Apps Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⣠⣾⣿⡿⠛⠋⣉⢉⣉⣉⣉⣉⣉⠛⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⣼⣿⣿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢷⣄⠙⣿⣿⣆⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⢹⣿⣿⣷⡀
⠀⢸⣿⣿⡇⢸⣿⣿⣿⠟⢉⣠⣤⣄⡉⠻⣤⣼⣿⡆⢸⣿⣿⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣤⣤⣼⣿⣿⣿⣧
⠀⣿⣿⣿⡇⢸⣿⣿⠃⣰⣿⣿⣿⣿⣿⣆⠸⣿⣿⡇⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⡇⢸⣿⣿⡀⢿⣿⣿⣿⣿⣿⡟⢀⣿⣿⡇⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠀⠀⠉⠉⠉⣿⣿⣿⣿⣿
⠀⢻⣿⣿⡇⢸⣿⣿⣧⡈⠻⠿⣿⠿⠟⢁⣾⣿⣿⡇⢸⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠘⣿⣿⣧⠘⢿⣿⣿⣿⣶⣦⣤⣴⣾⣿⣿⣿⡿⠁⣼⣿⡿⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠈⢿⣿⣷⣄⡙⠛⠛⠛⠛⠛⠛⠛⠛⠛⢉⣠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⠀⠀⠀⠿⠛⠉

⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⢀⣾⣿⣿⣿⣿⠟⢋⣉⣤⣤⣄⣉⠙⠻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⢀⣿⣿⣿⣿⠏⢠⣶⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣷⡀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⡿⠋⠀⠀⠈⠙⠩⣿⣿⣿⡆
⠀⣼⣿⣿⣿⠏⢰⣿⡏⠀⠘⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠉⠛⠻⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠀⣿⣿⣿⣿⠀⣿⣿⣧⡀⠰⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⡀⢻⣿⣿⣷⣄⠈⠛⠟⠉⠙⢿⣿⡏⢠⣿⣿⣿⡿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣧⡈⢻⣿⣿⣿⣿⣶⣤⣤⣤⣿⡟⢁⣾⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⣿⣿⡿⠿⠿⠂⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠻⣿⣿⣿⠃⠘⠛⠻⠿⣿⣿⣿⠿⠟⢁⣤⣿⣿⣿⣿⠏⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⣿⣿⣿⣴⣶⣿⣷⣦⣤⣤⣤⣶⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⢰⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠘⠉⠁⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⣶⣶⣶⣶⣦⡄⣤⣶⣴⣶⣶⣶⣶⣦⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣤⣤⣤⣤⣿⡇⠙⠛⠛⠛⠛⠛⠛⠛⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣨⣭⣭⣭⣭⣭⣤⣤⡀⣿⡟⠛⠛⠛⢻⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠉⠉⠉⠉⠉⠉⣿⡇⣿⡇⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣤⣤⣤⣤⣤⣤⣿⡇⣿⣧⣤⣤⣤⣼⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣉⣉⣉⣉⣉⣉⣁⣀⣀⣉⣉⣉⣉⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠠⠤⠄⣀⠀⠀⠀⠀⣀⠄⠒⠀⠉⠉⠉⠁⠐⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠑⠤⡀⡈⠀⠀⢈⣉⣉⣉⣉⣉⣉⣉⣉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠄⠒⠒⠢⡤⠂⠐⠢
⠀⠀⠀⠀⢠⠉⢢⡀⣀⠀⠀⣀⣠⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡇⠀⠀⠀⠀⢇⠀⠀⣠
⠀⠀⠀⠀⢸⠀⣸⠀⠘⠁⠀⠂⡄⠀⠐⡀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⡘⠢⡀⠈⠈⠈⠉⠉⠉⠉⠁⠉⠀⠀⠊⠀⡓⢤⠤⣀⠀⣇⠉⢲⠗
⠀⠀⠀⠀⠈⠄⢤⠁⠁⣀⣀⣀⡅⠀⡠⠁⠀⢀⣀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠁⠂⠠⠄⠀⠀⠤⠔⠒⠄⠀⠸⠄⡀⠀⠀⠀⠙⢣⠃⡄
⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠉⢽⠀⠀⠉⠘⠈⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠆⠀⣀⡶⠊
⠀⠀⠀⠀⠀⠀⡠⡇⠉⠀⣲⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠉⢀⠴⢄
⠀⠀⠀⠀⣠⠮⠠⠌⠈⠉⠁⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠁⢀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠀⡀⢀⠣
⠀⠀⠀⡼⠁⠀⠀⢸⠀⠀⠀⠀⠈⡌⢆⠀⠀⠀⠀⢀⠤⡚⢝⠷⠋⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠠⠊⠀⠀⠂⢁
⠀⠀⡜⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠱⡀⢀⠔⠁⠀⢈⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠂⠀⠀⠀⠀⢸
⠀⠰⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠘⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡚⢯⠐⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠈
⠀⠆⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠀⡑⠠⠀⢀⠀⠀⢀⠁⠀⠀⠀⠰
⢀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠲⡀⠀⠀⢀⠂
⠈⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⢀⢁⠀⢀⠂
⡄⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⣷⣶⡶⠷⠿⠶⣷⣶⣷⣶⣶⣶⣶⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣿⣾⣿⣾⣶⣾⣷⣾⣾
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠤⣤⣄⣀⡀⢀⣀⣤⡤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠀⠀⠐⠛⢉⠽⢛⡿⠋⠛⠻⠝⠂⠀⠉⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠎⡀⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⢠⠀⠀⡀⠀⠀⠀⢄⠀⠀⠀⠐⢦⡀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡟⢠⠃⢀⡏⢀⠃⠀⠀⡇⠀⠀⢀⡆⢸⠇⠀⠀⡼⣇⠀⢳⡀⠑⠄⠈⠳⣄⠈⠂⠀⠹⡄⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠘⢀⠏⢀⠞⠀⣼⠀⡀⠐⠀⠀⠀⣼⠀⠀⠀⢀⡼⠁⠹⡄⠀⠙⢦⡀⠀⠀⠈⢳⡀⠀⠀⠹⠀⢦⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⠀⠊⠀⢰⠃⢀⡇⡄⠀⠀⣰⣷⣡⠖⣠⠞⠁⠀⠀⠹⣄⢢⡀⠙⠢⠀⠀⠀⠁⠀⠀⠀⠀⠘⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⣣⣃⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠙⢦⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡄⠀⠀⠀⠀⠀⢀⡼⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡘⢧⠀⠀⠀⠀⠀⠀⠀⢸⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠶⡞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢧⠀⠀⠀⠀⠀⠀⠘⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣴⠀⢸⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠰⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⡇⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢰⠀⠀⢠⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠇⠀⠀⠀⢸⠀⠀⠘⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⠁⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠺⠀⠀⠀⠀⡿⠀⠀⠐⡇⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈⠀⠀⠀⣆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢆⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡀⠀⠀⠈⠂⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣎⣧⣦⢠⢠⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢃⡾⠀⢀⣾⡴⠀⢀⡾⡠⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣾⣿⣆⠈⠲⣝⢮⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣞⣔⣡⣿⣿⣯⣴⣿⣿⡵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠷⣽⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠟⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡔⢐⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠅⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠠⢁⠐⠒⠒⢃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⣦⢰⢠⢆⠄⠀⢀⡄⡠⣄⢀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⡅⠀⠀⡇⢹⠉⡇⡆⠀⠸⣿⣉⡿⢠⠀⠀⠀⠐⠋⠀⢠⣤⣴⠑⡀⠀⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⣦⠤⠤⠤⠞⠀⠀⠀⠀⠀⠀⠘⠀⠿⠸⠀⢠⢀⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠑⠀⠀⡟⠄⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠁⣀⠘⠀⠸⢸⠀⠀⠀⠀⣠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡂⠖⠚⢐⠀⢸⠃⡄⠀⠑⠂⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡆⠀⠀⠚⠋⠠⠀⢸
⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠈⠐⠒⠀⠐⠊⠀⣟⠀⡀⠀⢐⡴⠟⠢⠀⠀⠀⠀⠐⠀⠀⠀⠺⣔⠃⠀⠀⠀⢀⣘⠀⢸
⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠏⠀⢇⣁⠀⠀⢀⡘⠀⠀⠀⠀⠠⠃⠀⠑⠆⡏⠀⠀⠀⠒⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⣴⠀⡀⠀⠀⠀⠀⣘⠃⠀⠀⠎⠈⠉⠉⠀⠀⠀⠀⠀⠀⠒⠠⠐⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⡇⠀⡅⠀⠀⠀⢀⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠚⠁⠀⠀⠀⢰⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠲⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣅⡀⠀⠀⣙⠀⠀⠀⠇⠀⠀⠁⠐⠀⢰⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠯⢼⣚⡀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠐⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠒⠀⠄

⠀⠀⠀⠀⠀⣔⣐⠶⠶⢖⣰⣤⣤⡀⠀⠀⠀⠀⠀⢀⡤⣆⠒⠶⠖⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣖⡲⡄
⠀⠀⠀⠀⠀⠈⠩⢫⣎⡊⠛⡟⠛⠁⠀⠀⠀⠀⠀⠘⢽⠜⢰⣛⠆⠀⡇⠀⠀⠀⠀⠀⠀⢰⡶⢿⣦⠐⠢⠤⠗⡟⠁
⠀⠀⠀⠀⠀⠀⣀⣙⣛⣡⡀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⠉⣱⡀⡇⠀⠀⠀⠀⠀⠀⠘⠛⠿⠋⠸⠿⠭⠩⡭⠆
⠀⠀⠀⠀⠀⡀⠲⠶⠶⠶⣢⠦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠙⠉⢕⠭⡣⠀⠀⠀⠀⠀⠀⠀⣁⠿⠐⠿⠸⠗⡇
⠀⠀⠀⠀⠀⠻⠿⠿⠽⠿⠧⠡⠎⠀⠀⠀⠀⠀⠀⠀⠘⠴⠾⠿⠷⠦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠽⠿⠿⠃

⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠁⠉⠀⠈⠀⠀⠀⠀⠁⠉⠀⠁⠈⠁⠉⠀⠈⠉⠈⠀⠀⠀⠈⠉⠀⠀⠉⠈⠁⠈⠁⠀⠉⠈
⠀⠀⠀⠀⠠⣠⠠⠀⠀⠄⠄⠀⢠⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⡀⠀⣀
⠀⠀⠀⠀⠀⡃⠀⣠⠄⠒⠤⡀⠀⠁⠀⠀⠀⠀⠀⠁⣿⡷⢸⣻⠆⣿⡷⡃⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢠⡟⣭⢳⡄
⠀⠀⠀⠀⠀⣢⠴⡁⣤⣠⡄⠷⢴⡂⠀⠀⠀⠀⠀⠀⣒⣂⣀⡐⢀⣀⣂⣅⠀⠀⠀⠀⠀⢸⣯⣭⢽⡇⠐⠛⠿⠛
⠀⠀⠀⠀⠀⡂⠀⠑⣈⣘⡰⠁⠀⡀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣷⣾⠻⠽⠇⠀⠀⠀⠀⠀⠘⠻⠟⠚⠃⣤⡄⠐⠂⡄
⠀⠀⠀⠀⠠⡶⠠⠠⢿⣿⠇⠀⠰⡆⠀⠀⠀⠀⠀⠈⠉⣽⣿⣿⣿⣀⣂⣰⠀⠀⠀⠀⠀⠀⠀⣄⣀⣰⣈⣉⡩⠉

⠀⠀⠀⠀⠀⠀⠁⠂⠀⠐⠐⠒⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠐⠀⠂⠀⠒⠀⠒⠀⠀⠀⠀⠀⠘⠂⠒⠀⠐⠐⠠⠂

⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣀⠄⢄⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⢀⣳⡞⣠⠊⢤⠤⠜⠆⠀⠀⠀⠀⠀⠙⢛⣛⣛⣛⣛⣛⣛⠛⠀⠀⠀⠀⠀⠀⠀⢯⢷⣙⣋⡸⠿
⠀⠀⠀⠀⠀⡅⠀⠠⠈⠁⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⢘⣛⣛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⢾⡷⠰⣵⢎⠆⢾⡷
⠀⠀⠀⠀⠀⡇⡉⢈⢉⡙⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆⢸⣟⣻⡇⡔⡶⣖⣤⠀⠀⠀⠀⠀⠀⠀⠀⢰⠺⠙⠒⢢
⠀⠀⠀⠀⢰⣷⣶⣶⣶⣾⣶⣶⣶⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢞⣢⢘⠍⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣤⣤⡌

⠀⠀⠀⠀⠀⠀⠒⠐⠂⠀⠐⠒⠐⠆⠀⠀⠀⠀⠓⠂⠂⠀⠒⠂⠐⠒⠂⠒⠀⠂⠀⠀⠀⠀⠐⠂⠐⠂⠂⠐⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣻⣟⣿⣻⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣻⣿⣟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⢿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⠿⡿⡿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⢿⣿⠿⠿⠿⠿⣿⡿⠿⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠚⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⣤⣤⣷⣤⣤⣤⣤⣼⣦⣤⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠁⡠⠀⡄⠠⠄⢠⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⣇⠀⠀⠀⠀⠈⠊⠁⠊⠑⠈⠐⠉⠂⠀⠀⠀⠀⠀⢀⠐⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡠⠀⠁⠈⠁⢠⢤⡀⠀⠀⢀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠸⠧⣦⣴⣤⠧⠿⠀⠀⠀⠀⠀⣠⠤⡀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⢠⠗⠀⠀⠀⠀⡱⠤⠀⢈⠔⠀⣴⢒⡀⣤⢐⣊⡦⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢒⠁⠀⡀⠀⠑⠄⡐⡀
⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⡂⡄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⡔⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠠⠴⠚⣦⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⡐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢏⡗⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠅⠀⠀⠀⠀⠘
⠀⠀⢀⠀⠁⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢄⠀⠀⠀⠀⠣⡀
⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠑⠖⠲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠳⠶⠖⠁⠁⠑⠄⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣰⠁⡰⠃⢀⡀⠀⠀⠀⠀⠸⡄⠘⣆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣿⣰⠃⠀⡼⠀⡀⠀⢀⠰⣄⣧⠀⢸⡄⠀⠀⠀⠀⡜⠀⡏⠀⣰⠋⣀⡾⠃⠀⠰⡀⠀⢠⠈⣧
⠀⠀⠀⠀⠀⣿⣯⣀⣼⠃⠀⣇⠀⢸⠀⣹⣿⣴⠟⠁⠀⠀⠀⠀⢷⣸⣷⠿⠿⢛⡋⠀⢤⠀⠀⣇⠀⢀⣧⡿
⠀⠀⠀⠀⠀⠀⠉⡿⣝⡛⢶⣿⣄⣼⣟⣫⠕⠂⠀⠀⠀⠀⠀⠀⠀⠙⣻⡶⣤⣼⣇⠀⠘⣧⣼⠿⢟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠹⠜⠿⢿⣿⣋⢉⣉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣷⣽⡾⠛⣾⣿⢧⣞⡍
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠭⠋⠃⡉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣢⡆⠰⠮⠙⢷⡏
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⢻⡿⠷⢦⡴⠇⠹⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠈⠀⠈⢒⠦⢙⣂⡀
⠀⠀⠀⠀⠀⣼⣿⠏⣿⣿⣧⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠹⡟⢓⣶⠖⠓⠀⠛
⠀⠀⠀⠀⠀⠈⠧⠀⠘⠿⣿⣽⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣿⠃⠀⢀⠀⠀⠀⢀⠀⠀⠀⠈⣦⢷⠀⠀⠀⠀⠀⠀⠀⢾⣾⢄⣿⠀⢠⠀⠀⠀⠀⡆⢼⡌⡆
⠀⠀⠀⠀⣿⡤⠖⣿⠀⠀⠀⠈⡆⠈⠙⢲⣿⣿⠄⠀⠀⠀⠀⠀⠀⠘⣿⣏⣿⣀⡟⠀⣸⠁⠀⡷⣼⣧⡇
⠀⠀⠀⠀⢹⡿⢶⣿⣄⠀⠀⢠⣿⣶⣾⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣻⡷⢶⣧⣀⣸⡟⣻⠉
⠀⠀⠀⠀⠀⢼⣧⣾⣿⣷⣾⣿⣿⢯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣯⠻⡏⣘⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠈⠱⣿⣿⡯⠶⣷⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠃⠀⠋⠋⠉⠙⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⢟⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠞⠀⠀⣆⢀⣀⣐⢢⡄⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡱⠾⠛⢋⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠃⣰⡞⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣠⣾⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣎⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠾⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣁⣀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢰⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⣠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠒⠂⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢀⡄⢠⠀⡄⠀⠀⠌⠀⠀⠀⠀⠁⠀⡀⢀⣀⣀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠇⠀⡃⢱⠏⣜⡀⡶⠈⠀⡀⢰⣏⠤⢴⡇⠐⠀⠀⠀⠀⢀⡀⠒⠂⠐⠀⠂⠠⡀⠈⢙⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠀⠁⠀⡇⠘⠂⠨⠀⠇⡌⠀⠇⠘⠻⠃⠶⠋⠐⠀⠐⠒⠒⠂⠀⠀⠀⡬⠛⡿⠀⡇⠀⠈⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠁⠀⠈⣲⠖⠒⡲⠒⠆⠀⠀⠀⠀⠀⠀⢀⠀⠁⡠⠟⠀⡇⠀⢰⢀⠇
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⡀⢂⠀⢀⠟⠁⠆⠁⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⢁⣀⡐⠀⠀⡌⢠⠀⠐⠀⠀⠀⢀⡀⠢
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⡤⠤⠃⠀⠀⣘⠆⢀⠀⠀⠢⠤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠁⡌⠀⠀⠠⠶⠟⠉⠁⠀⡆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣉⣁⠀⢀⣠⠄⠀⣽⠀⠘⠀⠀⡀⠀⢤⡁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⡌⢠⠁⠀⠀⠀⠀⠀⢠⠀⠀⡇
⠀⠀⠀⠀⠆⠀⣈⡀⠁⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⡇⢀⠐⠢⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠙⡜⠀⠀⠀⠀⠀⠀⠐⢀⣁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⢄⣀⠀⠈⣀⠀⠁⠀⠀⠀⠀⠀⢒⠀⠀⠀⠙⠸⠃⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⣰⠀⢀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⠀⠈⠨⠁⠀⠀⠀⠀⠀⠀⠀⠘⠂⠤⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⡁⠀⠈⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠠⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠐⠒⠁⢠⡌⠀⠀⠀⠀⠀⡛⠂⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡎⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡆⠀⡀⠀⠘⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡈⢠⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠇⢠⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠇⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⡀⠒⠤⢤⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⡆⠛⠛⠓⡖⠆⠂⠤⠀⣀⠀⡈⠸⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⣀⣀⠀⢰⣀⡀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⡖⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠛⠤⢏⣎⡀⠀⠀⠀⠀⠀⠀⢰⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠐⠠⠤⠴⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠂⠀⠀⠂⠀⠀⠀⠐⠀⠄⢂⠤⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢂⡀⣀⠀⠈⠶⠀⠆⠰⠀⠆⠀⠀⢰⡔⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢎⣀⠀⡀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠉⠉⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠦⢤⣄⣀⣢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠐⠈⠅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣠⠀⠓⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⣧⡀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠄⠀⣀⢀⣲⠄⠀⠀⠀⣿⠈⠂⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢶⣄⡄⣩⡉⠉⠉⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⠠⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣽⣿⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣽⣭⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣛⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣟⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣞⣧⠀⠀⠀⠀⠀⠀⢿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣷⣿⡶⣿⣿⣾⡧⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⡉⠁
⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⣀⣀⣀⡀⠐⠿⠿⠿⠿⠿⠿⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀⣀⣀⣀⣀⡀⠘⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢀⣀⣀⣀⣀⣀⣀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⢀⣤⣤⣤⣤⣤⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⣤⣤⣤⣤⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⣀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠁⠀⢀⣤⣤⣤⣤⣄⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣟⣻⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡛⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣙⣁⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠁
⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠊⠉⠉⠉⠉⠐⠒⠤⣄
⠀⠀⠀⠀⠀⢀⠄⠤⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠑⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣀⠠⠤⢀
⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠀⠀⠀⢧⠀⢀⠖⠉⠁⠀⠈⠉⡙⠁⠀⠀⠀⢳
⠀⠀⠀⠀⡼⠓⠤⣄⡀⠀⠀⠀⠀⠀⢙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⠀⣸⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⢀⡼
⠀⠀⠀⠀⡇⠀⢸⠀⠉⠰⠒⠒⠒⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠷⡀⠀⠀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⠀⠀⢠⠏⠀⠟⢦⡀⣀⠀⠀⠀⣎⠉⠐⢦⣽⢤
⠀⠀⠀⠀⡇⠰⢻⢤⡎⠀⠀⢈⡉⠸⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⡉⠁⠉⠓⢄⣿⢢⠀⢸⠉
⠀⠀⠀⠀⢳⡘⠾⠀⠱⣄⠀⢀⡀⣰⠀⠀⠀⠀⢠⠎⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠊⠛⠒⠲⠄⢤⠤⠤⠖⠚⠓⠦⠤⠤⠷⠀⢸⠃⠀⠀⠀⠀⠀⢹⠞⢠⠇
⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠙⣍⣻⠁⠀⠀⠀⠀⣌⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣊⡷⠀⠀⢀⢼⠒⠁
⠀⠀⠀⠀⠀⢰⠓⠻⠶⣤⣤⠤⠃⠀⠀⠀⠀⠀⢹⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⡖⠊⠁⢘⡀
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠤⠖⠉⠈⠲⡄
⠀⢀⠔⣡⣄⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⣠⠃⠀⢀⡠⢤⣀⣀⠀⠀⢀⣀⣠⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠘⡄
⠀⢏⠎⠀⠀⠙⢆⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡤⠊⠑⢄⠀⠘⡄
⢸⢸⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢄⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢀⠌⠀⠀⠀⠸⠀⠀⡇
⢸⢸⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠅⠉⠟⠀⠀⠻⡑⢕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠓
⢸⢸⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣗⡡⡖⠁⠀⠀⠀⠀⠈⢦⢽⣗⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢨⠀⠀⠀⠀⠀⠠⠀⠀⢰
⢸⠘⡀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠖⠉⠰⠟⢁⠞⠁⠀⠀⠀⠀⠀⠀⠈⠢⡈⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⡆⠀⡆⠀⠀⠀⠀⠀⠠⠀⠀⢸
⢸⠀⢣⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢸⠀⢀⣀⠤⠚⠁⢀⡀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⢄⠉⠒⠂⠤⢀⡀⡇⢰⠀⠀⠀⠀⠀⢀⠃⠀⠀⢸
⢸⠀⠈⢆⠀⠀⠀⠀⠀⠀⢇⣀⡤⠔⠚⠉⠁⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠈⠁⠣⡀⠀⠀⠀⢀⠎⠀⠀⠀⢸
⢸⠀⠀⠘⡄⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⢡⠀⠀⢀⠎⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠘⡄⠀⠀⠀⡎⠀⢀⡠⠔⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠍⠁⠒⠢⠤⠊
⡇⠀⠀⠀⠀⠘⠦⠤⠴⠖⠊⠁⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡔⠢⣀⣠⠔⠂⠉⠒⠒⠤⡤
⠘⡖⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡏⠈⠁⠀⠀⠀⠛⠛⠛⠛⠓⠒⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡆
⣀⣰⣅⣀⣘⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣎⣀⣀⣥
⣿⣿⡏⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣤⠼⠿⢦⣤⡦⠀⠀⠀⠀⠀⠀⠀⢲⡶⠖⠛⠲⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠁⠀⠀⠀⠹⣇⣀⠀⠀⠀⠀⠀⢠⣼⠁⠀⣤⣤⣬⠁⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⠀⠀⠀⢀⣤⣿⣶⣶⣶⣶⠀⠀⠀⢸⣦⡀⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠳⢶⡄⡿⣛⣛⣛⣻⣿⡋⡄⠀⠀⠉⠁⠁⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢱⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡏⣽⢏⣿⢝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣾⣾⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣜⣛⣋⣶⣶⣶⡄⠀⠀⠀⠀⠴⢧⢦⠀⢽⢶⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢫⢻⣿⣿⣿⣿⣿⣷⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⣷⡀⠀⣿⣿⣿⡇⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢋⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⢻⡇⠀⣿⣿⣿⡇⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠒⠂⢄⠀⠀⠀⠀⡠⠒⢒⡐⠒⢄⠀⠀⠀⠀⡠⠒⠒⠐⠒⢄⠀⠀⠀⠀⡠⠐⢂⡐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⡭⢭⣦⠀⠃⠀⠀⠸⠀⣼⠋⠙⣧⠈⠃⠀⠀⠘⠀⢸⡆⠱⠆⠀⠃⠀⠀⠐⢀⡎⡍⠩⢱⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⣓⡚⠛⢀⠄⠀⠀⠠⡀⠘⢿⡾⠃⠀⠄⠀⠀⠠⡀⠀⠑⠶⠦⠀⡄⠀⠀⠠⡈⢇⣃⣺⣾⣦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠠⠔⠊⠀⠀⠀⠀⠑⠢⠄⠠⠄⠊⠀⠀⠀⠀⠑⠢⠄⠠⠄⠊⠀⠀⠀⠀⠑⠢⠌⠈⠅⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠒⢄⠀⠀⠀⠀⡠⠒⣀⣀⠒⢄⠀⠀⠀⠀⡠⠒⠀⠀⠒⢄⠀⠀⠀⠀⡠⠂⠈⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢾⡷⠀⠀⠃⠀⠀⠘⠀⠈⠁⠈⠁⠀⠃⠀⠀⠘⠀⣶⣶⣶⣶⠀⠇⠀⠀⠘⠀⡶⣶⣶⢶⠄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢼⡿⣿⠦⢀⠆⠀⠀⠨⡀⠀⣀⣀⡀⢀⠄⠀⠀⠰⡀⠿⠿⠿⠿⢀⠄⠀⠀⠰⡀⠾⠿⠿⠇⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠤⠤⠔⠁⠀⠀⠀⠀⠉⠢⠤⠠⠔⠁⠀⠀⠀⠀⠉⠢⠄⠤⠔⠉⠀⠀⠀⠀⠈⠢⠤⠤⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣀⠀⠀⠀⠀⣀⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⢗⡺⣹⣿⡆⠀⠀⢰⣿⠏⣴⣦⢹⣿⡆⠀⠀⢰⣿⡏⣻⣏⢻⣿⡆⠀⠀⢰⣿⢻⢶⡶⡟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠝⣧⣹⣿⡇⠀⠀⢸⣿⣧⡈⢁⣼⣿⡇⠀⠀⢸⣿⣿⣮⣛⢻⣿⡇⠀⠀⢸⣿⡸⣽⡏⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠿⠋⠀⠀⠀⠀⠙⠿⣿⣿⠿⠋⠀⠀⠀⠀⠙⠿⣿⣿⠿⠛⠀⠀⠀⠀⠻⢿⣶⣶⡾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⠀⠀⠀⠀⣠⣴⣶⣶⣶⣄⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡋⢙⣿⣿⡆⠀⠀⢰⣿⣿⣶⣶⣿⣿⡆⠀⠀⢰⣿⠩⢉⡉⠍⣿⡆⠀⠀⢰⣿⠛⠍⠉⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠁⠈⢹⣿⠇⠀⠀⠸⣿⡿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣀⣀⣀⣀⣿⠇⠀⠀⠸⣿⡏⠠⡒⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠋⠀⠀⠀⠀⠙⠿⠿⠿⠿⠋⠀⠀⠀⠀⠙⠿⠿⠿⠟⠋⠀⠀⠀⠀⠙⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠈⠍⠂⠀⠀⠀⠀⠀⢀⠤⠂⠉⠉⠉⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠤⠒⠒⠂⠒⠒⠢⢄
⠀⢠⠄⢀⡂⠬⠐⠀⠉⠀⠀⡀⠈⠠⠀⠀⠀⠀⠠⠁⡠⠰⠎⠉⣉⢦⣠⠌⡄⠀⠀⠀⡀⠀⢀⡀⠠⠄⠐⠀⠉⠑⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠂⠁⠀⠀⠀⠀⢉⣿⣾⣥⡄⠄⠆⠀⠀⠀⠀⠀⡀⢀⠜⠀⠱⠃⠋⡁⢰⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠀⠀⠀⠀⠀⠉⠟⢻⡀⠀⠰⠘⡀⠀⠀⠆⡀⠰⣁⠀⠀⠀⡱⡄⠇⠄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⣀⠀⢤⠚⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠇⠃⠀⠀⢀⡀⠤⠽⠳⠀⠀⢃⢁⠀⠀⢸⣡⢆⠀⠉⠀⠈⠀⢠⠘⠀⠀⠀⠀⠃⢀⡀⠀⠤⠉⠀⠀⠀⠈⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠸⠈⡄⠊⠁⢀⡀⠠⠀⠐⠂⣉⠰⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡇⠑⠒⠉⠀⠀⠠⠔⠂⠉⠁⠀⢀⠤⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠲⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠞
⠀⠀⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⡔⠒⠈⠉⠁⠀⠀⠀⠀⠀⡨⠂⠀⠀⢠⠖⢉⠇⠀⠀⠀⠀⣰⠖⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⣠⡤⠤⠄⠒⠊⠁⠀⠀⢰⠃⠀⠈⠲⡄⠀⠀⠘⣉⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠭⠀⠛⠘⠓⠈⠉⢡⠀⠀⠀⠀⠟⡄⠀⠀⠀⣇⠀⠀⠐⢓⣙⢒⡷⠀⢺⠀⠀⡔⠤⠄⠀⠀⠒⠒⢐
⠀⠀⠀⠀⠀⠀⠀⠔⠉⠈⠑⢄⠀⠰⡁⠀⠀⠀⢀⣀⣠⠤⠰⠀⠀⠀⠀⠂⣹⢾⣭⣭⡁⠀⠀⠘⣇⠀⠀⠀⡠⢿⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠈⡀⠀⠀⠁⠈⠉⡋⠀⠄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⠀⠀⠀⠀⠑⣆⡀⢰⢡⠂⠀⠀⣇⣀⡀⠀⠀⠀⢀⣸⡀
⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢱⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠘⡀⠀⢀⣀⠀⠀⣠⠗⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠘⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⡠⠖⠛⢉⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⢡⢀⡤⠶⠂⡡⣀⡴⡊⠁⠀⠐⡀⠀⠀⠀⡠⠶⠀⠐⠃⠄⢀⣰⠀⠀⠀⠀⠀⠀⡠⣀⠤⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⢸⠻⣓⠴⢾⣿⣿⣿⣦⠀⠀⠀⢣⠀⠐⠊⠂⠈⠀⠰⠦⢀⣄⠀⠉⠀⠒⠂⠀⠠⠖⠁⡠⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⢏⠀⠀⠐⣝⣛⡿⠟⢀⡠⠐⠁⠀⠐⠢⠤⣀⠀⠔⠒⠒⠠⡀⠛⠀⠓⠀⠀⠀⣰⡉⡄⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠈⢢⡔⠔⠊⡁⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢃⠀⠀⢀⠧⠀⠐⠐⠒⠒⠉⠁⠈⠁⠀⠀⠀⠀⠀⠈⠂⠤⠤⠤⠤⠤⠤⠤⠤⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠤⠤⠤⠬⢤⠄⡁
⠀⠀⠀⠀⠀⠀⠀⣇⠤⠔⣀⠔⠐⠀⢲⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠠⠤⢀⡀⠀⠀⠑⢄⠀⠀⢀⠔⠋⠊
⠀⠀⢠⠀⠀⡠⠁⠉⠢⣀⠋⠀⠀⠀⠈⠀⠀⠀⣠⡄⠼⠏⠁⠀⠚⠁⠉⠉⠉⢆⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠑⠐⠁
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠴⠦⠵⠶
⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⠀⡀⠔⠁⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠇⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠈⠐⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠀⠠⠤⠄⠐⠒⠀⠁⠁⠀⠀⠀⠀⠙⠛⠳⠶⣶⣄⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⡿⠘⠀⠀⢻⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣔⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⣠⡠⠀⠠⢤⠴⠄⠀⠀⢀⣀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢄
⡀⠈⠛⠙⠚⣰⢊⡋⡛⠟⠧⠿⠎⠉⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠤⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⠁⠐⠒⠒⠚⠃⠀⠉⠈⠀⠰⠷⠿⢕⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢄⠀⠀⠀⠸⣉⡀⠂⠄⢠⣢⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠤⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠂⠀⠀⢸⡹⣆⡄⠄⢀⠀⠀⠀⠀⡀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⠀⠀⠳⠈⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠘⡩⡺⢠⠀⠀⠀⠀⡀⠀⠐⢀⣁⠀⠀⠸
⠀⠄⠀⠠⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠐⠒⠀⠂⠀⠁⣀⡀⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠑⠁⠀⠀⠀⡀⠀⠠⠀⠀⠉⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠠⠤⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠁⠈⠀⡖⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠇⠄⠀⠀⠀⠀⠀⢦⡰⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠂⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⡀⣀⣀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⣰⣀⣠⠤⠤⠠⠯⠿⠯⠿⠗⠀⠀⠀⡇⠀⠉⠉⠉⠛⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⢁⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢤⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⠒⠀⠄⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡀⡐⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⢻
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠙⣆⠀⢀⡿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣿⣠⠞⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠒⠒⠒⠲⠦⣤⡀⠀⠀⠀⠓⠦⣤⡤⠾⠛⠁⠀⠀⠀⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣤⣤⡤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⠼⠿⢤⣤⡦⠀⠀⠀⠀⠀⠀⠀⢲⡶⠖⠛⠲⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡟⠁⠀⠀⠀⠹⣆⣀⠀⠀⠀⠀⠀⣤⣾⠁⠀⣤⣤⡌⠁⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⠀⠀⠀⣀⣤⣷⣶⣶⣶⣶⠀⠀⠀⢸⣦⡀⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠳⢶⣤⡿⣛⣛⣛⣻⣿⡋⡄⠀⠀⠉⠁⠁⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢱⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⡋⣽⢏⣿⢝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣾⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣜⣛⣫⣴⣶⣶⡄⠀⠀⠀⠀⢴⣯⣦⠀⣽⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢫⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⣷⠀⠀⣿⣿⣿⡇⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⢻⡇⠀⣿⣿⣿⡇⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⣀⡀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢻⡟⠉⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⣀⠀⠀⣿⢿⡇⠀⠀⠠⠤⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣼⣯⣤⣿⡄⠀⠀⠀⠀⣾⣿⣿⣇⠀⣠⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢳⣶⣦⣀⠀⠀⣀⣤⡀⠀⣰⡿⠛⡙⠛⣷⡄⢀⣴⣾⣿⣿⣿⡋⣴⣿⠋⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠘⣿⣿⣿⡶⣟⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣿⣿⣿⣅⣶⣿⣿⡇⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⣸⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡏⠀⠀⢀⡀⡄⣆⢳⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠀⠀⢀⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢺⡜⡎⣧⢳⢹⡜⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠧⠼⠘⠈⠁⠀⠀⣶⡄
⠀⠀⠀⠀⢀⣤⣤⣴⡖⠒⣶⣶⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣤⣤⡀⠀⠀⠀⣀⠉
⠀⠀⠀⠀⠀⠈⠙⠛⠷⠤⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢽⣽⣧⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣾⣿⣿⠀⠀⢸⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡷⠿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠚⠋⠁⠀⠀⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡄⠀⢱⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⠴⠦⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢳⣀⣀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠛⠙⠯⣭⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠋⠍⠅⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣿⣿⣿⠿⡀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⣴⣿⡿⡟⠻⠆⣽⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣼⡿⠋⡀⠀⢠⣼⡿⠃⢸⣿⣿⣿⣿⡏⠉⢻⡟⠀⢹⣿⡄⠁⠉⠻⠿⡉⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠙⠀⣸⡿⠁⠀⢸⣿⣿⣼⣯⡇⠀⠘⡁⠀⢀⣽⣿⠖⠒⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⢸⣿⠏⢹⣿⠇⠀⢠⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠀⠈⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠙⠂

⠑⢄⠀⠀⠀⠀⠀⣀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣢
⠀⠀⠑⣄⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠠⠄⠚⠉⠀⠀⠀⠀⠀⠀⠀⢣
⢀⠤⠒⠉⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠁⠀⠀⠀⠀⠀⠉⠢⣀⠀⠀⣀⠠⠤⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠒⠄⡀⠀⠀⠀⠃
⠀⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠉⠒⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⡤⠤
⠒⠄⠀⠀⠀⠀⠀⠀⠀⢐⣀⠤⠤⠒⠊⠉⠀⠁⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄⣀⡀⠤⠐⠒⠉⠁⠀⠀⠀⠑⡄
⣀⣀⢠⡠⠤⠴⠒⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢈⢃⠀⠒⠂⠈
⠢⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠄⠀⢀⡀⠀⠀⠀⠈⠀⠀⢀⠠⠀⠀⠉
⠰⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⢀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠖
⠰⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠈⠁⠀⠐
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⢤⠀⠀⢀⠙⡴⠢⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠐⠀⠀⠀⠑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⣶⠒⢂⠀⠀⠈⣠⡴⠂⡀⠂⠀⠀⢤⠄⠠⠀⠀⠀⠐⠀⠥⠤⠎⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⣦⢠⡀⢸⠀⢸⠀⠀⡀⠓⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⣀⠄⠰⠫⠄⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣬⣭⣛⠺⡁⠀⡙⠎⠀⠄⠀⢀⡸⠠⣀⠈⠀⠀⠀⠀⡄⠀⠀⠦⠀⠊⢡⣈⠀⠆⠀⠌
⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠉⠀⠀⢸⠏⠙⠖⡄⠀⠀⠁⠐⠀⠀⠁⠀⠀⠀⢀⠀⠄⠰⢅⠀⠀⠀⣠⠦⠀⠀⠍⠛⡐
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠄⠘⠵⢦⠋⠀⠀⡀⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠎⠀⠀⠀⠁⠒⣦⠀⣾⢁⠃
⠀⠀⠀⠀⠀⠀⢸⡸⠀⢀⡠⠚⠁⢀⡠⢊⢴⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠂⠀⠋⢊⠃⠄
⠀⠀⠀⠀⠀⠀⡈⠠⣄⡠⠭⠭⠀⢐⣈⢔⣣⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢲⠂⠀⠀⠀⠀⠀⣇⠌⡐
⠀⠀⠀⠀⢀⠎⠘⢆⢤⣉⠭⢿⡯⠭⢀⣻⣹⠄⠐⠂⠀⠁⠀⠀⠀⠀⠀⡐⣱⠒⠒⠚⡆⠀⠀⠰⣿⣆⡼⣰⠃
⠀⠀⢀⠀⠧⠤⢀⣀⣁⠀⠀⠀⠉⠒⡊⢁⠟⡀⠀⠀⠀⠀⠄⠀⠀⡀⣘⠢⣸⣐⣛⣙⣃⠛⠀⡀⣛⣛⢃⠏
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⢓⠂⠄⢤⡆⢀⡀⠠⠠⠐⠐⠀⠉⠁⠀⠈⠢⡈⠢⡀⠀⡏⠀⠀⣀⢧⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡈⠢⡂⠀⠫⢄⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃

⠀⠀⠀⡋⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣧⠤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠄⠀⠀⠀⠀⠀⠠⠡⠊⠀⠄⠀⠑⠀⠀⠀⠀⠀⢀⠤⠐⡶⢐⡟⠉⠓⣄
⠀⠀⠀⠁⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠇⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠈⠢⣌⠥⣝⡭⢯⠓⢺
⠀⠀⠅⠌⣉⠫⠀⠀⠀⠀⠀⠀⠀⠀⠠⡩⢀⠘⣦⠈⡱⠀⠀⠀⠀⠀⠈⢌⠠⠀⠄⠠⢈⠔⠀⠀⠀⠀⠀⠀⠀⠓⢥⠂⠋⠁⠁
⠀⠀⠐⠒⠛⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢰⣶⠠⠐⣀⠐⢀⠠⢢⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠢⡄⠀⠀⠀⠀⠀⢀⣤⣄⠁⠀⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⡃
⠀⡎⢀⡀⠈⡕⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⢔⡛⣆⠀⠀⠀⠀⠀⠀⠀⠿⠝⠠⡚⠙⢲⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠅⣈⠀⠅
⠐⡆⠢⡙⠚⠟⠡⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣠⠺⣠⣀⠇⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶


⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠠⠐⠤⠖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠁⠀⠁⠒⠫⡭⠂⠁⠀⠀⠀⠀⠀⠠⢀⠀⠄⠀⢁⣔⡤⠀⠀⠀⠀⠀⡁⠀⡀⠀⠀⠃⠃⠀⠀⠀⠀⠀⠀⣲⣄⠀⠶⠶⠖⠇
⢀⠀⠀⠀⠀⠀⡏⠀⡀⠀⠀⠀⠀⢐⣂⠀⡄⠀⠰⠍⡀⠀⠀⠀⠀⠀⠀⡈⠀⠓⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⢀⡁⠀⢀⣀⠀⠂
⠀⠀⠐⠐⠦⠄⠀⠀⠀⠀⠀⠀⠀⠻⠩⠈⠒⠒⠒⠒⠈⠀⠀⠀⠀⠀⠀⠙⠠⠀⠤⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢀
⠀⣠⠄⣀⣐⠠⡌⠀⢢⠀⠀⠀⠀⠀⠀⡀⠠⠀⠐⠶⣶⠀⠀⠀⠀⠀⢀⠴⠶⠲⡊⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⣠⠔⠀⠀⠁⠀⠀⠀⠀⠀⠈⣿⠈⠁⠃⡀⠉⠀⠀⠀⠀⠀⠀⠀⠒⠀⠓⠲⠒⢄⠀⠀⠀⠀⠀⠀⠈⠀⠛⠁⠈⠆⡄
⠁⠀⠀⠐⠁⠚⠁⡀⡀⠀⠀⠀⠀⠀⠸⣟⢲⡶⠦⢬⡽⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠠⢲⣀⠀⢀⡐⠋
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠛⠟⠲⠺⠟⠅⠀⠀⠀⠀⠀⠀⠀⣄⣣⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠓⠋⠛⠉⠁

⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⡀
⠠⡀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠠⠊⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠉⠑⡆⠂⠉⠀⠒⠒⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠉⠁⠀⠈⠐⠤⡀
⠐⡀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠤⣀
⠀⠐⡄⠀⠀⠀⠈⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁
⠀⠀⠈⢄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠑⢄⡀⠀⠀⢈⣆⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡁⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠑⢄⠘⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⣠⠦⠆⠐⠐⠒⠒⠒⠒⠒⢄⡀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠁⢀⡔⠉⠉⠂⠆⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠀⠀⠁⢆⠀⠀⠀⠀⠀⠀⡠⠊⠈⠀⠀⣀⠠⠀⠘⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⣀⠔⠁⠀⠀⠀⡀⣀⠠⠤⠄⠐⠓⢤⡀⠀⢠⢞⠘⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⠢⡀
⠀⠉⠉⠁⠀⠀⠀⠒⠂⠤⠔⠠⡀⢀⣣⣤⠮⠤⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⢈⠟⠀⠈⠛⠁⡱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠎⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢰⠀⢀⡀⠠⠠⠀⠒⠂⠁⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⡠⠔⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢀⠊⠐
⢀⠄⠀⡒⠨⠆⠒⠉⠁⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠃
⠐⠈⠁⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠆
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠙⢳⣄⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣠⡾⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠾⠋


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⣰⡖⢥⣃⡂⠄⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣂⡁⢀⣴⠾⣧⣼⢟⠘⢍⠀⠉⢳⢌⠢⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠊⠀⠈⠀⠉⠑⣊⡟⡄⣡⢀⠀⢀⡼⠀⠑⠌⢂⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠂⠡⠀⠀⠀⠀⠘⢄⡌⠙⢂⠀⠒⠁⠀⠀⠀⢈⡆⢃⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠈⡀⠸⠙⠂⠀⠀⠀⠀⠘⡷⢛⡀⡀⢀
⠀⠀⠀⠀⠀⠠⠂⣀⣀⣐⠂⠄⠀⠐⣄⠀⢀⠤⢤⠘⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⠚⠇⠁
⠀⠀⠀⢀⠤⠤⠤⠤⠤⠬⠧⠦⢤⡀⠈⠑⠴⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠃⠆⢠
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⠀⠀⠀⠀⠙⠉⠁⠁⠢⠄⡀⠀⠀⠀⠈⠀⡙⠠⠀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢁⢠⡄⠀⠀⠀⢠⠀⡄⠀⡀⠀⠀⠀⠈⠢⡀⠀⠀⠒⠚⠓⠒⠒⠒⠒⠗⠛⠉⠉⢝⡭⢭⣍⢂⠀⠀⠀⠀⡰
⠀⠀⠸⠀⠀⠸⠇⠀⠀⠀⢹⠋⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⡠⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸⣤⠂⣿⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠄⡀⠀⠀⢃⡈⠀⢀⣘⠂⠄⠀⢀⡀⢸⠄⠄⠊⢂⠈⠉⠁⠰⠀⠀⠀⠀⠠⠂
⡔⠐⡇⠀⠊⠀⠀⠀⠀⠀⠀⠀⠱⠀⠘⠉⢳⠂⠀⠈⠉⠁⠀⠐⠊⠒⠀⠈⠁⠀⠒⡀⠀⠀⠀⠣⠀⠀⡄⠀⢀⡀⠤⠐⡞
⡯⢁⠀⢠⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠍⠁⠀⠒⠀⠀⠒⠀⠉⡀⠀⠀⠀⠀⠀⠛⠀⠀⢀⢔⣑⡀⠃⠀⠀⠀⠀⠀⠐
⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠇⢈⢀⠀⣄⠀⠀⣠⢀⠈⢠⠀⠀⠀⠀⠀⠘⠈⡠⠢⠈⢹⡟⢻⠀⠀⠀⠀⠀⠰
⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠠⠀⠀⠀⠀⠀⠀⠃⡀⣄⣀⣀⣠⠀⠐⣋⢀⣀⣀⣤⠤⠼⠤⠤⠤⠤⠤⠴
⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉⠉⢩⡍⠉⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⠁⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⣿⡇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠙⢿⡿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣤⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢀⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣤⣤⣀⣈⣁⣀⣤⣤⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢛⣷⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠦⣄⠀⠀⠀⠀⠀⠀⣠⣀⠀⣠⠤⣤⡄
⠀⠀⠀⠀⠀⠀⢸⡈⢻⠁⠟⢡⠟⠀⠀⠀⠀⠀⠀⢀⡶⠃⠻⣶⠀⠀⠀⠀⠀⠀⠀⡇⢠⠞⠓⡌⢸⠀⠀⠀⠀⠀⠀⣿⠈⠛⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡶⣌⣷⠀⠀⠀⠀⠀⠀⠀⠉⡇⣿⠁⠀⠀⠀⠀⠀⠀⠀⣇⠈⠲⠖⠃⣸⠀⠀⠀⠀⠀⠀⣼⠧⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠈⣧⠀⠀⠀⠀⠀⠀⣼⠉⠉⣀⠀⠉⠹⡆⠀⠀⠀⠀⠀⡎⢰⡆⠐⠄⢹⠀⠀⠀⠀⠀⢀⡞⠁⢀⡀⣀⠘⡆
⠀⠀⠀⠀⠀⠀⢀⡽⠂⠀⠀⢻⡄⠀⠀⠀⠀⠀⢿⠀⠀⠛⠁⠀⢠⡇⠀⠀⠀⠀⠀⢧⠀⠑⠶⠆⡼⠀⠀⠀⠀⠀⠈⣇⠐⠋⠛⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠚⠋⠁⠀⠀⠀⠀⠀⠈⠛⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠡⠘⠙⠉⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⠤⠴⠋

⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⢄⠀⠀⠑⠀⢀⣀⣀⣇⠀⠂⠁⠀⠀⣠⠀⠀⢠⠃⠀⠀⡴⠁⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⡠⠷⡊⠉⠉⠀⠀⣀⣈⣦⣀⣀⡀⡔⠁⠀⢀⠎⠀⢀⠞⠀⠀⢈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣏⡠⠔⠊⠁⠀⠀⠘⡤⠒⠒⠉⠁⠀⠀⠂⠀⠈⢻⠒⡤⣋⠀⣠⠋⠂
⠀⠀⠀⠀⠔⠚⣇⡇⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⡀⠀⠈⠀⠀⢜⣔⠁⢀⡽⠧⣀⡀⢀⢂⠀⢀⣀⡠
⠀⠀⠀⠀⠉⠐⠪⠄⠀⠄⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⢄⢀⡴⠋⠈⣱⠮⣄⡀⠀⠈⢸⠁⠉⠄
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⣠⠜⠫⡀⢀⡜⠉⢣⠀⠉⠓⢦⣞⣀⣀
⠀⠀⠀⠀⣀⣤⢤⠧⠴⠦⡄⢀⣀⣰⠚⡟⠛⠋⠉⠉⠀⠀⠀⡼⠋⠀⠀⢨⡀⠀⢀⡜⠀⠀⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡏⠉⢇⠀⠀⡇⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣸⠈⠑⠼⡀⠀⠀⠀⠀⢀⠢
⠀⠀⠀⠀⡀⠤⡔⢳⢊⣹⣇⣠⡼⡤⠤⢵⠴⠶⠶⠖⠚⠁⠀⠈⠠⠀⢠⠃⠀⡀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⣱⠋⠉⠀⠳⡀⠀⢱⠀⢸⣀⣀⣀⣀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠠⠌⠀⠈⠣⡀
⠀⠀⠀⠀⠀⢠⠟⠦⣀⠀⠀⢘⣤⠔⠇⠀⠀⠀⡜⠀⠉⠒⠤⣀⣠⠃⠀⠀⠀⠐⠀⠁⠀⠀⠀⡀⠘⠢
⠀⠀⠀⠀⢠⠏⠀⠀⠈⢢⡔⠁⠈⠣⡘⠀⠀⢸⠀⠀⠀⠀⠀⢠⠋⠑⠢⠄⣀
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠳⣤⣄⣀⡙⡇⠀⠈⡄⢀⣀⣀⣠⣃⣀⣠⣤⣤⡤⡭⠶⠤⣤⡶⠖⠒⠛⠉
⠀⠀⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠉⣏⠉⢹⠋⠉⠉⢁⠏⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠉⠢⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⢉⠉⠉⠙⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤⢲⠤⣶⠶⡶⣶⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣠⣀⣀⣧⣦⣤⣊⣤⣡⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠉⠀⠀⠉⠁⠐⠠⡀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠂⠀⠐⠄⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢈⠃⠀⠀⠉⠉⠉⠉⠉⠉⠁⠁⠀⠈⠄⠀⡀⠀⠀⣀⠠⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠞⢄⡀⠀⠀⠀⢀⠄⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⢈⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠉⠍⠨⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡣⣠⢄⡀⢨⠁⢢⠷
⠀⠀⠀⠀⠀⠀⠀⢂⠺⠉⠣⢀⣀⡰⠀⢀⠃⠀⣀⢀⡀⠀⠀⠀⡀⠠⠐⠁⠀⠀⠉⠐⠠⠄⠤⠤⠄⠒⠠⠀⠈⠆⡁⠀⠀⠈⢻⠕⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⡀⠀⢓⠇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠂⡀⠼⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠆⢀⣩⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠔⠢⡀
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠂⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⢀⣾⣄⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠔⠀⠈⠄
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢄⠀⠀⡠⠀⠁⢅⠋⠀⠀⠀⠀⠀⠀⠀⠰⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠂⠀⠀⠀⢠
⠀⠀⠀⠀⡈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠈⠢⠊⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢽⡂⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸
⠀⠀⠀⢠⠁⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠍⠀⠑⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠑⠠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠈⠀⠒⢄⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⡆⠀⡐⠀⠀⠀⠇
⠀⠀⠀⠃⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢬⠉⠙⠒⠀⠀⠐⡆⠀⠐⠊⠩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣼⠀⢀⣀⣀⠀⠀⢇⣀⣀⣀⡀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠒⠊⠉⢀⠚⠛⠉⠀⠀⠀⡈⠋⠋⠉⠉⠈⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⢄⣀⠀⠀⢠⡉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠨⢆⠈⠀⠀⡸⠐⠒⠒⠒⠒⠒⠲⡀⠄⠀⠀⠄⠀⠉⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⢰⡐⠄⠀⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠒⠒⠈⣀⠠⠘⠋⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠔⠈⠀⠉⡠⠂⠀⠀⠀⠀⠀⠠⠐⠀⡡⠔⠋⠙⠉⠻⠲⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠔⠁⠀⡠⠊⠀⠀⠌⠀⠀⠀⠄⠈⢢⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄⠀⠀⢰⠁⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣠⠀⣤⣤⣶⣆⣀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡲⠄⢀⣀⡀⠉⠁⡒⠒⠒⠂⠤⠀⣈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡿⠧⡌⣯⠁⣹⠽⢿⣷⣧⠠⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠉⠁⠀⠀⣕⠂⡤⢠⠄⠀⠤⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠴⠃⣿⣷⣸⡦⠀⣿⠁⠀⠀⠁⠐⠠⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⢀⣄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠔⢈⡀⡀⠘⣆⣀⣀⣽⣿⣿⣷⣄⠀⢈⠂⠄⡀⠀⠀⠈⢄⢀⡴⠃⠀⠀⠀⠀⠀⢆⠠⠺⢉⡗⢒⠤⣠⢲
⠀⠀⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠠⠀⠀⠒⠁⠀⠀⠐⡄⠰⢊⡴⢁⡞⠀⣠⢆⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠁⠃⠈⠀⠀⠀⢠⣄⠀⢀⡜⠵⣋⣴⢏⣠⠞⠀⠏
⠀⠀⠀⠀⠀⠀⡘⠠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠄⠀⠀⠀⠀⠀⢈⣕⡶⢭⡋⢥⣠⠯⣣⡀
⠀⠀⠀⠀⠀⠀⠠⠰⠄⠤⠠⣤⠚⠓⢲⡴⠒⠒⢦⡀⣀⣀⣀⣀⣀⣇⠘⠁⠀⠀⠀⠀⠀⠀⠉⠐⠠⣈⡑⠪⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠙⠷⠔⠚⠛⠢⠴⠟⠉⠛⠃⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⠀⠀⠀⠀⠑⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠢⠂⠃⠂⠘⠞⠚⠘⠂⢀⠠⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡎⠀⠈⠁⠈⠀⠈⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠼⠔⠀⠉⠁⠈⠀⠀⠐
⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢰⠀⠂⢄
⠀⢀⠄⠪⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⢸⠀⠀⠀⢀⠄⢀⡀
⠀⠈⢄⠀⠀⠀⠈⠐⠢⠤⡀⡀⠤⠐⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠘⡀⠀⠀⠀⢸⠠⠐⠈⠀⠀⠀⠀⢰
⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⣰⡤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠠⠀⠈⠢⡀⠀⠀⠀⠀⢀⠤⠐⠈⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⣴⡄⠀⠀⠈⢢⡤⠐⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⠁⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⠄⠀⢀⠠⠐⠈⠀⠀⠠⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡁⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠁⢙⠁⠀⠈⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⡀⠄⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⢂⠔⣈⡔⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⣪⢚⠥⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡤⠔⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠰⠑⠁⢼⠀⠀⠀⠀⠀⠀⠂⢀⣶⠶⠞⠺⢿⡖⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠤⠄⢀⠃⠀⠀⢸⠀⠀⣤⡤⠴⢖⠛⠙⡇⠁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠁⠀⠀⠈⠰⠠⠆⠼⠶⢯⡇⠀⠀⢸⢸⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⠤⠖⢈⣀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠉⠀⠀⡘⠀⠀⠐⠗⠀⠀⢸⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠘⢀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠸⠀⢸⡇⠀⠀⢸⠀⢠⣷⠦⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠠⠀⠠⠀⠀⠀⢠⠰⠀⠀⠃⠀⠀⠀⠀⠐⠀⣹⡇⠀⠀⣸⣿⣻⡿⢶⣾⣯⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠂⠐⠨⠀⠀⠠⢰⡈⠋⠉⠙⢹⠀⢹⡗⠀⢨⣿⣿⠿⣧⣾⣯⣽⣿⡇
⠀⠀⠀⠀⠀⠸⡇⠄⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⣖⣊⡇⣁⣾⣷⣸⢶⣷⡿⢛⠚⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⡇⠀⠈⠉⠛⡟⡟⠛⠊⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠉⠐⠀⠄⡀⡗⠃⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄

⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⡇⢠⣄⣼⣮⣷⣿⣿⡿⠛⠙⠙⠈⠹⠿⠿⠍⠛⡋⠉⠁⠀⠀⠰⣤⡄⣀
⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠸⢿⣾⡽⣿⠏⠀⠀⠀⠀⠀⠀⠘⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠭
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⢸⡗⠂
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⣀⡀⠙⣿⡇⠀⠸
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠋⠁⠀⠀⠀⠉⣿⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⡷⠚⠛⠛⠛⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⡿⠁⠈⠃⠀⠀⣆⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠈⠁
⣿⣿⣿⣶⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠾⠉⠻⠿⠏⡽⠟⠁⠀⠀⠀⠀⠀⠃⠀⠀⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠲⠿⣆⡀
⢻⣿⡿⣿⣿⣛⣿⠿⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣤⡶⠶⢶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⠂⠒
⠈⢻⡆⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠐⠀⠀⠋⠁⠄⠛⠁
⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠰⢿⣷⣾⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠈⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⣿⡇
⡄⠀⡀⠀⠈⢻⣄⠀⠀⠀⠠⣶⣿⢛⠋⠉⠉⠉⠙⠛⠋⠀⠀⠀⠀⣰⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⠀⠀⠒
⢿⡀⠑⡀⠀⠀⠹⢦⡀⠀⠀⠈⢤⣤⣀⣀⣀⣤⠶⠃⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠘⣷⡄⠱⡄⠀⠀⠀⠙⢦⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢠⣤⠉⠀⠁⠀⠀⠀⠀⠀⡍⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⣀⣤⣤⣤⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢸⡇⠠⠤⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠸⡟⠿⠛⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣶⡆
⠀⠀⢠⠀⠀⡈⠁⠤⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠄⠀⠁⢄⠀⠀⠀⠀⢀⡆⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣠⣤⡀⠀⠀⢤⣤⣾⣿⠁⣿⡆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⠎⠀⠀⡃⠀⠀⠀⡆⠀⠀⢨⠀⠀⠀⢐⠀⠀⠱⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⣠⣮⣤⣤⣤⣮⣤⣤⣤⣧⣤⣤⣤⣥⣤⣤⣬⣤⣤⣤⣼⣤⣤⣤⣵⣤⣤⣤⣵⣄
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡸⢇⠀⠀⡨⢇⠀⠀⢨⢇⠀⠀⡸⢅⠀⠀⡸⢇⠀⠀⠨⢇⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠀⣠⣱⣪⣥⣤⣵⣪⣥⣤⣭⣨⣤⣬⣅⣬⣤⣤⣵⣊⣅⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⡟⠛⠛⠛⢻⡟⠛⠛⠛⢻⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣧⣠⣤⣤⣼⣧⣤⣤⣄⣼⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⡿⠿⠿⠿⢿⡿⠿⠿⠿⢿⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⢀⡀⣰⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣆⢀⡀
⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣿⣿⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠟⠛⠛⠛⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⢁⣀⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀⡉⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⡏⢹⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⣴⣿⣿⣿⣿⣿⠟⢋⣥⣶⣶⣿⠃⠘⣿⣶⣶⣬⡙⠻⣿⣿⣿⣿⣿⣧⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢀⣾⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣷⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⣿⣿⣿⣿⠏⣴⣿⣿⣎⠛⢿⣿⡇⣀⢀⢸⣿⡿⠛⣱⣿⣿⣦⠹⣿⣿⣿⣿⣷⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⣧⡀⣸⠃⠈⠓⠘⣇⢀⣼⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⣿⣿⣿⠥⠿⠟⠛⠛⠉⣍⡁⠀⡖⣡⣌⠢⠀⡬⠉⠉⠛⠛⠻⠿⠬⣿⣿⣿⣿⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⣿⣿⣿⣷⡒⣶⣤⣤⣄⣀⣉⠉⠀⢦⣛⣛⡴⠀⠓⣀⣀⣠⣤⣤⣶⢲⣾⣿⣿⣿⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⡿⠁⢹⡄⢠⡀⢠⡏⠈⢿⣿⣿⣿⣿⡏⣸⣿⣿⣿⣿⡇⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢿⣿⣿⣿⣿⣆⢻⣿⣿⢟⣠⣶⣿⡇⠐⠁⢸⣿⣶⣄⡻⣿⣿⡟⣰⣿⣿⣿⣿⡿⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠈⢿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣷⠀⠀⣾⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⡿⠁⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⢻⣿⣿⣿⣿⣿⣦⣌⡛⠿⢿⣿⡄⢠⣿⡿⠿⢛⣡⣴⣿⣿⣿⣿⣿⡟⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣇⣸⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⠋⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡈⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⢁⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⣤⣤⣤⣤⣤⣤⠶⠶⠟⠋⠉



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣤⣤⡀⢀⣤⢤⡀⢀⣤⣤⡄⠀⣤⣤⣄⠀⣤⣤⣄⠀⣠⡤⣤⠀⣠⣤⣤⠀⢠⣤⣤⡀⢀⣤⣤⡀⢀⣤⣤⡄
⠀⢸⣿⣿⡇⢸⡇⣼⡇⢸⣇⣠⡇⠸⣇⣀⡼⠀⣧⣻⣿⠀⣏⣃⣾⠀⢿⣁⣽⠀⢸⣿⣿⡇⢸⣿⣴⡇⠸⣹⣭⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠸⠀⠀⢸⡇⠀⠀⠲⠟⠀⠀⠺⠿⠆⠀⠸⠤⠀⠀⠰⡺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠀⠀⣷⠶⡄
⠀⠀⣀⡀⠀⠀⢈⡀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⢀⡀⠀⠀⢀⣀
⠀⢸⣿⣿⠆⢰⡟⣹⡆⠰⣟⣩⡇⠠⣏⣉⡷⠀⣏⢿⣷⠀⣾⢯⣿⠀⢼⡋⣿⠄⢸⣿⣿⡆⢰⣟⣹⡆⠰⡟⣛⡇
⠀⠀⠉⠉⠀⠀⠁⠉⠀⠀⠉⠉⠀⠀⠈⠉⠁⠀⠈⠉⠁⠀⠈⠉⠁⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠉⠉⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢠⡤⠀⠀⢠⣶⠄⠀⢠⡀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣢⣤
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠂⢤⡀⠀⠀⠀⠀⢀⡠⠔⠂⢉⠀⠀⠉⠑⢢⡀⠀⠀⠀⠀⠀⢀⠔⠊⠉⡁⠀⠡⡐⢀⠀⠀⢀⡀⠀⠀⢀⠔⠈⠣⠄⠠⠜⠁⠢⡀
⠀⠀⠣⡀⠀⠈⠐⠂⢀⠍⢠⠀⢁⠚⠥⠈⠀⠁⠈⠁⠀⠕⠀⠀⠀⢀⠃⠀⠀⠀⠁⠀⠀⠀⠑⢆⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⢀⠜⠂⣈⠕⠀⠈⠀⡡⠐⠒⠢⢄⠀⠀⠀⠀⡀⣀⠜⠁⠀⠀⢸⠠⠈⢈⡈⡀⠀⣠⠀⠔⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠘⠒⠫⠤⠄⠄⡤⠊⢀⠀⢀⡠⠚⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⢳⠀⠀⡆⠁⢀⠀⡘⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠮⠤⠴⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣢⡈⢲⡰⠁⠀⢘⠖⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⣀⡀⡠⠔⠢⢄⠀⠀⠀⠀⠁⠈⠀⠀⠈⠀⣀⠀⠀⠀⣀⠀⠀⠈⠒⣄⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠇⢯⡱⢸⠒⠀⠀⠆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⡤⠴⠎⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⢄⡠⠃⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠛⠁⠀⣠⠄⠒⠒⡤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠠⠁⣠⡀⡄⠀⢡⣧⠀⠀⠀⢨⠉⠉⡇
⠀⠀⠀⡀⠀⠐⠚⠀⠀⠐⠻⣄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⢰⠃⠀⣙⡷⠃⠀⣿⠇⠀⠀⠀⠈⠳⠞
⠀⠀⢰⠁⠀⠀⠀⠀⠠⡄⢠⠀⠃⠀⠑⠐⠊⠉⠉⠐⠢⠤⠀⠤⠔⠊⠀⠀⢀⠀⠀⠀⠇⠀⠐⠇⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡈⠀⠀⠀⠀⠀⠀⠁⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⢸⠂⣠⣀⡀⠀⠀⣼⠇⠀⠀⠀⠈⠁⠀⣀
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠲⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡈⠈⠁⢐⡏⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⡧⠀⠐⠒⠒⠀⢤⢄⠈⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠂⠚⠉⠢⣄⠀⠀⠀⠀⠀⠙⠶⠶⢥⣤⣤⡾⠁⠀⠀⠀⠀⡚⠓
⠀⠀⣇⠀⠀⠈⠀⠂⠈⣾⠘⠃⡅⠀⠀⠀⠀⠔⠁⠀⠀⠀⢀⣄⣴⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⡀⣠⣖⠠⠀⠐⠀⣷
⠀⠀⠉⡄⠀⠀⠀⠀⠀⠙⠐⡀⡇⠀⠀⠀⠊⠀⠀⠀⠀⢰⠃⠙⠋⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⢠⡄⠀⠀⠀⠀⠄⠀⢀⢸⣿⣿⡇⠀⠀⢸⡅
⠀⠀⠀⠲⠶⢤⠤⠤⡾⠡⡾⠐⠁⠀⠀⠀⠀⠀⠀⣀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⠈⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠙⠛⠶⠶⠶⢴⣄⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⣉⠀⢀⡂⠀⠀⠀⠁
⠀⠀⡀⠀⣀⠠⠖⠒⠊⠱⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠁⠀⠠⠔⠒⠂⡄⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⣤⣀⣀⣀⡀⢈⠀⠀⠀⠀⠀⠀⠀⢀⢄⠤⠄⠀⠀⠄⠀⠀⠰⠂
⠀⠀⢸⡀⠀⠀⠒⠡⡐⠀⠰⡀⠀⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⡄⠕⠁⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠈⡃⠀⠐⠂⠚⠁⠀⠀⡁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⡈⠀⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀⡀⠀⠀⠀⡧⡀
⠀⠀⠀⢣⠀⣤⠴⠖⠚⠀⠀⡁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣄⢣⣤⠇⠀⠀⠀⠀⠀⡀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠂⠀⠒⠊⠁⠈⠒⢄
⠀⠀⠀⠈⠆⡀⠀⠠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⠋⠘⠻⠂⠀⠀⠀⠈⠛⠀⠀⠀⠀⠈⠀⠀⠉⠉⠐⠲⠀⡀⠤⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⠒⣶⡀
⠀⠀⠀⠀⢰⣿⣿⣿⡶⠁⠀⠰⠧⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣯⣭⢟⡭⠿⠯⢍⢫⣿⣭⡁
⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⡞⠀⠀⠀⠀⢳⢻⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣻⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡳⣀⠀⠀⣠⢏⣾⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣇⣀⣀⣀⣀⣀⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⣭⣭⣷⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⢀⡴⢛⣉⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⡾⠁⣿⣿⣷⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠛⣿⣀⣀
⠀⠀⠀⠀⢸⡇⠀⠘⣿⣇⠀⢀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢷⡀⠀⠈⠻⣷⣿⣿⣷⢄⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠈⠻⢦⣀⡀⠀⢉⣉⡭⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣴⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡤⠖⠚⢹⡇⠉⠒⠦⣄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢷⣄⣀⠤⣾⡇⠠⢄⣀⣴⠟⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢈⠿⣿⣦⣿⡇⢠⣾⡿⢏⠀⠈⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣘⣁⣀⣈⣀⣈⣉⣻⣇⣼⣿⣷⣾⣦⣤⣼⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠹⡉⠛⢻⠛⣻⣿⠋⣿⣦⣠⡀⢠⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢈⣿⡿⠛⠀⣿⡟⠻⣿⣎⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢟⠉⠈⠙⠀⣿⠇⠉⠈⢙⢷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠒⠤⠄⣿⠤⠴⠚⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⢀⣴⣿⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⣼⣿⠁⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣿⣷⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⢺⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠻⣿⣦⡀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡈⠻⢿⣶⣤⣾⡿⠛⠿⣿⣶⣄⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⡈⠙⠋⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣶⣦⣤⣶⣿⠟⠁⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠁
⠀⠀⠀⣸⣿⣥⣶⣶⣿⠿⠿⠛⠛⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣴⣶⣿⠿⠛⠉
⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⠶⠿⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠶⠶⠿⣼⣧⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣽⣷⣤⣄⢀⢄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠁⠀⠀⣷⠢⠎⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢷⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢬⡆⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⣾⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⡇⠀⢠⠂⠀⠀⠀⠀⠀⠀⡏⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢐⠄⡸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⠀⠀⠀⡔⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢜⠄⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠊⡀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⢎⠎⣽
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠞⣸⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⡐⢈⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣧⠀⠀⠀⠀⠀⠀⢀⡾⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠊⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣬⠦⣄⣀⣀⣠⡴⡟⢰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⣷
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠴⢥⣾⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢪⢺⡆
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⠆⢀⠔⠀⠀⢀⠔⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡱⢣⢾⡇
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠐⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⡰⢣⠞⡇
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⡡⠃⣧
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡱⠃⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠱⢁⢺⡇
⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠳⠦⢼⠇
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠻⠤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⡸⢻⣿⣧⡀⣴⣶⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⢸⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣶⣾⠟⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣸⣾⣿⣧⣤⣤⣴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠋⠁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠈⠙⢷⣶⣴⣯⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⢀⣀⣾⣿⣿⣿⠋⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⣦⠀⠙⣿⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣧⡄⠨⣿⣿⣿⠃⠀⣾⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠙⠛⠿⣿⣿⠀⠀⢸⣿⣷⠀⠸⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⣾⣿⣿⣿⠀⢸⣿⣿⣿⣿⡿⠋⠀⣠⣴⣶⣶⣶⣦⣄⠀⠙⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣿⡇⠀⣿⣿⣿⣛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⡇⠀⣿⣿⣿⣿⣟⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣾⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣦⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⢀⣼⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣏⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣷⣤⣀⠈⠉⠉⠉⠁⣀⣴⣾⣿⣿⣿⣿⣿⠁⢀⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⢿⣿⣿⣧⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣼⣿⣿⣿⣿⣿⠛⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠶⣴⣿⣿⣿⣿⣷⣄⠀⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠀⣠⣾⣿⣿⣿⣿⡧⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣄⣀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠟⢿⡏⠉⠀⠀⠙⠛⠉⠛⠿⠍⠃⠈⠁⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠶⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠛⠉⠙⠛⠉⠀⠀⠀⠀⠤⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⠂⠀⠂

⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠛⠓⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⣰⠏⠀⠠⣤⣤⣤⣤⠄⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠠⠤⠤⠤⠤⠀⠈⢳⡀
⠀⠀⠀⠀⠀⣿⠀⠰⠶⠶⠶⠶⠶⠶⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠤⠤⠤⠤⠤⠤⠀⠀⡇
⠀⠀⠀⠀⠀⠹⣄⠀⠐⠒⠒⠒⠒⠂⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠐⠒⠒⠒⠒⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⣸⣁⡤⣤⣤⣤⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⣠⠤⣤⣀⣠⡤⠔⠋
⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁

⠀⠀⠀⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣶⡆⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⣿⡟⠁⣠⣤⣶⣶⣶⣶⣶⣶⣤⡈⠹⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡿⠋⣡⣤⣶⣶⣦⣤⡉⠻⣿⣿⣿
⠀⠀⠀⣿⠁⣸⣿⣿⡿⠛⠋⠛⠻⣧⣠⣿⠀⢹⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣶⣾⣿⣿⣿⠀⠀⠀⢸⣿⡏⢠⣾⡿⠻⣿⣿⣿⣿⣿⣦⠈⣿⣿
⠀⠀⠀⣿⠀⣿⣿⡏⢠⣾⣿⣿⣆⠈⣿⣿⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠉⠈⣿⣿⣿⠀⠀⠀⢸⣿⠀⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿
⠀⠀⠀⣿⠀⣿⣿⡇⠘⣿⣿⣿⠟⢀⣿⣿⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⡆⠀⠀⣶⣾⣿⣿⣿⠀⠀⠀⢸⣿⠀⣿⣿⣿⣄⠙⠻⠟⠛⢿⣿⡇⢸⣿
⠀⠀⠀⣿⠀⢻⣿⣿⣦⣄⣉⣁⣤⣾⣿⣿⠀⣸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡇⢘⣿⣿⣿⣿⣶⣤⣴⣾⠟⢠⣿⣿
⠀⠀⠀⣿⣧⡈⠻⠿⠿⠿⠿⠿⠿⠿⠟⠋⣠⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⠁⠘⣉⣉⠛⠻⠿⠛⢋⣡⣴⣿⣿⣿
⠀⠀⠀⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⠟⠀⠀⠀⠸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠂⠈⠀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠔⠒⠒⠒⠒⠦⣄⠕
⠀⠀⠀⠀⠀⣀⣀⢠⠴⠶⣒⡶⠶⣬⣱⡿⠖⢂⣰⣿⣦⠀⢀⣀⣤⣤⣿⣤⣤⡴⠦⣀⣒⠶⠦⠤⠤⠴⠤⠄⢄
⠀⠀⠀⠀⠀⡁⠀⢀⡠⠎⠉⠀⠘⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣼⠋⠀⢂⠀⠀⢀⠁⠆⡁⢸
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠐⠀⠐⠃⠀⠀⠈⢄⠉⠁⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⢛⠀⠀⠀⠑⢤⠚⠁⢰⡇⢸
⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠈⠉⠉⡇⠀⠀⠠⠀⠀⠠⠉⠀⠄⠀⠀⠀⠀⡈⠁⠀⣿⠀⠀⠀⠀⠀⡑⠄⠜⢣⠸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⡀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠑⠤⠊⠀⠀⠀⠀⠠⢰⡌⠁⢰⢸⠀⡇
⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠇⠆⢸⠘⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⡀⠀⠀⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⠙⠂⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⢀⠀⠀⠵⡠⠀⡉⠏⠀⡇⢸
⠀⠀⠀⠀⠀⠧⠀⠀⠀⠠⡀⠀⠀⡇⠀⠀⠀⠀⠒⠂⠀⠀⠀⠐⠠⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠁⠛⠀⠀⠁⢸
⠀⠀⠀⠀⠀⡄⢈⠢⠐⠈⠁⠀⠀⢡⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢂⢀⠀⠀⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠢⡇⢸
⠀⠀⠀⠀⠀⠧⠬⠤⣰⠤⠤⠄⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠀⠀⡇⠀⢸⠂⠀⠀⠀⠀⠀⠀⢀⣧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⠓⠒⠒⠤⠤⢭⡤⠎⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⠉⠀⠈⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⣰⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣦⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡄⠀⠀⣠⣤⣤⣤⣤⣤⡀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⢹⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠹⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⢀⣴⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠛⠋⠁⠰⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣤⡀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⢀⣈⣉⡉⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⢀⡀⠤⢠⢐⡀⡆⣂⢂⣐⣐⢒⡐⠂⡀⣄⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⡀⠄⢂⣡⡴⠼⠋⠉⢀⣀⠀⠠⠤⠌⠉⣍⠹⢓⠶⠬⣓⢤⡀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⢀⡠⠢⣀⠶⠚⠓⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠉⠙⠺⣆⣀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡰⠎⠡⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠐⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡔⢀⡶⠉⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠎⣿⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠂⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⡬⠀⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠌⢠⠃⣀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⠭⠥⢄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠁⠨⢁⡫⠤⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠨⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣓⠂⠀⠀⠀⠀⠀⠄⠈⠀⠁⠀⠀⢠⠀⡨⠋⠘⢲⡌⢽⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠥⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢌⣡⡞⠫⢽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢈⠠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠰⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠱
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⣨⡄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⢀⠞⠀⠀⠀⠀⡠⠀⠐⠁⠀⠀⠀⠀⠠⢤⠄⠀⠀⢠⠃⡙
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡯⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢀⠒⠈⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⠐⡶⢯⣇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⢥⠀⠁⠀⠀⠀⠀⠀⠀⡀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠠⠊⠾⠹⠜⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠢⡀⠀⠀⠑⠀⡀⠀⠀⠀⠀⢠⡧⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠔⢢⠶⠚⠆⡶⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠲⢄⡀⠀⠀⠁⠂⠤⢀⣈⡁⠀⠀⠀⢀⣀⠠⠄⠒⠛⠉⠁⠀⠀⠀⢀⡄⢂⠁⠈⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄⠙⠂⢀⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠡⠐⠀⡢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⡀⠈⠉⠒⠢⠠⠄⡄⡀⢀⠄⡤⡤⠤⠒⡈⠡⠀⠀⠣⠀⣠⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣄⣀⡀⠂⠀⠀⠀⠂⠠⠈⠀⢂⠈⣀⣥⠰⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡉⠈⠐⠒⠓⠒⠒⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠄⠊⠠⠂⠀⠐⢀⠄⠂⠡⠀⡠⠀⠀⠔⠀⠠⠂⠈⠄⠂⠀⠐⠀⡠⠒⢁⠔⠈⠄⠀⠔⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣐⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣉⣠⣤⣤⣤⣤⣤⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⣤⣤⣀⡀⠈⠑⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⣤⣶⣶⡿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⠳⣦⡀⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢻⡄
⠀⡀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠁⠁⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⢠⣿⠇⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣾
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⡱
⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠈
⠀⡄⠄⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⣴⠏
⠀⠈⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⠟⠁⣀
⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠋⠐⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠷⢶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⣞⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢌⡑⠂⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠉⠻⣦⣀⠀⠀⠙⣆⠣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠛⠷⣦⣀⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣝⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡀



⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡿⠉⡀⠈⠉⠈⢂⠐⣿⢿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠃⠤⠜⠀⡼⠋⢀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡆⠀⢀⠀⢙⠀⠀⠀⣤⣼
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠃⠀⠈⢠⠄⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠠⡇⠰⠄⠀⠀⠀⠀⠀⠀⣧⣠⣤⣤⣤⠴⠛⢦⣌⣉⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⢀⠒⠀⠉⠉⠉⠉⠶⠤⣤⠀⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠀⠀⠈⡄⢠⠙⠛⠃⠐⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠓⠠
⠀⠀⣶⠁⢠⠀⢀⢀⡀⢀⠀⠀⠘⣆⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠄⢸⢀⣤⣠⡶⠀⡀⠀⠀⢀⡞⠀⠀⠶⠀⠀⠲⣀⣀⣙⡀
⠀⠀⠋⠀⠸⠦⠚⠈⠃⠸⣈⠀⠀⡿⠀⠀⠀⠀⠀⠀⠑⠐⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠿⠃⠀⢀⠀⠀⠘⢰⡀⠀⠀⠀⡠⠂⠀⠀⠀⣀⠈⠃⣀
⠀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠆⠀⠁⠀⠀⠀⠀⠁⠉⠀⢠⠀⠀⠀⠀⠀⠰⡇⠓⠀⠀⠀⠐⠈⠂⠀⠀⠀⠑⠄⣀⣠⡇⠀⠋⠀⠀⠙⠀⠀⡷
⠀⠀⠀⠀⠀⠉⠐⡆⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠰⠃⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⢰⡇⠀⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠓⠀⠀⡀
⠀⠀⢘⡉⠀⠀⢙⠆⠘⠉⠒⠉⢁⠀⠀⠀⠀⢀⢂⡀⢠⡄⢀⡠⠄⠂⣀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠛
⠀⠀⠀⣻⠆⢸⠀⠀⣧⠀⡜⠉⠁⠀⠀⠀⠀⠶⠀⠄⡁⠀⢈⡠⠄⠀⢨⠆⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠛⠀⠸⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⣶⠀⠀⠈⠀⠈⠀⢸⠀⠀⡦⠀⠀⠀⠀⢰⠀⠀⠂⡀⠐⠀⠈⠀⡀⠀⠀⠀⠀⠀⠁⢤⣀⡀⠀⠰⠃⠠⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⠀⠂⠀⠀⡄⠀⠸⣀⢀⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢴⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠒⠒⠒⠀⠶
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠅⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡜⠀⣀⠒⠀⣰⠂⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠁⠄⠀⠃⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠤⠀⢠⡀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢂⡀⠀⢤⠀⠀⠀⠀⠁
⠀⠈⠃⠀⠰⠂⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠈⠀⠐⠚⠃
⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠞⡡⠈⠀⠀⠀⠀⢀⠀⠀⠃⠀⠻⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾
⠀⠘⡇⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠶⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢸⠀⠀⠁⡀⠀⢁⡘⢹
⠀⠀⠈⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⢠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠀⣤⡀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡔⠋⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠰⠆
⠀⠀⢀⡰⠋⠀⠀⠀⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⣀
⠀⣠⠎⠀⠀⠀⠀⠰⠀⠀⠈⢣⡄⠀⠀⠀⠀⠀⠀⠀⠛⢠⡀⢀⠴⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣈
⠀⠀⠀⡀⠀⣠⣀⣄⡀⠀⢂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠶⠤⠁⠀⠀⠀⠀⠀⠀⠀⣦⠀⠋⠀⠀⢁⠐⢀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⢀
⠀⠀⠙⣇⠀⡄⠀⠀⢀⠀⣹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢂⡐⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠁

⠀⠀⠀⠀⢰⣿⠿⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢾⣿⠷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣋⢛⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠟⠃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠬⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⠆
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⡴⠶⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠩⠟⠿⠀⠀⠀⠀⠀⠀⢠⣶⣶⢶⣶⣶⡆⠀⠀⠀⠀⠀⠀⢠⣾⣧⣄
⠀⠀⠸⣇⣘⣻⠆⠻⠃⠀⠀⠀⠀⠀⣾⣹⠿⠻⡿⢷⠀⠀⠀⠀⠀⢸⣿⣿⣠⣼⣿⡗⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣥⣤⣤⡿⠀⠀⠀⠀⠀⠈⠙⠋⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠛⠷⠖


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠲⢤⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢠⣶⣶⣠⣶⣶⡀⠀⠀⠀⠀⠀⡏⢸⡇⠀⠀⢹⠀⠀⠀⠀⠀⠀⡇⣠⠒⢶⢸⡇⠀⠀⠀⠀⠀⢰⡆⢰⡶⢶⣦
⠀⠀⠈⠻⠟⠉⠻⠟⠁⠀⠀⠀⠀⠀⣧⠀⠙⠺⢃⡼⠀⠀⠀⠀⠀⠀⣇⠘⠲⠊⢸⠇⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉


⠀⠀⠐⢶⡖⠀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠷⢶⣤⡀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⠿⣦⡀⠀⠀⠀⠀⠀⢀⡴⢋⡉⢳⡄
⠀⠀⠀⠀⢻⣴⠋⢰⡆⠀⠀⠀⠀⠀⠘⠻⣶⡌⢿⡄⠀⠀⠀⠀⠀⢸⣿⣦⣉⡓⢿⡇⠀⠀⠀⠀⠀⠘⠇⣿⡁⣸⠇
⠀⠀⠀⠀⠼⠷⠄⠨⠀⠀⠀⠀⠀⠀⠰⠷⠈⠿⠘⠿⠀⠀⠀⠀⠀⠈⠻⣦⣭⣥⣿⡟⠀⠀⠀⠀⠀⠀⢠⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣶⣶⣶⣶⠶⣶⡶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⡶⣶⣶⡶⡶⢶

⠈⢆⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠱⠀⠀⠀⠀⠀⣸⡀⠀⠀⠌⠀⠀⠀⢸⡀⠀⠀⠀⡞⠀⠀⠀⢠⠞⠁⠀⢀⠜⢶
⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⢳⣀⠤⠔⠒⠒⠊⠉⠉⠈⢣⡀⠀⠀⠀⠀⢀⠞⠀⠀⠀⡰⠃⠀⠀⣰⠋⠀⠀⠀⠁
⠀⠀⢀⡷⠀⠀⢀⣠⠴⢒⠁⠙⢆⠀⠀⢀⣀⣤⠤⠖⠒⠻⠉⠒⠲⠦⣏⣀⠀⠀⡴⠁⠀⢀⣼⢁⠀⠠⠎⠐
⠀⠀⢸⣠⡴⠚⠉⠀⠀⠀⠀⠀⠈⢷⡊⠉⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢸⡀⢩⠾⢄⡀⢠⡞⠀⠁⢄
⠴⠚⠹⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠐⠠⠄⣀⠀⠀⡊⠀⠂⠄⣜⣡⠋⠀⠀⡽⠻⢄⡀⠀⠀⠑⠀⠀⠀⠀⢀
⠒⠒⠦⣞⢁⠀⢀⡀⠄⠀⠀⠉⠀⢸⡀⠀⠀⠀⠀⠈⠁⠀⠀⠄⠀⣠⠞⠉⠙⢦⣞⡁⠀⠀⠉⠉⠉⡏⠉⠙⢉⠉⠁
⠀⠀⠀⠈⢩⠂⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠂⢙⣦⠞⠁⠀⢀⡴⠣⡈⠙⠳⢦⣄⡀⢠⠇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣀⣀⣀⣠⡤⠖⠋⠀⠱⣄⣠⠟⠀⠀⢱⠀⠀⠀⠈⢙⡿⠶⠦⡧⣤⣄⣀
⣠⣤⠤⠴⠷⠒⠒⠲⣆⠀⣀⣀⣹⠉⢿⢉⢉⠉⠁⠀⠐⠒⢂⠀⢠⡞⠃⠠⠀⠀⢼⣅⠀⠀⢀⡞⠀⠀⢀⠁
⠀⠀⠀⠀⡆⠀⠀⠀⡏⠉⢹⡀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⢀⡵⢏⠀⠀⠀⠀⠀⢸⠀⠑⠢⣞⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⣀⣧⠤⠴⢻⠃⠀⠀⢧⠀⡀⢘⣀⣀⣀⣀⣀⣀⣴⠟⠀⠀⠑⡀⠀⠀⢀⡇⠀⠀⠈⠈⠑⢦⣠⠀⠀⠀⢠⠃
⠒⠉⠩⣅⣸⡤⠶⠻⡖⠚⠛⠛⡏⠉⠉⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠞⠀⢑⠾⢤⣀⠀⢶⣞⠳⢦⣴⠇⠂
⠀⠀⠀⡼⠀⡆⠀⠀⠘⢦⠀⠀⢱⣀⣀⣇⣀⣤⠤⣤⣀⡀⠀⠀⠀⠀⠠⢠⡍⠠⢤⣉⠀⠠⠈⢹⠾⢄⠙⠦⠙⢦⠨
⠉⠉⣹⠛⠶⣄⠀⠀⠀⠀⣳⡤⠔⢇⠀⠀⠀⠀⢰⠃⠀⠉⠑⠢⢄⣀⢀⠎⠀⠀⡀⠀⢀⠂⠀⠁⠀⠀⠐⠄⡀⠀⠑
⠀⣰⠃⠀⠀⠈⠳⣄⡠⠚⠁⠙⢄⠸⡄⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢈⠟⠒⠤⣄⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⣰⠇⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠈⠣⡇⠀⠀⠸⡀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⠉⠛⠢⢤⡀⠀⠀⠀⢀⣀⣀⣤⣤
⣏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠦⢤⣽⣀⣀⣀⣧⣤⣤⡤⠤⢤⡾⠴⠶⠶⠶⠒⠺⡖⠛⠛⠛⠛⠻⢭⡉⠉
⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠉⠰⠇⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⠑⠦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠄⣐⠒⠒⠀⠀⢠⡄⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢐⠦⢛⡀⢓⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣘⣁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠁⢠⢾⡉⠓⡄⢀
⢇⠀⠀⡠⠄⠀⠀⡀⡄⢚⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠱⠆⠀⠀⠀⠀⡖⠄⡁⠀⠀⠀⠀⠸⠤⠤⠴⠁⠀⢁
⢸⣷⡞⠀⠀⠂⠑⠁⠀⠀⠀⣈⣉⣀⠖⠀⠀⠀⠀⠀⠀⠀⠠⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡎⠀⠄
⠀⠀⢅⠀⠀⠀⠈⠈⠛⠻⣿⡩⠍⠀⠀⠀⠀⢀⡰⢆⡄⠀⠠⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠒⠒⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⢧⡀
⠀⠀⠀⠀⠀⠀⠃⠤⠖⠒⢦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢹⠀⠀⢠⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠄⢀⣀⣀⣸⠀⠇⠀⠀⠀⠀⠀⠂⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⢸⠀⠀⣀⣶⡀⠀⠀⠀⡇
⠀⠨⠀⣠⣤⣤⡁⠀⢀⣤⣤⡀⡀⠀⠀⢀⡴⠀⠀⠙⠃⠀⠈⢀⣄⠀⡀⠀⠀⡀⠀⠀⠀⡟⠀⠀⢸⠀⠀⠉⠿⠉⠀⠀⠀⣇
⠀⠰⠄⠺⣘⡪⠷⠴⢯⣒⡾⠳⠂⠀⠀⠘⠄⠀⠰⣾⡧⠈⠠⠃⣺⡧⠂⠀⠠⠀⠀⠀⠀⠒⠀⡢⣬⡐⡄⠀⣴⣩⡑⡤⠤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠀⠀⠀⠻⠃⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠓
⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣇⣀
⣄⣀⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⢀⠀⡁⠀⢄⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⠀⡖⠀⠐⠄⣀
⠈⣸⠷⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠠⢌⠁⢈⡇⠀⢀⡎⠉⢱⠄⠀⠆⠀⠀⠀⣠⢐⣛⣛⠁⠀⠖⠁⣀⣈⡀⠈
⠐⠈⠓⠶⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠀⠋⠉⠀⠀⠀⠉⠒⠉⢠⣶⠀⠀⠀⣖⣋⡿⢽⡌⣷⣀⣠⣿⢹⡬⢽⣄
⠀⠀⠀⠀⠀⠀⠑⠠⠀⠉⠉⠈⠉⠗⠂⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠖⠚⢿⡎⠇⠀⠀⠀⠀⠙⠳⠚⠁⠀⠀⠈⠓⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠁⠈⠁⠐⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠁⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢀⠤⠀⠠⠤⡔⠂⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡷⢤⡀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢈⣉⣉⣉⣉⣉⣉⡁⠀⠀⠀⢰⠁⠀⠀⠀⠐⡀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⠀⡱⠂⢀⠈⠃⠀⠀⠀⠀⢀⠠⠄⠀⠚⢄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⠢⣠⢄⡀⢠⡉⠑⣼⠧
⠀⠀⠀⠀⠀⠀⠀⠈⡀⣹⠻⡀⠀⠐⠸⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠑⢤⡄⣀⣀⠀⣀⠀⢄⡀⠘⡄⠀⠇⠂⠀⠈⠚⣍⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠈⠰⣚⠎⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠲⣒⠄⠀⣠⠇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠛⠲⢦⠊⠀⠀⠀⠀⠡⠀⠀⣉⣉⣉⣉⣉⣉⣉⡁⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⢀⠤⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⠁⠀⢀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠰⡑⠁⠁⢄⠀⠀⠀⠈⡄⠀⠀⠀⠉⠒⠈⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠔⠒⠄⠈⡆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢃⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡆⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠂⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡠⣾⣋⠔⠁⠀⠈⢢⢱⡦⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⡁⠀⠀⠀⠀⠰⠀⠀⠀⢠⠀⠀⠀⢀⠔⠁⠖⣫⠊⠀⠀⠀⠀⠀⠁⠙⠀⠑⠄⠀⠀⠀⠀⠃⠰⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠇⠰⡀⠀⠀⠀⠀⡆⠀⠀⣨⠠⠄⠂⢁⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⡈⠀⠀⠀⢄⡀⠀⠀⠀⠠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠔⠈⠁⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠐⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⡇⠀⠀⠣⠀⠀⡘⢀⡀⠄⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠒⠀⠁⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠒⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠀⠀⣀⠀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⢢⠤⠀⠀⠀⠀⠀⣀⣀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠉⠉⠀⠀⠀⠀⠩
⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⠊⡀

⠀⠀⠀⠀⠀⠀⣤⠄⣀⣀⣀⣀⡀⣀⠀⣠⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠠⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡏⠀⠀⠛⠀⠳⣤⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⢸⠀⣿⢦⡾⣇⠀⣧⢀
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡆⢹⠀⠀⢻⡆⣿⠉
⠀⠀⠀⠀⠀⠐⠛⠗⠀⠀⠉⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠃⠘⠃⠀⠀⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠕⠈⠉⠉⠓⢌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡤⠤⡤⠤⡮⠀⠀⠀⠠⠀⠬⣮⣇⣤⡤⢄⡠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⠔⠁⢀⠇⡸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣆⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⢮⠥⡽⠀⠀⠀⠀⠀⠀⠀⠀⠮⡅⡽⠂⠈⠢⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠑⣄⢾⣼⡷⠀⠀⠀⠀⠀⠀⠀⠰⣞⣐⡳⠀⠠⠔⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⡎⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⠀⡰⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠛⠛⠒⠒⠒⠂⠀⠀⠀⠐⠓⠓⠒⠓⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠉⣿⠙⢱⡎⢹⡆⠀⠀⠀⠀⠐⠒⡶⠒⠂⢶⢲⠀⠀⢀⣶⡀⢰⡀⢰⡇⢺⠉⠀⣴
⠀⠀⠀⠀⠀⠀⢿⠀⠸⣇⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡿⣄⠀⢼⠗⢷⠀⢳⣼⠁⢸⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠘⠃⠈⠀⠛⠀⠈⠀⠀⠋⠀⠘⠋⠁⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⠶⢶⣶⣾⡧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣩⣿⣿⣥⣶⠶⠶⠾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⡶⢧⡀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⡾⣷⣦⣞⣱⠃⠈⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣟⡿⣿⣟⣿⣿⣶⣇⣀⡟
⠀⠀⠀⠀⠀⠀⢠⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⢻⣿⣿⣿⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡛⣾⣿⣳⢿⣿⡄
⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⣸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⡪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⣿⡟⢃⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣻⢡⣿⣗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇
⠀⠀⠀⠀⠀⠉⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣛⣛⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠙⠻⣿⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠁


⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠎⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠴⡶⠀⠀⢀⣴⡄⣠⣤⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠃⠀⢸⠀⠀⠀⣀⡄⠀⢀⡀⡄⢀⣀⣀⣀⣀⠀⠀⠈⠉⠉⠀⠘⠻⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⢸⠀⠀⠍⡏⢱⣠⣴⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⠄⣠⣄
⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⡀⠸⢻⠀⠀⠀⡇⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠀⣠⣶⠷⣾⠿⠻⠿⠄⠘⠛⠛⢻⣿⡿⠿⠿⠿⠿⡿⠿⠶⠼⠷⢤⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠛⢰⡏⠁⠐⣶⣦⣄⠀⠀⠀⠀⠀⠀⡀⠠⠀⢀⣠⣤⣤⣌⣛⣛⣀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⡧⠴⠶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡄⣿⢀⣄⠀⢸⡇⠐⠒⣿⣿⡧⠿⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡄⣤⣿⡇⣿⠘⠛⠀⠘⣷⠶⡾⠋⠀⠀⠀⠠⠄⠀⠁⠂⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈
⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣿⣧⣻⣶⣶⣶⣶⣶⡞⣰⣿⣿⣷⡀⠀⢰⡟⠛⣿⠛⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣻⡟⣶
⠀⠀⠀⠀⠰⢾⣿⣿⣯⠻⣿⣿⣿⠋⢻⡯⠭⣭⣿⣿⣿⣰⡿⣋⣉⣻⣷⠀⠈⠁⠛⠛⠛⠉⠀⠸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠸⡇⣿⡃⣿⣿⣿⣿⣄⣸⣇⣀⣏⠀⢼⣿⣿⣿⠿⠟⣿⡟⣷⠒⠒⠒⠒⠒⠒⠛⠒⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠙⠛⠻⠷
⠀⠀⠀⠀⠀⠤⠿⠿⣷⣿⣿⣿⣿⣿⣿⣭⣍⣛⣻⣿⣿⣿⣿⣷⣆⠤⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⣿⣿⣿⣿⣿⣿⠿⣡⣦⡇⣾⣤⣤⣤⣤⣤⣤⣤⠄⠀⠐⠀⠒⠒⣶⣶⣶⣶⣶⣶⣿⣿⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠻⢻⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⣿⣷⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣶⣶⡶⣶⣶⡶⢂⣴⣶⣶⣶⣶⣢⣶⡶⢂⡴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⣶⣻⣿⣿⠿⠿⠋⠴⠿⠿⠿⠟⠵⠿⠿⣫⣶⣿⡾⢃⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⣾⡟⠁⠁⣀⣀⣤⡄⣠⢀⢀⣄⣄⣀⡀⠀⠈⠉⣴⣻⣥⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣾⠁⢠⣾⣿⣿⣯⡞⣑⣵⢟⡡⣺⡞⠁⢡⣦⠀⢨⣿⠟⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⡃⠀⢸⣿⣿⣿⠋⠀⠁⠀⠀⠈⠙⢥⣤⡾⣻⠄⠀⡡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⣾⡇⠀⣹⣿⣿⠇⠀⠔⣫⣾⣻⢔⡀⠈⢫⠾⢋⠀⠀⡾⢋⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣫⡿⡃⠀⣼⣿⣿⠀⠀⠞⣩⢞⣵⣿⡧⠀⢠⠖⣡⠄⠀⣶⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣿⡇⠀⢸⢟⣵⢆⠀⠘⠿⡿⡿⠛⠀⢀⣴⡿⣻⠄⠀⢟⡵⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣫⡆⠀⠰⢋⣴⣿⣷⢄⣀⢀⣀⢀⣴⡿⣫⣾⣿⠀⠀⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣫⠖⠀⠀⠻⣿⣿⠗⡩⣪⢟⣴⣿⣿⣿⣿⠿⠃⠀⣼⢟⣱⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣵⣶⢛⣤⡀⠀⠀⠀⠀⠁⠁⠈⠉⠀⠀⠀⣀⡤⢚⣵⡿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡿⢋⡴⣫⣺⢞⣵⣟⣥⡶⣚⣵⣿⡿⢋⣴⡿⣫⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⠻⠛⠳⠟⠑⠻⠛⠿⠟⠻⠋⠚⠻⠋⠚⠋⠁

⠀⠀⠀⢠⠂⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣥⣀⡀
⠀⠀⠀⠟⠀⢞⠀⣶⠀⠲⡆⠀⢴⠖⠀⢨⣷⠀⢠⠖⠰⢂⠀⣴⠒⢲⡆⠘⡦⢠⡄⢰⡖⠲⠆⠀⣂⣰⣦⢐⣶
⠀⠀⠀⠀⠀⣿⠀⣡⡎⢈⠄⢀⠄⠻⣦⢘⡅⠀⡴⠀⢀⡿⠀⣿⠀⢨⣆⡀⠀⠛⠀⣿⠀⢀⡅⠀⣿⠃⣴⠏⢩⠀⡀
⠀⠀⠀⠀⠀⡭⠀⠋⠀⠀⠶⠋⠲⠖⠛⠀⠑⠊⠐⠗⠀⠛⠖⠛⠖⣹⡏⠀⠀⠘⠶⠛⠖⠊⠛⠖⠱⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠰⠦⢀⡀
⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣤⣬⣥⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⢉⣳⣿⣷⢦⣄⡤⠤⠤⢤⣀
⠀⠀⠎⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠀⣼⡟⠉⠹⡆⠀⠉⠛⠻⢅⣈⠙⠢⢄⡀
⠀⠀⣦⡏⠀⠀⢀⡟⡿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⢠⠀⠈⠐⠢⢤⣀⠀⠈⠉⠒⠶⣤⣷⣦
⠀⠈⠛⠃⠀⠀⢸⡌⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⢹⣷⡆⠀⠀⠘⡌⠉⠒⡦⠤⣀⠈⠙⠂⠤⡀
⠀⠀⠀⠀⠀⠀⡿⡇⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⢸⢿⡇⠀⠀⠀⣧⠀⠀⢸⠀⠈⡇⠑⡖⢤⣬
⠀⠀⠀⠀⠀⢀⣦⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣄⠘⡇⠤⠄⣀⣈⣀⡀⠈⡄⠀⠠⠀⢸⠀⢙⡄
⠀⠀⠀⠀⠀⢸⠃⠀⠙⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⢸⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⠈⢤⣿⡇
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⣀⠀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠘⡀⡇⠀⠀⠀⠀⠀⠀⠠⠆⣠⡀⠀⠠⠾⣿⡇
⠀⠀⠀⠀⠀⢸⣤⣀⣠⣤⣬⣤⣤⣤⠄⣤⡤⠠⠶⢶⡶⠶⣀⣀⣠⣤⣴⣶⣿⡀⠀⠇⡇⢂⣀⣀⡤⠤⠤⠤⠶⠶⠒⠚⠛⠻⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠃⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣔⣏⣿
⠀⠀⠀⠀⠀⢠⣘⣀⣀⠀⠨⣯⣄⠀⠀⠀⠀⠀⣰⣶⣶⠆⠀⢀⣀⣀⣀⣠⡤⢄⠀⠀⣿⣴⣿⣿⡆⠀⠀⢀⡀⠤⠀⠀⣿⡏⠉⠅
⠀⠀⠀⠀⠀⢈⣿⣿⣯⡄⠀⢺⣷⡂⠀⢤⡄⠀⣤⣽⠓⠀⢠⣿⣿⣿⣿⣿⣇⡨⠀⣀⢿⣿⣿⣿⣇⠈⠀⠀⠀⣀⣠⣴⣿⠁
⠀⠀⠀⠀⠀⢿⣿⣿⣿⡅⣀⢒⣶⣲⡶⠶⠶⠶⣶⠶⠶⠂⣐⣒⣒⣒⠒⠒⠒⢂⠀⠁⢸⣿⣿⣿⠏⠀⣤⣤⣼⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠘⠿⠿⠿⠍⠉⣉⣽⣋⣀⣀⣀⠀⠈⠁⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⡏⠀⢀⣵⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣟⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠿⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠳⣆⢤⣠⠤⢔⢂⣰⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠠⠀⡀⢀⠠⣄⣠⣤⣿⡚⡟⢁⡰⡎⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡡⠒⠉⢈⠹⠎⠉⠀⠀⠙⢾⣥⣹⡀
⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⢢⣴⠒⠒⠿⠋⠑⠄⠂⠙⣿⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠤⠄⢢⡀⠇⠀⡰⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠉⡆
⠀⠀⠀⡀⢠⠔⠚⠒⠒⠒⠒⠻⠟⠀⠘⠷⠯⠤⢒⠷⢾⣶⣦⠢⣑⡀⠀⠴⠀⠐⠄⠀⠀⠈⣴⡠
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠄⠀⢈⠏⠀⠀⠀⠀⠀⠐⣄⠀⡔⠜⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢸⡄⠀⠀⠐⠒⠖⠙⠐⡥⠤⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢸⠄⠀⠀⠀⠀⠀⠀⢆⠸⡐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠸⠀⡀⢀⢀⠀⢀⠠⢸⢐⠌
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣷⠶⠤⠤⠬⠠⠄⣊⡜⠋
⠀⠀⠀⠿⠦⢤⠤⣄⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⢀⢒⠂⢄⣔⣵⣷⣭⠨⠤⠴⠚⠉⠀⣀⣠⡠⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠙⠃⠒⠒⠻⠚⠛⠋⠋⠁⠀⠠⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠈⠈⠉

⠀⠀⠀⠀⠀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡤⠴⠖⠒⠦⢤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣁⣠⠤⠦⠤⣤⣀⣙⡆⠪⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⢔⢄⣠⣤⣴⡶⡟⣷⠾⣛⣽⡿⠶⢖⣿⣷⠲⠶⢶⣶⣾⣿⣬⡶⠮⣁⣾⣶⠶⠶⠴⠶⡶⢦⡀⢠
⠀⠀⠀⠀⠀⡁⣿⣀⠀⡠⠜⠉⠀⢸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢰⠏⠁⢂⠀⠈⠉⢐⣐⠀⣷⢀
⠀⠀⠀⠀⠀⠀⣗⢠⠋⠀⠀⢐⣀⣘⡃⠀⠀⠡⣈⠁⠀⠀⠀⠀⠀⠀⠀⣂⣀⣘⡇⠀⠀⠑⢄⠊⠈⣿⠐⡏⢸
⠀⠀⠀⠀⠀⠃⣼⠁⠀⠀⠀⠈⠀⢸⡇⠀⠀⠂⠀⠀⢊⠀⠀⠀⠀⠀⠠⠁⠀⡸⠄⠀⠀⠀⠀⣑⠰⠹⠀⣿⢸
⠀⠀⠀⠀⠀⠄⣿⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢱⠈⠀⠀⠀⠀⠀⠼⠄⠀⠀⠀⣿⢨
⠀⠀⠀⠀⠀⡆⡇⠀⠈⠶⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⡇⣧⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⣿⢨
⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⢑⡀⢀⠀⢤⠂⠀⠀⣿⢸
⠀⠀⠀⠀⠀⡂⢻⠄⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠠⠄⠀⠀⠀⠠⠀⠀⠀⠘⠀⠀⠂⠀⠈⠑⠲⠆⠀⠀⢀⡇⢸
⠀⠀⠀⠀⠀⡃⣧⠀⠢⡀⠐⠃⠀⠀⡇⠀⠀⠀⠀⢀⡀⠀⢀⠀⠄⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⠈⣷⢸
⠀⠀⠀⠀⠀⠃⢿⣐⣡⣈⣦⣤⣄⣀⣧⣀⡀⠀⠀⠀⠀⠀⠚⠃⠈⠁⠀⢸⠀⠀⠆⠀⠀⠀⠀⢀⠀⣹⣤⡟⢸
⠀⠀⠀⠀⠀⠠⠲⠠⠄⠘⠐⠀⠉⠘⠅⠐⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠺⠦⠴⠗⠒⠶⣤⣤⣥⡼⠋⠁⠖⢸
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒⠀⠒⠒

⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⢀⣴⣿⣿⣿⡿⠿⠿⣿⣦⡀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠛⠿⣿⣶⣄⠀⠀⠀⠀⣠⣾⣿⣿⠿⢿⣿⣿⣷⣄
⠀⠀⢠⣾⣿⣿⣿⡏⠀⣰⣶⣿⣿⣿⡄⠀⢀⣾⡿⠁⣠⡴⠶⠶⣤⡀⠹⣿⣆⠀⠀⣼⣿⣿⡿⠟⠀⠸⠿⣿⣿⣿⣧
⠀⠀⣾⣿⣿⣿⡏⠁⠀⠈⢹⣿⣿⣿⣿⠀⢸⣿⠁⢰⡏⢰⣶⠀⢸⣷⠀⢹⣿⠀⢸⣿⣿⣿⣧⡄⠀⢀⣤⣿⣿⣿⣿⡆
⠀⠀⢹⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⡿⠀⢸⣿⡆⠈⠓⣸⣇⣀⣼⠏⠀⣾⣿⠀⠘⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠃
⠀⠀⠈⢻⣿⣿⣿⡇⠀⣿⣿⣿⣿⡿⠁⠀⠀⠻⣿⣦⣀⡿⠈⠉⠁⣠⣾⡿⠃⠀⠀⠹⣿⣿⣿⣧⣀⠀⢀⣹⣿⣿⠏
⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠻⠿⣿⣶⣾⣿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⢀⣤⡾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⢠⣾⣯⣀⣸⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣾⣿⢡⣶⣶⣶⣶⡶⢦⠹⣿⣆⠀⠀⣼⣿⠟⢿⣿⣿⠟⠉⠙⠛⣿⣦
⠀⠀⣼⣿⣿⠉⢹⡏⠉⢉⡀⠉⢻⣿⣿⠀⢸⣿⡇⢸⡿⢡⣶⣦⠙⣿⠀⣿⣿⠀⢰⣿⣿⡇⠀⠉⠉⠀⠀⠀⢸⣿⣿⡄
⠀⠀⢻⣿⣿⠀⢸⡇⠀⣿⣿⠀⢸⣿⡿⠀⢸⣿⡇⢸⣷⡘⠻⠛⣰⣿⠀⣿⣿⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⠃
⠀⠀⠈⢿⣿⣀⣸⣇⣀⣿⣿⣀⣸⡿⠃⠀⠀⢻⣿⣌⠻⠿⠿⠿⠿⢛⣸⣿⠃⠀⠀⠻⣿⣯⣉⣀⣀⣤⣶⣿⣿⣿⠏
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠿⢿⣷⣦⡀
⠀⠀⢀⣾⣿⡿⣋⣥⣤⣬⣝⢻⣿⣷⡀⠀⠀⣼⣿⠿⠿⠛⠛⠛⠿⠻⢿⣿⡄⠀⠀⣰⣿⢋⣴⢶⣾⣷⣶⣦⡙⣿⣆
⠀⠀⣼⣿⡟⢰⡏⢙⣿⣿⣿⣧⢹⣿⣷⠀⢸⣿⡇⠀⠀⠀⣄⡀⠀⠀⠀⣿⣿⠀⢰⣿⡏⢸⣧⡀⣿⣿⣟⣿⡇⣿⣿⡄
⠀⠀⢻⣿⣧⢸⣿⣦⡙⠋⢻⡟⣸⣿⡿⠀⢸⣿⡇⠀⠀⠀⠛⠉⠀⠀⠀⣿⣿⠀⠸⣿⣷⢸⣿⣷⣌⡋⠙⣿⠇⣿⣿⠃
⠀⠀⠘⢿⡿⠐⣛⠻⠿⠟⣋⣴⣿⣿⠃⠀⠈⢿⣿⣤⣤⣤⣤⣤⣤⣤⣼⣿⠏⠀⠀⢻⣿⣧⣍⡿⣛⣛⣋⣩⣾⣿⠟
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠿⣿⣾⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣠⢖⣚⣭⣭⣭⣛⡲⢤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠟⣉⣭⣭⣭⣭⣍⣉⠛⣿⣿⣿⠀⠀⠀⠀⠀⡰⢋⣴⠟⢛⣛⢛⡛⠛⠻⢷⣝⢦⠀⠀⠀⠀⠀⣿⣿⣿⠛⣉⣭⣭⣭⣭⣭⣉⠻⣿⣿⣿
⣿⣿⡇⣼⣿⣿⠿⠟⠿⣿⣹⣷⢸⣿⣿⠀⠀⠀⠀⣸⢡⣿⠁⣾⣿⡿⠿⢿⣟⣿⡄⣿⣎⢧⠀⠀⠀⠀⣿⣿⡇⣾⣿⣿⠿⠛⠿⣯⣽⡇⢸⣿⣿
⣿⣿⡇⢻⣿⡇⣴⣿⣷⠘⣿⣿⢸⣿⣿⠀⠀⠀⠀⡇⣾⣿⠀⣿⡏⢰⣿⣦⢹⣿⡇⣿⣿⢸⠀⠀⠀⠀⣿⣿⡇⣿⣿⡃⣾⣿⣧⢸⣿⣯⢸⣿⣿
⣿⣿⡇⢸⣿⣧⣈⣛⣋⣼⣿⣿⢸⣿⣿⠀⠀⠀⠀⢧⢹⣿⠀⣿⣿⣌⣉⣡⣾⣿⡇⣿⡿⣸⠀⠀⠀⠀⣿⣿⡇⣿⣿⣧⣈⣛⣁⣼⣿⡿⢸⣿⣿
⣿⣿⣧⡘⠿⣿⣿⣿⣿⣿⠿⠋⣼⣿⣿⠀⠀⠀⠀⠘⢦⠻⣦⡙⠛⠛⠛⠛⠛⢛⣠⡿⣱⠃⠀⠀⠀⠀⣿⣿⣧⠙⠿⠿⠿⠿⠿⠿⠿⢃⣼⣿⣿
⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠳⢌⡻⠿⣿⣿⣿⠿⢟⣫⠞⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠀⣀⠀⢀⣔⡁⣸⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⢀⡠⠠⢄⡀
⠀⠀⠀⠀⢠⠉⠈⠀⠀⠀⢀⢍⠱⡀⠈⠉⢳⠀⠀⠀⡋⠀⢀⠤⠬⠤⠤⡀⠈⡇⠀⠀⠀⠀⢠⠀⠀⠀⠈⠑⠢⢈⠆
⠀⠀⠀⣀⠬⢉⡂⠆⠀⢠⠤⣭⠚⠀⡠⠤⠤⠃⠀⠀⣉⠉⢹⠀⣤⠞⢸⠉⠉⡇⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠰⠽⠑⢢
⠀⢘⠉⠁⠀⠀⠘⠦⠔⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡉⠉⠑⠒⠒⠂⠘⠁⠉⡇⠀⠀⠀⡀⢀⡠⠓⠒⠤⣄⣀⠤⠀⠴⣀⣀⡀
⠀⠀⠁⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣠⠤⠀⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠀⠀⠎⡠⠤⠈⠄
⠀⠀⠀⢀⠁⠀⠀⠀⠀⢸⠈⠊⡊⢂⠀⠀⠀⠀⠀⠀⢎⠉⠁⢺⠧⠀⠀⢀⡨⠂⠀⠀⠀⠀⠀⠀⡐⠘⠄⠠⠀⠣⠤⠁⡇
⠀⠀⠀⠸⡀⠀⠀⠀⠀⢸⡄⠁⠁⢸⠀⠀⠀⠀⠀⠀⠀⠑⠤⣌⢸⢅⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢀⡠⢀⠀⡇
⠀⠀⠀⠈⠉⡟⠛⠟⠛⠛⢲⠒⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣄⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⢲⠤⢎⠀⢀⠟
⠀⠀⠀⢂⣀⡈⠋⠀⠀⡀⠂⠛⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⡟⠃⡆⠀⡟⠋⠖⠒⡄
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉


⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀
⠀⠀⢰⠁⠆⠆⡔⠒⠀⠒⡆⣴⠉⢪⢂⠀⠀⠀⠀⠀⠀⠀⡐⡟⠁⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⠿⠓⠢⡰⠒⠒⡕⡄
⠀⠀⢠⠀⠑⠁⠈⠊⠀⠑⠁⠈⠂⠊⢸⠀⠀⠀⠀⠀⠀⣔⡀⢇⣀⣘⠀⠈⡆⠀⠀⠀⠀⠀⠀⡌⠀⡘⠂⠐⠊⠐⠂⣒⠁⡀
⠀⠀⠈⠂⢼⣀⡷⠀⠀⠀⠀⢎⣀⡗⠊⠀⠀⠀⠀⠀⠀⣇⣈⠖⠀⠐⣖⣒⠇⠀⠀⠀⠀⠀⠀⠈⢏⣀⡧⠤⠤⠤⢎⡀⡙
⠀⠀⠈⠭⠉⠍⠉⠭⠭⠭⠉⠩⠭⠭⠉⠀⠀⠀⠀⠈⠩⠭⠉⠉⠭⠭⠍⠉⠭⠍⠀⠀⠀⠀⠈⠩⠭⠍⠉⠩⠭⠉⠉⠭⠭⠍
⠀⠀⠉⠀⠀⠀⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠁⠈⠁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠃⡀⠐⠀⠀⠁⢀⠢⠀⠀⠀⢰⠄⠀⠰⠀⠐⡔⠀⠀⠀⠠⠀⡆⠀⢠⠀⠆⠄⢀⠀⢀⠀⡀⡀⠠⠠⠀⠈




⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⣇⠀⠀⠀⠀⣼⠃⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣾⡇⡀⠀⠀⠸⢷⣤⡀⠀⠀⠀⠀⢈⠁⠀⣠⠔⠊⣿
⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⣿⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠟⡀⠀⠀⠨⣿⣿⠥⠤⣄⡜⢛⣛⡃⠀⠀⠘⣷⣸⡄⠀⠿⠀⠀⣡⣾
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣉⡵⠀⠀⠀⠀⠰⠟⠛⠓⠀⠀⢠⡞⠁⠀⠀⠀⠀⠙⠀⠀⠀⠙⠿⣧⠃⠀⠀⠀⠻⢃⠇⠀⠀⠀⠐⣿⠛
⠀⠀⠀⠀⠀⠐⠻⣿⣯⣿⡿⠟⠁⠀⠀⠀⠀⠀⠠⢟⣀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⣶⣄⠠⣀⠀⣇⣐⣄⠀⠀⠀⢀⡆⠀⠀⠸⣿⠆⠈⢢⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⢉⠛⣿⣁⣿⡛⣷⡄
⠀⠀⠀⠀⠀⢸⣿⣷⣄⣀⣹⣿⣿⡆⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⡏⠉⣿⢿⡆⠀⠀⠀⠀⡴⠶⣾⡇⠿⠿⢧⣹⣿
⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣟⢁⠀⠀⠀⠹⠶⠶⠒⢢⣤⣴⡞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀⢿⡀⠀⠉⣿⣿⣿⢾⠟
⠀⠀⠀⠀⠀⠻⢿⣿⠿⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠞⣼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢱⡆⣿⠸⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⣀⣀⣀⠀⠀⠀⢀⣀⣀⡀
⠀⣠⡀⠀⠀⢠⣾⢷⠉⠃⡀⠀⠀⢠⣆⠀⠀⠀⢀⣀⣄⡀⠀⢳⣤⣼⢸⡿⣿⣿⢸⠀⢰⣿⣿⣿⣷⢀⣢⣀⡀⠀⠀⠀⠀⠀⠀⢀⡿
⠁⠀⠈⠿⠿⠟⠋⠀⠀⠞⠀⠀⠀⠈⢹⡆⠀⣰⠋⠥⠉⢻⣿⣿⡿⢁⡿⣄⠈⣿⡸⠇⠀⠛⢿⣿⣿⣿⣿⡖⢃⣼⡆⣤⠈⣷⣦⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣠⡼⠀⠀⢿⡸⣷⣶⢀⣿⠟⠁⠩⡐⣾⢶⣿⣧⣀⡀⠀⠀⠀⠀⠉⠁⣠⣿⣿⣧⠉⣰⠿⠋⠀⢀⣤⣤⠞
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠃⠀⠈⠻⣿⠇⠀⠈⠛⠷⣄⣀⣴⣃⣴⠄⢸⣟⢾⠲⢬⣛⠛⠀⡇⠀⠀⠀⠘⠿⠿⠟⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣄⠉⠉⠉⠁⠀⢸⡇⣸⣧⡎⠛⢁⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣿⣶⣤⣤⣶⣶⣽⡾⠟⠻⠿⠟⠛⠳⢽⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⡙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢀⣤⡶⠾⠿⢶⣤⡘⠿⠃⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣿⠋⠀⠀⠀⠀⠈⢿⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⣿⣧⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⢿⣄⠀⠀⠀⠀⣠⡿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿⣿⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠙⠻⠶⠶⠿⠛⠁⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠛⠛⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⣴⣾⣿⣿⣶⣴⣂
⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣶⣤⣄⣀⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⣿⡃⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠙⢿⣦⣀⣠⣦⣄⡀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠙⠻⠿⠿⠟⠁⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⡀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠙⠻⠷⠶⠶⠾⠟⠋⠁



⣿⢿⠿⡿⣿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣛⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⢤⣤⣤⣀⣀⣤⣤⡤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠉⠐⠋⠝⠋⠉⠛⠉⠀⠀⠉⠙⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡔⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡀⠀⠀⠠⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡼⢠⠁⣰⠁⡇⠀⢸⠀⠀⢀⠄⠸⠀⠀⡾⡄⠐⡄⠲⠄⠙⢦⡐⠀⠈⢦⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠎⡰⠃⢰⠁⡄⠀⠀⠀⣼⠀⠀⢀⡼⠁⢳⡀⠈⠢⡄⠀⠀⠑⠀⠀⠈⠄⢢⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠃⢠⢇⢂⢀⣼⣿⣖⡵⠋⠀⠀⠀⠳⡜⢄⠈⠂⠀⠀⠀⠀⠀⠀⠈⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣾⣾⠷⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⢦⡳⣄⠀⠀⠀⠀⠀⠀⠀⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢣⡀⠀⠀⠀⠀⠀⢸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⡞⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠣⠀⠀⠀⠀⠀⠘⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⡇⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⠀⢰⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠂⠀⠀⢸⠀⠀⢶⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡎⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⠀⠀⠀⢼⠀⠀⠘⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⢎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠈⠊⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣧⣀⠀⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢠⠇⢀⣄⡄⠀⡴⣀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣾⣷⡀⠢⣰⣽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣧⣢⣾⣿⣤⣾⣿⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠾⠿⠿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⢠⢂⡐⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⢈⣌⡠⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠎⡀⢀⢔⠜⠀⠀⠀⠀⠀⡰⠃⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠃⠠⣀⡡⠊⠀⠀⠀⠀⠀⠠⠀⠡⠊⠠⠂⠀⠀⠀⠀⠈⠢⡡⠠⠀⠀⠀⠀⠀⠀⠀⠢⠤⠘⠀⠤⠂


⠀⠀⠀⠀⠀⢀⡴⠶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢄⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠧⠀⠆⠠⠅⠀⠀⠀⠀⠀⠰⠌⠉⠉⠉⠁⠀⠀⠀⠀⠈⠂⡈⠐⢡⠂⠀⠀⠀⠀⠀⠀⠃⠤⠤⠃
⠀⠀⠀⠀⢐⡄⢀⡄⠀⡈⠀⠀⠀⠀⠀⢠⣡⣕⣢⡖⠀⠀⠀⠀⠀⠠⢔⠁⠒⡈⠄⠀⠀⠀⠀⠀⠀⣢⠤⢤⡄
⠀⠀⠀⠀⠈⠛⠋⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠇⣶⢲⡄⠃⠀⠀⠀⠀⠀⣾⡆⠀⠀⣿⠆⠀⠀⠀⠀⠀⢗⢄⠠⢪⢆⠀⠀⠀⠀⠀⠀⠀⠛⠘⢆
⠀⠀⠀⠀⠀⡇⠙⠚⠁⠀⠀⠀⠀⠀⠀⠈⠑⢲⠐⠙⠀⠀⠀⠀⠀⠀⢀⢕⠕⠈⠁⠀⠀⠀⠀⠀⢖⠁⡲⠀⠛⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠋⠈⠈⠋⠀⠀⠀⠀⠀⠀⠓⠀⠀⠒⠁⠀⠀⠀⠀⠀⠐⠁⠃⠒⠂⠁


⠀⠀⠀⠀⠀⠀⠒⠘⠢⠀⠀⠀⠀⠀⠀⠒⠀⣀⣠⡀⠀⠀⠀⠀⠀⠠⠽⢄⠀⡸⣀⠀⠀⠀⠀⠀⠠⣄⠓⠚⡦⠄
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠸⠸⠀⢸⠀⠀⠀⠀⠀⠀⠚⡐⠆⠘
⠀⠀⠀⠀⠀⠠⡁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠲⠃⠐⠳⠇⠀⠀⠀⠀⠀⣤⠀⠈⢰⠊⠀⠀⠀⠀⠀⠤⠚⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠈⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣷⣶⣤⣀⠀⠈⠻⠿⠋⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣶⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⡉⠉⠉⠉⠉⠁⠀⠐⠒⠒⠢⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢆⠕⠐⢀⣀⡠⡄⢴⢲⠰⡤⡤⢤⣄⣀⡀⠀⠀⠀⠀⠈⠉⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⠁⢀⡠⡒⣉⣦⡷⠾⠾⠟⣓⣓⣛⠺⠞⢲⡿⢇⣲⣠⡄⣀⠀⠀⠀⠀⠈⡒⢤⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⢆⣩⡶⠛⠋⣁⢥⡞⢁⣨⠿⠽⠯⠯⠭⠭⣽⣟⣗⡾⢟⣿⢭⣗⡦⣀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⡴⠁⠀⣠⢎⡱⠞⢃⡤⢾⣯⠟⠚⠉⡁⠐⣶⣹⠀⠀⠀⠀⠞⣯⣝⠙⠲⠤⣽⡷⣿⣻⢷⣤⡀⠀⠕⡈⢦⡀
⠀⠀⠀⠞⠀⢀⡴⣩⡾⠁⡰⢋⡴⠊⠀⠀⠈⠀⠀⠀⠛⠛⠀⠀⢀⣾⢄⡗⠈⠀⠂⡠⠀⠉⠛⢾⡹⠫⡟⢦⣈⢔⡤⠙⣦⡀
⠀⠀⠌⠀⢀⠾⣵⠃⢀⡾⡷⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢯⠴⢸⣓⠀⠀⠀⠀⠀⠀⠠⠄⠉⠢⡈⢢⡛⡬⢊⠕⡈⢷⢄
⠀⡜⠀⠀⡼⣹⡛⢠⢿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠃⣂⡣⣼⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡿⣜⡄⡪⢒⠈⣟⣆
⢠⠁⠀⢰⠳⡏⢠⢃⡞⠀⠁⠀⠀⢀⠀⢀⠤⠂⠀⠀⠀⣾⢃⠾⠩⠁⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠹⣮⢻⡔⠥⡢⠸⠬⣇
⠨⠀⠀⡧⣹⠂⣾⡿⠀⠀⠀⠀⠐⠩⠒⠁⠀⠀⠀⠀⣰⢡⡶⣚⢭⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡘⡆⢣⠪⢐⡀⡗⢼⡀
⡆⠀⢠⣳⡇⢰⢋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣲⣹⢡⡤⢙⣯⢸⣿⠀⠀⠤⢤⣤⣤⣤⡄⠀⠀⠀⠈⡟⠋⠇⢸⣿⢐⡥⢂⢸⠳⡇
⡇⠀⠸⣽⠅⢈⣸⠀⡁⠀⠀⠀⠀⠀⠀⢀⣀⠤⢛⡇⠘⠷⠶⠿⠛⣾⢶⣶⡲⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡧⣊⠅⢸⣝⡇
⡇⠀⠀⣿⠅⣻⣿⠀⢆⣀⠀⠀⠠⠶⠾⠿⠾⠿⢿⠀⠀⢀⡴⢀⡾⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠇⡆⢕⠭⠸⢬⡇
⢡⠀⠀⢿⡀⡸⢿⠀⣻⡿⠄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢠⣾⡏⡟⠛⠿⣦⣄⠀⠀⠀⠀⣀⢀⠔⠂⠀⠀⠀⠄⢀⣦⢁⠅⡊⡟⢾
⢸⠀⠀⠘⣆⢸⠈⡆⠩⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⣠⡟⢻⣧⢁⠀⠀⠀⠈⠀⢀⠤⠊⠖⠁⠀⠀⠀⠀⠠⠁⣸⡟⢴⡪⣰⡙⡎
⠀⣧⠀⠀⠘⣌⣧⣴⡈⠁⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣰⡓⠀⠀⢿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⢋⠗⡩⢰⢇⢹⠁
⠀⠘⣧⠀⠀⠘⢾⣯⣷⣄⠠⠀⡀⠀⠀⠀⠀⡟⠀⣴⡓⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠒⣰⣧⢞⣯⢶⠷⣌⡇
⠀⠀⠡⡱⣄⠀⠀⠙⢷⣎⡳⣄⠐⠠⠀⠀⢀⠇⡼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⢀⣘⣛⠛⣋⢠⡟⢦⡟
⠀⠀⠀⠹⣜⠣⡀⠀⠀⠙⠻⣿⣗⢦⡈⠀⢼⡞⡌⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠂⢀⡴⢋⢜⡥⡋⣠⠣⣘⠎
⠀⠀⠀⠀⠈⠣⣍⢳⢄⠀⠀⠀⠉⠳⢌⣓⣬⣐⡈⠀⠐⠀⠠⠀⠤⠀⠀⢻⣥⠀⠂⠘⠀⢀⣠⢴⣻⣶⢗⡵⠊⣴⠙⣦⠏
⠀⠀⠀⠀⠀⠀⠈⠺⣌⡝⠦⣄⠀⠄⢀⡈⡉⠓⠻⠿⢶⣒⡒⠂⢤⣤⣤⣤⣤⠰⢒⣒⡩⠿⢚⠟⡫⣶⠕⣫⠚⣌⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⣸⡹⠲⡮⣌⣐⡡⠢⠔⡤⣂⠄⡩⢍⡩⢉⠍⣉⠍⣠⢔⡠⣺⠕⢉⡪⡔⢫⠈⡧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠧⢥⣸⡉⡏⠖⢲⠠⠬⡤⣭⢤⢥⡈⣵⢯⠤⡥⢾⠓⡉⢏⢣⡸⠖⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠚⠂⠦⠵⢼⣌⣆⣣⣘⣄⣧⡴⠼⠖⠛⠉⠁
⠀⠀⠐⠭⢪⢕⡩⢒⡩⢐⡡⢔⡢⢒⠤⢂⠤⣢⠔⡠⢒⠔⣠⠔⡠⢀⠤⢀⠤⢀⠄⣀⠔⣂⠔⣠⠔⡠⢂⠔⡢⢒⠔⡪⣪⢔⡡⣪⢞⠔⡠

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠃⠀⠀⠀⠀⠀⢰⠋⠉⣉⣉⢩⠝⡆⠀⠀⠀⠀⣤⣤⣤⣦⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠐⢿⣿⠿⠇⠀⠀⠀⠀⠀⢸⠀⣾⠁⠈⣷⠀⡇⠀⠀⠀⢠⣿⣿⡏⢉⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠓⠚⠁⢀⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⢹⣷⣤⣼⣿⣿⡟⠀⠀⠀⠀⣾⠟⢉⣋⣀⢀⣰⣄⠀⠀⠀⠀⢨⣥⢠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢿⣄⣈⣹⡿⠈⠙⠋⠀⠀⠀⠀⢸⣿⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠐⠺⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠘⠛⠀⠛⠃


⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠤⣀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠶⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⡏⢠⡆⠀⠀⠈⣧⠀⠀⠀⠀⣼⡇⣴⡆⠀⢹⡇
⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⡁⠀⠀⠀⠀⠸⡇⠈⠳⢤⣤⠀⡿⠀⠀⠀⠀⠘⠃⣿⣅⣠⡿⠃
⠀⠀⠀⠀⠀⠙⠿⠿⣿⡿⠿⠛⠀⠀⠀⠀⢠⣯⠤⣤⣠⡤⠞⠁⠀⠀⠀⠀⠀⢸⡏⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⣀⡀
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣴⣿⣿⣿⣿⣿⣷⡀⠀⠀⣴⣾⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⡀⠈⠉⠉⠉⠛⠉⠉⠉⠁
⠀⠀⠀⠉⠛⠻⡟⠛⠋⠁⠀⠀⠀⠙⠛⠿⠟⠛⠋⠓⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⢠⣿⣿⣿⣿⣿⡀
⠀⠀⢠⣶⣶⣤⣶⣷⣦⣀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣶⣄⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠙⣿⣿⣿⣿⣿⠇
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠙⠿⢿⣿⡿⠁⠀⠀⠀⠙⠛⠛⠛⠥⡀
⠀⠘⠻⠿⢿⣿⣿⡿⠋⠛⠁⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠰⠋
⠀⠀⠀⢀⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⣠⣴⣶⣶⣦⣄
⠀⢀⣾⣿⣿⣿⣷⣶⣦⣄⠀⠀⢀⣠⣄⣠⣴⣶⣦⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⢰⣿⣿⣿⣿⣿⣿⡆
⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠈⠙⠉⠉⠉⠉⠉⠉⠀⠈⢿⣿⣿⣿⣿⡿⠃
⠀⢈⠟⠛⠛⠛⠛⠛⠛⠋⠀⠀⠛⠿⠿⣿⠿⠿⠟⠿⠃⠀⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠉⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣀⣤⣤⣀
⠀⢰⣶⣶⣶⣿⣿⣿⣿⣷⠀⠀⠀⣀⣤⣤⣤⣤⣄⠀⠀⠈⠿⢿⡷⠖⠒⠛⢻⡿⠃⠀⣼⣿⣿⣿⣿⣧
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆
⠀⠘⠛⠛⠛⢿⠛⠛⠛⠛⠃⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠃⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⢀⣴⣶⣶⣶⣶⣶⣶⣦⡀⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⠀⠙⠻⠿⠿⠿⠿⠟⣋⠀⠀⠹⣿⣿⣿⣿⡿
⠀⢘⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⢿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠀⠀⠈⠙⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠛⠛⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠛⠛⠛⠻⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠛⠻⢶⣤⡀
⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⣀⣤⣄⠀⠀⠙⢷⣄⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⣴⡟⠉⠀⢀⣀⣀⣀⣀⣀⠀⠈⠻⣦
⠀⠀⢀⣿⠃⠀⠀⠀⠀⣾⣿⠛⠋⠀⠀⠀⠈⢿⡆⠀⠀⢰⡟⠀⠀⣠⡀⠀⠀⢀⣴⣶⣦⣴⠀⠘⣿⡀⠀⠀⣼⠏⠀⠀⡾⠋⠉⢉⡉⠉⣭⢻⡄⠀⠹⣧
⠀⠀⢸⡇⠀⠀⠀⢠⣶⣿⣿⣶⡆⠀⠀⠀⠀⢸⣿⠀⠀⣿⠃⠀⠀⢸⣿⣷⣶⣾⣿⣿⣿⡇⠀⠀⢸⡇⠀⢰⣿⠀⠀⢸⡇⠀⡾⠋⠉⢳⡄⢸⡇⠀⠀⣿⡆
⠀⠀⢸⡇⠀⠀⠀⠈⠉⣿⣿⠉⠁⠀⠀⠀⠀⢸⣿⠀⠀⣿⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣸⡇⠀⠘⣿⠀⠀⢸⡇⠀⢷⣄⣠⡼⠃⢸⡇⠀⠀⣿⠇
⠀⠀⠈⣿⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠸⣷⡀⠀⢠⣤⣽⣿⣿⠿⠋⠀⠀⠀⢠⣿⠁⠀⠀⢻⣆⠀⠀⢷⣄⣀⣈⣁⣀⣀⡼⠃⠀⣰⡟
⠀⠀⠀⠈⢿⣦⡀⠀⠀⠛⠛⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠻⣧⣀⠀⠈⠉⠉⠉⠉⠁⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⣤⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⣤⣤⣤⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣦⣤⣀
⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠉⠛⢷⣤⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠈⠉⠻⣶⣄⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⢀⣾⠏⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⢠⡿⠃⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠘⢿⡄
⠀⠀⢰⡟⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣷⠀⠀⢸⣧⠀⠀⣼⡇⠀⠀⢀⣭⡁⢀⣤⣀⣤⣄⡀⠀⠀⢻⡆⠀⢀⣿⠁⠀⠀⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠈⣿⡀
⠀⠀⢸⡇⠀⠀⣿⣿⣿⡇⢀⣩⣿⣿⣿⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⢸⣿⡇⢸⣿⠏⠙⣿⣷⠀⠀⢸⡇⠀⢸⣿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⣿⡇
⠀⠀⠸⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣸⡟⠀⠀⢻⣇⠀⠀⢸⣿⡇⢸⣿⠀⠀⣿⣿⠀⠀⣼⠇⠀⠈⣿⡀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣷⡄⠀⢀⣿⠁
⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠈⢿⣆⠀⠈⠛⠁⠘⠛⠁⠀⠙⠋⢀⣼⠟⠀⠀⠀⠘⣷⡄⠀⠈⠛⠛⠿⠿⠛⠛⠁⠀⢀⣾⠃
⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⢀⣀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠛⢷⣤⣀⠀⠀⠀⠀⢀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⢀⣴⠿⠛⠉⠉⠉⠉⠉⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠉⠉⠉⠉⠉⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠉⠉⠉⠉⠙⠻⢷⣄
⠀⠀⠀⣰⡿⠁⠀⠀⢀⣠⣤⣤⣄⠀⠀⠈⠻⣦⠀⠀⠀⠀⣼⠟⠁⠀⢀⣤⠶⠶⠶⣤⡀⠀⠈⢿⣆⠀⠀⠀⢀⣾⠋⠀⢀⣠⣴⡶⠶⢦⣄⡀⠀⠙⣷⡀
⠀⠀⢰⡿⠀⠀⠀⣴⠟⣡⣄⠀⠙⣷⡀⠀⠀⢹⣇⠀⠀⣼⡏⠀⠀⣰⠏⣠⡄⠀⠀⠀⠙⣆⠀⠀⢿⡆⠀⠀⣾⠃⠀⢠⡟⠁⠈⢳⣄⣠⡾⢻⡄⠀⠘⣿
⠀⠀⢸⡇⠀⠀⠀⣿⡀⣿⡟⠀⢀⣿⠃⠀⠀⢸⣿⠀⠀⣿⠁⠀⠀⣿⠀⠹⣇⠀⢀⠀⠀⣻⠀⠀⢸⡇⠀⢸⣿⠀⠀⣿⠷⠶⠚⢛⣻⣥⣤⣤⣿⠀⠀⣿⡇
⠀⠀⢸⣧⠀⠀⠀⠈⢡⣿⢷⣤⡾⠋⠀⠀⠀⢸⡟⠀⠀⢿⡆⠀⠀⢻⡄⠀⠈⠛⠿⠛⣠⡟⠀⠀⣼⡇⠀⠈⣿⡀⠀⢹⣆⣠⡾⠋⠉⣿⠀⢠⡟⠀⠀⣿⠃
⠀⠀⠀⢿⣆⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠘⣿⡄⠀⠿⠶⠶⠦⣤⠴⠞⠋⠀⠀⣰⡟⠀⠀⠀⠹⣧⡀⠀⠙⢿⣤⣀⣀⣼⡷⠋⠀⢀⣼⠏
⠀⠀⠀⠀⠹⢷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠉⠉⠀⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠶⠶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⠶⠶⠶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠶⠶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⡄⣀⣀⡀⡠⠤⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠄⠈⢉⠇⡃⠈⠉⠁⠀⠒⢒⢒⡗⠢⠤⠤⣤⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠠⠤⠾⠓⠒⠚⠽⠒⠛⠒⠓⡟⠫⡀⠉⠀⠙⢷⠈⢹⡌⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣁⠀⠉⠉⠤⣠⡽⠟⠂⠀⣀⣀⣀⠀⠠⢤⠀⢢⣦⡶⣿⣶⠀⠶⢾⡟⢻⠇⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢠⢐⠐⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⡕⢺⣿⠀⢠⣠⡀⠴⠟⠛⠹⢻⠂⠀⢸⠇⢺⡠⠊
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠠⠄⣋⠀⠀⠀⠠⣀⣤⡽⠇⣈⡃⠈⠁⠀⠀⠀⠠⠀⢰⢾⠀⢀⣿⡴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣉⣱⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢈⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣟⠕⠁
⠀⠀⠀⠀⠀⠀⠸⢶⡼⠂⠀⠀⠀⠀⠀⠀⡆⡉⡦⠀⢀⢀⠀⢀⣦⣾⡿⠿⠛⠟⠃
⠀⠀⠀⠀⠀⠀⡠⠁⡒⠂⢀⣀⠠⠤⠄⠀⠈⠻⠉⠀⢨⣴⣿⣿⣿⠿⡗⠒⠂
⠀⠀⠀⠀⠀⠀⠑⢲⣧⡤⣟⣛⣿⣿⣄⠀⠠⢙⣀⣠⣯⣿⠿⠋⠁⠁
⠀⠀⠀⠀⠀⠀⢀⡩⠗⠋⠉⠉⠉⠒⠚⠒⠻⠿⢟⣭⣛⠁
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣰⠶⠶⠛⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠟⠉⠉⠙⢶⡀
⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⠀⠈⠉⠉⠉⠉⣉⣁⡀⠀⣀⢀⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⢽⣿⡇⠀⠀⠀⠀⢰⣹⣿⣸⠀⠻⣿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠁⣽⣿⡟
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡟
⠀⠀⠀⠀⠀⠀⠸⡄⡞⠉⣭⣭⣭⣄⢸⠀⡏⠀⠐⠀⠐⢸⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡇⡇⣸⣿⣿⣿⣿⠘⡀⡇⠢⠀⢴⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠻⠿⢿⣿⠿⠆⡇⢇⠀⠀⠀⠀⠄⠿⡿⢻⡟⠛⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡇⢈⣒⣒⣲⠶⠎⢍⣁⣨⠭⠭⠽⠿⠟⠛⢇⠸⡇⠀⠀⠈⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⢠⣀⠤⡀⢸⡇⠀⠐⣄⠐⠆⠀⢸⠀⣷⠀⠀⠰⣶⣿⣿⣿⣿⣤⣤⠄⠀⠀⣼⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⡇⡇⢀⡠⠂⠈⠐⠀⢸⣷⠀⠀⠀⠗⠦⠄⠸⠄⠛⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⡇⢸⢻⡇⠀⠶⠇⠀⠈⣿⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⣸⣿⣿⣿⡿⢃⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⣷⠘⠦⣤⣤⣤⣶⣖⣚⢉⣉⣉⣩⣭⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿⣿⣿⠟⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⢸⢀⡤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⠐⠂⠀⠐⠂⢸⢸⠈⠁⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠻⠃⠀⢸⠈⡠⠦⠆⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣅⡘⣒⣒⣒⣒⣊⣉⣀⣓⣀⣭⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⣀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⡻⢿⠿⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣻⡟⠉⠛⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠀⠀⠀⠐⠚⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠈⠐⢤⠀⠀⠠⠠⠤⠤⠤⠤⠄⠀⠁⠄
⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠑⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠐⠀⠀⢲⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠠⠀⠀⠐⠀⠂⠀⠀⠂⠀⠀⠀⠀⠂⠂⠀⠐⡄⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⡄⠠⡀⠀⠀⢐⠢⢄⣄
⠀⠀⠀⠀⠀⠀⢀⢘⠇⢄⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠑⠠⠀⣀⢀⢀⡀⠠⡀⠀⢂⠐⠈⠉⠐⠼⡢⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠈⠯⠅⠀⠁⠐⠈⠁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠄⠀⣰⠕⠁
⠀⠀⠀⠀⠀⠀⠀⡠⢆⠁⣀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢁⠀⠢⡀
⠀⠀⠀⠀⠀⢠⠞⠀⠠⠀⠁⠀⠑⠄⠀⠀⠀⠀⠀⠀⣼⣅⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠄⠀⠐⡀
⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠁⠑⡄⠀⠀⠔⠉⢨⠋⠀⠀⠀⠀⠀⠀⠀⢞⠢⡀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠀⠀⠀⢠
⠀⠀⠀⢀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⣇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢠⡀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠈⠙⠄⠀⠀⠄
⠀⠀⢠⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⠈⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⡟⠛⠋⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠉⠑⠄⠀⠀⢀⠀⠀⠁⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡀⠈⢀⡠⠀⢀⡀⠐⠤⠄⠀⡤⠂⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⠀⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠉⢣
⠀⠀⢀⠀⠴⠷⠿⠿⠟⠛⠶⠆⢀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠀⠀⠀⠀⠇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⡹⠀⠀⢹⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠁
⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠂⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠘⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⢀⢈⠃⠀⠀⠀⠀⠀⠘⠻⠿⠟⠀⠀⠸⡆⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡴⠒⢒⡀⠤⠞⠁⠀⠘⠉⢒⣋⠛⠈⠍⠀⢀⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⢉⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⡇⠀⠀⡞⠙⠛⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠲⠚⠁
⠀⢠⠀⡠⠊⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠠⠏⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆
⠀⢸⠀⣠⠎⠀⡠⠀⠀⠀⠀⠀⣹⡿⠀⠀⢰⡇⠀⠀⢄⠂⠀⠀⡠⠀⣰⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡄⠀⠐
⠀⠈⠀⠁⠀⠊⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠠⣛⡚⠲⠋⢝⣲⣄⣀⢀⣼⡍⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠨⠙⠘⠑⠀⠂⢸⢕⡀
⠀⠀⠈⠀⠶⠆⠀⠀⠀⠀⠲⠎⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠷⠦⠟⠀⠀⠀⠔⠛⢒⠒⠒⠢⠀⠔⠒⠒⠒⠛⠢⠀⠀⠀⠀⠀⠁⡀⠀⠀⡸⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠓⣼⢂⡤⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⡜⢁⠎⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⢠⠤⢭⣤⡤⣴⡶⢶⡖⠖⢴⠏⢺⠆⠀⠛⠛⠛⠛⠛⠛⠷⢼⠇
⠀⠀⠐⠂⠆⠀⠀⠀⠀⠀⠌⠀⠀⡜⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠸⡄⣠⠟⠁⠈⠁⠀⠂⠳⠏
⠀⠀⠠⢤⠈⠀⠀⠀⠒⢶⣶⣶⣞⣠⠃⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⠀⠀⠑⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⠏⣷
⠀⠀⠀⠀⠀⠠⠂⢠⣀⣸⣇⣀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡄⠰⠁⠛⠉⠀⠀⠀⠢⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢠⣄⠀⠀⠀⠘⡀⢻
⠀⠀⠀⠀⠀⡀⠒⠁⠉⠉⡇⠈⢈⣆⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⢸
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠘⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠋⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣇⡴⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠐⠲⠶⠴⠶⠦⣤⠴⠤⠤⠤⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡍⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⡎⡍⡝⡆⠀⠀⣰⣏⠀⠀⠀⣦⣴⡶⠀⠀⣶⡶⣶⡆⠀⠠⢪⠉⢢⠀⢀⣤⢴⣾⠀⠀⢰⣭⢱⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⠆⠀⠀⣉⣠⣤
⠣⠭⠡⠃⠀⠀⠸⠇⠀⠀⠀⠘⠛⠁⠀⠀⠙⠛⠛⠁⠀⠸⠄⠩⠊⠀⠀⠀⠙⠛⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠀⠀⠀⠛⠻⠘
⣤⣤⣤⡀⠀⢠⣤⠤⣄⠀⢀⣤⣤⣤⠀⠀⣠⣤⣤⡀⠀⢠⣤⣤⣄⠀⢀⣤⣤⣤⠀⠀⣠⣤⣤⡄⠀⢠⣤⣤⣄⠀⠀⣤⡤⣤⠀⠀⣠⣤⣤
⣿⣿⣿⡇⠀⢸⣏⢸⣿⠀⢸⣇⣁⣾⠀⠀⣯⣐⣀⡇⠀⢸⣿⣿⣿⠀⢸⣯⣅⣼⠀⠀⣿⣙⣣⡇⠀⢸⣇⣘⣿⠀⠰⡏⢇⣾⠀⠀⣏⣉⣍
⠉⠉⠉⠀⠀⠈⠁⠈⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉
⡄⠀⠂⠀⠀⠀⢠⡆⠀⠀⠀⢠⣤⡄⠀⠀⢠⡤⣤⠀⠀⠀⢠⠀⠀⠀⠀⢀⣤⡄⠀⠀⢠⣔⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠄⠀⠀⢐⣀⣀
⠁⠈⠀⠀⠀⠀⠸⠇⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠘⠙⠘
⢀⣤⣄⠀⠀⢀⣠⣤⡀⠀⠀⣠⣤⡀⠀⠀⢀⣤⣄⠀⠀⢀⣠⣤⡀⠀⠀⣠⣤⣀⠀⠀⢀⣤⣄⠀⠀⢀⣠⣤⡀⠀⠀⣠⣤⣀⠀⠀⢀⣤⣄
⣿⣿⣿⠇⠀⢸⣏⣸⡗⠀⠸⣏⣁⣿⠀⠀⢿⣀⣸⠇⠀⢸⣿⣿⡷⠀⠰⣯⣅⣿⠀⠀⢿⣸⣯⠇⠀⢸⣇⣸⡿⠀⠐⣏⢧⣿⠀⠀⢿⣉⣝

⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⣤⠄⠀⣤⣦⠄⠀⢰⡆⠀⢠⣶⡆⠀⠀⠀⠀⠀⠠⡀⠀⠀⣰⠆⠀⠀⣤
⠀⠀⠀⠀⣀⣀⠀⠀⣀⡀⠀⠀⣀⡀⠀⢀⣀⠀⠀⣈⡀⠀⠀⣉⡁⠀⢀⣀⠀⠀⢀⣀⠀⠀⣉⡀⠀⢀⣀
⠀⠀⠀⠸⣯⣼⠇⢸⣿⣿⠂⢾⣉⡽⠀⣏⣉⡇⠸⣏⣹⠆⢪⠐⣹⠀⣿⣿⡷⠰⣿⣿⠇⢸⣋⣽⠀⢾⣍⡷
⠀⠀⠀⠀⠈⡁⠀⠀⠉⠁⠀⠀⠉⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⣉⡁⠀⠀⠉⠀⠀⠈⠁⠀⠀⠉⡁⠀⠀⠉
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠛⠁⠀⠚⠟⠂⠀⠸⠇⠀⠘⠿⠇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠾⠁⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⠤⠤⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠋⠉⠑⠀⠀⠀⠀⠀⠀⢄⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⠁⠀⠀⠀⠀⠄⠀⠀⠹⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠐⠂⠀⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠀⠀⢰⠟⠛⠋⠙⠆⠀⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⢀⠆⠀⢸⠃
⠀⠀⠀⣶⠾⠿⠿⠿⠟⢻⡆⠀⠀⠀⠀⠘⢧⠀⠀⠂⠈⠁⠀⠀⣸
⠀⡠⠀⣿⠀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⡤⠞⠙⣆⣀⣀
⡄⠀⠀⢈⡄⠀⠀⠀⠀⠀⣟⠘⠄⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢠⠏⠈⠉⠙⠻⠗⠲⠶⠤⢤⣄⡀
⠱⠄⠀⢘⡂⠀⠀⠀⠀⠀⣿⠀⠐⠀⠀⢀⡴⠚⠣⠓⠦⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣄
⠠⠄⢀⣹⡇⠀⠀⠀⠀⠀⢻⡠⠃⣠⠞⠁⠋⠂⠀⣀⠀⠀⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀
⠈⠢⣤⠽⣇⣀⣀⣀⣀⣠⣼⠁⡼⠁⠀⠀⠀⠈⠲⢤⡉⠘⠂⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠉⠢⡀
⠀⠀⠀⠣⣿⠿⠿⠛⢻⠟⢛⢟⠇⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⢈⠋⠀⠀⣸⠀⠂⠈⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠀⠑⠄⣀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⡸⠀⠀⠀⢿⠂⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠬⠱⢄⡀⢀⣀⠀⠀⠀⠉⠑⠲⠤⣀⣀⠀⢻⣄⡤⠖⠒⠉⢏
⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠉⠢⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇⠀⠀⠙⣦⢣⡜⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠞⠙⠛⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⢦⡤⣄⣀⣀⣠
⠀⠀⠀⠀⢧⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠈⠣⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣆⣀⣀⣀
⣿⣽⣽⣭⣯⣭⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣯⣽⣯⣽⣽