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⠀⠀⠀⡗⣿⣾⣡⣇⣾⣿⣿⣴⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣿⢿⠻⠙⠀⠀⠀⣀⢀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⣧⢹⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡆⣿⠛⡍⠫⣾⣲⣇⢸⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠋⠛⠛⠀⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⣷⣾⣿⣶⣶⣶⣶⣶⣶⠠⠀⣿⡘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣾⣷⣿⣵⢿⡇⣶⣿⠘⠀⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣤⣭⢩⡏⣿⣿⣉⣉⣿⣿⣿⣿⢺⠒⠶⠶⠷⠾⠷⠿⠬⣤⠤⡤⣤⣤⣠⣄⣄⣀⣄⢿⡌⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠉⡞⣟⣿⣿⡯⣯⣿⠿⣿⢿⠛⠒⠖⠶⠶⠴⠤⣤⣤⣤⣠⣀⣁⣛⣴⣤⢦⠙⠈⠀⡇⣿⣿⢿⠙⠉⠟⣩⠀⠀⠀⣁⣭⠿⠒⠲⠒⠒⠙⠉⠉⠚⡖⢶⠓⣌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠏⢣⡿⣻⣌⣽⡿⣿⣿⣿⣾⣤⠹⠀⠀⠀⠀⠀⠀⠀⠁⠋⠚⠶⣶⠒⠛⠛⠛⠛⣞⠶⡴⣤⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣆⡸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠽⠿⠛⠀
⠃⣿⣾⣯⠟⢟⣿⣿⣿⣾⣠⠀⠋⣾⠤⠤⠤⠤⠤⠤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠂⠶⡿⢸⡀⣀⣂⣿⣄⣦⠳⠉⠀⠀⠀⠀⠀⣷⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣴⢀⣀⣿⢺
⡆⣿⣾⣗⣿⣿⣿⣾⣠⠀⠁⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⣿⠾⠶⣶⠵⣽⣫⠓⠚⠖⠤⠤⠤⠤⠤⡻⢮⠐⠀⠀⠀⡇⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣯⣠⠀⠀⠏⣿⢠
⠀⣿⣿⣯⣿⣾⣠⠀⠉⠛⡴⣧⠈⠀⠀⠀⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢛⡾⣴⣩⣛⢖⠴⡤⣠⣀⠀⠀⠀⣧⠘⠀⠀⠀⠀⠀⡗⣷⠹⠀⠀⠀⡀⢹⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⠽⠯⠛⡟⣿⢠⠀⠁⠟⣾⢀⠀
⠀⡆⣿⣿⣴⠀⠟⡴⣀⠀⠀⡀⢻⠀⠀⠇⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡫⢖⡤⣀⢀⢧⠁⠉⠛⠟⠿⠿⣶⣿⣿⣿⣶⣿⢿⠿⠻⣀⡀⣷⠘⠀⠀⠀⣆⣹⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⣞⣥⣾⢀⠁⠟⣿⣸⠀⠀⠀
⠀⠇⢸⣧⠛⡿⣾⠥⡿⣤⣤⠷⡌⢻⠀⡄⢶⣴⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⡼⣠⠀⠀⠉⠛⠾⣴⣤⣀⢀⠀⠀⠀⠀⣀⠀⠀⠀⡀⣇⣿⡇⢻⠒⡟⢻⠀⠀⠀⠀⣄⠹⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣿⣰⠏⣴⣀⠀⠋⣷⢸⣧⣿⠀⠀⠀
⠀⡧⢤⠉⣿⣾⢠⣤⣀⢀⠳⡿⣿⡿⢻⠀⠀⠟⣰⣀⣦⠻⠀⠀⠀⠀⠁⠟⡤⢀⢆⠋⠟⡴⣠⠀⠉⠘⠀⠀⠀⠀⠀⡀⢒⠀⠀⠀⠀⠀⡟⣻⣾⢀⠏⣿⣿⠸⠀⠀⠀⠀⡄⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣺⣹⠄⢠⠀⠀⠀⣀⡀⠀⡏⣿⠀⠀⠀
⠀⡆⠹⣧⣸⢀⠀⠀⠀⠀⠀⣇⣾⡿⣧⠸⡇⣰⠀⠀⠀⣿⠀⠀⠀⠋⣰⣧⠀⠋⡿⣴⢁⠋⠾⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⣶⢋⡿⣿⣿⣿⢿⠀⠀⠀⠀⠀⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠘⠀⠀⠀⠀⠀⠁⠟⣾⢠⠀⠀⠀
⠀⠀⣇⡌⢻⠀⠀⠀⠀⠀⠀⠀⣦⡇⣹⢸⡇⠠⠀⠀⠀⣿⠀⠀⠟⣷⠈⠉⠟⣾⢀⠋⡼⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠿⣿⣉⣿⣿⣿⣿⣿⣿⣿⢹⠈⠀⠀⠀⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣰⠀⠁⠋⠟⡿⣶⣠⢀⠀⠀⠀⠀
⠀⠀⠀⣧⣅⢻⠉⠀⠀⠀⠈⠀⠁⡟⢠⢸⡄⢻⠈⠋⡾⢠⠀⡏⣿⠙⣉⣿⣾⢀⠟⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠓⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠸⠀⠀⣻⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣾⢠⠀⠋⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡀⣷⠈⡈⣄⠹⠀⣧⣬⣠⢀⠀⣇⠈⠀⣀⢀⠀⠀⠃⣿⠙⣮⣏⣿⣿⠚⣁⢉⠀⠀⠀⠀⡀⣀⢀⠀⠀⠀⠉⠉⠛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⠀⠀⡆⣻⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣻⣴⠀⠋⡿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢷⣆⠹⡄⢹⡀⣷⠿⠛⠈⠀⢧⠈⠀⠀⠀⠀⡇⣿⣿⣻⠟⣿⣿⣿⠻⠛⠛⣿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣆⡾⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣞⢀⠁⠟⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⢹⣟⠸⡆⢻⡀⢿⡉⣷⠘⠀⢦⠘⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣉⣿⣉⣉⣙⣤⣥⢂⠿⣻⣍⣮⠸⠀⠀⠀⠀⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⣠⠀⠟⣻⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⡘⣷⠀⣿⠹⡄⢻⡀⣿⠀⠀⣇⠘⠀⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠾⣠⣀⠀⣆⣿⠘⠀⠀⠀⡿⡇⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣰⠀⠋⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⣦⠸⣆⣿⠹⡆⢻⣿⠀⠀⡀⢸⠀⠀⡆⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣴⣠⣀⡄⢹⠀⠀⠀⠀⡆⣿⠘⠀⠀⣧⣟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⣠⠀⠋⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣆⠘⢳⠀⣄⣧⠘⣆⢺⠀⠀⠀⢹⠀⠂⠙⣷⠘⡀⣄⡦⣾⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⣾⣿⣶⣴⣤⣤⣤⣀⣹⠀⠀⠀⠀⠀⠀⠀⣆⠙⠀⠀⠀⠀⣿⣷⠘⠀⡄⣿⢻⠀⠀⠁⠀⠀⠀⠀⠁⠟⣾⣤⢀⠋⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠹⠀⠀⣧⠈⣧⠘⠀⠀⣧⠈⠀⡗⡸⣧⢸⠀⡇⢀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣧⠀⠀⠁⠉⠉⠉⠋⠚⣶⠶⠖⠶⡷⣾⡏⢸⠀⠀⣆⣿⠿⡿⣺⣗⠿⠛⠟⣾⣠⠁⠋⡿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⣆⠹⠀⡀⢷⠈⢷⠈⠀⠀⢧⠈⡀⣧⠻⣍⠻⡻⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠁⣏⠉⠉⠉⠉⠚⠗⡭⣿⣾⣶⣵⠾⣿⣡⡿⣩⢏⠶⠴⡤⣶⣴⠀⠀⠀⠀⣧⣼⢀⢷⠀⡁⣾⣠⠁⠟⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠹⡄⢻⠀⡟⢻⡄⢻⠀⠀⠀⣆⠘⠀⣾⣷⢿⣛⢭⠿⠺⠒⠒⠶⣶⠶⠶⠷⠭⣥⣫⣛⣞⠶⠴⣢⣀⣉⡿⢹⠏⣤⢤⢶⡶⣒⠛⠙⠈⠄⠠⠀⠄⠸⠀⠀⠀⡇⢸⠀⡄⣷⣩⠛⡿⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⣇⢹⣷⡎⢻⡄⠹⠀⠀⠀⣇⠘⣄⠳⡝⣶⣿⣾⢶⠛⠿⠈⠀⣀⣄⢠⣃⣷⣼⢄⠤⣀⣀⠀⡄⢰⡄⢤⣀⢀⠀⠀⠀⠟⣾⡥⢋⠟⠾⠶⠶⠶⠓⠉⠀⣿⠀⠁⠉⠈⣄⠻⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣿⡀⣤⣦⠹⣇⠟⠙⠈⡇⢸⠧⠈⠀⠀⠀⣀⣀⢤⡤⣶⣛⠈⠃⠃⠙⠛⠛⠙⠛⠛⠙⠉⠌⠤⠀⠀⠁⠈⠀⠀⡏⣴⢋⡾⣠⠀⠀⠀⡄⠂⠀⣄⢷⣏⠿⣷⣋⢟⣾⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠘⠀⠟⣷⠘⣻⡞⣧⡿⢸⠀⢠⠀⠄⠠⠀⠃⠀⠀⠀⡁⢿⣽⣾⣴⣤⣀⣀⣀⣀⣀⣤⣶⢿⠻⠉⠛⠀⠀⠏⣼⡟⣼⠀⠀⠀⠀⠀⠄⣶⣴⠀⡃⣼⣷⣿⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⢿⠀⣷⣠⣀⣄⠻⡘⣿⢻⠀⠀⠀⠛⠀⠀⠀⠀⠁⠋⣿⣼⣀⠀⠀⠀⠀⠀⠁⠋⠛⠀⠀⡀⣧⣿⣠⠀⠃⣾⡯⣦⢻⠈⠀⠀⠀⠀⠀⠀⠁⠋⡾⢉⡄⢻⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⢻⡄⢹⠀⠀⡆⢸⣧⣄⢳⠈⠀⣆⠘⠉⠀⠃⡿⢇⣿⠀⢀⠀⠀⠀⠀⠀⡀⣤⣠⠀⠀⠋⣿⣼⠀⠀⡿⢡⢸⠀⣅⣶⣿⠾⠲⠓⠾⡶⣤⣿⢈⠀⠀⣇⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⠙⣇⠚⠀⠀⢷⡇⢸⡀⢧⠀⠀⠀⣷⠀⡷⣿⡈⣷⠻⠈⠀⠀⠀⠀⠀⠀⠀⠉⠛⡿⣿⣰⠎⠀⡄⣿⠀⢷⠒⡙⢄⡳⣆⣿⢿⠻⠉⠟⣿⣼⢠⠀⡇⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣿⠀⣧⠚⠀⡇⡇⢸⠀⡆⢸⠀⠀⡀⠀⡀⣷⢈⠀⡦⣶⢿⠿⠿⠿⠾⠴⣤⣍⣾⣤⢀⠋⢰⠀⠀⣿⠀⡀⢦⡙⣄⠤⠶⠶⠷⡿⣿⣽⣟⢿⠀⠀⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⠀⣦⠙⡀⡇⢿⠈⠀⢸⠀⠀⠀⠀⠀⠀⣄⠶⠿⠿⠿⣻⢟⣿⣿⢻⣛⣙⠽⣈⡯⣰⠀⠀⠀⣾⣦⠙⠂⡓⢮⠳⠉⠏⣿⣿⣿⣴⢀⡟⠀⠀⣇⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⢻⠀⠀⣇⣼⣦⡀⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣦⣲⠒⠓⢛⡛⣉⣉⣄⣤⣦⣶⣿⠿⠻⠛⠋⢠⠏⣿⠴⠥⣤⢧⡻⣟⣾⣶⢹⠁⠞⢠⠀⠀⠀⣿⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⢻⠀⡀⣿⠌⠀⣿⢰⡆⠹⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣄⣦⠲⠛⡙⣍⣿⣩⠟⣶⢤⣀⣀⣀⣀⣀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⡟⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢸⠀⡀⢶⠶⣴⠀⠀⡄⠹⠀⠀⠃⣾⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠶⣿⣿⣭⢭⡯⣾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⠋⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠓⠚⠚⠖⠴⣿⣿⣖⣦⠲⠖⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣳⣿⢶⠷⠿⠛⠉⠉⠈⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⠶⠶⠒⠒⠟⠯⡿⣿⣖⣤⣤⠤⣤⣄⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣲⣒⣽⣮⢶⡙⢳⠉⠋⠿⣽⣿⣭⡿⡛⣒⣴⡤⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠢⠒⠖⢴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀