⢀⣒⠒⠆⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⡛⠛⠻⣷⣶⣦⣬⣕⡒⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⢿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣳⠖⢋⣩⣭⣿⣶⡤⠶⠶⢶⣒⣲⢶⣉⣐⣒⣒⣒⢤⡀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠉⣩⣭⣽⣶⣾⣿⢿⡏⢁⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠲⢭⣯⣟⡿⣷⣘⠢⡀⠀⠀⠀⠀⠀
⠹⣷⣿⣿⣿⣿⣿⢟⣵⠋⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣾⣦⣾⣢⠀⠀⠀⠀
⠀⠹⣿⣿⣿⡿⣳⣿⠃⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠟⠀⠀⠀⠀
⠀⠀⠹⣿⣿⣵⣿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠛⣯⡇⠛⣽⣦⣿⠀⠀⠀⠀⢀⠔⠙⣄⠀⠀⠀⠀⠀⠀⣠⠳⡀⠀⠀⠀⠀⢿⡵⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣿⣿⣿⠿⢿⠟⠀⠀⠀⢀⡏⠀⠀⠘⡄⠀⠀⠀⠀⢠⠃⠀⠹⡄⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀
⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢸⠒⠤⢤⣀⣘⣆⠀⠀⠀⡏⢀⣀⡠⢷⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀
⠀⠀⠀⠸⣿⣿⠟⢹⣥⠀⠀⠀⠀⠀⣸⣀⣀⣤⣀⣀⠈⠳⢤⡀⡇⣀⣠⣄⣸⡆⠀⠀⠀⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠁⠀⢸⢟⡄⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⠁⠀⠈⠙⠙⣯⣿⣿⣿⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠇⢨⢞⢆⠀⠀⠀⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⡿⡇⠀⣠⢟⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡼⠀⢈⡏⢎⠳⣄⠀⡇⠙⠛⠟⠛⠀⠀⠀⠀⠀⠀⠘⠻⠛
⣠⠴⠒⢛⣋⣉⣉⣉⣉⣛⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠴⢚⡭⠖⠚⠉⠉⠁⠀⠀⠀⠀⠉⠉⠓⠲⢭⡓⢦⡀⠀⠀⠀
⠀⠀⠀⠀⣠⢞⡥⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡝⢦⠀⠀
⠀⠀⠀⣰⣫⠞⡤⡀⠀⢀⠀⠀⠀⠀⡀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣎⢧⠀
⠀⠀⢰⣷⠇⠈⠛⣵⠄⠀⢁⡆⠀⢠⠇⠸⢼⡀⠾⠻⠢⡄⠀⠀⠀⠀⠀⠘⡾⡆
⠀⠀⡏⡼⠀⠀⣼⠏⠀⢠⣾⠀⢀⡞⣳⡀⠈⣧⠀⠀⠀⢹⡄⢀⡶⣛⣓⣦⢹⣷
⠀⢸⠁⡇⠀⣸⠁⠀⣠⢯⡇⢀⣾⣀⠀⢳⡄⢻⡄⠀⠀⠈⣿⣸⣸⠁⠀⢸⠈⢹
⠀⢸⠀⡇⢠⠇⢀⡜⢁⣟⡴⠋⠀⠉⠉⠓⠻⡜⡇⠀⢀⣖⡿⠿⠋⠀⠀⠋⠉⢻
⠀⢿⠀⣇⢸⡞⠁⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠸⣟⠁⠀⠀⡟⢦⠀⠀⣸
⠀⢸⠀⠹⡾⡯⠿⠦⡄⠀⠀⠀⢀⣤⣦⣄⡀⠀⣧⠀⠀⠈⡷⠆⠀⣇⠸⡆⢾⡷
⠀⢸⠀⠀⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⣿⠀⠀⠸⣇⠀⢀⣿⠀⠹⣾⠃
⠀⢸⠀⠀⡇⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⠉⢸⠀⠀⢙⠀
⠀⠈⡇⠀⢧⢻⡀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⣿⠀⠀⢸⠉⢸⠀⠈⡇⠀⠀⢧
⠀⠀⢹⠀⢸⠈⢷⣄⠀⠈⠃⠘⠉⠁⠀⠀⠀⣠⣿⠀⠀⡏⠀⠘⡀⠀⢿⠀⠀⠈
⠀⠀⠀⢇⠀⢇⠀⠙⠳⣤⡀⠀⢀⣠⡤⢖⣋⡥⡇⠀⣸⠀⠀⠀⣇⠀⢹⡇⠀⠀
⠀⠀⠀⠈⢇⠘⣄⠀⠀⠀⠉⢩⢿⣷⣿⡉⠀⢸⠇⢸⠟⢳⠤⠤⠼⣄⡘⣿⡀⠀
⠀⠀⠀⠀⠈⣧⡙⣴⠋⠉⠉⣻⣾⣇⣿⣧⠀⣼⣰⠃⣰⠋⢀⡤⠖⠂⠈⢳⣧⠀
⠀⠀⠀⢠⡞⣫⠽⢿⣇⡴⡏⢻⣿⣿⣟⣟⣿⡷⠃⣰⠃⡴⠋⠀⠀⠀⠀⠀⣿⢧
⠀⠀⠀⢸⡇⠐⠚⠡⣿⢧⠁⠀⠛⢻⠄⡏⠞⠀⢰⢇⡞⠁⠀⠀⢀⠤⡀⠀⣿⠘
⠀⠀⠀⣸⡇⠀⠀⢸⡏⠈⠀⠀⠀⢸⣶⠛⢦⠴⣻⡞⣀⣀⣰⠮⠶⠚⠁⠀⣿⡄
⠀ ⢀⡏⡿⢧⡀⠀⠀⣧⠀⠀⢀⣠⠞⣿⣤⠞⢰⠋⠉⠁⠀⠀⠀⢀⣤⠀⢸⡏⢧
⠀ ⢸⠁⠙⢦⣙⠦⠼⣿⡖⠚⣉⣠⠖⠁⠸⡄⡿⠀⠀⠀⠀⠠⠚⠉⠀⠀⡞⡇⢸
⠀ ⡟⠀⠀⠀⠎⡍⠉⢹⢿⡏⠁⠀⠀⠀⠀⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣷⠀
⡼⠃⠀⠀⠀⠆⡇⢀⠟⡆⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⢻⠀
⠁ ⠀⠀⠀⠀⠀⠁⡾⠀⢹⡘⠃⠀⠀⠀⠀⠀⠈⢣⢤⡀⠀⠀⠀⢠⠇⠀⢸⢸⡆
⠀⠀ ⠀⠀⠀⠀⢾⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢧⠙⠆⠀⢠⠏⠀⠀⡟⠀⡇
⠀⠀ ⠀⠀⠀⠀⢸⠁⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀�