Milk shake Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠅⠂⠉⠉⢯⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡇⢀⣇⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠼⣼⣠⣉⠀⠙⡊⠒⠒⠢⡄⢀⣀⣔⡉⠉⠀⠀⠰⠥⠼⠄⠀⠉⠉⣳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠔⠒⠒⢄⢀⣉⡼⡶⠭⠭⣶⠺⡁⠐⠥⣈⡉⠀⠛⠛⠒⠚⠛⠂⠉⣉⡠⠇⠈⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠒⡄⠀⠀⠁⡠⠟⠀⠀⠀⠀⠱⡏⠁⠒⠒⠰⠾⠉⠉⠉⠉⠉⠻⠖⠐⠒⠊⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠈⠩⠆⠮⠤⢄⠀⣀⠤⡀⠀⠈⡶⠠⠤⠤⠤⠄⠀⠀⠀⠠⠤⠤⠤⠤⠴⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⠀⠀⠐⠀⠀⠉⠁⠂⣛⣀⠤⠧⠤⠄⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢰⠀⢰⠀⠀⡆⠀⠀⡦⠴⡟⠤⠤⠀⣀⣀⡀⠠⠤⠤⢻⠠⢄⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢸⠀⠀⠇⠀⢸⠓⠢⠭⠖⢒⣦⣤⠤⣤⣴⠖⠢⠭⠔⠚⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⠈⠒⡤⠤⠄⣀⣄⣀⣀⣀⣄⣀⡤⠤⢤⠒⠁⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢧⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢄⠀⠀⠀⠀⠀⠀⢸⠑⡖⠊⠭⠭⠭⠭⠭⠭⠭⠑⠒⢹⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⠤⢀⣀⠠⠐⣨⠄⠁⠀⠀⠀⡠⣶⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠈⠀⡇⠀⠀⠀⠀⡇⣿⢸⠀⠀⠀⠀⡌⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠲⣄⠀⠑⣤⣀⣀⠀⠘⠛⠃⠀⣀⣀⡤⠃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⡰⠀⠀⠆⠀⠑⠢⣽⠀⠀⠈⠉⠉⠉⠁⠀⠀⡇⠀⠀⠀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠠⠤⠤⠤⠐⠒⠊⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣀⣀⡀⣀⣀⣀⡸


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠐⠀⠀⠀⠀⠤⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣥⡉⠛⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠟⢻⣦⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢋⣿⣿⠏⣴⣿⠿⣿⡟⢻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⣼⣿⣿⡾⣿⡏⣸⣿⡁⠀⠏⠙⢿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣽⣯⣿⣀⠿⢻⣿⡇⣿⠁⣿⣿⡇⠀⠈⠀⠈⢿⣿⡇⠀⠀⠁
⠀⠀⠀⠀⢠⣾⡿⢿⢻⡿⢫⣼⣿⣿⣧⠹⣄⢹⣿⣿⣄⡀⠀⠒⣾⣿⣧⣤⣄
⠀⠀⠀⠀⢸⣿⡇⠸⣏⢿⣁⣼⣿⢿⣿⣷⣝⣧⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣨⣿⣿⣆⠹⣿⣿⣿⣷⡈⢿⣎⠻⣿⣽⣿⢿⣿⣿⣧⣾⣿⠟⢩⣿⣿
⠀⠀⠀⣾⣿⡟⢻⠛⣿⣿⠍⠛⢿⣷⣾⣟⠓⠾⠿⠶⠶⣿⡿⠟⠋⣠⣴⣿⣿⣿⣷
⠀⠀⠸⣿⣿⣅⠀⢷⣜⣷⡄⣀⠀⡟⣿⣿⣷⣶⣶⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠹⣿⡿⠗⠚⠛⠋⠋⠉⠁⠉⠀⠁⠀⠀⠀⠁⠀⠈⠉⠉⠉⠙⠛⠻⠿⣿⠋
⠀⠀⠀⠀⣿⠀⠀⠤⠴⠄⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢸
⠀⠀⠀⠀⣿⠀⢀⣀⣀⣀⣤⣤⣤⣤⡤⠤⠤⠤⠤⠤⠀⣀⡀⠀⠀⠀⠈⠉⠛⠟
⠀⠀⠀⠀⢿⡜⠋⠉⢈⡀⠻⢦⡀⢣⠀⡾⠛⠛⠛⠛⠋⠉⠹⡆⠀⡴⢀⡄⠀⣸⠂
⠀⠀⠀⠀⢸⣇⠀⢰⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡇⠀⡏
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠃⢰⠇
⠀⠀⠀⠀⠀⢻⡇⢀⠇⠀⠀⠀⠀⠘⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣸⠀⣾
⠀⠀⠀⠀⠀⠸⣷⠸⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡇
⠀⠀⠀⠀⠀⠀⣿⡆⠼⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠘⡄⢰⠃⢸⠃
⠀⠀⠀⠀⠀⠀⢸⣧⠀⡀⠀⠀⠀⡀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⡿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠇⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠀⡇⢀⡏⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢻⡇⢠⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠈⠀⠀⢸⡇⣸
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⡀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⢰⡄⡸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠇⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠀⠈⠀⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢠⠀⠀⠀⠀⣧⢃⠀⠀⠀⠀⠀⣠⠀⠁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡈⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠁⡏⢸⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⡄⠀⠀⠀⢻⢸⡄⠀⠀⠀⠀⡇⠈⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣸⠀⠀⠀⠀⢸⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠃⠀⠀⢸⣿⠀⠀⠀⠀⢸⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠠⠀⠀⠈⡏⠀⠀⠀⢸⣜⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⣆⠀⡗⣲⡀⠴⢞⠩⣭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡙⠉⠉⠉⠉⠉⠉⢀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠙⠢⠄⠀⠂⠲⠞⠋⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠛⠛⢛⠉⠁⠛⠛⠛⠀⠀⠱⣤⡀
⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀
⠀⠀⠀⠀⠶⣀⣤⡄⢀⣀⣀⣤⣴⣶⣶⣾⠀⠀⣾⣶⣶⣦⣤⣄⣀⠉⠀⣤⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠉⠉⠰⠒⠋⠉⠉⠉⠉⠉⠉⠙⠓⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⣉⡠⠄⠒⠋⠑⡤⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⠀⠀⠀⠀⠑⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⡄⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢃⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⠀⡀⠂⠉⠉⠒⣤⠤⢄⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⣠⠖⠋⠻⢆⣠⣠⠤⣄⡀⠀⠀⢸⠀⠀⣉⣉⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⣸⣁⣠⠤⠤⠤⢤⡀⠀⠀⠉⠙⠛⢾⣤⠞⣁⡈⠑⠤⡤⢷⡀
⠀⠀⠀⠀⠀⣀⡟⠀⠀⣀⣀⣀⣀⣀⣀⣀⠠⠄⠀⠸⠧⣄⣠⠟⣁⡀⠀⠀⠀⠀⠙⠦⠴⠒⠺⣍⡽⠋⠉⠉⠉⠉⠓⢦⡀⡧
⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠀⠉⢳⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢳⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠈⠓⠒⢤⡀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲
⠀⢀⡸⠇⠀⠀⠤⠤⠤⠤⣤⣤⡤⠤⠤⠤⠔⠒⠂⠀⠘⠛⠙⠳⣶⠒⠶⠶⠶⠶⠷⠶⠷⠶⠶⠶⣄⠀⢀⣠⠴⠦⣄
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠶⠶⠶⠶⠶⠶⠶⠖⠲⠒⠒⠚⠛⠛⠒⠒⠒⢾
⢨⡷⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢀⡀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⣀⠀⠀⢀⡇⠀⠀⠀⢰
⡏⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠶⠶⠖⠒⠒⠂⠉⠁⠀⠀⠀⠈⢧⣿⡇⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⢿⣧⡀⠀⠀⢸
⠹⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⠁⠀⠀⣿⠀⠀⠀⢻⡇⠀⠀⠀⣿⠀⠀⢸⡇⠙⣦
⠀⠈⣻⠒⠲⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⣿⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢿⡄⠀⢸⡇⠀⣿
⠀⠀⢸⡀⠀⢀⡴⠚⣆⠀⠀⣀⡀⠀⠀⠀⠒⠒⠀⠀⣠⣿⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⠃⠀⠀⠀⢸⡇⠀⢸⡇⠀⡿⡇
⠀⠀⠀⠻⡶⠚⠁⠠⠜⢛⠋⠉⠙⠶⣶⢶⠀⣠⠶⣾⠁⢸⠈⡇⠀⢹⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⠀⢸⠁⠀⢸⠇⢰⠀⡇⢠
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡑⠤⠒⠁⠀⣹⢀⡏⣰⠃⠀⠸⡄⢿⠀⢸⡇⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⣸⠀⡸⢠⡗⠁
⠀⠀⠀⠀⢹⠀⠀⠈⠣⡀⠀⠀⡀⠖⢢⡇⢸⣧⠇⠀⠀⠀⢧⠸⡆⠀⣇⠀⠀⢹⠀⠀⠀⢸⠀⠀⠀⠀⡟⠀⠀⡏⢠⠇⣼⠃
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠣⠁⠀⢀⡞⠀⣸⡏⠀⠀⠀⠀⠘⡆⢻⡄⠸⡀⠀⠘⡄⠀⠀⢸⠀⠀⠀⠀⠃⠀⠸⠁⡞⢰⡏
⠀⠀⠀⠀⠀⣇⠀⠐⣄⡀⠠⠄⠓⠙⠷⠞⡿⠀⠀⠀⠀⠀⠀⠹⣄⢳⡄⠱⡀⠀⠱⠀⠀⠘⠀⠀⠀⠌⠀⡰⢁⡜⢠⡟
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠑⢄⢀⠠⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣆⠙⣦⠈⠀⠀⠁⠀⠀⠀⠀⠈⠀⠈⣠⠏⣰⠟
⠀⠀⠀⠀⠀⢸⡄⠈⠒⠀⠉⠉⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⠛⢦⣀⠀⠀⠀⠀⠀⣀⡤⠞⣡⡾⠋
⠀⠀⠀⠀⠀⠘⡇⠘⠀⡉⠙⠁⡀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣈⡉⠙⠛⠋⢉⣁⣤⠾⠋
⠀⠀⠀⠀⠀⠀⣯⠀⢀⠈⠙⠁⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⠛⠛⢻⠉
⠀⠀⠀⠀⠀⠀⢹⠀⡈⠉⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡆⡈⠑⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠉⠉⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋⠀⢀⡞⠀⠀⠸⡄⠀⠀⠉⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢻⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⡀⠀⠀⠠⠋⠀⠀⠀⠀⠹⠀⠀⠀⠀⢀⣨⠗
⣀⣀⣀⣀⣀⣀⣀⣘⣶⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣒⣲⣦⣤⣤⣤⣤⣤⣴⣖⣒⣉⣉⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⣀⠤⢄⠀⢂
⠀⠀⠀⠀⠀⠄⠂⠉⠀⠀⠀⠡⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠐⠢⠤⠄⠠⢀⠀⢸⠀⡈⠄⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠒⠀⠀⠂⢀⠀⢀⡠⠽⠊⠤⠠⠈⠒⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠀⠒⠀⠀⠀⠀⠀⢀⡨⠃⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠤⠐⠈⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣄⡐⢩⡥⠤⡇⠄⢣⠔⢢⣀⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠾⠠⢁⠆⡂⡄⠀⢸⢀⠙⠠⢸⡈⡇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠤⠱⠄⡂⠶⢉⣾⠣⠝⣏⠁⡴⣘⠆⠀⢸⣿⡐⢨⠆⡌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢂⠡⡄⡄⢀⢇⠄⡈⠈⢸⠇⠃⡴⠂⡌⠲⢩⠈⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠦⠷⢠⡞⠃⠂⠁⡔⠚⣴⡠⢣⡁⠗⠁⠝⠀⠂⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠡⡆⠀⢠⠁⡄⠎⡑⠀⢀⠇⠘⠃⠒⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⢼⠀⢀⡀⠁⠖⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠈⠐⠠⠤⠀⠤⠐⠊⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠐⠢⢤⠔⠈⢉⠑⢤⡤⠚⡄⡠⠀⠀⠄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠨⠀⠄⠀⠀⢸⠀⠀⠁⠰⡀⠀⠀⠀⠈⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠸⠘⠊⠁⠤⠤⠄⠈⠚⠧⠉⠁⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠠⠠⠤⠄⠀⠠⠤⠤⠆

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣋⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠄
⠀⢀⠠⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠃⠀⢹⢳⣦⣤⣀⣤⣤⣤⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⣼⠿⡶⢾⡏⠹⠿⣇⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⢛⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣾⠋⢉⠙⠿⠛⠳⢤⣷⡍⠑⣀⣄⡘⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡆⠈⡀⠀⠤⠀⠈⠋⠉⠳⣿⠿⠃⠀⠀⠀⠀⠀⠀⢄⠀⠀⠾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡉⠀⠀⠛⠀⠀⠠⠄⠀⠙⡠⠇⠀⠀⠀⠀⠀⠀⠐⠌⠨⠀⢀⣘⣛⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⢹⣤⡄⠀⡀⠀⠀⠀⠈⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣄⢸⣇⠀⠀⠀⣶⣤⣾⣷⣿⣎⣿⣷⣤⡀⢀⣧⡀
⠀⠀⢠⡰⣶⡟⣿⡇⠭⠀⠀⠀⣟⣻⡳⣬⡿⠛⠿⣴⠿⣾⣳⠟⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠰⠾⣧⠙⠋⠀⠀⠀⠀⠀⠀⠈⠻⠟⢻⣗⡀⠀⠀⠀⠹⡅
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠀⠉
⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⡀⠀⠀⠀⠐⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡈⠤⢄⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠀⠀⠀⠈⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⡹⠂⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠱⣀⠀⠀⠀⢀⣀⣁⠀⠀⠈⠀⠉⢲⠒⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⠉⠀⠀⠀⠀⠀⠈⣳⠀⢠⢋⣀⡈⣉⡉⠉⠓⠢⢼⣠⠒⠑⢄⣨⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠼⠀⠀⠤⠤⠤⠤⠄⠀⠐⠳⢤⡏⠥⡀⠀⠀⠙⠒⠒⠻⡜⠉⠁⠉⠉⠢⣸
⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⠦⢀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠛⢄
⠀⠀⠀⠀⠀⣠⠗⠀⠀⠤⠤⠤⠤⠤⠤⠐⠂⠀⠘⠋⠓⣖⠒⠒⠒⠓⠚⠒⠒⢦⣀⡠⠔⢤⠀⠀⠀⡇
⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⠀⢠⠇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠒⠒⠲⠲⠤⠖⠒⠒⠀⠀⠀⠙⣶⡇⠀⢸⠇⠀⢸⠀⠀⢸⡇⠀⣿⡀⠀⢸
⠀⠀⠀⠀⠈⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⡇⠀⢸⠀⠀⢸⠀⠀⠘⡇⠀⣿⠈⡆⠈⡇
⠀⠀⠀⠀⠀⠀⡇⠀⢠⠶⡄⠀⣀⠀⠀⠀⠀⠀⣠⡆⡇⠸⡇⠀⣼⠀⠀⢸⠀⠀⠀⡇⠀⣿⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡞⠁⠀⠙⠉⠀⠑⠚⡆⡴⣻⠁⡇⣷⠀⡇⠀⢸⠀⠀⢸⠀⠀⠀⡇⠀⡇⢰⢑⡰⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠐⠀⠈⠉⠠⢰⠃⣧⠃⠀⢸⡸⡀⢣⠀⢸⠀⠀⢸⠀⠀⢀⠇⢀⠇⡆⡾
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⢀⣠⡏⣰⠏⠀⠀⠀⢧⢳⡘⡄⠀⠆⠀⠀⠀⠀⠸⠀⡌⡸⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠂⠀⠀⠀⠉⡟⠀⠀⠀⠀⠈⢧⠳⡈⠀⠈⠀⠀⠀⠀⠁⢈⡜⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠂⣈⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⠳⣌⠲⢄⣀⣀⣀⣠⠔⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠠⠤⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⡤⠭⢤⡶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣐⠂⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠬⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⡀⠀⡄⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡉⠀⠀⠞⠀⠀⠘⠄⠀⠀⢉⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢂⠩⡄⠛⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡄⢴⣾⡄⢀⣿⣿⠀⠎⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠰⠈⣤⠐⣃⠡⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠚⣿⠁⠙⠛⢃⠏⣀⠖⠉⠀⠀⠀⠀⠀⠀⣴⣿⡿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⢀⠀⣉⠀⣀⣈⠃⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠃⠀⠀⠀⣤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣩⣟⣅
⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⡉⠘⢿⣍⣻⣷⡀
⠀⠀⠀⠀⠀⠐⠙⠛⠈⠙⠛⠁⠙⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠉⢠⣨⠌⠙⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠻⠻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣽⣭⣭⣿⣭⡅
⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠭⠧⠭⠿⠀⡂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⢼⡴⠤⡠⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣄⠙⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠸⣿⣴⣇⠠⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣆⣼⠁
⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣭⡭⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⢐⣻⣿⠹⢳⡟⠐⣩⠂⠀⠀⠀⠀⠀⠀⢠⣦⡀⠹⠧⡿⣠⣿⣦
⠀⠀⠀⠀⠀⠀⠠⢉⣉⣉⣉⣉⡡⠇⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⣿⡧⢡⠀⠛⠋⠲⠉⡀⠀⠀⠀⠀⠀⠀⢈⡝⠿⠷⠂⠁⠌⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡜⢃⠙⣄⠃⢘⡁⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⡀⠠⣀⠃⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⣭⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣴⣾⠿⣾⣿⣾⡆
⠀⠀⠀⠀⠀⠀⢠⣤⣄⣴⣤⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⡿⠀⠛⠁⠿⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⠶⠂⠀⠒⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣴⣿⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⠏⠉⠁⠈⠛⠉⠉⠉⠻⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⠟⠋⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠟⠉⠀⠀⠀⠀⠹⢿⣤⡀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠿⠿⠾⠛⠉⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣧⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡾⠿⠃⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠰⠶⠶⠶⠾⠟⠋⠉⠉⠉⠀⠀⠀⠀⠀⢀⣀⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡶⠾⠟⠛⠛⠛⢿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣼⡿⠟⠛⠛⠿⠿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿
⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠶⠶⠆⠀⠈⢻⣷
⠀⠀⢀⣀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⣽⣶⣀
⠀⣠⡿⠟⠋⠀⠉⠁⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣦
⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣠⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿
⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠻⠿⠿⢿⠿⠛⠛⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠻⢿⠿⠿⠿
⠀⠀⣶⡆⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣶⡆
⠀⠀⣿⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⣿⡇
⠀⠀⣿⡇⢸⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⣿⡇⢸⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⣿⡇⢸⣷⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣿⡇
⠀⠀⣿⡇⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠀⣿⡇
⠀⠀⣿⡇⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⣿⠀⣿⠇
⠀⠀⢸⡇⣼⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⡄⣿
⠀⠀⠀⣿⡿⢻⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⢻⣿⡇
⠀⠀⠀⣿⡇⢸⡇⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⣿⡇
⠀⠀⠀⣿⡇⢸⣷⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⠀⣿⡇
⠀⠀⠀⢹⡇⢸⣿⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⣿⠀⣿
⠀⠀⠀⠸⡇⣸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢰⡟⠀⢸⣿⡄⠙
⠀⠀⠀⠀⢻⣿⠙⡄⠀⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡜⢹⣿⠂
⠀⠀⠀⠀⢸⡿⢰⣿⠀⢹⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣷⠸⣿
⠀⠀⠀⠀⢸⡇⢸⣿⠀⠈⣿⡄⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠃⢸⣿⠀⣿
⠀⠀⠀⠀⠀⢡⣾⢿⡀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢸⡏⠀⡸⢿⣤⠃
⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢿⡇⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⣿⡇⢰⣇⢸⣿
⠀⠀⠀⠀⠀⠸⣿⢸⣿⠀⠈⣿⡄⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠿⡆⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣰⡏⠀⡘⢿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⢹⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣿⡇⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠈⢻⣼⣿⡀⠀⣿⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⡿⠃⢸⣷⣼⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡄⢹⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⠀⣾⡇⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡿⣇⠀⢳⡄⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⢻⣇⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⡆⠸⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣶⠀⣿⡆⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡟⣧⡀⢡⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠿⣤⠛⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣇⠘⠇⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢹⡇⠀⡦⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡀⢸⣿⠉⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡌⢳⣦⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢳⣶⠋⣤⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡘⢻⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠛⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣄⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⢁⣼⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠙⢿⣶⣄⠀⠀⠀⠀⠀⢠⣤⣾⠟⠃⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠙⢿⣦⡄⠈⠙⠻⠿⠿⠿⠿⠛⠉⠀⣠⣾⠟⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⠀⠉⠻⠿⣦⣤⣤⣤⣤⣤⣤⡾⠿⠋⠁⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣶⣄⡀⠀⠈⠉⠛⠉⠉⠉⠉⠀⠀⣀⣠⣾⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣶⣿⣧⠀⠈⠛⠻⣶⣶⣦⡀⠀⣀⣠⣴⣶⣾⠛⠋⠀⢀⣼⣿⣶⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠋⠀⠀⠀⠈⢻⣶⡀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠁⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠈⠛⠻⣷⣦⡀
⠀⠀⠀⠀⠀⢰⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢷⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷
⠀⠀⠀⠀⢰⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠿⠿⠿⠷⠾⠿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⢿⣂⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣚⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠟⠛⢋⣉⣩⣭⣭⣥⣤⣤⣤⣤⣬⣭⣭⣍⣉⡙⠛⠿⠿⠟⠋⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⡿⢿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣴⣦⣤⣤⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣭⣿⣯⣿⣿⣿⣯⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠈⠑⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠉⠃⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⠽⣎⢑⠡⠐⠀⠐⣂⠄⣂⣠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠄⣀⣀⣀⠠⠤⢤⣶⣶⣶⣶⣶⣤⣤⣠⡤⠤⠒⠛⠋⢁⣀⣽⣿⣶⣿⠧⣴⣿⣿⣿⣿⣿⡿⠛⠁
⣤⣴⣾⣧⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠀⠚⢿⣿⣿⠋⠉⣠⣄⠀⠀⠀⠀⢀⣾⣿⡟⢋⣥⣾⣿⣿⣿⣿⡿⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣇⣴⣦⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⢠⣾⣿⣿⣿⣿⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠈⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣶⠄⠀⠀⠀⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣿⣿⣿⣄⣶⣄⠛⢻⣿⣿⣿⣿⣽⣿⣿⣿⣿⠻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣚⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡝⣿⣽⣿⣿⣷⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⢛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣾⣿⣟⣳⣶⣿⣿⣷⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⣠⣶⣶⣤⣶⣤⣶⣿⣿⡿⢋⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⣿⣿⣿⣿⠿⢫⣴⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⣟⣩⣿⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⢶⢄⠀⠀⠀⠀⠀⠀⡀⠀⡖⠤⠤⠴⣀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⠒⠉⠀⠀⠉⠉⠁⣸⠀⠀⠀⠠⡄⠐⠉⢁⡠⠤⠤⡀⠀⠀⠀⠁⠴
⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⢐⠒⠚⣧⡄⠀⠀⠀⠈⢢⠔⢁⣤⡀⠀⠈⠆⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠁⠈⠉⡈⠇⠀⠀⠀⠀⠑⠈⠀⠈⠊⠀⠀⢘⡠⠐⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠦⠆⠀⡖⠑⡔⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠚⠀⠖⠀⠀⠀⠀⡄⠐⠃⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠂⠀⠀⠢⡄⣀⡠⠘⠁⠀⠀⠀⠀⠈⠣⡀⠀⠀⣠⡜⡁⢠⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢠⡎⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠢⠜⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙⠛⡉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠁⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠀⠢⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢸⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢁⡀⠀⠀⠉⠒⠢⡤⢐⠶⠆⠢⣄⠀⣰⠃⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⢰⠃⢈⣒⣋⡵⣿⡖⠑⢤⣀⡀⣤⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠄⢀⢤⡤⣟⠒⠊⠐⠂⠡⠥⠋⠉⠀⠀⠘⡇⠀⢤⠈⢙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⣇⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⠀⠠⢴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠰⠈⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠀⠀⢰⠘⣤⠤⠤⡀⠀⠀⠀⠀⣀⣀⡄⠇⢸⣀⡤⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠂⠀⠘⠋⠀⠀⠀⠘⡆⠀⢠⠋⠁⠈⠑⠀⠐⠒⠒⠦⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣀⣠⡤⣄⣀⣀⣀⣠⡟⠀⠸⣄⢀⢀⣀⡀⠀⠀⠀⠀⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠭⠭⠽⠿⠛⠛⠛⠓⠛⠚⠚⠁⠀⠀⠈⠙⠋⠙⠓⠶⠶⠮⠽⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡦⣀⣤⠤⠎⠐⠉⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣤⣀⠀⣠
⠀⠀⠀⠀⠰⡛⢄⠀⠀⠘⢦⠀⠀⠀⠁⠈⠀⠂⢠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⣠⣂⠀⠀⢀⠀⠀⢠⡀⡀⠀⠺⡙⠛⠋⢿⠏
⠀⠀⠀⠀⠀⠑⡄⢂⠀⠀⠀⠑⠢⠄⠀⠐⠢⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣽⡿⢧⠆⠂⡀⠀⠀⡼⡆⠙⢦⣄⠂⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠘⢄⢣⡀⠀⢤⣤⣀⣀⣀⣠⠿⣷⡄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠾⠓⠒⠒⠒⠀⠀⠰⠀⠐⠂⠀⠀⠺⢧⡄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠓⠒⠤⣤⠈⠁⠀⠀⠀⠀⢹⣤⣴⡖⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢻⣤⠃
⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠋
⠀⠀⠀⠀⠀⠀⠱⡾⡄⣤⣤⣀⣀⣀⠔⠒⠒⠒⢦⣀⡀⠀⢀⡤⡅⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠉⠀⠀⠁⠄⠀⣀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡂⠀⠇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⣸⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠰⠦⠄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⡍⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⠀⡆⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⣤⢠⣄⣀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠂⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠙⠀⠀⠀⠈⢧⣆⠰⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⣉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⠂⠙⢛⡛⠓⠃⡀⠀⠀⠀⠀⠀⠀⠀⠸⠑⠊⠀⠀⣄⡀⢀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢦⠋⠂⠸⠆⠲⠈⠃⣷⡃⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠒⠁⠀⠁⠀⠀⠀⠀⠀⢀⡤⡙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠎⡦⠀⠙⠫⢄⣠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠾⠃
⠀⠀⠀⠀⠀⠀⠈⠐⠴⢠⠄⠠⠀⡉⢁⠀⡀⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⣽⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠍
⠀⠀⠀⠀⣀⣠⢶⠛⡛⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡇
⣠⠶⠞⣋⣥⠴⠞⠛⠳⡴⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠃
⠙⠒⠋⠉⠀⠀⠀⠀⠀⢳⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣇⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⠀⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡇⠀⡔⠛⠈⠛⠲⡶⠶⣄⡀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠛⠛⠉⠉⠉⢈⡟⠀⠀⣟⠉⠉⠙⠛⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠻⢄⣧⣬⣤⣄⣀⠀⠀⣿⠀⢀⣉⣉⠀⠙⢧⡀⣀⣤⢤⡿⢦⣄⣀⡀⠀⠀⠀⠀⠛⠳⠶⠞⠛⠀⠀⠀⠀⣀⣀⣤⠾⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣁⡤⠤⠶⠦⢤⡀⠀⠀⠉⠛⣛⣿⣴⣋⣁⣉⠳⠤⠴⣏⠉⠀⠰⣅⠀⠈⠉⠉⠛⠛⠛⠓⠒⠒⠒⠒⠒⠛⠛⠛⠋⠉⠉⠀⢀⡷⠀⠈⠙⣷
⠀⠀⠀⠀⠀⠀⣴⢋⣁⣀⠀⠀⠀⠀⠛⠶⠶⠒⠿⣥⠿⠋⠉⠈⠉⠙⠳⣦⢸⣧⣤⣀⣈⠛⠓⠶⠶⠦⠤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠶⠶⠖⠛⣋⣀⣤⡴⠖⠻
⠀⠀⠀⠀⢀⡼⠋⠉⠀⠉⢷⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⡁⠀⠈⠉⠉⠙⠓⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠛⠉⠉⠁
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠈⠛⠲⢦⡀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠔
⠀⠀⠀⠀⠷⠂⠀⠒⠒⠐⠒⠂⠒⠚⠓⠚⠓⠒⠒⠲⣄⣀⣠⡴⠶⠶⡄⠀⠀⠀⢸⡏⠉⠛⠛⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠖⠛⠋⠉⢹⡇
⠀⠀⠀⠀⠀⢰⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠓⠒⠒⠒⡿⠀⠀⠀⣸⣁⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⡆⠸⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⣸⡶⠖⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⣧⠴⠒⡿⠓⠀⠤⢄⣀⣀⡀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠚⣿⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠃⢹⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⣸⢧⣀⡀⠙⠶⢤⣄⣀⣀⣀⣀⠈⠉⠉⣁⣀⣀⣀⣀⠤⠴⠋⢀⣀⡼⡇⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢸⠆⠀⢸⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⢀⡟⠀⠈⠉⠛⠓⠲⠶⠶⠶⠾⠯⠽⠭⠭⠽⠿⠶⠶⠶⠖⠚⠛⠉⠁⠀⢳⡀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢀⢸⡄⠀⢀⠀⠀⠀⠇⠀⠀⠀⢿⠀⠀⠀⠙⢦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠖⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠀⠀⠀⡀⠀⠀⠀⠸⠀⠀⠀⠀⡄⢸⡇⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠈⡀⢿⠀⠸⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢃⠸⡆⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠛⡄⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠑⡶⢤⣤⣍⣉⣉⣉⣙⣛⣛⣋⣉⣉⣉⣉⣩⣤⠴⠖⠉⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠙⠲⢄⣀⠀⠀⠀⣀⠤⠚⢁⣼⡀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣿⠶⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣉⣉⣁⣀⠤⠒⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿⠐⣿⠀⢹⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⡆⣸⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢧⡀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠘⠷⠿⠿⠁⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⢠⠀⠀⡄⠈⠙⠦⣄⠀⠀⠸⡟⠓⠲⠦⠤⠤⢤⣤⣤⡤⠤⠤⠤⠤⠖⠚⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠀⠀⡴⠃⠀⠀⠹⡄⠀⠀⠈⠛⠶⢤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠠⠀⠀⠀⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⠈⠁⠀⠀⠀⠀⠑⠀⢀⣀⣠⣤⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠖⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣓⣒⣢⣤⣤⣤⣤⣤⣤⣤⣄⣒⣚⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠿⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡶⠿⠿⠿⠛⠛⠿⠿⢶⣶⣤⣄⡀⠀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣶⡶⠶⠶⣶⡆
⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠛⠛⠋⠉⠛⠛⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⣰⡿⠁⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠞⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠙⠛⠻⣧⡀
⢠⡿⠁⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣿⡇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⣿⡆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⢸⣧⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄
⠀⠹⣷⣄⠀⠀⠀⠹⣦⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⣄⣀
⠀⠀⠈⠛⠿⣦⣄⣀⠈⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠋⠉⠘⠛⠃⠀⠀⠈⠛⠛⢿
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠶⠾⠿⠿⠿⠿⠿⠿⠿⠶⠶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠶⠶⣶⣶⣶⡾⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠁⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⡄⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣴⠃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⣤⣄⠀⣀⣀⣤⠖⢶⣤⡶⢶⣄⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠉⠉⠀⠙⢷⣤⣤⣄⠀⠀⠀⠀⠀⣾⠁⠻⣤⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠏⠀⠀⠀⠀⣠⡶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⣾⠁⠀⠀⠈⠙⢧⣴⡟⠻⠶⠾⢦⣄⣀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⢀⣿⠀⠀⠀⠉⠙⠛⢲⣦⠀⢠⠶⢦⣀⠀⠀⠙⠷⣶⠟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠸⣿⡀⣀⣀⢀⣀⣤⣤⡿⠀⣿⡀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠻⢧⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠳⠶⢤⣶⣤⣄⠉⠉⠁⠀⠀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⣼⠿⠁⠀⠀⠀⢰⣿⠀⠈⠉⠻⣶⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠰⠿⠧⢤⣄⠀⠀⠀⠘⠿⠶⠶⠶⠾⠿⠀⠸⣧⣄⣙⣷⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣧⣄⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣉⣉⣉⣩⣭⣁⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣯⠈⠿⠻⣿⠏⠀⠹⣧⠀⠀⠀⠀⢀⣾⠋⠀⠀⠙⠛⠳⢶⣄⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠈⠛⠛⢶⡆⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣻⣿⠛⣿⣿⣟⠁⠀⠀⠀⠀⣼⠏⠲⠾⠇⠀⠿⠿⢿⡅⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⣶⠿⠀⢹⡇⠀⠀⠀⠐⢿⣤⡤⠤⠄⢀⣄⣠⣼⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣤⣤⡄⢸⣷⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠛⠉⢹⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠧⡾⠇⣼⠃⢸⣷⠀⠀⠠⣶⠾⠛⠋⠁⠀⣀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣶⡖⠲⣶⡄⠘⠛⠛⠃⠀⠀⠀⣿⡀⠀⠀⠠⠄⠛⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⠂⠀⢺⣧⣀⣀⣀⠀⠀⠀⠀⠉⠓⠒⠶⠆⢤⣤⣄⣀⣘⣇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠙⣿⠀⠀⠀⠀⢀⣤⢤⣄⠀⠀⠀⢉⣙⡛⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⡀⢾⠛⠛⠓⠦⠴⠿⠀⠀⠀⢰⡟⠁⣸⣯⡾⠛⣻⣿⡏⠉⢻⡆⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠻⡧⢾⣧⣤⣤⡀⠀⠀⠀⠀⠀⢸⣇⠀⠙⠿⠗⠈⠻⠿⠷⠀⠘⣷⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠈⢻⡆⠀⠀⠀⠀⠀⠙⠛⠛⠶⠦⠤⢄⣀⣀⡀⣸⡏⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠚⠂⢸⡇⠀⠀⠀⠀⠀⢀⣶⣦⡀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣴⣿⠁⠀⠀⠀⠀⢠⣞⠃⠀⠈⠁⠲⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⣷⡿⠙⢷⣄⠀⠀⠀⠈⠛⠛⣷⡆⠀⢀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⢴⡟⠉⠀⢠⣿⠻⣦⡀⣰⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡄⠋⠀⠀⠈⠛⣷⡄⠀⠀⠀⠀⠈⠻⢦⣤⡿⠁⠀⠈⠙⠟⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢘⣿⣶⣶⣦⠴⠴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢰⡟⠁⠀⠈⠙⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠸⣧⡀⢀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣶⣶⣶⣶⣶⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣾⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠐⣉⡉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠠⠐⠊⠁⠀⠈⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⠀⠀⠀⠀⠀⠀⡄⢃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢰⡇⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠠⠤⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠎⠀⠀⠀⠀⠑⢤⡀⠀⠀⡠⠒⠲⣄⣇⣀⣀⠀⠀⢱⠈⢙⣛⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣸⡥⠤⠒⠢⢄⠀⠀⢉⣉⣿⣴⣡⣬⣑⠦⠷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠴⠚⠀⠐⠀⠔⠒⠒⠒⠀⠀⠈⠙⢶⡥⠀⢤⠀⠀⠀⠉⠉⠉⣱⠎⠀⠀⠀⠀⠙⢦⡇
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠈⠳⠤⣄⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠠⠤⠤⠤⠤⠤⠖⠒⠂⠀⠉⠉⠑⣖⠒⠒⠒⠛⠒⠓⠒⠒⢦⣀⡠⠖⠦⡄⠀⠀⢨
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⢘⠇⠀⠀⣼
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠂⠰⠦⠤⠤⠤⠤⠤⠤⠆⠀⠀⠀⠙⣦⣷⠀⢰⡇⠀⠀⣷⠀⠀⢰⡆⠀⣿⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡟⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⣿⠈⣦⠀⢹
⠀⠀⠀⠀⠀⠀⢸⠉⠙⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠀⡇⠀⢸⡇⠀⠀⣿⠀⠀⠘⡇⠀⣿⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⢦⡤⠋⠈⠷⠶⠒⠦⣤⣤⠀⣠⣴⠛⡇⡇⠀⡇⠀⢸⡇⠀⠀⡟⠀⠀⠀⡇⠀⣿⢀⠸⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠤⠀⠀⡘⢸⢡⠃⠀⣧⢹⠀⣷⠀⠘⡇⠀⠀⡇⠀⠀⢀⡇⠀⡏⢸⢰⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢀⠀⠈⢩⠇⣸⡏⠀⠀⠸⡌⣇⠸⡀⠀⢇⠀⠀⠀⠀⠀⢸⠃⢠⠃⡏⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡀⠀⠁⠤⢯⠴⡟⠀⠀⠀⠀⢳⡘⣆⠣⠀⠈⠀⠀⠀⠀⠀⠌⢀⢂⡜⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⢠⣀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠳⡜⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⢎⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠡⢄⡀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⠲⢤⣄⣀⣤⠴⢊⣥⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠐⠤⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠴⠴⢶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣉⠂⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢄⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⠀⠀⡀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠚⠁⠀⠰⠃⠀⠀⠳⠀⠀⠀⠉⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠠⠤⠤⠤⠴⠖⠒⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣋⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠃⠉⠳⣄⣀
⠀⠀⢀⣀⡤⠴⠛⠋⢉⣠⣀⣴⡄⠀⠈⢹⡀
⣴⠛⠉⢁⣠⣤⠔⠒⠋⠉⠁⠀⠉⣶⠀⠀⢹⡄
⠙⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⡶⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⢇⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢿⠀⠀⠀⠁⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⡆⠀⠀⠔⠋⠉⠉⠀⠙⢳⣴⠶⣶⣄⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⣴⡇⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠉⠙⠛⠛⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠈⠙⠶⠿⠿⠛⠛⠳⠶⣤⣄⣀⡀⣠⠃⠀⣠⡴⠶⢶⣄⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣀⣤⡶⠶⠶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠉⠉⠙⣿⣤⡾⠋⣀⣀⠀⠙⠷⣤⡴⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠟⠉⠁⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⣤⣤⣶⡟⠛⣻⡿⠛⠛⠙⠉⠛⠛⠳⣦⣄⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⡶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠙⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢀⡿
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣤⣀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣹⣇⣀⣠⣟⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢀⡿⠛⠙⠛⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣦⡀⠀⣠⡤⠾⠟⠻⠷⣄
⠀⠀⠀⠀⠀⢸⡇⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⢶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠴⠶⠶⠶⢴⣿⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠘⣷⠀⣿⠀⠀⠀⠀⣤⣄⠀⠀⠀⢀⣤⡄⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⢠⣤⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⢹⡄⢻⡇⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⡄⠀⠀⢹⣿⣆⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢸⣿⡆⠀⠀⢹⣿⠙⢷⣄⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡆⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⣹⣧⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⣿⣯
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⣿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣇⠀⠀⣿⡇⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⣿⢸⡇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⠀⠀⢻⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡟⠀⢠⡇⢸⡇⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡀⠀⢸⣇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢸⡇⠀⣸⠇⣸⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢻⣇⠀⠘⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠇⢀⡿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠈⣿⡀⠀⢹⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡿⠀⠀⢰⡟⠀⣸⠇⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⣧⠀⠘⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣼⠁⣠⡿⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠹⣧⠀⠘⣧⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣰⠋⢠⡟⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠹⣧⡀⠙⢆⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⡰⠋⣠⡟⢁⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠘⢷⣄⠈⠳⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⢀⠘⢁⣴⠏⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠙⠳⣦⣄⣀⡀⠀⠀⠀⣀⣀⣤⡾⠛⠁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣤⡀⠉⠉⠛⠛⠛⠛⠋⠉⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣶⣶⣶⣶⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁⠀⢠⠄⠀⠀⢠⠀⠀⠈⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋⠀⠀⠀⣴⠋⠀⠀⠀⠘⣦⠀⠀⠀⠀⠈⠛⢷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣄⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣤⡴⠶⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣛⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣟⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⠿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣶⣦⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣷⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠿⣿⠿⠟⠀⠀⠘⢿⣿⣿⣿⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⣿⣿⣠⣶⣶⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣶⣶⠀⠉⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣆
⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦
⠀⠀⠀⢀⣾⠋⠀⠀⠀⣼⠏⠛⠷⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣎⢻⣿⣿⣿⣿⣧
⠀⠀⢀⣾⠃⠀⠀⢀⣼⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣧⡀
⠀⢠⡾⠁⠀⠀⢀⣾⠃⠀⠀⠀⠀⢠⣿⣿⣿⡿⠋⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⣷⡀
⢠⡿⠁⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣷
⢿⣤⣀⠀⢠⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣷⠙⣿⣿⣿⣿
⠀⠈⠙⠷⠟⠁⠙⡷⣠⣤⣄⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⡀⠀⠀⠈⠻⢿⣿⠟⠁⠀⠘⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣠⣾⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠻⢶⣤⡀⠀⠀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣴⣿⣿⡿⣡⣾⣿⡆⠀⠀⠀⠀⠈⠙⠷⣦⣄⡀⠀⠈⢻⡷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢏⣴⣿⣿⡿⣡⣤⣄⠀⢶⣤⣀⠀⠀⠉⠻⣶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠏⣼⣿⣿⡿⠀⠀⠈⠙⠻⣶⣤⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠘⠻⠶⠶⠶⠾⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡄⠀⠀⠀⠀⠀⢀⡴⠒⢶⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⡞⢀⠀⠀⠑⢮⡣⡀⠀⠀⠀⠀⠀⢀⠜⡡⢶⡂⢺⣇
⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡙⢮⡢⡀⠀⠀⣰⣃⠸⠷⠿⠃⣼⣛⢷
⠀⠀⠀⠀⠀⣼⠥⠤⠤⠤⠌⣆⠀⠀⠀⠀⠱⠤⠤⠤⠤⠤⠤⠤⠟⠊⠀⠀⡇⠀⠈⠉⠉⢸⠉⠀⢸⡀
⠀⠀⠀⠀⢰⠋⠒⠒⠒⠒⠒⢻⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡀⠀⢸⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠱⡤⣤⡭⠵⢴⣒⣠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡇⠀⠘⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢣⡀⠉⠉⠉⢩⣞⠲⣄⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⣯⡷⠤⠤⣴⠁⠱⣸⡄⠀⣧⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠛⠓⠒⠊⠉⢆⠀⣿⡇⠀⢸⣀⡀⠀⠀⠀⡇⠀⡠⠇
⠀⠀⠀⠀⠈⢧⣄⡀⠀⠀⣀⡼⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⢧⠛⠀⠀⠀⠀⠉⠉⠓⠒⠓⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⡰⣠⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠠⢞⠛⢯⢤⡠⠔⡀⠀⢸⡲⡄⠈⠓⢦⣤⣤⣤⣤⠞⠁⠀⠀⠀⠀⠀⠛⠻⠶⠶⠶⠶⠟⡇
⠀⠀⠀⠀⠸⠀⣔⡆⠀⡀⠀⡇⠀⠀⠙⢜⣄⠀⠀⣈⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠛⠀⠆⠲⠰⢻⡇
⠀⠀⢀⣀⣇⡚⠀⠀⢀⣯⢆⣿⠀⠀⢠⠞⢻⡄⣠⢤⡔⠒⣤⣌⣩⢵⡢⡄⠀⠀⢨⠀⠀⡄⠀⠀⢸⠁
⠀⠀⢸⠑⠒⠬⣍⣐⠚⢛⣉⣠⢱⠀⠈⣿⢿⢤⣤⣀⣀⣀⣀⣈⣡⠤⠟⡏⠀⠀⠀⡇⠀⡇⠀⠀⢸
⠀⠀⠸⢄⣘⠁⢙⠋⣩⡉⠠⠇⢯⠀⠀⠘⣿⣾⣴⢴⣤⣤⠤⡤⠶⣲⡟⠀⠀⠀⠀⡧⣧⣇⣥⠠⢸
⠀⠀⠀⠀⠈⠉⠒⠦⣽⣧⠔⠊⠁⠀⠀⠀⠈⠛⠿⢧⣿⡧⠴⠾⠛⠉⠀⠀⠀⠀⠀⠻⠤⠤⠤⠤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠿⠟⠛⠛⠻⠿⢷⣶⣦⣄⣀⠀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⡶⠶⢶⣦⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢀⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⣀⣤⡾⠟⠛⠉⠉⠉⠉⠉⠛⠻⣦⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣿
⠀⣼⡟⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠞⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠻⣦⡀
⣸⡿⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⣿⠇⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⣿⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀
⢿⡄⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠸⣷⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀
⠀⠈⠿⣦⣀⠀⠀⠙⢦⣄⣤⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠀⠀⠠⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠈⠙⠿⣦⣤⣤
⠀⠀⠀⠈⠛⠿⢶⣦⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⣤⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⢻⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢰⡇⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢾⠋⠁⠐⠶⠾⠉⠉⠛⠉⠉⠻⠟⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠇⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢷⣄⠀⠀⠀⣾⠁⠀⠈⠻⣦⡀⣰⠿⣆⣤⣄⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⣼⠋⠉⠉⠛⠳⢦⣤⣄⠀⢀⣤⣄⠀⠀⠙⢷⣤⣴⡟⠀⠀⠀⠀⠈⠙⠉⠀⠈⠁⠈⠛⠻⢶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣿⠀⣹⡇⠘⢳⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⢻⣇⣀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣤⣤⣤⣤⡈⠙⠛⠁⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠺⣧⣀⠀⠀⠉⣩⡿⠂⠀⠀⠀⢸⡏⠉⠘⠛⢦⡄⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠃⠠⣾⣋⣠⣄⠀⠀⠀⠸⣧⡴⠶⠶⠾⠇⠀⢻⣅⠉⢳⡄⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠼⣿⣀⣀⣀⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣉⣉⢉⣥⣼⠋⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠿⠛⣾⠏⠀⢹⡇⠀⠀⠀⠀⣀⡾⠉⠈⠙⠛⠑⠶⢦⣀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠙⠛⠓⣶⡄⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⠋⣿⣿⣏⠁⠀⠀⠀⢀⡿⠋⠳⠿⠁⠘⠿⠿⣏⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠛⠶⠏⠀⢹⡇⠀⠀⠀⠸⢷⣤⣤⣤⣤⣀⣤⣤⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡶⣦⡄⢸⡇⠀⠀⠀⠀⠀⣀⣤⡴⠾⠋⠉⠈⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠾⠃⣸⡇⢸⡇⠀⠀⢰⡿⠛⠋⠉⠀⢀⣤⣦⡛⠋⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢾⡟⠒⢶⡆⠈⠙⠛⠁⠀⠀⠸⣧⡀⠀⠀⠰⠊⠉⠉⠙⣧⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⢷⣤⣤⣄⡀⠀⠀⠀⠈⠙⠛⠛⠂⠴⠦⢤⣀⣿⡀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⢀⣴⠶⢶⡆⢠⣄⣀⣤⣭⣅⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⡛⠛⠛⠋⠛⠛⠀⠀⠀⢸⡇⠠⣮⣿⡏⣸⣿⣯⠀⠘⣿⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣷⠶⢦⣄⠀⠀⠀⠀⠀⠸⣧⣄⣈⡉⠀⠈⠉⠛⠁⠀⣽⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢀⡀⢹⣧⠀⠀⠀⠀⠀⠀⡀⠙⠛⠓⠲⠶⠶⠦⣰⡿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣟⡀⠈⢁⣼⠏⠀⠀⠀⠀⠀⣤⠟⠓⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣿⣿⣄⠀⠀⠀⠀⠾⣧⣄⡀⠀⠀⠉⠑⠶⣤⣀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠹⠃⠀⣹⡷⠀⠀⠀⠀⣀⣼⠟⠃⢀⣤⣄⠀⠀⣻⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡀⢠⠀⠀⢠⣾⣏⠀⠀⠀⠀⠀⠻⣧⡀⢀⣿⠁⠙⠷⣴⡿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⣧⣄⣀⣀⣀⣀⣽⠇⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⢿⣍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠙⠃⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠐⠂⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣶⣶⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠶⠶⠶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⡿⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠟⠉⠙⠛⠛⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣄⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠓⢄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⠄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠉⠛⠀⡄⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⡀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡆⠀⠠⠀⠀⠀⠴⠋⠉⠁⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠀⠒⠀⠐⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠈⠉⠛⠋⠑⠀⠀⠀⠀⠰⠄⠐
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⢂⡁⡄⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠉⠀⠀⠈⠧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⣶⠀⠀⠀⠀⠀⠀⡄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⢇⠀⠀⠀⠀⠀⠀⢠⠈⠀⠀⠂⠀⠢⡤⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠋⠀⠀⠀⠀⠈⠓⢆⠀⢀⠖⠉⠙⠲⠶⠒⠦⣄⣀⡁⣠⠤⢄⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⣀⡀⠀⢠⣏⣀⡼⠒⠉⠉⠉⠳⣄⡤⠤⣚⡿⠓⠒⠂⠯⡉⢇
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢹⡏⠉⠱⡄⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠸⣎
⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠠⠾⢅⣀⣀⣈⣉⣦⣠⣇⣀⣀⠀⠀⢀⣀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡷⠶⠶⠶⠤⠤⠤⠤⠬⠷⠚⠁⠀⡵⠀⠀⢀⠃
⠀⠀⠀⠀⢠⠗⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢾⡁⣄⠀⢠⡄⠀⢠⡄⠀⠀⣤⠀⢠⡇⠀⠀⢸
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⡏⠀⢸⡇⠀⢸⡇⠀⠀⣿⠀⢸⡟⢄⠀⠸
⠀⠀⠀⠀⠀⠈⡷⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢡⡇⠀⢸⡇⠀⢸⡇⠀⠀⢻⠀⢸⡇⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠻⣄⡠⠊⢳⣤⠤⢤⣀⣈⠉⢉⣠⠼⡇⡇⠈⡇⠀⢸⠃⠀⢸⡇⠀⠀⢸⠀⢸⡇⢸⡇⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢠⡀⠈⢹⢀⢏⡞⠀⣧⢻⠀⣧⠀⢸⡆⠀⠘⡇⠀⠀⢸⠀⢸⠁⡆⣷⠊
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⢀⡀⠀⠒⡿⢸⡾⠀⠀⢸⡜⡆⢹⠀⠘⡇⠀⠀⠁⠀⠀⡎⠀⡾⠰⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠠⢼⣡⡾⠁⠀⠀⠀⢳⡹⡄⢂⠀⠃⠀⠀⠀⠀⠠⠁⡰⢡⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⠁⣀⡀⠀⣰⠃⠀⠀⠀⠀⠀⠳⡝⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⡉⠤⡀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⠢⢤⣤⣤⡤⠖⣫⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠒⠄⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡶⠶⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⡉⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⡠⠀⢀⠀⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠀⠀⠜⠁⠀⠀⠣⠀⠀⢀⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠒⠒⠊⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠰⠞⠛⠉⠉⠉⠢⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⢿⡀⠀⠀⠀⠀⠀⠈⠉⠙⣆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣬⣭⡿⠗
⠀⠀⣸⠁⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠀⠉⢻⣿⠶⠶⠒⠒⠒⠒⠒⠂⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⣰⠇⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠤⢌⠙⢦
⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢳
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣾⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⡼⢁
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⣿⠀⣄⠀⡄⢠⠀⠠⡀⣿⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⣴⠞⠡⠊
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⣿⠀⠃⠂⠁⠈⠀⠀⠀⣿⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⢿⣷⣶⣶⣾⡿⠋⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣿⡀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠹⣷⣤⣀⣀⣀⣀⣀⣠⣴⡿⠃⠀⠀⠈⠻⣦⣄⠀⠀⢀⣀⣠⣤⣴⡶⠾⠛⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠒⠋⠙⠲⣤⣀
⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠁
⠀⠀⣀⣤⣴⣶⣏⣉⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⢹⣿⢶⣄⡀⠀⠀⠀⠀⠀⣀⣤⣶⣿
⢀⡾⠋⠀⠀⠀⠀⠉⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠊⠀⢀⣤⡠⡄⠀⠉⠙⠲⠦⣄⠀⢸⠇⠀⠈⠙⠳⣦⣤⡶⠛⠉⠁⠈⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⡇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢉⣉⣠⡤⠴⣛⠕⠀⣿⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠃
⢸⡇⠀⢀⠀⠐⠀⠀⠀⡠⠀⢸⡇⠀⠀⣠⣞⣡⣤⡴⠶⠖⠛⠋⠉⠀⣠⠀⡀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠸⣇⠀⠿⠀⢦⣄⠀⠀⠣⡀⢸⡇⠀⢾⡟⠉⠉⠀⠀⠀⢀⡤⠆⣀⠸⣧⡶⠃⠀⠀⣿⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠻⣦⡀⠀⠀⠀⠀⠀⡸⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⠾⠃⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⢸⠃⠀⠸⣧⡶⠄⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠁⠀⠀⠀⠀⠙⠶⢤⣤⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⠀⠀⠀⠀⠀⠉⠛⠁⢀⣠⠖⠶⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠿⡏⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠒⠒⠈⠀⠀⢀⠀⠀⢀⣠⣶⡂⠀⠀⠀⠀⠀⠈⠂⠀⠀⡀
⢀⡀⠀⠀⠀⠀⣰⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠎⠀⠀⠈⠁⠒⢤⡀⣠⠀⠀⠱⡀⠀⠄⠀⣀⢀⣌
⢸⣿⣿⣾⣤⣴⡿⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢀⠀⠀⣷⡀⠈⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⡇⣼⣿⣿⣦⣄⡀⠙⠒⠶⣤⣈⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠑⢄⠜⢳⣾⠿⣿⣿⣿
⢸⣿⣿⡿⠻⠿⠃⠈⠉⠛⢿⡉⠉⠐⠢⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠠⠀⠀⠀⠀⠿⠛⠉
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⠙⠲⡄⠀⠀⢅⠠⠀⡀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡀⠀⢸⠋⠀⣠⠇⠐⡄⠐⠢⡄⠀⠈⠱⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠠⠋⠀⢠⠧⢄⠀⡈⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠉⣈⡁⠒⠢⠤⢀⠀⠀⠠⡒⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢍⠉⠉⡹
⠀⠀⠀⠀⠀⠀⢀⠠⣔⡁⢈⠉⡅⠁⠀⣀⢀⡚⠃⠬⠒⡆⠈⢀⠎⣩⣍⠉⠉⣆⠀⠁⠴⠁⢀⠔⠉⠁⠀⠑⠠⡀
⠀⠀⠀⢀⠠⠐⢁⣀⠩⢤⣽⠉⠒⠀⠈⠂⠊⠀⡄⠀⠀⡇⢀⣊⣈⣤⣞⣀⣌⣀⡆⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠞⠓⢯⠼⠣⠀⠀⢅⡠⣏⣉⠄⠀⠀⠀⠀⠀⠀⠲⠇⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⠒⠒⠂⢄⢑
⠀⠀⠀⠂⠐⠀⠊⠀⠀⠀⠀⠅⡸⠀⢀⣤⣄⡀⠤⠀⠒⠁⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠘⢠⠀⠀⠀⠀⠀⢀⡀⠄⠀⠘⠉⠀⠀⢀⠒⠒⠒⠄⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠻⠆⠐⠂⠉⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⢀⠔⠁⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸
⠀⠀⠀⠀⢰⠒⠳⠤⠤⣀⠀⠀⠀⠀⠠⠤⠙⠒⡆⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠐⠊⢸
⠀⠀⠀⠀⢸⠀⠀⢨⡷⠉⣲⣶⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⢁⣀⡀⣀⡁⢀⣀⠈⡆⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠉⠫⡀⠀⠀⠀⠀⠀⡇⡔⠓⠆⢨⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⢀⠘⠉⠓⠛⠓⠚⠓⠀⡇⢸
⠀⠀⠀⠀⡜⠀⠒⠂⠠⡦⠤⠤⠬⠦⡄⠐⠂⢀⠋⠀⢠⠂⢸⣀⣀⣀⣀⣸⣀⣀⡀⠀⠡⢈⣉⣉⣉⣉⣉⣉⣉⣉⠠⠊
⠀⠀⠀⡐⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠈⠢⢄⣯⣄⣤⠂⠀⠀⠀⠀⡀⡀⡀⡀⠀⠀⣀⢀⡀⢀⠀⠀⢀⡀⢀⢀⡀
⠀⠀⠐⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠆⠀⣄⠆⠀⡧⠤⠤⡇⠀⠀⢸⠤⠤⢽⠀⠀⠀⡧⠤⠼⠅
⠀⠀⡓⠤⢀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠀⠀⠀⢀⠓⠒⠒⠆⠀⠀⡜⠒⠒⠚⠀⠀⢐⠒⠒⠒⠆
⠀⠀⡇⠀⠀⠀⠹⠁⠀⠀⠐⠒⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠘⡀⢀⠁⠀⠀⠀⢂⠀⠌⠀⠀⠀⠰
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠁⠀⠀⠀⠀⠋⡁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠏⢸
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠁⠈⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠈⢘⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠁⠒⠠⠤⠀⠀⢀⣀⣀⣀⡀⠀⠀⠠⠄⠒⠈⠀⠀⢐⣈⣀⣁⣀⣀⣀⣈⣁⣈⣀⣀⣀⣈⣉⣈⣁⣀⣀⣀⣉⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⢠⢖⡖⠀⠠⣴⠃⡖⠀⠀⠀⣤⣤⣀⣀⣤⣀⣀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡞⠀⢠⡃⣏⣸⣋⡃⠀⠀⣿⡿⣿⣿⠘⡏⠹⡇⡇⢻⣿⠇
⠀⠂⢀⡀⡀⠀⠀⠰⠀⣀⠀⠀⠀⠀⠀⠀⡤⣤⣤⣤⣤⡄⠀⢄⠀⠀⠀⠉⠀⠈⢻⣼⡷⠶⠶⢶⣾⣿⡂
⠀⠀⠈⣿⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⡟⢹⠃
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠌⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣾⡇⠀⢤⣀⠀⠀⠀⠀⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠂⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠖⠀⠀⠀⠀⢀⠄⣠⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠄⠀⠀⠈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠈⠄⠸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠂⠐⠆⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠐⠀⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠷⣄⣽⣿⡇⠀⠀⠀⠀⠀⠀⠻⡿⠂⠈
⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣿⡿⢡⣾⡿⣿⠛⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣾⣿⠃⣼⣿⣿⣿⡟⢸⣿⠀⠈⠈⠻⣿⣧
⠀⠀⠀⠀⣠⣴⣿⣿⡷⢊⣽⣿⡿⣇⢸⣿⣇⠀⠐⠀⣻⣿
⠀⠀⠀⢰⣿⡏⢷⣻⡆⣹⣿⣿⣷⡹⣌⣿⣟⣶⣤⣶⣿⣿⣿⣷⣄
⠀⠀⠀⢀⣿⣷⡈⢿⣿⣿⣧⠹⣯⡙⢿⣿⣿⣿⣿⣯⣼⡿⠋⣿⣿
⠀⠀⣰⣿⡟⢻⡻⣿⠏⠙⢿⣷⣿⡟⠚⠻⠶⢺⡿⠟⣉⣤⣾⣿⣿⡶
⠀⠀⢹⣿⣧⡀⣳⣽⣷⡄⣠⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢹⠋⠉⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢸⡇
⠀⠀⠀⢸⢀⣀⢤⠤⢤⠤⢤⡤⠒⢒⣒⣂⣀⣀⡄⠀⠀⠀⠀⠉⢻
⠀⠀⠀⢸⡎⠁⠀⠒⠈⠓⠀⠂⢸⠉⠉⠉⠉⠀⠀⠃⠐⠃⢰⠀⣸
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡏
⠀⠀⠀⠀⢹⡆⠐⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠃
⠀⠀⠀⠀⠘⣧⠀⡄⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠀⠀⠄⢸⠃⡾
⠀⠀⠀⠀⠀⢿⡀⠁⠀⠀⠀⠀⡄⡇⠀⠀⠀⠀⠀⠀⠀⣾⢠⡇
⠀⠀⠀⠀⠀⢸⡇⠸⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠘⠀⡇⣸
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⡄⢸⠃⡏
⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢰⢁⠀⠀⠀⠀⠀⠃⣼⢰⠃
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢰⠀⠁⣼
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠂⢸⢸⠀⠀⠀⠀⠈⠐⢂⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢸⠀⠀⠀⠀⣴⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⡞⠀⠀⠀⠀⡏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣇⡇⠀⠀⢰⠇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⢀⠀⢙⡇⠀⢀⢸⡆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠮⠤⠼⠿⠤⠭⠁⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠲⢄⠀⠠⢠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⠀⠒⠒⠂⠐⠒⠒⠢⠈⠱⣄
⠀⠈⠀⢀⠠⠴⠚⡉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤
⠀⠘⠀⠘⠡⠒⢂⠤⠴⠶⠾⠿⠿⠄⠀⠿⠿⠿⠶⠶⢤⣤⠐⠾⠂
⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠛⠛⠛⠛⠛⠛⠛⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠶⠶⠶⠾⣿⡶⠶⠶⠶⣶⡶⠶⠶⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣀⡀⠀⠀⠀⣺⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⡛⠉⠉⠉⠉⠉⠉⢛⣻⣷⠀⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠛⠛⠛⠛⠛⠛⠛⠛⢙⣿⠀⢸⡇⠀⠀⣠⣿⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⡇⠀⣰⡟⠀⢻⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⡇⠀⣿⡀⠀⢀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⢶⣶⣤⣤⣶⡶⠶⣿⡇⠀⢹⡇⠀⠈⠛⠿⠛⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢤⡄⢠⡄⢠⣤⠀⣿⠁⠀⢼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠶⠆⠰⠆⠰⠶⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⢘⡃⢘⡃⢘⡃⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣈⣁⣈⣁⣈⣁⣼⡇⢀⣀⣺⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⡿⢿⠿⠿⠿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠿⠿⠿⠿⠿⠿⢷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⡀
⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀
⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠙⣿⣄
⠀⠀⢠⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠛⠛⠛⠿⣶⣤⣀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⣿⣧
⠀⢠⣿⠏⠀⢹⣿⠿⠿⢷⣶⣶⣶⣾⠿⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣾⣟⣥⣤⣴⣶⣾⠿⠿⠟⢿⣧
⠀⣾⡏⠀⠀⣾⡏⠀⠀⢸⣿⠀⠀⠀⢀⣼⡿⠀⠀⣠⣶⡾⢷⣦⡀⠀⠀⣠⣾⠟⠛⠛⠿⣿⣍⠙⠻⣷⡄⠀⠈⣿⡆
⢸⣿⠀⠀⢰⣿⠁⠀⠀⢸⡿⠀⠀⢠⣾⠟⠀⢀⣼⡿⠁⠀⠀⠙⢿⣷⣾⠟⠁⠀⠀⠀⠀⠈⢻⣷⠀⠘⣿⡄⠀⢸⣿
⣾⡇⠀⠀⣿⡏⠀⠀⠀⣿⡇⠀⠀⠘⠿⣶⣾⠿⠋⠀⠀⠀⠀⣠⣾⠟⠻⣷⣦⡀⠀⠀⠀⠀⠀⣿⡇⠀⢻⣧⠀⠀⣿
⣿⡇⠀⢸⣿⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⢹⣧⠀⠸⣿⡀⠀⣿
⣿⡇⢀⣿⠇⠀⠀⠀⣾⡏⠀⠀⠀⣀⣀⡀⠀⠀⠀⣠⣾⠟⠁⠀⠐⢿⣦⡀⠀⠀⠙⠻⣷⣄⠀⢸⣿⠀⠀⣿⡇⠀⣿
⢿⣇⣸⡿⠀⠀⠀⣼⣿⣶⣄⣴⡿⠛⠛⢿⣦⣴⣾⣿⣧⣄⢠⣄⠀⠀⠙⠻⣷⣄⠀⠀⢸⣿⠀⢸⣿⠀⠀⣿⡇⢀⣿
⠸⣿⣿⣧⣀⣀⣾⣿⣦⣾⣿⡋⠀⠀⢀⣼⣿⠟⠁⠀⢘⣿⣬⡛⢿⣦⣄⠀⠈⠻⣿⣾⣿⣿⣶⠿⠃⠀⣰⣿⠁⣸⡿
⠀⢿⣯⠉⠛⠛⠋⠀⠈⠁⠻⣷⣤⣴⣿⠟⠁⠀⢀⣴⡿⠋⢹⣿⠀⠉⠻⣿⣶⣶⡿⠃⠈⠻⠿⣶⣶⡾⠟⠁⢠⣿⠇
⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠻⣷⣤⣴⣿⠋⢀⣠⣾⠿⣷⣶⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠈⢿⣧⡀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠈⠉⠉⠻⠿⠿⠛⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠻⣷⣄⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠄

⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⠀⠀⠈⢆
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⠀⠀⠀⣀⣀⣤⣤⡤⠤⠤⠤⠄⣀⡀⠀⠀⠀⠀⣀⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣤⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣴⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡖⠋⠀⠀⠀⣀⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣧⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠈⢹⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣮⣻⣿⣿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡠⠄⡌⠀⢙⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠣⡂⡜⠙⢻⣿⣷⣽⣿⣿⣿⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠼⠿⠿⠟⠙⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣠⠤⠖⠂⣤⣄⣀⠀⠀⠀⣀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢄⡀⠀⣰⠄⠀⠀⣭⣾⣧⠀⣠⡟⠉⠁⠀⠀⠈⡗⠛⠼⣿⣿⡇
⠀⠀⠀⢠⣷⣿⠀⠀⢀⣤⣶⣿⣿⠆⣀⣴⢿⣿⣷⡧⠀⠀⣼⣿⣿⣿⠀⣿⠁⠀⠀⠀⠀⠀⠶⠀⠀⢉⣛⡇
⠀⠀⠀⠀⢹⢿⣤⡀⢘⠟⠉⠿⠟⠀⠀⣧⣾⠿⣿⣧⣴⣿⣿⣿⠟⠓⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟
⠀⠀⠀⢰⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠃⠰⣿⠀⢿⡿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠘⡇
⠀⠀⢠⣽⡇⠛⠀⡴⠂⢠⡄⠀⠀⠀⠛⠉⢀⣠⣿⠀⠶⣴⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠘⡿⠛⠀⣸⢧⠔⠀⠀⠀⠀⠀⠀⠉⠁⠉⣹⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⢹⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠁
⠀⠀⠀⠀⠠⣠⡐⢼⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣄⢠⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇⠞⢰⢸⢰⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠈⠈⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠠⠬⠂
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⡔⠈⣾⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠨⡀⠙⠐⠂⠀⢤⠀⠀⠀⣀⣴⣶⣶⣴⣶
⠀⠀⠀⡸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⣠⣶⠟⠋⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠴⠀⠀⠀⠈⠉⠀⠈⠉⠉⠉⠑⠂
⠀⠀⠠⡀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣾⣶⣶⣴⣄⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠐⣦⣀⠀⢀⣀⣠⡀⠀⠀⠠⠀⠀⡀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠠⠆⠀⠛⠃