Nibble Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡴⠀⠀⠂
⠀⢀⠀⢠⣤⡱⠆
⠄⣸⠟⣾⣼⡧
⠈⠁⢶⠎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣦⣤⣤⢀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣸⣿⣿⣿⣼⣧
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠸⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡴⠤⠒⡶⠂
⠀⠀⠀⢁⠀⠀⠘⠂⠀⠀⠀⠀⠀⠐⣿⣾⣿⣿⣿⡿⠿⠿⠛⡿⢿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠈
⠀⠀⠀⠀⠆⠀⠀⡤⠙⡄⣀⠀⠀⠰⣿⣿⣿⣿⠃⠲⠂⠀⠸⠟⢾⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⡀⡤⠀⠀⠀⠀⡠⠘⠁
⠀⠀⠀⠀⠠⣷⣾⠃⠀⣷⠀⠶⠀⡀⣸⡿⠿⣿⠀⠀⢀⣠⡴⠀⠈⠉⠉⠀⠀⢀⠀⠀⠦⢄⠀⠙⠀⠀⠀⠔⠊
⠀⠀⠀⠀⠐⢻⡏⠀⠀⠘⠀⡁⠾⢹⡀⠀⠐⠁⠀⠀⣀⠙⡁⢴⣶⠦⠀⠀⠉⢻⠀⠀⠀⣠⡀⠀⠃⠈
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠇⢰⣿⣧⡀⢀⠀⠀⠀⠈⠻⣿⣼⡿⠀⠈⠁⠀⢀⡼⠂⠀⡹⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠶⠀⠀⠞⢁⣬⡿⢻⣇⢠⠟⡃⠀⠀⠀⠈⠇⠛⠀⠀⢠⡀⠈⡦⣠⠞⠁⠈⠠⠄⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣋⠁⠀⢿⣾⠎⠁⠀⣀⠀⡀⠀⠂⢠⡔⣲⡧⠞⠀⠀⠉⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡇⠀⠁⠂⠙⢶⢤⣦⣄⠀⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠉⣿⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⢀⣠⠀⠀⠀⣠⡀⢸⡆⠀⢠⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣒⠪⠷⢤⣀⢀⣬⣤⣾⣷⣆⢼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠀⣿⠈⠉⣁⡁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠂⠀⠀⠉⠘⢦⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣅⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⠈⠛⢻⡖⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢼⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠶⡇⠀⠀⠀⠆⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⢷⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣧⢌⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⡀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⣀⣰⣤⣀⣰⣶⣶⣖
⠀⠀⠀⠀⠀⠀⠰⢀⣰⠢⠖⠋⠉⠟⠉⠉⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠟⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠦⠤⠤⠤⠼⣇⣀⣠⡤⠖⠛⠉⠛⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⡁⡇⢸⢿⣇⠃⡇⠰⢠⣾⣷⣆⢿⣷⣮⠔⠊⠉⠙⠿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣷⣿⢳⣰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢻⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⡏⡿⣿⡇⣿⣿⢸⣿⣿⣿⣬⢻⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣿⢯⠹⣿⣻⢻⣿⡼⣿⣁⢿⣿⢸⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠈⠛⠋⠛⣧⠿⠋⢸⣿⠾⠿⡟⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠾⢶⣤⣶⣴⣦⣶⣤⣶⣤⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡌⠀⠀⠀⠀⢀⠀⡤⡀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢷⠠⠀⠶⡵⠷⠔⣿⣾⣾⣿⢰⣿⣿⣿⡿⣤⡶⠀⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡃⡔⠀⠙⠂⢠⠀⠀⣿⣿⣻⣿⢿⢿⣿⣿⣿⠟⣠⡾⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠀⣠⣾⣷⡆⣿⣿⣿⣧⠸⣮⣿⣿⣿⣾⣿⠀⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣿⣿⡟⠄⢻⣿⣿⣿⣿⠃⠀⣀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⡿⢿⠋⡌⠔⠈⢿⣿⡿⠁⠀⣴⣿⡿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣆⠀⠀⠀⣀⣣⡿⠀⢀⣼⣿⢿⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢛⣿⢿⣦⠁⡠⠀⠀⠀⠀⠈⢻⡧⠌⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠙⢿⣷⡷⠀⣁⣾⠇⣤⣀⡟⠰⢿⣱⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⣠⡼⠛⠳⢾⣿⡉⣀⡀⢙⡟⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠈⣡⡴⠟⠁⠀⠐⠂⢹⡟⠈⠀⢛⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⢉⣤⠾⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀⣦⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣁⣴⠛⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠃⡜⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⠾⠋⠀⠀⠀⠀⠀⠀⣤⣠⠀⠀⠀⢠⠄⠀⡼⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⡷⣄⡀⣠⣸⡀⣠⠁⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠘⠀⠙⢤⡏⠹⠇⠈⣦⠀⠀⠀⣅
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠰⠊⠉⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢘⣧⠀⠀⢹⣦⠶⠂
⠀⠀⠀⠀⠀⠀⠀⢈⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣽⡇⠀⠀⠓
⠀⠀⠀⠀⢠⣤⣴⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⡥⢀⡀⣀⠀⠀⠂⠀⠀⠠⠴⠖⠛⠉⠁⢻⠀⠀⠠
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣾⣷⣤⡀⠀⠀⠀⠀⢠⠶⠀⣠⣤⡤⠶⠖⢀⡀⠀⠀⢸⠀⣀⣠⣤⡤⢠⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣏⠻⣿⣦⡐⢄⠀⠀⠀⠀⠀⠀⢀⡉⠐⠋⠙⠒⣠⣹⣴⠿⠋⠀⠀⠘⡇⠤⠄⠰⣈⡝⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣌⠻⣿⣷⣕⢄⠀⠀⠀⠠⠤⠤⠰⠖⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠂⠀⢀⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣆⡈⠙⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢛⡗⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⡙⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⡃⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆⣠⣾⡿⢷⣀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⢿⣿⣿⣇⠘⠿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠿⢟⠿⣦⠈⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣁⣠⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⠀⡹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠠⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠄⣀⡀⢀⠎⠀⣱⣁⡀⠤⠤⠒⠒⠒⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⢀⠀⠀⠀⠀⠀⢸⠀⡜⠁⠀⠀⠠⠤⠀⠢⠂⠂⠀⠀⠠⠌⡓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢡⢆⠀⠀⠐⠈⠀⠀⠀⠰⣦⣣⣼⣻⡩⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠔⡂⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠐⠑⢀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠒⠈⠀⠈⠀⠀⠄⠉⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⠂⠤⡀⠀⠜⠐⡁⠀⠀⠀⠀⠀⠐⠈⠂⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡀⠓⠸⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠃⠂⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⠀⠂⢆⠙⣄⣀⢀⡀⠀⠈⠰⠐⠑⠈⠈⠂⠁⠀⠀⠠⢀⠀⡈⡐⠜⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⠠⢀⠀⠜⢄⢂⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠀⠔⠐⠀⠀⠠⢀⠁⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠠⢂⢀⠀⠈⠠⡇⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠊⠀⠀⠀⢀⢂⠆⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠑⠉⠁⠀⢂⠇⠀⠀⠀⠀⠀⠀⠠⢊⠄⢀⠀⡐⢠⢃⠂⠆⠀⠀⡆⢀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠐⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢁⠔⢁⠌⠰⠁⠂⡀⢀⠆⡔⢀⠃⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠡⢔⠀⠀⠁⠹⡆⠀⠀⢀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⡐⢀⠎⡘⢀⢂⠎⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠈⠸⠀⠀⠄⢊⠔⢁⡐⠀⡠⢀⠜⡠⢁⠜⡠⢊⠌⡠⢣⢂⠪⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⠀⣠⠃⠀⠀⠔⠁⠠⠊⠀⠔⡠⢊⠄⡠⢃⠜⡡⢊⠜⡱⢁⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⠀⠮⢈⡇⠀⠀⠀⠀⠀⠀⠀⠐⡐⢁⠔⡰⢁⠔⡵⢁⠎⡠⡡⠣⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⣶⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠊⡠⡡⢊⠔⢁⠌⠔⠔⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠪⠂⡰⢋⠔⠡⠢⢊⢔⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡠⠊⡠⢃⢔⠅⡡⢫⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠃⠀⠀⠀⠀⠀⠀⡠⠄⡀⠀⡀⠀⠀⠀⠀⠊⠠⢊⠔⡅⡠⢞⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠲⣄⡀⠀⠢⠕⢂⠡⠐⡨⠐⡠⢊⠀⠊⢀⢴⢄⠔⡡⢊⣨⣔⠏⢀⠡⢒⠠⢀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⠄⡂⠍⠛⠲⢦⠥⢀⣡⢤⣁⣐⡁⠐⣀⣉⣁⡥⢔⠺⢛⡡⢔⡀⢄⡪⠔⡈⠔⡊⠔⡩⢔⡠⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠉⠀⠐⠁⠂⠡⠐⢉⠠⠘⠩⠈⠡⠊⠄⠊⠁⠊⠁⠊⠁⠐⠉⠐⠉⠀⠁

⡎⠉⠉⠋⠙⠢⠔⠲⡤⠒⢄⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⡠⢄⣀⠠⠤⠤⠤⢤
⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠖⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠔⠉⠑⠊⠀⠈⠀⠀⠁⠀⠀⠀⠀⢠
⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠑⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢣⣀⡀⠀⠀⠀⠀⠀⠀⣀⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢱⠀⠀⠀⠀⠀⡎⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞
⠀⠠⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⠀⠀⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁
⠀⠀⢉⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢱⣀⡀⠀⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢕⣔⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡩⣊⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠊
⠀⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠢⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂
⠀⠀⠀⠀⠀⠀⠀⠫⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⢔⢄⠀⠀⠀⠀⠀⠀⠀⢐⠕⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⠤⢄⣀⡠⠦⠊⠀⠀⠀⠈⢢⡣⠀⢀⠀⠀⠀⢎⠊⠀⠀⠀⠙⠄⢄⠀⠀⡄⠀⠀⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⡑⣼⢸⡐⡰⠁⠀⠀⠀⠀⠀⠀⠀⠑⠚⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⣿⣿⣿⣆⢻⣿⣿⠆⠀⣸⣿⣿⡷⠀⠀⣿⣿⣿⡆⣿⣷⣦⡀⠀⣿⣿⣿⡇⣼⣿⣶⡄⠀⢸⣿⣿⣷⠀⠀⠀⠀⣾⣿⣿⣷⠀⢿⣿⣷⣿
⡈⢿⣿⣿⣿⡎⢿⣿⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⡇⣿⣿⣿⠇⠀⣿⣿⣿⡇⣿⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⡙⠿⣿
⣷⡘⣿⣿⣿⣿⡌⢿⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡁⣿⣏⡁⠀⠀⣿⣿⣿⡇⣹⣯⣁⠀⠀⣹⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠰⣾⡇⠀⣿
⣿⣷⡸⣿⣿⣿⣿⡘⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⠄⣿⣿⣿⡄⠀⣿⣿⣿⡇⣿⣿⣿⡆⠀⣿⣿⣿⣿⠀⠀⣰⡇⣿⣿⣿⣿⠀⠈⢃⣴⣿
⣿⣿⣷⠹⣿⣿⣿⣷⠀⠀⣿⣿⣿⡇⠀⠀⣿⣿⣿⡀⣿⣿⡿⠃⠀⣿⣿⣿⡇⣿⣿⣿⠃⠀⣿⣿⣿⣿⢀⣴⣿⡇⣿⣿⣿⣿⠀⣴⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣨⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢨⡗⠒⠒⠀⠐⠒⠰⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⢀⢀⢸⣤⡄⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠮⠿⠬⠗⠛⠁⠀⠀⠀⠐⡡⢂⠄⢀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠂⡐⡡⢂⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠜⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠊⢈⠔⣡⢊⠄⡈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠨⢄⡀⠀⠅⠀⠀⢀⠠⠀⠀⠀⠀⠀⠐⢁⠔⡡⠊⡜⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⠙⠀⠁⠀⠀⠅⠂⠅⠀⠀⠀⠀⠈⣠⠊⢠⠊⢀⠃⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠄⡠⢃⢂⠜⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⢂⠔⡰⡡⠂⢊⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢡⠐⢄⡠⢀⠄⡪⠀⡠⢊⠔⡡⢊⢄⠔⡡⢂⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢠⠊⡠⠅⡨⠔⢈⠄⡪⢂⠥⢊⠔⠁⢁⠔⡐⠡⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠈⡘⠀⢐⠅⠤⡚⠕⡠⠔⡡⢔⡁⢊⠔⡡⠊⠔⠅⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣀⠖⠉⠀⠐⠊⢐⡩⠐⡉⠄⡊⠔⣁⠔⡡⢊⠔⡪⡊⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡉⠀⠀⠀⠀⢂⠪⠅⢒⠩⠐⡨⠔⡪⠔⡨⢔⠥⡪⢎⡴⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⢄⡀⠉⠄⠐⠪⠥⢒⠥⢒⡩⠔⡩⠖⢁⣪⠴⢚⠡⠀⢂⠡⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠄⢘⠉⢒⡒⠒⡒⠔⢒⠢⠖⡒⠖⣚⠥⠐⡈⠅⢐⠨⠐⣈⠄⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠁⠐⠁⠀⠈⠀⠐⠁⠀⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠩⣻⡄⠀⠀⠀⠀⠀⠀⣀⠤⠴⡒⡒⡒⣲⣲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠱⣳⠀⠀⠀⢀⠔⢫⢰⠆⣇⡧⠗⠛⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣹⡄⠀⣰⢫⢸⣸⡼⠟⠉⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠶⠤⠬⡇⢘⣧⣤⢣⣾⠞⠁⠀⠠⠤⢀⣀⠁⢀⣾⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⡀⢀⢸⠘⣇⡼⠘⠁⠈⠉⠉⠉⠉⢀⡠⢴⠉⡀⠀⢢⣌⠙⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠰⢬⠻⠷⢝⢎⢻⡆⢛⡜⢫⠻⠖⠖⠶⣻⢋⡟⡰⢫⠞⡰⢃⡄⠘⠓⠂⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠆⠀⠀⠀⠀⠀⠀⣀⡚⠳⡇⣈⣅⣤⣶⢶⠎⡸⢁⠎⡼⠁⠋⠘⠁⠈⠈⠀⠠⢭⡒⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠐⡌⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣑⢮⡦⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⢇⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡳⡙⣆⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣀⠀⠃⡏⡜⡸⠸⠀⠃⠈⠀⠀⢀⠀⢠⢀⡄⠸⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠱⣽⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣝⡷⡄⠀⠀⡄⢠⠀⡇⠸⡄⢸⠸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⡈⢧⠀⠘⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣊⠷⣤⠀⠰⡈⡄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠧⠀⠀⢹⠈⡇⠀⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠵⣊⡅⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡃⠇⠀⠀⡆⠘⡇⢹⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣫⠔⠂⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠘⠀⠁⠀⢠⠀⡇⠀⡇⢸⠀⢸⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣉⠍⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠀⢀⠐⠀⠀⡄⢸⠀⡇⠀⡇⢸⠀⣼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⢒⡂⠀⠀⠸⡆⢀⠀⠀⡀⠀⠀⠀⡄⠀⠀⢀⠰⠈⠀⡀⠈⢀⠃⢸⢠⡇⢰⠁⡜⢀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠕⠒⠀⢀⡞⢀⠎⣸⢁⠃⠞⠘⠀⠀⡀⢰⠈⠀⡀⢠⠃⡇⢸⠀⡇⣸⠀⡜⢠⡇⣸⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣻⡭⠁⠀⢸⠀⠚⠀⠃⠈⠀⠀⢀⢰⠀⠃⠀⠀⡸⠁⡞⡼⢀⡏⡸⢀⡏⣰⠁⡞⢠⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡫⠭⠉⣀⡴⠋⠀⢀⠀⠄⡄⢰⠁⠃⠀⠀⢠⠃⣰⠃⡼⢱⠃⡼⢰⠃⡼⢠⠇⡼⢡⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡉⠉⠉⢉⡔⣰⢢⠇⠞⠈⠁⠀⠀⢀⡔⢠⠃⣰⠃⡜⢠⠏⡴⢡⠇⡸⢁⡟⣰⠃⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠉⠈⠁⡀⢀⠀⣠⠀⡰⢃⠎⣰⠃⡴⠁⡼⢡⠏⡰⢡⠏⡰⢁⡜⣰⢃⣴⠧⣤⣠⣄⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣷⣄⡀⠊⠕⢡⠞⣡⠎⡰⢃⡔⢁⠞⢠⠎⡰⠋⡼⣡⠃⡼⢡⠞⠐⣣⣞⣐⣒⣒⣒⣒⣒⣦⣴⣶⣶⣆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠽⠷⠶⠤⢤⣄⣀⣁⣀⣀⣈⣀⣁⣈⡁⠈⠀⠁⠈⣀⣨⠴⠿⠥⠥⠤⠥⠬⠤⠤⠤⠤⠤⠤⠬⠭⠭⠤⠥⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠶⠦⠭⠭⠭⠭⣍⣉⣋⣉⣉⣉⣉⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣓⡒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢦⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣈⣷⣤⣤⣤⡴⣫⣥⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠋⠁⠀⠀⡾⢱⡿⠉⣸⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⠀⠴⠏⠀⠀⠀⠙⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⢿⡟⠀⠀⠀⢤⠖⠒⣀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠙⣿⣿⣤⣠⡶⠿⠛⠛⠘⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⣤⡀⠀⠀⢀⣠⣿⠟⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣴⠞⠛⠓⠛⠛⠉⠀⠀⠀⢀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⡗⠓⡜⢷⣀⡴⢾⣟⠛⠉⠉⢻⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⣠⡀⠓⢚⣥⠤⣭⡀⠘⣿⠀⢀⣤⣼⣧⠀⠀⠀⢀⣠⣴⠶⠶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⣠⡶⢿⡁⠀⠘⠛⠃⠀⣾⠁⠀⣀⣷⣴⡟⢰⡿⠁⠀⠹⣧⡀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠻⣧⣼⠇⠀⣯⡿⠀⣀⣼⡷⠿⠛⣡⠟⠀⣿⡇⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠙⢿⣄⣠⣴⣖⣋⣭⣾⣿⠿⠾⠋⠀⠀⠹⣧⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠤⣤⣤⣤⣽⣷⣤⣀⣙⣿⣦⣤⣤⣤⣤⡤⠀⠀⠀⣦⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣥⣦⣀⣀⣤⣤⣾⣋⠙⠛⠋⠉⣉⣀⣤⣤⣤⡤⢤⣤⡤⠾⣧⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠛⠚⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠟⠋⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⣩⣭⣤⠤⢤⣭⣍⣉⣉⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⣁⣠⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⡴⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠲⠶⠶⠶⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⠀⢀⢀⠀⠀⢀

⠀⠀⢜⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⠀⠀⠤⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠿⢀
⠘⠁⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⢀⣤⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⣈⠁⢀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡐⠠⠀⠀⠹⡀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⢷⡀⠀⠀⠀⠐⡄⠀⠀⠀⠢⡄
⠂⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⣦⠀⠸⠀⠀⡧⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢅
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣠⢞⡡⠂⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⠙⠷⣄⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠛⠀⠀⠀⠁⠉⠀⠀⠀⠉⠒⢤⠤⠠⠀⠀⠀⠈⠉⠀⠠⠀⠀⠘⠃⠖
⢀⣤⠒⠀⠠⣤⣀⠀⠀⠀⠈⠋⢀⣀⡤⢾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⠀⠀⠠⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠉⠀⡀
⡛⠀⠀⠀⠀⢈⣿⡇⠀⢠⡴⠛⠉⠀⠀⠀⡽⢡⠀⠐⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠱⠀⠀⠀⠈⠁
⣧⣀⣀⣀⣀⡿⠋⠀⣰⠋⠀⠀⠀⠀⠠⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠂⠀⠀⠀⠀⠄⢈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠀⠰
⠈⠙⠛⠋⠁⢈⣠⡴⠗⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠈⠉⠀⢀⣠⣤⣤⢤⣄⡀⢀⠀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠤
⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⢠⠀⢰⠋⠀⠀⠀⡀⠀⣄⠀⠈⠋⠀⠀⠀⠀⠈⢀⣄⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠳
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⡀⠀⠀⠀⠀⠀⡹⠀⠀⢀⠀⠀⠈⠀⠐⣄⡀⠀⠁⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠳⠤⠖⠂⠁⠂⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⣫⠂⠀⠀⠀⠈⠐⠠⠤⠤⠊⠀⠀⠀⠀⠀⠁⠀⢀⠐⠀⠀⠀⠀⠀⡄⠀⠀⠁
⠤⠤⠀⠀⠰⠀⢈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣐⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠄⠀⠀⠀⠀⠈⠊⠁⠢⢀⠀⠀⢄⣵⠀⠀⢰⠏⠀⠀⠀⣠⢀⠆⠀⠀⠀⠠⠀⠀⢀⡤⠂⠀⠀⠂⠀⠀⠀⢀⡀⠀⠂⠀⢰⠋⠉⠓⠀⠠⡀⠸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠓⠠⠀⡿⣡⠄⠀⠀⠠⠤⠶⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⢻⣄⠀⠀⠀⠐
⠄⠀⠀⠠⢀⠤⠀⠀⠀⠀⠀⠠⠀⠐⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⢀⠀⠈⠹⡆⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣇
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡟⠀⠀⠀⠈⠙⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠘⢦⡀
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⢻⡄⠀⠀⠀⠐⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⠦⣄
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⣠⠀⢀⠓⠂⠀⠤⠾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠰⡄⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡠⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀
⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠍
⠀⠀⢱⡀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⡆⠀⠐⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠠⠤⠤⠠
⠀⠀⠀⠘⢷⣛⠓⣂⠔⠀⠀⢀⡼⣿⠀⠀⢐⠀⠀⠔⠉⠛⠁⠀⠁⠀⡠⠀⠀⠀⢾⡀⠐⢀⢂⣀⡔⢰⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠟⠐⠁⠀⠀⠘⠦⠤⠂⠐⠢⠀⠀⠐⠊⠀⠀⠀⠀⠈⠉⠓⠊⠉
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢢⡑⠂⠀⠀⠧⠥⠤⢤⠂
⠀⠀⠀⠹⠶⠄⠀⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣨⠇⠀⡄⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠧⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⣨⣿⣀⠀⠀⠀⠈⠂⠄⢀⣈⠭⠋⠀⠀⠠⠤⣤⣤⣾⠟⠁⠀⠀⠀⠀⠀⠈⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠈⠑⡀⡀⣦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠠⣄⣀
⠀⠀⠀⢦⣤⠤⠴⠆⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠁⠀⠈⠀⠀⢸⠀⠀⠂⠀⠐⡊⠀⠔⠀⠈⠻⢦⡀⣀⣠⠾⠃⠀⠘⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠰⠀⠀⠀⢀⡠⠄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣴⠖⠁
⠀⠀⢠⠂⢠⣷⠤⣀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⢀⡤⠀⢤⠀⠁⡐⠒⠲⢦⠀⠀⠀⠀⠀⠙⠛⠀⠁
⠀⠀⠘⢶⣿⣁⣠⣻⠇⣄⢰⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⡀⠘⡀⠀⣀⡾⠀⠀⠤⣤⣴⣶⣶⣶⣶⣶⢀⣀
⠀⠀⠀⠀⠀⠙⠛⠋⠀⣈⡛⠋⠀⠀⠀⠈⠓⢄⣀⣀⠄⠀⠀⠀⠀⢙⠚⠋⠀⢀⠈⣈⠉⠁⠀⢶⣾⣿⣿⣼⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⣀⣀⣴⡇⠀⠒⠛⠃⠀⢧⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⣅⠀⢐⠀⠀⠀⡌⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠊⠀⠐⠒⠛⠁⠀⠀⠋⠉⠉⠉⠉⠉⠉⠙⠃

⠀⠀⠀⢀⣀⠤⠔⠊⢉⠉⠑⢢⡀
⢀⠔⠀⠀⡀⠠⠈⠁⠠⠀⠂⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢢
⡏⠀⠈⠀⠁⠀⠀⠀⢀⠀⠀⠄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣴⡁⠀⠈
⢃⠈⢀⠀⠁⠀⢁⠀⠀⣀⠀⠀⢠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠼⠁⠲⠏⠘⡆
⠈⡆⢀⠀⢀⣀⠀⠀⡘⠁⠱⡀⠈⡆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠂⠀⠹⢄⣀⣀⡴⠣⡀
⠀⠘⡈⠀⡏⠀⠉⠊⠁⠀⠀⠙⠒⠃⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠂⠀⠀⠂⠀⠀⠄⠀⠀⠈⣆
⠀⠀⢡⡀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣀⣤⣶⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠈⠘⡄
⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣀⢔⠞⡿⠁⡿⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡱⠋⡜⠀⠀⢃⠙⠲⠧⣠⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡸⠁⢰⠁⠀⠀⠈⠳⡄⠀⠀⠑⢟⠲⣉⠆⡔⢦⡀⢀⣠⡀⠀⡇
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⣀⡠⠴⡾⠀⠀⡇⠀⠸⡀⠀⠀⠀⠀⠘⡄⠀⠀⢸⠖⣏⣀⡏⠉⠙⢍⢀⠝⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠊⠉⠹⡀⢀⠟⢄⡀⢱⡀⠀⠱⡀⠀⠀⠀⣠⣇⣀⠤⢺⡵⣤⠤⠜⠶⡒⢚⠏
⠀⠀⠀⠀⠀⠀⠀⡠⣖⡊⠭⣶⣓⡚⢄⡀⣨⠭⡍⢒⡶⢍⠑⡲⢭⡁⡠⢄⠀⣨⣄⣀⡱⣤⠤⡸⠃
⠀⠀⠀⠀⠀⠀⠚⠠⠤⢤⠤⢳⢄⣈⣑⣙⡅⠀⠈⡋⠀⠀⡙⠀⠀⡍⠀⢈⠏⢀⡯⠗⠒⠚⡉⢑⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⡀⠈⡄⠀⢣⠀⠀⠇⠀⠀⡇⠀⠀⡇⠀⣸⠖⢁⠀⠀⠀⠁⠀⡠⡀⠈⠀⠄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢱⠀⢱⠀⠈⡆⠀⢸⠀⠀⡇⠀⢰⠀⡰⠁⠠⠀⠀⡄⣰⡩⠮⠤⠬⣐⡆⠐⠀⠀⠈
⠀⠀⠀⠀⢀⠠⠄⣠⣇⣀⣀⡠⠤⣧⡔⠋⠒⢼⠀⠈⡄⠀⡇⠀⣘⢠⠃⠠⠐⠀⠀⢷⡁⠀⠀⠀⢀⡠⠃⠡⢀⣀⡀
⠀⠀⠀⢠⠃⠀⠀⠘⠃⠀⠈⢂⠀⠈⠀⠀⠀⢸⡇⠀⠃⠀⠂⠀⠃⠘⣤⢶⣀⠤⡀⠀⠈⠹⢉⠉⠅⠂⠈⣀⡜⠀⢈
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⠜⠀⠉⠉⠉⠉⠉⠉⠁⠈⠣⡀⠀⠱⠤⠔⠲⣌⣀⠖⠒⠔⠁⠀⡠⠊
⠀⠀⠀⠀⠈⠒⠤⢀⡀⠤⠊⠉⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⡀⠀⠀⠀⠀⣀⡠⠔⠊
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠋⠉⠉⠓⢲⠏⠀⠀⠀⠀⢀⡴⠷⠿⠦⣤⠴⠃⠀⠙⣆⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣏⠀⠀⠀⠀⠉⠀⠈⡇⠀⢀⡴⠀⠀⢀⡴⠓⠒⠒⠠⠤⠄
⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⢀⠗⠂⠄⠀⣿⣆⢀⡆⠀⠀⠀⢀⣷⠞⠛⠉⢳⣖⡭⠠⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣼⣧⡀⠀⢀⣠⡏⠀⠀⠀⢠⡼⠛⠛⢧⡀⠀⠀⠈⢷⣀⣀⣀⣼⣧⣤⣀⢀⠀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠊⠉⠉⢢⣀⣘⣿⡷⠞⡽⠁⠀⠀⠀⣾⠀⠀⠀⠀⠙⣆⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⠷⠶⠶⠛⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⣄⣀⡠⠤⠒⠒⠒⠒⠒⠲⢾⡀⠀⠀⡴⠋⠉⠑⠄
⠀⠤⠤⠤⠤⣄⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢠⠁⠀⠀⠀⡄
⢣⡄⠀⠀⠀⠈⠙⢦⡀⠸⡄⠀⠀⠀⢰⠃⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⠀⠀⠀⠀⣸⡇⡆⠀⠀⠸⢧⣄⡀⠠⠄⣄
⠀⠉⠐⠢⣄⠀⠀⠀⠹⡄⠈⠢⣄⣀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⠉⠀⠀⠀⠈⠙⠶⢤⣤⡴⠛⠀⠙⣄⡀
⠀⠀⠀⣠⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠁⠄⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⣇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⣀⣀⣤⡴
⠀⢀⡎⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠁⠀⠘⢦⣀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠈⠣⣄⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠄⠀⠐⢀⠀⠀⡀⠄

⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢋⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣽⣽⡇⠂⠀⠀⠀⠀⠀⢠⡿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠤⠀⠀⠀⠠⣄⣀⠀⠀⡁⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢤⡀⠀⠀⠀⠄⠠⠀⠀⢠⠀⠀⠀⠀⠀⣀⠠⡶⠆⠀⢆⠿⡁⡅⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠠⠇⠀⠀⠀⠀⠀⡠⠆⠀⠈⠁⣀⠀⠀⠐⠒⠹⠁
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⡀⠀⠀⠀⣄⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡄⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢀⠶⣭⠙⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⠀⠀⠴







⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠶⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈
⠀⠀⠀⡠⡖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣖⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠
⠐⠀⠐⣴⠔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣮⣯⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠤⠼⠂⠀⠀⠀⢤⣤⠂⠀⠀⣰⡿⠀⠠⠼
⠀⠀⠀⠈⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⣀⣄⠀⠀⣀⠀⡀⠀⠀⣀⣀⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣴⡓⢀⣲⣀⣄⠀⠀⠀⠀⡀⠀⢀⣀
⣿⡯⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠠⡀⠀⠀⠀⠀⢀⣴⣮⣤⣷⣶⣄⠀⠀⠀⠀⠀⣠⠦⠀⢤⠌⣄⠀⠀⠀⠀⢀⢖⣦⣾⣿⢦⣿⣇⠢
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣿⡆⠀⠀⠀⢸⠀⠁⡌⠤⠡⠐⠀⠀⠀⠀⢤⣿⣿⣧⣀⣀⣸⣿⡷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠡⣿⣿⣿⣿⣿⣿⣿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⠄⣀⠊⠀⠀⠀⠀⠀⠂⠦⠤⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠐⠊⠛⠋⠀⠉

⠀⠀⠀⠀⠀⠀⡐⠋⠉⠙⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⢀⠄⠠⢀⠀⡠⠐⠂⠄⠀⠀⠀⠀⠀⠀⢀⣴⣶⡖⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢤⣀⣀⣀⣀⣀⡤⡎⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⢀⠀⠀⠀⠀⠀⣛⡀⠀⠙⠉⣀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⢠⠀⠀⠀⠀⠀⠀⠏⡛⠶⠶⠷⠶⠖⢚⠑⠀⠀⠀⠀⠀⠢⢀⡘⢢⠐⠂⠀⠀⠀⠀⠀⣯⣭⣙⣛⡒⠶⠦⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠒⠋⠀⠀⠀⠀⠀⠁⠐⠀⠉⠍⠉⠛⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠄⡀⠀⠀⠀⠀⢀⣶⣿⠟⢻⣿⣿⣆⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣠⠤⣄⠙⣦
⠀⠀⠀⠀⠐⢁⣀⠀⠀⡀⠀⠀⣈⠄⠀⠀⠀⢸⠉⠛⠀⠀⠋⠀⣿⠀⠀⠀⠀⠀⠻⢿⣿⣶⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⡇⠸⡇⠄⠸⢀⡿
⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠠⡜⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠘⢦⣙⠳⠶⠛⠁
⠀⠀⠀⠀⠠⡀⠀⠆⠀⠀⠀⠰⡠⠁⠀⠀⠀⠀⠀⢄⠈⠉⢑⣆⠀⠀⠀⠆⠀⢃⡀⠀⠀⠀⠀⠀⣀⡸⠀⠐⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠈⠂⠤⠠⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠅⠀⠀⠀⠀⠒⠤⢈⠉⠉⠉⠉⠉⠁⠠⠀⠁⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌
⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢨⡙⢿⣿⣿⣿⣿⡧⠸⠅⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣬⠀⠀⠀⠀⠀⠀⠀⠄⠢⠐⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠂⠙⢿⣿⢋⠂⠈⠀⠀⠀⠀⣠⢶⠾⡿⣿⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⣭⡌⠀⠀⠀⢀⠴⠚⠒⠒⠶⣄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⣯⣯⣽⣿⣯⣟⣻⣻⣿⣿⠟⠀⠀⠀⢀⡀⠀⠀⣬⣤⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠙⠋⠙⠉⠋⠈⠀⠀⠀⠀⢂⣼⣀⣠⣤⡌⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢐⠇⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠀⠠⠄⠂⠀⠀⠀⠀⠘⠣⠹⠧⠐⠀⠀⠀⠀⠀⠘⠤⠠⠀⠀⠀⠼⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⡉⠈⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣀⠤⠐⠒⠂⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣠⣤⣤⠶⠖⢒⣻⣿⠿⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡿⠛⠡⠤⠾⢿⣾⡿⠆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡟⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠈⠉⢳⢤⣀⣀⡀
⠀⠀⠀⠀⣀⠤⠒⠊⣉⠤⢠⡗⣦⣤⣼⣇⡀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠠⠤⣈⠉⠛⠒⠦⣄
⠀⠀⠰⠊⠀⢀⣠⣬⣾⠿⢀⣉⣿⣿⠿⣿⣭⣽⣷⣷⣤⡤⣀⣀⠀⣷⠀⠀⠀⢸⣺⣿⠯⠝⠂⠀⠀⠀⠙⠆
⠀⠀⠠⡀⠀⠻⠿⠿⢟⡋⠉⠁⣀⣤⡴⢖⣛⣫⣭⠽⣿⠟⠾⢶⣿⣿⣶⣖⣦⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠈⠒⠦⣄⣀⡀⠈⠀⠈⠛⠛⠋⠉⠁⠀⢶⠿⠶⠚⠛⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⣀⡠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠲⠦⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀⣤⣤⣤⠤⠤⠴⠖⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⣠⠴⡒⠈⢛⡋⢐⠒⠦⢄⡀
⠀⠀⠀⠀⠀⢀⣠⠤⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠙⢦⠀⠀⠘⠁⠶⠶⠤⢤⡉⠁⠢⠈⣢⠍⠢⡀⠀⠀⠀⠠⠤⠄⢄⣀
⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠠⠑⠦⣀⠒⠈⠲⣄⠠⠘⠀⠀⠁⠀⡠⠐⠈⢉⢓⡲⣤⣍⡢⡀
⠀⠀⠀⡼⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠸⡄⢤⢦⡀⠳⢤⡈⠀⠑⠂⠀⠀⠀⠀⣷⠒⠋⠉⠉⠉⠉⠉⠙⠛⠦⣄⡀
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠋⠉⠀⠀⠀⠀⠈⢄⠣⢜⠃⢤⠚⠒⢤⣀⠀⠀⠀⠂⢀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠈⠙⠒⠶⠤⠤⠶⠒⠊⠉⠀⠀⢀⡀⠤⠤⠤⣄⡀⠀⠀⠀⠈⠣⡀⠳⢤⡉⠁⣠⠐⠀⠀⠀⣦⢌⠓⠶⠤⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠊⠉⠁⠀⠀⠁⠀⠐⠙⠆⠀⠀⠀⠀⠈⠢⣄⣉⠒⠦⠤⠌⣍⠢⣉⠒⢭⠒⢤⠬⠉⠳⣄⣀⣀⣀⡀⠤⠖⡫⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠶⠛⠋⠉⠓⢤⡈⠐⠤⠀⣀⡀⠀⠠⠀⠀⢀⠀⢒⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⡀⠀⠙⠁⠀⣩⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣤⣤⡤⠤⠒⠋⣁⣤⠖⠒⠒⠒⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠄⡠⠤⠴⢋⢁⡠⠤⠐⠊⠉⠙⠁⠀⠆⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⣠⠖⠉⢁⣀⣀⠠⠀⠀⠀⠂⣀⣬⠵⠖⢒⠛⠿⠅⡈⠳⠤⠾⠀⠀⢳⡄⠀⠀⠀⢀⡔⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⢠⠋⠔⠚⢋⣁⡀⠤⠀⣤⠀⠀⢀⣀⡀⠠⣄⠀⣀⠆⠀⠥⠤⠀⢀⠀⠀⡜⠀⠀⠀⠀⡞⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⡏⠠⠖⢰⣊⣁⠩⠤⠴⠚⠊⣉⠃⠁⠐⠚⠁⠤⠠⠄⠀⠠⡐⠂⠣⢀⠞⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⢻⡉⠋⠈⣈⣀⣠⠴⠔⠊⠉⠀⠀⠀⠠⠄⠀⠀⠀⠃⠀⠐⠀⣣⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⡀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠑⢄⠀⣀⣀⣀⠤⢀⠈⠀⣀⡤⠚⠁⠀⠁⠒⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠼⠤⠖⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠛⠛⢵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣖⡲⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢳⡏⢀⣀⣀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠸⡉⡝⣛⠛⠉⡆⠻⠀⢸⡿⠿⠛⢣⣴⠿⠿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢈⣀⢸⣶⠀⠆⣡⡀⣀⠄⠀⣥⠀⠀⠀⠀⠆⠀⠀⠐⢞⠛⠛⢛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡤⠀⠀⣈⣬⣤⣭⣌⠉⠉⠁⠀⢸⡇⠉⣩⡽⣿⠛⠛⢦⡘⢂⡀⢉⣥⠘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⣿⡇⠀⣜⣿⣿⣿⡝⣿⣠⣴⣾⣶⣿⢛⠏⡘⠀⠘⣷⠀⡸⣠⢴⠀⢸⣿⠘⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⠓⠋⠻⢿⣿⣿⢿⠉⠉⠉⣽⣿⡿⠘⢄⣇⠀⠀⣸⣿⣏⡗⠐⠀⣸⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⣀⣀⣑⣒⡚⠛⠃⠀⠀⠀⢈⣉⣉⡉⣀⠬⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⠶⠻⠿⢏⣸⠛⠻⣯⣹⣿⠿⡛⠫⣿⠿⠿⢿⣟⣷⣶⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡉⠇⣬⢄⡀⢸⡜⠦⠀⠛⠚⡟⠒⠂⠥⠿⠀⣀⣸⣾⣿⡿⡛⠛⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠸⠶⠆⠉⣀⡀⢀⠀⠫⢷⣴⣶⣿⣷⠶⣦⡴⠶⣶⣶⡾⠟⣏⣭⣇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢀⠀⠀⣸⡦⢄⣀⠀⠀⢀⣈⣴⢸⣽⣿⣿⣿⣷⢸⣿⠀⠀⠁⠀⣠⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠩⠭⣉⣑⣀⣄⡀⠀⠠⠤⠟⠉⠻⢿⣿⠿⠿⣞⣅⣀⠥⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⡿⢿⡉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣉⣉⣉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⠶⣯⣤⣀⣈⣁⡈⠐⠽⢛⣿⣭⣍⡉⠉⠉⡉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠋⠉⠉⠂⠒⠛⠛⠛⠉⠁⠉

⠀⠀⠀⠀⠀⢀⠠⠄⠒⠉⠈⠢⡀
⠀⠀⠀⡐⠉⠀⠄⠂⡀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⡄⠄⠀⠀⠠⠀⠐⠀⠈⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⡗⠄
⠀⠀⠀⠰⠀⠀⢀⡀⠁⡐⠐⢄⠈⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠘⢄⣀⣀⠦⡀
⠀⠀⠀⠀⢃⠀⠇⠈⠉⠁⠀⠈⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠈⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⣀⣴⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡩⢣⠂⠀⡑⠤⣆⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡰⠁⠐⠀⡆⠀⠀⠐⢄⠀⠉⠺⠲⡰⢠⢦⣀⣀⣄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⡀⠤⠔⠺⡇⠀⠀⠀⢃⠀⠀⠀⠀⡆⠀⢀⠏⠣⠼⣁⠉⢠⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢄⡧⢰⡈⠒⣘⠢⢀⡵⠤⢠⠐⢁⠀⠉⡋⠙⣄⠈⢢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠭⢠⠼⡄⣁⠒⣎⠀⢑⠁⠈⡒⠁⢙⠁⢱⠊⡽⠧⠈⠓⠓⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠇⠈⡀⠰⠀⠀⠀⠀⡁⠀⡄⠀⠖⠉⠀⠀⢀⣀⠤⢄⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠘⡄⡡⢀⣁⠀⠇⠀⠀⠀⠁⡌⠀⠀⠁⡲⠓⠈⠁⠐⡴⠀⠐⠀⠱
⠀⠀⠀⠀⠀⠀⠊⠁⠙⠇⠀⢪⠀⠙⠀⠀⢹⠄⠰⠀⠀⠰⠀⣄⣄⣀⡀⠈⠒⠄⠒⠊⠀⠀⡘⠑⡖
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⣰⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠉⠢⡀⠐⠤⠒⠀⡠⠒⠀⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⠤⠄⠠⠔⠂⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠉⠀⠒⠒⠦⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⣠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸⠁⠀⢀⠤⠐⠒⠊⠁⠀⠀⠀⠀⡔⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠒⠁⠀⡰⠁⠀⠀⠀⢀⠀⠀⠀⠀⡴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢀⠎⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡄⠀⠀⠜⠀⠀⠀⠀⠈⠀⢀⠖⠉⢁⠀⠈⢀⠎⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠒⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠛⠤⠀⠀⠁⣠⠊⠐⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⣠⠤⠐⠒⠊⠀⠀⠀⡀⠀⠀⠀⠘⠁⠢⠀⠀⠀⠀⡠⠒⠈⠁⡀⠀⢀⡼⠀⠀⠀⠀⠐⠀⠀⠤⢀⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⠀⠀⡀⠀⠀⢈⡤⠀⠠⡄⠀⠀⡠⠄⠀⠈⠀⠀⠠⠀⠈⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⣀⠤⠒⠁⢀⠀⠀⠀⣀⠜⡀⠀⠀⠦⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⠀⠀⠀⠈⠢⡀
⠀⠀⢰⠁⠀⢀⡰⠃⠀⡠⠀⣠⠁⠀⠀⡔⠁⢀⡀⠀⠈⠁⠐⢊⠑⠄⠈⢀⣀⡠⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⠀⠱⡀
⠀⠀⡆⠀⠰⠁⠀⡠⠎⡰⠋⠀⡠⠶⡊⠀⠀⠀⡠⠄⠀⠀⠀⢀⠔⠂⠉⠁⠀⠀⠀⢃⣀⣀⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠃
⠀⢠⠁⢀⠆⠀⠘⠀⢀⡀⠤⠊⠀⠀⠀⡠⠔⠊⠀⠂⡰⠀⢡⠃⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠁
⠀⠸⡀⡜⠀⠀⠁⠀⡏⡀⠀⠐⠀⢀⢎⡀⠈⠂⡠⠊⠉⢠⠂⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⢤⣀⡀⠑⣄⠀⡀⠠⠄⢒⡡⠊
⠀⠀⢣⡱⡀⠀⡔⠋⠀⠈⠂⠀⣀⠜⠀⢀⣠⠎⠑⢀⡴⠁⡜⠁⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢮⡆⠀⠐⠈⠁
⠀⠀⠀⠱⣁⠘⠀⢀⣀⡀⣠⠎⠀⣀⠴⠁⢀⡠⠖⠁⢀⡞⠀⢀⡀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸
⠀⠀⠀⠀⠈⠓⠦⠥⢀⣈⣀⣒⡊⠤⠤⠒⠉⠀⠀⠀⣎⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⡀⠀⠈⠛⠋⣉⣁⡤⠤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢸⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠛⡛⣁
⠀⠀⠀⠀⠀⠠⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⡐⠦⣄⣀⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢀⠈⠑⠒⠲⠔⠒⠒⢒⠇
⠀⠀⠀⠈⠑⠒⠒⠢⠤⠔⠊⡅⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⣿⣽⡆⠀⠀⠀⠀⠈⣷⣶⣶⣶⣤⣴⣾⡟
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⢁⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛

⠐⠀⠐⠀⠐⠀⠐⠀⠐⠀⡄⠀⠀⠀⢀⠀⡀⠂⢀⠀⠀⠀⠂⠀⣀⣀⢠⡄⢀⠄⠀⠀⠀⠀⠐⠀⠠⠄
⢈⠀⠈⠀⢈⠀⢈⠀⢘⠀⠁⠀⠀⠀⠰⠃⠀⠀⣈⡀⠠⠄⠀⠀⠉⠉⠀⠁⠉⠀⠄⠀⠄⠀⠀⠤⠀⣠⣤⣤⣄
⠈⠀⢈⣠⣬⣤⣌⠀⠀⠐⣾⣿⣷⣶⡀⢰⣿⣿⣿⣿⣿⣷⡆⠔⢀⣀⠦⠀⡐⠘⠀⢀⠀⢀⠐⠀⠀⣿⣿⣿⣿
⠀⠀⠿⣿⣿⣿⣿⢇⠀⢸⣿⣿⣿⣿⠀⡸⠹⠏⠏⣿⠙⠛⣇⠀⠈⠁⠀⠖⡆⢈⠄⠈⠂⠠⠤⠂⠀⣿⣿⣿⡟
⠀⠂⠓⠌⠉⠉⣡⠈⡄⠀⠙⠛⠛⠃⡀⠈⠀⡀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⣀⡠⡤⣀⠋⠉⠩⠑
⠀⠀⠠⠀⠀⠀⠀⠄⡠⠀⠀⠒⠄⡤⠁⠀⠀⠀⡨⡀⠀⠀⣔⠳⠠⢘⠍⠉⠩⠇⠠⠊⡩⠄⠀⠁⠀⠀⡤⠀⠄
⠰⠀⠠⠴⠀⠀⠠⠀⠀⢈⠠⢠⠴⠁⠈⠀⢀⠐⠀⣀⣤⣤⣤⣄⠀⡄⠀⠈⠀⠀⠀⠀⠇⠀⠀⢀⢀⡐⠆⠀⠘
⠀⠐⠀⠀⠀⢀⣃⠀⠀⠠⠊⠑⡸⠀⠀⠀⠀⠄⢸⣿⣿⣯⣿⡿⠂⠂⠠⠥⠈⠀⠀⠴⠋⠑⡀⠆⠪⠅⠦⠠⢐
⠀⠘⠄⠀⠀⠟⠛⢓⠀⠀⠀⠀⠖⢆⠁⠄⠀⠂⠈⠉⠉⠅⠀⠀⠀⠈⠉⠀⠀⠴⠀⢀⠄⠑⠃⠈⠢⠿⠁⠑⠬
⠀⣠⡂⠀⠀⢀⣤⡀⠐⡀⠀⣀⢸⠸⡀⠀⢚⡤⣶⣾⡿⣿⢿⡿⣿⣿⢿⠶⡦⣄⠨⠀⢀⠀⠀⠀⡠⠆⠀⠀⢀
⢀⠀⠀⢀⠀⠹⠛⠻⠀⠐⠊⠀⠊⠃⡓⠀⢾⣾⣷⣦⣿⣶⣿⣽⣦⣯⣾⣿⣧⣿⡆⠀⠀⡜⢀⠀⠉⠀⠀⠘⢨
⠈⠀⠀⠈⣤⡤⠤⠤⠤⠄⢠⠄⠀⠀⠀⡀⡘⠿⣿⣿⣯⣽⣽⣭⣭⣽⣿⣿⡿⠟⠠⠠⠼⣷⠚⢠⡁⠠⡄⢀
⠀⠀⠉⣶⠛⠒⠂⠀⠀⠀⠈⢈⠶⠒⠁⢀⠁⡀⢀⢤⣉⡉⠉⠉⠉⣉⡁⠀⠀⠢⢄⡀⠀⢠⠀⢀⠀⠈⠀⠂
⢀⡔⠁⠀⠃⡀⠤⡀⠀⠤⠔⢊⠀⠄⠐⠁⠈⠋⠓⠞⠛⢋⠀⠀⣾⣿⣿⡆⠀⢰⣄⣦⣶⡾⠀⠀⢁⣀⢈⡀⡀
⠀⡀⢀⡀⢀⡀⣀⠀⡀⢀⡀⠐⠢⠀⡆⠀⠈⠀⠁⠀⡀⢈⠀⠀⢹⠟⢻⡇⠀⠸⠛⢋⣡⡜⠀⢻⠀⠄⠀⠂⠂
⠀⡀⠀⠀⢀⠀⢀⠀⣀⠐⢄⣀⣱⢦⡅⠀⡘⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⢻⡿⠿⠁⠀⠊⠀⠀⣀⣤⣴
⠀⢀⠈⠁⠈⠙⢌⠀⢀⡀⠀⡙⠚⡐⢡⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠚⠤⠵⠀⠀⠀⢸⣿⣿⡷⠾
⠀⢈⠀⡀⠀⠡⡑⠄⠀⠀⠀⡄⠀⠉⠈⠁⠀⠉⠛⠛⠛⠹⠀⠀⢀⣠⣣⣤⡀⠐⠀⡀⠢⠀⠀⡀⠘⠋⠁
⠀⢨⠀⠈⠂⠀⢓⠀⢀⡀⠀⠄⠰⠶⠶⠶⠀⠀⠀⠂⠀⡣⠀⢰⡿⢿⡟⠏⠣⢈⠀⠁⢰⠂⠑⠀⠁
⠀⣀⡀⠠⣀⠀⢀⣀⠀⢀⢀⠀⠘⠛⠂⢃⠀⠘⠂⠀⠒⠀⠀⠀⠐⠀⠀⠨⠀⠀⠀⡀⠉⠡⠄⠐⣂⡀⠩⡤⠐
⠀⠓⠪⠁⠒⠀⠐⠂⠄⠜⠚⠀⠸⠿⠿⠿⠀⠺⠿⠹⠏⠿⠽⠧⠻⠼⠆⠀⠀⠤⠇⠃⠀⠀⢰⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡫⠉⠉⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⡀⢀⡏⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠋⠀⠀⠀⠀⠀⡴⠚⠉⠓⠲⠶⠶⠛⠉⠀⠀⠉⢢⠀⣠⠞⠉⠙⣿⡇⠀⠀⠀⠈⠒⠒⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠛⣿⠁⠀⠀⠀⢠⠖⠛⣇⣀⣀⣀⣀⠀⣠⠔⠒⠲⠦⣤⣴⠾⠋⠀⠀⠀⣿⠣⡀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⣿⡀⠀⠀⠀⢸⣴⢞⠋⠉⠈⠉⣩⠿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠙⢗⠢⣠⠖⠋⢳⡀⠞⠉⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠋⠁⠀⠈⠈⠙⠒⣤⠟⠑⠁⠀⠀⢀⡞⠑⠀⢻⣀⠀⠀⠀⠀⠀⠀⣀⠔⢋⠐⡲⢤⣄⣠⠜⠁⠀⠀⢸⠃⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣯⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡾⠰⠀⠀⠀⠈⡙⠛⠒⠒⠚⠻⣤⣰⡇⠁⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⠙⠻⠿⣿⣧⡀⠀⠀⢿⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⢀⣠⣯⡴⠞⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠈⠉⠛⠒⠾⠷⣤⣄⣤⣾⣷⡀⠀⠀⠀⢈⣇⣀⣤⡀⠀⠀⠀⢈⡃⣉⣓⣶⡶⠶⠞⠛⠉⠁⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠶⠾⠿⠷⠶⠚⠓⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣟⣛⡻⠿⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠖⠚⠛






⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⣠⠴⠖⠚⢉⡟⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢀⡜⠁⠀⢀⡰⠋⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠤⠒⠉⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⡀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣯⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣹⣦
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢄⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠈⡆
⠀⠀⠀⠀⠈⢢⡁⠀⠀⠀⠀⠈⠳⢄⠀⠘⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢱
⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣀⣀⣠⣤⠽⠶⠟⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠀⠉⠙⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠈⠻⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢠⠞⠋⠀⠀⠀⠔⠂⠉⠉⠉⠉⠉⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠔⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠒⠒⠀⣷⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠠⠊⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⣄⣀⣀⣀⠀⠐⠀⠀⠀⠀⠀⠠⣤⠄⠀⠀⣀⣤⡴⠞⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⡉⠉⠙⠛⠶⠶⠶⠶⠶⠶⠶⠶⠞⠉⠀⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⢤⣀⡀⠢⠤⢤⡄⠠⠄⠒⠂⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡒⠚⠙⠶⡚⠛⠦⣄⠀⠀⠀⠀⠉⠓⠶⠤⠴⠶⠚⠋⠛⠋⠉⠀⠀⠐⠤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠁⠠⣇⣴⠶⣄⠙⢦⡄⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠀⠀⣀⣀⣀⠀⠀⠄⢠⠂
⠀⠀⠀⠀⠀⠀⢀⠴⢦⠙⢄⡤⢬⠁⠀⠉⡷⠀⠧⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⡄⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⠂⡎⠉⠀⠠⠎⢱⡟⠓⠚⢦⠣⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣻⡀
⠀⠀⠀⠀⠀⠀⢀⢤⡂⢠⠞⠁⠀⣈⠒⠦⣌⠳⡄⠀⠀⠀⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡴⡆⣸⣶⠇⡀⡀⢀⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠈⣦⠁⠀⠣⣠⠜⢀⣉⣀⡈⠲⢬⡁⠂⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣿⢻⠃⠀⠘⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠲⠤⠆⠰⡉⠀⠈⠙⣇⡀⠙⢲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠇⠈⠀⡠⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⠀⡌⠀⠒⠒⠉⢻⡆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠐⣊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠒⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠒⠛⠋⠁


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

⠀⠀⠀⠀⠀⠠
⠀⠀⠦⢄⣀⠚⢀⠀⠀⠁⢀⠭⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣄⣐⢦⡄⠀⠀⠀⠂⠀⠄
⣀⡀⠀⢀⡭⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠐⠀⠀⠀⠩⠥⠶⠾⠇⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠤⡄
⠈⠉⠲⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠁⠀⠀⡅⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣑⠂⠤⣀⡞⠀⠀⠀⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⠀⠀⠀⠀⢁⠆⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⣁⠀⠀⠑⠒⠠⠤⠃
⠀⠀⢀⠀⠀⠤⠤⠤⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣃⣠⣄⡄⠀⡀
⠀⠠⠀⠀⢠⣥⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⣿⠽⠟⠇⠀⠸
⠀⠀⠀⠀⠀⠀⡀⠂⠈⡇⠀⠠⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⡼
⠀⠀⠐⡏⠉⠛⠓⠺⢼⡀⠀⢄⠀⠀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡄⠀⢀⡀⠀⢀
⠀⠁⠀⡇⠀⠀⠀⠠⠀⡏⠀⠀⠀⠀⠁⠀⢀⠀⠀⠄⡘⠐⠃⠴⢄⢀⡀⠀⠀⠀⠐⢤⡇⠀⠀⠀⠀⠉
⠀⢀⠀⠋⡉⠛⠒⠒⢼⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢂⠉⠒⠲⠤⢬⣀⣉⣂⠀⠀⠀⠑⣄⣀⣠⣤⡴⠞⠂
⠀⠀⠉⠓⠲⠭⠭⠭⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠶⢄⣠⣘⠐⠢⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⢀⡴⠚⠋⠉⢀⡼⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⠴⠂⠀⠀⠀⠀⢳
⠀⢠⠏⠀⠀⢠⡴⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡤⠖⠋⠁⠀⠐⢒⠀⠀⢠⡟
⠀⠁⣀⡰⠋⠁⠀⠀⠀⠀⠀⠀⢀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣧⣀⠈⠀⠠⠄⠂⣁⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⣈⣱⣄
⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠠⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⢹
⠀⠘⢌⠢⡀⠀⠀⠀⠀⠑⢄⡀⠀⠱⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠓⢤⣀⡀⠀⠀⠄⣀⣉⣶⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠀⠀⠉⠉⠉⠙⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⢰⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⢀⡀⠀⠀⠉⠉⠁⠀⠀⠀⠐⠄⠙⠷⣦⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡌⠰⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⠶⠋⠁⠀⠀⡠⠤⠶⠄⠒⠒⠒⠦⠄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠀⢹⡀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣁⣀⠀⠒⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠖⠂⣀⡴⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⠒⠶⢦⣤⣤⣌⣁⡀⠀⠀⠀⠀⠐⠛⢀⣁⡤⠴⠖⠛⠉⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠋⠉⠉⠀⠠⠄⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠉⠛⠲⠤⢤⣑⠒⠒⠶⠤⠔⢂⣉⣉⣠⣤⠾⠋
⠀⠀⠀⠀⠀⠀⣠⡔⠢⣍⠛⠉⠙⢛⡉⠉⠗⢦⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠛⠉⠉⠉⠉⠀⠀⠀⢀⡓⢦⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠰⣁⠁⠀⢿⣤⠟⢦⣄⠙⢶⠄⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡆⢀⣀⣀⠠⡄⠀⠀⠀⢠⠂⠁
⠀⠀⠀⢀⠖⢦⡈⢦⡤⠦⡄⠀⠀⢹⡇⠘⠆⢀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⡤⠘⠲⣄
⠀⠀⠀⠀⠀⢀⡽⠇⢴⠉⠁⠀⠴⠋⣼⠟⠓⠞⢤⠳⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⣼⠃⠀⠀⢸⣆
⠀⠀⠀⢀⣤⠆⠀⡴⠋⠀⢈⠓⠦⢄⡈⠳⡀⠀⠀⠀⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣦⡆⣸⣴⠏⡀⠀⠀⣾⠻⣆
⠀⠀⠀⠙⣎⠁⠀⠣⣀⣠⠋⢙⡂⠀⠱⢤⣑⠂⠠⡠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣷⢿⠋⠀⠑⣿⢸⣿⠀⠈⠁
⠀⠀⠀⠀⠫⡀⠤⣄⡀⢠⡒⠋⠈⠙⠳⡄⠈⠳⢤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡇⠉⠀⢀⠀⠘⢿
⠀⠀⠀⠀⠀⠈⠃⢀⢀⠀⢈⠂⠀⣤⡴⠻⣶⡄⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡀⠔⣉⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣈⣀⣠⣄⣀⣤⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠦⢤⣤⣤⠤⠶⠚⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣾⢳⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣽⡟⠛⠳⣦⢹⣀⡧⢀⣀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⢀⠀⠘⢄⠀⠚⠓⠦⠄⡠⢀⠀⠀⠀⠘⠷⠟⢸⡛⠢⢟⡀⠉⡠⠋⢉⡇⠀⠀⠁⢠⢂⠀⠀⠀⠀⠛⠀⠨⠀⠄⢀⠦⡄
⠀⠀⠀⠀⠀⠄⣀⠀⠀⠉⢳⡀⢀⣀⡀⠀⠑⠀⠀⠀⢠⠂⢈⣿⠶⠶⠃⠰⠥⠴⠟⠁⠀⠀⢠⡎⠀⠀⠀⠀⠘⠀⠋⡄⠀⡀⠀⠄⠦
⠀⠀⢣⡀⠀⠀⠈⢰⠳⠀⠀⡿⠉⠀⠀⠀⡰⠀⠀⠀⠈⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢤⣤⡘⢷⣦⡀⠀⠀⣀⣤⣢⠿⡀
⠀⠀⠀⠙⠲⠖⠚⢁⠀⢀⡼⠀⠁⠀⠐⠋⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡬⣍⣙⢉⣉⣈⣵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠢⡄⠈⠐⠢⠀⠀⠠⠀⠀⠀⠀⠭⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠃⠀⠀⠄⠁⠀⠀⠀⡁⠀⠀⠀⠀⠀⣠⠐⠄⠀⢀
⠀⠀⠀⠀⠀⢀⠴⠞⠋⠓⢦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠶⠞⠁⠀⠀⠀⣀⣀⣤⠤⠚⠀⠀⠀⠀⠈⢆⠀⢀⣀⣰⣄
⠀⠀⢀⡤⠚⠋⠁⣀⣤⡆⡈⠉⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠖⠛⠈⢀⠈⠁
⠀⠀⡃⣄⠀⢀⡞⠁⠉⠉⠛⢦⣤⣤⢄⠀⠀⠘⠀⠀⠰⢻⡇⡾⡀⣀⢰⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠂⢄⢰⡾⠿⠃
⠀⠀⠑⠦⠠⠶⢆⠰⡤⢤⣄⡀⠀⠈⢉⡷⠒⠁⠀⠀⠀⠿⠸⠗⠇⠏⠾⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠛⠶⢞⡉⠉⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⣠⢄⡤⣰⢆⣆⡤⣠⠄⡖⡌⣠⢄⡤⡄⠀⠀⠈⠓⠀⠀⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠓⠙⠚⠛⠃⠛⠚⠓⠓⠓⠙⠃⠓⠀⠀⠀⢤⠖⠀⡀
⠀⠀⠀⠀⣀⠄⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠦⡄⠀⢠⡇⡠⠊⢡⡀
⠀⠀⠀⢰⢇⠀⠀⠀⠀⢈⡶⠟⠛⠳⢤⡀⢀⡔⠃⠠⠞⠋⠐⠂⢸⠀⠀⠀⠀⠀⠀⢠⡾⠋⠈⠀⠘⠀⠀⡴⠋⠀⢠⠇
⠀⠀⠀⠘⠈⠓⠤⠶⢶⡏⠀⠀⠀⠀⢀⡏⠀⠳⠦⠀⠀⠀⠤⢖⠋⠀⠀⠀⠀⠀⠀⠈⠙⢀⣀⣀⣴⡀⡔⠀⢀⣤⠋⠀⠲⠖⢂⡁
⠀⠀⠀⠀⠐⢄⡀⠀⣠⡷⠄⠤⠐⠆⠻⢷⠀⠀⠀⠒⠒⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⠶⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡴⣾⡿⠇⢋⠁⡒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⣩⣥⣬⣍⡒⢴⡿⠞⠀⠀⠈⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⡟⠃⠉⠀⠉⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⢆⠘⠀⠀⠀⠀⠀⢠⠀⣿⣶⠆⠀⠀⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚⠿⠉⠉⠉⠙⣄⡀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠘⡆⠑⢤⡀⠀⠀⠒⢁⡰⠁⠉⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⣩⣖⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⠀⠐⢆⠀⠀⢀⡍⠀⠀⢁⠔⠀⠀⠀⠘⠯⣹⠆⠀⠀⠀⢀⠀⢴⡦⠄⠀⠠⠄⠀⠀⠀⡀⠒⠻⢶
⠀⠀⢌⠙⢙⣿⣽⠇⠀⣿⡿⠿⢧⣠⡆⠀⠀⢀⠀⢀⢀⣸⡦⠀⡀⠸⢷⣶⣿⠿⢠⡯⠀⠀⠀⢰⡿⠉⠈⠉⢰
⠀⠀⠢⠄⣭⡵⢖⡃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⢳⠇⠀⠁⠀⠀⠛⠃⠀⠈⠛⠀⠤⠂⢸⡿⠷⡆⠀⢾
⠀⠀⠀⠀⠒⠋⠁⠀⢀⠈⠁⠀⠀⠀⣀⣴⣀⣀⡀⠀⠈⠁⠀⠀⠈⢀⡀⢤⡤⡄⠀⠲⠲⠶⠂⠸⣧⣤⣤⠀⠤
⠀⠀⠀⠀⣤⣥⣀⠂⠤⠂⠀⠀⠀⠞⠫⠦⠭⣫⣄⠀⠀⠀⠀⠀⠀⠒⢂⠘⠊⠙⠙⠛⠛⢋⡁⢀⣀⣀
⠀⠀⠀⠀⠸⣾⡽⣿⣏⣷⢦⡀⠀⢈⣁⣀⡒⠠⢿⠀⠀⠔⠋⠀⠑⢛⣿⡇⠀⠀⠀⠀⠠⠬⠥⠍⠉⢩⣥⢾⠃
⠀⠀⠀⠀⠀⠙⠛⠓⠻⠮⡾⠁⠀⠉⠒⠢⢈⣱⣶⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠐⢶⣤⠒⠄⠐⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢲⠛⢶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⢟⠟⢡⠂⡰⢹⢻⠟⣦⡀⠀⣠⢞⠏⠍⠀⠀⠀⠈⠀⠁⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⢀⣾⠏⡌⡎⢀⠏⢰⠃⡎⣼⢀⢇⢻⣶⠣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠉⢉⡟⡏⡼⢸⢀⠞⠀⠀⡸⡐⡏⠸⡌⢠⢻⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠰⡄⣼⢡⡇⠇⣜⠂⠀⡆⢀⡟⢰⠃⣴⠁⡈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢨⡇⠘⢰⢠⢿⠀⡸⠃⡘⢀⠏⡸⢃⣴⢃⡿⡀⠂⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⠁⠀⡆⠌⡞⢠⢡⡶⠁⡞⠀⢀⠏⡈⣼⡇⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠒⠚⠋⣿⡸⠀⣤⠰⢡⠇⡞⠀⠸⢃⡴⢁⡜⣼⠓⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢸⡇
⠀⣀⣠⠤⠖⠚⠋⠉⠀⠀⠀⠀⠤⢀⡀⣿⡇⠀⠇⠀⡏⢰⠇⠠⢟⡽⡠⢊⡼⠃⠠⠀⠹⣆⠠⡐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠙⠳⢦⣀⠀⠀⠀⠀⠈⠦⠀⢀⡀⠙⣿⠇⡄⠀⡼⣡⠞⠀⡠⠂⣶⣡⢾⡀⠀⠀⠈⠦⢌⢧⡈⢦⡠⠀⠀⠀⠀⠆⠀⠀⠀⠁⣾
⠀⠀⠀⠀⠈⠙⠲⢦⣄⡀⠀⠐⠉⠀⠀⣿⠀⠇⠘⡰⠁⡠⠚⢁⣴⠿⠓⠒⠛⠶⣤⠤⠤⠤⠷⠽⣦⣙⠢⡀⠀⠀⠀⠀⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣀⡀⢹⣄⠀⡰⢁⠜⢁⣤⠞⠁⠀⠀⣤⠔⠊⠁⠀⠀⠀⠐⠚⠃⠈⠳⢤⡀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣶⡵⢾⣞⣋⣀⣀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣀⣠⡤⠴⠒⠋⠉⠛⠲⠶⠤⠴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡖⠁⠀⠀⠀⠀⡤⠽⠋
⠀⠀⠀⠀⠀⠀⠀⡄⠰⠒⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡜⠁
⠀⠀⠀⠀⣀⣀⠀⠰⡄⠀⢠⠀⠀⠀⠀⠀⢠⣴⢂⡀⠀⢤⡄⠀⠀⣉⠀⠀⢀⠀⠉⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠆⠀⢃⡀
⠀⠀⠀⠀⠀⠉⡠⠶⠈⣀⠋⣀⠀⠀⠀⠀⠘⠿⣅⠀⠛⠀⠣⠘⠒⠹⠶⡶⣥⡌⠁⢸⠿⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠁⠀⠀⢂
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠙⢯⣁⠀⠀⠀⠐⠒⠚⠂⠛⠁⡨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠐⢀⠀⠘
⠀⠀⠀⠈⠙⠳⠀⠀⠀⣠⣄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠒⢾⡷⠶⠤⠠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⢸⠀⠖⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠔⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡈⠉⠉⠈⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡀⠘⣦⠀⠀⠈⠁⠀⠀⠀⠔⠀⠀⠉⢷⠊⠁⠈⠂
⠀⠀⠀⠀⠐⡉⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⡠⠀⣿⡆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⠆⠀⠀⠀⡀
⠀⠀⠀⢀⠁⠄⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⣀⣀⣠⡴⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠑⠀⠉⠀⠀⠀⠀⠀⠀⠘⣦⣀⠀⢀⣼⠀⢀⡠⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⡨⠉⠹⡉⢢⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠻⢿⡝⠉⠉⢒⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡂⠤⠋⡄⠘⠦⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢴⠄⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⠳⣤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠹⠄⠁⠄⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠱⢄⠁⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢷⣄⡐⠠⣊⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏
⠀⠀⠀⠀⡘⠀⢀⡐⠀⠉⠐⠄⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢓⠀⠴⠦
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠋⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣴⣀⢄⡀⣂
⠀⠀⠀⣤⣀⣀⣤⡿⠶⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠆⠀⠓⠼⢋⣉⣉⡶
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠁⢀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣰⠎⢡⠒⠈⠁⢢⡎⢱⢘⠀⡆⣰⣄
⠀⠀⠀⠀⠀⠣⠅⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠀⠀⠀⠀⠀⠸⡟⠂⢤⠀⠐⠒⢁⡄⣸⡦⢀⡤⠟⡿
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠐⠀⠀⣠⠐⠫⠘⠁⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢦⡤⠀⠴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠋⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠏⠀⠀⣧⠘⣿⡅⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⣇⠀⠙⠀⣿⡇⠐⣇⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢉⣉⣩⡉⠉⠛⠓⠮⣭⣓⠢
⠀⠀⠀⠀⢸⣿⣿⡹⣿⣿⣧⠀⢹⣆⠀⠀⠘⣿⡄⠘⠀⠀⠀⠀⠀⠀⣼⣿⡏⠸⣆⠀⠀⠀⠛⠲⠀⠀⠀⠈⠻⢿⣦⡀⡀
⠀⠀⠀⠀⠈⣿⣿⣇⠹⣿⣎⢷⣄⠙⠦⠀⠀⠈⠻⢦⣄⣀⣀⣰⣶⣾⣿⣿⡻⣄⣀⣉⠓⠀⠀⠀⠀⠀⠀⠀⠑⢦⠙⢿⣎⢦
⠀⠀⠀⠀⠀⢹⣿⣝⣦⠈⠪⡳⣮⣷⣦⣀⣀⣀⣀⣀⠀⠉⠉⣉⠉⢹⣿⣿⣿⣾⣿⣷⣭⣕⡂⠀⠀⠀⠀⠀⠀⠈⢳⡀⠻⣎⢷⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣮⣳⣤⣬⣿⣿⡿⠿⠟⢛⣛⠛⢿⣦⡀⠈⠁⠈⢿⣿⣿⣿⣿⣶⣾⣍⠛⢶⣄⠀⠀⠀⠀⠀⠀⢳⣰⠹⣎⢧
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠿⠛⣩⡴⣺⠾⠋⠉⠀⢸⣿⣷⣶⣤⣄⣀⠙⢻⣿⣿⣿⣷⣾⣭⣝⣿⣧⡀⠀⠀⠀⠀⢆⠁⡇⢻⣎
⠀⠀⠀⠀⢀⣠⣶⡿⢟⣭⣀⣴⣾⣽⣺⠗⢀⡔⢠⢇⣾⣿⡇⢀⡉⠙⠻⣿⣿⣏⡏⠀⠀⠀⠀⠉⠻⣿⣿⡄⢤⠀⠀⠘⡆⠹⠸⣿⡀
⠀⠀⠀⣠⣾⠟⣩⡶⣫⣾⣿⣿⡽⠋⠡⠖⠉⠀⠟⣼⣿⣿⡇⠀⠉⠳⣦⡈⠻⣷⡀⠀⠀⠀⠰⡌⠀⠈⣿⣿⠈⡆⠀⠀⡛⠀⠀⣿⡇
⠀⢀⣼⣿⣷⠾⣫⢾⣿⠟⠋⣡⠆⠀⠀⠀⢀⠀⣰⣿⣿⣿⡇⢰⡀⠀⠈⠁⢀⠹⣷⡀⠀⠀⠀⠸⠀⠀⣿⣿⡄⢿⣶⡞⣼⠀⠀⣿⡇
⢀⣾⣿⡿⣿⣿⣿⡯⡠⣢⡾⠃⢀⡄⠀⣰⠋⢰⣿⣿⣿⡟⢷⡄⢳⡄⠀⣴⠘⠇⢹⣷⠀⠀⠀⠀⠀⠀⣿⣿⣟⢤⣉⣛⣁⡴⢎⣿⡇
⢸⣿⣟⣼⣿⡿⢫⢞⡼⠋⠀⣰⠋⢀⣼⠃⣰⣿⣿⣿⣿⣷⡈⠻⣆⠻⣄⠈⢇⠀⠀⣿⣇⠀⠀⠀⠀⠀⠹⣷⣍⣛⣒⣚⣡⣤⣾⡿⠁
⠜⣿⣿⣿⡟⢱⡫⠋⣀⠀⠈⠁⣠⡿⠃⣴⣿⣿⣿⣿⢿⡿⣟⢦⡘⢷⡙⢧⡘⢧⡀⢸⣿⡀⠀⠀⠀⠀⠀⠈⠙⠻⠟⣛⣛⠛⠉
⠘⣿⣿⣿⡇⠟⢡⠞⠁⣀⣤⡾⠋⣠⣾⡟⠈⢻⣿⣿⡷⣝⣌⠳⣿⣆⢻⣦⠀⠈⢿⣼⣿⣧
⠀⠘⠻⢿⣷⣄⡓⠶⣾⣿⣯⣴⡾⠻⠋⠀⠀⠀⠙⠿⣿⣮⡻⣷⡈⠊⠳⡙⣷⣔⣌⣹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⢶⣤⣄⣀
⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣲⣤⣐⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⣀⣴⡾⣟⡯⣿⠚⠋⠉⢁⣀⣤⣭⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣤⣄⠀⠀⠉⠛⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⣠⣾⢟⡽⡻⠵⠋⢀⣤⣶⢿⣿⣿⣟⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡽⠞⠋⠉⣿⡇⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣟⡥⠊⢀⣤⡶⣿⡿⠞⠋⢉⣠⣤⡿⠿⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠋⠀⣀⣼⡿⢡⣿⣿⠟⢿⣆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣫⢀⣴⣿⠟⢀⣿⣧⣶⠿⠛⣉⡠⢀⡀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠿⠿⠟⠉⠀⠘⣿⣿⣶⡈⣿⡐⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⣣⣶⠿⢛⡩⣀⡴⢚⠅⠀⢀⡴⣣⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠹⣯⢳⣷⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⢡⢖⣩⢞⡵⠊⠴⣞⡴⢋⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡛⣿⡆⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⣷⢑⡵⣫⠖⢋⡤⠴⣞⣯⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣏⣧⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠿⢼⣥⣤⣶⣶⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣌⡙⢠⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡇
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⡀
⠀⠀⠀⠀⣠⠄⠒⠉⢁⠀⠀⠁⢀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠰⠁⠐⠀⠂⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡌
⠀⠀⠀⠰⠈⢀⠀⠁⠐⠀⠀⠁⠀⠀⢀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⡜⠀⠶⠊⠆
⠀⠀⠀⠀⢇⠀⠀⢀⣀⠈⢀⠋⠙⡄⠈⡌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⠀⠱⢄⡀⣠⠓⢄
⠀⠀⠀⠀⠈⡆⠀⡇⠀⠉⠁⠀⠀⠈⠒⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠐⣄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⣤⡖⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡤⡪⢋⠏⠀⡗⢄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡔⠁⡎⠀⠀⠳⡀⠉⠒⠯⣣⣀⠤⡀⣀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣀⡜⠀⢰⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠘⣌⡖⠀⠬⠷⣔⠚⢣⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠒⠺⠁⢈⢧⡀⠘⡀⠀⢣⠀⠀⠀⠀⣸⠀⢀⢴⣣⣉⡈⠦⡤⠬⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⣒⣤⣇⠼⣀⠈⡡⣝⠂⡠⣛⠂⣀⣊⢁⢉⠀⢀⣃⣈⣢⣀⣈⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠬⠤⡤⢲⡄⣉⣒⢻⠀⠈⡊⠀⠈⡛⠁⠈⠁⠀⡕⠁⡭⠶⠐⠚⠚⡒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠈⡄⠘⡀⠈⡄⠀⢰⠀⠀⡇⠀⢸⠀⢀⠗⠁⠀⠀⠀⡀⢀⢤⠀⠁⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠰⠀⢱⡀⠸⠀⠈⡀⠀⡇⠀⡀⢠⠃⠐⠀⠂⡄⡼⠍⠃⠀⠬⣵⢈⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⡤⠒⠢⣬⠄⠤⡔⠒⠷⠉⠀⠑⣇⠀⣃⠀⠀⠀⡇⡌⠀⠀⠁⠀⠙⠄⣀⣀⡠⠔⠃⠐⢠⠦⢄⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡯⠤⠤⠤⠤⠤⠤⠜⢎⠒⠊⢆⠀⢀⡀⠄⠂⣈⢀⡔⠊⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⡠⠦⢄⣀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⡈⠉⠁⠈⠒⠊⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠔⠉⠳⠶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠔⠒⠲⣤⡀⠀⠀⠀⠰⣄⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⣀⣀⣀⣠⡴⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠹⣄⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⣀⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠸
⠀⠀⢠⠊⠀⡀⠈⠀⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⡰⠁⠀⠈⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠊⠉⠁⠈⠙⠳⡄
⢰⠃⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠇⠀⠀⠀⠈⠀⠀⠘⢦
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠂⠈⠆
⡇⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢸
⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡄⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⢸
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣤⣤⣤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠳⡄⠀⠈⠒⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠈⠲⠤⣤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠄⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠛⠛⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠈⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢀⣀⣤⠶⠛⠋⠛⢄⠀⠀⠀⢀⣰⠆⠀⠀⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠑⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⣶⠄⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡈⢀⡀⠀⠧⢄⠸⡇⢹⢰⠧⠜⢨⢀⡆⢠⠀⠀⣷⠋⢣⢸⠀⣸⠀⢸⠀⣙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣠⠄⠱⠜⠑⠀⠐⠚⠀⠀⠈⠈⠙⠋⠈⠋⠙⠃⠀⠀⠙⠀⠈⠈⠙⠁⠀⠀⠀⠈⠉