Butcher Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⣿⢉⡉⣁⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡈⠙⠛⠙⣶
⠀⠀⠀⠀⠀⡤⠚⢿⡀⣁⣈⣸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠮⠭⣤⣀⣻⠏
⠀⠀⠀⠀⠀⢫⠀⢸⣿⣼⣿⣿⢏⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠑⠢⡄⠀⠀⠀⠀⡰⠆⠰⠂⣹⠟
⠀⠀⠀⢀⡔⠩⠆⢸⠉⢹⠉⣸⣇⠀⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢨⠃⠀⠀⠀⠀⢸⢗⡶⣶⣿⡎
⠀⣠⣖⠯⡤⠒⠛⢻⠉⠉⠉⠑⢻⡀⠀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣸⠀⠀⠀⢀⣤⡼⣿⣿⣿⠟⢣⣄
⣼⠏⠀⢀⣧⣤⣤⡼⠀⠀⠀⠀⢸⣧⡀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣿⠀⠀⢰⡟⠇⠋⢳⠏⠉⢚⠕⠉⠡
⠻⠷⠶⠛⠁⢿⡏⠁⠀⠀⠀⠠⢬⠀⠘⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡏⣄⡀⣸⠃⠀⠁⠉⠉⠁⢸
⠀⠀⠀⠀⣀⣸⣷⣄⣒⣤⡔⣀⡎⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋⠶⢤⣏⣈⡆⠀⠀⠀⠀⠀⠸⡇
⠀⠀⣀⣀⣀⠀⢀⣤⣤⠖⠒⠋⢉⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠉⠛⠇⠀⠀⠀⠀⠀⣰⠁⠀⢀
⣰⣾⣿⣛⣯⣵⣏⠀⠸⣤⡤⡴⢋⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠸⣄⡀⠀⠀⢀⡉⠐⣲⡾
⠹⠿⠛⠛⠛⠁⠘⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠨⢉⡻⠖⠉⢘⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣶⣦⣤⣤⣤⡤⢅⣀⣴⠃⠀⡆
⠀⠀⠀⠀⠀⢀⡤⠒⠦⢤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢠⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠉⠒⠒⡄
⠀⠀⠀⠀⠀⠀⣿⠶⠒⠒⠚⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠖⠶⢾⡅
⠀⠀⠀⠀⠀⠀⣿⡈⠁⠘⠋⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢁⡉⢸⠇
⠀⠀⠀⠀⠀⠀⢸⣧⡐⠖⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⣾⡿⣿⣿⢿⣶⡤⢤⡀
⠀⠀⣠⢤⡖⡶⢏⠣⢼⣿⠿⢫⢷⠶⣄⣀⠀⠀⠀⡜⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣿⡇⠉⠛⠓⠁⢹⡇⠀⢹⡄
⠀⡜⠁⢠⡇⣯⠈⠑⠋⡏⠛⠁⢸⢠⠃⠈⢳⣀⠞⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡏⠳⠤⠤⠤⠤⠚⢳⠀⠀⢱⡀
⢰⠃⠀⢸⣧⣸⠀⠀⠀⡇⠀⠀⡏⢸⠀⢠⡼⢃⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣇
⡏⠀⣎⠉⠉⠉⠳⢦⣤⣧⡤⠞⣠⢼⡤⢮⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠷⠴⣾⠀⠐⠀⠀⠀⠐⠀⠸⣷⠤⠴⢿
⡇⢠⠟⢉⡷⠒⠒⠒⠛⠉⠉⠉⠀⠀⢈⣿⢏⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢻⠂⠀⠀⠀⠀⠀⠐⠘⡇⠀⢀⡟
⢸⣇⡀⣸⡀⢀⣀⣠⡤⠖⠾⣟⣳⣴⣋⣨⣮⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣾⠉⠦⣤⣄⣀⣀⣀⣤⠤⠏⠓⡞
⠀⠙⠛⣿⣿⡿⠋⠁⠀⠀⠀⠉⠉⠙⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣀⣸⡟⠻⠿⣿⣟⣇⣠⣰⣛⡄
⠀⠀⠀⢹⣿⠀⡀⠀⠐⠒⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡵⣿⢦⣄⣀⣉⣛⣿⣿⡿⠃
⠀⠀⠀⠀⠉⠑⠒⠲⠶⠶⠶⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣿⣾⣷⡟⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠁
⠀⠀⠀⢀⠆⠁⠀⠀⠃
⡌⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠁⢀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠈⡄⢀⢀
⠀⠀⠉⠒⠒⢩⠃⠀⠀⢉⡁⢠⡁⠁⠀⠈⢆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢯⠀⠀⠀⠈⠋⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠏⡄
⠀⠀⠀⠀⠀⠸⢌⡁⠀⠀⠸⣦⡄⠀⠂⠒⡄⠀⠀⠀⠀⠀⠘⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⣐⠀⠠⠀⠀⠀⠀⠀⡄⠒⡀⠀⢄⠀⠀⢠
⠀⠀⠀⠀⠀⠐⠑⠀⠀⠀⢀⡀⠦⠀⡝⠆⠄⠀⠀⠑⣄⠰⠐⠂⠁
⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠈⠀⢈⠠⠀⡀⢠⢠⠂⠰⠀⠀⢸⠀⢐⠀⠀⢀⠀⣠⣄⠲⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠗⠈⠀⠀⠀⠀⠀⠀⠀⢨⢥⠢⠆⠀⢅⠈⠙⠛⠘
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠀⡔⠀⠀⠀⠀⠀⢀⠐⠋⢇⣈⠇⢀⠆⠄⠀⠀⠈⡀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⠁⠈⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⢠⡁⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢸⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠤⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢠⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⡄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⢈⡁⠀⠀⠀⢸⠀⠀⡁⠀⠀⠀⣧⠀⠀⢸⢸⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡠⠊⠁⠀⢠⠀⠘⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠇⠉
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠜⠢⠄⠈⠀⠀⠀⠠⠈
⠀⠀⠆⠀⠀⠀⠀⠀⠄⠊
⣷⣿⡿⢿⠿⠿⣿⡷⣿⡿⢷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣶⣾⣿⣷⣿⣿⣿⣷⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠈⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢶⠴⠇⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡺⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⡶⠓⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣄⣤⣀⣿⡀⣀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⠛⢻⡿⢿⢟⣿⣤⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⡐⠀⠀⢰⡤⢸⡿⢿⣿⣶⣿⣿⣾⣟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠖⠠⡀⠀⠰⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣂⣼⣶⣦⣄⢠
⠀⠀⠈⠀⠀⢀⠀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣟⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠉⠁⠀⠀⠈⣯⠛
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⠛⠿⣛⠿⡿⣻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢸⡿⠿⢿⠏⣨⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠈⠃⠀⠘⠂⠉⠋⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣶⣶⣶⣶⣷⡾⠧⠀⠀⡀⠀⠀⠀⠀⠀⠀⢾⡇⣁⢠⣿
⠀⠀⠀⠀⡀⠀⠇⠀⠀⠐⠇⠐⠐⠀⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠼⠟⠛⠻⡏⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋
⠀⠀⠀⠐⠿⣷⣶⣶⣶⣶⣶⣶⣶⡾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠀⠢⠰⠐⠆⠆


⠀⠀⠀⠀⠀⠀⠐⣾⣷⣿⣿⣷⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢶⣦⠀⢠⣶⣾⣶⣄
⠀⠀⢠⣀⠀⠀⠀⠿⠛⠛⢹⡇⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣿⣽⠇⢺⣇⣤⣰⣿
⠀⠀⠾⢿⡏⣛⢗⣛⢲⡖⠚⢳⠛⣏⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠈⠙⠛⠛⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠶⠖⠀⣳⣾⠋⠰⠶⠀⠀⡆⠀⠀⠀⢀⣴⣶⣶⣄⠀⢀⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⠎⠈⠈⠳⣄⠀⠀⠀⠁⠀⠀⠀⢸⣏⡀⣀⣹⠇⢾⣋⣀⣈⣿
⠀⠀⢀⡀⠀⠀⠀⢾⣿⣿⣿⣶⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠋⠀⠈⠻⠿⠟⠋
⠀⠀⣼⣿⡖⠲⡶⠾⢦⡶⠷⢶⠖⡒⣾⣿⡄
⠀⠀⠀⠈⠉⠛⠚⠛⠚⠓⠚⠚⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠐⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⠀⠀⠀⢀⣀⣀⠀⠀⡇⠀⠀⠀⠀⠀⣧⣤⣤⠀⣿⡇⠀⣿
⠀⠀⢠⣄⣀⠀⠀⢻⣿⡿⠛⠉⠀⢀⣀⣤⠀⠀⠀⠀⢸⠀⠀⠉⠉⠁⠀⠀⠈⠉⠁⠀⠀⡇⠀⠀⠀⠀⢀⣿⣿⣿⠀⣿⡇⠀⣿
⠀⠀⠺⢿⣏⣙⣿⣹⡫⡟⣛⣹⣉⣍⣿⠿⠂⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢸⣿⣿⣿⠀⢿⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠉⠉

⠀⠀⠀⠀⣠⠴⠂⠉⠉⠛⠉⠐⠢⢄⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠲⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠐⡄
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣊⡿⠂⠄⠀⠒⠒⠈⠎⣧⢀
⠀⠀⠀⠀⠁⠒⠤⠄⠤⢴⠞⠛⠉⠉⠀⠀⠀⠀⠀⣈⠀⡌⠐⡢⠄⠀⠀⠉⠀⠈⠃⠎⡆⠀⠀⠀⢀⣀⣀⡤⠤⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⠁⠀⠀⠀⡇⠀⠀⠀⠀⡆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡐⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢤⣀⣀⣠⣴⡎⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡄⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠄⠀⠀⠀⠋⠙⠁⠈⠁⠀⠀⠀⠌⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠅⣀⢠⠀⠘⠛⠄⠀⠀⠀⠀⡠⠃⠀⠢⣀⠀⠀⠀⠀⣀⣀⡠⠀⠑⢂⠀⠀⠀⠀⠀⡇⢀⣀⠀⠤⢄⠇
⠀⠀⠀⠀⠀⠸⠠⡌⠁⣲⠂⡜⠀⠀⠀⠀⡸⡑⠁⠓⠀⠘⠳⣠⠤⢺⠁⢀⠦⡎⠀⠀⢣⠀⠀⠀⠀⡏⢉⣀⣀
⠀⠀⠀⠀⠀⠈⢗⡁⠀⡢⠀⠑⣄⠀⢀⣴⠟⡅⠀⠁⠀⠰⠆⠉⠐⠾⠀⠁⠀⠃⠄⠀⠀⢣⡀⡏⠛⠧⡜⢉⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡⠀⠀⠀⠙⡽⠃⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠘⠀⢀⢌⣵⠿⠂⢲⢹⠤⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡐⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠁⠐⠁⠀⠀⢸⠈⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠠⡀⠐⠂⠀⠀⠀⢀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⣢⣤⣀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠐⠐⠀⠀⡰⠋⠁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠒⠀⢠⠐⠒⠐⠒⠂⠒⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠄⠀⢀⣇⠀⣀⠤⢤
⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠄⣎⡄⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⡠⠀⠌⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡳⠊⠁⠀⠀⠀⠀⡎⠛⠀⠀⢠⠂⡓⡠⠊⠐⠄⠀⠀⠠⠂⠱⠉⡠⠂⠀⠀⠀⠐⠔⣊⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⡠⠐⢁
⠀⠀⠀⡀⠀⠀⠀⠺⠂⠀⠀⠐⠀⠳⠀⠘⢴⠁⠀⢀⠀⢀⠈⠀⣀⡄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠂⣁⠀⡠⠀⠀⢀⠼⠀⡀⠀⠀⠂⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠶⠀⠀⠀⠀⠌⠰⠀⠠⠠⠀⠀⠀⢄⣨⠀⠀⠀⠀⠂⢨⠀⠀⠀⠀⠀⢐⡆⠀⠀⠀⠀⠟⡌⠀⠀⢠⠁⠀⠀⠀⡔⠀⡆⠁⠌⠁⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠈⢀⢄⣀⢂⡆⠀⣀⣀⣀⣀⠀⡖⠀⠀⠀⠐⠐⠁⠀⠀⠀⠀⠀⠀⠘⠃⠨⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠔⠚⠀⠄⡀⠀⢡⠀⠀⠀⡀⠀⠁⠀⠉⠀⢐⠁⠀⡐⠀⠀⠀⠀⠀⢂⠀⠀⠄⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡌⠀⠀⠀⠀⠈⢢⢀⠄⢰⢠⠃⠈⠀⠀⠀⢀⠌⠀⠀⠀⠀⠰⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠒
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏⠀⠀⠀⠀⠀⠀⠀⡁⠀⣠⠌⣀⠠⢆⠀⠀⠄⠀⠂⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⣆⠀⠈⡠⠈⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⡁⢀⠓⢄⠀⠢⡄⠄⡀⠀⠂⢀⢼⠀⡂⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠄⠀⠀⠀⠈⠁⠀⠀⠄
⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠌⠇⠀⣗⠀⠀⡀⠔⢚⠴⠶⠀⠀⠣⠁⠀⠀⠑⠄⠇⠀⡆⠀⠂⠀⠀⠡⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠀⠀⠀⠀⠀⠀⢀⠂⠀⡰⠠⠂⠂⠀⠀⠀⠀⠰⠀⠀⢠⠀⠀⠐⠀⠀⠃⠀⠄⡀⠀⠀⠀⠀⠀⡅
⠀⢨⠀⠀⠀⠤⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠂⠄⠀⠊
⠀⠀⠉⠀⠀⠀⠒⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠇⠀⠀⡀⠀⠀⠀⠀⣠⠤⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢊⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⢰⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⢀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⡎⣱⢉⡁⣠⡀⢀⡀⠀⣀⢀⡀⡆⠀⠀⠀⠐⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠘⢖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⣀⣀⣀⣀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠭⠍⠠⠬⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠠⠄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠩⠅⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠑⠒⢶⣾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡳⣄⠀⠀⢀⣀⣀⠤⢴⣾⡍⠷⣤⣤⣾⡿⠛⢳⣦⡤⣀
⠀⠀⠀⠀⠀⠀⠀⢾⡉⠀⠀⠀⠈⠳⣞⠉⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠳⡄⠀⡀⣼⣿⣿⠶⣶⣶⠶⣶⣶⠾⣿⣿⣄⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⣀⡬⠖⠺⠿⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⡿⠟⠒⠤⡄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡞⣹⠋⡤⠀⠀⠀⠀⠈⠙⠛⠛⠒⠿⠿⠶⢉⣀⣈⡁⣀⣺⣄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠉⢻⣧⣊⡄⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢰⠏⠀⠙⠲⠚⠛⠁⠀⠈⠙⢷⣦⣄⡀⠀⠀⠀⠀⢸⠇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⡄⠀⠀⠀⠀⣀⣠⣤⣴⣶⠾⣿⣿⠿⣶⣤⣤⣤⣟⣠⣾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣶⡟⢻⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⠛⣿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠘⠛⠛⠐⠛⠛⠀⠛⠛⠂⠛⠛⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢢⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⢋⠁⢿⣿⡠⡄⠀⠀⠤⠤⠒⠂⠉⠒⠀⠶⠒⠒⠂⠀⠀⠀⣤⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⢶⠀⣤⠈⣿⣶⠀⢀⡀⠀⠉⠀⡲⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠶⠟⣤⢸⠦⣄⡤⠀⡀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⣰⣂⠄⠀⠸⠉⠁⠀⠀⠸⡏⠀⠄⠀⠀⠀⠨⠷⡚⠀⠀⠀⡆⡄⡄⡤⡄⠀⠀⢤⢠⢠⣤⣤⢠⣄⢀⢀⣀⡇⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠙⠻⠾⠀⠋⡉⠙⠂⠀⣸⠃⣾⠂⠀⠀⠀⠠⣿⡃⠀⢀⡆⣟⢇⢿⣏⡇⡆⢀⠀⠀⠀⠀⠀⠀⠈⠈⠈⢹⠁⣀⠤⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢷⣦⣄⣠⠀⡀⠸⠤⠗⢠⣿⣿⡁⠀⠀⠀⠁⡇⠵⠛⠏⠾⠜⠀⣀⠀⡀⢀⠏⢠⣞⠋⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠏⠚⠛⠒⡈⠉⢉⠉⡛⡟⠧⢥⣟⣂⡇⠇⠇⣶⢦⠆⡼⠁⠼⢀⠎⢠⣴⡙⠀⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣤⢸⢧⠆⠥⠳⠸⠘⢇⣷⠳⣠⡆⢌⠑⠲⣄⠀⠀⡬⠀⡦⢡⠞⠐⢦⡤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣡⣤⣦⠀⠀⠀⢠⣾⣯⣴⣦⣤⣌⡄⢤⠀⣄⢀⠀⢬⡤⠣⠳⠄⠒⡐⡂⢠⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⡀⠀⠀⡸⠛⠉⠉⠉⠉⠛⠷⢦⣬⡍⢹⡃⣾⢂⠶⠀⢓⡟⠛⠓⢸⡀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠿⠍⠆⠀⠀⠙⠂⠸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣤⡶⠃⠀⠀⢪⠇⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⢸⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⢀⠇⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣛⣿⣁⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣻⡟⠁⠀⢀⠜⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠁⠀⢰⣿⣶⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠴⠍⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⢀⣀⠶⠤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣀⣀⠤⠊⠉⠀⠀⣰⣛⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⢐⣥⣶⠿⠛⠛⠛⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠋⡩⠤⡀⠀⢀⠤⠀⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠀⠴⠖⠄⠀⠠⠶⠲⠀⣬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢀⠀⠂⠐⠂⢀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⠈⠛⣶⠋⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠄⠐⠖⣰⠙⡀⠐⠠⠀⠀⠀⡘⡶⠤⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠁⠁⠀⢀⣿⠘⡆⠐⠤⡀⠢⢞⠄⣿⠀⠈⠁⢤⠑⠐⠢⡄
⠀⠀⠀⣀⣠⠴⠯⠀⠠⠀⠀⠈⠀⠀⢸⡟⠀⠁⠃⠀⠈⠒⢈⠠⡿⠀⠀⠀⡀⠀⠀⠀⠀⠓⢀⡀
⠀⡴⠋⠉⠛⠓⠂⠀⠀⠀⠀⠀⡝⠀⠘⡇⠀⠐⢰⠘⠀⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠐⣣⠞⠓⠙⠒⣀⠀⠀⡤⢾⠉⠁⠀⢰⡇⠀⠀⠐⠀⠢⠀⠀⠀⣿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡤⣀
⠀⡏⠀⠀⠀⠀⠈⣇⢠⠃⠀⢧⠁⠀⢸⡇⠀⠄⠖⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠁⡤⢄⠀⠀⡀⠀⠀⠀⠀⠀⢨
⢀⡇⠀⢀⠀⠀⠀⠘⠣⡀⠀⢸⠀⠀⠜⢀⠓⠢⢧⡅⢀⣀⣤⡾⠁⠀⠀⠀⠀⡄⠀⠀⢹⡂⢠⠞⠀⠀⠀⠀⠸
⠀⠑⠒⠤⣀⠀⠀⠀⠀⠈⠢⢞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⠝⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠑⠀⣀⡀⠀⠀⠀⠉⠱⡀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠔⠁⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣲⢠⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀⠀⢀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠰⠐⠀⠀⠀⡀⡀⣀⡀⡟⢦⣀⠀⠠⠀⠁⠀⠀⠆⠀⠀⠁
⠀⠠⠤⠤⠤⠄⢀⣠⣄⠬⠀⠀⠀⠀⠀⠀⠈⠃⢿⡙⢿⠃⠄⠉⢱⡄⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⣿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠰⠶⠧⢄⣞⣁⠚⢚⢉⣀⡀⢀⣨⣅⣈⢛⠧⠀⠄⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠘⢺⠁⠁⡰⡅⠀⠐⠲⠶⠶⠖⠒⠀⠘⠙⠶⡀⠀⠀⣉⠿⣀⣀⣀⡜⠰⠤⠶
⠀⠀⠀⠀⠀⠐⠦⣌⣧⡀⠀⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⡤⠈⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠸⡻⢿⣆⡧⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠐⠋⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡷⢿⡿⣤⡀⠀⠢⠀⢀⡀⢀⢀⡀⠀⡀⡠⠐⠀⣀⣼⠷⠁⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣩⡳⢄⠑⠚⣀⣀⡀⣀⣠⠌⠁⠰⠚⠉⢉⠜⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⠀⠀⠀⠀⠐⠌⢀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢀⠀⠀⠀⠈⠂⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠂⠁⠀⠀⠀⠠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⡄⢀⡟⠀⠂⠀⠉⠣⢀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠁⠀⠱⠂⠀⠀⠀⠀⠀⢠⣀⠑⢤⠀⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠤⡀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠉⢅⠂⠀⠀⠀⠀⢀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠰⡄⠀⠀⠂⠸⡆⠠⢀⠀⠀⠀⢀⡄⠤⠀⡀⠤⠹⠂
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⠀⠀⠑⣤⡄⠀⠀⣄⣀⡋⠓
⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⢀⠀⠔⠈⠘⢃⠀⠀⠈⠉⠁⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠘⠀⠀⠀⠂
⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆
⠀⠂⠀⠈⠁⠀⠁⠀⠀⢄⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠄⠒⠂⠀⡀
⡀⠀⠀⠀⠀⠐⠠⢀⢠⣞⡣⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠈⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡞⣇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⣀⣡⠛⠈⠀⠀⠢⢀⠀⠀⢆
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⠄⠈⢀⢠⠄⢻⡀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⣀⣀⢀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢑⣀⣎⣅⣳⡠⠧⠤⠰⠖⢒⢘⡻⠛⠛⠛⠻⢄⡉⠑⠀⡉⠁⠠⡀⠀⠐⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠁⠀⠀⠀⠀⠀⠴⠋⠉⠐⠒⠀⢤⣀⠀⠝⠲⠀⠄⡐⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡀⢐⠂⠂⢄⠀⠀⠀⠂⠈⠓⠀⠄⠉⠉⠀⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⣂⠀⠀⡂⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣤⣄⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣖⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠙⠀⢉⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⡒⠒⡁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠈⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠉⠧⠈⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡞⠋⠻⣶⡶⢞⠿⡕⢦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⡇⢰⣯⣝⣛⣫⣄⡇⠘⡆⠈⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⡇⢠⣍⡍⣭⢩⡍⣅⢠⡸⡄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⣸⠃⣸⢹⡇⣿⢸⡇⣿⢸⣇⣷⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⣿⢯⡆⣿⢸⣿⣿⢸⡇⣿⠊⠀⢉⡗⡄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠉⠛⠻⣾⠃⣾⢠⡟⣿⢹⡇⢸⡧⠃⠀⢀⢞⡼⠛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠙⣀⡀⠀⠈⠑⠻⢼⣇⣿⣸⡇⢼⣁⡀⢠⢏⣾⣧⣤⣿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣦⣍⣩⣍⣛⣲⣒⡤⠀⠀⠀⠀⠈⣿⡷⠛⠩⢭⡲⢤⣀⣨⣉⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠻⢽⣦⣉⣿⠙⠿⣿⣿⣿⣏⣄⣤⣾⣿⣧⠀⠂⢶⠄⠀⠙⣿⠟⢛⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠲⣦⠻⢷⣦⣴⣿⣿⣿⣟⠿⣟⡻⢷⣦⣄⣀⣈⣴⣷⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣙⠛⢦⣬⡿⣿⣿⣭⣲⠭⣓⣯⣗⢝⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢯⣿⣌⡛⠿⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡊⢍⠉⡩⠷⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠁⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠔⠓⠒⠒⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⢖⣦⠄⠀⣤⠴⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⡁⠀⠁⠀⠘⠉⠉⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠐⣉⡁⠐⠛⡁⠀⠾⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠐⠒⠀⠀⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢔⢹⡄⢈⠓⢤⣤⣤⣾⢿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠊⠁⢸⠃⠀⣷⠀⠑⢄⣀⠜⠁⢸⡟⢹⠉⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡁⠀⠀⠀⠀⠏⢤⠀⢹⡀⡴⢻⠋⢂⣠⠋⠁⢈⠆⠀⠀⠈⡝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⡸⠇⠀⣀⠀⠀⠰⡄⠀⠀⢧⠀⣼⡇⠀⡆⠀⠖⣺⠀⡆⠀⣸⣴⢳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⡈⢻⠀⣘⠟⠓⠑⢎⡽⢦⠀⠘⡆⣿⣧⢰⠀⠀⡴⢹⠀⠁⠰⠏⠇⢸⡟⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠱⡀⠀⠹⠠⠠⠔⣈⠀⢀⡉⣉⣉⠉⠁⢉⡀⠀⠀⠘⡇⠀⣠⠜⠠⣿⣵⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠀⠀⠀⠉⣀⠀⡝⢄⢈⣠⠃⠀⢀⠀⠀⠙⠙⠀⠀⣰⡴⠀⢿⡀⣿⠀⢀⡿⠃⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⣨⣯⠭⠿⠒⠋⠉⠀⠀⡇⠀⣠⣟⠙⡄⣼⠀⠀⠀⠀⢠⡟⡰⣧⠀⣸⣏⢸⡄⠋⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣉⣶⠃⢆⠰⠀⠀⠀⠀⠀⠀⣏⡔⣡⠞⠁⢻⣸⢳⡄⠃⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⢯⡟⠀⠈⢆⢣⢀⠀⣀⠀⠠⢋⠀⠁⠀⠀⠘⠿⠎⢃⠠⣀⣀⣀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠤⣚⣯⡴⠞⠋⢡⣸⣡⠎⣀⠤⠖⠋⢦⢣⠀⠀⠉⠓⠛⢰⡆⠀⠀⣠⢶⡺⠋⠛⣒⠒⠂⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠉⠀⠀⠀⠀⢸⣿⢃⡜⠁⠀⠀⠀⠀⠹⣧⠀⠀⡔⢋⡴⢾⡇⢠⢸⣍⠀⠀⠀⠈⢁⣴⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣠⣤⣤⣄⣀⣾⢿⠏⠀⠀⠀⡀⠀⠀⠀⠀⢀⡎⣰⣿⣜⣵⡶⣣⢦⠞⣷⠀⣠⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⢀⠀⠀⠀⡠⠀⡐⠁⠀⠀⠚⢉⠀⠤⠀⢀⡴⣫⣾⣿⣿⣿⣿⣿⣧⣵⣿⠟⢻⣿⣿⣷⡒
⠀⠀⠀⣀⡴⠚⠉⠐⢁⠔⠁⠀⣐⠼⠁⡴⠳⠤⠦⠤⣀⠀⠀⠀⡠⢪⣾⣟⣿⠿⢿⣿⣿⠭⠙⢛⠉⠀⠀⠹⣿⣿⣿⣆
⣠⡴⢋⣁⣀⣀⣠⣂⣁⣈⣀⡘⠁⣠⠊⠀⠀⠀⢠⠆⠀⠙⠒⠢⠂⠛⠿⠛⠛⠋⢩⠀⠀⠀⠀⠀⢣⠰⠄⠀⠈⢻⣿⠏
⣿⣿⣿⣿⡿⣿⡿⣭⣭⣭⣭⣭⣭⣯⣭⣭⣭⣽⣯⣽⣽⣿⣿⣿⣿⣿⣿⣖⣒⣒⣺⣗⣂⣐⠶⠶⢾⠷⠶⠶⠶⠶⡷
⠙⠀⠀⠀⠀⠘⠈⠩⠭⠤⠤⠤⠼⢧⣤⣤⣤⣼⣧⣤⣤⣤⣤⣭⣭⣭⣽⣭⣭⣭⣽⣭⣭⣭⣭⣭⣽⣿⣿⣿⣀⣀⠃
⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⢿⣿⣿⣿⣿⣿⠁⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣿⣿⣿⣿⣿⡿⠀⠀⡿⠉⢟⣿⠿⣶⣦⣄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠸⠟⠛⠛⠟⠛⠛⠛⠛⠁⠀⠀⢰⣿⣿⣿⣿⣿⣧⣬⣟⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠿⠿⠾⠛⠒⠛⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠐⠂⠀⠀⠇⠂⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠝⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠰⣀⢀⡆
⠀⠀⠀⠀⠠⠀⢀⡀⠐⠙⠓⠺⠗⠀⠀⠠⠨⢙⠀⡄⢤⡀⡄⠀⠠⠐⢰⠁⠀⠀⠀⠁⠲⡞
⠀⠀⠀⠀⠀⠶⣖⠀⠈⠁⠈⠉⡄⢝⠀⡅⡀⠀⠔⡀⠀⢀⠀⠀⠀⠀⡇⠀⠇⠈⠰⠅⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⠒⠐⡙⢂⣀⠀⣀⣀⠀⠱⠘⠜⠁⠃⠓⢀⢡⠀⣀⡐⡃⡀⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈⡌⣈⢡⢩⣡⠀⠀⠀⣀⡀⠲⠚⠈⣼⣄⠋⠃⠱⠁⢇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠷⡀⠁⠁⢈⣂⠂⣙⠁⠀⣀⢀⡀⢴⠾⣳⡄⠰⣂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠉⠉⠙⠛⠳⠿⠤⠥⠒⠋⠻⣿⣷⣌⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡘⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢃⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠋⠛⠉⠀⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠁⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠑⢄
⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⢰⠃⠀⠀⠀⠀⠀⠀⢃
⢀⡤⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠁
⠑⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠸⡄⢄
⠀⠀⠈⠻⠤⡤⠼⣛⡆⠀⡀⠼⠗⠂⢀⡐⠓⠊⠁⠉⠳⡄
⠀⠀⠀⠀⠀⠀⢀⡟⠂⠀⠐⢀⠳⣶⠀⠛⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡼⡆
⠀⠀⠀⠀⠀⠀⠈⡖⠀⡀⠐⠃⠀⠀⡀⠀⠀⠀⠀⠠⡎⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠳⢌⣁⠀⠀⠀⠈⣿⣶⡖⠒⠚⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⡐⠂⠤⢀⠀⠀⠀⠀⣀⡔⠓⠄⡀⠀⠀⠀⠀⡸⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢾⠀⠀⠁⠀⠀⠀⠈⠉⠈⢻⣀⠈⢆⠀⠈⠢⡀⠀⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠃⠘⠠⠀⠀⠀⠀⡴⡘⣗⠂⢾⠹⠈⡟⠀⠀⢀⠈⢦⠤⠛⠹⠙⠣⡀
⠀⠀⠀⠀⠀⠀⢠⢇⠀⠀⠀⠀⠀⠈⠁⠀⢉⡤⠄⢀⡇⢰⠀⡔⠁⡴⠁⠀⠀⢸⠀⢐⢞⠀⠀⠀⡀⠀⣠⡄⠑⠆⢠⡀
⠀⠀⠀⠀⠀⠀⠘⠀⠳⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⢸⠇⠚⠋⠁⠀⠀⠀⠀⠀⠸⠀⢀⢻⠀⡴⣂⢉⠙⡅⠘⠳⠾⠴⠩⡆
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠑⠀⠀⠀⡜⠁⣠⠞⠁⠈⠀⠀⠀⠀⠀⠀⡴⢢⠀⠰⡆⠀⠋⡝⡊⠡⠜⠈⢵⠀⠀⠀⠀⠀⠀⠑⡆
⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠙⣅⠀⣇⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠘⢤⠶⠁⠀⡔⢁⠇⠀⠀⠀⡆⢆⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠠⡇⠈⠀⠀⠁⠀⠀⠀⠲⡁⠀⠀⠀⠀⠀⠀⠀⡌⠰⠁⠀⠀⠀⠀⠰⢸⠀⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⣟⠀⠈⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡔⠀⠀⠀⡉⠂⠀⠀⠀⠀⠈⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠰
⠀⠀⠀⠀⠀⢹⡆⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡇⠀⠀⠘⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠗⠀⡸
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠄⠚⠉⠀⠀⡇⠀⠀⠀⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠘⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠞⠀⠀⠀⢹⠳⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⣸⠘⠀⠀⢰⡆⠞⡇
⠀⠀⠀⠀⠀⠀⡇⠀⢤⠀⠀⡀⠀⠀⠀⠀⣀⠠⠔⠊⠀⢀⡇⠀⠀⠀⠀⠈⣸⠀⠀⢣⠀⠀⠀⠀⢸⣇⠀⠀⠀⡇⢸⢰⠀⠀⠐⡁⠃⡇
⠀⠀⠀⠀⠀⠀⣵⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠟⠛⠒⠠⣀⠀⠀⢿⡆⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⢀⡇⠘⠃
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡀⠀⠀⠀⣼⠀⠀⡠⠚⠁⠀⠀⠀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⡠⠂⠈⠀⠀⠀⠀⠈⠐⢠⡀⠞⠁⠉⠃⠠⠀⠀⠀⠤⠐⠊
⠀⠀⠐⢇⠀⠀⠀⠀⠀⠀⠔⠊⠁
⠆
⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠈⠈⠐⠂⠀⠀⠁⠀⠦⠀⠆⠀⠀⠀⠆⠐⠀⠀⠀⠀⠀⠂⠐⠀⠒⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⠛⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⠓⠶⠲⣄
⠀⠀⠀⠀⠀⠀⢀⡔⢻⣌⣤⣁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⠟⠥⣄⣺⠁
⠀⠀⠀⠀⠀⠀⢈⡆⠘⠿⣿⠿⡇⠑⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠉⡦⠀⠀⠀⢨⣁⡉⣸⡋
⠀⠀⠀⠀⣀⣔⣃⠤⢼⠂⠶⠐⢿⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠇⠀⠀⢀⣸⣿⣽⣿⢇
⠀⠀⠀⡾⠉⢀⣧⣤⡰⠀⠀⠀⢸⣃⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣸⠀⠀⢰⠟⠑⣿⠋⠱⠟⠙
⠀⠀⠀⠛⠞⠋⠀⣿⠁⠀⠀⠀⠺⠀⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠠⣀⢿⠀⠀⠉⠈⢸⡀
⠀⠀⠀⠀⠀⠀⠐⠛⠒⠒⡒⣰⠆⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠍⠙⠷⣾⠀⠀⠀⠀⠀⠇
⠀⠀⠀⡠⣶⡷⣖⣴⠋⠛⣀⣀⠔⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠘⠀⣠⠆
⠀⠀⠀⠻⠟⠛⠛⠁⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢙⡶⠂⢙⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠶⠶⠶⠒⠠⠔⠋⠈
⠀⠀⠀⠀⠀⠀⠀⡜⠉⡉⠉⠉⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡤⠄⠠⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⢴⡃
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠁⡘⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⣈⣸
⠀⠀⠀⠀⠀⠀⣀⣠⡗⢌⣡⣾⣄⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢲⡿⣿⣿⡿⢷⠒⢦
⠀⠀⠀⠀⠔⢉⠀⡏⠢⠽⡻⠕⢹⢸⠑⢢⠀⡜⢀⠂⠀⠀⠀⠀⠀⠀⢀⡎⠀⣼⢇⣀⣀⣀⠽⡆⠀⢧
⠀⠀⠀⡸⠀⢸⣆⡇⠀⠀⡇⠀⡄⢸⠀⡤⠋⢀⠎⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⢈⡄
⠀⠀⠀⡇⢺⣉⡉⠙⠲⣤⣤⣞⡡⠾⣾⣥⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⢺⡇⠐⠀⠀⠀⠀⣻⠶⠚⡇
⠀⠀⠀⣧⠊⢰⠋⠈⠉⢀⣀⣠⣄⣠⠼⡷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⡠⣇⠀⠀⠀⠀⠀⢸⢄⣠⠁
⠀⠀⠀⠘⠶⣾⣶⡶⠛⠉⠀⠙⠞⢳⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣇⢨⡿⢿⣿⣿⡏⣁⡴⡃
⠀⠀⠀⠀⠀⢸⣏⠀⠀⠐⠂⠀⢀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⢿⣦⣈⣉⣛⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠛⠃
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣟⣛

⠀⠀⠀⠀⠀⠀⢀⣠⢀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢀⡌⠁⠀⠀⣼⡏⠁⠀⠉⠙⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⡴⠋⠀⠈⠕⠠⠤⠤⣀⣀⠀⠀⢀⠬⣖⠎⠙⠲⢦⣤⣤⣤⣤⣤⣤⡤⠶⠶⠞⠛⠋⠉⠉⠛⠶⣄
⠀⠀⠀⣤⣥⠖⠒⠃⠂⠀⠀⣑⠂⠀⢐⠺⡖⠁⠀⠸⠽⠭⠇⠀⠀⠀⠀⠘⠒⠎⠚⠋⠃⠀⠀⣴⢲⠄⠀⣙⠆
⠀⠀⠀⠈⠉⠙⠒⠗⢮⠁⠚⠁⠀⠠⣝⠫⠀⠀⠀⠒⠲⠶⠀⢀⠈⣋⢀⠊⠂⠰⠆⠓⠙⠀⠀⠶⠫⠀⠀⣾⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢦⡌⠁⠀⠀⠀⣞⣶⡒⠀⠸⢉⠉⢉⡙⠘⠛⠙⠛⠓⠀⢠⡷⣊⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣤⢠⢄⣤⢠⢌⡀⠀⠀⠀⡀⠂⠀⠀⠀⠁⠀⠙⠓⠚⠓⠀⣴⣬⡇⠀⢀⡏⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠛⠉⠉⠈⠉⠈⠘⠐⢀⠰⡽⠈⢡⠆⣆⢠⢤⢠⠄⣀⠀⠀⠀⠀⠀⠁⠀⢺⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⣀⣄⣀⣀⣀⠊⠫⠉⠀⠀⣀⠀⠀⠀⣀⣩⡶⠛⢦⠻⠻⡘⠞⠟⠣⣼⠁⢮⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠛⡌⠈⠉⢠⡶⠿⠿⠟⠛⠛⠉⠛⠉⠀⠀⠀⠈⢳⡄⢰⡀⠀⠐⣿⡀⠀⠱⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢸⣧⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠹⣦⠀⢸⡇⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⢘⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⠇⡆⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⢠⠃⣿
⠀⠀⠀⠀⠀⠀⣄⣤⣤⣤⣶⣶⣮⣴⡷⢇⡼⢷⣶⡶⠴⠆⠀⠀⠀⠀⡀⣀⣠⣤⣤⣴⣶⣾⠁⣼⡾⢀⣷⡶⡶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⡟⠋⠉⢻⠀⠶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠿⠿⣦
⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⣿⣿⣿⣿⣿⣿⠏⠛⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣄⣾⣿
⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠻⠀⠃⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡾⠛⠉⠉⢹⡃⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠟⠁
⠀⠀⠀⠀⠸⣿⣷⣶⣶⣶⣤⣤⣶⣶⣶⣶⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠆⠰⠄⠴⠀⠶⠰
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⢿⡆⠀⣴⠿⠿⠿⠿⣆
⠀⠀⠀⣤⣀⠀⠀⠀⢸⠟⠉⠉⠹⡏⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣉⣽⣿⡟⠀⣿⣦⣤⣰⣿⡟
⠀⠀⠠⣿⣿⡏⢻⣷⡚⡳⣒⡶⠾⠛⡞⢻⡛⣿⣿⡧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠀⠀⠈⠻⠿⠿⠋
⠀⠀⠀⠀⠉⠙⠛⠒⠓⠛⠺⠓⠒⠓⠓⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⣀⠙⢦⣀⣴⠟⢁⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⠉⠁⢀⠴⠿⢯⡀⠉⠉⠁⠀⣸⠀⠀⠀⠀⠀⣼⡿⠿⠿⢿⣆⠀⣼⡿⠿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣄⣤⣼⡟⠀⣿⣤⣤⣤⣼⡟
⠀⠀⠀⣀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣷⡂⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠋⠀⠀⠈⠛⠻⠛⠋
⠀⠀⢀⣿⣷⡖⠶⣶⠴⢷⠤⣦⡧⠤⡶⠶⠶⣾⣿⣇
⠀⠀⠀⠈⠛⠓⠾⠥⠧⠷⢽⡧⠦⠦⠷⠾⠗⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠲⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⢰⡆⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠁⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⡇⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠠⠦⠄⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⡇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠘⡄⠀⠀⠀⠀⠀⢸⣧⣤⣤⡀⢸⣿⡇⠀⢸⡇
⠀⠀⠀⣀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠟⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠛⠛⠃⠀⠀⠀⠸⠛⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⡇⠀⢸⠇
⠀⠀⢀⣿⣷⡖⢶⣶⠤⢽⠿⣭⣤⠤⡴⠶⠖⣾⢿⣇⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠘⣿⡇⠀⢸
⠀⠀⠀⠈⠛⠷⠾⠭⠧⠷⣭⣧⣤⠦⠷⠾⠷⠛⠋⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠘⠇⠀⠈
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠰⠖⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠂⠀⢶⡄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠰⠾⡿⢁
⠀⠀⠰⠆⣶⣤⣄⡴⠄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠴⠤⠤⣄⣽⡿⠛⠃⠀⠐⠰⢦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠓⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢒⠀⠀⠀⠀⠀⢀⣤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢹⡁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⡀
⠀⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠈⠳⣔⠤⣀⠀⡀⠀⠀⠀⠀⠀⢀⠾⠟⠛⡄⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠸⠋⠀⢀⠀⠀⠀⠀⠀⠀⠰⣄⢀⡉⠲⠶⠶⠚⠀⠀⣀⠰⠊⠁⠀⠀⠁⠠⠊
⠀⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠀⠀⠀⠀⠀⣠⣄⣀⡴⠐⠋⠁⠀⢀⡀⣠⠰⠟⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠉
⠀⢀⠀⠀⢀⣼⣧⣠⣖⣀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠤⠂⠁⠈⢁⣀⠀⣸⠶⣦⠌⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢑⡻⠶⣤⡀
⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠄⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣩⠔⠊⢁⠈⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠁⡠⠊⠀⡀⠔⠒⢦
⠀⠀⠀⠛⠤⢤⡤⠤⠤⠿⠟⠶⠤⣤⣤⡴⠎⠉⠱⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⣿⣷⡤⠺⣤⡀⠀⠀⠀⠀⠊⠀⠀⢀⠊⠀⠰⢊⡤⠂⢈⣩⡀
⠸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⡏⠀⠀⠀⠀⠀⠀⠰⢤⣼⣿⣿⣹⠃⢁⠘⠻⣶⠟⢥⣿⡀⣀⣠⠁⡠⢊⠴⠋⠀⠀⠈⠐⠶⣦⡄⠒
⠀⠘⢦⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠂⢠⣤⣜⣲⣀⣠⣌⠿⡾⠧⣀⣸⣦⡴⠠⣿⠛⠿⠾⠶⠇⣴⡶⠶⠶⠞⠂⠀⠉⢓⠀⠁
⠀⠀⠀⠉⠛⠛⢻⣇⣀⣀⠀⣀⣀⣼⠟⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠉⠀⠠⠤⠬⠤⠄⠐⠈⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⣤⠦⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠛⠉⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣪⡤⠗⠋⠺⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠄⢀⠊⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠔⠁⠀⢄⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⢹⣤⡀⠀⠀⠀⠀⠀⣀⣴⡽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⠣⢦⡀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠱⡀⠀⠀⠒⢠⡶
⠀⠀⠀⠑⠿⣗⠶⠤⢒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⢦⡄⠀⠀⠀⠀⢨⡄⢀⡀⠠⠀⠀⣠⣴⣿⣧⣤⠊
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⡀⢀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠤⠤⠀⠙⠳⠦⡤⠦⡀⠤⡀⢀⣠⣐⣫⡴⣛⣡⢤⠄⣷⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⣀⣉⣐⣋⣙⣉⣀⣉⠁⠀⠁
⠀⠀⠀⠀⠀⢠⠀⠀⠒⢤⠜⢀⠀⠀⠀⠀⠀⠀⠀⡔⢶⣶⣄⠐⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠸⣷⣤⣀⡀⠀⠉⠉⠀⠒⠐⠂⠤⠀⠀⠑⠀⠋⢠⠇⣾⠀⠀⠀⠀⠀⠀⢰⣇⡀⠀⠀⠒⠤⠀⠀⠀⠀⠂⠀⠀⠀⠙⠢⣀⠀⠐⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠏⠛⠒⠤⣀⠀⠠⠄⠀⠀⠠⠄⠔⠐⣫⣾⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡌⠀⠀⠐⠶⠀⠀⢀⠰⠂⠄⡀⠈⠓⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⡀⠀⠀⠀⠠⣤⣤⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣶⣤⣄⣠⣴⡯⠄⠒⠀⠃⠀⠀⠒⠈⣙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣶⡶⠦⠴⠶⠶⠀⠀⠰⠒⠟⠛⠉
⠀⠀⠁
⠀⠐⠒⠃

⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⣾⣿⣿⣿⣿⡿⠉⠉⠉⠉⣹⣿⣿⣿⡏⠉⠉⠉⠉⣿⣿⣿⣿⠉⠉⠉⠉⢻⣿⣿⣿⣏⠉⠉⠉⠙⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⢰⣿⣿⣿⣿⡀⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠀⠘⣿⣿⣿⣿⡇
⠀⠀⣰⣿⣿⣿⡿⠁⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠈⢿⣿⣿⣿⣆
⢀⣼⣿⣿⣿⡿⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧
⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠘⠻⠿⣿⣿⣿⠻⠿⠿⠋⠀⠛⠿⠿⠟⠁⠘⠻⠿⠿⠋⠈⠛⠿⠿⠛⠁⠙⠿⠿⠟⠋⠈⠛⠿⠟⠋⠀⠙⠿⠿⢻⣿⣿⡿⠿⠛
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀
⠀⠀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠙⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠉⠉⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠒⠶⢶⠶⠶⠶⠶⠶⢶⡶⠦⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡄
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣧⣤⣤⣤⣤⣿⣤⣤⣤⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢿⠀⠀⠀⢠⡇⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣸⣄⣀⣀⣸⣅⣀⣀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⣉⣉⣉⣉⢉⣉⢉⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠛⠛⣏⠉⠉⣹⠟⠙⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢀⡿⠀⠀⢻⣀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢰⣷⡇⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢸⢸⣿⡇⠀⢠⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡥⠀⠀⠘⠀⢿⡇⠀⢸⣧⡄⠙⢷⣄
⠀⠀⠀⠀⠰⡀⠀⣠⠴⠊⠉⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣥⢸⣿⡆⠀⠀⠀⢸⡇⢠⢸⣿⣿⣠⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠱⣾⡅⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢀⣠⠴⠋⢠⢸⡿⢸⣿⠀⠀⠀⢠⠀⠀⣸⢸⣿⡿⠟⣠⢞⠝⠁
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠠⡄⠻⣿⣏⢹⡄⠀⢸⢸⡇⣸⣿⠀⠀⠀⣼⠀⠀⣿⢸⠏⣡⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⠀⢀⠦⠐⣄⠀⠹⣿⣦⣽⣆⠏⣸⡇⡿⡏⠀⠀⠀⣿⠀⠀⠋⣠⣞⠕⠋⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣿⡀⠆⢨⡃⠈⢧⡀⠘⣆⠀⣿⠁⠀⠘⣆⠛⡇⠃⡇⠀⠀⠀⠏⣀⣴⡿⠛⠁⣀⣀⣏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⡀⠹⣄⠈⣷⣤⠼⠛⠁⠀⠀⠀⠈⢧⠀⠀⠃⠀⣠⣴⡾⢛⣉⡴⠚⣩⠄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⠶⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣶⠿⠛⠁⠀⠈⡿⠀⠀⠃⠀⠀⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣸⠁⠀⠀⢾⠀⠀⠀⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠷⠤⠤⠿⣾⣆⠀⢰⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠲⠶⠶⠖⠛⠋⠉⢉⣙⣛⡛⠛⢛⣛⣩⣤⠀⢠⣤⣶⣶⡖⢀⣽⢀⣸⣧⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣉⣀⠿⢿⣿⣦⡀⠀⢿⣿⣷⣌⡛⢿⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⣫⣶⣿⣿⣀⡾⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡅⠘⠿⠿⣿⣷⣶⣿⣿⣶⡀⢻⣿⣿⣿⣮⣿⣿⣿⣿⠏⣠⣬⣭⣿⣿⣿⣿⣿⣿⠿⠃⣼⡿
⠀⠀⠀⠀⠀⠀⢶⣿⡿⠛⠲⠶⠦⣬⣙⠻⠿⣿⣿⣦⡙⠛⣩⣥⣤⣭⣭⡁⠘⣋⣭⣤⣤⣤⣤⡤⠀⢀⣠⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠠⠆⢠⢉⣛⠶⣤⣉⠙⠿⢦⣬⣭⣍⣛⣛⣡⣾⣿⠿⠛⢛⣉⣡⣴⠶⣻⣿⢣⡿⠁⠂
⠀⠀⠀⠀⠀⠀⠈⠀⢛⠻⠶⠦⣤⣩⣸⣹⡵⡀⠙⠻⠶⢤⣤⣭⣉⣉⣭⡭⠴⠶⠒⠛⠋⢉⣡⢰⠮⢇⡾⠛⢡⡀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣤⡐⠒⠤⠉⠛⠷⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣴⠴⡚⠉⣄⠃⠀⠬⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠂⠬⠐⠊⣉⠛⠶⢦⣤⣤⣤⣤⣤⡤⠤⠶⠖⠛⠉⠁⠒⠈⠉⣀⠀⠁⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠠⠄⠀⠐⠒⠀⠈⣁⡀⠀⠢⠄⡁⡠⠀⡁⠄⣒⡀⢀⠌⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣛⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⡟⢙⣍⠶⠟⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣀⢠⠄⣶⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠛⠙⠀⠁⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠰⠀⢀⠡⡀⢷⢫⡅⣠⢀⠤⢀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣥⣤⣄⣔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⡄⢃⠰⢄⠐⠀⠘⠁⠉⠛⠂⠛⣂⣠⡀⢀⢆⣤⣋⢰⣿⢟⣋⣉⣉⠑⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢩⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠙⠛⣦⣿⣿⣝⠛⠛⢷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⢊⣁⡀⠀⡀⠀⠀⠂⠀⠀⠀⠀⢰⠀⠉⠀⠀⠀⢠⠟⠿⢿⡇⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠘⣀⠁⣘⢦⣄⠈⠀⠀⠀⠀⢘⣀⠶⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡘⠁⢠⣉⡛⠛⠾⠿⠟⣋⡁⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣋⠛⠇⡷⠟⠏⡫⠃⣛⣓⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠲⣶⣤⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠈⠙⠛⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣿⣽⣿⣿⣇⠑⠀⣀⠀⣀⠀⣀⣽⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⠿⠿⠟⠻⠿⠋⠉⠉⠉⠙⠒⠒⠊⠁⠒


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

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⢀⠉⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠄⠀⠀⠀⠀⠠⠠⠶⠀⠂
⠀⠀⠀⢇⡁⠀⠀⠀⠀⠀⣄⣀⡀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡄⣠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣲⠀⢀⠀⡄⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠮⠦⠀⠀⠘⠁⠀⢀⠆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠰⣶⠁⢀⡀⠀⠙⠀⠀⠀⠀⣸⢀⠀⠀⠀⠀⠀⢹⠉⠉⠁⠀⢈⠞⠉
⠀⠀⢈⠙⠀⠀⠀⢀⠤⠤⠀⠀⠀⠀⠀⠈⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠁⠇⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠁⠀⢈⣀⡀⡐⠦⣀⡀⠀⠀⠈⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⡖⠶⠒⠚⠉⠀⠀⠀⠀⠖⠀⠀⠀⡐⠂⠉⠀⢀⠀⠀⠀⡀⢀⡄
⠀⠀⠀⠄⠠⠀⣀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠁⠀⠀⢣⡤⢀⠄⣎⡃⠀⠀⠁⠉⡀
⠀⠀⠐⠀⠈⠁⠘⠛⠍⠉⠁⠉⠋⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠉⠓⠖⠋
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠆⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠃⠀⠀⠀⠰⠈⠀⠀⡳⢀
⠀⠀⠀⠀⠅⠈⠉⠉⠉⢩⠾⠍⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠈⢥⠀⠀⠂⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⠠⣄⠄⡔⢘⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠆⢀⢁⠠⠂⠄⠀⠀⠀⠀⠀⠀⠁⠀⠂⠈⠀⠀⠀⠉⠉⠈
⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⡄⠀⢀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⣆⡠⠔⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣴⡶⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠢⠈⠶⠀⠀⠙⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠤⡤⡀⠀⠀⠀⠘⠀⠀⠘⠁⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠂⠀⢀⡘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠓⡶⢈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠂
⠀⠀⠀⠠⠠⠔⠀⠀⠀⠀⠀⠀⢄⡤⠀⠀⠀⠉⠀⢰⠇⠀⠀⠀⠀⠠⠀⠀⠀⠘⠳⣀⠈⠁⢄⣠⣀⣀⣀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠰⢢⠤⠀⠀⠀⡀⢀⡔⠆⠀⠀⠈⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠠⠀⠒⣠⠤⠆
⠀⠀⠀⠀⠀⠀⠚⠌⠀⠠⡀⢠⡼⡆⠀⠀⠀⠀⠀⠀⣿⠫⠀⠒⠂⠧⣹⡋⠀⠀⠀⠀⠀⠀⠀⠰⠔⠛⠓⠀⠀⠀⠸⢗⠻⣦⠠⠶⠀⠈⠟
⠀⠀⢠⠶⣶⠠⠄⠢⣶⣘⣷⠶⡞⢁⡄⠀⠀⠀⠀⠀⠉⠀⠀⠦⠤⠐⣽⠔⠈⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠇⠀⠚⠉
⠀⠀⠀⠚⠛⠨⡍⢂⠠⣯⠠⢠⠴⠛⠀⠀⠀⠀⣊⣟⡃⠀⣀⡐⣆⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢠⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⣿⠀⠀⡉⠀⢁⢿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈

⠀⠀⠀⠀⠀⠀⠛⢿⣿⣆⠀⣀
⠀⠀⠀⠀⠀⢀⣴⣻⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣯⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⢲⣶⣶⣶⣷⣷⣆
⠀⠀⠀⠻⠿⠿⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣏⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣧⣿⣷⣿⣿⣿⣿⣍⣩⣷⣿⢇⣸⡯⣝⠿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢍⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢿⢻⣿⡟⣿⣿⣿⠿⣿⢿⣿⣿⢿⣿⣶⣿⣧⣴⣿⣿⣿⢿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣮⣿⣿⢿⣿⣿⣽⣿⣺⣿⣿⣿⣿⣾⣞⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣯⣷⣵⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣯⣿⣿⣿⢯⡿⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⢿⣿⣧⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠈⣿⣿⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣿⡟⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢃⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠛⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣿
⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠉⡳⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⡟
⠀⠀⠀⢰⣿⡅⠀⠀⠀⠀⠀⡜⠀⢀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠂⣸⠇
⠀⠀⠀⠈⢿⢯⡆⠠⠀⡀⠀⠠⠂⠁⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠈⢠⡟
⠀⠀⠀⠀⠈⣿⣯⡀⠀⠠⠀⠀⠀⠀⢦⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣡⡀⠀⠃⢠⣿
⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⡀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⢀⡼⠁⣀⡟⠃⠈⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣷⣆⠀⠀⢠⠀⠀⠀⠀⢀⠙⣆⠀⠀⢀⡴⠋⠀⠀⠋⠁⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠇⠀⠀⠀⠀⠀⣨⣧⣠⠞⠁⠂⠀⠁⠀⠀⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠊⠀⣠⢴⣏⠠⡄⠙⢶⡄⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠶⠋⠀⢀⡽⣗⡄⠀⠈⠻⣷⣴⣦⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣠⠘⣿⣄⠛⠀⠙⢮⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⠀⣠⡾⠋⠹⣷⡄⣠⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⣼⠋⠀⠀⠀⠘⣧⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠙⠛⠋

⠀⢀⡀⠂⢀⢀⡒⢀⡀⠀⠀⡀⠂⠐⠄⠀⠀⣠⠀⠄⠀⠀⠀⢠⡖⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣤⠄
⠀⠀⠥⠀⢯⠈⠁⠅⠼⠀⠀⠐⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣸⠆⠀⠀⠀⠀⠀⠀⠀⡄⣀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠰⠾⠋
⠀⠀⠀⠒⢶⡷⠕⠁⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⡆⢠⠀⠀⠀⠙⠎⠄⠐⠤⠄⠀⠀⠀⠀⠀⠠⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⢀⡀⢄⠀⠀⠀⠀⠄⣠⢀⣀⢀⡇⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠰⠖⠤⣷⠆
⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠈⠐⠴⠄⠀⠀⠀⠀⠓⠃⠚⠁⢀⠀⣠⣴⣅⢁⢢⣴⠀⠀⠀⢄⠈⠁
⠀⠀⠐⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⠀⠀⠘⠓⠻⠿⠿⠴⠛⠋⠀⠀⠈⠉⠛⠿⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠚⠀⠀⠀⠉⢠⣵⣦⣼⣿⡟⠀⠀⢶⣠⣄⣀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠚⠉⠀⠀⠀⠀⠙⠴⠊⣙⠲⢄⠀⠙⢤⠀⢤⢄⡀
⠀⠀⠘⠷⢖⡄⠳⠖⠟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⢄⣀⣀⣀⣤⣀⠄⠀⠀⠉⠢⢌⡒⠀⠀⠀⠀⠀⠀⠉⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠴⠖⠒⠛⡋⠉⠉⠉⠉⠉⠙⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⣉⠀⣄⠠⢠⠀⠀⠀⡧⠘⡶⠹⠧⠸⠁⠻⠹⠁⡀⡄⠀⠀⠀⠀⠀⠉⠛⠶⣄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢠⣸⠄⠋⠒⠈⠉⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⢀⡄⡀⢀⡀⠀⠈⢟⠦⣄⣠⢎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⠤⡙⠄⠀⠀⣄⢴⡖⠦⠀⠀⢲⡆⠀⣰⠏⢳⠀⣇⢸⣷⡈⡇⠀⠀⣿⣀⢸⠓⢢⡏⣬⠀⠀⠀⢤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠑⠈⡂⢠⣴⡶⠓⠈⡤⡄⢲⠀⠀⠀⣧⠀⣹⡀⣸⠀⣿⠈⡇⠳⡆⠀⡀⠀⠀⡬⣍⣀⠑⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢸⣣⠄⠨⠁⠀⢶⡟⠖⠈⠈⠀⠀⠀⠛⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⢉⠘⢀⠀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠈⠚⣅⣠⠇⡀⠀⠀⡀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⡄⡇⢸⡀⠼⡇⡷⡴⡇⠀⣿⠁
⠀⠀⠀⠀⠀⢦⣸⡇⢩⢡⡄⠀⠀⠀⢂⡴⠚⡤⠀⠀⠀⣽⡍⠀⠀⠀⠀⢀⡀⡄⠐⣶⣸⡼⠗⠛⠀⠀⠀⠙⣄⠀⠀⠀⠁⠁⠀⠃⢸⡟
⠀⠀⠀⠀⠒⢯⣿⠀⢈⠚⡡⢠⡠⡀⠀⠐⣰⠗⠋⠀⢀⣿⠂⠐⢦⣿⠚⠿⠛⠛⠀⠀⠀⣀⢠⠴⣦⣌⡀⠀⠸⢷⣄⡀⢀⣴⡂⠀⢸⡅
⠀⠀⠀⠀⠀⢀⡇⢴⡤⣀⠸⡶⠵⠃⠀⠲⡀⠀⢀⠀⢠⡠⠀⠀⡉⠀⠀⠀⠀⢰⣧⡸⢦⡧⠎⢓⣃⣈⣁⡤⠖⠛⠛⠻⣦⠘⢿⣂⠀⠳⣄
⠀⠀⠀⠀⠀⢸⣇⠀⢼⡫⠗⠀⠀⢀⡰⣄⠘⣀⣈⠀⣭⠅⢠⣬⣥⣄⣀⣀⣀⣈⣯⣥⡴⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⣹⢳⣌⠲⡷⠀⣿
⠀⠀⠀⠀⠀⣼⠁⠠⡬⠡⠠⣼⣿⠓⢁⣴⠞⢉⠀⣸⠶⢠⠏⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⠜⠁⠀⠉⠳⠀⠀⡇
⠀⠀⠀⠀⢠⠟⣱⠏⠡⠠⣠⠾⠒⠒⠋⠁⠀⠀⣧⠍⠣⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠓⠬⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⡴⠚⠀⠀⠀⠀⠀⡀⠂⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣜⣀⣼⣤⣤⡀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠶⠒⠛⠛⠁⠐⠿⠶⠀⠶⣾⠷⠶⣥⠶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠉⠀⠉⠉⠉⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⣀⡀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠐⠖⠂⠀⠠⠄
⠀⠀⠀⠀⣠⠤⠶⠶⠒⠛⡓⠉⠉⠉⠉⣉⠉⢹⣇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢧⣀⣀⣶⣤⣤⣭⣤⠤⠤⠶⠾⠖⠛⠛⢶⡄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠁
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠤⠄⠀⠀⠀⠐⠀⠐⠒⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡎⡡⢬⡉⠓⠂⠀⠀⠤⠤⠤⠤⠤⠤⠶⠖⠒⠒⠒⠒⠒⠒⠒⠚⠋⠛⠁⠉⣩⠉⠉⠉⠉⠉⡉⠉⠉⡙⠓⠲⣆
⠀⠀⠀⠀⠀⠀⡸⠀⠓⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⠶⠖⠒⠒⠶⠤⠦⠤⠦⠴⠶⠴⣷⣄⣠⠃
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡤⡠⠠⠄
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠂⠂⠀⠊⠀⠈
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⢠⡠⠠⠄⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠒⢒⡶⠒⠒⡶⠒⠒⣶⠒⠒⣶⠒⠒⢶⠒⠒⢶⠒⠒⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣼⠃⠀⢰⡇⠀⠀⡟⠀⠀⢿⠀⠀⢸⡆⠀⠈⣧⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢰⡏⠀⠀⣼⠀⠀⢀⡇⠀⠀⢸⡀⠀⠀⣧⠀⠀⢹⡆⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠉⢉⣿⠉⠉⢉⣿⠉⠉⢹⣏⠉⠉⣹⡏⠉⠉⣿⡉⠉⠉⣿⡉⠉⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠛⠉⠛⠒⠋⠉⠛⠚⠋⠙⠓⠚⠋⠙⠓⠚⠉⠙⠒⠛⠉⠛⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣠⠖⠀⣠⠖⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢰⡆⣿⠀⣿⠀⠀⠀⣠⠞⠁⣠⠞⠁⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⣿⠀⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠛⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢮⡀⣶⢰⡚⣲⢰⣰⢴⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠉⠁⠈⠈⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⢀⣀⡠⠤⠴⠖⠒⠒⠲⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡋⣭⢩⡉⡍⠁⠸⠐⠆⠦⠘⠐⠚⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠡⠘⠃⡀⣀⣄⠀⢀⠀⢀⠤⡀⡄⣤⠠⠀⠀⡇⢰⠒⡤⡀⠀⠋⣑⣪⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠐⢠⡴⠖⣀⢅⢲⠀⠘⡇⡸⣀⠇⡧⠏⠳⠀⡀⠀⣬⣀⠑⠁⠀⠀⣿
⠀⠀⠀⠀⠀⡴⠃⠀⢸⠖⡀⠀⠘⠋⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢆⢰⢠⠀⡄⣄⡄⢠⡏
⠀⠀⠀⠠⣸⢓⣢⠀⠀⠉⣡⢇⠀⠀⢰⡆⠀⠀⠀⣀⡀⢤⠰⠞⠃⠀⠀⢪⠈⠀⠙⠉⠃⢼⠃
⠀⠀⠀⠙⡟⡀⠉⣂⣆⠄⢀⠚⠈⠀⠸⠀⠸⠟⠙⠋⣁⢠⣠⢀⣲⠶⠄⢀⣳⣦⡀⢶⡀⠸⡀
⠀⠀⠀⠀⡇⢩⣶⠌⠁⣀⣄⠂⣀⠀⡟⢀⣴⣀⣀⣀⣹⣋⡭⠵⠒⠒⠊⠁⠀⠀⢹⢎⠣⡄⢹
⠀⠀⠀⢸⢁⡴⠁⢢⠟⣉⡴⠋⣅⢼⢢⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡐⠁⠀⠙⠀⠸
⠀⠀⠀⠫⢚⠤⠔⠊⠀⠀⠀⠀⣹⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠴⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⣠⢤⣥⣾⣥⠤⢤⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠋⠐⠒⠂⠶⠷⠾⠶⢦⠄

⠀⠀⠀⠀⠀⠂⠄⠀⢉⠁⠀⠈⠁⠀⠀⠂⠒⠂⠀⠀⠀⠀⠉⠉⠉⠀⠒⠲⠤⠤⠄⠀⠄⢀⡀⠄
⠀⠀⠀⠀⠀⠌⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠀⠀⡀⠀⢤⠄⠀⠀⢀⣀⠀⠀⢀⡁⠀⣄
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⠀⠀⢀
⠀⠀⠀⠀⡅⡆⠀⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠂⠨
⠀⠀⠀⢠⡇⢰⡠⠀⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠙⠀⠀⠀⠉⠀⠀⠓⠀⠀⠀⢀
⠀⠀⠀⣾⡇⠀⡇⠀⠈⣠⣾⠃⠐⠳⠤⣄⣄⣀⣄⣀⣀⣀⣄⠀⠀⠀⡄⢀⠔⠁
⠀⠀⠀⡿⢀⠔⠅⠠⠂⠹⡏⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠣⢀⡽⣶⡇
⠀⠀⠀⠀⠘⠀⠂⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⡅⡀
⠀⠀⠀⠀⠀⠙⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢒⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠶⠦⠄⡀⠀⢀⠀⠄
⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡍⠀⠤
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢄⢀
⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠓⠐⠈
⠀⠀⠀⢠⡇⢸⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠠⣿⠇⠀⡇⠀⠀⣰⣿⠂⠈⠓⠶⢄⣤⣄⣤⣤⣀⣐⣄⠄⠀⠀⡌⢀⠜⠁
⠀⠀⠈⡿⢀⠔⢀⠀⠂⡘⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠀⡝⣶⡇
⠀⠀⠀⠀⠙⠀⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⡇
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠰⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⡅⡀
⠀⠀⠀⠀⠀⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠰
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠘⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠙⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠘⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠈⢎⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠘⢮⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠘⣿⣿⣿⣏⣹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⢄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣕⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣥⣤⣆⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣁⣹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⠿⠋
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠃⢀⡀⠙⠻⠿⠟⠋⢀⡀⠙⠻⠿⠟⠋⢀⡀⠘⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣿⣿⣶⣤⣤⣤⣶⣿⣿⣶⣤⣤⣤⣶⣿⣿⣶⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠉⠛⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣄⣀⣿⣿⠟⠉⠻⣷⣄⠀⠀⠀⠀⠀⢀⣼⡿⠃⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠙⢷⣦⡀⢀⣴⡿⠋⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣟⠁⣠⡾⠋
⠀⠀⠀⠀⣀⣴⣿⣿⣷⣀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⣴⣿⡟⠛⢻⣿⣿⣿⣿⡟⠁
⣼⣿⣿⣷⣤⣾⣿⣿⡿⠋
⢿⣿⣿⣿⣿⣿⣿⠏
⣈⣛⣿⣿⣟⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢀⠀⠀⠀⠀⠛⢓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢊⢉⣈⣀⣀⣠⣤⠶⠚⠋⠉⠃⠀⠀⠀⠀⠀⠀⠄⠤⢤⣀⣀
⠀⠀⠀⢀⣀⣠⣄⣤⣤⣤⡶⠶⠶⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠷⠶⣠
⠰⠺⠿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⢠⢤⠀⠀⢀
⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠧⡇⠀⠀⠀⠠⡍⢈⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠸⠼⠀⠀⢸⢀
⢠⢸⢻⠀⠀⠀⢸⠙⠀⠀⠀⠀⠀⢸⣆⣇⣀⣀⠀⠠⠷⠾⠤⠀⠐⠒⠀⠀⠘⠒⠇⠀⠀⠀⠀⠀⠀⢸⢀
⠸⠼⠾⠤⠄⠒⠚⠛⠒⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠠⠠⡋⣋⣉⢙⢛⢛⢿⣯⣴⣶⣶⣶⣶⣶⣶⣴
⠀⠀⠀⠀⢀⡆⠂⠀⠀⠀⣿⢾⠀⡟⠂⠁⠀⠀⠀⠀⣿⠒⠐⢐⠘⠶⡟⡐⠚⠒⠒⣾⠛⡿⠙⠋⠿⠗⠓⠛⠿
⠀⡀⠀⠀⢸⡇⢀⠀⠀⠀⡿⢼⠀⣿⣤⠆⠀⠀⠀⠀⣿⠀⠀⠀⠂⠀⡇⠁⠤⠐⠂⡆⠀⡇⢰⠀⢨⠀⠀⠂
⢘⠉⠁⠁⢸⣇⠬⠦⠤⠀⡇⠀⠀⠉⠉⠉⠀⠀⠀⠀⢿⣀⠀⢀⣤⠀⢈⣐⣐⣀⡀⠁⠀⢹⠸⠆⢸⡌⠈⠀⡀
⠈⠀⠀⠄⠘⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠆⠒⠒⠒⠒⠒⠚⢁⣊⣀⣀⣈⣁⣁⣈⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣋⢀⣅⠀⠀⠀⠀⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠀⠠⠤⢄⣀⠈⠧⡄⠴⠃
⠀⠀⠀⠀⠀⠄⣀⢀⡀⢀⡑⡉⢒⢛⠛⢀⢀⡐⠲⠠⠈⡅⢰⠆⠤⠔⠦⠐⠂⠲⠘⣰⠁⣀⠀⡀⠀⡀⠙⢾⡁
⠀⠀⠀⠀⠀⠀⠶⣖⡀⠀⠉⠁⠈⠙⣡⢨⣻⠀⡍⡀⡀⠠⢜⡀⠀⢀⢀⠀⠀⡀⠀⡏⠀⠸⠀⠇⠸⡠⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⠓⠶⠠⢋⠢⠄⠂⠀⠀⠀⠀⠀⡇⠸⡈⠿⠸⠃⠇⠀⢳⠀⠀⠀⠒⠂⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠐⠂⠻⠙⠂⠛⠻⠁⠀⠀⠀⠀⠀⢠⣤⣴⠻⢘⡄⢸⢸⠘⢇⡇⢻⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣘⡈⠺⠘⠾⠻⡇⢀⡀⢄⠦⠃⠀⠁⠀⠀⢛⠛⣦⡀⠀⠀⡀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⢠⣮⣤⣠⣤⣀⣀⢠⣆⠢⠭⠋⣛⣡⣷⣄⡩⢤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠚⠋⠉⠈⠻⣿⣷⢄⡖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣸⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢶⣶⡼⠻⠷⠛⠀⠲⠖⠒⠒⠓⠛⠂⠀⠀⠀⠀⠀⠀⠰⠟⣉⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢁⣀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⡟⢉⡷⠀⠀⠀⠱⣄
⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠣⡀
⠀⢀⡴⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⢔⠁⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠳⣄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤
⠀⠀⠈⠢⡀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠈⢢⡀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢁⣤⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⢀⡴⣪⠽⣷⡀⠘⠒⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠑⢄⠀⠀⢀⡠⢖⡥⠊⠀⠀⠙⣝⢄⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠈⣳⢔⣫⠖⠉⠀⠀⠀⠀⠀⠈⠳⡱⣄⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡾⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡳⣄⠀⠀⠀⢀⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡓⢄⠀⠫⠽⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⢄⣠⣴⠟

⠀⠀⠀⠀⠀⠂⠁⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡄⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢠⣠⡄⣄⠤⠀⣿⣿⠀⣤⣠⣤⣄⠀⠀⠀⠀⢸⣯⣼⣱⣻⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣄
⠀⠈⠉⠉⠉⠀⠀⡏⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⠛⠛⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⢹⠉⡯⢰⣧⢸⣟⠀⠀⠀⠀⡿⠏⠏⠯⠿⣏⡿⢸⠽⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠉⠉⠈⠈⠉⠀⠀⠀⠀⠰⠖⠲⠶⠶⣶⠶⠶⠶⠶⠄

⠀⠀⠀⡔⠒⠒⠒⢢⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠸⣾⣿⣶⠃⡆⣶⢶⢲⣴⡆⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠖⠿⠻⠗⣠⡀
⠀⠀⠀⠀⢙⢉⡇⠀⠶⠶⡆⠶⠰⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⢀⣼⡿⠋
⠀⠀⠰⣾⣾⣿⣶⣷⣿⠆⠀⣄⣀⡀⠀⠀⠀⠀⠀⠛⠏⠀⠋⠋⠉⠇⠀⠀⠀⠀⠀⠀⠀⠈⢋⠝⢯⠋
⠀⠀⠀⠋⠉⠉⠉⠉⠉⠀⠀⣿⣿⠀⠀⠀⠀⣀⣀⡁⣈⣀⢁⣁⣀⣀⠀⠀⠀⠀⠀⣶⣶⢶⢦⢶⣦⣶⣶⢶⠆
⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠃⠛⠃⠛⠛⠘⠛⠛⠛⠀⠀⠀⠀⠀⠉⠉⠈⠀⢩⡍⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⣶⡀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠸⠛⠻⠻⠅⠟⠳⠸⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄⣿⣶⣶⣦⠀⠀⠀⠀⠀⠀⠠⠾⠿⢿⡿⠿⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣈⠀⢀⡈⡁
⠀⠀⠀⣖⢰⣶⣦⡖⣶⢰⡆⣶⡄⠀⠀⠀⠀⠐⣿⠘⡏⣾⣶⣿⢺⡇⠀⠀⠀⠀⠀⡏⠿⠯⠿⠛⠸⠹⠿⠿⡇
⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⢶⣳⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠄⠠⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢣⡞⠉⣩⣆⠈⠛⣿⣄⠀⠀⠀⠀⠀⠀⠓⢄⠀⣑⡈⣳⣤⣶⡛⠋⠁⠈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⣨⠇⠀⠎⠛⠁⠀⠀⠀⠛⡆⢀⠀⡀⠀⠉⠻⣅⢠⣶⠟⣉⠙⡛⠛⠉⠈⢁⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣶⣄⣀⠀⠀⠉⠲⣄⠀⠀⢲⣄⣼⠦⠶⠃⠄⠀⣈⠀⠀⡀⠈⢉⡟⠉⠛⠉⠙⠋⠀⠐⠋
⠀⠀⠀⠰⠂⠀⠀⠀⠆⠀⢾⣿⢁⠹⣜⢦⠀⠀⠙⠶⣽⡮⠹⣿⣍⣷⠶⠶⠟⠿⠿⢷⣬⡤⠀⠁
⠀⠀⠀⠀⣨⠥⠀⠀⡤⠀⠈⢿⣟⣷⡜⢿⡇⠀⢀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠐
⠀⠀⠐⡤⠿⠔⠀⠀⢅⠀⠀⠸⣿⣿⣿⣛⣣⡄⠀⣀⠀⠀⠀⠀⠀⠀⠠⠄⡦⢀⡀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠡⣀⠀⠄⠀⠀⠀⢄⡀⠈⠻⠿⣿⠟⠁⠀⠁⠀⣀⠤⠀⠀⠀⣠⠠⢲⠇⢰⡆⢀⠀⠀⠀⠀⠀⠈⢶⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠑⠚⠋⠁⠀⠀⠀⢠⠊⠀⠀⠀⠄⢀⠘⣠⣷⣤⣼⣿⣿⠀⠀⠀⠀⠘⠛⠠
⠀⠀⠀⠀⣀⠀⣈⡄⢦⣤⠀⢄⡀⠀⠀⠀⠀⣰⡤⠀⠀⠀⢀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣷⡦
⠀⢀⠀⣀⡿⠟⣹⢧⣭⣶⣛⣳⠛⡆⠀⠀⠀⠋⢒⠘⠃⡀⣿⣿⣷⣿⡿⣟⠙⠙⠏⠙⠢⣅⣾⠁⠀⠀⠀⢀⠔
⠀⠘⣿⢿⠳⢞⢧⢺⣿⣟⠻⡿⣷⢤⣀⠀⠀⠐⠚⠒⠶⠚⠛⠛⣁⣈⠉⠻⡗⢲⠖⣢⣴⣯⣿⣦⠒⠆⠀⠁⠐⠶
⠀⠀⢰⣾⡖⣸⢋⡧⠌⠹⠇⢰⡜⣧⣌⣧⣄⠀⠀⠀⠀⠀⠀⢀⡿⠉⠀⠀⠀⠘⠓⠴⠼⠿⠟⠁⠀⠀⠀⠂
⠀⠀⠈⢛⣿⣽⡿⢶⠐⣆⡀⢈⡷⣼⠟⣿⣟⣆⠀⠀⢀⣄⣴⠰⣾⡆⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡤
⠀⠀⠀⠨⠙⢛⣛⣛⠁⣬⣿⣟⣿⣯⣯⣿⣿⠷⠂⠀⠀⠙⢿⠂⢩⠃⠈⠉⠉⠀⢧⣤⣡⣶⣿⣿⣧⣄⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⡀⠀⠀⠈⠁⢲⣍⢡⠀⡀⠀⠀⠿⢻⣧⣽⣷⢾⣤⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣾⡓⢸⠂⠀⠀⠀⠼⡦⠀⠁⠀⢀⡄⠈⣿⣿⣿⣸⣯⡐⠀⠀⠀⢠
⠀⠀⣀⠀⢀⡤⠴⠶⠚⠓⣒⠈⢉⠀⠀⠀⠀⠀⠸⣿⣷⠲⡤⣤⡤⠀⠁⠲⠂⠀⠀⠐⢃⡟⣿⣯⣿⣷⣷⡖⠀⡐⠀⡀
⠀⢠⣏⢳⣛⡅⠶⠾⠿⣷⡎⢠⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠤⠂⢉⡭⣿⣇⠀⠀⠀⠩⡰⠛⣿⣿⣿⣿⣷⣵⣤⡟
⠀⠀⣿⣿⢽⣷⣿⣾⣿⡟⠑⠁⠀⠀⡠⠞⠀⠀⠂⠘⠂⠀⡰⣯⣿⠿⠷⠛⠁⢀⠀⠀⠀⠠⠾⣛⠛⠿⢿⣛⠷⠚⠁
⠀⠀⠘⣿⣵⣿⣿⣿⣿⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠈⠐⠀⠒⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢷⠀⠀⠀⠀⠾⢥⣶⣴⠟⢿⣦⡀⠀⢀⠀⠀⠀⠀⢀⡤⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡒⢉⣡⢤⡾⠀⠀⣴⣤⣀⠂⢤⡀⠀⢾⠿⣿⠟⠻⣷⣄⡀
⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⣀⠤⢰⣏⢱⠍⠐⠋⠀⠀⢶⡶⢶⣿⢿⣦⣈⠿⠛⠳⢤⡀⠀⠀⠙⠳⢦⣄
⠀⠀⠀⠀⢤⣉⠂⠠⠊⠀⣠⠶⣯⣵⡿⠟⠋⠀⣀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠻⢿⣳⣦⡀⠙⠧⠀⠈⠀⠤⡉⠻⣿⣶⡆
⠀⠀⠀⠀⠠⢌⠲⢠⣰⡾⣱⣾⡽⠋⠀⠀⠀⢀⠀⠈⢰⣶⣾⣿⡷⠤⡀⠀⠀⠀⠀⠈⠙⠛⠦⠘⢦⠀⠀⣀⣀⡁⠠⠙
⠀⠀⠀⠀⠀⠀⠈⠒⠿⠾⠛⠁⠀⠀⠒⠂⢀⣷⣮⣓⣞⣟⣛⣻⣥⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⡆⠈⠻⠲⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣯⣒⠚⠛⠛⠛⠻⣿⣿⣿⣿⠟⠎⢀⠀⠀⠀⠀⡄⡠⠀⠀⠈⠓⠠⠄⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⣾⣿⣷⣷⡶⣞⣾⣶⣾⠗⡶⠁⠀⠀⢀⣻⣴⡌⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⠛⠛⠿⠇⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⡔⠶⢶⡄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠳⠤⠞⠁⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⢀⡴⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⢶⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠳⣄⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠈⠳⣄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⣀⣀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⣽⣯⠀⠀⠧⠼⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⣠⠖⣩⠞⠁⠀⢻⡳⡄⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⢦⠀⣀⡴⣋⡴⠋⠀⠀⠀⠀⠀⠙⢮⢢⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⡠⢟⡥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀⠀⠀⠀⣠⣄⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⡀⠀⠧⠼⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢦⣀⣀⣴⡿⠋

⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⠇⣿⢨⡇⢸⡇⣸⣀⣿⣦⣤⡀
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⣴⣷⣬⣟⡿⣿⣿⣧⣨⣿⡄
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⣿⡿⣿⣿⣿⣿⣿⣷⣯⣛⢷⡌⡷
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡟⠁⢿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣧⡖
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣷⠀⡀⠙⢿⡟⠀⠀⣀⡍⠻⣿⣷⡀
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⢰⣷⡄⠈⠃⠀⠀⢉⠁⠀⠈⠻⣿⡆
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⢸⡿⠀⠠⠀⠶⠤⠀⠀⠀⠀⠀⠘⣿⡀
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⠃
⣿⢸⡇⢸⡇⣿⠀⣿⠸⠇⠘⠁⠿⢆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣿⢸⡇⢸⡇⣿⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⠤⡀
⣿⢸⡇⢸⡇⣿⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢳⠀⠰⢤⡀⣿⠀⣿⠀⡇⡆⠀⢸⡄⠳⡀
⣿⢸⡇⢸⡇⠉⠀⠀⠀⠊⠁⠀⢀⣀⣴⣾⣿⣷⣶⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠇⠀⠀⠉⠛⠀⠛⠀⠇⠃⠀⠘⠀⠀⠙
⣿⢸⡇⠸⠁⠀⠀⣠⢸⣇⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⣿⢸⡇⠀⠀⠀⠀⣿⢸⡇⢹⣿⣯⣙⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠙⠦⠀⠀⢠⠀⠀⠀⠀⠀⢦⣄⠀⢸⡇⠀⠘⣆⠀⠀⡇⠀⠀⡇
⣿⠘⠁⠀⠀⠀⠀⣿⢸⡇⢸⡇⣹⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⡀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠈⠀⠸⠃⠀⠀⠿⠀⠀⠇⠀⠀⠇
⣿⢠⡄⠀⠀⠀⠐⢟⢸⡇⢸⡇⣿⢈⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢠⠃⠀⡀
⣿⢸⡇⢸⡆⣄⡀⠈⠙⢧⣸⡇⣿⠰⠏⠛⢻⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⠔
⣿⢸⡇⢸⡇⣿⠀⣦⠀⠀⠉⠂⠛⠀⢀⣤⣤⣴⣿⣿⣿⣿⣿⠋
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢠⡀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣄⠁
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⢠⣾⣿⣿⣟⠿⣿⣿⣿⣿⣿⣿
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⣼⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡶⢶⡶⣶⡶⣶⡶⠶⣶⣶⣶⡆
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⢽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠈⣿⣿⣿⣿⣿⣿⣧⣸⣿⣿⡿
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⢰⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⢸⡇⢸⡇⣿⠀⣿⢸⡇⢸⡇⣿⠰⡇⢸⡿⣿⣿⣿⣿⣿⣿⣿
⡿⣿⠿⠿⠿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⠀⣠⣴⣾⣿⣃⣁⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⡝⠙⣡⣿⣿⣿⣿⣿⣿⣿⣿⣟⣴⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⢛⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⠋⠁⠀⠀⣀⣴⣾⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠁⠀⠀⢠⣶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣀⢀⠒⠹⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣝⠻⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠂⠁⣾⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠛⠛⠟⠿⠛⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠉⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠈⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠵⠋⠁⢿⡧⠄⠀⠀⢐⠂⠈⡀⠐⠒⠒⠀⠀⠀⠤⢤⣀⣀⠀⡀⠀⠄⠠
⠀⠀⠀⠀⣀⠀⠈⠨⠅⠒⠘⣿⠀⠰⠀⠀⢨⣩⠀⠀⢀⠀⠀⠀⠀⠀⠐⠈⠁⠃⠋⠒⠃⢠⠀⠀⢰⡄
⠀⠀⠀⠀⠿⠦⠀⠒⠐⠀⢄⡇⣴⠀⠀⠀⢨⡵⠀⢀⢸⢆⣿⣿⠀⠀⠉⠉⠉⠉⠛⠚⠐⡆⠀⡀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣤⡄⡀⠨⠝⣠⣾⣏⡀⠀⠈⡄⠐⡛⠚⠂⢠⠀⡄⡰⠀⣼⠃⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢉⡉⠡⢠⢠⢠⢩⣉⢒⠣⢇⣃⠙⠓⠠⢃⠘⡰⢁⢚⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⣉⡄⠀⠀⢠⣾⣩⣌⣁⣀⣈⢁⠀⠁⣊⡐⢧⠈⠉⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⠀⠄⠞⠛⠉⠉⠙⠳⠦⠬⠻⠧⠾⠴⣒⣲⡛⠃⢠⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⠐⠀⣀⠁⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⢀⠁⡘⠀⠀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠀⠀⡘⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠽⢧⠤⠀⠀⠀⠀⠀⠀⠀⣠⣦⣿⠁⢀⣔⣲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡦⣄⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠄⡀⢠⡐⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣠⣤⡆⠀⠀⠀⠀⠀⠀⢠⣬⠄⠀⠀⠀⣠⣷⣸⣷⣄⣆⠀⠀⠀⠀⠔⠀⠈⠃⠖⠒⠒⠒⠚⠉⠉⠀⠀⣶⣀
⠀⢠⣿⣳⣿⡄⠀⠀⠀⠀⡀⣼⡇⠀⠀⠀⣷⣿⣉⣇⣸⣉⣯⣴⠀⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠆⢀⣾⠏⠁
⠀⢺⣓⢿⡏⣄⢀⡄⣶⡳⣽⣿⠇⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠉⠛⣿⣾⠀⣿⣿⣿⣿⣿⣀⢸⡟
⠀⠈⠻⢿⣿⣿⣬⣿⢮⣻⣾⠟⠀⠀⠀⠻⡈⢿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢠⡟⡅⡟⠀⠀⠈⢻⠋⢸⠇
⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⣶⠛⢻⡿⠛⢻⡋⠀⠀⠀⠀⠀⠀⠇⢣⣸⠃⠀⠀⠐⠚⡀⠜
⠀⠀⠀⠀⠀⠀⠁⠠⡙⡄⠀⠀⠀⠀⠀⠀⢰⠿⣟⣀⣇⣰⡿⢧⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣀⡏⠀⠀⠈⡏⠀⠀⢘⣇⠀⠀⣰⣼⣧⡆⠀⠀⢀⣤⡶⠿⣃⢾⣦⡦
⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢰⣧⠀⠀⠈⠉⠀⠀⣏⣧⣏⣿⠀⠠⣉⣴⣿⣿⣿⣮⡽⣿⣷
⠀⢀⣤⣀⠒⢿⣤⠁⠀⢠⣾⡗⢂⣠⣄⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠘⠻⠈⣿⣿⣯⣿⣏⢈⣿
⠀⠀⠻⢿⣷⣾⣷⡀⠀⣰⣿⣷⣿⠿⠃⠀⠀⠠⠀⢀⢀⠕⠤⢤⡤⢐⢰⢲⣢⠀⠀⠀⠀⣷⡦⣿⣿⣿⣿⡿⣰⠇
⠀⠀⠀⠀⠀⠈⣿⡇⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠁⠛⠸⠘⣿⠾⠆⠀⢠⢿⣱⣿⠿⠿⠟⣠⠏
⠀⠀⠀⠀⠀⠀⢻⢡⢠⢹⠃⠀⠀⠀⠄⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⢑⠒⠚⡏⠀⠀⢠⣷⣥⡿⠃⣀⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠈⠲⠷⠎⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠘⠀⠐⠗⠀⠀⠀⠳⠤⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⢒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠸⡏⢀⠛⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣀⣃⣠⠔⠻⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣌⡉⢁⣄⠀⢫⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⡇⠈⠁⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠞⢳⣒⠐⠂⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣧⣄⠀⠀⢀⣼⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⣾⠁⡇⠙⠻⣿⡟⢋⡜⢻⡈⢳⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢸⠀⢱⣏⣙⡛⠛⢫⣙⠀⡇⠀⢧⠀⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡟⠀⠀⠀⠀⠀⣸⠀⢘⡛⠛⠛⠛⠛⠛⠛⡃⠀⠈⣧⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⡟⠀⣼⠇⣿⢸⣿⢸⣿⢸⣧⢸⣷⠸⡇⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⡄⣼⠇⠀⣿⢠⣿⢸⡿⢸⣿⢸⣿⠈⡿⣆⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⢰⣿⢏⡴⢰⣿⢸⡟⣾⡇⢸⣿⢸⣿⡜⠁⠂⠉⣳⢦⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣶⠶⢶⣦⣤⣠⣿⠁⣼⡇⢸⡏⣼⡇⣿⡇⢸⣿⢸⠟⠀⠀⠀⣰⢋⣾⣥⣤⣴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⣿⠀⠀⠀⠈⠿⣏⢀⣿⠁⣿⡇⣿⡇⣿⡇⢸⣷⠎⠀⠀⠀⡼⢡⡾⠁⠀⣷⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠉⣀⡀⠀⠀⠀⠀⠉⠛⠤⣿⣇⣿⣃⣿⣇⣼⣇⢀⡀⢀⡾⣡⣿⣷⣤⣤⣿⣾⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣦⣬⣉⠋⠛⠓⠲⠶⠦⠤⢄⡉⠀⠀⠀⠀⠀⢀⠹⣿⣿⡶⠟⠛⣛⣭⣤⣄⡀⠈⣉⠙⡻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⡻⢿⣟⠛⠿⣿⠿⣟⢿⣿⣶⣯⣤⡤⢄⠀⡀⡀⣦⣿⣿⢀⠀⡌⢉⡙⠂⠉⠿⣿⣾⣷⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡙⠳⠾⠯⢤⠾⣇⢈⠛⠿⣯⣽⣿⣷⣴⣦⣳⣿⣿⣿⣿⣎⠢⠀⠻⠿⠀⠀⡀⢸⠯⠟⣉⣥⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣅⠒⠒⠺⣷⡘⠿⣿⣶⣦⣶⣿⣿⣯⣟⡞⡽⣭⣛⠿⢿⣷⢦⣄⣀⣀⣚⣡⣾⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠙⢿⣦⣄⣉⣳⣿⢿⣷⣝⡺⢬⣙⠲⢭⣛⢲⢍⡳⣝⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣚⠿⣿⣌⠳⣿⣿⣽⣲⢮⣽⣳⣾⣿⣾⣽⣾⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣿⣷⣄⡙⠛⣾⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⢀⣀
⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⣿⣿⣿⠀⠀⢀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⢠⣿⣿⣷
⠀⠀⣿⣏⣿⠀⠀⢸⣷⣿⣏⢋⣿⣿⡇⠀⠀⢀⣤⣤⣴⣶⣶⣦⡄⠀⠀⢰⣿⣿⡀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿
⠀⠀⣿⣇⣿⠀⠀⢸⣿⣿⣯⢵⢽⣿⣿⠀⠀⢸⣿⣿⡍⠝⣿⣿⡇⠀⠀⢸⣿⣿⣧⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⡧⢼⣿⡄
⠀⠀⣿⡍⣿⠀⠀⢸⣿⣿⣿⢂⣺⣿⣿⠀⠀⠈⣿⣿⣿⠌⣻⣿⣇⠀⠀⢸⣟⣛⣿⠀⠀⠀⢹⡟⡻⢿⠀⠀⠀⣿⠭⢿⠀⠀⢠⣿⣆⢹⣿⡇
⠀⠀⣿⣎⣿⠀⠀⢸⣿⣿⣿⡒⣾⣿⣿⠀⠀⠀⢻⣿⣿⣤⣼⣿⣿⠀⠀⢸⣯⠽⣿⡇⠀⠀⢸⣿⠒⣿⠁⠀⠀⣿⡗⣻⠀⠀⢸⣿⣞⣽⣿⡇
⠀⠀⣿⠏⣿⠀⠀⢸⣿⡿⣥⡼⣿⣿⡿⠀⠀⠀⢸⣿⣟⣓⣺⣿⡿⠀⠀⢸⣿⣃⣿⡇⠀⠀⢾⣥⡬⣿⠀⠀⠀⣿⡟⣿⠀⠀⢸⣿⡯⣽⣿
⠀⠀⣿⣿⣿⠀⠀⢸⣿⣷⣝⣋⣾⣿⡇⠀⠀⠀⢸⣿⣧⣛⣫⣿⡇⠀⠀⢸⣞⣛⣿⡇⠀⠀⢸⣬⣵⣿⠀⠀⠀⣷⣿⣾⠀⠀⢸⣷⣾⣿⣿
⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠛⠛⠛⠛⠁⠀⠀⠀⢸⣿⣿⠛⠛⠛⠃⠀⠀⢸⣿⣿⠿⠃⠀⠀⢸⣿⣿⡿⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⡏
⠀⠀⣿⣿⠋⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⢸⣿⡟⠀⠀⠀⢸⣿⡏
⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇
⠀⠀⢿⡿⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡗⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⢸⣿⡇
⠀⠀⡀
⠀⠀⢻⣆⠀⠀⠀⠀⠀⢠⡐⡄
⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⣶
⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⢹⣿⡇⠀⠀⠘⣿⡄⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⢸⣿⡄⠀⠀⠀⣤⠀⠀⠀⠀⠀⣤⣶
⠀⠀⠀⢸⡷⣿⡀⠀⠀⠀⢸⣏⡇⠀⠀⢐⣿⣇⠀⠀⠀⢸⣿⢘⣷⠀⠀⠀⣸⣿⡇⠀⠀⠀⣿⡆⠀⠀⠀⢸⡏⣿⠀⠀⠠⣆
⠀⠀⠀⢸⣯⢽⡇⠀⠀⠀⢸⡇⣏⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣞⣿⠀⠀⠀⣿⢯⣇⠀⠀⢰⣟⡇⠀⠀⠀⢸⡯⣿⠀⠀⠀⣿⡆⠀⠀⠀⣆
⠀⠀⠀⠈⣿⢸⡇⠀⠀⠀⠸⣇⣿⠀⠀⠘⣿⣿⠀⠀⠀⢸⣷⣊⣿⠀⠀⠀⣿⣙⡇⠀⠀⢸⣿⣇⠀⠀⠀⢸⡟⣿⠀⠀⠀⣿⣷⠀⠀⠀⣿⡀
⠀⠀⠀⠀⣿⣼⡇⠀⠀⠀⢶⣿⣿⠀⠀⢀⣷⣿⠀⠀⠀⢸⣧⣤⣿⠀⠀⠀⣷⣾⡗⠀⠀⢸⣿⡇⠀⠀⠀⣸⣷⣿⠀⠀⠸⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⢾⣿⠇⠀⠀⢸⣿⡿⠇⠀⠀⢸⣿⠏⠀⠀⠀⠀⣿⡿⠁⠀⠀⢸⣿⡇⠀⠀⢸⣿⡏⠀⠀⠀⢀⣿⡿⠀⠀⢠⣿⡇
⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⢿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⢨⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣻⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠈⣿⡇
⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⢻⣿⠀⠀⠀⠸⣿⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠘⣿⡆
⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢤⢤⠄⠀⠲⠒⠒⠒⠒⠂⢀⠌⢉⠉⠉⡩⠉⢉⠍⠉⠉⠉⠉⠉⠉⠩⢋⠉⡉⡉⢉⢉⠉⠉⠉⡟⠉⢹⠛⣉⠉⠉⣍⡭⠯⠧⣶⡶⠤⣂⠤⢀
⠀⠉⠲⢽⡳⢦⣤⣄⠀⠀⠀⠀⠁⠀⠂⠀⠔⠁⡀⠀⠔⠐⠁⢀⠄⠀⠁⠊⢊⠔⠑⠁⠀⠀⠈⣿⠀⣼⢑⠀⠐⣈⣥⠞⠀⡕⡤⢀⣼⣭⣡⣒⣉
⠀⠀⠀⠀⠈⠙⠺⠽⣫⣺⡶⣢⣤⣤⣔⠁⡀⢊⣀⡀⣀⢈⢀⢁⠀⣀⡈⢐⣁⣂⡀⣈⣄⣀⡀⣿⠀⢸⡤⠤⠂⠒⠦⣌⣴⢮⣴⣭⣾⣽⣂⡃⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠚⠥⠿⠿⠿⠿⠿⠿⠯⠾⠿⠧⠿⠿⠛⠘⠛⠛⠛⠓⠋⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠙⠧⠠






⠀⠀⠀⠀⡤⠖⠒⠲⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⠀⠀⡀⣀⣀
⠀⠀⠀⣸⠀⡴⠒⣦⠀⠀⡀⢈⠉⢉⠝⢛⠟⠛⠓⢖⡒⠒⢒⠒⠒⡒⠒⠒⠒⢲⢾⢯⣭⣿⣥⠶⣻⣶⠿⣒⡯⢖⠽⣚⡿⠶⣛⡿⠷⣖⣯⡢⡀
⠀⠀⠀⡇⠀⠑⠲⠋⠔⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠄⠁⠀⠊⠀⠀⡠⠀⣻⠰⠖⠣⣭⢴⣺⠿⠚⣉⡤⢪⠕⠺⣟⣋⡭⣗⠢⣽⣒⣿⣯⠜
⠀⠀⢸⠁⠀⠀⠀⠠⣊⠄⡠⠀⠀⢀⠄⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠈⠀⠀⠘⣌⠒⢯⢵⣛⣿⣒⡾⢷⣺⣿⣛⣭⠿⠯⣽⣳⣾⣋⣾⢿⡿⣰
⠀⠀⣸⠀⠀⠀⠠⢚⠁⠊⠔⠃⠀⠐⡠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠋⠉⠀⠀⠀⠉⠉⠘⠛⠓⠒⠚⠉⠉⠀⠀⠀⠀⠙⠛⠁
⠀⠀⡏⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠊⠀⠁⠀⠀⠠⠀⠐⠁⠀⠀⠀⠀⠀⠈⠀⠀⢸⠁
⠀⠀⡇⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠠⠀⠀⢀⠀⡀⢸
⠀⠀⡇⡀⣀⣀⢀⢀⣀⣀⡈⡀⣈⢈⢀⢀⠀⠀⠀⡀⡀⡊⡀⡀⢖⢐⠑⡃⡚⡑⢸
⠀⠀⠯⠿⠽⠵⠧⠯⠯⠮⠭⠽⠽⠥⠯⠯⠯⠯⠯⠮⠭⠼⣽⣥⣯⣯⣎⣘⣙⣙⣹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠔⢊⠉⠁⠀⢀⡤⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠑⣊⣀⠴⠒⠩⠤⠔⠂⠉⠀⠀⠐⠋⢁⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢈⣁⡤⠔⠋⠁⢉⣠⠤⠤⠀⠀⠒⠂⢀⠠⠐⠊⠁
⠀⠀⠀⠀⠀⠻⢦⡤⠚⠋⠉⠀⠀⡠⠔⠒⠉⠔⣂⠉⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠈⢿⣅⠀⠐⠒⣊⠤⢒⡡⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠈⠀⠀⠀⠤⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠚⣩⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠠⡴⠋⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠉⠐⠃⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡲⡀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣀⠠⠞⠡⠦⠆
⠀⠀⠀⠀⠀⡀⣀⣂⣀⣁⣀⠙⢒⣊⣉⣀⡀⠀⠤⠴⢒⡤⠀⠀⠀⠀⣀⡈⠒⡴
⠀⠀⢠⣼⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠉⠑⢲⣶⣽⢦⣴⠤⠈⠑⡂⠐⠋⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⢀⠠⠀⣠⡀
⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⢶⣶⣟⡃⣀⣖⢤⡄⠀⠛⠈⠁⠀⠀⠀⠀⠀⢂⠤⠋⠀⣀⠀⠀⠁⠀⡀⠖⠉⠀⣀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢀⠤⠒⢈⡤⠀⠉⢀⡄⠀⠁⠀⢀⠔⠊⠀⢀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢁⠀⢨⠀⠀⠄⠉⠀⠀⡦⠀⠁⡀⠀⠄⠨⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⠈⠁⠀⡤⠚⠀⠐⢀⠀⠀⠀⠀⢀⠁⠀⠀⠰⠄⠀⠀⠀⠀⣠⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣰⣃⠰⠀⠁⠀⣀⡄⠀⠀⠀⡄⠂⠀⣀⣠⢀⣠⡠⠤⡶⡒⠋⡰⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⣻⣷⣴⣶⣮⣀⢧⡤⡴⢲⠟⠋⠙⠋⠉⠆⠁⠂⣚⣼⡷⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣷⣲⣿⢿⣷⣽⠷⠦⠛⣤⡀⠤⠖⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠙⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡠⠂⡡⠒⢁⢤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡠⢊⠔⢉⡤⠚⡃⢠⠀⠀⡄⠀⠀⠀⠀⢰⠀⠀⠀⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⢠⢎⠔⠁⡖⡃⠀⠀⡇⢸⠀⠀⡇⠀⢰⠀⠀⢸⢀⣀⡤⠗⢛⣉⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢠⠃⠛⠒⢢⡇⡇⢠⠀⠇⠸⠀⠀⡇⣀⣾⠽⢛⡋⠹⠛⣞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣀⠤⠄⠀⡎⡀⠀⠀⢸⡇⠃⢸⣤⣥⣤⣶⠒⢫⠕⣿⠈⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡠⠊⠁⠀⠀⠀⢃⣀⣰⣀⣸⣧⣶⣚⡏⠀⠀⠀⢹⢸⠀⣿⠀⠀⠀⠀⠀⣯⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⢀⠀⠀⠀⣀⠰⢐⠀⠀⠀⠈⠉⠀⣿⡇⠀⠀⠀⢸⢸⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⡨⠴⠊⠉⢹⠀⠼⠖⢀⡀⠀⠀⠀⣿⡇⠀⠀⠀⢸⢸⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⡐⢀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡎⠀⠀⠀⠈⠋⠀⠀⠀⣿⡇⠀⠀⠀⢸⢸⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠓⠘⠀⠘⠁⠀⠀⠇⠀⠀⠁⠄⢀⠇⠀⠀⠀⠀⠀⠸⠀⠀⣿⡇⠀⠀⠀⢸⢸⢠⣿⣶⠆⠀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠆⣀⢀⢀⠀⠁⠀⠀⢠⠀⡄⡆⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣸⡞⢻⣿⣧⣴⣾⣯⡂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⢢⠀⠀⠀⠀⠐⠪⠀⢀⡘⠀⠀⠀⠀⢡⠄⠶⠠⠤⠤⢴⡀⠀⣿⣧⠀⠀⢶⡿⣿⣾⣷⢀⣿⣟⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠈⠘⠃⡀⠀⠀⠀⠀⡇⠀⣿⡇⡄⢊⣿⡟⠟⢉⣿⢿⣿⣿⣻⠗⣿⡆⡆
⠀⠀⠀⠀⠀⠀⠈⠻⠒⠂⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠰⠯⠭⣼⡇⡧⠾⢿⣟⣾⣻⣿⣿⣏⣠⠈⠄⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠀⠀⠀⠈⠉⢻⢹⠉⠙⠁⠁⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠉⠉⠒⠠⢄⡀⠀⢸⠞⠂⠒⠀⠈⠉⠁⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠤⠤⠤⠤⠤⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠘⠃⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣿⠟⠙⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⣠⣴⣤⡀⢀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠟⠻⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠉⠛⡛⠂⢈⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⢻⠀⠀⢁⣀⣀⡀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⡄⠘⠛⠿⠽⠛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠈⠂⢀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⢿⡇⠀⠀⠀⠀⠀⠘⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⢸⣿⠀⠀⠀⢠⡄⠀⠀⢿⡎⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠈⠀⠀⠀⠀⣿⡄⠀⠀⠀⢤⡀⠀⢸⣷⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣶⣾⣿⣿⣿⣾⣿⣤⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣠⠄⠒⠃
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⣠⠆⠀⢸⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠉⢆
⠀⠀⠀⠀⠀⡠⠛⠀⠀⠐⠠⢄⡀⣰⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⠔⠉⠓⡤⠤⠤⠤⠔⠒⠋⠀⠈⣷⡆⢸⠄
⠀⠀⠀⠀⢀⡇⣀⡤⠔⠂⠠⠤⣈⡇⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣼⣷⣾
⠀⠀⠀⠀⠘⣄⡁⠀⠀⠀⠀⠀⠈⠳⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠄⢀⠀⠠⠀⣀⡤⠔⠊⠁⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠈⠉⠲⢤⣀⠀⠀⠀⠀⠈⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠲⠞⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡄⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠈⠛⠛⠉⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⡇⢠⣤⡄⢠⣤⣤⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠹⣧⡀⠀⠀⢸⣇⠈⢉⡇⠀⠉⠉⢠⡿⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣁⡀⠀⠀⠘⢷⡄⠀⢸⣿⣶⡾⠷⠾⢷⣶⣿⡇⠀⠀⠀⠀⠀⣴⠟⠉⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠁⠀⠀⠱⡈⢿⡄⢸⣿⣿⣿⣾⣿⣾⣿⣿⡇⠀⠀⠀⢀⣾⠃⠈⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡰⢶⣦⣤⣵⡈⢿⣄⠻⢿⣿⣿⣿⣿⡿⠟⣡⣤⡀⢀⣾⠃⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣤⣤⣤⣽⡈⢿⡛⠦⠄⠉⠉⠁⠴⠟⣿⣿⢉⡿⠃⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡜⠛⠿⠿⠷⠘⣷⠀⠀⠀⠀⠀⠀⢰⣿⣿⡾⠁⠀⢀⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠙⣿⣿⡄⢀⣴⣶⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡄⢀⣾⣿⠏⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠸⣿⡿⠛⢉⡛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡉⠛⢿⣿⡏⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⢸⣏⠀⢢⠀⠐⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⡤⠂⢸⡗⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⣀⣿⠀⠀⠁⠰⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⡆⠈⠀⠀⣼⣇⡀⠀⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢀⣀⣽⣿⣿⠇⠀⠀⣠⡏⢻⣿⣿⣿⣿⣿⣿⣿⢹⣇⠀⠀⠀⣿⣿⣯⣀⣀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⡿⠟⠋⠉⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⡗⠀⠀⠀⠈⠙⠛⢿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣦⣠⣀⣠⣶⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣄⣠⡿⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠦⢤⣅⣈⡉⠀⠉⠛⠛⠿⠿⠿⠿⣿⡿⣿⣿⠿⠿⠿⠿⠟⠛⠉⠀⢈⣁⣈⡥⠴⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠶⣦⡀⢠⣌⠉⢉⡙⢓⡒⠒⠒⠦⠤⠤⠤⠤⠤⠤⠴⠖⠒⠒⠒⢋⣉⣉⣥⠀⣴⡶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣿⠇⢐⣿⠀⠀⡇⠈⠉⣿⡏⠉⣠⡞⠉⠙⠧⠀⣿⣇⣀⣿⠁⢸⣿⣀⡈⠀⣿⣇⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⣧⠸⣿⠀⢀⡇⠀⠀⣿⡇⠀⠹⣧⣀⣀⡴⠀⣿⡏⠉⣿⠀⢸⣿⠉⠁⠀⣿⡏⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡾⠃⠀⠙⣛⣋⣀⣤⣤⠭⠥⠤⠤⠤⠭⠤⠤⠤⠭⠤⠤⣭⣅⣘⣛⣛⠛⠀⠿⠇⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⡴⠶⠞⠛⠋⠉⠉⠀⠀⢰⣞⡶⠀⣶⣰⡆⢰⡞⣶⠀⣲⡶⣦⠀⢀⠉⢉⠙⠛⠳⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠄⢸⠇⠀⢴⣭⡿⠀⣿⢹⡇⠸⣧⣿⠀⢾⡟⠁⠀⣓⠄⢨⠁⠀⠀⠀⠀⠀⠉⠁



⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠉⢩⠋⠉⠉⡏⠉⠉⠉⡏⠉⠉⢹⠉⠉⠉⢹⠉⠉⠙⡍⠉⠉⠉⢆
⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⠆⠀⠀⢠⠀⠀⠀⢀⡃⠀⠀⢘⡀⠀⠀⠀⡄⠀⠀⠰⡀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠘⡟⠛⠛⠛⣿⠛⠛⠛⢻⠛⠛⠛⢻⡟⠛⠛⢻⡟⠛⠛⠛⡟⠛⠛⠛⣻⠛⠛⠛⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⠔⠈⠢⠤⠔⠃⠑⠤⠤⠊⠐⠠⠤⠊⠐⠤⠤⠊⠈⠢⠤⠔⠉⠢⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡟⠛⠛⠛⢻⡟⠛⠛⠛⢻⡟⠛⠛⠛⢻⡟⠛⠛⠛⢻⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣧⣤⣤⣤⣼⣧⣤⣤⣤⣼⣧⣤⣤⣤⣼⣧⣤⣤⣤⣼⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣶⣶⣶⣾⣷⣶⣶⣶⣾⣷⣶⣶⣶⣾⣷⣶⣶⣶⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣯⣉⣉⣉⣹⣏⣉⣉⣉⣹⣏⣉⣉⣉⣹⣏⣉⣉⣉⣽⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠄⠠⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠥⠬⠄⠠⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⣄⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⣧
⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⣸⣿⡆⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢰⣿
⠀⠀⠀⠀⠘⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢻⡿⢟⣄⠀⢀⣶⣝⠿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⣛⣛⠛⠛⠃⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡺⠏⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠨⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠘⠛