Axolotl Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄⢀⠀⠀⠀⠀⡄⠄⡀⢀⣤⢄⠀⠀⠀⠀⠀⠈⠃⡄⡄⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠀⠘⠰⡀⡀⠀⠉⠓⠒⢤⡀⠀⠀⠄⠇⠀⠀⠀⠠⠄⡄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⢆⠑⢌⠆⠀⠁⠠⠀⠀⠀⠀⠀⠘⠂⠀⠈⠀⡧⠀⡄⡠⠊⠠⠌
⠀⠀⠙⠢⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠚⠆⠀⠑⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠀⡀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠀⠤⠤⠤⠀⠈⢢⠙⠢⠂⠀⠀⠈⡵⠁⠀⠀⠀⠀⠀⠀⠘⠘⠃⠀⠀⠊⠀⢒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠩⠁⢀⠘⠀⠀⣀⡀⢀⡀⠀⣀⣀⠀⣀⣁⠀⠀⠈⡤⠐⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠗⢦⣀⣀⠤⠤⠣⡀⠀⠈⠉⠉⠉⠉⠐⠒⠒⠒⠒⠊⠰⠠⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣀⣀⠀⣀⠉⠑⠂⠀⠀⠀⠀⠤⢒⣈⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠊⠁⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⢆⠄⢠⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⢱⠌⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢸⡇⠀⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡆⠀⣿⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⠶⢧⣄⣿⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢸⣇⣤⠷⢶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⣀⠀⡶⠀⠀⠀⠈⠻⢦⣌⠉⠻⣏⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢈⡿⠋⢉⣠⠞⠋⠀⠀⠀⠰⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣇⣰⠇⠀⠀⠀⠀⠙⣧⠀⠘⣿⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢹⡟⠀⢠⠟⠁⠀⠀⠀⠀⢷⣀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠹⣏⢻⣄⣼⠁⢀⠀⠀⠘⣧⠀⠘⣿⠋⣀⣤⠴⠶⠒⠛⠛⠛⠛⠲⠶⢤⣄⡀⢻⡟⠀⢀⡟⠀⠀⢀⠀⢹⣄⣼⢋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠙⠷⣤⣾⠀⣴⠀⠸⣆⣤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⣄⡾⠀⢰⡄⢸⣦⡴⠟⠁⣼⠁
⠀⠀⠀⠀⠈⣷⣴⠏⢀⡹⣦⡀⠀⠙⠳⢿⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣸⠷⠛⠁⠀⣠⡾⣃⠈⢧⣴⡏
⠀⠀⠀⠀⠀⠘⣿⣦⡟⠀⡈⠙⠷⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡴⠞⠉⡀⠘⣧⣾⡟
⠀⠀⠀⠀⠀⠀⠸⣎⠳⣼⡇⢸⡇⢨⠏⠀⠀⠀⠀⣠⡶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣦⡀⠀⠀⠀⠈⢿⠀⣿⠀⣿⡴⢋⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠙⠛⠳⡿⠀⠀⠀⠀⢰⡏⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠈⣧⠀⠀⠀⠀⢸⡷⠛⠛⠉⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣰⡇⠀⠀⠀⠀⠈⠳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠋⠀⠀⠀⠀⠀⣷⣠⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣀⣀⣤⡤⠶⠖⠛⠋⠉⠉⠁⠉⠉⠉⠛⠓⠶⠦⣤⣤⣄⣤⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠓⠒⠒⠒⠒⠚⠛⠛⠛⠉⠉







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠘⣦⠐⠀⠀⡀⢠⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠃⠀⠀⠀⠀⠐⠄⠐⡕⡄⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⣧⠈⠀⠀⠀⠀⠈⢀⣘⡈⠀⢀⢆⠄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠈⠀⢫⢆⠀⠀⡀⠐⠋⠁⠀⠀⠀⠀⠈⠘⡜
⠀⠀⠀⠀⠀⠀⠠⠑⢦⣈⡂⠄⠒⠈⠎⠁⠊⠁⠀⠀⠀⠀⠀⠀⠙⠀⠂⠀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⡙⠪⠅⣒⣒⠂⠀⠀⠀⡴⠀⠀⠀⣀⡠⢀⡴⠗⠉⢀⠀⣠⠑⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣧⡠⠤⠔⠂⣇⠀⠀⠀⢀⣒⠭⠒⠉⠋⠀⡆⠀⠈⠀⠬⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠈⡡⠂⠙⠋⠁⠀⠀⠀⠀⠀⢰⠒⣩⠤⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢤⡀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡤⡔⠃⠀⠀⠀⠀⠀⠇⡈⠀⠀⢱⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⡜⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡤⠖⠉⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢉⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠒⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⠠⠠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⢻⡴⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡶⠿⣂⡤⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⠸⡐⣷⠡⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⢂⡸⢷⣿⢃⣤⠁⠀⢀⡤⠒⣆⠐⠊
⠀⠀⠀⠀⠠⠄⠁⠢⡀⠀⠌⣺⡁⢃⡿⠴⠂⠐⠚⠀⠢⠠⠄⠀⠀⡀⠈⡹⠁⣽⣏⠸⣶⣦⠔⡁⠧⠆⠀⠄⠂
⠀⠀⠀⠀⠠⡾⣦⢀⡈⠹⠁⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡬⢭⣽⠇⡚⣁⡄
⠀⠀⠀⠀⠀⠀⠸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⢊⣁⣼⠟⠀⠀⠈
⠀⣀⣀⣄⣀⡀⠐⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⡙⣅⢤
⠙⢦⠁⢨⣭⣟⠛⠃⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢽⣦⡼⠒⣩⡴⢁
⠀⠀⢶⣏⡿⣿⣿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⣾⣿⣶⣷⣿⣿⣍⠂
⠀⠀⠀⠀⢰⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⡿⡟⡏⢎⠈⠁
⠀⠀⠀⠀⠁⠐⠻⡀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⡀⠔⠀⣰⣿⣟⡅⢸⠁⠙⠐⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⣤⣀⣀⡠⠀⠀⠀⡀⠀⠀⠐⠒⠀⠒⣆⠉⡀⣀⣴⠀⠁⠉⠉⠲⡄⠀⠠⣄⠲⠭⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠁⠀⠞⢙⣋⠛⠓⠺⠛⠒⣤⣌⣷⣶⣾⣿⣿⣿⣿⠀⠓⢄⠀⠀⠀⠐⠮⠈⠙⠁⠂
⠀⠀⠀⠀⠀⠀⡜⠁⠀⢠⣾⠖⠉⠉⠓⠒⠤⠤⢯⣿⣿⣿⣿⡿⠿⠛⢿⡻⢿⣦⠈⠳⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠁⠀⠀⠐⡀
⠀⠀⠀⠀⠀⢸⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⡄
⠀⠀⠀⠀⢠⣰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠘⠁⡀⡰⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢲⡆⡄⢀⠀⠐⠑⠺⠄
⠀⠀⠀⠀⠀⠺⢳⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢹⢸⢧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢨⠇⠀⠡⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⣀⣠⠄⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡁⣟⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⢀⠾⠃⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⢦⡇⠡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠄⠊⢀⡜⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⣲⣌⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠛⠛⠎⡉⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠪⠍⢷⡴⠇⠀⠀⠀⠀⠀⢺⣤⡗⠀⠀⠐⠶⢶⠷⢴⣊⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠈⠛⠛⠀⠀⠀⠀⠀⡀⠀⠃⠀⠢⠄⠤⠂⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠤⠤⠀⠒⠈⠁⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⡆⠀⠀⠀⢀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠙⢦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠀⠀⠀⠀⢦⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠘⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠤⢄⠀⠀⠈⢢⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠉⡲⠂⠀⠄⠴⠀⠀⠀⢸⠅⠀⠀⠉⢦⡀⠀⢣⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠔⠀⠀⠀⠀⣰⠀⠀⠀⡌⠀⡇⠀⠀⠀⠱⠀⠈⡄⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⣀⠀⠀⠘⠢⠤⠊⠀⠀⠈⠒⡄⠀⠀⡇⠀⠇⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⠃⢰⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠐⠠⢄⠀⠀⠀⣀⡀⠀⢣⠀⢀⠎⡠⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡅⠒⠚⠒⠶⢅⡀⠈⠉⡩⠔⡡⠒⠁⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠈⠢⣄⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠙⠛⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⡈⠑⠠⢄⡀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠌⡢⠀⠀⡗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣬⠥⢲⣄⠀⠀⠀⠀⠀⢘⠃⢀⠀⠰⡀⠀⠀⠀⠀⠀⣴⡎⡀⣱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⣁⠾⣇⠀⠀⠀⢀⠊⠀⠠⠀⠀⠑⢄⠀⠀⠀⣸⡫⢈⣉
⠀⠀⠀⠀⠀⠀⢐⣲⠀⢚⣶⣦⡛⠧⠃⡾⠀⢠⡬⠥⠀⠐⠒⠒⠀⠀⠄⢣⡆⠀⢸⣸⠔⢋⣵⡿⢏⠁⣝⡭
⠀⠀⠀⠀⠀⠀⠀⠙⠃⢉⣄⢫⠛⠀⠀⢢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡜⠁⢀⡎⠡⣠⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣍⡸⠧⢦⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠜⢉⣩⣴⢿⠗⠂⢄⡀
⠀⠀⠀⠀⠀⠀⣨⣆⡀⡍⢙⢿⠣⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠮⣉⠀⣀⠁⠲⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠴⠗⠐⢣⢻⡆⠀⠺⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⠂⠀⠀⡇⢱⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠳⡀⠀⢄⠀⢀⣀⠠⠤⠤⢀⣀⠀⢀⠄⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⢲⠤⢀⡀⠀⠁⠀⠀⠁⠀⢀⡀⠤⢐⠃⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠒⠎⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠋⠙⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠌⣟⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⢸⣿⠀⡟⠀⠀⠀⠀⠀⠀⢀⣼⡏⢰⡿⠀⠀⠀⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠢⣀⣾⣇⠀⠛⠁⠀⠀⠀⠀⠈⠐⠛⠀⣼⡿⢀⠀⢊⣾⣿
⠀⠀⠀⠀⠀⠀⣴⣦⡀⡀⠛⣿⣦⡀⠈⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣀⣴⣾⠟⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶⣅⡉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⣉⣡⣴⡾⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢿⣆⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠄⠀⣼⣾⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⡀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡠⠐⠁⠉⠠⡀⠀⠀⠀⠀⠈⠦⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠊⢀⠄⠒⠀⠢⠔⠂⢐⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠢⣤⠔⠀⡐⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡺⠀⢁⠀⠈⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⠡⠀⣀⣐⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠔⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⢣⢙⠀⠀⢈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⡊⠐⡣⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢡⡁⠂⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠐⠂⠀⠀⠀⣤⣤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⢀⣀⣀⣀⣤⣠⣆⣤⠐⢛⣛⣋⣉⣁⣀⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢤⠀⠲⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠈⠈⠉⡉⠀⠈⠿⣿⣒⠄⠀⠀⠈⠉⠙⠂⠈⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠰⡂⠀⠉⠈⠉⠈⠀⠈⠀⠈⠠⠀⠆⠂⠀⠁⠀⠈⠀⠀⠀⡁⠀⠰⢶⣭⣍⣁⠀⠴⠀⠀⠐⠒⢋⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠙⠁⠀⠀⠀⠀⠀⢀⣠⠠⢠⠐⠀⡄⢄⣀⣆⢃⠀⣠⣄⣰⣤⣄⣥⣷⣼⣶⣿⣶⣤⠀⠠⠐⡀⠀⢀⣀⣛⡭⠞
⠀⠀⠀⠀⠀⡀⠠⡀⠉⢂⣡⣤⠴⠞⢺⣋⢉⢹⢸⣠⣼⣼⣶⣟⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⣴⡶⣾⠓⠦⡴⠞⠋⠀⠉
⠀⠀⠀⠀⡸⠁⣬⣴⣞⣿⣥⠶⠶⠾⠾⢟⣛⣻⠿⠻⠛⢉⡟⢻⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢴⠙⠋⠃
⠀⠀⡾⣠⣴⣿⠟⠋⠉⣀⣀⠤⠔⠚⠋⠉⠀⠀⠴⡴⠒⣏⡠⠈⠀⣠⠀⠀⡀⠀⠀⣿⠀⠀⠈⡟⢠⠺
⡀⠈⣐⢛⠭⠊⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢙⣰⡛⢀⣠⡞⠁⠀⠀⢰⠀⠀⣉⢀⡼⠀⠁⠈⠀⡀
⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⣩⢴⠰⣏⠓⠀⠀⡂⠀⠉⢶⡁⠉⠁⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠉⠀⠀⠀⠀⠀⠁⠸⠀⠉⠀⠀⠀⢀⡄⠀⢀⠀⠀⠀⢀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠃⠠⠤⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠔⠓⢆⡀⢐⣦⣠⠼⠷⡖⠀⠀⢀⠠⡾⠀⣤⣤⣤⣭⣥⣀⣀⡀⠀⠀⠘⠿⠃
⠶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⢶⣮⣷⢶⡚⠙⢯⣀⣈⣶⣤⠀⠀⠀⠀⠀⢱⠀⢒⣒⣒⣿⣿⣿⠿⠇
⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣧⠟⢾⡉⠉⢳⣄⡈⠀⠀⠠⠄⠀⠀⠀⢴⠚⠛⠩⠉
⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠺⠗⠀⠀⠀⠀⠀⣿⠶⠖⠛⠛⠩⡈⠀⠐⡀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣶⢆⣶⠁⢀⣀⠄
⠀⠀⠀⠀⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠰⠷⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⢸⣿⡆⢰⣿⢸⠇⣴⣿⣿⣿⣦⢠⡀
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡭⠋⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⣾⡄⢿⣿⣿⣿⡿⢰⡿
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣾⢿⣁⠀⠀⠙⠿⢦⣽⡿⣿⡁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠈⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⣤⣤⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠛⠷⣄⠀⠀⠀⣤⣦⠀⠀⠀⠜⠉
⠀⣴⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠰⠺⠶⠆⠈⠂⠀⠐⠃⠀⠀⠀⠀⠀⠀⢰⢋⠉
⠰⠇⣠⣴⣿⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠆⠀⠀⠀⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠷⠀⠀⠆⢀⠞⠿⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡰⠛⠙⠻⡄⠀⠀⠀⠈⡀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡿⠿
⠀⠀⠀⣠⣤⣤⣧⠀⠀⢀⡇⠀⣀⣀⠀⠃⠀⠀⠀⠀⠀⠈⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠈
⠀⠀⠀⠉⠉⠉⠉⠁⠀⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠘⠉⠁⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠖⢦⠀⠀⠂⠀⠀⢀⡘⠉⠀⠙⢷⣄⣰⠀⠀⣸⣤⠞⠛⠻
⠒⠆⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠹⣧⡀⠀⢀⣿⠋⠁⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⠖⢶⣦⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠁⠀⠼⠿⠶⠀⠀⠀⠀⠸⠷⠶⠄
⠀⠀⣠⣤⣄⢸⡄⠀⣰⠀⠀⢀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⡐⠀⠄⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠂⠂⠀⠀⠀⠀⠀⠀⠛⠀⠀⠠⠄⠀⠆
⠀⠠⡀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠄⠈⠂⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠐⠠⠀⠀⢆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⠀⢄⠀⠀⠀⠀⠈⠀⠀⠁⡄⠀⠀⡀⠠
⠀⠈⢀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠂⠐⠢⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⡀⠁
⠀⠈⠀⠀⠀⠀⠀⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠂⠀⢀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠐⠁⡠⢄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠢⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠅
⠠⠄⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠁⠠⠀⠄⠠⠂⠀⠀⠀⢀⠐⠂⠀⠀⡀⠀⠀⠉⠀⠂⠐⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠈⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠠⠰⠀⠁
⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⢀⠲⠀⠀⠀⢀
⠀⠈⠀⠀⠀⠄⠂⠀⠀⠀⠨⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠂⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠄⠀⠀⠠⠀⠀⠀⠏⠀⠀⠉⢩⠗⡆⠀⢀⣴⣒⣒⣦⡀⠀⠀⢶⠊
⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠄⠠⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠤⠤⠈⠀⡁⠀⣍⠿⠿⠿⠿⣿⠀⠀⠈⢧
⠀⠘⠀⠠⠀⠨⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠂⠂⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⡀⠀⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠠⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠰⠃⡰⠀⠀⢆⠘⠆
⠀⠀⠀⠀⠀⠐⠁⢠⡄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠁⠀⠀⠊⢀⠰⠀⠀⡀⠰⠂⠄⢀⠀⠐⠀⠀⠠⠀⠀⠀⠐⠄
⠀⠀⡀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠁⠁⠀⠀⠌⠀⠀⠀⢀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠤⠀⠀⢤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡀⠀⠀⢀⠄⠀⠀⠀⡠⠀⠀⠠
⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡡⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⢀⠀⠀⠠⠄⡀⠀⠀⠀⠠
⠀⠈⠂⠀⠄⠀⠁⠈⠁⠈⠄⠀⠀⠂⠔⠂⠐⠢⠐⠀⠠⠁⠀⠀⠀⠀⠀⠀⠄⠀⠁⢀⡀⠉⠂⠤⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⢀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⢀⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠢⢤⠀⢠⡠⠀⠀⣠⢀⡲⠶⠔⡉⢅⠉⠀⠀⢭⡉⠐⠦⡀⠀⠀⠀⠀⠨⠤⢉⡀⠄⠠
⠀⠀⠀⠀⠀⠠⠔⠀⠐⠀⠼⡋⠉⢹⠈⠑⠐⣀⠤⣶⣧⠴⠄⠊⢠⡦⢆⡷⠀⠽⠀⠀⡔⣩⣉⢀⡀⠴⣾⠇⣐⠀⠀⠀⠀⠤⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢄⠙⠟⠛⣆⣉⡔⣀⡠⣔⣎⠰⠤⠚⠁⠀⠀⠀⡂⠉⣁⠉⣠⣤⣀⠅⠉⣠⠒⠷⠦⠊⡶⠀⠒⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⢆⠤⣄⡀⢌⡨⢵⠀⠌⢰⡀⢠⠰⠞⠁⠠⢁⣄⡘⠿⠈⡃⣠⠈⡛⢲⣋⡴⢣⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⠈⠔⠂⡀⠰⣄⣈⠐⠀⡤⠃⠤⣈⣧⡀⠧⠭⠀⣀⣤⠃⠀⠉⠉⢉⠔⠁⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠢⢄⡄⠀⠐⠃⠀⠎⠙⠛⠛⣛⠉⡑⣲⠐⢀⣣⠀⠀⠀⡀⡄⡀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠐⢠⡠⠖⠀⠴⠆⣤⣤⣠⣤⠅⡥⢨⠟⠀⠀⠀⡆⣆⡗⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⠒⠒⠂⡠⢀⣐⡐⠲⠔⠒⠚⢖⠦⠚⠃⠀⠀⠀⠃⠓⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢀⠀⠀⠀⠀⠀⠈⠒⠀⠄⠀⠀⠀⠀⠀⠐⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠍⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡀⠀⠀⠀⠀⠈⣀⠤⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠐⢉⠁⠀⠀⠀⠈⡒⠰⢂⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠁⠀⠀⠂⠄⢀⠀⠀⠀⡀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣦⠀⠀⢿⣿⣷⣤⣀⣤⣶⣾⣾⣿⣆⠉⢠⣖⣺⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠙⠿⣿⣷⠒⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣷⡄⢠⣶⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢠⣴⣿⠟⠀⠀⠀⢰⣿⠻⣿⣿⣿⣿⣿⣷⠀⠸⣡⣤⡈⢉⡉⢻⡿⣾⣿⣿⡟⡉⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡿⠿⠿⠿⣦⠀⠈⠁⠀⠻⣿⣿⣿⣿⣿⡆⢠⣙⢛⣁⠻⡿⢚⠃⢿⡿⢹⣏⣁⣌⠁
⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⣿⣿⣶⣋⣤⡀⢰⣶⣾⣷⣿⣿⡿⠒⠈⠀⠀⠉⠉⠙⠈⢿⣯⣽⣶⣶⣿⣿⣿⣷⣾⣿⠟⠃
⠀⠀⠀⠀⠀⠀⢸⡿⠉⣐⣤⣽⣿⠙⠉⣡⣤⣀⡠⠟⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣿⠿⠈⠙⠻⢿⣧⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣟⡙⠹⢀⣻⣿⣾⡟⠁⠀⠀⠀⠀⠀⠒⠀⠀⠦⣀⣤⣿⣶⣶⣶⣶⣦⠈⠁⠀⢳⣾⣿⠋⠙⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⢜⣛⣥⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⡿⢿⡿⠿⢿⢿⡿⠿⠀⠀⡄⣾⡿⠟⢤⠀⣤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣷⣿⠛⠁⠀⠘⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣐⠰⡶⢲⣶⣾⣿⣦⣿⡿⠀⠀⠉⡀⠎
⠀⠀⠀⠀⠀⠀⣿⡿⠟⢿⣿⣿⡿⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⣴⣦⣄⠀⠀⠐⠂⠈⠉⠈⠟⡟⠙⠻⠟⢻⣿⡌⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠹⣿⠁⢀⣴⣶⣿⣿⡿⢇⡀⢸⡿⠋⠉⠙⢶⣦⣀⣠⣤⣤⣤⣸⡑⠂⠀⠲⢸⠋⠻⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠈⢀⣸⣿⣿⣿⡇⡀⠨⣍⣹⢀⡀⠀⣄⠸⣿⡟⠛⠿⣿⣿⣿⣷⣾⣽⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠙⣿⣿⣷⠀⠀⠠⣶⡶⣤⡴⣦⣤⣴⣿⡇⠀⠰⢿⣿⣿⡿⠉⠙⢹⡀⠀⠀⠀⢠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠶⠶⠶⠾⠿⠿⠟⣽⣿⣷⣤⣀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣷⠒⠒⠋⠠⣤⠄⠉⠉⢛⣿⣧⣄⣠⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣧⠀⠀⢀⣿⡄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠁⠀⢰⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡉⠐⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠦⣙⣤⠀⠀⠀⠀⠀⠀⠀⢮⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⣦⣫⡶⠋⠀⠀⠀⠀⠈⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠿⣷⣋⡦⠀⠀⠈⢻⢲⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡲⠆⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⡾⠀⠑⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡔⠁⠀⢀⠄⣢⡆⠀⠀⠀⠀⠀⠀⠘⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣻⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⢀⡈⢧⠀⠀⠀⡇
⠀⠀⠀⢀⠊⢠⠃⠰⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣾⡇⠀⠀⠀⢠⣿⡟⠀⢳⠀⠀⡇
⠀⠀⠀⠊⠀⠁⠀⠀⠀⢠⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠘⠛⢁⠀⠀⡇⠀⡇
⠀⠀⠶⢀⡵⠀⠀⠀⠀⢨⣼⠁⠀⠀⠀⠀⠀⠀⢀⣠⣖⣮⣽⣦⣤⣴⣦⣤⣇⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⢄⡀⠸⡄⡇
⠀⢘⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠛⠷⠟⠀⢻⡇
⠀⢨⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠻⣅⣀⠤⢊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠁⠀⠀⠀⠰⠀⣠⡇⣸⡃
⠀⣈⡀⠠⠀⠀⠀⣸⡿⢳⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠒⠈⠙⠲⠤⠤⠤⡤⠤⠤⠔⠒⠚⡉⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⣶⣤⣾⣿⡷⠀⢀⡴⠏⢀⣼⣿⢠⠟⡇
⠀⡍⡄⠰⣴⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠐⠀⠀⠉⠀⠀⠀⠀⠂⠀⢀⣀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡤⠖⠋⢀⣤⣿⣿⢿⣿⢘⡇
⠀⠳⡙⡄⠈⢿⣷⣤⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠤⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣠⣒⠋⠀⢀⣠⣴⣿⣿⣟⣵⣿⡇⢨⡇
⠀⠀⢹⣿⣷⣦⡙⢿⣿⣷⣤⣘⢮⣭⡹⠳⠂⠀⢀⢾⣷⠀⠀⠀⠀⠀⠀⠸⠶⠾⠿⠋⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠚⠀⢀⣴⣦⣴⣿⣿⣿⡅⣴⣿⣿⣿⠇⠰⡇
⠀⠀⠈⡄⠙⠿⣿⣜⠿⠿⠀⠙⢻⢞⡂⢀⡀⠀⠻⠞⣡⣶⡦⠀⠀⠀⠀⠀⠄⠀⣀⠠⠤⠤⠀⠀⠀⠀⠀⣀⣀⣠⣤⢰⣿⣿⣿⣿⡿⠟⠃⣼⣿⣿⣿⠏⠀⢸⡇
⠀⠀⠀⠱⡀⠀⠈⠿⢿⣶⣦⡀⠈⠛⢿⡿⣷⠿⠷⣾⣿⣯⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣯⣤⣴⣾⣿⣿⣿⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠛⠿⣿⣦⣤⣤⣤⣤⣀⣀⡀⠈⠛⢿⣿⣿⣿⣿⣿⠿⠟⠻⠛⢛⣿⣋⣽⣷⣶⣬⣟⣛⣉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠈⠉⠉⠛⠟⠿⢿⣿⣿⣦⣄⡀⠉⠛⠛⢉⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣴⠀⠀⠀⠀⠉⠈⠛⠿⣿⣷⣦⣤⣶⣿⠿⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⣤⣤⣀⠀⠀⠑⠛⠛⢿⣯⣶⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠾⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄⣆⢶⢰⣦⣤⣠⣤⣤⢠⡴⠄⣆⣤⣤⠄⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⣿⢸⣾⢹⣗⡀⣿⣏⢠⣙⡦⣿⠀⡇⢀⣛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⣀⣀⣀
⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠁⠀⠀⠺⣿⣿⣿⡗
⠀⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⢾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠻⠟⠁⠀⠀⠀⠈⠮⠁⠀⠀⣠⣿⣆
⠀⠀⢀⠄⠂⠀⠁⢠⣶⣿⣶⡄⠀⠀⠉⠀⠀⠀⢠⣶⠶⣶⡀⠀⠀⠀⠀⣿⡟⠛⠂⠀⠀⠀⢠⡶⠳⣦⠀⠀⠀⠀⣾⡏⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⣻⠇⠀⣠⣴⣦⡀⠀⠘⠓⠐⠚⠃⠀⣠⣴⣤⡘⢦⣠⡄⠀⠀⠀⢸⡀⠀⢸⠀⠀⠀⢀⠉⠁⠀⠈⠉
⠀⠀⢠⣶⣶⣦⠀⠀⠈⠋⠀⠀⠀⠟⠋⠻⠇⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠇⠀⢉⣀⣀⠀⠀⠀⠑⠒⠁⠀⠀⠀⣸⡿⠛⠓⠀⢀⣀⣤⣤⡀
⠀⠀⠹⣱⣤⡟⠁⠀⣠⣶⣶⣦⠀⠘⠿⠛⢀⣴⣷⣿⣶⡀⠀⢸⣿⡄⠀⠀⣾⡿⠛⠻⣿⡄⠉⢠⡾⠿⢦⠀⢰⣿⡇⠀⠀⠀⠉⠙⣿⡟⠁
⠀⠀⣾⠃⠉⠀⠀⠀⠙⠖⠰⠎⠀⠀⢀⠀⠘⠿⠉⠉⠿⠃⠀⠘⠿⠃⠀⠀⠻⣇⠀⢀⡿⠃⠀⠈⣛⣜⣋⠀⠸⢿⠇⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠛⠁
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣀⡤⠤⠤⠤⠤⠤⣄⣀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠄⠀⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⢀⠖⠉⡉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⠶⠶⠶⠶⠶⠶⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⢡⠖⠛⢛⢲⣞⠒⢇⠁⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠋⠉⠉⠓⢦⠤⠤⣤⠶⠤⣤⠤⠖⢉⣨⠽⠛⣿⣆⠀⠀⠇⢴⠊⢱⠛⠉⠁⠀⢓⠩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⢀⣀⣈⣷⢖⣚⡷⢀⡔⠒⠛⠉⠀⢀⣴⡿⠋⠀⠀⠀⠘⠑⠎⡳⠖⢟⡠⠳⡄
⠀⠀⠀⠀⣠⣶⠿⠷⠈⠙⢷⣦⣀⡏⠉⠉⠁⠀⠀⠛⠉⠳⣄⣀⣤⡶⠛⢁⠀⣀⠤⠤⢤⡀⠀⠀⠁⢴⠈⢱⡆⣿⠐
⠀⠀⠀⠀⠛⣿⣄⠀⠀⠁⠀⡀⠉⠛⠷⠶⠶⢤⠶⠶⠶⠛⠋⢉⣀⣤⠖⠃⠰⢑⡄⠆⣤⢹⣄⡤⠦⠉⠙⠈⠡⠃
⠀⠀⠀⠀⠐⠈⠛⢷⣤⡀⣎⠉⠉⠀⠀⠀⠠⠀⠠⣄⢀⣠⣴⠿⠋⠁⠈⠀⠀⣈⠃⣄⠿⣸⠃⣠⠰⢤⡘⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣤⣤⣤⠴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢹⠟⠉⢿⢦⡀⠗⣤⡺⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣴⣻⡌⡇⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠉⠂⠚⢉⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒


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

⠀⠀⠀⠀⠀⢂⠀⢀⠀⠀⠀⠀⠀⠀⢄⠀⣀
⠀⠀⠀⠀⠄⣁⠊⠈⠆⣀⠀⠀⠀⠀⠀⢀⣸⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠠⡂⢀⠘⣸⠃⠆⠀⢀⠀⠁⠙⠉⠈⠙⠙⣿⣥⡀⠀⠒⠀⠄⠀⠀⢀⡀⠔⠛⠀⠀⠠⣀⣀⡀
⠀⠀⠀⠈⢀⡙⣤⡀⠜⠈⠀⠀⠀⢰⠀⠀⠀⠀⠀⢈⣿⡇⠘⢦⡂⡒⢐⠒⠆⠲⡀⡶⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠈⠃⠁⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠉⠙⠚⠓⠛⠊⠉⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣻⣄⢀⣠⣿⣿⡟⠀⠀⠀⠒⡀⣀⠀⠀⠀⡇⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠛⠁⠀⠀⠁⠀⠀⠀⡆⠀⢠⠁⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠌⠀⠘⣷⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠙⠈⢀⣤⠃⠀⠀⢇⣀⠀⣀⣀⣦⠆
⠀⠀⠀⠀⡀⠀⠠⡏⠀⠀⠀⠀⢋⡀⠀⠀⠀⠹⣶⣶⣾⡟⣰⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⢁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠕⠚⠁⠀⠀⠐⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⡀⠀⣀⣶⠀⠀⡀⣀⢠⡄⢀⠀⠀⠀⠀⣼⠀⠀⣧⡀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠁⢸⠀⠀⠈⠳⠤⡧⡴⠟⠃⠠⠥⠼⡿⠟⠛⠻⣷⡄⠀⠀⣧⠀⠀⠈⠳⢦⣤⣤⡴⠷⠟⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠇⠀⠀⠀⣀⠀⠐⢄⠀⠀⠀⣠⣠⣼⠇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⣤⡼⠋⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⢠⠆⠀⠀⠀⢀⠀⠀⣠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣤⣶⣤⣤⣤⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⡞⠀⠀⠀⠀⡸⠿⠛⠏⣗⢀⡀
⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⠆⠀⠸⣤⣀⠀⠀⠀⠀⢀⣄⣀⣽⡿
⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⣿⡟⠉⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣤⣤⠀⠀⠀⠀⢰⣿⡟⠉⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣤⣤
⣿⡇⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣾⣿⣿⣷⣶⡶⣤⣿⣿⡀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣾⣿⣿⣷⣶⣶⣤
⣿⣷⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠘⡏⠹⠀⠀⠀⠸⣿⣿⣷⠀⠀⢼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠘⡏⠋⠀⠀⠀⠙
⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣧
⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡆⠀⠀⠀⠠⢤⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠁⠀⠀⣿⡆⠀⠀⠀⠠
⡿⡋⠛⡻⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⢠⣿⠇⠀⠀⠀⠀⣾⡿⡋⠛⡻⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣦⡄⠀⢠⣿⠃
⡇⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡟⡉⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢀⣤⣤⡀⠀⠀⠀⢸⣿⡟⠉⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢀⣤⣤
⣿⡇⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣶⣾⣿⣿⣷⣶⡶⣤⣿⣿⡀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣶⣾⣿⣿⣷⣶⡶⣤
⣿⣷⠀⠀⢾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠘⡏⠉⠀⠀⠠⠸⢿⣿⣷⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⠀⠘⡏⠉⠄⠀⠠⠹
⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠙⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⣿⣧
⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⡆⠀⠀⠀⠠⢤⣴⣾⣿⣶⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠁⣿⡆⠀⠀⠀⠠
⡟⡋⠛⠛⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⠄⠀⢠⣿⠃⠀⠀⠀⠠⣾⡟⠋⠙⠛⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠻⣧⠄⠀⢠⣿⠃⠀⠀⠀⠠
⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠍


⣀⣤⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⢿⠿⠿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢳
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⢫⢣⡀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠁⠀⠀⠀⠀⠉⠙⠒⢤⡀⠀⠀⠀⠀⠀⣠⢫⠋⣠⠞
⠀⠀⠀⠀⠀⢠⢤⣀⠘⣇⠀⠑⢍⡲⠤⣀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⡠⠴⣊⠔⠁⢀⡟⢀⣠⢤
⠀⠀⠀⠀⠀⢺⡈⠻⢷⣮⢷⣚⣆⠉⠑⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠉⢁⣖⣲⢯⣶⠿⠋⣸
⠀⠀⠀⠀⠀⠀⠉⠛⢆⡈⠉⢛⠚⠛⠒⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠚⠛⢚⠋⠉⣀⠞⠋⠁
⠀⠀⠀⠀⠀⢰⠲⢶⣶⣿⣿⣿⣟⠶⢲⡇⠀⣠⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢢⡀⠀⣗⠶⢞⣻⣿⣿⣷⣶⠶⢲
⠀⠀⠀⠀⠀⠈⠳⠤⠶⣄⣀⣀⡶⠤⠼⡆⠀⠹⠿⠿⠃⠀⠀⣦⣤⣤⡆⠀⠀⠻⠿⠿⠁⠀⡾⠤⠴⣆⣀⣀⡴⠦⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⠤⠜⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⠤⣤⣄⣀⣀⣤⡤⠤⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠐⠢⠐⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣄⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠐⠘⠀⠀⠛⠢⠀⠀⠈⠁⠀⠀⠀⠉⢀
⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠀⠘⠘⠀⠈
⠀⠀⠀⠀⠄⠀⣀⣀⠀⠄⠂⠁⠀⠀⠀⠀⠐⠠⢀⡀⢀⠤⠂⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠀⠠⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠂⠠⠄⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠊⠠⡔⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠢⡄⠈⠀⠀⠀⠀⠀⠗⢀⠀⠀⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠥⠄⠁⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡆⠀⠁⡀⠀⠘
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠰⢆⠠⠄⠠⠔⠀⠀⠀⠀⢠⠀⠀⠀⠘⡀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠲⠂⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠐⠒⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠦⠀⠀⠀⠀⡀⠀⠀⠀⠈⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠄⠀⠀⠘
⡄⠒⠠⡀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠁⠀⡀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠁
⠃⠀⠀⠈⠀⠉⠀⢀⠁⠀⠠⠂⠀⢀⠂⠉⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢐⡄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠑⠠⠄⠀⠤⠘⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡈⠣⡙⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠠⠍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⠣⠄⠀⠀⠀⠀⠀⠐⠀⣀⣑⡎⠀⠀⠀⠀⠀⢀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠉⠙⠒⠄⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⣄⣠⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡴⠁⢘
⠀⠀⠀⢀⠁⠠⠀⠈⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠀⠀⡰⠶⠄⢁⠠⡈⠦⠦⢠⠠⠀⠄⠀⢀⠀⠚⠀⠉⠳⠅⠀⢀⡀⢀⡜
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠈⡀⠐⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠩⠄⠁⠈⠨
⠀⠠⠂⠠⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠢⠀⠀⠀⠐⠕⠂⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⢒⢠⡂
⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠁⠀⠀⠉⠀⠀⠀⠀⠐⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢂⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠠⠖⠀⠺⠄⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⣄⠸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⡐⠀⠀⠀⢀⣀⡀⠀⢀⠀⠂⠀⠀⠂⠀⠄⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⢤⡀⠀⠠⣂
⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠈⠄⠄⠀⡘⡁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠍⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢨⠀⠄⠀⠀⠀⡀⠀⢠
⠀⠀⢄⠀⠂⡀⠀⠈⠀⠂⠀⠀⠂⠀⠀⠀⠀⢀⠐⣀⠆⠂⠀⠀⠀⡄⢒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠐⠓
⠀⠀⠢⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠐⠠⠴⡂
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠢⠉⠀⠄⠀⠂⢀⠌⠀⠁⠁⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠤⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠔⠀⠀⠠⠇⠸⢠⡢⡔⠁⠀⢬⡗⢠⡬⠀⠀⠠⢠⠲⠠⠀⠊⠀⠀⠀⡀⠀⢀⠐⠂⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠁⢀⣀⢀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⡔⠋⠉⠀⠄⢰
⠀⠀⠀⠀⠀⠀⠠⢀⢁⠀⠐⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠂⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠀⠀⠀⠀⠀⠛

⠀⠣⠀⠀⠀⠀⡠⠒⠉⠁⠀⠈⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠂⠁⠀⠁⠀⠁⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠙⢦⣀⠀⣀⣀⡴⠂⠀⠀⠀⠀⢁
⠐⡀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠢⢀⠀⠀⠉⠢⠤⢀⣀⠀⠀⠔⡣⠒⠒⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠄⢀⡠⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠰⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⠀⠐⠠⠄⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢄⡀⠀⡠⠂
⠀⠈⠀⠀⢀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠔⠁⠀⠀⠈⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠠⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⣠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠦⢠⡴⠶⣦⡀⣠⡶⠶⣤⠀⣶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠂⢿⡀⠀⢸⡇⣿⠀⠀⣸⠇⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠛⠛⠋⠀⠈⠛⠛⠋⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣾⡄⢠⠞⠓⠀⣦⠆⢠⠞⣓⡂⣾⣳⢠⠞⠓⡆⢶⢰⠆⡷⣄⡆⣾⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠘⠉⠙⠈⠓⠚⠀⠋⠓⠈⠓⠚⠁⠉⠑⠈⠓⠚⠁⠙⠚⠀⠃⠘⠃⠛⠚⠁

⠀⢀⣀⣀⡀
⠑⡈⠶⠆⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠖
⠄⢰⠸⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠁⠀⠀⢄
⠀⠀⡠⠀⠐⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠐⠢⠄⣀⠉⠂⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⢀⠀⠀⠀⣀
⠒⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠢⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⣀⠠⢔⡡⠒⠀⠀⠁⠒⠢⢄⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠂⠀⠀⣠⠖⠛⠛⠛⠶⣄⠀⠀⡴⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⡆⠐⠀⠀⠀⡅⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠘⡀⠈⠂⠄⣀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⣀⣀⠀⣀⡀⠀⣀⡀⢀⣀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢾⡇⣿⣒⢸⣇⣹⠆⣿⠰⣏⢀⢠⣯⣧⢸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠈⠉⠀⠉⠁⠀⠉⠁⠈⠉⠈⠀⠈⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⠆⣿⠭⠰⣯⡇⣾⠭⠀⣾⣧⢸⣏⡷⢰⡏⠙⢸⡤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠃⠛⠒⠘⠚⠃⠙⠓⠘⠉⠙⠈⠃⠙⠈⠛⠋⠘⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⡯⢽⡏⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡘⡇⠀⣿⢸⡇⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⢒⠖⢳⡝⠶⣇⣸⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠁⢻⡒⠋⠓⡾⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⣀⡤⠤⢶⡻⣖⡾⡷⠤⢤⣀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⢸⠁⡀⠀⠀⠑⠦⠞⠁⠀⠀⡈⢷⠀⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⡀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣠⠤⢶⠦⣄⠀⠀⠀⠀⠀⠐⣁⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡫⣶⠒⠒⢮⡳⡄⠀⢀⡽⠿⠿⠯⠀⢰⢡⠚⢢⠀⠈⣧⠀⠀⠀⣴⡛⢬⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠛⣯⠝⣳⡄⢹⢹⠠⠎⢀⣐⣒⣀⠀⠸⡜⠿⠃⠾⢂⡏⢀⣴⢊⠠⢙⣦⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⣄⠙⠺⢷⣗⡞⡜⣀⡀⠘⢻⣤⣟⠀⠀⠈⠓⠒⠒⠋⢠⣻⣌⠢⣴⣯⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⢽⣒⣺⠽⢾⡷⢤⡈⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠯⠛⠁⠈⢦⣸⡖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⡄⠀⠀⠀⠙⢦⡙⢦⠈⡇⢦⠀⠀⠀⢀⠀⣴⣒⣒⣒⣶⠀⢀⣀⣸⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡙⢤⣀⠀⠀⠀⠙⢋⣴⠇⠀⠳⣄⡰⠋⠀⠀⠼⣧⡷⣒⠒⠛⢲⣄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣒⠮⠭⠤⠴⣒⡽⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⢴⣛⣒⣒⣒⣚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠙⠲⢤⡟⠀⢸⠇
⠀⠀⠀⠀⠀⠀⣠⠟⡧⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣀⣠⠴⢾⣁⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣀⣀⣤⠖⠛⠛⣆
⠀⠀⠀⢀⣶⡈⠉⢻⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠁⣠⠖⠺⣅⣛⢳⡿⣆⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠉⣉⣀⡀⠀⠀⢿
⠀⠀⣤⣏⣤⠟⠉⠙⢷⣄⠀⠀⠀⠉⠓⠶⠤⣤⢶⠀⠀⠀⢠⣧⣯⡞⡿⠛⠙⢯⣹⠏⠀⢹⡀⠀⠀⠀⠀⠀⠈⠳⣦⠀⢠⠞⠉⠈⠉⢳⡄⠈⠳⢤⡀
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠉⠳⢦⣤⣀⣀⣀⡤⠿⣼⠀⠀⠀⠘⡇⠉⠙⢛⠒⠒⣿⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣠⠞⠀⢺⡀⠀⠀⠀⢸⡇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠈⠉⠙⠛⢦⠶⡆⠀⠀⠀⠀⠹⡄⠀⠉⠀⡼⠁⠈⠀⠀⠀⠸⡆⠀⠀⠀⠀⡞⠁⠀⠀⠀⠓⠦⠤⠶⠋⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣤⣤⣤⠴⢿⣸⠇⠀⠀⠀⠀⠀⠙⣆⢀⡾⠁⠀⠀⠘⠃⠀⠀⢻⡀⠀⠀⠘⣇⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⢀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⡄⠀⠈⠁⠀⠘⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⢳⣄⠀⠀⠄⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣩⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⡇⠀⠀⠈⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⣄⣴⠓⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⡄⠀⠀⠀⠀⣴⠂⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠻⣄⣽⢾⣄⣽⣴⠻⣦⢶⡀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣾⣼⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢠⡶⠧⠤⠽⢶⡄⠀⠸⡇⢺⠁⠀⠀⠀⣠⣾⠟⠀⠀⢠⡶⠤⣽⣃⣠⠟⡇⣸⣆⠈⢷⡃
⠀⠀⠀⠼⣧⡤⠤⠤⠤⠤⠴⠶⠶⠶⢶⡾⠇⠀⠀⠀⠀⠀⣸⠶⠶⠶⠶⠾⣇⡀⠀⣿⠘⢡⡟⠙⠻⣿⠁⠀⠀⠀⠘⠓⠒⣦⡉⠻⣼⡇⣿⠙⣆⠈⢳⣀
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠈⢳⠀⣩⡤⢬⣷⣄⣈⡿⠀⠀⠀⠀⠀⠰⣶⠿⢷⣤⣬⣷⣧⡼⠿⠖⢛⡏
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⢯⡀⠀⢘⡏⠉⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡟⠛⡻⣿⠳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⡴⠶⣴⣷⣴⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⡀⠁⠀⠙⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⣲⣾⠷⠮⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⣰⡯⠶⠓⠶⢭⣉⢿⣩⣽⣇⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡤⠶⠖⠒⣖⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣀⡀⢠⡄⠀⠈⠙⠶⣄
⠀⠀⠀⢀⡾⠁⠀⠀⠁⢀⠀⠈⠳⣄⢿⣍⢳⣈⠳⣄⠀⠀⠀⠀⢀⡾⢋⡐⠶⠀⣦⠀⠁⠶⠈⠻⣆⠀⠀⠀⠀⠀⠀⢸⡷⣄⡉⠙⠛⠦⣄⣤⠀⠀⠈⠳⣄
⠀⠀⠀⢸⡇⢀⡀⠀⠀⠈⠀⠠⠄⠈⢧⡈⣿⣩⡗⢹⠀⠀⠀⠀⠸⣇⠛⠀⠀⠀⠠⠴⠀⠀⠚⠃⠸⡇⠀⠀⠀⠀⠀⢸⣧⠉⡷⠀⢘⣂⣀⣙⠳⣴⠞⠀⠘⣧
⠀⠀⠀⠀⠙⢦⡀⠀⠃⠀⠀⠀⠀⠘⠂⢷⠀⣻⣿⢸⠃⠀⠀⠀⠀⣿⣉⣛⣛⡛⠛⢛⣻⣟⣛⢛⣿⣇⠀⠀⠀⠀⠀⢸⠷⠚⢁⡾⣫⣤⢲⢯⣳⣬⠷⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠃⠀⢀⠀⠘⣧⣿⣼⡟⠀⠀⠀⠀⠘⣯⣉⣁⣨⣭⣿⣭⣥⣤⣭⣭⣥⡾⠀⠀⠀⠀⠀⢸⣤⡀⠘⣏⣳⡼⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣈⡀⠀⢻⢡⡞⠀⠀⠀⠀⠀⠀⠘⢯⣉⠀⠀⠀⠉⠛⢶⣄⢀⣴⠃⠀⠀⠀⠀⠀⣿⣠⡽⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⠶⠖⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⢉⠀⢔⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣂⠀⠀⠉⠙⣳⡄⠀⠀⠀⢀⡠⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⡀⠀⠀⠀⠠⡟⠔⢀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢀⡹⡀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡸⢂⣤⠬⠗⢂⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⣬⣍⠁⠓⠺⣷⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠗⠉⠀⡴⢿⠉⠉⠃⠀⢀⢑⡒
⠀⠀⠀⠀⠀⠀⠀⡠⡀⠐⠀⠠⠉⠙⢆⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⡞⠐⠀⠈⣦⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣰⠇⢀⡣⠬⠵⡇⠀⠀⢰⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣶⠀⠀⠀⡟⠉⢉⣉⣱⣴⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢷⠒⠶⢤⣰⡀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣡⡔⠍⠃⠐⠉⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠤⠁⠀⠰⠀⠀⠇⡐⠩⠱⣄⠀⠑⠀⠐⠐⠦⣉⣉⡉⣁⠲⠂⠤⠤⠘⠀⢀⠴⠋⠁⡁⠐⠀⢴⡀⠀⠐⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⠀⠠⠟⠀⠀⢠⠀⠀⠙⠒⡤⠤⡄⣀⣀⣀⣀⣀⣀⣀⡠⠤⠔⠊⠁⠀⠀⠀⠃⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠡⢄⣀⡀⢀⣀⠤⠜⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣠⣮⠁⠀⠼⢤⣀⡮⡄⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠳⡗⢄⡀⠀⠘⠻⣧⠃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣱⡦⢹⢆⠀⢗⠬⡙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠁⠸⡀⢦⠀⠑⠢⠭⠔⡂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⠒⠠⠤⠐⠊⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⢠⡤⠄⡤⢤⡀⣤⢀⡤⠤⢀⣤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠿⠸⠯⠄⠧⠼⠃⠿⠘⠧⠤⠾⠻⠆⠧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢠⣤⢀⣠⡄⢠⣤⠀⣠⡀⢠⣤⡀⣠⣤⢀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⢯⢸⣯⠀⣝⡷⢸⣏⢰⠿⢷⢸⠻⡇⢿⣤⠸⡏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣖⣿⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢸⠀⢸⡇⣿⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠤⠬⢮⠳⣼⡃⣿⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⢱⠖⠛⠒⡾⠈⠲⢭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⢀⣠⡤⢤⡷⣖⠾⡧⠤⣤⡀⠈⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⢀⡏⡀⠀⠀⠑⠶⠚⠀⠀⢀⠘⡆⠀⠀⠀⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠸⠇⠿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⣭⣀⠀⠀⠀⣠⢤⣤⣤⠀⠀⡴⠒⠒⠲⣄⠀⠀⠀⠀⣘⣥⡔⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣕⣯⣉⡉⢺⡳⡀⢀⡼⠛⣛⠛⠀⢼⢸⣉⡇⣀⠘⡆⠀⢀⡼⢏⠳⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⣷⣫⢿⣀⡇⡇⠋⢀⣚⡛⣒⠀⠘⢮⣋⠈⣋⠜⢠⡶⣏⠈⣠⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡳⣌⣉⣽⢟⣽⡁⠶⢤⡘⠒⠚⠀⠀⠀⠈⠉⠁⠀⠻⣳⣬⡿⠳⡟⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⠒⠚⠉⠹⣍⠢⡀⠙⣆⡀⠀⠀⠀⠀⠀⣀⣀⣀⣙⡁⠀⠀⢸⡞⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢇⠀⠀⠀⠈⠳⡼⢂⡇⠙⢦⠀⢀⠖⠘⠓⣷⣳⣎⣁⣴⣒⡚⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⢝⣒⣂⣀⣠⢴⡿⠃⠀⠀⠱⠋⠀⠀⠀⠉⡿⠼⠧⠤⠤⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠈⠁⠒⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡘
⠀⠠⣀⡀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠖⠂⠀⠀⠀⠀⠀⠀⠠⢠⠄⠀⠠⠆
⠀⠀⠈⠀⠀⣠⠴⠉⠀⠀⠀⢀⡀⡈⠀⠠⠤⠒⢀⣰⡾⣍⣉⠜⠀⢂⣻⣄⠄⠀⢀⠀⠀⠀⡀⠘⠁⡠⠀⠀⠀⠀⢀⠀⡀⣣⠋
⠄⠀⠀⠀⠀⠈⢖⢒⣛⣥⡽⠁⠤⠖⠛⠓⠂⠀⣀⠀⠀⠀⠠⠀⠀⠀⠉⠁⠩⠭⠤⠔⠂⠉⠀⠀⠰⡁⠀⢀⡀⡄⠄⠈⣽⠏⠓⡲⠖⠚⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠈⠉⠉⠤⠤⠤⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⠀⠀⠨⣟⠓⠂⠈⠀⠀⠀⠆⠀⠨
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⡼
⠓⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠐⠀⣠⠞⠁⠠⠄⠀⠀⠁⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣽⡇⠀⠀⠀⠀⠀⢈⠀⠀⠉
⠀⠀⠀⠀⠒⠛⠖⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠸
⠀⠘⡿⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠄⠃
⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡊
⢀⣠⠌⢉⢻⡖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠄⠀⠀⠀⠀⠀⠘⠰⢒
⠀⠀⠀⠈⡟⢶⡤⠄⠒⠊⠁⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠔⠀⠀⢂⣤⠖⢃⠀⠀⠁⡨⢶⢀⡄
⠀⠁⠀⠀⠘⣟⠛⠁⠠⠀⠀⠀⠐⠊⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⡈⠀⠂⠀⠂⠀⠂⢀⠠⣾⠃⠀⡇⠈⠃
⠀⠁⡆⢀⠀⠘⣟⣀⣐⣃⡀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠄⠤⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⡀⠒⠘⢭⣁⡀⢀⣊⠀⠁⠂⠤⣖⡁⠀⣿⡧⠘⠁
⠂⠐⠁⠀⠀⠀⠘⡝⠋⠀⠀⠀⠰⠀⠀⢀⠇⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣶⡟⠠⢤⠤⣞⡀⠀⢠⡬⠗⢻⠁⠀⣿⡧⠐⠁⠀⠀⢀⣀
⠤⢄⠀⠐⠂⠰⠀⠙⢄⣀⣀⣀⣈⠀⠀⠁⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢻⡀⢠⣤⡀⢸⣯⠉⣷⡀⢸⡻⠐⠁⡀
⠀⢸⠂⢀⠀⢀⠔⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠿⣶⢆⠄⢀⡀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠈⠉⠁⠒⠻⠧⠽⠗⠈⠀⡀⠀⠀⠀⡀⠀⢀⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠉⠒⢦⣀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡤⢄⠐⠀⡀⠈⣆⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠖⠀⢀⡆⠀⠐⠒⠂⠰⠦⠂⠀⠀⢸⡶⣌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢺⣀⠐⣯⠂⠾⠋⠀⡀⠲⣀⣤⠀⠀⠀⠀⢀⣼⢡⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠈⢄⠉⢰⡞⠀⡾⢛⠛⠁⢀⣤⣤⣾⡿⠃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠰⠉⠀⠀⣷⣾⣶⣶⣿⣿⡿⠟⠁⠀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⡦⠒⡂⢶⢤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⠊⠢⡀⠀⠀⠀⠀⠀⠡⠀⢓⢈⠈⡆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠀⣀⠔⠉⠁⠂⠀⠀⠑⣀⡀⠰⠋⠢⡘⠀⠣⠁⠀⠀⡌⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠖⠘⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠅⠀⠢⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠚⡁⠀⠀⠀⢰⡆⠀⠀⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⡠⣴⣶⡶⠧⠶⠓⠒⠒⠛⠒⠒⠷⠴⠂⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠃⠀⡇⠀⠀⠀⠜⡄⠀⠀⡲⣤⡀⠀⠺⡄⠀⠈⠀⠀⠀⠀⠁⠒⠻⢧⡤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠤⣤⠶⠞⠃
⠀⠀⠀⠀⡰⠁⠀⠀⢡⠀⠀⡄⠀⢱⠀⠀⠙⣈⠻⣶⣄⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡷⡒⢲⠶⠒⠒⡒⠂⠢
⠀⠀⠀⡰⠁⠀⠀⠀⢸⠀⡐⠀⢰⠸⡄⠀⢄⠈⠓⠀⠙⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢱⠈⠢⠌⠀⣰⡇⠀⠀⢁
⠀⠀⠀⡇⠀⠀⠀⠀⠘⠴⠁⠀⠞⠀⠈⡲⢈⠏⢀⠀⠀⠀⠈⢃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢢⡀⠈⡁⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⢶⡖⠒⣋⡵⢲⠀⠀⠙⢶⣄⠀⠈⠓⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠐
⠀⢀⡜⣀⣀⣀⠤⣤⠒⠉⠀⠞⢁⡔⠁⠀⡎⠀⠸⡄⠀⠈⠻⢦⣀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠠⡄⠀⠀⠈⢠⡐⠂⠀⠀⠀⡀
⠀⠀⠀⠈⡁⠀⠀⠉⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠊⠈⠑⠒
⠀⠀⠀⠀⠑⠲⠄⠤⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠛⡿⢿⡷⠲⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠠⡄⠠⠄⠒⠂⠐⠒⠒⢲⠲⠾⠟⠚⠳⣿⣭⣙⠚⠒⠓⠲⠶⢤⡅⡢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠸⠤⠩⠀⠨⠀⠤⠀⠀⠀⡀⡄⢤⠀⠠⠐⠀⠀⠆⠀⢀⣩⣿⡶⡅⠀⢀⡀⠀⢀⣀⡤⠉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡅⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⡁⡇⠀⠀⠀⢀⠀⠀⡇⣄⢨⣙⣿⡟⠒⠀⠈⢀⠀⠀⠀⠐⣷⡤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⠄⠀⢠⣠⣀⡤⡤⢴⢶⠘⢸⢀⡀⣧⠥⣷⣧⣴⣬⣾⣷⣾⣶⣷⣿⣿⣿⠟⠛⢛⣻⣄⠈⠆⣤⣤⠐⠶⠒⠋⠁
⠀⠀⠀⠀⢀⡆⡨⢐⣨⣤⠶⢟⣛⣩⣸⣴⣴⣼⣼⣶⣾⡿⢿⣷⠀⠘⠛⠛⠛⠿⠿⠿⠿⠟⠛⠋⠁⢀⣿⡽⡟⠉⠙⠛⠉
⠀⠀⢀⠀⠌⣠⣶⣿⡿⠾⠛⠛⠛⣛⣩⡭⠽⠚⠋⡉⣑⣴⠋⠸⠆⠀⡀⠀⠀⠀⠀⣤⠀⠀⢠⡦⠐⢻⠈⠁⠁
⠀⢀⢏⣴⡿⢟⡉⠀⠀⠐⠐⠒⠉⠁⠀⠀⠀⠀⢚⣿⡉⣷⠎⠀⢀⠔⠀⠀⠃⠀⠀⣿⠀⢀⠀⠏⢱⠙
⢄⣠⠭⠅⠚⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠼⠅⠰⣶⡇⠀⠀⠀⠸⣀⡀⡾⣠⠟⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⡴⢫⡜⣧⠉⠀⠀⠇⠀⠀⠻⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⠆⠀⡤⠀⠀⢀⣀⡀⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠐⠒⠉⠀⠈⠁

⠀⠀⠀⠙⠛⠸⠸⠕⠍⠊⠐⠗⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠸⠕⠍⠪⠰⠗⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠨⠝⠩⠋⠐⠗⠤
⠀⠠⢐⠆⠴⠴⠰⠆⠆⠆⠤⠰⠶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠶⠰⠄⠆⠴⠴⠦⠆⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠰⠦⠄⢴⠰⠒⠀⠀⠆⠴⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⢠⣐⠒⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⡋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢻⣀⣉⡀
⠀⠀⠀⠀⠀⠄⠨⢀⣠⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢢⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣨⣀⣥⣍⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠄⠀⠀⠀⠀⢀
⠀⠀⠂⠀⠀⠀⠀⠘⠂⠄⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣁⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠒⠒⠒⠒⠒⠒⠃
⠀⠀⠀⢀⣀⠀⡄⠘⠀⢀⣃⣉⠀⣼⣽⠁⠀⠀⠀⠀⠀⢀⡞⣣⡌⢳⠀⢊⣁⠀⠼⠥⠤⢀⡀⠋⡽⠀⠀⠀⠀⠀⠀⠀⢸⠈⠄⠀⠁⠙⢀⠀⠀⠀⠀⠰⠆⠠
⠀⠀⠒⠄⠀⠎⠁⠀⠀⠀⠀⢀⣨⣡⢸⠂⠀⠀⠀⠀⠀⠀⠣⠌⠿⢯⠀⠈⠉⠀⠀⠀⠀⠹⠗⠚⠁⡀⠀⠀⠀⠀⠀⠀⢼⢸⡗⣿⡇⠀⢸⠀⡀⠀⠑⠊⠐⠂⠄
⠀⠀⠐⠓⠚⠁⠐⠄⠀⠐⡞⠁⠀⡀⣸⠁⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⢠⡕⠀⡀⠀⠻⣾⠂⠤⠈⠁⠀⠀⠀⠀⠀⠀⢺⠀⠥⠄⠀⢈⢸⠀⡀⠀⠀⢦⡀
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠓⠚⠒⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠉⠒⠓⠒⠋⠀⠀⠁⠀⠀⠛⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠘⠒⠐⠒⠒⠃⠘⠀⠁⠀⠀⠀⠙

⠀⠀⠀⠚⠛⠸⠘⠐⠂⠃⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠘⠘⠂⠂⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠘⠐⠐⠃⠐⠗⠂
⠀⠀⠀⠰⠐⠦⠐⠘⠒⠰⠶⠖⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠰⠄⠶⠐⠒⠆⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⢶⠰⠂⠆⠂⠒⠲⠒

⠀⠀⠀⠀⠀⠀⠀⠘⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢠⡀⢂⡄⠀⣠⠙
⠀⠀⠀⠀⠀⠀⠀⣡⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠔⠂⡈⠒⢀⠘
⠀⠀⠀⠀⠀⢸⢴⠃⠁⠤⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⣀⠀⠀⣈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⠈⠀⠁⠀⠀⠰⠀⠀⢀
⠀⠀⠠⢤⠤⢀⠠⡄⠀⠀⠀⢀⡀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠈⣤⢀⣀⠈⠉⠉⠉⠉⠀⣈⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠈⠂⣀⠀⠀⢀⡀
⠀⠂⠀⠈⢑⠂⠐⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⢹⠆⠀⠀⠀⠀⠀⠉⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠀⠀⠀⠀⠑⠉⠋⢇⠙⠙
⢀⠆⠔⢀⠒⠀⠀⡄⠀⢠⡤⠆⡰⢣⡌⠀⠀⠀⠀⠀⠀⠀⠀⠰⢴⠈⠶⠆⡀⠀⢠⣤⣀⠶⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⡶⣤⠶⠂⠀⠀⠐⣧⡶⣼
⠋⠀⠀⠀⠈⠀⡹⢃⠀⡀⠐⠂⠐⠂⠆⠀⠀⠀⠀⠀⠀⠀⡁⢠⠀⣥⠀⠀⠘⠀⠱⢶⠓⠒⠒⠓⠶⡎⠀⠀⠀⠀⠀⠀⠠⣉⣦⣎⣤⣝⣱⣀⠀⠂⠀⣧⣿⡞
⠁⠐⠒⠒⠊⠙⠁⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠉⠐⠈⠐⠈⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠲⠶⠺⠰⠰⠆⠦⠀⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠶⠰⠐⠀⠆⠰⠶⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢶⠐⠰⠰⠆⠰⠖⠤
⠀⠀⠀⠀⠀⠂⣔⡦⣠⢄⡠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⣦⢠⢀⣲⠤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣦⢶⡤⣰⢤⡆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠛⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁
⠀⠀⠀⠀⠀⠀⣬⠺⡄⠐⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠀⡉⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠰⠂⠶⣶⡞⠓
⠀⠀⠄⠂⠀⢠⠄⠀⣶⠀⣟⠀⠁⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⡐⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⣦⡼⠻⠛⠿⢹⠀⠢⢀
⠀⠀⠄⠀⠀⠸⠆⠀⠹⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠀⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠶⠦⠤⠄⠪⠰⠀⠀⠈
⠀⡀⠚⣘⡟⠈⠀⢀⠔⠒⠢⡠⠖⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⣀⠂⠀⠀⠀⠂⠀⠀⣂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠁⠀⠀⠀⠀⣳⢒⣀⣐⡒⣚⣌
⠀⠉⠈⢽⡇⠠⠀⢸⣄⣀⠤⠤⢄⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⠀⠰⠃⠀⢂⡐⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣠⡀⡀⠀⠀⣹⣭⣽⣭⣭⡍⣭
⠀⠲⡴⠈⡇⠀⠀⠤⢀⠤⣄⠐⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠨⠀⡼⢀⠀⢠⡏⠀⠀⠰⢠⡀⠀⠀⠀⠀⠀⢀⡞⠂⢸⡿⠃⠀⠡⠀⣠⢷⣠⢧⣤⢷⠞
⠀⠀⠇⠀⠃⠀⠀⠀⠈⠓⠁⠀⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠡⠾⠧⠶⠤⠂⠠⠃⠀⠀⠀⠀⠀⠀⠣⢀⣀⠗⠐⢄⠒⠀⠁⠀⠈⠉⠀⠉⠁
⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣄⣀⣠⠀⢀⡀⠠⠀⠀⠀⠀⠀⠊⢀⣀⣀⠀⢀⠘⠋⠋⠙⠀⠀⡀⠀⠀⠁⠀⠄⢢⠈⠀⣤⡀⠈⠀⢁⡄⠠⠑⠈⠁⠀⠀⠀⡈⠀⠀⢹⠂
⠀⠀⠀⢠⠯⣀⣀⠈⡆⠀⠀⣴⠋⠉⠾⠿⣿⣧⢳⡄⠀⠀⢀⠟⠛⠓⠢⡀⠀⠀⠀⠀⡜⠒⠑⢳⡀⠀⠈⠀⠀⡀⠀⠀⠳⠂⠀⠀⠀⢁⠈⠀⣀⠵⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠇⠀⢀⠃⢠⠀⠃⠀⠉⠐⢈⡄⠀⠀⡜⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢰⠇⠀⠰⠀⠀⣷⠚⠂⠒⢺⣌⣉⣉⣙⡎⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢰⠀⠀⢠⠀⠃⡀⠀⠐⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠰⠰⠂⠀⠙⢄⠰⠂⠈⠦⠤⠤⠤⠥⡀⠒
⠀⠄⠀⠀⢐⣦⣤⡆⠀⠀⠰⡀⠀⡰⠀⠀⢹⡀⠀⢨⠄⠀⠀⢈⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⡌⠂⠀⠀⠀⠀⠀⢠⡀⣼⡋⠂⠀⠀⠀⠒⠓⠡⠐⠀⠀⠈⠉⠈⠁⠀⣠⣄⢀⡉⠀⠀⡀⠀⠁⣴⠶⠦⡀⠀⢟⠢⡶⠓⡦⣤⠔⠠
⠀⠀⢃⠀⣀⠀⠀⠀⢀⠂⠁⠈⠊⡇⠀⠀⠀⣀⠑⠐⠂⠀⠀⠀⠀⠀⠀⠠⠀⠁⠐⠋⠄⠀⠀⠀⢸⡅⠘⠀⢻⡈⠀⠀⠀⢠⠉⠉⠓⠚⡇⠀⠀⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠘⡉⢉⡉⢉⠃⠀⠀⠀⣹⡆⠀⠀⢰⠆⠂⠀⠀⠀⠇⠀⣀⠀⢰⠃⠀⠀⠀⢸⠀⠀⠀⢸⠃⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠠⠉⠀⠀⠀⠀⠀⠀⠁⠨⠉⠉⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⢁⠀⠀⠀⠀⠀⢸⢢⠀⠠⣞⠀⠀⠀⠀⠀⠰⠀⠀⠆
⠀⠀⠀⡀⠀⡀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠥⣁⡨⠅⠀⠀⠀⠀⠸⠃⠀⢀⠳⠄⠀⠀⠀⠀⠁⣀⣀⠘⠀⡀
⠓⡶⠛⠻⠝⠓⠈⠉⡄⠀⠀⠀⠐⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⡲⣒⠳⣤⠀⠀⠀⠀⢠⣏⣀⠀⠙⡄⠀⠀⠀⠀⢀⠂⡖⠂⠀⠀⠀⠀⠀⠰⠆⡀
⠀⠃⠀⠰⠖⠒⠐⢂⠇⠀⠀⠀⠀⠀⠈⠀⠀⠈⠰⠀⠀⠀⡄⠀⠀⠀⢹⠀⠀⠀⠀⢰⠀⠈⠀⠀⠏⠂⡑⠍⠁⠀⠀⠁⢀⢂⠆⡀⠀⢨⡁⠀⠀⠀⣀
⠀⠀⠀⠀⢀⠐⠂⡀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠐⠂⠰⡄⠀⠄⠀⡟⠁⠄⠀⠀⠠⠴⡦⠠⠃
⠀⠀⠀⠀⡈⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⢀⠂⠀⠰
⡤⡤⠀⠀⠠⠐⠂⠀⠀⠂⠤⣀⠀⠀⠀⠀⠀⢀⡤⠀⠠⡀⠈⠐⠀⠂⠁⢀⠄⣀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠚⠘⠽⠄⠀⠀⠀⣀⠸⢅⠀⠀⠀⠀⠀⠀⠘⢀⠁⠀⠀⠀⠂⠀⠀⠀⢠⣀⠀⠸⡓⠀⠀⠀⠀⢀⣾⠋⠙⣶⡄⠀⠀⠀⠀⠜⠁⠉⡸⠆⠀⠊⠀⢰⡿
⠀⠀⢸⠁⠀⠀⠀⢾⠀⠀⠀⢘⡂⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⠀⣹⠿⠤⠴⢿⡄⠀⠀⠀⢘⣗⣇⣀⡟⡗⠀⠂⠒⠂⢸⠁⠀⠀⢸⡀⠀⠀⠈⡇
⠁⠀⠁⠀⠀⠀⠀⠈⣄⠰⢀⡤⠀⠀⠀⠀⠀⠣⠄⠐⠠⠏⠀⠀⠀⠀⡎⢄⠐⢀⡼⠀⠀⠀⠀⢸⡀⢀⣀⠀⣡⠀⠀⠀⠀⠘⠀⠨⠆⠘⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠖⠀⠀⠀⠀⢨⢏⠀⠀⢂⣉⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠁⠀⠀⠀⠤⠀⠀⠈⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠁⠀⠀⠉⠀⠀⣴⠰⢄⡅⠀⠀⠐⠀⠀⢀⡀⠀⠀⠈⠉⠉⠀⢀⡴⠶⠖⠂
⠇⠀⠀⠀⠌⠁⠀⠈⠁⠀⠀⢀⡰⠅⠁⠁⠜⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⡀⠀⢀⢰⠃⠀⠀⢱⠐⡖⠀⠀⢐⣀⠀⢸⠓⣒⣒⣒⣶⡩⠒⠸⠦⠤
⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠈⠓⡆⠀⡀⠀⠰⠀⠀⠀⠀⠀⢇⢀⣀⢠⠇⠀⠀⠀⠀⠘⡄⢀⠀⡘⠀⠁⠀⠀⣼⠿⠄⠴⢷⠀⠀⠀⠙⢾⡄⠠⠀⢠
⠀⠀⠀⠀⠈⣦⠒⣠⣿⠀⠀⠀⠀⠀⠈⠋⠁⠁⠀⠀⠀⠀⠀⢀⡀⠁⣀⠀⠀⠀⠀⠀⠀⠳⠈⠐⠁⠀⠀⠀⠀⡏⡀⠐⠀⣼⠀⠀⠀⠀⠀⠑⠀⠀⠈
⠀⠀⠀⡀⠃⠀⡀⠙⠙⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠨⠜⠀⠀⠀⠀⠀⠀⠃⢀⡀⠁⠀⠀⠀⠀⠓⠆⠀⠘⡗⠒⠀⠐⠀⠶⠆
⠀⠀⡐⢄⠀⠢⢌⠀⠜⠀⠀⠂⠀⡀⠀⠀⠀⠀⠔⠁⢤⣄⡀⠀⠀⠀⠀⠀⠏⠀⠀⠉⠀⠐⠉⠑⠀⠔⢈⢹⢶⠀⠐⢀⠂⠀⢀⡤
⠀⠀⠂⡀⣁⠘⠛⠫⢢⠃⠀⠀⢉⠁⠀⠀⠀⠃⠀⠀⠉⠙⣷⠀⠀⠀⠀⡧⠀⠀⠀⢀⡄⠀⠀⠀⡬⠀⠀⠀⠘⡆⠀⠀⠀⠀⣀⠓⢀⣀⡨⠍⠈⠄⠐
⠀⡀⠀⠴⠉⠀⠀⠀⠘⠧⠴⠦⠞⠈⠀⠀⠀⢁⡄⢀⡀⢀⠏⠀⠀⠀⠀⢠⡀⠤⠀⣸⠀⠀⠀⠀⠈⠀⠀⠄⠀⠁⠀⠀⠀⠰⠇⠠⠀⠀⠏⠀⠈⠀⠙
⠀⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠀⡍⠀⠂⠀⠀⠀⢡⠌⠁⣶⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡣⠤⠞⠃⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠨⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⡀
⠀⠀⡠⢀⠀⠃⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢀⢤⠴⠇⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠈⠃⠒⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠃⠈⠲⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⢀⠀⠄⠂⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊
⠀⠀⠀⢀⠀⢀⣀⡤⠀⠠⠖⠂⠈⢁⠀⠤⠀⠒⠒⠚⠁⠀⠀⡀⠀⠀⠀⠀⠐⠐⠀⠈⠈⠃⠉⠉⠉⠉⠙
⠀⡀⠀⠀⠑⠀⠠⠄⠰⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⢩⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠒⠈⡉⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠔⠉⢀⡂⠀⢸⠀⠀⢨⠁⠀⢀⠀⣄⡠⠄⡄⠤⠈⠡
⠀⠀⠣⣀⡁⠐⠒⠈⠅⠀⠀⠠⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠁⢂⠘⠈⠀⠐⢸⠀⠀⠸⠀⠀⢈⣉⠀⠈⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠜⠀⠈⠁⠀⢰⠈⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠘⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢁⠉⠁⢀⠀⢀⠀⠐⠀⠀⡆⠀⣥⠤⠀⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⡀⢤⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠈⡍⠍⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⠁⠠⠤⠃⠣⠄⠸⠯
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠄⢀⣀
⠀⠀⢀⡁⡀⣀⡀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡁
⠀⢀⠊⠈⠁⠢⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠄⠀⠐⡂⠀⠀⠀⠀⠀⠚⠀⠀⠰⡄⣈⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐⠇⠊⠀⠀⠀⠠⠀⠄⠀⠒
⠀⠀⠀⣀⠀⠨⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠄
⠀⢰⡄⠀⡶⢢⠀⡄⡄⠀⢸⠀⠀⠀⠀⠀⠀⠾⢁⣈⠷⠆⠀⣀⠁⠀⠀⠀⠀⠀⠰⠒⠠⠒⠃⠀⠐⡀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠘⠠⠀⠀⠠⠜⠀⠀⠈⠀⠀⠀⡄⠉⡁⠘⠒⣒⡓⣊⠉⠹⡄⠀⠀⠀⠀⠀⠀⢐⠠⠤⣃⡀⠀⠀⠂⠀⠀⠀⠁⡠⠒⠉⠀⠤⠠⠈⠉⠒⣄
⠀⠀⠀⠐⢤⡂⠐⠀⠀⠀⠀⠀⠀⠀⢱⡜⠥⠲⠷⠈⠇⠭⠆⢠⠇⠀⠀⠀⠀⠀⠁⢃⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⡴⠡⠠⠤⠤⠀⠤⠰⠔⠆⢸
⠀⢠⠀⠀⣈⠑⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣄⠀⠐⠒⠒⠀⢀⡠⠋
⠀⠘⢀⠀⠀⠀⠀⠈⠰⡀⠂⠀⠀⠀⠀⠀⠀⢄⡀⠀⡀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠉⠙⠛⠛⠋⠁⣀⡤
⠀⠀⠈⠁⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⣿⠤⠤⢄⣀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣹⣿⡇
⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣶⣄⠀⠀⠀⠉⠂⠰⣦⡀⠀⢤⣀⣀⣀⣴⣿⣿⡇
⠀⠀⣴⣿⣷⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠹⣿⣿⡷⢤⠀⠀⠀⠀⠙⣿⡄⣤⣈⣹⣿⣿⣿⣿⠇
⠀⣩⣿⡇⡟⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⢀⡏⠃⠙⠀⠀⠀⠀⠠⢄⣿⣿⣸⣷⣩⣿⡿⠟⠁
⠀⠀⠚⠋⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣯⣀⡀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠹⣧⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣤⡀⠈⠉⠛⢻⣿⣿⠿⢶⡜⢁⣤⣶⣶⣄⠀⢀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢾⣷⣿⠟⠉⠀⣶⣤⣤⣤⣾⣯⣤⣤⣤⣤⣼⣷⣾⣿⣿⣧⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠀⠋⠙⠛⠿⠛⣻⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣿⡆⠀⠀⠠⢴⠾⠟⠋⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣿⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⣠⣤⣼⣿⣿⣿⠶⠀⠀⠀⠐⠁⠐⡄⠀⠀⠀⡠⠤⠶⢶⣦⣀⡀⠀⠀⠀⠶⡄⠀⠀⠀⠀⠠⠞⠀⠠⠞⠁⠀⠴⠋⠀⠄
⠀⠀⠀⠉⠉⠋⡁⠰⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠄⠀⢾⣼⣿⡇⠀⠀⠀⠀⣿⠀⠀⢰⣦⣤⣴⣦⣀⣰⣤⣀⣠⣤⣄⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠃⠀⠀⠰⠀⡿⠀⠀⠘⠛⠈⠡⠜⠆⠛⠰⠼⠧⠴⠦⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠸⠟⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⠀⠀⢀⡀⠀⣠⡆⢀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⠀⠀⠀⠈⠁⠀⠀⢀⣴⡿⠛⠛⠻⠛⠢⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣽⣶⣿⣿⠻⠿⠇⠀⠉⠉⠀⠁
⠀⠀⢀⠐⠄⠀⠀⠀⠀⠂⢈⠄⠀⠀⠀⢀⣽⠏⠁⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⡄⠀⡀⠀⠘
⠀⠀⣄⠀⠁⠒⠠⠁⠀⠖⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠷⠀⠀⠀⠀⠇⠀⠀⢰⠘⡆
⠀⠀⠓⠺⢿⣈⡢⠞⠁⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀⡀⠀⠀⠔⠀⠀⠀⠀⠂⠀⠀⣠⠁⢀⠘⠞⢣⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⡷⠈⠀⠀⣤⣶⠆⠀⠀⠀⠀⠀⠀⡅⠀⢠⡇⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣟⣻⣿⣿⣟⣩⠁⠀⠀⠈⢂⠀⠀⠸⣿⣏⠰⡇⠀⠀⠀⠀⠀⢁⠀⠀⡇⡇⢸
⠀⠀⠀⠀⠀⡀⠀⠓⠂⠀⠀⠀⢀⡆⠀⠀⠀⠀⠿⠉⠉⠉⢙⠉⠹⠀⠀⠠⠀⠀⢻⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⡁⣹
⠀⠀⠀⠀⠈⢡⡆⢈⠜⢧⠠⠤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣄⣠⣄⠀⢀⠀⠀⣦⠀⠀⢆⠃⣿
⠀⠀⠀⠀⠀⠉⡤⠋⠀⠈⡆⠒⡀⠀⠀⠀⠀⢀⣠⠄⡐⢻⠷⠢⠀⠀⠀⠀⠀⠀⣸⠀⠀⡟⠛⠋⠉⠻⠀⠈⠙⠂⠀⠀⠀⢸⡃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢰⣮⣿⣷⣽⣭⣦⣴⣿⡤⠀⠆⠀⣠⠋⠀⠀⠷⠂⠀⠀⠀⠀⢀⡀⠀⠀⣀⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣐⠶⢿⣯⣝⡳⣆⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠰⠃⠀⠚⠀⠀⠘⠆⠀⠀⠀⠄⠀⣹⠀⢀⡳⢶⣶⡼⢷
⠀⠀⠀⠀⣀⠀⠀⠛⢷⣦⠋⠟⠁⠛⠁⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡜⠀⣴⠏⠀⠀⠉⠀⠋⠑⠚
⠀⠀⡆⠀⢹⡟⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⢀⣤⢴⡶⠀⠀⠀⠀⠜⠀⣼⠇⠀⠀⠀⢀⡀
⠀⠀⡇⠀⠈⡱⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠜⠋⠀⠀⠀⠀⠀⠤⣴⠏⠀⠀⠀⠠⢸⢃⠐
⠀⢀⡇⠀⠀⡷⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⢀⡴⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⣀⣤⡀⡀⠀⠀⠀⡘⠘⠀⣇⡁⡐
⠀⠸⡇⠀⢀⡘⠂⡁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠁⠁⠈⢹⡷⠁
⠀⠀⡇⠀⢠⠟⠀⠀⠀⠀⣄⡀⣔⡾⢤⠗⣤⢠⣆⠤⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣶⡄⠄⠆⢂⢐⡐⡀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⣾⡾⠂⠀⠀⢃⣀⠐⣛⣂⢛⡚⣘⣋⢳⠞⠋⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠸⡟⠒⠐⠂⠂⠃⠐⠀⠀⠀⠀⠀⠀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠛⣋⡉⠉⠉⠉⠙⠛⠒⠒⠦⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⠻⣤⡀⠀⠀⠸⡉⢇⠀⠀⠀⠀⠀⠀⡠⠤⠄⡀⠈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⡴⠞⠍⠻⣅⡴⠋⣹⢦⠀⡔⢻⡿⡆⠀⠀⠀⢀⠎⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⠙⠲⣤⡀
⠀⠀⠀⠀⣠⢞⠩⠀⠀⠀⠈⠻⣾⠁⢸⠀⠱⡝⣧⢘⠄⠀⠀⡎⠈⢣⡀⠀⢀⢠⢱⠀⠀⠀⠀⠀⠀⢨⡻⣷⣦⣀
⠀⠀⠀⣰⠯⠐⠀⠀⠀⠀⠀⠀⢈⣥⠀⢠⣞⠭⡏⠉⠀⠀⠀⠧⡀⣴⣧⣿⣼⣼⡾⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣿⣷⣄⣀⡀
⠀⠀⢠⣟⠭⠀⠀⠀⠀⢀⠠⡄⢏⠇⢰⠉⠀⠀⡆⠀⠀⠀⣀⣤⢧⢀⠽⣿⡛⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢿⣻⣯⠿⡻⣷
⠀⠀⢸⢒⠀⠀⠀⠀⢸⠹⠊⠁⠀⠀⢸⠀⠀⠀⡇⣀⣤⣾⠋⣼⢾⣡⢎⡔⠉⠓⣄⠀⠀⠀⢀⣠⢾⣻⠯⠑⠋⠉⠀⠀⠑⢍⡪
⠀⠀⢺⠀⠀⠀⠀⡠⠼⣇⠀⠀⠀⠀⢸⠀⠀⠀⣋⣥⣿⡿⢠⡟⣀⠕⢫⠒⠃⣪⣭⣦⣶⠿⠟⠛⠉⠀⠀⠀⣀⣀⡀⠀⠀⠀⠌
⠀⠀⢸⡄⠀⠀⠀⢯⣉⣛⣧⠀⠀⠀⠘⣄⣴⣾⣿⣿⣿⡇⢸⠚⢁⠴⠚⠀⠀⠉⢻⡿⣀⣀⣀⣀⣀⣀⣀⡼⣿⠛⢿⡷⡄
⠀⠀⣠⢛⣉⣽⣿⣾⣷⡤⠼⣇⠀⠀⠀⠙⠛⠛⠉⢹⣿⡟⡡⠊⠀⠀⠀⠀⠀⠀⠀⣧⡏⠉⠉⠃⠀⢸⢸⣣⠀⢤⡀⢙⡇
⠀⠀⡇⣿⣿⠟⠻⡟⢻⣻⠒⠛⠒⢒⣦⣤⠀⢀⡀⣼⡿⠈⠀⠀⠀⠀⢀⡜⣧⠀⢀⣿⣷⠀⠀⠀⢠⠸⠼⢏⣢⣤⠼⠃⢙⢦
⠀⢀⣽⣯⡅⠠⠀⢀⣿⠃⡇⠀⠀⠋⠁⢈⣷⣋⡽⠿⡇⠀⠀⠀⠀⣀⡼⠤⠇⠠⣽⣿⣸⢀⣀⣀⣸⡇⠀⡸⠃⢠⢶⠚⠛⠛⠓
⢠⣿⣿⣧⢼⡶⣴⣿⣯⢤⣿⠀⡀⠀⠀⢸⠁⠀⢀⠀⢹⠒⢒⢛⠁⢀⣠⣤⣴⢞⠯⣾⡯⢝⣂⣀⣉⣧⠜⢁⡼⡏⠀⢹⣶⣶⣶
⣿⣿⡿⠧⣤⣸⣿⣿⣾⠀⠈⠀⢸⡀⠀⠀⡇⠀⠘⢿⣷⣤⣾⣼⡀⣞⣯⡝⠊⠁⠀⣿⣷⢿⠁⠀⡿⠋⢠⣾⣹⠁⢀⣿⣏⠢⡀
⢻⣿⠀⢰⣿⡙⢿⣿⣿⠀⠀⠀⢠⣷⡤⠤⢳⣀⣀⣠⣤⣿⣿⣿⣿⣿⠟⡇⠀⠀⢀⣿⣿⡼⠀⠀⣇⣴⡿⢷⠇⠀⣸⣿⡪⠕⠘
⠈⣿⠀⢸⣿⣿⢈⣻⣿⡄⠀⣠⣾⡿⠗⠛⢹⠁⢸⣿⡿⠟⠛⠉⠀⠀⠀⢳⠀⢠⣿⣿⡿⢿⠀⠰⣏⠀⠀⡼⠀⢠⣿⣗⠯⠀⢠
⠀⢸⣄⣈⣿⣿⣼⣿⡿⠓⡏⠉⠀⣀⣠⣤⣾⢤⣸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠛⢍⠀⠀⠈⠳⠤⣴⣿⡆⢨⡢⠾⢯⣓⠅⠀⣼
⠀⢸⣿⠋⠀⠀⣿⠉⠉⠓⠛⢻⡿⣿⣟⣫⣵⡿⣿⠉⠉⠉⠛⠓⠒⠛⣿⠋⠀⠀⠀⠑⢄⡀⠀⠀⠈⠉⠁⠈⣿⣿⣷⣯⣓⢶⣿
⣶⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⣌⠠⠀⠀⡶⠂⢐⠀⠶⢣⠦⠀⠄⠲⠆⠀⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢀⡀⠁⠙⣿⠢⠀⡠⠀⠀⣌⣵⣀⡀⢂⠀⢤⠀⠀⠀⢄⡀⢠⣴⣄⣲⣶⢿⠦⠀⠀⣀
⠀⠀⢀⣴⣶⣶⢶⣿⡿⢿⣶⣶⣶⣶⣄⡂⡀⣀⠈⠀⠀⠉⠀⣀⠈⣷⠀⠈⡁⡗⣾⠷⡶⢜⡶⣿⠓⠖⠀⠀⠀⣶⣐⣶⢻⠯⣽⠿⡛⠛⠉⠛⣉⣀⡀
⠀⠀⣾⣟⠉⣁⡁⠙⠋⢽⣿⣿⣿⣿⣿⣿⣷⣦⡰⠀⠄⠂⠀⠀⣀⡤⠗⠸⠀⠫⠀⠁⠷⠈⠄⠙⠆⡅⠧⠴⠈⠉⠠⠄⠡⠒⠀⠎⠁
⠀⠀⢸⣯⡙⠐⠿⢳⣄⠀⠹⢾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣶⣿⣦⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠻⢿⡒⠄⠘⣟⡀⣥⠣⣿⣿⣿⣿⣿⣿⣛⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⡀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣸⣿⣿⣿⣿⣟⣿⣿⣉⠁⠁⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣯⣻⢿⣿⣿⣿⣷⣬⣦⠁⠀⣀⣴⣶⣶⣤⣶⣶⣦⣀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠭⣹⣿⣿⣿⡵⢉⡛⠄⡑⠆⣤⣤⣀⣻⣟⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣦⣴⣟⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣥
⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⢀⢠⣍⢻⣯⣄⠀⠀⢦⣀⠀⠸⢿⡿⣟⠉⡟⠉⠁⢾⡋⢋⡹⡟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡫⡚⠉⠉⠉
⠀⠀⠀⠀⠀⠘⠀⠂⣠⢰⣎⡆⢿⣇⠛⠹⢷⠀⠀⢙⣿⣄⠈⣑⡁⠺⠈⡁⠚⢈⠀⢨⠁⣯⡉⠹⠀⠛⢪⡏⡛⣯⡿⢿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠈⣱⢃⡐⡟⡟⠚⠻⠈⣁⣿⣷⣳⢙⣿⠿⣿⣤⣥⡐⠂⠁⠀⠀⠀⠀⠀⢣⣀⠴⣄⣥⣤⣿⣷⣶⣜⠃⣘⡛⢿⣿⣿⣿⣶⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡈⢊⠢⡀⡀⠈⢺⡋⢺⣿⠋⠙⠀⣦⡀⠙⢛⢷⣿⣬⣀⣶⣊⡐⡀⡤⣼⡻⢏⠉⡉⢿⣿⣿⡦⠻⢺⡍⠓⢹⠻⢿⣿⣿⣿⡀⡈
⠀⠀⠀⠀⠀⠀⠀⢠⣥⡀⠠⢿⣯⣶⣶⡿⠿⡃⠾⠀⡄⠸⠿⡔⢨⣘⠜⡏⣿⢁⢒⣂⡀⣶⠋⠁⢀⢢⣽⡿⠿⣿⣿⣿⣷⣶⣷⣌⢀⠋⡹⢿⣿⣿⡄⢀
⠀⠀⠀⠀⠀⠀⢐⠀⣄⢑⠄⡞⠉⠁⠐⠄⢦⣓⢤⡶⢀⠀⠀⠈⢛⣷⣗⣵⣿⣄⠈⢡⢜⠃⠀⡀⢀⣿⠿⢁⠄⠀⠄⠀⠉⠛⠻⢿⣷⣾⣀⡙⣿⣿⣿⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠠⠁⠜⣀⣟⠋⣟⢺⠀⣴⡆⢰⣿⡋⢹⣿⣧⡀⠀⠬⠐⢠⠖⠚⣇⢀⠪⡮⢃⢀⠠⡸⣄⠀⠠⠛⣿⣿⣷⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢬⣦⢊⣡⣤⢶⠻⢯⠣⡜⠌⠳⡟⠋⠊⣿⡄⢸⡿⡎⠻⢀⠀⣀⠈⣐⢄⣷⠨⡉⣽⠀⢤⡥⢡⣂⢋⠀⠀⠉⢭⢻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣿⢯⠁⠠⠈⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⣘⡇⠸⣷⢇⡴⡀⠁⠈⠁⠐⠿⢿⠀⠈⡀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠹⣿⠿⣯⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⢀⣠⠤⠀⠀⠀⠀⠄⢈⣧⡀⢿⣷⡄⣇⣿⢹⠸⠻⠘⠁⠆⢠⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠾⠻⠁⡾⢳⣧⠠⠀⢀⣁⣈⢿⠀⠘⣿⡿⡇⢯⣺⠅⣿⠐⠀⠀⠃⠀⠐⠀⠀⠀⠀⣶⣴⣶⢤⣽⠿⢻⡛⠿⣻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠈⠈⠀⠈⠁⠀⠉⠉⠀⠀⠉⠀⠉⠀⠀⠀⠀⢠⡀⢀⣴⣿⣏⣉⣿⣴⣎⣱⣶⣤⣴⣿⣿⠛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠿⡛⠛⡛⠛⠛⠙⠋⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀
⠀⠀⢠⢴⡧⠖⠚⡛⣷⠀⠀⠀⢀⠌⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢣⠀⢀⠔⣄⠀⢠⣄⣀⡀⠀⠀⣤⢤⡤
⠀⠀⢸⡄⠁⢁⡀⠤⠸⡆⠀⠘⠀⠀⠀⠀⠀⠀⠱⠑⡀⠀⢀⠔⠲⡒⡀⠀⠀⡆⢹⠀⢇⠀⢸⠀⢘⠿⢿⠂⠀⠀⡆⠀⡆
⠀⠀⠀⡧⠠⠀⢒⣂⠁⣳⠀⠰⣄⠀⠀⠀⠀⠀⢀⡴⠁⡠⠃⢄⡄⠈⢶⡀⠀⢁⠸⡆⠀⡕⡅⠀⢀⢳⠁⠀⠀⢀⠇⠀⢇
⠀⠀⠀⢳⡈⠭⢄⡐⠦⠝⠀⠀⠀⠍⠹⠹⠉⠍⡇⠀⣰⢁⣀⡈⠀⠀⣀⢳⠀⠈⢸⠃⠀⠀⡇⠀⠈⢠⠀⠀⢠⡋⠀⠀⠘⢷
⠀⠀⠀⠈⠊⠀⠒⠂⠁⠁⠀⠀⠀⠺⠈⠙⠛⠋⠇⠀⠈⠉⠉⠉⠉⠉⣉⣁⣀⣀⣀⣋⣀⣉⣁⣀⣈⣁⠀⠀⢠⠀⣉⡀⠈⠈
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠒⢲⣲⡒⠒⠒⢒⣖⡖⠒⠒⠒⠁⠀⢸⡀⣊⣈⣀⢀
⠀⠀⠀⡔⣡⠔⠂⠁⠐⢌⠢⡀⠀⠀⠀⢀⡔⢈⠉⠈⠉⠒⢄⠀⠀⠀⠸⠘⠉⣠⠖⠒⢦⡉⠙⣮⠀⠀⠀⠀⠨⣀⡀⠀⢀⡰
⠀⠀⠈⠘⠔⠒⡄⣀⢀⣀⢡⠡⠀⠀⠐⠑⠁⡎⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣿⣶⢠⣴⡇⠀⣿⠀⢀⠄⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⢀⢸⡀⢀⠇⡣⠿⢝⡜⠠⠀⡤⣦⣤⣤⡄⠐⠒⠒⠒⠒⠚⠢⡄⢰⢀⠀⠈⡷⠒⡏⠁⠀⠿⠀⠸⠼⡆⣷⠲⢷⢸⢈⢼⢃
⠀⠀⠀⠢⠋⠅⣀⣈⡒⢛⠔⢁⣀⡈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠈⠈⠉⢀⠀⠀⠀⠈⠉⠈⠀⠐⠒⠒⠒⠒⠒⠒⠒⠊⠁
⠀⠀⠀⢸⡸⠁⠐⠀⠀⠀⠠⣟⣒⡨⡆⠀⢀⠔⡒⡒⠒⠈⢕⠌⣇⠀⠀⡏⠀⠤⠀⠐⠃⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠌⠃⠹⠁⠀⣤⠰⠀⠃⠆⠃⣀⠴⡍⠀⠀⢳⠛⠉⣽⣟⡇⠀⠀⢹⠓⣛⡛⣛⠛⡛⢛⢛⠻⣻
⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠙⠦⠦⠄⠀⠀⠘⠵⣲⣖⡆⠽⠚⠉⠀⠀⠀⢸⡴⣶⠏⢹⠇⠀⠀⢧⠘⣅⠗⠟⠹⡇⠟⠾⢀⢿
⠀⠀⢰⠧⠤⠄⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠛⠀⠀⠀⠂⠁⠀⠈⠈⠀⠀⠀⠀⠁⠘
⠀⠀⢈⡺⠡⠀⠘⡂⠀⠀⢰⢑⡠⠤⠤⠤⠴⠥⠯⠮⠬⠤⠤⠤⠤⡄⡏⡇⠀⢀⠤⠐⣑⣒⣑⡒⠠⠤⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠘⡔⢄⣀⠰⡱⠀⠀⢸⢸⣈⣉⣉⠉⠉⠉⠋⢹⠉⠉⠉⣉⣉⣁⡇⡇⠀⢨⠢⠉⡇⠆⠀⡂⢉⠢⣤⠛⡂⢠⠇⠀⠘⡆
⠀⠀⠀⠈⠑⣲⠉⠀⠀⠀⢸⢰⠒⠒⡆⡇⠀⠀⡀⢸⠀⠀⢸⢰⠀⠀⡆⡇⠀⢸⡤⣀⡃⠂⠀⠃⡈⠴⠙⢄⡀⠀⢙⠉⠉⡅
⠀⠀⠀⠀⠰⠾⠄⠀⠀⠀⠸⡸⠀⠀⡇⠇⠀⠀⣅⡸⠀⠀⠸⡸⠀⠀⠇⠇⠀⠀⠘⠚⠩⠉⠍⠃⠊⠁⠀⠀⠀⠈⢤⣀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⣀⣀⡀⣀⡠⢜⠵⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢄⡢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠁⠑⠋⠭⠝⠋⠁⠀⠀⠀⢀⠔⡩⠢⠀⠰⠉⠀⠠⢆⠀⠀⠀⠀⠀⠀⠹⣿⣧⠎⠉⠀⠀⠀⠀⠀⠀⡔⢮⣹⠖⢤⡀
⠀⠸⡡⡁⠁⠁⠀⠀⠀⡇⠀⠀⠀⠈⠰⡁⢣⡄⠈⠂⠒⡡⡸⠀⠀⠀⠀⣠⡤⢦⣽⣦⢦⣤⡀⠀⠀⠀⠀⢸⡠⠤⠒⣊⡩⠇
⠀⠀⡱⠕⣂⣀⢀⡠⢮⡀⠀⠀⢄⠘⠂⠘⠒⠃⠀⠀⠁⠚⢁⠄⢠⡤⠼⠿⠿⠿⠿⠿⠿⠿⠷⠤⢤⠀⠀⡗⠐⣋⡉⠥⠔⠃
⠀⠀⠈⠁⠀⠉⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠃⢀⣀⡀⡀⠀⠀⠀⠀⠈⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢀⣀⡀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢰⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⠁⠲⣄⠀⠀⠈⣄⠀⠀⠈⠁⠸⠄⠀⠀⠀⠀⠀⡈⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⣤⠀⠀⣠⣤⣤⣤⡉⠢⢀⠘⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⣼⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠍⢠⡄⠀⢈⣤⠀⠀⠉⠂⠀⢷⡄⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠁⠘⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠃⠀⠀⠉⠂⠀⠀⠀⠀⢸⣧⠀⠀⠀⠸⠐⠢⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠁⠈⠄⠁⠤⠀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢄⠀⠀⠀⢀⣠⣤⣴⣆⣀⡀⠀⠀⠀⠀⢸⣤⠀⣈⠆⠀⠀⠈⠂⠀⠀⠀⠆⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⠂⠠⠄⠀⡀⠂⠀⠈⠙⠻⠯⣭⠍⠿⠛⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠴⠋⠀⢰⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠦⠤⠶⠒⠁⠀⠀⡰⠋⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢲⣿⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠉⠓⠦⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠒⠁⢠⠋⠀⠈⠸⣖⣤⣤⣤⠠⠄⡐⡅⠀⢀⣠⠂⣠⡊⠀⠀⠈⡉⣲⠶⢄⠀⢰⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠞⡵⠃⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⢉⠀⠐⡎⠃⢰⡟⠀⣦⠀⡾⢰⠃⠀⠀⠑⢬⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠔⡀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠀⢰⠀⣤⣼⠁⠀⠁⢸⠃⢀⡔⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⠁⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣿⡏⡜⠀⡠⡿⢸⣿⡧⠊⠀⣀⣈⢢⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡟⢹⢹⡇⣼⢡⠇⡾⡏⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠶⠀⢸⠚⠀⠀⢸⣿⠃⠸⠈⢱⡇⠀⠁⡀⠀⡂⠀⠰⡀⠀⠀⡰⠀⠦
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠄⢰⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡏⠀⠆⠀⠀⢧⡀⠋⣀⣾⡗⠄⠀⢈⠉⠉⠀⢀⢰⠂
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠙⡀⣿⢣⠐⣄⠀⠻⣆⠀⠀⠈⠈
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡏⠀⡀⠀⠀⠀⠀⠀⠇⠹⡈⡄⠈⢗⠀⠙⠂⠀⠀⡐
⠀⠠⠇⠀⠀⠀⠀⠀⠀⢀⢮⠀⢈⡇⠘⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⡇⠀⠀⠈⠀⢰⠁⠀⠀⠀⠀⡞⠀⠀⠀⠛⠒⠠⠀⠀⠀⠐⠈
⠀⡧⠘⠀⠀⠀⠀⢀⡔⠁⠰⠰⠊⡅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡏⠀⠀⠀⠀⣽
⠀⠸⡀⠃⠀⠀⡠⠋⠀⠠⠃⡦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠃
⠀⠀⠑⣦⠤⠐⠁⢀⡴⠕⠊⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠒⠶⠒⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣶⣶⣶⢶⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣫⣵⣶⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣡⣿⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡜⣿⣯⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⡜⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠀⠸⣿⣿⡿⠗⣽⣿⣿⣿⣿⣿⣿⣯⣶⣶⣶⢾⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠉⠑⢞⣣⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣵⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣭⣭⣭⣭⣭⣿⣯⣭⣭⣭⣭⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣒⢒⡒⢒⣒⣂⣿⣿⣿⣿⣿⣿⣿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⡀⠀⠀⣀⣠⣾⠿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⡿⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣶⣶⣶⣶⣶⣶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



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

⠀⠰⠲⠂⠀⡴⡄⠀⠀⠒⠂⠀⠀⡤⢤⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⡒⠀⠀⠀⠀⠀⠀⣰⢦⠀⠀⠐⠂⠀⡔⠆
⠀⢰⡆⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠁⠈⠁⠀⠈⠀⠀⠀⣴⠀⠠⣤⡆⠀⢋⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠱⡆⠀⠈⠀⠀⠀⠛⠓⠀⢶⡶⠀⢠⡆
⠀⠘⠇⠀⠀⠀⠀⠀⣈⣃⣃⠀⠀⠄⠠⠀⠀⠀⣰⣆⠀⠈⠁⠀⠉⠀⢀⣈⡀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠾⠷
⠀⠀⠀⠀⠀⠻⠗⠀⠻⠋⠿⠀⠀⠀⠀⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣿⢹⠀⠀⠀⠀⠀⢀⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⢀⣬⠀⠃⠀⢠⣄⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠁⠈⢀⣤⠈⠁⢡⣤⡀⠀⠀⣀⣅⠈⠁⣠⡀⠀⢀⡈⠉⠁⣀⡀⠀⠀⠀⠀⠀⢀⡐⠀⢀⣀⣐
⠈⠁⠀⠀⣠⣄⣤⡀⠀⠀⠙⠀⠀⣠⡀⠃⠀⢀⡀⠀⠀⠀⠀⠀⠈⠦⠃⠀⠰⠃⠀⠆⠀⠀⠹⠀⣘⣀⡀⠀⣥⠀⠀⣀⡀⠀⠀⠀⠀⠀⠛⠉⠉
⠀⠤⡄⠀⣿⣿⣿⣧⠄⢀⣀⣀⠀⠙⠁⠀⠀⣤⣤⠀⢘⡆⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠛⠓⠀⠙⠿⠁⠀⠿⠂⠸⠿⠿⠀⠀⢤⡄⠀⠀⠐
⠀⠰⠃⠀⢙⡅⠉⠀⠀⠸⠿⠿⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠿⠀⢸⡟⡇⠀⢸⣾⣶⡆⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩
⠀⠠⠀⠀⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠠⠠⠄⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠿⣆⠀⠀⠀⠀⡼⠿⡆⠿⠛⠛⠛⠀⠀⠀⢰⠛⠋⡷⠀⠀⠀⠀⣼⠛⠛⣿⠄⠀⠀⠀⠀⣼⡟⢻⣦⠀⠀⠀⠀⣸⠿⢿⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠠⠀⢰⣿⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⢠⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠂⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⢤⠄
⠀⠀⠀⠀⠚⠙⠛⢰⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠋⠋⠉⠁⢰⡏⠀⠙⣧⠀⠀⠀⠀⢠⣾⠋⢻⡆⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⣿⠀⠀⠀⠀⢸⣿⡆⢼⣷⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡧⠄⠀⠀⠀⠀⠀⢶⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠉⠀⠀⠀⠀⠀⠹⡇

⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⢀⣄⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣤⠀⣀⡰⢦
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠗⠲⠔⠂⠳⠀⠀⠀⠀⠀⠀⠀⠀⡐⣇⢠⠉⠄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠖⠀⣔⠉⢂⣸⡭⡤⠖⢈⠅⣠⠋
⠀⢠⣆⣀⣀⡀⢀⣀⣠⣀⡖⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠬⠕⠶⠀⠀⠀⠀⠀⠀⠜⢭⡀⢆⣐⠶⠶⠒⠉⠅⡀⢀⣠⠕⢋⣼⠑
⢤⠃⠊⣿⣓⣀⣐⣛⣓⡿⣅⣀⣄⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠃⠐⠒⠀⠘⠀⠀⠀⠀⠀⠘⣆⠘⢷⣺⡔⣺⠃⣠⢒⣓⡩⢿⠓⢚⡭⠊⢠
⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠤⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡉⠙⠶⠓⠯⠥⠖⠉⠉⣁⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣴⡿⢦⣠⡞⠁⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⢀⡜⢩⡀
⠀⠀⠀⠈⣾⠛⠀⡀⢉⠀⠘⠈⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⣶⠤⣞⣉⡉⣱⠞⢫⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡟⠝⠓⠈⠋⠢
⠀⠀⠀⢰⣟⡲⠦⠤⠬⠴⠾⠤⣺⣶⠀⠀⠀⠸⡁⠩⣍⡖⣲⠋⠀⠀⢈⢷⣓⡾⠧⣮⠏⡀⠀⠀⠀⠀⠀⢸⣤⣤⣅⣠⣤⣾⡇
⠀⠀⠀⠀⡏⠈⠉⠉⢹⠉⠉⠉⢹⠁⠀⠀⠀⢠⢹⣫⠍⡾⣻⠦⣤⣐⣫⡾⠤⠓⢔⣩⠿⡇⠀⠀⠀⠀⠀⠀⢛⠛⠛⠛⠛⡋
⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⡷⣝⠚⠚⠤⢞⡚⠋⠉⠗⣲⡶⠊⣩⣾⠃⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠄⡇
⠀⠀⠀⠀⠘⣦⣀⠀⢘⠀⢀⣠⠞⠀⠀⠀⠀⠀⠑⣌⠉⠓⠒⠶⢷⡀⢀⡼⠷⠚⢋⡡⠋⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠹⠄
⠀⠀⠀⠀⠀⠈⠫⠭⠭⠭⠭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⢦⣽⣯⠴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡀⣸
⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⣠⠀⢠⣀⣀⡀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⣠⠚⢱⠀⠑⣀⣹⣫⣏⣠⣮⢞⣥⡷⠀⠀⠀⠀⠀⠀⠀⣙⡦⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⢰⠃⢁⣌⣵⣷⠛⠁⣤⢸⡍⠁⢺⡀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠉⠙⠒⢄
⠀⣿⡤⢛⡻⣭⡇⠐⢾⣀⣀⡆⠀⣸⣷⠀⠀⠀⠀⠀⠀⢰⢻⠟⠲⠖⠒⠲⡗⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⢈⡀
⠀⣿⢮⣷⣾⣧⣵⣦⣤⣬⣥⣶⣿⡿⣿⠀⠀⠀⠀⠀⠀⢸⠸⡄⠀⠀⠀⢠⠇⡇⠀⠀⠀⠀⢀⣰⠂⠀⠀⠲⠁⠉⠉⠉⠈⠡⠃⠀⠐⣆⡀
⠀⠹⣷⣌⡉⠉⠛⠛⠛⠛⠉⠉⠁⣠⠇⠀⠀⠀⠀⠀⠀⠘⢦⣙⠲⣤⠖⣋⡠⠃⠀⠀⠀⠘⠃⢭⢀⣷⣆⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⡬
⠀⠀⠈⠳⣍⣙⠒⠂⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣉⣯⡁⠀⠀⠀⠀⠀⠀⠀⠸⣌⣛⣙⣛⣁⣀⣀⣀⣀⣈⣋⣀⡠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⡀⠀⠀⢀⣠⣄⣀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠋⣝⣺⣿⣿⣿⣿⣿⣿⣗⢄⣷⣫⡤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠑⡈⠉⠂⠺⢿⡛⠿⣿⡞⣫⣹⣧⡴⠾⠢⠄
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⣤⠞⢋⣴⣶⣶⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⣀⡀⠀⠐⠛⢃⠊⢿⣀⣼⣟⠛⢯⣍
⠀⠀⠀⠀⣠⠔⠈⢂⣀⣾⣿⣼⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣦⣀⣴⣶⣿⢿⣫⠥⠤⠄⠀⠈⠃⣀⣙⠋⡍⣙⠀⠈⠁
⠀⠀⠀⢸⣷⣶⣾⣫⡽⢛⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⢇⡀⠈
⠀⠀⠸⢿⣿⣾⣷⣶⣼⣶⣿⡿⢤⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣬⣽⡉⠉⠛⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⣟⣋⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⣥⣤⣀⠀⠀⠊⠁⠀⢡⣿⣶⠅⠉⠸⢿⣿⣿⣿⣷⣤⣀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠧⠀⠀⠀⠀⠀⠘⢽⣯⣥⣄⡀⠀⠉⠛⢿⣿⢿⣷⣤⠀⠈⠀⠉⠉⠁
⠀⠀⢀⣀⣤⣤⣶⣄⣠⣭⢷⣗⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⢷⠄⠀⠀⠈⠛⠿⢿⣿⣶⣤⣤⣤⣄⣀
⠀⠀⠁⠹⠿⠿⠿⠿⢿⣭⡿⡿⢉⣩⣷⣿⣏⣩⣤⣤⣤⣠⣀⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠛⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣯⣽⣾⣿⣿⣿⣿⠿⣂⠀⢡⡧⠤⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣈⣉⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣾⣷⢸⣟⣛⢸⡟⠛⣦⢸⡇⣴⠛⠻⠂⣸⢿⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠻⠋⠿⠸⡯⠥⠸⠧⠴⠟⠸⠇⠻⢦⡴⠢⠿⠚⠿⠼⢷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⡀⢀⣀⡀⢀⣀⣀⠀⢀⣀⠀⢀⣀⣀⠀⢀⣀⣀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⠇⣿⢭⠅⠿⣯⣅⢸⣯⡭⢀⣿⢻⡆⢸⣯⣽⠇⣿⠉⠉⢰⣷⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠻⠂⠿⠶⠆⠻⠶⠛⠸⠷⠖⠺⠋⠙⠛⠸⠃⠻⠂⠙⠷⠟⠘⠇⠀⠻


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⣉⣥⣤⠦⠶⢦⣤⣍⡙⠓⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⣴⠟⠉⠀⠀⢤⠄⠀⢀⠈⠙⢷⣄⠁⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠠⠄⠀⠚⠂⠀⠀⢤⡀⠀⣾⢷⣄⠀⠙⢷⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⡆⠀⠀⠀⠰⠆⢀⣠⣤⠶⣿⣦⣽⣷⠄⠘⣷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⠁⢦⠀⢴⠄⢠⣿⡉⠻⣦⣼⡇⠀⠀⠰⡄⢹⡆⣿⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⣤⣴⠷⠞⠃⢸⡇⢻⡄⠀⢀⣀⣀⣸⡏⠻⣦⣨⠟⠠⣄⠀⢠⡄⣼⠃⣿⠀⠛⠷⢶⣦⣀⡀
⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⠀⠀⠘⣧⠘⣧⠀⠙⢿⣍⢹⡟⠋⠉⠁⠀⢀⠀⠀⠀⢠⡟⢰⡏⠀⠀⠀⠀⠈⠙⢿⣄⡀
⠀⠀⠀⠰⣾⠃⠀⠀⠀⠀⠀⠀⠀⠘⣧⡘⢷⡀⠀⠙⢿⠇⠀⠀⠰⠆⠙⠁⠀⣰⠟⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⢴⡏⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠳⣄⡙⢷⣤⣀⡀⠙⠂⠀⣀⣠⣴⠟⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣿⢹⣿⠀⠀⠀⠈⠻⢶⣬⣉⣙⡛⠛⣛⣉⣩⣴⠾⠋⠀⠀⠀⠀⠀⣠⡶⢶⣄⠀⠀⢸⡟⠁
⠀⠀⠀⠀⢸⣧⡀⠀⣀⣿⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉⠁⠀⠀⠀⠀⣠⣄⣠⡾⠋⠀⢀⣿⠀⣠⠟⠃
⠀⠀⠀⠀⢀⣠⡴⢾⣏⣹⡇⠘⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⠙⠿⣄⢀⡴⢟⣡⡾⠛⠃
⠀⠀⣠⡴⠟⢁⣠⡶⠛⣿⣀⣀⣸⡇⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⣄⠈⢿⡄⠋⠉⠉
⣾⠛⣿⠀⣰⠟⠁⠀⠀⢹⣏⣉⣿⠁⠀⣿⣉⣉⣩⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣴⠟⠷⠞⠁⠀⢀⣀
⢹⡟⠋⢰⡏⠀⠀⠀⠀⠀⣿⣼⡯⠀⠀⢹⠏⠉⢹⡇⠀⠀⠀⠀⠀⣠⡾⠛⠛⢛⣿⠟⠁⠀⢀⣴⠾⠛⠛⠉⠛⣿⢦⣄
⢸⡇⠀⠛⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣼⡇⠀⠀⠀⠀⣰⠏⠀⢀⣴⠟⢡⣶⡀⢠⡟⠁⠀⠀⣀⣤⣤⣿⣄⣹⣧
⠈⢷⡀⣼⠋⠉⠹⣆⠀⠀⣤⣤⣤⣤⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⢿⣤⠞⠛⠁⢀⣿⡉⠀⣿⠀⠀⢠⣟⠙⢷⣄⣹⠉⠉⢹
⠀⠈⠻⣿⣧⣤⣾⣧⣤⣼⣧⣤⣤⣤⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⣾⠋⠁⠀⣿⠀⠀⣿⠙⢷⣄⣸⡟⠀⠀⢸
⠀⠀⢠⣾⣧⣤⣤⣤⣤⣤⣤⣤⣴⣿⡄⠘⠷⠶⠾⠁⠀⠀⠀⠀⣰⠟⣧⢀⣾⠋⠁⠀⠀⠹⣿⠛⢻⡟⠛⠛⠉⠀⠀⢠⡿
⠀⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇⠀⠀⠀⠐⢷⣄⡀⠀⠀⣿⣀⣼⠇⠀⠀⠀⠀⠀⠀⠈⠳⣾⣇⣀⣀⣀⠀⠆⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣿⣃⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢳⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢾⠀⠀⢸⠋⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⣿⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⢸⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣄⠘⡇⠀⢸⠀⠀⠸⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⣦⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿
⠀⠀⠀⠀⠀⡔⠒⣄⣀⠀⠀⢸⡄⠀⢹⡇⣠⠞⠛⠓⠶⠞⠛⠓⢦⠀⣿⠀⠀⠀⠀⠀⢠⠚⢲⣀⣀
⠀⠀⢀⡞⢻⡇⠀⡏⠉⡇⠀⠀⣧⠀⠈⠁⢿⠀⠀⠀⠀⠀⠀⠀⣸⠂⣿⠀⠀⠀⢰⠋⢻⠀⢸⡇⢸⡆
⠀⠀⢸⡇⢸⡇⠀⡇⠀⡟⠛⡆⢸⡄⠀⠀⠈⠳⣄⠀⠀⠀⣀⡴⠃⠀⡿⠀⠀⠀⢸⠀⢸⠀⢸⡇⢸⡏⢻
⠀⠀⢸⡇⢸⡇⠀⡇⠀⡇⠀⣧⠀⢳⡀⠀⠀⠀⠈⠳⣤⠞⠉⠀⠀⢠⡇⠀⠀⠀⢸⠀⢸⠀⢸⡇⢸⡇⢸
⣞⠳⣄⡇⠘⠃⠀⠃⠀⠇⠀⣿⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⡟⢳⣼⠀⠘⠀⠘⠁⠸⠃⠸
⢹⠀⢹⡇⢀⡤⢤⣠⠤⣄⠀⣿⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣧⠀⣿⠀⣠⠤⣤⡤⢤⡄
⠈⡇⠈⠁⢿⡀⠀⠀⠀⣸⠂⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⠈⠘⣇⠀⠀⠀⢀⡿⢀
⠀⢻⡀⠀⠈⠛⢦⣠⠞⠁⠀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⠀⠈⠳⣄⡴⠋⠀⢸
⠀⠀⠳⣄⠀⠀⠀⠁⠀⠀⢰⠇⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⣶⣶⠶⠶⣿⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣤⣤⣤⣶⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣻⣾⠿⠏⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾⣛⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠋⠁⠀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡛⠿⣦⣌⣉⣉⣉⡉⣻⠉⠉⠉⠉⠉⠁⠀⠀⠀⣉⣈⣀⣀⣠⡤⠤⠖⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣀⡍⠉⠉⠉⠉⠉⠀⠀⠉⠀⠀⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣀⡀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣿⠁⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢷⣶⠿⠶⢷⢶⣶⠶⠾⣿⠿⠋⠉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣅⣀⠀⠈⠉⠀⠀⠁⠠⠴⠀⠈⠀⠰⠒⠀⠀⠳⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣠⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣾⣦⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣏⢻⡛⠭⠽⠋⠿⠿⣷⣦⣀⢀⡀⠀⣀⠀⢀⣀⣠⣤⡶⠖⠛⠛⠛⠉⠉⠁⡀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡶⣦⠄⣀⡀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣤⣤⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣶⣾⡿⠛⠛⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⡿⢿⡟⠅⠁⠀⠀⠀⠀⠀⠀⣠⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⣿⣿⣭⣟⠉⠉⠙⠙⠀⠀⠀⠀⠀⠛⠋⠉⠉⠀⠀⠀⣁⣤⣄⣤⣤⠶⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⡳⠦⢙⠻⢿⣿⣿⣿⣿⣾⣾⣶⣶⣶⣶⣦⣶⣶⣶⣾⣷⣾⣿⣿⠿⠛⠋⠡⠀⠐⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⣈⡙⠛⠲⠶⠍⢉⡛⠛⠛⠛⠉⠉⠋⠙⠛⠛⠛⠛⠛⠋⠀⠐⠊⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠁⠀⠀⠀⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢹⡌⢿⡀⠀⠀⠀⢀⡔⠂⠁⠀⠀⠀⠀⠀⠀⢠⡾⣣⠶⣤⡀⠀⠀⠀⠀⠈⠉
⠀⠀⣀⣠⣄⠁⣤⢀⡀⡄⠀⠀⠂⣤⠤⠄⠐⠀⠀⠀⠀⢸⡀⢸⡧⠈⠣⡄⠀⠠⠉⠶⠀⠀⠀⠂⠀⠀⢀⡰⢿⣜⡱⢶⡌⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤
⠀⠀⠉⠉⠉⠀⠸⠼⠃⠇⠀⠀⠺⠶⠒⠺⠛⠁⠀⠀⠀⠘⡗⠈⠡⠀⣰⠇⠀⠀⠤⠼⠒⠈⠤⠀⠀⠀⠚⢵⢏⣺⡷⠋⠀⠀⠀⠀⠀⠂⠀⢺⣗⣤⠟
⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠛⠁⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠰⣦⠙⠃⢰⠀⠀⠀⠛⠿⣿⡿⠛⠁⠀⠀⠀⠃⣀⠈⠓⢄⣤⠀⠀⠀⢠⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢞⠁⣽⠆⠉⠀⠀⠀⠀⠛⠇⠀⢀⠴⠋⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢠⣴⠏⢠⣤⠀⠙⠃⠀⠀⠀⠀⢠⠙⠃
⠀⠀⠀⠀⡀⠻⠀⠀⠀⠀⠀⠧⠀⢠⣠⡤⠀⠁⠀⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠙⣁⣠⣤⣤⣤⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⣦⠤⡤⠀⠀⠀⠀⠀⠙⠇⢠⣄⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢘⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡉⠀⠀⠈⠀⣀⠀⠐⢦⡀⠀⠛⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡷
⠀⠀⠀⠀⠀⢾⡧⣴⠄⠀⠀⠧⠀⠁⠀⠈⠀⠀⠛⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡆⠀⠀⠀⠒⠃⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠘⢷⠜⠃⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄
⠀⠀⢀⣴⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠉⠟⡄⠀⠀⠀⠀⢰⠄⠸⣀⡴⠆⠀⡀⠀⠀⢄⠀⢰⠀⠀⠀⢠⣴⣶⣶⣶⡤⣄⡀
⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⡇⠀⠠⣠⡁⣠⡤⠘⠋⠀⠀⢈⡁⢀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠉⢀⡰⠶⠃
⠀⠀⠆⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠈⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⣩⡁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⡗⠀⠀⠰⠟⠆⠀⠀⢀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢤⠄⢨⠀⡀⠚⠁⠀⠀⢀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠈⠀⢀⠟⠀⠀⠀⠂⢀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣟⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠐⢣⠀⠈⠒⠂⠀⠀⠀⠀⠠⢠⡄⢠⣄⢹⡆
⠀⠀⠀⠀⠀⠀⠠⠘⠃⠀⠀⠀⠀⠟⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠯⠜⠃
⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣴⠶⠿⣷⣶⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣦⠀⠀⢠⣶⡄⠀⠀⠀⢦⠀⠘⢇⠀⠀⠀⠀⠀⢀⣤⣤⣠⡄⠠⠶
⠀⠱⣤⣤⣄⣄⣰⣤⠆⠀⠀⠙⢿⣤⣿⣦⡼⠇⠀⠀⡀⠀⠋⠉⠃⠀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠰⠀⠀⠸⠃⡰⣿⡟⢶⡏⠓⣤⠀⢿⠯⣍⡼⠇
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠴⠶⠋⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠈⢱⣏⣠⠼⠷⠞⠁⠀⠀⠀⠈⠁

⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡤⣤⡤⠀⠀⠀⠀⠘⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⣄⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠀⠀⠀⠆⣠⠆⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢲⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠺⠀⠀⠠⠀⠀⠀⠈⠻⠶⠶⠶⠟⠁
⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠠⠀⠀⢑⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠀⠀⠀⢠⣬⡑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣦⠄⠀⠄
⠀⠀⠀⠼⠃⣀⠴⢟⠀⠀⠠⠖⠐⠒⠀⠈⠆⠀⠀⠀⢴⣬⣿⣷⣤⡈⠀⠀⠀⠀⠀⣰⡀⠊⣱⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠒⠶⠐⠿
⠀⠀⠀⠲⠀⠙⢄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⠋⣹⡄⢣⡷⠀⠀⠀⠀⠂⠙⠁⡟⠁⠀⠀⠀⠘⠛⢃⣀⡄⢶⡄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠐⢠⣤⣤⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠐⠖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢱⡄⠀⠀⠀⠀⣀⣤⣴⠾⠟⠂⢀⠀⠀⡤⠈⠀⡀⠺⠆⠀⠀⠀⠀⠘⠛⠛⠂⠀⡄⠀⠀⠀⢈⠛⡀⠀⠰⣺⠉⣧
⠀⠀⠀⢶⣿⠿⠃⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⣶⠟⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠦⣿⡶⠀⠀⠀⢄⣠⡀⣀⣸⣀⡲⠐⠀⠀⠀⠀⢀⡀⠀⠀⢑⠊⠁
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠐⠋⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠺⢀⢈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡛⠏⠙⢻⡋⠉⡟⠛⢻⡙⠏⣙⡿⢛⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠔⢪⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⡄⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠀⠇⠀⠀⠀⡔⠰
⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡇⠜⡜⠀⡁⠀⠀⠀⢡⠀⠠
⠀⠀⠀⠀⠀⢈⠂⡀⢢⠀⠀⠀⠀⠀⢠⠘⡄⢸⠈⠆⠀⠀⠀⠀⠀⠀⠀⠈⠆⡙⠀⠇⡎⠀⠀⠀⢠⠃⢀⠞⡀
⠀⠀⠀⠀⠀⠀⣁⠘⢌⠣⡀⠀⠀⠀⠘⠀⡇⠈⠀⠆⢀⡠⠤⠤⠤⣀⠀⢸⢠⠅⢠⠀⠐⠁⠀⢠⠃⣀⠀⢐⠁
⠀⠀⠀⠀⠀⠀⠦⢁⡀⠀⠈⠢⡀⠀⠍⢰⠁⠀⠡⠚⠁⠀⠀⠀⠀⠀⠙⠂⠙⠀⢸⢀⠎⠀⡰⠁⠀⡛⠰⠁⠀⢠⠄
⠀⠀⠀⠀⠀⠀⣁⠀⢳⠀⠠⡀⠈⠒⠓⡢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⣠⠜⠁⠀⣐⣁⠀⢁⠜⢉
⠀⠀⠀⠀⠀⠀⠈⠳⢏⢯⠁⢈⣑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠥⠀⡠⠊⠦⠄
⠀⠀⠀⠀⠀⠀⠀⢂⣈⢢⠑⠦⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣐⡪⠔⠊⡠⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠤⢠⠆⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢰⠀⣀⡠⠔⠊⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⣠⠸⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢸⡄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⡀⠑⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢼⠖⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⢈⡐⠀⠈⠢⢄⣀⡉⠁⠀⠀⠉⠉⠉⠉⠉⣀⡠⠴⠃⠀⠀⢣⠀⠈⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠁⠘⠁⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⢠⣄⡀⢤⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⣿⣿⣿⣿⡿⠿⠋⠀⠙⣿⣿⣿⣷⣦⡀
⣿⣿⣿⠇⣀⡀⠀⠀⣀⣈⢻⣿⣿⣿⣿⠀⠀⡄⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⣴⣶⣶⣄⡀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⡏⠈⠁⠁⠀⠀⠀⠈⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣦⣤⡀⣀⣀⣻⣿⣿⣿⣿⣿⣄⣀⣤⣀⣀⣀⠀⠀⢸⣿
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣼⣿
⣿⣿⣿⣄⠀⠐⠀⠀⠀⠀⣠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⣿⣿⠟⠛⠉⠛⠿⣿⣿⣯⢸⣿⠯⠞⠿⠋⠕⠛⠁⢹⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠹⣿⡇⠸⠧⠴⠶⠂⠀⠀⠶⠶⠄⢹⣿⣿
⢻⣿⣿⣿⠇⠀⠀⠀⠀⠘⣿⢿⣿⡟⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠻⢿⡿⠿⣿⣆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⡏⠰⠒⠒⠂⠀⠒⠋⠓⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⢀⣀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⣠⡤⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⣉⣉⠉⠉⢉⣛⡻⣿⣿⡄
⠀⣤⣤⣴⣿⣏⣵⣶⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠄⠀⠀⠀⠤⠀⢺⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛
⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⡿⠻⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣿⡏⣁⣄⠀⠈⣤⣄⢙⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣾⣿
⡟⠁⠁⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠄




⠀⠀⠀⠀⣠⣤⣤⣠⣄⣀⡀
⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣶⡖⣖⣢⣦⣖⢂⣶⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⢠⡅⣬⠅⣄⢨⣤⣠⠄⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠛⠐⠛⠛⠛⠛⠛⠙⠙⠒⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⠭⢓⠚⠭⣇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠐⡀⢀⣀⣷⣌⢳⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢸⢸⠀⠐⢰⢯⣳⠏⠀⡂⡇⡧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⢏⢆⠙⢿⠋⢁⠠⠀⡼⡹⠁⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⢠⣤⠈⠳⢕⡢⠬⠤⣔⡫⠞⠁⠀⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⣴⣯⠹⡆⠀⠀⠈⠉⠉⠁⠀⢠⡲⣎⣠⣏⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⢋⠕⠋⣷⣲⠃⣖⣲⡄⠀⠀⠀⡠⠊⣹⢮⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢾⣀⠀⠘⠋⠀⣯⣸⠀⠀⢠⠎⣩⢟⡁⡴⠋⣉⣹⣓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣯⣨⣇⣴⣒⡂⡇⢸⠀⠀⠙⡋⢁⡞⠸⣁⣸⢯⣳⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠬⠭⠭⠭⠗⠈⠋⣄⣀⢸⣱⠊⠀⠀⠹⢽⣉⡁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⠤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠂⠀⠀⠂⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⢀⣀⣀⣐⣒⣒⣂⣀⣀⣠⣠⣤⣤⣤⣀⡄⡀⢠⣤⠤⠤⠤⠤⠐⠒⠉
⠀⠀⠀⠀⠠⠔⢶⠀⠀⠀⠈⠙⢲⣤⢀⣀⣀⣤⣤⠶⠛⠉⠉⠁⠀⣀⣴⡀⠀⠀⠀⠀⠐⠉⠈⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠶⢍⡉⠁⠀⠉⠉⠀⠀⢀⣀⣤⣤⣖⣋⣁⡀⡁⠂⢐⠀⣋⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡎⢭⠀⠀⠒⠬⠍⠉⠓⠒⠒⠊⢉⡀⠤⠛⠉⠉⠩⠉⠉⠻⠄⠀⡠⠂⠀⠹⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⢀⣠⣴⠶⡋⠉⠉⠉⢀⠀⢀⠀⠀⠀⢀⣀⣀⠰⠀⢠⠀⠀⢀⡀⠄⠁⢀⣀⣀
⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⠴⢋⠉⠙⠂⠈⠛⠛⠒⠀⠀⠘⠁⠤⠄⠈⠀⠀⠂⠀⠐⠶⠚⠉⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠔⠛⠇⠀⠀⢠⠶⠶⣿⡆⠀⠀⠀⢀⠴⠖⠶⠄⠀⢀⠞⠳⠄⠀⠟⡟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢾⠀⠀⠀⠐⠤⠐⠁⠀⠀⠈⠃⠐⠂⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⢀⣀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠐⠁⢀⠏⠠⠃⢄⡄⡄⠞⣵⡡⠊⡠⠆⠴⠀⡀⡈⠀⠀⡄⠀⠀⠀⢀⠠⡀⠀⢄⢄⢐
⠀⢀⠠⠈⠀⡀⡼⠠⡥⢊⠁⠣⠎⠐⠵⣨⠅⠠⠂⢐⣠⠁⡊⠉⠞⠰⢆⠠⠀⡄⠀⠨⠐⠉⡀⠀⠀⠉⡀⡠⠀⡀
⠀⢈⠂⡱⣸⣑⠡⠄⠖⠃⠈⠀⢀⠭⠏⡀⠠⣒⢲⠏⠀⢚⡉⣤⠒⢀⣬⠌⠤⠘⠄⡀⠄⠍⡀⠴⢒⣴⣋⢁⡠⢐⠀⠀⠲
⢡⡀⠈⠀⠁⠀⠀⠈⠠⠤⠓⡈⠁⠐⠋⢀⠠⣄⡖⢚⠛⣩⡍⣌⢿⡚⢫⠇⠖⠀⠀⠀⠒⠋⠉⢁⢃⡥⢾⡏⠔⠀⠄
⠀⠀⠀⠀⠠⠐⠐⠒⠂⠊⢁⠀⠰⠀⡈⣐⣖⠴⣷⢻⡔⢉⡭⡍⠥⠦⣒⠒⢚⡋⢚⠶⠩⠩⠡⠀⣄⠬⠗⠀⠉⠁⠈⠁⠂
⡄⠀⠰⢢⢜⣀⠤⠾⣎⡯⠜⣉⠀⠃⠓⠆⠭⡀⢒⠝⡾⠨⣷⣧⣍⣽⢚⡃⡃⣖⣒⣚⠻⢤⣄⡛⠀⡬⠧⠤⠄⠀⠐⠀⡀
⣸⠏⡹⢉⠇⡐⣴⡘⡎⣲⠗⠰⣯⡊⣢⣦⢔⠂⣩⠼⠲⢎⡋⠭⡏⣚⣷⡽⠛⢯⣀⣩⣻⣚⠲⠾⠦⣌⣱⡄⠺⠖
⠀⠀⠇⠀⠀⠀⠘⠃⢘⠙⠶⠉⡉⠛⠀⠉⠉⣁⠚⠃⠀⡹⢑⢃⢄⠁⣀⡮⠀⠂⢉⠒⠴⢇⠛⠋⢙⠉⠉⠥⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠓⠊⠉⠑⠐⠆⠀⠈⠁⠀⠀⠀⠱⠀⠀⢠⢀⠓⠀⠄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⢄⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣀⠄⠀⠀⠍⠄⠠⣝⠅⠀⠀⣦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠷⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠠⠀⢀⡐⡁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⡏⣼⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢂⣄⠀⠀⠀⠀⠀⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠆⠀⠀⠋⡋⠉⣠⣤⣴⣿⠃⠸⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⢿⣷⣾⣿⠿⠟⠃⠀⢸⢇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⡔⠁⠀⠢⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠋⠀⠀⢠⠄⠀⠐⡂⡘⠀⠘⠧⠤⠤⣀⣰⡀⢀⠄⣠⠀⠀⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠴⠃⠀⠀⣠⢆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡀⠀⠜⠁⠀⠐⠀⠀⠀⠀⠰⠀⠁⣰⠇⠘⢰⠁⠀⠀⠀⠀⠙⠂⠠⢶⣎⡁⠀⣤⡶⠿⠿⠉
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⣠⡏⡄⠀⠀⠀⢰⣿⣦⣡⣾⢿⡇⠀⣸⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿⠀⠀⠀⠤⠀⠀⠀⠀⢠⠀⠰⠃⠉⣷⠁⠙⠁⠀⠀⠀⣿⢏⣿⣿⡿⠀⠙⠔⢁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⠀⠀⠸⢇⠀⠈⣿⣿⣿⣿⣧⢀⡄
⠀⠀⠀⠀⠀⢀⠔⠟⠁⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⠁⠀⠹⣿⡷⠿⠿⠞
⠀⠑⠄⣀⣤⣶⣊⡤⠖⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⡜⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠂⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠢⢄⣀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠉⠀⠀⢀⠠⠔⠊⠁⢀⢀⡄⠀⠄⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⢸⠀⢠⠀⠁⠀⠀⠀⠀⠠⠤⡇⢸⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⡀
⠀⠀⠈⠀⠠⡀⠀⠀⣀⠤⢼⣠⣀⠀⠀⠀⢀⣀⡀⠀⢆⡇⢰⠇⡠⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡬
⠀⠀⢶⣀⡀⠈⢢⠊⢠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠉⠦⠊⠀⡼⠤⢀⡠⠄⠐⠨⠀⣠⠴⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉⠉⠁
⠀⠀⠈⠱⠤⡁⠔⠀⣤⡆⠀⠀⠀⠀⢀⣀⢨⠀⠀⠀⠀⠀⠉⣈⠥⠐⢁⠐⢀⡞⠁
⠀⠀⠀⠐⢅⣈⣅⠀⠉⠀⠀⠀⠀⠀⠈⠚⠋⠀⠀⠀⠀⠀⠫⢔⡂⠜⣀⢀⠾⣁⠑⠦⣀
⠀⠀⠀⠀⠀⠈⢧⡁⠈⠳⣐⣒⣒⣂⡴⢋⠠⠄⠊⠀⣠⠃⠉⠀⠀⠋⢡⠎⠀⠈⠒⢤⡀⠉⠒
⠀⠀⠀⠀⠀⡐⠈⢙⣦⣄⡀⠈⠉⠀⠀⠀⠀⢀⣠⡴⢃⣀⣀⣀⣀⠈⠡⡀⠀⠀⠀⢀⠇⡀⢰⡄⢳⠄⠄
⠀⠀⠀⠀⠠⠀⢸⠁⠀⠀⠉⠙⠓⠒⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⢣⠀⠐⢄⠀⠀⠁⠈⠥⠎⠈⠲
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡁⠄⡀
⠀⠉⠓⠈⠉⠂⡋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⢠⠖⢦⠻⡓⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠁⠀⠀⠑⠓

⣶⠈⠀⣀⠀⠀⠈⢻⣿⣿⡏⠁⠂⢤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⡇⠀⠀⠙⠃⢠⣴⣾⣿⡿⠇⢀⠀⠀⠀⠈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠉⣹⠟⠉⠉⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⢹⣶
⠁⠀⠀⠀⢠⣾⣿⣿⣟⣁⡀⣀⠀⠀⠀⠀⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠛⣴⣿⣶⡄⢀⣤⣀⠀⣿⠏⣿⣿⣿⣿⣿⠰⠆⠀⠒⠆
⠀⠀⠀⠀⣺⣿⣿⡿⠿⠿⢿⣿⡄⠀⠀⠀⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣆⠀⣄⠙⠛⠋⡁⠹⣿⣿⠃⠏⣀⣿⣿⣧⣤⣿⣤⣤⡶⡤
⣾⣿⣧⢸⡟⠉⠀⠀⠀⣀⣤⣼⣷⣀⣠⣤⣶⣶⣶⡶⠄⠉⠉⠉⠛⠛⠛⢿⠀⠸⣿⣿⣛⢳⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣁⣤⣤
⠛⢿⣿⣿⣴⣾⣿⡆⠀⠻⠿⠛⠿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⡿⠟⠛⢻⣿⣿⡇⠈⠉⠛⠻⠿⢻⣿⣿⡿⠟
⣤⣷⣟⣿⠌⠉⠁⣰⣶⣦⣀⣠⠜⠛⠛⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠰⠆⠀⠰⠦⠀⠈⣿⢟⠈⠑
⣟⢛⠫⢸⠀⢶⣾⣿⣶⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡀⠀⣀⣸⣷⣦⣤⣤⣤⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⣿
⣶⡆⢄⣸⣴⣶⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⢁⣴⣤⣤⡀⠀⢫⠏⡱
⣉⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⢰⣿⠿⠿⠿⠟⠛⢻⣿⣿⣿⠃⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡓⢤
⣵⣿⡿⠟⠉⠀⠀⠸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇⣤⣶⣶⣶⣦⣼⡟⠉⠉⠛⠋⠉⣿⣿⣷⣶
⣿⣿⣦⣄⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⠀⠀⠀⣠⣾⣿⣿⣶⣤⠀⠀⠓⣀⡀⠀⠰⠆⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⡄⠀⠠⣤⣶⣿⣿⣿⣿
⣿⣿⣿⡏⠀⢀⡀⠀⠀⢸⣿⡟⠃⠄⠀⠀⢸⣿⡿⠛⠛⠛⠻⢦⣶⣄⠉⠀⠀⠀⠀⠀⠘⠣⡏⠀⠀⠉⠉⠉⠀⣿⠁⠀⠀⠀⢿⡿⠛⠉⠙
⢹⣿⡏⠀⠀⢈⣀⣤⣴⣾⣿⣿⣶⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠚⡇⠒⠂⠀⠠⠦⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠙⠇⠀⢠⣿⣿⣿⣿⣿⠟⠛⠉⠛⠷⠶⠾⠡⠦⠄⠀⠠⠦⠀⢿⣿⣴⣶⣶⣦⣤⣤⣴⣿⣧⣠⡶⠶⣄⣠⣾⠀⠀⠀⠀⠀⠀⡶⠂⠀⠁
⠀⠀⠀⢤⣼⣿⣿⣿⣿⣏⢀⡀⠠⠶⠶⠶⠶⢦⣠⣴⣦⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠸⠀⠠⠄
⢀⣴⣾⣶⣾⣿⣿⣿⣿⡉⠈⠁⠀⢰⣶⣶⣶⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠉⠉⠃
⠈⣿⡿⠛⠛⠛⠛⢿⣿⣇⡀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⣹⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⡆⠀⠀⡀
⠀⠉⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⣿⡟⠛⡉⢉⠻⣿⡷⣶⡶⠀⠉⠉⠉⠙⠀⠀⠀⢨⣿⣿⣿⣿⠇⠂⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠉⠈⠀⠐⠆⠀⣾⣧⣤⣤⣿⣾⣿⣾⣿⣿⣿⣷⣿⣷⣶⣤⠀⠀⠀⠀⠀⠀⠈⢡⣿⣿⡿⠀⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡂
⣶⣜⣶⣶⡳⣄⣀⣀⣴⣿⣿⣿⣿⣯⢉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢀⠀⠻⠿⠀⠀⣿⡿⠟⠛⠛⠛⠻⣿⡇⠀⣠⣶⣿⣿⣿
⠻⣿⡘⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠛⠛⠛⠛⠛⠛⣿⢀⣠⣴⣶⣦⣄⠀⠀⢀⣀⠀⠚⢀⡀⠀⠀⢀⣀⠈⣁⣰⣿⣿⠛⠛⠛
⢀⠙⠃⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⢤⠀⠀⣀⠀⣵⣿⣿⡿⠿⠛⠛⢻⣾⣿⣿⣿⣦⡌⠁⣀⣀⡀⢁⣤⣹⣿⣿⣇
⠋⠀⠀⠀⠀⢀⣀⡀⠀⠀⠉⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣼⣿⣿⠋⠀⠀⠀⠰⠆⢻⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣯⣼⣿⡿⠏⠲⠆
⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⢸⡿⢿⣿⣿⣿⣿⣤⣀⣄⣴⣶⣿⣿⣿⣿⡄⠶⠀⠀⣀⣀⣬⣿⣿⣿⣿⣿⣿⠛⠛⠛⠃⠀⠘⣿⣷⡄
⠀⢀⠄⠀⠘⢿⣿⣿⣿⣧⣉⡃⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢀⣴⣏⣽⣿⣿⣿⣟⣛⠛⠉⠠⣤⢄⣠⣴⣶⣿⣿⣷⡀

⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⡐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢪⢧⡀⡇⠀⠀⠆⠡⠀⠁⢀⠀⠀⠀⠀⠄⠈⠀⠀⢀⠀⠀⠀⠀⠀⢀⠰⣬⠶⣂⡀⠀⠀⠀⠉⠁⡒⣷⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢀
⠀⠠⠂⡠⢁⠆⢵⠃⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠅⢀⢀⠀⠀⠀⠐⠀⠀⠀⠨⠑⢆⡃⣩⠶⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⢀⡀⢊⠔⠀⢠⠎⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠃⠘⡣⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⡤⠁⡤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠈⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠊⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⣿⢻⡟⠄⠀⠀⠀⠀⠀⠀⠀⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠠⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⢰⣦⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠷⠇⠆⠀⠀⠀⢀⠅⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠆⠀⠆⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⢀⣀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠄⠀⠀⠀⠀⠴⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠺⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⠅⠈⠀⠀⠀⠀⠀⠀⢀⢂⡄⠀⠀⠀⢀⠒⠑⢄
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡁⠀⠀⠀⠀⠀⢦⠆⠀⠀⠀⠐⠛⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠔⠀⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⢀⠠⠀⠈⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⢤
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠈
⠀⠀⠀⠀⡄⠀⠰⢄⠀⠀⠀⠀⠀⠥⠀⠁⠀⠀⠀⢀⡀⠸⡧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠈⠒⠂⠀⠀⠀⣀⠄⣬⠇
⠀⠀⠀⠰⠇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠿⣿⣻⣶⡝⢪⢁⢄⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠘⠛⣋⣽⢤⣾⣩⣌⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⡣
⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠄⠀⠀⠀⠀⠙⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠

⠀⠂⠀⠀⠀⠀⠀⠀⣧⠀⠀⠔⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠐⠂⠀⡩⠀⠀⠀⣀⣀⡀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠅⠀⠀⠀⢸⡇⠀⠀⢀⣤⣶⣤⡲⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡶⣫⣿⢻⣿⣷⣦⡀⠀⠀⠀⠀⠀⡀
⠉⠠⠀⠀⠀⠀⡀⠀⠛⠃⠀⠀⠀⠈⠉⠀⢰⣿⣿⣿⣿⣿⡜⣿⣿⡄⠀⠠⠄⠀⠀⠀⢠⣿⡟⠛⠁⠈⠁⠙⢻⣿⡄⠀⠈
⣀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠣⠉⠹⠍⠻⣿⠼⢻⣷⠀⠈⠀⠁⠀⠀⠀⠘⠀⢠⡀⠀⢀⣤⠀⠏⠀⠀⠠⡀
⠁⠐⠉⠀⠠⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠀⠈⠘⠃⠈⠉⠀⠈⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠐⠀⠀⠀⠀⠀⣰⣾⣿⡿⠻⡿⣿⣷⣄⠀⠀⠠⠄⠀⠀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⡈⠀⠀⠀⠀⠀⠐⢿⠏⠉⠀⠀⠀⠈⠙⣿⡆⠀⠁⠀⠄⠀⠛⠛⠉⠀⠀⣠⣤⢴⣦⣀⠀⠀⠀⠀⣈⡀⣀⡀
⠀⠂⡀⠀⠀⠀⠀⠘⠀⠰⠦⠀⠀⠴⠂⠉⠀⠀⠀⠓⠀⠄⠠⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡶⣤⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡟⠂⠙⠋⠛
⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠹⣿⠋⣧⠁⠐⢉⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾
⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢤⣄⣴⡄⠀⠀⠀⠀⣀⡀⠂⠀⠀⠫⣔⡆⠀⠀⢻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢣
⣀⡋⠈⡀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠤⠀⠠⠄⠘⡏⠀⠀⠀⠉⠓⡄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⣾
⠉⠀⠀⠁⠀⠀⢔⢂⡴⠔⠦⠆⠠⣄⡀⠂⠀⠀⣀⠀⠁⠀⠀⠉⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀
⠀⠠⠖⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠈⠋⠁⠀⠀⢸⣆⠀⠐⠂⢀⣾⡁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷
⠐⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⢀⠀⠳⠀⠀⠀⠠⡷⠀⠀⠀⠀⣿⡀⠀⠀⠤⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠈⠛⠀⠀⠀⠀⠉⠀⠀⡠⠀⣐⡄⠤⠸⠀⢠⡀
⠀⠀⢀⣤⠤⣤⣀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣀⣤⣦⣤⣀⠀⠀⠀⢀⠔⠈⠀⡰⠋⠀⠀⠀⠀⠈⠁
⠶⣾⣿⣿⣿⣾⣿⣦⠀⠀⢁⡨⠀⠀⣰⣟⣵⡿⠹⡟⣿⣷⣄⠀⠠⡀⠀⢺⣇⠠⠄⠀⠠⠄⠘⠁
⠋⠱⢞⣿⣿⣿⢻⠇⠀⠀⠀⠀⠀⠐⢿⡏⠉⠀⠀⠀⠀⠙⣿⠆⠀⠀⠐⠀⠈⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⣐⡂⠈⣼⡹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠦⠀⠀⠶⠂⠁⠀⠀⠀⢀⣀⠀⠠⠀⠉⠁⠀⠀⠀⢀⣴⣾⣿⣷⣝⢿⣶⡄⠀⠀⣓⡀
⠀⠀⠀⢀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠠⠀⠀⠀⠀⣾⠿⣿⣿⢿⣿⡎⣿⣿⡄
⠂⠀⢀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠀⠀⠀⠟⣂⠀⢸⣤⠙⠿⠉⢹⣇
⠀⠀⠀⢀⠀⠀⠀⢰⣀⠄⠀⠀⠰⢅⣢⠀⠀⢴⡄⣤⠄⠀⠀⠀⠄⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡇
⠀⠀⠀⠂⠀⠀⠀⣾⠃⣀⡀⠀⣀⠀⢽⠂⠀⠀⠀⠀⠀⠀⠀⠈⠒⠞⠉⠐⠁⠀⠙⢶⠄⠀⠀⠀⠀⠀⠘⠂⠀⢰⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣿⣿⡗⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⣴⣒⡀⣤⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠅⣼⣧
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠉⠉⠉⠛⠉⠁⠀⢠⣰⣿⠏
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⠀⠀⠀⠀⢠⣠⣴⣿⡾⠟⠂
⠀⢰⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠛⠉⠁⠄⠀⠀⠄⢀⣀⣾⠿⠉⠉⠁
⠀⢼⣻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠟⠁⠀⠀⣀⡀⠀⠀⣀⣀⣄⣀⣀⣀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡀⠀⣀⣠⣦⣤⣤⣤⣤⣾⣿⡟⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠳⢶⡿⠿⢿⣿⣿⣿⣿⡿⠿⠛⡿⠏⠀⠀⠀⠀⠁⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣀⠏⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠋⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠀⠀⢻⣿⣿⣿⣿⣇⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⢀⣴⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠉⠛⢻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⡀⠀⠻⠻⠟⠂
⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠐⠂⠀⠀⠀⠿⠛⠁⠀⠀⠀⠈⠻⠿⢿⣿⣿⡿⠿⠟⠛⢙⣿⠁⠉⠉⠙⣿⣧⠀⠀⠀⠀⠀⠀⠂⠹⠤
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢨⠿⡿⠀⠀⠀⠀⡀⡄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣤⣔⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⡀⡀⠛⠀⠠⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠒⠦
⠀⠀⠀⢠⡶⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⠀⠀⠀⠀⠀⠀⣠⠞⠂⠀⠐⠋⠀⠀⠀⠘⠋⠉⠀⡀⢀⠄⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡜⠁⠀⢀⣤⢀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⡀⠀⠀⢀⠀⠀⠘⡻⠋⠀⠀⡔⠁⠀⣾⠖⠀⠀⠀⠀⣀⡀⠉⠁
⠀⠀⢸⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣀⠴⠂⠀⠀⠀⠀⡛⠁⠀⣤⣄⣀⠤⠚⠁⠀⠀⢰⡗⠃⠀⠀⠀⠀⠀⠀⠀⠹⠏
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⡀⣠⣆⢒⣈⣀⣤⡤⠟⠉⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⡅⠀⠀⠀⠀⠀⠘⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢃⠀⠀⠀⠀⠚⠛⠃⠀⠀⠰⡿
⠀⠀⠘⠻⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠂⠀⠉⠁⠀⠀⠀⠀⠞⠀⠘⠟⠀⠀⠀⣠⣤⣄⠀⠀⣠⣤⣤⣤⣀⡀⢀⣾⢃⣼⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠘⠲⣿⠆⠀⠀⠈⡁⠀⠐⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⣠⣿⠃⠘⠟⠛⠙⠛⠛⠛⣿⡟⣛⡁⣘⠁⣤⢤⢿⣼⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢸⣿⠇⢀⣶⠲⡄⣼⡏⢹⢠⣿⣏⣼⢣⡿⢸⡧⢊⣔⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠛⢂⣾⣯⣠⣧⣿⠣⡼⢻⡟⢿⣄⠘⢓⣉⣙⡉⢸⣇⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⣠⠞⠻⣧⠟⠁⠙⠚⢁⣀⣥⣼⠿⢿⣍⣁⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠈⠿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠞⠃⠀⠈⠉⠁⢀⡀
⠀⠀⠀⠀⣴⠆⠀⠀⣤⠀⠀⠀⠈⠙⠁⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠒⠓⠚⠃⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⡾⠖⠋⠉⠁⠙⠒⠀⠀⠀⠰⠒
⠀⠀⠀⢠⠀⠘⠷⠀⠀⠀⠀⠀⣴⡶⠂⠀⠀⠉⠉⠀⠄⠀⠀⠀⡠⠂⠛⠁⠀⠐⠟⢃⡀⠀⢀⣤⡀⢀⣀⠀⠀⠀⠀⠘⢿⠁⣠⣤⠀⣀⣘⣀⣀⠠⣤⠀⠀⢤
⠀⠀⠀⣿⣧⠀⠀⣠⣄⢠⣴⣦⠀⠀⢠⣶⣤⠀⠔⢠⠆⠀⠀⣼⠃⠀⢛⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡄⢦⡤⠒⠉⠉⣉⠉⠉⠉⠓⢄⢀⡀⠁
⠀⠀⢰⣿⣿⣿⣧⣤⣤⣄⡀⢤⣄⣀⣀⣀⣀⣀⣴⡏⠀⠀⢀⡴⠀⠀⠙⠁⠀⠀⠀⠤⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⣀⠀⠀⠋⠀⠀⢀⡀⠀⠈⠡
⠀⠀⠘⢿⣽⣋⡉⣉⡉⠹⠿⠟⠛⠉⠉⢉⣽⡷⣀⣶⠀⠀⠈⠳⠀⠀⠦⢀⠐⠀⠈⠀⠁⠚⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⣏⠀⠀⠋⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃
⠀⠀⠀⢰⣿⣿⣿⣭⢤⣦⣦⣤⣤⣴⡷⠾⠿⠛⠙⠋⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠉⠀⣀⠀⠀⠤⠀⠀⣀⡀⠀⠀⢸⡇⣴⠄⠀⠀⠀⠀⢴⣆⠀⠀⠀⡀
⠀⠀⠀⢨⣥⣌⣉⠀⠀⣀⣀⣀⢠⠾⠆⠀⣀⣠⣤⣴⡛⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠉⠀⠀⠈⣿⠀⠀⣤⡀⠀⠀⠀⠀⠀⢠⡄⠛
⠀⠀⠀⢉⠾⠋⠉⢭⡉⠉⠋⢹⠟⢻⡏⠉⠉⠉⢈⣉⣤⠀⠀⠀⠀⠀⣀⣀⠀⠰⠖⠒⠒⠀⠉⠈⠁⠀⢠⡀⠀⠀⠀⠀⠘⣇⠀⠈⠁⠀⠶⠂
⠀⠀⢠⣿⡟⢛⡶⠶⣤⣤⣤⣤⡶⠶⠶⠞⠛⢋⡉⠡⢄⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢴⣦⡄⠀⠀⠀⠙⠁⢠⡆⠀⠀⠀⠈⠳⣄⣀⡀⠀⠀⢶⠆⣀⠤⠔⠁
⠀⠀⠀⠨⣷⣿⣿⣄⣀⠺⠷⠀⠀⠀⣀⡀⠀⣛⣣⠴⠊⠀⠀⠀⠀⠀⠀⠈⠁⣀⡀⠀⠀⠉⠁⠀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠃⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⠄⢀⠀⠀⣀⣀⣠⠤⣤⣴⣤⣀⣠⢦⣶⣀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡳⣄⡌⣹⠀⣠⣴⡮⠛⠒⠉⠉⠀⠁⠁⠙⣿⣙⢫⣿⣿⣿⣿⣾⣿⣾⣶⣴⣤⣀⠀⣀⡀⠀⣀⡤
⠀⠀⠀⠀⠀⠐⠪⡒⠣⠭⠴⠷⠚⣻⢏⡇⣀⠀⠀⠀⢠⣠⣶⣇⡉⢿⣟⣛⠛⢿⣿⡿⣿⣿⣿⣿⣿⠿⣿⡿⣿⣿⣿⠇
⠀⠀⠀⠀⠐⠀⣠⠂⠀⢀⡀⠀⠀⠈⠺⣛⣽⣵⣾⣿⣿⣿⠟⠛⠣⠸⠌⠉⠙⠓⠒⠀⠀⠀⠍⠉⠁⠀⠀⠀⠘⠋
⠀⠀⡴⠂⠀⢸⡁⠀⠰⠌⠁⠀⢀⣤⡺⢿⡟⢨⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⣀⠀⢢⠀⣀⠀⠀⠄⠤⢀⡀
⠀⠀⠁⠀⠀⠀⠉⠲⠶⠶⠿⠟⠛⠛⠋⠉⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠚⠣⠴⡬⠺⠀⡤⠒⠂⠈⢀⡻
⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡤⠔⠒⠊⠉⠉⠀⠀⠀⠀⠀⠁⠀⣀⣼⡶⠁
⠀⠀⠙⣌⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡨⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⣤⣾⠛⠛⠋⠂
⠀⠀⠀⠈⠳⣌⡐⠤⢀⡀⠀⠀⠊⣛⣢⣤⠶⠞⠛⠉⠉⠁⢀⣠⠤⠄⡀⢠⣤⣤⣶⣷⣿⣿⠃⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠦⣍⣉⡉⠁⠁⠀⠀⠀⠀⠀⢀⢀⣀⣸⣦⣤⣆⠈⢻⠿⠿⠟⠛⠁⠃⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠑⠄⣀⠉⠀⠀⠀⠀⠀⠂

⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡆⡆⡆⡆⡦⢴⠀⠀⠀⠀⠀⠀⠀⠠⢔⠄⠀⠀⠀⠀⠀⠲⠀⠀⡖⠂⠀⠀⠀⠀⡀⠀⡐⠒⡀⠠⡀
⠀⠀⠀⠀⢀⣇⣀⡇⣀⣇⣸⠀⠀⠀⠀⠀⢀⢔⡕⠈⡄⠀⠀⠀⠀⢴⣶⠄⢰⠷⡆⠀⠀⠀⠀⠱⣠⠟⡛⢇⡀
⠀⠀⠀⠀⠰⠄⠤⠄⠤⡤⢰⠀⠀⠀⠀⠀⠀⠁⡄⡔⠀⠀⠀⠀⠀⠀⢠⠀⢀⣭⣀⠀⠀⠀⠀⡔⢙⡣⢴⡏⠑⡀
⠀⠀⠀⠀⠀⠂⠀⠒⠂⠓⠊⠀⠀⠀⠀⠘⠀⠈⠁⠉⠃⠀⠀⠀⠀⠀⠒⠀⠂⠀⠑⠀⠀⠀⠀⠈⠁⠁⠀⠁⠉

⠀⠀⠀⠀⠀⢠⢢⠀⠀⡔⠢⠀⠀⠀⠀⠀⢀⠄⡀⡒⢄⠀⠀⠀⠀⠒⠒⠒⠒⣒⠲⠀⠀⠀⠀⡖⢲⠀⣖⠒⡆
⠀⠀⠀⠀⠀⠀⠉⡖⠐⡋⠈⠀⠀⠀⠀⠀⠀⠎⠀⠈⡆⠆⠀⠀⠀⠀⠡⡇⡸⠤⢣⠀⠀⠀⠀⡇⢸⠀⠤⠀⡇
⠀⠀⠀⠀⠈⠡⠀⠌⢊⣁⠀⠀⠀⠀⠀⡀⢾⠮⠐⠪⠊⠀⠀⠀⠀⠀⠀⠂⠊⠀⢐⠀⠀⠀⠀⠉⢹⢀⠋⠉⣡
⠀⠀⠀⠀⠠⠔⠒⠨⠍⠒⠈⠀⠀⠀⠐⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠫⠬⠄⠙⠚⠹⠀⠀⠀⠀⠢⠘⠢⠤⠤⠤⠆

⠀⠀⠀⠀⢀⡠⠔⠠⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣒⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢
⠀⠀⠀⠀⠀⢈⠍⠩⠅⡇⠛⠀⠀⠀⠀⠀⢀⢔⢆⡓⠉⠀⠀⠀⠀⢀⡀⠸⡀⢸⠘⡆⠀⠀⠀⡔⠈⠘⠄⢀⣠⠃
⠀⠀⠀⠀⠀⠐⡂⠐⠂⡇⣀⠀⠀⠀⠀⣀⢼⠤⠕⠁⠀⠀⠀⠀⢀⠃⠀⠀⠀⠿⠐⡇⠀⠀⠀⠣⠀⠠⢢⠂⠰⡀
⠀⠀⠀⠀⠠⠬⠤⠤⠤⠇⠲⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠬⠃⠤⠁⠀⠀⠀⠀⠀⠀⠈⠢⠐⠄

⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⣄⠀⠀⠀⠀⠀⠀⡠⠀⣤⠀⠀⠀⠀⢠⠀⠀⠀⠀⣠⡀⡄⠀⠀⠀⢀⠀⡀⠀⡄⠤
⠀⠀⠀⠀⠀⠀⠀⢸⢹⢀⡀⠀⠀⠀⢀⠔⠀⡖⢲⠀⠣⠀⠀⠀⢨⠘⠸⡤⢠⠤⠌⡆⠀⠀⠀⢸⡂⡅⠀⡇⡀
⠀⠀⠀⠀⠀⠐⠒⢨⠰⣀⠀⠀⠀⠀⠈⠠⠄⠧⢼⠠⠔⠁⠀⠀⢸⠀⠘⠄⠔⠰⠆⡇⠀⠀⠀⠯⠤⡭⠬⠥⠭⠆
⠀⠀⠀⠀⠸⠀⠀⠺⠂⠀⠸⠀⠀⠀⠀⠀⠀⠤⠜⠀⠀⠀⠀⠀⠀⠀⠨⠇⠨⠅⠀⠀⠀⠀⠀⠏⠀⠁⠈⠁⠉⠇

⣼⠁
⠸⣆⠈⢂
⠀⢹⣆⠀⠱⡄
⠀⠀⠻⣆⠀⡀⠲⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂
⠀⠀⠈⢻⣦⡀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⣄⣀⣀⣂⣀⣀⣊⣂⠀⠀⢀⡀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠹⣷⣄⠈⠢⢀⠠⠈⠂⠐⠀⠀⠀⠐⠀⠘⠂⠀⠀⠀⠀⠀⢉⡉⠉⠉⠉⠀⠀⠐⠉⡙⠛⠻⡆
⠀⠀⠀⠀⠀⠈⠛⣷⣤⡀⠁⠐⠠⡰⠀⡀⡆⡄⠀⡄⠀⢀⣀⡂⠂⠇⠀⠁⠀⠀⠆⠅⠀⣾⠁⠠⢀⠂⠀⠀⠀⠀⠀⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣤⣄⡡⣤⣠⣤⣠⠠⣆⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣀⣠⡀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠈⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠋⠉⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⢟⡻⢿⣿⣿⣿⣷⡄
⠀⠀⠀⣸⠛⠛⠋⠉⠉⠈⢳⡀⠀⠀⠀⢐⣁⠀⠉⠉⠁⠀⠉⠉⠀⣈⣆⠀⣻⣿⣿⣿⣿⠿⠋⠙⠳⢿⣿⣿⣿⣿⡆
⠀⠀⠀⢭⠀⣤⠀⠀⢠⡄⢈⡇⠀⠀⠀⢸⣿⣿⣿⣷⣤⣤⣤⣾⣿⣿⣿⡄⣽⣿⣿⡿⣧⠀⠀⠀⠀⢐⢿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠈⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⣿⣿⣿⣿⡇⠐⠐⠀⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠛⠿⠿⠛⠈⠉⠘⠻⠟⠛⠁

⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⣤⣤⣤⣤⣤⡀
⠀⠀⢠⣿⡿⠋⠁⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⢰⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⠋⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⢿⣿⠀⠀⠀⠀⠀⢸⠃⠀⠀⠙⠛⠋⠉⠈⠻⣿⡇
⠀⢸⣿⣧⡀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠁⠀⠀⠀⠻⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁
⠀⢸⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠂
⠀⢸⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠉⠉⠉⣀⣤⡀⠀⠈⠉⠉
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣆
⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⡚⠛⠛⠓⠲⠦⣄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⢸⠃⠀⠨⠍⠁⠀⠉⠭⠀⠈⠦
⠀⠀⠀⢻⣿⠟⠉⠁⠈⠛⢿⣿⣇⠀⠀⠀⠀⣿⣷⣦⣄⣀⣠⣴⣿⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠂⡀⠂
⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⢿⣿⣿⣿⣬⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⡆⠀⠐⠂⠀⠠⡧⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⢠⣄⣤⣤⣴⣶⣶⣦⣴⣦⡤⣦⢠⣄⡠⢄⣠⣤⣄⣠⣤⣦⣤⢤⣤⣀⢤⣀⣤⣔⠠⣤⣤⣤⣤⣤⣶⣦⣤⣴⣶⡴⠦⢤⣤
⡿⠉⣰⣿⣿⢟⢿⣿⣷⣛⣿⣿⣿⣿⡿⡛⢻⢿⣿⢿⣿⣿⣾⣯⣷⣾⣿⣿⣷⣿⣟⢿⣿⣿⡷⠿⣯⣴⣾⣿⣿⠿⡿⣿⣿⣿⣿⣿⣩⢴⣏⣩⣭
⣷⡟⢻⣿⠿⣭⣙⠛⠿⣾⣿⡿⣻⣿⣼⢇⡾⣘⣿⣿⣿⣿⡿⠿⠿⠿⠿⠽⠿⣿⣿⣿⣿⣿⠒⣼⣿⣿⣿⣿⣿⣷⣿⣿⣨⣿⣻⡿⢁⣾⣿⣿⣿
⣿⣿⣿⣦⣴⣾⣿⣿⡶⣮⡽⣶⣭⣾⡯⠿⠛⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠾⣿⣿⣿⡟⠿⣿⣿⣟⢿⣿⣿⣿⣿⣿⠿⣿⣿⣯
⠿⣿⣿⣟⣁⡀⠀⢈⠉⠻⣿⡿⠋⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢿⣷⣴⡈⣿⡷⣛⣽⣿⣿⣿⣿⣿⣶⣿⣿
⣿⡿⣹⣿⣽⣿⣿⣶⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣽⣿⣿⣼⣿⣿⣫⣽⣿⣿⣿⣿
⠛⠳⠿⠿⠿⠿⠛⠛⠉⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠋⠁⠀⠀⣠⡄⠀⠀⡈⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠐⡀⠀⠀⠄⠀⠀⣀⣤⣦⣀⣀⣀⣀⣠⣤⡄⠀⣀⠀⡀⠐⠔⠀⠀⡀⠯⡀⠀⢶⠀⠈⠁⠀⠀⠀⠀⣠
⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⡿⠛⠀⠀⠀⣠⣶⣶⣶⣿⢷⣶⣿⠛⣹⣟⠻⣯⣿⡿⠛⢡⣠⣹⣶⣷⣬⣒⡠⠠⠍⢤⣄⠀⠀⠀⠀⠀⠀⣀⣤⡶⢟
⠙⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢠⣴⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣖⣾⣷⣶⣿⣿⠿⡟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⡟⡡⠎⣩
⠇⣿⣿⡿⣿⣿⣬⣿⠿⣿⣄⠀⠀⠀⠀⢄⣽⣷⣿⣿⣻⣍⡻⠏⣹⡟⠻⡿⣿⣿⠟⣷⣾⣿⣿⣾⣿⣿⣿⣷⡝⣿⣿⠿⣿⣿⣿⣿⣿⣷⣶⣿⡗
⣾⣿⣿⣧⣶⣶⣿⣷⡺⣿⣿⡿⣶⣦⣀⣀⣸⣷⣿⡿⣿⣿⣷⣦⡙⣟⣿⣷⠾⢁⡾⣛⣻⣿⣿⣄⣛⠻⣿⡟⣿⣿⣿⣾⢿⣿⣾⣿⠿⣿⡟⢻⣿
⣿⣿⣏⣿⡿⣟⢛⣷⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⣊⣷⣽⣧⣤⣭⣭⣿⣟⣥⣿⣿⣏⠁⠀⣀⣤⣿⣿⣷⠼⣿⣿⣿⣋⠁⠀⠉⣻⡾⠁⡉⣡⣿⣿

⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⣄⣀⣀⠀⠀⠀⡀⠀⠀⠀⡀⠀⣠⣤⣤⡄⠀⠀⢠⡤⢤⡀⠀⠀⣀⡤⣤⠀⠠⣄⣀⣀⠀⢀⣀⣀⣀⣀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⡇⠉⠙⢆⠀⠀⢸⠀⠀⠀⠀⣇⠀⢀⡞⠀⠀⡇⠀⠀⠀⠀⠀⣟⣀⡠⠇⠀⠸⣁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠳⣤⠞⠁
⠀⠀⠀⠀⠀⢸⠃⠀⠀⣸⠀⠀⢸⠀⠀⠀⠀⢹⢀⡞⠀⠀⢸⠋⠓⠒⠀⠀⢀⡟⢆⠀⠀⠀⠀⠈⠙⣦⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⢀⡰⠃⠀⠀⢸⠀⠀⠀⠀⠘⡟⠀⠀⠀⣾⣀⣀⣀⠀⠀⠸⠃⠀⠱⣄⠀⠠⠤⠖⠁⠀⠤⠼⠤⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠚⠉⠀⠀⠀⠉⠉⠉⠉



⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣷
⠀⠀⠀⣿⣿⣶⡀⠀⠀⠀⠀⢀⠀⠀⠀⣷⣿⣿⡿⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣼⠻⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⡿
⠀⠀⢾⣿⣿⣿⠃⠀⢠⣶⣿⢿⣇⡀⠀⠘⣿⣿⣿⡟⠀⠀⠰⣾⣿⣷⣆⡀⠀⠘⣯⣀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠁⢙⡿⠀⠀⢀⣀⣶⣴⣴⡆
⠀⠀⢘⡿⢛⠟⣆⠀⠀⠙⢢⣤⠽⢥⠀⢀⣿⡿⠿⣤⠀⠀⠀⣿⣿⣿⠋⠀⠀⢸⡭⠤⠤⠼⡄⠰⣾⣿⣷⡖⠀⠀⠀⠀⢠⣟⣶⣛⣳⣀⠀⠀⢻⣿⣿⣿⣡⡆
⠀⠀⡞⡰⠋⢀⡿⠀⠀⠀⠗⠒⠉⢹⠀⢸⠐⠀⠂⢸⡀⠀⠀⣿⣿⣿⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠹⣿⣿⣿⠟⠀⠀⢠⠋⠁⠉⠉⠉⠉⡆⠀⠈⣿⣿⣿⣿⠁
⠀⠀⡟⢁⡴⠋⡟⠀⠀⠀⠱⠀⠀⢸⠀⢸⡀⠀⠀⠀⢧⠀⠀⣿⣽⡏⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⢿⣿⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⡠⠃⠀⠀⣸⡿⢿⢻⢻
⠀⠀⣧⠊⠀⢠⡇⠀⠀⠀⡆⠀⠀⣼⠀⠈⡇⠀⠠⠀⣺⠀⠀⣿⣿⣿⠀⠀⠀⠈⡆⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⢀⡜⠒⠒⠒⠙⣄⠀⠀⠀⡇⡇⠸⢸⢸
⠀⠀⡇⢀⠔⠉⡇⠀⠀⠀⡇⠀⠀⡇⠀⢀⠇⠀⠀⠀⢸⠀⠀⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⣾⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡄⠀⠀⡇⡇⡆⣼⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠛⣁⣴⠿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⢀⠀⠀⡠⠘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠾⡫⠋⠁⠐
⠀⠀⠀⠀⠀⠀⠸⣦⣀⣀⣒⡀⠀⠐⠛⠠⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⣦⣶⣦⠦⡀
⠀⠀⠀⠀⠀⠀⢀⠏⠉⠾⠉⠻⠝⡏⣩⣗⣜⢩⠗⠀⠀⠀⠀⠀⠀⠀⠙⡛⠉⠸⠛⠈⠙⠏
⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠀⠀⢡⠎⠀⠀⠁⠊⠀⠀⠀⠀⠀⢀⡶⠞⠃⣠⣾⠿⠋⣰⡾⠓⠐
⠀⠀⠀⠀⠀⠁⠤⢀⠀⠀⠐⠒⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠨⣤⡶⠟⠋⣀⣴⠾⠋⣠⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠠⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠶⠟⠋⣠⠴⠿⠫⠔⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣪⣭⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐
⠀⠀⠀⠀⠀⠀⠠⠞⣁⠀⡉⠉⣀⠬⠉⠃⠀⠀⠀⠀⠀⠀⡠⢀⠔⠀⠀⠀⠀⠀⠐⢄⠀⠀⠙⢷⣆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⢁⣀⠀⡆⠀⠀⠀⠀⠀⠀⢘⠠⠩⡀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⢐⡏⠃⢀⠀⠈⠠⣿⡇⠀⠀⠀⠀⠀⠈⠎⣓⠊⠒⣤⢄⡀⡀⢤⣊⡔⠁⣧⢤⡀⣀⡀⣀⡆
⠀⠀⠀⠀⠀⠀⢸⣬⡋⠅⣸⡿⠗⣀⢴⠈⠂⠤⠄⠒⠀⠀⡁⠌⠓⢒⠉⠁⠄⣀⡤⢋⣁⠀⠀⠉⣁⣙⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢬⡓⣶⢒⠭⠒⠋⠀⡄⠀⠀⢁⠀⠐⢘⠀⡀⠀⠠⠶⠘⠷⠢⠤⠊⠀⠀⠊⡀⢀⡑⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠁⠀⠁⠀⠐⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠀⠀⠀⡀⠀⡠⠀⠀⠀⠄⡀⠄⠒⠀⠉⠀⠉⠉⠀⠂⠀⠢⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⡀⠒⠰⠉⠘⢀⠉⣂⠈⠄⠀⠀⡈⠑⡄⠀⠀⠀⠰⠀⢠⠄⠀⠀⠐⠀⠀⡜⠛⡂⢎
⠀⠀⠀⠀⠀⠀⢀⡈⠣⠄⠸⢡⣾⡆⠈⠡⠢⠀⡄⠸⠀⠀⠠⠀⠅⣀⡀⠤⠖⡀⠘⠀⠀⠀⠔⠀⠄⢰⠀⡠⠈
⠀⠀⠀⠀⠀⠦⠤⠥⣤⣤⣤⠴⠶⠒⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠁⠄⠘⠃⠂⠀⠈⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣤⣤⣤⣤⡶⠶⠶⠾⣶⠿⠿⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠿⠛⠉⠉⠑⠒⠀⠀⠀⠀⠀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣤⣶⣇⣀⣀⣰⣶⣄⣀⠀⠀⠀⠉⠻⣿⣷
⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⢨⣿⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣧⣠⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣯⡓⠒⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⡾⠁⢀⡀⠖⣹⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⣿⣿⠞⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠐⠛⠿⠿⣇⠋⠉⠙⠿⠛⠁⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣾⣿⣿⣿⣿⣿⡋⢙⠿⣿⣿⠿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡯⠔⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣥⠀⠀⠹⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣦⣶⣶⣤⣴⣾⣿⣿⠀⠀⠀⠀⠈⡟⠛⠻⠿⠷⠦⠘⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡷⡶⣿⣿⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠛⣿⡟⣱⡃⢻⠷⠄⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠛⠁⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⢿⣯⣿⣟⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠋⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡄⣤⡄⣤⢤⡀⣤⢀⡤⠄⢠⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠃⠿⠅⠻⠔⠃⠿⠘⠦⠆⠛⠛⠸⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⢀⣤⡄⣴⡆⣤⣤⢀⣤⠀⣤⣤⢠⠴⠄⣄⣠⢠⣤⢠⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠊⠓⠂⠚⠛⠛⠒⠘⠙⠃⠋⠓⠘⠒⠂⠃⠙⠘⠓⠘⠋⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢤⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡁⠶⢀⣄⣹⢷⡄⣈⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⢌⣿⡤⣴⣵⢋⣁⣰⢟⣤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡘⠿⢉⣉⣀⡡⣼⣿⠋⢿⣌⢠⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠈⢗⢤⡸⠟⢹⡿⢠⡅⠀⢀⠴⡻⠁⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠑⠬⣑⣒⣒⣒⣒⣩⠕⠊⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣱⢄⣀⡀⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⣼⣯⡿⡼⣯⢯⡿⣽⢧⡖⡆⠀⠀⡇⣀⣼⡀⠀⢀⠞⡴⠂⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢹⡏⣽⢹⠋⡏⢹⠉⡏⡇⡇⠀⠀⢇⣓⣶⣃⠰⣁⣤⣟⠉⠉⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⣹⢸⠍⡇⢸⠀⡇⡇⡇⠀⠀⠸⡘⠥⣤⡙⠲⣉⢀⣝⡩⠈⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠉⣽⢸⠄⡇⢸⠒⡇⡇⡇⠀⠀⢀⢵⠴⠃⠙⣆⡈⢉⣇⡠⠤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢾⣼⣆⣿⣸⣆⣇⣾⣴⣧⡷⢧⣄⡰⠋⠀⢹⣭⠏⠀⠉⢹⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠈⠉⠀⠀⠀⠘⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠓⠚⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢀⣠⡰⠊⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠈
⠀⠀⠀⠀⠀⠀⡀⢀⡠⠠⠄⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠄
⠀⡀⠀⠀⠈⠉⠠⠤⠂⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠
⠀⢁⠀⡀⠀⠀⡀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⠀⠈⠀⢠⡀⠤⠄⠄
⠀⠈⠀⠂⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⡀⠀⠀⠀⠀⣠⡆⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⢀⢀⠀⠀⠀⢠⠠⠀⠀⠀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠈⠁⠉
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁
⠀⠀⠁⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠈⣠⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⢒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠴
⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⢁⠐⠒⣒⢂⠉⢱⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠠⠁⠐⢀
⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠱⠐⠐⠁⠀⠀⠀⠚⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⢂⡐⠐⠊⢠
⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢀⠑⠠⠤⠤⠤⠒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠶⠀⠰⠂⠀⠀⠀⣴⣿⣿⣿⡿⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠉⠀⢀⠘⣿⣇⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⠛⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣄⡀⣿⣿⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢫⣴⡤⡼⣿⠂⠀⢀⣤⣤⣤⣤⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⢸⣿⣿⣿⣿⡀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠖⠀⠉⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⡿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⣿⣶⣿⣦⣶⠘⠛⠀⠹⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢰⣿⣿⡟⠁⠀⠀⠣⠀⠀⠀⠉⠉⠙⣿⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⠟⠉⠉⠙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⣿⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣦⡀⠀⠀⠂⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣧⡐⠂⠀⠀⠀⠀⠀⠴⠀⠘⠃⣿⣿⣟⣉⡉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠁⠀⠘⠋
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠟⠃⠸⠿⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠄
⠀⠀⠀⠀⠀⢸⣿⡏⠙⠛⠛⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⡤⣤⣴⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⣿⣿⣿⣿⠏⠀⠀⢠⣾⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠙⣿⣦⣄⠀⠀⠀⠿⠋⠁⠀⠈⠀⠀⠀⢠⣾⣿⣿⡿⠛⠛⢿⣿⡏⠛⠃⠀⠀⠀⣿⣿⣿⣿⡿⠿⠿⠿⡿⠛⠉⠛⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⣿⣿⡏⠛⢁⠀⠀⢀⠁⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠁⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⣿⠻⡄⠀⢀⡄⢻⠃⠀⠀⠀⠀⠀⠸⣿⠃⠀⠈⠁⠀⣽⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠰⠆⠀⠉⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⠋⢀⡀⠀⢀⡀⠀⠀⠁⠀⠀⢀⣤⣾⣿⠀⠀⢀⣠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠰⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⢋⣭⡝⣿⣦⠀⠀⠀⠀⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠿⣿⢃⣾⡿⢡⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⡇⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡅⢿⣷⣥⣾⡿⣡⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⡿⣃⣬⣍⠻⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣎⢻⣿⡿⣡⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⢰⣿⣿⣿⣷⠘⠻⠿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣭⣵⣿⣿⣿⠟⣡⣤⣀⠀⠀⣿⣿⣿⣦⡛⠿⠟⠁⠀⠀⠀⠈⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣙⣛⣋⣭⣴⣾⣿⣿⣿⣿⣶⣝⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⣫⣥⣤⣭⡻⣿⣿⣷⡙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣷⢸⣿⣿⣿⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⣡⣦⡻⣿⣿⡿⠿⠿⠟⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣡⣾⣿⣿⣿⡎⣡⣾⣿⡷⢦⡹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣭⣭⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⠡⣿⡿⢋⣴⣿⡇⣹⣿⣿⡇⣀⣀⣀⣀⣠⠀⣠⣾⣿⣿⢡⡎⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡙⢿⣿⣿⠟⣡⡹⢶⣿⣿⠟⣡⣿⣿⡿⠐⠛⠛⠛⠛⣡⣾⣿⣿⣿⣿⣷⣶⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣶⣶⣿⣿⣿⣶⣶⣶⣾⣿⣿⠟⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠠⠤⡄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⣄⠀⠀⢀⠠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠀⠀⡜⠀⠀⠚⣇⠀⢠⠀⠀⠂⠀⠘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡇⠀⣾⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠘⠉⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠃⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠸⠋⠛⠇⠀⠈⠀⢀⠀⠀⢀⡈⡈⢉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠈⠻⠋⠉⠹⠋
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠠⠟⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠘⠀⠘⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⡴⠶⣆⠀⠀⠄⠀⠀⠀⠀⠠⠒⠦⠀⠀⠀⢀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠐⣢
⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⡁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂
⠀⠀⣰⡾⠿⣦⠀⠀⠀⠀⠀⠉⠀⠀⣀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⣄
⠀⠀⠻⠀⠀⠸⠀⢀⡀⠀⠀⠀⠀⡂⠀⠄⠄⠀⠠⠀⠀⠆⠀⠰⠈⠁⠁⢠⠀⢀⠀⠈⠀⠀⠿⠛⠻⠀⠀⣰⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠁⠀⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠃⠽
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠈⠀⠀⠀⠈⠀⠂⠀⠀⠞⠙⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⢠⡿⠉⠻⣦⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡆⠀⠸⠧⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠉
⠀⠀⠰⠂⠀⠄⠀⠀⡄⠦⠀⠀⠀⠈⠀⠀⠀⠀⢰⢥⢈⣆⠀⠀⠈⠉⠉⠂⠀⠀⠀⠀⢀⠀⠀⢰⡄
⠀⠀⣸⠁⠀⣆⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠜⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠃
⠀⠀⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠐⠂⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⡀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠣⠈⠁⠁⠀⠀⠘⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠄⣀⠤⠶⠒⠀⠤⡀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠘⠁⠀⠀⠀⠀⠀⠢⢀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢶⣦⣄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠈⠻⣿⣿⢦⡀⠀⠀⠀⠀⠀⠂⢠⠚⠁⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠀⣿⠿⢿⠳⢄⠀⠀⣸⣿⣷⡄⠀⣠⠟⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠚⠁⣀⣠⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⢃⡄⣷⠚⢄⣀⣀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡀⠀⠔⠉⠀⢈⠀⠀⢲⣦⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠛⠔⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠃⠀⠀⢀⠂⠀⠉⠁⠙⠿⠷⣤⡄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠠⠆⢀⡀⠀⠀⠀⠀⣬⡗⠠⠤⠤⠄⠒⠉⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢠⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢰⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⢀⣡⣄⢠⡤⠎⠁⠀⢣⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢈⠀⠀⠀⠀⢠⡂⠀⠁⠀⠀⠀⠀⠀⠀⠙⢦⣸⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠠⢚⠀⠀⠢⠄⠀⢠⣿⠁⡆⠘⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⢩⡍⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱
⠀⠀⠀⠀⠀⠀⡐⠀⠸⠀⠀⠀⠀⠀⠈⠉⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠑⣄⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡴⠀⠀⠀⡸⠀⠀⡄
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠉⠀⠈⠒⠂⣴⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣴⡾⠃⠀⠀⡇
⠀⠀⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⣤⡀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠰⠃⠀⢸⣿⠁⠀⠀⠀⢹
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢾⠁⠀⢀⡽⢰⠇⠀⠀⠀⠀⢸⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢸⡇
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⢈⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⡇
⠀⠀⣆⠀⠀⠀⠀⠠⠔⠊⣡⢀⡄⣸⠔⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⠀⠀⡇⡄
⠀⠀⠀⠙⠢⠤⠴⠶⣶⠾⠷⠛⠉⠀⠀⠀⣿⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠁⢁⠀⠀⠀⠀⠀⢠⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⠀⠀⠀⠀⠈⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠀⠀⠀⠐⠋⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠑
⡿⢿⠿⠿⡿⣟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣻⣻⣿⣛⣿⣿⣟⣿⣿

⠀⠀⠀⡀⠄⢀⠆⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⢀⡠⠔⡠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠯
⠀⢀⢢⢨⣰⠁⢐⣤⡆⠀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⠀⢰⠶⠂⠀⠀⡰⠉⠴⡀⢁⠸⠆⠀⠀⠀⠀⣤⠤⠤⠤⠾⠿⢦⡄
⠀⠸⠈⠉⠉⠉⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⢰⡆⠀⠀⠀⠀⠐⠿⣾⢉⡀⠒⢰⠀⠀⠀⠀⠣⠀⠀⢀⡀⠤⠀⡁
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣤⠁⠀⢀⡄⠄⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠉⡄⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⢡⡖⠀⠀⠀⠋⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⢣⠀⠀⠀⠁⠀⠀⣀⢀⣀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⢠⠖⠑⠊⢤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢨⠋⠁⠀⠈⠀⠄⠀⠀⠀⠀⠀⣰⠈⢷⠀⢠⣠⠀⠀⠀⠀⡄⠲⡀⢀⡀⠀⡀⠀⠄⢀⠸⠙⠀⠀⠀⠀⠠⠈⡃
⠀⠀⠔⠁⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡏⣘⢦⠀⠀⠀⠈⠢⡑⠄⢠⠀⠀⠀⢂⠀⠁⠂⠀⠀⡀⢀⠀⠀⢁
⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⢄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠈⡿⠔⠀⠀⠀⠀⠀⠐⠀⠄⠂⠀⠠⠔⠁⠀⠀⠸⡀⢀⠀⠀⠏
⠀⠀⠀⠀⠈⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⢀⠶⠁⠈⣀⣀⣀⠀⠉⠀⠀⠀⠈⣲⣷⡀⠘⣶⢧⠖⠀⠀⠀⠀⠀⠀⢈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⡀
⠠⠀⠤⠘⠉⡽⢏⠉⠐⠀⠀⠀⠀⢹⠀⠁⢸⡙⠳⠀⠀⠀⠀⠀⡠⠉⠉⠀⠁⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⡠⠗⠀⠀⠐⡀
⠀⠀⠀⠀⠉⢰⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠑⠚⢻⠟⠉
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⠈⡘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⠖⡄⠀⠀⠀⠀⠀⢠⡴⡆⠴⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠴⡀⠀⠀⠀⠀⢌⠄⡝⠁⠉⠀⠀⠀⠀⢠⡇⠂⠀⠀⠀⠀⠹⡀⠀⠀⠀⡠⠂⠉⠀⠀⠀⢀⠀⠆⠀⠀⡠⠚⠀⠀⠀⡌⠃
⠀⣀⠀⠐⠒⠛⠛⠛⠓⢲⠃⠀⠀⢀⢈⠂⢜⠖⢀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠄⠀⠀⠀⠀⠀⠨⠀⡁⠀⠀⢁⠄⠒⠀⠘⠢⣄⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢃⡠⠌⡠⠂⠀⠀⠀⠀⠀⠘⡆⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈


⢀⠉⠃⣶⣴⣶⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣄⣀⡀
⠈⠀⠀⠹⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⢰⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡟⠛⠁⠀⠀⠀⠠⠂⠀⠀⠀⠀⣀
⠀⠀⢾⠀⠀⡇⠀⢸⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣉⣷
⠀⠀⠘⠀⠀⡇⠀⠸⠀⠀⣠⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠄⠀⠀⠀⢁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠀⠀⠀⠀⢀⠐⠤⠀⠠⠌⠁
⠀⠀⠀⠂⠀⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠁⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠐⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡄⢥

⠀⠀⢀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⢀⠀⠀⠀⠀⣾⣿⠄⠀⠀⡀⡀⠀⠀⢰⣿⡧⠀⠀⢀⢀⠀⠀⠠⣿⣿⠄
⢀⣤⣤⣤⡀⣠⣼⣿⣤⡀⣠⣤⣤⣄⢀⣤⣿⣧⡄⢀⣤⣤⣄⡀⣠⣼⣧⣤⠀⣠⣤⣤⡀⢀⣤⣿⣦⡀⣀⣤⣤⣄⠀⣤⣾⣷⣄⢀⣤⣤⣤
⠉⣹⣿⡏⠙⠛⠛⠛⠛⠋⢉⣿⣿⠉⠉⠙⠛⠛⠛⠉⣽⣿⡏⠉⠛⠛⠛⠙⠋⢩⣿⣯⠉⠉⠙⠛⠛⠋⠉⣽⣿⡍⠙⠛⠛⠛⠛⠋⢹⣿⣿
⠀⣙⣿⣃⠀⠀⣀⣀⠀⠀⢈⣻⣟⡀⠀⢀⣐⣀⠀⠀⣙⣿⣁⠀⠀⣀⣀⠀⠀⣈⣻⣋⡀⠀⢀⣀⡀⠀⢀⣙⣟⣁⠀⢀⣀⣀⠀⠀⣈⣿⣏
⠾⠿⠿⠿⠷⠾⣿⣿⠿⠶⠿⠿⠿⠿⠾⢿⣿⡿⠷⠾⠿⠿⠿⠷⠿⣿⣿⠿⠾⠿⠿⠿⠿⠾⢿⣿⡿⠷⠿⠿⠿⠿⠷⠿⣿⣿⠿⠾⠿⠿⠿
⠀⠀⠤⠀⠀⠀⢿⡿⠃⠀⠀⠠⠀⠀⠀⠸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠿⡿⠃⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⡿
⣴⣾⣿⣶⣤⣶⣿⣿⣷⣤⣶⣿⣷⣦⣴⣾⣿⣿⣦⣴⣶⣿⣶⣤⣾⣿⣿⣷⣤⣶⣶⣷⣦⣴⣿⣿⣿⣦⣴⣾⣿⣶⣤⣾⣿⣿⣷⣤⣶⣾⣷
⠀⢾⣿⡇⠀⠀⢀⠀⠀⠀⠰⣿⣿⠀⠀⠀⣀⠀⠀⠀⢾⣿⡆⠀⠀⠀⡀⠀⠀⢰⣿⣷⠀⠀⠀⣀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⣷
⣠⣴⣿⣦⡀⣠⣤⣦⣄⢀⣤⣾⣧⣄⢀⣤⣤⣤⡀⣠⣴⣿⣦⡀⣠⣤⣤⣄⢀⣤⣾⣧⣄⢀⣤⣤⣤⡀⣠⣶⣿⣤⡀⣠⣤⣦⣄⢀⣴⣿⣧
⠉⠙⠛⠉⠉⠉⣿⣿⡉⠉⠉⠙⠋⠉⠉⢹⣿⣏⠉⠉⠉⠛⠉⠉⠉⣿⣿⡉⠉⠉⠛⠋⠉⠉⢹⣿⣏⠉⠉⠙⠛⠉⠉⠉⣿⣿⠉⠉⠉⠛⠋
⠀⣀⣀⡀⠀⢀⣹⣟⣁⠀⢀⣁⣀⠀⠀⣈⣿⣋⠀⠀⣀⣈⡀⠀⢀⣹⣟⡀⠀⢀⣀⣀⠀⠀⣈⣿⣃⠀⠀⣀⣀⡀⠀⢀⣻⣟⡀⠀⢀⣀⣀
⠺⢻⣿⡟⠳⠿⠿⠿⠿⠗⠛⣿⣿⠓⠾⠿⠿⠿⠷⠚⢻⣿⡛⠲⠿⠿⠿⠿⠖⢛⣿⣟⠓⠾⠿⠿⠿⠷⠚⣿⣿⠟⠲⠿⠿⠿⠿⠖⢻⣿⡟
⠀⠻⣿⠇⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⠀⠀⠻⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠠⠀⠀⠀⠻⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⠟
⣴⣿⣿⣿⣦⣴⣾⣿⣶⣤⣾⣿⣿⣷⣤⣾⣿⣷⣦⣴⣿⣿⣷⣦⣴⣿⣿⣶⣴⣾⣿⣿⣶⣴⣾⣿⣷⣦⣶⣿⣿⣷⣤⣶⣿⣿⣶⣴⣿⣿⣿
⠀⠀⢀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⠀⢸⣿⡷⠀⠀⠀⢀⠀⠀⠀⣿⣿⠄⠀⠀⢀⠀⠀⠀⢸⣿⡧⠀⠀⠀⡀⠀⠀⠀⣿⣿⠀⠀⠀⢀
⣠⣤⣶⣤⣀⣤⣾⣷⣦⡀⣤⣴⣤⣄⣠⣴⣿⣶⣄⢠⣤⣦⣤⣀⣤⣾⣷⣤⣀⣤⣴⣤⣄⣠⣴⣿⣦⣄⣠⣤⣦⣤⣀⣤⣾⣷⣤⣀⣤⣴⣦
⠉⣽⣿⡏⠉⠉⠉⠉⠉⠉⢩⣿⣿⠉⠉⠉⠉⠉⠉⠉⣽⣿⡍⠉⠉⠉⠉⠉⠉⢩⣿⣯⠉⠉⠉⠉⠉⠉⠉⣽⣿⡍⠉⠉⠉⠉⠉⠉⢹⣿⣯
⢀⣹⣿⣅⠀⢀⣈⣈⡀⠀⣈⣿⣏⡀⠀⣀⣁⣀⠀⢀⣹⣿⣁⠀⢀⣀⣀⡀⠀⣈⣿⣏⡀⠀⣀⣁⣀⠀⢀⣹⣿⣁⠀⢀⣀⣈⡀⠀⣈⣿⣏
⣿⠿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿
⣯⣀⣼⣧⣽⣭⣭⣭⣿⣼⣭⣭⣽⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣽⣽⣿⣭⣭