Cacti Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡄⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀
⠀⠀⠐⣆⢸⢠⣏⡴⠋⠀⠀⠀⠀⢽⡗⠀⠀⠀⠉⢀⠀⠀⠀⠀⠉⠳⣤⢠⠏⠀⣈⡆⢢⡾⣠⠆⠀⠀⢹⣧⠀⢀⣠⣼⣿⣶⣶⠾⠋
⠀⠀⠀⠈⢿⣿⣯⠶⠖⠀⠨⣿⠄⠐⡗⠀⢀⠀⠀⠀⠰⡄⠀⠀⢀⠀⠙⡇⠀⠀⢃⢳⣨⠀⠟⠋⠀⠀⢀⣿⣿⠟⠋⠉⢡⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠺⣎⡀⣿⠁⢠⣶⡂⠀⠂⠅⠀⠀⠀⠀⠀⠁⢂⠀⠀⢺⣾⠞⠁⠀⠀⣴⣿⡟⠁⠀⢸⣿⣿⣿⡿⠅
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣾⠂⣾⠯⢀⠀⠀⠘⠁⢤⠀⠀⡀⠤⠄⠀⠀⠰⠆⠶⠀⠀⠀⠉⠉⠀⠀⢀⡻⣿⠟⠋
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢌⣽⣽⠋⠀⠌⠐⣂⠔⠀⠀⠘⡸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦
⠀⠀⠀⠠⠀⠀⠄⠀⢸⠆⢈⡅⠀⡀⠛⠀⠀⠀⠣⡑⠊⠘⠀⠂⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣿⠀⢰⠇
⠀⣶⣦⡀⢰⣦⣤⡀⠘⣛⣴⠇⣰⠃⠀⡶⡿⠦⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⣿⢀⡼
⠀⣿⣿⡇⠈⣿⡿⠃⠀⢫⣿⣯⡉⠀⠐⣿⣿⡯⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⣴⠀⣿⠉⠁
⠀⠘⠿⠃⣀⠉⠀⠀⠀⠀⣝⣏⣴⠃⠀⢠⠤⣴⣯⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣿⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⠀⠀⠘⠿⠽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⣀⡆⢀⠀⠀⢸⣿⣿⣆⢀⡲⢨⡸⠃⠰⣓⠀⡍⠀⠀⢀⠓⡀⢀⠀⠃
⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠁⠀⢸⣿⣿⡟⢠⡑⠆⠙⠃⠀⡾⡬⠃⣀⣄⡀⠑⠜⠀⠀⡁
⠀⢠⣿⡁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀⠁⠃⠀⠁⠀⠉⠀⢸⣿⣿⣇⠀⠀⠙⠶⠚
⠀⢉⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⣿⣿⠀⠀⠄⠀⣀⠀⠀⠀⠀⢸⣿⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠀⠀⠂⠀⢸⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠟⠀⠀⠀⠀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⣠⢰⣿⡼⠃⠀⠠⣖⢀⡷⠀⠀⠀⠀⠀⠀⠤⠀⠰⠄⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡇⡗⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢻⣿⡿⠀⠀⣄⠈⣿⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⢮⡇⢠⢹⠃⡏⡆⠀⠀⡆⠤⠔⠀⠀⢀⡤⣤⡀
⠀⠀⠀⠹⠇⠀⠀⢻⣖⣯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⡀⠀⠀⢻⢸⣼⢰⡇⡇⠀⠀⢠⠀⡄⠀⠀⡟⡁⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠸⠆⣁⠄⠀⠀⢣⣿⣾⡿⠁⠀⠀⢀⢦⡇⠀⠀⢣⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⣷⣷⠄⠛⣼⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠠⣾⡇⠀⠀⠀⢣⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣶⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⡈⡀⡘⡘⡀⠀⠀⠀⠀⠀⠀⠠⢊⠋⠉⠈⢑⠀⠀⠀⠀⠀⠰⠁⠁⠘⠀⠎⠆
⠀⠀⠀⠀⠀⠀⠀⠇⡆⠁⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⡌⡈⢰⠀⠀⡆⡀⠀⠀⠀⢀⠃⠃⡄⠀⠈⢠⠈
⠀⠀⠀⠀⠀⠀⠰⢀⢠⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠁⡇⠀⠀⠀⠈⢸⠀⠃⢰⢰⠈
⠀⠀⠀⠀⠀⠀⡆⢸⢠⠀⡇⠀⢸⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠐⢸⠀⠀⠘⢸⠀⡇⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⢸⠀⡇⡇⠀⠀⠀⠀⢸⠀⠀⡇⠨⠀⡇⡇⠀⠀⠀⠀⢴⠛⠟⠦⡀
⠀⠀⠀⠀⠀⠀⠇⠀⠸⠀⠀⠀⠸⠀⡄⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠃⠇⠀⠀⠀⠈⠈⢠⢠⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⡇⠀⠀⠀⠀⢸⠘⠀⡇⠃⠀⠀⡄⠀⠀⠀⡀⡀⢸⢸⠀⡀⢰⠀⠀⠀⠀⠀⠀⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠃⡇⠀⠀⠀⠀⢸⠀⠀⠃⢀⠀⡆⢡⠀⠀⠀⠃⠁⡀⢸⠀⡇⢸⠀⡀⠀⠀⠀⠀⠀⢸⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⢀⠀⠀⡀⢀⠀⠀⠀⠀⠘⡀⡇⠘⠈⡄⠠⠘⡀⠀⢰⢀⠀⡇⢸⠀⠀⠈⡄⢁⠀⠀⠀⡄⡀⠈⠀⠀⡇⡆
⠀⠀⠀⠀⠀⠀⠀⡇⢨⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢡⠰⡀⡇⢡⠐⡀⠡⡀⠘⠈⠀⠇⢸⠀⢠⠀⠃⢸⠀⠀⠀⠇⡇⠀⠀⠀⡃⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢆⠱⠘⡄⢢⠑⢄⠑⢢⠀⠀⢀⠘⠀⢸⠀⡀⢠⠀⠀⢰⠀⠁⢸⠀⠀⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⢆⠣⡘⢄⠑⠤⠈⣹⠀⠀⢸⠀⡆⢠⠀⡇⢸⠀⠀⡈⠀⠀⡄⠸⠀⡇
⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⠢⡑⠢⠄⢸⠀⡄⠀⠀⡇⢸⠀⡇⠀⠀⢀⠃⠐⢠⠁⠀⢠
⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠇⢸⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣉⠐⢒⡀⡇⠀⠀⡇⢸⠀⡇⠀⢀⠜⢠⠁⠄⠀⠇⠘⢰
⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⡇⢠⠀⡇⢘⠀⡇⡴⠊⡠⠃⡰⠀⡜⢀⠃⡌
⠀⠀⠀⠀⠀⠸⠀⠀⠸⠀⢰⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⠀⡇⠘⢀⠟⢀⠜⢀⠔⠀⡐⠀⡌⢠⠁
⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠸⠀⡇⡸⢁⠔⢁⡴⠃⢀⠜⠀⡜⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⢡⠁⡠⠋⠀⡠⠊⢀⠜⢠⠎
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⡆⢠⢱⡆⠌⠀⡠⠊⢀⠔⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⢸⠀⣷⡔⠩⠄⠂⢁⠤⠊
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠈⠀⡆⢸⠐⠂⠉
⠀⠀⠀⠀⠀⠀⡆⢸⠀⡇⠀⠀⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⡇⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠇⢸⠀⡇⠰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠃⠘⠀⠃⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⢦⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢧⢸⣿⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠟⡀⠈⡳⠀⡄⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢉⣠⠄⠈⠻⢾⣮⡟⣽⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠦⡄⠱⠀⡄⣷⢀⣈⡠⠐⡇⠀⠀⠀⠀⠠⠋⢀⠔⠉⡠⠔⠈⢉⡠⠙⣧⡭⣿⠏⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⣥⡀⠈⢦⣘⣿⣷⠎⢁⠠⠾⣛⢶⡒⠦⣤⠃⡰⢃⡴⠊⠀⢀⡴⠋⠀⢠⠇⣿⣮⣻⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡑⢤⡉⣙⣿⣿⣿⣷⡿⠤⠲⣖⢮⠧⠱⡄⠈⠳⣡⠊⠀⠀⡠⠊⠀⠀⢀⠎⢠⠃⡃⠈⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣬⣍⣁⠔⢉⠼⡟⢿⠉⢳⡖⢌⡎⡄⠀⠘⡄⠀⠹⣀⡠⠊⠀⠀⠀⠠⠂⢀⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⣿⣡⢞⠋⡰⢣⠀⢛⢢⣧⠀⠁⢹⠀⠀⠘⡄⠀⢹⡀⠀⠀⠔⠋⠀⡠⠋⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠤⣠⠁⡌⠸⢇⠸⡀⠇⠀⣦⡄⠀⠻⠀⠀⠀⡆⠀⠀⠱⠀⠀⣃⠀⣀⠀⠔⢋⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠁⠒⠒⢶⠀⠁⠀⢸⠀⠈⡃⠀⡟⠀⠀⠀⡆⠀⠀⢠⠀⠀⠀⠃⠀⠹⠛⠒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠒⠉⠉⠉⠀⠂⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠉⠉⠁⠀⠂⠺⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⠑⠂⠤⠤⠤⠚⡃⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣑⠀⠠⠤⠴⢚⡇⢰⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠛⠁⢰⠀⡆⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠠⠀⢰⠀⠀⠀⠀⠇⠀⠀⢰⠀⠀⠀⡇⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠂⠀⠆⠀⠀⠀⢠⠀⠀⢸⠀⠀⢀⠁⠀⢰⠀⢸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡆⢰⠀⠘⡀⠘⡀⠈⡄⠀⢸⠀⠀⢸⠀⠀⣌⠀⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⢿⢿⣤⣧⣀⣡⣀⣣⣀⣡⡀⣰⣀⣀⣬⣀⣴⣷⠶⡟⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠾⢶⣴⣬⣹⣽⣹⣯⣹⣯⣉⣋⣩⣁⣥⣤⣤⠴⠟⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠄⠤⠄⠤⠤⠤⠤⠤⠤⠤⠒⠒⠊⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⣿⣷⡄⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠸⢿⣿⣿⠃⠀⠀⠀⠉⣶⠐⠀⠀⠀⠀⠀⣀⠀⢰⣿⡄⠀⠀⢠⣾⣿⡆⠠⣤⣿⣖⠀⢀⣀⠀⢸⣿⡀
⠀⠀⠘⢻⣿⣷⣶⣤⣤⡀⠀⠀⣸⣿⡇⠀⡀⠸⣿⣿⣾⡆⠀⠀⠀⢸⡇⠀⣿⡃⠀⢿⣿⡇⣿⣿⠀⢠⣾⣿⣿⣿⠃⠺⠿⠷⣿⠃⣾⣿⠀⣾⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⣼⣿⢼⣿⡇⠸⣿⣆⣽⣿⣿⣅⣸⣷⡄⢸⣿⠀⣿⠀⠀⠘⣿⣷⣿⡏⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠹⣾⣿⣿⠀⢸⣿⣷⣶⣦
⠀⠀⠀⠘⠿⠿⠿⠏⠀⠀⣿⣿⣿⣿⡇⠀⠈⣹⣿⣿⣿⣿⡟⠁⠀⠀⣿⡀⣿⠀⠀⠀⢿⣿⣿⠇⠀⢈⣿⣯⣿⠇⠀⢀⡀⠀⠀⣿⣿⣿⠀⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⢉⡅⢥⠀⢀⡀⠈⠛⠋⠀⠀⠀⠹⠟⠋⢠⣴⣾⣷⡶⢀⣿⣿⣿⠀⠈⢿⢿⡿⠁
⠀⠀⠀⠀⠀⠐⣿⡗⠀⠀⠈⠉⠁⠀⡀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠘⢦⡻⣘⣅⣜⣠⠶⠀⠀⣠⣤⣤⣤⣀⠀⢸⣿⣿⣿⠁⠸⣿⣿⡟⠀⠀⠀⣠⠀⣀
⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⢸⣷⠀⣸⣿⡆⢀⣄⠈⠙⠛⠉⣀⠀⢀⠀⠀⢸⣿⣿⣿⣧⠀⠀⣼⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⡆⠀⠉⠋⣀⠀⠀⠀⣿
⠀⠀⠀⣠⡄⠀⣿⡇⠀⠀⠘⢿⣷⣿⣿⣇⣿⣿⠀⢲⣜⣧⣿⣰⡟⠀⠀⢸⣿⣿⣿⡿⠀⠀⠹⣿⣿⣿⣿⣿⠃⠀⢿⣿⣿⣿⡆⠀⠸⣿⣧⠀⢸⣿⡆
⠀⠀⠀⣿⡇⠀⣿⣇⠀⢠⣶⡄⠈⣿⣿⠿⠿⠃⠀⠀⢿⣿⣿⣿⣵⡾⠀⠈⢿⣿⡿⠃⠀⣄⣀⠈⠙⠛⠋⠁⠀⠀⠘⣿⣿⣿⣷⡄⠀⣿⣿⡀⣸⣿
⠀⠀⠀⣿⡇⠀⣿⣿⠀⢸⣿⡇⠀⢻⡿⠁⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⣀⡀⠀⠉⠀⢠⠷⣿⣹⣿⠀⢠⣴⣶⣦⣄⠀⠻⣿⣿⡿⠁⠀⣿⣿⡇⣿⣿
⠀⠀⠀⢻⡇⢸⣿⣿⠀⢸⣿⡇⠀⠀⠀⣀⣄⣀⡀⠀⠀⠉⠛⠉⠀⠀⣿⣿⣦⣶⣦⠀⠛⠋⠚⠋⠀⣽⣿⣿⣿⡗⠆⠀⠙⠋⠀⠀⢿⣼⣿⣇⣿⡟
⠀⢸⣷⡸⣿⣼⣿⣿⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⣷⠀⠀⠠⣶⣶⠀⠀⢙⣿⣻⠛⠁⣤⣤⣴⣀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⢠⣷⠀⡘⣿⣿⣿⣿⡇
⠀⠀⣿⡇⠻⣿⣿⣿⠀⣸⣿⠇⠀⠀⠀⣹⠿⠿⠀⣠⣦⡀⢻⡟⠀⣰⣿⣿⣿⠀⠈⣿⣿⣿⣯⠀⠀⠀⢻⣿⡿⠃⢀⡄⠀⣼⣿⢰⣷⠈⠿⠿⠿⠁
⠀⠀⢹⣿⣤⣿⣿⣿⣿⠿⠟⠀⣿⣿⡆⠃⠀⠀⠀⠿⠿⠷⣾⣷⡆⢿⣿⣿⠏⠀⠀⠙⠉⠈⠉⢤⡄⠀⠀⠛⠁⠀⢘⣿⠀⣿⣿⢸⣿⠀⠀⠀⣴⣶⣦⡀
⠀⠀⠀⠉⠉⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⣄⠀⠀⣀⣦⣆⠀⠈⣻⣿⣿⣿⣅⠀⣀⢀⣶⢀⡴⠀⠈⣥⣴⣶⣤⣄⠀⠀⣿⣰⣿⣿⢸⣿⠀⠀⠈⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠀⣠⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⠀⣈⣿⣿⣿⣡⠖⣰⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡟⣾⣿⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠈⢿⣿⣿⠃⠀⠻⣿⣿⣿⠏⠀⠹⣿⣿⡿⠏⠀⢘⣿⣿⣿⠃⠀⠈⣿⣿⣿⣿⣿⠆⠀⠸⣿⣿⣷⡿⠏⠀⠀⢰⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉
⣿⣿⡿⠿⣿⠿⠿⢿⠿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣷⣶⣿⣶⣾⣷⣾⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣸⣤⣤⣤⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣹⡿⢋⡽⠋⠀⡟⠉⢿⣦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⡜⣀⠀⢰⡇⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣶⣤⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠸⡇⢸⡄⢸⠁⠀⣶⢸⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⠁⢸⡇⠈⣿⣿⡋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠇⠀⠸⢣⠀⠀⣫⠀⠀⠀⠈⡆⢨⣿⡀⠀⡀⠀⠀⠀⠰⣴⡟⢷⡏⠀⠀⢣⠀⢸⠉⣿⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣼⠈⣷⠀⡇⠀⠀⢠⡄⣿⠆⠘⣷⠞⠀⠀⠀⠀⠀⣿⠃⢸⡇⢦⡀⢸⠀⠈⣧⠸⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⡀⣿⠀⠀⠀⡇⠀⠀⣼⠁⣿⠀⠀⣿⠀⠀⠀⠀⠐⢶⣿⠠⣼⡇⠈⠁⠸⡀⢰⣇⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⡇⣿⠀⠳⣿⠀⠀⠀⡇⠀⠈⣀⠀⣯⠀⠀⢿⣆⠀⠀⠀⠀⠈⣿⠀⠹⡇⠀⢠⡄⣷⠈⢹⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡇⣿⡄⠀⣿⢀⠀⠀⢧⠀⠀⠿⠀⡿⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⠀⡄⣱⠀⠘⠃⣿⠀⢸⡆⢠⣿
⠀⠀⣀⠀⣼⣶⠶⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠁⣿⠁⠀⣿⠈⠷⠀⢰⠀⡀⠀⠀⣟⠀⠀⢸⡇⠀⠀⠀⠀⣀⣿⠀⠙⣿⠀⠀⠀⣿⠀⢸⡇⠘⣿
⠀⠀⢸⣿⣿⠁⠰⡇⠈⢿⢷⣄⠆⠀⠀⠀⠀⠀⠀⠈⣿⠀⡟⢴⠀⣿⠀⠀⠀⢸⣄⠇⠀⠀⣿⠃⣰⠸⣧⡀⠀⠀⠀⠈⢿⡆⠀⢸⠀⢠⡞⣧⠀⣸⡇⠀⣿
⠀⢴⡿⠁⡇⠀⠀⡟⠀⢸⠘⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⠀⣷⠀⠀⣿⠀⢀⡀⢸⡏⠀⠀⠀⣿⠀⠃⢸⡏⠀⠀⠀⠀⠀⢸⣷⠀⢸⠀⠈⠀⣿⠠⢿⠁⢸⣿
⠀⣾⡧⢀⡇⠀⢻⣇⠀⢸⡇⢹⣷⣤⠎⠀⠀⠀⠙⢾⣿⠀⡿⠀⠘⢿⡀⠘⠃⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠐⢾⡏⠁⢸⢠⠀⠀⡏⠀⡞⠀⢸⡇
⠀⣿⠀⢸⡇⠀⣾⠀⠀⢸⠃⢸⢹⡇⠀⠀⠀⠀⠀⠸⣿⠀⡇⠀⠀⢸⠁⠀⠀⢸⡇⢀⡟⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇⠀⢸⠈⠃⢀⠇⢰⡇⢀⣾⠇
⣸⣿⠀⢸⡏⠀⣿⢀⣴⠿⠀⢹⢸⣷⠀⠀⠀⠀⠀⠐⣿⠀⡇⢶⠀⢸⠀⠀⡆⢸⡇⠈⠀⠀⣿⠀⠀⣸⡟⠀⠀⠀⠠⡄⢸⡏⣇⣸⠀⠀⢸⠘⢯⠃⢨⡿
⢸⣧⠀⢸⡇⠀⣼⠈⠀⢰⠀⢸⣸⣿⠁⠀⠀⠀⠀⠸⣿⠀⡅⠀⠀⢸⠀⠸⠇⢸⠁⠀⠀⠀⡇⠀⠀⢻⡇⠀⠀⠀⠀⢱⣿⠁⢠⡟⠀⢀⡜⠀⡿⠀⣼⡇
⢸⡟⠃⢸⡇⠀⢹⡄⠀⢸⠀⢸⢹⣿⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣾⠰⡀⠀⢸⠀⠀⠀⠀⣷⠀⠀⣿⡇⠀⠀⢠⣤⡾⠃⢀⡞⣡⠴⣿⠁⢸⠇⣺⡟
⠸⣿⡄⢸⡏⡆⢸⠱⠀⢸⡄⢾⢸⡿⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣿⠀⠛⠀⢸⠀⡀⠀⢠⠿⠀⠈⣿⣥⣤⣴⠾⠋⣀⣴⡏⠀⢀⡞⠁⣠⠏⣰⣿
⢤⣿⠀⠸⡇⠀⢻⢀⠀⢸⠃⢸⠸⣿⠀⠀⠀⠀⠙⢶⣿⠀⡿⣄⠀⣹⠀⠀⠀⣼⠀⡇⠀⢸⠀⠀⠀⣿⣯⣥⡼⠗⠊⠁⣚⣤⠶⠛⢊⡽⠃⣰⠟⠁
⠀⢻⡆⠀⣧⡀⠀⡟⣧⠘⡆⢸⣴⣿⠀⠀⠀⠀⠀⠀⣿⠀⡇⠈⠀⣿⠀⣶⠀⡡⠀⠁⠀⢸⠀⠀⢤⣿⠤⠤⣴⠶⠒⠻⢯⣤⣤⡞⢉⣤⠾⠋
⠀⠘⣷⡀⢸⡳⠄⢷⡉⠀⢿⠈⡇⢻⡄⣀⠀⠀⠀⠀⣿⠀⡇⠀⠀⣿⠀⠁⠀⡇⠀⠀⠀⢸⠀⠀⠸⣿⣀⣀⠴⠤⠖⠛⢋⣁⣴⡿⠛⠁
⠀⠀⢻⡇⠀⢳⡀⠘⣟⠀⢸⡇⠱⡌⢿⣯⣀⣦⣴⣤⣿⠀⡇⠀⠀⣿⡄⠀⠀⣧⠠⡄⠀⢸⣼⠃⢸⣿⣤⣼⠷⣶⠶⠟⠻⠏
⠀⠀⠘⣧⠀⠈⣧⠀⠹⣄⠀⠻⣄⠉⠲⠿⠛⠿⠛⠛⣿⠀⡇⠀⠀⣿⠀⠀⠀⡏⠀⠉⠀⢸⠏⠀⢸⣇⡤
⠀⠀⠉⢻⣆⠀⠘⣷⠀⠘⢦⣀⠙⠳⠦⠶⣴⠒⠚⢉⣿⡆⡇⠰⡀⣿⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⣾⡏
⠀⠀⠀⠀⢻⣿⠅⢘⣦⡀⠀⠈⠓⠒⠒⠆⠛⠒⢊⣩⣽⡇⣿⠀⢷⡎⠀⠀⠀⡗⣠⠀⠀⢸⢠⡆⣿⠁
⠀⠀⠀⠀⠀⠙⣧⡈⠉⠙⠲⠧⠥⠤⠤⠤⡖⢛⣩⡴⢿⣷⣗⠀⠀⠇⠀⠀⠀⣧⡙⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣈⡻⢶⣦⣄⣀⣠⣄⣀⣴⡿⠟⠉⠀⢸⣟⣿⠀⠀⡇⠰⡄⠀⣿⠀⠀⠀⢸⡆⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠉⠉⠀⠀⠀⠀⠀⢺⡟⢏⡀⢀⣧⠀⠋⠀⣇⢀⣀⠀⣸⣧⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⡀⠀⠉⠀⠀⠚⠋⠀⠙⢁⣿⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢹⡇⠠⠶⠶⠄⠲⠆⠀⢠⠼⡿⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⣶⠀⠀⢰⡄⠀⢴⠀⣤⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢈⠀⢠⣏⠀⠀⢸⠀⠀⠀⢀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠘⠀⠀⡇⠀⠀⢸⡄⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⢰⣿⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠳⣄⠀⢸⠇⠀⢠⢸⡇⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⣿⡇⠀⠀⡇⠈⠃⢸⠀⠀⠈⢰⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠰⣇⠀⠀⢸⠀⠀⠀⢸⠇⢸⣧⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⣿⡀⠀⢸⠀⠀⢠⡿⠀⢸⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⠟⠛⠛⣿⡇⠀⠀⡏⠀⠀⢸⠀⠐⠃⣿⠀⢸⡏⠛⣛⠛⠻⠶⢶⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⣠⡤⠀⠀⠁⠀⣿⡟⠀⠀⣧⠘⠇⢸⠀⠀⠀⣿⢀⣾⠃⠀⠐⠲⠂⠰⠄⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⠄⠀⠀⠒⠀⠻⣿⣿⡵⠆⣿⠀⠀⢸⠀⠀⠀⣿⡾⠃⠀⠠⠔⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠤⠄⠙⠷⣤⣿⣀⣀⣼⣤⣾⠿⠋⠀⠀⠀⠤⠄⢀⣀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠹⠉⠉⠩⠥⠀⠀⠀⠛⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⢀⣄⠀⠀⠀⠶⠶⠂⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⢈⠀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠀⠠⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠐⠀⢰⡄⠰⠀⠀⠀⠀⠀⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⠀⠸⠁⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡧⠀⠀⠀⠁⠸⠀⠀⠜⠀⠁
⠀⠀⠀⠀⠀⢀⠸⣄⠀⠆⠀⠀⠀⠀⠄⠀⣴⠃⠀⠁
⠀⠀⠀⠀⠀⠈⣤⣬⣤⣬⣥⣤⣤⣀⣠⣾⣥⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⣴⣤⣦⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⢀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠦⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⢼⡿⣱⡄⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡇⠀⠀⠀⠀⠀⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠁⣼⡏⠀⠀⠀⣼⠁⣿⠁⢤⣿⠇⠀⢀⠀⠀⠀⠀⠀⠘⠀⡇
⠀⠀⠀⠀⢠⢰⣮⠈⣿⡇⠀⠀⠀⣽⠀⣿⠀⢸⡏⢀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⢸⣿⣿⠀⢼⡇⠀⠀⠀⣿⠀⡿⠀⣼⢁⣿⡿⠃⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⡀⢸⣷⡙⣆⠀⣷⠀⠀⠀⡏⢸⡇⠀⠏⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇
⠀⠀⠀⠐⡌⠻⣷⡈⠢⠉⠆⠀⠀⠇⣼⠁⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠰⣌⠻⣦⡀⠢⠀⠀⠀⠀⠘⠋⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠈⠁⠀⣝⣣⠈⠀⢀⣤⡖⠯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣞⣀⣀
⠀⠀⠀⠀⠀⠒⠀⠀⠚⠛⠻⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠘⠛⠛⠗⠚⠛⠛⠛⠛⠚⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠰⠆⠀⠑⠒⣯⣽⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠋⠀⠁⠈⠀⠈
⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠂⠀⠂⡖⠰⠀⢈⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠰⠀⣆⠀⠄⠀⠀⠈⠁⠀⢀⠘⠀⠀⠙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠒⠀⣈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠅⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⣄⠀⠁⠀⠆⠀⠀⡀⠁⠈⡀⠒⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠉⡀⠀⠄⠀⠀⡀⠀⠀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣄⠁⢀⠈⠃⡀⠀⠀⡉⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢂⣉⣄⣉⣀⣠⣴⣤⣤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⢀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠛⠛⠛⠛⠛⠋⠙⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢻⡟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠈⢹⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⢾⡇⢰⠀⣧⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⣸⡄⢿⠞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⣸⠀⠟⠐⣧⠀⠀⢠⣴⣼⣤⡀⠀⢠⠀⣿⠀⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⣿⠘⣾⠂⠾⢻⠀⢀⣛⣹⣿⣿⣧⡄⠈⢸⠙⠀⣹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⠀⣯⣶⣤⣦⣴⣧⠀⠸⣿⣿⣿⣧⣿⣷⡆⢸⠀⠂⡿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡇⣿⣧⢿⠏⡟⢙⢃⣦⣿⢸⣧⣧⣸⡏⠀⣸⠀⢠⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣿⡿⢾⢾⠀⠀⠈⡸⣿⡿⢸⡇⣿⣻⣇⠠⡇⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⡇⠀⠸⠀⠀⠀⠁⢻⡇⣿⣿⣿⣷⣤⣼⣧⡄⣿⠁⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⡇⠉⢸⠀⡄⢰⠀⢸⣇⣿⣿⠝⠿⣻⡟⡇⢻⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⢸⡀⠀⠸⠸⢈⣿⣿⠛⢸⠀⠸⠇⡇⡞⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢈⠘⡇⠀⢸⡀⢸⣽⣿⡇⡌⠀⠣⠄⠀⡁⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⠀⣇⠀⠘⡇⢸⣿⣿⡅⢁⠀⢀⠀⠀⢇⡿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢃⢹⡀⠀⡇⢨⣽⣿⡇⠀⠀⡾⠀⠀⢸⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣷⠸⡈⣥⠀⡇⢸⣿⣿⡅⠀⠀⣅⠀⢃⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠁⠙⢠⡁⢰⣿⣿⡷⢘⠀⣿⠀⡌⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⡄⠠⢃⣇⠸⣿⣿⣿⢸⢠⡟⣰⣿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣿⣠⡞⣧⣾⣿⣿⣿⣷⣾⣿⣿⣿⡿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠟⠉⠉⠒⠒⠂⠛⠓⠒⠂⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠂
⢶⣄⣀⡤⢤⡤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⣿⣭⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣧⣀
⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣦⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢦⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣧⡀⠀⠀⠀⠸⢠⡀⢀⣶⠀⠀⢐⣏⠀⢀⠈⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⠷⠤⣠⣴⠇⠈⠙⠉⠁⠀⠀⣺⢰⠀⢻⡆⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⣿⣸⡆⢸⢃⡿
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⠢⠀⠀⠀⠤⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⣿⣷⣼⣼⠃⠀⠀⢀
⠐⠀⠀⠀⠀⠀⠀⣿⡀⢁⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⢠⢄⠠⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠛⠃
⣼⠇⠐⠀⠀⠁⠠⠙⠅⠀⠀⠀⠀⠀⠀⠀⠸⠋⠳⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⠁⠀⢦⣠⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴
⠀⠀⣧⠀⠉⢀⡀⢠⠀⠀⠀⠀⢠⣤⡆⠀⠀⠀⢐⡄⠀⠀⠀⡇⠀⠀⠀⡀⠐⠦⠀⠀⠀⠀⠁⠀⠀⠀⡀⢀⠀⠀⠀⠉⠉
⠀⠀⠰⡎⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠰⢼⡆⠀⢺⠂⠀⠀⡸⠀⠀⠀⠀⠉⠀⡄⡤⠀⠀⠀⣘⡄⠀⠀⠱⠊
⠀⠀⠀⠀⠀⢪⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⡾⣿⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠔⠛⠁⠀⢰⡀⡤
⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠙⡇⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠙⠃
⠚⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣼⠀⠀⠀⠗⠀⠀⠀⢈⠉⠁⠄⠀⠀⠳⣤⠶⠘⠓⠀⣄⣀⡀⠂
⠘⡶⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠄⠈⣆⡼⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠴⠀⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣧
⡄⠀⢤⡀⠀⢀⠀⣰⠀⠀⠀⠀⣠⣄⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⢠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠷⢀⠈⣇⠀⠘⠐⡇⠀⠀⠀⠀⠛⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠁⠠⢠⡀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠘⠆
⢷⣼⠀⠙⠁⠀⠀⠁⠀⠀⣰⢫⠂⣸⢌⡅⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠈⢀⢢⡠⠀⠀⠀⠀⠠⠀⠀⡿⠀⠀⠀⠀⢀
⢠⠘⠀⢰⡆⠀⠀⠀⠀⠀⣽⣼⡀⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⣞⣇⠆⠈⣼⠗⠀⠀⠀⠀⠀⠀⠝⠃⠀⠄⠀⠀⠀⢻⡇
⠿⠁⢀⡟⠉⠄⠀⠀⠀⠀⠹⣿⣿⡽⠃⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⡄⠐⡂⠀⠀⡇
⠆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠂⢀⡀⣴⠃⠀⠀⠘
⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣶⣀⣰⠞⠁
⣈⣒⣋⣉⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣤⣠⣇⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠙⣩⡖⠮⢤⠀⠀⠀⠀⠀⠀⣠⢐⠖⡖⢄⠀⠀⠀⠀⠀⡀⢰⣈⠣⡀⠇⢀⡄⠀⠀⠀⠀⠀⡔⠂⣀⠀⠀⠀⠀⠠⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⡀⠀⠀⢆⢸⠀⢘⢀⠇⠀⠀⠀⠀⢹⣾⠢⠀⡁⠐⠁⠃⠀⠀⠀⠀⠘⠀⢸⡄⠀⠀⠀⢠⢹⠘⡏⡏⡆
⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠙⠷⠞⠋⠀⠀⠀⠀⠀⣼⡇⢻⠀⣷⠀⠀⠀⠀⠀⠀⢲⠂⠀⠀⠄⠀⠀⠀⢨⢸⢰⡇⢇
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡴⠈⠒⢄⠀⠻⣿⣜⣄⣇⣠⣟⡁⠀⠠⡀⢘⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⣳⡆
⠀⠀⠀⠀⠆⠀⠀⠀⡆⠀⠀⡀⠀⠠⠄⠀⠀⠀⠀⢸⠀⠠⠀⢰⠂⠈⠉⠛⠛⠛⠁⠈⠀⠀⢀⠠⡘⠀⠀⠀⠀⠀⠀⠀⠈⡜⡄⡇⢹⠃
⠀⠀⠀⠄⠈⢢⠀⠀⡇⠀⢠⢃⡄⢉⠁⠠⡏⠳⠀⡘⡆⢠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠘⠀⠀⠀⢰⡆⢀⠋⠀⠰⣇⣷⡿
⠀⠀⠀⠀⠠⢈⡅⠀⠃⠀⠈⡼⠀⠁⠀⠀⠈⠱⠉⠀⠉⢦⠀⠀⠀⠀⣀⠴⣾⣿⡦⢄⠀⠀⠀⠀⠑⠂⠀⠀⢘⠀⠀⢀⠀⠀⠙⠛⠁
⠀⠀⠀⢀⡄⠘⠂⠀⡤⠊⠎⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⡄⠀⠀⠀⡎⢁⡞⠁⠀⠙⡆⢱⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠈⢄⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡬⠒⠒⠻⢄⠀⠀⠀⠣⡀⢇⠀⠀⢀⣇⠼⠀⠀⠀⠀⠀⠀⠀⠘⠠⠁⡄
⠀⠀⠀⠀⠈⠒⢧⢠⠃⠀⠀⠀⠀⠤⡀⠀⠘⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⠉⠉⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠐⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠸⣸⠀⠀⠀⠴⠊⢲⣁⣀⣰⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠓⡴⠊⢠⠀⠀⠙⢦⠤⠖⠋⠀⠀⠀⠀⢀⠎⠉⢡⠀⠀⠀⠀⠀⢠⠴⣸⠀⠀⡄⠀⠀⠀⡄⠀⠠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⡠⠶⡄⠀⢠⢸⠇⠀⠃⠀⠀⠀⠠⠀⠘⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⣬⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⡤⢄⠠⠄⠀⠇⠐⠀⠀⠄⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣧⣴⠾⣄⡀⣀⠌⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠏⡇⠀⠀⠀⠀⠀⣠⣔⣛⣹⣶⣒⠢⡄⠀⠀⠈⠢⡟⠀⠀⠀⢛⠁⠀⠀⠀⠀⠀⠘⠼⠀⠀⢀⡀⢠⢣⠀⡀
⠀⠀⠀⠀⢀⡀⢺⢸⠀⡇⠀⠀⠀⢠⠞⢡⠂⠁⢱⠀⠀⠱⡘⡆⠀⠀⠀⡂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣍⣧⠀⣏⡅⠠
⠀⠀⠀⠀⢸⠻⣸⠸⠀⡇⠀⠀⠀⡇⠀⠈⠀⠀⠸⡄⠀⠀⡁⢧⠀⠀⠀⣷⠉⡅⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠤⠤⢽⣼⠧⠶⡁
⠀⠀⠀⠀⠀⠃⠻⠀⡇⡇⠀⠀⠀⢧⠀⢠⠀⠀⠀⡆⠀⢀⠃⡎⠀⡠⠶⠾⣏⡹⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⡆⠀⡇⡇⠀⠀⠀⠘⣆⠘⡄⠀⠀⡃⠀⡎⣰⠃⢰⠃⠀⠀⠈⣆⢀⠇⠀⠀⠀⢀⣀⠀⣠⠀⢀⣀⠶⡶⢖⠀⢀⢠⠖⠆
⠀⠀⠀⠀⠰⣇⢣⠀⢰⣇⡄⠀⠀⠀⠘⢆⠘⡄⠀⡅⣸⣰⠃⠀⠀⠆⠀⠀⠀⢸⢸⠀⠀⠀⠀⡏⠀⢠⣯⡆⣾⠀⠀⣷⢸⠀⣸⢈⠓⣦
⠀⠀⠀⠀⠀⢞⣶⡄⣸⣏⠀⠀⠀⠀⠀⠀⠳⢼⣬⣦⠟⠁⠀⠀⠀⠘⢄⠀⠀⣾⠀⠀⠀⠀⠀⠙⠋⠘⠀⣛⠈⠋⠁⠉⠈⠓⠃⠈⠛⠁
⠀⠀⠀⠀⠀⠈⠜⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣧⠇⠀⠀⠀⠀⠀⣎⠐⠷⣿⢶⠰⡀⢛⠠⢴⣱⠜⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣵⠟⣹⠋⢹⡏⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠰⢇⠀⠸⠁⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢿⠶⣦⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⡟⠈⠃⡇⠀⠘⢸⠈⢿⡀⠀⠀⠀⠀⠀⢠⣿⣹⠀⢠⡄⢸⠿⣆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⡏⢶⠀⡇⠀⠀⡀⣴⠋⣷⡴⠂⠀⠀⠈⣿⠁⡇⢀⠈⠇⠈⣦⢻⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠀⠀⡇⠀⠀⡇⠀⢠⠃⣭⠀⢸⡇⠀⠀⠀⢶⡏⢰⡇⠈⠀⢰⢀⣷⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣿⢀⠀⠻⡇⠀⠀⡇⠀⢠⠀⣿⠀⢸⣧⠀⠀⠀⠈⡇⠈⢳⠀⠠⢸⠀⢡⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⢸⡇⠀⡗⣤⠀⡇⠀⠘⠀⣇⠀⠸⣇⠀⠀⠀⠀⡇⠀⣾⠀⠀⠈⡄⢠⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⠉⣯⠹⣷⣄⣠⠀⠀⠀⠀⠀⢺⡇⠸⣄⠀⡇⠀⠀⠁⣴⠀⠀⣿⠀⡀⣿⠀⠀⠀⠐⣿⠀⠉⠀⠀⡶⠁⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⠃⢀⡿⠀⢁⢹⣇⠀⠀⠀⠀⠀⢸⡇⠸⠁⠀⡇⢀⡀⢸⠁⠀⠀⠃⠘⠰⣿⠀⠀⠀⠀⢹⡆⠀⡇⠈⢸⠀⡿⠀⣸⡅
⠀⠀⠀⠀⠀⠀⠀⢸⡗⢠⡇⠈⣧⠀⣿⠘⣿⡴⠃⠀⠀⠙⢺⡇⠀⠀⠘⣇⠈⠃⢘⠀⢀⠀⡄⠀⢀⡿⠀⠀⠀⠀⢿⡇⠀⣧⠀⢸⠀⣾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⡇⢰⠀⢀⡝⢸⠸⡇⠀⠀⠀⠀⢸⡇⡄⢀⠀⡇⠀⠀⢸⠀⠎⠀⡇⠀⢸⣧⠀⠀⠀⠀⢸⡧⠀⠇⠀⢸⣴⠏⢰⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢈⠰⠋⡇⢨⣀⣷⠂⠀⠀⠀⢸⡇⡇⠉⠀⡇⠠⠆⠘⠀⠀⠀⠁⠀⢺⡇⠀⠀⠈⢣⡾⠁⢻⠀⢀⡇⢸⠂⣼⡃
⠀⠀⠀⠀⠀⠀⠀⣿⠃⢸⡀⢨⣀⠀⠃⠘⢻⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⣀⠀⡆⠀⠀⠀⣦⠀⢸⡇⠀⠀⣠⡾⠇⣠⠃⠤⡿⠁⡞⢰⡏⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⠃⠆⠹⠀⢰⠴⢸⡇⠀⠀⠀⢀⢸⡇⣇⠀⠀⡇⠈⠀⡃⣀⠀⢰⠏⠀⢸⣧⡴⡾⢋⣠⠾⠃⣀⣞⣀⡜⢠⡿
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠸⡇⠀⣧⠀⢹⠀⢈⣷⠀⠀⠀⠈⢻⡇⡟⠳⠀⡇⠀⠀⡇⠙⠀⢸⠀⠀⣼⡗⠒⢋⣁⣤⡓⠚⢉⡵⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣿⠄⢡⡗⠘⡀⣾⢿⠀⠀⠀⠀⢸⡇⡇⠀⠀⡇⠘⠀⡇⠀⠀⢸⠀⠈⣿⡉⢉⣋⡡⠤⠝⢛⣿⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠸⠆⠈⣷⠀⣧⠡⡜⣿⣄⣠⣤⣼⡇⡇⠀⠀⣧⠀⠀⡇⢤⠀⢸⣇⠀⣿⣭⣿⣤⡴⠶⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⢺⣄⠙⣄⠘⢧⡈⠓⠛⠛⠛⣹⡇⡇⠀⠀⠏⠀⠀⡇⠈⠁⢸⠃⢀⣯⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠻⡂⠈⠢⢌⣉⢚⢳⣏⡩⠴⣷⡇⠙⣄⠀⠀⠀⡇⠀⠀⢸⠁⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠻⠦⣤⠦⣉⢈⣀⠤⠖⣸⣿⡇⠀⢹⠀⠀⠀⣧⠀⠀⢸⠇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣦⣤⣀⣀⣀⣀⣼⠶⠛⠁⢸⣿⠀⢸⠀⣀⠀⡟⠀⠀⢸⡄⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠀⠀⠀⠀⣿⢹⠀⠀⠀⠉⠀⠇⢀⡀⠠⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⠀⠸⣦⠀⢸⠘⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇⠰⠈⠀⢸⠀⠀⡄⡇⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⡇⢰⡀⠀⢸⠀⠀⠀⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠁⠸⠀⠀⢸⡄⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⠀⠀⢸⡇⠀⠀⡇⢸⣇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠀⢸⠙⡆⠸⠀⠠⠆⡇⢸⡇
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢰⠀⠀⢰⠀⠀⠀⠃⢸⣇
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⠀⢸⡇⠀⢸⠀⠀⣾⠀⣼⣇⣀⣀⡀
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠛⠋⠍⢹⣿⠀⠘⠀⡀⢸⠀⠊⢸⠀⣾⠉⢛⣉⠙⠛⠲⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠚⠀⣀⠀⣾⣿⣆⡀⡀⠉⢸⠀⠀⢸⣰⠟⠀⢀⡈⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⣌⠙⢧⣥⣇⣀⣸⣠⣶⠞⠃⠀⢠⡅⠀⡀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⣀⠀⠀⠘⠋⠉⠩⠍⠀⠀⠒⠀⠀⠀⠀⠉
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠄⠀⠀⠒⠛⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⡀
⠀⠀⠀⠤⢀⠤⠀⠀⠀⠀⠀⠀⠠⠂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⠃⠖⠂⡐⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⡁⠀⠡⠏⠉⠙⠀⣀
⠀⠀⢠⠀⠀⠄⠨⠁⡀⠀⠀⠐⠄⠁⠠⠀⠁⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠃⠀⠠⡄⠀⠸⠂⠉
⠀⠀⠀⢈⠀⠂⠀⠄⢁⠀⠀⠀⠀⠈⠠⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣤⠀⠀⠀⠀⠀⠀⣦⠀⠗
⠀⠀⠀⠀⠀⠅⠐⠈⠈⢆⠐⠆⠄⡠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣋⠙⠛⡙⢂⡀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠐⠂⠀⢀⡀⢠⡆
⠀⠀⠀⠀⠀⠀⠉⠰⠂⠤⠀⡁⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠁⠀⠉⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠙⠀⠀⡠⠄⠀⢠⠁⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠠⠈⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢘⠀⠀⠐⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠀⠀⠂⠐⠀⠀⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⡈⠐⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣤⠀⠀⠀⣦⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡁⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠂⠀⠀⠚⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀⠀⠐⠂⠅⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⢠⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⢀⡈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠉⠁⠐⠲⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠱⠀⠀⠀⠀⣃⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠂⠠⠀⠀⡁⠀⠞⠋⠙⠓
⠀⠀⠀⠀⠀⠄⠘⡀⠏⠇⠀⣀⠢⠃⡐⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠈⠁⠀⠀⠀⡁
⠀⠀⠀⠀⠀⢀⡀⢵⡀⢠⢀⠁⠀⠈⢄⠰⠊⣸⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠈⠀⢠⠀⠀⠁⠀⡂⠁⡄
⠀⠀⠀⠀⠀⠀⠻⠂⢈⠀⠀⠁⠀⡀⡸⣤⠞⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠈⠈⠀⠐⠇⠀⠀⠀⡁⢀⡅
⠀⠀⠀⠀⠀⠀⠒⠃⠲⠶⠆⠀⠰⠂⠰⠓⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢸⠀⠀⡦⠀⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠈⠈⠀⠀⠁⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⡉⠉⠀⠀⠐⠀⠀⠀⠀⠈⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠐⠂⠁⠂⠂⠐⠘⠐⠊⠁⠃
⠀⠀⠀⠀⠀⠀⡅⡀⠁⠈⠈⠀⠈⢈⠈⡀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠄⡀⢠⢀⢀⢀⠀⠄⡀⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⡀⠀⠀⠀⠀⣀⣠⠄

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⢀⠀⡀
⠀⡀⠤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠀⠛⠈
⠀⠀⢠⠄⠀⢠⠆⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡄⠰⡄⢀⢀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡆⠲
⠀⠀⠈⠚⠈⠁⠰⠐⠀⠀⠀⠀⠀⢀⠀⠓⠚⠀⠀⠀⠋⠈⡇⠀⠀⠀⠀⢠⠀⠀⠀⠹⠆⣠⠁⣰⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⣆⠀⠀⡘⣄⣀⠆⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢢⡁⢠⡇
⠀⠀⠀⠀⢀⣠⠇⠀⠀⠀⠉⠁⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠸⣄⡐⠀⠀⠀⠀⠀⠀⢈⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⡟⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⠀⢰⣿⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿⣿⣧⢸⣿⣇⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⣶⡄⢀⢰⡇⢠
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡄⢰⢀⡇⡇⠀⠀⠀⢿⣿⣙⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⡇⣼⠈⣷⣼⠀⣶⣦
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢸⣧⢸⣸⣿⠃⡇⠀⠀⠈⠛⣿⣿⡿⠿⣿⡿⠋⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣾⣿⡏
⠀⠀⢸⠀⠀⢰⣿⠁⠀⠀⢸⣿⣿⣿⠏⠸⠇⠀⠀⠀⠀⣿⣿⡇⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣶⣾⣾⣦⣼⣿⡇⠀⠰⣸⣿⣿⣿⠀⢤⣼⠀⠀⠀⣸⣿⡿⡇⢸⣿⣇⢀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡓⣿⣿⡖⣿⣿⣿⣿⣿⣿⣾⣿⣷⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⢿⣿⢟⣷⣿⣿⣿⣿⡿⢯⣬⢄⡹⣿⣿⣿⣿⣿⣿⡿⢹⣿⡿⣭⠞⡁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⡬⣯⣡⣽⠂⡽⠏⠟⣟⣷⣾⣇⡀⠀⢹⣿⠛⠻⣿⡿⢋⣹⣿⡁⠁⠐⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢰⣿⢻⠅⣈⣥⠹⡇⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠈⠃⠀⢾⣻⣿⣿⣿⣷⣾⡶⢶⡿⠿⠿⢿⠿⡿⠿⠿⠿⣿⣿
⢸⣿⠷⠀⠈⠉⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿
⠰⠆⠒⠤⠤⠠⠌⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠶⠶⠶⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠐⡀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⡈⠁⠘⠀⠀⠀⠀⠱⢑⡧⠀⠀⡀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡙⠢⠀⠀⣦⡀⠠⢄⠀⠒⠀⠀⠀⠀⡆⠠⠀⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⡀⣉⠀⠄⠀⠀⣧⠈⣀⠈⠀⠀⠂⢀⠟⠀⢠⡀⠀⢸⠀⠀⠇⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢦⡀⠀⠈⠄⠀⠀⠠⣴⠈⣿⡀⢙⠂⠀⣸⠂⠈⡀⠀⡘⠀⣀⠈⠄⡀⠀⡰⠁⠀⠈
⠀⠀⠀⠀⠀⠲⡄⡀⢀⡀⢸⡃⠐⠀⣀⠘⡃⠠⠄⠀⡀⢙⠂⡉⠲⣄⠛⠀⠁⠀⠁⠀⠃⢀⠋⢀⡴⠐⣠⠀⠀⠊
⠀⠀⠀⠀⠀⠀⣈⣻⣤⡨⣏⢀⠤⣀⡀⣠⡆⠀⠠⡄⠂⠀⡀⠈⠢⠀⠈⡿⠀⣀⠊⠀⠨⠼⡀⠈⠀⠀⠕⠀⠀⢠⢠⢀
⠀⠀⠀⠀⠈⠙⠀⢀⡼⠇⠘⡇⠰⡀⠙⠄⠁⡔⠰⠠⢴⡀⠘⡀⠈⢀⣀⠈⣋⠀⠄⢈⠀⠀⠀⠠⠈⠀⠉⢒⡒⠃⡉⠼⠓⠁
⠀⠀⠀⠀⠀⠀⠁⠞⠁⡖⠀⠿⠀⠹⢄⠀⢘⡆⠀⣰⣫⣎⠄⠃⠀⢸⡁⠀⠈⠀⠀⠀⠀⡄⢀⠀⠀⠀⣯⣈⢁⡾⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠬⠁⠠⢱⡄⠂⠀⠀⠇⢡⣀⠀⠀⠎⠀⠖⠀⠀⠂⠀⠀⠦⢀⠀⢀⠀⠈⡀⢠⡈⠀⠀⡽⡹⠃⡀
⠀⠀⠀⠀⠐⠂⠻⢄⠀⠀⠢⠋⠀⠈⣀⡀⠌⠃⠈⢁⠁⢠⠔⠁⠐⠦⣰⠁⠀⠀⠐⣰⣄⡦⠐⠀⠀⠈⠢⢮⡥
⠀⠀⠀⠀⠀⡀⢢⡀⠀⠀⠖⣧⣀⠀⢀⡀⠄⠀⡄⠀⠀⠀⠶⠄⠰⠃⡁⠀⠑⠂⠸⡛⠆⠀⠘⠐⢶⠃⠀⠈⡂
⠀⠀⠀⠀⠀⠀⡍⣅⠀⠠⠒⠊⠃⡉⠡⡀⠀⠑⠋⠀⠀⢴⡀⣀⡋⣤⢃⣀⠀⠀⠀⢈⡆⠀⡰⠀⠨⠤⠀⠠⠃
⠀⠀⠀⠀⠀⠀⢒⡘⠀⠀⠠⠐⡂⠅⠀⠈⠈⠀⣀⡀⢀⠀⢈⡐⠛⣭⠨⡅⠀⠐⠒⡀⣀⠖⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⢬⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⠣⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⣆⠆⢠⠀⠂⢠⠀⠀⠄⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠙⠀⠸⠀⠠⠘⠄⠀⠏⠀⠇⠃⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⡤⠴⠟⠒⠒⠦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⠟⠛⠛⢶⡀⠀⠀⢴⡴⢊⠅⣠⠂⡔⠀⢀⢠⠈⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⢡⢠⠀⣷⢸⠁⠠⣤⠞⢠⠊⣰⠃⡘⠀⠀⢸⡀⣇⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠘⠀⡟⢸⠀⢀⡟⢠⠏⢸⠃⢰⠁⢸⠀⢸⡇⢸⡀⠸⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⡄⢸⠀⣇⡏⡀⡾⢠⡏⢀⡏⢀⡏⠀⢼⠀⠸⡟⠈⡇⠀⣧⠀⠀⠀⠀⠀⢆⣸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢱⠘⣆⢸⡇⢹⠇⣼⠀⣸⠀⣾⠁⠀⡆⠀⠀⣧⠀⣷⠀⣯⡰⠃⠀⣠⠖⠛⠉⠙⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣷⠘⣧⠹⡌⢇⣸⢀⡇⢀⡏⢠⠇⠀⢠⠃⠀⠀⣏⠀⢻⠀⢻⠀⢀⡞⢡⡴⡴⠛⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡈⠳⢦⠄⣿⢸⠇⢸⠁⣾⠀⠀⣸⠀⠀⠀⣿⠀⢸⠀⢸⠠⣞⣰⠋⡼⢁⡄⣦⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠲⠶⠶⡇⣸⠀⡏⢀⡇⠀⠀⡏⠀⠀⠀⡿⠀⣸⠀⡾⣸⢡⡇⢸⠃⡾⢡⡏⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⣿⢠⡇⢸⡇⠀⢸⡧⠀⠀⢸⡏⢉⣛⡲⠧⣟⣸⢃⣞⡼⢁⡾⠁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡏⢸⠀⣿⡇⠀⢸⠁⠀⢀⣼⠃⠐⠢⢭⣙⣯⣵⡿⠞⣠⠞⢁⡾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡽⣯⡇⢸⠀⢸⡇⠀⣿⢀⡀⠀⣸⠀⣄⡐⠲⠒⢚⣩⡴⢞⣡⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⡇⢸⡆⢸⡇⠀⣿⠋⠀⠀⡟⠓⢶⠿⠿⠿⠭⠷⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⡇⠈⡇⠀⣿⠀⠀⢸⠇⠀⡞⢠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠀⣷⠀⣿⠀⣿⠀⢀⡟⠀⢰⠇⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⢹⡀⢹⡄⣿⠀⣼⠁⢀⡟⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⡤⠶⠶⡇⢻⠀⠸⡇⠸⡇⠟⢰⠇⢀⡞⢠⡟⠥⢤⡀⣀⡤⠶⠖⠒⠒⠦⣄⠀⠀⢀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠇⢸⣦⠀⣷⠀⣷⠀⡾⢀⡞⠀⡾⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⠒⠛⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣄⡀⢷⠀⣿⠀⡟⢰⡇⣾⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠽⢤⣰⠇⣸⠃⢸⢰⡇⢀⣃⡤⠤⠤⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣯⠤⠶⠾⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢦⠂⠠⡀⠄⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⡂⢄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⢀⡘⠀⡀⠀⢀⠀⠀⠀⠀⠀⡧⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢼⣧⣤⠄⠀⠀⠰⠒⠤⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣀⣧⣤⣤⠤⢽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⡀⠄⠘⠂⠀⠈⡏⠀⠀⠀⠀⠆⠀⠠⠿⠏⠉⠙⠳⡒⠶⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣄⡀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠉⠀⠈⢤⡀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠰⠦⣄⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⢿⣹⠆⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⠀⢸⠀⠐⠓⢀⡛⠛⠉⠰
⠀⠀⠀⠳⠛⠛⢇⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⢀⣴⡎
⠀⠀⠀⡜⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰
⠀⠀⠀⢱⡀⡘⠣⡄⠀⠀⠀⠀⠐⠂⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠐⠲⠀⣀⣠⠤⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⠦⠚⠁⠀⠀⠠
⠠⠀⠀⠀⠂⠀⠀⠀⠚⠀⠀⠈⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⡀
⠀⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢂⠀⠁⠐⣠⡀⠀⢀⠀⠐⠂⠉⠁⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⣴⠁⠀⠈⡏⠀⠀⠀⢠⠆⠀⠀⠀⠈
⠀⠀⠈⠁⠀⠠⠔⠂⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⠘⡷⠒⠂⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⢠⣈⣻⡇⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠐⠉⢀⡀⠒⠈⠉⠓⠂⡈
⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠨⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐⠁
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠟⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⠘⣋⡛⣹⣿⣿⡂⠀⠀⠈⠻⢧⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⣿⣿⣯⣿
⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠀⠀⠀⠘⣿⣿⣏⣾⣿⡇⠿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⢿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣿⢸⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿
⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣛⣛⣛⣟⣛⣛⣚⣣⣤⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⣤⣤⣼⣷⣿
⣷⠁⠀⠀⢦⡶⠀⠀⠀⠀⠀⠀⠀⣴⣞⣿⢺⣿⣿⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣶⣾⣿⣿⣷⣦⠀⠀⠀⠀⠉⣾⣶⣶⣶
⡟⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⣾⡿⣼⣿⢻⣿⢻⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢹⣿⣿⡟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠈⣿⣗⣿⣿⢻⣿⣿⣿⢺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃
⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⢻⡯⣿⣿⣻⣿⣷⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠀⣠
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣶⣿⣾⣷⣾⣶⡆⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⡌⣸⣷⣆⠡⠄
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⠀⠀⠀⠀⠐⠀⣿⣿⣯⠠⡄
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⢻⣿⣿⠀⢠⣴⣦⠀⠀⢸⣿⣿⣿⠄⠀⠀⠀⠉⠀⣻⣿⡷⠰⠆
⠀⠀⣤⣽⣿⣽⣯⣤⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢿⣿⣤⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠈⠈⣻⣿⣿⣘⡃
⠀⠀⠛⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⢹⣿⣿⣿⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠘⠃⣻⣿⣿⠄⠁
⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⣤⣥⣽⣭⣽⣤⣤
⠀⠀⠀⠸⠿⠿⠃⠀⢀⣶⣿⡄⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⣤⣤⣌⣿⣿⣿⣁⣀⣠⡀⠀⠀⠀⠀⠈⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣷⣶⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠐⣿⣿⣷⡀⠀⠀⠿⢿⣿⣿⣿⣿⣿⠿⠿⠀⠀⠀⢠⣤⣤⣬⣭⣭⣭⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢠⣶⣶⡄⠀⠀⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠉⣭⣭⣭⣭⣭⣭⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣿⣦⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⣿⣿⣿⡇⠀⢠⣿⣿⣿⠁⠀⠀⠀⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣽⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠃⢀⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⡄⠀⠀⠀⠀⠀⣤⣦⠻
⠟⠿⣸⣿⣷⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣞⣿⢺⣿⣿⣲⡄⠀⠀⠀⠀⠀⠀⠀⢈⣹⣭⣉⠁⠀⠀⠀⠀⢰⣿⣿⣇
⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣼⣿⣹⣿⣻⣧⢿⣆⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⡟
⣿⣃⣶⢻⡿⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣾⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⣿⣹⣿⣯⣿⣺⡷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⢿
⡿⠿⠿⠸⣃⡀⠀⠀⠀⠀⠉⣿⣷⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣹⣗⣻⣿⣽⣿⠻⠿⢾⣏⠀⠀⢠⣤⣤⣿⣿⣿⣿⣿⣭⣤⣤⡀⠀⢀⣻⡿⠿
⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⠲⢠⣅⡀⠞⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⢿⣿⣿⣿
⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⣾⣿⡷⠈⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠸⣿⣿⣿
⣿⣿⠿⠛⠁⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢤⠈⣿⣿⣟⢘⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠠⠠⣿⣿⡯⢨⡁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⠠⣿⣿⡷⠰⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢀⣼⣿⣷⠀⠀⠀⠀⠀⠀⢀⣀
⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠠⠠⣿⣿⣿⠐⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⠀⠀⠀⠀⠀⣀⣀⡿⠃⠀⢸⣿⣿⡿⠀⠀⠀⠀⣠⣾⣿⢿
⣿⠀⠀⠀⠀⢶⣶⣾⣿⣿⣿⣿⡷⠶⢶⡆⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠿⠂⠀⠀⣶⣷⡘⣿⣾⣿⡇⣤⣄⠀⠀⠀⢿⣿⣷⢠⣶⣾⣿⠿⠁⠀⠀⠀⢸⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⡠⠚⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠉⠀⠀⣠⡘⠄⠀⠀⠀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠠⡄⠀⠠⠊⠀⠈⠗⠀⠀⠀⠀⠘⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠃⠒⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠂⠀⠈⠀⢀⠀⡀⠀⠀⠀⠀⢙⣤⢦⣁⠈⠁⠀⠀⠀⠲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣈⢍⠀⠀⠀⠀⢀⢸⠅⠀⡆⢰⢂⣀⢌⢀⠀⠠⠄⠀⢀⠄⡪⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠘⠁⠈⢥⠉⠑⢠⡸⠌⠸⠟⠂⣠⡀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣄⠴⢤⠦⠠⠖⠋⡸⠈⠂⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠓⢦⠆⠁⠀⠀⠀⠀⢠⡄⣠⣄⡖⠀⠀⠀⠀⠈⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠿⠑⠤⢀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠅⠀⠀⠀⣀⡡⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠈⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠁



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

⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣆⡀⠀⠀⠀⠀⣿⡇⠀⠙⣿⣿⣁⠀⠀⠀⢿⠈⢠⡄⠀⣤⡄⢸⣿⠀⣀⣰⣿⣿⢀⣾⣿⣧⢠⣤⠀⣾⣦
⠀⠀⢸⣿⣿⣿⡟⠃⣴⣆⣿⡇⢰⣦⢙⣿⣿⠀⣤⡀⢸⡆⢸⡃⠀⢿⣿⣾⡏⠀⣿⣿⣿⡗⠀⠉⠉⣧⣾⣿⠀⣿⣿⣤⡄
⠀⠀⠘⠿⠿⠿⠁⠀⣿⣿⣿⡇⠀⢉⣿⣿⣿⣿⠋⠁⠘⣇⣾⠀⠀⠸⣿⣿⠃⠀⣿⣿⣿⠁⠀⡀⠀⢸⣿⣿⠀⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣶⠀⠀⣿⣿⠿⠇⠀⢸⣿⣿⣿⣿⠀⠀⠀⢡⡠⡄⢠⠀⠉⠋⠀⠀⠘⠛⠁⣴⣾⣿⡖⢸⣿⣿⠀⠘⠿⠿⠁
⠀⠀⠀⠀⢸⣿⠀⠀⢠⡀⢀⣤⡀⠀⠻⢿⣿⠟⠀⠀⠈⠓⣧⣷⣦⡞⠁⢠⣶⣿⣶⣦⡀⣽⣿⣿⡀⠸⣿⠏⠀⠀⢰⡆⠄
⠀⠀⢀⡀⢸⣿⠀⠀⠸⣷⣼⣿⣇⣾⡆⢀⢠⣰⣆⣴⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⠇⢸⣿⣿⣧⠀⠀⣶⡄⠀⣾⡄
⠀⠀⢸⡇⢸⣿⠀⢀⣤⠈⢻⣿⡿⠟⠀⠈⢿⣿⣿⣧⡖⠀⠻⣿⡿⠁⣀⣀⠉⠛⠛⠋⠀⠀⢿⣿⣿⣦⠀⣿⣿⢀⣿⡁
⠀⠀⢸⡇⢸⣿⡆⢸⣿⡇⠘⠿⠁⠀⠀⠘⢿⣿⣿⡟⢀⣤⡀⠈⠀⢾⣿⢿⡧⢀⣶⣾⣶⡄⠙⣿⣿⠏⢀⢻⣿⢸⣿⠁
⠀⣠⡘⣧⣸⣿⡇⢸⣿⠀⠀⢀⣶⣶⣄⡀⠀⢀⣀⠀⠘⣿⣿⣿⠇⠀⢉⠈⠀⠐⣿⣿⣿⡍⠀⠀⢀⡀⠸⣿⣿⣾⣿
⠀⢸⣇⢻⣿⣿⡇⢸⣿⠀⠀⠘⢿⣿⡟⢁⣀⠸⣿⠂⢠⣾⣾⠀⢰⣿⣿⣷⠀⠀⢻⣿⣿⠃⠀⠀⣼⡇⣴⠙⣿⣿⠏
⠀⠈⣿⣆⣿⣿⣷⡿⠟⢰⣶⡆⠁⠀⠀⠻⠿⢦⣷⡄⣿⣿⡿⠀⠀⠛⠋⠉⣤⡀⠀⠛⠁⠀⣿⠀⣿⡇⣿⡇⠀⢠⣤⣤⡀
⠀⠀⠈⠉⣿⣿⡇⠀⠀⣾⣿⣿⡄⠀⢠⣶⡆⠀⢹⣿⣿⣿⡄⢠⣠⣇⡴⠂⢈⣶⣾⣶⣄⠀⢻⣷⣿⡇⣿⡇⠀⢸⣿⣿⠁
⠀⠀⠀⠀⣿⣿⡇⠀⠀⢿⣿⣿⡏⢠⣿⣿⣿⡆⢸⣿⣿⣿⠇⢠⣿⣿⡷⠋⢼⣿⣿⣿⣿⡀⠸⣿⣿⣻⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠛⠛⠃⠀⠀⠈⠛⠋⠀⠀⠙⠛⠋⠀⠀⠙⠛⠉⠀⠀⠛⠛⠁⠀⠈⠙⠙⠛⠋⠁⠀⠙⠛⠛⠁⠀⠀⠙⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣤⡀⢷⠀⣼⢀⣴⠞⠀⠀⠀⠀⢐⣺⡯⠄⠀⠀⠉⠲⠀⠀⠀⠀⠀⠙⠻⢶⣄⠀⢰⠟⠀⠘⡆⢡⣈⡴⢀⡆⠀⠀⠐⣿⣆⠀⠀⠀⢀⣹⣧⣤⣤⣴⣾⠗
⠀⠀⠀⠈⢷⣼⣼⣷⢏⣀⣀⠀⠠⢤⠔⠀⣹⣇⠄⠀⠀⠀⠀⡘⢀⠀⠀⠀⠀⠀⠀⠻⣄⡋⠀⠀⠖⢢⢀⠟⢃⣯⡵⠂⠀⠀⢸⣿⣤⣶⡾⠿⠟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠙⠿⠟⠛⠉⠁⠀⠐⢺⣏⡀⢬⣧⠄⠀⢆⢀⡀⠀⠈⡬⡀⡀⠀⠔⠂⠀⡿⠀⠀⠀⠀⠀⡇⡆⢰⠂⠁⠀⠀⢀⣼⣿⡿⠉⠀⣀⣤⣤⣷⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣤⠀⣷⠄⠘⣾⡫⠀⠀⠉⠔⣐⠄⠀⠀⡀⡀⠀⠀⡅⠀⠀⡈⠿⠟⠁⠀⠀⠀⢴⣿⣿⠏⠀⠀⢀⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠷⣤⣿⠒⢰⠿⠄⠀⠀⠀⠐⠋⠀⠤⠀⠤⡀⢄⠔⠀⠀⠀⠐⠖⠒⠒⠀⠀⠀⠀⠉⠁⠀⠀⠀⣸⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣹⠟⠒⢠⡉⠶⠒⠤⠀⠀⠀⢠⠒⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢱⡄⠀⠇⠀⠀⠉⡿⠉⠀⠀⠰⢑⠣⢍⠀⠆⢀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠓⣿⡇⠀⣴⠀⠀⠈
⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⢨⣵⢀⣟⠀⣰⠀⠀⢀⣤⣄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⢀⠀⠀⠀⠀⠂⠀⣠⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠈
⠀⣿⣿⣿⡄⠸⣿⣾⣷⠀⢨⣴⢾⣯⣴⡍⠀⢀⣋⣛⣊⣵⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣧⡾⠃⠀⠀⠀⠠
⠀⢹⣿⣿⠇⠠⣿⡿⠏⠀⠀⢱⣿⡿⡦⠀⠀⠰⣷⣬⠿⠿⣟⣛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⠀⠀⠀⣿⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠻⡿⠀⣀⠉⠀⠀⠀⠀⠀⣭⣻⣠⡾⠁⠀⠠⠴⢶⣺⣭⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⣻⡇⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠏⠋⠀⠀⠀⠘⢟⣻⡿⠟⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠢⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠆⠀⠀⠀⠀⠠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣲⣞⣦⡀⠀⠀⡀⠰⠂⡀⠀⢂⡘⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⢀⠀⠀⢸⣿⣿⣿⠀⢠⡙⠰⡆⣁⠀⢠⠅⠀⠂⠀⠀⠀⠠⠀⠆
⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⢦⠘⡃⠘⠁⠀⢐⣒⡺⠀⣠⣴⣤⠀⠀⠂⢁⠀⠠⣀⠀⠀⠀⠀⠀⠀⠠
⠀⢠⣍⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡁⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠀⡀⠈⠁⠀⠈⠀⠀⠁⠀⢰⣿⣿⣿⡇⠀⠀⠈⠻⠾⠋
⠀⠂⠦⣯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠕⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠘⠀⠀⠠⠄⠀⢸⣿⣿⣿⠁⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣄⠀⠀⠀⠀⠀⠛⠟⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠩⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠛⠛⠛⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⣄⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⢀⡄⢸⣿⣼⠏⠀⠀⢸⣖⢀⡿⠂⠀⠀⠀⠀⠀⠀⠀⠤⠂⠐⠆⣈⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡀⡗⣦⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠸⣷⣿⡟⠀⠀⢀⠀⢘⣧⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⡆⠀⠀⠀⠱⣄⣧⢠⡄⣿⠃⡟⣠⠀⠀⠀⡄⣀⡀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠙⣿⡇⠀⠀⠼⣷⣘⣛⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢻⡀⣇⣿⢠⡇⣿⠀⠀⠀⡇⠀⡉⠀⠀⠀⡟⡇⡟⢧
⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣷⠿⠆⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⣁⠀⠀⠀⠀⠀⢧⢹⣾⢸⣇⡇⠀⠀⠀⣠⠀⣿⠀⠀⠀⡇⢁⠠⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡌⡀⠘⢋⣄⡜⠁⠀⠀⠈⢻⣿⣿⡞⠀⠀⠀⠀⢠⣼⣿⠀⠀⠀⠱⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢠⣿⠿⠄⠈⢡⡿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠰⡄⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠙⠋
⣿⣿⣿⠿⣿⡿⢿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣶⣿⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢆⠀⠀⠀⠀⢈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢕⠄⡀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠑⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠈⠁⠀⢄⠀⠈⠄⢇⠀⠀⠀⠀⠀⣀⠀⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢄⢰⡈⠀⠀⠀⡴⠋⠀⠀⠀⠀⠐⠄⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢳⠔⠂⠀⠑⠢⣀⠀⠀⠀⠠⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡈⣧⠀⠀⠔⠿⣿⠀⡀⠀⣀⡤⠠⢄⢀⡈⠀⠄⠐⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠦⣤⡈⠀⠀⠀⣄⠀⠀⠁⠀⠐⠀⢠⡎⠀⠀⠀⠙⢦⡈⠀⠘⡆⢀⠜⠁⠀⠐⠀⠙⡄⠀⠀⠀⠀⠀⠀⠈⠦
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⠀⡀⠀⠀⠀⡁⠀⢀⡜⠀⠠⡑⡄⠀⠀⢻⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⡀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠂⠀⠑⠤⣀⠀⠀⠃⠀⡘⠀⠀⠀⠀⠀⠀⠀⡰⠁⠰⠁⠀⠀⢀⡀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠐⠀⠀⠠⠀⠀⡀⠀⠀⢡⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠑⠦⠀⡼⠁⠀⠀⠠⠀⠀⠀⢀⣠⣄⣀⣤⠶⠚⠉⠁⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣀⣀⠉⠀⠛⠛⢉⣡⡀⠀⠀⠀⠑⠤⣄⠀⠀⢀⡠⠛⠀⢤⣄⡒⠒⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡄⠀⠀⠀⠉⠁⠈⠀⣀⠀⠘⠒⠀⠐⢈⢋⠉⡉⠁⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠱⡖⢄⠀⠀⠀⠀⢀⣠⠄⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢡⠀⠀⠀⠈⡀⠀⠀⠉⠙⢦⡀⠀⣀⡔⠉⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢳⠦⠤⠒⠋⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠂⡀⡀⠀⢀⠿⠐⠉⠀⠀⠀⠐⠢⠀⠠⠄⠚⢡⣀⠀⠀⠀⠀⢀⠀⠀⠀⡜⠒⠒⠂⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠞⠓⠒⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠉⠛⢧⣄⣀⠀⢀⡠⠞⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠄⠐⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠚⠑⢬⡂⠀⠀⠀⠀⢈⡳⣀⠀⠤⠔⢊⡼⡱⡄⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠐⠀⠬⠉⠠⡾⠉⠙⠒⠒⠉⠀⠁⢟⠲⣄⠀⠀⠀⢈⠔⠁⠠⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⠀⠀⠈⠢⡐⠀⠀⠀⠀⠰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠀⡂⢰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⢣⠀⠓⡄⢸⠀⢀


⣿⡟⣋⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⡻⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠶⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⢇⡄⠀⣰⠆⠀⠀⣺⠁⠀⡀⠉⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠹⠿⠦⢤⣴⡞⠀⠙⠉⠁⠀⠀⢸⠃⡆⠘⣷⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⢸⣇⣧⠐⡏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠀⢢⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠹⣿⣿⣶⣧⡟
⠐⠀⠀⠀⠀⠀⠀⣿⣁⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠛⠛⠋⠀⠀⠀⠘⠗
⣸⠇⠠⠄⠀⠁⢀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⠇⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣶⡦
⠁⠀⣧⠀⠋⠀⡀⢠⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⣀⠀⠦⠄⠀⠀⠀⠁⠀⠀⠀⢀⠀⡀⠀⠀⠈⠉
⠀⠀⢸⡖⠂⠈⠀⡼⠀⠀⠀⠀⠀⠀⠰⢼⣦⠀⢸⡇⠀⠀⢀⠇⠀⠀⠀⢨⠁⢢⢠⠀⠀⠀⢸⣀⠀⠀⠸⠶⠃
⠀⠀⠀⠀⠰⢪⡿⠃⠀⠀⠀⠀⠀⠀⠀⠐⣷⣶⢾⣧⣼⠷⠃⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⡤⠚⠋⠀⠀⡆⢠
⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠘⣧⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⢛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡅⠀⠀⢸⠀⠀⠀⠈⠋⢀⠠⠀⠀⠰⣄⡴⠀⠓⠂⢀⣀⣀⠰⠁
⠸⡤⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⡀⠀⣆⣸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢰⠀⡀⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢠⡄
⡀⠀⣀⡀⠀⠀⠀⢠⠂⠀⠀⠀⣠⣀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠈⢢
⠧⢀⠈⣇⠀⠘⠠⡇⠀⠀⠀⠀⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⡔⠀⠄⠀⠀⠀⠀⢦
⢷⣸⠀⠹⠃⠀⠀⠁⠀⠀⢠⢏⡆⢰⡞⡇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⢀⠠⡁⠀⠀⠀⠀⠀⡀⠀⢸⠇
⢀⠹⠀⢠⡄⠀⠀⠀⠀⠀⣹⣼⡆⣾⢰⠇⠀⠀⠀⠀⠀⠀⠀⠘⣇⣧⢡⠀⣇⡿⠀⠀⠀⠀⠀⠀⣘⠟⠀⢀⠠⠀⠀⠙⣿
⠾⠃⠀⡾⠛⠀⠀⠀⠀⠀⠻⣿⣷⣷⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠛⠳⠷⠋⠁⠀⠀⠀⠀⠀⢀⡀⠈⠀⣀⠀⠂⠀⠀⢻
⡅⠀⢸⠃⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⠄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠰⠀⠀⢠⡜⠀⠀⠈
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⣀⣥⠞
⠐⠀⠚⠛⠁⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣼⠀⠀⠙⠋⠉

⠀⠀⠀⠀⣀⣠⡤⣢⣆⡄⠀⠀⠀⠀⢀⡴⣶⣦⡦⣦⠀⠀⠀⠀⠀⠀⠰⡄⠀⢀⡀⠀⠀⠀⢀⡴⣤⣀⡠
⠀⠀⠀⠀⣴⠿⣾⣿⡧⣯⣷⡆⠀⠘⣷⢿⣷⠹⢷⣷⠀⠀⢠⠀⠄⣈⠳⣀⡀⠁⡧⠀⠀⠰⣯⡹⣽⣨⣃⣤
⠀⠀⠀⠀⢽⠻⠟⣻⣟⡓⠌⠀⠀⠀⠉⠛⠻⠛⠚⠁⠀⠀⠀⢑⡤⣙⣤⢻⣇⡴⢫⠀⠀⠀⡉⣽⠤⠿⠈
⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠵⣬⣟⣫⢿⡴⣿⡓⠀⢀⠄
⠀⠀⠀⠠⢶⣤⢤⣄⣤⠄⠀⣀⣴⢶⠑⢤⠷⣺⣼⣴⢦⡄⠈⡭⢉⣴⠟⠹⣾⡷⠠⣽⠄⠀⠀⠀⣠⢀⣸
⠀⠖⠀⢫⣽⣿⣶⣇⣼⠎⠀⢸⡭⣝⡳⢏⠴⡨⢏⢽⣽⡧⠈⠉⠁⠁⣠⠴⡇⠀⠐⠸⠀⠀⠦⢤⢿⡟⣃
⠀⠈⠾⢿⣍⣻⡿⠿⢉⡂⠀⠀⠙⢛⣻⠳⣾⣧⠾⡞⠋⠀⠀⠀⠀⠐⠁⠀⠐⠆⠀⠀⠀⠀⠢⠤⠀⠉⠁
⠀⠀⠃⠉⠛⡋⣸⠖⠛⠁⠀⣀⠀⠀⠀⢠⠀⠈⠉⠀⠀⣀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⡀⡠⢤⢢⣀⣲⡀⣀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⣠⣻⣷⣴⣾⡞⢀⡄⠀⠀⠀⠈⢿⠶⢾⡎⢹⠇⠄⠀⢀⠤⣼⢷⢼⣣⠟⣶⢷⣾⣀
⠀⠸⡇⣶⣶⠯⢀⠀⠠⣤⣿⣽⣏⣿⣿⣿⣿⣧⠞⠀⣠⡔⣾⣶⣿⣤⠷⠤⣄⠀⢾⣶⡿⣾⣿⣿⢿⢻⡿⣿⡟
⠀⠀⠓⣾⢻⠶⠛⠁⠀⠨⢽⠯⡭⣷⣿⠗⠛⠀⠘⠹⣯⠶⢿⣯⡏⣱⣆⠀⠉⠀⠈⠛⢿⣷⣽⠍⣾⠓⠶⡟⠁
⠀⠀⠰⠻⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⠉⠀⠀⠘⠎⠢⡀⠀⠀⠀⠀⠛⠘⠦⠜⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠈⠑⢀⠔⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠘⠇⠀⠈⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠑⠀⠈⠀⠀⠀⠀⠀⠙⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠠⠀⠘⠆⠀⠀⠈⠇⠀⠀⠿⢸⡇⠀⠀⣄⠀⣷⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠞⠀⡇⠀⠀⡁⢠⡏⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⡄⠑⣤⠀⢀⠀⢰⠀⠀⠀⠀⡇⢸⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⠛⠀⠈⠀⢠⠀⠀⠀⠀⠁⢸⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⣀⠀⠀⠀⠤
⠀⠀⠀⠀⠂⠀⣿⠀⠀⢸⠇⢠⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⢤⡀⠀⠀⠀⠀⡄⠀⡇⠀⠠⠀⡇⠈⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⣈⠀⠇⠀⠀⠀⠀⠀⠀⢀⠀⣠⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠸⣇⠀⠀⢿⠀⠄⠀⠀⠀⠀⣆⠀⠀⣠⡟⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠳⣄⡈⠃⠤⣈⡲⢀⡀⠀⠀⠀⠁⠀⠾⢋⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⣌⣀⣀⣀⡀
⠀⠀⠀⠐⠃⠘⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⢿⣾⠿⠿⠿⠿⠟⠿⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⡿⠾⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣄⣲⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠋⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢀⡀⠊⠀⠈⠙⢦⡀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠰⠀⠀⠀⠀⣾⣿⡏⣴⡆⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⡧⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⡶
⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⡿⢀⠀⠀⠀⠀⣿⡟⢡⣿⡇⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⢸⠀⠀⠀⠀⣿⠀⢹⣿⠀⠀⢿⣿⠟⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⢀⠀⣿⡄⠀⢹⣿⡇⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⣿⣿⠀⡄⣠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢁⠀⠀⢀⠀⠀⠀⠀⠀⠠
⠆⠀⠀⣿⣧⣿⣇⠀⠈⣿⡇⠀⠘⠀⠀⠀⣿⡀⠸⣿⠀⠈⣿⠇⢰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠈⠀⠀⠀⠀⠀⡃
⡄⠀⠀⢻⣿⢿⣿⠀⢁⢻⣧⠀⢸⠀⠀⢰⡟⠃⢸⡟⠀⢰⡟⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⡀⠰⠀⠀⠀⠀⢰⡇
⠰⡆⠁⣸⣿⣆⠙⣧⠘⠀⣿⡀⢸⠄⠀⢸⡇⠀⣿⠃⠀⢾⠁⣴⣿⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠸⣄⠛⢿⣿⣧⡈⢣⠀⠸⢧⠈⠀⠆⢸⡇⢰⡟⠀⠀⠀⣴⡿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠈⠂⡀⠙⢿⣦⠠⠖⠀⠈⠀⠠⠀⠀⠁⡞⠃⢀⣠⡾⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡀⠀⠈⢦⣀⠙⢷⣄⡀⠈⢤⠀⠀⠰⠂⠀⠀⠛⠉⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠁⠐⠒⠈⠉⠱⠦⣬⠻⠷⡄⠡⠀⠰⠀⢀⣤⠶⠚⠁⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣶⣿⣶⣤⣤⣤⣼⣿⣿⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣾⣿⣀⢀⣀⣨⣿⣿⣷⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠛⠻⠿⠿⠿⠿⠿⠿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘⠓⠘⠛⠈⠉⠃⠐⠀⠈⠉⠉⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠠⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢾⣄⣱⠖⢀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⣄⡠⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡖⢠⠚⠑⠶⠚⣯⣹⡖⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⢢⠜⠉⠀⠈⠀⠀⠠⠀⠀⠈⠁⠐⠠
⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⡐⠈⠀⠁⠠⠎⣿⠙⣏⡉⠳⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⠡⡀
⠀⠀⠀⠀⠰⠃⠀⠈⠀⠰⠁⠈⠁⠀⣉⠰⡏⠘⠃⠈⠱⠞⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠆
⠀⠀⠀⠰⠂⢰⡁⠀⠸⠀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠸⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⢠⡆⠀⡉⠛⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠃⠀⢧⡤⠐⠇⠐⠁⠀⠀⠀⡄⠀⢀⠀⠀⠀⠠⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀
⠀⠀⢠⡄⠀⠀⠀⠀⢠⠀⠆⠀⢢⠀⠁⠀⠈⡀⠐⠂⠀⠁⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⢁⠀⠰⠏⠀⠈⢃⠀⠀⠀⢀⠀⠀⠀⠱⠀⠀⠀⠀⠉⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠦
⠀⠀⠀⠘⠃⠀⠰⡶⠀⠈⠡⣄⠀⠀⠃⠀⠀⠰⠀⠶⠘⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⢀⠚⠃⠀⠀⡇⠀⠀⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡄⠈⠂⠀⠀⠘⢄⡀⠀⡄⠀⠰⢀⡀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠰⡷⠀⠀⠀⠀⠀⠀⡇⠀⡀⠈⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠻⠀⠈⠻⠀⠀⢀⣁⣈⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠤⣤⣴⣾⣿⣷⣶⣷⣶⣿⣿⠿⡿⠟⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣦⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⣄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡦⠠⠄⠀⠀⠀⠁⠦⢄⢁⠃⣠⠀⡔⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⢄⠰⠂⠀⡄⢀⡂⠀⠀⣈⡂⠀⡛⠀⠀⠄⢁⣀⠀⠚⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡆⠀⢲⠀⢠⠇⠁⠇⠈⢀⠁⠳⠀⠈⠁⠀⢦⡉⠣⡄⣦⠱⠃⠈⠀⡀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠀⠘⠑⠃⠀⢀⠀⠀⠉⡁⠐⠁⠄⠺⠄⠀⢋⡢⢌⡛⠄⡇⠈⣀⠔⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠑⠀⠀⠑⡤⡀⢀⠖⡔⠁⠀⠤⠘⠀⠀⣌⠀⠀⢀⠠⢶⠕⢤⡀⣠⠀⠂⠅⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠀⠐⣆⠠⣀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠁⠀⠈⠀⠀⠀⠀⠈⢢⠓⣀⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠝⠑⠀⠤⠀⠙⠉⠀⠈⡀⢀⠆⠐⠂⣄⠀⠀⠀⡀⠚⠙⠾⣦⠒⠙⠒⠲⠂⠀⠉
⠀⠀⠀⠀⠀⠣⠐⠢⠄⠀⠀⡀⠀⡠⠙⠂⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡔⠒
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡠⠂⠊⠀⠀⠄⠀⠙⠂⣀⠀⢠⠔⠈⠑⠄⠀⡀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⢀⠂
⠀⠀⠀⠀⠀⢀⡆⠀⠒⠉⠀⠀⠰⠴⠀⠀⠢⠀⠀⠠⡜⠁⠀⠀⠀⠀⠀⡀⠀⠀⠨⢴⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⡀⠐⠀⠀⢂⠀⠀⠀⠈⠐⡺⠀⠀⠀⠀⠀⠀⠀⠂⠐⠆⢀⠀⠤⠂⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠑⠀⣀⠀⠀⠈⠟⠀⠀⠀⠀⠋⠉⠀⠀⢀⠀⠀⠈⠤⢀⠄⠀⠀⢀⠤⣀⢀⠠⠀⠀⠀⡀
⠀⠀⠐⡄⠀⠁⠀⠂⠀⠀⠀⢁⣌⣱⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⡄⠀⠁⠄⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠤⠀⠃⠀⠀⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⢨⠄⢀⡂⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠐⠀⠈⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠍⠢⢁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⢀⠒⠂⡁⠀⢀⡠⠒⠄⠁⠀⠉⡄⢁⠒⠤⡀⠀⠝⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠉⠐⠀⠀⠰⠊⠑⠊⠚⠀⠀⠐⠁⠉⠀⠠⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠀⠀⠀⡀⠀⠀⠀⠠⠴⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡻⠂⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣆⠀⠀⠈⠁⠀⠀⠀⠀⠀⣤⣄
⠀⠒⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⣾⡄⠀⠀⠀⠘⣤⣀⣰⠇⠀⢀⡯⠀⢀⠈⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⢶⣾⠁⠈⠉⠀⠀⠀⢸⢱⡃⢸⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⣸⣿⣇⢸⢹⡏
⢀⠀⠀⠀⠀⠀⢰⡆⠄⠐⠀⠀⠀⠛⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⢿⣿⣿⠞⠀⠀⢀⣄
⢠⡄⢀⠀⠠⠀⠸⡶⠀⠀⠀⠀⠀⠀⠀⣠⢾⡄⠀⠘⠃⠀⠀⠀⠀⠀⢠⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡁
⠛⠁⡆⠠⠄⠀⠁⡁⠀⠀⠀⠀⢀⡀⠀⠀⠀⢅⠀⠐⠀⡇⠀⠀⠀⠀⢀⣀⠀⠈⠛⠣⠀⠀⠀⠀⠀⠀⠀⠙⠻
⠀⠀⢫⠠⠀⠒⢠⠇⠀⠀⠀⠈⠉⢁⣠⡀⠠⣟⠀⠀⠀⡇⠀⠀⠀⠓⢠⠉⡀⠀⠀⢰⠀⠀⠀⢦⡴
⠀⠀⠈⠁⡴⣲⠞⠀⠀⠀⠀⠀⠀⠀⢸⣥⣴⣇⣠⣶⠎⠀⠀⠀⠀⠀⠀⠷⠁⠀⢀⠼⠋⠀⢠⡀⡀
⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠓⠇
⢛⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣼⠀⠀⠸⠇⠀⠀⠈⠋⠀⠄⠀⠈⢦⡴⠄⠓⠂⣀⣀⣀⠄
⠸⠶⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⢀⠀⠸⣤⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠾⠀⠈⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢤⣴⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡾⠀⠀⠀⠀⠀⠰⡆
⡄⠀⢧⠀⠀⡄⢰⠃⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⡀⠀⠀⠀⠀⠀⠲⠟⢀⠀⠀⠀⠀⠀⢀⠸
⣟⣴⠀⣧⠀⠁⠹⠀⠀⠀⡤⡈⣁⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠁⠀⣠⠀⠀⠀⠈⠁
⠙⢳⠀⢀⠀⠀⠀⠀⠀⢰⣱⠁⣾⣸⠂⠀⠀⠀⠀⠀⠀⢸⣣⡄⠀⢢⢱⡄⠀⠀⠀⠀⠂⢤⡿⠀⠀⠀⠀⢠⣤
⣴⠄⠀⡾⠄⠀⠀⠀⠀⢺⣿⣧⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠳⠿⣥⡼⠚⠁⠀⠀⠀⠀⠀⠋⠠⠀⠀⢀⠀⠀⢸
⡃⠀⣼⠁⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⢀⡈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠁⣰⠂⠀⠈
⠁⠀⢹⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡀⢀⡴⠋
⠐⠤⠚⠋⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣰⠀⠀⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⣢⣆⠰⠦⠤⠀⠀⠀⠀⠀⠀⠀⡐⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠠⠄
⠀⠀⠀⠀⠀⢀⠈⢀⠐⠰⠃⠀⠀⠀⠀⢴⣠⠭⡁⠄⠐⢢⣴⠀⡀⠀⠀⡁⠀⠆⡀⢇⠀⠒⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⠰⠄⠠
⠀⠀⢀⠀⠀⠰⠀⢉⠈⠀⠜⠀⠀⠀⢀⠀⠨⠼⠂⠐⠄⠍⢋⣑⠂⠀⠠⠀⠐⠦⠒⡈⠂⠁⠒⠈⠀⠀⠀⠐⠐⠀⢈⠀⢁⡀⠐⠠
⠀⠀⠀⠀⠀⠸⠈⡠⠔⠂⠂⠐⠀⠀⠀⢀⣆⠋⠣⠠⡉⢾⠳⢇⠀⠀⠀⠂⠀⠚⠂⠀⠄⠱⠀⠂⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠾⠒⡤⠀⠀⠀⠀⠀⠀⠈⠀⠄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠦⠈⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠂⠀⠀⢂⠐⠈⠀⠄⠀⠀⠀⠄⠀⠀⡀⠰⠀⠆⠀⠀⠀⠀⠄⣁⡀⠒⠄⠀⠌⠀⢀⠣⠀⠀⠀⠘⠀⠂⠀⠀⡑⠀⠁⠠
⠀⠀⠀⠁⠁⠀⣶⣷⡄⠀⡀⠀⠀⠀⠀⠐⠀⠁⢀⣅⠀⡀⠀⠀⠀⠀⢀⠀⢀⠀⠢⡘⠀⡀⠂⠂⠄⠀⠈⠢⠅⡠⠠⠵⠂⠈⣀⠈
⠀⠀⠀⠀⢀⠈⠀⠑⠀⠀⠀⠄⠀⠀⠀⠤⠉⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⢀⠀⠐⠁⡀⠀⠈⡤⠂⠀⠀⠡⠐⠀⠄⢒⠈⠉⡁⠐
⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⣀⠀⠈⠂⠀⠀⠀⠀⠀⠉⠧⠰⠁⠔

⠀⠀⠀⠀⡀⠆⠠⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠐⢀
⠀⠀⠀⠀⠐⢴⠂⠀⠀⢀⠈⠂⠀⠀⠀⠀⠀⢀⠐⠠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠠⠔⠈⠠⡀⠀⠀⠀⢄⠠⢀
⠀⠀⢀⠄⠐⡤⢠⡉⠉⠌⠅⠐⠀⠀⠀⠐⢠⠀⠎⡱⠀⢀⠀⢀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠜⠯⠀⠁
⠀⠀⠀⠄⣀⠔⠲⠞⠠⠀⠄⠀⠀⠀⠀⠀⠄⠀⠂⠂⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠩⣀⠀⠀⠀⠈⠀⠂⠀⠠⠀⠐
⠀⠀⠀⠘⠁⠜⡋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠈⠁⠈⠃⠀⠀⠆⠜⢗⡢⠀⠀⠀⠒⠠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡄⠀⢠⠀⢀⢠⠀⡐⡂⡔⠂⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣀⠸⡀⠘⠄⠀⠉⠀⡇⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣶⢀⣤⡴
⠀⠀⠀⠀⠀⠀⠠⢀⣄⣃⠔⠠⠠⠀⠀⠀⠀⠈⢉⣛⢚⠫⠆⣀⢀⡠⣄⣤⡄⠀⠀⠀⠀⢠⠠⡄⠀⢀⡴⠀⠄
⠀⠀⠀⣾⣯⣶⡋⣓⡯⣽⢿⣃⢀⠄⠀⠀⠀⠀⢤⣔⣷⢫⢾⡷⣿⣷⡊⣇⡃⡀⠀⠀⠠⣤⣄⣿⣅⡀⢟⠻⠛⠀⢀⡄
⠀⢠⣠⣷⣚⣿⣟⣻⣿⣿⣶⣭⣄⡀⠀⠀⠠⠀⣳⠿⣿⠟⡊⢿⣽⣛⠟⣿⣿⡁⠀⠀⠀⣨⢽⣾⢾⢿⣀⣶⠈⡿⢋⡀
⠀⢸⣿⠿⣧⢿⣽⣿⣾⣟⣿⣿⢿⡿⠀⠀⠠⠼⣍⣻⣋⣭⣽⣷⣯⣹⡾⣿⣿⣦⠀⠀⠠⢿⢻⠧⢟⠻⢏⠹⠃⢛⠿⠖
⠀⠀⠠⣿⣛⡿⣿⣿⣟⣿⡻⠈⠉⠀⠀⠀⠀⠲⠿⢹⠘⢾⣻⣿⣿⢧⢟⣻⡿⠟⠗⠀⠀⠘⠙⢿⣋⡤⠀⠱⣮⣹⡇
⠀⠀⠀⠀⠈⠿⣿⠧⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢾⠯⠙⠊⠼⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠤⡤⠄⣀
⠀⠀⠐⠀⠈⠁⠄⠀⠀⠀⠀⠨⠀⠂⠄⡄⠀⠀⠀⠀⠀⠀⠋⠀⠁⡄⠌⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣤⠀⠌⠁⠀⢨⠠⡆
⠀⠀⠃⠄⠈⠈⡀⠆⠀⠀⡀⠀⠄⠁⠂⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠐⠈⠃⠀⠈⡀⢠⡄
⠀⠀⠀⠁⢀⠀⠀⠐⡀⢀⠀⡀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠗⢲⠴⠻⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠁⠀⠠⠄⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠐⢠⠅⣈⠀⠀⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠚⠀⠂⢁⠘⠆⠀⠀⠀⠀⠀⠀⠈⣀⠘⠂⠀⣀⡀⠀⢘⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠡⢈⠘⠀⠀⠀⠀⠀⠀⠀⠠⠆⠘⠃⠀⠐⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠓⠚
⠀⠀⠀⠀⠀⠀⠠⡄⠀⡁⠐⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠄⠀⠠⠆⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠠⢠⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢈⡀⠀⠀⡄⡁⢠⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⡀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢦⠀⠈⠁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠒⠀⠨⠁⠀⠀⠀⠀⠀⠀⢀⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡈⠀⠒⡇⠇⣀⠀⠀⠀⠀⠀⠀⠋⠁⠄⡁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⡆⠀⠉⢠⠁⠀⠀⢐⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠄⠀⠀⡴⠛⢛⠦
⠀⠀⠀⠀⢠⠀⠇⠞⠆⠀⡀⠼⢁⠊⠀⢠⡄⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⢈⠀⠁⡀⠀⠈
⠀⠀⠀⠀⠀⣄⠸⣄⠰⠨⠀⠀⠑⡠⠂⣸⠜⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠁⠃⠁⠀⠄⠀⠀⠀⠀⢡⠇
⠀⠀⠀⠀⠀⠘⠁⠠⠁⠀⠀⢠⠠⢣⢊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠇⠀⡀⠀⠄⢰⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢐⣘⡇⠀⢗⣄⢠⠾
⠀⠀⠀⠀⠀⠠⠠⠀⠀⢀⠀⢀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢀⠀⢀⢀⢀⢠⢀⠠⢠⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠄⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⣁⠀⠁⠁⠁⣈⣁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⡏⢠⠌⡌⢶⡀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠐⢅⡎⡜⠘⣄⢳⠀⢀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡄⠀⢰⠀⠀⢡⡇⠀⠈⠢⡷⠀⢀⡄⠨⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠄⢤⡀⠐⠀⢸⠀⢀⡜⠑⢄⠀⠀⡣⢸⠜⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣆⠈⠐⢧⡸⣤⠎⠀⠀⠀⢣⠎⠀⢸⠀⢠⡶⠣⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠄⠀⠀⠀⠘⡆⠀⠀⠙⡟⠀⢀⠀⠀⠄⠀⠀⠀⡖⠉⢀⣥⡆⢀⠆⠀⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⠢⡡⡀⢳⡀⠀⠀⢰⡀⡈⠑⠶⣀⠀⠀⢀⣧⠖⠉⠀⠀⢂⠄⠀⠐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢀⠀⠈⠻⡦⢷⡀⠀⠀⡿⠁⠀⠀⠈⠑⢦⡟⠁⠀⠀⢀⠞⠁⢀⠌⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⢐⠦⠤⠀⠀⠡⣄⠀⠈⢢⠈⠑⠲⣇⠀⠀⠀⠀⠀⠈⡄⢀⣀⣠⠎⠠⠤⠂⡀⠄⠀⠀⠀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡒⠦⠤⣀⡀⠈⠒⠮⣧⠀⠀⠈⠳⣄⡀⢀⣠⠴⠛⠉⠀⠀⡰⠋⠀⢁⣀⡠⠶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠈⠑⢦⣀⠈⠓⢦⣄⣲⠈⠛⠩⢄⠀⠀⢀⡠⢊⡠⠔⠋⠉⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢓⣦⣄⣀⠈⠙⠛⠋⡹⠃⠀⠀⠀⠀⣻⡛⠛⠛⠉⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠛⠈⣏⣏⠉⣻⢿⣷⣦⣤⣤⡴⢾⡿⡛⠓⣶⣖⣛⠿⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠁⠀⠘⠛⠒⠂⠛⠙⠃⠛⠛⠂⠀⠉⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠲⠤⠤⠄⠀⠀⠀⢀⣀⡀⠀⠀⠀⠤⡤⠴⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠀⠀⠀⠀⠀⠀⠠⠄⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⡄⠀⠀⠀⠲⡦⠀⢠
⠀⠀⢀⠀⠀⠀⢀⡆⣰⠃⡀⠀⠀⠀⠀⠀⢠⣾⣼⠀⠀⠀⠀⠀⠀⠀⠀⢼⣣⢀⡓⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⡀⠈⠳⠥⠅⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⢠⣉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠀⠀⠁⠀⠀⠀⢙⣋⠠⠤⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠂⠀⠀⢀⠠⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⠀⢢⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠌⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡘⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣹⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣔⠀⠀⠀⡀⠀⠀⠀⠀⠠⡄⡴⠀⠀⢰⣿⠃⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠢⢀⠠⠋⠀⡈⠈⠀⠀⢁⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠶⠀⢸⡀⠀⡇⠀⠀⢀⣸⣀⠀⠀⣱⢶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠎⠀⠀⠀⠀⡀⢠⠸⡇⢀⡇⠀⠀⠀⠉⠉⠀⠀⢹⢸⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢇⢐⣠⡗⠚⠁⠰⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⢀⠆⡄⠀⢄⠀⠀⠜⢀⠄⠈⢺⢸⠁⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠽⠿⠟⠀⠀⠀⠁⠁⢀⠁⠀⠀⠸⢼⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⣙⡁⠀⠸⠶

⠀⠀⠀⡀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⡂⠨⠀⠠⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢃⡇
⠀⠀⠄⠁⡠⢘⠆⠄⠀⠀⠀⠀⠀⠀⢀⠈⠰⣎⠐⡀⠀⠀⠀⠀⠀⠁⢄⠰⡲⠄⠈⠄⠀⠀⠠⡁⠁⣁⠀⠀⠄
⠀⠀⠀⢁⠁⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠡⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠠⣠⡀⢢⠴⠡⠔⠣
⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⢀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢀⡀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⠀⣀⣶⣦⣿⡿⣿⣴⣦⠀⠀⠀⠀⢸⣿⣾⣿⣿⣻⡇⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣧⡄⠀⠀⠀⢰⣄⣧⣴⢀⠄
⠀⠀⢹⣿⣿⣟⢻⣿⣿⣾⡟⠀⠀⠰⣿⣯⡿⢿⣟⣿⣿⠆⠀⠀⢾⣿⣿⡿⣛⣿⣿⣿⣷⠀⠀⣄⣦⣿⣿⣿⢿⡼⢀
⠀⠀⢀⣿⣽⣿⣿⣿⡿⠟⠉⠀⠀⠘⣿⣿⣭⣮⣿⣿⣿⠄⠀⠀⠘⢿⣿⢿⣽⣿⣿⡟⠁⠀⠀⠚⠿⣞⢿⢟⣿⣷⣋
⠀⠀⠈⠁⠋⠻⠟⠿⠇⠀⠀⠀⠀⠀⠉⠉⠹⡿⠛⠁⠀⠀⠀⠀⠀⠀⠻⠟⠙⠁⠉⠁⠀⠀⠀⠀⠈⠉⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢰⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠲⣄⠀⠀⢸⠀⠀⠘⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⡄⢹⠀⠀⢸⠀⠤⠀⠈⢠⠀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⢸⠀⠀⢸⠃⠀⠀⠀⢰⣠⠠⢻⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⢸⠀⢴⠷⠄⠀⠀⠀⠸⠁⢀⡜⢀⡞⠉⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⢈⠀⠈⠧⠀⠀⠀⠀⢠⠒⠁⠀⢸⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⢸⠀⢰⢶⡄⠀⢸⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠠⠀⠂⢸⠀⠀⠜⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢈⡀⠀⢠⠀⠀⢘⠀⢨⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⢀⠀⠈⢧⣀⣳⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⢀⠉⠁⠀⠀⠈⠀⠸⠀⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⢀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢶⠀⠀⠀⠘⠀⡆⠀⠀⠀⠀⠀⠀⢀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢰⠀⢰⠀⠀⢀⠎⠀⠀⠄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠃⠀⢸⠀⢸⣤⠴⠚⠁⢀⠊⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠂⠀⠸⠀⠀⠀⠀⠠⠀⠁⠀⠠⢢⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠠⠀⠐⠀⠀⠀⢀⡠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⠸⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠀⡁⠦⡃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣄⣤⡾⣿⣿⣿⡿⠷⢤⡀⠀⠀⢈⣷⠀⠀⡞⢀⣦⡀⡏⡀⡇⠀⣿⣼⠀⢾⣷⡇⠀⠀⣿⣿⠇⠀⠀⠀⣼⠃⠀⠀⠀⢸⣷⡆⣇⡀⠠⢸
⣿⣯⠟⠀⡔⠰⠀⠀⠀⠠⠙⣦⠀⢠⣿⣸⣴⣴⣿⣿⣣⣿⠿⠻⢾⣿⣿⣉⣾⠿⠛⠒⠚⠿⢧⣖⢀⣀⡸⣿⠀⠀⠀⠀⢸⣿⣿⣟⣛⣶⣿
⣿⣿⣾⡀⣶⣶⣠⣴⣆⣄⢱⣾⣷⡿⠋⠉⠉⠉⢻⣿⣯⠴⢤⣀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣯⣹⣿⣿⣤⠴⢦⣤⣼⣿⠛⣿⣿⠋⢸
⣿⣿⠛⠛⣿⠋⠉⠉⠉⠛⢿⣿⣿⢠⠀⠀⠀⠀⣷⣿⣧⣠⠖⠋⠉⠉⠲⣆⡀⠀⠀⣀⣤⣤⣤⣀⢾⣿⡿⠋⠀⠀⠀⠈⣿⡇⠀⢸⣿⣀⣸
⣿⡇⠀⢺⢹⡄⠀⠀⠀⠀⠀⠹⣷⣾⠀⠀⠀⠀⡏⣿⢸⡟⠀⠀⠀⠀⠀⢸⡷⠶⢴⣿⠃⠀⢸⣿⣿⠏⠀⠀⣠⣤⣶⣤⣿⣧⠶⠛⠉⠙⣿
⣿⡇⠀⠸⣆⣿⡄⠀⠀⠀⠀⠀⢘⣿⣴⣰⠀⣤⣇⣿⣿⣷⣤⣠⣠⣤⣶⣾⣿⣷⣄⣿⠀⠀⢰⣿⡏⠀⢠⡾⠋⠁⠀⠈⢻⣧⣀⡀⠠⣰⣿
⣿⡇⢶⡛⠛⠛⠛⠓⠶⠶⢤⣶⡿⡿⠿⢿⣿⣿⣿⡟⠉⠉⠉⡙⠿⣿⢘⣿⢻⢹⣿⢹⣿⣦⣼⣿⣇⣠⣾⠃⠀⠀⠀⠀⡀⣿⡉⠙⠛⠿⣿
⣿⣷⣠⣽⣦⡀⠀⠀⠀⡄⣾⠃⠀⠀⠀⠀⢻⣻⡿⠡⠄⢠⢠⢠⢀⡇⢸⢸⢸⢸⣿⡇⣷⣿⣿⡿⠋⠀⣿⠀⠀⠀⠀⠀⠀⢻⣧⣀⣄⣠⣿
⣿⠟⠀⠀⠈⠳⣄⣧⢲⣿⠇⠀⠀⠀⠀⠂⢀⢿⣧⠀⠀⢸⠸⡜⣾⡇⣿⢸⢸⢸⣿⡇⣿⣿⣿⣧⢀⣀⣿⠀⠀⠀⠀⠁⠀⢸⡇⠀⠉⣽⣿
⣿⣆⣀⣀⣤⠴⠿⠛⠻⣿⠀⢰⢸⠀⠀⠀⠄⣾⣿⡌⢸⠘⡆⣇⣿⣷⣿⢸⢸⢸⣿⣇⠏⠈⣿⣿⣿⣿⡿⣶⣄⠀⠀⡄⠀⢸⡇⢀⣼⠟⢸
⣿⡟⠋⠁⠀⠀⠀⠀⠠⣿⠀⠘⠸⠀⠀⠀⠀⣿⣿⣷⠸⡆⣿⢻⠋⠻⣼⢸⢸⢸⣿⣿⠀⠂⣿⡟⠁⠀⠀⠀⠙⣷⡆⡇⠀⢸⣷⠟⢁⣤⣿
⣿⣿⣤⡖⠂⣀⣄⣠⣼⣯⠀⡄⠀⠀⠀⠀⡇⣿⣿⣿⣧⣿⣇⣸⡀⠀⢻⣸⢸⢸⣿⢻⣇⢸⣿⡇⠀⠀⠀⠀⠀⠈⣿⣇⡆⣿⣥⠶⠛⣉⣿
⣿⡿⠞⣿⠉⠘⣧⠀⣾⣷⠆⡇⡄⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣏⣇⠀⢸⣿⣿⣿⣿⢸⣮⣿⣿⣿⣶⣦⣤⣤⣀⡀⠘⣿⣿⣿⣥⣶⣿⣛⣿
⣿⡿⢦⣜⣷⣄⣽⡾⢿⣿⠀⡇⡇⠀⠀⡇⡇⣿⣿⣿⣿⡏⣉⢻⡾⣿⢾⣿⡇⡇⣿⢸⣿⠟⠉⠀⠀⠀⠀⢙⣿⣿⣿⣿⡿⠛⠙⠛⠻⣿⣿
⣿⣿⡷⢮⣍⣻⡇⠡⠀⣿⡆⡇⡇⠀⠀⡇⡇⣿⣿⣿⠟⠓⡹⠛⢦⣸⡏⣿⡇⡇⣿⣼⠁⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠹⣧⠀⠀⠀⠀⠈⣿
⣿⡷⠟⠒⠀⠙⣿⠄⠀⢸⡇⡇⣇⠀⢀⡇⡇⣿⣿⣿⠦⢴⡇⠀⢸⣿⣧⣿⣇⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⢸
⣿⣇⣠⣴⣷⣼⣽⣿⣦⣿⣇⠁⢋⠀⠸⡇⡇⣿⣿⣇⠀⠀⢝⣦⣼⠁⢀⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠠⢸
⣿⣿⠿⠋⠀⠛⠁⠀⠙⢿⣿⣸⢸⢸⠀⡇⡇⣿⣿⣿⣿⣿⠋⠁⠈⢹⣿⣟⣫⡿⠟⠛⠛⠛⠻⢷⣤⡀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⣾
⣿⡁⠀⠀⢀⠀⠀⠀⠀⠈⣿⣿⣾⣾⣧⣿⡿⠿⠿⠿⢿⣇⡀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⡇⠀⠀⠀⢰⡟⠀⠀⠀⢀⣾⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⢿⣷⠿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⢀⣾⠃⠀⠀⢀⡾⠋⣻
⣿⠟⢦⡀⠀⠀⠀⠀⣴⡞⠛⢻⣿⡟⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣛⢻⠀⡀⣄⣤⢀⡇⠀⠀⠀⠀⠀⣽⡈⣿⡀⣼⠃⣀⢠⣴⢿⡿⢿⣿
⣿⠀⠈⣿⡇⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⣿⣆⣦⡏⠟⡾⣴⣠⠄⠀⠠⢀⣻⣟⢾⣿⣹⣶⣻⣏⢹⣿⣦⡈⣹
⣿⠀⠀⣿⡇⠠⠀⣸⣿⣷⣤⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢻⣽⣽⣮⠷⠾⣿⣙⠉⡰⢲⡟⠺⡿⣿⣿⣿⣿⣿⡿⢸⣨⣿⡿⢷⢻
⣿⠀⠀⣿⡧⢀⡼⠋⠉⠀⠉⠍⢻⣧⡆⠀⠀⠀⠀⠀⠀⢀⢠⢸⣿⡟⠁⠀⠈⢷⡀⠈⠻⣖⣿⠺⢷⡈⢧⠙⠿⡜⢿⡼⠥⣾⣛⣋⣴⠟⣻
⣿⣤⡴⠛⠛⠛⠛⢦⣀⠀⣠⠴⠾⣿⣧⠄⠀⠀⠀⠀⢀⢠⢸⣸⡇⠁⠀⠀⠀⠈⣧⢀⠄⣿⡟⢷⣤⣬⢾⠟⠋⠀⡟⠀⠀⠈⣧⠈⠙⠿⣽
⣿⡏⠀⠀⠀⠀⠀⠀⣹⣿⡇⠀⠀⠈⠻⣷⣴⣴⢀⣦⣸⣼⣿⣿⣿⣇⠀⠀⠀⢀⣿⣿⡗⣿⣿⣻⠏⢰⡏⠀⠀⢸⡧⠀⠀⠀⢸⡆⠀⡠⢹

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣾⣾⣷⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⣿⣆⠀⠀⠀⠀⠀⣸⣷⣾⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⢹⣿⡧⣷⣿⠀⠀⠀⠀⢀⡟⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣏⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⡟⣧
⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣏⣿⠀⠀⠀⠀⠀⢸⡿⣿⢿⡇⣿⣿⠀⠀⠀⠀⣾⣿⡿⣿⢼⣿⣇⣿
⠀⠀⠀⠀⠀⠀⣼⣿⡇⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⢸⡇⣿⣸⣷⡿⣿⠀⠀⠀⠀⣿⣿⡷⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣤⣠⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⢸⣿⡿⣿⠀⠀⠀⠀⠀⢸⡇⣿⣿⢻⣇⣿⠀⠀⠀⠀⣿⣿⣿⣧⣿⣼⣏⣿⠀⠀⠀⠀⢸⢹⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⣿⣽⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⣾⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣾⣧⣿⡆⠀⠀⢀⡿⣿⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣿⢹⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠸⣿⢹⡟⣧⣿⣹⣧⠀⠀⢸⡇⡿⣿⣽⣿⢻⣿⣿⡄⠀⠀⠀⣿⣼⣿⡏⣟⣇
⠀⠀⠀⠀⠀⢸⣿⢻⡇⣿⢻⣿⣿⣼⡇⠀⠀⠀⠀⠀⢿⣟⣷⢿⣽⣟⣿⣄⠀⣼⡇⣷⣿⣿⣿⣼⣿⣿⡇⠀⠀⢀⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣸⣿⣿⢻⡇⠀⠀⠀⠀⠀⠈⢿⡿⣞⢷⣻⣞⢿⣦⣿⡧⣿⢹⡿⣿⣿⣿⣿⡇⠀⠀⢸⡏⣿⣿⣧⣟⡟
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣿⣼⣇⠀⠀⠀⠀⠀⠀⠈⢿⡽⣯⢷⣽⣻⠾⣿⣇⣿⣾⣿⣿⣿⡟⣿⡇⠀⠀⣼⣧⣿⣿⢻⡿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⡳⣯⣛⣿⣿⣷⣿⣿⣿⣿⣿⡇⣿⡇⠀⢀⣿⣿⣧⣿⣾⢿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣯⣽⣿⣿⣿⣿⣟⣿⣿⡇⣿⠀⠀⣼⢿⡿⣽⣇⣿⣼⠁
⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣼⣇⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣇⣿⣠⣾⢯⣾⣳⣿⣽⣏⡿
⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣧⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⡿⣿⣿⣏⣴⣟⣵⡿⣵⣿⣳⡿⣼⠇
⠀⠀⠀⠀⠀⠀⣿⣻⣷⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢸⣟⣿⣡⣿⣯⡾⣫⣾⡿⣷⡿⣿⡟
⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣸⡿⢻⣯⣿⣫⣾⣿⢿⣾⣿⣽⡟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣇⡘⣿⣽⣿⢟⣵⡿⣫⣾⠏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⢹⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⣿⣿⣇⠙⢯⣷⣻⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⡟⣿⢸⡧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⣿⢹⣧⣿⣭⣯⠉
⠀⠀⠀⠀⠀⠀⣿⣧⣿⢸⡇⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⣼⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⢻⡧⣿⣸⡇⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⡿⣿⢸⡏
⠀⠀⠀⠀⠀⠀⠸⠇⠿⠻⠛⠇⠿⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠻⠻⠸⠗⠿⠻⠇

⣿⠿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠟⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣧⢙⣍⢋⣿⣿⡇⠀⠀⠀⠻⢧⣿⣿⣿⣿⠀⠀⠀⠀⠀⢻⡿⣯⣿
⠁⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠘⣿⣿⢧⣿⣿⡸⠿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣼⡇⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠨⣿⢿
⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣭⣭⣽⣫⣽⣭⣭⣶⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠰⢶⡶⠿⠿
⡇⠀⠀⠈⣻⡋⠀⠀⠀⠀⠀⢀⣾⢯⣿⣽⣟⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⢿⣿⣿⡿⠇⠀⠀⠀⠀⢸⣿⣿⣿
⠃⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⣿⣟⣿⣿⣽⣿⣽⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠘⠿⠿⠿
⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⢿⡧⣿⣿⣼⣿⣺⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣬⣿⣿⣿⣺⣟⣻⣗⣛⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣬⣀⠚⠂
⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣟⡛⠋⠀⠀⠀⣴⣿⣿⣿⣦⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⠀⠀⠀⡍⢰⣿⣿⠂⠁
⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⣀⣀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠆⢸⣿⣿⠅⣉
⠀⢀⣀⣿⣿⣿⣇⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠹⣿⣇⣸⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠂⢺⣿⣿⠂⠆
⠀⠀⠿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠙⠋⣿⣿⣿⠃⠀⣼⣿⡿⠃⠀⠀⠀⠀⠖⢺⣿⣿⡉⡁
⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣾⠟⠉⠀⠀⠀⠀⠀⢠⣤⣼⣿⣿⣧⣤
⠀⠀⠀⠻⠿⠿⠀⠀⣴⣶⡆⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣠⣀⣈⣿⣿⣿⣁⣀⣀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠹⠿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⣤⣤⣤⣭⣭⣭⣤⣤⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⣀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⢠⣶⣷⡆⠀⢸⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠉⢹⣿⣽⣭⣽⣿⡏⠉
⣿⣧⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⡇⠀⢸⣿⣿⠏⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⢠⣤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⣰⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣶⠀⠀⠀⠀⠀⣶⣶⣘
⣭⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢯⣿⣿⣟⣯⢷⡄⠀⠀⠀⠀⠀⠀⣤⣶⣶⣤⠀⠀⠀⠀⠀⣿⣿⣿
⣿⡇⠟⣿⣿⠀⠀⠀⠀⣀⣀⣈⠻⠿⠿⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣷⣿⣿⢿⣟⣿⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣯
⣿⣷⣷⣿⡇⠀⠀⠀⠀⠿⢿⣿⣛⣛⣛⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣿⣿⢿⣿⣿⣷⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢹⣿⣿
⣯⣭⣭⣽⣶⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⠰⠀⣠⡀⠀⠀⢠⣾⣷⣿⣿⣾⣯⣽⣽⣿⣦⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⢰⣾⣿⣭
⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣿⣶⡀⠄⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿
⣿⣿⣿⠟⠁⠀⠀⠀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⡃⢸⣿⣿⠄⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠙⢿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⣈⣭⣭⣉⠀⠀⠀⠀⠀⠀⠀⣁⣸⣿⣿⡑⡂⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⠄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⣶⣿⡆
⣦⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⡂⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠀⢀⡀⣿⠃⠀⣼⣿⣿⡇⠀⠀⠀⢀⣴⣿⣿
⣿⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⡶⣶⡆⠀⠀⠀⠸⢿⣿⣿⣿⣿⡿⠃⠀⠀⣶⣶⡙⣿⣾⣿⢠⣤⠀⠀⠀⢻⣿⣷⣠⣶⣯⡻⠟⠀⠀⠀⠀⣿⣻⣿⣾