July Emojis & Symbols

⠀⠀⠀⣤⡤⢤⡤⢤⡤⢤⣄⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⡿⠷⠮⠴⠼⠧⠿⣿⠀⠀⠀⠀⠀⠀⣻⣥⡿⠁⠀⠀⠀⠀⠀⠀⡀⠀⠹⣿⠁⣀⠀⠀⠀⠀⢨⡉⡶⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⡤⠻⣿⣿⠃
⠀⠀⠀⡇⠀⢀⡴⣷⠀⠀⣷⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠻⢷⡐⠀⡿⢀⡟⠃⠀⠀⠀⠈⢹⣿⣆⢀⢀⣾⣷⡀⠀⠀⠀⠀⣴⣛⠳⢶⡌⠉
⠀⠀⠀⡇⠀⠘⠛⠿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⢻⡆⠀⠀⠀⠀⠀⠀⠀⠒⠙⠄⠣⠊⠔⠛⠀⠀⠀⠀⢸⣿⠘⣿⠊⣿⡿⠁⠀⠀⠀⠀⡝⠏⠟⠃
⠀⠀⠀⠙⠖⠒⠒⠒⠒⠚⠛⠀⠀⠀⠀⠀⠘⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠛⠀⠛⠃⠀⠀⠀⠐⠛

⠀⠀⠀⢠⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⣠⠴⠂⠀⠀⠀⠀⠀⢠⡄⢲⠆⣤⡀⠀⠀⠀⠀⢀⣴⢀⠀⠀⠀⡀⡀⠀⠀⠀⢲⣀⣀⣀⣠⠤⢶⡲⠤
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⠀⠔⠊⠙⠓⠤⠀⡀⠀⠀⠀⠾⢦⣾⡟⢿⣧⡾⠇⠀⠀⠀⢈⡹⡉⣌⣡⣈⣏⣃⠀⠀⠀⢸⣿⣿⣿⣟⡯⠭⠭⡅
⠀⠀⠀⠈⠻⣿⡿⢻⣿⣿⠇⠀⠀⠀⢙⢻⢷⠶⠶⠾⠿⡟⠃⠀⠀⠘⣛⣻⣷⣀⣰⣿⣟⡛⠀⠀⠀⠸⣧⣧⢫⣧⢻⣦⡿⠀⠀⠀⢸⠭⠭⠵⣖⣒⣭⣭⣓
⠀⠀⠀⠀⠀⠈⠀⠀⠙⠁⠀⠀⠀⠀⢶⣬⣼⣘⣘⣃⣣⣧⡆⠀⠀⠀⠙⢥⡝⢻⡛⣧⡝⠃⠀⠀⠀⠐⣯⣰⣷⡀⣇⢸⡇⠀⠀⠀⢸⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠙⠁⠉⠀⠀⠀⠀⠀⠈⠉⠈⠀⠁⠉⠉⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠐⠜⠴⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣋⣀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠈⢣
⠀⠀⠀⠀⢲⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠈⣢⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⣄⠀⠀⠀⠀⠈⡍⠉⠉⠉⡍⠀⠀⠀⠀⠀⠀⢇⣤⣄⣄⣨⠂
⠀⠀⠀⠀⠈⠹⠻⠟⡏⠀⠀⠀⠀⠀⢸⣥⣴⣿⣿⣷⣶⣿⠄⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣾⠄⠀⠀⠀⠀⠇⠸⠿⢠⡇⠀⠀⠀⠀⠀⠀⠀⢻⠑⣽⠃
⠀⠀⠀⠀⠠⠏⢘⡇⠹⠄⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⠜⠀⠀⠀⠈⢍⣉⣉⣉⣉⣉⣉⠝⠀⠀⠀⠀⠀⢸⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠃
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢸⣟⣿⣏⣹⣿⣻⡇⠀⠀⠀⢠⣤⣤⣤⣤⣀⡀⢀⡄⠀⠀⠀⣴⣿⣽⣯⣿⣿⣷⡄⠀⠀⠀⠛⢉⠀⣀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣟⢹⡏⣿⢹⡇
⠀⠀⠀⢸⢩⢩⢽⣉⣽⡉⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⢁⠀⡰⠀⡴⣄⢠⢸⠀⠀⠀⠀⢸⠀⡎⣀⣀⣀⢸⠀⠀⠀⠀⠀⢸⣸⡇⣇⣿
⠀⠀⠀⢸⣬⢭⢬⡭⡥⣥⡇⠀⠀⠀⠈⠛⠟⠿⣿⠿⠟⢯⠀⠀⠀⠘⣦⣤⢤⢤⢤⣬⣤⡞⠀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣘⡀⠀⠀⢀⣄⢸⣿⣧⣧⡿⢀⣄
⠀⠀⠀⠀⠙⠺⠾⡷⠗⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠼⠼⠷⠋⠀⠀⠀⠀⠀⠘⠤⠼⠿⠿⠿⠿⠏⠀⠀⠘⠻⠷⠿⠥⠽⠿⠿⠛

⠀⠀⠀⢀⠀⡀⢀⣠⣀⠀⡄⠀⠀⠀⡀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣤⢠⣆⢰⢦⣴⠄
⠀⠀⠀⠉⢘⡇⠈⠛⠃⢘⡇⠀⠀⠀⢻⣷⣶⣨⣿⣠⣶⣾⡇⠀⠀⠀⠀⠀⢱⣶⠀⠀⠀⠀⠀⠀⠀⢶⣄⣠⣤⣤⣤⣤⣄⡀⠀⠀⢈⣭⣭⣭⣭⣼⣯⣽⡄
⠀⠀⠀⣀⠠⡇⠀⣹⠀⠀⡇⠀⠀⠀⠈⠙⢛⣿⣿⣿⠛⠋⠀⠀⠀⠀⠀⢀⠈⣿⣿⠀⠀⠀⠀⠀⠀⣻⡯⣥⣤⣤⣤⣤⡬⠇⠀⠀⠸⣿⣤⣼⣧⣧⣤⣬⡇
⠀⠀⠀⠉⢈⡇⠀⢺⠀⢠⣄⠀⠀⠀⠀⠐⠛⣼⣾⣦⠓⠂⠀⠀⠀⠀⣄⣸⣤⣿⣧⣦⣄⡀⠀⠀⠀⠉⠁⠀⠀⠶⠖⠀⠀⠀⠀⠀⢰⡇⢸⠰⣿⡂⣼⣷
⠀⠀⠀⠀⠀⠁⠀⠙⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠐⠚⠑⠋⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⡟⢡⠆⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃⡼⢡⡟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠏⠰⠃⠚⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣿⣿⡏⢀⡞⡽⢰⠏⠁⠀⠀⠀⠀⠀⢠⣤⠀⣞⣰⠃⣴⡇⢠⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢃⣾⣿⡟⠀⡾⣰⢃⡟⠁⠀⠀⠀⠀⣠⣤⡄⠀⡼⢩⢃⡾⣼⢀⡿⡼⢣⠏⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⣼⣿⡿⠁⠘⠓⠃⠚⢀⣀⣤⠴⠶⡾⠛⠋⠀⠀⠁⠁⠈⠀⠉⠚⠀⢠⡟⠚⢱⡵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⣸⣿⣿⠃⠀⠀⣠⣴⠞⠋⠁⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⢷⠀⠀⠀⠀⡜⠁⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⢰⣿⣿⠇⠀⢠⣾⠟⠁⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⡏⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⢠⣿⣿⡏⠀⢀⣿⡇⠀⠀⠀⣷⢀⣾⡏⠀⣀⡀⠀⠀⣀⠀⢠⣿⢣⠞⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣶⣶⣿⣿⣿⣶⡶⠈⢿⣇⠀⣀⡴⠃⣼⡟⠀⣼⡿⠁⢠⣿⠋⢀⣿⡷⠋⠀⣼⡿⠁⢀⣾⠏
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⣿⣿⡿⠛⠛⠁⠀⠀⠉⠉⠉⠀⣼⡿⢁⣼⡿⠁⢠⣿⠃⠀⣼⡟⠀⠀⣼⡿⠁⢠⣾⡟⠀⢀⡆
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠷⠋⣿⢁⡰⢻⣏⣀⠞⣿⡀⢀⠼⣿⢁⣰⢻⣿⠁⣠⠎
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠰⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠉⠉⠀⠀⠉⠁⠀⠈⠉⠁⠀⢉⣉⣠⣾⠷⠚⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⣡⡿⠃
⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⣤⡤⠴⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⡄⠀⢀⠀⠀⠂⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⡀⢢⠁⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠃⠀⡍⠀⠀⠀⠀⠀⠀⡀⠀⣎⢈⡃⠀⠈⠀⠁⠀⠀⠀⠊⠉
⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠀⢉⡁⠘⠀⠀⠀⠀⠀⠁⡇⢸⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠐⠀⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠁⠀⠀⠀⠀⠓⢚⠳⠂⠖⠀⠀⡀⠀⠓⢶⠸⠖⡀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⠀⢸⠀⠀⠀⠀⠀⠎⠀⠀⠀⢄⠀⠀⠲⠃⠠⠆⢀⠢⠆
⠀⠀⠀⠀⠀⠀⡀⠰⠷⠅⠤⠆⠖⠀⠀⠀⠶⠲⠂⠉⠁⠀⠃⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠋⠁⠠⢀⠀⠀⠀⠀⢀⠔⣦⠁
⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⢂⣠⣤⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⢏⡀⠀⠀⠀⠠⠔⠒⠈⠁⠀⠈⠁⠉⠈⠁⠂⠂⠠
⠀⠀⠀⠈⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠘⠴⠇⠀⣸⡀⢀⡀⢀⣠⠃⡀⣀⣀⣀⣆⣆⢀⣓⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠄⠀⠀⠀⠀⠀⠀⢀⠜⢎⡢⠄⣀⡴⠋⠉⠁⠒⠉⢰⡛⠛⠛⠛⠋⠁⠛⠿⠃⠀⠉⠉⠛⠳⢿⣿⣶⡆
⠀⠀⠀⠀⠘⠂⠤⢄⣀⠀⠀⠀⠀⣀⠤⠐⠈⠀⠀⠀⠩⠛⠉⠀⠀⠀⠀⠡⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠄⣀⠈⣁⠒⠒⠒⠀⠒⠂⠁⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠐⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⡇⠀⠀⢹⡇⠀⠈⣿⠀⠀⠛⡶⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣆⠀⠀⣠⡞⣿⠓⠲⣿⡀⠀⢸⣧⡄⢠⡟⠀⠀⣼⠃⠀⢀⣿⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⡴⠛⣦⡀⠈⠁⢿⠀⠀⠸⠧⠀⢸⡏⠉⠉⠀⠀⢰⡿⣇⣠⠾⠃⠀⣠⠞⠉⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⢷⡄⠀⠈⢷⡄⠀⠈⠷⠀⠀⠀⠈⠋⠀⠀⠀⠀⠲⠛⠀⠀⠀⠀⠀⢸⣇⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣀⣭⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡶⠶⠛⠛⣉⣉⣩⣤⣤⣤⣍⣉⡛⠳⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠶⠟⠛⣉⣉⣡⣤⣤⣤⣬⣉⣉⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⠶⠟⠛⣉⣩⣥⣤⣤⣤⣤⣬⣍⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠶⠞⢛⣉⣥⡤⠶⠶⠶⠶⢦⣬⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠛⠶⠶⢦⣤⣤⣤⣴⠶⠶⠛⣋⣭⡴⠶⠞⠛⠛⠛⠶⢦⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⢶⣤⣤⣤⡶⠶⠾⠛⠉⢀⣀⢀⡀⠀⠄⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢸⣶⣷⡆⠠⡀⣤⣤⢨⡝⡏⣩⢡⡄⠀⢤⡀⢨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⡇⠸⠾⠟⠗⡁⠁⠂⣿⢸⡇⠂⣾⢸⡇⠄⠈⢷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⢀⡤⠀⠀⠘⠛⣿⡏⠀⠀⠀⠀⠸⢧⣤⠟⠸⢧⣤⡟⢸⣧⣤⡄⢸⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⠢⡍⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔⣡⠄⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣄⠀⠹⡶⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠞⢡⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠏⡼⣵⠐⣠⢠⠀⡀⣼⠀⢀⢀⡀⡄⡀⠂⢠⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠃⠚⠘⠄⠧⠐⠧⠘⠇⠃⠙⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣰⠟⢷⡀⠀⠀⠐⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⠁⠀⢸⠇⠀⠀⠀⠀⠸⠽⠃⠀⢀⡶⢼⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠴⠃⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⣿⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀⢀⠀⠀⠀⡀⣿⠀⡿⠀⡀⠀⠀⣀⠀⠀⠀⠀⢼⠄⠀⠀⠸⡘⡆
⠀⠀⠀⠀⠀⢠⡜⠒⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢻⠁⠀⢰⡇⢹⣾⠃⢠⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢱
⠀⠀⠀⠀⠀⣲⠙⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⡇⢸⠀⢀⣿⡁⣸⣧⠀⢸⣿⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⣟⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⡇⠘⠷⠟⠘⠿⠃⠘⠷⠟⠻⣤⡾⢻⡄⣀⣠⣤⠶⠶⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡟⠉⠀⠀⠀⠀⠀⠀⠀⢮⡵
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⢀⠀⠀⠀⣾⠀⠀⠀⢠⢤⣒⡮⠽⠂⢀⡴⠋⠁⢸⡇
⠀⠀⠀⠀⠀⠛⡟⠂⠀⠀⣼⠃⠀⠀⣀⢰⠾⠀⠀⢰⠇⠀⠀⠀⠈⠁⠀⠀⠀⣴⠏⠀⡀⠀⢸⡇⠀⠀⢸⡉⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢄⣯⠉⠃⠀⢠⡏⠀⢀⣄⠀⠀⠀⠀⠀⣸⠇⢀⣸⡟⠀⣼⠃⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠉⠀⠀⣠⠏⠀⠀⠼⠼⠆⠀⠀⠀⠀⢿⡀⠘⠃⠀⣰⠏⠀⠀⢀⣀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠳⠦⠴⠟⠁⠀⠀⢹⡇⠘⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠲⢄⡉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡈⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠊

⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⣀⢠⢀⡀⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⢀
⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⢸⣅⢉⠀⠀⠀⡎⠉⠉⠉⠉⠙⠀⠀⣿⣿⣿⣿⡯⠭⠯⠍⠀⢸⣿⣿⣿⣇⣈⣈⡁
⠀⢰⣛⣻⣷⣿⡄⠀⠀⡊⢲⠀⠁⠘⠀⠁⠀⠀⠱⣠⢰⢠⣄⡶⠀⠀⠹⠿⠿⠿⠭⠭⠭⠁⠀⠈⠿⠿⠿⠷⠶⠶⠆
⠀⠈⠙⠛⠛⠛⠁⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⠀⠀⣤⣤⣦⡄⠀⠀⠀⠸⣷⢀⠀⠀⠀⠀⠀⠀⣰⢏⢁⢅⠉⢷⡀⠀⠀⠀⣼⣿⣏⣱⠀⠀⠀⠀⢀⣨⣿⣿⣇⣀
⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠸⢇⡄⠀⠀⠀⠀⢽⡈⠧⠥⠅⣸⠁⠀⠀⠀⢩⣉⢉⣹⠀⠀⠀⠀⠀⠂⠈⠈⠱
⠀⠀⠠⠤⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣿⠶⠶⣾⡇⠀⠀⠀⠀⠀⠡⡵⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠸⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⣠⣴⣿⣷⡆⠀⠀⣀⣰⢢⡤⣤⢰⣄⡀⠀⠀⣿⠿⠿⠿⡿⠀⠀⠀⠀⠘⢿⣿⣗⣲⡄⠀⠀⢸⠛⠛⠛⣛⠛⡇
⠀⢸⣿⣿⡿⠋⠀⠀⠸⠟⠋⠉⠓⠛⠉⠙⠻⠀⠀⠘⢆⣀⡰⠃⠀⠀⠀⠂⠀⠾⡟⢛⠛⠀⠀⠀⢸⠀⠀⠰⢿⠄⡇
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠢⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠉⢨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠛⠉⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠄⢂⡞
⠀⠀⠀⠀⠀⠀⠤⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠀⠀⠀⠀⠀⣾⠋⠉⠁⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡘⡠⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠑⠄⠀⠀⠀⠀⢀⡴⠋⢳⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢏⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣠⣴⣏⠀⠀⠁⠓⠒⠖⠊⠻⣧⣀⠀⠀⠀⢸⠀⠀⡆⠆⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠾⠋⠨⡁⠀⠀⠀⠠⠀⠀⠀⢀⠬⣻⣷⣌⠘⠀⡄⠀⠐⢀⣼⠃
⠀⠀⠀⠀⠀⢠⡀⠀⡴⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⣰⢛⣖⣇⣾⣻⡿⢷⣶⣧⣤⣼⠇
⠀⠀⠀⣘⠓⠢⠍⠂⠀⠀⠀⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⡁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡋⡋⠉⠉⣡⠾⠋⠀⠀⠀⠁
⠀⠀⠈⠉⣉⠁⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⡹⠋⠀⠙⠲⢤⣀⠀⠀⠠⠀⠈⠀⠀⠀⢃⣇⣴⠟⠁
⠀⠀⠐⠋⣠⠄⠀⠀⠀⢀⠀⡙⢦⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢏⠀⠅⡠⠊⠀⠀⠀⡉⣩⡻⣿⢚⡶⡿⣻⡿⠋
⠀⠀⠀⠀⠋⢀⡇⢸⠀⠸⡇⠁⠀⠁⠀⠀⣠⣴⠟⠁⡀⠀⠀⠀⠙⠢⢄⣅⣀⣠⢊⣾⢟⣗⡿⣏⣮⡿⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⢁⡀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠉⠉⡉⢛⠛⢛⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⡾⠍⠀⠀⠀⠀⠉⠒⠠⣤⣄⣀⣀⡀⣁⣸⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⡀⠂⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠑⣀⠀⠀⠀⠐⠤⣀⠀⠁⢠⣠⢅⣴⢰⡭⣏⣯⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡆⡧⠛⠢⢄⡀⠀⠀⠀⠘⠗⢶⢽⣽⢽⢭⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠹⣷⠁⠀⠀⠀⠈⠑⡲⡦⣄⣄⣀⣀⣈⣤⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⡶⠻⣷⡤⣀⢠⢄⡳⡂⠇⣀⡇⣯⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⠔⠋⠀⣠⠞⠉⠀⣠⡌⠳⣮⣽⣲⠿⣴⣗⣧⣷⡿⠋
⠀⠀⠀⠀⠀⠴⠊⠁⢀⡴⠞⠉⢀⡴⠛⢉⡿⠿⠶⢾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣀⡴⠋⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠔⠉⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣷⣶⣶⣶⣶⡾⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⡾⡿⠾⠷⠶⢶⣶⠾⠿⠶⠶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⢀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣀⡻⡦⠑⠘⠰⠉⠥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢒⣋⠁⠀⠀⠀⠀⢒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠰⠀⠐⢀⡀⠈⠁⠀⠉⠥⢂⡀⠀⠀⡘⠦⡉⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠐⠨⠋⠀⠀⠀⠀⠀⠐⡒⠀⡀⠀⠐⠋⠀⢸⡇⠇⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⣄⠀⠃⢸⠇⣴⠀⡴⠟
⠀⠀⠀⠀⠈⠀⠡⠄⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠈⢀⠇⠀⠀⠘⣂⠹⡶⠇⠈⠀⠀⠈⠀⣤
⠀⠀⠀⠀⠀⠀⢀⠔⠋⢠⠀⢀⢀⠀⠀⠁⠀⠀⠀⢸⠀⠀⣠⡤⠭⠀⠁⠀⠀⠀⠀⠀⠀⠰⠶⠖
⠀⠀⠀⠀⠀⠚⠁⠀⠀⠁⠀⡈⠈⠀⠀⠀⠠⠀⠀⡏⠀⠀⠀⠰⠆⡀⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⠀⠀⡇⠀⠀⠀⠴⠟⢁⠀⡀⢀⡄⢠⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡇⠀⠀⠀⢀⡴⠃⠈⠃⣼⠁⠈⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡇⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠃

⡷⣞⣷⣿⣶⣿⣾⢷⣾⡶⣿⣞⡷⣾⣷⠿⣶⢿⣾⣷⣾⣶⣿⣾⣷⣾⣷⣿⣾⣷⣾⣷⣿⡖⣟⣞⠓⣺⣷⣿⣾⣷⣾⣷⣿⣶⣿⣾⣷⣾⣷⣿⣾⣷⣾⣷⣿⣶⣿
⣧⣿⣧⣶⣿⡟⣷⣮⣿⣿⣿⣹⣷⣿⣴⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣳⣞⣫⣮⣛⣽⣾⣿⣿⣧⣿⣴⣿⣾⣧⣷⣾⣽⣧⣴⣷⣶⣶⣾⣿⣿
⠉⠈⠁⠈⠁⠱⡄⠁⠈⠁⠉⠁⠉⠈⡱⠋⢡⠟⠁⠁⠈⠁⠉⡀⢩⠈⠃⠉⡡⠉⠈⠅⠸⠟⡉⢤⠙⠈⠁⠙⠁⠉⠈⠃⠈⠁⠉⠀⠁⠈⡁⠉⠀⠉⠈⠁⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⡰⠁⠀⠁⠀⠀⠀⠀⠀⠀⣬⡀⠀⣠⠖⠃⠀⠀⠀⡈⠀⠅⢀⠀⢀⠀⠀⠂⠀⠀⢀⠀⠀⢄⠀⠀⠀⠁⠀⠄⠀⢀
⢀⠀⠀⠄⠒⠂⠤⠀⠀⠀⡀⠀⠀⡇⠀⣠⠆⠀⡠⠤⠒⡒⠄⠰⡀⢀⠀⠀⠓⡠⠀⡄⠁⠬⠤⢨⡆⢂⢀⠁⠀⠁⠀⠨⠓⣄⠀⠀⠀⠀⢀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡑⠀⠀⠄⠘⠁⠀⢀⡀⠀⠀⠑⠬⠁⡁⠖⠀⠠⠉⠀⠴⠁⠖⠀⠐⢁⡀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢀⡸⡖⣃⣋⣖⡧⠀⠀⠀⠒
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠐⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⠀⠀⠰⠗⢩⠐⠰⠀⠐⠁
⠀⠠⠊⠁⠀⢀⡤⠊⠀⠀⣠⠈⠀⠈⠀⠒⠀⠀⠉⠃⢀⠂⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠠⠛⡁⠀⠛⠃
⠀⠀⠀⠀⢀⠈⠀⡠⠂⢀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠢⠀⢀⠠⢈⡉⢄⡀⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⡄⠀⠁⠀⠘⡆⠀⠰⡄⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄
⠀⠀⠀⠀⢀⠼⠀⠤⠀⠀⣸⠀⠀⠅⠀⠀⢡⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠐⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠
⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣶⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠒⠶⠆⠂⠂⠒⠒⠒⢦⠤⡀⠀⠀⠀⢀⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠁⠀⠃⠀⠀⠀⡀⠀⠀⠣⠄⠀⠈⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠒⠀⠠⢀⣀⣉⠀⠔⠠⡀⠀⢀⣠⠀⡀⠄⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠉⠉⠈⠀⠈⠉⠉⠁⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⣀⡠⠌⠀⠍⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠚⠈⠁⠀⠀⠀⠀⠀⡰⠃⠀⠈⡙⠂⠀⠀⠀⠀⠁⠀⠀⠦⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣰⠒⠛⠋⠟⢥⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡇
⠀⠀⠀⠀⠀⢀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡤⠀⠀⠀⢀⠀⠀⠀⠀⠀⢈⡀⠀⠇⠀⠀⠀⠐⠁⠈⠃⡀⠀⠀⠀⠀⠀⠀⡇⠀⡄
⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠁
⠀⠀⠐⠄⠀⠈⠀⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠤⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⠀⣀⣤⣤⣄⣤⢤⣴⠶⠶⠶⣶⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣤⣀⣤⠶⠶⠶⣤⡾⢋⣉⠙⢷⣟⡉⠙⢯⣤⣄⠈⣷⣦⠈⣿⢲⡀⢸⣷⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡏⣴⣶⣆⢹⣧⣾⡿⡆⢹⠓⠛⠛⡆⢸⠋⣹⠀⣼⣤⡞⢀⡷⢾⣠⠟⠹⠧⠞⠛⠞⠁⢻
⠀⠀⠀⠀⠀⠀⠀⣼⠿⠛⣛⣿⢠⣧⣤⣴⢃⡾⠶⠶⣾⣡⠞⠛⠻⠾⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢀⡏⣼⣿⠁⠙⠛⠀⠀⠈⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⢀⣿⡸⣿⡇⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣀⣤⣤⡀⣤⣤⣤⠀⣶⠛⠙⠳⠶⠋⠈⣳⡄⠀⠀⣿
⠀⠀⠀⠀⠀⣸⣯⣧⣿⡇⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣿⠏⠹⠏⠈⣿⣿⠀⠸⣇⣙⠷⣤⠀⠀⣠⡾⠋⠀⠀⠀⢻
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢻⡀⢺⡟⢹⡆⠀⠀⠀⣸⢿⠀⠀⠉⢉⡇⣽⠀⠀⣿⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢰⣿⣿⣼⣿⡇⠀⠀⠀⠠⣶⠻⠾⠇⠈⡇⠈⢷⣀⣀⣠⠟⠘⠶⠶⠞⠛⠁⢻⣤⣤⠿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣾⢸⣿⢇⣿⡇⠀⠀⠀⠀⠹⣦⣀⣀⣰⠇⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⡏⣿⣿⢸⢸⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⣸⢃⣿⡏⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠰⠀⠀⠀⣷
⠀⠀⠀⣿⣸⣿⡇⡆⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⠶⠟
⠀⠀⠀⠈⠙⢿⣇⣧⠀⣇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣴⠶⠶⠶⠶⠚⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠤⠶⠶⠶⠖⠛⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⢛⣿⠟⢿⣿
⠀⠀⠀⠀⠀⣠⣾⣿⠟⢻⣷⣾⣿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣴⣿⣿⣋⣁⣀⣸⣿⣇⣴⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀
⠀⠀⣿⣿⣿⣟⠋⣽⣿⣿⠛⢻⣿⣯⣄⣿⣿⣿⡇⠀⠀⠀⠘⠈⠈⠀⠀⠀⠀⠀⠀⡀⠀⡰⢁⠔⢀
⠀⠀⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⡿⢛⣿⣿⠿⠿⠇⠀⠐⠂⠀⠀⠀⠈⠒⠂⠁⠐⠊⠘⠉⠉⠁⠘⡉
⠀⠀⠀⣠⠆⠀⠀⠀⠀⢸⡟⢻⣷⣾⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⠉⢲⣤⠊
⠀⢠⡞⠁⠲⠦⠦⢤⠄⠘⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣿⣶⡄⠉⠙⠛⠉⠁
⠀⠀⠠⠤⠶⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣄⠀⠀⣾⡿⠿⠿⣟⣛⠯⠇⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⣠⣶⣶⣄⠀⢠⣞⣽⣷⠀⠀⣴⡡⠚⡹⢦⠀⠘⠫⠭⣭⣖⠖⠋⠀⠀⠀⠀⠀⢰⣻⡿⣯⣿⡄
⠀⠀⠀⠀⢻⣿⣿⡿⠃⠘⠿⣷⠟⢀⣠⠟⣷⠁⠐⠉⠀⠀⠀⠀⠈⢁⣀⣀⣬⣭⣭⣤⠀⣿⣽⣿⣿⡾⠁
⠀⠀⠀⠀⡄⠈⠉⠀⠀⠀⣠⡤⠖⠉⠀⠀⠀⣤⡄⢠⡄⠀⠀⠀⣴⢿⣽⣯⣭⣥⣤⡤⠀⠓⠓⠛⠉
⠀⠀⠀⠀⢻⡀⠀⠀⢴⠟⠋⠀⠀⠀⠀⠺⣆⢻⣷⢸⣿⠁⠀⠀⢹⣿⡷⣶⣤⣤⣤⠂⢀⣔⠻⣶⣝⠢
⠀⠀⠀⠀⠈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡬⣿⢺⠻⠀⠀⠀⠀⠙⢿⣟⡾⠓⠀⠀⣦⡙⢷⣄⡙⠗
⠀⠀⢠⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⢁⣩⣴⣶⣶⡆⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⢨⠻⠶⠙⠁
⠀⠀⠀⣯⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁
⠀⠀⠀⢭⣉⣉⣉⣉⠀⠀⠀⠤⠤⠀⠀⢀⠀⠀⠀⢀⣀⣀⠀⣀⣤⣤
⠀⠀⠀⢸⣉⣙⣛⡻⠀⠀⠀⠸⠏⠀⠀⠀⠀⠀⠀⠐⣲⠂⠀⠘⣿⠇
⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠆⢠⠄⡀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠐⠓⡄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⠡⡀⠀⠇⠀⡔⠁⠀⠀⢀⠠⠒⡉⠤⠀⠀⠒⠂⠠⠤⡀
⠀⠀⠀⠀⠀⣀⠄⠀⠀⠠⠤⠤⢄⠀⠀⠀⠀⠀⠱⠀⠀⠈⡠⠊⠀⠒⠁⠀⠀⣀⣠⠤⠐⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⠁⠂⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠔⣋⠥⣀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⢐⠠⠄⠀⠀⠀⠘⠠⠅⠀⠀⠀⠐⠠⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⢈⠀⠀⠊⠩⠄⣀⠒⠀⠛⡠⠀⠀⠉⠉⠀⠒⠦⠀⠀⠀⠀⠀⠀⠈⠃
⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠊⠠⠁⠀⠀⠀⢀⡀⠿⣀⢐⢠⢩⠀⠁⠀⠤⣀⠀⠀⠀⠀⠁⠰⣄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢠⠊⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⢠⡀⠀⠈⠃⠀⠀⠀⢠⢠⠘⡆
⠀⠀⠠⠀⠀⠠⠇⠀⡀⠁⠀⠀⡀⠀⠀⠀⠰⠃⠀⢠⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠈⡤⠘⠄⠀⢄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⢄⠀⢡⠒⠀⠀⠊
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠰⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢀⡴⠋⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢠⡟⠀⠀⡼⠀⢀⡴⠂⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣿⠁⢀⡜⠁⠀⡾⠀⠀⠀⡟⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣸⣧⠔⠉⠀⠀⢸⠃⠀⠀⢰⠇⣰⠟⠉⣿⠀⢰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠒⣿⡇⠀⠀⠀⠀⣿⠀⠀⢠⡏⣸⡏⠀⣼⠃⠀⢸⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⡇⢠⡖⣶⠀⡏⠀⣠⠏⢀⣿⢀⡼⠃⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣿⡇⢻⡇⠀⠀⣿⠞⠁⠀⢸⡧⠞⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢸⣧⠀⠉⠉⠉⢹⡄⠀⠀⢸⡇⠀⠀⠀⣰⠃
⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢻⡄⠀⠈⢿⡀⢀⡼⠃
⠀⣠⡾⠋⠁⠀⠈⠙⢷⣦⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠦⠀⠀⠉⠁
⣼⠏⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠈⣧⠀⢀⡀⢀⣤⣄⠀⢀⡠⠔⠒
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡤⠚⠉⣸⣿⠀⢀⡤⠀⠀⢀⡾⠁⠀⢠⠇⠀⢸⡷⠟⠁⢘⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⡀⠀⠀⢻⣿⣠⠾⡇⠀⠀⢸⠇⠀⣠⠋⠀⠀⣼⠇⠀⣰⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢸⣿⡇⠀⠀⠀⠈⠁⠀⠹⣄⠀⣿⡤⠚⠁⠀⠀⢠⡿⠀⣼⠃⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢠⡿⠁⢰⡇⠀⠀⣼⠇
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⡴⠟⠁⠀⢸⡇⠀⣰⠏
⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠸⣧⣀⣠⡾⠋
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⢀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢰⡄⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⢳⡀⠈⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠦⢠⣤⠀⠀⢀⣤⡀⠀⠈⠧⠀⢻⠀⠈⠀⢀⠀⠀⠂⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣸⣿⡇⢀⣠⣤⣤⣜⠁⢠⣤⣬⣤⣄⠀⢠⣥⣤⣤⣄⠀⣤⡄⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⢻⣿⡗⢞⣫⣤⣼⣿⠆⢸⣿⠁⠈⣿⡇⢸⣿⠁⠈⣿⡇⠹⣿⣀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⢸⣿⠀⠀⢸⣿⠇⠸⣿⣤⣼⣿⡆⢸⣿⣦⣴⡿⠃⢸⣿⣦⣴⡿⠃⠂⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠀⠲⠄⠀⠀⠠⠀⠀⢸⡿⠀⠀⠀⠀⢸⣿⠀⢀⣠⠄⣤⣾⡿⠀⠀⢀⣀⣀⢰⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢤⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡈⠁⠀⠀⠀⠐⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⢀⣾⡿⠀⢀⣀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⢀⣾⡿⠁⠀⢺⣿⠃⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣾⣿⠃⢠⣬⡈⠛⠃⠛⠛⠛⠀⠄⠀⠀⠈⠀⠀⠠⠀⠰⢤⡉⠒⠶⢤⣄⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⢀⣾⣿⢃⣠⢸⣿⡇⠀⠀⡀⢰⣿⡆⢸⣿⠰⠈⢸⣿⠀⣾⡇⠀⠀⢿⣦⠀⣰⣿⠂
⠀⠀⠀⠀⠀⠺⠷⠀⠀⠀⠀⣾⣿⣧⣭⣤⣼⣿⣧⠠⠎⠀⢸⣿⡇⢸⣿⠀⡆⢸⣿⠀⣿⡇⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⡛⠛⢻⣿⡟⠀⣿⣆⣸⣿⠃⠸⣿⣄⣁⣼⡿⠀⣿⣧⣙⣀⣀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⣰⠈⠙⠋⠁⠀⠀⢨⠙⢛⡉⠀⣆⠉⠉⠉⠉⠉⠀⠙⠁⠻⠆⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢸⠀⠈⣇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠉⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⡀⠀⠀⠀⠀⠀⠀⠀⣻⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡀⠀⠚⠉⠙⠃⢰⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢻⡄⠀⢰⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢿⠀⠀⠀⢀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣼⠀⡀⠀⣰⠃⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢷⡄⠠⠀⠀⠈⡇⠀⠀⠏⠠⠁⡰⠁⡀⠀⢀⣠⠞⠁⠀⣠⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⣄⠀⠠⢀⣯⣰⡆⣰⣆⢠⡶⣦⣰⡶⣦⢰⣬⣆⡴⠋⠀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠙⠃⠦⠘⠇⠈⠘⠋⠤⠟⠹⠧⠟⠻⠼⠟⠉⠸⠏⠉⠀⠿⠀⠀⠛⠃⣀⣻⠳⠖⠛⠃⠀⠘⠃⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⡀⢀⣀⡀⠀⣀⣀⠀⠀⣀⠀⣀⣀⡀⣀⠀⢀⠀⣀⣀⠀⢀⡔⡒⢋⡉⢀⡀⢠⣀⠀⢀⡀⡛⠋⠁⠈⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢸⡿⣶⡏⢸⡏⣹⡆⣿⠼⠁⣿⡽⠇⣿⠬⠁⢻⢷⣾⠀⣿⢹⣷⢹⡧⠍⢸⡿⣾⡇⣿⡉⠛⢹⡧⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠉⠈⠁⠉⠛⠉⠀⠛⠛⠁⠛⠀⠀⠉⠃⠁⠙⠀⠉⠈⠛⠛⠁⠘⠋⠋⠘⠁⠈⠁⠉⠛⠁⠙⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠶⠶⠒⠂⠀⠀⠀⠠⠄⠂⢀⠀⠀⣀⣀⠀⢀⡀⣀⠀⡀⠀⠀⠐⠢⠤⣀⡀⠀⠀⠒⠒⠶⠦⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⢠⣦⠀⠀⣴⡤⠔⢲⡦⠀⠠⣿⣹⣇⣿⣷⠘⣿⠁⡀⣴⠀⠓⢠⣦⠉⠛⣶⢤⣄⣰⡆
⠀⠀⠀⠀⢀⣄⠀⠠⡴⠖⠂⠀⠀⠀⣀⡤⠖⠀⠀⠀⠀⣠⠊⠀⠉⠉⠈⢱⠈⠀⠉⢀⡀⢦⡀⠀⠀⠀⠁
⠀⠀⠀⠘⣿⣿⡏⠀⠀⠀⠀⠀⠀⠚⠉⠀⣠⠄⠀⢀⡼⠁⠀⠀⡼⠀⠀⢸⠀⡄⠀⠀⠻⡄⠹⣄
⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣴⠋⠀⠀⠀⢸⠇⠀⠀⢸⠀⢻⠀⠀⠀⠙⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠠⡞⠁⠀⡴⠀⠀⠀⠀⠀⠀⢸⠀⢸⡄⠀⣀⠀⠀⠀⠀⠙⠦⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢸⠀⠈⣇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠿⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢀⡴⢺⠃⣼⡝⣁⠀⠀⡀⠀⢀⢀⠀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⠴⠚⠁⢠⣏⡼⢋⡼⢡⠃⡜⢩⢧⠏⣸⡷⢁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⢰⢃⣼⠵⡧⡾⠴⢋⡞⠞⠁⣃⡽⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡵⠃⠀⠉⠁⠀⠀⠸⠁⠀⢜⣀⡴⢋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⠀⢀⡾⢀⣞⡈⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣠⣧⠈⡟⠠⠞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡟⠀⡤⠴⠒⠚⠃⠑⠒⢂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⢸⠂⠀⠀⠀⠀⣰⡫⢃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⠉⠀⠲⠖⡾⢠⠇⡼⢱⠟⢁⡎⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡿⠳⠄⠀⠀⣰⢃⣏⠴⠥⠻⠔⠛⠊⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠔⢡⠏⠀⠀⠀⢀⡠⠄⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣠⠏⠀⠀⠀⢠⡏⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠙⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡄⠀⠀⠀⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⠀⠀⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠈⠙⢦⠀⡴⠋⠁⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠃⠀⣿⡀⠀⠀⠀⠛⠀⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⡼⠃⠹⢦⣀⣀⣤⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠛⠶⠶⠞⠋⠀⠀⠀⠀⠀⢠⡄⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠡⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢠⣿⠃
⠀⠀⠀⠀⢀⣤⣤⣤⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠈⠓⠤⢤⣄⡤⠤⠴⠚⠋⠀⠀⣼⡟
⠀⠀⠀⠀⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠙⠳⢦⣀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄
⠀⠀⠀⠀⠘⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⣠⡼⠿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠲⠦⠤⠤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠄⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⣀⣤⣴⣾⣿⣿⠟⠋⢿⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀
⠾⠿⠿⠿⠟⠋⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡼⠛⠛⠻⠿⣷⣶⣤⣄⣀⣠⣿⠉⠉⠙⠓⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠋⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣁⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠿⢿⣿⣿⣿⣷⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠷⢀⡀⠠
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠠⠄⣀⣤⣄⣰⡌⠐⣿⠀⣵⣶⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠
⣶⡄⠁⢰⡆⣂⡤⣤⢡⡴⢶⣦⣿⣄⣼⠟⢷⣤⣿⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⡀⠙⠃⣴⣶
⠸⣿⣤⣾⣿⣩⣞⣿⡟⣷⠴⠟⢹⣏⣥⣄⣀⣼⡟⠀⢹⣿⣿⠠⠄⠀⠀⠀⠀⠀⠀⣿⣿⡇⠺⢂⡁⠰⠀⣿⣿
⠀⢿⣿⠀⢹⡏⢩⣵⣦⢻⡆⢸⡏⠿⢨⠙⠛⠉⠰⠶⢸⣿⣿⠀⠘⠿⠠⣦⢁⣤⡅⣿⣿⣷⢀⣿⣿⠀⠀⣿⣿
⠤⠘⠿⠀⠌⣱⣿⣿⣿⡄⣵⡬⣿⢶⣆⠐⣿⡖⣠⡶⠜⣿⣿⠀⣾⣿⡄⠀⢸⣿⣧⢸⣿⣿⠘⣿⣿⡀⠀⣿⣿
⠀⠀⠿⢆⣼⣿⢿⣿⣿⣧⠸⣇⡜⠀⠟⣀⣀⠠⣿⡷⠃⣿⣿⡆⣿⣿⡇⠀⢸⣿⣿⠘⣿⣿⡀⣿⣿⣷⣼⣿⣿
⠀⠀⢀⣾⣟⠋⠀⢉⣽⣿⣄⣭⣶⡄⢾⡏⢹⣷⢸⣷⠀⢹⣿⡇⢻⣿⣷⣦⣾⣿⣿⡇⢻⣿⡇⠙⢿⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣧⣴⣶⣿⣿⣿⠿⠛⠁⡈⠛⠿⠋⠈⣿⡆⢸⣿⣿⠈⠻⠿⠟⠋⠉⠛⢁⡈⠛⢃⡐⠀⣠⣿⣿⠏
⠀⠀⠻⠿⠿⠟⠛⠋⠙⣿⣿⡇⢰⣿⣿⣿⣷⣶⣤⣬⣤⣾⣿⡿⢠⣾⣿⣶⣦⣤⣀⣈⣁⣀⣀⣤⣶⣿⡿⠋⠰
⠀⠀⠀⠀⠰⠆⢼⡶⠀⢹⣿⣿⡀⠻⠿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⣰⡆⢴⡀⣠⢀⣀⣀⠤⠤⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠈⡿⢹⣏⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⢀⣠⣾⠟⣵⣿⠀⠀⣇⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠰⣿⣿⠷⣾⣿⣷⠄⠀⢀⡀⣀⠁⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⣿⢰⣿⠀⠀⠀⠠⠤⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⢿⡸⢻⠁⠀⠠⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡟⠀⠀⠀⠀⠀⣠⡄⠀⠄⠀⠙⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⠂⠀⠀⢀⠴⠚⠛⠉⣿⠀⠀⠀⠀⠀⣸⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢇⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣿⡷⠃⠀⠀⠀⠀⠀⣴⠄
⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⣀⣀⣈⠁⠀⠀⢸⡇⣠⠀⢀⣄⢀⣿⠁⠀⣿⠆⠀⣤⠀⠀⠀⠀⠀⢤⣼⣤⠄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⠟⠉⠉⠉⠛⣆⠀⢸⡇⣿⠀⣸⡿⢨⣿⠀⢠⣿⣀⣼⣿⠀⠀⠀⠀⠀⠐⠋⠓⠀⠀⠀⢀⡀
⠀⠀⠀⡏⠙⢆⠀⠀⠀⠀⣿⠀⢰⡇⠀⠀⠈⠀⢸⡇⠙⠶⠋⠳⠊⠹⠖⠁⠈⠉⠀⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡰⠋⢹
⣀⣠⠖⠃⠀⠈⢣⡀⠀⠀⢻⡄⠈⢷⣄⣀⡰⠀⣼⠃⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⢾⣿⠉⠀⠀⠉⠹⣆⠀⠀⢀⡜⡁⠀⠘⠲⣄
⠹⡄⢀⡾⢿⣍⣹⠁⠀⠀⠀⠙⢶⣤⣈⣉⣠⡾⠋⠀⠀⣠⡀⠀⠀⣰⠏⣠⢿⡃⣼⡇⣴⠺⠆⠀⠀⣽⠀⠀⠈⢏⣩⡷⢷⣄⢠
⠀⠙⡾⠁⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⢹⡄⠷⠛⣰⡟⠀⢷⣤⣤⣤⡾⠃⣀⡤⠖⠋⠁⠀⠀⢷⠊
⠀⣼⠁⢠⠀⠀⣴⢀⠀⠈⠙⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠞⠉⠀⠀⠀⣈⣉⡤⠖⠋⠁⢀⡀⠀⠀⢀⡀⠈⣧
⢰⠃⠀⠀⠀⣼⢃⡟⢰⢣⡖⡄⢠⠄⢉⠉⠀⠀⠐⠒⠒⠒⠲⠆⠀⠀⠠⠤⠶⠶⠒⠛⠋⠉⢠⡄⡀⢰⣦⠈⠻⣦⠀⠈⠁⠀⠘
⠈⠛⢦⣀⠘⠁⠞⣧⠏⡾⢠⠇⡿⠀⣼⢟⡆⡖⠀⡆⢠⢠⡄⡀⣤⠀⣤⠠⡄⣴⠁⢹⡄⠀⠈⣧⢸⡌⣇⢣⠀⠹⠆⠀⣀⡴⠛
⠀⠀⠀⠉⠓⠶⢤⣄⡈⠁⠁⠸⠇⠀⣿⠚⢸⡇⢀⡇⢸⢸⡇⡇⣿⠀⢸⡀⡇⢿⠀⠈⣧⠀⠀⠸⠆⠁⠙⢀⣠⡤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣄⣀⠁⠀⠘⠃⠘⠋⠿⠸⠇⠁⠸⠆⠸⠙⠟⠈⠓⠀⠈⠁⣀⣠⠤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢶⡆⠀⠰⠖⠀⠰⠶⠀⠐⡶⠀⠀⠾⠆⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⠀⢸⡇⠀⢀⡆⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⣆⠀⠀⣇⠀⢸⠇⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠈⠻⣦⠀⠘⣆⠀⠻⠀⠈⠀⠾⠁⣀⡴⠈⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢠⣿⠏⠀⢹
⠀⠀⠀⠀⣴⣋⠀⢀⡀⠀⠙⠳⣤⡀⠀⠀⣿⢃⡇⠀⠀⠀⠈⠀⠆⠉⠀⠉⠀⠀⠈⠀⠘⠉⠀⠀⢀⡤⠤⠤⠤⢤⣼⣿⡇⠀⠀⢀⣿⡿⠀⠀⡾
⠀⠀⠀⢰⠏⣏⢳⡏⣿⡀⠀⠀⠀⠙⠳⢾⣿⠟⠀⠀⠀⡴⡄⣶⡀⠰⡶⣶⡄⠀⡶⣶⡄⠀⣶⣶⡄⢐⣄⣶⡄⠀⣿⣿⡏⠙⠒⢾⣿⡧⠴⠊⠁
⠀⠀⠀⢸⡀⠘⡆⢀⣿⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⣀⠀⣿⣧⣿⡅⣿⣧⣿⡇⢸⣧⣿⠇⣸⣧⣿⠇⠿⢿⣿⡇⠀⣿⣿⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠈⢧⣀⣣⡾⠃⢀⣀⠀⢠⠖⢒⣿⡿⠤⠶⠋⠀⠻⢃⣿⠃⠙⠃⠻⠃⠹⠟⠀⠀⠻⠟⠀⣀⣀⠀⠻⠃⢰⣿⣿⠀⠀⠀⢿⣿⡇⠀⢀⣀
⠀⠀⠀⠀⠀⠉⠉⢀⡞⠉⠉⢳⡈⠀⢸⣿⠇⠀⠀⠀⢀⣴⣿⡉⢳⠀⠀⣼⣿⡆⠀⢰⣿⡗⠀⠀⣿⣿⡾⠻⣆⢘⣿⣿⠀⠀⠀⢸⣿⠁⡜⠉⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣸⠃⠀⣿⡟⠀⠀⠀⠀⣾⣿⢿⡀⢸⠀⢀⣿⣿⠁⠀⣾⣿⡇⠀⢠⣿⣿⠀⠀⠈⠉⣿⣿⠀⠀⠀⣸⣿⣾⠁⢠⣿⡿⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠉⢀⣼⡟⠀⠀⠀⠀⠀⢻⣿⠀⢉⡟⠋⠁⠘⢿⣤⡼⢹⣿⡇⣠⠏⢿⣿⠀⠀⠀⠀⠘⢿⣆⣀⡴⠃⠻⠇⠀⢸⣿⡇⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠴⠞⠋⠀⣀⣀⣀⡀⠀⠀⢉⣛⣉⠀⠀⠀⠀⢀⣀⡀⠀⢙⣛⠁⣀⡈⠁⢀⣠⡀⠀⣀⣀⠉⣁⡀⠀⠀⠀⠀⠈⠿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢱⠋⣿⣿⡆⠀⣥⣿⣀⠀⠀⠀⠀⢨⣼⡇⠀⡏⣸⠘⣿⣿⠀⢀⣸⡇⠀⣇⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡇⢸⣿⣿⠉⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⣿⣿⠀⣿⣿⡇⠀⣿⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⣿⣿⠇⠈⣿⣿⠀⠀⠀⠀⠀⢸⣿⡷⠀⣿⣿⣀⣿⣿⠀⢻⣿⣇⠀⠈⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠛⠛⠀⠀⠀⠀⠀⠛⠛⠁⠀⠈⠙⠛⠋⠁⠀⠈⠛⠛⠋⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠴⠶⠶⠶⠶⠶⠒⣒⣚⣋⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣿⣿⣿⣿⣿⣿⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⠰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸⣿⣿⣿⣿⣿⣿⣓⠶⢬⣙⡛⠶⠶⠶⢚⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣛⣛⣛⠻⠿⣭⣛⠲⢬⣍⣙⣛⣛⣩⡅
⠀⠈⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⢸⠁⠀⠸⢖⠀⠺⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣘⣩⣭⣭⣭⣙⡓⠶⣭⣙⠲⠶⠬⡭⠥⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣯⡴⠶⠶⢦⣬⣍⡓⠶⣬⣙⣛⠒⠒⢚⣫
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⠁⠀⠀⠀⠀⠀⠉⠛⠳⢶⣬⣍⣉⣉⣩⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣨⣀
⠀⠘⠒⠒⠐⠒⠒⠒⠒⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⢻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠁⠙⠟⡟⠃
⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠁
⠀⠀⣰⣶⣶⣾⡯⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢈
⠀⠸⠛⣽⡟⠻⣷⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⠀⠀⠀⠀⢠⠞⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⣄⠀⠀⠀⠀⠀⢠⠤⢄⣀⣀⠔⠁⠈⡀⠀⢀⡴⠁⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⣬⣷⡤⠤⠄⠒⠚⢣⠀⠀⠀⠀⠀⠀⠣⢤⣎⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠞⠀⠀⢸⡏⣟⢸⠦⡇⠀⡇⣴⢱⡄⡯⠁⠀⢀⡠⠝⠂⠀⠀⠀⠀⢧
⠀⠀⠀⠀⣀⠤⠒⠁⣠⠋⠀⡀⠀⢸⡇⠁⡤⠤⠥⠼⠤⡼⠿⢤⢡⡤⠶⡥⠤⢤⢠⡤⠤⢤⠀⣨⠿⢶⡦⢤⣀⡀
⢀⠤⠒⠉⠀⠀⠀⡴⠁⢀⣼⡇⠀⢸⣇⡀⠧⢤⠀⢠⡤⡇⠀⢸⢼⡇⠀⡇⠀⢸⠀⠱⡄⠈⠳⠃⢠⠎⠀⠀⠀⠉⠙⠒⣦
⠈⠑⠂⠤⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢸⡇⡇⠀⢸⢸⡇⠀⡇⠀⢸⠀⠀⠙⡄⠀⢠⠏⠀⠀⠀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠉⠛⢯⠉⠉⠙⡆⠀⢰⡏⢹⠖⠚⠀⢸⠳⣧⠀⠘⠚⠁⢰⡇⠀⠘⠒⠒⡦⡇⠀⢸⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠓⠒⠚⡡⢘⣶⣶⡒⠋⠀⠹⡓⠲⠶⠚⠁⠓⠒⠒⠒⠒⠃⠓⠒⠚⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠉⢹⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⣀⣀⡤⠴⠒⠛⠲⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠛⠷⣦⡀⠀⠀⠀⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣁⡘⠀⢶⣄⠈⢳⠀⣠⠖⢀⣠⣤⡶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⠉⠉⠛⠢⢌⠳⠈⠟⡡⠚⠭⢥⣔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠐⠀⠀⠀⠀⠐⠒⠲⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⢆⠀⢸⢙⡆⢸⣋⡇⠀⢆⡤⠀⠀⠻⠂⣠⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢷⠀⣼⠸⡆⢸⠉⠀⢸⠉⠀⠀⡜⠀⠠⣄⣀⣾⣏⣀⣀⣴⡿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⠀⠀⠧⠈⠃⠙⠀⠁⠀⠀⢀⣀⠀⣠⣌⠀⠀⠀⠀⣼⠇⠀⢀⣿⠟⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⣤⣤⣄⠀⢠⡄⠀⣼⣿⠐⢧⣯⣤⡄⠀⢰⡟⠀⠀⣾⣫⠞⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠀⠀⢠⣿⣧⣸⣆⢿⡇⠀⣿⣿⢀⡎⢰⡿⠀⢀⣾⠃⠀⣸⠟⡵⠋⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡐⠉⠻⣤⠽⠁⠘⠷⠞⠁⢿⠞⠀⣿⢁⡤⠋⣿⢀⡜⠻⠎⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡹⡄⠀⠀⠀⠀⠀⢠⠚⡆⢰⡏⠀⠙⢩⡾⣧⠙⠉⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⠀⣀⣤⣤⡀⢸⡀⡇⢸⠋⠀⠀⣾⠇⡇⠀⠀⠀⠀⢀⡘⠦⠀⢠⡄⠀⣀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠶⠛⠉⠁⠀⢻⣷⠀⠉⠀⠈⣰⡄⠀⣿⣸⠁⠀⣠⡆⠀⢸⣿⠀⢠⡇⡴⠛⠉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢸⣿⡄⣾⡆⠀⣿⣿⠀⣿⡇⠀⢀⣿⠁⠀⣼⣿⠀⠘⠈⠠⠚⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣤⣤⣄⡀⠳⡄⠀⠀⣿⡇⢿⡇⢸⢻⡏⣰⠹⣇⠀⡜⠻⣄⡰⠃⣿⠀⢀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡉⠣⠙⠀⠀⣿⠀⠈⠛⠁⠀⠛⠁⣀⣙⡛⠀⠀⠀⠀⢰⡏⢀⣾⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⠧⠬⣭⡉⠁⠀⠀⢰⡿⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠛⠲⣦⣴⠋⢠⠚⠾⠝⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠈⢻⡄⠀⠀⣼⠃⠀⠀⢀⢢⣀⠙⠒⠤⠤⠔⠒⠋⠁⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢤⠀⢀⡼⠁⠀⡴⠃⠉⠀⡔⢈⢧⡉⠰⠶⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⢀⡠⠞⠁⣀⢠⠞⠁⢸⡄⠙⠆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⠋⠀⠀⠃⠈⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣾⣿⣿⠿⠿⠿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⢠⡇⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣿⣇⣀⣀⣀⣤⣤⣴⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⠟⠛⠛⠛⠋⠙⣿⠈⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⣿⠁⠀⢀⡟⠀⠀⠀⠀⠀⠀⢻⡀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣾⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠶⠾⠿⠿⢿⣿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣼⣿
⠀⠀⠀⠀⠀⠀⣸⣟⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣶⠾⢿⣿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⢀⣀⡀⢀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡆⠀⠒⡖⠉⢳⡄⠀⢤⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⢲⠗⠮⣧⠀⠀⣇⡀⣸⠇⠀⣸⠃⠀⣿⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⠞⢳⡀⠈⠘⡆⠀⠸⠆⢀⡏⠉⠁⠀⢠⡿⠦⠴⠋⢀⡴⠋⠁⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠟⢳⡄⠀⠹⠂⠀⠙⠂⠀⠀⠉⠀⠀⠀⠈⠋⠀⠀⠀⠀⠸⣧⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⢛⣋⣉⣭⣭⣭⣭⣍⣛⡲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣭⡤⠴⠶⠶⠶⠦⢭⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣉⣭⡴⠶⢚⣛⣛⣛⣛⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣭⣭⣉⣉⣩⣭⡥⠶⢚⣋⣭⠭⠷⠯⢭⣝⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠦⢤⣤⡤⠶⠶⠛⠉⢁⢀⠀⠀⠀⠀⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢸⣿⣷⡀⠀⠶⣦⣵⠙⢰⢰⡄⠰⡄⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⠈⠉⠉⠁⣄⠀⡟⢿⡀⣸⢸⡇⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠐⠀⣡⡊⠁⠀⠀⠀⠉⠀⠀⠀⠀⠈⠋⠁⠈⠙⠁⠈⠉⠉⠈⠁⠀⠀⡀⢌⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠫⢔⡄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⠈⢶⠬⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢡⠒⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠓⠄⠔⡐⣠⢸⠀⡐⢠⢀⢠⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠹⡇⠀⠀⢹⡇⠀⠈⣿⠀⠀⠙⡶⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣆⠀⠀⢠⡖⣿⠛⠲⣿⡀⠀⢸⣧⡀⢠⡟⠀⠀⣼⠃⠀⢀⣿⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⡴⠛⣧⡀⠈⠁⢿⠀⠀⠸⠧⠀⢸⡏⠉⠉⠀⠀⢠⡿⣆⣠⠾⠃⠀⣠⠞⠉⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢷⡄⠀⠈⢷⡄⠀⠈⠷⠀⠀⠀⠈⠋⠀⠀⠀⠀⠲⠛⠀⠀⠀⠀⠀⢸⣇⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣀⣭⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡶⠶⠛⠛⣉⣉⣡⣤⣤⣤⣭⣉⡛⠳⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣟⡿⣿⣿⡶⠶⠟⠛⣉⣉⣡⣤⣤⣤⣬⣉⣉⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣿⣿⣿⣯⣷⠶⠟⠛⣉⣩⣥⣤⣤⣤⣤⣤⣍⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠶⠞⢛⣉⣥⡤⠶⠶⠶⠶⢤⣬⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠛⠶⠶⢦⣤⣤⣤⣴⠶⠶⠛⣋⣭⡴⠶⠞⠛⠛⠛⠶⢦⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⣤⣤⣤⡶⠶⠾⠛⠉⠀⠀⢀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢸⢶⣷⡄⠠⡀⣤⣤⢨⡝⠏⣥⢠⡄⠀⢤⡀⢨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⡇⠸⠾⠟⠗⡁⠁⠂⣿⢸⡇⠀⣿⢸⡇⠀⠈⢷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⢀⡤⠀⠀⠘⠛⣿⡏⠀⠀⠀⠀⠸⢧⣤⠟⠸⢧⣤⡟⢸⣧⣤⡄⢸⠇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⠢⠍⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠔⡡⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⠹⡶⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠞⢡⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠏⡼⣥⠐⣠⢠⠀⡀⣸⠀⢀⢀⡀⡄⡀⠂⢠⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠃⠚⠸⠄⠧⠀⠧⠘⠇⠃⠙⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣦⣄⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠆⢠⠀⣀⠈⠙⢷⡀⠀⠀⣀⠉⠛⠁⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⣤⣈⠛⠿⣆⠀⢷⢠⠞⣉⣤⠶⢞⡛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠉⠙⠲⠌⠃⠀⠣⠚⠅⠒⠒⠦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠁⠀⢀⠀⠀⠚⠉⠛⢿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡴⡄⠀⢸⠉⡇⠀⡿⢙⡆⠀⢦⡰⠀⠀⠘⠟⠀⣠⡄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣻⠀⢰⣇⣹⠀⢸⠋⠁⠀⡟⠉⠀⠀⡼⠁⢀⣀⡀⢀⣾⠏⠀⠀⣠⣾⠟⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⣧⠈⠧⠘⠇⠈⠃⠈⠀⠀⠀⠁⠀⣀⡘⠁⠀⠀⠈⢉⣿⠋⠉⠉⣹⣿⢿⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⡆⢸⠋⡇⠀⠀⠀⠀⣸⡏⠀⠀⣰⡿⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⠀⠀⠀⣾⣿⠛⣆⠀⣾⡇⠀⣸⣿⡇⠈⡟⢛⣿⠇⠀⢀⣿⠀⠀⢰⣿⠗⣡⠴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⣰⣿⠛⠦⣿⠞⢿⡇⢀⡏⣿⡇⡼⠀⣼⡟⠀⢀⢾⡟⠀⢀⣾⢃⠞⠁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⡍⠀⠙⠷⠶⠃⠀⠈⠛⠋⠀⠹⠟⠁⢰⣿⣠⠔⡁⢸⣇⡰⠃⠛⠃⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡹⣄⠀⠀⠀⠀⠀⠀⢰⡏⢳⠀⣾⠁⠀⠉⢠⡿⢻⠀⠉⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣽⠀⢀⣀⣤⣄⠀⢸⡇⣸⠀⣿⠀⠀⠀⣿⡇⡸⠀⠀⠀⠀⠀⢀⡈⠧⠄⠀⣤⠀⠀⢀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⠿⠚⠉⠁⠹⣿⣇⠀⠙⠁⠀⠉⣤⡀⠀⣿⢁⠇⠀⠀⣠⡄⠀⢸⣿⡄⠀⣰⠄⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢿⣿⠀⣠⡄⠀⢸⣿⡇⠀⣿⡟⠀⠀⢸⣿⠀⠀⣸⣿⡇⠀⡏⠘⢁⡤⠆⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⠋⣤⡀⠀⠀⢸⣿⠀⣿⡇⠀⣾⢿⡇⢠⢿⡇⠀⠀⣾⣿⠀⢀⡟⣿⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠘⠛⠛⠲⠦⣈⢳⡀⠀⢸⣿⠀⠹⣧⣠⠇⢿⣧⠞⠈⢿⣤⡼⠀⠙⠶⠋⠀⣿⠃⠀⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢠⣤⣤⡈⠂⠑⠀⢸⣿⠀⠀⠀⠀⠀⠀⠁⣀⣤⣤⣭⣀⣀⠀⠀⠀⣸⠇⢀⡾⣦⣍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠒⠲⢦⣄⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠠⡟⠉⠀⠀⠀⠉⠉⢛⣶⣾⡃⢀⠎⠙⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⡿⠀⠀⠀⠀⠐⣄⡀⠙⠒⠶⠶⠖⠒⠛⠉⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⠀⢠⣄⠀⠀⡼⠃⠀⢀⡾⠁⠃⠀⣴⢀⢳⡈⠋⢠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠁⠒⠈⠀⢀⡴⠋⠀⠀⢀⡼⠃⠘⡆⠙⢶⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠔⠚⠉⠀⠀⠺⠗⠈⠠⡤⠀⠿⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡃⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⣀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⣤⣦⠄⠀⠀⠀⠀⠀⠙⠀⠀⠘⡆⠀⢿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠘⠉⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⡄⠘⠃⠀⠀⠀⠀⠀⡼⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡼⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠰⠀⠀⠟⠐⠀⡜⠁⠀⠀⣠⠞⠁⢀⣠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⢀⣀⠀⢰⣄⣶⢰⣶⡀⣶⣲⢖⣖⣶⠰⣦⠆⠚⠁⠀⠒⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠀⠈⠓⠘⠃⠋⠚⠙⠃⠛⠀⠘⠏⠀⠀⠛⠀⠀⣀⣠⠴⠖⠋⠁⠀⠀⣀⣀⠀⣴⣤
⠀⠀⠀⠀⢠⣤⢠⣄⢠⡄⣤⣤⣄⢠⡤⢤⢠⣤⣄⢠⡤⣄⢠⣄⢠⡄⣤⢤⡀⢠⡭⡅⢠⣀⢠⡄⣠⣤⡈⣭⢥⡄⠉⠁
⠀⠀⠀⠀⢀⣿⢸⡟⢿⡇⣿⣀⡿⢸⣟⣣⢸⡗⠋⢸⣟⣀⢸⡙⢿⠁⣿⣠⡿⢸⣟⣢⢸⡛⢿⠘⣷⣤⡅⣿⣛⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⢤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⣴⠶⣄⢠⣦⠰⣄⡖⠀⠀⠲⢬⡉⠒⠦⢤⣀⡀⠈⠉
⠀⠀⠀⣤⣀⠀⡴⠖⠀⠀⠀⣀⡤⠖⠉⠀⠀⢠⠆⠻⠶⠏⠟⠻⠆⠿⢀⠱⡀⠀⠀⠉⠁⠀⠀⠈⠉
⠀⠀⠹⡿⣏⠀⠀⠀⠀⠀⠚⠉⢀⡤⠀⢀⡴⠁⠀⢀⡏⠀⠀⠀⡆⠀⠈⢧⡈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣰⠋⢀⡀⠀⠾⠀⠀⢰⡄⢰⠀⠀⠈⠁⠀⠙⣄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡞⠀⠀⠀⠀⠀⢸⡇⠸⡆⠀⣆⠀⠀⠀⠈⠃⠀⠀⠈⠳⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢸⡇⠀⣧⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠇⠀⢀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣄⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢻⡄⠀⢸⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠘⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢿⠀⠀⠀⢠⡄⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⡀⠀⣰⠋⠀⠀⠁⠀⣠⡾⠃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠁⠀⠀⠀⠆⠀⠀⠏⠐⠀⠰⠃⠀⠀⠀⣠⠞⠁⠀⣀⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠀⠀⠀⢠⣄⠀⢸⣿⣼⡇⢰⣿⡇⢸⣟⣿⠆⣿⣹⡷⠹⣶⠏⠊⠁⠀⠀⠚⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠆⠀⠀⠈⠛⠚⠟⠸⠇⠾⠛⠿⠸⠏⠀⠀⠿⠀⠀⠀⠿⠀⠀⠀⢀⣠⡤⠶⠛⠋⠁⠀⠀⠀⢀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀⠀⢀⣀⡀⠀⢀⣀⣀⠀⠀⣀⠀⢀⢀⣀⠀⡀⠀⢀⡀⢀⣀⡀⠀⠠⢒⣊⠉⣀⠀⢀⡀⠀⢀⡀⠘⣛⣋⡁⠈⠟⠳
⠀⠀⠀⠀⠀⠈⣿⠈⣿⣷⣼⡇⣿⡏⢻⣇⢹⣯⡍⠀⣿⣭⡷⢸⣯⡭⠁⣿⣷⣼⡇⢹⡏⢹⣷⢸⣯⡍⠁⣿⣷⣼⡇⣾⡏⠙⠆⣿⣭⠍
⠀⠀⠀⠀⠀⠰⠿⠀⠷⠈⠛⠃⠿⠷⠞⠃⠾⠷⠴⠃⠿⠂⠀⠸⠷⠴⠃⠿⠈⠙⠃⠾⠷⠞⠋⠸⠷⠴⠂⠿⠀⠙⠇⠙⠿⠞⠃⠿⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠶⠖⠀⠀⠀⢀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠐⠶⠦⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⠤⠊⠀⠀⣶⡶⣦⠀⣴⣦⠰⣦⣴⠂⠀⠀⠲⢤⣈⠉⠓⠶⣤⣀⡀
⠀⠀⠀⠀⡄⠀⠀⣠⡤⠆⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⢀⠆⣿⣧⡿⢡⡿⢿⡆⢹⡇⡘⢦⠈⠂⠀⠉⠛⠀⠀⠀⠈⠙⠃
⠀⠀⠰⣾⣿⡿⠀⠁⠀⠀⠀⠀⠴⠞⠋⠀⢀⠀⠀⢀⡴⠃⠀⠀⣴⠀⠀⢰⠀⡆⠀⠀⢳⡄⠳⣄
⠀⠀⠀⠚⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⣠⠏⠀⠀⠀⣰⠇⠰⠀⢸⠀⢰⠀⠀⠀⠻⡄⠈⢧⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⢠⡾⠁⠀⡤⠀⠀⠉⠀⠀⠀⢸⠀⢸⡄⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢸⠀⠈⣇⠀⢸⡄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⠃⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇

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

⠀⠀⠀⠀⠀⢄⠠⠉⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⡄⠀⢠⠀⠄⠐⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠧⡀⠈⠛
⠀⠀⠀⠀⠀⡀⠀⠉⠀⢄⠂⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡜⣿⣿⣯⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⣤⡄⠀⢰⣦⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠉⣁⡀⠀⢁⡀
⠀⠀⠀⠀⠀⢠⡄⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⠃⠹⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠃⠁⠛⠋
⠀⠀⠀⠀⢰⣾⣷⣄⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣰⣠⠏⣿⡇⠻⣿⣿⣿⢦⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏
⠀⠸⣿⡇⠀⣿⡇⠀⢸⣿⠀⠀⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠙⠁⠀⠙⠃⠀⠈⠙⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠍⠉⢉⠒⠒⠢⢄⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⣿⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⢸⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣄⠀⠀⣠⡾⠂⠀⠀⠀⠀⢸⠁⠀⠈⠁⠉⠁⢸⠀⠀⠀⠀⠀⣸⣿⡿⠛⣿⣿⡟⠻⣿⣷⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣤⣾⣿⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠁⠀⣼⠀⠀⠀⠀⠀⠈⠉⢱⣿⣿⣿⣿⣷⠉⠉⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠥⠁⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠈⠙⠛⠛⢿⣿⣿⣿⣿⣿⠿⣿⡏⠀⠀⠀⠀⠀⠀⢸⠀⠠⣤⣤⣭⣭⣤⣧⡀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠈⠻⠉⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠳⠤⠿⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠰⠶⠿⠿⠿⠿⠿⠿⠶⠶



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠻⡄⠀⠀⣠
⠀⣀⣀⢰⣦⣀⣀⡠⣶⢀⣀⡀⠀⠀⠀⠀⠀⠰⣿⡟⢻⣿⡟⢻⣿⡟⢻⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣁⣀⡰⣿
⠀⣿⣿⣼⣧⣿⣿⣯⣿⣼⣿⡇⡆⠀⠀⠀⠀⠀⣸⢻⡟⢻⡟⢻⡟⢻⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟
⠀⣿⡟⠛⡟⣿⣟⢻⡿⠉⢿⡇⡇⠀⠀⠀⠀⠀⣿⢸⡇⢸⡇⢸⡇⢸⡇⢸⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⡜⠀⡇⠈⡆
⠀⣿⣶⣷⣾⣷⣿⣾⣿⣷⣿⡇⡇⠀⠀⠀⠀⠀⠻⣼⡇⢸⡇⢸⡇⢸⣇⡼⠀⠀⠀⠀⠀⠀⡠⠖⢿⣽⣿⣋⣿⣏⡷⠢⢄⠀⠀⠀⠀⢰⠷⠶⡿⠶⠿⡀
⠀⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣁⡇⠀⠀⠀⠀⠀⠀⠈⠓⠾⢧⣼⠷⠚⠋⠀⠀⠀⠀⠀⠀⠀⠘⠶⢤⣌⣉⣉⣉⣠⡤⠖⠃⠀⠀⠀⢀⠇⠀⠀⠇⠀⠀⢣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠒⠋⠉⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢀⠄⡌⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠛⢧⠀⠀⠀⠀⠀⠀⠀⠆⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠁⠠⠠⠌⢷⣀⠀⠀⠀⠀⠓⠀⡾
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠈⠀⠀⠀⠀⠀⡄⣹⣷⣤⣈⣀⠁⡼⠁
⠀⠀⡰⠬⠃⠈⠈⠀⠒⠂⠀⠀⠀⠀⠀⣠⠞⢡⡀⠀⠀⠀⠀⠀⠒⠺⠞⠛⢛⡽⠋⠉⠛⠁
⠀⢈⡭⠁⠀⠀⠀⢀⡫⠀⠀⠀⠀⣠⠞⠿⠋⠀⠉⠂⠤⠄⣠⣀⣀⣠⣤⠔⠋
⠀⠀⠐⠃⡆⡄⢰⠓⠙⠀⢀⣠⠞⡁⠀⠈⠢⠄⣀⣀⢠⣶⣿⣗⣽⠞⠁
⠀⠀⠀⠀⠁⠀⠀⠀⢀⡴⢻⡡⠀⠀⠠⡀⠀⠀⠀⠉⠉⢍⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡼⢫⡀⠈⠁⢄⡀⠀⢀⢌⣯⣿⣶⡷⠋⠁
⠀⠀⠀⠀⠀⢀⡴⣷⠋⠑⠠⢀⣀⠈⠙⠛⠛⣿⡿⠋
⠀⠀⠀⢀⡴⠋⣠⠿⣦⣀⣀⣴⢨⣛⣛⣿⡿⠁
⠀⠀⠀⠈⡠⠚⢁⡴⠊⣳⢿⣿⣾⣿⡿⠋
⠀⠀⠀⠀⢀⠔⠉⡠⠚⠡⠊⠁⠉⠉
⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢤⡴⠒⢦⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⣾⣁⣻⡀⠀⢸⡇⠀⢸⡇⠀⢨⡏⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⣹⣆⠀⠸⠒⡇⠀⠙⣇⠀⢸⡿⠴⠋⠀⠀⣾⡄⢀⡼⠃⠀⣸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣍⠀⠘⢧⡀⠀⢻⡄⠀⠉⠐⠞⠀⠀⠀⠠⡼⠃⠉⠉⠀⠀⣾⠁⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣙⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣛⣉⣭⣤⠤⠶⠶⠶⢦⣬⣍⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣩⣤⠶⠶⠖⠒⠒⠶⠶⢬⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣥⠴⠶⢛⣛⣛⣛⣛⡛⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢤⣭⣉⣉⣉⣉⣉⣩⣥⠴⠞⣋⣩⣭⠭⠭⣭⣍⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢦⣬⣭⣍⣩⣭⣤⠶⠞⠋⠉⠀⠀⠀⠀⠀⢠⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⣦⣶⣄⠀⠀⣤⡄⣌⠙⢡⢈⡄⠀⣄⠈⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣿⠀⠟⠛⠗⢀⠀⠀⡇⣿⠀⢸⢸⡇⠀⠸⣾⠃
⠀⠀⠀⠀⠀⠀⠀⡠⠀⢂⡴⠀⠀⠈⠉⠿⠁⠀⠀⠀⠘⠷⠾⠃⠹⠦⠞⠘⠷⠶⠀⠟⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠢⡑⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢂⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⣄⠀⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠅⡔⢰⡀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠃⠰⠡⠡⡆⢏⢰⡈⢀⢠⠘⠄⠙⠂


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠂⠰⠒⠂⠂⠐⠐⠒⠀⠒⠀⠖⠒⠂⠀⠐⠐⠒⠀⠂⠀⠀⠀⢘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠤⠤⠤⠤⠠⢤⠀⠤⠤⠀⠤⠤⠀⠤⠄⠠⠤⠤⠤⠤⠄⠀⠀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢤⡀⣠⣠⣀⣤⠀⡄⢠⣠⣀⢠⠀⡄⢠⣄⣀⢀⠀⠀⠀⠀⢸⣿⠀⠠⣀⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⠀⢀⣀⣀⠀⠀⠀⡀⠀⣀⣀⡀⠀⢀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠸⣿⣆⠐⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣿⣻⣄⠹⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠈⠁⠉⠉⠈⠉⠁⠉⠉⠁⠈⠉⠉⠉⠈⠉⠉⠀⠀⠀⠀⢻⣟⣿⣿⣿⣿⣧⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠋⠀⠘⠀⠃⠂⠘⠁⠊⠙⠂⠙⠀⠁⠀⠂⠀⠀⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠀⠒⠒⠂⠒⠒⠂⠒⠒⠂⠒⠒⠒⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡹⣦⣀⣶⣶⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠄⠤⠤⠤⠴⠤⠄⠠⠀⠤⠦⠤⠄⠤⠄⠤⠴⠀⠤⠤⠀⠀⠀⠀⠀⣾⣽⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠠⠠⠤⠠⠀⢠⠠⢀⡠⠤⠀⠄⠤⠀⢠⡤⠠⠠⠠⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⣀⣀⣀⢀⣀⡀⢀⠀⢀⣀⢀⡀⢀⣀⣀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢟⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁⠀⠉⠁⠀⠁⠀⠉⠉⠁⠉⠀⠁⠀⠀⠁⠈⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠁⠉⠁⠁⠈⠁⠉⠁⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠀⣴⠄⣿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⣿⣿⠀⠸⠆⠟⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⣿⣿⠀⠀⢠⣄⢀⣄⠀⠀⣠⡀⢠⡄⠀⣤⡀⠀⢀⣤⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣴⣴⣿⣿⣤⠀⢸⣿⢸⣿⠀⠀⣿⡇⢸⡇⠀⠘⢿⣄⣾⠃⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⣿⣿⠉⠀⣸⡿⠸⣿⡀⢀⣿⠇⢸⣇⠀⠀⠈⣿⠃⠀⠀⠀⢴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠛⠛⠁⠀⠉⠛⠛⠉⠀⠘⠛⠛⠃⠀⠛⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⣤⡤⢤⡤⢤⡤⢤⣄⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⡿⠷⠮⠵⠼⠧⠿⣿⠀⠀⠀⠀⠀⠀⣻⣥⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⣿⠁⣀⠀⠀⠀⠀⢨⡉⡶⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⡤⠻⣿⣿⠁
⠀⠀⠀⡇⠀⢀⡴⣷⠀⠀⣷⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠻⢷⡐⠀⡿⢀⡟⠃⠀⠀⠀⠈⢹⣿⣆⢀⢀⣾⣷⡀⠀⠀⠀⠀⣴⣛⠳⢶⡌⠉
⠀⠀⠀⡇⠀⠘⠛⠿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⢻⡆⠀⠀⠀⠀⠀⠀⠀⠲⠝⠄⠣⠊⠔⠛⠀⠀⠀⠀⢸⣿⠘⣿⠊⣿⡿⠁⠀⠀⠀⠀⡝⠏⠟⠃
⠀⠀⠀⠙⠖⠒⠒⠒⠒⠚⠗⠀⠀⠀⠀⠀⠘⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠛⠀⠛⠃⠀⠀⠀⠘⠛

⠀⠀⠀⢠⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⠀⣠⠴⠂⠀⠀⠀⠀⠀⢠⡄⢲⠆⣤⡀⠀⠀⠀⠀⢀⣴⢀⠀⠀⠀⡀⡀⠀⠀⠀⢲⣀⣀⣀⣠⠤⢶⡲⠤
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣀⠂⠔⠊⠉⠓⠤⠀⡀⠀⠀⠀⠾⢦⣿⡟⢿⣧⡾⠇⠀⠀⠀⢈⡹⣩⣌⣡⣈⣏⣇⠀⠀⠀⢸⣿⣿⣿⣟⡯⠭⠭⣍
⠀⠀⠀⠈⠻⣿⡿⢻⣿⣿⠇⠀⠀⠀⢙⢻⢿⢶⠶⠶⠿⡟⠃⠀⠀⠘⣛⣻⣷⣀⣰⣿⣟⡛⠀⠀⠀⠸⣧⣧⢫⡧⢻⣦⡿⠀⠀⠀⢸⠭⠭⠥⣖⣚⣭⣭⣓
⠀⠀⠀⠀⠀⠈⠀⠀⠙⠁⠀⠀⠀⠀⢶⣬⣼⣸⣘⣋⣣⣧⡆⠀⠀⠀⠙⢥⡝⢻⡛⣧⡝⠃⠀⠀⠀⠐⣯⣰⣷⡀⣇⢸⡇⠀⠀⠀⢸⠉⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠙⠁⠉⠀⠀⠀⠀⠀⠈⠉⠈⠀⠁⠉⠉⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠜⠴⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣋⣀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠈⠣
⠀⠀⠀⠀⢲⣶⣶⣶⣶⡖⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠈⣢⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠠⣄⠀⠀⠀⠀⠈⡍⠉⠉⠉⡍⠀⠀⠀⠀⠀⠀⢇⣀⣄⣄⣨⠆
⠀⠀⠀⠀⠈⠹⠻⠟⡏⠀⠀⠀⠀⠀⢸⣧⣴⣿⣿⣷⣶⣿⠄⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣾⠄⠀⠀⠀⠀⠇⠸⠿⠀⡅⠀⠀⠀⠀⠀⠀⠈⢻⠑⣽⠃
⠀⠀⠀⠀⠠⠏⢘⡇⠹⠄⠀⠀⠀⠀⠀⢧⣀⣀⣀⣀⣀⠜⠀⠀⠀⠘⢍⣉⣉⣉⣉⣉⣉⠝⠀⠀⠀⠀⠀⢸⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠃
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢸⣟⣿⣏⣹⣿⣻⡇⠀⠀⠀⢠⣤⣤⣤⣤⣀⡀⢀⡄⠀⠀⠀⣴⣿⣽⣯⣿⣯⣷⡄⠀⠀⠀⠉⠙⠀⠀⠀⣤⣁⣹⠀⠀⠀⠀⠐⣿⢻⡏⣿⢻⡇
⠀⠀⠀⢸⢩⢹⢽⣉⣽⡉⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢸⢡⠀⡰⠀⡴⣄⢠⢸⠀⠀⠀⠀⢘⠀⣎⣀⣉⣉⢹⠀⠀⠀⠀⠀⢹⣼⣇⣿⣿
⠀⠀⠀⢸⣬⢭⢬⡭⡥⣥⡇⠀⠀⠀⠈⠛⠟⠿⣿⠿⠟⢧⠀⠀⠀⠘⣦⣤⢤⢤⢤⣬⣤⡞⠀⠀⠀⠀⢸⠀⠀⣀⣁⣀⣘⡀⠀⠀⢀⣄⢸⣿⣧⣧⡿⢀⣄
⠀⠀⠀⠀⠙⠺⠾⡷⠗⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠛⠾⠼⠼⠷⠋⠀⠀⠀⠀⠀⠘⠤⠼⠿⠿⠿⠿⠏⠀⠀⠘⠻⠷⠿⠥⠽⠾⠿⠛

⠀⠀⠀⢀⠠⡀⢀⣠⣀⠀⡄⠀⠀⠀⡀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣤⢠⣆⢰⢦⣴⠄
⠀⠀⠀⠉⢘⡇⠈⠛⠃⢘⡇⠀⠀⠀⢻⣷⣶⣨⣿⣤⣶⣾⡇⠀⠀⠀⠀⠀⢱⣶⠀⠀⠀⠀⠀⠀⠀⢶⣄⣠⣤⣤⣤⣤⣄⡀⠀⠀⢈⣭⣭⣭⣽⣼⣯⣽⡀
⠀⠀⠀⣀⠠⡇⠀⣹⠀⠀⡇⠀⠀⠀⠀⠙⢛⣽⣿⣿⠛⠋⠀⠀⠀⠀⠀⢀⠈⣿⣿⠀⠀⠀⠀⠀⠀⣻⡯⣭⣤⣤⣤⣤⡬⠇⠀⠀⠸⣿⣤⣼⣧⣧⣤⣬⡇
⠀⠀⠀⠉⢈⡇⠀⢺⠀⢠⣄⠀⠀⠀⠀⠐⠛⣼⣾⣦⠓⠂⠀⠀⠀⠀⣄⣸⣤⣿⣧⣦⣄⡀⠀⠀⠀⠉⠁⠀⠀⠶⠖⠀⠀⠀⠀⠀⢰⡇⢸⠰⣿⡂⣼⣷
⠀⠀⠀⠀⠀⠁⠀⠙⠀⠈⠁⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠐⠚⠑⠋⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘

⠀⠀⠀⠀⠒⠲⠴⠖⠒⠖⠲⠴⠒⠂⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡠⠀⠄⣀⡀⣀⣀⠀⠀⠀⡀⢀⡀⡀⢤⡀⠒⠒⠀⠀⠀⠃⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠈⢡⢠⠈⠀⠉⠠⠁⠄⠀⠀⠀⠐⢄⠃⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⣮⣑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡈⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡶⡀⠀⠂⠀⠀⠀⠀⡔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠘⠁⠹⠇⠀⠀⠀⠀⠀⠸⢉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠈⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡤⠀⠀⠀⠃⠀⠀⠀⢀⠆⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠚⠀⠀⠘⡀⠈⠀⠀⠀⠀⢈⡀⢀⠀⣠⢦⡄⠆⠠⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠀⠛⠉⠀⠈⠉⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⣤
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⡠⠀⠀⠰⠀⠀⠀⠐⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠛⠓⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠘⡄⠀⠀⠀⠀⠞⠛⠶⠶⠴⠶⠤⠤⠠
⠀⠀⠀⠀⠀⠀⠀⢁⠀⡀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠘⢶⡀⠀⠀⠀⠐⡗⠀⠀⠀⠂⠐⠩⠴⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⢀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠧⠀⠁⠀⠀⢡⠀⠀⠀⠀⠇⠀⠀⢊⣡⣬⡁⠀⠀⠀⠀⠀⠀⠀⡄⡠⠤⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠐⠂⠀⣈⠀⠐⠁⠀⠀⠀⠘⣶⣴⣃⣦⣼⠃⠀⠀⠀⢠⠀⠀⠀⠈⢀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠟⠻⠟⠋⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠋⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠉⠀⠀⠁⠀⠘⠀⠀⠁⠐⠀⠀⠐⠂

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⣀⣀⣀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠈⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠛⠋⠁⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⡞
⠀⠀⠀⠀⠀⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡄⠃⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⢁⠹⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⢀⡴⠋⠁⠛⢿⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⢱⠏⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢀⣴⠟⠂⢄⣀⠀⣀⣹⣦⠀⠀⠀⠀⠀⡀⢀⢰⡄⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢀⡴⢻⡗⠠⠀⠀⠈⠈⠉⠀⠙⢷⣤⠀⠀⡄⢇⠀⡈⡀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⡶⠋⠀⠈⠀⡀⠀⠁⠀⠀⠀⢀⡎⣡⢝⣿⣦⣅⣤⣆⠣⠀⣾⠃
⠀⠀⠀⢠⣄⡘⢦⠀⠃⠋⢀⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⠀⠀⠀⠀⠀⠀⠁⠂⠠⠤⡤⣿⢼⠾⠾⠷⢛⣭⠟⠛⠛⠿⠋
⠀⠀⠰⠶⠦⠌⠀⠁⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢥⡦⠚⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⢘⠀⣠⡼⠋
⠀⠀⢠⠴⠂⡀⠀⠀⠀⠀⠀⢌⡓⠀⠀⠀⠀⠀⢀⣤⠞⠉⠿⢋⠔⠁⡠⠈⠘⠓⠶⠤⣴⣤⣤⣠⣤⣤⣶⠞⠉
⠀⠀⠀⠠⠟⢀⡆⣰⠀⢰⠸⠆⠙⠀⠀⠀⢀⣴⠟⠁⠀⠐⠈⠣⢥⠊⢄⠀⠀⠔⣡⡾⣯⣾⢼⣹⣷⠟⠁
⠀⠀⠀⠀⠀⠸⠃⠙⠀⠈⠀⠀⠀⠀⣠⣶⠟⠁⠀⠢⠀⠀⠀⠀⠀⠉⠙⠓⠺⠶⢿⠾⠷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢷⡆⠏⠀⠀⠈⠂⠄⢀⡀⡀⠀⠄⠀⡄⢸⣠⡾⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢡⠀⠀⠈⠠⢀⡀⠄⠀⠀⡠⡢⢹⣋⢟⣟⣗⣻⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⡺⠷⣀⠀⠀⠀⠈⠑⠦⢦⣿⣾⣽⣿⣵⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢿⡏⠁⠀⠀⠉⠒⠦⢤⣀⣀⢈⠀⡉⣉⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⡴⠟⠁⣠⡼⢿⣦⡀⠀⣀⢰⢀⡸⢨⣩⢹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⠴⠋⠀⣠⠞⠉⠀⣨⠻⢮⣝⣷⣽⣨⣺⣽⣽⣾⠟⠁
⠀⠀⠀⠀⠀⡤⠊⠁⢀⡴⠞⠁⣠⡾⠛⣻⡿⠶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣠⠞⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠔⠁⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⣾⡿⢻⣿⡿⣻⡟⢻⣷⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣹⣷⣱⣽⣷⣷⣿⣿⣿⣷⣿⣿⣴⣿⣭⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠉⠉⢠⣶⣶⡆⠀⠀⠀⠀⠀⠉⠉⠛⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣿⡇⣩⠀⢸⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⣨⣿⣧⡀⠀⠀⠈⠦⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢛⣿⡟⠃⣴⢋⣷⣰⡿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣇⠀⠛⠚⠁⣿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢫⡿⢁⠀⡀⣰⢻⢂⠀⡉⢉⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⣸⢣⡏⣼⢡⡿⢣⡏⣰⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣴⠏⠘⠟⠻⠛⠗⣻⣿⣿⣀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⢸⣏⣼⠋⠉⠉⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣿⣷⣶⣶⣶⣶⣿⣶⣶⣶⣾⣿⡿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⣿⣿⣧⣼⣿⣯⣽⣿⣯⣿⣿⣤⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣀⣀⣀⡀⠀⠀⠀⠀⠀⡠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣦⣤⡾⠀⠅⠀⠀⡈⢑⠤⣀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⢱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡀⢅⠈⠀⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠉⠉⠉⠛⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⢨⡇⠀⠀⠐⠀⠐⠄⠠⠀⠀⠉⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⣿⡄⠀⠀⠀⠨⠀⠀⠀⠀⡀⠠⢀⢸⡇⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⡀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣾⠃⠀⠀⠀⢹⣷⡀⢠⠀⡋⠉⠈⠉⠑⠢⠤⣐⣘⣫⣵⠇⠀⠉⠒⢤⡀⠀⠀⠀⠂⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣰⣿⠇⠀⠀⠀⠀⠀⣿⣧⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⢀⠀⠹⣟⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⠁⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢂⠀⠹⣄⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠀⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⢄⠀⠙⢿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠣⠀⠹⣿⣿⣦⡀⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠛⠿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠘⠿⣿⣷⣤⡀⠈⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⢀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠂⠀⠈⠙⠿⣿⣿⣿⣿⣶⣶⠶⠊⠁⠀⠀⠀⠈⡍⠙⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢀⠴⢃⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡘⠀⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠰⠀⠂⠄⠀⠠⠂⣿⠈⠀⠀⠐⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠇⠀⠀⢀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⡌⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠡⠀⠀⠀⠆⠀⠀⠀⠀⠇⠀⠀⠀⠄⠀⠀⠐⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠆⠲⠦⠤⠠⠀⠤⠶⠒⠶⠒⠊


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

⠀⠂⢀⣒⠴⢃⠴⠇⠀⠀⠀⠆⠂⠀⠀⠐⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠐⠐⠌⠀⠀⠀⡤⡀⠀⠀⠈⠀⠀⠑⠀⠀⠀⠀⠡⡀⠀⠒
⢀⡄⠤⠉⢶⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⠀⠈⢀⡀⠈⠀⠀⠀⡘⢧⢀⠦⠀⠀⠐⠈⠈⠀⠢⠀⠃⠀⠊⠢⣀
⠒⠒⢈⡀⣆⢀⠀⠀⠀⠀⢤⣌⠬⠩⠉⢍⣠⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢇⠈⠀⢀⠀⠀⠀⠁⠈⠠⠀⠀⠁⠐⠒⠊⠁
⢳⡖⠫⡦⣉⠒⠁⠀⠀⠀⡀⡏⢙⡛⠟⠉⡃⠀⠀⢀⠠⠀⠀⠈⢆⠀⢀⠀⢂⠀⡠⢀⠀⠀⠰⠉⣉⢁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠰
⠡⠀⠆⠠⠤⢘⠇⠀⠀⠀⡐⠦⠤⠓⠣⠤⠜⡃⠀⠈⠈⡰⠀⠀⠀⢢⠂⠉⢈⠄⠀⠈⠀⠀⠀⠈⢄⡀⠀⠀⠠⡄⠀⠣⠀⠟⢀⡤⠀⠒
⠀⠀⠀⠘⠂⠁⠠⠤⢤⡄⠡⠄⠀⠀⠀⠀⡈⠣⠀⢈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠄⡹⡀⡰⠄⢅⠰⠀⠋⠘⡱⢤⠤
⠀⢀⠀⠀⠀⠀⠁⠀⠀⢸⡇⠀⠢⣀⠴⠋⠀⠀⠐⡥⠸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠰⡈⡥⠀⠀⠀⠂⠾
⠀⠀⠀⠀⠀⠀⠀⠈⢀⡞⠃⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠄⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠑⡄⠁⠠⠀⠌⠡⠀⡀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡇⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡙⠀⠀⠀⠰⡈⢀⠠⣈⣰⣂⢍⡀⠀⢀⠂
⠀⠀⠀⠀⠀⠆⡱⠀⠀⠀⠀⠀⠀⡐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⠀⢠⠈⠈⠶⠀⠀⡊⠻⢎⡱⠉⠁⢀
⣭⠥⠥⠀⢀⠀⡀⠀⠀⠈⠠⠀⢰⣃⢄⡀⢀⠤⣐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢐⡢⠀⠄⠀⠐⠀⠀⠀⠊⠀⠁⢉⢴⡚⢷⠁
⠁⠀⠀⣨⠓⠀⠁⠀⠀⢅⠀⠀⠀⣀⣐⡶⠒⠓⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠂⠀⠐⢈⠀⠁⠀⠀⠀⠀⠀⢰⠀⠈⠖⣉⠑⠁
⠀⠀⠘⠁⠀⠀⠀⠀⢀⠀⠄⡁⠀⠉⠀⠡⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠸⠀⠀⠐⡀
⠀⠸⠤⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⡀⠀⢠⠷⣦⠇⠠⠀⡀⠀⢠⠀⠀⠄⠀⢄
⠀⠒⡂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡶⠳⡆⢀⡿⣤⠿⠀⠈⠐⠠⠆⡼⠑⠰⠚⠂⠁⡀
⠀⠀⠐⢄⠀⠀⠀⢀⣀⠦⠁⠀⠀⢆⣤⢀⠀⡀⠀⠀⠋⠀⠀⠀⠀⠀⢀⠀⠐⢀⠀⠘⡄⠰⠃⠘⠖⠂⠀⠀⠀⠀⡠⠀⡀⠨⠈⣂⠄⠐
⠀⠀⠀⡂⠠⠀⠳⠠⢈⡀⠀⠀⠀⠀⠈⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠁⠤⠀⠁⠂⠉⠀⣠⣄
⠀⠀⡈⠉⠉⠉⢩⡀⠀⠁⠀⠀⠀⠊⠀⢁⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⢀⢴⢡⠋⠈⠍⢢⠈⠂
⠀⢠⠀⠀⠀⠀⠘⠃⠀⠀⢡⡀⠀⠃⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⡸⠀⠀⡘⠁⡄⠀⠀⢘⠛⣃⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⣿⠃⢀⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⡴⢁⣼⡟⠀⠀⢀⣤⣤⡀⠀⠀⠀⢠⣾⡇⠀⣠⣴⣄⠀⢀⣴⡆⠀⣠⣤⡀⠀⢀⡀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠌⢀⣾⠏⠀⢀⣾⠟⠁⠀⢀⢤⡀⢀⣿⣿⢃⡜⠁⣸⣿⣀⣾⡿⣣⠞⢁⣽⡷⠉⣸⡿⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠌⢀⣾⠃⠀⣰⣿⠃⠀⣀⠔⢡⣾⠇⣼⣿⢇⡞⢀⣾⣿⠃⣼⡿⡱⠃⡔⣹⣿⠃⣼⣿⡥⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠎⠀⠘⠧⠤⠊⠹⢿⡴⠞⠁⠀⢿⡯⢶⣿⡟⡜⠀⠈⠛⠃⣸⣿⡿⠁⠀⠛⠛⠁⠀⠉⠁⢠⣿⠥⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⣰⣿⡻⠁⠀⠀⠀⠀⠀⠀⡠⢴⣿⠏⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢠⡄⠀⢠⣿⣿⠃⠀⠀⠀⢠⣿⢧⠇⠀⠀⠀⠀⠀⢀⠞⢀⣾⡏⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⢀⣿⠃⠀⢸⣿⡏⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⢀⠃⢀⣾⡟⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣴⣶⣶⣾⡏⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠸⣀⣾⠏⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⣴⡾⠋⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠉⠉⠉⣿⣦⠀⠀⢸⡏⠰⠰⢀⠀⢰⠉⡆⡏⠀⠀⣰⣿⡿⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠘⠃⠀⠀⠀⠀⠀⠉⠀⠁⠀⣼⣿⣟⡠⠊
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⢠⣾⠆⠀⠀⢠⣶⠀⠀⠀⢰⣿⣿⠋⠀⠀⠀⠀⣠⣄⠀⠀⠀⣴⡶
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⢀⣿⡟⠀⠀⣠⣿⡟⠀⠀⢀⣾⣿⠇⠀⠀⠀⢠⡞⣹⣿⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⣹⣿⠉⠉⠐⣾⣿⠁⢀⠔⣿⡿⠁⣀⠔⠁⣿⣿⠀⠀⢀⡴⠋⢰⣿⣇⣠⣾⣿⣃⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣿⠇⠀⠀⠀⠻⠷⠖⠁⠀⢿⡧⠞⠁⠀⠀⠸⠿⠤⠞⠋⠀⠀⠈⠛⢉⣰⣿⠋⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢩⣿⠃⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢠⣿⠏⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢠⣿⠏⠀⠀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣼⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢵⣷⣊⠀⠀⡖⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠀⠀⢸⠃⠀⠀⢸⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠎⠀⠀⣾⠀⠀⠀⡏⠀⢀⡤⡄⢀⡠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣲⠄⠀⠀⢀⠠⠀⢇⠀⣀⡠⠧⢀⠀⠳⢌⠋⣐⡡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠁⠀⠀⠀⠹⡎⠀⠀⠀⠱⠀⠀⠓⠬⣁⠭⠗⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠰⡒⢦⠄
⠀⠀⠀⠀⠀⠀⢀⠔⣒⡓⢒⣋⣒⡄⠀⢰⠀⠀⠀⠉⢀⢇⠈⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡎⠀⠀⠀⠀⠓⠁
⠀⠀⠀⠀⠀⠐⠧⠊⠉⠀⢸⠀⠀⠀⠀⣠⠗⠤⠤⠔⠃⠀⠉⢋⣉⡿⠠⣔⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠃⠀⠀⢀⡼⠁⠢⡀⠀⠀⠀⣀⠤⠊⣸⠇⠀⠀⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠢⡤⠋⠔⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⡿⠀⠀⠀⠀⠀⢠⢞⡥⡶⠈⡭⠬⣵⠂⠀⠀⠀⠀⠀⠈⠑⠲⣔⣛⣒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⠋⢰⠐⢃⠇⠀⠀⠀⠀⠀⡔⠢⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⣴⠟⡽⠀⠀⠀⠀⠀⠀⣸⢣⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠛⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠐⠛⠓⠒⠃⠀⠀⠀⠀⠀⠀⠛⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠓⠒⠦⣤⠀⠀⠀⠀⠀⡼⠛⠒⠲⠤
⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⡀⠀⠀⠀⠀⣤⠤⢤⡏⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸
⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠇⠀⠀⠀⢸⠇⠀⢰⠃⠀⠀⠀⠸⠥⣤⣤⣄⣀⣸⠀⠀⠀⠀⣾
⣼⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⡇⠀⡜⠀⠀⠀⠀⡿⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢠⠇⠀⠀⠀⢸⠇⠀⢀⡇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡿⠀⠀⢸⠁⠀⠀⠀⣼⠉⠉⠉⠉⠉⡿⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⠃⠀⠀⡟⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢼⣀⣀⡀⠀⡿⠀⠀⠐⢧⣤⣀⣀⣸⠁⠀⠀⠀⠀⠸⣤⣤⣀⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣄⣀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣛⣻⣾⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢫⣾⢢⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢲⣀⣀⠠⠯⠭⡦⠤⢤⠀⠀⠀⠀⠰⠿⠥⡿⢡⡿⠁⠀⡿⠻⣶⣶⣦⡄⠠⢤⣤⣤⡶⣶⠒⢻⠟⢿⡋⣱⡀
⠀⠀⠀⠀⠀⠀⠴⠒⡏⠁⠸⠇⠀⠀⣀⣘⣃⠤⢼⡀⠔⠀⠀⠀⠀⠀⠸⡿⠁⠀⢸⣷⣾⣿⣤⣾⠀⠀⢸⣇⣿⡇⣿⠀⠘⣷⣾⠟⠿⣧
⠀⠀⠀⠀⠀⠀⢠⠴⡇⠰⠀⠈⠉⠁⠀⠀⠀⠀⠀⢇⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠈⠻⡟⠀⠀⢸⡷⠟⠧⣿⠀⠀⠹⠋
⠀⠀⠀⠀⠀⠀⢸⡌⣧⠀⠄⠀⢠⠀⢀⡆⠰⠾⣆⠘⡄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢸⠠⢹⡀⢄⠢⡈⠲⠐⠂⠀⠀⠈⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡦
⠀⠀⠀⠀⠀⠀⢸⡇⡌⢧⠀⠀⣀⣀⣀⡤⠤⠤⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢿⣕⣝⡿⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡚⠻⣶⣀⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡉⡻⣿⣆⡿⠋⠀⠀⠀⠀⠀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠁⠈⠓⠦⡿⠋⠀⠀⠀⠀⠀⢴⣛⣻⣿⠇
⠀⠀⠀⠀⡀⠀⢀⣤⡶⠖⣰⠿⠻⣿⡿⠻⢿⡄⠀⢀⠠⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣉⣻⠟
⠀⠀⠀⠀⠀⢰⣷⣶⣶⡿⣿⣧⣼⡿⣿⣤⣿⣿⡐⢿⣷⣤⣉⡛⢧⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠈⠀⠁⠀⠀⠀⠀⢀⣴⡿⠿⣄⣽⠃
⠀⠀⠀⠀⠀⣿⣤⣤⣤⣴⣿⣿⣿⣄⣰⣿⣿⣿⣷⣦⣉⠛⠿⠿⣿⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠳⢶⣿⠃
⠀⠀⠀⠀⠀⠸⡟⠿⠛⣋⣽⣆⣠⣿⣷⣀⣾⡏⢎⡛⢿⣿⣷⡶⠃⠀⠀⠀⠀⠀⡜⢀⠀⡠⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠐⠌⠻⠿⣿⡛⠙⢿⣿⣿⡿⠋⠀⠈⢿⡶⠖⠋⠀⠀⠀⠀⠀⠀⠘⠠⠷⠮⠊⠁⠀⠀⠀⠀⠀⠀⢀⡟⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡽⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠜⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡠⠁⠰⠐⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡌⣠⡤⠴⠂⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⣴⠶⣶⣾⣷⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠠⠆⢉⣠⣾⣿⢖⣯⣶⣿⣿⣿⣿⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡐⠆⣩⡅⠰⢂⡀⢿⣻⡟⣿⣯⢿⣿⢟⣿⣾⣿⣯⣿⣿⣇⠀⠠⣴⠄
⢀⠀⠶⢀⡀⢀⠀⠀⠠⠀⢀⣘⡰⣶⠛⢻⡾⣷⡀⢸⣧⢸⣿⣿⡎⣿⣿⣟⣿⣿⣗⣽⢟⡯⠿⠯⠽⣿⣿⣷⣄⠀⠀⢀⡀
⢿⣧⠀⠘⣿⣠⣾⣻⣷⢿⡏⢹⣿⢿⡷⠾⠃⠙⠷⣿⡟⠘⣿⣿⣇⢸⣾⣿⣿⣿⡿⣻⠃⢠⣶⣶⠀⣀⡈⠍⠀⠀⣼⣿⣿
⠘⣿⣷⠿⢿⣧⣿⣥⠿⠺⣿⠛⢋⡸⣷⠸⣷⣤⣶⡟⢁⠀⣿⣿⣿⠨⣿⣿⣿⣯⠞⠃⣀⢸⣿⣿⡇⠉⣠⣄⠈⠀⣿⣿⣿
⠀⢹⣿⡀⠘⣿⢀⣴⣿⣆⢿⠆⢸⣇⠛⠱⠆⢉⡁⠀⠛⠃⢿⣿⣿⠈⢉⣉⠉⠀⠀⣴⣦⠘⣿⣿⣇⢸⣿⣿⠀⠀⣿⣿⣿
⠰⠈⠿⠃⠤⢠⣾⣿⣿⣿⣀⣿⠆⣿⠾⣷⠀⠿⠿⢡⣶⠶⢸⣿⣿⠀⣿⣿⡇⠀⠘⣿⣿⡆⣿⣿⣿⢸⣿⣿⡄⠀⣿⣿⣿
⠀⠀⠿⠇⣰⣿⡿⣿⣿⣿⡇⢸⣧⡜⠁⠛⣀⣀⡀⢼⣿⠟⠚⣿⣿⡄⣿⣿⣇⠀⠀⣿⣿⣇⢸⣿⣿⠈⣿⣿⣷⣶⣿⣿⣿
⠀⠀⠀⣼⣿⡛⠁⠈⢩⣿⣿⣀⣩⣴⡄⢸⣿⠉⣿⡆⣿⡇⠀⣿⣿⡇⢻⣿⣿⣦⣴⣿⣿⣿⠈⣿⣿⡄⠙⢿⣿⣿⣿⣿⡏
⠀⠀⣼⣿⣿⣿⣠⣶⣼⣿⣿⣿⠿⠟⠃⠀⠙⠿⠿⠃⢹⣿⡄⢸⣿⣷⠈⠻⠿⠿⠟⠉⠙⠋⢀⠘⠛⠃⡐⠀⢀⣾⣿⡿⠁
⠀⠀⠻⣿⣿⡿⠿⠟⠛⢻⣿⣿⡄⢰⣾⣿⣿⣶⣦⣤⣈⣉⣠⣿⣿⣿⢀⣴⣶⣦⣤⣀⣀⠀⠛⠁⠀⠈⣁⣴⣿⣿⠟⠁⠤
⠀⠀⠀⠀⠀⣄⢀⣶⡄⠈⣿⣿⣷⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠸⢿⠿⠁⠤⠈⠉⠙⠛⠛⠛⠛⠋⠉⠀⠈⠃⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣴⣶⠀⠆⠐⠂⠒⠀⠖⠐⠂⠰⠀⠀⠀⠀⣿⣿⣿⣿⠟⠉⣿⣭⣿⣽⣯⣽⣯⣿⣭⣿⣽⣿⣿
⠀⠀⠀⠾⢿⣿⠌⣟⢹⡧⡇⠀⢼⢙⡆⣿⠅⠀⠀⠀⣿⣿⣿⣏⣐⠀⣻⡆⣾⢘⡃⣿⡏⢰⠌⡇⣺⣿⣿
⠀⠀⠀⣤⣬⣭⣤⣥⣬⣥⣥⣤⣬⣭⣤⣥⡄⠀⠀⠀⣿⣿⣿⡟⠛⠒⠛⠓⠛⠚⠓⠛⠛⠒⠚⠓⠻⣿⣿
⠀⠀⠀⣿⣿⢸⡇⢸⡇⢸⡇⢸⣷⡌⢁⣾⡇⠀⠀⠀⣿⣿⣿⡇⠀⣿⠀⣿⠀⣿⠀⣿⠀⠹⣶⠏⢸⣿⣿
⠀⠀⠀⠿⠥⠾⠷⠤⠥⠾⠧⠬⠽⠧⠼⠿⠇⠀⠀⠀⣿⣿⣿⣇⣘⣋⣀⣙⣛⣋⣈⣛⣚⣀⣛⣀⣸⣿⣿
⠀⠀⠀⣶⡖⠖⠀⣶⢶⡀⢐⣶⠀⠀⣶⡖⠂⠀⠀⠀⣿⣿⣿⡏⠩⣭⣿⡏⠉⢹⣿⠉⣿⣿⡏⢩⣭⣿⣿
⠀⠀⠀⣈⣻⡷⣸⡿⢾⣧⢠⣿⣀⡀⣿⣛⡁⠀⠀⠀⣿⣿⣿⡿⠦⠈⡿⠀⣙⠀⢿⠀⠿⢿⡇⠰⢾⣿⣿
⠀⠀⠀⠉⠉⠁⠉⠁⠀⠉⠀⠉⠉⠁⠉⠉⠁⠀⠀⠀⣿⣿⣿⣷⣶⣾⣷⣾⣿⣷⣾⣷⣶⣾⣷⣶⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣦⡀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠀⠄⣠⣀⠈⠻⣆⠀⠀⣠⡈⠉⠀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠶⢦⣤⣉⠛⢷⡀⢹⢠⠞⣡⡴⠶⠛⡛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣀⣈⣙⠢⠑⠀⠁⠚⣑⣒⡛⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⡀⠀⢀⣀⠀⠈⠉⠉⠛⠷⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⢰⢳⠀⠈⣇⡹⠀⢸⣀⡇⠀⢳⡴⠂⠀⠈⠛⢁⣴⠆⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢣⡤⣧⠀⣾⠬⣇⠀⡏⠀⠀⣼⠁⠀⠀⡼⠁⠀⢤⣄⣠⣿⣃⣀⣀⣴⣿⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡄⠀⠘⡇⠘⠂⠙⠀⠈⠀⠀⠀⢀⡀⠀⣠⣌⠁⠀⠀⠀⢀⣿⠃⠀⢀⣿⡟⢻⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠇⠀⠀⠀⣠⣤⡀⠀⢀⣄⠀⠀⣿⣷⠸⣇⣟⣀⡀⠀⠀⣸⡏⠀⠀⣼⣟⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢸⣿⡇⢹⡄⣸⣿⠀⢸⢿⡿⠀⡎⢁⣿⠇⠀⢠⣿⠁⠀⣸⡿⢋⡴⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡄⠤⠻⣯⠙⣻⠏⠙⣿⣀⡞⢸⣇⡼⠁⣼⡏⠀⡠⢻⡏⠀⡰⣿⡵⠋⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡻⣄⠀⠈⠉⠁⠀⠀⠈⣩⣄⠈⢫⡥⠀⠿⠶⣪⣤⠸⣷⠞⠁⠈⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡹⡆⠀⠀⠀⠀⠀⠀⡇⢸⡇⢸⡄⠀⠀⢰⡿⢹⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⣠⠴⠶⣿⣦⠀⢧⡸⠁⢸⠀⠀⠀⣾⡇⡼⠀⠀⠀⠀⠀⢰⣦⠙⠀⢀⠻⠀⣠⡤⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠋⠉⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⣾⣆⠀⣿⣧⠇⠀⢀⣾⠆⠀⢸⣿⡆⠀⡿⢠⠞⢁⡀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠈⣿⡇⢰⣿⠀⢰⣿⣿⠀⣸⡏⠀⠀⢸⣿⠀⠀⣼⣿⡇⠀⠃⠀⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢤⣤⣤⣀⠐⢷⡄⠀⠀⣿⡇⠸⣿⠀⣸⢸⡇⢰⠛⣿⡀⢠⠏⢿⣀⡴⠃⣿⠇⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠙⠆⠹⡀⠀⣿⡇⠀⠙⠛⠁⠈⠿⠃⠀⠘⠻⠋⠀⠀⠀⠀⢠⡿⠀⣠⣿⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣀⣛⡛⠛⠂⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣠⠖⠛⠛⠛⠓⠶⢦⣄⣠⠟⠁⡴⢿⣛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠈⠻⣦⠀⠀⠀⢸⡟⠀⠀⠀⠀⡀⠀⠳⢄⣀⣀⣀⣠⠤⠶⠛⠙⢦⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡟⠠⠀⢀⡄⢱⡙⠷⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠘⠃⠤⠚⠁⠀⣠⠟⠀⠀⢀⡾⠀⣆⠳⣤⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⣀⣠⠴⠚⠁⠠⣦⠐⠛⣀⠀⢻⡄⠈⠁⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⡿⠁⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⡿⢁⠔⢹⡿⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⠀⠀⢀⣀⠀⠀⣠⡄⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠂⣰⡟⠁⢀⣴⠟⠉⠁⢀⡀⠀⣾⣿⢀⠔⢉⣿⡀⣸⣿⢣⠞⢉⣷⠔⢈⣷⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⠀⣰⡟⠀⣠⣿⠃⠀⡠⠊⣴⡇⣸⣿⢇⠎⡠⣾⡟⣹⣿⡱⠃⢔⣽⡟⢠⣿⡣⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠻⠤⠀⠹⠿⠴⠊⠀⠸⠿⢴⣿⣏⠎⠀⠙⠋⢠⣿⡳⠁⠀⠛⠋⠀⠈⠉⢠⣿⠥⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⢀⣿⣻⠁⠀⠀⠀⠀⠀⡀⢐⣿⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⣶⠀⠀⣿⣿⠁⠀⠀⠀⣾⣯⠇⠀⠀⠀⠀⠀⠌⢀⣾⠏⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣀⣸⡏⠀⠀⣿⠇⠀⠀⠀⠸⣿⠏⠀⠀⠀⠀⠀⡐⠀⣾⠏⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⡄⠀⠀⠑⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠖⠒⢦⣄⠀⠀⣸⡇⡀⡀⠀⢀⠄⡄⡇⠀⠀⣰⣿⠏⢀⠆
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣾⣿⠀⠀⠻⠁⠀⠀⠀⠈⠒⠁⠃⠀⣼⣿⢏⡴⠃
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⢠⣦⠀⠀⢀⣴⡀⠀⠀⣸⣿⡟⠁⠀⠀⠀⣀⡀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢠⣿⠇⠀⢀⣾⡿⠀⠀⢠⣿⡿⠀⠀⠀⢀⠞⣽⡿⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⢉⣿⠏⠉⠀⣿⡟⢀⡠⢻⣿⠁⡠⠀⠀⣿⡇⠀⢀⡴⠋⢸⣿⣅⢴⣿⣯⠤⣄
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣼⡏⠀⠀⠀⠛⠓⠋⠀⠘⠷⠊⠀⠀⠀⠙⠓⠚⠁⠀⠀⠀⢉⣠⣾⠏⠀⠀⡼
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣼⡏⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⣼⡟⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⢀⣾⡟⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⡈⢀⠇⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⢀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠭⠿⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡐⠠⠒⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⠴⢐⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠊⠉
⠀⠀⠀⠀⠀⠰⠦⠾⠁⠀⠉⠉⠙⠒⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠓⠲⠤⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠑⡄
⠀⠀⠀⠀⢀⡜⠁⠀⠀⡈⠀⠰⠀⢰⠒⢲⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠐⠒⠒⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⢀⠎
⠀⠀⠀⢀⠎⠀⠀⠀⢠⠁⠀⠆⠀⠄⠀⡄⡰⠋⠀⣀⠈⠳⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠀⠀⠀⠀⡇
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⠀⠃⠀⡎⠀⡃⠀⠅⠀⠀⠌⠀⠉⢱⠀⢀⠀⠆⡀⠀⠀⠇⠀⠀⠎⠙⢢⠀⠀⣀⠜⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡆⠀⡆⠀⠳⡀⠈⠉⠁⠀⡌⢀⡄⠀⡀⠀⠑⠀⠀⠌⠁⠀⣀⣀⡸⠀⠀⠸⠒⠈⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⢃⠀⠀⠀⠀⠀⡈⠀⡘⠀⠸⠀⠀⠘⡄⠀⠱⡄⠀⠀⡘⠀⡘⠃⠀⡇⠀⠀⠉⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢸⡀⠀⠠⡀⠀⠣⠐⠁⢀⢃⠖⠀⡄⠘⠀⠀⣿⠀⠀⠀⠐⢀⠀⠀⠁⠀⠀⠀⢠⠊⠀⠑⠀⠀⢐⠂⡆⠀⡂⠀⠀⠀⠈⠀⢇
⠀⠀⠀⠀⠳⡀⠀⠐⠦⠄⠠⠔⠋⠸⡀⠀⢧⡠⠃⠀⣿⠀⠀⠀⠃⠘⠀⢰⠀⠀⠀⢀⠆⢀⠀⠀⠀⠀⠈⠀⠃⢀⠇⠀⠀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⡠⠞⡀⠀⠠⠀⠂⡄⠀⠈⠀⠀⠀⠌⠠⠏⠀⠀⠀⠆⠜⠠⢈⠜⠂⠀⠒⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠁⠀⠀⡇⠀⡆⠀⠀⠘⠀⠓⠀⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉⠲⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠐⠒⠒⠂⠀⠰⠀⠀⠓⠄⠀⠐⠁⠀⠀⠞
⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠖⠐⠡⠀⠀⠀⠀⠀⠀⠂⠁⢀⣀⣀⣁⠀⢁⣀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⢣⠀⢀⡀⣧⡀⡀⠀⠀⠀⠀⠀⠀⠘⢤⣀⡴⠲⠄⠐⠃⢀⡀⠉⢀⡤⠤⣤⣀⣠⠞⠁⠀⠀⠀⠉⠋⠀⠱⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢈⣟⡻⠵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡄⠀⠀⣠⠞⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠄⢀
⠀⠀⠀⠀⠀⠀⠐⣦⠉⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⡀⣜⠂⠀⠀⠠⡄
⠀⠀⠘⡁⠀⠀⠀⠰⠖⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠷⢼⣹⡵⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⢁⡀⡘⠁
⠀⠀⠀⢱⡄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁
⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠐⡀⠰⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⢄⡈⠳⡀⢃⠀⠰⠁⡔⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠈⠀⠁⠞⢀⡠⠄⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⢴⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢤⠤⠄⠒⠊⣁⠜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠠⠔⠊⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡠⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠈⠁⠀⣀⠜⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠒⠈⠀⢀⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠀⠒⠁⢀⡅⠀⠀⠀⠀⠀⠄⡀⠄⠀⠀⠀⠀⠀⢀⠜⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠤⠄⠒⠁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠔⠈⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⡀⠀⠀⢘⡀
⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠰⡤⠄⠒⡡⠊⠀⠀⠀⠠⡰⠀⠀⠀⠀⠀⠗⠠⠤⠩⢼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠠⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠠⠊⠀⠀⠀⠀⠑⢆⠀⡄⠁⡔⢁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠠⠤⠠⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠙⠢⠁⠀⠀⡰⢁⣀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⢀⠡⡀⠀⠀⠀⠀⠀⠀⠀⡘⠐⠀⠐⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢠⠁⠀⠀⠀⠀⠀⠐⣀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣄⡑⠀⠆⠀⠀⠀⠀⠰⠅⣁⣀⡘⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠂⠀⠀⠀⠀⠳⡀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠀⠀⠸⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢠⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠱⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⣴⡶⠶⣦⡀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣸⣇⠀⣸⣧⡽⣷⡀⣿⡟⠛⠋⠀⣿⠷⠤⠿⠃⢻⣆⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠋⠉⠿⠀⠛⠀⠀⠈⠁⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⣤⣀⣀⣀⣠⡤⠤⠴⢖⣒⣒⣒⡲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣯⠭⠭⠽⠿⠿⠭⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡛⠿⠿⠿⠿⣓⣒⣛⣭⠭⠭⠭⣭⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠭⠭⠭⠭⠭⠭⢶⣒⣒⣛⣛⣛⣓⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣄⢴⡆⠀⠀⠀⣶⡶⣶⠀⡶⢶⡆⠰⣶⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣿⢸⡏⢸⡿⡇⠀⣀⣿⡇⣿⠀⡇⢸⡇⡀⣹⡇
⠀⠀⠀⠀⠀⠀⢠⡟⣤⣤⢀⣠⡄⠉⠈⠋⠛⠛⠷⠀⠻⠿⠀⠻⠾⠃⠚⠛⠁⠀⠀⣤⢤⣀⣤⠴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠚⠺⠟⣾⣶⢴⡶⣴⣶⣤⣾⣦⣦⢴⣶⣴⣖⢶⡷⠀⠿⠞⠉⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠉⠁⠉⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿