Sneezing Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⢀⠖⠉⠉⠱⡤⠔⠂⠀⠒⠠⣀⡠⠐⢤⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⢈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡀⠚⠀⠘⠠⠴⠘⠉⠙⠠⠤⠆⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠀⠀⢀⣀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⡆⢀⠔⠐⡶⠐⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠠⠄⠀⣀⠀⠘⡇⠀⠞⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠛⠺⠁⠀⢠⠔⠂⠄⠀⠀⡬⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡆
⠀⠤⠀⠀⠀⠀⠘⠀⠠⠀⠀⠇⠀⢠⠜⠣⣀⡀⠀⣀⡀⠀⠤⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠐⠆⠁
⠀⠀⠀⢀⠀⠀⠀⢣⠘⠂⠀⠈⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠰⢎⣉⠀⠀⠀⠀⠀⠀⠀⢱⠒⢆⡀
⠀⠐⠊⠁⠀⠀⠀⠀⠉⠳⡀⠀⠀⠃⠀⠀⡸⠂⠀⠐⣤⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⡀⠀⠀⢀⠔⠀⠲⡀⠀⠀⠀⡈⠀⢠⠇
⠀⠀⠀⠀⢀⠤⠀⡦⠀⠀⠱⡀⠀⡌⠀⠞⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⡀⠀⠀⠀⢛⡀⠀⢀⠇⠀⠀⢀⠷⠐⠹
⠀⠀⠀⠀⡏⢀⠌⠀⠀⠀⠀⠈⣎⣀⠀⣀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡀⢡⠀⠀⠈⢢⠀⠀⠜⠈⠉⠁⠀⠀⢀⠎⠀⢀⠆
⠀⠀⠀⠀⠉⠁⠀⠀⠀⡀⠀⠀⠀⠈⠙⢻⡦⠄⢀⠘⠆⠀⠀⠀⠀⠒⢄⡀⠙⢣⠀⠀⠀⢳⠈⠀⠀⠀⠀⠀⡠⢊⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠂⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣄⣀⠀⠀⠀⠀⠘⠶⠆⠀⠀⢴⡀⢠⠀⠀⣀⠠⠊⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢇⡰⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋⢈⠉⠙⢆⠐⢒⡀⠀⠀⠀⠀⠹⠾⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⡈⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠙⠳⡄⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⡀⠀⣠⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢠⠁⠀⠈⠛⠀⠐⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⠀⠉⠉⠀⠐⢆⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠒⠒⠒⢚⠃⠀⠀⠀⠀⠰⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⢀⣀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢢⠄⠀⠄⠐⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⣀⢆⠀⠀⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠁⠈⠉⠀⠀⠦⣀⣀⡠⠔⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⢀⡤⡞⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠣⡀⠀⠀⢀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡍⠓⠦⣀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡒⠒⠒⠒⠶⠦⠼⠦⠄⠈⠛⠁⠓⢺⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡒⠊⠉⣉⣁⡀⠀⠀⣀⡤⠖⠒⠒⠛⢳⠂⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠊⠁⠀⠙⠒⠋⠀⠀⣀⣀⠀⠀⠨⣟⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠐⠛⠒⠀⠀⠀⠀⠊⠉⠉⠁⠀⠘⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠬⢏⢢⣄⠀⠀⠀⢀⣠⠖⠲⠀⠀⠀⢨⠇⣰⠷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⡄
⠀⠀⠀⢀⢀⣠⠔⠚⠉⡀⠀⠀⠐⣗⣉⠁⣀⣀⡄⣈⡃⠀⠀⠀⠀⠀⢸⣸⠁⠏⢠⠇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢱⠊⢠⣇⢤⡀
⠀⠀⠀⣾⠋⠀⠀⠀⠐⠳⠤⠤⣤⢷⠀⠗⠊⠛⣉⣁⡽⠂⠀⠀⠀⠀⠈⣡⠞⠉⠁⠀⠀⣤⠀⠉⠉⠙⠛⠒⠒⠒⠒⢶⠚⠛⡇⠀⡰⠋⢀⡼⠁
⠀⠀⠀⠹⣄⠀⠀⣀⠀⠒⠀⠀⠀⠸⡀⠀⠀⠠⢴⣎⣀⣀⣀⣀⣀⡴⠞⠉⠐⠒⠲⠤⣄⣀⠀⠀⠛⠀⠀⠀⠀⠀⠉⣹⠀⠀⢹⠀⢠⣖⠉
⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣉⡀⠀⢧⠱⢤⢲⡖⠉⠀⠀⠈⠉⢡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⣀⠀⠐⠶⠀⣿⣄⡤⠾⠤⣀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡟⠛⠚⠋⢰⡇⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠼⠃⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⠁⠀⠀⠀⢈⢰⡀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⡔⠢⠔⣹⠁⢠⠃⠀⠀⠀⡔⠊⠈⠙⡆⡞
⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⡇⡎⠀⠀⠀⠀⠙⠧⠠⠋⡰
⠀⠀⠀⠀⠀⠀⠉⠙⠚⠉⠀⣷⢤⡤⣤⣤⣤⣤⡤⢶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢓⡖⠒⢶⡳⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢹⠀⠀⠙⢻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢇⠠⣖⡉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡘⡆⠈⠥⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣱⣄⣀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠙⣏⢣⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢁⣙⣲⣇⡻⠀⢇⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⡜⠉⠀⠀⠈⠣⣇⠏⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⣄⣧⡀⠀⠀⠀⠀⠁⠀⣀⡴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣈⠙⠓⠒⠶⠒⠛⣉⣡⠴⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⢀⡀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠦⠶⠈⢙⣫⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⢠⠄⢀⡤⠖⠃⣀⡤⠤⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠃⠀⠀⣠⢿⡆⠀⠀⠀⣛⣠⠄⠀⠀⣀⣤⠤⠀⠀⠀⠀⠀⠐⠚⠛⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠞⠁⣸⠇⠠⠄⠈⠁⠀⣀⠀⠀⠀⣀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⢰⣡⡴⢛⣁⠒⠂⣤⠀⠉⠉⢩⢤⣤⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠙⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣄⠀⠥⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⠈⢷⡄⢤⠀⠀⠈⢙⡓⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣸⡇⠀⢀⠐⠦⠄⠉⠛⠀⠀⠀⠀⠈⠓⠲⠶⠄⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠉⠀⠀⠈⠙⠦⡀⠐⠲⢤⡀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠃⠀⠀⠀⠈⠉⠓⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠈⠑⠀⠀⠉⠛⠂⠀⠀⠀⠘⠲⢤⣀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⣤⣄⣀⠀⠀⠄⠠⢚⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠻⠆⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣧⣂⣯⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣤⣀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⡿⠖⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠋⠁⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠇⠀⠀⠸⠟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⡇⠀⠀⠀⢠⣶⠀⢰⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠛⠁⠈⠛⠀⠘⠛⠀⠀⣴⣾⣿⣦⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⡇⠀⠀⠀⠰⠿⠀⠰⠷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⣀⡰⠊⠉⠑⠦⠔⠂⠀⠒⠤⣀⡤⠢⢄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⢄⣀⡠⠔⠤⢀⣀⡀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⡀
⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⢀⠁⣠⠐⣠⠄⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠆⠀⠀⠀⠀⠀⠈⢣
⠀⠠⠀⠀⡀⠀⢲⠁⠰⠁⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠸⠓⡇⠀⢀⠔⠂⠄⠀⠠⡽⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢰
⠐⠐⠒⠀⠀⠀⢃⠀⡇⠀⢇⠀⢠⠚⠢⠠⠀⠀⠤⠀⠐⠐⠒⠀⠄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠰⠈
⠀⠀⢀⡀⠀⠀⠈⢄⢃⠀⠀⠉⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠺⢯⠀⠀⠀⠀⠀⠀⠀⢹⠑⢢⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠁⠀⢀⠜⠁⠀⠱⠆⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⢄⠀⢀⡐⠀⠈⢢⠀⠀⠀⡄⠀⣸⠁
⠀⠀⠀⢀⡔⠊⡜⠀⠀⠈⠢⣀⠆⠀⠁⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠖⠉⠑⢄⠀⠀⠀⡧⠀⠠⠊⠀⠀⠰⠃⠀⡘
⠀⠀⠀⠸⠄⠜⠀⠀⠀⠀⠀⠓⠠⣤⣦⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠱⡀⡜⠀⠀⠀⠀⠀⡠⢁⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⡠⢠⠄⠀⠀⠀⠀⠘⠋⠀⠠⠨⡅⠀⠀⠀⠀⠑⠢⣀⡐⠀⠀⠀⠃⠀⠀⠀⠀⣠⠞⠐⠉
⠀⠀⠀⠀⠀⠀⢰⠀⡈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠖⠶⠠⡄⠀⢠⠉⠁⠀⠀⠙⣤⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠦⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⠀⠀⠈⠂⠘⠃⠀⠀⠀⠀⠈⠀⠢⡀⠀⠀⠀⠰⢄⠀⠀⠀⠢⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⢀⡰⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠄⠀⠀⠉⠁⠀⠒⠒⠒⠒⠒⠒⠀⠀⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠘⠦⠤⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡓⠤⢀⣀⣀⣀⣀⠂⠀⠀⠀⢀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠒⠀⠀⠒⠛⣄⠀⠀⢀⡀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢘⡌⠁⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠒⠂⠐⠒⠉⠙⣄⠀⠀⣠⠞⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⢀⣠⡜⠀⠉⠉⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢃⠀⠀⠀⣠⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣤⣀⠀⠀⠨⠙⢦⠀⠀⠈⠓⠀⠂⠀⠀⠠⠀⠀⠀⠀⢀⣀⠸
⠀⠀⠀⠀⠀⢹⠛⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠐⡿⣶⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡰⡄⠀⠀⠠⣄⣀⠀⠀⠀⢀
⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠙⣀⠘⢂⠨⣦⠉⠐⠦⢄⠀⠀⠀⠘
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⣀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠈⠠⠤⠀⠳⡈⠁⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠸⢀⡆⠀⠀⠀⠈⠉⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⢂⠀⠀⣌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⢀⣀⠀⠀⠀⣤⡋⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠑⡀⠈⡆⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢣⠀⠀⠀⠀⠉⠘⠢⢀⠛⢄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠘⡤⠃⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠑⣄⠑⣀⣀⠏⠀⠄⠺⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠉⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠂⠐⡰⠂⠈⠑⠢⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢤⣄⣌⣹⣧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⣀⣤⣤⣤⣀⢄⠀⠀⠀⠀⠀⠀⡄⠊⢁⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⢀⡄⠀⢦⣈⣆⢷⣶⡿⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⠄⠀⠀⠀⠀⠢⡈⠓⢠⠙⢍⠟⡛⢷⠢⠔⢠⣾⡟⠁⠀⠈⢿⠙⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠚⠀⠀⠸⠿⠦⠔⠊⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠿⢿⣿⠯⠥⠐⠊⠙⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⢉⠀⠀⣁⠤⠀⠀⡠⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⡥⠀⠈⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣁⣀⡉⠔⠂⠀⠀⠀⠀⠤⡀⠊⠀⠈⠀⠀⠀⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⢤⣤⣴⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠁⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠄⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠿⠿⠿⠿⠷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠙⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣧⣀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢀⣀⣀⣀⣀⣠⣤⣤⣶⡾⠟⠛⠉⠀⠈⠻⣷⣤⣄⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠈⣿⡟⠛⢿⣏⠉⠁⠀⠀⠀⠀⠀⣀⣄⠀⠀⠉⠙⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⡇⠀⠈⠋⠀⠀⠀⢴⣶⣶⠿⠟⠁⠀⢻⣧⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⣷⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⣶⡄⢀⣹⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄⡀⠀⠀⠀⠘⠃⠀⠀⠻⠿⠟⠀⠀⠀⠀⠈⠉⠉⠁⠀⢸⣿⠙⣿⡇
⠀⠀⠀⠀⠀⣴⡿⠿⠆⠈⠙⠻⢷⣶⣦⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣾⣿⣤⣿⣇
⠀⠀⠀⠀⠠⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣦
⠀⠀⠀⠀⠰⣿⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⠿⠿⠿⠿⠿⠛⢻⣿⠿⠿⢶⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣠⣾⠟⢻⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠈⠉⠉⠛⠛⠛⣿⣿⢿⣿⡶⠶⠀⠀⠀⢀⣿
⠀⠀⣼⡿⠁⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⣀⣀⣀⣤⣴⣾⠟⠁⠀⢻⣧⣄⣀⣠⣴⣾⡏
⠀⣼⡟⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⢉⣿⡟
⢠⣿⠁⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⣿⣇⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠈⣿⣷⣦⣄⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⢿⠇⠈⠙⠻⠿⣶⣦⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠁⠀⠋⠘⠛⠣⣄⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠆⠀⠀⠠⠦⠀⠀⠀⠀⢈⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠁⣀⡠⠤⠀⠒⠒⠒⠄⠀⠀⠀⠀⠀⠰⠀⢀⠀⣀⣠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠀⠀⠀⠐⠂⠀⠀⠰⢂⠀⠀⢀⠔⠁⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⠉⠹⣀⣀⠀⠀⢀⣴⠣⠀⠳⢄⠁⠈⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡜⠖⠉⠀⠀⠀⠘⠜⠀⠀⠀⠒⠉⠊⠈⠢⢒⠐⠀⠉⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠬⠀⠀⠀⠀⠀⢀⠃⠅⠀⢰⠀⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡒⠉⠁⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠵⠱⠤⠄⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠊⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡰⠛⠶⠋⠈⠛⠉⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠘⡆⠀⠘⣄⡠⠖⢢⡤⢤⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠸⡄⠀⣼⠀⠀⠀⠀⠸⢄⠀⠀⡀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡀⢿⠀⢀⠀⠀⠀⢸⣆⣞⡝⣆⠀⠀⠘⣆
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠚⠂⠀⠀⠐⣿⢛⣡⠏⢳⡀⣰⠋⠳⡄
⠀⠀⠀⠉⠉⠉⠉⠉⠛⠓⠒⢀⡤⠤⠶⠶⠾⠤⢤⣀⣀⠀⠀⠀⠀⠀⢦⠀⠉⠁⠀⠀⢙⡶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠦⢤⣸⣆⠀⠀⠀⣠⢎⡴⠃⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠚⠶⠯⠤⢤⣀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⢯⠉⡏⠉⠀⠀⠀⠀⠀⠳⢤⣀⣤⠸⡄⡆⣿⣆⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣷⣷⠛⢎⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠈⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⣉⡙⠢⡄
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣦⡀⠀⠖⢋⢳⠳⣀⡀⠀⠀⠀⢀⠀⠶⠀⠀⡞⣤⣴⠒⠿⠧⠱⣄⠸⡄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠿⠙⠻⣿⣖⠛⡌⠈⠀⠁⡃⠀⠀⠀⠙⠁⠶⠒⠀⢻⠉⢢⢠⠰⠎⠀⠈⠚⢧
⠀⠀⠀⠀⢸⣿⣿⠉⢡⡀⣐⣧⣠⡃⡜⢣⠀⠑⠀⢠⠠⠶⠒⠒⠒⢒⣚⡑⠀⠸⡴⢿⠯⠀⠀⢢⢀⡖⠋
⠀⠀⠀⠀⠀⡿⠛⠤⡼⡫⢑⡠⢄⢙⠃⠀⠹⠂⠉⠉⡄⠀⠀⠀⠉⠡⡄⠀⠀⣀⠑⢄⣉⣓⣀⠤⡞⠋⠋⠒⠢⢄
⠀⠀⠀⠀⠀⠘⠒⠢⣇⠨⠄⢒⣡⡎⣀⡀⠀⡇⠀⠀⢇⠀⠀⢀⡠⠀⢀⡠⢚⠕⠀⡠⠊⠙⢤⡠⠃⠀⠀⢀⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠻⣍⠀⣴⣷⠀⠀⠉⠁⠀⠀⢸⠀⠀⠈⢉⠴⠋⠐⠁⢠⠎⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⡄⠀⠘⡆
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⡸⠉⠛⡇⠀⣀⣀⣀⡠⠊⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⣰⣙⡆⠀⠀⠀⢀⡠⠴⢥⣀⡼
⠀⠀⠀⠀⢰⠁⠀⠰⠒⠉⠀⢱⠀⢠⠃⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣏⠀⡀⣷⠀⠀⠀⣯⣤⣠⡠⠊
⠀⠀⠀⠀⠈⢇⠀⠀⠀⢀⣠⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠑⠲⢤⡀⢠⡆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣆⠙⠛⠒⠒⠒⠒⠷⠤⠀⠙⠃⠓⠺⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⡉⠉⢀⣀⣀⠀⠀⣀⠤⠖⠊⠉⠉⢹⣇⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠁⠀⠀⠙⠋⠀⠀⣀⣀⡀⠀⠀⣿⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠉⠂⠀⠀⠀⠈⠁⠀⠁⠀⠀⡷⠀⡎
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⢸⣌⣶⠄⠀⠀⠀⣤⡚⠉⠂⠀⠀⠀⡏⣰⢟⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⢶⡀
⠀⠀⠀⣀⣠⠖⠋⠉⠠⠀⠀⠀⢸⠏⢤⠠⣤⣴⣠⢬⡀⠀⠀⠀⠀⠰⣴⢃⣙⡠⠇⠀⠤⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡇⠟⠀⣼⠴⣦
⠀⠀⠀⣿⠁⠀⠀⠀⠉⢓⠒⠢⠞⡗⠈⠉⠁⠠⠤⡴⠋⠀⠀⠀⠀⢀⣠⣎⠀⠀⠀⠀⠲⠀⠀⣀⠀⠉⠉⠉⠉⣉⣿⠉⠉⡇⠠⠞⢀⡴⠋
⠀⠀⠀⠙⠦⣀⠐⠦⠀⢉⡄⠀⢠⠰⡀⠀⠐⣒⠿⠤⠤⠤⠤⢤⡶⠋⠀⠀⠀⠉⠓⠲⠤⣄⣀⡁⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠰⢯⡀
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⣤⣌⣧⣙⣯⡿⣀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⡘⠋⢠⠗⠒⠚⠉⠒⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣰⠃⠈⠁⠀⣿⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠋⢠⠃⠀⠀⠀⢀⡇⠶⣄⢀⠎
⠀⠀⠀⠀⠀⢰⡉⠉⠁⠧⡀⡎⠀⠀⠀⠸⣅⠀⢠⠜⡜
⠀⠀⠀⠀⠀⠘⠥⣄⡤⠔⢹⣇⠀⠀⠀⠀⠈⠛⢃⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣯⣹⣙⣋⣹⣉⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠲⡄⠈⠓⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢱⠀⢀⡤⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢇⠘⢖⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⡄⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⡄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡿⣷⢻⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠦⣽⢸⡇⢡⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡔⠋⠉⠉⠻⣽⣸⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣸⡀⠀⠀⠀⠀⠘⠁⠀⣀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢏⠙⠒⠦⠤⠤⠶⠒⢋⣡⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣑⣒⣒⣒⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣾⣿⣿⣿⣷⣶⣾⣖⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⡳⣆⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠺⠛⠉⣩⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡯⠁⠀⢘⣛⣿⣿⣟⣱⣯⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢠⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣋⣔⡥⠊⠁⠀⠈⠙⠛⠋⠸⣿⣿⣿⡿⣿⣖⠻⢥⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠙⠛⣫⣴⣿⣿⠟⠋⠀⡾⡱⣋⣤⣶⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣷⡏⣥⠤⣄⠈⢿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⠉⢹⠿⠃⠙⠈⠀⠈⡇⣾⠙⠫⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⢀⣀⠤⠀⠀⣀⣤⣴⡖⠀⠀⠀⠀⠀⠀⠘⠃⠹⡄⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⢠⠏⣠⣴⡶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣰⡏⠀⠈⠾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠙⢦⡘⣾⡿⠁⠐⠐⠚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠟⠀⠀⠀⠀⢀⡝⢃⣤⡖⠚⠋⠉⠉⠛⠒⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢰⠋⠀⢹⠀⠀⠀⠀⠀⣀⡤⠼⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠈⢀⡰⣏⠀⠀⣠⠶⠛⢁⡰⢶⣿⣿⢷⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠻⣤⠚⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠰⠟⠀⠀⢀⡙⠒⢒⠋⡠⠈⠱⠞⢅⣠⠄⢁⡴⠙⢡⡟⠀⠻⠀⠀⠀⣸⢀⡀⠀⠀⠀⠀⠙⠆⣾⠀⣶
⠀⠀⠀⠀⢀⣀⠀⠀⠾⣛⡀⠀⢀⣠⢖⡿⢋⠜⡵⣿⣥⠀⠀⠀⠀⠉⢠⡟⠀⣰⠟⠀⠀⠀⠀⠀⠀⣟⣾⠃⠀⠀⠀⠀⠀⣼⠃⢠⢟
⠀⠀⠀⠀⠈⠱⠖⠀⣶⢏⣡⠖⢋⡴⠋⠰⢫⠞⠸⠁⢁⣀⠌⠳⣄⠀⠺⣤⠾⣅⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⡼⠁⢠⠏⡾
⠀⠀⠀⣠⡀⡶⢀⣸⠟⠋⣠⠞⣩⢴⠀⣴⣋⣤⠶⠞⢁⣀⠀⢰⡏⠀⠀⠀⠀⠘⢷⣀⠀⠀⢀⡴⠋⠻⣄⣀⡀⠀⢀⡞⠁⢠⢏⡾⠁
⠀⠀⠀⢈⣽⠗⡋⢶⣤⠞⠁⢰⡙⢬⡿⠏⠾⠶⣮⠉⠉⠁⢰⡏⠀⠀⠀⣀⣀⣀⡀⠉⠛⠚⠋⠀⠀⠀⡴⠋⠉⢳⡞⠀⢠⠏⡼⠁
⠀⠀⠾⠋⠀⣀⡵⢋⠁⢄⣴⠊⡹⠯⣄⣀⠀⠀⠘⠷⢤⣤⣄⣙⠛⠛⠉⠉⠀⠀⠉⡇⠀⠀⠀⠀⠀⣾⢁⣀⢀⡞⠀⠀⠃⡼⠁
⠀⠀⠀⣠⠾⢋⡀⢸⠀⢸⣇⡞⠁⠤⠀⠘⠛⠳⣤⡀⠀⠀⠀⠉⢻⣆⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠉⠁⠀⢹⡃⠀⠀⣸⠃
⢀⣴⠿⡿⠳⢟⡅⢸⠀⣼⠿⣉⣩⣭⣤⡤⠴⠒⠻⠋⠀⠀⠀⠀⠈⣿⡀⣴⠋⠉⠀⢐⡶⢲⡶⠀⠀⠀⠀⢠⣾⣀⣀⡀⠏
⠛⠁⠀⢀⡴⢋⣄⢸⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠛⠶⠒⣚⡥⠞⠉⠀⠀⠀⠀⠀⠀⢀⡏⠈⢻⡆
⠀⠀⠀⠉⠀⠈⠱⠋⠈⠛⢶⡶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢾⣥⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⢘⣷⠦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⠉⠛⠛⠿⢶⣶⣶⣦⣼⣧⣼⣯⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⢦⣤⠤⠀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣶⡓⢟⣡⡶⠟⠋⠁⠀⠀⠀⠀⠈⠉⠓⢶⡟⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢠⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧⣤⣤⣭⣤⣤⣀⣘⣧
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣁⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣤⣷⣆⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢲⡷⠖⠛⠉⠋⠉⠸⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⠊⢸⠈⢆⠇⡒⢹⡅⠠⠄⣨⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠔⠁⠀⠈⠀⠀⠣⡍⠂⣂⡰⢺⣭⡓⣷⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣀⣠⣼⣦⣼⣶⡞⣽⢻⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⣿⠛⠛⠛⠉⢉⠉⣻⣆⡎⢻⢯⣙⣟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡱⠃⡇⠱⡀⠁⠀⠠⠤⡦⠉⡽⢿⣶⡹⣾⡆⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠎⠀⠀⠇⠀⠘⢎⠀⠀⠀⠉⢏⠛⣿⡈⢻⡻⣾⡂⠈⢆⠀⠀⠀⠀⠀⣀⣤⡴⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠁⠀⠀⠀⠀⠀⠀⠀⢣⡄⠨⣧⡴⢯⣽⡙⣦⣽⣼⠈⠛⠪⢧⡠⡴⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣤⣤⣤⠤⠴⢶⣳⣾⣿⢥⡥⢿⣶⠊⢿⡿⣄⢀⢄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢹⣟⠚⠛⡛⠛⠉⠩⠉⠋⣿⠯⣉⣽⡇⣳⣞⠷⣧⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠞⣸⠀⠣⡀⢈⠀⠀⠀⢼⣟⣃⣳⡚⣿⡿⣧⣼⣿⢿⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⢞⡴⠃⠀⣿⠀⠀⠱⣄⠆⠀⠀⢈⠜⢿⠉⠳⣾⣇⡙⢿⡛⢿⣄⡁⠱⡄⠀⠀⠀⣀⣠⣴⠶⠋⠃
⠀⠀⠀⠀⠀⠼⣡⠞⠀⠀⠀⠛⠀⠀⠀⠈⢦⡀⠀⣹⣄⣈⠵⣋⣿⡟⢦⣈⡿⡌⡇⠈⠑⠻⠄⠚⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣷⣄⢀⡏⡇⠏⢧⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠈⢿⣿⡄
⠀⠀⠀⠀⢸⣿⡿⠿⠋⢉⡄⢙⠛⢧⡘⠀⡀⠀⡇⠀⠀⠀⠀⠀⢤⠄⠀⢻⠛⠆⡆⠺⠀⠀⠉⡇
⠀⠀⠀⠀⢸⣿⡃⠈⡦⢖⠛⠚⢤⠁⠑⣄⠥⠤⡇⠤⠤⠐⠒⠒⣒⡒⠀⠘⡄⠠⡒⢢⠀⢠⣿⣿⣂
⠀⠀⠀⠀⠀⢆⣀⣩⠈⣒⠨⢔⠜⠀⠀⢰⠀⠀⠁⠀⠀⠀⠈⠁⠄⠀⠀⡀⢾⠂⠙⡗⠊⡍⠁⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣉⠴⡖⠒⣩⣆⠀⠐⠚⠀⠀⢸⠀⠀⠀⣠⠀⢀⠴⡪⠂⡼⢄⣀⠏⠉⠀⠀⠀⠐⢄⠀⠘⡄
⠀⠀⠀⠀⠀⡰⠊⠀⠀⠈⢰⠛⠿⡀⠀⠀⠀⢀⡰⠀⠀⠀⣀⠔⠁⠈⠀⢰⠁⠀⡸⢆⠀⠀⠀⠀⣀⣼⡀⢀⠇
⠀⠀⠀⠀⢸⠀⠀⠔⠊⠉⢡⠀⢠⠃⠈⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠁⢸⠀⠀⠀⣎⣄⣀⡽⠋
⠀⠀⠀⠀⠸⡀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⣧⣄⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⢚⣛⣫⣭⢽⠼⠶⠻⣆⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⢹⢿⠋⠡⡀⠀⠀⡆⡀⠀⠙⠂⢀
⠀⠀⠀⠀⠀⠀⡰⢋⡔⠁⣿⠀⠳⣄⢧⡐⠢⢽⠌⠐⢠⡄⣀⡱⣄⡀
⠀⠀⠀⠀⣠⠞⡰⠋⠀⠀⠻⠀⠀⠙⢎⠙⠢⡈⡏⢂⣤⣶⠋⠳⣼⣇
⠀⠀⠀⠜⣡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⠀⢳⡞⠠⣼⡷⣦⠤⣽⣦⣨⡶⠟
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠴⠿⣶⣲⣿⣿⡍⣳⣆⣿⣿⢋⠁
⠀⠀⠀⠀⠀⠀⢀⣀⢲⣾⠷⠿⠿⠛⠛⠋⠉⠉⢻⣎⣐⡌⣻⣿⡀⠳⡟⠧⡀
⠀⠀⠀⠀⢀⡴⢁⡼⢸⡟⢆⠀⠐⠂⠀⠀⠓⢀⡃⠻⡍⢦⣼⣀⡹⢆⣙⣇⠸⣆
⠀⠀⠀⣠⠎⣠⠏⠀⣸⡇⠈⢣⡀⢠⠀⠀⠑⠺⣿⣡⣩⣎⣿⡿⣧⣼⢿⠻⣀⠘⢢
⠀⢀⡞⢡⡞⠁⠀⠀⠼⠄⠀⠀⠹⣜⠂⠀⠀⠀⠀⢛⡈⠛⣾⣅⠈⢫⠛⢿⣍⡁⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⣤⢄⠐
⡐⠫⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣸⣆⣀⣵⡋⣹⡟⢧⣀⣻⡀⡣⠉⠳⠦⣽⡄⢀⣠⣴⣶⠽⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣀⣥⣾⠏⠠⢴⣾⣏⡉⢻⡿⣭⣧⠀⠀⠀⠈⠙⠁⠉⠁
⠀⠈⠀⠀⢀⣀⣠⠶⢶⣶⣚⣛⣛⣋⣩⣭⣽⣷⣿⣟⣿⣋⣿⡝⢣⠀⠙⣏⢻⡆⣠⢎⠔
⠀⠀⣀⠤⡎⣿⣟⠛⠛⠉⡉⠉⠉⠁⠠⠄⠈⠉⣯⡹⢬⣃⣽⡗⢈⡷⣟⠹⢻⣖⣳⡏
⢀⡴⢋⣴⠃⣿⠈⢣⡀⠀⢩⠀⠀⠂⠠⠀⣳⡶⠒⠳⣤⠞⣿⣿⣿⣅⣹⣷⣿⣟⠀⠣⡀
⠞⣡⠞⠁⠀⣿⠀⠀⠙⣄⠀⡆⠀⠀⠀⠸⠛⢳⣾⠟⢻⣆⣿⡯⠬⢿⣿⣽⣧⣽⠀⡄⠘⢆
⡼⠋⠀⠀⠘⡟⠀⠀⠀⠘⢧⡸⠀⠀⠀⣠⡎⠈⢹⣆⠀⣙⣿⣧⡤⠀⢹⣄⡉⢻⡆⠤⣄⠈⢆⠀⠀⢀⣀⣠⣤⡶⠿
⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠳⣄⡄⠀⣈⣳⣀⣀⡸⢞⣡⣿⡟⠙⣦⣀⡝⣧⠈⡇⠀⠀⠉⠛⠦⠘⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⢉⡭⠻⡉⢀⣼⣯⣿⣿⡍⠹⢏⠻⢏⣻⣷⠀⣠⢆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠤⢤⣽⡾⠗⢸⣿⣧⡼⠅⠨⢧⣬⣽⣿⣴⣣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⢿⢻⣾⡟⠹⣶⠥⣿⣿⣤⣼⠒⣺⡿⣿⣿⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⣛⡠⣤⣿⠀⠛⣳⣼⣿⣿⢻⣹⣿⢟⠩⣜⡿⣏⡹⡎⢯⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣋⣀⣈⣩⣼⣃⣨⣶⠛⣁⣤⠿⣿⣸⣷⣜⢿⣻⣾⣷⡮⢻⣿⡆⢫
⠀⠀⠀⠀⣀⠴⠊⢹⠀⠀⠀⣠⣡⣿⣔⣋⠤⠛⣯⡝⠙⣉⣿⣿⣯⣉⠛⣿⣥⣈⡷⢄⡹⣷⠀⠱⡄
⠀⢀⠤⠊⠁⠀⠀⢸⣜⠀⣠⣾⡟⠊⠉⠀⠀⣀⣳⠄⠉⢰⣿⢹⠇⢋⡾⣅⡙⣎⠙⠻⢿⣾⣷⣀⠙⡄⠀⠀⠀⣀⣀
⠾⣅⠀⠀⠀⠀⠀⠸⣜⠀⡙⢳⠨⠁⠒⣤⠞⠁⠀⠡⣠⠾⣿⢹⣇⣼⣣⡀⠙⢺⣷⣤⠀⣌⢿⣯⠙⠻⠆⠚⠛⠛⠉
⠀⠀⠙⠲⢄⡀⠀⠀⡇⢠⠁⡈⣷⠈⡵⠃⠀⠀⠀⠘⢷⠀⣿⣸⣿⡥⠼⠛⠙⠋⠽⠻⣦⡀⠃⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠓⢤⣧⡟⠉⠀⣨⣟⠁⠀⠀⠐⠀⠀⠀⢠⣿⡉⡿⢦⡀⠀⠀⠀⠀⢀⣽⣯⣿⣽⣯⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠖⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣦⠔⠋⠀⠉⠀⠀⠀⠀⠸⠧⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⢀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠏⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠧⢤⠀⠀⢀⡤⢄⡀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠸⡄⠀⠀⠀⠀⠀⠘⢦⢀⡏⣖⡀⣷⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠦⣀⠀⠀⠀⠳⡀⠀⢳⢠⡧⠆⠀⠀⠀⠘⠶⠃⠇⣤⡋⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⠀⠀⣸⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⡀⢀⣠⡀⠀⠀⠀⠀⢠⠏⠀⠧⠴⣲⠞⢋⣨⠷⢤⡀
⠀⠀⠀⠉⠓⠲⢤⠀⠀⠀⢀⡤⣀⠙⣩⠞⠁⠀⠀⠀⣰⠃⠀⣀⠴⠋⣡⠖⠉⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⡷⠋⠳⣌⠙⡆⠀⠀⡰⣧⠴⠊⢁⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⢾⣷⠞⠀⢸⡆⠑⠲⠊⠁⢸⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⠒⣿⡀⠀⢸⣇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠁⠳⠀⡼⢹⡄⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠤⠞⠁⢠⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡤⠊⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣶⣤⣽⣿⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣇⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠛⠁⠀⠘⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡂⠀⠀⠀⠘⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢛⠹⢷⣤⡀⠐⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠢⣀⢀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠰⡑⣄⠈⠇⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠃⠀⠀⠀⢣⠀⠑⠀⡉⠂
⠀⠀⠀⠀⠀⢀⠀⡞⠀⠀⠀⠀⠀⡎⠀⠀⠀⣙⢰
⠀⠀⠀⠀⢀⡃⢸⡇⠀⠀⠀⠀⣸⣀⣀⡴⠀⠈⠇⡆
⠀⠀⠀⠀⢸⢠⣾⣿⠀⠀⠀⠠⣬⡿⠇⣊⢗⣠⡇⢇
⠀⠀⠀⠀⡟⠈⢸⣿⠀⠀⠀⠀⡟⠙⠿⣷⣟⠁⢻⡇
⠀⠀⠀⠀⢷⢷⠸⣿⡀⢀⣀⡐⢧⠀⢰⣿⠀⠀⢸⡉
⠀⠀⠀⠀⢘⣿⣷⣏⣴⡒⠤⣌⣾⠀⣞⢿⡗⠔⠛
⠀⠀⠀⠀⣼⠈⢻⣿⡗⡥⠀⠈⠃⠀⢹
⠀⠀⠀⠀⢦⣰⣄⣿⣷⣭⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⠀⣶⣿⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡀⢹⣿⣇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡧⡄⠙⠿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠂⠀⢠
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣄⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⢿⣿⣿⣦⣘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢙⡮⠀⠉⠙⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡏⠑⠒⠤⢄⣀⣀⣲⡆⠴⠖⠒⡖⠒⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⢙⣛⠛⠿⠿⠏⠙⠋⠉⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇
⠀⠀⠀⢡⠀⢠⠖⠒⠤⠔⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠈⠙⠋⠀⠀⠀⠀⠠⠶⠄⠀⠀⡀⢠⣤⠀⡇
⠀⠀⠀⠀⢇⠘⢄⠀⠀⠀⠀⠀⠀⠀⡠⠠⣆⠀⠠⠂⠈⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⢀⡾⠛⢻⣤⣜⡁⠀⠀⢰⠃⣀
⠀⠀⠀⠀⠀⠳⢎⠀⠀⠀⠀⠀⠀⠐⣇⣀⣘⠈⠑⠒⠤⣀⠞⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠈⠿⣦⠾⣿⣿⣿⣿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⠀⠀⠀⠉⢈⡹⠂⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣲⣤⣤⢤⣤⣴⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣸⡓⠩⣹⣏⢧⠀⢀⡠⠊⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⣿⣿⣧⣙⣺⣿⣿⣿⡿⢟⠁⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⢰⡡⠒⡀⢹⠈⠑⠉⠈⠆⠗⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡇⢸⠀⠀⠀⠀⠸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢸⠀⠐⢾⣀⡎⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣛⣩⣹⢛⣿⣿⡛⣟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢱⠢⢤⡋⣘⡅⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣃⣞⣛⣛⣛⣛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢦⡏⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠛⠻⠿⠿⠿⠛⣛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠂⠀⠀⠒⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣯⣿⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸⢧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⣿⢙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠎⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⡵⠃⢸⣿⣝⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢓⡒⡴⠋⠀⢨⣑⣒⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡟⠀⠀⠸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠈⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⢀⠀⢨⠔⠄⠄⠄
⠀⠀⠀⠀⠈⠉⠁⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠁⢈⠆⠤⠤⠄⠀⠀⠀⠀⢀⠠⠤⡀⠏⠓⠒⠒
⠀⠀⠀⠐⠈⠀⠈⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣄⣀⠀⠀⠀⠀⠀⠠⠀⠐⠁⡚⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠅⠹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡘⠂⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣃⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣠⠖⠉⡙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠎⠁⠀⣰⡟⠁⢀⣼⠔⠊⠉⢉⡹⠆⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡎⣿⠁⠀⠀⠀⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢷⡇⠀⠀⠀⢰⠀⠀⠠⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠈⠉⢩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⡀⠸⠆⡀⢴⣦⠔⠈⠏⢠⠄⢐⣆⡄⠀⠀⠶⠃⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠄⠀⠛⠚⠀⠋⠈⠉⠀⠘⠋⠀⠀⠈⠙⠀⠀⠀⠀⢀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⣤⠖⠓⠂⠀⢰⠇⠀⠀⠀⠈⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠠⠞⠻⠶⠀⠀⠀⠁⠀⢀⠀⠀⠈⠻⡆⠀⠀⣀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡈⢣⠀⢀⣀⡀⠀⠀⠀⠀⠞⠋⠉⠀⠀⠀⠀⠁⠚⠡⠄⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢾⣄⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢂⠀⠀⠦⠀⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠆
⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⠀⣿⠀⠀⠞⠓⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠟⠛⠶⠀⠀⠀⠀⠀⣤⠖⠀⠈⠉⢦⡘⣄⠀⠀⠈⠲⠆⠀⡨⠃⠀⠀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⣹⠉⠲⣤⣀⠀⠁⠈⠀⠀⣠⠔⢶⠟⡗⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠘⢄⡀⠀⣀⣐⠒⠉⠙⠀⢀⠴⠛⡿⢶⠀⠐⠊⠀⠀⢀⠀⡇⠀⠀⠀⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠾⠟⠉⠉⠁⠀⠀⠀⠈⢳⠒⠉⠉⠒⣤⠛⡰⠃⠀⠀⣱⢄⣢⡄⢤⠒⡖⠠⠔⠀⢀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⡓⠒⠒⠀⣀⣠⠁⢀⡀⠄⠳⣤⣁⠘⠻⠆⢹⠁⠀⠀⢸⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠀⠀⠀⠀⡌⠁⠚⠓⠀⠙⠇⠀⠸⠋⢠⣤⠄⠀⠀⠀⠀⠀⣦⠠⡤⢤⣇⠀⠀⢀⠄⠀⠸
⠀⠀⠀⠀⠀⠠⠐⠛⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠀⡿⠠⣴⠦⠀⠀⠀⠀⢀⡷⠀⡀⠀⠙⠳⠶⠦⣄⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠂⠀⡇⠀⠉⠘⠃⠈⠛⠛⠛⢄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠴⠊⠉⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠆⢀⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⠙⣒⣢⣤⡤⠤⠴⠒⠒⠛⢓⣂⡈⣭⡥⠒⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠉⠁⠐⠒⠒⠒⠒⠒⠉⠉⠉⠁⠘⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠲⢄⣀⡠⠤⠄⠀⠀⠀⠀⠀⠀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⣤⠤⠴⠒⠫⠝⠷⢦⣤⣤⡤⠖⠺⠟⣁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⡶⠖⠀⢠⠐⠲⠆⢸⠒⢤⠃⢀⣀⡟⣉⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠴⠞⡉⢧⣟⣻⠇⠀⠀⠀⠸⣧⣷⡾⢏⣉⣁⣸⡟⡞⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⢶⠩⠤⠀⠀⢀⣀⢰⡮⠟⠋⠈⠉⠉⠉⠛⠃⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⣀⡤⣤⣤⣼⣠⣀⣙⡃⠴⠾⢿⡁⠀⠀⠀⢀⡀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠸⢎⡁⠀⠋⠀⠀⠈⢋⣡⠞
⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⣦⣶⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣤⣤⣴⣦⣤
⣿⣿⣿⡟⡏⠛⢿⡟⠙⡿⠛⢿⡛⠟⣻⣻⡿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣷⣶⣷⣶⣷⣶⣾⣿⣶⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⢅⣀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠀⠀⠀⠀⣿⣿⣿⠟⢋⡁⠀⠀⠀⣀⠀⠀⢿⣿⡿⠀⠀⠀⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠸⠛⣀⡇⠙⠻⠀⣿⠀⠉⣣
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠋⠉⠁⠀⠀⠀⠀⠑⣤⡀⠀⠀⠀⢓⣀⡀⠀⠈⠋⣤⡖⠁⠀⠀⠀⠀⠛⠛⠛⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⢀⣀⣠⣾⣿⣷⣄⠀⢮⣁⣀⡹⠆⣀⣾⣿⣧⣀⡠⠤⢤⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠀⠀⡠⠏⠀⠘⠛⣻⣿⠿⢷⠶⠚⠉⢲⡾⠿⣟⡛⠓⡆⠀⠀⣨⠇⠀⠈⠙⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⣨⠉⡠⠖⢇⠀⠀⢀⡎⠀⠀⠀⠀⠙⢧⡠⢄⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⢋⠴⠋⠀⠀⠈⡳⠖⠁⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣀⠔⠋⠀⡠⣄⣶⡒⢤⣤⡤⠴⠃⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⢻⠁⠀⠀⢰⣟⣒⠀⠀⢸⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⢟⣃⣠⡤⠼⠤⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣤⡄⠀⠀⠀⣠⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠿⣿⡟⠀⠀⠀⣽⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣭⡄⠀⠀⠀⠰⣷⣬⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣟⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣟⣹⡿⠂⠀⠰⠿⠟⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⣫⣿⡿⠟⠉⢸⣿⣥⣶⣦⡄⠀⠀⠀⣸⣿⣿⣿⣧⠲⡌⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⢸⣿⣿⡟⠃⡀⠀⠀⢀⣀⠘⠋⠀⠀⠀⡽⢿⡉⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⡰⢋⣤⠴⠛⠛⠉⠀⠀⠀⠀⠀⣄⣸⡇⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠀⠙⢧⣻⠿⠓⣒⣈⣉⡁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⡔⣡⠞⠏⠀⠀⠀⠈⠙⣦⣀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠃⣠⡇⠀⣀⡴⠚⢩⣼⣿⣧⡀⠀⠀⣀⠀⠀⠀⠻⣤⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠓⠛⠀⢀⣙⣒⣎⡁⠈⠟⠫⡴⢋⡞⢉⡿⠁⠓⠀⠀⣿⣄⠀⠀⠀⠙⢲⠇⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⡀⣈⡷⢀⡴⣾⠟⣽⣿⡿⠿⠀⣤⡀⠀⣟⣠⠞⠁⠀⠀⠀⢀⣿⠇⠀⠀⠀⣠⠏⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢰⡿⢚⡡⢞⣥⢠⣞⣠⣴⢂⡉⢀⡿⠀⠉⠁⠳⣄⠀⠀⣠⠞⢯⣀⡀⠀⣰⠃⡰⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⢛⣙⡶⠋⢐⣎⡼⠟⠛⠻⣯⠉⠁⢾⣁⣀⣀⠤⢤⣈⠙⠛⠁⠀⣠⠟⠉⣿⠃⡰⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠾⢫⡄⢱⢋⡞⠑⢒⡤⣄⡈⠑⠒⠲⢦⡀⠀⠀⢀⠜⠀⠀⠀⠀⠷⠒⢶⡇⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠷⣾⢸⡇⡸⢏⣸⣿⣥⡤⠼⠿⠀⠀⠀⠘⣷⢠⠞⠋⢀⡶⣶⠄⠀⠀⢀⣼⣀⡀⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡶⠫⣄⣿⣅⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⡓⣚⠽⠛⠁⠀⠀⠀⠀⢸⡇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡤⠈⢿⣉⣙⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠶⠶⠶⣤⣤⣄⣀⣸⡃⣾⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣭⣭⢀⣀⣤⣤⣤⣤⣀⠀⢠⡟⠀⠀⠀⠀⢠⡟⠉⠉⠉⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣯⠶⠛⠉⠀⠀⠀⠀⠉⠛⣿⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣸⣇⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠃




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣋⣙⣏⣨⣏⣹⣍⣉⣽⣫⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⢺⣿⡛⠛⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢤⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠴⡲⠏⢼⣿⡿⠶⢶⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠀⢸⣿⣇⠀⠸⠄⠳⠐⠒
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⢤⣾⣿⣿⢤⣤⣀⣀⣀
⠀⠀⠒⠀⠀⠻⠉⠹⠁⠇⠀⢸⣿⣿⣈⢀⣿⠩⣏⣣⣀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠑⠒⠁⠐⠉⣻⣿⣿⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⣿⠟⢋⣅⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡡⠶⠊⢹⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣍⡤⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠁
⠀⠉⠁⠈⠓⠀⠒⠂⠄⠲⠶⡆⢀⣈⢀⣦⣀⣀⢀⣀⣀⣀⣀⠠⢄⣀⣀⣀⡀⣠⣀⡠⠠⠒⠒⠤⠄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠠⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⠀⠀⠀⢀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠇⠀⢀⠔⠁⠆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠤⠂⠁⢀⠞⠀⠈⠉⢉⣥⠏⡁⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢀⢀⠀⠒⠃⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢄⠂⢄⡀⠐⠒⠒⠒⢆⡁⠀⠀⠀⠀⠀⠈⠒⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⡇⠀⠀⠀⠀⠀⠀⢲⢀⠀⠀⠀⡀⠈⠐⠠⠀⠀⠀⣥⠑⠒⠒⠦⣤⢤⠤⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⠀⠈⠐⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⣆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢃⠀⠀⠈⣷⠀⠈⠀⣤⣤⣴⡾⠏⠀⠀⠀⠀⠀⠙⠻⠶⠖⠂⠀⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⢢⠀⠀⢉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠨⠴⢠⣕⢄⡀⠀⠀⠀⠀⠘⠳⣦⡄⠀⠀⠀⠀⠀⣴⣿⣁⠀⠀⠀⣄⠸⠀⠀⠊⡀⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⡀⠙⠄⢈⠐⠀⠀⠀⠠⠖⠛⠁⠀⠀⣀⣀⡀⠀⠈⠉⠀⠀⠀⡉⠲⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠉⢹⠆⠈⠂⣄⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠈⠒⢀⡀⠀⠀⠀⠀⠀⢀⠔⠋⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠉⠉⠣⡀⠀⠀⡔⠀⠋⢀⡎⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠈⠒⠦⠀⠀⠀⠀⢀⠤⠖⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣠⠐⠁⡀⠤⠄⢤⣄⠀⠀⠀⠈⢀⠀⣘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣠⣤⠤⠤⠀⠐⠈⠇⠀⠀⠀⠀⠀⡈⢐⡌⠀⠀⢀⣾⢿⡗⠀⠁⠀⣸⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠤⣀⣀⣤⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠤⠄⠒⠊⠉

⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣷⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠶⠶⠶⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⡀
⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡷
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⢠⠄⢀⡤⠀⣠
⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⠀⠀⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⠒⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠐⢤⡀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⡀⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠉⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠦⣤⣤⣤⣤⣤⣀⣀⣤⣤⣤⣤⣤⡴⠶⠶⠟⠃
⣿⣷⠿⠿⠾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣧⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡀⠀⢀⠀⢀⠀⢀⡀⢀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⠆⠈⣇⠔⠹⠆⠈⠆⠁⠗⠉⢷⠈⢧⠤⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠃⠠⠈⠀⠀⠀⠢⠤⠀⠀⠀⢸⡠⠃⡮⣄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠐⠁⠀⠀⠀⠀⣠⣊⠤⢀⠀⠈⠁⠀⠁⠇⡸⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⣵⠶⢦⠀⢀⣴⠟⠒⠉⠉⠀⠀⠀⠀⠀⠖⠃⠀⣂⡀⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠐⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠤⣄⠁⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠀⠀⠈⠉⠙⠫⡉⠉⠢⡄⠀⠀⠀⠀⢀⡠⠛⠂⠐⠳⡦⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡚⠟⠋⠻⣄⡀⠀⠀⠀⠖⠛⠀⠁⠉⠀⣀⣤⠰⠋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⡀⠀⣌⠀⠀⠀⠘⣭⡓⣤⣬⡤⠤⠤⢴⣂⡉⠔⡁⠷⣄⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠳⣤⠀⠀⠛⢄⣹⠀⠀⠀⠀⠀⠉⠛⠻⢄⣀⠀⠀⠀⡠⠊⠀⠀⠈⢳⡀⢀⡜⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⢤⠀⡠⠝⠁⠀⠀⢀⣀⠑⠲⠤⢤⣀⡀⠀⠀⠀⠀⠉⠑⠊⠀⠀⠀⢀⡴⠋⠉⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢄⡁⠀⢛⡃⠀⠀⠀⠀⠉⢳⠢⢄⣀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠵⠦⠀⠀⠀⠓⠂⠊⠀⠀⠀⠀⠀⠀⠘⡖⠲⠼⠙⠒⠒⠙⠉⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣤⢄⡄⠀⠀⠀⠀⠀⠀⡀⠀⣠⠋⠀⣠⡞⠣⡈⢢
⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⣷⣄⠬⠌⠘⠘⠳⠀⠀⠀⠒⠢⡤⠄⢣⠴⣎⠀⢴⠀⠘⠺⡄
⠀⠀⠀⠀⣿⣿⠟⣋⡀⠆⠈⢉⠳⡀⠰⠀⡀⠠⠐⠒⠒⣒⡂⠀⠘⡴⢷⡇⠀⠢⢀⣶⠃
⠀⠀⠀⠀⢙⠋⣆⠬⠌⠊⢘⣸⡷⠈⡂⠉⢡⠀⠀⠀⠀⠰⠄⠀⡠⠘⠤⣨⡡⠔⡋⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⣿⣷⣵⡶⠥⢺⡟⠁⠀⠇⠀⠀⡀⠀⠠⠄⢀⠄⡪⠊⡠⠊⠀⠑⠒⠁⠀⠀⠢⡀⠈⢂
⠀⠀⠀⠀⢀⠅⠋⠁⠑⢠⠿⣷⠀⠀⠀⠀⢀⠇⠀⠀⠔⠁⠀⠀⢰⠁⠀⡰⠄⠀⠀⠀⠀⢀⡇⠀⡸
⠀⠀⠀⠀⡎⠀⠠⠔⠂⢫⠀⢸⠀⢐⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣤⠒⠁⢺⠀⠀⢠⣎⣁⢈⠕⠁
⠀⠀⠀⠀⢃⠀⠀⠀⣀⠼⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠈⠉⠉⠉⠉⠉⠉⠁⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠷⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠈⠉⠉⠀⠉⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⠜⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠱⡄⠀⠀⢀⡖⢉⡉⠱⡀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣤⣀⠀⠀⠀⠿⠞⠁⠀⠀⡀⠀⠀⠀⠙⠦⡠⠞⠠⡋⠉⠁⡇⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠉⢳⡀⠀⠀⠀⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⢀⡇⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡁⣀⡼⢣⡀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢻⣯⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣼⠀⠀⠀⢀⡴⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⠦⠴⠖⡋⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠟⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢰⣮⢭⣿⠖⢶⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠟⠀⠀⠀⠀⠀⠀⡿⢤⣀
⣀⣀⣀⣀⣀⠠⠤⠤⠤⠶⠤⠶⠒⠒⠒⠒⠒⢂⠈⠳⣄⠉⢻⠈⣠⡿⠁⠀⠀⠀⠀⠀⠀⣠⠞⣰⠃⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⣤⣀⠀⠀⠀⠖⠉⠁⠀⢀⠈⠳⣌⡛⠋⠀⠀⠀⠀⠀⠀⢀⡼⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⣠⠖⠉⠠⣄⡈⠒⠤⣌⠙⢦⠀⠀⠀⠀⣠⠏⠀⠀⣀⣹⡦⣀⡀⠀⠀⣠⠔⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⣠⠞⠁⠠⢄⣀⠀⠉⠳⣄⠈⣧⠠⠁⠀⠀⡴⠃⢀⡤⠞⠉⡜⠀⠈⠉⠛⡿⡁⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⣿⠀⠀⠀⠀⠀⠙⢦⠀⢨⠄⠱⠀⡇⢀⡞⠀⣴⠋⠀⠀⢰⠃⠀⠀⠀⠀⢇⢻⡎⢀⣠⣄⣀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⢿⠀⠀⠀⠙⣷⡀⢸⠀⢸⣀⣸⡖⠡⠋⠀⡞⠁⠀⠀⠀⢸⢀⡴⠊⠉⠓⢾⣾⠉⠁⠀⠀⠉⠳⣄⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠈⡆⠀⠀⠀⢸⡗⠘⠓⠋⠉⣸⠇⠀⠀⡼⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⣆⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠸⣄⠀⠀⠸⠇⠀⠀⠀⢰⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠸⡄⠀⢠⠇⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⡰⢷⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⠞⠁⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⣴⠛⣀⡤⠞⠁⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠿⠚⠋⠀⠀⠀⠀⣠⠴⠋⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠉⠉⠉⠉⣿⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⣀⡴⠛⠁⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⣿⠀⠀⣿
⠀⠀⠀⠀⠘⠶⡶⠊⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⢧⡀⠀⠀⠀⣴⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⢦⠴⠋⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⣀⡖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠂⠉⠉⠉⠉⠉⠉⠐⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠛⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⡤⠒⠋⠉⠉⠑⠒⠂⠐⠲⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⣄⣠⠞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠉⠀⠀⠹⡄⠀⠀⡴⢋⣉⡙⡀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡶⣤⣄⠀⠘⠛⠁⠀⣀⡄⠀⠀⠀⠈⠢⠚⠁⣯⠀⠁⡇⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⡼⣆⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⢠⡇⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠘⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢘⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⣄⡠⠴⠊⠀⠉⢲⡀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡎⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⢠⣞⣷⡶⢤⡄⠀⠀⠀⠀⠀⠀⠀⡸⢀⠞⠀⠀⠀⠀⠀⢱⢄⡀
⣀⣀⣀⣀⡀⠠⠤⠤⠤⠤⠄⠒⠒⠒⠒⢂⠈⠢⡈⠑⡇⢁⣾⠃⠀⠀⠀⠀⠀⢀⡴⣡⠋⠀⠀⠀⠀⠀⠀⡆⠀⠉⠓⠦⣀
⠀⠀⠀⠀⢀⡠⠔⠒⠒⠤⣀⠀⠀⠐⠉⠁⠀⣠⠈⠲⣍⠋⠁⠀⠀⠀⠀⢀⡰⢋⡜⠁⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⣠⠔⠉⠀⠦⣌⡙⠲⣄⠙⢆⠀⠀⠀⡰⠃⠀⣀⡤⡷⠦⣄⣀⣀⠴⠊⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⡾⠁⠀⠒⠦⢄⡀⠙⢦⠘⡇⢀⠀⢀⠞⠁⡠⠞⠁⢰⠁⠀⠀⠉⡟⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⡇⠀⠀⠠⣄⠀⢹⠀⢸⠀⣅⡈⢠⠏⢠⠞⠀⠀⠀⡏⠀⣀⠤⢄⣡⣹⠤⠒⠒⠢⢄⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⢣⠀⠀⠀⠸⣧⢸⣤⠼⠒⢻⠀⠁⢠⠃⠀⠀⠀⠀⣧⠎⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⠳⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⢆⠀⠀⠀⡇⠀⠀⠀⣴⠃⠀⢀⡎⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢱⠇
⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢹⠀⠀⡜⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⡰⢆⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⡇⠀⢀⡠⠊⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢠⡏⣡⡴⠋⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⢸
⠀⠀⠀⢘⡋⠁⠀⠀⠀⣠⠔⠋⠘⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣨⡇⠀⢸
⠀⠀⠀⠘⣇⣀⣠⠴⠊⠁⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠈⢩⠁⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⡀
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣇⠀⠀⠀⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⣄⡤⠚⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣤⣴⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢧⡤⢴⢒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣈⣞⠃⠤⠖⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠿⠛⢏⣿⡿⣿⡄⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠉⠒⣿⡽⢿⣴⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢿⡴⠚⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠅⠽⢿⠿⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣡⢄⣿⡄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠿⢿⣻⡟⣿⣶⣿⣅⣞⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠈⠛⡫⢿⣿⡿⣗⣆⣠⣄⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣾⣧⣤⣥⣬⣭⣥⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣍⣩⣬⣩⣏⣽⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⣿⡾⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⢮⣄⣀
⠀⠉⠉⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢉⣿⣭⡃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⡠⠰⠾⢳⣛⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⣯⣘⠀⠀⠀⡤⠀⠀⢰⡲⢬⢬⡀
⠀⠀⠠⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⠈⠀⠰⠒⠒⠓⠂⢈⠹⠴⢎⡄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⢩⡽⢿⠉⠉⠉⠉⠛⡉⠀⢈⢻⠒⠯⡁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠂⠀⢀⣠⠄⠀⠀⣚⡉⠨⡇⠀⠀⠀⣷⣿⠀⣞⣻⡁⣥⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⣀⠀⠀⠀⠀⠀⠀⣀⣶⠄⠀⠋⠀⠀⢸⢸⠀⠀⢠⣉⣁⣄⣻⠀⠀⠀⣇⢹⢀⠌⣿⡀⢸⣸⡆
⠀⠀⠀⡀⠀⠠⡀⢠⠀⡀⠈⠷⣄⢀⣀⣴⣛⣓⣚⣶⣄⣡⣤⣤⣼⠘⢰⣶⣺⣤⣭⣿⣼⣃⢀⣼⠇⠂⣧⢈⣯⡧⢸⣬⣇⣀
⠀⠀⠀⠇⢀⡿⣷⣾⣶⣿⣿⠿⠟⠟⠋⠉⠙⠛⠥⢴⣤⣩⣟⡻⠿⣼⠟⠟⣩⣿⣟⣿⣯⣝⣿⣿⣿⣷⣿⣿⣿⣿⠶⣿⣿⣿
⠀⠀⠶⣗⡚⣒⣧⢼⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠦⢤⣬⣉⡛⠛⠛⠛⠿⢿⣟⣨⣿⣿⣿⣿⣛⣛⡇
⠀⠐⢫⡷⢚⡭⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠂⠀⢀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⣷⣶⣬⣍⣉⠛⠻⠿⢿⠿⠏
⠀⣠⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛

⠀⠀⠀⠀⠇⠀⠀⢀⣀
⠀⠀⠰⢶⣿⣤⠠⠴⠪⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡠⢶⣾⡟⠗⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠉⠁⢨⢸⡇⣷⣐⡲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⣠⣴⣿⣿⡵⠂⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣦⠀⠬⠗⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠛⠉⢸⣼⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣖⡀⣠⣅⡀
⠀⠀⣈⣸⡷⣿⠉⠙⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢐⣼⣿⠚⠋⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣷⠦⣄
⠶⠊⠻⢿⡿⣬⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⢡⣸⣌⣀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠜⠛⠃⣻⣷⣀
⠀⠁⡣⢸⣏⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⠏⠉⠣⠀⠀⢀⣤⡀⢀⣅⠀⠀⠀⠀⢀⣀⣼⡯⠉⠑
⠀⢀⠀⢹⡧⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⢹⡟⠀⠀⠀⠀⠀⠀⠀⡀⢹⡷⠦⢀⠀⠀⠁⠀⣻⣷⡦⣄
⠀⠰⠁⢼⡟⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⡅⠃⠀⠀⠀⠀⠀⠉⠉⢿⣿⣤⡀⠀⠀⠀⠀⡹⡇⠂
⠀⡀⠀⢹⣷⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡇⢄⠀⠀⠀⠀⠀⠠⠀⢪⣏⡀⠁⠀⠀⠀⢀⠠⣇
⢀⠁⠈⣿⣇⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⡇⠠⠀⠀⠀⠀⠀⠀⠀⢚⡏⠉⠁⠀⠀⠀⠀⠰⣏⠐
⣸⠗⢆⣺⣿⢢⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠤⣴⡷⣤⡄⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⣀⣴⣯⣠⡆
⣿⣤⣤⣿⣿⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣤⣿⣷⣤⣧⣤⣤⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣧⣼⣿⣤⣮
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣤⣶⣶⣦⡀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⣤⡶⢶⣦⠀⠀⠀⠀⠀⣴⣶⣶⣦⡀⠀⠀⠀⢀⣀⣦⢴⣆⡀
⠀⠀⢸⣿⣏⣹⣿⡇⠀⠀⠀⠰⣿⣏⣹⣿⡇⠀⠀⠀⢸⣏⠀⠀⣹⡇⠀⠀⠀⢸⣿⣏⣹⣿⡇⠀⠀⠀⢈⣿⠀⠀⣿⡁
⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠈⠟⠻⠇
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢠⡿⢋⣙⢿⡄⠀⠀⠀⢠⡾⡯⢽⢿⡄⠀⠀⠀⢀⣾⡿⢿⣷⡄⠀⠀⠀⢀⡞⠉⠉⢳⡄⠀⠀⠀⢠⣞⣫⣽⣻⡄
⠀⠀⠘⣷⣌⣫⣼⠃⠀⠀⠀⠘⢷⣗⣺⣾⠃⠀⠀⠀⠘⢿⣿⣾⡿⠃⠀⠀⠀⠈⢧⣀⣀⡼⠃⠀⠀⠀⠘⢯⣝⣻⣽⠃
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⣤⣰⣦⣠⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠰⣟⣱⣞⣹⠦⠀⠀⠀⠠⣿⡫⠝⣿⡆⠀⠀⠀⢰⣿⡟⢹⣿⡇⠀⠀⠀⢰⣿⣟⢻⣿⣇⠀⠀⠀⢰⣿⡋⢙⣿⡆
⠀⠀⠀⠛⢳⡞⠛⠀⠀⠀⠀⠀⠻⠿⠾⠟⠁⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⠈⠥⡤⠿⠿⠃⠀⠀⠀⠈⠻⣿⣿⠿⠁

⠀⠀⢀⣾⡿⢿⣷⡄⠀⠀⠀⢀⣶⢿⡻⣶⡀⠀⠀⠀⢀⣶⡿⢿⣶⡀⠀⠀⠀⢀⡶⣿⣿⢷⡄⠀⠀⠀⠀⡴⠓⠓⢦⡀
⠀⠀⠸⣿⣦⣠⣿⡇⠀⠀⠀⠸⣷⣻⢟⣾⠇⠀⠀⠀⠰⣿⣄⣠⣿⠇⠀⠀⠀⠸⣿⣿⣿⣽⠇⠀⠀⠀⠸⣇⠘⠃⣸⡇
⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠛⠛⠛⠉⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠠⡤⠄⢰⣀⡀⠠⠤⠤⠤⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⣠⠔⠋⣱⡀⠄⠀⠀⠒⠐⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⠴⢦⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣏⣠⣒⠁⠈⢆⣀⠤⠒⢉⡠⠒⣽⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⢤⡀
⠀⠀⠀⠀⡠⠛⠀⠀⠹⣤⡤⠀⠀⢿⣿⣿⣿⣿⣿⠟⡥⠞⢻⣿⠉⠉⠹⢤⠖⢁⡠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠳⣀⡀⠀⢀⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⡄⠀⠊⠡⠽⡗⠒⠒⢞⠉⠉⠙⠟⠛⠛⠋⢩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢦⡀⠀⢸⠁⠀⠀⠘⣆⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠓⠦⣾⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠀⠀⠈⢳⣿⣿⡿⢏⡀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢀⣼⠀⠀⣸⣷⠀⠀⠀⠀⠀⡏⠉⠉⠁⠈⢦⣀⡀⠀⣀⣀⣸⣄⣀⣀⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⡤⠤⠴⠁⠀⠀⠀⠀⡿⠻⠴⠚⠁⢻⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠣⠤⠤⠤⠴⠦⠤⣄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠦⠤⠤⣤⣤⣤⡤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⡴⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⠉⠉⠙⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠠⠤⠤⠀⢀⣀⣀⠀⠀⠀⠀⠀⠸⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⣀⣠⡄⠀⠒⠚⠃⠀⠁⠀⢀⠀⠀⠸⣅⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠉⠉⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⣄⡙⠢⡔⢃⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠚⣃⠀⠀⢀⡠⠤⠐⠒⡆⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⢁⠀⠑⠊⠀⣀⣤⡀⠀⣹⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠉⠀⠀⠈⣀⡀⠀⠀⢽⢠⣇
⠀⠀⠀⢀⡠⠴⠒⠉⠉⠠⣖⡛⡀⣀⠐⠛⠀⠀⠀⠀⣇⠞⠆⡱⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡔⢩⣂⡀
⠀⠀⢼⠋⠀⠀⠐⠂⠤⠤⠆⠑⠈⠉⢩⠝⠀⠀⠀⠀⣩⡞⠈⠀⠀⠄⠈⢉⠉⠓⠒⠒⣲⡎⠙⡇⠠⢋⡠⠃
⠀⠀⠈⠢⢄⣒⠀⠡⠄⠀⡰⡀⣀⡰⠟⠠⠤⠤⡶⠊⠁⠀⠈⠑⠒⠤⠄⣈⠀⠀⠀⡀⢰⠁⢀⡇⠀⠫⡄
⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⡗⠮⠞⢰⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣁⡜⠉⠉⠀⠙⠒⠁
⠀⠀⠀⠀⠀⠀⢀⣠⠎⡝⠀⠀⠀⡜⣄⠀⡰⠁
⠀⠀⠀⠀⢐⠉⠉⢧⢰⠁⠀⠀⢎⡁⣠⢗⠃
⠀⠀⠀⠀⠘⠢⠔⠈⢩⣄⣀⣀⣀⣉⣡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢲⠐⠶⣲⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢇⠀⡨⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⡈⠓⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡱⡀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣷⣤⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⣴⢹⡘⡕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠊⠉⠉⠛⣤⠃⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⡼⢤⣀⣀⣀⣀⡠⠔⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠠⠬⠤⠴⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠰⡂
⠀⠀⠀⠉⠉⠈⠉⠁⠀⠈⠋⠃⠀⠀⠀⠀⠀⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠅⠈⢢⠤⠄⠀⠨⠄⠁⣄
⠀⠀⠀⠀⠀⢰⡖⠈⠒⠠⡌⠒⠂⢰⡤⠒⠀⢰⠆⠘⠋⢰⣦
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢙⠄⠀⠈⠋⠀⡠⡎⠀⠀⠀⢈⠏
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⠦⠀⠀⣴⠑⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠳⠀⣡⣤⠀⠷⠁⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣊⠀⠈⢁⠂⠀⠀⠀⠀⠀⠀⢀⡜⠧⣀⠀⡜⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡁⠐⡸⡄⠀⠀⠀⠀⠰⠏⠉⢲⡉⠸⠛⣸⠋⠉⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⡴⠁⢱⡀⠀⠀⠀⠀⠀⠀⠈⡳⠀⠰⡃⠀⠀⠀⠀⡀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡼⠹⣄⣀⣇⠀⠀⠀⠀⠀⠀⠀⢡⠛⢣⠁⠀⠀⠘⠁⠠⠘⠃⡌⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡼⠁⠀⠘⣄⣸⡀⠀⠀⠀⠀⠀⠀⡈⢠⠌⡄⠀⠀⠀⠀⠀⠰⢎⠀⠀⢀⠀⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡼⠁⠀⠀⠀⠈⣦⣥⠀⠀⠀⠀⠀⢠⣧⠎⢣⣳⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⣸⠏⠀⠀⠻⡇⠀⠀⠀⢰⠇⠈⢧⠀⠀⠀⡄⢀
⣀⣀⣀⣀⣀⣀⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣯⣤⣤⣤⣤⣿⣤⣤⣤⣮⣤⣤⣬⣦⣤⣴⣤⣬⣦⣤⣤⣧⣤⣤⣄⣀⣀
⣿⣇⣸⣯⣙⣿⣯⣙⣽⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⡚⠁⣠⡏⠐⠂⢀⣇⡀⠑⡂⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣐⠐⣌⣯⠛⡀⠛⠄⢻⠟⢠⠤⠙⠛⠀⠾⠃⡜⢋⡩⡗⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁⠙⠀⠛⠀⢻⠿⡦⠶⠛⢿⠀⠘⠋⠚⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⣿⡆⠈⠉⠠⣾⠦⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠰⠲⠊⠉⠉⠀⠀⠀⣿⣀⣐⣒⣁⣸⣂⠀⠀⠁⠈⠉⠲⠲⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠼⡴⠦⠶⠾⠂⠈⠙⠓⣀⠘⣟⠋⠅⣡⠉⠙⡟⢁⡚⠛⠓⠐⢾⠖⢠⠆⢨⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠒⠐⠴⠦⠤⢴⣿⣤⣤⢤⡀⠰⣷⠈⠀⠒⠊⠀⠛⠀⠀⠁⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠄⠀⠀⠀⢰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⣇⡀⠌⠋⠄⠈⣿⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢘⠃⠀⢸⡏⢉⠶⠶⢊⠁⣿⠀⠀⠛⠒⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⢂⣏⡁⠤⡄⠰⣖⠐⢿⠿⠷⣒⣓⡲⠿⣿⡗⠀⡦⠦⣤⣄⣩⣒⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠟⠲⠌⢠⣮⣡⣾⣤⡤⢉⡍⠱⣦⣼⡧⠉⠦⠜⠵⠞⠟⠃⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢑⣦⠴⠞⣉⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠚⠉⠁⠀⠉⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠀⠤⢀⣀⠤⠄⠘⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡇⠤⠀⠁⠀⠀⠀⠄⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡷⠀⠀⠀⠐⠐⠀⠀⡀⢸⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣿⠀⠉⠐⢀⣀⠐⠈⠁⣸⣇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠉⠠⠤⡀⠁⡠⠄⡉⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠉⠁⠀⠐⠒⠄⠀⠉⠑⢻⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⢠⡄⠀⠀⠀⠀⠀⠀⠀⣄⠰⡏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠋⠀⠀⠀⠀⣠⢤⡔⠂⠁⡀⠴⢧⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⢠⠐⠚⠓⢀⣀⠐⠉⠂⠀⠀⢰⠇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⢀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⣇⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣾⠀⠀⠁⠆⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠛⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣧⣤⣤⣤⣤⣬⣤⣤⣤⣾⣍⣤⣤⣤⣤⣼⣤⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⠅⠀⠀⠀⢀⣤⠿⠙⠋⠉⡩⢀⠀⠈⠉⠉⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠁⠉⢂⢄⠀⢻⡞⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⣯⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢺⣇⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠾⠉⠤⠠⠤⠤⠤⠤⠤⠴⠧⠤⠤⠤⠤⠤⠤⠤⠉⠽⠷⣿⡄

⠀⠀⢠⣄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀
⠀⠀⠀⠈⠓⢤⣀⠈⠛⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⡤⠞⠉⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠐⠒⠤⣀⠀⠀⠀⠀⣀⠤⠔⠂⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢈⠶⠀⠀⠀⠀⠀⠀⠶⡁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣄⡀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠉⠻⠿⢿⡿⠿⠟⠛⠉⠀⠀⢀⣠⣴⣶⠀⠀⠀⢠⣾⣿⣿⣶⣬⣿⣿⣿⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠘⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⠀⠀⢀⣾⣧⡀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⠿⢿⠿⠟⠁⠉⣿⣿⡄⠀⣾⣿⣿⣿⣶⣶⣦⣽⣿⣿⡟⠛⠻⠿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⣤⣤⠄⠀⢀⣿⣿⣿⣶⣼⣿⣿⣿⢿⣿⡿⠿⠟⠉⠀⠀⠀⠀⢤⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠃⢀⣴⣿⣿⣿⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠹⣿⣿⣉⠹⣿⣿⢟⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡏⣴⣿⣿⣿⡿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣴⠞⠛⠋⠀⠀⠀⠀⢿⣿⡟⠀⣿⣿⢣⢫⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⢀⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢻⠀⠀⢰⢃⠞⡵⠋⠀⠀⠀⠀⠀⠀⣿⠏⢀⣴⣿⡟⣴⣙⣭⣿⢿⣷
⠀⠀⠀⠀⠀⠔⠂⠁⠀⠁⣸⣿⣿⣿⣿⣏⠺⣧⠀⠀⢀⣀⡀⠀⠈⡀⠀⠀⠀⠀⡠⢋⠂⠈⠀⠀⠀⠐⠢⡀⠀⠈⠁⠀⢸⣿⣿⣳⡎⡏⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠁⠀⠀⠙⠲⢿⣿⣗⡭⡭⠿⠏⣿⠀⠀⠤⠌⠙⠲⡞⠉⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⣼⠟⣥⣻⡵⠶⠛⠀⠀⠈⢹⡀
⠀⠀⠀⠀⠀⢧⡀⢘⡟⢳⣶⣤⣀⠻⠥⠭⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣴⢟⡡⣟⣀⣤⡴⢾⢿⡃⢀⣸⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠀⢸⣿⣿⣮⡷⠶⠟⠛⠛⠒⠶⠦⢤⣤⣀⠀⢻⣤⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⣫⡥⢮⣭⣴⣻⢶⢷⡍⢺⡽⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣟⠉⠈⠀⠼⠁⠀⠀⢀⣠⡴⠛⠉⠟⠁⠀⠀⠀⠀⠉⠛⢿⡌⡳⢻⡆⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠓⠒⠒⠶⠾⣿⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣽⢵⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡳⣤⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⣽⢳⣦⣬⣉⡙⢻⠋⠉⠙⢿⣦⣀⡀⠀⠀⣸⠀⢸⠀⡾⠏⠀⠀⠀⠘⡀⠀⠀⢀⣠⡾⠛⠉⠁⠀⠈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣜⢸⣿⠿⠛⠛⠟⠀⣆⠀⠀⠘⢻⣄⣀⣠⣟⣠⠿⠚⠁⠀⠀⠀⠀⠀⢡⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡙⡶⣴⡾⠶⣛⢻⡆⠀⠀⠀⠀⢉⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠫⠄⠓⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣼⣾⣒⢻⣏⡾⢿⡄⠀⢠⠖⢻⡲⠤⠌⠳⠦⢄⣀⠀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⣟⡻⢾⢸⡇⢰⠃⠀⣠⡤⠆⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣾⣁⠘⢆⡼⠁⠙⠂⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣇⠀⠀⣰⠁⠐⠀⣠⡆⠀⠀⢠⡦⠄⠠⠤⠆⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⣇⠀⠀⣠⡟⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁⣄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠈⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⡄⠀⢀⡄⢀⢴⠀⡠⣦⢀⣤⡀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣗⡰⠉⣇⠔⠁⠷⠁⠘⠊⠀⠛⠋⠘⢻⠀⢳⡤⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠎⠘⠀⡄⠉⠀⠀⠀⠸⢤⡤⠄⠀⠀⠀⢸⣠⠞⢰⣡⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢠⠴⠁⠀⠀⠀⠀⠀⢀⠔⢀⡀⠀⠀⠘⠃⠀⠋⢰⠁⢸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠰⣤⣀⣀⠀⠀⠀⣰⣟⡮⠥⠖⠒⠀⠀⠀⠀⠀⢈⣱⣃⣀⡀⠤⢔⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠘⠋⢉⡝⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠶⠦⠥⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⣈⣓⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠒⠶⣇⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡄⠀⠀⠀⠉⠀⠈⠳⣄⠀⠉⠳⣄⠀⠀⠀⠀⠀⢀⡠⠛⠉⠉⠉⠻⣿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡒⠿⠓⠉⠻⣄⠀⠀⠂⡩⠀⠴⠚⠒⠚⠋⠉⠀⠀⣀⡤⢲⠋⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣉⠂⠀⠀⠀⠙⣟⡶⢤⣠⣒⣀⣀⣀⣀⣤⠴⠒⣉⠜⢐⣧⡀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⢀⠔⠒⣆⡀⠀⠀⢘⣦⠀⢹⡀⠀⠀⠀⠀⠉⠳⠶⣿⣿⠉⠉⠀⠀⠉⠉⠉⣡⠔⠉⠀⠙⢦⠀⠀⠀⣠⡇
⠀⠀⠀⡰⠛⠀⠀⠐⣿⡁⠀⠀⠈⠓⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣄⣀⣀⠞⠁⠀⠀⠀⠀⣠⠷⡄⠔⠁⡇
⠀⠀⠀⠓⠖⢇⣀⠴⠚⠀⠀⢀⡠⠤⣤⣀⠉⠉⠛⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣥⠄⠀⢛⡩⠂⠀⠀⠀⠀⠀⠈⡙⠲⢤⣀⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢀⡴⠁⠈⠷⣦⡀⠀⠀⠘⠒⠦⠜⠁⠀⠀⠀⠀⠀⠀⠀⠓⡖⠲⠬⡏⠓⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠸⣀⡄⠀⠉⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠑⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡤⠖⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣦⠴⠋⠀⠉⠁⠀⠀⠀⠸⠧⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠏⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠧⢤⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠸⡄⠀⠀⠀⠀⠀⠘⢦⠠⡏⣖⡀⣧⠀⠀⠀⠀⠻⡀
⠀⠀⠀⢤⣀⠀⠀⠈⠳⡀⠀⢳⢠⡧⠄⠀⠀⠀⠘⠶⠇⠇⣠⡏⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⣸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⠀⠀⣰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⡀⢀⣀⡀⠀⠀⠀⠀⢠⠏⠀⢧⠴⣲⠾⢋⣩⠦⢤⡀
⠀⠀⠀⠙⠒⠦⣄⠀⠀⠀⢀⣤⡀⠛⣫⠞⠁⠀⠀⠀⣰⠋⠀⢀⡴⠚⣡⠔⠋⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠙⣧⠛⠳⣌⠙⡆⠀⠀⣠⣧⡴⠚⢁⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⢾⣧⡖⠀⢸⡆⠓⠶⠚⠁⢸⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⠲⣿⠀⠀⢸⡇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡞⠉⢳⠀⣸⢹⡄⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠤⠞⠁⢀⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⢀⣠⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⣴⠋⠀⠀⠀⠉⠋⠀⠀⠀⠀⠙⣆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⣆
⠀⠀⠀⠀⠀⢀⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠲⠤⣤⠴⠞⠙⠶⠖⠦⢤⡤⠞⠁
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣤⣤⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⡼⠓⠀⠀⠀⠀⡾⣁⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣤⡀⠘⡇
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠸⡅⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⢳⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣳⣬⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁⠀⠲⠺⠯⣭⣛⠋⠉⠁⠀⣠⠏
⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠱⣜⠛⠓⠶⣄⡀⠈⠉⠛⠒⠚⡇⠀⠀⠀⢀⣀⣀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠶⠞⠁⠸⡿⢿⡦⣄⠀⠙⠲⣄⣀⣀⡼⠁⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠹⣄⣀⣀⡀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣳⠀⠀⣇⠸⣷⠈⠙⢦⡀⠀⠀⣿
⠀⠀⠀⠀⠉⠉⠙⠲⠴⠶⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢹⡄⠀⠀⠀⠀⢹⣦⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⣧⠀⠀⠀⢀⡾⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢯⡀⠀⠀⠀⠀⠀⢰⠛⠉⠀⠀⠀⠀⠀⠀⡴⠛⠒⠦⠤⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠉⠛⠲⠶⠶⠶⠿⢦⡀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⡼⠁⠀⠀⠀⠀⣸⠇⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢳⡀⠀⣸⠃⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠈⡇⣰⠃⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⣿⠃⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡴⠃⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⠞⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠴⠦⠾⣿⣿⠿⠶⠶⠶⠤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⠀⠤⢀⡲⣿⣿⢶⣒⠂⠤⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛⠛⡿⢿⠛⠛⠘⠓⠀⠸⠤⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣟⣺⡄⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢇⠀⠀⠀⠀⠀⢠⡯⢽⡇⠀⠀⠀⠀⠀⡤⠊⡇
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣀⢀⣸⡗⢺⣇⡀⠀⠀⠀⠉⠀⠀⡇
⠠⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⢀⣔⣤⡀⠰⠖⢿⣏⡡⠰⣮⣸⣟⣻⣯⣿⢿⠅⣒⣆⣰⢤⣥⣀⣀
⠀⠑⢦⡀⠀⠀⠀⠀⠀⠈⠐⠤⠀⣀⡀⠐⠁⣋⠀⠀⠀⢹⡏⠹⡁⢉⠩⣽⢏⡙⡏⠉⠉⠁⠉⠉⡟⠉⢩⠁⠈⠉⢳
⠀⠀⠀⠈⠁⠒⠀⠤⠄⠀⠀⠒⠋⠉⠀⠀⠀⣿⠤⠄⠀⢸⠇⠂⠙⡀⠀⣿⣤⡜⡇⠀⠀⠀⠀⢀⣇⠀⠸⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠘⡄⠀⡠⠋⠀⠀⠀⠈⠤⡿⣀⠤⣿⠀⠀⠀⠴⠉⡿⠀⢰⠄⠀⡜⣧
⠀⠈⢶⠤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⡀⠰⠊⠀⠀⠀⠄⠀⠀⢈⡿⣄⣁⣿⡤⠒⠀⠀⠀⡏⠀⠀⢱⠊⠀⢻
⠀⠀⠈⠙⠛⠿⠓⠒⠒⠀⠀⠉⠀⠀⠒⠚⠉⠀⠀⠀⠀⠄⠀⠀⠐⠀⢸⣷⣛⣿⣿⠀⠀⠀⠀⠀⢛⣠⠔⠈⢣⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢤⡴⢿⣿⠛⠳⣽⢦⣄⡠⠴⠖⡻⣧⠀⠀⠘⣷⢼⡇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠀⠀⠲⠂⠀⠀⠀⠀⠀⣼⣸⡗⣦⣈⠀⠀⠀⣠⡀⠙⣾⣆⡀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠈⣟⠛⣌⣨⣿⡷⣤⡀⠀⠙⠦⣌⣻⣎⠘⢶⣻⣿⣟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣟⡉⠉⢻⡟⠲⢌⡡⢄⡀⠀⠙⠛⠷⣏⢹⣏⢿⠻⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠟⠛⢯⣿⠀⠀⠀⠀⠉⠢⣤⣀⡴⠞⣿⣿⣺⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲⣤⣤⡖⢿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣿⣿⠈⣢⣥⡀
⠀⠀⠀⠀⣀⣠⣤⣶⣦⣄⣠⣴⣆⣀⣀⣄⠀⢀⣤⡀⠀⠀⠀⠀⠀⢼⠟⠋⠉⠉⠙⢻⡆⢀⣀⡀⠀⠀⠀⠀⠀⢠⣟⠿
⠀⠀⠀⠀⠙⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠻⠛⠿⠶⠾⠷⠶⣶⣶⣶⣾⣿⣿⣿⣾⣷⣾⣿⣿⣦⡶⢶⣤⣤⣼⣥⣬⣧⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣀⡤⠤⢠⠾⠒⣲⠞⠛⠛⠒⠚⠓⠒⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠈⠉⠉⠋⠀⠒⠂⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢖⠀⠀⠀⠀⠒⠂⠤⠄⡀⢋⠒⢄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠒⠒⠒⠓⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑⠊⢁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠲⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⢆⠑⡀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠀⠀⠀⠈⡆⢁
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣀⠖⠉⠁⠢⡀⠀⠀⠀⠀⠈⢢⠀⠀⠀⡇⠸
⢀⠀⡜⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⢋⡠⠊⠁⠸⡔⠁⠀⠀⠀⠀⠈⢂⣠⠀⠀⠀⠀⢡⠀⠀⠁
⡆⢰⠀⠀⢈⡴⠀⠀⠀⠀⠀⠀⠀⡄⢲⡠⠊⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠰⠀⠀⠠⡤⠆⠀⠀⠀⠀⡀⢀⠀⣀⢀
⡇⠸⠀⠀⠈⡄⠀⠀⠀⠀⢀⠻⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⢓⠀⠀⢠⠀⠀⠀⠀⠰⠀⠈⠁⠀⠀⡁
⢡⠀⢣⠀⠀⠁⠀⠀⠀⠀⡌⠀⠀⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠷⠂⢤⠀⠀⠀⣠⢂⡁⢀⠀⠀⠀⠉⣄
⠀⢢⡀⠁⢠⠀⢀⢤⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡃⠀⠈⠁⠀⠀⠈⣄⢀⠖⠐⠁
⠀⠀⠁⠀⠘⠀⠁⠀⠠⠀⠁⠀⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢳⡀⠶⠀⠀⠀⠀⠀⠀⣀⣀⣈⣀⡀
⠀⠀⠀⠀⠀⠲⣦⡀⠀⢶⠀⠀⠀⠤⠠⡄⠀⠀⠀⠀⠀⠀⠀⢠⠶⠄⠀⠈⠲⡄⠀⠀⠀⠀⠓⠤⡎⢰⠞⠒⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠠⠄⠉⠉⢆⠀⠈⢄⣀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠤⠠⠤⠄⠤⣸⠀⠀⠀⠠⠔⠈⠁⠙⢤⡀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠧⡈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠐⠠⠔⠁⠀⠀⠀⡃⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠒⠂⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠓⢤⡀⠠⠀⠀⠉⠐⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢄⠀⣀⠀⠀⠀⠀⣀⠀⠀⠤⠐⢲⠋⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠈⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠉⢣⡄⠄⠗⠀⠀⠀⠸⠀⠀⠰⡦⣄⠀⢀⢀⠀⠀⠉⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠉⠀⢀⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠄⠁⠁⠀⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠃⡰⠁⣀⠀⢀⠀⠀⠀⡇⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢇⠀⡀⠀⢀⠀⡨
⠀⠀⠀⠀⠀⠀⠠⠤⠄⠐⠒⠈⢇⣀⣀⣀⣀⢠⣬⡎⠤⠊⠀⠀⠀⢡⠀⠀⡧⠤⠀⠞⠒⠒⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠈⠣⠠⠊⠉
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⣀⢀⠠⠒⠁⢇⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠐⠈⠀⠀⠀⠃⠀⢠
⠀⠀⠀⠀⠀⠀⢖⠉⠀⠀⠀⠀⠈⡲⠀⠄⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⡠⠔⢛⠁⠀⠀⠀⣀⣀⠀⠀⢤⡤⠄⠤⠄⠀⣀⣀⡄⠀⢃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⡀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠉⢆⠀⠈⢢⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⡄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⠦⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠠⠀⠀⠀⠀⠀⠀⠀⡰⠁⠸⡀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠠⢈⠀⠂⠠⠄⠊⠀⠀⠀⠹⠀⠂⠀⣀⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠈⠁⠱⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⡁⠀⠀⠀⠀⠑⠤⢀⡀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠑⠲⢤⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢼⠄⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣀⡠⡔⠉⠙⠯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⢀⠀⠀⠀⠉⠉⠁⡀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠋⠁⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠼⠃⠀⠀⠀⠑⢦⡀⠀⠀⢀⣀⠽⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠉⠀⠞⠉⢧⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⣀⠀⡇⠀⠀⠀⠀⠀⠒⠛⠉⠁⠀⠐⣄⠀⡀⢀⠞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⡞⢉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠁⠀⠉⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠋⠈⠁⡠⢆⠀⠀⠀⠀⠀⣴⣊⠽⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠙⠋⠈⠑⠚⠉⠀⢸⠀⠀⠀⠀⡜⢹⠆⣠⠀⠀⠀⠀⠀⡠⢞⣡⠔⠊⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⢀⣀⡤⠖⠢⣀⢀⣸⠀⠀⠀⠀⣇⣠⠟⠁⠁⢀⡠⠔⠋⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⠨⠍⢋⠀⠀⠀⣀⣈⠤⠤⠒⠉⠓⠒⠢⠤⠤⠚⠣⢄⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⡄⠀⠈⠳⠚⢋⠀⠀⠀⢠⠒⠺⢍⠳⡄⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡴⢡⠖⠁⡼⠀⠀⠀⠀⠰⠌⢢⢀⡠⠚⣀⣱⠚⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡸⠚⠷⢜⣲⡾⠀⠀⠀⠀⠀⢸⠈⢢⣉⠔⠁⠀⢸⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⣸⠀⣀⣀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠉⠉⢫⣏⠉⠄⠀⠀⠀⠀⠀⠧⠊⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⢻⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣤⣤⣤⣤⣦⢤⣷⡒⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⣦⡀⠀⠖⢋⢳⢳⣀⡀⠀⠀⠀⢀⡀⠲⠂⠀⣿⣿⣿⡿⠟⠃⠈⢻⣿⡇
⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠛⠉⠻⡿⣖⠛⠌⠈⠀⢁⠁⠀⠀⠀⠈⠁⠲⠓⠀⢻⠛⢳⢰⠔⠫⠀⠀⠉⢹
⠀⠀⠀⠀⠸⣿⣿⠉⢀⡠⡐⠧⡀⠀⠜⢣⡀⠑⠀⢰⠀⠒⠒⠂⠉⣉⣉⠭⠁⠘⡔⢿⣟⡀⠀⠀⢀⣾⣿⠷
⠀⠀⠀⠀⠀⡟⠋⣲⣨⠥⠭⠊⠈⣆⠀⠀⠹⠊⠉⠉⡄⠀⠀⠀⠈⠀⠤⠀⠀⣀⣸⣦⣀⣉⡠⠔⢺⠙⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠈⠒⠢⣔⣤⡤⣊⢭⡃⣀⡀⠀⡆⠀⠀⠇⠀⠀⢀⡠⠀⢀⡠⢊⠕⢈⠝⠉⠈⠢⠤⠃⠀⠀⠠⣀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⢅⢀⣴⣷⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⢁⠔⠉⠐⠁⢠⠋⠀⠀⣄⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇
⠀⠀⠀⠀⠀⡰⠋⠀⠀⢀⣀⡸⠉⠛⡆⠀⣀⣀⣀⡤⠊⠀⠀⠀⠁⠀⠀⠀⠀⢘⠀⢀⣰⣉⡆⠀⠀⠀⢀⡤⠴⠣⣄⡰⠃
⠀⠀⠀⠀⢰⠁⠀⠐⠊⠁⠀⢱⠀⣠⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣏⠀⡀⣹⠀⠀⠀⢾⣤⣠⡠⠊
⠀⠀⠀⠀⠀⢇⡀⠀⠀⢀⡠⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠿⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⢀⣤⠀⢠⡄⠀⣤⡀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢸⣿⣤⣼⣧⣤⣿⡇⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢸⣿⠉⢹⡏⠉⣿⡇⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠉⠀⠈⠁⠀⠉⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⠀⠀⠀⠀⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⢿⣇⠀⠀⠀⠀⠀⠀⠙⠿⠶⠾⠟⠋⠀⠀⠀⠀⠀⠀⣸⡿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⣿⡇⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢸⣿⠻⣷⣄
⠀⠀⠀⠀⠀⣸⡿⠁⠀⣿⡅⠀⠈⠻⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠟⠁⠀⢠⣿⠀⠈⢿⣇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⢻⣧⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⣼⡟⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠙⠿⢷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡾⠿⠋⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤⠴⠚⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢲⣀⠴⠋⠈⠋⠁⠀⠀⠀⠀⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣠⠞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠈⠓⢻⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⢹⡀⠀⡴⣩⠙⣦⠀⠀⠀⠀⢰⡇
⠀⠀⠀⡀⠀⠀⠀⠈⢧⡀⠀⢹⡄⢠⠆⡀⠀⠀⠀⢹⣸⡇⡟⠂⣼⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠉⠳⢄⡀⠀⠀⠓⠀⠀⡇⠟⠋⠁⠀⠀⠀⠀⠉⠁⠁⢺⢧⡀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⣀⣀⣴⠷⣄
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠓⢲⣀⡴⢲⠄⠀⠀⠀⠀⡴⠃⠀⠙⢚⡵⠛⣡⠴⠚⠛⠲⣄
⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⣠⣴⠲⣄⡀⣾⣁⠀⠀⠀⠀⡼⠁⢀⡤⠚⢁⡴⠚⠁⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⣸⠋⠀⠙⣄⢸⡄⠀⢀⡜⢷⠞⠁⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡙⢿⡾⠁⠀⢸⠀⠉⠛⠉⠀⢸⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠙⢻⣧⠀⠀⢸⡄⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠈⠧⢀⡏⢹⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠴⠋⠀⢸⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣠⠴⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠿⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣋⡀⠀⢀⡀⠀⢀⣙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢻⠃⠀⢹⡏⠀⠘⡟⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠶⠶⢾⡷⠶⠶⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⣼⡄⠀⣸⣇⠀⢠⢧⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣍⠁⠀⠈⠁⠀⠈⣩⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠸⣿⣿⣿⣿⠇⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣧⠹⣿⣿⣶⣾⣷⣶⣿⣿⠏⣼⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢸⣿⣿⣷⣦⣭⣭⣉⣉⣭⣭⣴⣾⣿⣿⡇⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣋⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣦⣭⣭⣭⣭⣭⣭⣴⣶⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠴⠦⠾⣿⣿⠿⠶⠶⠶⠤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⠀⠤⢀⡲⣿⣿⢶⣒⠂⠤⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛⠛⡿⢿⠛⠛⠘⠓⠀⠸⠤⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣟⣺⡄⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢇⠀⠀⠀⠀⠀⢠⡯⢽⡇⠀⠀⠀⠀⠀⡤⠊⡇
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣀⢀⣸⡗⢺⣇⡀⠀⠀⠀⠉⠀⠀⡇
⠠⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⢀⣔⣤⡀⠰⠖⢿⣏⡡⠰⣮⣸⣟⣻⣯⣿⢿⠅⣒⣆⣰⢤⣥⣀⣀
⠀⠑⢦⡀⠀⠀⠀⠀⠀⠈⠐⠤⠀⣀⡀⠐⠁⣋⠀⠀⠀⢹⡏⠹⡁⢉⠩⣽⢏⡙⡏⠉⠉⠁⠉⠉⡟⠉⢩⠁⠈⠉⢳
⠀⠀⠀⠈⠁⠒⠀⠤⠄⠀⠀⠒⠋⠉⠀⠀⠀⣿⠤⠄⠀⢸⠇⠂⠙⡀⠀⣿⣤⡜⡇⠀⠀⠀⠀⢀⣇⠀⠸⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠘⡄⠀⡠⠋⠀⠀⠀⠈⠤⡿⣀⠤⣿⠀⠀⠀⠴⠉⡿⠀⢰⠄⠀⡜⣧
⠀⠈⢶⠤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⡀⠰⠊⠀⠀⠀⠄⠀⠀⢈⡿⣄⣁⣿⡤⠒⠀⠀⠀⡏⠀⠀⢱⠊⠀⢻
⠀⠀⠈⠙⠛⠿⠓⠒⠒⠀⠀⠉⠀⠀⠒⠚⠉⠀⠀⠀⠀⠄⠀⠀⠐⠀⢸⣷⣛⣿⣿⠀⠀⠀⠀⠀⢛⣠⠔⠈⢣⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢤⡴⢿⣿⠛⠳⣽⢦⣄⡠⠴⠖⡻⣧⠀⠀⠘⣷⢼⡇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠀⠀⠲⠂⠀⠀⠀⠀⠀⣼⣸⡗⣦⣈⠀⠀⠀⣠⡀⠙⣾⣆⡀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠈⣟⠛⣌⣨⣿⡷⣤⡀⠀⠙⠦⣌⣻⣎⠘⢶⣻⣿⣟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣟⡉⠉⢻⡟⠲⢌⡡⢄⡀⠀⠙⠛⠷⣏⢹⣏⢿⠻⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠟⠛⢯⣿⠀⠀⠀⠀⠉⠢⣤⣀⡴⠞⣿⣿⣺⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲⣤⣤⡖⢿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣿⣿⠈⣢⣥⡀
⠀⠀⠀⠀⣀⣠⣤⣶⣦⣄⣠⣴⣆⣀⣀⣄⠀⢀⣤⡀⠀⠀⠀⠀⠀⢼⠟⠋⠉⠉⠙⢻⡆⢀⣀⡀⠀⠀⠀⠀⠀⢠⣟⠿
⠀⠀⠀⠀⠙⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠻⠛⠿⠶⠾⠷⠶⣶⣶⣶⣾⣿⣿⣿⣾⣷⣾⣿⣿⣦⡶⢶⣤⣤⣼⣥⣬⣧⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣀⡤⠤⢠⠾⠒⣲⠞⠛⠛⠒⠚⠓⠒⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠈⠉⠉⠋⠀⠒⠂⠉⠉⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢄⣸⣶⣷⣾⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠛⠀⠠⣦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⠇⢀⣤⠀⢶⡆
⠀⠠⢼⣻⣿⣿⣿⡷⠄⠀⢀⣤⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠙⠃⠀⠀⠀⠉
⠀⠀⠊⣻⠿⡷⢟⠑⠂⠀⠀⠉⠀⣠⣦⣦⣼⣿⣦⣀⣄⣀⣴⣶⣶⣤⣄⠀⠀⠀⠀⠀⢸⣿⣦⣤⣤⣤⣤⣤⣤⣴⣤⣴⣶⣤
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣀⢀⠀⠿⠂⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⢸⠭⣿⣰⡆⠀⠀⢀⡶⠀⠀⠀⣆⠀⠀⢀⡀⠀⣀⠀⠰⡀⢸⣿⡇⠀⠀⢀⣦⠇⢠⡄⠀⠀⠀⠀⠀⡴⠀⠀⠀⢀⠄⠊
⠀⠀⢸⣴⣿⠈⡟⠀⠀⠸⡏⠁⠀⠙⣿⠀⠀⣾⣴⣶⣼⡆⠒⡇⢸⣿⡇⠀⠀⢸⣿⠀⣾⣿⠀⠀⡠⠤⠬⡷⠤⠐⠊⣁⣤⣾⡆
⠀⠀⠘⠛⠛⠀⠃⠀⠀⠀⠃⠀⠀⠀⠛⠀⠀⠛⠉⠉⠙⠃⠀⠃⠘⠛⠓⠀⠀⠀⠛⠀⠛⠛⠃⠀⠐⠒⠒⠓⠒⠒⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠩⠅⠻⠋⠉⡇
⠀⠀⠀⣀⠀⠀⢀⡀⢠⡀⠀⠀⠀⣤⢸⣿⣿⠀⠀⠀⢠⠍⢤⠀⠀⠀⢀⣀⠀⠀⠀⠀⠤⢠⡄⠀⠀⠀⡇⠀⠀⢀⣶⡀⣶⡇
⠀⠀⣿⡗⠀⠀⠈⠀⣿⡏⠀⠀⠸⣿⢺⣿⣿⠀⠀⠀⣟⠢⢺⠇⠀⠀⢈⣻⠓⠀⠀⢀⡀⣼⡇⠀⠀⠀⡇⠀⠀⢸⣧⠀⠙⡇
⠀⠀⠞⠛⠀⠀⠀⠀⠹⠁⠀⠀⠰⠋⠛⠛⠛⠀⠀⠀⠚⠀⠸⠀⠀⠀⠐⠉⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠧⠤⠤⠾⠼⠤⠤⠇

⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿