⣿⣿⣾⣿⣿⡿⠟⠀⢘⢍⣿⣿⣿⣿⣿⣿⣿⢿⣧⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣾ ⣿⣿⣿⡿⠟⠃⠀⠀⢀⢼⣿⣿⣿⡿⠟⠛⢏⠻⣭⡅⠀⠂⠀⠙⠋⣷⣜⣿⣟⣿ ⡻⣿⡿⠇⠀⠀⠀⣠⠩⣿⣿⣿⢏⣤⢆⣼⡜⣦⣈⢿⣦⠀⠀⠀⠀⠈⢛⣿⣿⣿ ⣿⠟⠁⠀⠀⢀⠒⣮⣮⣿⡿⠀⣾⣳⠟⠙⣿⣌⣿⡄⢿⣿⣂⠀⠀⠀⠀⠟⣿⣿ ⣾⠀⠀⠀⠠⢶⣮⣿⣿⣿⠃⢘⡩⠉⠐⠒⠛⠻⣿⣷⠘⣿⣿⣣⡀⠀⠀⠀⢹⣿ ⠃⡔⠀⠀⠀⠠⠈⢿⣿⡇⢀⣼⣽⠀⠐⡿⠷⠄⢻⣿⡀⣿⣿⣧⡇⠀⠀⠀⢰⣷ ⣸⡝⡀⠀⠀⠀⠀⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢥⣿⡇⡿⣿⠺⡇⠀⠀⢐⣿⣇ ⣝⣻⣷⡀⡀⠀⠀⠀⠘⢿⣷⠀⠀⣀⣀⢀⡄⢴⣿⣿⡘⣝⣿⣺⠃⠀⠀⠐⢿⣿ ⣺⣿⣟⡿⣕⠀⠀⠀⠀⠀⠉⢷⡔⢷⣤⠎⠁⠨⣿⢧⢴⠳⣿⣿⠀⠀⠀⠨⣿⣿ ⣿⣟⣳⣷⡷⣮⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣀⠐⣃⣂⣲⣟⡟⠁⠀⠀⠀⢨⣿⣿ ⢍⣏⣊⡟⣿⣾⣟⠆⠀⠀⠀⠀⠀⠊⠟⠛⠟⡨⣿⠦⡓⠟⠃⠀⠀⠀⠀⣸⣿⣿ ⣓⣶⣷⣏⠻⡽⣗⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣟⣿⣿ ⡘⣿⡉⣟⡿⣕⡅⣂⡉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣷⣿⣿ ⣺⣿⡬⣧⡫⠒⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿ ⣾⣿⠷⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣿ ⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿ ⡯⣷⠂⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⣼⣿ ⣿⣽⡂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿ ⡇⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠘⠗⡄⠀⠀⠀⠀⠀⠀⠀⠀⣬⣾⡿⣿ ⣿⣿⡟⣿⡖⣦⣔⣔⣀⡤⣶⠍⠀⠀⠀⠀⠀⠉⠉⠃⠒⠤⣤⣴⣶⣿⣿⣿⣿⣿ ⠙⣿⡗⠿⡿⣿⣿⣿⣯⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣟⣿ ⣿⡟⢷⡶⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⡳⣟⣿

⣿⣟⡳⠿⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⡶⢷⡟⣿ ⣿⣟⣿⣿⣿⣿⢿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣯⣿⣿⣿⡿⠿⡗⣿⠙ ⣿⣿⣿⣿⣿⣶⣴⣤⠤⠒⠃⠉⠉⠀⠀⠀⠀⠀⠍⣶⡤⣀⣔⣔⣦⡖⣿⡟⣿⣿ ⣿⡿⣾⣬⠀⠀⠀⠀⠀⠀⠀⠀⡄⠗⠘⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⡀⣧⣿⡇ ⣿⣿⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠿⡼⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⡂⣽⣿ ⣿⣼⠀⠀⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⠀⠀⠀⠀⠀⠀⡄⣠⠀⠂⣷⡯ ⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣛⣟ ⣿⣶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠷⣿⣾ ⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠈⠒⡫⣧⡬⣿⣺ ⣿⣿⣷⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡉⣂⡅⣕⡿⣟⡉⣿⡘ ⣿⣿⣟⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡷⣗⡽⠻⣏⣷⣶⣓ ⣿⣿⣸⠀⠀⠀⠀⠃⠟⡓⠦⣿⡨⠟⠛⠟⠊⠀⠀⠀⠀⠀⠆⣟⣾⣿⡟⣊⣏⢍ ⣿⣿⢨⠀⠀⠀⠁⡟⣟⣲⣂⣃⠐⣀⠀⡀⢦⠙⠀⠀⠀⠀⠀⠀⣮⡷⣷⣳⣟⣿ ⣿⣿⠨⠀⠀⠀⣿⣿⠳⢴⢧⣿⠨⠁⠎⣤⢷⡔⢷⠉⠀⠀⠀⠀⠀⣕⡿⣟⣿⣺ ⣿⢿⠐⠀⠀⠃⣺⣿⣝⡘⣿⣿⢴⡄⢀⣀⣀⠀⠀⣷⢿⠘⠀⠀⠀⡀⡀⣷⣻⣝ ⣇⣿⢐⠀⠀⡇⠺⣿⡿⡇⣿⢥⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠻⠀⠀⠀⠀⡀⡝⣸ ⣷⢰⠀⠀⠀⡇⣧⣿⣿⡀⣿⢻⠄⠷⡿⠐⠀⣽⣼⢀⡇⣿⢿⠈⠠⠀⠀⠀⡔⠃ ⣿⢹⠀⠀⠀⡀⣣⣿⣿⠘⣷⣿⠻⠛⠒⠐⠉⡩⢘⠃⣿⣿⣿⣮⢶⠠⠀⠀⠀⣾ ⣿⣿⠟⠀⠀⠀⠀⣂⣿⢿⡄⣿⣌⣿⠙⠟⣳⣾⠀⡿⣿⣮⣮⠒⢀⠀⠀⠁⠟⣿ ⣿⣿⣿⢛⠈⠀⠀⠀⠀⣦⢿⣈⣦⡜⣼⢆⣤⢏⣿⣿⣿⠩⣠⠀⠀⠀⠇⡿⣿⡻ ⣿⣟⣿⣜⣷⠋⠙⠀⠂⠀⡅⣭⠻⢏⠛⠟⡿⣿⣿⣿⢼⢀⠀⠀⠃⠟⡿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⢿⠿⠿⠾⣧⢿⣿⣿⣿⣿⣿⣿⣿⢍⢘⠀⠟⡿⣿⣿⣾⣿⣿