Fresh Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣤⣀⣀⣀⣤⣴⡖⠚⠉⠉⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣏⠀⠀⠉⠉⢢⡉⠉⠓⣶⢭⣀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣹⡛⠋⠉⠩⠽⢿⣄⠀⠙⠀⠈⢻⣏⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠉⠀⢲⣿⣷⡶⠉⠀⠀⠀⠘⢧⡀⠀⠀⠈⠀⠱⡦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠐⠁⠂⠔⠋⠉⠉⠙⠀⠀⠈⠀⠀⠈⠻⣶⣄⠀⠀⠀⠙⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠰⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠲⣤⣄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⢸⠸⡇⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡞⠫⣝⠛⡿⠧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠃⡆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⣂⡤⠞⠛⢏⡀⠘⢒⣲⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠎⡰⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠈⠑⣛⣽⢟⠀⢶⢹⢡⡑⠠⣹⣭⡓⢦⣄⡀⠀⠀⠀⠔⢁⠔⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢈⡶⣻⢇⡣⠛⡱⢸⡜⢎⢧⠳⢄⢢⣩⢟⡾⣿⠀⠀⠀⠔⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⣴⡛⡱⢺⠷⠇⠃⢘⣨⠒⠼⢛⣵⠟⢁⣿⣤⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠉⠛⠓⠛⠃⠛⠚⠚⣁⡤⠖⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠈⠉⠉⠁⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⣿⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠀⠀⠀⠀⠀⠸⢿⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⢺⣿⡇⠀⠀⠀⠀⢀⠀⣒⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠶⢶⢦⠄⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢯⣿⡇⠀⢀⡀⠀⢰⡄⣿⡷⠖⣘
⠀⠀⢀⣤⠀⠀⠀⠀⠈⡢⣀⡀⢊⠄⠒⠰⠾⠿⢿⡿⠿⠶⠀⠐⠀⡀⠀⠀⢾⣿⡇⠀⢄⠠⡄⠄⣿⡥⠶⠄
⠀⣰⠏⠉⡇⠀⢴⡞⠟⠟⡇⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⠿⢧⠀⣀⠁⢸⡞⠁⡔⠁⢀
⠸⠯⠀⠤⡀⠀⠀⣑⣦⢜⠀⢰⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣈⠐⠌⢳⣏⡡⣍⢉⡃⣴⠂⣠⠄
⠀⣠⠾⣆⠑⣀⡾⣋⡩⠈⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠸⢏⠑⢶⠄⣶⣠⡾⢿⣿⣀
⢸⠏⠁⢸⣤⡿⠳⣄⠐⢄⠘⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⠣⡄⠈⠛⠀⠊
⠀⠀⠀⠈⠛⠖⡚⠂⠉⢲⡷⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠐
⠀⠀⠀⠀⠀⡴⠿⢷⣤⣤⡶⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⢠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣵⠤⠠⠀⠚⠐⠃⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡏⣼⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⣿⡿⠿⠋⢩⣩⠆⢀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⡏⣋⠄⢠⣿⣿⣷⣦⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡰⣿⠺⠟⢃⣀⣿⣌⣡⣿⣻⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠇⡀⠃⠀⢰⣾⣿⠟⡻⣿⣿⠿⠟⠻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣎⠀⠟⡋⣻⣿⡁⣼⣷⣝⣿⣶⣿⠆⠀⠒⣶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⣄⡀⠀⠀⠀⠈⢙⠿⠉⢠⣄⣻⣾⠛⠾⠿⣟⣿⣿⣿⡧⠒⠀⠀⠀⠀⠉⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢹⣿⣪⣟⣵⡾⠗⠀⠒⣼⣿⣿⣿⠶⣶⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢠⣾⣿⡏⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣾⣿⣿⣶⣶⡀⣀⡀
⠀⠀⠀⠀⡠⠀⠀⠿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠛⠛⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠊⠁⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡖⠒⠛⠦⠤⣀⠀⠀⠀⢸⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣷⠀⠀⢄⡀⠈⠳⢄⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢳⡀⠀⠀⠙⢆⠀⠘⢦⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠐⠒⠢⠤⢭⠦⣌⣧⠀⠀⠀⠈⡆⠀⢸⠄⠀⣠⣴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⣿⣀⠼⠶⢟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⡬⣶⠖⠉⠙⠢⣄⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠁⠀⢀⠂⠀⡞⣧⡀⠀⠀⠘⣆⠀⠘⡆⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⡂⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣄⠀⠀⠘⠆⠀⠉⠑⠒⠒⠀⠀⠉
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢸⣈⠒⠤⡀⠀⡸
⠀⠀⠀⠁⠁⠒⠢⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⠊⠑⡼⠇⠇⠀⠀⠈⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⠂⠐⠉⠉⠀⠀⠀⠀⠀⠀⠘⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⢱⢸⢸⠁⠳⡄⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠌⢁⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⣿⠱⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⠂⠨⡉⠓⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢢⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢧⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⢀⠚⠃⠄⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠆⠀⠀⠀⠀⠀⠀⠢⠀⠇⠀⠀⠀⠀⠀⣸⠀⢠⠐⠿⠤⠛⢢⡔⠤⣔⣓⠴⣷⡼⠲⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡄⠀⠀⠀⠀⠀⢀⡇⠸⣄⠀⠀⢠⡀⠛⠀⣨⠐⢁⠈⢄⢙⣋⣉⣉⠙⡘⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⢶⡞⠀⣕⡤⢤⢆⣁⣒⣁⡶⠴⣷⢚⣖⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠧⣄⣠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣰⡾⠓⠒⣏⣀⣼⡟⠶⠾⠶⠮⠭⠽⠿⠿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠲⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠂⠁⠀⠀⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢰⠶⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠠⠄⡐⠂⠠⠈⠀⠈⡉⠞⠁⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠒⠀⠀⠀⠀⢀⠀⣠⣤⡤⠴⠊⠉⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡔⠀⢸⡀⠰⠂⠺⣟⠁⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠁⠈⠀⣨⠀⠀⠤⡀⢤⠀⢤⣇⣤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠀⠀⠀⠰⠁⠁
⠀⠀⠀⠀⠀⢰⠀⠃⠀⢹⠀⠀⠁⠀⠙⠀⠀⠘⠁⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠁⠠⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⣠⢈⠀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⢐⣦⣀⠀⠐⠂⠀⠤⠀⠠
⠀⠀⠀⠸⡕⠪⢄⡀⡆⠀⠠⠀⠀⠐⢄⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠠⠃⠀⠀⠀⠄⢃⡀⠸⡆⠈⢠⡈⢂⠐
⠀⠀⠀⠀⢀⠀⠀⠘⠐⠢⠀⡁⠀⠀⠀⠑⠂⠀⠀⣀⠠⠀⠀⠠⠄⡤⠀⢀⢠⢀⠂⠀⠑⢰⡇⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠘⣦⠄⢀⠀⠀⠐⠉⠉⠐⠀⠀⠁⠀⠀⠰⠀⠀⢐⡂⠀⠀⢰⠓⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣆⠨⡇⠀⠀⠠⣤⠀⠀⠀⠄⢦⠀⠀⠀⠲⡇⠀⠈⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠐⠄⠀⠀⠙⡅⠀⠀⠀⠐⡀⠀⠀⠀⢿⠀⠀⠀⠸⡄⠀⠀⢨⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⡀⠀⠀⢣⠀⠀⠀⠐⢁⠀⠀⠀⢸⡄⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠀⠀⠀⠇⡀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⣆⠀⠀⠀⠃⡀⠀⠀⢯⠀⠀⠀⠈⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣯⣦⣧⣾⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⣀⡀⠤⠒⠈⢈⠇⠀⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠀⠐⠀⠐⡄
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠷⡤⠸⢗⡈⠁⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⡇⠝⠣⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠐⠈⠁⠀⠀⠈⠀⢀⠄⠀⠀⡇
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⠀⠀⡴
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣼⠗⡯⣄
⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠁⠀⠀⠀⣤⣷⣖⠅⣅⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢨⣿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠿⡿⡔⠈⠀⠀⠀⠀⠀⠀⠠⠄⡄
⠀⠀⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⢧⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠁⠇⠀⠀⠀⠀⠀⢸⣟⣿⣷⡃⠀⠀⠀⠀⠐⠈⠉⠊⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡅⠀⢘⡀⠀⠀⢰⡌⣽⣾⣿⣿⢫⢡⠀⠀⠀⠆⠀⠀⠀⠀⠐⠈⢠⡔⠠⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⠄⢸⣻⣿⢿⠏⠀⠀⠀⠰⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠸⣯⡿⡟⢠⠀⠀⠀⠀⠀⠀⠐⠀⢰⠀⢀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⡀⠹⡷⠃⢸⠀⠀⠀⠈⠀⢠⠁⠀⠀⠁⠼⣄⠀⣀⡀⣀⠖
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠁⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠟⠁⠀⠀⠀⠏⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠘⠻⣷⡀⠘⠀⠀⠘⠈⡽⠃⠀⠉⠁⠂⠀⠀⠀⠀⠜⠀⠠⠀⠀⠀⣄⠀⠄⠀⠀⠀⠀⠈⠆
⡀⠁⠉⠐⠰⠦⡀⠀⠀⠀⠀⢠⣎⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⡤⠀⠘
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢀⣼⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠛⠛⠒⠀⠠⠀⠀⠉⠁⠀⠀⠂⠐⠂⠀⠀⠀⠀⠤⠀⢷⡀⠄
⠠⠀⠀⢀⣠⠟⠑⠑⠞⠚⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠒⠃⡸⣇
⣴⣶⠶⠋⠁⠀⠀⠀⠀⠀⠀⣀⣄⣠⠀⣀⡀⠀⠀⠀⠀⠀⠜⣦⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢀⣌⡀⡖⣢⠄⠀⠀⠀⠈⠳
⡀⠀⡀⠀⠀⠄⠀⠀⠀⠠⠜⠁⠀⠀⠀⠉⣿⣄⣀⡀⠀⠀⠀⠜⠳⣥⡄⠀⢀⡰⢃⡄⠀⠀⠀⠀⠛⠐⠬⡗⠻⣖⣺⣇
⡴⣒⠟⠳⠶⣄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠁⠀⠀⠀⠀⠐⠶⠝⠳⠏⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠈⣿⡧
⡾⡃⠀⠀⠀⠈⠳⠤⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧⠙⠉⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠃
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⣤⠀⠀⢀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⣦⣠⣤⠶⠂⠁⠀⠠⣰⣤⣟⠒⡀⠒⠋⠀⠀⠀⠀⠡⢠⡟⠈⠁⠀⠀⢠⡀⠑⢤⠀⠀⠀⠀⠀⢃⣠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡶⠟⠁⠠⠃⠀⢈⡅⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⢀⡄⠀⠀⠀⠀⠀⢻⡆⠀⡤
⢀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠃⠀⠸⠂⠀⠀⠀⠀⠀⠈⠲⢦⣤⠤⠶⠖⠛⠡⣈⠀⠀⠀⣱⣶⠊⠧⠄⠀⢸⠀⢀⣀⠁⠐⠂
⠈⠀⠀⠀⠀⠀⠛⠥⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⢾⡿⠉⠃⠀⠀⠀⢸⡆⠀⠈⠉⠀⠐
⣀⣤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠈⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠀⠀⠀⠐
⠟⢠⡈⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⢷⣦⣀⠀⠀⠠⠠⠒⠦⣄⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣔⣀⣀⡤
⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢸⡆⠀⢠⠀⢰⣡⢌⣠⣿⣷⡖⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⣤⡀
⠀⠀⠄⠠⣤⠇⢤⡰⠂⠀⠀⠈⢿⣂⠀⢡⡴⡷⣶⠋⠀⠚⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡖⠊⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠽⡃⢀⡀⠀⠀⠀⠀⠹⠿⣿⡶⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠿⠃⠀⠀⠀⠀⣀⣾⡇
⠀⠀⠀⠀⠀⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡦⠴⠋⠋⠀⠀⠀⠀⠀⠉⠁⣼⢆⡀
⣀⢀⡀⡤⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠃⠺⠙⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡝⠀⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⢀⠈⠁⠲⠉⠀⠀⠀⠀⠘⠃⣰⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠴⠂
⣀⣀⣐⣀⣀⣀⣀⣀⣀⣠⣄⣠⣀⣒⣀⣉⣛⣷⣠⣬⣃⣀⣁⣀⣀⣀⣀⣀⣀⣸⣋⣀⣃⣀⣂⣐⣃⣀⣀⣀⣀⣂⣸⣋⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢄⡀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⠻⡀⠀⠀⠘⠀⠁⣄⠀⠀⠀⢠⠆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠐⣦⣀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠹⣆⠀⠀⠀⠀⢻⠀⠀⠀⢁⡀⠀⢰⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠤⢄⡀⠀⠀⢸⠀⠀⠘⣦⠀⣀⡀⠀⣤⠌⣠⠛⠁⠀⡆⠀⠀⣠⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠈⠅⠀⠀⠈⣿⠏⠹⢦⠍⢰⠇⠀⠀⢰⠁⢀⡾⢁⠀⠀⠀⠀⣀⠤⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠈⠳⣶⠀⠀⢀⡌⠀⠆⠈⢻⡇⠀⡆⠀⣎⣰⠏⠀⠌⠀⢠⠄⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠉⠳⢤⣽⠀⠀⣼⠁⠀⠀⠀⠀⢱⡀⠇⢠⡿⠁⠀⣾⡄⠈⠁⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠰⢶⣶⣦⣄⢀⡀⠈⠳⣄⠀⠈⠳⢦⡟⠀⠀⢀⡀⠀⠈⣷⣶⠎⠀⢀⡾⠋⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢌⡋⢤⡉⠠⠙⣦⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠸⠃⠀⣰⣏⣀⣀⡀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡙⢦⣀⠙⢷⡀⠀⠀⠀⠻⣤⡁⠀⣰⡦⠚⠃⠉⠉⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠀⠀⡀⠀⠙⢀⠹⣶⠘⠛⠂⣤⣄⡀⠘⣧⠞⠁⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡀⠙⠦⡀⠳⣄⠀⠀⠈⠉⠲⣦⡀⠀⠀⠀⢀⠀⣤⣼⠀⠒⠒⠀⠀⠉⡡⠿⠟⠁
⠀⠀⠀⠀⠀⠈⠓⢂⡀⠶⠄⠘⠂⠀⠛⠶⢶⠀⠹⠆⠀⠀⠀⠀⠀⠻⡄⣀⡴⠞⠋⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⡖⠒⢀⠤⢄⣀⠳⠀⠸⠦⢄⠀⣀⠀⠤⠾⣁⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠻⠖⡄⠐⠀⠉⠛⠻⣦⣀⠀⠛⠁⠀⠀⠀⠈⠳⡆⠁⠀⢀⡄⢀⣀⣀⠠⠐⠒⠚
⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠐⠦⡄⢠⣄⠢⡔⢄⠀⠀⠙⠲⣤⡀⢀⣤⠄⠒⠚⠒⠂⠰⢿⣦⠈⠉⠉⠐⠒⣀⣀
⠀⠀⠀⠀⠀⠀⠠⠼⣿⣦⣤⣄⠀⠀⠈⠃⣀⡀⠆⠀⠀⠀⢀⣹⣧⠀⠀⠀⠀⡀⣤⣥⡴⠶⠖⠈⢉⠉⠉⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠛⠷⢶⣋⡉⠿⠶⣉⣀⠀⠀⠀⢀⣀⠴⠟⣤⠤⠞⠋⠀⣀⡀⠀⠠⢤⡤⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡒⠂⢠⠈⠳⠖⠠⢀⠈⠛⠷⡁⠀⠀⣀⣀⡈⠁⣤⠶⠋⢉⡄⠐⠀⠉⠁⠀⢠⡄⠀⠙
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣶⣶⠞⠿⠓⠚⠓⠨⢷⣄⠀⠹⠒⠀⠀⠈⠙⠛⢠⣤⢀⡈⠀⠈⠁⢴⣀⠤⠌⠃
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢈⣧⣤⣤⢠⡶⠒⠂⢠⡈⠣⣄⠘⣀⠀⠀⠀⢠⡴⠒⠻⡷⠖⠂⢠⣄⡉⠀⠀⠱⠃⡀
⠀⠀⠀⣀⠀⠀⡌⠁⠲⡀⠸⡇⠀⡤⠁⠤⠀⠀⠀⠘⠆⠙⣄⢉⡷⠉⠹⢦⣤⠈⠀⠈⠀⠁⠄⠘⡉⠀⠂⢲⠀⠑
⠀⠀⠀⠈⠓⢰⡿⠀⠀⣾⣶⠷⠦⣤⠄⣰⡆⠀⢰⡷⡤⠚⢻⡶⢀⣤⣀⠁⠀⠈⢠⡌⢱⣣⣄⠘⠗⠀⠈⠀⠶⡈
⠀⠀⠀⠀⣠⡋⠀⠀⡰⠋⠃⡀⠀⠀⠀⠙⡛⠃⠀⠛⠆⠀⠀⢳⣀⡄⢩⣐⡦⠈⠛⠀⢀⠍⠛⢳⡆⠀⠀⠀⣀⠙⠀⠀⠰⡆
⠀⠀⠀⡐⠿⠃⠀⠰⠁⠀⠀⠑⠀⠀⣀⠊⠀⣀⡤⢴⣤⣴⣞⠉⠁⡧⠈⠁⠐⣦⠄⠛⢫⡤⠀⡀⠘⣂⡀⠀⠁⠀⠀⢠⠄⠃
⠀⢰⡤⠃⢀⢀⡼⢤⡀⠀⢀⣤⠲⡖⠙⠓⢾⡋⠀⣸⡆⠀⠙⢇⠁⠀⠀⠀⡌⠁⠀⠀⢸⠀⠀⢹⡞⠉⠉⠖⠂⠀⢠⡦⠀⣤⠰
⠀⢸⠇⢀⡼⠁⠄⠀⢹⡟⠉⢀⡴⠃⠀⠀⢀⠉⠈⠉⠳⠀⠀⠺⣷⠶⠶⢤⡿⠀⠀⠀⠊⠀⠁⠰⡇⠀⠀⠋⣀⣼⡏
⡀⠘⢀⡌⠳⠖⠀⠀⠀⠛⠰⠂⢡⠀⠀⠀⠸⠂⠀⠀⠀⠀⣠⠞⠁⠀⡀⠀⠘⢣⡀⠀⠀⠀⠀⠀⢧⡀⠀⡀⠀⢸⡇⠀⠀⠰⡆
⠈⣄⡿⠁⠀⠀⠣⠄⢀⣀⠀⠀⠀⠀⢀⡼⠟⠛⡟⠓⠦⣠⡏⠀⠀⠀⠁⠀⠀⠀⣿⣠⠤⠴⣶⠴⢎⡁⠀⠀⠀⠸⣇⠠⠎⠠⡇
⠀⠉⠰⣧⠈⠳⣄⢀⡜⠋⠘⠓⣄⣠⡟⠀⠀⠀⠁⠀⠀⠹⠇⠀⠐⠀⠀⠀⠒⠂⣼⠃⠀⠀⠀⠀⠀⠙⢦⡤⡖⠢⡀⠀⠀⣠
⠀⢠⣾⣹⠆⠀⠘⣿⡀⢀⠀⠀⠈⠿⠀⣤⡴⠀⣆⠀⠀⠀⡃⠀⣀⣤⣤⣤⣄⢀⣿⠀⠀⠀⡀⢠⡤⣴⠟⠀⢀⡄⠀⣦⠐⢠⡦
⠀⢮⡄⠉⠀⢄⠀⠛⠑⠞⠀⠄⠀⠘⣇⠀⠀⠀⠈⠁⠀⠈⣡⠞⠁⠀⢄⠀⠈⠛⣏⠉⠀⠉⠁⠀⢠⡏⠀⠀⡞⠐⡿⠁⠘
⠀⠾⢫⣴⠶⢄⡀⠰⣄⣤⣄⣀⠀⠀⢙⠶⠉⠙⠋⠁⠶⣤⡏⠀⠀⠀⠈⠀⠀⠀⠈⣣⠶⠆⠀⢶⡜⠃⠀⢉⡀⠼⠇⣀⠀⡟
⠀⢠⠸⡇⠐⠀⠙⣶⠋⠀⠉⠈⠛⢶⡎⠀⠀⠀⠃⠀⠀⠈⢷⠀⠙⠛⠁⠀⠙⢠⠟⠁⠀⠀⢰⠆⢱⣆⣰⠋⢥⡀⣀⣥⣴⠇
⠀⢸⣧⠀⠛⡀⠀⠘⣷⠴⢀⡀⠀⠀⢻⡀⠢⣤⠀⠠⠄⠀⠠⣧⣠⣤⣤⣄⣰⠇⠀⠀⠀⡰⠃⠤⠋⢨⠋⠠⠜⢁⠙⠁⢼⠆
⠀⠸⠙⣧⡀⠑⢤⡀⢡⠀⠈⠑⠂⠀⢀⣧⠀⠀⠀⠀⠀⣠⡴⠋⠁⢠⠇⠈⠳⣆⠈⠁⢈⣤⠒⠶⢦⡀⠀⠀⠀⡮⠠⠂⣠
⠀⠀⣠⠀⠑⣄⠀⣨⡽⠶⣤⡀⣠⠖⠉⠉⠉⠉⠱⢦⠾⠁⠀⠀⣠⠘⡀⠀⠀⢸⣤⠖⠉⠀⠀⣷⠀⣴⣶⠶⢢⡀⢀⠾⠋
⠀⠀⠙⣶⡆⠀⢻⡁⢰⡄⠀⠹⣧⢀⣀⢀⡀⠀⠀⠈⣦⠀⠈⠉⠀⠀⢉⠁⠀⢀⣏⣀⣀⣀⡴⠛⠻⠃⠈⡇⢀⡼⣾⠃
⠀⠀⠀⠘⢷⠄⠈⠁⠙⢠⠀⠀⠙⡄⠀⠀⠑⠠⠄⠠⠛⢀⡠⠤⠛⠋⠁⠀⠙⠧⡀⠀⠀⠀⠀⠀⠇⢀⡀⠁⢨⠟⡀
⠀⠀⠀⠀⠀⠂⣰⣧⣀⡀⢑⡀⠠⣧⡤⠒⠒⠲⠒⠢⣴⠏⠀⡀⠀⠀⠀⣠⠀⣀⡿⠒⠒⠛⢶⣞⠓⠀⢀⡘⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠙⣯⠙⣇⠉⠁⠺⠏⠀⠀⠀⠀⠀⠀⠈⢣⠈⠉⠐⠀⠁⠉⠸⠋⠀⠀⠀⠀⠀⠛⠓⠫⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠂⠀⠀⠐⠄⠁⠂⠀⠶⠐⠂⠐⢷⣀⠀⠀⠀⢀⣇⠀⢀⠀⠒⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⢌⣀⣸⣆⠀⠀⠀⠀⣠⠆⠉⠉⠛⠀⠈⢙⡟⠉⣀⠤⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣛⣾⣿⣶⣶⣦⣤⣤⣤⣯⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠿⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⢰⡔⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⣗⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⣿⠾⠛
⠈⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣷⠉⣷⠀⢠
⠀⠢⡀⠀⠄⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⣿⡰⢻⢁⣦
⠀⠀⠐⡞⠀⠀⠀⠑⢦⡀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⣿⢀⣿⢷
⠀⠀⠀⠑⠀⠀⠀⠀⠈⣇⠀⣀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠣⣬⣿⡾⣫⣾
⠣⠀⠀⠀⠈⠀⣇⠀⠀⠀⠀⠀⢀⠀⠀⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⢢⠑⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇⣷⣿
⠀⠁⠀⠀⠀⠱⣝⠆⠈⠀⠀⠐⠁⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⢠⠾⠁⣜⠅⠀⠂⠉⠳
⠀⡖⠀⠀⠀⠀⠘⠋⠘⠓⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⠁⠀⣸⠐⠀⠀⠀⠀⠦
⠀⡄⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣟⠀⠀⠀⠀⠀⢠
⠀⠃⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⣾
⠀⢽⢸⠀⠀⠠⠀⠀⠀⢀⠄⠀⠘⡆⠀⠰⠀⠃⠆⡄⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠠⠌⠠⡆
⠀⠸⠀⠆⠀⠘⠄⠀⠂⠀⡃⠐⢆⡀⠀⠣⠄⠠⠊⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⠁
⠀⠈⠇⢠⠀⠀⠀⠀⣀⠒⠂⣶⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣏⠀⠀⠀⠀⡏
⢦⡀⠐⠈⡇⠀⠈⠀⠘⠗⠀⠈⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠴⠻⠀⠀⠀⡸⠇
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠠⠀⠀⡠⠄⠀⡄⠄⡄⠀⠀⠀⠀⠄⠀⠀⡀⢀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠄⡀⡀⠀⢀⢀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢤⠼⡗
⠀⠀⠀⠁⠈⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣿⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠄⠀⡀⠀⠀⠀⠀⠠⠀⠤⡀⠄⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠐⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⠄⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠀⠂⠐⠂⠉⠀⠆⠘⠀⠂⠐⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠂⠀⠂⠀⠈⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠐⣀⠀⢇⡂⠘⠉⠀⠀⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠐⠖
⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠐⠛⣁⠀⠀⠀⠁⠀⢠⣦⡄⠉⠀⢸⢀⠀⠈⢠⣤⡁⠀⠀⠀⠈⡀⠐⠀⠀⠆⡀⠀⠉⠃⢠⡴⠂⢤⡔
⠀⠀⠀⠀⠀⠀⠲⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠆⣀⡃⢰⠈⢈⢀⠀⠀⠀⠘⠃⠀⠼⠀⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠺⠂⠠⣤⢀⡀
⠀⠀⠀⠀⠨⠂⢀⡼⣷⡀⠀⠑⠰⠀⠀⠀⢀⠈⢠⣸⣆⣀⠀⡵⢸⠀⠄⢄⠦⠀⠀⠀⠀⠀⢀⡄⠀⠀⡄⡆⠀⠸⠞⠀⠘⠃⢠⣿⣷⣿⠀⠳
⠀⠀⠀⢀⠀⠀⠈⢏⣀⣠⡀⡂⠀⣀⡆⢠⣾⣌⡄⣘⣿⣹⣶⡇⣬⣰⡤⠘⣫⣅⣄⣴⣠⣦⣤⡷⡖⠀⣽⣷⣗⣴⣴⢶⣔⡄⠀⣩⢸⣿⡇⣡⡦⡄⡀
⠀⠀⠀⠈⠾⠰⠿⠾⠷⠿⠷⠿⠿⠿⠧⠿⠿⠿⠷⠿⠿⠽⠿⠷⠿⠿⠿⠿⠿⠿⠏⠭⠿⠿⠿⠷⠿⠻⠟⠿⠿⠿⠿⠼⠿⠧⠧⠿⠿⠿⠿⠿⠧⠧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡿⠋⠉⠹⣿⣿⣿⣿⣶⣦⣄⣠⣴⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣿⡄⢀⡴⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣤⣤⣴⣾⣿⣿⣿⣿⣷⣤⠀⠀⢸⡀⠐⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⣴⣿⣿⣿⣿⣿⡿⠿⠻⢿⣿⣿⣷⡀⢸⡅⠀⢀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢛⡻⠋⠱⠀⠀⠀⠀⢹⣿⣿⡇⠘⣇⠀⢀⠀⢁⡈⠁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⢳⠀⠀⠀⠀⠀⠀⣸⢯⣿⡇⠀⠻⠂⣸⣤⡶⠀⠀⣘⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣶⠋⣿⣿⠉⠇⠀⣶⣾⡋⠀⢠⠚⡿⠧⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠘⠃⠀⠀⠀⣀⠠⠀⠘⠷⠀⠀⣤⡾⢋⣼⣿⠃⠘⠆⠐⣻⠿⠃⠀⣸⣼⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⣤⣀⢻⠃⣠⣾⣿⣿⡆⣦⢀⡄⢻⡗⠀⠀⢉⣩⢠⡾⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠁⠉⢹⡀⠉⢹⣷⡾⠟⠉⠻⢿⣿⡀⢹⣤⠴⡃⣰⣇⣈⣧⣿⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠀⠀⠀⠂⠀⣾⠇⠀⠋⠁⠀⠀⠀⠀⠀⠈⠀⠈⢧⡴⠇⢿⣀⣩⡶⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢾⣆⠀⠀⠀⠀⠀⣀⣄⡀⢀⣿⣇⣀⣀⣹⣍⣀⣩⡿⠋
⠀⠀⠀⠀⠀⠀⢠⣼⣧⠀⢄⠀⠀⠘⠀⠀⠀⢀⣀⣴⣿⡄⠀⠀⢀⣾⣿⣿⢷⡟⠋⠙⠋⠹⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢾⡇⠀⠀⠀⢂⠀⠂⣙⣿⣿⡇⠀⠀⣼⣿⣿⡉⠀⠀⠼⠄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣟⣷⡀⠱⢣⣏⣤⣾⡿⣿⣿⠁⠀⠀⣿⣿⣏⠁⠈⠀⢤⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣛⣿⡗⣿⣫⣽⣿⣿⡿⠃⠀⠀⠀⣿⣿⡿⠇⠀⢸⠘⢖⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠸⣿⣿⣵⠀⣾⣇⣸⣗⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡐⠞⠷⢶⣤⣀⣠⣤⣤⣴⣿⣿⡿⠿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠀⠋⠀⡀⢻⠠⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣆⣀⠐⢡⣀⣤⣼⠏⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣾⣿⡿⠋⠀⠀⠀⠀⢿⣧⠀⠀⠠⠄⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⠒⠂⠀⢀⡼⠤⠀⠀⠀⢀⡨⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⣠⠴⠟⠒⠒⡂⠋⠈⠁⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⣀⣴⠞⠋⠀⠀⠀⠀⠀⠑⠒⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠅⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⣠⣄⣰⠏⠀⠀⠀⠀⠘⣧⣰⠻⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠟⢦⡤⢶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⢀⣴⣿⠋⠳⡀⠀⠀⠀⢠⡞⢉⣯⠻⡄⠀⠀⣠⠶⠦⠞⠃⠸⣟⠎⠳⢄⠀⠀⠀⠀⣴⠋⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠙⣦⣤⡴⠋⢰⡿⣌⣢⠈⠳⢮⣁⣀⣀⠀⠀⠀⠹⡗⢀⣀⣵⢶⣷⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣠⠴⣿⠁⠀⠀⠀⠘⢧⣀⡈⠑⠀⠀⠀⠀⠈⠑⠄⠀⠀⠉⠉⠁⠀⠸⣅⠙⠲⠦⢤⡴⢺⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⣤⣻⡍⠢⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⠇⢸⡄⠀⠀⡞⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠸⣟⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⢠⠘⣆⣿⣇⠀⡼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰⠀⢹⠀⠈⠙⠢⠀⣤⠀⠀⠀⢀⣿⣷⠀⠀⠀⣿⡆⢸⣿⣿⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⢄⠀⠀⣾⡇⠸⡀⠀⠀⠀⢠⣿⡆⠀⠀⢸⣿⣿⡂⠀⢠⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣦⣿⣦⣿⣷⠀⠙⢂⠀⠀⢸⣿⣇⠀⠀⣼⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡷⢦⡴⢄⣀⣿⣿⣿⣀⣀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣾⣧⣴⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠤⣄⠀⠀⠀⠀⠀⡠⠔⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⠔⠒⢒⡬⠖⠒⠒⠒⠾⣵⠒⠒⢄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⡀⣠⠋⠀⠀⠀⠀⠀⠀⠈⠳⡄⢨⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠃⢠⣤⡀⠀⣀⠀⢠⣤⡀⢹⠋⠀⢸⣳⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠚⠁⡜⠈⡇⠈⠛⠁⢸⠀⠀⣠⡏⢞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠹⣤⠃⣠⠖⢳⠊⠀⠀⡇⠙⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡑⠒⠒⣾⠁⣀⠏⠀⠀⠀⠳⢤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⢺⣀⡵⡄⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢸⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠋⠉⢢⡀⢸⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⢦⡀⠀⠀⠀⠈⠉⠒⠒⠲⡄⠀⠉⠒⠲⠤⠒⠊⣡⠜⢢⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠘⣄⠈⠓⢤⡀⠀⠀⠀⠀⠀⠳⡀⢀⠀⠀⢀⡴⠊⠁⢀⡜⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠢⡄⠀⠉⢦⠀⠀⠀⠀⠀⠈⠛⠀⡴⠋⠀⠀⡴⠋⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠇⠠⡡⠰⡹⠀⠠⠀⡎⠐⠁⢺⠰⠈⠉⢢⠂⠀⠰⡱⢘⠅⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠆⢰⠶⠔⠂⠢⠖⠶⠀⠆⠐⠢⠰⠰⠴⠄⠶⠆⠆⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⡀⠘⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠀⠀⠘⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠸⠈⠃⠀⠀⠀⠀⢀⠰⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠒⠀⠀⠀⠀⠀⠔⡀⠀⡠⠀⠁⠀⠀⠲⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠐⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠠⠈⠀⠈⠢⠔⠊⠁⠀⠀⡀⠄⠂⠀⠀⢎⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⢀⠇⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠤⠀⠀⣀⡠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠉⠐⠢⢀⠀⢧
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠸⡆
⠀⠀⠀⠀⠀⣎⠠⠂⠁⠀⡀⠀⠀⠀⠀⠈⠁⠀⠡⢄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀⣤⣄⣠⣬⣭⣷
⠀⠀⠀⠀⠀⡏⠡⠀⣀⣀⣀⣤⣄⣀⠀⠀⣠⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣇⠐⠋⠉⠉⠉⠀⠀⠀⣀⣀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⡿⠿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡟⠛⠳⢦⣠⣄⡀⠴⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⠀⠀⠀⠀⣤⣾⣦⡐⠛⠉⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢷⣦⡀⠀⠈⠁⠀⣀⣤⣾⣷⣦⣤⣄⣀⣀⣤⣦⣴⣶⣾⣷⣷⣶⣶⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠄⠺⠦⠴⠶⠴⠶⣤⣤⡤⣤⣤⣤⣤⣠⣤⣄⣀⣀⣀⣈⣉⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⢻⠖⠊⠈⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣬⣭⣭⢽⠶⠶⠶⠦⢤⠄⢀⣀⠀⠀⠀⠈⠉⠛⠛⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⡤⣿⠶⠶⣦⣄⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠅⠀⠀⠀⠀⠀⠀⠉⠙⢩⣙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣶⡒⠶⣿⡙⠻⣿⣍⠉⠻⣿⡙⢿⡖⢶⡶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠺⢿⣭⣉⡛⠷⢮⣝⡲⢬⣙⠳⢤⡉⠳⢤⡈⠳⣄⠹⡌⢧⢹⢸⢇⡟⣹⠖⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⣛⡿⠷⠶⢤⠤⠭⡙⠳⠦⣬⣙⠳⢮⣝⡲⠬⡓⠤⣙⠢⠈⠃⠈⠀⠈⠈⠈⠐⠡⢞⡡⠞⣋⣷⢤⡀
⠀⠀⠀⠀⢀⣴⣿⠿⠀⠀⠈⢲⡀⠀⣰⠃⠀⣨⠉⠓⣤⣌⣙⣒⠦⢍⡓⠤⢁⠀⠁⠀⠀⢠⠞⠉⠉⠉⠳⡄⠀⠐⠈⠥⠴⠶⢛⣳⣄
⠀⠀⢀⣴⣫⠔⠢⣅⣠⡞⠉⠳⢄⡀⠉⠀⠠⠉⠁⢀⣼⠷⢻⣿⣷⢶⡌⠉⠂⠀⢀⡴⢲⡇⠀⠀⠀⠀⠀⢸⣀⣠⠞⠛⣯⡩⠭⠭⠭⣷⣄
⠀⢠⣾⣿⣶⣾⣿⣿⣿⣷⣄⠰⠞⣉⡦⠴⠞⣳⠖⠋⠁⠀⠘⣿⡏⠀⠈⠓⣲⡯⣍⡀⣨⢷⠴⠚⠓⢦⣤⣾⣾⡃⠀⣼⡿⠻⢏⣹⢷⠚⠙⢦
⢠⣿⣿⣿⣿⣿⣇⣤⡤⣉⡛⠳⢿⡀⣀⣴⣞⠁⢀⠀⠀⠀⣩⣿⡿⠀⢀⡟⠙⠲⡀⠉⠳⢤⣴⡶⠾⡿⠟⡻⠉⠀⠀⣘⣷⠀⠀⢙⣷⣯⣴⣾⣇
⣼⣿⣿⣿⣿⣷⠟⣽⣻⣯⣿⣷⣶⡉⠛⢿⣿⣿⣶⡄⠀⣴⣿⠓⠀⣠⣿⣤⣤⣠⠞⢀⣀⢤⣬⣻⣮⣄⠈⠀⠀⢀⣠⣿⣿⣤⣾⣿⡿⣿⣟⣿⣿
⣿⣿⡟⣷⡿⣿⢻⡼⣧⣷⣿⣶⣿⣿⣶⣄⣌⡙⠻⢿⣼⣧⣤⣤⣾⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⢬⣿⣿⢿⡟⣿⣾⣿⣿⣻⣯⣿⣿
⣿⣿⢿⣿⣷⣞⣚⣿⣿⣭⣿⣿⣿⢻⣿⣶⡬⠝⠳⣤⣈⣙⠻⢿⣿⣿⣿⣟⡷⠾⠿⠛⢛⣋⣭⣭⣷⣶⣾⣷⣿⣿⠿⣾⣝⣗⣯⣷⣿⣿⢾⣿⣿
⢹⣿⣾⣿⣷⣮⣿⣧⣿⣭⣻⣏⡽⣻⣿⣿⣿⣷⣄⡙⠻⣿⡷⢯⣤⡿⠉⣿⣀⡀⠝⠻⠿⠷⠶⠯⢿⣧⢾⣛⣿⣶⡿⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣿⣆⣤⣍⣳⣯⡳⣄⣈⠙⠛⠻⠶⣬⣵⣾⣿⠿⠷⠿⠯⠿⢶⣿⣟⣿⣞⢻⡿⣽⣿⣿⣿⠃
⠀⠀⠹⣿⡽⢿⣿⣿⣾⣿⣿⣿⣿⣿⣯⣗⣺⠭⣿⡷⣷⣿⣾⣳⣾⣿⣦⣽⡷⠀⠀⠀⠈⠹⣿⣿⣿⣯⠭⠽⢿⣟⣒⣶⣭⣝⣛⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣷⣾⣷⣺⣭⣿⣿⣿⣿⣭⢟⡻⢿⡲⢭⣓⢪⣽⣿⡿⠟⠋⠁⠀⠀⠀⡀⠀⠀⢸⣿⣛⣛⣯⣭⡿⢾⣛⣛⣿⣭⣭⣭⡽⠋
⠀⠀⠀⠀⠀⠈⠛⢿⣞⣛⡻⣍⣯⣭⣝⣿⣮⡓⣭⣷⡾⠟⠋⠁⠀⠀⠤⠀⠀⠀⡀⠀⠀⢀⣼⡿⣟⣻⠽⢗⣛⣭⠭⠴⣶⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣽⣹⣯⣷⡿⣿⣭⠁⠄⠀⠀⠀⠒⡤⠀⠁⠀⠴⠀⣠⡶⣛⠽⣛⣭⠶⣚⡭⢵⣲⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣯⣶⣶⣖⢐⣠⣶⠖⠔⠐⠀⢢⣾⣷⣻⣵⣟⣯⣶⠿⠗⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠃⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠚⠉⠉⠛⢦⠉⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⠃⠀⠀⠀⠀⣠⠞⠉⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢠⡴⠚⠛⠃⠀⠀⠀⠀⠀⠀⠸⣦⣍⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚⢀⡴⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣴⠃⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠉⠙⠳⡴⠖⠒⠦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡼⠋⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⣦⠀⢸⡇⠀⠀⡀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠶⣠⠞⠉⠽⢤⠀⠀⢀⣀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢘⣧⢸⠃⠠⣄⣿⠀⠀⢸⡇
⠀⠀⠀⠀⡴⠚⠋⠁⢠⡤⠶⠛⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⠘⢧⡟⠀⠀⠈⣿⠀⠀⠀⢳⡀
⠀⠀⠀⡼⠁⠀⠃⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⣯⠀⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⢷
⠀⠀⠀⠳⢤⢤⡄⠀⠀⠀⠉⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣿⠐⡇⠀⠀⠀⠀⣿⠀⣠⠆⠀⣸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠶⠆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣿⠀⢻⡀⠀⠀⠀⣿⠞⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠈⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠂⣿⠰⠶⠻⢦⣀⠀⣿⢀⣀⡴⠋
⠀⠀⠀⠀⠀⢀⡿⠀⡖⠘⢦⣄⣀⠀⣠⠶⠦⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣀⣀⣀⣀⣈⡁⣿⠈⠁
⠀⠀⠀⠀⠰⠯⠥⠞⠁⠰⠯⠭⠥⠤⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠉⠉⠉⠁⠀⠀⠉⠁⠟⠘⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠆⠠⣤⠀⣤⡄⠠⡤⠘⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣧⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⣠⣷⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣦⣆⣾⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢶⣿⣷⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣟⠛⠛⠃⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣓⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠉⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣲⣤⣤⠤⠀⢃⣠⠀⣶⣦⢠⠰⢂⢤⠤⢀⣤⡄⣤⣠⢴⡂⣄⣦⢄⡠⢠⡀⢀⣠⠤⡆⢀⣂⠃⠀⢤⡤⢾⣂
⠀⠀⠀⠊⠉⠀⠂⠀⠉⠈⠙⠀⠁⠀⠈⠀⠁⠁⠀⠀⠀⠀⠙⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠈⠀⠁⠘⠉⠃⠁⠀⠀⠀⠉⠂
⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⢀⣀⠀⢶⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢂
⠀⠀⠄⢠⠈⠀⠔⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⢠⣀⠄⠠⡀⠀⠘⢼⢳⠝⠀⠐⢦⡧⡌⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠
⠀⠀⠄⠠⢰⣀⡼⢉⠀⠈⠀⠀⠀⠄⠀⠀⠠⢙⠁⠀⠀⢀⠀⠀⠺⣿⡆⠀⠀⠲⣧⡤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠂⠈⣿⣦⠀⠐⠀⠀⠀⢀⡀⣤⡆⠀⠙⠀⠀⠠⠂⠀⠀⡀⠯⠀⠀⠀⢀⠿
⠀⠀⠀⠀⠀⠛⠉⢠⠑⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠇⠀⠺⠀⠀⠀⠐⠛⡄⠀⠀⠐⣾⠈⠛⠛⠟⠉
⠀⠀⠘⠂⠀⡀⠀⠁⠈⠀⠀⠀⠂⠄⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⢂⠀⠆⠀⠀⢰⠁⣴⢷⡄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠢⠆⠀⠳⠆⢡⠀⠀⠀⠀⡁⠀⠀⠰⠀⠃⠀⠀⣾⠇⠁⢸⡇⠀⠀⠀⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠀⠀⠰⠀⠀⠄⠂⠢⠘⠁⠀⠸⢈⠁⠀⠀⠠⠀⠁⠀⠀⡏⠀⠘⡀⠇⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⣤⣲⡶⠀⠀⠲⠴⠃⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⣌⠁⠀⠀⠀⠀⢀⠐⠁⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡇⣤⣀⠠⣄⢁⡀⠀⠀⠀⠀⠀⡰⠀⠀⡰⠁⠀⠀⠀⣀⣠⡐⣄⡄
⠀⠀⠀⠉⠁⠒⠀⠉⠀⢀⣀⣸⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠳⠉⠀⠀⠞⣀⠀⠀⠀⠰⠁⠀⠁⠀⢀⠀⠀⠀⠰⡯⠙⠁⠕
⠀⢀⣴⣄⠀⠀⠀⠀⠀⠉⠛⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢁⠀⠀⡤⠒⠀⠀⠀⠐⢄⠀⠀⠀⠀⠁
⠀⠀⠀⣨⡷⠿⠏⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡴⢄⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⠎⠀⠀⢷⠀⠀⠁⡔⠁⠁⠀⠀⠀⠀⠀⣤
⠀⠀⢈⠉⠁⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠈⠐⠞⠳⠂⠤⠤⠀⠄⠒⠂⠁⠀⠀⠀⠀⠀⠁⠀⠀⠓⠶⠠⠄⠀⠀⠀⢰⡇
⠀⠀⠀⠁⡀⢄⠈⣧⢂⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠠⣀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⣁⢈⠠⠀⠀⠀⠄⠀⠫⠠⠀⠀⢀⠀⠰⣦⣿⣿⡇⠀⠀⢀⣿⣿⠆⠀⠀⠻⠄⠠⠄⢠⠄⠀⠀⠀⠀⠀⡇⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠡⡀⢀⣗⠈⡠⠀⠀⣀⣾⣿⣿⣷⠀⠀⠀⢻⣿⠀⠀⠀⠀⢢⠀⡄⢨⠂⠄⠀⠀⠀⠀⠁⣀⡎
⠀⠀⠀⠊⡴⠂⣒⣬⣙⢳⡄⠄⠀⠀⢺⠟⠀⠀⠀⠀⠋⡟⣟⣿⣿⡄⠀⠀⠈⡇⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⡌⡇⠀⢍⣁⣨⠀⡇⡤⠄⠀⠘⠂⠀⠀⠀⠀⠀⡇⡷⣿⣿⠀⠀⠀⠰⠷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀
⠀⠀⠈⠃⠨⡀⠠⠀⠤⡰⢁⠇⠀⠈⠻⠟⠀⠀⠀⠀⠀⣟⣿⡿⣿⠀⠀⢆⠀⠀⠀⠀⠀⠰⢃⠀⠀⠀⠠⠀⠀⠀⠉⠀⢀⡍⠈
⠀⠀⠀⠑⢀⢀⣀⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠈⢹⣿⠁⠀⠀⠀⠈⠉⠓⠒⠒⠂⠀⠀⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠠⠄⠀⠀⠀⢤⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣠⠾⠛⠃⠄⣀
⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡴⠟⠉⠀⢀⣾⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣿⣴⣷⣧⢀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠰⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣷⣿⣠⡀⣦⣷⢠⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣼⣧⣧⣼⣰⣇⢠⡀⣿⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⣠⢸⣷⣿⣦
⣿⣿⣿⣿⢿⢿⡿⠿⠛⠛⠟⠿⠛⠋⠛⠉⠉⠋⠉⠉⠋⠈⠉⠛⠁⠀⠋⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⣸⣧⡆⢠⢀⣿⣾⣷⣿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⣾⡧⢀⡀⣸⡇⣰⣠⣧⣴⣰⣿⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⢸⣿⣿⣾⣧⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣗⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣸⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡿⠻⣿⣿⢿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠃⠀⠀⠈⠁⠈⠀⠁⠈⠈⠉⠈⠉⠙⠛⠋⠉⠉⠛⠻⠟⠿⢻⡿⣿⠿
⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⢠
⣿⠃⢹⣿⣿⣿⣿⣿⡃⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣸⡇
⡟⠀⢐⣻⣿⣿⣿⣿⣷⣼⣿⣧⡀⢀⣦⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⢸⣿⣯
⠉⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣸⣿⡄⠀⢰⣾⣿⡇⠀⢰⡆⠀⠀⣿⣿⣿⡁⠀⠀⣾⠄⠀⠀⠀⢰⡧
⠂⠀⠴⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢺⣿⣿⣶⣤⣾⣿⠀⣘⣿⣿⣿⣶⠆⢸⣿⡇⠀⠀⠀⣿⣟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣘⣿⣿⣿⡟⢻⣿⣿⣦⣽⣿⣿⣿⣿⡥⣿⡿⠿⠀⠀⣽⣿⣿⠇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⣶⣤⣿⣿⣿⣷⡤⠀⠀⢰⡇
⠀⠀⠀⣤⣽⣿⣿⣿⡧⠀⠀⢽⣿⣿⣿⡿⢻⣿⣿⠦⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠠⢽⣿⣿⣿⣿⣿⣧⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠤⠼⣿⡟⠓⠀⠀⠙⢿⣿⣿⡃⠀⣿⡟⠃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⠙⢿⣿⣿⣿⣿⣷⡖⣸⣿⣿⡅⠀⢀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠒⠚⣉⠁⠀⠀⢤⣿⣿⡟⠀⠀⠹⡏⠁⠀⠀⣤⣿⣿⡿⠁⢿⣿⣿⣏⠁⠀⠀⢤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢁⣾⣇⠀⣸⣿⣟
⠀⠀⠀⠀⠠⠴⠒⠀⠀⠀⠀⠐⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠚⠻⠃⠀⠘⣿⣟⠀⠀⠀⠀⠐⢺⠻⣿⣿⠁⢻⣿⣿⡟⢻⣿⣽⣿⣧⣠⣿⣿⣿⣃⣾⠀⠀⣴
⠀⠀⠀⠀⠤⠦⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⢒⣿⠁⠀⢈⣿⣿⠀⠈⣿⠙⣿⣿⣿⠇⢸⣿⣿⣿⡆⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⣉⠅⠀⠀⠀⠙⠀⠀⠀⠋⠀⣿⣿⡿⠀⠈⣿⣿⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢦⣴⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣾⡷⠖⠀⠀⠀⠀⠀⣄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠻⠏⠻⡄⠀⠀⠀⠀⠰⠮⣿⣷⡶⠦⣄⠀⠀⠀⠀⠀⠘⠻⣟⠃⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢀⣸⣇⡀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⡏⠛⠁⠀⢹⣷⡀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠋⠁⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠘⠈⣿⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠛⢸⣦⡀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢿⠈⢧
⠀⠀⠀⠀⠀⣀⡀⣿⣼⡴⠖⠒⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣘⠀⠹⣦⡀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣄⠸⡇
⠀⠀⠀⠀⠀⠈⣩⠿⣿⣤⡆⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠾⠿⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⡏⢀⡇
⠀⠀⠀⠀⠀⣰⠃⠀⠸⠋⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠚⠀⡼⠁
⠀⠀⠀⠀⠀⢹⡀⠠⣤⣤⣤⠄⠀⢀⣤⣿⣄⡀⠀⠀⢀⡴⠶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣠⠶⠋⠀⠈⠉⠁⠀⣰⠏⠀⡴⠂⠈⠳⠶⠶⠖⠒⠛⠛⠓⠦⣄⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⠶⠶⢦⣄⠀⠀⠀⠻⣄⠀⠀⣴⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢀⣹⣾⣿⠿⣥⠀⠀⣈⢷⡀⠀⠀⠈⠳⣄⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⠞⠁⠀⢀⣠⣤⣴⣤
⠀⠀⠀⠀⠀⢀⡴⠋⡟⢧⠉⠇⠀⠀⠀⠘⠈⡇⠀⠀⠀⠀⠈⠛⠶⢤⣤⣤⣤⣤⠤⠶⠛⠁⠀⣠⡴⠋⠀⠀⠘⡇
⠀⠀⠀⠀⠀⢸⠁⠀⠃⠀⠀⠀⠀⠀⠀⡞⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣥⠖⠀⢀⡤⣰⠇
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠛⠩⠞⠋⠀⣀⠀⣉⡼⠃
⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣠⡴⠛⠁⠀⠀⠀⣠⠴⠶⠶⠶⠶⠖⢚⣋⣩⡴⠞⠃⠀⢠⡴⢚⣩⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠾⠿⣧⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⢀⣠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠦⠤⠤⠤⠤⠶⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⠿⠿⢿⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣩⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⡿⠿⠟⠛⠋⠉⠉⢿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⣀⣤⣶⣿⣿⣿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋⠁⢀⣴⣿⠟⠋⠁⠀⠈⠻⢃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⢀⣴⡾⠿⠿⠿⢷⣦⡀⠀⠹⣿⡀
⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠠⣿⠇⠀⠀⢠⣿⣧⡄⢠⣤⣤⣤⡄⢠⣤⣤⣤⠀⠀⣤⣤⣼⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⢿⣇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠁⠀⠉⠉⠉⠀⠈⠉⠉⢉⣀⠀⠈⠉⢹⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⣤⣤⣾⣿⣤⣤⣤⣤⣤⣿⣷⣤⣤⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⡄⠉⠁⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⢸⣿
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠰⣿⠟⠁⠀⠀⣠⣶⡿⡿⢿⠿⠿⠿⠿⠿⢿⡿⠿⣿⣿⣾⣿
⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⢀⣴⣿⠆⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⣿⡇
⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡟⠉⠉⠉⠉⠉⠉⠉⣿⣏⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣶⣶⣾⠿⣷⣶⣶⣿⡧⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢻⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡏⠀⠁⠀⠀⠀⠉⠀⣽⣇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣧⣀⣀⣀⣀⣀⣀⣀⣿⡗⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠿⠛⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⠿⠟⠛⠻⠿⣿⣷⣶⣶⣦⣼⡇⠀⠀⠀⠀⠀⢰⣦⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠇⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠏⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠋⠉⠁⠀⢀⣴⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡿⠟⠉⠀⠻⠋
⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠉⠈⠻⣿⣿⣦⣀⣠⣴⣾⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣶⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣀⣠⣾⣿⡿⠋⣠⠽⠻⢿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣦⣀⣠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠉⠉⠁
⣶⣶⡶⠶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⡿⣿⣿⣷⣶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹
⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣠⣿⣿⡟⠙⢿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⡀
⣼⠟⢤⠀⠀⠀⠀⠀⣀⣀⣠⣴⣽⣿⣿⣿⠟⠻⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⡟⢠⣯⡄⠀⠀⠘⠛⠻⠿⠿⣧⣀⣿⣿⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⢿⢿⣄
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣿⣿⣟⡉⢛⣉⡏⡀⣀⣸⣿⣿⡶⠿⠒
⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣄⡄⠀⠀⠀⠀⠀⢸⡏⣿⣿⠟⢿⣿⠿⢿⣿⣿⣿⡀⢀⣠⣶⡀⣠⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣀⣄
⡟⠀⠙⠃⠀⠀⠀⠀⠀⢸⡿⢯⣿⣤⣀⣻⣆⣠⠿⣿⠟⣿⣯⣨⣿⣹⡟⣹⣿⣿⢿⣋⡀⣄⣽⢳⣻⡿⠁⠀⠀⠀⠀⣼⣇
⠅⠀⢰⡀⠀⠀⠀⠀⠀⠈⢄⣈⣭⣿⣿⣿⣣⡿⠷⣯⣟⣯⣅⠉⣻⣿⣾⣿⡿⠿⣫⡻⣿⠿⢻⣿⣼⣧⠀⠀⠀⠀⠀⠈⢿⣧⡀
⡟⠀⢺⡇⠀⠀⠀⠀⠀⠀⢘⣿⡿⡿⡼⡟⢶⣅⣄⣀⣿⣾⣿⣷⣿⣿⣿⣍⣴⣶⡿⠏⣥⣤⢿⣷⠖⢯⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢗⡋⢱⣐⣯⣶⣽⣿⠿⠿⣻⣿⣿⣭⣔⡻⠿⢿⣾⣷⣚⣺⣛⣸⣗⡋⣻⡖⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣿⣿⡇⢠⡄⠀⠀⠀⠾⣷⡿⠷⠛⢫⣽⠋⠡⡶⡖⠀⠛⠿⣿⣿⣿⣥⣤⡀⠈⠉⢻⣿⣿⣿⣿⣵⣾⣷⠄⠀⠀⠀⠀⠀⠀⠈
⢸⣿⡿⣰⣿⡇⠀⠀⠀⠈⠛⠿⣿⠿⣿⣯⣤⣤⡍⢵⣶⣿⣿⣿⣿⣿⣿⡿⠟⠙⣛⠋⠛⠋⢻⣾⡿⠟⠛
⣿⣿⣧⣿⣿⠃⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣻⣶⣿⣿⣿⣿⡿⠋⠁⠀⣠⣤⣤⣤⡼⣿⣿⡫⢋⣤⣀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠐⢿⠇⡀⠀⢸⣿⢿⣽⣿⣿⣿⣿⢿⣿⣶⡶⣾⠟⡓⣿⣫⣿⣿⠋⢀⣈⠛⠃⠀⠀⠀⠀⠀⠀⢰⣾⡇
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣀⡀⠉⠀⠈⣿⠐⠙⣿⣥⣿⣇⣦⢻⠻⠐⡿⣾⣿⣧⣼⢿⣿⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⣈⠀⢿⣰⣿⣿⣿⣿⣿⣷⣼⠀⣰⣿⣿⣿⣿⠀⢘⣿⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⣦⡉⠙⣿⣿⣿⢿⣿⣿⠀⣿⣿⡿⠛⠃⠀⢘⣿⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⡏⢀⣶⣦⠀⠀⠀⠀⠈⠀⠀⠻⠟⠁⠀⣿⣿⣿⠀⢻⣿⣶⣿⠏⠀⠀⡀⠀⢸⣿⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝
⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⣿⣿⠀⢸⡟⠟⠡⣿⣿⡟⠀⠀⠘⠁⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠛⠿⠿⠀⠘⠇⠀⠀⠉⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣠⡇⠀⠀⠀⠀⢀⡶⠛⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⢟⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⢀⡠⠴⠃⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣾⡏⣸⣿⡇⠀⠀⠀⠀⡿⢀⡶⠲⣄⠈⢛⡛⠳⣆
⠀⠀⠀⠀⠀⠀⣠⡾⣋⡥⠖⠚⣩⣿⣿⡈⢿⡄⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⢸⢳⢣⣿⢫⣣⠀⠀⠀⣼⢇⡼⠁⠀⠈⠋⠉⠙⡇⢸
⠀⠀⠀⠀⠀⣼⠏⢰⠃⢠⠖⣫⢿⣿⢻⢳⠀⢿⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣀⣨⣧⠀⠀⠀⠀⡏⡾⠸⡿⢸⣿⠀⠀⡼⣡⠞⠀⠀⠀⠀⠀⢀⡼⢃⡾
⠀⠀⠀⠀⠀⣿⠀⢸⡀⣯⢰⠇⡜⡿⢸⢸⡇⢸⡇⠀⡏⠁⠀⢄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠁⡇⠀⠀⢈⡇⠀⠐⣇⠻⣄⣀⣀⡀⠀⠀⣸⢣⡞
⠀⠀⠀⠀⠀⠹⣧⠈⢧⢹⣼⣤⡿⢣⠏⡼⢀⡾⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠐⢺⠇⠀⠀⠀⣼⠈⡇⠀⠀⣼⠁⠀⠀⠙⠶⠤⣄⠈⠳⣤⡴⠋⣼
⠀⠀⠀⠀⠀⠀⠙⢷⣌⣧⣿⣿⡿⠷⠚⣡⡾⠁⠀⠀⠀⠈⠳⢤⠀⣠⣤⡤⠤⠖⠋⠀⠀⠀⠀⣿⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠷⠶⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠒⠲⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣆⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢤⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⣀⡤⠴⢶⠛⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣤⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⡼⠀⠀⠛⠂⠀⡸⠀⠀⠀⢀⡴⠚⢹⡆⠀⠀⠃⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢠⡴⠶⢿⠟⠁⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⠟⠲⠤⠤⠀⣠⠃⠀⠀⢠⣾⠁⠀⠈⠃⠀⠀⠀⠀⣄⠀⢠⠇
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⡾⠀⠀⠐⠒⢻⡏⠀⠀⠀⣾⠀⠀⢀⠀⠀⠀⠀⠀⢀⣽⠶⠋
⠀⠀⠀⠀⠀⢼⠀⠀⢠⡆⠀⣿⡄⠀⠀⢀⣿⣿⠀⠀⠀⠀⢀⡞⢸⠀⠀⠀⠀⠀⢰⠏⠛⠲⠀⢀⡞⠀⠀⠀⠀⠸⡄⠀⠈⠀⠘⣆⣠⠞⠉
⠀⠀⠀⠀⠀⢸⡀⠀⠸⠃⠀⠉⠁⠀⠀⢸⣿⡏⠀⠀⠀⠀⣿⡇⢸⠀⠀⠀⠀⠀⡿⠀⠀⠀⢚⡟⠀⠀⠀⠀⠀⠀⠙⠳⢤⡤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢀⣰⣿⡿⠁⠀⠀⠀⢰⡇⣧⡜⠀⠀⠀⠀⢰⣧⡀⠀⢲⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣶⠶⠾⠿⠟⠋⠀⠀⠀⠀⠀⢸⡇⣿⠇⠀⠀⠀⠀⢸⠁⠀⣠⠏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⢟⣵⠞⣛⡓⢦⣄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠿⢶⡶⣤⠀⠀⢸⣄⡴⠃⠀⠀⠀⣠⠶⢛⣉⡉⢳⡄⠀⠀⢰⣏⡟⣡⡀⠳⢃⡤⡙⡇⢹
⠀⠀⠀⠀⠀⢀⣠⠴⢶⠶⠶⣤⣄⡀⠀⠀⠀⠀⢀⡴⠋⢸⠁⠀⠀⢳⡈⢳⡀⠀⠉⠀⠀⠀⠀⡼⢁⡶⠋⠉⢹⡆⣿⠀⠀⢸⡿⣇⠷⢯⡴⣎⠛⢁⡇⣸⠇
⠀⠀⠀⠀⢠⡟⠁⠀⡟⠀⠀⠀⡿⠻⣦⡀⠀⠀⣾⠁⠀⠘⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⠀⣠⠾⣡⡿⠀⠀⠀⢸⡇⢸⡆⠀⠈⢷⡙⢦⣈⣛⣋⣠⠞⣡⠟
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⠁⠀⠘⣧⠀⠀⣇⠀⣆⠀⠀⠀⢀⠀⠀⣰⡇⠀⠀⢀⡾⠁⣼⠋⠀⢀⣄⠀⠀⢻⡄⢻⠀⠀⠀⠙⠳⢦⣭⣭⡴⠞⠋
⠀⠀⠀⠀⠀⠹⣿⡀⠀⣴⠂⠀⠀⡄⣠⠏⠀⠀⠹⣆⠸⡄⠀⠀⢸⣀⣴⠟⠀⠀⠀⢸⡇⠘⣧⣠⡴⠋⠹⣄⠀⣰⠇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⠶⠾⠛⠉⠀⠀⠀⠀⠈⠓⠿⠦⣤⣾⣟⠁⠀⠀⠀⠀⠈⠳⠦⣤⠤⠶⠛⢧⡙⠛⢉⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡗⠦⣤⠴⠒⠀⢲⡶⢄⠀⠯⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢀⣤⡀⠀⠀⢸⡇⣸⠃⠀⠀⣠⡔⢲⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠉⠙⠛⠛⠉⠀⠀⠀⠘⠧⠞⠉⣖⢻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⡆⠀⠀⠀⠀⠀⠀⠀⠰⠆⠠⣀⠀⠀⠀⠀⠀⠈⠓⠶⠃
⠀⠀⠀⠀⠀⠀⢠⡏⠀⡀⠀⢠⡇⠀⣀⣴⠄⠀⣀⣤⣤⣤⣀⠈⠙⢦⡀⠠⣀⠴⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠈⣧⣎⢀⣠⠞⠀⠈⡽⠹⢠⠾⣵⣧⣼⣬⣯⠷⣄⠀⢳⠐⣿⠀⠀⠴⠓⢒⡶⠆
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⢠⡇⠀⣯⣤⣯⣤⣼⣤⣼⣤⣼⠀⠘⡇⠸⠄⠀⠀⢰⡋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣣⣀⣜⠀⡀⣇⠀⢳⣀⣿⣀⣼⣀⣼⣀⡼⣀⢸⠃⠀⠈⢓⣶⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡾⠭⣤⠭⣶⠃⠘⣆⠀⠙⢬⣧⣽⣰⡧⠟⠁⣿⡯⠆⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⡖⣇⠁⣿⠈⣸⢲⠀⠈⠓⢤⡀⢀⡀⠀⠀⠀⠀⠉⠀⠀⠀⣦⢤⡖
⠀⠀⠀⠀⠀⠀⠀⠁⣼⠓⠿⠚⣧⠈⠀⢀⠤⢄⡀⢈⣁⣀⠀⣠⠤⣄⢀⡜⠉⣽⣹⣏⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⠞⠉⣉⣩⣉⠉⠓⣄⡿⠀⠐⠛⢳⣰⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡞⣵⠒⣺⢳⡀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢧⣈⣻⣁⣸⠃⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠈⠉⠉⠀⠀⠀⠸

⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡇⠀⠀⠀⣿⣿⣿⡆
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⢿⣿⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⣀⣉⣀⡀⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠟⠋⠀⢀⣀⣀⣀⡀⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⢀⣤⣤⣴⣶⣶⣶⣾⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠠⣿⣿⣿⡇⠀⢠⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡆⠀⠀⣷⣿⣿⡃⠀⢸⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠈⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇
⠀⠀⢸⣿⠀⠀⠸⣿⣿⣿⠀⠀⠸⣿⣿⣿⠀⠀⠸⣿⣿⣿⠀⠀⠸⣿⣿⣿⠇⠀⠀⣿⣿⣿⠇⠀⠀⣿⣿⣿⠇
⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⢀⡠⠀⠛⠀⠐⠒⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠉⠇⠀⠀⠀⠀⠀⣠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠀⠀⢰⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⡴⠁⡀⠀⠀⠀⠁⡼⠀⠀⢀⠊⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢠⠃⠀⡠⠁⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡜⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠜⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡜⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡌⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⡘⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⢠
⠁⠂⠠⠀⣀⠀⠀⠀⠀⠀⠐⠉⠀⠀⡆⠀⠀⠀⢀⣠⠔⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⡇⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠑⠠⢀⠀⠠⠤⡀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⠎⠀⠀⢠⠢⠀⠀⠈⠂⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⡎⠀⠀⢰⡧⠃
⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣻⡀⠁⣶⠁⣠⠞⡅⢀⡶⠁⣰⠃⢀⡖⣠⠄⣼⠁⢤⢀⡟⠁⢠⡆⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⡟⠀⠐⠇⠈⠣⣸⠃⠘⢅⠀⡏⠀⠘⠂⠹⢐⠟⢠⢯⢸⠁⠀⠻⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⡰⢋⡝⠉⠀⠀⠀⣰⠋⢀⡎⠌⢈⠁
⢃⠀⢠⡇⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠉⠀⡼⠁⠀⡖⣠⠀⡀⢠⠇⠀⡼⠃⢀⠁⡔⣰⠀⡴⠂⢠⡆
⡄⠀⠀⠁⠸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠰⡇⢀⡼⠁⠇⠘⠃⡟⠀⢸⠇⠀⠚⠔⠁⠣⢺⡋⠀⠨⡗
⠀⡀⠀⠀⠈⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠓⠁⠘⠂⣀⣀⣀⣀⣀⣀⣀⡈⠒⠁⠀⢀⠀⢀⣀⣀⣀
⠀⠡⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠐⠂⠐⠂⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡄⠙⠈⠁⠀⠀⢚⣰
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠄⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠈⡄⠀⠀⠇⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠁⡠⠔⠒⠀⠄⠂⠀⠀⠒⠀⠤⢄⠀⠀⠉⠉⠐⠒⠂⠤⠤⢀⣀⠀⠤⠊⢁⢀⡀
⠀⠀⠀⠰⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠢⠄⠀⡄⠴
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⡄⠀⠀⠀⠀⠀⢀⡠⠀⠠⠶⠀⠀⠤⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠌⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣤⣤⣤⣤⣶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⣀⣠⣤⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣉⠻⢿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠛⠷⢶⣤⣉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⡀
⠀⠀⢀⣤⡾⠛⠉⠀⣀⣤⣴⠶⠶⠿⠛⠛⠻⠟⠲⢶⣄⣀⠀⠈⠙⠻⢦⡈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣧
⠀⣰⡟⠁⠀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠣⣄⠀⠀⠹⣆⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿
⣰⡟⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⡀⠀⠈⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿
⣿⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⣿⡄⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣄⠀⠈⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣼⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣶⣄⠀⠈⠛⠷⣦⣤⣀⣀⣀⡀⠀⣀⣀⣀⣠⣤⡶⠟⠋⠀⣀⣴⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠈⣿⣿⣿⣿⣿⣶⣤⣀⡀⠈⠉⠉⠛⠛⠛⠛⠋⠉⠉⢀⣀⣠⣴⣾⣿⣿⣿⣿⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⠏
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⣿⣿⠏
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣾⣿⡿⠃
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠿⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠙⠆⠀⠀⠹⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⢠⠶⡄⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠂⠀⠂⠐⠀⠀⠀⢠⠋⠀⠹⣄⣭⣀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠹⡄⠀⠀⠈⠀⠁⠄⠁⠄⠀⠀⠀⠀⢻⡀⠴⢃⡟⠀⠈⢳⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣰⣂⡏⠀⠀⠐⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠉⠛⡙⢤⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⢢⡀⢹⠉⠀⣠⠤⣦⠀⠀⠁⣀⣤⢤⣤⣤⣀⠀⠀⠚⠁⠀⣤⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣙⣶⡃⢸⠀⣾⢡⠀⣼⠀⣠⠮⣵⣇⣸⣇⣹⣬⠷⡄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠀⣸⠳⠚⠁⢰⡇⠀⣟⠀⢸⠃⠀⣧⠀⢹⠀⢸⠓⠦⣄⣀⣀⣀⡤⠖⢻⠂
⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⣤⣽⣾⣥⣤⣤⠀⠸⡏⠉⣏⠉⢹⡏⠉⡿⠉⢹⠁⢸⣀⡴⠋⠀⠀⠈⠙⢆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⠻⡖⢺⡗⢲⠗⣶⠏⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠋⢩⠍⠩⠉⣧⠀⠀⠈⠓⠻⠾⠷⠟⠋⠁⠀⠐⢷⠦⢤⣈⣀⣀⣀⣠⡤⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠈⠓⠦⣤⣿⣬⣯⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢶⡶⣄⠀⠀⠀⣹⡟⠁⠀⢈⣧⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡵⠚⣧⠞⣇⠀⠀⠀⣇⠀⠀⠉⠁⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣋⣹⠆⠀⠘⢀⡀⠀⠀⢯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣉⣻⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⡿⡻⡛⡟⠟⢟⢿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠫⡡⡑⡑⡔⠜⢌⢌⢎⢊⢢⠢⡫⡻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠻⡡⡱⡑⡔⡔⣜⣌⣮⣮⣦⣦⣧⣥⣵⣕⣐⡜⠟⢦⣀⠀⠀⠀⣴⣶⣶⡄
⠀⠀⠀⠀⢀⣴⠿⡱⡑⣑⣴⠾⠾⠛⠙⠉⠉⢀⣀⣀⣄⣤⣤⣤⣤⣮⣴⣼⣯⣿⣦⣼⠓⢚⣿⠃
⠀⠀⠀⢠⡾⡓⠐⠌⠊⠉⠀⢀⣠⣴⣴⣾⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⡿⠤⠠⣿⣛⠦⣄⡀
⠀⠀⣰⡟⠑⠀⢀⣠⣤⡴⠿⢛⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣃⠀⣉⣹⣿⠷⠾⠧⢶⣤⡀
⠀⣼⣯⣦⠶⠛⠛⠉⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡀⢰⣿⣇⢐⣾⡟⠉⠀⠀⠀⠀⠀⠀⠙⢦⡄
⡼⠛⠁⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠁⠀⠀⠀⠀⢈⡻⠿⣿⢿⠣⣤⣤⣀⡀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠘⣦⠀⠀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢨⣤⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⣀⠂⠀⠀⠀⠀⠄⠠⠂⠈⠀⠀⠠⡀⣀⣠⣵⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣶⣶⣶⣶⣤⣶⣶⣶⣾⣿⣿⣿⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣿⣿⣿⣶⣶⣶⡄⠘⠛⠀⣠⣶⣶⣿⣷⣾⣷⢦⣶⠆⠈⠙⠛⠷⠶⠄
⠀⠀⠀⠀⢸⡿⠊⠉⠉⠙⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢰⣦⠾⠿⠛⠃⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⣶⡿⠀⠀⠀⢀⣾⠛⠋⠻⣿⣿⣤⣄⣀⣀⡰⠖⠀⠀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣤⣶⣤⣴⣿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣿⡇⠀⠀⠘⢿⣿⣿⣿⠀⠀⠈⠻⣿⣶⣷⡆
⠀⠀⠀⠀⣻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⠏⠀⠀⠀⠀⠀⠻⡿⠁⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⣠⣤
⠀⠀⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿
⠀⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⢀⡀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⠀⠲⣦⠀⠀⠀⠀⠸⠆⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠋

⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠧⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⠛⠛⠀⠂⠙⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠾⠐⠀⠆⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠤⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⢄⡀⠀⠀⠀⠀⠀⠀⠴⠫⠐⢀⡴⣤⠀⠀⠀⠀⡀⠀⠀⠀⠘⠠⣦⠬⠿⡀
⠀⠘⢄⠀⠀⠸⡇⠀⠀⠀⠀⢠⠀⠀⠀⣜⠀⢀⠀⢀⡈⠲⠍⠓⠒⠀⠀⠀⠀⠈⠐⠙⠉⠁⠀⠓⠀⠒⠊⠀⠀⠀⠀⢠⣒⡆⢯⡼⣭⣆
⠀⠀⠈⠙⠓⠂⠑⠀⠀⢀⡤⠞⠀⠀⠀⠹⡀⠀⠀⠀⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠁⠘⠶⠹⠠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⣀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠤⡀
⠀⠀⠀⠀⠐⠓⠄⢈⠤⠴⠆⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠐⡄⡀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠘⠓⡩⠷
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⢂⠜⠀⢊⠉⠁⠢⠀⠀⠀⢸⡀⠁⣖⠎⢻⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡔⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢣⠐⠀⡀⠀⠀⠀⠙⠯⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢦⣄⡠⣇⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⣧⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠳⣄
⠀⣤⣄⡁⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡹⠆⠐⠁⢡
⠀⠀⠉⠁⠀⠀⠀⠨⠉⠐⠦⢤⡀⠀⠀⠀⡉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠆⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠴⣦⣀⣤⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠍⠉⠤⠤⠶⠀⠂⠀⠀⠀⢀⠀⠀⣨⠃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠘⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢂⣰⣤⡀⠀⢀⠀⣀⡆⠊⠀⠀⠀⠀⠀⣀⠄⠀⠀⡀⠀⠀⡀
⠀⠐⠀⠃⠀⠰⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡘⠀⠀⠁⣿⢳⠃⠀⠀⢀⡴⠋⠀⣠⠄⠀⠀⠀⠉⠀⠐⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠢⠑⡄⠀⠀⠘⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠃⠃⠀⠀⠀⡈⠀⠀⠀⠀⢀⡠⠆⠠⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠑⠸⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⠟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧
⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧
⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆
⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣿⣶⢶⣦⣤⣾⣷⣶⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⡶⣤⡀⠀⠀⢀⣴⣯⣤⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣾⣋⣰⣾⣿⢷⣴⣏⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⣿⠀⢠⡾⢻⣿⣿⣿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠀⣿⢐⣿⣿⡿⣿⣿⢿⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟
⠀⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⢠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⡀
⠀⡀⡇⠀⠀⡀⣼⡀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐
⢰⡇⣿⣿⠀⣧⣿⡇⢰⢾⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠛⠿⣿⣀⣿⣿⡇⣼⣾⡆⣷⢀⡇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢿⡧⠇⢄⡀
⠀⠀⠀⠀⠓⠉⠛⠓⠿⠿⢯⣿⣤⣧⣾⣠⡆⠀⠀⠀⠀⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠇⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⠀⠀⢳⠀⢸⠄⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠑⠄⠀⡬⡆⢀⠂⢠⠈
⠀⠀⠆⠠⠒⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢀⠀⠀⠒⠣⣀⡤⡀⣸⣭⠆⠠
⠐⡆⢰⣛⣒⡀⣤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢘⠌⢨⠅⣀⠹⣷⣥⣕⠂⢓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡔⣤⠀⡤⣤⢄⠀⢖⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⠀⠀⡀⠘⢲⡏⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⡄⠠⠂⡌⠉⠂⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠁⠀⠰⢆⠀⠀⠈⠃⠂⢡⠀⠀⠀⠀⢀⠄⠀⠴⠚⠀⣆⠈⠈⡄⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠂⠀⡆⠀⠀⠀⢠⡸⡄⠀⠀⡔⠠⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠐⠰
⠀⠀⠚⠄⠰⡀⠀⠀⠱⢤⠀⢀⠀⠀⠀⠀⠀⡅⠸⠂⠤⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⡄⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢨⠀⠀⠀⠀⠀⠙⡀⠁⠀⠀⠀⠀⡠⠃⢠⡖⠀⠀⠀⠀⠀⠀⠄⠀⢣
⠀⠀⠈⠀⣀⠉⠂⡀⠀⣀⠄⠀⠀⡄⠀⠀⠀⠀⡇⡄⠀⠀⢀⠔⢀⡤⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠
⠀⠀⠀⠀⠈⠃⠀⠀⢀⡌⠀⠀⠄⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠀⠊⠀⠀⠀⠀⠀⠀⠠⠄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠏⠀⠐⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⡀⠀⠓⠈⡜⠌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠇⠀⠀⠀⡠⠂⠁⡰⠃
⠀⠀⠀⠀⠀⠀⡃⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣀⠀⠀⠀⠀⠀⠁⢂⠁⠌⣈⠭⠨⠔⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠘⠌⠐⠤⣀⣀⣠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠰⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⣋⠉⢑⣮⣭⣭⣗⣦⣀
⠀⠀⠀⠀⠉⠻⣯⣙⡛⠛⠛⠛⠉⠉⠀⣲⡤⡶⠛⣹⠃⠀⢀⡤⠬⠽⣷⣄⢀⡾⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠈⠻⢯⣉⠓⠒⠚⠻⠋⠁⠜⠁⠐⣁⡴⠞⠉⠀⠀⠀⠀⢙⡟⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢦⣤⡤⠶⣶⣿⣭⣶⣶⣶⣶⣶⣶⣶⣾⠁⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠛⠉⠉⠀⠀⠀⢀⣀⣼⣇⣰⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠙⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠋⠁⠀⠀⠀⠀⠉⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣀⠀⣿⣿⣴⣾⣿⠿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⣾⡟⣁⣾⠉⠙⠻⢿⣿⣿⠟⠁⣠⣤⣤⣄⡉⠻⢿⣷⣤⡀⠀⠀⠀⠘⢿⣷⣄
⠀⠀⠀⠀⠹⠿⣿⣤⡀⠀⢠⣾⡿⠃⠀⠀⠙⠉⠉⠛⢿⣷⡀⠙⠻⣿⣦⡀⠀⠀⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠈⠻⣿⣦⡀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠈⢻⣿⣆
⠀⠀⣠⣾⣿⠟⠉⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠙⣿⣷⡄
⠀⣴⣿⠟⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠈⠻⣿⣶⣄
⣸⣿⠏⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠈⠻⣿⣷⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠈⠻⣿⣦⡀
⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠘⢿⣷⣄
⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣶⣶⣶⣶⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⠀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣿⣲⡌⠈⠉⠉⠉⠉⠈⢉⣡⠤⣾⣏⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡂⢾⣼⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠸⢆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣿⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⣀⠀⠆⠰⣼⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠔⠀⠐⠂⢛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠁⠀⠀⠀⠤⠒⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢆⣖⡈⠂⠈⠻⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠨⠗⠋⣁⣤⣶⣭⣀⠀⠀⠂⠂⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⠁⠀⠀⠖⠂⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⢉⣀⠴⠾⣯⣭⡵⠟⢩⠿⠰⠶⣶⣄⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠈⠙⠀⠀⢺⣾⡏⠀⠀⠐⠀⠀⣀⡷⠒⠤⠐⢀⣠⠴⠚⢩⡷⠄⣘⡄⣁⢒⡞⢈⣇⢙⣳⡆⣈⠉⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡤⠀⠒⢠⣶⣾⠻⡇⢢⠲⣠⡀⠀⠈⠃⣠⡖⠉⢛⣳⠛⣟⢡⡴⠒⢻⡆⣠⠿⠏⠴⡖⢂⢰⡾⠘⣭⣦⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⣤⣶⣷⣺⣿⣦⣀⠁⠰⠷⣿⡵⣀⠀⢹⣿⢐⠿⣿⣿⠻⣿⣤⣤⣩⣾⠁⠚⠛⠀⠉⠈⠁⠀⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⢷⡶⠦⠉⠱⠯⠿⠛⠛⠨⠇⠏⠚⠟⠛⠛⠛⠚⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠀⣠⡴⢤⡀⣠⡴⣤⡀⢠⡤⠦⡄⢤⡀⣠⡄⣠⡤⢤⡄⠤⣤⡤⠄⣤⠤⠄⢠⣤⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠀⣿⠀⠀⠸⣿⠀⢸⡇⠘⠳⢶⡄⠈⢿⡟⠀⠙⠷⢶⡄⠀⣿⠀⠀⣿⠒⠂⢸⡟⣷⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠉⠛⠛⠁⠙⠛⠋⠁⠘⠛⠛⠁⠀⠘⠃⠀⠙⠛⠋⠁⠀⠛⠀⠀⠛⠛⠃⠘⠃⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⠫⠝⡇⠀⠸⣋⡣⠀⠀⠀⠠⠂⡰⠁⣤⠀⢀⠀⠀⠀⠀⠐⠑⢨⢂⣀⣀⠀⠀⠀⠀⣠⠈⠫⡭⢙⠀⡄⠀⠀⠀⠀⠀⢻⣀⣞
⠀⠀⠀⠀⠀⠘⠁⠊⡡⡒⡄⠁⠘⠀⠀⠀⢀⠀⠠⠆⠀⠄⢁⠀⠀⠀⢠⡜⡃⠰⡀⠓⢐⣤⠀⠀⢐⢠⠜⡒⠒⠨⢥⣀⠀⠀⠀⡆⡛⡿⠵⢹⠟⠈
⠀⠀⠀⠀⠀⢰⠠⠀⡈⠒⠡⠀⠠⠀⠀⠀⠀⠂⢀⠀⢀⠈⠀⠂⠀⠀⡅⠀⢈⠢⠀⢀⡋⠀⠀⠀⠘⡀⠖⣱⢔⡃⡖⡀⠀⠀⠀⠃⡁⠷⠭⠾⢆⡰⠂
⠀⠀⠀⠀⠀⠘⠳⠤⠇⠀⠸⠎⠈⠀⠀⠀⠈⠂⠈⠓⠋⠄⠂⠀⠀⠀⠈⠃⠀⠀⠀⠯⠏⠀⠀⠀⠀⠉⠠⢄⣀⠤⠐⠁⠀⠀⠀⠀⠁⠀⠀⠀⠈⠃⠄

⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠀⣀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠤⠠⠀⠀⠀⡠⠀⠒⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠓⠈⢠
⠀⠀⠀⠀⠀⠀⡌⠉⠤⠀⠁⠊⢀⠀⠀⠀⡂⡉⢰⠒⠑⠊⠛⡄⠀⠀⠐⠀⠒⠂⠂⠀⠂⠂⠀⠀⠐⡀⠘⠛⡤⠀⡐⠀⠀⠀⠀⡐⠗⠀⠘⠤⠄⠰⡆
⠀⠀⠀⠀⠀⠈⢓⠲⠀⡌⡔⡀⠘⠀⠀⠀⠀⢀⢦⢛⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⣸⠀⣿⡞⠀⠀⠀⢇⠠⠆⠀⢀⢴⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠐⠰⡬⠏⠉⠀⠀⠀⠀⠀⠈⢧⣣⡜⠆⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠚⠔⠘⠉⠉⠄⠐⠀⠀⠀⠈⠠⠤⣀⡈⠳⠂

⠀⠀⠀⠀⠀⠐⢀⠤⠀⠀⡀⠂⠠⠀⠀⠀⡔⠀⢀⠀⠢⢀⢀⠀⠀⠀⢀⢀⠢⠄⠄⠄⠀⢠⠀⠀⠀⠄⢄⠐⠀⠄⠐⠀⠀⠀⠀⢀⠀⣠⣴⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠡⠀⠔⠒⠬⠁⠁⠀⠀⠀⠀⠈⠠⠐⠠⠁⠀⡁⠀⠀⠁⠀⠁⠒⠒⠉⠍⠁⠀⠀⠀⠼⠤⠒⠒⢌⠸⠅⠀⠀⠀⠀⠀⠈⣀⡃⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠒⡤⠊⠀⠀⠀⠀⠀⠠⠆⠐⢴⠔⡘⢠⠄⠀⠀⢆⡆⠀⢠⡔⣠⢶⣆⠀⠀⠀⠁⠈⠣⡬⠊⠀⠈⠀⠀⠀⡀⠀⡘⢿⠗⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠁⠀⠀⠈⠉⠀⠈⠁⠉⠀⠁⠀⠀⠀⠀⠐⠈⠃⠐⠀⠀⠀⠀⠀⠀⠅⡀⠀⢐⣰⣆⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢤⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠄⣈⢣⡟⠾⡁⢄⠀⠀⠀⠠⠀⢤⢬⣤⠄⠠⠀⠀⠀⢠⡴⢉⣀⡁⠈⢢⡄⠀⠀⠀⠀⡄⡤⠥⡄⡄⡀⠀⠀⠀⠀⠀⣖⣹⣸⡃
⠀⠀⠀⠀⠀⠠⡤⣭⢃⠜⣑⢷⢤⠀⠀⠀⠀⠶⠚⡧⠈⠰⠇⠀⠀⠀⢰⡀⠀⠋⠨⠀⢀⡅⠀⠀⠈⠀⣸⡀⣗⣸⡀⠠⠀⠀⠀⠀⢀⣈⢹⡭⣀
⠀⠀⠀⠀⠀⠀⡄⠹⠮⠵⠄⡇⠰⠀⠀⠀⠀⢀⠀⢀⠠⢁⠀⠀⠀⠀⠀⠘⠔⡤⢤⠂⠃⠀⠀⠀⠀⠀⡁⠈⠎⠁⠀⠀⠀⠀⠀⠀⠇⡸⢫⡁⠈⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⡾⢹⡟⠆
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠹⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠁⠀⠀⣰⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⠟⠀⠀⢀⡴⠋⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⡾⠋⠀⠀⠁⠀⠀⠀⢠⣿⣷⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠘⢿⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⢋⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⣋⣥⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠦
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢞⣫⣥⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣠⡴⠀⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣬⣭⡷⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣤⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢿⣧⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⣠⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠐⠛⢁⡀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡀⠀⠀⠀⠀⠀⢠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢈⠛⠦⡄⠀⠀⣿⠀⠀⠀⠀⠀⠖⠋⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡿⠃⠙⣿⣆⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠤⠶⠋⢸⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠴⠞⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣤⠖⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣠⡴⠀⣿
⠀⠀⠀⠀⠀⣿⠀⢀⠴⠚⡁⠀⠀⠀⠀⠀⣀⣤⠀⡉⠻⢦⠀⠀⢸⡇⠀⠀⠀⠀⢀⣠⡆⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣀⣴⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠉⣠⠀⣷⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⢁⡤⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⣠⠀⣿
⠀⠀⠀⠀⠀⢹⠀⠀⠀⢠⣿⠀⠀⠀⠀⠐⠛⢁⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠚⠋⣁⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠐⠛⢁⢀⣿
⠀⠁⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⠀⠀⠀⠐⠖⠋⢀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠰⠚⠁⣾⡇⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠖⠋⣸⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠛⠛⠛⠟⠛⠛⠿⠛⠛⠛⠀⠀⠀⠀⠙⠛⠟⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠈⠛⠛⠛⠛⠛⠟⠻⠟⠛⠛
⠀⠀⠀⠀⠀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣲⣦⡄
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠛⠉⠁

⠀⠀⠀⠀⠡⠀⠀⢀⠀⠀⠀⠀⠀⠀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣷⣤⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣮⣩⡄⠀⣥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢳⠀⠀⠠⠀⡀⠀⠀⣤⣀⠈⢸⠘⢻⠛⠟⠛
⠀⠠⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠐⠀⠀⠱⡄⢸⣿⡿⠟⢻⡆⠖
⢲⣾⣻⠯⢀⣀⡀⢀⣄⠀⠀⢀⠄⠂⠀⢠⠀⠀⠀⠐⡄⢠⡈⠑⠄⣀⠀⢹⢨⣤⣤⡈⢻⠐⣿⣷⣦
⠘⡇⢨⠀⠫⠀⠀⢹⣿⠀⠀⣠⠀⠀⠴⠋⠀⣾⠀⠀⡅⠀⠁⠀⠀⠻⣤⡀⢢⠀⠙⠑⢾⣠⠐⠈⠁
⠠⠶⠾⠶⠴⣤⡄⠉⡉⠀⠘⣿⠗⠀⠈⠀⣤⣤⣤⣦⡥⣤⣤⣤⣥⣴⣴⣶⣶⣷⣶⣶⣼⡷⠶⠛⢻⣯
⢰⣦⢞⣀⣠⡀⡀⣀⣀⣒⣸⣿⣧⣤⣤⡤⠬⣿⠭⢭⠽⠟⢻⣿⣿⣿⣻⣿⣿⣿⡟⡙⣹⡄⢠⡀⣾⣿
⣀⡶⢚⣻⢲⣿⠌⣱⣿⠟⣿⡿⠿⠿⠃⠀⠀⠠⠴⠫⣷⣖⠶⢿⢿⣿⣽⠟⠉⠈⢰⡟⣿⡥⣿⣄⣿⣿⠄
⠡⠺⠯⠖⠁⠀⠀⠿⠷⠏⠁⠀⠐⠂⢚⡁⢀⣉⡉⠉⡉⠙⠛⠿⠓⡬⣁⠉⠃⠀⣷⡀⣿⣗⠥⣸⣿⣿⣦
⠀⠀⢐⣒⣀⠀⠀⠀⠀⠀⠒⠀⠠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠸⠦⠉⠀⠀⢠⣿⠀⣼⠁⠀⣿⣿⣿⣧
⢴⣾⠏⣽⡿⢿⡶⣴⣏⣿⠦⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢟⡃⢹⠅⠈⣻⡿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣙⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡄⠀⠁⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢏⣿⢰⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⣿⣿⡿⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢡⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⠷⠀⢸⠀⠀⣴⣾⡇⠀⠀⠀⣠⢆⣴⢰⣦⠰⣄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢦⢸⠀⠀⡫⠾⠃⠀⢀⣶⡆⣴⣭⢠⣭⡆⢶⣶⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣠⠞⠀⠀⠀⠀⢘⣛⡃⣛⣉⢀⣉⣁⢘⣛⡁⠀⠸⣿⡷⣀⣤⣤⣤⡐⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠈⠀⠀⠀⠈⢿⠧⠻⠿⠘⠿⠏⠾⡿⠁⠀⠀⢋⣾⣿⣿⣿⣿⣿⣦⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠻⠎⢿⢸⡟⠱⠓⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⣯⡽⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣭⣍⢛⣛⢛⣭⣥⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⣤⡀⠀⠀⠀⠀⠈⠉⠁⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⢰⣤⠀⠀⠀⠀⠂⣿⣿⡿⢟⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢵⡆⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠀⠀⠀⠀⠛⠿⠿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⡿⣿⣀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⡠⢂⣀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠄⢀⣠⣚⠃⠀⠰⠂⠀⠀⠀⠀⠀⠈⣿⣤⣾⡅⠀⣴⡀
⠀⠀⠀⠀⠹⣶⣴⡄⣠⣶⣾⣿⣿⣿⣿⣿⡿⠁⢀⠠⠀⠇⠀⠐⠂⠀⠉⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡅⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠂⠐⠀⠀⠀⠿⣚⢾⡄⠀⠀⢰⠆⠁⠀⠀⠀⠀⠀⡙⠛⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠈⠛⠢⣼⣦⡈⠛⠩⠷⠘⢃⠔⠀⠀⠀⠀⠀⠀⠈⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⠚⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⡂⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣠⣐⣤⠄⡠⢤⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣀⣙⡂⠙⠚⠴⢂⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⢶⡽⠿⠙⠛⣛⣁⡆⠀⡄⠀⠀⠀⠈⣷⣦⣤⣀⣀⡀⣐⠬⠶⣄⢀⠀⢠⢶⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⢙⣿⡅⠀⠀⣠⢆⣧⠖⠀⠠⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠠⣦⢹⠻⠿⠖⠙⠁
⠀⠀⠀⠈⢶⣤⣴⣶⣿⣿⡄⠀⠙⠛⡸⢀⣡⣜⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠿⣧⢠⣄⠰⠅⣼⣾⣿⣶⠴⠊
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠁⠀⠀⢀⣊⣴⠏⠀⠀⠀⠀⠀⠀⣀⣤⣈⡉⣀⣉⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⢀⡀⡀⣀⣀⡀⢀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠠⣤⣼⣢⠞⠀⠀⠘⢦⣸⠃⠀⠀⠀⠹⡄⠀⡄⠀⣠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣇⣀⣀⣻⡀⠈⢿⡀⠀⢀⣠⡖⢷⡄⢻⠞⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠈⡏⠉⣩⠍⠻⣄⠀⣷⠞⠋⠳⢤⠀⢳⣈⡆⠀⠀⢸⣀⣠⠀⠀⠠⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠓⣷⠚⠁⠀⠀⠙⢾⡇⠀⡀⠀⣄⠀⠈⣿⣀⣤⠶⠛⠙⠀⠁⠀⠀⢀⡤⠚⠻⣝⢩⠻⡏⣏⡙⠟⢦⣀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢼⠄⠀⠀⠀⠀⣿⡤⠞⠁⠀⠘⣇⣸⠋⠁⠖⡄⠀⡃⠀⠀⠀⡴⢋⣀⣀⠀⠈⢻⣴⣬⣤⣧⣷⣧⣽⣦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣸⣇⣤⣦⣶⣠⣏⣀⣀⣠⣶⠀⣸⠏⠀⡄⠡⣧⣤⢶⡤⣄⣼⡇⣯⢉⢹⡇⠀⠀⡇⣶⢶⠲⣆⠀⠀⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣬⣤⣤⣤⣤⣤⣥⣄⣉⣉⠉⠉⠛⠛⠛⠛⠛⢳⠲⠶⠷⠦⠼⣯⣍⣇⣹⡈⠀⡇⠀⠀⡇⠿⠾⠴⠟⠀⠀⣿⣉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠛⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠙⢓⠲⠷⠦⣤⣤⣀⡀⠀⣻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡶⠶⠶⠶⠴⠦⠶⠤⠤⣤⣤⣄⣤⣀⣀⡀⠠⢀⠀⠀⠈⠉⠙⠻⢦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⠤⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣶⡿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠳⣌⠠⠀⠀⠀⢀⠀⠈⠉⠉⠉⠙⠛⡓⠲⠦⠤⢤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⢀⡞⠳⣬⡛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⢶⣶⣶⠓⠚⡛⠓⠓⠺⠶⡶⢴⣤⣄⡀⠀⢂⠌⡃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠃⠀⢸⡳⣄⡞⣉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡌⠁⣀⡀⠁⡀⢀⠈⡀⣵⠟⢳⡄⢍⡓⠦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣞⣯⣹⢦⡀⠈⢇⣸⢉⡽⠋⠀⠀⢀⣀⣠⣤⣤⣤⡄⠀⠠⠀⠙⠲⢤⣄⠠⠀⣀⠀⣀⠙⢳⡟⠂⠠⡸⠁⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⡈⢹⡃⡴⠛⣿⣾⡟⣭⡄⢀⡤⢾⡏⠸⣇⡼⠿⡿⠁⠀⠀⠁⠀⢰⡟⠻⡟⢦⣠⣄⢀⡀⣹⡏⣈⡴⢦⣴⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠛⣟⠁⡴⢻⠍⣿⡿⣠⢾⡇⢸⣧⣞⡉⣩⠟⠁⠀⠀⠀⠀⠀⠈⡿⠛⠁⠈⣧⡶⣄⣤⣼⣏⣉⠷⣴⠛⠖⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡙⠲⢿⠞⠁⡼⠀⢸⣠⢿⣠⠿⢯⣤⡤⠛⠁⠀⠄⠀⠀⡀⠀⠀⢰⣇⣤⡀⠀⢸⣿⠉⡄⢼⡇⢉⣨⣏⢉⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠙⠲⢬⣇⠼⡁⠘⢿⡿⠿⠛⠛⠉⠁⠀⠀⢐⠀⠀⣻⡟⠛⢦⠀⣸⢿⣬⡿⠀⢸⣿⠤⠴⢾⡇⣤⠼⣯⢠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢴⣤⣿⣾⠷⣦⣄⣻⣠⣤⢀⣄⡀⠂⠈⡆⠈⠳⢹⣷⣊⡼⠀⢻⠀⣿⠀⠀⢸⢿⠄⠰⢸⡧⠄⠄⡧⠤⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠈⠹⡇⠀⠀⠉⠻⣏⣿⠟⠋⢠⠀⢀⡗⠀⢠⠏⠠⢻⠀⠀⢸⠀⢸⠀⠀⢸⢸⠖⠒⢺⡗⠶⠒⡷⠲⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣀⡀
⠀⢀⣀⣄⣂⣚⡛⠻⠟⠛⠹⠻⠛⠿⠿⣿⣷⣦⣄
⠀⠈⠙⠻⣿⣶⣏⣁⢘⠒⠒⠒⠶⠦⢤⣬⣬⣝⡻⡷⡒⢤⣌⣀⠄⡝⢿⣿⣷⣶⡆⠤⢄⡀
⠀⠀⠀⠀⠀⠙⠿⣿⣷⣧⣀⣀⠁⣠⣐⣤⠩⠋⣭⣛⠛⠶⣟⠻⣧⣿⢀⣁⣄⡬⠤⠂⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣯⣽⣷⣿⣿⣷⣿⣿⡶⠛⣿⣽⡹⣿⣥⣤⣄⣀⡀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠐⠈⠋⠛⠿⠟⠉⠞⠉⠀⠉⠻⢯⣩⣿⣿⣿⣿⣶⣀⡀⠀⠀⠀⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠳⢿⡟⠏⠁⠀⠀⠀⠀⠈⢮⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣤⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⡯⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡻⣻⣿⠆
⠀⠀⠀⠀⠀⠀⠈⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢐⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⡽⣅⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⣾⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣷⣄⠄⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣯⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⣤⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣧⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠺⣳⣤⣋⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣾⣿⣦⣾⣶⣴⡄⢢⣘⣿⣴⣿⣶⣷⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠃⠁⠀⢻⣏⠀⢀⣿⠀⠀⠀⢉⣿⣶⡖⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠚⠋⠹⠀⠀⠀⠀⢿⣿⡀⠀⢻⡀⠀⠀⢀⣀⣈⠙⠇⢼⣷⠄⠀⠃⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣓⡀⠀⢀⣠⠸⣶⣦⡜⣩⣷⣸⣏⠃⢀⡔⡏⠉⢋⠆⠀⠘⣁⣄⠀⢀⣷⡜⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠐⠿⠿⠂⠚⠑⢻⡀⣄⡠⠿⢿⣿⡿⣦⣩⡀⠀⣠⣿⣧⣤⣼⣿⣿⣷⣟⠁⠀⠀⠁⣀⠟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠿⣦⣀⣻⣃⡠⠞⠉⠁⠀⠀⠀⠀⠀⠉⠀⠘⠛⠳⣽⠆⢈⢿⡍⠻⣿⣿⠧⢤⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠁⠀⠀⠀⢠⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣯⣇⠼⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠸⠷⠚⠉⠀⢀⣠⣴⣇⣤⣀⠀⠀⠀⠀⠘⣭⣙⢦⣾⠿⠛⢇
⠀⠀⠀⠀⠀⠰⢛⣻⣷⣶⡶⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠏⢀⡀⠀⠈⠀⠀⠀⢁⡴⢌⣀⣀⠐⠆⠱⠄
⠀⠀⠀⣤⡀⠀⢘⣿⣿⣭⡤⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠐⠀⢀⠤⠓⠒⠛⠋⠉⠓⠀⡀⠰⠆
⠀⠀⠀⠈⠃⠀⣄⣙⣫⠽⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣀⣤⠦⣄⠈⠁⠀⠀⠀⠀⠀⢰⠀⢠⡴
⠀⠀⠀⠀⣀⡀⠁⢰⣶⢆⣸⠿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⡯⠐⠙⠓⠈
⠀⠀⠀⠀⠈⠁⠀⡈⢻⣿⣿⣄⢻⡀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⣞⠀⠀⠀⠀⠀⢀⡼⠄⠀⠀⠀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢠⣇⡀⠸⠿⢿⠷⡷⡄⠀⠀⠀⠻⠀⠀⠘⠀⠀⠀⠀⠻⡄⠀⠀⠀⢀⣼⣷⠚⢻⣟⣡⡶⠉
⠀⠀⠀⠀⠀⠀⠋⢯⡀⠀⠺⢺⣧⣨⠟⣦⣤⡤⠽⢾⣿⣶⣇⡀⠀⡀⠀⠀⠀⣆⠳⠚⢿⠹⣷⠿⠛⢉⡀⣴
⠀⠀⠀⠀⠀⠀⢷⣄⠀⠐⠢⡶⢿⢿⣿⣧⣈⣷⢲⣬⠡⠤⣀⣋⢀⣀⣗⡴⠊⠀⠀⠠⠆⠀⠸⡄⠀⠡⠙⠛
⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣤⡼⡺⢼⠛⢿⣿⣇⠀⠀⠀⠀⠡⠟⢐⣾⣿⠈⡠⣶⣿⠀⠀⠀⢠⠛⠉⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣤⣠⡓⠚⠋⠁⢻⣆⠂⠀⠀⠆⠋⠀⠰⠚⠛⠋⢙⠀⠀⠠⠀⠂⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣟⣿⣿⣷⣄⣀⠀⢹⠠⢤⡄⢠⣴⡶⠀⠀⠐⠒⠁⠀⠀⠀⠀⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠉⠉⠀⠀⠀⠈⠇⠘⠿⠯⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣆⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣶⠲⠂⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⠀⠀⠀⠀⠘⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⣸⡏⠀⠈⠻⣧⠄⠂⠀⠀⠀⠀⠰⠀⠺⡶⣶⣿⡿⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣦⣠⣦⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣉⡓⣦⠀⠀⠀⣿⡃⠀⢤⡀⠹⣦⡚⣾⡆⠀⠀⠀⠂⣁⣶⣿⡿⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⣣⠟⠀⠀⠀⢌⠛⢣⣜⡻⣄⠘⠶⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣽⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣁⣨⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⣶⡎⠈⢹⣿⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠄⠀⠀⠀⠀⠀⠀⠻⡶⢹⠷⠚⢿⣶⣿⠃
⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⢺⣿⣧⠀⠀⢀⣼⣏⠀⠀⠀⠀⠀⢀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠞⠛⠘⠀⣤⡠⡅⣠⠀⠀⠀⠙⠾⠶⠶⠼⠟⠉
⠀⠀⠀⣿⣿⣿⣷⣦⣤⣤⣤⣤⣽⣿⣿⠀⠀⢸⣿⣿⣦⣤⣀⣤⣶⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⠀⠀⢰⡒⢝⠶⣰⣿
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢙⣭⣉⣇⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠉⠛⠿⠻⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋

⠈⠀⠀⠀⣹⡀⠀⠀⠀⣷⠀⠀⣴⣀⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣄⣠⠶⠛⠉⠁⠀⡀⠀⣿⣷⢠⡿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠸⣇⠀⣿⣿⡾⢡⡏⡿⠈⠙⢄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠞⡄⠀⢀⠔⠀⠐⠂⠐
⡄⠀⠀⠀⠀⠀⠀⠹⣷⣿⣿⢁⣿⣿⠃⠀⠁⠈⢈⡀⢠⣤⣤⣤⣧⡔⠁⢸⠋⡴⠁⡀⢸⡇
⠂⠀⠀⠀⠀⠄⠀⠀⠈⣿⢾⣼⣻⡏⣠⣴⡆⣪⣶⣗⠉⣉⠛⣯⣝⠳⢄⣾⢉⣁⣠⢀⠏⠈⠐⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⣹⣿⣿⣿⣿⣿⡟⠟⠛⠛⠒⠛⠛⢯⡛⠓⣾⢿⣍⣀⣠⠟⠀⡀⠀⠀⠀⠉⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⡟⠁⢸⡀⠀⠀⠀⠀⠀⠹⢾⣃⠘⠓⡾⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠋⠀⠁⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠀⠀⢈⡄⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣄⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⠀⠀⠀⢸⠁
⠛⠒⠀⠘⠀⠼⢹⣿⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⠤⠤⠴⠤⠤⠤⠤⠤⠤⠄
⡀⠀⢠⠀⢀⡀⣾⣿⣿⣿⠀⡀⢠⠈⠀⠀⠀⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠙⣶⠞⢣⠸⡇⡸⠋⠉⠙⣨⣡⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣆⠀⠀⢠⠶⠆⡒⣂⠀⢀⠀⣔⢉⠰
⡷⠛⣿⡾⢻⣶⣧⡄⣠⠃⡟⢁⡶⠂⠀⢠⡐⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠚⠀⠌⠘⠛⠉⠀⠀⠀⠀⠈⠉⠀⠉⠀⡐⠋⠀⠀⠉⠘⠻⡟⠛⠂
⣁⣤⣯⣧⣾⣿⣾⡖⣹⣰⢴⠋⠀⠀⠀⠀⢙⣆⠙⣄⣀⣀⣀⣀⢀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣈⣡⣄⣈⢀⣀⣀⣄⣀⡀⢀⣄⣀⠀⣀
⠉⡁⣿⢹⠗⣿⣷⣧⣽⣿⡏⣉⡔⠁⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠂⠀⠤⢭⣝⣯⡙⠛⣛⠛⠛⠛⠧⠷
⠀⢰⢻⢸⡄⣿⠂⣿⢟⣸⠔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠘⡇⠸⣿⠃⠈⣯⣌⠃⠖⡾
⠲⣶⣼⣆⢻⢠⣾⡟⣿⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⣼⣾⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⡠⠆
⣽⠿⠿⢿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠔⠁⠈
⠀⠀⠀⠘⣋⢩⣿⡛⣯⠈⠙⢢⣴⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡂⢠⠮⠂⣴⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⡀⠀⠐⢒⠉⢤⣼⣿⣾⣷⣽⣿⡯⠭⢭⠹⣿⣿⡂⢀⣴⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡜⡩⠋⠀⠀⠿⠤⠄⠠⠀⠘⠀⠀⠀⢸⣻⡅⢀⣀⠺⠄
⡄⠔⠀⠀⠀⡀⢭⣥⣥⣨⣿⣷⣤⡶⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢀⣄⣠⢆⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡
⣄⣸⢀⣶⣭⣀⡨⠙⣻⣿⣯⣿⣇⣠⣼⣶⣾⠋⢻⠿⠿⢟⣿⣻⣿⡿⢿⣿⣿⣿⠋⣩⡿⠉⠀⠀⡀⢀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠁
⣯⢿⣿⣿⣿⣿⣿⣿⣾⠿⠻⠛⠙⣿⣾⣿⡿⣿⣿⠤⣴⢿⣭⣭⣿⣿⣿⣿⣿⣿⠀⠟⢿⣧⣤⠛⠉⠙⠺⠇⠀⠀⢈⣤⣄⡀⠀⠀⠀⠀⠀⢀⡀
⣟⣿⣿⣿⢿⣿⠋⡭⣄⠀⣀⣀⣼⣿⣿⣍⣟⠉⣃⡾⢣⣴⣶⠶⣶⡿⣿⣿⡏⠉⠉⠀⠀⠻⡇⠀⠠⣤⣤⢆⠀⠀⣸⠄⠈⠁⠀⠀⠀⠀⠀⠀⠈⠲⣤⣄⣀⣀
⣿⣿⣿⣷⠿⠁⢀⣀⣙⣿⡟⠋⠉⠙⣿⣿⣿⣿⣿⣾⡿⠛⠛⠛⠻⣿⣿⣿⣠⣤⣤⣤⣀⣀⣼⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠙⠛⠿⠿
⣻⣿⣟⣱⣟⠻⣧⡄⠀⠀⢈⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡶⠒⠒⢛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡀⣠⣤⣤⣤⣤⣴⣶⣟⠋⠉⠀⢄⣤⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⣿⣽⣿⣆
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠿⢿⣿⠀⠀⢰⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣶⣦⣄⡀⠀⠒⠀⠀⠀⠀⠙⠇⠀⠘⠳⠀⠀⠀⣠⣶⠿⠻⠟⠋⠉⠉⠉⣉⣉⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠈⠙⠶⣤⣤⣄⠀⢀⣤⣄⡀⠚⠈⣀⣠⣶⣦⣶⣾⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀⠀⢼⡟⢻⢷⣿⣿⣿⣿⣸⡿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⠈⠀⠼⣾⣿⣿⣿⣿⠿⢦⠴⠂
⠀⠀⢀⣠⣤⣤⣄⡀⠀⢠⣤⡀⠀⠀⠈⠙⠇⠀⢀⣸⠣⢢⠿⠛⠉⠉⠀⠀⢀
⠀⣴⣿⣿⣿⡿⠿⠛⠓⠈⠙⠻⠀⠀⠀⢀⣰⣾⡉⠀⠈⠁⣀⠀⠈⠐⠀⠀⠀⠈
⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⢿⢆⠀⠈⢳⣄⣀⣸⣄⢶⠶⠿⣿⣿⣿⣿⣿⣶⣶⣿⠟⠁
⠀⠀⣀⣤⠤⠶⠖⠒⠚⠛⠓⢲⢀⡴⠋⠀⠀⣵⣴⣿⣿⣿⡟⠉⠀⠀⠀⠀⠉⢿⡿⠿⠛⠋⠄
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡽⠊⠀⢀⣴⣾⣿⣿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠐⢈⣷⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠐⠂⠈⠁⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣦⣧⣀⣀⠀⡀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁

⠀⢻⣿⣿⠀⠀⠀⠀⠉⠙⣿⣿⣧⠀⢰⣿⣿⠉⠉⠛⠛⠀⠘⠿⠿⠿⠟⠁⠀⣨⣿⣿⠀⠀⣿⣿⠁⢸⣿⣿⡏
⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⡿⠀⢹⣿⣿⣄⠀⠀⠀⠀⣠⣴⣶⣤⡀⠐⠿⠿⠟⠁⠀⠀⣿⣿⡇⠘⢿⣿⠇
⡀⠘⣿⣿⣧⣄⠀⠀⠀⢰⣿⡿⠃⠀⠈⠻⢿⣿⣷⣦⡀⠰⠿⠿⢿⣿⣿⡄⢀⣄⣀⠀⢀⣠⣿⣿⠀⠀⠀⣠⣤
⣷⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⡄⠀⠀⠈⠛⣿⣿⡆⠀⠀⢸⣿⣿⠁⠈⠻⠿⠿⠿⠿⠛⠁⠀⣰⣿⡿⣿
⠏⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢿⣷⣀⠀⠀⣠⣾⣿⡏⠀⠀⢿⣿⣿⣄⣀⣤⣄⡀⠀⠀⠀⢀⠀⠙⠿⣴⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠘⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣿⣇⠀⠘⣿⣿
⣿⣿⣷⣆⠀⣼⣿⣿⠟⠛⢿⣿⣷⡀⠀⠀⠉⣁⣀⠀⠀⢀⣠⣤⣄⡀⠉⠉⠁⠀⠙⢿⣿⡿⠛⠻⠋⠀⠀⠸⢿
⠀⣸⣿⡟⠀⣿⣿⣿⣀⢀⣼⣿⣿⠇⠀⢰⣿⣿⣿⣷⠀⠘⠛⢿⣿⣿⡄⠀⠀⠀⠀⢀⣀
⣰⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣄⠀⢰⣿⣿⣷⣆
⠈⠻⣿⣷⡄⠀⠀⠈⠉⠉⠉⠀⠀⠀⢠⣾⣿⣿⠏⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠘⣿⠈⠻⣿⣿⣿⡏⠉⢿⣿
⠀⠀⠀⣿⡇⠀⢀⣤⡄⠀⢰⣦⣤⡀⢸⣿⣿⣷⣶⣄⠀⠀⠘⣿⣿⣿⣀⡀⠀⠀⠐⠺⠇⠀⢉⠻⠿⠃⠀⢸⣿
⠀⠀⠀⢸⣿⣾⣿⡿⠃⠀⠀⣿⡿⠃⠀⠉⢻⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⠀⠀⣾⣿⣿⣷⣦⣴⣿⡟
⣀⡀⠀⠀⠉⠉⢀⣤⣶⣶⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⡇⠀⠿⠏⠙⠛⠛⠛⠋⠁
⣿⣿⣷⣤⡀⠀⣾⣿⣿⠿⠛⠛⠁⣠⣴⣦⣄⠘⠻⣿⣿⣷⣶⣿⣿⠇⠀⠀⢀⣿⣿⠀⠀⠀⠀⢀⣤⣄⡀⢀⣾
⠋⠛⢿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣾⣿⠿⢿⣿⣷⡀⠀⠉⠛⠛⠛⠉⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⣸⣿⣿⡷⠸⣿
⢀⣤⡀⠉⠛⠛⠛⠉⠀⠀⠀⣿⣿⡇⠀⠀⠁⢹⣷⠀⠀⠀⠀⢀⣠⣤⣀⠀⠘⢻⣿⣿⣷⣶⣾⣿⣿⠟⠁⠀⠉
⣹⣿⣿⠀⢠⣶⣿⣿⣦⣄⠀⢸⣿⣷⣄⠀⠀⠈⢿⣧⠀⠀⣼⣿⡿⠿⣿⣷⠀⠀⠈⠙⠿⠿⠟⠛⠁⢠⣴⣤⣄
⣿⣿⠏⠀⣿⣿⡏⠀⣸⣿⠀⠀⠙⣿⣿⣧⠀⠀⠻⣿⣷⣾⣿⡿⠀⠀⠘⠛⠀⠀⢀⣀⠀⠀⠀⠀⠀⢻⣿⠛⠿
⠀⠀⠀⠀⠸⢿⣿⣟⠋⠁⠀⠀⠀⣸⣿⣿⠀⠀⠀⠈⠛⠛⠋⣠⣤⣶⣄⠀⠀⢰⣿⠿⢿⣷⣤⣤⣴⣿⡿
⣶⣤⣀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠘⢿⡫⠃⠀⠀⠀⠀⠀⠀⣼⡿⠛⠻⣿⣷⠀⢿⣿⡀⠀⠀⠈⠙⠛⠉⠀⣠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠀⠀⠀⠀⠀⠀⢠⣞⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⣇⠀⠀⠀⠀⠀⠀⠀⢠⠧⠘⣇
⠀⢰⠲⣄⡀⠀⠀⣀⡴⠚⠛⣿⠁⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣠⢴⡇⠻⠤⡿⠀⠀⠀⠀⠀⢀⠔⡁⠀⡀⠨⡑⢦⡀
⠀⠈⠳⣄⠉⠉⠉⠁⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⡫⠝⢏⠹⠻⡘⣁⣡⡞⠁⠀⠀⠀⠀⢠⡏⠸⠀⠀⠃⠀⠘⡀⢧
⠀⠀⠀⠈⠙⠓⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣰⡼⠀⠀⠀⠀⠀⠀⠈⠳⣤⣎⣠⣀⣧⠖⠋⠀⠀⠀⠀⠀⠀⠸⣄⢁⠀⠀⢐⠀⢀⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⣀⡀⠀⠀⠀⠀⢀⡤⠤⠖⠲⣄⡀⣠⠖⡾⢄⣒⣻
⠀⠀⠀⠀⢀⡤⣶⢾⢷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣻⣸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⠿⢻⠖⢟⠋⢭⡙⢦⡀⠀⠸⠤⣥⠬⡅⠂⣿⣧⢪⠶⠞⠈
⠀⠀⠀⢠⡏⠰⠋⣶⠛⠦⠘⡆⠀⠀⠀⠀⠀⠀⢀⢼⣲⣺⣺⣿⣤⡀⠀⠀⠀⠀⢀⡏⢠⠃⠀⠈⠀⠈⡆⠀⠱⡀⣧⠀⠀⠀⠀⠀⠙⠋⣉⣿⡋
⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⢸⡞⢻⣾⡟⠙⣯⣇⠀⠀⠀⠀⢸⡀⢸⠀⠀⡆⠀⠀⢠⠀⠀⠇⡿⠀⠀⠀⠀⠀⢠⠋⠅⠀⠉⢧
⠀⠀⠀⠈⠳⣄⣀⣀⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢻⣸⣿⣻⣅⢸⣝⠀⠀⠀⠀⠈⢧⠘⢄⠀⠇⠀⠀⡌⠀⡜⡰⠃⠀⠀⠀⠀⠀⠘⣄⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⣿⠅⠉⠉⠀⠀⠀⠀⠀⠀⠙⠚⠓⠚⠓⠒⠓⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠓⠞⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⡴⠏⡉⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⣿⠦⣀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠈⠀⠀⠀⠱⡄⠀⠀⠀⠀⢸⠇⠣⠀⡀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⡼⠁⠀⠄⢰⠃⠀⠀⠀⠀⠀⢀⣠⡞⠣⡻⡻⢾⢷⡮⢧⡀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⣀⣀⠀⡧⠀⠀⠀⠀⣏⠑⢄⠀⠐⠠⠀⡀⢤⣠⠇
⠀⠀⠀⠀⢠⡃⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⢸⡟⢊⠃⡎⣿⠊⡆⡷⡄⡇⠀⠀⠀⠀⠘⣤⣾⣻⣿⠁⠀⢻⠿⠛⠃⠀⠀⠀⠀⠈⢹⡟⢨⠁⠀⠀⠀⣼⠁
⠀⠀⠀⠀⡸⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⣧⠠⡢⣑⣿⡷⠰⣹⢁⣷⠃⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠸⡇⢈⠀⢀⠀⢀⡟
⠀⠀⠀⠀⣇⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣾⠿⠿⠿⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣶⠦⠞⠁
⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠒⠲⣄
⠀⠀⢀⡴⠊⠉⠉⠉⢢⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣌⣿⡦⢤⣀⠀⠀⠀⠀⠀⢀⡴⠉⣉⡤⢤⡞⠒⠲⠛⠦⣄⠀⠀⠀⠀⠀⣠⠴⠋⠉⠉⠉⠙⢦⡀
⠀⣠⠎⠀⠀⢀⡤⠴⠚⠋⠉⠀⠈⠳⡄⠀⠀⠀⡞⠡⠚⠉⠛⠶⠈⢳⠀⠀⠀⠀⢨⠗⠉⠀⠀⠀⣹⠀⠀⠀⠀⠨⡇⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠑⢦
⠀⡟⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢷⠠⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⣠⣾⢯⡷⣶⣶⢦⣤⠇⠀⠀⢼⡁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⣷⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠘⣦⠆⠀⠀⡌⢀⡏⠀⠀⠀⠀⠀⠉⠛⠙⢯⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⢀⡴⠃
⠀⠈⠓⠦⠤⠳⠤⠤⠤⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠈⠣⠴⠦⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠐⠀⢁⡧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⣒⣉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣶⣿⣿⡿⠁⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠰⢻⣭⡤⢤⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢳⡔⢡⡞⢠⣾⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣾⠁⣽⠀⣨⣿⠈⢷
⠀⠀⠀⠀⠀⠀⠀⡴⠁⢴⠃⢰⡇⠀⠼⣿⡄⠹⣆
⠀⠀⠀⠀⠀⢠⠞⠀⢀⡿⠀⢪⡇⠀⠘⣻⣷⡀⡉⠲⢄⡀
⠀⠀⠀⣠⠔⠁⠐⠄⡼⠁⠐⠚⣇⠀⠀⠟⠛⠳⡄⠀⢵⣪⡓⢄
⠀⢠⠞⠁⠀⠀⠀⡜⠀⠀⠉⠁⠈⢦⣦⡀⠐⢍⠪⡢⣈⠂⡙⢦⡱⡄
⢠⣇⠄⠀⠀⠀⡸⠀⠀⠀⠀⡀⠀⠀⢻⡟⡀⠑⢌⠊⠊⠳⡄⠀⠙⠈⢦⡀
⠜⡑⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⠀⠀⠀⠳⡍⢠⠀⠑⢄⠀⠘⢦⠀⠀⠀⠈⠒⢄⡀
⣯⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠎⡀⠀⠀⠙⣄⠱⣦⠀⠑⠄⠀⠑⢄⠀⠀⠀⠀⠈⠑⠒⠤⣀⡀
⣧⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⠐⣄⠀⠘⢆⢩⢳⡄⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⠤⠤⠤⠤⢄⣀⣀
⢷⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠏⣧⡀⠈⠳⣈⢸⢢⣀⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠦⣄
⢰⠆⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⢱⢄⠀⠙⢤⠀⠸⢳⢤⡀⠀⠀⠀⠀⠉⠺⠯⣷⣲⡢⡤⡄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠈⡏⠀⠀⠀⢠⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⡀⠀⠙⢦⡘⢰⢸⢓⠤⣀⠀⠀⠀⠀⠀⠈⠙⠓⠳⠴⣽⣝⡘⡝⠏⢳⠀⢇⠲⠐⡒⢖
⠀⢱⠀⠀⠀⠀⠇⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠙⢾⡀⠜⠀⡆⢉⢰⠢⡄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⠢⠷⠄⣠⣑⡬⠶⠋
⠀⠈⢆⠀⠀⠀⢈⣄⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠙⠣⣅⠡⠈⠀⡄⢡⠈⠏⢱⢲⢲⢤⢤⢤⢀⡀⣀⣀⡀⠀⠈⣷
⠀⠀⠘⣆⠀⠀⠈⠙⢦⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠙⠒⢤⣐⠀⠁⠘⡀⠀⠊⠌⠌⠌⠌⠂⠢⠑⡙⢷⣰⣻
⠀⠀⠀⠈⢆⠀⠀⠀⠈⠓⣄⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠈⠀⠂⢂⣀⡤⠼⠚⠋⠁
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠩⢣⡄⠀⠀⠀⠀⠑⢤⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢄⡀⠀⠀⠀⠉⠓⠶⡒⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠊⡗⣄⡀⠀⠀⠀⠈⢗⠳⢵⣐⡀⡀⠀⡀⠀⠀⠀⠀⠀⠈⠱⢖⠤⣀⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠁⡇⡋⠖⣄⠀⢠⠼⡄⠀⠈⠙⠳⠷⣰⣤⣀⡐⡄⠀⠀⠄⢀⢀⡍⡍⠁⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠁⠀⠁⠂⢧⣰⠃⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠼⠾⠾⠮⠾⠿⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢳⡤⣿⣀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠙⠛⠋⠀⠈⣯⣠⡿⠶⡄⠀⠰⢦⣴⢛⡉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠉⠙⠓⣶⠀⠀⠀⠀⠀⠈⠻⠶⠶⠃⠀⠐⢻⡇⠀⠁⣠⡼⠷⠒⠒⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣀⣤⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢷⡛⠉⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠠⠤⠄⢀⣀⠀⠀⠀⠉⢀⡀⠀⠀⠘⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠒⠒⠚⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠉⢻⡟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢳⡀⠀⠀⠀⠀⣤⢶⣿⡇⠀⢀⡤⢶⡿⢻⠛⢷⠶⣄⠀⠀⠙⣦⠀⠙⠟⠃⠀⠀⢀⡞⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢀⡀⢻⡄⠀⠀⠀⢀⡟⠸⠇⣴⠿⢦⣿⣤⣼⣤⣬⣷⠼⠷⡄⠀⠈⣧⠀⠀⠀⠀⠠⠟⢀⡀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠘⠃⠀⠹⣄⠀⠀⢸⠁⠀⢰⡇⠀⢸⠃⠀⢸⡀⠀⢸⡄⠀⢻⠀⠀⢸⡆⠀⠀⣠⠆⠀⠘⠃⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠐⠂⠀⠀⠙⣆⠀⢸⠀⠀⢸⡟⠛⢻⠛⠛⢻⠛⠛⢻⡟⠛⢻⠀⠀⢸⡇⠀⣰⠋⠀⠀⠐⠂⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠸⣇⠀⠈⢧⣀⣼⣧⡤⣼⡦⢤⣾⣄⣠⡟⢠⠀⣼⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠻⢦⣹⣄⢸⣃⣴⣣⡼⠋⠀⣾⣼⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣳⣤⣴⡃⢀⡀⠘⢷⣄⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠛⠋⠁⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣭⣥⣭⣿⡾⠂⠀⠀⠈⠛⠶⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡗⠲⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⠂⢸⠐⠂⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⢉⡟⢙⡏⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣳⣄⣼⣠⣼⡃⠘⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠘⢦⡤⢾⡉⠉⣹⢦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠉⠁⠸⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠸⡇⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠠⠄⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⠾⠛⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠟⠛⠉⠉⠀⠀⣤⣤⣤⣬⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠐⡿⠛⢻⣧⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠉⣿⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣀⣀⣀⡀⠀⠀⢸⡇⠀⢸⡿⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⢀⣠⡾⠁⠀⠀⢸⡟⠛⢻⡇⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡟⠛⢻⡇⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠐⠶⣿⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⣤⡤⢤⣤⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠘⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⣿⠀⠀⡿⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠠⠶⣿⠀⠀⠀⢸⠇⠀⣸⠀⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⡀⢀⣿⠀⠀⠀⠀⣧⣀⣠⣧⠀⠀⠀⢸⣧⣀⣸⡇⠀⠀⢸⣇⣀⣀⡇⠀⠀⠀⠀⣿⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠈⠛⠛⠛⣿⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⠛⢻⡿⠛⠛⠛⠛⠛⠛⠛⣿⠟⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡄⠀⠀⠀⣶⠒⠶⢀⠀⠀⠀⠈⠳⢤⡀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⢸⡇⠀⠀⠀⢇⣀⠄⠈⢷⡀⠀⠀⠀⠀⠉⠓⠒⠛⠂
⠀⠠⣶⣾⣷⣶⣦⣄⠀⠀⢠⣿⡏⠀⣸⠀⠀⠀⠀⠀⡥⠀⠠⢘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠨⡛⠿⣿⣿⣿⣧⠀⠘⣿⡄⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢀⢤⣾⣧⠀⠀⠀⠈⡀
⠀⠀⠀⣠⡴⣿⣿⣿⣿⡀⠀⠘⡿⠋⠀⠀⠀⠀⠀⣄⠀⠀⠐⡆⠀⠀⠀⠀⠀⠠⠀⢀⣺⣿⡟⠐⠀⠀⠀⠃
⠀⠀⣞⣡⢤⣤⠄⢋⠁⠘⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⢰⣾⣷⣶⣿⣿⡟⠿⠛⠀⠀⢀⡄
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢻⠯⠻⡟⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠠⠀⠄⠀⠀⠀⢀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠥⣀⣀⡈⠠⠈⣀⠤⠖⠈
⠀⠀⢤⣔⡛⠉⠛⣛⣳⣦⡀⡀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠈⠻⢷⣤⣴⣭⣽⣭⣿⣿⣤⣀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠆⠒⠒⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠙⠿⣿⠂⠀⠀⢠⡀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡇⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⠀⣠⣤⠄⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠘⡇⠀⠀⢠⣶⣾⠟⠻⣿⣷⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡇⠀⠀⠀⠀⡇⠀⠀⠀⠽⣿⣦⣴⣿⡿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⢿⣦⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠹⡄⠀⠀⠀⠙⠛⠉⠋⠁⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠙⠿⣧⣠⣀⣀⠀⣠⣤⣰⣦⣾⠟⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠀⠀⠐⠒⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⢯⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠓⠘⠀⣦⡀
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠰⠏⢩⣿⡿⣭⠁⠀⢀⣴⣦⡤⣀⠀⠀⠀⣿⣿⣦⣤⣶⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢰⡷⢶⢀⠙⠁⠀⠄⣤⡄⠀⠀⠙⠞⠉⠁⠀⢰⣯⢞⣻⠿⠞⠁⠀⣀⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣦⣸⣿⠦
⠈⠀⠀⠶⠀⠀⡀⠀⠀⠄⣴⣦⣦⠀⠀⠀⠀⠈⢁⣼⣷⠀⠀⠀⠀⠙⣏⠙⠛⠛⠛⠋⠙⢢⣶⡔⠁⢀⡔⠆⠀⠀⠀⠘⠛⠓⠂
⠀⠀⠀⠀⠀⢸⡿⠀⠲⠖⠀⠈⠛⠀⠀⠀⠀⢠⣟⡵⢫⣦⣵⠂⠀⠐⠁⠀⣤⠀⢶⡀⠰⢟⡟⠻⢄⢾⡷⠤⡀
⠀⠀⠀⠀⠀⠠⢆⡆⠀⠀⣠⣶⡆⠀⠿⠿⠆⣼⠅⠀⢸⡿⡟⠀⠀⠀⢀⢤⣽⣶⠀⡿⠠⠈⣟⠀⣿⣎⠀⠀⣻⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣤⣾⣿⣟⣡⠀⠑⠃⠒⡋⡅⡠⢋⢁⠛⣤⠀⠘⡄⡙⠂⣹⠯⠀⠀⠈⠀⣤⣄
⠀⠀⠀⠀⠋⠿⠀⠀⠀⢸⣦⡀⠀⠈⠻⣿⣿⣿⡿⠋⠀⢀⠤⣨⡖⢫⢣⣡⠀⢇⡅⢣⣴⠇⢿⡾⠛⢷⠀⠀⠺⣄⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠉⠁⢰⣦⣤⠈⢯⣟⡛⠀⠀⠈⠚⠋⠪⣵⣦⣬⡁⠀⠡⠵⢰⠀⠀⠰⣦⠟⠀⠀⢠⡄⡦⠀⠉⡉⠀⠘
⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⣲⣂⣔⡏⠛⢁⠂⣹⣿⠀⢀⡄⢠⡆⢺⣿⣿⣻⡟⣆⡀⠀⣀⠀⠀⠀⣎⢝⡉⢢⣤⠈⡡⢾⠛⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢸⠢⡤⠜⠪⡿⠏⠁⠀⣈⣄⣻⣿⠵⠛⣇⢸⡇⣸⠉⢉⠟⠉⢹⠙⠯⣾⣷⡶⠀⠉⠀⠉⣹⠲⠤⢥⡤⣀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠘⢧⡝⣈⢄⠐⠀⢁⣴⣿⣿⡜⣱⢦⡄⢸⡸⡇⡇⡴⢁⡤⢞⣵⣿⣿⣍⠛⠉⠀⠀⠀⠀⢸⠂⠀⠈⢽⣭⣷⠄⣸
⠀⠀⠀⠀⠀⠀⠀⡈⣧⣬⠀⢀⠿⢿⢉⣿⣿⣿⣻⠀⣌⢢⢟⡉⡉⠳⡫⠴⢾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⡀⠀⣰⣾⡿⣷⡰⠁
⠀⠀⠀⠀⡈⠂⠀⠀⠀⠊⠀⠸⡆⢸⠎⡼⠁⠐⢙⡀⠀⠉⠈⣶⠈⠂⠟⠿⡍⡫⢯⠉⠀⠀⣰⣶⣤⡀⠀⠀⠁⠀⠉⠺⣿⠛⠝⠟
⠀⠐⢄⠀⠑⠀⠀⠀⠀⠀⠀⠀⣏⢨⡴⡇⠀⣰⠟⣿⣇⠀⠀⠋⠀⠀⠀⠁⠊⣵⢋⣀⡀⢰⡿⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⠃⠁⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢙⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠦⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⣸⡁⣷⠴⠄⠳⡤⠀⢀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣉⠉⠛⢶⡔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢍⠑⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⣀⠐⠀⠀⠀⠠⡶⠀⠄⢀⡀⠀⠀⠀⠈⠈⠂⠈⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠐⠒⠧⠀⠀⠀⠀⢐⣋⡤⠂⠁⠀⢁⡀⠐⠃⠀⠀⡄⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠞⠀⠀⠀⠀⠀⠀⠑⡀⠀⡜⠞⠀⠀⠄⣰⠯⠀⣦⡠⢆⣈⠁⠈⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⡀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣦⣄⠀⣼⠿⠦⠐⠛⠒⠀⠥⢌⣉⠗⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠅⠁⢸⡀⠀⠀⠀⠀⠀⣴⣿⡀⣏⣼⢛⣋⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠈⡠⠂⠀⠀⢰⠃⡇⠀⠀⠀⢸⡯⣉⡹⣏⣿⡉⢤⣺⠃⠀⠀⠀⠀⠀⠀⣄⠀⠇⢀
⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠈⠀⣠⠆⠀⡼⠀⣄⣀⡤⠔⠛⠉⢙⣷⡟⡧⠙⠁⠀⠈⢢⠀⠀⠀⠀⠰⠞⢪⠀⠟⣠⣚⠅
⠀⠀⠀⢁⠤⠀⠐⠒⠀⠀⠀⠀⠠⠔⠊⠁⠀⡰⣡⢞⠍⠉⠀⠁⠆⣠⠋⣼⠟⠁⠀⣀⣤⠄⠈⠓⢏⠀⠃⠀⠀⠘⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠠⢀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡠⠊⡜⠁⠀⠀⠀⠀⠀⢰⠃⡀⡈⠀⠀⡾⡿⣮⠏⠀⠀⠈⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⠀⠀⠀⢧⠀⠐⠄⠀⠀⢀⡏⡐⠀⢣⣀⠄⠂⠉⠁⠀⠀⡠⢂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⣀⣀⠀⠠⠀⠈⠀⠈⠳⢦⠤⠤⠴⠊⠀⠀⠀⠀⠙⠦⠀⠀⠀⢂⠀⠔⠁⠀⠀⠀⠁⠀⠀⠐⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠓⠒⠒⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣖⠋⠉⢰⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⢤⣼⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠉⠳⢤⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⣠⠖⠒⡶⠛⠒⠒⠒⠒⠒⠒⠚⠓⠲⣄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⡇⠀⠀⢀⣴⣿⣿⡿⠿⠛⠛⠛⠻⣿⡿⣣⠞⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⣸⠀⠀⢰⣿⣿⠟⣡⣶⣾⣿⣿⣿⣿⡿⢰⣧⣄⣠⠟⠀⠀⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣀⠄⣩⠴⠚⣉⣁⣤⣀⡈⠙⢶⣄
⠀⢠⡏⠀⠀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⠞⢁⡴⠛⠉⠀⠀⠀⠙⣆⠀⣿⣧⡀
⣠⡾⠳⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡼⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣷
⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡾⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢰⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⢸⡀⠀⠀⠀⠀⢀⣠⠞⢁⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣦⣌⣻⣿⣿⣿⣿⣿⣿⡌⢧⡀⠙⠲⠶⠶⠒⢋⣡⣴⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⡿⠟⠀⠙⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣁⣀⣀⣀⣀⣀⣈⣛⣻⣿⣿⣿⣿⣿⣛⣋⣀⣀⣀⣀
⣿⣿⠋⢙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⣠⢸⣆⠀⢀⣴⣑⡄⠠⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠔⠀⢠⣄⢀⡐⢌⠐⣟⢹⣿⣿⡶⡻⢿⠉⣀⠐⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⡙⠉⠴⠿⠋⠤⠃⢀⣤⣍⣴⡿⢿⣷⣤⣠⣄
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣧⣿⣯⣀⣀⣀⡀⠂⠀⠀⠐⣢⡤⠶⡟⠇⠸⠟⠉⡧⠈⠁
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠟⣛⣡⢄⡀⣀⢀⡀⠄⢨⠍⣉⠁⣈⣙⠃⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⠛⣯⣵⣾⣿⣿⢏⡾⣿⡝⠂⠉⠛⣹⣿⣷⣶⣾⡯⣹⠟⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢠⡄⢤⡴⣻⣿⣿⣿⣿⢿⣿⡖⣿⣦⡀⠀⠐⠈⠲⣿⢿⢛⡼⠃⠀⢀⢆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠳⡀⠈⢕⢋⡡⠞⠛⣻⣵⣣⣿⠿⣿⣻⠏⣷⡿⠋⣶⠴⠀⠐⠉⠀⠀⠀⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠄⠈⠻⠱⣟⠊⠹⢻⣧⣷⣼⣿⣷⠀⠀⠚⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠙⠛⠛⠛⠟⠛⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠛⢿⣿⣿⣦⣤⣾⣿⣿⠟⠋⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠋⠀⠀⠀⠙⢿⣿⣿⡿⠟⠁⠀⢰⠆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⢠⡄⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣠⡀⣀⣄⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣤⣠⣶⠋⠀⠀⢀⣴⡤⣤⠘⠿⢿⡧⢘⣟⡃⠀⣀⠀⠀⣙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠈⣛⣃⣈⢁⠀⠀⠀⢘⣻⣿⣾⠟⠀⠀⠛⠴
⠀⠀⠀⠀⠀⠀⠀⠾⠀⢈⠉⠉⠙⠃⢴⣶⣦⠀⠀⠿⣿⡿⢸⣿⣷⠀⠉⠉⠉⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⣾⢻⣿⠀⠀⠀⠀⠀⢸⡏⣿⡀⠀⠀⠀⠀⠀⠀⢹⡿⣿
⠀⠀⠀⠀⠀⠀⢠⢿⡇⠀⠀⠀⠀⢠⡏⠘⡟⠀⠀⠀⠀⠀⢸⡇⠸⡇⠀⠀⠀⠀⠀⠀⣾⠁⢿⡀
⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠈⠃⠀⠁⠀⠀⠀⠀⠀⠀⠙⠀⠈⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠙⠛⡷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⡤
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣴⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⣧⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⣠⣿⠏⠀⠀⠀⠀⣤⠛⠙⣿⣄⠀⠐⣄⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣶⣤⡤⠀⡀⣠⣿⣿⣿⠋⠀⡀⠀⣠⣴⣞⠁⡀⠀⠀⠙⣳⣶⣿⣿⣿⠷⠦⠀⠸⠇⣷⣤⡄
⠀⠀⠀⠤⠈⣋⣾⣿⣯⣿⣿⣿⣿⡟⣿⣿⣶⠿⢛⡿⠟⠁⢤⣾⣿⣿⣿⣿⣯⠱⠶⢶⣄⠀⢀⠈⠁⠀⠄
⠀⠀⠀⠰⣾⣯⣿⣿⣾⣾⣿⣿⣿⣷⣿⣿⣿⣷⣾⣷⣾⣾⡆⠉⢻⣽⣿⣿⠿⠁⠀⢀⣨⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣟⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠋
⠀⠀⠀⠀⠀⠀⠻⠿⡿⣿⣿⣿⣿⣿⣏⠙⠻⣿⣿⣿⣿⡛⠀⠂⢀⣀⣠⣬⣯⣭⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣶⣶⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⣿⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠿⠿⠿⠟⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣽⣧⣿⢹⣟⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⢀⡛⣿⡿⣧⣿⣿⣿⣿⣿⣿⣿⡷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⢆⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟
⠀⠀⠀⠀⢠⣾⣶⣿⣾⡗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠚⠛⠉
⠀⠀⠘⠀⢨⣿⣿⣿⣛⣿⣷⡟⠉⢻⣿⣿⣿⣿⣿⣯⣽⠄⠀⠀⠀⠀⠀⢀⣟⠐⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀
⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⡿⣦⣠⣼⣿⣽⣿⣛⣻⠻⢫⠀⠀⠀⠀⠀⠀⠁⠈⠉⠑⠲⠀⠀⡄⠀⢠⠘⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⡀⠃
⠀⠀⠀⠀⠘⣟⢿⣿⣬⡿⣾⣿⢹⣿⣿⣿⣿⣿⣝⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣧⠘
⠀⠀⠀⠀⠀⠈⢣⣋⣿⢺⣿⣿⣸⣿⣿⣿⣿⣝⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠈⣻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠘⠾⢿⣿⣟⣹⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠒⠂⠁⠀⠀⢀⡀⢠⣴⣾⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠻⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡷⠀⠈⠻⣿⣿⠟⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⡆⠂⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⢰⣄⣀⠁⠀⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠤⠀⠀⡀⠀⠀⡁⢀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠤⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠠⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⢈⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠐⠀⣀⣀⠦⣠⣀⠄⠀⠀⠀⠀⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠊⣁⣤⣶⣶⣖⣷⣶⣿⣷⣦⡌⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠒⣹⣅⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠛⣿⣿⣷⣴⣿⣿⡿⣿⣿⣿⣿⣆⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠄⠀⠈⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⢀⣈⣸⣡⡦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⣠⣭⣿⣿⣿⣿⣿⡿⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⣁⡼⡿⣼⣿⣐⡿⣥⠀⠀⠂⠀⠀⠀⠀⠀⢠⣤⠤⠤⠶⢶⣿⣿⣷⣶⣿⢿⣿⣿⡟⣿⡟⢉⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⣙⢧⣿⣋⣏⠦⣧⠀⠀⠃⠀⠀⠀⠀⠀⠸⣇⣀⣀⣴⣿⣿⡿⢿⢿⠟⠀⣿⡿⠟⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠯⢓⡭⡿⠢⠚⡁⢀⠄⠀⠀⠀⠀⠀⠀⢢⡈⠉⠙⠿⠶⠶⡶⠶⠞⠛⠋⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠂⠉⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣤⣤⣄⡠⠠⣤⡄⠪⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⢟⠆⠀⢐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠶⠲

⡄⠀⠀⢠⠀⠀⠀⠀⠀⠘⠢⢌⣉⡙⠒⠣⣄⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⢘⣷⡂⠀⢻⠀⣇⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡇⠀⡇⠀⠀⠠⡒⡉
⠀⠀⢀⠎⠀⠀⠀⠀⠀⣤⣀⡀⠠⢈⠑⠀⠀⠀⢀⠘⠀⠀⠃⠄⠀⣠⣑⣒⡮⣧⠠⠀⠀⠏⣸⠀⠸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠸⣄⠀⠀⠄⣂⡱⠭⠖
⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠁⠀⢄⠀⠀⠈⢀⠀⢉⠉⠿⣷⣐⠀⠐⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠑⠂⠠⠔⠒⣂⢀
⠉⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠈⠈⠰⢀⠄⠀⠀⠀⠀⠀⠀⠡⠈⠀⡀⠀⠀⠤⡀⠣⠴⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⠐⣆⠐⠈⠉⠈
⠄⠀⠀⠄⣀⠤⠴⠶⠌⠀⡢⢂⡤⢖⣠⠴⠤⠀⠑⠀⠠⠀⠀⠨⡐⠀⠀⠀⠀⠄⠄⠔⠉⣤⠶⠖⠛⠐⢤⡤⢊⠔⣝⡲⢤⣄⡀⠀⠀⠀⠐⠀⢀⠀⠈⢦⠀⢀
⠁⠀⢀⡀⠀⠀⠀⠀⠀⢀⡰⠋⡴⠫⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢸⠀⠸⠀⢀⠴⠶⡋⠡⣴⡁⡢⣄⣙⠛⠲⣍⠳⠄⠀⠀⠀⠈⢣⡀⠀⠀⠀⠑
⠁⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠜⡠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⢀⠈⠀⠀⠀⠁⠀⠈⠘⠉⠈⡁⠀⡈⠆⠆⠀⠂⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠀⠀⠰⠀⠀⠠⠀⢁⡘⢦⠢⡠⡀⢦⣄⡤⠴⠶⡷⢶⡳⣶⣴⠖⠂⡀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠀⠀⠈⠀⠠⠂⠀⣀⠤⠶⣤⡀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠈⢿⠀⠂⠙⢦⠤⠠⠤⠀⡊⠠⢫⡾⠃⡀⠐⠄⡀⠀⠀⠀⡀⠀⠀⠀⠠⢀
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠀⠀⠔⠀⡠⠋⠀⠀⣀⡈⠙⠧⠊⡑⢀⠈⠀⠀⠀⠀⠂⠲⣆⠀⠀⠀⠀⠀⠀⠀⠠⠐⠹⠉⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⡌⢰⢃⠀⠀⠀⠀⠙⠲⢄⠀⢀⢘⡤⠠⠀⠀⠀⠀⠀⢀⡉⠳⠲⠄⠀⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠤⠀⠀⠀⠀⢀⡀⠀⡀⠠⠤⠤⡊⠀⠈⣸⢡⠐⠄⠀⠀⠀⠀⠔⠡⢂⢚⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠀⠀⠑⡀⠀⡀⠀⠀⠀⠀⣤⠔⠊⠑
⣀⣒⠒⠢⣄⡈⠂⠁⠀⠀⠀⣿⠀⠀⠀⡧⠈⠸⣆⠀⠀⠀⣟⣠⡇⢸⣸⡅⠀⠈⠉⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⢠⠔⠁⠊⠀⣀
⡁⠅⠀⠀⠀⠑⣄⠀⠎⠀⠁⣈⢧⠀⠀⠈⠀⠀⠌⠙⢦⡄⠈⠸⠳⠈⢳⢳⡒⠂⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⠂⠈⠀⠂⠤⠀⠀⠀⠐⠊⡀
⠀⠀⢀⣸⠀⢠⡏⡀⠀⢄⠈⠁⠀⠣⡀⠀⠀⠀⠀⢀⣒⣛⡷⡀⠄⠀⢸⢀⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠄⠀⠊⠀⠀⠀⢠⠀⠐⡀⡀⢰⠏
⠀⢌⢢⠇⠀⠞⠀⢁⠔⠀⠀⠀⠀⠀⠈⠀⠄⠠⢒⣀⠦⢤⠮⢯⣅⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢠⠆⢀⡎⣐⠋⠂⠀⢀⣀⠈⣆⢣⠀⢠⡞
⠫⠔⠇⣂⠊⡁⠑⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠜⠁⠀⠀⠀⠀⠋⠉⢀⠔⠈⠀⠀⠀⠀⠆⠀⠠⠁⠀⠀⠂⠀⢠⠏⠀⡚⢀⠁⠠⠀⠀⠀⠍⠈⢿⡌⣦⠟⢁⣰
⡥⠬⡂⡈⠺⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠄⠀⢀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃⠀⠠⠞
⠖⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⢠⠀⢀⣚⡀⠀⡃⠰⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠤⠤⢖
⠉⠀⠀⡀⠀⠀⣆⠀⠀⠀⠀⠐⠀⠀⣠⡤⢤⢀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠋⠉⠙⠳⣥⣾⡀⠀⠀⠀⡄⠀⠀⠈⠁⠀⠰⠚⠉
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⣠⣾⠗⠋⠱⣸⡇⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠐⡇⣾⡠⠐⢉⣛⢶⣤⢫⡟⣦⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣶⣯⢟⣭⣾⠧⣴⣿⣗⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⡞⠠⢫⢷⣎⠂⠀⠛⢿⣻⡝⡞⡅⠀⠁⠀⠰⠄⠀⡀
⠠⠄⠀⠀⠀⠀⠀⠀⠀⣻⠿⣽⣿⠿⠋⢰⡿⡜⢞⡷⠂⠀⠠⠀⠀⠀⠀⠀⠀⢈⠀⠐⠀⡀⠀⢹⡀⠃⠸⣎⡘⠦⣄⡀⠸⠿⣧⢳⣷⡀⠀⠄⡀
⠀⠀⠀⠀⠁⠐⠠⢄⡀⣿⠁⣿⠉⠀⠀⣾⠀⢃⡘⠇⡁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠈⢱⣄⠀⠈⠈⠂⠈⠻⣦⡀⠙⠀⡽⢻⡀⣀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠀⢀⠱⣏⠀⠫⣀⢚⣿⣃⡼⠡⠑⡌⠈⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠁⡀⠒⢀⣂⠐⣛⣷⡾⢿⣦⡈⢀⠂⠀⠀⠀⠁⠀⠀⢁⣀⣀
⣲⠀⠄⡀⠀⠀⠄⠀⠁⠈⢓⠶⠤⠽⠷⢁⠐⢀⠾⣍⠀⠄⠀⠀⢀⡠⠖⠐⠚⢶⣄⠄⠈⠀⠀⠀⠈⠀⠀⠈⠀⠈⠀⠁⠠⠈⠀⠉⠁⠀⠀⠀⠀⠀⢀⡜⣩⠄⠂
⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠋⠉⠙⠉⠛⠉⠀⠋⠱⢀⡜⢡⢟⠀⠀⠄⢤⡁⠙⢷⡐⢂⠀⠰⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣪⠞⢀⡀
⢣⢳⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠞⠀⡔⠋⠀⢁⡶⣀⠀⠀⠀⠙⠢⠀⠕⡡⢀⠂⠀⠀⠀⠀⠀⠀⠌⠀⢀⠀⠀⠀⠀⠀⠀⠒⡩⠚⡁⣴⣏⠀⢐
⠀⠃⠋⠱⠀⠀⠀⠓⠆⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠰⡇⠀⠀⢞⠐⠈⡆⠀⠀⢠⡄⢡⡎⠀⡟⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠈⠀⢠⠴⡑⢌⠠⡁⡈⠉⠀⣼
⠘⠘⠀⠀⡇⠀⠀⢀⠀⡈⠢⣀⠀⠀⠁⠀⠀⠀⢱⠀⠡⠀⠀⠈⠂⠈⠳⣄⠀⢨⡅⣧⠁⡆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢠⡎⠀⡇⠘⠀⠀⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⡀⠀⣀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠶⠿⠿⠿⠿⠷⣶⣼⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⣿⣄⡀⠀⠀⠀⠀⠘⠋⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠈⠙⠛⢻⣧⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣶⣦⠀⠈⢿⣆
⠀⠀⠀⠀⣠⡾⠋⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣘⣿⡄
⠀⠀⢠⣾⠏⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡏⠁
⠀⢠⣿⠃⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣤⣴⣶⣶⣶⣶⣶⣤⣤⣄⣀
⢀⣿⠃⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣶⣤⡀
⣼⡏⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠶⣶⣦⣤⣀⠀⠀⠉⠻⣦⡀
⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠘⣿
⣿⡇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢸
⢹⣧⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⢸
⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠈⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⣠⣿
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠾⠟⠋⠁⠀⠀⣠⣶⠟⣹
⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠙⠻⢷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⠿⠋⠁⢠⣿
⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣆⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠿⠛⠉⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣦⣤⣀⠀⠀⣀⣤⣶⠾⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣀⣡⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣴⣦⣀⡟⠀⢸⣿⣧⡀⠀⠀⣠⣶⣷⡀⠘⣿⣷⣶⣤⡀⠙⣿⣿⣶⣤⣄⠀⢻⣿⡄⢰⡿⠛⠻⠿⠏⠀⠿⠿⠿⣦
⡟⠉⠉⠳⠶⠟⠉⢹⣟⣿⣿⣿⠁⠉⣿⠏⠁⠀⠀⠙⣿⣿⠟⠉⠙⣿⡟⠀⠀⠙⣷⣾⡄⠀⠀⠀⢀⣤⣄⡀⢀⣏⣸
⠿⣦⣶⣶⡆⢠⡎⠙⣟⣿⣬⣿⠀⣴⡏⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢸⣧⠀⠀⢀⣿⡿⠛⠒⠲⢾⣿⠀⢈⣛⠉⠉⠙
⣠⣿⠟⣨⣤⣴⣿⠀⣿⠉⣠⠟⠀⢿⣿⣦⣀⠀⠀⠀⣿⣿⣦⣄⣀⣀⡛⠿⠿⢛⣡⣀⠀⠀⠀⠀⢻⣿⡿⠛⠛⠶⣾
⢿⣧⣴⡟⠉⣿⠏⠀⠈⣿⠏⠀⠀⠀⠉⢻⣿⣷⠀⣠⡀⠈⠉⠉⠙⢿⣿⡿⠂⣿⠟⠛⢧⠀⠀⠀⢠⡟⠀⠀⢠⣄⠙
⠀⠹⣿⡇⣸⣿⣄⣀⣠⣿⡀⠀⠀⠀⢀⣴⡿⠁⠀⣿⣿⣄⡀⠀⢀⣾⡏⠀⠀⢸⣷⣤⠈⣷⣦⡶⠟⠁⢀⣴⣿⣿⣿
⣀⣴⣿⠇⠈⠉⠉⠉⠉⠙⣧⠀⠀⢰⣿⣿⣧⣀⣠⠟⠉⣹⣿⠟⢋⣿⣷⣤⣴⣿⣁⣿⣷⠋⠀⡾⣿⠇⠘⠋⠀⠈⣿
⠛⠉⠁⢠⡾⠷⣄⠀⠀⠀⣿⠳⣤⣀⠈⠉⣻⡟⣡⣶⣾⠟⠛⠒⣿⡅⣸⡟⠁⠀⠀⠙⣧⡀⣠⣧⡼⣷⣴⣶⣄⢸⣿
⡀⠀⣠⣿⡇⢀⣽⣶⣤⣾⠿⠟⠳⠿⢿⣟⣉⣿⡿⠟⠁⠀⠀⠀⢸⣧⣿⡅⠀⠀⠀⠀⠘⢿⣿⣏⣀⣠⣌⡉⠛⣾⣿
⠿⠛⢿⣿⠋⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣠⣿⣿⡝⣿⡿⠛⠛⢿⡄⠀⠈⠉⠉⠛⣿⡉⢻⣻⡿
⠀⠀⠈⣿⣦⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣾⡿⠋⠉⠉⠙⢿⣷⠠⣤⣾⡇⠀⠀⠀⠀⠀⣼⣧⣾⣿
⠀⠀⠀⣿⣀⣻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠈⠻⣿⣄⠀⠀⠀⣠⣿⠃⠈⠙⢷⣀⠀⠀⢀⣴⣿⠁⠀⢻⣿
⣀⣤⣤⣀⠉⣻⣿⣦⣄⣀⣀⣀⣠⠴⣿⣿⡇⠀⠀⠀⠀⢠⠛⠉⢀⣴⣾⡿⣇⠀⠀⠀⣸⣿⣋⣻⠿⠿⣿⢧⣴⠋
⠻⣿⡟⠉⠙⣿⠉⣿⡏⠉⠉⣫⣥⣴⣾⣿⣿⣤⣀⠀⠀⣿⣦⣤⠞⠛⠛⢦⣀⠙⣶⣿⡟⠙⢿⡁⠀⣠⣿⡾⠋
⣾⡿⠃⠀⣼⣿⡇⠈⠑⢲⣾⡿⣿⠋⠀⠀⠀⠙⢻⣿⣦⡍⠋⠁⠀⠀⠀⠀⠹⣿⣮⠻⠿⠿⣿⣿⡄⠻⣿⠀⠀⣶⣶
⠋⠤⠄⠀⠘⠛⠓⠀⠀⠀⠛⠀⠘⠀⠀⠒⠒⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠐⠛⠛⠂⠀⠀⠀⠛⠁⠀⠙⠂⠀⠘⠂
⠀⠢⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣙⡛⠿⠆⢀⣀⢀⡀⠀⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⠛⠇⠀⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠉⠉⠛⠉⣩⣴⣾⡏⠀⠀⠀⠀⠀⠀⠀⠉⠈⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣄⣀⣀
⠀⠀⠀⠀⢰⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡿⠋⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣶⣬⣭⣭⣭⡄
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⢀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⠈⠙⠁⠀⠈⢿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣻⣿⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢧⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠙⠋⠁⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⣠⣤⠀⠀⠀⠀⠀⠀⠻⣿⣧⣭⣭⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⡀⠀⠀⢀⣠⣀⣀⣀⣀⣸⣿⣿⡇⠀⠀⠀⠀⢀⣠⣌⡛⠛⠛⣋⣡⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣀⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠀⠀⣿⣿⣿⡿⢋⣭⣭⣿⣿⣿⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠙⠿⣿⣿⣿⡿⠋⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠋⠀⠀⠠⠴⠶⠾⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠙⡏⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣷⡆⣿⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⢸⠇⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⣿⢡⡟⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⣾⠀⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡏⣸⣧⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⢸⢠⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠿⠋⠀⡿⢸⠇⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡌⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠸⡾⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡾⠿⠻⠛⠻⠉⠉⠉⠁⠁⠉⠙⠋⠋⢻⡿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠐⠛⣻⣠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡴⠁⡿⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⢀⣀⢀⣀⣒⣶⣶⡦⢀⢀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⣴⣦⣦⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⡦⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢈⣿⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣄⣀⠀⠐⠟⠻⠀⠀⠀⣼⣶⣦⡄⠀⠀⠀⠀⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⢿⢿⣿⣷⣾⢿⣿⣻⡻⠈⠁⠘⠛⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣟⢿⣽⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣧⣸⠁⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣿⡡⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣿⢤⡄⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡘⠁⠀⢀⣠⣴⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⠷⠶⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣠⣄⢠⡄⣄⣤⣠⠤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠛⠓⠚⠓⠋⠛⠛⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⡀⠈
⠀⠀⠀⠀⠀⢠⡎⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⣾⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⡋⠀⠰⠀⣼⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠂⠺⠃⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⡀
⠀⠀⠄⡀⠉⠁⢀⡀⠀⢹⣴⡴⠯⠉⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢠⡄
⠈⠀⠀⠀⠈⠠⢾⠕⠂⠀⢆⡀⣐⡫⠂⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠰⠂⠀⠤⠂⠀⠀⠀⠀⠀⠔⠉⠙⠀⠉⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠙⣄
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠖⠃⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⣧⠀⠤⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⠲⡲⣄⣌⡟⠀⠀⠊⠈⠛⠄⠀⢀
⠀⢆⣦⣶⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⣀⠀⠀⠀⢂⡢⠄⠈⢉⠁⠀⢔⣲⡀⠠⠈⠉⠁⠠
⠀⡮⢹⣗⠒⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠽⠋⠰⠞⠛⣘⠃⠀⠀⠀⠋⠁⡀⠀⠀⢀
⡰⣅⠠⠑⣤⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠬⣠⠏⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠁
⠁⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡴⠈⠀⠀⠀⠁⠀⠲⠄⠀⢀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⡇⠀⠀⠻⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠾⠿⠿⠿⠿⠿⠿⠶⢶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⢁⠀⠠⠠⠐⠐⠐⠀⠀⠀⠀⠄⠀⡉⠙⠻⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⡠⠔⠈⠀⣤⡰⠒⣄⡎⢹⠄⣤⠀⠀⠀⠀⠀⠁⠢⢀⠈⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢀⠀⠁⠀⠀⠀⢠⠇⣇⣰⠛⠦⠞⠀⠉⠁⠀⠀⠀⢀⣾⡇⠀⠈⠀⡀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠄⠀⠀⠀⠀⡀⠀⠈⠀⢠⡄⠀⠀⠀⣤⣠⠀⣠⠶⡶⢸⠟⠀⠀⠀⠀⠀⠠⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⠈⠀⠀⣼⡇⢸⠇⡤⣴⠌⡟⢡⡇⣸⠃⣯⡟⢰⡏⣼⣃⠿⠤⠃⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣿⣿
⠀⠀⠀⠀⠀⢀⣿⠃⢀⠂⠀⠀⢰⡏⣷⡟⣾⢁⡟⣸⣇⠼⠵⠻⠞⠀⠑⢉⣉⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠸⠀⠙⠃⠙⠋⣉⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⣹⡏⠀⣠⡄⢘⣿⡇
⠀⠀⠀⠀⠠⠿⠀⠐⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣟⣉⠉⠈⢣⡄⠀⣾⣿⡄⠘⣿⡇⠀⣿⣿⠋⢻⣷⡀
⢠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠟⠉⣉⠉⢻⣿⣿⠀⢠⠀⢻⣿⣿⡀⢰⡄⠙⠀⢻⣿⠇⠀⠛⢻⣄⣈⣁⣠⣾⣿⣿⡄
⠀⠻⣿⣿⣿⡿⠛⠛⠻⣿⣉⡁⢠⣤⠀⢸⣿⠀⢸⡟⠒⠚⢻⡟⠀⣠⡤⠀⠻⠟⠃⢈⣙⣦⣠⣼⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠹⣿⡟⠀⣼⣿⡄⠈⣿⡇⠀⣠⡀⠉⢿⡄⠈⠛⠃⠀⣿⠁⢠⣤⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⣭
⠀⠀⠀⢹⣿⡀⠸⠿⠇⢀⣿⠋⣀⣈⣵⣤⣤⣿⣷⣶⣿⣿⣿⡆⣶⣬⡛⢿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⠁⢰⡿
⠀⠀⠀⣼⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠁⣾⣿⣿⣦⡀⠀⠀⢀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠂⢀⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⣿⢟⣩⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⠂⢀⣾⠏
⠀⠀⠀⠉⠉⠉⠀⠐⣶⡄⠀⠄⠀⠀⠀⠀⠀⠀⠤⣶⣶⣿⣿⣿⣿⣿⣶⣌⡻⣿⡿⣿⣿⣿⠀⠀⠀⠀⠠⠂⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠐⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣻⡿⠿⠿⠿⣿⡔⣿⣿⣿⠇⠀⠀⠀⠂⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠁⠢⠄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣅⡛⠛⠁⠀⠐⠈⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⡈⠐⠠⠠⢀⢀⢉⠉⠉⠉⠉⠀⠄⠙⠒⠁⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣶⠾⠟⠋⠁
⣶⣶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢛⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠁⢳⡀⠀⠀⠀⠀⢀⡾⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠚⣇⠀⠀⠀⠀⢸⡃⢠⣴⡞⣆
⠀⠀⠀⠀⠀⢠⡞⢛⡷⢄⠀⠀⠀⠀⠀⠘⣧⣿⣄⠀⠹⡀⠀⠀⠀⢸⡇⠛⢀⣱⣿
⠀⠀⠀⠀⠀⠘⡄⠀⠑⠈⢆⠀⠀⠀⠀⠀⢻⠇⢁⡶⢿⣇⠀⠀⠀⠘⡇⠀⠚⢉⣽⡇
⠀⠀⠀⠀⠀⠀⢰⡀⠂⠀⣪⣢⠀⠀⠀⠀⠘⡆⠈⠀⠀⠈⡄⠀⠀⠀⣷⣯⡀⣿⡿⣇
⠀⠀⠀⠀⠀⠀⠀⢳⡸⠆⠀⠄⢣⡀⠀⠀⠀⠉⠀⠀⠀⠀⢺⡀⠀⠀⠟⠀⣰⣟⠃⢛
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⠀⠀⠀⢳⡀⠀⠀⢨⠀⠀⡠⠖⠚⣇⠀⠀⡄⠰⠋⠉⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠠⠻⣄⠀⠈⣇⢠⠀⠀⠀⢹⠀⢠⡅⠀⠓⠀⠐⠺⡆
⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡴⠎⠲⠌⢆⠀⠸⡀⣆⠀⠀⠘⡇⠘⡇⠀⡀⠠⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛
⡟⠡⠈⡓⢄⠀⠀⠀⠀⠀⠈⢶⠁⠠⠂⠂⠸⣄⢀⠃⠈⠙⠛⠋⠙⠚⠁⠊⢦⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠃⠂⣔⢀⡴
⠹⣤⣤⣤⣶⣷⣄⡀⠀⠀⠀⠘⣧⠀⠐⠠⠀⠘⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⢿⣄⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⡆⢀⣤⢄⡞
⠀⠈⠲⣀⠩⠉⠉⠙⠲⣄⡀⠀⠈⣧⠀⠸⣧⣄⠀⠀⠀⠟⠁⡀⠀⠀⢤⡄⣴⣂⣠⣾⣿⡀⠀⠀⠀⠀⠀⠀⡼⠣⠝⣿⠿⡿⡾
⠀⠀⠀⠈⠳⢆⠀⢰⣿⣀⢛⡶⠤⠞⠀⣄⣂⠀⠀⠀⠀⣠⣾⣿⣿⡦⠿⠃⢿⡿⢿⠀⠠⣿⣦⠀⠀⠀⠀⣸⠡⠾⠊⢍⡀⣾⠃
⠀⠀⠀⠀⠀⠀⠳⣟⠉⠀⢂⠠⢀⣴⠄⠉⠀⢠⡆⣀⡼⠟⢫⣥⣠⣀⠦⠀⢿⣵⠊⡷⢠⡷⠢⠷⣄⣀⣼⠏⠠⢘⠀⠝⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠁⠀⠀⠀⠠⡀⢀⠈⠁⠉⠀⠀⠀⢉⡿⠟⡷⣟⣶⡑⡓⢡⠟⣿⣠⠶⠈⠉⠉⡉⠐⣨⡋⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡙⢢⣐⠁⠀⠀⠀⠈⢀⠀⠀⣴⣦⡀⠀⣾⠟⠃⠦⠁⠼⠃⡯⢵⠄⣆⢰⣦⡀⢰⣎⣡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⠛⠟⢀⠐⠊⠓⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⢶⣽⡄⢀⣒⣋⢴⣓⠋⠉⠀⢺⣄⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣤⣴⣾⣿⣿⠶⠀⠀⠀⠚⠀⣿⡿⠀⠀⠀⠉⠁⠨⠈⣉⠀⣹⢻⡟⠀⢩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⣿⡟⡿⡆⢰⠀⠀⠀⠀⠈⠁⠐⠒⠀⢳⡻⣄⣿⠇⠀⢠⣄⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠈⠃⢀⠀⠘⡆⠀⠀⠀⢠⣀⡀⠀⡀⠉⠂⢝⣯⢀⣶⣾⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡠⠇⠉⠀⠀⠙⠒⠀⢀⡀⢉⠛⠃⠀⡀⠀⢀⣳⣌⡙⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣐⣒⣶⣂⣈⣉⠉⠉⣭⠀⠤⢅⣀⡀⠉⠉⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡠⣴⡯⣤⣀⠀⠰⠶⢿⠿⠂⠈⠀⠈⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⣤⡄⠀⠤⠤⠄⠀⠸⣿⠏⠡⠶⠶⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡌⠉⡄⢆⡶⣴⣶⡦⠀⢀⠀⠇⠐⠟⢻⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠷⢶⣼⢃⣄⢠⡄⠀⣾⢠⢆⡄⢀⣾⠸⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣴⣵⣶⣿⣼⣼⣮⣤⣼⣿⣼⣼⣼⣮⣧⣶⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⢈⠀⠀⠀⠀⠀⠀⢀⠔⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣦⡀⣀⢂⠀⠐⠒
⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠘⢋⡤⡐⢪⠀⠠⢠⠤
⢀⡀⠀⠈⠄⠀⠀⢋⠀⣬⡅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠑⡄⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡤⠂⠀⠁⢄⠐⣠⢎
⢻⣇⡄⠠⠠⠀⠀⠒⠂⠀⠚⠀⠀⢠⠠⠀⠂⡀⠀⠀⠀⠠⠆⠈⠢⠈⠃⠀⠀⣀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡋⠀⠀⢀⡜⡆⠙⠺
⠀⢿⠀⠀⠀⠀⠀⢳⡄⡠⠤⠃⠀⠙⢈⢢⡘⠁⠀⠠⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⡘⠢⠒⠀⠀⠑⠀⠀⠀⠀⠀⠀⠇⠘⠏⠉⢔⠁⢀
⠀⠀⠑⠤⡀⠀⠀⠀⠍⠀⠀⠀⠀⡔⠈⠀⡁⠀⠀⠀⠀⠀⠀⠀⢁⠠⠋⣑⡀⢈⢳⠀⢈⠔⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⠀⣤⡄⠈⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⣿⠂⠈⠀⠀⠀⢀⡀⠠⠶⠀⠀⠀⠠⢼⡄⠢⠍⠣⣬⠃⢀⠮⡔⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠃⠤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣆⠀⠀⠀⠉⠴⡀⠘⠄⠀⠀⠉⠉⡇⠀⢠⣀⡀⡔⠺⠀⠀⠀⠠⠀⠐⠂⣤⡁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠆⠀⠀⠀⣄⠀⠠⠄⠀⠀⠀⠀⡇⠀⠀⠀⠨⠀⠆⠀⠠⠀⠀⠀⠢⡄⠀⢠⠖⠀⠀⡛⠛⠉⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠡⣀⠀⢀⣘⠛⠋⠀⡰⠁⠀⠀⠓⢤⡄⣀⣀⣀⣹⠀⡠⠴⢄⠀⠀⠙⠛⠁⠀⢀⠔⢉⠆⠀⠀⠒⢧
⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠙⡍⠀⠀⢠⡟⠁⠀⠀⠉⢫⠀⠀⠀⠀⢾⡁⠀⠀⠈⣳⠄⣀⣘⣦⠀⠁⠒⠀⠠⢔⠈⠀⠀⠸⣄⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠰⠶⠾⠷⠀⠾⠷⠦⠠⠤⠽⠦⠀⠀⠰⠯⠤⠄⢠⣤⡬⠷⠄⠀⠼⢧⣤⡄⠉⠀⠀⠀⠀⠀⠴⢾⣅⠀⠠⣤⣬⣷⠄⠀⣾⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⡾⢛⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠋⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢲⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⢹⣾⣿⣿⣷⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⡾⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⣼⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣽⣿⣿⡀
⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡀
⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣧⣀⠉⣨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣦⣀⣠⡄⠀⠀⡀⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢹⣇⣠⡄⠊⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣎⣉⣉⢛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠟⠿⣿⡿⠿⠿⠟⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⡿⠛⠋⢛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠄⠀⠀⠀⠐⢻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢻⡇⠀⠀⠀⡀⣀⣤⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣥⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⡇⣸⣤⣤⣶⣾⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣶⣤⣴⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠒⠒⠲⠶⠖⠚⠳⡄⠠⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⢰⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠖⠒⠀⣰⣲⣦⡀⠀⢠⡾⠀⠀⠀⠰⠀⠀⠀⠀⠐⠠⠄⡤⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠈⠛⠟⡸⣿⣾⡇⠀⢳⡄⠀⡴⠀⢠⠀⠃⣠⣼⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢴⡀⠀⣸⣷⡜⢃⣿⡄⠰⠁⠠⡇⠀⠙⣠⢾⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⢟⠀⢀⠸⣷⠀⣾⠯⢠⣿⣿⡇⡆⠀⠀⠋⠀⣠⣾⡯⢞⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠸⣆⡸⢻⣿⣇⣼⣢⡄⣼⠟⢱⣷⡀⠀⠀⢰⣿⡿⣾⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⢀⡈⢳⢼⡟⣺⡿⣯⡿⣱⣶⣟⢿⡟⠀⠀⣿⣭⡦⢹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣍⢰⠈⣹⡿⣯⡏⢰⣿⣯⡙⣶⣤⡀⢰⣿⣙⣇⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠂⡄⢹⣿⣿⣳⣾⠄⣽⣿⢾⠋⡇⠨⣿⣷⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⢿⢸⣿⣿⠟⣡⠟⣸⣿⣧⣤⣙⠀⣿⣿⣵⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠙⣦⠸⢇⣿⡟⣰⠋⣿⣿⣿⠿⡆⢹⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⢷⣌⡋⢿⣿⣧⣌⠛⢲⣀⡷⢰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠟⢦⡙⢻⣗⠀⠈⣿⡇⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢸⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠛⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣾⣿⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠙⠋⠛⠛⢻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠲⠦⣀⣤⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣾⣷⣦⠈⢻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⢸⣿⠀⠐⣿⠀⠙⠋⢁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠙⠢⠄⠀⠸⠇⠀⠀⠿⠀⢰⡄⠀⢀⠠⠁⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣰⣿⣿⣿⣿⣿⠶⣤⣠⣷⡾⠛⠋⠛⠻⠶⠿⠇⣠⠞⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣀⢸⣷⡿⠻⡿⠂⠚⠁⠀⠀⠀⠀⠀⠈⠀⠐⢸⣿⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠛⢯⣹⣿⣿⡿⠇⣠⣤⣄⢀⠴⠴⠄⢰⡀⠀⠀⠀⠺⢿⣿⣦⣁⣀⡽⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣄⡀⢠⣿⣿⣿⠗⠊⠉⠻⠿⠿⠶⠆⠀⠈⠁⠀⠀⠀⠀⠸⡟⠛⠋⠉⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠃⣶⣦⠀⣀⢱⣶⡬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⣿⣿⣿⣶⣿⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡷⠀⠀⣾⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠺⢩⡾⠿⣿⣿⣿⣿⡗⠀⠀⠀⢀⡿⢻⣿⣿⣿⣿⡀⠀⡀⠰⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⡄⠺⣦⠟⣿⣿⣿⣿⣆⣀⣠⣿⣷⣿⣿⢟⠁⠉⡻⠷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣷⡆⠁⠀⣈⠀⠌⠍⠿⣿⡿⠏⠫⣥⣼⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣰⠎⠀⠰⠒⡂⠊⠉⠉⠀⠉⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⢞⠠⠀⠠⣊⡴⠔⠒⠒⠚⠓⠋⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⢀⣴⠋⠉⠉⠉⠑⠂⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣀⣶⣁⣤⣄⠀⠒⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠪⡁⡈⠋⠀⠀⠀⠈⠉⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠠⠐⠄⠰⠈⠁⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠋⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠋⠉⠉⣹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⡀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⣠⣶⠶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣛⣟⣛⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠛⠉⠛⠋⠙⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⣿⡶⠿⠿⠿⠿⢿⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢼⡇⠀⢸⣿⠀⣶⠀⠀⠀⠀⢠⣶⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⡇⠀⢸⣿⢀⣿⠀⠀⠀⠀⢀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠋⠀⠀⠀⠀⣿⡟⠛⠿⠛⠻⢿⡟⠀⠀⣿⡆⠀⠀⠀⠀⢹⡇⠀⠀⠻⠿⣿⠀⠀⠀⠀⠘⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⡁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠰⣿⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⠀⠀⣿⡇⠀⠀⠀⠀⢸⣧⠀⠀⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣿⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⢸⣏⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⣿⠀⢀⣿
⠀⠀⠀⠀⠀⢀⣤⣤⣼⣧⣤⣤⣤⣤⣼⣿⣤⣤⣿⣧⣤⣤⣤⣤⣼⣿⣤⣤⣿⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣿⣤⣴⣿⣤⣴⣿⣤⣤⣄
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉




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