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