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

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