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╓╖µ@▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒MÑ▒▒▒MM▒▒▒╜M▒▒▒ß▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒@@
⠀⢠⠴⡲⡒⡳⡱⡙⢝⠹⡙⢝⡙⢝⢒⠖⡖⡦⢤⣀⡀⠀⠀⠀⠀⠀⠀
⣀⢾⠵⠵⠮⠶⠵⢼⡨⡊⢎⢒⠜⡌⢆⢣⠱⡘⡌⣪⠮⡷⠦⡤⢤⣀⡀
⡇⠀⠀⣀⣄⣄⡀⠈⣗⠜⡌⢎⠜⡌⡪⡂⡇⢕⢼⠃⠀⣀⣀⣀⠀⠀⣧
⡆⠀⠀⠿⡿⡿⡇⠀⣿⠨⡊⢆⢣⠱⡨⡢⠣⡑⢽⡀⠸⣿⣿⣿⠀⠀⣺
⠦⣀⣀⣠⣀⣀⣀⡤⡗⡑⡕⢅⢣⢑⢕⠸⡘⢜⢼⡄⠀⠉⠉⠀⠀⣀⡏
⠀⢘⡇⡎⡢⡱⣸⠚⠺⢬⠮⠼⠴⣵⢬⢮⣎⢢⢑⢍⠝⡍⢏⢫⢫⠏⠀
⠀⠠⣇⢇⠪⡢⢺⡁⠀⢼⠀⠀⠀⢷⠀⠀⣾⢘⢌⢆⢣⢱⢱⡱⠋⠀⠀
⠀⠀⣷⠡⡣⡊⢎⢷⣀⡏⠀⠀⠀⢸⡀⣰⢇⢕⢜⣔⡵⠓⠋⠀⠀⠀⠀
⠀⠀⣷⢱⠨⡊⡆⡣⢫⢣⢤⣤⣤⡬⡿⠗⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢸⠨⡊⢆⠕⡅⡳⡙⡍⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡇⢕⡑⡅⢇⠪⡢⡱⡘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⡇⡇⡪⡘⡌⢎⢢⠪⡘⢼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣏⢎⢢⢃⢎⠪⡂⢇⢣⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠳⠵⢕⣕⣜⣜⣜⠼⠼⠞⠁⠀⠀⠀⠀⠀
⠀⢠⠴⡲⡒⡳⡱⡙⢝⠹⡙⢝⡙⢝⢒⠖⡖⡦⢤⣀⡀⠀⠀⠀⠀⠀⠀
⣀⢾⠵⠵⠮⠶⠵⢼⡨⡊⢎⢒⠜⡌⢆⢣⠱⡘⡌⣪⠮⡷⠦⡤⢤⣀⡀
⡇⠀⠀⣀⣄⣄⡀⠈⣗⠜⡌⢎⠜⡌⡪⡂⡇⢕⢼⠃⠀⣀⣀⣀⠀⠀⣧
⡆⠀⠀⠿⡿⡿⡇⠀⣿⠨⡊⢆⢣⠱⡨⡢⠣⡑⢽⡀⠸⣿⣿⣿⠀⠀⣺
⠦⣀⣀⣠⣀⣀⣀⡤⡗⡑⡕⢅⢣⢑⢕⠸⡘⢜⢼⡄⠀⠉⠉⠀⠀⣀⡏
⠀⢘⡇⡎⡢⡱⣸⠚⠺⢬⠮⠼⠴⣵⢬⢮⣎⢢⢑⢍⠝⡍⢏⢫⢫⠏⠀
⠀⠠⣇⢇⠪⡢⢺⡁⠀⢼⠀⠀⠀⢷⠀⠀⣾⢘⢌⢆⢣⢱⢱⡱⠋⠀⠀
⠀⠀⣷⠡⡣⡊⢎⢷⣀⡏⠀⠀⠀⢸⡀⣰⢇⢕⢜⣔⡵⠓⠋⠀⠀⠀⠀
⠀⠀⣷⢱⠨⡊⡆⡣⢫⢣⢤⣤⣤⡬⡿⠗⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢸⠨⡊⢆⠕⡅⡳⡙⡍⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡇⢕⡑⡅⢇⠪⡢⡱⡘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⡇⡇⡪⡘⡌⢎⢢⠪⡘⢼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣏⢎⢢⢃⢎⠪⡂⢇⢣⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠳⠵⢕⣕⣜⣜⣜⠼⠼⠞⠁⠀⠀⠀⠀⠀⠀⢠⠴⡲⡒⡳⡱⡙⢝⠹⡙⢝⡙⢝⢒⠖⡖⡦⢤⣀⡀⠀⠀⠀⠀⠀⠀
⣀⢾⠵⠵⠮⠶⠵⢼⡨⡊⢎⢒⠜⡌⢆⢣⠱⡘⡌⣪⠮⡷⠦⡤⢤⣀⡀
⡇⠀⠀⣀⣄⣄⡀⠈⣗⠜⡌⢎⠜⡌⡪⡂⡇⢕⢼⠃⠀⣀⣀⣀⠀⠀⣧
⡆⠀⠀⠿⡿⡿⡇⠀⣿⠨⡊⢆⢣⠱⡨⡢⠣⡑⢽⡀⠸⣿⣿⣿⠀⠀⣺
⠦⣀⣀⣠⣀⣀⣀⡤⡗⡑⡕⢅⢣⢑⢕⠸⡘⢜⢼⡄⠀⠉⠉⠀⠀⣀⡏
⠀⢘⡇⡎⡢⡱⣸⠚⠺⢬⠮⠼⠴⣵⢬⢮⣎⢢⢑⢍⠝⡍⢏⢫⢫⠏⠀
⠀⠠⣇⢇⠪⡢⢺⡁⠀⢼⠀⠀⠀⢷⠀⠀⣾⢘⢌⢆⢣⢱⢱⡱⠋⠀⠀
⠀⠀⣷⠡⡣⡊⢎⢷⣀⡏⠀⠀⠀⢸⡀⣰⢇⢕⢜⣔⡵⠓⠋⠀⠀⠀⠀
⠀⠀⣷⢱⠨⡊⡆⡣⢫⢣⢤⣤⣤⡬⡿⠗⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢸⠨⡊⢆⠕⡅⡳⡙⡍⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡇⢕⡑⡅⢇⠪⡢⡱⡘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢨⡇⡇⡪⡘⡌⢎⢢⠪⡘⢼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠐⣏⢎⢢⢃⢎⠪⡂⢇⢣⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠳⠵⢕⣕⣜⣜⣜⠼⠼⠞⠁⠀⠀⠀⠀⠀⠀⢠⠴⡲⡒⡳⡱⡙⢝⠹⡙⢝⡙⢝⢒⠖⡖⡦⢤⣀⡀⠀⠀⠀⠀⠀⠀
⣀⢾⠵⠵⠮⠶⠵⢼⡨⡊⢎⢒⠜⡌⢆⢣⠱⡘⡌⣪⠮⡷⠦⡤⢤⣀⡀
⡇⠀⠀⣀⣄⣄⡀⠈⣗⠜⡌⢎⠜⡌⡪⡂⡇⢕⢼⠃⠀⣀⣀⣀⠀⠀⣧
⡆⠀⠀⠿⡿⡿⡇⠀⣿⠨⡊⢆⢣⠱⡨⡢⠣⡑⢽⡀⠸⣿⣿⣿⠀⠀⣺
⠦⣀⣀⣠⣀⣀⣀⡤⡗⡑⡕⢅⢣⢑⢕⠸⡘⢜⢼⡄⠀⠉⠉⠀⠀⣀⡏
⠀⢘⡇⡎⡢⡱⣸⠚⠺⢬⠮⠼⠴⣵⢬⢮⣎⢢⢑⢍⠝⡍⢏⢫⢫⠏⠀
⠀⠠⣇⢇⠪⡢⢺⡁⠀⢼⠀⠀⠀⢷⠀⠀⣾⢘⢌⢆⢣⢱⢱⡱⠋⠀⠀
⠀⠀⣷⠡⡣⡊⢎⢷⣀⡏⠀⠀⠀⢸⡀⣰⢇⢕⢜⣔⡵⠓⠋⠀⠀⠀⠀
⠀⠀⣷⢱⠨⡊⡆⡣⢫⢣