Playful Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠀⠉⠉⠁⠒⠢⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⠀⠙⢆⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⢄⡀⡰⠁⡴⠁⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁⠾⡀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡏⢀⡵⣕⠀⠀⠀⠀⠈⢢⣀⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡏
⠀⠁⠢⠀⠀⠒⠄⡀⢀⠔⠀⠈⠊⠐⣈⡻⠃⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⢰⠁
⠀⠈⠉⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠌⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢡⡇⠀⠀⠀⠀⢸
⠀⢰⠁⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⡠⢂⡔⠛⠃⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⡇⠀⠀⠀⠀⢸
⠀⠘⠦⣀⡀⢀⡠⠃⠀⠀⠀⢀⠤⣚⡐⢛⣤⠤⣀⡀⠀⠈⠁⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⠀⠀⢧⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠞⠁⠄⠀⠣⠄⢠⠤⠊⠉⠓⠢⢤⠴⠃⠀⠀⠀⠀⢀⣀⡤⡞⠁⠀⣸⠀⠀⠈⠳⢤⡀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⡤⠒⢉⣉⡀⠔⠀⡠⠔⠁⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠁⠀⠀⠀⠀⡸⠀⠀⡱⠦⠴⡄⠀⠀⢰⡆⠠⣥⠀⢀⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⣇⣀⣀⣧⠀⠀⠀⡇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⢸
⠀⠀⠀⠐⠲⢄⣄⣠⢶⠊⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡁⠀⣀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢀⣄⠀⣰⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⡀⡀⠀⠐⠀⠀⠀⠀⢄⣠⠀⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠠
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠆⠂⠀⠐⠄⣀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠠⠀⠀⢀⠀⠘⠖⠀⠀⠀⠰⠐⡂⠐
⠀⠀⠀⠀⠀⠀⠤⡌⠀⠀⠀⠀⠀⠀⠷⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⡄⠀⠐⠈⠒⠉
⠀⠀⠀⠢⠂⠀⠀⡄⣀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⡠⠀⠀⠤⠩⠀⠀⠀⢄⠀⠀⠀⠀⡠⠀⡀⠀⠁⠀⠀⠀⠀⠠⠈⢁
⠀⠠⡀⠀⠀⠀⢀⠀⢈⠁⠀⠀⠀⠈⠀⣤⠄⠀⠘⠤⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠂⠈⠀⣀⣁⠈⠀⠀⠘⠁
⠹⠆⠀⠀⠐⠀⣁⣠⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢨⣤⠠⣄⡖⠢⠀⣀⠀⡀⠀⠈⠹⢆⡀⠀⠀⡀⡐⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡦⢀⠄⠀⠀⠀⠀⠙⠁⠐⠀⠀⠆⠈⠀⠁⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⡂
⠀⠀⠀⠀⠁⠀⢀⣄⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠳⡂⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠛⢄⡀⣀⠀⠛
⠀⢘⢀⠀⠀⡼⡏⠁⠀⠀⡀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠄⡀⠐⠂⠀⡓⢠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠴⠀⠀⠦⠄
⠀⠦⠀⠡⠔⠀⠸⠀⠀⠀⠀⠀⠀⢦⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠀⠈⠁⠗⠀⢦⡀
⠀⠠⣄⠓⠀⣆⠸⢧⢀⣀⣀⣀⠸⠏⠁⠀⠀⠀⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠢⠄⠐⠿⠀⠀⢠⠀⠀⠀⠀⠰⡦⠃
⠀⠀⠈⠁⠈⠁⠀⠤⠴⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠴⠆⠀⠰⠦⠆⠈⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣰⢁⡁⠀⣰⣆⠀⢰⡖⢀⡀⣀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⣤⣤⠀⠀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⢀⣀⠀⠀⠀⣀⣰⣾⢿⣷⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢸⡟⢻⣷⣴⣄⣻⣿⣆⠀⢠⣿⠛⣿⡄⣿⣿⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⣿⣿⢿⣿⣿⣿⣿⡿⣿⣦⣾⡏⠀⣿⣇⣿⡿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣷⣿⡇⠈⣿⡇⢻⣷⠀⠘⣿⠇⠀⠀⢹⣿⡿⠿⠇⠀⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠿⢷⣤⣴⣶⣬⡟⢃⣶⡿⠃⠀⢸⣿⠀⠀⢸⣿⣤⣾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣏⣀⣾⡟⠉⠉⢻⣿⣾⡟⠀⠀⠀⠀⣤⣄⣀⣾⡿⢿⣿⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠋⠋⢿⣧⣀⣀⣼⣿⠻⣿⣄⣀⣀⣤⣨⣿⣿⣿⣥⡄⣈⣉⣹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡉⠀⢠⣤⣽⣿⣟⣿⣥⣶⣾⠛⠛⣿⣯⣿⠟⢿⣿⠛⣋⣿⡛⠛⡏
⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⢸⣿⣇⣹⣿⢿⣿⣀⣀⠀⢀⣿⡋⣿⡇⢸⣿⣾⣟⠋⡀⠀⠁
⠀⠀⠀⠀⠀⠐⣿⣇⠀⠀⢀⢹⣿⣿⣿⣁⠸⣿⡟⠉⠀⢸⣿⠿⣿⣧⢸⣿⠘⣿⣿⠛⢀⠀⠤
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⣿⡇⠙⢿⡷⣿⣷⣿⠿⣿⡯⠀⢚⣿⣼⣿⠀⠘⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⣶⠖⠒⠛⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡞⠋⠉⠉⠓⠦⣄⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣁⣠⠞⠀⠀⠀⠀⠀⠀⠈⠙⠲⣾⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⡇⠀⠀⠀⢀⡴⠶⠶⢤⣀⠀⢀⣀⣀⣀⣀⡟⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⡾⠀⠀⠀⢰⡏⠀⠀⣴⣚⠉⠉⠻⢧⡀⠀⠈⠉⠳⣄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⣼⠁⠀⠀⠀⠈⢷⡀⢸⡇⠈⠙⢦⠀⠈⢷⠀⠀⠀⠀⠘⡆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠹⡄⠀⠀⠀⠀⠈⢷⠀⠓⠦⣤⠞⠀⠀⣸⠀⠀⠀⠀⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡟⠲⢤⣀⡀⠀⠈⣧⣀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⡞⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣘⡇⠀⠀⠈⠉⠛⢲⡇⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⣸⠋⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⢀⣠⠶⠚⠁⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢈⣩⠷⠒⠒⠋⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠈⠙⣳⠖⠛⠻⣍⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⢻⠀⠀⢠⡟⠀⠀⠀⠈⠉⠓⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⡟⢸⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⠀⣾⠃⣀⡤⠶⠒⠛⢛⣋⣩⡽⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣷⣸⣾⢗⣋⡤⠴⠖⠚⠋⠉⢁⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⡿⢟⣉⣠⣤⡤⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠾⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠆⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠀⠃⠀⠀⠀⠊⢀⢀⠄⠰⡆⢀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠐⠛⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠢⠂⠀⡀⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠔⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⣀⡠⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⠀⠀⠁⠀⠀⠀⠀⢀⡴⠇
⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠃⠐⠧⠒⠒⠈⠀⠈⠒⠂⠚⠀⠄⠄⠐⠈⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠁⠀⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠤⠀⠤⠄⠠⠤⠤⠄⠀⣀⡀⠀⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠉⠓⢄⡀⡀⠀⠀⠀⠀⠴⢠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⡀⠀⠐⠀⡇⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠆⠀⢻⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠘⠀⠀⠒⠊⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⣠⡀⠀⠀⠀⠀⡀⠑⠲⠴⠒⠁⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠁⠈⠐⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⢀⠄⠀⢄⠀⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠉⠢⢄⣀⣀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠘⡀⠀⠀⠄⠁⢠⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⡐⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⡄⠀⠀⠀⠀⠡⣬⠀⠸⡉⠀⡜⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⡜
⠳⠄⠀⠜⠁⠐⠀⡅⠉⠉⠈⠀⠀⠀⠀⠀⡠⠊⡜⠓⠂⠤⢤⠊⠉⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⢠⡄⠠⠤⠔⠈⣠⣾⣤⣀⡀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠈⢦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠤⠤⠐⠋⠁⠙⠁⡐⠀⢹⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⡄⠀⠀⠀⠑⢤⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠘⢦⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⣀⠵⠀⠀⢀⡤⠊⣀⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⠤⠤⠤⠄⣀⡨⠀⢨⠁⠒⠚⡄⠱⡤⠤⠄⠒⠊⡡⠐⠂⠉⠀⠀⢀⠔⠋⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠄⢀⠀⢠⠤⠤⠀⣠⠖⠒⠚⠒⠒⠢⢼⡄⠱⡤⣄⣄⣀⡟⠉⠉⠒⠒⠞⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢾⣀⣼⣀⡸⠀⠀⠀⡇⠀⡄⠀⠀⡀⠀⣄⠈⠂⠘⢄⠀⠸⣀⡆⠀⡄⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⣆⣀⣀⡧⠤⠇⠈⠒⠢⠚⠀⠀⠀⠈⠉⠙⠒⠚⠁
⣿⣿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⢄⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠀⠀⠀⠀⠈⠓⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣀⠠⢤⣀⡀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠴⠊⠁⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢲⠒⠄⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠀⠀⠀⠉⠁⠀⠲⢄⢀⠞
⠀⠀⠀⠀⠀⠀⠀⡈⢀⠴⠀⠀⠡⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢣⠀⠀⠈⣀⣀⡀⠼⡀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠔⢪⡁⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⢄⠁⠀⠀⠀⠀⠀⠀⠘⠁⠂⢢⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠈⣤⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⣄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢸⡀
⠀⡐⠂⠀⠂⢴⠂⠉⠀⠀⠀⠘⠿⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⣀⡇
⠀⡇⠰⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⡀⠀⠀⠀⠀⠀⠀⠤⠴⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⡐⠁
⠀⠙⠒⢳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⣰⡿⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠈⠓⠲⠤⠤⠶⠒⠻⣁⡠⠊⠉⠳⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠂⠀⡐⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣧⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⡜⣸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⢀⡴⠋⣠⠀⠀⠀⡜⢀⠇⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣠⠴⢋⠔⠊⠀⠀⠀⡘⡠⠎⠀⠀⠀⡴⠁
⠀⠀⠀⢀⢀⣀⣀⣀⠠⠄⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠑⢄⡀⠀⠀⠀⠀⠘⡅⠀⠀⠙⠢⠴⣅⠴⡴⠋⠀⠀⠀⠀⢸⠁
⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⠚⠉⠉⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠸⢆⡠⠀⠀⡀⣠⠏
⠀⠀⠸⢅⣀⣤⠤⣤⠤⠤⠠⠤⠔⠒⠒⠚⠛⠉⢉⠭⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⡀⠀⢀⡀⣀⡤⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠀⢰⡇⡀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣾⣿⠇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡜⣡⣾⣿⣿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣴⣿⣿⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⣄⢠⢣⣿⣿⣿⣿⠟⠋
⠀⣸⣦⡄⠀⠀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⡤⢊⣡⣴⣶⣿⣿⣿⣿⣶⣝⣿⣿⣿⠟⠁
⠀⢿⣿⣿⣿⣿⣷⣦⣭⣑⣒⣲⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⢎⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⣤⣥⣵⣿⣿⣿⣿⣿⣿⣿⡇⠀⡰⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠉⠛⠙⠛⠉⠉⠀⣹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢔⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣟⣿⣿⠏⠀⣿⣿⣿⣝⣿⣿⡟⣿⣿⣬⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⣇⠀⠐⣿⣿⡿⢿⣿⣿⣿⣝⠏⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡞⣿⣿⣿⣿⣿⣷⢠⡀
⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣯⠝⠋⡀⠀⠹⣎⣛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡟⢸⠁⣽⣿⣿⣿⠹⡟⢰⡇
⠀⠀⠀⠀⠀⠀⠸⠛⣿⡿⠇⠀⠐⠀⠀⠀⠹⠿⠟⠻⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⠃⡟⠀⢱⣿⠻⣿⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡄⠀⠀⡌⢠⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⡸⠁⠀⠀⢳⡀⠙⠃⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠻⠿⠿⠃⢀⠜⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡟⠁⠀⠀⠀⠀⠙⢦⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⠲⡟⠲⡞⢇⢀⣼⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡄⠀⡘⣦⡙⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⡿⣉⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⡼⣿⣿⣿⣿⣿⣧⢻⣿⡿⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢤⣴⣾⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣎⠭⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠐⠀⠘⡄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠺⣻⣿⠿⢿⣛⣻⣯⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠾⣄⣀⡰⠤⠜
⠀⠀⢪⡀⠀⠀⠀⣀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠛⠉⢩⢤⡍⠘⠩⠞⠁
⠀⠀⠀⠈⠉⠓⠚⠁⠰⡀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠼⠤⠂
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠺⣟⡛⠛⢲⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠙⢾⡓⠿⠉⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⣤⢤⣤⢬⣟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡿⠦⠉⠃⠉⠀⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢈⣛⣶⣤⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⡏⠉⠛⠿⣍⡉⠉⠛⠛⢩⣭⡭⠿⣿⣿⠳⢶⡶⠶⠶⠒⣶⣤⠴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⢀⡀⠀⠀⢸⡇⠀⠀⣤⣈⡙⢄⠀⠀⠀⠬⣽⣿⡗⠀⠀⠀⢀⣤⡶⠛⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠜⠉⠀⠀⠀⠀⢷⠀⠀⠞⠀⠀⠀⠀⠀⠀⠈⣿⡋⠉⠀⠀⠀⠘⠁⢀⣠⡤⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡟
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢻⣻⣿⡹⠀⠀⠀⠀⠀⢸⣿⣿⣳⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⣿⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠉⠁⠀⡀⠀⢀⠀⠠⠉⠉⠁⠀⠀⢀⣴⠏
⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠘⠀⣀⣉⣶⣏⣀⠐⠀⠂⢀⣠⠴⣿⠋
⠀⠀⠀⢀⣾⠇⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠉⠓⢦⣄⣀⠀⣀⡤⠴⠒⠋⠉⠀⠀⠘⢧⡀
⠀⢀⡤⠞⠁⢀⡀⠀⢰⡟⠀⠈⠻⣦⡀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⣴⢋⡤⠖⢠⡏⠀⢀⡿⠀⠀⠀⠀⢸⣿⡋⣀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠈⠙⠷⠤⠴⠛⠛⠛⠁⠀⠀⣀⡴⠋⠁⠘⢛⣷⡄⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⢀⣰⣿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠉⠀⣢⡀⠀⣨⣿⠿⠒⠛⠋⠛⠓⠶⠶⠶⠶⠚⠛⠋⠉⠛⠻⣦⡀⠀⢀⡐⢿⣿⠑⠀⠈⠛⢦⣄⡀
⠀⢀⡤⠶⠖⠚⠛⠉⠁⠀⠀⠀⢀⣾⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣿⡟⠃⠀⠀⠀⣶⣄⣈⠙⠳⠶⣤⣀⡀
⠀⠿⠧⣤⠖⠀⠀⣠⡆⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣼⡋⠀⠁⢀⠀⢠⣄⡀⠉⠙⢶
⠀⠀⠀⠻⠤⠴⠚⠁⠹⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⡅⠈⣳⣄⢈⡿⠶⠖⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣯⣥⣬⣽⣧⣤⣤⣤
⣿⣿⣋⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠙⣆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣸⣀⠀⠀⠀⠀⠀⡰⣻⡳⣀⠳⣦⣄⠀⢀⣠⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠊⠁⠈⠉⠓⠒⠒⠚⠣⢿⢫⣴⣵⠘⠀⠋⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⡗⠪⠒⠛⠋⠀⢀⠀⠀⢠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⢄⣀⣀⡀⢤⣾⠇⠀⠀⠀⠀⠀⠈⡗⠒⠁⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠒⠒⣒⠮⢡⠎⠀⠀⢀⡰⠃⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠉⠀⠛⡄⠀⠀⠀⠀⠀⢠⠃⠀⠀⡐⠑⣂⡥⠚⠒⢚⡿⠀⠀⠀⠀⣿
⠀⠀⠀⡄⠰⢆⠀⢸⣀⡀⠀⢠⠃⡤⠤⢀⡀⠀⠈⠒⠒⢊⠠⠒⠉⠉⡧⠖⣋⠀⠀⠀⠀⠀⡿
⠀⠀⡜⠻⠁⠘⠋⠉⠈⠉⠑⡇⢘⠄⠀⠀⢳⠀⢀⠔⠊⠁⣠⠔⢊⠼⠚⠉⡀⢱⠀⠀⠀⠀⡇
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠑⣭⢞⣀⡠⠁⣸⠐⣕⡀⢰⡟⡡⠚⠁⠀⣠⠜⣱⠃⠀⠀⠀⢰⠃
⣤⠇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡤⠞⠁⠀⠀⠉⢹⣞⢁⠄⢠⠚⠁⠔⠁⠀⠀⠀⠀⡞
⡍⠇⠀⠀⠀⠀⠀⡴⢋⠀⢀⣴⠋⢳⣀⡀⠀⠀⢀⡤⠋⠈⠘⢲⠋⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠇⠀⠀⠀⠀⠀⠀⠈⠛⡤⠄⠈⠆⢸⠀⠙⣶⠊⠁⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠸⡀⠀⠀⠀⢀⠀⡸⠳⠇⠀⠀⢸⠂⠀⠀⡽⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠱⣄⠀⠀⠘⡗⠁⠀⠀⠀⠀⠀⠀⢀⡴⠃⣀⡠⠔⠊⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠙⠢⣄⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠉⠉⠉⠁⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣁⡤⠤⠤⠤⢤⣀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠞⣆⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸
⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠀⠘⠀⡜⠀⢻⡀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠀⠀⠒⠲⢤⡞⠀⣠⠏
⠀⡀⢀⡠⠴⠒⠚⠉⠉⠉⠉⠐⠀⠀⠀⠀⠀⠀⡀⠀⢀⠃⠀⠈⢧⡀⠀⠀⠘⡄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠁
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⢊⣀⠀⢀⠤⡈⠀⠈⢀⠀⠀⠀⠛⢦⣤⡴⠃⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡰⠁⠀⡇⡇⠀⠘⣆⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⢧⠁⡷⡷⠀⢸⠀⠀⠘⢄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠦⠤⠋⠀⠹⣄⣀⡜⠀⠀⠑⡌⠢⣄⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠊⠉⠉⠉⠈⠉⠉⠙⢢⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣇⠀⠲⠀⠀⢀⡾⠆⠀⡼⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠘⠦⣜⣀⣆⣨⠧⡤⠞⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⣇⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇⠹⡄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⡤⠤⡞⠉⠳⣶⢶⡖⠛⡉⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢸⠁⠀⠹⣄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠛⠛⠉⠀⢹⠀⠈⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⣸⠃⠀⠀⡼⠂⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣠⡴⠯⠚⢀⡴⠁⠀⠀⣰⠃⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⡄⠀⠀⠀⠠⡜⠲⠖⠁⠀⠀⡀⠀⣀⡴⢚⠁⢀⠄⠀⣼⠁⠀⠀⢰⠃⠀⢠⠏
⠀⢀⡠⢤⣀⣀⡀⠀⠀⣀⣀⣠⠴⠞⠁⠀⠀⡟⠙⠓⠒⠒⠘⠲⣄⠀⠀⠀⠹⣎⠀⠈⠛⠖⠾⠴⠖⡵⠋⠉⠉⠉⠀⢠⠏
⣰⠋⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣤⠼⠗⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⠧⡜⠀⠀⡆⠀⢹
⣇⣠⡇⢠⠀⠀⢀⠀⢀⣀⣀⣤⠴⠞⢋⡥⠖⠒⠊⠉⠉⠉⠀⠀⠀⢀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠒⠚
⠀⠉⠛⠾⢦⣤⡼⠏⠉⠉⠀⠀⠀⠀⡟⢠⠂⠀⡖⠀⠀⣴⠶⠚⠋⠉⠉
⡀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠓⣻⣤⣴⣧⣤⡾⡁⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⡀⣀⢀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢀⡴⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠰⠤⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠀⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠐⠊⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠘⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⠄⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠉⠓⢦⡶⠒⠓⠒⠂⠀⠁⠀⠋⣀⢤⠀⠀⠀⠘⣤⣤⣤⣤⡤⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⡀⠀⢈⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠁⠀⠀⡴⠛⠂⠘⠀⠀⣤⣬⡁
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠙
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⠏⢸⠀⠀⠀⠀⠀⢀⢠⠀⢀⣄⠀⠀⣀⡀
⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⠰⠋⠀⣴⠀⠀⠐⡻⠛⠊⠀⠀⠈⠁⠀⠔⠻⢁⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⣲⣾⣿⡿⠿⠿⢿⣷⡄
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⣤⣤⣾⣿⣿
⠹⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢲⠞⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠘⠿⣿⣿⣿⣿⣷⣄⡀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⠀⠀⢢⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛⠋
⠀⠀⠀⠈⠙⠻⠿⢿⣿⠿⠋⠁⠀⢹⣿⣿⣶⣶⣶⣶⣶⡿⢻⣧⠀⠀⠀⠡⡀⠀⠀⠀⠈⠑⠒⢀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠙⢷⡀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠈⠰⡆⠦⠀⣀⡄⠀⠀⠀⠀⣀⠔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⡞⠀⢀⣴⣿⣿⣿⣶⣄⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⢸⠁⠀⢾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣶⣿⣿⣿⣶⡄⠀⠀⠉⠢⢄⠀⠀⠀⠀⠈⠐⠂⠼⠷⢦⡀
⠀⠀⠀⠀⠀⢸⡆⠀⠈⠿⣿⣿⣿⡿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠒⠄⣀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⠖⠢⡀
⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠐⣆⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠼⠿⡶⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠾⠿⠁⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡘⠀⠀⢄⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠘⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠈⠆⠐⠀⠀⠀⠀⠁⠀⠀⠂⠠⢀⠀⠀⢀⠀⠤⣀
⠀⠀⠀⠀⠈⠓⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⠀⠑⠄⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡈⢢⡀⠐⣀⢸⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⣀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⣶⣿⠉⣷⣄⠀⠀⠀⠀⡧⣿⢯⠷⡾⡿⢭⠂⠀⠀⠀⢾⡟⠉⠉⠉⣯⡆⠀⠀⠀⢀⣂⣂⣉⠈
⠀⠀⣿⣤⣿⣻⣏⣸⡆⠀⠀⠀⢈⣿⣯⣤⣼⣿⣁⠀⠀⠀⠀⡱⠆⢸⡷⠀⠶⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠹⢧⣼⣏⣨⠟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⢾⣧⣀⣀⣠⣟⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⣰⠁⠀⢘⡄⠀⠀⠀⢸⠙⠋⠋⢳⠃⠋⠋⢻⡇⠀⠀⣼⣛⣛⣛⣻⡄⠀⠀⠀⡠⠴⠟⠙⠋⠹⢶⣄⡀
⠀⠀⡼⡌⠀⠀⠀⡿⣆⠀⠀⢸⢀⣀⡀⣰⡀⣀⣀⣸⡇⠀⠀⠀⠙⣤⡜⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠘⠚⠒⠒⠒⠒⠚⠚⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⠠⠊⠀⠈⠢⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣀⣀⢀⡀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⣀⡠⠤⣲⣷⠀⠀⠀⣴⠤⣤⢦⡤⢶⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠻⡇⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⣭⣶⣾⣿⣿⣿⠀⠀⠀⢹⠀⣿⢸⡇⣾⠀⠀⠀⠛⢷⣾⢫⡙⣶⠟⠃
⠀⣴⡇⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠋⡟⠻⢿⣿⣿⣿⠀⠀⠀⢸⡆⣿⢸⡇⡿⠀⠀⠀⠀⢀⣿⡿⢿⣧
⠀⠉⠉⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠁⠀⠈⠉⠀⠀⠀⠘⠧⠿⠼⠶⠇⠀⠀⠀⠀⠚⠁⠀⠀⠙

⠀⠀⣀⣤⠤⣄⡀⠀⠀⠀⠀⢠⣺⣭⠷⣠⣚⣯⡷⡄⠀⠀⠀⢀⡤⡤⠤⠤⢤⢤⡀⠀⠀⠀⠀⡀⡀⠄⠄⠀⠂
⠀⣼⠛⣿⣤⡾⠻⡆⠀⠀⠀⠘⠯⣯⠝⠉⢯⣿⠽⠁⠀⠀⠀⠠⣛⠀⢠⣀⠀⣛⡇⠀⠀⠀⢰⣶⣶⣦⣦⣦⣤
⠀⣿⠟⢻⡾⠷⣶⡇⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠐⣭⠀⠘⠉⢨⣭⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠈⠳⠾⠷⠴⠋⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠉⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠛⠛⠿⠿⠿⢿⡟

⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⣬⠀⠀⠀⣣⠀⠀⠀⠀⡇⠁⠁⠁⠑⠁⠁⠁⠁⡇⠀⠀⠠⣯⣭⣭⣭⣽⠄⠀⠀⠀⡤⣶⣿⣁⠍⠠⠿⠷
⢀⣞⡇⠀⠀⠀⢨⢳⡀⠀⠀⡇⡀⡀⡀⡠⡀⡀⡀⡠⡇⠀⠀⠀⠀⢑⣴⡋⠀⠀⠀⠀⠀⢺⣿⣿⣿
⠘⠚⠒⠒⠒⠒⠚⠓⠃⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠔⠁⠀⠉⠢⠀⠀⠀⠀⠓⠒⠒⠂⠉⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣶⠀⠀⠀⢠⡬⣥⡤⣤⡬⣦⠀⠀⠀⠀⠀⠀⢰⣧
⢿⣿⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⢰⣖⣫⣥⣶⣾⣿⣿⠀⠀⠀⠘⡇⢸⡇⣸⠀⣿⠀⠀⠀⠲⣶⣶⠟⡟⢶⣶⠶
⣠⣿⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠘⠻⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⣷⢸⡇⣿⠀⡏⠀⠀⠀⠀⠀⣽⣾⣿⣾⡁
⠛⠛⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠈⠓⠒⠋⠉⠙⠻⠀⠀⠀⠀⣿⣸⣇⣿⣰⡇⠀⠀⠀⠀⠰⠟⠁⠈⠙⠧

⢀⡆⢠⢠⠏⢾⢦⠪⣃⡜⠁⠖⠒⠋⠀⢠⢠⠇⠠⠃⡷⠼⢂⡛⠀⠞⠠⠆⠴⢀⠀⠄⣈⣀⠠⠤⠠⡷⠈
⢈⡀⡉⣜⠦⣼⠾⠀⠁⡀⠰⠐⠐⠬⣄⢏⠆⠶⢤⠛⠁⠀⠇⠈⡆⠀⢷⠘⠛⠛⠃⢠⡀⠲⠄⠠⠤⠄
⠀⡇⠀⡟⢀⣸⠀⡾⢶⠶⠆⠀⣇⠄⢀⠀⠀⣄⠀⡀⠂⢱⠀⢜⠀⠶⠀⠖⠰⠀⠆⣸⠃⠂⠀⠀⣀⠀⡜
⠘⣀⣘⣁⠀⢰⣀⡇⣸⢀⡄⡴⠀⠀⠒⠒⠒⠀⢰⠉⢀⣁⣀⢈⠉⠀⢰⠀⡉⠉⠈⡁⣀⠀⠃⠈⠉⢠⠅
⡄⡂⢀⢀⠀⠆⠨⠤⠅⢈⠁⠖⠛⠠⠂⠆⠰⠐⠂⠀⣉⣈⡠⠀⠀⠹⣙⡆⢀⡤⡄⠀⠠⠀⠠⠖⠒⠀⠰
⠀⡁⢨⢤⡥⠀⠆⠄⠄⢸⠄⠂⠐⠀⠒⠖⠂⠀⠀⠁⢁⠀⠀⠀⠋⠀⢈⠀⡀⢀⠄⠀⠀⠆⠂⠁⠁⠒⠂
⠐⡇⡀⣸⢀⡄⠀⠈⠓⠀⠀⡘⠀⠠⠠⠆⠄⠀⣀⢀⡘⠀⠈⡁⡀⡉⠡⠀⠀⡄⠰⠃⠀⠆⠀⠱⠀⠤⠤
⣀⡀⠀⢀⠀⠠⢤⡘⠀⠂⠈⠁⠰⠒⠀⢀⡀⠈⠀⠠⠤⠤⠀⠀⠀⠠⠶⠂⠰⠁⠀⣀⣀⠀⣀⠀⠠⠠
⠀⠄⠀⡘⠀⠠⠀⠄⠀⠐⠒⠀⠀⠈⠀⣬⠁⠀⠀⠔⠠⠠⢀⣠⡄⠠⠀⠂⢀⡀⠠⠠⠠⠀⡉⠁⠀⢀⠇
⡄⠀⠈⠁⠠⠖⠂⠀⠀⠀⠈⠀⠸⡀⠀⠀⠀⠉⠓⠀⠀⠀⡈⢀⠀⠀⣀⠀⢀⢉⠀⠀⡀⠀⠀⣬⠄⠉⠰
⢠⠀⠀⠀⠄⠰⠀⠀⠊⡁⠀⠀⠀⠉⠀⢀⡀⠁⠘⠀⠀⡄⠁⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⢀⠀⠄⠀⠰
⠀⠀⠀⠀⡤⠀⠀⠈⠀⠀⠐⠲⠀⠀⢀⠁⠄⠀⠀⠀⡤⠁⠀⠀⠀⠁⠈⠀⠀⠀⠘⠀⠁⠀⠀⡤⠄⠀⢀
⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⢠⠀⠄
⠀⠀⠀⢀⡀⠀⠑⠀⠈⠄⠀⠀⠀⠠⠄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠⠄⠀⠀⠠⠀⢀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⠖⠊⠉⠁⠀⠈⠉⠉⠒⠶⣤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⠇⠀⠀⠀⣿⣙⠄⢀⡠⢤⡀⠠⣋⣿⠀⠀⠀⢸⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠤⠤⢤⣀⣉⡩⠔⣉⠤⠄⣈⠳⠭⣩⠤⠤⠤⠬⡇⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⡇⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠢⡴⠞⠙⡶⠖⠂⠀⠀⠀⠀⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠙⠦⠔⠃⠀⠀⠀⠀⠀⢀⡴⢻⠁⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠑⠒⠤⠤⠤⠄⠤⠤⠤⠤⠔⠒⠉⡇⠀⣎⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹⡎⠀⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢹⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⡇⠙⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢇⠀⠀⠀⠉⠒⢦⠔⠒⠉⠀⠀⠀⣸⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠦⠤⢘⣆⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⡃⠠⠴⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⢀⠀⡎⡀⠉⠉⠉⠀⢸⠀⠀⠈⢑⠋⢁⢹⠀⡀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠼⠤⠟⠧⢄⣧⠤⠴⠚⠑⠢⠤⠼⡤⠼⠞⠤⠧⠜⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠁⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣦⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⣧⣄⠀⡀⠀⢀⣶⣿
⠀⠀⠀⢠⣴⣾⣿⠿⠛⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⣾⣿⣯⠋⠉⡁⠈⠹⣿⣿⠃⠀⠀⢀⠔⠛⠻⣆⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠀⠀⣿
⠀⠀⠀⠘⢿⣿⡄⠐⠛⠆⢦⡿⠋⠀⠀⠀⠊⢠⡀⢠⣻⠀⠀⢠⣴⡞⠉⠙⠛⠙⠃⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠟⠁
⠀⠀⠀⠀⠀⠉⣷⢉⢦⣼⣥⠀⠀⠀⠀⠘⠀⠀⢤⠿⣸⠀⠀⢺⣿⡇⠀⠀⠀⠀⢀⣿⣿⠆⠀⣀⡤⠤⠤⢦⣄⠀⠀⠀⠀⠠⠖⣨⡿⠉⠟⠃⠀⠈
⠀⠀⠀⠀⢠⣿⣿⣿⣆⠺⣴⣶⣶⣦⡀⠀⠀⠐⠒⠁⠇⠀⠀⠀⠻⠇⢀⡀⣀⠀⠸⠿⠋⠀⣼⠏⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣬⣥⡤⠚⣞⣶
⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠝⣻⣿⣹⣵⢲⡀⠲⣶⡆⠀⢀⡀⠀⡃⠰⡀⣒⠀⡄⠀⠈⠀⡀⣿⠢⢤⠀⢠⠤⠀⠟⠁⠀⣿⡇⣿⣿⢷⡶⣿⣿
⠀⢸⣿⠟⢋⢓⣾⣿⣿⣧⣤⣿⠟⠋⠁⠸⣿⣦⣽⣏⡀⠘⣷⡀⠀⢀⠀⠭⠀⠀⠖⠀⡠⠻⣜⣷⣾⣤⡄⠀⠀⠀⠀⢰⢁⣼⣋⠿⣤⡽⠿⢾⡇
⠀⠈⠛⠳⣤⣿⣿⣿⣻⣿⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⢷⡤⣀⡙⢸⣋⣡⣀⡔⠁⠀⠈⢿⣿⣟⡛⠀⠰⠀⠀⢸⣾⣿⣿⡒⢂⣠⣐⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠁⠀⣄⣄⣰⢿⣿⣽⣿⡿⠿⠋⠉⠀⠀⠀⠙⠁⠁⠀⠀⠀⠀⠺⢿⣻⡿⠿⠀⠀⠐⠈⠁⠀⢹⠿⣿⣿⣿⣿⣿⡿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⡽⠖⠚⡎⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠹⣿⣭⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈

⣷⣦⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣴⣿⣦⡀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣠⣴
⣿⣿⣿⣦⡀⠀⢸⡇⠀⢀⣤⣾⣿⣿⣿⣿⣷⣄⠀⠀⢸⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣀⠀⠀⣿⠀⠀⣠⣾⣿⣿
⣿⡿⠋⠁⠙⢦⣸⣇⡴⠋⠈⠙⢿⣿⣿⡿⠋⠈⠑⢄⢸⢀⡴⠋⠈⠻⣿⣿⣿⡿⠋⠈⠳⣄⣿⣠⡞⠃⠉⠻⣿⣿⣿⠟⠁⠙⢷⡄⣿⣠⠞⠁⠙⢿⣿
⡏⠀⠀⠀⠀⠀⣹⣏⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⢀⣽⣏⠀⠀⠀⠀⠈⢻⠋⠀⠀⠀⠀⢈⣿⡁⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⢉⣿⡁⠀⠀⠀⠀⠙
⡇⠀⠀⠀⣠⣾⣿⣿⣷⣆⡀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⢸⠀⠀⠀⢀⣴⣿⣿⣿⣷⣀⠀⠀⠀⣿⠀⠀⠀⣀⣴⣿⣿⣿⣦⡀
⡇⢀⣤⠞⢿⣿⣿⣿⣿⡿⠟⢦⡀⢸⡇⢀⡴⠻⣿⣿⣿⣿⣿⡿⠳⣄⠀⢸⠀⢀⡔⠻⣿⣿⣿⣿⣿⠟⠳⣄⠀⣿⠀⣠⡞⢿⣿⣿⣿⣿⣿⠿⢦⡀
⣷⠟⠁⠀⠀⠙⢿⡿⠋⠀⠀⠀⠙⢾⡶⠋⠀⠀⠈⠻⣿⡿⠋⠀⠀⠈⠳⣾⠖⠁⠀⠀⠈⠻⣿⠟⠁⠀⠀⠈⠳⣿⠞⠃⠀⠀⠙⢿⣿⠟⠁⠀⠀⠙⢶
⣿⣦⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣾⣷⣄⡀⠀⠀⠀⢸⡄⠀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⣴⣿⣦⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣴
⣿⣿⣿⣦⡀⠀⠀⡇⠀⠀⣠⣾⣿⣿⣿⣿⣷⣆⡀⠀⢸⡇⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⣿⠀⠀⣠⣾⣿⣿
⣿⡿⠋⠀⠙⢦⣀⣇⡴⠋⠀⠙⢿⣿⣿⡿⠋⠀⠙⢦⢸⣇⡴⠋⠈⠙⢿⣿⣿⡿⠋⠀⠙⢆⣿⣠⡾⠋⠈⠻⣿⣿⣿⠟⠉⠈⠳⣄⣿⣠⠞⠁⠙⢿⣿
⡏⠀⠀⠀⠀⢀⣽⣯⡀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⢀⣽⣯⡀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⢀⣽⣏⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⢈⣿⡁⠀⠀⠀⠀⠙
⡇⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⢸⡇⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⢸⠀⠀⠀⢀⣴⣿⣿⣿⣦⡀
⡇⢀⡴⠛⢿⣿⣿⣿⣿⡿⠛⢦⡀⢸⡇⢀⡴⠛⢿⣿⣿⣿⣿⠿⠛⢦⡀⢸⡇⢀⡴⠻⣿⣿⣿⣿⣿⠟⠳⣄⠀⢸⠀⣠⠔⢿⣿⣿⣿⣿⣿⠟⢦⡀
⣷⠋⠀⠀⠀⠉⢿⡿⠋⠀⠀⠀⠙⢾⡷⠋⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠙⢾⡶⠋⠀⠀⠀⠹⢿⠟⠁⠀⠀⠈⠳⣾⠞⠁⠀⠀⠘⢻⣿⠟⠁⠀⠀⠙⢦
⣿⣷⣄⠀⠀⠀⢸⡇⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⣿⣷⣄⡀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣴⣿⣦⣀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⣾
⣿⣿⣿⡷⣄⠀⢸⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⠀⠀⣀⣴⣿⣿⣿⣿⣿⣷⣦⡀⠀⢸⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⡇⠀⠀⣠⣾⣿⣿
⣿⠟⠁⠀⠈⠳⣼⣇⠴⠉⠀⠙⢿⣿⣿⠟⠁⠀⠙⢦⣸⣠⠞⠁⠀⠙⢿⣿⣿⠟⠁⠀⠙⢦⣸⣠⠞⠁⠈⠻⣿⣿⣿⠟⠁⠈⠳⣄⣇⣠⠞⠁⠙⢿⣿
⡇⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⢹⡃⠀⠀⠀⠀⢀⣽⣧⡀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⣀⣿⣅⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⣨⣿⡁⠀⠀⠀⠀⠙
⡇⠀⠀⢀⣴⣿⣿⣿⣿⣧⡄⠀⠀⢸⡇⠀⠀⣠⣴⣿⣿⣿⣿⣦⡀⠀⠀⢸⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⠀⠀⠀⣿⠀⠀⠀⣠⣾⣿⣿⣿⣶⡀
⡇⣠⠖⠙⠻⣿⣿⣿⣿⠟⠉⠣⣄⢸⠇⣠⠞⠙⢿⣿⣿⣿⣿⠟⠙⢦⡀⢸⠀⣠⠞⠛⢿⣿⣿⣿⣿⠟⠳⣄⠀⣿⠀⣠⠞⠻⣿⣿⣿⣿⣿⠟⠢⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⠿⠿⠿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⢀⣤⣴⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠻⢷⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣙⣷⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠘⠻⣷⣄
⠀⠀⠀⣀⣴⣿⠟⠁⣀⣤⣶⣾⣿⡷⠀⠀⠀⢀⣼⠏⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⢷⡄⠀⠀⢰⣿⣷⣤⣀⡀⠈⠻⣷⣦⡀
⢀⣴⣾⣿⣿⣷⡿⠿⠛⠋⠉⠀⣿⡇⠀⠀⠀⣼⣇⣀⡀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⠈⣿⠀⠀⢸⣿⡍⠉⠛⠿⣷⣶⣬⣽⣿⣷⣤⡀
⣿⣿⣟⡋⠉⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⣿⣿⣏⣽⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣩⡇⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿
⠀⠙⠛⠿⣿⣶⣶⣤⣤⣤⣤⣾⣿⠁⠀⠀⠀⠙⠿⢿⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⡷⠟⠀⠀⠀⣿⣧⣀⣀⡀⢀⣀⣠⣤⣶⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⣍⣙⢲⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠈⠛⢿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⣀⣀⣀⣤⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡀⠀⠀⠀⠀⠈⣽⡿⠛⠻⠿⠿⠿⠿⠿⢿⣿⣥⣬⣿⠿⠿⠿⠟⠛⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢿⣧⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠈⢿⣷⣤⣀⣀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠈⠛⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⢀⣤⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣶⣶⣶⣶⣶⣶⣾⠿⠟⠁⠛⠿⣷⣶⣶⣶⣶⣶⣶⣿⠿⠿⠛⠋
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠉⠁⠀⠀⠁⠀⠀⠀⠈⢸⠂⠙⠀⠀⠀⠀⠀⠄⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⢀⠤⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄⠐⠀⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢁⣤⡖⠂⠉⠉
⠀⠠⠀⠠⠀⠁⠀⠉⠁⠀⠀⢐⡿⠀⠐⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢃⣼⠶⢋⣌⠀⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⣠⡾⠋⠀⠀⠆⠀⠀⠀⢈⣧
⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⡤⢠⣆⠀⠈⠀⠀⠀⠁⠀⠀⢀⣼⠃⠀⠀⠀⠐⠖⠛⡟⠛⠏⢁⠀⠀⠊⠁⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣟⠀⠔⠀⠀⠀⠀⠀⠀⠈⠂⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠠
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡂⣨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡈⠥⣀⠀⠀⠀⠀⠀⢈
⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠙⣧⡈⡀⠀⠀⡀⠀⠀⢠⡀⠀⠛⠀⢀⠀⠀⠀⢀⠀⠀⠀⢈⡓⠀⠀⠀⠔⠁
⢀⠀⠀⠀⠀⠐⠂⠘⠀⠉⠀⠄⢀⡷⢄⠘⣦⡀⠨⢽⣦⡀⠱⢄⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉
⢁⠤⠴⠥⢤⣀⡠⠄⠀⠀⠀⠀⣨⠁⠁⢨⠁⠑⠀⠀⠹⡝⠿⡸⣇⠀⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⣠⠛⠀⠉⡇⠀⠀⣧⠀⠘⡜⡆⢡
⠀⠀⠀⠀⠀⠀⠐⠃⠈⠀⠀⠀⠀⡴⠂⠀⠀⡰⠂⠀⡀⠊⠃⢀⠂⣴⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢤⠄⢁⡠⠞⠁⢀⠤⡂⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠑⢲⠆⠀⠀⠈⠔⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠘⠋⠉⠀⠈⢀⣀⠤⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠇⠀⢠⠃⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀⠠⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⢤⣾⢁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠀⠄⣼⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⡀⠀⠐
⡤⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠚⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠰⠞⠁⠀⠀⢁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⣉⣷⡄⠉⠂
⠀⠀⠀⠀⠺⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⡴⢾⣿⠋⠉⠀⠠⠀⢆
⠀⠀⡀⠀⠀⠨⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠒⠉⢁⠪⠕⠁⠀⠀⠀⠀⠀⠙⡤⠀⠀⠀⠀⢀⡀⣀⡄
⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤⣀⣠⡤⢴⠠⠊⣀⠀⠠⠄⠀⠀⠀⡆⣇⠀⢳⣁⡠⠂⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⡠⢖⣪⡷⠋⢈⡤⠞⠏⠀⠒⠒⠒⠲⠲⠾⠓⠛⠘⠋⠁⠀⠀⠈⢀⣼⣤⠏
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠤⠌⠉⠐⡡⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠤⠀⡀⠀⠀⠀⠀⠠⠆⣸⠁⢻⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠠⠀⠈⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⢀⠄⠉⠀⠤⠄⠀⠀⠈⠀⢀⣀⣀⣉⠀⠒⠀⠀⡀⢀⡀⠀⢤⠶⠊
⠀⠀⠀⠀⠀⠀⠀⣀⠀⡴⠁⠀⠄⡠⠀⠁⠠⠠⠆⠊⠀⠀⠀⠀⠀⠁⠀⠀⠁⠒⢄⣀⡀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠂⠐⡀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠉⠀⠘⠠
⠀⠀⠀⣀⣠⣤⣤⡤⡜⠉⠀⠀⠁⠘
⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠰⠀⠐⠀⠆⠄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⠀⠀⠄⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠘⠁
⠀⠀⡈⠀⠀⠀⠀⠀⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠁⠀⡠⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡀⠀⠀⠀⠀⠠⠂
⠀⠀⠐⠂⡀⣄⣤⡄⢠⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢴⡄⠀⠀⠀⣲⠂
⠀⠀⠀⠀⡀⠈⠐⠀⠀⠈⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠉⡔⡁
⠀⠀⠀⠀⠁⠖⣀⠶⢄⡀⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠲⠆⢸⡆⠀⡼⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⢀⠉⠐⠒
⠀⠀⠀⠀⠀⠂⠀⠙⠉⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⡆⢰⠁⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠐⠒⠠⢄⠄⠀⠈
⠀⢰⠋⠃⡇⣔⠀⡀⡀⢤⢠⠀⢆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠆⠀⠙⠂⠀⠉⠁⠀⠻⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣄⠀⡀⠀⠛⠛⣤⣀⠀⣀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠠⠀⢀⢀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⢀⡀⢆⠀⢀⠈⠉⡀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣦⡀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⢿⠀⡀⡞⠀⠉⢠⠸⢃⠗⢠⣀⡴⠀⠀⠀⠀⠀⢸⣷⠒⠋⢸⣧⠈⠒⣲⣿⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠘⢀⡀⠈⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⢐⣞⠠⠯⠬⠅⠡⠌⠋⢅⣲⠚⣄⡠⡴⠃⠀⠀⠀⠀⠀⢻⠙⠀⠀⠀⠀⠀⠀⠈⠀⢣⡀
⣧⣄⣀⠀⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠠⠠⠤⠀⠀⠀⠀⢀⠈⠉⠚⠁⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠄⠠⠠⠀⠀⠄⠀⠱
⠙⢿⣿⣤⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⢀⠁⢂⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣌⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⣄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣊⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠛⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢤⡀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀
⠀⠀⠀⠀⢀⠂⠀⠀⢠⠞⠀⠀⠀⠀⠙⡀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢳
⠀⠀⠀⠀⢸⠀⠀⣰⠋⠀⢀⣀⣠⡤⠤⠴⠤⠧⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢸⡇
⠀⠀⠀⠀⠈⢦⡴⠃⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣤⡴⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⢸
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣀⣤⠤⠤⠤⠤⣄⡀⠀⠀⡸⠀⡟
⠀⠀⠀⠀⠀⠠⢣⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⣧⠠⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢀⡽⠀⠀⠹⠞⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣛⡟⠀⢰⠁⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⣸⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠒⠉⠁⠀⠀⠀⠀⡷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⢄⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠌⢳⣤⣄⣀⣀⣤⡴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⢀⠤⠤⠀⠀⣠⠊⠀⠈⣩⠏⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⡏⢠⠂⠀⢰⠃⠀⢀⡴⠃⠤⠤⠖⠋⠉⠉⠒⠲⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⡇⠀⠀⡈⠳⠶⠋⠀⠀⠀⠠⠤⠤⠤⢤⣀⡀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠈⠢⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡡⠴⠒⠒⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠘⠢⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠈⠳⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢠⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡀⠀⢀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠦⣀⡤⠞

⣧⣿⢹⢳⣿⡿⣿⢸⡟⣿⢸⡇⣿⡈⣿⣸⡏⣇⢹⠻⡇⠀⣷⠀⠀⠀⠀⠀⠀⣰⠇⠀⣠⢞⡥⢖⣊⡩⠭
⣸⡿⡾⡞⣿⣿⡿⣼⠃⣿⢸⡇⢸⡇⣿⡇⣿⢹⢸⡆⠳⢿⠈⠢⣤⣀⠀⠀⢰⡏⢀⣼⢟⣵⣾⣷⠶⢿⣿
⣯⢣⣧⢇⡿⣸⠇⣿⢠⣿⢸⡇⢸⡇⣿⡇⣿⢸⠸⡅⠀⢸⡆⠀⠈⠙⠦⡄⣸⡇⣼⣿⣿⣿⢕⣪⡭⠵⠶
⠃⣼⢝⡾⢱⡟⣸⠇⢸⡟⢸⡇⣼⠇⣿⡇⣿⢸⢠⡇⠀⣼⡅⠀⠀⠀⠀⢌⢻⣽⣿⣿⣿⡷⢋⠤⣒⣨⣭
⣾⢏⡾⣱⠏⢠⡟⢀⡿⢁⡿⣱⠏⢠⣿⢳⣿⣿⡾⠀⠀⡟⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⣱⡷⠛⠉⠁
⡱⢋⡴⠋⣠⠏⣠⠟⣡⠟⣱⠏⣠⣾⣷⢋⣾⠞⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⡟
⡥⢛⡴⢊⡥⢞⣡⢞⣡⠞⢁⣴⣿⣿⣷⡿⠃⠀⠀⠀⢹⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⣚⡵⢚⡭⣖⡯⠖⢋⣠⣴⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏
⣵⣾⠿⣚⣥⣴⣿⣿⣿⣟⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⣽⣶⣿⣯⣅⣈⠀⠀⠈⠉⠛⠿⣿⣶⣤⣀⠀⠀⠀⠐⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⡀⠀⠈⠈⠉⠙⠛⠷⣦⡀⠀⠀⠀⠈⠑⢝⣧⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⡛⠻⠶⣦⣄⡀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⢹⣧⣠⡾⠋⠂⠒⠀⠀⠀⠀⠀⠀⢀⢀⣠⠃
⠙⠷⢤⣀⡉⠛⠷⣦⣄⠀⠀⠈⠳⣄⠀⠀⠀⣿⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠠⠀⠐
⠀⠀⠀⠈⠉⠓⠲⢬⡙⢿⣦⡀⠀⠘⢧⠀⣠⣿⠂⠀⠀⠀⠀⠀⠀⠀⢰⣾⢏⠠⠂
⠛⠛⠛⠲⠶⢤⣀⠐⠙⢷⣝⢷⡄⠀⢸⣿⣻⣥⣄⣀⠀⠀⠀⠀⠀⡄⠀⣿⠃⠀⠀⠀⠀⠀⠀⢀
⣭⣭⣭⣕⣢⢄⡈⠓⢆⠀⢹⡎⣷⣠⡟⠡⠄⠀⠀⠉⠙⠲⣄⠀⠀⢹⣾⣏⠄⠀⣀⠠⡰⠄⠊⠀⠉⠉⠉
⣶⠿⠳⠶⢮⡑⢯⣢⡈⢳⠀⣿⣿⣷⣦⠶⠤⣔⡢⠀⠀⠀⠈⠳⡄⠸⣿⢏⣴⠪⠔⠁⢀⡠⣶⠿⣛⣛⣛
⣉⣉⡛⠛⠦⡍⢲⣹⡱⡀⡇⣹⣿⣿⣭⣽⣛⢶⣭⡳⢅⠢⠀⠀⢹⢸⡿⠃⠁⢀⣠⡾⣛⠭⣒⠭⠒⣒⣲
⡤⢭⣉⠓⠦⡈⢆⢹⣧⢱⣧⡿⠉⠀⠀⠀⠈⠙⢪⣻⣮⠳⡱⡀⢸⣼⠃⢀⣴⡿⡫⡪⠔⠉⣀⣴⡿⢗⡯
⠤⢭⣐⠭⡢⡙⡼⡄⣿⢸⣿⣷⣖⡒⠲⢄⠀⠀⠀⢹⣟⢇⢻⣧⣾⠃⣴⣻⡫⡪⠊⢀⣴⣾⢟⡵⣪⠵⣚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠄⠶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⣶⡞⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠉⠢⡄
⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⣤⡜⠀⠀⠀⣛⣃⠂⠀⠀⠀⠀⠀⠀⠀⠙⢉⣀⡀⠀⠀⢹⣦⠑⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣻⠇⠀⠀⢼⣿⣿⡆⡐⠀⠀⠀⠀⠀⢁⡠⣿⣧⣽⠦⠀⠸⣿⣷⠀⠀⡄⠀⠘⢆
⠀⠀⠀⠀⢨⡇⢀⠀⠀⢸⣿⡀⠘⢀⠀⠉⠡⠄⠀⠀⠀⠀⠀⠀⠘⠇⠈⠉⠁⠀⢠⠅⢻⣿⡀⠰⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣮⡴⠟⠀⠀⠈⣿⠃⢀⡚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠤⢀⣿⣧⠀⠀⠀⠀⠀⠠⣘⣄
⠀⠀⠀⢰⣿⣦⡀⡀⠀⠀⢿⡆⣄⠁⠀⠀⠀⠀⢠⣀⣀⣀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠲⣠⡿⣿⡄⣦⣀⠀⢀⣤⡀⣬⡃
⠀⠀⠀⢸⣟⣿⣿⣧⣦⣦⢸⡇⡇⠊⣕⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠆⠈⡂⠀⢸⣾⡆⣿⣷⣿⡇⣿⢿⣦⣼⡟⣸⠿⠁
⠀⠀⠀⠀⣿⡟⣿⢱⣷⣾⢸⣧⠣⡄⢻⡇⠂⠀⠉⠹⢿⣿⣿⠿⠋⠀⠀⠀⣸⠟⢁⠼⣿⠿⣿⣷⢹⣿⣿⠄⡴⢏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⡁⢸⣿⠀⠀⠀⢡⡀⠀⠀⠀⢠⣈⡠⠀⠀⠀⠀⢠⡏⢀⢀⣀⡁⠠⣹⣿⠸⣿⣫⡠⢣⠁
⠀⠀⠀⠀⠀⠀⠹⢿⣿⣡⣏⣴⡗⠀⢀⠸⣿⢦⣴⣦⠾⢿⣿⣶⣶⣤⡴⣋⠞⠁⠀⠀⠀⠈⢟⢿⡇⢿⣻⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢺⠉⠁⠀⠀⠘⠓⠈⠻⣿⡄⠀⠀⠀⠀⣨⣿⡞⠁⠀⠀⠀⠐⠄⠀⠀⣑⣿⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⠀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣤⣴⡿⠋⠀⠀⢀⠀⠀⢠⡀⠀⢹⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⡀⠂⠀⠀⠀⠀⠈⠉⠋⠋⠉⠀⠀⠀⠀⠀⢿⡂⠀⣡⣤⣼⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠃⠘⠧⠾⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠁⠀⠋⠛⠋⠈⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⢷⣀⡀⠀⣄⡀⠀⠀⠀⠀⠢⠀⣢⡄⠘⠂⠂⠀⠀⠤⢀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠦⣳⡖⣶⣤⣿⠾⠗⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠂⠀⠀⠉⠉⠉⠁⠈⠉⠁⠀⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣴⣀⡁⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⣿⣿⠿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢟⣿⣟⣹⣿⣿⣻⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⣿⣯⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣳⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣏⡛⣛⣽⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠈⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⠀⠄⠀⢀⠀⢠⡄⠤⠄⠒⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⢠⣄⣀⣠⣴⣶⣷⣞⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠋⠁⠀⠀⠀⠁⠀⠀⣠⠊
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡄⠤⠛⠉⠀⠀⠀⠀⠀⠈⢧⣄⣀⡀⠀⢀⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠶⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠀⠀⠀⠀⠀⠠⠄⠤⠤⠤⠭⠀⠀⠀⠶⠶⠶⠶⠴⠦⠀⠀⠀⠀⠀⣤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣦⣞⣠
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠐⠒⠒⠒⠒⠒⠒⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⣀⣀⣰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣖⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠻⣿⣿⣿⣿⡇⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢿⣿⡇⠀⠀⠀⢘⡔⠚⠛⢃⠸⠓⣟⠟⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡇⠀⠀⠀⠘⠙⠛⠛⠛⠛⠂⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠀⠈⠣⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣌⣁⣴⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠉⠚⢱⣾⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣄⣀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⣴⣀⣄⣄⠀⠀⠀⢿⢿⠁⠀⠀⠀⠻⠿⠃
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣧⠘⠛⠀⠀⠀⢰⣶⣾⣶⣶⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣧⡀⠘⠂⠀⠐⠂
⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⣿⣿⣿⡿⠿⡫⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣶⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠹⠍⠋⡃
⠀⠀⠀⠀⠻⣿⣇⢻⡀⣷⣼⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⣟⣿⢿⣏⣻⠛⠛⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣼⣀⡔⠁
⠀⠀⠀⠀⠀⣽⠿⠿⠿⠛⠻⣿⣿⣿⣿⣿⡃⠘⣿⢯⣯⠿⣅⠿⣿⣮⣯⣯⣳⠒⠈⠘⠿⠟⠛⣹⣿⡋⠉⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠸⣷⣶⣶⣷⣶⣿⣿⣿⣿⣽⡉⠲⠈⠁⠙⠃⡀⡉⢘⠃⠒⠎⢳⣾⣿⣶⣾⣾⣿⣿⣿⣿⣿⣷⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⢶⠆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠒⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⢃⡀⠀⠀⠀⠀⠀⠀⠀⡄⠠
⠀⠀⠀⠀⠀⠀⣰⠀⠀⢰⠀⠀⠀⠀⠀⠀⣀⠾⠋⠁⠀⠠⠀⢐⣠⠄⠐⠈⠡⠒⠠⠤⠀⠉⠙⠻⣗⠁⠀⠀⠀⠀⠀⡡⠀⠁
⠀⠀⠀⠀⠀⠀⡍⠾⠃⢸⡆⠀⠀⢀⡠⠞⠁⠀⠀⠀⠈⠀⠠⠻⠁⠀⠀⠀⠀⠀⢩⡰⠊⠀⠀⠀⠈⠀⠀⠀⠀⢀⡚⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣻⣦⡄⠈⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠠⠀⠀⠀⠀⠀⠠⡈⠁⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡿⠁⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠻⢫⠆⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠈⢐⣬⣵⣦⣽⣿⣤⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⣀⢖⣨⣥⣭⣒⢶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⣼⣿⣿⣿⣿⡷⣷⣋⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠐⡱⢣⣿⣿⣿⣿⣿⣶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠐⢌⣿⣿⣷⣿⣷⠿⠛⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠱⢾⣿⣾⣿⣿⣿⢛⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠆⣐⠂⠀⠀⠀⠠⣙⠛⠻⠁⠁⠀⠄⠁⠀⣀⣴⣿⠶⠶⣾⣶⣄⡈⠑⢤⠀⠀⠐⢫⣭⢥⣞⡋⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⢸⣶⡷⠄⠀⠊⢀⡰⠜⠋⠀⠀⠄⠀⠀⠀⣼⠟⣥⣶⣄⣠⢠⣄⠉⢻⡄⠀⠐⠦⡀⠀⠹⢟⡩⠀⠀⠀⠁⠇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠯⠈⠀⠀⠐⠁⠀⠀⠀⠀⠙⣾⣧⣿⡟⣿⠻⣿⣦⣼⠁⠀⠀⠀⠘⢢⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣙⠃⣿⣄⣌⣤⠏⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⢀⢰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢟⣻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠁⠀⠰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠷⣖⠈⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣘⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣼⣿⣿⣿⣿⣷⣧⣀⠀⠀⠀⠀⠀⠀⠀⡠⠉⢤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⣘⠢⣀⠀⠀⠀⣴⡾⠛⠛⠛⠛⠛⣻⣿⡟⠋⠛⠛⢿⣿⡶⠢⢀⣆⡈⡹⣺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠙⠶⣽⣷⢺⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠙⣆⡘⣋⢉⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⡍⣋⣽⣇⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⡿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣏⡻⣦⣄⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢠⠟⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣭⣋⠛⠳⠶⡾⢿⣶⡶⢦⣶⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⠾⠶⠶⠖⠛⠊⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⡿⢿⠿⠿⠿⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡿⠻⣿⣿⢿⠿⠿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡬⢻⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠈⢼⠇⣾⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡦⢼⠆
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⠀⠀⠀⠀⠀⣤⣤⣜⠀⠀⠀⠀⢃⣤⣤⠀⠀⠀⠀⠀⢶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⣰⣿⣿⣧⣤⡀⠀⠀⠀⠀⠉⣿⣧
⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⣿⣧⡻⡿⢛⡃⠀⠀⠀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠙⣿⣷⣾⠚⠃⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠐⣻⣿⠿⠷⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⢘⣿⣿⠟⠾⠆⠀⠀⠀⠀⠈⢿⣧⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢠⣤⣤⣀⠀⠀⡀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⢋⣴⠸⣿⣿⡟⠀⠀⢧⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠀⠀⠉⣵⣇⣬⣴⠃⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣤⣀⣀⣈⣉⣸⡿⠋⠀⠀⠀⠀⠘⢶⣤⣀⣀⣀⣀⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠁

⠀⠀⣄⡀⢠⡀⠀⣠⡄⠀⠀⠀⠀⠀⣶⡦⢀⠀⠀⠀⠀⠀⢀⣤⣾⣦⣄⠀⠀⠀⠀⠠⠐⠒⣄⡒⠀⠄
⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⣼⣿⡗⣲⡄⠀⠀⠀⠀⠛⠛⢻⠛⠛⠃⠀⠀⠀⢃⢠⡦⢐⣴⡆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣯⠀⠀⠀⠀⠀⣐⣀⣸⣀⣐⡀⠀⠀⠀⠨⢑⡨⠤⢂⡰⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⣾⡟⠛⠛⠛⣿⡆⠀⠀⠀⢸⡏⠉⠉⢹⡇⠀⠀⠀⠀⣴⡺⡽⣖⢄⠠⠀⠀⠀⢀⣤⣤⡄⣤⡤⣄
⠀⠀⡟⠀⠰⡇⠀⠙⡇⠀⠀⠀⢸⡷⠤⠤⢼⡇⠀⠀⠀⢸⢞⢎⢏⣎⣾⠀⠀⠀⠀⢸⣿⣿⣷⣿⣤⣿
⠀⠀⣿⣲⣴⢳⣴⣾⡇⠀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⠈⣯⢗⣷⣮⣎⠀⠀⠀⠀⠻⠟⠃⠀⠈⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉

⠀⠀⣦⣬⣀⣀⣥⣴⡄⠀⠀⠀⢠⣶⣾⣷⠂⠀⠀⠀⠀⠀⠀⢀⣒⣒⡀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⡄
⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠱⢆⣾⣿⠀⠀⠀⠀⢀⣿⡿⣿⣷⠄⠀⠀⠀⢸⣿⡏⣄⡌⣿⣿
⠀⠀⠿⠿⢿⡿⡿⠿⠃⠀⠀⠀⠈⠀⣾⣿⠿⠃⠀⠀⠀⠀⣼⣿⣷⣶⣶⣆⠀⠀⠀⠀⠉⢡⣟⣣⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠉⠃⠀⠀⠀⠀⢠⠖⢻⠛⠲⡄⠀⠀⠀⠀⠾⠮⠴⠧⠷⠇
⠀⠀⠀⢸⡁⠀⠀⢀⡀⠀⠀⠀⠀⠀⣹⠶⠀⠀⠀⠀⠀⠀⡟⠑⣾⣷⠊⣻⠀⠀⠀⢠⠀⢴⠄⢴⠄⢠
⠀⠀⣀⣀⣙⣲⣒⣋⡀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⠾⣅⣨⠶⠃⠀⠀⠀⠈⢶⣾⣶⣾⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡄⣤⢠⢶⡀⡄⡄⢴⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠌⠀⢸⠿⢻⢸⢸⡇⣿⠇⢸⢸⡇⠸⠓⡀⠰⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠢⠔⠀⢁⠀⠀⠆⠈⠠⠀⠠⠉⠁⠒⢠
⠀⠠⣐⣦⣤⣄⡢⡌⠁⡀⠀⠘⠀⠘⠈⠛⠁⠘⠀⠚⠈⠓⠀⠀⠀⠁⠀⠀⠈⠀⠀⠃⠐⢤⠀⠈⠂⠀⠀⡠⠃⠈⠇⠀⠀⢐⡀⣥⠀⣀⠴
⠀⠌⠛⠛⠋⠉⠀⠃⠀⠈⡆⠀⠈⠄⠀⢀⠄⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠆⡠⠃⠀⣬⠆⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⢀⢐⡀⣀
⠀⠄⠀⢿⣿⡗⠀⡬⠀⢂⣀⠀⠀⡼⠰⠄⠀⡀⣀⠀⠀⠃⠀⠀⠠⠞⠀⠀⠀⢀⠑⠐⡂⠡⠄⣀⠀⠀⠣⠀⡔⠉⠢⡀⠀⡰⠊⠁⠀⠀⣄⠑⡄
⠀⠈⠂⠠⠭⠀⠊⠀⡈⣤⣴⣶⣶⣶⣶⣦⣤⠀⠀⠈⠀⠃⠀⠀⢀⢀⡀⠀⠀⠀⡄⠙⠤⢄⠀⣻⠈⢈⠁⠸⠀⠀⠀⠓⡀⣄⠀⢁⠀⠌⠠⢀⠇
⠀⢀⠄⠠⠠⡀⠀⠀⡇⣿⣿⣷⣿⣟⣿⣿⣿⠀⠀⠀⡆⢰⠀⠀⠙⠺⠹⠈⠠⠀⠰⠀⠀⢛⠒⠚⠀⠂⡃⠘⡐⠀⠀⣈⠃⠈⠐⠀⠀⠀⠀⠁
⠀⠊⠀⠀⠀⠈⢂⠀⡇⣿⣿⡟⡿⣿⡿⢿⣿⠀⠀⠀⠆⠀⣤⠆⠂⠐⠒⠒⠒⠒⡖⠀⠀⠸⠀⠀⠀⠨⠁⠀⢱⠀⠀⡄⠀⠀⢠⢴⣯⡀⠀⠈⠢
⠰⣅⣀⣀⢀⣀⠃⠀⠇⠛⠿⠿⠿⠿⠿⠟⠣⠀⠀⢀⠀⠀⠉⠀⢀⡠⠄⠐⠀⠤⡀⠀⠀⠀⠆⠀⠀⡠⠀⠀⠈⠒⠒⠁⠀⠀⠁⠀⠈⢿⣄⠐⡰
⠀⢽⠔⠛⢸⡇⠀⠀⠸⠋⠉⠉⢉⣉⡉⠉⡈⠉⠻⠅⡠⠐⡠⢤⣌⡰⢄⠀⠀⡠⠄⢹⠒⠄⡀⠀⠀⡴⠒⠒⢠⡀⠀⠐⠄⠀⠐⢀⠀⠸⠿⠋
⠀⢺⢤⡄⢾⠀⠀⠀⠀⢸⠉⠀⠀⣠⡤⠀⠃⠀⢀⡐⠀⠠⡀⠀⠀⠀⢀⠀⢸⠀⠀⣘⠢⠱⠈⢄⠀⠀⠀⠒⡆⣶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠙⠲⠧⠟⠂⠀⠀⠀⠈⡄⠀⠠⡤⠛⠀⠸⠀⠑⢄⠀⠖⡱⠆⢩⠀⢊⠐⢚⡁⢎⠠⢊⠜⢀⠒⠀⠢⠄⠤⠬⠤⠤⠤⠊
⠀⠀⠀⢀⣤⣶⣶⣦⣀⠀⢃⠀⠀⠶⠐⠂⠀⡆⠀⠀⠑⠠⢀⠀⠀⠉⠉⠀⠀⠀⠀⢁⠠⠐⠁⠀⠀⠀⠀⢀⠠⢀⠀⠀⣿⣻⠏⣿⡟⣿⡏⡉⣿
⠀⠀⣴⢟⣭⡶⣶⣭⡻⣆⠘⠒⠒⠈⠉⠉⠀⠀⠀⠀⢀⣀⡤⡀⠀⠀⠀⠀⠀⢀⢠⠶⠤⠤⠀⢄⠀⠀⢠⠁⠀⠀⢑⠀⠟⠛⠛⠃⡀⠈⠛⠛⠛
⠀⠰⠿⠟⠁⠀⠈⠙⢳⢿⠀⢠⣴⣶⣶⣶⣶⣶⣶⡄⠈⢥⠜⠁⣀⡤⡄⠀⠼⢁⣄⡀⠀⠘⠃⠃⠀⠀⢸⠀⠀⠐⠘⡄⠀⠀⢘⠀⠉⠈⠈
⠀⢃⣀⡀⠀⠀⠀⠀⣄⣠⠀⢸⡏⠁⠸⠀⡏⠠⢸⡇⢠⣀⢶⡄⢈⣀⠀⠀⠄⠈⠛⢀⠔⠒⠤⣀⡸⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄
⠀⠀⢹⣷⣄⠀⢀⣼⣿⠀⠀⢸⣇⠀⡀⡄⠃⠰⢺⡇⠈⠁⠀⢠⣼⣙⠃⠀⠈⠒⠒⠁⠀⣀⠀⠀⢀⡀⠀⠑⢰⡶⠒⠁⢐⠀⠀⠀⠐⠈⠀⠐
⠐⠂⠘⠋⡻⠀⠘⢋⡙⠀⠀⢸⣿⢾⣷⣿⣾⣤⣾⣿⠀⠀⢀⠀⠈⡉⠀⠀⠀⠀⠀⠀⢺⠁⠋⠙⠛⠛⣿⣆⠘⠷⠇⠀⠺⣶⣿⣛⣓⣚⣻⣷⣾
⠀⠈⣠⣉⠤⡀⠀⠀⣈⡄⠀⣰⣿⠀⡇⡆⢀⠘⢸⣿⠀⢰⠓⠲⠾⠶⢾⠄⢄⠀⠀⠀⠇⠀⣘⢀⡀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢀⠿⠏⢀⡠⣿⣿⠿⠷⠀⠉⢿⣶⡷⠶⠿⠶⠾⠟⠀⢸⠀⠀⠄⠠⠀⠀⠀⠀⢀⡞⠋⡧⠰⠎⠀⡤⠢⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢈⠅⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⡀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠀⢠⠆⠌⠀⠸⡄⠀⡀⠀⠀⠀⠃⠀⢸⠀⠂⠀⠞⣀⣀⡀⠙⠀⠈⠀⠁
⠀⢀⡀⠤⠤⠤⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⠀⠀⢀⣀⡀⠀⠑⠀⠀⠀⠊⠀⠀⠰⠀⠘⠒⠁⠀⠀⠀⠧⠴⠃⠐⠀⠀⢼⣿⣿⣿⡗⠀⡠⠀⠐⠄
⠀⠂⠀⠀⠀⠀⠀⣳⠀⠀⡖⠃⠀⣀⠀⠀⠑⡄⢸⠀⠀⠉⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠄⠀⠀⡄⠀⠀⠙⡍⠉⠀⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠇⠀⠈⠿⢿⠀⠀⠃⠈⡀⠀⠀⠀⠀⠀⡥⠐⠭⠂⠀⠀⠀⢀⠄⠠⣀⠀⠀⣀⠀⢀⠇⠀⠀⢠⠇
⠀⠀⠀⠀⢶⠂⠀⢸⡀⠀⠀⠀⣀⠀⢀⣀⡀⠀⠀⠇⠀⠀⢀⠔⡨⢔⠁⠀⢀⠀⠀⠐⣵⡿⢷⡌⡆⠀⠜⠀⠣⡀⠀⢔⠺⠂⡄⠀⢸⠀⠘⠃
⠀⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⠟⠣⠞⠃⠈⠀⢀⠀⠀⠈⠁⠀⠸⠀⠀⠀⠠⡊⠀⠙⠾⠋⠈⠀⢸⡀⠀⠀⡄⠀⠀⠀⣤⡆⠀⠈⡄
⠀⠑⠚⠚⠛⠛⠛⠋⠀⠀⠑⠆⠀⠀⠀⠀⠀⠐⠃⠀⠉⠑⠒⠒⠢⠤⠆⠀⠀⠀⠈⠢⠠⠊⠀⠀⠀⠈⠑⠀⠊⠁⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠿⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⠀⣠⡞⠉⠉⠛⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣶⣄⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠀⢰⡄⠀⠀⠈⠙⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠉⢉⠉⠛⢷⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠛⠉⠁⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡙⠻⣿⣆⠀⣿⣷⡄⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣰⡿⣧⡉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠹⡆⠘⣿⡀⢹⣿⣿⣄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣿⠁⠈⣿⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣸⣷⠀⣿⡇⠀⠙⣿⠿⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢸⠇⠀⠘⣿⣷⣤⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⢀⣿⠁⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⣿⡀⠀⠀⢿⣿⣿⡿⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣤⠾⢃⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⡾⠿⣷⣤⡀⠈⠻⣿⣤⡾⠃⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠙⢧⣴⠶⠒⠲⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⢿⣷⣤⣠⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠿⠿⢿⣷⠀⠀⠀⠀⢘⡏⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠉⠑⠛⠻⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀⠀⢀⣰⣿⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠙⢿⣿⠿⠿⠿⠟⠛⠁⠀⣠⣴⣿⠏⠀⠀⠀⠀⠠⠾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠛⠿⣶⣤⣤⣄⣠⣤⣤⣴⠾⠿⠗⠶⠾⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣾⠿⠿⠿⠿⣷⣄⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠿⢿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣶⣶⠞
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣤⣤⣶⣿⣿⡇⠀⠀⢀⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢠⡇⣆⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠏⢸⠀⠀⠀⢸⣧⠀⠘⣿
⠀⠀⠀⠀⠈⣇⠘⢦⡀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⡿⠀⠀⠀⢸⣿⠀⠀⠻⣧⣤⡀
⠀⠀⠀⠀⠀⠹⣄⠀⠙⠶⣤⣤⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⠿⠟⠛⠛⢦⡇⠀⠀⠀⠘⠿⠛⢦⡀⣄⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⣉⣉⣁⣀⢀⠀⠀⢀⣉⣄⡀⠀⣾⣇⠘⣧⡀⠀⠀⣤⠀⢰⠘⣧⣼⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⢿⣿⡿⠿⠛⠙⠛⠿⠿⠟⠻⠿⠛⠿⠿⠿⠿⠷⠟⠻⠟⠀⠈⠉


⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠆⠁⠀⠀⠰⡍⠙⠆⠄⡀
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⢰⠃⠀⠀⣴⠍⠠⡀
⠀⠀⣒⡈⠀⠀⠀⠀⠀⠀⠘⣆⣠⠾⢫⡆⠀⠈⢠⡀
⠀⠀⠉⠂⢀⣤⠤⣺⣫⠿⠀⠈⠁⠀⢹⠁⠀⠀⣀⡿⠙⣶⡀⢤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠠⢦⠶⠁⠀⠈⢀⠂⠀⠠⣼⠂⠀⢰⠋⠁⣠⣿⣇⠈⢻⣿⣿⢯⣍⣉⣉⣡⣭⣤⣈⡉⠉⠉⠁⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⢻⠀⠀⠁⠀⠀⠙⣿⡏⠀⠘⡟⠃⠀⣸⡿⠉⠳⠙⠃⠀⠀⠀⢀⡄⠀⠐⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⡜⠀⡿⠃⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢸⠠⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⠾⠋⠀⠀⠀⠀⠀⠀⢢⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠀⢹⣇⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⡂⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣢⡙⠄⠀⢀⡼⡥⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡟⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢙⣦⠀⠀⢰⡧⠤⠤⠄⠀⠀⠀⠀⠀⠀⠈⢷⣀⠙⢿⣷⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠸⣿⣿⣦⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡝⣿⣿⢷⡄⠐⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⣿⠀⠑⡀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢈⠁⢠⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇⠀⠀⠃⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠁⠎⢀⡈⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠧⣴⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠉⢴⣭⣍⣡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠛⠋⠀⢦⢠⣍⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⡴⣂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠈⠈⠸⡷⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⣀⣤⣤⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢰⡿⠀⢀⣾⡿⠋⠁⠀⠀⠀⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠑⠧⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⢠⣿⠃⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠘⠐⠲⠞⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠆⠁⠀⠀⠀⠀⠀⢠⣾⠏⠀⢀⣾⠇⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⢀⣾⠏⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢀⣾⠏⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠃⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣠⣿⠃⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣅⠀⣴⡿⠁⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⣨⣿⠟⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⣿⡇⠀⠀⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⡿⠛⠁⠀⠀⣠⣶⡿⠋⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣨⡷⠀⢀⣴⣾⠟⠉⠀⠀⢀⣿⠟⠉⠉⠙⣦⠀⠀⠀⠀⠀⠀⣴⣿⣷⣦⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣡⣴⠟⠁⢀⣾⡟⠁⠀⠀⠀⠀⠈⣿⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠻⣿⣿⣿⠇⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠁⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⡾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⡿⢷⡄⠀⠀⠀⣸⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⣿⣿⣿⣿⠀⠀⣴⣾⣶⣤⠀⠀⠘⢿⣿⣿⠏⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠙⠋⠁⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠨⢄⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⣦⣤⣤⣤⣤⣴⣶⡾⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠠⣄⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⢠⠀⡂⠀⠀⠀⣀⣤⣠⡈⡆⠀⠀⠀⠀⢰⠀⡄⠀⠀⢀⣴⠿⢿⣦⠀⠀⠀⠀⠀⡜⢃⠀⠀⠀⠀⠀⠀⣀
⠀⢸⣿⠻⠏⣿⡇⠀⠀⠀⣈⠀⠶⠀⠀⠀⣿⣿⠛⣿⡆⠀⠀⠐⣻⡏⠁⠁⠀⠀⢰⡇⢸⢀⡇⠀⠀⠘⣿⣤⣴⡿⠀⠀⠀⠀⠋⠠⠋⠀⠀⠀⣿⣫⣿⣻⡇
⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣒⢴⣲⠀⠀⠀⣠⣴⡞⢿⡆⠀⠀⠀⠉⠸⢃⡀⠀⠀⣾⢷⣶⡶⣶⠀⠀⢠⡤⡤⢠⢤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣠⣄⣄⠀⠀⠀⠀⠴⣷⡄
⠀⠀⢶⣿⣾⣿⠀⠀⠀⣷⣴⠿⠟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⣿⣿⣿⣿⠀⠀⢸⡆⡇⢠⣾⠀⠀⠰⣷⠀⠀⣾⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⢰⣿⡇



⠀⠰⠶⠆⠰⠆⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⣀⣠⣞⣟⡷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⢀⠀⠀⡀⠀⠀⢠⠤⠤⠤⠤⢤
⠀⢀⡀⠰⢆⡰⠆⠀⠀⢠⣄⢠⣤⠀⠀⠈⢿⡾⠾⠁⠁⠀⠀⣶⣦⣶⣤⣤⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⢺⣧⣼⠇⠀⠀⠀⢸⢡⡆⡟⠀⠀⢸⠹⠀⠇⠳⢸
⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠁

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣐⡿⢣⣤⡄⠀⠀⠀⠄⠛⣿⡆⠀⠀⣀⣀⣤⣄⡀⠀⠀⠠⠀⠀⢂⠀⠀⠀⠀⠀⢠⣮⠛⠀⠀⢠⠊⡉⣳⣀⡀⠀⠀⠀⢰⣦⡤⠀⠀⠀⣄⣰⡀⡄
⠀⠘⠿⢣⣾⠍⠀⠀⠘⣿⣦⡄⠈⠀⠀⠀⣿⡏⣶⢎⣿⠀⠀⠀⠱⣖⣻⡆⠀⠀⠀⡴⠟⠁⠀⠀⠀⠘⢄⣀⠜⠉⠁⠀⠀⠛⢻⣿⠟⠀⠀⠘⡘⢤⢼⡘
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠈


⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⣼⣿⣿⣧⠀⠀⢸⢾⡯⡭⡿⠇⠀⢀⣾⣶⣶⣾⣷⠀⠀⠠⠤⢤⠤⡄⠀⠀⢠⣼⣟⡷⣤⠀⠀⠀⠀⡖⠿⠀⠀⠀⠀⠀⡠⠚⠁⡀⠀⠀⣤⣶⠀⠀⡀
⠀⠀⠘⠾⠷⠃⠀⠀⠈⠀⠀⠁⠁⠀⠀⠈⠻⠟⠉⠻⠟⠀⠀⠠⠤⠦⠹⠄⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠶⠀⠚⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠛⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠐⠠⠢⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⡄⠀⠀⠀⠀⣿⠁⣿⠀⠀⠀⠀⠘⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄
⠀⢸⣿⡇⠈⠁⠀⠀⢰⣋⣟⣹⣏⡇⠀⠀⠘⠁⠀⠁⠀⠀⠀⠀⡏⠀⢹⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠦⢀⢀⠂
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠈⠁


⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣼⣿⣿⣼⣷⣶⣧⣼⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣷⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠏⠀⠀⣡⠀⢠⡀⠀⠀⠀⠀⣠⣶⣿⣤⣤⣴⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠄⠀⠀⠋⠀⠈⠀⠀⠀⠀⠘⡉⠛⠿⢛⡛⠛⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠰⣦⣤⣤⡤⠀⠀⠀⠀⠀⠸⣿⡀⠀⢸⣷⡀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠳⡦⠄⠀⠀⢀⣤⣶⣤⣤⣭⣶⣄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠯⠀⠠⡆⢲⣤⣾⣿⣿⣿⡏⠁⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢄⣧⡀⠀⠀⠛⠋⡟⠉⠸⠿⠇⠀⠀⠈⠟⠁⠀⠀⠀⠀⠀⠀⣤⣶⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⣀⣿⣇⣾⣇⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⡴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠿⠗
⠀⢀⣠⠖⠋⠀⠸⣿⣿⡟⠛⠛⠛⢻⣿⣯⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢻⣇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⡀⠀⠀⢸⣿⣿⣀⡀⠀⠀⠀⠀⠀⠚⠛⠻⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⡿⠃⠀⢼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡖⠛⠛⠲⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃⠀⠀⠀⠈⠣⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠉⢀⠴⠒⠒⠢⢄⠀⠁⠀⠺⡀⠀⠀⠀⠉⢢⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡤⠋⠀⠀⠀⠀⠀⠁⠀⣰⠶⢸⠀⠰⢶⡄⠀⠙⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠠⡦⠀⠀⡶⠰⠄⡀⠀⠀⣰⣿⣿⣟⠛⠛⠛⢿⣷
⠀⠀⢀⠀⠀⠀⢀⡔⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠐⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣼⠁⡇⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠃
⠀⢀⠀⠠⡇⠀⢷⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡄
⠀⠀⣄⠀⢧⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠇⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠓⢤⣀⠙⢦⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⠀⠀⢠⣔⡉⠉⠑⠒⠢⠤⠄⢀⣀⣀⣀⡠⠔⠂⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣲⠏⠁⠀⠀⢻⣿⣿⣿⣿⣶⣾⡿⠀⠘⢄⠀⠀⠀⠐⠺⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠿⠏⠓⠒⠶⠤⠤⠤⢦⠀⠀⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠄⣀⠂⠄⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡝⠂⠉⠀⠀⠀⠀⠈⠀⠐⠠⣄⠒⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠘⠚⢄⣀⠀⠀⠀⠀⠀⠀⠀⠢⡐⢂⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠂⠐⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⣗⣿⣿⡿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣗⢾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣭⠟⠂⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠘⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢷⡀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⣀⣠⣤⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⢻⠟⠉⠉⠉⠙⠛⠿⠛⢛⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣳⣾⣷⣿⠟⡡⠚⠁⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠟⠭⠓⠉⠀⠀⠀⠀⠀⠀⠐⠾⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠙⠛⠻⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠀⠀⠀⣀⣠⠶⠾⢿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡫⠄⠀⠀⣀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣧⠲⣄⣀⣠⣴⠞⣁⡤⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⢋⠁⠀⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣄
⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⢿⣿⣿⣿⣿⠿⣿
⣿⣷⣾⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⣂⣠⣄⡀⠀⠀⠀⠀⠀⠐⠒⠈⠉⠈⠀⠀⠀⠀⠀⠀⠈⢿⡟
⠿⠟⠛⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠵⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢡⠖⠒⠢⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢹⡀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊⠀⠀⠈⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠠⠂⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠊⠉⠉⠉⠉⠒⢄⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠉⠳⢤⡁⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⣀⠀⠀⠈⠀⠀⠀⢀⠋⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢠⠀⠀⠀⡌⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠚⠤⡀⢠⠁⢀⠟⠒⠲⠤⠤⣀⣀⡣⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢞⠓⠀⠀⠰⡄⠀⠉⠰⢏⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⣰⠁⠀⢙⡆⠀⠀⠀⠀⠠⢲⡆⢨⡴⠊⠘⡄⠃⠀⠀⠀⠀⢣⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⡏
⠀⠀⠀⢀⡸⠄⠀⠘⠄⣀⠀⢀⠀⠓⠈⠐⡙⢾⠅⢰⠀⡆⠀⠀⠀⠀⠀⠧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡃⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⢏⠀⢀⣄⡀⠀⢀⠜⠁⠀⠀⠀⠀⠘⠦⠔⠃⡸⠑⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡇⠀⠀⠀⠀⠀⡞
⠀⢠⠀⠈⠉⠁⠒⠰⢟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⡇⠀⠀⠀⠀⠀⡇
⠀⡆⠸⠂⠀⠀⢀⡀⠀⡗⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠈⠐⠢⠄⣀⠀⠀⣠⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣧⠀⠀⠀⠀⠀⡇
⠀⠣⡎⠀⠀⢀⠋⠂⠀⡇⠀⠀⠀⠀⠀⠀⡠⠊⠴⢦⣤⣀⡀⠀⠀⠉⠘⠃⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⠂⠀⠀⠸⡄⠀⠀⠀⠀⢻⡀
⠀⠀⠈⠑⠲⠼⣦⣤⡴⠁⠀⠀⢀⣠⡴⠊⠀⢠⠐⠂⠁⠀⠈⠁⢲⠀⠀⠀⡶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⢸⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠛⢩⠁⠀⠀⠀⠁⠉⠉⢸⠀⠀⠀⢸⡀⠀⠀⢱⠀⠀⠀⠀⠀⢀⣠⠴⠖⠋⠉⣣⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢣⠀⠀⡘⠀⣄⠀⠀⠙⠒⠚⠁⠀⠀⢸⣠⠞⠉⠀⠀⢀⡤⠊⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡠⠎⠀⢠⠇⠀⠈⣱⠒⠦⢴⡀⠀⠀⠀⢸⠁⠀⢀⠊⡉⠉⡀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡏
⠀⠀⠀⠀⠀⢀⡠⠤⠠⠤⠤⠤⠄⠀⠀⠤⢤⠤⠖⠋⠀⠀⢰⠃⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠘⠒⢦⠤⢇⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠦⠾⠀⠀⣸⠁
⠀⠀⠀⠀⢠⠎⢠⠀⡀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠿⠀⠀⠒⠒⠚⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⢺⣀⡃⢠⡇⠀⡷⡶⢋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠾⣀⣠⣇⠀⢀⡝
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠚⠹⣴⠋⠀⡞⠀⠀⠸⡏⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠦⠤⠤⠾⠃
⣿⣷⣶⣶⣶⣾⢷⣾⣷⣷⣿⣶⣶⣿⣶⣶⣶⣿⣷⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣷⣾⢷⠾⠷⠿⠷⢾⣿⠿⠿⠿⠿⠿⣿⠿⣿

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⢀⠤⠒⡤⡀⠀⢀⡠⠤⣀⠀⢀⡀
⠀⠀⢸⠏⢳⣝⣿⣦⣙⣷⣌⠻⣿⣕⡄⠈⣁⠤⠐⠒⠉⠁⢡⡁⡇⠀⠘⠻⠅⠀⡓⢓⣈⣅⢡⠔⠡⡄⢖⡄⠱⡈⠉
⠀⠀⡾⢄⣀⣦⣤⢀⣀⠀⠈⠉⠉⠉⠁⢂⢀⠀⡀⠀⠀⠀⠘⠞⡇⢸⠲⠤⣔⣒⠽⣼⣧⠔⠉⡇⠉⡥⡠⣒⢂⠇
⠀⢠⠁⠉⠙⠃⠶⠾⣛⣩⣵⡶⠦⣤⡄⠀⠉⡏⡝⠉⣀⡒⠒⠓⠁⠘⠚⡲⠢⢌⡉⠑⠺⣿⠒⠸⢦⣭⡡⠴⠊⢀⡀
⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠫⠃⠀⢀⠑⠃⠀⠉⣁⢀⡀⠀⠀⢠⠃⠀⠀⠀⠉⠡⠀⠀⠀⠀⠀⠈⢳⠀⠛⠃
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠽⢿⠃⡤⠂⠉⠀⢀⠈⠉⠢⣌⠒⡦⠤⣀⡀⠀⠀⢀⠀⠀⠀⢀⠎⠉⠁⡹
⠀⢀⣍⠁⠒⠠⠤⢁⣀⠀⠀⠀⠀⡇⠀⠀⢀⠎⠀⠀⢆⠀⠸⠁⢀⡠⠈⢣⠈⠁⡒⢩⡝⡒⠤⢌⡀⠀⣜⡀⠀⢰⠁
⠀⠘⠉⣀⡤⠔⠊⠠⣀⣈⠉⠒⠒⠀⠀⣠⡿⠀⣀⣀⠠⠆⣘⠂⠁⢀⡀⠈⡆⠹⣛⣀⣉⠐⠚⠓⢡⣌⠀⠈⠲⠃⣤
⠀⢠⠊⡀⠀⠐⠑⠂⠀⠌⢳⠀⠲⠖⠛⠁⢠⡀⠀⢀⣠⢴⡀⠺⡁⡡⠁⢀⠇⡴⠇⠤⢈⠓⡄⠀⡠⡔⠂⠀⢲⣄⠉
⠀⢹⣦⠤⣀⣁⣀⣀⣀⣀⣼⠀⢠⠿⠴⣄⢄⢢⡀⠉⠒⠰⠇⠀⠑⠁⢀⠜⠀⣇⢐⡒⢡⡅⡇⢔⠑⠒⠒⣂⡭⡊
⠀⠸⣿⠀⣿⠀⣿⠇⣿⢸⠇⢀⡖⢔⣒⠨⡉⠃⠙⠢⢄⣀⣀⣀⡠⠔⠃⠰⠀⣿⢨⠬⢸⡇⢱⠀⢷⢋⣴⢟⣴⢷
⠀⠀⣿⡄⣿⠀⣿⢰⡏⡞⠀⡾⢁⡨⠙⠃⡉⠀⡀⠖⠠⢀⠶⠰⣖⠀⠉⣿⠀⢫⠃⠫⠄⡧⢸⠀⠘⣟⣵⠟⣡⠾
⠀⣤⠙⠓⠻⠶⠿⠾⠓⠁⣸⠐⢌⠛⣣⡐⠀⡾⠂⡖⠄⡘⠄⠀⣿⠆⠀⢻⡆⠘⢄⡀⣓⣠⠚⢠⡄⠘⣥⢞⣥⡾
⠀⣉⣤⣀⣠⣄⣠⣒⣂⣄⡈⠐⠀⠀⡰⡠⠊⠀⠠⠛⠂⠌⣃⣄⢩⣇⣀⣸⣇⡀⠀⣍⠉⠀⠀⢠⡀⠀⠀⠉⠀⢤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⠀⠘⢠⣤⢄⠀⠀⠀⠀⠉⢉⠾⣿⣴⣟⣻⢆⢀⣸⣧⠰⠆⢠⣀⣀⡀⠀⠀⣠
⠀⠉⠢⠠⠠⠂⠒⠤⠤⠔⠊⠘⠛⠁⠘⠠⠀⠀⠈⠑⡇⢀⠔⠁⢦⢆⠀⣤⠈⣿⠀⠀⢿⡄⢰⣽⡃⠀⠀⠀⡀⣹⠢
⠀⠐⠂⠒⠂⡆⠀⠀⠀⢀⠀⠀⠀⠐⠈⠐⠐⠉⠁⠀⠉⠁⡀⢴⠟⢢⠠⠁⠀⠶⡇⠀⢹⡇⢰⣏⢁⣀⠀⢤⣠⠀⣽
⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⠐⠦⡀⠀⠀⠀⠀⠐⢿⢶⠶⠥⢐⠡⠀⠠⠱⠑⡀⢸⣥⡀⠸⠗⣀⡙⢦⠑⣷⡺⢃⡴⠁
⠀⢰⠀⠀⠐⠀⣸⣿⣷⣿⣬⣀⣵⠄⠃⠀⠀⡄⠈⢢⠣⠀⠀⠰⢐⡂⡂⠱⠝⠀⠀⣠⠚⠁⠐⡵⡌⢻⣟⢻⣟⠐⠗
⠀⢸⣄⡠⠂⠀⠸⣄⡜⢛⣻⣿⠏⠀⠈⢀⣀⡇⠀⠀⢣⠑⡈⠚⣉⠡⠌⣁⠂⠀⢸⡠⠉⢀⢀⡤⣧⠋⡹⢧⡑⢷⡀
⠀⢸⠻⣄⠀⠀⠀⠈⠉⠸⠋⠁⠀⠀⠀⣠⠟⡇⠰⣿⡇⠛⠊⠀⢈⢦⣤⣤⠚⢥⠺⠓⠭⠔⡉⠀⢡⡜⠁⠀⠳⣾
⠀⠈⠓⠚⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠒⠂⠁⠀⠈⠙⠂⠀⠘⠋⠀⠊⠉⠉⠉⠁⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⡤⠀⢒⣯⣻⣿⣿⣯⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⡄
⠀⠀⠀⠀⠸⡀⠂⠈⢟⣿⣽⣿⣿⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⡄
⠀⠀⠀⠀⠀⠈⠑⢤⣼⣿⣿⣿⣿⡟⠛⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⠏⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣋⡉⠛⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣷⣿⡿⠟⠷⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣷⣿⣿⣯⡉⣸⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⡇⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠘⠀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⣋⣩⣭⣦⣦⣄⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⠀⢘⡟⠛⠛⠿⠗⠒⠒⠛⠉⠉⠀⠀⠀⠘⢿⣧⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠆⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡳⣄⡐⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⢨⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠏⢻⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣥⣀⡼⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣁⠼⠀⢸⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣄⡜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠈⠉⣉⣀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠐⠒⠚⠿⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⢈⣿⡇⠀⠀⢰⣿⡅⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠛⠉⠛⢷⡄⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠐⠒⠂⠉⠉⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢻⠄⠀⠀⠀⠀⠻⣄⠀⠀⠀⠶⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⢠⠀⢳⡀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⢨⠿⠦⠤⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣤⣄⣀⣀⣀⣀⣀⢠⣤⠔⠋⠁
⠀⠀⠀⠀⢸⠀⡀⢢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⢸⠶⣽⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠄⣸⠀⠈⠙⣦⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠚⡏⠙⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⡜⠁
⡄⠀⠀⡆⢹⠖⠒⠒⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠉⠀⠀⠀⡇⠀⠀⠀⠈⠉⠲⠦⣤⡀⠀⠶
⢧⡀⠈⠉⢸⠆⠀⠀⠀⠈⠳⢦⠀⠀⠀⠀⠀⠀⣀⠴⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⢦⣀⣀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠙⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⠀⠀⠀⡘⠃⠀⠀⠈⠉⠛⠛⠢⠤⣄
⠀⠀⠀⠀⠀⣿⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠙⡄⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⡇⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⣆⠀⠀⡗⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢻⡄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⢧⣄⠐⠒⠈⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠈⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⣀⣰⡆⠀⠈⣧⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠳⣤⡄⠄⠒⠠⠄⠘⢷⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠀⠈⣿⠀⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠙⠠⠤⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠛⣦⣤⣤⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠀⠀⠈⣤⠁⠀⠀⠀⠀⠀⠀⡍⠀⠀⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⠁⠈⠁⠈⠀⠈⠉⠀⠈⠉⠁⠈⠈⠁⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣠⣤⣤⣤⣤⣤⣀⡀⠴⠖⠒⠒⠶⢦⣤⠀⠖⠒⠒⠖⠢⣄⡀⠰⠶⠒⠶⠶⣤⣀⡄⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠉⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⠃⠀⠀⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⡜⢁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣸⡆⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⢀⡆⠀⡄⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠸⡇⠀⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⡇⠀⡇⠀⠀⠀⠀⢀⠀⠀⣦⠀⠀⠀⢠⠀⣷⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⢿⠀⠀⠀⠘⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢰⡀⠀⢸⡇⠀⠀⠀⡇⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⠀⢩⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⢸⠁⠀⠈⠀⠀⠀⠀⠇⠀⠀⠸⡇⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢰⡄⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⢁⠀⠀⠘⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠘⠇⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⠀⠀⠀⠃⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⡄⠀⠀⠀⠀⡆⠀⠸⠀⠀⠀⠀⠸⠀⠀⡆⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⡇⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⢄⠀⠇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⣀⡿⢧⣀⠀⠀⠀⣀⡿⢆⣀⣀⣀⣀⡠⠘⠛⠲⠶⠶⠶⠖⠉⠛⠑⠶⠆⠉⠁⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠀⠀⠀⠈⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠶⡄⠐⠂⠀⠀⢲⡆⠐⠀⠀⠒⠒⠒⢶⠀⠐⠂⠐⠒⠀⠒⠀⠒⣤⠔⠂⠀⠀⠀⠀⢠⢰⣧
⣤⣤⣀⣤⣤⣤⣄⣠⣤⣤⣄⣤⣸⣷⣤⣷⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧⣠⣤⣤
⣿⣿⣿⣿⠿⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⢀⡈⠆⠐⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠑⡆⠁⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡠⠔⠁⡐⠁⠀⠀⠀⠀⢀⠀⢀⠀⠀⠘⡒⡀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⣠⢎⡀⠀⠀⠀⢀⠔⠁⠀⠀⠑⡄⠀⠀⠰⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢱⣿⣟⡀⠃⢀⠊⠀⣠⣄⢤⡀⠐⠀⠀⠀⠡⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠛⠻⠃⠀⠀⠀⢸⣿⣯⡄⡏⠀⡇⠀⠀⠀⠀⠑⠠⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢾⣍⣉⠉⠙⣦⠀⠉⠛⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠻⣿⡿⠿⠛⠀⠤⠀⠤⠔⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⡀⠔⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡶⠀⠂⠒⠂⠀⡈⠅⠂⡩⠂⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡔⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢛⡖⠂⠀⠀⢁⠠⠐⠁⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠁⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠻⢶⡒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢰⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⡇⠀⠀⠠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡴⢇⠀⠀⠀⢣⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⠀⠀⠀⢸⡄⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠸⠀⠀⠀⠘⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀⠀⢀⠔⠁⠀⠀⠀⣘⠤⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠣⠰⣥⠂⡄⠀⢀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠂⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


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

⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠛⠛⠛⠻⠗⣀⡀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣤⣾⣿⣷⡀
⠀⠀⠀⠀⠀⣤⣀⣀⣰⣿⠷⠶⠿⠿⢿⡏⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣀⣤⣴⡆
⠀⠀⠀⠀⠀⣿⠿⠿⢿⣿⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠈⠙⣻⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⢿⣿⠏⠉⠈⠁⠉⠉⠛⠿⠇
⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠖⠀⣤⣽⣿⣧⡄
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣯
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢴⠆⢶⠆⢠⣾⣷⣶⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⡀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⣾⠇⠀⢹⡇
⠀⠀⠀⠀⠀⠈⠉⢻⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠰⣦⠈⠻⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⢀⣤⠄⣠⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⢤⣶⣾⣿⣿⣿⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⢀⠔⢹⠑⢄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⣘⡿⠿⠿⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠂
⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣶⣶⣶⣶⡆⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⢹⡿⣿⣿⢿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠯⠿⠿⠽⠽⠽⠿⠿⠯⠯⠯⠿⠿⠽⠽⠽⠽⠿⠇
⠀⠀⠀⠀⢸⡁⢀⣀⢈⣿⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣼⣿⣼⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣶⣶⣶⢲⢲⢲⣶⣶⡖⡖⣶⣶⣶⣶⢲⣲⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣆⠀⠀⠀⡀⣀⣴⣆⣤⢠⡀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⢀⢠⣄⠀⢀⡀
⣿⣿⡄⠀⠀⡀⢀⣤⣿⣯⣶⣷⣾⣿⣿⣿⣿⣿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⡀
⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡿⠆⠀⠀⠀⠀⠀⠀⢰⠶⠆⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣇⣤⣤⣀⠀⣾⢶⠆⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠟⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⠻⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣦⣍⠀⣼⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⡗⠷⠻⠋⣽⣏⠀⢀⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠖⣀⠀⣶⣿⣿⣷⣿⣿⣦⡈⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠃⠸⣿⣿⣿⣵⣿⣿⣿⣧⡒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣯⠔⡁⠀⡀⣽⣿⣿⣿⠿⣻⣿⠋
⣿⣿⣿⡿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⢋⡾⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡟⣿⠿⡉⠀⠁⣳⣿⠿⠿⢁⣀⡚⠛
⣿⣿⡟⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠈⠀⠉⠀⠀⠀⠈⠛⢿⣿⣿⣿⣧⣡⣡⣆⣅⠈⠆⣿⣿⣶⣿⣼⠙⠃
⣿⣿⡀⠀⠀⠀⠀⠈⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠡⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣾⣧⣧⣶⣾⣿⠿⠿⡇
⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡀⠀⠈⠑⠲⠤⠀⠀⠀⠀⠀⠉⠉⠉
⣿⣿⡟⣀⣤⣤⣤⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⣿⡶⠤⠀⠀⣀⡀
⣿⢛⣼⣿⣿⣿⣿⣧⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⣰⣿⣿⣿⣿⣷⠀⢀⣾⣿⣿⣦

⠶⠚⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢌⡑⢌⣿⣿⢷⣝⡡⡢⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⠶⢛⣉
⠞⣋⣩⡄⠀⠀⠆⣠⠆⣠⠆⣠⠦⣹⠦⣹⠦⣽⣿⣻⢮⣼⠔⣡⡦⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⣋⣥
⣛⣩⣤⠦⠀⠀⠀⠁⠞⣡⡾⣍⡷⣍⡶⣍⡶⣿⣿⣝⡷⣡⣾⢋⡴⣿⣿⣳⣀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣏⣭⣴
⣏⣥⠶⠞⡀⠀⠀⠠⡘⢮⡽⢯⡵⢯⡵⢏⡵⢿⣿⣯⣿⢟⡵⢫⣾⢿⣿⣿⡿⣿⣽⣹⣱⣱⣻⣹⣻⣿⣿⣿⣿
⣽⣟⣾⣿⣅⡠⣌⢳⣌⣲⡌⣫⣽⣯⣽⣯⣽⣯⣹⣮⣱⠊⣠⠊⣠⢟⣛⣻⠑⠳⠳⢣⢣⢣⢣⢧⢯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⢿⣷⠿⣫⠞⣡⠞⣡⣟⣻⣿⠁⠀⠀⠀⠀⠀⠉⠋⢾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠞⢁⠜⢁⠜⢁⠔⢁⣟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⢋⡴⢋⡴⢋⣹⣿⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠋⡠⠋⣹⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠢⠢⠘⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠞⣩⣭⣽⣄⣀⣀⣀⣀⣄⣄⣤⣄⣤⣌⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣩⣽⣿⣿⣿⣿⢿⠝⠿⠿⠟⠽⠽⠿⠝⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡄⢰⡄⢻⣄⢿⣿⣿⡿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠀⣶⠈⣷⡈⣷⡈⢷⡈⢷⣬⣛⢿⣿⣿⡿⣫⠿
⠀⠀⠀⣀⠠⣄⠰⣦⠸⣇⢸⣧⢸⣧⡸⣧⠘⣧⠘⣧⠘⣧⣸⣽⣻⢿⣿⣿⣟⣷⠇⠀⠀⠀⠀⠀⠀⢀⡤
⡄⢻⡄⢻⡄⢻⡆⢻⡆⢹⡆⢻⡇⢹⣇⢹⣆⠻⣶⠹⣇⣽⣾⣝⡻⣷⣾⣿⣯⡞⠀⠀⠀⠀⠀⠀⢰⣿⠶⢿⣏
⢿⡈⢿⡀⢿⡀⢿⡀⢿⡄⢿⡄⢻⡄⢻⡄⢻⣾⣿⣶⣿⣿⣿⣿⡿⣿⣯⣿⡻⡝⣆⢧⢳⡸⡎⣷⢮⠶⢺⣋⣿
⡘⣧⠘⣷⠘⣷⠘⣷⠈⣷⠈⣷⡈⣷⡈⢿⡈⣿⣿⣿⣿⣿⣯⣿⢿⣿⣿⣿⢧⢹⡸⡌⣇⢧⠹⠘⠶⠞⣋⣻⣿
⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⢻⡹⡜⣇⢧⠹⠸⠜⠃⠃⠉⠀⠀⠀⠀⠐⢛⣩⡤⠶
⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡟⠆⠃⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⣥⠶⠞
⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⠢⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⠴⠞⣛
⣶⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣌⣿⣯⣷⣽⣣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣴⣖⣛⣩
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠒⠂⠒⠀⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⣤⣦⡤⠂⠀⠄⠚⠉⠉⣈⡆⠀⠀⠀⠀⠀⠀⠀⢀⣭⣐⢄⠀⠠⣦⣤⣶⡶⠦
⠀⠀⠀⠀⠀⡴⠋⠀⠤⡄⢸⡟⠁⠈⠀⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⠺⢦⡈⢻⡿⢀⡀⠀⣄
⠀⠀⠀⠀⢰⠁⠴⠀⠀⠀⡜⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣿⣗⠀⠉⠀⠁⠀⠈⠢⣸⡄
⠀⠀⠀⠀⣿⢸⣶⡦⠀⣞⠀⡤⠒⠲⣴⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣿⣿⠛⠳⢆⠰⣠⣄⣀⠈⢡
⠀⠀⠀⠀⡇⠘⠛⠁⣠⣧⣾⣴⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠧⣾⣿⠿⣿⣷⣼⣄⡟⠙⠿⠇⢸
⠀⠀⠀⠀⠙⠒⠢⠾⣿⣿⣿⣿⠿⣶⠿⠟⠁⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠈⠻⣿⢟⣿⣿⡿⣿⠦⠴⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡻⣿⣿⡾⠋⠀⠀⠀⠀⣰⢟⣭⣶⣿⣇⣩⠻⡆⠀⠀⠀⠀⠘⢿⣿⡟⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣧⠘⣿⠃⠀⠀⠀⠀⢠⣇⣾⣿⡟⣿⣿⣿⣷⣿⡄⠀⠀⠀⠀⠈⢻⡆⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡀⠀⠀⠀⠀⠀⠀⠘⣿⣛⠛⣹⣿⢿⣽⠟⣻⠀⠀⠀⠀⠀⠀⠘⡅⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣼⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⡇⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣸⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⢧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣿⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣯⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠻⠟⠿⠿⣻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣿⢁⠀⠀⠀⠀⠀⠈⠁⡡⢿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠄⠀⠤⠔⠂⠐⠉






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢿⡿⡿⢿⣿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣟⣛⣟⣛⣿⣟⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠄

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠈⠻⣆⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣷⣤⣤⡶⠖⠚⠛⠓⠒⠛⠛⠛⠓⠟⠹⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⡟⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⣻⣿⣿⣿⣿⠀⠀⠀⠃⠀⠀⣾⣮⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⣿⠘⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠒⠒⢦⡄⠀⢠⡇⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⣿⣿⡿⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⡇⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣡⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠒⠤⣀⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠹⢶⣶⣎⣉⣠⣤⣴⡶⠖⠊⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⣤⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠀⠀⣄⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⢀⡀⠀⠀⡀⠀⠀⠀⣠⣶⡿⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠒⠛⠛⠲⠿⠛⠹⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⣶⣶⣶⣶⣶⣶⣶⣴⣦⣴⣶⣶⠄
⠀⠀⡇⣿⢸⣼⣧⣷⣾⣿⣿⡇⣿⢸
⠀⢠⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈
⠀⢸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⡄
⣶⡘⠛⠛⠛⠛⠛⠛⠛⠛⠿⠛⠛⠛⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣄⡀
⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡖⣣⡾⢻⣿⣿⣿⣿⣿⡝⣦⢲⣾⣿⣿
⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣦⣾⣿⣿⣿⡿⠻⠿⣿⣿⢾⡇⠙⣿⣿
⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠈⣿⣿⣿⡇⠈⢹⣿⣿⣿⠉⠉⣿⣿⣿⡿⣿⣿⣿⣿⢡⣴⣶⡌⣿⣾⣟⣦⣽⣿
⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⠸⣿⣿⣿⡇⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⢠⣿⣿⣿⣏⣼⣿⣿⡇⣾⡧⠘⢸⣿⣿
⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠀⠀⣿⠟⢁⡈⢻⣿⣿⣬⣍⣟⠛⣻⠟⡇⠀⢸⣿⣿
⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⠿⠀⠀⠁⣰⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿⠡⡇⠀⢸⣿⣿⡄
⣿⣿⣿⠀⠀⣿⣿⣿⣧⠀⠀⠿⠛⠛⠛⠀⠀⡙⢉⡉⢁⣤⣄⣤⣴⣖⣸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣷⠀⢸⣿⣿⡇
⣿⣿⣿⠀⠀⣿⠟⠋⠁⠀⠀⠐⠲⣄⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⢸⣿⣿⣿⠶⣶⣤⣤
⣿⣿⣿⠀⣴⣯⣴⣶⣤⣤⣄⡀⠀⠈⠻⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⠀⠀⠀⠈
⣿⣿⣿⣾⣿⣿⣿⡿⠿⠿⠿⠿⠦⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⢏⣤⡈⠉⢉⣙⡀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣦⣤⣀⣈⣀⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡸
⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣟⠁⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢻⣿⣿⣷
⢿⣿⣿⣿⣿⣯⣛⠛⣿⣙⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿
⣿⣷⣦⣭⣭⣿⣿⣷⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠻⣿⣿⣟⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟

⠀⠀⠀⠀⠀⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠀⠀⠤⡴⠣⠂⣤⣀
⠀⠀⠉⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠃⠀⠀⠀⠀⠔⠃⠀⢀⠼⠁⠀⠀⠀⠈
⠠⠄⡁⠁⠀⢸⠀⠀⠙⠀⠢⠴⠀⠀⠀⠀⠽⠀⢀⠦⡀⠀⠀⠀⣀⡤⠤⠂⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠂⢰
⠈⠀⠀⠀⠀⠘⠆⠀⠠⠀⠀⠀⠀⠀⠀⠐⢢⡄⠀⠀⠀⠠⠤⢐⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠐⠁⠀⠈⠀⠉⠁⠀⢀
⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠠⠎⠀⢀⠄⠀⠀⠀⡀⡠⠴⠒⠀⠉
⢀⠠⠄⠀⠐⠐⠖⠄⠄⠠⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡠⠀⠁⠀⠀⢠⠾⠀⠠⠟⠋⠋⡡
⠀⢀⢀⠀⠀⠰⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠀⠀⠀⠀⠁⠀⠀⠀⡤⠊
⠀⠃⠀⠀⠀⣀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⡐⠀⠀⡟⠀⠀⠌⠀⠠
⠀⠀⠀⢠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠐⠁⠀⠀⠀⠀⠀⡖⠁⠀⢀⠃⠀⠀⠀⠠
⠀⠀⢠⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⠀⠀⠀⠀⠃⠉⠀⠀⠂⠀⢀⠀⠀⠀⢀⣀⢳⡀⣠⠂⠠⡄⠠⠀⠤
⠀⠀⣬⣇⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⡸⡆⠀⠂⢓⠀⠐⠂
⠀⠀⠏⠀⠀⠀⠀⠀⠩⠃⢀⣀⠀⠀⠂⠀⠀⠀⠀⠉⢠⠈⠀⠀⠀⠀⠀⢀⠀⠀⠠⣤⠀⠀⠀⠈⠀⠀⠀⠀⢀⣶⡀
⠀⣸⠀⠀⠀⠀⠀⡰⠁⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠉⠱⡀⠀⠀⠀⠀⠈⣧⠔⠚⠉⠢⠀⠀⡄⣀⢀⠀⠑⠌⠀⠁⡀
⠀⠧⠀⠀⢄⠀⠞⠀⠐⠀⠀⠠⠀⠠⠀⠀⢁⠐⠀⠀⠀⠀⢠⡀⠈⣀⠀⠂⠀⠇⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠘⠣⣄
⠀⠀⠀⢠⠀⠞⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠈⠀⡀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⣤⠔⠂⠐⠃⠂⠤⣀⠀⠀⠂⠈⠉
⠀⡆⠀⠀⢄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠇⢀⠀⠢⡀⠀⠀⡤⠤⠰⠂⠀⡥⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠙⠒⠂⠤⣤⡀
⠀⢣⡀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣇⡀⡜⠂⣀⠀⠀⠀⢀⡀⣆⡀⢤⠠⠀⢀⣀⡀⠀⠀⠠⡁
⠀⠀⣧⢠⡅⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡘⠉⠁⠉⠙⢍⡀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⢹⠂⠆⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⣠⣤⠀⠀⢀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢰⣾⢿⣷⣤⣾⡟⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⡿⢿⣇⣠⡀⣿⣿⡄⠀⢀⣾⡟⣿⡇⢹⣿⡏⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠿⠷⣿⣷⣿⣿⣿⣿⣿⣿⣿⡄⣼⡿⠀⣿⣧⢸⣿⠁⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣼⣿⠋⢹⣿⡜⣿⣏⠁⠹⣿⡟⠁⠀⢸⣿⣼⣿⣆⠀⢀⡓⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣿⣤⢈⣉⣁⣹⣿⠆⣠⣿⡇⠀⢰⣾⡋⠉⠉⣶⡆⣠⣴⣶⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠋⢉⣿⡿⠛⠻⣿⣦⣼⡿⠁⠀⢀⠈⣉⡃⠀⢸⣿⣿⣿⣏⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⢾⣿⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠻⣷⣶⣿⠟⠈⠛⠻⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠐⢻⡿⠇⠀⠀⠻⣷⣶⣶⡿⠋⣈⣻⣷⣶⣶⡿⢾⣿⣿⣿⣿⣿⢰⣶⣶⣿⠟
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠗⠀⠀⣿⣿⠿⣿⣷⣿⡿⠛⠛⠀⠀⣼⡿⣿⡇⢸⣿⣀⣴⣾⠗⠀⠸
⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⢀⣿⣿⣶⣿⠟⢻⣷⣴⡶⠀⢠⣿⣦⣼⣧⢸⣿⡙⣿⣤⣤⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢻⣿⣦⣀⣤⣤⣸⣿⠻⣷⣦⡸⣿⣅⣀⣀⣸⣿⠛⢻⣿⣸⣿⡇⠘⣿⣏⣠⣤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠛⠹⠿⠀⠈⠻⠟⠿⠿⠛⠛⠿⠗⠀⠸⠿⠿⠿⠇⠀⠸⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡴⠶⠶⡿⠿⠋⠻⠿⠚⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⢷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠆⣀⣴⠧⠉⠉⠓⠢⡀⠀⠀⠀⠀⠀⣀⠤⠔⠒⢒⣦⣄⣀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⢀⣼⣟⣁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⣳⣶⡀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣼⡿⡋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⠀⠀⠀⠈⢻⣿⡀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢀⣿⡿⠁⠀⠀⣠⣾⣟⣹⣿⣿⣷⠀⠀⠀⠀⣿⣯⣹⣿⣿⣿⣦⡀⠀⢤⣿⡗⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢸⣷⣶⣤⡴⠙⣿⣿⣿⣿⣿⡟⠒⠒⠘⠚⠟⠿⠿⣿⣿⡿⠃⢿⣴⢿⠙⠇⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠈⢹⠟⠉⠁⠀⣺⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠀⠀⢀⡶⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⢸⠆⠀⠀⠚⠁⠀⠀⠀⢀⣤⣶⣶⠶⣶⣦⣄⠀⠀⠀⠀⠉⠀⢀⣿⠁⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠀⠀⠀⠺⣦⣤⠄⠀⠀⠀⠀⠀⣿⣿⣿⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⢼⡏⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⣤⣶⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠈⠹⣆⠀⠲⣄⣀⡤⠾⠞⠁⠀⠀⠙⠛⠶⣶⣀⠀⣀⠞⢀⡼⠉⠛⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠳⣄⣀⣀⡀⠀⠀⠀⣀⣠⡴⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠁⡇⣿⠀⠀⠀⠀⢾⣿⣿⣦⡄⠀⠀⢰⣾⣷⣿⣶⠀⠀⠐⡀⠐⢆⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣴⣤⣤⣄⣤⡀⠀⠀⡀⠠⠤⢀⡀⠀⠀⠀⠀⣠⣶⡄⠀⠀⢰⡖⣒⣒⢺⣶
⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠆⠀⠀⣠⣾⣿⣿⠿⠀⠀⢸⡇⠧⡼⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠁⠀⠀⠓⠀⠀⠘⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠋⠉⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⡀⣄
⠀⠀⠀⠀⠀⠀⢸⣼⣶⣦⣦⡆⠀⠀⠀⠶⠾⠄⠀⠀⠀⣔⣻⢾⣳⡀⠀⠀⠀⢸⡛⠟⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣻⠞⠁⠀⠀⠀⣰⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⣀⡀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠀⠀⢼⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠹⣿⣿⣿⣿⣿⣆⠀⢀⣬⡄⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⡤⠀⠻⠻⣿⣿⣿⣿⣀⢿⡿⠃⠀⠀⠀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⢪⡿⣿⣿⣿⣿⣯⣀⡀⠀⠀⠀⠀⠸⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠅⣿⣿⣿⣿⣿⣿⣿⣿⡧⣤⠋⣸⣿⣿⣿⣿⣿⣿⣷⣿⣯⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠘⢿⣿⣿⣿⣿⣿⡿⣻⣷⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⣤⣈⣙⡿⣿⣿⠟⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣠⣤⣦⣄⡀
⠀⠀⠀⠀⠰⢶⣿⣿⣿⣿⣿⣿⡿⣿⣹⣡⣾⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⣠⠞⠁⠈⠙⠉⠟⠚⠋⠈⠋⠙⠛⠛⠛⠉⠉⠃⠈⠉⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠄⠀⠀⠀⠀⠀⣿⠁⠀⠈⣿⠿⠟⢻⣿⣿⡟⠉⠀⢈⣿⣟⠉⠉⠙⠋⢈⣿⣿⣿⣟⠀⠀⠀⠀⠰⠷⠄⠸⢿⠋⠀⠐⠀⣹⣿⣿⣿⣿⡇
⣇⠀⠀⠀⠀⣰⣿⣷⡖⠈⠀⠀⢀⠘⠛⠛⠻⠶⣾⡍⠉⠉⣠⣿⣷⡶⠈⠉⠙⠿⣄⣰⣶⡖⠀⠀⠀⠀⠀⢀⡽⣿⠏⠀⠐⠀⠀⢹⣿⣿⣶
⣷⡀⣀⣴⣶⡄⠀⠀⢱⡤⠀⠺⡟⠀⠀⠀⠀⠀⠈⡫⠈⠻⣉⣻⣿⡇⠀⠀⠀⠀⠹⠋⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠘⠉⠁
⠻⠿⠿⣯⣿⠃⠀⠀⠀⠁⠀⠀⢰⣄⠾⠀⠀⠀⢠⣧⡈⠂⠈⠁⠀⠸⣶⡦⣴⣶⣿⣶⡾⠟⠃⠀⠀⠀⠀⠀⣠⣎⣀⣀⣀⠴⠒⠂⣀
⣤⣀⠀⠀⠀⠀⣰⣶⡿⠈⠀⠀⣘⢡⣿⣷⣶⣶⣿⣿⠇⠀⠀⠀⠀⠀⡿⠦⢿⡏⠉⠙⣀⠀⠀⢀⣿⣶⡶⠞⠉⠉⣿⣿⣿⣦⣤⣴⣿⣿⣶
⣻⡿⠛⠛⠉⢉⣻⣿⡿⠿⠿⠿⠿⠿⠋⣻⣿⣥⣀⣠⣦⣀⣀⣠⣤⡀⠀⠀⣠⣦⣷⠤⠛⠋⠀⠽⢻⡿⠛⠓⢲⣴⠟⠋⠉⠉⠉⠛⠛⢿⡜
⣻⣇⣀⣠⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣟⠛⠉⠛⠛⠛⠛⠉⢉⣶⣿⣿⣏⣁⣀⠀⢀⣀⠐⠛⠃⠀⣴⡿⠿⠂⠀⠀⠀⠀⠀⠀⢀⣷
⣿⣿⠿⠛⠲⣄⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠈⠻⠧⠀⠈⠹⣿⠟⠋⠠⢹⣶⣤⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⠿
⠉⠀⠀⠀⠀⣾⠷⠀⣴⣦⣄⠀⠀⠀⢀⣴⣿⣽⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣀⣠⣆⢠⣿⣷⣦⣴⠿⠛⠦⡀⠀⠀⠀⣠⣆
⣀⣀⣀⣤⠂⠀⢀⣠⣷⣿⣿⡋⠀⠀⠀⠀⠉⠙⢻⡿⠋⠉⢡⠄⣄⣀⣀⠀⢀⠴⠟⠛⠻⠏⠉⠉⠙⠛⠟⠁⠀⠀⢀⡿⠖⠀⠈⠉⠉⠐⠚
⣿⠿⠛⠃⠀⠀⠿⣿⣿⠛⣿⣷⣦⣄⣀⣀⠀⢀⣠⡀⠀⠀⣀⠠⠚⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣿⠉⠀⠁⠀⢹⣿⣿⠋⠁⠀⠉⠋⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠗⠀⠀⠤⣾⣿⠿⠀⠀⠀⠀⣠⣿⠿⠿⢦⣄⣀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣀⣤⡆
⣧⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠁⠀⠀⠀⠈⢋⣠⡤⠀⠶⢾⡏⠀⠀⠀⠀⠈⠹⣿⣿⡅⠀⠉⠙⠛⠋⠀⠈⠉⠙⣄⡀
⣿⣷⡶⠖⠡⠛⡃⠀⠀⠀⠀⠀⠀⡀⠀⠀⢈⣇⡀⠀⠀⠀⠈⢢⣄⣀⣀⣀⡋⠟⠛⠓⢀⡀⢀⠀⠀⠀⠀⠀⢠⣽⡿⠦
⡴⠋⠀⠀⠀⣰⣿⣶⣤⣤⣀⣀⣀⣀⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢿⣿⣿⡟⠁⠀⠀⠀⠈⣿⣿⣷⣶⡶⠞⠛⠐⠉⠁⠀⠀⠙⠂⠀⢀⣀⣠
⣀⠀⠀⠀⣰⣿⣿⣶⡤⠀⢿⣿⣿⡏⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠿⠛

⠀⠀⠀⢀⠀⠒⠀⠒⠒⠒⠒⠀⠐⠒⠂⠀⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠒⠒⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⢀⣶⣶⣶⣆⠀⠀⣠⣶⣶⣶⣄⠀⠀⢀⣀⠀⠀⠀⣠⣤⡄⠀⠙⠛⠁⠰⣦⣤⡄⠀⠀⠀⠸
⠀⡀⠀⠀⢿⣿⣿⣿⣿⠃⢰⢿⣿⣿⣿⠿⠀⠀⠿⠿⠃⠀⠐⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⠧⠆⠀⠀⠄
⠀⡇⢀⣀⡑⠌⢛⡉⠞⠁⠀⠹⠏⢋⠿⠈⠀⠀⠀⠁⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⡀
⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠇
⠀⠀⠈⠙⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠇
⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣶⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠸⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣴⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛⠃
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠯⠴⡾⠇
⠀⣠⣤⣀⡀⢀⡀⣀⠀⣀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⣿⣿⣿⡇⠀⠀⢀⣄⣠⠶⠴⢦⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⡤⠤⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠘⠋⠀⠀⠀⠚⢹⣏⣀⣠⠀⠀⢠⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⢀⠈⠉⠀⠀⠀⢀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁
⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠘⠁⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠈⠀⠀⠠⠀⠀⢰⣿⠇
⠀⡀⢀⣠⡀⠔⠀⠄⢠⣶⣶⣶⣦⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢦⡴⠂⠀⠐⠠⠀⠀⢄
⠀⠀⣴⣿⣶⡀⠈⢳⠀⠀⠀⢼⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢳⡆
⠀⠀⣿⣿⣿⣿⣶⡇⢠⡄⠀⠘⠛⢉⣴⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠘⠃⠐⠀⠂⢀⣾⠇
⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣄⠑⢀⡞⠁⡔
⠀⠀⠀⠀⠛⢻⡿⠀⠀⠀⡤⢤⠄⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠐⠆⠀⠀⠀⠀⠀⣄⡀⠄
⠀⠀⢰⠀⠀⢽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⣂⡀⠀⠀⡀⠀⠈⠁
⠀⠀⠈⠀⠀⣾⠋⢀⠀⠀⢀⡀⢀⡀⣠⣄⣀⣠⣄⣄⣠⣠⣄⣠⣀⣄⠀⣀⠀⠙⠋⢀⠀⠈
⠀⠀⠀⠀⣴⠛⢷⣄⡀⡀⣸⡇⠈⣥⣬⣿⣟⣿⣿⠋⣿⣭⣿⣿⣿⢛⣤⡁⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠜⠁⠀⠀⠈⠉⠻⠋⠁⢀⠿⠘⠿⠻⠻⠗⡰⠿⢗⠛⠲⠿⠛⠿⠃⠀⠀⢠⡀⠀⠀⣀⣶⣿
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⠋⠀⠈⠀⠀⠀⠑⠋⠈⠙⠃⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠿⠛⠋⠉⠁
⠀⠀⠀⠈⠁⠰⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠔⢢⠀⠀⠀⠀⠈⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠔⢸⠃⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠻⠆
⠀⠀⠀⠀⠀⠗⠀⠀⣀⡀⢠⠀⠐⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⡤⠀⢆
⠀⠀⢄⡀⠀⠀⠀⠰⠿⠃⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡑⠀⠀⣰⠃
⠀⠀⠀⠙⠓⠶⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠶⠦⠀⠠⠶⠶⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠘⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⠂⡁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠀⠘⡀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡰⠀⡃⠑⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠈⠎⠡⠄⠀⠀⠀⠀⠀⠀⠀⡉⠓⠂⣤⠀⠀⡤⠤⢤⠀⠀⢀⡀⠀⠀⠀⢀⠌⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠨⡀⠄⢠⠺⠒⣄⠀⠀⡰⠁⠀⠀⠀⡁⣈⡿⣄⡁⠱⢄⣤⣏⢀⣹⠇⠀⠲⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡃⢰⠴⠈⠀⠑⠊⠀⠀⠀⠀⠠⡄⠤⢡⠀⠉⢀⡄⣘⡁⢀⡉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⢠⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠂⠳⠐⠺⣀⢢⡏⠀⠈⢻⠀⢸⡄⠓⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠁⣰⠀⢀⢇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⣹⢃⠙⠦⠴⢿⡇⢀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠃⡐⣄⠠⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⣟⣀⣀⡄⢀⡼⠄⣀⠛⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⡀⢆⠃⠀⠀⠀⠀⠀⠠⢰⠆⠠⠹⠈⠁⣿⠀⠉⣦⠀⠼⠀⠰⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣤⡀⠀⠀⠀⢄⠀⠀⠀⠆⠐⠹⡊⠱⡈⠓⣹⣵⡔⠢⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠐⡐⠆⠁⠉⠈⠀⢰⣿⣿⣿⣀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡻⣿⣿⣾⣀⠀⢄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠁⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⣿⣿⡆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠏⠁⠀⠀⠁⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠠⠀⠀⠈


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠒⠛⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠯
⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡔⢀⣀⣰⠃
⠀⣠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠠
⠀⠀⠀⠀⠀⡄⠀⡀⠚⠛⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠄⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠀⠄⠀⠀⠀⠀⠀⢀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠓⠀⠀⢠
⠄⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣀⠀⠀⠀⠀⠀⠀⠠⡌⠂⡀⢄⠈⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢲⡀⠀⠀⡤⠀⠠⡄⠀⠀⠀⠀⢠⠀⣤⠿⠤⡀⢠⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⡀⡀⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠁⠀⠀⠀⠀⠀⠀⠠
⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇

⠤⠤⢀⠀⢀⣀⠀⠀⠠⠦⠄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠠⠒⠒⠢⠀⠀⢀⠓⠤⠒⠲⢤⣀⠀⠀⢀⡀
⠀⢀⠀⠀⠉⠈⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠉⠀⠀⠤⢄⠀⠈⠁⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡀⠀⡀⠀⠀⠀⠀⠀⠈⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡀⠀⠀⠀⠈⠐⠀⠈⢀⡀
⠀⠀⠡⠄⠀⠀⠀⠀⠠⠇⠀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠀⠀⠀⠀⠐⠒⠀⠒⠃⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠉⢉⣽⣿⣿⣿⣿⠿⠟⠛⠉⠉⠛⢯⡉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣽⣻⡟⣽⢫⡟⣽⣋⡽⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋⠉⠁
⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠉⢻⡻⣿⣿⣿⣷⡙⣮⠗⠉
⣿⣿⡟⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢱⠀⠉⠻⣿⡟⠁
⣿⡿⠋⠉⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡸⠀⠀⢠⡟
⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣀⣠⣤⠴⠷⠤⠤⢄⣤⡀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴⠋⠁⡞⠁⠀⠀⢀⡴⠋⠁⠉⣑⣦⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠶⢶⣶⣶⣶⣶⣶⣦⠤⢤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣏⢀⣀⣈⣳⣄⣀⠀⢸⡇⠀⣰⡾⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⢀⡴⣻⣿⣿⣷⣦⣤⣾⣿⣿⡿⠛⠉⠁
⢀⠔⠈⠉⠉⠲⣄⣸⣶⡿⢻⠏⣩⣿⠿⠛⠛⠛⣳⣦⣿⣠⠴⢲⢻⢹⣇⠀⠀⠀⠀⠀⡾⢶⣿⣿⡋⠁⠀⠈⠉⠻⣉
⠃⠀⠀⠀⠀⠀⠸⣿⣿⠁⣿⢀⣿⠃⢀⣴⠞⠋⢉⣩⢻⡁⠸⣌⢯⣧⣿⣆⠀⠀⠀⠀⠹⣄⡈⠌⡯⡑⢄⠀⣠⣤⣬⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⣿⡬⣧⢠⣿⡇⠀⣴⠟⡇⠀⠳⢄⣈⣓⡟⠁⠙⣷⡀⠀⠀⠀⠙⣿⡿⠾⠃⠀⢻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀
⡀⠀⠀⠀⠀⣀⣀⣸⣿⣆⣙⣷⣿⣾⣿⣧⣼⠃⠀⠙⢤⣀⠀⢈⡃⢹⡄⠀⠈⠻⣦⡀⠀⠀⠈⣷⡄⠀⠀⣰⣿⡿⠛⠛⠛⠛⠿⣦⣴⣾⣿
⣿⡄⠀⢀⡎⠀⠀⠈⠙⠿⣟⣋⣁⣠⡴⠋⠈⢧⠀⠀⠀⠈⢉⠋⠙⠻⣷⠀⠀⠀⠉⠳⣄⠀⢀⣿⡿⢶⣴⣾⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⡁
⣿⣿⣄⢸⠀⠀⠀⠀⠀⠠⠚⠉⠁⠐⡄⠀⠀⠀⠙⠢⠤⣤⠞⠛⠻⢶⣼⡆⠀⠀⠀⠀⢙⣷⣿⣿⡠⣄⠈⠩⣾⠛⠷⣦⣀⠀⣠⣶⣾⣿⣿
⣿⣿⣿⣿⡄⠀⠀⠀⢠⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣴⡿⠛⣛⣿⣷⡿⠷⣒⣶⣶⡾⢿⣟⠁⠘⣿⣮⣵⣾⠃⠀⠀⠀⠙⠷⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡀⠀⠸⡆⠀⠀⠀⠀⠀⠙⠦⣄⣴⠞⠁⣴⢿⠫⠈⠁⠀⣼⡛⠋⠁⠀⠘⣿⣄⣠⣬⣽⣿⣧⣄⠀⠀⠀⠀⠀⠙⢿⣿⡿⠛
⣿⠻⢿⣿⣿⣿⣿⣷⣤⣹⣦⣀⣀⣀⣠⣴⣾⣟⡁⠀⠀⠙⢮⣶⣄⡀⢄⡻⣷⣤⡄⣀⣀⣈⣛⣻⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠈⢿⡄
⢻⣧⡠⢈⣙⣻⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⢙⣿⣿⣿⠿⠟⠛⠉⠉⠉⠋⢹⠉⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣷⠞⢻⣆⠀⠀⠀⠸⣧
⠘⣿⣉⠓⠀⣁⣼⣧⢠⢿⣟⠀⠀⠀⣠⢾⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠾⢻⣆⠀⠀⠀⢿⣦
⠀⢿⡟⠷⠤⠉⠀⣿⣼⠘⢿⣦⣤⣾⣏⣿⣿⠁⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣾⣆⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⠟⢻⡄⠀⠀⢸⣿
⠀⢸⡇⠀⠀⠠⠴⠛⣿⣆⠈⢉⣩⡿⢾⣿⣿⠀⠀⠀⢀⣴⣿⣿⠟⠛⠛⠛⠛⠿⡄⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⢾⣧⠀⠀⣸⣿
⠀⣸⠷⣤⣀⠀⠀⠀⣿⣷⣒⣺⡿⡗⠺⣿⣿⡄⠀⠀⢸⣿⠏⢀⣀⣤⣤⣄⣀⢀⠇⠀⠤⠀⠀⣰⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⢀⣀⣀⣐⡂⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⡤⠠⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⠆⣠⣾⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣟⣀⠛⠀⠤⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢿⣿⠿⢛⣥⣾⣿⣿⣿⣿⡙⠿⡧⠴⠾⠿⠟⠉⠉⠟⠛⠛⠉⠉⠀⠀⠀⠀⠩⠿⣏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⠉⢿⣿⢿⣿⣿⠀⢺⣧⣿⣿⣿⡟⠉⠀⢀⠤⠤⠀⣀⡀⠀⠀⠀⢠⣶⣿⣿⣆⣠⣶⡀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⣠⣴⣶⣦⣄⢻⣄⠈⠻⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⣿⣶⣾⣿⣿⠀⠹⣿⡦⠀⢐⣶⣴⣿⣿⣿⣿⣷⣶⣶⣤⣄⠀⠀⠀⠀⠉⠻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡆⠀⠸⣿⠿⠛⠁⠀⢴⠿⢃⣠⠘⡛⢹⣿⣿⣻⣿⣿⣺⣿⣿⣿⠃⠀⠀⠀⠋⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢠⣿⠀⣀⠀⢀⣠⣾⣿⣏⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡏⢸⣿⢦⣿⣿⣿⠂⠈⣘⣀⣼⣿⣿⠿⡿⠿⠸⣿⣿⠇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣯⠀⠙⢿⣾⣿⡿⠟⠛⡛⢛⠻⣟⠛⠻⠶⣶⣿⣧⣄⡀⠀⠀⠀⠀⠈⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡿⠋⢠⡄⠈⣿⡟⡀⢀⢑⡀⠈⠉⠈⠀⠀⢀⡠⠙⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⣧⠀⢿⣠⣾⠟⠀⡄⠀⠈⠛⠀⢂⠁⠄⠀⠀⢰⠃⢼⣦⣉⠉⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢿⠂⣲⠛⡃⠀⠠⠉⠠⠀⠀⠠⠌⠀⠀⠀⠀⡀⠀⡈⢁⡜⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣶⣗⣶⠊⠏⠐⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠲⠆⠀⠀⠀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⡆⠀⢾⣶⣆⠀⠀⠀⠁⠀⣀⣀⠀⠀⠀⠀⠐⠀⢀⡀⠀⠐⠆⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠠⣿⡇⠀⢸⣿⡿⠑⢄⠀⠀⠐⠈⠛⠷⢦⣤⣤⠄⠲⣾⣿⢶⡀⠀⠀⠙⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⡇⠀⢸⣿⣧⢰⣄⢁⡀⠆⠀⠀⠀⠀⠀⠄⢠⣤⣼⣿⡘⠳⠀⢠⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣏⡀⠁⣸⣿⣟⣁⣙⣾⣷⡿⠟⢢⣀⣀⠀⣀⣨⡟⠛⣿⡇⡀⢠⠃⣜⢸⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡯⣿⢾⢿⣿⣿⣿⣿⣿⣿⠷⠄⠬⠿⠟⢻⣿⣿⣿⣾⣿⣿⡇⢠⡈⣿⢠⠶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣹⠿⣥⣿⣾⣌⣿⣿⠿⣿⣿⣿⣿⣿⡷⠶⠶⣮⣭⣝⣿⣿⣿⣥⣇⠀⢖⡋⣨⡈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠉⠙⠉⠁⠀⠈⡿⠧⠿⡿⠤⠀⠃⢀⣾⣿⣝⣿⣿⣿⢹⣿⠀⡐⠀⢒⡉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⠀⢹⣟⣛⣿⠂⢰⣇⢠⣙⠦⠒⠀⣀⣀⠀⠀⠀⠈⠉⠉⠀⠿⢀⡱⣤⣤⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠈⠉⠉⠉⡠⠋⠙⠃⠉⠉⠀⠀⠉⠉⢹⡆⠀⠀⠈⠀⠀⠀⣩⡇⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣶⣶⡖⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣺⣶⣤⣠⣤⣤⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡿⠷⠂⠀⠀⠀⠐⠼⢿⣽⣿⠿⠿⡿⢏⡁⠀⢀⡀⠀⠀⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃⠀⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠉⠉⠁⠒⠦⣄
⠀⣀⡀⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠲⣄⠀⠀⠀⠀⡠⠊⡠⠔⠒⠒⠒⠒⠤⣀⠀⠀⢈⡇
⡞⠁⠀⠀⠀⠀⠉⠲⢄⣀⠠⠤⠒⠒⠒⠤⣠⠋⠀⠀⠀⠀⠀⠈⠣⡀⠔⣋⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉
⠑⠲⠴⠤⠤⣄⣀⠠⠤⠄⠒⠒⠉⠀⠑⢢⠀⠀⠀⠠⠀⠀⠓⠀⠀⠀⠺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠐⠃⠀⠛⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⣀⣤⠤⠤⠤⠤⢤⣀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⡴⠋⠀⠀⠀⠀⠀⢀⠀⢈⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡀⠀⠳⡀⠰⣄⣀⣤⣴⠫⠔⠉⠀⠀⠀⡼
⠀⢀⣀⣴⠛⢳⡤⣄⠀⠀⠀⠀⡜⢠⠃⢣⠀⠀⠀⠉⠉⠉⢻⡄⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢻⡀⠙⠀⠘⠀⢈⠇⠀⠀⠀⢇⠘⠂⣐⢧⡀⠀⠀⠀⠀⡘⠈⠲⠤⣤⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⢴⠉⢀⠀⠉⠢⡀
⠀⠀⠙⡄⢀⣀⢢⡏⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⠢⠤⠤⠚⡅⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠻⣆⣠⣀⡹
⠀⠀⠀⠹⡄⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⢰⠏
⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⡉⠓⠶⠤⣤⣀⣀⣀⣀⣀⡜⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢀⣀⡤⠞⠋⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⣤⣤⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣉⣉⣀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⣿⣤⠶⠶⠛⠛⠛⠶⢦⡀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠦⣄⡹⣄⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⠞⢁⡾
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠈⠐⠤⣀⡀⣀⠠⠔⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠖⠛⠳⠤⠤⠤⠄⠒⠉⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⣀⣀⠀⠤⢄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⢶⡒⠒⠒⠒⠒⠋⠁
⠀⠀⠀⠀⣠⠴⠒⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣈⣹⠏⠛⠛⠛⠛⠉⠙⠧⠤⠤⠶⠶⠶⠶⠶⠦⡄⠀⢀⠀⢀⢹
⠀⠀⠀⠀⠧⣴⣠⡀⢰⠆⠒⠒⠚⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠼⠥⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠉⠀⠀⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⡠⢤⡤⠚⠉⠀⠈⠉⠐⠢⣀⠀⠀⣀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⡠⠞⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⣀⠴⠊⢀⠌⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⢻⠢⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠉⠀⠀⣠⡊⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠙⢄⠀⠀⡄⢡⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣱⣿⡷⠈⢢⠀⢠⠃⠀⣀⡀⡀⠀⠘⡆⠀⡇⠀⢢⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠹⢿⣿⠆⠈⢀⠃⠀⣼⣿⡷⠈⢻⠀⢰⠀⡇⠀⠀⠑⠢⢀⡀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⣤⠶⠦⠤⢼⣀⠀⠙⢿⣿⠧⠊⠀⢸⠀⠇⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢿⣶⣦⣤⣤⣼⡇⠀⠀⠀⠀⠀⢠⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠙⡿⠿⠛⠉⠈⠀⠐⠒⠒⠊⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠈⠉⠉⠙⠉⠉⠁⠀⠀⣀⠤⢺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠶⡤⠀⠤⠀⠐⠂⠂⣉⠬⠖⢊⠔⠊⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢣⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠷⠤⠠⠤⠒⠊⠁⢀⠤⠊⠁⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠀⠀⢃⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⣀⠀⡀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠘⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢰⡹⠀⠀⠀⢱⡀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⡜⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣤⠾⢳⠀⠀⠀⠀⢇⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠐⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⣎⣀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣎⣀⣠⢃⠄⠀⠀⠀⢀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⢇⡠⠔⠃⠙⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠃


⣀⣀⣀⠀⡀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⢑⡀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⡀
⠀⠀⠀⠀⢰⣧⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⢻⢸⣏⠀⠙⠁⠀⠀⠀⠀⠹⠗⠀⠀⣀⡀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠉⠀⠠⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣟⠃⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠀⠀⠀⣀⣾⣏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⢩⢠⠋⣼⡆⠸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣷⣴⣾⣿⡻⢋⡀⠀⠤⢄⡀⠀⣆⡀⠠⡀⢠⣧⣰⣿⣨⡷⢙⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣿⠀⠄⠀⠀⣀⠠⠄⠀⠉⢨⣻⠗⣿⠛⢙⣿⣿⢥⣤⣶⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣭⣈⠓⠀⠐⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠉⠻⣫⣶⡶⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡷⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠅⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⢠⡄⣤⢦⢠⢠⡄⡦⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢢⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠁⠀⡿⡾⡇⡇⢸⠘⣾⠀⡇⢸⠆⠸⠇⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠠⠀⠀⠀⠀⠈⠁⠂⠂⣀
⠀⠀⢀⣀⣀⣀⡠⣀⠉⠀⠀⠀⠃⠀⠃⠙⠊⠀⠋⠀⠓⠘⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠑⢀⠄⢀⡁⠀⠀⢀⠘⠀⠰⠀⢀⡀⣀⠀⣁⠀⣀⠄
⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠁⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⢀⠊⠀⠉⠉⠁⠉⠉⠉⠄⢀⠄⠀⢠⡢⠀⠀⠀⠀⠁
⠀⡀⠀⣶⣶⡷⠀⢰⠄⠀⠀⠀⠀⢀⡄⢠⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠢⡈⢀⠐⠐⡀⠀⠀⡤⠂⠉⠀⠀⠉⠰⡀
⠀⠈⠠⠈⣛⡁⠔⠁⠀⢀⣡⣤⣤⣤⣤⣤⣀⡀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⣀⠀⢽⠁⠀⠀⠀⠌⠀⠀⠀⢆⢀⡀⠀⠀⠀⡀⠁⠀⠅
⠀⠀⠀⢀⠀⠀⠀⠀⢰⢸⣿⣿⣽⣿⢿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠀⠲⢸⢢⠐⢀⠀⢠⠀⠀⠰⠡⠨⠅⠄⠰⠀⠆⠀⠀⠀⠸⠀⠉⠀⠀⠀⠄⠀⠈
⠀⠜⠀⠀⠀⠑⠆⠀⢸⢸⣿⣿⢿⣟⢿⣿⣿⡇⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠠⠀⠀⡠⠀⠀⠐⠂⠀⠀⠀⡊⠀⠘⠀⠀⠀⠁⠀⠀⢀⣤⡆⠀⠀⠀⠄
⠀⡂⠀⠀⠀⠀⡔⠀⠘⠸⣿⣵⣾⣾⣿⣶⡿⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⣐⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠣⠀⠨⠀⠀⠀⠂⠈⠻⣢⠀⠀⢠
⠀⢸⡅⣷⢰⡇⠁⠀⠀⡦⠆⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠠⢀⠂⠘⢁⡀⠀⠀⠀⡁⠢⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⢄⠀⠀⠄⠀⠀⢹⣷⠄
⠀⢸⡁⠀⢨⣧⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠡⠀⠀⠈⡠⠁⢀⠁⠉⠐⠈⠈⠀⢰⠁⠀⠀⢇⠨⠑⡀⠀⠈⠀⠀⢀⢋⡄⠀⠀⠀⠀⠀⠈⠀⠉
⠀⢼⡇⣏⢸⡇⠀⠀⠀⠀⠇⠀⠀⢐⠫⡅⠀⠀⠀⢐⠁⠀⡸⠆⡀⠆⢀⠰⠀⠸⠆⠀⠊⡠⢠⠄⢈⠆⢀⠀⠀⠈⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠉⠀⣀⣀⡀⠀⠀⠰⠀⠀⢉⠁⣀⠀⢀⠀⠈⠀⢄⠁⠀⠀⠈⠄⠐⠁⠀⠂⠐⠀⠐⢀⠔⠁⠀⠀⠁⠈⠉⠉⠉⠁⠠⡤⢤⢴⣤⢤⣴⠤⠤⣤
⠀⠀⢀⣴⠿⢛⣛⠻⢷⡄⠀⣄⣀⠈⠤⠤⠄⠘⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠂⡀⠘⣷⣮⣬⠝⠘⢻⣴⣤⣿
⠀⠀⣾⣡⠞⠋⠻⠿⣦⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠲⠖⢡⠄⠀⠀⠀⠀⢀⠄⠀⠋⠁⠩⡄⣈⠂⠀⠀⡅⠀⠀⠀⠄⠀⠀⠀⡁⠀⠄
⠀⡈⠉⠃⠀⠀⠀⠀⠈⠉⠃⠀⣿⠿⠿⡿⢻⡟⠛⣿⡄⠀⠘⡁⠠⡰⠋⠆⠀⠈⢠⣷⠆⠀⣀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠘
⠀⠀⢤⣆⠀⠀⠀⠀⣴⡄⠀⠀⣿⠀⠀⠁⠸⡄⣃⣽⡇⠶⠞⠛⠂⢠⣤⡄⠀⠠⡀⢈⡠⠁⠀⠉⠒⠐⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⣷⡄⠠⣾⢿⡆⠀⠀⣿⡄⣸⢰⡀⡇⠋⣹⡇⠀⠀⠀⠘⠣⣴⠀⠀⠀⠈⠉⠀⢀⠀⡀⠀⠀⡀⠄⡀⠈⢫⠁⠀⠀⠇⠀⢀⡀⠀⢀⣀⡀⢀
⠀⠀⠈⣡⠌⠁⠀⠉⠢⠀⠀⠀⣿⡟⢻⢟⠿⠟⡟⣿⡇⠀⢀⠀⣀⣀⡀⢀⠀⠀⠀⠀⠀⡘⠁⠀⡀⠀⠀⠑⠓⠀⠈⠀⠀⠀⠙⠃
⠀⠀⣰⣤⠐⠀⢀⣀⣠⢶⠀⠠⣿⡇⢾⠘⢀⡄⡇⣿⡧⠀⠨⠉⠉⠋⠉⠙⠂⠠⠀⠀⢠⣁⡀⠈⠙⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⢀⠋⠃⠀⠄⠻⠟⠛⠛⠀⠀⠙⠿⠿⠛⠛⠛⠛⠛⠃⠀⢸⠀⠀⠂⠐⠀⠀⠀⠀⢀⡞⠀⠘⠀⠃⠀⢰⠁⢻⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢰⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠠⡀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⢰⠃⠂⠀⠘⢇⠀⡄⠀⠀⠀⢀⠀⢀⠇⠈⠀⠀⢡⣤⣤⣀⠀⠀⠘⠀⠃
⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠙⠀⠉⠀⠁⠀⠀⠟⣿⣿⠿⠂⢀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠐⠉⠈⣁⣍⠈⠉⢱⠀⠀⠀⠀⠀⠈⠁⠐⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠖⠀⠀⠰⠄⠀⠀⢱⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⠻⠇⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠴⠈⠕⠁⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⡀⠀⡠⠀⠀⠀⡌
⠀⠀⠀⠀⢻⠇⠀⢸⡁⠀⠀⠀⠀⠀⠀⢀⢠⠀⠃⠈⠀⠀⠀⢀⢒⠥⠞⠀⠀⠀⠀⠀⠀⣱⠿⠻⡦⠡⠀⡠⠀⠈⠄⠀⠰⣀⠓⢀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠜⠛⠐⠘⠀⠀⠀⠇⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠠⣴
⠀⠐⠒⠓⠉⠉⠉⠉⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠘⠀⠈⠉⠑⠀⠒⠀⠤⠂⠀⠀⠀⠈⠂⠠⠀⠀⠀⠀⠀⠉⠂⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣂⣈⣉⣉⣽⡷⢶⣤⠀⢶⡶⠀⢰
⠀⠀⢶⣶⣶⣶⡆⢰⣶⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠒⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢉⡛⠛⠟⢋⡠⢾⠃⠰⠈⠁⡠⡊
⠀⢰⣦⣬⣛⠻⢷⣸⣿⡀⢀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⢧⣿⣿⢶⣤⡷⢟⣣⣤⣤⠾⠃⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⡇⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡋⢉⣁⣠⣿⣿⡿⠉⣀⣤⢠⠜⣧
⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣶⣿⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡟⠃⢀⣘⣯⣿⠆⢀⣠⡄⣀⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⠧⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⠛⠋⠾⡴⢬⠅⠀⠘⠓
⠀⠠⠤⡤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⡀⠉⠛⢤⡀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿
⠀⢠⣿⡓⢄⠈⢯⡔⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣾⡿⣿⡿⣷⡿⣿⠿⣿⡿⣿
⠀⢠⠄⡀⠈⢤⡂⠐⠱⡊⣷⣦⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⡿⣿⡿⣿⡿⣿⡿
⠀⢸⡄⠀⡨⢀⣎⡂⠀⠑⢮⣙⣋⣉⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⣿⣿⣿⣟⣿⣟⣿⣟⣿⣟⣿⣟⣿
⠀⢀⣀⠀⠀⣈⠉⠈⣀⠈⠀⢀⣀⣉⡁⠀⠀⠀⠀⢀⢀⡀⡀⡀⡀⠀⠀⢀⡀⠀⠀⣈⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋
⠀⢸⣿⣦⡀⠘⢷⡀⠙⢆⣄⠨⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⣻⣋⢿⣠⣼⢿⡝⠤⣙⣻⡣⡥⡏
⠀⢸⣿⡌⠳⣦⡘⢷⠀⠀⠻⣷⡌⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⣥⣷⣁⣨⣿⣽⠣⣟⣷⣟⠘⣦
⠀⢸⣿⣿⣆⠙⣷⡌⢷⣄⠀⣸⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⡿⣶⣿⣿⣿⣷⣦⣻⣟⣰⣡⡇
⠀⢸⣿⣿⣷⠀⠀⠻⣿⣿⣷⡈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣿⣿⣿⣿⡟⣾⢏⣿⣧⣝⢣⡔⣃
⠀⠈⠉⠉⠉⠁⠀⠀⠙⠋⠙⠉⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠚⠃⠀⠀⠀⠀⠛⠓⠛⠛⠛⠚⠛⠛⠚⠛⠒⠒⠋
⠀⠘⠢⠘⠿⣿⣜⢿⣷⡄⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠈⠀⠙⠛⠣⡙⢷⡀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⠟⠋
⠀⢰⣤⡀⠀⠰⡀⠀⠀⠀⠙⡄⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢄⠀⠀⠙⢷⣄⢾⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠉⠛⡀⠀⢳⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⣀⣿⣿⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠛⠁
⠀⠀⠀⠀⠈⠀⠀⠘⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠿⠷⠿⠿⠿⠿⠿⠂⠀⠀⠀⠀⠶⠿⠿⠿⠇
⠀⣶⣶⣶⣶⣶⡰⣶⣶⢶⣶⣶⣶⣶⣶⠄⠀⠀⠀⠀⡶⠂⠀⡄⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣻⣿⣿⠂⠀⠀⠀⢀⣷⣄⠀⠻⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⠛⡶⢲⢦⣆⡀⠒⣠⠁⠀⠃
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣼⣿⣷⡄⢀⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣝⣆⠉⠚⢁⠿⢩⣄⢀⡀⠄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⢸⣿⣏⢻⣿⣿⣿⣧⣀⣀⣤⣾⣿⡇⠀⠀⠀⠀⠀⡀⠈⠣⠝⣶⢟⣻⡟⠀⣀⠐⠂
⠀⠿⢿⡿⢿⡿⢿⡿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⠀⠙⢿⣿⠷⠙⢻⡿⠿⠛⠁⠀⠀⠀⠀⠀⠉⠃⣴⠓⠚⠆⠀⠳⠈⠣⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠀⠀⠀⠁
⠀⣰⠆⢠⡶⣶⡶⢂⣤⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⢀⠀⠠⠀⠂⠄⠀⠀⣠⣤⠀⠀⠀⠠⡄⠀⠀⠀⠀⣠⠶⣰⢆⡴⠦⣴⢶⠶⣀⠶⡀
⠀⣿⠀⣼⠀⣿⣿⢋⡾⠟⠳⢶⣍⣏⡻⠇⠀⠀⠀⠉⠔⠣⠀⡔⡂⠀⢀⢌⡳⠆⠀⣱⣾⡇⠀⠀⠀⠀⣩⠿⣽⢮⡵⢿⣽⢿⠿⣩⠿⡅
⠀⣿⣆⣿⡀⢿⣿⣾⠃⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⢠⠐⣈⠂⠐⠠⠀⡀⣾⡗⣀⠂⠀⢨⠀⠀⠀⠀⠀⣭⠿⣽⢯⡝⢛⣽⣿⠟⣤⠻⡅
⠀⢿⣿⣿⣷⣄⡻⣙⠷⣤⣤⣾⢃⣿⣿⡇⠀⠀⠀⢦⣷⣴⣷⣤⣷⣦⣿⣿⣿⣎⠡⡈⠠⠀⠀⠀⠀⠀⣤⠛⣼⢫⡜⢋⣿⣿⠻⣤⠻⡄
⠀⢷⡙⠿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣿⣿⡄⠀⠀⠀⢌⣵⡫⣭⣻⣿⣿⣿⣿⣿⣿⣶⢬⣶⡂⠀⠀⠀⠀⣤⠛⣼⢣⡜⢫⣽⣿⠛⣤⢟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠃⠘⠁⠉⠉⠋⠀⠙

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀