Numeral Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠔⣠⠴⠒⠒⠒⠦⣌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣪⠴⠖⠒⠲⠦⣭⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⡠⠔⠒⠒⠦⣌
⠀⠀⠀⠀⠀⠀⢡⠎⠀⠀⠀⣶⠀⠀⠀⠙⣄⢀⠀⠀⠀⠀⠀⠀⢠⣳⠞⠁⠀⢠⠶⣦⠀⠀⠹⣎⢂⠀⠀⠀⠀⠀⢀⠊⠔⠁⠀⢠⠶⣦⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡄⡀⠀⠀⠀⠀⠀⣶⡏⠀⠀⠀⠈⢀⣿⠀⠀⠀⠸⡆⠆⠀⠀⠀⠀⡌⠾⠀⠀⠀⠀⢀⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⠇⠃⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⢰⠟⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠇⠄⠀⠀⠀⠀⠉⣿⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠡⡹⣄⠀⠀⠀⠿⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠰⡻⣄⠀⠀⢸⣤⣤⠀⠀⢀⡞⡐⠀⠀⠀⠀⠀⠘⡀⢄⠀⠀⠸⢦⠿⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠐⠘⡳⢤⣄⣀⣠⡤⠖⠩⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣳⣤⣄⣀⣀⣤⢶⡫⠊⠀⠀⠀⠀⠀⠀⠀⠈⠪⡳⢤⣄⣀⣀⣤⠔⡋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠴⠶⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⡴⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⡤⠶⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⢈⡴⠋⠀⣀⠀⣀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⡀⣴⠋⠁⠀⣤⣤⡄⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⢪⡞⠉⠀⢀⣤⣀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⡌⡾⠀⠀⠀⣿⠀⣿⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠰⣼⠃⠀⠀⠀⣷⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣈⡟⠀⠀⠀⣿⠀⠉⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠄⣇⠀⠀⠀⠻⠤⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠛⠙⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠟⣇⠀⠀⠀⣿⠛⣷⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠰⡹⣄⠀⠀⠀⠀⣿⠀⠀⠀⣰⠃⠁⠀⠀⠀⠀⠈⠜⣆⠀⠀⠀⣦⣠⡇⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠐⠻⡄⠀⠀⢿⣀⡿⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠐⢝⠳⣄⣀⣀⣉⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠪⡳⣤⣀⡀⠁⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⢝⠶⣄⣀⣉⣀⣀⡴⠞⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣂⡥⠶⠶⠶⢬⣔⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣠⡥⠴⠦⢬⣅⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⣢⡭⠥⠬⣥⣒⠤⡀
⠀⠀⠀⠀⠀⠠⢢⠞⠁⠀⢠⣤⣄⠀⠈⠳⣌⠀⠀⠀⠀⠀⠀⠀⠐⡱⠋⠁⢀⣠⣄⠀⠈⠙⢆⠠⠀⠀⠀⠀⠀⠀⠀⣼⡵⠋⠀⠀⣤⣄⠀⠈⠳⣌⢄
⠀⠀⠀⠀⠀⢡⡏⠀⠀⠀⠀⢰⠇⠀⠀⠀⢸⡄⡀⠀⠀⠀⠀⠘⣸⠁⠀⠀⢸⡇⢸⠀⠀⠀⠈⣇⢁⠀⠀⠀⠀⠀⡸⡿⠀⠀⠀⢸⡇⢸⠀⠀⠀⠸⡆⠄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⢨⡇⠇⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡗⢿⠀⠀⠀⠀⣽⠠⠀⠀⠀⠀⠀⠟⣇⠀⠀⠀⠘⠷⢾⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢣⢳⡀⠀⠀⢰⡇⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠘⡘⣄⠀⠀⢸⣇⣸⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠐⢻⡄⠀⠀⢰⣄⣸⠀⠀⠀⣼⢣⠁
⠀⠀⠀⠀⠀⠀⠑⢝⣦⣄⣈⡀⣀⣀⡴⢚⠔⠀⠀⠀⠀⠀⠀⠀⠀⠌⠳⣄⣀⠉⠁⣀⣠⠔⡃⠂⠀⠀⠀⠀⠀⠀⠀⠑⢟⣦⣄⣀⠈⢁⣀⡤⢞⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠩⠟⠉⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠍⠩⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠻⠙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢐⣒⣂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣡⠖⠋⠉⠉⠉⠙⠳⣮⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡾⠁⠀⠀⢸⠋⣷⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠃⠀⠀⠀⢸⠀⣿⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⡆⠀⠀⠀⢸⠀⣿⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡹⣄⠀⠀⠘⠶⠛⠀⠀⣠⠟⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢿⢶⣤⣤⣤⠴⣚⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⢀⣠⠴⠖⠛⠋⠉⠉⠙⠛⢶⣤⡀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣠⣴⣏⠡⠐⠑⣀⣀⣁⣀⠀⠀⠀⠙⢋⢦⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣾⣿⣟⣟⣿⣳⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠈⠙⢿⣧⠀⠀⢸⡇⠄⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠛⠿⢾⡧⡀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢸⡇⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⢀⣿⡑⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡽⠁⢀⡼⠑⠂⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣁⠄⠀⣠⡾⡛⢁⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣃⠚⠁⣠⣾⡿⠓⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡡⠒⠁⣠⣾⡿⠚⢠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣁⠂⠀⣠⣾⡿⠋⣠⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠔⠁⢠⣾⣿⢿⢁⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠌⠀⢰⣿⣿⠻⠛⠛⠛⠛⠛⠒⠛⠛⠛⠛⡛⢻⣿⣿⣷⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⠋⣠⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡟⠃⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣯⣾⣿⣿⣿⣿⡷⠿⣿⡿⠿⠝⠛⠻⠟⣿⣽⣿⣷⣄⣹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣿⣿⣿⣾⣶⣾⣶⣷⣶⣶⣶⣶⣷⣶⣿⣿⣿⣿⣻⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠿⠿⠿⢿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⣿⠀⠈⣿⠁⠀⠀⠀⠀⠀⣿⡇⠀⢹⡇⠀⢹⡇⠀⠀⠀⠀⠀⢸⡏⠀⠈⣿⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⡄⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣿⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠚⠛⠒⠚⠛⠓⠀⠀⠀⠀⠒⠛⠓⠒⠛⠓⠒⠛⠛⠂⠀⠀⠀⠐⠚⠛⠂⠀⠀⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠈⣿⠋⠀⠀⠀⠀⠈⢹⣏⠁⠈⢹⡏⠉⢹⣟⠁⠀⠀⠀⠀⠉⣿⡉⠀⠉⣿⠉⠉⣿⡏⠉⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡟⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡆⢀⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠘⣷⠀⣼⡇⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠁⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⣿⡇⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠄⠀⠀⠾⠿⠆⠀⠀⠀⠀⠀⠀⠸⠿⠧⠀⠀⠰⠿⠧⠰⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠐⢲⣖⠂⠐⢲⡖⠒⢲⣶⠒⠒⣶⠒⠒⣶⠒⠀⠀⠀⠀⠐⣶⡖⠒⢲⣖⠂⠐⣶⠒⠂⠀⠀⠀⠀⠒⣶⡂⠀⢲⡖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣼⡇⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⡆⣼⠏⠀⠀⠀⠀⠀⠀⠀⠘⣷⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣿⠀⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⡏⠀⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠇⠀⠀⢸⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣾⠃⠸⣧⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠄⠀⠀⠼⠿⠤⠤⠿⠤⠤⠿⠤⠀⠀⠀⠀⠠⠿⠧⠤⠼⠧⠄⠠⠿⠦⠄⠀⠀⠀⠀⠤⠿⠄⠀⠼⠷⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⠀⠠⣦⠴⠀⢦⡴⠀⠀⠀⠀⠀⠀⠀⠀⠶⣦⡆⠀⢰⡤⠆⠰⣶⠤⠴⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⣰⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢀⣾⠁⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢹⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠈⣿⡀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣏⠀⢀⣻⣆⣀⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡁⠀⣸⣧⣀⣀⣿⣀⣀⣿⣀

⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⢀⣴⣄⠀⣀⣦⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⣴⣄⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⣠⣤⠀⠀⢀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢹⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢻⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠉⣿⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⡆⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣷⢀⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠐⢿⠆⠀⠀⠀⠀⠀⠐⢿⠗⠀⠰⡿⠂⠀⠀⠀⠀⠀⠀⢾⡷⠀⠐⢿⠗⠀⠰⡿⠂⠀⠀⠀⠀⠀⠀⠺⡿⠂⠀⠀⠀⠰⡿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⡀⠀⠀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⢹⡟⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⢸⡟⠁⠀⢹⡟⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⢈⣿⠓⠀⠘⣿⠁⠀⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⡾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢸⠇⠀⠀⠀⣿⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡿⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⠀⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠄⠀⠀⠀⢠⣿⠄⠀⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⣿⠷⠀⠐⣿⠇⠀⠺⣿⠂⠀⢾⡗⠀⠀⠀⠀⠀⠀⠐⢿⡗⠀⠸⢿⡇⠀⠀⢀⣿⠷⠀⠀⠀⠀⠐⢿⣇⠀⠀⠀⣿⠿
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢠⡟⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣄⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣸⠁⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡏⠀⠀⠀⠀⣾⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠟⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡁⠀⠀⠀⢀⣿⡀⠀⣠⣷⡀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⢠⣴⡏⠀⠀⠘⣷⣤⠀⠀⠀⠀⠀⣴⡟⠀⠀⠈⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠁⠀⠈⠋⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠈⠛⠁⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢐⣾⡆⠀⢴⣷⠄⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⣾⡷⠀⠠⣾⠄⠀⢴⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢀⡾⠃⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⣼⠋⠀⠀⠀⣿⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⠁⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢳⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠻⣄⠀⠀⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⢻⣄⡀⠀⢀⣇⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠹⣦⡀⠀⠀⣿⡀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠂⠀⠀⠐⠻⠇⠀⠙⠟⠁⠀⠀⠀⠀⠈⠟⠃⠀⠀⠀⠛⠏⠀⠈⠛⠁⠀⠙⠟⠁

⣶⣶⣶⣶⣶⡾⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢾⣶⢿⠾⣷⠶⣶⡶⠶⠶⢿

⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣀⣀⣀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⠀⣀⣀⣀⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣧⠀⠀⢸⡏
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⡆⠀⣿⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣧⣸⡏
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠐⠓⠛⠓⠃⠀⠀⠀⠀⠓⠛⠓⠓⠘⠓⠛⠛⠃⠀⠀⠀⠘⠚⠛⠚⠂⠓⠛⠛⠚⠐⠓⠛⠓⠃⠀⠀⠀⠚⠚⠛⠒⠀⠀⠀⠚⠛⠛⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⢿⡍⠁⠉⣽⠏⠉⠀⠀⠀⠀⠉⠹⣿⠉⠈⢩⡿⠉⠁⠉⢹⣿⠉⠁⠀⠀⠈⠉⢻⡏⠁⠈⢹⡏⠉⠀⠉⢹⡏⠉⠈⠉⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣼⠇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⣿⠀⢀⣿⠁⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢰⡿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢹⡇⣸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠿⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠴⠄⠀⠀⠰⠴⠿⠴⠀⠀⠀⠀⠀⠀⠶⠾⠷⠶⠀⠀⠀⠶⠾⠷⠶⠰⠶⠿⠶⠆


⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡟⠃⠘⢻⡟⠙⠃⠛⢻⡟⠛⠀⠛⣿⠛⠃⠘⢻⣿⠛⠁⠀⠀⠀⠀⠀⠀⠛⢻⡟⠛⠘⠋⢿⣟⠃⠘⣻⡟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⣆⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣼⠏⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠼⠿⢤⠀⠀⠀⣤⠼⠧⢤⠠⡤⠿⠦⡄⢠⠼⠿⢤⠄⠀⠀⠀⠀⠀⠀⢤⠼⠧⣤⠠⡤⠾⢧⡄⢠⠽⠧⢤


⠀⠀⠀⠀⠰⠲⣶⡲⠂⠶⣶⡖⠒⠀⠀⠀⠀⠀⠰⠒⣶⡶⠆⠲⣶⡶⠲⠐⠖⣶⡖⠆⠀⠀⠀⠲⠲⣶⠲⠀⠖⣶⠖⠆⠰⠲⣶⠲⠆⠲⢲⡶⠲
⠀⠀⠀⠀⠀⠀⠘⣷⡀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⣰⡟⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠹⣧⠀⣼⠏⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢙⣿⡃⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣼⠟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢿⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⠛⣷⡀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣀⣾⣃⡀⣈⣿⣄⣀⠀⠀⠀⠀⠀⢀⣀⣼⣏⡀⣀⣿⣆⣀⠀⣀⣿⣇⡀⠀⠀⠀⣀⣠⣿⣁⠀⣈⣷⣄⣀⢀⣀⣿⣀⡀⣀⣸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢶⡶⡶⠶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⣠⣶⣖⠀⠀⠀⠀⠀⠀⠀⣴⡶⠿⢿⣶⣄⠀⠀⠀⠀⢠⡶⠒⠲⣶⡄⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡧⠀⠀⠀⠀⠀⠀⣶⠴⠶⠶⣴⠂
⠀⠀⠀⠀⠛⣯⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⣿⣿⠀⠀⠀⠀⢈⣀⡀⢀⣿⠇⠀⠀⠀⠀⠀⠀⣰⡏⢸⣿⡇⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠈
⠀⠀⠀⣀⠀⣯⡇⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⡼⠟⠃⢠⡀⠀⠀⠀⠑⠚⠛⢷⢤⠠⠀⠀⠀⠀⣰⠟⣨⢸⣿⡇⢰⡆⠀⠀⠀⠈⠉⠉⠋⢻⡿⣄⠢
⠀⠀⠀⠈⠀⣟⡷⢀⠀⠀⠀⠀⣶⣾⣶⡏⠁⠀⠠⢠⠈⠇⠀⠀⣤⠁⠀⠄⢸⣭⢡⠄⠀⠀⠀⣿⣾⡿⢾⣿⡷⠟⠁⠀⠀⠀⣤⣀⠀⠂⠀⡯⡿⠃
⠀⠀⠀⠀⠰⠿⠷⠄⠀⠀⠀⠀⠱⠟⠿⠿⠿⠿⠿⠿⠀⠀⠀⠘⠛⠳⠤⠴⠛⠃⢿⡀⠀⠀⠀⠛⠛⠳⠾⠿⠷⠞⠀⠀⠀⠈⠛⠷⠦⠤⠾⠛⠁


⠀⠀⠀⣠⡴⠶⢦⣤⠀⠀⠀⠀⠀⢠⡦⠶⢤⣦⣶⠂⠀⠀⠀⠀⢀⡤⠀⠦⣤⡀⠀⠀⠀⠀⠀⣠⡤⠖⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠲⢶⣄
⠀⠀⣾⡿⣏⣀⣀⠼⠤⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⣄⣾⣧⣤⣀⣿⡇⠀⠀⠀⠀⡼⣿⠀⠀⡂⢻⡷⠀⠀⠀⠀⠤⣼⣿⠀⠄⠈⣿⣧
⠀⢸⣿⣿⣋⡉⠙⣿⣆⠀⠀⠀⠀⡀⣀⢀⣾⢁⡀⠀⠀⠀⠀⢛⣾⣿⠿⣿⣿⣄⠀⠀⠐⠞⢿⣿⡀⠀⢀⣼⣛⡇⠀⠀⠀⢰⣿⡇⢀⣄⣀⣿⣿
⠀⣘⣿⣿⢛⣉⠀⣼⣿⢀⠀⠀⠀⣉⣹⣿⣿⠛⠀⠀⠀⠀⢀⢸⣿⠑⠓⠈⣿⣿⡗⠀⠀⠘⠁⠈⠛⠛⢛⣿⣿⢷⣶⠀⠀⡀⣿⣿⠈⣛⢻⣿⣿⠶⢆
⠀⣿⠛⠻⠦⣡⡴⢟⣁⠀⠀⠀⠀⠈⢸⣯⣿⡘⠁⠀⠀⠀⢰⠚⠻⢦⣎⣥⠾⠟⠛⠁⠀⠀⠀⠿⡦⣤⣾⡿⠷⠊⠀⠀⠀⠀⠈⠻⢦⣭⠼⠋⠀⠃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠀⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠆⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⣠⡶⠒⢢⡀⠀⠀⠀⠀⢠⡶⠒⣦⠀⠀⠀⠀⢠⡆⠀⠀⢰⠀⠀⠀⠀⡴⠖⠲⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠰⡟⠀⠀⠀⣷⠀⠀⠀⠀⠈⠀⠀⣸⠀⠀⠀⠀⣾⠁⠀⢠⡏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⢰⠇⠀⠀⣼⠀⠀⠀⠀⢰⣇⡠⠤⢤⣀
⠀⠀⠀⠀⠐⠋⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠸⠋⠉⠹⣆⠀⠀⠉⠉⠛⢻⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⢀⣼⠇⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠸⣆⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠐⠒⠛⠒⠀⠀⠀⠀⠛⠓⠒⠒⠒⠒⠂⠀⠀⠘⠛⠒⠒⠛⠁⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠁

⠀⠀⠀⠀⣠⠴⠖⠒⠒⢦⠀⠀⣰⠖⠢⡀⠀⣀⣤⠀⠀⠀⠀⣠⠖⠒⢲⡀⠀⠀⢠⡶⠒⠒⠦⣄⠀⠀⠀⠀⢀⡴⠒⠒⣄
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⠉⣹⠃⠀⠀⠀⢰⡏⠀⠀⣸⠃⠀⠐⠟⠀⠀⠀⠀⠸⣆⠀⠀⢠⡟⠀⠀⠀⢸⡆
⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⢷⣀⣴⠏⠀⠀⠘⣗⡀⠀⠀⠀⣀⣟⠀⠀⣿⠃⠀⠀⠀⢸⡇
⠀⠀⣿⠀⢀⣤⠶⠶⢤⣄⠀⠀⠀⠀⠠⠶⣾⠶⠖⠀⠀⠀⣠⠜⠛⢦⡀⠀⠀⠀⠈⠻⠦⠤⠶⠋⣿⠀⠀⡿⠀⠀⠀⠀⢸⡇
⠀⠀⢹⣴⠋⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣼⠁⠀⠀⠀⠙⣆⠀⢠⡄⠀⠀⠀⠀⢰⡇⠀⠀⣧⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠻⣄⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣠⠏⠀⠸⣇⠀⠀⠀⢀⡾⠀⠀⠀⢹⡄⠀⠀⣸⠏
⠀⠀⠀⠀⠈⠛⠒⠒⠋⠁⠀⠀⠀⠐⠒⠛⠒⠀⠀⠀⠀⠈⠙⠒⠒⠊⠁⠀⠀⠀⠈⠛⠒⠒⠋⠀⠀⠀⠀⠀⠙⠲⠚⠁

⠀⠀⠀⢴⠀⠀⠀⠀⢰⠀⢰⠆⠀⠀⠀⢰⡆⢰⡆⢰⡆⠀⠀⠀⠀⡆⠀⣆⠀⠀⢰⠀⠀⠀⠀⢰⡄⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⠀⠀⠀⠀⡇⠀⢻⡀⠀⡆⠀⠀⠀⠀⠈⣇⠀⢠⠁
⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⠀⠀⠀⠀⡇⠀⠘⡇⢠⠁⠀⠀⠀⠀⠀⢹⡀⡘
⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⠀⠀⠀⠀⡇⠀⠀⢿⡜⠀⠀⠀⠀⠀⠀⠘⣧⠃
⠀⠀⠀⠙⠀⠀⠀⠀⠘⠀⠘⠁⠀⠀⠀⠘⠃⠘⠃⠘⠃⠀⠀⠀⠀⠃⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⣀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⢀⡀⢀⡀⢀⡀
⠀⠀⠀⠀⣷⠀⠀⡘⠀⢸⠀⠀⠀⠀⠀⢸⡆⠀⢀⠇⠀⡇⠀⣿⠀⠀⠀⠀⠀⢿⠀⠀⡸⠀⢸⠀⢸⡇⢸⡇
⠀⠀⠀⠀⢸⡆⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⣷⠀⡸⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⢸⡆⠀⠇⠀⢸⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⣧⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡄⡇⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⢸⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠸⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠧⠀⠿⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠸⠄⠸⠇⠸⠇


⠀⠀⠀⣶⠀⠰⡀⢀⡖⠀⠀⠀⠀⠐⡆⠀⣶⠀⠀⠀⠀⠀⢂⠀⢰⠆⠀⣶⠀⠀⠀⠀⠲⡀⢀⡖⠀⢲⠂⢰⠂
⠀⠀⠀⣿⠀⠀⢣⡼⠁⠀⠀⠀⠀⠀⠘⣰⠃⠀⠀⠀⠀⠀⠈⢦⡏⠀⠀⣿⠀⠀⠀⠀⠀⢣⣼⠁⠀⢸⠀⢸
⠀⠀⠀⣿⠀⠀⣸⢇⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⡾⡀⠀⠀⣿⠀⠀⠀⠀⠀⣸⢇⠀⠀⢸⠀⢸
⠀⠀⠀⣿⠀⢠⡏⠈⡄⠀⠀⠀⠀⠀⡾⠀⢃⠀⠀⠀⠀⠀⣸⠃⠱⠀⠀⣿⠀⠀⠀⠀⢠⡏⠘⡄⠀⢸⠀⢸
⠀⠀⠀⠉⠀⠈⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠉⠀⠀⠀⠀⠈⠁⠀⠉⠀⠈⠀⠈⠁

⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠋⣀⣀⣈⣉⡉⠉⠉⠉⣩⣿⣿⠏⠀⠀⠀⠀⠿⠿⠿⠿⠿⢿⣿⣿⡆⠀⢀⣀⣀⣀⣀
⣿⣿⣿⡆⠀⣀⣴⣾⣿⣿⣿⣶⣦⡈⠁⠀⢠⣾⣿⣿⣿⣿⣿⣷⠀⠀⠻⢿⣿⣆⠀⠀⣀⣴⣶⣶⣶⣦⣄⠸⣿⣿⡇⢰⣿⣿⣿⣿⣿
⣿⣿⣿⠃⢰⣿⣿⡟⠉⠛⠻⣿⣿⣷⡀⢀⣿⣿⡏⠁⠀⠈⢻⣿⣇⠀⠀⢠⣿⣿⠀⢰⣿⣿⠟⠉⢻⣿⣿⡀⢿⣿⠇⠈⠛⠻⠟⠛⠛
⣿⣿⠏⠀⢸⣿⣿⡀⠀⠀⠀⠸⣿⣿⡇⢸⣿⣿⠁⠀⠀⠀⠘⣿⣿⣷⣾⣿⣿⠟⠀⣿⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰
⣿⠋⠀⠀⠸⣿⣿⣷⣤⣶⣶⣾⣿⣿⡿⢸⣿⣿⣶⣿⣿⣿⣦⡈⠙⠿⠛⠛⣁⡀⠀⢹⣿⣿⠀⠀⢰⣿⣿⡇⠀⣤⡀⠀⠀⠀⠀⣴⣿
⠃⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⠛⣿⣿⡇⢸⣿⣿⣿⠿⠿⢿⣿⣷⠀⠀⣠⣾⣿⡇⠀⢸⣿⣿⠀⠀⢸⣿⣿⡇⢀⣿⡇⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠸⣿⣿⡇⠀⠀⣠⣿⣿⢠⣾⣿⣿⣿⡇⠀⠘⣿⣿⣦⣤⣾⣿⣿⠃⢸⣿⡇⠀⠀⣼⣿⣿⡿
⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣿⣿⡇⠀⠀⠈⠛⠛⠿⠿⠛⠁⠀⠸⣿⠇⠀⣸⣿⣿⡿⠁
⠀⠀⢸⣿⣿⡟⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣉⣙⣛⣛⠛⠁⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠻⡿⠛⠁
⣄⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣀⣠⣤⣤
⠿⠀⣿⣿⣿⣇⣀⣤⣄⣀⠀⠀⠀⠀⠀⣿⣿⡟⠉⠉⢻⣿⣿⡇⠀⠀⠘⣿⣿⠃⠀⠀⢸⣿⣿⡿⠉⠀⠀⣿⣿⣿⡀⠀⠀⠻⠿⠿⠿
⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣠⡀⠀⠀⢸⣿⣿⣷⣄⡀⢀⣿⣿⣿⡇⠀⠀⠀⢀⣠⣤
⣿⡄⠘⠻⠟⠛⠛⠛⠻⢿⣿⣿⣿⣇⢠⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⢠⣾⡿⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣾⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠸⣿⣿⠁⠀⠀⠀⣿⣿⠇⠀⣰⣿⡿⢡⣾⣦⠀⠀⢀⣬⣿⣿⣿⣿⣿⣿⡀⠀⠀⠘⠻⠟⠁⢸
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⣿⣿⠀⠀⠀⢰⣿⣿⠀⣼⣿⣿⣦⣾⣿⡇⠀⢠⣾⣿⣿⠟⠋⠀⠻⣿⣿⡄⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⠸⣿⣿⣆⠀⠀⣸⣿⣿⠀⠙⠛⠛⠛⢻⣿⡇⠀⣿⣿⡿⠁⠀⠀⠀⢀⣿⣿⣿⠀⠀⢀⣾⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⣷⠀⢿⣿⣿⣶⣶⣶⣶⣿⣿⣿⠟⠀⢠⣾⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠹⢿⠏⠀⠀⠙⠻⠿⠿⠿⠿⠿⠟⠉⠀⠀⠘⠛⠛⠛⠿
⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⣠⣶⣿⣿⣿⣷⣤⠀⠀⣴⣶⣶⣶⣶⣶⠆⠀⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣄⠀⠀⠀⣠⣶⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢰⣿⣿⠟⠋⠛⢿⣿⣇⠀⠀⠀⢀⣀⣀⠀⠀⠀⣿⡿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⠄⠀⢰⣿⣿⠋⠉⠉⢿
⠀⠀⢀⣼⣿⣿⣏⡀⠀⠀⢸⣿⣿⡀⠀⢀⣼⣿⣿⠀⢠⣾⣿⣿⣿⣿⡄⠀⣿⣧⣤⣄⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⣾⣿⣯⣤⣤⣤⣀
⡀⠀⠸⣿⡿⠿⣿⣿⡆⠀⠀⠻⣿⣿⣾⣿⣿⡿⠁⠀⠻⠟⠁⠀⣽⣿⡇⠀⠻⠋⠙⣿⣷⠀⠀⠀⣼⣿⣿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⣼⣿⡇⠀⢀⣼⣿⠟⠻⣿⣿⣧⠀⠀⠀⢀⣴⣾⣿⡟⢀⣴⣦⣀⣤⣿⣿⠀⠀⣸⣿⣿⡏⠀⢀⡀⣿⣿⣿⠀⠀⠈⣿
⢣⣤⣤⣄⣠⣼⣿⡿⠃⠀⣾⣿⡏⠀⠀⠈⣿⣿⡇⣠⣾⣿⣿⣟⣉⣀⣈⣻⣿⡿⠿⠛⠁⠀⢰⣿⣿⡿⠀⢀⣿⣿⢻⣿⣿⣦⣤⣾⣿
⠘⢿⣿⣿⣿⡿⠟⠁⠀⠐⣿⣿⣧⣀⣀⣼⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣥⣤⣼⣿⣿⠈⠻⢿⣿⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⡋⠉⠀⣿⣿⣿⣿⣿⡇⠀⣿⣿⡷⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣴⣿⣿⠀⠀⢿⣿⣿⡿⠋⠀⠀⠈⠁⣀⠀⠀⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⡄⠘⢿⣿⡿⠀⠀⣀⠉⠁⢀⣤⣄⠀⠀⣾⣿⣿⡄⠙⠛⣛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⣿⣿⠀⠀⠈⢀⡀⠸⠿⠷⠀⠘⣿⣿⠀⠀⣿⣿⣿⣿⠀⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢿⣿⣿⣿⠀⢸⣿⣿⣿⡆⢀⣤⣤⣄⡈⠁⠀⠀⠈⠛⠛⠁⠀⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢈⣛⠋⠁⢀⣀⠉⠛⠛⠁⢸⣿⣿⠿⣿⣦⠀⠶⣿⣷⠄⢰⣶⡄⠀⢈⡉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⠀⠺⠿⠇⢠⣿⠟⠋⠁⠀⠀⠀⠈⢳⣄⡀⠉⠀⠈⠉⠁⢰⣿⣿⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢠⣿⣷⣄⠈⠻⢿⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠃⠀⠈⠻⠿⠟⠀⠀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠁⢀⣴⣦⠀⢀⣴⣆⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣿⣿⠇⢀⣾⣿⣿⠀⢾⣿⡿⠀⠀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢁⣤⣀⡙⠋⠀⠘⣿⣿⠇⠀⢀⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⢿⣿⣿⣿⣷⡄⠀⠈⠉⠀⠀⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠋⠀⠈⢿⣿⣿⡿⠃⠀⣴⣿⣦⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣶⣶⡄⠈⠉⠀⠀⠀⢿⣿⠟⠀⠀⠀⠀⣾⣷⡝⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⣄⣰⣶⣦⡈⠀⠀⢠⣾⣧⠀⠙⠛⣁⡀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡷⠀⠀⣿⣿⣿⠀⢠⣾⣿⣿⡇⢀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠈⠙⠁⠀⣿⣿⣿⡿⠁⠈⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣤⠀⠀⠙⠛⠋⠀⠀⣀⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⠀⠀⢨⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⢀⣤⣶⡆⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢻⣿⡿⠃⠀⠀⠘⣿⣿⣿⡿⠉⠲⢤⣄⣀⣀⣠⠞⠙⠛⠁⠀⠈⠻⠟⠁⠀⠸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠉⠀⣠⣶⣦⡄⠈⠉⠉⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⢠⣾⣿⡆⠀⢀⣤⣤⡀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠹⢿⠟⠁⣠⣴⣶⣶⣦⠀⠙⠿⢿⡿⠏⠀⠀⠻⣿⣿⠇⠀⣿⣿⣿⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠋⠀⠀⠀⣀⡀⠀⠹⣿⣿⣿⣿⠇⠀⠀⣀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠘⠻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣰⣿⣿⣿⣷⣄⠈⠉⠋⠁⢠⣶⣿⣿⣿⣆⠀⣾⣿⣿⣿⡿⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣇⠀⠀⠀⢿⣿⣿⣿⣿⣿⢀⣈⣻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠶⣶⠶⠀⠀⠀⠰⢶⡶⠆⠲⢶⠶⠀⠀⠀⠰⢶⡶⠆⠶⣶⠶⠀⠶⡶⠆⠀⠀⠐⠶⡶⠆⠰⢲⡶⠆⠶⣶⠶
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⣇⣿
⠀⠀⠀⣀⣿⣀⠀⠀⠀⢀⣸⣇⡀⢀⣸⣀⠀⠀⠀⢀⣸⣇⡀⣀⣿⣀⠀⣀⣇⡀⠀⠀⠀⣀⣇⡀⠀⠀⢀⣿⣇
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠀⠉⠉⠁⠀⠀⠈⠉⠉⠁⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠈⠹⣏⠁⢉⡿⠉⠀⠀⠀⠈⢹⡏⠁⢉⡟⠉⠈⢹⡟⠁⠀⠀⠈⠙⣿⠁⠉⣿⠉⠁⠉⣿⠉⠈⢹⡏⠁
⠀⠀⠀⠀⠀⠀⢿⡀⣸⠇⠀⠀⠀⠀⠀⠀⢿⠀⣸⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⡄⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣧⡟⠀⠀⠀⠀⠀⠀⠀⠸⣧⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⣧⣿⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢤⠿⢧⠄⠀⠀⠀⠀⠀⠀⢤⠿⢥⠀⠀⠠⡼⠧⡤⠀⠀⠀⠀⢠⠽⢧⠄⠀⠀⡤⠿⡤⠠⡼⠧⡄

⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⣀⣀⢀⣀⣀⡀⣀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⣧⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣿⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡞⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠒⠀⠀⠐⠚⠓⠂⠒⠚⠓⠂⠒⠛⠒⠀⠀⠀⠀⠀⠐⠚⠓⠂⠒⠛⠓⠐⠚⠓⠒

⠀⠀⠀⠰⠶⣶⠆⠴⣶⠶⠄⠀⠀⠀⠀⠶⣶⠆⠰⣶⠶⠆⠶⣶⠶⠀⠀⠀⠶⣶⡶⠠⢶⡶⠆⠰⢶⡶⠄⠶⣶⠶
⠀⠀⠀⠀⠀⠹⣆⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢷⣠⡟⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⢿⡀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⢀⣾⠁⠘⣧⡀⠀⠀⠀⠀⠀⢀⣼⠃⢈⣷⡀⠀⠀⣿⢀⠀⠀⠀⠀⣰⡏⠈⢻⡄⡀⠀⣸⡇⠀⡀⣿
⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠁⠉⠉⠉⠀⠀⠀⠉⠉⠉⠈⠉⠉⠁⠈⠉⠉⠁⠉⠉⠉

⠀⠀⣠⣾⠛⠱⣦⠀⠀⠀⠀⣴⠾⣷⠀⠀⠀⠀⠐⠾⠛⠿⣦⠀⠀⠀⠀⣴⡶⠤⡀⠀⠀⠀⠀⢀⣴⣆
⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠂⠀⠀⠀⢀⣀⣼⠇⠀⠀⠀⢠⣾⠛⣿
⠀⠀⢻⣇⠀⢀⣿⠃⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⠉⠙⣷⡀⠀⢴⣿⣥⣼⣿⣤
⠀⠀⠈⠻⠷⠿⠋⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠐⠟⠷⠒⠶⠂⠀⠀⠀⣤⣤⣤⡿⠃⠀⠀⠀⠀⠀⣿

⠀⠀⠀⢰⡶⠶⠶⠀⠀⠀⠀⢀⣤⣴⡶⠀⠀⠀⢠⣤⣴⣤⣴⡄⠀⠀⢀⣤⣤⣴⣤⡀⠀⠀⠀⣀⣤⢤⡀
⠀⠀⢀⣿⣤⣤⡀⠀⠀⠀⢰⣿⣋⣀⣀⠀⠀⠀⠀⠁⠀⣼⡿⠁⠀⠀⠺⣯⠀⣨⣿⠇⠀⠀⢰⣏⠀⠈⣿⡄
⠀⠀⠈⠉⠉⠻⣿⡆⠀⠀⢾⣿⠏⠉⠻⣷⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⣠⡿⠛⠻⣧⡀⠀⠀⠈⠿⠶⢾⣿⡇
⠀⠀⢠⣶⣴⣾⠟⠀⠀⠀⠘⢿⣦⣤⣴⠟⠀⠀⠀⣼⡏⠀⠀⠀⠀⠸⣿⣧⣄⣀⣿⠇⠀⠀⢠⣤⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣀⡀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⣀⣤⣤⠀⣤⣄⡀⠀⠀⣠⣤⡀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⡀⠀⠀⣀⣠⣤⣤⣤⣀⡀
⠀⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⣿⣿⣿⠁⠀⢾⣿⣿⠇⠀⣿⣸⡇⠀⣿⣿⣿⣿⡿⠿⠿⣿⣿⠿⠇⢠⣾⡿⠉⠀⠀⠈⠹⣿⣦
⠀⣿⣿⣯⣤⣬⣿⣿⣧⣄⠀⠀⣤⣤⣤⣴⣿⣿⡏⠀⠈⢙⣻⣿⡶⠤⠀⠀⠀⠀⠀⠾⠾⠇⠀⠀⠉⠉⠛⠛⠛⠿⠿⠟⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠿⠿⠿⠿⠿⢿⠿⣿⡿⠀⠀⣿⣿⡿⠿⠿⠋⠀⠀⠸⣿⣿⣿⡀⠀⢾⣿⣷⠀⠀⣴⢶⡆⠀⠀⢀⡤⠶⠶⢤⣀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⢠⣿⡿
⠀⣀⣀⡀⢀⣀⣀⡀⢀⣀⡀⠀⢀⣀⣀⠀⠀⣀⠀⠀⠀⠈⠙⠛⠛⠀⠚⠉⠁⠀⠀⠿⢶⡆⠀⢠⡏⠀⠀⠰⣄⠙⡆⠀⢠⣦⠀⠈⡛⠻⠶⠶⠾⠛⠋
⠀⣏⠉⠁⠘⠛⣿⡷⣿⣛⣿⡆⣿⡏⣿⡇⣾⠉⢹⡆⢰⣶⣶⣶⣶⣶⣶⣶⣶⠄⠀⢙⠛⠁⠀⠈⢧⡀⠀⣀⡿⠀⡿⠀⢸⣯⠀⠀⣟⠀⠀⠀⢀⣴⡆
⠀⠙⠛⢦⠀⢸⣿⢠⣿⠿⣿⡄⢿⡷⣿⡇⣿⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣿⣷⡆⠀⠀⠀⠉⠉⠉⠀⣰⠇⠀⢸⣷⣤⣤⣿⡀⠀⠀⠉⣿⡇
⠀⣀⣠⠞⠀⣿⡏⠘⣿⣦⣿⠃⢾⣦⣿⠇⠻⣤⡼⠃⠈⠛⠛⠛⠛⣿⣿⣿⣿⡇⠀⢿⡿⠁⠀⠀⢀⣀⣀⣠⠞⠃⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣤⣴⣤⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⢀⣤⣄⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠇⠀⠀⣴⣾⠟⠋⠉⠉⠉⠻⣿⣦⠀⢸⣄⠠⠦⠀⠀⢸⣿⣿⣿⡿⠀⠘⠳⣾⣅⣽⠂⠀⠐⣷⢦⣀⠀⠀⠀⠀⠀⠀⠒⢶⣄⠀⠀⠀⢸⡇
⠀⠀⠈⠉⠁⠀⠀⠻⣿⣦⣀⠀⠀⣀⣠⣿⠿⠀⢺⡇⢳⡞⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠉⠁⠀⠀⢸⣿⠀⠈⠛⠦⣤⣀⡀⠀⢀⣠⣿⠂⠀⠀⢸⡇
⠀⠀⠀⠠⡀⠀⠀⠀⣀⣭⡿⠿⠻⢿⣯⣄⠀⠀⢨⣡⣬⣩⠀⠀⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⡇⠀⠘⠛⠦⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠒⡅⠀⠀⠰⣿⣏⠀⠀⠀⠀⣹⣿⡇⠀⢀⢙⢬⣅⠀⢰⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⠁⠀⣴⢰⣦⠰⣶⡆⣴⢠⡄⣠⠖⠲⢤⠀⠀⠀⢸⡇
⠀⠀⠀⠒⠁⠀⠀⠀⠉⠛⠻⠶⠶⠿⠛⠋⠀⠀⠙⠛⠛⠉⠀⣸⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⠀⠀⣽⢺⣏⣰⢏⡀⠛⣂⠆⣇⠀⠀⢨⠇⠀⢀⣾⣇
⠀⠀⠲⣶⡖⠂⠀⢀⣀⣀⡀⠀⣀⣀⠀⣠⣀⢀⣀⣀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⡇⠀⠀⠉⠈⠁⠙⠛⠁⠉⠙⠁⠈⠙⠚⠁⠀⠀⠉⠉⠉⠁
⠀⠀⠀⣿⡇⠀⠀⡏⠀⠀⢹⠠⠍⣥⠘⢣⡿⢹⡇⣿⠀⠀⢠⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⠃⠀⣀⢤⣤⣤⠀⠀⠀⣀⣤⣤⣶⣦⣤⣄⡀⠀⠀⢠
⠀⠀⠀⣿⡇⠀⠀⠳⠤⠤⠞⠸⠇⠿⠱⠿⠦⠻⠇⠿⠀⠀⢸⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠀⠀⢉⡑⣦⡀⠀⠀⢾⣿⡏⠀⠀⠀⠈⣿⣿⠀⠀⠠⠉
⠀⠀⠀⣿⡇⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠐⢶⣤⠀⠀⣾⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⡇⠀⠀⣯⡝⢫⡝⠀⠀⠈⠛⣿⣶⣤⣴⣾⡛⠉
⠀⠀⠀⣿⡇⠀⠀⢸⣿⠉⠀⠀⠈⠉⠛⠦⣄⡀⢸⣿⠀⠀⠀⣀⣀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⡾⠷⣈⡧⠀⢠⣶⡿⠛⠉⠀⠈⠙⢻⣷⣄⠀⠀⠐⠂
⠀⠀⠀⣿⡇⠀⠀⠈⠛⠦⠄⠀⠀⠀⠀⠀⠀⠙⠾⡿⠀⠀⢸⣏⣹⠷⣦⠀⢠⣿⣿⣿⣿⠀⠀⠀⣙⣃⣘⡃⠀⠘⠿⣷⣄⣀⣀⣀⣀⣼⣿⠏⠀⠈
⠀⠀⠀⣿⡁⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠙⢉⣀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⣿⡇⠀⠀⠀⣸⣿⣤⣤⣤⠀⠀⢀⣴⠞⠉⠉⠉⠀⠀⢀⡿⣿⠀⠀⢸⣿⣿⣿⣧⣤⣤⣤⣤⢀⡶⠛⢦⢠⣾⠿⣷⣄⣾⡿⣷⡄⢰⣿⠀⣰⠚⠛
⠀⠀⠀⣿⠿⠃⠀⠀⠸⣿⠉⠉⣿⠀⠀⡾⠁⢀⣀⣀⡀⠀⠀⠘⠛⠿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⢸⢸⣿⢶⣷⡜⣿⣦⣿⠇⣿⡏⠀⠳⣄⣀
⠀⠀⠀⠁⠀⠀⠀⠀⠰⡿⠀⠀⣿⠀⢸⡇⢰⠏⠀⠈⠹⡆⠀⢠⣶⠶⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠸⣇⣀⣼⢸⣿⣨⣿⠇⣿⣏⣿⣶⣿⣁⡀⠀⠀⣹
⠀⠀⣠⣶⠶⠶⠶⢶⣦⣄⠀⠀⠋⠀⠈⣧⠈⠓⠀⠀⢠⡏⠀⢈⡋⣿⠀⠀⠀⣀⣤⡄⠠⣤⣤⣄⡀⠀⠈⠉⠀⠀⠉⠉⠉⠀⠉⠉⠉⠈⠉⠉⠁⠈⠉⠉
⠀⣾⣿⠃⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠈⠛⠲⠶⠚⠋⠀⠀⠈⢛⠛⠀⠀⠘⠿⠿⠗⠀⢸⣿⣿⣿⠀⢀⣤⣶⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢰⣶⡶⣶⣦⣤⣤⣀⣀⠀⢰⣿⣛⠀⠀⠀⠀⠀⠀⠛⢻⣿⣯⣄⠀⢸⣿⣿⡛⠛⠛⠛⠁⠀⠘⣛⣿⣿⡉⠉⢻⣿⣿⠁
⠀⠙⢿⣧⣀⣀⣀⣠⣾⡿⠁⢰⣶⣾⣿⣷⣶⣾⣿⣿⣿⣿⡇⠸⣯⣿⠁⠀⢾⣿⣿⠇⠀⣸⣿⣿⡿⠃⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⠄
⣀⣀⣀⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣈⣉⣁⣈⣉⣉⣉⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠈⠛⠛⣿⠟⠛⠁⠀⠀⠈⢻⣿⠛⣿⠛⠁⠀⠀⠙⢻⡟⢻⣿⠛⣿⠛⠀⠀⠀⠙⢻⡟⠻⣿⠛⠛⢻⣿⠛
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⢻⡇⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⣰⡿
⠀⠀⠀⠀⠀⣀⣠⣿⣄⣀⡀⠀⠀⢀⣸⣿⣀⣿⣀⠀⠀⠀⣀⣼⣇⣸⣿⣀⣿⣀⠀⠀⠀⣀⣼⣇⣀⣀⣿⣿⣇⣀⣀
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠘⠛⠛⠛⠛⠛⠁⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠈⠙⣿⡟⠉⠙⣿⡟⠉⠀⠀⠈⠙⣿⡟⠉⠙⣿⠏⢻⡟⠉⠀⠀⠀⠉⢿⡟⠉⠙⣿⠏⢻⡟⠙⣿⠋
⠀⠀⠀⠀⠀⠀⢸⣧⠀⢠⣿⠀⠀⠀⠀⠀⠀⠸⣧⠀⢸⡟⠀⢸⡇⠀⠀⠀⠀⠀⠸⣷⠀⢰⡿⠀⢸⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⣼⡇⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⣆⣿⠃⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣄⣀⡀⠀⠀⠀⣀⣀⣸⣿⣿⣀⣀⣸⣧⣀⠀⠀⠀⣀⣀⣸⣿⣿⣀⣀⣸⣷⣠⣿⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠈⠉⣿⡏⠉⠉⣿⠋⢹⡟⢹⣿⠉⣿⠋⠁⠀⠀⠈⢻⡟⠉⢿⡏⢹⡿⠋⠁⠀⠀⠈⠙⣿⡋⣻⡟⠉
⠀⠀⠀⠀⠀⠀⢸⣧⠀⣸⡟⠀⢸⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⠁⠀⢸⡇⢸⣿⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⡿⣷⡀
⠀⠀⠀⠀⢀⣀⣀⣸⣿⣯⣀⣀⣼⣧⣸⣿⣠⣿⣄⡀⠀⠀⢀⣼⣧⣠⣾⣧⣸⣷⣄⡀⠀⠀⢀⣠⣿⣅⣽⣧⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣏⢹⣿⠋⢹⣟⠉⠀⠀⠉⠹⣿⠉⣿⠏⠉⣿⠉⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀⢸⡇⠀⠀⠀⠀⠀⠹⣿⡏⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣆⠀⢸⣧⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣧⣸⣿⣄⣼⣿⣄⠀⠀⣀⣴⣿⣤⣿⣧⣠⣿⣤⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⢀⠈⣠⣾⣤⡄⣀⢀⡀⢇⣶⢀⢀⠀⠀⢀⢉⣤⣾⣤⡀⣀⢀⠀⣅⣶⠠⢀⠀⠀⢀⢉⣤⣾⣤⡀⡀⢀⠠⣅⣶⠠⢀
⠀⠀⠀⠀⢶⣾⣿⠀⢸⠋⢈⠈⠸⣿⣿⡕⠂⠁⠀⢾⡾⠋⠉⠙⢿⠋⢉⠀⠸⣿⡕⠀⠁⠀⢾⣾⠋⠉⠉⢻⠏⢉⠀⢸⣿⡕⠀⠁
⠀⠀⠀⠀⢹⣿⣿⠀⠸⠀⢸⠀⠀⣿⣛⣥⠀⠀⠀⣻⣷⡶⠃⢀⣼⠀⢸⡆⠀⣋⡥⠀⠀⠀⣿⣿⣶⠂⠀⠾⠀⢸⠀⠀⣋⡥
⠀⠀⠀⠀⠀⠛⢟⠀⢠⣀⠘⠀⢀⣹⡟⠂⠀⠀⠀⠈⠋⠀⠀⠘⢻⣀⠘⢀⣠⡟⠀⠀⠀⠀⠈⠋⠁⠁⠀⣠⡀⠘⠀⣠⡟
⠀⠀⠀⠀⠐⠋⣬⠙⡻⠿⠻⠧⠉⠉⠀⠀⠀⠀⠀⠘⢃⣤⠘⡻⠿⠻⠧⠉⠉⠀⠀⠀⠀⠀⠘⢣⣬⠘⡻⠿⠻⠧⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢸⣿⣧⣿⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⠃⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠋⠛⠁⠀⠀⠀⠠⠈⠂⠐
⠀⠀⠀⠀⠀⠰⢀⣠⣀⠀⠀⠁⠀⡄⣀⠀⠀⠀⠀⠀⠰⢀⣠⣀⠀⠀⠁⠀⡄⣀⠀⠀⠀⠀⠀⠖⢀⣤⣀⠀⠀⠁⠀⡀⣄
⠀⠀⠀⠀⣨⣴⣿⡿⠿⢷⡲⠸⠂⠹⣿⡎⠌⠂⠀⣸⣴⠛⠻⠛⢳⡳⠼⠂⢽⣿⡊⠄⠂⠀⣸⣴⠿⠟⠿⣷⡳⠾⠀⢹⣿⡪⠑
⠀⠀⠀⠀⢽⣿⡟⠁⠀⢸⠃⢰⡆⠀⠿⠃⠀⠀⠀⢿⣿⠀⠘⠛⠿⠀⣰⠀⢸⡿⠃⠀⠀⠀⢿⣿⠀⠒⠀⢾⠁⢰⡄⠀⡿⠆
⠀⠀⠀⠀⠘⠿⠁⢘⠁⠈⡀⠸⠇⠀⣾⠍⠀⠀⠀⠙⠿⠓⠛⠀⠀⠀⠿⠀⢘⣾⠉⠀⠀⠀⠙⠯⠀⢾⠀⢨⠀⠸⠇⠀⣾⠉
⠀⠀⠀⠀⠠⠦⡰⠫⢤⣼⢿⡆⠴⠞⠃⠀⠀⠀⠀⠠⠦⡐⠶⢶⣿⢶⡄⠶⠞⠃⠀⠀⠀⠀⠠⠆⡐⠤⢴⣿⢷⡄⠴⠞⠃
⠀⠀⠀⠀⠀⠀⠛⠀⠆⠈⠀⠉⠀⠀⡀⠀⡀⢀⡀⢀⣈⠛⠐⠆⠈⠀⠉⠀⣀⢀⣀⡀⣀⡀⠀⢈⣋⡐⠆⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣸⣿⣸⣇⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣽⡷⣟⣿⣇⣿⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠄⠀⠈⠉⠈⠀⠉⠉⠀⠁⠀⠀⠐⠆⠀⠀⠀⠉⠉⠁⠉⠈⠉⠁⠉⠁⠀⠐⠄
⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠂⠀⡀⢀⠀⠀⠀⠀⠀⢤⠀⣠⠀⠀⠀⠂⠀⡀⣀⠀⠀⠀⠀⠀⢤⠀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢐⣠⣾⣿⣿⣦⣦⠰⠄⢳⣿⢔⡐⠄⠀⢰⣠⡾⠿⢿⣦⣦⡴⠀⢳⣿⢔⡒⠄⠀⣰⣠⣾⣿⣿⣦⠦⠴⠀⢳⣿⢔⠒⠄
⠀⠀⠀⠀⣽⣷⣤⡤⠀⢀⠇⠀⡆⠀⣿⠇⠀⠀⠀⣿⣿⠀⢰⠀⣹⠃⢰⡄⠈⣿⠇⠀⠀⠀⣿⡿⠀⣠⠀⠹⠃⢰⡄⠈⣿⠅
⠀⠀⠀⠀⠸⣿⣿⠃⠀⣾⠁⢸⡇⠀⣴⡚⠀⠀⠀⠺⡿⠀⣴⠀⠙⠀⢸⡇⠀⣴⠒⠀⠀⠀⠺⣿⣄⡈⠀⢠⠀⢸⠇⠀⣴⠓
⠀⠀⠀⠀⢀⣄⠡⢠⣤⣿⣷⡄⢤⡴⠏⠀⠀⠀⠀⢀⡄⠀⢩⣀⣼⣦⡄⢤⡴⠏⠀⠀⠀⠀⢀⡄⠠⢈⣄⣼⣦⡄⢤⡼⠃
⠀⠀⠀⠀⠀⠀⠟⠠⡎⠉⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠠⡎⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠠⡎⠉⠈⠃

⠀⠀⠀⠀⣠⠤⢤⡀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⠤⣄⠀⠀⠀⠀⡠⠤⣄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⣶⣥⣄⠀⣷⠀⠀⠀⠘⠇⣀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢤⡟⢀⠀⠀⠀⡰⠋⡟
⠀⠀⠸⠏⢿⡋⣠⠟⠀⠀⠀⢘⡟⠟⠀⠀⠀⠀⣠⠞⡁⠀⠀⠀⠀⣄⢀⣶⠈⠀⠀⠘⠓⠚⣟⠂
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⣿⣉⠉⠀⠀⠀⠀⠀⣠⣎⣉⠁⠀⠀⠀⠈⠉⣹⠃⠀⠀⠀⣞⠉⣷⠀⠀⠀⠀⣴⠋⠙⣦⡀
⠀⠀⠀⠉⠨⣿⣿⠀⠀⠀⣸⣿⣯⠌⢹⠄⠀⠀⠀⣰⠃⠀⠀⠀⢠⡞⠉⢳⡄⠀⠀⠀⠙⠦⢾⣿⡗
⠀⠀⠀⠲⠴⠛⠉⠀⠀⠀⠈⠙⠓⠔⠋⠀⠀⠀⠐⠋⠀⠀⠀⠀⠘⠳⠤⠞⠁⠀⠀⠀⠐⠦⠔⠃

⣿⣟⣛⣛⣛⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢶⠒⡞⠋⠉⠉⠉⠻⡉⠹⣏⠉⠉⢹⠉⠙⢯⡭⠟⡿⠓⠒⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⣠⠋⠀⢹⡀⠀⠀⠀⣠⢇⡤⣌⠉⠉⠁⢀⣀⡀⠀⠀⣇⠀⢀⣠⠴⠊⠀⣈⣓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠓⠒⠉⣀⣤⡀⠀⠙⠒⠒⠋⠁⣏⠀⣈⠆⠀⣰⠋⠀⢹⠀⢀⣈⣉⠉⢠⠤⣄⢸⡁⠈⡇⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⣆⠀⢰⠁⠀⠙⢦⠀⡴⠦⡄⠀⣀⣉⣁⣀⠀⠸⣄⣀⡞⢠⡏⠀⠈⢧⠈⠳⠞⠀⠙⠞⠁⢀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⠀⠸⡀⠀⠀⢘⡆⠳⠚⠁⢞⠀⠀⠀⠀⢹⠄⠀⢀⡀⠈⢇⠀⠀⣸⠀⢰⠉⠉⣹⠄⣰⠋⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⠀⣀⣑⡶⠖⠋⣠⠤⢤⡀⠘⣆⠀⠀⢀⡜⠀⠸⡉⢹⠀⠈⠓⠚⠁⠀⠈⢓⣚⣁⡀⠘⢦⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⢭⣆⣰⣁⣀⣀⣷⣀⣈⣓⣚⣩⣖⣒⣦⡈⠁⢀⡴⠒⠢⡄⠀⢰⠋⠀⠀⠙⡆⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠆⢸⠀⠀⠀⠘⡆⠘⢦⣠⡤⠖⢃⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢺⠀⠀⠀⢀⡇⣀⡤⣄⠀⣴⠉⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠳⡜⢆⣠⠴⠋⡰⠁⠀⣸⠂⠘⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢹⠀⠀⠀⠀⠘⠒⠚⢁⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣉⣓⠦⠴⠒⢁⣠⠴⠚⠋⠓⢦⠀⡇⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡏⠀⠈⠉⠲⡀⣎⠀⠀⠀⠀⠀⢸⠀⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⠀⢹⡀⠀⠀⠀⡇⠈⠙⠒⠶⠤⠖⠋⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠙⢦⠙⠲⠶⠚⣡⠖⠓⡄⢰⡋⢱⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢧⡀⠀⠀⢀⡼⠁⢀⠀⠰⣇⠀⢀⡿⠀⠉⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠑⢦⠉⠉⠉⠉⡴⠋⠉⠹⡄⠈⠉⣩⢄⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠀⠀⡸⠀⣠⠤⡀⢣⡀⠀⢀⠇⠀⠀⡇⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⣍⠉⠀⠸⣁⢀⡇⠀⠉⠒⢋⣠⠤⢄⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠹⡄⠀⠈⣉⣀⠀⢀⡔⠋⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣰⠃⡰⠋⠀⠈⡆⢎⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡓⠦⣤⡤⠞⠁⠘⠥⠤⠴⠞⠁⠘⢦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠒⠒⢲⠀⢀⡤⠖⠚⠉⢳⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣏⣀⣞⣀⡠⠴⠚⠁

⠀⠀⠀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠙⣿⡿⠋⠈⠛⣿⡟⠋⠀⠀⠀⠀⠛⣿⡟⠋⠈⠻⣿⡟⠃⠈⠻⣿⡟⠁⠀⠀⠀⠙⢿⣿⠋⠀⠉⠻⣿⡋⠀⠈⢻⣿⠋⠁
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢻⣧⠀⢠⣿⠃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⣿⣆⣾⡏
⠀⠀⠀⠀⣨⣿⣄⠀⠀⠀⠀⠀⢀⣿⣧⡀⠀⢀⣿⣇⡀⠀⠀⠀⠀⢀⣿⣇⡀⠀⣠⣿⣇⠀⠀⣠⣿⣇⠀⠀⠀⠀⢀⣼⣿⡀⠀⠀⠀⠀⢘⣿⣟
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉


⠀⠀⠀⠀⡀⢀⢀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⢀⣀⡀⣀⠀⢀⢀⡀⢀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⡀⠀⢀⡀⠀⡀⠀⢀⠀⠀⡀⣀⢀
⠀⠀⠀⠈⠙⣿⡏⠁⠀⢉⣿⠟⠉⠀⠀⠀⠀⠀⠉⢻⣿⠉⠀⠉⣿⡟⠉⠁⠉⢻⣿⠋⠀⠀⠀⠀⠀⠉⠻⣿⡉⠀⠈⢹⣿⠋⠁⠈⠻⣿⠏⠁⠈⢻⣿⠏⠁
⠀⠀⠀⠀⠀⠘⣿⡄⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣰⣿⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢀⣿⠃⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⢹⣷⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣿⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣾⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣏⡀⠀⠀⠀⢀⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⡀⠀⠀⠀⢀⣠⣿⣄⡀⢀⣸⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠉⠉⠁


⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀⣀⣀⡀⢀⣀⣀⣀⡀⢀⣀⣀⣀⡀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⡀
⠀⠀⠀⠈⠙⣿⡍⠀⠀⢹⣿⠋⠁⠈⠙⣿⡏⠁⠈⠙⣿⡏⠁⠈⠙⣿⠏⠁⠀⠀⠀⠈⠹⣿⠏⠁⠈⠙⣿⣇⠀⣹⡿⠋⠁⠀⠀⠀⠀⠉⢿⣯⠀⣨⣿⠋⠁
⠀⠀⠀⠀⠀⠹⣷⡀⢀⣿⠇⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢻⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡿⠁
⠀⠀⠀⠀⠀⠀⢻⣧⣼⡟⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣾⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣷⡄
⠀⠀⠀⠀⠀⠀⣈⣿⣿⣀⠀⠀⠀⢀⣠⣿⣧⡀⢀⣰⣿⣧⡀⢀⣰⣿⣆⡀⠀⠀⠀⢀⣰⣿⣆⡀⢀⣠⣿⣏⠀⣹⣷⣄⡀⠀⠀⠀⢀⣠⣾⣏⠀⢘⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⡀⢀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣀⣀⢀⣀⣀⣀⡀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⠀⣼⡿⠉⠀⠀⢹⣿⠋⠀⠀⠀⠀⠀⠈⢻⣯⡀⣨⣿⠋⠀⠀⠙⣿⡏⠀⠀⠙⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣷⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣏⠀⣹⣿⣄⡀⢀⣼⣿⣤⡀⠀⠀⠀⢀⣠⣾⣏⠀⢈⣿⣦⡀⢀⣴⣿⣧⡀⢀⣴⣿⣧⡀

⠀⠀⠀⠈⣿⡏⠀⠀⠀⢹⡟⠀⢹⡏⠀⠀⠀⠘⣿⠁⢹⣿⠁⢹⡟⠀⠀⠀⠈⣿⠁⠈⣿⡁⢸⡟⠁
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢹⣧⣿⠃
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⢿⡏
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠈⠉⠁⠈⠉⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢹⣏⠀⣿⠏⠀⠀⠀⠙⣿⠁⣹⡟⠀⢹⡏⠀⠀⠀⠘⣿⡁⢹⡟⠁⢹⡟⠀⢹⡏
⠀⠀⠀⠀⠀⠀⣿⣴⡟⠀⠀⠀⠀⠀⢻⣧⣿⠁⠀⢸⡇⠀⠀⠀⠀⢹⣧⣿⠃⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡟⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠉⠉

⠀⠀⠀⠈⣿⡇⢸⡿⠁⢹⣿⠁⢹⣿⠁⢹⡏⠀⠀⠀⠘⣿⠁⠉⢿⡇⣿⠏⠁⠀⠀⠈⢻⣇⣸⡟⠁
⠀⠀⠀⠀⠸⣧⣾⠇⠀⢸⣿⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢿⡟⠀⠀⢸⣿⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣴⡖⣶⡄⠀⠀⠀⠀⣰⡿⢿⣆
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁⠉⠉⠀⠉⠉⠀⠀⠀⠈⠉⠁⠈⠉⠁⠉⠉⠁⠀⠀⠈⠉⠉⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣨⣿⠋⠈⣿⡋⠀⠀⠀⠈⢿⣇⣹⡟⠁⢹⣿⠁⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠃⠀⠀⣿⡇⠀⠀⠀⠀⠈⣿⡟⠀⠀⢸⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⣧⠀⠀⣿⠇⠀⠀⠀⠀⣰⡟⢿⡄⠀⢸⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠈⠉⠉⠀⠀⠀⠈⠉⠁⠈⠉⠁⠉⠉⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⢹⡏⠀⠈⣿⠁⠀⠀⠀⠀⠀⢹⡏⠀⢸⣿⠀⠈⣿⠁⠀⠀⠀⠀⠀⢹⡏⠀⠘⣿⠀⠀⢨⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠦⠀⠀⠀⠀⠀⠠⠾⠷⠤⠴⠿⠦⠀⠀⠀⠀⠠⠾⠷⠤⠾⠿⠤⠴⠿⠦⠀⠀⠀⠀⠠⠾⠷⠄⠀⠀⠾⠿⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣶⠂⠀⠲⣶⠖⠀⠀⠀⠀⠐⢲⡶⠂⠀⢲⣶⠒⠒⣶⠒⠀⠀⠀⠀⠐⢲⣶⠂⠀⢲⣶⠒⠒⣶⠖⠒⢶⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⣸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡏⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣾⠃⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣧⢠⣿⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡇⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣀⣿⣀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡃⠀⠀⣀⣿⣀⣀⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠉⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣿⠁⠀⢸⡇⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⣇⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⢰⡿⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢿⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣸⡇⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⠁⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣾⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠇⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠷⠀⠀⠰⠾⠷⠶⠾⠿⠶⠶⠛⠖⠀⠀⠀⠀⠰⠾⠷⠖⠾⠿⠆⠀⠶⠻⠶⠀⠀⠀⠀⠀⠾⠻⠆⠀⠶⠻⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⡖⠀⢐⣶⠒⠒⢲⡖⠂⠀⠀⠀⠀⠀⠀⠀⠐⢲⣶⠀⠐⣶⠖⠒⢲⣶⠒⠒⣶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⣼⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣸⡟⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢻⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠹⣧⠀⠀⢸⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣃⠀⢈⣿⣄⣀⣸⣇⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣏⡀⢀⣻⣆⣀⣸⣿⣀⣀⣿⣀
⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⡶⠒⣢⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣾⣿⠀⠻⠿⠛⠁⠘⢿⣿⣿⡿⠈⠙⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣥⣤⠀⠀⢀⡀⠀⣾⣷⡦⠀⣀⡀⠀⠀⣴⣿⡇⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡀⠉⠉⢠⣾⣿⣿⡆⠀⠁⢠⣾⣿⣿⡆⠀⢀⣤⣤⣀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇⠀⠀⣀⠉⠛⠋⠁⠀⢀⣸⣿⣿⣿⠇⠀⢿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠉⠀⠀⢿⣿⡇⠀⣾⡷⠊⠁⠀⠀⠉⠣⣄⣠⣄⠙⠛⠋⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣤⣤⡀⠉⠁⠀⠏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣇⣀⣈⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠹⣿⣿⡇⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⣀⣉⡀⠀⠙⢟⣀⠤⠲⣾⣿⣿⡟⠉⠁⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⣴⣿⣿⣿⣿⡄⠀⣨⣤⣤⡀⠀⠉⠋⠀⣴⣷⠀⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢿⣿⣿⣿⣿⠇⠘⠿⣿⡿⠇⠀⣿⣷⡄⠈⢉⣀⣀⡈⠉⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣦⠀⠉⠛⠛⢋⠀⠀⢀⣄⡀⢀⡤⠿⢿⠁⠀⣿⣿⣿⣿⣷⣦⠀⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⣴⣿⣧⠀⣾⣿⡿⠁⠀⠀⠀⠱⡀⠈⠙⠛⠛⠋⠁⠀⠿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣶⣿⣶⣄⠙⠛⠋⠀⠹⢿⠃⠀⠀⠀⠀⠀⢻⣦⠀⠀⣴⣾⣷⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠛⠛⠛⠋⠀⠰⣿⣿⣷⢸⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠻⠿⠃⠠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⡄⠀⢀⣤⣀⠙⠻⠟⠀⢇⠀⠀⠀⠀⢀⠏⢁⡀⠀⣠⣶⣶⣄⠙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣿⣿⣿⣷⡄⢠⣶⣮⡢⣀⣀⣠⣾⠀⠿⠇⠀⠻⠿⠿⠟⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠹⢿⣿⠿⠁⢸⣿⣿⡇⠀⣠⣬⣀⠀⠀⣤⣦⣄⠀⣴⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⢠⣤⣦⡄⠉⠉⠀⢸⣿⡿⠟⠀⠘⣿⣿⠿⢀⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⠀⣼⣿⡄⠀⣰⣾⣿⣦⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠛⠷⠤⠿⠛⠛⠋⠁

⠁⠐⠓⡆⠀⠀⠀⠀⠘⠋⠀⠀⠀⠠⠠⡄⠀⠀⢠⠖⢋⠒⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡷⠀⠀⠘⠦⠞⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢼⠁⣹⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⡇⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠩⠟⠀⠀⠀⠚⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢖⠢⠀⠀⠀⠀⠀⠈⡰⠀⠀⠀⠀⠃⠀⠀⠈
⠀⠊⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⠀⠀⠀⡐⢦⠀⠀⠘⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀
⠀⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⠂⠀⠀⠀⠁⠀⠀⢞⢈⡆
⠀⠀⠀⡀⠀⠀⠀⡇⠑⠒⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠚
⠀⠀⠲⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠨⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⡴⠲⢦⣄⠀⠀⠀⢸⡙⢦⣀⣸⠀⠀⠀⠀⠀⠱⠄⠀⠀⣀⣀⣀⣀⠀⠀⠀⠐⠋⠀⠀⠀⣰⡍⣰
⠀⠀⢧⣤⠜⢸⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⢄⠀⠀⠀⠈⠣⠟
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠁
⢀⣠⠀⠀⠀⠀⠀⠯⡄⠀⠀⠀⡀⠀⠀⢇⣘⠉⠳⠀⠀⢀⠔⣀⠀⠀⠀⠀⠐⣀⠀⠀⣀⡀⠀⠀⡖⠀⡆⡆
⠈⠐⠄⠀⠀⠀⠀⠁⠁⠀⠀⠸⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠊⣉⠇⠀⠀⠳⠉⠁⠀⠀⠒⠉⠀⠀⠙⠚⠁
⠀⠀⢀⡀⠀⠀⠀⢀⠀⠤⠀⠀⢀⢤⡀
⠀⠀⠈⢣⠀⠀⠀⠀⠓⠀⠀⠀⢳⡀⢹⠄⠀⠀⠀⠀⠐⡉⠀⠀⠀⠄⣞⡀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠀⠀⠀⠀⠀⠀⠋⡡
⢀⡴⡀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠀⠀⠀⠀⣰⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠃⠃⠀⠀⠤⡀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠼⠊⠁⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⡽⠀⠀⠀⡔⠒⠂⠀⠀⠀⡀⢤
⠀⠀⠀⠀⠀⠠⠉⠀⠀⢀⠀⠀⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⣀⡖⠀⠀⠘⠒⠚⠁⠀⠀⠀⠑⣖⢀⡄⠀⠀⠉⠈
⢠⢤⡀⠀⠀⠀⠀⠀⠀⡟⡠⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠘⠋⠉⡀⠀⢉⢉⠁⠀⠘⠓⠶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠀⢀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠰⣄⡈⢳⡀⠀⠐⣷⠀⠀⢸⡆⢸⢸⠀⠐⣾⠂⠀⠀⠀⣰⠃⠀⠀⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠈⠳⣄⢳⡀⠀⠀⠀⠀⠀⠷⠸⠸⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⢰⣶⡀⠀⠀⠈⠳⠛⣀⣤⠴⡖⠲⠒⠒⠖⢲⢦⣤⣀⠀⠾⠁⠀⠀⢐⣶⡆⠀⠀⠈⠛
⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⢖⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⡲⣄⠀⠀⠈⠁⠀⠀⠀⣀⡄⠀⣄
⠀⠀⠀⣠⠀⠈⠓⠲⠦⣤⣀⡀⠀⣠⢞⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡳⣄⠀⢀⣠⢖⣫⠵⠚⠁⠘⠂
⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠁⣼⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣧⠉⠖⠋⠁⠀⠀⠀⠀⢠⡄
⠀⠀⣀⠀⠀⠀⢴⣤⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣤⡦⠀⠀⠀⠷
⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⢰⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡆⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⢀⣀⣤⣤⡤⠶⠂⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡇⢐⣒⣒⣒⣒⣒⡆⢸⡇
⠀⢸⡇⠨⠥⠤⠤⠤⠤⠄⢸⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡇⠨⠯⠭⠭⠭⠭⠇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠇⠀⠀⠀⡀⠀⠀⠀⣸⠂
⠀⠀⢶⠀⠀⠀⠺⠛⢀⣤⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠛⠗⠀⠀⠀⠉
⠀⠀⠘⠃⠀⣀⠴⣚⡭⢖⡭⠄⢻⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡟⠀⠉⠳⢦⣀⠀⠀⠀⣠
⠀⠀⠀⠠⡄⠱⣚⡵⠚⢉⢀⡤⠀⠙⢮⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡱⠋⠀⠀⠛⠖⠦⢬⣝⠆⠀⠋
⠀⠀⠀⠀⠙⠀⠁⠀⢀⡴⠋⢀⡀⠀⢀⠙⠮⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠵⠋⠀⠀⢀⡀⡀⠀⠀⢀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⢦⡐⠋⠀⠸⠿⠁⢠⢏⡞⠀⡀⠉⠛⠳⠧⠴⠤⠤⠦⠼⠖⠛⠉⠀⢠⡀⠀⠀⠨⠿⠇⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⣰⢋⠞⠀⢸⠃⠀⠀⠀⠀⢰⠀⢠⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⡐⠣⠏⠀⢀⡟⠀⠠⡿⠀⠀⢸⠀⠸⡆⠀⠠⢿⠄⠀⠀⠀⠀⠹⠆⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠘⠁⠀⠀⠀⠀⠀⢸⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⢤⡄⠀⢀⣈⣀⠀⠈⣀⣠⡄⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠐⠒⠛⠛⠛⠓⠛⠛⠛⠃
⠀⠀⠀⢀⠆⡆⠀⠀⠀⢀⠤⠶⢦⣅⠀⠀⠀⠀⡤⠀⠦⠾⡤⠀⠀⠀⠀⡠⠹⢡⠀⠀⠀⠀⠀⠄⠴⠤
⠀⠀⣂⣁⠀⠆⠀⠀⠀⠃⠔⠒⠀⢸⠀⠀⠀⠀⠁⠐⠂⣔⠀⠀⠀⠀⡰⠁⠖⢠⠀⠀⠀⠀⠀⠀⠎⢁⠈
⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢀⠌⢀⠎⠀⠀⠀⠀⠈⠒⠆⠀⢡⠀⠀⣀⡀⠈⠀⠈⣰⠀⠀⠀⠀⠁⢢⠀⠱
⠀⠀⠀⢨⣀⡄⠀⠀⠀⠰⣁⣀⡀⠀⡱⠀⠀⠀⣏⣉⣁⡠⠎⠀⠀⠀⠀⠀⢁⢸⠁⠀⠀⠀⢸⣉⣁⣠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣤⡉⣄⠀⠀⠀⡀⠀⣠⡌⢢⡀⠀⠀⠀⣀⣀⣃⠀⠀⠀⠀⢀⡀⣠⢀⡀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠞⠀⣔⡒⠂⠀⠀⠠⠤⠤⡄⠀⣠⠇⠀⠀⡌⢠⣀⠀⡃⠀⠀⢠⠃⢠⠒⡆⢸⠀⠀⢀⠜⠡⠐⠢⡈⢆
⠀⢘⠀⠠⠀⡀⢳⠀⠀⠀⢀⠎⢀⠞⠁⠀⠀⢀⠜⢀⣀⠐⢅⠀⠀⠈⠦⣈⡉⠁⢀⠀⠀⢸⠀⡇⠀⠀⡇⢸
⠀⠘⡄⠐⠔⠃⡸⠀⠀⠀⡌⠀⡎⠀⠀⠀⠀⢸⡀⠡⠤⠃⣰⠀⠀⠀⡤⠐⠉⣀⠌⠀⠀⠘⢆⠈⠒⠊⢀⡜
⠀⠀⠈⠁⠒⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠐⠒⠊⠁⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠
⣤⣤⣤⣤⣄⣠⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠀⢀⡴⡏⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠸⠸⠀⠂⠘⠂⠀⠀⠀⠀⢻⢦⠈⢇
⠁⠀⠉⠀⠇⢠⠏⠀⠀⢀⣀⣀⣀⣠⠤⠀⠀⠀⠀⢸⠞⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡄⠳⠈
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠛⠒⠲⠤⢤⠀⠀⠀⡴⢻⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢤⡀⣧⠈⢣⡀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⣞⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠂⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡀⠀⢳⡀⠀⠀⢀⡀
⡀⠀⠀⠖⢚⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠳⠀⠉⢀⡀⠢⡙
⡙⠆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣩⡽⠶⠆⠀⠀⠀⠀⠁⠀⠀⠐⠢⢷⡀⠙
⠀⠀⠀⠀⠀⠀⣠⠞⢀⠀⠀⠀⠀⠀⠀⣠⠜⢂⡀⠀⠀⠀⢠⣤⣤⣄⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠑
⠀⠀⠀⠀⢠⣞⡥⠖⠋⣡⡀⠀⢀⡠⠞⢁⠴⢋⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠀⠀⠀⠈⠋⠁⢀⡴⠊⠁⠀⠀⠈⠡⠞⢁⡴⠋⠀⠀⣀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣉⠭⠟⠉
⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⢦⠘⣆⠀⠀⠀⢸⠃⡏⠘⣄⠆⠀⠘⣋⣀⡤⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⣦⠀⠀⢸⠀⡇⢀⢿⠀⠀⠀⠉
⠀⠀⠀⣀⣠⠤⠒⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠐⠃⠚⠘⠂⠀⠀⠀⠀⠀⢻⢀⡟
⠀⠀⢋⣡⠤⠖⠚⣉⡄⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⡤⠖⠚⠉⠁⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣸⠁
⠀⠀⠀⡶⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣧⠇
⠀⠀⢠⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠁⠀⠛⠀⠀⠀⠰⠦⢤⣀⣀
⠀⢀⡞⢠⠇⠀⠀⠀⠀⠀⠀⢲⡀⠑⢼⠀⠀⠀⠁⠉⠙⠒⠦⢤⠀⠀⠀⠀⠀⠀⠀⠶⠖⠒⠒⠛⠛
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⠓⢄
⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠈⡧⠸⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⡀⡀
⠀⠀⠀⠀⣿⡴⠋⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠈⠀⢇⡇⠀⠀⠀⠀⣄⠀⢦⠹

⠀⠀⠀⠀⠐⡟⠀⠀⠀⠀⢺⡗⠀⣿⠂⠀⠀⠀⠀⢿⠂⠘⡗⠀⢺⠃⠀⠀⠀⠀⢺⡗⠀⢻⡂⠀⣺⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠈⡇⢀⡏
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⡇⠀⣸⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣼
⠀⠀⠀⠀⠐⠷⠀⠀⠀⠀⠸⠗⠀⠿⠂⠀⠀⠀⠀⠿⠂⠰⠗⠀⠾⠆⠀⠀⠀⠀⠺⠗⠀⠀⠰⠷

⠀⠀⠀⠀⠀⠀⢺⡂⠀⢺⠇⠀⠀⠀⠘⣗⠀⢐⡟⠀⢺⡗⠀⠀⠀⠀⢻⡂⠀⣺⠃⠐⣿⠂⠸⡗
⠀⠀⠀⠀⠀⠀⠀⢇⠀⡏⠀⠀⠀⠀⠀⢹⡀⢸⠁⠀⠈⡇⠀⠀⠀⠀⠈⣇⢀⡏⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣼⠁⠀⠀⠀⠀⠀⠀⣧⡇⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⠀⠸⠗⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⠿⠂⠸⠗

⠀⠀⠀⠀⠸⡗⠀⢰⡟⠀⢺⡇⠀⣿⠀⢸⡗⠀⠀⠀⠀⠐⡟⠀⠺⣇⠀⢀⡟⠂⠀⠀⠐⢿⡀⠀⣸⠗
⠀⠀⠀⠀⠀⢹⠀⣸⠀⠀⢸⠀⠀⡿⠀⠈⡇⠀⠀⠀⠀⠀⡇⠀⠀⠘⢦⠎⠀⠀⠀⠀⠀⠀⠳⡴⠃
⠀⠀⠀⠀⠀⠈⣧⡇⠀⠀⢸⡀⠀⣷⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣠⠏⢧⡀⠀⠀⠀⠀⢀⡼⠹⣄
⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠺⠇⠀⠿⠀⠸⠗⠀⠀⠀⠀⠰⠷⠀⠶⠇⠀⠈⠷⠂⠀⠀⠐⠾⠁⠀⠹⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⢠⠟⠀⢺⡇⠀⠀⠀⠘⢧⠀⠀⡿⠃⠐⡿⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠏⠀⠀⢸⡇⠀⠀⠀⠀⠈⢣⡞⠁⠀⠀⡇⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣆⠀⠀⢸⡇⠀⠀⠀⠀⢠⠞⢳⡀⠀⠀⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠨⢷⠀⠸⠇⠀⠀⠀⠰⠯⠀⠀⠿⠆⠐⠷⠀⠸⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠳⡄⢤⡀⢀⠈⣆⣠⠖⠊⠀⠀⢠⣴⡆⠐⢶⡄⣤⡀⢀⠘⣆⡤⠶⠃⠀⠀⢠⢸⠀⠔⢷⡌⣤⡀⣀⠘⣂⡤⠖⠃⠀⠀⢠⢼⠀⠔⢶⡀⣄⡀⣀⠰⣀⡤⠖⠃
⠀⣃⡈⠉⠉⠤⢥⡄⠀⠀⢀⠄⠊⠀⢰⢀⠀⣇⡈⠉⠁⠤⢥⡄⠀⠀⣀⠀⠈⠀⢠⣀⠀⣇⠈⠉⠁⠤⢥⡀⠀⠰⡀⠀⠉⠀⠀⡀⠈⣇⠈⠉⠁⠤⣥⡀⠀⠐⡀
⠐⠉⢇⠄⢀⣀⡀⢀⠀⠀⡿⠀⠘⢳⡜⠁⠐⠉⠇⠀⢀⣀⠀⢰⢀⠀⡟⠀⠘⢷⠘⠁⠈⠉⢃⠀⢀⣀⠀⢠⠀⢀⠇⠀⠛⢷⠘⠁⠈⠙⢃⠀⣀⣀⠀⣀⠀⢨⠇
⡶⠖⢸⣦⠀⠈⠷⢸⠸⠣⣆⠀⠀⡸⠁⢶⡶⠖⢸⣦⠀⠈⠷⢸⠸⢠⡆⠀⠀⡜⠀⢶⠶⠖⢹⡄⠀⠉⠇⣾⠺⢠⡆⠀⠀⠜⠀⣶⠶⠆⢾⡄⠀⠙⡇⣷⠿⢠⡆
⠃⢠⡤⠛⢒⣦⣤⡈⠠⠴⣿⠛⠁⣀⣃⡈⠁⢠⡬⠛⢒⣤⣤⠈⠠⠶⣿⠛⠁⣀⣃⡘⠀⢠⠜⠛⣒⣤⣤⠈⠠⠶⣟⠋⠀⣀⣃⡘⠀⢠⠜⠛⣒⣤⣄⠉⠠⠶⣟
⠆⠀⣤⡴⠉⠀⠹⢷⠀⠀⢸⡤⢨⡁⠈⠹⠆⠀⣤⡖⠁⠀⠹⣶⠀⠀⢸⡄⢨⠁⠈⢻⠀⠀⣤⡖⠁⠀⠹⣶⠀⠀⢸⡄⢨⠁⠈⢻⠀⠠⣤⠆⠁⠀⢹⣶⠀⠀⣻
⣠⠴⠚⣇⠀⣀⠀⠘⠷⢶⡄⢰⠈⠳⠶⣂⣤⠴⠚⣇⠀⣀⠀⠘⠷⢶⡀⢸⠈⠳⠶⣂⡤⠖⢺⣆⠀⣀⠀⠘⠷⢶⡀⣶⠘⠳⠶⣂⡤⠖⢺⡄⠀⡀⠀⠹⠶⣶
⣀⡀⠀⠙⣻⣥⣰⣄⠀⠈⢳⡜⢧⡐⠿⣭⣀⡀⠀⠙⣫⣥⣸⣄⠀⠈⢱⠘⣦⡐⠿⣭⣀⠀⠀⠙⣫⣅⣸⣀⠀⠘⢳⠸⣦⡰⢿⣥⣀⠀⠈⠛⣫⣄⣾⡀⠀⠈⢲
⠉⢛⠀⠰⣄⠈⢳⠉⠉⢀⠀⢀⣿⡛⠃⠀⠉⣛⠀⢰⣄⠈⣷⢉⠉⣀⠀⢀⣛⡛⠁⠀⠉⣋⠀⢰⣄⠈⡇⠉⠉⡀⠀⣀⣟⡛⠀⠀⠉⣣⠀⢸⡀⠈⡇⠉⠉⡀
⠚⠁⠶⠀⠽⠁⠈⠼⠓⢸⡄⠀⠀⢻⠀⠰⠚⠁⠶⠀⠝⠁⠀⠼⠓⢹⡄⠀⠈⢳⠀⠴⠊⠁⠶⠀⠝⠁⠁⠼⠓⢹⠀⠀⠈⢳⠀⠴⠊⠑⠶⠀⠝⠀⠡⠾⠓⢻
⠖⠋⠀⠀⢠⣴⡇⠐⠻⡆⢴⣀⣀⠀⣇⡤⠒⠃⠀⠀⢠⢼⡄⠐⢻⡄⣶⣀⣀⠈⣇⠤⠒⠃⠀⠀⢠⢸⠀⠘⢳⡄⣦⣀⣀⠘⣆⠤⠚⠃⠀⠀⣠⢼⠀⠚⢳⡀⣦
⠀⠀⣀⠀⠈⠀⢀⣀⠀⣇⡀⠉⠁⠴⢶⡄⠀⠠⣠⠀⠈⠀⢀⣀⠀⣁⡀⠉⠡⠴⢦⡄⠀⠀⣀⠀⠈⠀⢈⡀⠀⣇⡈⠉⠁⠴⢦⡀⠄⠀⡀⠀⠁⠀⢀⡀⢀⣁⠈
⠁⠀⠿⠀⠈⢻⡎⠁⠀⠉⢃⠀⢀⣄⡀⢠⠀⠄⠏⠀⠉⢳⡎⠁⠈⠉⢣⠀⢀⣄⡀⠀⠀⡄⠏⠀⠉⢳⠈⠀⠈⠉⢇⠀⢀⣄⠀⡘⠀⠠⠇⠀⠉⢷⠈⠀⠊⠙⣇
⠸⠃⣆⠀⠀⠘⠁⢻⡶⠒⢸⣆⠀⠈⠗⢸⠸⠠⣆⠀⠀⠘⠀⢿⠶⠊⢸⡆⠀⠈⠇⢿⠸⢰⣆⠀⠀⠞⡀⢿⠶⠂⢸⡆⠀⠈⠇⣧⠻⢰⣆⠀⠀⠎⡀⣷⠶⠂⢿
⠠⠒⢿⠉⠀⣠⣇⣈⠁⠠⠖⠙⣛⣧⣤⠈⠠⠲⢯⠉⠀⣠⣇⡈⠀⠠⠞⠙⣻⣧⣤⠈⠠⠲⣯⠉⢀⣠⣅⡈⠀⠠⠞⠙⣻⣦⣤⠈⠐⠲⣏⠉⢀⣸⣅⡈⠀⠠⠎
⡀⠀⢸⡤⢨⡁⠀⠹⠆⠀⡴⡖⠁⠀⠸⢷⡀⠀⢸⡄⢨⡁⠀⢹⠀⠀⠶⡆⠁⠀⢸⢷⠀⠀⢸⡄⢨⠁⠀⠹⠀⠠⠶⠎⠀⠀⠹⣦⠀⠀⢨⡄⣭⠀⠈⠻⠀⠠⢶
⠳⢶⡆⢸⠈⠛⠖⣂⡤⠖⠛⣇⣀⣀⠀⠘⠳⢶⡄⢰⠈⠛⢖⣂⡤⠖⠳⣇⣀⡠⠀⠘⠷⢶⡀⣷⠈⠳⢖⣀⡤⠒⢻⣇⢀⡀⠀⠘⠷⢶⠀⣇⠈⠳⢒⣠⡴⠚⢹
⣀⡀⠱⡌⢷⣐⠻⢧⣄⡀⠀⠙⠩⢥⣸⣄⣀⡀⠱⠜⢧⣐⠿⢥⣄⡀⠀⠙⠯⣤⣸⣄⣀⠀⢱⠘⣦⡐⠿⣤⣄⡀⠀⠙⠭⣤⣺⣄⣀⠈⢳⠘⣦⡘⠿⣤⣀⡀⠈
⡉⢀⠂⢀⣭⡙⠁⠀⠈⣉⠀⠸⣄⠀⠷⢈⡉⢠⠀⣠⣭⡉⠁⠀⠈⣩⠀⢸⣄⠈⠇⢉⠁⣀⠀⣠⣭⡙⠁⠀⠈⣩⠀⢰⣄⠈⡇⢉⠁⡀⠀⣠⣭⡉⠀⠀⢉⣡
⠛⠸⠆⠀⠀⢹⠀⠴⠊⠁⠲⠀⠜⠁⠀⠜⠛⢹⠄⠀⠀⢹⠀⠴⠋⠁⠳⠀⠜⠁⠀⠜⠛⢹⠄⠀⠀⢿⠀⠔⠋⠀⠷⠀⠝⠀⠠⠞⠋⢻⠀⠀⠈⠇⠀⠖⠋⠐⠷
⠻⡆⢰⣄⣀⠈⣧⠴⠚⠋⠀⠀⢠⢼⠇⠘⠻⡆⢶⣀⣠⠈⣦⠴⠚⠁⠀⠀⢠⢼⠀⠘⠻⡄⢶⣀⡠⠘⣧⠴⠚⠁⠂⠀⢰⢾⠀⠚⢻⡄⣦⣀⡠⢐⡦⠔⠛⠁
⠀⣡⡀⠈⠀⠐⠶⡄⠀⠀⣠⠀⠈⠀⢰⣠⠀⣧⡀⠈⠀⠔⢶⡄⠀⠀⣤⠀⠀⠀⢰⡠⠀⣧⡀⠉⠀⠒⢶⠄⠀⠐⡠⠀⠁⠀⢀⡀⢈⣥⡀⠁⠀⠒⢶⠄⠀⠀⡤
⠈⠀⢃⠄⢀⣤⡀⢰⠀⡀⠟⠀⠈⢻⡎⠀⠀⠀⢃⠄⣀⣤⡀⢰⢀⠀⠇⠀⠈⢻⠈⠀⠈⠈⢣⠀⣠⣤⡀⠰⢀⠠⠇⠀⠈⢻⠈⠀⠊⠈⢣⠀⣠⣄⡀⡤⢀⠰⠇
⡷⠊⢸⣶⠀⠀⠛⢸⡘⠡⣆⡀⠀⠜⡀⢻⡖⠋⢸⣶⠀⠀⠟⢸⠘⠰⣇⠀⠀⠜⡀⢿⠖⠃⢸⣆⠀⠈⠇⢷⠛⠰⣇⠀⠀⠞⡀⢿⠖⠃⢻⡆⠀⠈⠇⣷⠛⢰⣇
⠁⠠⠖⠉⣫⡵⣦⡀⠀⠒⢿⠉⢁⣠⣥⣌⠁⠠⠖⠉⣫⡵⣦⠈⠐⠒⢯⠉⢀⣤⣥⡈⠀⠰⠞⠉⣫⣵⣦⠈⠐⠒⣯⠉⢀⣬⣥⡈⠀⠰⠎⠙⣫⣷⣦⠀⠐⠲⣯
⠇⠀⠶⡞⠀⠀⠘⢿⡀⠀⢸⠤⢨⡀⠀⠙⠆⠀⠶⡆⠀⠀⠘⢿⡀⠀⠸⢄⢨⡀⠀⠹⠀⠀⠶⠎⠀⠀⠸⢾⠀⠀⢸⠄⢨⡀⠀⠹⠀⠠⠶⠆⠀⠀⠹⣷⠀⠀⠹
⠴⠞⠋⣧⣀⡠⠀⠘⠻⢾⡆⢸⠀⠛⢚⣣⠴⠚⠉⣧⣀⡠⠀⠘⠳⢾⡄⢺⠈⠛⢚⣡⠴⠚⠹⣆⣀⡠⢀⠘⠳⢾⡀⣷⠈⠛⢚⣡⠴⠚⢹⣆⣀⡄⢀⠘⠳⢿
⣤⣀⠀⠉⠭⢦⡼⣆⣀⠀⠹⠎⣷⣜⡻⢦⣤⣀⠀⠉⠽⢦⡸⣄⣀⠈⢹⠈⣷⣜⡻⢦⣄⣀⠀⠉⠽⢦⣸⣄⣀⠈⠹⠘⣧⣘⠻⢦⣄⡀⠀⢉⠽⣦⣺⣄⣀⠈⠳
⠀⣩⠄⠸⣦⡀⢻⢈⡁⢠⠂⡠⢭⣍⠁⠀⠀⣩⠀⠸⣄⡀⠷⢈⡁⣀⠀⡠⢭⡉⠁⠀⢈⣩⠀⠸⣄⠀⡇⢈⡁⣄⠀⡨⢭⡉⠁⠀⢈⡩⠀⢺⣄⠈⡇⢈⠁⣐⠁
⠋⢀⠻⠀⠜⠁⠀⠚⠛⠸⠆⠀⠀⠹⠀⠔⠋⠀⠳⠀⠞⠁⠀⠚⡋⠸⠆⠀⠀⢻⠀⠖⠉⠀⠓⠀⠎⠀⠀⠚⡋⢹⠀⠀⠀⢻⠀⠖⠉⡈⠗⠀⠋⢀⠠⠚⠋⢹

⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⣤⡤⢤⣤⠄⠀⠀⠀⢤⣤⠤⣤⡤⢤⣤⠀⠀⠀⠀⣤⡤⢤⣤⠄⠠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⢿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⡇⠀⣿⠀⠘⡇⠀⠀⠀⠀⢸⡇⠀⢸⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⡇⠀⣿⠀⢀⡇⠀⠀⠀⠀⢸⡇⠀⠈⣷⣸⠃
⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⣸⡇⢀⣿⠀⠀⠀⠀⢀⣇⠀⣿⡀⢘⣇⠀⠀⠀⠀⣸⣇⠀⠀⣻⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠐⣶⠂⠀⢶⠖⠀⠀⠀⠐⢶⠆⠀⢶⡖⠰⣶⠂⠀⠀⠀⠲⣶⠀⠐⣶⠂⢲⡖⠐⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⣾⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⢠⡏⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢠⡏⠀⠀⠀⠀⠀⠈⣧⢠⡟⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆⣸⠇⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠇⠀⠀⠀⠀⠀⠀⢿⣸⠇⠀⠀⣿⠀⠀⠀⠀⠀⠘⣧⣿⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⢠⣿⡀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣸⣇⢀⣿⡀

⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⣿⠁⢹⡏⠈⣿⠁⢹⡏⠀⠀⠀⠀⢻⡏⠉⢿⡁⢸⡟⠁⠀⠀⠀⠈⢻⡇⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡀⢰⡇⠀⢸⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠈⣧⡾⠁⠀⠀⠀⠀⠀⠀⢷⣼⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠃⠀⢸⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⢸⡇⠀⣿⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⣰⠇⢹⡆⠀⠀⠀⠀⠀⢰⡏⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠀⠀⠼⠧⠠⠿⠄⠼⠧⠀⠀⠀⠀⠾⠧⠰⠿⠄⠠⠿⠄⠀⠀⠀⠠⠿⠄⠀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⣼⠋⠀⣿⠁⠀⠀⠀⠀⠀⠀⠈⣯⠀⣼⠋⠀⣿⠁⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢻⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢻⡄⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠚⠛⠒⠛⠃⠀⠀⠀⠀⠀⠀⠛⠓⠀⠚⠛⠒⠛⠓⠚⠛

⠀⠀⠀⠀⢀⡠⠤⡀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⡞⡠⢄⠈⡆⠀⠀⢀⠞⠁⠀⡇⠀⠀⢀⣀⡐⢂⢱⠀⠀⠀⠾⣤⠒⡀⡤⠀⠀⠀⢠⠎⠀⢸
⠀⠀⠀⢸⠅⡀⢸⠇⡇⠀⠀⠘⠋⡇⠀⡇⠀⠀⠀⠉⢀⡼⡸⠀⠀⠀⠀⠰⢞⡻⡅⠀⠀⢠⢃⡞⢻⣸⡀
⠀⠀⠀⠸⣆⠳⠞⢠⠃⠀⠀⠀⠀⡇⢸⡇⠀⠀⢀⡴⠛⠒⠠⡄⠀⠀⡔⠲⣀⠇⡐⠀⠀⠿⠬⡭⡁⣴⠇
⠀⠀⠀⠀⠈⠒⠒⠃⠀⠀⠀⠀⠀⠑⠚⠀⠀⠀⠚⠒⠒⠒⠒⠃⠀⠀⠈⠒⠢⠒⠁⠀⠀⠀⠀⠀⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠐⠀⡀⢀⠄⠀⠀⢀⠞⡁⣉⡂⠀⠀⢚⣋⡛⠋⠙⡇⠀⠀⡜⢁⠤⡍⢢⠀⠀⢠⡞⣋⣉⠲⡄
⠀⠀⠀⠀⣇⣰⡆⠄⠀⠀⠀⢾⠸⠄⠥⡄⠀⠀⠀⠀⢨⠃⡄⠀⠀⠀⣻⠌⠒⢃⡜⠀⠀⡟⢸⡃⣽⠀⢱
⠀⠀⠀⠀⣀⡁⢘⡆⡆⠀⠀⠘⠀⠀⠂⢹⠀⠀⠀⢀⠇⡀⠀⠀⠀⠀⡇⠰⡁⡇⢹⠀⠀⠙⣮⠿⢷⠀⡜
⠀⠀⠀⠈⢧⡁⢋⠐⠁⠀⠀⠐⢀⣁⣠⠎⠀⠀⠀⢸⣠⡇⠀⠀⠀⠀⠷⣄⠈⣀⠞⠀⠀⠘⢍⡑⢋⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠀⠀⠘⠀⠀⠙⠁⠀⠘⠀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡄⣤⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠁⠀⣤⡀⠉⠘⢷⡀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⠀⠀⠀⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠈⢷⡀⠀⠀⠀⠀⢠⠀⠸⣧⣽⠸⡧⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣬⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠐⠓⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠀⠐⠓
⠀⠀⠠⠄⠀⠠⠶⠶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢛⣭⠶⠛⠁⠀⠀⠤
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⢀⣠⣤⡶⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠛⠛⠛
⠗⠀⠀⢘⣋⣉⣀⣀⣀⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⣉⣉⣉⣉⣙⠀⠀⠐
⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⢀

⠘⠂⠀⠀⠀⠀⠀⠀⣀⣤⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⢠⡀⠀⢀⣤⠶⢛⣩⡴⠞⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠵⠞⣋⣥⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣄⣙⠳⢦⡄
⠀⠀⠈⠁⠀⠀⢿⠉⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠉
⠀⠀⠀⠐⠖⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠖
⠀⠀⠀⠀⠀⢠⠄⠈⠁⠀⠀⠀⠀⠀⢀⡾⢡⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢠⡟⣡⡟⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⡟⣰⠏⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡄⠀⠙⠂⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⠀⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⣤⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣰⣀⣀⣴⣄⣀⣰⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠈⢻⣿⠋⠁⠀⠀⠀⠈⢻⣿⠛⠁⠉⢻⣿⠋⠀⠀⠀⠀⠙⣿⡟⠋⠈⠻⣿⡟⠁⠈⢻⣿⠛⠁⠀⠀⠈⠛⣿⡟⠁⠈⠙⣿⡏⠁⠀⢹⣿⠋⠁
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⡀⢀⣾⠏
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢹⣧⣼⡟
⠀⠀⠀⢀⣼⣿⣄⠀⠀⠀⠀⢀⣸⣿⣄⡀⢀⣼⣿⣀⠀⠀⠀⠀⣀⣿⣧⡀⢀⣠⣿⣇⡀⢀⣸⣿⣄⡀⠀⠀⢀⣠⣿⣇⡀⠀⠀⠀⣀⣿⣿⣁
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠈⠉⠉⠉


⠀⠀⠀⢠⣤⣤⣤⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⢠⣤⣤⣤⠀⢀⣄⣤⣤⡀⢠⣄⣤⣤⠀⠀⠀⠀⠀⣠⣤⣤⡄⠀⣠⣤⣤⣄⠀⣠⣄⣤⡄⢀⣤⣠⣤⡄
⠀⠀⠀⠀⠈⣿⡇⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⣼⡟⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⢠⣿⠋⠀⠀⠈⣿⡏⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠘⣿⡄⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⢰⡿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⣾⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢹⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⡿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠤⠿⠿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠤⠀⠀⠀⠤⠾⠿⠦⠀⠀⠀⠀⠀⠀⠀⠠⠼⠿⠧⠄⠀⠀⠀⠴⠿⠷⠤⠠⠴⠿⠷⠄



⠀⠀⠀⠲⢶⣶⠶⠀⠰⢶⣶⠶⠀⠲⣶⣶⠶⠀⠶⣶⣶⠆⠀⢶⣶⡶⠆⠀⠀⠀⠰⢶⣶⡶⠂⠰⢶⣶⠆⠀⣶⣶⠶⠀⠀⠀⠀⠶⣶⣶⠀⠰⣶⡶⠖
⠀⠀⠀⠀⠈⣿⡆⠀⢀⣿⠇⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⢻⣧⣴⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣦⣼⡟⠁
⠀⠀⠀⠀⠀⠘⣿⡀⣾⡏⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⣿⣇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣾⠏⠙⣿⣄⠀⠀⠀⠀⠀⠀⢠⣿⠋⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠀⠀⠀⠚⠛⠛⠓⠀⠚⠛⠛⠓⠐⠛⠛⠛⠃⠀⠀⠀⠐⠛⠛⠛⠂⠚⠛⠛⠂⠀⠛⠛⠓⠀⠀⠀⠀⠚⠛⠛⠂⠐⠛⠛⠓



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⠁⢈⣿⠟⠋⠈⠻⣿⡟⠁⠀⠀⠀⠈⠙⢿⣏⠀⢹⣿⠛⠁⠘⢻⣿⠛⠀⠙⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⠏⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠈⢿⣶⡿⠃⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⡄⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠁⢘⣿⣆⡀⠀⣠⣿⣇⡀⠀⠀⠀⠀⣀⣾⣟⠀⢹⣷⣄⡀⢀⣼⣿⣄⠀⣀⣼⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠉⠁⠈⠉⠉⠉⠀⠉⠉⠉⠉
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⢶⠶⣶⡶⠶⠶⣶

⠙⢿⡟⠁⠀⠀⠀⠈⢻⡿⠋⠈⠻⣿⠋⠀⠀⠀⠈⢻⣿⠋⠈⠻⣿⠛⠀⠙⣿⡟⠁⠀⠀⠈⢻⡿⠋⠀⠙⣿⡏⠁⠈⣿⡟
⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣷⡀⣰⡿
⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣷⣿⠁
⠴⠿⠷⠆⠀⠀⠀⠰⠾⠿⠦⠠⠾⠿⠦⠀⠀⠀⠠⠾⠿⠦⠠⠾⠿⠶⠀⠴⠿⠷⠄⠀⠀⠰⠾⠿⠦⠀⠀⠀⠴⠿⠷⠄


⢀⣀⣀⡀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⡀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⡀⢀⣀⣀
⠀⠹⣯⠁⠀⢹⡿⠉⠀⠀⠀⠀⠀⠙⣿⡅⠀⢈⣿⠋⠁⠈⢹⣿⠁⠀⠀⠀⠀⠈⠹⣯⠀⠀⢹⡟⠉⠀⠈⣿⡏⠁⠈⢹⡟
⠀⠀⢻⣇⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⣼⠏⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢻⣇⢠⣿⠁⠀⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⢿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⠇⠀⠀⠀⠀⣹⡃⠀⠀⢸⣇
⠀⠀⠐⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠓⠂⠀⠀⠐⠛⠛⠓⠀⠀⠀⠀⠀⠀⠐⠛⠛⠒⠀⠀⠀⠚⠛⠛⠂⠐⠛⠛


⣤⣤⣤⠄⠠⣤⣤⣤⠀⣤⣤⣤⠄⢤⣤⣤⡄⢠⣤⣤⡤⠀⠀⠀⢠⣤⣤⡄⢠⣤⣤⡄⠠⣤⣤⠄⠀⠀⠀⢤⣤⣤⠀⢤⣤
⠀⠹⣧⠀⠀⣼⡏⠀⠀⠀⣿⠁⠀⠀⢹⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⢹⡏⠀⠀⠈⢻⣆⣰⡿⠁⠀⠀⠀⠀⠀⠙⣷⣀⣾⠏
⠀⠀⢻⣇⣸⡟⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇
⠀⠀⠈⣿⣿⠁⠀⠀⠀⢀⣿⡄⠀⠀⣼⣇⠀⠀⣸⣿⠀⠀⠀⠀⠀⣸⣇⠀⠀⢀⣾⠋⠙⣷⡀⠀⠀⠀⠀⠀⣰⡿⠉⢻⣆
⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠁⠉⠉⠉⠁⠈⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⠉⠉⠉⠀⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⡆⠀⢶⣶⠆⠰⢶⣶⠶⠀⠀⠀⠀⠶⣶⡆⠀⣶⡶⠆⠰⣶⣶⠶⠀⢶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⡿⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠹⣷⣴⡟⠁⠀⠀⢸⣿⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⠀⠀⠀⢸⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡏⠈⣻⣦⡀⢀⣸⣿⣄⠀⠀⠀⠀⣠⣾⡏⠈⣿⣆⡀⢀⣼⣿⣀⢀⣰⣿⣄
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⠀⢀⡀⠀⣀⠀⣀⣀⡀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣾⣟⡋⠘⢸⢶⡏⢻⡎⣓⡄⠉⣹⠁⠀⣇⣘⠉⣿⡁⠄⣶⠄⢱⣜⡧⠤⣿
⠀⠀⠀⠀⠀⠀⠝⠛⣿⢠⢸⡆⣴⣏⣠⡿⣦⢰⡯⠀⠰⡇⣲⢐⠶⡃⡅⠛⡈⣸⡏⣓⣶⡋
⠀⠀⠀⠀⠀⠀⣾⣇⣿⢠⢌⠨⠉⠉⢹⡧⣬⢰⠛⡆⢀⣅⣹⠹⢼⣧⣭⣟⠻⡟⠁⢉⣠⡿
⠀⠀⠀⠀⠀⠀⠨⢭⣡⠚⡏⡆⠀⠐⠸⣧⣿⢨⠛⡅⢀⣻⠙⢁⠈⠁⣾⢘⠋⠑⡄⣿⣥⡄
⠀⠀⠀⠀⠀⠀⠒⡴⢁⠮⢡⡶⣦⠛⣼⠠⣤⠘⠤⠃⠀⣇⡕⠘⠰⢐⡃⣿⣔⡊⡀⢿⣼⢧
⠀⠀⠀⠀⠀⠀⠈⠉⢸⣹⢸⡷⣿⢰⣶⠈⣳⠰⢯⡁⠀⣮⡇⡘⣴⢸⡇⣿⢸⡅⠗⠊⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠛⠛⠘⠋⠓⠋⠙⠚⠁⠈⠓⠁⠀⠛⠁⠈⠙⠛⠘
⠀⠀⠀⠀⠀⠀⡖⡂⢖⡶⣶⡖⣢⡞⣶⣶⢐⢴⣲⠀⢠⠂⢲⢰⡆⠀⠀⠆⠴⠶⣦⢰⡂⢴
⠀⠀⠀⠀⠀⠀⣇⡃⠿⢹⡆⣴⣃⡴⠇⡈⣐⠒⣿⠀⠀⢱⠎⢀⣷⣖⠲⣷⣾⣛⣋⠂⣉⠘
⠀⠀⠀⠀⠀⠀⡄⣿⣀⢻⡆⢿⠟⣹⢋⢅⢡⡆⣻⠃⠰⣿⡦⣷⡄⣍⡇⣯⣩⡏⠉⠴⢣⢦
⠀⠀⠀⠀⠀⠀⠓⠋⠙⠟⠱⢐⠘⣿⣮⣜⠈⡙⣿⠀⠀⠩⣲⡮⢶⡟⣶⣼⣌⠀⡂⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠺⣿⣼⠞⡇⠚⢸⢁⠙⢿⡇⢙⠡⠀⠠⣠⠿⠸⢠⡞⣷⡛⠳⣷⠀⢣⡶⣧
⠀⠀⠀⠀⠀⠀⢲⡶⠾⠗⢿⣽⠈⠁⡀⢭⡄⢀⢈⠁⠰⢳⡆⡇⣾⣷⢳⡅⣰⣹⢔⠘⠧⣿
⠀⠀⠀⠀⠀⠀⠚⡇⢮⡹⠸⡽⠀⠀⠀⢤⡇⠄⠠⠀⠰⣯⠄⡟⢯⡼⠿⠰⠈⠁⠸⠟⠷⠟

⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠲⠦⠀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒
⠀⠀⠀⠀⠀⠀⠁⠀⣄⠀⢶⡄⠀⠀⠞⠐⠂⠀⠒⠠⠑⠀⠀⠀⠈⠀⢰⡀⠰⣦⠀⠀⠀⠐⠈⡤
⠀⠀⠀⠰⣶⠆⠀⠀⠻⠆⠸⠃⠀⠀⢀⠂⠀⠀⠀⠀⡀⡀⢴⡾⠀⠀⠘⠿⠀⠟⠀⢀⠀⢊⣄⢀⡀
⠀⠀⠀⠀⠀⠀⣶⡆⣶⢳⡆⠀⠀⠀⢸⠀⠀⠀⠀⠐⠉⠑⠀⠀⢰⣲⢠⡞⣶⠀⠀⠈⠀⠙⢿⠙⠇
⠀⠀⠀⠀⠀⠀⣠⠄⠈⠉⠀⠀⠀⠀⣴⡄⠀⠀⠀⠐⠱⠄⠀⠀⢀⣤⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⢉⠁⢀⣠⠀⠀⠀⠀⢠⡀⠀⠠⠔⠀⠀⠀⠀⡀⠈⡉⠀⣀⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠌⠯⠝⠓⠚⡊⠀⢱⠀⠀⠀⠀⣰⢶⡖⠁⠁⠀⠀⡹⠭⠋⠒⠳⠁⠈⡆⠀⠀⣠⡴⠀⢀⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠀⠀⠀⠁⠁
⠀⠀⠀⠀⢀⡴⢶⣤⣤⣰⡦⢄⠀⠀⠀⣀⣠⣖⣐⡦⡀⠀⢀⡴⢦⣤⣄⢤⠤⡀⠀⢀⠄⣀⣴⡄
⠀⠀⠀⢠⣿⠛⢻⡋⠿⣿⡅⠞⢣⣠⣼⠛⡽⠏⡙⢳⣇⢠⣿⠛⢻⠉⠿⣿⡑⡞⠆⠂⢠⣲⣛⢧⣄
⠀⠀⠀⠸⠭⠀⠘⣏⣢⣹⡷⢚⡟⣿⡿⠄⠈⠒⢓⠍⣿⠨⠩⠀⠸⡋⣄⣿⡧⢓⠇⣠⡾⢻⣷⢱⡌⢧
⠀⠀⠀⠀⠀⠀⠀⠈⠋⡌⠛⠉⠀⣿⠆⠀⠀⠀⡃⣶⣿⢱⠀⠀⠀⢸⢫⡍⡟⠋⠀⠉⠓⣘⣿⡗⡖⢸
⠀⠀⠀⠀⡠⣖⠉⢦⡔⠀⠁⠀⠀⣿⠛⣶⠀⣀⣑⣴⣾⠁⡠⡖⡒⣦⡕⠂⠀⠀⠀⠀⠈⢓⣸⣋⡴⠋
⠀⠀⠀⠀⢷⣴⡷⢛⠇⢀⣀⡀⠀⢿⣟⠋⢸⡑⣷⣽⣿⠀⢧⣼⡖⠻⠇⢀⣀⠀⠀⠀⣾⣽⣿⡇
⠀⠀⠀⠀⠸⣽⣶⣦⣤⣿⣿⣿⠀⠈⠿⣶⢊⡑⣶⡷⠃⠀⢸⣻⣵⣧⣤⣿⣿⣷⠀⢀⡞⣢⣿⣷⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠉⠉⠉⠉⠉
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡉⡤⢤⠀⠀⠀⠀⠀⡠⢔⣬⢖⡐⡀⠀⢨⢙⡟⠂⡇
⠀⠀⠀⠀⢀⣠⣄⣤⣖⡔⡔⠀⠀⡠⠨⡠⡞⠁⠀⠈⠙⠾⢶⠀⠀⠀⠀⢠⠇⠀⡥⣕⣋⠉⣷⠃⢁⠈⢹
⠀⠀⢀⡴⠋⢀⡤⠤⡑⠗⢣⢀⡬⠣⢽⡁⠘⠚⠉⢹⠀⠀⢸⠀⠀⠀⠀⣼⠀⠘⠧⣀⠀⡹⠁⢠⢺⠀⢸⡄
⠀⠀⡞⠀⣰⠃⠀⠀⠘⣆⠼⠋⠀⢀⠼⡇⠀⣀⠴⠋⠀⣠⢏⠀⢀⡀⠀⠉⠉⢢⠀⠈⢻⠁⠐⠓⠚⠀⠘⠓⣦
⠀⢸⠃⠀⣇⠀⠀⠀⢰⠛⢦⡖⢻⠀⠀⡗⠉⠁⠀⣤⡚⢁⣮⣴⣥⣵⠖⠲⠤⠞⠀⠀⢸⠦⠤⠤⢤⠀⢠⡖⠟
⠀⠘⣇⠀⠘⠦⠤⠖⠃⠀⡼⠁⢸⠀⠀⣧⣄⣀⠀⠀⡸⠉⢈⠥⢍⠉⢳⣄⣀⣀⣠⠴⠃⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠈⠲⣄⣀⣀⣀⣠⠞⠁⠀⢸⠀⠀⢿⠀⠈⠉⠓⢧⡀⠘⠲⠚⢀⡼⠀⠀⠀⠀⡀⢦⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠘⢳⡖⠚⠀⠀⠀⢠⠖⠉⢀⣀⣀⠉⠲⣄⡠⠶⠶⣤⡸⣤⡀⢠⠚⢄
⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠲⠴⢞⠥⢹⣀⠀⠀⠀⣏⠀⠐⣇⣀⣸⠆⡰⠋⠀⣠⠴⠦⠤⣧⢆⡺⠫⠎⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠾⣤⣀⣀⡀⠈⠉⠁⣸⠤⢤⢡⡛⣐⣇⠈⠉⠁⣰⠁⠀⠀⠉⠉⠓⢤⡇⠀⡔⠉⠙⡆⡸⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣠⠔⠿⠤⣀⡉⠑⠚⡩⠋⠉⠉⣿⠀⢠⠋⠉⢱⠀⠘⣇⠀⠙⠶⠞⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⡴⠋⠀⠀⢠⠔⠊⠀⣠⠊⠀⠀⠀⠀⢹⡀⠈⠳⠴⠊⠀⣸⠉⠲⠤⡤⠴⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡞⠁⠀⠀⠀⠘⠶⢤⡀⠈⠱⡄⠀⠀⠀⠀⠙⠲⠤⠤⠴⠚⠁⠀⠀⣀⡤⠚⠁⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠻⠤⢤⡞⠀⠀⠀⠀⡴⠤⣤⠼⠃⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢥⣀⣀⣀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣍⠄⢰⠀⠀⠀⠀⢠⠒⣠⡆⣅⣀⠀⣄⡩⣛⡸
⠀⠀⠀⢀⡤⠶⠴⢾⢎⡎⠀⢀⡀⣠⠺⣁⣀⣀⠉⠛⢯⠀⠀⠀⠀⡎⠀⡴⠮⠭⢠⡟⠀⡤⠀⡇
⠀⠀⡰⠋⢠⠔⠒⠪⡉⢹⡤⠊⠑⢺⠀⠈⠀⣸⠃⠀⡼⠀⠀⠀⠰⢥⣀⠑⠢⣀⠞⢀⡎⡑⠀⡇
⠀⢰⠃⢠⠇⠀⠀⠀⡷⡏⢀⡄⠐⢸⣠⠤⠊⠁⣠⠞⠡⢀⠴⣀⣀⠀⢈⠆⠀⢹⡀⠀⠀⠁⠀⠉⢹
⠀⢸⠀⠘⢆⡀⣀⡴⠁⢹⠃⣧⠀⢸⡀⠀⠀⠛⢳⠔⠳⠚⠿⠻⡀⠉⠁⠀⢀⡜⠉⠉⠉⡇⠀⡏
⠀⠈⠣⣀⠀⠉⠁⠀⣠⠏⠀⢸⠀⠘⡏⠓⠒⠤⣾⠀⠸⣁⠕⠀⡟⠛⠒⡋⠁⣀⠀⠀⠀⠓⠒⠃
⠀⠀⠀⠈⠉⠓⠚⠉⠁⠀⢀⠸⢤⠤⠇⠀⠀⠀⡨⠓⠀⠀⠀⠺⢄⢀⣠⣤⣃⣹⣀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⡖⠤⠤⣡⡖⡍⢃⠀⠀⠀⢸⠀⠠⡏⠉⣱⠀⡼⠉⢀⡠⠬⣥⣏⣄⡿⠦⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠸⣅⣀⣀⡀⠈⠒⠁⡧⢄⡌⡼⣒⡇⠈⠉⠁⡜⠀⠀⠈⠉⠲⢤⠇⠀⡖⠉⢢⢀⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡤⠚⠧⠄⣈⠉⠚⡭⠋⠉⠉⡇⠀⡜⠉⢱⠀⢸⣇⠀⠓⠔⠋⠀⠀⢳
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⡴⠁⠀⠀⡔⠊⠁⢠⡊⠀⠀⠀⠀⢧⡀⠙⠒⠊⠀⡸⠉⠲⠤⠴⢶⠀⠀⡞
⠀⠀⠀⠀⠀⢀⡎⠀⢠⠏⠀⠀⠀⠀⠓⠒⡄⠀⠘⡆⠀⠀⠀⠀⠙⠒⠒⠒⠋⠀⠀⠀⡤⠚⠁⢀⡼⠁
⠀⠀⠀⠀⠀⠈⠓⠒⠚⠀⠀⠀⢰⠓⠒⠒⠁⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠤⠤⠒⠉
⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠰⣤⣀⣀⣀⣤⠾⠃⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠘⡉⠀⠀⠀⢀⡀⠀⠀⠈⠙⠛⠛⢋⣡⠖⠀⠐⠞⠛⠷⣦⠀⠀⢀⣀⣀⣀⠚⠋⠁
⠀⢀⣀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢠⡶⠟⠁⠀⠀⠀⠀⠒⠚⠉⠁⠀⠲⣤⣤⣀⣠⣤⠶⠂⠀⠉⠉⣉⠙⠛⠛
⠟⠛⠉⠁⣠⠄⠀⠀⢀⣠⣤⠆⠀⠐⠛⠋⠉⠉⠉⠀⠀⠰⠶⠶⠶⠶⠀⠰⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣬⡥
⠀⣀⣴⠾⠋⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠚⠶⠶⠂⠀⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠐
⠛⠋⠀⠀⠀⠀⠠⡾⠛⠛⠷⠀⢀⠀⠀⣠⡶⠶⠶⠶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⠀⠀⢈⣁⡀⠀⠀⠀⠀⠀⠀⠈⠛⣀⠀⢀⣤⡀⢶
⠀⠀⠀⠀⠀⢤⣀⡀⢀⣀⣠⡴⠋⠀⠀⠀⣀⣀⣀⡀⠒⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠛⢷⠀⠀⠀⠻⠛⠛⠛⠛⣃⣀⣡⣤⡌
⠿⠶⠀⢀⡀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⣀⠀⠐⠟⠛⠻⠀⠀⠀⠀⠀⢶⣄⠀⣀⣀⣤⠴⠁⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠰⠟⠀⣀⣤⠶⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠐⠶⠛⠛⢿⣆
⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⢤⣤⣴⠶⠶⠶⠶⠆⠀⠉⠀⠀⠀⠀⠀⠁⠀⡠⢤⡀⠀⠀⠀⠀⠀⠻
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠋⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠠⣀⣀⡁
⣀⣀⣠⣤⣤⡴⠶⠶⠛⠛⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣰⠿⣧
⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠟⠛⠁⢠⠇⠀⠀⠀⡤⠔⠁⠀⠀⠀⠰⠇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠟⠿⣶⣄
⠀⢀⡀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣤⣶⣶⣦⠀⠀⠿⠷⠀⢠⠀⠀⠀⠀⠀⠀⢻
⡶⠛⠁⠀⢀⣰⠏⠀⠀⠀⠉⠀⠀⣠⠀⠀⢠⣤⡴⠞⠋⠀⠀⠀⢠⡶⠛⠛⠻⣦⠀⠀⠀⠀⠀⢀⣀⣉⣀⣀⣀⣠⣄⠸⣧⡀
⠀⠀⡠⠀⠈⠁⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠈⠀⠖⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠈⠙⠷⠶⣴⠶⠾
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠐⠒⠈⠀⠀⠀⠀⠀⠀⣀⣤⡶⢶⣦⡀⠀⠀⠀⠀⠀⠤⠴⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢀⠀⠀⣀⣠
⠀⠀⠀⡠⠊⠀⠀⠈⠉⠀⢀⣀⣀⣠⣤⣤⠀⠀⠀⠠⠤⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠀⠀⠠⠀⠀⠀⠀⢳⡀⠀⠀⠉⠛⠋⠉
⠀⠀⠜⠁⢠⡴⠶⠶⠛⠛⠛⠉⠉⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣀⣤⠞⠁⠀⠃⠠⠀⠀⠀⠀⣀⣁⣠⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⣠⣶⣤⣄⠀⠀⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠠
⠶⠶⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠁⠀⠀⠀⡟⠁⠀⠀⠙⣧⠀⣀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⣠⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⢶⣤⡀⠀⠀⠀⠀⠀⣧⠀⢸⠟⠛⠛⠋⠉⢹⡟
⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠈⠓⠶⠶⣶⠆⠸⠏⠁⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⢹⣀⡀⠀⠀⠀⠀⠀⠸
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⣀⣀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠁⠀⠀⠚⠛⠳⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠾⠛⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣿
⡀⠀⠀⠀⢄⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⣴⠟⠛⠉⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢆⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠘⡇⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⣀⣀⣀⡀⠀⠀⠀⠸⢧
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢀⠇⠀⢀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣄⠊⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⣴⣏⠀⠀⠀⠀⠀⠀⠙⠲⡿⠛
⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣆⣀
⣿⠿⡿⢿⠿⠿⠿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⠛⣿⣿⡟⢿⡿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⢾⣿⠆⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⢾⡷⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⣿⠷
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡀⠀⠀⢳⡀⠀⠀⠀⠀⢠⡟⠁⠀⣀⣄⠀⠈⣦⠀⠀⠀⠀⠀⣴⠋⣀⡀⠀⣠⣀⠱⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⡇⠀⠀⢈⡇⠀⠀⠀⠀⣾⠀⠀⠐⠷⢦⠀⠀⢸⡆⠀⠀⠀⠀⡏⠀⢹⡇⢸⡇⢹⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠃⠀⢀⣼⠃⠀⠀⠀⠀⠸⣆⠀⠈⠓⠛⠀⢀⡾⠀⠀⠀⠀⠀⢻⣄⠘⠃⠈⠓⠋⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠤⠶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣰⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⠉⠙⣟⠁⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠉⠙⡋⠀⠀⠀⠀⠀⢀⡶⠋⠉⠉⠉⠉⢛⡁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠰⢶⠀⢰⣛⡃⠸⡇⠀⠀⠀⠀⣼⠃⠴⢛⡆⣴⠛⡆⢹⡀⠀⠀⠀⠀⡿⠀⢞⣳⢤⡞⢳⡈⣷
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢸⠀⢨⣬⡗⢰⡇⠀⠀⠀⠀⢻⡄⣠⣿⣅⢻⣤⠇⣸⠃⠀⠀⠀⠀⣷⠠⣬⣽⠚⣧⣼⢃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣀⡴⠏⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⣀⣠⡼⠃⠀⠀⠀⠀⠀⠈⠷⣄⣀⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠒⠒⢺⡿⠇⠀⠀⠀⠀⠀⢀⣤⠶⠒⠒⠒⢺⡿⠂⠀⠀⠀⠀⠀⣠⡴⠶⠒⠒⠒⣿⠗
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡄⢠⣤⡄⢲⡄⠀⠀⠀⠀⢰⠏⢀⣤⠀⣠⣤⡀⢶⠀⠀⠀⠀⠀⣼⠋⣠⣄⠀⣠⣄⠐⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⣇⠘⠓⣦⢈⡇⠀⠀⠀⠀⢿⠀⣾⠓⣦⣿⢀⡇⢸⠇⠀⠀⠀⠀⣇⠘⠧⣼⢸⡇⢸⠆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⠃⠈⠛⢋⡼⠃⠀⠀⠀⠀⠘⣧⡈⠛⠁⠘⠛⣡⡟⠀⠀⠀⠀⠀⠻⣄⠘⠋⠀⠙⠋⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⢚⠷⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠥⡀⠀⣠⠴⠦⡶⣥⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⠉⠓⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠰⣧⣛⣇⡞⠁⠀⣀⣀⠀⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⡴⡻⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢹⡉⠲⠋⠁⢸⡆⠀⢠⡇⠀⠀⠀⣀⠊⣰⢊⡙⢆⠀⠀⠀⢀⠔⠁⠀⠐⠣⠤⠃⠀⡟
⠀⠀⠀⠀⠀⠀⠀⡖⠁⢀⡄⠘⠉⣇⠀⠀⢀⠞⠀⢀⡾⠀⣾⠉⠉⠉⠑⠉⠮⠴⠋⢹⠀⠀⠈⠛⠲⠦⢤⣀⠀⠀⠀⠉⡶
⠀⠀⠀⠀⠀⠀⠀⠹⠶⠋⢹⡀⠀⢸⣄⠴⠃⠀⣠⣾⣤⣀⣿⠤⠤⠤⣤⠄⠀⠐⢁⡼⠀⠀⢀⠀⡠⠀⠀⡾⠀⢠⡟⠒⠃
⠀⠀⠀⠀⠀⢀⠄⣀⠴⡆⠈⣇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⠃⠀⢀⡖⠉⣠⣅⣶⢇⠷⣸⡀⠘⠧⣤⡼
⠀⠀⠀⠀⠀⣢⣤⢥⣄⡰⣤⢹⡄⠀⢸⡗⠒⠒⠒⠒⠒⠒⠃⢀⡞⠀⠀⣰⠋⢠⠞⠁⢀⡤⠤⣍⠀⠙⢦
⠀⠀⠀⣰⠋⠀⠀⣀⣡⣀⡏⠀⠓⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢰⠇⢀⡏⠀⢰⠃⠀⠀⠀⢳⠀⠘⡇
⠀⠀⣼⠁⠀⠠⠯⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡟⠀⢸⠃⡀⣿⡐⠆⠀⠀⢸⠀⠀⣿
⠀⠀⡇⠀⠀⢀⣠⣄⠀⠈⢳⠀⢠⠀⢀⣰⠄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⡼⣇⢤⡋⣌⡦⢤⣠⠞⠀⠀⡟⠀⠀⠀⢀
⠀⠘⡇⠀⠠⡏⠀⠀⣷⢀⡬⠧⡄⢮⡡⢮⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢁⣭⣬⣀⣸⠁⠀⢀⡼⣃⡤⠶⢶⠡⣰⠐⢶
⠀⠀⢷⡀⠀⠓⠦⠖⠃⢸⣇⣀⣈⡁⠈⠉⡴⠁⠀⠀⣀⠀⣠⡀⠀⠀⠀⠀⡇⠀⢸⣳⣦⣤⣤⠤⠶⠋⡼⠁⠀⣀⢬⣉⠫⠥⣎
⠀⠀⠀⠳⢤⣀⣀⣀⣤⠖⠃⡠⠊⠁⢀⡞⠀⠀⠀⣰⣤⣭⣤⣵⠀⠀⠀⠀⠧⠤⣄⡀⠈⠑⣆⠀⠀⢸⡃⠀⢸⡁⠀⢈⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢺⣀⣀⡀⠀⠉⠳⣤⠊⠁⣉⠭⡉⠉⢳⡀⠀⠀⠀⠀⠀⡷⠀⠀⢸⠂⠀⠈⢧⡀⠀⠙⠒⠋⠠⠔⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⣿⠀⠀⠧⡤⠟⠀⣸⠃⠀⡸⠉⠙⠉⠀⠀⢀⡼⢠⠶⠤⣤⣩⠷⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠛⠁⠀⠀⣠⣯⠷⠀⠀⠀⠀⠾⢅⠀⠀⠙⠶⠤⠤⠤⠖⠋⠀⢿⣀⡀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⢤⣤⠤⠴⠚⣽⠁⠀⣰⠚⠛⢦⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠹⠤⠤⠞⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡤⠞⠁

⣿⣿⠟⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣷⠃⠀⠀⠀⠀⠀⠘⣶⠀⢳⡇⠀⠀⠀⠀⠀⠘⣾⠀⢳⡇⠘⣾⠀⠀⠀⠀⠀⠘⣶⠂⠳⣖⠀⠀⢸⠟
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⡄⢀⠏
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣟⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡞
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈
⠀⠀⢀⣀⡀⠀⠀⣀⡀⣀⣀⠀⠀⠀⣀⡀⠀⠀⢀⣀⢀⣀⠀⣀⣀⠀⠀⢀⣀⠀⠀⠀⣀⠀⣀⡀⢀⣀⠀⣀⡀
⠀⠀⠀⢹⣆⠀⢀⠏⠀⢸⡇⠀⠀⠀⠈⣷⠀⠀⡼⠁⠀⣿⠀⢸⡇⠀⠀⠀⢻⡄⠀⢠⠇⠀⢸⡇⠀⣿⠀⢸⡇
⠀⠀⠀⠀⢻⡄⡞⠀⠀⢸⡇⠀⠀⠀⠀⠸⣇⣰⠁⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⢿⣀⠏⠀⠀⢸⡇⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠈⠿⠀⠀⠀⠼⠧⠀⠀⠀⠀⠀⠹⠃⠀⠀⠤⠿⠤⠼⠧⠀⠀⠀⠀⠘⠟⠀⠀⠠⠼⠧⠤⠿⠤⠼⠧

⠀⠀⠈⠙⣧⠀⡽⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⢀⡟⠁⠈⣿⠁⠀⠀⠀⠀⠀⠀⠈⢻⡅⢀⠟⠁⠈⣿⠉⢹⡏
⠀⠀⠀⠀⢘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣏⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⣠⠋⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠘⣷⣀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠘⣧⡀⢀⣿⠀⣸⡇
⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠁⠉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠁⠈⠈⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣴⠛⣷⠀⣰⡿⠀⠰⠟⣿⠀⠀⢶⣿⠀⠀⣼⠃⣾⠁⣼⠋⠉⠁⣴⠋⠁⠈⢛⣿⠋⠰⣟⣽⠇⢰⡟⢹⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⣰⠏⠀⣽⠃⢀⣤⣾⣡⡶⠀⠛⢉⣷⠘⠛⣿⠃⠀⠋⣹⡇⢸⡿⣻⡇⠐⣾⠛⠀⣴⠟⣳⠀⠘⢛⡿⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⠈⠁⠀⠉⠀⠀⠉⠉⠁⠀⠀⠉⠀⠉⠉⠉⠀⠀⠉⠉⠀⠀⠃⠀⠀⠈⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠉⣀⠀⠀⠄⣀⣀⠉⠛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⣁⣀⠀⠀⠀⣀⡈⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠁⡀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠉⠐⢤⡀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠉⠐⢄⠈⠹⣦⡀
⠀⠀⠀⠀⢀⣾⠋⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⢿⣆⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠘⢿⡄
⠀⠀⠀⠀⣼⠇⠀⠎⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⢣⠀⢿⡆⠀⠀⠀⠀⠀⣾⠃⠠⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠈⣤⠀⢿⡄
⠀⠀⠀⢰⣿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣷⠀⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠿⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⢸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠠⡇⢸⡿
⠀⠀⠀⠘⣷⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠃⢰⡿⠀⠀⠀⠀⢸⣧⠀⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇
⠀⠀⠀⠀⢻⣇⠈⢁⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⢀⠎⢀⣾⠃⠀⠀⠀⠀⠀⢿⡄⠘⢀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠂⠀⠀⠀⠀⠀⠠⠋⢠⡿⠁
⠀⠀⠀⠀⠀⠻⣦⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡾⠃⠀⠀⠀⠀⠀⠀⠈⢻⣄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣤⡈⠓⠤⢀⡀⠀⠀⠀⠀⣀⠠⠔⠂⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡈⠃⠤⣀⡀⠀⠀⠀⠀⣀⠠⠖⠁⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣄⣀⣀⠈⣁⣀⣠⣤⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣄⣀⣈⣁⣀⣀⣠⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠉⠁⣀⣀⣄⣈⡉⠙⠻⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⢁⣀⣠⣄⣈⠉⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠄⠂⠉⠀⠀⠀⠀⠀⠈⠁⠂⢄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⢀⠔⠂⠁⠀⠀⠀⠀⠀⠉⠑⠢⢄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⣼⠏⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢿⣄⠀⠀⠀⠀⠀⠀⢀⣾⠋⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⢷⡄
⠀⠀⠀⠀⣼⠏⠀⡌⠀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠈⢢⠀⢿⡄⠀⠀⠀⠀⠀⣾⠇⢠⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠘⣄⠈⣿⡀
⠀⠀⠀⢠⣿⠀⣤⠀⠀⠀⠀⠀⠀⠀⠉⣰⡿⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⣷⠀⠀⠀⠀⢸⡏⠀⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣇
⠀⠀⠀⢸⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⢿⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⢸⡇⠀⡅⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⡆⠘⣿
⠀⠀⠀⠘⣷⠀⠶⠀⠀⠀⠀⠀⠀⢀⣀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠃⢠⡿⠀⠀⠀⠀⢸⣇⠀⠇⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡇⠘⢂⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠘⠀⣼⠃⠀⠀⠀⠀⠀⢿⡄⠘⡀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⢠⠋⢠⣾⠁
⠀⠀⠀⠀⠀⢻⣆⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⣾⠃⠀⠀⠀⠀⠀⠀⠈⢿⣄⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠙⢷⣤⠈⠂⠄⡀⠀⠀⠀⠀⠀⢀⡀⠴⠂⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠘⠢⢄⡀⠀⠀⠀⠀⠀⢀⡀⠴⠋⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣀⡈⠉⠉⠉⠉⣀⣠⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣀⡉⠉⠉⠉⠉⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠛⠛⠛⠛⠻⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠿⠛⠛⠛⠛⠛⠻⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⢁⠤⠔⠒⠂⠀⠁⠒⠒⠠⣀⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⢀⠤⠀⠒⠀⠈⠀⠒⠂⠤⣈⠉⠻⣦⡀
⠀⠀⠀⠀⠀⢠⡾⠋⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠈⢻⣦
⠀⠀⠀⠀⢰⡟⠀⡰⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠱⡄⠙⣷⡀⠀⠀⠀⠀⠀⣰⡏⠀⠐⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠹⣧
⠀⠀⠀⠀⣿⠁⡀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⣇⠀⠀⠀⠀⢠⡟⠀⡌⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⢻⡆
⠀⠀⠀⢸⡟⠀⠋⠀⠀⠀⠀⠀⠀⠀⠛⠋⢿⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⢸⡇⠀⡃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣷
⠀⠀⠀⢸⣇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠃⢰⡟
⠀⠀⠀⠀⣿⡄⠨⡄⠀⠀⠀⠀⠀⠀⣿⣆⣿⠇⠀⠀⠀⠀⠀⠀⠰⠀⣸⡏⠀⠀⠀⠀⠘⣿⠀⢡⠀⠀⠀⠀⠀⠀⠀⢻⣧⣿⠇⠀⠀⠀⠀⠀⠀⠤⠀⣼⠇
⠀⠀⠀⠀⠘⣷⡀⠸⡄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⡔⠁⣰⡟⠀⠀⠀⠀⠀⠀⠸⣧⠀⠰⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⠜⠀⣸⡏
⠀⠀⠀⠀⠀⠈⢷⣄⠈⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃⣀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣤⣀⠉⠐⠂⠠⠤⠤⠀⠐⠈⢁⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠉⠒⠂⠠⠤⠤⠀⠒⠈⢁⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣶⣤⣴⣶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⣶⣤⣴⡶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⣰⣿⣿⣿⢟⣛⡻⣿⣿⣿⣆⠀⢠⣿⣿⣿⣿⠟⢿⣿⣿⣿⣷⡀⠀⣾⣿⣿⡿⢟⣛⢿⣿⣿⣿⡄⠀⣰⣿⣿⣿⣛⣛⢛⣿⣿⣿⣆
⠀⠀⠀⠀⣿⣿⣿⡇⣾⣿⣿⢸⣿⣿⣿⠀⣾⣿⣿⣿⣷⡇⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣷⣿⡿⢣⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣁⡻⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣧⡻⠿⢟⣼⣿⣿⡿⠀⢹⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠃⠘⣿⣿⣿⡟⠫⠶⢿⣿⣿⣿⡏⠀⢿⣿⣿⣿⡹⠿⢇⣼⣿⣿⡿
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢿⣿⣿⣷⡄⠀⢀⣾⣿⣿⡿⠿⠿⣿⣿⣿⣦⠀⠀⣴⣿⣿⣿⣿⡿⣿⣿⣿⣷⡀⠀⢠⣾⣿⣿⠿⠿⠿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⠟⣴⢸⣿⣿⣿⣿⠀⣼⣿⣿⣿⣇⠻⠿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⠋⠾⢿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣏⣘⣋⢘⣿⣿⣿⣿⠀⢻⣿⣿⣿⡻⣿⡿⢸⣿⣿⣿⡇⠸⣿⣿⣿⡇⢿⣿⢆⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣾⣿⣿⡿⠃⠀⠈⢿⣿⣿⣿⣶⣶⣿⣿⣿⠟⠀⠀⠻⣿⣿⣿⣶⣶⣾⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣾⣿⣿⣿⢱⣶⡎⣿⣿⣿⣷⠀⣸⣿⣿⣿⢣⣶⣦⢹⣿⣿⣿⡄⢠⣿⣟⡅⢸⡿⢡⣶⣦⢹⣿⣇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⡟⢡⣶⡎⢻⣿⣿⣿⠀⢿⣿⣿⣿⣦⣝⢋⣼⣿⣿⣿⡇⢸⣿⣿⡇⢸⣇⢿⣿⣿⢠⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠹⣿⣿⣿⣬⣭⣥⣿⣿⣿⠏⠀⠘⣿⣿⣿⣿⣵⣿⣿⣿⣿⡿⠀⠀⢿⣿⣷⣼⣿⣦⣭⣥⣾⣿⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠘⠻⢿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⠿⠿⠇⠀⠀⠀⠻⢿⣿⠿⢿⣿⠿⠂⠀⠀⠀⠿⣿⡿⠿⣿⡿⢿⣿⡿⠇⠀⠀⠀⠻⢿⣿⠿⢿⣿⠿⠿⠿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠰⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⣿⡄⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⢐⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢻⣧⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⢀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⣄⣿⠇
⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣄⣀⡀⠀⠀⠀⣀⣸⣿⣀⣼⣿⣀⠀⠀⠀⠀⣀⣿⣧⣀⣿⣇⣨⣿⣄⡀⠀⠀⠀⣀⣸⣿⣀⣀⣀⣽⣿⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⠿⣿⣿⣿⣿⠆⠀⠀⠀⠾⣿⣿⣿⠿⢿⣿⣿⡿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣾⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⣿⡏⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⢠⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⢸⣿⠀⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣾⡏⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣿⠇⠀⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡁⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⣿⣇⢀⣿⡇
⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗

⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⣿⡏⠀⣿⡇⠈⣿⡅⢸⣿⠁⠀⠀⠀⠀⠀⢹⣿⠀⠹⣿⡅⣸⣿⠃⠀⠀⠀⠀⠀⠀⠹⣿⡀⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⣸⡿⠀⠀⣿⡇⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢀⣿⠇⠀⠀⣿⡇⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⣿⡇⢀⣿⡃⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⠋⢹⣷⡀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢻⣧
⠀⠀⠀⠀⠀⠰⣷⣶⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠰⣿⣿⣿⣿⣿⡿⣿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣟⠉⣿⡟⠉⢹⣿⠉⠁⠀⠀⠉⠹⣿⡏⢙⣿⠏⠉⣿⡟⠉⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⡿⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠹⣿⣾⡏⠀⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣅⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠙⣿⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⣼⡟⠹⣷⡀⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣶⣿⣿⣶⣾⣿⣶⡄⠀⠀⣶⣾⣿⣷⣾⣿⣷⣶⣿⣷⣶⣿⣷⣦

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣀⡠⠒⢲⣦⣄⠀⠀⠀⠀⠀⠀⣠⡄⣰⣇⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠴⢠⡇⠀⠀⠀⠀⠼⣫⠈⠙⠋⢻⡎⡆⠀⠀⠀⠀⣰⣷⡞⠁⠘⢠⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⡇
⠀⠀⠀⠀⠀⠈⣟⣁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣏⣼⢞
⠀⠀⠀⠀⠀⠀⢸⢔⡂⠀⠀⠀⠀⠀⠀⣠⡶⢻⡦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣧⣻⡀⠀⠀⠀⠀⠀⠀⣠⠾⣿⠃⡸⣿
⠀⠀⠀⠀⠀⠀⢸⠋⡌⠀⠀⠀⠀⠠⢄⡣⠄⠊⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⢿⣶⣦⠀⠀⠀⠀⢀⣠⣟⠻⣧⢘⣿⣧⣤
⠀⠀⠀⠀⠀⠀⢠⠶⣏⠀⠀⠀⠀⠰⡦⣱⣤⡤⠠⣀⡄⠀⠀⠀⠀⠘⣺⠏⠠⠀⣌⣻⠇⠀⠀⠀⠰⠺⠟⠶⠷⠿⢿⣿⢻⠿
⠀⠀⠀⠀⠀⠀⠰⠻⠋⠀⠀⠀⠀⠑⠈⠛⠘⠛⠛⠹⠃⠀⠀⠀⠀⠀⠀⠘⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻


⠀⠀⠀⠀⠀⠀⣼⡶⢶⡖⢐⠆⠀⠀⠀⠀⠀⢀⣶⠂⣶⠆⢠⠀⠀⠀⠀⠀⢠⡀⢰⣇⢶⡶⠀⠃⠀⠀⠀⠀⣠⣀⢳⣲⣤⡄
⠀⠀⠀⠀⠀⢾⡀⡇⠀⠉⠉⠀⠀⠀⠀⠀⢰⣎⠸⠀⠈⢁⡵⠖⠀⠀⠀⠀⠀⠀⠁⢀⢀⣗⠂⠀⠀⠀⠠⡆⢷⠞⠈⠁⣴⠷⡄
⠀⠀⠀⠀⠀⣸⡯⠅⣀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣯⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢿⠏⠀⠀⠀⠀⠀⣉⣰⣀⡀⢀⠐⢁
⠀⠀⠀⠀⠀⣠⠝⠺⣧⣻⣷⣄⠀⠀⠀⠀⠈⣩⠳⣾⡔⣷⣶⣀⠀⠀⠀⠀⠀⠀⡰⠶⡏⠀⠀⠀⠀⠀⠀⠨⡿⣁⢱⡞⠈⠇
⠀⠀⠀⠀⢀⣀⡀⠀⠀⢐⣶⢻⠀⠀⠀⠀⢸⣯⡴⠀⠀⢀⡽⣿⠀⠀⠀⠀⠀⣸⣭⡄⠀⠀⠀⠀⠀⠀⠐⠻⣷⠁⠀⠀⣤⢶⠆
⠀⠀⠀⠀⠐⠋⣻⠂⡤⣺⠿⡯⠀⠀⠀⠀⠘⠛⡶⢢⣀⣾⢿⡟⠀⠀⠀⠀⢠⠟⠳⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣶⡤⣺⣷⡷
⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠈⠀⠀⠀⠀⠀⠋⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣂⠜⠫⢴⡾⠗⠀⠀⠀⠀⠀⣮⣧⡽⠛⠜⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⣫⠀⠀⠀⣼⣭⠀⠀⠀⠀⢈⢍⠙⠀⠀⠀⢣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣯⣤⠊⢍⠈⡿⠀⠀⠀⠀⠠⣿⠃⠀⠀⠀⣯⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⡟⠁⠀⠀⠀⢠⣏⡥⠀⠀⠀⡅⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⢲⡄⡀⣤⣟⢷⠀⠀⠀⠀⠸⢇⡸⣄⠀⠠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣛⡤⠿⠀⠀⠀⠀⠀⠀⠘⠳⣯⣤⠶⠖⠂

⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄⠀⠀⠀⠀⠀⠀⡠⠤⠤⠠⢄⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠀⠀⠀⠀⠀⠀⣠⣤⡤⣤⡤⣤
⠀⠀⠀⠀⠀⢈⡭⢾⣋⣻⠀⠀⠀⠀⠀⠘⠴⠚⠒⢦⡀⢐⠀⠀⠀⠀⠀⠣⠒⠓⢲⡀⠱⠀⠀⠀⠀⠀⠀⢀⣞⣿⡍⢹⠀⠀⠀⠀⠀⠀⡷⢾⠗⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠀⢸⠶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣒⣺⠀⠀⠀⠀⠀⠀⢤⢤⠺⣁⠜⠀⠀⠀⠀⠀⢠⠯⡼⠁⠥⢼⠀⠀⠀⠀⠀⢠⣟⣟⢒⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠋⠀⠀⠀⠀⠀⠀⠀⣠⣞⣒⡶⠁⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠑⡄⠀⠀⠀⢰⠯⣿⢤⣴⢯⢽⠦⠀⠀⠀⠀⠈⠁⠉⠙⢳⡀⢘
⠀⠀⠀⠀⠀⠀⠀⢰⠠⡆⠀⠀⠀⠀⠀⢠⢮⢵⠶⢧⠤⢤⠄⠀⠀⠀⢀⠦⣤⡤⡴⠏⢀⠇⠀⠀⠀⠘⠛⠛⠛⠛⡟⢺⠚⠀⠀⠀⠀⢠⢤⣀⣠⡾⠁⡔
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠚⠚⠒⠒⠒⠒⠚⠀⠀⠀⠀⠈⠓⠃⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠀⠀⠀⠀⠀⠘⠚⠒⠓⠛⠉


⠀⠀⠀⠀⠀⠀⣀⡤⡤⡖⠀⠀⠀⠀⠀⢰⢶⡖⡖⢲⢲⠲⠀⠀⠀⠀⠀⢀⠤⡒⣒⠦⣄⠀⠀⠀⠀⠀⢀⢄⠒⠒⠂⢄⠀⠀⠀⠀⠀⠀⡠⠤⠒⠒⢤⡀
⠀⠀⠀⠀⣰⠫⣤⠞⠛⠉⠀⠀⠀⠀⠀⠘⠚⠓⠓⣻⣾⡾⠀⠀⠀⠀⢰⠅⣼⠉⠉⡯⠨⡅⠀⠀⠀⢠⠍⢀⡟⠙⢣⠀⢓⠀⠀⠀⠀⢰⠁⡼⠋⢻⡁⠱
⠀⠀⠀⢠⣇⣷⢟⣏⡉⠐⢄⠀⠀⠀⠀⠀⠀⠀⣰⠯⡴⠁⠀⠀⠀⠀⠀⢣⡨⢷⣞⣭⣞⠀⠀⠀⠀⠸⠀⠸⣆⣀⢼⡭⢸⠀⠀⠀⠀⡇⢀⡇⠀⠀⡧⢩⡇
⠀⠀⠀⢸⡻⢿⠁⠀⢹⣂⢈⠀⠀⠀⠀⠀⠀⣰⠿⣻⠁⠀⠀⠀⠀⠀⠰⠫⣶⠋⠙⣦⠈⢢⠀⠀⠀⠀⠉⠂⠤⠐⡾⠋⡹⠀⠀⠀⠀⡧⢐⡇⠀⢠⡇⢸⠇
⠀⠀⠀⠀⢃⡘⠣⡤⠾⠁⡜⠀⠀⠀⠀⠀⢰⣋⣹⠁⠀⠀⠀⠀⠀⠀⠨⣀⠹⢤⢴⠟⢁⡆⠀⠀⠀⠀⢠⢠⠶⠋⢁⠘⠁⠀⠀⠀⠀⠹⡀⠹⠦⠞⢁⠜
⠀⠀⠀⠀⠀⠈⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠒⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠊⠁⠀⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠊⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠗⢆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⢫⠏⠀⠀⠀⠀⠀⠀⠀⠠⠈⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠃⠀⠀⠀⠂⠀⠈⠉⠁⠀⠀⠀⡞⡸⠀⠀⠀⠀⠀⠀⠀⢀⣞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠠⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⠙⢢⠀⡀⠀⠀⠀⠀⠀⣴⡇⠀⠀⡆⣥⣀⡀
⠀⠀⠀⠀⠁⠒⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠐⠁⠀⠀⠀⠤⠄⢠⡤⡀⠀⠀⠀⠀⢱⢙⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⡀⠧⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⢀⣴⣡⠊⠀⢀⡀⠀⠀⠀⠀⠀⠢⠷⠄⠀⠀⠀⡖⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣮⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠉⠉⠈⠈⠉⠁⠀⠁⠀⠉⠉⠀⠀⠀⠀⠉⠐⠐⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠊⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠖⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢒⠆⠀⠀⠀⠀⠀⠀⠒⢀⡤⡀
⠀⠀⠀⠀⠀⢀⡤⣠⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠀⢀⡎⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡌⠀⠀⠀⠀⡠⡴⠀⠀⠀⢱⢹
⠀⢀⠄⠀⠀⠀⠀⠀⠉⠙⢢⠢⡀⠀⠀⠀⠀⠀⠀⢀⣎⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠜⠀⠀⠀⠀⠀⠢⠧⠄⠀⠀⡨⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠱⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⡖⡶⠀⠀⠀⠀⠱⡈⡄⠀⠀⠀⠀⠀⠀⡜⠐⠁⠀⠀⠀⠀⠀⢀⠔⡶⠀⠀⠀⠈⢢⠱
⠀⠀⠀⠠⠤⣤⣀⠀⠀⠀⠀⠎⡐⠀⠀⠀⠀⠀⡇⢇⠀⢀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡸⠠⠁⠀⠀⠀⠀⠀⠀⡟⢸⠀⠀⠀⠀⠀⢨⠆⠃
⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⢜⡴⠁⠀⠀⠀⠀⠀⠉⠐⠓⠁⠀⠀⣰⢁⠆⠀⠀⠀⠀⣰⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠚⠂⠀⠀⠀⢀⠔⡸
⠀⠀⠀⠀⠀⠀⠴⠶⠾⠷⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀⣠⡤⠾⠵⠁⠀⠠⠤⠤⠤⠯⠾⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⠤⠤⠤⠴⠶⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⡠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠑⢬⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠀⠀⠀⠀⠀⠇⠇⠀⠀⠀⠀⠀⡠⡺⠋⠀⠀⠀⠀⠀⠀⠀⠱⡘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣱⣄⠀⠀⠀⢀⢇⡇⠀⠀⠀⠀⡘⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠊⡘⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠎⠀⠀⠀⠀⠀⠀⢡⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠑⠳⠤⠤⡄⠀⠀⠀⠀⢀⡌⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⢀⣠⣣⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠘⡏⠁⠹⡏⠀⢹⠏⠀⠀⠀⠀⠈⣿⠁⠈⣿⠁⠀⠀⠀⠀⠹⡏⠀⢹⠏⠈⢹⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢿⠀⡿⠀⠀⠀⠀⠀⠀⠸⡇⢸⠇⠀⠀⠀⠀⠀⠀⢿⠀⡿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠀⠚⠂

⠀⠀⠀⠀⢤⡄⠀⢤⡤⠀⣤⠄⠠⡤⠀⠀⠠⣤⠀⠠⣤⠄⢤⡤⠀⣤⠄⠠⡤⠀⠀⠀⢤⡤⠠⣤⠠⡤
⠀⠀⠀⠀⠘⣧⠀⣾⠀⠀⣿⠀⠀⡇⠀⠀⠀⢻⡀⢰⡇⠀⢸⡇⠀⣿⠀⠀⡇⠀⠀⠀⢸⡇⠀⢹⣼⠃
⠀⠀⠀⠀⠀⢹⣴⡇⠀⠀⣿⠀⠀⡇⠀⠀⠀⠘⣇⡿⠀⠀⢸⡇⠀⣿⠀⠀⡇⠀⠀⠀⢸⡇⠀⢰⣿⡀
⠀⠀⠀⠀⠀⢈⣿⡀⠀⢀⣿⡀⣠⣇⠀⠀⠀⠀⣻⣇⠀⠀⣸⣇⢀⣿⡀⣠⣇⠀⠀⠀⣸⣇⢀⣿⢈⣧⡀

⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⢀⣀⡀⠀⠀⠀⢀⣀⡀⣀⣀⣀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⢷⣸⠏⠀⠀⠀⠀⠀⠀⠸⣇⣾⠁⠀⡏⠀⠀⠀⠀⠀⠹⣇⡾⠁⠈⡇⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡾⢹⡆⠀⠀⠀⠀⠀⠀⢠⡏⢷⡀⠀⡇⠀⠀⠀⠀⠀⢰⡏⢷⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠈⠉⠀⠀⠀⠀⠀⠉⠁⠉⠁⠈⠉⠀⠉⠁

⠀⢀⣴⣶⣶⣤⡀⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⣠⣴⣶⣶⣄
⢰⣿⣿⢹⡟⣿⣿⡄⢰⣿⣿⣏⣿⣿⣿⡀⢰⣿⣿⣽⢝⣿⣷⠀⣸⣿⣿⡿⢹⣿⣷⠀⣼⣿⣿⣏⣿⣿⣷
⠘⣿⣿⣹⣧⣿⣿⠃⠸⣿⣿⣿⣿⣿⣿⠁⠸⣿⣿⣱⣿⣿⡿⠀⢹⣿⣿⣻⣺⣿⡿⠀⢻⣿⣧⣭⣽⣿⡟
⠀⠈⠛⠿⠿⠛⠁⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠉⠻⠿⠟⠋⠁⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠙⠻⠿⠟⠋
⠀⣠⣴⣶⣶⣦⡀⠀⠀⣠⣴⣶⣶⣦⡀⠀⠀⣠⣶⣶⣶⣦⡀⠀⠀⣠⣶⣶⣶⣤⡀⠀⠀⣠⣶⣶⣶⣤⡀
⢰⣿⣿⢹⡿⣿⣿⡄⢰⣿⣿⢽⢿⣿⣿⡀⢸⣿⣿⡿⣹⣿⣿⠀⣸⣿⣿⠽⢹⣿⣷⠀⣼⣿⡏⣿⢹⣿⣷
⠘⣿⣿⣛⣣⣿⣿⠃⠸⣿⣿⣛⣣⣿⡿⠁⠸⣿⣿⣳⣿⣿⡿⠀⠸⣿⣧⣻⣻⣿⡿⠀⢻⣿⣿⣚⣼⣿⡟
⠀⠈⠛⠻⠟⠛⠁⠀⠀⠈⠛⠻⠟⠋⠁⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠉⠛⠿⠛⠋⠀⠀⠀⠙⠛⠿⠛⠋

⠀⠀⢀⣀⣀⣀⡀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠈⠉⣿⠉⠁⠀⠈⣟⢹⠉⠀⠀⢹⡏⣿⢹⡏⠀⠀⢹⡏⢻⡉⢹⡏⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠈⠁⠀⠀⠈⠁⠉⠈⠁⠀⠀⠈⠁⠉⠀⠈⠃
⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⢸⠀⠀⠀⢸⡇⣿⢸⡇⠀⠀⢸⡇⠘⣇⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈
⠀⠀⠰⠶⠿⠶⠄⠀⠴⠷⠾⠶⠀⠀⠾⠷⠿⠾⠷⠀⠀⠾⠷⠶⠿⠷⠶⠄⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠖⠰⠂⠀⠀⠰⠂⠖⠰⠂⠀⠀⠰⠆⠀⠺⠇
⠀⠀⢀⣤⣤⣤⣤⣄⠀⢀⣤⣤⣤⣤⣤⣤⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⢀⡀⠀⣀⢀⡀⠀⠀⠀⣀⠀⢀⡀⣀⢀⡀
⠀⠀⠀⠸⡇⠀⡟⠀⠀⠀⠘⣇⢀⡟⢸⡇⠀⠀⠀⢿⠀⣼⠁⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠉⠀⠀⠀⠈⡀⠀⡁⠀⠁⠀⠀⠀⠁⠀⠨⠀⠁⠈
⠀⠀⠀⠀⢿⣸⠃⠀⠀⠀⠀⢻⣼⠃⢸⡇⠀⠀⠀⠸⣧⡏⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⣄⠂
⠀⠀⠐⠒⠛⠛⠓⠒⠀⠐⠒⠚⠛⠒⠚⠓⠀⠀⠒⠚⠛⠓⠒⠛⠚⠓⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠒⠀⠀⠀⠐⠚⠛⠂⠚⠃⠀⠀⠀⠒⠛⠒⠐⠛⠚⠃
⠀⠀⠠⣤⡤⠤⣤⢤⡤⣤⢤⡤⠀⠀⢤⡤⣤⡤⣤⠤⠀⠠⢤⡤⣤⡤⠀⠀⠀⠀⠀⠀⠀⢤⠄⠠⡤⢤⠄⡤⢤⠄⠀⠀⢠⡤⢤⠤⣤⠀⠀⠀⢤⡤⢤⠄
⠀⠀⠀⠘⣇⢠⡇⢸⡇⣿⢸⡇⠀⠀⢸⡇⠘⣷⠏⠀⠀⠀⠈⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⢻⣾⠀⢸⡇⣿⢸⡇⠀⠀⢸⡇⣰⡟⣆⠀⠀⠀⢀⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡜⠀⢀⠀⡀⢀⠀⠀⠀⠀⡀⢀⠋⡀⠀⠀⠀⢀⡈⢂
⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠛⠛⠛⠛⠛⠋⠀⠈⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠉⠈⠁⠀⠀⠈⠁⠉⠁⠉⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠲⣶⢶⡶⢶⡶⠀⠰⢶⡶⣶⠶⡶⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⡆⠰⠄⠀⠀⢠⠆⠦⠀⠆⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⢸⡇⠀⠀⠈⣿⠃⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⢲⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣹⣆⣸⣇⠀⢀⣰⣏⣧⣀⣇⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢉⣄⢀⡀⠀⠀⣠⡉⣀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠉⢉⠛⠷⣤⠀⠀⢀⠞⠈⠉⣩⢍⠉⠻⣦⠀⠀⠀⣠⠂⠛⣉⡙⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡠⣾⠀⠀⠘⡇⠀⣾⠀⠀⠘⠁⣸⠃⠀⢸⡇⠀⠀⡇⠀⠈⠸⣇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠹⢀⣠⡼⠃⠀⠹⡄⠀⠰⠯⠤⠄⣠⡞⠀⠀⠀⠹⣄⠀⠤⠼⣃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠉⠓⠶⠶⠚⠛⠁⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠚⠓⣦⠀⠀⠀⢀⡤⠀⠐⠛⠲⣦⡀⠀⠀⠀⢀⠴⠶⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢸⠀⡆⠀⢸⡇⠀⢠⡎⠀⢴⣉⡁⠀⠈⣷⠀⠀⢰⠃⢠⢊⣙⡂⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⠒⡇⠀⢸⡇⠀⠸⣆⠀⠈⠁⣹⠀⢀⣿⠀⠀⢸⠀⠈⠛⠒⠃⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣥⠶⠋⠀⠀⠀⠈⠓⠶⠯⠥⠶⠟⠁⠀⠀⠈⠓⠦⠴⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠴⠶⠦⣤⡀⠀⠀⠀⠀⠀⡀⠴⠖⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠐⠒⠊⢱⠂⠘⣷⠀⠀⢀⠖⠁⢖⡳⠈⠹⡆⠀⠀⢀⡞⠁⡖⠉⣲⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠐⠒⣾⠒⢀⡿⠀⠀⡏⠀⢠⡟⢳⠀⢠⡇⠀⠀⢸⠀⠀⢑⣊⡟⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣤⣤⡤⠶⠋⠀⠀⠀⠓⠦⢤⣭⠭⠶⠋⠀⠀⠀⠘⠦⣤⣈⣁⣤⡴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⢁⠔⣆⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠀⡼⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠉⠁⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⢔⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⡂⠀⠀⠀⠀⣜⡁⠔⠻⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⡦⠀⠀⠀⠀⠀⠀⠀⠱⢶⡏⢣
⠀⠀⠀⠀⣠⠦⠿⠯⣛⡸⢄⠀⠀⠀⠀⠀⢠⣐⢇⣚⡇⠀⣠⠖⠋⠛⠛⠾⠟⣆⠀⠀⠀⣤⠤⠴⣰⣎⠶⡼⢤⠀⠀⠀⠀⢠⠞⠒⠓⠲⡎
⠀⠀⢀⡞⠁⢠⠴⠒⠦⡀⠀⢳⡀⠀⣀⡴⠋⠀⠀⢸⡇⠰⢇⡀⣠⠶⢤⠀⠀⢸⡆⠀⠀⢧⣀⣀⣈⠀⠉⣰⠏⠀⠀⠀⢠⠏⠀⣰⠂⠀⡇
⠀⠀⡾⠀⢰⠇⠀⠀⠀⢸⡄⠀⣧⠀⣇⣀⣤⡄⠐⢹⡇⠀⠀⠉⠁⠀⣸⠀⠀⣸⠁⠀⠀⠀⣠⠔⠁⠀⣴⠃⠀⠀⠀⣰⠃⢀⡜⢸⠀⠀⡇
⠀⠀⡇⠀⢸⡀⠀⠀⠀⢸⠇⠀⣹⠀⠉⠁⢸⡇⠀⢸⡇⠀⠀⠀⢀⡴⠁⠀⣰⠃⠀⠀⠀⠈⣧⣠⣀⠀⠀⠙⢦⠀⣰⠃⠀⠈⠉⠉⠀⠀⠙⢻⡆
⠀⠀⢷⠀⠀⠳⣤⣠⡴⠋⠀⢀⡟⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⡔⠋⠀⠀⠚⠓⠒⢲⡆⠀⠀⠀⠀⢈⡇⠀⠀⢸⡖⠳⠲⠶⠶⠶⢶⠀⠀⡖⠚⠃
⠀⠀⠈⢧⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢸⡇⠀⢸⡇⠀⠐⣇⣀⣀⣀⣀⣀⣀⣸⡇⢀⡏⠙⠛⠉⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠈⠙⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠈⠓⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠒⡤⠒⠄⠀⠀⠀⠀⠀⠀⠠⠁⠐⠈⢣⡀⠀⠀⣠⠤⠤⠴⣐⣾⠱⠄⡧⣤⠀⠀⠀⢠⠀⡠⢦⠀⠀⠀⠀⠀⠀⡐⢁⣶⡉⢃
⠀⠀⠀⠀⡏⠑⠙⠣⠭⠏⠉⡇⠀⠀⠀⣠⠞⠛⠛⠓⠊⣹⠀⠀⣿⠀⠀⠀⠀⠀⠙⠋⠅⢸⠀⠀⣠⣧⣼⣶⣴⣄⠀⠀⠀⡴⠋⠙⢒⣙⠒⠋⠳⡀
⠀⠀⠀⠀⡇⠀⢰⠋⠉⠉⠉⠁⠀⠀⡼⠁⠀⣠⣒⡛⠙⠃⠀⠀⠛⠒⠚⢛⡷⠃⠀⢀⡴⠛⠀⡞⠀⢠⠴⢬⡀⠘⣇⠀⢸⠃⠀⣸⠉⠈⢱⠀⢰⢷
⠀⠀⠀⠀⡇⠀⠈⠑⠒⢦⡀⠀⠀⢸⠁⠀⠀⠉⠉⠉⠓⢆⠀⠀⠀⠀⣠⠏⠀⢀⡴⠋⠀⠀⠘⣇⠀⠙⠦⠞⠁⢠⠏⠀⠸⡄⠀⠘⠲⠶⠋⠀⠉⢸
⠀⠀⠀⠀⠉⠉⠙⢦⠀⠀⠹⡄⠀⣿⠀⠀⡴⠉⠉⢣⠀⠘⡇⠀⠀⣰⠏⠀⢀⡾⠁⠀⠀⠀⣠⠞⠃⠀⠀⠀⠘⠳⢄⠀⠀⠙⠦⢤⣤⣄⠀⠀⠀⡟
⠀⠀⠀⢠⠤⠤⠤⠞⠀⠀⢠⠇⠀⢸⡀⠀⠳⣄⣠⠞⠀⢠⡇⠀⢠⡏⠀⠀⣼⠁⠀⠀⠀⢰⡇⠀⢠⡎⠉⠙⡆⠀⠈⡇⠀⣠⣤⠤⠖⠁⠀⢀⡼⠁
⠀⠀⠀⢾⣀⡀⠀⠀⣀⡤⠋⠀⠀⠀⠳⣄⣀⠀⠀⣀⡤⠏⠀⠀⠸⣥⣤⣤⠇⠀⠀⠀⠀⠘⣇⠀⠀⠓⠒⠚⠁⠀⣠⠇⠀⣷⠀⢀⣀⣠⠴⠋
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠤⠴⠚⠁⠀⠀⠈⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣚⣭⣽⣒⠦⣄⠀⠀⠀⠀⠀⢀⡤⢖⣚⣭⣝⣒⠦⣄⠀⠀⠀⠀⠀⢀⡤⢖⣒⣭⣽⣒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⣾⣿⣿⠟⢻⣿⣿⣮⢳⡀⠀⠀⢰⢫⣾⣿⠟⣛⡛⢻⣿⣮⢳⡀⠀⠀⣰⢫⣾⣿⠟⣉⡙⢿⣿⣮⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⣿⣿⣥⡆⢸⣿⣿⣿⡇⣧⠀⢀⢇⣿⣿⣷⣾⣿⡿⢀⣿⣿⡇⢇⠀⢠⣇⣿⣿⣿⣾⡿⠟⣸⣿⣿⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣿⣿⣿⣿⡇⢸⣿⣿⣿⡏⡿⠀⠘⡌⣿⣿⣿⡿⢋⣴⣿⣿⣿⡏⡞⠀⠸⡏⣿⣿⣿⢿⣿⣷⡌⣿⣿⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡙⢿⣿⣿⣇⣸⣿⣿⠟⡱⠃⠀⠀⠳⡙⢿⣏⣀⣛⣛⣛⣿⠟⡱⠁⠀⠀⠳⡙⢿⣿⣌⣛⣋⣴⣿⠟⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢍⣛⣛⣛⣋⠵⠊⠁⠀⠀⠀⠀⠘⠲⢍⣛⣛⣛⣋⠵⠊⠁⠀⠀⠀⠀⠙⠲⢍⣛⣛⣛⣋⠵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⣀⡤⠔⣒⡲⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠴⣒⡢⠤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠴⣒⡲⠤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠴⣒⡲⠤⣄⡀
⠀⠀⢠⢞⣵⣾⣿⣿⠿⣿⣶⣝⢦⠀⠀⠀⢠⢞⣵⣾⠿⠿⠿⢿⣶⣝⢦⠀⠀⠀⢠⢞⣵⣾⡿⠿⠿⣿⣶⣝⢦⠀⠀⠀⢠⢞⣵⡾⠿⠿⠿⠿⣶⣝⢦
⠀⢀⡏⣾⣿⣿⡿⣡⢈⣿⣿⣿⡎⣇⠀⠀⣏⣾⣿⣿⠰⠿⠿⣿⣿⣿⡎⣇⠀⢀⡏⣾⣿⡟⢰⡿⢷⣼⣿⣿⡎⣇⠀⢀⡏⣾⣿⣿⣿⣿⢃⣼⣿⣿⡎⣇
⠀⢸⡸⣿⣿⠏⢴⠿⠸⣿⣿⣿⡿⣿⠀⠸⡳⣿⣿⣷⣴⣾⣦⠘⣿⣿⡗⡸⠀⢸⡔⣿⣿⡇⢠⣶⣦⠘⣿⣿⡷⡾⠀⢸⡿⣿⣿⣿⣿⠃⣾⣿⣿⣿⡿⣸
⠀⠀⢧⠻⣿⣶⣶⣶⢠⣾⣿⡿⢣⠇⠀⠀⢧⠻⣿⣧⡙⠿⠛⣰⣿⡿⢣⠇⠀⠀⢧⠻⣿⣷⡘⠿⠟⣰⣿⡿⢣⠇⠀⠀⢧⠻⣿⣿⡏⢸⣿⣿⣿⡿⢣⠇
⠀⠀⠀⠳⢭⡻⠿⠿⠿⠿⣋⠵⠃⠀⠀⠀⠀⠳⢍⡻⠿⠿⠿⠿⣋⠵⠁⠀⠀⠀⠀⠱⢌⡻⠿⠿⠿⠿⣋⠵⠃⠀⠀⠀⠀⠳⢌⡻⠿⠿⠿⠿⣋⠵⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣥⣶⣶⣶⣦⣝⠢⡄⠀⠀⠀⠀⡠⢚⣥⣶⣶⣶⣦⣝⠢⡀⠀⠀⠀⠀⡠⢚⣥⣶⣶⣶⣦⣝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣴⣿⣿⢡⣶⣦⢹⣿⣷⡜⡆⠀⠀⡜⣵⣿⡟⢡⣶⣦⠹⣿⣷⡝⡆⠀⠀⡞⣴⣿⣿⢁⣶⣦⠹⣿⣷⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣿⣿⣿⠆⣉⡁⢾⣿⣿⡇⣿⠀⢰⢣⣿⣿⣧⠸⠿⠟⠀⣿⣿⣧⢳⠀⢸⡇⣿⣿⡇⢸⣿⣿⠀⣿⣿⡧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢿⣿⣇⠸⣿⣿⢀⣿⣿⢇⡏⠀⠈⣇⢿⣿⣿⢻⣶⡿⢠⣿⣿⢇⡇⠀⠈⡇⢿⣿⣧⠸⣿⡿⢠⣿⣿⢇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡻⢿⣶⣤⣴⣾⠿⣫⠞⠀⠀⠀⠘⢮⡻⢿⣶⣤⣶⣿⠿⣫⠞⠀⠀⠀⠘⢮⡻⢿⣷⣤⣴⣿⠿⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠭⠽⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⠾⠭⠽⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠓⠾⠭⠽⠖⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⡠⠤⡀⠀⠀⠀⢀⣀⠤⠤⣀⠀⠀⠀⠀⢀⣤⣒⣀⡀⠰⠄⠀⠀⡔⡐⡆⠀⠀⠰⠈⠳⠀⠀⠀⡎⢉⠉⠉⡉⠐
⢀⠐⠊⡴⠛⢶⢀⢇⠀⢠⠆⢠⠒⠤⡀⠘⠆⠀⠀⠻⠊⠀⠀⡗⢀⠆⠀⠀⡇⢠⠁⠀⠀⢈⡡⢘⠁⠀⠀⡗⢁⠁⠀⠉
⣮⢥⠔⠀⠀⠸⠁⡌⠀⠘⠢⠝⠀⠀⢸⢀⡴⠀⠀⠀⣀⠴⣪⠵⡁⠀⠀⠀⡏⣀⠀⠀⠀⢨⠔⢸⠀⠀⠀⠏⠠⢔⠒⢀⡀
⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⡠⠊⡠⠁⠀⠀⠐⡡⠄⠠⡄⠈⣆⠀⠀⡋⠘⠲⢂⠊⣁⠔⠇⠀⠀⠀⠀⠀⠀⠹⡀⠨
⠀⠀⠀⠀⠀⡥⠂⡁⠀⠀⠀⠠⠚⣡⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡈⠀⠀⠈⠁⠁⠈⠁⣘⠴⠀⠀⠀⠀⠀⠀⠀⡠⠅
⠀⠀⠀⠀⠀⢇⣀⡝⠀⠀⠀⠏⠀⠌⠨⠠⠥⠽⠀⢠⠠⠤⠔⢉⡠⠁⠀⠀⠀⠀⠀⠀⠀⣅⢐⠀⠀⠀⡖⠋⠉⠫⠁⢂⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠐⠋⠁
⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⢀⡀⠤⠤⠤⣄⣀⠀⠀⠠⠔⠈⣋⣉⠒⢀⠀⠀⠀⡠⠀⠀⠊⠀⣢⠀⠀⠀⢀⠠⡖⢒⠀⠄
⠀⠀⠀⠄⠀⠴⠢⠄⢳⠀⠀⠀⠔⠓⠘⢢⠄⡚⠀⢰⠅⠤⠋⠀⠉⡆⢀⠀⠀⡰⠀⡰⠊⣶⡁⢀⠀⠀⠀⠚⢄⢠⣰⢀⠈
⠀⠀⠆⢀⠃⠀⠀⢇⠝⠀⠀⠀⠀⡀⢠⢞⡼⠤⠀⠸⡄⠀⠓⠒⠈⣡⠈⠀⠀⢡⠀⠉⠋⢁⢠⠔⠀⠀⡘⠠⣀⠃⠀⢃
⠀⠐⠀⡌⢀⠀⠀⠀⠀⠀⠀⠀⠅⠤⡔⡸⠒⠂⠀⠀⠈⡧⡄⠰⠶⣄⠀⠀⠀⠀⠑⠒⠀⠊⢹⠄⠂⠀⠆⠀⡈⠀⠀⢈⠠
⠀⠒⠀⠉⢠⡈⠈⢂⠀⠀⠀⠀⢀⡈⡠⠀⠀⠀⠀⢀⠊⠀⡢⠦⢤⡂⢑⡀⠀⠀⠀⠀⠀⠀⢨⠀⠆⠀⣀⠀⠤⠀⣀⠦⠄
⠀⠘⣄⠀⠃⠞⢀⠘⠀⠀⠀⠀⢌⠄⠀⠀⠀⠀⠀⢀⠀⠭⣀⣀⣜⠃⢠⠀⠀⠀⠀⠀⢀⡰⠁⢤⠀⠀⢇⠀⠀⠉⠁⠀⢢
⠀⠀⠈⠛⠒⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠁⠡⠤⠐⠁⠀⠀⢎⣉⠉⣁⠠⠖⠁⠀⠀⠈⠣⢄⣄⠀⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣦⠶⠀⠀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⡈⠆⠀⠀⠀⠀⠀⢀⣀⢀⡀⣀⣀⠀⠀⠀⠈⠚⠁⢀⠜⢁⠂⠀⠀⠀⠀⠠⢤⠤⠀⠤⢄
⠀⠀⠀⠠⣲⡒⣒⡁⢛⣠⠉⠆⠀⠐⠤⠡⠎⠴⠁⠊⠀⠀⠀⠀⠀⢀⠎⠁⠋⠀⠀⠀⠀⠐⠒⠒⡒⢒⡒⠁
⠀⠀⠀⠀⠀⠀⠉⢣⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢋⡘⠁⠀⠀⠀⠀⠀⣊⠉⡈⢁⣌⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠌⠀⠀⣜⡧⠢⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠛⢶⡄⠀⠀⣠⡶⠛⠛⠛⢦⡀⠀⠀⣤⠞⠛⠛⠳⣦⡀⠀⢀⣴⠞⠛⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣴⡏⣷⠀⢻⠀⢠⡟⠀⠘⣿⠀⠈⣷⠀⢸⡏⠐⢯⣽⠆⠘⡇⠀⢼⠃⠐⠫⣿⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⠓⠋⣠⡿⠀⠀⢿⣄⠐⠛⠀⣰⠏⠀⠈⢷⡀⠛⠛⢃⣼⠃⠀⠸⣧⡈⠓⠛⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⣤⡀⠀⠀⢀⣤⠶⠶⢶⣄⠀⠀⠀⢀⣴⠶⠶⢦⣄⠀⠀⠀⣠⡴⠶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣴⡆⠈⢿⡀⢀⡿⠁⢴⣶⡀⠘⣧⠀⢠⡟⠀⣴⣲⠄⠹⡆⠀⣸⠏⢰⠶⡶⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⠹⠿⢀⣾⠁⠈⣷⡀⠺⠼⠇⢠⡟⠀⠸⣧⠀⠿⠽⠃⣰⠇⠀⢹⣆⠀⠾⠃⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠟⠁⠀⠀⠈⠛⠶⠶⠶⠋⠀⠀⠀⠈⠳⠶⠶⠞⠋⠀⠀⠀⠙⠷⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢡⡤⣄⠙⣧⠀⠀⣾⠋⣠⢤⡈⠹⣆⠀⢀⡾⣡⡄⣠⢬⣻⡄⠀⢠⡟⠁⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢼⣛⣿⠀⣼⠀⠘⣧⠀⢽⣺⠇⢀⡿⠀⢸⣇⣼⡟⢿⣸⢿⡇⠀⢻⡄⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⣤⡾⠋⠀⠀⠘⢷⣤⣤⣤⠞⠁⠀⠀⠛⢦⣤⣤⣴⠟⠁⠀⠈⠳⣦⣤⣤⡴⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⡇⠈⠁⠀⡉⠱⠛⠀⠸⢠⠇⣀⠹⡼⢻⡛⢼⠁⠏⠅⡈⠄







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠀⠀⠀⠀⢠⠀⠀⡀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⠎
⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠤⢀⠀⠀⠀⢢⠰⢰⠀⠀⠀⠀⠰⠄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠲⣌⢆⠀⠀⠘⠤⠼⠀⠀⠀⡠⠁⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠐⠯⠇
⠀⠀⠀⠀⠌⢀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡀⣀⠐⡀
⠀⠀⠀⡈⠀⠀⠐⠲⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⠮⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠀⡀⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⡀⢸
⠀⠀⢰⠀⠁⠘⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠁⠸
⠀⠀⠈⠀⠀⠀⢀⡠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢁⠀⢀⠑⡭⢊⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠭⠆⠀⠀⠠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠡⠈⠁⠐⠁⠀⢠⢶⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⡠⠁⠀⠀⠀⢈⣏
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠐⠵⢁⠎⠀⠀⠀⡇⡆⠀⠀⠀⠈⠢⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠒⠈⠀⠀⠀⠀⠇⠐⠀⠀⠀⠀⠐⠂⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⡄

⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⣾⣿⣿⣿⠀⠀⢀⣾⣿⢿⣷⣄⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣤⣶⣶⠶⠆
⠀⠀⠈⠛⢻⣿⣿⠀⠀⠈⠛⠛⣼⣿⡏⠀⠀⠀⢰⣿⣿⣯⡀⠀⠀⢠⣿⣟⣴⣶⡄⠀⠐⠿⠛⠻⣷⣤⡀
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠈⠉⢻⣿⡷⠀⢠⣿⠿⠿⣿⣿⠇⠀⠀⠀⠀⠀⣹⣿⡇
⠀⠀⠀⠀⣸⣿⣿⡄⠀⢴⣿⣿⣶⣿⠃⠀⢠⣄⣀⣴⣿⡿⠃⠀⠀⠀⠀⢠⣿⣿⡂⠀⢴⣷⣦⣶⡿⠟
⠀⠀⠀⠈⠛⠛⠛⠁⠀⠈⠉⠉⠉⠉⠀⠀⠘⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠈⠉⠁
⠀⠀⠀⣀⣤⣀⠀⠀⢀⣀⣀⣀⣀⣠⣄⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣠⣀⣀
⠀⢀⣾⣿⠿⠛⠁⠀⠈⠛⠛⢻⣿⣿⠏⠀⠀⣾⣿⡋⣹⣿⠂⠀⠀⣰⣿⠿⣿⣿⣦⠀⠀⣰⣿⡿⠻⣿⣷⡀
⠀⢸⣿⣿⣶⣶⣤⡀⠀⠀⢀⣾⣿⡏⠀⠀⠀⢨⣿⣿⣿⣿⣷⡄⠀⢿⣿⣄⣼⣿⣿⠀⢰⣿⣿⠁⠀⢹⣿⡇
⠀⢸⣿⣿⡟⢈⣿⡇⠀⢀⣾⣿⣿⠁⠀⠀⢠⣿⣿⡇⠀⣹⣿⠇⠀⠀⡉⠋⣹⣿⠟⠀⠘⣿⣿⣆⣀⣿⣿⠃
⠀⠀⠛⠿⠿⠾⠛⠀⠀⠈⠛⠿⡟⠀⠀⠀⠀⠻⠿⣷⠶⠛⠉⠀⠀⠘⠻⠾⠛⠉⠀⠀⠀⠘⠻⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⢻⣿⡄
⠀⢀⣠⣿⣧⣤⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⣶⣶⡦⠀⠀⢀⣠⣽⣥⣄⠀⠀⢴⣶⣶⡶⠀⠀⠹⠇⢀⣼⣿⠏
⠀⠈⠉⢿⠏⠉⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠙⠛⠋⠀⠀⠈⠉⣽⡍⠁⠀⠀⠛⠛⠛⠋⠀⠀⠀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡍

⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⢤⣴⠀⠀⠀⠀⠀⠀⠀⢄⠐
⠀⠀⢀⡠⠚⢸⠁⠀⠀⠀⡠⠊⢉⠙⠛⡄⠀⠀⠀⠀⣎⣉⡛⠘⡹⠁⠀⠀⠀⠀⡜⢈⠐⡇⠀⠀⠀⠀⢰⠉⣋⡟⢩
⠀⠀⢧⠤⡄⠘⡀⠀⠀⠀⠉⠚⠉⡇⠀⡇⠀⠀⠀⠀⢠⠊⠁⠸⢅⠀⠀⠀⢀⠎⣠⢻⠀⡇⠀⠀⠀⠀⢸⠀⠓⠠⡀
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡠⠊⢀⣞⣀⡀⠀⠀⠀⢀⠉⣱⠀⠈⡆⠀⠀⣎⣀⣀⣀⠀⡨⠇⠀⠀⠀⢀⠀⣱⠀⠘⡆
⠀⠀⠀⠀⣇⣠⠇⠀⠀⠀⠀⣅⣄⣀⣀⣠⠇⠀⠀⠀⣏⣉⣀⡠⠞⠀⠀⠀⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⢦⣀⣀⡠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡠⠶⠶⠔⡆⠀⠀⠀⠄⠐⠐⠷⣢⢦⠀⠀⠀⢀⠬⠴⡤⣄⠀⠀⠀⠀⡠⠦⠼⠂⢦⠀⠀⠀⠀⢀⠴⠶⢶⢥⡀
⠀⠀⡞⠀⠴⠭⣉⠁⠀⠀⠀⠦⠤⡤⠀⢀⠼⠀⠀⠀⡆⠰⢄⠆⢸⠀⠀⠀⢰⠁⢐⠉⡱⠠⣇⠀⠀⢰⠃⡔⠈⠑⡄⢱⡀
⠀⢰⠀⢀⠔⠢⠀⢣⠀⠀⠀⢀⡞⠀⡴⠁⠀⠀⠀⢠⠜⢀⡀⡀⠓⡄⠀⠀⠈⠦⣀⣉⠀⠀⡇⠀⠀⣎⠀⡇⠀⠀⡅⠀⡇
⠀⠈⢆⠈⠢⠚⢀⡜⠀⠀⠀⡜⠀⡸⠁⠀⠀⠀⠀⢸⡀⠰⠤⠞⠀⡄⠀⠀⠀⡄⠐⠋⢀⡜⠁⠀⠀⠸⣄⠈⠒⠊⠁⡸⠁
⠀⠀⠈⠑⠒⠒⠉⠀⠀⠀⠀⠓⠒⠃⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⠀⠀⠀⠀⠑⠒⠈⠁⠀⠀⠀⠀⠀⠈⠑⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠠⢀⠐⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⡨⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⣤⡶⠦⠀⠀⢠⠆⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠐⢶⣦⣤⠤⡤⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠄⠀⠀⣻⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠂⠀⠀⠀⠀⣻⠀⠀⠀⡀⠀⠀⠈⠀⣠⢞⠝⠁⠀⠐⠂⠀⠀⠀⠈⠻⠰⢿⠄⠀⢀⡴⡻⠁
⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⡀⠀⠀⢸⢸⠀⠐⠐⠁⠀⠀⠀⡰⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠈⠙⢦⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⣼⠃⠈⠀⣠⢘⠇⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢐⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⡇⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠑⢄⣤⣤⣠⣤⡦⠈⠀⠀⠀⠀⠁⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⡌⡨⠀⠀⠄⠀⠀⠀⠒⢤⡀⠀⠀⠱⣄⠀⠀⠀⠀⣀⡮⠀⠀⠀⠀⠀⢂⡀⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠶⠶⠷⠇⠀⠀⠀⠀⣤⣤⠀⠀⠹⡦⠀⠀⠈⠉⠓⠐⠚⠋
⠀⠀⠀⠀⠤⠰⠂⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢰⠇⠀⠀⡠⠀⠀⠀⠀⠀⠀⣤⣤⣼⡜⠀⠄⠀⢀⣽⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⣿⠁⠀⠀⠀⠲⠶⠼⠇⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⡀⠀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠙⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣠⡴⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⠁⢭⡉⠉
⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⠀⣀⢀⣿⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣦⠀⠀⠀⠀⠀⠈⠀⣀⢀⣀⢤⣄⡀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠁⠀⠀⢻⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣔⡟⠋⠀⠀⠀⠀⠰⠤⣤⠤⠤⣤⣤⣴⣿⠀⠀⠀⠀⠋⠀⠀⠀⠉⠛⠁⠀⡠⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠐⠈⢉⠁⠁⠀⢀⡀⠀⠀⠀⠀⢠⢪⡁⠉⠉⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣀⡀⠈⠢⠀⠀⠀⠀⠀⢿⡋⠉⠑⠀⠀⣷⠀⠀⠀⠀⠀⠀⢴⡮⠑⠦⠀⠀⣿⠄⠀⠀⠀⠀⠙⠶⣤⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠎⠈⠁⠀⢸⡇⠀⠀⢣⡀⠀⠁⠀⠀⢀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣔⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣠⡄⠀⢸⡇⠀⠀⠀⠙⠳⠶⠶⠾⠗⠊⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⠀⠉⣄⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⠁⠇⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢯⡎⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣽⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠉⠀⠀⠀⡠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢠⣤⠲⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⠶⠆⠋⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿
⠀⠀⠀⠈⢩⣭⣭⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠉⠛⣿⣿⣷⠀⠀⠀⠀⠈⠉⠉⢉⣽⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣻⣥⡀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃⠀⢰⣴⣴
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⢨⣬⣼⣥⣤⣤⢼⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⢶⢿⢿⢿⠛⠁⠀⠀⠀⠀⠀⠀⢰⣶⣶⣄⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠨⠯⠿⠿⠿⠯⢽⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣾⣾⡆⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣦
⠀⠀⣚⣛⣛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⢻⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠿⢻⣿⣿⡇
⠀⠀⣿⣿⣿⣸⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⣼⣿⣿⢯⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⣹⣶⣿⣿⣿⣿⢇
⠀⠀⠿⠿⠿⠼⠛⠻⣿⣿⣷⠀⠀⠀⠀⣼⣿⣿⠗⠛⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⣾⣿⣿⠟⠙⠫⣿⣿⣆
⠀⠀⣤⣤⣤⡀⠀⠀⣼⣿⣿⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⢀⣿⣿⣿
⠀⠀⠘⢿⣿⣿⣶⣾⣿⣿⠏⠀⠀⠀⠀⠙⣿⣿⣿⣶⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⠀⠈⢻⣿⣿⠀⠀⠀⠀⣸⣿⣿⠏⠉⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⣀⣀⣾⣿⡿⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣟⣾⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣧⣀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠴⢶⡶⠦⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⡋⠉⠀⠀⠀⠈⢀⠈⣁⣀⠁⠀⠀⠀⠉⢙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠓⠀⣄⠀⠀⠀⠀⠀⠸⡆⣿⣿⠀⠀⠀⠀⠀⠀⢀⠚⠈⠓⢤⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠄⠀⠀⠙⢦⠘⣆⠀⠀⠀⠀⠀⢧⣿⣿⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⣠⠋⠀⠁⠀⠀⠀⠀⠀⠳⣜⠦⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⡴⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⣨⢦
⠀⠀⡼⠡⠀⠐⠶⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠀⠀⣀⡤⣚⠽⠂⠀⠈⢧
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠈⠁⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⢮⠉⠀⠀⠈⠗⠋⠁⠀⠀⠀⠀⠘⡆
⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣶⣟⠂⠀⠀⠀⠀⠀⠀⠀⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠊⠻⠷⣄⡀⠀⢀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡷⠄⠤⠖⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣟⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣭⣭⣭⡏⠠⠶
⠀⡇⠄⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠠⢸
⠀⡧⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠸⡄⠀⢀⡤⣖⡭⣚⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⢠⠇
⠀⠀⢳⠐⠀⢫⠗⠋⢁⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠮⠝⠀⠂⡞
⠀⠀⠀⢳⡚⠀⢀⡴⠋⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡞
⠀⠀⠀⠀⠱⣌⠀⠀⠀⠀⠀⣠⢫⠏⢠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⣡⠎
⠀⠀⠀⠀⠀⠈⠣⣀⠄⠀⠰⣳⠃⠀⡞⠀⠀⠀⠀⢹⠀⣶⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠠⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⣤⠀⠸⠃⠀⠀⠀⠀⢸⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣤⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⣀⡀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠀⠀⠀⢀⣨⠤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠲⠤⠼⠧⠤⠖⠒⠒⠋⠉
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣻⣿⣟⣿

⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⠠⣾⠟⠛⣿⡆⠀⠀⠀⠀⠀⠾⠟⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠻⠗
⠀⠀⠀⠀⠈⠁⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠰⠿⣿⡁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣏⣀⡀⠀⠀⠀⠀⠀⣤⣄⢀⣼⡷⠀⠀⠀⠀⠀⠀⠀⢶⡦
⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠛⠟⠛⠁

⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⢀⣿⣟⣛⠛⠁⠀⠀⠀⠀⢀⣾⡏⣉⠻⠃⠀⠀⠀⠀⠀⠻⣿⣶⣿⡿⠃
⠀⠀⠀⢠⣾⠋⣿⣿⠀⠀⠀⠀⠀⠸⠿⠛⠻⣷⡄⠀⠀⠀⠀⢸⣿⡿⠛⣿⡆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀
⠀⠀⠀⠻⠿⠿⣿⣿⠗⠀⠀⠀⠀⢰⣶⣤⣴⣿⠇⠀⠀⠀⠀⠈⢿⣧⣠⣾⡟⠀⠀⠀⠀⠀⠙⠋⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋

⠀⠀⠀⠸⠿⠿⢿⣿⡇⠀⠀⠀⠀⢠⣾⠿⢿⣦⠀⠀⠀⠀⠀⠀⣴⡿⠿⣶⡄⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠘⣿⣷⣾⣟⠀⠀⠀⠀⠀⠘⣿⣇⣠⣿⣷⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⢸⣿⠁⢸⣿⡆⠀⠀⠀⠀⠀⣈⡛⠛⣻⡿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁

⠀⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⢰⣿⡏⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣇⣀⣀
⠀⠀⠀⢸⣿⡄⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠿⠿⢿⣿⡿⠿⠟
⠀⠀⠀⠘⢿⣷⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇
⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⠲⡀⢄⠂⠀⢠⢲⣤⡟⢇
⠀⠀⠀⠀⠀⡀⠀⣀⢀⢄⠀⠀⠀⠠⠀⣠⠴⠒⠺⢶⣜⡍⡇⠀⠀⠀⠀⢠⠏⠑⠛⢔⡦⠧⣄⡜⠲⠓⠤⡎
⠀⠀⣠⠴⠚⠺⠛⣵⣆⡇⢠⢠⡎⢬⡎⠣⣀⡤⢤⡀⠉⠙⡆⠀⠀⠀⠀⡼⠀⢰⠛⠒⠲⢤⡟⠀⣰⡆⠀⡇
⢀⡜⠁⢠⠔⠚⠓⢎⠀⢹⡤⠋⠉⠹⡇⠀⠀⠀⣠⠃⠀⢠⠇⠀⠀⠀⠀⠧⣄⡈⠑⠦⣀⠞⠀⡼⢡⡇⠀⡇
⣼⠀⢠⠇⠀⠀⠀⢸⢶⠉⢀⣀⠠⠂⣇⣀⠤⠚⠁⢀⡴⢋⠤⣀⠶⡀⣀⠀⠀⣱⠀⠀⢹⠀⠀⠉⠉⠀⠀⠉⢹
⡇⠀⠸⡄⠀⠀⢀⡼⠘⢻⠏⢹⠀⠀⣏⠀⠀⠀⠲⠯⣄⠼⡶⢷⣶⢿⡉⠉⠛⠁⠀⠀⡼⠛⠛⠛⢻⠀⠀⡏⠉
⠹⣄⠀⠈⠓⠒⠉⠀⢀⡞⠀⢸⠀⠀⣿⠲⠤⣄⣀⢰⠁⠀⡖⠒⡄⠀⢳⠦⠤⠤⠴⠊⠀⠀⠀⠀⢸⣄⣠⡇
⠀⠈⠳⠤⣤⣤⣤⠴⠋⠀⠀⢸⠀⠀⢸⠀⠀⠀⠈⠙⢆⠀⠙⠋⢁⣠⠋⠀⠀⡔⠠⠄⢷⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣻⣏⠉⠀⠀⠀⢀⠖⠁⢀⡤⠤⡀⠈⠳⣤⠔⠛⠓⠶⠜⣦⡤⢠⣊⢣⣀
⠀⠀⠀⠀⠀⠀⣼⠉⠓⠚⠼⢏⠶⢨⣄⡀⠀⢀⢸⠀⢀⢻⣀⣀⡿⢀⠞⠁⢀⣤⡒⠒⠶⣣⠦⠽⢛⡊⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠧⢤⣤⣀⡀⠀⠉⠑⣸⠦⠤⡠⣜⢩⣻⡀⠀⠀⣀⡞⠀⠀⢀⣀⠉⠑⢤⡇⠀⡜⠉⠉⡇⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⣠⠖⠻⠤⢄⣉⠉⠒⣩⠟⠉⠉⢩⡇⠀⢰⠉⠈⢳⠀⢸⣇⠀⠙⠲⠖⠁
⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⡴⠋⠀⠀⢀⠴⠊⠁⢀⡔⠁⠀⠀⠀⠀⢧⠀⠘⠢⠔⠃⠀⣸⠉⠲⢤⣤⠤⡦
⠀⠀⠀⠀⠀⣰⠃⠀⢀⡞⠁⠀⠀⠀⠸⠤⢤⡀⠀⠙⣆⠀⠀⠀⠀⠈⠓⠦⣤⣤⠤⠞⠁⠀⠀⢀⡠⠔⠁⠀⣠
⠀⠀⠀⠀⠰⠧⣤⣤⡞⠀⠀⠀⠀⡤⣤⣀⣠⠇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⡀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⣿⠀⢸⢸⢰⠀⡆⢧⢸⠀⠀⡆⡜⠀⢸⢀⠃⡇⠀⡇⡸⢸⢸⠀⢸⢠⠇⡇⣺⠀⢸⠘⣤⠃⠀⢣⡜⠀⠘⣤⠃⡇⠀⢧⡎⡆⡇⠀⢸
⠀⠀⡇⠀⣿⠀⢸⢸⢸⠀⡇⢸⡞⠀⠀⢷⡇⠀⠘⣾⠀⡇⠀⢳⡇⢸⢸⠀⠘⣾⠀⡇⢿⠀⢸⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⡇⠀⣸⡄⡇⡇⠀⢸
⠀⠀⠃⠀⠙⠀⠘⠘⠈⠀⠁⠀⠃⠀⠀⠘⠀⠀⠀⠋⠀⠃⠀⠘⠁⠘⠘⠀⠀⠋⠀⠃⠙⠀⠘⠘⠀⠃⠀⠃⠘⠀⠘⠀⠃⠃⠀⠃⠑⠁⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⢀⠔⠋⠉⠙⠲⡄⠀⠀⢀⡴⠛⠉⠙⠲⣄⠀⠀⢀⡴⠛⠉⠙⠳⣄⠀⠀⢀⡴⠚⠉⠙⠳⣄⠀⠀⠀⡴⠚⠉⠉⠳⢄
⡏⠀⠀⢺⡇⠀⢹⠀⠀⡞⠀⠐⢻⡇⠀⢸⡄⠀⣾⠀⠀⢻⡇⠀⢸⡆⠀⣼⠀⠀⣾⡇⠀⠘⡆⠀⢸⠁⠀⠿⣧⠀⠈
⢳⡀⠀⠘⠃⢀⡼⠀⠀⠻⡄⠐⠛⠂⢀⡼⠀⠀⠹⣄⠀⠛⠃⢀⡼⠁⠀⠸⣄⠈⠙⠋⠀⡼⠃⠀⠸⣄⠀⠛⠛⠀⣰
⠀⠉⠓⠒⠚⠋⠀⠀⠀⠀⠈⠓⠒⠒⠋⠀⠀⠀⠀⠈⠓⠒⠒⠋⠀⠀⠀⠀⠈⠓⠒⠒⠋⠀⠀⠀⠀⠈⠑⠒⠒⠋⠁
⠀⡠⠖⠒⠒⢦⡀⠀⠀⠀⡠⠖⠒⠒⢦⡀⠀⠀⠀⡤⠖⠒⠒⢦⡀⠀⠀⠀⣠⠖⠒⠒⠦⣄⠀⠀⠀⣠⠖⠒⠒⠦⣄
⡾⠀⢠⣶⡆⠀⢹⡄⠀⡾⠀⠀⢲⡆⠀⢹⡀⠀⡾⠁⠠⣶⡆⠀⢹⡀⠀⣸⠁⠀⣾⣦⠀⠸⡆⠀⢸⠁⠀⣶⣶⠀⠘
⢳⡀⠘⠿⠇⠀⣸⠁⠀⢷⡀⠀⠾⠁⠀⣸⠁⠀⢷⡀⠘⠿⠇⠀⣸⠁⠀⢹⡀⠀⠿⠟⠀⣰⠃⠀⠸⡄⠀⠿⠟⠀⣠

⠀⠀⢀⣄⠀⢀⣄⠀⠀⣀⣀⠀⣀⠀⣀⠀⢀⣄⡄⠀⠀⣀⣀⠀⣠⣠⣄⠀⠀⣠⡀⠀⠀⣀⣀⠀⠀⣀⣄⡀
⠀⠀⠛⣿⠀⢋⣸⠇⠈⠥⣾⠀⣿⢤⣿⠀⠸⠲⣦⠀⣾⣥⣄⠀⠀⣤⣿⠀⣠⣿⣿⡀⠸⣿⣿⡇⢸⣿⣿⣷
⠀⠀⠀⠿⠀⠿⠷⠆⠐⠶⠟⠀⠀⠀⠿⠀⠰⠶⠛⠀⠙⠿⠟⠀⠀⠿⠁⠀⠙⠿⠟⠁⠰⠶⠟⠀⠈⠻⠿⠃

⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠛⠛⠛⠛⣤⠀⠀⠘⠛⠛⠛⣳⡄⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠈⠛⠛⠛⢫⣄⠀⠀⢠⡄⠀⠀⠀⢠⡄⠀⣤⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣯⠀⠀⢸⡧⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⣴⣶⣶⣦⠛⠀⠀⢠⣶⣶⣶⡝⠃⠘⠃⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠘⠃⠘⠃⠘⢫⣤⣤⣤⡜⠃⠀⠛⣤⣤⣤⣤
⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠘⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣷⠈⠃⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢰⣿
⠀⠀⠀⠀⣿⠇⣀⣀⡀⠀⠀⠀⠀⡀⢀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣮⠉⠉⠉⢱⡆⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠉⠉⠉⠉⣶⠀⠀⠀⠀⠉⠉⠉⢱⡆⠀⠀⢰⡆⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⣉⠁⠀⠀⣀⠶⠶⠶⠶⠉⠀⠀⠀⠠⠶⠶⠶⢞⡁⠀⠀⠈⠱⠶⠶⠶⢎⡁
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠸⢟⣀⣀⣀⡸⠇⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠿⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡸⠗⠀⠀⠀⠀⠀⠀⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⣠⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⢸⣷⠈⠁⠀⠀⠀⠀⠀⢺⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⣿⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⢸⡧⠀⠀⢸⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⢣⡄⠀⠀⢠⡞⠿⠿⠟⣦⡀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⢀⣽⠻⠿⠿⢻⣄⠀⠀⠀⠙⠿⠿⠿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡼⠃⠀⠀⠹⣣⣤⣤⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠘⢿⣤⣤⣤⣼⠇⠀⠀⠀⢠⣤⣤⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⣠⠐⠒⠲⣶⣄⠀⠀⠀⣠⠐⠒⢶⣦⡄⠀⠀⢠⣶⣶⡀⠀⣀⡄⠀⠀⢠⣶⡶⢶⣶⣤⣤⠆
⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⣿⣄⣤⠀⣹⣿⡇⠀⠀⣿⣤⠄⢈⣿⡿⠀⠀⠈⠀⢹⠇⢻⣿⡇⠀⠀⢸⣿⡇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠙⠛⠋⣰⣿⡿⠁⠀⠀⠈⠁⠀⠾⣟⡁⠀⠀⠀⠀⠌⠀⢸⣿⡇⠀⠀⠸⠛⠓⠒⢶⣤⣄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠀⣀⣀⠀⠀⢹⣿⡆⠀⠀⡈⠀⠀⢸⣿⡇⠀⠀⠀⣀⣀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣜⣋⣀⣀⣀⣀⠀⠀⢼⡿⠛⠃⠀⢸⣿⡟⠀⠀⠁⠀⠀⢹⣿⡏⠃⠀⢼⡿⠻⠃⠀⣸⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⠄⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠈⠣⠄⠀⠤⠿⠋⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠈⠣⠄⢀⠴⠿⠋

⠀⠀⠀⠀⠀⣠⡶⠊⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⣴⣾⠉⢿⣦⡀⠀⠀⢠⣴⠏⠉⢳⣦⡀⠀⠀⠀⠀⣤⡾⠉⠹⣶⡄
⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣠⠏⠀⠀⠸⣿⣿⠀⣸⣿⠇⠀⢀⣿⣿⠀⠀⠘⣿⣷⠀⠀⠀⣾⣿⠃⠀⠀⢻⣿⡆
⠀⠀⠀⣸⣿⣿⠋⠈⣷⣦⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⢙⣻⠦⣿⣋⠀⠀⠈⣿⣿⠀⠀⢰⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣷
⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⡇⠀⠀⢰⣿⡟⠀⠀⠀⠀⣴⣿⠃⠀⠈⣿⣧⠀⠀⠈⠻⠦⠠⠾⣿⡿⠀⠀⠸⣿⣿⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠸⣿⣇⠀⠀⣸⣿⠇⠀⠀⣿⣿⡇⠀⠀⠀⠀⢿⣿⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢻⣿⡄⠀⠀⣾⡿⠁
⠀⠀⠀⠀⠙⠻⠦⠤⠟⠋⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠈⠛⠷⠄⠼⠛⠁⠀⠀⠀⠀⠤⠞⠋⠀⠀⠀⠀⠀⠀⠙⠷⠄⠼⠛⠁