Ingredients Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢴⡦⣸⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠼⣇⣠⣶⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢤⣤⠘⢶⠛⠀⠀⠀⠀⠀⢀⣴⣶⠿⢿⠻⠻⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⢾⣶⣖⣼⣧⡸⢷⠀⠀⠀⠀⣰⡵⠋⠀⣬⢱⣤⡄⣸⠻⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠈⠢⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⠀⠀⠀⣯⢃⠔⠚⣻⢆⡈⣿⠃⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⡅⠀⠈⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠁⢹⣧⣾⡿⡮⢱⣷⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠐⠒⠨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣽⣝⣳⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣀⡀⠀⠀⠀⠘⠤⠀⠈⠑⡄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠛⠛⠛⠉⠂
⠀⠀⠀⠀⠀⠀⢸⡿⡊⢹⣧⠀⠀⠀⠀⠀⠀⡴⠖⠁⠀⣀⣲⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣇⣧⠘⣿⠂⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢹⢹⣇⢸⡖⠀⠀⠀⠀⠀⠀⠀⠣⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠⡤⠤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣻⡂⢻⣠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡠⠄⣀⠀⠀⠘⠸⠾⠀⢀⣐⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⠳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⠳⣽⣄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠚⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠉⠳⠭⣰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠛⠓⣢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡒⠶⡂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣅⡈⡩⠁⠀⣇
⠀⠀⠀⠀⠀⠀⢠⠄⠋⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⢀⠈⡎⠀⠀⠀⠈⠮⣀⠄⠀⠀⠀⠀⠀⠒⣶⡦⢐⠘⠃⡈⠀⣸⡿⣠
⠀⠀⠀⠀⠀⠀⡏⠀⡠⠂⠀⠀⠀⠈⠑⢜⠇⠀⠀⠀⠀⠄⠄⠈⠀⠀⠀⠀⠀⠀⠀⠫⠧⠀⠀⠀⢀⣰⡇⡈⡍⠛⠈⢡⡼⠋⣠⠎
⠀⠀⠀⠀⠀⢘⡇⡌⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡴⠀⠀⠀⠈⠓⠠⠤⢤⠴⠿⠯⠖⠋⠁
⠀⠀⠀⠀⠀⠈⠛⣇⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠈⢿⢆⢀⠀⠀⠀⠀⠀⢀⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠜⢿⡂⠀⠐⠒⡩⠞⠋⠀⠀⠀⠀⠀⠀⠈⠑⠉⣂⠀⠠⠔⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠉⠀⠒⠠⠤⣀⡀⠀⠀⣠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⡙⠀⠀⢘⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⢀⢀⠄⣀⡀⠀⠀⠀⠀⠁⠀⠀⣀⣠⠷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⣀⡤⢤
⠀⠀⠀⠀⣷⠀⠀⠠⠂⠀⢼⡃⠀⠀⠀⠀⠀⡜⣧⠀⠈⠉⠉⠉⠉⠉⠉⠩⣿⡏⠸⠀⠀⠀⠀⡀⣀⣀⠈⢡⠀⠀⠈⠀⠀⣰⠟
⠀⠀⠤⠚⠁⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢡⢹⣄⠀⠀⠀⠀⠀⠀⢀⣾⡟⢡⠃⠀⠀⠀⢠⡏⠀⠈⠉⢸⠀⠀⠀⠠⠰⣯⡀
⠀⠀⠀⠀⠀⠀⣧⠀⠁⠈⡟⠁⠀⠀⠀⠀⠀⠀⠣⣙⢆⠀⠀⠀⠀⠀⢼⠟⡠⠃⠀⠀⠀⠀⢀⢇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⠃⠀⠀⠀⢰⣿⡏⡆⠀⠀⠀⠀⠀⠀⠊⢢⠀⠀⣸⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣸⠀⠀⠀⠀⠀⢵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠄⠀⠀⠀⠠⢾⠟

⠀⠀⠀⠀⠀⠄⢠⣶⡒⠂⠀⣀⠖⠒⠂⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠇⣽⣂
⠀⠀⠂⠀⠀⣰⠟⠁⠀⠀⡸⠃⠀⠀⠰⠋⠀⠀⢸⣖⠄⠀⠀⠀⠀⡴⠊⠉⠀⠀⠀⠀⠀⠉⠃⠠
⠸⣿⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈
⠀⠉⠙⠒⠂⠒⠀⠀⠀⠀⠰⠒⠀⠶⠶⠦⣶⡶⠿⠟⠋⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠼⣇⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⣠⣄⣠⡀⠀⠀⢀⡀⠂⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤
⠀⠀⠸⣆⠁⠠⠃⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣶⣿⡂⠀⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠘⠃⠀⠀⠀⢰⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢸⡭⢽⡗⠒⠒⠂⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡗⠐⠒⠀⠀⠀⠀⣰⣟⣻⣿⣿⣳⡄⠀⠀⠀⣠⣄⠀⢀⣤⡀
⠀⠀⠀⠀⠀⣄⢀⢠⠀⠀⢀⡴⢳⡄⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢫⣿⠿⣧⡿⢿⠇⠀⠀⠀⠛⠛⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⣧⠀⠀⠀⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢻⡀
⠀⠀⠀⠰⠶⠶⠶⠖⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠏⡳⠿⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⢿⣿⣿⡿⠰⠁⠀⠀⠀⠀⢠⣀⣤⣀⣤⣀⣤⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠻⠆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠛⠉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣿⣿⣿⣿⢀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠛⠒⠿⠿⠿⠿⠿⠿⠿⠗⠛⠓
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⡄⠀⠀⠀⢀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⢠⣤⣤⡀⣀⣀⣀⣀⣀⣠⣤⡀⠀⠀⠀⢸⣿⣿⡇⠸⠿⠿⠿⠀⠀⠀⠀⣿⣷⣶⣦⣤⣶⣶⡆⠀⠀⠀⠀⢠⡶⡄
⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⡿⠀⢿⡀
⠀⠀⠘⠟⠿⠃⠻⠟⠻⠛⠟⠛⠿⠃⠀⠀⠀⠘⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠻⣺⡷⠲⠦⣄⠀⠀⣴⠞⣉⡀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡶⠻⠋⠁⠀⠀⠈⣧⠀⢷⣻⣭⣽⣳⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢈⡿⠁⢸⡟⠋⣠⠴⠚⠛⠛⠛⠓⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⢧⠀⡀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠓⠒⠛⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⠛⢛⠲⣌⠛⠦⣤⣤⡤⠖⠋⠀⢀⣠⣤⠶⠶⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⠐⡀⠁⢸⡆⠀⠀⠀⢀⣀⠀⣴⠛⠁⠀⠀⠀⢹⡆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠞⠀⠀⠀⢀⣿⣽⠀⢿⡀⠀⠀⠀⣀⡼⠃⢸⡇⠀⠀⠀⠀⠀⢀⣠⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢺⠟⠟⠀⠀⢀⣰⠏⢀⢸⠇⠈⠳⢦⣴⢾⢿⠁⠀⣼⠁⠀⠀⠀⣠⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠶⠒⠚⠋⠡⣐⡵⠋⠀⠀⠀⠀⢾⣤⡼⠇⢸⡃⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣲⣶⣶⠿⠭⠶⠶⠶⠶⠶⠶⠶⠶⢶⣦⡼⢋⣿⣾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠉⠁⠀⠀⢀⣀⣀⣠⠴⠛⣧⠀⠀⠐⣏⣉⡀⢻⡅⠀⠉⠙⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠐⠀⠀⠺⣥⡉⣀⣀⣸⠏⠀⠀⠀⠈⠙⠷⠾⠃⠀⠀⠀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠉⠛⠲⠶⠭⣤⣬⣉⣙⣉⣁⣀⣀⣀⣈⣁⣠⣤⡤⠤⠶⠒⠋⠉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠶⠷⠼⠾⠶⠶⠛⠛⠉⠁

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

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

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

⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠒⠂⠉⠉⢻⡉⠉⠁⠒⠢⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⣀⣄
⠀⠀⠀⠀⣯⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⣀⣴⠤⠶⠿⢶⡿⠼⢷⣤⣤⣤⣀⡀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⢤⢽⡋
⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⢁⢀⣴⣾⣿⠏⡰⣾⡿⢀⣴⡑⣶⣶⣼⣷⣼⠟⢉⠛⠦⣄⡀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⣐⣾⠿⠛⣼⣿⢠⣄⣤⠀⣈⠛⠃⣼⠋⠛⠁⡸⡀⠀⠀⠐⢈⢿⣦⠰⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⢀⢒⣼⢙⣄⠿⠁⠺⠿⢷⣼⣅⢀⣜⣘⡦⢿⣄⠀⠀⡘⠰⢣⣷⣆⠈⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢠⣿⡟⠂⣟⣯⣬⣿⡆⢿⡷⡶⢶⣾⣏⣥⣿⠀⠙⢿⣧⣾⠛⠻⢦⣤⡶⢿⣥⡙⣦⠀⠉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢐⠋⠀⢷⣝⣻⣴⠿⣸⣘⣿⠠⠀⠀⠰⠄⢀⣽⣾⣂⣽⣮⢻⡧⢤⣴⣯⣽⣿⡿⠟⣙⣃⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⣭⡄⠻⢧⣹⣮⣹⡬⢷⣟⣿⣿⠚⣉⠁⠲⢻⠏⠉⢹⣿⣷⢼⡿⢛⡿⢿⣿⣿⠁⠀⣤⢤⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢸⠿⡁⠀⠀⠀⠀⠀⠚⢿⠿⣿⡀⠀⠀⠀⠘⣻⡆⠑⢶⣯⡿⠣⢿⡏⠀⢧⡸⣧⠈⠀⠀⣸⡏⠀⠐⡄
⢰⡿⣧⡄⠀⠀⠀⠀⡇⠀⠀⠠⣋⣁⣀⣀⡀⠀⠀⠉⣴⣿⡃⠀⢀⡀⠀⢻⣿⠛⡻⣯⣀⣀⣈⣿⣠⠜⣓⢿⡄⢀⣀⣴⣷⠂⢀⡁
⣮⡆⣿⠇⠀⠀⠀⠀⠓⠀⠡⡦⠯⣿⠋⡍⠍⢮⡷⣿⠚⠈⠛⠶⢻⣦⣴⠖⣿⣶⣎⣻⠁⢈⠻⣿⡟⠋⢫⣤⣍⠿⣶⡿⣾⡗⠈⡇
⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠨⠀⠆⢹⣤⠇⠃⠀⠁⢾⡶⢦⣤⠔⣛⣓⣞⣩⡿⠑⡛⠋⢿⣭⡼⡏⠰⣦⡈⠛⠡⣦⢸⣷⣌⠃⠀⠇
⠹⣇⣻⠀⠀⠀⠀⠀⠘⠀⠀⢀⣶⣮⣾⣷⣀⡀⠀⣠⡶⡼⠱⣊⣹⠿⡉⠃⢿⡄⠁⠐⠊⠉⡸⣧⣸⡿⣡⣦⣦⠋⣼⣹⣏⠁⠈⠀⠀⠀⠀⣀⠤⠊⠁⣡
⠀⠿⣹⡄⠀⠀⠀⠀⠀⢁⠀⠘⣿⣿⣿⣷⣼⠛⠉⢉⡱⢟⣵⣨⣯⣿⣷⡈⢻⣧⢀⢂⣠⣾⣿⣌⣷⣤⣽⣯⣵⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠝⠃⠀⠐⢁
⠀⠀⠻⢷⡄⠀⠀⠀⠀⠀⢇⠀⠈⢻⠟⠷⣿⡀⠀⢸⡃⣛⣛⣉⣭⣭⠻⢇⣼⣿⣿⣟⢡⣀⣿⢻⣯⢀⣐⠷⣿⡈⢿⡀⢐⠂⠀⠀⠀⠀⠀⠘⠄⠀⢂⡀⠀⠁
⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠈⠣⡄⠈⠀⠀⠈⠻⣾⣿⣧⠛⠿⠇⢿⣿⡿⠷⠾⢿⣿⡯⢝⣽⣛⠓⠌⣭⡽⠞⣩⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢖⠊⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠙⠲⡄⠈⠀⠰⣏⣬⣿⡹⡷⠶⡺⢧⡀⠀⠀⠈⠑⣶⡄⠰⠟⠾⡹⣿⣿⠿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠈⠙⠋⣉⣛⣤⠘⣅⣽⡿⢶⣶⣶⣾⠿⠵⠮⢁⡄⠼⠃⠀⠸⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠙⠛⠯⠧⠄⢈⠿⠴⠶⠃⠚⠉⠁⣀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⣤⠤⠤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣆⣱⢄
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣲⠿⣋⣥⣴⣮⣿⣿⣧⠸⡂
⠀⠀⠀⠀⢀⣥⢞⢉⠵⣟⣾⣿⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⣻⣏⣫⣾⢋⢻⣿⣻⣿⣥⢿⣦⡙
⠀⠀⠀⢰⣓⠳⣎⣿⢱⡾⠚⣽⣶⡗⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣶⣿⠿⣩⣿⣯⣭⣤⠿⠿⣧⢀⣿⣿⠆
⠀⠀⢠⣿⠼⣯⡛⡏⢻⠏⢞⢿⣻⣽⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⢩⣗⣶⣶⣝⣯⣿⠛⡙⠲⣿⣏⠰⣷⣶⣾⡝⣿⣿⡇⡆
⠀⠀⠈⣽⠶⠥⡞⠻⢧⣿⡟⢯⡻⣟⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠎⣿⣟⣿⣿⣿⣭⣿⣿⣿⣿⣧⣏⣤⡹⢟⣿⠷⡇⢹⣿⣼⣿⣿⡇⠃
⠀⠀⠀⠹⣧⡝⣟⢞⣷⣩⠅⣟⣻⣜⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⣾⢿⣾⣏⣙⢿⣿⣿⣿⢿⣟⣴⣿⣿⣁⡨⠙⠿⢾⣾⣫⡟⣿⣛⢁⡆
⠀⠀⠀⠀⠈⠛⢮⣾⣭⣱⢷⡁⣤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠓⠛⠿⠍⠿⠶⢿⣮⣶⡮⠿⣿⣡⣶⣿⠋⡸⠁
⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣥⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣥⣭⣷⣥⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠀⠀⠉⠀⠀⠀⠀⠈⠀⠐⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡉⣀⣠⠤⠤⠶⠒⠒⠒⠒⠲⠦⠤⢄⣀⡀⡀⠀⠀⠁⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠤⠖⠋⠉⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠁⠀⠀⠘⠛⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠈⢠⠘⠠⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠋⠐⠀⠀⠀⠐⡀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠢⠔⡀⠀⠀⠀⠀⢀⡀⠤⠀⠂⠀⠀⠂⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠀⠀⠀⠐⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⢀⠁⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⢠⠔⠛⠛⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡄⠀⠀⠀⠀⠈⠂⢀⣀⣀⣀⣀⣀⣈⣀⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣤⣤⣀⢠⣃⣪⠔⠂⣴⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⣴⣶⣿⣿⣟⣛⠛⠛⠛⠛⠙⠛⠙⠛⠛⠛⠛⣿⠿⠷⣶⣦⣄⡀⠀⠀⠀⡰⠋⠐⢠⠐⣈⣷⢤⠈⠢⡄⢾⢇⡿
⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⡟⠉⠉⠁⠀⠀⠀⠈⠙⡞⠓⠶⢶⡋⠛⠶⠶⠖⠋⣁⣠⠴⠋⠉⣻⣿⡅⠀⠀⠇⠴⣏⠀⢸⠍⠀⠀⡂⠀⠯⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠁⠘⠻⣿⣆⠀⠀⠀⠀⢀⣀⣀⣹⡶⣎⣉⡹⠆⣠⠖⠚⠋⠉⠀⠀⢀⣴⡿⠋⡁⠀⠀⠐⢌⠣⠛⠌⣳⠞⠿⣇⢜⠳⣄
⠀⠀⠀⠀⠀⢠⣤⣾⡿⠦⠈⠻⢷⣦⣀⠰⡏⠉⠉⠉⠁⠀⠀⠳⠞⠙⢧⣄⠀⣀⣤⡾⠟⠋⢀⠄⢀⣤⣤⣄⡀⠀⠀⠈⠃⣠⠆⠉⢲⡄⢹⠀⠂
⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠈⠢⢀⠉⠛⠿⢿⣦⣤⣄⣀⣀⣀⣠⣤⣤⣶⠿⠟⠋⠉⣀⡤⡎⠀⠞⡡⢒⡔⢈⠹⣆⠀⢀⣀⠸⠃⡤⠺⢃⡞⡈
⠀⠀⠀⠀⠀⢀⠻⢿⣦⡀⠀⠀⣠⠤⢦⡤⢀⡀⠈⠉⠉⠉⠉⠉⠀⢀⡀⠠⣠⣶⡿⠋⡠⠁⠘⠐⢾⡁⠀⣻⡆⣿⢞⠉⢀⠡⠀⣤⠀⠉⠔
⠀⠀⠀⠀⠀⠈⠀⠀⠙⠻⢷⣤⣹⡄⠀⠀⠀⠀⠁⠀⠁⠀⠀⢻⣤⣤⣶⠿⠛⠁⡠⠊⠀⠀⠀⢠⣬⣁⣧⣙⡱⠏⢠⡖⠈⠱⣶⢸⡇⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠉⠙⠛⠿⠶⢶⣶⣶⡶⠶⠾⠛⠛⠉⠁⣀⠀⠂⠁⠀⠀⠀⠀⠀⠀⡟⠋⠀⢻⡷⣦⡀⢛⢴⡘⢏⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢤⣴⣻⡇⢹⠄⠂⠀⢀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠁⠒⠠⠄⢀⣀⠀⠀⠀⠀⢀⡀⠀⠏⠲⠀⠾⡛⢃⡞⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠈



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

⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⠠⠤⠤⠤⠠⠤⣤
⠀⠀⠀⣰⣖⠀⣶⢈⠁⠀⠾⠋⠉⠙⣀⠀⠠⠄⢲⠂⢀⡀⢡⠀⡠⠊⠀⠀⠀⠐⡀⠀⠀⠀⠐⠒⢤⡀⠘⢦⡀⠀⠀⠀⡠⠃
⠀⠀⢀⡈⣇⣘⡏⠀⠀⠱⡌⠛⠛⠩⢵⠂⠀⠢⣉⣛⣻⠄⠁⠀⠅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⢈⡁⠐⠉
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠔⡲⠃⠀⢣⡀⠀⠀⠀⢠⡜⠀⠠⠖⠇⢰⠀⠠⠄⠀⠠⠄⠀⠰⠰⠆⡀
⠀⠀⣠⢻⡀⠀⠀⠔⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⣘⠁⠊⠀⠀⠀⠀⠉⠒⠒⠒⠁⣀⠊⣤⠀⡰⠀⠀⠠⠄⠀⠀⠠⠀⠀⣀⢀⠋
⠀⠀⠁⠰⡇⠀⢸⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠳⢤⣀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠩⣤⡔⠈⠀⠐⠂⠀⠰⠃⠠⠠⠀⢀
⠀⠀⠒⠀⠇⠀⠀⠀⠀⠄⠀⡐⠂⠀⠁⠀⢠⠂⠙⠢⠇⠀⠀⠀⠄⠀⡠⠴⠒⠒⠀⠒⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠁
⠀⠀⠈⡄⠜⢄⠀⠀⠀⠒⠤⠄⠂⠀⠀⠀⡇⠀⠈⠀⠈⠂⠤⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡠⠐⢠⣼⣯⢧⡜⠁⠢
⠀⠀⠀⠈⠂⢀⠂⣀⠀⠐⣆⠀⣠⡀⠀⠀⠈⠒⠂⠀⠀⠀⠤⣚⠒⢌⠁⠀⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠐⠁⠀⠀⠀⠈
⠀⠐⢦⣻⠇⡀⠉⠂⠙⠒⢃⡴⠋⠱⢄⠀⠀⠀⠀⠀⡀⠀⠑⢌⠐⠤⢽⣦⣄⠌⠐⠐⠀⠂⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡐⢿⣴⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⢠⠊⠁⠀⠀⠀⠈⡀⠀⠈⡉⠀⠀⠀⠀⠀⠀⢀⠷⠀⡆⠐⡀
⠀⠀⡙⠢⣹⣇⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣀⠀⢀⣹⡲⢞⠣⡀⠀⠀⠀⠀⠀⢘⠛⠆⠑⠄⣡⠀⠀⢠
⠀⠀⠈⠑⠐⠼⢷⠀⠀⠁⢀⣀⠀⠀⠀⢀⠔⠀⠀⠉⠒⠒⠁⠀⠏⠀⣿⠈⠛⠃⠀⢀⠤⠀⢀⠇⢸⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠤⠥⢀⡀⠀⠉⠳⠟⠈⠀⠀⠀⢀⢀⡀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠠⡎⠠⠁⡁⢀⠋⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⡄⣶⠖⣰⣶⣮⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⢈⣐⡒⠚⠁⠀⠀⢀⠀⠔⠁⠀⢄
⠀⠀⠀⠀⢼⣏⡙⢣⡼⠛⠈⠀⠀⡄⠀⢀⢤⠀⢁⠌⠀⡠⠆⠁⠀⠀⠀⠀⠄⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠂
⠀⠀⠀⠀⠌⢠⣠⣍⣡⣃⡽⠀⠀⠀⡨⢾⣿⣊⡷⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠀⠘⢉⣭⠖⠊⠀⠀⠀⠎⠀⠀⠰⠈⠉⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⣸⠀⠀⠀⠀⠀⠈⠒⠄⠀⠠⠀⠠⠂
⠀⠀⠀⠀⠀⢶⣤⣂⣠⣆⠀⠀⠀⣄⣐⠔⠁⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⠀⠀⢀⣠⠄⠀⣠⠄⣠⠤⠄⣀
⠀⠀⠀⠐⠙⠛⠋⠉⠉⠄⠈⠑⢄⠈⠀⠀⣀⣀⠀⣤⢤⡀⠈⠉⠉⠉⠉⠑⠒⠒⠒⠒⠚⠀⡜⢩⠫⡭⠉⠁⠉⢩⠍⢓⢤⢑⡄
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡼⠀⠈⠛⠀⠀⣻⠀⠀⣀⠤⠒⠘⠓⠒⠢⣄⠀⠀⣏⠂⡀⠁⠈⢠⠀⠑⠄⠚⣸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⠀⠀⡒⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢧⠀⢹⡀⠠⠤⡁⠀⢣⠤⠒⠈⣼⠀⠆
⠀⠀⠐⠄⣈⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠈⠲⠠⠔⠁⠀⠀⠘⢧⠀⠔⠃⠀⠀⠀⠀⣸⠀⠀⠣⣄⣀⡀⢘⡀⠀⠄⢀⡿
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠐⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⠒⠒⠦⣀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡀⣀⠠⡀⠇⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢤⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠐⣳⡟⠛⣼⠃⠀⠀⢂⠀⠈⢆⠀⠀⠀⠀⢰⠉⠁⠀⠀⠀⡈⢂⢸⡠
⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⠁⡐⢬⠯⢦⠈⠁⠀⠘⣿⡄⠀⢸⠀⠀⠀⠀⠄⠀⠀⠀⠀⢺⢀⠜⡏⠃⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⣤⠟⠀⠀⠻⣔⣟⡡⠁⡼⠀⠀⠀⡘⠀⠁⠀⠀⠀⠀⠁⠉⢅⡸⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠐⡀⠀⢰⠀⠀⠀⠀⠈⢧⠀⢷⣻⢦⠜⡤⠀⠄⠀⠀⡴⠁⠀⠀⢀⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠢⢑⡚⣆⠈⡐⠀⠀⠀⠀⠈⠳⠤⣬⣙⣉⣀⣀⣠⠴⠋⠁⠀⠀⠀⡘⠀⠃⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣑⣂⣀⠠⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡗⠆⢀⠁⠀⠀⠀⠀⠀⠌⠀⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠄⠀⠀⠀⢀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⣈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠀⣠⣪⠤⠚⠁⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢀⣐⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠑⢤⣀
⠀⠀⠀⠠⠀⠰⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠄⠡⠼⠁⠀⠀⠀⠀⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢔⢤⣤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠸⣌⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⢀⠔
⠀⠀⠀⠀⠀⠤⠤⠐⠲⠁⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡐⠀⠀⠀⠾⠦⠄⠠⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠑⠢⡀⠀⠀⠀⠀⠀⠙⣄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠂
⠀⠀⠀⡐⠁⠀⠀⠄⡀⡠⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⢄⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⠀⡴⠊⠀⠀⢀⠠⡄⡀⠀⠀⠐⡀
⠀⠀⢠⡁⠀⠀⠀⡸⠢⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠳⢵⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠐⣠⠀⠀⡌⠀⢜⡅⠂⠀⠀⠀⡴⠀⠀⠡⠰
⠀⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠆⢔⠏⡀⠘⠋⡁⠈⣀⠘⡔⠀⠀⡇
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣀⣠⠞⢁⡞⠁⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢆⠘⠣⣉⠅⠀⡀⢣⢽⣟⡠⢀⢠⠃
⠀⠀⠀⠀⠈⠓⠦⣤⣀⣈⣋⡥⠖⠋⠀⠀⡆⠸⠆⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠸⠀⠀⠀⠀⠈⢢⡑⠄⡀⠙⣄⠮⠞⠀⠀⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠉⢉⣀⠤⠚⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠢⠀⣀⣀⣀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠰⠦⠤⠴⠇⠄⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠠⡄⠀⠀⡇⡠⠀⠀⠀⢀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⡆⣿⠀⢰⠁⡇⠀⡠⢖⣵⠥⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣿⠀⡎⣸⡡⣪⠔⠉⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⢀⠇⢀⢧⢿⡾⣰⡿⠋⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠱⣦⠀⠀⠀⣼⠀⣸⡞⡾⠕⢻⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠏⢧⠀⢠⠇⣰⡿⢁⣠⣴⣿⣟⣖⣒⣒⡒⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⡇⡸⣸⣀⠎⣴⠟⠩⢉⣛⠿⠉⠁⠀⠀⠈⠙⠳⣄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡈⢂⢰⢡⡵⢛⣛⠛⠲⢾⣯⣉⣉⠙⠓⠢⢤⡀⠀⠀⠀⠈⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣚⣷⡼⣠⡴⠶⣭⠙⠉⠙⠳⢽⡄⠀⠉⠑⠢⣀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⢟⣵⢿⣝⠢⡀⠈⣷⠈⢆⣀⣀⡀⠀⠀⠀⠀⠈⠳⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣚⡽⠑⣹⡟⢸⠈⠳⠃⣀⡼⠗⠋⢁⠔⠁⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⣫⠵⠚⠁⣇⣴⡟⣠⢃⡤⠖⠋⠁⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⡀⠀⠀⠀⡀⠀⠈⠀⣴⡄⠀⣨⠟⠴⠋⠁⣀⣤⡶⠯⠥⠐⣲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⡈⢢⠀⢰⠃⠀⣠⢾⢃⣷⣞⣁⣤⣴⠚⠉⠁⢀⡠⠤⠖⣛⡛⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠱⠈⣇⡟⢸⢞⣡⣫⣞⣉⠀⣤⣔⣛⠻⠿⢿⣯⣉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣑⣀⡴⠠⢟⣴⡿⢭⣍⡉⠙⠛⠿⢷⣮⣝⡫⣙⠒⠤⣍⡛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠴⣋⣭⡤⠤⣛⠫⢭⡙⠗⠚⠛⠿⠶⢤⣄⡈⠙⢿⡻⢷⡄⠀⠉⠲⠬⣻⣄
⠀⠀⠀⠀⣠⢞⣭⠖⣻⢫⢷⡈⢢⠀⠙⠢⡈⠢⣀⠀⠀⠀⠀⠀⠉⠒⢤⡉⢦⡙
⠀⠀⠀⠀⠈⠉⠀⠀⠘⠊⠈⢧⡜⠀⠀⠀⠘⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⢠⠛⠂⢲⠀⠀⢀⣶⣤⣼⡀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠚⠛⠒⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠚⠛⠃
⠈⢷⡄⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⢰⠿⢿⡄
⠀⠀⠀⠀⠀⣠⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣀⡀⠀⠀⠀⠀⣴⢶⣶⣶⢦⡀
⠀⠀⠀⡀⠠⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣻⣾⣟⣿⣿⡇⠀⠀⠐⢿⠇⠀⠿⠿
⠀⠀⠀⠁⠀⠁⠀⢀⡿⠀⢿⠀⠀⠀⠂⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠙⠓⠛⠛⠊⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⡀
⠀⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡽⣳⠿⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠀⠀⠀⢸⣿⣿⣿⣷⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⣘⠿⣿⣿⠏⠊⠀⠀⠀⠀⠐⣤⣴⣤⣶⣤⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠀⠁
⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠤⠼⠿⠿⠿⠧⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⠛⠛⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣶⣶⣶⣦⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡀
⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠈⠉⠉⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠃⠀⠀⠀⢰⡏⢹⡆
⠸⠿⠿⠸⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠸⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢿⡀
⣿⣿⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⠀⡲⠂⠀⠀⠀⢀⠔⣁⠔⢁⡤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠊
⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⣠⠆⠖⡤⠋⠀⠈⠀⠀⠀⠀⠐⠋⢚⣡⠖⠉
⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢀⣠⣴⡤⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡀⠀⡀⢀⡀⠀⠀⠀⡀⡀⡀⠀⠐⠐⢀⠀⠀⠕⠋⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠠⢄⡩⣿⡗⢮⠤⠀⠀⠈⠀⠅⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡀⠀⠈⠤⠟⠢⠹⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡆⠀⠀⠀⠀⠀⡀
⠀⢮⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠁⠀⠀⢐⢶⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠚⠁⡀
⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠆⡀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠆⠀⠀⠀⣀⠂
⡀⠀⣀⠀⠀⡀⣕⠠⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⢀⡠⠀⠀⣀⡤⠀⢀⠀⠀⠀⠐⠀⠒⠘⠀⠀⢀⠈⠳⢌
⡙⠆⠀⠀⠀⠱⢌⡑⢤⡉⠒⠀⠀⠈⠁⠀⠀⠀⠔⠀⠀⠀⠀⠈⠓⠀⠛⠫⣁⠙⠁⠛⢡⠀⠀⠀⠐⠌⠀⠀⠲⣄⠀⠠⣀
⠁⠀⠈⠲⠀⠀⠀⠙⠦⠈⠁⠀⠀⣤⣄⡄⠀⠲⠄⣀⡤⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⠀⠀⠀⠀⠠⠄⠀⠄⠰⠠⠠⠤⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⢴⠖⣒
⠀⠀⠀⠠⠀⢀⡰⠄⠀⠀⡠⠍⠌⠃⠛⠁⠀⠀⠀⠂⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠊⠉⠄⠄⠈⠁⠈⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣴⡶⠀⠀⠸
⠠⠀⠀⠀⠀⠀⡄⠉⠀⠁⢀⡀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⣀⠔⠉⠠⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠉⠉⠉⠁⠀⠀⠀⠀⠀⡄⠀⠐⠤⠤⠀⠀⠀⠀⠀⠀⠀⠁⠖⠁⣠⠴⠚⠀⠀⠀⠲⢤⣴⣀
⣀⠀⠂⠀⠀⠀⠀⠀⠉⠻⠋⠀⠀⠄⠀⠆⠀⠀⠀⠀⠙⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠛⣂⡭⠴⠂⠀⠀⠀⠙⠒⢸⣿⠨
⠁⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠞⠀⠀⠀⠘⠻⠟⠀⠀⢣⡀⠀⣀⠄⠉⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁
⠀⠀⠀⢀⣡⠶⢀⣄⢩⣢⣄⠀⢤⡀⠀⠊⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠂
⠤⠄⠀⠀⠀⠀⠀⠊⠉⠀⠐⠈⠁⠀⠀⠐⢶⢴⣼⠧⣝⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠐⠁⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠚⣿⡌⠬⢦⡶⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠂⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠈⠀⠈⠀⠀⠀⠉⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢔⠁⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠄⠠⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠙⠛⠛⠶⣶⣀⣐⠠⠄⡀⢀⠀⣠⣶⠛⠋⠉⣈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡶⢖⠉⠙⠩⠏⠓⢦⠈⠉⣅⠠⣀⠁⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⠀⠄⠀⢦⠀⠀⠀⢠⠄⠄⠠⢤⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠟⠀⠀⡘⠀⠀⠀⢠⠁⠀⠀⢀⠊⠀⠀⠀⡎⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠸⠁⠀⠀⠠⠇⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⠀⠀⠀⠰⠤⠴⠁⠀⠐⠒⠐⡆⠉⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⢂⠀⠀⠀⠐⣀⠀⠀⠒⡤⢤⠀⠀⢀⣄⢁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠥⠀⠀⡀⠀⠉⢁⣠⣶⠛⠀⠀⠂⢈⣀⡀⠀⠀⠀⡱⠒⠢⢀⡀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠲⠶⠛⠉⣀⣠⡴⠖⠚⠋⣇⣀⣴⡶⢛⠡⠒⢈⣉⠀⠀⣊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠷⣤⡤⢶⠶⠋⠉⠉⠀⣐⠁⡬⠭⠉⢁⣀⣤⠶⠛⠋⠛⠛⠛⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡤⠲⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⢠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣠⣼⣀⣠⣮⡄⢀⣀⡀⠀⠀⠀⠀⢀⣀⣄⣀⣀⣤⣤⣄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠈⠉⠉⠛⠿⢿⣿⢷⣼⣷⣦⣤⡾⠿⠿⠛⠛⠋⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠸⡐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⡾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠈⠀⡤⠐⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠒⠒⠒⠒⠒⠐⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠂⠧⠤⠚⠉⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⠀⠠⠔⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠶⠚⠈⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡄⠠⠔⠀⠀⢀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠤⠄
⠀⠀⠀⠀⠀⠐⠋⢁⣀⡤⠄⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⠀⢀⠀⢂
⠀⠘⠀⠑⠀⠠⠀⢒⠉⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠀⠆⠃⠠⠀⠀⠀⢸⠀⠀⠓⠂⠉⠂⠉⢀
⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠁⠊⠀⢸⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⠀⡀⢀⠀⠀⠀⢈⡤⠤⠀⠀⠀⠀⢀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠤⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀⢠⠡⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠐⠈⠘⠒⠘⠻
⠀⠀⠀⡀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠄
⠀⠀⡰⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⣀
⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⢀⡀⠈⠐⠀⠀⢰⠀⠀⠀⠀⠀⢀⡴⠒⢢⣄⠀⠀⠨⠀⠀⠀⠀⠀⣀⡀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠃⣈⠁⠉⣈⠌⠀⠸⠀⠀⠀⡐⠢⠄⠭⠭⠬⠥⠔⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⢀⠤⠐⠒⠀⡒⠤⢄⡀
⠀⠀⠀⠠⢀⠀⠄⠀⠀⠀⠀⠀⠀⢃⠐⡠⠰⠄⠒⠐⡠⢀⡇⠀⠀⠀⠀⠘⠢⢃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⡈⢀⠀⣄⠄⢰
⠀⢀⠀⠀⠘⠑⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠴⠄⠀⠀⢀⠞
⠀⠀⡀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠑⠒⠒⠒⠉⠁⣠
⠀⠀⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠀⠀⠁⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠀⠤⣤⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠥⢀⣀⣀⣀⣀⣀⡒⠘⠁⠓⠀⣀⣃⣙⣀⠁⠥⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠉⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⢽⡩⠳⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢁⣄⣈⡛⠋⢡⡒⠤⢀⠀⠀⠀⠙⢆⣈⠻⣭⣉⠉⡑⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠙⠻⢇⣀⣄⠁⢒⠛⠋⠲⠶⠢⢄⣬⣴⣮⡉⢲⣄⠀⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⢄⣀⠉⠐⠚⠓⠀⢀⣼⣤⢌⣉⠃⠉⠻⣶⠿⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⡶⠟⠛⠃⠈⠉⠁⣠⡾⠁⠈⠁⠀⠨⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣙⣒⣞⡛⠛⠛⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣤⠛⠉⠉⡷⠊⠉⡩⠇⣸⢏⡤⠀⠀⠀⠀⠀⠀⠀⠀⢴⣥⠔⠂⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠉⠀⠀⠤⠖⢂⣠⣶⡀⠤⠴⠞⠛⠉⡠⠔⠒⠙⠟⠀⠀⠐⠰⣋⣀⢤⣾⣃⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠈⠀⡀⡠⠀⢠⠀⠈⠈⠓⠀⠠⣄⠀⠀⣀⣤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠴⠖⠶⡽⠤⠄⠀⡄⠙⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢄⣤⠄⢠⠄⠀⠀⠀⠀⠀⠁⢁⠀⢀⡀⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⠌⠋⠉⢈⠶⠶⠤⣐⣄⣂⡰⠃⠀⡍⠁⠁⠈⢉⡀⠬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡉⠀⠀⠁⠀⢀⣀⠀⣀⣾⢀⣤⠖⠛⠋⠁⣈⠍⠌⠛⠛⠓⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢏⣋⢣⣤⠀⢄⣠⣭⠴⠚⠛⠋⠁⠄⠀⠀⢠⠤⠄⠀⠀⠀⠀⠀⠉⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⣄⠶⡀⠀⠀⠀⠠⠀⠐⠓⠚⠓⠛⠀⣀⠰⢈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣯⣀⠀⠀⢀⠐⠊⠉⠉⠈⠉⢀⣀⣠⢤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⢒⡒⢢⡤⠬⠤⣚⠵⢿⣄⣠⣉⣼⣿⣫⣙⣿⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⢂⠘⢉⠍⠁⠀⡀⠰⠀⠖⣀⠀⣨⡧⢤⣄⡤⠄⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠱⠄⠙⣸⣇⠀⠙⠁⠛⢐⣤⠖⠋⠀⠀⠊⠀⠀⠀⠀⠀⠙⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠐⠒⠚⠋⠉⠀⠂⠐⠲⠎⣀⠠⠀⠀⠀⠀⠦⠄⠀⠀⣀⡈⠇⠀⠈⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢄⡀⠀⠀⠀⠉⠓⠂⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⡀⣀⡀⠀⠉⠑⠒⠤⠧⠤⠶⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠉⠉⠁⠈⠁⠀⠈⠀⠀⠀⠀⠉⠛⠓⠲⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠂⠀⠀⠐⠒⠒⢒⠢⡠⠣⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⣐⣂⣀⣀⣀⣘⣁⣀⡘⠷⠾⠛⠉


⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣶⣶⣶⣶⣶⣾⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣶⣶⣿⣿⣷⣶⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⢻⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⢛⣻⠋⠈⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣿⣿⣯⣉⣙⡹⠛⢲⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠉⠀⠙⠀⢀⣠⣾⣿⣿⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠀⠀⠀⢀⣀⣤⣶⠿⠛⠛⠉⢉⡀⢀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠙⠃⠈⠉⠉⠀⠀⠀⠀⠀⠀⠑⠘⣩⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠀⠠⠀⠀⣀⣀⣀⣀⣀⣠⣤⠤⠤⠲⣖⣟⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢂⣄⢀⣀⡀⡀⠀⡄⠈⢡⣸⣶⣔⣨⣰⢮⣿⣞⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠓⠚⠩⡿⢻⡴⠋⠻⢇⠈⠻⣿⡄⢉⡿⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠀⡄⠀⠀⠀⣸⢠⡄⠀⣾⡄⢀⣿⡇⢸⣧⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣷⠀⢹⠀⢸⣾⣾⠀⣿⡧⢸⣿⡁⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⣿⣄⣿⣆⣿⣿⣯⢸⣿⡇⣼⣿⣼⣿⣿⣿⣠⣴⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢿⡇⣿⡿⠸⢿⣿⢾⣿⡇⣿⣿⣼⣿⣿⣿⣶⣶⢞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠳⠾⠿⠿⢿⣿⣿⣿⣿⣿⡯⠿⠷⠄


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠶⠶⠶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⣾⡿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠻⠛⠛⠛⠛⠛⠿⠿⠿⠿⠟⠛⣿⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⡇⠀⠀⠀⣠⠀⢠⡶⠛⢷⣆⠀⢀⡀⣴⠞⠳⣆⠀⠀⠀⣰⠞⠳⣦⠀⠠⠄⠀⠀⠀⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠛⠃⠘⢷⣤⡾⠃⠀⠘⠃⠻⣦⣴⠟⠀⠀⠀⠻⣦⣴⠟⠀⠙⠁⠀⠀⠀⣾⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⢛⡿⠟⠉⡀⠀⠐⠀⠄⢉⡿⠛⠋⠉⠍⠉⠙⠻⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡁⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⣹⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⡴⠃⠀⠀⠔⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⣿⣿⣿⡿⠋⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠶⠶⣶⡶⢶⣾⠇⠙⠻⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠛⠛⠉⠙⠛⠛⠋⠉⠉⠉⢹⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⣠⣿⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣈⣻⣷⡄
⠀⠀⠀⠀⠀⠀⣿⣟⣛⣛⣛⣛⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⣭⠭⠭⠭⠽⠿⠿⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠇



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

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠈⠀⠀⢄⠀⠀⠀⢀⣠⡂⣶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⣀⠀⠀⠀⣁⡀⠀⠀⠀⣄⠀⢀⣤⡶⠋⠀⠀⢔⠃⠀⠈⠀⠘⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⣷⠉⠉⠀⢙⡟⠁⠀⣼⠁⠀⠀⠀⡿⠀⠠⠤⠄⠈⣻⣧⠀⠀⠆⠀⠀⠀⠢⠀⠂
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⠀⠀⣠⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⣥⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣇⠀⠀⢰⠀⠀⠀⡄⠀⣠⡗⠀⠀⠀⠀⠀⡀⠀⠂⠀⠃⢀⣀⡀⠀⠀⠀⠈⠰⠰⠄⠠
⠀⠀⠀⠀⢰⠏⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⣠⣿⡀⢀⣰⣇⣴⠟⠁⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠈⠉⡅
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⢰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⣴⠀⡀⣠⠀⠀⢀⠠⡂⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠆⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠄⠀⠀⠈⠃⡏⠀⠅⠹⠆⠀⠈⣳⠀⠀⢤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡄⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣾⠂⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠄⡐⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠉⠛⠃⠀⡠⠄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠆⠀⠀⠀⣄⣠⣧⠈⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠠⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐
⠀⠀⠀⠀⢀⡀⢀⠀⣀⡌⠀⠀⠀⠀⠨⠟⠉⠊⠋⠉⢙⠈⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠘⠀⠀⠀⠀⢺⠁⠀⠁⠀⠀⠀⠀⠀⢀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠩⠀⢀⡀⠀⡀⠀⡠⢀⣠⠆⠀⠀⢠⠐⠄⢀⡠⠄⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠠⡄⠀⠀⠀⠀⡄⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠂⠀⠋⠀⠀⠀⠀⠉⠒⠦⠴⠾⠓⠁
⠀⠀⠀⠀⠀⠀⢀⡄⣂⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠂⠀⠀⠻⠛⠃⠀⠠⠶⠶⠥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠅⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠈⠉⠉⠱⠆⠀⠰⠄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠘⠶⠶⠦⠤⠀⠀⠀⠀⠂⠐⠂⠒⠂
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣒⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡂
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠁⠀⠀⣠⠀⡅
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢠⡄⠀⠺⠷⠂⠀⠀⠀⠀⠀⠀⠀⠯⢀⣇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⢈⠴
⠀⠀⠀⢿⣿⣛⡛⡟⣟⣿⢻⢛⣿⢻⣛⣟⣿⣿⠀⠀⠈⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠍⠙⠉⠑⠛⠛⠻⠼⠇
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⢀⣠⠜⠀⠀⠀⠀⠒⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠚⠋⠁

⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣷⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠠⠖⠿⢗⠀⠀⡐⠀⠂⠀⠀⠀⠀⠈⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡴⠄⠀⠀⠀⠤⠀⢀⠀⢀⠀⠀⠀⠀⠀⠂⢀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠠⠀⡀⠀⠀⠕⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠁⠈⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⢀⠀⠀⠈⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡸⠄
⠀⠀⠀⠣⡀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠤⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠟⠃
⠀⠀⠀⢆⠈⠂⠤⣀⠀⠀⠀⠉⠐⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠬⠌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠆⠊⠁
⠀⠀⠀⠀⠑⠢⣄⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠈⠐⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⢤⠖⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⠈⠁⠐⠂⠀⠀⠀⠐⠂⠀⠀⠀⢀⣠⡤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠦⠤⣤⣤⠤⢤⣄⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢠⡄⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠈⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⠀⠀⠀⠠⣈⣸⢿⣂⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⢀⣄⠀⠒⠀⠐⢰⠈⠀⠁⠀⡅⠄⢀⢠⠀⠀⠀⠀⠀⠅⠀⠘⠙⡂⢸⡈⡃
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠁⢀⠈⠂⡀⠀⠃⠁⠉⠋⠉⠀⠉⠀⠐⢀⡀⠘⠈⠂⠈⠊⠁
⠙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠒⢛⠃⠁⠀⠀⠀⠐⠂⠀⠀⠀⡈⠀⠀⠀⠀⠀⠠⠴⠈⠀⠀⠀⠀⠀⠀⡀⠀⠆
⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢐⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⠐⣀⠂⢀⡀⠤⠀⢀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡿⠴⠆⠀⠀⠀⠀⢀⡀⠀⠤⣴⣶⣤⠄⣂⠀⠂⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡔⠀⠀⢀⣀⣀⠖⠈⠀⠀⠀⠀⠂⠉⢿⡌⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠀⠀⢀⡈⠛⣃⢀⠀⠀⢁⠀⢀⢀⢸⠇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠙⢌⡀⠀⢐⠢⢀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠑
⠀⠀⠀⠀⣴⣿⣿⣿⠀⠈⠁⠀⢀⢀⡌⠀⠀⢀⠞⣀⠀⠄⠐⠒⡦⠓⠛⠁⠐
⠀⠀⠀⣼⣿⣿⡿⠿⠣⠄⢲⢾⣏⠊⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡐⠠
⠀⠀⠀⢈⣟⣿⣗⠠⠀⠐⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠀⠀⠓
⠀⠀⠐⢸⢿⣿⡟⡎⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⢀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⣿⣿⣿⠏⠀⢚⠁⠀⠀⣀⠀⠀⠀⠹⠀⠀⠐⠂⠢⣀⠖⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⢤⡠⠆⠀⠁⡀
⢀⢿⣿⣿⠋⠀⠀⠈⠤⠀⣴⠀⠀⠀⢀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠛⠆⠀⠌⠀⠱⠒⠫⠈⠁⠀⢀⣰⣤⣰⡇
⠐⣾⣿⠇⠀⠀⠀⠀⠀⠀⠐⠱⠤⠀⠙⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡿⣿⡇
⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⡀⠓⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿⣽⣿⠁
⠘⠳⣆⢦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢱⠆⠀⠀⠑⠀⠀⠀⠀⠀⠂⠀⢀⡈⣌⠗⠀⠀⠀⠀⠺⠛⣿⣿
⠀⠀⠀⠜⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠄⠀⠀⠀⠂⠀⠀⠠⢎⡁⠜⠀⠀⠀⠀⠀⠀⠀⠜⠻⠟
⠀⠀⠀⠁⠀⢻⡓⢲⣦⡤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⡉⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠓⡺⠒⠐
⠀⠀⠀⠀⠀⢀⢐⣬⡿⠁⠀⡄⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠀⠈⡍⠁⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⢨⡛⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠈
⠀⠀⠀⠀⠀⣮⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠀⠠⠄
⠀⠀⠀⠀⠘⠝⠿⠁⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠂⠀⠸⡏⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠠⠀⠀⠀⠠⠄⠛⠧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡤⡀⠠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠃⠀⠐⠀⠀⠄⠀⠀⠜⠁⠤⠶⠂⠠⠀⠠⠈⠀⠤⠠⠓⠄⠃⠢
⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠂⠐⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⠀⠀⠠⠀⠀⠀⠀⠀⡀⢄⠠⠀⠀⠠⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡯⠰⠀⠀⠀⠀⠀⡀⠀⠄⣴⣦⡤⢐⡉⠂⠀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⡔⠀⠀⢀⣀⠐⠈⠀⠀⠀⠀⠀⠹⣷⠉⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⢠⠌⢩⠄⠀⠀⠠⠀⠀⡀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠁⠄⠠⠨⠁⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠄⣢⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⡀⠀⠀⠘⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⣀⢂⣠⢀⡀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠰⠄⠀⠀⠀⢠⠀⡔⠈⠀⠄⠀⠀⠀⠘⡳⡔⠀⠀⢀⢀⡟⠂⣄⠀⠈⠁⠀⢠⡃⠀⠀⡈⠁⠁⠀⠙⡖
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠂⢀⣀⣴⡀⢀⠈⠂⠀⠖⠁⠀⡄⠊⠀⠀⠀⠀⠀⠠⢡⠜⠣⢗⡫⠂⡀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⢸⠁⣀
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢀⠈⠀⠈⠁⠀⠀⠐⠦⠀⢀⠎⢠⠞⠆⠀⠀⠀⠀⣔⡄⣴⠨⠌⠠⠔⡧⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠆⠀⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢠⠀⠀⢤⡄⠀⢧⠀⠂⠀⠀⠄⠀⠅⠠⣤⠔⠚⢀⡠⠆⠀⠀⠀⠙⠀⠤⠄⠠⠤⠤⠂
⠀⠀⠀⠀⠀⣀⢰⡄⠀⠀⠀⢠⠀⠀⢀⡀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠸⢓⣸⠭⡅⢎⡑⠀⠀⣄⢶⠖⠀⠀⣀⠀⠀⢦⣆⡀⠈
⠀⠀⠀⠀⡶⠈⠁⢁⡀⡀⠀⣀⠀⠀⠘⢁⠾⣸⠀⠀⠀⠀⢀⡀⠀⠀⠀⠦⠀⠀⠈⠉⠛⠃⠉⠀⠀⠴⡉⠀⠀⠀⠀⠁⠀⠀⠀⠈⢱⡄
⠀⠀⠀⠀⠀⠀⡔⠋⢀⡠⠴⠨⢄⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠠⡤⡀
⠀⠀⠀⠀⠀⠀⠹⠶⠃⠁⠀⠀⠀⠈⠆⠀⠀⣥⠀⡆⡔⢰⢰⠀⡄⢀⠇⠀⠀⢰⠠⠰⠄⠂⣦⠀⠀⠀⠀⠀⠀⠘⢸⣁⠄⡓⣧⢆
⠀⠀⠀⠀⠃⠀⠀⠘⠀⠁⠀⠀⠀⢀⠀⠉⠀⠤⠐⠣⠁⠬⠘⠄⠇⠈⠤⠀⠀⠃⠱⠐⠢⠀⠇⠀⠄⠁⠀⠰⡦⡄⢉⠭⠶⠒⠈⠆⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠉⠸⠖⣠⡀⠟⢬⠘⣣
⠀⠀⠀⠀⣠⠀⠀⠢⡆⡀⢀⠀⣠⠄⠀⠀⠙⣣⡆⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⢀⡱⠎⠁⠀⠀⣀⠀⠀⠀⠀⠐⠳⠴
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠂⠀⠀⠚⠃⠀⢀⠀⠀⡠⠄⠆⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⣄⣀⣄⣀⡀⠀⠀⠠⡄
⠀⠀⠀⢠⠀⠈⠀⠀⠀⢠⡀⠠⠔⠀⠀⠀⢠⠀⠀⠁⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠁⠲⠀⠀⠀⠀⠘⠀⣴⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠻⡿⠄⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠘⡀⢀⠄⠄⠁⡀⠀⠰⠀⠀⠡⣰⠃⠀⠀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢢⣟⠁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠾⠃
⠀⠀⠀⠀⠀⠲⠈⠈⢀⢀⠉⠈⠀⠈⠀⠀⠈⠁⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢒⣁⡤⣠⣦⣤⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞⠛⠛⢻⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⣤⠀⡏
⠀⠀⠀⠀⠀⠀⢠⡲⣿⣿⡆⠀⠀⠀⣠⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠙⣀⢰⣿⡄⠀⠀⠀⠀⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠟⠁⢀⣀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠈⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠀⠀⠀⡀⠒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣇⠂⠀⠀⠀⠁⡴
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⡻⣿⣿⣷⣄⡀⠶⣾⡁
⠀⠀⠀⠀⠀⢀⠖⠛⢢⡀⠙⢮⡛⠿⠿⢿⣿⣿⡻⡢⡀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠹⡄⠀⠱⡄⠀⢰⣿⣿⣿⣇⢡⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢹⡀⠀⠙⣄⠀⢹⣿⡿⣿⣿⣇⠀⠀⠀⠀⢾
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⢧⠀⠀⠈⠉⠈⢿⣷⠘⠿⠸⡄⠀⠀⡰⠛
⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢱⠀⡸⠁⠀⠘⢿⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣰⠁⠀⣤⠀⢺⡏⠁
⠀⠀⠀⡇⠀⠀⠀⢀⠀⢾⣣⡟⠀⠀⠀⢀⣀⣠⠀⠁⠀⠈⢁⡠⠂⠀⠙⠛⠛⠀⢀
⠀⠀⠀⢡⠀⠀⠀⡡⢖⢛⡷⠒⠘⠉⠉⠁⠀⢰⠀⠀⠀⠀⢸⣽⣇⠤
⠀⠀⠀⠘⠀⠀⠈⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠖⠒⠉⢸⠐⠄⣾⣛⠛⠛⠛⣛⠛⠃⡄
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠏⠀⢀⠀⠀⢸⡄⡆⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⠲⠆⠶⢶⠒⢚⠋⠍⠅⠤⢨⡧⠷⠶⠶⠾⠶⠶⠞⠣⠶⠀⠀⠀⠀⠀⠠⠀⠼⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡆
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⣿⣿⠟⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⡶⠒⠒⠒⠒⠒⢲⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⡇⠠⠴⠆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠒⠒⢒⣒⡒⠒⠒⠒⠒⠒⠚⠃⣠⠗⠒⠒⠒⠒⠒⠚⢧⡀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣠⡽⣛⡛⢦⡀⠀⠀⣞⢓⣒⣒⣒⠒⣒⣒⡒⣒⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠞⠹⡟⠁⠉⢻⠇⠀⠀⠉⠉⠉⠉⠉⣩⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⡶⢶⣏⣀⠀⠀⠀⠀⠀⢯⠀⢸⠆⢸⡄⠀⠀⠒⠒⠲⡖⠒⢲⡖⠒⢶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠉⠉⠀⠈⣷⠀⠀⠀⠀⢘⣀⣤⣄⣘⠁⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⡴⠀⠀⡶⢳⢄⣿⡀⠀⣀⣰⠯⠥⠤⠤⠭⢷⣀⡀⠀⠀⠀⡇⠀⣸⣇⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣅⠀⠘⠳⢦⣠⣟⡏⢠⠈⠓⠶⠯⣿⠀⠀⠀⠀⠀⢸⠉⠁⠀⠀⡞⢹⣆⡏⢹⢰⠋⢳
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⡶⠴⣇⣹⠇⢺⠶⠶⠶⠶⢾⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠙⠚⠙⠓⠚⠈⠓⠋
⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠳⠶⠶⠶⠶⠞⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⢸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⣶⠶⠶⣶⣶⡶⠶⢶⡶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⣿⠸⠭⠇⠸⠭⠭⠿⠀⠯⠟⢸⠀⠘⠚⠂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢛⣛⣛⣛⣛⣛⣛⣛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣈⣉⣉⣉⣉⣉⣉⣉⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⠐⢀⠠⣄⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠈⠁⠈⠃⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠲⠖⠐⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠈⠉⠉⠀⠀⠒⢌⢀⡠⣖⡁⠀⠀⢀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⣿⡽⠳⡶⣮⠀⠐⢆⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠈⢀⢀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠇⠉⠉⠁⠀⠀⠀⠀⠀⡬⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢽⠀⠀⠄⠀⠀⠈⠀⠀⠀⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠀⠀⢠⠄⠐⠂⢤⢺⡀⠀⠐⠂⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢢⣌⢦⢤⡀⢀⣸⣳⣤⣀⡀⠀⢀⢀⠶⠥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⢱⡁⠀⠈⢣⡁⡉⣘⢈⡀⣀⠀⣀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠐⠢
⠀⠀⠀⠀⠀⡐⠉⠉⠛⠓⠂⠠⠤⢧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠂⠉⠀⠀⠖⠁⠂⠐⠔⠂⠘⢆⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⠀⡎
⠀⠀⠰⠿⠉⠑⡄⠚⠂⡤⠒⢦⠤⠂⣾⠿⠄⣀⡀⠀⠀⠀⠀⠀⢈⡤⣀⠀⠀⢀⣠⠷⠀⠀⢀⠂
⠀⠀⠀⠑⣄⡼⠁⠀⠀⠐⣤⠇⡄⢠⠇⠀⠀⠀⠀⠈⠈⠉⣉⡉⠁⠤⠤⠨⢉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠸⠷⠷⠶⠶⠶⠿⠶⠶⠎⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠐⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⠀⠀⠀⠀⣀⡀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠯⠋⠁⠀⠀⠀⠈⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡇⠀⠀⢀⣀⠀⣀⡀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢻⣠⠎⡅⠀⠀⡀⢀⠱⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠃⠠⠲⢏⠃⠐⠇⢀⠀⣆⣠⠃⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠃⡀⠀⢀⠾⠁⠀⠀⠀⠀⠀⠀⢄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡐⠃⢀⣤⡟⡀⠀⠀⠒⠀⠀⢤⠊⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠶⠊⠉⢉⠤⠀⢹⡀⢄⠀⠠⠄⣀⠜⠒⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⢁⠀⠞⠁⠐⠂⠀⠀⡑⡌⠛⠒⠛⡂⢃⠏⠀⠀⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡔⠃⠈⠻⣀⠀⠀⠐⠆⠀⠘⠈⠄⢀⣼⠀⢸⠀⢀⠀⣈⣿⢯
⠀⠀⠀⠀⠀⣀⡠⢧⡀⠀⢒⡏⡿⠒⠸⠴⢲⠊⠀⠈⠁⠀⢀⠷⠤⢼⡾⠋⠁⠀⠱⢄⡀
⠀⠀⠰⢖⠉⠀⠀⣀⠍⠋⠩⠳⢧⠀⠀⠀⢸⠀⠀⠀⠀⢀⠎⠀⠀⠀⠙⢦⡀⠈⠀⠀⠙⢦⡀
⠀⠀⠠⠮⠤⡴⠊⠀⠂⠀⡀⠀⠻⠀⠀⠀⠈⠳⡘⠋⠛⢧⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠑⡄
⠀⠀⠀⢠⠎⠀⠀⣀⠀⠀⣀⠀⠀⢳⡀⠀⠀⠀⠙⣄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠘⠆⡀
⠀⠀⢠⡣⠐⠊⢁⡠⠔⠂⢹⠀⢀⣀⣱⣄⠀⠀⠀⠘⢤⣤⠇⠒⠒⣒⣒⣊⡉⠭⠭⠥⠟⠒⢆⠀⡀⠈⣂⡀
⠀⠀⡚⠒⠂⠁⠀⠀⠀⠀⢸⠉⠀⠀⣀⣈⡑⠤⣀⠀⠀⠀⠀⠙⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠊⠁⠈⠉⠂
⠀⠀⢰⠀⠀⠀⠟⢂⠀⠀⠸⠀⠸⣍⡀⠀⠀⠀⠀⢆⣲⠦⠧⠣⣎⣤⠤⠤⠤⠴⠒⠒⠒⠊⠉⠂⡍⠉⠒⠢⠤⢄
⠀⠀⢸⠄⠀⣀⡀⠸⣰⠀⣒⠀⠀⠀⠈⠉⠒⠢⠤⣀⡈⠑⠒⠤⠤⣠⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⣨⢤⢄⠀⠐⣀⠅
⠀⠀⠈⡃⠈⠓⢤⡉⠂⢄⡺⠀⢀⣀⣀⠀⠀⠀⠀⠀⢈⣑⣒⠤⢄⣈⠣⡀⢫⠁⠂⢒⢰⠛⠂⠐⠚⢳⠘⠒⠉
⠀⠀⠀⠉⠉⠉⠀⠉⠑⠢⣄⡊⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣮⠉⠛⡾⠯⠥⠤⠜⢻⠉⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠛⠒⠓⠤⠤⠤⠤⠤⠤⠔⠒⠒⠊⢉⡇⠀⠀⡇⠲⠴⠶⠆⢸⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠜⠀⠀⠀⡇⠀⠀⠀⠀⠈⡇⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣤⡄⠀⠀⠀⣀⣀⣤⠖⠁⠀⠀⠀⠀⢇⠀⠀⠀⢀⣠⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⢿⡿⠿⢿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠂⠀⢀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⠳⡖⢋⠕⢊⣾⠟⠓⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⢀⣿⠃⠀⠉⠉⢠⣿⠇⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢧⠀⠀⠀⣾⣿⣀⣀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⣧⣀⣼⡇⢀⣿⣿⣿⣿⣿⣿⠀⠀⠸⣄⠀⣀⣠⣤⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣟⢶⡀⠀⠀⠀⡼⠁⠀⣰⠋⠉⠁⢸⡇⢐⣿⣿⣿⣿⣿⣿⠀⠀⠀⣽⢫⠁⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢠⠿⠀⢹⡆⠀⡰⠁⢀⡜⠁⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣇⢀⣠⠗⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣦⡿⣄⢀⣀⡼⢀⠔⠁⠀⡎⠀⠀⠀⠀⠀⠈⡇⢸⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⢷⡿⡆⣤⠀⢁⠀⡀⢰⠃⠀⠀⠀⠀⠀⣰⠃⣬⣿⡿⠟⠋⠉⠀⠀⣀⣤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡿⣔⣿⡻⠛⢡⡀⠀⠀⠀⠀⡴⢁⣾⣿⣿⡄⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣷⠀⠈⠁⠙⠉⠳⠤⠏⢹⣄⣀⢀⣜⡡⢟⣫⣥⣾⣤⣤⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠉⠀⢀⣺⣷⣤⣦⡀⠀⢀⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠸⣿⣏⠀⠉⣷⢀⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠓⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣙⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⢀⡠⠔⠒⠀⠀⠐⠒⠤⣀
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⢀⠎⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀
⠀⠀⡘⠀⠀⠐⢤⢀⠆⠀⠀⣴⢀⠀⢤⢀⢀⠘⠀⠀⠀⠀⠀⢼⠃⢀⣀⡀⠻⣷⣄⠀⠀⠀⣠⡀⠘⣯⠀⠀⠀⠀⠀⠀⠀⠈⢀⡏⢮⡁⠄⢰⣣⡀⠰⣀⣠
⠀⠀⢃⠀⠀⢀⡎⢈⡶⠈⠆⠚⠒⠀⠈⢩⠃⢀⠀⠀⠀⠀⠀⢿⡀⠘⠛⠀⢀⠈⠻⣷⣄⠀⠛⠁⠀⡯⠀⠀⠀⠀⠀⠀⠀⠤⠎⠐⠊⠉⠉⠁⠉⠀⠀⠀⠃
⠀⠀⠘⡄⠘⠊⠀⠁⠀⠀⠠⠐⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠹⢇⠀⠀⠔⠃⠀⠀⠈⠙⠦⠀⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠦
⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠑⠦⢄⣀⠀⠀⢀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⣠⣾⠟
⠀⠀⠀⠀⡀⠀⠀⠈⢿⣦⡀⣠⣾⠇⠀⠀⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣛⣸⣷
⠀⠀⠀⢨⡇⠀⠀⠀⢠⣿⣑⣿⡇⠀⠀⠀⠘⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣷⣾⣿⣧
⠀⠀⠀⢾⡆⠀⠀⠠⢾⣿⣷⣿⣷⠄⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦
⠀⠀⠀⢘⣧⠀⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⢬⠃⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠿⣷⣄⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⢠⡤⣄⠸⠿⢿⠏⢹⡿⠿⠀⡀⢤
⠀⠀⠀⠀⠘⠁⠀⠘⠿⣿⠛⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⣻⢳⢳⢻⡟⡟⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠿⠴⢦⢾⡼⠷⠷⠿⠿⠈⠁


⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢰⠂⢠⡄⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠘⠒⠚⠓⠸⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⡌⠀⠀⢠⣶⣿⣿⣷⣿⣿⣷⣦⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⡀⠀⣀⢀⡄⣀⠀⠀⡀⠀⢀⡀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⢿⡀⠀⠈⠉⠛⠛⠛⠛⠛⠋⡉⠀⠀⢠⠇⠀⠀⠀⠀⣤⣴⣶⣦⣤⣾⡟⣿⡇⠛⢸⡇⡆⣿⠈⢡⣿⠘⢻⣿⠸⢃⣿⡘⣸⣿⢛⣷⣦⣤⣶⣶⣤
⠀⠀⠀⠀⠈⠁⠀⠀⠃⠃⠁⠨⠬⠘⠇⠧⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠙⠿⠿⠇⠛⠸⠇⠶⠸⠸⠧⠻⠜⠋⠿⠰⠌⠿⠇⠿⠿⠿⠏⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠐⢧⣰⠒⣶⣲⣙⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠁⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⣸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣉⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⡿⢿⠙⠶⠖⠀⠀⠈⢛⡄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣌⣀⠠⠀⠀⠀⠀⠈⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⣄⠤⠀⠠⠀⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⠆⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⢷⣶⠾⠛⣉⡤⠞⣡⣿⡿⠛⠷⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢡⣾⡟⠁⠀⠿⢤⡼⠥⢤⣴⣿⡿⠁⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠀⠀⠀⠀⣾⣿⠁⠄⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣯⡀⠀⠀⠀⠀⢀⣼⣿⡏⠀⠀⠀⠀⠀⠈⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠈⢷⡀⠀⠀⠀⣸⡿⠛⢿⣶⣤⣤⣤⣤⣤⣼⣿⣿⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⣷⡀⠀⣠⣿⡇⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣀⣀⣀⣀⣿
⢀⠀⠀⠀⠀⠀⠀⣾⣆⢠⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣰⠞⠿⠷⠛⠉⣿⠃⠀⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣷⣴⠞⠋⠉⠉⠉⠙⣿
⣼⡄⠀⠀⠀⠀⠀⢻⡜⠛⣧⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣻⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢰⡿⠹⡆⠀⠀⠀⠀⠀⢿
⣿⣧⠀⠀⠀⠀⢠⡜⡇⠀⠸⣷⡇⠀⠀⠀⡼⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⡧⠚⠁⠀⠀⠀⠀⠀⣸
⣿⣿⣆⠀⢰⡄⠸⠀⠀⠀⠀⣸⠇⠀⢀⡼⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿
⢹⡟⢿⣆⣺⢷⡜⢦⣀⢀⣠⠟⢀⡴⠋⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠈⣧⣈⣿⣯⣠⣿⡆⠈⢉⠁⠀⢸⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⠛⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠘⣿⣇⠙⢿⠙⢿⣀⣿⡀⢀⠘⡴⢀⣴⢆⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢀⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡏
⠀⠀⠈⣿⡄⠀⠀⠘⣿⡿⣇⢸⣷⡙⡟⠼⠋⢁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢠⣾⣿⣿⣿⣡⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡀
⠀⣧⠀⢹⣷⡀⠀⠀⢻⡇⠹⣾⡏⢿⡆⠀⠀⣼⠿⣆⠀⠀⠀⠀⠀⢀⡾⠁⣤⣿⡿⠿⠛⢉⡝⠀⡔⣠⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⢳⣾⣿⡇⠀⠀⠀⠀⡀⠈⠀⠀⠙⠳⠛⠋⠀⢹⣧⣀⣀⡀⢠⣞⣡⠶⠋⣁⣤⣶⣿⣿⣤⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⡀⠈⠋⠋⠀⠀⠀⢦⣿⣦⡀⢠⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠘⣧⠀⠀⠀⠀⠀⣷⣾⣿⡯⠻⢿⣿⣦⠀⠀⠀⢸⣿⣿⡿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠘⣧⡀⠀⠀⠀⢻⣿⣿⡁⠀⠀⠈⣿⣿⣀⣤⢿⣛⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⢷⣤⣤⣀⠹⠿⠿⠶⣖⣒⣭⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠈⢻⡉⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠙⠷⣤⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣭⣷⣶⣾⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⠹⠡⢃⠎⡲⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠀⠈⠛⠒⠦⣊⢌⠜⠅
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠤⡆⠀⡠⢡⣆⢠⠀⠈⠳⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠞⣁⣨⠔⠋⠊⠈⠈⡘⣆⠀⢀⣤⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠩⢁⣀⠄⠀⠊⠀⢀⡈⣢⣶⢫⠉⠙
⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⠀⠀⢀⣴⣿⣯⣙⡇⠀⠘⢣⡌
⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢁⢀⣤⣶⡛⣲⡞⠬⠽⠟⠋⠀⠀⠀⡠⣁
⡗⠠⠀⠀⠤⠒⠁⠄⠀⠂⠉⠐⠢⡀⠀⠻⣘⣻⠿⠧⣤⡠⠖⠂⠀⠀⠀⡐⠀⡆⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠰⠂⠒⠡⢼⠐⠁⣂
⡇⠉⢀⢀⠀⠀⠀⠀⡡⢆⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠉⠁⠀⠄⡀⠀⡺⠃⠀⡇⠀⠀⢀⠙⣤⣡⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠀⠂⠀⠀⠀⠀⠁⢄⠀⡐
⡇⠀⠈⠘⠂⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠒⠈⠀⠈⢉⡉⢀⠘⠀⠈⠀⠀⠀⡋⢀⠯⠥⠆⠀⠀⠀⠀⠈⠀⠒⠀⠀⠀⢄⠀⠀⠀⠀⠈⡅⠄⠒⠂
⡦⠤⣀⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠋⠰⢊⡔⠁⠠⡀⠠⡀⠀⡀⠀⠀⠆⠀⠀⢰⠖⠁⠀⠱⠐⢄⠐⠄⠀⠀⢾⣧⠀⠀⢀⡀⠨⠂⠀⠀⠀⡄⠀⠐⠃⡄
⣟⣓⠒⠢⠤⠭⢉⣉⣓⠶⠶⠀⠀⠀⡤⠈⡡⠂⠙⠒⠀⣐⠮⠑⢽⡒⠚⣩⣍⡀⠀⢀⠊⠂⠀⠀⠀⠡⢀⡉⠀⠀⠀⠀⠐⠉⢀⠻⠇⠀⠀⢀⡴⢴⡀⠀⡄⠀⠁
⣧⣬⠭⠽⠓⠊⠉⠀⠀⠀⠀⢀⡔⢨⣄⠀⠹⡇⠐⢒⡦⠩⡄⠈⢠⡔⠂⠌⠘⠻⣶⠁⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⠈⢀⡀⠈⠁⠀⠀⠀⣀⠴⠤⠦⠤⠤⠴⠶⠖
⡏⣉⣐⣓⣒⡒⠒⠒⠤⣤⣤⠀⢌⠲⡵⠃⠐⢖⠆⢨⣄⡈⠿⣀⠸⠋⡩⠠⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡸⠉⠉⠝⠋⠉⠉⠓⠀⠶⢐⠈⠁⠀⢄
⡗⠒⠲⢤⣤⠭⠝⢛⣉⠅⠠⡀⠠⠑⠄⠙⢆⢠⢦⣠⣦⠀⠹⠋⠰⠠⠄⠔⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡈⠂⢂⠀⡔⠀⠀⠀⠀⠀⠢⡀⠀⡠⠅
⡿⠛⠋⠩⠄⠀⠀⠈⠀⠀⠀⠀⠂⠈⠢⡈⠢⡙⠋⠀⠈⢉⠔⠓⠀⠀⠠⠄⠠⠤⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡠⠀⠀⡀⠈⠁⠑⠈⢡⠈⣠⠠⢀
⡇⠀⠀⠀⠒⠀⠀⠀⠀⠠⠀⠀⠀⠄⠂⠉⠀⠈⠑⠤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⡜⠙⠋⠀⠢⢡
⡏⠢⠀⠀⡀⠔⠀⡀⠀⠀⠈⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡂⠀⠠⠄⠀⢤⠀⠀⠰⠀⠀⠀⠁⠀⠀⠘⠑⠀⢀⡉⢀⡀⠀⠀⠀⠀⡷⠐⠀⠀⠄⡈
⡏⠢⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⢀⡀⢀⡀⢤⠐⠂⠁
⡇⠄⡁⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⡃⠀⠀⠀⡑⠠⠈⠂⠀⠀⠀⠀⠀⠀⢀⡄⣀⠀⠀⡀⢀⡄
⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠈
⡇⠀⠀⠀⠠⠐⠈

⠀⠀⠀⠀⠀⣀⠄⡤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠐⡠⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠁⢂⡄
⠀⠀⠀⠀⡔⣕⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠀⠀⢀⠄⠀⠀⠉⠱⣀⢀
⠀⠀⠀⠀⠁⣍⡑⠒⠂⠀⠤⠔⠒⢂⡀⠀⠀⠀⠀⣁⠁⠈⠀⠘⠀⠀⠆⠀⠑⣉⡔⠀⠀⠘⣦⡠⢄⣠⠴⠋⠀⠀⠀⣄
⠀⠀⠀⠀⢸⡡⣄⣀⣀⣀⡭⠭⣉⣋⠌⢳⠀⠀⢀⢘⠫⠀⠀⠀⠀⠐⢒⣋⠭⠚⠈⠀⠀⠀⢹⣼⣨⣭⣧⣠⢄⣠⢄⡜
⠀⠀⠀⠈⠒⠭⠤⠀⣀⣀⣐⡚⠩⠅⠂⠁⠀⠀⠈⠒⠤⢄⣀⣀⣀⣀⣀⡠⠤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠘⣏⣭⣭⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠀⠠⠒⠀⢲⡀⠀⠀⠀⠀⠀⠀⢀⠤⣢⣄⠀⢀
⠀⠀⠀⠄⠓⠤⢤⣄⣀⣀⣀⣀⡀⠼⠖⠵⠀⠀⠀⠀⠀⠀⠌⠀⠈⠈⠀⠀⠀⢸⠃⠀⠀⠀⢀⡠⠒⡁⠀⠂⠂⠢⢊⡩⠈⡀
⠀⠀⠄⠰⢤⣤⣀⣀⣀⡀⢀⣀⣀⣠⣴⠆⠀⠀⠀⣠⣖⠀⠠⠀⠀⡀⠀⢄⡰⠃⠀⠀⢀⠴⠈⠐⢠⠀⠁⠐⡁⣀⠄⠀⠄
⠀⠀⢃⠀⠀⡉⠈⠉⠙⠋⠉⠉⢉⡨⠋⠀⢀⠀⠀⠈⢍⠳⣇⠁⠐⣀⡴⠋⠀⠀⠀⠈⠪⢧⡄⠘⠊⠐⠀⠀⡂
⠀⠀⠀⠑⠊⣀⣤⡅⢐⡒⠒⠚⠉⠀⠀⠀⠁⠀⠀⠀⠀⠐⢹⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢄⠉⠉⠄⡀
⠀⠀⠀⠀⠀⠳⠄⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢱⠀⠀⠀⠀⠐⠉⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠎⡅⠤⠤⠄⠒⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠈⣀⣤⠞⡫⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⣆⢀⣼⢢⡇
⠀⠀⠀⠀⢀⠀⠈⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠟⠋⠁⠈⠱⡘⢄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠻⡿⠃⢈⠇
⠀⠀⠀⡠⢰⢄⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⠳⡄⠀⠀⠀⢠⠚⠀⠀⡏⣽⠶⠾⢸
⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣳⠷⠁⠀⠀⠀⠀⠁⠚⠂⠀⠐⠒⠊⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⣤⠖⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣠⠄⠀⠰⠆⠀⠀⠰⠶⠂⠀⠀⡐⠀⠀⢠⠖
⠀⠀⢠⠋⠀⢀⣀⡀⠀⠻⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠠⠆⠀⢀⠀⠀⠀⠀⠀⢟⠊⠀⠀⠔⠀⣴⠶⠀⠀⠀⣀⡀⠙
⠀⠀⡆⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠒⠀⠀⠀⢀⠋⠀⣰⣆⡠⠔⠉⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠆⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⠶⠭⠤⠴⠖⠊⠁⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⣠⣄⠀⠀⢀⣀
⠀⠀⢿⡄⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣀⡀⠀⠘⠁
⠀⠀⠀⠐⠀⠐⠻⠀⠀⠀⠀⡶⠀⡾⠃⠀⠀⣀⣀⠀⠀⢀⣀⣀⠀⠀⢀⡾⢹⠀⠀⠀⠀⣀⠀⠀⠀⠁⢤⣤⠀⠀⠙⠃⢀⡠⠶⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⣼⠇⠸⠟⠛⠛⠛⠿⣿⢟⡋⣘⢂⣤⡼⣧⠃⠀⠀⠀⠀⠈⠁⠐⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⣿⡏⢠⡶⢲⢰⡟⢹⣸⣿⣡⠏⣿⢸⡗⡡⣋⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⢁⣿⡧⣼⢻⣏⡞⠻⠏⢷⣄⡭⠤⢥⡈⠣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⡴⠋⠈⠓⢡⣤⣤⣴⡶⠞⠋⠙⠓⠶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠴⠆⠀⠚⠛
⠀⠀⠀⢠⠄⠀⢀⡄⠀⠀⠈⠛⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢠⠤⠶⠒⠒⠈⠛⠢⠀⠀⠀⠀⠀⠀⣠⣏⣶⠶⠂⠉⠑⠂⠀⠁⠀⠶
⠀⠀⢀⡄⠘⠳⠀⠀⠀⠀⠴⠖⠀⠀⠉⠉⠀⠀⠀⠀⡠⢈⡋⠀⠐⠛⢂⠀⠀⣤⠀⢠⡄⠀⠀⠀⠹⠏⢠⡦⢀⣀⣃⣠⣠⠄⠀⠠⡄
⠀⠀⢸⣷⣄⡀⠶⠆⠺⠷⠀⠀⠾⠳⠆⠊⡜⠀⠀⢼⠁⢨⣅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠖⠋⠀⢠⡄⠀⠀⠉⠂⢴
⠀⠀⢿⡿⠿⠿⠿⠿⣦⣯⠷⠶⠶⢶⣖⠛⣀⠀⠀⢏⠀⢀⡀⢀⠀⠠⠀⠈⠷⠀⠀⡀⠁⠀⠀⠀⠸⠏⠁⠶⠄⠀⠀⠀⠐⠦
⠀⠀⠀⣽⣿⣶⣛⣠⣀⣀⣀⣠⣤⣿⠿⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⠀⣸⢀⡄⠀⠀⠀⢀⣄
⠀⠀⢀⣭⣍⡉⠁⢈⣉⡉⣩⠿⠀⢀⣀⣤⣴⠂⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠁⠀⠀⠀⠊⠙⠀⠀⢸⡇⠀⣤⡀⠀⠀⠉⠀⢠⠈⠇
⠀⠀⢈⣜⡋⠩⠿⠉⠉⠹⠏⠿⠉⢉⢉⣉⡥⡄⠀⠀⠀⠠⠤⡀⠰⠂⠁⠂⠈⠀⠁⠀⣄⠀⠀⠀⠀⠻⡀⠈⠁⠐⠂⠀⠀⠀⠀⢀
⠀⠀⠺⡿⣩⣟⠻⢶⣶⠲⠓⠓⠚⠋⣩⡄⢐⡴⠀⠀⠀⠀⠀⡄⠀⠀⠀⠿⠖⠀⠀⠀⠁⢠⡆⠀⠀⠀⠙⠒⠠⢄⣀⡘⠃⠔⠒⠁
⠀⠀⠀⠙⠛⠛⠲⠮⠉⢤⣤⠤⠶⠤⠶⠚⠉⠀⠀⠀⠀⠀⠤⠀⠴⠄⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠘⡤⠔⠀⠉⠉⠉⠉⠉⠁⠐⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣀⢀⣀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣠⡟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢸⠀⠀⠀⠀⠠⣄⡀⠀⠀⠤⠄⠒⣩⠏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢻⠀⠀⠀⠀⠀⢀⠶⢆⡀⣀⠰⠚⠁⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠖⠓⠀⠤⠤⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡛⢌⡦⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠻⣦⠈⠡⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⢶⠶⠶⠶⠆⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠘⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⠔⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢋⡆⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⠏⠦⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠰⠀⠳⣄⠀⠀⠀⣀⢠⠔⠒⡝⠁⠈⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠈⠷⠐⠊⠁⠀⢀⡠⠟⠲⠦⣤⣀⡀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⠱⣤⡜⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠈⠉⠈
⠀⠀⠀⠀⠀⠀⡠⠛⠻⠉⠉⠉⠁⠀⠀⠈⠒⢄⡀⠀⢀⠞⠀⠈⠙⠃⠤⠤⠌⠿⠿⣧⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠙⠓⠤⣀⣀⣀⣀⣀⣀⣀⡀⠀⡨⠛⢷⣄⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢈⣳⣤⡚⢠⡄⠀⠀⠀⠀⠀⣤⣤⣤⡀⣀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠒⣒⣖⡚⠛⣻⣿⡛⢻⣿⣖⠒⠒⠖⠲⠚⠷⠲⣶⣶⡶⠶⣶⣶⡿⢵⣶⣤⢶⣤
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠘⠋⠉⠃⠈⢉⠉⠃⢹⣏⣹⠃⠀⠀⠀⠀⠀⠰⣿⣽⣿⢺⣿⣹⡿⢺⣯⣽⣿⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡦⠤⠴⣦⠤⠤⠤⣤⡤⣥⣤⣤⣤⠤⠤⣤⣤⣤⣬⢭⣥⣤⣭⣭⣥⣬⣭⣉⣠⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡀⠀⢠⣀⣀⣠⣘⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣻⣻⣯⢸⡇
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠐⠒⠚⢦⠔⡄⠤⠀⠀⠀⠤⠄⠤⠤⠤⠤⠤⠤⠤⢤⣤⣄⠀⠀⠈⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠰⣆⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⢸⠀⠀⠀⠀⣿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠍⢹⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⢘⣄⠀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠭⠥⠤⠬⠤⠤⠤⠤⠤⠤⠤⢴
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠓⢤⣤⣇⠀⠱⢦⣄⠀⠠⣄⡀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣀⢀⣀⠀⠀⢀⣀⣀⣀⣀⡀⣀⣀⣀⢀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠛⠓⠒⠚⠛⠛⠛⠒⠛⠓⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃

⠀⠀⠀⠀⢀⣠⣄⣠⣤⣀⣤⣤⣴⣶⣤⣴⣶⣤⣶⣶⣶⣶⣦⣶⣦⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⣿⠛⠛⠛⠉⠉⠉⠉⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠋⠙⠛⠛⠙⠉⠙⠉⠉⠛⠛⠛⠛⠛⠙⠛⠛⠁
⠀⠀⠀⠀⣴
⠀⠀⠀⠀⣿⣤⣄⣀⣀⣄⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⣤⣀⣤⣀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣸⡏⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠻⣦⣀
⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀
⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⣠⣼⢿⡆
⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢀⣠⣶⠿⠉⠀⢸⡇
⣸⣇⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄⣤⣀⣠⣀⣀⡀⠀⣰⣿⠶⠛⠉⠀⠀⠀⠀⢸⡇
⢸⡉⠉⠀⠀⠀⠈⠉⠀⠈⠉⠁⠈⠀⠈⠈⠁⠉⠀⠉⠁⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢸⣧
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⠀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣽⡀⠀⠀⠀⠀⢸⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠉⢹⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣸⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣴⠿⠛⠁⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⡇⠀⠀⠀⠀⣿⠁⠀⠀⠀⢀⣴⡏⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢠⡅⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⣿⡀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣹⡇⠀⠀⠀⠀⣿⡇⠀⠀⢼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⠶⢤⣤⣀⣀⣠⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⡇⠀⠀⠀⠀⣿⡇⣀⣀⣀⣀⣀⣀⣀⣈⣁⣉⣭⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⣿⡟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡁⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡁⠀⠀⠀⠀⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⠃⠀⠀⠀⠀⣾⡄
⢼⡂⠀⠀⠀⠀⣿⢣⣶⣶⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣦⣶⣤⣴⡄
⣾⡇⠀⠀⠀⠀⠿⣦⠼⣯⠭⠭⠭⠭⠭⢭⠤⠿⢿⣿⣿⠥⠬⠭⠿⠭⢭⣬⡭⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠁
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⣹⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢤⡀
⠀⠀⠀⠀⠊⠁⠯⠽⠭⠇⠤⠀⠿⠿⠼⠵⠸⠥⠁⠸⠿⠫⠼⠯⠼⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠔⠁⠀⠀⠀⠀⠈⠶⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛⠂⠀⠀⠀⠢⣤⣀⣠⣴⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠙⠢⢄⣀⡀⠀⠀⢀⣀⣠⠟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠅⠠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢁⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡊⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⠒⠂⠀⣀⠄⠀⠀⣀⡄⣀⡤⠞⣹⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⠀⠈⠉⠁⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⣉⠙⠛⠛⠉⠁⠉⠁⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢅⣀⠤⣤⢤⣤⢤⡤⠼⢑⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⡄⠀⠜⣀⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠼⡇⠂⠀⠒⠒⠒⠒⠂⠀⠐⡁⠀⠠⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠣⠜⠉⡤⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡖⠂⠉⠉⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠢⣀⡠⠆⠀⠀⠀⠀⠀⠀⡠⢶⠁
⠀⠀⡀⠀⠠⠀⠀⠀⠀⠇⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠀⠀⢀⣀⠀⠀⠀⠀⠑⠢⢄⣀⣀⣀⣀⣀⣤⣤⡲⠯⠖⠋
⡀⢀⡍⠀⠐⠒⠒⠂⠀⢸⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⢀⠀⣤⢯⡑⢢⣀⠀⢀⡔⠙⣏⡙⠉⢹⠏⠀⠀⠙⣄⠀⠀⡀
⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡦⢀⢀⡀⠀⠀⡀⠀⣀⠠⠤⠌⠀⠠⠀⠘⢯⣻⠄⠈⠒⠚⠳⠆⠀⠀⠉⢹⠀⠀⠀⠀⡇
⡇⠠⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠓⠠⠀⢀⠀⢀⡀⠀⢀⠤⢄⠀⠀⢀⡤⠴⠖⠊⠷⠀⠚⠀⠘⠒⠲⠤⢄⣸⠒⠤⣀⡴⠁
⡇⠀⠈⠦⠤⢤⠤⠤⠴⠏⣄⠀⠀⢩⠀⠀⠀⠁⠀⡯⠉⠐⠅⢤⣀⠀⠀⠘⡄⠀⠈⠁⠠⠠⠠⠄⠀⠀⣀⡤⠞⠋⠀⢠⣧⡴⢲
⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣟⠀⠀⠀⠐⡬⠤⣈⡤⠼⡆⠁⡀⠀⠀⠀⣺⠌⠉⠀⠀⢀⣠⠔⠉⢹⣤⠶⠥⠤⠤⠤⠤⠤
⡇⠁⠈⠁⠀⠉⠁⠉⠉⠉⠉⠁⠈⠈⠉⠁⠁⠁⠁⠉⠐⡀⠀⡌⠁⠉⠉⠁⠉⠁⠐⠠⠄⢀⣀⠳⣊⣤⠤⠚⠉⠀⠀⠀⠸⡎⡅⠉⠁⠉⠉⠈⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠦⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡖
⡇⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠉⢹⠃⠀⠒⠂⠒⠁⢧
⡇⠀⠀⠀⠀⠀⠈⠉⠒⠂⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄
⠧⠤⠤⠤⠤⡌⠀⠀⠀⠀⢨⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡔⠉⠑⠲⠤⢤⡼⠀⠀⠀⠀⠀⠀⠀⢣⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢣⡀⠀⠀⠀⢀⠷⠤⣄⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠐⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⣄⠀⠀⠀⠉⠉⠐⣒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠂⠉⠁
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠊⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢙⢀⣄⡤⠀⠀⠠⠀⣤⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⠀⠀⠀⠀⠀⠀⠛⡟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡖⠀⠀⠀⠀⠈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⠃⣴⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡀⠠⠤⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠤⠂⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣿⣷⣼⣦⣴⣾⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠉⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣆⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢾⣿⠇⣿⣿⡀⢀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⡖⠀⢠⡀⠈⣧⠀⠀⠀⠀⠀⠀⣿⣿⠀⢹⣿⠆⣇⡞
⠀⠀⠀⠀⠀⠀⢸⠡⢜⡲⢽⣶⢻⠀⠀⠀⠀⠀⠀⠘⠁⠀⠸⡏⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠙⣺⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡭⢬⡍
⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠘⣮
⠀⣀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠔⠛⠁
⠀⠻⠦⠘⣷⠖⠤⠤⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡐⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⠉⠉⠑⠒⠒⠲⢤⣠⣤⣤⠤⢤⣄⣀⣀⣀⣀⠀⠀⠀⢠⠁⠶⢛⣃⡈⠛⣁⡒⢠⡤⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠁⢸⡀⠚⢦⡬⠀⠀⠩⠡⠄⠂⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⢦⣄⡀⠂⠝⠛⠀⠘⠛⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⢤⣄⣀⣀⣉⡛⠓⠶⠶⠦⠤⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡇⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⣀⠤⠤⠴⠒⠒⠉⠀⠀⠀⠨⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡟⢠⠁⠀⣀⣤⣠⣇⣡⣴⠀⢱
⠀⢀⠐⠂⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠁⠀⢀⠄⢀⢤⠀⣴⣿⣖⣽⠇⠈⠀⡸⠇⠳⢃⠿⠗⠛⠀⣼
⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠁⠀⠠⠁⣰⣇⣼⢀⢾⣭⢯⠜⠀⠁⠀⠹⣶⠶⠤⠤⠤⠖⠋⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⢠⠃⣔⣟⡮⢙⢛⡻⠋⠀⡠⠊
⠀⠀⠀⠀⣀⡤⠤⠴⠶⢤⢄⡀⠀⠀⠀⠀⡎⢀⡿⠗⠃⠉⡁⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠴⠋⠁⠀⠀⠠⠀⡎⠀⠀⠑⠀⠀⢸⠀⡀⠠⠐⠂⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢲⡖⠁⠈⠍
⢠⠃⠀⠀⠀⠀⠀⠀⢀⢷⡄⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠙⠍⠀⠀⠀⠁⠀⡀⠄
⠚⠉⠀⠑⣦⡀⠤⠒⠁⢘⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠔⠀⠀⠀⠒⠀⠀⠀⠀⠄
⢰⡠⠀⠈⠉⠒⠂⠄⠀⠀⠀⠀⣀⣀⠄⠈⠺⡇⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡀
⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⣲⣤⠖⠁⠈⣿⠜⠉⠁⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡿⠁⠀⢠⠟⠁⠀⠀⣰⣫⠌⠛
⠀⠀⠀⠀⡀⠄⣀⣄⡀⠤⣀⠀⠀⠠⠀⠀⣀⣈⣁⡀⠐⠀⢄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⣀⠔⠁⠤⠤⢤⣍⠉⣛⡼⠀⠎⠀⠾⢭⡤⠧⠌⣩⡽⡳⠀⠁⠈⠕⠂⠤⠀⣀⣀⣀⣀⣠⠤⠤⠐⠒⣹
⡼⣁⣬⠙⡓⠲⢀⠼⠊⠁⠀⠀⠀⠀⠀⠈⠓⠒⠒⠓⢉⠀⠀⡀⠀⢰⡀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⣰⠃
⠙⠉⠛⠛⠃⠖⠁⠀⠀⠀⠀⠀⠐⠦⣀⡀⠀⠀⠀⣀⣀⠔⠊⠀⠀⠀⠉⠓⠢⠤⠥⠥⠥⠬⠤⠴⠚⠁

⠀⠀⢀⣤⣴⣶⣶⣾⣿⣿⡟⣿⣿⣿⣻⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⣸⣋⠉⠙⠛⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⣰⣧
⠀⠀⡹⠋⠙⠛⠛⠻⠶⠶⠶⠦⠤⠤⠶⠶⠶⠛⠛⠛⠉⢨⡏
⠀⠀⢹⡾⠀⠀⠀⠀⠀⠀⠀⠦⠬⠤⠄⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⡏⠉⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠒⠒⠚⠛⠛⠉⢹⡇⠀⠀⠀⠠⢴⡒⡽⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀
⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⡇⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⢀⢤⡄⠀⠀⢸⡇⠀⠀⠀⠀⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⢰⣟⢭⢁⠠⠀⠀⠀⠀⡈⢋⣷
⠀⠀⠀⡇⠀⠀⣿⡤⢠⠀⠀⡖⢲⠘⡇⠈⢸⣤⡏⠀⠀⢸⡇⠀⠀⠀⠀⠿⣼⠀⡋⣦⠛⣰⣾⠀⣟⢹⡽⠈⢳⡀⠀⠀⠀⢸⣿⡖⠀⠉⠈⠍⠁⠀⠀⢪⣿
⠀⠀⠀⡇⠀⠀⣿⠀⢸⡀⠀⡇⢸⢀⡇⠀⢸⠀⠙⠀⠀⢸⡇⠀⠀⠀⠀⠉⠘⠞⠧⠟⣄⢛⣻⣀⣥⠼⠼⠀⠛⠁⠀⠀⠀⢸⡇⡀⡀⠆⢢⠰⠖⡄⠀⠈⣿
⠀⠀⠀⡇⠀⠀⠿⠀⠸⠦⠆⠓⠚⠀⠉⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⡀⠀⡀⠀⠀⠀⢀⠀⠀⠀⢸⡇⡣⠷⢒⣁⣘⣒⠃⢄⡌⣿
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠂⠸⠀⠁⠧⠘⠃⠀⠀⠀⠸⠀⠀⠀⢸⡇⠀⣰⣿⡯⢉⢿⣷⠀⠈⣿
⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢰⠙⢀⡖⣤⢀⡤⡄⢠⠦⡀⠰⣿⠀⠈⠀⠀⠀⢸⣇⠀⢿⢿⡼⢷⡼⢿⠀⣠⣿
⠀⠀⠀⣏⠛⠻⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠖⠎⠛⢹⡇⠀⠀⠀⠀⠘⠴⠈⣇⡽⢸⡀⡄⢻⣘⣇⣟⠻⠔⢀⠀⠀⠀⢸⣿⡷⣌⡪⠟⠪⠕⣣⣶⡿⣿
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠉⠀⠀⠀⠀⣌⠀⠀⠀⢸⣇⡙⢷⣇⡅⢐⢾⡧⢟⣠⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠀⠀⠀⢸⣿⣙⡂⠀⠉⡈⣀⣐⡛⣽⣿
⠀⠀⠀⠀⠉⠒⠀⠀⠀⣀⣀⣀⢀⡀⣀⠀⠀⠤⠤⠐⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠠⠭⠉⠉⠭⠄⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣤⣀⡤⠤⢤⡀⠀⠀⠀⠙⠆⣰⠿⠃⠀⠀⠀⢀⣶⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢱⠀⠀⢀⡀⠀⠀⢠⡞⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠞⠀⠀⢸⣧⠀⢰⡿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢀⣴⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢧⡉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⡴⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⠃⠀⠀⠀⠚⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠈⠲⠤⠞⠋⠛⠿⠿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠈⢧⣄⣀⣠⡞⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⢀⣤⠀⠀⠀⢸⡏⠉⠉⠉⠉⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⡂⠀⠀⢸⣧⣤⣤⣤⣄⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣴⣿⣿⣿⣄⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⠇⠀⠀⢸⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⢠⣿⣿⡿⣿⣿⣿⣷⡀⠀⠀⠛⠻⠛⠀⠀⠀⢸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣇⣽⣿⣿⣿⡇⠀⣀⣀⣀⢀⣀⣀⠀⠨⣿⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⡿⠁⠀⢨⡟⣱⣿⡇⠀⢿⣿⣿⣿⣿⣿⠁⠈⣿⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣷⠀⠀⠀⠁⠙⢿⡇⠀⠀⠛⠻⠿⠛⠁⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣾⡇⠀⢀⠀⠀⠤⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⡇⠀⢈⠀⢁⠀⠆⠀⣠⣴⣿⣤⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⢠⣄⣀⣀⣀⣀⣤
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠇⠀⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠙⠻⠟⠛⠁⠀⠀⠀⠙⠛⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡤⠤⠤⠀⠤⠀⠐⠂⠒⠒⠠⠤⢤⠤⠤⠤⠤⣤⠤⠄⠒⠐⠒⣒⡒⡒⡎⠉⠉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⣀⣀⠁⢁⠀⣤⡄⠀⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⣠⡾⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠂⠁
⠀⠀⠀⠀⢺⡏⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠠⠤⠤⠤⠆
⠀⠀⠀⠀⢸⡇⠀⢀⣀⣼⣶⣶⣶⠤⠤⠤⠤⠤⠶⠖⠒⠒⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠻⠛⢿⣿⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⠀⠀⠀⢀⣤⠲⣤⠀⠈⠑⣄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠁⠀⢀⣠⣼⠿⣧⡼⠀⠀⠀⠘⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣫⣥⠿⠋⠀⠀⣄⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⢃⠀⢢⡀⣴⠉⣩⢷⡽⠃⢠⠇⠀⠀⣼⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠘⢄⠀⠀⢣⠀⠙⠆⠀⣠⠟⠀⢀⠞⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⠑⠀⠀⠑⠂⡴⢚⣁⠤⠚⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⢀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣤⣄⣀⣀⣀⣀⢀⣀⠴⠒⠉⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⣀⡀⠀⣴⡶⠀⡤⠢⣤⣞⣏⠈⣿⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢀⣤⡀⠫⣤⠆⢹⠘⡿⢿⠀⠿⣿⠁⠀⢼⠥⠀⠑⠒⠀⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⢀⡈⠀⠨⠿⠃⠛⠛⠃⠈⠀⠉⠈⠀⠣⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠤⠤⠖⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡃⠀⠀⠀⢀⣀⣀⣀⣤⣠⡤⠤⠤⠴⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⢉⡀⢀⡀⠀⢉⠀⠉⠀⠀⠀⠁⠀⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠄⠀⢀⡀⠀⠘⣀⢀⠀⣀⣠⡀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣍⠀⠀⠀⠀⠀⠉⣤⠀⣀⠀⠀⠄⡄⠉⠀⠉⠉⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣀⠀⠀⡀⠀⢠⡄⠀⠀⠁⡀⠀⣰⠣⠀⠀⠀⠤⠀⠀⡠⠔⠁⠔⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠉⠀⠀⠀⣀⠔⠀⣀⠾⠭⠄⠁⠁⠉⠈⠠⠄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠓⠀⠀⠠⠀⠀⠂⠁⠀⠀⠚⢅⡀⠁⠠⡀⢀⠄⠀⢀⡀⠀⠐⠂⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠂⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⡠⠔⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠐⠀⠀⠄⠈⢆⠀⠀⠀⠁⠀⢀⡠⠔⠉⠀⠤⠤⠤⠤⠒⠀⠀⢀⡴⢧⡀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠙⢤⡀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⢻⠀⠀⠀⠀⠀⠄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠈⢀
⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠑⠄
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠄⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠀⠈⠢⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢄⣀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡅⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠹⣧⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠙⠒⠂⠉⠉⠁⠀⠈⠀⠀⠀⠑⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⣦⠤⠀⠀⠀⠄⠒⠈⠀⠀⠀⠀⠀⠀⠑⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⣰⠁⠀⠀⠑⢦⡀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⡇⢀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠢
⠀⠀⠠⠔⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠇⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆
⠀⠈⠓⠒⢤⡀⠀⠀⠀⠸⡀⠀⠀⢀⡧⠀⠀⠀⠀⠡⣤⢃⠀⠀⠀⠀⠌⠢⡀⠀⠀⡸⠀⠰⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⢀⣀⣀⣀⣈⣳⣄⢀⣀⣉⣁⣀⣈⣿⣄⣀⣀⣀⣀⣀⣈⠀⠀⠀⠀⢀⠠⠀⠀⢀⣁⡀⢇⠀⠀⢀⡀⠠⠔⠋⠁⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠁⠀⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠉⠉⠉⣉⢩⠍⠉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠁⠰⠦⢀⠀⠀⠈⠑⠁⠀⠀⠀⠤⠀⠀⠀⢀⣀⣤⣶⣿⠿⠋⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠐⠀⠠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⢢⡀⠈⠲⣀⣤⣶⣶⣶⣶⡿⠿⠟⠋⠉⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠂⢀⠀⠀⠀⠀⠐⠉⠉⡁⠀⠀⠀⢀⠀⠀⣄⢀⡀⠀⣀⡀⠈⢆⠀⠐⠂⠭⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡄⠈⡁⠀⠀⠉⠀⠀⠀⣈⠉⠉⠉⢠⣀⠈⠢⣄⠠⠄⠈⠑⠀⢤⠤⠤⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠰⠂⠒⠚⠀⠉⠉⠛⠓⠛⠉⠀⠀⠉⠉⢓⣓⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠲⢤⣠⣤⣀⣀⡤⠀⠙⠦⢤⣤⡤⠤⠄⠀⠙⠲⠶⠤⠤⠓⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠴⠴⢶⠶⠆⠀⡀⠀⠀⠶⢶⠶⠆⠡⠈⠛⠛⠛⡟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⡶⢶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⣇⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⡻
⠀⠀⠀⣼⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⠳⣄
⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⠙⢦⣀
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢀⣠⠽⣇
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⡴⠞⠋⠁⠀⣿
⣾⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⡿⠛⠁⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⢰⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⢶⠟⡟⣹⡷⢦⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⣿⣿⡼⠀⠖⠼⠱⣄⣿⣷⣦⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⢸⡇⠀⠀⢠⣾⢿⠋⡌⢡⠈⠰⢁⢀⡍⢁⠘⠿⣿⡄⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⢸⡇⠀⠀⢺⣿⠷⣇⠅⡆⠇⠇⢈⠾⢁⡎⠈⡞⣿⠟⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠛⠻⠶⢽⣬⣧⣹⣤⣭⠴⠖⠛⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡇
⡇⠀⠀⠀⠀⢸⡇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡇⠀⠀⠀⠀⢀⡇
⡇⠀⠀⠀⠀⢸⡇⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⡇⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⢸⡇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡇⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⢸⣥⣭⣭⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣩⣭⣭⣭⣭⣤⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡴⠚⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠖⠋⠁
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣭⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⢄⡠⡀⠀⠀⠀⠉⠀⠀⠀⠐⠚⠒⠢⠀⠠⠤⠆⠤⠄⠀⠀⣴⣿⣿⡆⢀⡟⢹⢹⠀⢴⣶⣶⣶⠄⠀⠀⠠⠀⠁⠑⡀
⠀⠀⠀⠀⠀⠀⣠⣮⡄⢀⣦⣹⡏⠀⠀⠀⠸⠀⡆⠀⠀⠀⠀⠀⠀⣆⣄⣀⣀⣸⡀⠀⠙⢿⡿⠃⠀⢯⣼⡼⠀⢸⣿⣿⣿⠀⠀⠀⠤⠀⠀⠀⠠
⠀⠀⠀⠀⣠⠞⢾⡟⡿⢿⣿⣋⣱⡀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⣿⣷⡗⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠸⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣠⠞⠁⢀⡼⣧⣶⠿⣿⢿⣿⠃⢰⣿⣷⣿⡆⠀⠀⢲⡎⠀⢸⣿⢋⠄⢙⢿⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠘⡟⠀⠀⠀⠁
⠀⢸⣿⣤⢴⣿⡾⢋⡵⠊⠙⠛⣿⣦⡄⠛⠿⠛⠀⠀⠀⢼⡧⠀⢸⣧⡠⠖⠉⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠻⢿⡟⢁⢀⣥⣒⣦⡄⠀⠘⣿⣛⢉⠂⠀⠀⠀⠀⢸⡇⠀⢸⣇⠀⡀⠀⣸⡇⠀⠀⢈⣁⠀⡀⢀⣁⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠉⡇⠆⣿⣿⡇⣴⣿⣿⣿⣿⣿⣿⣿⡦⠀⢸⡇⠀⢸⣿⣦⣤⣴⣿⡇⢀⡐⣿⣿⠀⠃⢸⣿⡷⢀⠀⢸⢹
⠀⠀⠀⠀⠀⠀⡇⠸⣿⣿⣷⣽⣿⡇⠁⡇⢸⣿⣿⡇⠀⣞⣳⠀⠘⠾⢿⣿⡿⠿⠃⢸⣧⣹⣿⣆⢀⣾⣿⣡⣾⠀⠀⠁
⠀⠀⠀⠀⠀⢰⡇⡇⣿⣿⣿⣿⣿⡇⠀⡇⢸⣿⡿⠁⠀⠈⣡⣤⣶⣦⣤⡀⠀⠀⠀⠈⢿⣿⡿⠉⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡠⠞⠁⢃⣿⣿⣿⣿⣿⣿⣦⣧⣼⠛⠂⣄⠀⣾⣿⡽⠛⠲⣜⢿⣆⠀⠀⠀⠀⠈⠛⠐⠀⠘⠉⠁⠀⣴⢤⣤⣤⣤⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠘⠷⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⢸⣿⢸⡁⠀⠀⣸⢺⣿⢀⡠⡀⢠⡄⠠⣀⠄⢠⡤⠀⣰⣿⣿⣿⣿⣯⣆⠀⠀⡀⣿⢸⡇⡷
⠀⠀⠀⠀⠀⣠⢐⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣂⡄⠀⠀⠻⣷⣝⣒⣚⣹⡾⠃⢸⣗⡣⡿⢿⠸⠿⡆⢤⣓⠀⣿⣿⣀⣀⣀⣻⣿⠀⠰⡇⢹⢸⢣⡇⣶
⠀⠀⠀⣰⡾⢿⣿⣿⡿⢿⣟⡩⠉⢉⣭⢍⠉⣰⠁⠀⣠⠤⠈⢉⠙⠉⢁⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⢀⣷⠿⠿⠿⠿⠿⣼⠂⢀⣇⢸⣸⡾⣇⣿
⠀⠀⠀⠹⣧⣀⢹⣿⣿⣇⣿⠀⠀⣼⠇⠀⡟⠄⠀⠀⠐⠀⣠⣽⣶⣶⣤⣌⣉⣲⢈⣉⣀⣙⠾⣯⣩⠟⠀⢰⣿⠀⠀⠀⠀⠀⢻⡆⢰⡼⣸⢧⣇⡿⣼
⠀⠀⠀⠀⠈⠙⢿⡿⢿⣿⢿⡀⢀⣿⢀⡼⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁⠉⠀⠀⠀⢸⠿⢿⣿⣶⣾⣿⣿⡇⢻⡇⣿⢸⡅⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠯⠉⠭⠟⠀⠀⠀⠀⠀⠀⢮⡤⢾⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⠶⢬⡵⠀⠸⢤⣴⣿⣿⣿⣿⠿⠇⠘⠇⠿⠸⠇⠇⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠴⠶⠶⠶⠶⠶⢶⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠗⠒⠒⠒⠶⠶⠿⠟⠻⠿⠶⠶⠶⢤⣤⣄⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣉⣀⡤⠴⠶⠶⠶⠶⠟⠛⠻⣦⣤⠴⠦⢤⣤⡾⠋⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠉⠙⠛⠛⠷⠶⠶⠶⢶⣶⠶⠶⠶⠖⢲⡟⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⠶⠖⠚⠋⠀⡇⢀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠲⣿⠛⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⣏⠉⠉⣦⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⡿⠓⠀⣿⢠⡟⣳⡄⣿⢀⣷⠸⣿⠛⠀⣿⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⠃⠀⠀⠛⠈⠛⠛⠁⠙⠛⠛⠀⠛⠀⠀⣿⠀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⣿⠛⠉⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠞⠛⠁

⠀⠀⠀⠀⠀⠀⢀⠤⠔⠢⢤⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡤⣤⢤⠀⡠⢠⣄⢀⣄⢀⣀⠀⢠⣤⡀⣠⠄⡤
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠀⠁⠉⠉⠉⠉⠈⠁⠁⠈⠉⠀⠉⠉⠁
⠀⠀⢀⡴⠊⠁⠀⠀⢀⡤⣄⠀⠀⠀⠀⡼
⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠙⠒⠒⠊⢳
⠀⠀⠈⠓⠒⢷⠒⠂⠸⠤⠖⠉⠛⣄⢀⡮⣀⡀
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⡨⠋⠀⠀⠉⠓⢤⡀
⠀⠀⠀⢀⠎⠈⠙⠒⠒⠒⠒⠋⠁⢀⠀⠀⠀⠀⠀⠀⠘⢉⡆
⠀⠀⠀⡜⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠑⠄⠀⠐⠠⠀⣀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⢳⠤⣀⣈⡠⢄⣀⠈⣀⣤⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠈⡄⢀⠀⠀⠀⠀⠀⢧⠀⠤⠀⠀⠈⠉⠁⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢐⠀⠀⠀⠀⡀⠠⠤⣌⠢⡀
⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⢸⠀⣀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠉⠉⠉⢨⠀⡠⡖⠁⠀⠀⠀⠀⠀⠈⡖⢄
⠀⠀⠀⡇⢠⠀⠀⡆⠀⠀⡇⠀⠀⢀⡀⢀⡠⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠳⡌⠉⠭⠭⠭⠭⠍⠋⠥⠎
⠀⠀⢴⠃⠠⠀⠀⠀⠀⢀⣇⣀⣀⠀⠈⣉⣠⣴⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⡀⠀⠀⠉⠳⣄⣠⣄⡀⢸⠉⠙⢏⠙⠛⢡⡟⢦⡀⠀⣀⠄⢢⢧⠄⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⣤⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢘⡀
⡇⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠘⡏⠉⠀⠰⠚⠂⠀⠀⢴⠋⠂⠄⡀⠀⠀⠐⠂⠤⠔⠒⣁⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠶⣼⣄⣀⠤⢞⡥⠒⡂⠉⠁⠙⠁⠀⠊⠓⠲⠦⣅⠀⠀⠁⠀⠀⠀⠈⠀⠈⠗⠀⣤⠀⠀⣸⡀⠀⠀⠀⠀⠀⢸⠗
⠇⠀⠀⠀⠀⠀⠈⠂⡤⠏⠡⡀⠈⠑⠨⠑⣒⠀⠀⠀⠀⠒⠒⠂⢁⠅⠀⠀⢠⣀⣀⣀⣠⠀⠰⡀⠀⠇⠀⡀⠩⣷⣦⣤⣤⣤⣶⡧
⡆⠀⠀⠀⠀⠀⠀⡔⢸⠁⠀⠘⠢⠄⡀⠀⠀⠰⢁⠀⠀⠀⢀⡠⠂
⠁⠀⠀⠀⠀⠀⠀⣗⠃⣀⠀⠀⠀⠀⠈⠐⠒⠚⡳⣶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡬⠤⠭⢭⡭⠄⡾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠙⢄⠀⢀⡾⠄⡀⢥
⠁⠀⠀⠀⠀⢀⠞⠁⠉⢦⠤⠉⣽⠂⠠⠐⠚⡦⡀
⠁⠀⠀⠀⠀⠘⡀⠀⠀⠘⢄⣀⠼⡄⠀⠉⠈⠀⠈⠆
⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡳⠄⣀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠚⠁
⣶⡶⢶⢶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⢶⣶⣶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⣶⣿⣿⣿⣿⣦⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠴⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⠦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⠒⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⣰⠋⠉⠉⠉⣗⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣧⣄⠀⢀⣀⡈⠲⣀⣤⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢘⡷⡆⠀⢠⣄⠁⠀⠋⠀⣹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⢸⠀⣄⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⢰⡬⢤⡤⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⣆⠓⠊⠀⠀⣠⠔⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⠒⠉⠀⠀⠹⣷⣄⣀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⢧⡀⠀⠀⢀⡏⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠉⠓⠢⠞⠀⠀⠀⠀⠀⠘⢆
⣠⠶⠿⣽⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠁⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣧⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠦⣤⣀⣤⠖⣫⡥⢭⣑⣶⠚⠛⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⣤⠖⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠔⠋⠀⠀⠀⢯⠙⢷⡄⠀⢧⡀⠀⠀⠀⠀⠀⠀⣸⠀⣞⢇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠻⣦⡀⠱⣄⠀⠀⠀⠀⠀⡇⠀⠘⢾⣷⢄⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠈⠻⡓⠾⢦⣄⣀⣀⠀⣷⣄⠀⠀⠻⣮⠳⡄⠀⢀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠳⣄⠈⠓⠒⢶⡙⠲⣝⢷⠈⠓⠦⣄⣹⡷⡈⠢⣼⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⢄⡀⠀⠹⢤⣈⣻⡆⠀⢀⣀⣩⢃⣷⣄⣈⣳⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⠛⠛⠛⢻⠿⠆⠀⠀⠉⡿⠯⢭⣉⣽⣟⣋⣉⣉⣉⣉⣉⣉⣉⣩⠭⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠘⠒⢾⠀⠀⠈⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⠤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡏⠙⠲⢤⣄⡀⠀⠀⠉⠳⣶⣦⣤⣤⣤⡤⢤⣤⣤⡶⢶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠒⠤⢄⣉⠉⠉⠁⠀⠀⢀⣤⣤⣭⣭⣥⣤⡴⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣤⡤⠶⠴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⢤⣀⣼⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡇⠉⠓⠲⢤⣉⡙⠲⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡇⣰⡄⣄⢠⡀⣼⡇⢸⡇⢢⣰⢠⢠⣠⠋⡿⡶⣤⣬⣙⡶⡦⣶⣀⣠⠂⣼⣦⣾⣾⢦⠀⠀⡀⠀⠀⢉⠧⡎⡦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠁⠈⠀⠁⢹⠉⢹⡏⠉⠈⠈⠈⠈⠀⠁⠁⠋⠉⠉⠛⠧⢬⣉⠉⠛⠻⠇⢿⢹⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣓⣦⣄⣸⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢀⣠⣴⣛⣉⣉⣉⣉⣁⣈⣉⣉⣉⣉⣉⣀⣉⣉⣉⣈⣡⠴⠛⢹⠃⠀⣠⣴⣞⣋⣁⣉⣉⣁⣈⣉⣉⣉⣈⣉⣉⣁⣉⣁⣀⣉⡥⠟⢻⡇
⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠁⠀⠀⢸⡆⠸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⢰⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢠⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⢈⡇⢠⠦⢤⡀⠀⡀⠀⣤⠀⠀⠄⠀⢀⠀⠀⠀⠀⢰⡇⠀⠀⢸⡇
⠀⠀⢸⡇⠀⢀⡀⠀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⢸⠃⢸⡇⢸⠒⠺⡄⣈⠭⡇⣿⣞⠁⡇⢸⠉⡇⣼⠉⣿⢸⡇⠀⠀⢸⡇
⠀⠀⢸⡇⠰⣯⣙⡃⣼⠋⠉⣷⢸⡏⠉⣷⠀⣼⢻⡄⠀⢸⠀⠀⠀⢸⡀⠀⡇⠘⠒⠚⠁⠓⠚⠃⠙⠈⠃⠁⠙⠀⠋⢈⣒⡿⢸⡇⠀⠀⢸⡇
⠀⠀⢸⡇⠰⣦⣬⠇⠹⣦⣤⠟⢸⣧⣤⠟⢰⠟⠛⢷⠀⢸⠀⠀⠀⢸⠇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⢰⡇⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀⣖⠲⢠⠖⢲⣀⡔⢺⡇⠔⢲⡄⠀⠀⢘⡇⠀⠀⢨⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⢬⡽⠘⢦⡼⠉⢧⡴⠕⢯⡼⠇⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠘⡇
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⡆⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⡇
⠀⠀⢸⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣤⠶⠛⠉⠀⢰⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣧⡴⠚⠉
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⣻⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⠀⠊⠑⠀⢙⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⣀⠄⡀⠀⠀⠀⠀⠀⠘⣰⣤⠔⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠋⠐⠲⠟⡩⢆⠈⠀⠀⠀⠀⠀⠀⢇⣀⠀⢠⡴⠂⠸⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣢⣬⣤⡀⠀⡄⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⡇⠀⠙⣄⠀⠀⢨⡛⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠈⢣⡀⠀⠁⠀⠀⠀⠀⠀⡴⠀⠀⠀⠈⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠱⣤⠁⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠳⣄⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⣀⣤⣤⣄⣀⠀⣀⣀⡄⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⣴⣻⠃
⠀⠀⠀⠀⢀⣠⣴⣶⣆⠈⣿⡟⢳⡄⠈⢹⣿⠿⠟⠋⢉⣭⣅⣀⡀⠀⠀⢰⢻⣆⡀⠀⠀⠀⡠⠀⠁⠀⠀⠀⢀⣴⡾⢡⡏
⠀⠀⠀⠀⠈⢛⠻⣿⣿⣶⣿⣭⣬⠍⢠⡀⢲⣿⠻⠇⠈⠳⣮⣛⣄⡈⠀⣿⠘⠿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠁⣼
⠀⠀⠀⠀⠀⠈⢦⡹⣿⣿⣿⣿⣿⠦⣈⠁⣼⠿⠀⠀⠀⠀⠈⣿⣾⢁⣀⡏⠀⠀⣿⣿⣦⣄⠀⢀⣤⣶⣿⡿⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠿⠛⠛⠛⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⠇⠀⠀⠈⠙⢿⣿⣿⣿⡿⠛⠉⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣜⡻⢿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⣶⠄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠚⠛⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠋⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣸⠃⣿⣿⡟⠁⠀⠀⢀⣴⣷⠀⠀⢀⡾⠀⡟⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⢿⠀⠁⠈⠁⠀⠀⠀⡼⠛⠛⠀⣠⠞⠀⠀⡇⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡏⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⠀⢰⡇⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⢺⡇⠀⢸⡇⠀⠀⠀⠀⢀⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⢠⡞⢀⣴⣄⠀⠀⡿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢸⡇⠀⠘⣧⠀⠀⠀⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠿⠿⠁⠀⣸⠃⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠘⣇⠀⠀⠈⠳⢦⣀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⣀⣈⠳⣄⡀⠀⠀⠈⠙⠛⠒⠶⠶⠶⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⢰⣿⣯⠀⠈⠙⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣷⣄⡀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠶⠶⠒⢒⡒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⡴⠚⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⢻⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡏⠀⠀⠀⠀⠀⣀⣤⡴⠚⣹⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢸⡆⢸⡆⠈⡇⠉⣿⠓⣶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣬⣥⡤⣤⠶⢶⡟⢙⡏⢀⡇⠀⡿⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⡇⠘⡇⠀⣇⠀⢸⠀⣿⠀⢸⡇⠀⣿⠀⢸⠀⡏⠀⣾⠀⣾⠀⢸⡇⢸⡇⢸⠃⢰⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⠀⣿⠀⢿⠀⢸⡄⢸⠀⠈⡇⠀⣿⠀⢸⠀⡇⠀⣿⠀⣿⠀⣸⠀⢸⠁⣸⠀⣸⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡆⢹⡀⢸⠀⠸⡇⢸⡇⠀⡇⠀⣿⠀⣾⢰⡇⠀⡇⠀⡏⠀⣿⠀⣿⠀⡟⠀⡿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣧⢸⡇⢸⡇⠀⡇⠸⡇⠀⣿⠀⣿⠀⣿⢸⡇⠀⡇⠀⡇⠀⡟⠀⡏⢰⡇⢰⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⠀⣇⠘⡇⠀⣷⠀⡇⠀⣿⠀⣿⠀⣿⢸⡇⢀⡇⢸⡇⢠⡇⢰⡇⢸⠃⢸⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⡇⢻⠀⣷⠀⢻⠀⣿⠀⣿⠀⣿⠀⡏⢸⡇⢸⡇⢸⡇⢸⡇⢸⠃⣿⠀⡿⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⢸⡄⢿⠀⢸⠀⢿⠀⢻⠀⣿⠀⡇⢸⡇⢸⠇⢸⠀⢸⠀⣼⠀⡏⢠⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢹⡈⡇⢸⡀⢸⡇⢸⠀⢸⠀⣿⠀⡇⢸⡇⢸⠀⣾⠀⣾⠀⡟⢸⡇⢸⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⣇⣷⢸⡇⠘⡇⢸⡇⢸⡇⣿⢠⡇⢸⡇⢸⠀⣿⠀⡿⢀⡇⢸⢁⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠤⣧⣨⣇⣸⣇⣟⢸⡇⢸⡇⣿⣀⣟⣀⣧⣼⠷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⢄
⠀⠀⠑⠦⣀
⣀⠀⠀⠀⠈⠉⠒⠀⢀
⣿⣷⣦⣄⣀⣤⡀⠀⠀⢱⣄
⠉⠛⠛⠛⢿⣯⠔⠀⠀⠀⠙⠛⢦⡀
⠀⠀⠀⠀⠀⢷⣾⠀⠀⢠⠀⠢⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢻⣿⢁⡀⠀⣱⠀⠙⣦⢄⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡄⢠⡏⠀⣶⡏⠀⣿⠈⣇
⠀⠀⠀⠀⠀⢸⣿⡿⢀⣿⡁⢠⣿⣇⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠛⠿⠾⠿⣧⣾⣿⣿⡀⠙⣷⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠻⣍⠓⢆⣻⡀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣹⡇⠈⡇⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠸⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠚⠛⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠅⠀⠀⠀⠙⠲⢌⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠙⢴⡠⠀⢰⠁⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠠⠀⣀⣀⠛⠁⠀⠀⠦⠀⠸⡀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣆⠀⢰⣶⣄⣀⢤⣤⣤⣦⣴⣥⣀⣀⣀⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣷⣾⣿⣿⣮⡻⠛⠻⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠓⠒⠛⠛⠛⣛⣿⣿⣿⣿⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠦⠤⣤⠤⠤⠤⠴⠾⠿⠛⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡀⠙⣦⡠⠄⠒⠒⠒⠒⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⢰⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠋⠀⠀⡴⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠁⣀⠰⡟⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢠⣼⠀⠀⠀⠀⠀⠙⠋⣀⠀⠉⠉⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠋⠉⠲⠄⠒⠉⠀⠀⠀⠀⡄⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⣀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡰⠋⠁⠐⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠤⡱⢄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠹⣦⡈⠋⠴⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⣤⣤⣤⠤⠤⠐⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠘⢷⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣀⠠⠄⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠸⢡⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣾⠢⠄⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠂⠘⢆⠀⠀⠀⠀⠀⢀⡀⡤⢸⠇⠀⠂⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠓⣤⠠⠔⠒⠈⠁⠀⣸⢤⣄⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠦⡀⠀⡴⠁⠀⠀⢀⡠⠔⠋⠀⠀⠈⠉⠛⠲⠦⠴⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢟⡤⠤⠤⠤⠴⠀⠉⠳⢄⠀⠀⠀⠀⢀⡜⠛⠦⢤⡄⠉⠀⠀⢦⣤⣄
⠀⠀⠀⠀⠀⢀⡴⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡄⣠⠊⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠛⢷⣄⡀
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠉⠑⠒⠒⠒⠀⠐⠒⠒⠢⣤⠔⠁⠈⠻⣦⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠵⠾⠅⠴⠂⠀⠀⠀⠐⠀⠒⢾⣶⣦⣠⡄
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢐⠋⢉⣉⣉⡙⢛⣛⣛⡛⢛⣛⣋⡉⠉⠉⠉⠀⠉⠛⠛⣛⣛⣛⠛⣛⣛⣛⠁⣀⣦⣀⢰⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠿⠉⠉⠁⠘⢋⣉⡟⠸⣏⡉⠟⠀⠀⠀⠀⠀⠀⠸⣿⣩⣿⠺⣿⣭⣿⠺⣿⣭⣿⢿⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷⠦⠤⠴⠦⠤⠬⣭⠤⢤⣤⢤⣤⠤⡤⢤⣤⣤⣤⣤⣬⣭⣥⣤⣬⣭⣥⣤⣈⣉⣅⣸⡇
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡧⠀⠀⣴⣀⣀⣂⣆⣀⣀⣀⣠⣀⣀⣒⣲⣒⣒⣒⣚⣓⣚⣛⣛⣛⣛⣛⣛⣛⣿⠍⢹⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡅⠀⠀⠀⠀⡤⠤⠄⣠⡀⣀⢀⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⠁
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠂⢰⠒⠒⠒⠒⡖⠲⠒⠒⠒⠒⠋⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⡇⠈⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠧⢤⡤⢤⣤⣤⡤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠙⠲⠤⢧⡀⠘⠒⡤⢄⡀⠠⢄⡀⢀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠒⠛⠛⠋⠛⠓⠛⠛⠃⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⡟⡏⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⢀⣴⣄⣸⢿⡀⣾⡇⣤⡻⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠁⣙⣻⠛⠙⠹⠟⢸⣟⡿⠇⢰⣿⣧⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠞⠋⠉⠁⠀⠀⢀⡆⠞⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣠⣶⡊⠀⢀⣠⣤⡶⠿⡟⣛⣉⣽⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⢠⣌⠁⣀⣀⣠⠞⠁⠀⠠⣦⣼⣷⣿⣿⣿⡟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⣶⣿⣿⣿⣭⠟⠁⠀⠀⠘⡑⣿⣿⠟⣭⣿⣿⡷⠼⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡞⠉⠀⣀⢭⣟⣯⡅⣤⣄⡴⠗⢊⡽⢋⣡⣾⣟⣡⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⣼⣿⣦⣽⣿⡓⠻⠁⢀⣴⢟⣴⣿⣿⣟⠋⠉⣀⣴⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⣿⣿⣿⡟⠁⠀⠀⣰⡟⢁⣾⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣭⠙⠿⢿⣷⣶⣤⣾⠿⠴⠿⠿⠻⠿⣿⣿⡿⣿⣿⣿⡷⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣭⢿⣿⡀⣀⡈⢴⠑⢯⡉⠁⠀⢦⣿⣶⠷⣆⣿⣡⣿⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣻⣿⣿⠳⢦⣤⣤⠁⠧⠀⢳⠟⢷⣴⣆⣿⣿⣯⣿⣿⣿⡛⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⠹⣿⣤⣿⣿⣿⢸⠀⢰⣾⣶⣼⣿⣿⡝⢿⣿⣿⣿⣯⠘⣿⡟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠀⢻⣿⠉⢿⣿⡀⣦⣿⣿⣿⢿⣿⣿⣧⠈⢿⣿⣿⠁⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⣧⠈⣿⡇⡀⠀⣾⣿⠀⠈⣿⣏⠀⢰⣿⡯⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢹⣿⡄⣿⡇⣷⠀⣿⡿⠀⢰⣿⡇⠀⣿⣿⠇⣼⣿⣿⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣿⡇⢸⡿⣿⢠⣿⡇⠀⣸⣿⡆⣸⣿⣿⣰⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠈⢳⢻⢸⣿⣧⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣼⣏⣈⣿⣟⣀⣻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣆⣦⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠀⠤⠅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠄



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

⠀⠀⠀⠀⠀⣀⠠⣤⣰⣶⣶⡶⣾⣿⣿⠿⣿⡿⡟⠻⢲⡟⢺⣿⠟⡛⣿⢻⣯⡴⢶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⡴⣿⣾⣿⣍⣬⣽⣾⣿⣷⣿⠛⢳⣾⡛⣿⠛⣾⣻⡟⡛⣷⢾⣿⣶⣾⣷⣶⣼⣿⣈⣿⣿⣿⣾⡷⣄
⠀⠀⢸⡗⠽⡻⠿⢿⡉⢹⡟⠛⣻⡇⠶⣿⡴⢿⡯⠶⣿⠷⢿⣿⣶⢿⢷⣶⡞⠻⣿⣿⣛⣻⣿⡿⠿⣛⡥⣿
⠀⠀⢸⣧⣀⠀⠈⠀⠀⠀⠉⠀⠉⠛⠒⠛⠓⠛⠓⠤⠿⠶⠼⠿⠛⠦⢼⢛⣛⠓⠋⠉⠭⠉⠑⠂⢈⣁⣤⣿
⠀⠀⢸⣿⣿⣿⣷⣶⣶⣤⣤⣠⡀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣾⣿⣿⣿⡟
⠀⠀⢸⣅⡉⠙⠛⠛⠿⠿⢿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⢉⣠⡇
⠀⠀⢸⡇⠀⠉⠁⠒⠒⠀⠤⠄⢀⣀⡀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣀⣀⡀⠤⠄⠒⠊⠁⢘⡇
⠀⠀⢸⡇⢸⡇⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣤⡀⠸⡇
⠀⠀⢸⠃⠸⡜⠃⡘⢠⠤⡄⣀⣀⡀⠀⠀⠚⠓⠀⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⣟⣤⢄⣿⠻⢸⡇
⠀⠀⢸⠀⠘⣧⣰⡇⠠⠘⠛⢇⢾⡃⠀⠀⠀⠀⠀⠘⡟⠀⠛⣻⡛⡄⢰⢫⠟⡜⣭⢱⠈⣏⢰⣶⢛⡾⠞⡇
⠀⠀⢸⡇⠀⠉⠁⠷⢠⡴⢠⡦⠆⣱⢀⡀⠀⠀⡀⠈⡧⠀⠄⡇⠀⡇⢸⢸⡀⠇⠷⣸⢀⡟⢸⣷⠿⠏⠀⡇
⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠙⠃⠘⠒⠟⠑⠟⠈⠛⠃⠲⠃⠈⠢⠞⠈⠓⠁⠈⠁⠀⠀⠀⠀⢰⡇
⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣦⣀⣄⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡆⠀⠀⠀⣀⣤⣦⣶⣶⣶⣾⣿⡿⢿⣿⣶⣿⣿⢿⣿⣿⣿⣿⣾⣟⢻⣿⣿⣶⣶⣦⣤⡀⠀⠀⠸⡇
⠀⠀⢸⠀⠀⣠⡾⠋⣉⠀⠀⠀⠀⠀⠉⠻⠟⠉⠙⠿⠿⠀⠀⠻⡿⠖⠉⠹⠿⠋⠁⠀⠀⠈⡙⠻⣦⡀⠸⡇
⠀⠀⢸⠇⢰⡏⠀⢸⣿⢻⣷⠄⠀⣰⣴⠀⠐⣤⡄⠀⣤⡄⠀⣤⣤⠀⢠⣤⣄⢴⣶⢀⣴⠿⣯⡀⠹⣷⠘⡇
⠀⠀⢸⡃⣼⠃⠀⢸⣿⣻⣿⣄⣰⣿⣿⡆⠀⣿⣯⣾⣯⠀⠀⣿⣿⠀⢸⣿⣿⣾⡗⢸⣿⠀⣿⠇⠀⣿⢀⡇
⠀⠀⢸⠅⢿⠀⠀⠘⠛⠛⠛⢵⡿⠛⣿⣿⠖⣿⡏⠹⣿⣧⠀⣿⣿⠀⢸⣷⠙⣿⠷⠈⠻⠟⠋⠀⠀⣿⢸⡇
⠀⠀⢸⡇⢸⡇⠀⢸⣶⣶⣤⠀⣀⣠⣀⠀⠀⣈⠀⠀⠉⠁⠀⠈⠉⠀⠀⠉⣀⣀⣤⠤⣴⡶⣶⡀⢀⡿⠘⡇
⠀⠀⢸⡁⠈⣷⠀⢸⣿⣼⣿⢺⣿⠋⢹⣷⠆⣿⣇⣾⣿⣸⡗⢼⣿⠛⣿⡖⢹⣯⡝⠀⣿⣶⡟⠁⣸⠇⢸⡇
⠀⠀⢸⡇⠀⠸⣧⡼⢿⡇⠀⠸⣿⣇⣸⡿⠀⠸⣿⡟⣿⡿⠁⢸⣿⣀⣿⣇⣼⣧⣤⡖⣿⠞⢻⣴⠏⠀⢸⡇
⠀⠀⢸⠇⠀⠀⠈⠿⣦⣀⠀⠀⠈⠙⠉⡁⠀⠀⠛⠀⠙⠃⠀⠘⠛⠛⠋⠀⠈⠉⠉⠁⠀⣠⡾⠋⠀⠀⢸⠇
⠀⠀⢸⡃⠀⠀⠀⠀⠈⠛⠿⣶⣶⣤⣶⣿⣤⣀⠰⣶⣦⠀⢀⣶⣶⢄⣠⣿⣷⣶⣶⣶⠟⠋⠀⠀⠀⠀⢸⠂
⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠲⠿⠏⠉⠉⠿⠿⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡭⠏⢳⡜⢳⢐⠛⡆⢰⠂⣲⡍⢢⢹⠰⢶⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⢰⣦⣀⠀⠀⠀⠀⠀⠀⠠⣧⡆⠐⠋⢸⡘⠖⢠⡇⢸⢀⡯⣸⡅⢼⣘⣛⠆⠀⠀⠀⠀⢀⡀⣞⢽⡇
⠀⠀⢸⠘⡟⢙⠏⢱⡖⠀⣤⡀⠀⣀⣀⠀⠀⠀⠉⣭⣉⢤⢨⣭⠄⠁⠀⡀⠀⠀⡠⢤⡀⡶⢶⠏⣿⣿⢸⡇
⠀⠀⢸⠆⣳⠿⣼⢸⡇⣏⢹⠃⡞⡵⢌⢳⠀⡏⣷⠀⠀⡞⢩⣭⡿⢰⠡⢾⡃⡎⠔⡆⣹⣿⣤⣶⡿⢻⢿⡇
⠀⠀⢸⣦⣈⠛⠻⠬⢛⡠⢿⠀⠣⣑⣊⡼⠀⡇⠿⢤⡀⡇⠰⠶⣤⣜⠓⢖⡸⠑⠤⠤⢋⠛⠉⠒⣀⣤⣾⡇
⠀⠀⢸⣿⣿⣿⣶⣤⣤⡀⠉⠀⠒⠈⠀⠠⠤⠙⠉⠛⠁⠉⠉⠉⠩⠄⠀⠀⠐⠂⢀⣀⣠⣤⣶⣿⣯⣿⢿⡇
⠀⠀⢸⣇⠈⠙⠻⠿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⠿⠟⠋⠉⢀⣸⡇
⠀⠀⠈⠛⠷⣶⣄⣀⠀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠀⠀⣀⣠⣤⣼⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢶⣦⣤⡄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⡶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉