Kiddie Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠠⠂⠉⠑⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⢦⢀⠀⠳⠆⠀⠀⠀⠀⡇⠀⠀⠀⠠⠀⡠⡀⠀⠀⠀⠆⢑⠀⡅
⠀⠀⠀⠀⢠⠀⢂⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠘⠆⠘⠋⠀⠀⠀⠀⠀⠀⠀⡁⠂⠀⢠⠲⠴⠦⠀⠀⠀⠀⠢⠤⠊
⠀⠀⠀⢠⠏⠀⠀⠛⡙⡤⢤⠤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠿⠀⠀⢸⠀⠂⠀⡀
⠀⠀⣀⡙⠀⠀⠀⠈⢈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠋⠀⢺⢬⠇⠀⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⡐⠁⠑⠢
⠀⠀⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⡼⠀⠀⠀⠀⠀⠀⠘⠚⡀⠀⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⢀⠀⠀⢠⣶⠄⠀⠜⣀⠞⢁⠁⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⡒⡎⠁⢀⢬⣡⠆⠀⡰⠣⠔⠂⠀⠀⠀⠀⠀⢠⢁⡆⢢⡀
⠀⠀⢀⠔⠐⠄⠀⠀⠀⠢⠴⠀⠀⠀⠀⠀⠯⠁⠷⠀⠀⠉⠁⠀⠀⠁⠀⠀⠠⣀⠀⠀⠀⠀⢿⡀⠁⡜⢳
⢀⠠⣲⠤⠤⠂⠀⠀⡤⡀⠀⠀⠀⠀⢀⣖⢶⣆⠀⠀⠀⠀⡒⠒⡀⠀⠀⠈⢄⠔⠀⠀⠀⠀⢎⠟⣶⠀⠀⢂⠂
⠣⠬⠅⠀⠀⠀⠀⠀⡧⢷⠀⡆⠀⠀⡼⠯⣡⠋⠀⠀⢀⡞⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⡲⠢⢼⠙⡄⠀⠀⡸⠒⠃⠀⠀⠀⣎⠠⡜⠀⠀⡠⠊⠄⠈⠂⠀⠀⠀⠀⠀⠀⠰⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠉⠀⠀⠰⠁⠀⠀⠀⠀⢸⣡⡶⠁⠀⠘⡇⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀⠀⠉⡄
⠀⠀⠄⠀⠀⠀⠀⢀⠀⠠⠀⠄⠄⠀⠀⠀⠀⠀⠐⠲⠼⠀⠀⠀⠀⢃⠰⠔⠊⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠠⠀⠃⠀⠀⠀⠀⠤⠀⠒⠀⠂⠒⠄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠑⡦⠠⡔⠁⠀⠀⠀⠀⠀⣔⠄⢀
⠀⠀⠀⠀⠀⠐⠧⠠⣶⠄⠀⢺⡖⠂⠀⠀⠀⠀⠈⢣⣷⡼⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⠐⠉⢀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠒⣂⣠⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⣴⣤⣾⣿⣶⣾⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⢫⣶⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣇⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⢠⣿⣿⠛⠻⢿⣿⣿⠿⣿⡿⠆⠀⠀⢸⡿⠋⠉⠛⠿⠿⠿⢿⣿⣿⠁
⠀⠀⣴⠧⣀⣴⣿⣿⣿⣿⡍⠙⠀⠁⠀⠉⠁⠀⣧⡄⢸⣿⠡⠤⠀⠀⠀⠒⠀⢹⡇⠀⠀⢀⣼⠃⣀⡁⠀⠀⢀⡒⢀⣿⡏
⠀⠈⠑⠠⠀⣿⣿⣿⡇⠻⠁⠈⠁⠀⠀⠈⠁⠀⡅⠀⠾⣿⢈⣿⡆⠀⠰⣿⡅⢸⢋⣀⠀⠀⢸⠈⠿⠀⠀⠐⢿⠄⢈⠟⠆
⠀⠀⠀⠀⠀⢀⠙⢿⣿⣿⠀⠀⠠⣤⣤⡄⠀⠀⠀⠀⠐⠼⠀⠉⠀⡀⢀⠀⠀⠸⠛⢫⠄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⣴⣿⣿⣷⡀⠹⠻⢅⠀⢀⡀⢁⡠⠀⠀⠀⠆⢀⠈⠡⠀⠈⠛⠛⢁⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⣀⠀⢠
⠀⠀⠀⢿⣿⡟⠉⠉⠄⡀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠨⠁⠀⠀⠀⠙⠂⠈⠃⠠⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣶⣾⣿⣶⣤⡀
⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠔⠀⠀⠀⠀⠀⠀⢢⠄⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠉⠐⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠠⠀⠀⠀⠀⠄⠀⠂⠀⠈⠰⠂⠠⠀⠀⠀⠀⠤⠐⠒⢀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠔⠂⠀⠘⢀⠀⠀⡀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⡘⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠐⠒⠇⠀⠀⠀⠰⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠇⠃⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⡌⠢⢤⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣸⣀⡠⠂⠀⠀⠀⠰⢄⡀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡤⠞⠀⠀⠀⠀⠳⢤⠘⡀⠀⣃⡤⠚⠀⠀⠀⠀⠀⠑⠀⣀⡀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁



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

⠀⠀⢀⠠⠠⢄
⠀⠠⠁⠀⠀⠀⢂
⠀⠁⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠠⠁⠀⠀⣀
⠀⠢⣀⡀⠄⠁⠀⠀⠘⠤⠅⠀⠀⠂
⠀⠀⠢⠓
⢀⠀⠀⠀⠀⢐⢶⡄⣆⣀⢠
⠚⠃⠀⠀⠰⠚⠉⠁⠈⠉⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠐⠀⠀⠀⡈⠀⠀⠀⠠⢬⠄
⠀⠀⠂⡀⠀⢀⠀⠀⠁⠀⢰⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⡀⠐⢄⠀⠂⠄⠀⠄⠁⡠⠊⣀⡀⠀⠀⠀⠂⠀⢀⠼⠀⠀⠠⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⢁⠀⠀⠉⠐⠒⠒⠂⠁⠀⠀⠉⠠⢀⡌⠀⠀⠀⠁⠀⠐⠄⢐⠄⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠐⢀⠇⣀⣀⡃⠀⠀⠀⠀⡘⡎⠀⠀⠀⠁⠀⠀⠀⠆⠀⠑⠠⠁⠀⠀⠐⢝⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠠⣂⠀⡀⢀⣁⠀⠀⠐⢢⣀⢃⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠐⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡠⠂⠀⠀⠈⠜⠒⠲⢂⣤⠄⢀⠀⠡⠄⠑⠤⠠⠔⠀⠀⠀⠀⠈⠀⠦⡀⠀⠀⠀⠀⠁⢤⣹⣠⡢⠀⠀⠀⠀⠀⢀⠄⠊⠙⠳⠟⠦⡤⣆
⠀⠀⠋⠀⠠⠀⠈⠉⠒⠨⠴⢤⡤⠔⢉⠢⡄⡑⠀⠁⠒⠒⠀⠀⠭⡉⠉⢀⠂⡠⠂⠀⡄⠀⠀⠀⠈⠉⠛⢶⡅⡀⠨⠁⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠠⠄⢃⡀⢀⠠⠀⠆⠀⠂⠁⠀⠀⢰⠎⡀⠀⠀⢠⠀⠀⠀⣱⠀⢸⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⣇⠐⠀⢄⠀⠀⠀⠀⠀⠀⢀⡀
⠰⠆⢀⡀⠔⢀⠁⠀⠀⢀⠀⠀⠠⠀⠀⠀⢀⠁⣇⣀⣀⠈⠤⠠⠐⠁⠀⢸⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⠀⠑⣤⣀⠀⠠⠐⠁
⠀⠀⢈⢃⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠠⠸⠈⠁⠀⢆⣀⣀⠀⢀⠀⠄⢆⠀⠉⠰⠆⠒⠁⠀⠀⠀⢀⠆⠀⠀⣔⠀⣀⠀⠈⠀⡀⠀⢠⠀⠠⠶
⠀⢠⠀⠉⠑⢄⠀⠈⠀⠀⠀⠒⠁⢀⠠⠊⠀⢀⠘⠀⠀⠀⠀⠉⠉⡀⠐⠀⠀⠀⢱⡄⡀⠀⠀⠀⠀⠀⣀⡠⢊⡤⠂⠀⢰⠀⠀⠁⠀⠈⠁
⠀⠙⠐⠢⢄⣀⣈⣀⠀⢰⠲⣖⡚⠱⡐⠀⠐⠋⠀⡀⢤⠀⠀⢐⡇⠀⠀⣷⠀⢀⠃⠐⠉⠑⡖⠀⢈⠩⠅⠊⠁⡤⣄⠀⠀⠀⢀⠀⠀⠀⠀⠺⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣷⣶⣶⣄⠀⠀⠀⠠⠴⠶⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠿⠿⡇⢀⣶⣿⡿⣿⣿⣷⣮⣿⡇⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⢠⣾⣿⠿⣿⣿⣿⣿⣿⠆⠀⠀⠀⢛⠋⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⣾⣟⠁⠀⠀⠉⠁⠈⢹⠀⢠⠄⠀⣤⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠉⡐⠀⡀⠏⠉⠉⠁⠈⠀⠹⣿⣿
⠀⠀⠀⠍⠛⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠷⣤⣄⡀⢀⣰⣅⠲⠀⠀⠀⠈⠉⠀⠀⢀⣼⠧⠀⠙⠀⠀⠀⠀⠀⠀⠀⠙⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠁⠈⠉⠁⠀⠀⠀⡓⠶⠀⠶⠟⣋⡵⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⢺⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒


⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠐⠁⠔⠊⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡑⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⢁⠤⠀⠀⠈⠉⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠦⠀⡀⣀⠀⠀⠀⠀⠀⡀⠋⠀⣠⠕⠁⢀⠠⠐⣀⠄⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠔⠀⡆⠁⠒⢄⣀⠨⠃⠀⠈⢀⣀⠊⠀⠀⠀⠀⠸⠀⠀⢐⣧⡞⠉⠐⣀⠥⠐⠊⠁⠠⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⡀⢁⢁⠀⠀⠈⠁⠀⠀⠀⠀⣠⠀⠀⡀⠀⠀⢠⠀⠀⡠⠂⠊⠃⠀⠀⠡⠄⠀⠀⠀⣠⡁⠈⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢐⠀⠢⠀⠀⠀⢿⡆⠀⠀⡀⠻⠃⠀⠂⠀⠀⠀⠀⡜⠀⡀⠀⠂⠈⠀⢸⣷⠀⠀⠀⠹⠃⠀⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠩⠂⠀⡀⠀⠀⠀⠀⠀⢇⠀⠋⡄⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⢀⣣⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠐⢄⠀⠀⠀⠀⠁⠤⠚⠀⠀⠜⠀⠀⠀⠀⠀⠘⡜⣄⣴⠖⡀⠀⠀⠀⠀⠈⠒⠀⠀⡠⢋⠏⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⢀⣀⡠⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⣷⠤⠀⠐⡦⠀⢠⡤⠄⠒⠉⠅⢨⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⢃⢱⢰⡯⢛⡒⠚⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠘⠀⠀⠀⠄⠀⠡⠰⣄⢆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢍⡳⡜⠞⠚⠉⠉⠁⠀⠐⠒⠓⠀⠐⠀⠒⠀⠀⠀⠀⠌⠉⠠⠅⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⠢⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⡄⠀⠀⠀⠀⠀⡒⠬⠝
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠐⡖⠶⠤⠤⠄⠤⠤⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠀⠀⢰⠄⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠠⡶⠀⡘⠋⢠⡄⠐⠶⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡙⠁⣶⠄⠈⠋⢀⣄⠀⠰⠇⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⢠⣄⠀⠿⠀⣈⠁⢰⣦⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠠⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡀⠂⠀⠀⠀⠀⡆⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡨⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠦⢤⣀⡃⠀⠀⠀⠀⠀⢀⣀⡤⠔⠚⠀⡀⠀⠀⠀⠀⠀⠀⠠⠥⠒⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣀⣑⣈⡆⠀⠀⠀⠀⠨⣠⣀⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠐⠤⢌⣈⡀⠀⠀⠀⠀⠀⠐⠄⠆⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⣀⠀⣖⣤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣢⠀⡠⢂⡀
⠀⠀⠀⠀⠀⠀⢟⢿⠇⠿⡿⣽⣱⣢⠆⠀⠀⣠⠖⠲⣞⢷⡴⠶⣆⣖⣦⠖⠛⢲⡀⠀⠀⢛⣉⠷⢶⣄⡀⠀⠖⢶⣄⣀⣀⣽⢻⣿⢿⣷⢿⡀⢀
⠀⠀⠀⠀⠀⢠⠎⠀⠄⠠⡄⠈⠛⢟⠀⠀⢰⠃⢠⠞⠁⠈⠀⠀⠀⠈⢯⠙⡆⡸⠁⣤⡖⠉⠈⠰⠋⠏⣿⢷⢄⣸⣿⣝⡿⠉⠛⠙⣿⡍⢿⣿⣿⣶⡞
⠀⠀⠀⠀⡠⡏⢀⡀⠐⠀⠀⠀⠀⢸⣀⠀⢸⢠⣯⠀⢻⡀⠀⠀⠀⡤⠘⣶⢣⡇⠀⢸⠀⢼⠀⠁⠂⠀⠀⢈⡎⠻⣿⡏⠀⡆⠀⠀⠀⢠⠀⣯⣿⣯⣟
⠀⠀⠀⠀⠈⢳⡀⠳⣄⣀⣠⠞⢀⡞⠋⢀⣾⠞⠈⢆⠀⠙⠒⠒⠋⢀⡼⢻⠘⡇⠀⠈⢦⡘⢤⡤⠞⠁⠀⡼⠗⠈⠃⢇⠀⠳⢤⣠⠴⠃⢠⠇⠻⡥
⠀⠀⠀⠀⠀⠀⠑⣦⢄⣀⣠⠴⠋⠀⠙⠃⠁⠀⠀⠀⣙⡶⠤⠴⣞⠉⠀⠘⢦⡹⠆⠀⢀⣹⠲⠤⣤⠴⠊⠀⠀⢞⣶⠈⠳⣤⣄⣀⣤⠖⠋
⠀⠀⠀⠀⢠⠖⢋⣏⡤⢤⣼⡗⣄⠀⠀⠀⣀⣠⠴⠋⣹⡇⢢⠒⢼⢦⠀⢀⣀⣀⣴⠋⣩⠃⠀⠀⡟⠉⣷⠤⠖⠃⠀⠀⣞⣁⣠⡀⢈⡇
⢠⣤⡔⠚⢹⣀⡞⠀⠛⠁⠈⣧⣼⢦⡀⠈⠑⠇⠀⡰⠃⠈⠽⠂⢸⡀⠱⣜⢋⠀⢸⡞⠁⠀⠀⠀⣿⠢⠟⠀⠰⣶⠖⢩⠏⠉⠶⠉⢣⠈⠲⢤⡔
⠀⠁⠃⠀⢠⡞⠀⠀⠀⠀⠀⢳⠀⠀⢹⣾⠀⠀⢼⡁⠀⠂⠀⠀⠈⣇⠀⠘⠋⠀⢯⣀⡀⠀⠀⠀⢻⠀⠀⠀⠘⢁⣴⡁⠀⠀⠀⠀⠈⣆⠀⠚⠉
⠀⠀⠀⠀⠀⢹⠗⠶⠠⠤⢤⠞⠀⠀⠈⠀⠀⠀⠀⣸⠓⢲⢶⠒⢶⠚⠀⠀⠀⠀⣠⠋⠁⠀⠈⠉⡏⠀⠀⠀⠀⠈⠛⠯⢿⣲⢞⣿⡽⠭⠆
⠀⠀⠀⠀⢠⠏⠀⢀⢴⡀⠈⣇⠀⠀⠀⠀⠀⠀⢠⠇⢀⡏⠈⣇⠈⡇⠀⠀⠀⠰⢧⣀⣰⠳⡄⣠⠹⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⠀⢣⣀
⠀⠀⠀⣔⠉⠀⢄⡜⢈⣧⠄⠚⡆⠀⠀⠀⣀⠤⠼⣶⡞⠀⠀⢹⣤⣟⣀⠀⠀⣀⠴⡃⠀⠀⠀⠘⣄⣀⡀⠀⠀⢀⣴⠣⡼⠀⠀⠀⢫⡭⢦⣀
⠀⠠⣎⢉⣙⠦⠞⠀⠈⢧⣔⡒⣳⡤⠀⠈⠓⠒⠲⠚⠁⠀⠀⠘⠫⠤⠼⠇⠚⠶⠶⠃⠀⠀⠀⠰⠧⠤⠞⠃⠈⠓⠒⠒⠃⠀⠀⠀⠀⠳⠴⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠘⣿⣿⣿⣿⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣶⣶⣦
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡀⠀⠀⠀⢀⣤⣤⡈⠻⠷⣦⣬⣿⣿⣯⣤⣶⠶⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⢀⣴⠶
⠀⠀⠀⣤⡀⠙⢿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⣹⣿⣿⡏⠁⠀⠀⠀⠀⠈⢠⣴⣤⡄⠀⠀⠈⠷⢤⣤⣀⣛⣽⣿⣿⣠⡶⠋
⠀⠀⠀⠈⠙⠳⣾⣿⣿⣧⣤⡀⠀⠀⣨⣿⣿⡅⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠐⢻⣿⣿⡿⠀⠀⡀⠀⠀⠀⠙⠛⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⢀⣼⣿⣿⣿⣿⣆⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⣿⣿⡷⠾⠛⠃⠀⠀⠀⠀⣰⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⠘⢿⡀⢸⣿⡿⣿⣿⠀⠀⠀⠀⠀⣼⡿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢰⣿⠏⢿⣿⢠⣿⡟⠻⣿⣿⠀⠀⠀⢸⣿⠀⣸⣿⠀⠀⠀⠀⠐⢟⣵⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠈⣿⡏⣿⡏⠉
⠀⠀⠀⠀⠀⣠⣿⣿⠀⢸⣿⠀⠙⠃⠀⢿⠿⠀⠀⠀⢸⣿⡗⣿⣿⡀⠀⠀⠀⠀⠈⢿⡏⠀⠈⢹⣿⠀⠀⠀⠀⠀⠀⣿⡀⢸⡇
⠀⠀⠀⠀⠀⠻⣿⡿⠀⣾⣿⠀⠀⠀⠀⣾⡆⠀⠀⠀⠘⠛⠃⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⣠⣾⡷⠀⢺⣗⠀⠀⠀⠀⢲⠃⠀⠀⠀⢠⣤⡄⢸⣶⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢻⣷⠀⣘⣷⠀⣴⣂⢀⣾⡧⠀⠀⠀⢸⣾⠃⢺⣿⠀⠀⠀⠀⠀⡀⠊⣡⣤⣤⣤⡟⠀⠀⠀⠀⠀⠀⣾⡀⣸⡁
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣟⡃⠀⠸⣿⣿⣿⡷⢀⣴⠀⢈⢿⣦⣾⣿⠀⠀⠀⠀⠀⠹⣦⣽⣭⠿⠁⠀⠀⠀⠀⠀⠐⢶⣟⣷⣿⣿⠖
⠀⠀⠀⠀⠀⢀⡀⢸⣿⡿⠿⠂⠀⠙⠫⣿⣿⠟⠁⠀⠀⣮⣼⣿⡟⠀⠀⠀⠀⠀⠀⣈⣿⣿⡋⠀⠒⠂⠀⠀⠀⠀⠀⣽⣿⣿⡁
⠀⠀⠀⠀⠀⢁⣴⣿⣿⣷⡄⠀⠀⠀⢾⣿⣿⠆⠀⠀⣀⣙⣿⣿⣂⡀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠄⠒⠂⠋⣙⣻⣿⣛⠛⠦⣄
⠀⠀⠀⠀⠀⠘⠿⠛⠿⠛⠀⠀⠀⠀⠀⠀⠈⡤⠖⠉⠉⣭⣿⣿⣯⡉⠉⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠈⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⢠⣤⣀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣠⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⢴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⣿⣿⣿⣿⣿⣿⢿⣿⠿⠋⠻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠋⠁⠀⠀⠈⠉⠙⠛⠻⢿⣿⡇⠀⢿⠃⠉⠁⠉⠁⠀⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⠖⡆⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢠⡀⠀⠄⠀⠀⠀⣠⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠙⣱⠂⡄
⠀⠀⠀⠀⠀⠀⠀⣦⡅⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢡⠔
⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⣀⣠⡄⡁⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⠄⠰⢿⣿⣿⣿⣧⠀⠀⠀⠀⠐⠀⢈⡁⠀⢠
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠈⢿⣿⣿⣿⡆⠀⠀⠈⠠⠀⡈⠀⠀⠀⠉⠀⠠⡀
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⢅⠀⠀⠀⠀⠀⠀⢽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⠁⢂
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠇⡄⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠤⢨⠀⠀⠀⠀⠀⠀⢀⠀⡷⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠁⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠐⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋⡃⠀⠀⡋⠃⠀⠀⠀⠀⠀⠄⡤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⠅⠀⠀⣏⣑⡢⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠈⠙⠉⠁⠀⠀⠘⠛⢿⣿⣿⡏⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠻⠷⠗⠀⢨⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⡠⠶⠶⣦⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣉⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣇⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠠⣤⣤⣤⣾⣿⡁⠻⣮⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⠛⢿⣿⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⠀⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⣾⣿⡀⢸⣶⢂⡸⣧⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⢈⠿⠿⢿⣿⣿⣿⣿⣯⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣦⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠉⡟⠛⠳⣤⣀⣀⣨⣿⣿⣿⣿⣿⣿⣷⢹⣿⡾⢿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠁⠀⠀⠀⠉⠉⣉⣩⣩⣿⣿⣿⣿⣿⠆⠀⣴⣿⣷⡙⣿⣿⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⠀⠀⠀⠀⣠⡴⢶⣛⠉⣛⣛⢿⣿⣿⣿⣿⡆⠠⡘⣋⣬⣿⣿⣿⣿⣿⢷⠌⢁⣽⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣷⣶⣦⣴⣷⣴⠾⠋⠙⠋⠋⣈⣿⣿⣿⠔⠻⠿⣿⣮⣿⣿⣿⣿⣷⣾⣿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣏⣉⣩⣤⣤⣤⠀⢁⣴⡟⢁⣠⣶⣿⣿⣿⢿⣿⣯⡛⠛⣻⡿⣿⣿⣿⣿⣿⣿⡿⠦
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣠⣿⣿⣿⡿⠟⠛⠛⠉⠉⠛⠒⠾⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⡿⠟⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣆⣤⣤⣶⡄
⠀⠀⠀⠆⠀⢠⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⣤⣴⣾⣿⣷⡀⠀⠀⠀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠁⠀⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⡅⣄⠀⠀⡇
⠈⢳⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣷⡏⢷⣄⣧⠈
⠀⠈⢻⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣷⡇⢀
⠀⠸⢧⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣷⣹
⠀⠀⣾⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⣤⣦⣤⡄⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⣿⣯⣿⣤⡠⠤⠒⢒⣒⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠐⠉⠉⢹⣇⢻⠀⠂⣀⣉⣭⣭⣑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⠀⠀⠀⠀⣀⡀⠚⢿⡆⢡⣈⡀⠀⠀⠀⠈⠛⣔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠁⡤⠒⡉⠤⢶⡶⠇⠉⠈⠛⠒⠶⠾⢏⠛⠊⣀⠈⠓⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡷⠊⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆⡘⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣸⣾⠟⠁⠀⠀⢀⢄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⢳⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠛⠁⠀⠀⠤⢚⠟⣹⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠀⠀⠀⠀⢺⣶⠏⠀⠃⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠓⠀⠀⠀⢈⡍⠀⠀⡈⠈⡀⠀⠩⣽⣷⠀⠀⢀⡔⢒⣺⡇⣺⣷⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⣿⡇⠀⠀⠀⠀⣾⠁⠀⠘⠿⠿⠹⠗⠀⡿⢿⡆⠀⢸⡟⠃⠘⡇⢿⠙⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠣⠉⢃⣀⡀⢀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈⠁⠀⠀⡇⠸⡀⠀⠀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠈⠉⣠⣾⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠑⠄⠀⠨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠋⣿⣾⡆⠀⠀⣄⠀⠀⠀⠀⠀⠀⠤⣤⣶⡶⠄⠀⠰⢻⣆⠑⢄⡀⠀⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⠸⠇⠀⠀⢸⡃⢧⡁⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢰⡿⢻⣦⡀⢽⠂⣄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⡇⠀⠀⠀⡀⢸⠣⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠈⠁⣠⠿⠁⣾⡿⢿⣦⡇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠇⠀⠀⣰⠃⠀⠳⣷⡀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠘⠖⠚⠃⣰⡟⠀⠀⡟⣡⠶⠚⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢿⡟⠀⠀⢀⡏⠀⠀⠀⣿⡗⠈⣿⣿⣷⣦⣀⠀⠀⢀⠀⠀⢀⣰⣿⣧⠀⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠈⣀⠀⠀⢰⠀⠀⠀⣀⠉⢀⠾⣿⣿⣧⠈⠻⣿⡿⠿⠶⢾⣿⢿⣿⡿⠤⣄⠰⣼⣦⡀⠀⢤⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡯⠀⠀⠀⠀⠀⣾⠛⠘⣏⠀⠀⠙⠹⡀⠀⠀⠀⠀⠀⠀⢻⡈⠻⠷⣀⠘⠃⠘⢿⣿⣶⠄⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠀⠀⠀⠀⠀⢀⡏⠀⠀⠹⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⢿⠆⠀⠀⢄⠀⠀⢀⠻⡆⠀⠠⠀⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡶⠁⠀⡜⠁⠀⠀⢄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢧⠑⢄⠀⠠⡴⣼⡆⠃⠀⠀⢣⠀⠈
⠀⠀⠀⢀⡀⠂⢰⡆⠀⠀⣴⡏⠀⣼⣿⠀⢸⣿⠀⠀⠀⢸⠆⠹⣦⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠸⠇⠀⢠⣴⣿⡟⠀⠀⠀⢱⢿⡇
⠀⠀⠀⠀⢳⠀⢸⣧⢀⣤⢸⡇⠀⢿⣿⡄⢸⣿⠀⠀⠀⢀⡴⠶⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠏⠀⠙⠀⠀⠒⠀⠘⠋⠃
⠀⠄⠀⠀⠘⠀⠀⠙⠘⠃⠀⠻⠀⠀⠙⠋⠀⠁⠄⣠⣶⠏⠀⠀⠐⠈⢳⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠈⠀⢀⠔⣪⠐⠀⠈⠁⠨⠏⠀⠒⠭⡢⣄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡰⣣⠊⠙⣦⠀⠀⠀⢰⠂⠀⠀⠀⠈⣪⢢⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⡘⡘⠀⠀⠀⠀⠳⠄⠀⠉⠀⠀⣠⠐⠋⠀⢣⠁⠀⠀⠁⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠶⠤⠤⢤⡤⠀⢀⣠⢄⡀⠀⠁⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⢨⠸⡀⠀⠀⠀⠀⠀⠀⠟⠰⠀⠀⠐⠦⠠⠤⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠃⠄⠀⢀⡤⠚⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⡜⡼⠀⠀⠀⠀⠀⢀⣚⣠⡀⠀⢀⠀⠠⠞⠁⠀⠀⡀
⠀⠀⠘⠌⠖⠋⠀⠀⠌⠘⡇⠀⠀⢃⢢⠀⠀⡐⡜⠁⠁⠀⠀⠀⢀⢌⡄⠁⠀⠁⠁⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠈⠦⡀⢄⡌⡀⢰⡇⠀⠀⢀⣢⢕⡪⠊⠀⠀⠀⡀⠀⢀⣮⠎
⠀⠀⠀⠀⠈⢀⠗⠪⠥⢽⡓⣚⠤⠭⡖⠋⠀⡀⠠⡀⠄⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠌⠠⠁⠀⠈⣃⠀⠀⠀⠐⠀⢣⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⠎⢀⠃⠀⠀⠀⠀⠐⠀⠀⠀⠱⢀⢣
⠀⠀⠀⠈⠈⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠈⠁⠀⣀⠤⠒⠀⠂⠀⠈⠀⠠⡄⠀⠀⠀⠀⠄
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢄⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄⠂⠁⠀⠀⠀⢀⣠⠐⠄⠀⠀⠤⠤⡀⠀⠀⢡
⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⡀
⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠰⢠⠐⢰⡘⠍⡇⠀⠀⠀⠀⠀⠀⠘⣵⠇⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠁⠀⠀⠈⢷⠀⠀⠀⠀⠇⠟⠄⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠂
⠀⠀⠀⠠⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠣
⠀⠀⠀⠀⠀⠀⣤⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣓⣀⡛⠂
⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠿⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣴⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⣿⣿⣿⣿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣏⣈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⡁
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣗⣄⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠹⣀⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⢀⠀⠀⠀⠀⠀⠄⠀⠏⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⢇⢰⡀⢠⡀⢠⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣌⠁⠈⠍⢸⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⣦⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⢠⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢹⣿⣿⣿⣿⣿⠫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⣿⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣶⣤⣾⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣶⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠛⢻⡿⡿⢿⣿⣿⣿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣠⢴⢖⣒⣾⣒⡒⣤⣄⡀
⠀⠀⠀⢀⡴⣏⠔⠚⡇⠀⡇⠀⠸⠓⠪⣹⢦⡀
⠀⠀⢀⣞⡴⠁⠓⢄⠘⡄⡇⢠⠃⡠⠊⠈⢢⣱⡄
⠀⠀⣼⢸⠉⠐⠢⢬⣳⣽⣷⣯⣎⠤⠔⠊⠉⡇⢷⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡟⢛⠒⠒⠒⣒⣾⣿⣀⣿⢗⡒⠒⠒⠒⡛⣻⠀⠀⠀⠀⠀⢠⠿⣆⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⢻⡸⡄⠒⠉⡠⠊⡽⣿⣯⣳⣌⠉⠒⢠⢧⡏⠀⣀⣤⣤⠦⠇⠤⠸⠵⠤⢀⠀⠀⠀⢰⢑⡃⠀⡀
⠀⣠⣌⣷⡙⣤⣎⣤⡼⢸⣿⣏⣆⣈⣳⣤⢋⠞⢀⡏⣁⣸⣹⡏⠹⠉⢻⠘⢳⡁⠤⠰⠲⢸⠼⣱⠀⢺⢽⠂
⠀⠀⠀⠁⣙⣦⣝⣺⠅⣼⣿⣯⡸⡟⣫⠴⢋⣠⡾⣟⡩⢁⡼⢹⣧⣀⣌⠀⢸⢿⢲⣾⣾⡶⣖⡿⠀⠎⠀⠃⠀⠀⡤⢀⣢⡄
⠀⠀⠀⣀⣤⣤⡈⢉⣞⣓⣷⣾⣿⣿⣿⣾⣯⣥⣤⡼⡟⢻⠛⠙⣇⠚⣸⠃⠐⠂⠙⢋⣛⠉⠁⣠⣤⣤⣤⣤⣤⣅⣐⣻⣀⣂



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⡀⢔⢢⡙⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠱⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⣈⣦⣤⡤⠶⢒⢲⡈⢳⠀⣧⠕⠃
⠀⠀⠀⠀⠀⠀⠀⠨⢀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠐⠀⡴⠞⢞⣉⡤⠞⢳⡧⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢺⡾⡝⣧⠀⠀⠀⠀⠀⢱⣓⡒⢾⡄⠴⠚⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⢀⠀⠀⠈⠁⢤⡈⠳⠀⠀⠀⠀⡔⠦⣍⡾⠓⠒⣋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⡜⢬⣓⣞⣁⣋⡉⣡⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠾⢯⣳⡾⠬⠭⢤⡇⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠀⠀⠁⠀⠀⠛⠙⠉⠁⢻⣓⣒⣚⣃⡯⣭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣰⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠌⠀⠘⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⢠⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⡞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢁⠀⠀⠀⠸⠀⠘⠀⠀⠀⠀⠀⠀⣸⠈⠓⡋⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠁⠀⠀⢠⣂⡄⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡑⠀⣄⠀⠁⠀⠀⠀⠀⠀⠀⣿⣀⡀⠙⢢⣌⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠶⠶⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣖⣀⡀⠒⠂⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠉⢉⣥⠫⢭⠤⠀⠒⠒⠒⡆⠰⠯⠤⠤⠤⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡥⠀⣠⡴⠶⢦⣇⠀⠀⠀⠀⠀⢄⠀⠹⣮⣁⠒⣄⠀⠀⠀⠀⠀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢰⡏⠉⠇⠀⢹⣦⣤⡴⠖⠛⠶⣄⠀⠩⡀⣹⡏⠀⠀⠀⠀⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠘⠺⡇⠒⠀⠁⣸⠇⣾⠁⠤⢰⢲⢹⣇⢀⠜⢍⠈⢆⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠖⠉⠙⠢⢴⠾⠋⠀⣿⡀⠀⠸⠐⣸⠟⠻⣷⡦⠖⠛⠁⠲⣄⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠞⠋⠀⠀⠀⠀⠈⠉⠉⢀⢧⡀⠀⠀⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⣏⠶⠀⢰⠢⠤⠤⠔⠳⡠⢱⣄⡴⠙⠃
⠀⠀⠀⠀⠀⢠⠄⠤⣈⢻⡄⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⡠⣁⣀⣀⣀⣤⠄⢻⡋⠈⡆
⠀⠀⠀⠀⠀⠀⠑⠂⡤⠿⣷⠤⠤⡀⠀⠀⠀⠈⠳⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢊⠒⠄⠀⠀⠀⣈⣆⠀⠀⠀⠀⠀⢀⣈⠉⢹⠿⢿⡏⣉⠁
⠀⠀⠀⠀⠀⠀⡠⢎⠺⣀⢀⠀⡘⢤⡀⠙⡆⠀⠀⠀⡀⢈⡶⣧⠤⢼⠜⠳⠁
⠀⠀⠀⠀⠀⠘⠤⢎⣰⠋⠀⠤⠤⠊⠀⣴⠀⣠⠖⠚⠀⣸⣄⡏⠀⣸⠀⠊⡶⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠤⠐⠒⠢⣀⠀⠉⢹⡰⠉⡏⢁⡤⢧⠀⠃⠀⠘⠀⠀⠔⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣟⠉⢀⢔⡋⠁⠀⠀⠉⣿⠿⡟⠐⠚⠳⡀⠀⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣀⠋⣀⠀⠀⠀⠀⢸⠀⡇⢠⠂⠴⠃⠀⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠉⢻⠻⠻⠷⠤⢼⡆⣧⠈⠐⠒⡄⠀⠀⠸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠱⣦⠀⠀⠸⢗⣿⡀⠄⠲⠡⠾⠼⠦⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡄⠛⠋⠲⢆⠂⠀⠀⠀⠀⠀⡜⠒⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠀⠈⠛⡛⠚⠲⠤⣦⣼⣗⣢⣤⡔⢪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠀⠉⠀⠀⠀⠀⠈⠁⠘⠦⡠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠤⡀⠀⠀⠀⠀⠀⠀⣠⣶⢛⠉⠉⣉⣭⣵⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠀⠒⠄
⠀⠀⠀⠄⠂⠚⠀⠀⠀⢨⠀⠀⠀⠀⢠⡾⠁⠀⠉⣴⠟⠉⠉⠻⣿⣦⡙⢷⡀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠐⠀⠐⠂⠠
⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢰⡟⣀⠀⢠⡞⠁⠀⠀⠀⠀⠈⠿⣿⣆⢻⡄⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀
⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⢡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⢻⡀⠀⠀⠑⠀⠤⡀⣀⠀⠀⠀⡀⣀⠀⣀⠀⠠⠃
⠀⠀⠀⠁⠀⠒⠄⠀⠴⠀⠀⠀⢸⠇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠘⡇⠀⠀⠀⠀⠀⠀⠈⠒⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⡆⣠⠄⣿⠀⠀⠀⠀⠀⢸⣿⢦⡀⠀⠀⡿⠀⡿⢀⠒⠒⢀⠀⠀⠀⢀⠂⠀⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣇⠀⠀⢸⡆⠀⠀⠀⠀⣾⢿⣇⠙⢦⣀⠃⢰⡇⠸⡀⢀⡘⠀⠀⣀⠀⠁⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣻⡄⠀⠀⠀⡇⠘⣿⡄⠀⢹⡁⢸⡇⠀⠈⡋⠀⠀⠀⠆⠢⠀⠀⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠻⣆⠉⡀⠹⣆⠀⢠⡇⣶⣽⣿⣀⡿⠀⠀⣇⠀⠀⠃⢄⠀⠄⠀⠂⠁⠁⠀⠐⠠⠴⣀
⠀⠀⠀⠀⢠⡔⠁⠰⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣦⣈⡳⠾⣇⡿⠿⠛⣹⠇⠀⠀⢹⡀⠀⣇⣤⢍⡁⠐⠂⠠⠀⠀⡀⠀⠀⠀⠉⠪⠄
⠀⠀⠀⢀⡀⠳⣤⠔⠀⠀⠀⠀⢀⣠⠀⠀⢠⡟⢻⣿⣷⣶⠶⡷⡶⠋⡿⠀⠀⠀⠈⣇⠀⠂⠀⠀⠸⡇⠬⠐⠶⣤⠤⣈⣈⣀⠂⠀⠠
⠀⠀⢀⡞⢧⠀⢸⢀⠀⠀⣄⠰⡁⠀⠈⣰⣾⣴⢋⣿⣹⣿⢾⡿⣄⡼⠁⠀⠀⠀⠀⠸⣆⠂⠀⠀⠘⠃⠀⠲⠐⠉⠀⠀⢁⡉⡙⠁⢚
⠈⢠⡼⠁⠘⣆⢸⢠⢧⡀⠻⣐⣃⠐⢂⠛⡛⠻⣽⣧⣞⢹⢹⣯⠟⠁⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢸⡁⠀⠀⠀⠀⠐⠀⢤⣀
⣀⣼⠁⠀⠀⠹⣾⠙⠒⠠⠄⣈⠀⡶⠆⢠⣷⢂⣼⠛⢮⣻⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠈⠙⠀⠀⠀⠘⠃⠓⠲⠚
⢱⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⠷⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠨⣙⠦⠤⠐⠊⠀⠀⠀⠀⠀⠀⣀
⠘⣇⠀⠀⠀⣠⠇⠈⠀⠁⠀⠀⠀⢂⡀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠈⠀⠀⠀⠁⠀⠈⠅⠐⠎⠁⠀⠀⠀⠀⠠⠀⠀⠐
⠀⠈⠉⠻⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⡃⠄⠻⠛⠋⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⡀⠀⡁⠀⠀⠀⠀⠈⠀⠤⠐
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⢳⣭⣤⡾⢃⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡐⠐⠀⠀⠀⠐⠈⠀⠀⠅⢐⠂⠂⢠⠸
⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠠⠀⠒⠀⠀⣈⠀⠈⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡶⠶⣶⣶⣶⣾⣿⣿⡖⢶⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠿⠿⠿⠿⠿⠿⠷⠾⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢃⣴⣿⣷⣶⣤⣌⡉⠛⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⣿⣿⣿⣷⣄⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠋⠀⠀⠀⣠⣾⣿⣿⣿⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢠⣤⣤⣤⣤⡆⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⣹⣿⡿⠟⢋⣉⣉⡁⠀⠸⠿⠿⠿⠿⠇⠀⢈⣉⣉⡙⠻⢿⣿⣏⣉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⣠⣾⣿⣿⣿⣿⣿⣶⣶⡆⢰⣶⣶⣿⣿⣿⣿⣿⣷⣄⠙⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠐⠐⠒⠂⠒⠐⠒⠒⠂⠂⠒⠒⠒⠂⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢠⢰⡆⢰⠀⣆⠀⢰⠆⢰⠀⣶⠀⡆⢰⡂⢔⡀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣶⣾⡄⣶⣖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠
⠀⠀⠀⠀⠀⢀⣶⣶⠘⠿⠋⣀⠉⢀⠈⠛⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢐⡒⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠥⠤⠖⠀⠠
⠀⠀⠈⠀⠐⢌⠻⢿⡿⠂⢸⣿⣿⠿⠃⠀⠀⠀⠀⠁⠀⠀⢁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⢈⠐⡤⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡁⡂⠐⡀⢐⠀⣂⢡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠅⠤⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⢌⢂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢰⡶⠄
⠀⠀⠀⠀⠀⢂⢐⠐⠂⠐⠀⡃⣈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠙⠋⠈⣡⣴
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⡀⠁⠠⠤⠄⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣀⠠⠆⠀⠤⡀⠣⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⢨⣤⠀⠀⠀⠀⠀⠀⠰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡅⢠⣳⡶⠀⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⢀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠤⡅⠛⣀⠈⢀⠁⠀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠢⠀⠀⠀⠀⠆⠀⠀⠲⠒⠀⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣴⣶⠦⠀⠀⠠⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢀⣄⣸⣶⡟⣹⡏⢿⡇⠀⠠⠃⠀⠀⠀⢀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠂⠀⢸⡶⢋⣿⠛⣿⡍⢛⠂⠛⠃⠊⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠿⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠔⠂⠂⡀⠀⠀⠀⠀⢀⡴⢟⡍⢈⣠⣤⣾⣶⢦⣀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠁⠐⡀
⠀⠀⡐⠀⠀⠀⠀⠀⠠⠀⠀⠀⣰⠏⠀⠀⡼⠋⠀⠀⠙⢿⣷⡌⢧⡀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠲⢠⡾⠁⠀⠀⠀⠀⠀⠹⣿⡞⢷⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠤⡀⠀⣀⠀⠉⢀⡟⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠘⡇⠀⠀⠀⠀⠀⠒⢄⣀⠔⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡿⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢀⠤⣧⠀⠀⠀⠀⢸⣷⣄⠀⠀⢹⠇⣿⢠⠐⠂⡀⠀⠀⢀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡄⠀⠀⠀⣼⢿⡆⠙⢦⡉⢰⡇⠸⣀⡠⠃⠀⠀⠀⠁⠒⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡀⢷⡄⠀⠀⡏⠘⣿⡄⢈⡇⠸⡇⠀⠈⠀⠀⠀⠀⠁⠀⠐⠂⡀
⠀⠀⠀⠀⠀⣀⡀⠀⠄⠀⠀⠀⠘⢧⣠⣄⠹⣄⣀⡇⣿⣿⣷⣼⠁⠀⢷⠀⠀⠘⠦⢀⠀⠁⠀⠀⠀⠁⠂⠦⣄⡀
⠀⠀⠀⠀⢋⠀⢈⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣮⣉⣓⣏⣩⣴⡏⠀⠀⠸⡄⢠⠓⠋⢒⡄⠀⢉⣀⠐⠀⠀⠀⠀⡉⡠
⠀⠀⢀⢷⠀⢹⠁⠀⠀⠀⡐⠈⠀⢀⣼⡠⢾⡿⣿⣯⣷⠉⡼⠁⠀⠀⠀⢳⡀⠀⠀⠀⡇⠉⢀⠘⠋⠉⠳⠒⠦⠄⠥
⠐⢀⡞⠈⣧⢸⢈⣆⠈⢇⠜⠀⠄⠿⠿⣗⣿⣩⢻⡷⣟⡿⠁⠀⠀⠀⠀⠀⢻⡀⠀⠠⡇⠀⠈⠀⠀⠀⢠⡉⠁⠀⠑
⢀⡼⠀⠀⠘⣿⠹⠘⠤⠀⡁⣴⠯⢨⡧⢈⡟⢪⣻⠶⠋⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⡀⠁⠀⠀⠐⠀⠀⠘⠃⠓⠦⠂
⢹⠃⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡆⠈⡷⢚⡛⠉⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⢽⡦⠄⢒⠀⠀⠀⠀⠐⢀⡀
⠘⢦⣀⣀⣠⠎⠀⠉⠀⠀⠀⠐⡄⠀⣀⣠⡀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠃
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⠀⢠⡄⠠⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠛⠟⠛⠔⢁⠀⠀⠂⠄
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢀⠄⠀⠠⠀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠤⣤⣴⣤⣶⣶⡿⢶⣶⣶⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠴⠿⠿⠿⠿⠿⠷⠾⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢠⡏⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⠃⠀⠀⠀⠀⠀⠈⢿⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣸⣿⠀⢹⠀⢀⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠉⠉⠉⠉⠉⠻⠀⠈⠀⡾⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠴⠛⠉⠀⣠⡤⠶⠚⠛⣻⡆⠀⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⣀⠤⠴⠚⠉⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣀⣤⣤⡶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠘⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⡿
⠀⠀⠀⢀⣠⣴⡶⠿⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⢀⣴⠟⠋⠀⢀⣤⠴⠖⠒⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢶⣤⣤⣤⣤⣴⠟
⢠⡟⠁⠀⠀⠜⠉⠀⠀⠀⠀⠶⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⠟⠁
⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠰⣶⣤⣤⣤⣤⣴⡶⠾⠛⠉
⠀⠈⠻⢷⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣸⠁⢀⡆⠀⠀⢿⡇
⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⣦⡀⠀⠀⠋⠀⣼⠁⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢀⡏⠀⣼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠘⣇⣰⠏⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⠀⠈⠁⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⣾⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⣥⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣭⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣉⣉⠉⠉⣉⣉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⠐⠒⠒⠒⠂⠀⠀⠈⠉⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⢀⡠⠄⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠴⠛⠒⡒⠈⠉⠉⠉⠉⠁⠐⠐⠂⠀⠀⠀⠸⢤⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢀⣴⣛⠛⠳⣦⠀⠀⠀⠀⠀⠐⠀⠈⢻⡦⢍⣱⡄⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣼⣧⢠⠁⠀⢸⡶⢶⡶⠛⠉⠛⢶⡀⠈⢆⢀⡿⡀⠀⠀⠀⠘⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠋⢻⡏⠚⠀⠀⣸⠃⡾⠀⠠⠐⡉⠀⣿⣀⡴⠛⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⢠⠊⠉⠉⠲⠶⠚⠁⠀⢷⡀⠀⠰⠤⢀⡟⠙⢻⣷⠾⠛⢉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠞⠋⠀⠀⠀⠀⠀⠋⠁⠁⢀⢇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢟⣱⠄⠀⡶⠤⠤⠤⠔⢣⠨⠱⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣜⠀⠀⢀⡀⡠⠈⢓⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣰⣧⠀⠀⡀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡖⠒
⠀⠀⠀⠀⠀⠀⠀⢀⡔⢀⠃⠀⠀⠀⢀⠈⠀⢀⠀⠀⠀⢀⠊⠑⣤⣇⣀⢸⡩⢯⠃
⠀⠀⠀⠀⠀⠀⢰⠁⡘⢁⡔⠚⣆⣈⡠⠋⢀⠜⠀⣀⠤⡾⠀⢼⢀⡇⠀⠸⢀⠴⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⡀⠀⠀⡡⣄⠀⠈⠓⠒⠇⡠⢧⠔⠋⢙⡄⢀⠋⠀⢠⠃⠀⢈⠝⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠲⢄⡠⠛⠀⡨⠤⠊⠁⠘⠄⣤⡄⣦⢠⠀⢅⡀⠀⢣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢊⡗⠀⠀⠀⠀⠀⢹⠀⠁⠀⠀⠀⡣⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠂⠄⣠⣤⣄⠀⠀⢘⡀⡀⠘⠀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠩⡹⠉⠉⠛⢻⣇⣿⠀⠀⢀⠔⢠⠀⣀⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠈⣧⣀⡀⠈⠻⠿⠔⠊⠉⠒⠚⡋⣩⡐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣼⣄⣀⠀⠈⠣⢀⡀⠀⠀⠀⢀⡜⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣀⡀⡀⢘⣅⣉⣉⣒⣶⠾⠯⢿⣶⡎⠹⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠀⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠠⠀⠆⠄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠉⠟⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⡤⠔⢺⠒⠤⣴⣃
⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⣀⢀⡠⡟⠲⣀⡒⠒⣢⣤⡔⠒⠒⡖⠠⣄⠀⠀⠀⠀⠀⠀⠠⢤⡜⠁⡽⡆⢻⠃⡲⢅⠙⣤⠄
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢰⠊⠀⡇⠀⠀⢱⠮⣀⠈⢣⠀⠀⠁⠀⢨⠑⠀⠀⠀⠀⠀⠛⡟⠈⡟⠢⣼⣾⣶⡥⠚⠋⠘⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣚⣆⡀⣇⢀⠀⣺⣀⣀⣹⡟⠂⠤⡦⢀⣸⣰⣀⣀⡀⠀⣈⡉⢏⠉⡏⣩⣿⣿⣿⣯⣉⡙⢉⣏⣭
⠀⠀⣠⠀⠒⠂⠉⢹⠉⠁⠉⠀⠑⡧⣀⠀⣈⣉⡉⢨⠤⠀⠛⠃⢀⢼⠁⡘⠆⡇⠀⠉⢉⡽⣖⠛⣾⣿⣼⠈⣿⡞⢙⡾⣄
⠀⠀⠘⠒⠸⢠⡷⢾⠀⠒⡟⠋⠉⡏⠉⠉⠻⢠⣀⢈⡁⣀⢠⣿⣯⣘⠀⠙⠃⡇⠠⠀⢼⡇⠈⢱⣿⣬⣽⣇⡼⣷⠋⠀⠶⠆
⠀⠀⠀⠀⣰⣿⣧⣴⣀⣴⣷⣄⣀⣷⣦⠤⡤⢾⡟⠺⠻⠿⠿⣿⣿⠿⠿⠿⠒⣷⣿⣆⠘⠋⣩⣿⣿⣦⣼⡇⠀⣿⣧⢀⣄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠷⢤⣅⣸⣇⢀⠠⡴⡇⣽⣿⣠⣴⡆⣸⣿⣿⣿⣿⣠⣴⣿⣸⣄⣟⣷⢿⣼⣿⣿⣿⣷⡆
⠀⢤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠶⠶⣿⣿⣿⣶⢶⣶⣶⣿⣿⣾⣶⣶⣿⣿⣿⣿⣿⡶⣾⣿⣿⣷⣾⡷⠿⣶⣿⣿⣿⣿⣷
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠲⢄⡀⡴⠉⠀⠀⠀⠀⠈⢢⡀⣠⠴⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠈⠑⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠋⠉⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢀⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⢠⠞⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⣄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⣀⢀⣠⠾⣄⠀⠀⢀⡠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⡴⠋⠀⠀⠁⠀⠀⠀⠉⠉⠉⠀⠈⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠤⣀
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠠⡤⠔⠋⠀⣰⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⡼⠉⠀⣠⣙⢆⠀⠀⠀⠀⠀⠀⠀⡴⠚⢉⠛⢷⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠉⢇⠀⠸⢿⠟⣸⡠⠒⠉⠉⠑⢦⣸⠀⢸⣿⡷⠀⡟⠂⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠈⠓⠤⠤⠚⢹⠁⠀⠀⠀⠀⠀⡏⠣⣄⣀⣠⠜⠁⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠶⡏⠀⠀⠀⢀⡴⠒⠒⠒⠺⢆⠀⠀⠀⠀⣠⣃⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣄⣀⣀⣀⣀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢼⠀⠀⠀⠀⠀⠀⢉⠓⢒⠋⠁⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠘⣆⠀⠀⠀⠀⠀⠈⠓⠊⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠈⠉⠒⠲⠤⠤⠤⠤⠤⠖⠚⠉⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢄⣀⣀⣀⣀⣀⣀⠤⠤⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⣜⡆⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠰⠤⠄⠠⠤⠄⠀⠒⠒⠒⠂⠀⠀⠀⠀⠠⠬⠍⠉⠉⠭⠉⠉⠥⠄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠿⠅⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠔⢄⠀⠀⠀⠈⠒⠶⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣤⣄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⡁⢃⠀⠀⠀⠀⢠⠖⢁⠀⠀⠀⠀⠉⠳⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⣠⣐⡢⣤⣤⡀⢀⡄⠀⢠⠁⡇⠀⢃⢸⠀⠀⠀⢰⠃⠀⠀⠄⠀⠤⠀⠀⠀⠈⡄
⠀⠀⢀⠀⠠⣿⠋⠐⠊⠀⠀⠀⢀⠀⠀⠹⡀⠀⠀⠀⠀⠉⠀⠀⠈⠁⣄⠀⠀⢈⠀⡀⠀⠀⢀⠀⠀⠀⢀⡀⡀⢠
⠀⠀⠈⠀⠀⡎⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠆⠀⠀⠣⡉⠒⠊⠁⠀⠀⠀⠈⡰⠁
⠀⠀⠀⠀⠈⠻⡀⠀⠀⢀⠀⠀⡰⢀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⣄⠀⠀⠈⣐⡄⣤⠤⣤⠒⠊
⠀⠀⠀⠀⠀⠀⠈⠢⠄⢀⣈⡉⣀⠁⢄⠀⡴⠤⣀⣀⠀⠀⠀⠠⠄⠀⠀⢡⠘⡦⠤⠊⡌⠐⠁⠀⡇⠈⢢⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠈⠓⠋⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣧⢀⡀⢠⡥⠤⠋
⠀⠀⠀⠀⠀⠀⡜⠀⠚⣢⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⡄⢀⣀⠀⠀⠀⠀⠀⡃⢠⡀⠰⠀⠀⠀⠀⠀⡔⠢⡀⠀⢀⡀⠢
⠀⠀⠀⠀⠀⠀⠈⠀⠘⡡⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⣹⡎⢠⣔⡇⠀⣀⡀⡍⠁⠁⢎⠁⠀⠀⠀⠀⠀⠰⠄⠴⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠵⡧⠤⠖⠂⠀⠀⠀⠀⠀⠀⠀⠈⠒⢣⢝⠁⠌⠰⠀⠀⠁⠈⠁⠐⠯⠋⠀⠀⠀⠀⠀⠀⠀⠇⠐⣈⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⢧⡀⠲⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⣉⠁⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠄⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠊⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢀⠔⠂⠀⠀⠀⠀⠺⣇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⢸⠠⡀⠀⠀⠀⠠⣺⠆⠿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠸⠀⠉⠛⠷⠿⠛⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠐⠻⣦⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢶⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣐⠲⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⣰⠋⠃⠒⠂⠀⠀⠀⠀⠀⠀⢶⣤⣀⡀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠘⠁⢰⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠛⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣐⣤⢀⣽⠃⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠸⠁⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠯⠵⠐⠒⠒⠃⠼⠭⠒⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⡽⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢮⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⡀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡇⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣼⠛⠛⣧⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡃⠀⠀⠀⠀⠀⠀⠀⢳⠀⣰⣿⠷⠾⣿⣦⠀⡞⠀⠀⠀⠀⠀⠀⠀⢘⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡃⠀⠀⢘⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢣⠀⠀⠀⠀⠀⢠⣾⢯⠃⠈⠉⠉⠁⠘⡽⣷⡄⠀⠀⠀⠀⠀⡜⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠳⡀⠀⠀⣠⣿⢯⠏⠀⠀⠀⠀⠀⠀⠹⡽⣿⣄⠀⠀⢀⠞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠜⢢⣴⣿⢏⡎⠀⠀⠀⠀⠀⠀⠀⠀⢱⡹⣿⣦⡔⠣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡾⢄⣀⠀⠀⠀⠀⠀⠀⣀⣠⢷⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⡾⠉⠐⠂⠯⠽⠉⠉⠯⠽⠘⠂⠉⢷⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⡼⠁⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢧⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶
⠀⠀⠀⠀⣰⣾⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣆
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠈⠻⢿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣿⣿⠿⠛⠛⠛⠻⢿⣿⡿⠟⠁⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠤⡄⠀⣀
⠀⠀⠀⠀⠀⢀⣠⣀⠀⢱⡀⠡⠦⠁⣴⠁⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠜⠀⠹⢦⠀⠃⠀⠀⠀⠀⠀⠶⠇⠈⢇⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⡿
⠀⠀⠀⠀⠈⠐⠲⠄⠀⠀⡐⡘⡘⠰⢂⠀⠀⠜⠊⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀
⠀⠀⠀⣤⢦⡤⠦⠄⠀⣒⠠⢕⠉⡥⠐⡂⠀⠠⠤⢤⣤⣠⡴⣻⢟⡽⢹⡇⣯⢻⡻⣿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢿⡀
⠀⠀⠀⠁⠂⠁⣠⠤⠀⠐⢢⢡⠳⠨⡐⠀⠐⢤⢆⣬⠞⣫⡾⢣⣾⢃⣿⠁⣿⡎⢿⣌⢷⣍⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠈⢷⡀
⠀⠀⠀⠀⠀⠉⠀⢠⡔⠀⢠⠎⠀⠳⠀⠒⣲⡐⠛⠃⡚⠛⠐⠛⣣⣼⣿⣤⣻⣷⣼⠛⠂⠛⠓⢘⡛⠂⠒⠂⠀⠀⠀⠀⢀⡟⠀⢸⠀⠘⣧
⠀⠀⠀⠀⠀⢠⠶⣧⠀⢰⠟⠀⡦⠰⠹⡄⠀⡽⢶⡄⡇⣀⡀⠀⣿⣿⣿⣿⣿⡿⣿⠀⠀⠀⠀⢸⠀⣀⡀⠀⠀⠀⠀⢀⡾⠁⠀⢸⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠆⣤⠧⡄⠢⠀⠀⣁⠀⠀⣿⣿⡇⠀⣿⠿⣿⣿⠁⢀⣸⠀⢀⣀⠀⢸⣿⣿⡇⠆⠀⠀⢀⣾⠃⠀⠀⢸⠀⠀⠀⢹⣦⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⢼⣯⣿⣿⣿⢿⡿⠃⣣⡞⠀⠀⣀⡀⣅⠠⣾⣽⣿⣿⡿⢿⡿⠁⠀⠀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠙⡇⡇⠰⠃⠀⣼⣿⣧⣿⣿⣯⣿⠀⠃⠀⠹⣽⠀⠼⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠚⠓⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠚⠓⠒⠒⠒⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠈⠉⠁⠐⠒⠢⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠀⠀⠀⠒⠠⢀⠀⠀⠈⣀⡠⠂⠐⠒⠀⠢⢄⠀⠐⠤⡀
⠀⠀⢀⠔⠈⣀⡀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢱
⠀⢀⠀⠠⠊⠀⠈⢆⠀⠀⠀⠀⠀⠀⢱⠀⡜⢀⣀⠠⠤⠤⠤⠤⣘⡄⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠣
⠀⢐⠂⠀⠀⠀⠀⠈⠂⠒⠢⠄⡀⠀⢸⢢⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠈⢑⡎⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡽⡀⠀⠀⠀⠀⠀⡠⠂⠀⢀⠎⠕
⢀⡀⠀⠢⡀⠀⢄⠀⠀⡀⠀⠀⣠⠊⠀⡘⠀⠈⢄⠀⠀⠀⠄⡤⠋⠀⠀⠀⠀⢈⠛⠢⣄⡀⠀⠤⢀⣠⠔⠋
⠈⠉⠒⠄⠬⣠⠤⠬⠭⡤⣔⡊⢤⠔⠉⠁⠀⠒⠈⠑⡤⠀⢤⣬⡵⠒⠒⠒⢒⣃⠀⠀⠀⠬⢋⠉⠉⢦⠠⣄⡀
⠀⠀⠀⠁⡐⠁⠀⠀⠀⠀⠈⠆⠐⠀⠀⠛⠉⠉⠇⡐⠀⠀⠀⠈⣅⡨⠒⠉⣤⠑⠉⠉⡀⠀⠀⠉⠀⠀⠱⡃⠈⠉⠛
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⡂⠀⠀⡀⡀⠀⠀⠀⢀⣰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠐⢍⠉⠀⠂⠠⠌⠃⢁⠀⠀⠱⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⢉⠂⠀⠀⠁⡀⢉⣉⠤⢛⡖
⠀⠒⠋⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⢤⠤⠤⠤⠒⠢⡉⢀⡀⠀⠈⡙⠉⠉⠁⠉⠀⠀⠀⠼⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠧⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⠚⠀⠐⠶⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡛⣃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⢀⡠⠔⣤⠞⢡⡇⠸⢦⠙⠦⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⢠⣾⢼⠧⡧⣷⢰⠀⠀⠀⠀⠀⠀⣠⢸⢦⢀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣿⣽⣯⣴⣴⣍⣴⣴⣥⣶⣴⣥⣦⣴⣿⣯⣽⣶⣿⠁
⠀⠀⠀⠀⠀⠀⡜⢸⡇⢊⣆⢿⢸⡄⡄⠀⠀⠀⡗⣾⠇⢟⢸⡟⣗⠚⠀⠀⠀⠀⠀⠀⢿⢿⡿⡿⡿⢿⢿⣿⣿⣿⣿⣿⣿⣻⡿⣿⢿⣿⡿⡿⢿
⠀⠀⠀⠀⠀⢠⢃⡿⢀⣼⣿⣌⠁⢧⠠⠀⠀⡰⢡⡟⢀⣾⣧⡑⠹⡌⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠁⠈⠀⠚⠛⠛⠛⠂⠈⠓⠁⠘⠁⠁⠀⠛⠛⠛⠛⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⣷⣿⡿⠟⣿⣿⣿⣸⣿⣿⣿⠀⠀⠀⢀⣴⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⣿⣿⣿⣧⡀⣿⣿⣿⡿⠋⠉⣛⣴⡦⣤⣾⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢶⡀⢀⣀⣤⣾⣤⣀⣀⠀⢀⡶⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠯⠀⠘⠏⠀⠋⡙⠛⠁⠀⢰⣿⠸⢃⣿⠛⠹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡾⢿⠉⠁⠀⢹⠁⠀⠉⢛⡾⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡟⢠⣶⡆⣦⣿⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠠⠤⣄⣀⡼⠋⠀⢈⣷⡒⠋⢻⠋⠓⢲⣞⠀⠈⠳⣄⣀⡤⠄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣿⣷⣾⣿⣷⣿⣿⣀⣀⣄⣀⣀⣀⣠⡀
⠀⠀⠀⠀⣤⣤⣬⡟⠳⢤⣴⠁⠈⢳⡀⣸⠀⣠⠏⠀⢑⣤⠶⠛⣧⣤⣤⠀⠀⠀⠀⠀⢲⣼⣦⣾⣦⣿⣴⣷⣼⣧⣾⣦⣿⣴⣷⣼⣧⣾⣦⣿⣴⠆
⠀⠀⠀⠀⠈⠉⣼⠁⠀⡸⠉⠙⠦⢄⣱⠼⢔⢉⡤⠞⠉⠸⡄⠀⢹⡀
⠀⠀⠀⠶⠶⠶⣿⠶⠒⡷⠒⠒⢒⠒⣇⠀⢀⢗⢒⠒⠒⠒⡗⠒⢺⡗⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠸⣶⣶⠆⢹⡄⠀⠸⣀⡤⡮⣬⡖⢩⠑⣮⠾⡶⢤⣰⠁⠀⣼⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⡧
⠀⠀⠀⠀⠀⠀⠀⣳⡴⠚⠙⢤⣍⡟⠀⢺⠀⠘⣯⢥⡴⠉⠓⣶⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⢻⠁
⠀⠀⠀⠀⠀⠒⠋⠁⠹⣦⡀⣜⡺⠓⠦⣾⠤⠖⠻⣫⡄⣠⠞⠁⠈⠉⠁⠀⠀⠀⢀⡠⣠⢎⡏⣧⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠈⢸⡆
⠀⠀⠀⠀⠲⠶⠾⠀⠀⠈⣹⣢⣧⣄⣀⣸⣀⣀⣤⣗⣻⠁⠀⠀⠘⠿⠟⠀⠀⠘⠛⠛⠛⠛⣿⡟⠛⡟⠛⠋⠀⠀⠀⠀⡠⠊⠀⠀⠀⡀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⡯⡝⠀⠀⠀⢹⠉⠀⠀⠸⣖⡷⠄⠀⠀⠀⠀⠀⣠⡄⣴⠀⣤⠀⣿⣇⠀⢳⡀⢀⣄⠀⢤⣾⣁⡀⠀⠀⠀⡇⠈⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢽⠃⠀⠀⠀⠉⠁⠀⠀⠀⢯⢵⡖⠀⠀⠀⠀⠀⠙⠃⣿⡀⡷⢀⣿⡟⡶⠈⢿⣄⠛⠁⠈⠻⣿⣮⣭⣍⣒⠃⠀⣄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡟⠀⠀⠀⠘⠿⠟⠀⠀⠀⠘⣏⣇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢚⣿⣇⠙⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡸⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢺⡀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠿⠿⠿⠿⠿⠿⠿⠿⠦⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⡻⢿⠛⡻⠿⡿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠑⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⠤⠄⠀⠀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣀⡤⠶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠀⣀⣿⣤⣤⣄⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠄⠀⠈⠷⣤⣄⠀⠈⠉⠁⠀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢓⠐⠒⠘⢖⠀⠀⢙⡟⣠⠶⢲⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠧⠀⠀⠤⠳⣰⠟⣰⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠰⡀⠀⠀⠑⣄⣠⡞⠃⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠀⠐⡄⠀⠀⠀⠙⠶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡈⢃⠀⠙⠂⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢣⡈⠳⠐⠒⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠙⠁⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⡄⠈⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⢦⠈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠋

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⣄⡤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣄⣄⣄⣀⣀⣠⣀⣤⡤⣤⢀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⢨⣾⡿⢿⣿⣿⣟⡛⣿⣷⣿⣿⣷⣟⣻⣗⡘⡾⣿⣽⢿⡿⣺⢽⣾⣻⣏⢙⣟⠿⣷⣿⣷⣿⣥⡿⠿⣿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠺⠿⣟⢚⣿⣿⣿⣻⢡⢏⣩⢯⣍⡿⣿⣾⣛⣮⣿⣼⣻⢹⣿⣻⢮⡟⣽⡿⢿⣻⡿⠕⢭⠏⡐⢻⣖⣯⢿⣯⣽⠋
⠀⠀⠀⠀⠀⠀⡸⢶⡾⠟⣿⣾⣿⣧⡟⣼⣻⣾⣿⣛⣟⠿⣿⣷⣭⣏⢻⣞⣿⣟⣿⣧⡏⢰⣬⣿⣿⡾⢷⣖⣯⣼⣝⣿⣾⣏⣷⡀
⠀⠀⠀⠀⠀⠀⢴⣯⣿⣴⠻⢾⣾⡻⡷⣾⣿⢿⣏⠻⢂⡼⣿⣽⣿⠏⠸⣿⠿⣋⣾⠿⣴⣛⡶⠈⣛⠗⠂⣯⣿⣰⣿⣟⣻⣝⡻⠯
⠀⠀⠀⠀⠀⠀⢨⣷⣿⣿⢁⣾⢧⣴⣾⡾⠏⢀⣠⣶⣋⣐⣿⣺⣿⣷⣶⣾⢿⣿⣾⡞⣷⣹⣯⣽⣅⣹⡏⣰⢿⣿⣟⣽⡷⠏⣶⢷
⠀⠀⠀⠀⠀⠀⢹⣝⢿⠓⣿⢽⣾⣿⢛⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⡿⣼⣿⣷⣟⣫⣥⣿⡛
⠀⠀⠀⠀⠀⠀⠀⢉⡌⠀⢻⡎⢻⣧⣾⣿⣿⣯⣉⣭⣹⣿⣿⣿⣿⣿⣟⢹⣏⣻⣿⣿⣿⣿⣿⢿⣿⣿⡇⣻⣶⣎⣵⣯⣿⠯⡄
⠀⠀⠀⠀⠀⠀⢂⡀⡄⠀⢸⡆⠹⢸⣿⣿⣿⠀⠁⠉⢹⣿⣿⣿⣿⣟⠉⠉⠉⣷⢸⣿⣿⣿⣷⣦⣞⣿⣿⣿⣿⣾⡋⠀⠉
⠀⠀⠀⠀⠀⠀⢿⡄⢢⠀⠈⢄⠀⢺⣿⣿⡿⠦⡐⠀⠾⣿⣿⣿⣿⣿⣄⡀⠀⠻⢾⠿⣿⡿⠿⣿⣿⣯⣿⡿⢟⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠟⠋⠁⠀⠀⠀⠃⠀⠀⠈⣿⣿⠛⠃⠉⠶⠂⠀⡀⠙⠃⠠⣾⡟⢠⣶⡾⠏⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⠒⠢⠅⢀⠢⡷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⡗⠀⠀⣦⣸⡇⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⢽⣯⡓⣽⡷⣤⠤⠤⠤⠴⠀⢹⣿⠏⠀⠀⠀⠀⠀⠇⠀⢠⣾⣿⣷⠹⡏⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢿⡁⠀⠀⡄⠀⠀⡀⠟⣃⠀⠀⠀⠀⠀⠀⠠⠀⢀⣿⢿⣯⡅⢰⣾⠆⢈⠂⡈⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠲⢷⡀⠀⢹⣾⣿⣤⣴⠉⢱⡆⠉⢲⣿⣯⡀⠀⠙⠁⢻⡏⠁⠈⠚⠠⣍⠄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠻⠛⠁⠀⡘⠙⠀⠈⠛⠻⣯⣦⣄⠀⠸⣇⢀⡀⢀⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠙⠀⠢⠀⠸⢿⣿⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⢧⠰⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⣟⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣡⡀⠀⢿⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠂⣻⣿⣿⣧⣤⠏⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⣅⣿⣏⣻⣿⡒⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⣾⣇⣼⣿⣾⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠉⣻⡿⠓⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠛⠉⣀⣀⣀⣀⣸⣿⡿⠁⣶⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠰⣿⣿⣿⣿⣿⡿⠟⠁⠀⣿⣿⣿⣧⡀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠻⣿⣿⣦⡀⢰⣿⣿⣿⣷
⠀⠀⠀⢠⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣰⣿⡟⠉⠁⣾⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣸⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠄⢸⣿⣿⣿⣿⡟
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⡟⢩⣿⣦⣤⢠⣄⠀⣾⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣾⡏⣰⣿⣿⣿⣿⠇
⠀⠀⠀⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠏⣿⢧⣿⢡⣿⣿⣿⣿⠏
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠉⣸⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⡀⠀⠀⢀⣠⣴⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⣿⣿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⠦⢤⢄⡀
⠀⠀⠀⠀⢀⡴⣫⠽⡖⠋⢹⠉⠓⡾⢭⡛⣤⡀
⠀⠀⠀⣴⢫⠞⠣⡀⠘⡄⢸⠀⡸⠀⣠⠞⢣⠱⡄
⠀⠀⢰⢓⠗⠤⣀⠘⢦⣹⣸⣰⣣⠞⢁⡠⠔⢳⢹⡄
⠀⠀⣿⣼⠀⠀⠀⠩⢵⣿⠋⢻⣷⠯⠁⠀⠀⢸⡤⡇⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢹⢸⡀⣀⠤⠒⣪⢿⣿⣿⢯⡓⠢⢄⣀⢰⢒⠇⠀⠀⠀⠀⡠⡞⠈⢗⢀⠀⠀⠀⠀⠀⠀⣔⡕⠂
⠀⠀⠘⣎⢫⠀⢠⠞⠁⡎⣿⣿⢗⠛⢦⡀⢠⢏⡟⢀⡴⠚⠿⢯⡬⣥⠭⡬⢭⢥⠕⠀⢀⣀⢸⢴⢂⠀⣰⣤⡀
⠀⠲⠦⠿⢧⡟⢿⡞⡟⢀⢿⣿⠾⡶⣼⠟⣣⠞⠀⣸⣤⢶⠗⣾⢦⠅⠀⠳⠀⢸⣦⣈⢨⣨⢘⣋⣿⠀⢰⠋⢏
⠀⠀⠀⠀⠐⠘⠳⢼⣑⣾⣺⣛⣶⣽⣴⣏⣥⠶⠟⠙⣷⣇⣶⣣⣾⡖⣖⢲⡀⢸⡛⢿⣯⣿⠿⠿⠋⠀⠁⠀⠘⠀⢠⠙⣣⡜⢚
⠤⠤⠤⠴⠶⠶⠦⠤⠾⠤⠽⠽⠿⠷⠿⠿⠷⠶⠾⠿⠿⠧⠬⠤⠼⠧⠥⠾⠥⠤⠥⠤⠤⠴⠤⠤⠴⠷⠶⠶⠶⠾⠾⠶⠷⠷⠾⠤⠤

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡔⣴⢲⡢⣄
⠀⠀⠀⠀⢠⢴⣯⠯⡷⡦⠄⠀⠀⠀⢀⣴⣄⡀⠀⠀⠀⠀⠀⣷⣶⣿⣯⣤⣭⣤⣭⣤⣥⣤⣴⣾⣷⣴⡇
⠀⠀⠀⠀⡘⣼⢀⣧⠣⢧⠀⠀⢀⢣⡏⢫⡹⢻⠁⠀⠀⠀⠀⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⠟⠛⢻⠛⠛⠃
⠀⠀⠀⠐⠑⠁⠾⠿⠧⠈⠂⠀⠊⠊⠰⠿⠷⠀⠓⠀⠀⠀⠀⠀⠀⢠⣶⡶⣿⣿⣿⣿⣿⠀⠀⢸⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢳⠿⢿⡆⣿⣿⡿⠋⢙⢴⢦⣾⣿⣏
⠀⠀⠀⠀⠀⠀⣈⣹⡤⠔⠚⡿⠓⠦⣤⣏⡁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⡀⡍⣁⡀⣻⠈⠸⠁⠘⠁
⠀⠀⠀⠠⣄⣀⠞⠁⣹⡤⠒⡗⠒⢤⡏⠙⢧⣀⡤⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣷⣿⣷⣿⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠶⢶⠏⠓⡾⣁⠘⡄⡇⡰⠃⣨⢶⠊⢻⠶⠆⠀⠀⠀⠲⠿⠾⠾⠷⠷⠾⠾⠶⠷⠷⠾⠾⠶⠷⠇
⠀⠀⠠⢤⣼⠤⢼⠤⠬⠍⡎⠉⡦⠭⠤⢬⡤⢼⡦⠤
⠀⠀⠶⠶⠸⡄⠈⣄⢴⢭⡌⡎⢦⣷⠦⣼⠀⣸⠱⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢹⡆
⠀⠀⠀⢀⣠⠷⣏⠉⣖⣟⣀⣇⣈⣷⡞⠁⡹⠳⠤⠀⠀⠀⠀⢀⣰⣆⡀⠀⠀⠀⠀⠀⠀⢀⠔⢉⢻
⠀⠀⠀⢤⡤⠀⠈⢳⢿⣀⣀⣏⣀⣸⣵⠊⠁⠰⠶⠆⠀⠰⠶⠿⢾⡾⠾⠷⠆⠀⠀⠀⡰⠃⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠐⣿⠇⠀⢈⣏⠁⠀⢳⠗⠀⠀⠀⠀⢰⣦⡆⡄⢸⣧⡀⣦⠠⣄⠰⣮⡤⢀⡀⡀⢰⠃
⠀⠀⠀⠀⠀⠀⢻⠽⠀⠀⢠⣤⠄⠀⠘⡽⠁⠀⠀⠀⠀⠘⠃⠯⢼⡏⠧⠘⠃⠀⠀⠈⠻⠿⣶⡇⢸⡾⠂
⠀⠀⠀⠀⠀⢀⣞⡇⠀⠀⠀⠀⠀⠀⠀⣩⣇⠀⠀⠀⠀⠰⠶⠶⠿⠿⠶⠶⠆⠀⠀⠀⠀⠀⠀⡇⢀⡀
⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠒

⣿⣿⣿⣿⣿⣿⡿⣻⡷⠀⠠⡴⣿⣾⣿⢎⣿⣷⣶⢼⣷⣼⣾⢿⣿⣭⣯⣿⣿⠿⢿⢿⣿⣿⣿⣇⡉⠛⠿⠇⢨
⣿⣿⣿⣿⡿⡿⠀⠛⣀⡼⠠⢆⡶⡋⣾⠋⡋⠔⠓⠾⠻⠿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⡻⢿⣿⡟⣷⣶⡆
⣾⣿⣩⣿⠱⢀⣤⣿⣋⣀⣾⢫⣿⠟⠉⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣷
⣶⣿⣿⠏⣰⠼⣯⣽⣯⣽⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿⣿⣿⣿⣿⣷⣾⣝⡛
⣿⣿⠋⣶⢩⣿⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⣿⣿⣿⡿⢿
⣿⡟⡴⣁⣿⣿⢿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠛⠿⣧⡿⢿⣿⣷⠸
⢋⣪⣼⣿⡙⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢉⡅⠈⡇⣿⠂
⣡⡿⣽⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⣿⣿⣿⣿⣶⣦⣬⡇⠀⢃⠁
⣿⣿⣿⠋⠁⠀⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡅⠠⠤⠄⢈⡏⢻⣿⣿⣷⡀⢾
⣿⣿⣿⣣⣾⣿⣿⠟⣿⣟⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠈⠉⠹⣿⣇⠦⡄
⣿⣿⣿⣿⣿⠀⠻⣄⠈⠉⠀⡸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢦⡇
⣿⣿⡿⠛⠛⠒⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⠀⠀⠀⠛
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⣿⣿⡯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣿⣿⣷⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁
⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⡻⣿⣮⡘⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡯⠚⣼
⣿⣦⣙⠻⠿⣿⣿⣿⣷⣦⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡏⣠⣶⣿
⣶⣶⣾⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⠿⠟⠻⢻⡋⣘⣛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣟⣛⠿⣿⣿⣿⣷⣶⣶⣢⣤⣤⣶⣶⣶⣿⣿⡍⠀⠘⠥⢞⣓⣉⣥⣿⣶⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣼⣻⣿⣿⣷⣿⣿⣷⣽⣿⡿⣟⣻⣿⠻⠿⠍⢿⣿⣿⣻⣷⣶⣷⣬⣿⣽⣍⣛⣛⣻⡿⢿
⣻⣿⣭⣯⣭⣿⣿⣯⣭⣓⣺⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣞⣷⣶⣶⣾⡤⢡⣥⡬⠭⣭⣩⣙⣻⣿⢛⢻⡿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣛⣋⣉⣉⣿⣷⣦⣶⣶⣷⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠤⠀⠀⡤⣀⢐⠉⠂⠲⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠠⣀⡀
⠀⣅⠳⢤⠔⢄⠀⠠⠹⢀⣀⣣⠞⢀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢘⠢⠏⠡⠡⠈⡀⠸⢹⡞⠀⢆
⡠⠃⠀⢀⣠⠛⠃⠀⠀⠢⠜⢸⠧⡄⢠⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢉⡁⣠⣘⢄⢀⢇⢀⣇⣰⡼⢻⡖⠊
⠃⠤⠊⠣⣀⡱⢦⡡⠌⣐⡰⠃⠑⠒⠂⠀⠀⠤⢀⠐⢌⣭⣔⡒⡒⢄⠀⠉⡧⠃⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠥⠤⠤⠴⠄⢻
⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠠⠤⢀
⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠀⠰⠀⠤⠤⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠤⠅⢁
⠀⠀⠀⢸⡄⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠊⠀⢄⠱⠄
⠀⠀⠀⠈⢌⠒⠄⢉⠒⠀⠐⢊⠅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣀⠄⠂⠠⢀⣀⠀⠈⢈⡀⠀⠀⢀⢠⢖⡀
⠀⠀⠀⠀⠈⠱⠤⣀⣀⡩⠝⠁⠀⠀⠀⠀⡠⣄⣀⠀⠀⠀⠢⠀⢈⣁⠀⠀⡀⠐⠈⡄⠀⠀⠈⠀⡑⠏⣠⠲⠊
⠀⠀⠀⠀⢀⠃⡐⠀⠀⠀⠀⠀⠀⣀⠠⠚⠒⠀⠘⣤⣄⠀⠀⠀⡀⠈⠐⡄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⢀⠎⡘⠀⠀⠀⠀⠀⢴⡋⠄⠀⠀⠀⠀⡊⠀⠈⠉⠁⠚⡍⢣⠀⠷⠊⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⢄
⠀⠀⠀⢎⣠⠀⠀⠀⠀⠀⠀⠠⢈⠑⠈⠀⠙⠉⠈⠖⠉⠙⠆⠀⡠⠸⠁⠀⠀⢀⠔⠊⠁⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠚⠀⠈⠓⠀⠉⠓⠈⠀⠀⠀⠀⢀⠏⠀⢀⠔⢋⠑⡦⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⣄⠀⠀⠀⠀⠀⠸⡀⠉⡇⠀⣭⠤⠣⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠲⢚⢉⠉⢫⡤⢀⠃⠀⠀⠀⠀⠀⠙⢤⡛⢮⣀⣀⡧⢏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠂⠉⠀⠑⠄⠀⠈⣎⡤⠊⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢂⠠⡀
⠀⠀⠀⠀⢲⠠⠠⠅⠀⢂⠑⠄⡄⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡘⢆
⠀⠀⠀⠇⠀⡑⢒⠔⠣⠤⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠒⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠁⡀⡀⠐⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠉⠀⠀⠀⠀⡠⠈⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⡠⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠁⠤⠤⠠⠄⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⠀⠀⠀⠀⠀⠈⢀⠀⠀⠆⠀⡰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣈⡂⠤⣀⣈⠀⠀⠀⡀⠈⠀⠀⠀⡊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠓⠀⠀⠄⠄⢀⢀⣱⠀⢠⠴⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠰⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⠀⠈⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠐⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⢸⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠳⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠘⠌⠁⠀⠀⠀⠀⠈⠃⠐⠂⠁⠀⠀⠤⠄⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠶⠦⡀⠀⠀⠀⠀⣆⡙⢄⠐⠀⡀
⠀⠀⠀⠀⠅⠀⠀⠀⠀⠈⠡⠚⣁⠀⠀⠀⠀⠄⣢⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⣶⠢⢹⡆⡴⢋⡩⠉⠻⣆⠴⢋⣽⡄⠠
⠀⠀⠀⠀⡅⠀⠈⡀⠀⠠⠀⠀⢠⣿⡄⢀⡀⠀⢻⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢧⡸⢟⣀⡼⢻⡇⣾⡿⠀⠀⣿⣤⣉⠈⠀⠀⠂
⠀⠀⠀⠀⠠⠀⠑⠚⣢⠅⠀⠀⠨⠟⠁⠀⠉⡷⠀⠀⢀⠀⠀⠀⢐⡀⠀⠀⠀⠐⠀⠀⠀⠙⠙⠃⠀⠀⠳⢬⣀⣀⠴⠟⠀⢹⠆⣀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢅⠈⠥⡀⠀⠀⠀⠀⠦⢠⡦⠀⠀⠀⠌⠀⠀⠀⠘⣭⡀⠀⠀⠐⠠⠒⠃⠤⠀⠀⠘⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠘⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣜⡤⢢⠴⠀⠀⠀⠀⠈⠂⠀⠀⡀⠀⠀⠀⠤⡀⣀⣀⡀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⢯⣤⣬⠦⠄⠠⠠⠀⠰⠀⠀⠀⠘⠭⠅⠀⠀⠀⢠⣀⡀⠀⢀⣤⢠⣅⠀⠡⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢰⢀⠋⡍⢸⠈⣿⡄⠀⠠⠆⣼⢃⠕⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠘⣷⡋⠀⠤⠀⠀⠛⢧⢊⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠀⠴⠀⠀⠋⢀⢨⡇⡀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠢⠤⠤⠤⠤⠤⠤⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡭⠥⠤⠤⠤⡯⢤⠌⠰⠇⠐⠆
⠀⠀⠀⠀⠀⠀⢀⠈⢀⢄⡰⢀⣀⣻⣤⣤⡀⠀⠀⠶⢒⣲⣤⠴⢶⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⢥⡐⠅⠀⠁⠀⠉⠛⠛⠛⠁⠀⠀⠀⣀⣀⣀⠐⠨⠋⠉⠉⠙⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠩⠴⡮⢄⢀⡀⣂
⠀⠀⠀⢀⡄⢉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠈⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠓⠐⠒⠀⠀⠀⠒⠀⠂⠀⡁⠈⠑⠈⡋⣂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢸
⠀⠀⠀⢸
⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠠
⠀⢀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⢀⡨⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⡀⠀⣤⢤⠀⠀⠈⡲⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⢀⡶⠟⠒⠖⠓⠀⠀⢉⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡆⠅⠘⠀⠀⡁⠀⠀⠠⠀⢀⡀⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠉⠀⠀⠡⠊⠀⡄⠀⠘⠃⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠐⢏⠡⠴⠄⠐⠰⠀⠀⠀⠀⠀⠀⠌⠀⠀⠄⠀⠀⠀⠀⠀⠃⠀⠀⠂⠈⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠸⠁⠘⠐⠀⠀⠀⠀⠀⠀⣀⠰⠃⠀⡄⠈⠀⠀⠀⠀⠠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⢀⠂⠘⠔⠀⠉⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠆⠘⠊⠀⡀⠀⠀⠐⠀⣀⠂⡈⣀⠒⠠⡤⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠒⠄⠠⠊⠁⠴⠀⠀⠄⠀⠀⠄⠉⠀⠰⠆⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⡅⠀⠤⠂⠂⢀⠂⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠈⠀⢀⠀⠐⠂⠠
⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠠⠤⠀⠐⠃⢀⠀⠀⠀⠀⠈⠀⡀⠀⠰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⡦⢀⣈⡀⠀⠀⠈⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠚⠓⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⣀⠀⠀⠀⠀⠀⣟⠀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠙⠦⠙⢦⡜⠳⢤⡄⣀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠛⡁⠀⠀⢀⡶⠀⠈⠁⠀⠀⠀⠀⠀⣹⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠏⠁⢀⠀⠈⡆⠀⠈⠁⠀⣀⠄⠁⣀⣀⠀⣈⣵⣮⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⠀⡇⠀⠀⠀⠀⣠⣏⠩⠥⠶⣰⣿⣿⣷⣮⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡟⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⣿⡻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠟⠂⠤⡀⠬⠁⢀⠀⠀⠀⠀⣿⠛⣻⣉⣩⠻⠋⢹⣿⣿⣿⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠲⢤⣀⣑⢦⡀⢀⡫⢤⣙⠟⣉⣧⣴⣆⣽⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠦⣄⡀⠀⠀⠀⠉⠁⡄⢀⣠⣾⣧⣼⣶⣿⣯⣵⣾⣿⣿⣯⢻⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⠙⠛⠒⠒⠋⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠞⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠘⠁⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢤⣤⣤⢤⣶⣖⣯⣠⡆⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠰⠶⠶⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⣠⠞⢋⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣇⡟⠿⢿⡟⡿⢿⠿⡿
⠀⠀⠀⢠⡞⠁⢀⣸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⡉⣠⠶⠋⠀⠀⣀⡤⠁
⠀⠀⠀⠘⠚⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠉⠁⠈⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⢀⣔⠒⢢⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⠀⠀⣀⠤⣠⣀⢀⠀⠀⠀⠀⣠⣴⠀⢤⣄⣀
⠀⠀⣘⣷⡄⢰⠉⣠⠒⠚⠢⠀⠔⠒⠢⡀⣴⣿⣯⣼⡁⠀⠀⠀⠀⢰⣿⣾⡛⠟⢷⡀⠀⠀⢰⡇⠸⣆⠀⡽⠿⢷
⠀⣾⣛⢧⣿⠜⣲⠧⠀⢀⣐⠆⠆⠀⠤⡇⢿⣯⣿⣿⢁⣤⠀⠀⢰⡸⣿⣽⣇⣉⣬⣷⠀⠀⢺⣿⣦⡈⠉⣳⣾⣿
⠀⢸⣿⡿⡟⠀⠙⣷⣾⣴⠋⠀⢴⣶⡶⠁⠘⣿⣳⡟⢛⣉⣀⣀⣸⠀⠻⣿⣯⣿⣼⠏⠀⠀⢸⣿⣿⣻⣷⣿⣿⡟
⠀⠘⣿⣿⠃⠀⠀⢿⣻⡍⠀⠀⠘⡝⠁⠀⠀⢿⣿⠇⠀⢿⣭⣼⠃⠀⠀⣠⣿⢹⣀⠀⠀⠀⠀⣇⠀⠈⡉⠈⣿
⠀⠀⢹⡇⠀⠀⠀⠈⣭⠃⢀⠀⠀⠑⠀⠀⠀⢸⣻⠀⠀⢸⣗⣿⠀⠀⠀⠉⠁⠈⢉⣴⠖⠂⠀⠻⣄⡀⣀⣠⡿
⠀⠀⢈⠁⠀⠀⣀⣀⡙⠀⣿⢯⣿⠀⡞⢻⡆⢀⣭⣤⣀⠀⠃⠃⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣨⣄⠀⠈⠉
⠀⠀⠈⠀⡄⢠⣿⣿⣽⡄⣿⣾⡟⠀⡃⢸⡇⣾⡏⢹⣿⣇⠀⠀⠀⠀⠀⠀⢀⡀⠸⣷⢦⣤⠿⠿⠿⠿⠿⠿⣶⡄
⠀⠀⠀⠀⢡⢸⣿⣿⡇⡁⣿⣽⣿⠀⡆⢸⡇⣿⡇⢈⣿⣿⠀⠀⠀⠀⠀⠀⢙⣇⣤⣶⣭⣁⡄
⠰⡟⠀⢬⣿⣾⣿⣿⡇⡅⣿⣿⣿⠀⡇⢸⡇⠻⣧⣠⣿⠏⢀⣀⣠⢤⣄⠀⢈⢻⣿⣿⣯⣿⠧⠄⣶⠀⠀⡀⡴⡄
⠀⠉⠉⠋⠉⠘⠻⠿⠓⠀⠙⠛⡏⠀⠳⠾⠃⠀⠀⠈⠀⣼⣿⣥⣿⣿⣿⠢⣀⣼⢀⣀⣘⣿⠀⣦⢸⣦⣶⣶⣶⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠇⠀⠈⣻⠿⠿⣿⠁⠀⢸⣯⣻⣸⣟⢻⡬⡀
⠀⠊⠁⠉⢳⠀⢠⠖⠒⢤⡀⡠⠒⠒⢦⢀⡴⠒⠒⢆⢹⣶⣾⣿⣬⣿⡆⠀⠀⠉⡀⣠⠃⠀⠀⠘⣿⣷⠿⣿⢿⣿⠇
⠀⣷⠀⣀⣼⠆⣗⠀⠀⢰⠇⣷⠀⢀⣸⠘⣆⠀⣠⣾⠰⣟⠀⠀⢹⣯⠁⠀⠀⢞⡓⣻⡄⠀⠀⠀⠈⣿⢿⢻⣿⡇
⠀⠈⠉⠉⠉⠀⠈⠁⠉⠉⠀⠈⠉⠉⠀⠀⠈⠈⠉⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⠂⠘⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠑⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⢂⡕⠉⠉⠑⡤⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠀⢀⠤⠂⠁⠀⠀⠀⡠⠁⠸⠂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡠⠐⠈⠀⠀⢀⡀⠄⠐⠈⠠⠂⢀⠥⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⢁⠀⠠⠶⠠⠬⠄⠒⠀⠈⢉⠰⠂⠁⢀⢆⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⢀⠤⠂⠁⠀⠀⢀⠤⠐⠈⠀⢀⠠⠐⠁⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡠⠊⢁⠀⠠⠐⠈⢁⠀⠠⠐⠂⠁⠀⠀⢀⠴⠄⠒⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠔⠁⡀⠄⠂⠁⠀⠀⠀⣀⡀⠤⠀⠀⠁⠀⠀⡠⠊⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠔⠉⠀⢠⣊⠀⠀⢀⠀⣀⢀⡄⠀⠁⠀⠀⠀⠄⠀⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠄⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠠⡤⠀⢄⣄⠀⣀⡀⠀⠄⣤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⣀⠈⠙⠢⢀⡀⠀⠠⠒⠂⢤⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠓⠲⣀⠉⠉⠑⡠⠤⠊⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠢⢤⠄⠑⠒⠄⢀⣀⠄⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⣈⠰⠤⢄⠈⠈⡡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡁⠈⠑⠠⣀⡀⠠⠈⠉⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠑⠌⡉⠀⠉⡀⠖⠮⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠛⠃⠀⠒⠂⠉
⣿⣿⣻⣻⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣛⣿⣿⣛⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠁⠀⠀⠀⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠹⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡤⠴⠒⠋⠁⠀⠀⣀⡤⢾⡇
⠀⠀⠀⠀⠀⢸⠒⠚⠉⠉⠀⠀⠀⢀⣠⡤⠖⠋⠁⠀⢸⠁
⠀⠀⠀⠀⠀⠈⢦⣠⣤⠤⠔⠒⠋⠉⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠴⢶⠛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢝⢢⣀⡠⠴⢲⠶⠦⣄⡀⢧⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠠⡅⠉⠀⣰⠋⠀⣰⠃⠙⣎⣇⠹⣄⣀⣠⣄⣀⡀⠀⠀⣠⠴⠶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣰⠒⠀⠀⢀⡏⠀⢰⠇⠀⠀⠘⢻⡶⢫⠇⠀⣾⠀⠉⢲⠞⠔⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢼⣘⣿⣠⠴⢦⠀⢸⠀⠀⣾⡋⠉⠭⣛⠿⠀⢸⡀⠀⢹⠀⠀⠀⠐⣃⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⡄⠀⡏⢳⡄⠀⠒⠀⠀⠀⣇⠀⠸⡆⠀⠀⢀⠀⠩⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡟⠀⡪⠀⣄⠀⠸⣄⠀⠹⡄⣠⠏⠙⠲⠯⠥⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠾⣢⠞⠉⠙⠲⠾⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠄⠠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣶⣀⠀⡤
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⣱⢤⡀⠤⠄⣀⡀⠤⠤⡄⣀⠀⠀⠀⠀⠀⠀⢀⣠⠟⢫⡄⠶⠀⣜⠻⣅⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡅⠉⠁⠀⠉⡧⢎⠉⠓⠀⠀⠁⠀⠓⠀⠀⠀⠀⠐⢺⠋⡒⠤⣱⣶⣾⠤⢒⠙⡖⠂
⠀⠀⠀⠀⠀⠀⣿⠀⢀⣷⣀⣂⠀⠀⣇⣀⢀⠒⠀⠀⠀⠀⢠⢀⡀⠀⢀⣬⣹⡉⢋⣩⣿⣿⣿⣍⡙⠉⢯⣥
⠀⠀⡔⠀⡋⡉⢹⠀⢀⣀⣈⣳⣄⣀⡤⠤⠀⡄⠀⠈⣀⡀⡀⣤⡂⠀⠀⠀⣭⠻⣉⣿⢧⣦⠸⣷⢉⠟⠤
⠀⠀⠉⠈⣣⡟⢛⠈⢨⡅⠀⢀⡀⠀⠁⣶⣄⣤⣤⣼⣿⣦⣤⣀⣁⣆⣀⣀⣻⢀⣬⣿⠒⢿⠖⢻⡅⠀⠙⠁
⠀⠀⠀⣴⣿⣿⣿⣾⣿⣿⣶⣟⣟⠉⠏⢹⠁⠉⢉⡍⣿⡏⠙⣉⢩⣿⣿⣷⡌⠘⣿⢿⠻⣿⣤⣾⣿⣴⣷⣄
⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣙⣷⣿⣇⣍⣉⣡⣿⣯⣿⣁⣼⣿⣿⣿⣯⣽⣿⣼⣯⣿⣷⣯⣿⣿⣿⣿⡆
⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠙⠛⠛⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⣀⣀⣀⣀⢀⡠⠉⠀⠸⠏⠀⠀⡀⠀⠀⠀⢀⡨⠕⠢⢦⠀⠀⠀⠀⠸⠀⠀⠻⠇⠀⠀⣂⣀⣀⣀⣀⣀
⠀⢠⣶⣿⡿⠿⠿⢿⠁⢀⡀⠀⠀⡄⠀⠀⠡⣀⡇⢀⡜⠁⠀⠀⠈⢧⡀⠂⢀⠀⠀⠀⠐⠀⠀⢀⡁⠘⡿⠿⠿⢿⣿⣦⡀
⢠⣿⡟⠁⠀⠀⠀⡘⡓⠀⠑⠄⢀⢣⡄⠤⣤⠗⠋⠉⠀⠀⠀⠀⠀⠀⠉⠛⠣⡤⠤⢴⡌⢀⠔⠁⠀⢞⠁⠀⠀⠀⠈⢿⣿
⢸⣿⡇⠀⠀⠠⠂⠉⢹⡀⠀⠀⡠⠀⠀⠠⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠅⠀⠀⢀⡏⠉⢰⠀⠀⠀⢸⣿
⠸⣿⣧⡀⠀⠀⢠⠖⠉⠁⠀⠊⠀⠀⣠⣤⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠒⠂⠈⠁⢲⡁⠀⠀⢀⣾⣿
⠀⠙⢿⣿⣷⣶⠁⠀⠀⢠⣠⠆⢠⡞⣱⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡌⢷⠄⠢⣀⡀⠀⠈⠄⣶⣾⣿⠿⠃
⠀⠀⠀⠀⠉⠉⠤⠂⠀⠀⠈⠀⢸⡇⢿⣿⣿⣻⣿⢿⣀⠤⠤⠠⠤⣀⡿⣿⣿⣿⣿⡿⢸⡇⠀⠀⠀⠀⠁⡤⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠘⠻⢿⣿⡧⠋⠐⣇⡀⢀⣽⠈⠑⣽⢿⡿⠿⠃⠚⠃⢠
⠀⠀⠀⠀⠀⠀⢂⢀⡀⠠⠆⠀⠀⠀⠀⠀⠀⠰⡇⠒⠦⡴⢿⠿⢤⠴⠂⢸⠀⠀⠀⠀⠀⠀⠀⡱⠄⢀⡀⡀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢫⣀⣀⡝⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠐
⠀⠀⠀⠠⠀⠀⠅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠈⠓⠦⠶⡺⠁⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢠⢠⡤⠤⠤⠴⠦⢄⡀⡀⠀⠀⠈⠀⠀⠀⣠⠼⠦⠦⠤⢤⣄⡘
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⠄⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠉⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡷⠆⠀⣿⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⠃
⠀⠀⠰⠄⠀⠈⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⡀⠑⣾⠅⠀⠀⠸⣧⠖⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠈⠀⠀⠢
⠀⠂⠀⠀⣀⣤⡴⢶⣶⠶⣤⣄⡙⠲⠤⣤⣤⣤⠬⠿⠋⠀⠀⠀⠀⠉⠶⢯⣤⣤⣤⢤⠖⠋⣠⡤⢶⣶⡶⢦⣄⡀⠈
⠈⠀⢠⣶⣍⣿⠧⣾⡟⠑⣿⠻⣷⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⣾⠈⣻⣦⠾⣯⣙⣦⡀⠈
⠀⠀⣾⡟⠉⣧⣀⣿⠷⠞⠛⠓⠿⣿⡀⠀⠀⠀⢀⠤⠄⡔⠁⠀⢢⠤⠤⡀⠀⠀⠀⢠⣿⠟⠚⠛⠶⠿⣧⣀⣾⠉⣽⣧
⠂⠠⣿⡟⢾⠟⠁⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠁⠀⠀⢀⡀⢠⠀⠀⠀⠈⠀⠀⠀⣶⠃⠀⠀⠀⠀⠀⠀⠈⠻⡗⢻⣻⠄
⠀⠀⠸⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠂⠀⠁⢠⠂⠀⠀⠀⠀⠀⡄⠈⠁⠐⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠏
⠂⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠂⠐⢀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣤⣀⣤⠾⠋⠐⠀⠀⠁⠀⠘⠲⠤⠤⠔⠃⠐⠊⠀⠀⠊⠙⠦⣄⣀⣠⡤⠖⠋⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡈⢄⣡⡞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠚⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠀⠛⠈⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠂⢕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⢿⠥⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣡⢔⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠐⠒⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠣⠄⣀⡀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢐⢀⡇⡇⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠺⠺⠧⣄⠀⠀⠀⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠃⡤⠠⡄⢰⠀⠀⠀⠀⠀⡰⠋⠀⠄⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⡀⠀⠀⠀⣠⠒⡈⠀⠠⢤⣬⣑⡲⣶⣆⠀⢱⡆⠀⠀⡎⢸⠁⠀⢡⢘⡄⠀⠀⠀⢸⠁⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠸
⠀⠀⢀⡂⠀⢰⣿⠋⠐⠊⠀⠀⠀⠀⢀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⢠⠀⠀⠀⢠⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠉⠀⠀⡇⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢣⠀⠀⠈⢦⡘⠒⠒⠊⠀⠀⠀⠀⠀⢋⡜
⠀⠀⠀⠀⠀⠸⢧⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠃⠀⠀⠀⠉⠢⣄⡀⠀⠀⣀⣄⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠑⠤⠤⠊⠾⡀⠔⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⢧⣀⢀⡠⠞⠏⡪⠏⢉⡏⠒⢄⠀⠀⠀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢲⣒⡶⠀⠘⠆⠐⠋⠓⠒⠒⠂⠀⠀⠈⠈⠁⠀⠀⠀⠳⡸⠏⠉⠀⣾⠀⠀⠀⠀⠗⠀⣨⠇⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠢⡄⢸⠀⠉⠀⠢⣤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠤⠄⢺⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢎⠀⠘⣉⡆⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣂⢀⡀⠀⠀⠀⠀⠀⠀⢆⢀⣦⠀⢸⡀⠀⠀⠀⠀⠀⡎⠱⡄⠀⠀⣤⠎⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢃⢀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⣮⣸⡾⠀⣦⣚⠀⠀⣀⡀⢨⠉⠀⠙⡏⠀⠀⠀⠀⠀⠀⠉⠰⢆⠰⠆⡸⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠭⠼⠤⠤⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢠⣋⡇⢰⠁⡌⠀⠀⠓⠈⠋⠀⠶⠭⠛⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⢌⠁⠐⠰⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢼⡀⠀⢤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠒⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⢀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⡭⠆⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⢟⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡍⢻⣦⡉⠻⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⡿⠋⣾⡿⢿⠘⡹⠉⢿⣣⣴⣿⣿⣿⣦⡌⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⠉⢁⠈⣌⠘⢦⣤⣌⠉⠋⠉⢹⣿⡿⢸⢿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣠⣗⡀⠀⢀⡘⢿⣿⠻⠶⠀⠉⠀⠀⠀⢼⠿⡟⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣿⣿⣯⠟⠫⣿⢀⣈⣭⣅⠀⠀⠀⠀⠀⢠⣌⣁⠘⠀⠀⢻⣧⣿⣿⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣤⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠚⠁⠀⠀⢠⣾⣷⣿⠏⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠝⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠕⢶⣼⣧⡀⠀⠀⠀⠀⠲⠤⠒⠀⠀⠀⠀⠀⢠⣯⡤⠠⡔⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠⠄⠈⠓⠲⠞⠣⠹⣿⣶⣤⣤⠉⢛⡒⠛⠉⢀⣀⣠⣶⣿⣴⠶⠂⠀⠈⠁⠉⠐⠒⠈⠑⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠹⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣷⣦⣭⣤⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⡀
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠹⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢳⠀⠀⠀⠀⣠⠴⠶⢿⣂⡅
⠀⠀⠀⠀⠀⢀⣣⠆⠀⠄⠀⣰⢀⠈⠣⠀⠀⣤⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⡌⢁⠀⡠⠀⠘
⠀⢀⣀⣠⠐⠋⡎⠄⠁⠀⠀⠁⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠛⠻⠿⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠋⠀⠃⠘⡐⡆
⠀⠙⣟⠈⣠⠌⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⢏⠐⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⢀⢀⢸⡀⠦⠀⠠⠤⠦⠶⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⠶⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠃⠁⠀⠀⠈⣄
⠀⠘⠀⠀⠀⢀⠀⠀⠀⠐⣧⡙⢶⠑⠀⠀⡠⠁⡀⠀⠀⠀⡩⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠁⠠⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠔⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠆⢠⡞⣀⡤⠀⣀⣠⣴⣾⣶⣦⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣟⢸⣸⢃⠗⠁⠀⠀⢀⡀⣀
⢸⡂⣿⢋⠀⠀⢨⣿⣿⣿⣿⣿⣿⡏⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣿⢾⡷⠀⠀⠀⠏⠈⢻⠇
⠀⢷⣿⠊⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⣤⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢾⣇⡀⠀⠀⠻⢛⢉⡀⠀⢰⣶⡀
⠈⣾⢿⣷⠄⢴⣿⣿⣿⣿⣿⣿⣿⣿⡟⢩⠟⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠈⠻⣿⣿⠃⠀⣷⣾⣇⣤⣿⡿
⣠⡏⣼⢋⠠⠾⡿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠁⢀⣀⡀⠀⠀⠀⠀⣿⣇⠀⣠⣿⣇⡀⢸⣿⡟⠛⠟⠋
⣿⣿⣿⠃⣴⠾⢷⢤⡀⠀⠀⠀⠀⠀⢠⣤⣤⣶⡀⠈⠀⠀⠀⣾⣿⣿⠯⠀⠀⠀⠀⠙⠉⣰⣿⣿⣷⣟⢻⣿⡅⠀⠂
⣿⠟⠁⢺⡉⣀⠀⠀⠅⠀⠀⠀⠰⠿⢻⣿⣿⣛⡁⠀⠀⠀⢀⡘⠿⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢿⣿⣞⠻
⠁⠀⢀⣴⣿⣋⣶⢶⣿⣶⣦⣄⠀⠀⢸⣿⡏⡿⣃⣤⣶⣾⣿⣿⠒⢲⠀⠀⠀⠈⠁⠀⣼⣿⣿⡇⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀
⠀⣀⣾⣿⣿⣿⡷⠈⢣⢰⠀⠉⢶⡀⢸⣿⡇⣾⡿⣵⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠂
⠟⢻⣿⣟⣩⡵⠆⠀⠈⠋⠀⠀⢸⡇⢸⡿⠀⢸⣇⢻⣿⣿⣟⣁⡠⢿⠒⠒⢒⡦⠀⣺⣿⣿⡿⢋⣽⣿⡏⠀⠀⠀⢰⣧⣤
⠀⣼⣿⠋⣫⡶⠻⡅⠉⠙⢶⣤⡾⠃⣙⡃⠀⠐⠿⢶⣤⣤⣉⣁⡀⢈⣇⠀⠈⠀⠾⠛⣱⣿⣿⣎⣿⠟⠁⠀⠀⠀⠚⠿⠟
⠆⣿⡟⢀⣿⠁⠀⠈⠈⠙⠋⣻⠀⠀⠉⠙⠀⠀⠺⢿⣿⣻⣿⡄⣿⠋⣹⣆⣤⣄⡀⣼⣿⣿⣿⣿⠁⡀
⠙⣿⠇⠘⠟⣆⠀⠀⠀⠀⢀⡟⠀⠀⢀⡀⠀⠀⢀⣼⣿⣿⠻⣿⡿⣾⠋⢻⡀⠈⢹⣿⣿⣿⣿⣿⣾⡿⠀⡀
⠀⠠⠀⠀⠐⠈⠓⠲⠶⠖⠋⠀⣠⡾⠛⢻⠛⣶⣏⢘⣿⡏⣠⢿⣾⣧⠀⠈⣧⠀⠙⠻⢿⣿⣿⠈⠁⠀⠚⠁⠀⠀⠀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠢⢸⣾⣡⣿⡾⣿⡿⠁⠸⠿⠿⡄⠀⢠⣤⣶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠁⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⠻⣌⠀⠀⢀⠰⣾⠃⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⣛⣛⣯⣟⣋⣬⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣁⣤⣄⢠⣦⣐⡎⠀⠀⣴⣯⣬⠁⠀⠈⣧⠀⠀⣿⣿⣟⣭⣭⣿⡿⣻⡦
⠀⠀⢀⡴⠖⠛⠲⣤⡀⢛⣿⡏⠙⢉⣹⡿⠁⡴⠏⠁⠀⣀⡵⠶⠴⢿⣀⠀⢾⣿⣶⣤⣿⣶⣾⡉⠁⠀⢀⡿⣦⣀
⠀⢠⡏⠀⠀⠁⠀⢈⣷⠈⡿⣿⡿⣿⣿⠇⢰⡝⠂⠀⣼⠇⠀⠀⠀⠀⢈⡄⠸⣯⣏⣻⡟⢋⣿⡏⠀⠰⣏⣆⢻⣿⢳⡀
⠀⠈⢏⠀⠀⠀⣠⣬⣟⠀⢹⣿⡷⣾⢿⠀⠈⢹⢲⡴⣯⡀⢀⠀⠀⠀⠠⣾⠀⢹⣿⣟⣛⣿⡿⠀⠴⣴⠿⠼⣿⢘⣿⣧⡄
⠀⠀⢋⡀⢀⢠⣀⢢⡼⠀⠸⣿⡷⢮⣿⠀⠀⠺⣼⣗⠀⠣⣠⡀⠤⠤⢶⡋⠀⠀⣿⢹⣿⣿⡇⠀⠼⣯⣾⣱⠚⣜⣿⣹⠃
⠀⠀⢠⡾⣷⡾⡿⡾⠀⠀⠀⠛⠓⠚⠃⠀⠀⠀⠈⢿⣿⣶⣶⣦⣴⡻⠉⠀⠀⠀⢽⢾⣤⣿⠃⠀⠀⢻⣿⣿⣾⣛⣿⡿
⠀⠀⠀⠜⣧⣻⠓⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣧⠃⠀⠀⠀⠀⢸⣿⣩⣿⠀⠀⠀⠘⣟⣿⣹⣯⣽⠇
⠀⠀⠀⢸⣶⢋⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠻⣖⡏⠀⠀⠀⠀⠀⠀⣿⣻⡿⠀⠀⠀⠀⢻⣿⣙⣯⣿
⠀⠀⠀⠈⡟⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣻⣽⣩⠁⠀⠀⠀⠀⠀⠀⠹⢿⠇⠀⠀⠀⠀⠈⣿⡟⣿⠇
⠀⠀⠀⠀⠙⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣰⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠹⢦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⠶⣿⠀⠃⣰⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠖⠋⣁⡤⠴⠒⡦⠀⢙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠒⢋⣡⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠻⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢲⡶⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡄⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣴⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠃⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⠴⠚⠉⢉⡤⠆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣶⡶⠋
⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⢠⣤⣀⣀⣠⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⡀⠀⠀⢠⠇⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦⠀⠀⠀⡏⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠐⣇⡼⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠞⠁


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

⠀⠀⢀⡀⢀⡀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⠕⠊⡀⠀⠀⢉⡤⠃⢄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣥⠉⠠⠀⠀⠀⢀⢤⡀⡀
⠀⠀⠬⢀⠐⡂⠀⠀⠈⢃⠀⠮⠂⠀⠀⠀⠀⠀⠐⠸⠃⠀⠈⠀⠀⠀⠀⠠⣠⡤⠤⠐⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠨⠈⠚⠁⠂
⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠛⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠁⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⣿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⢠⠀⠀⠀⠊⡁⠃⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢐⣀⠀⠄⠀⠀⠀⢯⡟⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡦⠚⠀⡀⠀⠙⢀⡄⠀⠀⠀⠀⡰⢸⠀⠀⠀⠀⠀⠀⠰⠷
⠀⠀⠀⡬⠙⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢⡀⠱⡀⠀⠤⠀⠀⠀⠀⠉⡄⠀⠐⣁⡘⠀⠀⢠⠖⠀⠀⠀⠸⡆⠁⠀⢠⡀⠄
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠣⠈⠀⠀⠀⠀⠤⠀⠦⠀⠀⠀⠠⠞⠙⠆⠀⠀⠀⠀⠀⠰⠆⠀⠀⢬⠀⠠
⠀⠰⡗⠐⠂⠀⠀⢧⠆⠀⠘⠺⠀⠀⠀⠀⠈⠉⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡸⠀⠀⠀⠀⠐⠁
⠀⠀⠁⠀⠀⠀⠀⠁⣀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢴⠆⠀⠺⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⡉⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠀⠈⠁⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠦⠀⠀⡄⠐⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠉
⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⣀⡀⠀⡇⠀⣠⡄⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠂
⠀⠀⠀⠀⠠⠀⠗⠀⠀⠁⠀⠀⠀⠀⠀⣄⣤⠄⠀⡀⠓⠿⡁⠐⠀⠈⠙⣓⣷⣓⠀⠀⠀⡀⢨⠋⠉⠄⠀⢰⣦⡤⠀⠀⠀⠄
⠀⠀⠀⠀⠓⠀⠈⠀⠠⡀⠀⠀⠀⠀⠀⠚⢋⠰⠀⠀⠀⠘⠁⠈⠀⠲⠋⠙⣁⠁⠙⠂⠀⠀⠈⠀⠀⠀⠸⠂⠈⠁⠀⠀⠀⠍⠀⠃⠀⡉⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣿⠿⠿⠿⢿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣯⠀⠀⠀⠀⢀⠜⢧⠀⠀⠈⠀⠀⠀⠀⠠⠁⢠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠈⠙⢦⠀⢧⠉⠀⠒⠈⠁⠀⢸⡇⠂⠀⠀⠖⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠰⣄⣀⣀⣨⡇⠘⣆⠀⠀⠀⠀⠀⡜⠀⠔⠀⢀⠀⠀⢀⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠚⠉⠉⠉⠉⠉⠙⠒⢼⣄⠀⠀⠀⢰⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⠤⠄⢀⠤⠒⠉⠉⠉⠓⢄⠙⢦⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⠴⠒⡟⠓⠢⣄
⠀⠀⠀⠀⠀⣠⠋⠀⠀⢁⠤⢴⡁⠀⠀⠀⠀⠀⠀⠈⣇⠈⣧⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢰⠇⠀⠘⡀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⢠⠃⢀⡀⢰⠃⠀⣸⠃⠀⠀⠀⠀⠀⢱⠀⢸⠀⢸⡖⠉⠉⠉⠳⢤⣀⣀⣀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢣⠀⠀⠀⠀⢳
⠀⠀⠀⡀⡾⠀⢎⠀⠘⠦⠖⠁⠀⠀⠀⠀⠀⠀⠈⡆⢸⠃⠈⡇⠀⠀⠀⠀⠀⠙⣤⠀⢸⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⢣⡀⠀⠀⠈
⣠⠞⠉⠉⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⠀⢸⠇⠀⠀⠀⠀⢀⠔⠁⢠⠟⠊⠉⠉⠉⠙⠓⠦⣄⢀⠞⠁⠀⠀⠀⠀⠀⠑⢤⣀⣰
⡏⠀⠈⠓⢾⡀⠀⠀⠀⣇⠀⠀⢠⡀⠀⠀⠀⣠⠞⣰⠇⢀⡞⠀⡀⠤⠤⢀⠣⣄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠏
⢻⡀⠀⠀⠀⢳⡀⠀⠀⠘⢦⡀⠀⠉⠓⠒⠋⢁⡴⠃⣠⠞⡔⠁⠀⠀⡀⠁⡼⢲⠄⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢀⣠⠖⠋
⠀⠙⠲⠤⠶⠋⠳⣄⡀⠀⠀⠉⠒⠦⠤⠖⢚⣡⡴⠛⠁⡘⠀⠀⠀⡔⢀⠎⡡⠀⡀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠈⣧⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠦⢤⡶⠖⠚⠋⠁⠀⠀⢠⠁⠀⠀⠌⡠⡡⠒⣁⢔⠅⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⣀⠀⠀⠀⠀⠀⠘⡀⢀⠎⠔⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠈⠙⢲⠒⢤⡴⠀⠓⢁⡜⣰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⢀⣴⠋⠀⣀⡀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠈⠉⠢⡀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⣰⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⣄⠀⠀⠀⠀⠀⢀⡤⠊⢁⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠙⠓⠶⡶⠾⠷⠞⠛⠉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠐⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⢰⡇⠚⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠒⠒⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⢀⡾⢣⡄⠀⠀⢰⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⣠⠞⠀⠀⢠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⣸⣀⡴⠞⠁⠀⠀⠀⣀⠇⠀⠺⣀⡈⠀⢨⠁⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢄⣀⣤⡤⠖⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⡠⠐⢢⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢼⠤⣀⣠
⠀⠀⠀⠀⠀⠀⡇⠀⢸⢀⣨⠓⢆⡒⢀⣤⡤⠀⠀⡄⢀⡀⠀⠀⠀⠀⠠⢤⡜⢉⢦⢺⠂⡴⡉⣣⡤
⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⢹⠂⠀⣈⠀⠀⠀⠀⠉⠀⠀⠀⠀⣉⣟⣈⣑⣠⣿⣾⣔⣉⣀⣏⡁
⠀⠀⠀⢀⡀⠀⡧⠠⢼⠡⢴⠀⠀⠸⠤⠤⠯⠁⣘⠃⠀⡶⠠⡤⠄⠰⠦⣭⣈⣤⣾⢿⢿⣷⢤⣀⠗⠶
⠀⠀⠇⢀⡀⣄⣇⡀⢼⠤⠬⠷⠦⢶⠒⠀⠋⠀⢀⣤⠊⠇⠶⠅⠀⠀⢐⡏⠳⢼⡟⢺⡆⢻⡤⠊⣁⡀
⠀⠀⠀⢀⣾⣅⡁⣠⣾⡀⢀⣤⣀⣠⢼⡧⠷⣶⣾⣿⣿⣷⡶⠤⣤⣦⠈⡇⣒⣿⣯⣹⡏⢉⣷⡀⣀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠤⣄⣸⡇⠠⠤⠆⣿⡧⣤⡆⢸⣿⣿⣿⠠⣽⡏⣏⢿⣷⣯⣿⣾⣿⣷⡀
⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⢾⣿⣷⠷⣶⣾⣿⣷⣷⣶⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣦⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣶⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠿⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⣀⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣤⣤⠀⠈⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢿⣿⠂⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣾⣿⠀⠀⠀⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠸⣿⣿⣶⣶⣾⣿⠟⠀⠀⠀⠀⠀⠀⠸⣿⣷⣤⣤⣤⣿⣿⠀⠀⠀⠐⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢿⠏⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠛⠉⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⡿⠋⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸⣿⡁⢀⣠⣿⠇⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠈⠻⠿⠿⠛⠁⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣽⣦⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⡄⠙⢃⠀⠀⠀⠀⢠⠀⠋⡀
⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣦⡌⠀⠀⠀⠀⠀⢰⢠

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⣾⣟⣼⠄⠀⠀⠀⠀⢠⣴⣦⡄⠀⠀⠀⠀⣠⡐⡦⣀⠀⠀⠀⠀⠀⠀⠂⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠘⣷⢣⢠⡍⠀⠀⠀⠀⡀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⡰⣟⡲⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⣀⢸⡶⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⢠⣿⣿⡗⠀⠀⠀⠀⠀⠿⠮⠙⠁⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠰⣬⡳⠁⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡿⠃⠀⠀⠠⣿⠊⠁

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠉⢙⡇⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⢠⣴⣿⠃⠀⠀⠀⠀⢠⣿⣷⡆⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠻⢿⡿⠏⠀⠀⠀⠀⣸⣷⡿⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠾⣟⡀⠀⠀⠀⠀⣴⢿⣿⣷⡄⠀⠀⠀⠀⣀⣾⣿⣦⠀⠀⠀⠀⢾⣿⣿⠇⠀⠀⠀⠀⣶⣤⣴⣦⣶
⠀⠀⠀⠀⠀⠠⣤⣤⠀⠀⠀⠀⠘⠁⣾⣿⣿⡿⠀⠀⠀⠀⠉⠛⣛⣽⠃⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⠀⠀⢀⠄⢼⠷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠆
⠀⠀⠀⠀⠀⢠⣾⣿⡿⠀⠀⠀⠀⢀⠮⠁⠀⠀⠀⠀⠀⠐⡃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⢀⣯⡀
⠀⠀⠀⠀⠠⣾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠂⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⢰⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⠒⠂⠤⢤⡴⠋⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠈⠹⢉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣅⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⢰⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠖⢮⡀⠈⠙⠲⢄⠀⠀⠀⢀⠔⠁⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠞⠀⠀⡻⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢠⡄⠒⠳⡤⣀⣀⡀⠀⠀⠀⣀⡀⠀⣀⡠⢶⠀⠀⠱⠴⠚⢣⠀⠀⠀⢑⡤⠀⠀⠀⠀⠀⠀⠀⣀⣤⢀⣀⠽⠦⡀⠀⠀⠀⠀⠀⡾
⠀⠀⣠⠞⠁⠀⢸⠤⠄⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⡎⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠉⠛⠻⠛⠓⠒⠒⠋⠁⢉⡉⠀⠀⠀⡏⠳⣌⠀⠀⢀⠇
⠀⠀⢹⠋⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⠇⠈⠳⣄⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡇⠀⠈⢣⣀⠞⢄
⠀⠀⠓⠤⠲⢖⢽⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢄⣀⣤⣆⣠⠎⠀⠀⠀⠈⢧⠀⢰⡀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠣⠤⠶⢹⡏⠀⠀⠱⡄
⠀⠀⠀⠀⠘⠋⠀⠳⣄⠀⠑⠒⠚⠀⠀⠀⠀⠀⠀⠀⣀⡥⠊⡸⠀⠀⠀⠀⢀⣬⠆⠀⠑⢄⡀⠙⠋⠁⠀⠀⠀⠀⠀⠀⢀⡠⡖⠁⠘⣄⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣢⣄⣀⣀⣀⣀⣠⣤⠔⠚⠑⠢⢄⡧⢿⠀⢀⣦⡸⠀⠀⠀⠀⣀⠬⢵⣦⣤⠤⢤⣤⠔⣲⠮⢥⡒⠓⢄⠀⠙⠦⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⣿⠉⠈⢁⡤⣇⡙⢖⠒⠒⠮⣷⣠⡷⠋⠀⠀⠀⠀⠀⢠⠃⠀⠐⡇⠉⠉⠋⠀⠀⣏⠀⠀⠙⢍⠙⣗⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⣰⠏⠀⢠⠮⠀⠈⢱⠀⠑⢦⡀⠈⠻⡁⠀⠀⠀⠀⠀⠀⢸⡀⠀⣴⠃⠀⠀⠀⠀⠀⠻⣄⣀⣀⢼⠀⡏⢡⠜⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠋⠁⠀⠀⢸⠀⠀⠀⠀⠣⡀⠀⠱⡀⠠⠹⡀⠀⠀⠀⠀⠀⠀⢇⢻⡝⠀⠀⠀⠀⠀⠀⢄⠙⠻⡄⠀⡆⠹⢀⣰⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡟⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⢀⣴⠗⡐⠄⢡⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⢁⠎⠀⠀⠇⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⡹⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⢼⣀⣀⠀⠀⠀⠀⢀⡠⠊⠀⠀⡜⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠠⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢥⣀⣁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠉⠍⠉⠉⠙⢰⣢⢀⡴⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⡶⠤⠤⠤⣤⠤⢤⠲⠿⣜⡢⠜⢁⠦⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⢆⣠⠤⢄⡀⠀⠈⡷⢫⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⡟⠀⣸⠀⢐⠂⠈⠑⢭⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢹⡤⠊⠀⡴⠡⠉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡉⠢⣄⡀⢀⡼⢧⡔⢁⡴⠻⡀⠀⠀⠀⢳⠤⠔⠃⠐⠤⣤⣤⣄⡤⡞⢄⠀⠀⠀⡎⠱⣖⡋⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢀⠖⠉⢇⠀⠈⣳⠆⠀⠹⠉⠀⠙⣧⣀⡠⠃⠀⠀⠀⢠⠂⠀⠀⠀⡜⠁⠀⠀⠀⠉⠢⠉⠒⡺⠀⠉⢙⠀⠰⠀⠀⠀⠀⡾⠀⢀⡀
⠀⠀⠀⠠⠀⡏⠀⠀⠀⠉⠈⠁⠀⠀⢸⠀⠀⠀⢳⡀⠀⠀⠀⠀⣠⠎⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢫⠀⠀⠀⠀⢀⡞⠁⠈⡀⠙⠢
⠀⠀⡂⠀⠀⠹⣄⠀⢀⠀⡀⠀⠀⣠⠇⠀⠀⠀⠀⠙⠶⠶⠖⠚⠁⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠑⠦⠤⠴⠋⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠠⢀⠀⠈⠙⠈⠁⠓⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠉⠁

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

⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠛⠂⢤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣯⡗⣿⣾⡯⡇
⠀⠀⠀⠴⣿⢿⠦⠀⠀⠀⣠⡾⣿⣷⣄⠀⠀⠀⠸⠷⠂⠀⠀⠀⠀⠀⠀⠂⠿⠀⠀⠰⠶⠆⣤⣤⠀⠶⠖⠀⠀⠳⣷⣿⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡇⣿⢸⡟⡇⠀⠠⡦⠰⠀⠀⠀⡾⡆⠀⠀⠐⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣾⢷⣿⡾⣇⢻⡀⠀⢀⡄⠢⠀⢸⠃⢳⠀⠠⠂⣄⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠰⢤⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣌⡟⠐⢸⡏⣄⠀⠛⠀⠀⠀⠀⠀⠴⠁⠠⡀⠀⡠⠀⠙⠄⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣷⣾⣶⣿⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⡀⠀⠀⠀⠀⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣤⠀⠙⣦⡊⢀⣧⠈⣢⡾⠁⠀⠘⠃⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠙⠛⠀⠀⣠⣴⡟⢹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⠟⠀⠀⠀⠙⢸⣿⠘⠁⠀⠀⣠⣄
⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠰⠶⠿⠿⣾⣧⣴⣷⠿⠿⠶⠦⠀⢀⠀⠀⠀⠈⠉⠉⠀⠀⣀⠀⠀⠀⠈⠉⠀⢠⣴⣿⣻⣟⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣿⣿⡿⣿⠀⣀⡤⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⠀⠀⠀⠀⢀⠀⠀⢀⡀⡀⡀⢀
⠀⠀⠀⠠⠶⠶⠆⠆⡆⠀⠀⠀⠘⠉⠉⣿⣩⣤⣿⠈⠋⠉⠀⠀⠀⢰⠲⢲⠰⡾⢇⡀⢘⣛⣌⣯⣄⠀⠀⠀⠛⠶⠣⣿⡧⠧⠷⠛
⠀⠀⠀⠀⠤⠤⠴⠤⠀⠀⠀⠘⠘⠙⠃⠋⠛⠙⠙⠙⠃⠃⠓⠀⠀⠸⠓⠿⠀⠿⠫⡅⠌⠹⠷⠬⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⢀⢀⡀⣀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⡇⠀⠀⡜⣱⡏⣼⠃⣿⠀⣷⢸⣇⢻⡎⣦
⠀⠀⠀⠀⠸⠁⠉⠁⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠈⠀⠀⠁⠀⠀⠈⠁⠀⠀⠈⠀⠁
⠀⠀⠀⣀⣀⡀⠤⢀⠀⡄⠀⠀⠀⠈⠀⠐⠘⠙⠋⠀⠀⠈⠀⠀⠀⠐⠀⠁⠀⠀⠸⠷⢶⠆⠀⠀⠀⢀⣠⡃⠶⠦⢘⣄⡀⣤⣼
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠈⠙⠻⢿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢀⡂
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⡀⠀⠀⠀⢀⡀⠀⠈⠁⢰⢤⣀⡈⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢷⠯⢃⣀⠀⠀⣿⠋⠉⠉⠁⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠲⢤⣄⡰⠁⠈⠉⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠐⠀⠀⠀⢀⠀⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢀⠌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠁⠘⠘⠒⠓⠒⠒⠈⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠾
⠀⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄
⢨⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⡀⠀⠀⠀⠘⢢⣤⣠⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⢄⡀⠀⠀⠠⠐⢦⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠹⠂⠓⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠠⠔⠉⠰⠄⠀⠀⠀⠀⠈⠓⢶⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠘⠁⠀⠀⢀⣰⠂⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢐⠂⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⣿⣿⢟⠿⡟⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠐⠚⠛⠛⠒⠒⠤⣀
⠀⠀⠀⠀⡀⠄⠒⠈⠀⠀⠈⠁⠒⣤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄
⠀⠀⡀⡪⠔⠁⡠⠐⠈⠀⠀⠀⠀⢙⡀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⢀⢊⠜⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⡜⢣⡀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠤⠤⠤⠔⠒⣺⢋⡀⢠⠆⠀⠀⢀⠴⢠⠀⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡜⠀⠈⢅⢀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠐⠂⠀⠈⠐⠂⠉⠒⠂⠉⠀⠀⠄⢣⡁
⡇⠀⠀⠀⠀⠀⠀⡠⠔⡡⠔⠋⠀⠀⠀⠀⠣⡀⢣⡖⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠁
⢁⠀⠀⠀⢀⡂⠩⠐⠈⠀⠀⠀⠀⠀⡄⠀⠀⠈⢹⡍⠃⠀⠀⢀⠀⠀⢀⢼⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠈⢆⠋⠁⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⢐⠒⠇⢈⣍⠈⡆⠀⠠⠬⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡟⢢
⠀⠜⣾⠀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠞⢀⡴⠊⠀⡍⠁⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠤⠔⠀⠀⠀⠀⠀⠀⠔⠀⠁
⠀⠑⢅⢳⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⣔⡩⠞⠋⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⣀⠀⠀⠀⠀⠀⣀⠠⠔⠁
⠀⠀⠀⢸⢹⠂⡤⢀⣀⣀⣀⡠⠠⠐⡨⢉⡏⠡⡀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢺⣍⠂⠭⠙⣹⢄
⠀⠀⠀⢸⠀⠄⠁⠀⠀⠀⡰⢧⣅⡨⠃⢩⠃⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠘⠁⠛⠋⠁⠀⠉⠢⡀
⠀⠀⠀⠈⠂⡀⢰⠀⢀⠌⠈⡄⠀⠁⠁⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠨⣅⢀⠀⢢
⠀⠀⠀⠀⠀⠀⠉⠀⠆⠀⢀⡄⠀⠀⠀⢀⡀⠀⠀⠀⠆⣀⣀⣀⣀⣀⣬⡀⠈⠑⠛⢲⠄⠤⠤⠀⠀⠀⡴⠢⡃⢀⡰⠀⣀
⠀⠀⠀⠀⠀⠀⠲⣺⣀⠀⠈⠙⠓⠉⠡⠀⠈⠀⠀⠀⢀⠈⢱⢤⡀⠀⠀⠈⠁⠘⠒⠊⣀⣀⣀⣠⣄⠤⠗⠒⠚⠁⠀⠀⠀⠉⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣉⠈⠉⠐⠑⠂⠀⢀⣉⣉⣩⣤⡤⠤⢤⣆⡀⠠⠤⠤⠤⢬⣭⠀⠀⠐⠒⠒⣒⢖⠒⠒⠒⠀⠀⢹⢹⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠙⠛⠛⠛⠉⠉⠁⠀⠀⠉⢢⡀⠀⠤⠤⠤⠤⠆⠀⠀⠀⠘⡾⢀⠀⠀⠀⠉⠲⡤⠀⣀⢸⠸
⠀⠀⠀⠀⠀⠀⠀⢲⣀⠀⠈⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⢢⡄⠀⠀⢠⡀⣈⣢⠄⠠⠀⢸⠤⠄⢸⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣴⢰⣄⠀⠀⣀⣀⣀⠠⠤⠄⠒⢸⠒⠂⠀⠉⠉⠉⠉⡀⠀⠀⠈⠀⠀⡈⠀⠀⢀⡃⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠈⢄⠀⣈⡄⠀⠀⠀⠃⢒⠇⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⡇⠀⠢⣄⣠⡞⠢⢕⠠⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⠢⡀⠀⠀⠀⠈⠳⡀⠱⡀⠀⠀⢧⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠩⠃⠀⠀⠀⠀⠀⠀⠀⠈⠂⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⡑⠀⠀⠀⠀⠈⠛⠃⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⢈⣀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⠟⢩⡀⢠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣧⣸⣇⠀⢀⣿⣠⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠛⣁⣽⠏⢿⣈⡻⠀⠀⢠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⣾⠟⢉⡤⠴⠀⢌⠻⣦⠴⣿⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⡀⢀⣸⡿⣁⡴⠁⠀⠀⠀⠀⠱⡌⠀⣯⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⠟⢉⡴⠋⠁⠀⠀⠀⠀⠀⠀⠙⠢⠙⠻⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⣼⣿⣿⡏⠻⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣴⣶⣷⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡞⠛⣿⣱⠇⣰⠃⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠠⠀⢧⣼⢿⣧⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠉⠛⣐⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢷⣤⢰⣿⡆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⣠⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢷⡜⠳⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣇⢁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠠⠔⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠜⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⡇⠀⡀⠀⠀⠀⠀⠈⠻⢶⣶⣿⣷⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣦⠀⠀⠀⠈⠁⠿⠀⠀⢠⡀⠀⢀⣦⣀⣠⣿⡿⠿⠛⢛⣉⣠⡆⣀
⠀⠀⠀⠀⠀⢀⣤⣤⣄⣠⠴⠈⢻⣏⠘⠛⠛⣆⡀⠀⠀⠀⠀⠠⣴⣿⣿⠟⠋⣰⠾⠟⠛⠛⠛⢻⡿⠙⠁
⠀⠀⠀⠀⠀⠈⢿⡟⠟⠀⠀⠀⢀⡏⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠈⠉⠙⣷⣴⡿⣿⣟⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣼⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠉⠙⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⣤⣤⣴⣶⣄⣤⣀⣀⣤⢀⣠⣤⣤⣤⣤⢠⣤⣄⣀⢀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠏⠹⡿⢿⣿⠟⠛⠛⠉⣽⡏⠛⠿⠿⠋⠉⠃⠛⠛⠛⣿⡿⠛⠏⠀⢛⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡏⠛⠀⠀⠈⠿⠀⠀⠀⠠⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⣦⠸⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡁⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢧⠘⠀⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠛⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⣿⡀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠾⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠶
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠆⣀
⠆⠀⠀⠀⠈⠉⠂⠀⠀⠀⠀⣶⣶⡶⠦⣶⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡶⣴⣶⠄⠀⠀⠰
⡆⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⢦⡴⠖⠚⠋⠉⠉⢉⣉⣉⣭⡽⡱⠊⢷⠤⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣿⠀⠀⡹⢤⡶⠖⣶⡿⢻⣶⠶⠊⣼⡁⠀⠈⣧⠀⠀⠘⢿⣿⡉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⣿⠀⠀⠀⡸⠁⢸⡟⠀⣾⠁⠀⠀⠀⠁⠀⠀⢸⡄⠀⠀⠘⣿⡇⠀⠀⠀⠙⣦⣄
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⠇⢀⣀⠀⠁⠀⠞⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⣿⠓⢄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⡠⡞⠀⠈⠉⠓⠀⠀⠀⠀⠀⠠⠖⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢸⣿⠀⠀⠱⣄
⠀⠀⠀⠀⡴⠃⠀⠀⠀⡠⠊⠀⡇⠀⠀⠀⠀⠀⢺⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⣽⣦
⠀⠀⠀⣸⠃⠀⠀⢀⠈⠀⠀⢀⣷⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⢠⣿⡏⢣
⠀⠀⢰⠇⠀⠀⠠⠁⠀⢀⡴⠋⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⢀⣾⠟⠀⠀⠇
⠀⠀⡿⠀⠀⠀⣴⣠⡠⠋⠀⠀⠀⠀⠑⢤⡀⠀⠀⢀⣀⣀⠀⠀⢀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⣾
⠀⢰⡇⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢀⡽⠛⠉⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⢀⣾⣿⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣀⠔⠂⠉⠉⠈⠉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠛⠁⡇
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⣄⣰⠊⠀⠈⠒⠄⠀⠀⠀⠀⠴⠶⠚⠛⠉⠁⠀⠀⠀⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠇⠈⠀⠀⠀⠀⠀⠀⣠⠴⠒⠤⠤⠐⠚⠉⠉⠀⠀⠉⠐⠢⢄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡀⠀⠈⠓⠶⢦⣤⣶⣾⡿⠿⠇
⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⣿⣊⣼⣷⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠲⢶⣤⣌⠁⠀⠀⢮
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢻⣟⠩⢿⣿⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠹⣄⡼⠀⠀⠀⠀⠀⠐⠿⠿⢿⣧⠀⣀⠹⡄
⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠈⢷⣢⣿⠿⠛⢄⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣸⠖⠁
⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠫⡀⠀⠀⢈⢦⡀⠀⢇⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠐⢤⣤⣾⠟⠉⠓⢼⡄⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⢦⡀⠀⢀⣼⣿⡄⠀⣠⡦⣤⣤⠄⠀⠀⢶⣶⣿⣯⣁⠠⠐⠉⠈⢀⣘⠫⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠉⠓⠿⣿⡋⠀⠀⢸⡗⣿⡏⠀⠀⠀⢀⡿⠛⠉⠁⠀⠀⠀⣤⡀⠈⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠉⠀⠛⠛⠛⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡈⠟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⡀⡂⠀⠀⠀⢀⡀⠤⢒⣒⠀⢩⣍⣐⣒⠢⢤⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⢀⠔⣩⡖⠈⠀⠀⠀⠀⠸⠀⠀⠉⠓⠬⡓⢄⠀⠀⠇⠐⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠠⠤⠄⡀⠈⠈
⠀⠀⠀⡴⣡⠊⠉⢛⢄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⢢⠱⡀⠀⠀⠠⠀⠀⠂⠂⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡞⡜⠁⠀⠀⠈⠈⢢⡀⠀⠀⠃⠀⠀⠀⠀⡔⠔⠁⢳⠱⠀⠀⠀⠇⠀⠰⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣸⢸⣀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠚⠈⠀⠀⠀⠐⠃⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⡅⢌⠉⠉⠈⠉⠒⡂⠀⠐⢦⠗⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⡇⢪⠄⠀⠀⠀⠀⠀⠀⠀⠚⠁⠓⠀⠀⡐⠁⠂⠐⠖⠠⡆⡜⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⢰⠰⠀⠀⠀⡠⠐⠓⠀⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣰⢡⠇⠀⠀⠀⠀⠀⠀⠀⡜⡃⣄⠀⠀⠀⡀⢀⡠⠚⠀⠀⠀⢂⡀
⠀⠀⢃⠣⡴⠞⠁⠀⠀⡜⠀⢿⠈⠀⠈⢇⢡⡀⠀⠀⢠⢣⠞⠐⠂⠀⠀⠀⠀⢀⠘⣁⠌⠁⠁⠒⠊⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⢣⡑⢄⠀⠀⡜⠠⠀⣼⠀⠀⠐⡈⢆⠢⣀⠔⡡⠃⠀⠀⢀⠀⠀⠀⢀⠞⡰⠁
⠀⠀⠀⠀⠈⠂⢅⡚⠤⣆⣸⣏⠀⣃⣀⡡⠜⣊⠵⠊⠀⠀⠀⠀⠀⠍⠀⢀⠚⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡜⠉⠗⠒⠲⡤⠤⠶⠒⠂⢋⠉⢀⠀⠄⠀⠂⢀⠂⠀⢠⠞⠁⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⡜⠀⡜⠀⠀⠀⠛⡀⠀⠀⠀⠈⢆⠈⢇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢀⠜⠀⡸⠀⠀⠀⠀⡇⠀⢰⠀⠀⠀⠘⡄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠘⠠⠴⠇⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠼⢾⠾⠇⠄⠀⠀⠀⣠⢄⣀⡀⠀⠙⢦⣀⢸⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡰
⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⣀⠀⠀⢄⣳⡀⠀⠀⠈⠙⣧⡀⠀⠀⢀⡴⢙⠦⣤⡴⠊
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠⠴⠂⠈⠀⠀⠀⠀⠀⠀⠀⢀⠁⡀⠀⠀⠀⠸⡍⠳⣶⠏⡅⡐⢰⠃
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⢀⣀⣴⠙⣇⠀⠀⠀⠤⠫⣄⠀⠀⠀⠹⠀⠉⠀⠁⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢞⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢃⢰
⠀⠀⠀⠀⠀⢀⠀⡐⠀⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⠀⠀⢀⡀⡀⡤⢠⠀⡆⢲⠀⠀⠀⠀⢀⠀⠀⠀⠈⡼⢸⠄⠀⠀⠀⠀⢀⠢
⠀⠀⠀⠀⠂⠀⠀⠂⡀⠀⠀⠤⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⣇⢳⢃⠘⢧⣃⠘⡆⠀⠀⠀⠐⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠘⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⡇⠀⠀⠀⠉⠄⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠤⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡎⡞⡕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣡⡞⢰⣇⠹⣆⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡏⠁⣾⡟⠀⢸⣿⠀⢹⣷⡄⠙⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⠐⡿⠓⠠⣾⣿⡆⠘⠛⠓⠀⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⡂⢀⠀⣿⣺⡇⣠⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠿⢿⠚⠂⣿⣺⡇⠁⡿⠿⡇⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣀⣆⣀⣴⣿⣾⣷⣄⣀⣦⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣠⠤⠤⠴⢦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢽⣢⢀⠀⠀⠀⠉⠉⠛⠻⠷⣶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣶⣤⣀⠀⠀⠀⠀⠀⠉⠑⠻⢶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠫⠗⠒⠤⠀⠀⠀⠀⠀⠉⠪⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠒⠋⠉⠉⠉⠉⠢⡀⠀⠀⠀⠉⠐⠂⠀⠤⠥⠬⠥⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡤⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠐⢦⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡴⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⠋⠉⠉⠉⠙⢯⡀⠑⠄⢀⡔⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣀⣀⠈⡇⠀⠀⠁⠣⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡀⢀⡇⠀⠀⠀⠀⠀⠀⢿⣿⠖⠁⠢⡀⠀⠀⠀⠈⢹⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠹⠁⠙⢦⡀⠀⠀⠀⠀⢸⡅⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠹⡋⠀⠀⣠⠫⠀⠀⠀⠀⠐⠀⠀⠈⠉⠂⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣀⠀⠀⠀⠀⠀⠁⠈⠀⢁⠆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠃⣀⡴⠋⠓⠂⠐⠊⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠈⠉⠉⠉⠀⣀⣀⡤⠖⠺⢅⣀⠀⠀⢀⡠⡴⠂⡀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡝⠻⠶⠲⣖⡺⠟⠉⠁⠸⡄⠀⠀⠀⠈⠉⠉⠁⠾⠅⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⠁⠀⠀⠀⠀⠀⠀⢄⣠⣤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⡝
⠀⠀⠀⠀⠀⠀⠀⣄⠂⠈⠑⠠⠤⠄⠀⠀⠀⠤⠔⢍⡉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣤⣄⣀⣀⣀⣀⣀⡀⠠⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠚⢻⠭⠭⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣎⠉⢣⡤⠐⢞⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠂⠬⠁⠛⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠖⠐⠂⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐

⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠛⠛⠛⠛⠿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠉⠉⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⣤⠀⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣏⠈⣦⠄⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣦⢛⣣⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣵⠆⠠⡄⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡟⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⣿⡇⢀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣇⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⠘⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠘⠀⠀⡀⠀⠀⡀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣄⡰⠀⠀⠀⠀⠀⣹⣿⣄⠀⠀⠀⠀⢧⠀⠀⣧⠀⠘⠃⠀⠀⠀⠠⡆⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣧⠀⠀⠀⢰⣿⣿⡿⠋⡄⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⢠⡾⠀⠲⠄⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣿⠟⢀⠀⠀⠀⠀⠀⣀⡄⠒⠀⠀⠀⠀⠀⣼⢃⠄⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣤⣈⡉⠙⠛⠛⠛⠛⠛⠋⠉⣉⢀⡄⢨⡅⠀⠻⣷⣄⠀⠀⣾⣿⡀⠀⠀⠀⣀⣤⡄⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⢿⡇⣾⡇⠀⠀⠸⣿⡆⠀⠀⠙⠓⠀⠀⠀⢹⣿⣿⣿⣦⣄⣀⡀⠉⠉⠉⠉⠉⠉⣉⣀⣀⣀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠃⠏⣷⠀⢠⠀⠈⠁⠀⠀⠀⣡⣶⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡿⠻⢿⠀⠀⠀⠀⠀⠀⢿⣷⢿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣷⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣄⠀⠀⠀⠀⠇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣫⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠈⠛⠳⠛⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⣤⣿⣄⡀⠀⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣿⣁⡽⢀⣀⠈⠛⣦⡴⠞⠋⠁⠀⢀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢀⣀⠀⠀⠠⡏⣹⠇⢀⡼⣧⣠⣤⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣧⠀⣏⣈⡷⠀⠀⠉⠁⠀⠈⠓⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠶⢋⠀⠀⠉⡴⢤⡀⠠⡞⢳⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠰⣏⣹⠀⠀⠙⠦⠇⠀⠉⠉⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⠈⠁⠀⠀⠀⣀⡤⣄⠀⢰⣣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⡤⠇⠀⣞⣹⠆⠐⢧⡤⠏⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⣸⣷⡀⠀⠀⢁⣤⣄⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠀⠀⣠⡾⠋⠀⠙⠷⢦⣼⡧⣾⠟⠋⠁
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⢸⡇⠀⢹⡄
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠸⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡴⠛⠉⠻⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣿⣛⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⡇⠀⢸⣷⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⡿⠋⠙⣿⣿⣿⣷⡄
⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⢻⣿⣿⣿⣆
⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆
⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣷⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡄
⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⣠⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷
⢰⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣠⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠋⠁⠀⢀⣀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢀⡀⠀⠈⠙⠻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣄⣴⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠋⠀⣀⠀⠰⣿⣿⠆⠀⣤⢀⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠉⠀⣠⣿⣿⣿⣿⡿⠋⠁⣠⣾⣿⣆⡀⠈⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿
⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⢿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿
⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⡿⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃
⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⡿⠋⠀⣠⣾⣿⣅⣀⣠⣤⣤⣤⣤⣄⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠙⣿⣿⣿⣷⡀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣦⣴⣿⣿⣿⡿⠋⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉
⣿⡟⣙⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣠⡄
⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠘⠿⠀⣡⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⢠⢞⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡶⢤⠄⠀⠙⠃⠀⠀⠀⠀⢰⣾⡲⡆⠀⢰⠀⠀⠀⠀⠀⣀⡀⣰⣿⣫⣦⡄⣤
⠀⠀⣼⣧⠀⠓⢢⣼⡀⠀⠀⠀⠀⠛⣿⡇⠀⠀⣽⠤⠀⠀⠀⠀⠀⢸⣿⣷⡿⣿⣿⣗⠀⠀⠀⠀⠽⣟⠿⢽⣷⡷⠛
⠀⢰⠇⠸⡇⠰⠚⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣵⣶⣿⣶⣦⠀⠀⠀⠀⠀⠈⠉⣠⣶⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⡄⠒⠐⠃⠒⢀⠀⠀⠀⠀⠀⡠⠖⠛⠷⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠞⠀⠁⣀⣄⠈⠄⢳⠀⠀⠀⠀⢀⡀⣀⣤⡄⠀⠙⠂⠀⠀⠀⠀⣠⣤⣾⣿⣿⣦⣤⠀⠀⠀⡉⠀⠈⢂⡠⠤⡀⠀⡠⣀
⠀⣇⠠⢀⡝⢻⡀⠌⣘⠀⠀⠀⠚⠸⠡⣭⣿⣟⡱⢆⡀⠀⠀⠀⠀⠉⠉⠋⣿⡏⠋⠉⠀⠀⠀⠀⠀⠀⠁⢡⠀⠑⠊⠀⢸
⠀⠈⢦⣜⠀⠀⣣⡰⠁⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠠⠴⠘⣿⡇⠳⠶⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠐⠁
⠀⠀⠎⠀⠈⠁⠈⠱⠀⠀⠀⠀⠐⠻⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠺⠿⠿⠿⠿⠿⠟⠂⠀⠀⠶⠶⠶⠶⠶⠦⠶⠶⠶⠶
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢠⣠
⠀⠀⣯⣅⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣾⡶⣹⣧⣤⡀
⠀⠀⡟⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⢨⡇⠀⠀⠀⠀⠘⡀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⢛⣵⣿⡫⢝⠻⠁
⠀⠀⣧⣤⣤⣤⣤⣴⠀⠀⠀⠀⠀⣰⡏⠓⠤⠀⢀⢸⡇⠀⠀⠀⠀⢸⣿⣿⠷⠢⣤⣄⠀⠀⠀⠀⢠⣯⣽⡥⠊⠁
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡴⠋⣷⠀⠀⢀⣼⣽⣇⡀⠀⠀⢰⣾⣿⣷⣶⣶⣾⣷⡶⠀⠀⠀⠘⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠛⠛⢛⡟⠛⠛⠁
⣀⠠⡤⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⠀⠀⣦⡄⠀⠀⢀⣄⢀⣀⣸⣿⡟⠃⠀⠀⠀⠀⠀⠀⠈⠃
⠈⢛⣿⣉⣉⣀⣀⣀⣀⠀⠀⠈⢩⡿⢧⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠘⣿⣟⠡⠉⣿⡇⠀⠀⠀⠀⠀⢠⡄⢀⣤⣠⣤
⠀⠀⣸⢷⡀⠀⠀⠀⠀⠀⠀⣀⡞⢷⠀⣉⣀⣤⣤⣤⣿⣿⡇⠀⠀⠀⠈⠛⢲⡞⠋⠁⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠈⠃⠀⠓⠀⠀⠀⠀⠀⠀⠉⠀⠙⠀⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠊⠐⠙⠋⠐⠑⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡇⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠲⡄
⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣈⡆⠀⠀⠀⠀⠀⠀⡸⢭⣙⣳⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢢⡀⠀⠀⠀⠀⠀⢸⠤⠖⠤⢾
⠀⠀⠀⠀⠀⠀⠀⢻⢮⣑⡏⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠘⡇⠀⠀⠀⠀⢸⡀⣀⠀⢀⡀⢈⠆⠀⠀⠀⠀⣏⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⣷⡼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⢹⠁⠀⠀⠀⠀⠀⠙⣄⣍⣡⡸⠁⠀⠀⠀⠀⠀⠈⠓⡖⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⣴⡁⣹⡀⠀⠀⠀⠀⠀⢠⠞⠓⠛⢤⠗⠀⠀⠀⠀⠀⠀⣀⣟⣆⡀
⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠙⠦⡀⠀⠀⢠⠞⠓⠒⠛⠓⢛⡆⠀⠀⠀⠀⢮⣀⣀⣀⣼⠄⠀⠀⠀⠀⠀⢸⠶⠤⠤⢧
⠀⠀⠀⠀⠈⠻⣍⣑⣉⣉⣊⣩⠗⠁⠀⠀⢸⠟⠛⠛⠛⣛⣛⡇⠀⠀⠀⠀⠀⢣⣶⣶⠃⠀⠀⠀⠀⠀⠺⢍⣛⣛⣛⡩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡇⣃⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⡀⠀⠀⠀⠀⠀⢀⢔⡒⣒⠢⡀⠀⠀⠀⠀⠀⢀⡤⠒⠢⢤⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⢠⢊⡩⣍⠲⡄⠘⡄⠀⠀⠀⠀⡇⡏⣞⠶⡱⣱⠀⠀⠀⠀⠀⣏⢀⡀⢀⠀⣱⠀⠀⠀⠀⠀⣺⣿⣽⣽⣿⡇
⠀⠀⠀⠀⠀⢤⢸⠰⣀⡧⢸⣀⠇⠀⠀⠀⠀⠱⣕⣮⣭⠷⠋⠀⠀⠀⠀⠸⡍⣿⢹⡏⡿⢸⠇⠀⠀⠀⠀⣿⣿⣯⣭⣽⡇
⠀⠀⠀⠀⠀⠈⠣⣳⣬⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⢳⣻⣸⣧⣇⡟⠀⠀⠀⠀⠀⣗⣀⣈⣉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⡉⢢⠀⠀⠀⠀⠀⠀⠀⣠⡼⣝⢢⡀⠀⠀⠀⠀⠀⢺⢀⣀⡅⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⢸⠁⠏⠀⢀⠀⠈⡆⠀⠀⠀⠀⢠⠞⡄⢣⢸⠋⠁⠀⠀⠀⠀⢎⡉⠀⠈⢋⡱⠀⠀⠀⢀⡾⡀⢣⠀⣰⢃⡼⡆
⠀⠀⠀⠀⠀⠘⢄⣀⠀⢀⣁⡼⠁⠀⠀⠀⠘⣍⠢⡵⠜⠁⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠻⡀⠀⠀⠀⠀⠳⢼⠍⠉⠉⣽⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠋⠙⠦⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠎⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⠶⠤⣴⣒⠒⢤⣼⢥⢡⢼⠬⢽⡄
⠀⠀⠀⠀⠀⠀⠀⣠⢴⡏⢄⣣⣹⠶⠾⠛⠾⠞⠊⠉⠉⠉⠙⠓⠤⡀
⠀⠀⠀⠀⠀⠀⡰⠁⢸⢵⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣠⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣦
⠀⠀⠀⠀⢰⠁⠱⣤⠃⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢣
⠀⠀⠀⢀⠞⡄⠀⡟⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢀⡀⠘⡄⠀⡦⡀⠀⠈⢧⡀⢇
⠀⠀⠀⣼⠀⠙⢼⠁⠀⠀⠀⢰⠁⠀⠀⢰⡆⠀⠀⠈⡑⡄⡇⠀⢸⠹⡀⡀⣸⢧⣸
⠀⠀⢰⠛⡄⢀⣸⠀⠀⠀⠀⡌⠀⠀⠀⡿⢇⠠⠤⠤⠃⠑⠛⠒⠉⠀⠉⠁⠀⠘⡈⡶⡄
⠀⠀⣠⠀⡸⠁⢸⠀⢀⣀⣰⠓⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠳⠀⡇⢡⠆
⠀⢰⠉⢣⢇⣀⡼⡄⡏⠀⡝⠀⡆⠀⠀⠀⠀⠞⠳⠀⠀⠀⠠⣄⠄⠀⢀⡠⡀⠀⡇⢸
⠀⠸⣴⠁⠀⣠⠃⠱⡕⠤⣆⠀⡇⠀⠀⠀⠀⠀⠀⡀⣀⢀⡠⠤⠐⠰⠯⢄⣳⢀⡇⡸
⡰⠑⠦⢭⠏⠀⠀⠀⠈⠒⢼⠀⡇⠀⠀⠀⠀⠀⢸⢀⠈⠁⠀⠀⠀⠀⠀⠀⠙⢇⣷⠃
⣧⠆⡇⡸⠀⠀⠀⠀⠀⠀⠈⡆⢸⠒⠢⢤⣤⣤⣀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⣧
⠈⠛⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⢮⡆⠀⡇⠀⠀⠑⢇⡀⠀⠀⠄⠀⠘⠀⠀⠀⣀⡷⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢧⠀⠀⠀⡠⣻⢆⣀⡠⠤⢄⡀⣠⠋⠀⢈⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⠣⡀⡜⡵⠁⠀⠈⠑⢆⠀⢸⠙⢤⡤⠾⠚⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡠⢔⡪⠋⠓⢦⣄⣀⣀⡠⠞⠚⠉⠀⠀⠀⠀⠀⢸⠹⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠖⠁⠀⠀⠀⠀⠈⠉⡞⢳⠤⠒⠲⡖⠐⡲⠋⠑⡌⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⢠⠃⡎⠀⠀⡰⠀⠀⠃⠀⠀⡗⠚⢾⠥⡖⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⣀⣀⠀⢀⠎⡜⠀⠀⡰⢇⣀⣀⣄⠀⡠⠓⠠⠴⠤⠧⠷⠒