Hairless Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠑⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢷⣤⡉⢶⢄⡀⠀⠀⠀⠀⠀⠀⢸⣧⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⡄⢹⣿⠆⣼⠏⠀⠄⠀⠀⠀⠙⠚⢿⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡌⢸⣯⡴⠁⠀⠀⡀⠀⠀⠠⣄⠀⠀⠙⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⠟⠀⠀⠀⠀⣀⣤⣜⠃⢸⠰⠇⠰⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠄⢈⡥⠒⡈⠻⠿⠿⣟⠛⠀⠀⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡞⠃⠀⣠⠍⡷⠂⠀⠀⠀⠀⠀⠀⢈⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠑⣖⡀⣾⣻⠔⠁⠀⠀⠧⠤⠀⠀⠀⢠⣴⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⡁⣀⣉⠸⢧⣄⡀⠀⠀⠀⠀⢀⣘⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣧⣾⡟⠻⣿⣍⣛⣶⣤⣬⣬⣴⣷⡿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠾⠋⣀⣾⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠻⠀⢀⡜⠈⣼⣿⣿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡮⠀⠩⠀⢀⣸⣻⣾⡟⢙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⣃⠀⠀⠈⠏⣽⠟⠏⣸⡟⠏⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⢱⠆⠀⢀⣼⡷⠀⢸⣏⠀⢀⣿⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠘⣷⣀⠀⠀⣠⣾⠃⠀⢀⡟⠀⢠⠿⣁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠈⠛⠧⠶⠛⠀⠦⠀⣾⢀⠠⠾⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⢾⣿⢿⡿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣊⣁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡙⠛⠀⢘⣿⣿⣤⠄⠄⣄⠀⠀⡀⠀⢀⣔⣿⣿⠿⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡶⠀⢨⣿⡿⠁⠀⠀⠉⠀⠀⠀⠠⠀⠀⠙⢿⠀⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣼⡿⠃⠀⠀⠀⠀⠀⠰⡷⢠⠀⠀⠀⣤⠱⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣅⠀⣄⣠⡤⠶⣿⣿⣦⡤⠀⠀⠰⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠗⠉⠁⠠⣤⡀⠀⠀⠁⠀⠀⠀⠈⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⣰⣆⠈⠁⠀⠀⢀⠀⠀⠀⠀⢈⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢧⣼⣿⡿⠀⣂⠀⠠⠶⠆⠀⠀⠀⠟⣭⣭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠘⠳⠰⣶⣴⣿⠀⡀⠀⠀⠀⠀⢀⢘⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⡴⠋⣹⣿⣿⣿⣿⣶⣶⣶⣶⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠁⢒⠀⠁⠐⣿⠁⢈⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢸⡌⠀⠋⠈⠆⢀⠋⢱⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢺⠁⢸⡶⢻⢠⠀⢠⡀⢠⣾⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢐⡀⠀⠀⢿⢹⠘⣷⡟⢧⡌⣿⣿⡟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠋⠿⡀⠂⠁⠺⡂⠼⢃⡘⢠⣿⡟⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣄⠀⢁⠙⡆⠸⣀⠠⢦⢸⡟⠁⠄⢠⣻⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡝⡆⠀⢼⣧⣦⠈⢤⠈⡇⢀⡄⣠⣾⣟⠊⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⠀⠀⡤⣤⡀⠘⠻⢷⡄⢾⣼⠏⣴⢋⠿⠋⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃⠀⠀⠀⠻⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⢙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠠⠀⢙⢾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠀⠀⠀⠀⠈⠻⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣞⡀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡎⠓⠄⠀⠀⠀⠀⠘⢦⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣴⣾⡟⡡⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡱⠌⠀⠀⠀⠀⠀⠀⠐⢝⠢⣍⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⣾⣿⣿⣿⣠⠆⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣇⠠⠀⠀⠀⠀⠀⡀⠈⢢⣱⣮⣦⡀⢿⣤⣤⣤⣤⣤⣤⣤⣄⣤⣼⠃⢸⣽⣿⣿⣿⡏⠀⠀⢀⣎⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠀⠀⠉⠒⠄⠠⠁⣴⣼⢿⣿⣿⠇⠜⠘⠈⠠⠀⠀⠀⠀⠀⠈⠁⠀⠈⢿⣿⣿⡟⣡⠔⠀⠸⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠦⠀⣴⣿⡿⢿⣿⠁⠀⣀⠀⠀⠓⠁⠀⠀⠀⠀⠀⠀⠑⠀⡀⢉⡻⢿⣏⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢡⠘⠂⠀⠀⢀⠳⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠉⢀⣌⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢶⣴⡄⠏⠐⡠⠀⢀⠀⠀⠀⣀⡤⠴⣦⣤⡀⢼⠀⠘⠀⠀⠀⠀⠠⣯⠖⣾⡶⡄⢹⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⡀⠀⠀⢨⡆⠀⢸⡀⠠⠀⡏⠀⢶⣿⠇⠘⡆⢃⠠⠀⠀⠀⠀⢰⡇⠸⣿⠇⡟⠈⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⡉⢉⡀⠂⠀⢧⠀⠀⠙⠄⠈⠋⠀⣼⠟⠀⠀⠀⠀⠀⠀⠈⣷⠠⠥⠞⢁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠀⣤⡄⠀⠈⢧⠀⠀⠀⠀⠁⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠤⢺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠠⠐⢄⠀⠀⢝⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⡌⠂⠀⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⠂⠀⠈⢕⡢⠤⠉⠉⠈⠀⠀⠀⠀⡀⠀⠈⠉⠻⣿⣿⠋⠁⢀⢰⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⢧⡀⠀⠀⠍⡁⣒⡀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⢨⠁⠀⢐⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⡈⢀⣀⣠⠴⠞⠳⢤⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠑⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢍⡉⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⠝⠛⠃⠙⠓⢒⠠⡴⢢⠟⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠐⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢄⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠗⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢹⣿⣧⣠⠀⠀⠀⠀⠀⣤⣿⣿⡔⠸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢰⣿⠟⠁⠀⠀⠸⡖⠀⠀⠙⢿⡟⢘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣬⠋⠀⠀⠀⡀⠀⠀⢠⣀⡀⠀⢳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡤⡾⢹⡄⣤⠀⡫⠖⣦⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡉⠳⣦⠌⠀⠀⠀⠑⠶⢃⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠈⠠⣖⣐⡄⢳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⣿⣇⣁⡀⣿⣿⡀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⣿⣿⡿⢿⣷⣶⣶⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡧⠀⢸⣿⣇⢀⡉⢡⡿⣇⠆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠈⡿⠃⣿⡇⠛⣿⠇⠀⠁⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⡾⠁⡄⠀⣷⣴⡿⠀⠀⠀⠇⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢠⠏⢀⠃⠀⠀⣿⠁⠀⠀⡛⠀⣿⢰⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣾⠀⣼⡀⠀⢀⠀⠀⠈⠀⡟⣼⡇⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠄⣠⠟⢩⡄⡉⢳⣀⠀⠄⠀⢀⣼⣰⣿⡀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⣶⣿⡇⡿⣦⣿⣆⡀⠀⢱⣿⣿⣶⡆⠀⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⣿⡏⠉⠳⢷⣮⣹⣿⡆⠀⢸⡁⠈⢿⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⠃⠀⠀⠀⠀⠀⢹⡇⢠⡎⠛⣿⣿⡘⣄⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡟⠀⠀⠀⠀⠀⠀⢸⠁⢻⠀⢀⣾⡿⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⡇⠀⠀⠀⠀⠀⠀⣾⢰⣧⣶⣿⣿⠃⠀⠀⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⣿⠂⡏⠛⠋⠁⠀⠀⠀⡏⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡇⠀⠀⠀⠀⠀⠀⡟⠠⡇⠀⠀⠀⠀⠀⢰⣷⣖⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣸⠇⠀⠀⠀⠀⠀⢸⠁⠀⡇⠀⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⠇⠃⠀⠀⠀⠀⠀⠀⠻⠿⠘⠷

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⢿⡆
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠉⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠢⡉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡴⠊⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⢦⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⣠⠏⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣇⢱⡀⠀⠀⠀⠀⠀⠀⣿⠀⠿⠶⠶⠖⠛⠛⢻⠟⣟⠛⠛⠲⠶⠶⠾⠃⢸⠁⠀⠀⠀⠀⠀⠀⡰⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠳⣤⠤⢤⡄⣠⠞⣁⣤⠴⠖⠚⣋⠙⡄⢾⠀⢸⠀⠜⢉⡓⠒⠶⢤⣌⡙⢦⠀⣤⠤⣤⡼⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣶⡦⠞⣰⠷⢋⣡⠴⠒⠋⠉⠀⠣⠀⠸⠀⠘⠀⠐⠁⠈⠉⠓⠶⢬⣙⠺⣷⡘⣤⣶⣦⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣇⠀⣡⠞⢋⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣉⠳⣮⡁⢀⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡻⢋⡴⢡⣴⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣬⠳⡌⠻⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡾⠁⠀⢷⡀⠀⠉⠻⣧⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠁⠀⣰⠇⠀⠻⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⢀⡄⢀⡴⠂⠀⠀⠀⠀⠀⠀⠦⣄⠠⡀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡔⢉⣴⠏⠀⢀⣤⢤⠄⢤⢤⡄⠀⠘⣧⡈⡓⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣿⠁⠀⠀⠈⠛⣶⠀⢰⠞⠁⠀⠀⠀⢻⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣤⣤⠴⠋⠳⢤⣤⣤⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣀⣀⣀⣠⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣹⡿⠟⢿⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣰⠏⠀⠀⠀⣿⢳
⠀⠀⠀⠀⢀⠤⣒⣶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢇⡟⠀⠀⠀⠀⠻⢸
⠀⠀⠀⠀⠁⣾⡟⠛⠻⢦⣄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢸⠁⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠈⠳⡝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢸⠀⠈⠀⠀⠀⠀⢠⣞⣡⣆
⠀⠀⠀⠀⢸⡇⢠⠀⠀⠀⠀⠰⣌⠢⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⣆⠀⠀⡶⢠⣤⠞⠈⠉⣿
⠀⠀⠀⣶⠸⡇⠸⡄⠀⠀⠀⠀⠘⣧⠀⠈⢿⣷⡀⣀⣤⡤⣔⢻⡛⣏⡁⣰⣿⣿⠀⠀⣧⣸⠇⣀⡜⢠⣿
⠀⠀⠀⢻⡄⠁⠀⢧⠀⠀⠀⢀⣦⢸⠀⠀⠀⠙⣿⣏⡓⠣⣌⣿⡧⢻⡵⢌⡉⠻⣦⡘⠉⠁⢸⡏⢠⣾⡿
⠀⠀⠀⠈⢿⢄⠀⠘⣆⠀⠀⣤⠀⠈⠀⠀⠀⢀⣞⣹⡏⡄⡈⡏⢻⠀⠙⣓⠲⠤⠈⠛⠿⣖⢦⡛⢶⣿⡇
⠀⠀⠀⠀⠈⢧⠳⡆⠘⢷⣼⠿⢋⣳⣴⠀⡴⢻⠟⠋⣨⠖⡡⣟⡻⠳⡁⢸⠉⠛⠒⠂⠀⠈⠁⠑⠀⣿⠃
⠀⠀⠀⠀⠀⠘⡇⢧⡀⠀⠀⠒⠻⠉⠀⠀⠀⠀⠀⠈⠀⠉⠀⠜⢳⠀⠙⠘⠀⠀⠈⢷⡈⡙⠶⢤⣸⡇
⠀⠀⠀⠀⠀⠀⠁⢸⣿⣦⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡄⠀⠀⠱⠄⠀⠀⡜⠁⣴⣾⣿⠿⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⠶⢠⡇⠀⣧⠄⢠⡾⠵⠒⡒⠈⠳⣀⢰⡀⠀⠈⣾⡇⣸⠝⢿⣿⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣧⢸⡇⢠⡟⠀⠋⢴⢾⣿⡿⣿⣦⡈⠻⣇⠀⠀⠹⡆⢹⣦⣀⡠⠜⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠙⢧⠃⠸⣧⠀⠀⢇⠈⠻⠏⠀⣸⡷⣄⠹⡆⠀⠀⢷⣸⡆⠠⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⠀⢿⡄⠀⢀⠑⠂⠐⠚⠁⣠⣾⣦⡇⠀⠀⠀⢹⣧⠀⠈⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠳⡈⠻⣦⡈⠙⠿⣿⣿⣿⡿⠟⠹⡇⠀⠀⠀⠀⢻⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠘⢦⡈⠛⠲⢤⠀⠀⠀⠀⠀⠀⢹⣀⣤⣤⣤⣾⡗⠀⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣄⣀⠀⠠⠄⠤⠠⠈⠿⣿⡍⢡⡜⠀⢂⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⢹⠿⠷⣦⣄⣀⠀⠁⠀⢀⣹⠿⢤⡶⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣩⣴⠟⢀⡟⠀⠀⠀⠉⠛⠳⠶⠾⠏⠥⠔⠋⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣤⠶⠋⡽⠋⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠉⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠿⠋⠀⠀⣸⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠛⠉⠉⠀⠀⠀⣀⣤⡾⠋⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⡄⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⠀⠀⢀⣀⣤⣤⣴⠶⠛⠋⠁⣀⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⢀⡴⠿⠛⠛⠉⠀⠀⠀⠀⠀⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢣⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠹⣯⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢉⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣣⡞⠀⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠙⢿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠈⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢠⠀⢨⣿⠉⠙⠀⣀⣠⡤⣤⣠⡤⢤⡄⠈⠋⢉⣿⡄⠠⠃⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⣾⡟⠁⠀⠀⠀⠄⠀⠈⣧⠀⠀⠀⠀⣆⠀⠙⢦⠀⠰⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠃⡼⠃⢀⡴⠁⢀⣀⠀⠀⡀⠃⠰⠀⢀⡀⠀⢱⣄⠀⠁⢤⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⡼⠗⢀⣠⡻⠗⠛⠃⠀⢰⡄⠘⣏⣤⡀⠻⡆⢰⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣼⡇⣴⣿⣽⣽⡆⣿⠀⢠⠈⢧⢠⣟⠿⣻⠆⣵⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢷⣌⠁⠈⢌⡙⠁⠀⠀⠀⠈⠃⠁⠈⢁⣴⠟⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⣀⠙⣷⠷⠋⠄⠀⠀⠒⠀⠀⠰⣗⢿⢿⡉⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠘⣶⢠⡆⡼⠃⢠⣶⡛⠛⣲⡄⠘⣶⢠⡷⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⣽⣴⠛⡇⠀⠸⣿⣿⣿⣿⠏⠀⢷⢞⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡅⠸⢇⠀⠀⡼⢻⡟⢫⡀⠠⣾⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢻⡿⣿⣶⣟⣾⢾⡟⠛⠛⡻⣧⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡝⠀⢾⣿⣿⣿⣶⣥⣤⣤⣶⣿⡿⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⠄⠈⡉⣿⣿⣏⣿⣿⡟⢹⡿⠀⣺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠹⡷⠀⠀⠑⣿⣿⢟⠟⢛⠁⢷⡖⠤⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠻⢛⡇⠀⠘⣿⡃⠀⠐⠜⠀⣘⠃⠀⢈⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠠⢹⣇⠀⠀⠳⡦⠀⠀⠀⠀⢾⠈⠀⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣇⠀⠀⠀⢹⡄⠀⢸⡷⢆⡀⣠⣾⠏⠀⡰⠇⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠀⠙⢷⡀⠼⣡⣼⢧⡄⡟⠀⢸⠁⠀⠀⡀⢜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠛⣧⠀⠀⠀⢸⣧⠀⠙⠀⠆⠁⠁⢠⡟⠀⠀⢶⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠙⣟⡀⠀⠈⠛⣀⡀⠀⠀⡀⢀⡿⠇⠀⡀⠀⡀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠔⠀⠀⠀⠀⠞⣡⣦⠀⡪⢿⢁⠆⢴⡃⠺⠰⠀⢰⡿⡶⢬⠀⢠⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠛⠀⠐⠒⠁⠈⠁⠐⠁⠂⠐⠀⠀⠘⠃⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⡀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠂⠀⠀⠀⠀⠀⢴⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣾⠇⠁⠀⠀⠁⠸⣦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠐⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⡴⠂⠀⣄⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠲⠂⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠭⢶⠞⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⣄⣀⣀⣠⠀⠐⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⢠⠘⢋⠉⠙⠋⠀⠁⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢸⣡⡴⠄⣸⢃⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠸⣿⣏⠠⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⠃⢽⢛⣤⡵⠶⣛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠋⠶⠶⠉

⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⢳⣄⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⢠⣾⣿
⠘⠂⣼⡇⠃⠀⠀⠓⢸⣆⠸⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣶⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣿⣿⣿
⠀⠹⣯⠐⣰⠄⠠⣄⠈⡿⠆⠀⠀⠀⠀⠀⠀⠈⢻⣏⢙⣿⣿⣿⡋⣹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠘⣦⠀⠶⠆⠈⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢸⢶⣖⣦⡾⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⡧⠀⠁⠈⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣼⠁⠀⠀⠀⠀⠀⡸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢰⠈⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⡆⢸⡀⣀⡀⣠⡆⠰⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⠃⢃⠸⠟⠛⠛⠟⠀⠃⢸⠄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠁⠀⠾⠀⢸⣂⣬⠄⣸⠖⣸⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⢶⣶⣇⠸⣿⡟⢠⡿⣾⠋⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣄⣀⡍⣹⢞⣈⣫⣤⢖⣻⠀⠀⠀⠀⠀⠀⠠⣾⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⣿⣿⣿⣿⣿⣿⡏
⠈⠁⠀⢬⣭⠿⣥⡼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⣿⡿⢿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⣿⣿⢿⣿⡏⠉⠁
⣿⣿⡿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⠖⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠢⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⠀⢸
⠀⠀⠀⠀⠰⡀⠀⠹⡄⠸⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡽⠏⣠⠏⠀⢀⠆
⠀⠀⠀⠀⠀⠁⠀⠀⠉⠂⢈⠻⣦⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⣴⡟⠁⠐⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢫⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠉⠲⣤⣠⠠⠀⠀⠄⣄⣤⠖⠉⠀⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢀⢸⡿⠀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠻⠀⠀⢀⣀⠀⢿⡇⡀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠈⠾⠁⠚⠁⠀⢀⣀⠄⠀⠠⠄⠀⡠⣀⡀⠀⠈⠃⠈⠷⠁⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⡟⠋⣀⣀⣀⠀⠨⣧⡄⠀⠀⢀⣴⠅⠀⣀⣀⣀⠙⢻⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣹⣻⡿⡟⣿⣿⣷⡎⣀⠀⠀⣀⢱⣾⣿⣿⣻⢿⣟⣏⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡙⠦⣙⣩⣿⢿⣿⡟⠀⠀⢻⣿⡿⣿⣍⣋⠴⢋⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⢻⣿⡇⠀⠀⢸⣿⡟⠀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠃⠀⠘⣿⠋⠀⠀⠙⣿⠃⠀⠘⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠀⠈⠲⣶⣶⠖⠁⠀⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣀⣠⡠⣨⣅⢤⣄⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠶⠶⠞⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⢄⣀⣭⣑⠢⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⢄⣒⣥⣬⠢
⢀⢻⣿⡇⠀⠉⡙⠮⡢⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⢻⠿⢿⣿⣷⢧
⢸⣸⢰⡇⠀⠀⢙⡇⠐⢈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁⠈⠀⠀⢈⠆⠁⣾
⢸⣟⢠⡜⠀⠀⠀⠀⠀⠀⠳⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣽⢏⣴⡿⠀⠀⠀⠈⠀⡐⣿
⢘⣏⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣥⣿⠯⢻⠟⠀⠀⠀⠀⠀⢰⡇⣿
⣿⣯⢸⣿⠀⠀⠀⠀⠀⠀⠳⣄⢿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⠁⢀⠀⠀⠀⠀⠀⣰⣿⢃⡏
⣿⣿⠀⠹⢇⠀⠀⠀⠀⠀⢀⢹⣻⣿⡟⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢿⣿⡇⣿⢀⡟⠀⠀⠀⠀⠉⠩⠉⠸⡇
⢸⡘⠧⠀⠈⠀⠈⠀⠀⠀⢸⣆⣿⣿⣧⣿⣿⣫⢟⡿⠛⡏⡉⣯⠙⣟⠻⡻⣿⣯⢇⣿⢸⣿⡇⣿⣼⠃⠀⠀⠀⠀⠀⠀⠜⣣⣿
⢸⢿⣦⣌⢲⣀⢁⡀⠀⠀⣸⣿⡌⣻⣿⣿⣝⣡⡾⠃⡈⣹⡇⢸⡇⢋⡴⡄⣽⣿⣿⣿⣿⣿⣡⣿⣿⣄⠀⠀⣴⠊⠀⣠⣼⣿⣿
⠘⣿⠟⠁⠘⣿⣿⢇⣶⡄⣿⣿⣿⣾⣿⣿⣿⡿⣁⢌⡥⠛⣧⣾⢠⡋⣦⢰⣿⣿⣷⣿⣿⢿⣿⣿⣻⣿⢂⣾⣧⣡⡞⣱⣦⢹⡟
⠀⢻⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⢟⢿⣿⣭⡛⣏⣬⠇⡀⠙⠃⡾⢣⠿⣬⣉⡝⢻⣿⣿⠷⣿⣿⣿⣶⣾⣿⣿⠟⣰⢟⡡⠀⣸
⠀⢸⣷⣄⠀⣄⢙⡻⣿⣿⠿⣿⣱⣷⣾⣿⣿⣿⣮⡛⣰⠀⢲⣶⡆⢸⡇⢺⣋⣴⣯⣿⣿⣿⣾⣿⣿⡿⠿⣿⢋⡾⣱⢟⣤⣾⣿
⠀⢸⣿⣿⣦⣿⣎⠛⠋⣠⠎⢱⣯⢿⣿⣿⣿⣿⣿⣖⠿⢇⣸⣿⣿⣿⡏⠘⢟⣽⣿⣿⣿⣿⣿⢛⡿⣧⣴⣦⣈⡀⣫⣿⣿⣿⣿
⠀⣾⣿⣿⣿⣿⣽⣶⣷⡇⢸⠀⠹⣷⣬⣝⣿⣿⣿⣿⡆⠹⣿⣿⣿⣿⠿⣷⣿⣿⣿⣿⣿⣋⣥⠊⡀⠏⠙⣿⣿⣾⣿⣿⣿⣿⣿
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣇⣸⣄⠐⢌⠛⠛⢂⡀⠉⡏⠹⣶⡏⣿⣽⡏⠀⠿⠹⠀⢛⡏⠉⠉⢠⠖⠀⢠⢐⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠹⡛⢦⣄⠀⠰⣾⡇⠀⠀⡸⣿⣶⣶⣶⣶⣶⡦⠂⠀⢈⠀⢀⠴⠋⣰⣧⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡐⢿⣿⣿⣿⠀⣀⠀⣀⣼⣿⣿⣿⣿⣿⡓⠀⢠⡄⠀⣿⣿⡿⢛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⣿⣷⡀⣬⣦⡡⣯⡿⣿⣿⠿⣄⡑⢦⣤⣴⢇⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠩⠴⢛⣵⣿⣿⣿⡿⣶⣍⠲⠶⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣛⣿⣟⣀⣆⡀⢸⡟⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡜⢿⡿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣯⣵⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⠙⣿⣆⢻⡟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢻⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠘⠃⠘⡏⢿⠃⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⡿⣼⣿⡿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⢿⡝⢂⠰⣄⢳⡿⠀⣼⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡆⢸⡟⣼⣿⣿⡇⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡇⡈⠇⠀⢲⣿⣼⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⢸⡿⣹⣿⣿⠁⢸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠛⣧⠰⣄⠀⠙⠛⠤⣿⣿⣽⣿⣿⣿⣿⠞⢿⣿⡿⣫⣿⡇⢀⣿⣿⠏⢀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡻⢶⣿⣧⡒⠬⢢⣿⣿⠘⣿⣿⣿⣿⡗⢘⣿⣷⣿⣿⣇⣾⣿⣿⢦⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⡈⣙⠙⣳⡾⢿⡏⠀⣿⣿⣿⣿⡟⢾⣿⣿⣿⣷⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⣋⢁⣾⠇⢰⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠄⢿⣿⣿⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⣿⠿⢿⣎⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣰⡟⠁⠀⠀⢻⠸⡄
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢆⡿⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠠⢁⣶⣶⣶⣬⣑⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣸⠃⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠄⣼⡟⠀⠀⠀⠙⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣿⠀⠟⠀⠀⠀⠀⠀⢠⡎⢀
⠀⠀⠀⠀⠀⣿⠃⡀⠀⠀⠀⠀⠈⠳⡈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣿⠀⠀⠀⣀⠀⠀⣰⠟⠶⢿⡄
⠀⠀⠀⢠⠀⣿⠀⣇⠀⠀⠀⠀⠈⢳⡌⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⠃⢸⣿⣦⠀⠰⡏⢰⡶⠋⠀⡀⢸⣇
⠀⠀⠀⢸⠀⢿⠀⢻⡀⠀⠀⠀⠀⠀⢹⡄⠀⠈⢿⣷⣄⣤⡶⠞⢯⡹⣎⢱⣦⠠⣿⣿⣿⠀⢀⣿⡾⢃⣤⠞⢀⣿⡟
⠀⠀⠀⠘⣧⡀⠀⠈⣧⠀⠀⠀⠠⠽⢾⡇⠀⠀⠀⠙⣿⣮⣉⠓⢦⣽⣯⠘⣯⣓⠦⠈⠻⣦⣈⡀⠀⠘⣧⡀⣾⣿⠃
⠀⠀⠀⠀⠸⡷⣀⠀⠸⣆⠀⢀⣴⣀⡀⠁⠀⠀⢀⣴⣫⣿⢃⠎⡆⢃⡹⡇⡈⢫⣛⡓⠶⠈⠛⠻⣟⠳⡌⠻⣿⣿
⠀⠀⠀⠀⠀⠹⣎⢳⡄⠙⢷⡼⠟⢋⣹⣴⠆⢠⠞⡽⠛⢁⡤⢞⡡⡻⡱⠝⣆⠀⡏⠉⠉⢑⠂⠀⠀⠁⠙⠀⣹⡏
⠀⠀⠀⠀⠀⠀⢡⠘⣅⠀⠀⠀⠒⠻⠉⠀⠀⠈⠀⠀⠀⠊⠀⠋⠀⡘⢻⡀⠈⠃⠡⠀⠀⠘⢧⡀⣙⠲⢤⣄⣿
⠀⠀⠀⠀⠀⠀⠈⠀⣿⣷⡄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠘⢦⠀⠀⢀⡜⠁⣠⣶⣿⣿⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣼⣷⣤⠀⡇⠀⢰⣠⠀⢠⣾⡡⠤⠤⠀⢿⡀⠀⡄⠀⠀⢰⣼⠇⣸⠿⣿⣿⡇⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣆⠀⡇⠀⣾⡇⠰⠋⣡⣴⣶⣶⣦⡄⠈⠂⣿⠀⠀⠈⢿⡀⢿⣄⠈⠉⣠⠆⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠻⣆⢧⠀⣿⡄⠀⢨⡉⠸⣿⣷⠂⢹⣶⣄⠘⣧⠀⠀⠘⣇⢸⡍⢛⣉⣡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢂⠀⢹⣇⠀⠀⠑⢤⠈⢀⣠⠞⠋⢹⣆⢹⠆⠀⠀⠙⢾⣇⠈⠛⠻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢦⠈⢿⡄⠀⠲⣤⣤⣤⣤⣤⣴⣿⡿⣿⠀⠀⠀⠀⠘⣿⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠱⣄⠙⢷⣄⡀⠉⠛⠛⠟⠛⠋⠀⠹⡄⠀⠀⠀⠀⢸⣧⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⠉⠳⠄⠀⠀⠀⠀⠀⠀⣿⠴⡶⠶⠶⢿⠇⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣶⣤⡀⠀⠂⠐⠀⢂⠈⠛⢿⣆⣤⠇⠀⣁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣿⠇⣹⠛⠻⠷⣦⣄⣀⠈⠀⠄⣀⡼⠛⣲⠞⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣈⣴⣾⠋⢰⡏⠀⠀⠀⠀⠉⠛⠛⠛⠿⠁⠰⠞⠁⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣠⡴⠞⢩⠟⠁⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠏⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠟⠃⠀⠀⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⠾⠟⠛⠛⠉⠁⠀⠀⢀⣠⡾⠃⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠛⠉⠀⢀⣀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠉⠀⠀⠀⠀⠀⠀⢠⡿⠛⠁⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠉⠉⠀⠀⠴⠾⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⢠⠟⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠻⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣤⣄⠙⢿⣷⣄⡀⣀⣀⣠⣤⣤⣀⣀⡀⣀⣴⣿⠟⢁⣤⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣷⣤⡈⠻⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠋⣀⣴⣿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠘⠛⠛⢛⣛⣛⠛⠃⠘⠿⣿⡿⠟⠀⠙⠛⣛⣛⡛⠛⠛⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠘⠛⠉⣉⣥⠶⠛⠀⠀⣼⡄⠀⠘⠳⢦⣌⡉⠙⠛⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠚⠉⢠⣤⡤⠶⠚⠁⠙⠲⠦⣤⡤⠈⠙⢃⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣶⣶⣶⣾⡿⠿⠟⠋⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⣀⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠲⣾⢏⡾⣁⠤⠀⠁⢀⠈⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣿⠄⢰⢏⠎⠀⣉⠐⠐⠀⠀⣀⢢⠄⠈⣿⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠊⡌⡠⠴⠀⢀⣴⡄⠄⢹⡇⣀⡄⠘⣧⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡴⢾⢢⣀⡰⠆⠘⢋⣽⣧⠀⠈⠀⠸⡿⠂⢼⢤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡅⢀⠀⣿⠋⠁⠀⠂⠀⡀⠈⠠⠀⠀⣀⠀⡎⠘⣧⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⡾⠙⣦⡄⠀⢀⣠⢂⠀⠀⠀⠀⢀⣀⠴⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⠁⠀⠈⣇⠀⣪⣯⠾⢶⠀⠀⠀⠀⠻⢦⡸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡩⠈⣂⢠⠀⠙⣷⡆⡚⣋⠍⠒⠀⠀⠀⣶⢞⣑⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⠗⠤⣼⣎⠁⠀⠙⢿⣿⣡⡴⠂⠀⠀⠀⠸⢿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣲⡇⠀⠀⠸⣿⣆⡀⠔⠘⢻⣿⣿⣿⣛⣐⣿⢳⠶⢥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣅⣿⠅⠀⠀⠀⠈⢿⡿⢒⠀⡈⢻⣁⠀⣲⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡟⠧⠀⡐⠨⠄⠀⠱⢿⣷⣬⢙⣷⣾⠏⠀⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡗⠀⢁⡄⠀⠀⠢⡄⠀⠉⠳⠞⠉⡁⠊⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢈⣿⠀⠈⠀⠘⠡⡂⠈⠀⠃⠸⠠⣄⠁⠄⠁⠁⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⠘⠄⠀⡠⠂⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡈⡆⠹⣂⠄⠀⠁⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⡀⠈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⢰⡂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢄⣤⢀⡆⠀⠀⠀⣀⠃⠀⠁⠀⢁⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠁⣁⣀⠀⠀⢀⣀⣼⣤⠞⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠐⠛⠋⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠉⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠄⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣆⠀⢻⣆⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢠⣿⠀⠸⣿⣆⠀⠀⠀⠀⢀⣿⡟⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣾⡏⠀⣸⣿⣿⠧⣤⣄⢀⡾⠿⣧⠐⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡆⢸⠟⢠⣿⡿⠣⡄⠛⡍⢑⡶⣄⠠⠈⠺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⣾⣶⣿⡿⠁⠀⠀⢀⣴⠮⠭⡈⢡⢿⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡿⠁⠀⣀⣀⣠⣀⣴⣾⣿⣿⡎⢧⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡧⣐⣷⠛⠛⠻⣧⣍⠉⢛⡹⠃⠀⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠛⢿⠀⣾⠃⠀⠀⠀⠺⣟⠳⠛⠋⠀⠀⠀⠀⠀⠉⣠⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣿⣆⢿⡓⠀⠤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠹⣷⠬⢿⣀⣀⣤⡄⠈⠛⢿⣒⣦⣄⡀⠒⢀⣤⣙⣻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡈⢹⣗⠀⠀⠀⠬⠛⠻⢶⣦⣬⠝⠉⠭⠿⠻⠿⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠿⣿⡾⣻⣧⡀⠀⡀⢀⠐⢋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⡏⢿⠀⠰⢿⡆⢼⣿⣇⠀⠀⠈⠀⣸⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠺⣦⡀⠘⣵⠾⣿⣿⡆⠀⠀⠰⠀⢰⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⢀⠚⣿⡀⠰⣷⣿⣿⣇⠀⠄⠃⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⠂⠠⠄⢻⣷⡀⠘⢿⣿⣿⡄⠀⠀⢰⣿⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⢿⣄⠀⠠⠏⣿⡄⠈⠉⠉⠁⠀⠀⠈⠁⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢼⣟⡀⠀⠀⠘⠛⠷⣦⡀⠀⠀⡤⡸⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡀⠂⣺⣯⡄⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⢐⣿⡋⠀⠀⠀⣀⠀⠀⢀⠀⠀⡀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⠿⠏⠛⠃⠀⠐⠒⠋⠐⠀⠈⠀⠘⠑⠂⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣞⣓⡒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣀⠀⣀⣤⡤⢤⣤⣴⣿⣿⣟⡚⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢁⣿⣱⣿⣿⣿⣋⣻⣧⢸⣿⣿⣿⣿⣿⣎⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⣯⣟⣿⣿⣿⣿⣷⣿⣿⡿⣿⣿⣿⣿⣯⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⣿⣿⣿⣿⡿⣿⣇⢶⣆⣿⣮⣿⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣽⣿⡗⡋⠉⠉⠥⠈⠙⢣⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⣝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠲⠦⢌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⠈⠐⠢⠠⢤⣤⣄⣠⣶⣤⣤⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠛⠛⠺⢮⣍⢝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠖⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⡶⠤⠤⠶⢶⡶⢿⣿⣿⣷⣦⣀⣤⣀⣠⡶⠌⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠻⠓⠺⠿⢿⣿⣿⣿⣿⠫⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠿⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠐⠷⠦⣤⣀⣴⠿⠻⡆⠀⠀⠀⠀⠀⠀⣿⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⣀⡀⠀⠀⠀⠉⠻⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⡆⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠠⠿⡵⠀⠀⠀⣀⡀⠀⢴⠁⠀⣀⣀⣀⣀⣀⣘⣿⣄⠀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠰⣦⣄⠻⠼⠃⠁⢸⣿⠛⠛⠋⠙⠛⠛⠛⠿⢿⣷⣄⡀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣀⠀⠤⠔⣇⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠓⠦⠤⣤⣤⣤⠴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠒⠒⠀⠀⠀⠀⢹⣿⡄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⣠⡾⠁⠀⢀⣠⣄⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢁⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢋⣤⡶⠿⠛⠋⠉⠀⠀⣀⣀⣽⣿⣦⣤⣤⣤⣄⣀⣴⣿⣿⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠟⣩⠞⠋⠁⠀⠀⢀⣤⣶⠾⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠀⠰⠋⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣶⡄⠀⠀⠀⠀⡴⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⠃⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣠⣤⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠲⠚⣋⣍⣽⡷⣄⡀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠀⣀⣀⠀⣐⣺⡥⠚⠼⠛⠷⠛⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⣏⠀⣴⠟⠁⠉⠉⠁⡾⠛⠃⠀⠀⠿⠷⠀⠀⠹⣆⠀⠀⠀⠀⢰⠟⠻⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣷⠹⡾⣇⠀⠀⠀⠀⣸⢳⡆⠀⠀⡰⠆⠀⠀⠀⠀⢸⡄⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠘⢷⡻⠾⠀⠀⠀⡴⠃⠘⠋⠀⠀⠘⠇⠀⢰⣿⣿⣿⣇
⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⢀⣼⠟⠂⠀⠀⢰⠁⠀⠺⠤⣤⠈⢦⠀⠀⠀⠙⢛⡿⢉⠇
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⢸⠀⣷⠀⢤⣄⠀⠈⠃⠀⠀⠀⣬⡴⠋
⠀⠀⣾⠁⠀⠀⢀⣀⣠⠶⠿⣿⠄⠀⠀⠀⠀⠀⠀⠘⣆⠘⣆⠀⠈⠉⠀⠀⠀⠀⠀⣼
⠀⠀⠉⢷⡀⠀⠉⠉⠀⢠⡾⠛⠛⠛⠿⣦⣤⠶⠶⠶⣬⣷⣌⠳⠶⠶⠀⠀⠀⣠⠾⣇
⠀⠀⠀⠀⠻⣦⡀⠀⠀⠋⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⢀⣽⢿⣷⡶⠤⠖⠋⠀⣠⢾⣿⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣴⠟⢁⡿⠈⣧⠀⣠⡴⠛⢡⠏⢸⡇⠈⠙⠛⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⣀⢀⡆⠀⢀⡽⠿⠋⣼⠇⣠⣾⣻⣇⠀⢠⠟⣀⣸⣧⠀⠀⠀⢀⡀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢠⡇⣼⠁⠀⢸⡇⠀⣸⡟⠋⢀⣿⡿⠛⢷⡏⠈⠻⣏⡉⠀⠀⠀⣾⠁⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣳⠃⠀⠀⢸⡇⢀⡿⠁⢠⣿⣿⠇⢠⡟⠀⠀⣠⠏⠀⠀⠀⢸⡏⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⢸⡇⢸⠃⠀⣿⣿⣿⢀⣿⠁⣠⠞⠁⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠇⠈⠀⠸⠟⠻⣿⣼⠃⠐⠁⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠿⣶⡿⠟⢀⡉⠛⠙⠛⢱⠟⡻⡿⣶⠞⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣴⣾⠃⠢⡄⠘⣿⡀⢀⣾⠀⢂⣤⣐⣿⣶⡸⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢰⠿⠁⠠⢾⡿⣰⡟⣷⠿⢿⣦⣿⣟⠧⠌⠙⠿⡜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⢠⡦⢠⣾⣿⣷⡿⠹⠁⠀⠸⠿⣿⣿⣷⣦⡁⢠⠁⠘⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⣽⢇⣿⡤⣶⠋⠈⢹⡗⣀⣤⠀⠀⠀⠚⢠⣍⡁⠈⢻⡄⣧⠀⣶⣌⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣿⢃⡟⢹⡇⣧⣲⣾⡇⢁⣤⣶⣦⣤⣴⣦⡈⢧⣹⡦⢢⡇⢹⠀⠉⠸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⢱⠊⠁⡞⡅⣿⣿⡟⣠⣮⣿⠏⠁⠈⡉⣶⣿⡆⠙⣷⣸⡇⠼⣁⠀⣶⣾⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣼⡆⠀⢃⠃⣿⣿⠁⠹⡟⠁⠻⣯⣾⡟⠉⠋⠷⡈⣾⣿⡇⢠⣏⠰⠁⢻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡖⣼⣇⣿⣏⡀⠀⣤⠜⣈⢻⡿⠂⣘⢂⠈⣅⠹⣿⡇⣜⢹⣦⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡼⠻⢻⡿⡙⢠⣧⣾⠟⠻⠧⠸⣿⣿⣷⣿⣸⡿⠓⠘⣞⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠃⣰⠸⣧⠇⠸⣿⣿⣿⣶⣦⣾⣿⣿⣿⣿⡿⣷⣴⢄⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⢻⡀⠀⡈⣿⣿⣿⣿⣿⣿⢇⡟⠏⣹⠟⣸⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⣀⢀⢷⣦⣻⣷⡳⡜⢻⣟⣡⣎⣠⣾⡃⣰⣂⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠖⠀⠙⣦⠘⠇⢉⡿⠛⠛⡿⠛⠻⡇⠹⣄⣿⡏⠫⠉⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢋⠤⠀⡤⢻⣄⣾⠅⢀⣾⣽⡆⡀⣥⣴⢟⠛⠓⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⡆⠀⠀⠉⢈⠉⠘⢳⡶⢴⡶⡟⢣⣧⡀⢽⡢⡀⡄⣀⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣡⠜⣡⣞⣴⢃⠇⢸⣆⡼⠁⣆⠱⣅⠀⠋⠑⠆⠑⡘⠳⡌⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢀⠠⠠⢹⠺⣇⡆⡎⠈⠁⡴⠹⡄⣿⠘⣄⠘⢶⠰⡛⢂⢀⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢡⣾⠃⢼⣾⠱⢨⡱⣿⠆⡿⠱⠸⠀⣿⣄⢹⡇⢸⠑⡇⣼⣤⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠟⢡⢀⣼⠻⠀⣀⠱⠏⠀⢡⠇⠣⢀⠉⡍⠹⣏⠀⣼⣣⡇⠀⠙⢻⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⠂⣿⣿⢹⠃⠈⠏⠀⠀⡄⢈⡀⠀⢀⡀⠁⠀⢋⣼⡿⠙⠛⣰⣄⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠔⠀⡋⠋⠸⠀⠰⡖⠄⣆⠀⠸⠃⣷⣾⡇⡀⣦⣿⣘⣴⡇⢀⡏⠈⠈⢿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣵⡶⠋⠙⣴⠀⣧⠀⠹⣌⠛⠃⢀⢸⣿⣿⣱⢉⣿⠿⠛⡻⡀⢸⡇⢳⣴⣶⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⡡⢀⡿⣦⢠⡀⠐⢿⣇⠀⠘⠀⣯⡿⠋⢰⣿⡀⠀⠈⡡⣹⠉⠈⢻⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠟⠐⡫⣼⣿⢦⣻⣄⣙⣿⢠⣄⢀⠟⡥⢸⣿⣿⣷⣴⡞⢷⠙⠀⠘⣿⠻⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣃⡀⠀⠀⣼⢘⠈⢳⣌⣿⣿⢸⠛⡎⠀⠃⡌⣿⣯⢾⡟⢹⠋⢆⠑⠐⣾⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢿⣿⠀⢼⡿⡉⢠⠸⢿⣯⠹⣿⡠⡇⠀⢸⣷⢋⣵⠟⠐⠻⠀⠈⣆⠠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣾⣧⣠⣡⡆⣤⣰⣿⡷⠻⢷⣿⣼⠟⠻⢿⣷⣿⣠⣇⣿⣧⣹⣗⣼⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠁⠉⠁⠈⠉⠉⠁⠀⠀⠉⠁⠀⠀⠈⠉⠉⠉⠈⠉⠉⠉⠉⠀⠉
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⡀⠀⠀⠀⠀⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠀⢻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠃⠀⠈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠀⠀⢀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⠃⠀⠀⠀⠈⠉⠹⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⠀⠀⢠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⣠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠏⠀⠈⠹⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⢹⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⠸⠿⠟⠛⠀⠀⠀⠸⠿⠿⠇⠀⣿⣿⣿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣤⡶⠟⠛⠛⠻⣶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⡀⠀⠀⣠⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢶⡿⣷⠀⢸⣿⣯⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣷⠏⠀⠸⣷⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⣤⣦⣄⠸⣿⣿⣿⣿⡟⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣇⠀⠙⡟⠁⢠⣿⣿⣿⣿⣿⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠛⠛⢚⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠉⠉⠉⠉⠉⠉⠉⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⣰⠀⠀⠀⠀⢸⣿⡄⠀⣿⡿⠋⠉⠙⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠸⣿⣿⠀⢻⡇⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠹⣿⡆⢸⡇⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠘⣧⠀⠀⠀⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⢹⠀⠀⠀⠀⠀⠀⢸⣧⠀⢻⡆⠀⢰⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⢻⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠛⠶⢶⡌⠉⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⡴⠟⠁⠀⣸⣤⣤⣤⣤⣀⣀⣀⣸⣧⣀⣀⣰⣤⡷⢦⣾⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⠴⠖⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⡠⠴⠻⢷⣷⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⡀⠀⠀⢀⣼⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣷⣽⡝⢏⢻⣿⣿⡭⠿⠿⠿⠿⣫⣋⣉⣁⣀⣀⠈⠉⠻⣆
⠀⠀⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⠠⠗⠒⠦⠤⢤⣤⣍⡁⠘⠋⠱⣄⠀⠹⣆
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣶⣤⣀⡀⠀⠈⠐⠙⢦⡀⠀⠈⠳⡀⠹⣆
⠀⠀⠀⢉⡟⣹⣿⣿⠋⠉⠉⠙⢷⣜⣟⢿⣿⣿⣿⡿⣗⠺⠉⠙⠛⠿⣿⣿⣶⡄⠀⠀⠙⢦⡀⠀⠘⢦⣹⣆
⠀⠀⠀⣸⠃⠈⠿⣿⠀⠀⠀⠀⠀⠙⠿⠦⠉⠛⠋⠁⠈⠛⠦⣤⣀⠀⠠⠉⠻⣿⣦⠀⠀⠀⠙⠆⠀⠀⠉⢻⣆
⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⢲⡀⠀⢻⡄
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣧⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠃⠰⡌⢿⡄
⠀⢸⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⣷
⠀⠸⣏⠉⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢹⣧
⠀⠀⣿⢠⣤⣈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⣴⠏⡄⠉⢿⣿⠶⣄⠀⠀⠀⠀⣿⣷⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⣾⣏⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⢸⡏⠀⠙⠲⠄⠀⢠⡟⠀⠀⡴⠂⢠⣭⣭⣟⣛⣛⠻⠿⢿⣷⣦⡀⠀⠀⠹⣯⡿⢿⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⣿⡇⠀⠀⠀⠀⢀⡿⠁⠀⠀⠁⠀⢠⡘⠂⠈⢿⣿⡿⠶⣄⠈⠉⠁⠀⠀⠀⠻⠏⠾⢁⣼⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⢸⡇⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠛⠶⠆⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠠⣿⠡⣤⡙⢿⣤⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣆
⢸⣿⠀⠀⣴⠟⠁⠀⠹⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⡃⢀⡙⢷⣄⡀⠀⠀⠀⣠⡾⠁⢀⣿⣆
⢸⣿⠀⢀⡙⣷⡀⠀⣠⣄⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠅⣠⠟⣵⠋⠀⠀⠻⣷⡀⠀⣴⠟⠀⢀⣾⠋⢻⣆
⢸⣿⠀⠸⣇⠀⠀⠀⠀⠉⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠶⠛⢁⡾⠁⠀⠀⠀⠀⠙⣧⡾⠋⠀⣰⡟⠁⠀⠀⢹⣆
⢸⣿⠀⠀⠘⣿⠦⣤⣀⣀⠀⠀⠀⠀⠀⠉⠳⢄⡀⢸⡇⠀⠀⠀⠀⠀⢠⣿⣧⣤⣤⡶⠋⠀⠀⠀⠀⠀⢠⡾⠋⠀⢀⣾⠋⠀⠀⠀⠀⠀⢻
⠘⣿⠀⠀⠀⠹⣦⣄⣈⡉⠙⠛⣛⣿⡿⠂⢀⡟⠀⣾⠃⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁
⠀⢻⡇⠀⠀⣄⡀⠉⠉⠙⠛⠋⠉⠁⠀⠀⠈⠀⠘⠃⠀⠀⠀⢀⣴⡿⠁
⠀⠘⣿⠀⠀⠀⠉⠛⠲⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠁
⠀⠀⠀⠻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⡀⠀⠀⡘⠀⠀⣈⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠁⢀⠄⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⡡⠚⢁⣀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⡐⠁⠀⠁⠀⠑⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣃⠀⠀⠀⠀⠴⣅⠘⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⢳
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠐⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡂⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡟⡚⠀⠀⠀⠀⠙⢎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣵⣿⡃⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠘⡇⡋⡀⠀⠀⠀⠀⢀⢫⣦⠙⣆⠀⣀⣀⣀⣀⠀⢀⠏⣾⣿⣿⣷⠃⠀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠠⢀⣼⢿⣿⠷⠘⠉⠁⠈⠀⠈⠉⠉⠀⠹⣿⣿⣋⠔⠀⠋⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡞⠿⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⠻⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡐⢤⣀⠐⠈⠀⠀⠀⠀⢀⣠⣤⣀⠀⡀⡆⠀⠀⠀⣴⠤⣤⡀⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢬⣀⣀⡸⠀⢰⡀⠀⠏⠰⣾⠃⢳⠁⠀⠀⠀⠀⡏⠺⠏⡟⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⣀⠀⢣⠀⠈⠀⠀⠐⣋⠀⠀⠀⠀⠀⠹⠀⠉⢰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠉⢀⠀⢱⣤⡀⠀⠀⠀⠀⠀⣀⣤⣀⣤⡐⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠡⠄⡁⠁⠀⢀⠀⠀⠀⠉⠙⠿⠃⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠁⠀⠀⠀⠐⠀⠠⢄⡀⠀⠀⢀⡠⡦⣀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣀⢀⠀⠈⠉⢍⣁⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠐⠈⠉⠀⠀⠀⠈⡜⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠛⠓⠾⢟⠆⠈⢣⡔⢹⠇⠀⠀⠀⠀⠀⢀⣀⠴⠞⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡜⡰⠋⡱⠒⠀⠀⠀⠀⠃⣼⠀⠀⡴⠒⠒⠊⠉⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠘⠒⢁⠜⠁⡴⢦⡀⠀⠀⠀⠳⠴⡞⠀⠀⠀⠀⢀⠤⣄⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣁⣠⠞⠛⢦⡙⠦⣄⣀⡠⢴⡁⠀⣠⠔⠊⠁⠀⢹⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣴⡋⠩⡈⠳⣄⡄⠙⢷⣄⠀⠀⠀⠓⠋⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣷
⢀⡤⠄⠠⠤⣴⠋⠀⠑⠄⠙⠂⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⣀⣀⠀⠀⠀⢸⠀⠀⠀⠈⣿
⠻⠀⠀⢀⡞⣿⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡜⢁⠈⢣⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⢠⡏⠀⣿⠈⠨⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⢀⡟⠀⣸⣶⡦⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠀⣇⠀⠀⠈⢏⢲⡄⠀⠀⠀⣀⣴⡾⠟⠁⠀⠈⠁⠀⣧⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⣠⣤⡄⠀⠻⢿⣄⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠛⠿⣶⣦⣿⠀⠀⠀⢰⣿
⠀⠀⢀⣤⣤⣿⣿⠈⠻⣦⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⢸⡏
⠀⠀⢻⣏⠻⣯⠙⢷⣄⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⢸⡇
⠀⠀⠀⠙⠷⣿⠀⠀⠉⢉⡤⠾⢅⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⣠⠞⠉⠀⠀⠀⠙⠲⣌⠉⢿⣶⣄⠀⠀⠀⠀⠀⢀⠇⢸⡄⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡙⠛⠃⢰⡄⠀⠀⢸⠀⢸⡇⠀⠀⢸⡛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠈⠀⠀⠀⡆⠀⢸⡇⠀⠀⠈⠃⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⢀⣼⠀⠀⠘⣇⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⡜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠘⢨⣿⣿⣿⣦⡀⠛⡧⠀⠀⠀⠀⠀⣿⣷
⢀⡴⠚⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⢈⣿⣿⣿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠸⣿⣧
⠘⣆⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⢀⠟⠀⣿⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆
⠀⠘⣆⠀⠀⠀⠈⢦⡤⢦⡀⠀⢀⣀⠐⣧⠈⠳⡄⠀⡠⠋⠀⢰⣿⣷⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠘⢦⠀⠀⠀⠸⣄⠀⠈⠉⠁⠀⠉⠈⠳⣄⠹⠊⠁⠀⠀⢸⣿⣿⡆⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠳⣄⠀⠀⢈⠋⠻⢄⡀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⠀⢀⠞⠙⠖⣺⣄⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠀⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟
⠀⠀⠀⠀⠈⠲⠤⠊⠁⡌⠉⢻⠂⠸⠃⠘⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠁⠀⣰⣠⠟⠳⢄⣀⣀⠀⠄⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡰⠃⠀⠀⣄⡀⠃⠀⠀⠀⠀⠀⠀⠘⢿⠇⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⢀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠗⠀⠀⠀⢠⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠲⠒⠒⠦⢤⣤⣀⡀⠹⡆⠀⠀⠀⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣅⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠂⠐⠒⣶⠀⠀⠀⠀⠸⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⣷⣞⠻⠇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⠗⠈⠉⠀⣠⡄⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⠀⠀⣀⡴⠞⠉⠳⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠟⠛⠿⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠉⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣞⣧⣀⣀⣠⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣵⣿⣿⣿⡇⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣠⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠙⣮⡛⢦⣀⠀⠀⠀⣀⣠⣤⣤⣤⡀⢀⡴⠟⠁⢀⡄⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠈⢷⠀⠈⠁⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠘⠳⠄⠀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡇⢴⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⡾⣯⣿⡟⠂⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣿⣋⠁⠀⠀⠀⠀⠀⠀⠀⠠⣽⣯⡶⠃⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠛⠉⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⢁⡀⠤⢄⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠙⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣄⣀⠈⠙⣛⣻⠏⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠶⠶⣤⣶⣤⢤⣄⣀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠻⣷⣾⡷⠉⠀⠈⢉⡉⠉⡱⡌⠃⠉⠈⠳⣮⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠘⣿⡿⢡⠏⠀⠀⡆⠀⠀⠀⢬⣉⠈⣆⠀⡀⠀⠸⣧⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡗⠀⠀⣿⢡⡏⠀⠀⠀⠩⣦⠄⠚⣉⡍⠙⣿⡄⣷⠄⠀⣈⢷⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⡄⠀⠀⠃⢸⣁⠄⠀⠀⠀⠁⣐⣴⣭⡇⠈⢉⠃⠻⠀⣴⠷⣾⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢹⣿⣄⣦⠀⢸⣷⣤⣴⣶⣞⠛⢡⣙⣸⣻⣠⡟⠀⠄⠀⠹⡤⢴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠹⡿⠃⢰⢸⡏⡀⠀⠀⠘⢦⡀⠉⠁⢀⢟⡔⠀⠳⠂⣦⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣧⠀⠀⠀⠀⣸⢸⣳⡟⠀⢸⡠⠀⠙⣻⣿⠏⠟⠀⠀⠀⠀⠈⠓⣤⣉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢷⣙⠇⠀⡄⠀⠙⢺⣿⣆⠐⣻⣿⡁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡝⠛⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠻⡄⠀⠁⠀⢠⡆⡟⢿⡿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠈⠻⣧⣴⣶⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣣⣀⣀⣀⠞⢀⡏⠀⠑⣤⣀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢰⣓⣶⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢍⠉⠁⣠⣾⣟⠀⠀⠀⠙⣳⣬⣅⢴⣄⡀⠀⠀⠀⠀⢀⣤⠞⣜⣭⡙⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡯⠀⠀⣠⡶⠛⠁⡱⠶⠾⢡⣤⣀⣀⡤⠶⠟⠛⠋⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢻⣈⠀⠀⠀⠀⠰⠋⠀⠠⣴⡃⠀⠀⢸⠏⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠈⣿⡄⠀⠀⠐⡁⠀⠀⠀⠙⠳⣶⡀⣸⠤⢀⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢃⣄⣾⣿⠟⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠙⠀⠹⣯⠀⠀⢀⡴⠆⠀⢀⠐⠉⠀⢚⣿⠟⡵⠦⠟⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡉⢳⣦⡄⢨⣿⠃⠀⠀⠀⠀⠀⠀⣀⣦⡞⠁⣀⡹⢒⠇⠀⠏⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠲⣏⠈⠐⠿⣯⡆⠀⠀⠀⢀⡶⣼⡿⠋⣀⣼⡛⢡⠏⢰⠥⣄⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣻⠄⠀⠀⢻⣧⡀⠀⣠⣼⠟⠉⠀⣰⡎⠃⣠⠋⠀⢠⡔⢸⡀⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⣧⣤⣄⠰⠙⠙⠇⢠⠿⠿⣤⣶⡾⠟⠀⣾⡛⢀⣶⠇⢀⣾⠃⢸⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢺⡭⠛⣧⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣼⢏⣱⡜⠋⠀⣼⣿⠀⢻⣿⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠙⢷⣭⠿⣄⠀⠀⠀⠀⠐⠀⢠⣾⣿⡽⠋⠁⠀⠀⠀⢐⣞⠀⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠶⣿⠃⠄⠀⠐⠀⠀⢸⠿⠃⠀⠀⠀⠀⠀⠀⣼⣿⠀⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠊⠠⡀⠀⠀⠀⠀⣠⣮⣽⣤⡀⣿⢁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠀⠁⠀⠀⠀⠀⠚⠀⠀⠀⠀⠐⠒⠀⠐⠖⠛⠓⠚⠋⠛⠛⠘⠛
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⠉⠀⠈⢻⣷⡀⠀⠀⣀⣤⣶⠿⣛⣩⣥⡶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠁⣠⣴⡶⢾⣿⡆⣀⣿⡷⢰⣿⠟⣫⣴⣿⠿⢋⣡⣤⣶⠶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣀⣴⡶⢿⡿⠟⠋⠀⠀⠀⣾⣿⣿⣷⣾⡿⢛⣉⣀⣤⣤⡤
⠀⠀⠀⠀⠀⢀⠀⢠⣿⠇⠀⠀⣠⣾⡿⠩⠶⠾⢷⣆⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣛⣉⣀⣀⣀
⠀⠀⠀⠀⠀⣿⣷⣌⠻⢷⣶⡾⢿⣿⠁⠀⣠⡄⠀⠙⠀⠀⠀⠀⠶⢶⣶⡄⠈⠹⠿⠿⣿⡋⠉⠉
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣄⠀⣿⡿⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⣀⡄⠈⢻⡀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠏⠀⣹⣷⢸⣿⠁⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠈⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⢠⣿⠇⠈⠉⠁⣠⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⣾⣟
⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⢾⣿⠀⠀⠀⠐⣧⣀⣠⠀⠈⠉⠀⠀⠀⠀⠀⠀⠟⣡⣴⣌⢻⡇
⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠘⣿⣆⠀⠠⢤⣈⣉⠁⠀⣶⠀⠀⠀⠀⠀⣠⡄⠴⠋⠐⢋⣾⠇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠉⠉⠛⠻⠆⠀⠀⢀⣴⣿⣷⣤⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣤⣤⣶⣿⠟⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠋⠛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⠁⠀⠈⠻⣿⣿⣿⣧⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣶⣶⣷⣴⣶⣿⣿⣿⣿⡇⢸⣿⠿⠟⠷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠉⢻⣿⣿⣿⡿⠛⠃⠘⣿⣤⠀⠀⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣼⣿⣿⣿⡇⠀⠸⣿⣿⣿⣧⣤⣤⡄⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠟⠙⠻⠃⠀⠀⠿⠟⠙⠻⠿⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠻⣿⣿⣷⣄⣤⣤⣤⣶⣶⣤⣤⣤⣠⣾⣿⣿⠟⠋⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠛⠛⠛⢛⣧⠀⠀⠀⠀⣽⡟⠛⠛⠛⠛⠛⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠛⣛⣉⣩⡿⠟⣻⣷⡆⢰⣾⣿⠻⢿⣍⣉⣛⠛⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⢋⣭⣶⣿⡿⠟⣡⣌⠻⢿⣿⣶⣬⣙⣻⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⢿⣫⣽⣟⢩⣯⢽⣿⣋⡿⣿⢳⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⡟⣻⠃⠹⡎⠹⡿⢷⡖⢩⡿⣤⡽⢂⠁⢋⢾⣟⣭⡿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢬⡽⠉⡰⣞⡱⡤⢤⣴⡀⠂⠀⠒⠵⠂⢀⢀⡀⠙⢠⠁⠉⠳⠔⠊⣷⢒⣯⢽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⢫⡹⢾⡁⠚⠙⠋⠐⡧⠆⡸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢋⠻⣎⡑⢟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠙⠛⠤⢈⠀⠆⠀⠆⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠢⠼⢿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⠛⠰⠄⠓⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠐⣣⣤⣶⣦⡘⣫⠽⣿⣿
⣿⣿⣿⣿⣿⣿⡿⣿⠾⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠈⠛⣯⣸⠟⢿
⣿⣿⣿⣿⣿⣿⡿⣙⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠠
⣿⣿⣿⡿⢿⡙⠢⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢹⣿⣿⣿⡶⢾⢤⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⢻⠻⠟⠀⠀⠀⠀⠈⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠄⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠧⠀⠀⢹⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠉⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠈⠻⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⣿⣷⣄⣀⢀⣀⣀⣤⡄⠢⡄⠰⠈⠙⠻⣏⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⣼⣿⣿⠋⢈⠏⢹⠀⠇⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢸⡷⢿⣠⣬⡶⠂⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠁⡰⠈⠀⠸⠀⠀⠀⢀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠀⠻⠿⠶⢦⣀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⢀⠴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠂⠀⢀⠀⠁⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠠⠙⠃⣀⣠⣴⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠑⢄⠀⠘⢶⣶⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠎⠉⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠅⢀⣠⠤⠴⠶⣄⠐⠀⠀⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠲⢦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠦⣤⣤⠀⡀⠁⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⣄⣀⡀⠀⠀⠠⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠱⡄⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠉⠀⠀⠀⠀⠀⠂⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⠂⠀⠀⠀⠀⠐⠉⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣠⣀⣤⡤⠀⡠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⢀⠐⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠂⢾⠎⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⣶⡋⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⢿⡿⠶⠶⠶⠿⣿⠇⠀⠀⠀⠀⠀⢹⢇⣴⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⠘⠻⡏⠀⠀⠀⠀⠀⠈⠙⢷⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⣿⡯⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣅⠀⠄⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠠⠀⠀⠀⠀⠀⣸⣿⡇⠀⠙⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⢬⡏⣹⢻⣶⣤⡀⠀⠀⠀⠀⠀⣠⣴⠶⠶⢶⣤⢤⣤⣴⠞⠑⢸⡁⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠛⣿⣿⡋⣤⠙⢿⠀⠀⠈⠄⢙⣿⠿⣿⣶⣾⣋⡉⠀⠀⠀⢀⣀⣶⡾⠋⠉⠀⠀⠈⠀⠀⠀⠀⠀⠘⡀
⡀⠀⠀⠀⠀⠀⠀⣠⣶⠞⠛⠁⠀⢀⠰⠋⢸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠟⠛⠛⠻⠿⠷⠿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⣦⣤⠀⠀⢀⣰⠾⠋⠀⠀⠀⠀⠀⠁⠀⠀⢸⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⣿⣿⣶⣶⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⣿⣿⡟⠁⠼⠗⢢⠁⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣿⠋⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠠⡀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⡿⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣇⠀⠀⠈⣿⡻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⢹⡟⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢣⡄⠀⠀⢿⠀⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⣿⠁⣠⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⢷⣾⣶⠛⣀⣿⡿⠛⢻⠶⠶⢶⣦⡀⠶⠎⠙⠳⣴⣿⠇⣼⠃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠀⠀⢻⣿⣆⣿⡟⠀⡀⠀⠀⠀⠀⠊⠁⣛⣄⠀⡄⠈⠛⣶⠁⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⣼⣿⣿⠟⠀⠘⠀⢐⡲⠒⠂⠀⠀⠈⠈⣷⠘⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⣁⡟⠀⡠⠐⠚⣽⡥⠄⠀⠀⠀⢶⣏⠙⣆⠐⡀⠀⠐⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣋⣀⡀⠀⠠⠀⢀⣠⠀⣠⣤⣤⣼⡟⠁⢿⡄⠁⣦⠸⢇⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢄⣶⠾⠛⠛⣿⡉⠉⠻⠻⣾⣿⣆⣼⠃⠀⠙⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠊⠈⢀⠀⠠⠀⠈⢿⣦⣀⠀⠀⠁⠽⠫⠀⠀⠓⡈⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⢫⣄⠈⢫⣄⣠⣶⡦⠈⣽⡛⠉⠀⠐⠀⠀⠀⠀⠀⠀⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠻⣇⡘⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠘⠿⣿⡾⠿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡛⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠂⠀⠀⠀⠀⠀⠀⠠⢄⣀⠱⠐⣶⣄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠐⠀⡀⠀⠀⠀⢈⣃⣀⣀⡙⠻⢦⣄⠀⠀⠀⠀⠀⠀⣀⣹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⡀⠀⠀⠀⠀⠠⠐⠛⠛⢫⠜⠻⡋⠀⢠⣈⠛⠶⠴⠲⠶⠿⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡄⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢷⠂⠀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⣿⣷⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢻⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡿⠋⢀⣿⣿⡿⠉⠋⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠘⣻⣶⠏⠀⠀⠀⠀⠀⠀⣾⠿⠋⠀⣤⣾⣿⠹⡀⠀⠀⢠⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠢⠀⠉⠛⠀⠀⠀⠀⠀⠀⡈⠉⠀⠀⣼⣿⡿⡧⠒⠌⢀⣰⡟⠳⠌⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠁

⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⣴⠉⠀⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠁⠉⢦
⠀⠀⠀⡇⠀⠔⢀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⡀⠦⠀⢸
⠀⠀⢰⡃⠀⠀⢰⢦⠀⢻⣯⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣵⡟⠀⡰⡇⠀⠀⢈⡆
⠀⠀⠀⠧⠀⠀⠀⠚⣤⠀⠈⢷⣷⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢨⢾⡾⠁⠀⣤⠃⠁⠀⠀⠼
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠁⠀⠄⠻⣿⢪⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⡴⣷⠟⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠳⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠞⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠐⠳⢄⡀⠀⠀⠀⡀⢀⡀⣀⢀⠀⠀⢀⡠⠞⠂⠀⠀⣵⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡆⠀⠀⠀⠊⠙⢳⣟⠀⠇⠈⠁⠸⠀⣳⡞⠋⠁⠀⠀⠀⢸⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠃⣧⡀⠀⠀⠀⠀⡀⢸⣿⠧⠀⢀⣠⡀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⢀⣄⡀⠀⢼⣿⡇⢀⠀⠀⠀⠀⢀⣼⠘
⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠘⣼⠟⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠀⠸⣧⠉⠀⠀⠀⢠⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣴⡀⡀⠀⣩⣤⠤⠀⠀⠀⠠⠀⠛⠦⡁⠀⠀⠀⠀⠀⠀⢈⠴⠛⠀⠄⠀⠀⠂⠤⣤⣍⠀⢀⢀⣢⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣾⣟⣀⢀⣤⣤⣤⣄⣀⡀⠑⣮⡦⣀⠀⠀⣀⢴⣥⠎⢀⣀⣤⣴⣤⣤⡀⣀⣹⣷⣾⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠸⣏⢻⡿⡿⢻⣿⣿⣿⣶⡌⠀⡀⠀⠀⢀⠀⢩⣶⣿⣿⣿⡟⢿⢿⡟⣫⠇⣽⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡙⣿⡀⠹⠞⢛⡷⣻⣿⣴⣾⠇⠀⠀⠸⣷⣦⣿⣟⢾⡟⠳⠏⢀⣿⢋⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣧⠈⠙⠒⠒⠿⠟⢛⣼⣿⣿⠀⠀⠀⠀⣿⣿⣧⡙⠻⠿⠒⠒⠋⠁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⢀⣼⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡶⠠⠤⠀⢻⡿⡿⠆⣀⣀⠰⢿⢿⡟⠀⠤⠄⢶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢐⠀⠀⡄⠄⠻⣄⡀⠀⠀⢀⣠⠿⠠⢠⠀⠄⡂⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠄⠀⠠⠐⠀⠌⠻⣿⣿⠟⠡⠀⠂⠄⠀⠠⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣘⡀⢃⣈⣀⣀⣸⣇⣀⣀⣉⡘⢀⣃⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⣦⣭⣄⣠⣭⣴⠿⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢃⡘⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠟⠋⠉⠛⢿⣿⣿⣿⣿⣧⡼⠿⠿⠿⣦⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡿⠿⠛⣁⣤⣤⡴⠶⣤⡄⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⢶⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠀⠟⣉⣤⡴⠶⠶⠶⠄⠀⠀⠀⢹⣿⣿⣿⣧⣤⣤⡀⠙⣷⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡄⢙⣋⣥⠀⣴⣶⣶⣤⡀⠀⠀⠀⣿⣿⣿⣿⣿⣤⣧⡀⠈⣿⣾⠟⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠿⠋⠁⠀⠈⢀⣉⣙⣛⠀⠀⠀⢸⣿⣿⣿⡶⠶⣬⠉⠀⠹⣿⡀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⣾⡿⢷⣴⣿⡿⠉⠛⢷⡄⠀⣾⣿⣿⣁⣠⣤⣤⠀⠀⠀⠈⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠀⢈⣿⠀⠀⠀⠀⢸⣿⠀⢹⣿⣿⠋⣿⠏⠁⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⣤⡾⢿⣄⠀⠀⠀⣸⡏⠀⢸⣿⣧⡀⢿⡀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠙⣷⣶⣾⣿⣴⠒⠿⣿⣍⠻⣄⢻⡆⠀⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡍⠉⠀⠀⢸⣯⠈⢁⣿⣿⣿⣿⡟⢷⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠻⣦⠀⠀⢸⡿⠀⢸⣿⣿⣿⡘⢷⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⢹⣇⠀⠀⠀⠠⠎⣿⣿⡍⠁⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣀⡀⣀⣀⣤⣾⡿⠉⣿⡀⠀⠀⢻⡆⣤⠀⠀⣰⣿⢿⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠿⠋⠁⠀⠀⢸⣇⠀⠀⠈⣿⠹⣧⣴⡿⠃⢸⣿⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡟⠀⠀⠀⣿⠀⣿⠉⠀⢀⣿⡿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠻⣿⣷⣦⣄⠀⠿⠀⣿⠀⠀⣾⡿⠁⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣿⣉⣉⡁⠀⠀⠀⣿⡀⢸⣿⠃⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⢻⡿⣟⠁⠀⠀⠀⢹⡟⢿⡏⠀⠀⢰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⠇⣻⡆⠀⢀⣠⣾⣿⠛⣷⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣏⠙⣷⠻⣾⠟⣿⡿⢿⡟⣿⣿⣧⠏⣠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠻⣦⠸⣇⣹⣧⣼⣥⣠⣧⣾⠟⠋⣰⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⣦⠀⢿⣤⡿⢻⣿⠉⠉⠉⠉⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢴⡟⠀⣼⠟⢁⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣎⠻⠟⠋⣰⣿⠟⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣌⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢷⣶⣿⣻⣧⣄⣿⣐⡇⣶⢰⡆⣻⡆⣹⣧⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣦⣿⣾⢿⣿⡟⠛⠻⠿⠿⠿⠿⠿⠟⠛⠛⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⣿⢨⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⢿⣾⠇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⣶⣶⣿⣿⣶⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣄⣀⣠⣤⣤⣴⣿⣶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠙⠛⠛⠛⠉⠀⠈⠉⠛⠛⠛⠛⠛⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣍⣭⣭⣩⣭⣭⣭⣭⣤⣭⣉⣿⣉⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣬⣥⣤⣤⣥⣥⣼⣿

⠀⠈⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⡀
⠁⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠈⢹
⠀⠀⡀⠀⠀⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠰⠋
⡀⢀⡀⠀⠀⠃⠀⠀⠋⠈⠛⠂⠀⠑⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⢘⣦⣀⠀⠀⠀⢠⡈
⠀⠈⠱⠃⠙⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣴⡈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠴⠀⢺⡄⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⢠⡄⢀⢠
⠀⠀⢠⠀⠀⢸⠏⡂⠀⠀⠀⢀⡔⣦⠀⠀⢀⠈⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠤⡄
⠀⠀⠈⡄⠀⠀⠈⡁⠀⠀⠀⠈⠃⠈⠀⠀⠨⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠁
⠀⠀⠀⢊⡀⠄⠀⠠⠀⢠⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡁⠀⠀⠀⢀⡎⠦⠀⠀⠀⣠⠞⠋
⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⢋⡰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⠋
⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⡄⠀⠈⠉⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⣤⢰⠷
⠀⠀⠀⠀⠀⠀⠐⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⢀⢠⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀
⠀⠀⠘⡁⠂⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸
⠀⠀⠀⠐⠆⠀⠀⠰⠀⠀⣡⠀⠀⠀⠀⢀⠐⠆⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡜⠃⠘
⠀⠀⠀⠀⠀⠘⠆⠀⠁⠀⠁⠀⠀⠀⠀⠈⠑⠂⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⣀⠠⠰⠀⠀⢀⡄⠀⠀⠀⠀⢶⠀⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠐⠀⢠⡄⠀⠀⠠⠀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣮⠑⠀⠀⠀⠀⠀⠻⠆⠰⡜⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⣄⡀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠐⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢘⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠐


⠀⠀⠀⠀⠀⢀⡴⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠂⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢃⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⢀⠀⠠⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⡠⠰⠞⠀⡆⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠉⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡄⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠰⠆⠀⠀⣠⡆
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠰⠈⢁⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡂⢦⣰⡾⠁⠀⠘⠀⣀⡀⠀⠀⠀⠀⠙⠁⠀⢀⢠⡟
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⡀⢤⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⠉⠀⠀⠐⠀⠈⢠⡍⡀⠀⠀⠀⠀⠠⢐⡤⡎
⠀⠀⢀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣀⠀⠀⠀⠐⠇⠀⠀⠀⠠⠗⠈⢀⠁
⠀⠀⠀⠁⠒⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠒⡄⠀⠀⠀⠀⠀⠀⠙⠄⠘⠃
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢾⡐⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⡈⢃⠀⠀⠀⠐⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣈⠁⢀⣀⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠐⡉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠴⠶⣶⠦⢤⣄⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⠤⠶⠛⢉⡀⣠⡀⠦⠀⢠⡙⠀⠸⠁⠚⢷⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⡻⠶⣦⢸⡟⡻⠋⠀⠉⠒⠀⢀⠀⣄⢀⠀⠀⠀⠙⢿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠛⠉⠀⠀⠐⢡⢿⡾⠁⠀⠀⠘⠧⣀⠸⣧⣿⡌⣾⣰⡦⠀⢞⣿⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⣌⠀⣤⡞⠑⠀⡎⣾⠆⠀⠐⠀⢽⡛⢋⣥⡄⠙⣿⣿⣟⠀⠐⣤⠻⣇⢸⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣟⠁⣸⠏⢘⣽⣦⡇⠀⢰⣿⠆⠀⠘⠒⠁⢀⢘⣿⠀⢀⣾⢻⣿⠀⣰⣧⣆⣽⠈⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⣿⡀⡕⠀⠈⠉⠻⡇⠀⢸⣿⣧⣤⣤⣴⡾⣯⠿⣿⡂⣼⡟⠈⣿⢿⡟⢛⡌⣿⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⢸⣿⡇⠀⠀⠀⠀⢹⡄⢸⠿⡿⠿⣷⣈⡳⠶⠞⠻⣄⡿⠀⡀⠷⣄⠻⠌⣰⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢿⣧⠀⠀⠘⢂⣼⡇⣾⠀⠀⠈⣽⢿⣶⡆⢠⣤⡿⠅⠀⢉⠢⡉⠃⠘⣿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠻⠂⠀⣤⣾⡿⢡⣿⠀⠀⡀⣼⠏⠙⢱⡝⠏⡠⠖⠁⠀⠀⠼⣂⠃⡈⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⢘⣿⣿⠟⢡⣾⣿⣷⣾⡏⠿⡧⠔⠡⠀⠀⠀⠀⠀⠀⠀⠰⠛⠟⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠇⠈⣿⣯⣥⣶⣿⡁⠙⠾⢿⣗⠀⢸⣟⠁⠀⠀⠀⡀⠀⠀⠀⠘⠻⣿⡛⠳⠣⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣫⡿⠀⠀⠘⣿⣿⣇⠀⢲⣄⠀⠀⠻⣤⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⣠⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⡏⢀⠀⠀⢾⣿⣿⣧⠀⠀⠀⠀⠀⡌⠃⢘⠿⣦⡁⠀⠀⠈⠁⢀⠀⢠⢼⣯⣽⣿⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⠃⣨⡀⠀⠀⢿⣿⣷⣈⠉⠀⠀⠀⢀⣾⠏⠿⠀⠻⢦⣄⡀⠀⢈⣰⣶⣿⣿⣿⣣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣿⣧⢀⠀⠈⠛⢿⣯⣥⠀⢀⠞⠁⢠⢀⣴⡾⣃⠀⠈⠙⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢿⣽⣃⣄⠀⠀⡀⠈⠉⠁⠐⠲⠻⠉⠉⠋⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⣼⣿⡿⣴⡄⢤⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡟⣷⣼⣿⣾⡷⢀⣴⡿⠐⠀⣴⣾⡿⢻⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠈⣿⣼⣿⣿⣿⠋⠀⠁⠀⠀⠰⡿⡏⣷⠟⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⠀⢀⢇⣸⣿⣾⡟⠀⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠻⣿⠀⠚⡆⣬⣦⣹⣿⡏⠀⠀⠀⠀⣺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⡀⠀⠀⠀⠀⠀⠙⠀⠘⠻⣿⣿⡿⠉⠁⠀⢄⢤⣤⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⣬⣵⣢⣦⣆⡀⡀⠀⠀⠀⠀⠘⠁⠁⠀⠀⣶⠎⣑⣊⠙⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡒⠠⣤⣤⡞⣻⣿⣷⣶⣆⠀⠀⠀⠀⠀⠀⠿⣿⡟⠉⠁⢀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠈⠛⠉⢸⠿⡹⠋⢿⢷⡄⠀⢠⢠⡇⣀⡀⠀⢀⡒⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠃⠘⠑⠟⠋⠑⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠲⣄⡀⠀⠀⠀⠀⠀⣼⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⢿⣦⣤⣤⣶⣾⣿⣦⣄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠋⠈⠻⠟⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢠⣤⠀⠀⠀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠉⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⡄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠹⣿⣿⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⠀⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⡇⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡀⠀⠀⣤⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⡇⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⡠⠀⢱⠀⠀⢉⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⠿⠿⠿⠟⠛⠉⠀⠀⢊⠁⠀⠘⢀⠀⠈⢦⣀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠏⠉⠁⠈⠢⠀⠀⠈⣂⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠀⠀⠀⠒⠲⠤⠂⠀⠀⠀⠀⠀⠁⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢠⣌⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⡿⠛⣧⡀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣻⠟⡋⠉⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢀⡟⠀⠀⢹⣷⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⠴⠚⠁⠀⠀⠀⢸⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡼⠀⠀⠀⢨⠃⠣⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠞⠁⠠⠄⠀⠀⠀⠐⢯⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡏⠁⣰⠇⢀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠳⡄⠀⠴⠈⠠⠀⢳⠀⣠⢿⣷⠖⠻⣶⡶⠦⢲⡿⠉⡷⠶⣿⠋⠁⠀⢀⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠒⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⣠⠟⠀⠀⠐⢢⣀⠜⠀⠁⡸⠃⡆⠀⠏⠘⡠⠚⠁⠘⠀⠀⠙⠀⠀⠀⠘⣿⢄⣀⡀⠀⠀⠀⠀⠀⣠⠂⠈⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡏⠀⢀⣠⡤⠟⠁⠠⣶⣉⠀⠀⢧⡀⠒⠁⡀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡉⢦⡀⣀⠀⠶⠊⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠿⠗⠋⠁⠀⠀⠀⠀⠀⠀⠉⢆⠈⢷⠔⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⠐⠒⠂⠀⠀⠑⠤⠌⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢠⠛⢩⣿⣷⣦⣄⣠⠀⠀⠁⢸⠀⠈⠀⠀⣠⡖⠀⣀⣯⠶⠒⣻⣖⡶⢦⣄⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣾⠀⣼⣿⣿⠷⠙⣿⡄⠈⠀⠀⠀⠀⣠⠈⠙⠁⣠⠋⠀⢀⣹⣿⣿⣏⠀⠈⣳⠂⠀⠀⠀⠀⠇⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠢⣭⣿⣳⣥⡶⠋⠀⠀⠀⠀⠀⡠⠃⠀⠀⠛⡿⠀⠘⠲⢿⣿⡟⡭⠀⣸⠇⠀⠀⠀⠀⢀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⠼⠀⡞⠀⠀⠀⠶⠗⠒⠦⢾⣏⣭⡤⠞⠁⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣄⡴⠞⠁⠀⢀⣀⣀⣧⢀⣴⠇⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⣋⠵⣿⡏⠀⠀⠀⠀⢮⣤⡉⠻⠟⠛⢧⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁
⠀⠀⠀⢀⡴⠋⠁⠀⢀⣀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠸⢇⣀⡴⠋⠉⠀⠀⠀⠀⢹⡇⢀⣴⣧⡤⠎⢀⡠⠀⡾
⠀⠀⠀⣼⠇⣶⡾⠋⠁⠀⠀⠈⢻⢷⣄⡀⠀⠀⢀⣠⣾⣿⡀⠀⠀⠀⠀⢀⣠⡿⠁⠀⠀⣤⣴⠞⠉⠀⢠⡇
⠀⠀⠸⡇⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠛⠙⣿⡉⠀⠈⠙⠒⠒⠖⠚⣿⠿⠀⣀⣴⡞⠃⠀⠀⠀⠀⣾⠃
⠀⠀⠀⢧⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⢈⡙⠳⠶⣤⣤⣤⣶⣾⣿⠟⠋⠁⠀⠀⠴⢀⠀⠀⣼⡟
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠻⣷⡄⠀⠀⠀⠠⢂⠌⠀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⢻⡄⠀⣸⠄⠀⣠⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⣋⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠋⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠿⠛⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠟⠋⠁⠀⠀⠀⠀⠻⣿⣦⣤⣴⣶⣿⣷⡄⠀⠀⠀⣴⣿⡟⠁⣀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⠿⠛⠋⠉⠙⣿⣷⠀⠀⠰⢿⡿⠀⢾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⡄⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠟⣿⣷⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠈⠻⠟⠋⠉⠉⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣾⣿⡿⠛⠋⠁⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⡿⠟⠁
⠀⠀⠀⠀⣀⣀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣄⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢠⣿⡟⠁⠀⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⡀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⣆⣀
⠀⠀⠀⠀⠹⢿⣷⣤⣀⡀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣇⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣷⣦⣀
⠀⢸⣿⣧⠀⠀⠉⠛⠛⠃⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣀
⠀⠀⠙⠿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠈⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣾⣿⠟⠁

⠀⠀⠀⠀⣼⠟⠻⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠛⣿⡄
⠀⠀⠀⠀⣿⠀⢀⡀⠀⠉⠙⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠉⠀⠀⣀⠀⢸⡇
⠀⠀⠀⠀⣿⡇⢸⣿⣷⣦⣤⣀⣈⡙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⣉⣀⣠⣤⣶⣿⣿⠀⣿⡇
⠀⠀⠀⠀⢹⣧⢈⡻⣿⣿⣿⣿⣿⣿⣷⡌⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣴⣿⣿⣿⣿⣿⣿⡿⣋⢠⣿
⠀⠀⠀⠀⠈⣿⡄⠻⣦⣍⡻⣿⣿⣿⣿⣿⠀⣈⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣏⡀⢸⣿⣿⣿⣿⡿⣋⣥⡾⠃⣼⡏
⠀⠀⠀⠀⠀⠸⣿⣤⡈⠻⣷⣿⣿⣿⣿⣧⡀⠉⠩⣿⡿⣿⣟⡿⣿⡿⣟⣯⡿⣿⡯⠉⠁⣠⣿⣿⣿⣿⣿⡿⠋⣠⣼⡿
⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠻⡟⣿⣿⠛⠿⠃⣀⣾⡽⢞⣽⠟⠁⣿⡇⠙⢿⣝⠾⣽⣆⡀⠻⠟⢻⣿⡟⡿⠃⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠘⣿⡇⣾⠃⣸⡏⠀⣠⡶⠛⠉⠀⠈⢉⡀⠀⠀⠹⠁⠀⠀⣈⠉⠀⠈⠙⠳⣦⡀⠘⣿⡀⢻⡄⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣝⠷⠟⠁⣼⣋⣀⣀⣐⠒⢦⣌⢻⣦⠀⠀⠀⢠⣾⢋⣤⠖⢂⣀⣀⣈⣻⡄⠙⠷⢟⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠘⠁⢸⡏⣹⠿⣿⣦⡻⣆⢻⡆⠀⠀⣿⢃⡾⣣⣾⡿⢿⡉⣿⠀⠙⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⡜⣧⡹⠶⠟⠘⣧⢹⡜⡇⠀⠀⡏⣼⢡⡟⠘⠷⠾⣡⡟⣼⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⢿⣮⣛⣛⣛⡛⢻⣆⠁⠀⠀⠀⠀⢁⣾⠛⣛⣛⣛⣫⣾⠏⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢤⣈⣉⣉⣉⡤⠂⠙⣦⠀⠀⠀⢠⡞⠁⠢⣌⣉⠉⣉⣠⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠉⠛⠋⣽⠞⠋⢁⣤⣤⣄⣤⣤⣄⠉⠛⢾⡉⠛⠋⢁⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡄⠁⠀⡀⠘⠿⣶⣽⣵⡾⠟⠀⡀⠀⠁⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠈⠀⠄⢙⡀⢈⣿⣏⠀⣘⠁⠄⠉⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣭⣐⣢⣤⣾⠃⢻⣶⣄⣒⣨⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠐⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠁⠂
⠀⠀⠰⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠆
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠨
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⢆⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡰⠃⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠸⡀⠀⠀⡂⠀⠀⠀⠀⠈⢦⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡴⠃⠀⠀⠀⠀⠐⠀⠀⢀⠇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣼⠁⠀⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢂⢀⡀⠀⡀⠄⣀⣀⠠⢀⠀⠀⡀⡐⠀⠀⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⡒
⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠚⠃⠈⢧⠀⠘⠮⡄⠄⠀⠀⢀⡀⠀⠀⠠⢠⠵⠃⠀⡼⠁⠘⠓⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠈⢇⠀⠀⠀⠠⣄⡴⢤⡇⠀⡾⠃⠀⠐⠁⢀⡀⠀⠀⠀⠀⢀⠀⠈⠂⠀⠘⢿⠀⢸⡤⢦⣠⠄⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠱⡀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⢀⠎
⠀⠀⠀⠀⠀⠡⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠌
⠀⠀⠀⠀⠀⠀⠈⢤⠀⠀⢀⣄⣤⠤⣤⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣤⠤⣤⣀⡀⠀⠀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠘⣿⠀⢰⡆⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢰⡆⠀⣿⠃⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠓⠢⠄⠠⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⠄⠠⠔⠊⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⠀⠀⠀⠈⠲⢬⠑⠊⡥⠔⠁⠀⠀⠀⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⢠⡄⠁⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢭⣉⣉⡭⠟⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠻⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠿⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣘⢻⣷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⢃⡀⢀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⠀⣂⣈⠀⣿⣼⣷⡄⠀⠀⠀⠀⠀⠀⠰⠛⠲⢮⣷⡉⢰⢟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠆⠉⠻⣀⣿⠏⠀⠐⣐⡩⡂⡈⡯⡕⢀⠁⠀⠀⠉⢳⣸⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⡄⣀⡿⢁⡤⠀⠈⠣⠐⠅⠅⠠⠈⡀⢢⠄⠀⠀⢀⠘⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢾⣠⣉⠁⠀⠰⢆⠤⠀⣈⣥⡰⢼⠀⣤⡇⠰⣶⣄⠁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡚⣃⠀⠈⣐⣂⣻⠿⢶⣤⠀⢻⠻⣆⢡⠾⢶⠾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⣞⠛⢝⣛⣷⡼⠁⠀⠀⠈⠈⠙⠛⢁⡒⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⢘⣷⣦⣤⡂⢀⡤⠀⣾⠟⠀⠈⠒⡟⢰⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣸⡇⣾⡄⠀⠉⠀⣠⣿⡀⠀⣶⣈⣉⣉⡄⢱⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⢸⣿⣿⣿⣶⣶⣼⢫⣿⡥⡘⣛⣻⣿⣏⡅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⡆⢻⣿⣿⣎⣫⡉⠄⣿⣧⠈⣹⣿⣟⣿⣃⠀⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⢿⣎⠛⣄⢻⣿⣿⣿⣷⣤⣙⣉⣴⠿⠿⠭⠛⣿⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠭⠀⠻⣧⡈⠳⢝⣿⣿⣿⡏⢿⡿⣷⣶⣶⡾⠟⢠⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⡇⠉⣀⠀⢹⠟⢦⣄⣉⣻⣿⣧⣴⣶⣿⣩⢬⣧⣤⡇⣿⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡏⠸⣇⡉⣉⠵⠄⠎⠻⣎⢻⣱⣿⣾⡿⡯⣧⣤⠄⠙⢉⡼⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣼⡃⠀⠻⣧⡀⠁⠲⢀⠀⢽⠻⣿⣶⡙⠷⢧⣧⠿⢤⣴⣿⠃⠈⠀⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⣿⣀⠀⠙⠿⣦⣄⠈⠀⠀⠓⣨⣿⡅⠀⠀⠀⠀⢸⣿⡟⠣⡠⠄⠃⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⢸⣿⠄⠀⠈⠁⠩⠻⠦⣶⠖⡀⠛⢷⣄⠀⠀⠀⣸⡟⢱⣤⠴⠔⠉⣩⣺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡈⣿⣄⡒⢀⠲⠶⠲⠶⣮⠈⡁⣿⠘⠟⠻⣦⠞⠛⢋⣾⠟⠀⠀⢀⠗⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠸⣿⡧⡄⠐⣷⣄⠀⠀⠛⠓⠛⠞⠘⠀⠈⣀⠀⠈⠀⠀⢀⣼⡋⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡤⢿⣟⣹⠟⡛⠈⠽⣲⣦⣦⣀⣤⣠⡔⢠⣏⣰⣂⣼⣿⣿⣿⣷⠶⢆⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣿⡇⣸⠟⠻⣋⡴⠶⢿⡟⠩⢽⣽⣯⣿⣿⣿⠯⠍⠉⠉⠉⠉⢷⡟⠋⣉⢁⣹⣇
⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠛⠛⠛⠓⠚⠓⠒⠒⠂⠀⠐⠛⠃⠚⠙⠛⠋⠀⠀⢀⠀⠀⠀⡘⠛⠐⠛⠚⠋⠛
⣿⣏⢹⣟⡻⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠈⢳
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢿⣆⠈⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⢠⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣿⡆⠓⠒⠒⠋⠁⠀⡀⠀⠁⠉⠀⠣⠹⠀⠀⠐⠀⠄⢲⡄⠀⠀⢡⠀⠀⢇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠰⡂⠀⣿⡉⢸⡟⠀⣠⠂⡀⠀⠀⠀⠃⠂⠀⡀⠀⠀⠉⠀⠀⢠⡞⠓⣾⣡⠄⠀⠞⠀⠀⡜
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠽⡠⠢⡿⢈⡠⠊⠑⣁⠤⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠰⣄⠀⢀⡼⡰
⠀⠀⠀⠀⠀⠀⠑⢄⠰⠀⢀⠀⠀⠀⠀⠔⠁⠀⠐⠉⠴⠂⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢬⡀⠀⠀⢀⡠⢤⡤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠴⣖⣲⠒⡄⠀⠀⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠸⡀⠸⡿⠀⢹⡆⠀⡀⠀⠀⠀⠀⠀⢸⡅⠀⠻⠋⡰⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠢⡉⠀⠤⠐⠺⠇⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠉⠀⠁⢀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⡵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⣭⡀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠈⠱⢀⡐⠁⠀⠀⠀⠀⢀⠞⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠸⠄⣀⠀⠀⢀⠄⠃⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠒⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣀⣴⠾⠛⠉⠉⠑⢦⣀⠀⢀⡖⢰⠆⠛⠛⠒⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⡔⠊⠁⠀⠀⠀⠀⠀⠀⣀⣉⢿⣿⣇⡿⠀⢀⡴⠋⢀⠘⠂⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠟⠋⠁⠀⠀⣠⣤⠶⠶⢻⣿⡿⠋⠙⠈⠁⠈⠀⠒⣯⠀⢠⠞⠀⠀⠈⢲⣄
⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⢀⣠⣾⣿⣿⠂⢠⣾⠋⠀⠀⣠⣤⣶⠗⠀⠀⢹⡖⠻⣤⢐⡇⠀⠀⠙⢧⡄
⠀⠀⠀⠀⢰⠁⠀⠀⠀⣠⣿⠿⣛⠉⠀⠀⢸⡏⠁⣴⠻⠟⠻⠛⠀⠀⠀⠘⠓⣶⣌⢻⡙⡀⠀⠀⠀⠹⣀
⠀⠀⠀⠀⠇⠀⠀⠀⢠⣿⣧⣾⣿⣦⣴⡦⠺⠇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣇⣱⡄⣀⠀⠀⠉⢶⢤⡄⡀
⠀⠀⠀⡿⠀⠀⠀⠀⣾⣿⣿⡿⠉⠙⠁⠀⠀⢀⣡⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠾⠘⠁⠉⢧⣀⠀⠀⠀⣴⠀⠹⡌⠲⢄⡀
⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣿⣷⡶⠶⠶⠆⢀⣨⠋⠀⠀⠀⠀⢀⣤⣤⣴⣄⠀⠀⣼⡄⠀⠀⠈⠙⣋⠀⠘⠁⠀⠀⢘⠓⠛⠛⠛⠳⣦⡀
⠀⠀⢸⡇⠀⠀⠀⠀⢻⣿⣿⡏⢴⢾⡤⠰⣦⠈⠀⠀⠀⠀⠀⠋⢁⣠⡀⠀⠀⡀⣩⠃⠀⠀⠀⠀⠈⠳⣄⠀⠀⣠⢾⡗⠀⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠸⡇⠀⠀⠀⠀⢸⣿⣿⡇⢰⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠈⠃⠆⠐⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢰⡈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⢿⣄⠀⠀⠀⠘⣿⣿⣧⠈⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠙⣦⣄⠀⠀⢹⣏⠻⣿⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠤⠀⣠⠿⠀⣀⣠⣤⣀⣤⡄⣠⣴⠿⣤⣤⣴⠶⠶⠤⠤⣀⠀⠀⠀⠀⢀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠙⠛⠷⣿⣿⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⡄⠀⡜⠁⠀⠀⠀⠹⠀⠀⠁⠈⡀⢉⠉⣸⠟⠁⠀⠙⠭⢄⣀⡀⠀⠀⠈⠑⠒⠲⣤⣾⠇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⢁⠀⠀⠀⢣⣄⠀⠀⠀⠀⠀⡁⠀⠀⠘⠻⠶⢟⡦⠀⠀⠀⠀⣷⠈⣰⡿⠀⠀⠀⠀⠀⠈⠉⠉⠛⢶⡠⠄⠀⠂⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⢀⡼⠏⠻⣿⡇⢨⠇⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠛⡇⠀⠀⠀⠀⣿⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⢢⠀⠓⠀⠀⠀⣠⠞⠁
⠀⠀⡠⠖⢻⡿⠁⠀⠀⠹⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⢿⠀⢸⡄⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⢾⡇⠈⡀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⣼⠟⠲⠒⠛⠻⠁⠀⠀⠀⠀⢈⡇⠸⣇⣿⠁⠀⢀⠄⠀⠀⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠈⠷⡀⢁⡀⠀⠀⢠⣿⡦⢀⡀⠀⠀⠀⠀⠴⠎⢠⡿⠐⠲⢶⣄⡀⢣⡀⠀⠀⠀⠈⠃⢠⣿⡟⠀⣴⠏⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⣾⣿⠃⠀⠈⠑⠢⢄⠀⠀⢀⡞⠁⠀⠀⠀⠈⠛⢾⡇⠀⠀⠀⠀⠀⢸⣿⠀⠞⣁⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣾⣿⠃⠈⠁⠒⠒⠒⠀⠈⠑⢿⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣧⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠈⠁⣀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣉⣭⣿⣦⣤⣄⡀⠀⠀⠀⣀⢀⣤⣤⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣋⣶⡾⣛⡩⢁⣤⠤⣎⡙⠷⣤⣴⡇⣾⠉⠀⢀⡤⠙⢣⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢟⢫⡵⢶⣭⣤⣿⣷⣶⣶⣾⣿⣿⣿⢷⣍⣀⡴⠋⠀⣴⠀⠀⠘⣄
⠀⠀⠀⠀⠀⢀⣴⠞⡋⢔⡋⢠⣴⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣼⣯⣾⣹⣷⣀⣼⡁⢠⡄⠀⠘⢷⣄
⠀⠀⠀⠀⢀⡿⡁⢺⡵⢏⣼⣿⣿⣿⣟⣿⣹⣿⣿⣋⣵⣿⣿⡿⠛⠛⠉⣿⣯⣽⣿⣶⢿⠀⠀⠀⠙⢧
⠀⠀⠀⠀⣼⢃⣹⠘⣡⣿⣿⣿⣿⣧⣽⣟⣿⣿⣷⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⢧⠀⠀⠀⠈⠲⣄⡀
⠀⠀⠀⣼⢣⡜⡋⠆⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠗⠾⣷⠲⠀⠀⠀⢹⡿⣷⣦⣄⡀
⠀⠀⢀⡿⢇⠼⡿⢤⣿⣿⣿⣿⣴⣦⣿⣿⣯⣿⡿⠁⠀⠀⠀⠀⠀⣛⣐⡀⠀⠀⣙⡇⠀⠀⠻⣷⣤⣤⣴⡿⣧⣜⢿⣿⣿⣦⣤⣄⡀
⠀⠀⢸⡇⢊⣰⣧⠸⣿⣿⣿⡟⣯⣻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠶⠟⠛⠛⠛⠀⠀⠿⡇⠀⠀⠀⠈⠻⣿⣻⣟⠻⢇⣽⣧⣷⣷⣶⣽⡿⣦⣄
⠀⠀⢸⡇⣸⢿⣿⡇⣿⣿⣿⡇⢘⣽⡏⠛⠛⠀⠀⠀⠀⠀⠀⢀⡴⢻⡇⡀⢠⠶⡚⠀⠀⠀⠀⠀⠀⠈⠙⢷⣾⣿⢻⣿⢗⡼⠷⣉⠾⣃⣝⠳⣤⡀
⠀⠀⠈⣷⠉⣎⡻⠆⣿⣿⣿⣇⠸⣭⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠤⠀⠁⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⣿⢩⠂⠴⢷⣌⡳⠬⣈⡳⣬⡻⣦⡀
⠀⠀⠀⠘⢷⣌⠈⡣⠘⣿⡿⣿⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡀⠀⣀⣿⡘⢋⣬⣭⣭⣤⣌⠙⠶⠦⠐⣉⣷⠋⢿⣄
⠀⠀⠀⠀⠈⠙⠿⣶⣤⣿⣷⠀⠙⠷⠿⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠇⠈⠉⢀⢿⡁⠴⠶⣿⣻⣷⡿⣳⣾⠟⠿⣿⡿⡟⠛⠏⠛⣛⠷⣶⣭⣤⣧⣼⣷⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡆⠀⠀⠀⣄⠀⠀⠀⠀⠀⠘⡟⢼⠁⢤⣤⣤⣴⣜⢯⡂⢰⠀⣿⢿⣧⣿⡇⣎⢼⣄⠛⢿⣿⣷⣶⣤⣝⣪⣭⣽⠿⠿⢛⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⢰⡄⠀⠀⠘⢿⣄⠀⠀⠀⠀⢇⠀⠀⠀⢨⣭⣴⣿⢤⣧⢸⠀⣿⠈⣿⠿⣻⡏⢀⣤⠉⠰⠒⣿⣎⡿⣿⡛⠿⣦⢔⣴⠞⠁
⠀⠀⢀⣠⣤⣾⣿⣿⣹⣿⠃⠘⠁⠀⠀⠀⠀⠉⠀⠁⠄⠀⠈⠀⠀⠀⠀⠀⠀⣿⢸⡜⢠⠀⣿⡇⣿⡆⣿⡇⡼⠡⠖⣮⠉⢁⠻⢦⣠⠏⣩⣼⠟⠁
⠀⠀⠻⣏⣿⣿⣿⣟⣷⣌⢳⣄⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣠⣤⣤⣠⣴⣶⠿⡘⢣⡞⣤⣿⣇⢹⣧⣿⡇⣼⢁⣶⡎⣛⢯⠴⣊⣵⡾⠋
⠀⠀⠀⠈⢻⣿⣿⣿⣻⣾⢃⠜⣧⣀⠀⠀⠀⠈⠉⠀⣀⡭⠉⣿⣉⣯⣝⡡⢿⣷⣹⠎⣧⢙⣹⡟⢸⣿⣿⠁⢡⣿⢏⡾⣋⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠙⠛⢸⣇⢱⢾⣿⣿⡿⠻⢦⣄⣀⠀⠀⠉⠀⣸⡟⣍⣉⡙⠻⣶⣽⣧⡸⠇⣨⣿⣧⢸⣿⡏⣴⡟⣡⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣼⣿⡟⡷⢾⣧⣬⣭⣟⣦⣄⣴⡟⢰⣌⣬⠱⠕⠪⠛⣿⠀⡄⠙⣿⠉⣿⣿⣿⣽⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠿⠟⠉⠁⠚⠫⠍⢽⣿⣷⣮⣹⣿⡡⠜⠣⠞⠴⠛⠰⢧⡄⣠⣾⠛⣾⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠛⠓⠚⠛⠚⠛⠛⠒⠚⠓⠒⠂⠉⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⣿⣿⣶⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⠋⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠙⢿⣿⣿⠿⠛⠋⠉⠁⠀⠀⢸⠋⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠀⠀⠀⢠⡿⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣀⣤⣴⣾⠿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣠⡤⠤⠤⠤⠤⠀⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠉⠉⠀⠀⠈⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⢢⡀⠀⠙⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠈⢷⡀⠀⠈⠙⠻⠛⠁⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⣀⣀⣀⣤⣴⣾⣿⣿⡿⠿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡶⠶⠀⢤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⡿⠋⠁⣀⠘⠀⢀⣤⠉⠉⠉⠛⠛⣶⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⡟⣀⠤⣾⣿⠀⢠⣿⣟⣲⠠⠶⢖⠋⣿⠆⠈⠹⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣰⠟⢡⣿⣷⣿⡿⢀⣿⠟⢩⣿⣏⠀⣿⡆⢸⡇⠠⡀⠺⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣠⣿⠾⡯⠿⠛⣹⠇⡼⣿⣿⢷⣿⡉⢰⡈⢯⢸⡟⠀⢹⡦⣨⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠁⣻⠟⠐⠋⠈⠉⠁⣸⠛⣿⣷⣾⡻⠿⣾⣷⢀⣿⡟⠀⣿⡇⠀⢺⣟⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣮⣥⡀⣀⣶⣶⡀⠀⠈⣿⠌⡿⠈⠉⡁⣈⣿⣿⣿⣿⢠⣿⠁⢠⡄⣹⣧⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡇⡏⢾⣿⣿⠿⢿⢿⠂⠀⢸⣾⣷⣤⢷⣿⣟⡁⢸⣿⡇⡘⢻⢃⡞⢡⠟⢸⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣰⢻⣆⠀⠨⢿⢿⣉⡩⠱⠠⠄⠹⡿⣿⣧⣀⣠⣶⡄⢸⣿⠃⢴⠣⠞⠛⢃⣴⡼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡸⣿⠀⣾⡶⠾⣿⠛⢳⡖⢠⣽⣿⣾⣿⠛⣿⣿⡗⢸⡿⣆⣰⣷⣦⣴⢿⢡⡔⣬⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⡖⠙⣧⣹⠀⠲⠶⡇⠛⢦⣤⣮⣫⣤⣯⣀⣿⣿⣴⣿⣇⠸⡛⠟⠟⢁⡼⡀⢠⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣧⣞⡹⢻⣿⠀⣄⡉⡀⠺⢿⣽⣏⣬⣴⣿⢿⣿⣿⣿⡟⢀⣧⠀⠲⠹⠄⣳⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡟⢈⣰⣿⠃⣤⠹⡿⣿⣷⣴⣶⣽⣯⣥⣾⡶⠀⠥⢿⣷⢫⣶⣮⣬⣬⣆⣽⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡿⠋⢡⡘⠛⢓⡚⢹⢿⣿⡿⣿⣽⣿⣿⠛⠲⠀⣠⣽⣷⣾⣿⣇⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣇⠘⣿⠛⠷⢋⣿⣱⣿⣿⣷⣄⣰⣾⣿⡿⠟⢻⣿⣿⣿⡗⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣿⠀⠘⢳⣾⠷⠛⣫⡴⣫⡟⣻⢋⡯⡳⣬⡈⣩⡟⡙⢋⠷⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣤⢻⣿⣿⣿⢿⢿⣿⣭⣞⣡⣜⠷⣌⣻⢟⣻⠀⠆⠜⠓⠒⢂⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠽⠦⣛⢲⣟⡥⣚⣿⠟⢈⣟⠢⠝⠛⠷⢸⢟⠃⠂⠐⣭⠜⠋⠈⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠀⠀⠀⠀⠀⠉⠿⣯⣭⣽⢖⡼⠈⡼⠳⠆⣶⣶⢿⡇⢠⣁⡐⠎⢁⠀⠈⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠺⠃⠀⠀⡠⠖⢖⣩⠵⣶⢏⡒⢁⠴⣃⣴⡛⢆⠙⢆⢠⠙⠎⣦⠆⠨⢂⣈⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣫⠛⡀⢀⠎⠀⠀⠋⠀⡔⢀⡾⠿⣿⠋⠣⣌⢻⡈⠃⠀⢢⢁⣰⠝⣆⡶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⠀⠈⢄⠀⠀⠀⠀⢠⠟⠁⠸⠞⠀⠸⣄⠀⡇⡄⠰⠀⣸⣅⠀⡝⢀⣢⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢠⣀⢸⠀⢃⠀⠀⡀⠀⡧⠀⡲⠀⠀⠃⠀⢳⡇⢀⣤⠿⣿⣆⣠⣬⣿⠅⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⣆⠈⢦⡀⠀⠂⠣⣰⠇⠃⣼⠀⠠⠟⣠⣾⢇⣴⠠⡿⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣌⣻⡆⠀⣷⣏⣠⡾⣡⣶⣿⡿⣡⠿⠛⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠿⠿⣿⠿⠾⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⢀⣤⡴⠦⢭⡢⡀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⡠⣖⣮⣿⣮⢀
⠀⠀⠀⠀⠀⢸⣯⡇⠀⠰⣌⠈⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠄⠉⠙⠟⣛⡀
⠀⠀⠀⠀⠀⣆⠀⡃⠀⠀⠈⠀⠐⢬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡆⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠈⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣵⠧⣢⠏⠀⠀⠀⠀⣤⢼⡧
⠀⠀⠀⠀⢰⣿⠸⣷⠀⠀⠀⠀⠀⢲⣼⢿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢋⠀⡀⠀⠀⠀⢀⣴⡿⣰⠇
⠀⠀⠀⠀⠘⣿⡄⠘⠆⠀⠀⠀⠀⢄⢟⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡞⣿⣇⣾⣠⡇⠀⠀⠀⠀⠉⢀⣛⡄
⠀⠀⠀⠀⠈⣧⡁⠀⡀⠠⠀⠀⠀⢸⣞⢿⣿⣾⢯⠟⣽⠉⢿⡄⢷⣸⠎⡉⢻⣿⣵⣧⣿⡟⣼⡇⠀⠀⠀⡀⠀⠀⣡⣾⡇
⠀⠀⠀⠀⠀⣻⣿⠇⢾⣶⡖⢠⣀⣿⣿⣆⣿⣿⣷⣟⠁⢐⡰⣇⣘⠃⠞⠁⣼⣿⣏⣿⣿⣷⣿⣿⣷⢀⣼⢁⣰⢞⡛⣿⡇
⠀⠀⠀⠀⠀⢸⠁⠀⠀⢿⣿⣿⣷⣿⣿⣿⢿⣿⣋⠷⣏⣿⠀⠹⢯⡾⣸⣏⡛⠻⢿⣿⣷⣿⣿⣾⣥⣾⣿⡿⢣⡿⠋⠉⣤
⠀⠀⠀⠀⠀⢠⣷⡄⠠⡌⡻⣿⣿⠿⣏⣼⣶⣿⣿⣿⣟⢣⡄⢰⣴⠄⣿⢘⣟⣱⣿⣿⣿⣿⣿⣿⣿⣿⡟⡵⣫⢎⣤⣾⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣶⣷⡙⠋⣠⠀⠹⣝⢿⣿⣿⣿⣿⡼⢗⣼⣿⣿⣿⡈⢿⣿⣿⣿⣿⣿⢏⠟⣷⣰⣦⡀⣱⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣾⠀⠛⢷⣾⠿⠿⣿⣿⠈⣿⣿⣿⠟⢻⣿⠿⣿⢿⣿⠶⠃⠀⠁⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣿⣆⠐⠂⢀⣠⡄⠈⠀⣿⣃⣻⣟⣁⡙⠈⠀⠈⠀⠀⣰⠋⣀⢌⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣤⣆⢻⣶⣤⡿⠁⠀⠀⢙⣿⣿⣿⡿⡻⠄⢀⡀⢠⣼⣶⡾⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⣿⣧⢈⣉⢈⣿⣿⣿⡿⣯⡑⢤⣀⣤⢊⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠭⢾⣧⣿⣿⢿⢷⣮⡒⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣤⣤⢀⣿⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠘⠇⢻⡣⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡎⠹⣿⣿⢏⣿⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⣿⠃⢠⡀⣧⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹⣧⣿⣿⠘⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡇⠛⡀⢰⣿⣿⠁⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⣇⡼⢺⣿⣿⠃⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢰⡄⣤⡀⠙⠋⢰⣿⡹⣿⣿⣿⣿⠻⣿⡿⣿⣿⠀⣼⣿⠃⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠿⣷⣬⣀⣾⣿⡔⣿⣿⣿⣿⣔⣿⣿⣿⣿⣸⣿⣿⣠⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣠⡿⢛⡿⠀⣿⣿⣿⣿⣞⣿⣿⣿⣿⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠾⠇⣈⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠄⠁⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠈⠙⡕⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣴⡅⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡏⢜⠠⠀⠀⠀⠀⠈⢦⡙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⣾⣿⡕⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠘⡟⡄⢀⠀⠀⠀⠀⠀⢌⠪⡳⡈⢳⣀⣀⣀⣀⣀⣀⣀⢀⡼⢰⣿⣿⣿⣿⠁⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠂⡀⠈⢠⣜⢿⣿⡿⠨⠉⠉⠁⠉⠈⠉⠉⠉⠁⠈⢿⣿⣿⢋⡄⠀⡘⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡀⠀⠠⢀⠾⣿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡻⢿⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠢⣀⠀⠀⡤⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⣀⠀⢦⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠏⠂⠀⢔⠀⢠⠀⠀⢰⠊⣉⣿⠓⣌⠆⠃⠀⠀⠀⢸⡏⣽⡯⢳⠸⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣶⠂⠋⠀⠈⡆⠀⠘⠄⠘⠟⢀⡾⠈⠀⠀⠀⠀⠘⣆⠈⡡⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢠⡤⠀⠘⢄⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡀⠀⢷⣤⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣶⠈⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢤⠀⠀⠪⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠪⡁⠀⠀⠀⠈⠉⠀⠤⣀⠀⠠⠀⠀⢀⣠⢆⡀⣂⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢀⠄⠛⠃⠘⠂⠠⠰⢲⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⣀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠀⠀⠉⠀⠀⠀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡅⠉⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠋⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⢾⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⣠⠞⠋⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⠀⢀⠰⠖⠛⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠛⠉⠛⠻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣌⠙⠁⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢀⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⠿⢿⣿⣿⣆⠀⢀⣠⣶⡿⠿⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠀⠀⠉⠛⠿⣿⣿⣿
⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⢀⣀⡀⠈⠻⣿⠀⠛⠉⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣠⣤⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⢿⣷⣄⣀⡀⣀⣹⣿⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠹⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠶⢶⣴⣶⣶⣾⣿⣿⠟⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿
⠀⠙⢿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⠿⠋
⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠁⠀⠀⠀⠀⢠⡔⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢄⠀⠀⠀⠀⢸⠾⡀⠀⠀⠀⠀⠀⠉⠉⠙⡆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡤⠈⠉⢂⡇⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⠀⢀⣚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠈⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠇⠀⠀⠀⢠⠆⠱⠋⡄⠀⠀⠀⡜⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⠇⠀⡴⠚⠒⣤⠒⠓⢄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣀⢠⠞⣧⠀⠀⠤⠀⠂⣼⠢⡤⢤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠃⡞⣉⣤⠤⠶⠤⢤⡉⢳⠳⣤⠾⠋⠉⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠴⠒⠒⠓⠤⠟⠁⠀⠐⠀⠀⠀⠈⠻⠤⠛⠐⠚⢦⡀⠈⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠯⢼⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠲⢤⡀⠀⡼⠉⠑⠲⠦⠤⠤⢤⡤⠤⠤⠤⠴⠒⠋⠁⠀⠀⠀⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡔⠋⠉⠉⠳⡌⣾⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⠤⠴⠶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⡖⢰⠀⠀⣸⠇⠀⠀⢸⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠃⣘⠒⠀⡉⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⡁⠨⣉⠀⠁⠀⠀⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡌⠀⠀⠀⡗⣲⠾⢆⠀⠀⠀⠀⠀⠀⠀⡠⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢳⡴⢦⣿⡇⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⠀⢹⠷⡀⠀⠀⠸⡅⠀⢠⠇⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣸⡙⠀⠌⢠⠉⠁⠒⠒⠑⠀⠞⠒⠂⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠰⡀⠀⠀⠐⠂⠀⢀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⢡⡀⠀⠀⠀⠀⠀⠈⠁⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠱⡂⠀⠀⠀⠀⡀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⣦⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠘⢤⠀⠠⠀⠀⢀⡀⣄⡀⠀⠀⠀⠀⠀⢀⡠⠄⠀⢄⡈⠳⡀⠀⠀⣠⠞
⠀⠀⠀⠀⠈⠲⡇⠀⡜⢡⣶⢶⡉⢡⠀⠀⠀⢠⠃⣼⡟⢻⡄⣷⠀⢰⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠃⢀⢇⠸⢷⡾⢃⡇⠀⠀⠀⠘⢄⠻⠿⠿⡡⣋⠀⠸
⠀⠀⠀⠀⠀⠀⠘⡀⡙⠋⠤⠘⠉⠀⠄⠀⠀⢀⠀⠉⠙⠓⠈⢡⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠑⡌⠂⠀⠀⠀⠑⠒⠀⠖⠊⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⣀⣀⣠⣄⣀⠠⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⣀⠀⣀⠤⠤⠤⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠇⠈⠁⠀⠀⠘⠇⠀⢸⡇⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⢸⠇⢹⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⢀⠀⠀⠀⠀⣦⣀⢠⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠁⠢⢄⠐⠁⠀⠀⠀⠈⠉⠛⢀⠀⠀⠀⠀⠀⠖⠓⠤⠄⣀⡀⠐⠠
⠀⠀⠀⠀⠀⠐⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⢀⠀⠀⠀⣄⣠⣀⡠⠆⠁⠀⠀⠀⠀⠈⠱⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⢀⡰⣀⠀⢀⡧⠀⠼⠣⠤⠲⠄⠠⠤⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⣉⣀⠒⠒⠒⠀⠒⠒⠀⠀⣁⣀⠤⠔⠚⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣿⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠈⠙⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢍⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⡩⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠳⣌⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣡⠞⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣦⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⣴⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⡇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢹⡄⠀⠀⠀⠀⠀⠀⢨⡇⠈⠿⠾⠛⠛⡋⠉⢩⡏⢹⡍⠉⢙⠛⠛⠿⠟⠁⢸⡁⠀⠀⠀⠀⠀⠀⢠⡇⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠻⡤⠶⢶⡦⢀⡾⢋⣤⠴⠖⠛⣉⣉⠙⠆⢸⠀⠀⡇⠰⠉⣉⣉⠓⠲⠦⣤⣙⢶⡀⢰⡶⠦⢤⠟⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣶⣶⠸⢡⡿⠚⣉⡤⠶⠛⠉⠁⠀⠱⡈⠘⡇⢸⠃⢁⠎⠀⠈⠉⠛⠶⢤⣉⠓⢿⡌⠇⣶⣶⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣏⠀⢉⣴⠟⣩⠴⠂⠀⠀⠀⠀⠀⠁⠀⠆⠸⠀⠈⠀⠀⠀⠀⠀⠐⠦⣉⠻⣦⡙⠀⣿⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠿⠟⣡⠞⣡⣴⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣦⣌⠳⡌⠻⠞⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⠏⠀⢸⡇⠉⠉⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠉⠉⢸⡇⠀⢹⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠛⠶⠶⠖⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠲⠶⠶⠋⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⡠⠚⢡⡾⠋⠀⢀⠀⠀⠀⢀⡀⠀⠉⢷⡌⠒⢄⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⣔⣴⠛⠁⠀⠐⢯⣍⠉⠉⣩⡿⠂⠀⠈⠻⣶⣢⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠙⠆⠰⠋⠀⠀⠀⠀⠀⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⠶⠶⠛⠁⠈⠛⠶⠶⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣤⣤⣤⡶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠛⢿⣿⣿⣿⣿⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⣿⣿⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣶⣦⡈⠋⠁⣴⣶⡖⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⢦⣍⠛⣧⠀⣠⡟⢉⣥⡾⢿⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣃⣍⢙⣷⠌⣷⢋⣴⣌⣿⡛⠏⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⠀⠀⠉⠀⠉⠉⠅⠘⠣⡁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠒⣀⡀⠀⠠⠤⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣆⣀⡀⠀⠐⠒⠒⠒⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⠙⠌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡯⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣽⣿⣿⣿⣦⡶⠀⠀⠠⣤⣤⣄⣀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠈⢻⣿⣿⡇⠀⠀⠀⠐⠐⠈⠉⠋⠑⠶⠄⣰⣿⣧⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣛⣿⣿⣄⠀⠀⢿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⢀⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠉⠈⠆⡀⠀⠘⠿⣶⣦⣀⣀⣀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⢱⣤
⠀⠀⠀⠀⠀⣸⣿⣿⣿⢟⣿⡇⠀⠀⠀⠘⠲⢄⡀⠀⠈⠙⠻⠅⡀⠀⠁⠀⠈⠳⡄⠄⠂⠀⠈⠝⢿⠆⡀
⠀⠀⠀⠀⢠⣿⣟⠙⠙⠦⣿⣾⣤⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠘⢢⠀⠀⠀⠀⠙⠆⠀⣶⠐⠀⠀⢹⡇
⠀⠀⠀⠀⣼⣿⢿⣿⣗⡀⢈⣿⡛⣛⣄⠀⢀⣤⡄⠰⠂⠚⠓⠲⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋
⠀⠀⠀⣸⣿⣿⢸⣿⣿⣷⣄⢿⠛⣈⡤⠶⠟⠛⠛⠁⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠒
⠀⠀⠀⣿⣿⣿⣆⣿⣿⣿⣿⢷⣿⣿⣷⣦⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⢟⣦⣽⡿⠙⠁⠀⠀⠀⠀⠠
⠀⠀⠀⢸⣿⣿⣷⣻⣿⣷⢊⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠷⠎⢠⡄⠰
⠀⠀⠀⢨⣿⣿⣿⣏⠿⡃⠀⠀⠀⡀⣀⢠⡴⡁⠀⠀⠀⠀⠐⢀
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠐⠀⢠⠿⠛⠁⠀⠐⠒⠛⠁⠘⠃⠁⠀⠀⠀⠀⢀⡀⣀⣠⣤⣶⣄⣀
⠀⠀⠀⣼⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⠐
⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⣿⣿⣿⣶⣦⣂⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠿⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠻⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⡀⠴⠶⠶⠾⠿⠿⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠦⣄⠀⠀⠀⢣⡀⠀⠀⠀⢰⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠙⢦⡀⠀⠸⡀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⣀⡀⠀⠙⢦⡀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡴⠋⠉⠉⠉⠙⠀⠀⠱⡄⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠞⠀⠀⡹⠄⠀⠀⠀⠀⠀⠀⠀⠈⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢥⣤⡤⠀⠸⣤⣤⣤⣀⣠⣤⠤⠤⠖⠚⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠟⠉⠻⠿⢷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡃⡘⡏⠁⢀⣠⡶⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣿⣾⠟⠁⢠⣿⣵⠂⢀⣻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡅⠔⠉⠀⠀⠀⣾⣿⣿⣷⣦⣻⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠧⢄⡀⠀⠀⠀⠀⢿⠉⠻⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣿⣿⣶⣽⡆⠀⠀⠀⠈⣷⣤⣴⣿⡿⠛⣡⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢹⠟⠋⠉⠀⠀⠀⠀⠀⢨⡏⠉⣁⣴⢾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣰⠺⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡈⠛⢷⣌⡳⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣤⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡾⢿⡁⢹⡟⢳⣽⣿⣾⣿⣶⣶⣣⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣇⣠⠟⢹⡆
⠀⠀⠀⠀⠀⠀⢸⡓⣶⡟⣋⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣀⡙⣿⣉⡏
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⣴⢀⢄⣀⡀⣀⣀⣰⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠜⠻⠘⠷⠷⢧⡇⠿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⣧⡀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠹⣧⠀⠀⠀⠀⠀⠀⣾⠃⠀⠸⣷
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢿⣶⠶⠶⠶⢶⣾⡏⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠿⠃⠀⠀⠀⠀⠹⠿⠁⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢸⡇⠠⠤⣄⣀⡀⠀⣀⣀⠀⠀⣀⣀⡤⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠒⣾⡇⠸⣅⣸⠂⣽⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⡸⣇⣀⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⢷⡄⠀⠀⣼⡆⠘⠛⠛⡟⠛⠛⠀⢀⣴⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⢠⡏⣷⠀⠀⠀⡇⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⣥⣼⡆⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⡆⢠⡏⠀⠈⣧⠀⠀⡇⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠞⠁⠼⠁⠀⠀⠹⠀⠘⠇⠀⠀⠀⠈⠙⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⡠⣻⣿
⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⣷⣀⠀⠀⣰⣾⢱⣿⣿
⠀⠀⡿⠉⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣾⣿⣿⢛⠘⠋⠉⠋⣻⠿⣿⣿
⠀⠀⡗⠀⢰⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⢳⣙⢻⣟⢞⡴⠴⠀⣤⠈⠁⢹⡅
⠀⢸⡇⢀⣿⣿⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣀⣴⡿⠋⠹⣿⡷⢉⡍⠁⣶⣠⣾⣿⣿⣇⢸⢺⣿
⠀⢸⡏⢸⣿⣿⣧⣤⣠⣤⡶⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠿⢾⣿⡿⠀⠀⠀⢹⡇⠈⡀⣠⠄⠈⣿⣻⣿⣿⣟⠛⢻
⠀⠘⣧⡀⠹⣿⣿⣿⣿⣿⡿⠛⠁⣀⠙⢿⡟⢁⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢰⡿⠉⠀⠀⠀⡀⠀⢡⡀⠈⠓⣟⣍⣉⢥⣿⣿⣿⣷⡼⢻⣄
⠀⠀⠙⠷⣦⣤⣭⣭⣿⣿⠃⠀⠀⢉⡄⢸⠁⢼⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⡴⠀⣽⠇⠀⠀⠀⣴⡷⠀⠹⣿⡔⣦⣳⣹⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠀⣿⠂⠀⠀⠘⣇⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸⡇⠀⢻⣇⢠⡀⠀⠻⢷⣀⡀⠈⠉⣿⣿⣦⣝⣛⠻⣿⣟⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠻⠈⣷⠀⢿⣿⣿⣿⣿⣿⣿⡇⠠⣿⡷⠀⠀⠉⠀⣷⣄⠀⠈⣿⣿⡆⠀⠘⢻⣿⠛⣿⠛⠛⠛⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⡙⢷⡀⠘⠿⢿⣿⣿⣿⣇⢀⣿⡇⠀⠀⠀⠀⠙⢿⡆⠀⢹⣿⣿⠀⠀⣼⣿⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⠀⠀⠀⠀⡿⢀⠀⡀⠀⠀⠉⠛⣿⣧⠀⣿⣿⣇⠀⠀⠀⠀⢸⣿⠀⠈⠻⡿⠀⣰⠟⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠀⠀⠀⠀⠀⠁⢨⣿⣿⣶⣤⣀⠀⠈⠻⠀⠈⣿⠁⠀⢠⣴⣀⡿⠁⠀⠀⠀⢁⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⢤⣀⣀⣀⣴⡿⠿⠿⠿⠟⠉⢷⣄⠀⠀⠀⣿⠀⣠⠼⠿⠷⢤⣶⣄⣠⣶⣿⠃⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠻⡄⠈⢹⣿⣿⡃⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⡟⠀⠠⠤⠶⠒⠀⠀⠀⢀⡀⠀⠉⠙⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢡⠀⣼⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣤⣤⣠⣄⣀⣀⣤⣤⣀⣰⣦⡀⠀⠈⠑⠒⠂⠠⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠀⢸⢠⡇⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠻⣭⣉⠀⠀⠈⠙⣟⠷⣤⣀⡀⠒⣤⣑⣮⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠝⡟⠃⠸⡳⡳⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⣀⠀⠀⠘⢦⠈⠙⠻⠷⠏⡿⠬⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡍⠑⣄⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣄⢄⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣧⡀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣀⡉⠑⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣇⣿⡬⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠝

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡛⠿⠯⠩⣭⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⣤⣉⠙⠓⢄⠈⠦⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣿⠁⠀⠙⠿⡝⠿⠛⠫⣄⡉⠙⢿⣆⠀⠑⠄⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠙⢷⠀⠀⠰⢠⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣧⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⣬⣃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠲⠌⢉⡇⢠⠌⢻⢿⣿⡿⢷⣤⡀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡞⠀⠀⠀⠲⠄⠛⠛⠓⠠⠀⠀⠉⢈⡾⣛⣦⡀⠀⠀⠀⢈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣏⠀⠑⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢃⣼⡌⠻⣦⠀⣠⠏⣨⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣌⡀⠉⠁⠀⠱⣄⠀⢀⠀⠀⠀⢀⡄⠐⣫⠎⠀⠀⢘⡷⢃⡴⠃⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠸⢭⣙⣒⣲⡶⠀⠇⡼⠀⠀⢠⡞⠉⠉⠁⠀⠀⠀⠉⠀⠞⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠐⠲⠤⠄⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠀⠀⣀⣠⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉





⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣦⣧⣾⣤⣷⣴⣯⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⢤⡀⠀⠀⠀⠀⠀⠀⢠⡖⠂⠉⠉⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣍⣁⣀⣄⢠⣼⡦⠀⠀⠀⠀⠈⠀⠙⢻⣦⣚⣭⠞⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠛⢿⣯⡿⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⢨⣙⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⣺⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣼⠃⠀⢀⣴⣾⡇⠀⠀⠀⣷⣶⡄⠀⢸⡍⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠚⠙⠛⠁⠀⠀⠀⠙⠉⠘⣆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠃⠀⠀⠀⢠⢠⣴⣓⡤⢄⠀⠀⠀⠙⣆⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠂⠀⡆⢀⢁⠈⠻⡿⠃⢈⢃⠀⠀⠀⠈⢱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡄⠀⢹⣜⣻⢿⠛⠛⣻⠿⣿⡐⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠈⠹⡿⠀⠟⢛⠅⠀⢸⠃⢀⣰⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡬⠜⠳⣤⢹⣤⣄⣡⣤⣠⣾⠷⢏⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⣠⠔⠁⠘⠛⠘⠉⠁⠑⠄⠀⠀⠁⠲⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠚⠁⠀⠀⢀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⣿⡆⣦⢸⡀⠀⠀⠀⠀⣦⠀⣦⣶⠖⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⡄⠸⠟⠘⡝⠋⢲⠎⠂⡈⠫⣆⡏⠉⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠙⢿⣇⠀⢂⠈⠀⢦⡄⠄⠋⡂⣴⠟⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡆⢀⣀⣿⡄⠁⠀⠑⣤⣟⠐⠀⠳⠁⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣉⣉⣹⡗⠀⠀⠀⠈⢻⠀⠀⠀⡧⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⢱⡄⠁⠀⠀⢀⠄⠀⠀⠃⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠈⠀⢘⠀⠀⠀⠀⢧⣀⡀⣀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠄⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⣀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠙⣿⡿⣿⣶⣄⠀⠀⠀⠀⠀⠀⢻⣿⢋⢡⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠔⢂⡥⠂⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠐⢍⡒⠤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠔⠁⠀⠀⠀⠀⠀⠀⠐⠚⠋⠉⠓⠂⠀⠀⠀⠀⠀⠀⠙⢦⡈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁




⡶⡶⢶⠶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⣶⣶⣶⣶⣶⠶⣶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⡒⠒⢽⡍⠑⣄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡋⠉⠈⠁⣀⡠⠔⣠⣦⠀⣐⠊⠉⠸⠏⢒⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠛⠛⠻⢷⡦⣄⠀⢀⡥⢀⡴⠞⠁⠀⢤⣌⡑⠢⠐⠐⢉⡁⠀⠈⠯⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⣨⠶⠖⠲⠦⣄⠙⠈⠀⡟⡴⢋⠔⠠⠄⠀⡼⢻⠉⡄⠀⠐⢉⡴⠚⢻⡁⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠈⢀⣁⡀⠀⢉⣉⣻⣦⣤⢤⡀⠀⠀⢀⡴⠿⠯⠴⠏⠀⢉⠇⡠⠥⣤⣀⡼⢹⣸⡟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⡴⠛⠉⠉⢉⣻⣯⣍⡉⠙⣧⡄⣧⠘⣦⠏⠀⠀⡀⢀⣠⢶⣿⡖⠒⠚⠛⠋⠀⠾⠁⢿⣀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡞⢀⡄⠀⠀⠀⠁⠀⠀⠉⢣⣸⡇⣧⠀⢸⡀⢀⠞⢠⠟⠁⣾⡟⠀⣠⠔⣒⣒⠠⠀⠐⠠⡉⢳⡀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢠⡏⠀⢠⡴⠒⠋⠉⠉⠒⢆⠙⡇⠸⠀⠈⠇⠈⠀⠘⠀⡸⠣⠁⠞⠀⠋⠄⠒⠒⠦⣤⡀⠈⠀⠡⠘⢧⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⢠⠀⠀⠉⢀⡵⠶⠀⠀⢀⣀⠀⠀⡀⠀⠀⢠⣆⣄⣤⠀⣠⣴⡀⡀⠀⣀⡠⠤⠭⣦⠉⠘⠄⠀⠙⢦⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⠞⢁⡜⠀⡤⠔⠋⣀⡴⠶⣶⣶⣾⡔⣦⠸⠾⢀⠈⠟⠋⠙⠃⠸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⡀⢾⠀⠢⣄⡙⢦⡀
⠀⠀⠀⢤⣤⠶⠒⠊⠁⠘⠿⠍⠀⠀⠀⣹⠋⠉⠀⠀⠉⠛⢛⣱⠾⣌⠁⠸⠀⠀⠀⠀⠀⠀⠚⢁⡶⢄⣀⠀⢴⠀⢍⠢⠈⢆⢢⠐⠄⢻⠀⡇
⠀⠀⠀⢠⣤⠈⣠⠀⠚⡡⠒⠀⠀⠀⠀⡇⠀⡇⠀⠀⣄⠀⢀⡺⡃⠀⠀⠀⠀⠠⠁⠀⠀⣀⠀⠀⠀⠈⠉⢱⡆⠂⠈⢧⡀⢸⢘⡄⠀⠸⠀⡇
⠀⠀⠀⠀⠀⡰⢁⡄⠘⢀⣗⠒⢹⠆⢆⠐⠀⣻⠖⠀⠉⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢤⡈⢹⠃⠛⠓⢤⡀⠀⠒⠦⣄⡀
⠀⠀⠀⠀⠀⢇⡸⣧⠀⠈⠩⢀⠸⡇⠀⢀⠾⠂⠀⠀⠀⠀⠐⠂⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡼⠀⠀⠀⠤⢀⣀⠀⠠⡈⢳⡀
⠀⠀⠀⠀⠀⠈⠃⢠⢀⠰⣆⠊⠀⠈⠀⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠉⠐⠂⠄⠀⠐⢄⢣⠀⠀⠑⣄⠀⢠⠉⠢⠘⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠘⣮⠇⠈⠑⠀⠀⠘⣶⠖⠊⠀⠀⠀⠄⠐⠀⠀⠘⢿⣿⣻⣿⣹⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⠀⠀⠘⣄⠸⡀⢀⡈⠶⢤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⡄⠀⡠⠀⠀⠏⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠛⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠟⢦⡈⠈⠂⠌⠉⠉⠀⠋⡵⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡇⡇⢧⡀⢘⠀⠀⠀⠀⠐⠁⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠡⡀⠀⠂⠀⠘⣴⢦⡀⠉⠙⠛⠉⠁⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡠⠈⠒⠥⠤⠿⣦⠀⠀⠀⠀⠀⠀⠀⠃⡄⢀⣠⡤⠉⠈⠉⠉⠷⢤⣦⠄⣀⠈⣲⣤⠀⠰⡇⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢨⠋⠀⡀⢀⠀⣀⡠⠀⠈⢳⡀⠀⠀⠀⠀⠀⡆⣣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢁⣎⠀⠀⠈⢢⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢰⡵⠛⠉⢰⠁⡀⠀⢳⣰⢄⣄⡦⠔⠛⠁⠀⠀⠀⠀⠀⠀⣀⠀⣠⡀⢀⡰⠋⠁⣀⠑⠀⠰⡄⠇⢯
⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⡿⢠⠁⠀⠘⢄⠳⡀⢄⣙⢀⠁⢬⡢⠶⢄⡀⣤⠀⠀⠤⠔⢟⠉⡄⠉⠁⠠⢄⣀⣀⡁⠀⠀⠀⠀⠀⢑⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠌⠧⣄⡀⠀⠈⠓⠈⢳⠱⡄⡇⠀⠠⡀⠀⠀⠀⠀⠀⠘⣄⠣⠘⢄⣀⣀⠨⡉⠉⠳⠈⡆⠀⠀⢀⡈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⠉⠂⠀⠀⠀⠊⠘⠁⠓⠀⠀⢧⠀⢢⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣾⠛⠛⣷⠶⠶⢾⠿⠾⣿⡟⢿⠾⠾⢶⠿⠷⠾⢿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠶⠾⠿⣶⡿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠒⠀⡆⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠤⠀⢠⡂⡀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢠⠎⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡄⠀⠀⠀⡂⠘⣦⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠈⠁⠀⠀⠉⠀⠁⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠘⠀⠀⢀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠁⢠⠤⠐⠁⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠀⡖⠈⠸⡗⢠⣤⣤⡤⣤⣤⣦⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠚⠐⠀⠀⠀⠈⠈⠉⠉⠁⠈⠍⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠠⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⡈⠁⠀⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠘⠶⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⠀⠀⣄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠈⠉⠻⠤⠃⠀⠴⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢤⣀⣀⡀⢀⣀⣠⣔⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣼⣧⠘⡆⠀⠀⠀⠀⠀⠀⠀⣸⢓⡿⣯⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣸⣰⣿⡀⠀⠀⠀⠀⠀⢀⣿⣼⡇⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣺⡇⣧⣽⣿⡟⠛⠛⠛⠛⠛⠉⠙⢻⣿⣟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⣿⣾⡿⠋⠀⣀⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢛⠁⣀⣹⣿⡿⠀⠀⢸⣿⣏⣤⣠⡌⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠘⠿⠙⣿⣿⣿⠆⠀⢿⣿⡟⠛⠿⠃⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠈⠛⠛⠁⠶⠟⠃⠻⡿⠃⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⣦⡀⠀⣀⡄⠀⢀⡀⠀⣶⣾⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⣿⠇⢎⢱⣦⢀⣼⢝⠀⣿⣇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⠀⢾⣿⣿⣿⣿⡿⠀⣿⣟⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠻⣿⡀⠙⢻⣿⣿⣿⠓⠀⣿⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡀⢷⣿⣿⡿⠻⠟⠯⣿⣿⡇⢰⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⠇⠀⢱⣟⠲⣶⣶⣶⠞⢹⣦⠀⠛⣥⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⣡⣌⣠⠀⠀⣿⠀⠛⠋⣉⣴⡟⠁⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣿⣿⣿⣧⠀⠙⠷⡶⠜⠛⠏⣁⣴⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣟⠙⠛⢶⢶⡶⠶⣶⠛⠉⠁⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠦⠾⠼⠧⠧⠾⠶⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢠⣿⠛⠿⣦⡀
⠀⠀⠀⠀⠀⢀⣿⠁⢀⡀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴
⠀⠀⠀⠀⠀⢸⣿⡀⢀⣧⠀⠘⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⢠⠇
⠀⠀⠀⠀⠀⣼⣿⡁⡈⢁⣠⣤⣽⣿⣿⣿⣿⣿⣶⣦⣤⣤⣴⣾⣿⣿⣿⣯⡁⠀⢰⠏
⠀⠀⠀⠀⠀⣿⣿⣷⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⡿⣿⣿⣟⢛⣿⣷⣤⠏
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢳⡽⣴⣽⢹⡿⣿⣿⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⡿⣟⢫⡛⠿⠟⠛⠻⠜⣿⠘⠷⠿⡾⠏⣷⠹⠘⢿
⠀⠀⠀⠀⣰⣿⣿⣿⣵⢬⣴⣴⣷⠶⠶⣶⠟⢻⠻⣶⡌⢻⣧⠀⠀⢰⣧⠶⣶⣦⡇
⠀⠀⠀⠀⣿⣿⣛⣷⣿⣿⣿⣿⣿⣿⣦⣝⡆⠈⢀⣼⣿⣌⣇⠀⠀⠉⡈⢀⠜⣴⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣭⣉⠙⣿⣿⣿⣿⡷⡦⠀⢿⣿⣿⣷⣀⣀⣻⡕⢺⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠡⠤⠮⠯⠉⠙⢿⣏⡝⠀⢿⣿⡟
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⡀⠂⠀⠀⢀⣠⣏⠀⠀⡜⠹⠃
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠚⢻⠋⢹⣷⠞
⠀⠀⠀⠠⠿⠿⣿⠿⠿⠟⠿⠿⢿⢿⡿⣿⣿⣿⣿⣿⣅⣀⣀⣀⣠⠟⠁
⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠶⠉⡙⠆⠉⢦
⠀⠀⠀⠀⠀⡠⠔⠣⢄⡐⢺⡧⠬⣿⠉⣿⠀⠀⠀⠀⠀⢀⠀⠄⣀
⠀⠀⠀⠀⢸⠀⣰⣂⢾⡋⠴⠛⠈⠉⠉⠑⠢⣄⠀⠀⡰⢁⠖⠀⠀⢣
⠀⠀⠀⠀⢸⠀⠙⠶⠉⠀⠀⠀⡾⠛⠛⠳⠂⠀⠑⣄⠃⠘⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⢆⡌⠀⠀⠀⠀⠀⠀⣠⣪⣤⣄⡀⠀⠈⠀⠐⢆⠀⠀⢀⠃
⠀⠀⠀⠀⠀⢸⣱⠞⠃⠀⠀⠀⠀⡟⠁⣠⡌⠳⠀⠀⠀⠀⠘⠀⣠⠎
⠀⠀⠀⠀⠀⠀⡍⢀⣀⣀⣀⠀⠀⠢⡀⠙⣁⠔⠀⢠⣠⠄⠘⠧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠈⠀⠈⠒⢄
⠀⢠⠊⣉⣉⡁⠙⢸⠋⢡⣬⢑⡀⠀⢈⠥⠥⠊⠁⠐⠃⢄⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠘⡄⠁⠀⠀⠇⠘⠦⡀⣭⠊⠁⢀⠅⠚⠁⠀⠀⠀⠀⠀⡇⠀⠀⡧⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢠⠖⠉⡔⢛
⠀⠀⠘⢆⡀⠀⠈⢓⢀⣤⡃⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢇
⠀⠀⢀⠜⠉⢱⢲⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⠃⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀⠀⠉⠐⠒⠉
⠀⢀⠎⠀⢀⠃⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡠⠋⡆⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠎⠀⠀⠘⠀⠡⡑⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⡠⠊⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡘⠀⠀⠀⡀⠀⠀⠑⢄⡉⠐⠒⠒⠂⠈⠉⠁⢀⠤⠊⠀⠀⠀⠀⠇⠁⠀⡀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠘⠀⠀⡆
⡇⠀⠀⠀⢁⠀⠀⠀⠀⠈⠁⠒⠂⣤⠔⠶⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠓⢄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡄⠀⢠
⡇⠀⠀⠀⠘⣄⠀⠀⠀⠀⢀⡠⠚⠁⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠈⠣⡀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⢁⠀⠘
⢣⠀⠀⠀⠀⠈⠁⠐⠂⠈⠁⠀⠀⠀⠀⠀⢀⠵⡄⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢡⡀⠀⠀⠀⠙⠀⠀⡇
⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠘⠄⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⢢⠀⠀⠀⢸⠀⠀⡇
⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡎⢢⠀⠀⠀⠀⠑⢄⠀⢈⠀⠀⡇
⠀⠀⢧⠓⠜⠧⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠀⣾⠃⠈⠀⠀⠃
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡇⠀⢠⠃⠀⢠⢓⡔⢠⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃⢀⠆⠀⠀⠂⠀⢠⠇⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠤⣀⠀⠀⠀⢸⠀⠀⠈⠑⠦⡀⠀⠀⠀⠀⢨⠀⠀⠀⢰⠀⡌⠀⠀⡘⠁⡠⠋⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠑⠢⣀⠈⡀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡜⠀⠀⠀⠈⡘⠀⠀⢰⡥⠞⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢀⠀⠀⠈⠑⠶⠀⠀⢣⠀⠀⠀⠈⠳⡎⠀⠀⠀⠀⣷⠁⠀⢠⠋⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠉⢦⡀⠀⠀⢡⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⣸⠃⠀⢠⣃⡠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠻⡦⡀⠀⢃⠀⠘⡀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢠⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠤⢤⣀⠠⠤⠤⠠⠶⢦⡽⣌⠲⠤⣆⠀⢱⠀⠀⠀⠀⡠⠞⡜⠀⢠⠃
⠀⠀⣠⣶⣉⠀⠂⢀⡉⠠⢀⣀⠲⠦⠤⠤⠤⠴⠚⠆⠀⢬⣦⣤⣏⠈⠉⠁⠀⡶⠶⣤⠗⠈⠉⠁⠀⠀⠀⠀⢈⣉⡐⠒⠠⢄⡀
⠀⠸⣯⡙⣁⠴⢊⡤⠄⠂⠀⠈⣀⠠⠄⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠑⠢⢍⡳⢄
⠀⠀⠀⢸⣧⠞⢣⠀⠤⠚⠁⠀⠀⠀⠀⣀⡀⠦⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢠⠚⠃⠀⠈⠁⠀⠲⢤⡀⠀⠉⡾⣥⡀
⠀⠀⠀⠀⠩⣷⡟⠛⡄⠀⢀⡠⠔⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠓⠤⢀⣀⣀⣀⠀⠀⠀⠁⠂⠷⠟
⠀⠀⠀⠀⠀⠘⠼⠶⠧⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠐⠄⡈⢓
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡊⠉⠠⢀⠒⠒⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⣤⣼⡟⠀⠀⢀⣹⣮⣎⣀
⠀⠀⠀⠀⠀⠀⠀⡐⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⠟⠛⢿⣿⣇⠀⠀⠈⠹⡿⠟⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢲⣾⣿⠀⠀⢄⡤
⠀⠀⠀⠀⠀⠀⠀⠅⢠⣾⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⣿⣿⣿⣿⠯⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣧⢈⣿⣿⣿⣿⣷⣣⣧⡀⡀⠀⠀⠀⣀⣼⡇⡀⠀⠀⠀⢸⠾⠟⠃⠰⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⡟⠙⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣆⠀⠀⠀⠘⠁⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠟⣻⡿⡹⣿⣟⣫⡈⠙⠿⣿⣿⣿⡿⠿⠿⠿⣿⣄⡀⣴⣄⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠰⠚⠙⢡⠹⣿⣿⠟⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⣿⠁⠛⢿⡴⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠠⡿⠀⢻⡟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⡇
⠀⠀⠀⢀⠀⣄⠀⣟⠀⡀⠀⠀⠈⢇⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠄⠀⡁⢀⠀⢀⡠⣀
⠀⠀⠀⠉⠨⠿⠶⠿⠿⠽⠴⠾⠿⠿⣿⢿⣶⡷⠖⠲⠶⠶⠞⠓⠶⣿⣴⣾⡦⣿⣿⣷⣴⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⠶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢻⣦⣍⠳⣄⠀⢀⣠⠶⠚⠋⠋⠁⠛⠙⠛⠻⠶⢤⣄⠀⢠⢛⣵⣶⡟⠋⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢠⠀⠀⣿⣿⣿⣾⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣓⣡⣿⣿⡃⠀⢠⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠳⣦⣼⣿⣿⠉⠁⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⠎⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⣛⡛⠁⣴⠞⢛⣛⣛⡛⣿⣦⠀⠀⢠⣴⠿⣛⡛⠻⢶⡆⠈⠛⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠸⢃⢖⡍⠉⠉⠩⡿⣿⠀⠀⣿⡷⠟⠋⠃⠉⡲⣝⠆⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢿⢸⠀⢴⡦⠀⢀⣿⠀⠀⣿⠀⠀⣴⡄⠀⠙⢹⠀⠀⠀⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢘⣐⠀⠀⠀⠀⡰⢻⠀⠀⢻⠄⠀⠀⠀⠠⣠⣥⠤⠐⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠈⠛⠷⠦⣶⠞⠋⠸⣶⣶⡷⠀⠳⢦⣴⠾⠟⠁⠀⠀⢠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⡀⠀⠠⣾⠃⠀⠀⠀⠙⠋⠀⠀⠀⠀⣽⣦⣤⣤⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣾⣿⣷⣤⣀⣀⠉⠉⢁⣀⣠⣶⣿⢿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⠿⣶⣿⡋⠙⠙⢻⠟⠻⠟⢏⣡⣭⣾⢋⠉⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣾⣿⣷⡿⡁⠀⠈⢿⠛⠓⣾⡷⣺⣶⡖⠋⣉⣤⡏⠀⡠⠰⣨⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡎⢢⠔⠙⠿⣦⡀⠀⠀⠈⡟⠶⠟⣳⠟⣏⠙⠛⠁⣸⠆⠀⣹⡾⠃⠈⠁⠸⠆⠙⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠔⠁⠐⡄⠀⠈⠙⡷⠀⠀⢲⡄⠀⣧⣾⠟⡀⠀⢀⠃⠀⠀⠙⠃⡄⠠⢀⠋⠀⠁⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣘⠀⠀⠀⠀⠘⡀⠀⡞⠁⠄⠀⠈⢷⣸⡿⠃⣴⣇⠀⡈⠀⠀⢀⠀⡜⢠⠃⡀⠀⠀⠀⠘⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⡀⠀⠂⠘⢄⠀⠀⠀⠸⡟⢡⣾⡿⠩⢰⠃⠀⠀⢀⠾⠄⠉⢀⣌⣤⣄⣀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⡀⠀⠀⠈⠁⢀⡌⠀⠈⢷⡀⠀⠀⢷⣿⠋⢀⣼⡇⠀⢀⣴⡋⣈⣉⣶⠞⡫⢛⠅⣩⠃⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠠⣐⢸⡇⢀⠠⠈⢷⡉⠀⠸⣇⣴⣿⣏⠀⢀⣼⣿⢁⠀⣴⠃⠀⠀⠡⢊⣆⠀⠀⢁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠠⠀⠀⠀⠀⠄⣼⣿⣾⠶⠶⣿⠉⠐⠓⠛⠿⠛⠓⠒⠻⠿⠿⠾⠿⠥⠤⠤⢰⣒⠺⠧⢀⡀⢺⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠂⠀⠀⠀⠀⠁⡿⠋⠀⠀⢠⡇⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⢼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣸⣶⠶⠶⢶⣾⠖⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠀⠀⠠⠊⢀⠈⠈⠃⠙⠛⠢⢤⣄⣂⠐⠂⢠⣀⣄⡀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⣴⣿⣟⣻⣶⣄⣀⣈⣀⣀⣐⣷⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⡀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⣿⡿⠿⠚⠉⠉⠈⠉⠹⠛⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠷⣷⣦⣠⣴⣾⣿⣧⣶⣤⣤⡤⠤⠶⠖⢻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠩⢍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇