Old school Emojis & Symbols

⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠛⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⡈⠘⢿⣿⣿⣿⣿⣷⡦⣤⣀⣾⣿⣍⢿⣿⣿⣿⣶⠆⢶⣶⣶⣶⣦⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠿⢿⣿⣷⣿⣿⣿⡿⢋⣱⣾⣿⣿⣿⣿⡆⣿⣿⣿⣿⠀⢼⠏⣵⠄⢿⡿⠿⠋⢿⡷⣽
⠀⠀⠀⠀⠀⠀⠀⠀⣒⣒⣒⣒⣲⣿⣿⡿⠟⣡⣰⣿⣿⣿⣿⣿⣿⣿⠰⣷⣿⠿⢿⠀⠸⣧⣙⣣⠎⠁⠀⣐⡾⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡬⢭⣽⣿⠟⢡⣴⣿⣿⣿⣿⣿⣿⣿⡿⣁⣳⠿⢏⠀⠈⠀⢄⠀⠉⠀⠀⠀⠀⠃⠛⠒⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠂⠉⣉⣵⣿⠟⠡⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠶⠄⠀⠀⠀⠀⠙⡆⠀⠀⠀⡄⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠒⣊⠭⣿⣿⠏⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠠⡄⠀⠀⠀⠀⢳⣀⠀⠀⠒⣤⠖⠁
⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⠋⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢣⡀⠀⠀⠠⠴⠒⠳⢤⣈⣙⡷⠛⠁
⠀⠀⠀⠀⠀⠉⠁⠪⣻⠇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠡⠸⠽⠠⣄⡀⠈⠁⠀⠐⠋⠁
⠀⠀⠀⠀⠀⢀⣴⣿⡏⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣾⣷⣀⠀⠀⠀⠁⠀⠁⠁
⠀⠀⠀⠀⠈⠠⢈⣽⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠞⠿⡟⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⣤⣤⣴⠛⠉⠁
⠀⠀⠀⠀⠀⢀⣴⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⣿⣿⣻⣿⢿⠀⢠⡞⣰⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠐⠉⢛⣧⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣹⣾⡿⢯⡷⡁⢰⣹⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⢀⠞⢯⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠶⡔⠙⣯⡵⣦⣝⡹⠛⠁
⠀⠀⠀⠀⠀⠄⠀⣾⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠂⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄
⠀⠀⠀⠀⠀⢠⠈⠉⣧⠸⣿⣿⣿⣿⣿⣿⣿⡾⣡⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠿⣿⣿⣭⣛⢿⡛⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠈⢄⣠⠛⡄⢹⣿⣿⣿⣿⣿⣿⣿⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠉⠀⠀⠀⠀⠈⠉⠛⢷⣝⢿⡿⣿⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠐⣷⡄⠓⣄⢿⣿⣿⣿⣿⣿⣯⢟⠴⣭⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠑⠙⣷⢳⢤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠉⣜⣻⣿⣿⣿⣿⣿⣿⣽⢃⠄⠀⠀⠀⢀⣤⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠜⠸⣼⡄⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠆⣿⡇⠹⢿⣿⣿⣿⣿⣿⣾⣳⢆⠐⢶⣟⣛⣛⣡⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⡇⠀⠀⠀⠀⣠⣾⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡇⢸⣦⣻⣿⣿⣿⣿⣿⣯⣿⢂⠀⠉⢋⠀⠀⠚⠳⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠞⣉⢻⣧⣶⣶⣿⢟⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠡⠀⣿⢶⣬⡛⢿⣿⣿⣿⣿⣿⣧⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢰⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠊⢠⣀⢿⣳⠈⠹⠿⢿⣿⣿⣿⣿⣵⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⣠⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢠⣄⣄⡀⠉⠙⢿⣿⢿⢿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣷⡾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠲⠦⠶⠶⠿⠽⠿⠿⠾⠿⠟⠛⠛⠉⠁

⠀⠀⠀⣀⡠⠤⢖⠂⠶⠤⠤⣤⣀⣀⠀⠀⠀⠀⠀⢀⠄⣠⣶⣣⣴⣄⡀
⠀⠰⣭⠤⠂⠈⠘⠃⠉⠧⠶⡦⠤⠤⠃⠀⠀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⣿⡿⣿⢭⡹⠁⠈⠹⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⢤⠌⠀⠰⠶⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢀⡀⠀⢀⣀⡀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⡩⠭⠔⠗⠰⠯⢭⣽⣳⠆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠂⠈⠉⠁⠠⠂⠄⣀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠀⠀⡠⠀⠀⢀⢀⣉⢛⡂⢠⠁⠱⠀⠀⠀⠋⠆⠀⠀⠀⡴⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⢶⣋⣠⡤⠶⠾⢦⣟⠃⠐⠋⠛⠋⠉⠉⠈⢡⠀⠉⠀⠚⠀⠐⠐⠀⠠⠅⠀⠀⠀⢃⠐⠐⠀⡆⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣄⢉⣡⣤⡴⠶⠶⠇⠀⠆⠀⠀⠈⠈⠉⠈⢠⡴⠁⠒⠒⠀⠰⠠⠤⠤⠄⠀⡀⣀⣀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠶⣤⣈⠙⠤⡤⠤⠤⠶⠶⠀⠠⠆⠀⠄⠀⠀⠀⠀⢖⣣⡄⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢦⡀⠹⠆⢠⣤⣤⣤⣤⣴⠀⠀⠈⢀⠄⠀⡀⠐⠻⡌⢳⡈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠰⢴⣄⠈⠀⠰⠶⢦⡀⠻⠀⠀⢠⣀⣀⣠⣀⣤⡄⠀⠈⠁⠀⠀⠀⠀⢠⡟⡸⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸
⠀⠀⢸⠀⢠⠀⠀⠘⢳⢀⠀⠀⠀⠟⠀⠀⠀⢠⣤⣬⣥⣤⣀⣠⠀⠀⠉⠈⠁⠀⠁⠉⢀⠀⠀⠀⠀⠀⠀⠤⠤⠇⡀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣾⣦⣤⣶⣶⣶⡆⠀⠁⠀⠀⠀⢠⣶⠀⡀⠀⡖⠰⢻⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⢠⠀⠀⠀⠀⠀⠁⠈⠳⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠄⢠⠀⠀⢰⠉⢯⠃⢀⢹⣾⣏⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠙⠎⠐⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢈⡀⠸⠇⣧⣾⣿⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠁⠀⢸⣿⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸
⠈⠉⢺⣠⢦⣀⣤⢠⡀⣀⠀⣀⢀⣄⡈⢁⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡆⠠⠤⠠⠼⠀⢼⢿⣿⣧⠀⠘⣿⡇⠠⠀⢀⣀⡴⡀⢀⠛⡿⢟⠀⡀
⠀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣯⣟⣿⠛⠛⠛⠙⠏⠀⠀⠀⠀⣼⣯⣶⣿⣾⣶⣾⣧⠀⣿⡿⣿⣿⡄⠀⣿⣷⣿⣾⣿⣽⣾⣵⣿⣷⣿⣿⣿⣧
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠉⠉⠉⠉⡉⠉⢠⠋⠁⠹⠿⠇⠀⠛⠠⠌⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠤⠔



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣥⣤⢦⣤⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠙⠒⠾⣿⡿

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡴⢶⡟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠡⠀⡠⠀⠀⠀⠀⣠⣤⣄⡄⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⡠⠿⣧⠁
⠀⠀⠀⠀⠨⠔⣏⣿⠋⠛⠀⠀⠀⢀⣤⣰⣦⠀⠀⠀⠀⠑⠤⢤⠦⠉⠀⠀⠀⢿⣿⡟⠁⠀⠀⢾⠿⠣⠀⠀⠀⠀⠀⠀⠀⢸⣯⠰⡀
⠀⠀⠀⠀⠀⠀⠈⣿⢀⠀⠀⠀⠀⢿⣿⢿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠀⠈⣭⡆⠴
⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠘⠿⡿⣿⣻⠃⠀⠀⠀⠹⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠐⠛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⣶⠀⢨⠷⠞⠀⠀⠐⢸⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣆⣶⣞⠇⠀⠀⡀⢣⢀⣄⠠⡀⠀⠀⠱⠀⠀⠀⠀⠀⠊⠁⢀⠁⠀⠀⠀⠀⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⠋⠉⠁⠀⠀⠀⡀⠀⣙⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⠀⢴⢨⡀⠀⠀⠀⣀⠀⠀⠀⣄⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠰⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠰⠆⢤⡄⠀⠀⠺⠿⠂⠀⡠⣪⡄⡚⠁⠀⠀⠀⠄⠀⠀⠀⢀⣤⣤⠀⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠤⢘⣃⣤⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡿⢱⣆⠀⠀⠠⠀⠀⠀⠀⠀⠈⢸⠟⠀⠀⠈⠛⡓⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣋⠀⠀⠀⠘⠃⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⠀⠀⠀⠾⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔
⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡀
⠀⠀⠀⠀⣡⠞⠿⢛⢷⢤⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡛
⠀⠀⠠⠋⣀⣤⣴⣈⠂⢸⣿⣟⠀⠈⣧⠀⠀⠀⠀⣾⣮⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠙⢖⡀
⠀⠀⠀⠀⠉⠁⣀⠀⠀⡀⠉⠙⠢⠒⢾⣷⠶⣶⣯⣍⡛⠺⠶⠤⠤⠀⠀⠀⠠⣤⡄⠀⠐⠒⠓⠳⠴⠦⢠⡶⠿⠓⣻⡄⠁⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣉⠉⣛⣿⠷⢶⡶⠦⣀⣹⣆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠒⠒⠛⠀⠀⢀⣠⠤⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⢠⣶⣆⣈⡈⠳⣄⡙⠂⠤⣍⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⠶⠶⠶⠠⣦⣤⣤⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠹⣿⠋⢠⡀⠈⠹⠖⢶⣶⣦⡿⣷⡀⠀⠀⠀⠀⠀⢀⡴⠛⠈⠛⠙⠻⠶⠛⠙⠟⠋⠀⠒⠚⣩⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣟⡿⠋⠀⠊⢉⡐⠒⣀⡁⠈⠢⡀⠀⢀⠴⠏⠃⠀⠀⠘⢧⡀⠀⠤⠀⢠⠄⡀⠀⢠⡟⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠒⠀⠀⠀⠀⠀⠄⠿⠀⠀⠁⠸⠾⠭⠁⠉⠀⠐



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⡀⠤⠐⣒⠒⠂⠤⠤⠤⡀⠀⠀⠀⣠⣠⣶⣷⣶⣄
⠀⠙⡖⠀⠀⠈⠀⠉⠙⠒⠲⠁⠀⠀⣤⣿⣿⣿⡟⠻⣿⣧
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⣉⠓⠠⡤⠘⢟
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⣀⡀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡒⠬⠽⠇⠭⠥⣶⣶
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠈⠁⠀⠁⢠⣀⠀⢀⢆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢛⣀⣄⢰⣄⢠⢤⡤⠤⠄⠦⠀⠄⠀⡄⠀⢀⡀⠸⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣤⡉⢚⣉⣡⣤⣽⠀⠀⠀⠀⠐⠒⠀⣡⠄⠤⠄⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠶⢤⡉⠫⠥⠤⠤⠴⠀⠰⠂⠀⠀⠀⠀⢰⣢⡀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠀⡀⠀⠀⢀⠐⠓⣄⠙⠀⠶⠶⠶⠶⠂⠀⠀⠄⠀⠀⠈⢷⢹⡄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠀⠈⠛⢆⠀⠈⠙⢦⠈⠀⠀⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠠⠟⠘⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣿⣿⣯⣿⣿⣄⣤⣤⣤⡄⠀⠀⠀⠀⢠⡄⠀⢀⠄⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡇⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠈⠻⡁⡈⢶⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⠀⠋⠷⠿⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠰⢦⡄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢀⣀⡛⢠⣤⣤⡀⠠⣿⠂⠀⠀⠀⡀⠀⠤⣤⡇
⢠⣦⣿⣿⣿⣷⣷⣿⣴⣷⣿⣷⣾⣿⣿⠿⠿⠛⠟⠉⠉⠉⣹⣿⣼⣶⣤⣴⡄⢸⡿⣿⣇⠀⣿⣴⣦⣾⣿⣽⣾⣷⣷⣷⣶
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡉⢁⠎⠁⠻⠿⠀⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠟⠭⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣳⣻⠟⣁⣠⣤⣄⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⡈⠙⠃⠉⠉⣽⣿⠛⣾⣿⣆⣨⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⡅⠉⠀⠀⠀⣼⣯⣈⣰⣿⢀⠄⣮⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⡿⣼⣿⣟⡁⠁⢸⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣼⣧⣿⣿⠉⠻⢦⣄⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⣿⢩⣻⠝⠿⣶⣶⣿⣿⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣼⣟⢻⣜⢋⣿⡶⠤⢛⣿⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣶⡟⣹⠛⢳⡾⠛⠀⠀⢉⡿⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⡸⠛⢻⣿⡍⣤⠈⣁⡾⠀⠀⢀⠁⠀⣩⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡝⠁⠀⠘⣁⣿⣽⣾⣏⣁⣠⡠⠾⠗⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠾⣛⣿⣿⣷⣦⡀⠀⢻⣷⣿⣿⣿⢿⣿⣿⣦⣶⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣣⣿⣾⠏⠿⣆⢸⣿⣿⢿⣿⣷⠋⠉⡀⠙⢻⣵⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠋⠀⢸⣦⠀⠻⣿⡿⠃⣨⣯⡁⠠⣏⢉⡇⠈⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢻⣿⣷⣿⡟⠁⣠⣿⡿⢿⣤⡈⢉⣀⣾⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠙⢟⠳⡿⠁⣈⡻⠿⣿⠗⢾⣿⣷⡽⠃⠈⠉
⠀⠀⠀⣠⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠸⣅⡽⠀⡀⠀⢀⣽⣦⣤⡀
⠀⠀⣼⣿⣿⠟⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠⠿⠟⢰⡦⠀⠀⠘⠋⠀⣾⣿⣿⠈⠻
⠀⠀⢻⣿⣷⣄⣀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⡏
⠀⠀⠀⠙⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣻⣿⣿⣿⣻⣿⣿⣿⠃⡴⣽⡋⠀⣈⣩⣇⠀⠈⢣⠀⠙⢧⠈⠙⢿⣍⠉⠻⠷⣄
⠀⠀⠀⠀⠈⠋⡙⢛⠛⠿⡛⠛⠻⢻⡟⠛⠛⢿⡿⠻⠻⠟⠛⡿⢻⠿⠿⠛⠿⡷⠛⠿⡷⡾⢛⡿⣷⠶⠲⢾⠿⠄
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠙⠄⠠⣠⣱⡄⠀⠈⢣⠀⠀⡀⠀⡇⠘⠸⠀⠀⢐⠀⣀⣜⡡⢒⠥⠖⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠰⡁⠀⡅⠀⡇⠀⡂⠀⣰⢏⣨⡾⠕⠊⠀⠀⢀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠀⠀⠈⠉⠳⢤⠀⢦⠀⣷⣠⣧⣾⠿⠈⠉⠀⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⣸⢧⣯⣧⠀⢀⠂⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⢣⣿⣼⢬⡛⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⢟⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡥⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠜⠂
⠀⠀⠀⠀⠀⠀⢠⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂
⠀⠀⠀⠀⠀⡀⢸⢳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠂
⠀⠀⠀⠀⠀⢀⡻⣼⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣬⡇⢆
⠀⠀⠀⢀⡤⠻⠁⠉⠠⣎⠋⣷⣰⣄⠀⠰⣆⠀⠀⠀⠀⠠⢀⣀⠄⠤⠴⠀⠒⠒⠂⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡠⢶⣷⣤⣀
⠀⠀⠀⠋⠠⣴⠾⠿⠧⠃⠀⠺⣿⣧⠀⠀⠹⣧⠀⠀⢀⣠⣾⣷⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢀⣿⢇⣈⡙⠤⠠⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⡀⠀⠘⠒⠋⠻⣿⡟⠿⠿⠷⠦⣍⠙⠓⠓⠒⠒⠂⠀⠀⠀⠲⣶⡖⠐⠀⠉⠛⠛⠛⠚⠛⢢⡿⠟⠛⢉⠿⠦⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣈⠉⢙⣻⡿⠻⣶⡖⠢⢄⣀⣿⡀⠀⠀⠀⠀⠁⠀⠀⠒⠀⠀⠀⠐⠒⠚⠋⠁⠀⠀⣀⣤⠤⢴⡘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠆
⠀⠀⠀⠀⠀⠀⢠⣶⣄⣀⣁⠈⢦⣀⠙⠂⢔⣉⣉⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⢶⠶⠤⠶⠶⠠⣤⣤⣤⡀⠀⠀⠈⠉⠒
⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠋⡀⠀⠉⢻⡖⣠⣤⣭⣙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠏⠙⠿⠻⢿⣦⡴⠖⠲⡶⡏⠁⢯⠬⠟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⣰⢿⣶⡖⠀⠤⠶⠟⢉⡉⠩⠟⠛⢦⠀⠀⠀⠀⢀⣴⠧⠄⠈⠀⢰⡄⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⣈⡿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠧⠄⠀⠤⠄⠒⠂⠀⠚⠃⠀⠀⠱⠄⢀⣴⣉⠁⠀⠀⠀⠀⠀⠉⢶⡀⠈⠡⠂⢸⣡⠦⢤⠠⠟⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉




⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢩⣿⠋⢠⣽⡿⠝⣻⣿⣿⠀⣻⣿⡇⠙⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⣴⡿⠁⢠⣾⡟⠀⢠⣿⣿⠉⠀⣿⣿⡇⠀⢹⣿⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⣿⡟⠀⢠⣾⡿⠀⠀⣾⣿⡇⠀⢀⣿⣿⣿⠀⠀⣿⣿⡆⠀⢹⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⣽⡿⠁⢀⡿⣿⡇⠀⢠⣿⣿⠇⠀⢐⣿⣿⣿⠀⠀⢻⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⠁⣼⣿⡇⠀⣼⣆⣿⠀⠀⢸⣿⣿⠀⠀⠸⣿⣿⣿⠀⠀⢸⣯⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠠⣾⡟⠀⣿⣿⠁⢀⣿⣿⡏⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⠨⣟⣿⠄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⡇⢀⣿⣗⠀⢸⣿⣿⡇⠀⠀⣿⣿⣯⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⡇⠐⣿⣿⠀⢸⣿⣿⡇⠀⠀⣿⣿⣯⠀⠀⢸⣿⣿⣿⠁⠀⢐⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⠀⠘⣿⣿⡇⠀⠀⢻⣿⣿⠀⠀⠈⣿⣿⣿⠀⠀⢸⣿⣿⠃⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣄⣹⣿⣤⡀⣿⣿⣿⠀⠀⢸⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⣼⣿⡿⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⢼⣿⣿⡇⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣴⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣆⣠⣼⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢸⣿⠇⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣿⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠛⠇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠄⠀⢠⣀⡄⣤⣤⣦⣠⠀⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠆⠀⠸⣿⣷⣿⣿⣿⠟⠣⠄⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣧⣼⡆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⠉⠛⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠈⠁⠠⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠁⠀⠄⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⣷⠀⠀⠀⠹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠠⠿⡀⠈⠁⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠑⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠐⠶⠟⠃⢀⣇⠀⠀⠀⠀⢀⡀⢠⡇
⠀⠀⠀⠀⡀⠀⠀⡀⠀⠠⠤⢤⢰⡶⠞⠋⠀⠙⢶⣴⡰⠊⠀⢰⡇
⠀⠀⠀⠀⠁⠀⢁⣀⣥⣴⠖⠀⠀⠀⠀⠀⠀⠀⢘⠗⠀⠀⠀⠘⣿⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠒⣠⣳⣦⣿⠃⠀⠀⠀⠀⠀⠀⣠⡘⠀⠀⠀⠀⢘⣿⣿⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⢈⣉⣭⡄⠀⠀⠀⠀⠀⣠⣾⡋⠀⠀⠀⠀⠀⣼⡏⢡⡄⠀⣴⠉⡞⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⢁⣾⣿⡿⢀⠀⠀⠀⠀⠀⣿⣇⡈⣦⠚⠈⣑⠇⠀⠀⠀⠹⣿⣷
⠀⠀⠀⠀⠀⢀⣤⣿⣿⡇⠀⠀⣴⡿⣱⡿⠁⠀⠀⠀⠀⠀⠀⠧⠋⡿⣿⡶⠾⠛⠀⢠⡀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⢽⣿⣿⡏⠁⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⢈⣿⣟⠀⠀⠀⢻⡟⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⢅⢠⠀⠀⠀⠀⠈⠀⠀⠄⠈⠀⠀⠀⠈⢇
⠀⠂⠀⠀⠀⣾⣿⠟⡄⢀⣼⡍⢸⡯⠄⢠⠀⠀⣓⡂⢀⠆⢐⠿⠙⡤⠄⠀⠀⠆⠈⡀⠘⡄⠀⢠⠱⡄⠘⣧
⠀⠀⠀⠀⢀⣿⣿⠀⢠⣿⠁⢀⡿⠃⠀⣬⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠈⠀⠘⡆
⠀⠀⠀⠀⢸⣿⡏⠀⣾⣁⠀⣼⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⣿⣿⠀⣼⡿⡜⢰⠇⡜⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣿⣷⣠⣿⢡⠁⣾⢦⡄⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⣻⣿⣿⣏⡞⣽⠃⠀⠇⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠘⡇⠀⠀⠈⠁
⠀⠀⠀⠀⠙⣛⣿⣛⠁⣿⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⡇⠀⢀⣶⣄⠀⠀⠃⠀⠀⠀⠀⡀
⠀⠀⠀⡈⣾⣿⣿⣇⣰⣧⡀⠀⢸⠋⠀⢀⡴⢤⡀⠀⠀⠀⠀⣾⡆⢹⠳⣤⣀⣀⠀⡎⢇⠀⠙⠀⢴⣀⠄⠢⠀⠁⢀⡀
⠀⠀⠐⣇⢻⣧⣹⣿⣿⣿⣿⠄⢐⣷⠎⣿⠃⢸⠁⢲⡤⢤⣴⣿⡇⠈⡆⢰⠘⡿⣄⢷⠈⡆⠀⠀⠘⠉⠀⠀⠀⠀⠀⠃
⠀⠀⢸⣿⣦⡙⠿⠿⠿⢟⡋⣼⡿⣿⠀⣿⠀⢸⠀⢘⡇⠀⠀⢼⢷⠀⢧⠈⠀⢡⠘⢾⣇⠹⡀⠀⠀⠆
⠀⠀⢀⣿⣿⣿⣷⣿⠿⣿⢑⣿⢹⡏⠀⡿⠄⢸⠀⠈⡇⠀⠀⢸⢸⡄⢸⡄⢠⠀⠆⠰⣿⡆⢇⠸⠀⢦⠀⡆
⠀⠀⢸⣿⣿⡿⢹⠏⢰⡇⢸⡿⢸⡇⢸⡗⠀⢀⡆⠀⣿⠀⠀⠀⢈⣧⠸⣿⠈⡇⠀⠀⢹⡇⠈⠀⠃⠈
⠀⠀⢻⣿⣧⡀⡀⠀⡞⠀⠞⠀⠟⠁⢸⠷⠆⠸⠗⠀⠈⠁⠸⠀⢸⡤⠀⡇⠀⣃⠀⣀⣠⣧⣀⣤⣀⣤⣴⣤⣤⣶⡶⠊
⠀⠀⠸⣿⣿⣿⣿⣿⣷⣾⣶⣶⣤⣼⣧⣤⣤⣦⣤⣤⣷⣿⣧⣴⣾⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠂
⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠐⠒⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠠⣤⣀⣙⣿⣿⣿⣶⠦⣠⣾⣯⢿⣿⣷⡖⢲⡶⢶⣦⣤⣤⡀⡀
⠀⠀⠀⠀⠀⢀⣀⣈⣙⣿⣿⡿⢋⣵⣾⣿⣿⣿⢸⣿⣿⡇⢸⡸⢇⡿⠉⢉⠿⠋
⠀⠀⠀⠀⠀⣀⣭⣭⣽⡿⢃⣴⣿⣿⣿⣿⣿⠏⡾⠟⠀⠁⢄⠉⠉⠀⠀⠛⠒⠶
⠀⠀⠀⠀⣀⢠⣴⣾⠋⣰⣿⣿⣿⣿⣿⣿⣿⣦⠈⠃⠀⠀⠀⢹⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⣀⣬⣿⢃⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢄⠀⠁⠠⠄⢦⣑⣲⠖⠁
⠀⠀⠀⠈⢀⣹⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠘⠓⠦⠀⠀⠀⠉
⠀⠀⠀⠀⢙⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶
⠀⠀⠀⠐⢻⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⠀⣀⣶⣶⠊⠉
⠀⠀⠀⠰⢿⡃⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡟⢀⣿⣾⡿⠟⠁
⠀⠀⠀⠀⠞⡇⣿⣿⣿⣿⣿⣿⣗⠫⠌⠿⢶⣾⠟⠋
⠀⠀⠀⠀⠠⢿⢸⣿⣿⣿⣿⣿⡷⠁⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⢁⡘⡃⢿⣿⣿⣿⣿⣮⡖⠀⠀⠀⠀⠀⡰⠛⠉⠁⠉⠉⠙⠻⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠈⣷⡈⠞⣿⣿⣿⣿⣿⣾⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠙⡌⠘⢿⣦⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠈⢻⢸⣞⠻⣿⣿⣿⣿⣟⡄⠠⣴⣿⣋⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢀⡞⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠇⢻⣜⢿⣿⣿⣿⣿⣄⠈⠁⠀⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⣡⣽⣶⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠠⢋⡑⣾⠛⢿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⢤⣌⣉⡻⠿⡿⣿⣿⣷⣶⣶⣾⣿⡾⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⢀⠀⠀⣀⡀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⠀⠄⠀⠀⠀⠆⠀⠀⡀⠀⠀⢀⡀
⠀⢀⠀⢸⣿⣿⣷⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⣄⡘⠿⠃⠀⠀⠀⢀⣾⠀⠀⡼⢀⡔⠁⠀⠀⠀⡀⢀⣽⡆⠓⠀⠀⢠⣦⡄
⠀⠀⠀⣼⣧⣜⠿⣛⣩⢿⣿⣦⠀⠀⠀⠀⣀⣿⡟⠀⠀⠀⠀⢠⣿⣿⠀⣸⣷⠏⠀⠈⢀⣤⠞⡁⠘⠟⡁⢠⠶⡄⠘⠛⠁
⠀⢀⣿⣿⣿⣿⣯⣷⣶⣿⡯⠥⠀⠀⠀⢸⣿⣿⣧⡄⠀⠂⠀⠘⠿⢿⣷⣿⣿⣧⣶⣶⡿⠋⠀⠀⠀⠀⠀⠈⠛⠁⠰⠤
⠀⠨⠁⠀⠙⠻⠿⠟⣿⡇⠈⠀⣀⠀⠀⢸⣿⣿⣯⣷⠀⠀⠀⠀⠸⣯⣿⡭⠉⠉⠛⠉⠀⠀⠀⠀⠄⠘⠷⢶⣶⣶⡀⠠
⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⢈⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⡀⢠⣴⣄⣀⣤⣤⣄⣰⠂⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠁⠠⠄
⠀⠀⠀⠂⠀⢸⣆⠀⠈⡆⠀⣠⠂⠀⠀⠀⢻⣿⣿⠃⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⠂⠐⠂⠀⠠⠀⣤⠶⢯⢤⣀
⠀⢳⣤⣄⠀⣸⣿⣧⠀⣿⡾⠁⠀⠀⠀⠀⠜⡛⠟⠦⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣭⠁⢀⠀⢤⣤⡖⣣⢨⣤⢒⡽
⠀⠀⢻⣿⣿⣌⢻⣿⣷⡿⠡⠀⠀⠀⠀⠙⠛⠒⠛⠛⠃⠀⢠⠶⣿⣿⢿⣿⡿⠋⠻⠟⠃⠀⠠⠀⠉⠁⡀⠀⢅⣂⡴⠀⠂
⠘⠀⠀⢀⣼⣿⡧⣿⡟⣵⠀⢀⣀⠀⠂⠀⠀⠀⠀⠀⣊⠁⠀⠀⠙⠉⠘⠈⠃⠈⠀⢀⡄⠀⠀⠀⠈⠛⠃⠀⢐⢿⡓
⠀⢤⠀⠀⠻⢿⣅⣿⠕⠃⠀⠻⣿⡿⠀⠁⠀⠈⠓⠛⠋⣀⠘⢁⠀⠠⠀⠀⠀⢐⠀⠿⠇⠀⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⡠⠡⠈⠀⠀⠠⠄⠐⠂⠐⠟⠭⢀⠀⠀⠀⠀⠀⠄⠀⠐⣀⠀⠀⠀⠆⠀⠀⠀⢠⡴⢦⡀⠀⠁
⠀⡀⠁⠀⠀⣀⠀⣜⣻⣾⣶⣿⣷⡄⠀⠀⠙⠀⠈⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡃⠿⣷⡾⣥⣤⡀
⠀⠁⠠⣀⣿⣿⣿⡬⠛⠛⠻⢿⠛⠋⡁⠀⠄⠀⣤⡄⠀⠀⠀⠀⢠⣄⣸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠈
⠀⠀⢄⣈⣯⣿⢁⢀⣶⣦⡀⣀⢱⠀⠀⠀⡴⠒⠉⠳⠮⠁⠀⡀⣠⡟⢣⠶⣄⠀⠀⠴⠀⠀⢉⠀⠐⠂⠀⣿⡏⠐⠂
⠀⠟⢲⣿⣿⣿⡏⣘⠽⡯⣣⣹⡿⠀⠲⣾⡅⢰⣛⠆⠘⠀⠘⠛⣼⣧⡜⠶⢻⣄⣀⣀⠀⠀⣾⡄⠀⡠⢀⣿⠁⠀⠀⠀⡉
⠀⠀⠀⠙⠻⠟⣿⣨⠟⠚⢳⣸⡇⠀⠀⠠⠳⠤⢄⡤⠎⠈⠁⠀⠉⠻⠿⠇⣾⣬⣾⣽⡇⠀⠉⢧⣬⣀⣼⣿⡀⠀⢤⣾⠃
⠀⠄⠀⠉⠐⠿⠋⠛⠿⠾⠟⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠀⠀⠀⠘⠃⠛⠙⠛⠋⠃⠀⠂⠀⠘⠋⣥⠙⠛⠛⠋⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠘⢆⢠⠴⠚⡉⢽⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠫⡙⠉⠈⡉⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⢨⡟⠀⠀⢠⡾⠀⡉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠽⢦⡀⠆⠈⢀⠈⢷⡀⠀⠠⠲⢤⣀⠸⡇⣿⣿⠀⠠⠈⣼⠃⢀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠙⠣⣄⠀⠀⠀⠙⡖⠀⣰⣦⣬⣉⠻⢿⡿⠐⠀⣴⣃⣀⡀⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠉⣳⣤⣀⡞⠀⣰⣿⣿⣿⣿⣷⣤⡷⢟⡉⠉⠉⠉⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣾⠟⠋⠿⡿⠀⢠⣿⢿⠿⡛⢻⡸⣶⣒⣾⣿⣿⣿⡆⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⠀⠀⠀⠀⠀⢶⣿⣿⡇⠀⣠⣶⡇⠀⡞⠹⡌⢿⠁⠀⢹⣿⣿⣞⣹⣿⣿⡇⢸⡟⠉⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠉⠒⠒⠒⠦⣌⣿⣿⡇⠀⣿⣿⣷⣮⣾⠀⠙⢾⣀⡴⠾⣯⣉⠀⣈⢿⣿⠇⣸⠇⠀⠀⡼⡁⠤⠒⠚⠉⠛⣲⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡉⠻⣷⣶⣿⣿⣿⣄⠈⢿⣿⣿⠟⠀⢀⡼⢻⡇⠀⢣⠈⠓⠿⠼⣿⣞⣁⣀⠄⣰⣧⣶⡶⠖⢁⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⢉⠛⣻⢣⡿⠿⣿⣷⠀⠉⠳⢤⡒⠉⣠⠞⠀⠀⠈⠳⢤⡤⢴⣾⣿⣿⡭⠞⠉⠛⢯⠒⠚⠉
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣠⡴⡶⢚⠋⡿⠀⠀⢠⣿⡍⠛⠒⠶⠤⣍⡻⠤⣶⣶⣦⣤⣤⣴⢠⣿⣿⣿⣿⡗⠀⠀⢀⠀⠳⡄
⠀⠀⠀⠀⢀⠞⢡⠤⢺⠛⠁⡰⠁⠂⢸⡇⠀⠀⢸⣿⣿⣦⣀⢠⣤⣤⣽⣦⡈⣙⣛⣿⣿⣵⣿⣿⣿⣿⣿⡥⠀⠐⢋⡠⢾⡁
⠀⠀⠀⡠⠞⠊⠣⣄⡁⠀⠐⢀⣠⠶⠺⣇⠀⠀⠈⠻⣿⣿⣿⣷⣯⣟⣻⣿⣿⣿⡿⢿⣿⣧⣈⠉⠉⣉⣡⣶⣶⣿⣿⣦⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠈⠑⢦⡀⠀⢀⣉⡻⣿⣿⡿⠦⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡏⠠⣌⠛⣿⠿⠟⢉⣀⡽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣄⠈⠻⢿⣿⣿⣿⡿⠅⠀⢀⣠⣿⣿⣿⣿⣿⣿⠃⠀⣿⠆⣟⣀⡴⢋⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣿⣿⠓⠤⣀⣀⣤⠶⠒⢶⣶⣿⣿⣿⣿⣿⡿⠟⠁⠀⠜⠋⣰⠿⣄⢀⠁⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠟⣩⡏⢀⠄⡈⢱⡇⠀⠘⢧⡹⠿⣿⡍⠉⠁⠀⠀⠀⠀⢀⡼⢁⠀⠈⠳⡄⠁⠀⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣃⠤⠊⢹⢃⠅⠊⠀⣼⠀⠂⠀⠀⢹⣆⠀⠀⠀⠀⠀⣀⣠⣴⣿⡀⡀⡀⠀⠀⡉⢳⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⢸⡀⠔⢀⠠⡇⠈⠀⠀⠀⢸⠏⠓⠒⠚⠉⠀⠈⡇⢸⣿⠙⣧⡀⠀⡀⠃⠀⠙⢄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡐⠁⢸⡏⢄⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⣇⢸⡟⢠⠏⠙⠶⠤⣤⣤⣄⣈⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡾⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡗⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣼⠿⢿⣿⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠉⠉⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠐⠉⠁⠀⡄⣼⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⣀⠀⣠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣅⣠⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠞⣿⣿⠿⠇⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡂⢠⠿⣆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠫⠄⣀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⠀⣀⣠⣶⡾⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠀⠈⠋⠁⢀⣀⡼⠓⢄⡀⠀⠀⠀⠀⣤⠄⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠒⠲⡶⢾⣿⠟⠋⠁⠀⠈⠹⣷⢶⣤⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠈⠀⠉⠉⣑⣧⣴⡶⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⢻⡶⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⡤⠈⢿⣛⣫⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⣿⡷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣼⠗⠀⠀⠀⠀⠀⠀⢠⣿⣷⠏⠀⠀⠀⢀⡡⢄⡀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠀⢠⣤⣤⣶⡆⠀⠀⠀⠀⠀⠀⢀⣾⣿⡁⠀⠀⠂⠀⠀⠀⠀⣼⡿⠀⢸⠆⠀⠠⣮⠀⣎⠁⠀⠀⠀⣠⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡇⠀⠀⠀⢀⠁⣴⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠘⣦⠼⠃⠈⣇⡿⠀⠀⠀⠀⠉⠾⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⠁⠀⠀⠀⣠⣾⠟⣹⣿⠃⠀⠁⠀⠀⠀⠀⠀⠀⣇⡹⢻⣾⣿⣤⣤⣶⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠆⠀⠀⢠⣿⢏⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠭⠙⣛⠉⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⡿⠀⠀⠀⢀⣿⣯⣟⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⢀⠀⠁⠀⠀⢤⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢉⣿⣾⠁⠀⠀⠀⠈⣿⡟⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⣄⠀⠀⠀⠀⠀⠈⠀⠀⠐⡄⠈⠡⠀⠀⠀⠀⠸⣇
⠀⠦⠀⠀⠀⠀⢀⣿⣿⡿⢃⡀⢀⢸⡟⠋⣼⣟⣁⠀⣀⠀⠀⠰⠶⠀⠀⣰⠀⢤⣾⠟⣇⣀⣀⠀⠀⢀⡄⠀⢇⠀⠸⡀⠀⠐⠀⣱⡀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⣸⣿⣿⠃⠈⠁⣾⠟⠋⢡⣿⡇⠉⠀⡟⠀⠀⠐⠉⠁⠀⠁⠀⠾⠈⠠⠘⠁⠈⠀⠀⠈⢙⠀⠘⠀⠀⢳⠀⠀⠘⠀⠙⠄⠈⢻⡆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣼⣿⣿⡀⠀⣾⠟⠀⠀⣼⠏⠁⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣸⣿⣀⠆⢠⡟⢠⠇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⢾⣿⣿⠀⢠⣿⡇⡿⢠⣿⠁⡞⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⢸⣿⣇⠀⣾⡟⢸⠃⣼⣧⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣷⡇
⠀⠀⠀⠀⠀⣾⣿⣿⣾⣿⢁⡿⣠⡿⠈⢿⠀⠀⡘⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠠⠀⠀⠀⢻⡇⠀⠀⠀⠰⣄⠀⠐⠂
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⣼⠃⣿⠇⠀⠸⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠿⢛⣿⣛⠋⢰⣿⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢴⠀⠀⠀⠀⠈⡇⠀⠀⢠⣶⣄⠀⠀⠀⢃
⠀⠀⠀⠀⠰⣠⣾⡿⣿⡿⠀⣼⢉⠀⠀⠀⣰⠟⠀⠀⠀⣊⣁⠀⠀⠀⠀⠀⠀⠀⣸⣧⠚⣶⣶⣀⠀⠀⠅⠀⣤⠹⡅⠉⠱⠆⠀⣠⠄⠀⠀⣄⠂⠘⠆
⠀⠀⠀⢠⡆⣹⣿⡛⢿⣷⣾⣿⢿⣧⠀⠀⢸⡤⣀⣤⣾⠋⢹⡷⢄⣀⠀⠀⠀⢀⣿⣿⡄⢹⡀⠹⡛⢶⣾⠄⢿⡄⢱⡀⠀⠀⠈⠙⡿⡎⠁⠈⠀⠀⠀⠰⡇
⠀⠀⠀⢸⣧⡈⢿⣷⣬⣿⣿⣿⣿⣿⠟⢀⣤⣿⠏⢠⣿⠀⠀⡇⠀⢻⡿⠓⠶⠾⣿⣿⠁⠀⡇⠀⡇⠨⡟⢷⡘⣷⡀⢷⠀⠀⠀⠀⠣⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⣿⣿⣈⡛⠿⢿⡿⠿⠟⡋⢰⣿⢿⣿⠃⢸⡏⠀⠀⡇⠀⢈⡿⠀⠀⠀⢾⣿⣇⠀⢿⠀⠁⠀⢱⠀⠳⢿⣇⠘⡇⠀⠀⠀⠲
⠀⠀⠀⢸⣿⣿⣿⣿⣶⣾⣶⣷⣿⠇⣿⡟⢸⣿⠀⢸⣿⡀⠀⡇⠀⠈⣷⠀⠀⠀⢸⡀⣿⠀⢸⡆⠀⣀⠀⣆⠀⣸⣿⡆⢹⡀⢰⠀⢰⡀⠀⡆
⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⠃⣸⡟⠀⣿⡇⣾⡟⠀⣾⣇⠀⠀⣇⠀⠀⢻⠄⠀⠆⠘⠁⢿⠀⢨⣿⡄⢹⡄⠀⠀⠈⣿⣇⠈⡇⠘⡄⠘⠇⠀⢣
⠀⠀⠀⣼⣿⡿⠟⠋⠸⠏⠀⣿⠁⢸⡿⠁⣿⡇⠀⣿⠇⠀⢀⣾⠀⠀⢻⣤⠀⢀⠀⠀⣾⠗⠘⣿⠇⠀⡇⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⢿⣿⣷⣆⡀⡀⠀⢸⠃⠀⡾⠁⠸⠏⠀⢈⡿⠿⠂⠘⠿⠃⠀⢈⠀⠀⠸⠀⠀⣷⠦⠀⠿⠀⠀⣁⠀⢀⣤⣤⣿⣤⣤⣶⣄⣴⣶⣶⣴⣶⣾⣿⡿⠋
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣶⣾⣤⣶⣦⣤⣴⣿⣀⣀⣀⣼⣄⣀⣠⣾⣾⣾⣧⣤⣴⣷⣤⣤⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣉⠉
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⣿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⡿⠿⠛⠿⠟⠛⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣤⢀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⡀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣾⣟⣻⣗⠀⠀⠀⠀⢠⣶⣶⢿⣿⣿⣏⣠⡄⠀⠀⣹⣿⣇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣪⣿⡇⠀⢀⢻⣾⠿⣴⢇⡀⠀⠘⠻⠟⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⣟⣿⣯⣤⠀⠀⣻⣿⣟⡴⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⢤⣘⣿⣿⣿⣻⡿⣡⡤⠀⠠⠴⢾⣿⣿⣿⢿⣿⣟⣯⣿⣹⣿⠛⠟⠂⠀⠠⣿⣿⣻⠤⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⠿⠿⠟⣿⠿⠿⠿⠂⠀⠀⠐⠉⠁⣨⣿⣯⣿⣿⡿⢿⣷⡦⠀⠀⣠⣶⣿⣿⣿⣿⣷⣏
⠀⠀⠀⠀⠀⠀⠀⠒⣾⡿⢿⣷⠖⠀⢀⣶⣿⣿⣿⣦⠀⠀⢀⣤⣠⣤⠈⠉⣽⣻⡟⠉⠀⠈⠙⠓⠀⢠⣧⣿⣿⣿⣯⣷⣺⣿⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣏⠀⢠⡾⣷⣿⣿⣿⣿⣷⡀⣸⣿⣿⣿⣦⠘⠋⠁⢀⣤⣴⣶⣦⣤⠄⠈⣿⣿⣿⣿⣿⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢠⣿⣿⣿⣿⣿⣿⣻⡄⠈⠙⠿⠏⠀⠀⠀⠀⠀⠘⢿⣶⡿⠇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣀⡀⠈⢛⣿⣿⣿⣿⣾⡏⠀⣀⣀⣤⠖⠀⠀⢀⡶⠒⢶⡄⠹⠏⠁⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣈⣙⠿⠛⣟⣉⣱⣿⡿⠟⠛⠉⠀⠀⠘⡧⣿⣼⠃⠀⠀⠀⠐⠂⠀⢻⣿⣿⣿⣿⣿⣯⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠙⠷⣯⣿⣿⣽⣿⣽⡯⠿⠃⠀⠒⠀⠘⠻⠿⠿⣭⠿⠿⠟⠂⠀⠀⠀⠀⢠⡛⠛⠿⠛⣋⣉⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⣶⣤⣿⣴⣻⣶⠆⠀⠀⠀⠀⠀⢙⣴⠒⠋⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠆⠀⠀⢸⣿⣷⣦⡀⠀⠀⢠⣆⠀⠈⢛⣿⣻⣻⣿⣿⣁⠀⠀⣰⡄⠀⢰⠋⠀⡧⠀⢠⣴⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⢿⠷⠀⢠⠀⠈⠻⢷⣿⣷⡀⠀⠻⣽⠃⠰⢿⣿⢿⣿⡿⣿⣿⣅⠐⣯⠟⠀⠘⠲⠖⠁⠀⣿⣏⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠈⠉⠁⠀⠀⠘⢦⣄⣈⣁⣼⣿⣧⣈⣙⣋⣴⠃⠀⣠⣤⣤⣤⣀⠀⠙⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣾⣟⣿⣷⣿⣳⣶⡀⢀⣀⣀⡀⠀⠉⠛⠛⢿⣿⡿⠛⠛⠉⠀⠀⠘⠿⣿⡿⠿⠋⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣷⣼⣿⣯⣿⡽⣿⣿⣿⠟⢿⣻⡾⠀⠀⠀⠀⠀⠀⠉⠀⣀⠀⠀⠀⠀⣤⣄⡀⢀⣀⡀⣠⣶⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⣿⣿⣷⣽⣿⣟⣿⣫⣿⣿⠾⠋⠀⡀⠀⠀⢀⣠⣄⣤⣘⣍⡀⠈⢿⣿⡿⣯⣧⡿⢿⣿⣭⣟⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⣶⠝⣛⠛⢿⣿⣿⣿⠿⠿⡀⢴⣶⣿⡥⠀⣠⣿⡿⣛⢿⣿⡛⠁⡀⠀⠙⢙⣿⡿⣿⣛⡞⣿⣿⡀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡤⣄⣉⣉⣁⡤⣼⣿⡟⠉⠁⠰⠮⠼⣿⣷⣭⣾⣿⠁⠀⠀⢀⣾⣿⣵⣿⣮⣭⣾⣿⣞⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠻⠥⣿⣼⣼⣯⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⣀⠀⠀⠈⠉⣽⡷⠏⠉⠈⠉⠹⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣠⣿⣿⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢯⣿⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⡏⡀⢠⡌⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣠⣉⠁⠀⠀⢠⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠆⣄⢀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠈⠉⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⣩⠉⠄⠰⣿⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠⡂⠀⠠⣄⠀⣿⡆⠀⣙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠈⢳⡀⠀⠉⠀⢸⣷⠀⠋⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢁⣀⠈⢻⣦⣄⣀⢸⣿⣤⣆⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡅⠋⠁⠹⠚⠛⠻⡿⣿⣿⡿⢯⣦⡜⣷⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠁⠀⠀⠀⠀⡤⠂⡰⠋⠀⠀⠄⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣡⡀⠀⣀⠀⠐⠁⠀⠃⠈⣷⡀⠀⠀⣶⡆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠡⠞⠁⢀⠃⠀⡼⠲⣼⣿⡟⣾⠃⠹⠏⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⣤⠁⢠⡖⠀⠈⢻⠂⢠⡇⠀⡈⣿⡇⢻⣇⢀⡀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠟⢁⣤⠏⠀⠀⣰⠿⠀⣾⡇⠀⠁⣿⣧⠸⣿⡌⠃⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣤⣶⠿⠉⡀⣠⢶⡄⠂⢠⣿⣇⢀⠈⣹⣿⠀⣹⣧⠸⠖⡀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠸⢠⣾⣿⣿⠤⢾⣿⡿⠂⠈⠥⣆⠦⠂⢠⣿⣿⡿⠸⠐⢻⣿⠄⢽⣿⣆⠀⢁⠜⣿⣇⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢰⢀⣿⣽⡿⢶⠶⣶⡟⠀⠀⠐⠂⠙⠀⠀⣼⠷⢿⠇⠀⠐⠀⣿⡆⠀⠘⣿⡆⠻⣷⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣏⣾⣿⣯⣿⣻⠿⠉⠀⠀⠠⣰⣸⠆⠀⣘⠃⠀⠁⠀⠀⠈⠁⢹⡇⠀⠡⡼⣿⡄⠘⢷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢄⣿⣿⣿⣿⡟⣁⣴⠞⣡⣤⠴⠟⠋⠀⣼⣿⡏⢘⠀⠀⠀⡀⠀⢸⣇⠀⢀⠀⠘⣿⣄⠘⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣡⡾⠋⠁⠐⣇⣠⣿⢀⣠⣾⣿⣿⡀⠸⠀⠀⠀⢱⡀⢹⣿⠈⡄⠀⠀⣿⣿⣆⠸⣿⣷
⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠋⠀⠄⠀⢀⡼⠻⠄⣉⣿⡏⢸⠋⣧⡄⠀⠀⠀⢙⠃⢸⣿⠀⣿⣦⡀⠈⣿⣿⣷⡿⣿⡇
⠀⠀⠀⠀⢳⣿⣟⡟⣋⢶⡿⠄⠀⠟⠉⠁⢴⣾⣿⢻⠇⢾⠀⢹⡇⠀⠀⠀⠘⠀⢸⣿⡀⡟⠺⣷⠆⢛⣻⡙⢷⣿⣷
⠀⠀⠀⠀⣴⣿⢟⣷⣿⣃⡝⠐⠆⠀⢀⣠⠾⢋⣿⡆⠀⡀⠀⣀⠇⠀⠀⠀⠀⠀⣸⣿⠇⣡⠀⠀⠀⣨⣿⣯⠈⢿⣿⡇
⠀⠀⠀⢀⢿⣿⡙⠿⢿⣹⠇⣌⢀⣾⡿⢡⡀⢿⡏⢿⣄⡵⡧⠬⣦⡀⠀⠀⠀⠀⢹⢻⡇⣽⣄⠀⠀⡙⠿⣗⣻⡄⢻⡇⡀
⠀⠀⠀⣿⣦⠙⠿⠃⢸⣿⠟⣣⣿⣿⡷⠈⢷⡌⠃⣸⣿⣆⠁⠀⢎⣁⣄⣼⣁⠀⢸⠘⡇⢉⣻⣤⠐⠛⠀⣾⠿⠇⠀⣾⠃
⠀⠀⢰⣿⣿⣷⣶⣶⣶⣶⡈⠿⣾⣿⡇⠸⣦⣱⣶⣿⣿⣿⣷⣀⠈⠉⢠⠟⢉⡄⣿⠀⡇⢈⣟⡿⠋⣠⠆⠀⢲⡇⠀⣿⡃
⠀⠀⣸⣿⣿⣿⣿⣿⣷⠸⣷⠀⣿⣿⡄⠀⠙⢻⣿⣿⣿⠇⣿⡿⢷⣤⣀⠀⠘⠃⣽⠀⣷⠀⠈⣡⡴⠃⠀⢀⣾⣿⡀⢸⣷⡆
⠀⠀⣿⣿⣿⣿⣿⠟⠙⢧⠀⢼⣿⣿⣿⡄⠀⠀⢻⣿⣿⢠⣿⠃⠀⠛⠛⠛⠶⢤⣽⠄⢻⠶⠛⢉⡇⠀⠞⠉⢸⣿⠃⠸⣿⡇
⠀⠀⠛⠛⠻⣿⣤⣤⣀⣀⣀⣼⣿⣿⣿⣧⡈⠀⠈⣿⣿⡎⠁⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⣺⣇⢀⡍⠀⢸⣿⠀⠀⣿⣧⡀
⠀⠀⠀⠀⠀⠐⠛⠻⠟⣻⣿⣿⣿⣽⣯⣿⣇⣠⣴⣿⣿⣷⣶⣦⣤⣄⣈⣀⣀⣀⣀⠀⢀⣀⣰⣾⣿⣄⣀⣠⣼⣷⠤⠞⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣽⣟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠈⠉⠉⢻⠿⠿⠟⠛⣿⠿⠻⠿⠛⠿⠿⠿⠿⢿⠿⣿⣿⣿⣿⣏⣽⡛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠠⡂⢀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠠⠘⠁⠲⢈⡥⣸⡤⠢⢤⠀⠀⠀⠀⠀⠀⢾⣿⣶⣿⡟
⠀⠀⠀⢠⡶⢘⡢⠁⠀⠁⠃⠀⠀⣠⡠⠤⣍⢠⣙⣿⣻⣲⣩⣀⠀⠀⠀⠀⠀⠀⠙⠟⢡⣶⡦
⠀⠀⣰⠇⢰⠋⣅⣂⠂⠀⢀⠀⠀⣾⣹⣒⠋⡾⣿⣿⣤⣴⣶⣩⠀⠀⠀⠀⠀⣀⡜⢀⣈⠉⠁
⠀⢀⠇⣰⠞⣾⠃⡀⠈⢄⡀⠀⠀⠹⣷⣏⣐⢐⠚⢻⠿⠇⠀⠀⠀⢀⡀⠀⣐⣿⣿⣿⣿⣿⢶⣆⡀
⠀⢸⣾⣿⡞⣳⡏⠀⠀⠰⠦⡀⠀⠀⠘⠻⣿⣿⣋⣧⡜⢀⣠⣠⠗⠀⠀⣤⣿⣿⣿⣟⣏⠟⠀⠘⣡⡆
⠀⠸⣿⣾⣿⣳⣤⠉⠦⠀⠀⠈⠂⠀⢀⠀⠀⠘⠙⠿⠇⣸⠈⠂⠰⣤⣿⣿⣿⣿⣿⠻⣿⡄⠀⠀⠉⠔
⠀⠀⠹⠿⠻⠙⠉⠀⠀⠀⠀⠀⠀⣷⣤⣆⣶⠇⠀⣦⠀⢸⠀⡰⠀⠿⣿⣿⢿⣯⣤⣬⣿⡓⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⣤⣳⣤⣈⠛⡟⢻⢠⣴⣿⣆⡈⡴⠁⢢⠘⣿⡿⢿⡿⢿⢿⠋⠀⠹⢦⣉⠂
⠀⠀⠀⡀⠀⠀⠀⠈⠽⣿⣿⣿⣿⣇⣅⠺⡄⣿⣿⣿⣿⣧⠇⠀⡼⠃⢸⠿⣟⣡⢀⡎⡇⣅⣆⠿⠋⠁
⠀⠀⠀⣷⣆⠀⠰⢶⣶⣿⣿⣿⣿⣿⣿⣶⡾⣏⢻⣿⣿⢸⢧⡞⠀⢠⢃⡠⡌⠁⠊⠋⠛⠈
⠀⠀⠀⢨⣩⡷⣧⠄⠨⢿⣿⣿⣿⣿⣿⣿⣿⣙⣼⣿⣿⣬⠏⢀⡄⠸⢈⠟⠃⢀⣄
⠀⠀⠀⠉⠉⠰⢧⡀⣢⢀⡸⠿⠿⠿⠻⢿⣿⣿⣿⣿⡿⠁⠀⢉⣧⣼⣿⣄⡿⠛⠁
⠀⠀⠀⠀⠀⣀⡤⢻⡏⢤⣤⣴⣶⣦⣴⣾⣿⣿⣿⣿⠇⣡⣶⣿⡟⡟⣿⢿⡟⠛⠋
⠀⠀⠀⠀⠈⠀⠀⠠⣴⣿⣿⣿⣿⣿⠿⣯⣹⡟⠋⣤⣄⠿⣿⡟⡸⣈⣥⣤⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠛⠁⣴⣿⠯⠄⢈⣙⣻⣧⠹⣻⣿⣿⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠹⠿⣿⢠⣿⣿⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡀⠀⠆⠀⢀⡄⠀⠀⠀⠀⣤⣤⣄⠀⠠⠄⠀⠀⠀⢀⣶⣆⣤⠄⠀⠀⠀⢠⣤⡄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⣄⢸⣷⢀⠀⠀⠸⣿⣽⣿⠀⠀⣀⣀⣼⣿⣟⣿⣿⣿⣴⠆⠀⠀⣼⣿⣧⢀⣀
⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⡿⠇⠀⢲⣽⣿⣹⣿⣴⠀⠀⠉⠁⣀⣤⣴⣿⣿⣿⣿⢿⡿⣿⣿⣷⣖⠂⠀⣸⣿⡗⠋⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣶⣿⣿⣿⣿⣵⣞⠁⠀⢉⡽⠟⠻⣿⣻⣯⣿⣷⣿⣛⠃⠉⠀⢀⣤⣿⣿⣾⣉⡗
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣠⠀⠉⣩⣼⣷⣍⡉⠀⠀⠀⠀⣀⠀⠾⢿⣷⡟⠟⠉⠻⢿⡅⠀⡴⣿⣿⣿⣿⢟⣟⣧⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠸⢿⣾⡿⠀⢀⣴⣿⣿⣿⣿⣷⡄⠐⣿⣿⣿⣄⠠⠟⠛⠁⢀⣠⣤⡀⡀⠀⣧⣿⣿⣿⣿⣿⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⢈⣷⣿⣿⣿⣿⡿⣇⠘⠛⢿⡿⠋⠀⠀⠀⠈⢻⣿⣽⡿⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠀⠘⢿⣿⣿⣿⣿⣿⠋⠀⢀⣀⡤⠀⠀⢀⡴⠶⣄⠙⣿⠒⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣶⣘⡻⠿⠻⠟⣋⣶⣾⠿⠟⠛⠁⠀⠸⣇⣦⣼⠀⠀⠀⠀⠖⠀⢸⣿⣿⣿⣿⣿⣇⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠿⣯⣿⣟⣿⣿⣿⡿⠟⠀⠐⠀⠐⠺⠿⠿⣽⠿⠿⠖⠀⠀⠀⠀⠠⡟⠻⠿⠟⣋⡁⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣴⣿⣞⣷⡶⠀⠀⠀⠀⠀⢙⣴⠚⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠇⠀⠀⢾⣿⣷⣄⠀⠀⢀⣶⡀⠀⣉⣿⣿⣽⣿⣯⣀⠀⢠⣧⠀⢠⠏⠀⡧⠀⣴⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠻⠟⠀⠴⠀⠈⠻⠿⣿⣧⠀⠘⢻⡃⠘⢻⡿⢻⣿⡟⣿⣯⡀⢻⠟⠀⠈⠓⠚⠁⠘⣿⣇⣨⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣤⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣿⣿⣧⣤⣭⡶⠋⠀⣤⣶⣶⣶⣤⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⢰⣿⣯⣿⣿⣯⣽⣧⣠⣤⣶⡆⠀⠀⠈⠉⠻⡿⠋⠉⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⣿⣿⣻⣿⠿⣿⣜⣷⠟⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢤⣤⣼⡶⣦⣴⣶⣤⠾⣧⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣙⣿⣿⣿⣿⣿⣷⣿⣿⡿⠋⣁⣠⠖⠀⠀⣴⣾⣶⣿⣶⡶⠂⠈⠻⠯⣿⣿⣯⣽⣻⣿⣾⠛⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢧⣷⡀⠙⠻⠟⠋⠉⣳⣦⠿⠟⠋⣀⢺⣿⣇⣒⣿⡿⠀⠀⠀⢀⣴⣟⣿⣝⣶⣧⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣏⣟⣿⣻⣻⣝⣿⠟⠀⠀⠀⠈⠈⠙⠿⠿⠟⠁⠀⠀⠀⠿⢻⣯⡿⠟⠙⠿⢻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠀⢠⢀⣒⠓⣤⡞⠋⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢸⣶⣾⣾⣿⣿⣦⣽⣶⣁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠐⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣀⣿⣶⣿⡧⢿⣿⣿⣿⣿⡿⢚⣇⡠⡤⣄⠾⠂⠀⠀⠀⢲⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⡗⢠⢻⣿⠀⣿⡿⣿⣧⢼⣿⣿⢿⡿⠲⢺⣾⠭⠁⠍⠀⠀⢀⠄⠀⣸⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣤⡅⠀⠰⠄⠰⠐⢠⠄⠄⢻⠄⣸⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢻⡹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⣤⣤⡀⠄⠀⠀⢸⠉⢹⣿⣷⡀⠄
⠀⠀⠀⠀⠀⠀⢰⢸⡇⠀⣸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡗⢀⣼⣿⣿⣇⠀⠀⢂⣾⠤⣾⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠘⣾⣷⠀⢻⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢵⣾⣿⣿⣟⣿⣦⡄⠀⢸⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⣹⣿⣶⣶⣶⢻⣿⣿⣿⣿⣿⢻⣬⠟⣯⣿⣿⣾⣿⣿⣿⣛⣋⣉⣉⣠⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⢀⣀⣶⣿⣿⣿⣿⡏⠀⣿⣿⣿⣻⣿⢸⣽⣧⢿⣷⣿⣿⣿⣿⣿⣹⣹⣛⣟⣻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠐⢤⣿⣿⣿⢹⡟⠚⠛⠶⠾⠹⠿⠺⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠁⢠⣿⣿⣿⣟⣼⣿⣄⠐⢶⣒⢲⠤⡀⢁⠀⠀⠀⠀⠀⠀⠚⠒⣾⣿⣿⣿⣾⠄
⠀⣄⣻⣿⣿⣿⣿⣿⣿⠃⢰⣾⣿⢿⣿⣿⣿⣟⣿⣦⠀⢻⣿⣆⢹⣆⠁⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣄
⢀⣿⣿⣿⣿⣿⣿⣿⢋⣶⣿⣿⣿⣾⠋⠡⣼⣿⣿⡿⣷⡀⠙⣿⣠⣿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣆
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⢿⣿⣿⣷⣿⣷⡄⠈⠛⠛⠛⠿⠄⠡⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠿⠿⣟⢧⣼⢿⣿⣶⣶⣶⣶⣶⣶⣶⣼⣤⣶⣶⣶⣶⣶⣾⠿⠿⠿⠿⠿⠂
⠀⠀⠀⠐⠲⠤⠄⣀⠉⠉⠉⠉⠙⠻⠛⠚⠿⣦⣠⣶⣷⣾⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⠿⠛⠿⠿⠿⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣡⣀⣀⣀⠀⠀⠀⠀⣠⣤⣭⣶⣶⣤⡀⢰⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠓⠀⠙⠻⣿⣿⢿⠃⠉⠉⠉⠁⠀⠀⠀⠀⠀⠒⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⣧⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠘⣯⡿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⡘⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣦⣿⡟⣡⠴⠾⣿⣿⣿⣿⢃⣴⣄⡀⠀⢠⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠂⠀⢠⣠⡄⠀⠋⠁⠀⠀⢠⣾⣿⡋⠙⢿⣿⣿⣧⣠⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢸⡏⠠⠋⠀⠀⠀⠀⢠⣿⣟⡁⠁⣠⣾⠃⠀⣠⠤⣌⠋⡁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⡟⢩⣿⣾⣿⡿⠣⠊⢁⣾⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⣿⣧⣄⢀⠀⠸⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣀⣼⣿⢴⣿⣿⡿⠈⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠟⣻⣜⠻⣿⣧⣄⣀⣲⣼⣿⣧⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢀⣾⣇⣘⠷⢞⡂⣍⣛⠛⠻⠛⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣀⣸⣿⡏⢩⢦⣎⢃⣿⣿⡿⠦⠞⢉⣿⠏⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦⣥⣤⣾⠟⡿⠷⠾⣦⣾⡿⠂⠀⠐⠒⢻⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⢹⣿⣿⣿⣧⡼⠟⠀⠐⢿⠃⢠⡀⠀⠀⠀⠸⠏⠀⠠⠿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣁⠿⠉⠉⣿⠛⣧⢀⣶⠀⣀⣰⡟⠇⠀⠀⠀⣄⠀⠀⠀⣤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣝⠟⠀⠀⠀⢹⠀⣹⣧⣭⣾⣿⡏⠁⡀⣀⢀⣼⣿⡷⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣼⣿⣏⣀⠀⠀⠀⠀⣿⣿⣛⠾⣿⣿⣿⣷⣿⣿⣯⡀⢀⣁⣶⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠛⢉⡥⣴⢿⡿⠻⣿⣷⣄⠀⠀⢉⣿⣛⣷⣿⣿⣿⡙⢿⣿⣿⠟⢾⣿⣿⣿⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣰⢏⣼⣿⣿⣿⢌⣿⣷⡀⢸⣿⣿⣿⡿⣿⣿⣿⡟⠉⠉⠈⠀⠙⠛⣧⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡾⣽⣿⡿⠋⠈⢹⣧⡀⠀⣸⣷⣤⣿⣿⠏⠀⠛⡟⢋⠀⢀⡶⠛⢲⡀⠀⠻⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠉⠀⠀⠀⢸⣿⣿⡄⢀⣹⣿⣿⠃⠑⣴⣿⣿⣦⠀⠈⠷⣤⠾⠁⠀⣤⣼⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⠁⠀⣶⣿⣿⡿⢻⣦⣤⡀⠀⢀⣤⣼⣿⣿⣿⣷⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠻⣿⡟⢧⣴⡞⠋⠀⠻⣶⣿⣿⣿⡧⢴⣿⣿⣷⣌⣿⠏⠀⠉⠛
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠃⠈⠋⠀⢰⠞⠛⢧⠉⠙⠋⠁⠈⠻⢿⠛⠋⠁
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣸⡄⠀⠙⠦⣤⠾⠀⣀⡀⠀⠀⣠⣿⣿⡶⢦⣄
⠀⠀⠀⣼⣿⣿⣿⡿⠿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠟⠠⣦⣄⠀⠀⠀⠠⠿⠃⠀⣼⣿⣿⢹⡧⠈⢻⡇
⠀⠀⠀⣿⣿⣿⣏⡀⠄⠉⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠐⣿⢯⣿⣻⠇⠀⠀⠁
⠀⠀⠀⠸⣿⣿⣿⣷⣶⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⣿⠿⡟
⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⣤⣀⣀⠖⠁⢤⢨⠁⠀⠀⠙⢼⠋⠃⠀⠀⢸⣵⠁⢸⠈⣇⣤⠶⠿⠿⠿⠛⠉⠁⠀⢠⠛⡄⠈⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⢀⠝⠱⠏⢢⣈⢤⡇⠀⠀⠀⠀⠀⠀⠀⢀⠄⢿⠀⠀⢀⣾⠀⣄⠀⢠⠀⢀⣀⠀⢴⠁⠠⣅⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢜⠥⢄⢀⠣⠘⣊⣽⠓⡆⠀⠀⠀⠀⠀⠐⠁⠀⠘⠀⢀⠈⠚⠀⡻⢆⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠜⣁⠈⠠⢤⡹⠆⠀⡠⠙⡄⢘⡒⠒⢦⡀⠀⣸⠀⠀⠀⡌⠀⡹⠄⠒⠓⠂⠽⣤⠀⠀⢇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢆⠫⢄⠶⡷⠀⠠⠊⢀⠴⠇⠀⠉⢐⠄⠚⠉⠉⠉⠀⡀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠐⢌⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠏⠀⠱⠎⠈⣄⣠⡔⠘⣇⢾⡿⠀⡀⠀⠀⢸⡞⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠡⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢰⣤⡀⠀⠈⠐⡇⠀⠸⡀⠐⠀⠀⠀⠀⡘⠁⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⡏⠉⠐⡄⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡼⢆⠀⠉⠙⠒⠀⠄⡇⠀⠀⢳⣤⢤⣠⣤⡖⠑⡄⠀⠉⣡⣤⠸⣿⣿⣷⢀⠌⠀⠀⠀⢰⣢⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⢂⡄⠀⠀⠀⠀⢰⠀⢁⢀⠯⠉⠈⠀⠑⡔⢹⠀⠈⠛⠿⠀⠈⠉⢁⠆⠀⠀⠀⠀⠀⠈⠑⢀
⠀⠀⠀⠀⠀⠀⠀⢠⢂⣀⡀⠀⣏⠛⠁⠀⢈⡁⠻⠷⣌⡾⠠⢃⣀⠈⠘⡆⠁⠠⡀⠀⢀⡴⠺⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠈⠦⡇⠀⠀⠲⠄⠂⠀⢀⡞⠛⠳⠋⡤⠉⢲⡧⡀⠀⠀⠀⣈⣠⠠⠅⠰⡀⠀⠀⣀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⣁⠀⠀⢀⣀⠻⡈⠀⠀⠈⠠⠂⡠⠗⠘⠛⠈⠉⠀⠀⠀⠀⠀⢏⡲⠋⠀⢀⠀⣩⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠖⢦⡐⡾⠉⠙⠶⠁⠈⠻⡟⠀⠀⠐⠁⠸⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⠈⠻⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⡴⡏⠁⠀⠀⡀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡠⠛⡀⠀⠀⣀⣀⠨⠤⠂⠠⠔⠀⠹⡎⢁⢀⠠⠦⢄⡠⠤⠤⢤⡤⡖⣊⠵⠒⠛⠶⣂⠤⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⣈⣡⠀⣀⣀⣀⡀⠀⢠⠶⠀⣤⠚⢂⢃⣶⠂⢀⠭⡆⡔⠁⢩⠏⠁⠀⢀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⢋⠄⠊⠁⠀⠀⠀⠈⠑⢇⠐⠀⠀⠀⣬⠞⣟⣦⡆⢀⠇⠀⢐⡢⢀⠉⠙⠻⢿⣶⣶⣦⣀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⢤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⡂⢀⣤⠁⡉⠀⠣⠋⢢⠄⣁⡐⢀⣑⠤⠤⣀⠀⢀⠀⠉⠁⢀⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⠘⣼⡅⠀⠙⠒⠠⢁⠠⡀⠰⡚⣯⠖⠁⠀⠀⠀⠀⠙⠀⠀⠑⢖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢹⢄⠀⣠⣴⣶⡄⢀⠛⠟⠋⠀⡜⠀⢻⣦⣀⠀⠀⠑⢤⡀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⠀⠀⠳⠙⠿⠟⠁⣾⡿⠆⠀⣾⢃⠀⠀⠀⠉⠁⠐⠂⠀⠉⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡱⠀⠀⠦⣤⢤⣄⠈⠀⠀⠀⠙⢈⠤⠃⠒⠒⠒⠒⠒⢢⠔⠓⣀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠋⠐⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣇⠀⣈⣈⠉⣓⣦⠂⠀⠀⣸⢀⠀⠀⠀⠀⠀⢀⠂⣠⠀⠋⠉⠁⠉⠁⠲⢞⠀⢀⠟⠀⡰⠤⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠸⠂⠀⠠⠜⠋⠀⠨⡔⠌⢧⠀⠤⢚⠍⡉⡽⠀⠀⠀⠀⠆⢀⣥⠀⠀⡀⠀⠀⠀⠀⠀⣑⣋⠤⣠
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⢢⡪⠖⠉⢿⢁⠀⠀⠀⠂⠀⡐⠉⠣⠀⠀⢀⠀⣀⡁⢰⡀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡴⡒⠒⣾⠎⠻⣦⣀⡀⣐⣀⣀⣤⠀⢀⠌⡄⢀⡴⠛⠒⠒⠁⠀⠈⠛⢌⣡⠀⡁
⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣉⣹⣦⣾⣋⣄⣐⣗⣯⣱⣀⣉⢓⣞⣀⣁⣊⣷⣊⣀⣀⣀⣀⣀⣤⣤⣀⣀⣙⣢⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣀⣤⢠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠂⠀⠀⢄⡀⡀⢀⠄⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣻⣿⣿⣿⣿⠟⠋⠀⠀⠐⠀⠀⠀⠰⠀⠑⢯⠻⡱⠊⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡄⣄⠀⠘⠀⠀⣿⣶⡟⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡇⣿⢀⡀⠀⠀⣿⣿⡇⠀⠀⠖⣈⠤⠄⣤⡮⠢⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⢀⠀⠀⡀⠀⠐⠀⠀⣾⣿⣿⣳⣯⠀⠀⠀⢹⣿⠀⠀⡰⠐⠓⠰⠢⢜⡦⣤⠐⠂⡄⠀⠁⠀⠀⠀⠀⠂⠀⠁
⠀⠀⠊⠀⠀⠀⠀⠠⠀⠀⠀⠹⠍⠿⡍⡟⡇⠀⠀⠈⠉⠀⣾⣶⡶⠚⠙⠒⠖⡰⢭⣉⡡⠂⠀⠀⠀⠠⠀⠃
⠀⢀⣀⣤⡀⢀⣄⣀⠀⠀⠀⠰⣶⣶⣶⣶⠁⠀⠀⡀⠀⠀⠁⠟⠹⡄⢿⠆⣄⠀⠁⠉⠀⠀⠐
⠀⠀⠘⡋⠸⠎⣛⠩⠀⠀⠀⠀⠩⢭⠩⠁⠀⠀⠀⠀⠀⠀⠸⠸⣮⠁⢠⡖⠚⣦⣄⣧⡄⠀⣠⣴⣶⢶⠤⡦⡀
⠀⠀⠀⠐⠂⠒⠀⠀⠀⠠⠀⠀⠸⣐⣰⠀⠀⢸⡇⠀⠀⠀⠀⠐⠇⠁⢈⢷⠾⠛⠛⠉⠀⠀⠡⠛⣿⣏⣾⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⠀⠀⢸⡇⠀⠀⠐⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠄⡠⣟⣿⣿⣧⡀⠀⠀⠠
⠀⠀⠀⠀⠀⡁⢀⠬⠤⠀⡀⠀⠀⠸⠅⠀⢀⣨⣇⠀⠀⠀⡀⠀⣄⠀⠀⠈⠐⣫⣆⠀⠀⠀⢀⣿⡽⠟⠉⠹⢿⡄
⠀⠀⢀⠀⠺⡀⢀⠲⠂⡓⢌⠀⠀⠀⠀⠀⠀⠾⡗⠀⠀⠀⠐⠋⠔⡳⢿⣋⠆⠉⠐⠂⠀⠀⣱⣿⠡⠋⠀⠀⠈
⠀⠀⠀⠐⢄⠈⠇⣩⠾⢿⡇⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢂⡀⠀⣭⣼⠁⣶⡴⠂⠀⠀⠀⠛⠃
⠀⠀⠀⠢⠄⠉⠁⢧⢦⣼⣇⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠈⠀⠏⠁⡤⠂⠶⡂⠀⠀⠠⠀⠀⠀⢀⢳⣤⣑⣂⣤⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠄⢀⡀⠂⠀⠀⠀⠱⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠲⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⣔⡄⢴⡀⠀⠄⣇⢘⠂⢀⠈⠁⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⠄⠀⠳⣖⢤⠾⢁⡉⠉⢁⠼⠀⠀⢠⡧
⠀⢀⣤⣄⠰⠶⠀⠀⠐⠐⠂⠀⢿⣳⢄⠀⠀⠀⠀⠀⠀⠉⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢦⡈⠁⠙⠳⠴⠖⠚⠛⠒⠖⡶⢛⠄
⠀⠀⠉⠻⣷⣄⠀⠀⠰⠀⠑⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠐⠻⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠹⣦⣀⠀⠀⠀⠀⠀⢐⡾⡠⠊
⠀⠀⠀⠀⠈⠙⢿⣶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠈⠉⠉⠁⠀⣠⠞⢩⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠇⠀⠀⠀⠀⢠⠀⠀⣀⣤⣄⠀⢀⣤⣄⡀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠘⠀⣼⣿⣿⣿⠇⢸⣿⣿⣿⡆⠈⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⢁⡀⢀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⠿⠿⠋⢠⠈⠛⠿⠿⠋⠀⢦⠀⠀⠀⠀⠠⠀⠟⠐⠀⠀⠤⠊⠀⠀⠀⠀⠀⠠⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⢿⠇⠀⠀⠀⠀⡀⠈⠀⠀⠀⡤⠄⠁⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢀⠀⣀⡀⠀⠀⣴⣿⠃⠀⠀⠀⢠⠀⢀⢀⣠⡶⠶⠶⢄⠀⠀⠀⠠⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠤⠀⠠⠶⠞⣻⠟⠀⠀⠀⠀⠈⠀⠐⠛⠦⠉⠈⠁⠀⠹⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⡁⠠⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⠚⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⣀⠸⠃⠀⠈⠀⠶⣶⣤⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⣾⡀⡆⠀⢀⠀⠀⠈⠀⠋⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠈⢣⡄⢄⣼⠀⠁⠂⠀⠀⣁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠘⠁⠀⠀⠐⢀⠀⠀⠀⠀⠀⠤⠤⢤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠳⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⢶⡄⠘⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⢻⠓⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⡕⠦⣄⡐⠂⢰⢸⠀⠀⠘⠾⠙⠀⠀⠈⡖⠀⠇⢣⠴⠚⠛⠛⠋⠉⠀⢀⠘⠆⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠡⡤⠉⠙⠙⡦⣾⡇⠀⠀⠀⠀⠀⠠⠂⢻⠀⠀⣾⠀⣤⠀⠂⠠⠄⠐⠃⠀⢢⠔⠉
⠀⠀⠀⠀⠀⠀⠔⠀⢈⡑⣤⠁⠐⠧⠈⢤⢀⡀⠀⠀⡀⠀⠀⠀⠢⣀⠀⠏⢢⣄⠀⠀⠀⠀⠀⠈⠐⡆
⠀⠀⠀⠀⠀⠀⡰⣂⣨⡯⠀⠀⢀⡴⠄⠑⠀⡌⠗⠚⠓⠠⡀⣦⠈⠀⠀⠀⠀⠈⠢⡀⠁⢄⠂⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠈⠦⠈⢄⣤⠀⢲⠺⠷⠀⠀⠀⢱⡇⣀⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢲⣤⡀⠀⠹⠀⡈⣄⠀⠀⠀⠀⡌⠘⢿⡿⠆⢀⣀⣀⠀⠸⠁⠈⢂⠀⠰
⠀⠀⠀⠀⠀⠀⠆⠀⠘⠣⠀⠀⠀⠀⠐⠀⠀⠸⡿⠒⠖⢋⠈⡆⠀⣴⣷⠘⠿⠟⡱⠁⠀⠀⠘⠳⠇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡺⠄⠀⠀⠠⣧⡀⡴⠁⠀⠀⠠⡁⠃⠀⠀⠀⡠⣤⠔⠁
⠀⠀⠀⠀⠀⠐⠓⠉⠉⢶⠁⠀⠠⠌⠀⠀⡸⠓⠶⢩⡅⢲⡇⠀⠀⠀⣈⣠⠬⠠⡄⠀⢀⣀⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⠀⡤⣈⣌⠀⠀⢀⠈⠠⠓⠈⠉⠉⠀⠀⠀⠀⢫⡟⠁⠀⠀⣭⡄
⠀⠀⠀⠀⠀⠀⢠⠢⠋⢲⡬⠁⠀⠉⠀⠈⠛⢄⡀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠈⠠⠀⡬⠀⠀⠀⠀⡀⢀⠀⡀⠛⣦⠄⠀⢐⡀⠀⠀⣀⣀⣀⠠⣔⠳⢤⣀⣀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠈⠐⡀⠈⢀⠀⠀⢀⠥⢀⡨⠆⢂⣤⠀⢙⣄⡀⠉⡳⠊⠀⠀⠀⠈⠀⠀⢄
⠀⠀⠀⠀⠀⠀⢀⡜⠉⢢⠑⠉⠁⠀⠀⠁⠪⡐⠀⠀⠠⡞⣟⢴⠀⡄⠀⢐⠄⡀⠙⠻⢷⣶⣦⣀⠈⡄
⠀⠀⠀⠀⠀⠀⠈⠢⣒⠁⠀⠀⠀⠀⠀⠀⣀⢁⢠⠀⢴⡀⠀⠈⠊⠡⢂⡤⠁⠬⠒⠂⠤⡀⠄⡀⢀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⢀⣀⡀⠰⣿⡿⠈⡿⢠⣀⠁⠀⠂⠀⠈⠠⡟⠁⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⣧⠈⠑⡜⢿⡿⠃⣶⣤⠀⣰⠃⠀⠛⠓⠀⠀⠈⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡣⠀⡰⢤⣀⣄⠉⠀⠀⠘⢀⠔⠒⠒⠒⠒⠂⡤⠂⡀⠀⠀⠀⠀⢀⣀⡠⠋⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢬⠉⣱⠄⠀⢀⣄⣀⡀⠀⠀⠀⠄⠠⠀⠉⠉⠀⠀⠐⢇⢀⠎⠀⠒⠜
⠀⠀⠀⠀⠀⠀⠔⠉⠀⠐⠉⠀⠀⠊⢈⢒⠂⢉⣢⡰⠁⠀⠀⠘⠐⠶⡄⠀⠀⠀⠀⠀⠠⠹⠐⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣴⠷⣏⠁⠈⠃⠀⠀⠀⢀⠄⠀⢀⠤⠀⠔⠒⠠⢗⠦⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⢛⣆⣴⣃⠀⢿⣟⣢⠑⠪⣝⡀⡠⣺⡔⠁⠀⠀⢀⣠⣀⣀⠙⢧
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⢀⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⢄⡀
⠀⡠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠢⡐⢦⡙⠓⠢⠰⣎⠀⠀⠀⠀⠀⠠⠑⢂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀⠀⠀⢁⡍⠑⣦⡄⢠⠀⠀⣀⣀⣤⣄⣀
⡈⣼⣿⡎⣿⡅⠀⠀⠀⠀⠀⡀⠀⢠⠈⣿⡄⠀⡁⢻⡀⠀⠀⠀⠀⠀⣷⠈⣗⡢⣬⡀⡀⣀⣿⣀⣄⣀⢀⣿⣆⡀⢘⣿⠄⢻⡇⠀⢣⡐⣿⡄⠀⠉⣿⡷⡄
⠇⣿⣿⡇⣽⣧⣿⣠⣤⣣⣸⣷⣆⣿⣷⣿⠇⠀⣆⣼⣅⠀⡀⢀⠠⣦⣿⡀⣾⣵⡿⠷⢛⣉⠩⠍⠁⠀⠈⠉⠉⠛⠻⣿⣧⣿⣷⣶⣺⡇⣣⡇⣷⣤⣾⣷
⠈⠪⠿⠕⠋⠉⠉⠉⠉⠛⠻⠿⠿⣿⣿⣏⣄⣼⣿⣿⣿⣖⣠⡾⠾⣛⣛⣭⣿⢛⠖⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠛⢿⣿⣧⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠛⣿⣿⣿⣿⢏⣡⠖⠋⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢷⣄⠊⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠙⠿⣿⢸⡃⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⢛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠋⢸⠀⠀⡴⣾⠟⣩⢉⡀⢠⣉⠙⣦⡀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠛⠉⠉⠉⠃⠲⢤⠀⠸⠒⠖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡓⢤⡀⢀⡁⠸⠀⡾⠐⠀⢠⡎⢐⣄⡄⢈⠵⡄⠹⣎⠋⣁⣀⣤⣾⡟⠁⠀⡠⢖⣾⢰⣶⢀⠀⠑⡄⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢲⠌⡑⡆⢸⣼⣷⡂⠀⡿⠤⣾⣥⣻⡤⠤⢭⠀⣿⣿⣿⣿⣿⡿⠀⠀⠼⠛⢛⡟⢻⣄⠴⠆⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠸⣆⣤⠑⠂⢞⣿⣇⠀⢒⡒⠘⢿⠛⠝⢢⣿⠀⡟⠀⠀⠀⠸⣷⠀⠀⢲⠂⠈⣿⠿⠟⠲⠂⠀⠷⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⠉⠛⠛⠛⣛⣿⣆⠈⠙⠦⠿⠤⡿⠟⢁⣔⣀⣀⣀⣤⣤⣿⣦⡀⠈⠲⠆⣀⡄⠔⠁⢰⡖⠀⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠶⠦⠤⠤⠤⠶⠟⠻⠿⠿⢿⠿⠿⠟⠛⠛⠶⣄⡠⢄⣀⣠⣴⣾⣿⣿⣿⣿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⣿⣿⣿⠟⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠻⢿⣿⣷⣦⣷⣌⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⠀⠙⢿⠟⢿⣿⣿⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠛⠀⠀⠀⠀⢻⣿⣷⣇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⡠⢿⣿⣿⣮⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠔⠊⠀⠀⠀⠉⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣠⣤⠔⠆⠘⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⡀⠀⣀⠀⣴⣹⠇⢖⠀⠀⠀⠀⢰⣦⣙⡀⠀⠀⠈⢿⡟⠠⠀⠀⢸⣿⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠶⠾⢶⠞⠋⠉⠛⠛⡉⠀⣄⢀⣀⣸⡀⢀⠀⠀⣿⡃⠀⢐⣧⣀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣐⣒⠒⠒⠂⠀⠲⠤⠈⠁⠀⠀⠀⢠⡀⣸⡅⠀⠀⠁⠡⠀⢄⣼⣿⣿⣿⣮⡅⠈⢳⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠃⢀⡀⣽⣿⣧⣄⣠⡀⠘⣀⣾⣿⣿⣿⣿⣿⣿⣆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠤⣦⡄⣴⣶⡾⠿⠛⣽⣙⡔⣱⣾⣿⣿⣿⠋⠉⠉⠉⠙⠛⠙⠋⠉⠠⠙⠇⠻⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢠⠔⣎⣼⣏⣡⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠀⢈⣧⣠⣦⡤⢄⡈⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⣜⡐⣠⣯⣛⣿⣭⡻⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣰⣿⣷⣿⣿⡿⠻⠉⠀⠀⠀⠉⠠⠀⡤⠀⡀⣀⡀⠀⠀⠀⠀⠀⣠⣦⣀⣴⣾⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⣽⢿⣁⣿⣿⣧⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣬⣿⣿⣿⠟⣹⡿⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢉⣉⢙⡧⢼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣯⣾⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠠⡷⣿⠃⠀⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢙⣿⣽⣟⡋⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠿⣿⣿⣾⡇⢘⢓⣶⣦⠀⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⢿⣿⣿⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠏⣀⣾⣯⣽⣿⠀⡾⢠⣿⠃⠀⠘⢦⡀⠀⠀⡌⠀⠀⠀⠀⡀⢹⠸⣿⣧⣾⣿⣰⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⡿⣿⣿⡷⠊⣀⣿⣿⣆⣤⣶⣦⣩⣶⣰⠇⠀⠀⠀⣼⣇⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣀⣀⣠⣿⣿⣶⣾⣿⣿⣿⣿⣟⣿⣿⡟⠿⠿⣷⣿⣿⣿⣿⣿⣸⣿⣿⠿⠿⠿⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠿⠿⠿⠽⠿⠿⠿⠿⠿⠿⠏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠤⠀⠀⠀⠠⠠⢠⠀⠠⠠⠐⠀⠀⠠⠀⠄⠀⠀⠀⠀⠐⠀⠀⠠⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣴⠦⠴⣊⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠔⠧⠄⢸⠶⡔⠋⠀⢸⠋⣀⡀⠔⠃⣼⣿⣧⣠⣾⣅⠐⢠⣀⠼⠓⠓
⠀⠀⠀⠀⢠⠀⠀⣤⠞⠃⠀⠀⠀⠐⠛⠠⠋⠈⠀⠘⠀⡛⣁⠀⡖⢈⡏⠀⠹⠛⠛⠄⠀⠋⠉⠐⢶
⠀⠀⠀⠀⠄⠀⢤⡟⠐⠀⠘⠀⢨⠗⠀⠠⠰⠀⠐⠀⠀⠃⠊⠀⠁⠀⠋⠀⠹⠇⠴⠢⠤⢤⣦⡤⠴⡄⢀⡀
⠀⠀⠀⢈⠀⠀⠈⣇⢀⠀⠀⡀⢇⣀⠀⢂⡀⡀⢄⡀⠀⡄⢀⠀⠀⢤⠄⠤⠁⠀⠀⠀⠀⢠⠁⠃⠄⣿⣿
⠀⠀⠀⠈⠃⠀⠠⠂⠛⠀⠐⠃⠈⠃⠂⠀⠁⠁⠈⠀⠃⢇⠸⠀⣟⠀⠀⠁⠐⠂⠐⠈⠃⠈⠀⠁⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⢀⣠⣀⠀⢑⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡄⠀⣰⢰⢠⡄⣉⠶⣏⠁⢈⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⣶⣿⣯⣿⣿⣿⣿⣦⣼⣷⣧⡀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢂⢠⣿⡈⢨⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣶⠀⠀⠀⡴⠆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣯⣰⣿⣗⢸⣿⣿⣿⣿⣿⣿⣯⣽⡋⠁⣉⣉⠉⣠⣆⠀⠀⠀⠀⢸⡃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⣼⣗⠆⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⣟⡁⣷⣋⠖⣹⠭⡗⠉⠁⠀⠀⠀⠀⠀⣗⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠎⢻⡟⠃⣿⣿⢹⣿⣷⣸⣿⣿⣿⢛⡷⢩⡉⠹⣿⠓⠲⠀⠃⠀⡀⠂⡜⠀⠀⢠⡏⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠀⣾⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣤⡆⠈⠁⠷⠄⠸⠀⠒⢶⠀⠴⠙⡷⠀⣸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡗⠒⠚⣿⢰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠀⢀⣐⣀⡀⢀⠌⠀⠀⠐⡟⠉⣿⣿⣷⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⠀⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣸⣿⣿⡇⠂⠀⠀⡀⠠⡇⠀⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⡇⠀⠰⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠏⠀⣾⣿⣿⣿⣿⡂⠀⠀⠴⢻⡏⢉⣿⣿⣿⣟⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⡄⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡿⣿⣿⡻⣿⠚⣿⣿⣿⣿⣯⣿⣿⣿⡆⠀⣸⣿⣿⣿⣿⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠚⠀⠀⣹⣿⣷⣶⣷⣿⠻⣿⣿⣿⣿⣿⢿⡏⣧⣼⠇⣣⣾⣿⣿⣧⣿⣿⣿⣿⣍⣉⣉⣉⣉⣠⣿⣿⣿⣿⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⢀⢠⣼⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⢻⣸⡇⢿⣿⣧⣿⣾⡏⣿⣳⣿⣿⣿⣿⢻⣛⠟⢿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⢰⣴⣿⣿⣿⣿⣿⣿⣿⡿⣀⠀⣼⣿⣿⣿⢾⣯⢧⣹⣿⣽⣬⡟⣭⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣽⢿⣿⣿⣿⢈⣷⡀⠀⢀⡉⠉⠁⠉⠋⠈⠻⠿⠛⠛⠛⠋⠉⠉⠻⢿⣿⡻⣿⣿⣿⣿⡟⣿
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⢲⣿⣾⣿⣿⣯⣾⣿⢿⣄⠈⠻⣏⣍⢹⠳⣆⠐⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⢿⣿⣿⣿⣿⣝⠂
⠀⢠⢈⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢮⣿⣿⣻⣿⣿⣿⣿⡟⣺⣿⣆⠀⠙⣿⣿⡆⢹⣧⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⡄
⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⠟⢤⣶⣿⣿⣿⣯⡿⠛⣏⣹⣿⣿⣿⣿⣷⡀⠘⢿⢿⡄⣽⣿⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣷⣀⠼⣿⣿⣿⢿⢡⣿⣷⡄⠀⠻⣾⣿⣿⣿⣦⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠛⠛⠛⠿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣻⣿⣿⣿⠟⠃⣿⣿⣆⠀⠀⠀⠀⠈⠉⠁⠀⠱⣄⠀⠀⠀⠀⣀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠙⢿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⢻⡅⢻⡿⠏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠒⠲⠶⠤⢄⣀⠈⠈⠉⠉⠉⠙⠛⠿⠛⠻⠿⣧⡀⣴⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⣿⣻⣿⠿⠟⠿⠿⠿⠿⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⢂⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣉⣉⣩⣭⣤⣄⡀⠀⢰⣶⣦⡄⠀⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠳⠶⠶⢶⣦⣤⡐⠙⠿⣿⣿⣿⣿⣿⣷⠰⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠶⠒⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠭⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠠⡂⢀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠠⠘⠁⠲⢈⡥⣸⡤⠢⢤⠀⠀⠀⠀⠀⠀⢾⣿⣶⣿⡟
⠀⠀⠀⢠⡶⢘⡢⠁⠀⠁⠃⠀⠀⣠⡠⠤⣍⢠⣙⣿⣻⣲⣩⣀⠀⠀⠀⠀⠀⠀⠙⠟⢡⣶⡦
⠀⠀⣰⠇⢰⠋⣅⣂⠂⠀⢀⠀⠀⣾⣹⣒⠋⡾⣿⣿⣤⣴⣶⣩⠀⠀⠀⠀⠀⣀⡜⢀⣈⠉⠁
⠀⢀⠇⣰⠞⣾⠃⡀⠈⢄⡀⠀⠀⠹⣷⣏⣐⢐⠚⢻⠿⠇⠀⠀⠀⢀⡀⠀⣐⣿⣿⣿⣿⣿⢶⣆⡀
⠀⢸⣾⣿⡞⣳⡏⠀⠀⠰⠦⡀⠀⠀⠘⠻⣿⣿⣋⣧⡜⢀⣠⣠⠗⠀⠀⣤⣿⣿⣿⣟⣏⠟⠀⠘⣡⡆
⠀⠸⣿⣾⣿⣳⣤⠉⠦⠀⠀⠈⠂⠀⢀⠀⠀⠘⠙⠿⠇⣸⠈⠂⠰⣤⣿⣿⣿⣿⣿⠻⣿⡄⠀⠀⠉⠔
⠀⠀⠹⠿⠻⠙⠉⠀⠀⠀⠀⠀⠀⣷⣤⣆⣶⠇⠀⣦⠀⢸⠀⡰⠀⠿⣿⣿⢿⣯⣤⣬⣿⡓⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⣤⣳⣤⣈⠛⡟⢻⢠⣴⣿⣆⡈⡴⠁⢢⠘⣿⡿⢿⡿⢿⢿⠋⠀⠹⢦⣉⠂
⠀⠀⠀⡀⠀⠀⠀⠈⠽⣿⣿⣿⣿⣇⣅⠺⡄⣿⣿⣿⣿⣧⠇⠀⡼⠃⢸⠿⣟⣡⢀⡎⡇⣅⣆⠿⠋⠁
⠀⠀⠀⣷⣆⠀⠰⢶⣶⣿⣿⣿⣿⣿⣿⣶⡾⣏⢻⣿⣿⢸⢧⡞⠀⢠⢃⡠⡌⠁⠊⠋⠛⠈
⠀⠀⠀⢨⣩⡷⣧⠄⠨⢿⣿⣿⣿⣿⣿⣿⣿⣙⣼⣿⣿⣬⠏⢀⡄⠸⢈⠟⠃⢀⣄
⠀⠀⠀⠉⠉⠰⢧⡀⣢⢀⡸⠿⠿⠿⠻⢿⣿⣿⣿⣿⡿⠁⠀⢉⣧⣼⣿⣄⡿⠛⠁
⠀⠀⠀⠀⠀⣀⡤⢻⡏⢤⣤⣴⣶⣦⣴⣾⣿⣿⣿⣿⠇⣡⣶⣿⡟⡟⣿⢿⡟⠛⠋
⠀⠀⠀⠀⠈⠀⠀⠠⣴⣿⣿⣿⣿⣿⠿⣯⣹⡟⠋⣤⣄⠿⣿⡟⡸⣈⣥⣤⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠛⠁⣴⣿⠯⠄⢈⣙⣻⣧⠹⣻⣿⣿⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠹⠿⣿⢠⣿⣿⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣀⠀⡀⠐⠀⠄⠀⠙⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠲⢤⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⡴⡅⢀⡟⠀⣀⢸⡄⠰⠀⢈⠙⠃⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠲⠄⠀⠀⠀⠉⢣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⣇⠘⢷⣼⣉⣠⡾⠐⠓⠳⠀⣺⠄⢀⢀⡟⠀⠐
⠀⠀⣀⠀⠀⣀⡀⠀⠠⡄⢀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠐⣄⠒⠿⠾⢷⣍⣉⣀⣤⣾⣥⣤⣤⢾⡏
⠀⠘⠻⢿⣦⡉⠁⠀⠰⡄⠰⡀⠀⠙⡯⠏⠀⠀⠀⠀⠀⠀⢠⣽⣷⠖⠲⠆⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⢷⣄⠀⠀⠉⠉⠈⠀⠀⢀⣰⠃⡰⠁
⠀⠀⠀⠀⠙⢿⣦⣄⡠⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠙⠷⠦⠤⠄⠀⠄⣠⠴⣻⡎
⠀⠀⠀⠀⠀⠀⠉⠛⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⡀⠀⠀⠀⢀⣠⠞⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠈⠛⠓⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠇⣤⣰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⠃⠀⠀⠀⠀⢰⡆⠀⣠⣴⣶⣄⠀⣴⣶⣦⣀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠈⠃⣼⣿⣿⣿⡿⠀⢿⣿⣿⣿⣦⠀⢱⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠐⠆⢤⠀⠤⠗⠀⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠻⠿⠛⢁⣶⡈⠛⠻⠟⠃⠀⢻⡀⠀⠀⠀⢀⠐⡟⠛⠃⢖⠐⠒⢃⠀⠀⠀⠀⠀⠠⢊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠀⠁⠀⠘⠿⠇⠀⠀⠀⠀⡠⠊⠁⠀⠀⡰⠱⠉⠇⠀⠀⠀⠉⠁⠀⠀⠀⠠⠀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⡀⢀⣀⡘⠀⢀⣴⣿⠇⠀⠀⠀⠀⠃⠀⡺⣊⣴⠶⠶⢶⢄⠀⠀⡀⠤⠄⠠⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠠⠌⠏⠰⠶⠾⣿⠟⠀⠀⠀⠀⢸⠀⠀⠻⢷⣌⠁⠋⠁⣀⡹⠋⠁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡴⠛⠁⢀⠀⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠞⠁⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣴⠞⠀⠈⠙⠻⠃
⠀⠀⠀⢰⠀⠀⢀⡠⡷⠁⠀⠊⠠⣶⣦⣄⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠐⠩⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣬⡇⢠⠄⠀⠀⠀⠀⠙⠉⠟⢡⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠈⠳⡌⢂⠀⣟⠀⠢⠄⠀⠀⠛⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠀⠐⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠋⠠⣿⡇⠀⠀⠰⠆⠀⠉⢢⠄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠽⢿⡀⠀⠠⣄⠀⠀⠀⠲⠆⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠒⠒⠶⠦⣤⣤⣀⣀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣤⣄⡈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠘⠻⠓⠶⠶⣦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⡿⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣾⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⣻⣿⣿⡿⣟⣿⣿⣿⢋⣉⣻⠟⠉⠛⢛⡟⠉⠙⢛⠛⠻⣟⠛⠿⢿⣟⠛⠻⣷⣄⡀
⠀⠀⠀⠀⠀⢾⠿⡿⠿⣿⠿⠿⢿⣿⣷⡿⠿⣿⣷⣶⣷⣿⣶⣶⣶⣿⣽⣶⣶⣬⣦⣤⣤⣵⣤⣤⣽⣦⣤⣤⣬⣿⣦
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⣄⢀⠀⠹⣄⠀⠀⠹⡅⠈⠈⠀⠀⡇⢸⢹⠀⠠⢀⠋⠀⢀⡼⣋⠵⣊⠝⠋⠁⠀⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠠⡉⠻⠿⣆⠀⠀⢱⠄⠀⠂⠀⡇⠀⡈⠀⠀⡰⠢⢐⣟⡪⠕⠊⠁⢀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢄⠀⠈⠛⢦⡌⠂⠀⡃⠀⣧⠀⡆⣠⣾⢱⢾⠟⠉⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣿⢤⣿⣾⡿⠟⠋⠀⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⢨⡝⡿⣍⠀⠀⢀⠂⠀⣠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠠⡀⡾⢲⠷⣿⡀⠠⠁⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣿⣾⣳⣎⣿⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣖⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⡤⠀⠀⠀⠂⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⢤⡀⡀⠀⠀⣀⡀
⣀⣾⡞⣧⣀⠀⠀⢀⠀⣠⢹⡆⠀⢸⡄⠀⠀⠀⣶⠹⡦⣤⢀⣠⣧⡄⠄⣾⣆⣀⣷⢸⡇⠀⡄⣿⠉⠙⣿⠄
⠙⣿⡧⠿⠟⠶⠿⣾⣷⣿⣿⠃⣴⣾⣇⠀⣠⣼⢿⣾⡿⡋⠅⠀⠀⠀⠀⠀⠀⠉⠛⢾⣿⣷⣷⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⢿⣿⡿⣋⠔⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣍⢹⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⡇⠀⣀⣠⠴⠶⠤⠤⡀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⢉⠛⠋⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡢⣄⢀⡀⠇⡼⠉⢀⠃⣃⡝⡲⡙⢦⠒⣀⣀⣼⠏⠀⡠⣤⣤⡄⠁⢄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣖⠍⡂⢶⣿⠀⠛⡰⣯⣷⡒⣦⢸⠿⠿⢿⡇⠀⢘⠉⣟⣷⡘⠀⢸⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠘⠺⠤⠼⢿⣆⠐⢆⣸⣈⡴⠏⡈⠀⣀⣈⣧⡀⠘⢄⢘⡉⠌⢠⠈⠁⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠲⠤⠄⠐⠛⠛⠿⠿⠟⠛⠛⠢⠤⠤⡤⢴⠾⠾⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣀⡀⠀⢀⣠⣴⣶⣶⢶⣦⣄⡀⠀⠀⠀⠀⠄⠀⣀⣀⡀⢰
⠀⠤⢕⣃⠀⣀⠀⠀⠈⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢀⠄⢤⡴⠀⠀⠙⠀⣀⣼⣿⠛⠛⣉⠛⠻⣿⣧⣀⠀⠀⠀⠀⡴⢟⡓⡿⠈
⠀⠀⠀⠀⠀⠘⢿⣶⣦⣤⠄⢿⡏⠡⠀⠀⠀⠔⠋⣡⠤⢉⠝⠀⠀⠀⠀⠚⠛⠉⣰⣦⣭⣴⣄⠉⠛⣃⡀⠀⠘⠛⠳⣞⢛⣶⣤⣤⡀
⠀⠰⠀⠀⢹⣦⣀⠙⢿⣿⣇⢸⣧⠀⢀⣀⡀⠲⠏⡤⠴⠃⣀⣀⣄⠀⠀⠲⢾⣻⣟⣿⣿⣯⣩⡥⢐⡻⠀⢀⣤⠀⠀⣼⡿⢦
⠀⠐⠤⣴⣾⣿⣯⣻⣿⣿⣿⣄⠻⣾⡿⠛⢣⠀⠀⠄⠀⢼⡿⣻⣿⣷⠄⢀⣤⢻⣿⢿⢻⣷⡻⣇⣈⠀⠀⣸⠋⣠⠤⣿⡟⠋⠀⡷⠄
⠀⠀⠀⠀⢈⠉⠉⠉⢻⣿⣿⣿⣿⣿⣶⡴⠡⡌⡋⡤⠀⠻⣿⣾⣿⡟⠠⠟⠛⡙⡛⢿⠿⡿⠛⠾⠛⠓⠀⢿⣷⣧⣾⣿⣷⣒⣦⣼
⠀⠀⢀⡠⣾⣧⣀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠐⢦⣤⣄⣀⣀⠈⠁⠀⠀⠀⠀⠟⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠎⠙⠛⠛⢷
⠀⠘⢿⣿⣿⣿⣿⠟⠀⠐⠂⠀⠐⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡄⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣴⣦⠀⠀⠀⠀⠀⠁
⠀⠀⢸⣿⡟⣿⣿⠀⠀⠂⠐⠩⠂⢐⠀⠠⡀⠀⠀⠀⠈⣻⣿⣿⣁⣀⡀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠶⠆⠀⣿⣿⣿⣿⠆⣤⡄
⠀⠀⠈⠀⠀⣀⣈⠀⠀⠀⠢⠀⠐⠀⠀⣨⣿⣶⣄⠀⠀⠛⠻⣿⡟⠉⠉⠉⠛⠁⡠⠤⢶⢶⣶⣊⣅⠄⠁⠀⣄⠙⠋⠉⠁
⠀⢠⡶⣶⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠛⠻⢿⣟⣿⡿⢡⣿⡿⢿⣿⣶⡖⠀⠀⠀⠻⣼⣻⣷⣾⣯⠎⠀⢀⣼⣿⣿⣿⠁⢠⣦⡀⠠⠄
⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⣴⣶⣄⣤⡄⠀⠀⠀⣩⣵⣿⣿⣾⡿⠟⣋⠀⠀⠀⢀⡀⠈⠛⠿⢟⡀⠀⠀⠈⠻⣿⡿⠿⠄⣿⣿⡇
⠀⠀⠈⠛⠿⠿⠟⠀⠀⠀⠻⣿⣿⡿⠃⠀⢀⠔⠛⠉⠀⠀⠀⣴⡞⢻⣦⠀⣀⡀⠀⠀⠸⠿⠿⠟⣀⣠⣤⣤⡁⠀⠀⠀⣿⢿⣯
⠀⠀⠴⣄⠠⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢠⡶⢶⣤⣤⡀⠀⠘⠿⠟⡋⢹⣋⣻⣓⣀⣤⣴⣾⣟⣿⣽⣿⢿⡧⠘⠿⢤⣿⣷⣷⡤⠿
⠀⠀⡇⠹⡀⠷⠀⠀⠀⣀⡷⣤⠆⠀⠀⠀⠘⣿⣿⣿⡾⠇⠀⢀⢠⣞⠀⠨⣿⣽⣻⣿⣧⣷⠿⠛⡁⠸⣮⠼⠟⠀⠀⠀⣿⣴⣿
⠀⠀⢹⠈⡃⢰⠀⠀⡀⠉⢿⠟⠃⠀⠀⠁⠀⠈⠛⠉⠀⠠⢂⣵⣾⡃⠀⠀⠈⠉⠉⠉⠁⠀⢐⡀⣠⠀⠀⠄⠀⠀⠀⠐⠠⠤⡭⢀
⠀⠀⠀⢦⣃⡌⠀⣠⠏⠀⠀⢠⡄⠀⠠⣶⣤⡄⠀⠀⠀⢠⣿⣿⠏⢀⠀⠀⠀⠀⠀⠀⠀⠁⡙⠋⡀⠐⠀⢠⡀⠀⠀⠀⢲⣦⣥⠁
⠀⠀⠀⠸⠁⠀⢸⣟⢰⡇⢰⣨⣧⠀⠀⠚⠃⡤⠿⣿⣶⣼⣿⡟⠀⠀⢀⣠⣶⣃⣀⡀⠀⡀⠁⠄⠀⠸⣷⣽⣧⡾⠃⠀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣠⣼⡏⠀⠀⠀⠀⠰⣠⡾⣿⣿⣿⣿⣿⣿⣿⠷⠞⠋⠁⣀⠤⠅⠀⠀⠘⢛⣿⣿⣿⣟⠟⠀⠀⣿⡇
⠀⠘⣿⣷⢦⡄⠀⠈⠙⠛⠛⠋⣠⡴⣿⣿⠀⠀⢈⢃⣿⡿⠿⠟⠁⠀⠀⠀⢠⠔⢈⡀⠐⠢⠋⠁⠀⠘⠋⢿⡏⠛⠂⠈⠀⠸⠇⠀⠄
⠀⠀⢹⣿⣿⣿⣷⣤⣤⣤⣠⣾⣿⣿⣿⡇⠀⡀⢂⣾⣿⠃⠀⠀⠀⠄⠀⠀⢀⠐⠉⡠⠋⡤⠀⡖⠀⠀⠀⢠⠀⠀⡇⠂⣤
⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠁⣸⣿⣿⠀⢠⣤⣶⣄⡀⠀⠛⠀⠊⠀⢠⠀⡜⠀⠄⠀⣀⠀⣈⣢⣥⣎⡀⣄
⠀⠀⠘⠿⢫⣿⣭⡵⢾⠷⣯⣭⣯⡹⠟⠁⠀⠀⠘⣿⡿⠀⢸⣿⣿⣿⣷⣶⣦⡄⠀⠀⠱⣜⡀⠆⠀⠀⠀⠀⠠⠒⡉⠢⢀⠁
⠀⢀⠀⠀⣿⣿⣿⠏⠛⠊⢻⣿⣿⣿⠀⠀⣴⡄⠀⠹⡇⠀⠀⠙⠋⢻⣿⣿⣿⡇⠀⠀⠘⠁⠀⠀⠠⠀⠀⠚⠀⠀⡥⠀⠘⠀⢀⠂⡂
⠀⠀⠀⠀⠻⠟⠋⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣴⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣄⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣷⣶⣶⣄⡀
⠀⠀⠀⠀⢀⣠⡾⣟⠁⠰⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀
⠀⠀⣀⣤⣾⣿⣗⣨⣿⣦⣌⣿⣿⣿⣿⣿⣿⢸⣿⡟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⠋⠙⣿⣿⣿⣿⣷⣤
⠀⠀⠻⠆⢀⣤⣭⢙⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣿⣭⣍⡀⠀⠀⠰⠿⣿⣿⣿⡟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠘⠿⠓⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣤⣄⣀⣤⣿⣿⣿⣿⣴⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠉⢿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣿⡀⠀⠀⠹⣿⡿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣿⠋⣸⡿⠁⠀⠀⠀⠀⢀⣀⣀⣠⡤⠀⠀⣽⣿⡿⠀⠀⢄⣨⣶⣿⣿⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣟⣿⣿⣿⠷⠶⠿⠿⠛⠛⠛⠛⠙⣫⡿⣅⣮⣾⣫⣤⠦⠂⠈⠹⢿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣁⣭⣿⣿⣾⣿⣿⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣉⢻⣿⣿⣿⡿⠟⠉⣙⡛⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡆⠻⠞⢛⣋⢠⣴⣾⣿⣿⣿⣷⣜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢀⠛⢻⡿⠟⠋⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠑⠽⠿⠿⠖⠁⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠙⠲⠀⠀⠀⠀⠤⠖⠢⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⣤⣤⡲⠀⠀⡴⣠⣤⣀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠛⠁⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣁⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣏⣹⣷⡆⠀⠀⠰⣞⠛⠛⢳⣦⠀⠀⠀⣷⣿⣿⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡄⠀⠀⠉⠛⠛⠋⠁⠀⠀⣰⣿⣿⣿⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣟⠻⣿⣶⣬⣝⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⠙⣿⣧⠀⠀⠀⠉⠉⠉⠙⠋⠻⣿⣿⣷⣞⠙⢿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣽⣿⣿⣏⣸⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡻⢿⣇⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠉⠺⢿⣿⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣴⣦⣀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠿⠿⢿⠓⠋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⣆⣠⣦⡜⠛⢂⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡌⣻⣿⣠⣠⣤⠎⠙⠉⠹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⣶⠛⠋⠀⠉⠙⠉⠉⠿⣿⣿⣶⣶⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⡀⣷⠃⢀⣠⣦⣤⣤⡦⠤⣤⣿⣿⣿⣿⣿⣿⣥⠀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣄⡤⠼⢿⡆⢉⠹⣿⠿⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣀⠀⣿⡄⠀⠀⠀⢀⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⡿⠋⠁⣠⣦⡿⣹⡔⠻⡄⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣟⠀⢸⣿⣤⠀⣨⠀⢿⠷⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠋⠁⠀⠸⠿⣿⠃⣿⣿⣦⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⠈⠙⣇⣠⠏⠘⢺⡟⠋⠂⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠐⢾⣿⣶⢏⣻⣿⣿⣿⣤⣠⣶⠃⠀⢀⣀⠀⠀⢸⡟⠂⠘⠻⣷⣾⡇⠾⠿⠟⠛⠋⠉⣁⠀⠐⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⡄⠀⠀⠹⢿⣿⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣠⣿⠟⠃⠀⢀⡏⠀⣼⣧⠖⠴⠔⠲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠠⣖⣿⡖⠀⠀⠘⢿⣿⣄⢛⠛⣿⣿⣿⣿⣿⣿⣿⣏⢽⠿⠛⠁⠀⣤⠞⠀⠀⠙⢿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠴⠖⠚⠛⠛⠻⠦⣿⣄⢳⣾⣆⠀⠘⠛⢛⣿⣿⣧⣤⣉⣹⠏⠉⠁⢀⡘⠻⣷⣤⣴⣾⠋⠀⠀⠀⢐⡈⠻⣍⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⡶⠛⣡⠤⠶⠿⢌⠹⣿⡷⠀⠀⠈⠁⠊⠸⠏⠙⠻⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣷⠀⠀⣀⠈⠉⠙⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠥⠶⠋⠁⠀⠀⢀⠀⠡⡟⠁⠀⢿⡏⠀⠀⠀⠀⢻⣿⣿⣿⠟⠄⠀⠀⣼⣿⣷⡵⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠛⠋⠄⠰⡄⠀⣿⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠐⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⡰⠚⠁⠀⠀⠈⠆⣿⠀⣀⡀⠤⠤⣀⠠⠤⢤⢤⣤⣴⣾⣾⣿⣛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠁⣰⡿⠃⠀⠀⠀⠀⠀⠀⣿⣞⠁⠀⠀⠀⠈⠳⣦⣦⡀⠀⠉⠛⠷⣶⣷⣿⠛⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠚⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⢀⡄⠈⠻⡛⢦⠠⣄⠀⢄⡈⠉⣉⣉⡭⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠈⠀⠀⣄⠙⠾⣧⡀⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠛⠟⠳⠤⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠄⠠⠤⠤⠤⠄⠰⠢⠖⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⣲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢟⠿⠟⠋⢡⣴⣞⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠠⡑⡄⢈⠿⠋⠙⣷⣄⠀⠀⠀⠀⠀⠌⠀⠀⠖⠀⠐⢛⣻⢯⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠈⠀⠀⠀⢀⣾⠿⠆⠀⠀⠀⠀⣀⡀⠀⠀⠐⣤⣀⢈⠉⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠸⢫⠉⠀⠀⠀⠛⠋⠐⡄⢸⣿⣿⣿⣿⡏⡇
⠀⠀⠀⠀⠀⢘⠁⠨⡽⡆⠀⣠⣤⣄⣸⣿⣿⡟⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣹⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣸⡋⠑⠚⢿⣿⣿⡆⠀⠀⠀⢈⣀⠔⢀⡀⠀⠀⠀⠀⢠⡝⠛⠉⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢀⠀⠘⠀⠠⣯⡇⠀⣠⣿⣿⡿⠀⠀⠀⠀⠀⠈⠠⢤⠄⠀⠀⠀⠀⣼⠇⠀⠀⣿⣿⣿⠿⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢩⣄⠋⠄⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣠⣿⡏⠀⠀⠀⣿⠿⠋⣰⡿⠿⠦
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠐⠿⡿⢱⣦⣀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⠾⠿⢿⠁⠀⠀⠘⠃⠀⣰⡿⠁
⠀⠀⠀⠀⣀⣤⠀⡎⠏⠀⠔⠺⠛⠁⢸⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣀⣀⡀⠀⠀⠑⢤⠀⠀⠀⣰⡿⠁
⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠂⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⡸⣼⠆⠀⣰⡿⠁
⠀⠀⠀⣯⣿⣇⠀⠀⠀⠂⠠⠀⡠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣷⣷⠀⣰⡿⠁
⠀⠀⠀⠉⢻⣿⠀⠀⠀⠀⢀⣾⣣⣿⠷⣿⢯⠯⢭⣵⣿⢿⣫⣿⣿⣿⠟⠋⠀⣼⣿⣿⣷⡿⠁
⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣾⢝⣾⡟⣸⣇⠃⠠⠿⠟⠖⠋⢱⣟⠟⠁⢀⠀⢠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢆⠑⠀⢀⣶⠛⣯⣿⣿⠃⢹⡽⡣⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣸⢻⣻⡿
⠀⠀⠀⠀⠀⠢⡀⠸⣏⣾⣿⣇⢟⣴⡷⠉⠈⠁⠀⠀⠀⠀⡄⢀⠀⡐⠀⠀⡏⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢦⠈⠉⠿⢿⢶⠫⠿⠁⠀⠀⠀⠤⠊⡀⠂⠈⡆⠀⠀⠀⠛⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠉⢳⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠈⠋⠀⠒⠉⠉⠉⠘⠛⠛⠿⠿⠿⠿⠿⠿⠿⠷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⡀
⠀⠀⠀⠀⣠⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡖⠉⠉⣿⣿⣿⣶⣖
⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣿⣿⣿⣧⠀⢀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⡀
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⣻⣿⣿⣿⡄⠀⠀⣿⣿⠃⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠛⠛⠿⠇⠀⢀⢀⣁⣄⣿⣿⡟⠀⠀⠀⢀⡀⠞⠻⣿⣿⣿⠏⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣤⠺⠋⣺⣿⣿⠉⠁⠀⠀⢀⣤⡻⡿⠶⠌⠉⠉⠿⠿⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠈⣻⣿⡄⠀⠀⠀⢈⣙⠛⠳⠀⠀⣀⠀⠀⢀⢙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢴⣿⣷⠀⠀⠀⠈⠛⠠⠶⠀⠀⠉⢳⠀⣿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⣦⣄⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣻⣿⣧⠀⠀⠀⠀⠀⢀⠀⡀⠀⠈⠉⢘⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡀⠀⠀⠀⠀⠀⢈⣿⠆⠀⠀⠘⠿⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⢿⣿⡇⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢝⣩⣿⣿⡀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣿⣿⣇⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠿⣿⣿⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠄⣽⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢛⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⢯⡘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢷⡟⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⢟⣰⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣈⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⢁⠄⠉⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡷⠋⠀⠘⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠰⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠐⠁⣠⠊⠀⠀⠀⢢⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣰⣧⠀⠀⠀⠙⠀⣃⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣮⡂⠀⠀⣷⡤⠶⠀⠶⠶⠶⣿⣿⣿⣷⣄⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⠞⠁⠀⠀⣴⣿⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡡⠤⠲⢤⣀⢿⠋⠋⠀⠀⠀⠀⠀⣿⡟⢻⣉⡛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠻⣏⢈⠀⠀⠀⣀⡠⠾⣍⣸⡿⣋⣡⣤⣤⣄⡀⢀⡀⠰⣄⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣀⣤⣄⠀⠀⣰⣿⠐⢃⠀⣆⡈⠀⠀⠙⢁⣼⣿⠷⠚⠙⠺⢿⣦⠁⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠿⠻⠙⠁⠙⣿⠾⠿⠟⠓⠋⠀⠁⠙⢦⡀⠀⢸⣿⣟⠀⠒⠀⡄⣸⣿⣦⠀⠀⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡤⠋⢀⡐⠀⠀⡁⠀⠀⠀⠀⠂⡈⠛⢷⣦⣉⠀⢠⣿⣿⠀⠀⢀⣴⣿⠋⣈⣆⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠆⠈⠀⠀⠙⢸⠁⠠⠀⢈⠸⠶⢸⣦⣽⣦⢸⣿⣿⣗⣿⣿⠟⠀⢀⠘⠻⢧⣀⠾⠿⣦⢻⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠟⣸⣿⣿⣦⣤⣤⣶⣤⣾⣿⣷⠀⠙⢿⡉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠡⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢃⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡎⢧⢹⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠃⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠘⣷⠈⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣋⢻⡟⠣⠿⢿⣿⡷⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋⢠⣾⣿⣿⠋⣙⣿⣿⣿⡍⣿⡷⠂⡄⠰⣦⣶⣄⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡞⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣞⠀⢸⣿⣿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⡜⠁⠀⠀⠀⠀⠀⠀⠘⠁⠀⣼⠋⠀⠐⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡼⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⡀⠂⣴⣤⠐⠃⠀⠀⠀⢠⣤⡶⠂⠀⠀⢠⣜⠏⣀⠀⣾⢋⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⣿⣯⡼⣿⣏⠙⠟⣠⣦⡀
⠀⠀⠀⢼⢁⣦⠈⠁⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⡰⠋⢁⡴⠃⠀⠇⢾⣥⣾⡏⢠⣿⣿⡇⠙⣻⢿⣏⡑⠀⡀⠙⢊⣉⣰⣾⡿⠋
⠀⠀⠀⢈⠉⠁⢀⠀⠀⠀⠀⡀⠉⠀⠀⠀⢀⠀⠁⠀⠞⠀⢀⡄⠀⠀⡄⠉⢤⢸⡿⢿⣁⣀⣛⣿⣯⡷⠺⢷⡀⠹⠛⠋⠹⠄
⠀⠀⠘⡵⠚⠋⠀⠀⠀⠀⢀⠤⠒⢀⡰⠟⠀⠀⠀⠀⠀⠀⢀⠀⢠⣾⣤⣴⣦⣿⡉⠀⢻⡶⠀⠀⡤⠈
⠀⠀⠀⠰⢦⠤⢶⣤⣄⣀⣤⣄⡀⠀⣀⣠⣤⣤⣶⣄⣀⡀⢁⣄⣽⣶⣿⣦⣀⣀⣁⣀⣀⣧⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠
⠀⠀⠀⠀⠀⢀⣬⣿⣿⣷⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣷⢶⣤⣤⣤⣤⣔⣺⠋⠏⠁
⠀⠀⠀⠀⠀⢾⣿⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⠿⡏⣛⣙⠋
⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠛⠛⠛⠀⣾⠛⢫⣤⣿⣦
⠀⠀⠀⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡻⠿⢿⣿⣿⠘⠛⠢⠀⠲⠘⠣⠶⢿⣿⣿⣿⣤⠖⠐⠂
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⢩⣽⣿⡆⠀⠀⠀⠀⠀⢼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⢀⣴⣶⣎⡟⢀⣼⣿⣧⠀⠀⠀⠀⠀⣹⣇⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠒⠂⣀⣴⣿⣿⣿⣿⣦⣬⣭⣿⡏⠀⢀⣀⠀⠀⣼⣿⡀
⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⣾⣿⣏⣽⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢋⣙⣦⣄⡀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠿⠋⠁⠀⠀⠸⣿⡟⠉⢉⠶⣄⡉⢀⣴⠈⠛⢻⣶⣼⣿⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⡀⠀⠀⠀⠈⠙⣦⣎⡐⢾⣿⣿⣿⣷⡀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡜⠁⣻⣿⣿⣿⣟⡿⢟⡅⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢃⣺⣿⣿⣿⡿⠿⠟⢿⠃⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⣰⡟⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢸⣿⣿⣿⣿⡇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏
⠀⠀⠀⠀⣰⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠁⢼⣿⣿⡿⠛⠛⠂⡀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⢰⡟⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⡞⣿⣿⣧⠀⠠⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⢿⡆⠀⠀⣠⡼⠛⠁
⠀⠀⢠⣿⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣬⣫⣽⣆⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⡅⠀⠀⠀⠃
⠀⠀⣼⠇⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠡⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⡿⢏⣴⣿⡿⠿⠋⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣶⡛⢻⣿⣳⣦⡀⠀⣽⣿⠋⠁⠀⡠⠂⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⢺⣭⣿⣿⣷⣜⣿⠋⠀⠀⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠲⡦⢀⠀⠀⠀⠀⠀⠀⢳⠈⢿⢯⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠈⢤⣀⡀⠀⠀⢀⡀⠀⡇⢠⣿⡿⣛⣿⣿⡿⣿⣿⣿⣿⣷⣦⣀⡸⠃⠀⢀⣠⣴⣤⣤⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢠⠀⠀⠘⣌⣻⡅⠻⣿⣯⣾⣭⣫⣿⣿⣿⣿⣿⣿⣒⣺⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠿⣷⣜⣻⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣯⣽⣿⣿⣿⡛⠛⠋⠉⠡⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢙⡿⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠁⠀⠀⡔⣊⣉⣭⠶⠃⠉⠛⢿⣿⣿⣿⣷⣦⡀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣴⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣷⣤⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣀⣼⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠀⠀⠀⠙⢻⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡄⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡖⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣤⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⢛⡶⠀⠘⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣅⠀⣠⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢠⠛⠀⠀⠈⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠲⠶⠖⠦⠟⢧⣉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠰⠀⠈⠀⠀⠀⠀⠀⠐⡄⠃⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⢠⠴⠒⠈⠉
⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣶⣎⠁⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠲⠶⣤⠊⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⡂⠀⠃⠀⠀⠀⡀⠀⠀⠀⢠⠅
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣤⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⣘⡿⠟⢠⣶⣄⣲⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠢⠁⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠿⠟⠛⠻⠿⣿⡿⠿⠿⠿⢿⠿⡿⠿⠿⠿⠻⠿⠿⠛⠛⠛⠛⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠇⣀⠀⠀⠀⣿⠀⠀⠀⣀⣂⠀⠙⢁⠂⠀⠰⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢆⠀⣋⣛⣺⣛⣿⣿⣿⣟⠛⠻⢿⣦⢫⠀⠀⡂⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡔⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⠿⠟⠒⠒⠲⠒⠒⠶⠿⠆⠀⠀⠀⣶
⠀⠀⠀⠀⢀⠠⢼⣄⠀⡇⠀⠀⠉⠻⠙⢻⣿⠿⠛⠛⠿⠷⠿⣿⡿⣭⣭⣤⣼⣾⣶⣤⣄⣀⠀⠀⠀⠈⠴⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢰⣿⣷⣿⣿⣷⣷⡄⠀⠀⠀⠀⠾⢿⠐⠐⠒⠂⠐⠰⠤⠦⠤⣧⣴⣦⠤⢭⣍⣩⣩⣹⣿⢟⣿⣾⣿⣿⣿⣭⣽⠂⠀⢀⣤⡲⠾⡟
⠀⠀⠀⣿⣿⣭⣝⣿⣿⣷⠀⠀⠀⠀⠀⠐⠸⡄⠀⠀⠀⠀⠀⠀⣀⣸⣇⣿⠃⣶⠈⡁⠈⠡⢸⣿⢿⣽⣸⡇⣽⣿⣿⣼⠀⠀⣿⠙⢲⠀⣇
⠀⠀⠀⣿⣿⣿⣝⣿⡟⠻⣇⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⡿⢻⣿⡇⡀⠞⠀⠀⢸⣿⣽⣯⣼⡇⣨⣽⣿⣿⣶⣿⣿⣼⣍⣠⣥⣾⣷⣦⣄
⠀⠀⠀⢻⣿⣿⣹⣿⣧⠀⢻⣧⣶⠆⡀⠀⠀⠀⠀⠀⠀⢀⡴⢯⣥⣤⣭⣭⣽⣿⣷⣦⣴⠀⢸⣿⢸⡿⢚⡇⣸⣿⣿⢻⣿⣯⣭⡛⣿⣿⣿⣿⣿⣿⡀⠇
⠀⠀⠀⢸⣿⣿⢻⡟⣿⠒⢹⣟⣿⣄⡹⠁⠺⠟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣽⡟⠉⠉⢸⣿⠀⢸⣿⢹⣿⣽⡧⣾⣿⣿⣾⠋⠛⠿⣻⣿⠟⢿⣿⣿⣿⡓
⠀⠀⠀⠈⣿⣿⡟⠃⣿⣾⢎⠛⠺⠯⣝⣿⠐⠰⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⣤⡾⢹⣆⢸⣿⣿⣿⣿⡟⣿⣿⣿⣗⠰⡶⠀⢸⡇⠀⠀⠹⢿⣿⣷
⠀⠀⠀⠀⠹⣿⣿⣾⣿⠇⠀⠉⠂⢠⡀⠈⠛⢻⣿⣿⣿⣿⣿⢫⡆⠂⠸⣿⣿⣿⣾⣶⣿⣟⣿⣯⣿⣿⠿⠷⠿⠟⠛⣿⣧⣤⣄⣿⣷⣶⡄⠀⢙⣿⣿⡇
⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠈⠀⢀⣿⠿⠿⢻⣿⡿⢃⠁⠰⢀⠹⣧⢿⣿⣿⣿⣿⣜⣷⢔⣒⣀⣞⣶⣿⣿⣷⣿⣿⣿⡿⣿⣿⣿⠁⢨⣹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⡄⠀⠶⢬⢆⣿⠘⣿⣿⣿⣯⣿⣿⣿⣿⡿⣿⠛⠛⠉⠉⣁⣠⣬⣤⣿⡿⠇⠀⣼⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡠⣾⣾⡇⡧⢾⡇⣿⣿⣿⣿⣇⣸⣼⣿⣃⣿⠷⠾⠛⠋⠉⢿⣿⣿⣥⣀⣠⡴⡏⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⢒⠈⡿⣿⠦⢸⡇⣿⣯⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡎⢠⠁⠐⠀⣼⡇⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡙⢑⢄⢀⡿⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣯⣡⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡝⢿⠁⢀⣀⣀⡀⠀⠀⢀⣀⠀⠀⠰⣬⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡏⢠⣿⣿⣿⡿⠀⠀⠈⣾⠆⠀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⣼⣿⠋⠀⠀⠀⠀⠛⢀⠎⠀⠀⡠⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⠷⣦⢀⠘⠁⠀⠀⠰⠀⠀⠑⠊⢀⡴⠒⠒⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣛⡛⠆⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢾⡄⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠋⠉⠉⠓⠀⠀⢰⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣦⠀⠘⠛⣛⡿⠶⣄⠀⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠛⠀⠀⠀⢠⣾⡿⠟⢋⣟⠉⠋⢾⡻⣗⡀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⣶⠤⠘⢋⣶⢞⣻⣿⣁⠀⠀⠀⠈⠓⠀⠀⠂⠠⡤⠒⠦⠜⠃
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠀⠀⠾⠳⠒⣯⣿⣿⠁⠀⠀⢀⣉⠀⠀⠠⠀⢀⡀
⠀⠀⠀⠀⠹⢿⡉⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⣯⠟⠃⣠⣶⠞⡉⠹⠀⠀⡄⠀⢸⡷⠖
⠀⠀⠀⠀⠀⠀⠉⠙⠓⣄⠀⠀⠀⢀⠀⠀⡐⠀⠀⣠⢿⠁⣄⡟⠉⢫⠿⣧⣀⠀⠀⠀⣀⢈⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⢀⠀⠞⠁⠀⠀⣀⣀⠁⢾⠀⠀⠀⠀⣿⣿⠆⠳⣦⣿⣦⠈⠁⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣸⡿⠇⡎⠀⠀⠀⠀⠈⠻⠁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣄⣠⣿⣾⢶⡀⢸⣇⠀⢰⠷⣶⣤⡆⠀⠀⣠⣄⡀
⠀⠀⠀⠀⢀⣤⣴⢶⢶⡄⠀⣀⣸⣻⣿⣇⠙⢿⣦⠻⡄⡞⢹⣆⠁⠀⢻⡿⠃⠀⣿⣉⠋⣥⣴⡿⣓⣬⠶⠦⠄
⠀⠀⠀⠘⠋⠁⠀⠁⠉⠴⠟⠛⠛⠛⢛⣯⡤⠄⠩⡄⠠⡇⠀⣿⡄⠀⣨⢤⣦⣤⣴⣤⣄⠀⠉⠙⠻⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠷⠂⠀⠀⠀⢰⠀⠈⣣⠀⣀⣀⣼⠾⠽⡟⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠂⡆⢠⠁⠈⠙⠻⠟⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃


⣿⣿⣿⣿⣿⣿⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⡿⠿⠿⠿⠿⢿

⣿⣿⡿⢟⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣄⣿⣾⣶⣿⣿⣟⣠⣴⣶⣆
⣿⠿⣿⢻⣯⣥⣄⣀⡀⠍⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⠠⣾⣿⠿⠻⠿⠟⠿⠟⠿⠿⣿⣷⣶
⠃⠀⡏⠈⠿⣿⣿⣿⠉⢳⣦⣹⣿⠃⠀⠀⠀⣀⣀⣐⠋⠁⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠆
⠀⠀⠆⠀⠀⠈⠛⠫⠄⠈⠙⠋⠀⠀⣴⣿⣿⡿⠟⢻⠇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⢣⠀⠀⠀⠐⠲⠖⠃⠀⠀⠀⠀⡝⣿⣯⢙⣷⠋⠀⠀⠀⠀⠀⠀⢸⣧⢴⢯⣵⣦⣄⣀⣺⣯⣭⣦⣬⡅
⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⢭⡌⠁⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠁⢈⡟⠻⠀⠉⠀⠈⡽
⣧⠀⠀⠹⡄⠀⠀⠀⡄⠉⠁⠀⠀⢰⠀⠙⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⡫⡇⠀⠙⠒⠒⠊
⣿⠁⠠⢤⣘⣦⡀⠀⠻⣿⣿⣦⣤⣴⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀⢈⠃
⡇⠀⠀⠀⢈⣻⣿⣦⣤⣜⣿⣿⡿⣰⡿⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡿⠂⠋⠁⠉⠳⠀⢀⣀
⣿⣶⠖⠀⠀⢨⡙⠿⣿⣯⣿⣿⣷⣿⣥⠤⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠺⣿⡇⠐⡣⠸⠃⠀⠀⠄⠀⣸⣿⣿⡶
⣿⣿⠓⠀⠀⠚⠻⢶⣤⣌⣭⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⣠⠟⠁

⠁⠀⢀⠈⢀⠈⠀⠀⡀⠁⡀⠀⠀⢐⠈⢐⠀⠀⠀⡀⠁⡀⠀⠈⢐⠈⢀⠀⠀⠁⡀⠁⡀⠀⠨⢀⠈⢀⠀⣀⣁⣠⣤⣦⣤⣬⣀⣨⣀⣥⣀⠁⡀⠁⠈⠀⠨⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣶⣶⣴⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢈
⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠄⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠄⠠⠀⠠⠀⠠⠀⠀⠀⠄⠀⠄⠀⢀⢠⣼⣿⠿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣯⢻⣆⠀⢐
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠀⠀⢀⣾⡿⣣⣾⣿⣿⠟⠋⠉⠉⠙⠛⠛⠛⢿⣿⣝⢿⣰⣿⠀⠐
⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡠⠤⡀⠀⣼⢻⣳⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢾⣿⣿⡇⠠
⠄⠀⢐⠠⢐⠠⠀⠄⠀⠄⠀⠀⠀⢐⠠⢐⠀⠀⠀⠂⠄⠀⠀⠠⢐⣀⣐⠀⠀⠸⣄⣀⡸⢀⣿⣼⡿⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⠃⠠⠀⠠
⠀⠀⠐⠠⠐⠀⠀⠀⠀⠀⣀⡴⠶⠒⠛⠛⠛⠒⠂⠂⠄⡠⠖⠉⠉⠉⠉⠉⠒⢄⡂⠁⠀⠰⣿⣿⢧⣿⣿⠠⠦⣄⡀⠀⠀⣠⠴⠛⠃⠀⠀⢿⣿⢿⣿
⠀⠀⠠⠀⠀⠐⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢨⣿⣿⣼⣿⡷⠖⣾⡟⠣⠀⠈⠑⠺⣿⠟⠗⠀⠈⡅⠉⡟
⠀⠀⠈⠀⠈⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣷⠀⠐⠀⠐
⠀⠀⠀⢀⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣵⣿⡆⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⣿⣆
⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⣾⣷⣿⣿⣿⠨
⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⡀⠀⠻⢿⢿⠟⠁⠀⠀⣠⣾⣿⣿⣿⣇⠛⠈⠀⠈
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣠⢾⣿⣿⣿⣿⣿⣿⣦⢈
⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠈⢰⣝⣯⣻⣿⠟⠻⡎⢳⠒⠒⠋⠀⢸⣿⣯⢿⣿⣹⣿⣿⣷⣨⣀
⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠁⠀⠀⠀⠀⠉⠉⠛⠻⠟⠃⠀⡴⠁⠀⠁⠀⠀⠀⠀⠙⠻⣧⣿⣷⣿⡿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠒⠒⠒⠒⠒⠒⠈⠁⠁⠀⠘⠟⠀⠀⠀⠀⠀⠀⣈⣿⢹⣿⣧⠟⣿⣷
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡀⢀⣀⠀⠤⠤⠔⠒⠒⠈⡅⠀⠀⠀⠀⠀⠀⣠⡴⢁⡼⢿⡏⠀⠛⣿
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⣀⣀⠄⠴⠈⠀⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠀⢾⣿
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⣀⠠⠠⣶⣷⠀⠀⠀⠘⠄⢔⡈⠒⠀⠀⠀⠀⠀⢀⣴⣿⠋
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠉⠉⠀⠀⠀⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷
⠀⠀⢀⠈⢙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⣿⠛⠢⣀⠀⠀⠀⠀⡄⢀⠞⣿⣿⠋⠙⣿
⠄⠀⢐⠠⢀⠠⠀⠍⡉⠍⡃⠘⠊⢐⠠⢘⠢⣄⡀⠀⠀⠀⠀⢀⣠⠠⢀⠤⠤⠤⡤⠶⣷⠀⠀⢸⠀⠀⠀⠀⠀⢳⣿⣿⣷⣶⣿⣷⣄⢣⣸⢠⣷⣾⣿⣿⣷⣾⣿
⠀⠀⠐⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠉⠛⠛⠛⠙⠉⠐⠀⠐⠀⠀⠀⠀⠀⠘⡀⠀⢸⠀⠀⠀⠀⠀⠈⡋⠉⣿⣿⠋⠉⣿⣦⣿⠉⣿⣿⠋⠙⣿⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡶⠛⠻⢿⣷⣤⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠠⣠⣾⡟⠁⠀⠀⢘⣷⣿⢿⡄⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⡃⠀⢁⣬⣿⣿⠅⣸⣿⣄⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠻⣿⠛⠒⢂⠘⣿⣿⠀⣿⣿⣿⣀⡀⢀⢠⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠁⣰⠀⠀⠈⠉⠨⡀⠀⠀⠐⣨⠃⢲⡙⠛⠫⣽⣆⡀⢨
⠀⠀⠐⠆⠈⢉⠛⣋⠲⠖⠛⢋⣽⠀⠀⠘⣧⡩⡉⢛⢻⣟⣲⠿⠃⠉⠀⢸⣷⡄⠀⢾⣿⣾⣿⣦⠤⠤⠤⠤⠤⠄
⠀⠀⠀⡇⠀⠄⠀⠱⠈⠀⡹⠎⠀⠀⠘⡟⢿⣥⣿⣿⣿⣿⡑⠂⠀⠀⠀⠜⠀⠹⠀⠈⠁⣿⣿⣟⣐⠤⠄⠀⠁
⠀⠀⢸⢥⠤⠴⠤⢤⣴⠎⠀⠀⠀⠀⣰⣳⣿⣷⣿⣿⠏⠀⠈⠀⠀⣤⡀⠀⠀⢺⡧⠀⠈⢿⣿⣿⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠟⠀⢉⡳⠋⠁⠀⠀⠀⢀⣠⣼⣧⠤⠀⠀⠀⠀⠀⢼⣿⣧⢠
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢤⣥⡸⣬⡄⣿⣀⠀⣀⣠⣶⣿⣿⣿⣭⡑⠂⠀⠀⠀⠀⢀⣿⣿⣷⡒⠂
⠀⠀⢰⣷⣶⣾⣿⣶⣶⣶⣶⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣤⣵⢶⣶⣾⣿⣿⣍⠛⠐⠤⣄⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠷⠖⢿⠛⢿⣿⣿⣿⡟⣷⣤⡈⠇
⠀⠀⢘⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣿⡿⢛⡿⠉⠃⠔⠋⠀⠀⠘⠀⢰⢸⣿⣿⣿⣿⣿⣵⡆
⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡏⠁⣠⡴⠖⠫⠉⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠚⠀⣧⢻⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⡦⠙⣿⣿⣿⣿⣿⢿⣹⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣵⣶⣿⣿⡿⠋⠀⡘⠁⠀⢠⣿⠃⠐⠀⢀⠀⠀⠢⠤⠀⡀⠀⡀⠀⡀⠀⠀⠂⣀⡍⢸⡟⣿⣿⣿⣧
⠀⠀⢨⣥⠼⣿⣿⣿⣾⠛⣴⠂⠁⠀⠀⣹⡝⠀⠀⠀⠈⠀⠀⠀⠀⠉⠱⡶⠟⠁⠄⠀⣠⣾⣿⣄⣴⣧⣿⣿⣿⡗
⠀⠀⢸⣿⣿⡷⢶⡟⠛⢿⣏⣓⣦⡾⢭⣽⣗⣤⠀⠀⣀⢀⣀⠀⠀⡴⠟⠏⣅⠀⢂⣿⣿⢷⣿⠟⣿⠉⢻⣿⠑
⠀⠀⢸⡟⣿⠀⠀⠛⠄⠀⠻⣿⣿⣿⣿⣿⣾⣿⣭⢟⣺⣭⣥⣥⣭⣵⣶⣶⣶⣴⣿⡿⣟⣻⣿⣿⣿⣿⡿⣿⠀⠁
⠀⠀⢸⡷⠋⠀⠀⣠⣇⣠⣤⣽⣣⡶⠟⠛⠛⠛⠛⠛⠛⠛⠈⠉⠉⠿⠟⠻⠟⠛⠛⠛⠙⠛⠻⠿⠟⢿⡇⣿⣷⡆
⠀⠀⠸⠁⣀⣩⣾⣿⣟⣁⢀⡘⣧⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠇
⠀⠀⢰⣾⡿⠟⠛⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠓⢦⣀⣀⣠⠔⠋⠁⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⣠⠾⢉⢙⡙⢶⡄⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⣏⠀⠀⠐⠀⠨⢍⠲⠦⣄⡀⠀⠀⠀⠀⢹⡆⢿⣷⣄⣶⣴⣿⠇⢠⡿⠁⠀⠀⠀⣀⣠⠔⠊⠀⠄⠀⠈⠈⠑⡆
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠁⠈⠁⠀⠀⠐⠀⠉⠓⠤⢄⡀⠀⢹⣿⣩⡿⣿⣻⠻⣿⠛⠁⣀⡤⠖⠋⢁⠀⡄⠀⠐⠀⠂⠁⠈⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⡐⠐⠀⢀⢀⡀⠀⠀⠀⠀⠉⢙⡚⣷⣿⣇⠍⠁⠈⣛⢐⣋⠁⠀⠀⠀⣁⡀⠁⡀⠠⠂⠀⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢒⠊⠔⠐⠒⠒⠐⠂⢂⣠⢼⣿⣿⣿⡾⣞⣾⣧⢄⣀⡀⠁⠒⠒⠢⠤⠀⠁⣤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⢚⣿⠋⢀⣙⣿⣿⣿⣟⣿⣿⣗⡈⠹⣯⠓⠂⠤⠤⠤⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠁⣸⡟⣿⣿⡿⣿⣿⣽⣿⣿⡟⢷⡉⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⢰⣻⠀⣿⣿⣷⣟⣛⡛⣹⣹⡇⢸⣱⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣻⠀⢻⣿⣟⣷⣿⣓⣿⣿⠇⠀⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠃⠀⠘⣿⣿⡷⣿⣷⣿⡟⠀⠀⠀⠙⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠘⠿⣯⣿⡿⠟⠀⠀⠀⠀⠀⠀⠙⣧

⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⢸⣿⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⣠⢶⡿⠇⣠⡔⠶⣖⠀⠀⠀⠀⠀⢀⣤⣶⡶⠆⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠈⣁⠉⠚⢠⣦⠈⠀⠉⠀⣶⣿⣿⡻⠆⠀⠙⠃⠀⣶⠟⠋⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⢠⠈⠉⠠⡿⠀⠀⠀⠠⠀⠉⠉⠁⠰⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠈⠄⠀⠈⡧⡀⠀⠀⢀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠈⠃⠰⠃⠈⡀⢀⣬⠀⠀⠠⡄⠀⠁⠀⠰⡄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡟⠁⢁⣤⣾⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣴⣾⣿⢟⣿⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠛⠛⠁⠚⠟⠋⠁⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⢠⡄⠤⡄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠗⠈⠛⠘⠇⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⢨⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠐⢠⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠠⣤⠉⠙⠋⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦⣤⣤⣼⡇⠀⢠⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⠀⠀⢁⣼⣿⡶⢾⣯⠟⠂⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠞⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⠴⠦⠶⠶⠾⠿⠓⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢿⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⣣⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠋⠀⢁⡄⠀⣷⠀⠀⠀⢠⡤⠘⠉⣀⣭⢴⠀⠀⠀⢰⣌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢷⣄⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⠄⠀⠀⢺⡇⠀⣿⠀⠀⠀⢀⠀⢠⣾⣿⣦⡇⠀⠀⠀⢸⡟⠀⠀⠀⣠⣄⠈⠛⠛⠃⣤⣶⣤⣤⣄⠘⡃⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠠⣄⠸⠣⠀⣿⣶⣄⠀⠀⠀⠀⠸⠋⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠛⠉⠁⠀⢀⠀⠀⠛⠛⠉⠻⡧⡇⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⡄⠀⢠⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡀⠀⠀⠀⡿⠀⠀⠀⠀⣿⠁
⠀⢸⣿⠀⠀⠀⠀⣤⠀⠀⠸⠧⠀⠰⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⣬⣍⣄⣀⣉⣧⡀⠀⠀⢸⣠⣤⣀⣤⣀⣶⣦⣼⣿⣿⣿⣿⣦⡀⠙⢷⣆⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠟⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠏⠀⠠⠐⢂⡀⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠲⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡆⠀⠀⠀⠈⠀⠈⡀⢠⣈⠻⣶⣤⣤⣤⣤⣦⣴⣤⣴⣾⠏⠁⠀⠈⠃⠀⠀⣿⠄
⠀⢸⣿⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⠀⢰⣷⠀⠁⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠇
⠀⠘⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⢀⢐⠊⠙⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⢀⠀⠂⠀⡀⢚⠋⡀⠰⣦⡇⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣯⡷⣰⡾⠁⢀⡈⠁⢲⣄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠻⢗⠏⡀⠰⣿⣆⠄⠉⣉⣿⣷⡶⠃⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⡇⠀⠀⠀⣹⠀⠈⠘⢁⡒⠿⠛⠉⠀⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⡢⡝⢼⡲⡠⢞⡵⠖⢲⡟⣷⣀⠀⡴⠁⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣗⡠⢳⡸⠸⣵⡇⢿⠃⠈⠻⣙⠇⢹⠉⣠⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡓⢉⣠⠷⢹⣿⡜⢦⣤⣄⣈⡼⣴⠈⠛⠤⡤⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠞⠘⠁⠨⣼⣧⡀⠂⢈⣉⠙⢈⡉⢀⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⢠⠀⠈⠠⠖⢍⠒⠿⠙⠉⠀⠀⠀⠀⠠⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠄⡀⢡⡴⠬⣾⠦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣞⢔⣫⣽⡓⣮⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣍⠨⣿⣟⡵⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠏⠸⣥⣴⣄⣀⣀⣀⠀⡄⡀⣺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢀⣼⣿⣥⣾⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠿⢿⣿⠿⠛⠁


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣠⣤⣴⢶⣤⡶⢦⡤⢦⣀⣤⡀⣀
⠀⠀⣤⣾⣯⣿⣶⣿⣶⡿⣿⣿⣿⣾⣿⣴⣿⣹⣶⢦⣀⣄
⠀⠀⠹⣿⣿⣯⣹⣿⣺⡿⣿⣼⣿⣿⣯⢻⣟⣿⣿⣾⣯⣽⣿⣇⣀
⠀⠀⠐⡇⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠛⡿⠛⠛⠙⡛⠙⠃⠒⠠⢄⡠⠀⢀⠀⢀⡀⢀⢀⠤⠄⠒⠐⠉⢐⠉⠒⠖⠠⣤
⠀⠀⠀⢠⢐⡀⠄⢩⡈⠉⠈⠉⡈⠋⡀⠁⠀⢀⣂⣀⡤⠌⢧⠝⡄⠸⠁⠶⠈⡡⠀⢠⡄⣴⡆⣀⠀⠶⠀⠿⠀⠛⠤⢯⠴⣷⠰⡆⡄
⠀⠀⠀⠀⠎⣿⠲⠀⠤⡄⠁⡀⠧⢤⠀⠐⠈⠋⠙⢡⠆⠐⢺⠀⡀⠀⠀⠀⢸⡔⣇⣤⠀⣼⡇⣬⣗⠲⣼⠁⠀⠀⠀⠀⠀⢹⠤⠆⣧
⠀⠀⠀⠀⠸⠸⠃⡰⡆⢱⠈⡁⠀⠻⡄⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠄⠀⠀⠸⠁⠀⡽⠀⡏⠀⢿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠞⣠⢹⣆⢶⣡⡀⠀⢳⠀⠀⠀⠀⠀⡴⠀⠀⡇⠀⠀⠀⠀⡆⢀⢠⡇⠀⡇⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⠀⢸
⠀⠀⠀⠀⠀⠈⠀⢡⡎⢻⡘⣧⣧⠀⠀⢧⠀⠀⠀⠀⠃⠀⠀⢹⠀⠀⠀⠠⠃⠀⠘⡇⠀⡧⢀⠀⠄⢸⠃⠀⠀⠀⠀⠀⡾⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢟⡀⢣⠘⣏⢧⠀⠈⢣⠀⠀⠀⢰⡆⠀⠸⡀⠀⠀⢠⠀⠀⢸⠁⢸⣤⣼⠆⠀⢸⠃⠀⠀⠀⠀⡼⢃⢠⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠀⢃⠘⣌⡄⠐⠘⣦⠀⠀⠀⢁⠀⠀⡇⠀⠀⢸⠀⠀⣿⠀⢸⠀⢰⡇⠀⢸⠀⠀⠀⠀⡼⣁⣆⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⠸⡄⢹⡾⡥⠈⠈⢆⠀⠀⠛⠀⠀⢹⡄⠀⢸⠀⠀⢻⠀⢸⠀⠘⠃⠀⣾⠀⠀⢀⡾⣻⢫⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢠⡄⢣⡹⣂⠐⠌⣆⠀⠨⡇⠀⠈⢠⠀⢨⠀⠀⢸⠀⢠⠀⠀⠀⠀⣿⢠⣀⣾⢷⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠁⠌⠷⢻⡄⠘⡘⣧⠀⢠⠀⠃⠙⡀⢈⠀⠀⢸⠀⢸⠀⠀⠀⠀⡿⢬⣿⣧⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠘⠀⠐⢃⢿⡀⠐⠘⣧⠘⠀⢠⠀⡇⢸⠀⠀⣸⠀⢿⠀⢀⠀⠀⡇⣸⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⢣⠈⡌⢳⠀⢢⠙⡄⡇⠀⠀⢴⢸⠀⠀⣿⠀⢸⠒⠺⠀⠀⣇⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠸⠀⢷⠈⡁⠸⢠⠁⠂⠈⡾⠀⠀⡏⠀⢸⠀⢸⡄⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡀⢃⠼⡗⠀⠀⠻⡠⠀⠀⢷⠀⠀⠀⡄⠈⠀⠰⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⠘⡆⢳⡀⠀⠀⡇⠀⠀⠈⡇⠀⢠⡇⠀⡇⠀⣤⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠃⡌⣷⠰⠀⢰⠀⠀⠄⠇⠀⠀⢸⠀⢋⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠃⠘⠀⢸⡆⠀⠈⣴⠀⠃⢺⠀⠁⣸⡀⢸⠂⠀⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠇⠀⠀⡄⠈⣿⠐⠇⠻⡄⢠⠸⠒⠀⠈⡧⠀⣟⠀⠠⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣾⠀⠀⢱⠀⠉⡟⠠⠸⠇⠃⡆⡧⠐⠀⢷⠀⢻⡄⠸⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⣘⣧⣿⠀⠀⠈⠀⠐⢁⠆⡆⢼⠀⢡⢡⡀⠆⠸⡄⠘⢇⠈⡇⡼⣱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣧⣱⢊⢡⡇⠀⠀⢀⠀⠀⠸⢆⠁⠀⡆⠈⠸⡇⠁⠀⡇⠀⠸⠀⢸⢀⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢿⣥⣷⡅⠀⢰⡇⠀⠀⣾⠀⠀⠀⣏⠀⠀⢃⠀⠀⢿⠀⠀⢸⡀⠀⡇⠈⣾⡸⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⡠⢫⡾⠉⠩⡳⠁⠀⠀⢈⠇⠀⠀⣿⠀⠀⠀⢿⠀⠀⢸⠀⠀⢸⡇⠀⠀⣇⠀⢹⠠⢿⡄⠾⢸⣿⣿⣿⣦
⠀⠀⠀⠀⠀⡰⢋⣴⡿⠋⠎⡴⠃⠀⠀⠀⣾⠀⠀⢡⠅⠀⠀⠀⢸⡄⠀⠈⡆⠀⠀⣧⠀⠀⢹⠀⠸⡀⠘⣧⠀⠋⡿⣿⣿⣿⣷⡀
⠀⠀⠀⢠⠞⡡⠛⠋⠀⢀⠞⠁⠀⠀⠀⢠⡇⠀⠀⢸⠀⠀⠀⠀⢸⡅⠀⠀⡇⠀⠀⢺⠀⠀⠸⡇⠀⡇⠀⢿⠀⠀⢱⠈⠉⣿⣽⣿⡄
⠀⠀⢠⣏⢰⠏⠀⠀⡀⠎⠀⠀⠀⠀⠀⡘⠇⠀⠀⡌⠀⠀⠀⠀⠈⡇⠀⠀⢷⠀⠀⢸⡆⠀⠀⣧⠀⢳⠀⢸⡇⠀⢸⠀⠀⡟⠉⣹⣷
⠀⠀⣿⣵⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠈⡇⠀⠀⢼⠀⢸⠀⠘⣇⠀⠘⡇⠀⠀⡇⢸⣿
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠁⢰⠁⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⢸⡄⠀⣿⠀⠀⡇⠀⠀⡇⡟⢹⠃
⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⢀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⢸⠂⠖⣿⠀⠀⣷⠀⢰⠇⢃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⠿⠿⠷⠦⢔⠢⠀⠀⡧⢸⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⢸⠀⠀⣿⠀⠀⣷⠈⠀⢋⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠌⢃⠀⡁⡾⠀⡀⢀⡇⠀⠀⣸⠀⢸⠀⠀⣟⠠⠀⣏⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡃⠀⠉⣸⠧⢀⢀⡟⠀⣼⠀⢰⡏⡀⢌⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠬⢀⣀⠨⠅⠉⡇⢀⡪⠅⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⢽⠙⠫⡍⢙⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠀⢺⢐⡆⡈⣇⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⠶⠛⠀⢀⣂⣩⣜⠈⣰⡇⡈⠡⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢧⣀⢀⣀⣀⣠⣤⣿⠟⣿⣰⣿⣇⣸⠖⡴⢡⣾⠳⡄
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⣀⣈⣂⡀⠉⠁⠈⠉⠉⠈⠛⠀⠉⣿⣿⣿⣾⡿⣡⣾⣯⠂⡁
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠙⠙⠙⠻⠿⡿⣷⣶⣶⠤⣤⢄⣠⣤⢰⣿⣿⣿⡟⣼⢿⣿⠄⠀⢸
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣠⣤⣶⣿⣿⣿⣽⣿⣿⣿⠟⠁⠈⣿⣧⡀⠈⠓⢄⣀
⠀⠀⠀⢠⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⠏⠁⠀⠀⠀⠘⠿⣧⣇⡄⣀⣈⠑⡦⠄
⠀⠀⣠⣀⣀⡁⠀⠀⠀⠙⠻⠿⠛⠛⣻⣿⣿⣿⣿⡏⢿⠫⣿⣿⣿⣿⣧⣀⠀⢂⡦⣄⡀⠀⠀⠉⠛⠿⠇⠎⣑⣷⠶⣄⡀
⠀⢰⣿⡟⡁⠀⠀⠤⢤⡀⠀⠀⣠⠞⡿⠉⠁⠔⠋⣠⣶⠾⡛⠿⣿⣿⣽⣇⣀⡀⠀⡈⠻⠶⡄⠀⠀⠀⠀⢸⣏⡥⢲⠯⠴⢻⡏⠀⠆⣠
⢠⣿⣿⠿⠷⠂⢀⡀⡀⠀⢠⣾⣡⠀⠀⢶⣶⣶⡿⢋⠀⣀⣶⡟⠉⠉⠉⠛⠛⢓⣦⠀⠀⠀⡀⠀⠀⠀⠀⢉⠁⣀⣀⡀⢠⣿⣿⣀⣄⣯⠇
⣾⣽⠏⠀⠀⠀⠘⢷⣿⣦⣌⣙⡙⣗⣿⡿⠛⠁⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠉⠈⢥⠻⣿⠿⠟⠋
⢻⠟⠀⠀⠀⠰⣄⡀⠈⠙⠻⢿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⠀⠀⠀⠀⠀⠀⢀⡼⠷⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡟⠻⣿⣦⡀⠀⡀⢤⣤⣤⣠⣤⣀⣴⠦⡀⠀⠀⠀⠀⢀⣼⡇⠏⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣤⣀⣀⠉⠀⣀⣺⡿⣿⠾⣿⠢⡝⣯⠰⣿⣷⡧⢘⣃⠀⠀⠀⢀⣾⣽⠃⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡁
⠀⠀⠈⠉⠀⠘⠃⠉⠛⠙⠒⠂⢹⣷⣿⠾⣥⣟⠛⠜⠏⠋⠀⠀⠀⠾⣏⣐⣷⠞⠁⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢧⣍⡛⠛⠒⠦⠄⠀⠀⢸⣿⣿⣿⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠖⠛⠁⠁⠀⠄⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣶⣦

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣴⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣶⣄
⠀⠀⠀⠛⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡟
⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃
⠀⢀⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⢠⡀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣧⣤⡄⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣧⣤⣄⡀
⠀⣸⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⡿⠁⠀⠀⠁⣰⠀⠀⢀⣤⡤⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣇
⠀⣿⠁⢻⣿⣿⣿⣿⠀⠀⠀⠀⣰⡟⠁⠀⠀⡀⠐⠻⣇⣰⠟⠀⠀⠀⠀⣿⡟⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢰⡿⠉⣿⣿⣿⡏⠈⣿
⠀⢿⡄⠈⠟⣛⣿⣿⡆⠀⠀⠀⠘⣷⠀⠀⠁⠙⢰⡖⠻⠁⠀⠀⠀⠀⠀⣿⡁⢹⣿⣿⣧⣀⠀⠀⠀⠀⠀⢸⣷⠀⣹⣿⡟⢃⡀⣿⠇
⠀⠈⣿⠀⢼⣿⣿⣿⡧⠀⠀⠀⠀⠈⢧⣀⠀⠀⠸⡇⢠⠀⠀⠀⠀⠀⠀⢹⣷⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠹⣯⠀⠋⠉⠠⡐⡟
⠀⠀⣿⡆⠈⣽⣿⣿⣿⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣁⡀⠁⠀⠀⠁
⠀⠀⠈⠋⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠨⣀⡀⠘⠒⢠⠀⢢
⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠂⠉
⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠃
⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢰⡟⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⢀⡾⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢀⣿⠃⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠰⣿⠃⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠊⠉⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡖⢦⣀⣣⣤⠱⣶⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⠈⠐⡡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢈⠿⠧⠽⣟⠀⠀⡠⡒⡀
⠀⠀⠀⠀⠀⢀⣤⠤⠒⠛⠛⠚⠀⡠⠁⢀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢵⠀⠀⠀⠀⠀⠁⠨⠾⣿⣷⡀
⠀⠀⠀⠀⠀⡏⢰⠂⠀⠀⠀⠀⠀⢹⣷⠋⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠌⠀⠀⠀⢀⠄⣤⣀⡠⠀⢉⣧⡀
⠀⠀⠀⠀⠀⡇⣟⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠐⣄⠀⠘⠛⠚⠾⠅⣀⠘⠿⠷
⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⣟⣋⠠⠀⠀⠀⠒⠂⢄⣠⠙
⠀⠀⠀⠀⠀⣇⢸⠂⠀⠀⠀⢀⠴⢆⠀⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢓⢻⣔⠂⠀⠀⢤⡉⠲⠾⠃⠉⢢⡀
⠀⠀⠀⠠⠀⢻⠘⡄⠀⡀⠠⣸⠀⠀⢢⠀⠀⢠⢠⠆⢰⠒⠀⠄⠀⠒⠂⠀⠈⠂⠀⡛⠀⠸⠘⡯⣄⠀⠀⠰⡄⠀⠀⠠⢊⠁⢳⡀
⠀⠀⠀⠀⢳⢘⡇⢂⠀⠃⣀⣿⡆⠀⢿⢉⣁⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⢵⠈⣂⠀⠀⠹⡀⠐⠃⠈⠀⠈⠳
⠀⠀⠀⠀⣸⡄⢳⢸⡀⠎⢉⣁⢇⠀⢰⣼⣿⣧⠀⠲⣶⣦⠈⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⢑⠐⠊⢸⡇⣰⣥⡓⠆⠀⠀⠀⠀⡀⠀⠃
⠀⠀⠀⡘⢡⠄⢹⣦⣈⠀⠀⠀⠊⠀⣀⣀⠉⠋⣦⢀⠈⣻⣆⠀⠀⠀⠀⠀⣠⠉⠃⠊⠁⠀⠀⡀⠀⣿⠛⢠⠙⠚⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠇⠀⠀⠀⣻⣯⣻⢦⣕⡀⠤⠘⡍⠉⠹⠿⠏⢋⡉⠘⣤⣀⣤⠴⡞⠋⠀⠀⠀⠀⠀⠤⠁⠀⣾⠀⠘⠄⠀⠀⠀⠀⠀⠠⠀⠒⢤⣀
⠀⠀⠀⠀⠜⠀⠀⣿⢯⣖⠴⠫⠂⡯⠀⢇⠀⠀⠀⡀⠀⠘⠀⠀⠀⠸⠃⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⢢⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀
⠀⠀⠀⠀⠈⠄⠀⣿⠈⠁⢀⠂⠀⡗⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡝⡀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠋⢰⠀⡦⢰⠀⣃⠐⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⡀⡇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠸⠈⡾⠁⠸⠄⠹⡀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠃⠃⠀⡿
⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠰⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠈⠀⠀⠀⠁
⠀⠠⠦⠄⠀⠀⠀⠀⠀⠀⢀⡠⠄⠐⠞⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢾⡭⣀⠀⠐⠀⣤⣜⢷⣺⡇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⣼⣍⡁⠀⠀⠀⠀⢀⣠⣤⣤⣤⣾⣳⢷⣜⣻⣦⣤⢠⣤⠀⠀⠀⠅⠠⢠⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠋⠉⠉⠉⠙⠓⠂⠀⠛⠙⠛⠛⠿⣦⣤⣱⡾⠋⠉⠀⠀⡀⠙⠃⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢈⣎⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⡠⣶⣶⣿⣍⠉⠐⠒⠂⠤⣄
⠀⠀⠀⠀⠀⡀⠀⠈⠙⢿⣿⣿⣶⣦⣐⢀⡤⣠⠀⡄⠀⠀⠀⠄
⠀⠀⠀⠀⡒⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠒⠒⠒⠒⠆⠀⡀
⠀⠀⠀⣔⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠈⠩⠐⣂⡲⠆
⠀⠀⠀⢪⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣠⣤⢾⣿⡿⠃
⠀⠀⠀⠸⡀⠀⠀⠀⠐⠐⠒⠂⠀⢽⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⠟
⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⣄⠂⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠈⢦⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣼⣻⡅⡮⣀⢘⢏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣛⡾⣿⡽⡒⡋⠀⡃⠀⠀⠀⠀⠀⡠⠞⠉⠈
⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣀⣀⣀⣠⣄⣀⠉⠓⢾⢿⣿⣜⠧⢶⡠⠓⢠⠟⠀⠀⠄⣀⣀⣠⠄⠀⠂
⠀⠀⠀⠀⠀⠉⠉⠉⠻⠿⢿⣿⣿⣿⣿⠿⠛⠒⣾⣿⣿⣿⣿⣛⣁⣤⠟
⠀⠀⣰⡇⠀⠁⠂⢀⣤⣴⣾⣿⣿⡟⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⢸⣆
⠀⢰⣿⣃⣠⣴⣾⣿⣿⣿⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⢸⣿⣿⣿⣿⡿⠟⠋⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠱⡀⠈⠙⠲⠀⠀⠀⢀⣀⡀⠤⠤⠀⠚
⠀⠘⠟⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠂⣬⡶⠿⡏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡄⠀⠀⠀⠐⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢻⣿⣦⣶⣾⣿⣿⡿⢿⣊⣥⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣧⣯⣹⣿⡊⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠃⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠘⡀⡀⢀⠀⠀⠀⠱⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡿⠿⠿⠛⠻⠿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠂⡁⡎
⠀⠀⠄⠀⠰⡃⠇⠀⢀⠄⡀⢰⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣿⣿⣧⠀⠀⠀⠀⠀⢠⣿⣟⡤⠟⠀⠀⠀⠀⠀⠀⠀⠐⠀⢜⠀⣀⡄⠀⠀⢃⡇⠀⠠⠂
⠀⠀⠀⠀⠀⠁⢠⡄⠀⠀⠉⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⠀⠀⠀⣴⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠈⠁⠀⠀⡆⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⢈⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⠟⣿⣿⡇⠀⠀⠀⠈⠻⠿⠿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⢀⣠⣶⣟⣿⣿⣿⡟⠁⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⢿⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⡀⠀⣀⣠⠞⠋⠓⠀⣈⣁⣴⠿⠀⠀⣾⣻⣿⡁⠀⠀⠀⠀⣠⠀⠀⠀⠸⣦⣤⡀⡀⠉⠉⠹⠷⣤⡀⠀⡄⠀⠀⠀⠀⡺
⠀⠀⠀⠀⠀⡆⠀⢠⡀⠘⠃⣾⠟⠁⠀⢀⠤⠊⠀⢻⣇⠀⠀⠀⣿⢏⠁⣿⠂⠒⠓⠀⡇⠀⣡⠀⠀⣿⣟⠂⠀⠑⠠⡀⠀⠈⠻⣆⠀⠀⡤⠀⠀⠆
⠀⠀⡀⠀⠀⠀⡄⠀⠁⠃⠘⢡⠀⢀⠔⠀⠀⠀⠀⡾⠻⣦⠀⠰⣿⠈⠀⠉⢄⡤⠂⢈⠀⢀⡟⠀⢸⡇⠹⡆⠀⠀⠀⠀⠂⡀⠀⡈⠀⢀⠀⠀⡄⠀⠀⢠⡄
⠀⠀⠀⠀⠠⠄⠅⢠⡞⠀⢠⣟⡾⠁⠀⠀⠀⠀⣔⠧⠴⡏⠀⠀⣿⣧⠀⠀⠏⠀⠀⠀⠀⣸⣇⠀⠀⣗⠄⠗⣄⠀⠀⠀⠀⠘⢧⣱⡀⠀⠳⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⣞⣹⠁⠀⠀⠀⣠⣾⢿⣴⣾⠃⠀⣼⣿⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⡄⠀⢹⣵⢴⡟⢳⣄⠀⠀⠀⠸⡇⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠑⡣⠆⠐⠂⠀⠳⣥⣼⡽⠃⠀⢠⣿⣿⡿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠹⣮⡧⠼⠃⠀⠀⠒⡒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠁⢼⠇⠀⠀⠀⠀⠀⠸⠁⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⢻⣆⠀⠀⠈⠀⠀⢷⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠠⠔⠆⠀⡀⠎⠀⠀⡆⠀⠀⠠⠁⠀⠀⢻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣌⢿⣧⡀⠈⢿⣿⣄⢀⡇⠀⠸⠀⠄⠠⠐⠐⠂⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣷⡀⠀⡌⠻⣦⠁⠀⠐⠂⠁⠈⢁
⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠐⠀⠀⣴⠁⠀⠀⠠⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠈⠀⢹⣧⡄⠐⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⢹⡄⠄⠀⠀⢠⢠⣴⣃⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠹⣿⣧⠀⠀⠘⡄⢻⣇⢄⠀⠀⠀⡄⣿
⠀⠀⠁⠸⠀⠀⡈⠃⣠⠀⠀⡈⠉⠠⠏⠖⠑⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⠀⠙⢿⣧⡠⠀⠀⢾⡇⠌⣀⠀⢀⢀⠋⡁⠐⠙⠐⠁
⠀⠀⠀⠀⠇⠰⠈⠛⠹⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣼⡟⣿⣆⠀⠀⠹⣿⡄⠄⢺⠇⡀⢹⠀⢘⠘⠃⠙⠀⠇
⠀⠀⠀⠀⠀⣄⠀⠈⠀⢁⠈⠀⠀⠀⠀⠀⠈⠀⠀⢠⣿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡿⠁⣿⠹⣧⠀⡆⢹⣧⠀⠘⡅⡇⠀⡄⠛⠉⡁⠀⡀⠀⡀
⠀⠀⠀⠀⠢⠈⡀⠈⠀⠘⡏⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣼⡇⠀⣿⠀⣿⡆⠁⢸⣿⠀⠀⢸⡇⠀⠜⠀⠀⠀⡀⢐⠂⠁
⠀⠀⠀⠀⠐⠸⠃⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣷⠀⣿⠀⠹⣿⡆⢸⣿⠀⠀⠠⠑⠰⠀⠀⠀⠀⠑⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⠁⠀⠀⠀⠀⠀⠀⢻⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢻⣿⡏⠀⠘⠀⠹⣿⡟⠀⠀⠀⢱⠂⡄
⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⢁⡔⠈⠀⠀⠀⠀⠀⠀⠈⠳⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣯⣿⠀⢄⠀⢠⡿⠃⠀⠀⠀⠈⣀⠁⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⠸⡇⠀⠀⠈⢀⠉⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠈⠑⢢⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠰⡏⠀⢈
⠀⠀⠁⠀⠀⠀⠆⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠄⠀⠐⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠂⣼⠀⠀⠀⠀⠲⣄⡀⠀⠀⠀⠀⠐⡿⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠚⠂⠀⠀⠀⠀⠀⣠⠴⠂⠀⠀⠀⢧

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠰⣍⡶⣀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⡀⠀⠀⢸⡿⣿⡇⠀⠀⠀⠀⢈⣁⠆⡈⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⢠⡞⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠓⠀⠀⠀⠀⠀⠸⢻⠯⣿⠣⠀⠀⠈⠛⠟⠁⢀⡀⠀⠀⢈⠉⢀⠷⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠏
⠀⠀⠀⡀⢊⣖⣿⢶⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⢩⠔⡀⠻⠆⠀⠀⠀⠀⢠⣈⠋⠉
⠀⠀⠀⠀⡿⢾⢫⣔⠣⡄⠀⠀⠉⠀⠀⢠⡶⠁⠠⠀⣇⣾⠀⠀⠀⢠⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡄⣠⡠⠀⠀⠀⢠⣀⠉⠣⠚⢋⡀
⠀⠀⠀⠀⡛⢠⠘⠿⠖⠃⠀⠀⠀⠀⠀⡰⠁⠀⢀⡀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠠⡤⠢⡀⠀⠗⠀⠀⠀⠀⢿⡇⠀⢾⣿⣿⠋
⠀⠀⠀⠀⢀⠀⡀⢠⣠⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠌⢓⣀⢁⣀⠀⠀⠀⠀⠀⠀⢰⠈⠛⠁
⠀⠀⠀⠈⠢⠄⠹⢩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⡄⠀⠀⠀⢋⡙⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⡀⠀⣠⢦⡀⠀⠀⠐⢧⣞⣟⣷⠆⠀⠀⠀⡈⠋⠁⠀⠀⢀⣤⡀⠀⠀⠀⠘⢫⠝⠶⠀⠀⠀⡤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠁
⠀⠀⠀⠈⠇⠀⠀⢘⡤⠛⠀⠀⠀⠘⠓⠟⠋⠀⠀⠀⠀⠳⡔⠂⠀⠀⠚⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⠻⠛⣿⠀⠀⠀⠐⠢⠄⠀⠀⢀⡀⠀⠁
⠀⡆⠀⠀⡀⠀⢠⢿⣿⠁⠀⠀⠀⢘⣷⣄⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠰⠿⠀⠐⠀⠀⣀⢤⡄⠀⠀⠀⠀⢰⠆
⠀⡃⠀⠐⠂⠀⠀⠀⠈⠃⠀⠀⠐⠦⠹⣏⣼⠃⠀⠀⠈⠳⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢛⣷⡄⠀⠀⠀⠈⠘⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠇
⠀⡄
⠀⡄
⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⡄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣿⠁⠀⠀⠀⠀⠀⢀⣠⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠼⣻⣿⣿⣿⣿⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⣾⣶⣤⣀⡀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡟
⠀⠀⣀⣄⣀⠠⡀⠀⠀⠀⣙⣻⣿⡿⡻⠋⠉⠙⠳⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣀⠠⠈⢻⣿⣿⣿⡷⠶⢶⣿⡿⠿⡿⠿⠋⠀⠀⠀⠀⢀
⠀⣾⣿⣿⣿⣷⣏⣧⣀⣾⣿⣿⣿⣏⡇⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣿⠀⠀⠀⠈⣿⠟⠁⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢾⣧⠀⣿⡄⠀⠀⢀⡀⠀⠀⠀⢸⡇⠸⡿⠀⠀⠀⠀⠉⠀⠀⢉⠀⠀⠀⠀⠆⠀⠀⠈⠤
⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠿⢽⡄⠀⠀⠘⢿⡆⠹⠧⠂⢰⣿⣿⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆
⠀⠺⢿⣟⣿⡿⠟⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⢀⣤⣀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⡀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣀⣾⠈⠀⠀⣰⣦⣤⣤⣤⣴⣶⣶⡄⠁
⠀⠀⠠⣴⣶⣶⣶⣶⣶⣿⣦⡀⠀⠏⠙⣿⣶⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣛⡋⣠⣴⣶⣿⣿⣿⣽⡿⢿⠛⠛⠃⠚⠒
⠀⠀⠀⢹⡿⠿⠛⠛⠙⠛⠛⢿⣿⣮⣀⠀⠀⣛⡛⣵⡄⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⣳⣿⣿⣿⣿⣿⣿⠟⠀⠀⠱⡄
⠀⠀⢀⠂⠀⠀⡠⠄⠀⠉⣽⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣦⣀⢀⠄⠐⠀⣀⠠⢀⣤⣴⣾⣿⣿⣯⠟⢫⠎⠙⠿⠿⠿⠟⠋⠁
⠀⠀⠨⡀⠀⠜⠀⠀⢀⡀⠘⠿⣿⣿⣿⣿⣿⣿⡟⠙⢿⡏⡠⠀⠀⠠⢀⠀⠀⠀⢙⡿⠿⠟⠋
⠀⡀⠀⠀⢰⠀⠀⠐⠁⠀⠀⠀⠀⣉⠉⠉⠉⠁⠱⠀⠈⢧⡀⠀⠀⠐⠁⠊⠀⠀⠀⠀⠄⠀⠆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠡⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢢⠀⠆
⠀⠀⣀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠄⡑⠀⠀⠘⠄⠀⠀⠀⠆⠀⠰⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣾⣿⣿⡿⠆⡀⠀⡤⢀⡀⠀⠀⠀⠀⠀⣠⣶⣦⡝⠀⠀⠀⢀⣀⣁⠀⠀⠀⠀⠀⠀⠠⢄⠂⠀⣤⣤⣤⣄⣂⣀⣀⠀⠀⠀⣤⣴⣶
⠀⠱⣿⣿⣿⣦⣌⠈⣠⠊⠀⠑⢄⢀⠀⠈⠿⣿⣿⣷⡄⠠⠊⠁⠀⠀⠈⠓⠄⠀⠀⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⡏
⠀⠒⠛⠻⢿⡿⠟⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠃⠀⠀⠀⠈⠉⠁⠢⡄⠀⠀⠀⢸⠀⠈⣿⣿⣿⡟⢻⠟⠃⠰⣎⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠹⡿⠟⡡⠂⠀⠈⠰⣿⣿⣿⣿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⡀
⠀⣀⣀⣀⣠⡤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⣀⡀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠀⠀⢀⠁⠀⠙⢿⣿⣿⣿⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⢀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠂⢄⠉⠛⠙⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠀⠰⠃

⠀⠀⠀⠀⠀⣠⣴⡦⣦⡀
⠀⠀⠀⠀⢰⣿⡟⠠⠘⣁⢀
⠀⠀⠀⠐⠸⣿⠟⠀⡀⠉
⠀⠀⠹⠈⠘⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢠⡞⢈⡙⢷⡄⠀⠀⠀⠀⢿⠛⠿⣿⣿
⠀⠀⠀⠰⠄⠀⠀⠀⢀⠀⢘⡄⠀⠀⠀⠀⠀⠀⣼⡟⠉⠀⢁⡅⠀⠀⠀⠀⠈⠀⠀⠘⠫
⠀⠀⠀⠀⠈⢴⠀⢊⠗⢋⠿⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡄⢀⠀⠀⠀⢠⢄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⢀⢠⣾⣥⠃⠀⠀⠀⠀⠘⠃⠀⠠⣦⠓⠀⠉
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣥⠐⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠰⠂⣁⣤⣤⣤⡁⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢩⠁⣸⠋⣿⡏⠀⠀⠀⠉⠁⠀⠀⠀⠄⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⡁⠠⠏⢰⡇⢠⣿⠃⠀⠀⠄⠀⡄⠀⡀⢦⡀⠀⠀⢖⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠙⣄⢀⣼⡇⣼⣇⠀⠀⠀⠀⡀⠀⠀⠀⢨⣷⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⢏⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠈⡆⠀⠀⢐⡆
⠀⠀⠀⠀⢤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡦⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣽⣿⣿⡟⠀⠀⢶⡆⠀⣴⠂⠀⢀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⡻⣿⠁⢀⠴⠉⠐⠂⠀⣶⠄⢈⣂⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠥⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠛⠂⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡖⠒⠀⠦⡤⡤⣤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣴⡞⠛⠴⢴⡿⢋⣿⡯⠀⢸⣷⣴⡟⠷⠖⢶⠿⠾⠇⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣠⣤⡴⢿⠟⠋⣩⡽⣿⣁⣤⣬⣯⣿⣿⣗⠔⣤⣘⣟⣓⣒⣈⣍⣙⣞⢻⠭⠟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡉⠀⢹⣤⣘⡦⣷⣿⣴⣦⡜⢯⢵⡟⡟⠉⡙⢻⡌⣽⡿⠿⠫⡈⢿⣿⣿⠯⣵⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⡙⢟⣢⣤⣽⣏⠠⠘⢘⠇⠨⣙⣻⢉⣺⣿⢊⡟⠋⢀⣿⣯⣤⣼⣾⣾⡻⠥⣴⣼⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⢾⡧⠀⣿⢋⢼⣿⣿⣾⣿⣿⡾⠟⢉⣛⣛⣯⣽⣷⢰⠟⢿⣿⣿⣟⣭⣠⣿⣿⣿⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⣼⣷⣟⣟⠺⣄⣼⠏⠘⢋⡟⣷⠄⢠⡴⣿⣿⢯⡛⠛⠶⢿⠏⠉⣿⠟⠿⣿⣟⣉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⢶⡍⠻⠿⠷⣴⠨⢹⣷⣀⣡⣼⣹⣦⣊⣰⣁⡙⡯⠙⢂⣉⣹⣶⣦⣀⣀⣱⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⡀⢀⣶⣾⣿⢟⣻⣿⣿⣷⠟⠛⣉⢟⣯⡭⠟⠁⠀⠈⠁⢀⣘⣛⣿⠛⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣐⣣⠬⣿⣧⣌⣧⡾⢿⣿⣿⣿⠓⢤⢤⠞⣻⠀⠀⠂⠀⠠⣶⠛⠛⣿⡏⡀⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠍⠢⡿⡛⠿⣼⡀⣿⣿⣿⣿⢿⣟⠛⣶⠿⠀⠀⠀⠀⠀⠈⠢⠴⠟⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⣷⣷⣱⡀⡵⣝⠊⠭⠄⢿⣿⣩⠛⣽⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣎⡼⢛⠿⢟⣄⣸⠟⠷⠶⠟⠣⠙⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠳⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣠⡌⣱⣶⠻⢻⡌⠀⠀⠂⠘⠲⠃⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡿⠷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⢛⠻⠟⣻⣇⡿⠀⡀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢹⡻⠶⠼⢿⣇⠀⠐⠇⠀⢧⠀⠠⠀⡤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⢻⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣋⠰⣶⣿⠟⢢⠀⠀⠀⠀⠛⢤⣤⣄⢋⠉⠁⢀⢤⣀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⣄⣿⡌⠠⠎⠁⠀⠀⠀⠀⠀⢘⡍⠛⠻⢮⣤⣄⣀⣀⣀⢀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢡⠜⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄⡠⠄⠙⢻⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡈⢈⢰⣅⢈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢥⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⢄⡀⣍⠱⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⢸⡁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠑⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠫⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠠⠀⢠⡌⠁⠠⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠿⢦⣤⣄⢰⡀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠓⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀⠀⠀⠀⠀⢀⠤⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠦⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⠶⠶⠚⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⡧⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢶⡴⠚⢉⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠶⠋⠘⠓⠛⢷⣴⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣿⠠⣴⣶⠶⠒⢺⣿⣿⣿⣿⡀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⢀⣽⣶⡸⠇⠀⠀⠀⠻⣿⣿⣿⠃⢼⣇⠀⠂⣶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⣛⣟⡸⣷⣾⣄⠀⣀⠀⠀⠀⠘⣧⠈⣥⣞⡈⣻⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠸⣿⣗⢿⣿⣿⣿⣿⣶⣶⣆⣰⡷⠀⢀⠋⢡⣭⠤⠤⠴
⠀⠀⠀⠀⠀⢀⣀⣤⣠⣀⡐⢾⣃⠀⢸⣿⣮⣍⠻⢿⡿⠿⠻⣽⣋⢁⣰⠞⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠉⢀⡤⢒⡨⠽⠆⢻⡧⠀⠐⠉⠻⠟⠾⣶⣶⠖⠈⢻⣿⣿⠀⠀⠀⠂⠈⠂
⠀⠀⠀⠀⠀⠀⠑⠚⠁⠀⢀⡄⠘⡁⢈⡏⠀⠀⠈⠻⠟⠋⠀⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡠⠂⠀⠐⢼⡇⣀⠀⢀⡀⠠⠠⣤⣴⣿⣟⢃
⠀⠀⠀⠀⠀⠀⢄⣋⡠⠛⠀⠀⠀⠀⠘⣯⠀⠀⠀⠙⢶⣦⡀⠉⠛⠿⠿⠵⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠁⢀⡑⢵⡉⠒⠲⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠠⠀⠀⠠⠀⠐⠄⠀⠰⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⢀⠆⠰⠂⠄⠀⡴⠀⠲⣄⠀⠀⢀⣰⣶⡆⠀⠀⡿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⡀⠘⠲⢶⡐⢠⡄⢀⢚⠁⠹⣵⣾⡍⢯⠀⢤⡀⠳⠛⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠊⠀⠀⢠⠀⠂⠀⠀⠀⠀⠐⢄⡾⢧⠀⠀⠈⠛⢧⠀⠀⠀⠹⠇⠻⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠒⠆⠀⠈⠁⠀⡄⣃⢉⣤⣄⡀⢀⡤⠓⢁⠀⢠⡄⠀⠀⢀⠀⠘⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢰⣻⠰⣷⣴⣤⠀⠨⠰⠀⢸⡿⠉⠉⠙⡆⠀⠀⡀⠛⠎⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠛⠛⠃⠀⠀⠀⠀⡨⠁⠄⠂⠀⠁⡀⠀⠈⢻⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠑⠀⠁⠀⠀⠀⠀⢠⡀⠀⠐⠲⠀⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠃⠻⠦⡄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣀⣀⣤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢴⡻⣏⢹⡿⣿⢿⠉⢉⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣶⣶⢲⣿⣿⣦⣄⠙⠋⢀⣼⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣾⣿⣿⣿⠛⠂⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠈⠻⢿⣿⣿⣿⡿⣿⣳⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠀⠙⣿⣿⣦⣤⣴⡀⣩⣽⡇⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⠡⣾⣻⣿⣿⣿⣿⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⢨⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢀⣘⡀⠴⠟⠁⠑⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⡈⣸⣿⡶⢶⣿⣷⠠⣄⡀⠀⠀⠀⠹⣿⠃
⠀⠀⠀⠀⠀⠐⠃⠐⠂⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣶⣶⣿⣿⣿⣿⢷⣄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⢻⠛⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡛⢻⡟⠛⠉⠀⠀⠀⣠⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣀⡈⡀⠀⠀⠀⠀⣀⠀⣻⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣾⣿⣟⣉⠉⠀⠉⢙⡖⠁⠀⢩⣿⣾⣿⡄⠢⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠰⣾⣦⣀⠀⠀⠀⣀⠛⠛⠛⠿⠻⠷⠦⠀⠀⠼⠦⠿⠿⠿⢿⣿⣆⢦⡀⠀⠀⠀⢘⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠦⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⠀⢠⡿⠿⠛⠁

⠀⠀⠀⢻⣦⡀⢀⣴⣿⠀⠀⢠⣤⣀⠀⠀⣀⣤⡄⠀⢰⣦⡀⠀⠀⢀⣤⡦⠀⢰⣦⣀⠀⠀⢀⣤⡆
⠀⠀⠀⢘⡏⢻⣿⠩⡇⠀⠀⠈⢃⣤⣷⣾⣥⣜⠃⠀⠘⠻⣾⣶⣶⢷⡞⠃⠀⠈⢿⡿⣧⣴⢿⣿⠃
⠀⠀⠀⢸⡾⠁⠀⢡⣟⠀⠀⠀⠺⠽⠋⠙⠯⠿⠀⠀⠀⠺⣿⠊⠑⢿⠿⠀⠀⠀⠻⣿⠎⠉⢾⡟

⠀⠀⢀⣄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⢠⡄
⠀⠀⠀⢿⣿⣦⣴⣿⡿⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⢇⡀⣠⣶⣀⡰⠇⠀⢠⡀⠒⣢⣖⠖⠂⡀
⠀⠀⠀⢸⣿⠏⠋⣿⡷⠀⠀⠀⠐⠁⠘⠇⠀⠂⠀⠀⠀⢿⣰⡟⠿⣆⡽⠀⠀⠀⠙⢟⡻⢟⡻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁

⠀⠀⠀⣗⠲⣤⣤⠔⢲⠆⠀⠰⡒⠐⢦⡴⠒⢒⠶⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣶⣆⠂
⠀⠀⠀⠸⣲⠺⠛⣖⠏⠀⠀⠀⠀⢳⠞⠳⡾⠁⠀⠀⠀⠀⢠⡄⢡⡄⠀⠀⠀⠀⠘⣯⣿⢿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁