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⠐⡈⢜⡳⣞⢥⣚⠉⣆⣱⢍⣞⣨⣵⣤⣴⣶⣷⣾⣷⣶⣶⣭⣚⠥⢂⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡱⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⣑⠺⣤⡹⣝⡞⣭⠆⣹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⡭⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⡛⠦⣝⣦⢫⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡱⣃⢾⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⢏⠳⣎⢧⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢋⠉⠋⠻⠱⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⣃⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⡑⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡙⢾⠀⠀⠀⠀⠀⠀⠀⠀ ⡐⢣⠴⣩⣿⣿⣿⣿⣿⣿⢻⡟⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣙⠾⠀⠀⠀⠀⠀⠀⠀⠀ ⣍⡓⢎⣽⣿⣿⣿⣿⣿⠯⠟⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠻⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢥⢫⡄⠀⠀⠀⠀⠀⠀⠀ ⢬⠳⣍⢾⣿⣿⣿⣿⣿⣧⠢⠔⡁⠀⠀⣠⣦⣄⠀⢀⡀⣀⣤⣶⣷⠿⠛⠛⠲⢝⠻⠿⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⡗⡇⠀⠀⠀⠀⠀⠀⠀ ⢊⠷⣘⢺⣿⣿⣿⣿⣿⣿⣻⡙⠀⠁⠀⠉⠏⠃⠸⣷⣷⣿⣿⣿⣁⣤⣄⣀⢀⣀⠀⠀⠙⣿⣿⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡼⡜⡇⠀⠀⠀⠀⠀⠀⠀ ⠈⠂⡑⢚⣿⣿⣿⣿⣿⣏⣖⣠⣴⣦⣯⣤⠀⠟⠀⠉⠈⢻⣿⣿⣯⣤⠶⢾⣿⠿⠀⠀⠀⠙⣿⣧⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢳⣃⠀⠒⠒⠒⠀⠀⠈ ⠀⠐⠤⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⢀⠀⠀⢹⣿⣿⣿⣿⣡⡾⠟⠀⠀⠀⠀⠈⡘⣧⡈⢳⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣳⣽⠈⠀⠀⠀⠀⠀⠀ ⢄⡀⣀⡽⢺⣿⣿⣿⣿⣿⢋⣼⡿⣛⠭⠿⣿⣿⣧⣢⠀⠀⠘⠪⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢐⣻⠓⢨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⢺⠘⠰⡀⠀⠀⠀⠀ ⠰⣌⣳⢻⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⢏⢳⢄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⡌⣌⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⣧⠀⠀⢧⠀⠀⠀⠀ ⠑⡼⣹⢳⣞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⢨⣿⠎⢆⠀⠀⠀⠡⡐⠀⠀⠀⠀⠀⠀⠈⠄⢳⠸⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⣾⠀⠀⠎⡀⠀⠀⠀ ⠃⠄⡍⢫⢞⣱⣻⣿⣿⣿⣯⣹⠟⠛⠉⠀⠀⢁⣸⣿⣦⣤⣤⣴⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⢀⠞⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣹⡇⠀⡈⠇⠀⠀⠀ ⠈⠓⠜⣂⡫⣖⡻⣌⣿⣿⣷⡧⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠏⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⢿⡄⠀⠈⢆⠀⠀⠀ ⠀⠴⣒⣍⣇⠌⠑⣧⣇⢻⣿⣿⣧⢡⢀⡀⠀⠀⠀⠈⢟⣻⣦⣼⣿⣿⢿⢿⣶⣶⠆⠀⠀⠀⡄⠇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣉⡄⠀⠀⠌⡀⠀⠀ ⡬⢓⡼⢖⡩⣅⠋⠉⠸⣧⢙⢿⣿⣿⣾⢼⣣⠄⢾⢡⣾⣿⣿⣿⡛⠥⣀⣮⢫⡁⠀⠐⠠⠃⠔⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣏⠀⠀⠐⡡⠀⠀ ⢒⡱⣈⢧⣕⢺⣝⢢⠀⠠⡺⢍⣹⣿⣿⣿⣷⣽⡳⢾⡿⢿⣿⣶⣼⣿⣿⣿⠟⠐⠈⠀⠀⡠⣽⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣣⠀⠀⠀⣁⠂⠀ ⣌⡳⢭⠳⡼⢀⢺⣧⣳⠲⣈⠨⣖⢾⡻⣿⣿⣿⣿⣷⣻⡝⣾⢻⡿⠿⠋⠁⠀⠀⠀⠀⣰⣿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣡⠀⠀⠀⠀⠀⠀ ⠈⠹⢲⣝⣣⠤⠿⣶⠻⢀⡙⣷⡈⠤⠀⠉⢿⣿⣿⣽⣷⣿⣎⣷⣂⣄⢤⡰⢴⣢⣦⣴⣿⣿⣣⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷⠀⠀⠀⠀⠀⠀ ⠀⠐⠷⢙⠏⡿⠖⠞⡻⣈⠗⣩⢹⣄⡴⡶⣄⣻⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⡟⣧⢁⠃⡆⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⣾⡀⠀⠀⠀⠀⠀ ⠀⢈⡶⠷⠿⣅⡴⠄⠰⠍⣼⢀⣆⣭⠿⣔⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⣡⠂⠌⣇⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣳⡇⠀⠀⠀⠀⠀ ⢀⣨⣞⠫⡍⢺⣌⡵⣼⡃⢻⣳⣄⣩⣴⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢎⣳⢢⡉⠄⣹⠀⢄⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⡇⠀⠀⠀⠀⠀ ⢸⣝⣼⠓⢫⣎⣻⣴⢳⡖⣚⠞⠋⠑⠐⠈⠜⢈⠙⢷⣟⢿⣯⣟⡿⣿⣻⣽⡾⣿⡽⣫⡖⢧⣃⠐⠠⣗⢀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢯⡇⠀⠀⠀⠀⠀ ⠪⢵⣬⠿⢾⣼⣳⠮⠜⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⢝⡻⣓⠻⢳⠻⠵⡋⠷⠛⠋⢴⠀⠀⠀⢣⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣇⠀⠀⠀⠀⠀ ⡱⢋⢾⠯⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠷⡢⡙⠒⠐⠦⢤⣦⣌⠀⠀⠀⠀⢇⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⠀⠀⠀⠀⠀ ⠡⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣽⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡠⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⢾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡢⡢⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⣿⣻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣳⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⡢⢄⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⢺⣽⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⣓⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠈⠽⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⡷⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⢇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣸⣟⣯⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣸⠰⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣵⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⣇⠯⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡗⡎⡔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣧⣯⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⢷⣈⠧⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⢋⠦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡟⢆⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠙⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣳⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠿⠀⢴⣃⣎⡴⣠⢀⠤⣀⠀⡀⢀⠄⢾⣿⣿⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⢷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡘⠻⢿⢿⣿⣿⣾⣯⣞⠰⡁⠈⠄⣿⣿⠀⠀⠀ ⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣽⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢺⣿⡝⢢⠘⡀⢂⢹⣿⡆⠀⠀ ⠌⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⣼⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣴⣦⢤⡀⠀⠀⠀⠀⡀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⠄⠂⠐⡀⢚⣿⡇⠀⠀ ⡐⠠⠂⢀⠠⠀⠀⠀⠀⠀⠀⠀⠠⡁⣿⣿⣿⣯⣃⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣆⣀⠐⠈⣰⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠿⣿⡂⠀⠠⠐⠀⣿⡇⠀⠀ ⢀⠃⠌⡀⠂⠀⠠⠀⡀⢀⠠⢀⠡⢒⡿⣿⣿⣿⣿⣼⣄⡢⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⠇⡂⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢸⡇⠀⢂⠇⣤⣿⣇⠀⠀ ⢌⠢⡁⢐⠠⢁⠂⠌⢀⠡⠐⠠⡑⢪⣽⣿⣿⣿⣿⣿⣾⣥⣋⡄⡀⠀⠀⠀⠀⠀⠀⣉⠽⠿⢻⢏⣺⣭⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡧⣴⣬⠇⠠⢸⡝⠙⣿⣿⠀⠀ ⡌⢆⡑⠠⢂⠂⡌⡐⠤⢂⠉⡔⣡⢓⡾⣿⣿⣿⣿⢿⣿⣿⣿⣶⣝⣦⣹⡌⢦⡑⣮⣱⣎⣷⣯⣿⡿⢋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣿⣤⣿⡀⢡⡟⠀⠀⢸⣿⠀⠀ ⡚⡔⡨⢁⠆⣡⠔⡀⢂⠡⢊⠔⡡⢎⡽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠻⣌⠡⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠆⠉⠙⠓⠋⠀⠀⠀⠘⣯⠀⠀ ⠳⣌⠱⢌⠒⡄⠆⡱⠈⡔⠡⢊⡔⢫⢾⣿⣿⣿⣿⣿⣿⣷⣯⣟⡿⣿⢿⣿⣿⣿⡿⡿⣟⠻⣌⠳⣄⠣⡁⠆⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱⣧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀ ⡏⢦⡙⣂⢇⡘⢌⠰⡁⢆⡑⢢⢜⣹⣾⣿⣿⣿⣿⣿⣿⣿⣷⣯⢿⣼⢳⡞⣴⢣⣞⣱⣎⠿⣌⠷⣌⡱⡘⢤⠡⣈⠐⠠⢀⠀⣀⣄⣠⣡⣗⢦⠛⡝⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣫⠖⡱⡌⢦⡘⢢⠱⡈⢆⡸⣃⣾⣿⠟⡋⠟⡙⢏⡛⢟⡻⢟⡿⢿⣯⣿⣾⡷⣟⣾⣳⣯⣿⣭⣟⡶⣵⢭⢦⡳⢤⡋⠶⡑⢞⡛⠛⠿⣯⣛⠛⢶⣄⡀⠁⠈⠐⠢⠄⡀⠀⠀⠀⠀ ⣧⢫⡕⣚⢤⡙⢆⢣⡙⢤⢃⠿⠋⠡⠈⠀⠁⠌⡐⠈⢆⡑⢊⠔⠣⢎⠱⠩⡍⢍⠳⣩⠛⣌⠫⡙⠬⠑⢊⠆⠡⠃⢈⠀⠁⠀⠀⠀⠀⠹⣿⣛⡀⠙⢧⣡⠀⢀⠀⢀⢈⢄⠀⠀⠀ ⣷⣓⢮⡱⢎⡱⢎⢦⡙⢦⡉⠰⡀⢡⠀⠄⡈⠀⠄⡁⠂⠀⠡⠈⡐⢈⠂⠡⠐⡈⠐⠠⠁⠄⠂⢁⠠⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⢈⢻⣆⠀⡀⠂⢼⣸⠀⠀⠀ ⣷⢯⣞⣱⢫⡞⣭⢶⡹⢦⣍⠳⣜⢢⡑⢢⠄⡡⢂⠐⡀⠄⠐⠠⠐⡀⠄⠁⠄⠠⠀⠁⠀⠀⠄⠀⠀⠀⢀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣁⢿⣟⡂⠄⡌⣷⣀⡤⠎⣀⠙⡀⠀⠀ ⣿⡿⣜⣎⢧⡻⣜⢧⣛⢧⢺⡝⣎⡳⣜⢣⢎⡕⡪⠵⣐⢊⡌⡡⢒⠰⣈⠒⡌⣀⠂⠄⣁⢂⡐⡈⢄⠡⢂⠌⣢⠐⠤⡡⢌⠢⠡⢌⡀⢢⠯⣼⣷⠏⡰⣘⡿⣀⠆⡕⣺⡶⠑⢀⠀ ⣿⣿⣽⣜⣮⢳⡝⣮⡹⢎⡳⣜⢣⡳⢎⡳⢎⡼⣱⢫⡔⣣⢜⣡⢣⢓⡤⢓⡔⢢⢍⠲⣄⢲⡘⡴⣊⠶⣩⢞⣴⣫⢗⣵⣮⢷⣽⣾⣽⣯⣷⣿⡯⢖⣵⣿⢧⢣⣟⡹⣭⠁⠀⠀⠈ ⣿⣿⣿⣟⣾⣧⣟⡶⣽⣫⣵⢮⣷⣹⢯⡽⣞⡶⣧⣻⣼⣱⣞⣦⣻⣜⣞⣳⢾⣹⣮⢷⣞⣧⣿⣷⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣯⡿⠞⠋⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢟⡛⢭⠛⣭⢛⠿⣻⠿⣿⣻⣟⣿⣿⡟⡔⠂⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢏⡿⡼⣳⡝⣮⣙⠦⣫⠴⣩⠞⣥⣻⣼⡿⣯⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡷⣯⣻⡼⣻⣜⢷⣣⢟⡴⣭⢞⣥⡻⣜⣯⣷⢿⣽⣞⣿⣟⢣⠀⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⢯⣟⠿⣽⡻⣟⣿⣻⣟⣿⣻⣟⡿⣿⣿⣿⣷⣯⣷⣟⣮⣷⢯⣾⣝⣾⣻⣮⣽⣿⣿⣾⣯⣷⣿⣿⢏⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣽⣛⣾⣛⣷⣻⡽⣾⢷⣻⣟⡿⣟⢿⡻⢟⡻⣛⢟⠻⣹⢛⡻⢛⠻⡛⣛⢛⡛⢏⡛⢻⠿⣿⣿⣿⡿⢊⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣽⡲⣏⢶⡹⢞⡵⢫⡑⠎⡴⠡⢎⠱⣉⠖⡱⢊⠕⢢⢁⠆⠩⡐⡁⠆⠢⠘⡠⠉⠆⡱⢈⡛⠿⣽⢌⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡳⣝⣎⢧⡝⢪⠔⠣⠜⡨⢐⡉⠆⡱⠈⠆⡑⠈⢌⠠⠈⠌⡐⠠⠁⠌⠠⠁⠄⡁⢂⠐⠡⢈⠆⠹⢮⡂⢅⠂⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣳⣚⢦⡹⢡⢚⠱⡈⠔⡡⢐⠈⡄⢁⠂⠄⢉⠀⢂⠁⢂⠐⠀⡈⠀⠠⠈⢀⠀⠂⠈⡐⠠⠌⡁⠆⡛⣦⠈⡅⢊⠤⣁⠢⡐⢠ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡹⢎⡵⢃⡎⡱⢌⠢⣁⠂⠆⡐⠠⢈⠐⠀⡈⠄⡈⠄⠂⢁⠀⡈⠄⠠⠀⠠⠈⢀⠐⡀⠒⡀⠒⡈⢜⢳⣌⢣⢚⠤⡓⡜⡤

⡤⡜⡓⠤⢚⢣⣌⢳⢜⡈⠒⡀⠒⡀⠐⢀⠈⠠⠀⠠⠄⡈⠀⢁⠂⠄⡈⠄⡈⠀⠐⢈⠠⡐⠆⠂⣁⠢⢌⡱⡎⢃⡵⢎⡹⣷⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢠⡐⠢⣁⠤⢊⡅⠈⣦⡛⠆⡁⠌⠠⡐⠈⠂⠀⢀⠈⠠⠀⡈⠀⠐⢂⠁⢂⠀⢉⠄⠂⢁⡄⠈⢐⡡⠔⡈⠱⢚⢡⡹⢦⣚⣳⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠂⢅⡂⢮⠹⠆⢈⠡⠐⢂⡁⠄⠁⠠⠌⠁⠠⡐⠌⠈⠠⢌⠈⡑⠆⠈⡱⠆⡉⢐⡨⠜⠣⠔⢪⡝⢧⣎⣝⡳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⢌⣽⠿⡛⢈⡱⠆⠉⡠⠘⠢⠆⡁⡐⠩⠆⢁⢢⠕⢊⡱⠖⣉⠱⢎⠡⡴⠎⡑⢫⡵⢞⡹⢶⣏⡲⣽⡞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⢊⡿⣿⣿⣿⠿⢻⡛⢏⡛⢛⣛⡛⠻⢛⡻⢛⣹⠻⢟⣛⡻⢟⡻⢿⣟⡿⣟⣻⢷⣾⡽⣻⣷⣛⣾⣛⣽⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢏⣿⣿⣷⣯⣾⣿⣿⣽⣮⣻⣾⣝⣾⢯⣷⣮⣟⣷⣯⣷⣿⣿⣿⡿⣟⣻⣿⣟⣻⣿⣟⡻⣽⠿⣟⢯⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠂⠀⢣⣟⣿⣞⣽⢿⣷⣯⣜⡻⣥⢞⣭⡴⢟⣣⢷⣜⣻⡼⣻⣯⡷⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢿⣯⡿⣼⣻⣥⠞⣩⠴⣫⠦⣙⣮⡝⣳⡼⡿⢏⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠂⡔⡟⣿⣿⣟⣻⣿⠿⣻⠿⢛⣭⠛⢭⡛⢟⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠋⠞⡿⣯⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣯⣷⣿⣧⣞⢷⣮⣹⢾⣳⣞⣜⣻⣦⣞⣱⣼⣻⣧⡶⣞⡽⢯⣹⣷⢮⣵⣫⣽⡶⣟⣧⣾⣟⣿⣿⣿ ⠈⠀⠀⠁⣭⡹⣟⢣⢧⣿⣵⢖⡯⣿⣷⣯⣽⣾⣽⢷⣮⣵⢗⣫⣴⢞⣩⠶⣊⡴⡘⢲⣄⠲⢍⢢⡔⢓⡤⢓⢣⣡⢜⣣⡔⢫⣱⡼⢎⡳⢎⡳⢣⣜⡳⢎⡹⣮⡝⢳⣮⣜⣽⣿⣿ ⠀⢀⠑⡶⣺⡕⠆⣀⡿⣘⡰⠏⣷⣼⠯⢢⡀⢌⠡⠢⢌⡡⠤⠐⣢⠌⢂⠡⢄⡈⡐⢂⣁⠄⠂⣀⡌⠒⣈⠰⢒⡡⡌⢊⣐⠵⡪⡕⢎⢣⣜⡳⣎⡝⢺⢧⣛⢧⣜⡻⢧⣎⣜⡿⣿ ⠀⠀⡀⠙⣀⠎⡤⣀⣷⡌⠄⡂⣟⢿⣁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⠀⠄⠀⠀⠁⠀⠠⠄⠁⠄⡀⠐⠠⠐⠄⡀⠐⢂⡡⠄⢢⡑⢢⣜⠳⣍⢦⡹⢶⣭⡞⢫⣱⣞⢯⣷ ⠀⠀⠀⣸⢼⠂⡀⠀⣆⢻⢈⠀⣧⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠠⢁⠂⠄⠁⠠⠐⡈⠐⠡⠂⢈⡐⠈⠡⠀⠂⡁⠄⠀⡈⠄⠀⢡⡀⠰⡉⢦⡙⢦⢎⡱⢎⡱⢮⣓⣷ ⠀⠀⠀⢄⢈⢀⠀⢀⠀⣡⢧⠙⡀⣛⣿⠹⠀⠀⠀⠀⠁⠀⢈⠃⠡⠆⢊⠑⠬⡙⠫⣌⠛⣩⠳⢍⡍⠩⠱⢎⠣⠔⢊⡑⢆⠈⡐⠌⠁⠀⠈⠡⠋⠿⢃⢤⡙⢣⢆⡙⢤⣚⡕⢫⣧ ⠀⠀⠀⠀⡀⠄⠢⠐⠈⠁⡀⣄⢶⠛⣛⣯⠿⠛⡛⢞⡑⠶⡋⢤⡳⢦⢭⣵⡶⣟⣭⣿⣯⣳⣾⣟⡷⣾⣿⣯⢿⡿⢟⡻⢟⡛⢏⡙⠟⡋⠟⣿⣾⣃⡸⢆⡈⠱⢢⡘⢦⡌⡱⠖⣫ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡝⠛⢦⣗⣡⣠⣄⣀⠀⢀⠠⠐⣈⠡⢤⡘⡱⣌⠷⣌⠿⣎⣱⣞⢣⣴⡞⢳⣼⢿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣾⣹⢜⢢⡑⢆⡁⠰⢌⡘⢇⣂⡙⢦⡏ ⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⣧⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠆⡁⠣⣄⠳⣌⠻⣟⡿⡿⣿⣿⣿⢿⣿⡿⣟⣯⣷⣿⣿⣿⣿⣿⣿⢾⢫⡔⢊⠡⡔⠈⡱⠆⡄⠒⢌⠱⣌⠳ ⠀⠀⣯⠘⠀⠀⠀⠋⠓⠙⠉⠆⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠡⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡽⢎⡡⠔⢊⠡⢂⡀⠔⣡⠆⢁⡨⡔⡚ ⠀⠀⣿⢸⠀⠀⡟⢡⡀⣿⣤⣿⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢋⡿⣿⣯⣷⣎⣱⣮⡑⢦⡌⣹⣦⣝⣶⣿⣿⣿⢿⣿⣿⣿⣿⡾⢓⣡⡔⠉⢂⠤⡐⡌⠂⢂⠠⡑⢆⡌ ⠀⠀⣿⣿⠙⡝⢸⠠⠇⣬⣴⡧⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣭⣺⢏⢻⠿⠽⣉⠀⠀⠀⠀⠀⠀⡀⡄⣋⣥⣾⣿⣿⣿⣿⣿⣽⢪⡑⠠⠐⠡⢀⠌⠂⢁⠠⢐⡁⠢⢌ ⠀⠀⣇⣿⣤⠇⢂⠀⡇⢸⠀⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣾⢀⡂⠇⣿⣿⣿⣿⣿⢼⠀⠀⠀⠀⠀⠀⠀⡀⡢⣄⣼⣿⣿⣿⣿⡿⢒⠡⢀⠠⢀⡀⠀⠠⠀⠂⡀⠌⠃⢀ ⠀⠀⡇⣿⠀⠐⠠⠀⡂⣿⠿⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⣰⠈⠐⣀⣆⣿⣿⣿⣿⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⣃⣯⣿⣿⣿⡁⠠⠀⠀⠀⠀⠀⠀⠀⠠⢀⠂⠠⡐ ⠀⠀⡇⣿⢚⡀⠐⠂⠄⣟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣰⡀⠀⠀⠀⠀⡀⢤⣦⣴⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣼⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠌ ⠀⠀⡆⣿⢹⢂⡀⠘⢢⡝⣿⢺⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⣿⣽⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐ ⠀⠀⠀⣿⣿⠄⠈⡁⠰⣞⣯⣾⣿⣿⢿⢿⠻⡘⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣻⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⣿⣿⢾⠄⢀⡀⠀⣀⠤⢀⣠⡴⣎⣃⢴⠀⠿⠛⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣳⣿⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠼⠙⣶⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢆⡟⣿⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠦⢋⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠧⣈⢷⣿⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡃⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⣯⣧⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⡎⡗⣯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡄⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠯⣇⠂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣵⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠰⣸⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣯⣟⣸⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢇⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⡷⢸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠽⠈⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⣯⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⣓⢡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣽⢺⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⢄⡢⠱⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⣳⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣻⣿⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⡢⡢⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢾⣿⠈⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡀⡠⠳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣽⣾⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠸⠀⠀⠀⠀⠙⠈⠀⠀⠀⣀⠪⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠡ ⠀⠀⠀⠀⠀⣻⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⢇⠀⠀⠀⠀⣌⣦⢤⠦⠐⠒⡙⡢⠷⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠯⢾⢋⡱ ⠀⠀⠀⠀⠀⣇⣯⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢣⠀⠀⠀⢴⠋⠛⠷⡋⠵⠻⢳⠻⣓⡻⢝⠦⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠜⠮⣳⣼⢾⠿⣬⢵⠪ ⠀⠀⠀⠀⠀⡇⢯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⢀⣗⠠⠐⣃⢧⡖⣫⡽⣿⡾⣽⣻⣿⡿⣟⣯⢿⣟⢷⠙⢈⠜⠈⠐⠑⠋⠞⣚⡖⢳⣴⣻⣎⢫⠓⣼⣝⢸ ⠀⠀⠀⠀⠀⡇⢧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⢄⠀⣹⠄⡉⢢⣳⢎⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣴⣩⣄⣳⢻⡃⣼⡵⣌⢺⡍⠫⣞⣨⢀ ⠀⠀⠀⠀⠀⡇⣳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣇⠌⠂⣡⠟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣣⣔⠿⣭⣆⢀⣼⠍⠰⠄⡴⣅⠿⠷⡶⢈⠀ ⠀⠀⠀⠀⠀⡀⣾⡽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡆⠃⢁⣧⡟⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣻⣄⡶⡴⣄⢹⣩⠗⣈⡻⠞⠖⡿⠏⢙⠷⠐⠀ ⠀⠀⠀⠀⠀⠀⣷⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣣⣿⣿⣴⣦⣢⢴⡰⢤⣄⣂⣷⣎⣿⣷⣽⣿⣿⢿⠉⠀⠤⡈⣷⡙⢀⠻⣶⠿⠤⣣⣝⢲⠹⠈ ⠀⠀⠀⠀⠀⠀⣡⣯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣰⠀⠀⠀⠀⠁⠋⠿⡿⢻⣾⡝⣻⣷⣿⣿⣿⣿⡻⢾⣖⠨⣈⠲⣳⣧⢺⢀⡼⠳⢭⡳⣌ ⠀⠂⣁⠀⠀⠀⣣⣧⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣽⡠⠀⠀⠈⠐⠟⣿⣿⣿⣼⣶⣿⢿⡿⢾⡳⣽⣷⣿⣿⣿⣹⢍⡺⠠⠀⢢⣝⢺⣕⢧⣈⡱⢒ ⠀⠀⡡⠐⠀⠀⣏⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣡⠔⠃⠠⠐⠀⡁⢫⣮⣀⠥⡛⣿⣿⣿⣾⢡⢾⠄⣣⢼⣾⣿⣿⢿⢙⣧⠸⠉⠋⣅⡩⢖⡼⢓⡬ ⠀⠀⡀⠌⠀⠀⡄⣉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠇⡄⠀⠀⠀⠆⣶⣶⢿⢿⣿⣿⣼⣦⣻⢟⠈⠀⠀⠀⡀⢀⢡⣧⣿⣿⢻⣇⣧⠑⠌⣇⣍⣒⠴⠀ ⠀⠀⠀⢆⠈⠀⡄⢿⣯⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣰⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠏⡿⣿⣿⣿⠈⠀⠀⠀⠀⠀⠀⡧⣷⣿⣿⣌⡻⣖⡫⣂⠜⠓⠈ ⠀⠀⠀⠇⡈⠀⡇⣹⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡁⠞⢀⠀⠀⠀⠀⠀⠀⠀⠃⡶⣿⣴⣤⣤⣦⣿⣸⢁⠀⠀⠉⠛⠟⣹⣯⣿⣿⣿⣻⣱⢞⢫⡍⠄⠃ ⠀⠀⠀⡀⠎⠀⠀⣾⡝⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠸⢳⠄⠈⠀⠀⠀⠀⠀⠀⡐⠡⠀⠀⠀⢆⠎⣿⢨⡽⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣞⢳⣹⡼⠑ ⠀⠀⠀⠀⢧⠀⠀⣧⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠾⣌⡌⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢄⢳⢏⣿⢻⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣹⢻⣳⣌⠰ ⠀⠀⠀⠀⡀⠰⠘⢺⣽⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢨⠓⣻⢐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠪⠘⠀⠀⣢⣧⣿⣿⠿⠭⣛⡿⣼⢋⣿⣿⣿⣿⣿⢺⡽⣀⡀⢄ ⠀⠀⠀⠀⠀⠀⠈⣽⣳⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢳⡈⣧⡘⠈⠀⠀⠀⠀⠟⡾⣡⣿⣿⣿⣿⢹⠀⠀⢀⣄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⠤⠐⠀ ⠈⠀⠀⠒⠒⠒⠀⣃⢳⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣧⣿⠙⠀⠀⠀⠿⣿⢾⠶⣤⣯⣿⣿⢻⠈⠉⠀⠟⠀⣤⣯⣦⣴⣠⣖⣏⣿⣿⣿⣿⣿⢚⡑⠂⠈ ⠀⠀⠀⠀⠀⠀⠀⡇⡜⡼⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⣿⣿⠙⠀⠀⣀⢀⣀⣄⣤⣁⣿⣿⣿⣷⣷⠸⠃⠏⠉⠀⠁⠀⡙⣻⣿⣿⣿⣿⣿⣿⢺⣘⠷⢊ ⠀⠀⠀⠀⠀⠀⠀⡇⡗⣎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣇⣿⣿⠿⠻⢝⠲⠛⠛⠿⣷⣶⣤⣀⡀⢀⠀⣄⣦⣠⠀⠀⡁⠔⠢⣧⣿⣿⣿⣿⣿⢾⣍⠳⢬ ⠀⠀⠀⠀⠀⠀⠀⡄⢫⢥⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⢿⠻⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠶⠟⠯⣿⣿⣿⣿⣿⣽⢎⡓⣍ ⠀⠀⠀⠀⠀⠀⠀⠀⠾⣙⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠒⡟⢻⣿⣿⣿⣿⣿⣿⣩⠴⢣⡐ ⠀⠀⠀⠀⠀⠀⠀⠀⢾⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⢿⠙⠀⠀⠀⠀⠀⠀⠐⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡑⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡱⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⠱⠻⠋⠉⢋⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢧⣎⠳⢏⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⢾⣃⡱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢫⣦⣝⠦⡛⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡭⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣹⠆⣭⡞⣝⡹⣤⠺⣑ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡱⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢂⠥⣚⣭⣶⣶⣷⣾⣷⣶⣴⣤⣵⣨⣞⢍⣱⣆⠉⣚⢥⣞⡳⢜⡈⠐