Ant Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡐⠤⣀
⠀⠀⠀⠀⠐⢄⡀⠐⠂⠤⢀⡀⠀⠈⠒⠄⣁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠘⣧⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠀⠀⠒⠤⡀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣀⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠄⡀⠀⠀⠀⠑⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⠃⠀⠀⠀⠘⠛⠢⡀⠀⠀⢀⠤⠀⠀⡔⠁⠀⠀⢀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢀⣤⡀⠀⠀⠀⢀⣤⡀⠈⢆⠀⡂⡤⠃⠰⠀⠀⠀⠀⠀⠈⡁⠢⢀⠀⠀⠀⠡⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠠⢜⠛⠁⠀⠀⠀⠈⠛⣃⠀⠀⢣⢱⠈⣸⢏⠑⠄⠀⢀⡔⣩⠠⡑⢄⠑⠄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⡆⢠⠱⠇⠘⢀⡠⣋⠅⠶⡘⡌⢌⢆⠀⠂⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠋⠀⠀⢀⢧⢢⢧⣧⠔⡊⡾⠁⠀⠀⢡⢰⠈⡌⠆⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠐⠈⠀⠀⢀⠠⠂⢂⠆⡔⣡⠚⠇⡇⠀⠀⠀⠀⡆⡆⠈⠌⣄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡖⠒⠒⠒⠲⠖⠒⢎⠁⠀⠀⠋⠀⠈⡰⠂⢦⣴⠦⠤⠤⠤⣦⣵⠒⢳⡰⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡉⠉⠘⡄⠀⠑⠀⠀⠀⠒⠈⠀⠀⢸⣁⠀⠀⠀⠀⢰⣨⠀⢠⣆⣉⣉⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⠂⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⠀⠀⠀⠀⢠⠼⡤⢤⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠠⠤⢀⠀⠸⣀⣀⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠨

⠀⠀⠀⠀⠀⠀⠀⠀⢺⡛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⠋
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⢆⢳⠀⠀⠀⠀⠀⠀⠀⣠⢶⡆⢰⡦⣄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠹⡟⢆⠀⠀⠀⠘⡌⡆⠀⠀⠀⠀⠀⢰⠁⠸⣇⣸⠇⠈⡆⠀⠀⠀⠀⠀⢰⢡⠁⠀⠀⠀⣠⢻⠏
⠀⠀⠀⠀⠀⠀⢹⡌⢇⠀⠀⠀⠘⡸⠀⠀⠀⠀⠀⣸⡟⠉⠉⠉⠉⢻⣇⠀⠀⠀⠀⠀⢇⠃⠀⠀⠀⣼⢡⡏
⠀⠀⠀⠀⠀⠀⠀⢣⢸⡄⠀⠀⠀⣷⣓⣒⣶⠾⢻⡏⠀⠀⠀⠀⠀⠀⢘⡟⠷⣶⣒⣚⣾⠀⠀⠀⢠⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠘⣼⡇⠀⠀⠀⠈⠉⠁⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠈⠉⠁⠀⠀⠀⢸⣧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠙⢦⡀⠀⠀⠀⠀⢀⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⠀⠀⠀⠀⢀⡴⠋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣌⡳⢤⡀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⢀⡤⢖⣩⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⡟⠲⡄⠉⢛⣿⠶⣶⡲⠶⣿⡛⠉⢠⠖⢻⡵⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡙⣄⣾⠁⠀⠀⠀⠀⠈⣷⣠⢋⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡿⣄⠀⠀⠀⠀⣠⠿⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡖⠲⣄⠀⠈⠳⣏⠁⠀⠀⠈⢹⠖⠁⠀⣠⠖⢲⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⣫⠔⠋⠉⠓⠦⢝⣲⠶⡿⠂⠀⠀⠐⢿⠶⣖⡫⠴⠚⠉⠙⠢⣕⠢⣄⡀
⠀⠀⢀⣀⣀⠠⢴⡞⢉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢾⡇⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠈⠳⢄⡉⢓⣤⣀⣀⣀
⠻⢤⣤⣤⠤⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⣄⣀⣀⣠⠿⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠤⣬⣭⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠖⠒⢊⣩⠷⠴⡏⠉⠉⢸⠦⠾⣍⣓⠒⠲⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡷⠒⠋⠉⠀⠀⢠⡟⠀⠀⢻⡄⠀⠀⠉⠙⠲⢾⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⠃⠀⠀⠀⢀⡴⢾⣧⡄⢀⣼⡷⢦⡀⠀⠀⠀⠘⣇⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢡⡏⠀⠀⠀⣰⠏⠀⠀⠈⠁⠈⠉⠀⠀⠹⣆⠀⠀⠀⠸⡄⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡾⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢷⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡷⠞⠁⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠳⢶⡛⢦⡀
⠀⠀⠀⠀⣀⡤⠞⢉⡴⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠙⢦⡉⠳⢤⣀
⠀⣴⡚⢋⣁⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣈⣙⢳⣦
⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⠉⠒⠒⠀⠐⠒⠒⠉⢁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡒⠤⣄⣀⣀⣠⠤⢒⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣠⡴⠟
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣋⢀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠈⠁⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⣀⡤⠴⠒⢯⣀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⡏⠉⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠠⢒⣷⡢⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠱⢌⣛⠵⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⢿⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⣠⠴⠚⠉⠉⠁⠀⠀⠈⠉⠙⠲⢤⣠⠔⠚⠛⢲⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠐⠛⢇⡀⠀⢀⡼
⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢈⣷⢄⣀⠀⠀⣀⣀⡭⠟⠋
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢹⣄⠀⣄⢀⣿⠦⣄⣀⣳⣤⠞⠉⢣⡈⠉⠉⠉
⠀⠀⠘⢦⡀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣀⡴⠋⠈⠛⢻⠁⠈⣇⠀⠀⠀⠹⡄⠀⠀⠙⣆
⠀⠀⠀⠀⠉⠓⠲⠦⡾⠤⠤⠶⡖⠚⠉⠁⠀⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⠀⠹⡄⠀⠀⢘⣦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠀⠀⢳⣀⣀⠘⠦⠤⠚
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣧⣤⣀⠀⠀⠯⣤⠬⠃
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠥⠤⠜
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⠟⠒⢦⠀⠀⠀⠀⠀⢰⣛⢉⣱
⠀⠀⠀⠀⠀⡴⠟⠒⡄⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⢍⠉⠉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢳⡀⠀⠀⠀⡌⠙⢦⡀
⠀⠀⠀⠀⠺⠛⠛⠳⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⡇⠀⠀⠀⡄⠀⠀⡝⢦⡀
⠀⠀⠀⢀⣀⣤⣄⠀⠀⠸⡆⠀⠀⠀⠀⣠⠴⠖⠦⢤⡾⠦⣄⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡄⠈⡿⣄
⠀⠀⢰⡏⠀⠀⠈⠑⢤⣠⣧⣄⣀⣠⢼⡁⠀⠀⠀⠀⢷⠀⣸⡆⠀⢠⠇⠀⠀⢀⡇⠀⠀⠀⢀⠀⣙⣷⠤
⠀⠀⠈⠁⠀⠀⠀⣠⠎⢠⠔⢦⡙⣦⠀⢱⠀⡄⠐⣦⡾⡗⠻⣟⠦⣌⣀⣀⣀⣎⣀⣤⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣦⡿⣣⣟⣖⣽⠋⡟⣏⠹⣆⠷⠲⣿⣦⣬⣭⣭⣭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣆⣬⡽⣺⢡⡖⠒⢺⡿⢿⣞⣤⡿⠆⠀⠘⣆⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠘⢠⡟⣾⠇⠀⣸⠀⣿⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⢡⡿⠀⠐⠋⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠁⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⢷⡀
⠀⠀⣀⢤⡲⠟⠳⣦⡀⠀⠀⠘⣇
⠴⠮⠓⠉⠀⠀⠀⠈⢳⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠿⠒⠒⠙⠒⠦⡀
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣴⣀⠀⠀⠀⢱
⠀⠀⠀⠀⢀⠜⠀⠀⠀⠘⢿⡿⠁⠀⠀⠈⠲⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⣀⣠⠞⠁⠈⠒⠒⠢⢄⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⣇⠤⡄⢀⠤⠤⢲⢋⡼⢠⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠈⠐⠛⠁⠀⡰⢁⡾⢡⠃⠀⠀⠉⠲⣄⣄⣀⣀⣀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⢻⢁⠎⠀⠀⠀⠀⡸⡜⠀⠀⠀⠀⠀⠱⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⢀⣠⠞⡴⢣⢃⡎⠀⠀⠀⠀⡰⡹⠀⠀⠀⠀⠀⠀⠀⠱⡘⡍⠒⠦⠄⣀⢀⣀⣀⠠⡊
⠀⠀⠀⠀⠘⠓⠒⠛⣠⠇⡼⠀⠀⠀⠀⠾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⡐⢄⡀⠀⠈⠓⠬⠷⠓⣝⡢⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⢾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣦⣼⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄
⠀⠀⠀⠈⠛⠿⠟⢷⣶⡄⠀⠀⠀⠀⠀⠘⠿⠋⠛⠋⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠈⠙⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡿
⠀⠀⠀⠀⠀⣠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠂⠀⣠⣼⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢯⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏
⠀⠀⠀⠀⣹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡏⠉⠁
⠀⠀⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣷⣤⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠋
⠀⠀⠀⠈⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠗
⠀⠀⠀⠀⠙⣿⡁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⣠⣤⣤⣶⡄⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿
⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠻⢿⣿⡿⠋⠙⠛⠁⠉⠀⠀⠀⠀⠀⠀⠈⠙⣷⣶⡆⠄
⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⢤⡀
⠀⠀⠀⠀⠀⡠⠚⠠⠎⠉⠢⡀⠈⢦
⠀⠀⠀⣠⠂⢀⡜⠁⠀⠀⠀⠘⣦⣤⣧⣤⣀
⠀⠀⠘⠃⠀⠈⠁⠀⠀⠀⣰⣿⣿⢟⡉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠘⠃⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣤⣤⣤⣾⣿⣶⣶⣄⠀⢀⡀⣠⣴⣾⣿⣿⣿⣎⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠛⠛⣻⣿⠏⣿⠙⢿⣿⣿⣿⣿⣿⣿⡷⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⣠⠔⠊⠁⡞⠀⡟⠀⠀⠈⠉⠉⠉⠉⠉⢧⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⢰⠃⠀⠀⢸⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠀⣀⡤⠁⠀⠀⠀⠸⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠳⣀⠀⠀⢀⡰⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⣄⠘⢆⡀⠀⠀⣀⠞⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣿⣿⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠉⠹⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⢻⣿⠋⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⡶⡞⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣿⣿⡏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢹⠀⢸⢉⡀
⠀⠀⠀⠀⠀⠀⣀⠴⠊⠉⠉⢻⣿⠋⠉⠉⠳⢄⡀⠀⠀⠀⠀⢀⡠⠞⠉⠉⠙⣄⡜⠉⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⡞⢉⣽⣿⣍⠙⡆⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⢀⠋⡉⠻⢯⡍⢳⡀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⣿⣿⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠐⡇⠀⠀⡖⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠻⡿⠋⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠙⢄⠜⠁⠀⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠏⠀⠀⠀⠀⠀⠀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⠀⢀⣀⣀⡀⠀⢸⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡸⠊⠁⠀⠀⠀⠀⠈⠚⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠓⢍⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠩⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣕⢄⠀⠀⠀⠀⢀⡖⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⢦⡀⠀⠀⠀⢀⠔⡫⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡱⢄⠀⠀⠈⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⡠⢎⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠁⠀⠀⠀⠈⠁⠒⠒⢒⡖⠖⠒⣦⠠⠤⠤⠐⠁⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠃⠂⠤⡀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⠄⠒⠙⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠈⢢⠄⡘⠀⠀⠀⠀⠀⠀⠀⠈⣆⠤⠞⠁⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠚⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠓⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⠀⣀⠀⠀⣀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⡄⠀⠉⠈⠐⠠⢄⡀⡠⢄⠀⠀⠀⠀⠀⠀⡤⢄⣀⡠⠔⠂⠁⠀⠀⣠⠉⠢
⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⠁⠁⠒⠠⠤⠀⠀⠼⣀⣈⠉⠉⠉⠉⠁⠉⣃⣀⠧⠀⠤⠤⠀⠒⠉⠘⡀⠀⢃
⠀⠀⠀⠀⠀⠀⢠⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢄⠀⠀⠀⠀⣠⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⡄
⠀⠀⠀⠀⠀⠀⡄⢀⠎⠀⠀⢀⡀⠤⠄⠐⠀⠒⠚⣄⠀⣓⣂⣀⣚⢀⣘⠃⠒⠀⠐⠀⠤⢀⡀⠀⠀⠱⡀⣡
⠀⠀⠀⠀⢀⢔⠝⠁⠀⡴⢎⣀⡀⠤⠄⠒⠀⣀⠝⠋⠉⠀⠀⠀⠀⠈⠉⠛⢄⠂⠐⠂⠤⢀⣀⡩⢆⠀⠈⠫⡣⡀
⠀⠀⢀⢔⠕⠉⠀⠀⢰⠀⠀⡇⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢸⠀⠈⡄⠀⠀⠈⠪⡢⡀
⣠⡴⠕⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡜⠒⠒⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠒⠒⠸⡀⠀⠀⠈⠀⠀⢠⠀⠀⠀⠀⠈⠊⠦
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢇⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠁⠀⠀⠀⠀⣇⣀⣀⠀⠀⠠⠤⠤⠤⠤⠤⠀⠀⣀⣀⢀⡆⠀⠀⠀⠈⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡸⢀⠆⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠰⡀⢄
⠀⠀⠀⠀⠀⠀⡐⠁⡜⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢣⠈⢂
⠀⠀⠀⠀⢀⠜⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠐⠒⠂⠀⠀⠀⠒⠒⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠣
⠀⠀⠀⡠⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠀⠀⠠⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢄
⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢛⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡟⠛⠋⢳⡀⠀⠀⠀⠀⠀⠀⣰⡶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠔⠀⠀⡈⣧⠀⠀⠀⠀⠀⢠⡏⠀⠀⣠⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⣧⢀⣴⠀⠀⠸⡄⠀⠀⠀⠀⠘⡇⢰⡟⠻⢆⣷
⠀⠀⠀⠀⠀⠀⢸⠋⠀⢿⠙⣆⠀⠀⠀⠀⠀⠀⢹⣿⡿⠖⠀⣀⣧⠀⠀⠀⠀⠀⡇⠀⠈⣰⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠁⠘⢇⠀⠀⠀⠀⠀⠀⣿⠃⢠⡿⠻⠾⡄⠀⠀⠀⠀⣷⠀⡈⠁⣰⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠂⡀⠀⣮⢧⠀⠀⠀⠀⠀⢸⡄⠈⠀⠀⠀⢱⠀⠀⠀⠀⢸⣿⣥⠈⣿⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⡷⠀⠨⠀⢳⡀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⢧⠀⠀⠀⠸⠀⢀⣰⡟⠃⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠄⠀⠀⠈⢳⡀⠀⠀⠀⢃⠀⠀⢀⡤⠴⠾⡄⠀⠀⡄⠀⡾⠋⠉⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠻⣄⠀⠀⠸⡆⢀⠊⠀⠀⠀⣧⠀⠀⡇⠀⠰⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠈⢀⡠⢀⡙⢦⠀⠀⢻⡘⡀⠀⠀⠀⢹⡀⠀⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤
⣰⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢷⢠⡟⡁⠀⠉⠈⣇⠀⠈⡇⠙⢦⣀⣀⣨⣇⣀⡇⢀⠔⠀⠁⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠇⢀⠀⢈
⣏⢠⠂⠨⠉⢢⡀⠀⠀⠀⠀⠀⠈⢿⡀⠠⠃⠈⠀⠙⣆⣠⠁⠀⠀⠈⠍⠀⠈⠉⠀⠈⠈⢷⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠓⠈⠀⠨⠅⢰⠏
⠘⢦⡦⢶⣮⣿⣛⣦⣀⠀⠀⠀⠀⠈⢷⡀⠀⠁⠔⠀⠈⠁⠀⠀⢀⣠⠀⠀⣀⡀⣀⡀⠀⠘⢿⡄⠠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⡦⢀⣶⡖⣰⠃
⠀⠈⠳⣆⠀⠅⠀⠁⠉⠓⢦⣀⠀⠀⠈⢿⡀⠀⢿⣦⡀⠀⠀⠀⠸⠋⠁⡀⠀⠀⢤⣄⢠⣶⢁⣠⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⠟⠪⠟⣿⡿⣿⢶⠇
⠀⠀⠀⠀⠙⢦⡂⣀⠐⣶⡇⠘⠓⡤⢀⢼⠃⣀⠐⠊⠉⠀⠀⠀⠀⣤⣾⣷⣷⣦⣼⠯⢘⣿⣯⣿⠀⢠⣼⣧⡀⠀⠀⠀⠀⢠⡏⣤⢶⠨⡍⠀⢰⡞
⠀⠀⠀⠀⠀⠀⠙⢦⡾⠛⠋⠫⠌⢁⠀⣀⡀⠜⠋⡁⣀⡄⠈⢠⣾⠿⢛⣋⢉⠁⣀⡀⢰⡞⣠⠜⣦⢀⡿⣥⣹⣆⠀⠀⣠⡿⠣⡀⢦⠐⡺⣉⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡆⠴⠊⠍⠐⠛⠁⠀⠐⠀⠺⠁⡳⠎⠁⠀⠛⠟⣿⣿⢶⣡⠎⣹⢱⣬⠇⢸⣿⠄⢨⣌⠛⠻⠛⠦⠢⡬⢺⠦⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣀⢄⡀⢀⡤⠑⠀⠚⠀⢄⠀⢀⠀⠀⣀⠘⠛⠁⢛⣽⣖⠓⠃⡆⢘⡧⢼⢷⡚⠉⠀⢀⡁⠐⢀⡀⡿⠖⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⢹⣮⣄⡀⠀⠀⣀⡀⠐⡂⠀⠐⢿⣷⣄⠀⠻⠋⠀⠜⢃⣄⠘⠁⠘⢒⣟⢀⡧⣸⣟⡦⠀⣹⠧⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠉⠚⠠⠤⡉⢀⣉⠀⠁⠀⠀⠈⣿⢿⣷⣄⠀⠀⠤⠷⣟⡇⠠⣨⣭⣭⢾⣍⣃⡀⠀⢈⣷⣆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣤⣶⣾⣿⣟⠿⠀⠀⠀⠀⠛⠀⣽⡿⠇⠀⠀⠈⠉⠑⠀⠄⢀⡍⠀⣽⢻⡿⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣿⣆⠀⡆⠀⠀⠀⠀⠈⠁⠀⠒⠤⠘⢶⣺⣆⢸⡿⠀⠀⢠⣀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠋⠹⠆⠁⠁⠀⢧⡀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠚⠅⡸⢿⡃⢀⣤⣾⠋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢠⡄⠶⠀⠀⠘⢤⡀⠀⠀⠈⠻⢿⠶⠜⠁⠀⠀⠁⢻⡅⠸⢿⢿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⠀⠀⠀⣀⣀⣀⠈⢠⣴⡦⠴⠦⠤⠄⠰⠆⠀⠀⠶⠿⢶⣤⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠲⠶⣭⠽⠗⠒⠶⠖⢀⣀⣰⡖⠀⠉⠡⠴⣤⣠⣤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡔⠶⠿⠶⠦⠀⢀⠘⠛⠻⠛⣋⣀⣀⡀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⣦⣤⠀⠠⠶⠶⠦⠀⠀⢿⡿⠍⠱⠶⠶⠶⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡈⠙⣠⠰⡐⣦⣴⣶⣶⠄⠀⠀⠀⠇⠀⠾⠛⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢲⣬⡄⡽⠅⡀⢁⡌⠀⢱⡇⢰⡄⡄⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣇⣡⣹⣇⣸⣹⣘⡃⢒⣮⡇⣸⣸⢓⣴⣿⣡⣸⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⡶⠶⢶⣾⠿⢷⣦⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠒⡒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡀
⠀⣿⠀⣥⢼⡇⠻⢺⣇⠶⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡇⢎⡰⠾⠠⣀⠠⠦⠂⠄⢖⡀⠀⢨⠀⠀⠀⢀⠀⠀⠈⠀⣀
⠀⠙⠳⠶⠚⠛⠿⠿⠟⠿⢿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠄⣀⠀⠀⠤⠤⠀⠀⡄⡠⠤⠊⠀⢀⠞⢁⠀⣆⣀⠀⠌⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠀⠒⡁⠆⡏⠒⠢⠁
⠀⠀⠴⡇⡀⠀⠀⢀⠈⡢⠭⠥⠐⠂⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⣀⡀⠀⣀⢀⡀⠀⠄⠀⡆⠀⠀⢀⣠⡄⠀⠀⠀⡀⠀⠁⠙⠁
⠀⡎⠈⡇⠱⡄⠄⠈⡜⠄⠀⠀⠠⠘⡄⠁⡀⠀⠀⠀⢻⡗⠋⣰⠁⠁⣼⠁⠈⡧⠰⠮⠞⠀⡀⠀⠀⠋⠃⠀⠀⠀⠈⠂⠀⠃⠀⠀⠐⠁
⠀⠣⣰⡇⠐⠁⠀⠃⢡⠀⠀⠀⡀⢀⠁⠦⠀⠀⠀⠀⠀⠉⠉⠈⠙⠋⠈⠛⠋⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⠁⠀⠀⠈⠀⠤⠕⡂⢉⠀⡈⡆⠐⠀⠀⡔⢀⠀⠬⠀⠀⠀⠐⡄⠀⡀⠀⠤⡀⠀⠀⠀⠀⢠⡀⠀⡀⣀⠤⠛⠀⢰
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠈⠉⠲⠀⠀⠀⠀⠀⣷⢀⠤⠀⠀⠠⠉⠛⠁⣸⠀⠒⢆⢹⠀⠐⠇⠀⠀⠀⠈⠉⠀⠀⠀⠠⠶⠄⠐
⢀⢰⡀⠂⡀⠀⠀⡤⠀⠄⠠⡀⠀⠀⣠⠉⠉⢢⣟⡀⠀⠀⠰⣄⠀⠀⠀⢻⠀⠀⠊⢨⠃⠀⠀⠀⣀⠤⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⡄
⠣⠔⢪⠰⠀⠀⠡⠳⠄⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠈⠉⠁⠀⠈⠙⠛⠁⠀⠻⠶⠒⠁⠀⠀⠀⡎⠀⠀⠀⠀⠀⠰⠠⡀⠈⠀⠀⢰⣆⠀⠐
⠀⠀⢀⣤⠔⠒⠒⠒⠢⣤⡀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠉⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈
⠀⣠⡛⢿⡇⠠⠄⢚⣩⣿⣿⣦⠀⠀⠀⠀⡈⠘⠠⣍⠀⣼⠳⠹⠀⠀⠀⠡⠓⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⢀⠇
⢰⠹⢛⣆⠀⠀⠰⠟⠛⠻⢿⣿⡇⠀⠀⠠⠃⠀⠈⠉⠢⠈⠇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⡇⢸⠒⠉
⢸⣿⣿⡏⠀⠀⢀⣾⣿⣷⣬⡛⡇⠀⠀⠄⡀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠠⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣾⣿⣆
⠀⢯⣀⣠⡄⠀⠈⠛⠛⢿⣿⢰⠃⠀⠀⠀⠩⠀⠤⠀⠀⢰⠁⠀⠀⡆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛
⠀⠈⠻⣿⣿⡇⠀⠀⠀⠘⠇⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠑⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠀⠀⠀⠀⢀⢐⡐⢂
⠀⠀⡀⠀⠈⠁⠀⠀⠈⠀⠀⢀⠀⢀⡠⢦⡀⠚⠓⠒⠀⢠⠀⠀⠀⠀⢠⣤⠀⠀⠀⣦⠀⠀⠀⢠⡴⠦⣤⡶⢶⣦⠀⠀⠀⠀⠣⠌⠁
⠀⢸⠠⢀⠄⠤⢀⠄⢤⠀⡀⠨⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⣿⣐⢃⣸⣀⣀⣿⣁⠀⠀⢀⠀⢀
⠀⠈⠒⢈⡀⠀⠉⠈⠈⠀⠁⠀⠀⠀⠀⠀⠚⠀⠀⠑⠀⠀⠀⠈⠁⠀⠀⢀⠤⠀⢰⡮⡀⠀⠀⠈⠙⢻⡟⢵⠿⡏⠻⣷⡄⠀⠀⠈⠧
⠀⠀⠀⠀⢀⠔⠂⠒⢂⣤⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠸⠀⠀⡴⠉⢁⣠⠟⠀⠄⠀⠀⢠⡴⢾⢿⡶⣾⠶⣷⡿⠁⠀⠀⠀⡆
⠀⠀⠀⢀⡦⠶⠒⠚⢉⠅⠁⠀⠀⠀⡄⡀⠀⠉⡉⠭⠁⢠⠀⠀⠀⠸⣀⡴⠚⠁⠀⠐⠀⠀⠀⢸⣇⣤⣸⣇⣷⣛⣿⡷

⠀⠀⠀⣴⣿⡏⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠲⣄⠀⣤⠖⠀⠀⠀⣤⣶⣤⠂⠀⠀⠀⠀⠹⣷⠀⠀⠀⡤⠊⠀⠉⠒
⠀⠀⠀⢣⣿⠇⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠁⠻⣿⠿⠀⠀⠀⢼⠇⢀⣀⣀⠀⠀⠁⠀⠀⢀⡈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠛⠒⠓⠒⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠒⠋
⠀⠀⢀⠤⡄⢄⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⢀⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⡀
⠀⠀⠿⠃⢀⣾⣷⠀⠀⣺⣺⡃⣄⣄⠀⠀⣴⡿⠀⢹⡄⠀⠀⣶⢰⡖⡆⢶⠀⠀⠄⢠⣿⡇⠠⠀⠀⢛⣹⣇⣤⣀⡀
⠀⠀⠢⣛⠀⠘⠀⠀⠀⣶⠸⣦⣓⣒⠀⠀⢸⣧⢠⣼⡇⠀⠀⠁⢊⣶⡓⠚⠀⠀⠈⠀⢵⠅⠀⠀⠀⠸⠿⡏⠁⢩⡅
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢠⢉⡤⠀⠀⠀⠀⢠⣍⣰⡀⠀⠀⠀⠠⡦⢀⠀⠀⠀⣀⠼⢐⡡⠄⠀⠀⢠⠆⢀⠢⣄⠀⠀⠀⡄⠀⠀⡀
⠀⠀⠀⣤⢠⡀⠀⠀⠀⠀⣿⡀⠉⠁⠀⠀⣰⣿⣦⠆⠔⠀⠀⠨⠄⡧⠡⠙⠀⠀⠈⠦⣷⠫⠘⠀⠀⣾⣟⠀⣸⡿
⠀⠀⠀⠛⠟⠁⠀⠀⠀⠘⠁⠃⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠙⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣀⡀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠯⡇⡀⠺⠵⠀⠀⢰⣿⡿⠈⠀⠀⠀⢠⣸⣿⣿⠀⠀⠀⠠⠀⠀⣄⠀⠀⠀⡴⠀⢤⡄⠀⠀⠀⢰⡆⣴⢠⡄
⠀⠀⠀⢾⣸⠇⠀⠀⠀⢿⡟⠀⠒⠆⠀⠀⠀⢯⣉⣹⠀⠀⠀⠿⡿⠶⢿⠷⠀⠀⢿⠦⠼⠿⢾⠆⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⡄⢰⠆⠀⠀⢶⠀⡦⠀⡦⠀⠀⢀⢤⣼⡁⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠐⢼⡴⠃
⠀⠀⢰⢡⣦⠙⡄⠀⠀⠀⢸⡇⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⡇⣈⣀⠀⠀⠀⠘⢯⠁⠀⠀⠀⠀⣸⡇⠰⡗
⠀⠀⠈⠢⠥⠚⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠸⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠑⠘⠃
⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠐⢡⣧⠙⡆⠀⠀⡾⢷⠠⡾⢧⠀⠀⠀⠻⡿⠇⠀⠀⠀⡞⠁⣴⡈⢱⠀⠀⠀⣤⡼⢿⡆⠀⠀⣼⣿⡄⣿⣷
⠀⠀⠘⠄⠎⠴⠃⠀⠀⠣⣠⣿⣄⠌⠀⠀⠘⠒⠐⠛⠁⠀⠀⠳⡄⢉⣡⠞⠀⠀⠈⠋⠀⠼⠃⠀⠀⠹⣿⣇⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⢂⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⢈⡇⠉⢑⢦⡀
⠀⠀⠀⢀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣀⠌⠀⠀⠀⠘⠤⢷
⠀⠀⠀⠄⠀⠲⣤⠂⠈⠂⠀⠀⠀⠀⣰⢋⡑⡄⠀⠀⠀⢸⠹⣠⠃⠀⡎⢆⣀⠀⠀⢨⡇
⠀⠀⠀⠈⠂⣤⣋⡤⢚⠀⠀⠀⢀⡘⠡⠎⢰⣈⢹⠀⠀⠀⢆⠀⠀⠀⢣⠀⠀⠃⣄⣼⠀⠀⠀⡠⠐⠒⡨⠋
⠀⠀⠀⠀⠈⠈⠆⠜⢣⡀⠀⡪⢀⡵⠀⠀⠀⠈⢩⢠⡀⢰⠸⠶⣄⡀⠚⠀⣀⡤⣿⢰⠀⠀⠈⠀⣠⠞⠁⡀
⠀⠀⠀⠀⢀⠀⠀⠈⢫⠃⢠⠁⢸⣱⣐⣠⠎⠃⠘⠀⡇⠀⠢⠀⠀⢩⠉⠉⠉⠀⠀⡄⠀⠀⢀⡾⠥⠄⠊
⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠘⠲⡐⠧⠋⢸⠳⠆⠀⠀⠁⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⡜⠙⠑⠰⢐⣠⠂
⠀⠀⠀⢀⠃⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠆⠀⠰⡀⠀⠀⡄⠋
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⡄⠀⠀⠠⠀⠀⠈⢢⠀⠈⠢⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠡⠀⠀⠙⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠰⣤⣤⣤⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠙⢶⣾⣏⢹⣿⣷⣾⣿⣷⠈⠠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⡈⢳⣶⣿⡋⢘⣉⣻⣿⣿⠻⣧⣴⣾⣿⣶⣶⡎⢛⣀⣁⣤⣤
⠀⠀⠀⠀⠀⢶⣄⣀⣤⣿⣿⣿⠿⠻⣿⣧⡌⠉⠋⢰⣿⣾⠻⠇⢙⡿⠛⠿⣿⡿⢿⣿⣿⠿⣷⣶⣦⡀
⠀⠀⠀⠘⢇⣀⣿⣿⣿⠿⠀⠈⠃⢀⠰⣿⡁⠘⠃⠀⢰⣿⡄⠚⠛⠁⣀⣼⠸⣷⣌⣿⡆⠘⣻⣿⠛⣿⣀⠑
⠀⠀⠀⠀⠈⢻⣿⣿⠿⣀⠲⢼⣷⣾⣷⣟⠛⢶⡄⠀⢼⣿⣿⠂⢐⠃⡍⠀⡀⢠⣄⡸⢿⡏⢻⠷⣾⣿⣿⣤⣤⣄
⠀⠀⠀⢷⣀⠀⣿⣿⣶⠉⣷⣾⠛⠟⣳⣾⠂⠈⢁⠀⠈⠻⠇⢰⣾⠀⠉⠀⢳⠆⢻⣷⣬⣿⢺⣶⡿⢉⣠⣋⠙⠡⣄
⠀⠀⠀⠀⠈⠁⢿⣿⣿⣷⣿⣿⣿⡶⠌⠻⢿⡃⠈⢷⣶⠰⠃⡛⢸⡶⠀⢰⢴⡗⠙⣿⠟⢿⣿⣏⣠⣾⣿⣯⡈⢷⡄
⠀⠀⠀⠘⠃⠀⢸⣿⣿⣿⠋⠉⢩⣥⣤⣦⣼⣷⡇⢰⣿⣶⣾⣿⢰⠆⠁⠺⠈⠛⣮⡷⢠⣬⡟⠙⣧⣼⣿⣿⠃⡀⠉
⠀⠀⢠⡀⢻⣤⣼⣿⣿⠆⡿⠓⢴⣦⢙⣿⣿⣿⢷⣿⡟⣻⣧⡍⣘⠀⢛⣀⣎⡐⢿⣀⢸⡛⠷⠴⢦⡀⣼⣿⡦⠋
⠠⠆⠈⣿⣤⣾⣿⣿⠁⠘⠃⢀⣾⣿⣿⣿⡹⣿⣾⡟⣾⣿⣿⡶⠛⠀⠈⣩⣽⡗⠈⠁⠀⠀⢀⣀⣀⠁⢈⣿⡗
⠀⠀⣾⣿⣿⣿⣿⣿⡁⢸⡅⠺⠻⢡⣿⣿⣷⡼⠇⣸⣿⠻⣿⣤⣇⠘⣷⣿⣿⣠⣶⣇⠀⠀⠈⠁⠈⠑⢾⢿⣿⣶⡄
⠀⢚⣿⣿⣿⣏⢣⢀⣿⠄⢹⣆⠠⢈⣿⣾⣿⣧⢰⣿⣿⣴⣿⣶⣿⢰⣿⣿⣻⣿⣩⡏⣼⡗⠀⢀⡿⣧⣾⣶⣿⣏⠁
⠀⢿⣿⡟⢋⡉⠛⠁⠉⠠⣼⡿⢿⣽⡟⡿⢻⣿⡌⣿⣿⣿⣿⢻⣿⣿⣿⠳⡿⢿⣿⣿⠇⡹⢦⠘⢣⣄⠘⣿⠛⠿
⠀⢻⡟⣿⣿⣧⣶⣜⠃⠰⠈⠁⣤⡜⠻⣿⠿⣿⣷⠸⣿⣿⣿⢸⣿⣿⢃⣴⣾⣿⣿⢻⡾⣷⠀⡀⢼⡉⢠⣿⣗
⠀⠀⡀⠘⠋⢙⣿⣟⠁⠘⠂⠘⣅⢀⡾⠛⢾⣿⣿⣇⢻⣿⣿⡼⠟⣡⣾⣿⣿⣿⠃⣼⣷⡀⢲⡀⠈⣷⣿⡇⢸
⠀⠀⣠⠐⠃⡘⢿⣿⣦⣠⣤⠾⡇⠀⣠⣾⡾⢿⣿⣿⡌⣿⡿⢃⡴⠿⠿⢻⣯⣽⣿⣿⣿⡟⢻⣟⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣯⣀⣶⣀⣿⣶⣧⣼⣿⣿⣇⠘⢠⡾⠗⠀⠘⠋⠉⣿⣿⣿⣿⣿⡟⢹⣿⡋⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠉⣿⣿⡿⢿⡻⣿⡏⠹⣿⣏⠀⣿⣷⣿⣧⣴⣿⣿⣿⣿⠿⢿⡏⢹⡇⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠴⠊⣻⣟⠁⣄⣿⡏⢸⣯⣿⡏⢹⡏⣹⠙⡿⠈⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡁⢿⣿⠃⢸⡿⠋⠉⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡋⠉⢲⣤⡟⢡⠟⠁⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⢻⣿⠡⠟⢀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⢌⣿⠀⠀⢸⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⢷⣮⣻⠇⠀⠀⣿⡿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠠⡟⠛⠓⠿⠾⠷⢦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠛⠶⣿⣶⣶⣶⣤⣤⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣿⣿⡾⡟⠏⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⡀⠀⠀⢒⣿⣿⠀⠀⢀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠟⡿⠻⢿⣽⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠀⠈⠀⢛⣿⠀⠀⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣤⢺⡏⠀⣦⡇⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⠀⣿⣸⡇⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⣄⣀⣼⣿⣹⣧⠀⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⣿⢹⡋⢹⣿⣿⡀⢸⡏⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡁⠘⡇⠘⡇⣟⠁⠈⠁⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⠇⢸⠁⢰⠇⣼⡇⢀⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠷⠴⠾⢀⡿⠦⣿⠀⢿⡇⢨⢠⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⣷⠘⡇⢠⠀⠀⣿⠃⠀⣈⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠙⣿⣿⣟⣷⢄⣿⠇⢠⡏⠸⣿⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠼⣿⡿⠿⠾⠿⠟⢻⣿⣫⣴⠿⢷⣦⣿⣿⣷⡿⠿⠶⠶⠤⠠⣤⣀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡉
⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠄⢀⣾⣿⡶⡁⠀⠀⣀⣀⣀⠀⠀⡆⡀⠀⢠⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠠⠀⠄⠉⠀⠾⠂⠀⠒⠋⠉⠉⠀⢀⢨⡄⠒⠀⠁⢀⠤⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠘⣶⠠⢄
⠀⠀⠀⠀⣀⡀⠀⡀⢠⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣙⡇⠀⠀⣸⠂⠈⠳⣄⠀⠀⠀⣂⠀⡀
⠀⠀⠀⠀⠀⠛⠉⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠠⡄⠀⠀⠀⠀⠄⠀⢾⢁⡄⠂⠀⠁⢿⠀⠁⠸⠋⠀⠀⠀⠘⢧⣄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⣇⡠⠔⠂⠀⠠⣤⡀⠀⢈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠉⠀⡠⠔⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⣦⠀⠀⢀⡀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠠⠄⢾⣁⣤⣀⡄⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢦⣀⢀⡀⠀⠀⠀⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠠⢀⣴⡀⠀⠀⠄⠀⠀⠴⠄⠰⠆⠀⠀⠀⠀⠀⠀⠐⠚⠓⠀⠈⠁⠑⢦⠤⠤⠤⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠲⣞⠿⠤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠿⠆⠄⢀⣁⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠣⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠶⠶⠶⣞⠙⠉⠉⢉⣡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣋⢀⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡇⠰⡄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠒


⠀⠀⠀⠀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠘⠋⠛⠋⠛⠃⠂⠘⠙⠛⠉⠙⠁⠘⠙⠋⠛⠀⡙⠉⠉⠋⠛⠈⠋⠙⠛⠛⠙⠉⠛⠛⡛⠀⠀⠀⠀⣀⡀
⠀⠘⠛⠛⠛⠀⠛⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛⠐⠛⠓⠛⠛⠛⠃⠘⠛⠓⠘⠛⠃⠛⠛⠛⠻⠇⠘⠛⠛⠛⠀⠛⠛⠛⠛⠓⠛⠛⠛⠃⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣿⡷⣶⠀⣶⣾⣻⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⠿⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⣯⣏⣁⣀⣈⢻⣯⢏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⣠⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣏⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⢰⣿⡟⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⢿⡦⣦⠀⣦⣼⢿⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⢁⣧⣽⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡟⠁⠀⠙⢿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡆⣺⣿⣟⣿⡿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣻⣟⣿⣟⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡍⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠋⠛⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣾⢀⣤⣰⣧⣄⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⣿⣿⣿⣯⣸⣿⡗⠛⣼⠛⣥⣾⡇⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⠻⣿⣿⡿⢨⣭⣭⣈⠛⣱⣆⢈⢸⣿⡿⣃⠉⣵⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣧⡁⣠⡍⣴⣄⠻⣿⣿⣿⣿⡿⣿⠆⣡⣾⣇⣴⣿⡿⢣⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣻⡿⣯⣿⣅⣿⠇⠹⣿⠇⣮⠉⢛⡍⣶⠛⠃⣻⣟⢁⡍⠉⣐⣤⣽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⡣⠙⡿⠿⢧⡲⢿⣿⣷⢯⣰⣿⠇⢸⣇⣴⣯⣥⣟⡃⢀⣿⣿⣟⢁⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣾⣿⢇⣚⢳⣤⣀⣿⣄⣘⢿⣷⢿⡄⣦⣾⡟⣁⣠⣾⣯⣷⠿⣹⣿⠀⠸⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠛⢹⣿⡿⠇⢰⠟⠉⠉⠛⠿⣷⣾⣷⣾⣿⡿⠋⠉⠀⠈⠛⠃⠻⣿⣧⠀⠉⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠿⢿⢿⣿⣦⣄⣀⠀⠀⣀⣀⢠⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢻⣽⣭⣶⣾⡿⢿⣁⡦⠉⠉⠙⠿⣿⣿⣿⣿⣇⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣥⣶⣿⣿⣿⣿⣿⡿⠇⣠⣤⣀⠀⠀⠀⠈⠻⣿⡿⠀⠰⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣡⣿⣿⣿⣿⣿⣿⣿⣿⠗⠊⠉⠙⠛⠟⠳⠆⠀⠀⠘⢷⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢈⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠻⢿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢺⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣶⡆⠀⠀⠀⠀⢀⣼⣿⣿⡇⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⡇⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⡾⣹⣿⡿⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢺⣿⣿⣧⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣰⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠁⠀⠀⠋⠻⣿⣧⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠀⠀⢸⠷⢿⣿⣿⣿⠿⠿⢿⣿⢿⣿⣿⣿⣿⣿⢟⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣤⣬⣥⣤⣵⠶⠛⠉⠀⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⣿⡟⣿⠏⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣿⡀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⡠⠐⠠⢀⠀⠀⠀⠀⢰⣿⠟⡤⣄⠀⠀⠀⠀⠀⢸⡿⣿⡇⠀⠀⠀⠀⡀⠀⣠⣧⡀⠀⡀⠀⠀⠀⣿⠛⠛⠻⣷
⠀⠀⠀⠀⠐⡀⣿⡿⢀⠂⠀⠀⠀⢸⠁⡾⡷⢈⡇⠀⠀⠀⠀⢸⣤⣰⡇⠀⠀⠀⠀⠿⡇⣾⢽⡴⡿⠁⠀⠀⠀⣿⠈⠀⢀⣿
⠀⠀⠀⠀⠀⠐⠠⠐⠀⠀⠀⠀⠀⠈⠢⢤⠥⠞⠀⠀⠀⠀⠰⠾⠿⠿⠷⠄⠀⠀⠀⠀⠛⠊⠘⠚⠂⠀⠀⠀⠀⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⡀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⢀⣀⡀⣀
⠀⠀⠀⠐⣜⡔⢮⡵⢦⣣⠂⠀⠀⣠⠴⠋⠙⢦⡀⠀⠀⠀⢰⢻⠟⠀⠹⡆⠀⠀⠀⠴⣿⢫⡝⢿⠦⠀⠀⠀⠀⢞⣗⣗⣻
⠀⠀⠀⢀⡟⣆⡜⢇⣸⢳⠀⠀⠀⢧⣀⣀⣀⣠⠟⠀⠀⠀⠘⣄⢸⠗⡠⠃⠀⠀⠀⠀⣯⣍⣽⣼⡀⠀⠀⠀⠀⠒⢒⣖⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣬⡍⠀⠀⠀⠀⠀⠀⠀⣠⡜⠂⠀⠀⠀⠀⣰⡖⠒⠒⢲⣄⠀⠀⠀⢠⣶⠿⠿⣶⡄⠀⠀⠀⠀⢀⡎⠉⢣
⠀⠀⠀⠀⠀⠈⢸⡟⠂⠀⠀⠀⢀⡤⢜⢻⣉⡥⢄⠀⠀⠀⠉⡷⣶⣶⢾⠁⠀⠀⠀⢸⣿⢤⡤⣿⡿⠀⠀⠀⠀⣼⢷⣶⣾⡆
⠀⠀⠀⠀⠀⠠⠎⠹⡄⠀⠀⠀⠘⠦⠜⠈⠙⠤⠜⠀⠀⠀⠀⠟⠉⠉⠛⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠜⠛⠛⠙⠆

⠀⠀⠀⠀⠀⠀⡴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠸⣿⠿⠿⣿⠃⠀⠀⠀⢠⣎⣉⣉⣧⠄⠀⠀⠀⢀⠀⣿⣷⢀⡀⠀⠀⠀⢠⣿⠟⠻⣿⡄⠀⠀⠀⠀⣀⠛⠘⢷⡀
⠀⠀⠀⠀⠀⣧⡻⢧⣽⠀⠀⠀⠀⣾⣿⡥⣽⣿⡇⠀⠀⠀⢸⣏⣻⣟⣹⡇⠀⠀⠀⠘⠻⡄⢠⠟⠃⠀⠀⠀⠰⢯⣤⢠⣬⣿
⠀⠀⠀⠀⠀⠙⠉⠉⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂

⠀⠀⠀⠀⢀⢰⣸⣴⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠠⡆⠠⡶⠀⠀⠀⠀⠀⠤⣄⡤⠤⣀⠤⠀⠀⠀⠀⠀⡤⡤⡤
⠀⠀⠀⠀⠘⣿⡿⢿⣧⡖⠀⠀⠀⠺⣿⣦⠛⠛⠁⠀⠀⠀⠀⠙⢲⣶⣶⠀⠀⠀⠀⢦⣉⡊⠙⡉⡰⠀⠀⠀⠀⣦⣴⣿⣤⣄
⠀⠀⠀⠀⠀⠹⣤⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⠈⠙⠇⠸⠏⠁⠀⠀⠀⠀⠁⠈⠉⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢴⠃⢢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠔⠈⠁
⠀⠀⠀⠀⠀⠀⢠⣾⠛⠻⣆⢸⡇⠉⠣⢠⠗⠀⠀⠀⠠⠠⠠⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢸⡇⠀⠀⠀⠁⠀⠀⠀⠂⠀⠉⠉⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⢸⡇⣠⣄⠀⣠⣄⢀⡀⠀⠀⠀⠀⣀⣿⠀⣀⠀⣠⣄⠀⢀⡀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢸⣇⡟⢹⣦⡟⢹⣼⣷⢿⡆⣇⠀⡟⣿⣾⢻⣴⡏⢹⢰⠟⣿⣸⠿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡇⢸⣿⡿⠟⢻⡿⠟⢻⡏⢸⡇⢿⢠⡇⢿⡇⢸⣿⡿⠛⠉⣶⣼⢿⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⡇⢸⡏⣷⣼⠋⣷⣼⢻⣷⠟⠀⠸⣿⠃⢸⠀⢸⠹⣧⣼⠘⣇⣻⠈⢷⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈⠁⠈⠁⠀⠈⢁⢸⡇⠀⠀⠀⣿⠀⠈⠀⠈⠀⠉⠁⠀⠙⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡨⠸⡇⠀⠀⢷⠇⠀⠀⠀⠀⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄⠋⠀⠀⠀⠀⠄⡀⡀⠀⠀⠀⠀⠀⠁⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠐⠐⠂⠂⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠐⠀⢃⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠠⢅⠅⠀⠀⠀⠀⠀⣨⠀⣅
⠀⠀⠀⠀⠉⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠂⠀⠀⠀⠀⠀⠠⠥⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠨⢩⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡞⠉⡇
⠀⠀⠠⢅⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠒⠉⠁⠉⠀⢸⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡴⠁⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠂⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⣀⡤⠐⠤⠤⠊⠁⡜⠀⠀⠀⠀⣠⣞⣻
⠀⠀⠀⠀⠀⠀⠀⠌⠁⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣀⣀⣀⣡⠞⡇⠀⠀⠀⠀⠰⠁⠀⠺⣉⠉⠡⠀⠌⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⠝⠊⠉⠉⣉⠉⠉⢓⣧⡀⠀⠀⢀⠇⠀⠀⠀⣨⠃⢀⠂⠀⣠⠒⠁
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⢀⠟⠁⠀⡴⠊⠁⡈⠱⡞⢡⢌⢳⡀⠀⡸⠀⠀⠀⡰⠧⠒⠉⠱⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⢠⠋⠀⠀⠀⡇⠀⠈⠀⢀⠠⠄⠀⡼⡇⢠⡷⡄⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⣃⠔⢁⣷⡏⢰⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⡔⠂⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠴⠊⠉⢰⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠈⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣠⡿⠋⠀⠀⠀⢠⡤⡀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠂⠀⠙⠒⠶⠖⠒⢉⡟⠀⠀⠀⠀⠀⠙⣇⠉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠊⠉⠉⢉⡞⠀⠀⠀⣀⣀⣠⡄⠀⠀⢈⡀⣒⣦⠏⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠯⠑⠦⠚⠁⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠂⡠⠋⠀⠀⠀⠀⠈⠉⠉⠁⠉⠁⠄⠛⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠀⠸⣍⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⣄⠀⢉⣉⠙⣀⠀⠀⠀⠀⠀⠐⢶⠛⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣤⣀⣀⣀⣐⠀⣀⣀⣤⣷⠚⠉⠀⠀⠀⠀⠀⠄⠠⠄⠀⠀⠀⣍⠙⠁⠀⠀⠉⠉⠛⠀⠀⠀⠀⠀⠀⠙⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢉⠿⡁⢀⡼⢻⣄⠀⠀⠀⠀⠀⠐⠀⡠⠒⠀⠀⠈⠁
⠀⠀⠐⠀⠀⠀⠀⠒⠀⢈⠁⠀⠀⠀⠀⠐⠿⣶⠿⠈⠙⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠀⠣⠄
⠀⠀⢀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠤⠤⢤⡤⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠈⣤⠄⠀⠙⠀⡀⡀⠂⠆⠀⠜⠃⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠈⠀⢀⣀⡨⠡⡤⠰⠀⠄⠁⠀⢀⠀⠀⣈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡁⠀⠀⠀⠀⠀⠁⠈⡁⠀⠤⡔⠀⠀⠀⠀⠓⠐⠀⠂⠁⠀⠲⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣰⡆⡠⠄⣀⠀⠀⠀⠈⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢀⠧
⠀⠀⠀⠀⠀⢠⣀⡀⠀⠐⢀⡜⠀⣁⡀⠀⠈⡂⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠃⠀⢀⢀⣳⣾⣧⠀⠠⠤⠄⠒⠒
⠀⠀⠀⠀⠀⠀⡀⢌⠁⠒⠒⠧⢀⡙⠛⠮⡀⠑⠀⠀⠠⢀⠀⡂⢄⠀⡀⠀⠔⠀⡠⠂⢀⠴⠓⠉⠀⠀⠀⠀⠀⠀⠊⠘
⠀⠀⠀⠀⠀⠀⡇⢀⡱⡀⠀⠀⠀⠀⠉⠒⠽⣇⢜⠚⡀⢁⠈⠂⠕⠈⡀⠐⠐⣡⢾⠖⠁⠀⢀⠀⠀⠀⠀⠀⡐⠁⡊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠈⠑⢮⡂⠑⠈⡂⠀⠄⠦⠰⣋⠖⠁⠀⠀⡎⠀⡑⠀⠀⢀⠊⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⢈⠢⡀⠀⠀⠀⠀⠀⠀⠙⢄⠀⡪⡰⢘⢅⡢⠉⠠⡀⠀⠘⡄⠀⢃⣄⠔⠁⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠙⢀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢢⠞⠀⠇⢀⡜⠀⠀⠈⢛⠟⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠨⠍⠀⠀⠀⣑⢄⠀⠀⠀⠀⠀⠀⢹⣴⠋⠀⠀⠀⠉⠀⠀⠠⠂⠁⠀⠀⠀⠄⣀⡠⠃⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠠⠀⠀⠂⢀⡹⠦⡀⠀⢀⠀⠀⡇⠀⠀⠀⠀⣠⠐⠁⠀⠀⠀⡀⠄⡥⠖⠉⠀⠀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡢⠚⠉⠉⠉⠉⠙⠓⠒⠂⠤⠤⠄⠤⠖⠛⠈⠉⢙⢂⣀⡤⠖⠉⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠇⡠⡸⠁⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⡀⠀⠀⠕⠊⠀⠀⠀⠂⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠁⠀⠐⠀⠐⠒⠀⠀⠀⠀⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⢐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⣠⣴⣇⣰⣶⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣛⣿⠖⠛⠛⠰⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⠡⠹⠋⠈⠨⢆⠙⠎⠉⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠛⠀⠸⢇⠀⠄⡾⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢌⠀⠀⠀⠀⢨⠃⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⣷⣿⠉⢠⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣭⠄⣴⠛⣧⠀⠀⠀⣰⠀⠀⠀⣾⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⡀⠙⣿⡃⠀⠈⠓⣡⡖⠁⠀⠂⠀⠀⠀⢀⣀⠀⢸⠧⣰⡧⠨⠋⠀⠰⠤⠿⠦⠤⢤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⣄⠈⠃⠐⠀⠀⠹⣷⠉⠠⠀⠀⠀⠀⢿⣿⠗⠚⠒⠛⠛⠛⠃⠈⠍⡂⢀⡲⣶⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠸⣏⠲⣀⠀⠀⢤⡀⠈⠣⠠⠴⠒⠂⠀⡈⠛⠃⠀⠀⠒⠒⠀⠀⢀⠀⠰⣾⣧⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⣸⣿⢿⡿⢸⠇⠀⠘⣄⠈⠦⣔⢑⡢⠈⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡇⠘⠿⢿⣿⣷
⠀⠀⠀⠀⢠⣿⣿⡞⢧⣾⠁⠀⠀⠙⢦⡀⠉⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⢿⣿⣿⢡⠁⠚⢂⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⠅⢰⡿⠀⠀⠀⠀⠈⠃⠀⠀⢀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠂⠀⢠⣿⡿⢞⡃⠀⠨⢁⣀⣾⠻⠛⠁⢀⠠⣦⣤⣄⡀
⠀⠀⠀⠀⣾⣿⡿⠃⠁⡅⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠉⠀⠀⠀⠀⢀⣠⣄⣀⢀⠀⠀⠉⠁⢠⣾⡟⠂⣶⣾⠀⠀⡀⠉⣻⣷⣤⠀⠘⠃⠨⡉⠝⢻⢶⡀
⠀⠀⠀⠀⣿⣿⡷⡔⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⣧⣶⣤⣶⡨⢭⣋⣿⡟⣙⣻⡟⠀⢠⣿⡟⠀⠀⠀⣰⡗⠈⣠⣀⡐⠶⡟⠑⢦⣈⣞
⠀⠀⠀⢰⣿⣿⡇⠘⠈⣢⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⢿⣷⣄⠀⣿⣇⠀⢀⠅⠀⣸⣿⣾⡿⣿⢃⡀⠈⠋⠀⠀⠠⠾⠿⠀⠚⠿⠗⠃⢠⠀⠀⠀⢹⣿
⠀⠀⠀⣸⡟⢻⡧⠠⠀⠀⠉⡟⠃⠈⢿⠀⠀⠀⠀⠀⢿⣿⣶⡤⣿⣏⡀⠘⠂⠀⣿⣿⣾⣿⠟⣿⢿⣶⣤⣤⡀⣠⠃⣠⣤⠤⠤⠶⣶⣵⣿⣷⡀⠈⢹
⠀⠀⠀⣿⡇⢿⡁⠀⠀⠀⢀⠃⠀⠀⢸⠀⠀⠀⠠⣞⣻⣿⣿⠂⣿⣿⡁⠀⠀⠀⢻⣿⣿⣿⣾⣿⠈⢿⣯⣿⣆⡀⠀⡈⢧⣴⣿⡏⠀⠉⢿⣿⣇⠀⣼
⠀⠀⢘⣛⠷⢜⡟⢀⢀⣀⢸⢁⣀⣀⣸⣀⣀⣰⣶⣿⣿⣿⣿⣿⠉⢙⣠⠀⠐⡔⢸⣿⠠⡿⡻⢿⣷⡾⢿⣾⣻⣧⣿⡄⠀⠻⡿⠁⠀⠀⠈⠛⠻⠄⢾
⠀⠀⢼⣿⣿⣟⣛⣟⣼⣿⣿⣿⣿⣧⣤⠉⠉⠉⠉⠙⠛⠛⠉⠙⠛⠓⠀⠲⠋⠑⠛⠙⠃⠘⠛⠛⠻⣧⣾⡗⢰⣤⣿⣷⣄⠀⡠⣰⢟⡇⢠⣩⡾⠂⣈
⠀⠀⠈⠉⠉⠛⠛⠛⠛⠻⠽⠧⠬⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠉⠉⠓⠲⡿⠾⠁⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣀⣄⣠⣄⣤⢤⣤⡤⢤⢤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡠⠀⠀⠀⣀⠂⡀⠀⠀⠀⣤⢲⠀⠀⠀⠀⠀⢀⠀⢠⣤⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠉⢉⣹⠀⢒⣁⠛⣣⣤⡉⣀⣀⣇⡏⣀⡀⠸⠷⢀⣴⣦⡈⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⣿⡀⠐⠊⣵⣰⡏⣉⣷⣟⣹⣿⣋⣭⣿⠙⣯⣽⣀⠀⣺⡏⢻⣷⣾⣿⣦⠃⢀⡠⠴⠒⡶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠸⣿⣿⣶⣶⠏⣈⣻⣿⣬⣿⣏⣈⣛⠋⠙⠿⢟⡉⠛⠳⢼⡇⠘⠟⢦⣼⡿⠐⢋⢶⡲⢸⠴⠈⡈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⡌⠛⢫⣵⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⣶⣦⣌⠛⠘⣠⠈⢧⡀⢡⡾⠟⠁⡳⢫⣶⠷⠛⠺⢦⡘⣡⠞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⠀⡋⠀⣠⣴⣦⣤⢠⠶⣴⣯⢙⠛⢿⡿⠿⠿⠟⡃⠀⠈⠙⠃⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠘⡖⢙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀⠉⢛⣍⠀⢩⡟⠛⠚⠉⠷⠿⠻⣼⢁⣶⣦⣼⣽⡀⢀⣠⠂⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢠⡍⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣶⠌⠳⢾⡏⢠⣿⠇⠀⢀⢀⡀⣠⣄⠘⢋⡀⠈⠁⣩⢿⡏⢠⡄⠀⠀⢚⠀⠀⠀⠀⠀⠀⣠⢎⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣾⣟⠛⣷⢾⠉⢸⡱⣹⢻⡷⣋⣿⣦⣸⡇⠀⣾⠁⢈⣷⠈⠁⠀⠀⣆⣀⣀⣀⣠⣴⣚⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⠻⢿⣿⡿⠈⠳⠛⠟⠉⢁⡧⠛⣛⡉⠉⢳⡄⠻⣷⣿⠏⠀⠀⠀⢸⡱⣴⠤⢦⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⣄⣾⣿⡇⣿⠆⠀⠐⢸⡿⠁⣹⣿⠰⣠⣿⣿⡿⣦⡘⠿⠀⢠⣇⠳⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠨⡏⣹⣶⣴⣿⣦⡿⣦⢻⣦⣿⡿⢰⣿⡏⣸⣷⠀⠁⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠹⣿⠰⣽⢾⣽⣷⠿⡼⣶⡿⢧⣌⠻⣿⣿⡟⣠⠃⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠶⠌⠛⠿⡾⠿⠛⣁⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠚⠓⠚⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⣀⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⣠⠃⠰⡧⠒⠐⣭⣸⣛⢟⡛⣧⣄⡶⠒⠲⢄⠀⡇⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠊⠁⡠⠟⠀⠀⡰⠉⠀⢹⡟⠉⠛⢿⣷⡄⠀⠀⠑⠷⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠊⠀⠀⠀⠜⠀⠀⠀⠀⠼⢄⠀⠀⠈⠻⣧⡀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⠀⠀⡰⠊⠀⠀⢀⠎⢀⠀⠀⠙⢆⠀⠀⠈⠙⠷⠶⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠐⢊⣄⠀⠀⡔⠁⠀⠀⠑⢦⠀⠀⠑⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣡⠤⢞⡂⠀⠠⠗⠀⢀⣁⣤⣤⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢠⡼⢟⠁⠉⠳⣦⠀⠀⠀⠀⠐⢛⡥⢲⠒⠢⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡾⢧⠄⠀⠀⠀⠀⡤⢚⠋⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀
⠀⠀⢀⣤⣉⠁⣴⡆⠀⠀⠀⠀⠀⠀⢿⠟⣿⣿⣿⡟⣿⠀⠀⠀⠀⢀⣴⣿⢋⡉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠙⠛⠃⠉⠁⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣤⣄⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠦⠆⢦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠴⣿⣿⣁⣨⣿⣿⠦⠀⠀⠀⠀⠀⠈⠃⣤⠈⠁⠀⠀⠀⠀⠀⠀⣾⢿⣧⣸⣶⣆⠀⠀⠀⠀⠀⠀⠙⢯⣅⠸⣿⠀⠀⠀⠀⠀⠀⠀⠸⣽⣿⡇
⠀⠀⠐⢿⣿⠟⠿⣿⡿⠂⠀⠀⠀⠀⠘⢷⣘⣿⣣⡾⠁⠀⠀⠀⠀⢀⣻⣶⣛⣛⣫⣝⡀⠀⠀⠀⠀⠀⠢⢈⢃⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⢿⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣤⣴⣦⣠⣶⣦⡀⠀⠀⠀⠀⣠⡶⠿⠿⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠄⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⢾⡆⠀⠀⠀⠀⠀⠀⠀⢶⣼⣧⡴⠆
⠀⠀⠺⢫⡄⠀⠻⣿⣿⡿⠀⠀⠀⠀⠈⣧⣦⣆⣿⣸⠀⠀⠀⠀⠀⠀⠀⢂⣀⣀⡘⠀⠀⠀⠀⠀⠀⣼⣏⣿⡿⠿⡏⣤⠀⠀⠀⠀⠀⠀⢠⡉⠉
⠀⠀⠠⠀⠀⠼⠇⠬⠁⠀⠀⠀⠀⠀⠀⢯⡿⠿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠁⠀⠀⠀⠀⠀⠀⢾⣿⣿⣤⣾⣿⣿⠆⠀⠀⠀⠀⢀⠠⠄⠀⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈

⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢏⣶⣿⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣠⡄⠀⠀⠀⠀⠀⠈⣿⣄⠸⣿⡷
⠀⠀⠀⠋⠝⢷⣺⡵⠟⠀⠀⠀⠀⠀⠀⡾⠿⣻⠛⣧⠀⠀⠀⠀⠀⠀⠀⢘⢷⣤⢦⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⠾⣶⣤
⠀⠀⠀⠐⠠⠆⡁⠔⠂⠀⠀⠀⠀⠀⠈⣷⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⡐⠻⠸⠃⡈⠂⠀⠀⠀⠀⠀⠀⠞⢈⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠴⠟⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⢐⠛⠓⠛⠓⠛⡀⠀⠀⠀⠀⠀⢸⠉⠍⠉⠍⠹⠀⠀⠀⠀⠀⠀⡄⣶⣿⣶⠘⠋⠀⠀⠀⠀⠀⠀⠉⢠⣾⣁⣀⡀
⠀⠀⠀⠘⠛⠀⢡⣤⣄⠀⠀⠀⠀⠀⠨⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣘⣀⢾⣶⠞⢀⠀⠀⠀⠀⠀⠀⠇⣿⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⡟⠻⣿⡇
⠀⠀⠀⠀⠀⠐⠘⠳⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠚⠀⠀⠀⠀⠀⠈⠻⠿⠆⠉⠀⠛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁

⣿⣿⣿⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠛⠰⣦⣀⠀⠀⢀⣤⣶⣦⣤⣶⣶⣾⠂⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠧⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⠀⠛⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⡿⠟⢇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠙⠻⣿⡿⢹⣿⣿⡟⠉⡆⠀⢸⡿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢼⣷⣶⣶⣶⣶⠒⠋⠉⠁⠈⠉⠉⠛⣴⣷⠶⠿⠿⠿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠚⠛⠿⣟⣿⣿⠀⠀⢀⣾⣷⣄⠀⠀⢸⡿⢲⠀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠠⠀⠄⡐⢹⣾⣿⠀⠀⣿⣿⣿⣿⡀⠀⢸⡇⢸⡇⣸⢨⡇⠐⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢀⢸⣿⠀⢸⣿⣿⣿⣿⡇⠀⢸⣇⢸⡇⡛⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢴⣤⣀⣀⣸⣿⣀⠈⠛⠿⠿⠟⠁⣀⣼⡇⢸⡇⣿⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠛⠿⠿⢿⢷⡿⠿⠛⠋⠀⢸⡇⣽⢸⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣇⣛⣘⡇⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣠⣰⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠁⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠒⠒⠐⠂⠀⠀⢠⡀⠀⣠⣤⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢀⣠⣤⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣯⣭⣾⣿⣿⣽⣏⡳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠙⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢆⣀⣠⣴⣶⣶⠶⠶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣡⣠⣶⣶⣦⡄⠀⠀⠈⣿⣷⠂⣸⣿⣿⣿⡴⠶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣹⣿⣾⣿⣿⡿⣧⣤⣤⣤⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⡿⠊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⡿⣿⣿⣿⠀⠙⣻⣿⣿⣤⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⣴⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⣿⣿⡿⠿⠿⣿⣿⣿⣯⣿⣿⣿⡟⢀⣿⣿⡿⠟⠿⣿⣍⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣾⣿⣿⠋⣿⡿⣿⣷⢸⣿⣿⣇⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⡟⠛⠛⣿⣿⡿⢹⣿⣿⣿⣿⡀⢿⣿⠿⠛⠁⢹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⣿⠛⢿⣿⣿⣿⣧⠀⠹⣷⣾⣿⣿⣷⣾⠿⠻⡉⢻⣧⠸⡿⣦⣤⣶⡏⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣧⠀⢻⡀
⠀⠀⠀⠀⠀⠘⠁⠈⠁⠀⠁⠀⣿⣿⣿⣿⣿⣦⡀⠀⠉⢀⣹⣿⠃⠀⠀⠀⠀⢿⣷⣄⣈⣉⣹⣶⣿⣿⣿⣿⣿⣿⣿⣧⠈⠃⠀⠻⣧⡾⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⢸⡿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠋⣻⣿⣿⣿⣿⣿⡟⠉⠻⣧⠀⠀⠀⣿⡷⢘⣿⣄
⠀⠀⠀⣠⠇⠀⠀⢠⡟⠀⠀⢻⡇⠀⢹⣿⣿⠛⠉⠹⡏⠉⠙⠧⡀⠀⠀⠀⠀⣠⣿⡛⠛⠷⠀⠋⠁⠉⢿⣿⡿⠀⠀⠀⠙⠀⠀⠀⣿⣷⣿⣿⣿⡆
⠀⠀⣴⣿⣴⣶⣾⣿⡇⠀⠀⠀⠃⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣶⣶⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠁
⠀⠘⢿⣿⣿⣿⣿⠙⢿⡄⠀⠀⠀⠀⠈⢻⣿⡀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⡟⠂⠀⠀⠀⠒⠦⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠋
⠀⠀⠈⠛⡟⠉⠉⠀⠀⠳⡄⠀⠀⠀⠀⠀⢿⣷⠀⢠⣶⠗⠒⠒⠲⢾⠤⠽⠟⠃⠀⠀⠀⠀⠤⣴⣿⢆⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⢀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣶⣄⣤⣤⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠛⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣀⡇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⡀⠀⡀⠀⢀⠀⠀⢀⠀⠀⢀⠠⢤⡁⠂⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⣤⡷⠓⠉⠉⠀⠀⠀⠀⠀⢉⢀⡰⡋⣒⠛⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡐⢦⡴⡋⠻⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠑⠀⠊⢘⠁⠧⡠⡄⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣹⠃⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠈⠈⢨⢐⣷⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡠⢔⣱⣤⠠⡀⠀⠀⠀⠀⢠⠄⢰⠴⣤⡀⠀⠌⠣⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠠⠚⡅⢾⣯⠞⠀⠀⠀⠀⠀⠐⠷⡾⠞⠐⡄⠀⢶⠳⢄⠀⠀⠐⠟
⠀⠀⠀⠀⡄⣶⠘⢺⠀⠀⠀⠈⠀⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢚⠁⠀⠐⠊⡄
⠀⠀⠀⠠⡛⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣁
⠀⠀⠀⠀⠈⠃⢰⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠜
⠀⠀⢀⠠⠤⠠⠌⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⠀⡀⣶⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠁⠙⡄⠀⢀⣴⠀⠀⠀⠀⢀⣀⣀⠰⠾⢫⠃⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠀⣀⠼⠏⠀⠀⠀⢀⠀⠒⠒⠴⢤⣠⡤⢊⣧⠥⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠂⠀⠡⣴⣤⣄⠔⠀⣈⡴⠛⡉⠙⢹⣯⣀⢌⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠋⠉⠉⠉⠉⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠍⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡤⢚⣭⣶⡂⠉⠉⠁⠒⠬⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡴⣫⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠢⣣
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠞⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡞⣼⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⢃⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⣧⠀⠀⢸⠸⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠱⣄⠀⣇⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠻⣇⠀⡠⠋⢑⠼⣎⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣤⣴⠧⣠⠈⠓⡟⠛⠛⠻⠿⠷⣶⣶⣾⡿⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⡀
⠀⠀⠀⣠⣴⣶⣿⣿⣿⣧⡀⠩⢃⠀⠀⠀⣸⠃⠀⠀⠀⠀⢠⣿⠟⠛⠃⠀⠈⠙⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⣄⣀⣀⣀⣀⣀⣀⠀⠚⠁⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⡙⠻⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣼⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣤⣤⣀⣘⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣋⡒
⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣿⣿⣿⣛⣻⡭⣯⢩⡭⠝⠻⣿⣟⣫⣽⣶⣶⣶⣤⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⢻⢡⡟⣃⣛⡈⠛⢷⣦⣬⣭⣙⡛⠻⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢳⣦⠠⠹⣇⠻⢻⢿⣿⣷⣦⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠻⠂⠀⢸⣤⡾⣦⠹⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠙⢑⡀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⣦⠀⢀⡘⣀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣰⣶⡄⠀⢾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠿⠋⠀⣀⣙⣩⡄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡇⠀⢈⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣌⢂
⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣁⡴⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⢿⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠠⣀⣈⢢⣆
⠀⠀⠀⠀⣰⠂⢰⠀⠀⠀⠀⠀⠀⠠⡀⣦⢉⢉⠀⠀⠀⠀⠀⠀⠀⢀⢉⡸⠄⠀⠀⢀⠤⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠀⡀
⠀⠀⠀⣤⡇⡠⠊⣤⣄⠀⠄⢠⠀⠀⠀⠸⠛⠋⠀⠀⠀⠐⠀⠀⠀⢰⠯⠄⠊⠀⠀⠁⠉⠉⠛⠻⠿⣿⣿⣉⠪⠀⠀⡰⠁⠃⠀⠀⠸⣷⣾⣷
⠀⠀⠀⠘⠟⠀⠀⠿⠋⠀⠀⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⣠⣤⠀⢠⣤⣮⠙⢿
⠀⠀⣿⡷⠀⢠⡶⠀⠀⠀⠄⠠⡤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠛⠉⠀⠀⠈⢙⠀⣀⡤
⠀⠀⠏⠀⠀⠈⠈⠀⠀⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠠⠳⣶⡖⠀⠀⠀⠀⢀⣝⣿⣶⣀⠀⠂⠀⠈⡇⠀⠐⢷
⠀⢄⡥⠀⡀⠀⠀⠀⣼⠁⠰⠀⢠⠀⢰⠢⠰⣶⡦⠀⠀⠀⠀⠀⠀⢀⠀⡐⠀⠀⠀⠀⠀⠃⠉⠉⢰⠀⠀⠈⠉⠉⠒⠈⡟⠀⠀⠀⠘⠁⣀⣖⢄
⠀⢬⡴⠀⠀⠢⠭⠼⠃⠀⠀⠀⢃⠐⢱⡰⠁⠀⠀⠀⠀⠀⠀⢀⠓⢤⣑⢤⣤⠀⠀⠀⠀⠀⡀⠀⠸⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⣶⠈⡒⢻⣼⠲
⠀⠶⣴⠇⠀⠀⣰⡆⠠⠀⣠⢤⣤⢀⡿⠁⠀⠀⠁⠀⠀⠀⢀⣦⣞⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠈⢁⠔⠀⠀⠀⠀⠑⠀⠻⠂
⠀⠰⢦⡴⠀⠀⠙⢣⡇⠂⠈⠉⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠸⠈⠛⢇⠀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠄⠀⠀⠠⠀⠀⠀⠀⠀⢠⣤⣤⡶⠆
⠀⠐⠶⠆⠀⠀⠀⠀⠭⠳⢖⠂⠀⡄⠉⠀⠀⠀⠁⠀⠀⡀⠀⠀⢀⠹⣥⡀⠈⠀⠐⣀⠄⠀⠀⢠⠜⠀⡐⠠⡀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠉⠉⠀⣄⠂
⠀⠀⡛⠀⠀⠀⠀⠠⠤⠤⠤⠸⠧⠶⠀⠀⢀⣦⠀⠀⠀⠀⠀⠁⠈⢣⢫⠀⠀⠕⠀⢀⡀⠤⠖⠡⣈⡤⠃⣠⠤⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆⠹⠖
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⡀⠃⠀⠀⢄⠛⠁⣼⣻⡤⢀⠀⠀⠀⢋⢦⣀⠀⠀⠀⠀⢀⣤⡾⠷⠒⠋⠁⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣬⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⢈⡆⠈⠹⠛⠃⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⢰⡏⠤⠒⠋⠉⠉⠙⡟⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠐⠶⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⣶⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⣡⠟⠁⠀⢸⠀⠀⠙⢧⡉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⢦⣀⣰⠃⠀⠀⠀⢸⠀⠀⠀⠈⢷⣀⣠⠟⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⢹⠟⠶⠤⣤⣄⣼⣤⣤⡤⠶⠚⣿⠁⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣾⣤⣤⣤⣤⣤⣤⣷⣤⣤⣤⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢻⡀⣀⣠⣤⠤⠾⠦⠤⣤⣀⡀⣼⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢀⣤⠞⢿⠉⠀⠀⠀⢸⠀⠀⠀⠈⣹⠿⢦⣀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⢷⡀⠀⠀⢸⠀⠀⠀⣴⠋⢀⣠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢿⣦⣄⣼⣤⣴⣾⠷⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠉⠢⠀⢄⠀⠄⠀⠀⢀⣀⣀⣠⡴⠖⠛⠉⠉⠉⠑⠂⠀⠀⠀⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡤⠖⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣳⡶⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⠤⠤⠤⠤⠤⠤⠤⠴⠒⠒⠂⠀⠀⠀⠉



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿