Pokemon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣾⣿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣧⢸⣿⡁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠃⢀⣼⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⢼⣏⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⣾⣿⣷⡘⠿⠿⣿⠋⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠹⣿⣶⣤⣤⣾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣦⣾⣿⣿⣿⣿⣿⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢸⣿⣤⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣼⡿⢯⠭⠙⠻⣿⣜⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⠿⠶⠟⠛⠋⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⢀⣄⣾⣇⣷⣀⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡟⢝⡟⣫⡏⢛⣿⣃⣘⢷⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣿⣿⣿⡇⣼⣿⣿⡟⣶⡽⣧⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣲⡚⣣⡭⢻⢦⣄⠀⢰⣟⣸⣿⣋⢿⠻⠘⣷⡟⠙⡽⣛⣿⣧⢹⣧⠀⣀⣠⡴⣚⡹⠿⣶⣄
⠀⠀⠀⠀⠀⠈⠻⣟⢉⣓⣸⣯⢿⢱⡜⣻⣿⣿⣿⣿⣅⡸⣿⢟⣨⣾⣿⣿⡿⣾⢳⣿⣏⣽⠏⠼⡛⢾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣍⣼⡞⣿⣿⣮⣭⣭⣉⣉⣁⣈⣀⣉⣤⣴⣶⢿⢨⣏⣿⣇⠿⢛⣿⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⢿⢿⣟⣂⣉⣸⣽⡿⣿⣿⣿⣿⣿⣿⣟⣿⠹⠬⣼⣿⣿⡟⣷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⣏⡼⣋⣭⣭⣿⣿⡘⣻⣸⢇⣿⣿⡸⠟⢢⣬⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠘⠂⠀⠀⠀⢀⡄⠔⣡⣾⣿⡿⠿⣿⣿⣿⣎⣟⣿⢿⡿⣿⣛⢿⣿⣿⣿⡿⣿⣿⣿⢿⣦
⠀⢠⣞⣿⡷⠶⠖⣚⣿⢦⣾⣻⣿⣿⣧⡇⣸⡿⣻⣿⠀⢤⡌⠻⣽⣿⣇⣿⣮⣝⡮⣾⠟⢿⣿⣿
⠀⣾⣿⠱⣿⡎⣿⣟⡙⣷⣿⣿⣷⣯⣭⣾⣿⣿⣿⣿⣻⣿⢠⣾⣊⠉⣭⣭⣭⣉⣛⣮⡀⢚⣽⡿
⠀⢸⠙⠿⠿⠵⠋⠷⠿⢿⠇⠹⣷⣝⣮⣛⣿⣟⡼⣯⣿⢅⣴⣯⠗⠂⡙⠿⠿⠿⠟⠋⣁⢄⡄⠀⠀⡠⢠⠿⣿⣷⣦
⠀⠀⠰⣧⠴⠾⡆⣡⣶⢿⣿⣧⣬⠉⡍⢉⡀⣍⡴⠚⠁⢀⡼⣣⣪⣾⣟⡖⢲⠖⠞⡙⣣⠈⠀⠀⢾⣚⣿⣭⣽⣏⠃
⠀⠀⡄⠀⠀⣠⢃⡉⣵⠋⠉⢻⣿⢰⢶⣌⣵⠟⠀⣀⣴⣹⣾⣛⣭⣿⡝⣦⣴⣾⡾⠟⠁⠀⠀⠀⠀⠉⠉⠁⠉⠛
⠀⠀⠀⠀⣰⠃⣿⣵⠏⠀⠀⢿⣿⣶⡿⠟⠉⠾⠂⠉⠿⠷⢮⣽⠿⢿⣞⡻⠏⢁⣀⢀⣄⡀
⠀⠀⠀⠠⣿⣄⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠉⠁⠀⢠⣿⣿⠇⣻⣿⣧
⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣾⣿⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡏⠀⠉⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟
⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⡿⠁
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠁⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⢰⠁
⠀⠻⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⣰⠿⠃⠀⢀⠀⠀⢀⣜⢷⡀⠀⢀⡤⠚⡇⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⢸⠷⠂⠀⠉⠉⠉⠒⠠⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠖⠀⠀⠀⣠⡟
⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⡄⠀⠀⠀⠰⠀⠀⢠⡇⠀⠀⢠⡾⠟⠁
⠀⠀⠀⣠⡟⠀⠀⠀⢿⢿⠃⠀⠀⠀⢀⠀⠀⠀⠠⠀⠚⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⣇⠀⠀⢻⣇
⠀⠀⢨⡟⠫⣙⠒⠦⣌⣧⠁⠀⠀⠁⠀⠄⠀⠁⠀⣀⠔⠀⠀⠀⠀⠀⠀⡂⠀⢰⠀⠀⣀⡀⠈⣷⡤⠀⠉⠛⠷⣤
⠀⠀⠸⣇⠀⠘⠢⢄⢰⠉⠁⠀⠰⠏⠀⠀⠀⠀⠀⠁⣀⠠⠈⠀⠐⠒⠀⠉⠀⠀⠀⠈⠀⠀⠀⣉⡩⠥⠤⠒⠀⢘⡧
⠀⠀⠀⠹⢷⣴⣒⡺⠯⠿⡄⠀⠐⠆⠀⠀⠀⠀⠀⠁⠀⠠⠄⠀⡀⠀⠀⠀⠀⢀⠀⠤⠴⠲⠈⠁⠶⣀⡀⠀⣠⡾⠃⠀⠀⢀⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⡀⠐⢳⢦⠀⠒⠀⠠⠃⣻⠄⡋⣷⠞⠋⠀⠀⠀⢠⠎⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡰⢀⠀⠀⣤⡀⠀⠀⠂⠀⠀⠈⡠⠀⠀⠁⠜⢀⠨⡀⠻⣀⣀⠬⠧⢤⡤⢤⣀⡏⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⢌⡞⠹⡀⢰⠀⠑⢦⡀⠀⠀⠀⠊⠁⠠⣑⠆⠀⠀⢀⠆⠀⠸⠉⠐⠄⠀⠀⠀⠀⠂⠀⠸⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⢧⢸⠀⠀⠀⠙⠦⣄⡀⢀⠠⠐⠉⠐⠄⡠⠄⠀⠀⠐⠀⠀⠘⠀⠀⢀⠀⠀⡀⠀⠁⢘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠙⢤⣀⡀⠀⠀⠂⠀⠀⠀⢀⣒⡀⠀⣰⠂⠀⠟⠀⡚⣡⠊⣀⠄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣤⣀⣤⠀⠀⠀⢀⣀⣄⠠⡴⠚⠚⢹⡀⢸⠉⠑⣦⠘⡝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡇⠀⠰⠖⠀⠀⠀⢣⣚⠀⢸⠉⠁⠆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⣦⠇⠀⠀⠀⠀⠉⢠⡏⢀⢀⡀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠋⠱⠋⠿⠉⠶⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠀⠀⡤⠖⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣔⢠⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⡄⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡟⡁⠢⠀⢢⠀⠀⠀⢢⠀⢀⢀⠠⠐⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡀⠀⠔⠀⠀⡠⠂⠀⠀⠀⡸⢄⢠⡜⠁⠀⠀⠀⠆⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⡀⠠⠜⠀⢀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠄⠀⣀⠀⠀⡔⢁⠀⠀⡀⢈⠀⠀⠀⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢠⠋⠈⠀⡎⠀⠠⠀⠸⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠠⡀⠀⠀⠙⣥⣀⠸⠀⠈⠀⠀⡆
⠀⠀⠰⢀⠀⠠⠁⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢄⠀⠀⠘⢯⣑⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠉⠁⠠⢀⡀⡸⢀⠀⢸⠐⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡨⠂⠀⠀⠘⡆⠄⠀⠀⢀⠀⠀⠰⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠑⠰⢄⠀⡌⠀⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠢⢄⣀⠄⠤⠆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⢈⣁⡀⠐⠀⠀⢸⢀⣢⠐⠄⠀⠀⢀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠠⠄⡀⠈⠄⠀⠑⢀⠀⠀⠎⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠈⠂⠐⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⢀⢿⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⡒⣏⣼⠀⠀⠀⠁⢀⡀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡆⠈⠲⠀⠘⠀⠰⠀⠀⠺⡆⠀⡛⢢⠁⣀⠈⠀⠀⠀⠀⠁⠀⠄⢀⠀⠀⢰⠁⠀⠘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠡⠀⣮⠀⠡⢀⠀⠀⢀⠐⠀⠀⠀⠀⢀⠤
⠀⠀⠀⣦⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡘⠀⠀⠀⢦⣾⣦⡌⣤⡰⠂⠀⠛⠛⠁⠒⠀⢀⣀⣠⠄⠀⠠⠂⠒⠠
⠀⠀⠀⡀⠀⠰⠆⠀⠮⠀⢠⣤⠀⠈⢠⡄⠀⠀⠀⠹⠦⠀⢮⣝⣤⡘⠂⠀⠀⠴⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠈⠁⠀⣀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠙⢿⣿⠆⢀⠀⠀⣤⡅⠀⠀⠀⠈⠁⠀⠀⠀⠀⠇⠀⠀⠀⡀
⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⠀⠻⠃⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⠀⠀⠀⠸⡇
⠀⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠈⠁⢀⠀⡀⠊⠂⠀⠀⠠⠆⡀⠀⠀⢀⣠⠤⠀⠿⠉⠀⠀⠀⡀⣧
⠀⠀⠒⠒⠛⠀⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠦⠀⠀⠀⠀⢰⡆⠈⠶⠃⢄⣤⡄⠀⢁⠀⠀⢂⣠⣾⣤⣤⡄⣣⠀⠉⠀⠀⠀⠁
⠀⢶⣦⠶⠿⠉⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⣴⠔⠃⠀⠋⠁⢀⠀⢠⠀⠱⠀⠰⠋⠀⠀⠼⣿⣾⡿⠋⡀⠀⠠⢄⠀⠀⣀
⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⢰⡄⠀⢸⡆⠀⠈⠀⠠⠀⠀⣃⠈⠀⣨⠀⠀⠀⠀⠀⠀⠰⠂⠈⠁⠀⠘⠃⢀⠀⠈
⠀⠀⠀⠀⠀⠙⢷⠆⢃⣀⡀⢭⠉⢲⡤⣀⠠⠀⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⣡⣦⣀⠀⠠⢀⠀⠀⠀⠀⠐⠺⣷⢤⣠⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠐⠿⠀⠘⡁⠀⣀⡄⠀⢀⠘⠃⠀⠐⠓⠘⠃⠀⠀⠉⠁⢠⠐⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠀⠈⠀⠘⠑⠀⠠⠈⠀⠀⠋⠑⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢀⣀⣠⣀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠌⠠
⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⣿⣿⣿⡿⣿⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢦⡔⠶⠶⢩⣴⡄
⠀⠀⠀⠀⠀⠀⢸⡾⢾⣿⣿⣿⡟⠀⢹⣿⡏⠁⠠⡀⠀⠀⠐⠐⣰⠟⢁⠀⠀⠀⠀⢠⠀⠀⠁⢺⡿⠛⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠚⠛⠀⠉⢻⣿⣧⣤⣾⣿⠡⡇⢤⠈⠀⠲⠶⢛⠉⢀⡾⠇⢈⣀⠀⠀⣤⣙⣦⠈⠁⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠉⠀⠟⠋⠀⠀⠀⠈⢦⣤⣤⡤⢟⠙⠋⠀⢱⠎⠉⠀⠀⠀⠀⠸⠆⡁⠀⠐⠂⢛⠳⡆
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣠⠀⠀⠀⠁⠀⢸⡇⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⢀⡠⠂⠀⠀⠊⠑⠈⢓⡤⠀⠀⠋
⠀⠀⠀⢀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢀⣠⠀⠉⠀⠀⠄⠀⠴⠊⠀⠀⠀⠀⠀⠋⠉⠋⠉⠀⠀⠃⠠⠂⢻⠁⠈
⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠉⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢉⠠⡄⠀⠀⠈⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⡸
⠠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⣠⡖⠋⠁⠀⠀⡇
⠀⠉⠛⠻⢶⡀⠀⠀⠀⠀⣰⡫⠁⠰⠶⠢⢀⠐⠃⠓⠤⠔⠊⠀⠀⠀⠀⠀⠀⠱⣄⣀⠀⠀⠀⢱⠄
⠀⠀⠀⠀⣸⠏⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⡀⠀⠀⠀⡄⠀⠀⡞⠁⠀⢀⣴⠟
⠀⠀⠀⣰⠏⠀⠀⢴⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⢇⠀⠀⣿⡁
⠀⠀⢹⡿⢖⠒⠤⣈⣆⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠈⣧⡤⠈⠛⠳⣦⡀
⠀⠀⢸⡅⠈⠓⢄⢰⣉⠀⠐⠚⠁⠀⠀⠀⠀⠁⡀⠄⠁⠀⠒⠀⠁⠀⠀⠀⠁⠀⢀⣉⠩⠤⠔⠂⠈⣷
⠀⠀⠀⠛⠶⠶⠮⠓⠛⣄⠀⠐⠂⠀⡀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠶⠚⡊⢀⠚⣠⠀⣀⡼⠃⠀⠀⢀⢲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠞⠀⠈⠙⢢⠈⡁⠐⠁⣸⠢⠁⣿⠉⠀⠀⠀⡠⠃⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢔⣤⠀⢐⠳⣀⠀⠀⠀⠀⠀⠜⠠⠀⠀⠀⠂⢂⠈⠦⠔⡘⠓⠒⡒⠲⠇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠏⠀⡇⢸⠀⠈⠱⣄⠀⠀⠀⠀⠀⠎⡀⠀⡐⠀⠀⢈⠀⠈⡄⠀⠀⠀⠀⠀⠨⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⠀⠀⠀⠀⠙⠲⣀⠀⠀⠀⠀⠐⠉⠐⠀⠤⠀⠀⣠⠀⣰⠂⢰⢂⠄⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠣⣄⣀⣀⡀⠀⠈⠁⢀⠈⣁⠴⠦⠲⡁⢹⠒⢯⡄⢞⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠛⡇⠀⢸⠄⠀⠀⢣⡾⠀⡜⠉⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⡼⠀⠀⠀⠀⠉⣰⡃⣀⣀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠁⠛⠹⠃⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⣀⠜⢹⣀⡠⠒⣩⠈⠀⠀⠀⠀⠀⠀⡠⠂⠉⣀⠀⠀⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⢴⡠⠔⠒⠊⢧⠀⠀⠀⠀⠀⠀⡌⠀⢀⣞⣹⣷⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠰⣖⠋⠈⠀⠀⢀⢀⠜⠀⠀⠀⠀⠀⡜⠀⠀⠸⣿⣿⡿⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⢀⡎⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠓⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣆⣠⡤⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠓⠒⠦⠤⢄⣀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡄⠀⠀⠀⠀⠀⠀⠔⢉⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠱⠀⠀⠀⡠⠂⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢧⠁⠀⠺⣆⡠⠄⣺⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⢴⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢆⠑⠀⠉⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⢦⠀⠑⠀⢎⡠⠤⠔⠒⠒⠋⠉⠉⠓⠒⠤⡘⠉⠑⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠳⣄⠀⠀⠉⠓⠲⠄⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⠤⡀⠈⠉⠙⠒⠒⠤⠤⠤⣰⡶⠋⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣛⡓⡶⠀⠀⠂⠒⠚⠁⠀⠀⢀⠴⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡄⢀⡞⠀⣹⠃⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠈⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠁⢠⠎⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠐⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠓⠒⠚⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⡀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠜⠀⠈⠢⡀⠀⠀⠈⢀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠴⠄⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠆⠀⠀⠀⠆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠈⡄⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢃⠀⠀⠀⠀⢐⠀⠀⠀⠼⠄⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⠄⢀⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢀⠌⠁⠀⠀⡠⠐⠐⢀⠀⠀⠠⡄⠀⠀⠒⢕⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⢀⠔⠁⠀⠀⠀⠀⠑⡀⠰⠐⡄⡐⠀⠀⠑⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡐⠁⠀⠀⣤⠶⣄⠀⠀⠈⠃⠀⠈⠀⡴⢦⡀⠐⠁⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⣿⣶⣿⠀⠀⠀⠀⠀⠀⢸⣷⣿⡇⠀⢹⠋⠀⠈⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠰⠀⠑⠖⠀⠀⢢⠀⡃⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠤⠀⠀⠻⠟⠁⠀⢸⠀⠀⢀⡈⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⢆⢃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⡐⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠢⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡤⠂⡠⠊⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠈⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⠀⠀⠠
⠀⠀⢆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡠⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠴⠂⠁
⠀⠀⠀⠀⢀⠠⠄⠐⠒⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠈⢌⡀⠀⠀⠆⠀⠀⢀⠀⠤⠀⠀⠀⠀⠢⠤⠊
⠀⠀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠤⠤⠤⠝⠒⢒⠴⠂⠈⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡀⠀⠤⠐⡊⠀⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠬⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠤⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠀⠂⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣄⣀⣀⣀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠁⠀⠀⠀⠈⠉⠙⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⣠⣀⣀⣀⡀
⠀⠀⠀⠀⢀⡶⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣀⣀⠶⠖⠛⠛⠉⠉⠁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⣠⠏⠀⣰⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠿⠛⠁
⠀⠀⢠⡏⠘⠀⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠶⠚⠋⠁⠀⢀⣀⣤⣤⣤
⠀⠀⢸⠃⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣠⣷⠀⠀⠀⠀⠈⢻⠁⠈⠁⠀⠀⠀⢀⣀⣤⡤⠶⠞⠋⠉⠁⠀⠀⣸
⠀⠀⠸⡧⠊⠀⠀⠀⠀⠀⠉⠢⠄⠀⠀⠀⠘⠿⣿⠿⠋⠀⠀⠀⠀⠀⢸⠀⢀⣀⣤⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⢄⠀⠀⠀⢀⣠⡾⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⡀⠤⠐⠌⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⠐⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⡘⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⣀⠀⠔⠁⢀⡠⠚⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠹⣆⠀⠀⠀⠀⢠⠤⠄⣀⣀⣀⡀⠀⣼⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⣄⡀⠔⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠉⠉⠉⠰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠉⠉⠉⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠷⠶⠶⠦⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠶⣶⣶⣶⣶⣶⣤⣤⣤⣀
⠀⠀⠀⠀⠀⢀⡼⠋⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠔⠒⠋⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⢠⡿⡀⢰⣿⣦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠛⠉
⠀⠀⠀⠀⡎⠀⢰⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠂⢠⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠀⠒⠒⠊⠉⠁⣀⡀
⠀⠀⠀⠀⡇⢀⡌⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠘⣿⣷⣤⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣤⠔⠒⠋⠉⠁
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⢸⡇⣀⣠⡴⠚⠋⠉
⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⠀⠘⠄⠀⠀⣀⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠠⠖⠊⠃⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠠⠆⠁⠀⡤⠋⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢻⣆⠀⠀⠀⢸⡟⠶⠶⠶⠶⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⠀⢀⣼⡴⠞⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⠛⠒⠒⠲⢤⣀
⠀⠀⠀⠀⠀⠀⡔⠒⠶⠤⢤⣀⣀⣀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣟⣲⢦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠃⠀⠀⡇⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⢀⡤⢒⣞⠏⠳⣄⠀⠉⠙⠲⢤⣀⡤⠔⠢⡄
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠞⠦⣤⠎⠐⢄⠀⠀⠀⠈⠀⣀⣤⡄⠀⠀⠀⠉⡏⠀⠀⠈⢣⡀⣠⣴⣊⣡⠖⠙⢦⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠈⠐⠪⠀⠿⠿⠃⠀⠀⠀⢀⡇⠀⠀⠀⠀⢹⡟⠁⠠⠙⡉⠙⡉⠳⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⢀⡜⠀⠀⠀⠀⠀⠸⣧⣀⡠⡶⠃⡰⠁⠀⢳⡘⣧
⠀⠀⠀⠀⠀⣀⣤⡖⠚⠉⠉⠣⡀⢳⣤⡄⠀⠀⠀⠠⠤⠤⠀⠒⠁⣸⢎⠴⠊⠉⠉⠑⠢⡀⠈⠑⢶⡓⠉⠉⠉⠉⠈⢳⡘⣧
⠀⠀⠀⡠⠚⠁⠀⠈⡆⠀⠀⠀⢳⢸⢸⠉⠲⠤⢀⣀⣀⣀⠤⠴⣺⡧⠇⠒⠒⠒⢤⡀⠀⢹⠀⠀⠀⠱⡄⠀⠀⠀⠀⢀⡇⢘⡆
⠀⠀⣸⠃⡦⢠⡄⠀⡅⠀⠀⠀⣸⡞⡎⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠑⢄⠀⠀⠀⠀⠹⡄⢸⠀⠀⠀⠀⠹⣄⣠⠴⢚⣡⡴⠋
⠀⠀⠹⡛⣗⣉⣠⡼⡥⠠⠤⠒⠛⢿⠉⠲⠤⣄⣀⣀⣮⡧⢄⠀⠀⠀⠘⡆⠀⠀⠀⠀⣧⠎⠀⠀⠀⠀⢀⠽⡤⠒⠉⠈⡇
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⠉⠯⣤⠞⢄⠀⠀⠀⣇⣀⡀⣤⣚⠋⠀⠀⣀⡠⠖⠉⠀⢱⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠘⠓⠒⠚⠂⠈⠉⠀⠀⠀⠀⠀⠉⠉⠹⡄⠀⠀⠀⠀⠀⢳⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠈⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣀⣀⠀⠀⠀⠀⢳⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠹⣟⠓⠶⢤⣤⣤⣤⣀⣀⣀⣀⣤⠄⣠⢤⡴⠒⠉⠁⠀⠈⠉⠓⢄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡞⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣀⠴⠋⠀⠀⠈⠓⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⣌⠀⠀⠀⠀⠀⠀⠀⣏⠀⠉⠓⠒⠦⠤⢤⣀⣸⡟⢆⡀⠀⠀⠀⠀⠀⣀⠞⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠈⢣⣀⡄⠢⡀⢀⣰⣋⣳⡄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠒⠀⠂⠒⠈⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠈⠉⠉⠉⠙⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣆⠀⠀⣀⣀⠀⠀⠀⢰⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠘⢳⡏⠀⠀⠀⢱⠔⠣⠤⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦
⠀⠀⠀⠀⠀⡀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠘⠁⠀⠀⠘⠉⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠲⢰⡶⠀⠄⠀⢰⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠀⠀⠇⠈⠀⠀⠀⣾⠘⠻⣿⣷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢤⠼⠋⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠓⠢⣤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠉⣛⣛⣀⣀⠀⠀⣀⣤⣤⡀⢀⣞⡽⠂⣀⣠⣤⡀⠀⣀⠀⠀⠀⠀⢀⣀⣀⣠⣇⣀
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠐⣏⡀⠀⣤⡈⣇⣀⣷⠈⢁⣸⠋⡵⣨⣿⠁⠘⠀⣧⠤⣯⠉⣷⠓⡆⢸⣻⠁⠘⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡀⢈⣼⠁⠦⢈⡆⣬⣙⠦⣤⡤⣾⢠⣄⣸⠉⠓⢸⠂⠈⣸⠁⠀⠛⠗⠚⠛⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡏⠓⠖⠚⢶⠇⠈⠑⠺⢀⡈⠉⠉⠳⠿⠚⠧⣾⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣄⡠⣴⢶⡤⣀⣴⡔⡻⣾⣓⢰⢣⠤⣤⣀⡤⢬⢩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⢐⠚⠓⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢠⣅⠀⠀⠀⠀⠙⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣠⣾⣿⣈⡀⠀⠀⠀⠀⠘⠈⠄
⠀⠀⠀⠀⠀⠀⠀⡠⢠⣤⣀⠀⠀⠀⠀⠀⣇⣀⠠⠐⠂⠓⠂⠤⢀⣀⠀⠀⠠
⠀⠀⠀⠀⠀⢠⠊⢸⡅⠘⠘⠗⢢⠀⢀⣴⣫⠤⢀⣀⣤⣤⣄⡀⠀⣀⣁⣒⣴⣀⡀
⠀⠀⠀⠀⢠⠁⠀⠘⠶⠭⣤⠠⠦⣾⣿⣿⣇⠀⠌⣽⢴⣿⠟⠕⠻⠃⣶⠹⣿⣿⣿⣾⡆
⠀⠀⠀⠠⠛⠒⠀⢄⣀⡠⠘⠀⠒⠀⠛⢿⣿⠀⢠⡏⠘⠁⠀⠀⠀⢰⡟⠰⡯⣿⣿⠟⠱⡄
⠀⠀⠀⡤⠤⣀⡀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠡⡈⠉⠀⣋⣀⡀⠀⠰⠏⠁⣰⣡⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⣾⠿⢂
⠀⠀⢠⠁⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠦⡀⠣⣀⡠⠃⢀⡀⠴⢍⠉⠁⢀⠄⠐⠁⠀⠀⠐⠒⠁⠀⠀⢀⠜⠁⢠⠊⡀
⠀⠀⠂⠀⠀⠀⡘⠀⠀⠀⢀⡀⠠⠴⠁⠎⡀⠀⠀⠀⡓⠀⠒⠉⡘⠀⠀⠀⠁⢢⣾⠀⠀⠀⣼⣿⠄⠀⠀⡠⠊⠁⠀⡰⠁⠀⠰
⠀⠠⠀⠀⠀⠀⠄⠀⢸⡁⠀⠀⠀⢈⡀⠀⠈⢆⠀⣴⠁⠀⠀⠴⠀⠀⠀⣀⣤⡋⣉⡀⡀⠀⠈⡅⠂⠄⠀⠱⠀⠀⠔⠀⠀⣀⠔
⠀⠇⠀⠀⠀⠀⠓⠈⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠞⠂⠀⠀⢰⡁⠔⠊⠁⠀⢰⠁⠘⣌⠀⠀⠀⠑⠐⠁⠀⠀⠄⠘⡄⠀⠘⢅
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⠠⢋⡀⠀⠀⠀⠀⠊⠢⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⠘⠀⠀⠀⡱
⠐⢄⠀⠀⠀⠀⠀⣀⠠⣼⠀⠀⠀⠀⠀⠀⠀⠺⠥⠃⠀⢀⠢⠂⠀⠀⡀⠀⢠⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⡐⠁⠀⡠⠒⠁
⠀⠀⠒⠀⠀⠀⠁⠀⠀⠘⠂⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠑⣤⡄⠀⠘⡄⠀⠐⠀⠀⢀⠀⠸⢔⡨⠂⢀⡨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠈⡅⠱⣀⣰⢀⡂⡠⠐⠁⠀⢠⣪⣄⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠓⢀⡈⢢⡔⢍⢁⡊⠀⠀⠀⢠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡴⡄⠀⠀⠀⠘⠢⢄⣀⠀⠀⢱⠀⠀⠐⡙⣦⠰⠐⡀⢳⠀⢪⠀⠆⠀⢐⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠎⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⣀⡆⠀⠀⠈⢿⢶⢷⠲⠤⠗⠘⢃⠾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⢿⣯⠀⠀⢸⢻⣷⠀⠀⠀⠀⠳⣱⡌⢃⠉⠓⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠐⠀⠊⠁⠈⡄⠀⠀⠀⠀⣉⡤⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⠔⠆⠄⠀⡤⠀⠀⠀⡄⠀⠀⠀⢡⠤⠖⠠⠛⡂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢄⣰⠀⢠⢀⠄⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡼⠁⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⠀⠀⢀⠞⠃⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣅⠌⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⢀⠀⠂⠀⠀⢰⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢂⠀⠸⠣⠈⠑⠌⡆⠀⠀⠐⠄⡴⠄⠊⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡔⠁⠀⠀⠠⠊⠂⠚⠠⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡠⠄⠂⠉
⠀⠀⠀⠌⠀⠘⠢⠄⠊⠰⠀⠀⠂⢠⠀⠀⠀⠀⠀⠁⣆⠀⠀⠀⢀⠀⠀⠀⢤⠁⠀⠄⠀⠄⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠀⡠⠃⠀⠀⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⢻⡳⠄⠀⠀⠀⠆
⠀⠀⠀⠐⠐⠀⡀⠀⠀⡆⠀⠸⠠⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢫⢊⠀⠀⢀⠀⠀⢀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠤⠄⠀⡐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢉⣈⠀⠢⠀⢠⠅⣢⡐⠄⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠂⠠⢀⠀⡆⠀⠁⢀⠀⢀⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⢱⡜⣇⠀⠀⠀⠄⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠩⢧⠟⠀⢀⢀⠠⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡏⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡃⢀⣠⡰⡆⠋⡰⠛⢱⡎⠋⣇⣴⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠈⢳⡈⣧⣁⣠⡰⢬⣰⠾⠥⣶⣄⣥⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠈⠛⠉⡠⠊⠁⢢⣀⠴⠈⠀⢦⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⣿⠀⢎⠰⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠙⠂⠤⠚⠈⠑⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠞⠛⠓⠒⠒⠒⠶⠦⢄⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⣠⡴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⢀⣠⣤⣶⣾⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠘⠿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠉⠛⠛⠿⢿⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠻⣷⣆⠀⣿
⡟⠓⠲⠶⢤⣤⣀⡀⠀⠉⠉⠙⠛⠛⠛⠒⠒⠲⠶⠶⡶⠂⠀⠀⠀⣠⡶⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣴⣿⣿⠀⢸⡆
⣷⠀⠀⠀⠀⠀⠉⠉⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢰⣿⣷⣤⣾⣿⠀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⠘⠻⠿⠟⠃⠀⠀⢿
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡓⠶⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠻⢿⣿⠿⠃⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⢀⣴⣴⣄⡀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⠋⠹⠛⢦⣉⠛⠦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣀⣤⠴⠚⠉⠀⠀⠈⠻⣶⠞⠁⠀⠀⠀⢀⡞⠁⢹⡀⢀⣤⠶⠋⠁⠁⠈⢿
⠀⣷⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠈⠑⠦⣈⡄⠀⣠⠤⠤⢄⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⢸⡇⠀⢸⡟⠋⠀⠀⠀⠀⠀⠀⢘
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡜⠁⠀⠀⠀⢳⡀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠈⢧⡀⣸⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⡼⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠛⠶⠦⣤⣄⣀⣀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠴⠃⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠠⣾⣥⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢉⣿⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⠀⢀⡴⠛⠳⢤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣵⣷⠟⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠶⠦⣤⣄⣀⣀⣀⣀⣠⠴⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠈⠙⠢⣄⠀⠀⠀⠀⠘⣆⢦⣋⣠⣇⠼⢤⣘⣁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⢁⠈⠁⢦⠔⠀⠢⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠙⢆⠀⠀⠈⠢⠀⠜⠢⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠊⠉⠀⠀⠒⠂⠀⢳⡀
⢀⣠⣤⣶⡖⠚⠛⠉⠉⠉⠉⠛⠓⠒⠲⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠙⠻⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠘⡄
⡶⠤⠤⣀⣉⠉⠓⠒⠒⠦⠤⠤⠤⡤⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣿⡆⢣
⡇⠀⠀⠀⠈⠉⠒⠦⢄⣀⠀⠀⠀⡇⠀⠀⢺⣷⣾⡇⠀⠀⠀⠀⠂⠀⠀⠈⠛⠋⠀⠘⡆⠀⠀⠀⢀
⢻⠀⠀⠀⠀⠀⢀⠴⠒⠺⢕⠢⢼⡇⠀⠀⠀⠉⠉⠀⣀⣀⠔⠊⠉⠒⢦⠔⠀⠀⢀⠔⢳⠀⣠⠴⠋⠋⢶
⠸⡄⠀⠀⠀⠀⢺⠀⠀⠀⠀⠉⠢⡇⡠⠒⠲⡄⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡀⢸⠋⠀⠀⠀⠀⣸
⠀⢇⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢹⣇⠀⠀⡘⠀⠀⠀⡆⠀⠀⠀⠀⡎⠀⠀⠀⠀⠑⡎⠀⠀⠀⠀⡰⠁
⠀⠈⠓⠒⠢⠤⣤⣀⣂⠀⠀⠀⠀⠀⢫⠁⠈⠀⠀⠀⠀⠘⢄⠀⢀⡜⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡠⠔⠁⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⣏⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢼⣀⡤⢤⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⣼⢄⡠⠋⠙⠲⠤⢤⣤⠤⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣴⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⠀⠀⢹⢁⣿⠗⠠⠆⠀⠀⢶⣿⣷⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠀⠀⠀⡟⠘⠃⠀⠀⠀⢰⡇⠸⢻⣿⣿⣶⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠉⠀⠄⣰⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠀⡀⠀⠀⠀⠐⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠿⠋⠓⢦⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣴⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠀⠀⠀⠀⠈⣛⣛⣅⣀⣀⠀⠀⢀⣠⣤⣤⣄⠀⢠⣎⡼⠃⣀⣀⣠⣤⡄⠀⠀⡀⠀⠀⠁⠀⠀⠀⣀⣀⣀⣠⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⢰⡋⠁⠀⢀⣀⠙⡆⠀⠸⡆⠘⠋⢈⡷⢋⣭⠉⣳⡟⠀⠹⠀⣧⣀⣀⣏⠙⢳⡶⠶⡤⢸⡟⡏⠁⠹⡏⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠘⠿⣠⠟⣭⣉⢳⡀⠀⠻⢧⡈⠁⠊⣙⡇⢀⠀⢀⡟⢵⣠⢹⡄⠘⠁⣸⠁⠈⢿⣷⡤⠴⢿⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⣹⡀⠈⢁⣼⠀⣟⠲⢤⣉⣻⠋⠹⠦⠼⢿⡏⢧⣀⣠⡞⢠⠀⢠⡇⠀⠀⠀⠈⠀⠀⠀⢙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣨⡇⠉⠉⠉⠘⠻⠋⠀⠀⠈⣙⢠⢤⠀⢀⡀⠙⠛⠃⠈⠛⢻⣀⡾⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡠⡔⣾⣳⠲⣄⢔⣶⢺⠸⣺⢘⠂⣸⢳⠶⢢⣄⣀⡔⠶⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣭⠽⠶⠿⠟⠒⠙⠚⠓⠚⠛⠉⠛⠋⠙⠚⠺⠾⠿⠧⣤⣏⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀⠚⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣠⠦⠄⠀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠊⠻⠒⠂
⠀⠀⠀⠀⢀⠔⢠⠙⠓⠦⠀⠀⢀⣼⣂⢁⢀⣀⡀⠀⠁⠂⠠⣠
⠀⠀⠀⠀⠊⠀⠡⠴⢥⡠⢦⣼⣿⣿⠀⠈⡿⣽⡿⠷⠲⢻⡟⣿⣿⣷⣶
⠀⠀⠀⠊⠀⠀⢄⡀⠔⠁⠀⠘⠻⢾⠀⣸⠇⡉⠀⠀⠀⣼⠇⠿⢿⣿⠋⠦
⠀⠀⠐⠒⠀⠄⣀⠁⠀⠀⠀⠀⠀⠈⢄⠀⢠⠅⠠⡄⠘⠁⢠⣷⠿⠋⠀⢀⠀⠀⠀⢀⠠⠐⠀⢨⠿⢋⡄
⠀⠀⠂⠀⠀⠠⠁⠀⠀⠀⠀⣠⢀⠖⠀⠁⠢⡁⠀⠀⠤⠀⠉⠢⣀⣴⠀⠀⢀⣤⠈⠀⠀⡀⠔⠁⠠⠂
⠀⠈⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠑⠄⠀⡰⠂⠀⣠⠁⠀⠀⢀⡜⠛⠀⠀⠘⠛⢁⠀⠘⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠆⠀⠉⠀⠀⠀⡼⠀⠀⠈⠞⠀⠀⠀⢂⠀⠒⠈⠨⠂⠙⡉⠀⠀⠀⠐⠀⠀⠀⠰⡀⠀⢊
⠀⠀⠀⠀⠠⠂⠀⠀⠂⠀⠀⠀⠀⠀⠐⠒⡀⠀⠌⠄⠀⠀⠀⠈⠱⠄⠀⠀⠀⠀⠀⠀⠔⠀⢀⠜⠀⠀⡱
⠈⢄⠀⠀⡀⠀⠄⠰⡃⡀⠀⠀⠀⠀⢘⠚⠀⠀⡀⠂⠀⠠⡀⠀⠀⢀⠀⠀⡀⠀⠀⠀⡰⠰⡁⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠀⠘⠇⢀⠀⠀⠀⠀⢀⠔⠀⢉⠖⢁⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⡰⠀⠓⣃⠰⠒⠔⠀⠀⠁⡓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠘⠤⣀⡀⠀⢠⠀⠀⢐⢧⡨⠁⠘⡄⢱⡁⠄⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⣀⣀⠀⢀⣠⡆⠀⠀⠻⡲⠆⠣⠘⠀⢃⢞⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⢸⣿⠇⠀⢈⡹⢷⠀⠀⠀⠘⠵⠈⡄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡐⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠉⠀⠉⠀⠀⠀⠀⡀⠀⠉⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⠎⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⣀⣴⡇⣼⡀⣼⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⠖⠵⡟⢟⡟⠿⡿⡗⢁⢿⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣯⢰⣿⣷⣿⡇⢰⣿⣿⣿⢢⣝⢿⣄
⠀⠀⠀⠀⠀⠀⠠⣤⣿⠛⡳⢦⣀⠀⠀⢀⣸⠏⣿⣿⢸⡿⣿⢹⣧⣾⠟⢟⡿⡼⣿⡘⣿⠀⠀⠀⠀⣀⡤⠶⣿⣛⣀
⠀⠀⠀⠀⠀⠀⢶⣿⣶⠿⣅⢹⡝⣷⢦⡈⡿⣴⣿⣿⣦⣿⠄⢦⣿⣯⠀⣺⣴⣿⣿⣷⣹⣇⣴⡖⢿⡯⢐⣾⣍⣽⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣱⣶⣿⠿⢸⡖⣿⣼⣟⠿⠿⠿⠿⣷⠊⠿⠃⠾⠟⠛⢛⣛⡍⢷⡸⣿⡗⣿⣧⣭⡴⢉⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣷⣾⣷⡛⠿⠞⣿⣿⣶⣶⣴⣦⣴⣶⣶⣶⣾⡿⡏⠯⢼⡇⣿⣷⡉⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⡹⠻⣾⣥⣤⣴⣗⡻⣟⣿⢿⡿⣿⣿⠿⣿⠸⠇⣑⣸⣿⣟⣿⣇⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡾⣧⢞⣭⣶⣶⣾⣿⣧⡈⢵⣼⣣⣿⣿⣄⣟⡈⢶⣾⣿⣿⣿⣿⣿⣿⣳
⠀⠀⠀⢀⠋⠀⠀⠀⠀⣠⠆⢞⣵⣿⣿⡿⠛⠻⣿⣿⣿⡞⣯⠿⢻⣏⣿⣭⡛⣿⣿⣿⣿⡻⣿⣟⣿⣿⣷⡀
⠀⢀⣾⣻⡿⠿⡛⣛⣻⣷⢦⣿⣻⣿⣿⣧⣽⢠⣿⢟⣹⣿⠀⣤⡄⠻⣾⣿⡿⣸⣿⣦⣝⠮⣮⠏⢻⣿⣿⡆
⠀⢸⣿⡃⢿⣷⢹⣿⣹⣹⡾⣿⣿⣷⣯⣭⣷⣿⣿⣿⢿⣟⢻⣿⢀⣼⣃⡉⢩⣭⣭⣍⣙⣛⢮⡀⠚⣽⡿⠁
⠀⢸⡙⠿⠿⠯⠜⠙⣧⡿⣿⠏⠹⣷⣝⣧⡛⢿⣿⣋⣾⣽⣿⢁⣴⣿⡥⠂⡈⠻⣿⣿⡿⠿⠋⢁⣀⡤⠀⠀⢀⠤⠼⢿⣿⣶⣄
⠀⠀⠁⣞⣠⡶⣶⡘⣠⣶⣾⣿⣧⣝⠉⢉⠙⡋⢡⣉⡤⠟⠁⠈⡽⢋⣔⣴⣿⢦⠠⣤⠤⡖⠻⣋⠘⠁⠀⢰⠿⢾⣟⣋⣿⡟⠃
⠀⠀⣀⠈⠁⠀⡸⠑⠛⣵⠞⠛⢿⣿⣇⣬⣌⢛⣴⠟⠀⢀⣤⢪⣴⡿⢟⣻⡜⢯⣀⣄⣶⣼⠖⠃⠀⠀⠀⠈⠙⠛⠋⠉⠛⡇
⠀⠀⠉⠀⠀⡼⢡⡖⣲⡏⠀⠀⣼⣿⣯⣵⣷⡿⢫⣦⠘⠛⣷⣯⣝⣻⣿⣿⣧⠾⣿⠛⠋⠁
⠀⠀⠀⠀⣼⡇⠘⠿⠟⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠿⢿⠖⠴⠟⠋⠁⢠⣾⣿⡘⣿⣷⣄
⠀⠀⠀⠀⠻⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣰⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⡟⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠐⠉⠉⠁⠒⠢⣄⡀
⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⢦⠤⠤⢤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠭⠓⢶⣤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⡜⠀⠀⡸⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠠⢔⣨⣻⠃⠑⣄⠀⠈⠉⠲⣤⠤⠒⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠙⢲⡞⠀⠳⢄⠀⡀⠀⡀⣤⣶⡆⠀⠀⠀⠰⡇⠀⠀⠈⠣⣤⣴⠯⢥⣞⣉⣙⣆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠈⠁⠀⠚⠙⠁⠀⠀⠀⢸⠃⠀⠀⠀⠀⣿⠁⠀⠃⣡⠀⡅⠈⢆⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠞⢏⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡜⢣⣠⠃⣀⡀⣀⣀⠀⠹⣧⣄⣻⣃⣠⣃⣀⠨⣆⢻⡄
⠀⠀⠀⠀⣠⠔⠚⢍⠀⠀⠀⢳⡀⡟⡶⡀⠀⠀⠐⠒⠒⠀⠉⣠⡾⡱⣊⣀⡀⠀⠈⠱⡄⠀⠈⢣⡀⠀⠀⠀⠀⠘⣆⢻⡄
⠀⠀⢠⡞⠀⠀⠀⠈⡆⠀⠀⠀⣇⣧⠃⠀⠙⠒⠒⠒⠒⢒⡉⠾⢟⠁⠀⠀⠈⠓⣄⠀⢳⠀⠀⠀⠳⡀⠀⠀⣀⠤⠛⣠⠇
⠀⠀⣿⣤⡏⠜⠀⡰⠃⠀⢀⣰⣿⡾⣄⡀⠀⠀⠀⣠⣶⠉⠀⠀⠀⢣⠀⠀⠀⠀⢸⢀⡏⠀⠀⠀⠀⠱⡔⢋⡥⠖⡏
⠀⠀⠘⠲⠓⠒⠚⠙⠃⠉⠁⠀⠈⡇⠀⠉⠑⠒⠶⣿⠋⣱⠀⠀⠀⠀⡇⠀⠀⢀⣼⠞⠀⠀⠀⢀⡠⠊⢹⡁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠈⠟⠁⠱⠄⠠⠔⠓⠂⠈⠛⠒⠢⠴⡖⠊⠉⠀⠀⠀⢣⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠻⡶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠒⠛⠒⠒⠤⣀⠀⠀⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢦⡀⠈⠉⠉⠛⠛⠛⠋⠋⠉⠉⢉⡟⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⡴⠃⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢇⠊⠁⠀⠀⠀⠀⠀⣿⠉⠒⠦⠤⣄⣀⣀⣀⣸⢣⡀⠀⠀⠀⠀⠀⠀⣠⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠈⠳⡀⢀⠤⡀⠀⢀⡏⠢⡀⠀⠀⠀⠀⠈⠉⠙⡇⠈⠒⠀⠤⠄⠐⠊⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠒⠒⠒⠚⠙⠓⠒⠋⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡠⢿⡀⠀⠀⠀⠀⠀⠀⠀⡾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠤⠤⠷⣴⠋⠀⠀⠐⡤⠾⠤⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣄⣀⣀⣀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠁⠀⠀⠀⠈⠉⠙⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⣠⣀⣀⣀⡀
⠀⠀⠀⠀⢀⡶⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣀⣀⠶⠖⠛⠛⠉⠉⠁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⠀⣠⠏⠀⣰⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠿⠛⠁
⠀⠀⢠⡏⠘⠀⠹⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠶⠚⠋⠁⠀⢀⣀⣤⣤⣤
⠀⠀⢸⠃⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣠⣷⠀⠀⠀⠀⠈⢻⠁⠈⠁⠀⠀⠀⢀⣀⣤⡤⠶⠞⠋⠉⠁⠀⠀⣸
⠀⠀⠸⡧⠊⠀⠀⠀⠀⠀⠉⠢⠄⠀⠀⠀⠘⠿⣿⠿⠋⠀⠀⠀⠀⠀⢸⠀⢀⣀⣤⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⢄⠀⠀⠀⢀⣠⡾⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⡀⠤⠐⠌⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⠐⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⡘⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⣀⠀⠔⠁⢀⡠⠚⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠹⣆⠀⠀⠀⠀⢠⠤⠄⣀⣀⣀⡀⠀⣼⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⣄⡀⠔⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠉⠉⠉⠰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠉⠉⠉⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠷⠶⠶⠦⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠶⣶⣶⣶⣶⣶⣤⣤⣤⣀
⠀⠀⠀⠀⠀⢀⡼⠋⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠔⠒⠋⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⢠⡿⡀⢰⣿⣦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠛⠉
⠀⠀⠀⠀⡎⠀⢰⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖⠂⢠⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠀⠒⠒⠊⠉⠁⣀⡀
⠀⠀⠀⠀⡇⢀⡌⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠘⣿⣷⣤⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣤⠔⠒⠋⠉⠁
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⢸⡇⣀⣠⡴⠚⠋⠉
⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⠀⠘⠄⠀⠀⣀⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠠⠖⠊⠃⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡀⠀⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢟
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠠⠆⠁⠀⡤⠋⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢻⣆⠀⠀⠀⢸⡟⠶⠶⠶⠶⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⠀⢀⣼⡴⠞⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⣀⠜⢹⣀⡠⠒⣩⠈⠀⠀⠀⠀⠀⠀⡠⠂⠉⣀⠀⠀⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⢴⡠⠔⠒⠊⢧⠀⠀⠀⠀⠀⠀⡌⠀⢀⣞⣹⣷⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠰⣖⠋⠈⠀⠀⢀⢀⠜⠀⠀⠀⠀⠀⡜⠀⠀⠸⣿⣿⡿⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⢀⡎⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠓⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣆⣠⡤⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠓⠒⠦⠤⢄⣀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡄⠀⠀⠀⠀⠀⠀⠔⢉⡏⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠱⠀⠀⠀⡠⠂⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢧⠁⠀⠺⣆⡠⠄⣺⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⢴⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢆⠑⠀⠉⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⢦⠀⠑⠀⢎⡠⠤⠔⠒⠒⠋⠉⠉⠓⠒⠤⡘⠉⠑⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠳⣄⠀⠀⠉⠓⠲⠄⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⠤⡀⠈⠉⠙⠒⠒⠤⠤⠤⣰⡶⠋⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣛⡓⡶⠀⠀⠂⠒⠚⠁⠀⠀⢀⠴⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡄⢀⡞⠀⣹⠃⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⠈⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠁⢠⠎⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠐⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠓⠒⠚⠓⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⣿⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣈⣿⣇⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⡁⣀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⢰⣷⡝⢿⣿⣿⣿⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠃⢻⡿⣿⣦⡙⠛⠿⢃⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣿⣿⣶⣶⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⣼⡿⢿⣻⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠟⠟⠀⣿⣷⠾⣿⣿⣿⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣹⣏⣀⣬⣿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢐⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡌⠙⢡⡅⠈⠆⠀⡄⠀⠀⣦⡀⠀⠶⢄⠃⠀⠐⠀⠀⠀⠀⠐⠀⢀⡀⠀⠀⠀⠠⠒⠀⠠⠆⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠂⡌⠀⠰⡄⢈⡅⠀⢂⠘⠀⠘⠀⠠⠀⠀⠀⠀⠀⠀⣀⠘⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠑⢀⢀⣥⡀⠷⠂⣈⡔⠀⣤⣴⠦⢠⡀⠀⠀⠀⠈⠉⠀⢀⡀⣀⡀⠀⠈
⠀⠀⡀⠹⠃⠀⣀⠀⢀⡀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠈⠻⣟⠛⠒⠻⣦⠀⢠⡄⠀⠀⠀⢀⣤⣴⣶⠟⠁⠀⠀⠀⠀⠈⠁⠀⠦
⠀⠀⠀⠂⠀⠀⠉⠄⠚⠁⠀⠸⠟⠀⠀⠐⠧⠀⢄⠀⠀⠉⠁⠀⠙⣶⣿⣤⡀⠀⠂⠈⠙⠿⠟⠁⠀⠀⠤⠤⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⡙⠻⠋⢠⡄⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⡀⢀⠄⠀⠀⠀⢁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣴⣦⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢀⣤⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠋⠀⠀⢤⠀⡀⠁⠁⠀⠀⢀⠺⢣⠄⠀⠄⢠⡤⠒⠀⡘⠁⠀⡀⠀⠠⣘⡧
⠀⠀⠚⠘⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠲⠄⠀⠀⠀⠀⣼⡇⠈⠲⠁⢠⣤⡴⠀⢀⡀⠀⠈⢠⣴⢶⣤⣴⣄⢹⠀⠁
⠀⠲⣶⠶⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⡰⠚⠀⠀⢰⡦⠚⠀⠘⠉⠀⢀⠀⢠⠀⠸⠀⠀⠟⠁⠀⠠⠿⣿⣾⡿⠃⡀⠀⠠⢤⡀⠀⢠⡀
⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⢰⡄⠀⠸⡆⠀⠀⠁⠀⠤⠀⢐⡂⠈⠀⣈⠄⠀⠀⡀⠀⠀⠀⠶⠃⠈⠁⠀⠒⠃⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠙⢿⣦⠐⡇⠀⠀⣏⠙⢦⣀⡑⠀⠀⠀⠀⢀⠂⠀⠀⠀⠈⠁⠀⠀⢀⣤⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠺⣷⣤⣀⣀⣀⣤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⠏⠰⣶⠀⠸⠃⠈⠁⡀⠀⠀⠀⠶⠆⠀⠰⠖⠰⡆⠁⠈⠉⠉⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠂⠉⠁⠁
⠀⠀⠀⠀⠂⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡃⠀⠀⠃⠀⠖⠠⠀⢀⠐⠀⠀⠲⠰⢀⠆⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀⠊⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣠⣶⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣀⣀⣀⠰⢁⡀⠁
⠀⠀⠀⠀⠀⠀⠂⣄⣈⣼⣿⣿⣿⣿⠃⢹⣿⣶⠆⠀⠀⠀⠀⠀⣀⢀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠐⠍⣽⣧⣭⠙⠰⠿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣿⣿⣿⡏⠀⢠⣿⡷⢠⠀⠳⠄⠀⡀⣀⣬⣾⠋⢰⡄⠀⡄⠀⠀⠆⠠⣀⠀⢻⠏⠁⠀⠀⠠⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠀⣹⡿⠿⢾⣿⠿⠃⠛⠘⣆⠈⠀⠙⠋⣡⣄⣠⠟⡅⢀⣴⡄⠀⠰⠲⠶⣯⢀⠀⠀⠀⠀⢀⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠋⠁⠀⠀⠀⠀⠘⠷⠶⠶⠞⠣⠈⠁⠀⠠⡇⠀⠀⠀⠀⠀⠀⢛⠃⠄⠀⠈⠁⢩⠍⠻
⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠾⡠⠆⠀⠀⠈⠀⠀⠻⠄⠀⠀⡀⢠⡀⠀⠀⠀⢀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠎⠀⠀⠠⠀⠀⠀⠐⢂⠀⡀⠐⠁⠀⠀⠀⡀⠀⠀⠀⠻⣤⣀⣐⣀⣀⠔⠁⠀⠀⠊⡙⢀⠛⣤⠀⠀⠈⠁
⠀⠀⠀⢀⡀⠀⠀⢿⡏⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠀⠀⠠⠀⠀⠖⠊⠀⠀⠀⠀⠀⠙⠉⠉⠉⠁⠀⠈⠁⠰⠂⢹⠃⠈
⠀⠀⠀⠀⠉⠻⠗⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢤⠀⠀⠀⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠛⠒⠚⠋⠉⠓⠒⠒⠲⠤⣄⣀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠀⠀⠀⢀⣀⡤⠖⠚⠉⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢠⣤⢶⣴⣆⠀⠀⡼⠀⢸⣿⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢺⢀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠙⢦⣴⠃⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡉⣻⣷⡀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢰⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢺⠀⠈⡇⠀⠀⠀⢲⣤⡤⠖⠒⠲⣤⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠸⣆⣠⠇⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠉⢻⡞⠁⠀⠀⢀⡴⠶⢦⣄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢰⡏⠀⠀⠀⠘⡆⢀⡏⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠸⡆⠀⠀⠀⢀⡼⠁⠀⠀⠀⠈⢧⡀⠀⢀⡴⠁⡼⠀⠀⠀⠀⣀⡤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠙⢦⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣀⡞⠁⠀⠀⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⣿⣄⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⢀⡴⢻⠈⢧⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠹⡋⠉⠀⠀⣀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣧⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠛⠶⣟⢲⡄
⠀⠀⠀⢰⣶⣦⣀⡴⠋⠀⠀⠀⠀⠈⠙⠆⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠣⠖⠛⠛⠻⣏⠀⢀⣤
⠀⠀⠀⢸⡿⣏⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠘⡷⢻⣿⠁
⠀⠀⠀⠈⢷⠈⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠉⡿
⠀⠀⠀⠀⠘⣇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⢦⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠘⣆⠀⣤⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠙⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⢹⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⣧⣤⠤⠴⠦⢤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠟⠁⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠋⠉⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡞⠀⣴⣿⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢀⣰⡾⠋⠛⠻⣄⠀⣼⠁⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶⣄⠀⠀⠀⠀⠀⢸⣧⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢺⡅⠀⠀⠀⠀⠈⣿⠃⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢰⣿⣤⣾⣿⡇⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢠⡟⠛⢦⠀⠀⠀⠀⡀⠀⠀⢀⣈⡁⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠸⡇⠀⢸⠀⠀⠀⠀⢹⣶⠟⠉⠉⠙⠲⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢻⣤⠟⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣤⠞⠋⠛⢦⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⣷⠀⡞⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠸⡄⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠳⣤⣀⣠⠼⢃⡾⠁⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠙⠦⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠁⠀⠀⢺⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠋⠁⣻⢧⡀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⣶⣻⣄⣹⡆⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠉⠀⢀⣀⣤⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠾⢥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠙⠳⢿⢳⣦
⠀⠀⠀⢰⣾⣦⣀⡴⠋⠁⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠣⠖⠛⠙⠛⢯⠀⢀⣤⡄
⠀⠀⠀⠘⣿⢷⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⢳⢿⣿⡇
⠀⠀⠀⠀⢳⠈⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠘⢹⡇
⠀⠀⠀⠀⠈⣇⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣄⣠⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡿
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠙⠧⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡒⠀⠒⠈⢉⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠡⠄⢀⡄⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠉⡀⠒⣀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠐⠒⠀⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠇⠠⣰⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠛⠁⠀⣀⣀⠀⢀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠁⢁⠘⠢⠀⠀⣀⣠⣄⣀⠀⣀⣠⢴⡎⡀⢀⣤⠟⠉⠀⠀⠈⠆⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⣀⢠⠉⣴⣿⢟⠿⢻⣿⣿⠖⣁⠟⢉⠀⠄⣸⣃⣤⣤⣤⣤⠀⠃⠀⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠈⠉⠀⢀⣤⡴⠖⠏⣡⣾⡿⠏⢠⣼⣿⣿⠃⠰⠉⠀⠋⣀⣴⣿⣿⠿⠛⠉⠁⣀⢠⠐⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⡴⣰⡳⢭⣥⣴⣶⣿⠟⠉⡠⢴⣿⣿⠟⢳⣤⣴⣴⣾⣿⣿⣿⡟⠁⠀⣴⣶⣾⣭⣴⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢠⣤⡟⢻⠊⢁⣠⣾⣿⣿⣉⡠⠂⣉⢴⣿⠿⠁⠀⠀⠀⣼⣿⡿⠿⠿⠿⠖⣛⣫⣿⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰⣿⡏⠻⣿⣿⣿⣿⣿⡉⠡⢐⣫⣴⠿⢃⡐⠂⠀⣠⣺⣾⣿⣿⣿⣤⣤⣿⣿⡿⠿⠛⣋⣩⣼⠯⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠉⢻⡓⣲⣮⣿⣯⣥⣶⠾⠛⠉⠋⢀⡀⣀⠄⣪⡷⠟⠀⢿⣿⡍⡙⠋⠉⠁⣀⣴⠾⠋⠉⠀⠀⠀⠈⠻⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠤⣫⣼⣿⠿⣊⣽⣿⣿⣿⣿⣿⣿⣿⣦⣔⣒⣠⣽⣶⠟⠋⠀⠀⠀⠈⠻⢿⣿⣯⣿⣿⣏⣱⣶⣿⣿⣷⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣇⣾⣿⠟⣡⣾⣿⣿⣿⣿⣿⣶⣮⣭⣽⣯⣽⣿⠟⠋⠀⠀⢠⣄⣼⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠐⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢈⡝⢁⣾⣿⣿⡿⣿⣙⡟⠛⣻⣿⣿⡿⠛⠛⠿⣿⣶⣤⣤⡄⠉⠁⣰⣾⣿⣿⣉⣀⣼⣿⣿⠟⠛⠉⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠚⠀⣿⡟⢻⣿⣷⣽⣿⣧⣶⣿⣿⡿⢿⣶⣿⣿⠿⣿⣿⣿⡁⠀⢰⣿⣿⠿⢿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣀⣤⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢈⠤⢡⣾⢋⡼⢳⣿⣿⡟⠩⣿⡇⠠⠻⠿⠿⠿⠟⠛⠛⠁⠀⣿⠛⢿⠿⠿⡿⠋⢹⡇⠀⣈⣴⣾⣿⣿⣿⡶⠞⣻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣡⠔⢛⢧⣈⠇⣾⣟⣻⣇⣀⣿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀⠙⠀⠇⠀⢀⣿⠋⣾⣿⡿⠛⠿⣿⡿⡟⢩⠽⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⢀⣿⣽⣦⠞⠋⣠⠌⣸⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣸⣧⡀⠀⠀⣠⣿⡏⢰⣿⣿⣷⡆⠰⠹⣧⣬⣴⣶⣶⣾⣷
⠀⠀⠀⠀⠀⠀⡈⠀⢐⢴⠋⡉⠁⡀⠀⠀⠀⣴⣿⣄⡛⠳⢦⡇⠀⠀⠀⠀⠘⠻⣿⡿⠋⠀⠀⢸⡿⣿⠁⠀⠻⠿⠿⣷⣄⣐⠈⢛⠻⠥⠀⢈⡿
⠀⠀⠀⠀⠀⠀⢹⠀⠈⠜⠙⠒⠂⠀⠀⢀⠄⣽⣿⢿⣿⣷⠈⣧⠀⠀⠀⢀⣠⣴⣤⣴⣤⡀⠀⡿⢁⣿⣧⠀⠀⠀⠀⠠⠉⢿⣿⣀⡀⣀⡴⠟
⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠠⠐⢂⣡⣴⣿⣿⠎⣻⣽⠇⠍⠀⠀⠀⠻⣟⢛⣻⣿⣿⡟⠀⢁⣼⡿⣿⣦⡀⠀⠀⠀⠀⠀⠙⢿⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣄⣐⣈⣥⣿⡟⠉⢀⢒⣭⠶⣿⣄⡀⠀⠀⠀⠐⠻⢿⠿⠋⠀⣠⣿⣿⡇⠹⣿⣿⣷⣶⣶⣶⣤⣤⠾⡿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠛⣩⣿⣻⣿⡀⠀⢆⣾⣿⠀⠘⢿⣿⣦⣄⠀⠀⠀⠀⢀⣠⣾⣿⠟⣿⣿⣤⣤⣄⣻⣿⣿⣷⣦⡀⠀⠀⠁⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣼⣿⡿⠟⠛⠛⠛⠿⣿⣾⣿⣏⢇⠀⠀⣙⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡄⠾⠿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣶⣆⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⢀⣀⣠⣄⠀⠀⠙⢿⣿⣦⣾⣶⣤⣬⠹⠙⠻⠿⣿⣿⣿⡿⣿⠿⡀⠀⠀⠉⠙⠛⠛⢷⡈⢻⣿⣿⣿⡗⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣾⣿⣿⣿⣿⣿⣦⣀⠈⠻⢿⣿⣿⡿⢿⠿⢀⡀⠀⠀⠈⠙⣿⠹⣧⠻⡄⠀⢀⠀⠀⠉⠀⠻⢦⣿⡿⠟⠁⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⢿⣿⣿⣿⣿⣿⣿⣯⡀⢠⠒⣨⠥⠶⠦⠄⠀⠈⠓⠦⢤⡀⠘⠷⣽⣷⣽⣦⣄⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⣾⣿⠏⠁⠀⠀⠈⠙⠿⠷⢬⣤⡀⠀⠀⠀⠀⠀⣀⣀⡤⠇⠀⠀⠀⠀⠀⠹⣿⠛⢛⡿⢿⣶⣤⡤⠤⠤⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠁⠉⠀⠀⠀⠀⠀⠀⢀⣼⠏⣠⡿⢃⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣦⣤⣤⣶⣶⣿⡿⠾⢋⣴⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠛⣿⣷⣶⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⢿⠻⣿⡿⠻⡿⢿⡿⡿⢿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣶⣶⣶⣾⣧⣶⣿⣦⣾⣿⣴⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣒⠖⣀⣤⣶⠾⡇⠉⠀⣠⣦⣴⣄⠀⠉⠹⠷⢶⣤⣄⢖⣲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣮⣳⣌⣛⣛⣟⣟⣀⠀⣼⡏⢰⡆⢹⣧⠀⣀⣻⣻⣛⣛⣥⣟⣵⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⠣⣼⣿⣿⣿⣿⣿⣿⣿⠛⠛⠻⣷⣿⣿⣾⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣷⠌⠛⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢧⠀⠀⠄⠛⢿⣟⠛⠠⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⣤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡏⢉⠛⢻⣿⠟⠋⠻⢿⣫⣷⣶⣶⣶⡮⣣⣾⣿⣿⣷⣼⢷⣶⣶⣶⣾⣝⡿⠟⠉⠛⣿⡿⠛⡉⢹⣯
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠘⠀⠘⣿⣀⣰⣾⣯⡄⢠⣠⣿⣿⣿⣿⣿⣿⢱⣿⠃⡰⢆⠙⣿⡎⣿⣿⣿⣿⣿⣷⣆⡄⢀⣼⣷⣤⣀⣾⠃⠀⠃⣤
⠀⠀⠀⠀⠀⣠⠶⣾⣋⣦⣠⣴⣾⠛⠋⠻⠁⣠⣴⣶⣮⣝⠻⣷⣟⡿⠖⠛⠉⣁⣈⠉⠛⠲⢿⣻⡿⠟⣯⣵⣶⣤⣄⠈⠟⠉⠛⣿⣦⣄⣴⣉⣷⠶⣄
⠀⠀⠀⠀⢰⢣⣮⣻⣿⣿⣿⣿⣧⡀⠀⣺⢰⣿⠁⣤⣀⡿⠟⢋⣁⣤⣴⣾⣿⣛⡛⡿⣷⣦⣤⣈⡙⠳⢯⣀⣤⠈⣿⡆⣖⡀⢀⣼⣿⣿⣿⣿⣟⣽⡬⡆
⠀⠀⠀⠀⠘⢣⣦⢹⣿⣿⣿⣿⡿⣳⣿⣿⣎⢿⣄⡼⠋⣴⣾⣿⣿⣿⣿⠃⠀⢽⣧⠀⠘⣿⣿⣿⣿⣷⣤⡙⢦⣤⡿⣱⣿⣿⣞⢿⣿⣿⣿⣿⡏⣴⣄⠃
⠀⠀⠀⠀⢠⡿⣿⢸⣿⣿⣿⣿⢹⣿⣿⣿⢿⣖⡾⢁⣾⣿⢰⣷⣔⠀⣿⣶⣶⣈⣁⣦⣶⣿⠀⣠⣾⡦⣿⣷⡈⢷⣰⡿⣿⣿⣿⡏⣿⣿⣿⣿⡇⣿⢿⡆
⠀⠀⠀⠀⡾⠇⠛⢻⣿⠛⠉⠃⢸⣿⣿⣿⣿⡽⠁⣼⣿⣿⠀⠙⡿⢋⢿⣿⣿⢷⡾⣿⣿⡿⠙⢿⠛⠀⣿⣿⣧⠈⢯⢿⣿⣿⣿⡇⠙⠉⠛⣿⡏⠛⠸⢷
⠀⠀⠀⠀⠁⠀⣀⣤⣿⡀⠀⠄⠾⣯⣵⡶⣼⠁⣸⣿⠿⠋⢻⣿⣿⣷⣻⣮⠿⣛⣛⠻⣷⣟⣾⣿⣿⡟⠙⠿⣿⣇⠈⣯⣶⣾⣽⠷⠠⠂⢀⣿⣤⣀
⠀⠀⠀⠀⢠⣾⢋⣉⣽⣿⣿⣦⣾⣿⢉⡠⠇⢰⣿⢃⣀⣤⡔⠻⢿⣟⣿⢣⣾⢛⡟⣷⡌⣿⣻⡿⠟⣲⣠⣀⡜⣿⡄⢸⢄⡙⣿⣷⣄⣻⣿⣯⣉⠙⣷⡄
⠀⠀⠀⠀⠐⢿⣄⣉⣻⣿⣿⠕⢿⣿⣌⠑⡆⠘⣿⡜⠉⠛⠫⣴⣾⣯⣿⡘⢿⣽⣥⣿⢣⣿⣽⣷⣧⠍⠙⠙⢥⣿⠃⢰⠊⣁⣾⡿⠃⣿⣿⣟⣉⣡⡿⠃
⠀⠀⠀⠀⡀⠠⠉⠛⣿⠁⠀⠀⢶⣟⡻⠿⢻⡀⢹⣿⣶⣄⣼⣿⣿⡿⣵⢟⣦⣭⣭⣴⡻⣮⢿⣿⣿⣧⣤⣶⣿⡏⢀⡟⠿⢟⣫⡶⠀⠀⠈⣿⡛⠉⠄⢠
⠀⠀⠀⠀⢷⡆⣤⣼⣿⣤⣀⣤⢸⣿⣿⣿⣿⣳⡀⢻⣿⣿⠀⣠⣵⣌⣾⣿⣿⣾⢿⣿⣿⣷⣠⣾⣄⠀⣿⣿⡟⢀⣾⣾⣿⣿⣿⡇⢠⣀⣤⣿⣧⣤⢰⡾
⠀⠀⠀⠀⠸⣷⣿⢹⣿⣿⣿⣿⣸⣿⣿⣿⣾⠯⢷⡈⢿⣿⠺⡿⠻⠀⣿⠿⠻⣩⡉⠟⠿⣿⠀⠙⢿⠗⣿⡿⢁⣞⠹⣿⣿⣿⣿⣇⣿⣿⣿⣿⡟⣿⣾⠇
⠀⠀⠀⠀⢠⣝⠟⣼⣿⣿⣿⣿⣷⡽⣿⣿⣏⣾⠃⠳⣄⠻⢿⣿⣿⣿⣷⡄⠀⢺⣗⠀⢠⣾⣿⣿⣿⡿⠟⣠⠞⠛⣿⡹⣿⣿⢿⣾⣿⣿⣿⣿⣇⠻⢋⡄
⠀⠀⠀⠀⠸⡞⢟⣽⣿⣿⣿⣿⣟⠁⠈⠽⠘⣿⡀⠛⠉⣳⢦⣌⡉⠛⠻⢿⣶⣭⣥⣷⡿⠿⠛⢉⣡⢴⣚⠁⠛⢀⣿⠇⠯⠀⠈⢻⣿⣿⣿⣿⣯⣻⢳⠇
⠀⠀⠀⠀⠀⠙⠦⢿⡍⠟⠙⠻⣿⣤⣀⣴⡀⠙⠻⠿⢟⣫⣴⡾⣯⣷⡦⣤⣀⣉⢉⣀⣠⠴⣺⣽⣷⣧⣝⡻⠿⠛⠋⢀⣦⣀⣤⣿⠟⠋⠻⢉⡿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⡟⢀⠠⢠⣿⠩⠙⣿⡟⠁⠘⠙⣿⣿⣿⣿⣿⣿⡸⣿⣄⠱⠎⢠⣿⢇⣿⣿⣿⣿⣿⣿⠏⠃⠈⢻⡿⠏⠉⢿⡄⠄⠄⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣈⣤⣼⣿⣤⣀⣴⣾⣝⡿⠿⠿⠿⢗⡝⢿⣿⣾⡿⢫⡺⠿⠿⠿⢿⣻⣷⣦⣀⣤⣿⣧⣄⣁⣸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠋⠛⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⣤⣽⣭⣤⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⡟⠁⠀⠉⠛⠙⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⡔⢻⣿⣿⣿⣿⣿⣿⣿⣤⣤⣴⣿⣿⣿⢿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⢂⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡿⢟⣽⢋⣭⣭⣭⣯⠉⠀⢻⣇⠘⠆⣸⡟⠀⠉⣿⣭⣭⣭⡙⣯⡻⢛⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠯⠤⠝⠻⠷⢶⣇⡀⠀⠙⡿⠻⠋⠀⢀⣰⡶⠾⠟⠋⠶⠭⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠐⠐⠂⠹⢿⣿⣃⣤⣀⣀⣀⣠⡀⢀⠀⠀⣀⣀⢀⣀⣀⢀⣀⣠
⣶⣶⣾⣿⣿⣷⣵⣶⣤⣦⣷⣾⣶⣦⣶⣾⣷⣦⣴⣶⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣛⣿⣟⣯⣽⣿⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⣀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣩⠖⠪⠥⠶⠶⣿⣿⣭⣉⠛⠛⠶⣤⡙⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡾⠡⡠⠊⢀⡶⠞⠛⣛⣛⣿⣿⣦⣌⣲⣿⣾⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣼⡇⠁⣵⠗⡁⢄⣐⣤⣼⠞⠛⠛⣿⣿⣿⣿⣿⣿⣧⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡡⣻⢃⣷⠀⣿⡮⠚⠋⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⡫⠋⢯⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣫⣞⣥⣿⣿⠄⠷⠶⠄⠀⢀⣤⣤⣀⡀⠀⠹⣿⣿⡪⡛⠮⠲⣄⠑⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢫⠗⣫⣿⣿⡾⠳⢦⠄⠀⠀⠀⢀⣄⡉⠢⠀⠹⣿⡻⣦⠈⢲⣄⠱⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢹⢸⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⡿⣿⡪⠳⣅⠱⢕⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢣⢣⢹⢹⡇⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣿⡗⡕⢬⣙⣒⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⢈⢘⢸⡇⢀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⢈⠘⢇⣿⣦⣍⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠈⠀⠌⣼⡇⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⡌⡎⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⣴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣙⡪⢿⣿⣷⣤⣤⣤⡄⠤⠄⠐⠀⠀⠀⠀⠀⡏⡀⣦⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⡿⢻⣿⣿⣿⡿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢧⡱⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡱⢋⡀⣸⠺⠟⣿⡇⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣌⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠿⠚⠁⠀⣨⢾⡷⢹⡿⣿⢻⡀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠉⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⡥⢂⣤⠂⢈⡴⢋⡆⢰⢇⡿⢸⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡇⠏⢟⠀⢸⢡⠟⡠⢣⢎⢆⣿⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣜⢿⣦⣬⡇⠸⠋⡔⡱⢣⣮⡾⣻⡇⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡽⣿⡇⢠⢰⢁⢡⡟⡫⢚⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡽⠳⣿⠸⠸⠸⠘⢡⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⣷⣰⡄⢢⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠫⠾⢟⠧⠞⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣧⣀⠀⢉⣣⢳⣜⡓⠚⣧⠆⠍⣳⠽⢿⣽⣿⣯⣿⣿⣎⣻⣯⢭⡝⠁⠀⢹⠋⢰⠀⠹⡇⠈⠻⠈⠛⢿⣵⣆⡼⠃⠈⡾⠃⠀⣛
⣿⣿⣿⣿⣿⣿⣤⣄⣛⠃⠀⠘⠲⡄⠘⡷⣼⠟⠾⠷⣿⣿⢿⣻⣭⣟⣧⡖⠙⢐⡗⡀⠐⠠⡄⠀⠀⠀⠀⠀⣿⠃⠀⠰⠄⡑⣀⡤⠻
⣿⣿⣿⣿⣿⣍⣻⣷⡄⣿⣆⣤⡄⠀⠌⠀⣴⣼⡛⠻⢿⠟⠾⢳⢯⣎⠐⠁⣰⠼⣿⣿⣿⡇⠀⢠⡄⠀⠀⣄⠘⠀⠠⠂⠀⢻⣁⣠⣷
⣿⣿⣥⣄⣤⡟⢹⣿⣡⣯⡴⠁⣀⠄⠀⣀⡻⠄⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⣂⢀⡟⡜⠘⠁⠖⠐⠃⠄⠀⡁⠁⠀⠐⢺⡟⠉⠈
⣿⣿⣿⣿⣿⣷⣿⣟⣭⣥⣾⡿⣛⢢⡬⠽⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠃⠀⠀⠀⠀⠛⠂⣶⣀⢀⠁⣿⠂⠐⠀⠘⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢲⠛⠈⠀⠀⠀⠉⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⡦⢽⣔⡏⠀⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣾⣰⣶⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢺⢻⣥⡿⡽⡽⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣴⡆⠀⠀⠀⠀⢚⠉⠉⠀⠀⠀⢀⠀⠈⠃⢀⠤⠚⠋⢸⡅⠊⢱⠛⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⢠⡀⠈⠃⠀⠀⡈⠥⠖⡿⠀⠀⠁⠀⠀⠀⠛⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠾⢛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠗⠙⢤⠀⠀⠀⡀⠀⠀⠀⠀⠘⢉⣱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡾⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠁⠛⠀⣀⠀⢤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣾⡅⠀⠀⠀⠀⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡆⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⡨⣾⣯⣀⣣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⢁⣹⠋⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣶⣄⠀⠀⠁⠀⠀⠀⢀⢘⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠳⠀⢱⡶⣂⣂⠀⠀⢺⠹⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⢡⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠺⠟⣒⢰⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢁⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡜⢁⡦⣤⠀⠘⠇⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢂⣈⣉⣁⣧⣿⢙⢾⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢥⣠⣭⢿⠛⣚⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡄⠀⠀⠀⠀⠀⠀⠠⢾⠈⠹⠧⣽⡟⠉⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠠⢞⡒⠂⠈⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡞⠁⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣷⢩⣠⠀⠀⠀⠀⢿⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠁⠁⡀⢀⣀⠀⢡⡀⠀⠨⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⠏⠀⣠⣶⣾⣿⣿⣿⡿⣷⡀⠀⠀⠆⠀⠁⠀⢀⡄⠀⠀⠀⠀⠁⠈⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠻⡶⠾⠄⠀⠘⠂⢼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠀⠀⠀⢀⣴⡶
⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⢦⣐⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⢗⠀⢀⡀⠀⠈⠋⠁⠠⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠰⠾⠿⢿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⢀⡘⠛⠛⠀⠀⠈⠉⠙⠉⠛⠀⠀⣤
⠀⠀⠀⠀⠂⠀⠀⠀⣠⠀⡄⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣶⣿⣿⣿⣿⣿⣇⠀⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠂⠉⠁⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡉
⠀⠀⠈⠉⠓⢀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⡀⠤⠀⠕⢀⣀
⠀⠀⠀⠀⠀⠉⠦⣵⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠙⠆⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠈⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢩⣍⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠍⡙⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⡿⠦⠈⢈⡡⡄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⡿⢉⣿⣿⣿⡿⣿⣿⣿⢹⣿⣿⣿⣿⠀⢁⠼⠟⠚⢇⠀⠀⠈⢁⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⢿⡟⣼⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠔⠈⠀⠀⠛⠆⠫⣵⣦⣌⡁⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠁⣄⠙⢿⣯⠀⠀⢠⣼⣦⣀⣄⣤⣶⣾⣿
⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠛⢃⡘⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣤⣀⢀⣠⣄⣀⠀⠀⠀⠸⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡴⢄⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣥⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠰⠋⠀⠉⠀⠀⠐⠛⠓⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠐⣾⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣦⠀⠁⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣽⣿⣿⣿⣖⠀⠀⠀⠀⠀⢸⡎⣽⠀⠀⠀⠀⢀⠋⣸⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣤⣼⣿⣻⣿⣿⣦⣄⠀⠀⠀⠈⠛⠟⠀⠀⢀⣴⣿⣶⡿⠟⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣬⣍⠉⠛⠛⠛⢿⣿⣷⣤⡀⣀⠀⠀⠀⠀⠼⣿⣿⣿⣿⢿⣥⡀
⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⣿⣿⠤⠶⠶⡖⠺⣍⠙⠿⠭
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣠⣤⢤⠀⠀⠀⠂⠀⢀⣿⡿⠿⠀⠀⠀⠈⠀⠈⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⢠⣿⣯⣼⠇⠀⠀⠀⢠⡾⠛⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠹⠀⢀⠀⣀⠀⠀⠈⠉⠀⣀⣤⠄⠀⣿⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣦⣴⣿⣿⣷⣶⣶⡋⠀⠀⠀⠀⣢⣿⣿⣶⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠻⠟⡿⠉⠙⣿⠟⠿⠟⢻⠋⠀⠀⠀⠀⠘⠻⠟⠁⠀⢸⣿⣧⢀⡤⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⣤⣤⡄⠀⣤⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣸⠸⣿⡏⣠⡞
⠀⠀⠀⠀⣀⡶⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⡆⢈⢁⣀⣀⡀⠲⢤⣤⣿⢁⡶⠁⣸⣿⣿⠏
⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⣠⡼⠋⠉⠀⠀⠀⠈⠙⠘⠃⢰⣿⣿⣇
⠀⠀⡀⠀⠀⠀⠀⠀⠄⠠⢷⡿⢿⡷⠄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣶⠟⠁
⠀⠀⠸⠆⠀⠀⠄⠀⠀⠀⣙⣛⣭⣁⠀⠀⠀⣴⡚⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠋⠉⢩⠄
⠀⠀⠀⠰⢶⣄⠀⢠⣶⠿⢿⣿⣿⡍⠀⢰⡿⢹⠇⠀⠀⠀⠀⢀⠍⣌⡿⡄⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠉⠣⢀⣠⣴⣿⣿⣿⣿⣦⡯⠀⢸⡦⠀⠀⠀⠀⠈⠿⠿⡑⠃⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠤⠶⢟⣿⡿⠿⢹⠿⡎⢙⣁⣀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠠⠶⠛⠉⠀⠀⠀⡇⢿⡈⠉⠽⢃⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣧⠀⠀⠀⠻⠦⣤⣄⡀⠀⠀⠀⢀⡴⠀⣰⡟⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠰⣾⣿⠟⠱⠿⠞⢋⣵⣤⡀⠉⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣶⡿⠛⠁⠀⠀⠀⠀⠘⣿⠋⠃⠀⠀⠀⢸⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⢧⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠛⠛⠿⠿⣿⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠨⣭⡻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣪⣴⣶⣿⣿⣿⣿⣶⣶⣦⣄⢺⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣶⣆⠀⠐⣤⡴⠇
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣯⣟⣡⣿⡿⠟⠋⣀⣽⣿⣿⣿⣿⣿⣿⣦⠀⠻⣿⡶⠋
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇⢰⣀⣲⡄⠀⢀⡀⡀
⠀⠀⠀⢠⣾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠀⣈⠁⢡⣾⠟⠛⠻⢿⣿⣿⣿⣦⡙⢻⣧⢠⣟⣧⣿⠂
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣛⣯⡅⢸⣿⢀⠀⠀⠀⠙⢿⣿⣿⡇⠀⠉⠛⢋⣷⡎⠛⢣
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⣶⣾⣿⣧⢢⡀⠀⠀⡀⠹⣿⣿⣶⣶⣶⣿⣿⣿⣤⣄⣀
⠀⠀⠀⠀⢈⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⠟⢳⡱⡀⠀⣹⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⢰⡏⣀⡵⣰⣿⣻⣿⣿⣿⣿⣿⣿⣿⣟⡽⠋⢁⣴⡿⠟⠛⠿⠿⠀⠠⢿⣿⡀⠰⣿⣦⡈⠻⢿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠓⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣴⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⡠⣿⣿⣿⣤⣀⣹⣿⣷⣿⣿⣯⣭⣭⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⢿⣃⣈⣿⣿⣿⣯⣿⣿⣿⣿⡿⣉⡉⢉⣻⣿⣷⣤⣤⣶⣶⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠈⠁⠙⠛⠛⠛⠿⠿⠋⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⠛⣛⣫⣿⠿⠛⠻⠿⠿⣿⣿⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣀⠀⠀⠄⠀⠀⠠⠄⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠀⠀⠀⣠⣁⠀⠀⢀⣀⠀⠴⠐⢍⡲⠃⠀⢀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠋⠃⠠⠂⣈⣀⡀⠰⠶⡎⠄⠀⠀⠄⠀⠸⠒⠢⡈⠁⠁⠄⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠙⣂⠠⣤⡴⠀⠈⠀⠀⡎⠀⠀⠴⠀⣂⠀⠄⠀⠀⠥⠰⠂⠔⠘⢟⣔⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠈⠀⠁⢂⠏⠀⢀⠄⠃⠀⡇⠀⣐⢄⠾⢠⠆⢸⠀⠀⢈⠂⠀⢄⡒⠉⠂⠔⢀⠘
⠀⠀⠀⠀⣀⠀⣢⠀⠀⠠⠈⠀⡠⠀⠂⣧⠀⠀⠀⠀⠀⠦⠘⠈⠀⠀⠈⠀⠀⠀⣀⠊⠉⠐⠀⣤⠀⠀⠈⠔⠀⣁⡈⠳
⠀⠀⠀⠀⠈⠀⠀⠡⢀⡈⡗⠀⢠⣷⣤⠋⠀⢀⠀⠀⣒⡆⠡⠦⣀⠀⡠⢄⠉⠻⠋⠀⠀⠠⠠⣤⡷⠀⠄⠀⠂
⠀⠀⡀⠒⠀⢁⠀⠁⠈⠑⠳⠀⠑⠀⢀⠠⠐⠀⠗⣋⠀⠃⠀⠀⠈⢅⠀⢈⣱⡠⠀⢷⡂⡄⠀⠋⠀⠐⢀⡼⠁⠛⠉
⠀⠀⠀⠰⠀⢆⢡⢀⠀⠁⠀⠖⣂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠀⠀⠀⠂⠈⠁⠀⠀⠁⡀⢀
⠀⠀⠀⠛⠃⠀⠋⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣾⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡛⡟⢿⢟⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡟⠿⢻⢛⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣾⣶⣯⣤⠾⠇⠀⠀⠀⠀⠀⠀⠰⠷⣦⣤⣶⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀




⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣤⣿⠓
⠀⠀⠀⠀⠀⠀⢀⣀⡴⢛⡓⠈⠙⢷⡀⢠⣤⢄⣀⣤⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⣠⣠⣤⣶⣿⣿⣿⣿⠏⠀⠀⠀⠁⠀⠙⠶⡉⠉⠙⢦⢤⣾⠿⠷⢤⣄⡠⠛⠻⠆⡀
⠀⠀⠈⠉⣃⣙⠃⣴⣿⡿⠂⠀⠀⣠⣶⣾⣧⢦⣀⠀⠀⠶⢤⡄⠠⠔⠛⣿⠁⠀⠀⢀⠉⠒⠛⠘⠢
⠀⠀⠀⠀⠉⠉⠃⠈⠉⠦⣤⣴⣾⣿⡿⠿⢿⣤⣤⡀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⢀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠉⠁⠀⠘⡽⠿⠻⠀⠀⠀⠀⢴⣿⣏⠀⠀⠀⣸⣿⡇⢀⡀⡆
⠀⠀⣿⣷⣦⣤⣀⠀⠀⠀⠀⣠⠀⠀⠁⠄⠊⣀⣶⣦⣶⣄⠀⠀⠀⠈⠿⢶⠂⢀⣿⣿⣿⡃
⠀⠀⠈⠁⠀⣿⣿⣷⣿⣴⣆⣿⣇⣴⡄⠀⠀⢘⠛⠿⣍⡁⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣯
⠀⠀⠰⢴⣷⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢀⣿⣶⡆⠀⠉⠂⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣷⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⠛⠛⠿⠻⠿⠿⠛⠿⠿⢿⣄⣼⡆⠀⠀⣠⣠⣿⠿⠿⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠘⡆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠓⠲⠤⣄⡀⠀⠀⡰⠋⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠞⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⣤⠴⠖⠋⠉⢸⠇
⠀⠀⠀⠀⠀⠀⣀⣤⣠⡀⠀⢀⡏⢠⣿⣏⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣠⡴⠖⠋⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢠⡾⠋⠈⠁⠳⣄⡜⠀⠈⠿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⣷⡄⠀⠀⠀⢀⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⡇⠀⢹⠀⠀⠀⢱⣦⠴⠒⠒⠦⣄⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠹⣤⠞⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⢹⡏⠀⠀⢀⡴⠒⠲⢤⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⡞⠀⠀⠀⣿⠀⠀⠀⢈⡇⢸⠁⠀⠀⠀⠀⢀⣀⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠈⠳⣄⠀⠀⠘⣆⠀⠀⣠⠎⠀⠀⠀⠀⠈⠳⠤⠴⠚⣰⠃⠀⢀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⠳⢄⡀⠈⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣧⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠚⠉⠀⣠⢏⠳⣄⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠙⢻⠒⠋⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡧⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⢧⣀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢠⠆⠙⠲⣟⣦
⠀⠀⠀⣾⣷⣤⠞⠉⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⡴⠓⠚⠉⠉⠻⣄⢀⣴⡄
⠀⠀⠀⢹⠻⠜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣸⢫⣿⠇
⠀⠀⠀⠘⣇⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣼⠁
⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠹⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠘⠲⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠳⠴⠋

⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠐⠀⠀⠘⠃⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡾⢿⣿⣿⣿⣿⣏⠢⠈⠑
⣿⣿⣯⠀⠁⢢⠙⠿⣿⣟⢿⢿⣿⣿⡆⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡶⠛⠋⡉⣿⠃⠀⢀⣰⣶
⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⠷⠘⠻⣿⣿⣤⣀⠀⠀⠀⠀⠁⠙⢿⣿⣿⣶⣦⡀⠀⠀⠀⠀⢹⠏⣀⡴⠃⠌⠀⢠⣞⠁⣿
⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⣷⣤⡀⠀⠈⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⣈⠁⠀⠁
⣿⣿⣿⣿⣇⢠⡶⠛⠀⠉⠁⠀⠀⠀⠀⠀⠘⠋⠛⠛⠿⣿⡀⠀⠀⠀⠀⠈⠉⢳⡀⠀⠀⠀⢰⣿⣟⠀⡀⠀⠉
⣿⣿⣿⣿⣿⣯⣿⠟⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⣿⣏⢙⡿⠁
⣿⣿⣿⣿⣿⣿⣟⡛⠶⣤⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠻⡄⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⠟⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣶⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠘⢦⣳⠀⠀⠀⠀⠀⠐⠀⠀⣿⠃
⢸⣿⣿⣿⣿⣿⣿⠟⣿⣿⡆⠙⣿⣿⠷⣤⣀⡀⠀⠀⠀⡀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠈⢿⣿⣿⡿⣿⣿⣼⣿⣿⣿⠀⠈⢿⢷⡄⠀⠀⠀⠂⠀⠘⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⣿⣷
⠀⠀⠉⠋⢻⡆⠀⠀⢸⡟⢿⣷⣦⣀⠣⠉⠂⠤⡤⣀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣼⣿⠋⠁
⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⣿⣿⣿⣦⠑⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⢮⣾⠟⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠈⣿⣿⣿⣿⣶⠶⣦⡀⠀⠀⠀⠀⠀⡇⠀⣰⣿⣿⣿⣿⡿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⢿⣿⣷⠘⣧⠀⠀⠀⠀⢀⢁⣼⣿⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⡿⣿⡇⣸⣿⢟⡴⠃⠀⠀⠀⠀⣼⣾⣿⣿⡟⠉
⠀⠀⠀⠀⠀⢠⣷⣴⣿⣿⣿⣿⣿⣿⣾⣿⠿⠛⠉⠁⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠟
⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠋⠻⠁⡾⠋⠀⠀⠀⠀⠀⣠⣤⣴⣿⡿⠋
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠢⠀⠀⠀⠀⠀⠀⣤⣤⠶⠋⠈⠉⠁
⠀⠀⠀⠀⠀⠈⢿⣿⠿⠟⠿⠂⠀⠀⠀⠂⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠻⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣄⣀⡀⠀⠀⢸⣿⡟⠁⣼⠇⠀⡀⣇⠀⠀⠀⢿⣿⣏⣉⡹⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠸⣶
⠛⢿⣷⣤⣀⣼⡏⠀⠀⠀⠰⠇⠀⠙⣧⡄⠀⠀⠸⡏⠉⠃⠀⠀⣸⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣴⠾⣿
⠀⠈⠉⠙⣿⣿⣆⠀⠀⠀⢀⡄⠈⣶⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣰⡿
⠀⠀⠀⠀⢹⣿⣿⣷⣤⣤⣤⣿⣴⣿⣿⣿⣇⠀⢠⡟⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⡍⣿⡿⠃
⠀⠀⠀⣴⣾⣿⡟⣿⣿⣿⣦⣿⣞⠛⠛⢻⣿⣿⣿⠇⠀⠀⠀⣸⣿⢻⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢿⡟⠀⠀⠀⢀⡜⠃⠈⠁⠠
⠀⠀⠈⠻⣿⠿⢷⣿⣿⣿⠿⠿⠹⣷⣤⣸⣿⣿⣿⠀⠀⠀⠀⣿⣿⡾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⢀⠞⠀⠀⣤⡾⠛⠈⠛⠄
⠀⠀⠀⠀⠀⣄⡘⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⢀⡠⢐⣠⣶⣶⣿⣥⠀⢠⠎⠀⢀⣼⠗⣠⣦⣀⣤⠀⡀
⠀⠀⠀⠀⠀⢻⣿⣻⡛⠛⠻⣦⣠⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣾⡀⠀⣤⣖⣿⣿⣿⣿⣿⣿⣿⠋⡰⠁⢀⣴⣿⣿⣶⣿⡿⠛⢿⣀⣤⡄
⠀⠀⠀⢀⠀⠀⠙⢿⢷⣤⠀⠘⢻⡟⣿⣿⣿⣿⣿⡷⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⢁⠀⠀⠀⣼⣿⣿⠟⠛⠛⢁⣤⣿⣿⡏
⠀⠀⠀⠘⣧⣀⡀⠀⠁⠜⠻⢆⣠⡄⢉⣷⡞⠛⠁⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⡴⠁⠀⠀⠀⠁⠈⠏⠀⠀⠀⢸⣿⣿⡿⠄
⠀⠀⠀⠀⠀⠉⢿⣦⡄⠀⠀⠈⠙⢇⠀⠙⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠁⠀⠀⠈⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠟⠉⠘⠃
⠀⠀⠀⠀⠀⠀⠈⠓⠿⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠴⣦⠸⣿⡿⠋⠀⣀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢦⣿⡇⠋⠀⢠⡏⠙⣿⣷⠀⠀⠐⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣰⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣉⠀⣀⡀⠈⠻⣿⣿⡿⢀⣤⡅⡈⠁⣠⡏⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣀⣠⣤⣄⡀⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⢻⡿⢿⣦⣤⡶⢦⡁⠀⠀⢀⣡⣴⣅
⠀⠈⠁⠀⣈⣙⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⠈⠉⠛⡁⠝⢻⣿⣿⡶⠤⢤⠙⠋⠉
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢀⡀⠀⠀⢹⡿⠿⠖⠊
⠀⢸⣿⣿⣿⣿⣿⣿⣿⢟⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢤⡗⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⢿⣿⣿⣿⣿⣿⠃⠁⠀⠀⢀⣴⣯⣬⣽⡝⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠜⠁
⠀⠀⢀⣽⣿⣿⣿⣟⢂⣠⡄⣴⣿⣿⠀⠀⠿⠻⣷⣤⣶⣶⣄⠀⣀⠀⢶⣬⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢰⣿⣿⣿⣿⣿⣿⣶⡿⣧⣿⣧⣈⠀⢠⠀⠁⠙⠿⠿⠛⠙⠛⠃⠀⠀⠙⣆⠀⠀⠰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠂
⠀⠈⠻⢿⣿⣿⣿⣿⣿⡗⠀⢿⣿⣷⣷⣦⣤⣶⠿⠏⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⠀⣠⠏⠀⠀⠀⢀⡀⠀⠀⢠⣾⣶⡜⢧⡀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⣄⣨⣿⡿⢿⠉⠁⠀⠀⢨⡅⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡟⠀⠀⠀⠀⢺⡧⠒⣰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣼⣷⣄⠀⠘⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠠⢤⣘⠃⢀⠰⣿⡁⠈⠹⣿⣿⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡏⢻⣿⣷⡀⠈⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣿⣿⣷⣼⣿⠛⠛
⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠃⠐⢡⣷⣿⣿⣷⡀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣿⣿⣿⣿⣿⣷⡀
⢦⣄⠀⣠⣶⣿⣿⣿⣿⣿⣦⣄⣬⠿⠟⡿⠿⠋⠀⠀⠀⠀⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢄⠈⢿⣿⡿⢻⣿⣿⣦⡀
⠈⢻⡙⣿⡿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣪⡤⣤⣶⣦⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⠘⠏⣼⣿⣷⣾⣿⠋⢿⣯⢲⣄⡀
⠀⠀⠹⣎⠻⢿⣿⣿⣿⣿⠟⠁⢠⣿⣿⣴⣿⣿⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⡀⢀⣄⣿⠿⣿⣿⣿⢴⠿⠉⠛⠿⠁⠤⠦
⡀⠀⠀⠙⢧⠠⠈⠉⠛⠙⠶⣤⣾⣿⣿⣿⣿⡿⠟⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⣬⣯⣼⡄⢻⣿⣿⡶⠂⠀⠀⢀⣀⣤⠤
⡉⠛⠲⠶⣬⣷⣄⠀⠀⠁⡁⣛⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⣉⣩⡤⠶⠒⠋⡉⢁⢀⠐
⠀⠀⠠⠀⠄⠈⠱⠀⠀⠀⠀⠠⠀⢹⣿⡿⡿⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠄⠀⠰
⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⣣⠚⠃⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⣿⣿⣿⣿⠀⠘⣿⣿⣿⣷⠀⠀⠀⠀⠀⡁⠀⢈
⠂⠀⠀⠂⠂⠐⠀⠀⠀⠂⠀⠐⢀⣾⣿⣷⣿⣿⣿⡆⣀⠼⠁⠈⡓⠦⡤⠴⠖⠛⡉⠈⢀⣾⣿⣿⣿⠗⠀⡇⢹⣿⣿⣿⡇⠀⠀⠀⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⠀⠀⠑⡀⠀⠀⠀⠀⡠⠀⠀⠀⡆⠀⠀⠀⣀⠁⠀⠀⠀⠀⡠⠞⠋⠉⣿⣿⡄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⢀⠀⠀⠀⢸⡇⢿⠀⠀⠀⠘⠀⠀⠀⠀⠠⠶⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⢠⠎⠀⠀⠀⢠⡟⣹⠁⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⡞⣨⡟⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠘⢆⠀⠀⡜⠛⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢿⡿⠁⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠣⡀⠙⠦⣀⡀⠀⠀⢀⣴⠋⢣⠀⠀⠀⠀⠀⠀⠀⢠⠞⢲⡄⠀⠀⠀⠀⠀⢀⡤⡃⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣄⡉⠀⠀⣾⣿⣤⣾⠀⠀⠀⠀⠀⠀⠀⣾⣄⣸⣿⡀⠀⠀⠐⠚⠉⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢀⡀⠠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠘⣄⠀⠀⠀⠀⠀⠀⠠⠶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢠⠊⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠠⠚⠁⠀⠀⠀⢀⡤⠔⠒⠛⠉⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢱⣶⣶⣶⣶⣾⣿⣶⣿⣿⣾⣶⣶⣶⣶⣿⣿⣿⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣶⣖⢻⣿⡇⣿⠄⡟⠟⣟⣿⢹⣿⠉⢸⠙⠻⡿⢻⣛⢛⣟⢻⠻⣟⠛⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣿⣦⣧⣶⣽⣿⣾⣿⣾⣼⣶⣿⣶⣮⣿⣼⣿⣾⣧⣽⣦⣿⣿⣿⣿

⣿⣿⣿⣿⡿⠟⠛⠉⠛⠛⠛⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿
⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⣤⣀⣀⡀⠠⠾⣿⣿⣿⣿⣿⣿⣿
⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⠀⡀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠋⠙⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⣶⣭⣴⣾⣷⣿⣷⣄⡀⠀⠀⠀⠀⢳⠀⠀⣹⠄⣤⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣢⣤⣤⣴⣾⣿⠋
⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⠂⣀⠀⠀⣴⣾⡇⠀⡿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣡⣶⣶⣶⣦⣤⡄
⣿⣿⣿⡿⣿⣿⣤⣤⣿⣿⣿⣾⣷⣄⠈⠋⠄⠀⠀⣠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣷⠹⣯⣛⠻⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠁⢀⣈⣽⣿⣿⣿⣿⣿⡄
⣿⡟⢩⣷⣶⣶⣬⠁⠀⠈⠃⠙⠟⠁⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣴⣶⣾⠿⠁⣾⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠀⠀⠙⠉⠐⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢠⣾⣿⡿⠋⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣄⠠⡄⢠⡄⢠⠰⢀⠀⠀⠀⠀⢀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠉⠉⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉
⣿⣿⣿⣤⠄⠲⢤⡍⠁⠀⢀⡀⠐⠁⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣶⣿⣿⣿⣇⠀⠠⣿⣿⣶⣤⣄⣈⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠂⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡅
⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⠾⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣶⣦⣀⣀⣀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠦⠤⠍⠉⠉⠙⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠊⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠣⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠶⠶⠖⢒⡲⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠑⠠⢄⠠⢄⠀⠀⠀⠀⠀⠘⢮⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠤⡀⠀⠀⠈⢿⡙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠚⢉⡠⠄⠂⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠶⡬⠛⠀⠀⠀⠀⠀⠀⠙⣦⠈⣑⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⢠⡧⠚⠉⠀⠀⠀⠀⢀⠀⠀⠀⠈⠑⠢⠄⠀⠀⠀⠠⠖⠋⠀⠀⠀⠀⢈⡀⠐⠐⡄⠀⠀⠀⠁⢀⠈⠳⡀⠙⢦⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⣰⠋⢀⢠⣴⠖⠋⠀⠀⠚⠤⣴⠶⠶⠢⠄⠀⠀⠀⠀⠀⡠⠶⠶⠶⣦⠄⢶⡀⠀⠈⠀⠀⠀⣀⠤⠾⠖⠄⢙⣦⣀⠈⢦
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢠⠣⠂⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⢤⡔⠰⠃⠀⠀⠀⠀⠈⠻⡎⠢⡀⢇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡞⠀⢀⢾⠃⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⡀⠀⠠⠀⠀⠀⢘⡀⠰⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡡⠐⠁⠈⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠐⠀⠈⡆⠀⠀⠈⠀⠁⡿
⠀⠀⠀⠀⠀⠠⠐⠀⠀⠁⢀⠀⠐⠁⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠃⠉⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠊⠁⠀⠀⠀⠀⠒⠒⠒⠋⠀⠀⠀⠀⡠⠋⠀⠀⠀⠰⡀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⣤⣙⠒⠒⢦⠀⠈⠀⠈⠣⠀⠀⠀⠀⠀⠈
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⡰⠛⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠋⠐⠃⠀⠺⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠘⢦⣤⠄⠥⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠉⡄⠀⠤⠤⠤⠄⠈⡞⠀⠀⠀⠈⠣⠈⠃⠀⠀⠀⠀⠀⠀⡞⢶⠐⠒⠺⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡞⠁⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠠⣀⠀⠦⠄⡄⠀⣠⠂⠐⠟⢆⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢄⡒⠤⠈⣀⠀⠀⠒⣚⠉⢁⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⢀⣲⡀⠀⠀⠀⠀⠈⠶⠀⠤⠦⢀⣜⡴⢀⠴⣾⠓⠂⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡒⠂⠤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠢⢤⡤⠠⢴⣀⡠⠄⠀⠀⢹⠔⠉⢀⣿⡄⠀⡜⠀⠙
⠀⠀⠀⡴⠈⠁⣉⡁⠀⠈⠀⠀⠀⠄⢤⡤⠖⠊⠀⢀⣠⠶⠋⠀⠀⢀⠊⡴⠓⡀⠈⠒⠇⠀⠀⠀⠀⡆⠀⠀⡿⠁⠀⢻⠆⡀⠀⠀⠞⢸⠃⡘
⠀⠀⠀⠁⠀⠀⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠀⢠⣤⠀⢀⡵⠚⢁⡄⠉⠀⠀⠘⠐⠂⠢⠞⠃⠄⠠⠄⠀⠀⠀⠓⣌⠖⠁⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣀⡀⠐⠗⠀⠀⣀⠜⠁⡔⢉⣀⢊⠉⠁⠀⠀⠑⠄⣀⡄⠊⠀⠀⠀⠂⠀⠀⢀⠼⠂⠀⢁⣴⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢤⡤⠬⠿⠗⠒⠈⠀⠀⢼⠴⠋⠠⠐⣆⠀⠀⠀⠒⠂⠠⠴⠆⠀⠀⠀⠐⠀⠔⠎⣀⣠⠴⠋⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠤⠅⠅⠤⠐⠃⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠒⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣹⣛⣉⣙⣛⣟⣹⡿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠛⠒⠒⠒⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⣰⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⢰⡸⣧
⠀⠀⠀⠀⠀⠀⠀⡜⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣿⣿⣦⠀⠀⠀⣿⡇⢹⡆
⠀⠀⠀⠀⠀⠀⢠⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣠⣿⣿⣿⣇⠀⠀⣟⣓⡏⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣻⡍⢇⢻⡟⢢⡀
⠀⠀⠀⠀⠀⠀⢠⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠷⠃⣠⡜⢩⢳⣃⣿⠇⢸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠻⣯⡵⢾⡏⠀⢸⣿⣿⣿⣷⣄
⠀⠀⢠⡶⠶⠶⠶⠾⠿⣟⡲⢤⣀⣀⣈⣠⣤⣤⣤⣤⠤⠤⠤⠶⢢⠞⠁⡰⠦⢄⠀⠘⠷⣄⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⣷⢰⡞⠃⠀⠀⠈⠙⠲⣬⣭⣉⣀⡀⠀⠀⠀⠀⣀⣠⣤⣿⣦⠀⠻⠷⠏⠀⠀⠀⠘⢧⡈⢻⣿⣿⣿⣿⣷⡀
⠀⠀⠺⣁⠘⠋⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠛⡛⠛⢛⣛⠛⠋⠉⠅⠹⣆⠀⠀⣀⠀⠀⠀⠀⠈⢷⠀⠹⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⡀⠀⠀⠬⠀⠒⠀⠀⠀⠀⠹⣦⣎⡫⢉⣵⠦⣀⠀⢸⡇⠀⢹⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⢸⠃⠉⠉⠙⠛⢻⠟⠛⠓⠒⠒⠛⠋⠙⢷⣜⡷⠋⠻⠾⣁⣿⠀⠀⢸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣴⣏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣷⠾⠾⢛⡿⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣆⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⠐⢸⡇⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⡴⠒⠋⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⢣⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠘⣇⠀⠘⣿⣿⣿⣿⣿⣿⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⡽⠓⠲⠶⠦⢷⡤⢤⡤⡤⠤⠤⢮⣀⠀⠀⠀⠀⠀⠘⣆⠀⠘⢿⣿⣿⣿⡟⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⣀⣠⣽⣧⠀⠈⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣠⠴⠶⣦⡄⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠳⣄⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⣨⠟⠉⠀⠀⠉⠟⢷⡄⠈⣿⡿⢄⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢻⠄⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⠓⣤⡀⢄⠠⡻⣦⣀⡀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠘⡊⣿⣴⣿⠴⢯⡄⠀⠀⠀⠠⣇⠀⠀⠀⠀⠙⠀⢀⣺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢛⢷⣮⣀⣿⠛⠛⠿⢶⣿⠀⠀⠀⠀⠀⠀⠀⣟⢻⣯⢂⣚⣷⠧⡄⠀⠀⠀⢿⡤⣀⠀⢀⡠⣔⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠳⡝⣿⠛⠳⠶⠶⠶⢿⠀⠀⠀⠀⠀⠀⢀⡟⢼⡷⣮⣤⣭⣭⣭⣥⣦⣤⣬⣿⠶⠷⠷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡗⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣠⠀⠀⠀⠀⠀⠀⣀⣸⠆⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⣟⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⠀⢠⣬⣤⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖
⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢏⡟⠁
⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠐⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠎⠉⠀⡜
⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡝⠀⠀⠀⠀⠀⠙⣦⡄⠀⠀⠀⢀⡤⡞⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠛⠛⠳⣶⡄⠀⠀⠀⠀⠀⢠⢏⠈⠀⠸⠴⠦⢀⡀⠚⠂⠓⠦⠤⠖⠁⠀⠁⠀⠀⠀⠀⠀⠱⣄⣀⡀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠋⠀⠀⠀⣠⣼⠏
⠀⠀⠀⠀⣠⡿⠁⠀⢀⣠⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠠⠠⠀⠈⠇⠀⠀⠀⠐⠀⠀⠀⢻⠀⠀⠀⣴⡟⠁
⠀⠀⠠⣤⣿⣀⡀⠀⠈⢏⠺⡄⠀⠀⡀⠤⠀⠀⡀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠘⣆⠀⠀⠹⣧⣀⡀
⠀⠀⠀⣿⠙⢢⡉⠑⠒⢼⣧⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠅⢀⢈⣂⣀⣦⣐⠂⢘⣷⣂⡀⠀⠉⠻⣷⡄
⠀⠀⠀⣿⡀⠀⠙⠢⣄⢭⣀⠁⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⠤⠔⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⠊⠓⠀⢈⡿
⠀⠀⠀⠘⠫⣖⣒⠦⠭⠽⠳⡄⠈⠑⠖⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠞⠂⢁⠠⢳⣀⠀⠀⣠⡾⠁⠀⠀⠀⡠⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠃⠀⠀⢠⠀⠀⠀⠀⠀⣠⠾⡐⠘⢓⠦⡀⠘⡂⠀⠞⠀⣷⠘⡉⣷⠞⠋⠀⠀⠀⠀⡜⠀⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⡀⠀⠀⠀⢠⡄⠀⠠⠀⠂⠀⠁⠈⢢⡂⠀⠑⠬⠃⣀⢄⠐⢿⠁⣀⠩⠦⣀⡤⣄⣀⡜⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠠⠌⡵⠚⡆⠀⡆⠙⠦⣄⠀⠀⡀⠠⠐⠑⠄⠐⢤⠀⠀⠀⡠⠂⠀⠍⠁⠢⡀⠀⠀⠄⠈⠡⠀⠀⢮⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠚⠁⠀⢳⠀⡇⠀⠀⠈⠢⣄⠀⠀⠀⢀⠀⠈⠢⢀⠀⣄⠁⠀⠀⢠⠀⠀⠰⠀⠀⠀⠀⠀⠂⠀⠰⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠁⠀⠀⠀⠀⠀⠉⠫⡁⠀⠀⠀⠀⠠⠘⠀⠀⡐⠀⠄⠀⠀⢠⠀⠀⡰⠀⢠⠏⡠⠂⢀⠉⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠉⠀⠀⡠⠋⣀⡴⠤⠴⡎⢘⡖⠲⢅⣀⢴⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠦⠤⠶⢲⠊⠂⢈⡇⠀⠀⠀⢃⢨⡇⠀⡸⠳⠈⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡈⡅⠀⠀⠀⠈⠺⠀⢠⠇⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡟⠁⠀⠀⠀⠀⠀⢠⠿⣀⢴⡴⢄⡐⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠈⠁

⠀⠀⠀⠀⠀⠤⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⡄⠀⠀⣀⡀⠀⠈⡀⠀⠀⠀⣴⠔⣶⡶⣶⠥⣄⠀⠀⠀⢀⠄⣂⠜⠣⣀⠢⡀⠀⠀⠠⠐⠀⠁⠀⠂⠄⠀⠀⠀⡠⠂⠈⠁⠀⠢⡀
⠀⠀⠸⣉⣉⣹⣏⣿⣉⣉⣉⠀⠀⢸⡵⠋⠙⠟⠋⠑⢮⡃⠀⠀⡄⡜⠡⠤⠦⠌⢳⠰⠀⠐⠀⢀⠐⠀⠂⡀⠀⠂⠀⠈⠀⠀⠐⠒⢀⠀⠘⡀
⠀⠀⠀⠢⡀⠀⠉⠁⠀⢀⠂⠀⠀⠸⡀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠆⠛⡄⠀⠁⠠⠸⠠⠀⢀⠀⡶⠇⠀⠸⢶⠤⠄⠀⠀⠀⠐⠆⠐⠆⣀⢀⠃
⠀⠀⠀⠀⠈⠀⠒⠒⠈⠀⠀⠀⠀⠀⠈⡢⠤⠤⠤⢀⠁⠀⠀⠀⠈⡣⣀⣀⣀⣀⠜⡃⠀⠀⠀⡔⠀⢤⠀⢢⣢⠄⠀⠈⠢⡹⠧⠤⢿⡕⡂
⠀⠀⠀⢀⠔⠀⠉⠁⠐⢄⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠑⡀⠀⠀⢋⠉⠉⠛⠛⠉⠉⠙⠀⠸⡉⠉⠙⠛⠋⠉⢉⠃⠀⠈⠉⠉⠙⠚⠉⠉⠩⠁
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⡀⠀⠀⠤⠀⠀⢠⡇⠀⠀⠀⠐⠄⠀⠀⠠⠀⠀⠀⠀⠀⠢⠀⠀⠀⠔⠁⠀⠀⠀⠑⠠⠀⠀⠀⠔⠁
⠀⠀⠘⣝⠦⣀⡤⢄⡠⢜⡵⠀⠀⠀⢈⠒⠳⠤⠖⢊⠕
⠀⠀⠀⠘⠗⡚⠿⠟⡒⠟⠁⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⢤⡔⠊⠉⠁⠈⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⢢⣀⠀⢀⣀⡠⠒⠓⢉⣿⡆
⠀⠀⠀⢀⠐⠂⠒⠀⢀⠀⠀⢰⠀⠀⠀⡄⠒⠐⠒⠀⡀⠀⠀⡆⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡖⠀⠀⠀⠀⠀⠐⡤⠒⠉⠀⡄
⠀⠀⠀⠠⠰⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠅⠦⠤⠐⡀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠂⠤⠠⠤⠀⠀⠀⢇⠀⡇⠴⠄⠀⠀⠴⠄⣇⣀⡠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣇⡀⠀⠀⠀⠀⣀⡏⠹⡄
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠯⠥⣤⠤⢤⡤⠭⠶⠯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠈⠉⠉⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠠
⠀⠀⡃⠀⣞⣳⠀⢘⠀⠀⡯⠒⠳⠛⠂⢵⠀⠀⢠⠊⠠⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⢈⠀⠈⠀⢈⠀⠀⠀⠚⠀⠘⡒⠀⠀⠀⢠⡃⢘⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠘⠐⠶⠖⠀⠂⠀⠀⠃⠶⠆⠒⠃⠀⠄⠒⠯⠼⠒⠢
⠀⠀⡆⠀⠀⠀⠀⢰⠀⠀⡆⠀⠀⠀⠀⠰
⠀⠀⢫⣂⣔⣦⣀⡝⠀⠀⠀⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⠄⠠⢀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡉⠣⡀⢀⠀⢀⡨⠆⢠⡄
⠀⠀⠀⠐⠀⠂⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⡂⠀⠀⠀⠀⠦⠒⠉⠈
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡇⠚⠀⠀⠓⠠⢴⠂⠁
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡟⢀⡀⢀⡐⢧⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠉⠉⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠤⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡏⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢫⣄⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣡⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⣤⡀⠀⠀⠀⠀⠀⠠⢇⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⣿⣶⣄⣠⣁⠙⠛⠁⠀⠀⠀⠀⢀⣀⠘⢏⡳⣷⣄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨⠹⣿⣿⣇⠈⠀⠀⣶⣤⣤⣄⠀⠹⠟⡿⠃⠻⣺⣿⣗⡄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣶⡘⢿⣯⣥⠀⠀⢸⣿⡿⠁⠀⣠⣿⣿⣄⣠⡬⣿⣿⣿⣆⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠛⠁⢈⡿⠉⣦⢀⠈⠋⠀⠀⣀⣨⣿⡿⣿⣿⣧⣾⣿⡟⠉⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⠐⣷⣎⠛⣍⠀⠒⠀⠈⠁⠀⠈⠙⠛⣿⣿⣁⡛⠁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⣤⣿⣷⣴⣭⣄⡠⠀⢠⣴⣷⣦⣤⣾⣿⢻⡏⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢾⡟⢿⡿⣥⣿⣿⣷⣶⣾⣤⣾⣿⣿⠛⠛⠛⠁⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⡏⣡⣞⠁⢿⣾⣿⣿⣿⣿⣿⡿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣧⣿⣿⠏⣽⣿⡿⢛⣿⣿⣿⣿⣷⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠻⣿⣯⣜⣻⣿⣷⢬⡟⣿⠛⢛⡿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴⣾⠿⠿⠛⠉⠉⠈⠉⠉⠙⠻⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣶⣿⣿⣿⣦⡙⢿⣶⣄
⠀⠀⠀⠀⠀⠀⣰⡟⢛⣷⣼⣿⣿⣿⡟⣭⣙⣿⢸⣿⣿⣀⣴⡶⠄⢀⣠⣤⣀
⣀⣤⣤⠀⠀⣀⢸⣿⣿⣽⣿⣿⣿⣿⣧⣙⠛⣡⣾⣿⣿⣟⠻⣷⡶⠿⣿⣿⣿⡇⣠⣴⣶⣦⣄
⠿⣿⣤⣶⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣧⢸⣿⣿⣾⣿⣍⢻⣿⣿⣷⡀
⠀⠈⠁⠀⠙⣿⣿⣧⣾⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣽⣥⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢰⣿⣿⣧⡽⢿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠁⠀⠀⢀⠀⠛⠦⠀⠈⣻⢿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣫⣽⡻⣿⣿⣿⠇⠀⡦⠁⠀⠀⠀⢿⣿⠟⠷⠀⠀⢠⣧⣌⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠸⢛⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠇⢠⡆⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠁⠀⠀⠹⢦⣄⠀⠀⠀⠀⠉⠛⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠇⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⢀⣴⠶⠿⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⣾⣁⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⡿⠈⢻⢿⣶⣄⡀⠀⠈⠙⢷⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⡀⠁⠀⠈⣌⠻⣟⠋⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣁⣤⣀⡠⠙⠀⠘⣇⡛⠧⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣀⡿⢡⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠿⠿⠿⠛⠉⠉⣉⣩⣿⣍⡰⠟⠀⠀⠉⣡⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⠷⠀⣀⣀⣸⡿⠋⣠⡶⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⣠⣴⣿⣿⡿⠋⢠⣾⠋⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⠛⠛⠋⠉⠉⠁⣀⣤⣶⣿⣿⣿⡿⠋⢀⣴⡟⢁⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⡿⠟⠁⣀⣴⣿⠏⠀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣁⣠⣴⣿⣿⡿⠁⠀⢰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢿⣿⣏⠉⢁⣀⣤⣤⣶⣾⣿⣿⣿⡿⠋⣠⠖⠀⡼
⠀⠀⣸⠀⠀⠀⠀⠀⣾⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢁⣤⡾⠃⠀⣸⠇
⠀⠀⣿⠀⠀⠀⠀⢀⠉⠀⠀⠀⠘⣿⣿⣿⣿⠿⠛⢉⣁⣤⣾⣿⠟⠁⠀⣼⡏
⠀⠀⡟⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⣿⣅⣠⣴⣶⣿⣿⣿⡿⠃⠀⠀⣼⣿⠃⣠
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠋⠀⠀⣠⣾⣿⡟⢀⣿⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⢀⣠⣾⣿⣿⡿⢀⣼⣿⡇
⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⢀⣴⣿⣿⣿⣿⡟⢁⣾⣿⣿⣷
⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣶⣿⣿⣿⣿⣿⠏⣠⣾⣿⣿⠿⠋
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⢃⣴⣿⡿⠛⢁⡴
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢏⣴⡿⠟⠉⢀⣴⠏⠀⠀⢀⣶⣶⣤⡀
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠡⠛⠁⢀⣠⣾⡟⠁⠀⠀⢠⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⣴⣿⡿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⢁⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣿⣦⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⣈⢻⣷⣦⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⡇
⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹
⠀⠀⠀⠙⢿⣿⣿⣿⡏⠛⠓⠒⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠉⠻⢿⣇⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⡀⠀⠀⣀⣀⣠⣤⡤⠤⠤⢤⣬⣇⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⢤⠤⠤⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠈⣇
⠀⠘⣆⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⢤⣀⡀⠀⢸⠀⠀⠀⢠⣾⣉⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣧⣼⣿⡆⢻
⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣿⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⠐⠂⠀⠀⠛⠿⠛⠀⠈⣇
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣀⠀⠀⠀⠀⢤⣀⡤⠖⠋⠙⠲⣤⡄⠀⠀⣠⠖⠻⡄
⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠋⠀⠈⠱⡄⠀⠀⠸⡄⠀⠀⠀⠀⠀⢻⠀⠀⠀⢇⠀⠀⡇
⠀⠀⠀⠀⠀⠹⠤⠤⠤⠤⠤⠤⣤⣀⡀⠀⠀⠸⡙⢆⣀⣀⡼⠁⠀⠀⠀⢧⠀⠀⠀⠀⢠⠇⠀⠀⠀⠈⠓⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣠⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⣠⠏⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⡼⠁⡸⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⡠⠞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⠦⣤⡇⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⣠⢼⣇⡀⢄⠀⠀⠀⠀⠀⠀⠀⢰⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⡬⠷⣄⠀⢀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⢻⠀⠀⠀⠉⢹⡄⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠙⡞⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠃⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢸⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠇⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣼⣀⣀⣀⣀⣀⣀⣹⡄⠀⠀⠀⣸⣄⡀⡀⣀⣾⣤⣤⣤⣤⠤⠤⠴⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉⠛⠋⠛⠉⠉⠙⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠔⠆⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⠸⣿⣦⡈⠉⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢸⣿⣿⣇⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣼⠿⢿⣯⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⢺⡟⠁⠀⡔⠉⠻⠛⣄⢀⡀⠀⠀⠀⠠⠂⠋⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⢄⡀⠀⠛⠃⢀⣪⡾⣻⠂⠀⢘⣉⠀⢠⣶⢁⡦⠀⣠⠁⠀⠀⣄
⣤⣀⠀⠀⣠⠴⢛⣀⣠⣂⣀⡀⠀⢀⠀⣀⣶⣾⣿⡄⠀⠀⠈⠁⠀⠐⠀⠀⣾⠁⢠⠤⠙⠯⠀⠀⠀⠠⢤⡀⠈
⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⠿⠿⠿⠿⠟⠛⠁⠘⢳⣤⣀⡀⣀⣢⡤⣀⢀⣏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠊
⠿⣿⣿⣿⠿⠛⡁⠀⢠⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠟⠁⠹⣏⣽⠀⠀⠀⢠⣼⣿⣷⠀⠀⠀⠀⢀
⠀⠘⣿⠀⡀⠀⠹⣦⡀⣀⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠀⠀⠀⣠⣿⣿⡅⠀⠀⠸⣟⣻⣟⡁⠀⣀⡶⣸
⠀⠀⢸⠀⠘⢃⣠⣝⡃⠉⣠⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠿⠿⢷⡉⣷⢰⣾⣉⣽⣿⣿⠛⠛⠛⠟
⢀⡀⠈⢻⣿⣿⣿⣮⣽⣷⠏⠀⠀⠀⢀⣰⢦⠀⣀⠂⣦⣤⣤⠀⠀⠑⠂⢀⣾⡁⠛⠈⠉⠉⠉⠻⠿⣱⣏⢹⣳
⠀⠓⠁⠀⣹⠋⠻⣿⠛⣿⣀⢈⠑⠀⠘⢃⡐⠀⠙⠉⠛⠟⠀⠀⠀⠀⠀⠘⠋⣶⠼⠃⠈⣩⣽⠃⣶⡚⠷⠿⠟
⠀⠀⢰⣦⠁⠀⠀⠁⠀⠉⠉⠀⠀⠀⢀⠉⠁⠀⠀⠀⡀⡰⠶⠄⠀⢀⠀⠀⣾⡏⠀⠜⠀⠈⣷⣰⣿⡏
⠀⢠⣬⠃⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠨⠀⠀⠀⢀⣰⣦⣿⣆⣦⣽⣿⠵⢾⠟⠷⠀⣰⠇⠀⠈⠉⣴⠇⢶⣶⣄
⠢⢂⠀⢓⠿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⢾⠞⢋⣩⡿⠻⣿⠛⣿⡀⢀⠀⠀⡀⠝⢒⠀⣿⡀⠁⠀⠀⢘⣿
⠠⡞⣠⣿⠀⠀⠐⠒⠒⢀⠀⠡⠀⠀⠀⠁⢾⡇⠰⠛⠛⠿⠓⠉⢨⡿⠟⣠⢿⠋⢠⣸⣷⣴⣿⣷⠠⠛⠛⠋⠹
⠒⢻⣿⠿⠐⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠈⢡⡄⠀⠀⣤⡘⢉⡀⠀⠈⣢⣍⣁⡸⠇⠹⢿⢿⣿⡈⠃⣶⣠⣦
⠈⠉⠁⠀⠀⡀⠀⠀⠀⢠⠤⠀⠀⢴⡶⠒⠻⣦⠁⡾⠶⠉⣿⢀⠀⠘⠃⢰⣿⣿⣿⡶⣾⣾⣇⡋⠀⢾⣯⡍⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠴⠚⠋⠀⢠⠈⠀⠠⠀⠀⢀⠾⠓⠀⠘⠈⠉⠁⠘⠛⠋⠛⠛⠁⠀⠚⠻⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⣀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣇⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿

⠀⠀⠀⠐⡈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠡⠃
⠀⠀⠀⠀⠀⢄⠀⠈⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠁⠂⠄⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⡀⢀⠠⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⠀⠜⠣⡀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⠜⠣⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠎⢀⣤⣌⠢⠀⢀⠀⠀⠀⠀⠀⠀⠔⣡⣤⡀⠡⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣧⣸⣆⠑⠀⠀⠀⠀⠀⠀⠂⣼⣇⣾⠇⠀⡀
⠀⠀⠀⠀⠀⠐⠀⠁⠑⠠⠀⠀⠀⠀⢸⠋⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢹⡇⠀⠀⠀⡀⠔⠉⠈⠀⠂⠄
⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⢑⠁⠀⠀⠁⠈⠀⠀⠄⢠⠊⢑⡄⠠⠀⠈⠁⠊⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠉⡁⠖⠀⠀⠀⠀⠀⠀⠘⠄⠠⠁⠀⠀⠀⠀⠀⠀⠢⢈⠉⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⢀⡤⠐⢐⠃⠂⠠⡄⠀⠀⠀⠀⠀⠀⡀⠀⢠⠄⠀⠘⡂⠂⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⡀⠁⢀⠖⠁⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠡⠀⠐⣀⠶⢰⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠤⠼⠁⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⠀⠀⠘⠒⣒⠦⠆⠀⠎⠽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁⠀⠀⠀⠠⠃⢄⠀⠀⠀⠆⠀⠆
⠀⠀⠀⠀⠀⠀⢰⡆⠀⢨⠠⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠄⠈⠀⠜⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠀⢀⠴⡠⠂⠁⠨⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠁⠂⠄⣄⠐⠁⠀⡀⠀⠔⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢒⢆⠚⠁⠢⡀⢂⠀⠴⣂⡐⠁⠀⢀⢀⣀⠠⠐⠀⢀⢀⣠⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢌⣵⣂⠀⢬⠒⠈⠀⠀⠀⠀⠀⠀⠈⠤⠤⡀⠀⣠⣠⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠉⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⢢⡀⠀⠀⠀⠀⣰⠁⠀⡤⠤⣄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠱⡀⠀⠀⢰⠃⢀⡞⠀⠀⠈⣷⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⠒⠢⣄⠱⠀⠀⡏⢀⠎⠀⣀⡴⠋⠁⠀⠀⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠁⠀⠈⢢⡀⢰⠁⢀⡴⠞⠁⣀⣠⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠒⠍⠁⠐⠒⠒⠭⠗⠶⠤⣄⣽⣿⡾⠿⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠠⠤⠖⠒⠒⠒⠛⠛⠋⠛⠙⠛⠛⠛⠛⠛⠓⠒⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⡶⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠒⠶⠶⠦⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡕⡷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡱⣧⢏⡜⡰⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣭⣬⣤⣥⣿⣥⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⠟⠋
⣟⣀
⣿⣿⡷
⣿⣁⡀
⣿⣿⡿⠄
⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣿⣿⣤⡀
⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣼⣿⣄⣀⣀⣤⣾⣿⣿⣁⣠⣤⣠⣤⣤⣤⣄⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣒⠒⠒⠒⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⣭⣽⣛⠶⢤⣤⣴⣾⣿⠿⠄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠃⡟⠛⢿⣿⣧⡀⠀⠀⠀⠈⠙⠻⣷⡙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⢀⣘⣳⡤⢤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⠻⠿⠶⠶⠖⠛⠛⠻⣿⣿⡆⠀⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠀⢰⣷⡄⠀⠰⣆⠀⠀⠘⣿⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⡇⢻⣦⣀⢻⣦⣀⠀⢉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠙⢿⣿⣿⡿⢿⣶⣿⡚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢾⣿⡷⠀⢳⡄⢸⣿⠈⡇⠀⠈⡃⣿⡆⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠂⠀⠀⣀⠐⠈⣿⡾⠁⢈⣤⣶⡟⢡⡟⢁⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢴⣿⣿⡏⢰⠏⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⣿⠻⣾⣿⡙⢧⡀⢾⡏⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣹⡇⠀⠈⢻⣿⠦⣵⡌⠛⢾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠁⠀⠀⢰⣿⡀⢿⣷⡀⠀⢠⠟⠀⣻⣷⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠈⠙⣷⡅⣠⡴⢻⣿⡁⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⣾⠋⡞⠁⠀⠸⣿⣿⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡇⠙⢶⡇⠀⠀⡄⠈⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢷⡀⠘⣷⡄⠀⠳⢄⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠃⣠⡿⠃⠀⠀⠀⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣻⣿⣯⣟⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣵⣾⠟⢻⢿⡿⡟⠻⣷⣮⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⢄⠀⠀⠀⢀⣀⣀⣰⣋⣾⠏⠀⠀⢀⣲⣖⡁⠀⠀⠹⣷⣙⣆⣀⣀⡀⠀⠀⠀⡠⣖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⣦⣶⡾⠟⠛⡛⠛⠛⠿⣷⣤⠺⡱⡟⢻⢎⡗⣤⣾⠯⠛⠛⢛⠛⠻⢷⣶⣴⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢻⣶⡢⡀⢃⢸⠠⠀⢸⣳⠏⠀⢎⡱⠀⠹⣞⡇⠀⠀⡆⡘⢀⢔⣶⡟⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⠪⣿⣿⡸⡈⣠⣜⣰⣯⡴⠞⠛⠛⠳⢦⣽⣆⣣⣀⢁⢇⣿⣿⠕⠁⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠈⣉⣑⡒⠨⡿⣻⠥⢭⣟⢏⣤⢶⣻⣟⠖⣤⡹⣿⡭⠬⣝⣿⠅⢒⣂⣉⠁⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣫⣽⣿⡄⠀⠀⣀⢾⡅⣇⣿⢟⡇⠾⠱⢏⡡⢌⡹⠎⠿⢸⡻⣵⣸⢨⡷⣀⠀⠀⢠⣿⣯⣝⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣱⣿⠋⠁⠙⣿⢶⣲⡴⣲⡿⢟⣩⡏⡀⠉⡉⢸⠀⠀⡇⢉⠉⢠⢩⣭⡻⢿⣶⢦⣖⡶⣿⠋⠀⠙⣿⣎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣳⣿⣁⡀⢀⢞⡲⠋⠁⣰⠏⢠⣟⡵⢆⣃⣈⣮⣿⡦⢴⣿⣷⣁⣘⡰⢮⣻⡄⠹⣆⠈⠙⢔⡳⡀⢀⣈⣿⣞⣧
⠀⠀⠀⠀⠶⡷⡷⠶⡷⣾⣿⡷⣸⢾⣿⣉⢎⡱⣿⠀⣿⢸⡁⢎⠀⠄⢈⣏⢾⡷⣹⡁⠀⠀⡱⢈⡗⣿⠀⣿⢆⡱⣋⣿⡷⡏⢾⣿⣿⢾⠶⢾⠾⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⣿⡉⠁⠈⢮⠵⣄⡀⠹⣆⠘⣬⡳⠎⡍⣉⢿⣿⠗⠺⣿⡿⡁⢩⠱⢞⣭⠃⣰⠟⢀⣠⠪⡵⠁⠈⢉⣿⢯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⣿⣄⡀⣠⣿⠾⠽⢳⢿⣷⣮⣛⣃⢃⣀⣁⢸⠀⠀⡇⣈⣀⠸⣘⣛⣵⣾⡿⠞⠯⠷⣿⣄⠀⣠⣾⢏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣝⣻⣿⠃⠀⠀⠉⢾⡗⡏⣟⣎⡇⣶⡰⣎⡑⢊⣱⢆⣶⢸⣱⣻⢹⢘⡷⠉⠀⠀⠘⣽⣟⣫⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢀⣉⠩⠥⢔⣷⣽⡒⣚⣿⣎⠛⠾⣽⣭⠥⠛⣱⣿⣓⢒⣯⣾⡢⠬⢍⣉⡀⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⢀⢔⣿⣿⢱⢁⠙⢫⠹⣟⠳⢦⣤⣤⣴⠞⣻⠇⡝⠉⡈⡎⣿⣿⡢⡀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼⠿⠕⠁⡎⠸⠀⠀⢸⡽⣆⠀⢌⡱⠀⣰⢯⡇⠀⠀⡇⢁⠈⠪⠿⣧⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠟⠿⢷⣦⣤⣥⣤⣤⣶⡿⠛⢴⡱⣧⣽⢎⡦⠛⢿⣖⣤⢤⣬⣤⣴⡾⠿⠻⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠊⠀⠀⠀⠈⠉⠉⠹⣏⢿⣄⠀⠀⢈⠽⠯⡁⠀⠀⣠⡿⣹⠏⠉⠉⠁⠀⠀⠀⠑⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡻⢷⣦⣼⣾⣷⣧⣴⡾⢟⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣽⣻⣟⣯⠷⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠛⠋⠉⠁⢸⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⡼⠧⠤⠤⠦⠤⠤⠤⢤⣀⣀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⣿⣅⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡞⠛⣦⡀⠀⠀⠀⢳⠀⠀⠀⣀⣠⡤⠶⠒⠛⠉⠉⠁⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠘⢿⣿⠿⠃⠀⠀⡤⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇⠀⠀⠀⢸⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠧⣄⠀⠀⠀⣀⢀⣠⠴⠲⢤⣀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⣧⠀⠀⠈⣿⠃⠀⠀⠀⠈⠉⢻⠁⠀⠀⢀⡴⠒⠒⠢⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣠⠇⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⡁⠀⠀⠀⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠓⠦⠴⠞⢡⠇⠀⠀⠀⣶⠒⠚⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡀⠀⠀⠀⠈⠳⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠳⡀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⢸⠀⠙⣆⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣦⠔⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⠴⠒⠋⠉
⠀⠀⠀⣠⣦⡀⠀⢀⣤⢯⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⣯⣄⡀⢀⣴⡄
⠀⠀⠀⣿⢿⡻⡖⠉⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢳⡎⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠁⠀⠀⣹⠏⡿⣿
⠀⠀⠀⣿⠈⠀⢳⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠠⠏⠀⢀⡇
⠀⠀⠀⢸⡄⠀⠈⡇⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠈⢧⡀⢀⡀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢸⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠉⠛⠛⠛⠛⠿⠶⡴⣦⠶⠷⢦⡤⣤⣤⢼⠖⠒⠒⠶⠶⠶⠒⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡟⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠬⠷⠦⠤⠤⠄⣀⡀⠙⣆
⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⢀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⣠⣴⣾⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠈⠙⠻⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⢱
⠀⡦⠤⢤⣀⣀⠈⠉⠛⠒⠒⠦⠤⠤⠤⠤⢤⡤⠀⠀⠀⣠⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣠⣿⣧⠈⡇
⠀⡇⠀⠀⠀⠈⠉⠓⠢⢤⣀⡀⠀⠀⠀⠀⢸⠃⠀⠀⢸⣿⣦⣼⡷⠀⠀⠀⠀⠀⠤⠀⠀⠈⠛⠿⠟⠃⠀⢹⡀
⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣀⢍⣗⠦⣄⡀⢸⠀⠀⠀⠀⠛⠿⠟⠁⠀⠀⠀⣀⠠⠤⠤⣀⠀⡀⠀⠀⠀⠀⡸⢇⠀⠀⠀⣠⠶⠶⣄
⠀⢸⡀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠓⠤⣙⠻⠀⠀⢀⣀⠀⠀⠀⠀⠒⡖⠊⠁⠀⠀⠀⠘⣿⠁⠀⠀⠀⡘⠀⢹⣤⠖⠋⠀⠀⠀⠨⣧
⠀⠈⡇⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⠹⡄⡞⠉⠉⠑⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢱⡀⢨⠁⠀⠀⠀⠀⠀⣴⠁
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⢀⠇⠀⠀⠀⢱⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⢙⠏⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠈⠓⠒⠢⠤⢤⣀⣀⡘⡄⠀⠀⠀⠀⠀⠀⢆⠉⠈⠁⠀⠀⠀⠀⠀⢣⡀⠀⠀⡠⠃⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣄⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠊⠁⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢢⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠰⠷⠾⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠤⠤⢤⣄⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠀⣠⠞⠙⠲⠤⣀⣀⣀⣀⣀⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⢶⡄⠒⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣰⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠉⠉⠉⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠶⠶⠷⠴⠶⠦⢤⣏
⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⢀⣠⣤⠴⠶⠶⢶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⢀⡴⠋⢠⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠾⢡⠀⣿⣷⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡿⠿⠛⠉⠁
⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⣤⠀⠀⠀⠀⠀⣤⠤⠄⠀⠒⠚⠛⠉⠉⠁⣀⣀⠤⠴⠖⠚⠛⢛
⠀⠀⢸⡀⠞⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠸⣿⣿⣾⡟⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⣠⡤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⡉⢡⡀⠀⠀⠀⠀⢀⣬⣤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⣀⢀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠆⠀⢠⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠰⠂⠁⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⣀⠂⠀⣀⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢃⠀⠈⢧⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⡄⠓⠀⠀⠀⠀⡇⠀⠀⠉⠉⠉⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠚⠛⠓⠒⠒⠢⠔⠋⠀⠀⠀⠀⠀⠀⠀⠇




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⡀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠊⠉⠉⠉⠉⠉⠒⠛⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⢀⣀⠤⠴⠚⠛⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⢀⡜⠁⢠⣾⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⡾⠉⠀⠸⠿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠰⠞⠋⠉
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣼⡆⠀⠀⠀⠀⢸⡇⠁⠉⠉⠁⠀⠀⣀⣤⠤⠐⠒⠀⠒
⠀⠀⠀⠀⢧⠈⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⢸⡇⠀⣀⣠⠴⠞⠋⠉
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⡀⠀⠀⢀⣠⡼⠷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠴⠒⠂⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠈
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠄⠃⠀⡀⠚⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⣷⡀⠀⠀⠀⣶⠶⠶⠤⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⡀⠀⣫⡴⠞⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⠀⠴⠄⡄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠋⠀⠀⠁⣶⠂
⠿⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⢠⠔⠁
⣾⣶⣖⢸⡟⣳⣶⣤⣄⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠌⠀⢀⠉
⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠛⠿⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⢰⡴⠁⠀⠄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣶⣶⣿⢯⣭⣤⡤⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣾⣁⣈⠀⢀⣤⣤⠀⢘⡿⣷⢽⣻⣿⣿⣿⣿⣿⣿⣶⣶⣾⣧⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣤⣤⣤⣤⣤⣤⣄⣀⣀⣰⣿⣉⣀⣀⣀⣀⡙⢒⣾⣒⣺⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⣉⡁⠈⠉⠈⣿⣿⡉⠁⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⡈⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠀⣀⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠟⠛⠛⠟⠋
⠀⠁⠉⠀⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣖⣒⠒⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣿⣿⣿⣿⣽⣛⠯⣍⢒⠮⣝⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⡻⣝⠮⣑⠭⣒⠭⢄⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣥⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣮⡢⢕⡪⠝⠒⠍⠒⢯⣮⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠁⠀⠈⠂⠀⠀⠀⢸⣿⣿⣿⢿⣾⣝⠯⣲⢍⡙⠲⠤⣄⡀⠪⣻⣿⣾⣟⠯⠍⡉⠒⢄
⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠈⠓⠒⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣭⡓⢝⠢⣕⠪⣐⢄⡪⣝⢷⣌⢿⣿⢗⡫⠭⠭⠍⠲⣵⡀
⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣮⣝⢦⠱⡌⢳⣜⢦⠙⢮⣷⣽⣿⣿⠏⣠⣽⡿⣿⣶⣸⡇
⠀⠀⠀⠀⠀⠰⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣦⡳⡹⣄⠙⣦⡀⢮⡻⣿⣿⣟⠜⡵⠋⠀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠢⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⢀⠀⠀⠈⣷⡑⡑⡜⢆⢪⡻⣦⣙⢿⣿⣿⠀⡄⡌⢠⣏⡟⡇
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄⠘⣮⡳⣝⣮⣝⣿⣿⣿⡄⡇⣸⢸⢸⢱⠇
⠀⠀⠀⠀⠘⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣞⢞⢦⡘⢿⣮⣿⣿⣿⣿⣿⣷⣿⡷⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠒⠂⠒⠀⠀⠀⠀⠀⠀⢀⢯⣿⣿⣿⣞⢎⢦⣙⠶⠭⠽⢛⣭⣿⣿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣿⣿⢿⡝⣮⡳⢬⣛⣛⡛⣋⡴⢻⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⢮⡻⣮⣙⡒⠒⢒⡛⢉⣴⢏⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣝⠲⠭⠭⠭⠵⢞⠋⣡⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⠭⠍⢓⣊⠭⢴⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠒⠲⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣴⣶⣶⣶⣖⡒⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠓⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⣤⣤⣴⠶⠿⠟⠛⢋⣉⣥⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣛⣫⣇⣻⠏⠀⠙⣋⠧⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢒⣒⡩⠭⠀⣀⣤⣶⡿⠛⠁⠀⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⠂⠁⠀⠀⢃⡾⢻⡄
⠀⠀⠀⢀⠤⢒⣊⣭⣴⡶⠟⠋⣁⣤⣶⣿⡿⠛⠁⠀⢀⣤⣾⣿⣿⣿⣿⣿⡿⣟⣻⡽⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⠇⣈⣀⣀
⠀⠀⢀⠁⡼⣎⣽⡟⡉⠀⠀⠉⠙⠛⠛⠁⠀⠀⠴⣾⣿⣿⣿⣿⣿⣿⣫⡵⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠰⠂⠀⠀⠀⡼⠁⠐⢿⣿⣿⣿
⠀⠀⢸⡇⠣⢻⣿⠐⡷⠀⡀⣨⣁⣐⡒⣒⠒⠂⠀⠠⠤⠄⠀⢴⣾⠟⠉⠀⠀⠴⣠⣴⣦⣄⠀⠀⠂⠀⠀⠀⣴⣿⠟⠛⢲⠀⠀⠀⠀⠀⠠⠎⠀⢀⠰⢸⣿⣿⡿
⠀⠀⠈⠙⠛⠁⠙⠀⢀⠀⠈⠟⠿⣿⣧⡿⣾⢲⢃⡏⡠⠀⠀⠘⠁⢠⠻⡆⠈⢰⣍⣙⡍⢿⠶⠁⠀⠀⠀⢐⠟⠁⠀⠀⣼⠀⠀⢀⣤⣾⣷⣤⣤⣾⠀⣾⡿⠋
⠀⠀⠀⠀⠀⢀⡒⠶⢴⣾⠷⢶⣤⣤⣬⣭⣭⣭⣌⣁⣁⠀⠀⠀⠢⣄⡻⠁⣀⠠⢿⡛⢁⡿⠀⠐⠏⠀⠀⠂⠀⠀⠈⣴⡇⣴⣾⣿⣿⣿⣿⣿⣿⣿⡷⠋
⢀⣴⣿⣶⣶⣦⣽⣷⣀⠌⢑⠒⠒⠛⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⡶⠶⢶⣤⣽⣶⠶⠾⠫⠇⠀⠀⠀⢀⠍⠀⠀⢰⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣉⣉⣐⠒⢶⣶⣶⣶⡂⠀⠀⠤⠍⢉⡉⠀⠒⠀⠀⠀⠀⠁⠀⠀⡠⠊⠀⢰⠰⢸⡟⣸⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣖⣒⣤⣤⣤⣀⡀⠀⠀⠀⠀⣀⣠⡴⣀⠀⡀⢠⣀⡿⢃⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣦⣧⢸⡏⠀⣼⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋

⠀⣠⡄⠀⠀⣤⠀⣀⠀⣀⠀⠀⠀⡀⠀⠀⢀⠀⣠⠀⡤⡄⣤⡀⣤⡀⠤⣀⣤⢀⣤⢠⣤⣠⣄⣠⣄⣠⡄
⠀⠨⠁⠠⠀⢬⠀⠠⠀⣤⠀⠄⠀⠄⠀⠀⠀⠀⠈⠀⣬⡅⣭⡄⣭⡄⣭⣀⡍⢠⢭⢨⣭⣨⣅⢨⡅⣨⡅
⠀⠤⠄⠀⠀⠰⠀⠀⠀⠠⠀⠢⠀⠆⠀⠆⠰⠄⠀⠀⣼⡄⣈⠀⣼⡄⣭⡠⣥⢠⣧⢠⣧⢠⡥⣨⡅⣬⡄
⠀⠰⠆⠰⠀⠐⠀⠒⠀⠶⠰⠶⠀⠀⠀⠀⠰⠆⠰⠂⣜⡄⣴⡄⣾⡄⣶⠤⣥⠠⣷⢠⣧⢴⡦⢔⡆⣼⡆
⠀⢠⠉⡂⢠⣾⡆⠀⠊⣠⠀⢾⣧⠀⠘⢡⡄⠀⢁⡄⢞⠆⣶⠆⣶⠤⣶⠤⣶⠰⣶⢰⡦⢴⡆⢴⡆⢶⡆
⠀⢀⡭⠀⢀⣭⡀⠀⠨⠅⠀⣨⣅⠀⢠⣍⠀⢀⣍⠀⢶⠆⢶⠆⢶⠤⣶⠴⠶⠰⡶⠰⡲⢴⡦⢴⡆⢶⠆
⠀⠐⠴⠋⠈⠻⠛⠀⠠⠞⠀⠻⠟⠁⠐⠞⠃⠘⠿⠃⢎⠆⢎⠄⠾⠆⠷⠰⠳⠰⡷⠰⡱⠰⠆⠼⠆⠶⠆
⠀⠀⠀⠰⠀⠐⠀⠐⠀⠓⠀⠃⠀⠂⠀⠃⠀⠀⠘⠃⠳⠾⠀⠔⠀⡀⠀⠒⢆⠀⠀⠶⠰⠂⠸⢔⢂⠒⠆
⠀⠀⠀⢘⠁⠙⠀⠊⠈⠛⠈⠃⠀⠃⠈⠃⠘⠃⠘⠁⢢⠱⠶⢹⠆⡐⠆⠠⣿⠈⡙⠏⠐⠀⠿⠎⣀⣨⡁
⠀⠈⠀⠘⠁⡈⠀⠀⡀⠀⠀⠉⠈⠃⠈⠁⠀⠃⠈⠃⠤⢄⡤⠌⠀⠁⠟⠃⠀⠀⠈⠂⣠⣶⣦⡀⠛⡛⠃
⠀⠰⡾⠄⠀⡿⠀⠀⠸⠀⠀⠐⠀⠀⠰⠂⠀⠹⠞⠀⠠⣭⣤⠃⠖⣖⠀⢀⠸⠇⡌⡁⠻⣿⡿⠣⠻⠊⣁
⠀⠀⣀⡀⠀⣠⣀⠀⠠⣀⠀⠀⣄⠀⢀⣄⡄⢀⣀⠀⢒⡀⣛⠆⣌⣉⣠⠛⡣⢥⣾⢋⠲⢦⢈⣑⠐⢀⡃
⠀⠀⢈⠀⠀⠘⠉⠀⠀⠀⠀⡀⠉⢀⠈⠀⠀⠈⠁⠀⠦⠀⠉⠤⢧⣶⡴⣘⢃⡐⠟⢣⡋⢰⣾⡿⢳⡈⡃
⠀⠀⠐⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠛⠁⠚⠛⠁⠉⠀⠐⠘⠀⠒⠚⠂⠐⠂⠒⠛⠛⠋

⠀⣀
⠀⢻⣿⣷⣶⣤⣀
⠀⠀⠻⣿⣿⣆⠨⠛⠶⣤⣀
⠀⠀⠀⠈⢿⣿⡆⠀⠀⠘⠫⣟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⡤⢤⣦⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠈⠱⣮⡳⣄⣀⣀⣠⣤⣤⠤⠴⠶⠶⠶⠶⠶⠦⠤⣤⠴⠖⠚⠛⠉⠉⠁⠀⠀⠀⢀⡶⣠⣿⣿⡿⠟⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⢷⣥⣀⡀⠀⠀⠈⢳⠈⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠾⣋⣾⠿⠋⠁⠀⠀⠀⠀⠀⢀⣴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣦⣤⣤⣾⡷⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⢾⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢏⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡜⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡣⠞⠁⠀⠎⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡾⠀⢀⣤⣤⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡤⢶⣤⣄⢰⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠀⠀⠀⠀⣴⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠃⢰⣿⣀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣠⣿⣿⡆⢣⣿⡀⠀⠀⠀⠀⠀⠀⣠⡾⠍⠁⠀⠀⠀⠀⠀⢹⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠸⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠘⠿⣿⡿⠟⡡⠘⡜⣧⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⢨⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡟⠀⠂⠈⠉⠉⠀⠀⠀⠀⠀⠰⢶⣶⠶⠀⠀⠀⠀⠀⠀⠂⣈⣤⣴⣌⣻⡄⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣴⡷⣊⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣡⣶⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⠁⠀⠀⠀⠀⢀⢰⣿⣿⣿⣿⣿⠇⣠⠞⠅⠀⠀⠀⠀⠀⢀⣤⡾⣿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⣿⣿⣿⡷⠈⠄⠀⠀⠻⣶⠶⢛⠋⠙⠛⠶⠟⠀⠐⠀⠈⠿⣿⣿⢟⡿⠸⣇⠦⡀⠀⠀⠀⠀⣰⠛⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⡛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠄⣴⠞⢷⠀⠈⠻⣯⢂⠀⠀⠀⢿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣛⠐⣶⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⡸⡆⠀⠀⠈⣻⡄⠀⠀⢀⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠅⠀⠀⣀⡀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣿⠀⣠⡾⠋⠀⢀⠀⣪⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡠⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠙⠻⠿⠛⠉⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⣿⢹⡟⢹⡣⠀⣨⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣿⣿⡟⢳⣅⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢠⡾⠙⡏⣷⣾⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢷⣝⣤⡀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⠀⠀⠀⣠⡟⠀⠀⣇⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠂⠀⠙⢿⣽⣄⠀⣨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣦⡴⠋⠀⠀⠀⡗⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠈⠙⠿⠋⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⡒⠀⠀⠀⠀⢀⣀⣠⣶⣶⣶⣦⣤⣤⣤⣄⣀⢠⣤⣤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠿⠛⣸⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⢙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡷⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠢⣵⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⢠⠏⠀⠀⠀⢀⠞⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⠀⠀⠀⣀⠀⠀⢣
⠀⠀⠀⡎⠀⠀⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⡘⠀⠀⠃⠀⠀⠀⠀⠈⡟⠢⡀⢣⡀⠀⠀⠀⠀⣀⠤⠒⠚⢲
⠀⠀⢠⠁⠀⠀⠀⠀⠇⠀⠀⠀⠘⠑⠢⣀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⢆⡿⢆⡠⠔⠋⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⢻⠀⡜⠇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢻⡈⢧⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⠀⠀⠀⢸⠓⢤⡀⠀⠀⠀⡇⠈⢶⠀⠘⡄⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠇⠈⡆⣀⠴⡆⠀⢰⠁
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡀⠀⠙⢦⠀⠀⡇⠀⠀⠀⠀⠘⢄⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⢰⠁⠀⡎
⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠼⢄⣀⡀⡇⠀⠀⠈⡇⠀⠀⠀⠳⡀⠸⡄⠀⠀⠀⠀⠈⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢀⠇⠀⢰⠁
⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⢇⠀⠀⠀⠀⠙⡄⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡜⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⠞⠁⠀⠀⠀⠀⠀⠀⠀⣰⡆⢸⡀⠀⠀⠘⡄⠀⠀⣠⠞⠁⠀⠀⠙⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡜⠀⠀⡼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣧⠋⢇⠀⠀⠀⠱⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢇⠀⡼⠀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠘⠄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠳⡄⠀⠀⠀⡰⠉⣷⠀⠀⠈⡶⠁⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣇⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⢧⣀⡅⠀⠀⠀⠣⡠⠃⣀⡀⠀⡇⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠈⠉⠉⠙⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠙⡄⠉⠀⠀⠀⠀⠀⠀⡼⠁⢘⡀⡇⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⠀⠙⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠑⣦⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣥⠖⡏⣧⠋⠉⢉⣠⠿⠒⠒⠂⠃
⠀⠀⢀⠞⠉⡄⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⣩⠗⡇⠀⣼⡓⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡇⢸⣢⣀⡇⠀⠀⠀⠀⠀⠀⢸⠿⢀⢧⣏⡠⢒⡩⠼⠛
⠀⢀⠇⠀⠀⠈⠢⢄⣀⣠⠔⠁⠀⠀⠀⡜⠁⠀⢣⡜⢮⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢧⠈⠁⡸⠃⠀⠀⠀⠀⠀⠀⢸⢀⢌⡼⠈⣉⠟
⠀⡜⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠸⡀⠉⠉⠒⠲⣖⠀⠀⠀⠀⠀⠀⠈⠒⠗⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⡹⠗⠋
⠀⡇⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡷⢄⣀⠀⠀⢐⡷⡀⠀⠀⠀⠈⠑⠦⣀⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡳
⠀⠑⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⠉⠉⠁⢰⠉⠲⡤⣀⠀⠀⠀⠨⣍⠒⠲⠬⠭⠂⣀⣀⣀⡀⠤⣤⠤⠤⠖⣒⣻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡇⠀⠀⠑⢌⣉⡲⠦⢤⣈⣑⣢⣄⣀⠀⣀⣀⣀⠴⠊⠁⢀⠞⠉⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠑⠦⣀⡎⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣿⣷⣄⠀⠀⠀⠀⠒⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣤⣿⣯⣿⣧⣀⠀⠀⠀⠀⢹⡟⣿⣶⣦⣾⣰⣾⣧⣶⣷⣤⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣭⣿⣿⣿⡿⢿⣿⣿⣿⣿⣶⣄⣿⣅⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⢁⡾⠋⠉⣉⣉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡇⣈⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⡯⡽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣩⣬⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠰⠾⠿⣿⡷⣶⣤⡀⠀⠚⢻⣿⣿⣿⣿⣿⣿⣿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠸⣦⣤⣼⡿⢀⣤⣴⣿⣿⣿⣿⣿⣿⣇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⣀⣨⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢀⢀⡀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡆⢸⠀⠀⠀⠀⠀⢸⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⢈⠆⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⡀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣇⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠋⠉⠁
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣷
⣿⣿⣿⣷⡄
⣿⣿⣿⣿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⣸⣿⣿⡿⠋⢁⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣤⣿⣿⣯⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣿⣿⣿⡿⠿⠊⠀⠀⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠙⠻⢿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣆⠉⠻⠆⠀⠀⠀⠀⠈⣿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⢻⣿⣿⣿⣿⠟⠉⠈⢿⣿⣿⣷⡝⠀⠀⠀⠀⣀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡄⣰⣿⣿⡀
⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⠿⡆⠙⠿⠉⠁⠀⠀⠀⣼⣿⣿⣿⣽⣿⠀⠀⠀⠈⢷⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢀⣾⡿⢻⡿⣏⠀⠀⢁⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⡿⠟⠿⣦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠈⠋⠧⠙⢨⣵⣾⣿⣿⡀⠀⠀⠀⠀⢋⣿⢿⣿⣿⣻⣿⣗⡈⢣⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⠃⣾⢾⣟⣿⣯⣝⢿⡜⣇⢀⣾⣿⣿⣿⡿⠟⠋⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⡀⠠⣀⠀⠀⣱⣾⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣿⣿⣿⣃⠀⠀⠀⠉⠉⠁⣹⣿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠴⢾⣿⣿⣿⠿⠿⠿⠿⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠐⠲⠶⠶⢶⣶⣶⣶⣾⣿⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠋⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⠃⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡠⠔⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠻
⠀⢰⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣠⠞⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⡀
⠀⠸⠀⠀⠀⠀⠀⠉⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠃⠀⣠⡶
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠈⡇
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⢹
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⡇⠀⠀⠀⠀⢀⠠⠖⠒⠉⠉⠉⠉⠉⠁⠐⠀⠀⠀⠀⠒⠒⠉⠉⠉⠉⠉⠛⠓⠒⠦⣤⣀
⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⢀⣙⠷⠆
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠷⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⢰⣿⣇⣸⣷⠀⠀⠀⠀⠀⠀⠀⢾⣁⣹⣧⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡏⠀⠀⠀⠘⢮⣽⣿⠟⠀⠀⠀⠀⠐⠂⠀⠘⠿⣯⠽⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⠀⠀⢠⡆⢸⠇⣠⠖⠂⠢⡄⠀⠀⠀⠀⠀⢀⣀⡴⠶⣄⣀⠀⠀⠀⢀⠔⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⠀⢸⣶⡇⠀⠀⠀⠘⡆⠀⠀⠀⣿⠉⣁⣈⣷⣿⡞⠀⠀⠀⡞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⣱⠈⡟⢿⣦⣀⣀⣠⠃⠀⠀⠀⢿⠋⠁⠀⠀⡽⠁⠀⠀⠀⢳⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⢠⠇⢀⣿⡈⠉⠛⠉⠀⠀⠀⠀⠀⢸⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⣠⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠖⠋⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣀⠀⢀⣤⣿⣁⠉⠻⠋⠁⠀⠀⠀⠀⠀⣤⣀⣀⣀⣀⣀⠀⠀⠐⠊⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣿⣿⣿⠃⠀⢀⡄⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠢⣤⡤⠤⡀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠀⢄⢀⡤⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡄⠲⣤⠀⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠦⢤⠞⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠘⡄⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⢧⠀⡔⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⠃⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣧⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⢧⠀⠀⣠⠀⠹⡄⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⢠⠞⢁⡆⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣌⣳⠴⠏⠀⠀⠹⣄⠀⠀⠀⠀⢠⠏⠘⡄⠀⠀⠀⢰⡏⠀⠘⣧⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠛⣄⣀⠀⣀⣸⠒⠒⢳⣀⣀⣀⡼⠉⠉⠉⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢰⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⡦
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠻⢿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⡿⠿⠟⠛⠛⠛⠛⠉⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠉⠛⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠛⠋⠉⢹⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⡄⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠀⢀⣼⣿⣷⡿⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⠾⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⣠⣴⣿⠟⠉⠀⠀⠘⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣦⡀⣀⣀⣠⣤⣶⣾⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⡟⠛⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⢀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠈⢻⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⢸⡿⣽⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣈⣿⣿⡇⠀⠀⢸⣿⠟⠋⠛⣿⣧⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠟⠛⢺⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠋⠙⢿⣿⣿⣿⣷⣶⣤⣿⡏⠀⠀⠀⢸⣿⠃⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡿⣏⠀⠀⠛⢃⡀⢀⠀⠀⠀⠀⠀⢠⣿⠋⠁⠀⠉⣿⣿⣄⣀⣠⣿⣿⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⠀⠸⣇⣻⡆⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⢀⣿⠋⠛⠛⠋⠉⣿⡀⠀⠀⠘⢿⣿⣧⠀⣀⣴⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣛⡆⠘⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠾⠛⠁⣀⠀⠀⠀⠀⣿⢷⣄⠀⠀⠈⠻⣿⣿⣿⡿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡁⠀⠀⢠⡉⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⣿⠀⢻⣧⠀⣠⣾⡿⠛⠁⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠋⠀⠀⢉⣴⣿⡿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠻⢿⣦⡀⠀⠀⢹⣧⣶⡖⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠙⢿⣦⡀⢸⣿⣿⡇⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠁⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢏⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡀⠀⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⣿⣇⣠⣤⣤⣀⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣏⣤⣤⣤⣤⣭⣿⣿⣷⣶⣶⣶⣶⣿⣿⣥⣀⠀⠈⠁⣀⣠⣴⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⡔⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠢⣀⠞⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠙⠀⠀⠀⠀⠀⢸⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠾⣿⣾⣿⣿⣷⣶⣤⣄⣀⣀⣤⣶⠟⠁
⠀⠀⠀⠀⣠⠔⠊⣻⢝⠯⢄⣀⣶⣿⣿⣿⣿⣿⣭⣽⠿⠻⣿⣟⡁
⠀⠀⢠⠞⡁⠀⠀⢂⠵⠚⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣉⣙⢦⡀
⠀⠰⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣆
⠐⢢⣄⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠾⠟⠛⠟
⠀⠀⣿⡆⢿⣿⣿⣿⣶⣤⣄⣤⣾⣿⣿⢟⡽⠿⠛⠛⠛⠛⠛⠛⠛⢛⣻⣿⣿⣷⠀⠀⣠⣴⣿⠿⠋⠉
⠀⠀⣸⡇⢸⣿⣯⣉⠻⣿⣿⣿⡿⣫⡾⢉⡀⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⡄
⠀⣼⠿⠃⣼⣿⣿⣿⣧⡘⣿⣿⣿⣿⠈⡁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⢸⡟⠳⣿⣿⣿⣿⣿⣿⣷⢻⣿⣿⣽⣦⣄⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠸⣧⠀⠈⠻⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣶⣄⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡀
⠀⢻⡆⠀⠀⠈⠛⠿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠋⢹⣿⡀
⠀⠈⢻⡄⠀⠀⠀⠀⠀⠙⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠈⣿⣇
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠢⡐
⠀⠀⠀⠀⢿⡄⠀⠀⠀⢠⣿⡼⣿⣿⣿⣿⣿⣿⡟⠛⠋⠙⢄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠉⠀⢳⡹⡿⠉⠙⣍⠁⠠⠦⠤⣀⡈⠢⡀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠳⡑⡀⠀⠈⠣⡌⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠙⢎⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⣑⠠⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⣿⣃⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠸⠋⠉⠉⠉⠙⠛⠛⠷⢶⣤⣀⣀⣤⣤⣶⠶⠾⠿⠿⠛⠛⢛⣿⣿⣷⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⠉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠟⠛⠉⠉⠁⣼⠏⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣀⣤⣤⣤⣶⣿⡿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⣀⣤⣴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⣴⣶⡄⠀⠀⣾⠃⠀⢠⣶⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉
⣀⣤⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠘⠁⠘⠻⣶⣼⣏⣀⡀⠸⢿⡿⠃⠀⠀⠀⣀⠀⠀⠀⣠⢤⡀⠀⢸⡟
⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⢀⣀⢀⣀⣛⠀⠀⠀⢿⣾⡿⠀⣾⠃
⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⣷⣤⠤⠀⠀⠀⣠⣿⠀⠀⠀⢀⣀
⠀⢿⡆⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠁⠀⠀⣼⡇⢹⣇⠀⠀⠀⠀⠀⠹⡍⠀⠀⠀⠀⠀⡇⠀⠀⠉⣻⠃⠀⠀⢠⣾⣿⡟⠛⠛⠛⠛⢿⣷
⠀⠘⣿⡀⠀⠀⠀⣠⡾⠟⠉⢸⡟⠀⠀⢀⣿⡿⠟⠛⡆⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢧⠀⢀⡔⠁⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠘⣷⣀⣴⠿⠋⠀⠀⠀⣾⡇⠀⠀⠀⠁⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠠⠚⠉⠀⠀⠀⠀⠀⣠⣾⠟⠉
⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⣿⠀⢀⣠⣴⣾⣀⣀⣾⣯⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡶⠟⠋⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢫⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠃⠠⢤⣤⣤⣤⣤⣴⣶⠶⢶⣶⣶⣆⣀⣀⣀⠀⠀⠀⢀⡴⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣯⣴⡶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⢿⣶⣤⣤⣤⣜⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⢀⠀⣀⠀⣀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠈⡀⠀⡁⠀⠀⠀⠀⠀⠉⠀⠂⠀⠐⠀⠀⠀⠀⢐⠀⠀⠄⠀⡊⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠁⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⡀⠀⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠆⠸⠀⠀⠀⠀⠖⠶⠀⠀⠀⢀⠀⢅⠩⡀⠂⠀⠀⠂⠀⡚⠣
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢄⠄⡦⢄⡄⢰⢠⡠⠀⠀⠀⠀⠃⠀⡉⢉⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠘⠃
⠀⣀⢀⡀⠀⠀⠀⠀⢆⢀⠀⠀⡆⠀⠊⠂⠓⠊⠁⠚⠀⠑⠀⠀⠀⡇⢨⠀⡤⢈⠀⠘⠀⢰⡆⠀⠀⠀⠀⠀⠀⠁⢠⠀⠿
⠀⠀⠀⠀⠀⠀⠄⠸⡶⠾⣷⣾⡇⢸⡢⠀⠀⠤⠀⠀⠄⠀⠀⠀⠀⡇⠸⠀⠇⠈⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⢈⠁⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠇⠀⡤⠀⢠⠊⡉⢆⠀⠀⣀⠀⡀⠁⠀⠈⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠄⠠⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠈⠢⠄⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⡤
⠀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⢘⠃
⠀⠠⣤⣤⡄⠀⠀⠀⠠⠆⠠⠀⠆⢠⠀⠀⠀⠀⢀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⠀⠸⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣷
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠘⢿⣿⣿⣿⣿⠋⠛⠓⠲⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠻⢿⣿⡆⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣹⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣴⠚⠛⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠋⠀⠀⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢢⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠸⡉⠉⠉⠛⠓⠒⠲⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠳⣶⡄⢸⡄
⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⡀⣾⠀⠀⠀⠀⣿⣧⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⡗⠈⣇
⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠙⠿⠿⠟⠁⠀⠀⠀⠀⠀⣉⠀⠀⠀⠉⠛⠉⠀⠀⢹⡄
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣀⣀⠀⠀⠀⠀⢤⣤⠤⠖⠋⠁⠉⢳⣦⠖⠀⠀⢠⠞⠉⢳
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠏⠀⠀⠈⢧⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⡘⣆⠀⠀⢀⡞⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⠓⢤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⣧⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣰⠋⢸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠖⠁⠀⠀⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣼⠁⠀⡟⠀⠉⠳⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣄⡀⠈⠙⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣄⣠⠴⠾⠦⣄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⡰⠀⠀⠀⠀⠀⠀⠀⠀⡯⠰⠞⠳⢤⡀⢠⡾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠙⣧⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢹⠏⡷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠂⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸⠇⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⡀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⣿⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢀⣀⣄⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠓⠒⠒⠒⠒⠒⠛⠿⠦⠤⠴⢤⠖⠻⠲⠶⠶⠶⠟⠋⠉⠉⠉⠉⠉⠀⠈⠉