Japanese culture Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡟⡗⠂⠀⠀⠀⠀⢠⣤⣿⣶⣿⣶⣾⣤⡄
⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠿⠁⠀⠀⠀⠀⠀⠀⠠⠤⣷⡇⢸⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁


⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠈⢛⣿⣻⣟⣿⡛⠁⠀⠀⠀⠀⠀⠛⠛⣿⣧⠀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣄⠠⣶⠀⣴⠄
⠀⠀⠀⠈⣿⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠾⢿⣯⠿⠻⠛⠓⠀⠀⠀⠀⠀⢀⣿⣧⣤⣼⣿⡆⠀⠀⠀⠀⣠⣌⡻⣧⣿⣾⣏⣴⠿
⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠉⠉⠛⠻⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⣴⡏⢡⡄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⢼⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠫⣽⣿⣿⡿⠂⠀⠀⠀⠀⠀⢤⣦⠄⠷⣿⣿⡿⠁
⠀⠀⠸⣿⣿⡟⢻⣿⢀⠄⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠿⠗⡂⠀⠀⠀⠀⠲⣾⠿⠶⠶⠾⠿⠶⡶⠖
⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠛⠉⠁


⠀⠀⠀⠀⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀
⠀⠀⠀⢀⣈⡷⢾⣁⣀⡀⠀⠀⠀⠀⢠⣿⣿⣏⠻⣽⣿⣿⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡤⠀⠀⠀⠀⠀⠀⣀⢠⢰⡂⡆⣲⢠⢀⡀
⠀⠀⠀⠉⢉⡷⠺⣅⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣀⣿⣿⣿⠀⠀⠀⠀⠀⠠⣤⣾⣶⣷⣧⡤⠄⠀⠀⠀⠀⣧⠾⠞⠛⠛⠛⠾⢦⡇
⠀⠀⠀⠀⠘⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠏⠇⠭⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣡⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡛⠉⡁⠀⠀⠸⣿⣿⣿⠀⠀⢀⣴⣶⡶⣄⠀⠀⠀⣰⣷⡀⠀⢠⣯⡭⡷⢙⣧
⠀⠀⠀⠀⠀⠀⢀⡃⠀⣃⠀⠀⠀⣿⣿⡟⠀⢀⣾⣤⡀⠀⣹⣆⢀⣸⣿⣿⣿⣀⠈⢯⣫⣾⣯⠟
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠴⠾⠿⠷⠄⠀⠈⠉⠉⠉⠉⠀⠙⠙⠋⠁⠙⠋⠁⠀⠈⠉⠁⡄
⠀⠀⢠⠶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⣤⣤⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠘⢄⣸⣿⣿⣿⣿⠇⠀⢀⣤⣤⣶⠾⡃⠀⣸⡶⢾⣿⠉⠑⢸⡿⢿⡿⠧⢤⣠⠖⣛⣛⣛⣛⣛⣛⣛
⠀⠀⠀⠀⠭⣽⣿⣿⡯⠍⠂⠾⠻⠯⠿⠛⠀⠀⠁⠃⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⠿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠒
⠀⠀⠀⠀⠀⠀⢹⣠⠀⡇⠀⠀⣠⠞⠉⢲⡀⠀⢠⣸⣾⣧⢖⡀⢾⡛⠃⠘⠙⣷⠆⣴⣾⣿⣤⡆
⠀⠀⠀⠀⠀⠀⡆⢠⡀⡇⠀⠴⠿⠶⠰⠼⠿⠄⠀⠈⠙⠉⠉⠁⠀⣿⣀⣄⣸⡅⠀⢹⠏⠹⡇⠈
⠀⠀⠀⠀⠀⠀⠃⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠉⠁⠈⠉⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣷⠀⠀⣠⣶⣿⡿⠿⣿⣶⣤⠀⣰⣿⣿⣷⡀⢠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠴⠶⠶⠶⠶⠐⣿⣿⠍⢶⡦⠩⣿⣿⠈⠻⠿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠻⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⠀⠤⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣅⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⠀⠀⠀⡐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠛⠀⠀⠉⠁⠀⠀⡸⠓⠈⠀⠈⢷⡄⠀⠀⠀⠀⡀⠐⠤⢈⠈⠀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⣖⡓⠀⣤⠀⠸⠆⠀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠞⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠞⠓
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣤⠴⠶⣗⣃⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣦⣦⣦⣤⠶⠤⣄⡀
⠀⠀⠀⢀⣀⠀⢰⣿⣧⡀⠀⠀⠚⣛⡟⠉⠉⢛⣛⣇⡀⠀⢸⣟⣟⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⢠⣾⣿⣆⢿⡇⡈⠃⢀⣄⣶⣯⣍⣲⡆⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠰⠉⠉⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠸⠇⠀⠿⠀⠀⠑⠀⠀⠀⠀⠀⠀⡘⣿⡆⠀⠀⠀⠀⠀⠙⠛⠋⠀⣶⣴⣶⣶⣶⣤⡆⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋
⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠀⠠⣿⣿⣿⣷⣿⣿⣦⠀⢉⣙⣋⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣽⣿⣽⣽⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣠⠶⠚⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣘⡛⠛⠛⢛⣛⣿⣄
⠀⠀⠀⠀⠀⡀⠽⣿⣖⣶⡿⠇⠈⢀⢀⠻⠃⢀⣴⣾⣿⣷⣄⠀⠀⠀⠀⣀⣈⡉⠉⢩⡽⡷⣶⣄⡉⠩
⠀⠀⠀⢠⣬⣽⣳⠮⠿⠿⢥⡉⠀⣀⠋⣢⣶⣿⣿⣿⣿⣿⣿⣷⣤⣜⣛⣯⣭⣽⣥⣀⢀⢀⠆⠉⠋⣗
⠀⠀⠀⠀⠀⠉⢿⠟⠛⠙⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣖⠚⠿⠿⡛⣷⣱⣾⣿⣷⣦
⠀⠀⠀⠘⠛⠒⣄⣠⣶⣿⣿⣿⣿⣷⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣤⣼⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠋⠀⠙⠛⠿⠿⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⢡⠐⠟⠋⠀⠙⠃⠉⠻⢿⣿⣿⠵⠚⠁⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠙⠟⠋⠉⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣤⠤⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠀⢀⣀⠟⠁⣱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠜⢩⠁⢠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⣫⣷⡏⠀⠀⠐⢻⣭⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⠟⠡⠺⠃⣴⠎⠉
⠀⠀⠀⢤⠴⢖⣿⣷⢾⠲⢤⣂⡄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⢀⣀⣙⣿⡽⠾⣛⠀⠀⠘⠉
⠀⠀⠀⠙⠽⡶⡞⣏⣿⠀⠀⠰⠆⠈
⠀⠀⠘⢷⣾⣿⣯⡵⣖⠀⠀⢀⣠⡴⠂
⠀⠀⢤⣤⣬⣧⣷⣷⣫⠀⠀⠀⢁⣀⠄
⠀⠀⠀⠉⢻⢻⢻⡏⡇⠀⠀⠀⠙⠁
⠀⠀⠰⢶⡿⣿⢻⡟⡿⠊⠄⠀⢀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢤⡀
⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣦⣔⣦⣤⣤⣤⣀⣀⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀

⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠸⣿⣿⡷⠀⠀⠀⠀⠀⣀⠤⣀⠀⠀⠀⠀⠀⢀⣺⣄⠀⠀⠀⠀⢠⡤⠏⠻⢤⣄⠀⠀⠀⢠⣶⣷⣦
⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⣴⣇⢀⣸⣦⠀⠀⠀⣀⣼⣿⣿⣄⡀⠀⠀⠈⣷⢀⡀⣾⠃⠀⠀⠐⢻⣿⣿⣿⠛
⠀⠀⠐⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠙⠋⠙⠛⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣤⣾⠿⣷⣤⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⢀⣠⣋⣉⣃⡀⠀⠀⠈⣿⣇⢛⣸⡿⠀⠀⠀⠐⠿⢿⠿⠟⠀⠀⠀⠸⠿⠻⠿⠶⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠟⠃

⠀⠀⠀⣾⠿⡆⠀⠀⠀⠀⠀⡏⠉⢱⠀⠀⠀⠀⣀⣠⣤⣤⡄⠀⠀⠀⢀⡶⠿⡛⣶⡄⠀⠀⠀⢀⣤⣤⡄⣄
⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠁⠽⣿⣿⠇⠀⠀⠀⢸⢿⡕⣋⣴⣿⠀⠀⠀⢿⡿⠿⣿⠹
⠀⠀⠰⣥⣤⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠲⠶⠿⠞⠁⠀⠀⠀⠘⠁⠈⠃

⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⣆
⠀⠠⢴⣦⣦⣶⣦⠀⠀⠀⠀⢔⠉⡂⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢀⣼⣿⣤
⠀⠐⢚⣿⣿⣿⡋⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠰⣿⠇⠀⠀⠀⠀⠀⠀⠸⠋⠓⠀⠀⠀⠀⢀⣾⣿⣿⣾⣤


⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⣶⣄⣿⡿⠷⠀⠀⠀⢴⣷⣶⣷⣀⠀⠀⠀⢀⣔⣆⣗⡴⡀⠀⠀⠀⣰⠻⠿⢳⡄
⠀⢰⣿⣿⣿⠗⠀⠀⠀⠀⠛⠃⠛⠃⠀⠀⠀⠀⠙⠉⠉⠉⠙⠁⠀⠀⠀⠈⠙⠋⠋⠁⠀⠀⠐⠻⠷⠤⠴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣄⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣤⣤⣄⣀⡀⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣀⣠⣤⣶⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣭⣻⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣲⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠙⠛⠿⣿⣿⣿⠀⠀⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠟⠛⢻⡟⠛⠿⣿⣿⣿⣿⠟⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⡄⠀⠉⠙⠉⠉⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⢻⣿⠃⠀⠀⠀⠉⠉⠉⠓⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠛⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠁⠀⢠⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠶⠂⠘⠋⠀⠀⠀⠀⠀⠒
⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢠⠀⠺⠁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠰⠆⠀⠈⢠⠀⠀⠀⠀⠀⢀⣠⣦⡀
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⡄⠀⠒⠀⠈⠀⠀⠀⢀⣴⣿⣿⣿⣿⣄
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⢀⡠⠟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆
⠀⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠈⠉⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⠀⢀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠀⡀⠀⠀⠀⠀⠀⠂⡀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁
⠰⠉⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢍⠆
⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠐⠤⠐⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⣠⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠌⠈⢿⣿⣿⣿⣿⣿⣯⡀⠈⢐⠀⠀⠀⠀⠀⠀⡀⢆⢀
⠃⠀⠡⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠒⠒⠚⠛⠒⠒⢒⣶⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠐⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⠀⠀⠀⠀⠈⢻⣿⢿⣿⣿⠿⠟⠁⡀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣦⣀⣀⠀⠙⡶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠉⠉⠉⠙⠛⠛⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠤⠀⠁⠐⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠹⣶⣶⡄⠀⠀⠀⠀⠀⠰⠅⠨⠴⢥⣀⣼⣴⣦⣥⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣷⣈⣿⡧⢖⣩⠀⠀⠀⠀⠠⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣻⠏⠉⠉⠻⣷⠀⠉⡒⡈⣭⠈⣰⢟⣩⣤⡉⠉⠻⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣿⣧⠀⠈⠻⡏⠙⢶⠀⢠⢶⣦⡀⠀⣁⠈⠰⣿⣻⢿⣿⣾⣧⠀⠀⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡤⠘⣿⣆⠈⠂⠁⠀⣤⠀⠘⠜⠟⢃⠀⣰⡷⠻⢹⠛⣧⠹⠃⢻⣶⡀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡈⠻⢷⣄⣈⠀⠶⠈⣀⣿⠗⠀⠀⠋⣤⣤⣀⠀⠈⡔⠛⠢⠘⠛⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⢦⣉⠘⠈⣁⢿⡼⣇⣢⣿⠇⠘⡆⣠⡏⠀⠀⠈⠛⠻⣯⣥⡤⠀⠹⠶⠯⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠍⠈⠁⠀⢘⣷⣿⡿⢡⠀⢂⠳⠽⡇⠀⠀⠈⡀⠂⠀⠙⢻⣀⣀⠀⣤⢷⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢸⠀⠀⢰⡦⢄⢉⣗⡬⠃⠀⠀⠀⠀⠀⠙⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢸⡆⠀⠀⢻⠠⠞⠷⣟⢣⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠆⠻⡄⠀⠹⠰⣶⣤⡜⢯⣝⣧⣒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣄⣂⠀⠀⠀⠀⠙⣯⣿⣶⣿⣯⢹⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡀⣹⢻⣿⣿⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢂⣟⢺⡏⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣡⠛⢸⡇⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢅⣿⣀⡾⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠠⣤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⢠⠄⠴⠄⢠⠠⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠠⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⡏⢉⡀⢀⢀⠀⡀⡀⢀⡀⢀⠀⢀⣀⡀⡀⡀⠀⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⡄⠀⣀⡷⣏⢸⢸⢸⢧⡁⡆⡄⠀⢾⠐⠛⢣⣼⡇⠛⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡀⠀⠀⠁⢀⣉⡁⠈⠉⠘⠉⠀⠉⠁⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣧⡀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⠌⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈
⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠉⠀⠘⠀⢀⡀
⠀⠀⠋⠀⠀⠘⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢀⡠⠤⠄⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡜⠁⠀⣀⠀⠙⣆⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡇⠀⢘⠿⡄⠀⣹⠀⠀⠒
⠀⠠⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⠀⠀⠀⠤⠀⠀⠘⣤⣂⢀⣠⡜⠃⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡄⢠⠃⠈⠈⠀⠹⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⠋⠆⠀⠆⠀⠲⠑⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣤⣤⣤⣤⣬⣬⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢈⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠚⠻⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⢸⣿⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⠋
⠀⠀⠀⠀⠀⠀⠀⣾⡁⠁⣹⡆⠉⠈⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠠⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣷⣷⣷⣶⣾⣓⣲⣤⣄⡀⠀⠃⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠒⢀⡀⠀⠀⡿⣿⠷⡇⠀⠀⡀⠐⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢠⠖⠒⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⣶⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⡀⠈⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣷⡘⢿⡡⠂⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⣆⢸⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣉⣙⡙⠻⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡿⠆⠙⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⡧⠀⠀⢤⡖⢬⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿
⠀⠀⠀⠀⢹⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣷⣷⣦⠀⠀⠀⣀⡀⠰⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠁⢠⣤⠀⠀⠀⠉⠻⠿⢿⣿⣿⡧⠀⣶⣮⣅⢨⣅⢈⣃⡄⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠲⡠⣄⠛⠿⣿⣷⣶⣿⡿⠃⠀⠀⠘⠁⠀⠀⠀⠘⠋
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠆⠀⠈⠛⠛⠁⠠⠆⠀⠀⠀⠀⠀⠀⠀⣀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆
⠀⢼⣿⣿⠟⢠⡐⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢠⡄⠀⠀⠀⠐⠀⠀⠻⠛⠋
⠀⠘⠋⠁⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⠀⠄⢀⠀⠀⠀⠀⠀⠘⣿⣧⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⣦⣈⡈
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠚⡀⣀⠿⣿⣿⣿
⠋⢁⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣰⣿⣾⣿⣿⣷⣄⠀⠀⠂⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠘⠀⣀⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⢀⣤⣭⣽⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠈⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠂⡠⠤
⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠀⠀⠈⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠻⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⣤

⠀⠀⠀⠀⠀⠀⠒⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠲⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡔
⠀⠀⠀⠀⢀⠀⠀⠐⣀⡀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⢿⡿⠛⠛
⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠺⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⡿⠛⠛⠛⠛⠛⠛⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⢀⣀⡠⢠⣆⣴⢰⣆⣤⣄⣢⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⢀⣴⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣦⣄⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠿⢿⣹⣿⠿⠞⡿⢻⣿⣻⣿⣿⣻⣿⠿⢿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣛⣿⣷⡐⢠⠀⠀⠐⠘⠻⠃⠀⠐⠂⠋⠙⠛⠛⠻⠛⠉⠉⠀⠀⠙⠁⠀⠀⠈⠉⠉⠉⠉⠉⠑
⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⢿⡿⢿⣿⣿⣷⠀⠀⠠⡆⢀⠠⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠃
⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠈⣻⣿⡟⠀⠀⠀⡛⠁⠀⠀⣠⣤⡉⠒⠀⢲⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⡇⠀⠀⠀⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠄⡀⠀⠀⠄⠀⠀⠀⠀⠁⠶⣿⣿⣿⣶⣤⣀⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠏⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠈⠻⠿⣿⢿⣄⠀⠆⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⠊⠉⠙⠉⠩⠒⠀⠀⠀⠀⠀⣤⣤⡜⠁⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠄⠀⠀⠀⠀⠀⠠⠌⠡⡀⠀⠀⠀⠀⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠢⠀⠀⠀⡀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⣄⣛⣃⣀⡄
⠀⠀⠀⠀⠀⢸⣿⡶⠀⠚⠐⠪⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢂⠔⠀⠀⠀⠁⠀⠐⠂⡐⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠰⡎⣁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠲⠨⡀⡘⡀⠈⠠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣠⠁⠈⠀⠀⠀⠀⠀⠐⠄⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢤⡄
⠀⠀⠀⠀⠀⠀⠸⠳⢶⠶⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⡀⠀⣀⣠⡤⠶⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠃⠀⡠⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠼⠛⠋⠉⠉⠛⠛⠓⠲⠶⠶⠀⣤⡀
⠀⠀⠀⠀⠀⣴⠀⠀⠀⢗⣐⡈⢰⣆⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠈⢨⣦⡀⠑⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⢀⠀⣀⡄⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⣿⠀⠀⢗⠀⠀⠈⠀⢿⡆⠀⠀⠐⣀⠈⢉⣠⠃⠀⠀⠀⠑⣴⠄⠈⠛⢦⡀⠀⠀⠀⠀⠀⢀⠀⠶⠖⢀⣾⣷⣬⣭⣥⠆⠀⣷⣬⣭⣥⡾
⠀⠀⠀⠀⠀⠁⣀⣤⣬⠦⠤⢄⣀⡺⠀⠀⠀⢠⣌⣉⣉⣡⡾⠀⠀⠀⠀⠈⠚⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⡿⠀⠀⠿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣉⣭⣶⣶⢶⣦⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣿⣿⣿⣿⣿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⡟⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠀⡁⣀⣀⢄⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢀⠅⣀⡀⠀⠀⠋⠀⠀⢈⡉⠚⠠⡌
⠀⠀⠀⠀⠀⠀⠏⠀⠠⠄⡀⠡⠒⠈⠉⠉⠈⠑⠠⡈⠓⣀⠠⠲⠤⡀
⠀⠀⠀⠀⠀⠀⢥⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠠⡄⠘⠤⠁⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⢀⡂⠈⠀⢄⠀⢠⡄⠀⢱⠀⠀⠀⠀⠉⡠⠔⠛⠦⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠘⡇⠀⠀⠈⠆⠀⡁⠀⠀⢣⠀⠀⠀⠸⠶⠤⣀⠀⠈⠠⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢃⠀⢸⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠓⠲⠆⠄⣙⠓⠶⢌⣢⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠸⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⣀⠀⠀⠈⠁⠒⠤⠈⡅⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠈⠀⣈⠀⢦⡀⠀⠀⠙⣠⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢠⠁⠂⠀⠫⠟⢝⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠐⠁⠀⠻⠀⠀⠉⢡⠡⠀⠠⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠈⠢⠠⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⠀⠆⠣⠀⠰⡈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢀⣀⠔⠀⠀⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⡘⠄⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢻⠀⠀⠀⠀⠀⡡⠔⡡⢀⠎⠁⠀⠀⡄⠀⠀⠀⠀⠡⠀⠄⠡⠈⢦⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠀⢋⠀⠊⠀⠁⡀⠀⠈⠀⡅⠀⠀⠀⠀⠀⣁⢈⠄⢡⠘
⠀⠀⠀⠀⠀⠰⠊⡀⠀⠀⢠⠀⠀⠰⠖⠁⢀⠀⠀⠐⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠄⢠⠂⠄⠃
⠀⠀⠀⠀⢸⠀⠀⢡⠀⠀⠀⣅⣀⡤⠤⠒⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢀⡠⠚⠁
⠀⠀⠀⠀⠈⠀⠀⢀⠂⠀⠀⠈⠁⣀⠔⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠉⢀⠤⠒⠁
⠀⠀⠀⠀⢀⠀⠀⠀⢢⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠓⠀⢀⠀⠀⠀⠀⡀⠴⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⢀⡔⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠳⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣧⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠵⡶⠾⠑⠦⠐⣶⡎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⡴⠀⢀⠀⠀⢠⠀⠀⢠⠀⠈⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡀⠀⠀⠀⠐⡀⠀⠐⠤
⠀⠀⠀⠀⠀⠑⡤⠐⢹⡃⠀⠀⠑⠂⠀⠀⠀⢇⣀⣥⠀⠀⠀⠐⠂⠀⠀⠲⢆⠝⠁⠀⠀⠀⠉
⠀⠀⣠⠇⢠⣁⠂⢠⠟⠀⠀⠀⠀⣀⡀⠀⠀⠈⠝⠁⠀⠀⠀⢀⣀⣤⣀⣀⣀⣀⠂⠀⠙⠏⠺⠒⢐⠂⠑⠀⡀
⠀⠊⠁⠀⠈⠉⠀⠘⠀⠀⠺⣕⢦⡈⠀⠔⠀⠀⡀⠀⠀⠲⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠃⠀⠈⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⡃⠀⡾⠆⠀⠀⠀⠰⠀⠀⠀⠈⠲⠒⠲⢒⢞⠁⢈⣧⣥⡀
⠀⠀⢀⣀⡀⠀⠀⠀⠚⠘⠂⠀⠐⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⠵⢾⠀⠀⠀⠠⠀⠀⠀⠄⠀⠟⣽⣄⢻
⠀⢀⣄⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢡⠃⠸⡈
⠀⠀⠀⠀⠀⠀⠂⠤⠄⠂⠆⠀⠀⠀⠉⠀⠀⠀⠀⠀⣲⡄⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠠⢄⣀⠈⠋⠙
⠀⠀⠀⠕⠂⠀⠀⠶⠤⠆⠀⠠⡶⠀⡄⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣀⡋⣨⣭⣧⣤⡉⣫⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠆⡀⠐⠐⠀⠡⠅⢤⠼⠿⢤⠄⠥⠅⠸⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣤⡀
⠀⠀⠙⠂⠀⠀⠀⠈⣺⡧⠂⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢦⠘⢃
⠀⠀⠀⠄⠀⠀⠀⠀⠌⠁⠀⠀⠀⢀⠀⠤⢀⠀⢸⠀⠀⢈⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠐⡆
⠀⠀⢈⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢰⡀⡽⢔⣷⠀⠀⢄⣁⣀⠀⠀⢀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⡄⠀⠀⠰⠂⠀⠀⡀⠠⠜⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠊⠈⠀⠀⢀⠄⠀⠠⠄⠀⠒⠀⠈⠐
⠀⠀⠁⠀⠀⠀⠉⠀⢠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠄⠀⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣻⣿⣏⡷
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠐⢠⣶⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⡀
⠀⠀⠀⠀⣀⣀⡀⠰⡟⠀⠀⠀⠀⠀⣰⣿⠛⠛⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⡀
⠀⠠⣾⣯⣽⣿⡿⠂⢳⠀⠀⠀⠀⠀⠈⠁⠉⠀⠈⠀⠋⠀⢀⠚⠀⠀⠀⠀⠈⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⣠⢞⣿⡯⠟⠀⠀⠀⠀⠐⠄⠰⠀⠀⠀⢨⣄⠀⢀⣤⣤⣤⣤⣄⣀
⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠘⠂⠀⠁⠀⠘⠻⠿⠿⢿⣥⡽⠇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡴⠶⠶⣤⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢿⣷⣾⠇⠀⢀⠀⠀⠀⠀⠋⠀⠀⠈⠀⠛⠀⠀⠀⠀⣿⡘⠀⠰⢈⣧⠀⠐⣃⠘⠃
⠀⠀⢀⡠⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣠⣐⣀⣀⣒⣀⣀⣀⡀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠈
⠀⠤⠀⠁⠋⠀⠀⠀⠀⠀⠀⢠⣿⡯⡽⠋⣿⢩⡟⡙⡿⡙⣽⡇⠀⠀⠉⠉⠉
⠀⠀⠘⠃⠀⠀⠀⠀⠀⡀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠒⠒⠒⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠿⠶⣶
⠀⢠⣶⣖⣛⣟⣟⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠻⠾⢂⠀⢀⣤⠀⠀⠀⠀⢀⣀⠀⠁
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠲⠾⢿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠴⠖⠚⣷⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⠀⣆⠀⣿⢋⠕⠛⠓⢯⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡷⠼⠀⠀⠀⢈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢰⡇⠀⠀⢀⡠⢎⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣾⡴⣒⣫⣥⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣩⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠉⠉⢳⠀⠀⠀⣶⣀⠀⠀⠀⢀⣆⣸⣁⣉⣽⠿⠛⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠉⠁⠈⠣⢤⣄⣙⣒⣒⣪⣭⣭⠷⠛⠈⠁⠈⠉⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢶⣖⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⢖⣲⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠒⠒



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢰⠏⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠘⢷⡄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠸⠇⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⡶⠛⠉⠁⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠙⠳⣄⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⣶⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣻⣭⣭⠹⣦⠀⠙
⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠈⣿⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⣿⠿⠿⠛⠛⠛⠋⠉⠁⣸⠏⠁⠀⣸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣤⠶⣿⢦⣄⠀⠀⠀⠀⠀⢠⣿⣠⡴⠟⣡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢻⣆⠄⠀⠀⠀⠀⠀⣿⠀⠋⠀⣿⠀⠀⠀⠀⣠⣿⣩⣥⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣙⣧⡀⠀⠀⠀⠀⣿⣀⣀⣀⣿⠀⠀⢀⣴⣟⡉⠁⠀⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠉⠉⠙⠷⢦⣤⣤⣬⣥⣭⣭⣤⡤⠶⠋⠉⠉⠙⠛⣦⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⢤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⡟⠛⠛⠂
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⣠⣄⠀⠀⡾⠁⠀⠀⠀⡇⢀⣤⡄⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡇⢸⡇⢿⠀⢠⡇⠀⠀⠀⢿⢈⡇⠰⡷⠄⠀⠀⠀⡇⠸⣷⣃⡸⣷⢷
⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠶⠛⠀⠻⠞⠁⠸⡗⠋⠀⠀⠀⠀⠈⠋⠀⠀⣷⠀⠀⠀⠀⠃⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠛⣦⡄
⠘⢶⡶⠶⣶⠞⠂⠀⠀⠀⠀⠀⠀⠀⢸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣰⣆⣤⠀⠀⠀⠀⠀⠀⠡⠀⠌
⠀⢻⡟⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⡠⢺⠜⠁⣦⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣾⣧⡛⣼⣷
⠀⠈⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠘⠛⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⡄⠀⠀⠀⠀⠀⠀⢠⣄⠀⣠⡄
⡠⢤⣴⣿⣧⣴⠆⠀⠀⠀⠀⠀⠒⢼⠤⠤⠴⡇⠂⠀⠀⠀⠀⠀⠀⠉⣡⠶⣦⣷⠀⠀⠀⠀⠀⠀⠰⣿⣶⣿⡆
⠑⢾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣹⣋⣙⣋⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡄⠀⠀⠀⠀⠀⠈⠉⣿⠉⠁
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀
⠀⠀⢬⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿
⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⢠⡈⠀⠀⠀⢅
⠀⠐⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠉

⠀⠀⣠⣤⡄
⠀⣴⠿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣠
⠘⠏⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⡀⠶⣆⣀⠀⡀⠀⠀⠀⠀⠀⠀⣲⣽⣿⣯⣖⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿
⠀⠠⣔⠑⣦⠄⠀⠀⠀⠀⠀⠀⠊⠛⠶⢮⡜⠫⠀⠀⠀⠀⠀⠀⠀⠴⣻⣿⣟⠮⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣶
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣀⠀⣿⣿⡿⠀⣀⠀⠀⠀⠀⠀⠀⢾⣷⣻⣿⣼⡷⠀⠀⠀⠀⠀⠀⠀⣠⢼⡁⣹⢦⡀
⠀⠀⠀⣿⣿⣷⠀⣉⢀⣾⣿⣿⠀⠀⠀⠐⠿⢷⣿⢟⡻⣿⣾⠿⠂⠀⠀⠀⢠⠖⢷⣤⠟⢷⣤⠟⢦
⠀⠀⠀⠈⢉⣁⡈⠛⢑⣈⡉⠁⠀⠀⠀⠰⣿⢿⣿⣿⣿⣿⡿⣿⠆⠀⠀⠀⠈⠳⣞⢙⣷⣟⢙⡷⠛
⠀⠀⠀⠀⢿⣿⡿⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠿⠟⣿⣿⠻⠿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⣽⠋⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣿⣿⡦⢀⡀⠀⠀⠀⠀⠀⠀⣠⣶⣄⣴⣶⣀
⠀⠀⠀⠀⠀⢀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⣾⣿⡿⡿⠿⢿⣿⣷⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣽⡿⠃
⠀⠀⠀⠀⢀⣶⡀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠛⣻⣿⣦⣴⣿⣟⡛⠀⠀⠀⠀⠀⣴⣿⣿⣷⣿⣿⣷⡄
⠀⠀⠀⠠⠿⠿⠿⠤⠿⠿⠿⠄⠀⠀⠀⠀⠘⢿⣿⡿⢻⣿⡿⠃⠀⠀⠀⠀⠀⠈⠙⠿⠋⠻⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠞⠋⠉⠛⠳⣄⠀⠀⠀⠀⠀⢀⣴⠟⢻⡟⠻⢦⡀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣧⣀⣀⡀
⠀⠀⠀⢰⡿⠿⠿⠿⠿⠿⢿⡆⠀⠀⠀⠀⣾⣅⣀⣸⣧⣀⣨⣷⠀⠀⠀⠀⠀⠘⣿⣿⠟⢿⣿⡟⠁
⠀⠀⠀⠘⣿⠿⠿⠿⠿⠿⣿⠃⠀⠀⠀⠀⢻⣄⠀⢸⡇⠀⢠⡟⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⣿⡄
⠀⠀⠀⠀⠈⠳⠶⠤⠶⠞⠁⠀⠀⠀⠀⠀⠀⠙⠷⠾⠷⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏

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

⠀⠀⠀⠀⢠⣤⡄⢀⡀⠀⠀⠀⠀⠐⣶⠆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⣼⣿⠘⣿⣅⠀⠀⠀⠀⢸⣿⢇⡀⠀⠀⠀⠀⠀⢺⠉⠛⢻⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠐⠦⠔⠚⠻⠄
⠀⠀⠀⠀⠉⠉⠀⠿⠿⠂⠀⠀⠀⠘⠛⠋⠃⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣻⣿⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣄⣀⣀⣀⡄⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⢘⡼⠒⠒⠒⢽⡂⠀⠀⠀⠀⠀⠔⢀⡐⠄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⣯⣯⣿⠀⠀⠀⢴⣾⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣦⠀⠀⠀⠀⠀⠙⢿⣿⣦
⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣶⣶⣦⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⠛⠁⠀⠀⢰⠀⣀⠐
⠀⠀⣀⣤⠀⠀⠀⠀⠀⠠⣦⣶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠠⠀⠀⠀⠀⢀⡀⢆
⠀⠀⡟⠋⢀⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢆⠀⠀⠀⢀⣀⣴⣄⣀
⠀⠀⠁⠰⠿⠃⠀⠀⠀⠀⠀⠁⠀⠀⠐⢾⡷⣥⣶⡄⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠈⠋⡀⠀⠀⠀⡇⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠋⠁⠀⠀⠀⠀⠀⠐⠖⢯⠗⠖⠂⠀⠀⠀⠀⠀⠀⠀⠁⠃
⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠻⣤⠞⠁⠀⠀⠀⠀⠀⠀⣤⣀⣀⣤⠀⠀⠀⠹⣵⢄⡀⠀⠀⠀⠀⠐⣿⢀⣾⣀⠀⠀⠀⣶⣶⢤
⠀⠀⠀⠀⢠⠞⠁⠱⡦⠀⠀⠀⠀⠀⠀⠈⠉⠍⠁⠀⠀⠀⠀⠈⠺⣷⡄⠀⠀⠀⠀⠻⠿⠿⠏⠀⠀⠀⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢸⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠸⠁⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⢀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠊⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢄⣀⠀⠐⠈⠉⠁⠀⠒⠒⠒⠛⠓⠲⠶⠀⠉⣉⣀⠴⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠀⠀⠐⠐⠒⠒⠛⠋⠉⠉⠉⠁⠀⠀⣸⡥⠔⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⢠⡏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣉⡉⠉⠉⠉⠀⠀⢀⡾⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⡖⠁⠀⠈⠀⢹⡆⠀⠀⠀⢀⡾⠁⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠳⣄⠀⠀⡠⠞⠁⠀⠀⢀⣾⠡⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣄⣀⣀⣀⣀⣀⡤⠘⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⢠⡿⠁⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠘⢷⣄⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠈⢻⡆⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠟⠁⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⣠⣶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⢀⣀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣄⣀⠀⣸⣷⣤⡶⠶⠶⣶⣄⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⡶⠶⠿⣶⡄⢻⡆
⠀⠀⠀⠀⠀⠀⠤⣤⣤⣤⡄⠀⠀⠀⢻⣇⠀⠀⠈⠉⠙⠛⠛⠛⠛⠻⠿⠿⢿⡿⠿⠛⠛⠛⠛⠋⠉⠉⠀⠀⢃⣿⠃⠀⠀⢀⣾⠇⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⢄⣼⡏⣀⣤⡶⠟⣁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠸⡗⠈⣿⡇⠀⠀⠀⠀⠀⠀⣴⡿⠟⠛⣉⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠄⠀⠀⠀⠙⣷⣎⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣼⣿⡷⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣦⡀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣿⡇⠀⠀⢀⣠⣾⣏⣀⡀⠀⠀⠀⠀⠀⠀⠀⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠉⠉⠉⠻⢷⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⡶⠟⠋⠉⠉⠙⠛⠷⣦⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣄⣀⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣀⣤⣤⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠿⠿⠿⠷⠶⠶⠶⠾⠿⠿⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⡟⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡶⠀⠀⠀⠀⢸⡇⠀⢀⣀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⡄⠀⣴⠀⣾⠛⠛⢻⡇⠀⠀⠀⠀⣼⠛⢷⡀⠀⣿⠀⠀⠀⠀⠀⢸⡇⢀⡟⣹⠆⢀⡾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢀⣀⠈⣧⢀⣿⡀⢻⡄⢀⣼⠃⠀⠀⠀⠀⢸⣆⣼⠃⠘⣿⠛⠀⠀⠀⠀⢸⡇⠈⢿⣯⣤⠌⠷⠟⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢶⡶⠶⠛⠁⠀⠻⠟⠉⠁⠘⣿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢹⡄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠿⠖⠿⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⠀⠀⠀⠈⠰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢁⡀⠨⠗⠀⠐⠒⠂⠀⠀⠠⣿⠯⠚⠀⢘⣯⡄⠀⠀⠀⠀⠀⠀⠤⣀⠰⠐⠀⠁⠂⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣼⡀⠀⡀⠀⢠⡌⠉⠀⠀⠀⠀⠈⠰⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⣆⣴⠏⠀⠈⠀⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡀⣤⡄⠀⠀⠀⠀⣸⣟⣩⣽⡿⣶⣀⣀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠠⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⣉⣳⣦⣤⡀
⠀⠀⠀⢀⣄⡄⠀⣽⣿⣷⡄⠀⠀⠈⠩⣭⡅⠀⠀⢩⣭⣭⠄⠀⠀⢼⣽⣯⡿⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⣾⠿⢿⡆⢿⠄⡠⠃⠀⣴⣴⣿⣧⡌⣷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⡳⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤
⠀⠀⠀⠿⠀⠰⠇⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠸⣿⡦⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⣶⣤⣶⣶⣶⣦⣤⡃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠋
⠀⠀⠀⠀⠠⠆⠀⠀⢐⠀⠀⠀⠀⠀⣴⣷⣿⣿⣵⣿⣶⣦⠀⢘⣛⣛⡛⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠘⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⢠⠀⢃⠁⠟⠀⠙⠆⠴⠄⢀⠀⣀
⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣀⠺⠷⠝⠆⠃⢸⡟⠐⠛⢲⠦⢾⣬⠉⣥⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠹⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠶⠼⢗⣟⣉⣠⣋⡛⣾⢷⣀⡼⠣⣖⡸⠛⠀⢙⠿⣟⣭⡖
⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⢮⡽⠻⠟⢻⣧⣭⡤⠿⠗⣶⡿⠿⠛⣻⣿⣷⡟⢿⡁
⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢠⠟⢁⡀⠵⠸⣿⠉⠉⣀⠫⠜⢏⠀⣙⢿⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣶⣶⣦⣶⣶⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠘⠀⠚⠁⠘⠈⠛⠑⣿⣭⣑⢎⠰⠝⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠘⠛⣻⠻⣄⠘⣿⡀
⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠓⠂⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠻⣦⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀
⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣷⠤⠀⠀⠀⠀⠀⢠⣾⣿⣿⣄⠠⠀⠀⠈⠃
⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⠿⣿⠿⠟⠁⠀⠀⠀⠀⣀⣸⣿⣿⣶⣶⠀⠀⠀⣠⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠰⢾⡷⠶⠛⠳⠶⣿⠶⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⡉⠀⠀⠀⣀⣿⣿⣿⣯⣤⠀⠀⠀⠀⣼⣿⠿⠿⠿⣿⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠏⠉⠁⠀⠀⠀⠈⢿⠿⠿⠿⠀⠀⠀⠀⠀⠻⡿⠀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⢀⣤⣾⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⢀⡀
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠛⠀⠀⢸⡇⠀⠀⠚⣿⣟⢛⡿⣿⣿⣛⣷⣾⣿⣶⡄⠀⠀⠀⠀⠀⢀⣴⢿⣹⡏⣿⣿⣾⣽⢧⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠛⠛⠛⠛⠓⠀⠈⠙⢯⣍⠉⠁⠀⠀⠀⠀⣤⣻⢮⣷⣳⣿⡿⡟⡻⣳⣿⡽⣳⡀
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣠⠆⠀⠀⢸⡇⠀⠀⠀⠀⠶⠶⢾⣿⣷⡷⠶⠶⠿⠿⣿⣿⣿⣦⠄⠀⠉⠓⠿⢃⣴⣶⣶⣮⠛⠓⠋⠁
⠀⠀⠀⠀⠀⠘⣿⣰⣶⣌⡿⠀⠀⠀⠘⡇⠀⠀⢠⣤⣤⣄⣀⣀⣴⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣄⣀⠀⠀⠈⣿⠀⠀⠀⠉⠛⠛⠛⠛⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡾⣷⡆⣾⡿⢿⣷
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣾⡸⡇⣿⢹⣏⣿
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⣧⣿⣇⡇⣏⣿⣿⣹
⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢿⣿⣿⡿

⡶⣶⢶⢶⠶⠶⢶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⣶⣶⠶⣶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠤⠀⡀⠀⠀⠀⠀⠤⢄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀⠒⠐⢂⡉⠉⢄⠉⠐⡆⠤⣀
⠀⠀⠀⠀⠄⣄⣠⣀⣀⣀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢅⡀⠀⣤⠀⠘⣖⠀⣸⣆⡀⣸⠄⢻⠲⡀
⠀⠀⠀⢁⠚⢸⡃⡩⡆⠀⡗⠁⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⢰⠎⠉⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⡀⠈⠳⡂⠸⠒⠈⠉⠐⠀⠈⠁⠈⠑⢇⣰⠅
⠀⠀⠀⣖⣂⡯⠀⢴⡁⣨⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⢲⡀⢂⡸⠀⢘⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠅⠀⠠⠄⠀⠀⠀⠀⠐⠂⢈⠈⠋
⠀⠀⠀⢠⡠⠕⢞⡷⣿⡿⢾⡀⢨⠀⠀⠀⠀⠀⡆⢃⠡⠴⠀⠘⠾⠇⠀⠉⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠐⠂⠀⠀⠐⠀⠀⠄⠆
⠀⠀⢠⠈⠲⠆⠘⠉⠻⠛⠉⠠⢀⠠⠀⠀⠀⣜⠩⠀⠾⣀⣀⡀⠀⠀⠀⠎⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡁⢀⠀⠀⠀⠉⣿⠀⠀⡌⠱⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠇⠈⢰⡯⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂⠘⠉⢁⢈⠁⢈⢐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢄⣹⢤⠛⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠜⠁⡌⡄⠘⠈⠢⠈⢸⣄⢀⡸⠀⠀⣸⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⡅⠀⠀⡴⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢦⠀⢇⠀⡨⠤⠄⠉⠀⠀⡘⠉⠙⢀⠙⠷⠺⢍⡔⠠⢤⡀
⠀⠀⠀⠠⡎⠀⠰⠃⠀⡠⠁⠀⡴⠁⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠘⠉⠉⢃⠐⠀⠀⠡⠂⠀⠴⠂⠈⠀⠐⠀⠀⠀⠙⢦⣀⡴⠆
⠀⠀⣿⠀⠉⡒⠚⠁⠒⠓⠄⣠⠃⠀⡞⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣾⡀⢠⠄⡘⢤⣶⢀⡄⢹⢀⠜⢁⡼⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠙⡀⠘⠀⡹⠂⢠⠚⠃⠘⡧⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠁⠐⢤⢱⠈⠰⡤⠠⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⣘⠁⠀⠀⢸⡇⠀⠐⠉⠂⠖⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣌⠁⠀⠀⠀⠀⠀⠀⠐⢄⣀⡀⠀⡇⠀⠀⠀⢸⠤⠬⠿⠻⠃⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠗⠛⠛⠛⠂⠹⢻⠀⠀⠀⢸⠙⠈⠳⠚⢃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢺⠤⢮⠹⢟⣂⣀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⠀⣄⠀⠨⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⣴⠩⠗⣈⡑⢦⠈⢂⡬⡀⡎⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⠂⠈⠱⡀⠀⠀⠀⠀⠀⠅⠈⠚⠤⠝⠘⠏⠹⠀⠎⠐⠑
⠀⠀⢀⢀⠀⣁⣉⠉⠙⣏⣩⡟⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣄⡄⠀⡀⢠⡄⠀⣴⢀⢠⡄⡀⢀⡖⠲⢰⡆⠢
⠀⠀⢸⠀⠀⠉⢠⣷⣋⠉⠁⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡹⣿⠞⣋⡉⢶⠄⢉⣴⠒⣁⣤⠉⠀⠄⣊⢨⠟
⠀⠀⠀⠀⠀⠰⢸⡥⠐⠙⠿⠍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠄⠘⠆⠀⠀⡜⠀⠀⢰⠈⠘⡆⢵⢀⢰⠃⠛
⠀⢀⠀⠀⠠⠀⠉⠀⠈⠀⠀⠀⠀⠰⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠱⠀⡴⠀⠀⠀⠃⠀⣠⠃⠀⠐⡀⠀⢟⠃⢸⠂
⠀⠀⠂⠄⠀⠀⠀⠄⠀⠀⠀⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠰⠁⡴⠁⠀⡔⠁⣠⠀⠁⣀⠊⣼⡅⡠⠴⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⡁⠠⠌⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂
⠀⠀⠀⢀⣀⠀⠈⠀⠀⠀⢀⠔⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠂⠀⠀⠠⠀⠄
⠀⠀⠀⠄⠌⠐⠆⠁⠠⡀⠃⠀⣠⣶⣿⣷⡆⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⣿⡀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠁⠄⠈⡈⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢴⣾⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢷⣶⣀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠰⢀⠄⠒⢊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠦⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡾⠴⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠤⠥⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠆⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣨⣯⡭⠽⠷⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡭⠀⠋⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⣀⡶⢆⡀⠀⠲⠶⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤
⠀⠀⠀⠀⠀⠺⠺⠷⠿⠇⢿⣄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣧⠹⢟⠤⠀⣰⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣬⢟⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢱⡄⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣤⣶⣴⣤⣱⣦⣶⢤⣄⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠶⠿⠗⠀⠃⠐⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠷⠿⠿⠿⠶⠷⠷⠴⠤⠿⠥
⢀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠱⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠟⢠⠂
⠀⢠⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⣇⠀⡀⠹⢦⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠈⠁⠉⠀⠀⠀⣦⣤⡄⡀
⠀⣏⠀⢱⣶⠀⣧⠀⢸⠁⣄⠀⠀⠀⠲⢿⣷⣶⣾⣿⣿⣛⣛⣛⣻⣛⣿⣿⣷⣶⡾⠟⣃⠸
⠀⠹⣦⡄⢹⣶⡻⠀⡖⣠⡘⢆⠀⢴⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣻⣿⠁⣆⣲⣦⣄⢲⡀
⣀⣀⣈⠳⣄⣹⡇⢰⠃⣿⡇⢸⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⠋⠁⠀⡼⣸⠇
⠘⡍⢶⣄⣩⣭⣽⣿⣦⣿⣧⠟⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠇⣎⣠⠴⢊⣼⠟
⠀⠈⠢⣀⠜⠋⠹⠛⣿⠿⣁⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛⣸⢋⣤⠾⠛⠁
⠀⠀⠀⠈⠐⠒⠒⠁⠀⠀⠙⠷⠆⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⠏⡰⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢾⣒⠁⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣫⣞⠓⢤⣤⣐⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠀⠉⠙⠋⣆⠰⢍⡛⠷⠶⠶⠶⠶⠾⡿⢿⣿⠿⠋⠻⢂⠽⠂⢉⣆⡕⠀⠀⢀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣀⣤⡴⣞⡋⠠⡆⠀⢀⠀⢀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣻⣲⣿⣻⣿⣻⣻⣿⣷⣿⣿⣿⠿⣿⠛⠋⠉⠀⠀⠉⠙⠣⡀⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣏⠙⠶⣤⣤⠤⠴⠒⠚⣷⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣿⡀⠀⠀⠀⢀⣽⣬⠿⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠮⣿⣷⣠⠤⠚⠋⠁
⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠸⠄⠀⠘⠇⠀⠸⠀⠀⠐⠂⠀⠀⠇⠀⠘⠀⠀⠸⠀⠀⠐⠇⠀⠀⠶⠀⠀⣶⠀⠠⡄⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠐⠒⠀⢀⡀⠀⢀⠄⠀⠀⠀⠀⠀⡆⠀⢀⡄⠀⢠⣤⠀⢠⣄⠀⠀⠀⠀⠀⡁⠀⢈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠆⠀⢀⡀⠀⠀⠀⠀⠘⠁⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠳⠀⢀⡀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠠⠠⠀⠈⡁⠀⠀⠄⠀⠀⠓⠀⠀⠄⠀⠀⠁⠀⠀⠛⠀⠀⠙⠄⠀⣶⡀⠀⠃⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢈⡁⠀⢠⡄⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⢀⠀⠀⠐⠒⠀⠀⠶⠀⠀⣠⠀⢀⡶⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢈⡀⠀⠀⣀⠀⠀⠇⠀⠈⠀⠀⠀⠁⠀⠀⠁⠀⠀⡄⠀⠀⠃⠀⠀⣶⠀⠀⢉⠁⠀⡦⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⢀⡄⠀⠀⡄⠀⠀⠆⠀⠀⠀⠀⠐⠢⠀⠐⠃⠀⠀⠀⠀⠀⡿⠀⠀⢄⠀⠀⠾⠀⠀⡉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠁⠀⢀⠁⠀⠀⠀⠀⠈⠡⠀⠀⡀⠀⠀⠆⠀⠐⠓⠀⠀⡆⠀⠀⣉⠀⠀⠶⠀⠀⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠀⠠⡄⠀⢰⠆⠀⠀⡀⠀⢠⡄⠀⢸⠂⠀⠀⡄⠀⠀⠛⠀⠀⢤⠀⠀⡆⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠓⠀⠀⠀⠀⢀⡀⠀⠀⡄⠀⠀⣁⠀⢀⡀⠀⢀⠄⠀⠀⡑⠀⠐⠰⠀⠀⠉⠀⠀⡄⠀⠰⢧
⠀⠀⠀⠀⠀⠀⠀⠈⣉⠀⠀⠃⠀⠀⠆⠀⠀⡀⠀⠀⠁⠀⠀⠁⠀⠈⡁⠀⠀⡆⠀⠀⠧⠀⠀⣀⠀⠸⠿⠀⠀⡌⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠘⠓⠀⠀⠃⠀⠀⠁⠀⠈⠀⠀⠀⡆⠀⠀⣉⠀⠀⠙⠀⠀⠶⠀⠈⠉⠀⢀⣦⠀⠀⣉⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠗⠀⠀⠀⠀⠘⠂⠀⠀⠐⠀⠀⠁⠀⠀⠉⠀⠈⠉⠀⠀⠲⠂⠈⠘⠀⠀⠀⠀⠈⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⢎⠁⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠓⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐
⠀⠀⠀⠀⠃⠀⠂⢀⠀⠐⡆
⠀⠀⠀⠠⠀⠂⣀⡘⠀⢈⣀⠀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⢠
⠀⠀⠀⠤⠐⠂⠑⠀⠠⠈⠋⠀⡀⠈⠉⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡐⠾⠀⠀⠀⠀⠐⠀⠀⠀⠀⣠⣶⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠝⠿⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢈⣽⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠚⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⢸⣿⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⠋
⠀⠀⠀⠀⠀⠀⠀⣾⡁⠁⣹⡆⠉⠈⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣤⣶⣿⣷⣷⣷⣾⣾⣓⣲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠀⠀⠀⠀⡿⢿⠷⡇⠀⠀⡀⠘⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⡿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠛⠛⠚⠁⠀⠀⠀⠃⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠷⠂⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢠⠖⠒⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⣶⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⡀⠈⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣷⡘⠿⠡⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣾⣿⣿⣿⣿⣷⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠓⣆⢰⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⡙⠻⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡿⠄⠙⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠿⠁⠉⠉⠩⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠁⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⢦⣀
⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣤⣶⣶⣾⠯⠟⠓⠒⠒⠒⣂⡈⢳
⠀⢸⢇⠀⠀⠀⠀⢀⡠⠔⣒⠭⠕⢒⣉⠽⣿⣿⣿⣿⣍⣉⠩⠭⠭⠤⠤⠌⡷⣄
⠀⠈⢎⢣⡀⠀⠀⣿⡈⠩⠴⠒⣉⣩⠤⠒⢊⣻⣿⣿⣿⡶⠒⠒⢒⡒⣒⠊⢹⠈⠣⡀
⠀⠀⠈⢣⡱⡄⠀⢰⠈⠓⠢⠬⠥⠒⠒⢩⡍⢸⣿⣿⠿⣇⠀⢈⠥⠭⣍⢁⣼⣄⡀⠈⠢⡀
⠀⠀⠀⠀⠱⡜⢆⠸⡀⠐⠒⠒⠀⠀⠀⢀⣠⡚⢻⠀⠀⠀⣟⣇⠀⠀⢈⡇⠀⠀⢸⠉⠙⢿⢦
⠀⠀⠀⠀⠀⠘⢎⢣⣧⡀⠀⠀⠤⠆⢰⠁⢠⠝⠚⠢⣤⡞⠉⠈⣷⠊⠉⠳⣶⠖⠋⠳⣄⡸⠉⡗⢄
⠀⠀⠀⠀⠀⠀⠈⢢⠱⡉⠓⠒⠒⠚⣿⣦⣧⣀⠀⠀⣸⢳⡤⠤⠻⣀⠀⣠⢧⣀⣀⣴⣿⣤⣶⡇⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡙⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⢛⡿⣟⠓⠒⠒⠤⢤⣈⢦⣤⣤⡤⢒⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠳⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢡⠖⢉⡥⣀⠉⠲⠼⠃⢸⠀⠀⠀⠀⠀⠈⣗⣉⠶⣍⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡑⣄⠉⠛⠻⠿⣻⠟⢋⢄⠀⠀⢸⢀⠋⠀⠀⠉⠑⢒⣒⣁⠀⠀⠀⣀⣀⣀⢟⠛⠛⠋⢟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⢆⠀⡴⠋⠀⠀⠸⣌⠲⠤⠞⣸⠀⢀⡠⠔⠊⠉⢀⠀⠀⠀⠀⠀⢀⠀⠘⡄⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢣⣧⠀⠀⠀⠀⠈⠉⣛⡩⠕⠚⠉⠀⠰⠒⠒⠉⠁⠀⠀⠀⢠⠋⠀⢰⠁⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠹⡗⠤⠤⠔⢒⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣠⠔⠁⠀⠀⠀⢀⣠⠤⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⢾⡄⠀⠈⠙⠓⠀⠀⠀⠀⣀⣀⣤⠤⠤⠖⠒⠉⠉⠀⠀⠀⣀⡤⠖⠊⠁⣀⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢫⡳⠤⠴⠖⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⢀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⢆⠀⠀⠀⣀⡠⠔⠚⠉⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢳⠒⠉⠁⣀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠤⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠒⠒⠒⠛⢻⠛⠛⣿⠛⠛⠛⠒⠲⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣼⣄⣀⣀⣠⣤⡤⠤⠤⠤⠤⠴⠦⠤⠤⠤⢤⣤⣄⣀⡀⣙⣿⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠳⣶⠒⠒⠛⠋⠉⠁⣿⠶⢦⣄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⡧⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣄⠀⠀⠀⠀⠀⢰⣇⣀⡤⠔⢁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⣴⡉⣿⠀⠀⠀⢠⠿⠤⠶⠖⠚⠉
⠀⠀⠀⠀⠀⢀⣀⣠⣤⡼⠿⣦⡀⠀⠀⠀⠀⠀⠀⣿⢾⡓⠀⢸⡄⢀⡴⠓⠶⠤⢤⣀⡀
⠀⠀⠀⠀⣾⠋⠉⠀⠀⠀⠀⢨⣿⣶⣤⣀⠀⠀⠀⠻⠾⠶⢚⣫⣴⣿⡄⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣶⣶⣶⣿⣿⠿⠟⠛⠁⠀⠀⢀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠓⠶⠶⠶⠶⠶⠒⠚⠛⠛⠋⠉⠁

⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠠⠀⠂⢁⠠⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠤⠄⠀⣄⠀⠀⠔⠉⠀⢈⣄⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⡤⠄⠚⠁⠀⠀⠢⠐⠄
⠀⠀⠈⠐⠀⠉⠠⠔⠂⢀⣤⣾⣿⣿⠇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣄⡀⠀⠀⠀⠐⠀⠀⠀⠄⠈⠀⠂⠐⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡈⠐⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣯⠇
⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴
⠀⠀⠀⠀⠀⠀⢤⡿⡷⠚⢻⡧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠕⠊⠁
⠀⠀⠀⠀⠀⡀⣤⣟⡣⣄⠀⠛⠛⠁⠀⠀⠠⠀⠀⠀⠀⢀⢐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶
⠀⠀⠀⠀⠈⠉⠉⠉⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⣛⠐⣀⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⢀⢀⠀⢄
⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣼⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣇⠻⠃⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣾⣿⣾⣿⣛⣛⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣤⣀⡘⠁⠀⠀⡼⠈⠀⠀⠀⢿⣵⠤⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⠀⠀⠀⠈⠓⠀⠐⠋
⠀⠀⠒⠀⠀⠠⠄⠀⠀⠃⠀⠡⠀⠀⢿⣿⣦⣿⣿⠀⠀⠘⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠄⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠋⠀⠀⠀⠀⠁⠀⠀⠔⠀⠀⠀⣿⣟⣿⠁⠀⠀⡀⠶⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠠
⠀⠀⠀⠀⠐⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠀⠉⠩⠀⠂⠀⠀⣤⣭⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⢀⠀⠒⡦⠀⠀⠀⠀⠐⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡦⣤⡆⠀⠀⠀⠀⠀⠐⠘⠄⠀⠤⠃⠂⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⢰⣬⡿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠐⠁
⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠠⠆⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⠒⠦⠄
⣴⣶⣴⣦⣴⣴⣴⣴⣤⣶⣤⣴⣶⣤⣶⣶⣴⣦⣶⣶⣶⣶⣤⣴⣦⣴⣴⣶⣶⣶⣶⣦⣶⣶⣴⣶⣤⣶⣶⣶⣤⣦⣶⣶⣦⣤⣦⣴⣴⣦⣦⣦⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⢄⠀⡀⢲⣾⣻⣍⣯⣿⣦⣾⣤⣌⡓⣒⣠⣤⡤⢤⣀⠀⠀⠀⠀⠀⠀⣰⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣺⡿⠻⠩⠿⣯⡿⠛⠀⠀⠀⠠⠤⢀⣤⣦⣲⠀⠀⠉⠙⠻⢯⠿⠷⠶⠿⢿⣶⣤⡀⡞⡵⠚⠉⠉⢝⠺⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⣧⣶⠐⠗⠃⠀⠀⠀⠀⣤⣄⢸⣎⡙⣣⠜⣻⠠⣴⠒⡦⣀⠀⠀⠀⠀⠀⢠⡄⢙⣿⡿⣇⢿⡀⠀⠀⠀⠀⢹⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡯⡋⡷⢻⣿⣦⠀⠀⠐⣠⣦⡽⣿⣷⡿⢿⣧⠲⣌⠶⢏⠁⠀⠀⠀⠀⠀⢀⣴⢎⡴⢣⣿⡷⡁⢸⣷⠀⠀⠀⠀⢈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡻⡃⠑⡘⢛⣩⢈⠀⠀⠀⠸⠾⠃⠛⣀⠨⣅⡐⠛⠭⠈⠁⠀⠀⠀⠀⠀⠀⠙⠉⢀⡠⡾⣔⣻⠿⠶⠀⠀⢀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢶⣥⣬⣉⣊⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠆⠀⠀⠀⠀⡠⢤⣲⣖⣠⣥⠶⠿⠋⠀⠖⡦⢧⠀⠧⠄⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠟⠃⢀⠀⠈⠉⠙⠛⠛⠓⠿⠿⠛⠛⠖⠲⠟⠷⠿⠿⠿⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠐⡦⠔⠀⣁⡤⠐⢫⡀
⠀⠀⠀⠀⣠⣮⠀⠀⢀⠰⡇⣀⣂⠀⠄⠀⠀⠀⠄⡀⠀⢠⣄⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣄⣦⡀⠀⠀⠀⠀⠠⢋⠴⢂⣉⣉⠀⠀⠀⢻⣚⣀
⠀⠀⠀⢠⣿⡇⠀⠀⠋⡐⢛⠉⠼⣣⠀⠀⠀⠀⣼⣇⡀⢈⣁⡜⣠⠤⣶⠚⣯⢣⢄⠀⡀⠀⠛⢾⠏⡀⠀⠀⠀⠀⢀⠊⠈⣋⢬⠏⠉⠀⠀⢀⠉⢹⣷
⠀⠀⠀⢾⡏⡀⠀⠀⠒⣤⣿⡛⣾⣀⢀⠁⠀⠘⠛⠻⠛⢀⣍⣤⢧⣉⡰⢇⡿⡞⠂⡞⣉⡶⠗⠛⠛⠀⠀⠀⠀⢾⣋⠈⠁⠉⠅⠀⠀⣂⢢⢾⣴⢎⡿
⠀⠀⠀⠘⢿⣿⠿⠦⠀⠈⠓⠉⠀⠁⢴⠆⠑⡀⠀⠀⠒⠁⠠⠀⠸⣿⠊⠁⠀⠉⣡⠟⠛⠇⠀⠀⠀⠀⠀⡀⠐⠯⣭⠔⠀⠀⠀⠀⠀⣤⣴⣿⠔⠋
⠀⠀⠀⠀⠈⠙⢶⣢⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠀⢠⢀⡤⠀⠀⣀⣈⣤⠼⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠾⣦⢶⣤⣀⣀⡀⠀⠀⠀⢫⡑⠂⠤⢤⣤⣠⣤⣤⣔⣶⣴⡬⠴⠖⢋⣝⣀⣤⣬⣭⠬⠖⢛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⡀⠉⠉⠓⠒⠒⠛⠒⠒⠶⠦⠴⠶⠒⠒⠒⠒⠒⠒⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⢶⣶⣤⣦⣤⣤⣤⣴⣰⣶⠤⠤⠆⣲⠖⠲⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⠿⣿⣿⢿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠐⢲⣾⣿⣿⡆⣿⡟⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡿⢀⣿
⠀⠀⠀⠀⠀⠀⠉⠟⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣆⣸⣿⣿⢀⣤⣶⣤⣤⠄⠀⠀⠀⠀⠀⠰⠶⢿⣿⠷⠿⠿⢾⣿⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⡇⠾⠤⠄⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⡿⠿⠿⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⡧⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣷⣾⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠤⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢿⣿⣿⠈⠙⠻⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⣀⣠⣤⣴⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⢠⣾⣿⣿⡇
⠀⠀⠀⠀⠛⠛⢿⣿⣿⠿⢿⡿⣿⠛⠛⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⠿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢺⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣸⣇⣼⠀⠀⠀⠀⠀⠀⠀⢘⣿⢿⣋⣁⣤⣾⣧⣀⣸⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠿⣿⣭⣯⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠈⠋⠈⠉⠙⠑⠟⠻⠿⠿⠏⠁⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⠟⠉⠉⠁
⠀⠀⠀⠀⠀⣿⣶⣾⣿⣿⣿⣷⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠁⡄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⣀⣴⠄
⠀⠀⠀⠀⠀⣀⣤⣶⣿⣶⣶⡄⠀⠀⠴⡇⠀⠀⠀⠀⠀⠀⠀⢠⣴⢀⣀⠀⠀⠸⠛⢦⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢀⣤⣠⡴⠞⢋⡀
⠀⠀⠀⠐⣾⣿⠟⢛⣻⡟⠋⠁⠀⠀⠀⢸⡆⠀⠀⠀⠀⣠⡄⣾⣇⡎⢨⠖⡶⠘⠿⣾⣧⣌⣻⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠙⣿⡿⠿⠁⠀⠻⠃
⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⢠⡤⠀⣰⣿⣯⠄⠀⠀⠀⠻⣧⣙⣿⣿⣿⣿⣷⣶⣠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣈⡿⣗⡀
⠀⠀⠀⠀⣰⡤⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢠⣤⣶⡀⠶⠒⢺⠿⠛⠀⠛⠷
⠀⠀⠀⠀⠙⠄⠀⠀⠀⠈⠛⠛⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⠚⣯⣽⡿⢿⡻⠿⠿⠛⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⣰⣏⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⡀⠄⠀⠶⠂⠖⠒⠒⠒⣶⣶⣦⣤⣄⣀⡜⠲⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡤⠀⠀⠀⡀⠠⣍⣀⣀⣤⠈⠉⠉⠂⠛⢛⡛⢿⣷⡆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠰⣇⠀⠀⠀⠀⣡⠀⢩⡀⠈⠹⠷⣤⣈⣁⣼⡿⢃⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢤⣒⡐⠀⠀⠀⠀⣠⣶⡀⢼⠭⢽⢟⠉⢰⣏⣹⡷⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠴⠖⠀⠉⠙⠀⠋⡿⣿⠃⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠻⠶⠒⠋
⠀⠀⠀⠀⠀⢀⡔⠟⠛⠉⢛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⣶⣤⣀
⠀⠀⠀⠀⠐⠈⠀⠀⠀⣰⠻⡿⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠤⣻⣿⠵⣺⡀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣛⣷⠋⡷⢲⣦⣧⣀⡀⠀⡀⠀⢀⢃⣠⣶⣟⢓⣏⣹⣿⣧⠆⠀⠀⣘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢋⠥⢠⠈⢉⡛⠛⠛⠿⠛⠿⠛⠻⣿⣯⣯⣯⠋⠁⠀⢀⣠⣸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠛⠁⠀⣀⣀⠀⠀⠀⣀⠀⠈⢀⣤⠄⢰⠿⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠉⠉⠁⠀⠓⠚⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠴⠿⠛⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣀⣼⣄⡀⠀⠀⠀⠀⠀⠀⢾⠆⢿⡿⣠⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⣟⣛⣻⡋⠁⠀⠀⠀⣀⣀⠼⠮⡵⣷⠊⠁
⠀⠀⠀⢀⣀⣰⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠛⣿⣿⣿⠛⠁⠀⠀⠋⠀⠀⠀⠀⠉
⠀⠀⢰⠍⠞⠃⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣇⠀⠀⠀⠐⠻⣿⠿⢿⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⣙⣿⣛⣛⣛⣛⣻⣟⠁
⠀⠀⠀⠀⠀⢀⢀⡀⠈⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⡟⠀⣠⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣬⡭⢸⣯⡞⠋⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠤⠾⠿⠿⠿⠿⠿⠿⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠤⢸⡧⠙⠂⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⡿⠯⠯⡇⣴⠏⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦
⠀⠀⠀⠀⢈⣦⣛⣶⣶⠂⠀⠀⠘⠳⠻⢼⠃⠀⠀⠀⢀⠴⡐⡉⠉⠇⡲⢄⠀⠀⠀⠛⠄⠀⢀⠟
⠀⠀⠀⠀⡈⠱⠿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡀⠀⣐⠣⢑⣴⣴⣶⣬⣔⠡⢣⠀⠀⠤⠊⠀⠑⠤
⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠻⡟⠛⠃⠈⠀⠠⠇⠀⠠⠰⠄⠀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⡠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣁⡤⠄⠀⢀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡠⠊⢉⢠⡄⣀⠔⠁⠀⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣵⡶⠿⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢠⣤⢴⡾⣿⠶⠚⠛⠶⣶⣤⣄⣀⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⡴⢋⠔⠁⠀⣰⠤⠿⠛⠛⠛⠛⠛⠓⠒⠛⠛⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⠟⠡⠃⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠠⣊⠔⠁
⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣤⣤⣼⣧⣤⣤⣿⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣼⣷⡀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⢠⣾⣦⠀⠀⣰⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡀⢸⣿⣿⣏⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣽⣿⣿⡅⢀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⣿⢿⡄⣼⢿⡿⢯⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⡿⣿⠿⡇⢨⡿⣿⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠒⠒⠒⠚⠓⠒⠒⠒⠛⠛⠒⠒⠒⠒⠒⠒⠛⠛⠒⠒⠒⠚⠒⠒⠒⠒⠛⠒⠂

⠀⠀⠀⠀⠀⠀⠛⣿⠛⠀⣴⠛⠳⣆⠀⢰⡟⠓⣦⠀⠐⡆⠀⢰⡆⠀⠀⠀⡴⠛⠓⠀⠀⠀⡶⣆⠀⠀⠚⣿⠛⠀⠀⣟⣛⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣤⣴⠟⠀⠸⡟⠻⡇⠀⠸⡇⠀⠸⡇⠀⠀⠀⠳⣤⣼⠇⠀⣼⠓⠻⡆⠀⠀⣿⠀⠀⠀⣯⣭⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠇⠂⠁⠂⠐⠒⠒⠠⠐⠑⠇⠡⠂⠅⠓

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣠⠀⡀
⠀⠀⠀⠀⠀⢀⡠⣴⣿⣷⣶⣄⢀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⢷⣶⣧⣼⡀⢠⠆
⠀⠀⠀⠀⠔⠃⠀⠀⢸⠋⢹⡿⣿⣷⣄⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿⢸⡏⢹⡟⢻⣦⡾⠂
⠀⠀⠀⠀⠤⠒⠒⠤⢤⣀⠸⣇⣿⣿⣿⣷⡀⠀⢸⡀⠀⠀⠀⠀⠀⠐⠁⠰⠃⡼⢃⣠⠇⣺⡷⡿⠚⠯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣿⣿⣿⣿⣿⣷⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠿⣄⣁⣦⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠟⠃
⠀⠀⠀⠀⠀⢀⣤⠤⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⣴⣾⣷⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⢤⣀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠀⢰⣿⢯⣾⢻⣷⣤⣄⣀
⠀⠀⠀⠀⠈⢓⡦⣴⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸⣷⣿⣖⣿⣿⣿⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡗⣤⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠁

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠤⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠀⠀⡡⠀⢀⣀⡟⡤⢠⣠⡄⡄⣠⢠⣠⡤⣄⢸⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠰⠀⠐⠅⠀⠀⠀⢀⣀⠀⠘⠃⠀⠈⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠂⠄⠀⠀⠀⢘
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠟⠹⠦⠀⠀⠈⠁⠶⠀⠂⠰⠆⠈⡀⠃⠠⣠⢤⡀⠀⠀⠁⣠⠀⠈⠀⠀⠀⠀⠠
⠀⠀⠈⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⡆⠰⠀⠀⠐⠀⠘⣮⡀⠈⠀⠀⣿⠀⠀⠀⠀⢺⡆
⠀⠀⠂⠥⠀⠀⡏⠀⠀⠀⢀⠖⠛⢏⠀⠀⠰⠤⠄⠀⠦⠴⠀⠀⠀⠁⢊⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⣧
⠀⠀⠀⣾⡖⢺⠃⠀⡩⢿⠆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠈⠁⠀⠀⠀⢿⠆⠀⠀⠀⠀⣿⡄
⠀⠀⠀⣹⣿⣿⡀⠀⠀⠎⠀⢠⠀⠀⠰⠓⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⣠⣎⡟⠀⠀⠤⠀⠲⠀⠒⠂⠴⠀⠀⠀⠀⠀⢀⣀⡠⠔⠈⠀⠈⠢⣄⣀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣽⡳⣦⡀⠀⠈⠢⡆⠀⠀⠀⠀⠀⠀⠹⠀⠈⠛⠁⠀⢠⠐⢖⠒⡒⢒⠛⠓⠁
⠀⠀⠀⠀⠘⠀⠀⠀⣴⣶⡜⠁⠀⠀⠀⣀⠀⠀⠀⠒⠒⠀⠀⠀⠄⠑⠀⢀⠀⠀⣱⡭⣤⣽⣎⡀⠀⡀
⠀⠀⠀⠀⠀⠃⠀⠈⠘⠁⠙⠀⠀⣤⠒⠃⠀⠀⠀⠠⠂⢠⡧⠀⠀⠀⠀⠈⣙⡏⡙⣟⠀⣚⠉⢩⡋⠁
⠀⠀⠀⠀⣤⣬⡉⠉⣽⢂⡀⠀⡄⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡿⣛⠙⣛⢚⡟⠃
⠀⠀⠀⠈⠟⠙⠻⠘⠁⠚⠃⠀⠙⠁⠀⠀⠀⠀⠀⡅⠄⠀⠀⠀⠀⠚⢷⠶⠶⣮⠽⣭⠽⡹⢼⡿⠶⠶⠾⠒
⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⣶⣿⣶⣷⣾⠓
⠀⠀⠀⠀⠀⠁⠃⠉⠀⠀⠠⠐⡠⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⠛⡅⠉⢭⠉⠉⡍⠉
⠀⠀⢄⢀⠀⠀⢀⠀⠀⠀⠐⣄⠤⠀⠀⠀⠀⣄⠀⠀⠀⠀⢢⡀⠀⠀⠀⠈⠿⠯⣽⣿⠓⠛⠲⣚⠿
⠀⠛⠻⣭⣆⣼⢶⣷⠆⠀⠠⣤⣤⠀⠀⠀⠀⠻⠶⠁⠀⠀⠀⠀⠠⣶⣤⣤⣤⣚⣲⣛⣖⣛⣚⣗⣦⣤⣤⡦⠄
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠉⠎⠉⠏⠀⣏⣀⡏⠠⠏⠁⠜⠈
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠔⢂⣠⣴⣿⣿⣦⣄⡈⠁⠀⠀⠀⠀⡄⠀⠄⠀⣼⣿⡇⠀⡤⠀⡄
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠉⠉⠉⠀⠀⠀⠀⠁⠉⠉⠛⠛⠛⠛⠊⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄
⠀⡀⠀⠀⠀⢠⠗⠒⠂⡤⠀⠀⠀⠀⠀⠀⠀⡀⣠⣐⠐⠀⢠⠀⠀⠀⢀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠘⠛⠀⠀⠀⠹⠃
⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⡄⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⢠⣾⣹⣹⣿⣹⣏⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟
⠀⠀⣠⡶⠿⢶⣄⡀⠀⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⡀
⠀⠀⣴⣾⣿⡳⣮⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠐⣾⣿⢿⣽⡷⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣿⣿⣿⣭⣯⣽⠇
⠀⢈⣯⡶⠻⢾⣏⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠠⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⡠⢔⢲⣶⣔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⣀⠠⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠃⠉⠉⠉⠁⠀⠄
⠀⠀⠀⠚⢶⡗⡀⠀⠙⢤⠶⠋⠄⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡀
⠀⠀⠈⠁⠤⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠁
⠀⢀⣤⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠔⠀⠀⢠⣾⣿⣹⣏⣿⣳⡆
⠀⠘⠻⠿⠟⠛⠛⠋⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡨⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⣰⣯⣽⣦⠀⠀⠀⠀⣸⡏⠀⣶⣖⣒⣶⣖⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⡀⠀⡠⠤⠤⠄
⠀⢰⡟⠉⠁⢹⡇⠀⠁⠀⣿⠃⠀⠈⢭⠍⣩⠉⡭⡄⢀⡄⢠⡄⡀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠔⠋⠀⢀⠀⠁
⠀⠀⠑⢀⠀⢀⠀⠀⠀⢸⡿⠀⠀⠠⠎⠞⠙⠐⠉⠐⠉⠁⠚⠈⠃⠀⠀⠀⠘⠋⠀⠀⠀⠄⠐⠀⠚⡇⠀⠀⠀⠀⠀⠂
⠀⠀⠛⢀⣀⠘⠀⠀⠀⣿⠃⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠘⡀
⠀⠀⡀⠠⠄⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⢼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠂
⠀⠀⠰⠂⢀⡀⠀⣼⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣴⣶⡶⣶⣶⣶⢶⢶⣶⣤⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠛⢛⠛⣛⡿⠖⠛⢋⣉⡤⠄⢖⣊⣳⡂⠑⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠁⠀⠀⠀⠀⢸⠘⠷⠶⠖⠛⠉⠁⠀⣀⣀⣤⣬⣽⣦⠘⣄⣠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠛⠛⠛⠻⠷⢖⡤⡒⠋⠉⢉⣒⣂⣠⣬⣧⠘⣦⣤⣄⣬⡍⢻⡆
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠁⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣈⣛⣛⣛⠻⠿⠿⠿⠿⣛⣛⣛⣫⣭⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠁⠘⠲⠤⣤⣤⣀⣤⡔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠚⣧⠈⣉⡉⢁⠀⢀⡀⣀⣀⣀⣀⠤⠴⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠲⠶⢦⣤⣤⣤⣤⣤⣤⠴⠞⠋⠁⠀⠀⠀⠀⢿⡀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⢀⣠⣼⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⣦⣤⣤⣄⣀⠀⢀⣠⣤⠤⠀⠀⠤⠤⠤⣤⣤⣤⣤⣴⣾⣍⣀⣀⣻⡀⠉⠉⠉⠉⠉⡼⠋⠉⠈⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⡿⠛⠁⠀⢠⡰⣄⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⢿⡍⠉⠛⠛⠛⠲⡾⠷⠶⢤⣤⣤⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠟⠋⠁⠀⠀⠀⠀⠀⠱⡌⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⣇⣤⡶⠶⠟⣾⠓⠚⠓⠲⢦⡀⠀⠈⠉⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠳⣄⠀⠀⢀⣤⠶⠚⣩⣶⡾⠛⠁⠀⠀⠁⠶⠞⠃⠀⠀⠀⢹⣦⣤⠞⠁⢸
⠀⠀⠀⠀⠀⢠⣶⡛⠋⠙⣇⠀⠉⠉⠛⠛⠛⠷⠶⢶⣤⣤⣤⣤⠼⡧⡙⡂⠜⣋⡤⠖⢿⣿⡟⢀⠔⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠙⠛⠛⠾⠿⠿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣤⣤⣷⣽⣿⠞⢉⣤⣴⠋⣹⡇⠼⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⣈⠉⠉⠉⠛⠛⠛⠛⠻⠿⠶⠾⣷⣶⣾⣍⣷⡀⣀⣀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡼⠂⣰⢂⡿⠂⠀⠀⠀⠀⠀⡔⠒⠲⠦⣄⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⡴⠁⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠈⡷⠟⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⣤⡜⢀⠀⠈⠣⣄⣀⣀⣀⣀⡀⢀⣀⣴⠏⠀⣴⠃⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣙⣒⣒⣂⠀⠀⠀⠀⠈⠉⠉⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠶⠶⠞⠛⠉⠀⠉⠉⠙⠓⠲⠶⠦⠤⠴⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠤⠀⣀⠀⣰⡧⠴⡗⠚⣻⣁⣸⣦⡤⠖
⠀⠀⠀⠀⠀⠀⠤⠴⣿⣚⡽⠛⠁⢸⠀⢠⡿⡆⢸⠀⢰⡇⢰⡇⢈⡽⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣠⣴⣟⣁⡤⢤⡤⢼⠁⢸⠃⢻⣼⠀⢸⡇⠀⠛⠋⢠⠀⠀⢀⠀⠀⢀⡼⣣⠖⠁
⠀⠀⠀⠀⠀⠈⠉⠉⣇⡤⠖⠋⠀⠻⠴⠺⠀⠀⠛⣤⠀⢠⡄⣷⠖⣾⡴⣦⠞⠀⢀⣞⢞⡵⠊
⠀⠀⠀⠀⠀⢀⡤⠾⡏⠀⠀⠀⠀⠀⢠⣀⣿⣠⠄⡟⠿⠿⢹⡏⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⣦⢶⠾⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⢀⣀⣤⣾⡜⠳⣻⠿⠂⠧⠖⠂⢀⣀⢀⣀⣤⣴⠶⣖⣉⣉⣉⠉⠒⢬⡁⠁
⠀⠀⠀⠀⠀⠀⠀⣷⣲⣾⡧⠛⠉⡏⠟⠈⠋⠀⠀⣀⡠⠊⠁⠀⠫⣴⢣⣀⠷⠈⡧⢄⠈⢳⠀⠀⠈⠳⢄⠀⠀⠐⠂
⠀⠀⠀⠀⠀⡰⠂⡏⠀⠸⠀⠀⠀⠁⢀⣠⣴⡖⠉⡱⠁⠀⠀⠀⠁⠙⢗⣭⠷⣴⡳⠌⡇⢸⠯⡉⢳⡀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠑⠞⠁⠀⠀⣀⡤⠖⠋⠁⡟⠋⡻⢤⡃⠀⡔⠒⠂⠉⢂⡜⠁⠂⠀⠙⣞⣠⠷⣄⡹⢸⡣⢚⣶⠤⡈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⡀⢀⡀⠄⠠⡈⠒⠌⠒⢦⣶⣆⡀⡌⠀⠀⠀⣀⣀⠈⢏⡲⠗⠧⣞⠔⣱⠋⡰⣁⠠⢠⠈⠲⡀
⠀⠀⠀⠀⠀⠀⣼⠡⣴⢤⠐⠢⣀⠢⡕⠂⢁⠠⠐⡧⠠⠠⡈⠛⢶⡃⠀⡎⠀⠀⠈⣤⠋⠀⠀⠀⠈⢾⠃⢜⠔⢁⠔⡦⢀⡦⢿
⠀⠀⠀⠀⠀⠀⡟⣆⠀⠸⡇⠦⠀⠂⠒⣈⠠⡄⠰⣄⠢⠀⣴⣦⣶⡌⠑⠧⣶⡄⢐⠁⢠⠄⠐⠒⢢⠈⢟⠳⣪⡭⠞⠋⠁⠀⡼
⠀⠀⠀⠀⠀⠀⡇⠀⠙⢦⡃⠘⠙⠣⠉⢮⢹⣈⠃⢈⣀⠴⢯⡁⡠⠛⠉⠙⢪⡑⠧⡀⢢⢠⢰⣄⣤⠤⠚⠋⡁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠳⣍⡀⡳⡜⠛⠛⡿⠉⠀⠀⠀⡸⢁⡴⠒⢢⠀⣇⣀⣨⠽⠚⠋⠁⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠉⠳⢤⣀⢸⠁⢠⠊⠑⡄⣇⣸⣠⡤⠜⠒⠉⠁⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠒⣚⠋⠉⠁⠀⠀⠒⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠁⠁⢀⣀⡤⠴⠒⠋⠁⠀⢀⠀⣠⡀⣴⣠⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠙⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⢠⠟⣷⠁⠿⠘⠃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⡀⠀⠀⠀⡀
⣿⣯⢭⣟⡛⣛⣛⠛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣤⣴⡶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⣲⣶⣄⠀⠀⠀⢀⢤⠄⠶⠀⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⢀⣉⡉⢉⡉⠉⢢⠀⠀⡁⠀⠀⠀⠀⠀⢠⡴⣏⣤⣾⣿⢟⠋⠹⠃⠀⠀⣧⣿⣶⡾⠛⠛⣋⡙⢻⣆⠀⠀⠀⠀⠀⣰⡷⠺⣿⣯⡭⣿⣆
⠀⠀⠀⢸⣿⢶⢻⣽⠀⢸⣷⣾⡇⠀⠀⠀⢀⣴⣛⢠⣶⣿⡟⠁⠰⠈⠀⠀⠀⠀⠈⠉⠙⢀⢰⣿⣻⣿⠀⠃⠀⠀⠀⢀⣾⠏⠀⢂⢬⣿⣷⡄⠾⣧
⠀⠀⢠⠐⣯⣿⣷⣿⡆⢼⣿⣿⠇⠀⠀⢠⣾⣓⣮⣿⣽⢟⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠗⠉⠀⠀⡀⠀⠀⢠⣿⠟⠰⠤⠜⡷⠬⣿⣷⢶⡿⠃
⠀⠀⠈⠢⠀⠀⠈⠉⠠⠞⠋⠁⠀⠀⠀⠉⠲⠾⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠁⠠⠒⠃⠀⠀⠈⠛⠒⠒⠂⠀⠀⠀⠼⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⢠⠄
⠀⠀⠀⠀⠀⢀⣠⡶⠞⠓⠀⡀⠀⠀⠀⠀⠀⣴⡚⢫⡭⣭⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⣧⣅⣼⠦⡀⠀⠀⠀⠀⣀⢠⠒⢠⠀⠀⢶⣶⢂⡄
⠀⠀⠀⢰⠋⠀⠀⠑⢈⡧⢤⣴⣪⠄⠀⠀⠀⣟⢷⡈⠙⠛⠁⠠⠄⢳⠀⠀⠀⠀⠀⠜⠁⣀⠄⠀⠈⠹⣠⣧⠀⠀⠀⠀⡏⠨⠁⠀⠀⠀⠲⣿⡿⡇
⠀⠀⠀⣅⠡⠶⠒⠀⠘⢃⠘⢁⢼⠂⠀⠀⠀⢃⠈⠿⢶⣆⣴⡴⡶⢤⡆⠀⠀⠀⢀⠀⣸⡭⡳⣆⠀⢸⡏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡗
⠀⠀⠀⢶⡒⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣤⣈⡉⠈⠃⠀⣸⠇⠀⠀⠀⠘⠀⢿⣿⣎⢯⡇⠈⣷⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣷⡿⠃
⠀⠀⠀⠘⠓⠒⠒⠚⠃⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠓⠛⠃⠁⠀⠀⠀⠀⠀⠦⡀⠉⠉⣩⢅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣄⠂⢀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠑⢂⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠰⣾⠿⠁⡆
⠀⠀⣀⢈⡉⠀⠈⠱⢿⣄⣤⡷⠗⠋⠍⠀⠀⢀⠀⢠⡄⠴⣖⡫⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣶⡞⠁⠀⠀⠀⠀⠀⣾⣁⠎⣁⣹⣥⣿⣾⡇
⠀⠀⠑⠫⠤⠆⠐⠟⣽⠿⠟⠋⠀⠀⠀⠀⠀⠈⠀⠀⠉⠇⠸⠟⠁⠀⡐⠀⠀⠈⠁⠀⠤⠠⠄⣰⣇⢸⡗⠈⠀⠐⠀⠀⠀⡿⢘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠛⠃⠐⠈⠀⠀⠀⠀⣇⢸⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣠⠔⠄⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠰⠀⠒⠰⠆⠀⠀⠀⠀⠀⠀⡀⠐⡠⠒
⠀⠀⠀⠀⢠⠀⠄⠄⠀⠄⢰⡆⠆⠀⠀⠀⠀⢰⠤⠀⠒⠐⠒⣀⣈⣀⣀⠀⠀⠀⠀⠀⣤⠈⠀⠀⡀⣀⣤⠽⠞⠛⠀⠀⢰⠁⠀⠑⠀⣄⡀⠀⢀
⠀⠀⠀⠀⢸⣄⡀⣀⣀⣰⠀⣿⣤⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢀⡜⢁⡠⠴⠞⠋⠁⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢉⡐⢀⠀⢰
⠀⠀⠀⠀⢀⠁⠀⣿⣿⣿⠀⣿⡿⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠘⠳⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣀⠐⠁⠐⣈⣴⡿
⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠰⠋⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠼⠿⠿⠟⠃⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠄⠀⠀⠠⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣠⡟⢡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡋⠉⠛⠛⠋⠉⠉⠳⣄⠀⠀⣴⠏⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⣉⣤⠶
⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠛⠛⠋⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⢁⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⢋⣡⡴⠟⠉
⠀⠀⠀⢀⣠⣤⢶⣿⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠀⠀⣰⠟⣰⡟⠉⠙⠛⢶⡄⠀⠀⠀⠀⠀⢀⣠⡶⠛⣉⣤⠾⠋⠁
⠀⢀⡴⠛⣁⣤⠾⣗⠶⠀⠀⣤⠶⠄⠀⠀⠀⠀⠿⠀⠀⢀⡾⢋⣼⠋⠀⠀⠀⠀⠀⡿⠳⣦⣀⣴⠞⢋⣡⡴⠛⠉
⣰⡏⣠⡾⢯⡜⠓⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣡⡿⠁⠀⠀⠀⣀⠀⢘⣻⡶⠟⣉⣴⠞⠋⠁
⣿⠀⣿⣹⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⠏⠀⠀⠀⠀⣀⣼⠷⢋⣥⡶⢻⡏⢸⡇
⢻⣦⡟⠷⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣠⡴⠞⣩⡴⠞⠋⠁⠀⢸⡇⢸⡇
⠈⣿⣿⣗⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣥⠶⠛⠉⠀⠀⠀⠀⠀⢈⣹⣿⠁
⠀⠘⣿⡙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⣿⠃
⠀⠀⠘⢷⡝⠶⠍⠛⠻⠶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣶⠶⠟⠛⠉⠀⣼⠏
⠀⠀⠀⠈⠻⣾⠛⠦⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠙⠷⣝⡛⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⣭⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢦⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢼⣿⡧⠄⠀⠐⠊⠃
⠀⠀⠀⠠⣒⣁⠰⠃⢀⡠⠄⠀⠀⠀⠀⠀⠀⠄⠀⠸⣿⣇⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠆⠀⢤⡀
⠀⠀⠀⠀⠋⠈⠉⠁⠲⢄⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⡎⣿⣿⡀⠈⠀⠀⢪⠉⣲⡄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠻⣿⣧⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⡀⡀⠀⠈⠲⡏⠀⠀⠙⢿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄⠀⠀⠠⠈⡀⠀⠀⠀⠐⠂⠈
⠠⢴⠀⢰⠒⠰⠢⣀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⣾⣿⣿⣿⣷⣶⣶⣿⠃
⡲⠚⠛⠉⠐⠒⣄⠉⠒⠀⠀⠀⠈⠉⠉⠉⠁⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠠⠄⠀⠖⠠⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢠⠈⠀⡰⠁⠈⠙⠀⡀
⠀⠀⠀⠀⠀⠀⡾⢭⠹⢸⡁⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋⠉⠁⠐⠓⠠⢆⠀⠠⢐⡀
⠀⠀⠀⠀⠀⣾⢿⣕⣐⣨⣿⣿⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⣀⢤⣀⠤⠤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢳⣀⠠
⡿⠊⠀⠀⠀⠙⠷⣦⠴⠶⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⡴⡎⣀⣄⣄⣵⣬⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⢿⣷⣤⠤⠀⠀⠀⠀⠀⢀⡽⠛⠉⠉⠉⠙⠛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛
⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢾⡀⢠⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⡀⠂⣀⣀⣤⡾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠒⠂⠉⠁⠙⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢀⡀⢀⠄
⠀⠀⠄⠤⠤⠤⠤⢤⣀⣀⠀⠀⠰⠀⠀⠀⠀⠀⠺⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⠊⡁⠁⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠴⣾⠋⣽⣹⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⠖⢋⣩⠖⠁⠀⠀⣀⠀⣾⣰⡇⡜⣿⢸⣇⠞⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⣠⠖⡋⠁⣧⠴⠟⠒⠛⣻⠆⢰⡷⡟⡿⠑⠟⠀⠏⠀⡁⠀⢰⠇⣰⠇⠀⢀⣠
⠀⠀⠀⠀⣴⡯⠖⠋⠀⠀⣧⠀⠀⣠⠞⠁⠈⠙⠚⢠⠀⢀⢠⠀⣤⢸⣷⢛⣾⠞⢹⠀⠀⢋⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠚⠁⠀⠀⠀⠀⠀⣸⠀⠿⠻⠞⣿⣼⠙⠋⣿⠀⠘⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿⠀⠀⠀⣠⢤⡖⠀⠀⣿⣠⡴⠀⢸⡇⠛
⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠋⠁⠀⠀⠀⢀⣀⡠⢤⠔⠶⣒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠛⠉⠁⢢⡗⠀⠒⢠⠙⢆⠈⢲⠤⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠊⠁⠀⠀⣠⡄⡰⠒⠾⢭⡢⢤⡊⢀⣠⠤⠃⡠⠗⠒⠐⢸⠀⡰⢀⡬⠔⢊⣉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⣄⠎⠲⠃⠈⠁⠀⠀⣀⠓⠂⠉⠒⢤⣠⠊⢀⡀⠴⣒⠡⠶⠵⢍⠀⢎⢹⣂⠇⠀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⡰⠒⠃⡄⠀⠀⠀⠀⠀⠀⠤⠏⠁⣨⡤⠒⠂⣏⢙⠤⣠⠊⢠⠂⡏⠌⡲⠑⣤⣈⡤⠖⠊⠁⡇
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠐⠀⢀⣀⣶⣲⠃⠀⠀⡇⢀⣀⣰⣾⠄⠑⢩⠛⠲⣝⣓⣨⠴⠚⠉⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠉⠳⢤⣀⡔⡉⠀⠀⠀⣱⠼⠾⣔⠋⠀⠀⠈⢣⣀⣠⠷⠒⠋⠁⠀⠀⠀⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠙⠧⣄⣀⡞⠠⠀⠀⠈⣧⣠⠴⠒⠉⠁⠀⠀⠀⠈⠁⠀⢀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠀⠀⠀⠀⠀⠈⠉⢛⣒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣈⣁⣀⡤⠴⠚⠉⠁⠀⠀⠀⣀⡴⡴⠖⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠸⠛⠻⠃⠀⠀⠀⠀⡠⠤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣨⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⠀⠀⠈⡐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠁⠀⠉⠁⠀⠀⢰⠿⠓⠁⠀⠹⣦⠀⠀⠀⠀⠀⠀⠂⠄⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢠⠺⠀⢀⡄⠀⠶⠀⢀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣧⠻⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⡶⣶⣖⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⡤⣀⡀
⠀⠀⠀⠀⠀⠀⢐⣾⣧⡀⠀⠀⠠⠾⠷⠛⠋⠹⣶⣶⡀⠀⠀⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠒⠚⠛⠛
⠀⠀⢀⣼⣿⣄⢸⡏⠉⡃⠀⣀⣠⣼⣛⢦⡄⠈⠙⠋⠁⠀⠀⠉⠉⠉⠁⠀⠀⠰⠚⠛⠛⠒⣆⠀⠀⠀⢀⣀⠀⠀⢀⠤⣀
⠀⠀⢸⡏⠉⣹⠈⠁⠩⠄⠀⠉⠉⠉⠉⠈⣿⣄⠀⠀⠀⠀⠀⠰⠶⠶⠂⢠⣄⣠⣤⣤⣄⣀⠁⠀⠀⠀⠀⠈⠀⠀⢿⣿⡿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣶⣾⣽⣶⣤⠀⠐⠶⠶⠆⠀⠀⠘⢿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠐⠒⠂⠀⠀⠁⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠁⠈⠻⠟⠁⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⢀⠤⠔⠒⠒⠢⢄⡀⠀⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⣀⠄⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⡀⠀⠀⠑⠢⢄
⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⢀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠔⠒⠢⠤⠋⠙⣦⣀
⠀⡠⠔⠋⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⠊⠁⠑⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠜⡠⠔⠒⠒⠠⠄⣶⠤⣑⠂⣄
⠸⣀⠀⠀⢠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠃⠀⠨⠀⠀⠀⡠⡔⠋⠀⠀⠂⠈⡹⠯⠶⡄⡀
⠀⠈⠑⢢⢄⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⢀⠤⠂⢡⠁⠀⡄⠀⠂⢇⡔⠉⠀⠀⠀⢋⠤⠒⠉⠠⠄⠀⢹⣌⡑⠢⣄
⠀⠀⠀⢸⠀⠉⠒⠤⡈⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡄⠤⠀⠀⠘⠢⡀⠀⠄⢀⣠⣦⡲⠀⡀⠂⠁⠀⠈⢀⡀⠄⠊⠁⣠⢹⠀⠀⠉⠂⢄
⠀⠀⠀⠈⠢⢄⡀⠀⠀⠑⠢⢌⠑⠢⢀⠀⠀⠀⠀⠀⢀⠤⠒⡋⠀⣰⠥⠴⢦⣤⣌⡂⢁⠈⠢⢄⢩⣴⡶⢶⠵⣄⠑⢀⣞⡉⠀⠂⠀⠀⠁⠀⡇⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠉⠒⠄⡉⠒⠀⠒⠊⠀⡰⠧⢭⣚⡥⢤⣥⣇⣀⣼⠚⠉⠉⠂⠆⠀⠀⢰⠁⠀⠀⠙⠉⠁⠙⢢⣀⣀⠀⠀⣀⢇⡠⢶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠈⠑⠠⢀⠀⠀⠑⢤⢾⡁⠀⠀⠀⠀⠉⠛⢦⠀⢀⠀⢠⣄⠠⡀⢀⠠⠴⡁⠀⠀⠀⠈⠂⠈⡉⠄⠊⠁⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠉⠒⢄⡀⠉⠃⠀⠀⠀⠀⢀⡀⠜⣀⣀⢠⣌⡨⠏⣘⠁⡀⢠⠈⠁⠀⢀⡠⠒⠉⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠁⠀⡎⠀⢀⠀⠀⢙⡄⠃⠀⠓⠁⣀⠤⠊⠁⠀⢀⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠁⠢⢄⡀⠀⠃⠐⠀⠀⠀⠈⠃⢀⡠⠔⠈⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠀⠈⠐⠤⣀⠀⠀⣀⠤⠂⠁⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠈⠁⠀⠀⣀⠤⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠠⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⢤⣴⣤⢦⣄⡀⠀⠀⢀⣠⡿⢧⠈⡷⣠⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⣿⡟⣾⣇⣿⢦⣍⣵⠀⢠⣿⢻⣏⠦⣈⠀⣾⣀⣉⣀⡀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠌⠑⠢⡀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⢰⠙⠋⠉⠉⠀⠀⠻⣿⣿⡀⠘⣿⣦⡉⠛⠶⢾⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⣷⣄⣑⠂⠄⠀⠀⠃⣠⡇⠀⠀⢸⡿⢿⢻⢛⣿⢿⢿⠅
⠀⠀⠀⠀⠒⠀⠀⠀⣀⠄⢱⠀⢸⣼⠃⠀⡰⠛⠛⠻⠿⣿⣿⡿⠤⠤⠄⠀⠀⠊⠂⠀⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⠀⠀⣾⡗⣚⡂⢼⣿⣼⣇
⠀⠀⠀⠀⢘⠀⠀⡈⢰⠁⡮⠀⢸⣿⠇⠀⡁⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣧⣼⣥⣤⣽⣿⣾
⠀⠀⠀⠀⠘⢀⣀⠀⡈⠈⢀⠠⠾⠋⠀⠀⠁⠠⠄⣀⠀⡈⣿⣿⣧⣀⣤⠀⠄⠊⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣽⡿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠚⣡⠠⡿⢥⣿⣿⣟⡀⠀⡲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠋⠉⠀⠂⠀⠀⠉⢿⣿⡇⠀⠀⢸⠀⠈⠀⢀⠠⣾⣿⣿⠄⠀⠎⠩⢀⡀⠙⡤
⠀⠀⠀⠀⠀⢰⠤⠴⠖⣿⣿⣿⠒⠒⠒⠒⠒⠒⠋⠛⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠘⣿⡇⠀⠀⠘⢶⠞⠁⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠘⡇⠑⢄⠂
⠀⠀⠀⠀⠀⢸⡀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⢄⠀⠀⢔⢀⠌⣼⡟⠀⠀⠀⠀⠸⡀⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⡰⠁⠘⢼⡖
⠀⠀⠀⠀⠀⠈⠓⠠⠀⠈⣿⣿⣧⣀⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠓⠀⠦⠀⠹⠿⠿⠆⠀⠐⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠄⠀⠀⠀⠀⠀⢀⢠⣴⣶⣶⣶⢶⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣒⣒⢒⠒⣒⣒⣒⣒⣒⣲⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠠⠤⠴⠒⠒⣚⢒⢒⣐⣐⡇⠀⠠⠤⠤⠤⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠉⠉⠀⠐⠒⠒⠒⠒⠒⠂⠠⠬⠭⠭⠭⠭⠍⠉⣹⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠒⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣉⣛⣟⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣶⡄⠀⠀⠀⠙⠻⠿⣿⣿⣿⣶⡀⠀⠀⠙⠻⠿⢿⣿⣶⡀⠀⠀⠀⠀⢠⣾⣆⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠾⣿⡿⠄⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⠀⠀⣠⣤⠄⠀⠀⠀⠀⢀⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⣤⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠈⠙⣿⡿⢥⣄⣀⡄⠀⠀⠀⠈⢻⣿⠯⢤⡀⠀⠀⠀⠀⠈⢹⣿⠿⠿⣿⣿⡆⠀⠀⠀⠈⠙⣿⡿⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣀
⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣐⣖⡸⢶⡶⡇⠀⠀⠀⠀⠀⠀⣀⡈⠹⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠿⡿⣷⣯⣵⡆⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉


⣿⣿⢟⠿⠛⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠐⠂⠤⠤⠤⣀⣀⣀⣀⣀⡀⢠⠤⠤⢤⠤⡄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠿⠿⠿⢦⡀⠀⠰⠄⠀⠀⠀⣀⣤⣴⣤⣄⡘⠀⠸⠵
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⡟⠿⢣⠀⠀⡬⠿⢣⠀⠂⠀⠤⠶⠿⡿⠿⢿⠿⠿⠿⠷⠦⠄
⠀⠀⠉⠀⠀⢀⡀⣀⣤⣤⣤⣶⣦⣄⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⣇⠠⠄⠀⠀⠠⠀⣸⠀⣀⣀⣀⣀⣀⡀⠀⢰
⠀⠀⠀⠀⠀⠸⠍⠿⠿⠿⠿⢿⣿⠒⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⢛⠙⠋⠟⣻⠇⠀⣿⡍⣹⣿⢹⡿⠀⢰⠀⢸⣗⣶⣶⡟
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠀⠠⠠⠀⣠⣴⠆⠈⠉⠀⢠⣀⠀⠀⠀⠠⣄⠀⠀⠀⢀⣤⠀⠀⠀⠀⠙⢿⣷⣷⡾⠃⠀⠀⣿⡛⢻⣿⢻⣿⠀⢨⠀⢸⡇⠀⢈⡇
⠀⠀⠀⠀⠀⠘⠛⠿⠿⠇⠀⠠⠠⠀⠘⠷⠄⢠⠀⠀⠀⠀⠰⠀⠦⢀⠹⣷⢆⡰⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠿⠷⠾⠿⠼⠿⠀⠈⠀⢠⣿⣧⣿⡇
⠀⠀⠀⠀⠀⢀⣀⢠⣤⠀⠠⠀⠀⣠⡴⠀⠀⢨⠀⠉⠀⠀⣀⠀⠀⠋⠀⢉⡈⠃⠀⠀⢠⠶⡆⠀⡟⡻⡇⢠⡟⡻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠻⠛⠛⡛
⠀⠀⠀⠀⠀⠘⠛⠻⠟⠀⠠⠀⠂⠘⠷⠀⠀⢘⠀⠁⠀⠀⢿⣷⠀⢠⣾⣿⣿⣷⡀⠀⠈⠛⠁⠀⣴⣷⡄⠀⣴⣷⡄⠀⣤⣦⣀⠀⢴⣶⣦⡀⠀⢠⣤⣠⣤⡤
⠀⠀⠀⠀⠀⣀⣀⣤⡄⠀⠀⠀⢠⡴⠀⠀⠐⠸⠀⠀⠀⠀⠛⠁⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⢁⡀⠴⠶⢏⠋⠀⠉⢛⣛⠛⠀⠻⠿⠿⠁
⠀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢤⣄⣀⣀⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣤⡤⠀⠀⠀⠀⠀⠀⢻⣿⣖⣂⠔⠑⣷⠿⣿⡉⠁⠀⠀⠀⠀⡤
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡍⠉⠉⣩⡍⠉⠉⣩⡅⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠿⠦⢦⡀⠀⠛⠛⠀⢀⣾⣷⡀
⠀⠀⢰⠏⠉⠙⣷⠀⠀⠀⣤⣤⠿⠋⠀⠀⠀⠘⠃⠁⠀⠀⠀⢠⡄⠀⠀⠙⠃⠀⠀⢤⡄⠀⠀⠀⠀⠀⣠⣄⣠⣤⡄⠀⠀⢀⡀⣾⣆⣀⠀⠀⠀⠽⠿⣿⣯⣄
⠀⠀⠘⣀⠀⢀⡘⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⡇⠀⢠⣤⣾⣾⣿⣿⣿⡿⠃⠀⠀⠘⠛⠛⠛⠛⠀⠀⠀⠙⠀⠛⠛⠉
⠀⠀⣾⡿⠟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠸⣨⠆⢸⡇⠀⠀⢀⡄⠀⠀⢸⣇⠀⡈⠙⠛⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢤⡀
⠀⠀⣿⣧⣾⣦⣿⡄⠀⠀⠀⣠⣼⣿⣿⣿⣿⣾⣿⣷⡄⠀⠀⢸⣇⣴⣿⣿⣿⣾⣧⣾⣟⣿⣿⣦⡀⠀⠑⠀⢸⣿⡶⣀⣀⡀⠀⠀⠀⠀⣀⣤⣶⣄⣀
⠀⠀⣿⣿⣿⣿⣿⡇⠀⠐⠛⠿⠿⣿⠿⢿⣿⣿⣿⠿⠛⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣡⣔⣭⡁⠀⢠⣤⡘⢷⣮⣵⣭⣯⣷⠀⣤⣄
⠀⠀⠉⠉⠉⠉⢩⣥⣄⣠⣤⣄⣀⣤⣤⡄⠀⠀⡠⠀⠀⠀⠉⠀⠀⢉⣉⣩⣍⣉⠉⠈⠈⢉⣉⠉⠉⢉⣡⠀⠰⠟⢨⣛⠁⠀⠨⠿⢦⣤⠶⠶⠶⠶⢦⣤⠾⠧
⠀⠀⢦⣼⣦⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⡇⠻⠿⢴⣤⠀⠒⠀⣠⠞⠉⢠⣾⡦⠈⠙⢦⠀⠘⠼⠃⠀⢺⣿⡀⠀⣠⠔⠉⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠉⣁⣀⣀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣶⣶⣶⢟⣠⣄⠐⠃⠀⠀⣠⣼⣤⡀⠀⠀⠃⠀⠀⠈⠻⣶⣽⣿⠇⠀⠀⠀⠀⠀⠀⠐⠄⡑⠀⢀⣀⡀
⠀⠀⢠⠾⣿⣿⣿⢷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⡄⠀⠸⠇⠀⠀⡠⢚⡳⣶⠼⠧⡀
⠀⠀⣄⠛⢲⣤⡖⡟⣤⠀⠀⠀⠛⠟⠿⠋⠙⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⡀⠀⢀⠂⠀⠀⠂⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣦⣤⣤⠄⠀⣷⣶⣶⣾⣶⣶⡆⠐⠿⠂
⠀⠀⠡⠟⣩⣿⣍⠷⠁⠀⠀⠀⢀⣠⣦⣀⠀⠀⠈⠙⠛⠿⠿⠟⠓⠀⠀⠀⠀⠀⠌⠀⠀⠁⠀⠁⠀⠀⠀⠈⣿⣟⣿⣿⣻⣻⠁⠀⠀⠈⠻⣿⣿⡿⠏⢀
⠀⠀⠀⠺⣿⠿⣿⠗⠀⠀⠀⠀⠈⣿⢿⡏⠀⡶⠆⠀⠶⡄⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⣴⣦⠄⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣄⠀⡀⢀⣄⠸⢀⡄
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠖⠂⠀⠀⠀⠀⠀⣷⣾⣿⣶⡇⣻⡇⠀⠀⠀⠀⠂⢀⢀⡄⠀⠀⠀⡉⠙⠀⠠⣤⣿⣷⣿⣿⣾⣿⣤⠄⠀⢤⡙⠄⠇⠰⠞⣿⠛⠦
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡉⠁⢰⠀⠀⠀⢀⡿⢿⡿⠿⣥⣿⡇⠀⠀⠀⠀⠀⠎⠳⠀⠀⠁⠱⠀⠀⠀⠀⠈⣿⣟⣿⣿⣻⣿⠁⠀⠀⠀⠀⢰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠀⢸⠠⠀⠀⣼⣷⡄⠁⣠⣿⡏⠀⠀⠂⠹⡂⠈⠀⠀⠀⠀⠀⠀⡤⢤⠀⠘⠻⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⣴⣶⣶⣶⡶⣦⠀⠀⢘⠀⢸⠈⠥⢠⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⡿⢶⡀⠀⠀⠀⢀⡀⠙⠚⠀⢠⣠⣿⣷⣿⣿⣾⣿⣀⡀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠈⢻⣿⣳⡿⠋⠀⠀⢰⠀⢸⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⠁⠀⠹⣶⡾⠧⣶⡾⠁⠀⠈⣿⣟⣿⣿⣻⣿⠁⠀⠀⠀⠀⢸⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡹⡆⠀⠀⠀⠀⢠⡀⠀⣠⠄⠶⣇⠤⡨⠂⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⢀⠴⠚⠋⢙⠀⠀⠀⠈⠀⠀⢗⣆⠀⣨⠅⣀⠄⠀⠀⠀⠀⠀⢠⠏⠸⠄⠈⢊⠀⣄⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⢀⠠⠴⠚⠋⠀⠀⠀⠀⠢⠀⠈⠛⠫⠀⢂⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢠⣎⣠⠄⢋⣘⠁⣄
⠀⠀⠀⠀⠀⠀⣀⣠⠄⠴⠋⠀⡀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⣀⠀⠀⡤⢯⡇⠈⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠰⠛⣉⠔⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠦⠰⠚⠁⠸⣏⠲⠀⠀⠀⢘⡇
⠀⠀⠀⠀⣰⣎⣁⠔⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠐⣒⠂⠀⠀⠈⠀⠀⠀⠐⠒⠂⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡔⢢⣤⠛
⠀⠀⠀⠀⠙⢿⡧⠊⠀⠀⠀⠀⠀⠀⠀⢀⡤⣚⠭⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠳⣄⡀⢀⠠⢄⡤⠤⣄⣠⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⣀⣴⡯⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢀⣀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠘⡆⠑⡶⠉⠑⠂⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠍⠚⡅⢰⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⠷⠚
⠀⠀⠀⢠⣍⣤⠞⡙⠠⡤⡌⠄⠀⠄⠀⠀⢱⠘⡧⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⢣⠏⡠⠊⠙⡆⢳⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠉⠚⢣⡼⠲⠔⠼⠀⠀⠀⠀⠀⢃⢧⠈⠑⠒⠤⠤⢄⣀⣀⣀⣀⣀⣀⡀⠤⠤⠒⠊⠉⢀⣮⠏⠉⠁⠀⠜⢁⠌⠀⠀⠀⣠⠘⢃⠀⠙
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣟⡠⠐⣀⠄⠂⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡞⣡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⣠⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣠⣞⠋⠉⠉⠉⠉⢉⣁⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣟⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢹
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⠀⠀⣀⣈⣉⣢⣶⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣫⡄⢸
⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠛⠋⢉⡴⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠈⢐⡇⢸⡆
⠀⠀⠀⠀⢀⡃⣀⣀⣀⡰⠂⠀⢠⠎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠒⢻⣟⠁⡈⠀⠈⡇⢸
⠀⠀⠀⠀⠈⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣿⣷⠿⣡⣶⡽⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢠⠈⠁⠱⣈⠳⡴⢁⡎
⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡹⢉⣺⣷⣤⣄⠀⠀⠀⠀⠴⣒⠉⠡⣀⣆⠀⣬⣀⠀⣲⠿⠉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢸⠅⠒⠀⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⣵⠿⣿⡍⠁⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣉⣉⣀⣉⣉⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣮⣦⣤⣀⣀⣀⡀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣺⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣯⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣲⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⣾⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠙⣿⣿⣿⣿⠟⢉⣉⣈⣹⡿⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⣿⣿⣿⣤⣿⡇⢺⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⡄⠘⣿⣿⠁⢠⣾⣿⠿⢋⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡘⣿⣿⣿⠀⣿⡇⢻⡇⢸⡇⢸⢿⡧⢾⡏⠴⣦⣽⣧⠈⣶⣾⣿⡿⠁⢰⣿⣿⡄⠘⣿⠀⠸⣟⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠻⣿⠇⣿⡃⢸⡇⠘⡇⠀⠊⠁⢸⡟⠳⠖⢸⣷⠀⠿⢿⡿⢧⣰⠿⠟⠛⠻⠀⠘⡧⣀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡘⢿⣿⠿⠋⠁⠂⠀⠐⠒⠁⠈⠻⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⠶⠋⣠⢞⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡴⣋⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⠋⣠⡶⡫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⠉⣤⢞⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⠷⣄⡀⡀⠀⠀⠀⣀⡴⠞⢁⡴⢚⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⣀⣉⣛⣛⣛⣋⣉⡤⠶⣋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣉⠉⠉⠉⠉⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⢿⣟⠛⠛⢻⣟⢻⣿⣿⣿⣿⣿⣿⡿⣟⠛⠛⠛⢻⣿⣿
⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⢸⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠃⢻⣧⠀⠀⢹⡆⣿⣿⣿⣿⣿⣿⣇⢻⡆⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠤⢤⠀⢸⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢿⣿⡟⣿⡿⣿⣿⣿⣟⠛⠿⠙⠾⣿⣿⣿⣆⢠⣻⣇⠀⠸⣿⣾⣿⣿⣿⣿⣿⣿⠈⢻⡄⠀⢸⣿⣿
⣿⣿⡇⠀⡇⢸⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⢿⣷⣿⡏⣸⡿⣧⢸⣧⡟⢿⣷⣄⡨⣿⣿⣿⣿⣿⣆⣿⣿⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⡄⢸⣿⣿
⣿⣿⡇⠀⢡⠈⠀⢸⠀⠀⠀⠀⢸⣿⣿⣿⠸⣿⣿⣷⣿⠃⢸⣾⣿⡇⠀⠙⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⣿⣼⣿⣿
⣿⣿⡇⠀⠈⠒⠀⢸⠀⠀⠀⠀⢸⡟⣿⣋⣀⣛⣻⣿⡏⠀⠈⢿⡇⢳⣠⡤⠾⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⢸⣿⣿
⣿⣿⡇⢰⣦⣔⡆⢸⠀⠀⠀⠀⢸⡇⣿⣇⢀⣩⣉⠛⠀⠀⠀⠀⠀⠈⢁⣠⣶⣶⣷⣵⣮⡽⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⡟⣼⣿⣿
⣿⣿⡇⠸⠰⡇⠁⢸⠀⠀⠀⠀⢸⣷⣿⣿⢿⢻⣿⡟⠂⠀⠀⠀⠀⠀⠘⠻⣿⡟⠀⠀⠞⠀⠀⣿⣿⡿⢹⣿⣿⡿⢻⣿⣿⣿⣿⢿⣿⣿⠟⠁⢸⣿⣿
⣿⣿⡇⠀⠀⠠⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⡏⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⡏⣴⣿⣿⣿⠁⢸⣿⣿⣿⣿⡇⣿⣿⡀⠀⢸⣿⣿
⣿⣿⡇⠀⠂⠠⠀⢸⠀⠀⠀⣸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢁⣿⣿⣿⣿⣾⣿⣿⣿⣿⠈⠀⢸⣿⣷⡀⢸⣿⣿
⣿⣿⡇⠀⢀⡤⠀⢸⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣼⣾⣿⣿⠀⣼⣿⣿
⣿⣿⡇⠀⠘⠄⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣧⣸⣿⣿
⣿⣿⣇⣀⣀⣀⢀⣸⠀⠀⣿⣿⣿⠁⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡇⠀⠈⢻⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡀⢹⣿⣿⡿⣿⣿⣿⣤⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢹⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿⠟⣸⠇⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⢿⣿⣿⣶⣿⣿⣷⣿⣿⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢹⣿⣿⣿⣿⣿⣧⣾⣿⡿⣻⣿⢃⡴⠃⠀⠀⠀⢼⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠙⢿⣿⣿⣿⣿⣿⣿⣾⢿⣿⡿⠏⠑⠀⠤⠀⠀⠀⠀⠀⠐⠼⣿⣿⣳⣿⣿⣿⡿⢋⣼⠿⠻⠋⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⢹⣿⣿⣿⠿⠏⠸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣱⣿⡿⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠵⠚⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⠀⠀⠉⠉⠉⠉⠀⠀⠐⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡨⠐⠂⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⡘⡠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠠⢐⠡⠊
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡨⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠢⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠐⠁
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣂⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢋⡤⠒⠂⢀⠀⠀⢙⡆⠀⠀⠀⠀⢀⣠⠔⠚⢉⠀⠀⠀⡉⠉⢑⠀⠀⠀⠀⢀⣤⣴⣶⣮⣍⣉⠉⠒⢤
⠀⠀⠀⠀⠀⢀⠎⣀⠈⠁⠀⢀⢀⣨⠇⠔⡊⢠⠀⠀⣠⡖⢩⠀⠀⠀⠀⡨⠖⠈⠀⠀⠁⠀⠀⡠⠂⠉⠉⠉⢛⠤⣀⣀⣱⡆⠈⢱
⠀⠀⠀⠀⣠⣧⡊⢀⡰⠆⠒⡉⡠⠀⣀⠬⠐⠁⠀⢰⡡⠄⠒⠒⡠⠔⠉⠀⠀⢀⣁⠔⠀⠀⢸⡁⠀⠀⢀⠔⣡⠤⠺⣿⣿⣿⠔⠉
⠀⠀⠀⡜⠘⣡⠞⠲⠤⣌⠭⠉⠒⠉⠀⠀⠀⠀⠀⠸⣉⠒⠒⠩⠄⠀⢐⡮⠔⠁⠀⠀⠀⠀⠘⢆⠉⠀⡉⠉⠀⢀⡘⠿⠛⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠛⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠤⣞⣩⠊⣙⣯⠵⡤⢄⠀⠀⠀⠀⠀⢀⡴⢉⡯⢥⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠠⠤⢤⣴⣀⡀
⠀⠀⠀⠀⠀⡴⢳⡴⣏⡠⢏⣀⡽⢤⠚⠚⡄⠀⠀⠀⠠⣾⠀⠊⣀⣠⢥⡴⡗⠲⠦⡀⠀⠀⠀⢀⣤⡄⡀⢠⣙⣃⠨⡀⠽⣃⢠
⠀⠀⠀⠀⠀⠑⣾⣀⣸⣀⣀⣽⣄⣠⠶⡞⠀⠀⠀⠀⢠⠛⡚⠿⢸⢉⣳⡾⠢⢤⡈⠀⠀⠀⠀⢀⠝⣶⣾⣵⣮⣷⣬⣥⢲⣮⠞⠳
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠄⠀⠇⠀⠀⠀⠈⣈⠂⡘⠦⠊⣎⣠⠓⢀⡾⠁⢠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⡄⠸
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⣀⠀⠀⠀⠀⠀⠈⠁⢧⡐⠀⠓⠛⠉⣁⡤⠒⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠠⠀⠂⢄⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠀⢀⠠⠂⠁⠀⢀⡠⠖⠃⠂⢄⠀⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⡀⡀⣤⣦⣀⠀⡤⠒⠁⠀⠀⢀⠠⠚⠁⠂⠄⠀⠀⠀⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⡄⣤⣤⢤⣀⠈⢁⡬⡝⣦⣤⣤⡀⠂⠁⠀⠀⢀⠠⠊⠉⠑⠀⡀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⢠⠔⠋⠁⠀⠀⢀⣤⣤⣤⣀⠈⠁⡬⡜⢶⣶⢧⣅⠈⠁⡀⡥⡤⢄⡀⠊⠀⠀⠀⢀⣠⡞⠉⣹⡤⠠⡀⠀⠀⠉⠓⢤
⠀⠀⠀⢸⠀⠀⠀⠀⠰⠋⠉⠛⢉⣽⣧⣄⣡⡄⠀⠁⠀⢈⢀⣺⠉⠀⠀⠀⠈⡆⠀⣠⡞⠅⣹⠭⢾⠿⢀⣴⠷⠉⠁⠀⠀⠸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠋⠁⡌⠗⠚⠲⢤⠋⠀⠈⢱⠒⠀⠨⠤⣕⢤⣌⣩⣞⣧⢀⣼⠗⠋⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠂⠀⠀⢀⡀⠇⣀⡄⠘⠠⢀⠀⠀⢢⠤⠙⢩⡄⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠆⠀⠈⠉⠁⡠⢒⣂⠳⢜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠁⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠠⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠖⠂⠒⠒⣾⠀⠀⠐⠦⠞⠱⠏⠀⠧⢸⡁⠟⠰⡥⠼⠇⠟⠉⠧⠀⢿⣿⣿⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠐⠀⠀⠈⠂⠀⠂⠀⠀⠀⣀⣀⠀⠀⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠯⠞⠃⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⠅⠀⠀⠀⠠⠀⠀⠀⠀⢻⠟⢹⣦⠀⠀⠀⠈⠁⢀⡆⠀⠶⠀⢰⠄⠉⠀⠀⠓⠀⡄⢀⢀⡀⠀⠀⠀⠈⠀⢉⠀⠀⠓⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠰⠀⠀⠀⠀⢐⠀⠀⡀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢀⡀⠀⡀⠀⢠⠄⢁⡀⠀⠂⢀⡄⠀⢧⡐⠛⠂⠐⠂⠀⢨⣶⡀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⡐⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⣁⠀⢠⠷⠶⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠈⠐⠡⠀⠀⠠⡵⠀⠀⠀⠀⠀⡰⠟⠉⠳⡈⠁⠀⠀⠥⠤⠄⠀⠀⠤⠼⠅⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⢘⣽⡄⠀⠀⠀⠀⠀⣷⢧
⠀⠀⠀⠀⣔⡶⠶⠚⠃⠀⠀⣒⣿⣦⠀⠆⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠓⠀⠀⠀⠀⢸⣮⡅⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⢹⢗⣀⣆⠀⠀⠐⠉⣸⠃⠀⢀⠀⠀⠀⢀⣌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠈⠬⠁⠀⠀⠀⠀⠀⠈⣷⣇
⠀⠀⠀⠀⡼⣄⣸⣟⠄⠀⠀⠀⠃⠀⠀⢰⡀⡀⠀⠚⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡞⠻⢇⡀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⢀⣴⡡⡏⠁⠀⠀⠲⠀⠀⠳⠀⠈⠋⠁⠲⠃⠀⠀⠀⠂⠀⠀⢀⣀⣀⡤⠒⠉⠀⠀⠀⠉⠢⣄⣀⣀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⣛⡻⢦⡄⠀⠀⠀⠀⢢⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠚⢋⡁⣀⣀⣀⢀⢀⠀⠒⠦⠈⠙⠛⠶
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣈⡙⠟⠄⠈⠀⠀⠀⠀⠀⠙⠃⠈⢀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠈⠀⠁⠌⠡⠠⠉⠄⢈⠥⠀⠈
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⢿⡟⢿⡄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣘⣛⣛⣓⣚⣻⣤⣄⣀⣤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠊⠀⠀⠙⠀⠀⢠⣔⠛⠃⠀⠀⠀⠀⠀⡐⠁⢀⣾⠀⠀⠀⠀⠀⠀⠀⣈⣡⣉⣉⣡⣂⣀⣠⢂⣀⣠⣂
⠀⠀⠀⠀⠀⣀⣀⣒⠛⠛⠛⣻⡦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢘⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠨⠿⠧⢤⠺⠧⠶⠿⠶⠶⡾⠿
⠀⠀⠀⢀⠤⢶⡿⢻⣿⠀⡼⠋⣰⣿⠀⠀⢳⡤⠀⠀⠀⠀⠀⠀⠀⡤⠠⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⣠⠰⠆⠴⠃⠤⠾⠄⠺⢤⣄⣀⣀⣠⣀⠄
⠀⠀⠀⠀⠀⠊⠀⠋⠘⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⡐⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢛⣝⠋⢩⡍⠙⣍⠋⣩⡛⠛⠛⠋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣾⣾⣷⣿⣷⣾⡚⠛
⠀⠀⠀⠀⠀⠀⠐⠁⢿⠈⠃⠀⠀⠀⣀⠤⢀⡀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⠻⠵⠾⠖⡐⠀⠀⢚⠻⢝⢛⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⢶⣷⠶⢶⣼⡤⠄⣾⡀⠀⢰⣷⠆⠀⠀⠀⠀⠐
⠀⢠⣐⣂⣠⠀⠀⣀⠀⢀⠀⠀⠀⠀⠸⠇⠚⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⠈⠷⠠⠄⠀⠀⠀⠀⠋⠛⣒⠲⢚⡩⠉⣉⡉⢉⡭⠛⠁
⠀⠘⠛⠻⣦⣎⣀⣼⢷⣶⡾⠀⠀⠀⢤⣤⣤⠀⠀⠀⠀⠀⠀⠣⠾⡁⠈⠀⠀⠀⠀⠀⠰⣶⣶⣤⣤⣤⣖⣛⣐⣎⣁⣒⣉⣁⣉⣓⣲⣦⣤⣴⣶⠴
⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠸⠀⠀⠀⠈⠋⡉⠉⠳⠜⠀⠲⠂⠈⣾⠉⠡⠋⠉⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠀⠀⣀⣤⣤⣀⠀⠀⠢⠔⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⣿⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡠⣴⠾⣿⣿⣿⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⣖⠀⢒⡀⣀⠸⣿⣿⣇⡀⣐⠂⠐⢒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⠿⣿⡏⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⢻⢯⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⡅⡰⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠶⠒⠒⠒⠶⠶⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠛⣛⣉⣉⣭⣭⣭⣭⣭⣉⣉⣙⠛⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣼⣿⣤⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠘⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃⠀⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢹⡷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣠⡾⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⢁⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺
⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐


⠀⠀⠀⠀⠰⣮⣶⡄
⠀⠀⠀⠀⠘⣻⣿⣷
⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠐⡻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠤⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠀⠀⡡⠀⢀⣀⡟⡤⢠⣠⡄⡄⣠⢠⣠⡤⣄⢸⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠰⠀⠐⠅⠀⠀⠀⢀⣀⠀⠘⠃⠀⠈⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠂⠄⠀⠀⠀⢘
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠟⠹⠦⠀⠀⠈⠁⠶⠀⠂⠰⠆⠈⡀⠃⠠⣠⢤⡀⠀⠀⠁⣠⠀⠈⠀⠀⠀⠀⠠
⠀⠀⠈⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⡆⠰⠀⠀⠐⠀⠘⣮⡀⠈⠀⠀⣿⠀⠀⠀⠀⢺⡆
⠀⠀⠂⠥⠀⠀⡏⠀⠀⠀⢀⠖⠛⢏⠀⠀⠰⠤⠄⠀⠦⠴⠀⠀⠀⠁⢊⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⢸⣧
⠀⠀⠀⣾⡖⢺⠃⠀⡩⢿⠆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠈⠁⠀⠀⠀⢿⠆⠀⠀⠀⠀⣿⡄
⠀⠀⠀⣹⣿⣿⡀⠀⠀⠎⠀⢠⠀⠀⠰⠓⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠻⠃
⠀⠀⠀⠉⠉⠉⠀⠀⠀⣀⣠⣎⡟⠀⠀⠤⠀⠲⠀⠒⠂⠴⠀⠀⠀⠀⠀⢀⣀⡠⠔⠈⠀⠈⠢⣄⣀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣽⡳⣦⡀⠀⠈⠢⡆⠀⠀⠀⠀⠀⠀⠹⠀⠈⠛⠁⠀⢠⠐⢖⠒⡒⢒⠛⠓⠁
⠀⠀⠀⠀⠘⠀⠀⠀⣴⣶⡜⠁⠀⠀⠀⣀⠀⠀⠀⠒⠒⠀⠀⠀⠄⠑⠀⢀⠀⠀⣱⡭⣤⣽⣎⡀⠀⡀
⠀⠀⠀⠀⠀⠃⠀⠈⠘⠁⠙⠀⠀⣤⠒⠃⠀⠀⠀⠠⠂⢠⡧⠀⠀⠀⠀⠈⣙⡏⡙⣟⠀⣚⠉⢩⡋⠁
⠀⠀⠀⠀⣤⣬⡉⠉⣽⢂⡀⠀⡄⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡿⣛⠙⣛⢚⡟⠃
⠀⠀⠀⠈⠟⠙⠻⠘⠁⠚⠃⠀⠙⠁⠀⠀⠀⠀⠀⡅⠄⠀⠀⠀⠀⠚⢷⠶⠶⣮⠽⣭⠽⡹⢼⡿⠶⠶⠾⠒
⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⣶⣿⣶⣷⣾⠓
⠀⠀⠀⠀⠀⠁⠃⠉⠀⠀⠠⠐⡠⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⠛⡅⠉⢭⠉⠉⡍⠉
⠀⠀⢄⢀⠀⠀⢀⠀⠀⠀⠐⣄⠤⠀⠀⠀⠀⣄⠀⠀⠀⠀⢢⡀⠀⠀⠀⠈⠿⠯⣽⣿⠓⠛⠲⣚⠿
⠀⠛⠻⣭⣆⣼⢶⣷⠆⠀⠠⣤⣤⠀⠀⠀⠀⠻⠶⠁⠀⠀⠀⠀⠠⣶⣤⣤⣤⣚⣲⣛⣖⣛⣚⣗⣦⣤⣤⡦⠄
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠉⠎⠉⠏⠀⣏⣀⡏⠠⠏⠁⠜⠈
⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠔⢂⣠⣴⣿⣿⣦⣄⡈⠁⠀⠀⠀⠀⡄⠀⠄⠀⣼⣿⡇⠀⡤⠀⡄
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠉⠉⠉⠀⠀⠀⠀⠁⠉⠉⠛⠛⠛⠛⠊⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠