Squirrel Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠉⠁⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠀⢀⡀⢀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⠟⣷⡐⣴⠀⢰⣄⣼⡿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣾⠏⢠⣿⣧⠏⠀⣿⠿⠋⠀⢀⠀⠀⣀⣴⣆⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣍⠉⢀⣞⡅⠀⠀⠀⠀⠉⠉⠉⢿⠟⠁⢰⣧⣦⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⠙⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣤⣄⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣵⠀⣿⠀⠀⠀⠀⢠⣶⡶⣶⣤⡀⠀⠚⠿⠯⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣦⣿⠀⠀⠀⠈⠐⠫⡻⣝⣿⣿⣿⠷⠖⠊⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣹⠏⠀⠀⠀⠀⠀⡇⠈⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⠀⠀⠀⠀⠀⣸⣣⡄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠿⠦⠌⠿⠿⣷⠿⠄⠴⠆





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

⠀⣀⠠⠤⠀⠒⠒⠒⠒⠒⠀⠿⠅⠐⠒⠀⠤⢀
⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡀
⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⠲⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠢⡀⠀⠀⠀⠀⠀⠠⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠰⠀⠀⠀⠀⠠⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⡓⠀⠀⠐⠓⠠⢀⣀⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡄⠀⣄⠇⠀⠠⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⢠⠁⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⠔⠋⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠲⠄⠀⠀⠀⠀⢸
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠚⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃⣠⣿⣾⠀⠀⠀⠀⠀⡄
⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠦⠽⠿⠋⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠙⠄
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠢⡀⠘⣄⠀⠀⠀⠘⡤⠔⠊
⡗⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠲⠀⢣⠀⠭⠱⠶⠒⡪⡄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠃⠀⠀⠁⠀⡹⠖⢶⡚⠁⠐⠂⠄
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⣤⠀⠀⡀⣠⠊⠀⠀⠉⠁⠀⠀⣀⢺⢦
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠘⡯⠄⠰⣄⠠⠠⠀⠒⠈⠀⠀⣿
⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠂⠀⢀⣉⡉⠹⡀⠀⠀⠀⠇
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⣀⡀⢠⡤⠤⢘⣧⠀⣀⣀⣀⣐⠎⠀⠀⢀⠌
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⠘⠃⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠉⠒⠀⠐⠂⠁
⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢾⠃
⠀⠀⠀⠀⠰⡛⠂⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⡠⢊⠌
⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⣤⡠⠖⢁⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡠⠔⠁⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠁⠀⠀⠀⠀⠰⠥⠤⠤⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠠⣤⣤⣤⣀⡀⠈⠉⠉⠂⠍⠙⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⢶⠐⠂⠒⠂⠐⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡄⠀⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠹⡇⢠⠟⣭⣿⠀⠀⠀⢀⡄⣠⣠⢄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠿⢳⠋⢸⣤⣿⠀⠀⣠⡞⠗⠹⠋⠉⠳⡰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⣀⠀⠰⢋⠃⠀⣀⠟⠃⠀⠀⠀⠀⠀⢸⣾⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠾⠿⠀⠀⠈⡄⠀⢿⠀⠀⠀⠀⠀⠀⠀⠘⠋⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠷⠔⠀⠐⠀⠀⠀⢀⠀⠀⠘⣦⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⣦⠤⠶⠚⠃⠀⠀⠀⠈⠙⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠈⣆⡠⠊⠀⠀⠀⢀⡔⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣰⠏⠁⣀⡠⠤⢤⠴⠟⠒⠒⠒⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢠⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠉⠑⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⢦⣀⡀⢧⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣠⣴⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣭⠭⢬⣽⣻⡧⠄⠀⢀⣀⢀⣠⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⠭⠥⠒⠒⠒⠉⠈⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣴⢶⡶⠆⠈⠒⠶⠰⣤⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠐⠂⢠⡏⠛⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⡱⠂⠀⠀⠀⢢⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣦⠀⠀⠐⠋⠀⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣰⡄⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡦⠠⠀⠀⢹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣆⠁⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣇⡐⠀⠀⠈⠈⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠻⢾⡏⣿⣿⣶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡈⢉⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡆⠠⠄⡸⢿⣿⣬⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⡷⣄⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⣖⠀⢀⢿⣿⣮⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⣏⠀⠀⠀⠀⠃⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣄⠀⠀⢍⣛⢻⠟⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠷⣿⠄⡀⠀⢀⡀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⠟⣻⣿⣷⣦⣬⣯⣵⣧⡟⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣯⠐⠇⠀⠀⡁⣤⣴⣿⣿⣿⡿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡀⠀⠀⣻⡿⠟⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠄⠀⢸⡄⣹⣾⣿⣿⣿⣿⠧⡾⠛⣅⠸⢿⣿⣿⣿⣿⣯⣿⠻⢻⢿⠁⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡁⠀⠀⢸⢹⣿⣿⣿⡿⣿⠛⣶⠁⢰⢶⠀⠈⢀⢻⣿⣿⣿⣷⡟⠫⠜⠆⠀⡼⣃⠀⣠⣴⣾⣷⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣖⣀⠀⠀⢀⣿⣿⣗⡽⢂⠳⠄⠉⠈⠀⡀⠀⠀⢀⠈⣿⣿⣿⣿⡦⠐⠀⠂⠐⠢⢞⣽⣻⣿⢕⢌⣻⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡟⡄⠐⠀⢼⣿⣿⣿⣡⡜⠁⠀⠀⠀⠀⢠⠀⠀⠈⡙⣹⣿⣿⣿⣿⣿⣶⣶⣤⣶⣿⣿⣿⣿⡲⠄⣿⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠁⠀⠰⣼⣿⣿⡿⡀⠄⣠⣤⣶⣶⣶⣦⡀⠂⠀⠰⢾⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧⠀⠀⣰⣿⣿⠿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⢟⠀⣟⡯⠂⣰⣿⢋⠃⢀⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⢨⣿⣿⣿⣿⣿⣿⣿⡟⠉⠈⡰⣿⡇⢠⣿⣿⡏⠘⣀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⣿⣆⣸⣿⣿⣿⣿⣿⣿⡏⠀⠀⢠⣷⡏⡎⢻⣧⣙⠷⢦⣸⣿⠇⠀⠄⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢹⣿⣿⣿⣿⣿⣧⡔⠂⣡⣾⡿⠁⢿⣾⣿⣧⣾⣽⣿⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢤⣄⣀⣀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⢉⣦⣜⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠈⠉⣩⠛⠛⠻⣿⣿⣿⣿⡷⠿⠿⢷⣿⣥⣯⣵⣿⣽⣿⣉⡛⡿⠦⠶⠶⠶⢤⡶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡈⠂⢃
⠀⠀⠀⠀⠀⠈⠉⢉⣷⠂⠀⣀⣽⣷⣦⣤⣄⠀⠈⠋⠄⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠂⠛⠒⠒⠓⢸⢁⡼⠏⠐⢦⣤⡈⠀⠀⢀⣿⣷⠊
⠀⠀⠀⠀⢠⠔⠚⠋⠀⠀⠀⠈⠈⠉⠙⠻⡏⢿⠷⣄⠂⡧⢠⢀⣤⣤⣨⡤⠀⢀⣤⣤⣀⣀⣀⠀⠀⠀⠀⢘⠀⡁⣀⠀⠀⠘⢻⡦⣀⠼⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠓⠈⠙⠉⠛⠛⠉⠺⠀⠁⠘⠁⢾⣿⠾⠦⣄⠚⢿⣿⠟⠛⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠦⠤⠀⠀⠀⠀⢀⠀⢀⡀⣧⡀⡀⠀⠀⠀⠀⠀⠁⠀⢤⣴⠶⢯⣵⣤⠀⠀⠀⠀⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⠀⠀⣯⣈⠀⠈⠰⡄⠀⠀⠀⠀⣴⠛⠛⠓⠀⡹⢿⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠤⢌⡀⢸⣄⣰⡝⠨⠁⢀⣲⣿⣷⣧⣶⡿⠦⡤⣤⣀⢪⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣻⣤⣶⣏⣽⣿⠅⠀⠀⠀⠀⣀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⠛⢩⠃⢿⣿⡿⢤⣀⠀⠀⠀⣋⢹⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⣁⠂⠘⠋⡉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢟⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣱⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⡀⢀⣤⠀⠀⠀⠀⠀⠀⣼⠃⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡀⠱⠡⠃⠀⢸⠀⠀⠀⠀⡏⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⢀⠞⠀⠠⣀⠀⠇⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⡶⠛⠓⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣿⣿⣿⣿⡇⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⢸⣇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⢢⠞⠉⣉⠉⠁⢠⠀⠀⠀⠀⣠⠀⠀⠀⠘⣿⣷⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠏⠀⣠⢿⡀⢀⡞⠀⠀⠀⣰⠏⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢠⣾⠟⠛⠛⠺⢧⣼⠃⠀⢀⣼⣋⠠⠄⠀⠀⠀⠀⠘⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣙⣄⣰⣿⠇⠀⠀⠀⢀⡼⠁⣀⡴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⡟
⠀⠀⠀⠀⠔⠚⠉⠉⠉⢹⣿⡄⢙⣻⣶⣷⠖⢛⡁⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣐⣋⣁⣤⡾⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡻⠟⠃⠀⢳⣤⣈⠻⣷⣤⣀⣀⣀⠀⠀⠀⢰⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⡠⠶⢻⠿⣛⢛⡋⠉⠉⠉⠉⢁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠸⠥⣏⡠⠴⠖⠚⠛⠉

⠀⠀⠀⠀⠀⢠⡴⠒⠦⠀⣠⠖⢦⡀⢠⡆⠀⢠⡆⢰⡆⢰⡶⠲⢦⠀⠠⣶⠒⢶⡄⠀⣴⠶⠶⠒⠀⡶
⠀⠀⠀⠀⠀⠈⠓⢶⡄⣼⠁⣀⢀⡗⢸⡇⠀⣸⠇⣾⠀⢸⡧⢶⣏⠀⠀⡿⠶⣞⠁⠀⡿⠓⠛⠀⢰⡇
⠀⠀⠀⠀⠀⠐⠒⠛⠁⠈⠛⠛⢿⠀⠀⠙⠛⠉⠀⠙⠀⠘⠃⠀⠉⠓⠀⠃⠀⠈⠛⠊⠛⠋⠉⠁⠘⠓⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠐⢀⠀⠐⠀⠊⠠⠴⢀⡀⠀⠀⠀⠀⠀⡉⠀⠈⠁⠘⠁⡀⠀⠈⠬⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⠶⠶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⡟⠉⠉⢿⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⠁⠀⠀⣼⣿⣿⡿⠋
⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠰⣿⣿⣿⣿⣿⡟⡀⠀⡴⠿⠛⠁
⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣀⣿⣿⣿⡄⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⡀
⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣶⣄⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⣧
⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡀
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢃⣄⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⡟⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠈⢋⣴⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⡇
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⡇
⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡼⠟⠿⡿⢿⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣽⣿⣿⣿⣿⣿⡿⠃⢀⣿⣿⣿⡇
⠘⣿⣿⣿⣷⠀⠀⠀⠀⣰⢿⣤⣤⣶⣿⣸⣿⣵⣿⣿⣿⣿⣿⣿⣿⢟⡽⠛⠉⣹⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⠟⠁⠀⣼⣿⣿⣿
⠀⠹⣿⣿⣿⣧⠀⠀⠀⠸⠮⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡿⣱⠏⠀⢀⣼⣿⣿⣿⣿⣿⠏⠾⠿⠿⠟⠋⠀⠀⠀⣰⣿⣿⣿⠇
⠀⠀⢻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⢿⣿⣿⡇⠈⠛⠓⠶⣾⣿⣿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡏
⠀⠀⠀⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⠗⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣄⠀⠀⠀⣴⣶⣶⣶⣿⠿⠛⠉⠀⠀⠀⢴⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣤⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣾⠏⠀⠀⢀⣄⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠐⠃⠀⠀⢖⡠⣤
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⢸⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢃⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣀⣾⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣤⣖⣯⣱⡾⣛⡉⣿⣌⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡈⠁
⠀⠀⠀⣴⣿⣿⣿⣿⠟⣉⣙⣿⡏⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠈
⠀⠀⣼⣿⣿⣿⣿⣏⣴⣿⣿⢻⣧⡘⢿⣿⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⢡⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⣠⣦⣾⣿⣆⡀⢀⡆⣀⢀⠐
⠀⠀⠉⡛⢻⣟⠙⠿⣷⣤⣴⣾⠁⡇⠀⢡⠕⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣾⣛⠀⢠⠠⠀⠐⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣦⡑⠎⠀⠄
⠀⠠⣤⣾⠀⠻⠇⠀⣻⣿⣿⣿⣾⢆⡁⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣆⣴⡖⣀⢶⣾⣿⣷⣿⣿⣿⣿⠋⠀⠙⠙⠂
⠀⠀⠀⠓⢤⡦⠦⠘⠛⠛⠛⠛⠛⣋⣴⡿⣛⣃⣀⠀⠀⠀⠀⠉⠉⠿⡟⡲⠶⣤⣬⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠑⠲⠖⠶⠚⠛⠋⠙⠁⣻⣿⣿⡿⡙⢃⠀⠐⣤⡄⠈⠋⠀⠋⠐⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠷⣨⡈⢿⣿⣾⣏⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢷⡄⢿⣿⣿⡿⠀⠀⡀⠀⠀⠀⠰⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣵⣷⡝⣿⣿⣿⣷⣐⣁⣡⣤⣤⣄⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⢁⣜⠃⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣣⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣨⠿⠟⠿⣟⣿⣿⣿⡿⠁⠀⣠⣴⣾⠺⠉⠨⠀⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡶⠁⡀⠁⠀⣠⣶⣿⣿⡿⡋⠐⠠⣴⠋⠛⠁⠀⠀⠀⠂⢹⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢏⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⣤⣾⡿⠿⠟⣋⣵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣿⣿⣿⣿⣿⣿⣿⡟⣴⣷⣿⡷⣿⡷⣿⣟⡁
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡎⣠⣖⣃⠜⠉⠁⠀⠀⠈⠉⠀⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣾⣿⢙⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠟⠏⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠘⠏⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣼⣾⣇⢴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣀⠀⢠⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⣤⣤⣤⣤⣤⣤⡶⠾⠿⠿⢿⣿⠆⣌⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣾⣷⣿⣿⣭⣤⣔⡴⢒⣋⣁⣀⣀⣈⣩⣿⣿⣿⣿⣿⣿⡿⣿⡿⢿⣿⣿⣿⣿⡟⡛⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠋⠛⠛⣿⣾⣿⣶⣿⠿⠿⠿⠛⠛⠛⠻⠿⠛⠛⠛⠛⠙⠃⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢈⣁⣀⠀⠀⢀
⣿⣿⠿⠻⡿⠛⠿⢿⠿⢻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⠀⠀⠀⠤⣠⡆
⠀⠀⢰⠓⢤⠀⠀⠀⡇⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠋⠉⠉⠉⠉⠙⠒⠶⢤⣀
⠀⠀⠸⡀⠀⢳⠀⢠⡇⠠⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⢇⢀⡴⠋⠙⡇⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦
⠀⠀⠀⡊⢏⢀⠤⠹⡌⠀⠃⠋⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠤⣄⣀⠈⠳⡀
⠀⠀⢸⢠⣶⣿⢠⣲⣾⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢷⢦⣳
⠀⢀⠊⠙⠋⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⡀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠙
⠀⡮⠠⡀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⡀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⡜⠀⠀⠈⠢⠀⠀⣰⢁⠇⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢷
⢣⣀⠀⡀⢀⣧⠔⢿⣫⠞⠙⡇⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠉⠉⠉⠋⠀⣆⠬⠆⠀⠀⣷⡎⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠈
⠀⢀⣀⣀⡈⠉⡡⠤⠐⠒⠒⠋⠀⢰⢃⣠⣤⠤⠴⠶⠶⠶⠦⠤⠤⣀⠀⠀⠀⠀⢹⡄⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⡔⠁⠀⡅⢺⡥⠀⠀⣐⢒⣒⢶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇
⢷⡤⠞⠀⠀⠑⠶⠴⡋⠉⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⠏⡇⠀⠀⠀⠀⠀⠀⢠⡇⣸⠁
⠀⠑⠤⣀⣀⣀⣠⠾⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣀⡴⠋⢀⠃⠀⠀⠀⠀⠀⠀⢸⣣⠇
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋
⠀⠀⠀⠀⠀⠀⡔⠂⠉⠐⠒⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠑⠚⠉⠉⠉⠓⠚⠿⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠛⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⠀⠀⠀⠀⠹⣌⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠣⣴⠀⢀⡖⠒⠒⠚⠛⠛⠓⠒⠒⠒⠶⠦⠤⣤⣄⣠⡼⠀⠀⠀⠉⠓⠶⠶⠤⠶⠶⠚⠉
⣶⣶⡶⣶⡶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠙⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠉⢀⣀⣀⣐⣿⣆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠼⡟⠇⠀⠀⠺⣿⣷⣿⣿⣟⣷⡆⢾⣇⠀⢢
⠀⠀⠀⠀⠀⠀⠀⣐⠃⠀⠀⣶⣶⣾⣿⣶⣿⣿⣿⣷⣼⡿⢀⠰⠁⠤⣄⣤
⠀⠀⠀⠀⠀⠀⣿⠟⡃⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠘⠓⠈⠁⣸
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⡀⠀⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠘⠹⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢓⣿⣧⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⢼⣿⣿⣿⣿⣾⣿⣿⣿⣗⡀⣀⣉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣧⣤⣀⡿⢿⡿⠛⠽⢿⣿⣿⡿⢋⣅⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢹⣿⣿⣿⠀⠀⠀⠀⠈⠙⠏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠁⣿⣿⣿⡟⢠⡆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⣼⣿⣿⣧⠀⣰⣆⡀⣠⣡⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⠽⠿⠜⣧⣥⡿⠿⠿⠿⠛⠚⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⢠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣄⠀⠹⣌⣧⡣⠀⠀⠐⠂⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⠀⣿⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣄⣀⡈⢝⣦⢻⣿⣧⡅⠀⢸⣧⠀⠘⠀⠀⣞⢻⣿⠀⠀⠀⠀⠀⠀⣿⡿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⢤⣀⠉⠙⢦⠁⠛⢿⣿⣷⣸⢸⣟⡄⠀⠀⢸⡟⠀⢿⡆⠀⠀⠀⠀⠈⣿⣇⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⡿⠿⠿⠁⠀⠈⠂⠀⠁⠀⠀⠉⢿⢹⣼⣿⣧⡄⢀⣿⣇⠀⣻⠷⠶⢤⣤⢤⣴⣿⢿⣧⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠭⠶⢒⡀⢤⠤⠤⢀⡀⠐⠀⠀⠀⠀⠀⠘⢘⢻⣿⡿⡖⢸⢹⣧⡴⠃⢀⠀⠀⠀⠀⠛⠛⠛⢬⡆
⠀⠀⠀⠀⠀⠀⣀⣠⠤⢶⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⢠⡇⢸⠘⠏⢀⣈⠛⠆⠀⠀⠀⠀⠀⠀⠘⢹⣄
⠀⠀⠀⠀⠀⠍⣀⠴⠒⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢸⢯⣦⡟⣀⡧⠰⠁⣾⣯⡆⠈⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⢒⡥⣪⡿⠁⠀⠀⠀⠀⢀⣨⠀⠀⠀⠀⠀⠀⣓⣿⣍⠿⠋⢽⠇⠀⠰⣙⡉⠁⠀⠀⠀⠀⠒⠀⡀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠐⠡⡺⠋⡀⠀⠀⠀⠀⠈⠉⣙⣁⣠⠄⠀⠬⢨⣅⠹⠂⠀⣧⡞⠀⠀⠀⠋⠀⠀⢀⡤⠀⠀⠈⠀⠁⠈⠂⠘⠀⠀⠀⢀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⡄⢔⡄⠀⠠⣾⣿⠝⠁⠀⠀⡀⠀⠸⣷⣠⡄⠀⠇⡆⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⡀⠀⠀⡀⣰⢦⣀⡔⣆⢸⡎⡟⣇
⠀⠀⠀⠀⣀⣀⣀⣀⣰⣣⣿⣿⣃⣀⣤⠏⠔⠁⡄⡀⠀⠃⠀⠀⣿⣙⣠⣦⣤⣄⣀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠘⠷⠂⣸⣿⣿⣿⣣⡿⣸⡷⣹⣿⣿⣭⠍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠯⠻⠭⠿⠿⠿⣦⣴⣼⡏⠀⠀⠀⠀⢹⠟⠛⠻⣿⣋⣉⣛⣛⣿⠿⠷⠬⣀⡀⢀⣶⣤⣼⠿⠷⠂⠉⠻⡿⠿⠿⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⢰⡄⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⢳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢋⣉⡉⠹⠝⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⣀⣤⣄⠀⠈⠁⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⡰⣽⣴⢞⡭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢰⣵⣿⣷⢏⠔⠊⠁⣀⡀⠀⠀⠀⢬⡼⠀⢸⣇
⠀⠀⠀⠀⠀⣿⣿⢻⡇⣠⣴⣿⣿⣿⣿⣦⡀⠈⡾⠍⡆⠀⣿
⠀⠀⠀⠀⢸⢿⡇⡟⢸⣿⠟⠉⠉⠺⣿⣿⣿⠀⠀⠀⠃⢀⣿⡇⠀⠀⠀⠀⠀⢀⡟⠤⣀⡾⢀⡀
⠀⠀⠀⠀⠘⣸⢰⡇⣿⠏⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⢸⡌⢳⣌⢧⠴⢿⣤⣄⣀
⠀⠀⠀⠀⠈⢟⡄⢹⡟⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠘⣷⠀⠉⠀⡀⠢⡀⢬⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠁⠈⠇⠀⠀⠀⠀⢀⡞⡟⠉⣿⣇⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⣼⠛⠀⠀⠀⣰⣷⣾⠀⠃⠘⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⢠⡉⠀⣼⡟⠀⠀⠀⠀⠀⠀⣰⠛⠀⠀⠀⡀⡙⠉⠁⠀⢀⠀⠀⠈⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡆⠀⠘⠁⣼⣿⠇⠀⠀⠀⢀⣠⠞⣅⣁⣀⠀⠂⠈⣿⣿⣿⣿⡟⠀⠀⠘⣶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢻⡾⠀⠀⠀⣼⣿⡟⠀⢀⡠⠒⢯⣭⣿⣿⣿⣟⠉⠒⠀⣛⣛⣫⣭⣴⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣿⠀⠀⣠⣿⣿⣧⠔⣫⠀⢜⣷⣿⣿⣿⣿⣿⣶⣄⠀⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⢀⢸⣿⣿⡿⠃⠀⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⢧⠘⡄⠀⠀⠀⣀⣠⠄⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣾⣿⡿⠁⠈⢀⣴⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⠀⠘⢦⡈⠲⢤⣼⡿⠁⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⡯⠀⠀⠉⣿⣿⣿⣿⣿⣷⣄⡀⠉⠓⠚⠛⠃⠀⠒⠂⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⠃⠀⠀⣴⣾⣿⣿⠋⠀⢀⡤⠞⠛⠉⠙⠛⢿⢿⣿⣿⣳⣖⣚⣤⣤⣤⣤⣷⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⠟⠃⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠟⠋⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣟⠀⠀⣸⣿⣿⣶⣶⣦⣴⣶⣟⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣖⡤⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠠⢞⣻⣿⣿⣿⣿⣿⣿⣟⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⡄⠀⠀⠱⢿⣿⣿⣿⣿⣿⣿⢟⣫⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣦⣄⠐⠛⠛⠻⢿⣛⣯⣶⣿⣃⣒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣟⣀⣛⣿⣭⣭⣍⣀⣀⣢⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣶⣶⣾⣻⣭⣵⣷⣟⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣦⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠐⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠂
⠀⠀⠀⠀⠀⣳⣿⣿⣿⣿⣿⡿⠿⠿⠟⠟⠿⠿⠻⠛⠻⠛⠟⠛⠋⠁
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⣠⣤⣴⣶⣶⣶⣤⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣥
⠀⠀⠀⠀⣿⣿⡟⣡⣴⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣦⡀⣀⣼⣶⣦⣄⡀
⠀⠀⠀⠀⠙⣋⣼⣿⣿⣿⣥⠀⠀⠈⠟⠿⣿⣿⣿⣿⡿⢿⡿⠿⠛⠿⠏⠀⣟⢻⣷⣦⡉⢛⣶⣄
⠀⠀⠀⠀⠀⣫⣿⣿⣿⣿⣿⡏⠀⠀⠀⠠⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠐⠀⠈⠳⠍⠭⡆⠀⠈⠀⡱⠀⠀⠀⢀⣄⢠⣶⣤⣀⣀⠀⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠠⣿⠏⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⠀⠀⠀⠀⠳⠄⠠⠂⠀⠀⠀⣶⡾⠛⣉⣍⣑⠊⠉⠁
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣫⠄⠀⠀⡰⠏⠀⢀⣀⣀⣠⣤⡴⠖⠤⣠⣄⣀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⡿⠤⠑⣆
⠀⠀⠀⠀⠀⠈⢿⣿⠻⠛⠛⠁⠀⣀⣾⣧⢀⣀⣦⣛⣿⣿⣿⣵⡾⣦⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⠾⣯⣭⣶⣶⣿⣿⣿⣿⣿⣙⣿⣿⠠⠘⠛⠏⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⣠⣴⠟⠟⠈⠉⢀⣀⠀⠀⠀⠀⠉⠉⠛⠿⣷⣄⡀⢀⠀⣤⣄⣄⣀⣴⠿⠿⢷⣤⣴⠶⠆
⠀⣐⣤⣔⣶⣄⣠⣶⡶⠟⠋⠁⠀⢠⣶⣮⡙⣿⣅⣀⡀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣙⣾⣿⠾⡋⠑
⠐⠛⠛⠛⠛⠒⠛⠛⠲⣆⡃⠀⠀⠍⠠⣽⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣷⡆⠀⣂⠉⠻⠧⡙⣿⢿⣯⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠈⠛⢳⣦⣴⣶⠦⡀⠀⠀⠈⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢺⠛⠿⢶⣄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠙⣧⣄⡀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⣿⣿⣿⣿⡇⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣿⣿⣿⣟⣁⣀⣀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢟⣁⣀⣀⣀⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣵⣾⣿⣿⣿⣿⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠓⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠻⡴⠀⣠⣦⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠘⢰⣧⣤⣿⣟⣵⣋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣻⣠⢋⣿⣿⣿⡿⣞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢱⣷⣾⠟⠫⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⣿⣷⡃⠀⠀⠀⠀⠀⠀⢘⣾⠃⠘⢿⣿⡄⠀⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠙⠟⢰⣿⣿⡖⠀⠀⠀⠀⠀⠀⢨⣻⣧⠀⠘⢜⢿⡠⡈⣾
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡦⣨⡂⠙⣧⠰⣤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣿⣷⣻⡿⣌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣷⣽⠀⠀⣀
⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣧⠀⡉
⠀⠀⠀⠀⠈⠛⣁⠀⠀⠐⠀⠀⢀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⢠⢠⡀
⠀⠀⠀⠀⠀⢀⡠⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢨⡄
⠀⠀⠀⠀⠀⢺⡅⠠⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢆⢀⠕⡠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⠀⠀⢀⠤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⣿⡷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⣿⣿⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⢶⣖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣸⣿⣷⡯⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠁⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⡒⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣛⡋⠀⠀⠻⢵⣹⣬⣝⡆⠀⠀⢀⣀⡀⣀⠠⠘⠿⢿⡿⠿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠈⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡒⠀⠾⣿⡞
⠀⠀⠀⠀⠀⠀⠶⠀⠘⠛⣃⠈⠀⠉⠋⠂
⠀⠀⠀⠀⠰⢆⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠲⠶⠂⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⠀⣹⣗⣿⡷⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠈⣽⣿⣿⡿⢣⠆⠀⠀⠙⣿⣧⡀⡀⡀⣀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢠⣤⣤⣾⣿⣿⣿⠿⠔⠁⢀⡆⠈⢠⢾⣿⣷⣉⠱⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠽⠈⠉⠉⠉⠛⠉⠀⠠⠤⠒⠉⠀⠀⢺⣼⣿⣿⣏⣽⣽⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⣿⣿⣿⣿⣿⣿⣿⡻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⠀⠠⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⣞⣜⣤⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⡤⠤⠶⠒⠛⢂⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣁⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠶⢗⣶⣖⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠒⠉⠉⠁⠀⢉⡴⠟⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠀⢀⠂⡀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣿⢧⠂⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⠀⢸⣿⣿⣓⡀⠀⡠⠀⠠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢸⡇⠰⡀⠀⠀⠀⠀⢰⣧⠻⡄⠀⠀⠀⠈⢿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠀⢠⣄⠀⠋⣠⡀⠘⠢⡀⠀⠀⣾⡻⠀⠀⠀⠀⠀⠀⠀⠋⢻⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡗⠷⣣⠟⠀⠀⠈⢻⠆⠀⠘⠦⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠆⠀⠉⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠙⠶⣤⣀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠴⠶⠀⣿⠤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣉⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣄⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⣿⣿⢿⣆⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⢿⣿⣶⡀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠛⢿⣾⣦⣴⣆⣀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡘⣿⣿⡇⠀⠀⠀⠀⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡀⠀⠈⠉⠛⠿⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣿⣿⡠⠀⠀⠀⠈⣹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢦⣄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⠀⠀⠀⠀⣠⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠆⠀⠀⢛⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠅⠀⠀⠀⢉⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣤⡀⠀⢠⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⡍⠙⣧⣄⣴⣄⣸⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠬⡿⠆⠀⠀⠀⣸⣿⠟⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠚⠛⠋⠉


⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⡿⠻⡿⠛⠿⢿⠿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠑⠊⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣐⣻⡖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣟⡄⠀⣠⠴⠊⣉⣥⣤⣴⣶⣶⣦⣬⣭⣐⠢⠄⡨⠽⣯⡤⣼⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⡧⣦⠞⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠘⢿⠶⢟⣟⡡
⠀⠀⠀⠀⠀⠀⠀⣀⣹⡤⠀⣰⡯⢽⡿⢁⣼⣿⣿⣿⣿⡿⠿⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣷⡌⢦⣙⣯⡴⠂
⠀⠀⠀⠀⠀⠀⠀⢬⣼⠛⣡⣭⣯⡟⢀⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡌⢯⣹⣦⡤
⠀⠀⠀⠀⠀⠀⠢⡴⣿⣋⠵⢾⡿⠀⣾⣿⣿⠏⠀⠀⠀⠀⠀⢀⠀⢀⠎⠁⠀⠀⠀⠀⠈⣿⣿⣿⠸⣭⣧⣄⡄
⠀⠀⠀⠀⠀⠀⠐⠶⡟⠻⠒⣻⡇⢰⣿⣿⡏⠀⠀⠀⠀⠀⡠⡀⠈⢺⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⣏⢹⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣯⠙⠛⢻⠁⣸⣿⣿⡇⠀⣀⠀⠀⠀⠀⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⡼⡿⣿⡇⢸⠘⡇
⠀⠀⢀⣀⣀⣀⣠⣤⣿⠤⠤⠼⠀⣿⠛⠁⠸⡌⠷⠀⠀⠀⠀⠀⡰⠥⠤⠤⠤⣠⢠⠤⠞⠁⢀⣠⠟⠘⠓⠓⠒⠒⠒⠂
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡄⠉⠦⣄⣀⠐⠒⣚⠁⠀⠠⠀⠀⠀⠀⣐⣤⠖⠋⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠦⢬⣥⣴⣤⠤⠷⠴⠖⠚⠋⠁⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠛⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑
⠀⠀⠀⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠢⠀⠀⠸⠄⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣩⣝⣻⣫⣿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠚⠛⠛⠛⠛⠛⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⢸⠁⢀⡤⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⢾⠀⣿⠀⠠⠄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⢠⠟⠀⠈⠓⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠉⠁⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⡞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠴⠏
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⢀⣀⠀⠀⢰⣿⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣿⣿⣤⣶⡿⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣠⠤⠶⠚⠋⠁
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣤⣤⠤⠔⠋⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⣤⣤⡤⠴⠖⠛⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣴⡆
⠀⠀⠀⠀⠀⢀⢠⣼⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠈
⠀⠀⠀⠀⠀⠤⢺⣿⢿⣿⣿⡟⠀⠀⠀⢀⠀⠀⠀⠀⣠⡆⠀⠀⢴⡧⠠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠡⠀⠀⢠⡦⠀⣀⣤⣶⣿⠏⠀⢰⣿⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣇⣶⣶⣾⠷⠊⠙⠉⠀⠀⠀⠀⢸⡏⣠⠤⡄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⣿⣿⠃⠀⠀⠀⠀⢀⣄⡀⠀⠀⠛⢉⣤⣄⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢤⢿⣿⣦⡤⠶⠃⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⣦⠀⠀⣰⣀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⢠⡞⠃⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣾⡿⠀⠐⣛⣋⣉⠙⡁⠐⠂⠀⢸⣧⣀⣰⣶⠾⠿⠇⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢋⣉⡉⠹⠏⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣀⣤⡤⠀⠈⠁⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⡰⣽⣵⢟⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⢰⣵⣿⣷⢏⠔⠊⠁⣀⡀⠀⠀⠀⢼⣼⠀⢸⣇
⠀⠀⠀⠀⠀⣿⣿⢻⡇⣥⣴⣿⣿⣿⣿⣦⡀⠈⣟⠎⡄⠀⣿
⠀⠀⠀⠀⢸⣿⡇⡟⢰⣿⠟⠉⠉⠺⣿⣿⣷⠀⠀⠀⠇⢀⣿⡆⠀⠀⠀⠀⠀⢀⡟⠤⣀⡾⢂⡀
⠀⠀⠀⠀⠘⣹⢰⡇⣿⠏⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢸⡈⢳⣌⢧⠴⠿⣤⣄⣀
⠀⠀⠀⠀⠈⠿⡄⢸⡟⠀⠀⠀⠀⠀⢿⣿⣿⣷⡄⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠘⣷⠀⠉⠀⣀⠠⡀⢬⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠁⠈⠇⠀⠀⠀⠀⢀⡞⡟⠉⣿⣇⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⣼⡋⠀⠀⠀⣰⣷⣾⠀⠃⠘⠛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠇⠀⢠⡍⠀⣼⡟⠀⠀⠀⠀⠀⠀⣰⠛⠀⠀⠀⡀⡙⠉⠁⠀⢀⠀⠀⠈⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡆⠀⠘⠁⣰⣿⠇⠀⠀⠀⢀⣠⠞⣁⣁⣀⠀⠂⠈⣿⣿⣿⣿⡟⠀⠀⠘⣶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢻⡾⠀⠀⠀⣴⣿⡟⠀⢀⡠⠖⢯⣭⣿⣿⣿⣟⠉⠒⠀⣙⣛⣫⣭⣴⠤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣿⠀⠀⣠⣿⣿⣧⠔⣫⠂⢜⣷⣿⣿⣿⣿⣿⣶⣄⠀⠉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢀⢸⣿⣿⡿⠃⠐⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⢧⠘⡄⠀⠀⠀⣠⣤⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣾⣿⡿⠁⠀⢀⣴⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⠀⠘⢦⡈⠲⢤⣼⡿⠁⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⡿⠁⠀⠀⢺⣿⣿⣿⡯⠀⠀⠉⣿⣿⣿⣿⣿⣷⣦⣀⡙⠓⠾⠿⠓⠡⣶⣶⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⠃⠀⠀⣴⣾⣿⣿⡋⠀⢀⡤⠞⠛⠀⠁⠐⢮⣿⣿⣿⣒⣶⣾⣥⣤⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⠟⠃⠤⠖⠋⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠠⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣟⠀⠀⣸⣿⣿⣷⣶⣦⣴⣶⣟⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣷⣒⡤⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠠⢞⣻⣿⣿⣿⣿⣿⣿⡟⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣷⡄⠀⠀⢱⢿⣿⣿⣿⣿⣿⣿⢟⣫⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣦⣄⠀⠛⠛⠻⢿⣟⣯⣷⣿⣃⣒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣟⣀⣛⣻⣭⣭⣍⣀⣀⣢⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⠉⢉⡉⠈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⠊⢀⠔⠈⠤⢚⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠏⢺⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠈⠸⠀⠀⠀⠀⠀⢀⡀⢼⣾⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠂⠀⠀⠀⠀⠀⠠⢋⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠀⠀⡀⠀⠀⠀⠀⢠⣾⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡅⡀⡄⡇⠠⠀⠀⢀⣽⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡗⢿⠀⠇⠀⠀⢀⡾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⣤⡘⢻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠸⡇⠀⣼⠁⠉⢼⡯
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⢨⣷⣾⡟⣽⡄⢀⣀⣀⣤⠶⠟⠉⠁⠀⠩⠉⠉⣑⣦⢤⣿⣦⣰⡆⠙⠀⣀⣛⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⠙⠊⠿⣿⠉⡙⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠻⣷⣿⣻⣛⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢉⠀⠀⠀⠀⠀⠁⠀⡅⠀⢳⡆⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠐⠀⣿⣿⡿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⢀⡀⢄⠀⠀⠀⠌⠁⠀⠈⠀⠀⠷⡄⠀⣀⠀⢸⡇⠀⠀⠀⠀⠀⠠⢹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢏⠈⠀⠀⠀⣠⠀⠀⠀⡀⠀⠀⣾⣿⣿⠿⠿⢯⠀⠀⠀⠀⠀⠀⠀⣹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣶⠖⠛⠆⢀⡴⠃⢀⣶⡿⠛⣁⢠⣄⡒⣂⡀⠀⠀⠀⡀⢼⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⣥⢐⡌⣠⣾⣀⡤⣿⣭⣤⣿⣻⣇⣤⣍⣈⣽⣦⣀⣤⡥⣼⡿⡋
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠉⠁⠀⠐⠒⠉⠉⠙⠛⠛⠻⠿⠿⠛⠉⠁
⠀⠑⢄
⠀⠀⠀⠑⢀
⢀⡀⢀⣀⠀⣑⢄
⣤⣤⣤⣶⣴⣤⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣽⣽⣭⣭⣬⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣼⣿⣿⣯⣽⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣶⡄⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁
⠀⣠⣾⡇⠀⢀⡎⠀⠀⠆⠈⠉⡆⠐⣿⣿⣀⣮⡅⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⣿⣿⡄⠀⠀⠀⢽⣷⢀⠀⠀⠃⢨⣿⣿⣿⣿⣾⡿
⢸⣿⣿⣷⣠⠆⠀⠀⠀⠀⢄⠀⢤⣾⣿⣿⠉⢡⡰⡄
⢸⣿⣿⡿⣿⣶⣆⡐⠀⠀⠀⠑⠀⠉⢿⣷⣤⣸⣿⣦⢄
⢸⣿⣿⠀⢈⡛⠛⠻⠆⠈⠰⠒⠘⠈⠘⣿⣧⡙⢶⠽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⢸⣿⣿⢿⣿⣿⣿⣯⣵⣤⡤⡀⠀⠀⠀⠼⠃⠀⡂⠁⢰⣿⡖⣠⣦⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⣾
⠘⣿⣿⠹⠯⣄⠀⠉⣿⣿⣿⣧⢠⠀⠀⠀⠀⡴⠁⠀⠸⣿⣷⣟⣭⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠂⠀⠀⠒⢺⣿⡿
⢠⣿⣿⠂⠀⠀⣀⣀⡘⠛⠛⣿⣧⠸⣦⣶⣇⠀⠀⢀⣬⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡟⢴
⠈⠙⢿⣷⣼⣿⣿⣥⣶⠿⠿⠟⠋⠁⠀⠀⠈⠉⠻⠍⠁⠐⠖⠀⠔⠁⠟⢒⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⣾
⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⢤⣶⣦⠀⢀⡀⡈⠁⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⡾⡅⠀⠀⠀⠀⠀⠀⠀⠐⣶⣤⣤⣤⡤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠐⠁⠈⠀⠛⠁⠉⠑⠃⠘⠉⠀⠉⠈⠉⠙⠀⠛⠈⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠁⠐⠘⠀⠛⠀⠁⠘⠛⠋⠉⠘⠛⠃
⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣴⣶⣶⣶⣾⣿⣿⣿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢟⡭⣶⣶⢞⡩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⣩⡾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⢰⢷⡯⢾⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣶⢻⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣼⣿⣷⣿⣿⠏⠀⠀⠀⣀⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⠋⢀⣾⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠇⠀⣼⣿⡾⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣿⣿
⠀⠀⠀⠀⢀⠀⢠⣿⣿⣯⣾⣿⡏⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⠇⢸⣿⣿
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣧⣿⣿⡿⣿⢿⣿⠿⠉⣿⣿⣿⣿⣿⣿⡀⣼⣿⣿
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣷⡀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⢨⣿⣷⣄⠀⢀⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣄⢀⣠⣾⣿⣿⣿⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠟⢻⡛⣿⣷⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⣀⠀⠀⠀⠀⣠⣾⣿⣿⣧⡿⠋⣰⠾⡟⢧⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣁⣈⣤⡾⠁⢀⡜⠋⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣾⠉⢉⠹⠀⠀⠂⠀⠀⠈⣨⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣶⠄⠠⠞⠀⠀⠀⣀⠀⢈⡰⡿⢿⣦⣀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣤⠂⠀⠀⠀⠀⠠⠍⢩⣥⣈⢛⣻⠿⠟⠃⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠻⣿⣷⣙⡿⢷⡔⢃⣰⠆⣔⠀⣰⡏⣻⣿⣿⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡌⠙⠻⡧⠀⠀⠀⠻⣿⣿⡿⠿⠋⠪⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣚⠓⠂⠀⠀⡁⠀⠁⠀⠈⢛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣠⣴⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠉⠻⠟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⣦⣦⣠⣀
⠀⠀⠀⠀⠀⠀⠀⢴⣾⠿⡟⠭⠙⠻⠛⢾⡻⣶⣦⡀
⠀⠀⠀⠀⠀⠀⣲⠟⣛⠁⠀⠠⠀⠀⠀⠀⠙⠘⢟⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢄
⠀⠀⠀⠀⠀⠠⣟⣧⡤⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡙⣷⠶
⠀⠀⠀⠀⠀⠀⢿⣿⠶⢦⢄⣀⠤⠬⠂⠀⠀⠀⠀⠀⢠⣽⠀⠀⠀⠀⢀⡴⠅⠞⢻⠈⠀⠠⠠⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢶⣄⡀⠠⡄⢠⡀⠀⠀⠀⣞⢿⠂⠀⠀⢠⣾⡤⠠⠄⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢉⠳⠄⠀⠇⠀⠀⠀⠸⣿⠁⢠⡖⠋⠉⠉⠉⠂⠀⣀⣦⣀⠀⠠⢌⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢧⠐⠄⠀⠀⠀⢠⠀⢧⣿⠖⢉⠀⠀⢤⣀⣤⡀⠀⠉⠸⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⢵⠀⠀⡀⠀⠈⠀⡼⠃⠀⠀⠀⠀⠐⠛⠛⠘⠀⠀⢿⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣻⠀⠀⢹⢀⠀⣸⠃⠀⠀⠀⠐⠀⣇⠀⠀⠀⠀⣀⠘⠃⠉⠁⠰⠦⣤⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣇⠀⠀⠘⢺⣤⠏⠀⣠⠀⠆⠀⣀⠹⣏⣤⡄⣦⣄⢠⣤⡤⠶⢤⡀⡜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡹⢀⡀⣖⣾⣿⠄⠀⠘⢻⠄⠈⠋⠋⠉⠙⠛⠿⡉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡙⠓⠀⢽⣿⣿⣷⠀⠀⢶⢸⡆⠀⠘⠆⠀⠀⢰⠗⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⠠⢠⣾⣿⣍⣆⠀⡀⠀⡇⠁⠀⠀⠤⠀⣰⡿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⠿⡿⠿⢿⡛⢄⠁⠀⣄⠀⠀⠀⠀⣠⣿⡄⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠤⠤⣭⣭⡷⣶⣿⣶⣶⣤⣼⢶⣤⣴⡟⢡⣘⢷⣮⣵⣮⣶⣶⣤⣀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⣿⣐⣰⣭⡿⠿⠿⠍⠀⠀⠀⠀⠉⠛⠛⠉⠉
⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠈⠢⡀⠈⠡⡀
⠂⠁⠐⠀⠀⠌⠒
⣿⡿⡿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⠿⣿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢼⣿⣿⠙⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣿⣿⡏⢘⠿⠧⠐⠋⣹⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⣾⡿⡿⠐⠂⠀⣄⢶⣿⣧⡀⡈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣶⠟⡹⠛⠛⠿⢿⠿⣶⣶⣆⠀⠀⠀⢀⣰⡿⠋⠀⣰⠏⠀⢠⡆⣀⠀⢻⣮⣙⣫⠅⠀⢠⡾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⠋⠀⠀⢰⠁⠀⠀⠀⠀⠀⠙⠛⢻⣿⣇⣰⣾⠿⡀⠀⠀⠀⢠⣄⢸⣷⣞⣧⣤⣈⢉⣅⣀⣠⣬⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⡿⠡⠇⠆⠀⠀⠊⠀⠀⠀⠀⢀⣠⠄⠒⠚⠛⣟⣿⢁⠠⠀⢀⠀⠀⠀⣙⣦⣻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣼⣿⣿⡀⠀⠈⠀⠐⠀⠻⠦⣽⣿⣿⣿⣿⠿⠿⠛⢉⣤⠞⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⣠⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠀⠀⢀⡀⢀⠠⠌⢹⣿⣿⠊⣀⠀⠀⠀⠀⢧⠻⣿⣿⣿⣿⣧⠀⠀⢀⣯⠴⠒⠛⣧⣄⡀
⠀⠀⠀⠀⠀⠀⣰⡟⢻⡟⡀⡇⠀⠀⢀⣤⠔⠚⠋⠀⠂⠀⠉⠉⠉⠉⠉⠉⣙⣁⣼⣿⠟⡀⠀⢀⡀⠀⠈⣸⠏⣽⠿⣿⣿⣿⣴⠖⠫⠀⠈⠀⢰⣿⣿⡟
⠀⠀⠀⠀⠀⢸⡿⢳⡾⠋⠃⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⣶⣶⣿⣿⠟⠉⠀⠁⣠⠈⣁⠆⠀⠉⢾⢇⣾⠟⠡⢈⠇⣈⣼⣿⣶⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⡿⠃⢸⡇⠐⡁⠄⠀⠀⢀⠤⠀⠀⠀⠐⢒⣴⣶⣶⣶⣾⣿⣿⡿⠛⠇⠘⢄⠀⠀⠀⣿⣾⣷⠁⠀⠐⢛⡀⠀⣸⣿⣿⠟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⢀⣿⣿⠀⡇⠇⠀⡿⠀⠀⠀⠀⢀⢰⡴⣾⣿⣾⣿⣿⣿⡿⠟⠋⠋⠒⠀⠀⠠⠀⣡⢓⣽⣿⣿⣿⣿⣦⣀⣨⣿⣿⡿⠛⠁
⠀⠀⠀⣼⣿⣯⠀⣹⠈⣀⠀⠀⠀⣄⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠇⢒⠀⡄⠀⠀⠥⠘⣁⣤⣽⣿⣿⣿⣿⣿⡿⠙⠛⠋⠁
⠀⠀⠀⣼⣿⡅⠰⠉⠣⢹⣄⣤⠘⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠠⠀⠀⠀⠀⢃⡶⠛⣉⣩⣤⣤⣼⣿⣿⣿⠃
⠀⠀⠀⣿⣿⡇⠂⢳⡀⠠⣿⢾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢂⠀⠀⠐⠀⠀⠁⡴⠚⠛⠛⠋⠀⠀⠂⠉⠙⠳⣤⡀
⠀⠀⠀⣹⣿⡷⡀⠌⠟⠀⣹⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠑⣿⣷⣄
⠀⠀⠀⢸⣿⣿⣼⣦⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⠺⠀⡀⠐⠀⠀⠁⠠⡀⠠⠀⠀⣀⠤⠀⠀⢂⠐⣿⣿⣯
⠀⠀⠀⠀⢿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢐⠈⠀⢺⢆⠀⠀⠀⠀⠛⠀⠀⢸⣿⣧⠀⢠⢠⣝⣿⣿⣿⡅
⠀⠀⠀⠀⠈⣿⣿⣿⣷⣽⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠇⠠⡀⠨⠀⢀⠘⢽⣶⣿⣶⣿⣿⠟⠀⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⢶⣾⣆⠘⠀⢈⠃⠈⡀⠋⠛⠛⠋⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣆⣦⡀⣽⢆⡂⠎⠈⡼⠟⠀⠀⠀⡀⣀⢢⣿⣸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣤⣤⡎⢸⡄⠈⠄⡤⢠⠀⠀⢰⡇⣿⣌⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣧⣴⣃⣏⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⡿⣏⣷⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠛⠿⢿⣿⣿⣿⠻⡟⢯⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⣤⣤⣤⣶⣶⣶⣶⣿⠿⢿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠉⠀⠀⣠⣾⣿⣿⣿⣀⣿⣿⣿⡏⠙⠛⠷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⢠⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⡄⠀⠀⠈⠙⠛⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⡇⠀⠀⢀⠀⠀⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣧⠀⣼⣷⡀⠀⠉⠛⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢠⣄⡜⠀⠀⣠⣾⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠹⣿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⣴⡾⣿⢻⡀⡸⠉⠀⣠⣾⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⢰⣿⠀⠙⠁⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠛⠀⠀⠀⢀⣾⣥⣤⣀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⢀⣠⣾⣿⠀⠀⠀⠀⣠⡟⠁⠀⠀⠉⠻⣦⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⣷⡀⠀⠀⠈⣿⡀
⠀⠀⠀⠘⠋⢸⣿⠀⣴⠀⣴⠏⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣿⡇⠀⠀⠀⢹⡅
⠀⠀⠀⠀⠀⢠⡟⠀⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢴⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⣶⡀⠀⠸⣧
⠀⠀⠀⠀⠀⣼⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡿⣤⣄⠀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣇⠀⠀⣿
⠀⠀⠀⠀⢠⡟⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢀⡿⢫⠖⣲⣽⠟⠉⠉⠀⠀⠀⠉⠛⢷⣤⡤⢴⣿⣿⣿⣿⣿⣿⣿⢀⡀⣿⡀
⠀⠀⠀⠀⣼⠇⠀⠀⣿⣇⣀⣀⠀⠀⠀⠀⢀⣾⣫⣿⠀⠀⠀⠀⢸⣇⢸⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢡⠖⠲⡌⢿⣿⣿⣿⣿⣿⡿⠁⢸⣇⣀
⠀⠀⠀⢠⡟⠀⠀⢀⣿⠉⠉⠙⠻⢶⣄⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⢙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢟⣼⣿⣿⣿⣿⠟⠀⠀⠀⣿⡟
⠀⠀⠀⣼⡇⠀⠀⢸⡏⠀⠀⠀⠀⠀⠹⣷⠟⠁⠀⠀⠀⠀⣀⣀⣠⣾⣻⡇⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣶⠟⠙⠿⣿⣿⠏⠀⠀⠀⢀⣿⠁
⠀⠀⠀⡿⠀⠀⠀⣼⣃⡀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⠋⠉⠉⠙⠻⣷⣩⠟⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⢠⡿⠀⠀⠀⢽⡇⠀⠀⠀⠀⣼⠇
⠀⠀⢰⡇⠀⣀⣠⣿⣉⣩⣿⣿⣶⣤⣼⣷⣄⠀⠀⢀⣀⣀⣀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⣾⣇⡀⢀⣠⣼⢿⢦⣄
⠀⠀⣾⡷⠟⠛⠉⠙⠋⠉⠉⠉⠙⠻⠶⢦⣿⣿⠾⠋⠉⠉⠙⠷⣦⡀⢹⣿⣿⣿⡷⢀⡖⠀⣀⣠⣤⡶⠾⠋⠁⠀⠀⢀⣴⠟⠋⠉⠋⠁⠀⠀⠀⠸
⠀⢸⣏⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠈⠳⢶⣿⡛⠿⠒⣫⣶⣿⠛⣯⣠⠆⣠⠀⣀⣠⡶⠋⠁⠀⠀⠀⣠⡦⠀⣀⠀⢠
⠀⣠⡟⠀⠻⣦⣤⡿⠳⣄⠀⢹⡷⣦⠀⣶⣄⢠⣄⣸⣧⣤⡀⠀⣄⡀⠀⠈⠻⣷⠛⣿⠁⣿⣴⣿⣏⣴⣣⠞⠋⠁⡀⠀⢠⠞⠳⠚⠉⠐⠛⠉⠛⢻
⠀⣿⣥⣤⣤⣤⣶⣤⣤⣈⣙⠛⠀⠈⠳⠟⠙⠷⠏⠉⠀⠀⠉⠛⠛⠳⢦⡀⠀⣜⣷⣿⠶⠿⠋⠀⠉⢹⣯⣴⣦⣾⣃⡴⠋⣀⣤⣤⠶⠚⠙⠛⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣶⢶⣶⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⣀⣀⣭⣓⣋⣀⣹⣷⣶⠶⠶⣤⣾⣥⣬⡥⢬⣭⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⡏⠉⠁⠀⠉⠉⠋⠁⠀⢀⡴⠾⠛⠉⠁⠀⠰⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⡀⠀⣀⠀⠄⠀⠀⠠⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢀⣤⠶⠻⠛⠛⠛⠓⣦⣄
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡏⢀⣤⣹⣹⣷⡄⠀⠀⠀⣴⣿⠆⠀⠀⠘⢀⢀⡠⣽⣻⣿⣶⣦⣄⣠⣼
⠀⠀⠀⠀⣸⣿⢣⣿⣿⣻⣿⠀⣿⣿⣿⣿⣿⣿⣄⣀⣾⣿⣵⠐⠀⢢⣳⣌⣺⣟⣽⡝⣻⣿⣿⠟⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⡟⢠⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡂⠀⠀⠉⠈⠟⣿⠿⢠⣿⣿⡏⣉⢽⣿⠃
⠀⠀⠈⠘⣿⣿⣿⣿⣿⣾⠁⠀⠀⠀⠉⠛⠿⢿⣿⣟⢿⣿⠮⠿⣿⢳⣿⢄⣀⣿⡷⡭⡘⣷⢿⣿⠼⡟
⠀⠀⠀⢄⠙⣿⣿⣿⡿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠭⣼⣾⣧⣾⡟⠚⠲⠝⣷⣄⠀⢃⡛⠀⠀⠠⡀
⠀⠀⠀⠈⠛⢠⢉⠉⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠛⠋⠍⠉⠥⣬⠆⠀⠈⢻⣄⣬⠉⠉⠂⠀⠀⠰⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠀⠀⠀⠀⠈⠉⠙⠓⠐⠤⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣤⠴⠶⣶⣶⣶⠛⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⢀⠀⣼⣿⣿⣿⣾⣿⣿⡇⠈⠉⠛⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⠀⠀⠀⠀⣿⣤⣿⣿⣿⣿⣿⣿⣿⣷⣿⣰⡆⢠⣦⠈⠙⠳⢦⣤⣀
⠀⠀⠀⠀⠀⢀⣴⡟⢡⡤⠃⢀⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢹⡿⠆
⠀⠀⠀⠀⠐⠋⡿⠳⠜⠀⣴⠟⠛⠋⠙⠉⠙⢛⣿⠿⠟⠛⠉⠙⠛⠛⢿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣧
⠀⠀⠀⠀⣠⠞⠁⠀⢀⣾⣉⣀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠀⠀⠀⠀⢿
⠀⠀⣴⢿⡇⠀⠀⢠⡟⠁⠀⠉⠙⣄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⣧⠀⠀⢸⡆
⠀⠀⠁⢸⡇⢸⣴⠛⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢀⠀⠈⣇
⠀⠀⠀⣼⠁⢸⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⣹⣦⣀⢀⣀⣤⣄⣀⡀⠀⠀⢸⣿⣿⣿⣼⡇⠀⢻
⠀⠀⢠⡇⠀⢸⡇⠀⠀⠀⠀⠀⢠⣟⡀⠀⠀⢠⡏⡔⣰⠟⠋⠉⠀⠀⠈⢙⣶⠶⠾⣿⣿⣿⣿⣿⣠⢸⡆
⠀⠀⣼⠁⠀⣼⠳⠶⢤⣄⢀⣴⣿⠟⠀⠀⠀⠘⢧⣽⠃⠀⠀⠀⠀⠀⠀⠀⠁⠉⢙⣾⣿⣿⣿⡿⠃⠈⣷
⠀⢠⡏⠀⠀⣿⠀⠀⠀⠉⢿⡿⠃⠀⠀⢀⣀⣀⣾⣿⣀⣠⠀⠀⠀⠀⠀⠀⠠⣬⡽⠛⢿⣿⡟⠀⠀⠀⡿
⠀⣸⠃⠀⢰⣯⣤⣄⡀⠀⣿⠀⠀⠀⠀⠈⠉⠉⠉⢻⡿⠃⠀⠀⠙⠁⠀⠀⠀⢰⡇⠀⠀⣿⠀⠀⠀⣸⠃
⠀⣿⣤⠶⠾⠿⠟⠛⠿⢷⣿⣷⣤⡴⠶⠶⢦⣄⠀⣿⣤⣤⡄⣀⠀⢀⣀⣠⡴⠏⠀⠀⢀⡿⠶⠴⠞⠛⠛
⢸⣋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠈⠳⣽⡿⠯⢚⣵⡞⣿⣩⢁⡀⣀⣠⠞⠁⠀⠀⣠⡄⣀
⣴⣿⣿⣦⣾⣿⣦⣀⣿⣦⣰⣦⣰⣤⣷⣶⣄⣢⣀⠀⠙⢿⢻⣁⣷⣾⣯⣾⡔⡉⣠⠀⣰⣿⣾⣿⣿⣿⣿
⣿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⡿⠟⠋⠉
⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠉⠛⠿⠟⠋⠉⠉⠛⠋⠉⢡⡴⠟⠋⠉⠡⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣽⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⢉⣿⡿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢛⣽⣿⠇⡸⠛⠉⣈⣴⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢶⣶⣶⣶⣤⣄⣀⣀⠀⠀⠀⠀⢠⣾⠿⠁⣸⠟⠉⡀⠁⠀⣧⠻⣽⠷⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠛⠉⠁⠎⠀⠀⠉⠋⠙⢿⣿⣶⣆⢀⣴⡟⠉⠀⠀⠋⡀⢠⣷⣲⢄⠙⠓⠒⠋⠀⡀⣯⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⢱⢁⠀⠀⠘⠀⠀⠀⠀⠀⣀⠠⠤⠿⣿⣿⠋⢁⠀⠀⠀⠀⠻⣆⢻⣶⣿⣿⣿⣾⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠙⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣉⣿⣾⠀⠀⠐⠀⠆⠸⢮⣽⣿⣿⣿⣿⣿⠿⠟⣀⡴⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⣠⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠀⠀⣀⡀⠈⠤⠙⣿⣿⠒⡀⠀⠁⠀⢠⡴⣿⣿⣿⣿⡇⠀⠀⣸⡭⠴⠺⢧⣀
⠀⠀⠀⠀⠀⢀⣾⠻⣿⡄⡇⠀⠀⣠⠤⠒⠋⠁⠂⠈⠉⠉⠉⠈⠉⢉⣋⣼⣿⠟⡀⠀⢠⠀⠀⢀⠏⣹⠿⣿⣿⣷⡴⠚⠅⠀⠀⢰⣿⣿⡗
⠀⠀⠀⠀⣀⣿⠃⣾⠋⡃⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⣼⣿⣿⣿⡛⢁⠀⠀⡴⢀⡔⠀⠉⠳⠇⣾⠋⠐⣸⣀⣤⣿⠷⠿⠿⣿⡿⠁
⠀⠀⠀⢀⣿⡉⢀⣻⠀⣄⠂⠀⠀⠔⠂⠀⣀⣀⢡⣶⣿⣿⣿⣿⣿⡟⡋⠓⠈⠢⡀⣠⢸⣿⣿⣏⠀⠀⠈⣄⣀⣾⣿⠟⠁
⠀⠀⠀⣼⣿⠇⠜⠨⠀⠟⠀⠀⠀⠀⢀⣻⣿⣿⣿⣿⣿⣿⡋⡉⠀⠈⠀⢀⢠⡄⠔⣼⣿⣿⣿⣿⣿⣶⣶⣿⠿⠋⠁
⠀⠀⠀⣿⣿⠆⡸⠦⢶⠄⡀⢸⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⠈⠀⠐⠀⢠⢈⣨⠶⠿⠟⠛⣿⣿⣿⡟
⠀⠀⠀⣿⣿⠀⢀⠈⢈⣷⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠐⢋⣤⣶⡿⠟⠋⢉⡙⠻⢧⡀
⠀⠀⠀⢿⣿⡄⢈⢷⡀⢹⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠀⠀⠢⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⠀⠢⣽⣧⡀
⠀⠀⠀⣿⣿⣆⣦⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢮⢈⠈⠄⢀⠈⠀⠀⠀⠀⠀⣱⠀⠀⠋⠈⢻⣿⣟
⠀⠀⠀⠘⣿⣿⣿⡷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠘⠀⢷⡀⠈⠀⡀⠳⠀⠀⣰⣿⡍⠁⣀⣝⣿⣿⣿⡁
⠀⠀⠀⠀⠹⣿⣿⣿⣽⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠘⠇⢂⠀⠅⠀⠘⠳⣶⣿⣾⣿⡿⠃⠀⢘⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠤⡶⣿⣆⠁⠀⡌⠈⣀⡉⠛⠛⠉⠀⢀⡀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣧⠧⠐⡟⡨⠘⠀⠼⠋⠃⠀⢀⣀⡄⣿⣧⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣧⣿⣀⠐⣴⢱⣤⡀⣼⣯⣷⣿⣿⣿⣿⣿⣿⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⡿⠛⢯⣣⡿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠙⠛⠷⣼⠮⠷⠃

⠱⠀⢄⠀⠀⠈

⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡈⠑⠀⠀⠀⠀⠠⡀
⠀⠀⢀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠀⡀
⠀⠀⠀⠑⢄⠀⠢⣇⠀⠈⠓⠒⠒⠁⢦⡄⠀⡖⠸⠐⢄⡀⠢⠀⠁⡆
⠀⠀⠀⠀⠀⠁⠀⠈⠓⢤⠀⠀⠀⣄⡀⠐⡆⢁⠀⠈⠀⠙⠠⡇⠀⠁⠆⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡈⢣⡉⠉⠀⠀⠀⠀⠀⠑⠜⠶⠶⠶⣄⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠢⡈⢂⠉⠀⢀⢇⠀⠀⠀⠀⠈⠢⣐⠘⠿⠧⠤⢄⣀⣀⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⠑⡄⠣⢀⣯⡜⢆⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠈⠉⠒⢶⣦⡄⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠙⠂⢹⣽⣇⣞⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠈⠹⣦⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣄⣀⣘⣿⣿⣿⣿⡇⠉⠓⢶⣤⣀⡀⠘⢦⡀⠀⣾⠀⠀⠀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡦⡀⠘⠻⠿⠿⣷⢄⠛⠆⠘⢆⠀⠀⠂⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢾⡵⠢⠄⡀⠈⠁⠀⠀⠀⠀⠙⠠⢀⣀⡀⣀⣀⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⡠⠀⣹⠗⢔⡀⠁⠂⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠉⠒⡶⡰⣠⠃⠀⠀⠈⢀⠭⣔⣂⣉⠁⢰⠀⠀⠀⠀⢀⡴⠒⠘⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣈⠀⠁⠉⠲⢄⠀⠔⢁⢴⠋⠁⠈⠉⠉⠁⠈⠀⠀⠀⡀⠀⠀⠰⢊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⢀⠎⠠⠁⠮⠄⣀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⣀⡀⠀⠀⠉⠑⠒⡖⠋⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠒⠚⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣤⣄⣀⠂⡄⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠈⣉⠙⡌⠋⢿⣟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠈⠑⢀⣬⢻⡻⣇⠀⠀⠀⠂⠀⣠⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡠⠄⠀⠀⠉⠼⠳⠿⡀⠀⠀⠀⢀⣿⣷⣿⣿⣿⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⡿⠂⠀⢀⣊⠀⠀⠦⡀⠀⠀⣀⣀⣴⡿⣿⣿⣿⣿⣿⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⢀⢘⣷⡄⢀⣸⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣻⣜⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⡏⣙⠉⠱⢄⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣿⣿⢿⣧⠠⠈⣻⡿⠀⠨⠅⠀⠈⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣇⣠⣈⢒⠲⠲⠀⢀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣾⣿⡮⠛⠛⠻⠿⠟⠃⠀⠀⢈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣿⣾⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⣿⣿⣿⣿⣿⣿⣵⣦⠴⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢢⡙⡷⠶⠓⠳⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠋⠉⠉⠉⠉⠉⠏⠈⠛⠃⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢴⠃⢢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠈⠁
⠀⠀⠀⠀⠀⠀⢠⣾⠛⠻⣆⢸⡇⠉⠣⢠⠗⠀⠀⠀⠠⠠⠠⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢸⡇⠀⠀⠀⠁⠀⠀⠀⠂⠀⠉⠉⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⢸⡇⣠⣄⠀⣠⣄⢀⡀⠀⠀⠀⠀⣀⣿⠀⣀⠀⣠⣄⠀⢀⡀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢸⣇⡟⢹⣦⡟⢹⣼⣷⢿⡆⣇⠀⡟⣿⣾⢻⣴⡏⢹⢰⠟⣿⣸⠿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡇⢸⣿⡿⠟⢻⡿⠟⢻⡏⢸⡇⢿⢠⡇⢿⡇⢸⣿⡿⠛⠉⣶⣼⢿⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⡇⢸⡏⣷⣼⠋⣷⣼⢻⣷⠟⠀⠸⣿⠃⢸⠀⢸⠹⣧⣼⠘⣇⣻⠈⢷⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠁⠈⠁⠀⠈⢁⢸⡇⠀⠀⠀⣿⠀⠈⠀⠈⠀⠉⠁⠀⠙⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡨⠸⡇⠀⠀⢷⠇⠀⠀⠀⠀⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄⠋⠀⠀⠀⠀⠄⡀⡀⠀⠀⠀⠀⠀⠁⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠐⠐⠂⠂⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⡆⠈⢀⠷⡆⢉⡆⠀⠐⠀⡈⠆⡈⠁⠀⠘⣄⠀⠂
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠈⢲⠠⣀⡸⠊⠸⣤⢄⡇⠀⠃⠀⢀⢠⠀⠀⡇⠀⠃⠀⣄⠴⠂
⠀⠀⠀⠀⢀⢋⡘⠀⠀⠀⡠⣄⣵⢹⠀⢹⠀⣸⠀⢣⡊⠠⣀⡀⠈⡄⠀⠈⠙⢆⡀⣸⠤⢤⡀⠀⠄
⠀⠀⠀⠀⠈⠺⡄⠀⠀⠀⡠⢈⡀⣿⠀⠈⠳⡇⠀⠀⢳⠀⠀⠘⢾⠁⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠉⠉⢳⡀⠀⠀⠹⢀⡏⠙⠶⢤⣀⣇⠠⡀⣞⠀⠀⠀⢸⡄⠀⠀⣀⣼⢎⣷⠄
⠀⠀⡀⠠⢀⣄⣀⠽⠛⠳⣦⡘⣇⠀⠀⠀⠀⠉⠲⣥⡏⠀⠀⠀⠀⢹⣦⠾⠋⠀⠠⠀⠀⢀⠃
⠀⠀⢀⡍⠁⠀⠀⠀⠀⠀⠀⠳⢼⣦⣀⢀⣀⠀⠀⢿⠀⠀⡖⠀⠀⣼⠃⠀⠀⠀⣨⣜⢁⡤⡊⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⢒⠀⠀⠈⠉⠙⢿⡅⠀⢸⡇⠉⠀⠀⢠⣿⠀⠀⠀⣼⠁⠀⠀⡴⠁
⠀⠀⠀⠠⣀⣀⠀⠀⠀⠉⠙⣄⠀⠀⣀⡄⠈⣿⡄⢸⡇⠀⣠⣴⠿⠁⠀⣀⡴⠋⣀⣤⣞⣀⠂⢠⠀⠁
⠀⠀⠀⠀⢁⡩⠷⠶⠶⠦⢤⣜⣆⣸⣿⣁⠀⠘⣿⣾⣧⣾⣿⠷⠲⠶⠶⠿⠖⠚⠉⠀⠀⠁⠉⠑⠢
⠀⠀⠄⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠻⣷⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠠⣴⣶⣶⠶⣶⣶⣶⣶⣶⣶⡶⢆⣀⠉⣙⡛⠋⢛⠛⢓⡀⠲⠶⠶⣶⣶⣶⠶⢶⣶⣶⣶⣶⣒
⠀⣀⣀⣴⣿⣿⣿⣿⢿⠿⢉⡉⣡⣴⣶⣿⣿⠸⣿⣧⣧⠸⣦⣬⠹⣷⡺⣷⣶⣤⣚⣿⣷⣶⣾⣿⣿⠯⠄
⠀⠠⣿⣿⣿⣿⣿⡿⣫⣶⠟⣼⣿⣿⣿⡟⢁⡄⣿⣿⣿⡰⣮⡻⢦⡙⢿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣷⣆
⠀⢛⣿⣿⣿⣿⣏⣾⣿⣯⣾⣿⣿⣿⣿⣧⠸⣧⣙⣛⠻⢿⣞⣿⣶⣽⡆⢙⡛⣛⠻⢿⣭⣿⣿⣿⡟⠙
⠀⢈⣻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣌⡻⢿⣿⣿⣿⣿⣷⡹⣿⣿⣶⣦⣿⣽⣿⣛⣉⡁
⠀⠀⠤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣰⣮⣿⣿⣿⣿⣷⣶⣯⣻⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⠷⠶
⠀⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣀⡀
⠀⠀⠰⠾⣿⠿⠿⢿⣿⣿⣿⡿⠿⠟⠿⠿⢿⣿⣿⣿⠿⣿⣿⠿⠿⣿⢿⣿⡿⠿⢿⡿⠿⣿⣿⣿⢯⡍

⠀⠀⠀⠀⠐⠀⢃⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠠⢅⠅⠀⠀⠀⠀⠀⣨⠀⣅
⠀⠀⠀⠀⠉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠂⠀⠀⠀⠀⠀⠠⠥⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠨⢩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡞⠉⡇
⠀⠀⠠⢅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠒⠉⠁⠉⠀⢸⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡴⠁⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠂⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⣀⡤⠐⠤⠤⠊⠁⡜⠀⠀⠀⠀⣠⣞⣻
⠀⠀⠀⠀⠀⠀⠀⠌⠁⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣀⣀⣀⣡⠞⡇⠀⠀⠀⠀⠰⠁⠀⠺⣉⠉⠡⠀⠌⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⠝⠊⠉⠉⣉⠉⠉⢓⣧⡀⠀⠀⢀⠇⠀⠀⠀⣨⠃⢀⠂⠀⣠⠒⠁
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⢀⠟⠁⠀⡴⠊⠁⡈⠱⡞⢡⢌⢳⡀⠀⡸⠀⠀⠀⡰⠧⠒⠉⠱⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⢠⠋⠀⠀⠀⡇⠀⠈⠀⢀⠠⠄⠀⡼⡇⢠⡷⡄⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⣃⠔⢁⣷⡏⢰⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⡔⠂⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠴⠊⠉⢰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣠⡿⠋⠀⠀⠀⢠⡤⡀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠂⠀⠙⠒⠶⠖⠒⢉⡟⠀⠀⠀⠀⠀⠙⣇⠉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠊⠉⠉⢉⡞⠀⠀⠀⣀⣀⣠⡄⠀⠀⢈⡀⣒⣦⠏⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠯⠑⠦⠚⠁⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠂⡠⠋⠀⠀⠀⠀⠈⠉⠉⠁⠉⠁⠄⠛⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠀⠸⣍⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⣄⠀⢉⣉⠙⣀⠀⠀⠀⠀⠀⠐⢶⠛⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣤⣀⣀⣀⣐⠀⣀⣀⣤⣷⠚⠉⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⣍⠙⠁⠀⠀⠉⠉⠛⠀⠀⠀⠀⠀⠀⠙⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢉⠿⡁⢀⡼⢻⣄⠀⠀⠀⠀⠀⠐⠀⡠⠒⠀⠀⠈⠁
⠀⠀⠐⠀⠀⠀⠀⠒⠀⢈⠁⠀⠀⠀⠀⠐⠿⣶⠿⠈⠙⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠀⠣⠄
⠀⠀⢀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠁

⢀⡠⠄⠀⠀⠒⠒⠒⠂⠀⠻⠀⠐⠀⠀⠠⢀
⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄
⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡤⡀
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠢⡀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠸⠀⠈⢄⠀⠀⠀⠀⡄⠀⠂
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡃⠸⠄⠀⠠⠬⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⡌⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡠⠊⠁⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠔⢁⠄⢓⢆⠀⠀⠀⠀⠇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣤⣿⣿⠀⠀⠀⠀⢰
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠘⠚⠛⠁⠀⠀⠀⠀⠈⠄
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠰⡀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⢀⠀⡠⠃
⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠤⡀⢥⠀⠓⢠⣄⠤⣊⠁
⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠐⠀⠀⠂⠈⢲⠤⡴⠖⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⣄⡀⠀⠀⢀⡌⠀⠀⠋⠀⠀⢀⠸⢦
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⣿⠅⠰⢄⠄⠀⠐⠀⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠂⠀⠠⠭⠅⡣⠀⠀⠀⡀
⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣀⣀⣀⠀⠀⠤⠀⠰⠂⠂⢽⠀⠤⠤⣤⠜⠁⠀⣀⠜
⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⡵⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⡀⡠⢊⠌
⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡀⠔⠁⠁⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠀⠀⠘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠒⠁⠀⠀⠀⠠⠡⠄⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⢠⣤⡤⢄⡀⠈⠉⠑⠪⠉⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡉⣳⠐⠐⠐⠐⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠠⠲⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠆⣦⣰⣶⣯⣼⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⠿⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣿⣻⡿⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢻⣤⣥⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⠀⠄⠀⠀⠀⠀⣀⡀⠤⡾⠷⣧⠎⠉⢠⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⣿⣿⡿⠂⠀⢀⡤⠀⠈⠀⠀⠚⠀⠀⠘⠏⣤⣽⣿⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣟⠕⢀⣴⠊⠁⠀⠀⠀⢀⠈⠓⡶⢦⡤⠩⣌⠉⢙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⣰⠏⠀⠀⠀⠀⠀⡀⠀⠀⠀⢣⡁⠈⠉⠓⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣿⠟⠰⠃⠁⠀⠀⠀⠀⠀⢶⠀⠀⠐⠀⠱⣄⡐⠉⠉⠁
⠀⠀⠀⠀⢀⣀⡀⢀⣤⣿⣿⠀⡊⠀⠀⠀⠀⠀⠀⠀⠸⣦⣄⠠⠠⠀⠀⡠⠤⣤⣽⠇⠁
⠀⠀⠀⠀⠠⠠⣽⣿⣿⣯⣽⣄⣽⠀⠀⠀⠐⠸⠃⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠓⠺⠞⣿⣿⣷⡇⠀⠀⡗⡾⠀⠙⣦⣵⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣃⡌⠀⠀⠃⣀⣄⠙⣿⠉
⠀⠀⠀⠀⠀⠀⠂⢀⠀⡠⠀⠹⠿⠿⠿⠆⣴⣀⣷⡞⠘⠻⠿⢿⣶⡶⢤⣄⢀⠀⠀⠀⣠⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⠁⢢⣤⣤⣼⠷⢛⡽⠛⡳⠶⠶⢾⣅⣀⣠⠿⡿⠶⠰⠂⠈⠢
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠤⠛⠩⠟⠛⠛⠉⢉⣀⣀⠴⠛⠛⡀⣈⡙⠁⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣬⣿⣶⣶⣿⣿⣼⣦⣶⣶⠲⣿⣷⣿⣷⣗⣾⣾⢶⢶⠴⠦⡠⠄
⠀⠀⠀⠀⠀⠛⠉⠉⠉⠛⠒⠂⠁⠉⠉⠛⠛⠋⠩⠝⠛⠛⠛⠛⠛⠛⠛⠛⠓⠓⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⣠⣴⣇⣰⣶⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣛⣿⠖⠛⠛⠰⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⠡⠹⠋⠈⠨⢆⠙⠎⠉⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠛⠀⠸⢇⠀⠄⡾⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢌⠀⠀⠀⠀⢨⠃⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⣷⣿⠉⢠⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣭⠄⣴⠛⣧⠀⠀⠀⣰⠀⠀⠀⣾⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⡀⠙⣿⡃⠀⠈⠓⣡⡖⠁⠀⠂⠀⠀⠀⢀⣀⠀⢸⠧⣰⡧⠨⠋⠀⠰⠤⠿⠦⠤⢤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⣄⠈⠃⠐⠀⠀⠹⣷⠉⠠⠀⠀⠀⠀⢿⣿⠗⠚⠒⠛⠛⠛⠃⠈⠍⡂⢀⡲⣶⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠸⣏⠲⣀⠀⠀⢤⡀⠈⠣⠠⠴⠒⠂⠀⡈⠛⠃⠀⠀⠒⠒⠀⠀⢀⠀⠰⣾⣧⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⣸⣿⢿⡿⢸⠇⠀⠘⣄⠈⠦⣔⢑⡢⠈⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡇⠘⠿⢿⣿⣷
⠀⠀⠀⠀⢠⣿⣿⡞⢧⣾⠁⠀⠀⠙⢦⡀⠉⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⢿⣿⣿⢡⠁⠚⢂⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠅⢰⡿⠀⠀⠀⠀⠈⠃⠀⠀⢀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠂⠀⢠⣿⡿⢞⡃⠀⠨⢁⣀⣾⠻⠛⠁⢀⠠⣦⣤⣄⡀
⠀⠀⠀⠀⣾⣿⡿⠃⠁⡅⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠉⠀⠀⠀⠀⢀⣠⣄⣀⢀⠀⠀⠉⠁⢠⣾⡟⠂⣶⣾⠀⠀⡀⠉⣻⣷⣤⠀⠘⠃⠨⡉⠝⢻⢶⡀
⠀⠀⠀⠀⣿⣿⡷⡔⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⣧⣶⣤⣶⡨⢭⣋⣿⡟⣙⣻⡟⠀⢠⣿⡟⠀⠀⠀⣰⡗⠈⣠⣀⡐⠶⡟⠑⢦⣈⣞
⠀⠀⠀⢰⣿⣿⡇⠘⠈⣢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⢿⣷⣄⠀⣿⣇⠀⢀⠅⠀⣸⣿⣾⡿⣿⢃⡀⠈⠋⠀⠀⠠⠾⠿⠀⠚⠿⠗⠃⢠⠀⠀⠀⢹⣿
⠀⠀⠀⣸⡟⢻⡧⠠⠀⠀⠉⡟⠃⠈⢿⠀⠀⠀⠀⠀⢿⣿⣶⡤⣿⣏⡀⠘⠂⠀⣿⣿⣾⣿⠟⣿⢿⣶⣤⣤⡀⣠⠃⣠⣤⠤⠤⠶⣶⣵⣿⣷⡀⠈⢹
⠀⠀⠀⣿⡇⢿⡁⠀⠀⠀⢀⠃⠀⠀⢸⠀⠀⠀⠠⣞⣻⣿⣿⠂⣿⣿⡁⠀⠀⠀⢻⣿⣿⣿⣾⣿⠈⢿⣯⣿⣆⡀⠀⡈⢧⣴⣿⡏⠀⠉⢿⣿⣇⠀⣼
⠀⠀⢘⣛⠷⢜⡟⢀⢀⣀⢸⢁⣀⣀⣸⣀⣀⣰⣶⣿⣿⣿⣿⣿⠉⢙⣠⠀⠐⡔⢸⣿⠠⡿⡻⢿⣷⡾⢿⣾⣻⣧⣿⡄⠀⠻⡿⠁⠀⠀⠈⠛⠻⠄⢾
⠀⠀⢼⣿⣿⣟⣛⣟⣼⣿⣿⣿⣿⣧⣤⠉⠉⠉⠉⠙⠛⠛⠉⠙⠛⠓⠀⠲⠋⠑⠛⠙⠃⠘⠛⠛⠻⣧⣾⡗⢰⣤⣿⣷⣄⠀⡠⣰⢟⡇⢠⣩⡾⠂⣈
⠀⠀⠈⠉⠉⠛⠛⠛⠛⠻⠽⠧⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠉⠉⠓⠲⡿⠾⠁⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣄⣠⣄⣤⢤⣤⡤⢤⢤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡠⠀⠀⠀⣀⠂⡀⠀⠀⠀⣤⢲⠀⠀⠀⠀⠀⢀⠀⢠⣤⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠉⢉⣹⠀⢒⣁⠛⣣⣤⡉⣀⣀⣇⡏⣀⡀⠸⠷⢀⣴⣦⡈⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⡀⠐⠊⣵⣰⡏⣉⣷⣟⣹⣿⣋⣭⣿⠙⣯⣽⣀⠀⣺⡏⢻⣷⣾⣿⣦⠃⢀⡠⠴⠒⡶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⣿⣿⣶⣶⠏⣈⣻⣿⣬⣿⣏⣈⣛⠋⠙⠿⢟⡉⠛⠳⢼⡇⠘⠟⢦⣼⡿⠐⢋⢶⡲⢸⠴⠈⡈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⡌⠛⢫⣵⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣶⣦⣌⠛⠘⣠⠈⢧⡀⢡⡾⠟⠁⡳⢫⣶⠷⠛⠺⢦⡘⣡⠞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⠀⡋⠀⣠⣴⣦⣤⢠⠶⣴⣯⢙⠛⢿⡿⠿⠿⠟⡃⠀⠈⠙⠃⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠘⡖⢙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀⠉⢛⣍⠀⢩⡟⠛⠚⠉⠷⠿⠻⣼⢁⣶⣦⣼⣽⡀⢀⣠⠂⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢠⡍⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣶⠌⠳⢾⡏⢠⣿⠇⠀⢀⢀⡀⣠⣄⠘⢋⡀⠈⠁⣩⢿⡏⢠⡄⠀⠀⢚⠀⠀⠀⠀⠀⠀⣠⢎⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣾⣟⠛⣷⢾⠉⢸⡱⣹⢻⡷⣋⣿⣦⣸⡇⠀⣾⠁⢈⣷⠈⠁⠀⠀⣆⣀⣀⣀⣠⣴⣚⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⠻⢿⣿⡿⠈⠳⠛⠟⠉⢁⡧⠛⣛⡉⠉⢳⡄⠻⣷⣿⠏⠀⠀⠀⢸⡱⣴⠤⢦⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⣄⣾⣿⡇⣿⠆⠀⠐⢸⡿⠁⣹⣿⠰⣠⣿⣿⡿⣦⡘⠿⠀⢠⣇⠳⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠨⡏⣹⣶⣴⣿⣦⡿⣦⢻⣦⣿⡿⢰⣿⡏⣸⣷⠀⠁⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠹⣿⠰⣽⢾⣽⣷⠿⡼⣶⡿⢧⣌⠻⣿⣿⡟⣠⠃⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠶⠌⠛⠿⡾⠿⠛⣁⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠚⠓⠚⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⡀⣀⣴⢿⣿⣄⣡⠊⣥⣧⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣚⣿⣿⣿⣿⣿⣿⡿⡻⢿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡏⣛⣿⣿⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠋⢲⣶⣿⣦⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇⠀⠀⣸⣿⣿⣿⣧⣾⣦⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢙⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣃⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠋⣠⣼⣿⣿⣿⣿⠋⠈⢻⣿⢿⡏⢀⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣶⡀
⠀⠀⠀⠀⠀⠀⣸⣤⣼⣿⣿⣿⠏⣰⣾⣯⢿⣷⢺⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣞⣻⡛⣿⣧⣾⢻⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢿⣏⣀⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢾⡟⣥⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠙⢏⣈⣿⣿⠏⢉⣿⡿⣁⣸⣿⣿⣿⣿⣿⣿⣿⢇⣽⣴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣿⠛⡀⢸⡋⣠⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⣿⣶⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠞⢑⡻⠃⠀⠀⠀⠻⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠈⡏⠻⣿⣀⠀⣼⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣼⣿⣿⣏⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⣀⣨⣟⢷⣼⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠞⠛⠿⠿⠛⠛⠛⠛⠛⣻⣷⣟⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡿⢏⣿⡿⠿⠾⠿⠿⠄







⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠻⠛⢿⡟⠛⡿⠻⣟⠿⢻⣻⠟⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣾⣿⣿⣷⣾⣿⣶⣾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠤⠶⣠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⢋⠁⠘⠅⠈⢄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢸⠃⠀⠈⢀⡎⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠤⠌⠁⠀⠀⡰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⢇⠐⠊⠀⠀⠀⠐⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡉⠉⠄⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⢬⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠐⠃⠀⠀⡀⠄⡈⠀⠀⢠⡀⠀⢀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⢁⣭⠐⠉⠀⠀⠀⠐⠧⠀⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠐⠤⠠⠴⡒⠀⠀⠀⠀⠀⣼⠿⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⡂⠠⠒⠋⠁⠀⠀⠀⢜⢄⢠⣿⡗⠀⢸⠁⠀⣭⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⢱⡶⢀⠀⠀⠀⠀⠘⠌⠂⠰⢿⠝⠋⠙⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⣡⠋
⠀⠀⠀⣠⠶⠚⠛⠙⠋⠘⠀⠒⠤⡀⠀⠀⠀⢀⡀⢠⣤⣄⠀⣷⠀⠀⠀⠀⠀⠀⠠⣟⡄
⠀⠀⣼⠁⠀⠀⠀⠀⠄⠀⠀⢄⡢⣄⢻⡙⢲⣎⠀⣶⠀⠙⢆⡠⠠⠖⠀⠀⠀⠠⠐⣿⠇
⠀⢸⡏⠀⠀⠀⠀⢒⡛⣒⡳⠦⠝⠾⠵⡭⠚⠛⠛⠋⠀⠀⠀⡈⠉⠉⠀⠀⠀⠀⠐⣿⡄
⠀⢸⡇⠀⠀⢀⣲⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠒⠀⢀⠀⠀⠀⢀⣿
⠀⠈⢻⣆⡊⢙⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠋⠁⠄⠁⠀⠀⠌⢿⡄
⠀⠀⠀⠉⠙⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠈⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢣⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠦⣄⣀⣸⡓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⢰⡌⠉⢀⡨⣩⡓⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⠉⠙⠊⠀⠀⠚⠻⠊⠁⠙⢦⡀⠀⠉⠉⠛⠒⠲⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⢀⣰⡅⠖⡂⠀⠀⠀⠀⠸⢾⣷⠶⠶⣿⡿⠟⣳⠦⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣍⣁⣀⣀⠈⣱⡶⠒⠒⠛⠛⠛⠛⠻⣿⣿⡿⠿⣦⣽⣿⣭⣽⡿⠛⠋⣀⡴⢚⡡⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣘⢿⣿⣿⣾⣿⣿⠀⢠⠀⢀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⣠⢏⣄⡴⢞⣩⠖⠉
⢦⣀⠠⣄⡀⠀⠰⣤⢤⣄⡀⣦⣄⡀⠀⠀⠀⠈⠳⣍⠻⣿⣿⣿⠀⣾⠀⡾⠀⣰⠏⠀⠀⠀⠀⠀⢀⣼⣯⠞⣫⠴⠋
⠘⣏⠓⠻⠍⠉⠛⠛⠂⠀⠈⠙⠀⠙⢦⡀⠀⠀⠀⠈⠳⣌⢿⣿⣼⢇⣾⠁⣴⠋⠀⠀⠀⠀⢀⣴⣿⢟⣥⠞⠁
⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⣀⣀⣽⢸⣿⣿⡿⢃⡾⠃⠀⠀⠀⣀⣴⣿⢟⡵⠛⠁
⠀⠀⠻⢭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡽⣣⣿⣿⢟⣵⣟⣀⣠⣤⣶⣿⣿⡿⣱⠟⠁
⠀⠀⠀⠀⠉⠛⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣤⡴⠾⣿⣾⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣽⣁⣠⣤⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣧⠃
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢤⡀⡄⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠝⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠂⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠈⠉⠉⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠁⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⡔⠂⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⢀⠂⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘
⠀⠀⠠⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⠀⣀⠀⠠⠄⢄⡀⠀⠀⠀⠀⠃
⠀⠀⠂⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠠⡀⠐⢀
⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢰⡇⠀⠰
⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⡝⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠔⠋⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠡
⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡀⠑⠐⠃⠀⠄⠠⠀⠀⠀⠀⡎⠻⢟⡛⡲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⡐
⠀⡔⠈⠓⠒⡈⠒⠄⠀⠐⠀⠀⠀⠀⠔⠁⠀⠀⣰⠇⠈⠳⢦⡀⠀⠀⠃⠀⣼⠋⠉⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠆
⠀⠀⠀⠀⠀⠁⠄⢤⠄⢀⠀⠀⢀⠂⠀⠀⢀⡠⡽⡀⠀⢢⡀⢹⢠⠔⡉⢄⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⣀⢁⢣⡀⢀⣸⠱⢠⠵⠤⠚⠉⠁⠘⣼⢡⠄⠁⠀⠠⠤⠤⠡⠄⠐⠊⠀⠀⠀⠀⠀⠀⠀⣸⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠈⠡⠀⠀⠄⠠⠤⠀⠠⠄⠠⢀⠀⠈⠛⠀⠀⠀⢀⢴⠂⠀⠀⠀⠀⠀⣠⠀⠀⠀⡀⠘
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⢀⣠⠚⣥⠓⢀⡔⠁⠲⠖⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠤⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⣀⠀⣀⠀⠤⠐⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠉⠉⠉⠀⠐⠠⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠀⠀⢀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣾⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣋⣿⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣏⡉⢁⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣛⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠐⠒⠋⠹⡿⠿⠿⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠈⠲⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠒⠂⠈⢆⠣⡀⢆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠲⡄⠀⠈⢣⡀⠈⡶⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠇⠀⠀⠀⠀⠑⡼⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣤⡀⠀⠀⠀⠀⠀⢀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣗⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠓⢄⠈⠂⠀⠀⢆⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠂⠀⠀⠄⠀⠱⢶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡠⠊⠃⠀⠀⠰⡄⠀⠀⠄⢂⠙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢴⢊⡁⠶⠋⠁⠀⠀⠁⣹⡀⠀⢀⢾⣿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡀⠀⠀⠀⠀⠀⠠⠾⠆⠁⠆⠀⠀⠀⡀⢀⠉⠙⠀⠈⢷⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠠⠤⠄⣠⠴⢋⠃⠀⠐⢄⠀⡀⠈⢢⡼⣻⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠖⠀⠀⠀⠀⠀⡰⢆⠐⢀⣲⣟⡧⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠰⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⢤⠘⣆⠑⠘⡿⣾⢥⣠⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⠢⡘⠿⠿⠊⠁⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⣰⠂⠠⠿⠛⣶⡀⠀⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠠⠄⠀⠤⢀⠢⣄⠢⣄⠪⣅⡩⣙⢧⡲⡀⣼⡃⠀⠀⠻⡀⠐⠤⠴⠟⠀⠀⠀⠐⡐⢄⠘⣾⡿
⠀⠀⠀⣾⠙⠀⠀⢀⣀⡠⠤⠶⠾⡷⠶⠶⣤⣍⣳⣮⣑⣬⣙⠮⢝⠿⡶⠾⠇⠀⠀⠀⠀⠙⠓⠒⠛⠀⠀⠀⠀⠀⠈⢰⣿⣄
⠀⠀⠀⢛⠀⠀⠀⠀⠀⢀⠤⠀⣠⡿⠆⠀⠀⠁⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀⠀⠀⠀⠀⠀⠁⠈⠲⡿⠃
⠀⠀⠀⢸⣄⠀⠀⣀⣀⣬⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠉⢉⡀⢀⣀⠀⠀⠀⠀⣀⡙⠰
⠀⠀⠀⠘⣿⣇⡓⠨⣕⣤⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠂⠉⠰⢄⠙⠀⠀⠀⠤⠄⢁⣦
⠀⠀⠀⠀⠈⠻⠿⠃⣉⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠐⠄⢂⠀⠀⠀⠀⠀⠀⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠈⠃⠁⠀⠀⡆⠀⠀⠀⠀⠀⢰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠄⡧⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠁⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠒⠒⠐⠂⠀⠀⢠⡀⠀⣠⣤⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢀⣠⣤⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣯⣭⣾⣿⣿⣽⣏⡳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠙⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢆⣀⣠⣴⣶⣶⠶⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣡⣠⣶⣶⣦⡄⠀⠀⠈⣿⣷⠂⣸⣿⣿⣿⡴⠶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣹⣿⣾⣿⣿⡿⣧⣤⣤⣤⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⡿⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠙⣻⣿⣿⣤⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⣴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⣿⣿⡿⠿⠿⣿⣿⣿⣯⣿⣿⣿⡟⢀⣿⣿⡿⠟⠿⣿⣍⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣾⣿⣿⠋⣿⡿⣿⣷⢸⣿⣿⣇⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡟⠛⠛⣿⣿⡿⢹⣿⣿⣿⣿⡀⢿⣿⠿⠛⠁⢹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⣿⠛⢿⣿⣿⣿⣧⠀⠹⣷⣾⣿⣿⣷⣾⠿⠻⡉⢻⣧⠸⡿⣦⣤⣶⡏⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣧⠀⢻⡀
⠀⠀⠀⠀⠀⠘⠁⠈⠁⠀⠁⠀⣿⣿⣿⣿⣿⣦⡀⠀⠉⢀⣹⣿⠃⠀⠀⠀⠀⢿⣷⣄⣈⣉⣹⣶⣿⣿⣿⣿⣿⣿⣿⣧⠈⠃⠀⠻⣧⡾⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⢸⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠋⣻⣿⣿⣿⣿⣿⡟⠉⠻⣧⠀⠀⠀⣿⡷⢘⣿⣄
⠀⠀⠀⣠⠇⠀⠀⢠⡟⠀⠀⢻⡇⠀⢹⣿⣿⠛⠉⠹⡏⠉⠙⠧⡀⠀⠀⠀⠀⣠⣿⡛⠛⠷⠀⠋⠁⠉⢿⣿⡿⠀⠀⠀⠙⠀⠀⠀⣿⣷⣿⣿⣿⡆
⠀⠀⣴⣿⣴⣶⣾⣿⡇⠀⠀⠀⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣶⣶⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠁
⠀⠘⢿⣿⣿⣿⣿⠙⢿⡄⠀⠀⠀⠀⠈⢻⣿⡀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⡟⠂⠀⠀⠀⠒⠦⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠋
⠀⠀⠈⠛⡟⠉⠉⠀⠀⠳⡄⠀⠀⠀⠀⠀⢿⣷⠀⢠⣶⠗⠒⠒⠲⢾⠤⠽⠟⠃⠀⠀⠀⠀⠤⣴⣿⢆⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⢀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣶⣄⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠛⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⡇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⡖⣰⢒⡶⠂⢈⡱⣒⣆⣰⣶⣶⣶⣀⠀⣲⣶⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⣰⡷⢾⡴⠊⣹⣾⣿⣿⣿⣿⡏⠀⠀⠙⢿⣺⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⣰⢛⣫⢿⡿⢀⣴⣹⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠐⠀⠲⣀⡀⠀⠀⠀⣀⠠⠇⠀⣩⡿⢏⣾⣱⣿⣿⠏⠉⠻⣿⡙⣿⣿⣷
⠀⢀⠀⣀⡀⠀⢠⣴⣴⠿⣴⣮⣺⠀⢰⡄⠐⠁⠀⠀⠀⠈⠀⠘⢁⣿⢿⣿⠀⠀⢘⣽⡇⠘⢿⣿⡇
⢀⢀⠀⠀⠄⠀⠈⠛⠋⠁⠙⣿⣼⠇⣸⡀⠄⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⠞⠤⣾⣿⡇⠀⠈⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣏⣢⡟⠀⠀⠀⠀⠀⢁⠀⠀⣰⣶⡻⠏⠁⠀⠀⠘⢿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢚⠟⠉⠀⠀⠀⠀⠀⠀⠈⠀⠌⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠐⠰⠆⢠⣀⡅⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠦⣹⡧⠀⠀⠀⠀⠀⠓⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣻⡧⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⣿⠃⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠐⠂⠨⠅⠐⠳⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⡇⠀⠀⠀⠀⣀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠗⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⡇⠀⠀⠠⡜⠋⢀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡇⠀⠀⠘⠀⠀⢸⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠻⠍⠕⠁⠀⠀⠀⠀⠀⠐⠨⢤⡀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢄⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⠠⠀⠄⠀⠀⢀⡀⣰⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣴⠁⠀⠈⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡇⠀⢀⠐⢛⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢣⠀⠀⠀⠀⠀⢰⣾⠋⠁⠀⣩⣭⡉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡖⠦⠤⠀⠺⠇⢠⡄⠶⣤⣜⡃⠟⣷⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢥⣉⣤⠐⠋⠀⢿⡁⢂⠄⠢⠬⠟⡀⠙⠀⠑⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠠⠖⠀⣀⢘⣆⠤⣴⠞⠾⡿⠿⠟⠂⡀⣤⣤⡤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠿⠟⠓⠙⠉⠀⠀⠀⠒⠈⠊⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣍⣟⣿⣿⣏⣭⣉⣿⣿⣿⣽⣩⣙⣿⣿⣹⣯⣽⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠋⠉⠉⠉⠉⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠍⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡤⢚⣭⣶⡂⠉⠉⠁⠒⠬⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡴⣫⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠢⣣
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠞⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡞⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⢃⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⣧⠀⠀⢸⠸⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠱⣄⠀⣇⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠻⣇⠀⡠⠋⢑⠼⣎⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣤⣴⠧⣠⠈⠓⡟⠛⠛⠻⠿⠷⣶⣶⣾⡿⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⡀
⠀⠀⠀⣠⣴⣶⣿⣿⣿⣧⡀⠩⢃⠀⠀⠀⣸⠃⠀⠀⠀⠀⢠⣿⠟⠛⠃⠀⠈⠙⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⣄⣀⣀⣀⣀⣀⣀⠀⠚⠁⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⡙⠻⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣼⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⣤⣀⣘⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣋⡒
⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣛⣻⡭⣯⢩⡭⠝⠻⣿⣟⣫⣽⣶⣶⣶⣤⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⢻⢡⡟⣃⣛⡈⠛⢷⣦⣬⣭⣙⡛⠻⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢳⣦⠠⠹⣇⠻⢻⢿⣿⣷⣦⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠻⠂⠀⢸⣤⡾⣦⠹⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠙⢑⡀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⠒⠸⠿⣿⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠉⢿⡦⣗⣶⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣞⣟⣣⠃⠉⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡎⠙⠂⠀⠀⠙⣿⣷⣦⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣐⠄⠰⠊⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⡆⠀⠐⡀⢀⢿⣿⣯⡀⠘⠙⢮⡸⠳⠆
⠀⠀⠀⠀⠀⢠⣿⢢⣆⡀⠠⢤⡀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⣀⠀⢨⣷⣿⣅⣴⣡⢯⣾⣿⣿⡁⠀⠀⠀⠷⠀⠡⣤⠄
⠀⠀⠀⠀⠀⢶⣷⠶⢺⣷⣆⣿⣿⣅⣀⡠⣶⣿⣿⣷⡀⠄⠀⢻⠤⢿⣿⣿⡿⣿⣯⣿⣿⠟⠛⠛⢯⣤⠀⠂⠀⢀⠗⢻⣆
⠀⠀⠀⠀⠐⣿⣟⣀⣤⣬⣭⣽⣛⠿⠭⠗⠀⠉⠙⠟⠷⣷⣦⣦⡙⠾⣟⠈⠙⢻⣿⣿⡟⡀⠀⠀⢀⣿⡂⠂⠀⠀⠀⢁⢻⡆
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⡀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣧⣉⠃⠀⣸⣿⡉⠁⠀⠉⢠⣾⣿⠆⠅⠀⠀⠀⠰⠾⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⡁⠉⠉⠉⠀⠈⠓⠶⣶⠾⢿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣇⣀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⢺⡅
⠀⠀⠀⠀⠀⣻⠿⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣯⠁⠀⠀⠀⣾⣧⡿⠆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣇⠀⠈⠁⠀⣀⠀⠀⠮⣽⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠁⠈⠛⢻⡄⠂⠘⠗⠀⡄⠇⣸⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠈⠰⢠⢳⡄⢁⠀⠴⣦⣤⣬⣶⣿⣿⠏
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⢀⠀⠀⠉⣈⣠⣄⣤⣜⣟⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘⣤⣶⠦⣕⣢⡄⠀⠀⠨⡄⣀⡘⣻⣾⠶⣽⣿⣿⣿⣿⣿⣿⣵⡿⠁
⠀⠀⠀⢪⠾⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠠⠖⠀⠈⠙⣲⣾⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢡⠋⣰⣲⣤⡇⠀⢀⢀⠀⠀⠀⠀⢀⠀⠈⠁⣨⣠⠦⠀⠌⠟⠻⠿⠛⠛⠉⠛⠛⢿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠂⢿⠿⣿⣷⣎⣬⣯⡴⠒⡠⢀⠁⡀⢀⣄⣤⣤⣤⣴⣶⣤⣤⣴⣶⣶⣶⣶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠛⣿⣷⣿⣷⣿⣿⣿⠻⠃⠛⠏⠽⠟⠙⠻⠿⠟⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠰⣤⠀⠀⠀⠀⢠⠞⠁⠀⠰⠁⠄⠁⠀⠀⠀⠀⠁⠲⠀⠐⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠒⠦⠄
⠀⢠⠄⠀⠻⢀⣠⠤⠤⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⢄⣠⠄⠀⠀⠀⠀⠀⠈⠁⡀⠀⢀
⠀⠈⠱⠀⠒⠁⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠠⠃⣀⠀⠀⣀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⢀⠀⠀⠑⠼⠀⠀⠀⠀⠀⠀⠀⠤⣤⠺⢀⣀⡀⡠⠄⠘⣠⢀⡄⠈⠑⠲⠤⠤⢀⠀⢴⠄⢠⡤⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠃⡀⢀⡀⢀⠠⠃⠀⠊⠀⠂⢲⡇⠀⠀⢱⣦⣸⠀⢸⠵⠉⠉⠉⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⢤⠀⠀⠀⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⢠⣽⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⠀⠤⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡧⢸⣿⡄⠀⠀⠀⠀⠀⠀⣤⠀⠛⠁⠀⠀⠀⠀⠀⠁⠀⠀⠡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⡇⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⡀⠀⠀⠱⡀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⡀⣴⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡆⣀⢠⡂⣾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡘⠒⠀⠈⠀⠀⠀⠀⠀⠀⠙⠻⣷⣾⣿⣾⣷⠁⡸⣳
⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⠀⠻⠠⠀⠦⠤⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢿⣇⠞⢡⣟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠷⢷⠦⡄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡌⢉⢞⠰⠅⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢟⠗⠋⠁⠀⠂⠔⠂⠀⠀⠀⠈⣿⡇⣛⣉⣴⡾⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⣿⣴⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⣀⠀⠀⠀⣈⣵⣿⣿⣿⣿⣿⣻⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡷⣄⠽⠷⢿⣾⣦⣠⡼⠿⢿⣿⣿⣿⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠓⠀⠐⠊⠉⠉