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How to Calculate Size of the PCB

Introduction to PCB Size Calculation

Printed Circuit Boards (PCBs) are essential components in modern electronic devices. They provide a platform for mounting and interconnecting electronic components, ensuring proper functionality and reliability. When designing a PCB, one of the critical factors to consider is its size. Calculating the appropriate PCB size is crucial for ensuring compatibility with the enclosure, optimizing manufacturing costs, and meeting the desired form factor. In this article, we will explore the various methods and considerations for calculating the size of a PCB.

Factors Affecting PCB Size

Before delving into the calculation methods, it’s essential to understand the factors that influence PCB size. These factors include:

Component Placement and Spacing

The placement and spacing of components on the PCB play a significant role in determining its size. The dimensions of each component, along with the required clearance between them, contribute to the overall PCB size. It’s important to consider the component footprints, pin spacing, and any specific layout requirements when calculating the PCB size.

Trace Width and Spacing

The width and spacing of the traces on the PCB also impact its size. Traces are the conductive paths that connect components together. The minimum trace width and spacing are determined by the PCB Manufacturing capabilities and the electrical requirements of the design. Wider traces and larger spacing between them can increase the PCB size.

Layer Count

The number of layers in a PCB directly affects its thickness and overall size. Multi-layer PCBs allow for more complex routing and higher component density compared to single-layer boards. However, adding more layers also increases the PCB Thickness and may require adjustments to the overall size to accommodate the increased thickness.

Mechanical Constraints

Mechanical constraints, such as the enclosure dimensions, mounting holes, and connectors, must be considered when calculating the PCB size. The PCB must fit within the available space in the enclosure while providing room for proper mounting and connection points. It’s essential to account for any mechanical features or constraints that may impact the PCB size.

PCB Size Calculation Methods

There are several methods for calculating the size of a PCB. Let’s explore some of the commonly used approaches:

Manual Calculation

The manual calculation method involves measuring the dimensions of the components and determining the required spacing between them. This approach is suitable for simple PCB designs with a limited number of components. Here’s a step-by-step guide for manual PCB size calculation:

  1. List all the components and their dimensions (length, width, and height).
  2. Determine the minimum spacing required between components based on manufacturing guidelines and electrical requirements.
  3. Arrange the components on a grid or graph paper, considering their placement and orientation.
  4. Measure the total length and width of the component arrangement, including the necessary spacing.
  5. Add any additional space required for mounting holes, connectors, or other mechanical features.
  6. Consider the layer count and adjust the PCB thickness accordingly.
  7. Round up the dimensions to the nearest standard PCB size or manufacturing tolerance.

While the manual calculation method provides a rough estimate of the PCB size, it may not be accurate for complex designs with a large number of components.

CAD Software Calculation

Computer-Aided Design (CAD) software tools are widely used for PCB design and size calculation. These tools offer automated features and libraries that simplify the process of determining the PCB size. Here’s how CAD software can assist in PCB size calculation:

  1. Create a new PCB project in the CAD software.
  2. Import or create the component footprints and symbols in the library.
  3. Place the components on the PCB layout, considering their placement and orientation.
  4. Define the trace width and spacing rules based on the manufacturing guidelines and electrical requirements.
  5. Route the traces and optimize the component placement to minimize the PCB size.
  6. Use the software’s built-in tools to measure the PCB dimensions, including the length, width, and thickness.
  7. Generate manufacturing files (Gerber files) that include the PCB outline and dimensions.

CAD software provides a more accurate and efficient method for calculating PCB size compared to manual calculations. It takes into account the component footprints, trace routing, and manufacturing constraints, resulting in a precise PCB size estimation.

PCB Manufacturer Specifications

PCB manufacturers often provide specifications and guidelines for PCB size calculation. These specifications are based on their manufacturing capabilities and standard PCB sizes. Here’s how to leverage PCB manufacturer specifications for size calculation:

  1. Consult the PCB manufacturer’s website or contact their support team to obtain their PCB size specifications.
  2. Review the available standard PCB sizes and their dimensions.
  3. Consider the minimum and maximum PCB sizes supported by the manufacturer.
  4. Determine the number of layers required for your design and check the manufacturer’s specifications for the corresponding PCB thickness.
  5. Ensure that your PCB design falls within the manufacturer’s size and thickness guidelines.
  6. Communicate any specific size requirements or constraints to the manufacturer for Custom PCB sizes.

By adhering to the PCB manufacturer’s specifications, you can ensure that your PCB design is compatible with their manufacturing processes and avoid any potential issues related to size and manufacturability.

PCB Size Optimization Techniques

In addition to calculating the PCB size, it’s important to optimize the size to reduce manufacturing costs and improve overall efficiency. Here are some techniques for PCB size optimization:

Component Selection and Placement

Selecting components with smaller footprints and optimizing their placement on the PCB can significantly reduce the overall size. Consider the following tips:

  • Choose components with compact packages, such as chip-scale packages (CSPs) or quad-flat no-lead (QFN) packages.
  • Place components on both sides of the PCB to maximize space utilization.
  • Arrange components in a way that minimizes the trace lengths and reduces the PCB size.
  • Use surface-mount devices (SMDs) instead of through-hole components whenever possible.

Trace Routing Optimization

Efficient trace routing can help minimize the PCB size. Consider the following techniques:

  • Use the smallest trace width and spacing allowed by the manufacturing guidelines and electrical requirements.
  • Optimize the trace routing to reduce the overall trace lengths and minimize the PCB area.
  • Utilize diagonal or 45-degree trace routing to save space and reduce the PCB size.
  • Employ via-in-pad or blind and buried vias to maximize routing space and reduce the PCB size.

Multi-Layer PCB Design

Utilizing multi-layer PCBs can significantly reduce the PCB size compared to single-layer boards. By distributing the traces and components across multiple layers, you can achieve higher component density and more efficient routing. Consider the following tips:

  • Use four-layer or six-layer PCBs for complex designs with a large number of components.
  • Assign power and ground planes to dedicated layers to improve signal integrity and reduce the PCB size.
  • Utilize blind and buried vias to interconnect between layers without consuming additional PCB area.
  • Optimize the layer stackup to minimize the overall PCB thickness.

Design for Manufacturing (DFM)

Designing your PCB with manufacturing considerations in mind can help optimize its size and ensure smooth production. Consider the following DFM tips:

  • Adhere to the manufacturing guidelines for minimum trace width, spacing, and Hole Sizes.
  • Provide sufficient clearance around the PCB edges and mounting holes.
  • Avoid placing components too close to the PCB edges to prevent handling and assembly issues.
  • Use standard component footprints and packages to simplify manufacturing and reduce costs.
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O2DYMpA+VEHGOnqcmhB4i8LDxBrMx13RhDJo+hRRyHULTy3kjudTZ0Vt+CVDKSM/xD156ysi3/wCRl1z/ALAfh7/0r1agCM+I/BxlSU+ItH3okkagatbCMiQoxLRiXYT8owSuRzjG47qlpqPw9sZWlttc0ZX8sxRiTWo5o7aEsGMNpHNOyRxnC5VFUfIvHyAL0UssUEUs00iRQwo8s0krKkccaDczu7EAADJJzVG21VJ544ZbO+s/tG42D36RRrehVMhEapIzq+35tkio+Mnb+7bywDLj1H4exXZvU1zRhN5ksyodaja2imlBEk0Nq05gWRsvuZUBO9sk+YdxJqPw9luxevrmjGbzIpmQa1GttLNEAI5prVZxA0i4TazISNi4I8sbby67A81mFsr7+z7ydba21U/ZBp8juG8tgTN5+12GyJvK2sWXaSJFLrJrM32rULW10XVbz7BPHbTzWz6WkXmvbw3e1Rd3cb8LIufk/lQBDda94Hvba7s7nXdDktrqCW2uE/tS1XfFKhjddyShhkEjgipv+En8H/8AQw6H/wCDKy/+OVr0UAfI1FFFAH0X8N/+RL8Pf9xH/wBL7ioY4ZLLS/EWpxXd8NUsNV8RSWdobmVYPPl1G4ntrN7FCI2+0b0K7kZ2E67GHyGOp4A1iwtPCWh28sOqtJH9v3G20fV7mL5r2dhtltrd4z15wx9OowN99S8NSXcOoSaXqT30CGKG7fwzrLXMUZDAokps94B3NwD/ABH15AMjxDLqrWPi65u9D1EmPR9e06xmhm0o2lvYyRktO2bsTsZNkbt+6yoUKq5DNcdnE7yRxO8UkTOiO0UpjMkTMASjmJmTI6HDEe5HJyZdc0aeOWGaz1mWGZHimjl8O648ckbjayOjWhBBGcjFP/4SHTP+ffXP/Cf17/5EoA16yNW/4/8Awb/2HLj/ANM2p0f8JDpn/Pvrn/hP69/8iVlanrunPe+E2EGsgQ6zPI+/Q9aQlTpOoR4RXtQWOSOACcZOMKSADrK5Cfjwl4ztjxctP4vtVhP+tNxfXt29tEE+9ulEsRjGMt5i4zvGdWTXNGmUJLZ6xIgkilCyeHddYCSJ1lRwGtCMqwDKexAPbNQvqXhqS7h1CTS9Se+gQxQ3b+GdZa5ijIYFElNnvAO5uAf4j68gBrMem61BrOnHWntE01NusQI8ccPlywpdKL5mCzeSV+9snj3Auu7g7KcEB1bV/tN+NRsDe+GdBuRZQ3lzZSeek968yNLb+VOTB5iKw3ADzRuXJUpcuNT8NXctpNdaXqU81nJ5tpLceGNZlkt5NytvhZ7MlTkKcgjoPSi81Lw3qESw3+l6ldwrIJVjvPDOszxrIAVDhZbMjOCRnHf3oAvaLc3F3p0U87+afPvooZ9qr9qtobqWG3ufkAQ+agSTKqFO7KgKQBpVkf8ACQ6Z/wA++uf+E/r3/wAiUf8ACQ6Z/wA++uf+E/r3/wAiUAGk/wDH/wCMv+w5b/8Apm0ypdRubht+nae+3UriBmWYKrpp0T7kF5OGBU4IPlJj52UjhUeSHF0zXdOS98WMYNZIm1mCRNmh605CjSdPjw6pakqcg8EA4wcYYEvuZPBF7NJc3nh+e5uZNvmTXPhHVZZX2qEG55LEscAADnt7UATGwjXUrbTLCefSUsNDtI7ee08p7i8t0leEW4+2pJGyW+1SxKOwNwMMgdhdXtAdX0q0KRIiCS7RXiMhjuglzIgvUaVmcifHnAmRyfMzvfO96M974Uuba3srnR76ezt/L+z20/hbV5LeLy1MaeXE9kUGASBgdDjvVz/hIdM/599c/wDCf17/AORKANeisj/hIdM/599c/wDCf17/AORKP+Eh0z/n31z/AMJ/Xv8A5EoAPE//ACLXiv8A7Aerf+kkla9cn4i13TpvD/iWJINZDy6NqcamXQ9aijBa2kUF5JbUIB6ksAPXArV/4SHTP+ffXP8Awn9e/wDkSgCPxRFEfD/ieZo4zNHoGtRRyFVMiRyWxZ0VsZAYqpIz/CPThurtqUl5aQf2RfXmmQfZb5msJdOVpr2GcyxRyfbLmF1SMoknyg7iQMhUZLg/tfQPs32L+z9V+x+R9l+zf8I3rf2fyNvl+T5X2PZsxxjGMcVN/wAJDpn/AD765/4T+vf/ACJQBhadNLJB4dnmtZ7WOHxx4l803LQEJ9obWIU3NBI6DMkiwjLDL8DIZTJb1CDTrrUfEpvpp4tPhsfCa3NxavJGYJ7PULy/2NNCCybQ0TyHKlUcPlQQ4uf2v4fMM1sdP1U28/2jzoT4b1sxS/aGZ5d6fY9p3lmLZHOTnrRbavoFnBHbWen6rbW8e7y4bbw3rcUSbmLnaiWYUZJJPHf3oAfaobDV4tOtZrua0m065vbpby6ub2S1nSeGKAia5d5VEoM3ylyD5GVAIcyPuP8AkZdD/wCwH4h/9K9JqtZ6l4b0+JobDS9StIWkMrR2fhnWYI2kIClysVmBnAAzjt7VTn13Tj4g0aUQaztTRtdjYHQ9aEhaS50xgVjNrvI+U5IUgcZxuAYA6h4oZGgeSONngcyws6qxikKNEXQkZBwzLkdmI74ONoVzbWXhHw/eXL7Le08Oadc3D7WbZFFZJI7bUBY4APQGpv8AhIdM/wCffXP/AAn9e/8AkSof7X0D7N9i/s/VfsfkfZfs3/CN639n8jb5fk+V9j2bMcYxjHFAFOa2uYfC1jpl0m2/1n7JY6nGrK0r3GrzhtTkhCErvUPcSjAKrsJxsTFCWVs+peMri71G+svIvra9hMV41pFBB/ZVmn210BCOhaN1/eh0/csMcOHvvrmjSNA8lnrDPA5lhZ/DuusYpCjRF0JtMg7WZcjsxHQ8w3Gp+GruW0mutL1Keazk820luPDGsyyW8m5W3ws9mSpyFOQR0HpQBTt7vxBdvpF7qPh7UnNra2d3bxWL6bFGL65sQtxLKt9eRzgp5ksSoVwOWJcsv2fR8KO7+GfCzNE8RGjacgWQxklUgRA48tmGGADLznBGQDkCT/hIdM/599c/8J/Xv/kSmRa5o0EcUMNnrMUMKJFDHF4d1xI440G1URFtAAAMYGKAH+Hv+PC6/wCw54n/APTze1oXNzb2cMlxcSbIo9oJCs7MzsEVERAWZ2JCqoBJJAAJODzWha7p0Vlcq0GsEnWfEUg8vQ9akGJNWu5AC0dqRnBG4ZyDkEAggWbm+8KXiSR3mj31yklwt1Ilz4W1eVXnWIQCVg9kQWCgKD1wMdBigCtq1pdvp+o6ldNJa3N3qXhpyUMLyaXpljqVvMPMchoCYszTyMVZV3kbnSIM01zaQRSahonn6jLpl/oGqS6kGnu9Ru7RiYreJoHnM0wMqtNtU7gTB8qgh/MfZX3hTTfO/s7R76z87Z532LwtrFv5mzdt3+VZDOMnH1PrT7PUvDenxNDYaXqVpC0hlaOz8M6zBG0hAUuViswM4AGcdvagAiSCxvPD/wDZd3d3MGrPN9oS41G71KNrJLSW4W8ha6lkZQr+Um5WCnzwCCWQx5ekQyadofhG6gu76TUZP7D0u4tbi5lkiYF47W7tRZAiJXt1WRjtjV1+zkuWAcS6lvqfhq0lu5rXS9SgmvJPNu5bfwxrMUlxJuZt8zJZgscljkk9T60JqXhqO7m1CPS9SS+nQRTXaeGdZW5ljAUBHlFnvIG1eCf4R6cAFnxD/wAeFr/2HPDH/p5sql1qDT7jTpU1GaeGzSexuJprd5Ini+z3UVwrmWIb1QFQXbI2rlty7dy4uu67p0tlbKsGsAjWfDsh8zQ9ajGI9WtJCA0lqBnAO0ZyTgAEkA6v/CQ6Z/z765/4T+vf/IlAGbfXE+gvfw6dJPcgaHqF+sGoXN3fsmpLLDBYxLJPI0/+kszoqb/mMXyAMGMj49OEN9Y6TZ3d1p403QLKGG8hFs13qMEUjQCJhcRPARDtVmPkkg3IwYw5Fy+3vfClrCba10e+gtjPHdGG38LavFEZ42R0lKJZBdwKoQcZ+UenD7zUvDeoRLDf6XqV3CsglWO88M6zPGsgBUOFlsyM4JGcd/egC3oDq+lWhSJEQSXaK8RkMd0EuZEF6jSszkT484EyOT5md753vq1kf8JDpn/Pvrn/AIT+vf8AyJR/wkOmf8++uf8AhP69/wDIlAGvWRb/APIy65/2A/D3/pXq1H/CQ6Z/z765/wCE/r3/AMiVlQa7pw8QazKYNZ2vo2hRqBoetGQNHc6mxLRi13gfMMEqAecZ2kKAa/iKKefw/wCJYYY5JZptG1SKKKJWeSSR7aRVRFUEkk8AYqpEEs7zw+1jf3d8msPM141xeSXkc1qtpJci/hTcY0AfylzGqJ+/A28p5cp1zRmlSY2esGaNJIo5D4d10yJHIUZ0VvseQGKqSM87R6cRW+p+GrSW7mtdL1KCa8k827lt/DGsxSXEm5m3zMlmCxyWOST1PrQBZn/4m9zbwRc6dp99HPezH7lzd2jl47WAjDfupAjysCAGiEfzEutvlXNrYadYa9qWlXmpHULO71O4SCW9vjC+pzzvcLZNp7sISJWdUQCIMyyqytudZCRDwHBLDND4aeKaF0liki8H6mkkciMGV0ZbEEEHkHParj6l4aku4dQk0vUnvoEMUN2/hnWWuYoyGBRJTZ7wDubgH+I+vIB0FFZH/CQ6Z/z765/4T+vf/IlH/CQ6Z/z765/4T+vf/IlAHy7RRRQB9F/Df/kS/D3/AHEf/S+4rWOrXjvNPa6f9o0u2nuLa4nSZzetJbSNBO1tZLES6IwKn94rHY21H+Xz8n4b/wDIl+Hv+4j/AOl9xVN7bS7W31qJUgTxi99r9zowdg2pGS5vbi5s2sy5LeQQymTb+75l34xIAAdFqWrXlgl/cRaf5tjpkElzqU88z2zeXHF57rYxmJhIwXk5ZFyQu/IYQbFczrkvhi/a407WpLu2a3dVtY5mnij1GRkhuFaztuYbko20BDFJhhgp+8Al3bB76Sx0+S/iSG+e1t3vYoiDHFctGplRCGYYByB8x+p6kAs1kat/x/8Ag3/sOXH/AKZtTrXrI1b/AI//AAb/ANhy4/8ATNqdAGvWLNrU0a3l8lnG+i2D3Ud7eG4ZLlDZu8VxJDaeUQ0cbKwbMqsdjbUb5fP1pJYoVDyyJGheKJWkZVBklcRIgLEDLEhVHckDqcVyNzLCmh+JvD7yRrrV/J4pSxsCyi5uRqd3dzW8kKZy0ZEilnGVXDbivkt5YBtalq15YJf3EWn+bY6ZBJc6lPPM9s3lxxee62MZiYSMF5OWRckLvyGEE2o3WsWu+W2tdKezigaa4n1HU5rLytm5nLBLSVdoABJLjvxxk5euS+GL9rjTtaku7Zrd1W1jmaeKPUZGSG4VrO25huSjbQEMUmGGCn7wCWa/e+udL8O2V/FHFqGsXekwX0KkG2DRL/aV9bvhmzGyRTR4ywbcAflYsADU0y5vLywsLu8tPsdzcwRzyWpkeRrfzBuEbtJHG24DG4bBg5HOMm5RRQBkaT/x/wDjL/sOW/8A6ZtMp02o3zXF1Dptgl2lg6R6g0l0LaQSvElwIbRGjZXk2MrHc8a/Oo3/AHvJbpP/AB/+Mv8AsOW//pm0yqF/cQ2F/fLHqkelPfvFLNHdWq3M2oyCCO3E2jYlyZsKsZQxy8oh8rEmbsAvT6/p0MWmXSN5lneWN1q8k+JU8nSra2E73fllCxwXhTbgN+9zj5CBNbXmqNNHHfaZ9miudxtXhuDdMhUGTy75UiCxuR0KvImQRvyV8/l7fTdRudH1TTvJ33mmeB7Xw3DF5kS+Vqt1YmW7t924KcgWZ3FivoR81XE/s77Ra/8ACH/Yf7R/0z+1t3m/d+xXHlf23/y283zvKzv/AHv+sxx5lAGzcaxDDqemabFDJM11dPaXMyFRDZyfYp79I3J5MjBM7R0DBmI3qJtWuOeHXrW98IRz2GmjzdflmuLkarcXNzdTtpN8kks2bCJchAdoGANioAiAGLsaAMjxP/yLXiv/ALAerf8ApJJWvWR4n/5FrxX/ANgPVv8A0kkrXoAytb1iHRrG6ujDJc3Edrd3cVpCVWSWO1j82SRmbhY1GNzH1AALOqSXrm5t7OGS4uJNkUe0EhWdmZ2CKiIgLM7EhVUAkkgAEnBy/EUsM/hbxLNDIksM2ganLFJEyvHJG9nIyujKSCCOQc0up2+uzX1q8Ftp11p9ukU0cF3fXFmTfLIzCWVY7SYOEAQxDcoDZYgsqNCAEGuPPYW1yLGSO9vNS1HSrOxlmjybm0nuYiJpo9yKAsLyORvwAQvmHAkeNa8iO8TUbbyb+0+w77a0l+0pP/aEzW1p9nmkWIHzHBj+dU2spzhMSPhWDXi2Wk317FBBBp3jHxPdXskE7zxwQSSavatNIzRRsEWSTaTtICje20BhE/UY11htavbEyXWnOnhCMXOnySEyrpmrz314bSS2IkYojDBjJO7KqS6FVAOitLrUnla31CxS3mKGaJ7OeW8tJIwyqVM7wRFZASDtKDIOVLbWENe4/wCRl0P/ALAfiH/0r0mqelf2P/aSf8I39h/sf7Dd/wBpf2T5P2D7f5tv9m2+T+683b52/bzjZv42VcuP+Rl0P/sB+If/AEr0mgC3Je+XqVjp3l5+1WOo3vm7sbPsktpFs2453ednORjb3z8pJe+XqVjp3l5+1WOo3vm7sbPsktpFs2453ednORjb3z8uXqlnBfeINBime7RF0fxBIDZ3l5ZyFhc6UuDJZyI5HPTdj2yOGRada2HiXSPIkvn83Q9e3fbdQv73Gy70rGz7bLJjqc4xnjrgYAOjooooAKKKKAMjw9/x4XX/AGHPE/8A6eb2r15cTW8S+RbSXFxLIIbeJdyx+YQW3TzBSEjABLMQemAGZgklHw9/x4XX/Yc8T/8Ap5val1LWtH0q2uLq8u4FWCeO0ZPOhV2u5VWSO3zIyoHYFW+ZlAU7iQoLAArprc0K6lHqlmlveWb2Ajt7G4a7F1HqDi3tWillihUF5A8WGC4KZJCsGMq6ndWsV7JrNolmtraz37TWcs99afZoFzJmX7PG4kXrtMfIPyltrCHDmFjq2m6rNb39rqV7NqOgXuqDRLw3D2dna3sEv2e2ktmFxhESV0xhmcuyqrSbFZcW1heW2u2fhNLGSwu/Dmt210mlNbrYPqkqxR2iq0ZEAlKmbfg5xs38bKAOitrzVGmjjvtM+zRXO42rw3BumQqDJ5d8qRBY3I6FXkTII35K+fpVy1l/Yf8AaOlf8I55Hm+fN/wkP2fP2j7N9lnx/a3mfvPP83y8eZ+8z5nbzK6mgDI8Q/8AHha/9hzwx/6ebKtesjxD/wAeFr/2HPDH/p5sql1iLV57aOLTfI3POouxLdTWbtabH3JBcwRSurk7QSEztLYKth0AGafrEOo32o20EMn2e2tbC6t7tivl3sd1JdRb4FHPlgxHaxxuzkAqQ8pp+sQ6jfajbQQyfZ7a1sLq3u2K+Xex3Ul1FvgUc+WDEdrHG7OQCpDy52kDUo/EGrQz2Gm2cMOgaDFHFp93LPHFHHc6isKRq1rCMY3gjAxtXGd58qy1zbWeueJ7y5fy7a18OaJc3D7WbZFFcavI7bUBY4AJ4BoAf/bU00s1vY2aTXLXV/DYia4aCCaDTjDBd3E0gid1CSsYQBG5YgEDYxeO9Be5tp576P7E1p5gvfPfEEflqJGljuHCo0WMMGwOOGCsrJHy7abZ28fhOfxHDAtrFpWq/wBsteuhsRrGozWV7J9rAYwbGdZmXcNgYKBhigqVLbWLqKWHTYLG48OG+mNpbXV3NaRXNgLa18uKJ47eZjamT7RhdqhlCBSYDslAN3S9T/tM6ri1nthZXy2aC5GyWVGtLe8WZoiNy7hIMK3zDuFYlEit/wDkZdc/7Afh7/0r1aq3h99Se98Zfbbe1hb+2bUkWt1LcjzP7JsAVzJBEcABCDjqxGAEDSWbf/kZdc/7Afh7/wBK9WoA0Lq5trO2ury5fZb2kEtzcPtZtkUSmR22oCxwATwDVS2vNUaaOO+0z7NFc7javDcG6ZCoMnl3ypEFjcjoVeRMgjfkr57Neje70jXNNtyj31/o2qx2luZESSZjAYcqHIGAXQE5wNwyRmsZP7O+0Wv/AAh/2H+0f9M/tbd5v3fsVx5X9t/8tvN87ys7/wB7/rMceZQBs3GsQw6npmmxQyTNdXT2lzMhUQ2cn2Ke/SNyeTIwTO0dAwZiN6iaKbWpo1vL5LON9FsHuo728NwyXKGzd4riSG08oho42Vg2ZVY7G2o3y+fkPDr1re+EI57DTR5uvyzXFyNVuLm5up20m+SSWbNhEuQgO0DAGxUARADElzLCmh+JvD7yRrrV/J4pSxsCyi5uRqd3dzW8kKZy0ZEilnGVXDbivkt5YBuzajfNcXUOm2CXaWDpHqDSXQtpBK8SXAhtEaNleTYysdzxr86jf97ydGKRZo4pUEgWVEkUSxyRSBWAYB45QHB9QVBHpxiuVntvDUGq+IZdeSBbi8vre50drhnM8ka6faWxbSghLifejA+ViTIj9UJ6LTP7R/s3Sv7S/wCQj9htPt/+q/4+/KXzf9T8n3s9OPTigD5SooooA968AahfweEtDii0LVbqNPt+2e2l0hYpM3s7HaLi8jk46HKDp3HJ6j+1tU/6FjXP+/2g/wDywrI+G/8AyJfh7/uI/wDpfcVb/ty4nvGW1udK+We9gh0eZ1XV79bGea1nmt3adUX5o5PLUxMCI+XTzD9mALn9rap/0LGuf9/tB/8AlhR/a2qf9Cxrn/f7Qf8A5YU6+PiaVrldLOm2wgQiFtThluBezFA42/ZZ0McanCliHJOfkAQGe5YXkOoWWn6hCsiw31pb3kSyhRII541lUOFJGQDzyf60AUf7W1T/AKFjXP8Av9oP/wAsKytT1PUWvfCbN4d1lDHrM7ory6KTKx0nUE2JsviM4JbkgYU85IDdZWRq3/H/AODf+w5cf+mbU6AD+1tU/wChY1z/AL/aD/8ALCj+1tU/6FjXP+/2g/8AywrXrn5tW1FbfUtZjFqNI0x9SS4tZIpTfXEemyywXE0c4lESkFHMaGNtwUZdPNP2cAs/2tqn/Qsa5/3+0H/5YUf2tqn/AELGuf8Af7Qf/lhUOuanqmmW2p6kv2G30/SoDPIL4F5NSYKHENu8cyrHk4jVmVyWY/JhAbixd3WpSXy6bYSWttMLQXzT6hby3EcyGQwmK3hjmiLFTgyt5ny74xhvOzEAN/tbVP8AoWNc/wC/2g//ACwo/tbVP+hY1z/v9oP/AMsKt6be/wBoWVvd+V5fm+YMK/mRP5cjR+bBLgbonxuibaNyspwN2BcoA5PTNT1Fb3xYy+HdZcyazA7qkuigxMNJ09Nj774DOAG4JGGHOQQur/a2qf8AQsa5/wB/tB/+WFGk/wDH/wCMv+w5b/8Apm0ynXx8TStcrpZ022ECEQtqcMtwL2YoHG37LOhjjU4UsQ5Jz8gCAzgDf7W1T/oWNc/7/aD/APLCj+1tU/6FjXP+/wBoP/ywqGfUL+fTYNcsr+xstLfSo9UkGo6ZcXdxHEYjcl2NreRjhcZUK3IPJzgaOmNqj2Fg+qrAmovBHJeR2yFIopXG4xKDJJnb90nec4zwDgAFT+1tU/6FjXP+/wBoP/ywo/tbVP8AoWNc/wC/2g//ACwrXooA5PxFqmoyeH/Esb+HdYiR9G1NGlll0UxxBraQF3EV8z4HU4Unjoeh1f7W1T/oWNc/7/aD/wDLCjxP/wAi14r/AOwHq3/pJJWvQBkf2tqn/Qsa5/3+0H/5YUf2tqn/AELGuf8Af7Qf/lhR4g1O80rTdQubK1+0XUNjfXieaHW0iS1iMrPcSKPoFUHLE9lDSQ3r28hsbd7mVZHAkghjjiCmSWe4lW3hiTcQuWZlUEsAM5JABIAKP9rap/0LGuf9/tB/+WFH9rap/wBCxrn/AH+0H/5YUafq0j6Rd6pqogt/sU+trefZjLLFFFp15cW5ZSVDthUyTsGf7oztDtIv76+fW1vLZLZ7LUktYoVcSSLC9ja3i+e6kp5n7w7tpIHQFsb5ABv9rap/0LGuf9/tB/8AlhWVNqeonxBo0n/CO6yHXRtdQRGXRfMcNc6YS6kXxTC4AOWB+YYBwSnWVkXH/Iy6H/2A/EP/AKV6TQAf2tqn/Qsa5/3+0H/5YUf2tqn/AELGuf8Af7Qf/lhViW8mTV9NsAqGG503VLuRiG8wSWs9jEgU5xgiVs8dh0xzfoAyP7W1T/oWNc/7/aD/APLCj+1tU/6FjXP+/wBoP/ywrXooAyP7W1T/AKFjXP8Av9oP/wAsKP7W1T/oWNc/7/aD/wDLCteigDk9C1PUUsrkJ4d1mUHWPETbo5tFADPq125Q+ZfKcqSVbjGQcEjBOr/a2qf9Cxrn/f7Qf/lhR4e/48Lr/sOeJ/8A083tXrx75Y1WyijeeWQRCSYjyLYEEmeZQwdgMcKpyxIGUBMkQBR/tbVP+hY1z/v9oP8A8sKP7W1T/oWNc/7/AGg//LCmW9xrzy6vpk1zpv8AaVsljd211FY3H2Q2l0ZIwJbZrvzPMDRTA4mxgoeSSoZY3fiA3utxXUtje2+mwQoBp1jJaXEuoSR/aTbqbu9dPlQxEE4BMw+YeWRQBN/a2qf9Cxrn/f7Qf/lhR/a2qf8AQsa5/wB/tB/+WFRpda9a3+lx6lJpz2uqSXFrFFY29ws1rdrA94ivPLMVeMJHKrN5MZzt+UBiI9ugDk9d1PUXsrYP4d1mIDWPDrbpJtFILJq1o4QeXfMcsQFXjGSMkDJGr/a2qf8AQsa5/wB/tB/+WFHiH/jwtf8AsOeGP/TzZVo3MlzHDI9tB9on+VYojIsSszMFBeRgcIM5YhWOAcKxwrAGd/a2qf8AQsa5/wB/tB/+WFH9rap/0LGuf9/tB/8AlhSWlzq8OpjT9Tnsbj7VYy3tlLYWk1rt+yyxxXCTrNcTf89YTGQ39/IGAXXTtTvL3U9UtpbX7PawWOmXll5odbuRLqW8iL3EbAbM+UCq43AH5sMTHCAH9rap/wBCxrn/AH+0H/5YUf2tqn/Qsa5/3+0H/wCWFMivdav1uvsMdrFGdR1C1gurmNpEt4bBxaSefbpMjvI8qy+XtdRswxIZfLmSx1O/1LSre6sltJp5rq9sluY2BsQLW5mtTfbRJvMbbNyIrsSXVd4GZkAJP7W1T/oWNc/7/aD/APLCsqHU9RHiDWZP+Ed1ku2jaEhiEui+YgW51Mh2JvgmGyQMMT8pyBkF9fTbrUjd6np2pSWktzapZ3kU1jby28L2l35kaB45ppWEgeKXPzEbdp6khG2//Iy65/2A/D3/AKV6tQAf2tqn/Qsa5/3+0H/5YUf2tqn/AELGuf8Af7Qf/lhV6/vIdPstQ1CZZGhsbS4vJViCmQxwRtKwQMQMkDjkf1rO07UL64u54JLrRr0RyNFdxaTIDNo8wDkRXZkmYuCVZN3lxnKj93hybYAf/a2qf9Cxrn/f7Qf/AJYUf2tqn/Qsa5/3+0H/AOWFZuja1ea1L5lrrvhx4jPcTrYQWzzX401LkpE8jLfgq7psJ3QDaXwVyNtTf25cT3jLa3OlfLPewQ6PM6rq9+tjPNazzW7tOqL80cnlqYmBEfLp5h+zAFz+1tU/6FjXP+/2g/8Aywo/tbVP+hY1z/v9oP8A8sKh1zU9U0y21PUl+w2+n6VAZ5BfAvJqTBQ4ht3jmVY8nEasyuSzH5MIDcbtAHyNRRRQB9F/Df8A5Evw9/3Ef/S+4pJLWSDTtf0OOynXVNTvtZvbO5gtJTaGe9upLm2vpL1E8tXgymdzBwYPkVvkMud4Am8Rp4R0JbPTtKmth9v8uS51S5t5W/02cndElhIowcgfvD68ZwOp+0eMP+gTof8A4O73/wCVlAFPWdQhnmn0ae21UWDwBdSnt9J1S6W5imUg2dvJawOvzD/Wvu4B2r87F7TfikWaOKVBIFlRJFEsckUgVgGAeOUBwfUFQR6cYrM+0eMP+gTof/g7vf8A5WUfaPGH/QJ0P/wd3v8A8rKANesjVv8Aj/8ABv8A2HLj/wBM2p0faPGH/QJ0P/wd3v8A8rKytTn8Um98Jl9M0dXGszmAJrF2weT+ydQBVydOBAxuOcNyAMfNuQA6iWRIlDsJCC8UY8uOSQ7pHWMErGCcZI3HGAMk4AJHL3EN0uk6/wCHPs1219qkniIWkqW87WJj1a4ubhJpLtVMShBJiRWYNmM7Vfcvnav2jxh/0CdD/wDB3e//ACso+0eMP+gTof8A4O73/wCVlAFbU3sZ7iWDVPD93cNbvt0W6trY3UkrSRRMz29zAN1vIH+UM7xD5QwfgmGtcW0i/wBnHxRa/wBq266VYQkW+ny6jbpq6eZ9qne0ghLfvBs8p/JwoRx+783FxpfaPGH/AECdD/8AB3e//Kyj7R4w/wCgTof/AIO73/5WUAWNJjvorCCO9MnnB7lkWaQSzRWzTyNbxTSAtukRNiu29slSdzZ3NfrI+0eMP+gTof8A4O73/wCVlH2jxh/0CdD/APB3e/8AysoANJ/4/wDxl/2HLf8A9M2mVT1nUIZ5p9GnttVFg8AXUp7fSdUuluYplINnbyWsDr8w/wBa+7gHavzsXtK2mT+KRe+LCmmaOznWYDOH1i7UJJ/ZOngKhGnEkY2nOF5JGPl3Pq/aPGH/AECdD/8AB3e//KygA1QSX0OhQwxT+VearplzJK0MytaxWTf2sGmikUONxhWI7tuDKOpGxtesj7R4w/6BOh/+Du9/+VlH2jxh/wBAnQ//AAd3v/ysoA16KyPtHjD/AKBOh/8Ag7vf/lZR9o8Yf9AnQ/8Awd3v/wArKADxP/yLXiv/ALAerf8ApJJWvXJ+Ip/FJ8P+JRNpmjpCdG1QSvFq93JIkZtpNzIjacoJA6Auv1GcjV+0eMP+gTof/g7vf/lZQAmuh73w34gFtFPJJd6HqIt4vJlW4dpbV9ieS6iQMcgbSoOeMZ4ov9O1i41C2vbTULGOO2g2QQX2nzXawzsZFkuIzFdwjcykJyrEAEKQJWDr9o8Yf9AnQ/8Awd3v/wArKPtHjD/oE6H/AODu9/8AlZQBj6fpHiOW0g82+sYmttc8Q3Zt7rSbloJ3fU5JYLhovtqP8p3yRZcjEiHBaFZTpaFb6xBeeK21GSCTztVtpIXgs5rVJcaZZRtIglnlynATqfmRuTnbFN9o8Yf9AnQ//B3e/wDyso+0eMP+gTof/g7vf/lZQBr1kXH/ACMuh/8AYD8Q/wDpXpNH2jxh/wBAnQ//AAd3v/ysrKnn8U/8JBoxOmaOJho2uiNBq92Y2jNzpm9mf+zgQQduBsOcnkbcOAa88U58QaNMI5DDHo+uxSShW8tJJLnTGRGbGAWCsQM/wn041ayPtHjD/oE6H/4O73/5WUfaPGH/AECdD/8AB3e//KygDXorI+0eMP8AoE6H/wCDu9/+VlH2jxh/0CdD/wDB3e//ACsoA16KyPtHjD/oE6H/AODu9/8AlZR9o8Yf9AnQ/wDwd3v/AMrKADw9/wAeF1/2HPE//p5val1LVBYW1xNHZ311LHPHapDb2d7JulkVXDs0ELt5Sg5d1RsYIAZx5ZxtCn8UiyuRFpmjOn9s+IiTJrF3GRIdWuy6gLpzDAOQDnkAHAztXU+0eMP+gTof/g7vf/lZQAmhyWzrfMhvnup50u9QmvNNv9OWad41gBgivI1G1VjVFALEBRuLMxeQ0UPa6LDc3MU8clx9u1m4t/Jlee3bUJ5dSe28pFMjNHvKcJklfugnaF+0eMP+gTof/g7vf/lZR9o8Yf8AQJ0P/wAHd7/8rKAKel6hDqGoRXlzbarBePBPbWNvcaTqtvFZWshSaRZ7mWBYTK/loX+faNoRc4Mlz0dZH2jxh/0CdD/8Hd7/APKyj7R4w/6BOh/+Du9/+VlAB4h/48LX/sOeGP8A082VXr67SxtLm7aC7nECF/IsYJLi5mbIASKKMEkk4HYDqSACRzuuz+KTZWwl0zRkT+2fDpBj1i7kJkGrWhRSG05RgnAJzwCTg42tqfaPGH/QJ0P/AMHd7/8AKygCHRrmG6ubu5lS+GpXUEP2gzaZqtnaQ29u7mK2glvbeJW2mRySfmYsxwqgRwOdprTV/Ed+bW7mhj0DR2jW2iZ5LiS3n1SV4YBwGkwy4Gf4x/ezUn2jxh/0CdD/APB3e/8Ayso+0eMP+gTof/g7vf8A5WUAUxB/Z+k6Npmq6V/aVmbEDWp4IPt6fb0MMhlks9hnk82Qu5YRsQw3MPmLoQ3c+kabe3CWN9Jay3yroVhDa3ck1vaSRRqqzxQRSSxxBhLIAUJRGVAoZRAtz7R4w/6BOh/+Du9/+VlH2jxh/wBAnQ//AAd3v/ysoATQ5LZ1vmQ3z3U86XeoTXmm3+nLNO8awAwRXkajaqxqigFiAo3FmYvItv8A8jLrn/YD8Pf+lerUfaPGH/QJ0P8A8Hd7/wDKysqCfxT/AMJBrJGmaOZjo2hCRDq92I1jFzqexlf+ziSSd2RsGMDk7sIAbWs273+m6vpUJ23Oo6VqVvA8iS+QrSReQDLKilRy4wOpAJAOw4oxFLy88PrY2F3Ypo7zLeLcWclnHDataSWwsIX2iNwX8psRs6fuAd3CeZZ+0eMP+gTof/g7vf8A5WUfaPGH/QJ0P/wd3v8A8rKAKcrSXcelaZb6bPZXun32mTnZbypYWVvaTRmb7LeiNYmSSPdEgT5iJdrIg3iGnJayQadr+hx2U66pqd9rN7Z3MFpKbQz3t1Jc219Jeonlq8GUzuYODB8it8hl2PtHjD/oE6H/AODu9/8AlZR9o8Yf9AnQ/wDwd3v/AMrKAK2pvYz3EsGqeH7u4a3fbot1bWxupJWkiiZnt7mAbreQP8oZ3iHyhg/BMOvYJfR2Onx38qTXyWtul7LEAI5blY1EroAqjBOSPlH0HQUftHjD/oE6H/4O73/5WUfaPGH/AECdD/8AB3e//KygD5dooooA+i/hv/yJfh7/ALiP/pfcU5Namu7q4kh1J4ZoNSvNNisGtC2ktJbXUlmsV/qC27FJpiNyYmXHmxfu5P8Al7b8N/8AkS/D3/cR/wDS+4qxPYan9g1nw+lpI8OqvrRTU1ktxbW8OrTz3EhmiaQT+ZH5jhVVGDYXLp5h+zgFvW7zVrb7CbNUit/7S0OO6uJQjmWO71KC0a2gjzkHDEuzDgEBQS5e226zdZtri7tIIoE3yJquhXLDcq4ittTtbmVssQOFVj+HqcHSoAKyNW/4/wDwb/2HLj/0zanWvWRq3/H/AODf+w5cf+mbU6ANeuZnv9T+waz4gS7kSHSn1oJpix25triHSZ57eQTStGZ/Mk8tyrK6hcrlH8s/aOikZ0UMsUkpLxIVjMYIV3CFz5jKMKDubnOAcAnAPOz2Gp/YNZ8PpaSPDqr60U1NZLcW1vDq089xIZomkE/mR+Y4VVRg2Fy6eYfs4AeJNRu9NiuLk6olrMqMND023SGefWbsBAIZopImmIZ2RNsW0gEsX/eAW965kvb3UrnTLe9nsI7Oysr6We1S1kuJmvJbqFIx9rikjCL5TFvkJJYcqEImLuXWfM1C1k0eDULG7/c2ZjnhWMRPCiSJqiXZBCFi3MaS5X+DK4mqXWnXkNto8VxBfat9jsYbRrnTbx9P1czqqrLM87XcO6KXapdfOyGRTiTO63ANTSrya+s/OmVBNFd6jYzGIMsckljdzWTSojEkBihYLubGcZbG5r9Zui6d/ZWnQ2e2CPE99c+VajFvb/a7qW78iH5Vyke/Yp2rkLnaudq6VAGRpP8Ax/8AjL/sOW//AKZtMpNTg1aVL+Zda/si3toHa3mhjs5l4j3vcXxvoiuxT0VWXhSS58wLbrpP/H/4y/7Dlv8A+mbTKrarLqs921m2h6jdaQiI0xtJtKA1GRhkwyrc3cbiFf412/OeDhFK3QBTn1ya5lsrWabUtImfRtN1ea306ybUNT33rTI0LQtazERwlMSN5H3pEGUxtn6OxlmmtLWaWW1leRA4msWZraeMklJotxJAcYbG5sZxuYDe2bINQtr59Xi026uRf6dp9nPZwyWSXdpJayXM6ljNOsDA+cytibgoMbw5MVzSrOaxs/JmZDNLd6jfTCIs0ccl9dzXrRI7AEhS5UNtXOM4XO1QC/RRRQBkeJ/+Ra8V/wDYD1b/ANJJK16yPE//ACLXiv8A7Aerf+kkla9AGJ4lvNXstI1WfTVRJoNO1G8a7mCPHbC2gaUBYSctIx4XjaMFjnaI57+oXv2KFGSPzrm4nhtLOANtM08zbQCQC2xRl5CFYqiM2Dswa2sQ3eoeH9bt4beRbu+0a+hitpXhEizz2zosTurmLIJwTvI98c0XekSXV8uoQ6rqVnMtqLMLarp8kYj8wysUF7bSkFjt37SN3lpkHywQAVtN/tXUtL/0jVZ4LyLVdZglutOt7NPMS01C6tURYruKdQmFXHVvlHzHJLP0A6hLFf3VxqV3fWk92y6U11HZI/2OECLzwbOCNSJWDvGckFDGRgk5i02z1zS9D1hI2e71P7X4hvLCO8NqBJJNd3E1uHNsI0xJlXbJGDIR8oAWPXsLOHT7LT9PhaRobG0t7OJpSpkMcEaxKXKgDJA54H9KALNZFx/yMuh/9gPxD/6V6TWvWRcf8jLof/YD8Q/+lek0Aa9ZujXNxd2k8s775E1XXbZTtVcRW2p3VtEuFAHCqo/D1OSX8urW91ZT2ttPeWYgu4rq0tGs1nM7tA0Mwa8kjXaoWUNiTOXX5TjMZottc2tiUuE8uWa+1W+MZZWaJb6+nvUjcoSm5Q4VsMRkHBI5IBpUUUUAFFFFAGR4e/48Lr/sOeJ//Tze1evEvpIljs5UhaSQJLOwDSQQ4Ys8EbKUMnQLu4GdxDbPLlo+Hv8Ajwuv+w54n/8ATze1LqV3q0FtcHTtMnuroTxwQjfZhNjqrtdbZbiPKJkjaXQsy4+VW80AFO0XUnn13Sn1e+m+z/YJ4dTWLThcW7Tgl7JlW2+zFlCCQ5iztuV4GA7t02LVZrvXAdb1K4sYUXTraSaHSg4vhua4nha3tFQiPKRrnIDpKGU7BVvR/MSO4R9N1K0kLrNPcanJp8k99O42tK7WM8gyAqjG1QBtVQFQKj9Etrm10yzS6Ty7ybzr6+jDKyxXt9M97cRxlSRsV3YL8x4A5bqQCjZxaqNbaBdb1K8srG1LX6XUOlCN7u4x5EKvaWkbZRQ0ki7lP7yI8q5B6Cs3Sra4h/ta4uU8u51DVby5dAysgii22NsybSfvRRRM2WPzMen3U0qAMjxD/wAeFr/2HPDH/p5sq05ZYoIpZppEihhR5ZpJWVI440G5nd2IAAGSTmszxD/x4Wv/AGHPDH/p5sqsanpw1KK1jN3d2pt7uK8R7T7MxaSJW2CRLuKSIgEhxlOGRWGCgIAM7TdR1q7vtX8yJI0OjaPqOm2Fwr28kDXUl+oS9l2s4kby08zCEJ90BtheZmnahK+tz6amr/2r5djc3GqmOGBYNNvEuIoYreJrZBt3/v8AKSSyOBEOeCZSDS9etdS1+8i1Ce7ebQ7G2099VWxWB72KW9kCzrYQRybE3IeAMiVvvFR5T5zrl1NbXi6RJBc6PHfTbWu7XGqSSW0kQsbaaNiwhd9khaRI+Yoz5ZOTbgFCXXLlpRBLez2keoX2v/Zms7Vbu+ii0W5g0021pCIZC7yNvnYmF9q7lxhfNi14NS+z6TcX9zP9sig8xbeSCPZeXm0iNIJLZ1QLdF8wlBjLjohfyoq8emXekxeGZbeOTUDoujSaLJDD5ME88cosx9oh8+QRZBhXKtIvDk7iUCSsTQrq6uJtTlvb7Trqe+mv47e1NhN9n8yytbACX7VDNEZQsXLKPl810DMp3SgFzRbnVJ5fEMeovA0tpqscESWykRQRPp1ldCJXYB22mRssQM9cKCEQt/8AkZdc/wCwH4e/9K9Wpmi6dqFhdeJXuru7uUvNRt5rZ7oWQaSNNPtYTLizijAJKlCCBxGDjktK+3/5GXXP+wH4e/8ASvVqALep3v8AZum6rqPleb9gsbu98rds8z7PE0uzdg4zjGdp+nasvSr2ae7Cx6u9+syPLMl3ZNZQ+WBkXGjOIFEkIYqpzLLxIh83jF1o6ravqNjqWljzI01HTb+1N0FjeOAyxiEbkLq5J3EjAx8hyRkbqmzU9RvNIe5sJLFNJu5byR5J7eeO6ma0uLER2nksX8v94zlnSM/Ko2fOfIAKzW+rxatpVnD4g1W4C+Zf6klxDo5jWyQGNI2aCyVw0rkBeRlY5cEMlWL681aPV9AhjVIdPn1GWznLhJJr0/2ZeXgKEEhI0KKOm5iD91Uzc2bS2uBqeu306bPN+wWNntZSsllawm4EjKCWD+ZNOpzjhF4/ikNRtrme78NSxJujs9Vmubk7lHlxNpl9bBsEgn5nQcZ6+gyACvv1PUbzV0tr+SxTSbuKzjSOC3njupmtLe+Ml35yl/L/AHioFR4z8rHf848i9pl7/aWm6VqPleV9vsbS98rdv8v7REsuzdgZxnGdo+nasvVbKae7LSaQ9+syJFC9petZQ+WBg2+soZ1EkIYswxFLxI48rjN1qaZZf2bpulad5vm/YLG0svN27PM+zxLFv25OM4zjcfr3oA+UqKKKAPefAEPiN/COhNZ6jpUNsft/lx3Ol3NxKv8Aps4O6VL+NTk5I/dj05xk9T9n8Yf9BbQ//BJe/wDy0rI+G/8AyJfh7/uI/wDpfcVGl9Ncvf6hMdZt3tNS1SzGoo7DRLGOyvJrVFuLJrhDJGQoM0nlNt8xv3sXk/6GAbf2fxh/0FtD/wDBJe//AC0o+z+MP+gtof8A4JL3/wCWlQrC+q32uia7voP7KvobKw+w3MtusZawtb0zyRodkjlpMYkV0wgGz5m869o15NqGkaLfzKizX2m2N3KsQYRrJPAkrBAxJxk8cn+tAFf7P4w/6C2h/wDgkvf/AJaVlanB4pF74TD6no7OdZnEJTR7tQkn9k6gSzg6iSRjcMZXkg5+Xa/WVkat/wAf/g3/ALDlx/6ZtToAPs/jD/oLaH/4JL3/AOWlH2fxh/0FtD/8El7/APLSteuTuJrptK1/xH9pu1vtLk8RG0iS4nWxEek3FzbpDJaKwiYOI8yMylsyHaybV8kA1fs/jD/oLaH/AOCS9/8AlpR9n8Yf9BbQ/wDwSXv/AMtKoeJ76+On+IINNneA2Gjald317b4822mjt/NgtY2IwJJAd7EZKqo4UzpItu4Q6lq95p0813HaWWnabeotjdXNnJLPeT3kRMs1q6SkKIhtAcD52JDEKYgCT7P4w/6C2h/+CS9/+WlH2fxh/wBBbQ//AASXv/y0qXRbm5urEvcP5ksN9qtiZCqq0q2N9PZJI4QBNzBAzYUDJOABwNKgDk9Mg8Um98WBNT0dXGswCYvo92weT+ydPIZANRBAxtGMtyCc/NtTV+z+MP8AoLaH/wCCS9/+WlGk/wDH/wCMv+w5b/8Apm0ymavYwSQapeajqmpW1pbWs0kTaZc3dk1lDHCXlnb7K+ZJMgsNysAFUBM7jOAP+z+MP+gtof8A4JL3/wCWlH2fxh/0FtD/APBJe/8Ay0rIujrl5c6Ot/pWuP8AZ9Dhnvo9C1AWMDaleuoeNpft8GfJ8pgAHk4m524Bl6LTTZGytzZSzy237zY11NdT3AYSMHSZ7xjPuVsqyscqRtwNuAAVPs/jD/oLaH/4JL3/AOWlH2fxh/0FtD/8El7/APLSteigDk/EUHikeH/Epm1PR3hGjaoZUi0i7jkeMW0m5UdtRYAkdCUb6HGDq/Z/GH/QW0P/AMEl7/8ALSjxP/yLXiv/ALAerf8ApJJWvQBkfZ/GH/QW0P8A8El7/wDLSj7P4w/6C2h/+CS9/wDlpUPiptUTRNaksrn7KINK1O6luISRdq0NuzxxwZUqNx+8+cgLhRukEkF7Ubya3WC3tFSTUbyRY7WNwzBIw6LNdSKpB8uIHc3zrk7UDBpVyAV/s/jD/oLaH/4JL3/5aUfZ/GH/AEFtD/8ABJe//LSsq1nvv7M0y2nvbt47rxNrmlX9/JIEuVto73UUiAmjCqhdkhhUqq48wKmxipRt7cXlvH4r0XS5L67e3sdHS38m5e51Kxn1ia4tZCJ5pQ/7pQk675QRuPzqhXyQDX+z+MP+gtof/gkvf/lpWVPB4p/4SDRgdT0czHRtdMbjSLsRrGLnTN6sn9okkk7cHeMYPB3ZS/pEdlFcyIYdcs70wOy2us6rdXvm229A00Km8uLc7ThWw25cjIAlBkmuP+Rl0P8A7AfiH/0r0mgA+z+MP+gtof8A4JL3/wCWlH2fxh/0FtD/APBJe/8Ay0qPUL5bLWtLaeeSO0/sfW5JI1MjCSZbvS4ogsSAlpCXKRgKSS+AMvgzaTLNqMVvrMkkiw31rFLp9qrMI4bScLMrzqDhpmG0seQv3V/ikuQBv2fxh/0FtD/8El7/APLSj7P4w/6C2h/+CS9/+Wla9FAGR9n8Yf8AQW0P/wAEl7/8tKPs/jD/AKC2h/8Agkvf/lpWvRQBymhQeKTZXJi1PRkT+2fEQIk0e7kJkGrXYdgV1FRgnJAxwCBk43NqfZ/GH/QW0P8A8El7/wDLSjw9/wAeF1/2HPE//p5vavXlvNdRLAly9vG7gXLQ7lneDBzHDKrAoWOAWAJAzt2sRJGAUfs/jD/oLaH/AOCS9/8AlpR9n8Yf9BbQ/wDwSXv/AMtKzc3lgni2HT7qdrWx/s+Vp9RvXuJrWZoxLfQwT6lIV+WHypYt5Kb5TubaCsVnR5UN9cQ6fJqJ0+O1WW6j1ptQN2l1JJthe3XVD9rEbKsgcsNmVXZ8wkwAWfs/jD/oLaH/AOCS9/8AlpR9n8Yf9BbQ/wDwSXv/AMtKh0xtUGua3Hf3PmE6VolytvESbS0aW41JGjt8qGPCLudgCxGcKuI4t2gDlNdg8UiytjLqejOn9s+HQBHo93GRIdWtAjEtqLDAOCRjkAjIzuXU+z+MP+gtof8A4JL3/wCWlHiH/jwtf+w54Y/9PNlWnKZhHKYUR5gjmJJXaONpADtV3VWIBPU7D9DjBAMz7P4w/wCgtof/AIJL3/5aUfZ/GH/QW0P/AMEl7/8ALSmaGb8T+KIry8e6kg1mJFdlEcaB9LsJzHBECQsYLNtG4nnksxLuzTG1Qa5rcd/c+YTpWiXK28RJtLRpbjUkaO3yoY8Iu52ALEZwq4jiAJvs/jD/AKC2h/8Agkvf/lpR9n8Yf9BbQ/8AwSXv/wAtKhsG1S9srq5gudh1LVb1kncmRLbTopGtIJtOjdWQ+Ykcci5JXdM0mGX91JmpqN4vhvwGHe+mfWINMtrx7Uu+oT79KmvCIpiwKtIyBWcsNodm3IR5kYBsfZ/GH/QW0P8A8El7/wDLSsqCDxT/AMJBrIGp6OJho2hGRzpF2Y2jNzqexVT+0QQQd2TvOcjgbcvqaM5H2u3330fk+S/2DVpPPv7PzN53NdedL5kUmMod74Idd/yeVbLb/wDIy65/2A/D3/pXq1AB9n8Yf9BbQ/8AwSXv/wAtKPs/jD/oLaH/AOCS9/8AlpVjWbybT9I1q/hVGmsdNvruJZQxjaSCB5VDhSDjI55H9ay9Nbyr23+fXLf7X5nOuyedHq2I2k320XnHyJR9/wAvyovlLjyv3WbMAufZ/GH/AEFtD/8ABJe//LSj7P4w/wCgtof/AIJL3/5aVkWl1O1zp+Li+OuzX32XUvNkuzoUiwu/2uG03n7Idqo/kiP96Cg8z7s2LGq6XbyX2nWtvdazHd6hdPe3Dxa1rCJDY2skctwyQi4EWGLRwBVwV87cBiIgAF/7P4w/6C2h/wDgkvf/AJaUfZ/GH/QW0P8A8El7/wDLSsq9Fzcaxq0l3p3iZtPtUsrOCTS7+e2tsJGbqa6EVteQzuT5oQhYJD+5+UszFI+ltTbm2tDbS+dbGCI283nNcebFtGyTznZmbI53Fjnrk5zQB8m0UUUAfRfw3/5Evw9/3Ef/AEvuKvTaTqLW+paNGbU6Rqb6k9xdSSyi+t49SllnuIY4BEYmJLuI3Mi7Qwyj+UftGB4A0+/n8JaHLFruq2sb/b9sFtFpDRR4vZ1O03FnJJz1OXPXsOB1H9k6p/0M+uf9+dB/+V9ACSWmsWt1qMumCxkTVJ47m5a+kmRrOdLeGz8yOOGMiRCqIdheM5U/PiQeRfsLOHT7LT9PhaRobG0t7OJpSpkMcEaxKXKgDJA54H9Ko/2Tqn/Qz65/350H/wCV9H9k6p/0M+uf9+dB/wDlfQBr1kat/wAf/g3/ALDlx/6ZtTo/snVP+hn1z/vzoP8A8r6ytT0zUVvfCat4i1lzJrM6IzxaKDEw0nUH3pssQM4BXkEYY8ZAKgHUyGYKDEkbsXiBEjtGBGXUOwZVY5AyQMckAZAO5cKbSdRa31LRozanSNTfUnuLqSWUX1vHqUss9xDHAIjExJdxG5kXaGGUfyj9os/2Tqn/AEM+uf8AfnQf/lfR/ZOqf9DPrn/fnQf/AJX0AU9U8LWF3Ya5BZvfQ3F/BqZjU6tq0dl9rvBI5d7ZJzFsLsWYeWRyeDnBty2N/Z3IvdLSC4kksbPTZ4NTvLiPMVm00kMq3QimkLjzHD7lbdkHcpQiZf7J1T/oZ9c/786D/wDK+j+ydU/6GfXP+/Og/wDyvoAt6dZfYLUW5l82Rp7u7ncLsVp7y4ku5SiZJCbnbaCzEDAJJGTcrI/snVP+hn1z/vzoP/yvo/snVP8AoZ9c/wC/Og//ACvoANJ/4/8Axl/2HLf/ANM2mVDqEHiOfUEeOz0q50228mW1huNSubZpLtTv8+4RLKVTsOPKG/AI3nLBfs1DTNM1Fr3xYq+ItZQx6zAjskWikysdJ099777EjOCF4AGFHGSS2r/ZOqf9DPrn/fnQf/lfQBLP/wAJAvkT20djK7wRx3Vjc3MkVvFKMsZbe7jtnkPUqQ0PICkbCpE82nWX2C1FuZfNkae7u53C7Fae8uJLuUomSQm522gsxAwCSRk1P7J1T/oZ9c/786D/APK+j+ydU/6GfXP+/Og//K+gDXorI/snVP8AoZ9c/wC/Og//ACvo/snVP+hn1z/vzoP/AMr6ADxP/wAi14r/AOwHq3/pJJWvXJ+ItL1GPw/4lkfxFrEqJo2pu0UsWiiOULbSEo5isVfB6HDA89R1Gr/ZOqf9DPrn/fnQf/lfQBLqdpealoeq2OIIry/0q7tMeY7wRz3Fu0ePN8sMUBPXywcdu1F3o2m3lybyU30dy0EVs72WpajZb4onkkRXWzmRTgu5GQfvGov7J1T/AKGfXP8AvzoP/wAr6P7J1T/oZ9c/786D/wDK+gCtaaHc2Ok3VjDJHK0uo6tdvBfzT3lreW13cTsLS4e6DyAMjLuKg/OCxEmWWd1ho9xbR3s0K2Ol3c8FpbW9vpkazWFpFaTT3CKVeOIv5jSyGXCR8PgbWXznn/snVP8AoZ9c/wC/Og//ACvo/snVP+hn1z/vzoP/AMr6AHWtrqU19FqWpR2sE1taXVjbW9lcS3Mey5kgmlllmmhiOSY0CqIxjBOW8wCFtx/yMuh/9gPxD/6V6TR/ZOqf9DPrn/fnQf8A5X1lTaXqI8QaNH/wkWsl20bXXEpi0XzEC3OmAooFiEw2QTlSflGCMkOAbVxp/n6zo+pOsDR6fY6tAm9cyxz3b2m2SLKkD5UkVjkH58cgnD7W0mtLu+MRQ2F5I94YyWV7a7YIriFVGzy5MGRuhDlj8/n/ALiv/ZOqf9DPrn/fnQf/AJX0f2Tqn/Qz65/350H/AOV9AGvRWR/ZOqf9DPrn/fnQf/lfR/ZOqf8AQz65/wB+dB/+V9AGvRWR/ZOqf9DPrn/fnQf/AJX0f2Tqn/Qz65/350H/AOV9AB4e/wCPC6/7Dnif/wBPN7Uupf8ACQPbXCaWlity08ccUtxcyR7bUopklGLaRRLncqAo69GOeYji6FpmovZXJTxFrMQGseIl2xw6KQWTVrtC58yxY5Ygs3OMk4AGANX+ydU/6GfXP+/Og/8AyvoAhj03UJ9PewntbHT1gnsruye0vbjUd11b3S3wkuvtFvA5y6q0nzln3N8ysdxsWtrqU19FqWpR2sE1taXVjbW9lcS3Mey5kgmlllmmhiOSY0CqIxjBOW8wCFv9k6p/0M+uf9+dB/8AlfR/ZOqf9DPrn/fnQf8A5X0AWIrOZNX1K/LIYbnTdLtI1BbzBJaz30rlhjGCJVxz2PTHN+sj+ydU/wChn1z/AL86D/8AK+j+ydU/6GfXP+/Og/8AyvoAPEP/AB4Wv/Yc8Mf+nmyrXrk9d0zUUsrYv4i1mUHWPDq7ZIdFADPq1ogceXYqcqSGXnGQMgjIOr/ZOqf9DPrn/fnQf/lfQBYsbSa2utfmkZCmoalFeQhCxKxrp9nZ4cEAZ3Rsep4I7nAhls9SS+1y/s2tfOudGsLOxW5Mnli7tZL+UG4CDPlkypnBJ4PAwMt/snVP+hn1z/vzoP8A8r6P7J1T/oZ9c/786D/8r6AL1hZw6fZafp8LSNDY2lvZxNKVMhjgjWJS5UAZIHPA/pWVBo95Bo/ha3WSA6joEFk0QLP9knnhsXsJI3cLvCMruFbbkEhtrBTG8/8AZOqf9DPrn/fnQf8A5X0f2Tqn/Qz65/350H/5X0AS2FpeC5vdSvhBHeXcFpaNBaSPNbwwWjTvGBNJGjs5MrljsUYIXHyF5Yrf/kZdc/7Afh7/ANK9Wo/snVP+hn1z/vzoP/yvrKh0vUT4g1mP/hItZDro2hOZRFovmOGudTARgbEphcEjCg/Mck4AQA6DULT+0La806UYs7+xvLS5ljl23CecoiAiQxsnILkktwQOG3ZSnHaaxdXWnS6mLGNNLnkubZrGSZ2vJ3t5rPzJI5owI0Cu52B5Dlh8+Iz56/2Tqn/Qz65/350H/wCV9H9k6p/0M+uf9+dB/wDlfQBWh0nUVt9N0aQ2o0jTH017e6jllN9cR6bLFPbwyQGIRKQUQSOJG3BThE80fZ9EWczavJfysjQxabHaWKgsJIpJp3luywAAIcJbY5OPLOMZPmV/7J1T/oZ9c/786D/8r6P7J1T/AKGfXP8AvzoP/wAr6AJblfECTSfYWsZoLjbzfvJG2nsFCFo0t4j5qH721njOcjzMSAW9mws4dPstP0+FpGhsbS3s4mlKmQxwRrEpcqAMkDngf0qj/ZOqf9DPrn/fnQf/AJX0f2Tqn/Qz65/350H/AOV9AHy7RRRQB9F/Df8A5Evw9/3Ef/S+4qGXTUhm17WNf8N6Hc2r313d3N3M8V1ew6fbKLWGRLaS1K7RHGkjqLknliF3EQib4b/8iX4e/wC4j/6X3Fa91pV5dfa7RtQzo995ovLWaF5btkmz5sEF4ZRtifkEGJioZgrIAogAM29/sP8AtHVf+Ej8jzfPh/4R77Rn7R9m+ywZ/sny/wB55/m+Zny/3mfL7eXWvoVzcXuieH7y5fzLm70rTrm4faq75ZbdJHbagCjJJPAoubPVGmkksdT+zRXO0XSTW5umQqBH5lizyhY3I6hkkTIB2ZLefbtba2s7a1s7ZNlvaQRW1um5m2RRKI0Xc5LHAAHJNAE9ZGrf8f8A4N/7Dlx/6ZtTrXrI1b/j/wDBv/YcuP8A0zanQBr1xtzFC+h+JvEDxxtrVhJ4pexvyqm5thpl3dw28cL4ysYEahkGFbLbg3nN5nXyCYqBE8aMHiJMiNIDGHUuoCspyRkA54JBwQNrZE2izSLeWKXkaaLfvdSXtmbdnuXN47y3EcN35oCxyMzFsxMw3ttdfl8gAzfFEs2o6R4njt5JF02x0bWjeTRM0Zub6GAhLaORTkxxkP5+MDcFTLBZIxc8X280/h/Xz9pkit4dG1aaaKHckk8iWzNErTKwIjByWUD5uATt3JM/U/CvhzUrbVY/7L0qK8v4LtPt39n2z3Ec9wrD7Ru2hiwJ3feBz371ev8ATYrvSNQ0iHZaw3OnXGmxeVEvl28csDQLsiUqMKCMDI6Y4oAv0UUUAZGk/wDH/wCMv+w5b/8Apm0yodb0zw/Lbane61Z/2jGICkMMyRyyRBlEQt9OX5SJZWOFIYOzMo3YRVjm0n/j/wDGX/Yct/8A0zaZUd5p2uz6kt7BqWnLDCgWytrzTLi4FtIylJJw0d7EDIwJXJT5V+UY3sZgBqNqlzFpukyXO+7ggtV8TXtoTEFb7NuaG3lRVKyysVb5UBWMlsxs8Zebwx/yLXhT/sB6T/6SR06TQdCu2FxqWk6NeX7pELq5k063JmkRFQsPODuBx8oLtgYGTjNTaPpsOkaXpemQ7Cljaw25eONYRLIqjfMUUkAu2Wbk8k8nOSAX6KKKAMjxP/yLXiv/ALAerf8ApJJWvWR4n/5FrxX/ANgPVv8A0kkrXoA5/wAX280/h/Xz9pkit4dG1aaaKHckk8iWzNErTKwIjByWUD5uATt3JMeINPvtSudEiTS9N1CxtnvL65i1OcQwG5WIWsCsPInLAiSZseV1RTuG3bLo39jNqGk6hps06LNfabcWMs8ULCNZJ4GhaVIWkJxkkhfMPpnvT722vJvJlsrv7NdQ7whlje4tJEk27kntlkjz0BUh1II67WZJQDOsbHR7mzuLCKwg09La+8vV9OsY4Y7WafyI5DHI0cah4nVon6KWXCuAC0NGiWtnbXviFdMt4LbSRPaxJDbRJHC+pQxsl3NAIxt248mJsEYeGT5QQWkdNpOpGxuobPU47e/1C6S61O8a1lYTHy0heOCOG4jaMFUSNSJCwVc7jIfNq5pttqVrH5N1PprwxJDFaR6bp8ljHBGgK7Nr3MwxjbtAC4x3z8oBfrIuP+Rl0P8A7AfiH/0r0mtesi4/5GXQ/wDsB+If/SvSaAIdb+x/adM/tfyP+Ef8i++2/bNn2H7dut/sv2vf8mzHnbd/y7tn8eyshLm2vbHV9Jsn36fd+I7LRNOhCssb6XLaWd9ewwO4GIjEbpoiGxt2iM42Cuovba8m8mWyu/s11DvCGWN7i0kSTbuSe2WSPPQFSHUgjrtZklpwaN5d1Z3k9z50yT3WoXWIvLWbUpreOxjuIwGO1Y4g8SplshwWLOm9wDL1u1FtdWd4lg7zLqVhd3niG6ktgNN09LoSS28bR5uFj2L5ZCxKm2Vnd+Xdr+t6Z4flttTvdas/7RjEBSGGZI5ZIgyiIW+nL8pEsrHCkMHZmUbsIqxum0e/mW8spdVkm0i+kumvLe6gEl4Yrl3eS1t7xHULDg7ADCzBSQrr8phLzTtdn1Jb2DUtOWGFAtlbXmmXFwLaRlKSTho72IGRgSuSnyr8oxvYzAGlYJfR2Onx38qTXyWtul7LEAI5blY1EroAqjBOSPlH0HQWajiEwjiEzo8wRBK8SNHG0gA3MiMzEAnoN5+pxkyUAZHh7/jwuv8AsOeJ/wD083tXryzhvolgnaQ25cNcQqVEd1GAR5M+QSYycFgCN2NpyrFHo+Hv+PC6/wCw54n/APTze1LqVprF3bXFvaajBZtLPGRL9lmkdbQIvmQ7o7mNw7Hd86spCtgAMBIADD+z29nD4t/skwadpYnsIkS2RoY7jUYmEd4lq1mrOPOXybUGMFlkR9qeYv723pEcEGpSQ22m/wBhwGxaRtMZLRPtsnmov2uNLJ3tx5Y+Ryrlj5q7wojjMtyPSrySyewv7ixMEf2I2A0mwew+xPaSLNE6LNcTodjLGUGwD5cEMGwJbWwvBcrfaldQXV5FBNaWxtLZ7SCGCZo5JAInmlcu5RNxMhGEGAuWMoBR0y3mt/EGvie5kuLiXR/D81xK25Y/MNzqq7YISxCRgABVBPTJLMxeSnJaix1zQ5EsJIUF3Iup6/dyWwm1Rp7SSKG0drfMhDSOpAdYkUwoiDlFroI7Ly9SvtR8zP2qx06y8rbjZ9klu5d+7PO7zsYwMbe+floQ6PfhbO0vNVkvdNsntJ4VuIANQmmtXSaE3l4rhWCsAw2wITtXczDcJwCTxD/x4Wv/AGHPDH/p5sqvXl5DZxq7q8kkriG2t4QrT3M7AsIoVYgZwCSSwAALMVVCy0fEP/Hha/8AYc8Mf+nmyq9eWOnahEsN/Z2t3CriVY7yCKeNZAGUOFlBGcEjOO/vQBzltHrVrfeKZFKXeuv4Z0S68tpHNo+oeZq22CBXKBYQQFUZXjliXZnY0bStN0WbRre58P6NaXJT7Fp2oWTRXdzNPDbOzrcTGzt5BI6K7bgpB2sCVJCy6Vr4b0WyvtSu7O0tLVb3TrbTjHp8CWckSpJPJJJHNbFXBfemcYI8pTngbEk0rV5+bjVkea0S5Ojzx2KRyW11LbyWq3d2pkMckiqzYCpGh3N8nK+SAYCfab6XTFFjBqUPiD/hItceC8lWCxuYobmyt9OubsbHO1bcxhU8lvmKMyhkMkWvbXv2WzutP0+Lbq6zz2lrpkreda2E6wQy4SRAjfY0DxyZyCqyrGArFbdL0mkJFFpf9lyJZz6VatYWLTRyXUC2biJWgmiMqOwPlxkHzFbKD5iCyysXw/pEyO2qWdjqV3NPJd3E15aQyKZ5IooGMEUoYIoWONAAScINxZsu4BFoEH2a58XQ+dPOV1yJnmuX3yyO+j6a7MxACjJJwFCqOigKAqzW/wDyMuuf9gPw9/6V6tTtK0TTdHm1mSyt7SBNRu4bgR2ttFbiKOK2itxD+74IyruOBzIeMklm2/8AyMuuf9gPw9/6V6tQBpyxRTxSwzRpLDMjxTRyqrxyRuNrI6MCCCMgjFc7p2j6ENev7yy0vTbQaKg0yI2tpbwSPd3cMN5NK3lpyFRoUjOQfnlBBDAnoiJjLGQ6CEJIJEKMZGkJTYyvuAAA3ZGw5yORtw9ewsvsSXQaXzpbm+vbyWYrtd/PmZ40ckkny02RKc/djA4ACqAczbRQpofhnxAkca61fyeFnvr8Koubkand2kNxHM+MtGRIwVDlVwu0L5K+XNrdqLa6s7xLB3mXUrC7vPEN1JbAabp6XQklt42jzcLHsXyyFiVNsrO78u7aUOizRrZ2L3kb6LYPayWVmLdkuUNm6S28c135pDRxsqlcRKx2Ludvm89JtHv5lvLKXVZJtIvpLpry3uoBJeGK5d3ktbe8R1Cw4OwAwswUkK6/KYQCLxHbzSR6fO1xILeDWfDJit4t0YedtZtUaSdg2WABwi4AByx3EKYOgqnqNl9vt44PM8vZfaZe7tu/P2K9hvdmMj72zbnPGc84wblAHyNRRRQB714A0ewu/CWh3Es2qrJJ9v3C21jV7aL5b2dRtitrhIx05wo9epyda5j8EWU0lteeIJ7a5j2+ZDc+LtVilTcocbkkvgwyCCOO/vUXw3/5Evw9/wBxH/0vuKsFdd0OPX9WubjTZ7T7VqGrXlvFa3C3b2kQ2Rhbkz+V5iQpGAPs4DFMFssZqAJrjTPDVpLaQ3WqalBNeSeVaRXHifWYpLiTcq7IVe8BY5KjAB6j1qz/AMI9pn/Pxrn/AIUGvf8AyXVC5F+954oXTrO11BJUt7bURqLAGGQWYYWdvGw2yx7HWTy2eFd0zfvSZmFrtaY1u+m6S9tcz3Vs9jaNb3VyWae5iMSlJpmdQ29hgtlRyeg6UAVP+Ee0z/n41z/woNe/+S6ytT0LTkvfCaifWSJtZnjffrmtOQo0nUJMoz3RKnIHIIOMjOGIPWVkat/x/wDg3/sOXH/pm1OgA/4R7TP+fjXP/Cg17/5Lqs+m+Gku4dPk1TUkvp0MsNo/ibWVuZYwGJdIjebyBtbkD+E+nHQVyE/PhLxncnm5WfxfdLMf9aLixvbtLaUP97dEIohGc5Xy1xjYMAGrLoejQRyzTXmsxQwo8s0kviLXEjjjQbmd3a7AAAzk5qG803w3p8SzX+qalaQtIIlkvPE2swRtIQWCBpbwDOATjPb2rC8UaxoWo2Pie2m1XTkh0/TtatYrGe7t1uLzVY42RJDbFhJiFlZYgwO5m3hR5KSS9dJLpMarrTyRujWkUUFyjPOHgmcOiWqoWBMpKABFJchB821QoBUi0PRp44pobzWZYZkSWGSLxFrjxyRuNyujrdkEEYwc0/8A4R7TP+fjXP8AwoNe/wDkupdEtri00yzhuE8qU+dObYMrLZLcSvOlkjIShSAMIlxgYQYAHA0qAOT0zQtOe98WKZ9ZAh1mCNNmua0hKnSdPky7JdAsck8kk4wM4UAWb2x8Kab5P9o6xfWfnb/J+2+KdYt/M2bd2zzb0ZxkZ+o9auaT/wAf/jL/ALDlv/6ZtMp2pCxs7fUp/saXd3qaC0S0mYu2oyCF1jsh5gYCMjeWG3aoMkhABZiAVLzTfDenxLNf6pqVpC0giWS88TazBG0hBYIGlvAM4BOM9varP/CPaZ/z8a5/4UGvf/JdMaw1WysbJrD7Lf61b6bBpn23V7i6ijKpH885VFmbLuEaQAqWwMv+7XEvh8Qpouj28TyOLG1j0yQyoscgnsP9CmV1VnXKsjA4dhxwzAhiAN/4R7TP+fjXP/Cg17/5Lo/4R7TP+fjXP/Cg17/5LrXooA5PxFoWnQ+H/EsqT6yXi0bU5FEuua1LGSttIwDxy3RQj1BUg+mDWr/wj2mf8/Guf+FBr3/yXR4n/wCRa8V/9gPVv/SSStegDFl0PRoI5ZprzWYoYUeWaSXxFriRxxoNzO7tdgAAZyc1Deab4b0+JZr/AFTUrSFpBEsl54m1mCNpCCwQNLeAZwCcZ7e1Hi+zhuvD+vvM0jR22j6tMsBK+Q862zNFLKuMkxkZQbsAndgsitHY1Sw1e7vdGuLK6sYIrD7bOwvbaa5zdyRrbxOiQzQnhGnU5kx84+UkBogCvZ6b4b1CJprDVNSu4VkMTSWfibWZ41kADFC0V4RnBBxnv71Mmh6NI06R3msM8DiKZU8Ra6xikKLKEcC7yDtZWwezA9DzQvfEaW8VxptzfWNhq/n3GnfbZ5IoLGJktre5N9GLtiDtWaIiIliWO3JRDOr/AAtNorT+LYtKubSe3TWbeYG2uUuSwl0qxUzPIGZmLusm5ixLMGySQTQBf/4R7TP+fjXP/Cg17/5LrKn0LTh4g0aIT6ztfRtdkYnXNaMgaO50xQFkN1vA+Y5AYA8ZztBXrKyLj/kZdD/7AfiH/wBK9JoAjOh6MsqQm81gTSJJLHGfEWuiR44yiu6r9syQpZQTjjcPXmT/AIR7TP8An41z/wAKDXv/AJLouP8AkZdD/wCwH4h/9K9JrXoAyP8AhHtM/wCfjXP/AAoNe/8Akuj/AIR7TP8An41z/wAKDXv/AJLrXooAyP8AhHtM/wCfjXP/AAoNe/8Akuj/AIR7TP8An41z/wAKDXv/AJLrXooA5PQtC06WyuWafWARrPiKMeXrmtRjEerXcYJWO6AzgDccZJySSSSdKXQ9GgjlmmvNZihhR5ZpJfEWuJHHGg3M7u12AABnJzT/AA9/x4XX/Yc8T/8Ap5va0Z7a3ufs/npvWCeO5jUswTzY8lGdQQp2n5lyDhgG+8gKgGLZ6b4b1CJprDVNSu4VkMTSWfibWZ41kADFC0V4RnBBxnv70Wem+G9Qiaaw1TUruFZDE0ln4m1meNZAAxQtFeEZwQcZ7+9Vpra41SPX72yTfZ3s+iCKBGVY9WtbCZJrqdd5VD9oQm3G7CusKHeY5AUo63qhll1a4sY9RtSvgrxS5uZra50+SWe1No8O1LhY5yYd7lW2YHnHaxJYKAa9vpnhq7lu4bXVNSnms5PKu4rfxPrMslvJuZdkypeEqchhggdD6VZ/4R7TP+fjXP8AwoNe/wDkuo7+KG2vfBSW0ccKpqVxYKsKrGFtP7JvZfs6hAB5eY4m29MxqcZQY26AOT13QtOisrZln1gk6z4djPma5rUgxJq1pGSFkuiM4J2nGQcEEEAjV/4R7TP+fjXP/Cg17/5Lo8Q/8eFr/wBhzwx/6ebKtG5tre8hktrlPMgl2iWMswWRQwYo4UjKHGGU8MCQQQSCAYVlY+FNS87+ztYvrzydnnfYvFOsXHl7923f5V6cZwcfQ+lPt9M8NXct3Da6pqU81nJ5V3Fb+J9Zlkt5NzLsmVLwlTkMMEDofSpljXUdXvZ4jIlnb6dPpNxPbySRG8uZJ8tGssTK+bbawVgThrhwCrRsDWSO8ttf0prmCxtNOSx1DRdDisC8u93aK7Inykax/u7cGNVRlG1wXztWQAfPpnhq2ju5rjVdShhtHSK7km8T6ykdvI6oypMz3gAJDoQCR94f3uX/ANkaB9m+2/2hqv2PyPtX2n/hJNb+z+Rt8zzvN+2bNmOc5xjmodKgefTLXWILaC5v7ye91iyF7cywL5WpSl4TO6RygSxwFIgfLbaFKKwRiS/QrVJLA2uo7Jb/AE7Wb26v441kjtk1G4nfU12JvYNGBMjxbif4WISRNsQAWem+G9Qiaaw1TUruFZDE0ln4m1meNZAAxQtFeEZwQcZ7+9U4NC04+INZiM+s7U0bQpFI1zWhIWkudTUhpBdbyPlGAWIHOMbiW1NL/wBIvdZ1OH5bG8+xQ2mz/V3n2aNt+oL0/wBZuEQO35lt0YMyOu1bf/kZdc/7Afh7/wBK9WoAZLoejQRyzTXmsxQwo8s0kviLXEjjjQbmd3a7AAAzk5qhbR+CL2aO2s/EE9zcybvLhtvF2qyyvtUudqR3xY4AJPHb2rqayLT/AEvWtZupOP7J8vRbVOu3z7e21K4myMff3QLgg48jIP70gAEZ0PRllSE3msCaRJJY4z4i10SPHGUV3VftmSFLKCccbh68xPpvhpLuHT5NU1JL6dDLDaP4m1lbmWMBiXSI3m8gbW5A/hPpwfY4rfxTp04Z5Li60bxA000xVpPLW80sxwrtAAjQEhQAOpY5aRnkzrozfYPEZREbRW1K+nvtVd2Gp25t5wLia3h2kMbZkZYXMiMohXbHL5C/bADRuNM8NWktpDdapqUE15J5VpFceJ9ZikuJNyrshV7wFjkqMAHqPWrP/CPaZ/z8a5/4UGvf/JdULkX73nihdOs7XUElS3ttRGosAYZBZhhZ28bDbLHsdZPLZ4V3TN+9JmYWu1pjW76bpL21zPdWz2No1vdXJZp7mIxKUmmZ1Db2GC2VHJ6DpQB8pUUUUAfSngWzm0/wzp1hM0bTWN3rNnK0RYxtJBqd1ExQsAcZHHArQl0W2lllH2i6SxuJHlu9MQwfYLqVyXdpA0ZlAc8yKsiqxzuVvNbzSigB9zpSTzyTRXt9Z/aNovksHijW9CgRgyM8bOrbfl3xsj4wN37tfLvRRwwRxQQxxxQwxpFFHEqpHHGo2KiKoAAAGAMUUUASVkat/wAf/g3/ALDlx/6ZtToooA05Vd1VVlkiIeNy0YjJKo6uyHzFYYYfKeM4JwQcEZ0ui20sso+0XSWNxI8t3piGD7BdSuS7tIGjMoDnmRVkVWOdyt5reaUUAW7+0h1Cx1CwmaRYb21uLOZoiokEc6NCxQsCM4JxwaqX+kSX15Z3a6rqVo9pHKsEdqunvCryAq0228tpT5mDsDZ4BIGPMbzCigC/bQywQxxS3U906bt09ysCyyZYsNwto44+Ogwg6evJmoooAyNJ/wCP/wAZf9hy3/8ATNplJc6NNcX8mox61qttK0C20ccCaW8UEQIZlhF1aSON5AZ/m5wueI1CFFAD5tHEksd1FqOpW2oC1t7Ke9t3tjJcwQNI6ia3mhe0zuZm3CBSMkAhWKm9bW1tZwx29umyJNxALM7MzsXZ5HclmdiSzMSSSSSSTklFAE9FFFAGR4n/AORa8V/9gPVv/SSSteiigCnc2Ed7pt3plzPPJHd2MthcT/ulndZYjC0nyIIwxyTwgGe2OKL2wS88mRZ57W7g3C3u7TyvtESybRJGBMjxlWwNysjDIDYDRqyFFAD7O0hs42jRnkklczXNxMVae5nYBTLMygDOAAAAAAAqhVQKpb2cNtNqU0bSF9Quku5g5Uqsi2sFoAmADjbGp6nkn1wCigCzWRcf8jLof/YD8Q/+lek0UUAS32lm9ubK8i1C+sbm0gu7ZHshZNviumgkdXW8glXrGhGAO/rVmzt57aJo5r67vXLlxLeLaLIqlQNgFpDEmOp+6Tz17AooAs0UUUAFFFFAGR4e/wCPC6/7Dnif/wBPN7UupaW2p21xayahfQwzzxSuLcWRzEiKptWE9u6mJiNzhgc5Kk7G2UUUAEels0N1b3+oX2oxT+UVF4LKJoGjYuskD6fbwsHB2sGzlSoKkEZJBpMC/aGvZ59Tlmge0eTU0tGxaSYL26xW8McIVv4/3eWwAxIjUIUUAFtpSQTxzS3t9efZ9wsUv3ikWyDAxkxskauzbfl3yM74yN37xvM0qKKAMjxD/wAeFr/2HPDH/p5sqvX1s97aXNot3d2hnQxm4sXjS5jBIyYnkRgCRxnbkZyCCAQUUAUINDWO2uLC51G+vNOmsZNPNlPFpsECQOoiIj/s+1hcYXKjD4APTIBVToaOkyTalqs37ieCweWaLzdNE0TQmS1lSMSGUKcLJI0jjn5v3jeaUUAS3GkWc32F7d57CfT4JbWwm09kj+zQSeUHiWCRWtipCIAGiYDAIwVBENzoUFxYSWAvb6EXE63N/cxfZHuL98AOLr7RC8ZVsKGURgbVCACMeXRRQBcsrS6tfO8/U76+37dv21LBPK25zs+xW8PXPOc9BjHepb/8jLrn/YD8Pf8ApXq1FFAGoUcyRyCVwipIjRAR+W7MyEOxKl8rggYYD5jkHAKQ2VpDZQyQwtIyPdX94TIVLeZeXUt3IMqAMBnIXjpjr1JRQAj2kL31rfs0nnW1reWaKCvlmO6e3mcsMZyDEuOR1PBzxUl0W2lllH2i6SxuJHlu9MQwfYLqVyXdpA0ZlAc8yKsiqxzuVvNbzSigB9zpSTzyTRXt9Z/aNovksHijW9CgRgyM8bOrbfl3xsj4wN37tfLvRRwwRxQQxxxQwxpFFHEqpHHGo2KiKoAAAGAMUUU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PCB Size Calculation Examples

To better understand PCB size calculation, let’s explore a couple of examples:

Example 1: Simple PCB Size Calculation

Consider a simple PCB design with the following components:

  • 1x microcontroller (10mm x 10mm)
  • 2x resistors (2mm x 1mm each)
  • 1x capacitor (5mm x 2mm)
  • 1x LED (3mm diameter)

Assuming a minimum spacing of 1mm between components and 2mm from the PCB edges, let’s calculate the PCB size:

  1. Component placement:
  2. Microcontroller: 10mm x 10mm
  3. Resistors: 2 x (2mm x 1mm) = 4mm x 1mm
  4. Capacitor: 5mm x 2mm
  5. LED: 3mm diameter

  6. Total component area:

  7. Length: 10mm + 4mm + 5mm + 3mm = 22mm
  8. Width: 10mm + 1mm + 2mm = 13mm

  9. Add spacing between components:

  10. Length: 22mm + (4 x 1mm) = 26mm
  11. Width: 13mm + (3 x 1mm) = 16mm

  12. Add spacing from PCB edges:

  13. Length: 26mm + (2 x 2mm) = 30mm
  14. Width: 16mm + (2 x 2mm) = 20mm

The resulting PCB size for this simple design would be approximately 30mm x 20mm.

Example 2: Multi-Layer PCB Size Calculation

Consider a more complex PCB design with the following requirements:

  • 50 components of various sizes
  • 4-layer PCB
  • Minimum trace width: 0.2mm
  • Minimum spacing between traces: 0.2mm
  • Minimum spacing between components: 0.5mm
  • Mounting holes: 4 x 3mm diameter

Using CAD software for this example:

  1. Create a new PCB project in the CAD software.
  2. Import or create the component footprints and symbols in the library.
  3. Place the components on the PCB layout, optimizing their placement and orientation.
  4. Define the trace width (0.2mm) and spacing (0.2mm) rules based on the manufacturing guidelines.
  5. Route the traces on the four layers, optimizing the routing to minimize the PCB size.
  6. Add the mounting holes (4 x 3mm diameter) to the PCB design.
  7. Use the software’s measurement tools to determine the PCB dimensions.

The CAD software will calculate the precise PCB size based on the component placement, trace routing, and manufacturing constraints. Let’s assume the resulting PCB size is 80mm x 60mm x 1.6mm (length x width x thickness).

Frequently Asked Questions (FAQ)

  1. What is the minimum PCB size that can be manufactured?
  2. The minimum PCB size depends on the manufacturing capabilities of the PCB fabricator. Typically, the smallest PCB size that can be reliably manufactured is around 10mm x 10mm. However, some advanced manufacturing processes may allow for even smaller sizes.

  3. How does the number of layers affect the PCB size?

  4. Increasing the number of layers in a PCB allows for more efficient routing and higher component density. By distributing traces and components across multiple layers, the overall PCB size can be reduced compared to a single-layer board with the same functionality.

  5. Can I reduce the PCB size by using smaller components?

  6. Yes, selecting components with smaller footprints, such as chip-scale packages (CSPs) or quad-flat no-lead (QFN) packages, can help reduce the PCB size. However, it’s important to consider the availability, cost, and manufacturability of smaller components.

  7. What is the impact of trace width and spacing on PCB size?

  8. Trace width and spacing directly affect the PCB size. Using narrower traces and smaller spacing between them allows for more compact routing and reduces the overall PCB area. However, it’s crucial to adhere to the manufacturing guidelines and ensure the traces can handle the required current and voltage.

  9. How can I optimize the PCB size for manufacturing?

  10. To optimize the PCB size for manufacturing, consider the following tips:
    • Adhere to the manufacturing guidelines for minimum trace width, spacing, and hole sizes.
    • Provide sufficient clearance around the PCB edges and mounting holes.
    • Avoid placing components too close to the PCB edges.
    • Use standard component footprints and packages.
    • Utilize multi-layer PCBs and efficient routing techniques.
    • Communicate with the PCB manufacturer for specific size requirements and constraints.

Conclusion

Calculating the size of a PCB is a critical step in the design process. It involves considering various factors such as component placement, trace width and spacing, layer count, and mechanical constraints. By understanding these factors and utilizing the appropriate calculation methods, you can determine the optimal PCB size for your design.

Manual calculation, CAD software tools, and PCB manufacturer specifications are common methods for calculating PCB size. Each method has its advantages and limitations, and the choice depends on the complexity of the design and the available resources.

To optimize the PCB size, techniques such as component selection and placement, trace routing optimization, multi-layer design, and design for manufacturing (DFM) can be employed. These techniques help reduce manufacturing costs, improve efficiency, and ensure compatibility with the manufacturing process.

By following the guidelines and best practices discussed in this article, you can accurately calculate and optimize the size of your PCB, resulting in a well-designed and manufacturable product.

Factor Impact on PCB Size
Component Placement Proper component placement and spacing affect PCB size
Trace Width and Spacing Narrower traces and smaller spacing reduce PCB size
Layer Count Multi-layer PCBs allow for more compact designs
Mechanical Constraints Enclosure dimensions and mounting holes impact PCB size
Calculation Method Description
Manual Calculation Measuring component dimensions and spacing manually
CAD Software Automated calculation using PCB design software
Manufacturer Specs Following the manufacturer’s guidelines for standard PCB sizes

Remember, calculating and optimizing the PCB size is an iterative process that requires careful consideration of design requirements, manufacturing constraints, and overall system functionality. By approaching PCB size calculation with a systematic and informed approach, you can create efficient and reliable PCBs that meet your project’s needs.