Chicken soup Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠚⠻⣷
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠀⠰⠆⠒⠐⠂⠂⠀⢹⠋⠹⠉⠀⠉⠐⠰⠷⣒⠖⢠⣠⣤⣤⡔⠋⠁⠀⠀⠀⠘⠁
⠀⠀⢀⠴⠚⠁⠀⠀⠀⠀⠀⢀⡀⢤⢀⠀⢠⡿⠄⠀⠀⠄⠠⠅⠄⢢⣤⡙⣲⣴⡟⢑⠿⢳
⠀⠀⠻⣦⣄⣀⡤⠚⠉⠈⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠄⠀⣠⡶⠏⢁⣻⣦⡿⠋
⠀⠀⠀⠙⡯⢍⠉⡒⠲⠶⠤⠤⣤⣤⣄⣀⣀⡠⠤⡤⠤⠤⠤⠄⠔⠛⠛⠒⠉⠉⠁⠺⡅
⠀⠀⠀⠀⠆⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⡠⢪⡇
⠀⠀⠀⠀⣶⠹⠊⡠⡀⠢⠜⠀⣀⠠⣐⠄⠀⠀⢔⡢⠀⡀⠂⠅⠀⠄⡐⠁⠐⠴⠀⠘
⠀⠀⠀⠀⠱⣀⣈⣉⠀⠀⠀⠐⠒⠃⠀⠀⠬⠥⠀⠀⠰⠓⠂⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠨⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣦⡤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⠒⠈⠉⠉⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠊⠉⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠠⠐⣀⣀⣠⡤⠄⠀⠀⠀⠀⠠⣤⣤⣄⣀⣀⣀⠀⠀⠌⠑⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⢋⣀⣤⣶⣾⣿⠿⠋⣁⡤⠖⣒⠒⠀⠲⠤⠤⠙⠩⠿⣿⠿⠿⠿⢶⣦⣄⣈⠢⡀
⠀⠀⠀⠀⠀⢀⡞⣠⣿⡿⢿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠤⠄⠀⠁⠀⠈⠉⠉⠉⠻⡿⣿⣧⡙⡄
⠀⢀⡠⠔⠒⢺⢠⡿⠉⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⣠⡘⠃⠠⠄⠀⠀⠒⢺⣧⢹⡀
⠀⡞⠀⠀⢠⣿⡘⣧⣀⣀⣀⡀⠀⠉⢀⣤⠍⠠⠄⡀⠀⠀⠄⠀⠸⠀⠒⢁⠐⠁⠀⠿⠂⠀⠀⠀⣼⣿⢸⣧⡀
⠀⠘⢄⢠⠟⠀⢳⡘⣿⣿⣷⣤⣀⠀⠉⠁⢶⡆⠛⢣⣶⣀⣘⠉⢠⣄⠀⠀⠂⠐⠂⢠⡤⠔⣩⣾⡿⢃⣾⡄⠻⡄
⠀⠀⢸⠏⠀⠀⠀⠙⢮⡙⢿⣟⡻⠓⠀⠀⣴⣶⣄⠙⢿⣿⡏⠀⠈⠁⠀⠀⠀⠀⢀⣠⣶⣾⠷⢋⡴⠋⠉⢡⠳⣼⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠲⢬⣙⠛⠲⠾⢿⣿⣿⣤⣄⣀⣠⣤⣴⣶⣶⣦⣶⠧⠿⠛⣉⡤⠖⠋⠀⠀⣠⠏⠀⠀⠙⢦⡀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⢤⣤⣀⣈⣉⣉⣉⣉⣁⣀⣤⡤⠶⠚⠋⠁⠀⠀⣀⠤⠚⠁⠀⠀⠀⠀⢈⣷
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⣤⣤⣤⣀⣀⠤⠔⣱⠃
⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⣠⠤⠶⣶⣶⡖⠉
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⠤⣤⣤⣀⣤⣤⣤⡤⠤⠤⠖⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⡦⠐⢄⣀⠀⣀⠀⠀⢀⣠⡤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠁⠀⠀⠀⠀⠸⣷⣺⡄⠈⠀⠀⠀⠀⡠⠚⠀⠀⠀⠀⠈⠀⢶⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡓⠾⢦⠄⠀⢀⠾⠟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠇⠀⣁⠈⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣲⣤⠀⠀⠛⠿⠆⣀⠀⠲⠆⣀⠀⠀⠀⠀⢀⠀⣰⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⢴⡶⠶⣒⡲⠸⠟⠁⠈⠀⠀⠀⢠⠿⣷⣄⡀⠻⠛⠚⠓⠂⠂⢶⣿⣿⣿⠍⢁⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠸⡀⡘⣶⣿⣶⡤⠀⠀⠀⠀⠀⠙⢭⣉⠐⠁⠀⠉⠀⠊⢡⠨⡁⢀⠙⢿⠟⠀⢠⠖⠂⠀⠀⠀⠙⢋⡡⢶⣌⣉⠂
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠑⢈⠷⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣀⣀⣠⡷⠈⠀⡀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢀⡿⢢⡍⠷⠊⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠧⣘⣆⠀⠀⠀⠀⠀⠀⡀⠈⠉⠒⠐⠒⠒⠾⣧⠶⠆⢠⣤⠹⣆⠀⠀⠀⠀⠀⠀⠀⣠⡎⣀⠟⢃⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢦⣤⣉⠓⠤⢔⣁⣀⣠⣴⠁⠀⠀⠀⠀⠀⠀⣿⢲⣿⠌⢫⣄⠻⣷⣦⣀⣀⣤⠴⠛⠋⣀⡤⣾⡯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠒⠦⠤⠉⠉⠙⠑⠀⠀⠀⠀⠠⠠⠿⠮⠵⠿⠟⠉⠓⠀⠈⢀⣡⣤⡶⢒⠽⠃⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠂⠐⠂⠒⠒⠒⠟⠛⠛⠀⠀⠄⢠⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠶⡇⠁⣴⢍⣠⠀⢓⣡⢶⣈⠁⢲⣼⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠡⠛⠓⢧⠐⠦⣈⡡⠀⡉⠡⠌⠍⠁⣀⢻⡖⠀⠂⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⠲⣄⡀⣐⡀⠀⠀⢘⡇⠀⠀⠀⢀⠀⠀⠚⠋⠁⢉⡛⢄⡲⠝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⣀⣹⡦⠬⠫⠀⣤⣘⡀⠀⠀⠞⠁⠀⠀⠀⠀⠀⢀⣀⣤⠷⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢩⠞⠉⠁⠀⡰⠂⠈⠛⠉⠉⠤⡀⡆⠀⠀⡤⠀⠈⠀⣀⣀⣀⣀⣀⣀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡇⠀⠀⣀⠟⠀⠀⠀⠀⠐⠀⠀⠈⠑⠀⡘⠀⢀⡤⠋⠉⠀⠠⠀⠠⠭⣣⠄⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠂⠈⣇⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡇⢀⡎⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡦⠤⣤⡏⠀⠀⢀⣤⡤⢤⡀⢠⠀⠀⠐⠃⠀⠀⠁⠘⣆⠠⠀⠀⣀⡀⠀⠁⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡀⠄⢈⢹⡀⠀⠞⠁⠀⠀⠙⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠈⡸⠇⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⡄⠀⠀⠸⢷⣄⠢⣀⢆⡠⢃⣴⢻⡾⠋⠙⢛⠋⠀⠀⠀⠀⠀⠀⠀⠘⢻⠁⢄⡡⠰⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠩⢬⠑⣀⠒⠒⠭⢁⣜⠃⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡾⢀⠐⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠀⠋⠈⠁⠉⡐⠢⠤⣞⢋⣠⡆⠀⡄⠀⠀⠀⠀⠀⢀⠆⠀⡾⠛⠘⡇⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡄⠈⠁⠀⢌⣭⣍⡀⠰⠟⢀⠀⠀⠐⠒⠋⢀⡺⠂⡶⠁⠻⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠈⣥⠀⢰⠀⠻⠧⠛⠀⠀⠠⠃⠀⠀⢂⠰⠃⣠⣤⣼⠃⢠⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠐⠣⠀⠈⡛⠢⠀⠀⠀⠁⠀⠀⠴⢁⠿⣧⡀⢁⠀⠿⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⢀⣀⣀⣠⠠⡤⠺⡇⠐⠀⡄⠈⠉⠙⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⠿⠷⠶⣮⢻⣄⠀⠠⠟⠈⠓⠉




⣿⣏⢹⣟⠻⣿⢛⠟⣻⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠐⠤⠤⠠⠀⠤⠤
⠀⠀⠀⡤⣦⢤⣀⡀⣀⡀⣀⣠⣤⢀⡀⡀
⠀⠀⠀⠐⠃⠏⠓⠛⠓⠛⠓⠓⠓⠛⠛⠚
⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠤⠤⡤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠠⠠⢀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠌⢁⡄⣀⣠⣶⣤⣄⣀⣀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡭⠔⠒⠛⣿⠁⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⠀⠈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠄⠀⠀⠀⠀⠸⠗⠊⠁⠸⡄⠀⠀⠀⠀⠀⠀⠉⠑⢢⡀⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠚⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠈⠓⢦⣀⣀⣾⠑⢂⠉⠁⢃⣤⣴⣾⣋⡡⠁⠀⢀⠀⠀⠀⠀⠀⢘⠀⠀⢠⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⡔⠛⠉⠉⠀⠉⠀⠀⢨⠀⠏⠉⠻⢧⠀⡀⠀⡖⠲⠄⠦⠻⠁⠁⠀⡨⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡇⠀⠀⠀⠀⠀⢱⢀⣴⡦⢼⣾⣾⣷⡿⣧⠐⠈⡄⠀⠀⠀⢀⣀⡀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⣤⡔⣷⠀⠀⠀⠀⠀⠈⡾⠁⡀⠠⠈⠻⣿⣁⡸⠀⠀⠈⠢⢤⡴⠚⠛⠳⢶⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠁⠀⠸⣤⣤⡄⢰⣦⠘⢧⠀⠙⠂⠀⠀⠈⣮⣭⡄⠀⠀⣤⡆⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠈⡁⠀⠀⠀⠀⠀⠀⢳⡜⠀⣐⠀⢀⣿⣿⣷⢞⡟⢿⡧⠀⣴⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⢦⣄⣣⠀⠀⠀⠀⠀⢠⠀⠳⢀⠈⠀⢺⣿⣿⣟⣾⣷⡟⡀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠁⠀⠀⠀⠀⠈⠀⢀⡾⠀⢀⣼⣏⡿⣻⡿⣚⣜⠄⠄⠀⠀⠐⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠀⠤⢄⣀⠠⠞⢤⣀⣉⣿⣽⢏⡻⡿⢿⣸⣼⢷⡶⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠛⢦⣀⠀⢀⠿⣿⢿⡿⠷⠻⠑⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣴⣶⠋⠁⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠗⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠋⠀⡀⠲⡞⠄⠀⠀⠀⠀⠉⠛⠛⠋⠉⠹⣦⡀⠀⠀⠀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡀⠀⠀⠀⠀⢀⠀⠁⢀⡆⠲⠆⠠⠀⠀⠀⠄⠁⠈⠀⠀⡈⠛⠛⢳⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠆⣠⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠠⣄⢀⡠⠒⠙⠀⠈⠁⠀⠘⣧⠀⢁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⢿⣸⣡⣁⠀⣀⠐⠃⠰⠂⠀⠀⠀⣠⠎⠀⠍⠂⠀⠀⠑⠀⠄⠀⠀⠀⠈⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⢮⠉⠉⠁⠹⢣⢇⡀⠀⡠⠁⠀⢠⡶⣓⢀⡆⠘⠇⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⣵⠒⠀⠀⠀⠀⡀⠋⠔⡀⠠⠒⠰⠛⠁⠈⠙⠂⠀⠀⠀⠀⠀⠜⠀⠀⠀⡇⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢃⢠⢩⡄⠀⠂⠀⠀⢉⣤⣈⣉⡖⠓⠂⠀⠀⠀⠀⢠⡱⣤⣄⡀⠜⠀⠀⠀⠀⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⢧⠣⡻⣄⠲⡐⢛⠿⠽⠏⡩⣟⡽⡃⠀⠀⠀⠀⢀⡹⣣⠊⣱⡄⠛⠄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⢳⡑⡌⢷⢸⠃⠀⠀⠈⠙⠂⠼⣱⡆⠀⠁⠀⠀⠀⠀⠛⣕⡤⢵⠈⢀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⣷⢹⡸⡼⡇⠀⠀⠀⠁⠀⡀⣜⡢⠚⠀⠠⠄⠀⠀⠀⢸⠅⡾⠀⣾⢰⠰⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⢿⡎⠇⢧⠈⢶⣦⣄⡀⡀⢡⢸⣅⠂⠀⣠⡠⠤⠀⠐⠭⠞⢁⣤⢁⢹⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⠸⡌⢣⣀⠭⠭⢚⣡⢎⣚⡭⠵⣂⠀⣀⠀⡀⠤⠴⠒⠋⠑⣋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠦⠭⠛⠋⠁⠠⠌⢕⣚⣭⡤⢒⡡⣬⠭⢕⣒⣤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠷⣬⣭⣭⣭⣶⣾⣷⡤⠶⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠙⠭⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡄⠄⠸⠦⠵⢦⣄⣀⣀
⠀⠀⢀⣴⡉⢉⣱⠶⠒⣉⡡⠤⢄⣲⡶⣂⣐⣒⡒⠒⠒⠢⠤⢍⣙⡒⠤⣄⡀
⠀⣰⠁⣠⠖⢉⣤⣲⣭⠴⠶⣟⠫⢱⠖⣿⠋⠉⢉⠿⣗⠒⠒⠲⠶⢭⣕⡢⣈⠢⢄
⢀⣿⠞⢁⣴⠟⣩⢴⡃⢀⣠⢼⡷⠊⠉⠉⠉⠲⣁⣠⠂⠀⣀⣠⣄⠈⢙⣿⣿⣷⡄⠱⡀
⣸⠃⢠⡟⠁⠀⠙⠚⣋⣉⡀⠀⠧⣀⠀⠀⠀⢠⡏⣲⠬⠑⢊⠥⠊⠙⣯⡇⠐⢿⣿⡆⠘⡄
⣿⠀⡎⠀⠀⢀⢠⠊⠁⠈⠑⡦⠁⣈⠑⠲⠢⠞⢱⣃⣠⠚⠁⡰⠃⠉⢹⣤⣤⣭⠟⣿⠀⢣
⢻⠀⢷⠾⣆⠀⢿⡀⣠⣴⡚⣧⡘⠭⠟⠀⠀⣀⣄⡉⠀⣴⠋⣀⡀⢀⡿⠀⠀⠀⠀⠸⠀⣾⡀
⠀⣄⠘⡄⠀⣳⣠⠽⣹⡗⠀⠀⠋⠳⡴⣄⠀⡃⠀⠉⢣⠈⠋⠋⠙⢉⣤⠀⠀⠀⡤⠃⣰⣯⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢒⠟⡇
⢰⠏⠢⡈⠲⣇⠈⠒⠉⢯⡀⠀⠀⠀⠑⢹⠂⠱⠤⠤⠎⠀⠀⢀⣠⣷⣴⢋⡠⠎⢀⣴⣏⠈⢻⣶⣑⢄⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⡇⠀⢇
⡜⠀⠀⠈⠒⢌⡒⠤⣀⠀⠉⠳⠦⡵⠷⡛⢀⣢⣀⣀⡈⢀⡖⠉⣀⡠⠜⢋⣠⡶⠋⣀⠈⠳⠀⡇⠉⢢⡓⣄⠀⠀⠀⡠⠉⠀⠀⢀⠀⡘⠀⠀⠘
⡇⠀⠀⠀⠀⠀⠉⠑⠲⠭⣉⡒⠒⠣⠴⠾⠯⠤⠤⠭⠛⢛⢋⣉⠤⠒⠊⠉⠉⠣⡀⠜⢳⠀⠀⠇⠀⠀⠑⣌⠢⣀⡴⠀⠀⠀⣄⡠⠊
⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠃⢀⡜⠀⠀⠀⠀⠀⠳⣌⠙⠶⠶⠚⠉⠀⠀⠀⠀⠀⢠
⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⡀⠀⠀⣀⠴⠃
⠀⠀⠘⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⣿⡏⠳⡦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢶⠟⢩⡿⠀⠀⣀⣀⠤⠤⠴⣒⣒⣒⣒⣒⣒⠰⠦⢤⣀⡀
⠀⠀⠀⠸⣧⠀⠑⣀⠀⠉⠙⠒⠒⠦⠤⠤⠤⠤⠤⠖⠒⠚⠉⠉⠀⡠⠋⣨⣾⡿⠟⢋⡡⠴⠒⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⢤⣉⠓⠠⣀
⠀⠀⠀⠀⠈⠧⣄⠈⠑⠦⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠒⠉⣡⣴⡿⠋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⣀⠀⠀⠉⠉⠉⠙⠉⠉⠉⣁⣀⡤⠶⠋⢹⡏⠀⠀⡐⠀⠀⠀⠀⢀⠤⠒⠉⠉⠉⠀⠉⠉⠒⢤⠀⠀⠀⠀⠱⠄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠻⠟⠛⠻⣏⠀⠀⠀⢸⠀⠀⠀⢁⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⢃⠀⠀⠸⡀⠀⠀⠈⢦⡀⠀⠀⠀⠉⠒⠂⠤⠤⠤⠤⠴⠒⠁⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡢⠤⠊⡄⠀⠀⠱⡀⠀⠀⠀⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠃⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠘⢆⠀⠀⠈⠳⢄⠀⠀⠀⠉⠛⠻⠶⠖⠰⡤⢖⣶⣶⠾⠟⠋⠁⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠢⡀⠀⠀⠀⠉⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⠒⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠆

⠀⠀⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⣿⠋⠉⠙⢿⣦⡀
⠀⠀⠀⠀⠻⣦⣀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠉⠻⣦⣤⣤⣴⣶⠶⠶⠶⠾⠿⠿⠿⠶⠶⠶⢶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣷⣤⡀⠈⠻⣧⣀⣀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⢉⣻⣶⣄⠈⠙⠛⠻⣶⣤⣼⠏⠀⠀⠀⠀⢿⡄⠀⠀⠀⠘⣷⣄⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣴⠟⠉⠉⢻⣧⠀⠀⠀⠈⣹⣷⣤⣦⣤⣤⣤⡾⠃⠀⠀⠀⠀⠈⠙⠻⣶⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠉⠀⢀⣀⡀⠙⢷⣄⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠿⢶⣶⡶⠟⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⢿⡟⢷⣦⣀⡀⠙⠛⠛⠂⠀⢹⡟⠀⠀⠀⠀⠰⠶⢶⡆⠀⠀⠙⠁⠀⠀⠀⠀⣀⣠⣶⠟⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠈⠙⠛⠷⢶⣦⣤⣤⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣴⠶⠟⠛⠉⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠛⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠛⠻⠷⣶⣤⣀
⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⡶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⣷
⠀⠀⠀⠀⠘⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⣶⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠒⠛⠛⠛⠛⠓⠶⣄
⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⢀⣤⣤⠤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁
⠀⢀⣠⠴⠒⠋⠁⠀⠀⠈⠓⢄⣸⠁⠀⠀⠀⠀⢠⠱⡄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖
⠘⠫⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠧⢶⡖⡟⠋⠻⠋⠉⠉⠉⠏⢉⠉⠙⠛⠛⠓⠒⠶⠤⢤⣤⡖⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠉⠁
⠀⠀⠀⠰⠯⢤⣀⣀⡀⠀⠀⠀⠐⠠⠀⠀⠀⠉⣌⣥⣄⣠⠤⠂⠚⠛⠛⠻⠿⠿⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠈⠑⠠⢄⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠒⠒⠛⠛⠓⢤⡀⠹⣏⠉⠀⠀⠀⠀⠀⡀⠠⠤⠄⢀⠚⠛⠿⠿⠿⠒⠶⠶⠶⣤⣄⡀⠀⠸⡶⡏
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⣈⣀⣸⣟⠓⠒⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠂⠐⠂⠀⠀⠉⠉⠙⠛⠷⢶⣄⡘⢦
⠀⠀⠶⢤⣤⣤⣤⣶⣋⣀⣠⣴⠾⠿⠟⠚⠛⠛⠛⠛⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠉⠐⡀⠀⠀⠀⠈⠐⠀⠀⠀⠙⢮⣧
⠀⠀⠀⢸⢸⣿⢿⢟⣛⡓⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠚⠛⠻⣿⣿⡉⠉⠉⠉⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⠠⠀⠀⠀⣸⣿
⠀⠀⠀⢸⡄⠻⣯⡉⠉⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⡴⢫⡏
⠀⠀⠀⠸⡟⢄⡈⠛⠳⢤⣀⡀⠉⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡖⠀⠀⠐⢂⠠⠄⠀⠀⠀⠀⠀⠈⣋⣁⡴⠞⢉⣴⢿⡇
⠀⠀⠀⠀⢳⠐⠹⠦⣄⡀⠈⠛⠻⠷⢶⣦⣤⣤⣄⣈⣀⡀⠀⠀⠀⠂⠁⠀⠈⠀⠐⠒⢈⣀⣀⣀⡤⠤⠴⠒⠟⠋⣀⣤⠶⠛⠁⣸⠁
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠉⠓⠒⠦⠤⢄⣀⣀⡈⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⢛⣉⣉⣁⣈⣤⡤⠴⠶⠚⠛⠉⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠹⡷⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⡀⠀⠠⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢠⠀⡄⡠⠰⠂⢠⠀⡂⢰⠂⡄⢠⡠⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠛⠀⠉⠃⠐⠃⠂⠘⠂⠀⠘⠃⠀⠃⠐⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠒⡆⠀⠁⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡽⠂⠀⠉⠀⠐⠉⠉⠀⠂⢸⡈⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢂⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠷⢾⣩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⡼⡷⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣷⣖⣏⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡈⣮⣿⢵⣃⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢎⣩⠿⣿⠉⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⢛⠚⢶⣦⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠞⠀⢀⡏⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠰⠂⡀⢉⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⢐⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⣰⠦⡀⡘⢀⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠛⠛⢾⢃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⡱⠦⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡤⠔⠒⣡⣁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠛⠩⢧⣏⡀⢠⢿⣷⣶⣖⠟⠧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢀⣀⠀⠘⠲⢋⣽⣿⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢐⠆⠁⠠⢔⡂⣀⣀⣀⠒⠂⠠⠌⣁⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡡⢂⠬⣀⠄⠈⠂⠌⣐⣆⠈⡀⢋⣕⣃⢰⣥⡐⢌⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡀⠩⠊⡔⣉⣀⣈⠀⠈⠐⠘⠀⠈⠙⠉⠀⠀⠀⠑⡝⢗⢕⢀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⠖⠂⠈⠁⠀⢀⠢⠐⠀⠀⠀⠀⠀⠢⠪⠀⠀⠀⠀⠰⡀⠁⢧⣃⠘⡀
⠀⠀⠀⠀⠀⠀⠀⡌⠀⡇⠀⠀⠀⡢⠀⠁⠀⠀⠀⠀⢀⠀⠀⣀⠀⠱⠀⠀⠀⠀⣛⠠⡍⢫⠀⢡
⠀⠀⠀⠀⠀⠀⠰⠃⠘⣧⠀⠁⠈⠢⡀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠈⠑⢅⠀⠀⡐⡃⠀⠈⢸⠁⡘⡄
⠀⠀⠀⠀⠀⠀⠀⢨⡀⢻⣗⠖⠂⢄⡠⠊⠉⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠔⣢⠐⠲⡄⠏⢠⡅⠁
⠀⠀⠀⠀⠀⠀⢀⠘⡘⢄⠙⢄⠠⠀⠈⠒⠬⢀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢑⡲⠋⡠⢡⠀⡆
⠀⠀⠀⠀⠀⠀⠈⡄⠐⡀⠐⢄⠙⠲⣤⣁⠀⠀⠀⠉⠁⠢⣄⣠⣴⣯⣾⣾⡃⠜⢋⠠⠊⢠⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠢⡀⠉⠒⠤⢈⡙⠓⠒⠤⠀⠼⠿⠿⠓⠚⢉⡁⠤⠒⠁⢀⠔⢡⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⣈⠐⠤⣀⠀⠀⠉⠁⠀⠐⠂⠀⠀⠉⠉⠀⠀⣀⠤⠂⣁⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡉⠐⠐⠀⠀⠀⠀⠀⠀⠀⠂⠂⣁⣤⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠤⢒⡤⠒⠀⠒⢴⣲⠤⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⣋⣉⠉⠉⠉⠉⠓⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢂⣐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⡤⠴⠚⢉⣁⣉⣹⠆⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠴⣎⠳⠀⡞⢹⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣉⡥⠔⠋⠉⣹⠆⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢢⣤⠽⠆⠾⣭⣁⡈⢉⠗⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣏⣩⡵⠞⠋⠙⡆⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⢈⣹⡆⠐⡄⢿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡤⠷⠾⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣭⠭⠬⣧⠁⣃⢁⡏⡄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠲⠤⣌⣀⡴⠋⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢘⣮⡓⠾⠟⢻⡄⠀⠀⠀⠀⠀⣾⠓⠛⠛⠛⠳⣶⢲⡟⠖⢶⡦⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣀⣀⣠⡜⢧⡀⠀⠀⠀⠀⠈⠙⢒⡶⠖⠒⢛⠙⢧⣀⣨⠵⠿⠎⠉⠛⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⢦⡀⠀⣀⡤⠞⠉⠀⠀⠘⠉⠀⠀⠋⠀⠀⢀⣠⠞⢫⠉⣙⠶⠄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠟⠋⠁⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⠶⣚⡯⠬⢷⣚⣋⣥⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡉⠙⢯⡉⠉⠉⠉⠉⠙⠓⠒⢲⣶⣶⠏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠲⣌⠳⢄⡀⠀⠀⠀⢀⠞⢩⠏
⠀⠀⠀⠀⢠⠤⠤⣤⠤⠤⠴⠶⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣈⢳⣄⠉⠲⣄⣠⡟⢀⡾⢤
⠀⠀⠀⠀⠻⣀⣘⠓⠦⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠭⢍⣳⡤⠞⠉⠀⢁⠀⣸⠉⠉⢉⣓⠲⣄
⠀⠀⠀⠀⠀⢸⠉⠉⠉⠙⠓⠒⠒⠂⠀⠈⠉⠉⠩⠭⠭⠭⠭⠍⠙⠛⠛⠛⣛⣛⣛⡲⢌⠙⠢⣄⠀⡏⢀⠏⠭⠭⠭⠭⣴⠛
⡤⠖⢐⢒⣋⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡈⠛⠄⡼⠀⠀⠀⠀⠀⡇
⠹⣄⠘⢯⡀⢸⣀⡤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⡸⠁⠀⠀⠀⠀⢠⡇
⠀⠈⢳⡄⠉⠉⣠⠔⠢⢞⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠙⠳⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⢠⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⢸⠇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⣼
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡟
⠀⠀⠀⠀⠀⠈⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠄⢠⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠤⠒⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡴⠊⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⢀⠄⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠐⠀⠀⠁⠀⡀⠀⠀⢀⣀⠀⠘⡄⠂⠀⠠⣀⠀⠀⠀⠀⠃⠀⠡⡀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠂⠄⠘⡀⠀⠀⠁⠀⠀⠀⠀⠹⢆⢳⢐⠀⠰⠺⠃⣀⣤⣄⣸⡎⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⠀⢢⡤⡜⣼⠋⠃⣡⣷⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠏⢸⠆⠀⠈⡯⢻⡵⢢⠍⣌⠁⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢠⠁⢀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⣸⣶⡻⣶⣃⠿⠿⠚⢧⠜⠀⠠⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢸⠀⢈⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⢻⡑⣘⣿⣿⣿⣶⣠⠉⠉⢡⣼⡆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠱⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⢠⠉⢸⠗⠉⠁⠂⠈⣉⢻⠀⣠⡜⠘⢣⡆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠠⠆⠀⠘⡆⠠⠀⠀⠀⢸⢸⣉⠝⠀⣀⠎⠑⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⢀⣃⣶⢐⠄⡀⠈⢿⡍⠈⠀⠐⢠⠁⠄⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠡⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢡⡌⢺⣰⠅⠠⡾⠛⠧⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⢉⠐⠆⠀⠀⠀⠉⣤⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠄⠀⠀⠀⠀⠈⠂⠀⠒⠠⠀⠀⢀⠔⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠡⠀⠀⠀⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⠄⠀⠀⠄⠀⠀⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠷⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠰⣶⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡙⢿⡂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠀⠀⠀⠈⠹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢘⣶
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠤⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠠⠀⠛⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⠀⠀⠒⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢠⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠐⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠠⠀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠐⠉⠀⠀⠠⠀⠀⠀⢸⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣰⠆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⡀⠀⠀⡇⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠛⣶⠤⠀⠛⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⠀⠀⣀⠘⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⡶⡇⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣤⣤⣀⣠⣄⣙⣾⣏⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡰⠋⣠⠘⠀⠆⠀⠀⠀⠀⠀⠠⡀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⠉⠄⠀⠀⠀⢀⡀⠠⡬⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⢀⡀⠀⠀⠀⣠⠞⠁⠀⠈⠀⠀⠀⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣾⣾⡅⠐⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠲⢶⣦⠴⠃⠀⠀⠀⠀⠀⠘⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⢀⠀⠀⠀⠀⠀⠂⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀
⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⣺⡦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣄⣀⣀⡀⠙⣶⣶⡶⢀⣤⡀⢨⣅⣀⡤⣦⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈⠛⠛⠒⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠍⠀⠶⠯⢤⣤⣙⣛⠟⠐⠛⠛⠛⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣼⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠸⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⡌⢻⠚⠀⣠⣄⣤⣀⡀⠀⠀⢠⣰⠀⠀⠀⠺⢶⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⠀⣼⣿⣿⣿⡿⠇⠀⠀⠀⢾⡇⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⢩⣿⣿⠟⠁⠀⠀⠀⠀⠿⠀⣰⠋⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣤⣀⠀⠘⠿⠃⠀⠀⠀⣤⠀⠀⠆⣰⠃⠀⣀⣀⣁⡀⣠⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠿⣉⡽⠓⠂⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠞⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣙⣉⠓⠀⠀⠀⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠠⡀⠘⠋⠀⠀⠀⠀⠀⣷⡄⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢙⡇⠀⠼⠛⠛⠛⠦⠀⠀⠀⢠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⡀⠀⠘⢿⣤⣤⣶⣤⡀⠀⠀⠀⢀⣠⣷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⢭⣙⡿⣿⣤⠀⠀⠀⠀⠀⢀⣀⣄⣀⣿⣷⠾⣿⢄⣀⣀⡉⠲⠿⠙⠛⠆⠀⣠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢉⣃⠀⠀⠀⣼⣿⡿⠟⢉⣸⣏⡠⠈⠸⢭⠽⣯⡄⢀⡀⠀⠈⠘⠁⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡦⠤⠛⠉⣴⣾⢛⣿⣿⡁⠀⠀⠀⠀⠀⠛⠀⠀⠘⠂⢀⣤⠖⠺⠦⠜⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡄⠀⠀⣴⠯⠶⢽⣣⣿⣿⡍⠀⠀⠀⠀⢛⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢶⣟⡛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⣾⢿⣻⡟⠀⣀⣤⡴⠞⢻⡂⠀⠀⡁⠀⠀⣷⣀⡀
⠀⠀⠀⠀⠀⠈⠙⠷⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠘⢣⡿⠊⠡⣤⣾⣿⢯⣤⡄⠈⠀⠀⠠⠃⠀⠰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠦⠄⠀⠀⠀⠠⠈⢀⣰⠁⠀⠠⠴⠉⢇⠘⣷⠏⠀⠀⠟⢹⣿⣠⡀⢈⠀⠀⣤⡦⢶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠀⠀⠀⣡⠤⠜⠁⠀⠀⠀⣀⣀⡈⠠⢿⠀⠀⠀⠀⠈⣿⣷⡇⠈⠻⣶⣿⣷⡄⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢨⣿⣿⢠⡏⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠙⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⣀⡀⠀⢰⣶⣽⣯⡏⠀⣼⠇⠀⢠⣶⣤⣤⣀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⣿⣿⣿⣿⠻⣿⣿⡙⣿⡇⢆⡿⣷⡀⠠⠉⠸⣿⣿⡶⠀⢰⣶⢞⡿⠒⡀⣠⣤⣄⠲⢄⣀
⠀⠀⠀⠀⢀⣴⡶⠿⣛⣛⡻⠃⣤⣤⣦⣬⣼⣿⣿⣄⠘⠻⣿⠀⠳⢸⠁⢸⣷⠀⠀⠀⢻⠟⠁⠀⠸⠡⠤⠀⠚⠿⣿⣯⣼⣿⡋⠉⠉
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠚⠛⠉⠉⠉⠉⣉⣽⣶⠖⠃⠐⠦⠀⠾⡀⠀⢿⣦⠃⢀⠴⠶⣷⣶⣾⣿⣷⣦⡀⠀⠀⠉⠛⠛⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠖⠁⠀⠀⠀⠀⣇⠀⠀⢋⡄⠀⣀⣀⣤⠷⠧⢿⠟⠛⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠠⢠⡀⢀⠏⠀⠙⠟⢿⡿⢿⣿⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡎⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇



⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠿⢿⡿⢿⡿⠿⣿⠿⠿⡿⠿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣷⣾⣿⣿⣿⣶⣶⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣹⡿⠋⢠⣿⡿⠗⣿⣿⡟⠩⣿⣿⡏⠹⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢁⣴⡟⠀⢠⣾⠏⠀⢰⣿⣿⠛⠀⣿⣿⡗⠀⢸⣿⣷⡊⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⢰⣿⠏⠀⣠⣿⡏⠀⠀⣾⣿⡏⠀⠀⣿⣿⣷⠀⠀⣿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠓⢐⣿⡟⠀⢰⣿⣿⠁⠀⢸⣿⣿⠃⠀⢸⣿⣿⣿⠀⠀⢹⣿⣿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⡟⢀⣿⣿⠀⢀⣯⢠⡏⠀⠀⣾⣿⣿⠀⠀⢸⣿⣿⣿⠀⠀⢨⣿⣿⡆⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣼⣿⠁⢸⣿⡗⠀⢸⣟⣿⠇⠀⠀⣿⣿⡯⠀⠀⢸⣿⣿⣿⠄⠀⠐⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⡿⠀⣿⣿⠁⠀⣿⣿⣿⠁⠀⢠⣿⣿⡇⠀⠀⢸⣿⣿⣿⡁⠀⠀⣿⣿⣇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⠂⠀⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⠆⠀⠀⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⢺⣿⡇⠀⢿⣿⣿⡀⠀⠘⣿⣿⣇⠀⠀⠸⣿⣿⣿⠁⠀⠀⣿⣿⡇⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠸⣿⡇⠀⢸⣿⣿⡆⠀⠀⢿⣿⣷⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣷⣼⣿⣿⣗⠘⣿⣿⣧⠀⠀⢸⣿⣿⡄⠀⠀⣿⣿⣿⠂⣀⣼⣿⣿⣡⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣆⠀⠀⣿⣿⣇⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣶⠚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠫⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠘⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠀⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡛⠁⠊⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⣿⠇⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣿⣀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠀⠀⢄⢀⡄⣠⣠⣤⣀⡀⢀⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠄⠀⢻⣿⣷⣿⣿⣿⡿⢳⡀⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠛⠛⠛⠋⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠂⢊⠀⢫⣟⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢻⣿⣷⡔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣀⣲⡶⠒⠒⠒⠒⠀⠙⢻⠇⠀⠀⠀⠀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⢠⡀⠀⠀⠀⠀⠹⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⠹⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣼⠀⡸⢠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠨⠛⣹⣿⡆⡄⠀⠁⠇⠀⣰⣿⠃⣀⣀⡀⠀⠇⢸⠇⠀⢰⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⡰⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠀⠘⣿⣆⠐⣯⡃⠀⢠⣤⢾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣾⡅⠤⠈⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⣷⣬⠀⢀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠬⠄⢀⡀⠀⠀⠀⠔⠀⢀⣿⣿⢰⠃⠏⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⡀⠠⢤⠀⠀⠀⠀⠀⠀⠀⣠⣿⡷⠃⡸⠀⠀⡀⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢋⠿⠇⠀⠀⠀⠀⠀⢀⣠⣴⠾⠿⠋⠠⠞⣁⠀⣰⠁⢀⠄⠁⠂⠀⠸⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡟⢻⡟⠫⠆⠀⢀⠉⠀⠀⠊⠁⠊⠑⠀⠈⠜⡸⢁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠁⣰⣶⠖⠂⠉⢀⡀⠀⠀⠀⢅⠋⠎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⠋⠀⠀⠀⠀⢀⡠⠋⠁⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠔⠋⠀⠀⠀⡀⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠉⠁⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⢀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠬⢾⣷⠓⠂⠀⠀⣀⣠⣀⠀⠀⠀⠤⠤⠘⠀⠀⢹⣿⠃⠀⠠⠿⠏⠀⠀⠀⠀⠀⢺⡁
⠀⠀⠀⠀⠀⡇⡀⠀⠀⠘⣿⣿⣿⡀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⢈⡗⠒
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠋⠛⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣦⠖⠀⠀⢄⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣾⠅⠀⡀⢄⣄⠠⠀⠀⠂⠀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠈⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡌⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢀⠀⠀⠰⠂⠀⠀⠀⠆⢤⠀⠀⠿⠃⠀⣼⡄⠋⠀⠀⠀⠀⠀⠀⣤⡄⠀⢈⣄
⠀⠀⠀⠀⠐⢨⠴⠀⠀⠶⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡞⠚⠦⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣹⡅
⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠄⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⡉⣵⣍⣦⣾⣧⡄⠀⠀⠆⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠀⠀⠀⠠⠀⠀⠀⠀⣀⡽⠾⣛⠿⣿⣳⣌⡀⠐⡿⣴⠀⠁⠐
⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⣠⡿⢿⣿⠉⡿⣟⣻⣄⣠⠤⡄⣙⢡⣶⡮⠉⣠⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠁⠀⡐⠀⠘⢿⣿⣶⣏⣤⣲⣻⣽⣿⢻⣿⣯⣶⣎⣸⢷⣤⡈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⡡⠀⠀⠀⠀⢀⣔⣷⠿⣿⣿⣫⠫⢒⡿⠽⣿⣿⣯⢤⣾⡿⡿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⣇⠉⡉⠟
⠀⠀⠀⠀⠀⠀⣄⠄⠀⠠⠀⣤⠀⠀⠀⡘⢿⣿⣴⣿⢷⣎⢹⣿⣿⡀⢿⣮⣿⣾⣿⣿⣾⣿⣿⣇⠀⠀⠀⢀⣴⡶⢟⡀⣀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡠⠄⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠐⠀⢸⠷⣏⣠⣎⡂⠀⢻⣿⣿⣿⣿⣿⡙⢿⡇⣀⣿⡫⢃⣿⠟⣿⣯⣼⣿⣆⠀⣠⡟⣡⣴⡟⠁⠁⠀⠀⡀⠀⣀⣤⠀⡎⢩⡇
⠀⠀⠀⠁⠷⠀⠀⠈⠀⢜⠁⡓⠹⣿⣿⣿⣷⣾⣿⣿⣋⣿⣿⣷⡶⠟⢛⣻⣭⣿⣿⣻⡯⠟⡋⠁⣙⣶⣧⠜⢡⢁⠃⠔⢁⣠⡤⣔⠏⠀⠁⢨⠃⢸
⠀⡀⠀⠀⠀⠁⠀⠀⠀⠨⠀⠡⠀⢿⣿⣿⣿⣿⡿⣷⣽⣿⣽⣯⣶⣿⡛⣻⡢⢊⡩⣥⣶⣿⣶⣿⣿⣿⠀⠠⢘⣬⢼⠒⠛⢗⣱⠀⡇⢰⡄⢸⠀⠸
⡀⢀⣠⡀⠀⠀⠀⠀⠀⠀⡎⠀⠠⡆⣿⣿⣯⣿⣿⣿⣛⣫⣭⣴⣯⣶⣏⣽⣾⣾⣿⣿⣿⠿⠛⠛⣿⣿⣴⡾⣏⠙⢺⡀⣀⡀⠻⣀⡇⠸⡅⡎⠢⡂
⢹⠀⠀⠀⣀⠀⣀⠀⠀⠀⣴⡶⣦⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⡿⣄⠀⠀⣛⣿⣿⠁⠟⠠⡌⠇⣸⠃⡀⢳⡣⣞⢙⣏⠁⡁
⠀⠂⠀⠀⠀⠀⢊⡶⠄⢀⢿⣃⣸⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⢉⣉⣼⣶⣿⣿⣿⣧⠠⠘⢼⣿⣿⡔⣇⠐⢧⣃⡏⢀⡘⣯⡉⠉⠉⠹⣧⡀⠠
⠀⠳⢀⠟⡄⠀⠉⠀⡰⡍⠘⣏⠀⠙⠺⠛⣾⣿⣿⠛⠻⢻⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢄⠈⠟⠿⣿⣡⣠⣇⣿⡻⠿⠄⢹⣷⡀⠀⠀⠘⣷⡀
⠀⠆⠀⠘⡀⠆⣀⠀⠠⠀⠈⣵⣄⠶⣼⣸⠟⢿⣿⣇⠀⠀⣿⣿⣧⣻⣿⣿⣿⣿⡿⡛⠋⢻⣿⣦⣔⣲⣋⣿⢹⣿⡿⣿⣷⡄⠀⠀⠙⢿⡄⠀⠀⠈⢿⡄
⠀⠀⠐⠀⠁⢠⣗⣤⠖⣪⡵⢾⣮⡄⠙⠛⠀⣿⣿⣿⣿⡎⣿⣿⣿⣽⣻⣿⣉⠇⠹⣽⣄⢴⣹⣧⢿⣿⣿⣿⣧⠈⢣⣻⠟⢿⡄⠀⠀⠈⢿⡄⠀⠀⠀⠻
⠀⠀⠀⠤⢖⣾⡵⢿⡋⢹⣇⣸⣿⡇⣤⡬⢷⣿⣼⣿⣿⣹⣸⣿⣿⣿⢿⣿⣿⣖⣻⣼⣿⣿⣿⣹⣯⠛⣿⣿⣟⣷⠑⠿⠀⠉⢿⡄⠀⠀⠀⠻
⠀⠀⠰⣞⡏⢽⡇⢸⠇⢸⡅⢿⡟⢏⠀⢤⡈⠛⣽⣿⣿⣷⣵⣻⣼⣿⣿⣿⣿⣿⣿⣷⣿⡿⢿⣟⢿⡆⠈⣿⣿⣿⣷⠀⠀⠀⠀⠛
⠀⠀⠈⢸⡇⢸⡇⣽⠄⣸⡇⢾⡧⢠⠀⢺⣾⠇⢸⣧⣼⣾⣿⣿⣿⣿⣿⠻⣿⣿⣿⢻⣯⢶⣰⣿⣿⣿⡄⠈⠛⠿⠋
⠀⠀⢀⣿⠀⣿⢁⣿⡦⣿⠀⡏⣙⣺⣄⣿⡏⠀⣸⣿⣿⣿⢿⣿⣿⣿⣿⡖⠺⣿⣿⣿⣿⣞⡄⠋⠻⠋⠁
⠀⠀⠈⣼⡖⣿⢞⣿⣷⣿⡖⣿⡝⠋⢸⣿⣿⣾⡿⢟⣫⣿⡀⠀⣾⣿⣿⣿⠄⠉⢿⣿⡿⢿⠂
⠀⠀⠀⣽⣿⣿⣹⢿⣿⣿⡇⣿⠁⣿⣿⠉⢹⣤⣾⣿⣿⡿⣏⠄⠿⣿⣿⠘⠃⠁
⠀⠀⠀⠛⢿⣿⣿⠘⢿⡿⠇⢸⢢⠨⠙⣷⣼⡆⣅⣏⠋⠁⣿
⠀⠀⠀⠀⠀⠉⣻⠀⠣⣆⢯⢸⠟⠀⠀⠿⠃⡃⠹⠋⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢸⠀⠘⠁⠛⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡾⠋⠉⠉⠉⠉⠻⣿⣿⣿⣇⠀⠀⠀⠀⣾⡟⠋⠉⠉⠉⠙⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠈⠻⢿⡿⠛⢿⣿⠟⠛⠻⠿⣿⠀⠀⠀⠀⠀⠠⠴⠄⠠⠦⠤⠀⠸⣿⣿⣿⣧⠀⠀⠀⠻⣤⣤⠀⣤⣤⠀⠀⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠘⠃⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠙⠀⠀⠙⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠘⠃⠀⠘⠃⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣾⣿⣿⣿⣷⣶⣶⡄
⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣆⠀⠀⠀⠀⢸⣿⠿⠛⠛⠛⠛⠛⣿⣿⣷⠀⠀⠀⠀⢈⣿⡿⠟⠛⠛⠛⠛⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣯⣤⡄⠀⣤⣄⠀⢻⣿⣿⠀⠀⠀⠀⠈⢃⣀⣀⠀⣀⣀⠀⢻⣿⣿⠀⠀⠀⠀⠸⣿⠤⠴⠄⠠⠤⡤⠀⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⣀⣀⡴⠶⢶⣄⣀⣀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⠀⠀⠉⠀⠀⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠉⠀⠀⠀⠉⠐⢳⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠰⠁⠀⠀⢈⠂⠀⠀⠀⠀⠴⠒⠀⠀⠀⠒⠀⢳⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠰⠆⠠⠀⠂⠒⠉⢸⠀⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡠⢊⡠⠊⠁⠒⠤⠤⠤⠤⠤⠤⠤⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠆⠀⠀⠀⠀⠀⠐⠀⠠⠁⠀⡇⠀⠄⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠬⠙⡆⠀⠀⠀⠠⣤⣤⠤⠴⠋⡼⢄⡀⠀⡀⣀
⠀⠀⠀⠉⠉⠙⠁⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠰⠀⠆⢀⠏⠀⠈⠓⠄
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠕⡦⢀⠀⢀⣠⠆⠀⠀⢸⠀⠀⠀⡰⠈
⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⡌⠀⣠⡈⠓⠢⢸⡀⠀⠰⠁⢱
⠀⠀⠌⠀⠀⠑⡄⠀⠀⠀⠜⠀⠀⠀⠀⠠⣀⠘⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆
⠀⡸⠀⠀⠀⢦⡇⠀⠀⠀⠀⠀⠠⠀⠄⠀⠈⠑⠢⢄⢰⡀⣀⠄⠀⣸
⠀⠁⠀⠀⠀⠤⣙⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢦⠀⠀⣀⣀⡴⠃⠀⢠⠃
⡄⠀⠀⠀⠀⢀⠘⠐⠂⠤⠀⠀⠀⠀⠀⠉⠁⢠⠀⠘⡀⠀⠀⠀⠀⢸⠀⢸
⢷⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⢀⡇⠀⢸
⠀⠳⡇⠀⠀⢸⡤⠤⠤⠤⢀⡀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⡾⠀⠀⢸
⠀⠀⠹⠄⠠⠒⠀⠐⡄⠀⠀⠈⠑⠢⠤⠤⠤⠜⠀⠦⡀⠀⠀⢠⠇⠤⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠁
⠀⣁⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣷⣤⣶⡄⠀⠀⠀⠤⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⠉⣽⢻⣿⣄⡀⠀⠀⠀⠆⠀⠄⠶
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠐⢠⣿⣿⡀⠀⡀⢀⢀⣝⣿⣿⠫⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣟⠁⠀⣀⣶⣽⣿⣿⠀⢰⣿⣷⡄⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠓⠢⠖⠐⢿⣿⣿⠀⣿⣿⣿⡗⢀⠀⠀⠀⣀
⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠐⠂⠀⠀⠀⠀⠒⠂⠀⡀⠀⠋⠛⠒⠌⡃⠀⠀⠈⠁⡌⢻⠏⣤⠻⡿⢿⠛⢻⡅⠘⠁⢻
⠀⠀⠀⣀⠀⠠⠤⣤⣠⣤⣀⣀⣠⣤⣤⣤⠀⠉⠘⣤⠠⠤⢤⣤⣤⣹⣦⣀⣤⡆⠴⠇⠀⢸⣇⠀⠀⢉⣿⣿⣢⣰⣟
⠀⠀⠀⢸⠀⠀⠀⠄⢰⡄⢘⠉⣉⠁⡶⠗⠀⠀⣀⣽⣧⠲⣆⣸⣬⣿⣤⡿⠋⠀⠀⠀⠀⢸⡟⢷⠀⠀⢻⡝⢿⣿⣿⡿⠛⠛⠚⠓⢈⡛⠛
⠀⠀⠀⢸⠇⠂⢒⠀⠀⠓⠠⠀⡨⠿⠃⠀⠀⠈⣻⢛⣷⣴⣯⣽⣿⣿⢯⡈⠃⠀⠀⠀⠠⠞⠁⠰⠇⠀⠀⠄⣾⣿⣿⣯⡈⠤⠒⠀⠀⠀⠄
⠀⠀⠀⣿⣄⣤⣼⣤⣤⣄⣴⠎⠀⠀⠀⠀⠀⢠⣿⣾⣿⣶⣾⣿⡿⠁⠀⠉⠀⠀⢠⣄⠀⠀⠀⠰⣿⡇⠀⠀⢿⣿⣿⣇⡤⠤
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢠⠀⣿⠉⠙⠛⣭⠟⠋⠁⠀⠀⠀⠀⠀⣈⣿⣄⣀⠀⠀⠈⠀⠀⠀⣈⣟⣿⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠠⡆⢱⡐⠦⢸⣦⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⠿⢄⡀⠀⠀⢀⠀⠀⠈⢹⢾⡇⣌⣁⣀⡀
⠀⠀⠀⢀⠄⣀⠀⣤⡠⠀⠄⠀⠀⢀⠀⣿⣲⣎⣻⣿⣸⣿⣦⣤⣲⣶⣾⣿⣿⣿⣿⡟⠳⡦⠉⠐⠠⡀⣀⠀⣀⣾⣿⣿⣿⣅
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠿⠿⣿⣿⣿⣿⣧⣦⡉⠀⠳⠶⣄⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⠿⠿⠷⠶⠟⣿⠛⢿⣿⣿⣿⣿⡟⢛⣶⣄⡈⡇
⠀⠀⠀⢿⣅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟⣾⡗⠹⢂⡴⠞⠀⠀⠀⠚⠀⢠⡅⢻⣿⣿⣿⣿⣿⣯⣥⡆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⢁⣀⡴⠛⠛⠁⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡄⢹⡟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠠⠐⠻⠋⠁⠘⠁⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠸⠀⢸⣿⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⡟⠏⠩⣿⣿⣿⣿⡿⠿⢣⡼⠛⠗⢤⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡟⢠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣶⣶⣿⣿⣿⡿⠋⠀⢀⡉⠀⠀⢠⣼⣯⠃⠘⠀⠁⡀⠀⠀⠃⠐⠂⣀⡀⠀⣀⠐⠠⠄⠐⠀⠁⣀⣴⠇⡹⣏⢻⣿⣿⣿⣷
⠀⠀⠀⣩⣥⣽⣿⣿⣿⣷⣾⠛⢤⡖⠊⠁⠀⠀⢸⣏⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠉⣶⡶⠟⠛⢀⠐⠀⢀⣶⣿⣯⢀⣼⣇⣿⣿⣿⣷⡷
⠀⠀⠀⣿⣷⣶⣿⣭⣝⠿⢿⣷⡜⠳⢤⣠⣴⣒⢻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡗⠺⠀⢠⢠⣶⣿⣿⣼⣿⣿⣿⠛⣿⣿⡟⠍⠉
⠀⠀⠀⣿⣿⣿⠒⠈⢻⣤⠀⠙⢿⣷⣿⣿⣶⣭⣿⣛⣶⣿⠤⣤⣘⡶⠶⠖⠖⠢⠾⣅⣀⣠⣝⠀⢲⣾⣿⣿⣶⣿⣿⣾⣻⣶⣴⣿⡷⠠⠅
⠀⠀⠀⣿⠉⣿⠀⠀⠀⠈⡃⠀⠈⠻⣿⡿⢛⠷⣻⣿⣿⣿⣶⣁⣶⣿⡿⢿⣷⣾⣿⣿⣿⣿⣻⣿⣿⣿⣽⣷⣾⣿⣿⣿⣿⣿⡿⢻⣇
⠀⠀⠀⣿⠟⠁⢀⠀⣀⣾⣥⣤⠼⠶⣯⣶⠟⠋⠑⠛⠉⠉⠉⠉⠉⠉⠉⠐⠀⠀⠙⠛⠛⠛⠛⠛⠛⠉⠉⠈⠙⠛⠛⠻⠛⠻⡷⣸⣿⣿⡇
⠀⠀⠀⠏⠀⡀⢉⣵⣿⣿⡋⢀⠀⡀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠇
⠀⠀⠀⣤⣵⣿⣿⠿⠟⠛⠋⠙⠉⠛⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠆⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣽⣿⣿⣷⣿⣶⣶⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⠀⢀⣀⠀⢀⡀⠀⢀⣀
⠀⠠⠁⠀⠲⡄⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠈⠉⠀⢫⡀⠀⢀⡈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫
⢀⠀⠀⠀⢀⠀⠉⠀⠂⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠙
⡎⡀⠀⢀⠂⡀⠀⠀⠀⡌⠀⢸⡀⢠⠤⡴⡂⠉⠀⠀⠂⠀⠒⠀⢒⣀⣾⣷⡶⢠⣐⡀⠀⠀⠀⠀⠀⠂⠐⢻⡂⠀⠀⠀⠀⢧⠙⡄
⢠⠁⠠⠃⢠⠁⠀⠀⢀⠆⠀⠈⠀⣼⢀⠀⢉⠄⣀⠀⠀⣀⡀⣺⡟⡉⢡⢔⠀⠀⠈⡕⠒⢤⡆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠐
⠇⡰⠃⢠⡇⠀⠊⡁⠀⠀⠀⠀⠀⡄⠘⢀⢸⠂⣿⠴⢋⢹⢭⠉⠉⣡⠱⠛⠓⢤⣤⣄⠠⣠⣶⠀⠃⠀⠀⣴⡈⡀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢡⢀
⠐⠋⣥⡄⠀⠰⠍⠠⢄⠠⠄⠠⢈⣧⠟⣬⡇⠨⠄⠠⢘⣼⠖⣏⠚⣧⡟⢿⡉⢸⡆⡿⠒⢘⣿⣄⠀⡴⠀⠄⡡⠶⠀⠔⠀⡐⠀⠀⠀⠀⠀⡀
⠢⢄⠈⠑⠢⣄⠀⠑⠠⡐⠀⠑⢼⠉⡖⢦⢄⡑⠦⣀⢸⣛⠲⠦⣌⣧⠥⡤⠦⢤⠭⡿⠆⠹⣿⣧⣾⡢⠄⢠⠀⠀⢂⢀⣌⠄⠊⡀⠄⠂⡀
⢸⠀⠹⢢⣄⡀⠙⠢⣀⠈⠐⠄⡆⠀⡇⠸⠨⠘⡑⠠⢙⣎⣂⣁⣚⣛⡛⣶⣯⡴⣊⢀⡤⠤⣭⠿⡏⠀⠰⠈⡄⡈⠌⢋⡠⠐⢀⠠⠂⠁⣀⠴⠞
⠇⢀⠇⡸⢘⡏⢰⠤⠀⠙⠢⢀⠃⢀⠇⡆⠈⠦⠥⠀⠀⠉⠁⠦⠄⣀⠀⠀⠀⠞⣁⣩⠜⠋⠀⠀⠀⠀⠀⠀⠉⢡⠈⢌⡄⠊⢀⣠⠔⠊⢅⠘⡄
⠀⡼⢠⠇⢸⠁⢸⡂⠀⠁⠂⣼⣄⠈⠠⠄⠀⠀⠔⠀⠀⢄⠀⠠⠀⠈⠙⠒⠶⣶⠿⠀⢀⣤⣄⣠⡄⢀⣠⡄⢂⡔⠀⣪⡼⡖⠉⠀⠀⠀⠈⢢⠐
⠀⣇⣞⠀⠛⠀⠈⠁⠐⠂⠈⠉⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⣴⡿⢶⠐⢂⡁⠲⠀⠀⠀⠀⠀⣠⡴⠚⠉⠒⠒⠶⠶⠶⠶⠶⠶⠷
⣸⣿⣟⣉⣙⣑⣀⡒⠒⠂⠒⠒⠖⠖⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⠠⢀⠑⠦⠖⣊⠴⠊⠁⠀⠀⠀⢀⣠⡖⠛⠁
⣍⣁⣀⣀⣀⣉⣉⣉⣉⣙⣛⣛⠛⠒⠒⠒⠒⠖⠚⠻⠦⣄⡀⠁⠂⢀⠉⠒⠋⣀⡤⠊⠁⣀⣴⠾⠉⢁⣀⣀⣀⣀⣀⣀⡀⠀⠈⠁
⣿⣽⣯⣭⣭⣭⣭⣭⣭⣭⣙⣛⣛⣛⣛⡛⠛⠛⠓⠶⠶⠾⠿⢶⣄⡀⠑⠲⠟⠁⢀⣴⠾⠯⠤⠤⠤⠤⠤⠤⠄⠀⠠⠤⠤⠤⠤⠤⠄⠤
⣿⣭⣽⣯⣭⣯⣭⣭⣭⣩⣍⣩⣉⣉⣉⣛⣛⣛⣛⣛⣓⣶⣶⣶⣮⣿⣶⣤⣤⣾⡛⡒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠄
⣿⣯⡛⣿⣯⣝⣯⣿⢿⣭⡋⠩⠻⣿⣍⠉⠙⠻⣯⣍⡉⠛⢿⣍⠉⠉⠉⠙⠛⠉⠉⠉⣉⡿⠛⠉⠙⣻⡿⠛⠛⠛⣓⡿⠛⠒⢒⡶⠛⠒⠒⣲⡶
⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣖⢹⣿⢷⣌⡠⠐⠉⠻⣶⣄⡙⢷⣄⠀⠀⠀⢀⣤⠾⠋⠀⣀⣴⠟⠉⠀⢀⣤⠞⠉⠀⣠⠶⠋⠀⣀⡴⠛⠁
⣿⣿⣿⣽⣿⣿⣾⣿⣿⣿⣽⡯⣿⢷⣧⡶⣉⠻⣦⣔⠉⡈⠙⢿⣦⡙⢷⣶⡾⠛⠁⢀⣤⠞⠋⠀⢀⣤⠾⠋⠁⣀⣴⠟⠁⢀⣤⠞⠉⠀⠀⣠⠴
⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⡻⣿⣿⣦⣗⡬⣻⢷⣤⡀⠀⠙⢻⣦⡉⠀⣀⣴⠟⠁⢀⣤⠾⠋⠁⣠⡴⠟⠉⢀⣠⡶⠋⠁⠀⣠⠴⠋⢁⡴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣮⣿⣷⣤⡷⣝⡿⣦⣄⠀⡈⢿⣿⡟⠁⢀⣴⠟⠁⣀⣴⠟⠉⠀⢀⣴⠟⠁⠀⢀⡴⠋⠁⣠⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣠⣾⣗⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣿⣿⣷⡞⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⡏⠀⢈⣉⠻⣿⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃⢈⡛⠃⠈⠁⠀⣿⣿⡧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⡦⡈⠀⠠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⠛⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠛⠖⠀⢀⣶⣬⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⡄⠋⢀⠀⠀⣹⡆⠀⠸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡅⠘⣆⠀⠀⠛⠀⢸⣷⠀⠾⠆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠘⣷⣀⠀⠀⢈⣿⡆⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢁⡴⠒⢴⣬⣿⣷⣶⣾⣿⣿⣿⢂⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠃⠀⠀⠉⠀⠀⡈⠉⡹⠟⠛⠁⠛⠃⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⠀⠀⠀⢀⠟⠁⡼⠠⢄⠀⠉⠀⢀⣀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡶⠀⣠⡶⠀⡄⠀⢀⣀⢀⣼⣷⣀⡄⢸⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⢿⠏⠁⢚⠁⢀⣤⡀⠀⣾⠉⠻⣿⡟⢻⡇⠀⠛⠰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣿⡇⠀⣴⠋⠀⢀⣽⠁⢰⡟⠀⠄⢹⣷⠸⣷⡄⣦⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠛⢋⣤⡾⠁⠀⠐⠚⠛⠀⣿⣷⠀⢢⢼⣿⠈⢻⣧⠈⡀⠀⢹⣷
⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣿⡿⠷⣶⣾⡿⠋⢠⣀⠔⢻⠆⠁⣰⣿⣿⢠⠀⣬⣿⡄⢠⣿⡌⠋⢡⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠒⠀⠀⢃⣾⣿⡿⠗⠚⢿⣿⠏⠁⠐⠚⣧⠓⠁⢰⡿⣿⡟⠘⠃⠉⣿⡇⠸⠿⣿⡄⠀⣴⢹⣿⡆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡆⣿⣷⣿⣛⣛⣻⡿⠃⠀⠀⠈⣀⠘⠀⢀⡾⠟⡻⠃⠀⠀⡀⢹⣇⠀⢀⢻⣿⡈⠻⡇⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣼⣿⣿⣿⣿⡿⠋⠀⠀⠀⢆⣻⡼⠃⢀⣌⣉⢀⠀⠀⠐⠀⠀⢸⣿⠀⠉⠦⢻⣧⡀⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣿⡿⢋⣤⡾⢋⣴⡶⠾⠛⠁⠀⣼⣿⠏⢸⠀⠀⠀⡀⠀⢸⣿⠀⠀⡄⠀⢹⣷⡀⢹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢫⣴⠟⠉⠀⠺⣄⣼⣇⣀⣴⣾⣿⣿⡄⠘⠀⠀⠀⢉⡆⢸⣿⡀⣧⠀⠀⠸⣿⣿⣄⢻⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⡁⠠⠀⠀⣠⡟⠿⢀⣩⣿⡏⣾⠋⣧⡄⠀⠀⠀⠘⡋⢸⣿⡇⢸⣷⣄⠀⢹⣿⣿⣮⢿⣿
⠀⠀⠀⠀⢸⣾⣟⣻⢛⡴⣿⠧⠀⠸⠟⠉⢡⢶⣾⡿⣻⠃⢶⠀⢹⡇⠀⠀⠀⠘⠁⢰⣿⡇⣸⠚⢿⡶⠘⣛⣇⠹⣷⣿⣧
⠀⠀⠀⠀⢠⣿⣿⣳⣿⡗⣸⠃⠲⠀⠀⢀⣴⠿⢋⢿⡄⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⢸⣿⡇⢨⡀⠀⠀⢀⣭⣿⡇⠸⣿⣿⡀
⠀⠀⠀⢀⣸⣿⡝⢿⣷⣏⡿⢄⡃⣠⣾⠟⣁⠸⣿⠘⣷⣀⣷⣦⣬⣤⠀⠈⠀⠀⠀⢸⡟⣷⢸⣥⠀⠀⢈⠿⣿⠇⣷⠈⣿⠇⡀
⠀⠀⠀⣼⣧⠹⢿⠗⢀⣿⡷⢟⣵⣿⣿⠆⠹⣦⠙⠂⣼⣿⡄⠑⠀⠌⢃⣄⣰⡂⠀⢸⡇⣿⠈⠻⣧⡀⠺⠃⢰⣿⣿⠀⢨⣾⠁
⠀⠀⢠⣿⣿⣷⣤⣴⣦⣶⡄⠺⣿⣿⣿⡄⢷⣝⣷⣤⣿⣿⡿⣦⡀⠘⠛⢉⣽⠉⡂⢸⡇⣿⠀⣻⢻⡗⠂⣠⠌⠀⣶⠆⠀⣿⠆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡌⣿⡄⢸⣿⣯⠀⠈⠻⣿⣿⣿⣿⠇⣿⣿⣦⣀⠀⠀⠰⠇⢸⡇⢸⡄⠉⠉⣠⡜⠁⠀⠀⣿⡇⠀⣿⣦⡀
⠀⠀⣾⣿⣿⣿⣿⣿⠟⣧⠈⢁⣾⣿⣿⣦⠀⠀⠸⣿⣿⣿⢀⣿⠇⠈⠽⠿⠶⢦⣄⣸⡇⢸⣧⡴⠟⢻⠀⢠⠔⠋⣿⣿⠃⢸⣿⡇
⠀⠀⢿⣿⣿⣿⣋⡁⠀⠈⠁⢀⣿⣿⣿⣿⡀⠂⠀⢹⣿⣿⠘⠋⠀⠀⢀⠀⠀⠀⠈⠉⠁⠈⠁⠀⠠⣿⠁⠀⠖⠀⣿⡗⠀⢸⣿⣁
⠀⠀⠀⠀⠀⠉⡿⣿⣿⢶⣾⣿⣿⣿⣿⠿⣿⠆⠀⣨⣿⣿⣆⣤⣀⡀⠀⠐⠃⠀⠀⠀⠀⠀⠐⠀⣨⣿⡇⠈⠀⢀⣽⣇⣀⡼⢿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣍⣛⣿⡿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠻⠿⠿⣴⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠀⠀⠠⠄⠀⠉⠉⠙⠉⠙⠿⠛⠛⠿⠻⠿⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⡄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠌⡀
⠀⠀⠀⠉⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠢⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠑⠄⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠂⠀⠀⠁⠀⠘⠐⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑
⠖⢺⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠠⢀⠆⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠐⡁
⠀⠐⠅⠀⡄⠐⠈⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⡀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⡍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠈⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠄⠀⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣦⣄⡀⠀⠀⣠⡤⣤⣤⣤⣀⣀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠩⢶⣶⣤⣽⣿⣿⣿⡿⠏⣳⣾⣿⣿⡞⣿⣿⣿⡟⢈⡿⢛⡛⣿⣿⣿⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠤⢤⣭⣭⣿⣿⣿⠿⣉⣴⣿⣿⣿⣿⣿⡇⣯⣿⣿⡷⠘⣇⠻⢆⡟⠁⠀⣌⠿⠋
⠀⠀⠀⠀⠀⠀⣀⣉⣭⣭⣽⣿⠟⢡⣼⣿⣿⣿⣿⣿⣿⢟⣲⠽⠟⠀⠑⢄⠈⠉⠁⠀⠀⠘⠑⠶⢴⠄
⠀⠀⠀⠀⠀⠀⠊⣉⣩⣾⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠲⠄⠀⠀⠀⠉⠦⠀⠀⢠⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠚⠍⢿⣿⡟⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⠄⠀⠀⢀⠰⢄⣀⢀⡠⠞⠁
⠀⠀⠀⠀⢀⢴⢾⣿⠏⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢙⣄⠀⠀⠐⠍⠉⠲⣦⠼⠋⠁
⠀⠀⠀⠀⠀⢀⣼⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠈⠖⠀⠠
⠀⠀⠀⠀⠐⠹⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⠄
⠀⠀⠀⠀⠠⢾⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣄⣤⠖⠒
⠀⠀⠀⠀⢀⣴⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⡆⢠⣖⣰⣶⣿⡿⠃
⠀⠀⠀⠀⠉⢙⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⡽⡼⣾⣟⠯⢮⣰⣼⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠋⢣⢸⣿⣿⣿⣿⣿⣿⣿⣯⠘⠆⠘⠷⠻⠶⠽⠋
⠀⠀⠀⠀⠐⠀⢿⡀⣿⣿⣿⣿⣿⣿⣿⡷⢁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠘⠃⠀⠷⠹⣿⣿⣿⣿⣿⣿⣜⢠⠌⠀⠀⠀⠀⠀⠀⣰⠾⠛⠋⠉⠉⠛⠻⢮⡳⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃
⠀⠀⠀⠀⠀⠘⣏⡐⢇⣹⣿⣿⣿⣿⣿⣿⢫⣖⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠫⠻⣽⣆⡀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠸⣧⡘⢁⢻⣿⣿⣿⣿⣿⣿⣎⠄⠀⠀⠀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠏⣧⣇⠀⠀⠀⠀⠀⢠⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠉⣷⣸⣯⠙⢿⣿⣿⣿⣿⣿⣳⡂⠰⣾⣟⣟⣡⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣿⣿⠀⠀⢀⢀⣴⡏⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⡯⠸⣧⠹⢿⣿⣿⣿⣿⣟⣄⠀⠉⠀⠀⠙⠛⠚⠀⠀⠀⠀⠀⠀⠀⠂⠀⢋⣌⣿⣶⣶⣿⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⡻⢳⢪⣭⠻⢿⣿⣿⣿⣦⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣼⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠙⠪⣟⠃⡀⠉⠻⠿⢿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣤⣶⣥⣤⣠⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⠶⠦⣭⣩⣭⣿⣻⣿⣟⣿⡿⠿⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢈⠉⣁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠈⠁⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠀⢄⠔⠒⠢⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠈⠉⠂⢀⠀⠀⠈⠂⠀⣀⡀⣀⠤⠄⠊⠀⠀⠀⠀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄
⣤⡒⠁⠁⠀⠈⠈⠝⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠀⠚⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡎
⠑⠈⠦⣄⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⠠⠁⠀⠈⠀⠀⡤⠄⠚⢡
⠀⠀⠀⠈⠢⡀⠉⡀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠁
⠀⠀⠀⠀⠀⠈⠁⠙⡄⠀⠀⠙⠄⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠄⠠⠀⠰⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠈⠐⢲⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠁⠒⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⢄⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠁⠺⠀⠀⠱⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠑⢄⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⣀⣄⠐⠂⠀⠠⢄⠀⢤⠃⠀⠀⠀⠀⠠⠄⠒⠂⠒⡠⠴⢤⡀⠀⠀⠂⠀⠀⠁⠢⡀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⢏⠙⢳⣻⠁⠀⠀⠀⠀⠀⠀⣀⡘⠀⠀⠀⠀⠁⠀⠀⠀⡠⢡⡀⠤⢈⠀⠀⠀⠰⡀⠀⠀⠈⠑⠠⣀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡋⠀⠄⡀⢐⣠⢜⠤⠉⠀⠀⠀⢄⠀⢠⡄⠀⠀⠁⠀⣀⣀⠚⠁⠀⠀⠀⠈⠐⠢⢀⡀⠀⠀⠈⢛⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠤⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠍⢐⡀⠀⠀⢄⠀⠈⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠁⠁⠀⠄⢛⣒⣐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⢀⢀⡀⠀⠀⠘⠁
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣾⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣰⣿⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠁⢸⠀⠀⠀⠀⠀⠀⠈⣉⣙⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣀⡾⣿⣿⠆⡀⠀⣿⣿⣶⣠⣾⣧⡀⣀⣬⠀⠀⠀⠀⠀⠠⠟⠟⡿⣟⠻⢻⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣏⢙⣳⣿⣷⣆⡈⠉⠻⣿⣿⣷⢾⣇⣨⣿⠶⠄⠀⠀⠀⠀⠀⠠⣧⣿⣾⣩⣢⣆⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡮⢍⣿⣿⡿⢿⣿⡦⢩⣵⡑⠄⠙⠛⡳⠄⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⣿⣿⣿⡇⢀⠙
⠀⠀⠀⠀⢄⡀⠀⣾⣿⣿⣛⢻⡏⣅⣩⣿⣟⠸⣤⡌⡂⠀⠀⠑⠖⣀⣶⠆⠀⣀⠉⠉⠛⠛⠛⠛⠛⠛⠃⢀⣀⣀⣀⢀⣀
⠀⠀⠀⣼⣿⣿⣿⣿⣭⣝⣛⣛⡿⠿⠿⢿⣿⠀⣿⣿⣷⢀⣆⢰⣿⢏⢤⣤⠶⠷⠶⠖⠒⠒⠚⠛⠛⠉⠉⠉⠉⠀⡀⠉⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣶⣿⣭⣬⣭⣌⣭⣬⣭⠥⠴⠶⠖⠒⠚⠛⠳⠒⠀⠀⠀⣀⠸⠷⠃
⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠘⢿⣿⣿⣿⣿⣯⠅⣀⣿⠀⠀⠀⠀⠀⣠⣤⠀⠀⠐⠀⠈⠉⠁
⠀⠀⠀⠀⢀⠀⠀⠍⠉⠙⠻⠿⠿⣿⣿⠛⣿⠀⠠⠄⠉⠉⠙⠛⠶⢤⣿⠀⠀⠀⠀⠀⠙⠑⠢⢾⡈⠀⠁
⠀⠀⠀⣀⣤⢀⣄⡦⢀⡅⢠⠀⠀⠀⠉⠓⢾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣶⣿⣿⣿⣶⡖⠶⠄
⠀⠀⠀⠘⠿⠻⠯⠠⠟⠂⠆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⣿⠿⠷⠖⠖⠀⠀⠀⠚⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢷⣄⠀⠀⠀⠀⠀⣠⡖⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠁⠉⠉⠉⠉⠉⠊⠀⢀⡇⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⣄⠀⠤⠄⠀⣤⡀⠀⠀⡼⠑⠒⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⢍⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⣳⡄⢆⣰⣆⡠⠀⣒⡾⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡌⢢⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣉⣠⠓⢤⣀⣀⣠⠴⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢱⡀
⠀⠀⠀⠫⡉⠈⠀⠀⠀⠀⢹⡀⠀⠈⠉⠀⠀⠀⠀⠀⡔⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢱⠀⠀⠀⠀⢀⣠⣷⡀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠈⡇⠀⠀⠀⣞⠒⠒⠛⠒⠒⠲⠤⠤⠤⠈⢧⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠳⣄
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠻⠦⠴⠒⠒⠒⠒⠒⠒⠒⠒⠮⠷⣄⡀⠀⠉⠒⠦⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠄⠐⠒⠒⠀⠠⠤⠤⠤⠤⠄⠐⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠔⠒⠊⠉⠉⠉⠉⠒⠒⠲⠤⠤⠤⠖⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣤⣾⣦⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⠟⡛⣿⡿⠚⠿⠿⡿⠛⠿⢿⠿⠿⣿⠿⢿⣿⣿⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⣾⣿⣿⣿⣭⣽⣿⣿⣏⣼⣗⣿⣀⣠⣤⣴⣻⣀⣀⣈⣂⣀⣉⣣⡀⢀⣛⣦⡀⠀⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠈⠢⡉⠈⠉⠫⣍⠉⠙⠛⣏⠉⠉⠙⣿⠋⠻⠹⠉⠉⡟⢹⢿⡛⠉⠙⢻⠋⠉⢛⡟⠟⣩⠟⡻⠛⠛⢛⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂⠈⠊⠒⢴⣬⣦⠀⠀⠈⢆⠀⠠⠀⠀⡇⠘⠸⠀⠈⠀⡁⢀⢴⡪⢔⡫⠔⠋⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠄⠈⠙⢷⣄⡀⠪⡀⠀⡄⠀⡇⠀⡃⠀⢀⡾⣠⣴⠯⠒⠉⠀⠀⢀⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠙⠦⣇⠀⣆⠀⣿⢠⣦⣾⡿⠗⠉⠁⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠻⢵⣿⠿⠋⠁⠀⠀⠁⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡐⠄⠀⠀⢀⣰⣋⣟⣷⠀⠀⡰⠁⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠘⣌⣏⢸⣙⠻⣧⡐⣁⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣿⣿⣾⣷⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠔⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡯⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠋⠀⠈⠃⠀⠀⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠘⡄⠀⠀⠀⣀⣀⣀⠀⠂⠀⡰⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠈⠢⣄⡀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠉⣭⡉⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⡟⠈⢆
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠀⠀⠀⢤⡀⢀⠀⢨⡄⠀⠀⢂⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡇⠀⠆⢸⠁⠀⠀⠰⣿⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠐⠒⠤⣐⢕⠠⡀
⠀⠀⢠⠠⠤⠤⠤⠤⠤⠄⠀⠐⠒⠀⠒⠒⠒⡄⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⡀⠈⠑⢕⡌⢂
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠈⢫⠀⠃
⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢁⠀⠀⢀⣀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠈⠐⠢⠤⣀⡀
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢀⠜⠀⠀⣖⡄⠁⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠠⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⢀⣀⡀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢎⠆⠀⠀⠀⠉⠑⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠊
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⢀⡼⡿⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠁⠄
⠀⠀⠔⣁⣤⣤⠑⠰⣿⣇⠀⢳⡄⠀⠀⣰⣶⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⢆⡀
⠀⠀⠀⠈⠀⣤⣀⣀⣈⠙⠒⠺⢷⠒⠿⠯⢍⡙⠒⠒⠂⠀⠀⢰⡶⠀⠈⠙⠛⠓⢒⡰⠞⠛⠿⠆⠀⠀⠀⠄
⠀⠀⠀⠀⢀⣂⠀⠛⢍⠻⢭⠒⠾⠧⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⢀⣀⣀⣒⡋⣂⠀⠀⠀⠀⠤⠀⠀⠈
⠀⠀⠀⠀⠘⢿⡿⠋⠈⠑⣦⢬⣭⣖⣶⡄⠀⠀⠀⠀⠀⣠⠶⠻⠿⢿⣭⠤⠦⠿⠋⠍⠶⡂
⠀⠀⠀⠀⠀⠀⠁⢼⣿⠂⠐⠚⡋⠀⣐⠉⠢⡀⠀⡠⠾⠃⠀⠀⠢⣀⠀⠄⠀⡄⠀⠀⣤⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠐⠘⠂⠀⠀⠓⠋⠁⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡒⡳⠓⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠅⠚⠙⠣⠴⣶⠪⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢗⠉⠑⠿⠤⣄⢈⢀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠸⠛⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠂⢀⡔⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⡠⠞⠉⡅⠀⣠⠞⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣁⠀⠀⠀⠈⠙⠒⠤⣀⣀⡾⠀⠀⠀⠈⠙⠁⠀⠀⡠⠕⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⣠⣶⡟⠓⢄⡀⠀⠀⠀⠀⠀⠀⡍⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢄
⠀⠀⠀⠀⣀⣤⠶⠋⠁⢀⢤⠂⠀⠙⠋⠐⠠⡎⠈⠉⠉⠁⠀⠀⠾⢁⠃⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠈⢦
⢀⣠⠴⠚⠉⠀⠀⠀⠀⠈⢈⠢⡀⠀⠀⠀⠀⠈⢣⡒⠤⣀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠑⢌
⠻⣧⡀⠀⠀⠀⠀⠀⠀⠠⡊⠑⢌⠢⡀⠀⠀⡀⢸⡁⠀⠈⣡⠾⢻⢀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡇
⠀⣿⠙⠷⣄⠀⠀⢠⠀⠀⠘⣄⠈⠢⠟⣖⠭⠒⢉⣠⣶⣋⡥⠴⡇⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⡸⠁
⠀⣿⠀⠀⠈⠻⢦⡈⠘⡄⠀⠈⠢⠖⠉⣀⡤⠞⠋⠁⠀⠀⢀⡄⠈⠒⠤⣀⠀⠀⠀⠀⢀⠀⠀⢀⠞⠁⠐⢀⠞
⠀⣿⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠉⠀⣰⠟⢴⢡⠄⠈⠧⠚⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠶⠋⢹⡆⠀⠀⠐⢼⡶⠋⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠋⠁⢀⡸⣃⡠⠎
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣸⠀⠀⠀⢀⣤⡤⠖⣾⠛⠒⠒⠒⢶⠚⢻⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⢹⡀⠀⠀⠀⠙⡆⠀⣿⠀⠀⠀⠀⢸⡇⠸⣿
⠀⢹⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⡇⠀⠀⠀⡏⢳⡀⠀⠀⠀⠹⡀⣿⠀⠀⠀⠀⢸⡆⠀⣿
⠀⠘⢧⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⠀⢳⡀⠀⠀⠀⢳⡟⠀⠀⠀⠀⢸⠁⠀⣿
⠀⠀⠀⠻⣄⠀⠀⠀⠀⢸⠀⣀⣠⡷⠤⠴⡖⠃⠀⠀⢳⡀⠀⠀⠈⡇⠀⠀⠀⠀⠚⠂⠀⢹⡄
⠀⠀⠀⠀⠈⢷⡀⠀⠀⢸⠋⠉⠀⣀⣀⣀⡗⠀⠀⠀⠀⢳⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠸⠷
⠀⠀⠀⠀⠀⠀⠙⣆⠀⢸⡛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⠤⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣶⣶⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠒⠀⠀⠀⣠⣴⠶⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠈⠀⠀⠀⠀⠈⠉⢁⣶⡆⠀⠀⠉⠐⠆⠈⠉⢛⣿⠶⣥⣈⡠⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣠⣄⣰⡤⠀⣠⠀⠀⠀⠀⠀⠀⠉⠻⠄⠀⠀⠀⠀⠈⣿⣿⣿⣶⠄⢀⣀⡀⠠⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⢀⣴⠳⠔⠛⣠⣤⣌⣼⣿⠂⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⣻⣿⠟⠁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣼⣏⢹⣵⣾⣿⣿⣿⠿⠣⣄⣀⣠⡴⣶⣶⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⠟⣿⠁⠀⣀⢻⣿⠟⠘⠋⠁⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠉⠀⠂⠀⠹⣤⢂⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⣶⠀⣠⣄⡤⠀⡀⢠⣇⠀⢺⣿⣿⣿⣿⡿⢀⡤⠶⠒⠀⠀⠲⣿⣦⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠈⠛⠛⠛⠁⠀⠀⠀⠈⠞⢵⡉⠀⠀⠀⠀⠀⠀⢾⣿⡿⠟⠓⠢⠤
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠂⣧⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⢀⡀⣸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⣶⣶⣾⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣦⣡⡎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠹⠟⡿⣷⣶⡄⠀⠀⠀⠀⠈⢷⣶⣿⣶⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⡾⣿⢈⣰⣿⠟⡋⠀⠘⠒⠢⣝⣷⣿⡆⠀⣠⣄⣘⣉⡀⠀⠀⠀⠀⠀⠀⣼⣯⣿⠟⢄⣀
⠀⠀⠀⠀⠀⠘⣯⡍⠓⠲⢍⡩⣌⣀⣬⣳⡙⣦⣀⡀⠀⠘⠻⠿⣷⢸⣿⣄⠉⠀⢝⡳⣶⣄⣀⣴⠊⠉⠉⠉⠀⠠⣍⠙⠓
⠀⠀⠀⠀⠀⠠⠋⠀⠀⠉⠢⣙⢾⡿⠛⠉⠁⠘⡏⠙⠣⠀⠀⠀⠿⢸⠋⠻⣧⡀⠈⠻⣾⣿⡿⠿⠷⡄⢀⣀⡀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡁⠀⢀⣀⣀⡅⠠⢶⡿⣛⣠⣴⣿⣤⣤⣬⣷⣦⡀⣰⠋⠀⠀⠀⠀⠁⠺⣽⣢
⠀⠀⠀⠀⣀⣀⠀⠀⣀⣤⣄⣰⣶⣧⣤⡿⢱⡿⠁⢀⣤⡶⠟⠛⠫⠯⡭⣤⢄⡈⠉⣹⣯⣇⠐⠂⠀⠀⠀⠀⠈⠻⣧
⠀⠀⠐⠋⠉⠀⠀⠀⠀⠢⢤⢬⣙⣿⣿⣇⡿⠁⢀⡘⢹⢇⡀⠐⢛⣍⠉⠛⠛⠙⢿⣿⣿⣛⠛⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠻⣄⠀⢸⣧⣴⠂⠀⠈⢲⡦⣄⣺⡁⢀⠟⠈⠉⠁⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣼⣷⣼⣿⣿⠇⣠⢴⠟⣿⠈⣿⣿⣿⡶⠄⠀⢀⠀⠀⠀⠀⢇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⠜⠛⠁⠀⠀⠀⣩⣿⣶⣯⣿⠀⢹⣄⣸⣿⡿⠛⠀⠀⠚⢷⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠁⠀⠀⠀⢀⡤⠒⠉⠙⠛⠛⢫⣿⣯⣿⣿⣿⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡿⠁⠈⢿⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⠀⣀⣀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠠⢌⡑⠂⢄⠀⠀⠀⣀⣤⣤⣶⣿⣿
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⣂⡐⠲⠿⣓⡀⢄⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿⣾⡿⣻⣡⣿⣾⣿⣿⣿⣿⣟⠿⣏⠟⠻⠛⠛
⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⠀⠐⠀⠀⣠⠀⠀⠀⠀⠀⠀⢺⢷⡶⠿⠻⢛⠟⣹⣟⢿⡻⣌⢣⠙⣄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠅⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢠⣾⣿⣿⢦⠳⡈⢀⢡⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠠⠀⠀⠀⠰⣟⡻⠯⡹⠽⠖⢱⡀⠀⠃⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣐⠀⢀⡀⠄⠀⠀⠀⠂⢀⠀⠀⠀⠀⠒⠉⠉⠁⠂⠀⠀⠀⠀⠀⠚⢸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣨⣷⣄⡀⢤⡁⠀⠁⠀⠀⢈⢲⣴⣋⠀⣀⠀⢀⠀⣀⠀⣀⣀⣀⣀⡀⡉⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⠠⠾⠻⠙⠋⠦⠈⠑⠈⠙⠭⡙⠽⡿⣿⢯⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠈⠑⠀⠀⠀⠀⢸⢦⡀⠀⠑⠤⠑⢌⠛⡾⠁⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⢀⡀⠠⠄⡒⠈⠁⠀⠀⡀⠀⠀⠀⠀⠏⡙⢦⣀⠠⠈⠢⠈⠃⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠌⠷⣶⡾⠁⠀⠀⠀⠔⠀⢞⠀⠀⠀⠀⠁⠈⢻⣷⣄⠐⠄⠐⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠋⠀⠀⠀⢀⠄⡠⢁⣾⠀⠀⠀⢸⠀⠀⣛⣷⡍⠳⠄⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢁⡴⠠⣿⣿⠁⠀⠀⠈⠀⠛⡡⢋⠔⢁⠄⠉⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠄⠀⠒⠀⠈⠒⠀⠉⠑⠀⠀⠀⠀⠘⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠃⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠄⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⡀⣠⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⢀⠑⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠉⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠝⠒⠙⠨⣿⣔⣦⠀⠀⡀⡀
⠀⠀⠀⠀⢀⣤⠔⠶⠒⠂⢀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠈⠁⠪⢿⣿⡀
⠀⠀⠀⠀⡇⡔⠀⠀⠀⠀⠈⣷⠋⠀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⣀⣤⣄⠀⠈⣷⡀
⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠙⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⡦⠀⠉⠉⢙⠂⠄⢉⠃
⠀⠀⠀⠀⡇⡇⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢹⡢⠁⠀⣀⠀⣌⡞⠢⡀
⠀⠀⠀⠄⢧⢀⠀⠀⠀⡇⠀⢠⠀⠀⣀⡄⠠⠄⠀⠀⠠⠀⠀⠀⠉⠂⠈⠒⣯⡀⠀⠨⡁⠀⠀⠔⠙⣆
⠀⠀⠀⢰⢸⡀⡀⢀⣤⣿⠀⢹⢩⣤⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢵⢑⠀⠀⠹⠀⠃⠈⠀⠘⠂
⠀⠀⠀⡼⠂⣇⠣⠉⠠⠌⠄⠘⠿⢿⡆⠉⢿⣇⠀⠀⠀⠀⠀⢠⡆⠀⠈⠄⠅⢺⣰⠓⣍⡂⠀⠀⠀⠄⠈
⠀⠀⢸⠐⠁⠹⣷⢦⡄⡀⢀⠰⠒⠶⣾⡶⠖⠛⣂⠀⢀⣠⣴⠁⠀⠀⠀⢀⠀⢸⡃⠸⡀⠀⠀⠀⠀⠀⢨⣀
⠀⠀⠀⠐⠀⢈⡿⣭⡽⠋⢸⠀⠇⠀⠀⠀⠈⠂⠈⠉⠹⠘⠂⠀⠀⠀⠀⠀⠀⠈⣃⠀⠀⠀⣠⠀⠀⠀⠀⠀⠉⠂⠄⡀
⠀⠀⠀⠈⠀⢸⡇⠁⠀⠀⢸⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⣏⣠⠏⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⡀⣀⠇⢀⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠃⠈⡴⠁⢸
⠀⠀⠀⠀⠀⠀⠁⠋⠀⠈⠀⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠇⠐⠀⠀⡜
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠐⠄⠀⠀⠀⠀⠀⣀⠤⢀⡚⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠲⣯⢀⠀⠂⠤⡼⢷⡧⠀⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠦⣤⡀⠀⣀⣤⣶⣶⡶⠿⣝⣷⠽⠗⠒⢶⡆⠀⠀⠀⢰⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠙⢳⡟⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣾⣷⣿⣾⣥⣾⣿⣷⣞⣛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣾⣿⣷⣾⣿⣿⡿⠿⠟⠛⠛⠛⠻⠿⣿⣯⣁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢟⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠻⠋⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣥⡾⣻⣿⠟⠁⠀⠀⡀⠀⠀⠀⡀⠐⠋⠉⠀⠀⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡿⠃⠀⠀⠐⠋⡉⢁⡀⠋⠉⠀⢠⠟⠁⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢸⣏⠉⠁⠀⠀⠀⠀⠠⠛⠾⠿⠤⠴⠞⠉⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡟⠉⠀⠀⠀⠀⣠⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⢶⣦⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣄⡀⠰⠋⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⡄⠫⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣴⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⣀⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠒⠚⠋⢰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠀⠀⠀⠦⣝⣳⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠰⠤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⠶⠶⣬⣓⣶⠋⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⢌⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀⠀⠙⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠾⠿⠆⠀⠀⣶⡇⠀⢿⣧⡤⠴⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣁⠀⠀⠀⠀⢀⣸⣿⡇⠀⠀⠀⢀⣀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠙⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⣠⣧⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠟⠛⠿⠶⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠠⠤⠀⠀⢨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄⠀⠀⠀⢁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣀⠀⠈⠀⢺⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⢻⡿⠿⠀⠀⠀⠀⢻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠞⢳⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠐⠂⠂⢀⢀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣢⠀⢲⠾⠛⠀⢰⣇⠀⠀⠀⠀⠀⠀⡀⢰⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⢤⡄⣶⣶⠾⠋⠀⠙⢶⣤⣄⡤⠉⠀⢸⡇
⠀⠀⠀⠀⠘⠀⠀⠊⠉⣖⣠⣦⠌⠁⠉⠀⠀⠀⠀⠀⠘⣷⠉⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡤⠈⢟⣋⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⢸⡿⣶
⠀⠀⠀⠀⠀⣀⠐⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⣤⡾⠃⠀⠀⠀⠀⠀⢼⡿⠞⡀⠀⠀⣨⠖⣄⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⡟⠀⠀⠀⢀⠀⣠⣾⣿⠄⠀⠀⠀⠀⠀⢀⣿⡃⢸⡇⢀⡸⢦⢸⡄⠀⠀⠀⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢂⣼⠿⣿⠟⠠⠀⠀⠀⠀⠀⢠⠿⣷⣄⣿⠋⢀⣰⡞⠁⠀⠀⠀⠈⠻⣿⡁
⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡇⠀⠀⢰⣿⢏⣼⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠡⣟⠿⠿⠛⠛⠁⠀⢰⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⠁⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⢙⣷⡏⠀⠀⠀⠘⣿⢋⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⡅⢠⠀⠀⠀⠀⠀⠁⠀⠀⡄⠈⠄⠀⠀⠀⠸⡆
⠐⠂⠀⠀⠀⠀⣿⣿⠟⣄⢀⣸⣏⠁⣾⣯⠀⢠⠀⠀⠐⡆⠀⣰⠀⢲⣿⠻⣀⣀⠀⠀⣠⠀⢱⠀⠸⡀⠀⠀⡸⣄⠀⢻⣄
⠀⠀⠀⠀⠀⢰⣿⡿⠀⢀⣾⠏⠁⢰⡿⠀⠀⡊⠀⠀⠈⠀⠀⠁⠀⠃⡀⠀⠁⠀⠀⠀⠀⡅⠀⠁⠀⢳⡀⠀⠁⠈⠂⠈⢻⡀
⠀⠀⠀⠀⠀⣾⣿⡟⠀⣼⠏⠀⢀⡟⢠⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⢠⣾⣿⠁⢰⣿⢳⠇⣾⠁⡎⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⢸⣿⡇⢀⣿⠏⡟⢸⣏⠘⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢸⣿⣷⣾⡟⣰⢀⡿⠙⢿⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢤⡀⠀⠄
⠀⠀⠀⠀⢨⣿⣿⣿⣷⡏⢸⠇⠀⠚⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠈⢛⣩⣿⡍⠀⣿⠀⠀⠀⢸⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⢐⡆⠀⠀⠀⢸⠀⠀⢠⡷⣤⠀⠀⠨⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢱⣿⣿⣿⣇⣸⣧⡄⠀⠀⡿⠁⠀⣀⡵⢦⡀⠀⠀⠀⠀⢀⣿⡆⢸⠻⣦⣄⣀⡀⢰⠈⢇⠀⠉⠀⢤⣆⡠⠐⠮⠀⠉⠀⡄
⠀⠀⠀⣿⠸⣿⣎⣹⣿⣿⣽⣿⡄⠀⢺⣴⠞⣿⠁⢸⠋⠲⣦⡤⣀⣼⣿⡇⠈⡇⢸⡌⢻⣯⡸⣧⠘⡆⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⣿⣷⡘⢿⣿⣿⣿⡿⠟⢡⣾⢿⡇⢠⡿⠀⢸⠃⠀⣿⠀⠉⠉⣿⣧⠀⢿⠀⠃⠘⡄⢣⣿⡆⢹⠀⠀⠀⢠
⠀⠀⠀⣿⣿⣿⣷⣤⣷⣶⣶⡇⣿⡟⣼⡇⢸⣿⡀⢸⠀⠀⣿⠀⠀⠀⣿⢹⡀⢸⡆⠀⡀⢡⠀⢸⣿⡄⣇⠀⡀⢠⡀⠠
⠀⠀⠀⣿⣿⣿⣿⢹⡟⢀⣿⠀⣿⡇⣿⠃⢸⣇⠀⠘⡁⠀⢸⡆⠀⠄⠛⠸⡇⠀⣿⡀⢧⠀⠀⠈⣿⡇⠸⠀⢧⠈⠇⠀⠆
⠀⠀⢰⣿⣿⠛⠃⠛⠀⣸⠃⢠⡟⢠⡿⠀⣸⣃⠀⢰⣧⠀⠸⠧⠀⢠⠀⢰⠛⠀⡿⠃⢸⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠄⠀⠀⣀⣀⣠
⠀⠀⠈⣿⣿⣷⣤⣄⣀⣏⣀⠋⢀⠚⠁⣠⡟⠛⠁⡈⠋⠀⢰⢀⣀⡁⠀⣸⠛⠀⣉⣀⣰⣤⣠⣶⣾⣿⣶⣾⣷⣾⣿⣷⣾⣿⣿⠟⠁
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣶⣶⣿⣶⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇
⠀⠀⠀⠈⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡋⠐⠂
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⡿⢿⠿⠿⣿⡿⣿⣿⣿⣿⠿⠿⠿⡿⠟⠻⠿⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠⠤⣄⠀⣩⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠗⣀⣰⢱⣶⣦⣤⠛⢧⡀⡴⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡃⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠒⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡤⢸⣷⡀⣾⣿⣿⣿⣿⣿⡿⢭⡿⠿⠿⠿⠇⢀⠀⠚⠁⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⡀⣿⣿⣿⣿⠦⣿⣿⣿⣿⣿⣿⠟⣟⢆⡀⡶⢦⡰⠿⠀⠀⠀⠀⠘⣆⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠂⣐⢿⣷⠄⣿⡿⢿⣿⡄⣿⣿⣿⡿⣿⠵⠶⢿⡶⠅⠋⠨⠁⠀⢀⠀⡄⠀⢀⡷⠀⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠐⠂⣸⠇⠐⣿⣿⣿⣿⣷⣿⣿⣿⣷⣯⣬⣴⣈⡋⠱⢰⣄⡀⡔⠡⢉⡀⢀⠸⣧⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠤⠤⣿⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠤⠁⠀⠐⠁⠀⠀⡷⠒⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣾⣿⣿⠀⠁⠀⠀⢀⡇⠀⣿⣿⣿⣦⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢘⡇⠀⠠⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣾⣿⣿⣿⣖⠀⠀⠡⢾⡗⢘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⡇⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⣿⣿⣿⣿⢺⣿⣿⣿⣿⣹⣿⣷⣦⠀⣈⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠃⠀⣘⣿⣷⣶⣷⣿⠻⣿⣿⣿⣿⡿⣿⢹⣤⡗⢫⣾⣿⣿⣿⣿⣿⣿⣯⣭⣭⣉⣉⣡⣾⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⡏⣯⣿⢸⣽⣷⣼⣾⣏⣿⣿⣿⣿⣿⣟⣟⣻⠛⣿⢻⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⣿⣿⡿⠤⣀⣿⣿⣿⡟⣿⠾⠬⠿⣯⣥⣟⣶⣾⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣾⣿⣿⣿⡇⣼⣧⡀⠀⣤⣀⣀⣀⣁⠀⠛⠛⠉⠉⠉⠀⠀⠈⢻⣿⣝⣿⣿⣿⣿⡹⡇
⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣹⣿⣿⣿⣿⣾⣿⣟⣷⡄⠈⢷⣶⣼⠉⣧⡀⢆⠀⠀⠀⠀⠀⠀⠀⠐⣘⣻⣿⣿⣿⣿⡍
⠀⣶⣼⣿⣿⣿⣿⣿⣿⣿⠇⢀⣱⣿⣿⢸⣿⣿⠿⣿⣽⣿⣿⣄⠀⢻⣿⣧⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣄
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣏⣸⣿⣿⣿⣿⣿⡍⠐⢶⣾⣿⣿⡟⣿⣦⠀⠙⣼⣠⣿⣿⣆⠐⢄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣄⡀
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡿⣿⣿⣯⣧⡟⣿⣷⡀⠈⠛⠛⠛⠛⠳⠀⠣⡀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠶⢿⣿⣟⠧⣤⡿⣿⣷⣶⣶⣶⣶⣶⣶⣦⣤⣽⣤⣴⣶⣶⣶⣶⣶⣾⡿⠿⠿⠿⠿⠿⠦
⠀⠀⠀⠀⠤⣤⣉⣀⠉⠙⠛⠛⠛⠛⠻⠿⡿⠦⢶⣶⡀⢉⣦⣷⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠦⠴⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⡙⠛⣛⣻⣉⡉⠉⠉⣥⣤⣀⠉⠉⠉⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠶⠶⢦⣤⣤⣤⣄⠞⠾⣿⣿⣿⣿⣿⣖⠴⠿⣿⠿⠄⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⠿⡿⠭⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⡦⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣿⠃⠀⠐⡿⠖⠒⣉⣀⠠⠴⠶⡄⠀⢀⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠿⡠⠄⢨⡷⢧⠘⠁⠀⢸⠟⢀⡀⠀⠔⠃⢠⣿⣿⣦⣠⣾⣯⡐⠒⢀⣀⢠⠟⠛⠓⡀
⠀⠀⠀⠀⠀⣀⠀⠄⢀⣀⡼⡃⢀⠀⠀⠀⠰⠾⠀⡸⠃⠊⠁⠘⠄⠰⠏⠉⠐⡦⠎⢻⡏⠈⠙⠿⠿⢇⠄⠀⠛⠉⠃⠲⣼
⠀⠀⠀⠀⠀⠉⠀⠀⢸⡿⠤⠉⢠⡇⠀⢲⣆⡀⠀⡀⡀⠀⢐⠀⠀⢸⢂⠓⠀⠸⡀⢹⡧⠤⢤⣖⠐⣠⣀⠀⠀⣔⠀⢀⣩
⠀⠀⠀⠀⡄⠁⠄⠊⢿⠀⡐⠀⠀⠁⢠⡏⠀⠀⢀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣘⠁⠈⠁⠈⡉⠙⠻⡻⠏⠙⣇⣴⡗
⠀⠀⠀⠀⢀⠀⠀⠀⢸⢤⢰⠀⠀⡠⠘⣤⠤⠀⢨⣤⠀⡄⢦⡄⢀⠰⡀⣤⠀⡄⡀⠖⠸⠙⠠⠀⠀⠈⠀⠀⢸⡇⢈⠐⠂⣿⡏⠇
⠀⠀⠀⠀⠀⠁⠀⠀⠚⠈⠋⠀⠀⠉⠀⠈⠒⠃⠀⠀⠀⠁⠈⠀⠘⠸⣀⠿⠀⣿⠀⠀⠀⠀⠈⠋⠀⠛⠈⠁⠈⠀⠀⠁⠍⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣷⣿⣿⣶⣶⣶⣤⣲⣞⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡾⡻⣿⡁⢿⣿⣿⣿⠿⡌⠙⠉⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣥⣤⣠⣏⣳⣾⣇⠈⠁⠱⢷⣶⠃⠀⢠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣾⣿⣿⡇⠻⢿⣿⣿⣷⣵⣤⣀⣀⠀⣴⣿⣿⣿⣿⣿⡿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠻⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠢⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⣄⣠⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⣿⠛⡿⣿⣿⣷⡄⠀⠀⠈⠛⠻⢿⠿⠿⣿⠘⣿⣷⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠘⠀⠀⢸⣿⣿⣿⣶⣷⣶⣿⡆⣠⣶⣾⣿⠰⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠉⠁⠀⠛⠈⠉⣴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣳⣷⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣷⠟⠷⣿⣿⣯⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⢸⡟⡿⠿⣿⣿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢀⠀⢘⡀⢠⣴⠟⠋⠀⠑⠆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠹⣿⣷⣄⣈⣛⣿⣏⠆⠀⠀⠀⠀⠀⠀⠀⠒⠿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠐⠂⡀⠰⠀⠀⠀⠀⢰⠁⣴⣿⣿⣯⡙⠿⠿⣻⣤⣙⣲⣦⣄⡀⠀⠀⠀⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠙⠂⠀⠀⢀⠀⠀⠀⠀⠀⡈⠀⢿⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⡿⢛⣦⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⢷⢽⣿⢇⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠷⠋⠀⠀⠹⠠⠄⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢘⢉⡉⣻⣟⠉⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣼⢿⡷⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣐⠛⠿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠂⠀⢀⣈⠁⠀⠀⠀⠂⠀⠀⠀⠄⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⠶⠿⠟⠁⠳⠶⢶⣀⡤⠀⠀⠛⢷⣦⣭⣼⣷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠴⢧⠠⣤⠀⢸⣷⣽⣿⣿⣿⣷⡀⢃⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⠿⠷⠢⠀⠀⠠⠿⠶⠼⠿⠿⢿⣿⣿⣿⣷⡀⢷⡄⠀⠀⠀⠀⠀⠈⣥⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄⣀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣉⡀⠀⠀⠀⢠⣼⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠀⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⡀
⠀⣲⣄⢤⡄⠀⠀⠀⠀⠀⠀⠂⠹⣄⠀⠁⢻⡄⠀⠀⠀⠀⢀⠩⢄⡀⠀⠀⠀⢠⠀⠀⠀⢈⣄⠀⠀⣦⠈⣿⡀⢒⠀⣤⡶⠶⢦⣤⡀
⡆⣿⣿⢸⡇⣥⠀⢀⡄⣰⡀⣸⣆⣿⠀⠀⢘⡇⠀⠀⠀⢀⣸⡇⣹⣞⣿⣦⠶⠾⠷⠒⠒⠘⠿⠶⢦⣿⡇⣼⣇⡄⣷⢼⣧⣄⡀⣿⡅
⠀⢿⣟⠼⠛⠛⠛⠻⠿⢿⣿⣿⣿⡟⢀⣼⣿⣿⣤⢁⣴⡼⠿⢟⣾⡿⡭⠐⠀⠈⠉⠀⠀⠀⠀⠁⠀⠙⠻⣿⠿⣿⣿⣸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⢿⣿⣿⣿⡟⣉⠴⠚⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣍⠉⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⣿⠀⠇⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⢟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡀⠀⠀⠘⢸⠀⢠⠾⠟⠩⠄⠤⢤⣌⠹⢦⡀⣀⡀⠀⠀⣠⣴⠚⠉⠁⠀⠉⠑⠢⠀⠘⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⠢⢄⡆⢘⢀⣏⠀⢀⡪⢀⡦⣆⠔⠳⠀⢷⣤⣤⣤⣾⡟⠁⢀⣴⣩⣧⡽⠇⡄⠈⣆⣀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣏⠀⠥⡘⣻⣿⠀⠘⢁⠻⣾⣿⢏⢹⡇⢸⠟⠛⠛⣿⡃⠀⢘⡀⠼⣭⣿⣎⡁⠀⣟⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠛⠦⠤⢾⢿⣧⠀⠲⣄⣸⣀⣴⡾⢃⠈⠀⠀⠀⣘⣧⡀⠘⢄⡀⠛⠉⡤⢁⣤⠉⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠿⡷⡦⣤⣈⣀⣡⠴⠿⢿⣿⣿⣿⡿⠿⠷⢦⣀⣈⡉⣀⣠⣴⣷⣶⣶⣿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⠚⠓⡓⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡓⣨⠰⠏⠟⢥⠄⣴⠎⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠔⠛⠶⢧⣄⡠⢈⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⠀⠹⠶⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⢠⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⢤⠐⠁⠀⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠛⠲⢤⣀⠀⠀⠀⢀⡔⠉⠀⠈⠢⢠⠎⠁⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠉⣀⣤⠆⠀⠀⠀⠀⠀⠈⠙⠲⢶⠎⠇⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠋⠀⢀⠴⣮⠟⠁⠑⣄⣠⣀⣀⠀⠀⠀⠀⡌⠰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⣤⢒⠊⠀⠐⠉⠈⠑⠺⣁⠀⠀⠀⠀⠀⠀⠛⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣄⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠈⢨⡑⠄⠀⠀⠀⠀⠀⠈⢮⠑⠢⣄⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠈⠳⣄⠂⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠛⣦⣄⠀⠀⠀⠀⠀⠀⠀⢰⠉⠑⢄⠠⡀⠀⠀⢀⠀⢺⠀⠀⢀⣡⡾⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢸⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠷⣄⡀⠀⠀⡄⠀⠀⠑⡄⠈⠳⠼⠦⣚⠥⠒⢁⣠⣶⣛⣁⠴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠲⠃⠀⠀⠀⢀⡏⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⢦⡀⠰⢰⡀⠀⠘⢦⠴⠂⠁⣀⣤⠾⠋⠉⠁⠀⠀⡠⠈⠳⢤⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡠⠋⠁⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⢷⣄⠁⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠙⠒⠒⠀⢠⡾⣠⠒⣈⠁⢲⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⠶⠛⡇⠀⠀⠀⢀⣦⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠋⠀⢸⠗⠁⣀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣉⣁⣀⣠⡤⢴⡏⠙⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠒⢿⡋⠁⣸⡇⠀⠀⠀⠀⣿⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣷⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢷⠀⣿⡇⠀⠀⠀⠀⣿⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⠀⢳⡀⠀⠀⠀⠈⡇⣿⠁⠀⠀⠀⠀⣿⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⢳⡀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣿⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⣿⠀⣀⣴⠿⠒⠒⢶⠛⠀⠀⠀⢳⡀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠛⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣿⠋⠁⠀⣀⣀⣀⣼⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⣿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⣠⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⡶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣤⣤⠴⠛

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠧⠐⢧⣠⠴⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠰⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠒⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠳⠄⡨⢤⣹⣤⠍⠦⢧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⠟
⠀⠀⠀⠀⠀⡤⣦⠘⠇⡞⠀⢀⠃⠘⠆⠀⠀⠀⠠⠀⣀⣘⡗⢠⡙⠾⣻⠟⡶⣖⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⠛⣀⡴⣤
⠀⠀⠀⢀⡶⠋⢡⡔⠎⣉⢀⡠⠀⠀⠁⠀⠀⠈⣿⠧⣀⣨⡯⢰⣿⣾⣿⠙⠉⠉⠋⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠥⠀⠻⠿⠟
⠀⠀⠀⡿⠁⢀⡏⢀⣼⠤⢤⢄⠀⠀⢴⡀⠀⠈⣷⠶⢧⡄⠒⠾⠲⣿⢿⢿⣿⠿⠿⠄⢧⠀⠀⠀⠀⠀⠀⢠⣴⣇⣠⣤⣄⣀
⠀⠀⣰⠇⢰⡶⢙⣾⠓⢒⠤⠀⠇⢀⠔⠀⠀⠀⢹⣿⣿⣉⡉⠉⡛⠛⢻⢏⠾⡀⢀⠄⠀⠀⢀⣀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⠎⣶⢠⡀
⠀⠀⣷⣼⠟⣦⡾⣯⡾⠻⠀⠀⢀⣥⣀⠀⠀⠀⠀⠑⡿⣻⣿⣿⡷⠚⡏⢀⣆⠀⢠⡀⢰⠦⠈⠁⠀⣀⣿⣿⣿⣿⡿⣿⠟⡿⠀⠁⢸⢓⡄
⠀⠀⣿⡿⢟⡿⣷⣞⠑⠠⠔⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠉⠻⢻⡷⢿⣿⡏⠈⣗⠻⢏⠁⢀⠀⣦⣼⣿⣿⣿⣿⣿⣷⣿⣞⠀⠀⠀⠠⠾⠃
⠀⠀⢹⣿⣿⣿⣷⣿⢷⡅⠐⠛⠀⠀⠀⠀⠈⠀⠀⠰⠈⠀⠀⠄⠈⠈⠋⠃⠠⣿⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⠟⠜⢳⣻⡆⠀⠀⠀⠀⠐
⠀⠀⠀⠻⠿⠛⠟⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣜⣠⣾⡟⠀⢀⣦⠀⠀⢻⠀⢠⠇⠀⠿⢿⣿⣿⢿⣻⣥⣬⣬⣽⣿⠚⠁⠀⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣦⣤⡀⢀⣷⣄⠀⠛⠿⣿⠿⣿⢠⠀⣸⣿⡇⠀⠸⢠⡏⠰⡄⠸⢿⣿⣷⣿⣿⣿⣿⣿⡿⠉⠀⠱⣬⡉⠛⠦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣶⣾⣿⠒⠤⡘⡄⠸⡆⣿⣿⣿⣿⣿⢰⡏⠀⠀⢹⡤⠛⣿⣫⢝⡿⠁⠻⣸⢰⠀⠄⡀⣍⣿⡷⠆
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⣿⣿⣿⣆⣶⡈⠻⡄⢷⣿⣿⣿⣿⡿⢸⠀⠀⣴⠋⠀⢀⠟⠻⣯⣴⡇⢠⡇⣼⡀⣆⠷⡽⠞⠁
⠀⠀⠀⠀⢿⣿⡂⠀⠐⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡾⣯⠹⣿⣿⣿⡇⣿⠀⡼⠃⠀⢠⡜⣀⢤⡄⠉⠈⠋⠛⠙⠃
⠀⠀⠀⠀⠉⠛⠳⣦⡖⢀⠈⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⡄⢻⣿⣿⣀⢟⡿⠃⢈⠀⢸⡇⢻⡶⠇⠀⢀⠐
⠀⠀⠀⠀⢼⣿⡿⠋⡿⠫⢀⠈⠙⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣵⠊⠀⣠⣾⠀⢠⢠⣮⠀⣠⣤⣯⠒
⠀⠀⠀⠀⠀⠀⠀⠺⠓⣄⣀⣾⣀⠤⢙⠛⠛⠛⣛⠙⠛⢿⣿⣿⣿⣿⣿⡿⠃⠀⠄⢀⣼⣶⣿⣿⣷⣴⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⢻⠏⣤⢤⣤⣴⣷⣶⣦⣴⣶⣿⣿⣿⣿⣿⣿⡗⢈⣤⣶⣿⣿⠋⡟⢻⣿⣿⡻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠚⠉⠋⠀⠙⣠⣼⣷⣿⣿⣿⣿⣿⣿⣿⠛⢿⣯⡿⠛⠉⠁⢸⡟⣿⣿⡏⣾⠡⢋⣁⠈⣙⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠿⠿⣿⣿⣿⣿⠟⠋⣹⣷⡾⠋⠀⣰⣿⣷⣮⠓⣿⡟⣠⣣⣴⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⢠⣾⣿⡿⠗⠊⠀⢠⣌⣭⣻⣇⠹⢡⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠀⠿⢿⣿⣿⢀⣿⣿⣟⣛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠿⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠒⠒⠀⠒⠀⠈⠀⠀⠉⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠰⠀⠆⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠈⠐⠤⣀⠒⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⣀⠊⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢀⠀⠁⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠐⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠤⠀⠀⠀⠀⠒⠂⠀⠀⠆⠈⠠⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⣀⣉⠄⠀⠈⢄⠈⠢⡀⠀⠀⠀⠀⠀⡠⠊⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠁⠁⠀⠀⠐⠀⠀⠀⠑⠄⣈⠁⠒⠒⠂⣉⠄⠊⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⣁⢀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⡀⠀⠉⠉⠉⠁⢀⠀⠄⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠊⠀⠀⡸
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠄⡐⠀⠀⠀⠑⠒⠊⢀
⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⠊⠀⠀⠀⠀⠀⠈⠦⠊
⠀⠀⠀⠀⠀⠀⠀⠑⠬⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢾⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠈⠁⠀⠀⠀⠀⠀⠟⠃⠀⠀⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠂⠠⠤⠤⠠⠤⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠎⠡⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣵⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡏⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠓⠷⠧⠤⠤