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