Burger Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠁⢠⡀⠈⠁⠠⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠢⠂⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠤⠀⢠⠄
⠀⠀⠀⠀⠀⠀⡋⠀⠐⠂⠀⠀⠠⠠⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠣⠤⠀⠀⠀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠠⠄⠀⠐⡀⠄
⠀⠀⠀⠀⠀⠀⢠⠃⠏⠩⠴⠤⠤⣄⣀⣀⣠⣠⡍⣍⡍⣩⢩⢀⣀⣄⡄⠲⠤⠤⠤⠤⠄⠤⢛
⠀⠀⠀⠀⠀⠀⢦⢀⡀⠀⠂⠀⠀⢀⡄⠀⠀⢀⡄⠀⠀⠀⡀⠀⠀⠀⡤⠀⠀⠠⠄⠀⠀⢀⡠⢤
⠀⠀⠀⠀⠀⠀⠳⢅⣄⢪⠪⡣⡑⢞⠆⠂⠀⠐⠐⠒⠐⠀⠁⠒⠀⠒⠒⠂⠀⠀⠈⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠐⠒⠃⠀⠉⠱⣘⡉⠒⠓⠒⠒⠂⠐⠒⠒⠒⠒⠐⠒⠒⠀⠒⠂⣀⠐⠐⣛⣉⡤⠊
⠀⠀⠀⠀⠀⠒⠂⠀⡀⡐⠀⠄⠀⠀⡑⠀⠄⣀⢀⠀⠀⣠⠄⠀⡄⠐⠒⢛⡋⠀⠈⠃⠉⡤⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡊⠉⢁⠀⠀⢀⠮⠒⣄⡴⠐⠒⠀⣰⠧⠃⡈⠐⠳⡄⠘⠪⠧⠀⠀⣀⠐⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠈⠉⡀⠀⠄⠀⢀⠀⠀⠀⣀⠐⠀⠀⠀⠉⠀⠒⠀⠐⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⢠⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⡀⢀⡀⠀⢀⠀⠀⢁⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⠶⣖⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢖⣻⣯⣽⣿⣖⣶⣿⣿⣭⡍⠻⢛⣛⠙⠫⠑⠉⠓⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡿⣿⣻⣷⣟⣿⡷⣿⣿⣷⡊⠁⠔⠀⠀⠁⠁⢠⣀⠀⠀⠀⠤⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⣿⣫⣿⣿⣿⡿⢟⢉⡉⠁⠀⠀⠀⠀⠀⠠⠀⠈⠀⠠⠀⡀⢤⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⠏⠙⣋⡀⠉⠀⠀⠀⠇⠀⠀⠖⠀⠀⠦⠀⠀⠀⣄⠀⠢⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠎⢸⣿⣿⣿⣿⣿⣿⡿⠛⠃⣀⡀⠀⠀⠀⠀⠐⠀⠀⠠⡄⢲⡀⠀⠀⠆⠀⠀⠀⠀⠄⠀⠀⠹⡆
⠀⠀⠀⠀⠀⢸⠀⣾⣿⣿⣿⣿⣿⣿⣏⠁⠶⠕⢠⡀⠀⠀⠈⠓⠀⢠⠆⠉⠀⠀⠈⠃⠀⠘⠀⠈⠀⡀⠹⠉⠀⣷
⠀⠀⠀⠀⠀⠸⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣥⡤⠀⠁⣤⡀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⡀⠀⠀⠘⠀⠉⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠈⢢⣤⣌⣉⣙⣉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣇⣀⣠⣤⣤⡶⠖⠈⠀⠀⢠
⠀⠀⠀⠀⢠⠊⠈⢛⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣟⣛⣋⠛⠛⠿⠿⣿⠿⢿⠛⠓⠚
⠀⠀⠀⠀⠈⠉⣘⣧⣄⣤⣾⣿⣷⣶⣽⣌⠈⠙⠟⠉⣨⣾⡿⢿⣶⣤⣄⣈⠉⠛⠻⠿⢿⠛⣻⣶⣶⣾⡓⠦⣌⠐⢤
⠀⠀⠀⢀⠎⠁⠀⠑⠋⠉⠻⢿⣿⣿⡛⠿⣆⣀⣤⠞⡉⠀⠊⠁⠛⠛⣻⣿⣿⣷⠶⣤⣀⣴⣯⣭⣤⣉⡉⠀⢻⡒⠲⠃
⠀⠀⠀⠘⠖⢲⠞⠋⠉⠉⠙⠛⠛⠋⢹⣷⣌⠁⠀⠁⠀⠀⣀⡤⠶⠛⠿⠿⢝⠓⠀⠈⠉⠉⡉⣀⠠⠈⠈⠛⢋⣻
⠀⠀⠀⠀⠀⠡⣀⣄⢀⠀⣀⠀⣄⣤⣔⣥⣛⠳⣦⣴⡶⠛⣿⣴⣉⢀⢀⣠⣤⣤⣴⣴⣶⣿⣿⣿⣿⣦⣴⣴⣾⠟
⠀⠀⠀⠀⠀⢀⡿⢛⣿⣿⣿⣿⠿⠿⣿⢿⣿⣿⣿⣶⣶⣶⣿⡶⠿⢿⣿⣛⣛⣋⣭⣥⣶⣿⣿⣿⣷⣾⣶⡴⠿⣄
⠀⠀⠀⢐⠦⠼⣆⢈⠛⠛⠿⣿⣷⣤⡀⠀⠀⠀⢀⡤⠐⢀⣠⣴⠾⠿⠿⠿⠿⠿⠋⠉⠉⠉⠉⠁⠀⠀⢀⣠⣤⣿⣛⠋⣱
⠀⠀⠀⢨⣁⣰⣿⣿⣶⣶⣶⣿⣿⣿⣷⣄⠀⠘⣡⣴⣾⣏⣭⣥⢀⡀⠀⠀⠆⢀⣀⠀⢀⣠⣷⣿⣧⣾⣿⡿⡿⢉⡙⣾⠁
⠀⠀⠀⠀⠉⠙⣧⢙⣿⣿⢿⣿⣟⠙⠛⣿⡷⣿⣿⡿⠿⢿⣿⣿⣿⠿⠿⣷⣶⣿⠿⠿⠿⣛⣻⣿⣿⠏⣉⣤⢦⠏⠙⠁
⠀⠀⠀⠀⠀⠀⠸⡌⢿⣿⣿⣿⣟⣴⣿⣿⣿⣿⣿⣷⡶⠶⠶⠶⠶⠶⠶⠿⠾⠷⠶⠛⠳⠼⠋⠛⠿⠚⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⣿⣿⣿⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠆⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣷⣾⣧⣦⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣍⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡄⠀⢠⡀⢹⠀⣀⠀⠀⠰⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⢻⡦⠀⢸⡇⢸⠀⡏⢠⢶⠀⣿⠁⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠳⣘⡁⠈⡟⠃⣸⡀⠃⣼⠟⢠⡟⢠⠀⣃⡀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⠷⢄⢹⡆⠀⣦⠀⣾⡇⠈⠙⠀⡜⠀⡴⢰⡏⠀⡈⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡄⠈⠀⢧⠀⢹⡖⠙⣧⠀⠀⣰⠁⠀⡴⠛⡀⣴⡇⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣧⠀⡄⠈⡆⢘⡇⠀⢡⠀⡤⢯⡄⣰⣿⢠⠋⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠁⠀⠀⠀⢻⡀⠥⠘⠛⠀⢸⠀⠀⡞⠀⣿⡿⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠚⠧⠀⣀⣸⣄⢰⡯⠘⠋⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⣻⠟⣯⡍⢛⠟⠉⣭⣟⣹⣿⡟⣶⠶⢦⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣯⣔⣸⣿⣿⣿⣶⢶⠛⠛⠛⣦⣄⡈⠉⠛⠚⠛⣛⣥⣯⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠤⠀⣆⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠾⠿⠛⣛⣯⣿⣿⣿⣿⣿⣶⠿⠿⠿⠶⠶⢿⣿⣿⣛⣋⡛⠃
⠀⠀⠀⠠⠟⠉⠉⠛⠛⠳⠶⣤⣤⣄⣀⡈⠉⠑⠂⠠⠀⣀⠀⠀⠀⠀⢀⣁⣀⢤⣤⣤⠤⣤⠤⠶⠯⠭⢿⣾⣉⡉⠉⠉⠉⠉⠛⣻⠁
⠀⠀⠘⣿⠛⠓⠒⠦⢤⣌⣀⠚⢋⡩⠟⠛⠻⠷⣦⣤⣄⣀⡀⠀⠒⠺⠿⢿⣧⡀⠀⠀⠀⠀⠀⣠⣶⣞⣋⣉⣉⣩⡟⣛⣿⣶⣤⡅
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠦⡈⠢⠐⠊⠉⠙⠛⠿⢶⣶⣤⣠⡈⠙⠂⠀⢀⣴⣿⣿⣿⣯⣝⣻⣯⣭⣽⣽⣿⣥⣬⣥⡄
⠀⠀⠀⠈⣿⣧⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⢄⣈⠃⠠⢭⠙⠻⢶⣦⡄⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠇
⠀⠀⠀⠀⠈⠹⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠂⠰⣁⠊⠍⠁⠺⠷⠄⠤⠀⠀⠀⠀⠤⠀⠀⠐⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠙⣦⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⣤⣄⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠶⠤⠤⠤⣤⣀⡀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⢿⢿⠍⠃⠚⠫⠛⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⢿⡟⠁⠀⠀⠀⠀⠘⠀⠀⠀⠉⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣃⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⢐⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣆⢊⣠⡄⠀⠠⣄⢰⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣶⣴⣶⣿⠿⡷⢿⣏⡙⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⣿⣿⠟⠛⠿⠉⠉⠠⢀⠹⠟⠛⢻⣿⣿⣧⣶⣧⣬⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⠷⠶⠴⠦⢤⠤⠄⠀⠤⠤⠾⠿⠿⠟⣱⣿⣿⣭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢛⣋⣤⣴⣶⣌⠛⠛⠋⠙⠉⠉⢉⣥⣶⣤⣄⣼⣿⣿⠟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⠯⢉⡛⣿⣿⣿⣧⡀⠀⢀⡴⣿⢿⣟⣩⣿⣿⣿⢿⠿⣿⡳⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠗⣤⠞⡯⡣⠎⣠⣝⢶⠏⠇⢀⡐⠟⠉⠑⢉⠅⣠⣴⢇⡦⢻⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⣰⣩⣤⣶⣌⣛⠀⣤⡭⢀⣉⣀⡀⢠⠾⠿⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠯⣼⣄⣉⢁⣀⠀⠀⠁⢉⡉⠪⠴⠷⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠈
⠀⠀⠀⠀⠀⠀⠀⢳⠈⢲⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠠
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣤⡀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠈⢿⡻⣿⣦⣙⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠋⢐⣀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢈⣷⣠⣏⣿⣷⣤⣌⣛⠛⠒⢦⣤⡈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢲⠀⠠⣦⠀⣦⢈⠉⢈⣠⣠⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠙⠻⣾⣿⣟⣿⠉⠩⠛⢶⣾⣧⣤⣽⢿⣏⠻⠂⡴⢦⡜⡐⠆⢀⣰⠞⣰⢺⣖⠶⠃⣁⣄⠈⢁⣼⢿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠂⠀⠉⠙⢷⣧⣤⣈⡈⠝⠛⠛⠿⣿⡶⣾⢷⣶⣆⣤⢶⣀⣠⣴⣿⣈⣀⣶⠾⢟⠥⠞⢋⡰⠛⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠨⣍⢹⣿⡿⠶⢾⣤⣿⣤⣿⣾⣿⣿⣧⣿⣾⠶⠟⠛⠛⠉⠁⠀⠀⠀⠈⠁⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⣠⠖⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠙⠛⠛⠛⠐⠃⠒⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠀⠒⠢⠤⠤⠤⠄⣄⣀⣤⣀⡠⠤⠤⠤⠔⠒⠚⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠦⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⣀⠤⠔⠂⠀⠀⠀⠀⠀⣀⣀⡀⠠⠤⠤⠄⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡁⠔⠈⠀⠀⣀⡠⠤⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠄⠀⢀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠉⢒⠒⣋⣞⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣠⡀⠀⠀⠀⠀⠀⠀⣠⠦⢤⠀⠀⢀⠁⠈⠁⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠄⠠⠚⢡⠀⠄⠇⠰⠂⢷⣀⠤⠥⠤⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⠀⢹⣈⠦⣀⡀⠖⠑⠀⠂⠀⠀⠀⣉⡀⠠⠆⠀⡀⡀⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠀⢀⢦⠀⠀⠚⠁⠀⠀⡠⢀⣀⡤⠖⢈⣀⢀⠀⡔⠂⣂⠠⠀⠒⢉⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠠⠬⠄⠤⠘⠙⠒⠀⠀⠈⢁⣤⡤⠤⠀⠀⢀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠒⠖⠒⠒⠀⠉⠁⠀⠀⣀⠄⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⢤⠐⠂⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠘⠓⠒⠂⠉⠉⠉⢂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠘⠦⠀⠀⠀⠀⣀⠀⢀⣀⠀⠤⠤⠤⠤⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠀⠠⢠⡤⠄⠠⠶⠀⠀⣀⠠⠊⠀⠐⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠂⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢄⢀⠀⠁⠑⠒⠀⠠⣀⣀⠈⡶⠀⣀⠠⠂⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠱⡀⠀⠀⠀⠈⠁⠀⠒⠒⠒⠒⠒⠀⠈⠁⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠈⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠙⠓⠶⠤⠤⠤⠤⠤⠶⠒⠚⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠻⡟⡻⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠀⠉⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⢠⣤⠀⠁⠈⠁⠒⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠴⠰⠀⠀⠀⡀⣀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠆⠆⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⣄⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢔⡠⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡔⡄⠀⠀⠀⠘⠘⠁⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⠉⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠰⠄⠦⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢐⠈⠁⠄⠬⠊⣥⢌⠁⡉⠉⠉⠉⠉⠉⠉⢉⠁⠀⠀⠀⠀⠒⠒⢒⠒⢲⠒⢒⠒⠒⢒⠀⣀⣐⠂⠈⠁⡉⠹⡄⣀
⠀⠀⠀⠀⠀⠀⡀⠅⠀⡃⢠⢴⠄⠀⠓⠚⡀⠄⠠⠀⣤⠌⢁⢱⡀⠀⠀⠀⢠⣄⣊⡒⠉⠀⠁⠈⣢⣄⠠⡊⣉⣢⡀⣈⡀⣱⡍⢢⠇
⠀⠀⠀⠀⠀⠀⢇⢐⠉⠀⡧⠤⡴⠄⠀⡸⠀⠀⠀⠀⢀⡀⠀⠀⠈⢉⢀⣈⢁⡀⡀⢀⡀⠀⠈⠀⠀⢩⠐⢧⣀⢀⣀⢀⣀⣈⠈⠁
⠀⠀⠀⠀⠀⠀⡾⠀⡇⢀⠃⠈⠒⠂⠁⠀⠄⠀⠀⠠⠀⠁⠂⠀⡄⠐⠊⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠉⠁⠘⠲⠀⠓⠃⠘⢂
⠀⠀⠀⠀⠀⠀⣟⠚⠂⠁⠀⠀⠀⠐⠂⠀⠀⠤⠀⠀⠀⠀⡈⠈⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠈⠠⠄⠀⢸
⠀⠀⠀⠀⠀⣘⢀⣑⠤⠠⠄⡠⠔⠢⠄⠀⠄⠀⠤⢀⣤⠤⣀⠀⣀⠀⢀⣀⣃⡀⣀⣀⠠⠄⢀⣀⠀⢄⣄⣀⠀⠀⠀⠀⢠⠤⠋
⠀⠀⠀⠀⠀⠉⠙⡤⠐⢤⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡈⠁⠒⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⢀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢆⡰⠉⡆⢀⠰⡉⠫⢄⠀⡰⠁⠘⢀⠠⡀⢰⠓⣀⠥⣐⠤⡀⢀⣔⡁⠤⡄⠀⡎⠑⠨⡱⢈⠆⠑
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠀⠙⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠤⠄⠀⠓⠃⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉





⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⣶⠒⠋⠩⠋⠉⡉⠉⡉⠉⢉⠉⠉⢙⠛⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⣠⠴⣚⡉⠀⠀⠀⠁⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠃⠠⠄⠀⠐⠀⠐⠋⠓⢦⡀
⠀⠀⠀⡼⢋⠀⠀⠀⠀⠀⠃⠀⠈⠁⡀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠐⠀⠀⠄⠀⠈⠀⣙⢦
⠀⠀⡾⠁⠁⠀⠈⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀⠈⢧
⠀⢸⡗⣔⠀⡀⠀⠀⠀⢀⠀⣀⠀⡀⣀⠀⣄⣠⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⡇
⠀⢸⣿⡿⠾⢥⣷⣶⣤⣿⣶⣿⠿⠿⠟⠛⢛⡋⣉⣋⣉⠉⠛⢛⣿⣗⡒⠒⣶⠦⠤⢤⣤⣤⣀⣀⣠⠃
⠀⠀⠻⣿⣿⣿⠿⠟⠛⠉⢁⡤⠚⢉⠍⠉⠁⠉⠁⠀⠈⠉⠉⠉⣀⠀⠀⠈⠀⠉⠉⠲⢤⣤⠤⣄⣬⣵⣤
⠀⠴⢺⣵⡾⠛⢉⠉⢙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠠⠀⠀⠀⠀⢀⠍⢸⡄
⠀⠀⠘⣧⣤⣄⠀⢀⢈⣀⣴⣾⣯⠿⠷⠶⠶⠶⠶⣆⣠⡄⠀⣤⣤⠾⠿⠶⢶⡆⠀⡀⣠⣙⣀⣀⣀⡼⠁
⠀⠀⠀⠀⣿⣿⣃⠏⠉⠀⣀⣀⣀⣀⣠⣤⠤⠤⠤⠼⠿⢿⠼⠿⠋⠓⠒⠒⠶⠿⠼⢍⣉⣈⡉⢉⡏
⠀⠀⣤⣞⣻⡟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠈⠉⠢⡀
⠀⣾⠿⠿⣿⠟⠻⠶⢦⣄⡀⠀⠀⢰⡀⠋⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⡄⠀⠀⠀⠈⠙⠚⢻⡄⢀⣄⡖⢻
⠀⢻⣤⣤⡷⠀⠠⠀⠀⠉⠛⢶⣄⡀⠁⠀⢀⡴⠋⠀⡀⠒⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠻⠼⠈⠄⢠
⠀⠀⣽⣿⡷⠶⣶⣶⣶⠶⣶⣶⣼⣿⣷⣠⡯⣤⣤⡴⠾⠶⢶⡶⢲⠶⢶⣤⣴⠶⣤⡤⣤⢴⡷⣶⣶⣶⠋
⠀⠀⠛⣿⣷⡼⠁⠉⠁⠀⠸⣄⡜⠛⠛⠛⠁⢸⡇⠀⠚⠦⠞⠀⢸⣤⠜⠀⠉⠛⠁⠀⢿⡀⢰⠏⠙⣇
⠀⠀⠀⢻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⢠⡇
⠀⠀⠀⠘⢿⣿⣿⣷⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠳⠦⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⠤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣿⣟⣛⣟⣛⣻⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠈⠉⠉⠁⠁⠀⠀⠀⠉⠉⠒⠦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⣀⣀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠦
⠀⠀⠀⠀⠀⠀⣀⠀⠙⠒⠢⠶⣖⡒⠖⠒⠒⠒⠖⠖⣾⣿⣿⠿⠿⠛⠛⠐⡰⠛⠋⠉⠉⠉⡠⠀⠤⠀⠀⠄
⠀⠀⠀⠀⠀⠋⠉⠇⠀⠀⠀⢀⡤⠿⠇⠲⠶⠶⠛⠛⠉⠀⠀⠀⣀⣀⠶⠟⠢⢀⠀⡀⢀⡄⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠷⠞⠉⠓⠠⠤⣤⣀⣀⣀⣀⣀⡤⠴⠒⣿⡷⠶⢤⣤⢤⣤⡤⠦⠴⠐⠂⠈⣀
⠀⠀⠀⠀⠀⠀⠀⢪⣸⡄⠀⠀⠉⠀⠀⣀⣈⣭⠥⡄⠤⠐⡊⠁⠀⠀⠀⠂⠀⠈⠉⠀⡄⠋⠄⠀⠃⢹
⠀⠀⠀⠀⠀⣀⠀⠀⠈⠃⠀⢀⣤⣶⣟⡻⣀⣀⣀⡈⠰⠀⢤⡀⠀⠀⢠⠤⠤⠀⠁⠠⠆⠀⣂⡴⠒⠀⠀⢠⠤⠆
⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠴⢋⣄⠀⠉⠉⠉⠉⠉⡉⠉⠀⠒⠂⠓⠀⠀⠘⠂⠃⠀⠀⣉⠉⠁⠀⣀⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠐⠋⠙⠀⠀⢀⡼⠛⠛⣿⡇⠀⠀⠀⠠⠞⠛⠛⠢⠀⠀⡞⠙⠳⠄⠘⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠐⠒⠁⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⡄⠤⣤⣤⣤⣤⣤⣤⣠⢄⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠟⠋⠀⠒⠀⠀⠀⠘⠁⠀⠀⡉⠁⠁⠀⡁⠛⠒⠲⡶⣶⣤⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⡖⠼⠁⠀⠀⣀⠄⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⠙⠓⠀⢋⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠞⠛⡁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠀⠀⠁⠁⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠃⠀⠀⢀⡀⠀⠘⢽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢨⡿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢲⠄⠈⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣱⣿⣶⣾⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⠿⣶⣦⣤⣀⣀⣀⣀⣤⣀⣀⣀⣤⣤⣀⠀⡀⢀⣀⣀⣀⣀⣀⣤⣤⣀⣤⣤⣤⣤⣶⣾⣿⣿⣿⠿⣟⡛⡭⢄⣀⡴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣆⡈⠉⠉⣛⣛⠛⠛⣛⣿⡛⠛⡛⠿⢿⢿⣿⣿⣿⣿⣍⣩⣭⡭⠍⠵⣬⠉⠁⢀⣶⠟⢉⠾⠛⢽⡲⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠶⠚⠉⠺⡿⣿⣙⡛⣿⣿⣿⣟⢻⣿⣿⣷⣄⣀⣤⣴⣿⡯⠾⢿⠽⠺⢿⡿⣧⠖⠻⢮⡙⣿⡿⢿⡷⠃⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣋⣁⡀⠀⠒⠛⠛⢿⠿⣷⠶⢿⣿⠿⣿⣿⡟⠛⠒⠛⠚⠁⠠⠤⠀⠚⠁⠀⠀⠀⠈⠀⠀⠀⠀⣀⣤⣤⣶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣌⣿⣷⣦⣤⡖⠺⠒⠀⠀⠠⠖⠄⠩⠚⠁⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⠿⣻⣿⣏⢹⡏⣠⣿⢉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣈⠻⠿⣏⡉⠿⡷⣦⡀⠀⠀⠀⠀⣠⣴⣿⡟⣉⣭⣿⡟⣡⣿⡟⣩⡿⠋⢩⣽⣻⣿⢷⡾⠟⢻⣿⡿⣱⣿⢋⡼⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠠⠤⠟⠻⠝⢷⡚⢿⣿⠶⣶⣿⣿⣧⣀⣠⣾⣿⠿⠻⣿⣿⢟⣻⣿⠿⣫⣴⣿⣧⣴⣿⠟⣸⡏⢸⣷⢶⣾⣿⡵⣟⢯⡜⠙⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡠⠋⠀⠁⠐⠒⠀⠛⠛⠿⠟⠿⠛⢃⢀⡽⠉⣿⣉⠛⣷⠚⠋⡭⠉⠉⠱⠾⠙⡇⠛⠋⠛⡿⠁⣯⣿⣠⣬⣶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠙⠃⠐⠚⢤⣄⣶⡶⣴⣶⣾⣿⢿⣷⣦⡤⣮⣤⣅⣤⣴⣦⣶⣶⣶⣶⣾⠿⠚⠻⠟⠷⢶⣿⠟⠉⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⢀⡇⢈⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣹⣶⡂⢀⣠⣾⣦⣿⡿⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠒⠚⠒⠒⠲⠖⠂⠰⠶⠶⠶⠖⠾⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⡤⣖⣦⠶⠚⢋⣁⣤⣴⠶⠶⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⠶⠶⣮⣭⣛⡲⢤⡀
⠀⠀⠀⠀⢀⣴⠞⢋⣥⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣮⣓
⠀⠀⠀⠰⢋⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⣰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄
⠀⢀⣠⠼⠛⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠾⠻⢥⣼⠁
⠀⠘⢤⠀⢰⣏⣇⣤⢉⡽⡿⠛⠿⠶⠶⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠾⠿⢟⣛⣛⢉⡭⢤⠔⡆⢀⡶⠼⠂
⠀⠀⠘⣟⠶⠯⢍⡈⢹⣯⣅⢰⣲⡄⢴⠚⣇⡴⢦⡀⠀⢠⣤⠀⢠⢶⣀⣀⠀⣼⢻⣌⡇⣺⢌⣹⢃⠂⠹⣋⣽⣿⠄
⠀⠀⣤⣸⠲⢦⣤⣽⢷⡄⠻⠚⠻⠤⠞⠀⠈⠀⠸⠶⡦⢈⡟⠒⠋⠈⢉⣿⠴⠟⠒⠶⠶⠿⠿⠖⠒⠚⠋⢁⡸⣏
⠀⠀⡇⣿⠀⣸⠀⡏⠓⢻⡄⠀⠀⠀⠀⠀⣀⣠⡤⠴⠿⠯⠤⠴⠶⠛⢻⡁⠉⣓⣒⠶⠶⠦⢤⡴⠶⠖⠚⠋⠀⣼
⠀⠀⠙⠹⣄⠙⠞⠡⠂⠀⢷⡀⢀⣠⢶⡿⠿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠓⠽⠋⠁⠈⢷⠀⡎⠉⠀⠀⠀⠀⢀⣴⠿⠃
⠀⠀⡠⠦⠜⢻⢶⢦⣤⣄⣈⣙⣉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠤⠃⢀⣀⣠⡤⠶⠋⠙⣷
⠀⠀⢙⡰⠂⠘⢎⠓⠾⢭⣍⣉⣛⣛⣻⣿⣿⣿⡿⠶⠶⣶⣶⣖⣒⠒⠒⠒⠚⠛⠛⠛⠛⠋⢉⡽⠁⠀⠀⠀⠸⣏
⠀⠀⠘⠒⢻⣰⣾⢙⡲⠤⣤⣀⣈⣉⣉⣁⣀⣀⣤⠤⣴⣚⠁⠀⣩⣍⠛⣲⣦⣄⡀⠀⠀⣠⡾⢣⣠⢤⢸⢛⡟⡃
⠀⠀⠀⠻⣌⠷⣷⠻⣇⡞⠶⠟⠁⡸⠁⡞⣣⢰⠛⠞⣩⠟⣠⡌⢧⠘⠋⠩⣧⢦⣍⣛⣛⣿⠀⠀⠁⠈⣩⡟⣸⡇
⠀⠀⠀⠀⠙⢷⣌⠛⠶⣤⣀⠀⠀⠘⠚⠁⠙⠃⠀⠘⠳⠖⠋⠛⠋⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⣠⡾⠋⣴⠟
⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠉⠛⠲⠶⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠛⠉⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣠⠀⢀⠀⠐⠖⠀⠀⠀⠚⠖⠀⠠⠀⠠⣄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠉⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⣀⠀⠰⠆⠀⠀⠀⠛⠒⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠁⠀⠀⠀⠀⠰⠼⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠺⠆⠀⠀⠀⠀⠙⠤⡀
⠀⠀⠀⠀⡐⠀⠈⠉⠀⠀⠀⠦⠋⠀⠀⠀⠀⠠⣈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⠀⢠⡄⠀⠀⠀⢀⣰⠀⠀⣐⡄⢅
⠀⠀⠀⢨⠇⠀⠀⢄⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⢠⡤⠂⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠉⠙⢒⠢⠄⠀⠀⠀⢀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⡀⠄⠀⠒⠀⠀⡒⣃⡠⠤
⠀⠀⠀⠀⢸⢥⣒⣒⣒⣀⡠⠤⠭⠤⢁⣀⣀⣀⣀⣀⣈⣛⣛⣛⣛⣉⠉⡙⣃⢀⣀⣀⣉⠑⠤⣄⣀⣈⣀⣁⣀⣀⣀⣀⠽⡋
⠀⠀⠀⢀⠝⠠⢀⠀⠀⠍⠉⢉⠉⡙⡓⡒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⡉⡉⢉⢉⠉⠉⠉⠄⠂⠐⠨⠧
⠀⠀⠀⡼⣶⠠⣄⢀⣀⠙⡋⠀⠀⠀⢣⣧⠔⠐⠸⠀⣥⡅⠀⠀⠀⠀⢀⡥⠁⠀⠘⠀⢠⠆⠃⠂⠀⠘⠖⢁⣀⣀⢀⢤⠴⠒⢢
⠀⠀⠀⠻⣌⠑⣭⢢⠌⢶⡝⢍⠙⣕⠺⣥⠰⠒⠛⢗⠲⡢⠤⠄⠖⠒⠒⠒⠲⠒⢒⠒⠶⠒⠒⠒⠈⠋⠉⠁⠀⠀⠀⢁⠀⠀⡼
⠀⠀⠀⠀⢀⠉⠒⠱⡬⢢⡉⢢⣛⣄⡱⣬⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣊⡀⠀⢀⣀⡲⡶⠖⠀⣤
⠠⠀⠋⠉⢉⠉⠑⠐⠆⠀⠬⣥⣀⠈⠉⠛⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⢉⣀⣀⣈⣉⣁⣀⣩⣤⠶⠋
⠀⠒⠒⠶⠀⠀⠄⢀⡡⠄⣀⡤⠀⠀⠉⠑⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠐⠐⠂⠶⠶⠫⠉⠀⠀⠹⠄⠈⠉⣀⠀⠀⠰⠛⠉
⠀⠀⠀⠀⢀⣠⣪⠤⠧⠀⠀⠆⠀⢀⡔⢙⡄⠀⢀⠞⠉⣋⡇⠀⢀⡍⢳⠀⠀⣟⣁⢦⡀⠀⢠⠀⠠⡀⠀⠘⠀⠀⠘⠨⣵⣄
⠀⠀⠀⠀⠸⢁⠀⠀⡥⡉⠀⢂⣠⠎⠶⠉⠹⠤⠧⠇⠉⠀⠐⣄⡼⠔⠋⠡⠤⠀⠀⠉⢳⠄⠌⠍⠛⠚⠢⠔⠀⣬⡄⠉⠠⡞
⠀⠀⠀⠀⠀⡈⡃⠀⠀⠀⠀⠨⠉⠃⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⢀⠀⠀⠫⠁⠀⠰⠆⠀⠠⠆⠀⠈⠠⠖⢀
⠀⠀⠀⠀⠀⠐⢦⡀⠘⠓⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠋⠀⠀⣤⠀⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠒⠄⠀⠻⠇⣀⣀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⡤⠦⠀⠀⠰⠂⠀⠀⠀⣤⡄⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣘⣛⣀⣀⣀⣀⣠⣄⣉⣁⣀⣀⣈⣉⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⡛⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠖⠂⠀⠂⠀⠀⠒⠒⠠⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⣯⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠹⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢰⣿⣂⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠚⣳⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣾⣷⣾⣿⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡷⢬⣭⣙⣿⣿⣿⣿⣯⣭⣉⣉⣀⣿⣿⣿⣤⣍⣩⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣖⡈⠁⠁⠀⠉⠉⣾⡉⠻⠛⣛⣻⡿⢿⣿⣿⣿⣿⣿⣿⠿⣫⡬⣇⠀⢆⡀
⠀⠀⠀⠀⠀⢀⠐⣿⡻⣷⣶⣶⡀⠀⣀⠈⠉⠀⠀⣨⣽⣶⣾⡿⣿⣿⣿⡿⣷⡜⣫⡴⣿⡃⣜⠁
⠀⠀⠀⠀⠀⠉⠙⣿⣷⡦⢿⣿⡿⠻⢿⣷⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⣟⣛⣻⠟⠒⠃⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠃⣿⣍⣽⣟⣠⣤⣮⣭⣽⣿⣿⣿⣷⣿⣶⣿⣷⣟⣼⣥⣾⣿⡧⠤⠠⠤⠤⠠⠀⠀⠶
⠀⠀⠀⠀⠀⠀⢀⣤⠧⣌⣉⣙⣿⣿⣿⣿⣿⠿⠿⠿⠟⠻⠟⠻⢿⣭⣩⣿⣿⡿⠧⢤⡀⠀⠀⢠⣾⣷
⠀⠀⠀⠀⠀⠀⠙⢪⢳⣤⡂⠀⠀⠀⠈⠉⠻⠶⢶⣶⣶⣶⣶⣾⣿⣿⣿⣭⡥⠤⣴⣄⠹⡆⣰⣿⣿⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠹⣇⢀⠄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠼⠷⢶⣿⣿⣿⣿⣇⣼⣿⣿⠉⠛⠻⣿⣷⣀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣴⣶⣾⣿⣿⢋⢻⣿⣿⣙⠻⢷⣶⣜⠛⠛⠉⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠳⠦⣿⣝⠛⠲⢦⣄⠉⠛⣿⣿⡁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠉⠉⠁⠙⠻⠆⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠲⠶⠿⠛⠉





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀⠰⠒⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⣀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢸⡜⡖⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⢀⠀⠉⠁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠁⠀⢁⠃⠀⠀⠀⠀⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣶⣶⣾⣠⣦⣭⡛⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⢀⣨⣴⣄⣀⣀⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣈⣉⣛⡳⢿⣭⣿⣿⡿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣯⠛⢰⣿⣿⣿⢹⣿⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⣿⣷⣀⠉⠉⠑⠲⠯⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡯⠀⠸⣿⣿⣿⣿⣿⣾⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡿⣷⣿⣿⣿⣷⣄⠀⣀⣀⣨⣭⣶⣤⣡⣾⣿⣷⣦⣤⣌⡇⠀⡀⣨⡀⣈⣹⠾⠟⠻⠃⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢶⣬⡻⢾⢋⠋⢿⣛⠻⣿⣿⣿⣿⢿⣷⣿⢿⣿⡿⢿⣿⡿⣅⠀⣹⠈⠛⡉⠀⡜⠀⢸⣿⣧⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⢿⣷⠏⣠⣧⣤⠿⣶⣉⡿⡿⣿⣭⣿⣿⣥⡤⠾⠛⢅⠙⠛⠁⡶⠀⡘⠉⠡⠀⠋⢀⡧⠤⠠⠜⠁⠀⠈⢙⣳⣶⣦⡄
⠀⠀⠄⣀⡀⠀⠀⠀⠈⠙⢷⣿⣧⣾⣿⡿⠓⠟⠻⣿⣿⣧⣮⣄⢰⣧⣀⣠⣄⡶⠔⠀⠜⠀⠀⠁⠀⠀⡠⣢⠿⠀⢠⣶⣴⠚⡀⢀⣼⣟⢉⣿⠂
⠀⠠⢤⣄⣉⠛⠒⠢⢄⢀⣀⠀⠉⠙⠛⠷⠶⢶⣶⣿⣿⣿⣿⡿⢀⣿⡿⠃⠈⢄⡀⢀⢀⡤⠀⢒⡀⢠⡞⢀⣠⡖⣻⠟⠀⠀⠘⠚⠿⣿⣯⣁⡀
⠀⠀⠀⠀⠉⠙⠛⠾⠶⣦⣄⡉⠀⠒⡤⢤⣄⡀⠀⠀⠀⠉⠁⠈⠉⠀⠑⠶⣀⣠⠀⠀⣴⠁⠀⠀⣠⡶⠟⠋⣁⣉⣀⠉⠀⠀⠀⠀⠀⠀⠀⠉⣍⡙⢳⣶⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⠿⣶⣤⣀⡉⢒⠢⠄⠀⡀⠀⠀⠀⠀⠈⠉⡳⢞⣀⣠⡾⠋⢁⣥⣴⣿⣿⣿⣍⡉⠉⠒⠒⠪⠥⣤⣄⣀⡀⠴⢊⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⢦⣤⣄⣀⠀⠐⠤⣤⣀⣀⠠⢈⣡⠴⠚⢉⣿⠿⠛⠁⠀⠉⠉⠛⠓⠲⠦⣤⣤⣄⣉⣉⣿⣧⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠶⣿⣭⣽⡟⣿⣯⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠾⠿⠿⠶⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⡉⠉⠉⠉⠉⣉⣭⣭⡉⠉⠉⠉⠉⣉⣭⣭⣉⠉⠉⠉⠉⢉⣭⣭⣉⠉⠉⠉⠉⢉⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣦⣄⣤⡾⠋⠀⠈⠹⢦⣄⣠⡾⠋⠀⠈⠙⢷⣄⣠⡴⠋⠁⠀⠙⢷⣤⣠⣴⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠙⠛⠛⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⠛⠛⠛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣤⣀⣀⣠⣬⣽⠿⠶⢦⣤⣀⡀⠀⢀⣴⠞⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⢰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⣾⠃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠒⠚⠛⠓⠒⠲⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⡉⠀⠘⠃⠠⠄⠈⠁⠠⠄⠙⠀⠀⠆⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠀⠀⢁⠀⠈⠁⠀⠈⠁⠀⢠⠀⠀⠉⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⣙⡒⠦⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠤⢶⣒⣋⣁⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣟⠯⢍⣓⣲⠦⢤⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⣉⡥⠴⠶⠭⠭⠒⣩⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⣷⣶⣶⣶⣶⣾⣿⣿⣷⣦⣄⠲⠔⣂⣴⣾⣿⣿⣶⣶⣶⣿⣿⣿⠿⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⣄⠈⠛⠉⠛⠛⠛⢻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁⠀⣈⠁⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣤⣶⣶⣶⣄⣀⣤⣄⠀⠤⠀⣀⣀⡀⠀⢀⣴⣶⣶⣮⣥⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⠦⠤⠤⢤⡤⠤⠤⠤⠤⠶⠶⠖⠚⠛⠉



⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⣀⣠⣤⡄⣀⣀⣀⣔⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠒⠈⠩⠁⡯⠐⠀⠀⣀⠀⠀⠓⠚⠁⠈⠉⡟⡝⢒⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⢁⠀⡀⠀⠀⠀⠈⠀⠀⠀⠐⠆⠀⠰⡠⡄⢄⡇⠀⠑⠁⠀⠒⠃⠈⣑⠪⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠀⠦⠋⠘⠁⠀⠀⠀⠀⠀⠲⠉⠀⠀⠀⠓⠁⠔⢢⠀⠀⠀⣀⠆⠀⠄⠠⠃⢰⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠑⣳⠀⠀⠀⠐⠃⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⠤⠀⠀⡔⡄⠘⣼⠆
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⡀⠀⠠⣤⠀⠀⠀⠀⢆⡄⠀⠀⠀⠐⠥⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⢠⠉⠀⠀⠉⢋⡱⠀⢰
⠀⠀⠀⠠⡞⠁⢑⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡠⣷⣾⣷⣿⠉⡆⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⠀⡠⠀⢰⣶⠢⡀
⠀⠀⠀⢣⣿⣿⣿⠏⠐⣿⣾⠨⣤⡾⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⣴⣤⡸⢿⣠⡿
⠀⠀⠀⠀⠈⣷⣶⣲⣄⣀⣥⣀⢀⡷⠶⢿⣿⡟⠚⣰⠶⣶⡂⢲⣤⣖⠐⡦⠐⣿⠈⣡⣴⡧⢤⣎⢑⠶⠶⢇⢰⣿⣭⠘⢛⣅⠀⠘⢄
⠀⠀⠀⠀⠀⠻⣿⣿⣏⠁⠀⠈⠁⠀⠒⣶⣿⣿⡟⠁⠀⠙⣷⠚⠖⠛⣿⣿⣶⠿⣤⣟⡭⠃⠈⢻⣾⣤⣤⣿⣶⡈⢁⣠⣿⣿⣗⣀⠌
⠀⠀⠀⠀⠈⢱⣦⠈⠉⠉⠛⠛⠛⢛⣉⣩⣭⣿⣤⣀⣀⣠⣿⣷⣶⣾⣿⣿⣿⣭⣉⡉⠛⠤⠄⠚⠛⠉⠉⣹⣿⣿⣿⣿⣿⣿⣦⠃
⠀⠀⠀⠀⠀⣾⣿⡄⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⡃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡀
⠀⠀⠀⠀⣾⠻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣛⣉⣭⣭⣤⣿⠛⠛⣿⡷⡰⡁
⠀⠀⠀⠀⠹⡏⢘⣿⠙⣦⠈⣭⠭⠍⣡⡤⣤⣶⣾⣿⠗⠠⣭⣌⣉⣉⣉⣉⣉⣽⡽⣾⣿⡛⠉⢹⣿⡿⠠⣿⣿⡿⠃⠀⣿⣛⡙
⠀⠀⠀⠀⠀⢹⣏⣉⡘⠻⣿⠋⢠⣤⡄⠀⠙⠟⠉⢸⣧⣨⣥⠀⠻⣿⠿⣇⠉⣯⠈⠛⢫⡅⢠⡶⠎⡷⠀⠉⠋⠴⣶⣦⣽⣿⡿⠊
⠀⠀⠀⠀⠀⠘⡉⠉⠓⠒⠛⠛⠛⠛⠿⣿⣶⡀⢰⣦⣴⣿⡃⠠⣤⣆⣤⣤⣄⣙⠥⣦⣤⣤⣼⣿⣬⣿⠿⢿⣷⡴⠞⠋⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠖⠋⠙⠿⠷⠖⠛⠛⠉⠛⠿⠿⠾⠛⠉⠁⠁⠀⠀⠀⠀⠀⠀⢄⣀⣲⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠠⠨⠜⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠒⠒⠂⠂⠀⠀⠄⠤⠤⠀⠄⠀⠒⠂⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠖⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣀⠋⠁⠀⠈⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢁⡀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠊⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣯⠁⠈⠀⠀⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠘⠤⠠⡘⠂⠹⠀⣿⡆⡄
⠀⠀⠀⠀⠀⠀⢠⣾⡰⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠁⣠⣤⣶⢇⣿⣷⣿⡆
⠀⠀⠀⠀⠀⠀⡀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠷⢛⣋⣥⢞⣿⡍⡥⠃
⠀⠀⠀⠀⠀⠀⢅⠋⢾⢿⣿⡿⠗⠶⣶⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡞⠻⣿⠻⠌⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢆⣼⡿⡏⠀⠀⠈⣷⣶⠿⡟⠛⠻⣯⠹⣿⡿⠙⣿⣯⠉⣻⣿⣿⡦⢻⡟⠈⢧⣻⣿⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⠀⠳⢶⣾⠋⠃⠀⠀⠀⠂⢁⡄⠇⠁⢀⡿⣏⣼⠜⠀⠉⢁⣾⢷⣴⣾⢿⣿⣿⣥⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢹⣿⠓⣦⣀⠈⠑⠒⠀⠀⠀⠀⠉⢣⡴⡶⢟⣩⠿⠿⠷⠦⠴⠛⠛⢉⣠⣴⣿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠈⠉⠉⠑⠒⠦⠤⢤⣤⣬⣽⠶⣿⡛⣻⣷⣶⡤⠤⢖⣶⣿⣿⣿⣭⣧⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣶⣾⣿⣿⣿⣿⣿⢶⣶⣭⣝⡒⠒⠀⠰⠒⠒⠺⠏⣼⣿⣿⣿⣿⣿⣿⣿⡋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢟⠛⠿⠻⠿⠿⠿⠿⠶⠦⣀⣀⢀⢰⠟⠛⠛⠛⠛⢑⣲⠲⣦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠉⠀⠀⠀⠂⢋⣁⢴⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢔⣫⡵⠟⠉⢉⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠠⠄⠀⠀⠤⠄⠒⠀⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠒⣒⡒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠛⠃⠀⠀⣀⠀⠉⠉⠓⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢁⣀⠀⠀⠀⠀⣔⣲⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⣠⡄⠀⠘⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢡⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢃⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⠆⠀⠀⠀⠠⢊⠁⣶⠇
⠀⠀⠀⠀⠀⠀⠀⣴⡋⠉⠳⢥⣀⡀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡤⠔⠚⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠉⠙⠒⠦⢤⣀⣀⠀⠀⢤⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⢰⣲⠮⠭⠒⠊⠉⢁⣀⣀⣀⣀⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠖⢚⣻⡆⠀⣀⣠⡄⠈⠉⣩⣹⠟⠓⠒⠒⠒⠒⠛⠉⢉⣉⡤⠤⠶⠒⢚⡋⠩⠉⠁⡤⠀⢻⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠛⠂⢩⣭⣡⡤⠳⠖⠊⠳⣄⠀⠀⠀⢀⣀⡤⠒⢫⡉⢠⣴⣆⠁⠠⡭⠝⠸⢆⣠⣠⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⠿⢿⣦⣤⣿⣅⡁⠈⠳⠟⠄⠸⣄⡤⠞⠉⠔⠻⣄⠺⣗⣀⣀⣉⣤⣤⣴⣶⡶⠿⣛⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡂⠀⠉⠉⠛⠛⠛⠿⠿⠷⠶⠿⠶⠾⠿⠷⠿⠿⠿⠟⠛⠛⠋⠉⠉⠁⠀⢀⡉⠥⢞⣛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢐⣪⣽⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠷⢤⣄⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠄⣀⣀⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠓⠒⠒⠒⠒⠒⠚⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣄⠀⠀⠀⠀⠐⡃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠐⠳⣤⣀⣀⣀⣀⣀⣠⣴⠿⡀⠀⠀⠀⣈⢳⣦⣀⡀⢀⣀⢀⣀⣰⠇⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡀
⠀⠀⠀⠀⠠⠳⠾⣓⣘⣾⢤⣦⠯⣠⣶⡀⠀⠀⠀⢰⣾⣤⣼⣯⣙⠉⢩⣭⣀⠁⠀⠀⠀⢎⣱⠶⣶⡤⣤⣤⣶⢶⡿⠕⠃
⠀⠀⠀⠀⠀⣿⣾⣍⠉⣉⣡⣤⣾⣿⣿⠇⠀⠀⠀⢸⡛⢿⣿⠿⣿⠿⠿⠿⢿⡁⠀⠀⠀⢸⣿⣭⣉⣨⣭⣭⣼⣿⣶⣾
⠀⠀⠀⠀⠀⢹⠿⠿⠿⢿⢿⣿⢛⡿⣿⠂⠀⠀⠀⠘⢧⣴⣶⣯⣽⣯⣽⣻⣿⡗⠀⠀⠀⠸⣝⠛⠻⠿⠿⠿⠟⠛⣩⠟
⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠐⠚⠋⠁⠀⠀⠀⠀⠈⠷⣬⡉⠉⠛⠛⢻⣿⠾⠁⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⠀⠒⠒⠒⠂⠀⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣴⢁⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⡾⡀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠒⠀⡈⠈⠂⣿⣦⢀
⠀⠀⠀⠀⠀⠺⣧⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⣳⡿⠿⡇
⠀⠀⠀⠀⠀⠠⢸⣿⣶⣤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣩⠵⢶⣿⡑⠛⠈
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣻⣼⠿⠛⠻⣏⢻⣿⠛⣿⡏⣻⣿⣿⠝⡿⠉⢆⣾⡆
⠀⠀⠀⠀⠀⠀⣰⣷⡈⠓⠾⣏⠁⠀⠀⠀⣠⠘⠀⣠⣟⣷⡟⠁⢉⣰⣟⠶⢟⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⢳⣿⠙⠶⠤⢄⣁⡀⠀⠀⢠⣖⣩⣽⣾⣛⣛⡉⣉⣡⣤⣶⠿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⠦⣤⣤⣴⣶⣭⣽⣯⣟⣛⠭⠄⠙⠻⠭⢥⠞⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠛⠿⠻⠿⠿⠷⠶⢄⣀⡀⡸⠛⠛⠛⠛⣳⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⣡⣴⣶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⢀⡀⢠⠽⠞⠋⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢸⣿⡇⠿⣸⡿⡿⣿⢿⠿⠿⣿⣿⣷
⠀⠀⠀⢸⣿⣇⣛⣤⣥⣵⣄⠙⣠⣷⣵⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢤⣀⣀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠈⠩⠉⠉⠉⢁⡏
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣨⠷⢈⡰⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠖⠒⠒⠒⠒⠒⠒⠲⠤⠤⣀⣀⠀⢸⣀⣀⣀⡠⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠩⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢹⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⢈⣾⣐⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⡢⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢹⣌⣋⣉⣉⣙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠋⣩⠜⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⡿⠲⠶⠟⠻⣍⠙⠒⠲⠶⠶⠶⠖⠒⠖⣲⢶⣷⣶⠶⡤⠖⠒⠒⠒⣶⣞⠛⠊⣹⠛⠳⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⣀⣀⠙⠒⠛⢷⣄⣁⡴⠋⠉⠉⠀⠀⢈⡻⢷⡤⠊⠙⠳⠛⠀⣀⣉⡈⢁⠴⢆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⠀⠀⣇⢀⠔⠤⣀⣀⠴⠊⢆⠐⠀⠊⠁⠘⣄⠀⠀⡴⠒⠲⠚⠁⠀⠑⠞⠀⢸⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠠⠂⢀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⣀⠈⠉⠐⠄⠀⣀⣀⣀⡂⠠⠄⠉⠀⡀⠀⠉⠒⠀⠀⠀⣀⣠⣤⣄⣀⡠⠊⢉⣥⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠹⡇⠀⢀⣤⣀⠀⣀⣀⠉⠛⢋⠉⠀⠀⠀⠀⠀⠉⠉⠡⡀⢀⡀⣀⣤⣄⣀⡌⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠛⠒⠉⠀⠈⠁⠠⠌⠉⡛⠻⣵⢀⠞⣛⡒⠛⣛⡳⠦⠴⠋⠀⠉⠀⠚⠋⠈⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠒⠒⠂⠀⠒⠒⠲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⢐⠀⠀⠀⠐⠂⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠁⠀⠢⠀⠀⠀⡠⠄⣄⠀⠀⠀⢀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡆⠴⠂⠀⠀⠀⠀⠀⠀⠀⠣⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠁⠀⠀⠋⠀⠈⠓⡂⠀⠀⠁⠀⡀⠀⠁⠀⠀⠈⠂⠀⢀⡄⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⠀⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⣷⣶⣤⣤⣖⡒⠒⠒⠛⠛⠉⠙⠋⠛⠓⠒⠒⠶⠤⣤⣤⣀⣀⣀⣀⣀⣠⠞⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⡟⠁⠀⠀⠀⠈⠍⠙⠒⠢⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣷⡀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⣤⣄⠀⢀⣤⣤⡄⠀⠁⠂⠬⡉⠲⢤⠴⠒⠂⠉⠉⠡⠄⠀⠀⠐⠒⣩⣥⢳⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⠢⣝⣋⠀⠸⠿⠿⠃⠀⠀⠠⣤⣤⠁⠒⠀⠁⣾⡇⠀⠀⢿⣿⠀⠀⠠⠿⣃⢾⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⡟⢇⠀⠀⠉⡉⠉⠉⠐⠒⠒⡖⠒⠒⠒⠒⠒⠒⠒⠒⢒⠒⠒⠒⠚⠋⠉⢩⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⢦⡀⣸⠙⡆⠀⣤⢤⡀⠀⠀⠀⠘⡆⢀⡀⠀⠀⠘⣆⣴⠋⠙⠳⣤⡞⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠁⠀⢳⣀⣸⠆⠘⢦⣀⣀⣀⠟⠉⠹⣄⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣕⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠭⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡔⠒⠒⠒⠒⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⠒⠒⡒⠒⢒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⡔⠣⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠒⣓⡆⠀⠀⠀⠀⣠⡚⠢⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⣊⣳⠄
⠀⠀⠀⠀⠀⢸⣤⣶⣄⣠⣬⣍⠉⢉⣉⡉⢉⣩⣍⣤⣶⣤⣼⣿⠀⠀⠀⠀⠀⠀⢿⣝⡋⠑⣒⣤⣍⡉⠉⠉⠉⣉⣥⣒⣒⣀⣩⣿⣇
⠀⠀⠀⠀⠀⢞⡉⠛⠛⠛⠿⡿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⡋⢠⠇⠀⠀⠀⠀⠀⣎⡙⠛⠛⠻⠿⡿⠿⠷⠤⠾⠿⠿⠿⠛⠛⢛⠃⡼⠃
⠀⠀⠀⠀⠀⠰⡟⠒⠒⠒⠦⠴⢤⣀⡤⠤⣄⡤⠖⠓⠒⠊⢉⡏⠀⠀⠀⠀⠀⠀⢸⡙⠒⠒⠲⠤⠶⢤⣠⡤⢤⣄⡤⠚⠒⠒⠋⢹⠇
⠀⠀⠀⠀⠀⠀⠈⠲⠤⣄⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠢⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠊⠩⠉⠉⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⠀⢀⡴⠧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠓⡄
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⢹⣟⠻⠉⠉⠉⣉⠙⠛⡛⢛⢛⣫⣽⣿⣿⣟⣿⣿⠁
⠀⠀⠀⠀⠀⣔⣓⣢⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠄⣚⣉⡷⠀⠀⠀⠀⠀⣔⡙⠻⠿⠿⢿⣿⣿⣯⣭⣭⣿⣯⣿⠿⠿⠛⠿⢩⡷
⠀⠀⠀⠀⠀⠘⣿⣍⣉⣛⣲⣤⣄⡀⠀⡀⢁⣤⣔⣛⣀⣤⣼⡿⡀⠀⠀⠀⠀⠀⣸⣿⣦⣴⣶⣤⣤⣄⣀⣀⣤⣀⣀⣴⣶⣮⣾⣿⣞
⠀⠀⠀⠀⠀⢸⣥⠉⠛⠛⠛⠻⠿⠿⠷⠾⠿⠿⠟⠛⠋⠉⣉⢀⡞⠀⠀⠀⠀⠘⡧⠤⠭⠙⢛⡛⠿⠿⠿⠿⠿⠿⠿⠿⣛⡛⠭⠥⣼⠇
⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣷⣶⣶⣤⣤⣶⣤⣤⣾⣿⣷⣾⣿⡟⠀⠀⠀⠀⠀⠀⢙⡶⣶⣦⣤⣮⣕⢢⣄⠀⣠⣔⣶⣭⣴⣶⣶⣾⡏
⠀⠀⠀⠀⠀⠀⣇⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⢀⡞⠀⠀⠀⠀⠀⠀⠘⣆⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⢀⣀⠀⠀⢀⣀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠠⠆⠀⠀⠚⠀⠐⠀⠁⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠀⠀⠤⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠈⠀⢀⠀⠀⠲⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠘⠒⠀⠀⠀⠑⠢⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⠐⠃⠀⠬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠐⠋⠀⠀⠀⠠⠐⠀⠀⢀⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡀⠀⠤⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⠹⢋⢦⣀⣬⣀⡄⠁⡄⠠⠀⢈⠉⠉⠉⡉⠩⡁⢠⠀⢉⠡⡦⣄⣀⣀⣁⣅⠁⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⣀⠀⠀⠈⠉⠈⠁⠈⠉⠉⠁⠉⠀⠁⠈⠀⠉⠉⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡑⢝⠢⡲⢐⢆⠠⡄⢼⡁⡀⠤⠄⡋⣀⣀⣀⠀⠂⢀⡀⠀⣈⡁⣀⠤⠄⠄⠒⠒⠀⠐⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠕⠔⢬⡓⣕⣌⡣⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⣀⣀⣀⡤⠤⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠰⠤⠀⡉⠉⠈⠈⠉⠉⠉⠀⠉⠁⠀⠁⠁⠀⣀⠀⢉⣁⠄⠀⣀⠠⣥⠴⠖⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⢈⠀⡄⠂⢰⠀⠀⢀⡈⠀⠀⢠⢀⣀⠀⠀⢠⠄⠀⣤⠀⠀⠉⠉⣅⠀⠀⠘⠀⠀⡦⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⢁⠀⠠⠀⡰⡅⠘⣄⣴⠁⠒⠒⡀⣰⠡⠃⣀⠁⠒⢲⡀⡘⠠⠵⠄⠀⠀⠀⠘⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠙⠀⠈⠁⠀⠉⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠑⠀⠤⠀⠠⠄⠀⠁⠤
⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠐⠆⠈⠓⢀⡀⠈⠁⠀⠀⠀⠀⠁⠀⠤⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⠀⠀⠋⠀⠄⠀⠀⠈⠁⠠⠄⠀⠀⠠⠀⠈⠀⠚⠀⠀⠈⠀⠀⠐⠚⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀


⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠒⠒⠒⠒⠒⡒⠒⠒⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠆⠀⠀⠚⠂⠀⠀⠈⠁⠀⠀⠤⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠆⠀⠀⠀⡤⠀⠀⠀⠠⠆⠀⠀⠀⣤⠀⠀⠀⢤⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠁⠀⠘⠋⠀⠀⠀⠉⠀⠀⠀⠘⠃⠀⠀⠚⠁⠀⠀⠀⠐⠖⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⢀⣻⣧⠀⠀⠠⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⢀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⣸⡇⢄⡀
⠀⠀⢤⠤⢤⣉⠉⠙⢷⣄⠀⠀⠀⢰⠄⠀⠀⡀⠀⠀⢠⡄⠀⠘⠃⠀⠀⠀⠀⢰⡄⠀⠈⠁⣀⣴⠟⠀⠀⠘⡆
⠀⠀⠈⠑⠠⢌⡹⡄⠀⠉⣻⣶⣤⣀⡀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠘⠂⠀⠀⠀⠀⣀⣠⣴⠾⠟⠓⢠⡂⠘⠋⠁
⠀⠀⠀⡴⠂⡿⠀⠁⠀⠀⠀⠤⠾⠛⠛⠻⠷⢶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠟⠛⣋⠿⠂⠤⠴⠖⣋⠀⠉⢱⡆
⠀⠀⣠⠇⠀⠙⢄⠀⠀⠀⣀⣠⠴⠶⠶⢤⣄⣀⣀⠤⠚⠓⠦⠤⠤⠀⠤⠀⠒⠊⠁⠀⠀⠀⣠⠴⠟⠒⠂⠈⠙⣧
⠀⠈⠳⣄⡀⠉⠉⠙⢦⣀⣀⠀⠀⠀⢀⠠⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠃⠀⢀⢒⠲⠶⠚⠁
⠀⠀⠀⠀⠉⠳⡄⠀⠀⡴⠛⠳⢤⣐⣀⣀⣠⣤⣶⣶⣤⣤⣤⢴⡾⠟⠓⠚⣛⣉⡉⠑⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠻⣤⣄⣀⣀⣀⣤⠴⠶⢤⣀⣀⣠⠶⠥⣤⣀⣈⣀⣤⠖⠋⠉⠉⠉⠙⠛⠛⠉⡼
⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠦⢤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⠉⠉⠰⠊⠙⢟⠟⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠛⢋⠈⣀⠀⡰⠀⠀⠀⠐⠀⢐⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠻⠀⠀⠈⠀⡄⠀⠀⠀⠀⢀⠀⢉⣙⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠶⠀⢠⡀⢀⡄⠘⢃⡉⠐⠙⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣤⣤⣼⣥⣤⣭⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠭⢽⣿⣿⡿⠟⢛⣻⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⢿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠒⠛⠉⠉⣉⣉⠭⠭⠶⠿⠃⠀⣚⣩⡽⢟⣋⠉⡐⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣄⣴⣶⣶⣿⠿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣌⣶⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣇⣀⣠⣤⣦⣼⣧⣽⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠦⢄⣉⣛⣾⣿⣿⢿⠉⠉⣛⣿⠿⣿⣯⠭⠽⠿⣿⡂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡿⣾⠄⠴⠤⠴⠷⠦⠉⠚⠹⠶⠖⠢⢼⣲⣶⣶⣾⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣘⣁⣴⣿⣿⣿⣿⣿⣫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣶⡶⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⣙⡛⠛⠒⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠘⠒⠁⠀⠀⢶⡄⠀⠀⠰⡿⠀⠀⠀⠓⠛⠀⠀⢴⣠⡤⢩⡿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⡠⢲⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⢀⡀⠀⠀⠈⠉⢷⣭⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠈⠓⠋⠀⠀⠈⠃⠀⠀⠀⢀⣘⠆⠀⠀⠀⠈⠀⠀⠀⠀⠘⠭⠀⠀⠀⠘⠊⢕⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠖⣫⣥⠶⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠴⠶⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⢐⣷⡸⠯⠖⠛⣋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⢟⢻⢻⡟⠛⠟⠟⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡟⡿⡟⡟⠻⠛⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠶⢤⣾⢾⢾⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠲⠶⠶⠗⠳⠳⠗⡳⣲⡶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠊⠁⠋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⠒⠓⠒⠒⠒⠒⠒⠒⠒⠚⠛⠚⠓⠛⠚⠚⠛⠓⡖⠒⠒⠒⠒⡶⠒⠒⢒⠚⠲⠖⢚⠉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢲⢊⢹⡂⠀⠀⠀⡂⠀⠀⠀⠀⠙⣦⣀⠝⣇⠀⢀⣼⣅⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⣶⠛⣉⣈⣧⣤⣤⠖⠳⠤⠘⠉⠛⢻⡀⠀⠀⢋⠶⣄⠰⠆⢀⡟⢀⣠⣼⢿⣟⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣥⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠋⠀⠈⠙⠿⢯⡴⣿⣟⣯⣿⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠿⠿⠛⠛⠉







⣿⢿⠿⠿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣻⣿⣟⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠶⠋⠐⠈⠉⠙⠋⠉⢉⡉⢉⡙⠲⢶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠶⠒⠁⠀⠐⠀⠁⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠈⠁⠈⢿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆⠀⢀⠙⢹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠐⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣑⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠸⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣸⣿⣶⣿⣿⠿⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠰⣯⣿⡳⠶⠶⡶⠶⣶⣶⢿⣷⣶⣦⣶⣶⣶⠶⢶⣶⣾⣛⡛⠛⠛⣿⠿⣯⣿⣏⠶⠚⠃
⠀⠀⠀⠀⠀⠀⠤⠒⠻⣿⠟⣓⣾⣿⣷⢾⣿⣧⣉⣩⣽⢿⢿⣿⠿⠿⣿⡧⠺⣗⢶⣾⣿⠎⠀⠀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⢬⡥⣤⣀⠋⢙⣛⡻⠛⢿⠛⣿⡿⠛⠙⠋⠁⠀⠐⠉⢀⣀⣠⣄⣁⣤⣤⡴⣶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢸⡓⢿⣿⠿⣷⣤⡀⠀⠉⠁⣀⣤⡶⢖⣿⡟⣻⡿⣻⡿⢿⣿⣿⣯⡽⢿⣷⣟⣾⢃⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠤⠛⠟⢷⠻⣿⢶⡾⣿⣆⣠⣾⣿⠟⣿⣿⣻⣿⢿⣵⣿⣴⣾⢯⣿⣸⣶⣾⣿⣟⠫⡛⢂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⡁⡀⣈⡁⠉⣉⣛⣉⣩⣤⣟⠘⣫⢹⠏⢋⠊⣀⣈⣋⣯⣉⣉⣝⣀⣿⡶⠾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠈⢻⢋⣖⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣻⣶⣊⣤⡿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠋⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⠀⠀⠤⠆⠀⠀⠀⠀⠀⠪⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠰⡄⠀⠀⡄⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠐⠂⠀⠘⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⣼⡃
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠈⠉⠙⠛⠛⠛⠓⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠴⠤⠤⠤⢤⣤⣤⣤⣤⡤⠴⠴⠶⠶⠚⠋⠉⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢧⡴⢻⡿⣧⠀⢀⣠⣤⠤⣤⣄⡀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣠⠶⢦⡀⣾⡓⠶⢦⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠙⢾⢏⡁⠀⠀⠀⠈⠛⢶⣶⡾⢿⠉⠻⠾⠋⠙⡷⢦⣴⡏⠉⠉⠙⠳⢶⣿⣠⠜⢻⠏⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠈⠲⢍⣉⣛⣛⣛⣉⢭⡤⠶⣇⡀⠀⠀⠀⠀⣳⡤⣄⣈⣉⣉⣉⣉⣉⡥⠴⠒⠉⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠂⠀⠀⠀⠀⠀⠀⠉⠒⢤⡉⠓⠲⠯⠽⠷⠯⠯⠟⠚⠁⢀⣠⠜⢋⢁⡀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠓⠶⠶⣦⣤⣤⣄⣈⣀⣀⠀⠨⠵⠦⣄⠒⠠⠤⠤⢂⡠⠞⢉⣀⣀⣠⣤⡤⠤⠶⠒⠚⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠓⠚⠛⠲⠶⠖⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠮⣭⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠶⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠋⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣢⡉⠙⠓⣲⡶⠶⢦⠤⡦⣤⡤⡤⢤⢤⡤⡶⠶⠶⠶⠲⠛⠛⣉⠁⠀⢀⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠩⠿⠻⠋⠿⢦⣀⠀⢀⣠⣶⠿⠶⣤⡀⠀⣠⠞⠶⢤⣠⡾⠉⠹⡶⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⠼⠛⠻⣥⣀⣀⣀⣠⣽⣻⢿⣀⣀⣀⣀⣀⣀⣤⠟⠻⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣝⣒⡒⠖⠚⠁⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⣀⣠⠼⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⣒⡶⢿⣭⠭⠭⠭⠭⣭⣉⣉⣙⣛⣻⣛⣛⣛⣛⣛⣉⣉⠭⠭⠥⠴⠖⠒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠈⠳⠤⠴⠚⠋⠛⠦⣄⠀⠀⠈⠁⢀⣤⣄⢀⡴⠒⠦⣤⠴⢻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⣀⣀⣀⡀⠀⠈⠙⠓⠒⠒⠋⢀⣈⣉⣁⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⠈⠉⠉⠉⠁⠐⠒⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠎
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠓⠒⠒⢒⡲⠒⠒⠒⠒⠒⠒⠛⢛⡉⠉⠉⠉⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡉⠁⠒⠒⠀⠀⠀⠀⠀⠶⠒⠒⠈⠉⠀⠀⠈⠀⠀⠤⠤⢀⡀⢀⣀⠀⠀⠀⠤⠤⠒⠀⣇
⠀⠀⠀⠀⠁⠨⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠂⠠⠀⢀⣀⠀⡀⠀⠤⠀⠂⠁⠀⠐⡶⠢⠄⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠐⢀⣀⣀⠀⠠⠤⠀⠀⠀⢠⠀⠀⠀⠀⢈⡀⠀⠀⣀⠀⠀⣀⢀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠈⠄⡀
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠄⠐⠀⠀⢄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡀⠄⡀⠀⠀⠢⠀⠀⠀⠀⠀⠂⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠛⠛⠉⠉⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠴⠶⠀⠀⠀⠀⠙⠉⠀⠀⠀⠙⠛⠀⠀⠀⣤⡤⠀⠀⠀⠀⠉⠛⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⠁⠀⠀⠴⠖⠀⠀⣤⡀⠀⠀⠀⠴⣦⠀⠀⠐⠚⠃⠀⠀⢠⣤⡄⠀⠀⣀⡀⠀⢤⣤⠀⠀⠈⠙⢿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠘⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⣠⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣴⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣶⡀
⠀⠀⠀⠀⠀⢻⣿⡤⠈⠉⠉⣀⣀⣀⠈⠀⠀⠀⠀⣉⣉⣉⠉⠀⠀⠉⠉⣉⡉⠉⠉⠉⠉⠉⠉⣉⠉⠉⠉⠛⠛⠛⢋⡉⠉⠉⠉⠉⠙⢋⠉⢁⣘⣿⣷
⠀⠀⠀⠀⠀⠈⢿⣷⣴⣶⡿⠟⠛⠿⣿⣶⣤⣶⣿⠿⠛⠻⢿⣶⣤⣶⣿⠿⠿⣷⣦⣤⣴⣾⡿⠿⢿⣶⣤⣤⣴⣾⠿⠿⣿⣶⣤⣶⣿⠿⢿⣾⣿⡟⠃
⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠋⠉⠉⠉⠉⠉⠉⠉⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢘⡔⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣈⣿⣤⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣀⣠⡽⢷⣽⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⢊⡿⠀⠈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣷⠀⡠⢦⠙⠛⡳⠶⢥⣜⣀⣤⣰⣐⣒⣂⣂⣂⣤⣉⣠⡤⣾⣟⡂⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣽⣾⠄⠀⠀⣖⠻⣤⣉⡩⠭⢭⡍⠉⠉⠉⠉⠫⣤⡁⠀⠈⢻⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣶⣶⣿⣿⣿⣶⣤⣤⣀⡀⠉⠛⠛⠙⣲⣤⣼⣧⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⣼⣿⣿⣿⣿⣿⣯⣶⣞⣿⣯⣿⣟⣿⣷⣤⣼⣿⣿⣿⣿⣿⣯⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡙⢿⡧⢛⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⣿⣿⢙⣿⣟⠇⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣍⡲⢤⣈⡛⠛⠛⠚⢋⣈⣩⣾⣶⣤⡈⠙⠓⠦⣴⣉⡉⢭⣥⣾⡇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢹⣿⡟⠓⠂⠭⠭⠭⠭⠽⠛⠛⠛⠿⠷⢋⣙⣻⣶⢿⠿⣫⣿⣿⣿⣈⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠠⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣼⣿⣿⣯⣽⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣶⣠⢏⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠟⠉⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣟⡻⣦⣤⡤⠤⠤⠤⠤⣬⡽⠶⠶⠾⠿⢶⡿⣷⢾⣷⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣤⣀⡠⢀⣀⢀⠀⣀⢀⣀⣠⣴⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠁⣠⡀⠀⠰⠦⢀⡀⢛⠀⠀⠶⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠶⠆⠀⠉⠚⠀⢶⠄⠈⣁⠉⠀⠠⡶⠀⠤⠛⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣴⢟⢻⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡾⠛⠛⣿⣿⣿⡾⠷⣄
⠀⠀⠀⠀⠀⠀⢰⡏⡏⠀⠛⠿⣽⣟⣟⠛⠿⣷⠶⡟⣿⣿⣽⣿⣿⣿⣿⣿⣍⣂⣴⡿⣋⣭⣿⣧⢸⡆
⠀⠀⠀⠀⠀⠀⣿⣿⠀⣤⣾⣿⣿⣷⣯⣭⣉⣙⠻⣉⡉⠉⠙⠛⠿⠿⠿⠿⠿⢟⣩⣾⣿⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠹⣏⣸⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣭⡲⣄⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⠿⢿⣷⣿⣿⣽⣿⣽⣯⣭⣿⣿⣎⢆⠀⢀⡾⣿⣿⣿⣿⣿⡿⠟⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠿⣦⣄⡀⠀⠀⠈⠙⠛⠿⠿⠷⠾⠷⠾⠿⡎⢀⡾⠿⠿⠛⠛⠋⠁⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⣶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠹⠞⣀⣀⣀⣠⣤⣴⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄
⠀⠀⠀⠀⢃⣑⡒⢂⡀⠀⠀⠀⠀⠀⠀⣐⣊⣡⡞⠀⠀⠀⠀⢳⡾⠶⣦⢀⠀⠀⠀⠀⠀⣀⠴⠂⣳⡶⠁
⠀⠀⠀⠀⣜⠛⠿⠿⢿⠷⠾⣿⡾⠿⠿⠿⠛⠋⡱⠀⠀⠀⠀⢜⡛⠷⠾⠿⡿⠶⣤⡶⠿⠿⠿⠛⠛⢩⠆
⠀⠀⠀⠀⠸⡑⠒⠓⠒⠲⠤⠴⠦⠤⠚⠓⠊⣩⠇⠀⠀⠀⠀⠘⣝⠒⠓⠒⠒⠤⠤⠦⠤⠒⠛⠚⢉⠏
⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⠤⠤⠤⠤⠖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠤⠤⠤⠤⠤⠖⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠄⠒⠒⠠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⢀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⡀
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠳⣖⠟⠴⢄⣐⠒⠒⠒⢒⣂⠶⠊⣰⣶⠃
⠀⠀⠀⠀⢮⣵⡦⣤⠄⠀⠀⠀⠀⠀⠠⡤⠄⢮⣭⠂⠀⠀⠀⢰⣉⠛⠛⠻⠿⠿⠶⠶⠿⠿⠛⠛⢛⣁⠇
⠀⠀⠀⠀⡸⠷⣤⣼⣿⣶⣦⣀⣤⣶⣷⣷⠶⠿⢓⡄⠀⠀⠀⣔⡻⠿⣿⣷⣶⣶⣴⣶⣦⣾⣿⣿⠿⢛⡄
⠀⠀⠀⠀⠸⣷⣤⣶⣤⣤⣀⣀⣄⣀⣴⣶⣴⣶⡎⠀⠀⠀⠀⠸⣤⣤⣁⣀⡠⣈⠉⢉⣠⣔⣠⣬⣤⣾
⠀⠀⠀⠀⠸⡀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⢁⠇⠀⠀⠀⠀⠀⢇⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⢁⡜
⠀⠀⠀⠀⠀⠈⠑⠒⠤⠤⠤⠤⠤⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠢⠤⠤⠤⠤⠤⠤⠔⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠢⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣄⠲⠙⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠸⣿⣷⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠏⠁⢿⠿⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢒⣍⠀⢀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⠀⠀⠈⢠⡇⠀⠀⢀⣃⠐⠀⡐⠂⠄⠤⠠⠄⠠⠤⠀⠀⣢⡄⢀⣲⠀⠈⣀⠐⠄⠀⠀⢰⡟⢯⣈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠀⠁⠀⠟⠉⣀⠀⢨⠞⠃⢀⠿⠀⠀⠐⠢⡀⠀⢠⣄⣠⠏⠙⠌⢶⠀⠀⠻⠂⠀⠀⠐⠊⢠⢦⢱⣽⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠷⠶⠦⣄⣀⣀⠉⠀⠈⠉⠀⢉⣁⣠⣴⣿⣿⣿⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⣠⡾⠛⠿⢥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣤⣭⣍⣉⡉⠛⠛⠟⠛⠉⠉⠉⠛⠢⢤⣤⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣻⣿⣯⢿⣟⣻⣿⣛⣿⣿⣿⣿⣶⣆⡈⠐⢄⡀⠀⠀⠀⠀⠽⣫⣿⣿⣿⣿⡿⠿⢻⣿⣿⡟⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣷⡷⢹⣿⣷⣤⡙⢆⠀⠀⣠⣾⣿⣯⣸⣥⣏⡎⣸⣿⣿⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠻⠿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⣀⣴⣿⡿⣿⣿⣿⢿⡿⣟⣼⣻⣿⡿⠿⠿⠿⢛⢽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠿⢻⠿⣿⣯⣿⠿⠿⢿⣿⣻⣦⣿⣟⠛⠟⢾⡛⠍⠛⠋⠉⠄⠔⠰⢒⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⢶⠖⠶⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⢤⣅⣀⡌⠀⠀⠉⠈⡿⢻⣿⡷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡿⠀⣤⠀⡸⠁⠀⠚⠂⢰⠧⣼⣿⣇⢀⢸⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⢀⠁⠀⠋⠀⠚⠀⢠⢇⣤⣿⣿⠙⡄⠀⢳⡸⣧⠀⠀⠀⠀⠀⢰⡆⠀⣾⢿⠀⠀⣷⣤
⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠈⢿⣄⡝⠉⡛⠂⢰⣧⣤⣾⢿⣇⣾⡗⠒⢛⠉⠙⣄⣽⠀⠠⢤⣤⣶⣼⢠⣴⢿⣜⣧⠀⣿⡏
⠀⠀⠀⢠⣔⣋⠟⠫⡉⠉⠿⡶⣄⠙⠿⡿⢷⡶⢿⣏⣩⣧⣾⡯⠀⢷⠐⠚⡊⢉⣿⡏⠀⠀⠀⠀⠈⣿⠘⣻⣆⠟⢻⡸⡇⡇⢲⡤
⠀⢀⣔⣫⠚⠳⣀⠄⠛⢇⣀⠔⠛⣣⡀⠀⠈⠁⠀⠈⠁⠻⢟⢻⡶⢾⠶⠶⣿⠻⠟⠀⢀⣠⣤⠴⡶⠿⣿⣿⣽⣄⠈⣿⣿⡇⣠⠉⠓⠚⠁
⠀⣼⠋⠙⣦⡂⠉⢢⡤⠈⠹⣄⡀⠙⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠉⠀⢀⣼⢋⣏⡈⣹⡂⢠⠧⠈⣿⣿⡀⢹⣿⡇⣸⡆
⠀⣿⠷⡂⠀⢑⣖⠉⠙⣤⡐⠉⢳⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠛⣶⡛⠛⣿⣿⣿⣿⡿⠁⡈⠀⠀⠉⠉⣧⠘⡟⡇⠈⡿
⠀⢿⣆⣸⠾⡁⠈⡳⡆⠀⢱⡤⠀⣠⠃⠀⠀⠀⠀⠀⠀⢀⣴⠛⢈⣦⡖⠋⠀⠱⣼⡿⠿⣿⣾⡧⠰⠁⠀⠺⠂⢤⣿⡇⢸⡇
⠀⠈⠿⣧⣀⠹⠏⠀⢈⠶⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣼⣽⣖⠉⠀⢱⣄⡤⠾⠛⣄⠀⢀⣿⣿⠃⠀⢤⡆⠀⣐⣿⡇⣘⣭⣤⣠⡀
⠀⠀⠀⠈⠙⢻⣶⡶⣶⡾⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣦⡔⠊⠉⢦⠀⢀⡸⢷⡁⢠⣿⡆⠀⡀⢀⣤⡿⢫⣷⢿⣄⣸⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣁⣠⡤⠴⣶⠶⠶⠤⢤⣤⣀⣀⠀⠸⣶⠊⠉⢣⡀⢀⡤⠿⡁⠀⢀⣿⣿⣿⣷⣾⣷⡿⣋⣿⣿⡛⠿⡿⠓⠟
⠀⠀⠀⠀⠀⠀⢠⡞⣯⣤⠛⠂⢄⡀⠶⠎⣁⠠⢄⣫⣷⠀⠹⢷⣤⣤⠿⡅⠀⢀⡸⢶⣴⣿⣿⡿⢶⣿⣿⣛⠋⠉⣹⠇
⠀⠀⠀⠀⠀⠀⠘⠟⢷⣶⠷⣶⣤⣤⣴⣦⣤⣴⡿⡟⡿⠀⠀⠀⠛⠹⠿⢾⣶⠿⠛⣿⣵⣟⣼⡁⠀⠀⡏⢈⣩⠿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠃⠄⠸⠇⠨⠿⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠙⣿⠺⣿⣾⠛⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡿⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠟⠋⠁⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣳⣿⣿⡿⠻⡿⢣⡀⠀⠀⠀⠀⠀⡖⠻⠉⠉⣀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠁⠛⠉⠁⣤⠀⢠⣰⡃⠀⠀⠀⠀⠀⠳⢦⠀⠀⠉⠀⠀⠀⠐⠟⠀⠀⠸⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠘⠃⠀⠀⢀⠀⠀⣸⣿⣿⣶⣶⠀⠀⠀⠀⠈⢧⣄⠀⠘⠒⠒⠀⠀⠀⢀⡼⠤⠞
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣷⣄⡀⠈⠚⠉⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣀⣈⣹⠀⠀⠀⡴⢒⣚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⠀⠀⢸⣿⣟⠋⠁⠀⠀⠀⠀⠀⣰⠋⠀⠀⠹⢄⣀⠴⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⢢⠈⢏⠐⠉⠃⢹⢃⠀⠀⠀⠀⠀⢰⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣸⠃⠈⠦⠤⠃⠸⡟⠀⠀⠀⠀⢀⡟⠳⣼⠇⣠⣀⠀⠀⣀⢄⠀⢸⣠⠞⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢸⠀⠀⠀⠀⡠⠷⣧⣰⣶⣄⡀⢸⠁⠀⣜⠚⢯⣉⣩⠟⠹⠆⢳⣸⡇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣧⠀⠘⢦⣀⣠⠜⠁⠺⣍⡩⣀⣔⣳⣾⠀⠒⠉⣿⣅⡟⠀⠙⣍⠀⡀⠛⠿⠞⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⢧⣀⣀⣤⠤⠦⣄⣀⢠⠶⢯⡾⠃⠹⣄⣠⢾⠁⠀⣀⣠⣄⣈⠉⠉⢳⠦⣤⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣀⠤⣶⠖⠀⠉⠙⢦⡀⠀⠀⠀⠀⣀⠼⠛⠘⠛⠂⠾⠻⠃⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⡠⠖⠋⡠⠚⠁⠀⠀⠀⠀⠀⠙⢦⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⣀⣀⣀⣀⣤⠤⣄⣀⠤⠠⠤⠤⣀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢸⡠⣤⣤⡤⠴⠚⠋⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢠⣏⣀⣀⣀⣀⣀⣠⣤⡤⠤⠤⢤⠤⠶⠶⢲⠖⠒⢲⣖⠚⠛⠋⠉⠁⠀⣀⣠⠤⢼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠤⢶⡞⠀⠀⠀⡼⠀⣠⠏⠈⠉⠛⠛⠛⠉⠉⢉⡇⠀⣸⠀⠀⠀⠀⣀⣀⣤⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡤⠦⣤⠞⠀⠀⣠⠾⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⡞⠉⠓⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⠴⣞⢁⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢰⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠋⠉⠉⣉⠉⠈⠠⠉⠉⠋⠿⢟⣳⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⣡⠖⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢟⣧⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠀⠀⠀⠀⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠀⠀⠉⢻⠿⣿⣿⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⡀⠐⠸⢿⣭⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠠⠀⠀⠋⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠁⠓⢰⢹⣿⠋⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⠀⠀⠘⠁⠀⠐⠃⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠆⠀⠒⠁⠀⠀⠈⠀⠈⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣙⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢦⣀⣀⠀⠀⠀⠀⠀⠀⢠⣄⢀⢠⣀⣀⣀⣀⣀⣀⣠⣀⣄⣬⣬⣤⣤⣾⣤⣶⣶⣶⣶⠿⢿⣿⣿⠁⢄⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠏⢰⣦⡾⠉⢙⣻⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠛⠛⠉⢩⣭⣿⡛⠛⠛⠛⠛⠁⣠⣾⣿⣿⣿⣶⠗⠈⡇
⠀⠀⠀⠀⠀⠀⡞⠉⢀⣠⡴⠶⠶⠿⠟⠻⣯⣃⣀⣠⣴⣞⡂⠀⠀⣠⡤⠶⢤⣄⣀⣴⣿⡛⠋⠙⠷⢶⣤⣴⣾⡿⠁⠀⢀⣀⣀⣀⠀⠁⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠻⠤⡾⠉⣆⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠙⠲⠛⣋⣡⣤⣶⣿⣯⣍⣉⠉⠑⠢⣄⠀⠀⠀⠀⠀⢀⣴⣟⣛⡻⣯⣍⣁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣉⣧⠀⢀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⠿⠟⠛⠉⠉⠀⠀⠉⠛⠻⢷⣦⣄⡉⠒⢄⡀⢀⠞⠛⠻⠻⠍⢻⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢶⣧⠀⠀⣠⣴⣾⣿⣿⣟⣋⣁⣠⣤⣀⣀⣀⣀⣀⣀⣤⣤⣀⣋⣸⣿⣿⣷⣦⣀⣾⣶⣶⣶⣶⣶⡋
⠀⠀⠀⢸⣆⠀⠀⠀⠀⢨⣄⠀⢸⣦⣾⣽⠾⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⠛⠻⠿⠿⠟⠿⠿⠿⢿⠛⠻⠿⠻⠟⢿⠯⡟⢻⠻⡉⣿⣤⠄
⠀⠀⠀⠀⣯⠣⡠⣄⣡⡘⣿⣿⣦⣍⣉⣀⠀⠀⢶⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣠⣧⣘⣂⣴⢦⣤⣿⣿⣾⣿⣿⡿⢗⡛⣛⡿⠋
⠀⠀⠀⠈⠳⣶⠿⠀⣵⣶⣬⡉⠙⠻⠿⢿⣿⣿⣿⣿⣶⣾⣦⣶⣤⣄⣀⢰⡖⣐⠀⢌⠟⢈⣿⣿⠿⡿⠿⠟⠻⠿⠿⠿⠿⠛⢟⣭⠞⣫⣿⣋
⠀⠀⠀⢀⣀⠈⡁⢀⡤⠖⠀⠀⣀⣤⣀⠘⠛⠿⢏⣵⠶⣆⠀⠀⣰⣄⣌⣙⠚⠛⠻⠿⠟⠛⣉⣤⣷⣾⣿⣴⣣⣀⣀⠀⠐⠝⢿⣷⣶⣤⡀⢿⠷⠂
⠀⠀⠀⠈⠙⡟⣩⠞⣫⢵⠦⠴⠿⠛⠛⠛⢿⣧⡴⢶⣻⢿⣆⠀⣿⣿⣾⣿⣿⣿⠛⠛⠛⠶⢶⣶⣶⣾⡿⠿⠛⠛⡟⠻⣦⣤⣸⣿⠇⠈⠛⠿⠄
⠀⠀⠀⠀⠀⠛⣇⣼⠇⠀⢿⡄⠀⠀⠀⠀⠀⠉⠀⠀⣡⡟⠛⠷⠿⠛⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡜⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⣡⣶⣾⣷⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣤⣀⣤⣤⣤⣴⣴⣴⣶⣶⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉

⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠈⠉⠁⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢀⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠒
⠀⠀⠀⠀⣴⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢲⠖⠊⢀⡴⡇
⠀⠀⠀⢾⡀⠘⣌⠳⣄⡀⣀⡴⠾⢉⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠾⠒⡷⠒⡶⢿⡾
⠀⠀⠀⠈⠻⢲⡦⣟⣶⣿⡍⠀⢲⠾⠧⠀⢯⠙⠒⢛⣲⣦⣤⣊⡽⠀⢀⣀⣀⡜⢓⣊⡱⡢⠷
⠀⠀⠀⠀⠀⠸⡌⠙⢕⣮⡉⢿⣿⡟⢐⣷⢎⠑⠀⢙⡯⢤⠤⠟⠒⢒⣊⡡⠛⠉⠉⠑⠊⠀⣠⣆
⠀⠀⠀⢀⣀⣜⢿⣷⣤⣀⠀⠀⠈⠉⠙⠛⠓⠩⠘⠀⠛⠐⠉⠉⠙⠛⠂⠁⠀⠀⢀⣀⣤⡞⠋⢹⣇
⠀⠀⢠⡋⢇⣘⢮⠋⠛⠲⢿⡒⠲⣤⡤⠀⣀⣀⣀⣀⣀⣀⡠⢤⣤⠤⣲⣶⡦⣭⣥⠚⠃⠉⢑⡾⠉
⠀⠀⠈⠙⢾⡻⡄⠁⠠⠄⢄⡈⠑⠺⣝⡛⠛⠋⠉⢱⠄⣠⠴⠛⠙⠒⠈⠁⠀⠁⣀⣤⡤⢞⡹⠂
⠀⠀⠀⠀⠀⢳⣈⡩⠛⠉⠙⣝⠲⠶⣒⠍⣒⣤⣰⢋⣠⠖⠉⡉⣒⠶⠦⣴⠊⠉⠋⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣠⠟⠋⠁⠉⠉⠉⠀⠈⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠺⠁⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠋⠭⠁⡀⠰⠂⢀⠀⠌⠉⢙⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠀⠘⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠄⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣋⣙⡲⠦⢤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠤⣒⣋⣁⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⠻⠍⢓⠶⠤⢤⣉⠉⠉⠉⠉⠉⠉⠉⢉⣩⠴⠶⠭⠭⢐⣩⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⢿⣶⣶⣶⣾⣿⣿⣿⣷⣤⣒⢒⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣦⡀⠉⠈⠉⠉⠉⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⡀⢀⣤⣀⣸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⣿⣿⣷⣤⣶⣶⣄⣒⣠⣤⣤⣤⣀⣴⣿⣿⣿⣶⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣻

⠀⠀⡠⠀⢠⢤⡀⣀⢠⢠⢀⠀⡀⠀⡤⡀⡀⢀⡀⢀⡀⡄⣀⠀⡀⠀⣠⣄⢀⠀⣀⠀⡀⠠⢀⡀⢀⠀⢀⢤⡀⡀⣀⡀⣀⠀⠀⣀⢀⡀⠀⡤⡄⢀⢀
⠀⠀⠘⠃⠘⠒⠋⠛⠙⠘⠚⠃⠃⠀⠋⠙⠋⠹⠋⡿⠃⠛⠛⠛⠚⠀⠛⠁⠛⢹⠟⢹⠚⠘⠋⠛⠓⠃⠘⠋⠘⠋⡷⠋⡗⠛⠙⠘⠛⠚⠀⠋⠉⠛⢹
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡶⠿⠟⣻⡿⠃⣠⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⣿⠀⠀⠀⣰⣿⣷⣿⡏⠀⠀⠀⠀⠸⣿⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠍⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣆⣀⣀⡼⠿⠿⣛⣿⣟⣩⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣾⣿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⡀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠢⡀
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣠⡀⢤⠤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⡗⣠⣤⣶⠿⠟⠛⠛⠛⠛⠺⠽⠛⡋⣉⣭⣤⡤⠄⠠⠍⠩⠉⠽⠿⢶⣶⢶⣤⣀⣰
⠀⠀⠀⠀⠀⣀⣱⣿⠏⣠⠄⠤⠄⠲⢴⡤⠐⠒⠤⢈⣿⣀⣤⣤⣤⣤⣤⣤⣀⡤⠄⠀⠠⠽⢿⡛⠛⢤
⠀⠀⠀⠀⢠⣿⣯⣿⣿⣥⣤⣀⡀⠀⠉⠉⠉⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣿⣤⡀
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⡙⠿⠻⠿⢟⣻⣛⠛⠻⣿⡿⠿⠿⢿⣿⣿⠿⠿⠿⢿⣿⣿⣿⡿⠿⠿⣿⡿⠿⠻⠿⠿⠿⢿⠋
⠀⠀⠀⠀⠈⠉⢹⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠀⠀⠀⠈⠉⠒⠢⠄⠚⠉⠙⠚⠙⡍
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠙⠋⠉⠉⠉⠉⠛⠛⠛⠓⠒⠛⠒⠒⠒⠂⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⢀⣤⡤⠀⣠⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣼⡿⠁⣰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⠀⠀⢰⡟⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⢠⠏⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⠀⠈⠀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣤⣬⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⢹⠋⠉⠉⣿⠉⠉⠙⡏⠉⠉⢻⠉⠉⠹⡏⠉⠉⢹⠉⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⢿⠿⠿⠶⣿⠿⠿⠿⡿⠿⠿⢿⠿⠿⢾⡿⠷⠷⢿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣼⣦⣤⣤⣷⣤⣤⣴⣧⣤⣤⣶⣤⣤⣴⣧⣤⣤⣼⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣸⣁⣀⣀⣿⣀⣀⣈⣇⡀⢀⣹⣀⣀⣸⣇⣀⣀⣸⣀⣀⡀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⣛⠝⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⢀⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡻⡫⠊⠀⠀⠀⢀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠲⠦⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣠⣤⣴⣶⣤⣤⠬⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠒⠂⠀⠐⢤⠀⢀⣀⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠁⠀⠠⠤⣄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠓⠑⠀⢀⠈⠀⠀⢀⠸⠀⠀⠈⣖⠏⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠢⠀⠀⠀⠀⠀⠀⠤⠷⣄⡀⠀⠀⠄⠀⠀⠀⠀⢠⠀⣀⢀⣀⡀⠀⠀⡠⠀⠄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠄⠂⠈⢣⠀⠀⠀⢀⠀⠉⠢⠀⠀⠉⠃⠠⠐⠉⠩⠉⠀⡀⠀⠈⠐⢄⠰⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⣄⠀⠀⠀⠀⠀⠳⡀⠀⠁⠀⠀⠐⠀⠐⠀⠀⠀⠐⠀⠀⠠⠀⠐⠀⠀⠀⢀⣡⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢉⠳⠲⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠴⠒⠊⠍⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠒⠒⠒⠒⠂⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡉⠠⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣀⣂⣠⡥⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠉




⠀⢀⡀
⣿⣏⢽⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⡠⡈⠩⠄⠀⠬⠉⡠⢄⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠄⠠
⠀⠀⠔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠗⠀⠀⠐⠷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠈⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠉⠉⠁⠀⠀⠀⢀⠀⣈⡀⠀⠀⢁⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡀⠀⠀⠀⣠⠠⠀⠀⠀⠀⠐⠀⠐⠀⠃⠂⠀⠀⠀⠀⠒⢀⠀⠀⠀⠀⠠⠐
⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠂⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠂⠐⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠂⠀⢀⢀⠀⡀⢀⠀⠘⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⠲⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⢀⠀⠀⢀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⡂⠀⠐⠀⠚⠀⢇⠅
⠀⠠⠰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⠀⡁⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢌⠠⠀⠀⠐⠀⠀⠀⠛⠛⠛
⠀⠀⠔⠄⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠈⠀⠀⠐⠈⠀⠀⠈⠰⠀⠀⠈⠀⠀⢀⡀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠
⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⢘⠁⡃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠢⠄⠀⠀⠀⠤⠐⠒⠄⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠤⠠⠄⠀⢊⠁⠀⠀⠀⠛⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠂⡀⠂⠀⠀⠀⠀⠀⠀⠂⠕⠂⠀⠀⠀⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠄⠀⠀⠀⢐⠀⠂⢀⠀⣀⠀⡂⠐
⠀⠀⠀⠂⠀⠀⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⡀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣤⡴⠂⢀⠄⠛⠉⢹⡞⠛⠛⠻⠟⠚⠐⠤⣤⣰⣄⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠈⠋⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠚⠂⠀⠠⣿⠟⠻⢿⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⡾⠛⠁⣠⠀⠀⠀⠁⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠛⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣔⠉⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠀⠀⠀⠈⠋⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢰⣼⣿⡷⣄
⠀⠀⠀⠀⡠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠌⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⡄⠀⢙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢹⣃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⣾⣷⣴⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠙⣛⠿⣶⢤⣤⣀⣀⣀⣠⣄⣀⣀⣠⣤⣀⠀⣀⢀⣀⣀⣀⣀⣀⣤⣀⣀⣤⣤⣤⣴⣴⣿⣿⣿⡿⢿⡛⣯⢍⣀⡴⡇
⠀⠀⠀⠀⠀⠀⡹⣿⣷⣄⣘⠋⢙⣛⡛⠛⢛⣿⡛⠻⠟⡛⣻⡿⣿⣿⣿⣿⡭⣭⣭⡽⠒⢷⡍⠉⠈⣡⡟⢋⡽⠛⠻⡒⠋⠁
⠀⠀⠀⠀⠶⠊⠉⠻⠿⠏⣉⣙⣿⣿⣿⡛⣿⣿⣿⣦⣤⣤⣴⠿⡯⢾⡯⠿⠻⢿⢟⡷⠚⠳⢌⣙⣿⠿⠿⠊⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢬⣭⢥⣀⠀⠺⠉⠻⠿⠻⠷⢚⣿⠟⣿⣿⣯⠓⠚⠋⠉⠀⠒⠂⠐⠉⠀⠀⠀⣀⣀⠀⣀⣀⣀⣤⣶⣶⡶⣦⣤⡀
⠀⠀⠀⠀⠀⠸⡿⢬⣿⣿⣶⣶⣚⠋⠑⠒⠂⠒⠓⠚⠊⢁⣀⣤⣤⣤⣶⡤⣤⣤⣴⣶⣿⣿⣯⣿⣿⠿⣻⣿⣧⣸⡏⣤⣿⢀⡁
⠀⠀⢀⠀⠀⣰⣷⣤⡹⣻⣧⣈⠻⢿⣦⡀⠀⠀⠀⣤⣶⣿⣏⣡⣴⣿⣋⣴⣿⠃⣼⡟⠀⣴⡿⣿⣟⣿⠛⠙⣿⣿⣱⣿⢥⣾⠀⠀⠠⠃
⠀⠀⠀⠐⠒⠋⠙⠘⠫⣙⡻⡟⢻⡿⢿⣿⣤⣴⣾⣿⡛⠉⢿⣿⣭⣽⣿⡛⣷⡿⣿⣶⢿⡿⣣⣿⣀⣿⣛⣿⣿⢷⣫⠹⢎⠉⣠⡇
⠀⠀⠀⠀⠀⠀⠈⠷⣞⣁⣀⣀⣈⡁⠈⠉⣉⠛⢉⢉⣩⣤⡜⠀⠳⠤⠈⡟⠒⠓⠖⠐⠀⣉⣃⣹⣈⣁⣀⣼⡁⢸⣾⡶⠶⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠶⠾⠟⠛⠛⠟⠿⠹⠿⠓⠞⠻⠾⠷⠶⠿⠾⠟⠿⠛⠟⠛⠉⠉⠉⠛⠙⣿⠋⠀⠢⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣤⣀⠀⠀⢀⣂⢤⣾⣐⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢤⣤⣤⣄⣀⣀⣄⣀⣀⡀⣀⠀⣀⢀⣀⣀⣤⣤⣠⣄⣄⣠⣤⣥⡿⠧⠴⠶⠿⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠶⢶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠟⠛⠋⠉⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠈⠉⠙⠻⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠦⢤⣀
⠀⠀⢸⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⠶⠶⠚⠋⠁⠀⢠⡶⠿
⠀⠀⡞⠁⠈⠉⠙⠛⠻⠶⠶⣦⣤⣤⣄⣤⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⠤⠤⠤⠶⢶⡶⠶⠖⠛⢛⣛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶⠾⢣⡀
⣠⡼⠿⠶⣶⠿⠛⣿⣦⣀⣴⢶⡄⠈⣨⣭⠉⠉⢉⣄⡀⠀⠀⢀⣤⣀⣀⣴⠞⠛⠻⣤⣀⣤⠶⠋⠉⠳⣤⣀⣀⣴⠛⠻⣦⣤⣤⣏⡴⠛⠀⠀⢻
⢿⣤⣤⡀⠀⠀⠀⠹⣦⡉⠁⠀⠙⠛⠁⠘⢧⡴⠟⢉⣷⣤⡴⠋⠻⢯⣝⡃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠉⠉⣉⠛⢛⣛⣿⣯⠴⠴⣶⠒⠛
⠀⠀⢸⡟⠓⠶⢬⣁⡊⠛⠓⠶⠤⠤⠤⠴⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠶⠶⠶⠛⠋⠉⠠⢀⣂⣤⠴⠖⠛⠉⠉⠀⠀⠀⠀⣼
⠀⠀⠸⣇⠀⠀⠀⠉⠙⠓⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣂⣬⠾⠛⠳⣄
⠀⠀⠀⣼⠿⢶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠶⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠤⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠖⠛⠉⣡⣤⣤⣤⡾
⠀⠀⠀⢧⣄⣤⣀⠈⠙⠛⠷⠶⢤⣤⣤⣀⠀⠀⠀⠀⠈⠉⠙⠛⠶⢦⣴⣴⠞⠉⢀⣀⣤⣠⣤⣤⠤⠖⠚⠋⠉⣹⠏⢀⣤⠶⠶⠶⠟⠀⢻
⠀⠀⠀⠀⠀⣿⠙⢧⡀⠀⠀⢀⣀⣀⠀⠈⠉⠉⠛⠛⠓⠲⠶⠒⠒⠚⠛⠛⠛⠛⣉⣩⣭⣀⠀⠀⣠⣾⣛⣛⣛⣫⠶⠋⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⣿⡀⠈⠙⠻⠛⠛⠉⠉⠻⢦⣀⠀⠀⣀⣴⠾⠛⠛⠷⠶⢤⣤⡴⠞⠋⠁⠀⠉⠛⠛⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠘⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⠤⠶⠶⠚⠛⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣯⣫⣴⣭⣿⣧⣿⣽⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠴⠶⠶⠶⠦⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡈⢢⡀
⠀⠀⠀⠀⠀⠀⣠⠋⠄⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣆⡠⠞⠳⣄
⠀⠀⣰⡓⠤⣏⠠⢀⢊⠊⠄⡠⠃⢀⠔⡔⠠⠠⠀⠄⡀⠀⠀⢀⢀⡐⡀⣠⢂⡌⣀⣀⣀⣀⣀⣤⣤⣴⠾⢛⡥⠞⠡⠔⠒⠲⣾
⠀⢀⠏⠙⠂⢾⠻⠷⣿⣷⣾⣶⡶⡶⠾⠒⣒⣓⣛⡩⠽⠛⢋⣭⣋⣩⣉⣉⣩⣍⣉⣩⠥⠤⠒⣊⡩⢴⢚⡁⠀⢌⡑⠒⠒⢸⡰
⠀⢸⠤⣀⡀⠈⢱⠦⢤⢌⣉⣉⡝⢹⣉⣉⣁⣀⣤⣤⠖⠚⠙⠤⣤⠛⠻⣭⣥⡤⢤⡴⠒⠾⡭⠥⠒⠁⢸⠉⠲⣄⣈⣑⡠⠃
⠀⠀⠑⣢⣤⣔⣁⡀⠈⠲⠴⠚⠀⠸⣏⣉⣥⠞⠁⠀⠹⡒⠒⡲⠃⠀⠀⠑⢄⡩⠟⢀⣀⣀⣈⣢⣄⡤⠋⠀⠀⠀⠙⢄
⠀⡠⠤⠖⠒⠶⡏⢉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⠤⡤⠖⠒⠺⠛⠋⠛⠛⠛⠓⠛⠿⠿⠉⠉⢉⠙⠓⢶⠦⠗⠐⡖
⠘⠤⢴⡒⠒⠀⣇⠀⡀⠀⠈⠳⣄⠀⠀⠀⣀⠤⠖⠊⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣄⣸⢀⣀⠴⠁
⠀⠀⠀⡇⠐⠁⢨⠋⠉⢣⠀⠀⠀⠓⠒⡩⠴⢤⡀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⢀⢀⡜⠉⠑⡦⠄⠠⠂⡼⢔⠂⠉⠉
⠀⠀⠀⠁⠐⠚⠓⡖⠲⢼⠓⠤⣠⣀⠞⠀⢀⣀⣳⣉⠒⣀⠀⡘⣀⠠⣈⣷⠤⠬⠄⣰⢗⡐⠑⠳⠤⠤⠞⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠹⡰⢄⡓⠆⠒⠉⡡⠶⠂⠄⠉⡣⣍⣁⠴⠉⠁⠔⠄⠈⠓⠒⠚⠡⡠⠄⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⣀⠈⠀⠀⠁⠈⠀⠀⠐⠀⠂⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⠉⠀⠀⠀⠍⠀⠀⠈⠍⢛⡟⢿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⢻⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠃⠈⢬⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⣬⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣿⣧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣦⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠤⠀⠐⠂⣉⣥⣤⣴⣾⣿⣿⢿⠟⠛⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣴⣶⣾⣾⠿⠿⠟⠛⠛⠁⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣀⡀⢤⠤⠞⠻⠛⠛⠻⠿⠿⣋⣉⣉⣹⣝⣋⣃⣀⡀⠄⠀⣀⡶⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣜⠫⠉⠙⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⢉⣁⣤⣤⣤⣤⣴⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠠⢀⣂⢧⠻⡆⣠⡄⡉⢹⣿⣧⡀⠀⠀⠀⠀⢀⣠⣴⡶⢟⣿⣏⣛⣿⡷⣺⣿⣿⣿⣇⣯⡄
⠀⠀⠀⠀⠀⠀⡀⠟⢾⣄⣧⣼⣇⠈⣺⣿⠋⡝⣆⠀⣠⣶⠟⢿⣧⣠⣼⡟⣻⠿⠗⠚⢃⡀⠉⠙⠛⠃⠅
⠀⠀⠀⠀⠀⠀⠁⠘⠀⠜⠁⠙⠟⠙⠹⠛⣿⠗⠿⡟⠯⠹⠷⣟⣍⣩⣉⣿⡉⠀⠴⠚⠊⣹⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢐⣾⣀⣀⣠⣶⣾⣤⣤⣤⣤⣶⢶⣾⣷⣶⠶⠦⢶⡶⣶⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢥⣬⣿⣧⣧⣄⠀⠀⣀⡁⠀⠀⠀⠿⣃⣀⣤⣾⣷⣾⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠓⠈⠙⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠏⠉⠙⠃⠐⠀⠀⠂⠀⢀⠉⠉⢉⠓⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡚⠉⠀⠂⠀⠀⠀⠐⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢒⡫⣚⠄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢏⢏⠉⠑⢒⡲⡤⠤⠤⢤⣄⣄⣀⣀⣀⣀⣀⠤⣤⣤⠤⢤⣶⣒⣪⣭⣋⠡⠭⠍⠓⠉⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠪⢷⣮⣭⣥⣤⣽⣿⠶⠿⠟⢻⡙⠳⠤⠤⠤⠤⠷⢄⣀⣉⣀⣁⣀⣀⣠⡤⠤⠴⠒⠚⠉⣇
⠀⠀⠀⠀⠀⠀⣀⠀⢳⠚⠉⠉⠉⠉⠓⠺⢖⡢⢄⡀⠀⠀⠈⠙⠒⠒⠒⠒⠚⠉⠉⠉⢀⣄⣐⣂⣐⣒⣒⣒⣒⣂⣀⣸
⠀⠀⠀⠀⠀⠀⡏⠉⠺⣄⠀⠀⠀⠀⠀⠀⠀⠉⠢⣍⠢⡀⠀⠀⠀⣀⠠⣀⡤⠔⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢥
⠀⠀⠀⠀⠀⠀⣹⠄⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⢄⡠⢊⡵⠊⠁⠀⠀⠀⠐⠊⢀⣉⣁⠔⠒⠲⠤⣀⡠⠇⠈⡇
⠀⠀⠀⠀⠀⠰⠧⠤⢤⡀⠈⠳⠤⢶⣤⣤⣤⣀⡀⠀⣀⠳⢤⠔⠋⠀⢀⣀⡤⢄⡀⣠⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡧⢤⡀⠀⠀⠀⠀⠀⢀⣉⠉⠉⠉⠉⠉⠙⢋⣉⡴⠢⣄⣩⣀⣀⢀⣠⠖⠒⠤⢤⠤⠤⠤⢤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠓⠤⠖⠒⠦⠔⠋⠀⠉⠙⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠟⡛⢿⣧⠀⠀⠀⡐⠉⠀⠀⠑⢀⠀⠀⢀⠊⠁⠀⠀⠉⢂⠀⠀⢠⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠀⠀⠀⠘⠿⠂⠁⠺⠟⠀⠀⠀⠀⠀⠺⠂⠀⠘⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠛⠛⠑⠗⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⣜⣧⢧⣯⢖⣀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣾⣿⣿⣷⡄⠀⠀⢀⣤⣶⣾⣶⣦⣄⠀⠀⣠⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠙⠚⠁⠤⠀⠿⠶⠀⠀⠀⠀⠙⡟⠁⠀⠀⠀⠀⠿⠿⢛⡛⠿⠟⠀⠀⠘⠻⠟⣉⡙⠿⠛⠀⠀⠛⠛⠁⠆⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⣴⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⣔⣶⣷⣢⢄
⠀⠀⠀⠀⠺⠿⠟⠭⠻⠿⠗⠀⠀⠀⠀⠾⣿⠆⠀⠀⠀⠀⠀⠰⢾⠷⠄⠀⠀⠀⠘⠛⠛⠿⠟⠛⠛⠀⠀⠘⠚⠁⠄⠙⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠿⠁⢤⣶⡄⠹⠇⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠐⠟⠛⠻⠛⠛⠿⠀⠀⠀⠀⠐⠆

⠀⠀⠀⠀⠀⢠⣶⣿⣷⣄⠀⠀⠀⠀⣴⣿⣿⣷⡆⠀⠀⠀⠀⣴⣶⣶⣤⡀⠀⠀⠀⠀⢀⡤⣤⡀
⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⠹⠿⡿⠿⠃⠀⠀⠀⢼⣿⡏⢹⣿⣷⠀⠀⠀⠀⠸⣔⣨⠇⠀⠀⠀⠀⠀⠠⡦
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠙⠋⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠜⠺⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠶⠦⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠂⢦⣠⠀⠀⠠⠀⠀⠀⠀⠐⣇⣸⠛⣀⣰⡄⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠎⣶⣶⡶⠀⠳⠄⠀⠀⠀⢳⠿⡄⢀⠠⠀⠂⡠⣊⡟⠄
⠀⠀⠀⠀⠀⠈⠃⠀⠊⠀⠀⠀⠀⠀⠀⠀⠙⢷⣀⢏⢻⢿⣆⠄⠀⠀⠀⠀⣀⣨⡁⠃⠀⢀⠀⠐⣂⡀⠰⠀⠀⠰⣝⠲⠀⢐⠈⠬⡁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠆⡸⠁⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠙⠘⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⢠⡀⠉
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠾⠂⠀⠾⣿⣉⣙⠀⣀⡀⠀⣼⠄⢀⡀⠉⠗
⠀⠀⠀⡀⢰⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠆⠀⠀⢈⠾⠪⠈⠤⣀⣙⢤⡤⠞⠀⠀⠀⢸⣿⣬⣿⣿⢶⣷⣎⣩⣽⠇⠀⠀⠀⠐⠤⠀⠑
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠶⣶⣦⣤⣴⣶⣶⣶⣶⣾⠗⠀⠀⠠⢄⡍⢙⢛⠉⠉⠉⠈⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠀⢰⣦⣀⣀⡀⣀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡀⠀⠀⠀⣀⣀⣤⠀⢀⠠⠤⠖⠀⠒⠂⠀⠀⠀⠉⢀⣼⣧⣄⡄⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⡀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠓⠠⠄⠀⠘⠒⠀⠀⠀⠁⠀⠀⠀⠉⠛⠋⠙⠋⠉⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣌⡷⢆⠁⠄⣸⣽⢿⡏⠙⠉⠙⠂⠠⠄⠅⠆
⠀⠀⠀⠘⣠⣀⣠⣀⣀⣀⣬⣅⡩⠕⣖⠲⢦⠤⣤⠄⣤⡞
⠀⠀⠀⠀⣽⢟⣦⣤⣤⣶⣴⣮⣶⣶⣾⡼⡇⠊⠉⡦⣿⡧⠀⠀⠀⢠⠛⠘⠒⠠⣄⠄⢠⠀⡄⢠⢀⡀⣠⡀⢤⠄⠠⠖⠃
⠀⠀⠀⠀⠙⠓⠷⠶⠶⣾⣾⣭⣬⡶⢯⣿⠿⠟⠛⠛⠙⠁⠀⠀⠀⠀⠈⣁⠾⠇⢠⠠⢀⣠⠀⠠⠘⠃⣤⡀⣠⠤⠿
⠀⠀⠀⢀⢤⣄⣀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠪⠄⠤⠀⠶⠀⠀⠀⠀⢉⣉⠀⠀⠀⠀⠀⠀⠈⠐⠛⠛⠉⠙⠑⠒⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠏⠉⠉⠁⠲⠞⡄⠁⠃⠄⠀⠀⠀⠀⠀⠀⠘⠿⣿⣯⣿⣶⣤⣤⣶⣿⣟⣿⣻⣝⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠐⠄⢄⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣶⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣶⡀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠁⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠉⢹⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⠀⢸⣿⣿⣿
⠀⠀⠀⢸⣟⠁⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⢶⣙⡇⠀⠀⠀⢸⣿⣿⣿⣿⠠⢾⡷⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠶⣉⠶⢈⣿⣿⣿
⠀⠀⠀⢸⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⢸⣿⣿⣿
⠀⠀⠀⠈⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⡀⡀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⣀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⡶⠶⠶⣶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠦⣄⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⣀⡀⠀⣄⣀⣠⠈⠐⢄⠀⠀⠀⡀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠘⠛⠂⣠⢈⠀⣠⡔⣮⠉⢳⣤⣭⠠⠀⠀⠘⠁⡁⡀⠄⠀⢠⡿⠀⠀⠠⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⠠⠟⠓⠠⣀⣉⡤⠔⢈⡭⣬⣈⣻⡆⢀⡀⠁⠀⠀⠀⢷
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⢲⣿⣿⠿⠃⠀⠀⠃⠀⠀⠀⠀⠀⠉⠁⢀⡜⠀⠁⠀⠀⠐⡒⠉⠀⠐⠈
⠀⠀⠀⠀⠀⠙⢀⣠⣥⣤⣬⣉⣡⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣮⣤⣤⣄⣀⠀⠉⢀⡶⣿⠟⠹⣿⠿⠆
⠀⠀⠀⠀⠀⠈⠀⠙⠩⠼⠿⢿⣿⣟⠛⣿⣿⣧⣀⣤⣾⠿⣛⣛⣿⣿⢩⣽⣿⣿⣽⣦⣭⡴⠟⢓⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠀⠀⢀⣀⣀⣴⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠂⠈⠉⠁⠉⠉⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠒⠒⠒⠒⠒⠒⠒⠢⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠉⡠⢠⠀⠀⠑⠃⠀⠀⢠⣘⠀⠰⠿⠃⠀⠉⠑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠈⡃⠀⠄⠀⣦⣦⠀⠀⠀⠐⠢⠀⠀⠙⠿⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⢐⠀⠀⠀⢨⡏⠀⠀⢀⠀⠀⠀⠉⠀⣤⣄⠀⠀⠀⠄⠲⠄⢀⡠⠈⢧
⠀⠀⠀⠀⠀⢈⠀⢀⣀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠘⠾⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠄⠀⠈⡧⡄
⠀⠀⠀⣀⠼⠉⠀⠀⠂⠒⢠⣤⣤⡀⠀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠄⣀⣈⣁⣉⣤⠤⠴⠒⡚⡡⠜
⠀⠀⠀⠑⠐⢂⣲⠳⢦⠤⠤⢤⠦⣄⣀⠀⠉⣁⣀⡐⢒⣒⣒⣚⣉⡩⠭⢥⢴⢒⠢⣄⡴⠲⠞⢹
⠀⠀⠀⠀⡎⢁⠆⠁⠸⢊⠐⠺⠶⠤⠤⠭⣭⠭⣈⣈⡼⠛⠯⠥⠦⣤⠤⠼⠬⢼⠤⠶⠷⠶⠚⠉⠱⡄
⠀⠀⠀⠀⠑⠶⠚⠿⠷⣄⣠⣤⣤⠀⠄⠠⠀⠀⠀⢀⣤⣤⡐⠆⠀⡀⢤⣄⣀⣡⡒⢒⣄⣀⡤⡅⠁⡇
⠀⠀⠀⢀⠀⣠⠐⡖⢤⣤⡀⠀⠉⠳⡀⠐⠀⢊⠔⠁⠩⠁⠛⠛⠛⠋⠉⠉⠉⠙⠉⢡⠈⠁⠀⠈⡎
⠀⠀⢰⡀⣀⣄⠁⠂⠠⠤⢈⣁⣀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⠐⠒⠒⣀⣀⠤⢊⣹⣄
⠀⠠⠥⠢⣄⠈⠁⠀⠀⠶⢄⠔⠒⠀⡭⠹⢫⢌⣉⡡⢄⡒⠒⠒⠒⢈⡉⠉⢉⣉⠉⢁⡤⣀⠀⢸⡤⠜⠃
⠀⠀⠀⠀⢸⠓⡆⠀⠁⠀⠀⡀⠤⠤⢄⢤⣠⠐⠤⣈⡈⠳⡄⠀⢰⣉⣙⣑⡉⡂⢫⠁⠐⢠⠳⣠⠇
⠀⠀⠀⠀⠈⣇⡕⠄⠈⡄⠀⠀⠀⠠⠤⠀⠀⠀⠀⠄⠈⠉⢩⠉⢁⠀⠀⠀⠀⠈⠱⠔⠒⡏⢠⠃
⠀⠀⠀⠀⠀⠘⢮⡂⠄⠁⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⢐⣂⡘⠠⠄⠀⠈⡇⠀⠇⠀⠀⣀⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠐⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠶⠶⠶⠖⠶⠶⠶⠶⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠉⠓⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢙⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠣⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡌⠀⡠⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠞⡙⣇⡀
⠀⠀⠀⠀⠀⢰⣶⠚⠻⠛⠷⠿⠤⣴⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠶⠶⠶⠖⠚⠛⠉⣉⡀⡠⢰⠶⠮⠟
⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⢀⣠⣤⠤⣀⠀⠀⡴⠒⢦⣀⡤⠤⣄⠀⠀⢀⡴⢶⠤⣤⡴⢫⠉⢭⣻⠻⣦
⠀⠀⠀⠀⠀⠀⡬⠟⡛⡊⠬⠖⠶⠋⠁⠂⠔⠀⣱⣞⣁⡉⠈⠉⠁⠀⠀⢓⠶⠚⢦⣍⣁⠀⠀⠐⠒⠀⠀⣀⡾
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣈⢁⠄⠀⠌⠙⠉⠉⠉⠉⠉⠉⠉⠁⢀⡀⠐⠂⠔⠄⠈⠀⠒⠒⣿⠿⣍
⠀⠀⠀⠀⠀⠀⠀⣉⣽⠿⣽⣻⣆⣀⣤⠀⠐⠀⢈⠂⠤⠭⣀⠠⠂⠒⠀⢀⡀⣀⣀⣀⣀⣠⣤⠴⠚⠁⠀⠘⢧⡀
⠀⠀⠀⠀⢀⣴⡾⠛⠒⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⠭⠭⠿⠷⠶⢶⣦⢤⣄⣀⠀⠈⣧
⠀⠀⠀⢠⣿⠥⠶⢚⣿⣽⣃⡶⠀⠀⠐⢂⣀⠀⠀⠀⠈⠩⠍⣁⣶⣄⣀⣀⣄⣀⣈⣉⣀⣤⠮⠗⠉⢈⢿⡍⠲⠟
⠀⠀⠀⠀⠀⠀⢠⡏⠨⠉⠉⠉⠙⠙⠓⠒⠒⠒⠒⠚⠋⠉⠉⠉⠋⠉⠉⠁⠀⠁⠀⠉⠀⠀⠀⠀⠀⠐⢈⣿
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢩⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠴⠶⠚⠛⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣭⣦⣧⣿⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣵⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⢉⠉⠉⠉⢉⡉⠓⠒⠒⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠰⠶⠀⠰⠟⠀⠀⠀⠛⣋⣀⠰⠶⠆⠀⠀⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠘⠛⠁⢀⡀⠀⣰⡆⠀⠀⠘⠻⠆⠀⠉⠉⠀⠀⠀⠀⠀⠾⠓⢀⣀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢀⡄⠀⠛⠁⠀⠈⠀⠶⠆⠀⠀⠶⠶⠀⠀⠰⠟⠀⣀⡀⠀⠀⣙⠉⠀⠀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠲⣄⠀⠀⠀⠀⠀⠀⣠⣶⡗⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢠⣶⣿⣷⣶⡄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠲⢤⡀
⠀⠀⢖⠒⠂⠉⠉⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣠⠃
⠀⠀⠀⠑⢄⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⢧⡀
⠀⠀⠀⠀⠀⠙⣦⡀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠙⣄
⠀⠀⠀⠀⢀⡜⠀⠙⠢⡈⠓⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⠲⣄⠀⠉⠉⠒⠒⠤⠤⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠴⠶⠒⠛⠛⠑⠊⠉⠉⠉⠉⢹⡖⠒⠤⠿
⠀⠀⠀⠀⠈⢳⠦⢄⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠖⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢺⡇
⠀⠀⠠⣤⠒⠚⡄⠀⠈⠉⠉⠉⠉⠉⠑⢄⠀⠀⠀⢀⣀⡤⠤⠖⠒⠋⠉⠀⡸⡏⠑⠦⣀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠐⠒⠒⠊⠉⠀⠀⢸⠧⣄
⠀⠀⠀⠈⠉⢲⠞⠑⡖⠒⠒⠒⠒⠒⠒⠚⠛⠒⠛⠛⠓⠒⠒⠒⠒⠒⠒⠉⠀⠈⠒⠒⠚⠛⠒⠒⠒⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⠃⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢪⡀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢻⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠈⢱⠦⢤⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⡭⠭⠭⠭⠭⠭⠭⣭⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣩⣥⣶⣥⠤⠤⠤⠤⠤⢤⣘⠄
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠉⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⢀⣠⠤⠔⠒⠒⠉⠉⠉⠉⠁⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⡀⣀⣀⠤⠤⠲⠒⠚⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠠⠤⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠤⠔⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠻⠙⠉⡁⠉⠴⠂⠩⠳⡚⠽⠟⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⢿⠎⠘⠀⠀⠀⣀⠀⠀⠀⠀⠅⠀⡠⢜⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠂⢠⡄⠐⠀⠙⠆⠐⠊⠀⠀⠀⠂⠀⠀⢘⠿⠚⣻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠭⠀⠀⠈⠁⠀⠀⠀⠀⠲⠄⠀⠀⠤⣀⠐⣴⠀⣚⣵⢾⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣀⠀⣂⡀⠠⠟⠀⠐⡦⠀⢀⡆⠈⠛⣠⡄⠉⠁⣹⣿⣷⣾⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣦⣤⣀⣷⣅⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢛⣛⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⣭⠭⠽⠿⠿⠧⠤⠒⠚⢛⣫⣿⡟⢋⠁⡥⠴⠾⣿⣿⠿⠟⢋⡉⠽⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⣀⣀⣀⣠⣶⣶⣒⣛⣭⣭⣍⣥⣤⣤⣴⣶⣿⣯⣔⡒⢄⡂⣹⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⣴⣾⣿⡿⠿⠿⢻⡿⢟⣿⢿⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣹⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠩⢿⣃⠀⣀⣤⣤⣦⣼⣿⣤⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣀⡉⠉⠻⢫⣽⣿⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣛⣛⣙⣻⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣰⣔⣩⠏⢉⡉⠉⣙⣟⣈⠒⠦⠬⢟⣋⣩⣬⡛⢹⣉⣉⣀⣈⣻⣧⣤⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣓⣛⠋⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣤⠬⠙⣶⣿⣿⣿⣿⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣯⣄⣀⣀⡀⢀⠀⣀⣀⣀⣀⣀⣛⣠⣤⣬⣿⣿⣿⣿⣿⣿⣿⣯⣾⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠉⠙⠙⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⣀⠐⠒⢲⠶⠲⠶⠶⠴⠠⢤⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡤⠘⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠓⠀⠀⠾⠉⠻⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠿⠿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠠⠄⠐⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⡌⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠄⢈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣾⣿⣿⠿⢿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣭⣟⠳⠶⠶⣶⢶⣶⣶⡾⣿⣶⣶⣦⣶⣶⣶⠶⠾⣶⣾⣛⡛⡛⠛⢛⣻⠟⣩⣷⣞⡵⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠤⠒⢿⣿⡗⠶⢶⣿⣶⢶⣾⣿⣌⣉⣉⣭⣿⣿⣟⣿⢿⣿⣯⠴⣽⠲⣴⣾⣧⠌⠀⠀⠑⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠠⣍⣠⣀⠐⠟⠻⠿⠻⡶⢻⡿⢿⣿⣟⠓⠛⠊⠁⠀⠀⠊⠁⠀⢀⣀⣉⣁⣀⣀⣤⣶⡶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⣿⣿⣶⣦⣉⠁⠀⠐⠃⠀⢈⣠⣤⡴⣶⡶⢶⣶⠶⣶⣿⣿⣿⣿⢛⣿⣿⣆⡿⣤⡿⣸
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡶⡌⣿⣦⣝⣻⣷⣄⠀⢀⣴⣿⣿⣴⣶⢿⣧⣾⣏⣼⣏⣠⣿⢻⡏⣿⣁⣸⣿⣽⢿⠰⠇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡉⠂⠙⠈⠏⠙⠿⢶⠿⠿⠛⠀⠟⢳⡛⢻⡆⡻⣛⠛⠛⠷⠿⡗⠞⠛⠿⠛⣿⣈⣱⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠂⠒⠲⢤⣴⡶⢶⣶⣿⣿⣶⣤⠾⣴⣥⣤⣦⠶⣶⠶⠾⠓⠚⠚⠗⢶⡿⣋⡉⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⠀⠀⣼⣤⣷⣸⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠦⠤⢤⣤⣤⣤⣄⢤⣤⣠⣤⣤⣴⣦⣤⠤⠴⠷⠾⠿⠶⠞⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⣀⣀⠀⡀⢀⢀⡀
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠟⠑⠚⠘⢿⠋⠉⠉⠨⣽⠧⠄
⠀⠀⠀⠀⠠⢼⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠆⠀⠀⠀⠀⠀⠈⠀⠀⣀⡤⠖⠁⠈⠁⠤⣄⠘⠢
⠀⠀⠀⠀⠀⣶⢿⣠⡆⠒⢀⡴⣶⢶⠶⣄⠀⡌⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⣽⣷⣿⣷⣤⣬⣀⣑⣨⠑
⠀⠀⠀⠀⠀⠻⢷⣶⣇⣸⣛⣐⢄⣀⢈⣹⡂⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠃
⠀⠀⠀⠀⠀⢐⣦⣬⢭⡽⠿⣟⣛⡛⠛⢉⣡⠄⠀⠸⠁⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠣⠏⠻⠏⠉⠓⠓
⠀⠀⠀⠀⠀⣼⠛⠧⠂⠄⡀⠀⠉⠉⣇⠉⠤⠐
⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠐⢀⠁⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠤
⠀⠀⠀⢀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠐
⠀⠀⠀⠀⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠙⠛⠷⠿⠟⠛
⠀⠀⠀⠀⠸⣧⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣴⠋⠁⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠄⠀⠀⢀⢀⣤⠰⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠞⠛⢋⠉⠉⠉⠉⠉⠉⠛⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠨⠙⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⢀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣌⠂⠄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠲⠶⠶⠶⠦⠤⠤⠤⠤⠤⠶⠶⠖⠚⠋⠉⠀⠐⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣶⣤⣤⣄⠀⠀⠀⢀⡀⠤⠤⠤⠤⠄⢀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣀⣠⣤⢤⡤⠴⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⣀⣠⣧⣉⣻⣷⣶⠶⠶⠛⠛⠛⠓⠶⢦⣤⣤⣴⠾⠋⠉⠉⠙⠛⠛⠛⠉⠀⠀⠀⠙⢤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠍⡁⠀⠀⠀⠭⠍⣙⡓⠲⠦⠤⣤⣀⡀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠄⠒⣀⣀⢠⡽⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠉⠙⠒⠢⢬⡉⠓⢶⠚⠉⡁⠠⠐⠂⠋⠉⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠢⢄⣀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⡈⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⠉⠙⠒⠲⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠖⠒⠋⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⣀⠀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠲⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠲⠶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠙⠒⠤⠤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠒⠋⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⡶⠛⠛⠀⠀⠛⠙⢲⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢰⡋⠀⠈⣷⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠖⢲⠀⠀⡶⠶⠛⠀⠀⠀⠀⠀⢠⠏⠀⠈⢳⠈⠷⠤⠴⠋⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢦⡤⠇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠾⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⠐⠄⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠁⣠⠈⠀⠈⣡⠀⠉⢉⠑⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⣡⠀⠀⠀⠈⢁⠀⠁⠀⣄⠀⠀⠦⠀⠉⠀⠀⠀⣀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠴⠀⠀⠋⢀⡀⠀⠀⣀⡀⠀⠀⡤⠀⠀⠀⠀⠀⠖⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠐⠆⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⢦
⠀⠀⠻⣍⠉⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡴⠁
⠀⠀⠀⠈⠳⣄⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⠱⣄
⠀⠀⠀⠀⠀⡸⠓⢄⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠈⢆
⠀⠀⠀⠀⡰⠁⠀⠀⠑⢄⡈⠑⠢⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠤⠶⠯⠤⠤⠤⠤⢤⡤⢄⣘
⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣉⣉⡍⠭⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠁
⠀⠀⠀⣤⠄⢺⡀⠈⠉⠐⠂⠀⠙⠢⡀⠀⠀⠀⣀⡠⠤⠔⠒⠉⠉⡹⡁⠲⢄⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠄⠒⠊⠉⠀⢠⠦⣀
⠀⠀⠀⠈⠉⠲⠋⢲⠂⠀⠀⠐⠐⠂⠙⠒⠛⠋⠁⠒⠒⠐⠀⠂⠉⠀⠉⠒⠒⠛⠒⠒⠒⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⡃⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠣⣀⠈⠦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⣫⠁⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠟⠒⠂⠀⠀⠒⠀⠤⣤⠤⠀⠒⠒⠒⠂⠀⠀⠀⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠠⠤⠒⠚⡷⠒⠒⠀⠒⠒⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⢀⣀⠭⠶⠤⠤⠔⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠤⠤⠄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠤⠤⠴⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁



⡿⠉⢙⡟⡿⠻⠿⠟⠿⡛⠿⠻⠿⠿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⡿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠦⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠰⠗⠃⠀⠀⣤⠀⠀⠀⣶⠀⠀⠘⠫⠇⠀⠠⣤⣭⢛⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢀⠔⡆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⢀⠀⠀⠈⢊⢷⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠘⠋⠀⠀⠈⠁⠀⠀⠀⢠⠕⠀⠀⠀⠈⠀⠀⠀⠀⠣⠁⠀⠀⠘⢫⣺⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⣢⣊⢥⣖⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣀⣀⣀⣤⣤⣤⣤⣽⣽⣵⣭⣭⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣘⣝⣁⣏⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣨⣯⣈⣄⣈⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠙⠋⠝⠉⠈⠉⠉⠉⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠝⠉⠈⠈⠐⠁⡪⠚⠽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠴⠵⠦⠤⠦⠤⡤⠤⠤⠤⢤⡤⠤⠤⠤⢤⣤⡴⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠶⠒⡆⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡺⡆⠀⠀⣳⡀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡶⢚⣉⣯⣀⣠⠔⠢⠤⠚⠓⠛⡇⠀⠀⢋⠤⣀⠴⠀⣸⢁⣀⣬⣷⣞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣯⣀⣀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠉⠀⠈⠛⠛⣵⣾⣿⣿⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠚⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠒⣒⡒⠒⠒⠒⠒⠒⠒⠲⠦⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠛⠃⠀⠀⣀⠀⠉⠉⠓⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢁⣀⠀⠀⠀⠀⣴⣲⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆⠀⠀⣠⡄⠀⠘⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢁⠀⠀⠀⠠⠶⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢇⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⠆⠀⠀⠀⠠⢊⠁⣶⠇
⠀⠀⠀⠀⠀⠀⠀⣴⡋⠉⠳⢥⣀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡤⠔⠚⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⠉⠙⠒⠦⢤⣀⣀⠀⠀⢤⣀⣀⡀⠀⠀⠀⣀⡀⠀⠀⣰⣒⠾⠭⠒⠊⠉⢁⣀⣀⣀⣀⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠖⢚⣻⡆⠀⣀⣠⡄⠈⠉⣩⣹⠟⠓⠒⠒⠒⠒⠛⠉⢉⣉⣤⠤⠶⠒⢚⡋⠩⠉⠁⡤⠀⢻⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠛⠆⢩⣭⣡⣤⠳⠖⠚⠳⣄⠀⠀⠀⢀⣀⡤⠖⢫⡉⢠⣴⣆⠁⠠⡭⠝⠺⠆⣠⣠⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⠿⢿⣦⣤⣿⣅⡁⠈⠳⠟⠄⠸⣄⡤⠞⠉⠔⠻⣄⠺⣗⣀⣀⣉⣤⣤⣴⣶⡶⠿⣛⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡂⠀⠉⠉⠛⠛⠻⠿⠿⠷⠶⠿⠶⠾⠿⠷⠿⠿⠿⠿⠛⠛⠋⠉⠉⠁⠀⢀⣈⠥⢞⣛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢒⣺⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⣤⣄⣀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⢀⣀⡤⠴⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠓⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢴⠆⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⢰⢶⡄⠒⡀⣤⠘⠙⠛⠁⠀⠈⡡⠍⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣀⠀⠀⠀⠀⠀⠀⠙⠇⢠⠀⡀⠀⣀⡹⢦⠾⠨⠉⠀⠀⠓⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⡀⠀⠀⠀⠀⠀⠘⠈⠁⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠔⡩⠄⢀⡄⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠰⠚⠍⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠂⠆⢠⣄⡄⢀⢀⡀⡄⡀⢀⡀⢠⡄⢠⠴⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡾⠧⢡⠠⢁⣄⠀⠀⠋⣭⡁⣀⡠⡷
⠀⠀⠀⠀⠀⠐⠀⠵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣀⠀⠀⠀⠀⠈⠓⠚⢛⣊⠉⠑⣂⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡁⢨⡀⠀⠀⠀⢀⠀⠀⠀⠀⠛⠿⠿⣿⣶⣦⣶⣾⣿⣽⣯⣯⣿⣿⣿⠿⠿⠁
⠀⠀⠀⠀⠈⠀⣀⠤⠐⠃⠀⠀⡃⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠀⠀⠀⠀⢀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠓⠐⠁⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡤⠀⢓⡀⣀⣠⣴⣾⠅
⠀⠀⠀⠀⢿⣴⣞⣿⣛⢲⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠘⠗⠻⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣷⣿⣽⣿⡏
⠀⠀⠀⠀⣇⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡖⣦⣤⣤⡴⢰⠀⠘⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⡿⣿⣿⠇
⠀⠀⠀⠀⠙⠢⠄⠀⡀⠀⠀⠀⠀⠀⡀⠤⣤⣿⣋⠙⢫⠘⢿⣿⠷⠟⠀⠀⠉⠁⡀⠀⠀⠀⠀⠀⢿⢻⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠉⡃⠀⠀⢀⡠⠄⠔⠓⠂⠀⡀⢳⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠣⣛⣋⡀⠀⠀⠂⠀⠘⠂⠀⠀⢳⡟⠓⠠⠦⠠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠛⠛⠛⠛⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠓⠶⣄
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢠⡟⠀⣠⣤⡴⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠖⢢⣤⣄⠀⢷⡄
⠀⠀⠀⣼⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣧
⠀⢠⡾⠁⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣄⣀⣀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣄⣀⠀⠀⠀⠀⠉⢷⡀
⢀⡞⠁⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⠈⢳
⣈⠃⠀⠀⠀⠀⠀⣿⠀⢸⠛⢿⡛⠛⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠸
⣧⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠘⢷⡄⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⢻⡄⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠈⣿⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⣴⠃⠀⠀⠙⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⢁⡄⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⣶⠶⠛⠁⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠈⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠰⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⣦⣀⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄⠀⠀⣰⣿⣿⠏⠀⠀⠀⣠⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⣉⣀⡈⠉⠉⠉⠉⠛⠻⣦⣄⡀⠀⠀⠀⠹⣿⣿⣧⣀⣿⣿⡟⠀⠀⢠⡾⢋⡅⠀⣿
⡿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠛⠛⠛⠛⠶⢶⣄⡀⠀⠀⠈⠙⢦⡀⠀⠀⠈⢿⣿⣿⣿⣿⠃⠀⢠⣾⠁⠠⡇⠀⣿
⣧⠀⠀⠀⠀⠀⠀⣿⠀⢸⣶⣤⣀⡀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠙⣦⠀⠀⠀⢿⣿⣿⣿⠀⠀⢸⣇⠀⠀⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠉⢻⣄⠀⠀⠀⠸⣇⠀⠀⠀⠀⠸⣷⠀⠀⠸⣿⣿⣿⡀⠀⠈⢿⡄⠀⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠄⠀⠀⠀⣿⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢸⡇⠀⠀⢻⣿⣿⡇⠀⠀⠈⢳⣦⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⣰⠟⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠙⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠃⢀⡴⠋⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠰⡇⠀⣿
⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⡾⠋⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⢰⡇⠀⣿
⢿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⢠⡇⠀⣿⠀⠀⠀⠀⠀⢀
⢸⡆⠀⠀⠀⠀⠀⣿⠀⠸⠶⠶⠶⠶⠿⠷⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠷⠶⠶⠶⠶⠃⠀⣿⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠻⣤⣤⣀⣤⣤⣤⣄⣠⣄⣀⣄⣀⣠⣄⣀⣠⣤⣄⣀⣤⣀⣠⣄⣀⣤⣀⣄⣀⣄⣀⣠⣴⠏⠀⠀⠀⠀⠀⢸
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣇⠀⠀⢀⣠⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠄⠤⢤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈
⠀⢸⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⡴⠋⠁⠀⠀⢀⡀⠀⠀⠈⠹⢦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡇
⠀⢸⡇⠀⠈⠛⠻⠿⢿⣿⣿⣿⡇⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢸⣿⣿⣿⡿⠿⠛⠛⠁⠀⢸⡇
⠀⠈⣿⠗⠶⣤⣤⡀⠀⠈⠉⠉⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢉⡉⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠋⠉⠁⠀⢀⣤⣤⠶⠺⡿
⠀⠀⢿⠀⠀⠀⠀⠉⠛⠳⠶⠦⣀⡀⠀⣼⠀⠀⣴⣶⣶⠀⣼⣿⣿⡇⢠⣶⣶⡆⠀⠈⡇⠀⢀⣀⡴⠶⠞⠛⠁⠀⠀⠀⢀⡟
⠀⠀⠈⣦⠀⠀⢀⣀⡀⠀⠀⠀⠈⣷⠀⢹⡄⠀⠈⠉⠁⠀⠘⠛⠛⠃⠀⠉⠉⠁⠀⢰⡇⠀⣿⠁⠀⠀⠀⢀⣀⡀⠀⠀⣼
⠀⠀⠀⢿⡀⠠⣿⣿⣷⠄⠀⠀⠀⢻⡀⠘⣧⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⣾⠁⢠⠏⠀⠀⠀⠰⣿⣿⣿⠀⢀⡟
⠀⠀⠀⠘⣷⠀⠙⠛⠃⠀⠀⠀⠀⠈⣷⠀⠈⠳⣄⠀⠀⠀⠀⠛⠛⠀⠀⠀⢀⣠⠟⠁⠀⣿⠀⠀⠀⠀⠀⠙⠛⠋⠀⣾⠁
⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠉⠻⢦⣤⣤⣄⣀⣤⣤⠶⠟⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠈⢷⡀⠀⣤⣶⣦⡄⠀⠈⢧⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⢀⡞⠀⠀⢠⣶⣶⣄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠻⠿⠿⠃⠀⠀⢸⡇⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⡇⠀⠀⠘⠿⡿⠟⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣼⠁⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⣿⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⡿⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢄⣨⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣅⡠⠶⠞⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣦⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⠿⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣁⣀⣀⣀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠟⠁⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠚⠛⠛⢛⡛⠛⠛⠛⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⡉⠀⠀⠛⠀⠠⠀⠈⠁⠠⠄⠈⠃⠀⠐⠆⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢥⠀⠀⢁⠀⠀⠁⠀⠀⠘⠂⠀⠀⡀⠀⠈⠁⠀⠀⠐⠂⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⣶⣤⣬⣍⣛⡓⠒⠶⠶⠶⠤⠤⠤⠤⢤⣤⣤⠤⠤⠤⠶⠶⠒⣚⣫⠭⠵⣶⢶⣶⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣌⠓⠲⠬⠝⠛⢓⣶⣤⣀⡀⠀⠀⠀⠀⢀⠀⢀⣠⣴⣚⡛⠓⠒⣚⣉⣥⣾⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡑⠚⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⡀⠐⠋⠈⠉⠉⠙⠛⠿⠛⠛⠻⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠁⠀⠀⢀⡈⠀⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣤⣤⣶⣶⣶⣄⣀⣠⣤⡀⠀⠤⠀⣀⣀⡀⠀⠀⢀⣴⣶⣶⣮⣭⣶⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⢤⠖⠒⠛⡿⠋⠉⡉⠉⡉⠉⢉⠉⠛⠓⡒⠳⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠖⡛⠉⠀⠀⠋⠀⠂⠀⠴⠀⠀⠁⠀⠀⠀⠈⠁⠴⠀⣁⠀⠀⠤⠀⠩⡗⠦⣤⡀
⠀⠀⠀⢀⡶⠞⠉⠀⠉⠁⠠⠄⠀⠀⠖⠀⠀⢀⡀⠀⠂⠀⠀⠀⠦⠀⠀⠄⠈⠀⢠⠀⠀⣀⠀⠐⠎⠑⢆
⠀⠀⢠⡞⠰⠂⠀⠖⠀⢠⠄⠀⠀⢀⠀⠐⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠊⢳⡀
⠀⠀⣿⣇⡀⠀⠀⠀⠀⠀⡀⠀⠔⠁⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠀⠀⠀⠒⠀⠀⢳
⠀⢸⣏⣾⡄⣠⢤⡄⠀⢀⣤⣄⣾⣶⣦⣼⣴⣼⣶⣷⣶⣶⣦⣦⣤⣤⣀⣀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠈⣿⣿⣻⣻⣼⣿⣿⣾⣿⡿⠿⠟⣛⣉⣉⣩⣥⣠⡤⠤⢤⣄⣀⣀⠽⠿⠯⢭⣭⢿⣛⣛⡒⠶⠶⠶⠦⠴⢾⡀
⠀⠀⠘⣿⣿⣿⣿⣛⣋⣉⡀⢀⡴⠋⠁⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠂⠈⠙⠲⢶⠲⠲⢴⣶⡽⠦
⠀⠶⠟⣷⣾⡟⠉⣏⠉⢉⠉⠉⠀⢀⠀⢀⡀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡤⠁⢹
⠀⠀⠀⢿⣭⣶⡀⠀⣀⢈⣀⣤⣾⣯⡽⠿⠶⠶⠶⠶⠶⣄⣠⣄⠀⣠⣤⡴⠿⠿⠶⢶⡆⠀⠀⢀⣌⣃⣀⣀⣠⠞
⠀⠀⠀⠀⢹⣿⣿⢰⠙⠋⠉⠀⠀⠀⣀⣀⣀⣀⣤⡤⠤⠽⢿⣿⣤⡿⠿⠓⠒⠲⠤⠼⠿⣴⣛⣋⠉⠉⠉⢹⡇
⠀⠀⢀⣴⣾⣿⠟⠛⠂⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⠉⠉⠉⠳⣄
⠀⢰⣿⣿⡿⠿⠶⣶⣤⣀⠀⠀⠀⠀⠀⡄⠰⠒⠀⠀⠀⣀⣤⠶⠛⠋⠉⠉⢉⠉⠉⠉⠉⠙⠳⠴⠶⣄⠀⠀⠀⡼⣷
⠀⢸⣐⣉⣹⣋⠀⠀⠈⠙⠛⢶⣄⡀⠀⠓⠂⠀⠀⢠⠞⠋⠀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠒⠀⠹⣄⡟⠛⠀⢘
⠀⠈⢻⣿⣯⣅⣀⣉⣀⣀⣀⣀⣙⢻⣶⣦⡀⢠⡟⠉⠀⢀⣢⣀⣀⣀⣠⣄⣀⣀⢀⣘⣂⠀⠀⠀⠀⣤⡉⣁⣀⣡⠞
⠀⠀⣾⣿⣿⠉⣹⠿⡿⠟⠉⢻⡟⠻⣿⣿⣷⡿⠛⢿⠛⠋⣉⡉⢉⡏⠉⡟⠉⣻⠛⢯⣯⡿⠋⣿⠙⠛⢻⠿⣿⡇
⠀⠀⠀⢸⣿⣷⠃⠀⠀⠀⠀⠈⠳⠞⠀⠈⠉⠀⠀⠸⣄⣰⠉⠓⠋⠀⠀⠻⠞⠁⠀⠀⠀⠀⠀⠸⣧⣀⡟⠀⢸⡇
⠀⠀⠀⠸⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠻⢿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠾⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠴⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠟⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠛⠷⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⢠⡿⢛⣿⡿⠿⠿⠿⠿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⡿⠿⠿⠿⠿⣿⣟⠻⣷
⠀⠀⢠⣿⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠙⢷⣼⣧
⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿
⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠹⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⢠⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣧
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠀⠠⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠲⠒⠈⠉⠀⠊⠀⡀⠀⠠⠀⠨⠉⠋⠂⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⢀⣀⠀⡀⠀⠀⠀⠀⠐⠉⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⢀⢻⣺⣶⠷⢟⣶⣿⣿⣞⢿⣿⣷⠷⣶⣶⣤⡆⣤⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢞⣛⣽⠿⣿⣿⠟⢛⣘⡉⠭⢭⡬⠝⠛⠻⠿⠿⠿⣷⣟⠿⠽⣿⡿⢿⠂
⠀⠀⠀⠀⠀⠀⠘⢻⠿⣶⣟⣁⣴⣿⣿⣤⣤⣶⣶⡶⣤⣶⣶⣷⣦⡖⠙⠛⢿⣿⣦⣹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣮⣭⣟⣛⡻⢭⣝⣾⣿⣿⢶⣭⣛⣛⣟⣟⣚⣯⡽⣿⣿⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣿⡟⠛⠿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣷⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣦⣶⣶⠀⣾⣶⣦⣤⣀⡀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣤⠄
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠻⣿⣳⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⣭⣭⡄⠶⠎⠀⣠⣀⣙⠛⠉⠉⠙⠛⠛⠛⠛⣉⣉⡉⣭⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠁⢻⣯⣄⡀⠹⠔⣋⠉⠀⠀⠀⠉⠐⠀⢀⠤⠔⠊⠉⢹⡄⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣴⣀⣈⣉⡁⢀⡀⠀⠘⠀⠒⠀⠐⠒⠚⢀⣸⢡⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠷⠶⠟⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣄⡀⠀⠀⠀⢀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣾⠁⠀⢹⡆⠀⠶⣿⠶⠆⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠘⠷⠶⠞⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⣤⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣴⠚⠛⢦⡀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡾⠋⠈⠻⣦⡀⠀⠀⠒⢺⡗⠂⠀⢻⣄⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡾⠋⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠛⢶⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⢷⣄⣀⣠⡾⠁⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠉⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⢰⠇⠀⠀⠀⢀⣄⠀⠀⣠⣄⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣴⠆⠀⢀⡴⠋
⠀⠀⠀⣿⠀⠀⠀⣴⠋⠈⠳⠾⠋⠈⣳⡄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣴⠟⠁⢀⡴⠋
⠀⠀⠀⣿⠀⠀⠀⠈⣳⡄⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠴⠏⠁⢀⡴⠋
⠀⠀⠀⢸⡄⠀⠀⢾⡋⠀⣠⣄⠀⠈⣻⠄⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠞⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢻⡄⠀⠀⠙⠾⠋⠈⠳⠞⠁⠀⠀⢠⡴⠒⠒⢦⣄⠀⠈⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⣠⡾⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠉