Pets Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠁⠀⠀⠉⠐⠂⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠐⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⡤
⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢐⣿⣾⣷
⠀⠀⠀⠀⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠣⣽⣿⣿⣷⠀⠀⠀⠀⠰⣄⣀
⠀⠀⠀⠠⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⡇⡀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠗⣿⣿⡛⠓⠀⠀⠀⠀⠀⠉⢻
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⣿⣿⠛⠂⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠘⣃⠀⠀⠀⠀⠀⠀⠐⠀⠰⢿⣿⣿⣿⣿⣼⣂⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣠⣏⣿⠌⠙⠃⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⣷⡁⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠻⣿⣿⣿⡿⠶⢀⠀⠀⠈⠋⠙⢿⣿⣦⣶⣦⣄⣾⣿⠏⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⠟⢡⣌⠹⠙⠆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡤⠄⣤
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠈⠩⠭⠟⠩⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢦⣾⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢰⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡏⠁⠀⠀⠀⠀⠀⠀⠰⠞⠉⠀⠀⢠⠀⠃⡀⢮⢃⡕
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⡀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡅⢠⣤⣿⣿⠻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡆⣰⡷⠉⣿⡟⡆
⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢩⣿⣾⣿⣿⡏⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣷⢸⠃⣀⡿⣿⡇
⠀⠀⢰⣼⣿⡿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡟⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⣿⡆⠀⢹⣿⣿⡇⠄
⠀⢠⣿⣿⣿⣷⣾⣇⣠⠄⠀⠠⠀⡀⠀⠀⢀⣠⠀⠀⢸⣿⡿⣿⡭⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢠⣏⡿⢃⣶⢈⣿⡿⡇
⠀⠈⠿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣤⡤⠷⠛⠋⠁⠀⠀⠹⢻⣟⠻⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠃⢠⡿⣻⣇⠀⠃
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⠘⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡃⣼⣾⡷⢰⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⡏⠁⠄⠀⠀⠰⣴⣤⡆⠀⠀⠀⠀⠀⠀⣀⠆⢰⡄⣧⠀⣿⣽⣿⣿⠁⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⡀⢠⣶⣯⣿⡿⠀⠂⠀⠀⠀⠀⣽⠇⡈⣴⠏⢰⣿⣿⡟⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⠁⠀⠀⢠⠵⡋⣗⠀⢀⠦⠊⣠⠟⠐⣹⠊⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠂⠀⢀⠀⠀⠁⠻⠴⠛⠒⢀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⣆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⢖⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢉⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠿⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⢀⡉⠀⣤⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠣⣀
⠀⠀⠀⠀⠀⠀⠃⠀⣈⡏⠀⠀⣒⡀⠀⠀⠀⠀⠀⠀⠒⢂⣀⠀⠈⢷⡐⠀⠀⠈⢢
⠀⠀⠀⠀⡎⠀⠀⢀⣿⠀⠀⠾⣿⠿⠀⠀⠀⠀⠀⢁⡴⢿⣾⠗⢀⢸⣿⠆⢀⡄⠈⠣
⠀⠀⠀⢰⢇⡄⠀⠘⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⢿⡇⠘⠂⠀⠀⠀⠄
⠀⠀⠀⣾⣋⠀⠀⠀⣿⠀⠒⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠁⡁⣻⣿⡀⡀⠀⠀⡈⢚⠂
⠀⠀⠀⣿⣿⣿⣤⣤⢸⣾⠁⣦⠀⠀⢰⣿⣿⣿⣿⣿⠆⠀⠀⢰⣴⢸⣯⣿⡏⣿⣧⣼⡏⣾⠟
⠀⠀⠀⢿⣟⣏⣾⡾⢸⡜⠦⠹⡗⠀⠈⠙⠿⡿⠟⠋⠀⠀⢠⠟⠠⢾⠟⢿⡇⣻⣿⠄⡜⡇
⠀⠀⠀⠀⠘⣿⣿⡇⡼⢣⡀⠀⢰⣄⠀⡀⣰⣤⣀⣀⠀⣀⢟⡄⠠⠢⠐⣾⣿⢹⣿⣖⡽
⠀⠀⠀⠀⠀⠈⠿⣿⠛⠋⠀⠰⠌⢻⣿⡟⠉⠙⠛⢙⣿⡕⠉⠀⠀⢀⠀⠐⢽⡎⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠘⣷⣄⣀⣠⡿⠏⠀⠀⠀⠀⢄⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣆⢀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢸⠀⢈⣦⣼⡿⣅
⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠙⠋⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢀⠈⠈⠁⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹⢶⣄⣷⣠⣀⣤⣴⠄⠘⠃⠀⠀⠀⠀⠉⠀⠙⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠀⠀⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔

⠀⠀⠀⠀⠀⡀⠀⠀⢀⠤⣀
⠀⠀⠀⠀⠀⢡⠄⠀⢨⠄⠈⢀⡄⡀
⠀⠠⢔⠀⠀⠈⠁⠀⠨⣄⣠⠞⡅⠈⠀⡀
⠀⠈⠑⠀⠤⢔⣮⠽⠀⠈⠁⢸⡇⠀⢀⣽⠛⣶⡀⣤⣤⣤⣀⣀⣠⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠐⠒⠂⠀⠈⢠⡀⠀⢾⠅⠀⠞⠁⢰⣿⡇⠈⣿⡿⠓⢤⡥⡴⢶⠦⠤⠀⠉⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⢀⠌⣿⠇⠀⠹⠀⠀⠟⠁⠈⠀⠀⠀⠀⡰⠃⠀⠑⡄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠞⠁⠀⠀⠀⠀⣄⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠸⡆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡀⠀⠀⠀⠀⠀⠀⠸⢦⣄⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢴⣝⠀⠀⠜⡗⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣸⠇⠀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⣿⣦⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡹⣿⣷⣄⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠙⡏⠘⠄⠙⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠁⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠐⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢦⡤⠋⠠⡤⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣑⡾⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠉⠉⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡀⠀⠙⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢱⠀⠹⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠄⢠⣴⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡈⢻⣦
⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣆⢿⡄
⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠐⠉⠀⠈⠉⠉⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣸⣷
⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣓⣶⣤⣀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢿⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⢿⣧⡈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⢻⡆
⠀⠀⠀⠀⠀⠙⢿⣦⣧⡐⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣌⠀⠀⠀⠀⠀⣾⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⣰⡿⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣽⣿⣿⣿⣿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣨⣵⣿⣿⣿⣿⣿⢟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⠿⠛⢁⣴⣾⣿⠛⠋⠹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡄⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠑⠀⠐⡜⠝⢸⠇⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⢳⡀⠀⠀⠀⠑⠀⠀⢀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢳⡀⠀⠀⠀⠀⠀⠀⠱⡔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⣄⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠠⢂⡟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠜⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣷⣦⣀⣀⣤⠤⠤⠤⠤⠤⠤⠤⡾⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢠⠔⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⡏⠀⢀⣄⢤⡀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠈⠉⠀⣼⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣿⠹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠋⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡴⢚⣛⣛⣦⡀⢠⠇⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣠⠤⠶⠤⣀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠹⢶⣶⣎⣉⣤⣤⣶⠖⠊⢛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⡀⠀⠀⠀⠈⠉⠛⠛⠛⠉⢀⣠⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣦⣀⣠⣄⣀⣤⣴⣿⠟⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⡶⠤⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣶⣶⡼⣿⠷⡇⣤⢴⣷⢀⡄⠄⣾⣿⠓⠂⢴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡟⣋⡉⢠⡯⢇⠀⠿⣴⢼⣿⡿⠸⡯⠿⢫⣼⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠍⠃⠀⠆⢠⠁⣄⣾⣷⢭⡟⠀⣴⡿⢂⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⣑⠢⠄⢳⣿⡟⢾⢹⡆⠝⡑⠚⠟⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⠛⠛⣥⣌⣷⣉⣹⡆⠀⢸⢡⡏⣠⠴⠖⡶⢶⠿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⠀⠀⠉⣻⣿⣤⣷⠀⠀⢾⣷⣟⣷⣾⣿⣟⠂⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⢀⣽⠯⢿⠀⣀⣽⣿⣿⣟⠻⣿⣋⣙⣯⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣤⠀⠀⠀⠀⠀⠉⡿⠛⠙⠙⣿⠶⣤⣭⣽⣿⣻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⡀⠀⠀⠀⠐⠶⠄⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢼⡷⢦⣄⣀⡀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣦⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⠀⢰⠋⣸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢻⠟⢽⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣺⣿⢻⣿⣾⣿⣿⣟⢿⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⡿⢾⢿⣏⣹⣿⢿⠿⠻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠐
⠀⠀⠀⠀⠠⠀⠈⠁⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠤⠂⠀⠀⡀⠀⠀⠐⠤⠄⠀⠀⣦⡔⠀⠄⠀⠀⠄⠀⢤⡾
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠿⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠆⠀⠀⠐
⠀⠀⠀⠀⠈⠠⠠⠈⢠⠠⠘⠊⠀⠀⠀⠀⠀⠀⠀⢈⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠒⠂⠀⢀⠀⠀⠀⠀⠈⠧⠀⠀⠂⡐⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠁⠒⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠁⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠄⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠂⠄⠀⠄⠂
⠀⠀⢀⠰⣀⠌⠀⠀⠀⠀⣀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠈
⠀⠀⠀⠀⡁⠤⠀⣀⡀⠤⠀⠀⠀⠀⠀⠠⣀⠁⠐⠀⠀⠐⠂⠀⣀⠄⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡄⠈⣛⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠩⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠬⠉⠧⠸⠀⠀⠀⠀⠀⠀⠀⠂⠀⢁⠀⣀⠀⠐⠁⠀⠀⠀⠀⠐⢄⠀⠂⠑⠀⡀⠀⠀⠀⠀⣇⡀⠀⣀⣀⣀⠀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠣⠦⡉⠀⢉⢴⠜⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠠
⠀⠀⠀⠈⡀⣀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠔⠀⠀⠁⠀⠁⡀⠢⡀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⡄⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠲⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢁⡀
⠀⠀⠈⠀⠉⢀⠘⡟⢀⠈⠀⠊⠀⠀⠀⠀⠀⢀⠄⠉⣄⠉⢠⠀⠀⠀⠀⠀⢀⠀⢠⠀⠰⠆⠀⡄⠀⡀⠀⠀⠀⢷⠀⠁⣀⠈⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠟⠒⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠃⠀⠈⠀⠀⠀⠀⠀⣧⡀⢘⠀⣠⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠤⠄⠀⠀⠂⠀⠀⠀⠀⢈⠀⠀⠀⡈⠀⠠
⠀⠀⠀⠀⠀⢠⡀⠀⢠⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠺⠆⠀⠠⠟⠂
⠀⠀⠆⡀⢀⡀⠀⣛⡀⢀⡀⢀⠰⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢴⠀⠐⡄
⠀⠀⠀⠀⠀⠁⠂⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⡈⠀⠄⠀⠀⠀⠀⠀⠀⠑⠄⠈⠅⠀⠐⠀⠀⠀⠀⠀⠸⠤⣀⡘⣀⣤⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠓⡄
⠀⠀⠀⠀⡠⠖⠚⠒⢦⠀⠀⠀⣀⡀⠀⣠⠤⠒⠴⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠳⣄⡴⠋⢹⡄⠀⠀⠀⠀⠀⠱⡸⡄
⠀⠀⠀⢸⢧⡷⠨⠤⠔⠀⠀⠘⣄⠈⠳⠁⡀⡄⠠⠇⠚⢹⡆⠀⠀⢀⡤⢤⡤⠤⠤⠬⠶⠿⣼⣹⠓⠜⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⢱⢸⡀⠀⠀⠀⠀⠀⠀⠀⢙⡖⠒⠈⠁⠀⢮⡽⡀⣻⠀⠀⠘⢦⠴⠃⠀⠀⠀⠲⠖⠀⠀⠉⠓⠒⠒⡖⠒⠋⡩⠟⢀⠇
⠀⠀⠀⠈⢣⡳⢄⠤⢴⠒⢻⠉⡏⠉⠱⡆⠀⠀⠐⠤⠞⣡⠇⠀⠀⠀⠸⡀⠀⠀⠀⠀⡗⠀⣠⠞⡦⢄⠀⠀⠓⠤⠖⠁⢠⢾
⠀⠀⠀⠀⠀⠈⡇⠀⠘⠀⠀⠀⠀⠀⠀⡞⠓⠦⠤⠖⠊⠁⠀⠀⠀⠀⠀⠈⠲⠤⠤⠾⠓⠋⠀⠀⢸⢷⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⣠⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣏⡷⠤⠤⠔⡶⣿⠁
⠀⠀⠀⠀⠀⠀⡇⢻⡟⡟⠒⠋⡝⢸⡔⠧⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠚⡸⢹⢻⠀⠀⠀⡅⣟⡄
⠀⠀⠀⠀⠀⠀⢧⣈⠧⣉⠆⠀⣇⠈⢓⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠹⡥⠞⠀⠀⣖⣻⠿⠭⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⢰⠄⠐⠰⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡊⠉⠛⢢⡀⠀⠀⠀⠁⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢣⣤⡊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⡴⠛⢥⠀⠀⢩⣿⡄⠀⠀⠆⡀⠘⠋⢀⢚⠃⠀⠀⠀⣤⡆⠀⠘⣰⠋⢹⠛⣶⣦⠠⠂
⠀⠀⠀⠀⠀⠤⠂⠀⢁⣐⠦⣍⡂⣙⠪⠗⠆⠀⠚⠛⠁⠀⠀⠈⠱⠴⠂⠘⠁⠀⠀⠀⠀⠌⠀⠀⠀⠉⠀⢈⠁⡋⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣛⠦⣝⠊⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠂⠀⠀⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠘⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠶⠂⠀⠛⠃⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⡼⣇⡄⠀⠠⠆⠸⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠄⠃⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠈⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢤⡄⠒⠀⠀⠀⠙⠄⠀⠂⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠬⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢐⡒⢊⠙⢡⠀⡀⠃⠀⠀⠀⠀⢰⡀⣄⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠘⠃⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡥⠀⠐⠊⡀⠐⠀⠀⠁⠀⠀⠀⠀⠸⢡⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⡴⠂⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⣠⣚⣰⠀⢈⡁⠛⠀⠶⠉⠰⠸⠀⠀⠀⠀⢰⡈⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠃⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠰⠆⠀⠀⠚⠂⠀⠛⠀⠀⠀⠀⢸⣇⠀⠙⠿⣣⡄⢠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⡄⢀⡉⠡⡖⠈⠀⠀⠀⠰⢲⣤⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡋⠀⠙⠁⢠⡓⠀⠀⠀⠀⠐⠋⠁⠐⠆⠻
⠀⠀⠀⠀⠀⠀⡠⠂⡒⠤⡴⠋⠈⠑⠶⠞⠁⠀⠀⠁⠀⠀⠀⠀⠀⠤⠱⠆⠀⠐⠃⠙⠀⠀⠀⢸⠒⠀⠀⠀⠑⠻⣦⣤⡀⠒⠢
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠟⠛⠛⠛⠉⠑⠋⠘⠃⠙⠀⠀⠰⠶⡶⠶⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠉⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣶⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠼⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⡿⠿⠛⠃⠀⠀⠈⠻⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣶⣶⣦⢻⣿⣿⡿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣤⡈⠻⠿⢋⣼⡿⠁⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⢻⡟⠛⣻⠋⢠⣶⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠛⠿⠋⠀⣸⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠿⠿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⢻⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣿⡇⠻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⠀⠀⠐⣷⡄⣴⣿⣿⠇⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⢿⣿⣿⡟⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠁⢻⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡿⣂⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠁⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⢹⡄⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠉⠉⢸⣶⣤⣴⣶⣤⣤⣤⣴⣶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣠
⠀⠀⣿⣿⣿⠿⣿⣿⣇⠀⠀⠀⠀⣴⡖⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢠⣤⢀⠢⡄⢠⣤
⠀⢘⣿⣿⡃⠒⢸⣿⣯⠀⠀⠀⣼⠿⠿⡘⠿⠿⡇⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠉⠀⠒
⠀⠀⠚⣿⡇⠀⢸⡟⠗⠀⠀⠀⣿⣤⣤⣤⣤⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⢀⣀⣠⡄
⠀⠀⠀⠘⠛⠻⠿⠇⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣫⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿
⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠀⠘⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⡟⠋⠁
⠀⠀⠀⠀⣀⣄⠄⠀⠀⣤⡐⠂⠀⠀⢣⢸⠀⢼⡄⣷⣦⡇⢸⢸⢾⠠⣷⢲⠀⡇⢼⡆⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠊⡟⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⣀⡀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢠⡄
⠀⠀⢀⣄⢀⣀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢰⣿⡶⣾⣷
⠀⠀⠀⠉⠈⠉⠀⠉⠀⠀⢴⡄⠀⠀⠀⢠⣦⠀⠀⢀⠸⣷⠟⠚⠛⣶⠗⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⠺⢺⣿
⠀⠀⠀⠶⠆⠠⣤⡆⠀⠀⠘⣿⠀⠀⠀⣼⠏⠀⠀⠸⢿⡏⠀⠈⠀⠘⡿⠇⠀⠀⠀⠀⠛⢻⣲⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿
⠀⠀⠀⣤⣤⣤⣾⡇⠀⠀⠀⠘⠀⢀⠀⠉⠀⠀⠀⠸⠟⣧⣀⣀⣀⣴⡻⠏⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⢻⣀⣸⠋
⠀⠀⠀⠘⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢸⠿⡧⠻⠃⠀⠀⢀⣀⡀⠀⠿⠿⠃⠀⣀⣀⡀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠙⠋⠁⢀⣾⣿⣷⠀⠉⠉⠁⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠂⠀⠁⠉⠉⠉⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣈⠁⠀⠀⠀⠓⠀⠀⠄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠀⠘⠛⡁⠀⠀⠈⠭⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢸⠀⠀⠐⠄⢀⠀⠀⠀⢀⠀⢠⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠜⣄⢣⢀⡠⠤⠤⡤⢴⠋⡠⡞⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠢⡹⠀⠀⠀⡖⡡⠊⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡇⠀⠀⡇⠀⠀⠀⡋⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⡀⠀⠱⢄⡠⠔⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⡞⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡆⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠱⡀⠀⠀⢰⠀⠀⠀⢛⠀⠀⠀⠀⠀⡜⢇⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠄⠑⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⢠⠞⠀⠈⢆⠀⠀⠘⡀
⡔⠋⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢣⠀⠀⠘⡄⠀⡰⢻⠀⠀⠀⠈⢣⠀⠀⢃
⡇⢄⠀⠀⠀⠀⠀⢸⠀⠀⠂⠀⠀⡟⠀⠀⠀⠀⠀⠘⡄⠀⠀⢣⠐⠁⣸⠀⠀⠀⠀⠀⢣⠀⠸⡀
⢣⠈⢦⡀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠹⡀⠀⠘⡤⢖⣁⠀⠀⠀⠀⠀⠈⢇⠀⢣
⠀⠑⢤⣈⠉⠛⠉⠉⢳⡄⠀⠀⠢⣇⣀⠀⠀⠀⠀⠀⢀⣱⠀⠀⢸⡁⠀⢙⡆⠀⠀⠀⠀⠀⢣⠈⠓⠤⢄
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠢⠼⠤⠴⠼⠀⠉⠉⠉⠉⠉⠁⠸⣀⢀⠀⢈⢻⠉⠁⠀⠀⠀⠀⠀⠀⠣⣀⣰⣀
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠚⠋⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠲⢄⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⡄
⠀⠀⠀⠀⢰⠀⠀⠀⡴⠁⠀⠀⠀⠈⢃⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡀
⠀⠀⠀⠀⢠⠀⢀⡞⠀⠁⣀⡤⠤⠶⠖⠒⠺⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⡇
⠀⠀⠀⠀⠈⠦⠊⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠞⠛⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⡇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠁
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⡠⠴⠒⠒⠒⠒⠒⠤⠄⠀⠘⠀⡟
⠀⠀⠀⣀⠄⠈⡼⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠐⣌⠀⠀⠉⠁⠀⠀⠀⠀⠀⣠⣦⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢰⠁⣠⣤⡀⠀⠀⠀⠀⠀⠀⠧⠞⠀⠐⠀⠀⢀⡠⠴⠒⠒⠓⠲⡄⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⢃⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠇⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠈⠀⠘⡟⠛⠃⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠥⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⢀⣀⠀⠀⢢⠜⠙⠛⢛⠟⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⡜⢁⡄⠀⢰⠃⠀⠀⡴⢃⣀⣀⡤⠖⠀⠤⢄⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠡⡎⠀⠀⠸⣤⡤⠞⠁⠀⠈⣀⣀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠑⠄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡤⠤⠼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠳⢄⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠹⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠆⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠳⣄⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠄⠐⠒⠂⠠⠄⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢡⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⡄⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⢀⠃⠀⠀⢸⣯⠆⡠⠤⠤⡀⢯⣿⠀⠀⠀⠇⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠸⠒⠒⠒⠐⠒⢊⣤⣒⣠⣌⠑⠒⠒⠒⠐⠺⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠇⠀⠀⠀⠀⠀⣀⣉⡿⣏⣁⡀⠀⠀⠀⠀⠀⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠫⣀⡨⠁⠀⠀⠀⠀⠀⡰⡖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠒⠢⠤⢀⣀⣀⣀⣀⠀⠤⠄⠲⡋⢠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣷⠃⠉⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢣⠀⠈⠢⣀⠀⠀⠀⢀⡠⠊⠀⢠⠃⢱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⡆⠀⠀⠈⠉⢲⠊⠁⠀⠀⠀⡜⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠂⡜⠢⠤⠤⠀⢸⠀⠀⢀⡀⠜⣄⠚⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣰⣘⣴⡀⢰⠀⣀⠼⢄⡀⢐⠀⢰⣼⣰⣀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢉⠉⣀⠀⠉⠐⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⢠⡙⣿⠁⣼⠟⣀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠉⠁⠃⠄⠹⠀⠋⢈⣷⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢈⣿⣷⠀⠰⢲⢳⠢⠀⢠⣿⢽⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃⣿⡀⣤⢠⣇⢠⠀⢸⣿⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢧⣥⢟⡹⢦⣀⣸⣏⣷⡍⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣽⠃⢲⣿⠿⠊⠑⣫⣾⣿⠇⠘⡆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⢘⡇⠀⠀⢠⣿⣿⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣾⣷⣆⣴⣿⣿⣿⠁⠀⠀⠀⣾⠁⢠⠀⢸⣄⣤⣤⠀⠀⠀⠻⠦⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠀⣰⣿⠀⣾⠀⢸⣿⣿⣿⣤⡀⠀⠀⠀⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠄⠀⠀⠙⠻⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⣿⣿⣾⡟⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⣸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⣀⡀⠸⣧⣤⣀⠀⢀⣠⣤⣀⣠⣶⠃⠀⢰⣿⣿⣿⡿⠛⠛⠻⢟⡁⠙⠻⡷⣷⡀⠰⠁⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣠⡝⠁⠀⠀⠈⠛⠿⣿⣿⡿⠿⠟⠋⠁⢀⠀⠀⠛⠉⠀⠀⠀⠀⠀⣼⣿⡤⠔⣃⡼⠃⠀⠁⠀⠹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⡰⠋⠁⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣠⣤⠞⠋⠁⠀⠀⠀⠀⠀⠈⢌⡉⠟⠋⠀⢸⡋⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿
⠀⠀⠄⠒⠉⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒
⡤⢀⢀⡄⣠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁⠀⠀⠁
⠓⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢠⠀⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢀⡴⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠰⠤⣀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠀⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠐⠊⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠘⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⠄⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠉⠓⢦⡶⠒⠓⠒⠂⠀⠁⠀⠋⣀⢤⠀⠀⠀⠘⣤⣤⣤⣤⡤⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⡀⠀⢈⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠁⠀⠀⡴⠛⠂⠘⠀⠀⣤⣬⡁
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠙
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢠⠏⢸⠀⠀⠀⠀⠀⢀⢠⠀⢀⣄⠀⠀⣀⡀
⢀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⠰⠋⠀⣴⠀⠀⠐⡻⠛⠊⠀⠀⠈⠁⠀⠔⠻⢁⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⣲⣾⣿⡿⠿⠿⢿⣷⡄
⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⣤⣤⣾⣿⣿
⠹⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢲⠞⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠘⠿⣿⣿⣿⣿⣷⣄⡀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⠀⠀⢢⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠛⠋
⠀⠀⠀⠈⠙⠻⠿⢿⣿⠿⠋⠁⠀⢹⣿⣿⣶⣶⣶⣶⣶⡿⢻⣧⠀⠀⠀⠡⡀⠀⠀⠀⠈⠑⠒⢀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠙⢷⡀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠈⠰⡆⠦⠀⣀⡄⠀⠀⠀⠀⣀⠔⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⡞⠀⢀⣴⣿⣿⣿⣶⣄⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⢸⠁⠀⢾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣶⣿⣿⣿⣶⡄⠀⠀⠉⠢⢄⠀⠀⠀⠀⠈⠐⠂⠼⠷⢦⡀
⠀⠀⠀⠀⠀⢸⡆⠀⠈⠿⣿⣿⣿⡿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠁⠒⠄⣀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⠖⠢⡀
⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠐⣆⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠼⠿⡶⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠾⠿⠁⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡘⠀⠀⢄⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠘⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠈⠆⠐⠀⠀⠀⠀⠁⠀⠀⠂⠠⢀⠀⠀⢀⠀⠤⣀
⠀⠀⠀⠀⠈⠓⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑⠀⠑⠄⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡈⢢⡀⠐⣀⢸⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠛⠛⠀⠙⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠴⠛⠹⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⢀⡤⠞⠃⠀⠀⠀⣠⠤⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠢⢤⣄⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉
⠈⢳⣤⣀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡿
⠀⠀⠉⠉⠡⣴⠶⠊⢹⡇⠀⠀⠀⠀⠀⠀⣰⡯⢶⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡤⣰⠟⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣀⣤⣾⠋⠀⠀⢠⠟⠀⠀⠙⠓⠆⠒⠷⠒⠋⠀⠀⠀⠀⣸⢱⡇
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡴⠋⠉⠀⠾⢦⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⢷⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣿⠈⠓⢤⣀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣤⣭⠆⠀⠀⠀⠀⠀⠈⠓⣦⠀⠀⠘⠦⣤⡴⠞
⠀⠀⠀⠀⠀⠀⠱⣦⣄⣀⣨⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⢰⣬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡠⠔⠒⠉⠉⠷⠿⣶⣦⣭⠭⠉⠉⠉⠙⠳⣆⠠⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣴⠶⠆⠀⠐⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢺⡏⣠⠀⢠⠂⠀⠀⠀⠀⠀⠀⠈⠀⠢⡀⠀⠀⠘⡇⠀⠄⠀⠀⠀⠀⠈⣏⢧⠸⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣾⠁⠀⣨⣴⡇⠀⡇⠀⠀⠀⢀⡀⠀⠀⣀⡆⣠⠇⠀⠀⠀⠁⢦⣠⣶⣀⠤⠀⠀⢸⣾⠀⠃⠉⠻⣄
⠀⠀⠀⠀⠀⠀⣼⢸⣿⡇⠸⣿⣿⡇⢰⡇⠀⠀⣀⡾⣿⣻⣿⣿⣆⢿⠀⠀⠀⠀⠀⠀⠻⣿⣽⣷⠄⡀⠈⣟⡇⠀⠀⠀⠿⢷
⠀⠀⠀⠀⠀⠀⢹⣆⢻⡇⠀⢻⣿⡇⢸⡇⠀⠉⠉⠁⢼⡿⠉⣿⡏⠀⠀⠀⠀⣷⠀⠀⠰⡙⠧⠀⢀⡄⠀⣯⡇⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⢿⣷⠀⡿⡄⠀⢤⣀⠀⠀⢈⣿⠆⠀⠀⣀⣸⡟⠃⠀⠀⢀⣰⠿⠋⠀⠀⣿⣇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⢸⣿⡀⡇⠀⠀⠀⠙⢻⡇⠀⡏⢀⡴⠛⠉⣠⣤⣄⠐⢶⣦⠙⣦⠀⠀⠀⣿⣏⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⢸⣿⢣⣇⠀⠀⠀⠀⠊⠀⠀⠀⡜⠁⠀⠀⣭⣷⠄⣀⠸⣯⡅⠸⠀⠀⢠⣿⣿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠾⣃⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⣿⡷⠞⠀⠀⠠⢇⠀⡿⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⢿⣿⡇⠀⠋⠘⣵⣆⠀⠀⠀⠀⡀⡀⢸⣿⣿⢈⣶⡆⠄⠀⢾⠃⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠈⣿⣷⡀⠀⠀⠻⣿⣆⠀⠀⡄⡄⢤⠴⣿⢻⣾⣿⣷⣍⣀⠌⡄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⢹⠈⢳⣄⠀⠀⠘⡿⢿⣶⣤⣤⡴⣚⠛⠯⠋⠀⢹⡛⣉⠞⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡼⡆⠀⢇⠀⠉⠑⣦⡀⠈⠙⠛⠻⣏⣴⡙⠦⣀⠀⠀⠘⣿⠃⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠈⣆⠀⠀⠈⠛⠂⠰⢤⣀⠙⠻⠿⠶⠶⠖⢚⡶⠋⠀⠀⠀⣼⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠈⠀⠀⢠⢠⠀⠀⠀⠈⠑⢶⣶⣶⠃⠈⠁⠀⠀⠀⠀⡀⢸⡟⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣻⣿⠃⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⡾⣿⣿⡀⠀⠀⠀⠀⠀⢠⠀⢸⠃⠀⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⣿⡀⠀⠀⠀⠀⠀⠘⢱⠃⡀⠀⠀⠀⠀⠙⢿⣟⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠁⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢿⣇⣤⠀⠀⠀⠀⠀⢸⣿⡇⢀⡄⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡇⠀⠀⠀⠻⡿⣆⠀⠀⠀⠀⠈⠈⢿⣿⣧⣆⠀⣠⣶⣄⠀⣀⠀⠀⠀⠠⣹⡆⠀⠀⠀⡏⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⡀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠁⠙⠻⢶⡏⠀⠉⠻⠇⠈⠁⠀⠀⢹⠃⠀⠀⡼⠃⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠳⣄⢀⡀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠈⠛⢷⣾⣷⣄⢲⣄⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣷⠖⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⠖⠊⠉⠁⠀⠈⠉⠉⠒⠶⣤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⠇⠀⠀⠀⣿⣙⠄⢀⡠⢤⡀⠠⣋⣿⠀⠀⠀⢸⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠤⠤⢤⣀⣉⡩⠔⣉⠤⠄⣈⠳⠭⣩⠤⠤⠤⠬⡇⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⡇⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢸⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠢⡴⠞⠙⡶⠖⠂⠀⠀⠀⠀⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠙⠦⠔⠃⠀⠀⠀⠀⠀⢀⡴⢻⠁⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠑⠒⠤⠤⠤⠄⠤⠤⠤⠤⠔⠒⠉⡇⠀⣎⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹⡎⠀⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢹⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⡇⠙⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢇⠀⠀⠀⠉⠒⢦⠔⠒⠉⠀⠀⠀⣸⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠦⠤⢘⣆⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⡃⠠⠴⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⢀⠀⡎⡀⠉⠉⠉⠀⢸⠀⠀⠈⢑⠋⢁⢹⠀⡀⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠼⠤⠟⠧⢄⣧⠤⠴⠚⠑⠢⠤⠼⡤⠼⠞⠤⠧⠜⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣤⣄⣉⠀⠀⠀⢉⣡⣦⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⢟⠅⠀⠀⠀⢙⣷⡀⠀⡿⠁⠀⠀⠀⠀⠈⢽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟⢰⣿⣧⠀⠀⠀⠀⠰⣜⣿⢸⣡⣾⣉⠀⠀⠀⠘⣆⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠃⠀⣿⣟⡴⣉⡰⣶⣴⣼⣿⠘⣿⣿⣿⣻⣦⠈⠣⣽⡿⠀⠙⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⠂⠀⠀⠀⡀⣽⠏⠰⠟⣫⠛⢻⣿⠏⠀⠘⠿⣿⡟⠟⠓⠀⣻⣷⠀⠰⣆⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⡘⢻⣶⡄⠀⠀⣿⡏⠀⣀⢀⡀⣠⡟⢁⢾⡷⠘⢳⣞⢿⣦⣄⠀⠻⣿⣧⠘⣿⡆⠐⢾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⡙⠃⣴⡞⣹⠃⣨⣽⣿⠿⣿⠀⢠⣞⣡⣦⣈⡻⠀⢻⣧⠀⠀⠙⣿⠀⣿⡇⠀⢦⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⣿⣴⡟⠀⣉⠠⠄⠀⠇⠀⢰⣶⣿⣻⣭⡄⠀⢨⠙⠒⠤⣄⢻⣄⣿⣧⣀⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠙⣿⡿⢻⠖⠉⣴⣞⡂⠀⠀⠀⢸⣿⣿⣯⡻⠃⠀⠈⠀⣢⠀⠸⡎⣿⣿⡿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣋⣴⠁⠀⣿⡤⠀⠀⢻⣿⣦⣤⣴⠖⠻⣿⡿⠟⠓⢶⣴⣾⡁⠀⠘⡟⠻⣯⣾⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⠟⣡⠀⠀⢻⣧⣀⠀⠸⣎⡛⢿⡾⡀⠀⠈⠀⠀⢰⣿⣋⣾⠇⠀⠠⠇⠀⢈⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⠁⠀⠀⠈⢿⣧⠄⠀⢀⠙⢿⣄⠱⡘⠒⣀⡠⢎⡽⠁⠀⠀⠀⡄⠀⠀⢤⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡻⣄⣶⡆⠀⠘⢿⠠⠀⠀⠙⠲⡌⠓⣂⠀⠠⠴⠛⠁⠀⠀⡀⣶⠇⠀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠘⣿⠇⠀⠀⠀⠸⢿⣤⢀⡄⠀⠀⠀⠉⠁⠀⠀⠀⠀⣴⣿⠟⢠⣾⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇⢹⣴⡇⡀⠀⠀⠀⠙⣿⢧⡿⢶⣶⡄⠀⣤⡀⢀⡶⠟⠁⠀⠛⢉⣻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⣿⣿⣴⡆⠙⢿⡟⢦⣷⡄⠀⠀⠀⠀⠀⠀⠉⠀⠹⣷⡏⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⢀⠀⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣡⣿⣿⣿⣿⣿⣿⣄⣷⡀⡄⠀⣠⠶⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⢠⠾⣿⣿⡟⠁⠙⠿⣿⣿⠿⣿⣿⣄⣇⢸⣿⣀⠀⠀⠀⠀⠀⠀⢀⢠⢠⡀⢡⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣠⡟⠀⠈⢻⠇⠘⣿⢿⣿⣆⠉⠉⠀⠀⠀⠀⠀⠀⢸⠾⠁⢱⡟⠉⠻⣧⢻⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⣿⡿⠁⠀⠀⠀⠀⠀⠀⠚⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⢹⡿⣿⠈⢿⣮⠁
⠀⠀⠀⠀⠀⠀⢸⣿⢿⣇⣈⠁⠀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡧⠁⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⣆⠀⢰⡿⣧⡟⢷⣦⢰⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⡏⠃⠀⠀⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⢻⣷⣿⠀⠈⠻⠀⠿⠙⠿⣿⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣸⡿⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠉⠀⠀⠀⠘⠉



⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣭⣞⣿⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢸⠟⠉⠉⢩⣳⣲⢿⣟⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⢦
⠀⠀⠀⠀⠀⠘⢄⠌⠀⢨⢋⣿⣵⣾⣿⣿⣿⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠉⠯⢠⣼⣿⣿⣿⣿⣿⡿⠛⠃⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⣿⡏⠁⠀⠀⠀⠀⠀⠈⢳⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⠶⠦⣤⣤⣤⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠇⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⣿⣟⣿⣻⣯⣿⣟⣿⣿⣿⠿⣿⣶⣤⣤⡈⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠁⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡗⣿⠿⣿⢿⣿⣿⣛⠉⠻⠾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣦⢄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣺⣿⣻⣾⣯⣿⣿⣿⣿⡅⢄⣻⡏⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠘⣆⠀⠀⢰⣟⣿⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡦⠋⠟⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣧⠀⠀⠘⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠟⠟⢛⡉⣉⡁⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⢣⠀⠀⢫⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣭⠴⠶⠛⠛⠛⢻⣿⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠇⠀⢸⠇⠈⠉⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢳⠰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡳⣆⣀⠮⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠘⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⡞⢻⡀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣋⠁⢠⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡒⠁⢰⠁⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡴⢛⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠊⠁⢀⠠⠣⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⠴⡤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠤⣤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣽⠀⠀⢠⠄⠀⠘⠇⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡝⠀⠀⠈⠛⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠀⠀⠀⠀⠀⠠⣇⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠓⠀⠀⠄⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡗⠲⠛⠦⡀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠙⡄⠀⠘⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⠤⠶⢤⡀⠀⢢⠀⠀⠀⡔⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠉⠀⠀⠀⠀⠹⡆⠈⡄⠀⠀⡇⠀⣠⠀⠸⡇
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢧⠀⠀⣧⠞⠹⡄⠀⡇
⠀⠀⠀⠀⢸⡷⡄⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⠀⠀⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠰⣧⠙⢦⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡠⠚⡇⠀⡇⠀⠀⢇⠀⠇
⠀⠀⠀⠀⠀⠈⣷⣄⠈⠓⠦⢄⣸⣄⣀⠀⠀⠀⢀⡤⠚⢁⣠⣖⠉⠉⠙⡇⠀⢧⠀⠀⠈⢣⠘⠂
⠀⠀⠀⠀⠀⠀⠈⠛⠢⠤⠄⠠⠤⠾⣅⣀⣀⣀⣈⣉⣉⡀⣠⡠⠏⠉⠀⠙⢄⠀⡁⣠⠀⠀⠁⠠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⣶⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⢀⡀⠿⠇⣀⡀⠛⠃⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣷
⠀⠹⡿⠻⣿⣿⣿⣿⣷⣶⣿⣿⣷⣿⡁⠀⠀⠀⠀⠀⠀⠸⠇⠀⠈⢿⠟⠀⠀⠀⠀⠀⠀⠙⠻⠷⢦⣄⣀⣀⣀⣀⣠⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠼⠆⢀⡔⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠻⣿⡟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢻⡿⢹⣿⠀⠀⠙⣿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠡⣾⠟⠁⠀⠀⠈⣿⠻⣿
⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠼⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠿⠄⠀⠀⠀⠀⣿⡀⣿⡀
⠀⠀⠀⠀⠀⠛⠃⠸⠿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠹⠸⡈⠠⠹⢸⢘⠸⠰⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠻⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣠⣼⠇⠀⠀⢠⣾⡿⠿⢿⠿⠿⠿⠶⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⠿⠿⠿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⢀⣤⣴⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠻⢷⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣙⣷⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠉⠁⠀⠀⠀⠀⠀⠀⠘⠻⣷⣄
⠀⠀⠀⣀⣴⣿⠟⠁⣀⣤⣶⣾⣿⡷⠀⠀⠀⢀⣼⠏⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠙⢷⡄⠀⠀⢰⣿⣷⣤⣀⡀⠈⠻⣷⣦⡀
⢀⣴⣾⣿⣿⣷⡿⠿⠛⠋⠉⠀⣿⡇⠀⠀⠀⣼⣇⣀⡀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⠈⣿⠀⠀⢸⣿⡍⠉⠛⠿⣷⣶⣬⣽⣿⣷⣤⡀
⣿⣿⣟⡋⠉⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⣿⣿⣏⣽⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣩⡇⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿
⠀⠙⠛⠿⣿⣶⣶⣤⣤⣤⣤⣾⣿⠁⠀⠀⠀⠙⠿⢿⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⡷⠟⠀⠀⠀⣿⣧⣀⣀⡀⢀⣀⣠⣤⣶⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠋⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣯⣍⣙⢲⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠈⠛⢿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⣀⣀⣀⣤⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡀⠀⠀⠀⠀⠈⣽⡿⠛⠻⠿⠿⠿⠿⠿⢿⣿⣥⣬⣿⠿⠿⠿⠟⠛⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢿⣧⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠈⢿⣷⣤⣀⣀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠈⠛⠻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⢀⣤⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣶⣶⣶⣶⣶⣶⣾⠿⠟⠁⠛⠿⣷⣶⣶⣶⣶⣶⣶⣿⠿⠿⠛⠋
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣶⣶⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣎⠁⠈⠋⢹⠟⢘⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡈⠀⠀⠀⢸⣏⣸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢺⣿⡿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣼⣿⢹⠿⢿⣿⠏⠀⠀⠀⠀⢠⣄⣀⣀⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣏⠁⠀⠀⠁⠀⠀⠀⠀⢢⣶⣿⣿⣿⡇⠀⠻⢿⠿⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠿⠁⠀⠀⠀⢀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⣘⣿⠿⣅⠀⠀⠀⠐⠂⠺⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⢀⣉⠁⣀⣤⡗⠀⠀⠀⠀⢀⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⢐⣰⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠌⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣟⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡙⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠙⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡏⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣴⠞⠋⠁⠸⠇⠀⠀⠀⠀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⢀⣤⠶⠦⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⢀⣀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄
⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠙⣳⣤⣄⠀⠀⠀⠀⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣾⠃
⠀⠀⠈⠉⠉⠡⣤⣶⠞⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢀⠄⣼⠟⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⣤⡾⠁⠀⠀⢀⣾⠃⠀⠈⠻⠶⡤⠠⠴⣶⠤⠞⠁⠀⠀⠀⠀⢠⡏⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⠶⠛⠋⢹⣇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⢀⣴⡟⠁⠀⠀⠀⠈⠙⢷⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢹⡇⠀⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣤⣦⡼⠇⠀⠀⠀⠀⠀⠀⠀⠉⠹⣄⠀⠀⠀⠛⢦⣤⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⣀⠀⢀⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣦⣹⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠉⠛⠛⠛⠛⠛⠻⠾⠿⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⡀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡟⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⢻⡻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⢀⣤⣿⠇⠀⠀⣠⣤⣴⣶⣆⠀⠋⠀⢀⣷⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⣤⣴⣿⣿⣿⠀⠀⠐⠿⡿⢛⡿⠇⠀⠀⠀⠻⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣻⢿⣿⣿⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠈⠑⠮⣭⣥⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠛⠿⠟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⡇⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⣿⣿⣿⣷⣭⡛⠿⠟⣡⡿⣧⣉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⣠⠄⢸⣿⣿⣿⠀⠈⠙⠛⠛⠋⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣀⠀⠀⢿⡆⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣷⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⠀⠀⠀⠀⠀⣰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⠈⡇⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢁⣾⠀⢱⣤⣤⣿⣿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⡇⠀⣿⣿⣿⣿⡻⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡇⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣆⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏⠉⣭⣽⣆⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⢹⡿⠃⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⢻⣿⣧⡀⠠⣄⡀⠀⠀⠀⠀⢹⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠙⢿⣿⣶⣤⣭⣷⣶⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠙⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣯⣍⠉⠛⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⡄⠀⠀⠀⢠⣤⣴⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⠀⠀⠀⠉⠛⠿⠿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⢀⣤⣴⣶⣿⣿⣧⣼⣿⣿⣿⣿⣿⣻⣇
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⣿⢟⣽⣿⣿⡄
⠀⠀⠀⠈⠻⠿⠿⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡼⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⣿⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⣿⣿⣿⣿⡟⣿⣿⢟⣫⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢋⣴⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⣿⡟⠹⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢊⣿⣇⠀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⠾⠿⠟⠸⣫⣯⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠟⠃⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠟⠛⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⠋⠋⠉⠉⠉⠉⠛⠓⠲⠦⠤⠤⠤⠤⠤⠤⢤⡞⠛⣶⠛⢳⠚⠙⣆⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⢸⠀⠀⡿⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠃⠀⠘⠀⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣸⠅⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⡴⠋⠉⠉⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⣀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣨⣧⣠⣠⡔⠋⠀⠀⢺⣀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠾⡁
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣘⣲⡇⠀⢸⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠓⠶⠛⠲⠞⠓⠶⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⣦⠤⠤⠤⠤⠤⠤⠼⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⢸⡇



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡌

⡤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠⠤
⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡔⠠⡀⡄⠠⡄⠀⣄⠀⡤⢠⢠⠀⠀⡄⠀⠀⡠⠂⠀⡄⠀⠔⣄⢠⠀⢄⢠⢀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⡇⠀⠆⡇⠀⠇⠼⠘⠄⣏⠱⠈⡀⠀⡇⠀⠀⢈⡲⠀⠇⠀⠓⠇⠣⡀⡸⢸⠛⠄⣏
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⢟⣹⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣯⡙⢾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⢿⣮⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠿⣍⢦⣿⣿⣿⣿⣿⣿⣼⡿⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⡟⢉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣷⣦⡙⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⡏⣿⠟⠁⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⠿⠛⠉⠉⠀⠉⠀⠙⢿⡾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣾⠿⠿⢿⣆⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣶⣦⣤⣤⣶⠟⠁⠀⠀⠀⠻⣷⣦⣦⣤⣲⣾⣿⣿⣿⣿⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠉⢻⣿⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣤⣾⣿⣿⣿⣿⣿⣦⠀⢻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣷⣹⣿⣏⢿⣿⣿⣿⠃⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠹⢿⣿⣿⣿⠟⠀⠀⠀⢸⣿⣿⣽⣿⣿⡹⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣿⣿⡿⣿⣿⡿⣿⣿⡉⠁⠀⠀⠀⠀⠴⠞⠹⠷⠆⠀⠀⠀⠈⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣽⡿⣿⣿⣿⣧⡀⠀⠀⠀⣀⠔⠚⠷⠦⣀⠀⠀⠀⣠⣿⣿⣷⣭⣛⠻⣿⣿⣟⣹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢫⣾⣿⣿⣿⣿⣿⢷⣶⡙⢤⣤⣤⡀⠐⣾⣿⣶⣾⣿⢽⣿⡝⠻⣿⣶⣿⣼⣿⣿⣝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡏⠀⢻⣿⣦⠀⠈⠀⠀⠿⣿⣿⢻⣿⣮⣻⣿⣦⢹⣿⣿⣿⣿⣿⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠠⠂⢹⡿⠄⠀⠀⠀⠀⠹⡅⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠈⠀⠀⠀⠑⣠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⡠⡪⠉⠀⠀⠀⠀⠀⠑⠔⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⡀⠔⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⡀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⣦⣄⠀⠀⢀⠌⠀⠀⠀⠡⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢿⣿⠄⠁⠂⢠⣾⡮⢰⠄⠃⢀⠀⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⢠⡒⠒⠲⢄⠈⠻⠿⠀⠀⡀⠈⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠿⣿⡶⠟⠣⠀⣀⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠉⠁⠀⠀⠠⢐⠹⣄⠀⠀⠀⠀⠀⠀⠀⠸⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡀⡀⠠⠀⠂⡁⠔⠁⠀⠈⠐⠠⢄⠀⠀⠀⠀⠡⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢼⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⡼⡄⠀⠀⢡⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢸⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠠⠂⠀⠀⠨⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣄⣀⣈⠀⠀⠀⢠⠊⠈⠁⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠀⠂⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢤⡠⠤⢤⡤⠤⠴⠤⢤⣀⡀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡎⠉⢠⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠉⠙⢻⣿⢿⣿⣷⣤⡀
⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⠟⠋⠀⠀⠁⠀⠠⠂⠀⠀⠀⢠⠀⠈⠢⡀⠀⠀⠀⠀⢻⣏⣿⣿⣿⣿⣷⣾⣿⣶⡀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠠⠤⣄⠀⠀⠀⠻⣮⣟⣿⣿⣿⣿⣿⣿⠃
⠀⠀⢿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠈⠀⠀⣀⡈⠀⠀⢠⠀⠀⠀⢀⣀⡀⠀⠉⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡟
⠀⠀⠈⢻⣿⣿⣿⣾⡇⢠⢒⣤⣶⣶⣶⣿⣿⡿⡰⠀⣘⣀⠀⣄⢻⣿⣿⣷⣶⣦⣄⢱⠀⠀⡿⣿⣿⣿⡟
⠀⠀⠀⠀⠹⣿⣿⣿⡇⠁⣿⡟⣿⣯⣽⣾⣿⣿⣷⣿⠿⢿⣿⣾⣿⣿⢿⣯⣽⡟⣿⠇⠀⠀⣿⠘⠻⠟
⠀⠀⠀⠀⠀⠘⠿⢿⡁⠀⠙⢿⣾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⢻⣿⣿⣮⣿⣿⡿⠋⠀⠀⢄⠸⡆
⠀⠀⠀⠀⠀⠀⠀⣼⢰⠁⣴⣶⣾⣿⣿⣿⣿⣿⣶⣿⡛⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠁⣷
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢿⣏⣙⢿⣿⣿⣿⣿⣿⡿⢇⢿⣿⣿⣿⣿⣿⣿⢟⣥⣾⣿⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢿⣿⣦⣝⣛⣛⣋⣽⢾⣿⣷⣮⣝⣛⣛⣯⣵⣿⣿⡿⠁⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⢿⣿⣮⣟⡟⠀⠀⠸⠀⠀⠈⣟⣫⣵⣿⡿⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠉⠛⠿⣿⣦⣤⣀⣀⣠⣼⣿⠿⠛⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣈⡉⠙⠉⢉⣉⣀⣤⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉



⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣟⣿⣟⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⠲⢽⡍⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠉⠉⠉⣀⠥⠔⣠⡦⠠⣘⠊⠉⠟⢒⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠚⠛⠙⠛⢷⡢⡄⢀⡠⢂⡴⠚⠁⠀⢶⣌⡙⠂⠂⢉⡁⠀⣀⡛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠩⠞⠛⢉⣓⣄⠑⠈⠸⠑⢁⠔⠁⢂⣠⠏⡧⢸⡀⠀⢁⠖⠋⢹⡄⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⣤⣤⣄⣠⡴⠿⣿⡗⢦⠀⡀⣠⠞⠛⠛⠛⠁⢀⡄⣐⢒⣶⣦⠞⢠⡼⡏⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠃⡼⠉⠀⠀⠒⠼⠓⠒⢤⡈⣷⢸⡇⢸⡇⠀⣠⠀⡴⠞⣿⡯⠁⢉⣁⣀⠀⠉⢀⠳⢦⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠸⣀⢡⠎⠀⢀⣠⡤⠤⠤⢄⠑⢿⠘⡇⠈⡇⠀⠇⠸⠁⣸⢻⠀⠔⠩⢒⣒⣈⣀⠀⠑⠂⠱⠘⣗⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡉⡼⠀⠀⠛⠂⢤⣄⠐⠀⠑⠈⠀⠀⠀⠀⢀⡄⠀⡀⠁⢀⡀⠀⠀⠀⠀⣀⣺⡛⠂⢤⠀⠱⣌⠳⡄
⠀⠀⠀⠀⠀⠀⢀⣦⡴⢃⡇⣀⣠⠖⠉⣠⣤⣤⣼⣧⢠⠐⣦⡄⡜⡿⠟⠻⠊⣿⣿⣾⡖⠊⠉⠀⠀⠁⠀⢠⡄⠠⣈⠑⢦
⠀⢀⣠⡤⠄⠒⠈⠸⠖⠋⠀⠀⢐⠖⠋⠁⠀⠛⠿⢛⣤⢥⠃⠸⡆⠀⠀⠀⠀⠨⠟⣩⣄⡀⠀⢤⠈⡐⢄⠱⡰⡀⢌⢳⡌⡇
⠀⠀⣤⡀⢠⠀⠔⡡⠂⠀⠀⠀⢸⠀⡞⠀⠀⣀⠀⣈⢟⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠉⢳⣆⠂⠘⣆⠀⡇⣇⠀⠸⠁⡇
⠀⠀⠀⢰⢃⡄⠈⢸⡖⠊⡇⠰⠈⠀⢹⠦⠈⠉⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠛⠈⠋⠠⣀⡀⠒⠢⣄
⠀⠀⠀⢸⣺⠿⠀⠈⠀⡄⠻⡀⢀⡸⠂⠀⠀⠀⠈⠉⠀⠀⢀⣠⣤⣤⣤⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢱⡆⠀⠀⠂⠤⢀⣀⠢⡌⢳
⠀⠀⠀⠀⠉⢰⢠⠸⢍⡀⠀⠀⠔⠁⢀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠒⠀⠀⢆⠃⠀⠈⢳⡀⢰⠈⠑⠀⠈⠣⠤
⠀⠀⠀⠀⠀⠀⠿⡃⠀⠀⠀⠈⢹⠋⠁⠀⠀⠐⠈⠁⠀⠀⠙⢿⣻⣿⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⡀⡄⠳⢌⣦⠠⣄⣓⡶
⠀⠀⠀⠀⠀⠀⢠⠗⢧⠀⠂⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢨⠹⡷⢤⣌⡥⢄⢀⡀⡠⠋
⠀⠀⠀⠀⠀⠀⡄⠀⠈⢮⣓⠄⣣⡆⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠄⣶⣶⣦⣦⣀⢀⡀⠀⠑⢄⠀⠀⢠⡏⠀⠘⡄
⠀⠀⠀⠀⠀⠰⠆⢀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢸⠀⢠⡞⠋⠀⠀⠀⠀⢈⠛⠋⠑⡲⠚⠛⢉⠉⠀⢢⡀⡬
⠀⠀⠀⠀⠀⠎⠠⠃⣔⡥⠖⠈⠀⠀⠈⢧⣠⣀⠀⣄⠼⠞⠁⢱⠀⠀⠀⠀⠀⠘⢀⠔⠖⠁⠀⠠⣈⠳⠐⠂⠆⠑⢄⣀
⠀⠀⠀⠀⠠⠀⠀⢰⡏⡐⠀⠀⢆⠰⡀⢀⡛⠈⠋⠙⠖⠤⣄⣸⡆⠀⠀⠀⠀⢘⠁⡠⠀⠠⡈⠑⠦⡁⠀⡀⠀⠀⠐⠣⡀
⠀⠀⠀⠀⠀⠆⠀⠸⡄⢣⠰⣄⡀⠀⠈⠂⠈⢆⢣⠈⠑⠂⠐⡌⢷⣀⣀⣀⣀⡜⠀⡇⢠⡀⠈⢆⢄⠘⠄⢰⠀⠀⢚⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁⠀⠉⠑⠀⠀⠀⠂⠌⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠘⠈⠀⠀⠈⠀⠀⠘


⡿⠿⠿⠿⡿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿

⠀⠀⣄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠉⠊⠉⠁⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣶⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣿⣶⣶
⠀⠀⠀⠀⠖⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠂⠀⠀⠀⠀⢰⣿⡿⠿⠛⢿⣿⡀⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⠍⠀⠀⠈⠛⠋⠋
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠘⠟⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣀⣀⣂⣆⠀⠀⠀⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠐⠀⠘⠿⠧⠀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠈⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣧⠀⢀⣾⣿⣆⠀⠀⠀⠀⡞⠃⠌⢁⠀⠀⠀⠰⠟⡿⠃⠀⢰⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⡄⠀⠀⠰⢦⣖⣰⠞⠀⠀⠀⠀⠀⠀⣘⣃⡈⠃⠀⠀⠀⣆⠀⠀⠀⢠⠀⠀⠈
⠀⠰⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠇⠀⠂⠀⠀⠘⠟⠛⠛⠃⠀⠀⠀⠀⠙⠙⠀⠀⠀⠀⠀⠀⠘⠽⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡀⠤⡤⠀⢀⠄⠀⠀⡀⠀⣺⣦⣄⡖⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠰⠆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠈⠋⠀⠀⠀⠳⠂⠀⠀⠀⠀⠲⠞⠁⠀⠀⢠⣶⣿⠛⣧⣹⣎⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣤⡄⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠹⣋⠠⡆⢀⡈⠀⠀⠀⠀⡸⢧⡏⣤⠀⣧⡛⠀⠀⠀⠀⠀⠀⠀⠄⢠⡄⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠳⢶⠖⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢤⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣤⣦⡦⣣⠔⣶⣄⠀⠀⠈⣷⣿⡿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠰⣇⣽⠛⢫⣻⡃⠀⠀⠀⠀⣀⠀⠀⢀⠉⢡⡟
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⠿⣿⡿⠄⢠⡾⠯⠙⠂⠀⠀⠟⠋⣤⠝⠛⠃⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠰⣿⣿⠲⢾⣟⣿⠀⠀⠀⠘⠿⠀⣄⢙⣁⠄⠡
⠀⠀⠀⠀⣓⠈⠀⠀⠀⠀⠀⠀⠀⠞⠻⠏⢻⡟⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠐⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠢⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢶⣶⣤⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠈⠋⠀⢹⠿⠃⠀⠀⠀⠀⠈⠈⣡⣴⠀⠁⠀⠀⠀⠘⠀⠀⠂⠀⠀⠀⠰⣶⡆⣶
⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠂⣥⣄⢀⡹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⢀⠀⠀⠀⠀⠀⠀⡖⠁⠈⡏⠀⢀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠀⠿⣁⠙
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢿⠟⠘⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠲⣴⣼⠬⡵⡃⠀⠀⠀⠀⠀⠀⡇⠀⡂⠈⠀⠠⠀⠀⠀⠐⠐⠗⠈⠀⠀⠀⠀⠀⠉
⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠟
⠀⠀⠘⠙⠁⢸⡿⣶⣶⡆⠀⠀⢠⢀⠐⣦⡴⡆⠀⠀⠀⣟⣿⡄⣤⣾⡿⠂⠀⠀⢀⣠⣸⣶⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⣤⠞⠚⢷⣦⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⣿⣿⠘⠃⠀⢐⣿⡿⠀⠸⢦⡟⠀⠀⠀⣼⣻⠇⣟⣿⠀⠀⠀⠀⠀⢩⠿⠛⠛⠛⠄⠀⠀⠀⠀⠀⢀⠀⠿⠛⠓⠚⠂⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣙⢿⡿⠀⠀⠀⠸⣿⠴⣿⢷⣴⡿⠀⠀⠀⠙⠁⣀⠈⠃⠀⠀⠀⠂⠀⠃⠀⣶⡆⠀⠀⠄⠀⠀⠀⠠⠆⢀⣶⢀⣀⢰⣤⢀⡄⠀⠀⠛⢿⠿⠿⡟
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠛⠒⠿⠾⠟⠁⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠘⠀⠀⠼⢄⣀⡠⠀⠀⠀⠀⠀⠓⢺⣿⣬⣋⣼⡷⠜⠁⠀⠀⠀⠘⠦⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡤⠄⠀⣀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠁⠀⠀⠐⠉⠉⠀⠀⠈⠁⠀⠀⠐⠀⠒⠒⠂⠶⡶⢄⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢀⣿⡏⠠⠂⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢀
⠀⠀⠀⠀⡀⢀⠀⠀⠀⢰⡆⠀⠀⣤⠏⡤⠀⠀⠀⠐⠂⡰⠦⠀⠀⠀⠄⠂⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⢹⣷⠈⠛⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡄⢀⣴⣏⣜⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢳⢦⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⣡⡄⠀⠀⣀⣤⣔⢄⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡆⢿⠘⢠⠁⠀⠀⠀⣿⠀⡄
⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⣼⣟⣵⠶⠓⢠⣿⣿⣧⣿⡌⠹⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⢷⣶⡀⠀⠈⠛⢾⡇⠀⡇⠀⠀⠀⢉⠀⡿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠉⣿⣿⡿⣀⠀⠀⠑⠘⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠺⠻⣟⡽⠳⠀⣸⠸⣿⠁⠀⠀⠀⠀⠀⠈⢸⠃
⠀⠀⠀⠀⠰⡟⡀⠀⠀⠀⡟⢰⣿⣿⠀⠈⠹⣿⣶⠀⠀⠀⠀⢀⣤⡄⠠⠀⡀⣀⠀⠀⠀⠣⡀⠀⢀⣤⠀⠘⡓⢿⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠈⠻⣆⠀⢀⠁⣾⠏⡿⠀⠀⣀⢹⣿⡀⠀⠀⣰⡿⣋⡀⠀⠌⠁⠈⠻⣄⠀⠀⠐⣶⣿⡏⠀⠀⣿⣿⢸⣇⠀⠀⠀⢰⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢇⡜⢴⣿⢸⡇⠀⠀⠛⡿⡭⠁⠀⢠⣿⣶⣿⣿⠁⡀⢺⣿⣷⣼⡄⠀⠀⠻⣿⠀⠀⠀⣽⣿⡘⢿⡀⠀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣼⡇⣸⠗⠋⠁⠈⠀⠃⠀⠀⠀⠑⣧⡈⢡⣼⣗⣠⠉⣻⠿⠇⠀⠀⠀⠉⠲⣀⢀⡿⣹⣇⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⢃⣿⢀⡴⣶⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⢠⠈⠻⠟⠁⠀⠀⠀⠀⠀⠀⣀⠀⢸⡇⡿⣿⠐⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣻⡯⠸⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⢄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠈⣧⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣩⣿⠚⣧⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣤⣿⣦⣡⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⡼⢏⣼⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠸⡇⢻⣿⣿⣤⣄⣀⣠⣴⡿⣿⣟⣙⣧⣀⠀⠀⠀⠀⢠⠎⠁⠔⠃⠛⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣇⣿⣿⣿⣿⠗⠒⠂⢺⣿⡋⠀⠿⣷⣶⣶⣶⡿⠐⠀⠀⠛⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡷⠞⣨⠛⠁⠀⠀⠀⠙⠋⠁⠀⠀⠸⣯⣽⣟⠓⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠹⠿⣿⡿⠿⠛⣷⡶⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠃



⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠀⠁⠈⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡺⠑⠤⢲⡞⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡖⠒⢤⣐⡊⠁⠠⠀⠀⠀⠉⢽⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⣽⠁⠞⠀⠀⠀⠀⠀⢠⢜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠁⠝⠛⠛⠛⠋⠀⠀⠀⢠⠄⠐⠂⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠸⡅⡜⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠼⢶⠤⠔⠋⠙⠁⠀⣇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢀⡘⠀⠀⠈⠙⢦⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣏⣉⠉⠒⠒⣚⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠐⠣⠋⠉⠉⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⠀⠀⠀⠘⠳⢤⡀⠀⠉⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠸⠞⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⠀⠀⣦⠀⠀⡆⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠸⡄⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⢸⠀⠀⡇⣠⠖⠚⠛⠓⠲⢄⡠⠁⠹⢄⠀⠀⠀⢳⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠙⣇⠀⢻⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢳⡀⢠⠏⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠸⡄⢸⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠜⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⡄⣀⡬⠽⢧⣸⡆⢀⡵⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢧⡰⠂⠀⠀⢀⣾⠀⢀⠀⠀⣠⣀⡀⠀⠀⢀⣀⣀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠉⠈⠙⠛⠒⠚⠁⠀⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠞⠻⣏⠛⠫⠉⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⢀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠲⠒⠚⠋⠉⠁⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠈⣇⠀⠀⢀⡴⣫⡟⠁
⢠⠤⠤⠤⠤⠴⠚⣉⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠙⣷⠦⣄⣀⣀⡿⠀⢠⠏⢠⡏
⠙⠲⠤⣄⡈⠛⠛⠋⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡏⠙⣿⠀⣿⣀⡀⠉⠀⠀⡰⠃⠀⡾
⠀⠀⠀⠀⠙⠳⣤⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣶⣦⣼⡆⢹⡅⠉⠉⠉⠛⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠶⣿⣿⡇⠀⠀⠀⠀⠀⢹⣿⣭⣽⣿⠟⠀⡇⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠛⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⢰⡇⠀⠀⠀⠀⠀⠀⢀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⠀⠀⠀⠀⢸⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢰⣶⣶⣶⣿⡆⠀⠀⠀⣰⠋⠀⠀⠸⡆⠀⠀⠀⢀⡇⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠘⢿⣿⣿⡿⠁⠀⠀⡼⠃⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠠⢤⣤⣿⣤⠴⢂⡞⠁⠀⠀⠀⠀⢀⡇⣀⠜⠉⠉⢧⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⢀⡴⠓⢦⠤⠤⠤⠲⣏⠀⠀⠀⠀⠀⠀⢸⡏⢫⠀⠀⠀⠀⠑⠲⣄⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢰⡏⠀⠀⡟⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢸⠁⢸⡆⠀⠀⠀⠀⠀⠘⢦⠀⠳⡀
⠀⠀⠀⠀⠀⠀⣤⠖⠊⠁⠀⠀⠐⠁⣀⣸⠃⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣸⢀⣸⠇⠀⠀⠀⠀⠀⠀⠈⢧⡀⠱⡄
⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠓⠶⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⣤⣴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡠⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⢶⣶⢶⢶⡶⠿⣯⣍⠻⢿⣦⠙⣿⣟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣦⡴⠾⠻⠉⠁⠠⠀⠈⡜⠉⠈⠁⠀⠠⠙⣷⣄⠻⣦⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣶⠟⠿⢻⣽⣿⠏⠀⠀⠀⠀⠀⣧⡀⠀⢠⣥⢀⣄⠀⢀⠀⠹⣿⣦⠀⢲⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡋⢸⠁⠀⠀⣾⣿⠏⠀⠀⠀⠤⢴⣾⣾⣧⠀⢠⣿⣿⡿⣧⣾⣿⣤⣤⣿⣷⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⣤⠾⠿⢿⣿⣆⢸⣿⠁⠀⠀⣿⡿⢬⠉⠻⣿⠟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢠⣿⣿⠀⠀⠐⣼⣧⡀⠀⠀⣿⣿⠈⢿⣷⣦⣾⣿⣷⢶⣼⣿⣿⡆⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣸⣿⣿⠀⠀⠈⢡⢴⣾⡓⢸⡿⠛⡆⢀⡛⢯⣼⣧⣵⠞⣼⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⠏⢸⣷⣠⣶⡞⠻⢌⡙⠷⣾⡁⠠⠐⠀⠉⠘⠙⢷⣶⣾⣿⡄⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢚⡟⠁⠀⢐⣦⣀⣀⣠⠏⠀⢰⣶⣦⠀⠀⠀⠀⠈⠉⠹⠇⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠐⠛⠿⠛⠃⠀⠀⣈⡉⠀⠐⣲⣶⣤⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣄⠀⠀⠀⠀⠀⠀⠀⠙⠁⣴⣾⣿⣿⠗⠀⠀⠀⣼⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡷⢿⣿⣶⣦⡀⠀⠀⠀⠀⠐⣼⣿⢻⠿⣖⣆⠀⠀⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⣴⣽⣿⣿⣷⡄⡀⠀⠀⢸⣵⣧⡼⠦⠀⢉⣴⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠼⢿⣿⣿⣿⣿⣿⣉⠐⠛⢀⣠⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⢈⡋⠈⣩⣾⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⣀⣉⠽⣿⣿⣿⣿⢿⡇⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⠋⠀⠘⠲⠿⠞⢻⣏⣾⣸⠃⠹⣿⢳⣿⡿⣏⠻⠿⠛⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠁⠀⡄⢀⣤⠀⠀⠀⠈⠙⠁⠀⠀⠀⠊⠋⠉⠀⠀⠀⢀⣀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠛⢿⣿⣷⣶⣖⣫⣴⣸⡀⠀⠀⠀⠀⠀⢀⣾⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢠⠄⠚⠛⠻⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠘⣿⠏⢙⡿⢿⣿⣿⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠈⢻⣿⣿⡿⠛⠿⠷⠿⠳⠖⠚⢿⡀⠛⠀⠀⠀⠀⠉⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⢰⡆⠀⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠀⠀⠆⠀⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣤⠀⠀⠰⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠃⠀⢸⠀⠁⡀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢧⡰⣿⢶⣄⣸⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣄⠀⣿⣄⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠿⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⠀⣠⡞⠉⠉⠛⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣶⣄⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠀⢰⡄⠀⠀⠈⠙⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠉⢉⠉⠛⢷⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠛⠉⠁⠀⠀⠀⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⡙⠻⣿⣆⠀⣿⣷⡄⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣰⡿⣧⡉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠹⡆⠘⣿⡀⢹⣿⣿⣄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣿⠁⠈⣿⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣸⣷⠀⣿⡇⠀⠙⣿⠿⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢸⠇⠀⠘⣿⣷⣤⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠇⢀⣿⠁⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⣿⡀⠀⠀⢿⣿⣿⡿⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣤⠾⢃⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⡾⠿⣷⣤⡀⠈⠻⣿⣤⡾⠃⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠙⢧⣴⠶⠒⠲⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⢿⣷⣤⣠⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠿⠿⢿⣷⠀⠀⠀⠀⢘⡏⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠉⠑⠛⠻⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀⠀⢀⣰⣿⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠙⢿⣿⠿⠿⠿⠟⠛⠁⠀⣠⣴⣿⠏⠀⠀⠀⠀⠠⠾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠛⠿⣶⣤⣤⣄⣠⣤⣤⣴⠾⠿⠗⠶⠾⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣾⠿⠿⠿⠿⣷⣄⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠿⢿⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣶⣶⠞
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣤⣤⣶⣿⣿⡇⠀⠀⢀⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢠⡇⣆⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠏⢸⠀⠀⠀⢸⣧⠀⠘⣿
⠀⠀⠀⠀⠈⣇⠘⢦⡀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⠀⡿⠀⠀⠀⢸⣿⠀⠀⠻⣧⣤⡀
⠀⠀⠀⠀⠀⠹⣄⠀⠙⠶⣤⣤⣿⣿⣧⠀⠀⠀⠀⠀⣸⣿⠿⠟⠛⠛⢦⡇⠀⠀⠀⠘⠿⠛⢦⡀⣄⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⣉⣉⣁⣀⢀⠀⠀⢀⣉⣄⡀⠀⣾⣇⠘⣧⡀⠀⠀⣤⠀⢰⠘⣧⣼⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⢿⣿⡿⠿⠛⠙⠛⠿⠿⠟⠻⠿⠛⠿⠿⠿⠿⠷⠟⠻⠟⠀⠈⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠶⠶⣶⣾⣶⣤⣤⣤⣤⣤⡄⣶⣠⣦⣴⡆⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⡷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾⣿⣿⣷⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢹⣿⠟⠉⠉⢩⣥⣿⣿⣿⣿⣿⡇⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣤⣄⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⢸⣿⣿⣿⣿⣿⣴⣶⣶⣶⣿⣿⣷⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠬⢸⡇⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡓⣄⣹⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣷⠚⠁⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⢄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢀⢀⡤⢄⠀⠀⠀⠀⠀⠀⠂⠸⣆⠟⠛⠉⠑⠀⠰⢶⣶⣿⣀⡀⠺⠀⠀⠄⠠⠄⠆⠀⣄⢻⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⠀⠀⡁⠀⠀⠀⠲⢤⡘⠀⠀⠄⡴⠆⠋⠀⠀⠀⠀⠀⠁⠀⠁⢀⣿⣄⣤⡈⡉⣊⢳⣗⣦⡧⠕⣨⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠁⢀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⢠⣾⣷⠐⣿⣆⠉⠉⠀⠉⣽⣿⠀⠁⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⢀⠀⠷⣦⠻⠀⠀⠀⠀⢾⠀⠀⠘⢦⣤⠒⠖⠒⠲⠤⠤⣤⠴⠞⢿⡑⢳⡜⠃⠋⠀⠀⢠⣞⠻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠐⠒⠀⠀⠀⢰⡆⠀⣀⠀⢸⣿⣆⣴⣦⣀⠀⠀⠠⣤⠀⢈⣿⡟⠀⠀⠀⠀⢄⣤⠈⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⣿⣄⠀⠀⢀⣠⣴⠀⠀⡗⠀⣿⣦⣼⡻⡟⠁⠉⠛⠿⠶⠿⢿⣤⡾⠋⠀⠀⠀⣤⠂⠄⣀⡄⡀⣱⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢻⡿⠛⠀⢸⣿⡿⢦⡌⣗⣴⣻⠛⠏⠁⠈⣤⠀⠀⠀⠀⠀⣀⡻⢧⡀⠀⠀⠐⠋⢀⠀⡟⣇⢉⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⣮⣄⣀⣈⠐⣿⣧⠈⠦⠀⡿⠉⠁⢠⡆⢠⣶⣶⡀⠀⠀⠀⠀⡠⠃⠈⠴⣜⣿⠉⢀⡝⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡏⠀⠙⠿⠀⠀⠀⠀⠠⠀⣿⡁⠙⡿⣿⣿⠀⠀⠀⠠⡗⡀⠀⢀⣿⡿⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠠⠀⢿⠇⠒⠀⠻⠿⠀⣤⣴⣿⠋⣠⣿⣿⣿⣦⣄⠀⠀⠀⣈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠟⠀⠙⢻⠷⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠘⣿⡟⠠⣿⣿⣇⠘⠻⣿⠻⢷⡈⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⣀⣉⠣⠄⠀⠀⠀⢉⡁⠴⢛⣟⠉⢲⡀⠠⠆⢸⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠰⠘⠋⠋⡀⠀⠀⠀⡗⠄⠀⠀⡄⠀⢠⡄⣻⣷⣶⣦⣿⣿⣿⣇⠀⠁⣀⠀⢠⠷⢲⣿⡿⣁⢎⡇⠀⠀⠘⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⣙⣾⠀⠀⠇⣔⣿⠄⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢱⠀⡺⢴⡺⡟⠀⠀⠀⡃⠀⠐⡄⠰⠀⠙⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠈⠁⠀⠀⠀⢸⡷⠀⢹⡀⠸⣿⣿⣿⣿⣿⡟⢡⠀⠀⠈⠀⠁⠘⢃⠀⣄⢀⡇⢠⣀⣤⠆⠀⢀⡀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡀⠂⠑⠃⠸⠟⣿⠟⠻⠃⠀⠀⠄⠄⠠⠄⠄⠾⠀⠿⠿⠧⠈⠿⠋⠐⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠋
⣿⣿⡟⠛⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠓⠀⠀⠰⣶⣆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⡀⠀⢀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⠐⠗⠀⢀⣀⠀⢹⠟⠀⠀⠀⠀⠀⢀⢸⡿⠃⠄⢀⣿⣄⠲⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠄⠿⠀⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠀⠀⠉⠀⣼⠀⠀⠀⠀⠀⣴⣿⠛⠳⣆⠀⠀⠉⠃⠀⣴⣆⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣶⣦⠉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠰⣆⠀⠀⣀⣄⡝⠀⠀⠀⠀⠀⠸⣿⢄⠣⢄⡀⠀⢶⣀⣀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢽⢥⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠀⢩⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⢻⣿⣿⣿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⢒⡤⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠲⢀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣂⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⣤⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⣴⢰⡆⠛⠀⠈⠓⣿⢺
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢀⡙⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣀⡀⣀⡰⠿⠁⠀⠀⠀⠀⠀⢻⠀⣷⣄⣀⢀⢸⣏⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡏⠐⢿⣏⢈⣿⣿⡇⠀⠀⠀⠀⠀⠐⢄⠀⠈⣿⡇⢉⣛⣛⡛⠟⠀⠀⠀⠀⠀⠀⢀⡀⢋⠀⢼⣧⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠁⠐⠛⠙⠉⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠑⠊⢛⡀⢸⠏⢹⠁⠀⠀⠀⠀⠀⠀⠀⢘⠳⣄⠲⠸⠷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠰⠄⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡼⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠂⢄⠐⡆⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡄⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡷⠀⠀⢠⣄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠶⠀⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢸⡇⠛⠀⠀⠛⢸⠁⠡⠀⠀⠀⠀⠀⠀⣠⡶⣿⣅⠈⠁⠚⠻⠀⠐⣄⠀⠀⠀⠀⠀⠀⠈⠠⡆⠀⠀⠂⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣅⠈⢻⠟⠀⣨⠷⠂⠀⠀⠀⠀⠀⠘⣿⣇⠳⠈⠂⠀⢂⡀⠀⢸⣿⠂⠀⠀⠀⠀⢠⡇⠀⢿⣄⠲⠶⡦⣭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢿⣾⣷⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠁⠈⠳⠀⠀⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠲⠺⣇⠘⡟⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣲⣥⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢄⡀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⠴⡊⠉⠓⠢⢤⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠞⠉⠀⠀⡠⠀⡩⠶⠶⠞⠁⠀⠘⠓⠒⠶⢥⡊⠈⡀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡇⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠶⠅⠤⢄⠀⠀⠀⢀⣠⠱⣄⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡴⠁⢠⣴⡆⠀⠱⡄⠀⡜⢠⠀⠈⣿⢧⡀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣇⠀⢻⣿⣷⡆⢠⡇⠀⢹⣿⣦⡆⣿⡈⠳⣄⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⣰⡿⠀⠀⣈⡦⠤⣌⣁⣤⠿⢒⠖⠚⠛⠻⡒⠃⠉⢢⡈⠳⢦⣀⣀⡷
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢀⡾⢻⡅⠀⠀⠁⢠⢖⠀⠀⠀⠀⠀⠓⠦⡤⠋⠀⢀⣄⢸⡇⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢧⣀⣤⠞⠋⠀⠀⢷⠀⠀⠀⠀⠀⠑⢦⣀⣀⣀⣀⣠⣄⣀⠴⠃⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠤⣀⣀⢀⠀⠈⠫⡉⠉⠛⣿⠟⢀⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠈⢏⠙⠳⠤⣄⣀⣈⣉⣠⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠌⠀⡙⡄
⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⡖⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢙⢧
⠀⠀⡇⣇⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⠁⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠉⢸⡆
⠀⠀⡇⠹⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⣾⠃
⠀⠀⢻⡀⠙⢦⣀⣀⡴⠶⠾⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠖⠀⣇
⠀⠀⠀⠻⣦⣀⢀⡏⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⡐⠁⠀⢸⠈⣧
⠀⠀⠀⠀⠀⠉⠹⡇⠀⠀⠀⠀⠙⡄⠀⢺⠀⠀⠀⠀⢸⠖⡟⠉⠀⠀⠀⡞⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢹⠀⡿⠀⠀⠀⠀⢸⣰⡇⠀⠀⠀⢠⠃⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠸⢤⡇⠀⣀⣀⢀⣀⣏⡇⠀⠀⠀⢸⣰⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⣆⠙⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣰⣄⣠⣦⣤⣇⡀⠀⢀⡆⠀⣠⣸⣧⣤⣀⣀⣨⣀⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⢸⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⡙⠢⣀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠽⠊⠁⠀⣸⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠁⠢⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⠏⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⠀⠀⠈⠲⡄⠈⠛⣿⣿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣟⠉⠀⡞⠀⠀⢀⡤⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡦⣀⠀⠀⢇⡴⢉⢜⡵⠚⠓⠲⣤⡴⠒⠒⠒⢤⣣⠑⢶⡇⠀⣴⠧⣺⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡞⠣⣄⡸⣱⢣⠋⠀⠀⠀⠀⡇⠈⢆⣀⣤⣄⡹⣧⣈⣧⠞⣡⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⡠⣷⡇⣾⣪⣭⣥⣻⢳⡇⠀⢸⠃⣢⡶⣶⣿⣄⣿⣋⣵⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢞⣽⢿⣿⠞⠘⢿⠟⣄⣟⣼⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠊⢙⣏⠴⡎⠉⠑⠺⡎⠻⠍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣼⡏⣠⣗⣲⣮⣵⣼⢄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⡁⢸⠿⣿⣿⠿⠻⣆⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣼⠴⣾⣷⣤⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡖⠛⠛⠲⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃⠀⠀⠀⠈⠣⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠉⢀⠴⠒⠒⠢⢄⠀⠁⠀⠺⡀⠀⠀⠀⠉⢢⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡤⠋⠀⠀⠀⠀⠀⠁⠀⣰⠶⢸⠀⠰⢶⡄⠀⠙⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠠⡦⠀⠀⡶⠰⠄⡀⠀⠀⣰⣿⣿⣟⠛⠛⠛⢿⣷
⠀⠀⢀⠀⠀⠀⢀⡔⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠐⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠀⠀⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣼⠁⡇⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠃
⠀⢀⠀⠠⡇⠀⢷⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡄
⠀⠀⣄⠀⢧⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⠇⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠓⢤⣀⠙⢦⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⠀⠀⢠⣔⡉⠉⠑⠒⠢⠤⠄⢀⣀⣀⣀⡠⠔⠂⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣲⠏⠁⠀⠀⢻⣿⣿⣿⣿⣶⣾⡿⠀⠘⢄⠀⠀⠀⠐⠺⢿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠿⠏⠓⠒⠶⠤⠤⠤⢦⠀⠀⡼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⠀⠀⠀⠄⣀⠂⠄⣸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡝⠂⠉⠀⠀⠀⠀⠈⠀⠐⠠⣄⠒⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠘⠚⢄⣀⠀⠀⠀⠀⠀⠀⠀⠢⡐⢂⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠂⠐⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢀⣤⣴⣶⣤⣄
⠀⠀⠀⠀⠀⢀⣀⣀⣼⠿⣤⣾⡿⢿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠘⣿⣿⡿⠂⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⡀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠻⢝⣲⡤⣤⣤⠼⠉⢹⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠹⡆⠀⠀⡆⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣅⣠⠀⠀⢸⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣴⣧⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣦⢻⣿⣿⣿⣿⣿⣿⣯⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢿⣟⢛⣱⠋⢈⣿⣿⣿⣿⣿⣿⣿⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⡆⣫⡁⠀⠀⢈⣧⣼⣿⣿⣿⣿⣿⣿⣿⣷⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡋⣦⣈⢿⣦⢶⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢾⣿⠻⣿⣾⡆⠀⢻⣿⣿⣿⣿⠋⡟⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⣿⣆⠘⢻⣷⡀⠀⠹⡝⢿⡇⢰⠁⠈⢿⣿⣿⣿⣿⠟⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⣿⡄⠘⢿⣷⡀⠀⠀⠈⢳⠃⠀⠀⠈⠉⠛⠻⢷⣤⠄⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣦⡀⢸⡇⠀⡀⢀⢸⠀⠀⠀⠉⠀⣴⡾⠶⠧⣤⣝⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡺⠛⣿⡇⠙⢿⠀⢡⣘⣮⡀⠀⠀⢀⡴⠁⠀⢠⣴⣶⣾⣿⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣃⠹⣷⠀⠀⡇⠠⢹⣻⡁⠈⡆⣼⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣇⣿⡄⠀⡇⠹⣼⣿⣿⣷⣼⣿⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⣿⡇⠀⢈⠘⣿⡯⠙⣿⣿⣿⣇⠀⠸⣿⣿⣿⣿⣿⡿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡛⢿⠇⠀⠘⣤⣿⣇⣄⣈⣻⣿⣿⣦⠀⠈⠻⠿⣿⡞⠁⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡐⢶⡯⢆⣤⣿⠀⠀⡾⢠⢻⣿⣿⣿⣿⣿⣿⠾⣷⣄⠀⠰⢽⣿⣶⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠿⠤⠟⠓⠁⢠⣞⡴⣡⠋⣿⠀⢰⣣⢋⡵⢞⣻⣶⣶⠾⠿⠟⠛⠛⠛⣻⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋⠀⠘⠛⠛⠷⠾⠛⠧⠀⠀⠒⠒⠒⠒⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⣁⣤⣤⣤⣤⣤⡴⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢉⣴⣟⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⣾⣿⣿⡿⣿⡿⠉
⠀⠀⠀⠀⠀⣀⠄⠒⠒⠉⢀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠈⡀⣺⡟⠁⠉⠠⠔
⠀⠀⠀⠀⠠⣅⡀⠀⠄⠰⡟⢠⣿⣿⣿⣿⣷⣄⡈⠁⠈⠉⠁⠀⠀⠀⠛⢛⣿⣶⣶⠤⠔⠋⢀⣼⣿⡿⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢠⣿⣿⣿⡿⡿⠋⢉⣀⣀⠀⠀⠀⠀⠀⢀⣻⣾⣿⠟⠁⠀⠀⠀⠀⢸⠋⠁⠀⠀⠀⣠⠃
⠀⠀⠀⠀⢀⡯⠶⠀⢀⡴⢏⠛⣿⠻⠃⠀⠀⣽⣿⣿⣿⣦⡀⠀⠀⠀⠛⠛⠁⠀⣀⣤⣤⣶⣧⣦⣀⣄⠀⠀⢀⡏
⠀⠀⠀⠀⠐⠄⠤⠖⠋⠀⠘⢦⠉⣱⣄⢀⣨⡛⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠶⢮⡻⣿⣿⡆⠀⠀⠀⠀⣿⣿⡿⣻⣭⣍⠻⢿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⠰⣾⠇⣿⣻⣿⠁⠀⠀⠀⠀⠻⢿⡟⢡⣶⠌⣷⣢⡿⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣶⣾⣿⠏⠁⠀⠀⠀⠀⠀⠀⠈⠐⠲⠥⠞⠋⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣾⣿⣿⣿⣿⣿⠋⠁⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣾⣿⣿⣿⠟⠁⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⠻⢿⣟⡀⠀⠀⢀⠀⠀⠛⣿⢿⣿⡿⠿⠋⠀⠀⠀⠀⣰⡟⠋⡀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠻⢿⢷⣌⠻⣷⠀⠄⣈⡁⣂⠹⡟⠛⠏⢒⡀⠀⠁⠀⠀⣿⣶⡿⠏⠻⠉⠀⢄
⠀⠀⠀⠀⠀⠀⢠⠖⠛⠻⣦⣀⠀⠀⠀⣿⡆⠈⠀⠒⠀⠀⠶⣂⣿⣦⣐⠒⠰⠄⠆⠀⢠⡿⠋⠀⠀⠀⠀⠀⣸⢆
⠀⠀⠀⠀⠀⠀⢻⣾⣿⡦⠈⠙⠷⣄⡀⠈⠛⠦⣀⡀⣫⣤⠾⠟⠋⠙⠟⠻⣦⣍⣈⣵⠯⠁⠀⠀⠀⣀⣤⠞⠁⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠙⣧⣤⣶⣦⠀⠀⠙⠓⠶⣤⣄⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣁⣤⣤⣶⠞⠋⠉⠉⠀⠰⢛⡿
⠀⠀⠀⠀⠀⠀⠀⢰⡄⠙⠿⣿⣇⠀⠘⢁⣤⣌⠉⠉⠛⠛⠛⠳⠶⠶⠚⠛⠛⠛⠉⠋⠀⠀⠀⠀⠀⢸⣿⣿⡶⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠉⠛⠿⣿⣿⣿⣦⠀⠲⠶⠃⣠⣶⣦⣄⠠⠒⠛⣠⣾⣷⣦⣀⣠⣤⠾⠛⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠈⠉⠛⠛⠶⠶⠿⠿⠿⠿⠿⠶⠶⠾⠿⠛⠛⠋⠉⠁⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣄⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠘⣶⡟⣛⣛⡛⣳⣤⠏⣸⣶⡾⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣉⠺⠥⠚⠛⡒⠒⠤⢭⠶⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣆⡀⢿⣿⣿⣿⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⣿⡿⣉⣿⠿⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠠⡉⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⣀⣀⠀⠀⠈⢢⢀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⣾⣿⣿⣿⣿⣶⣄⠀⠱⡀⢤⡘⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠱⡘⠿⠀⠈⠉⠉⢹⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⣸⠁⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠛⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⠀⠀⠀⡀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⢿⠀⠀⠀⠈⠳⠦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣦⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠿⠤⢤⣤⣤⣤⠽⠶⠚⠉
⠀⠀⠀⠀⠘⢦⡀⢀⠠⠐⠁⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠈⠙⢻⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⠀⢸⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⡄⠈⠙⠛⠻⠟⠛⠉⠀⠀⠀⡠⠒⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠹⠿⠛⠉⠀⠀⠀⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠐⠉⠉⠐⠠⢀⠀⠀⠀⠀⣀⠔⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡀⠀⢀⣤⣀⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠑⠒⠊⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⢀⠔⢀⡴⠋⢀⡼⠉⠛⠒⠲⠶⠶⠶⠶⠖⢺⡇⠀⠀⠀⡴⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠂⠁⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠙⢦⣀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠳⣝⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠐⠀⠰⠀⠀⢠⣄⣀⠀⠀⠠⠴⠠⠀⠴⠀⠀⠀⠀⠀⠐⠀⠤⠀⠀⠌⠀⠘⠐⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠀⠀⠐⡀⠀⠻⠟⠋⠀⠀⠀⣈⣤⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠘⠟⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠰⠂⠰⡆⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠰⠮⠖⠁⠐⡄⠀⣿⠒⠧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠛⠃⠀⠀⠈⠉⠀⠐⠊⠰⠃⠑⠂⠠⢠⡀⠀⠀⠀⠀⠀⢠⠠⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⡀⠀⠈⠀⠁⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⡷⣦⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠛⠙⠿⠀⠄⠀⠀⠁⠀⠁⡀⠀⠁⠀⠀⠀⡀⠉⡀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⠰⠦⠈⠓⠒⠀⢈⢉⢉⠻⠀⢈⡄⠀⢤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣣⡔⠢⠤⢤⠀⠀⠀⣠⠠⠀⡄⠀⠀⠀⠀⠈⠛⠛⠗⠠⠀⠀⠀⣠⠄⣈⣀⣀⠀⠀⠀⠀⢀⢃⠰⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⢀⣀⡀⡀⠀⠀⠀⡀⣠⣤⣤⣤⣄⠁⡀⠀⠁⠀⠀⠀⠀⢆⠀⠀⠈⠁⠘⠷⠲⠖⠒⠐⠏⠃⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠈⠁⠀⠀⠚⠇⡙⠛⠛⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠢⠦⠀⠀⠀⠀⠈⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣹⣷⠄⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠐⠀⠀⠉⠏⠀⠀⠘⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠦⠄⠀⢐⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠂⠀⠀⠀⠀⠀⠀⢀⣤⡀⠒⠒⠂⠀⠂⠤⠄⠀⠴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠒⢦⡀⠀⠀⠀⠀⠀⠀⢘⣿⣧⠀⠀⢄⠀⠀⢀⠀⠀⢀⠒⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⡿⢿⣀⣀⠐⠂⠀⠀⠀⠄⡀⠀⠰⠀⠀⠘⣿⣿⣷⣶⠄⠈⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠠⠀⠀⠀⠐⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⡀⠀⡟⡏⠀⠀⠛⠀⣀⠀⠈⠀⠀⠃⠀⡀⠀⠀⠀⠐⠉⠀⠀⠀⢰⡾⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⡆⡄⠈⠁⠈⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⠀⡆⠀⠀⠀⠐⠀⠀⠀⢈⠁⠁⠀⠀⢠⠙⠁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢴⣷⠄⠸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⠶⠤⠤⢤⣤⣤⣤⠤⠤⢶⠶⠋⠁⠀⠺⠀⠀⠀⢀⣰⠛⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠁⠀⠀⠀⠀⡴⠖⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠠⢤⣀⣀⣀⣠⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⣄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠿⠷⠶⠄⠀⢀⣠⢦⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⡞⡼⠃
⠀⠀⠀⠀⠀⠘⠛⠋⠁⠀⡿⠀⠀⠀⠀⠀⠀⠀⣠⡿⠚⠻⠁⢠⡄⠀⠀⣤⣀⠀⠀⢀⡀⠀⣼⠇⠀⠀⠀⠀⢠⠎⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⢀⣠⡴⠾⣟⠀⠀⠀⢠⡟⠁⠀⠀⠈⠉⠉⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⣠⡶⠋⠀⠀⠰⠻⣦⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⡇
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⣷⠈⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣈⢙⡆⠀⠀⠀⠀⠀⠀⠘⠇⣦⠀⠀⠀⠹⣄⣀⣰⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠈⢓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢈⡙⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠏⠀⡀⠀⠀⠀⠀⢱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠮⠁⠶⣿⠆⢘⢋⡀⠒⠦⠀⠬⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣆⡈⢥⡤⣯⠍⠁⣤⠐⢠⠐⢨⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣯⡿⢿⠷⡒⠗⠀⣤⣴⣷⠶⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣯⣿⡷⣞⣼⡏⠀⣆⠀⠉⠁⠀⠀⠀⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⢾⣿⣿⣿⣶⡜⣆⠀⠀⠀⠀⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⢼⣄⠂⠀⠀⠠⠸⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣍⠘⡟⠓⢻⣿⡿⢿⣓⣻⣏⢸⠛⢛⡱⠞⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢡⠀⢁⠈⡷⠄⠀⠀⠉⠻⢿⠉⠁⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠄⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⠾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣦⠀⠛⠻⣿⣤⡀⠈⣁⣄⠀⠀⠀⠀⢀⠦⢤⣴⡟⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⡀⠂⠐⠄⠹⣝⣳⣮⠵⠀⠁⠀⠰⠋⠀⠈⢻⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠁⠆⠀⠀⠁⢻⣿⡆⢐⠀⠀⠀⠗⠀⠀⠀⠀⠓⠤⠤⢀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⣀⠄⠀⠀⠰⣿⢿⣤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢶⡌⠀⠀⠈⠉⠓⢮⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⠀⡘⣀⠂⡽⠤⠴⠬⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣿⣟⣛⣻⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠒⠚⠛⠛⠛⠛⠋⠉⠉⠙⠛⠛⠛⠛⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣮⠙⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣵⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠈⠋⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠸⣿⣿⡄⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡿⠁⢸⣿⣿⣿⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⢀⣾⠋⠀⠀⣿⣿⣿⣿⠋⠀⣀⣤⣤⣤⡀⠀⠀⢠⡆⠀⠀⠀⠀⠀⣿⣆⠀⣀⣠⣾⠿⣿⣿⣿⣦⣀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀
⠀⠀⠀⣴⡿⠁⠀⠀⠀⢹⣿⣿⣿⢀⣾⣿⣿⡿⢿⣷⣤⣴⡟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣽⣝⣛⣴⡾⠋⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆
⠀⠀⣼⡟⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣷⣜⣛⣽⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠁⠀⠉⠁⢀⣠⠎⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⣿
⠀⢰⣿⣿⠁⠀⠀⠀⠀⠘⣿⣿⣿⠻⣆⠈⠉⠉⠉⠈⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠸⣿⡟⠁⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿
⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠙⢶⣷⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠹⠃⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿
⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⢀⠀⠀⠀⡄⠀⠀⣴⣿⣿⣉⣀⣀⣿⣿⣿⣷⠀⠀⠀⢦⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿
⣿⣿⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⢸⠇⠀⠘⣿⣿⣿⣿⣿⢿⣿⣿⢿⡿⠁⠀⠀⠘⡆⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿
⢹⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠉⢿⣯⣿⣿⡟⣿⣷⡿⠃⠀⠀⠀⠀⡇⠀⡀⢰⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠈⣿⣇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⡀⢰⡄⠀⠀⠀⠈⠙⠻⢿⣧⡟⠁⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⠟⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣿⡘⡇⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⠀⠀⠀⠀⠀⠀⢀⡿⢣⠟⠁⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠙⣿⡀⠀⠀⢀⣴⣾⠟⠛⡿⠋⠻⡷⠲⣤⣄⣤⡿⣱⠋⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈⠻⣶⣶⡏⠉⠛⠀⠀⠁⠀⠀⠀⠀⣿⡟⣉⡼⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⣀⣀⣠⣴⣿⠟
⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠛⠁
⠀⠀⠀⠘⢿⣧⣄⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⣄⣀⣀⣀⣠⣤⠶⢛⣵⠟
⠀⠀⠀⠀⠀⠙⠛⠿⢿⣶⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠿⠿⠿⠽⠶⠾⠋⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣆⢀⣀⣀⡞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡏⠉⣿⣿⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢃⡘⢿⣿⣷⢶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣬⣧⣼⠟⠁⠀⢻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⡀⠀⠀⣰⣿⢿⣿⣿⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣿⣿⣦⠙⣿⣤⣟⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⠀⡘⣠⢃⣿⠇⠀⠀⢧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠁⠒⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡚⠲⡄
⢠⠐⠒⠀⠉⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠠⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠇⠈⠁
⡇⠀⠀⠀⢀⡀⠀⠈⠁⢀⡈⠀⠠⠀⠿⠀⠱⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠀⠀⠀⢦⠈⢆
⢱⡀⠀⠀⠁⠀⠀⠀⠎⢉⣿⣿⣦⠀⠀⠀⡀⠀⠀⠀⠈⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⢀⣀⡀⠀⡼
⠀⢱⡀⠀⠀⠀⠀⠀⠁⢈⣻⡿⠟⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢹⠀⠀⢰⠀⠈⠀⠀⠊⠀⡀⠠⣿⠏
⠀⢀⠃⠀⠀⠀⠠⣀⡠⠴⠢⡀⠀⢀⠀⠀⣸⠇⠀⠀⣀⡤⠖⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢋⠉⠘⠁
⠀⠸⡀⡄⠀⠀⠀⡀⠀⠀⠀⠈⠉⠁⠀⠀⢱⠁⢀⠎⠁⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠢
⠀⠀⠈⠀⣸⠀⠀⠇⠀⠀⠀⣰⠀⠀⠀⠀⢏
⠀⠀⠀⢠⠇⠀⠀⠘⠦⣤⠴⠃⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⠀⠀⢀⠄
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠂⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠠⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⣶⡈⢦⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⣀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⣀⠄⠈⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢣⠀⠀⠑⢄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠠⠴⠶⣤⡀⢘⢀⠀⠀⠑⠄⠀⠀⠳⣄
⠀⠀⠀⠀⢠⠔⠐⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⣶⣾⣻⡇⠀⠲⡄⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠁⢠⡀⠀⠀⠀⠛⡟⠋⠀⠀⡠⠓⠀⠀⠤⠤⠤⠶⠶⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⢀⡈⠆⠐⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⢀⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠑⡆⠁⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡠⠔⠁⡐⠁⠀⠀⠀⠀⢀⠀⢀⠀⠀⠘⡒⡀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⣠⢎⡀⠀⠀⠀⢀⠔⠁⠀⠀⠑⡄⠀⠀⠰⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢱⣿⣟⡀⠃⢀⠊⠀⣠⣄⢤⡀⠐⠀⠀⠀⠡⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠛⠻⠃⠀⠀⠀⢸⣿⣯⡄⡏⠀⡇⠀⠀⠀⠀⠑⠠⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢾⣍⣉⠉⠙⣦⠀⠉⠛⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠻⣿⡿⠿⠛⠀⠤⠀⠤⠔⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⡀⠔⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡶⠀⠂⠒⠂⠀⡈⠅⠂⡩⠂⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡔⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢛⡖⠂⠀⠀⢁⠠⠐⠁⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠁⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠻⢶⡒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢰⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⡇⠀⠀⠠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡴⢇⠀⠀⠀⢣⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⠀⠀⠀⢸⡄⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠸⠀⠀⠀⠘⠃⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄⠀⠀⢀⠔⠁⠀⠀⠀⣘⠤⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠣⠰⣥⠂⡄⠀⢀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠂⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


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