Sweet Love Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠦⢤⡀⠀⠀⠀⠀⣀⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠗⠀⢀⡀⢀⠀⠈⢢⡀⡠⠞⠁⠀⠀⢀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠈⠓⠈⠀⠀⠀⣷⠁⠀⠀⠀⠄⡸⠀⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠋⠀⠀⠀⠀⠀⢠⡞⠉⢳⠋⣆⢀⡔⠐⣄⠀⠀⠀⠀⠈⠦⡌⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⠃⠀⠀⠀⠀⠀⠀⠀⡇⢀⡞⠀⢈⣾⣆⠀⢂⠂⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡎⠀⣴⠿⠋⠉⠓⠧⠀⠀⠀⠀⠀⠀⠀⠙⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣣⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣹⣧⢠⠀⢀⣀⣀⠀⠀⠀⠀⠀⣤⢤⣄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⣇⣀⣀⣠⡖⢲⣤⣤⣴⣴⡟⣾⡶⣿⡷⣾⢿⢻⡄⣬⣿⣾⡶⢶⣿⡝⣮⣿⣯⣇⣀⣀⣀⣀⣀⡀
⠀⣀⣠⣤⡶⠞⠛⠙⡉⢹⣽⡿⢻⣿⣷⣶⢻⢎⣯⠷⡿⠃⢤⢸⣿⠿⣿⣷⣷⣿⡿⣧⣷⢨⣉⢛⣿⣾⣇⣀⣈⣻⣹⣿⡟⣯⣷
⠀⠉⣿⣿⠃⢴⣔⣺⣿⣽⣿⣷⣶⣿⣿⣿⣦⣶⣿⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⣿⡏
⠀⠠⣷⣶⡿⠿⠿⢻⣿⣻⠉⠉⠉⠉⠉⠉⢉⡉⣩⢉⣽⠋⠀⠀⠀⢹⢓⡀⠀⠀⠀⠀⠘⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠚⠉⠀⠀⠀⠀⠀⣿⢷⠀⠀⠀⠀⠀⢠⣿⣿⠟⠋⠁⠀⠀⠀⠀⠈⢿⡇⠀⠒⢠⣀⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢠⠀⣠⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⡲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠠⠀⠀⠀⠀⢀⢠⢤⠣⡉⢝⣠⡀⠀⠀⢀⣠⡄⠀⠀⠀⠀⢀⠔⠃⠈⡄
⠀⠀⠀⠀⠀⠀⣀⠀⠑⢜⠃⢧⠑⠤⠊⡀⠀⠘⠗⠁⢠⠀⠀⠠⠁⠈⠀⠄⠒⠄⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠘⡡⠫⡢⠀⠉⠚⢀⡴⠋⠄⠀⠐⠃⠀⠀⠀⠀⢠⠀⣶⠄⠀⢀⠄⠀⠀⢀⣳⠁⠀⠕
⠀⠀⠀⢏⠣⡀⠑⠤⠡⠀⡀⠔⠁⠀⠑⠘⠀⡀⠀⠀⢀⠈⠁⠀⠆⢋⠠⠐⠁⠀⠀⠀⠈⠁⢢⡄
⠀⠀⠀⠈⢆⠙⡸⠀⠀⠀⠁⠀⠀⠀⣀⡴⡿⢠⡣⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣰⢳⣤⢃⣾⠁⠂⠀⠀⠀⠠⠀⠀⠀⠀⢀⡤⠀⠀⡤⠀⠀⢁
⠀⠀⠀⠠⠀⠀⠀⠀⢀⠄⠀⠀⢠⠟⢋⣠⠿⢃⠈⠀⠰⠡⠙⣀⡄⠀⠀⣀⠀⠁⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠄⡠⠀⠀⠀⠑⠏⢁⠄⠈⠀⠀⠀⠒⢦⡼⠀⠈⠁⠀⠒⠀⠨⠉⠀⡨⠁⠊
⠀⠀⢀⡠⠂⡲⠄⠀⠀⠀⠀⢀⡐⠀⠀⠁⠀⢀⣠⡶⢂⠀⠀⠱⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⢣⠔⠋⠀⠐⠄⠀⠀⠀⠀⢀⠤⡀⠀⠀⠈⢃⠀⠊⠀⠀⠀⢧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠵⡀⠀⠉⠀⠀⢀⠄⠀⠄⠀⠘⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠂⠌⠀⠀⠀⢰
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠠⡀⠀⠀⠀⢰⠀⠘
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠈⠙⠂⠀⠺⠀⠀⠀⠀⠠⠀⠀⢀⠀⢀⡄⢀⡤⠀⠀⠈⠂⠀⠀⠃
⠀⠀⠀⠀⠀⠉⠓⠦⠇⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⡘⡛⣿⠍⠰
⠀⠀⢀⠀⠈⠀⢈⠈⠀⠀⠀⢀⡔⠁⠘⢮⡧⠀⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠶⠾⠙⠓
⢀⠀⠀⠉⠣⠦⠀⠀⠀⠀⠀⠈⠉⢀⡔⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠉⠉⠉⠀⠀⢠⠄⠀⠈⠵
⠀⠀⠤⠤⠴⠤⠀⠀⢀⠊⠁⠀⠀⠈⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠖⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⡄⠰⡀
⠀⠐⠀⠀⠄⢀⠀⠀⠇⠀⠀⢠⠎⡄⠐⠄⠀⠀⣰⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⡂⠈⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠃⠠⠉
⠀⠀⢀⠀⠑⠀⠀⠀⠀⠀⠀⢂⡨⠀⠠⠔⠁⠠⡍⠑⠀⠠⠄⠀⠒⡀⢡⡄⠀⠱⢄⠀⠀⠂⠀⠀⠣⢀⡀⠀⠀⢀⡤⠀⡔⡄⠀⡀⠀⢀
⠀⢀⢀⡀⠀⠀⠀⠀⠠⠀⠁⠀⠁⠀⠀⠂⠀⠀⠘⠄⠀⢂⠈⠀⠠⠅⢠⡄⣠⠀⠠⠊⠉⠀⡀⠀⠀⠀⠀⠄⠂⠀⠀⠄⠈⢀⠞⠂⠀⠈⠑
⠀⠀⠘⠂⠀⠐⠒⠐⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠁⠀⠀⠈⠠⠀⠀⠂⢀⣍⠂⠀⠈⠂⠀⡀⠁⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⠂⡀⠀⣤
⠀⠀⠀⠠⡈⢀⠁⠁⢈⠁⠁⣀⠩⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠈⠔⠀⠀⢀⠑⢄⠀⠀⠥⡜⠀⠀⠀⠀⠀⠰⠁⠀⢀⠤⠳⠠⠂⠈⠓⠁
⠀⡐⠂⠀⠀⠀⠔⠀⠀⢄⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⣁⡀⠀⢪⠀⡠⠄⢠⣄⠀⠁⠀⠠⡄⢢⡤⢶⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠢⢄⣀⡠⠽⠀⠀⠄⠄⠀⠒⠐⠂⠉⠁⢀⠀⠀⠉⡀⠈⠻⢿⠀⡀⠀⠀⠃⣀⣠⣄⡑⢄⣀⠔⠁⢀⡀⠀⠐⠅⣈⠺⠀⠂
⠀⠀⠤⠄⠁⠀⠀⡀⢀⠀⠀⡀⠀⠈⡀⠀⠄⠀⠀⡄⠊⡤⠂⠈⠀⠄⠂⠄⠄⠊⡄⡆⠀⣾⣿⣿⣿⣻⡆⠀⣀⡐⠀⠈⠡⠈⢀⠀⠀⠣
⠀⠑⠀⢁⠀⠀⠠⠇⠐⠗⠀⠄⠀⢠⠐⢄⠀⠀⠀⠤⡀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠋⠁⠀⢿⣯⣿⣿⣿⠇⠀⣌⡁⠐⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠖⠁⡠⠀⠠⠀⠀⠀⠀⠀⠠⡀⠉⠛⠻⠅⠀⢀⠀⠏⠀⠀⠀⠒⠐⣈⠁⠐⢁
⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠀⠄⠈⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠠⠀⢣⠀⠀⣀⡀⠒⠀⠀⠀⡉
⠀⣄⠀⠀⠀⠀⠐⢂⠤⠢⠀⣴⠟⢻⣿⣿⠟⢿⡇⠀⠀⠀⠀⠀⢄⠀⠀⡐⠀⠀⠀⠄⢀⡀⢄⠈⠀⠠⡁⠜⠋⣀⢐⡉⣀⠠⠠⣄⡠⠄⠃
⠀⠂⡍⠀⠀⢀⠜⠁⠐⣃⠰⣟⠀⠎⠀⠀⣄⣨⡿⠀⠀⠀⠈⡀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠠⡲⠙⠈⠀⠀⢰⠀⠀⠀⠀⢈⠆⢠⢃
⢀⢢⠀⠀⠀⠘⠀⠀⠀⢊⠆⠘⠷⠶⠾⠿⠿⠛⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠄⠉⠀⠀⢀⠀⠀⠀⠂⠤⠀⠀⠳⡐⠒⠀⠉⠀⠀⠁
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⡤⠁⠀⠀⡕⠆⢠⡀⡀⠀⠀⠀⠀⠂⠐⠀⠈⠐⠠⠈⠀⠤⡀
⠀⠘⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⡘⠐⠀⠐⠋⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠁⠈⠉⠐⠂⠥⠀⠀⢠⢲⠀⢀⣠⣅⣀
⠀⠸⠰⢀⠄⠩⠀⢀⠒⠒⠆⠀⠈⠀⠓⠄⠂⠀⠀⠀⠁⠈⠀⠄⠀⢀⠀⠠⠀⡀⡀⠀⢁⣠⢶⡄⠀⠂⠀⠊⠀⠀⠀⠈⠁⣰⣿⠛⠛⣿⣧
⠀⠀⡄⠁⠀⠀⠀⠀⡀⠁⣄⠂⠉⡀⠀⠀⠁⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠘⣿⣛⣀⢐⡂⣠⠄⣴⠆⢀⠰⡄⠹⣿⣶⣴⣿⡟
⠀⡀⠔⠀⠀⠀⠀⠎⠀⠀⠀⠀⠱⣠⠂⠀⠀⢀⠀⠀⠀⠈⠀⠀⠐⠀⢠⠆⢀⠀⡀⢀⠀⣿⣿⣞⣸⠇⣹⡆⣹⡇⠈⡁⠱⠀⠈⠹⠋⠉
⠀⠈⠒⠀⠀⠀⠀⠀⢀⡠⠀⡀⠀⢹⠀⣤⣴⡄⠀⠀⠱⠆⡆⡇⠐⠀⡃⠀⠀⠀⠀⠀⠁⠈⠀⠉⠁⠈⡉⠁⠉⠀⠀⢠⠀⠐⠀⡀⠠⠢⢀
⠀⢚⠉⠉⠉⢉⠂⢰⠀⠈⠀⠐⠀⢸⡀⠘⠿⠀⠀⠀⢇⡄⠃⡀⠀⠀⠀⠀⣤⣤⡀⠀⡁⠀⠐⣅⠀⡐⠂⢀⠔⠀⠀⡆⠠⠄⠀⠀⠄⢂⡀
⠀⠀⠀⠠⠀⠀⠑⠀⠀⠔⠂⠀⠀⠀⠣⠀⠀⢀⡀⠰⠮⠇⣠⡇⢤⢀⠀⠀⠙⠟⠀⠀⠀⠀⠀⡀⠁⠀⡈⠁⢀⠀⠀⠡⠀⠀⠀⠀⠐⠈
⠀⢠⡄⢠⡄⢠⡄⡀⢂⠈⣀⠀⠄⠀⠐⠀⠀⠐⠁⠰⠀⠀⠀⠀⢰⢘⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⠠⠌⠀⠔⠀⠀⠀⠀⠈⠆⠀⠀⠁
⠀⠀⢡⡌⢤⠈⠀⠀⠀⠀⢐⠂⠀⠀⢎⢐⠀⠀⠀⠀⠄⢰⡶⠀⠄⠀⠀⠐⠀⢐⠀⣀⡀⡀⠀⠀⠀⠀⢐⢒⠄⠀⠀⠀⠀⢀
⠀⠁⠂⠀⠀⠐⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠊

⠀⠀⠀⠀⠀⠀⢀⢔⠋⠉⠉⠑⢦⡤⠚⠉⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⡏⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣸
⠀⠀⠀⠀⠀⠀⠘⢎⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣣⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠰⡵⠁⠀⠀⠀⠀⠀⡴⡩⠀⠀⠀⠉⢢⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢰⣵⠁⠀⠀⠀⠀⠀⠋⠁⠀⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⢸⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠠⣤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠀⠉⠳⡀⠀⠀⠀⠀⠀⠸⡄⢀⡠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠑⠋⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠳⠋
⠀⠀⠀⠀⠀⠀⡞⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢳⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠹⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠜

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⠋⠉⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⠊⠁⠈⢹⡿⠥⠀⠆⠁⠀⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡆⠀⠈⢀⣏⣀⣀⣠⡻⠗⠂⠤⣐⠄⠰⣆⢴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠛⠉⠉⠉⠁⠀⠀⠀⢅⡊⠐⠄⠈⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠐⢅⠐⡅⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠆⠀⠄⠄⢀⢶⠀⠀⠀⠀⠀⠀⠀⠢⡄⣀⠀⠀⠀⠀⠀⣀⠀⠸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠉⠘⡇⠀⠀⠀⠀⠀⠁⠀⠃⡟⠁⠀⠊⠈⢣⢀⡆⠀⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡳⠀⠀⠀⠀⠀⠀⠘⡾⠁⠀⠀⠀⠀⠈⠀⢠⠀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⢪⢀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡿⠀⠀⠀⠀⠀⠂⣠⠞⡀⠀⠀⢀⡀⢠⡀⠠⠀⠿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠀⠇⠀⠀⢠⣂⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠈⠰⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⢾⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⡀⠀⠌⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⡐⠀⠀⡁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠝
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⡐⠀⠄⠀⠁
⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠀⠆⠄⢀⠀⠠⠀⠀⠠⠀⡀⢰⠀⠁⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⣦⣔⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⣤⣿⣿⣿⡿⠛⢛⣿⣿⣿⣿⡿⠟⢿⣿⣿⣿⣿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣿⣿⣿⣿⣒⣲⠶⠛⠛⣿⠛⢿⣶⠿⠟⠏⠉⠙⠛⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣥⣤⣾⣿⣿⣿⣿⣿⣿⣦⣤⣤⣿⡆⢸⡧⠀⠀⠀⠀⠀⠀⠀⢹⣧⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⡏⠁⠀⠀⠀⠀⣿⣯⡇
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡏⠙⠛⠫⠭⠭⠿⠿⣿⣿⣿⣷⣄⠀⠀⠙⠻⣅
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣧⣿⡄⢸⠋⣹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠰⠶⠾⠿⠛⡻⠁⣿⠀⠀⠀⢾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⣻⣻⣼⣿⠇⠀⠀⠀⢀⣀⠀⠀⠀⠀⢠⠃⠀⣿⡆⠀⠀⠀⠈⢧⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠙⣻⣶⣄⣠⣆⣠⣾⣿⣿⣄⠀⠀⢰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⣿⣾⡿⠉⠉⠛⠻⠷⠤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⢀⠤⠎⢱⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⡣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠈⠂⠤⠐⠀⠀⠀⠀⢀⣀⢰⠚⢦⠳⡀⠐⢇⡠⢄⠀⠀⠀⠀⢀⡠⢚⣆⠀⠀⠀⠀⠀⠀⣀⡠⡞⠉⠉⠑⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠙⢦⠘⡆⠙⢆⠀⡠⠃⠀⠀⠀⢲⡭⠖⠉⠀⣂⠀⠀⠀⢠⠋⠀⠉⠆⢀⣀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠤⡀⠈⠓⢤⡀⢱⠀⠀⠉⣠⡾⠂⠀⠀⢀⣥⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⢠⠛⡟⠐⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢟⠳⡜⢆⠀⠀⠈⠉⢀⢄⠜⢁⠖⡄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⡄⡼⠁⠀⠈⠒⠁
⠀⠀⠀⠀⢸⠉⠳⡀⠀⠘⢦⡑⠋⢰⠀⠀⡀⠀⠑⠁⠀⠙⠤⠔⠀⠀⠀⠀⠀⠀⠠⠀⠊⢱⠀⠈⡄⠻⠇⠀⡠⠔⠉⠀⠀⠀⠀⠀⠈⠙⠓⠤⡀
⠀⠀⠀⠀⠈⢇⠀⠙⣄⡠⣀⠈⠉⠁⠀⡈⠈⠀⠀⠀⠀⠀⠀⠀⡠⣾⠣⡄⠀⠀⠀⠢⠠⠃⠀⠀⠰⡠⠒⠉⠀⢠⠒⠤⡀⠀⠀⠀⠀⠀⠀⠰⡩⠆
⠀⠀⠀⠀⠀⠀⢳⡀⠈⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣰⠃⡼⢨⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡁⠄⠒⠒⢄⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣆⢐⡏⢰⢃⠇⢠⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠐⠀⢈⡀⠀⠀⠀⣀⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣠⠾⠻⣄⢏⠎⢀⠏⠀⠀⣀⠤⢤⡌⣁⠱⠀⠀⠀⠀⠀⠘⠯⠌⠀⠀⠀⠋⠄⠀⠀⠀⠑⡄
⠀⠀⠀⡀⠔⠑⠀⠀⠀⠀⠀⢀⣀⠔⠄⠀⠀⠀⠠⡟⠋⢁⡠⣖⠝⠫⣀⠌⠀⠀⠀⡇⡖⢀⣊⢀⠸⠀⠀⠀⢀⢀⠀⠀⠀⠀⣄⣀⠀⠀⣠⢄⠀⢀⠇
⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⡄⠀⠀⠀⠀⠈⠲⡽⠊⠁⢀⠤⠋⠀⠀⠀⠀⠑⢔⣤⡀⣯⠃⠀⠈⠉⠀⠈⠣⠄⠠⢄⠓⠈⠀⠀⢃⢈⠠⠊
⠀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠢⠖⠁⠀⠀⠀⢀⣄⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠁⠀⠀⠀⠀⣀⠂⢱
⠀⠀⠀⢀⠠⠞⠁⣠⠟⢢⠀⠀⠀⠀⠀⠀⠀⢠⠴⠉⡆⠀⠀⠀⠀⠀⢀⠔⣣⠞⠑⡀⠀⠀⠀⠻⡄⠀⠀⠀⠀⣀⠢⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⠑⠀⠈
⠀⠀⠀⢇⠀⡨⠒⠁⢀⠄⣥⠀⠀⠀⠀⠀⠀⠀⠁⢒⣁⠀⠀⠀⠀⠀⠈⢏⠁⠀⢎⡇⠀⠀⠀⠈⣭⠀⠀⠀⠈⠢⠠⠃⠀⠀⠀⠀⠀⠠⠆⠀⠀⠈⢆
⠀⠀⠀⠀⠫⡀⠀⠀⠸⢄⠜⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠑⡄⠀⠀⠀⠀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠈⠢⠀⠀⢈
⠀⠀⠀⠀⡠⠺⡄⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⡠⠊⠉⠓⠾⠀⠀⠀⠇⠀⢸⡇
⠀⠀⠀⠀⠑⠔⠁⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣆⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⢤⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠉⢀⠆⠀⠰⠉⠉⠢⠀⢀⠖⣉⠙⡄⠀⠈⠢⡀⠀⠀⠀⠀⢸⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠠⣄⡆⠆⠀⠀⡀⠀⠀⠀⠀⠈⠁⠉⠉⠩⠱⡀⢀⠀⡀⠀⠈⠂⠊⠀⠀⠰⡜⢄⠁⣥⡄⣀⣔⠔⠁⠀⠀⠀⠀⠑⠂⠀⠤⠃
⠀⠀⠀⠠⠀⠀⢠⢂⠉⡛⢸⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠲⠷⢿⣿⣛⣓⣲
⠀⠀⠀⠀⠀⡠⠂⠎⡰⢁⠌⡰⠉⠑⠀⠀⠀⠀⠀⡠⠚⠻⡌⠳⡀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠒⠈⠉⢹⣽⠁⠀⢘⡀⠀⠀⣀⣀⠤⠤⢴⡄
⠀⠀⠀⢠⡔⢀⠊⠜⢠⠊⡔⠀⠀⠀⠀⠀⠀⢀⣎⠀⠀⠀⠙⢦⡼⠂⠀⠀⢀⠎⠀⠀⠀⠀⠑⠀⠀⢸⡿⠀⠀⠀⡇⠀⠀⠷⠒⠚⠋⠉⢁⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⡘⠀⢛⠮⣠⢁⠜⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⢀⠔⠁⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠘⠄⠐⠚⠛⠋⠉⠉⠀⠀⠀⢸⣀⠀⠀⠀⠸⣒⡄⠀⠀⠠⠀⠴⠃
⠘⠀⠀⠀⠀⠸⠀⠏⠈⠁⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⢰⠓⡆⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠃
⠀⠀⠠⡆⠶⠲⠒⠇⠗⠀⠀⠀⠐⣍⠁⢨⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⣄⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠆
⠀⠀⠀⠐⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠄⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣾⡿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣿⣿⣷⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣤⡀⠀⠙⠛⠋⢁⣤⣶⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣤⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣤⣶⣶⣶⣦⣀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡋⢉⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿⡉⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡟⠉⣹⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣏⠉⢻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⠿⠁⠀⣠⡀⠀⠀⠀⠀⢀⣄⠀⠈⠻⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠐⠺⠖⠀⠀⠒⠷⠂⠀⠀⠉⠙⠛⣿⣷⠀⠐⣿⡇⠀⠀⠀⠀⢸⣿⠂⠀⣾⣿⠛⠋⠉⠀⠀⠐⠾⠒⠀⠀⠲⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧
⢀⢿⢀⡔⣶⡄⣶⣴⡄⠀⠀⠀⠠⠾⣿⣶⢆⣏⣹⣷⢦⣴⣞⣠⠀⠀⠀⣯⡄⣠⣄⡤⡄⢠⣀⢀⣿⡁
⠀⠸⠞⠯⠏⠑⠋⠻⠴⠃⠀⠀⠀⣼⠟⠛⠉⠉⠛⠶⣬⡿⠟⠃⠀⠀⠘⠁⠷⠿⠾⠤⠧⠻⣧⠾⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡂⠀⠀⠀⠀⠀⠀⣀⠀⣤⡄
⠀⣰⠒⠒⢤⠞⠉⢢⠔⠪⠗⠂⠀⠀⢶⡦⠹⠟⠀⠙⠁⠀⠀⠀⠀⠀⠀⠠⣄⡀⣠⣤⡀⣠⣤⡀⢀⡤
⠀⠘⣄⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⠄⢀⣀⡀⢀⠀⠀⠀⠤⠄⠻⣿⣿⣿⣿⠇⠤⠤
⣀⡤⠞⢫⡀⣠⠎⠀⠀⢀⣄⡀⢀⣤⡀⠀⠀⢤⡂⢙⣦⠸⡤⠇⠊⠔⠀⠀⠠⠔⠂⠙⢿⠟⠁⠰⠦
⠉⠁⠀⠀⠙⠁⠀⠀⠀⣇⣶⣌⣡⡦⢸⠀⠀⢁⠄⢀⢀⣀⣦⢠⡶⠁
⠀⣠⣤⡀⣠⣤⡀⠀⠀⠈⠣⡉⢟⡴⠃⠀⠀⠻⠴⠺⠾⠁⠷⠚⠛⠁⠀⠀⠐⡶⠀⠀⠀⠀⢀⡤⣀
⠀⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀⡤⠖⢤⠀⠀⢠⡄⠀⣴⣋⣀⣀⣑⣢
⠀⠀⠙⢿⡿⠃⠀⠀⢠⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣼⠶⢄⠈⠀⠀⡸⠁⠀⠈⠀⠈⠀⢠⣦⣶⠄
⠀⡀⠀⠀⠀⠀⠀⠀⡸⡖⢺⡀⢠⢠⢶⣀⠀⠀⠀⠘⣄⠀⢀⡎⠀⣠⠞⠁⠀⢰⠧⠀⠀⣀⣀⣙⣃⣀⣸
⢀⡧⠄⡴⣦⣏⢙⣼⡧⠧⠾⠙⠋⠉⠀⠀⡀⠀⠀⠀⠈⠳⠋⠘⠖⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⡄
⠀⠳⠔⠓⠃⣨⠿⡇⣴⠀⠀⡀⣀⢠⡀⡾⣧⠿⠶⠀⠀⠀⠀⠀⣠⣠⢠⠦⡠⢶⣠⠀⠀⠀⠀⣤⠀⠛
⠀⠀⠀⠀⠀⠓⠴⠁⢻⣵⡿⢧⠿⠏⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢽⠘⠚⣁⡈⠛⠀⡴⠒⠒⢄⡠⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⢤⢀⠤⢶⠀⣀⡀⠘⢧⣸⢠⣄⡉⣤⡄⠀⠱⡄⠄⢠⠀⠉⠄
⠠⣖⠂⣠⣤⡀⣠⣤⡀⢒⡲⠀⠀⠀⠀⠑⠴⠁⠑⠊⠸⣩⠃⠀⠀⠀⠘⠉⠁⠛⠂⠀⠀⠘⢆⠰⠂⣡⠞
⢾⣉⡀⢿⣿⣿⣿⣿⠇⣈⣙⠆⠀⠀⠀⢰⢖⠒⠒⠒⡶⡆⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⡈⠳⠞⠁
⠀⠸⠥⠤⠙⢿⡟⠡⠤⠽⠀⠀⠀⠀⠀⢸⣠⠿⣿⠯⡀⡇⠀⠀⠀⠀⠀⡿⢠⣖⣶⡄⢘⣿⣥
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣒⣒⣒⣛⣃⣀⣀⣀⣀⣈⣣⣞⣤⣃⣳⣞⣙⣖⣃⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠰⣶⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣶⣶
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⢙⡿⠿⢿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠈⠙⠻⠿⢿⡿⠿⢿⠋⠁
⠀⠀⠀⠀⠀⠀⠐⢯⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠻⢦⣤⡾⠛⠿⣷⡀⠀⠀⠀⢳⡀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⣤⡙⠀⠀⠀⣿⠃⠀⠀⠀⢠⠿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣀⣀⠀⠀⠈⠻⣦⠀⢹⠁⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠛⠛⢦⡾⠋⠙⢿⣧⠀⠀⠀⠉⠳⣤⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢠⣦⠁⠀⠀⢸⡟⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠇⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣿⣇⣾⡇⠀⣠⣄⣠⣤⠀⢸⣿⣴⣿⡇⠰⣿⣷⣴⣿⠿
⠀⠀⢰⣿⣦⡀⣼⣿⡇⠀⠀⠀⢿⣿⣿⠇⠀⠻⢿⣿⠟⠀⠀⢿⣿⡿⠁⣀⣀⠉⢉⣥⡀
⠀⠀⠘⢿⣿⣿⣿⣿⠃⠀⠀⠀⠘⣿⡿⠀⢠⣀⡄⠀⠀⠀⠀⠈⠻⠃⠀⠹⢿⣷⣿⠿⠃⠀⠀⠈
⠀⠀⠀⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⠘⠁⠀⠈⠻⠁
⠀⣠⢄⣀⢤⡀
⠀⠹⣄⢋⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⠉⠀⢠⢞⡷⣆⠀⡠⢤⣄⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⠉⢳⡴⠉⣷⠀⣴⢦⡴⢦⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢸⣋⠞⣹⣞⡵⢁⣼⠀⠀⣇⠈⠽⠶⠋⠉⡇⠘⣆⠘⠁⢠⠏⠀⠘⠢⡤⠋
⠀⠀⠀⠀⠀⠀⢳⡎⡠⢋⡴⣣⠇⠀⠀⠈⠓⢤⣀⡤⠞⠁⠀⠈⢦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢵⣋⠴⠃⢀⡄⣄⠀⣀⡀⠀⠀⢀⣀⡀⢀⣤⣄⠀⠠⣿⣦⣾⣷
⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠨⣿⣿⣾⣿⣿⠀⠀⢺⣿⣿⣾⣿⣿⡇⠀⠹⣿⣿⠃
⠀⠀⡎⠉⠑⣄⡴⠉⠀⡇⠀⠀⠀⢹⣿⢿⣟⠇⠀⠀⠈⠻⣿⣿⣿⡟⠀⠀⠀⠉⠁⢠⠤⢄⡠⠒⠢⡀
⠀⠀⢣⡀⠀⠈⡀⠀⢠⠇⠀⠀⠀⠀⠻⠷⠉⢀⠀⠀⠀⠀⠈⠙⠋⠀⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠙⢦⣈⠁⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠈⠀⡄⠀⠀⠀⢀⠀⢁⠀⠀⠀⠘⢆⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠄⠀⠀⡠⠀⠀⠀⠀⠑⠠⠈⠀⠀⠀⠀⠉⠒⠊
⠀⠀⣠⣤⣄⠀⣠⣶⣄⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠈⠈⠀⢀⣀⡀⢀⣤⡀⠀⠀⢠⣤⡀⢀⣤⣄
⠀⠀⢿⣿⣿⣶⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣦⣠⣾⡆⠀⠸⣿⣿⣾⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠈⢯⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠈⠻⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⡄⠀⠀⢀⣾⠻⣧⡀⠀⠀⣠⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢈⣿⠀⠀⢸⣇⣀⣽⠇⠀⠠⣿⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⢀⣉⣛⣉⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣧⠀⠀⢸⣿⠉⣿⠀⠀⠀⣿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣯⣀⣠⣼⣿⠀⣿⣤⣄⣀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⢿⣇⣸⣿⠉⠉⠹⣿⣤⣿⠉⠉⠉⣿⣄⣸⡟⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣌⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣡⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣾⣯⠉⠛⠛⢻⣿⠛⠻⠿⠟⢻⣿⡟⠛⠛⢉⣿⣧⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠙⠷⣦⣴⠟⠻⣷⣤⣀⣤⡾⠛⠷⣦⣴⠾⠃⠈⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⢻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣀⡈⠉⠛⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠛⠉⣁⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡟⠛⠿⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠟⠛⢻⣯⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠾⠛⣷⡀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⣸⣿⣄⠀⠀⠀⢠⣾⠻⢷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠻⠷⠶⠾⠋⠈⠻⣶⣤⣤⣤⡾⠟⠈⠛⠷⠶⠾⠛⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⡀⠀⡀⠀⠀⣀⡀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⢸⣧⣼⠀⣼⣷⠀⣿⢹⡆⣿⢹⡎⢷⣴⠏⠀⠀⣿⣽⡇⣿⢸⡏⣷⠉⣿⠋⢸⣧⣼⡇⡟⢻⡆⣸⣷⡙⣧⡾⠁
⠀⠀⠸⠇⠹⠰⠟⠛⠇⠿⠋⠁⠿⠋⠁⠀⠿⠀⠀⠀⠿⠾⠇⠿⠸⠟⠿⠀⠿⠀⠸⠇⠹⠃⠷⠾⠳⠟⠛⠧⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠋⠹⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⡳⣞⡵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠖⢿⣤⣉⣉⣤⣿⠲⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠉⣀⣤⣀⠀⠀⣸⢧⡈⠓⠤⣏⠀⠀⣀⣤⣀⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠐⡇⠀⠈⠉⠉⠹⣆⠉⠲⢤⡏⠉⠉⠁⠀⢸⡂⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡖⠒⠋⠀⠀⠀⠀⠀⠀⢯⣑⣂⡼⠀⠀⠀⠀⠀⠀⠙⠒⢲⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠉⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏⠙⢦⣄⠀⠀⠈⠧⠤⠴⠒⠒⢦⠀⠀⠀⠀⡴⠒⠒⠦⠤⠼⠁⠀⠀⣠⡴⠋⢸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣇⠀⠀⠈⠙⠲⠦⣤⣀⣀⠀⠀⠈⠑⠶⠖⠋⠁⠀⠀⣀⣀⣤⠴⠖⠋⠁⠀⠀⣸⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⡟⠓⠚⠙⣆⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⣰⠛⠓⠚⢻⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢿⡀⠀⠀⠘⣆⢀⡴⠛⢦⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⡴⠛⢦⡀⣰⠃⠀⠀⢀⡿⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⢷⣄⠀⠀⠈⠉⠁⠀⠘⢧⣀⣠⡞⠁⠀⢳⣄⣀⡼⠃⠀⠈⠉⠁⠀⠀⣠⡾⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣆⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⣰⠟⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠤⠤⢤⣤⠤⠤⠶⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣼⢦⣀⣀⣤⣄⠀⠀⠀⠉⠉⠛⠒⠶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡤⠴⠶⠒⠛⠉⠉⠀⠀⠀⣠⣤⣀⣀⡴⣇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⠉⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠈⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠘⣧⠀⠀⣰⠞⠛⣦⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⣴⠛⠳⣆⠀⠀⡼⠃⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠈⠓⠞⠃⠀⠀⠸⣆⠀⠀⠀⢠⡟⠀⠀⢻⡄⠀⠀⠀⣸⠇⠀⠀⠘⠳⠚⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠋⠀⠀⠀⠀⠙⠶⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠴⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⠤⠤⠤⡀⢠⠔⠒⠒⢤⡀⡠⠤⠠⢤⡀⠀⣀⣀⣀
⠀⠀⠀⠀⣀⡤⢄⡀⣰⣋⣀⡤⠽⠖⠓⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠓⠾⠥⢄⣈⣱⡄⣀⠤⢄⡀
⠀⠀⠀⡞⠁⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢄⠀⠘⡆
⠀⠀⠀⣧⠒⠋⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠓⢦⡇
⠀⠀⠀⡇⠀⠀⠀⠀⣷⠊⠉⠉⠑⣄⣠⠔⠒⠦⡀⠀⣠⠤⢤⡀⢀⡤⠖⠒⢤⣀⡔⠉⠉⠉⢲⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠑⢄⣀⣀⠴⣇⠀⠀⠀⠀⣸⠁⠀⠀⠀⢸⡏⠀⠀⠀⠈⡟⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⡷⢄⣀⣀⠔⠁
⠀⠀⠀⠀⠐⡅⠀⠀⠈⠢⠤⠤⠖⠙⢆⡀⠀⣀⡼⢧⠀⠀⠀⣠⠿⣄⠀⠀⣠⠞⠑⠤⠤⠴⠊⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⠳⡄⠀⠀⠀⠉⠉⠁⠀⠀⠉⢒⠊⠁⠀⠀⠉⠉⠀⠀⠀⢀⡴⠳⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡗⠒⠊⠁⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠳⣄⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠙⠒⠒⡇
⠀⠀⠀⠀⠀⡟⠢⢄⣀⠀⠀⠀⠀⠉⠲⠤⠤⠤⠖⠉⠀⠀⠀⠈⠑⠦⠤⠤⠴⠊⠀⠀⠀⠀⢀⣀⠤⠚⡇
⠀⠀⠀⠀⣠⡏⠒⠤⣈⡉⠓⠒⠦⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠖⠒⠋⣉⡠⠔⠊⣧⡀
⠀⠀⠀⢰⠁⡇⠀⠀⠀⠉⠉⠒⠒⠦⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠤⠖⠒⠊⠉⠁⠀⠀⠀⡇⢹
⠀⠀⠀⠈⠢⣈⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⢊⡡⠊
⠀⠀⠀⠀⠀⠈⠓⠦⣤⣈⣉⠙⠒⠒⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠚⢉⣉⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠷⣖⣒⣶⠤⠤⠤⠤⠤⠤⠤⠤⠤⣴⣖⣒⡶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡭⠭⢿⠉⠉⠉⢹⠯⠭⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠶⠶⠶⠿⠿⠟⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠦⡄⠀⠀⠀⠀⠀⠀⠙⠲⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⢀⡟⠀⠀⠀⠀⠘⠄⣀⣴⠇⠀⠀⠀⠀⠠⡊⠉⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⢠⢥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⣧⠀⠀⢃⢾⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠄⢺⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡟⠀⠀⢣⣾⠟⠿⠶⣶⡀
⠀⠀⠀⠀⢀⡴⠛⠁⠀⠈⠠⣒⣦⣆⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠢⠀⠐⠂⠉⠀⠀⠀⠀⠀⢁⠤⠖⠛⠁⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠍⠻⠿⡁⡀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠄⠀⠐⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⢸⡧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠊⠀⡅
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠒⠂⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣼
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠤⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠰⡄⡐⠘⡄⠀⠸⣿
⠀⠀⠀⣇⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⢸
⠀⠀⠀⢹⣶⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠊⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡤⠋
⠀⠀⠀⠈⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡷⣼
⠀⠀⠀⠀⡟⠔⠀⠀⠂⢦⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⣰⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠀⠐⠀⢀⣀⡀⠄⠂⠐⢄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢩⡟
⠀⠀⠀⠀⠸⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠤⠔⠂⠁⠀⠀⠀⠀⠀⠁⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⡏⠛⠐
⠁⠀⠀⠀⠀⠀⠺⠗⣣⠘⢸⣶⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡴⠞⠉
⠀⠀⠀⠀⠰⠀⠀⠀⠈⠛⠢⢄⡁⠙⠛⠳⠶⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠈⠉⠒⠲⠤⣄⠀⠈⠈⠉⠉⠑⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⠤⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣈⣄⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄⢸⢚⡲⠄⡄⣄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠙⡟⠂⢠⣀⢂⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣤⣀⣀⣀⣀⣈⣀⣀⣭⡶
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠉⠉⢉⡉⠉⠉⠉⠁⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠁⠠⠤⠀⠀⠀⠤⠄⠐⣀⠀⠀⠂⠐⠀⠀⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⢀⢀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠈⠁⠀⣀⠀⠀⠄⠀⠐⢄⢖⡠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣧⣴⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⣁⣀⣀⣤⣤⠶⠞⠛⡃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⣤⣤⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⡀⠄⢂⠀⠡⠂⠄⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠍⠀⠀⠈⢵⡄⠈⠐⠢⢦⣶⣄⣀⣀⢀⡀⠀⠀⣀⢀⣀⠀⣤⠴⣖⡞⢀⠀⠀⠀⠀⠘⣡⠀⠀⠑
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠂⠀⠱⠀⣀⣋⠀⢠⢙⠃⢠⠀⢼⠉⠷⢶⠀⡀⠠⢐⠃⠀⠊⠙⠂⢠⠀⠐⠤⠌⠀⢀⠀⣀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡷⠧⠉⠒⠄⠁⣄⡀⠂⠈⠀⠠⠀⠀⠂⠀⠙⠀⠁⠀⠈⠀⠀⠀⠁⠀⡀⠀⠀⠂⡙⠃⠢⠐⢉⡂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣇⡀⠀⠀⢀⠐⠒⠄⠈⠁⢀⠐⡀⢠⠀⠀⠀⠐⠀⠐⠀⠀⠀⢤⠦⠀⡄⠀⠀⠀⢐⣤⣶⣶⣿⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⠛⠻⣶⣦⣤⣤⣄⡂⠀⠀⠀⠀⡉⠀⠑⠂⠀⠀⠀⢈⠀⠀⠀⣀⣠⣤⣦⣴⣶⣿⡿⠛⠋⠁⡐
⡇⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠑⠀⢬⡀⠀⠍⠉⠛⠻⠿⢿⠿⠿⢶⣶⣶⣶⣶⣶⣿⣿⡿⠿⡿⠟⠛⠛⠉⠉⢁⠀⢈⠀⠄⠊⠀⠐⢄
⡇⠀⠀⠀⠀⠀⠀⠈⢻⡀⣀⠀⠀⠀⠀⠉⠒⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⣈⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠤⠾
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⣤⡤⣆⠀⢀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠒⠃⠀⠀⠒⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⢠⡖⠟
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⢧⡤⢤⣀⣠⡀⠀⣀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⢀⣀⢀⡦⣄⡞⠲⠾⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠒⠈⠉⠉⢛⠋⠉⠷⢞⢹⡶⠎⠳⢶⠉⢲⠋⡙⠛⢋⠛⠁⠉⠠⠤⠤⠤⠤⠀⣀
⡇⠀⣀⠠⠀⠀⠒⠈⠉⠉⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⣀⠄⠂⠘⢀⠀⢀⡘⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⢠⢀
⡇⠁⠀⠀⡤⠀⠀⠀⠀⠤⠀⠀⠀⠤⡦⠀⠀⠀⠀⢠⠄⠰⡀⠀⠀⠩⠄⡆⠠⠣⠈⡃⠀⠐⠀⡠⠀⠀⣀⠐⡄⠀⠶⣀⠀⣀⢀⠀⢀⡀⢀⠀⠀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡂⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠂⠀⠤⠬⢀⠤⠄⠀⠀⠐⠁⠀⠀⢀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠐⣨⠂⠀⠘⣈⠂⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠶⠀⠘⠠⠒⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠑
⠏⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⡔⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣧⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⠋⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣅⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⡾⠛⠉⠭⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠩⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠶⠶⠶⠶⠶⠶⠷⠶⢤⣤⣤⣀
⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣀⣀⡀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣧⡀
⠀⠀⠀⠀⠘⣧⠀⠀⠀⣠⡞⠉⠉⠻⣦⡀⢀⣴⠞⠛⠛⢶⡀⠀⠀⠐⠀⣠⡶⠛⠋⠙⠳⣦⡀⠀⠀⠠⠀⣠⣤⢤⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⢷⠶⠟⠉⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠙⠶⣤⠴⠞⠉⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠛⠉⠀⠀⠈⠻⢦⣤⡾⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣸⡀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⠶⠛⠛⠛⠉⠉⠉⠉⠉⡉⡉⠛⠛⠛⠓⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣀
⠀⢸⡇⠠⠄⠀⠀⠀⠀⣀⣀⣀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉⢷⡀
⠀⠘⢷⣀⠀⢀⣀⣴⠟⠉⠉⠉⠻⢦⣄⣀⣤⡴⠖⠛⠲⢶⣄⡀⠀⠀⣀⣠⣤⠤⢤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠖⢀⣀⣀⣀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⢹⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⠀⠈⠙⠷⣤⣤⣤⣤⠶⠞⠋⠉⠀⠈⠙⠳⠶⣶⠞⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣴⠞⠉⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⢦
⣼⣿⠀⠀⠀⠙⠷⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠛⠁⠀⢸
⣿⠙⠷⣤⣀⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠳⠶⠶⠶⠶⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠞⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⣠⣾
⠘⠷⣤⣀⠈⠙⠛⠶⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠶⢛⣩⠞
⠀⠀⠀⠙⠳⠶⣤⣄⣀⡀⠀⠈⠉⠉⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⢤⣤⠤⠦⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠋⢉⣉⣡⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠚⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠙⢄⣠⠴⠚⢉⡀⠙⠒⢦⣀⡠⠞⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⣄⡞⢁⣤⣶⣄⠀⠙⣦⣾⣿⣿⣷⣆⡜⠁⣠⣤⡀⠈⠳⣀⣠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢁⡰⠃⠈⣵⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣦⠞⠉⢀⡴⠈⠳⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⢋⡱⣄⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⠉⢀⠔⠋⢠⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠒⢋⡔⣈⢦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠏⡀⢠⠎⢸⠄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⠤⠖⡉⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠙⠲⢤⣁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠈⡞⠁⠤⠚⢡⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠁⠀⡇⢲⠀⠈⣷⠛⡇
⠀⠀⠀⠀⠀⠀⠀⡿⡀⣇⠀⣀⡤⠊⠀⢀⠜⠋⡰⠉⠻⢿⡿⠿⣿⡿⠛⢿⣿⢿⡿⣿⠟⠋⠰⢈⠙⢧⠀⠊⢀⡜⠀⠀⡼⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠘⢾⡦⣄⣀⢀⣰⠃⢀⡴⠃⡟⠀⠀⢻⠞⠁⢠⠏⠀⠙⢦⡾⠁⢀⡰⠃⢸⠀⠀⣇⣀⠀⣀⡠⠞⣡⠋⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⢬⣁⠹⣄⠀⢀⠔⠁⠀⢀⣾⠐⠚⠁⠠⠃⠀⠀⣧⡀⠈⠀⠰⠃⠀⣠⠏⠉⠉⢁⡠⠞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠠⣄⡀⠀⠀⠈⠑⠺⠷⣶⣶⠖⠒⠋⠘⠦⣀⣀⣀⣀⡤⠞⠀⠉⠒⠲⠶⠖⠚⢁⣠⠤⠒⠉⠀⢀⡠⠄⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣄⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠶⠶⠶⠶⠶⠖⠒⠒⠚⠋⠉⠁⢀⡴⠒⠒⢀⣞⢀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠈⠙⠒⠒⠒⣞⠉⠉⠓⠦⡀⢀⣀⣠⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠖⠒⠂⠀⣮⣀⣀⡠⠞⠀⠉⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠈⠙⠲⠤⠤⠖⠻⣄⡀⠀⠉⢓⣠⠖⠉⠉⠉⠃⣀⠜⠡⠤⠤⠴⠊⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠓⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⢀⣀⢛⡦⢄⠀⣀⣀⣀⡳⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⠚⠛⢇⣀⣭⠙⠤⡶⠆⠸⢉⣵⡐⠲⠗⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢣⠖⣂⠄⠀⢁⡀⠀⡀⢀⠀⡀⣤⠄⡤⠤⣢⡎⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠤⢬⡕⣴⣆⡿⠁⢈⢰⠴⡇⣉⣣⣇⣰⠀⡷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠶⡒⣄⡀⣫⠈⢉⢁⢸⣆⣀⣏⣉⣉⣀⣤⣭⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣁⠒⠤⠤⣌⣉⣈⣂⠉⡙⠉⠉⠈⠉⣉⣉⣠⣥⠴⠞⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣄⣉⡸⣂⠤⣠⡄⢤⣈⡩⣉⣉⣉⢉⣉⣠⢁⠄⢰⡆⠚⢠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⡌⢒⠛⠛⠲⠨⢤⣼⣤⣙⣁⣼⣀⣹⣌⣧⣭⣭⣲⠟⢟⢛⣹
⠀⠀⠀⠀⠀⠀⣀⣠⣸⠧⣄⠉⠃⠙⠓⠖⠶⢲⡤⡬⣀⣩⣭⣥⣤⣤⣽⡴⠶⠶⢛⢋⣩⣀
⠀⠠⡀⠒⠐⢅⠀⠀⠙⠲⢄⣁⠘⠙⠼⠶⠤⢤⣤⣨⣄⣄⡤⣤⣤⣤⣔⣦⢴⠶⠟⣋⣹⠏⠉⢓⠅⣀⠂⠄
⠀⠀⠀⠁⠐⠀⠠⠄⠀⠀⠀⠀⠉⠀⠂⠠⠄⠤⠤⠤⠤⠤⠀⠠⠤⠤⠤⠶⠒⠒⠉⠁⠀⠀⠀⠁⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⡀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠛⠉⢹⠁⠀⠀⠀⡏⠉⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠣⣄⣠⠜⠁⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡠⢄⠀⠀⡠⠤⠀⢀⡀⢀⡀⠀⠀⢀⠀⣠⠲⡄⡠⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣠⠇⢸⠀⢰⠃⠀⠒⠋⡇⡏⠘⠀⠀⡏⠉⠁⠀⠧⠇⢸⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠸⢤⠼⠀⠀⠀⢠⠃⢹⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠘⣤⠎⠀⠳⠴⠃⠀⠀⠀⠀⠀⠀⡏⠉⠓⠦⣀
⠀⠀⠀⠀⠀⢀⣞⠁⢰⠉⡳⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⢞⠉⡦⠈⡳⡀
⠀⠀⠀⠀⠀⠸⡌⠂⠀⠀⠀⠀⠀⠀⠀⠉⠩⡙⠓⠒⠒⠒⠒⠒⠒⠒⢋⠍⠉⠀⠀⠀⠀⠀⠈⡠⠚⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⡀⢢⠀⠀⠀⡀⠀⠘⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢠⠇⡜⠁⢸⠀⠀⠀⠈⠋⠀⢱⠀⠀⠀⠀⢰⠙⢦⡀⠀⠀⢀⠀⠀⠀⣼⠵⠤⣄⠀⣴⡸⡀
⠀⠀⠀⠀⠀⠈⢲⠃⠀⠸⡄⢀⠆⠀⠀⠀⣼⠀⠀⢀⡀⢸⠀⠀⡇⠀⠰⠛⣆⠀⢀⡇⠀⠀⠘⠚⢹⠃⢣
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠑⠊⠀⠀⠀⠀⢹⠀⠀⣼⠐⠁⠀⠀⢧⣠⠇⠀⣿⠀⠈⡇⠀⠀⠀⠀⠸⣆⡼
⠀⠀⠀⡠⠤⡴⢺⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠁⠀⠀⠀⠀⢈⡗⢦⠤⣄
⢀⣠⠞⠧⠴⠃⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠘⠦⠼⠳⣄
⡏⢯⠀⠀⠀⠀⠀⠀⣙⣒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣒⣋⠀⠀⠀⠀⠀⠀⡽
⠘⢆⡓⢤⣀⠀⠀⠐⢅⡨⠂⠀⠈⠉⠉⠓⠒⢒⣶⠶⠶⠶⠶⠶⠶⣶⡒⠒⠚⠋⠉⠁⠀⠐⢅⡨⠂⠀⠀⣀⡤⢚⡱
⠀⠀⠙⠲⢬⣙⠓⠶⠤⣤⣀⣀⡀⠀⠀⠀⠀⢧⣠⠇⠀⠀⠀⠀⠸⣤⡼⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠒⣋⡥⠖⠋
⠀⠀⠀⠀⠀⠈⠉⠒⠶⠤⢤⣉⣉⡉⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⢉⣉⣉⡤⠤⠖⠚⠋⠁

⠀⢐⡀⠀⣂⠀⠀⠀⠄⠀⠀⠀⢜⠀⠀⠆⠀⠀⠀⢤⢀⠠⡀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠠⠄⠄⣠⢀⠄⡀
⠠⠈⠂⠐⣈⠂⠀⡄⠂⠄⠀⠁⠉⠀⠂⡥⠆⠑⣈⢰⣇⡠⠋⠢⡀⣿⣰⣧⣝⣀⣇⣷⣅⣿⢀⠔⠀⠀⡤⠀⠠⡄⠀⢠⡔
⠀⡀⢀⠀⠄⠄⡀⢔⢊⠌⠀⡨⣀⠀⠀⠰⠀⠰⠢⢓⠀⢳⡄⠐⠀⠙⠛⠛⢻⡿⢛⡛⠛⠁⢨⠀⡳⠆⠀⣼⡄⢡⣶⡄⠁⢳⡇
⠀⠁⠁⠂⠀⠸⠅⠃⠀⡂⢀⠦⢀⠀⠁⢉⠀⠀⠾⠂⢠⠂⠀⡠⠊⠖⠀⡀⠈⠀⢠⡄⠀⠈⠀⠁⠠⠘⠠⣀⠔⠢⣀⠄⠁⠤
⠀⡠⢂⠅⠰⢈⢐⠀⡨⠇⣀⠪⠂⠁⢀⠰⢁⠀⠀⠠⠂⢰⡁⠄⠀⠀⠀⢧⢀⠀⡇⢩⠀⡞⢰
⠠⠠⠠⢐⠀⠂⠂⠂⠰⠃⠀⠄⠡⠂⠂⠀⠠⠃⠠⠄⠠⠊⠧⠤⠤⠀⠂⠈⠄⠀⠀⢸⠀⠇⢸⠀⡀⡤⠀⠠⡢⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡀⠐⢖⠂⠡⠀⠁⠀⠀⠔⠀⠈⠀⠀⠈⣹⡄⠀⠀⠐⠤⠘⠀⡄⢼⠀⠀⠈⢀⠀⠀⠀⢀⠅⠘⢂
⢀⠄⠀⢠⢀⠀⠀⣉⣂⠐⠻⠲⡶⠲⡶⠆⠀⠰⢆⠂⢒⠶⡀⠁⡁⠈⠁⡀⠀⡐⠈⠀⠁⢀⠀⠀⠀⣄⠀⢠⠀⠀⠌⠈⡀
⢀⣤⣤⣄⡏⢄⢾⣿⣿⠀⠀⠀⠹⠜⡀⠈⠤⠂⠈⠳⠎⠀⠈⠒⠀⠀⠂⠂⠀⠀⠀⠀⠀⢀⠀⠀⣄⠈⠘⠈⠑⠠⠆⠀⠀⠠⠘
⠀⢿⣿⡟⠀⠀⠈⠋⠙⢆⠀⠀⠀⢀⢆⠀⠀⠠⠀⢀⠀⠲⠲⠒⠒⠒⠖⡤⢄⠀⠀⠀⠀⠞⠉⠀⠐⠄⠀⠀⠆⠀⠀⠀⣀⡀
⠀⠀⢖⠀⠀⠀⡠⠒⡀⠘⠣⢀⠠⠼⠸⠄⢀⠀⠀⡞⠀⢀⠀⢀⠐⠀⡆⠀⢘⠆⠘⠋⠁⠀⠀⠀⡀⠈⢆⠈⠀⠀⠃⡀⠉
⠀⠂⠛⠑⠀⠀⠅⠀⠀⢂⠀⠔⡀⠀⠀⠀⢰⡀⠀⡁⢈⠁⠄⠁⠈⠀⠁⠀⠀⠀⠀⠀⢢⡀⠀⠀⡀⡀⠀⠁⠀⠈⠂⠁⠀⠐
⠀⠀⠀⢰⡄⠸⡀⠀⠀⡘⢸⠠⠄⣁⠀⡀⠡⢸⠀⢃⢄⠀⠐⠐⠢⠀⠠⠄⢀⠇⠀⠀⠀⠀⠀⠤⠀⠸⠄⠀⠀⡀⠈⠁⠈⠂
⠈⡐⢠⠃⠱⡀⢡⠀⢀⠀⡸⣀⠀⠀⠀⠀⢐⠸⠀⠀⠘⠀⠤⠤⠤⠤⠄⠐⠁⠀⠰⠆⢰⣶⠞⠉⠁⠀⠙⢶⣶⠀⠀⠐⠈⠄⠁
⠀⠀⠎⠀⠀⠰⠀⠉⠈⠀⣈⠂⢩⠄⠀⠬⠀⠊⠀⣄⠀⠀⠀⢀⠀⠢⠉⠁⢐⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⢸⠁⢀⠠⠀⠒⢐⠢
⠀⢸⢀⡀⣀⠀⢇⠀⣸⠀⠉⠀⠙⠁⠀⠀⣠⠊⡀⠊⡀⣀⡂⠘⡬⢄⣲⠅⠈⡀⠓⠁⠀⠈⢀⡀⠀⠀⣠⠊⠀⢀⠘⠂⢒⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⢐⠀⠀⡰⠁⠀⠀⢠⡅⠃⠀⠀⠀⠀⠀⡀⢀⠅⠀⠴⠢⠀⣤⣬⣷⣯⣤⣇⠀⠀⠑⠀⠐⢂⠁
⠀⢀⡀⠙⢋⢄⠀⠈⠢⠈⠈⠈⠀⠀⠐⠧⠐⠂⠉⢀⡀⡀⠀⠀⠀⠉⠐⠒⠁⠐⡿⠠⡤⠤⡄⡉⠉⣉⣉⣀⣀⢀⠀⠠⠄⠺⠃
⢀⢮⣈⠻⠧⣔⠢⡄⠐⠠⠀⠀⠀⢀⠆⢀⠀⢠⠞⠁⠀⠰⠞⠉⠁⠀⠀⠀⠂⡀⠀⢠⣀⣀⡃⠀⠀⠀⠀⣰⠀⠀⠀⡀
⠘⠉⠀⠤⠀⠐⠀⠅⠐⠀⠊⠀⠈⢂⣀⡈⠀⠐⠀⠁⠂⢐⠆⠼⠀⠷⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠈⠁⠈⠁⠉⠀⠁
⠈⠢⡀⠀⠀⣀⠤⠀⠚⠒⠀⠀⠂⠀⠙⠀⠀⠃⠒⠀⠀⠌⢸⠀⣇⠀⠍⠀⠀⠀⠘⠄⢱⠀⢉⠀⠀⠎⠂⠰⡰⢢⠚⠁
⠀⡠⠬⠉⠀⠀⢄⠀⢀⢆⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠌⠀⠀⠲⠀⢀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠃⠀⠊⠀⠐⠂⠀⠈
⠀⠀⠀⡖⠲⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣰⡌⢄⡸⠀⠀⡂⢀⠀⢀⠂⡂⠀⠚⠈⠇⢹⠈⠐⠄⠀⠡⠀⢡⠋
⠀⠒⠀⠀⠀⠀⠚⠀⠁⠂⠤⠁⠁⠀⠈⠉⠈⠒⠒⠒⠒⠒⠀⠂⠀⠁⠀⠑⠀⠈⠂⠘⠑⠃⠐⠂⠐⠁⠊⠐⠒⠀⠀⠀⠂⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠘⢲⣄⠴⠶⠄⠠⠀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠴⠀⠁⠀⠄⠈⠀⠀⠐⡮⠃
⠀⠀⠀⠂⢀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠈⢈⣃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠁⠘⠉⣀⠦⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠨⠀⠉⠆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠣⢠⢴⡄⠀⠀⠁
⠀⠀⠀⠑⠆⢂⠠⢄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⡁⠀⢸⢱⠒
⠀⠀⠈⢀⠊⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠓⠚⠀⢍⣀⡀⠺⢠⠀⠂⠔⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⢠⡀⠄⠠⠀⢀⠀⣀⠀⢀⡤⠤⡄⠀⢸⡑⠀⢀⣨⣥⣤⣢⣰⣄⣀⣀⣤⣤⣄⣀⣄⣄
⠀⠀⠀⠀⠑⠀⡀⠀⠈⠁⠶⡲⠢⠈⠀⠉⠓⢸⢜⢦⣆⣦⢋⠍⠐⢈⣇⣁⣠⣁⣤⣭⣈⣥⣴⣦⡙⣿⣷⢿⣃
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠍⠀⠀⠸⠗⠶⣔⠲⠶⠴⠦⠠⢶⣔⣠⠿⠟⠼⠛⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡆⢀⠘⠎⠉⠁⢀⣶⠎⡦⠋⠀⠀⠀⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⣀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠀⠈⠰⠃⣟⡇⢐⠲⠈⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⢀⣶⠖
⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣶
⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠃⠀⠀⠀⣀⣀⣀⣴⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠿⠟⠋⠀⠀⠀⠀⢠⣖
⠀⠀⠀⣈⣿⣁⠀⠀⠰⣤⠉⠀⠰⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠿⠿⠿⣿⣇⠀⠀⠘⠀⣆⣀⠠⠀⣤⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠰⠟⠉⢹⡇⠀⠀⠀⠀⠀⣼⠁⢸⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠉⠃⡈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⢀
⠀⠀⠀⠀⢀⠀⠀⣴⣤⣤⡀⠀⣿⣠⣤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠛⠂⠀⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⣠⣷⣦⣄⡘⢿⠿⢷⠀⣿⣿⣿⠏⡀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⣿⡇⠀⠀⠀⠀⠀⠀⣬⣁⣴⡿⠋⠁⠀⠀⠀⠀⠀⠸⣿⠄⣿
⠀⢠⣴⢛⡛⠛⠛⠁⠀⠀⢀⡀⠉⣶⣤⣶⣷⣤⡀⠙⢿⣧⡀⠀⠀⠿⠀⢸⣦⠀⣴⣦⣼⣃⠀⠀⠀⠀⠀⠀⠛⣙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠛
⠘⣿⣿⣾⡏⢀⠀⠀⠀⠀⠀⠃⠀⠉⠘⠛⠉⠁⠀⠀⠀⠈⠻⠞⢿⡗⠀⠀⠋⣀⣿⣿⠟⠛⠻⣦⠀⠀⠀⠀⠘⣿⡦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰
⠠⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡄⢷⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠛⢿⡗⠀⠀⠀⠿⣿⣆⣰⣜
⠀⠀⠉⠻⠀⠀⠀⠀⠀⠰⣾⣿⡇⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠠⠬⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠙⠃⠀⠀⠶⠂⠀⣠⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⣶⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣾⣿⠟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘
⢸⡁⠀⠀⠁⠀⣀⣠⣤⣤⣀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⠃⠀⠀⣤⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠛⠃⠀⢶⡄⠀⠀⠀⠀⠀⣰⣆
⢸⣷⡀⠀⠀⠀⣽⣿⣿⣗⠀⠀⠀⠀⠸⠛⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠆⠈⠁⠀⠀⠀⠀⠸⣿⣿⡆
⠈⢹⣷⡆⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇
⢀⣾⡁⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒
⢸⣟⢁⣌⣅⠀⠀⠀⠈⠻⢷⣦⢴⣿⣸⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢟⠁⠇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠋⠁
⢈⣉⠉⠻⢿⡇⠀⠀⠀⠀⠀⠀⠘⠋⣩⡄⠀⣀⡠⠘⠉⠀⣹⣿⠿⠿⠗⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⣷⠀⠘⢠⠄⠀⢈⣿⣂⠀⠀⠀⠀⠀⠀⠐
⠸⠿⣿⣦⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⠀⠀⠀⠉⠆⢩⡄⠀⠀⠀⠀⠙⠉⠛⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣿⢻⣧⠀⠀⠀⠀⠠⣤⣄⠀⢾⠁⠀⠀⠀⠀⠈⣥⡀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡇⢰⣶⣶⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡿⢸⡇⠀⠀⠀⠀⠀⠀⢹⣷⣾⠇⠀⠀⠀⠀⠀⣿⣷⡈⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣍⣛⡛⣧⠟⠉⠛⠿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠹
⠠⠀⠀⢀⡄⠀⢀⡀⢀⣀⣀⣀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⠏⠉⠈⠉⠻⣿⡿⠛⠿⠃⠀⠀⠀⠀⢹⣏⣽⡆
⠀⠀⠀⣼⣣⣶⣾⣿⣿⣿⣿⣿⣷⡶⠈⡅⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣿⣠⣤⠀⠀⠀⠀⠀⠀⣁⣀⡴⣶
⠀⠠⢾⡿⠿⠿⠿⠿⡿⠿⠟⠋⠁⠙⠰⠀⠀⠀⠀⠀⠀⠀⢾⢿⠿⠿⠿⢶⡦⡤⠏⠀⠀⠀⠀⠀⠸⠹⡿⣿⠀⠀⠀⠀⠀⠈⠉⠻⣧⢷⠀⠀⠀⠀⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⠀⢀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡎⠀⠇⠀⢀⠔⠉⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⡌⠙⠒⢼⠠⠐⠛⠠⡟⢀⣔⡿⠒⠒⡤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠡⡀⠀⣠⠏⠸⠁⢈⡒⢢⡀⠘⣄⠀⠁⠀⠀⠀⠀⠘⢏⠉⠁⢈⡸⠁⠑⣏⠈⣧⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣣⣱⡯⠣⢴⡆⠙⡤⠸⠊⢙⣶⣿⣷⣶⣄⠀⠈⠀⠀⠸⠶⣈⣁⠴⡄⢴⠁⠈⢦⢠⡯⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢤⣾⠑⢦⢸⠀⠋⢁⡔⠛⣾⡿⣺⣘⠽⢼⡽⣦⣄⢤⡧⢊⡥⢖⠛⠃⠀⠱⠀⠣⡀⣁⠸⣆⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠒⡇⠀⠀⠀⠀⠀⡰⢻⡿⠒⣤⢞⣿⢿⢷⣷⣲⣏⢏⢱⣳⡿⠼⠒⠛⠲⠧⢄⣠⠁⠉⡤⠐⢇⠈⡦⢜⠉⠓⢤
⠀⠀⠀⠀⣠⠊⠁⠐⠀⠱⡀⠀⠀⠀⢠⡀⠀⠀⣼⣯⠮⣗⣏⠿⣻⣟⣿⣻⡾⠋⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠓⡄⠸⠣⣀⡸⠈⠃⠀⠱⡀
⠀⠀⠀⡸⠁⠀⠀⠀⣀⡀⠈⠑⠒⠒⠟⠳⢄⣀⣿⣟⣿⣿⢎⣸⣛⣿⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠛⠶⠚⠁⠀⠀⠀⣀⠀⠇
⠀⠀⠀⡇⠀⠀⠃⠀⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⢿⣻⣮⣾⣿⠿⠃⠸⣏⡒⠄⢒⣒⣒⠦⣄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠪⠤⠷⠀⠀⠀⡄
⠀⠀⠀⡼⣄⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣀⡈⠉⠉⠀⠈⠀⠉⠢⣕⠢⣄⠀⠀⢠⡇⠀⠀⠤⠄⠀⠀⢀⠔⡇
⠀⠀⠀⡇⠈⠳⡌⠀⠄⠀⠠⠤⠀⠀⢀⣀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠙⠲⠭⠿⠟⠁⠀⠀⠀⠀⠀⢠⠃⢀⠇
⠀⠀⠀⡇⠀⠀⠈⢦⡀⣀⢀⡀⠀⠠⠌⢉⡀⡀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠶⠶⠄⠀⠀⠀⡰⠆⠠⠀⠀⠈⠁⣀⠤⠒⠒⠊⠁⣰⢻
⠀⠀⠀⠘⣄⣀⡀⠀⠀⠀⠀⠈⠒⠒⠒⠦⡀⣁⣉⣀⣁⢀⣀⠈⠀⠉⠀⠁⠒⠂⠀⢀⠀⠀⠀⠀⣀⣀⣀⣀⣴⡿⢦⡀⣰⠿⠛⠛⠉⠨⡇
⠀⠀⠀⠀⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠀⠀⠄⠊⠁⠈⠁⠀⠉⠀⠀⢀⡾⠁⠠⠀⡇⢻⡀⠄⢀⠔⠁⣧⣀
⠀⠀⣠⢴⠈⠣⣉⡇⠀⣀⣤⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⢒⢶⣄⣀⣀⣀⠀⠀⣾⠀⠀⠀⠀⡇⢸⣢⠐⠀⠀⠀⡧⠈⠓⣄
⢀⡔⠁⣸⠀⠀⠈⡇⠠⡟⢘⠥⡂⢙⢿⣷⣄⠀⠀⠀⠀⠀⣠⠖⠏⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⡧⠀⢿⠀⠀⣀⠠⡷⡏⠀⠀⠀⢀⣠⠃⠀⠀⠈⢦
⡜⠀⠀⠈⣦⣄⠀⠑⠚⠀⠉⠀⠛⠐⠀⠨⢿⡆⠀⠀⠀⢸⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠃⣿⢠⠞⠛⠉⣻⠀⠀⠀⠀⠈
⡇⠀⠀⠀⡯⠘⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡎⠀⠀⠀⢀⣇⣸⠎⠀⠀⠀⣹
⢳⠀⠀⠀⠓⢦⡀⠙⢿⣦⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⡇⢀⣠⠞⠉⠉⠁⠀⠀⢀⡴⠉⠀⠀⠀⠀⡸
⠀⠳⡀⠀⠀⠑⠉⠢⣀⠉⠛⠿⠷⣦⡤⠒⠶⣾⠀⠀⢷⣤⣤⣤⣤⡀⠀⠀⣀⣤⣤⡤⠞⠋⠉⠓⣏⠀⡸⠁⠁⠀⠀⠀⠀⢀⠴⡪⠊⠀⠀⠀⢀⡔⠁
⠀⠀⠈⠢⣄⠀⠀⠀⠀⠉⡒⠤⣀⠀⠀⠀⠀⢸⡀⢀⡎⠀⠉⠉⠙⠻⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⡀⠄⡪⠁⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠁⠀⠉⠔⠒⠠⢬⡅⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠆⠁⠀⠁⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⢄⣀⡀⠀⠀⢸⠁⠀⡧⠋⠁⠈⠩⠟⠭⠬⠬⠛⠋⠀⠈⠙⠀⠀⠁⠀⠀⠀⢀⣀⣠⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⡏⠀⠀⢸⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⡶⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⠜⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠤⠄⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢔⡊⠁⠀⠀⠁⠂⠤⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⡀⠀⠉⠛⢟⠁⢐⡢⠔⠀⣉⠉⠉⢁⡒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⡦⠋⢉⠱⠂⢄⠙⡅⠀⠠⠤⠠⠌⠙⠚⠧⡄⠀⢨⢒⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠠⠒⢢⠁⠀⠀⠀⠀⠀⠌⠀⠊⠀⠀⠀⠀⠉⠁⠀⠂⠀⠀⠀⠀⢤⣀⠀⡀⠀⣀⣨⣽⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢀⡰⠞⠃⠀⠀⡄⠀⢀⠎⠀⠀⡶⠂⠉⠀⢈⡄⠀⠀⠀⠠⠄⠊⠁⣄⣀⠷⠘⠒⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⡄⠀⠀⢸⣿
⠀⠀⢰⡂⠉⠁⠀⠀⠀⠀⠀⣧⠔⠁⠀⠀⠀⡧⠄⠒⠈⠁⠀⠀⠀⠀⠈⠀⢈⠥⠀⠣⠄⠠⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⣿
⠀⠀⠐⡈⠢⡀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠈⠈⠐⠂⠄⣀⠑⠂⠤⠤⠤⠄⠠⠔⠀⠀⠀⢸⣿⠄
⠀⠀⠀⠈⠢⡈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠀⠀⠐⠒⠒⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⡀⠀⠀⢠⣓⡄⠀⠀⢀⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠇⠀⠀⣿⣩⡇⠀⠀⢿⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣭⡇⠀⠀⣟⢩⡇⠀⠀⣟⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣵⡇⠀⠀⣟⢥⡇⠀⠀⣟⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⡇⠀⠀⣯⣵⡇⠀⠀⣿⣥⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣴⡇⠀⠀⣯⣴⡇⠀⠀⣯⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠆⠒⠛⠛⠓⠀⠉⠉⠉⠉⠉⠁⠉⠛⠓⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⡖⠉⢢⢀⡴⡄⡎⢸⠀⢸⠁⢸⠀⡇⢡⠀⡎⠀⢱⢠⠒⠀⢴⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢴⠁⠀⢸⠈⡇⠓⠂⢸⠀⠸⠀⢼⠀⢃⠼⠀⡇⠀⣆⢈⠀⠓⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠒⠁⠀⠀⢨⠀⣸⠃⠈⠒⠂⡇⠀⢸⠀⠈⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⠤⠤⠆⠒⠒⠒⠚⠛⠉⠀⠉⠉⠈⠁⠒⠚⠒⠂⠤⠤⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠒⢤⠀⢀⣀⢀⡊⢦⠀⡰⠋⢱⡀⡎⠱⠀⢠⠊⠑⡄⢀⢤⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⠇⠀⢰⠀⢂⠸⣠⠆⠘⠀⢃⠀⢘⠃⢣⢀⠀⢣⠀⠀⡇⢸⠐⠤⣼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⣄⡸⠀⠀⠀⡇⠀⠸⠀⠹⣀⡸⢸⠀⠈⡄⠀⠣⠞⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠼⡄⠀⠀⠀⠀⠀⠀⠀⠳⠤⠚⠀⠀⠀⠀⣈⠀⠀⡇⠀⠀⠀⠀⢠⠧⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⢠⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠁⠀⠀⠀⠀⡜⠒⡄⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠈⠲⠤⠍⣐⣒⠒⠐⠲⠆⠀⠀⠤⠤⠤⠄⠀⠀⠐⠶⠒⠒⣒⣒⡩⠤⠖⠁⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠂⠤⠤⠬⠭⠍⣉⣉⣁⣀⣀⣀⣀⣈⣉⣉⠉⠭⠥⠤⠤⠐⠒⠂⠉⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣽⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⡿⣷⣿⣿⠀⠀⠀⠀⠀⢾⣿⣿⣙⣿⣿⣙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠉⠉⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⣉⣙⣛⣛⣋⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣄⣠⣴⣿⣀⣠⣶⣶⡆⠀⠀⣰⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢿⣿⣿⣿⠈⠁⠀⠈⠛⣦⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠘⠿⢋⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡿⢸⣷⣤⡀



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠒⠄⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢄⠠⠊⠀⠠⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠁⠠⠐⣂⠠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣉⡀⢀⢈⠉⣀⡠⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈⠁⠃⠉⠀⠀⢀⢠⢄⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠠⡐⢀⠁⢀⠥⠼⡁⢄⠑⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⡗⡌⢄⡤⢾⢉⠉⠉⠑⡓⠀⠀⠘⡦⢀⣲⠃⠀⠀⠀⠈⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠄⠀⠀⠈⣉⣁⣈⣂⣀⣀⣒⡀⠀⠀⠀⠉⠠⠀⠀⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠠⠤⡀⠀⠀⠀⠠⡀⢀⠀⠐⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠒⠤⠠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠤⠐⠈⠁⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠐⠒⠂⠀⠤⠤⠀⠀⠀⠤⠤⠀⠒⠒⠒⠂⠉⠉⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡬⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⣁⡃⠀⠀⠀⠀⠀⢱⠚⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠺⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⡀⠀⠀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢀⠠⠀⠀⠐⠀⠑⢄⠈⠂
⠀⠀⠀⠀⠀⢀⠀⢤⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠔⢁⠄⠀⠈⠀⠀⠄⠀⠀⠠⠀⠔⠀⠀⢸⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡠⢂⡄⠀⢈⣨⡄⠉⠛⢄⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣐⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠈⠀⣀⡣⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠀⠀⠀⠠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠞⠉
⠀⠀⢀⠂⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠁⠈⡆⠀⡠
⠀⠀⡀⠁⠈⠀⠐⠀⠀⢳⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⡯⡊⢀⠴⠁⠀⡀
⢸⡂⠧⠀⠀⠀⠀⠀⠀⢄⠁⠠⡄⠀⠀⠀⠗⢄⠀⢀⡀⠀⠀⠊⢀⡌⡀⠀⠀⠀⠀⢀⠇⠀⠁⠀⠈⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⡀⠔⠑⠐⣦⣤⠀⠘⡀⠐⠁⠀⠀⠀⡠⠊⠉⠀⠐⠀⠀⠒⡤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⢑⠶⠀⡀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠘⣷⣦⣄⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⣀⣴⣿⠟⠀⠰⣿⣿⢿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣶⣶⣿⣿⡟⠁⠀⠀⠀⢻⣿⣼⣿⣷⡘⣆⡻⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣧⣼⡇⢻⣿⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣇⠀⠀⠀⠀⠀⢰⣿⢹⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣷⣏⠀⠀⠀⠀⠀⢸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣇⡙⢻⣁⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠟⠋⠼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢀⣄⣠⣼⣿⣿⣿⣿⣿⠏⠀⠁⠀⠀⠀⠹⣦⣤⣤⣄⡀⠀⠀⠀⠀⠉⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣴⣟⣰⡄⣤⠘⣿⣿⣿⣿⣷⣶⣤⣬⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣇⢹⣿⠇⠀⠹⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠞⠄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠂⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⡀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇
⣄⠀⠀⠀⠀⠀⠀⠌⠀⠀⠈⠉⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⣷⡶⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡇⠀⠀⣠⡄
⣿⣆⠀⠀⠀⢀⣥⣤⣤⣤⣾⣷⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣦⠃⢰⣿⣿⣅
⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⡄⣃⠀⠙⢿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣵⣿⣾⣿⣿⣿⣿⣿⣦⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⢦⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⡄⠀⠀⠀⠀⢠⠃⢆⢣⠀⠀⠀⢀⠇⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡆⢱⠀⠀⠀⠀⢯⢸⢸⢸⠀⠀⠀⢸⢠⠱⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣄⣄⡜⠀⠀⠀⠀⠈⣻⣿⢿⡄⠀⠀⠘⣼⣾⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠿⣯⢲⡀⠀⠀⠀⡞⠛⢩⣼⠃⠀⠀⡴⠻⠛⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣴⢸⡇⠀⠀⢸⣴⣿⡗⣿⠀⠀⠀⣷⣰⣧⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢚⣿⡇⣀⡀⢈⣿⠦⣌⣏⠀⣀⠀⢸⣿⠽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⠶⣤⣶⣾⣿⣻⡏⠭⠛⣿⣿⣭⣿⡯⣑⠢⣿⣿⣭⣿⣿⠿⣋⣿⣷⣶⣶⡴⢶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣤⢾⣿⣷⣿⣛⣛⠋⠉⠉⠉⣸⡧⢐⣫⣧⠀⠀⢰⡗⠠⢍⣿⠀⠀⠀⣿⣈⠤⣿⠉⠙⠛⠛⠛⣷⣶⣽⣟⣛⣳⣆
⠀⠀⠀⠀⠀⢾⣷⢻⣽⣶⣿⣭⣭⣿⣶⡞⠲⣮⣩⣭⣭⣥⣤⡶⢮⣭⣛⣋⣭⣴⡶⢦⣭⡿⡿⢭⣴⡞⣛⣛⠺⣿⣷⣴⡟⣿⢻⡿
⠀⠀⠀⠀⠀⠈⠙⢿⣿⣯⣚⣿⡸⣿⣿⣿⣿⣾⣽⣶⢶⣾⣿⣿⣶⣮⣻⢯⣯⣭⣿⣶⣿⣯⣿⣷⣭⣿⡿⣿⠿⢿⣿⣿⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡯⣽⣽⠿⣿⣿⣿⣮⣿⣯⣿⣾⣿⣯⣽⣿⣽⣿⣿⣟⣟⣫⣾⣯⣿⣷⣿⣷⣷⣿⡿⣿⣻⣿⣟⡾⢻
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡷⡏⣵⠟⣿⣿⣿⣞⣭⡭⢿⣟⣯⣿⣿⣟⣯⣭⢯⣟⣿⣯⣷⣿⣿⣷⡿⠞⢾⣿⢿⣿⢫⡷⣿⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠘⣯⠉⣸⠇⠀⢹⡟⣿⠉⣿⡝⣹⠟⠉⣿⣯⡿⠁⠹⣟⣿⣿⠿⣿⡿⢡⡟⠀⠀⠀⢻⣏⢃⡾⠀⣿⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡋⠀⠀⠘⣷⣻⡿⠃⣴⠏⠀⠀⠉⠉⠁⠀⠀⢿⣭⣿⣠⣿⠇⣼⠃⠀⠀⠀⠀⠙⠛⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣤⣘⣻⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣹⠟⢁⣴⡟⠀⣀⣀⣀⣠⣤⣴⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣭⣿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠿⣫⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠩⠻⣯⡛⠿⠗⢒⣺⣾⠶⢾⣖⠾⣿⣿⠿⢟⣫⡶⠞⠛⠻⢮⣟⣟⣩⡴⠞⠉⠉⣇⡀
⠀⠀⠀⠀⠀⣀⣀⣠⠶⣻⣄⣀⡀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠉⠓⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠈⠉⠁⣀⣀⣠⡶⠿⣟⣷⣄⣀⡀
⢀⣠⠴⠞⠋⠉⠉⢿⡟⣽⢿⣯⣟⢛⣶⡶⢦⣤⣤⣄⣤⣤⣀⣤⣤⣤⣀⣀⡀⢀⣤⣤⣤⣤⣤⣤⣶⣶⣿⣻⣭⣽⣿⣿⣿⡿⠋⠉⠉⠛⠶⢤⣀
⣾⣧⣄⡀⠀⠀⠀⠈⠻⠾⢿⣽⣿⡿⡷⣿⣿⣷⣷⣿⢿⣿⣫⣴⣶⣮⣿⣿⣛⣿⣭⣴⣦⣽⣷⡾⠿⣶⣾⢿⣻⣿⣵⠟⠋⠀⠀⠀⠀⠀⠀⣀⣽
⠈⠛⠿⣿⣷⣶⣦⣤⣄⣀⣀⣀⠈⠛⠿⠿⠻⠷⡿⠿⣿⣯⣿⢾⣿⣿⠿⣯⣭⣽⡽⠿⣿⡿⠟⠛⠛⠛⠛⠛⠉⠀⢀⣀⣀⣀⣤⣤⣶⣶⡿⠟⠋
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠿⠿⠟⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⢠⢠⢠⢤⢤⢠⠰⣤⠀⡇⠀⠀⠂⠙⠂⠃⡋⠟⣀⢄⣄⢠⡀⠀⠀⠀⠀⡇⠸⠘⠠⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠈⣨⣀⠤⣌⡈⣈⣈⠀⠧⠘⠁⠈⠀⠨⠀⣭⠀⠉⠉⣋⣈⡁⣠⡀⣄⠀⡇⢸⡄⠐⠒⠐⠰⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠒⠘⠒⠃⠀⠀⠀⠠⠤⠤⠤⠄⠶⠲⠶⠒⠰⠶⠀⣲⠀⠀⠀⠉⡁⠑⠉⠁⡁⠀⠁⠚⠀⡛⢠⢄⡤⢰⠀⢴⢦⡤⠄
⠀⠀⠀⠠⠀⠢⠠⠤⠄⠋⠃⠁⠓⠁⠚⠃⠸⣿⣿⣿⡇⠐⢠⢐⣀⣆⣄⠀⣴⠀⡿⠀⢳⢡⣗⣱⡗⣺⡊⣃⣘⣷⣾⠂⣓⠀⡀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠑⠃⠘⠀⠆⠆⠰⠶⠲⢸⣿⡇⠀⢠⡄⠀⢀⣤⣬⣄⠀⣠⣤⣤⡄⢠⣤⣤⡄⢀⣤⣤⣄⠀⡈⡄⡀⢀⠀⢀⠀⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⣋⢰⠃⡶⠶⡆⡆⡆⡶⠀⣄⠀⢸⣿⡇⠀⠰⡄⠀⣾⡿⠛⣿⣇⠙⣿⣿⠁⠘⣿⡟⠃⣾⡟⠙⣿⣇⠁⠈⠉⢈⠈⠉⢀⡄⡀
⠀⠀⠀⢀⢀⡉⢈⠉⡉⢈⡉⠉⠁⠉⠀⣶⠀⢸⣿⡇⠀⣤⣤⢰⣿⡇⠀⣿⣿⠀⢸⣿⡄⢸⣿⠃⢰⣿⣧⣤⣿⣿⠘⠆⠈⡚⡈⢨⠀⠂⠛⠂⠀⡀⢀
⠀⠀⠀⠈⠈⠁⠉⠀⠁⠐⠃⠃⠘⠘⠀⢤⠀⢸⣿⡇⠀⣿⣿⢸⣿⡇⠀⣿⣿⠀⠀⣿⣇⣾⡟⠀⢸⣿⡏⠉⠉⠉⠸⡥⠀⢠⠅⢸⣬⣗⣿⣺⣏⣿⢘⢸⢚⡃
⠀⠀⠀⢰⣀⣐⢀⡀⣁⢁⡉⣉⠉⢉⠀⢦⢀⣸⣿⣧⣀⣿⣿⠀⣿⣧⣀⣿⡟⢰⡂⢸⣿⣿⠃⢴⠀⣿⣧⣀⣾⡖⢰⣳⠀⠐⡆⢀⣀⣀⣀⣐⣡⣀⠀⠈
⠀⠀⠀⢸⣧⣸⣹⣎⣧⢿⡋⣿⠀⢤⠀⠀⠘⠛⡛⠛⠛⠛⠛⠀⠈⠻⠿⠛⠀⠨⠃⠀⠛⠛⠀⢸⠅⠈⠛⠛⠋⠁⢸⣿⣿⣭⣭⣬⣭⣭⣭⣬⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢠⠄⡄⡤⠄⠤⠀⠘⠀⠍⠇⠇⠅⠘⠛⠚⠃⠑⠘⠃⠄⠀⠀⠰⠄⠐⠖⠂⠲⠸⠏⠉⠀⢉⡇⣀⡈⢉⣉⣙⠋⢋⢻⣺⢓⣟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠴⠴⠰⠰⠶⠲⠀⢸⣱⣬⡇⣯⢸⡅⡇⣟⣾⣻⠀⠰⠆⠶⠒⠂⠶⣶⠆⢨⡁⠈⡇⢈⠉⠉⣀⠘⠉⠉⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠓⠶⠶⠒⠒⠒⢀⡄⡇⡄⠒⡂⠸⠁⣈⣉⣉⠈⠁⡁⠉⠈⠍⠀⠐⠂⢒⡂⠀⠄⠀⠂⠤⠄⢘⡇⠘⡃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⣤⠔⢠⡄⣆⠠⠠⠀⠃⠀⠀⠀⠀⠈⠀⢀⡀⠀⣦⠖⠒⠒⡆⠀⠃⠈⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠉⠉⠉⠉⠉⠁⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣆⠀⠀⠀⠀⢀⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣦⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠖⣊⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⡠⢚⣿⡦⠀⠀⢸⠀⣿⣿⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⡰⠀⠀⠈⠟⠒⠀⠞⠀⠺⣿⠇⠀⣠⠞⠀⠀⡿⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠂⠀⣿⠶⣤⡀⣀⣀⣀⣀⣀⠜⠁⣠⠋⠀⠀⣤⡾⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢿⡀⠀⠉⠈⠉⠉⠉⢁⡠⠾⠃⠀⢀⣴⣿⡇⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢱⣸⠛⠦⣄⣀⣡⣴⣶⣿⣧⣀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠏⠀⠀⠀⠁⠀⠈⠻⢿⣿⡟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣰⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢰⣿⠀⠀⡄⠀⣀⡀⢠⡎⠁⠀⠀⠠⣄⡜⠘⢨⠾⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠟⠀⠔⠒⠓⠊⠉⠂⠺⠉⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣉⢉⠉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⢿⣻⠿⠗⠊⠈⠀⠀⠀⠁⡈⠶⠂⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⢻⠟⠧⠈⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⠀⠀⠀⣠⣼⣿⣿⡿⡋⠓⠈⠀⠀⠀⠀⣀⠄⠂⠁⠀⠀⠀⢀⡀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣣⡀⣰⣿⣿⣟⠉⠈⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⢟⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢻⣿⣿⣿⡇⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠋⣠⠴⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣹⡄⢸
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠟⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⢿⡿⣿⣯⣿⣾
⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣦⣄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠙⣫⣽⠏
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣞⠁⠀⠀⢀⣀⡀⣠⣄⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⠾⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠹⣎⣩⠉⢙⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠶⠾⢄
⠀⠀⠀⠀⠀⠘⣧⠬⢤⠠⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠶⠆⡸
⠀⠀⠀⠀⠀⠀⠈⡿⣌⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⠁⠀⠀⠀⠀⠀⠀⡀⠄⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠸⡌⢈⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⡟⠋⠋⠉⠀⠀⠀⠀⠀⢀⡠⠔⠂⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣘⣉⣀⣠⣤⣴⣶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣥⡀⡄⠀⢀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣯⠾⠗⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⡿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡙⠿⠿⠿⠟⡛⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠛⠑⠉⠀⢾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢗⡿⣽⡷⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠟⠁⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡏⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⣦⣠⡀⠀⠀⣠⣴⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡋⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⠷⠄⠂⠉⠙⢿⣿⣿⣿⣿⣷⣄⠀⣀⣤⣴⣿⣿⡿⠛⡆⠈⠙⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣾⡿⠋⠙⢿⡉⠀⣀⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⡀
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡠⠀⠀⠀⠀⢀⡦⢄
⠀⠀⠀⢸⠀⡸⠁⠙⢉⠇⠠⠀⣠⢐⠚⣓⠢⢀⠴⠂⠀⣴⢿⡭⠭⡻⣧⠀⡀⠀⠀⠇⢰⠙⠒⡉⡂
⠀⠀⠀⢸⣰⠁⠀⠀⣌⠀⠐⠄⡁⠬⣶⡟⠁⣇⡄⠀⠸⢟⡸⡀⠀⡀⣸⠀⠀⠒⠊⢊⠓⠘⠉⢏⡿
⠀⠀⠀⢀⠏⠀⠀⠀⠘⡄⠀⠀⠉⢄⡀⢀⡜⠁⡂⠁⡄⠑⢯⢮⣯⠾⠋⡀⡀⠀⠀⠈⠦⠀⠠⠼⠃
⠀⠀⠀⠈⠉⠉⠉⠉⡉⢁⠀⡀⢠⣤⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⡌⣳⡁⢸⠂⡒⠄⠀⠀⠀⠒⡱
⠀⠀⠀⠀⠀⡲⢠⡀⠂⠠⠃⢱⡟⣷⡎⡆⠐⠂⢰⠀⢰⠅⠀⠀⠀⠈⠁⠉⠁⢸⠀⡃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⢵⠐⠃⠀⣀⢀⢀⢉⡒⠊⠀⠀⠀⠈⠀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠰⠥⠤⠤⠤⠤⠤⠱
⠀⠀⠀⠀⠀⠀⠤⣸⣆⠹⢯⣟⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠇⠑⠈⠠⠥⠀⠀⠀⠀⠀⢀⠰⠄⡀
⠀⠀⠀⠀⠀⢀⣀⡈⣁⡀⠀⠀⠀⡀⠀⠀⠙⠰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡍⣔⠁⠀⠀⠈⡴⡆
⠀⠀⠀⠀⡊⠁⠀⠀⠀⣈⠄⢀⠙⢋⡇⠀⠳⠀⣉⣀⣀⠈⢸⢓⣲⢀⢨⣿⣔⡁⠀⢿⠀⣴⣶⡀⠃⣤
⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠸⠤⠼⠆⠀⠀⠂⠡⣀⡠⠒⠉⠉⡀⠘⠿⠟⠉⠀⢁⠀⠈⠛⠞⠁⡀⠽
⠀⠀⠀⢸⡑⢒⠒⠠⢂⡄⠀⠰⢪⢍⢢⠀⠀⢶⠀⡀⠀⠀⠀⡼⣁⣥⠀⠀⠐⠉⠂⠉⢢⣀⣀⡜⠁
⠀⠀⠀⠘⠁⠀⠒⠒⠂⠝⠀⠰⢌⡈⠜⠐⠟⠀⠐⠘⠀⠀⠀⠀⠃⠔⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣟⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠈⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡞⠗⣶⣹⠇⠀⢠⣤⡈⡆⠀⢠⡇⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣿⡁⣺⠗⠋⠀⠀⠀⠈⠙⣷⠀⠈⠀⠑⠀⠀⢀⠱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢹⣿⢿⢇⠈⠀⠀⠀⠀⠀⠀⢄⠉⠀⠀⣀⣀⡀⠀⠈⠀⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⠀⠹⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⠍⢻⣖⠂⣭⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠑⠀⢸⡯⢳⣻⣿⡄⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠣⠀⠀⠀⠀⠀⢀⣬⠁⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠔⠋⣀⠞⣡⢿⣇⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠤⠐⢚⡡⠞⣵⣿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡩⢒⣷⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⢶⣿⠻⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⠐⠋⠁⠃⠀⣏⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⢀
⣿⣟⣟⣿⣟⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣛⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠋⠁⢳⠀⠀⠀⠀⠀⠂⠀⠑⠀⠀⠀⣠⡀⠔⠄
⠀⠀⠀⠀⢐⠉⠈⠉⠒⠠⠥⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠉⠀⠐⠢⢤⡀
⠀⠀⠀⠀⠈⠒⠂⠐⠢⣀⠀⠈⠀⠀⢂⠀⠀⡀⠀⠀⢠⠊⠀⣀⠔⠊⠉⠲⡦⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣤⣄⠆⠀⠀⠀⢰⠃⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢉⣾⢿⠈⣀⠀⠀⠊⠀⠈⠣⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣾⣷⣿⡤⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠀⡠⢶⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠰⠿⡸⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⡤⠤⠒⠊⠉⠐⢛⣾⠆
⠀⠀⠀⠀⠀⠀⣸⣧⠔⠙⠄⣰⡾⠃⠀⠀⠀⠀⣠⣾⣿⣯⣿⣿⠦⠶⠚⠉⠀⠀⠀⠀⠀⠀⢸⣿⣠⡀
⠀⠀⠀⠀⢀⠄⠛⠁⠀⠰⣷⣿⠁⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠾⠛⢋⠵⠧⡄
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⠞⠛⠋⠉⠉⠀⠀⠀⡀⠀⣀⠇
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠐⢻⡇⠀⠀⠁⢀⣿⣿⠃⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⡔⠲⣬⣦⡱
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⣴⣾⡿⠛⠁⠀⡀⠀⠀⠀⢰⡏⠀⠀⣰⠦⡀⠀⠀⡇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠿⢿⡏⠀⢀⡼⠋⠉⠀⠀⣠⣿⢃⡴⠞⠁⠀⠘⢢⣀⠆
⠀⠸⠀⠀⠀⠀⠀⣄⣠⣿⠋⠀⠀⠀⠈⠓⠠⣎⠀⠀⠀⠀⠀⠿⢷⣾⡁⠀⠀⠀⠀⠈⢹
⠀⠘⣂⠀⢀⣴⣾⠟⠁⡽⢄⠀⠀⠀⠀⠀⠀⡎⠱⣼⠧⢀⣄⠀⠈⣯⠀⡄⠀⠀⠀⠀⢨⠂
⠀⠀⢇⢀⣾⡏⠀⠐⠋⡇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣼⣧⣼⣄⡀⠀⢀⡾
⠀⠀⢈⣿⣿⠇⠀⠸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠙⠻⣿⣿⣿⣿⣷⡀
⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⢆⠀⠀⠀⠀⠀⠼⢿⣇
⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢓⠔⠊⡋⡔⠁⠈⢧⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠒⣹⠞⠁⠀⡐⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⢁⢶⡀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡜⡠⠁⠘⣧⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⡀⠀⠀⢀⡜⣰⠃⠀⠀⠈⠁⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠠⡶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠊⢠⠇⠹⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣦⣤⣤⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠟⠋⠁

⣾⠛⠳⡄
⣿⠀⠀⢹⡄
⢹⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠄⠂
⠸⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠁⠀⡔⠁⢀⠔⠉
⠀⣇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠦⣧⡀⢀⠇⠀⡞⠀⡴⠁⢀⡴⠞⠋⠉⢹⡇
⠀⢿⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⢹⣾⣀⣼⠤⠾⠶⠶⠏⠀⠀⠀⠀⣸⠃
⠀⢸⠀⠀⠀⠸⣆⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⢸⠀⠀⠀⠈⣂⡛⠉⠀⢸⡉⣿⠙⡆⠀⠀⠠⣾⡁⢀⡀⠀⠤⠤⠀⠤⠤⠄
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠆⠀⠀⣎⣿⣝⡆⠀⠀⠉⠛⠋⠁⠀⠀⠀⠔⠛⣧
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠲⢦⣀⣠⠴⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⢺⡏⠉⠉⠉⠉⠉⠐⠀⠄⡀
⠀⢸⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣀⡀⠀⠀⠀⠑⣼⣏⠁⠂⠄⡀
⠀⠘⡇⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢀⠔⠘⣧⣀⠔⠂⠀⠀⠀⣠⠟⠀⠈⠉⠛⠛⠛⣻⠇⠀⠑⡀⠀⠈
⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠐⠁⠀⠀⡸⠛⠓⣶⠾⠖⠛⠁⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⠄
⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⣠⠴⠛⠁
⠀⠀⠀⠈⡇⠀⠀⡆⠀⠀⣾⠓⠒⠲⠶⠶⠶⠶⠶⠶⠖⢲⡄⠀⠀⢰⡄⠀⢀⡖⠒⠛⠛⠛⠋⠉
⠀⠀⠀⠀⣇⠀⣰⣿⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣸⡇⠀⣸⠃
⠀⠀⠀⠀⠘⠚⠋⠘⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣴⠟⢧⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣴⠋⢹⡄⢻⡀⣾⠀⣼⣭⡭
⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣤⣀⣙⣶⣞⣁⣈⣛⣃⣀⣘⣲⣶⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗

⠀⠀⠀⠀⣠⡄⠐⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⠀⠀⠀⣶⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠂⢀⡄⠀⠀⠀⢠⠀⠀⠀⠿⠀⠀⠀⠀⠈⠓⠀⠀⠘⣿⣦⣾⡏⠀⠀⣠⣡⣄
⠀⠀⠀⠀⣠⣄⠀⠀⢡⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠙⠿⠁⠀⠀⡒⠄
⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠈⠉⠀⣴⣶⣶⠀⠀⢸⣿⡇⠀⠀⠰⢿⣿⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆
⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⣿⡏⣿⡇⠀⠈⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣿⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢹⡇
⠀⠀⠀⠀⠀⢄⠀⠀⠤⠀⠀⢀⠀⢻⠀⢹⡇⠀⠻⠛⣇⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⢀⡀⠀⣀⠀⡀⠀⠟⠀⠸⠇

⣶⣶⡶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣰⢦⠲⠀⠀⣶⡄⠀⢰⠂⢤⠶⣄⠲⢄⡜⢢⠀⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⣡⣽⣦⡖⢀⡷⣤⠾⣆⡰⣄⠈⡃⠈⠀⡘⠀⡰⠃⣻⠰⢆⡰⠀⢣⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠠⣄⢀⢆⠀⠙⡁⢠⠼⢫⠟⢉⡝⠣⢤⡤⠏⢹⣤⠑⣾⣦⠼⣧⣄⡀⢨⡏⠢⣼⠱⡀⢀⡟⠀⢇⠀⣠
⠀⠀⠀⠀⠀⢠⡀⠀⡆⠐⣆⠀⡏⠈⣦⠊⠙⠁⢸⠷⢄⣰⠈⠢⣄⡇⠔⠁⠈⣿⢥⡝⢢⡼⣤⠭⣧⣾⠀⢸⠀⠐⠆⠀⠀⡰⠋⠀⡄
⠀⠀⠀⠀⠀⢸⠈⠓⣦⠀⠈⡆⠀⠀⠂⠀⣦⡤⣎⠸⣀⠞⢱⠆⣜⠡⢻⠔⡎⢋⣠⣛⣬⣧⡬⢦⠀⠙⡀⢘⢀⠸⠀⡠⠎⠀⣠⠔⠋⣃⣀
⠀⠀⠸⠂⠦⣀⡆⠀⠘⠀⢀⡛⢀⠈⠐⢠⠉⠄⠀⠘⢏⡰⢦⢶⡼⡦⡌⡼⠢⣼⣤⢫⣇⠦⢱⡄⢣⡀⡡⣾⠶⡶⢶⣷⣄⠈⡠⠆⠚⢉⡹⢦
⠀⡖⠀⠷⢄⡀⠙⢦⡴⢿⡉⣩⣉⣹⠷⣇⡄⠰⠞⣄⠋⢱⠊⠁⠚⣽⠛⡒⠩⠿⣬⠛⣏⣢⣶⡘⠳⢐⣾⣠⢏⡉⠉⣤⠿⣇⠄⠒⠉⠀⣠⢃⣀
⠰⡞⠒⠂⢤⡈⣢⠋⡤⠼⣁⠤⣁⣰⣤⣬⠀⢳⡀⢫⠀⢸⠀⠀⡿⠁⠀⡗⠀⣦⠘⠋⠉⢢⡔⠊⢳⡴⣇⣼⡠⣍⣩⣁⣦⣻⣨⡤⠒⠉⢀⣠⣼
⠀⠘⢦⡀⠀⢠⡟⠙⡤⠴⢉⠤⡾⠄⣥⣠⠀⠀⠱⠘⡀⢸⠀⠀⠀⠀⢰⠀⢠⠁⢀⡥⠚⠁⡌⠀⠇⢀⡏⣄⠧⡜⠳⣧⣌⣹⠧⠄⠂⢋⠉⡤⠎
⠀⠀⡠⠙⢒⠶⡗⠺⡶⠐⢿⡓⣥⠤⠼⣿⣶⣿⡟⢳⣯⣸⢀⣀⡞⠦⡟⢁⣮⠀⡬⠀⠀⢀⡇⠸⠀⣨⠱⠞⢷⠯⢸⡦⠺⣓⡒⠒⠂⠉⠑⢄
⠀⡞⠒⣀⠔⢻⠀⢠⠛⠦⠆⢿⣶⠀⣌⢷⠊⠟⠈⡇⣇⡝⢻⣭⡅⢠⣀⠡⡆⠹⣶⠞⠋⠙⡑⡆⠀⠙⠢⡴⢩⣵⣾⠇⢸⣿⢉⡽⠶⠒⠒⠒⠓
⠀⢲⠞⣁⡀⢼⡀⢈⠜⡀⢷⣸⡉⠢⢭⡎⠰⡇⠀⡷⡘⡇⠸⠶⣦⢤⣤⢋⠇⠀⣀⡠⠔⠁⠘⠃⢸⠇⣴⠁⢻⣸⣇⠰⢨⡞⣹⠀⣦⠀⢶
⠀⠈⠁⠭⢀⡠⠛⠦⠊⠉⢦⣤⡁⠀⠀⢈⣦⢛⡶⣜⣷⣣⡘⣿⠒⢶⢺⢣⠚⢀⡋⠀⠀⠀⢀⣆⠸⠆⣢⠗⠤⢞⡾⡦⢹⠿⠞⡰⢀⡴⠇⡲
⠰⠆⠰⠗⠫⠷⠝⠒⠒⠛⠢⣄⠀⠉⠁⠶⣏⡩⠚⠂⠈⠉⠛⠚⠵⡚⠏⠠⢆⠞⠛⢅⠉⠩⠤⠬⠷⣞⢡⠼⠖⠺⣑⡣⠞⠒⠲⣥⠊⢀⡜⠁
⠀⡦⠘⠢⣄⡀⢆⠀⠀⠀⣠⠛⠒⠒⠒⡸⠋⠀⠀⠀⢀⠶⡀⠀⠀⠈⠻⠢⠊⠀⢀⣞⡒⢳⠀⠀⢀⣞⣠⠀⠀⠀⢠⠒⠄⡀⠀⡗⠨⢀⡀⣤⡈
⠀⠘⣤⣞⠉⢈⠺⠀⠀⠀⣿⠀⠀⠉⢈⠁⠀⠀⠀⠀⡌⠀⠃⠀⠀⠀⠀⢃⢃⠀⠈⢧⠀⡸⠀⢀⠶⠀⢸⡇⠀⠀⠈⠙⢛⠌⠋⢹⡓⠈⠀⣠⠝
⠀⣀⣰⡄⠙⠠⢴⠀⠀⠀⣿⠙⠃⡀⢽⠀⠀⠀⠀⠀⠰⠤⠇⠀⠀⠀⠀⢸⠈⡀⠀⠈⠒⠁⠀⡸⠤⠤⠸⡇⠀⠀⢈⠁⠋⠀⠀⡞⠧⡉⠉⢄
⠀⠙⣤⡘⢦⣑⠾⠀⠀⠀⠈⠦⠠⠴⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠃⠀⠀⠀⠀⠀⠧⡔⠂⠐⡇⠀⠀⠈⠑⠒⠒⠊⢹⠒⢤⣀⡈⢣
⠘⢧⡀⠙⡤⢉⠃⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠡⡀⢠⠀⠀⠀⠀⡸⠶⡤⠒⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⠷⣄⠢⠈⢋
⢀⣀⠱⠾⠃⠚⣄⣀⠀⠀⠀⠀⣀⣀⠴⢡⠈⠑⠄⣀⡀⠀⢀⡀⢴⠋⡀⠢⡘⢦⡑⢄⣀⡴⠁⢠⣄⡴⡁⠀⠀⠀⠀⠀⠀⠀⢀⡞⢢⣼⡛⠦⢠
⣈⠵⠦⠤⡤⠩⠹⠤⡯⡼⢇⡽⣼⠴⠾⠡⠴⠋⠐⢀⡧⠄⠘⠂⠤⢀⡏⠤⢙⠦⠍⠶⠺⠤⠤⢀⣈⡦⣉⠨⡯⠭⠭⠿⠭⠥⠼⠵⢾⠈⣁⠔⠋
⠈⢢⡀⠐⠆⠀⠀⠀⠱⠗⢬⣤⠃⠀⠀⠀⢠⠀⡰⠁⠀⠀⠀⠀⠀⠀⠙⢆⠘⠁⠀⠀⠀⠀⠀⠀⠀⠉⠣⡀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⣠
⠘⢦⡌⣓⣣⠀⠀⠀⠀⠹⡶⠆⠀⠀⠀⠀⠀⡀⠁⠀⠀⡰⢚⠓⣄⠀⠀⠘⡀⠀⠀⠀⠀⡟⠛⢢⠀⠀⠀⡱⡇⠀⠀⠠⠎⠋⡳⠛⡻⠂⢁⡝
⠰⢥⠾⣛⣻⠀⠀⠀⡄⠀⠉⠀⢀⡄⠀⠀⠀⡷⠀⠀⠀⡇⠈⠋⢹⠀⠀⠀⡿⠀⠀⠀⠀⠓⠈⠁⠀⣀⢴⠧⡇⠀⠀⠀⠙⠛⠚⠺⣆⠴⠛⢀⡝
⠀⠉⠿⣍⣿⠀⠀⢰⠙⡄⠀⠀⡜⡇⠀⠀⠀⠿⠀⠀⠀⢃⠀⠀⠘⠀⠀⠀⣿⠇⠀⠀⠀⡤⢄⠀⠀⠉⢢⢴⠃⠀⠀⠀⠤⠀⠤⣖⠳⠤⡒⠉⣉
⠀⠀⠶⠲⢾⠀⠀⢸⣄⠘⢤⠾⡀⡇⠀⠀⢸⣯⡆⠀⠀⠈⠲⠎⠁⠀⠀⡰⢁⡇⠀⠀⠀⡏⠙⠇⠀⠀⠀⡾⠃⠀⠀⠈⠓⠁⠃⠉⢹⡇⠖⢉⠍
⠀⠀⠀⠀⢸⣀⣀⣨⣍⡑⢤⣀⢼⣇⣀⣀⡘⣳⠼⠦⣀⠀⠀⠀⠀⢀⡴⠁⠸⣧⣀⣀⣀⠧⠤⢼⣀⣀⣀⡟⢃⣀⣀⡀⢀⣀⡀⣀⣸⠆⠚⢧⣀
⠀⠀⠀⠀⠀⢖⡉⠀⠀⠀⣈⣉⣻⡔⢣⣊⣱⡟⠤⢓⣚⣯⡀⠐⢏⠁⡼⢼⠚⡶⠧⡌⠲⢆⠖⠡⠚⣀⡄⣸⠴⢼⡩⠿⣍⣹⢀⡏⠢⢕⣂⠀⢫
⠀⠀⠀⠀⢠⠎⠉⠢⣤⠤⠄⠒⣣⣼⣽⣥⠜⣳⣉⠯⣀⠀⠈⠑⣠⠋⡗⢚⠓⠖⢲⡞⣅⣎⢠⡴⠃⠘⢤⣀⡶⠊⠣⡔⢁⡹⠏⠀⠐⢄⣀⠈⢣
⠀⠀⠀⠐⠷⠀⢤⠎⠀⠀⡀⣀⠈⢣⣸⡄⣿⢠⣝⣠⠋⡙⠶⠤⡟⠺⣠⣯⢟⣙⣯⣱⢿⢉⠆⠀⠀⣌⠂⡼⢹⠓⠚⠛⢣⠀⠈⢷⢄⡀⠨⠁⠛
⠀⠀⢀⠞⠣⣄⢈⡁⣿⠟⠁⠀⠀⠁⡸⢒⠛⢲⠿⠍⣀⣀⣀⣀⣶⠚⡤⠓⣮⠭⣴⠋⣻⠋⠤⡴⢡⡄⠈⡆⠀⠀⠇⠀⠀⢣⡀⠈⡄⠉⠚
⠀⢴⣇⠒⢂⠟⠁⡐⣌⢀⣀⣠⠤⢾⠀⠀⢠⡇⠈⢀⣀⡔⢁⡨⣭⢶⡉⢡⠦⡄⣹⡾⢉⠈⠙⢷⠺⠇⢀⡇⠀⡆⠘⠀⠀⠸⠙⢄⡇
⠀⠀⠀⠘⠋⠲⣶⠀⢀⣬⣅⡼⠀⢸⠀⣰⠋⠉⣶⢾⡆⠘⠓⢴⠁⢊⣼⠛⣳⠛⠹⣆⠈⠑⠦⣤⣹⣖⠉⠇⢀⣵⣀⠿⣀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠒⠉⠖⢡⠀⡔⢹⠀⠙⢆⠀⠀⡷⠉⠈⠰⠉⡀⠀⡂⠑⠄⡀⢀⠀⠉⠀⠘⠋⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠑⠤⢄⣣⡜⠀⠀⣶⠁⠀⠣⣀⠇⠀⠀⠈⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⣈⣉⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡢⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⡉⡅⠀⠀⠀⠀⠈⠗⠑
⠀⠀⠀⠀⠀⠀⠀⠸⢂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠐⠤⠀⠀⠀⠁⠀⠑⠀⠐
⠀⠀⢀⠀⢀⠀⠐⠖⠒⠂⠀⡄⠀⡀⠀⠀⠀⠀⠀⠁⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢴
⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⢀⠀⡀⠀⠀⠀⠀⠊⠠⠀⣾⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠄⠀⠖⠀⠠⠒⠓⠀⠈⠢⡀⠀⠀⠀⠠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣀⡴⠇⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠄
⠀⠀⠐⠀⠈⠂⢀⠀⠰⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠐⢁⡄
⢠⠠⣂⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠼⢁⠈⠀⠀⠀⢨⠀⠀⠉⠀⠀⠂
⠈⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠢⠶⣥⠀⠀⠄⢺⠛⠋⠀⠀⠐⠀⠻⢯⣚⠏⠈⣡⣖⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠕⠀⠀⠉⠉⠀⠀⠑⣬⣭⠤⡠⠈⠁⠉⢛⠓⠤⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢺⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⢻⡅⠈⢇⡴⠛⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠈⣛⣓⣚⣓⡰⢦⣴⣚⣵⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠻⢿⠿⠛⠿⠷
⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣀⢀⣀⡄
⠀⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⣠⡝⠒⠶⠶⠶⠶⠶⠖⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣌⠙⠟⠁
⠀⠀⠀⠘⠿⢿⣷⣶⣦⣤⣤⣴⣶⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠙⠗⠲⠶⠶⠶⠶⠲⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠘⠀⠇⡇
⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡓⠂⠀⢠⡿⡀
⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠠⢦⣉⣉⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠻⢦⣬⣭⣭⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣤⣤⠾⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢛⣛⣶⣄⡴⠖⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⣿⣿⣿⣿⣴⣾⣿⣿⡾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣻⣿⣿⣿⣿⣿⣿⣿⢧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠻⣿⣟⡻⣿⣽⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣿⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡴⠶⠶⠶⠶⠶⠶⣤⣤⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠄⠀⣠⣴⣶⣦⣤⣴⠶⠛⠋⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⢠⣿⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣷⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣷
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣾⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢀⣿⠿⠟⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠻⣧
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠈⠛⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠉⠛⠿⢶⣤⣄⣀⣀⠀⣴⣿⣿⣿⣿⣿⡄⢀⣀⣀⣠⣤⠶⠞⠋⠁⠀⠀⠀⠉⠛⠶⣤⣀⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⣀⣀⣤⡴⠞⠋⠁

⠉⠈⢷⡠⠂⠀⠀⠘⠃⠀⠜⠩⢉⠉⠲⡕⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠽⣧⢏⠀⠀⠀⠠⡄⠀⠖⠀⠀⠀⠀⠆⠀⠉
⠀⠄⠊⠀⠀⠄⠁⠀⠀⠀⡘⠣⠀⠀⠃⡽⠃⠐⡶⠆⠠⠂⠶⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠴⣄⠰⣦⡶⠂⣤⣌⢳
⠀⣤⣰⡼⠀⠰⢒⠠⡀⠂⠈⠗⠂⠀⠀⠀⢀⢄⡀⠄⠀⠐⠴⠃⠀⠀⠼⠂⠀⠀⠠⢀⣀⢀⠈⠄⠈⠀⠰⢮⠿⠋
⣷⠙⠃⠀⣀⣀⡀⠀⠢⠀⠀⠀⢀⡀⠀⠀⠻⠑⠄⡻⠓⢀⡀⢆⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⢀⣰⡆⠀⠀⠁⠀⢀⣄
⠘⠀⠀⠀⡀⠀⠙⠀⠀⠀⠶⣤⣾⣧⣄⡀⠀⠀⠀⠀⣀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠛⢀⠄⡀⠘⡯⠀⢰⡇⣶⡶⠏⠃
⢀⠠⣀⡠⢌⡐⡀⠀⠀⠀⠰⠟⠛⢿⡅⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠆⠀⠀⠀⠆⠀⠡⠀⠀⠀⢨⠀⠀⠻⠋⠁⢾⣦
⠃⠀⠀⣀⣀⣄⠓⠄⠀⢠⡤⣀⣀⡀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠠⢄⠀⢠⠎⠀⠀⠀⢠⡄⢈⠁
⡇⠀⠀⠋⣹⠋⢠⠃⠀⠉⠀⠳⠴⢣⢿⢱⡲⢲⠄⠀⠁⠀⠀⠀⠂⠀⡠⢶⣠⣆⠉⠁⠀⠀⠀⠀⠀⡲⠾⣯⢷⠜⠂
⠁⠤⠀⢀⠀⣰⠃⠀⠀⢰⣦⡀⠀⢀⣤⡆⠙⠁⣀⠀⠀⠀⠀⠉⠀⠀⡘⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢚⢸
⠀⠐⠀⠀⣠⣤⣤⣶⣄⡀⠈⠉⠒⠬⣙⠃⡀⠫⠟⠀⡀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠄
⠉⢠⠀⠈⠛⢿⣿⣿⠟⠁⢀⠄⢀⠀⠀⠙⠋⠄⠀⠈⢯⡿⠁⠀⠐⠊⠉⠛⡄⠀⠠⠀⠀⠀⠠⠀⣠⣀⣀⡀⠉⠠⠶
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢡⠀⡄⢀⠀⣠⠀⢤⣤⠀⠀⠀⠀⠀⠈⡁⠀⠀⠜⠀⠀⠀⢦⠶⠀⠀⠘⣿⠟⠁⠀⠐⢄
⠃⠰⡾⢠⣽⠅⠀⠂⢀⠀⢤⣀⡀⣠⠞⠁⠀⠈⠋⠀⠀⠀⠀⣠⠀⠀⠀⡀⢲⠖⠠⠀⠀⠀⠀⠀⠀⠀⠶⢖
⠀⠀⢀⣀⠙⠃⠄⠀⣇⠀⠀⢰⠘⠁⠲⡶⠀⠀⠀⠐⠁⠀⠘⠋⠀⠠⣴⠁⣖⡤⡀⡀⡀⠀⠀⠀⠀⠀⡀⣙⠁⡄
⣀⡀⠃⠀⠀⠀⢸⡄⠈⠈⢇⠋⠀⠀⠀⠀⠀⠚⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠉⠀⠞⠙⠟⠦⠄⣤⠀⠀⠀⠀⠎⠀⣶
⠛⠃⠀⠀⣄⠠⠘⠀⢀⡤⠤⡀⠀⣀⠄⠠⠐⠀⠀⠂⠀⠀⡁⠐⠉⠀⠄⠀⠿⠃⠀⣀⡀⠀⠠⢤⣐⣅⣀⠀⠀⠀⢻
⢀⡀⢀⠄⠀⠀⠀⠰⠁⠀⠃⠱⠀⠃⠁⢠⡤⠄⠀⠀⠶⠃⠘⢆⣠⠮⠊⠀⢨⢷⣭⣽⣥⠄⠀⡠⠋⠁⠀⠙⣄⣄⣤
⣘⢧⢆⠐⠀⢀⡠⠞⠁⠀⠀⠄⠀⠀⠀⠃⠀⢀⠄⠀⢀⣀⡄⢀⠡⢀⠀⠑⢓⠖⠋⢫⠁⠁⠀⢀⠀⠀⠀⡰⠁⠹⢃
⠀⠀⠀⠀⠀⠉⠀⠤⣴⠈⠂⢀⠃⠀⠀⠀⠈⠀⠀⢠⠘⣤⣤⡄⠀⠈⡆⠀⠘⠈⡂⠜⠁⠀⠀⠀⠑⠒⠈⠀⠀⠂⠈
⠀⠈⠀⠤⡖⠣⢠⠇⠈⠀⠀⠀⡐⢀⢀⡈⠀⠀⡀⠈⢃⡘⠃⠀⠀⠀⡃⠀⠀⠀⠡⡀⠠⠄⠀⠀⠀⠀⠀⠲⠄
⡀⣠⣠⠄⠁⠀⣴⢦⡤⡆⠂⠤⡣⠘⠺⠃⠀⢂⢁⡈⠀⠂⠀⠂⠐⠂⠁⠀⠀⠀⡖⠓⠐⢢⠀⠤⣤⠀⠀⢀⡠⠈
⢿⣶⢿⠶⠂⠀⠘⣇⣱⠃⠈⢀⣀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡔⠵⠤⠤⠊⠀⠀⠈⠀⠀⠉⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⣴⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡔⠒⠒⠢⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠀⠂⠑⠀⠈⢦⣇⠂⠀⠀⠀⠀⠹⠦⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠂⠱⠾⠷⢂⣾⣯⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠰⠂
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠑⠂⠈⢩⠟⠻⢄⠀⠀⠀⠀⠀⠀⠀⠠⠐⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣾⡎⠀⠀⠠⠷⣄⡐⠀⠀⠀⠠⠀⡴⢠⠄
⠀⠀⠀⠀⡠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡐⢾⠶⣌⡱⠀⠀⠀⠀⠘⠳⡀
⠀⠀⠀⠀⣧⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⢨⡱⢳⡂⣀⣈⠂⠀⠕⢀⠃
⠀⠀⠀⠀⠙⣇⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢈⠠⠂⠈⡝⣞⠋⠉⠉⠛⠫⡲⡄
⠀⠀⠀⠀⡖⠁⣀⢐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠮⡡⠎⠀⢀⠁⠊⣀⠉⠀⠀⠂⠈⣿⡆
⠀⠀⠀⠀⡧⠀⠢⡀⢰⠠⢀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⡱⠆⠜⡁⠀⢈⡿⠀⠉⠀⠐⠀⡿⡇
⠀⠀⠀⠀⠂⡱⠮⡀⢰⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⣀⣇⡔⠰⠀⠀⢀⡀⠒⠀⠀⠆⢰⡷
⠀⠀⠀⠠⢸⡶⠆⠁⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡈⢶⠍⠊⠄⠈⣀⠀⠃⠀⣰⡿⢁⠦
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠄⢼⡤⠤⠥⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣽⡟⠁⠨⡇
⠀⠀⠀⠀⠨⠀⠀⠐⡀⠀⠰⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⢇⣦⠂⡇
⠀⠀⠀⠀⡸⠄⡀⠂⠐⠆⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⣷⠀⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠡⠐⠚⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠦⡀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⢾⣿
⠀⠀⠸⠏⠢⠈⠉⠀⠀⠐⠀⠀⠀⠀⢠⣤⠀⠠⠀⠀⠀⠀⠀⠘⠂⠈⠛⠀⠀⠀⠀⠀⠐⠀⢨⠉⠉⠃⢪⠀⠁
⠀⠀⠀⠐⢬⠀⠀⠀⠀⣤⠂⠀⠀⠀⠈⠁⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠠⠀⠄⠀⠀⠉⠀⠀⠀⢀⢀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠤⠄⠂⠉⠡⠄⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠀⠘⠂⠀⠀⠀⠀⠀⠠⠀⠘⠀⠞⠉⠠⠀⢀⢀⣕
⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠬⠭⠭⠥⠤⠤⠬⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠤⠦⠼⠦⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣳⢠⡾⣻⡄⠀⠀⠐⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢸⣿⣿⣙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣿⠟⠁⠀⠀⠀⠄⠀⠀⠀⠀⡞⠳⢦⣰⠋⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⠃⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠹⣄⠈⠃⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠲⢤⡀⠀⠀⠀⢀⡾⠋⠀⠈⢻⣧⠀⠀⠀⠘⢦⠀⣰⠇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠙⣦⠀⠀⣾⠁⠀⠀⠀⠘⣿⡆⠀⠀⠀⠈⣦⠃⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⢷⣸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣴⣦⣰⣿⡇⠈⢷⡄⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠘⣾⢛⡟⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡀⠀⠀⠀⢀⣠⠴⢦⣄⠀⢶⢤⠚⡆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⠫⡙⣦⡀⣰⡟⠁⢆⡄⣹⡆⠈⠢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢈⣿⣿⢇⠀⠃⠈⣿⣿⠘⣤⢹⣥⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠀⠀⠀⠈⢧⠀⣰⣿⡿⠙⢿⣄⣸⡄⢊⢇⠀⢃⣦⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠈⠛⢿⡈⣬⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠶⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢳⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠉⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣠⣶⣿⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣤⣶⣿⣿⣿⠟⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⡟⠿⠟⠋⠀⠀⠀⣠⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⣽⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿⠶⣶⣶⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢾⡿⠋⠉⣲⣄⠀⠀⠀⣰⠃⠀⠀⣀⣴⣿⣿⣧⢀⣀⣤⣾⣿⣿⠟⠁⣾⣀⠀⠀⠀⠐⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣀⠀⠀⠀⠈⠛⠳⡄⠀⣷⣶⣾⣿⣿⣿⠟⠋⠀⠙⢿⡿⠟⠉⠀⢀⡜⢻⡿⠂⠀⣠⣄⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢽⣿⠆⠀⢰⣿⣦⠀⢻⠀⣿⡿⠛⠋⠁⠀⠀⠀⢀⣴⣿⠀⠀⠦⣶⣯⡀⠀⢀⡀⠀⢿⣿⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠀⢠⡄⠈⠛⠋⠀⢈⡆⢡⠀⠀⠀⠀⢀⣤⣾⣿⡿⡟⠀⣠⠀⠙⣿⡇⠀⠈⠁⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠈⠁⠀⠀⠀⠐⣿⡇⠀⠣⣤⣶⣾⣿⣿⠟⠋⣰⠁⠀⠀⠈⠀⠉⡀⠀⠀⣶⣦⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠀⠀⠐⣿⡇⠀⠀⣠⠇⠀⠀⠙⠻⠛⠉⠀⢀⡴⠃⠀⠀⢀⠃⠀⠀⠑⠀⠀⠙⠋⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⣀⣀⡀⢀⠟⠀⠀⠀⠀⠀⠀⠙⢚⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⢷⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠙⠻⠿⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢿⡇⠙⣿⡀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠘⣿⡀⢀⣤⢤⡀
⠀⠀⣴⡶⣤⡀⠀⢀⡴⠒⠳⣦⢸⣿⠻⣦⢀⡤⢤⡀⠀⠸⣿⡀⢸⣧⠀⠁⣼⠀⠀⢀⣶⢿⣦⠀⠀⠀⠀⠸⣿⡀⢸⣧⠈⠀⢀⡷
⠀⠀⣿⡄⠈⢿⠄⠋⠀⠀⣸⠇⠀⢿⡆⠛⠀⠀⠀⡿⠀⠀⠹⣷⡈⠋⠀⣠⡏⠀⠀⠈⣿⡀⠹⣧⠀⣤⠶⣄⠻⣷⡘⡿⠀⣠⡞⠁
⣀⠀⠘⣿⡄⠀⠀⠀⢀⡾⠋⠀⠀⠘⣿⡄⠀⢀⣼⠃⠀⠀⠀⠻⣷⣤⡴⠋⠀⠀⠀⠀⢻⣧⠀⠻⠀⠀⢠⡿⠀⠙⠷⠶⠞⠋⢀⣀
⢹⡇⠀⠘⢿⣆⢀⣴⡟⠁⠀⠀⠀⠀⠘⠿⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣾⡟⣷⡄⠊
⠟⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⣠⠶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⢀⣀⠀⠀⠀⠀⠀⠸⣷⡈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇⠹⣧⡘⠁⣸⠇⠀⣴⣶⣆⠀⠀⠀⣠⣤⡀⠀⠀⢠⣿⠛⣷⡀⠀⢀⣤⡀⠙⣿⣶⡿
⠀⠀⠀⣴⡿⠷⣦⡈⠁⣸⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠙⠀⣰⠏⠀⠀⣿⡇⢻⣆⠀⠚⠁⢠⡿⠀⠀⠈⣿⡄⢸⣧⠀⠁⣸⡇
⠀⠀⠀⣿⡇⠀⠈⠃⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣼⡏⠀⠀⠀⠸⣷⡀⠿⠀⢀⣴⠏⠀⠀⠀⠀⠹⣿⡄⢀⣠⡾⠋
⠀⠀⠀⠘⢿⣦⣀⣾⠏⠀⣴⡿⢿⡄⠀⠀⣀⡀⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀⠹⣷⣄⣴⠟⠁⠀⠀⠀⠀⠀⠀⠘⢿⠟⠁
⠀⠀⣠⣦⠀⠉⠛⠁⠀⠐⣿⡀⠀⣿⡄⠊⠁⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢷
⣷⡈⠀⣿⠀⠀⠀⠀⠀⠀⢻⣧⠀⠘⠁⠀⢀⡼⠃⠀⣴⡿⢷⡄⠀⢀⣠⡀⠀⠀⠀⠀⢠⣾⠶⣦⡀⡴⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠈⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⣠⡞⠁⠀⠀⢿⡇⠀⢻⡆⠋⠀⣿⠀⠀⠀⠀⢸⣷⠀⠘⠏⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⣄⣠⡿⠀⠀⠀⠀⣠⣤⣄⠀⠈⢻⣷⡾⠋⠀⠀⠀⠀⠘⣿⣄⠈⠁⢠⡾⠁⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢠⡟⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠻
⠻⠟⠀⢠⡾⢷⡔⠁⠀⣽⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⣴⠟⠀⠀⠀⣠⢶⡆⠀⠈⢿⣦⣀⣴⡟⠀⠀⢰⡿⠋⠻⣦⢠⠞⠉⢹⡆
⠀⠀⠀⠘⣿⣄⠀⠀⣰⠏⠀⠀⣠⣶⣤⡀⢀⣠⣤⠀⠀⠀⠈⠛⠁⣴⡿⢷⡜⠁⢸⡇⠀⠀⠀⠙⠛⠋⠀⠀⠀⢸⣇⠀⠀⠿⠁⠀⢀⡾⠁
⠀⠀⠀⠀⠈⢻⣦⣼⠟⠀⠀⠀⣿⡇⠈⣷⡋⠀⡿⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⣠⣄⠉⠋⠀⠀⠀⠀⢿⣇⠀⠙⠁⣼⠃⠀⠀⠀⠀⠀⠀⠸⣷⡀⠈⣸⠏⠀⠀⠀⣠⣄⡀⠀⣤⢦⡄⠀⠹⣿⣤⣴⡾⠋
⠻⣦⣄⠈⠀⢸⡇⠀⢀⡀⠀⠀⠘⢿⣦⣠⡾⠃⠀⣠⣤⡀⠀⠀⣀⠀⠙⣿⣾⠟⠀⠀⠀⣼⡟⠙⣷⠈⠁⢠⡗⠀⠀⠈⠉⠉⠀⠀⠀⠀⢸
⡀⠈⠉⠀⣠⡟⠀⢰⣿⢿⣆⠀⠀⡀⠉⠉⠀⠀⢸⣿⠉⢻⡶⠋⣿⠀⠀⠈⠁⠀⠀⠀⠀⢸⣧⠀⠈⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣷⡄⠀⣰⠟⠀⠀⠈⣿⡄⢻⡆⠋⠙⣦⠀⠀⠀⠘⣿⡀⠈⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣠⡾⠁
⠙⠿⠿⠏⠀⠀⠀⠀⠹⣷⡈⠁⠀⣠⠏⠀⠀⠀⠀⢻⣷⣤⡾⠃⠀⠀⠀⣠⣄⠀⢀⣀⠀⠀⠀⢻⣿⠟⠁⠀⠀⢠⣿⢿⡀⠀⡴⠚⢻⡆
⠀⠀⠀⠀⠀⣠⠶⣦⡀⠙⣿⣤⡾⠋⣶⣦⡀⠀⡀⠀⠉⠉⠀⠀⠀⠀⢸⣿⠹⡗⠉⠉⣷⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⢸⡇⠈⢀⣴⠏
⠀⣾⠛⠿⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢿⡏⡿⠈⠉⣷⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢀⣴⡟⠁
⠀⢿⣆⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠘⣿⣄⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠋
⠀⠈⢻⣦⡀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡂⠀⢀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡿⠂⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠰⣶
⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠠
⠀⠀⠅⠀⠀⠀⠀⣶⡶⠸⡆⠀⣸⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⠀⠀⢦⡀⠀⢻⠟⠀⠙⢦⣽⣥⠾⠁⠀⣦⠀⢀⣇⠀⢰⠆⠀⣦⠀⢀⣆⠀⠀⠀⢠⡄⠀⣠⣇⠀⣾⠀⠀⢰⣀⠀⠀⣀⠀⡀⠀⠀⢀⣄⠀⢀⡆
⠀⠈⠀⣀⣻⣋⣠⠏⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⢦⣙⣟⣤⠟⠀⠀⠘⢦⣙⣟⣠⣄⡀⠀⠹⣦⣙⣯⡴⠃⠀⠀⣙⣿⣤⠴⠋⠀⠙⠶⣤⣘⣟⣠⠞⠁
⠀⠀⢸⡍⣿⣿⠀⠀⠀⠀⢀⣼⠋⠻⣄⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⡇⠀⠙⠂⠀⠀⢹⣿⡇⠀⠀⣞⠹⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⡇⢀⡀
⠀⠀⠀⠙⣿⣿⠀⠀⠀⢠⡾⠁⠀⠀⠙⣧⠀⠀⠀⣿⢻⡅⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠙⠀⣿⠻⣆⠀⠀⠀⠀⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡿⡏
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠁⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠘⠃⠃⠀⠀⠀⠘⠃⠘⠋⠀⠀⠀⠀⠘⠋⠃

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠐⠀⠀⠐⠠⠌
⠀⠀⠀⠀⢠⡾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣄⣀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⣿⢋⡿⠋⠙⠁⠀⠀⠀⠀⠀⢐⣯⣽⡛⣿⡏⠛⠁⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠳⠀⠘⠀⢰⡃
⠀⠀⠀⠀⠀⠀⣿⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⠛⢷⣄⠀⠠⠄⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⡄⠄⠀⣠⣤⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣼⡀⠀⢈⣻⡆⠘⢿⣿⣿⣿⣷⡿⠁⠀⠂⠉
⠀⠀⠀⠀⠀⠘⠋⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠟⠁⠀⠀⠀⠀⣾⣿⡄⠀⠀⣾⣿⣇⠀⠀⡌⠻⣷⣶⣸⣿⣿⣏⣀⡀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠿⣦⣤⡻⢿⣋⣠⡄⢟⢆⢸⡿⣿⣻⡟⣿⣿⣿⠀⠀⢀⣠⣾⠇
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠐⢿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣯⡿⣧⣬⣭⣥⣴⡶⠟⠋
⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣶⣿⣿⣟⣯⣴⣮⣥⣼⣿⢿⣿⠀⣿⣿⣿⣿⡀
⠀⠀⠀⢙⣛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢸⣿⣻⣷⣸⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⡷⠶⠶⠾⠀⠀⠸⠶⠶⢶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⠙⣿⣹⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡿⠿⣿⣿⣿⢸⣿⢸⣿⢹⣿⢻⣿⠟⠘⠿⠘⢛⣿⠟⣿⡏⠁
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡿⠿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢸⣿⠁⠉⢸⣿⢸⣿⢸⣿⢸⣿⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⢸⣿⠀⠀⠈⠉⠀⠉⢸⣿⢸⣿⠀⠀⠀⠀⠐⠿⠃⠿⠃
⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠸⠿⠘⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀⠠⠀⠐⠒⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠒⠪⠅⠀⣀⡀⣀⣈⠁⠒⠻⡉⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠠⣄⣀⣀⠈⠙⢍⣀⡈⠕⠒⠁⠣⠄⢀⠀⢀⡏⠁⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⢘⠖⠁⡠⠔⠋⠑⢤⣙⡆⠀⡔⠂⠐⠒⠒⠈⠉⠛⠢⠀⠀⢶⠱⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠊⣨⡎⠀⠀⠀⠀⠀⠀⡰⠁⠀⡊⠀⢀⣀⠀⣀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠦⠤⣄⠣⡀⢨⣤⠤⠾⠛⠦⢤⣀⣀
⠀⠀⠀⠀⠀⢀⡀⠼⠛⠉⠀⠀⠀⣦⠀⢀⠔⠁⠀⠀⣾⠉⠀⠀⢀⡨⠂⠀⠀⠀⠀⡔⠊⢁⡀⠦⣤⠜⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢰⠏⡁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠐⠁⠀⠀⠀⢀⠧⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠐⠈⠉⢂⡀⠐⠒⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠣⡈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠉⠐⠂⠄⣀⡁⠒⠒⢀⣒⣒⠒⠊⢨
⠀⠀⠀⠀⠈⠢⢄⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉

⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡄
⠀⢸⡟⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣉⣛⢹⡿⢿⣷⣄⠀⠀⣀⡤⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⠁
⢀⠾⡇⢠⣾⣩⡿⣇⢸⣇⣟⡗⠀⡀⠀⠀⠀⠚⠛⣻⡟⠿⣛⣼⣧⣼⢫⡟⣻⣿⣿⣧⣴⠆⠀⠀⠀⣼⠷⡆⣰⣾⢤⠖⢲⡄⣼⢦⡄⢤⣿⡥
⠀⠀⣷⠏⠳⡼⠃⠹⠟⠙⠻⠶⠞⠁⠀⠀⠀⠀⣸⡿⠟⠋⠉⠉⠉⠛⠷⣶⣭⣾⡿⠟⠃⠀⠀⠀⠀⠟⠸⠧⢿⡵⠿⣤⢾⡵⠃⣏⣴⢿⣃⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠀⢀⣀⠀⠀⢀⣀⣀⠀⠰⢚⣩⢖⡀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠀⢿⣿⠇
⠀⢀⡞⠉⠉⠓⣴⠋⠀⠈⢳⠞⠋⠤⠒⠁⠀⠀⠀⠻⣿⡿⠈⠻⠏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣀⠀⣴⣶⣤⣀⣴⣶⣤⠀⣠⡴⠆
⠀⠀⢧⡀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠈⣿⣿⣿⣿⣿⣿⣿⠃⣀⣠⡄
⠀⠀⠀⣻⣴⠂⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣏⡁⠠⡟⠛⣦⢠⠖⢀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟⠁⠀⠈
⣴⣶⡛⠁⠘⢦⠀⣴⠋⠀⠀⠀⢀⡴⠶⢤⣀⡤⠶⢦⡀⠀⠀⠘⠲⢌⠠⠶⠿⠂⠳⠞⠁⠈⢚⣉⠀⠀⠀⠈⠛⠉⠀⠀⠘⠿⠋⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⢸⡀⣾⣄⡙⣡⣿⡄⣿⠀⠀⠈⢉⣤⠀⣀⠀⡀⣰⣆⢠⡖⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⢹⢟⡿⢋⡴⠃⠀⠀⠀⣟⢀⡄⣏⣼⡇⢽⣁⡸⣯⡵⠂⠀⠀⠀⢀⣠⠆
⠀⢰⣟⣿⣦⣴⣟⣿⣷⡀⠀⠀⠀⠀⠈⢳⣌⡵⠋⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⠂⠀⠀⠀⠀⣠⠞⠉⠲⢤⡀
⠀⠘⣿⣿⣿⣿⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠂⢄⢀⠴⠂⠐⢦⠀⠀⠀⢶⣆⠀⢠⣞⣁⣀⣀⣀⣀⣉⣳⡄
⠀⠀⠈⠻⣷⣾⡿⠋⠀⠀⠀⠀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡧⣤⡄⠀⠃⠀⠀⠀⣼⠀⠀⠀⠉⠀⠀⢸⠀⠀⣤⣄⣤⡄⠀⠀⡇
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⣇⣀⣹⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠙⠃⠀⣸⠀⠀⠀⠀⠜⠁⠀⢀⣠⠆⠀⠀⢸⠀⠀⠙⢿⡿⠃⠀⢠⡇
⠀⢠⠀⠀⠀⠀⠀⢀⣀⠀⢀⣌⢻⠉⢸⣤⡄⣾⣆⡟⠻⡤⠆⠀⠀⠀⠀⠙⢦⡀⠀⣰⢯⠀⢀⡴⠋⠀⠀⠀⠀⡟⠓⠀⠀⢸⣤⣤⣤⣤⣤⣤⣤⣼⠇
⠀⣸⣤⠄⢰⣶⣤⣿⠈⢳⣸⣿⠼⣧⠾⠇⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠁⠈⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⢹⣇⣀⣾⣤⠏⠘⢓⣿⠃⢁⡄⠀⠀⠀⠀⠀⠀⠀⢠⣤⡿⢰⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⡀⠀⠀⠀⠀⠈⠁⠀⠙⠁⢰⣦
⠀⠀⠉⠁⠀⠀⠀⡴⠋⢸⠀⢸⣅⡀⣤⡤⢠⣶⣼⢷⣨⡏⠳⠟⠈⠉⠁⠀⠀⠀⠀⠀⠀⠰⢷⣼⠃⡏⢹⡏⠹⣷⣿⠀⠀⠀⠀⡀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠞⠀⠹⣧⣞⣷⠷⡼⠿⠋⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⠀⠙⢋⣤⣀⠀⠉⠀⢠⡞⢉⠉⡓⢆⣰⠞⠛⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡠⣄⠀⠀⠀⠀⠸⣇⡀⢸⠀⣀⠀⠻⢀⣀⠀⠀⠘⣧⠈⠀⠁⢈⠁⠘⢛⡀⢘
⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠐⣏⠉⣹⠘⣇⣡⡏⣴⠲⢶⠀⠀⠈⠙⠛⢸⡟⡟⣇⣾⣟⣀⠀⠀⠈⢷⡉⠀⢉⠀⠰⠀⣡⠟
⠀⣯⣌⠉⣴⣶⣶⣄⣠⣶⣶⣄⠉⣡⣽⠀⠀⠀⠀⠀⠀⠈⠳⠃⠀⠀⠉⠀⠘⠦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠹⣄⠘⠁⣠⠞⠁
⢼⡉⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⠈⢉⡷⠀⠀⠀⠀⠀⢰⣶⡒⠒⠒⠒⠒⣶⣶⠀⠀⠀⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢦⠞⠁
⠀⠉⣿⡋⠀⠙⢿⣿⣿⣿⠟⠀⢙⣿⠉⠁⠀⠀⠀⠀⠀⢸⠀⠙⣶⣶⣶⠟⠁⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣠⣤⣀⡀⠀⢾⣦⣞
⠀⠀⠈⠉⠉⠉⠀⠻⠟⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣤⠊⠉⠻⠋⠓⣄⣿⠀⠀⠀⠀⠀⠀⢀⣸⡇⢰⡿⢤⡟⣧⠀⣼⣷⡽⢃
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⢀⣈⢉⡉⢉⣉⣉⣉⡉⣉⢀⣀⣀⡀⣀⠀⢀⡈⣷⡏⠳⠞⡁⣹⣶⠃⣘⠓⣋⢀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡸⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠘⢧⡙⣷⡧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⠇⢠⠖⢛⣷⡴⠛⠁⠀⠀⣘⣀⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⠀⠳⡞⠉⠈⡇⢸⠀⢠⠋⢹⡉⠉⢁⡰⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜⠀⠀⢰⡅⠀⣠⠁⠘⣦⡜⠀⠀⠙⠛⠋⡀
⠀⠀⠀⠀⠀⠀⠀⢈⠟⠀⠀⠀⡀⠙⠋⠁⠀⠀⠀⢰⣟⣷⣦⠖⢛⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠘⠉⢧⣀⡤⠞⠀⠀⠀⠆⠀⢰⡄⠀⣴⡄⠈⢧⢸⡀⡠⢿⣀⣀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⣄⡠⠃⡇⢀⡽⣤⠤⠃⠀⠉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡷⠋⠀⠀⠀⠀⠀⠀⠀⣴⣲⣦⡤⢶⣥⡄⢀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣠⠴⠖⠋⢉⣁⣼⠀⢀⣀⢀⡴⢶⠀⢸⠉⠀⡇⡸⠋⠀⡎⡰⠁⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠛⠓⠶⠒⡟⠉⠘⡴⠋⢹⠏⢀⠆⠀⡘⠷⠚⠀⠷⡤⠞⠻⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⠴⠊⠀⠀⣼⠁⠀⣿⠀⣎⡠⠚⠁
⠀⠀⠀⠀⠀⢀⣀⡀⢀⡔⠒⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⣄⠀⠹⣾⠀⣸⠁
⠀⠀⠀⠀⠀⠉⠛⢦⣉⢰⡇⣾⠓⠊⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠈⢷⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠊⠈⠐⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⢻⢀⡾⣆⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠁⠀⠈⠀⠤⠀⠀⠀⡀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠸⢫⡜⣷⡆⡠⣴⢻⡇⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⡄⠁
⠀⠀⠀⠀⠀⠀⠈⠂⣠⣤⠀⠀⠀⠀⠀⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡴⢻⡇⣵⡏⢟⣵⢸⡷⢋⣼⠂⠀⠀⠀⠘⢄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⣤⣄⣿⣿⡀⠀⠀⠀⠐⢡⠀⢁⡀⠤⠄⠀⠀⠀⠀⠨⢾⠰⢟⡥⣧⢞⢹⣀⣴⠟⠁⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠁⠄⡀⠈⠀⠀⠀⢈⡀⠄⠂⠀⠀⠀⠀⠀⢹⣴⠏⡇⣡⣻⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠊⢡⡐⠋⠢⣀⠀⠀⣀⠔⠛⢀⡌⢱⠀⠀⠀⠀⡌⠀⠀⠉⠢⡄⠀⠀⢀⠔⠊⠁⠀⢱⠀⠀⠀⠀⣾⣿⣯⣕⠦⡀⠀⠀⢀⠔⠉⠀⠀⢡
⠀⠀⠀⠀⠀⢋⡝⠑⣬⠔⠙⢀⡐⠋⠢⣥⠊⢫⡙⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⢂⣠⠋⠀⠀⠀⠀⡰⠀⠀⠀⠀⢿⢻⣿⣿⡯⣙⣄⡐⠁⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠣⠁⠋⢑⣶⠚⠓⣶⡊⠙⠈⡜⠀⠀⠀⠀⠀⠀⢣⡀⡃⠀⠀⠚⠃⠀⠀⠀⠆⡰⠁⠀⠀⠀⠀⠈⢿⣫⢾⣿⡷⡺⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠹⡎⠁⣈⢹⡏⣅⠈⢱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠁⠀⢀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠈⠳⡨⢿⣽⣿⣔⡀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡍⣤⣤⣹⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡠⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡻⣿⣿⣇⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢞⣸⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢏⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡐⠉⠉⠑⠢⡀⠀⠀⢀⡤⠂⠈⠉⠑⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢣
⠀⠀⠀⣠⡖⠉⠀⠈⠉⠒⠴⣯⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠈⢆⢠⠊⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⢀⠄⠒⠉⠉⠉⢳
⠀⠀⠀⢓⡡⡀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈⠃⠀⠀⠀⣀⣠⣁⣶⡄⠀⠀⠀⠀⠡⠀⠁⠀⠄⠟⠁⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠙⢽⣢⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⡀⠣⡀⢀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠉⠚⠽⣢⠄⣀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠈⢻⣿⣿⠂⠙⢍⠁⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣀⡄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠟⡶⣤⠆⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠑⢄⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠞⠁⠀⠀⣀⣀⡤⡀⢰⣦⠀⠀⡆⡄⠀⣠⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⢀⣾⡟⠉⢣⡇⢼⣿⠀⠀⢹⠄⣰⡟⠀⣸⠃
⠀⠀⠀⠀⠀⢀⡴⢻⣿⠀⠀⠀⣾⣿⠀⠀⣼⠀⠸⣿⡇⢀⡇⠀⣿⡏⠋⠁⢀⡀
⠀⠀⠀⠀⢠⠎⠀⢸⣿⠀⠀⢠⣿⡇⠀⣰⠇⠀⠀⢿⡇⡼⠀⠀⠹⣇⢀⣠⣎
⠀⠀⠀⠀⠂⠀⠀⢸⣿⠀⢀⠎⢻⣷⣴⠏⠀⠀⢀⡈⠛⠁⠀⠀⠀⠀⠉⠙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⠞⠀⠀⠈⣉⣀⠀⢠⠋⣽⡆⠀⢀⣴⡾⣏⣆⡴⠋⣳⡄⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢰⠁⣿⢠⠇⢠⣿⡇⠀⣾⡏⠀⢸⠃⠀⣼⡿⠁⢠⣾⡟⢩⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡇⢸⣿⡿⠀⣼⣿⠀⢸⣿⠀⠀⡞⠀⢸⣿⠃⠀⣿⡟⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⠇⠀⣿⡟⠀⢸⣿⡀⣼⠃⠀⣿⡿⠀⡸⢿⡇⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠸⣿⠀⢰⣿⡇⠀⡎⠈⠛⠁⠀⠀⠘⠧⠞⠁⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠘⣿⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⠏⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣤⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣤⣀⠀⠀⠈⠻⣿⠿⠛⠁⣀⣤⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣶⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⣶⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡟⣻⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⣿⣿⡏⠀⠀⠀⠀⢹⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣯⣼⠿⢿⣿⣿⣿⣿⣿⣦⣤⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣅⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣨⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠈
⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⣤⣤⣤⠀⠀⠉⠙⠛⠿⠿⣿⣧⡈⠢⢰⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡄⠔⢁⣼⡿⠿⠿⠛⠋⠉⠀⠀⣤⣤⣤⠀⠀⢠⣤⣤⡄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⢿⣿⠇⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠸⣿⡿⠐⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⣴⣻⣷⣆⠀⡠⣾⣿⠿⢿⡦⠀⠀⢰⠁⠀⠀⠈⢂⡠⠁⠀⠀⠀⡀⠀⠀⠀⣠⣤⣤⣤⡀⠀⣠⣴⣶⣆
⠀⠀⠀⣿⣿⠀⠻⣿⡾⠋⠀⠀⠸⢀⠆⠀⠀⢀⠀⠀⠀⠘⠡⠀⠀⠀⡰⠁⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣿⣻
⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⣠⢞⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠈⠻⣷⡀⢀⡤⣘⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠢⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠙⠿⣯⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⣴⣤⣀⡀⠀⢀⢀⡄⣤⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⣀⣤⣄⡁⠀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠠⣄⢀
⠀⠀⢠⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣷⠀⠀⠀⢰⣿⠉⢿⣿⡾⠉⠙⢿⣷⠀⠀⠀⠀⠄⢹⡗⠚⠋⠀⠀⠲⠀⠢⠆
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⣿⣿⡏⠀⠀⠂⠸⣿⣆⠈⠉⠁⠀⣴⡿⠃⠀⠀⠀⠀⠠⣀⠠⠆⠈⡉⠑⠒⠓⠴
⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠉⠻⣧⠀⢀⣾⠟⠁⠄⠀⠀⠀⠀⠀⠘⢃⡐⢂⠈⠡⠈⡀⠁
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠘⣳⡿⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⢡⠎
⠀⠀⠀⠀⠀⠀⠙⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡀
⠀⠀⠀⢠⡾⠛⠛⢶⣄⡔⠋⠉⠙⢧⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢉⣀⠘⠁
⠀⠀⠀⣼⠀⠀⠀⠀⠁⠀⠀⠂⠀⢨⠀⠀⠀⠀⠀⡓⠀⠋⠀⠀⠀⡰⠀⠀⠀⠀⣠⠒⢶⣤⡎⠀⣸⠇⢀⣤⣤
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠠⠀⢰⡀⠐⠀⠄⢠⡀⠀⠀⠀⠀⢻⡄⠀⠉⠀⣿⡿⣶⣿⣿⣿⠁
⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠢⠀⠰⠀⠄⠀⡟⠀⠀⠀⠀⠀⠀⢻⣄⠀⢀⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠳⣄⠁⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢧⠎⠀⠙⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡚⣧⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠇⠀⠀⠀⠀⠀⠀⣀⠤⣶⠂⠛⣀⠒⢤⡀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⡬⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⡀⠉⠠⠀⠉⠀⠀⠋⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡔⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠛⠀⠀⠈⠀⠐⠗⠀⠀⠂⣠⣷
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢸⠑⠊⠁⠀⠀⠀⠀⣴⠄⠀⠀⢸⠀⠂⠆⠀⠀⢴⠄⠐⠀⡀⢀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠘⡜⠃⠀⠀⠄⠀⠀⠀⠈⢁⢮⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠘⠑⠒⡢⢄⡀⠀⠀⠀⠀⠀⠈⢺⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣔⠷⠀⠀⣶⠀⠀⠒⣥⢄⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡁⠀⠀⠸⠇⠀⠈⠀⠉⢦⡀⠀⠀⠀⠀⠀⠢⡀⠀⢈⢈⠇⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⣀⣀⡥⠖⠋⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠘⠟⠀⠀⠀⠀⠀⣀⠀⠠⣤⢧⠀⠀⠀⠀⠀⠀⠈⠀⠚⠣⠄⠀⠤⠆⠀⠀⠀⢠⠖⡸⠻⡽⡀⠀⠀⠀⠀⠀⠀⠎⡨⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠐⠀⠀⢠⡄⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠙⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣇⢄⠀⠁⠀⠀⠀⠠⠀⢠⣄⠀⡸⠀⠀⠀⠀⡀⠑⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡰⠆⠀⠀⣴⡆⠀⠈⠁⡴⠃⠀⠀⠀⠘⠄⠉⠀⠀⠀⠐⠟⡸⠀⠀⠀⠀⠧⣹⠴⠂⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣆⣀⣀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠿⠀⠀⠀⠠⢤⡜⢳⠖
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⠟⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⠄
⠀⠀⠀⠀⠀⠀⢴⢁⡦⠀⠀⠀⠀⠈⣓⡛⠁⠀⠀⠀⠀⠀⠀⠀⡰⠋⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠣⡎⣀⡽⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⡃⡇⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⢀⡸⠀⠀⠀⠀⠀⠀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠿⡗
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠛⠀⠀⠘⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢣⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⢀⣠⠔⠁⠀⠀⠀⣠⠲⡀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢉⣿⡿⡟⠒⣄⠀⠀⠀⠀⠑⣄⠃⠀⠀⠀⠀⠐⠠⢀⣰⡂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠻⣤⠖⠀⠀⠀⠀⠘⠲⠔⠚⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠉⠒⠒⠁
⠀⠀⠀⠀⠀⢮⠈⠆⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣸⠚⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠰⠇⡸⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠂⠈⠉⠀⠐⠂⠄⠀⠀⠀⣠⣴⠟⠀⠀⠀⠀⠀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⢀⠀⠠⡇⠀⣼⡟⠻⣿⣶⣄⡀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢠⠔⠀⢀⠀⠀⠀⠀⠀⣠⢔⠥⠀⠀⠇⠀⠙⡇⠀⠬⣝⢿⣿⣦⣀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢀⠇⠀⠀⢰⠤⣀⠀⠈⡡⠾⠀⠀⠔⠂⣣⠀⢀⠁⠐⠄⠀⠀⠿⡟⢻⣷⣤⡀⢼⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡳⣀⠀⠀⢣⠀⠀⠀⠀⢴⠇⠀⠀⡇⠀⠀⠀⠀⠀⣡⣾⣿⣿⡏⠢⣍⠲⢄⡀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡇⠈⠑⡶⠋⠀⢒⠦⣄⡔⠀⡠⢴⠳⣄⣀⢤⡖⠂⢘⡿⠟⠋⠈⢑⢞⠛⠒⠁
⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⣿⡒⠊⠀⠀⢠⠋⢻⣿⣿⣿⡆⠈⠳⢌⠢⠈⢣⠔⠋⠀⠀⠀⠈⠉⠉⠉⢣
⠀⠀⠀⠀⢠⣾⣿⠀⢠⢠⣿⡇⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⠉⢸⠀⢲⠢⠤⠤⠐⠀⠄⠀⠀⠚⡆
⠀⠀⠀⠀⣾⣿⣿⢀⣾⣿⣿⡏⠒⠒⠒⠊⠁⣼⣿⣿⣿⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⣿⣿⣧⣾⣿⣿⣿⠃⠀⠀⠀⠀⢰⣿⣿⣿⢻⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⣿⣿⣿⡏⢸⠀⠀⠀⠀⠀⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣀⠠⠿⠟⠋⠁⠀⠀⠉⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⣿⣿⣿⣿⡿⠟⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢱⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢠⡞⠀⠀⠀⠀⠀⠀⠹⣆⠀⣠⠇⠀⠀⠀⠀⠀⠀⠸⡄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣌⣫⣍⡀⠀⠀⠀⠀⠀⠀⣴⠞⣛⣥⡀⠀⠀⠀⠀⠀⠀⣀⣩⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⠑⠚⢿⠀⠀⠀⠀⠀⠀⣯⠉⠉⠙⡏⠀⠀⠀⠀⠀⠀⣻⠳⠾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠒⠶⢾⠀⠀⠀⠀⠀⠀⡏⠉⠓⠲⡇⠀⠀⠀⠀⠀⠀⣿⠲⠦⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣄⣀⣸⠀⠀⠀⠀⠀⠀⡿⠢⣄⣀⣯⠀⠀⠀⠀⠀⠀⣿⣄⡀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⢻⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⡿⠀⠀⠀⠀⠀⠀⣿⠀⠉⠒⢿
⠀⠀⠀⠀⠀⢀⡴⠢⣤⣀⠀⠀⠀⣀⣀⣀⣿⣦⣄⣀⣸⣄⣤⣤⣤⣄⠀⡿⢢⣤⣤⠷⠤⣤⣀⠀⠀⣀⣿⣄⡀⠀⣸⠀⣀⣀⣤⣀⡀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠉⢳⣴⠛⠉⠉⠉⠉⠑⣦⡝⠋⠁⠀⠀⠀⠈⢻⣧⡞⠉⠀⠀⠀⠀⠉⢧⡞⠉⠀⠈⠙⢿⣿⡞⠉⠁⠀⠈⠙⣦⠞⠉⠉⠉⣷
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⣷⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⠷⣄⣀⣀⣀⣾⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠉⠀⠉⠛⠲⠤⠴⠚⠋⠉⠓⠤⠤⢄⣤⠤⠞⠋⠙⢦⣀⣀⣀⣀⡤⠞⠻⢤⣀⣀⣠⠞⠉⠓⠦⠤⠴⠋⠀⠈⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⣤⣄⡀⠀⡇⠀⠀⢀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡼⠋⠀⠀⠉⠛⢧⣤⠞⠁⠀⠀⠀⠀⠈⠻⣄⣠⠶⠛⠋⠉⠉⠉⠛⢶⡄⢀⡴⠚⠋⠁⠀⠈⠉⠻⣆⣠⠶⠊⠙⠋⠑⠶⣄⣠⠶⠚⠛⠛⠛⠛⢶⣜⡶⠞⠋⠙⠶
⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠟
⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢀⣼
⠀⠀⣟⠉⠉⠓⠚⠋⠙⠶⢤⣤⣤⣤⣤⡤⠖⠲⢦⣤⡀⠀⠀⠀⣀⣤⡴⠖⢶⣀⠀⠀⠀⠀⠀⣀⡤⠾⣄⡀⠀⠀⠀⣠⠞⠳⣤⣄⣀⣠⣴⠏⠀⠙⠒⠒⠚⠉⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠑⠒⠶⠖⠊⠉⠀⠀⠈⠉⠓⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⡞⠛⠛⠳⢦⡀⠀⢀⣀⠤⠤⠦⠤⣤⡀⠀⢀⣀⠴⠶⠶⠖⠶⠦⣄⠀⠀⣀⡴⠆⠛⠛⠓⠶⢦⡀⠀⣠⡤⠤⠤⢄⡀⠀⠀⢀⡤⠶⠶⠶⠦⣄⠀⢀⡤⠦⠤⣮
⣯⠀⠀⠀⠀⠀⠙⣶⠋⠁⠀⠀⠀⠀⠀⠙⠷⠛⠀⠀⠀⠀⠀⠀⠀⠈⢣⡼⠋⠀⠀⠀⠀⠀⠀⠀⢹⡾⠁⠀⠀⠀⠀⠙⣦⡼⠋⠀⠀⠀⠀⠀⠘⣷⠋⠀⠀⠀⠈
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠
⠀⠈⠛⠲⠶⠤⠤⠶⢦⣄⡀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⢀⡜⠛⠶⣤⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠉⠛⠓⠶⠶⠶⠞⠛⠁⠀⠈⠳⠆⣀⣠⣠⡴⠞⠋⠈⠛⠶⠦⠤⠶⠛⠁⠀⠙⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈