Healthy foods Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣀⠤⠤⠔⠒⠒⠂⠤⠤⢄⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠔⠊⠁⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠞⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠛⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⣀⢀⡊⣠⠴⢠⠙⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣴⣶⡾⠿⢟⣛⠉⠉⠉⣉⡉⠉⠛⣛⠿⠷⢶⣦⣄⡀⠀⢀⠊⣀⠤⣊⡿⠦⠁⢤⠸⢡⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠘⣏⣉⠻⣅⡉⢛⣉⡥⠴⠚⠁⢨⣿⠧⠀⠈⠈⡧⣀⢧⣀⣠⠄⣘⠀⠁
⠀⠀⠀⠀⢀⣠⣴⡌⠻⣦⣄⠀⢰⠒⠶⠚⠉⠒⢯⠔⢧⡀⠀⢀⣠⡶⠟⠁⠀⣀⣀⠀⠀⠀⠰⢁⡝⠮⣌⢳
⠀⠀⠀⠀⣾⣟⠁⠀⠀⠄⠙⠻⢾⣦⣄⣀⣀⣀⣀⣤⣤⠿⠞⠛⢉⡠⠀⠠⠊⢁⡈⡙⣆⠀⣀⡨⠂⡄⠟⡼
⠀⠀⠀⠀⢈⠻⣷⣄⠀⢠⠶⠶⠄⠀⠀⠉⠉⠉⣁⠀⠀⣀⣴⠾⠋⠀⠀⠁⢺⡅⢨⡇⣸⠊⢁⡀⠀⣆⠈
⠀⠀⠀⠀⠀⠐⠀⠙⠻⠾⣧⣄⣀⣀⣀⣀⣀⣤⣽⠶⠛⠋⡁⠀⠀⠀⠀⠐⣲⡾⠷⣴⡁⢸⣅⡨⡗⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠉⠉⠉⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⣏⢻⠀⠈⠁⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠰⠨⠟⢋⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅



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

⠀⠀⠀⢠⠄⡐⢀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⢀⠤⢒⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿
⠀⢀⢢⢠⣸⢀⢸⣴⠀⠀⠀⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢸⠖⠀⠀⢀⠜⡡⢆⠈⠀⠷⠀⠀⠀⠀⢠⡤⠴⠤⠾⠿⢷⣄
⠀⠘⠈⠉⠉⠉⠁⢠⠀⠀⠀⠃⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠸⠆⠀⠀⠀⠀⠘⠷⣎⣁⠀⢀⡆⠀⠀⠀⢙⠀⠀⠀⡀⠤⠀⠅
⠀⠀⢂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⢠⢶⠁⣀⠀⠀⠀⠀⢤⠁⠀⣠⠄⠂⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡖⠀⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⡀⠀⠀⠸⠀⠀⠠⠤⠤⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠰⠉⠠⡀⠀⠀⠀⠀⠀⢞⣁⠁⣐⡆⠀⠀⠀⠀⠀⠀⠀⢄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢠⡖
⠀⠀⠀⡄⠀⠀⢄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠸⠀⠺⣅⡰⢴⠀⠀⠀⠀⢄⠡⡄⠰⠀⠠⠀⠐⠀⢄⢁⠁⠀⠀⠀⡐⠀⡇
⠀⠀⠈⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠮⡵⠂⠀⠀⠀⠑⠌⡀⠧⠀⣂⠈⠄⠀⠀⠀⠀⠄⠐⠅⠀⡠
⠀⠀⠢⢀⠠⠤⢀⡀⠃⠀⠀⠀⠀⠈⠂⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠡⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠂⠀⠂⠀⠁⠄


⠀⣀⠄⠲⠂⠐⠒⠢⠄⠀⠀⠀⢤⣠⡄⠐⣆⣸⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠘⠁⢀⠤⠖⣶⡶⠤⣀⠀⠀⠀⠐⡟⠓⠀⡼⣼⡁⠀⠀⠀⠀⠀⠤⠴⡉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠃⢃⢠
⠈⠀⠁⠀⠼⡩⠗⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⢀⠁⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢀⠈⠄⠀⠀⠀⠀⠈⠆⣡⣶⣴⠦⠃
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠃⡆⠀⠀⠀⠀⠀⠀⠘⠂⠉⠀⠈⠲⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢡⡁⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠈⠁

⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢄⠀⠀⠀⠀⠀⢀⣠⠄⣠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠠⠄⢀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢠⠢⢀⠂⠘⠀⠀⠀⠀⢀⡎⠅⠁⠀⠀⠈⢣⠀⠀⠀⠀⠠⠐⠒⠂⠀⡀⢀⠠⠀⠀⢀⠤⢆⠀⠀⡈⠢
⠠⣀⠀⠠⠐⠒⠚⠛⠢⠼⠀⠀⠀⡀⠁⠁⠣⠂⠀⠁⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠨⡀⠀⠀⠀⠀⠈⠁⢘⠀⠀⠒⣄⠴⠀⠐⠇⣀⠓
⠀⠈⠂⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠱⣁⡀⢁⠔⠀⠀⠀⠀⠀⠘⣆⡀⠠⠤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠑


⢀⠉⠃⣶⣶⣶⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣤⣀⡀
⠈⠀⠀⠻⣿⠃⠐⠌⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⡁⠀⠀⠡⡀⠀⠀⠀⣴⣿⣿⠇
⠀⠀⠃⠀⢻⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⡽⠛⠋⠀⠀⠀⠀⡖⠀⠀⠀⠀⣀⡀
⠀⠀⣿⠀⠸⡆⠀⡾⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠹⡃⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢠⣭⡽
⠀⠀⠐⠀⢠⠃⠀⠀⠀⠀⠞⠒⠒⠲⠶⠶⠶⠶⠖⠶⠾⠶⠀⠀⠀⢠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⡚⠁⠀⠀⠄⠀⠀⠀⠀⠔⡒⠂⠀⠆⡀
⠀⠀⠀⠁⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠦⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⣄⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⡀⣤⡞⠀⢰⡆⠀⡆⣼⠛⡇⠀⣀⣀⠀⣴⣶⠽⣟⠛⠁⢀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⢀⡘⠮⣿⠀⢸⢃⢰⠀⡏⣰⢡⣾⣿⣿⣷⣆⠀⣾⣩⣶⠀⠀⠀⠀⠀⡸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢶⠄⠀⢸⣾⣾⣾⣱⠃⢺⣿⣿⣿⣿⡿⠀⡟⢸⣥⢟⣀⠀⠀⠰⡿⠀⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠙⢿⣿⠋⠁⠀⠁⠀⢠⣿⣿⣿⣿⣧⣄⠼⠧⡀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆⡀⠘⠛⠻⠛⠀⠀⠀⠀⠘⠋⢠⠂⡖⡔⠀⠈⠛⣿⣼⢿⣿⣿⣄⣾⠟⣿⠛
⠀⠀⠀⠀⠀⢀⣀⡀⣬⣥⡹⡄⡇⣄⢳⠀⠂⠀⠃⠘⠘⠀⠀⠁⠃⠘⢹⠀⣿⡿⠋⠙⠛⠉⠑⠿⠿⠛
⠀⠀⠀⠀⠀⠘⠿⢁⣈⠉⠁⢳⣷⡸⣎⣇⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⢋⠸⣿⠁⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠼⠛⣠⠙⠪⣿⣧⢻⣼⣆⠸⠃⠇⠺⠀⠆⠇⠀⣴⣿⣷⣶⡀⢀⠀⠀⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠞⢸⠀⣠⣼⡟⣯⣿⢻⡄⠁⣼⣆⣤⣾⡄⠀⣿⣿⣿⣿⠃⠛⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣙⠋⣿⣿⡿⠇⠛⣴⣿⣿⣿⣿⣿⡇⣿⣿⢟⣵⣶⠺⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⢧⠀⠀⠀⠀⠘⢿⣿⣯⣿⣿⠟⣠⣭⠡⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⡀⠻⢟⠉⣠⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⡁⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠐⠒⠒⠒⠒⠂⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠁⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠆⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠳⢄⡀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣀⠀⡐⠁⠀⠀⠀⢀⣀⠸⠦⠄⠒⠒⠤⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠈⢦⡀⢀⡤⠶⠐⠒⠠⠤⢄⡀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⣀⣀⠠⠤⠄⢀⣀⠔⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠠⡀⠀⡜⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡠⠚⠉⠄⠀⠀⠀⠀⠠⠆⠑⢶⡛⠉
⠀⠀⠀⠀⠀⠀⢀⠜⢲⠁⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⡄
⠀⠀⠀⠀⠀⠀⠮⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⠄⠀⠀⠀⠀⡤⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠈⠦⠜⠁⠀⠀⠀⠀⢠⠂⡟
⠀⠀⠀⠀⠀⠀⢀⣀⠔⡿⠆⠤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠌⠀⠄⢀⠌⠂⠘⣆⠀⠀⠀⠀⢀⡀⠔⢳⡀⠂⠄⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠂⡰⠃
⠀⠀⠀⠀⠀⠘⠋⢀⠐⠠⠀⠀⠀⡅⠈⠉⣩⠭⢅⡀⣀⡀⠣⡀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠉⠀⠈⢢⠈⠑⠤⣀⢀⡀⠀⣀⡠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠈⠐⢋⡥⠒⠛⠂⡀⠘⠄⢀⠀⠐⢷⠀⡀⠠⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⢀⠃⠀⠀⡇⠀⠀⠀⡤⢄⠀⢀⠔⠒⠀⠒⠒⠤⣤⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡁⠘⠂⢠⠖⠉⠢⢀⠀⠃⠀⣀⡰⠃⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠙⠢⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠉⠀⠀⢀⡄⠀⠀⠸⡄⠀⠀⠸⢄⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠔⠉⠑⠤⠀⠁⠀⡔⠀⠀⠀⣾⠀⠈⠀⠂⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⣆⠀⢀⡄⠁⠄⣀⠐⠀⢢⡤⠔⠓⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠧⣀⠠⠚⠤⠤⠊⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⣀⢤⡚⠃⠀⠐⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠢⠦⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⡰⠋⠆⠀⠀⠀⠀⠀⠀⠀⢸⡏⢲⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠈⠁⡄⠁⠀⠀⠀⠀⠀⠀⠀⢸⢂⠪⡒⠽⡄⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠠⠦⣀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠬⠣⠘⣳⠀⠀⠀⡔⠁⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⠀⠈⠑⢆⠀⠀⡇⠀⢸⠀⠀⠀⠀⢠⠊⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⢷⠊⡂⠚⡸⡆⠀⢰⠀⢶⣤⢤⣬⣯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⡇⠀⢸⠀⠀⠀⠀⠸⣆⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣽⣠⣭⡇⠀⠸⠀⢠⣿⣿⣟⣏⣤
⠀⠀⠀⠀⠀⠑⠴⠚⠉⠀⠀⡰⠁⣠⠏⠀⠀⠀⠀⠀⠀⣹⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢭⡉⠀⠀⠁⠀⠛⢿⣯⣿⣿⡿⠓
⠀⠀⠀⣀⣀⣀⣀⣀⣀⡴⠊⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⢻⣿⡗⠂
⠀⠀⠀⠈⠙⠋⠉⠤⠄⠒⠛⠁⠀⣀⣀⣀⣀⣀⣠⣤⡤⠴⢶⠒⠛⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⡀
⠀⠀⠀⠀⢀⣠⣤⢀⡀⠀⠀⡘⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⣬⡥⢻⡄
⠀⠀⠀⡴⣡⠖⠀⠀⠈⠂⠀⠈⠒⠦⣤⣤⣤⣤⣤⣤⠤⠶⠒⠊⠉⠀⠀⠀⠀⠀⠀⡀⢉⡓⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⡇
⠀⠀⠀⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠔⠀⠀⠠⡌⠹⡆⠀⠀⠀⠀⠀⡇⠀⠀⣀⣨⡇
⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡴⠒⠲⡞⠛⢯⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⢳⡹⠄⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⢃⠀⠃⠀⠀⣿⠀⣸⢰⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⠀⠈⠀⣸
⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡇⢠⡷⠏⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠨⣷⡀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠀⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⡰⣹⠃⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠠⠀⠀⠄⣀⡥⡄⠀⠀⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠭⠖⠃⢀⣀⢀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡎⣀⣠⠤⣀⣀⣀⡼⠃⠀⠀⠀⠰⠀⠀⠀⣀⠄⢚⠑⡀⣾⣇⠀⡠⠄⠀⠀⠀⢠⡮⣸⡐⣠⣿⡛⠦⣷⣤⡀
⠀⠀⢠⠀⠀⠀⢸⡷⢥⣄⠀⣠⣄⣀⣀⣠⡀⠀⣀⢀⠀⠀⢀⣤⠶⠋⣢⠶⠿⣷⠶⢦⣄⠀⠀⠀⠸⣦⡅⠃⡚⠋⣿⡞⢋⠡⡇
⠀⠀⡠⠃⠀⠀⠘⣇⠁⠈⠉⣡⢬⠇⠈⠀⠋⢛⡏⠘⠀⢀⣾⠋⠀⠐⠁⠀⠀⠈⠀⠀⠙⠆⠀⠀⠀⠉⠘⠀⠉⢙⠻⢷⣦⡼⠃
⠀⠀⠈⠹⠀⠀⠀⠙⢦⡀⢠⠽⠀⠀⠀⠀⣠⠞⡠⠁⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡞⠱⠋
⠀⠀⠀⠓⠤⣀⡀⠀⠀⠉⠛⠶⠴⠤⠒⠋⠁⢀⠇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⣸⢠⠱
⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠤⠄⠠⠤⠊⠀⠀⠀⠀⠀⠙⠦⣄⣀⡀⠀⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⣧⣼⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡐⠑⡄
⠀⠀⠀⣉⠑⠀⠀⠀⠀⠀⢀⣾⣴⠀⣠⣀⠀⣀⠤⡄
⠀⠀⠀⢿⡌⠀⠀⠀⢠⠦⡔⡏⠜⢀⣐⣄⣯⣀⣤⠃
⠀⠀⢖⡐⣧⡠⢄⠀⡤⠳⠀⡀⢶⠈⡤⡻⢇⠠⠚
⠀⠀⢀⣀⣩⡗⣸⠓⣌⠐⡀⡥⠊⠐⢠⡉⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀
⠀⠀⠙⢄⣌⠞⣮⠢⡏⡁⠱⡐⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠊⠐⠂⠁⠀⠑⡀
⠀⠀⠀⠀⢙⣻⡢⣉⢹⠂⣄⣈⣺⠴⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠀⢙⠒⠀⢀
⠀⠀⠀⠀⠛⠄⠘⡢⠍⣓⠒⠨⣍⠀⡀⠵⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠤⠼⠄⠺⠀⢴⠉⢊⠀⠀⢀⠗⠄⣀
⠀⠀⠀⠀⠀⠀⠘⠒⠈⠀⠀⠀⢈⠊⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢀⠇⠘⠰⠀⠀⢠⠀⢠⠇⠀⠀⣆⡔⠁⠀⠀⠀⠑⠤⠔⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⣠⠀⠀⠀⠀⠘⡀⠀⠀⠀⡀⢰⠀⠀⢠⠖⠃⠀⢠⠃⢠⠋⠀⠀⢠⠃⠈⠒⢤⠊⢀⡠⠊⠀⢸
⠀⠀⢀⣀⡀⠄⠂⢄⡀⢿⣿⣃⠘⣒⠟⠁⠀⠀⠀⢀⡴⠑⡀⠀⠀⠉⢡⠂⠀⢁⡞⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠖⠁⠀⠀⠀⠾
⠀⠀⡠⢬⣍⢉⣋⠁⠤⡙⡿⢃⠭⠒⢷⡤⠤⡀⠉⠉⠀⠀⠡⡀⡌⠑⠁⠀⠀⠎⠀⠈⢀⣀⡤⠴⠒⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠠⠊⠀⠣
⠀⠜⠀⢀⠀⠀⠀⠑⠂⠀⠞⠁⠐⠁⠀⠀⠀⠈⢢⡤⠂⠀⠀⢻⠁⠀⠀⠀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⠃
⠈⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠴⠊⢆⣤⡶⠟⠋⠁⠀⠒⠒⠒⠉⠀⠒⠂⠠⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠔
⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⡀⠀⠀⠈⡗⠒⠒⣀⡀⠀⠀⠀⢀⡠⠆⡀⠀⠀⢀⣀⡌⠢⡄⠀⢀⠤⢄⣀⠆
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠛⢦⠖⠃⠐⡞⠀⠂⠠⠬⢉⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠈⠂⠂
⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠑⢄⡠⠒⠛⠄⠀⢡⠀⠀⠀⠀⡀⠔⠒⢄⠀⢠⠊⠐⠂
⠀⠀⠈⠐⠂⠄⣀⣀⣀⣀⣀⣀⣀⣀⠠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡇⠀⠐⠈⠀⠀⠀⠀⠈⠁
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇
⠀⠀⢀⣀⡤⣤⣖⠒⠉⢉⣹⣼⣍⡉⠉⠓⠒⣤⣄⣀⣀
⢠⠞⠁⠀⠀⠀⠀⢑⠖⠁⠀⠀⠀⠈⠳⡔⠋⠀⠀⠀⠀⠙⢦
⡏⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀
⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠉⠲⣄
⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡤⠒⣫⣿⡿⡆⠀⠀⣄⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢢
⠸⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠯⠭⠚⠀⠀⠀⠉⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣸⠞⠑
⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⠀⠀⠀⢰⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣠⠗⢲⣴⡋⠀⣠
⠀⢱⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠠⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⠏⠀⡼⠁⣹⠖⠁
⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠱⡀⠀⠀⠀⡀⠀⠀⠘⠇⠀⠀⠀⢀⡠⠔⣋⠉⠓⢦⡀⢀⡼⠋⠀⠞⢁⡔⢉⣧
⠀⠈⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢦⡀⠀⠉⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⢿⡄⠀⠀⠱⡟⠁⠀⠀⣀⡤⠿⡏⢉⡧
⠀⠀⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⢀⣠⣮⠽⠦⠒⠒⠉⢻⡄⠀⠀⠀⢀⡀⠀⠈⠿⠀⠀⠀⣧⣤⡤⠼⠷⠖⠛⠋⠁
⠀⠀⠘⢆⠀⠀⠀⠙⣄⠀⠀⠀⢀⡤⠒⠉⠁⠹⠆⠀⠀⢀⠀⠀⠈⢿⡄⠀⠀⠈⢿⡄⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠉⠒⠒⠒⠋⠑⠒⠒⢞⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠈⠿⣀⣀⡠⠖⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣵⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣯⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢴⡦⣸⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠼⣇⣠⣶⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢤⣤⠘⢶⠛⠀⠀⠀⠀⠀⢀⣴⣶⠿⢿⠻⠻⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⢾⣶⣖⣼⣧⡸⢷⠀⠀⠀⠀⣰⡵⠋⠀⣬⢱⣤⡄⣸⠻⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠈⠢⠀⠀⠀⠀⠀⠀⠈⠳⠞⠁⠀⠀⠀⠀⣯⢃⠔⠚⣻⢆⡈⣿⠃⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠮⡅⠀⠈⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠁⢹⣧⣾⡿⡮⢱⣷⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠐⠒⠨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣽⣝⣳⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣶⢴⣀⡀⠀⠀⠀⠘⠤⠀⠈⠑⡄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠛⠛⠛⠉⠂
⠀⠀⠀⠀⠀⠀⢸⡿⡊⢹⣧⠀⠀⠀⠀⠀⠀⡴⠖⠁⠀⣀⣲⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣇⣧⠘⣿⠂⠀⠀⠀⠀⠀⠘⢆⠀⠀⠈⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢹⢹⣇⢸⡖⠀⠀⠀⠀⠀⠀⠀⠣⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢠⡤⠤⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣻⡂⢻⣠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡠⠄⣀⠀⠀⠘⠸⠾⠀⢀⣐⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣖⠳⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⠳⣽⣄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠚⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠉⠳⠭⣰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠛⠓⣢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡒⠶⡂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣅⡈⡩⠁⠀⣇
⠀⠀⠀⠀⠀⠀⢠⠄⠋⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⢀⠈⡎⠀⠀⠀⠈⠮⣀⠄⠀⠀⠀⠀⠀⠒⣶⡦⢐⠘⠃⡈⠀⣸⡿⣠
⠀⠀⠀⠀⠀⠀⡏⠀⡠⠂⠀⠀⠀⠈⠑⢜⠇⠀⠀⠀⠀⠄⠄⠈⠀⠀⠀⠀⠀⠀⠀⠫⠧⠀⠀⠀⢀⣰⡇⡈⡍⠛⠈⢡⡼⠋⣠⠎
⠀⠀⠀⠀⠀⢘⡇⡌⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡴⠀⠀⠀⠈⠓⠠⠤⢤⠴⠿⠯⠖⠋⠁
⠀⠀⠀⠀⠀⠈⠛⣇⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠈⢿⢆⢀⠀⠀⠀⠀⠀⢀⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠜⢿⡂⠀⠐⠒⡩⠞⠋⠀⠀⠀⠀⠀⠀⠈⠑⠉⣂⠀⠠⠔⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁

⠀⠀⠀⠀⢠⠆⠀⢀⠠⠤⢤⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠠⢀⠤⢲
⠀⢀⠀⠀⠀⠀⠀⢘⠉⠉⠉⡁⠀⠀⠀⠀⠀⢠⠕⠠⢀⡀⠀⠀⠀⠀⢠⠖⠉⠉⣐⣂⠤⠚⠚⠉⣰⠔⡇
⡠⠫⣻⠫⣀⠼⢟⣟⣀⣀⠀⠅⠀⠀⠀⠀⠀⠸⠀⠄⠀⠇⠀⠀⠀⠀⡄⠿⣴⡪⡽⢁⡠⢂⣲⡮⢔⡾⢃
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠧⠄⠀⠀⠀⠀⠀⠈⠲⢤⣉⣙⠚⠛⠕⢊⣉⣡⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⢀⣤⣄⡠⠊⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠰⢂
⠀⠀⠈⣷⠋⠀⢀⠀⠋⢂⠀⠀⠀⠀⢀⣀⠀⣦⣴⣋⣉⠖⢫⠀⢀⡀⠀⠀⠀⠀⢨⠛⠓⠚⠓⡀
⠀⠀⠐⡯⠒⠒⢒⠚⢓⢿⠇⠀⠀⠘⣄⣦⣏⣏⠁⠀⡘⡾⢞⢳⣿⡌⠀⠀⠀⠀⠸⣶⣦⣤⣾⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⣽⢧⢭⣋⠽⠶⢺⣭⣠⠵⢊⡇⠀⠀⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠱⣄⡀⢀⠀⣀⡜⠀⠀⠀⠈⢫⡑⠒⠦⠵⡀⢀⠾⠗⢚⡽⠁⠀⠀⠀⠀⠀⠇⠀⠀⠆
⠀⠀⠀⠀⠘⠛⠋⠛⠛⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠿⠿⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆
⠀⠀⣠⢴⠒⠒⢲⣤⠆⣰⡶⣢⠀⠀⠀⠀⠘⠣⣄⣀
⠀⡘⠁⡐⣰⡾⠋⡉⣞⠋⢞⠉⠀⠀⠀⠀⠀⡖⠋⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠢⢄
⢰⣷⣚⢿⣽⠀⠮⣀⠴⢀⣼⡆⠀⠀⠀⠀⠰⠛⠒⠒⠒⠚⢢⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡁
⠘⣟⠻⠿⢶⣿⣶⡶⠿⠟⢻⠇⠀⠀⠀⠀⢸⠸⣄⠀⣀⠆⡀⠀⠀⠀⡤⠎⢠⡀⠁⠀⠀⠀⠀⢁⠀⠘⠄
⠀⠘⢿⣒⠤⠄⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠑⢲⠛⡗⠊⠁⠀⠀⠀⠀⢇⠻⠿⠟⠀⠀⠀⠀⠰⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠠⠠⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠆⠰⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣀⠀⢀⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠐⠉⠀⠈⠋⡀
⠀⠀⠐⣧⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠀⠀⠀⠁⠁⠒⠦⠴⢤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠐⢿⣾⣿⣿⣿⣿⣿⣿⣾⣿⡶⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢰⣤⢬⣉⡅⡉⠽⠉⠿⠯⠶⠷⠳⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠘⠻⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠤⠽⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠄⠀⠀⢤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢄⠀⠁⡀⢠
⠀⠀⠀⠐⢪⣷⣻⠯⡑⠀⠳⠟⣓⡃⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⠹⠧⠃⡁⠤⠚⡤
⠀⠀⠀⠀⢸⡋⠚⠧⢵⠒⢲⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡜⣒⠙⠉⣀⢐⠸⡆⣀⡚⡀
⠀⠀⠀⠀⠀⣷⠋⠠⢈⣵⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡟⠻⡶⢄⠻⣯⠑⣾⡟⢘⡟⣾
⠀⠀⠀⠀⠀⠘⣆⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢛⢯⠟⣾⣠⣿⣯⣽⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠁⠚⠾⠉⠒

⠀⢀⡀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠤⠄⡀⠀⠀⠀⢀⡀⠀⠀⠀⡀⣠⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠄
⠀⠘⠀⠀⠀⠀⠀⠈⢄⠀⠰⠁⢀⠀⠉⠆⠀⠀⠌⠠⠊⠠⠀⠟⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠈⠀⠡⣈⢀⡄⠐⠰⣲
⠀⠀⠐⠀⠐⠀⠀⢉⠣⠀⠀⠣⡀⠈⠀⠈⠆⠈⢠⠴⡀⠊⠀⠀⠀⠂⠀⠠⠀⠄⠀⠁⠀⠀⡠⠁⠀⠒⠄⠀⠉⠉⠀⢐
⠀⢀⠀⣋⡀⠀⠀⠀⠈⣀⢀⢀⠈⠒⠈⠄⢀⡴⠀⡯⢚⠁⠀⠀⢠⠐⠂⡐⠠⢀⢀⠀⢀⠜⠀⢣⢄⣀⡀⠀⠀⠀⠤
⠀⠘⠀⠀⡆⠀⡠⠊⡁⠀⠃⠂⢌⡑⢄⠀⠸⠋⠀⢸⡵⠀⠀⢸⠃⠀⢀⡅⡀⠘⠄⠐⠁⢀⠀⠠⣀⡀⠀⡀⠠
⠀⢠⠖⢦⠀⢄⣠⠒⡂⢜⣊⠼⠓⢊⠁⢠⠒⠒⠤⡀⠃⠀⠀⠀⠁⠨⠉⠁⠀⠀⠀⠀⠠⠂⢤⠀⠠⠀⠀⠁⠀⠈
⠀⠀⡆⣈⢂⠀⠀⠀⠀⠒⠒⠒⠈⠁⠀⡌⠀⠀⢰⠀⠰⢠⠀⠀⠂⠆⠀⢀⣴⣶⢻⣟⣳⡆⠀⡀⠀⢀⠀⢀⡰⠉⡘
⠀⠀⡄⠂⢠⠀⠀⠀⢖⠒⠀⠠⠀⢲⠆⠑⠀⠲⠈⠀⠀⠁⠃⠀⠀⠀⠀⢀⢀⠽⠉⠉⠉⠉⠀⠀⡀⠐⠀⠀⠉⠉
⠀⠀⠈⠉⠁⠔⢄⠀⡄⠉⠀⠒⠀⠁⢀⠀⣴⡢⡄⠀⠠⠀⠀⠀⢀⠖⡆⠀⠀⠀⠀⠍⠀⠁⠀⡀⠃⠀⠀⡔⠉⢆⠁⢠
⠀⠦⠀⠀⠈⠀⠀⠀⠀⢀⠀⢈⠈⠡⠏⠓⢉⠠⠣⢶⠠⢅⢤⡤⠀⠀⠀⡀⠈⣁⠀⠈⠈⠀⠂⠀⠀⠀⠨⠀⡠⠊⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠀⠂⠈⢀⣐⣃⡠⠤⠗⢉⠀⠀⠀⠀⠰⠀⠀⡀⠼⢑⠀⠉⡂⠲⢀⠑⢀⡱
⠀⠀⠐⠀⠘⢀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠀⠈⠉⣤⠀⠀⢘⠭⠁⣀⠀⠐⣁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢈⠀⠀⠀⠎
⠀⠐⠂⠀⠀⡠⠄⠀⠀⠊⢟⠀⠀⢠⠶⠛⠉⠐⢹⣶⠄⠈⡠⠀⠀⠀⠀⠈⠀⢠⠄⠀⠀⠀⠀⠀⠀⣡⠀⠀⠘⠀⠂⠄
⠀⠰⠠⠍⢀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢈⠠⠒⠀⠀⠀⠀⠉⠉⠉⠈⠐⠡⠄⢀⣀⠀⠂
⠀⢠⠀⠀⡀⠄⠈⡆⡕⠀⠈⠀⠐⠀⠀⠠⠒⠃⠀⠀⠀⢰⠀⠀⠀⠌⠀⠀⠄⠠⠏⠀⡀⠀⢀⠠⠀⠀⠙⠇
⠀⠀⠀⡀⢀⡄⠀⢡⠁⢀⡀⠌⠀⡄⠂⠂⠀⠀⠀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡰⠒⠀⠀⠒⢅⡀⢀⠰
⠀⠠⠐⠊⠸⠈⠆⠈⢀⠡⠀⠀⠦⠠⢖⠀⠀⠀⠈⠁⠀⠈⠀⠐⠀⡄⠀⢠⠂⠉⠀⠀⠀⠈⠀⢀⠜⡀⠀⠀⢻⠧⠂⠁
⠀⠀⠠⠨⠄⠀⠂⠀⠀⠒⠈⠀⠀⠀⠀⠄⠀⠀⠀⠠⠒⠃⠀⠀⣀⠀⢌⢀⠢⠤⠬⠔⡀⠤⠔⢊⠈⠃⡀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠈⠠⠂⠀⣀⡀⡔⠒⠒⡆⠀⢢⠀⠐⠀⠀⠁⠀⠈⠀⠠⡈⡀⢄⠀⠠⠀⠈⠀⠀⠀⠀⠐⠁
⠀⢀⡀⠐⠀⠀⠀⠀⠂⠄⠁⠀⠀⠘⠄⠂⢘⣀⣸⠀⠀⡀⠀⠐⠄⢤⠆⠀⠀⠈⠚⠁⠡⠊⠈⠠⠁⠀⠤⠀⠐⠀⠒⢤
⠀⠀⣠⡶⢀⡶⠀⢀⠀⠃⡀⠂⠈⠠⠀⠀⡀⠄⠠⣀⠀⠀⠘⠀⢀⠀⠀⠀⠃⠀⠠⣀⣠⣤⠄⠀⠀⠀⢄⠀⠀⠀⠀⠔
⠀⢸⣆⠅⠊⠀⡀⠁⠀⡂⠀⠀⡀⢊⠀⠌⡠⠊⢉⡉⠠⠀⠈⠠⠊⠀⠀⠀⠁⠀⢀⠜⠈⠡⡀⠀⠀⠀⡈⠀⠈⠁⠁⢠
⠀⠀⠁⠂⠀⠀⠃⠀⠀⠈⠀⠉⠀⠈⠀⠋⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠉⠀⠒⠠⠤⣀⡀⠀⠀⣠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⡙⠀⠀⢘⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⢀⢀⠄⣀⡀⠀⠀⠀⠀⠁⠀⠀⣀⣠⠷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⣀⡤⢤
⠀⠀⠀⠀⣷⠀⠀⠠⠂⠀⢼⡃⠀⠀⠀⠀⠀⡜⣧⠀⠈⠉⠉⠉⠉⠉⠉⠩⣿⡏⠸⠀⠀⠀⠀⡀⣀⣀⠈⢡⠀⠀⠈⠀⠀⣰⠟
⠀⠀⠤⠚⠁⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢡⢹⣄⠀⠀⠀⠀⠀⠀⢀⣾⡟⢡⠃⠀⠀⠀⢠⡏⠀⠈⠉⢸⠀⠀⠀⠠⠰⣯⡀
⠀⠀⠀⠀⠀⠀⣧⠀⠁⠈⡟⠁⠀⠀⠀⠀⠀⠀⠣⣙⢆⠀⠀⠀⠀⠀⢼⠟⡠⠃⠀⠀⠀⠀⢀⢇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⠃⠀⠀⠀⢰⣿⡏⡆⠀⠀⠀⠀⠀⠀⠊⢢⠀⠀⣸⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣸⠀⠀⠀⠀⠀⢵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠄⠀⠀⠀⠠⢾⠟

⠀⠀⠀⠀⠀⠄⢠⣶⡒⠂⠀⣀⠖⠒⠂⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠇⣽⣂
⠀⠀⠂⠀⠀⣰⠟⠁⠀⠀⡸⠃⠀⠀⠰⠋⠀⠀⢸⣖⠄⠀⠀⠀⠀⡴⠊⠉⠀⠀⠀⠀⠀⠉⠃⠠
⠸⣿⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈
⠀⠉⠙⠒⠂⠒⠀⠀⠀⠀⠰⠒⠀⠶⠶⠦⣶⡶⠿⠟⠋⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠼⣇⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠁
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢿⠈⣧⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢀⢞⣵⣺⢦⠀⠀⠀⠀⠀⠁
⠀⠠⠶⠶⠆⢱⢰⢄⡆⠀⢁⣒⣂⣂⡤⠀⠀⠀⢸⡄⠸⠂⠈⡦⠀⠈⠈⣁⡀⠀⠀⠀⠀⡴⣩⢟⣾⡽⠃⠀⠀⠀⠀⠀⣰⡞⢹⡆
⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⢧⣄⣥⠔⠃⠀⠀⠉⠁⢀⣨⠀⠀⠀⠈⠉⠺⠋⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣄⠓⢀⡄⠀⠐⠳⢿⣾⠟⠃⠀⠀⠰⢀⡁⠂⢀⡄⠀⠀⠀⣾⣶⣶⡿⠆
⠀⠀⠀⠈⢀⡀⠀⠀⠀⢀⢰⡁⣼⠂⠁⠀⠀⠀⠙⠇⠀⡠⠊⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⣰⡾⠁⡤⠀⠙⠀⠀⠀⠀⠨⠙⠂
⠀⠀⠀⣀⡘⠁⠀⠀⠀⠘⠀⠀⠤⠖⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠡⠤⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠸⠉⠃⠀⠀⠀⢀⣈⠁⠚⡆⢀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠐⡷⠀⠀⠀⠀⠀⡐⠀⠀⠙⣷⡀
⠀⠀⠀⠀⢠⣆⣠⡀⠀⢰⡁⠂⠀⠀⠀⠸⠀⠀⠉⠂⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡄⠀⠀⠨⠽⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⠉
⠀⠀⠀⠀⠰⢷⡽⠂⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠋⠁⠀⠀⠀⠀⠐⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠰⠆⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠙⣡⠀⠀⢀⠀⠆⠀⣢⠴⠁⢀⠀⠀⠠⠀⠰⠀⠀⠠⠶⣶⣶⠶⠢⣤
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⠀⠀⣠⠀⠀⠀⠀⢠⡄⠀⠠⣀⡝⠀⠐⠶⠀⠶⠋⠁⠀⠀⠰⠠⠆⠀⣤⠄⠀⠀⠀⠃⢄⠀⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⠀⡀⠛⠀⠀⢀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠂⠉⠻⠃⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢀⣾⣠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠤⠊⠀⠀⠀⠀⠀⠚⡄⠈⠒⠀⠀⠀⠀⠀⢠⡄⣤⡈⡷
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠓⠃
⠀⠀⠀⠐⠗⠀⢀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⣄⠀⠀⠀⢀⠀⡀⠀⠠⣿⡟⣭⡛⣷⠀⠀⠀⠀⡴⢤⠀⠀⠀⠀⠛⠃⠀⠀⠛⢃⠀⠀⣬⠃⣠⣥⣀⡤⣀⠀⣠⣾⠿⢶⠃⠉⠁
⠀⠈⠻⠿⠾⠿⠟⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠰⣤⣀⣀⡤⠂⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⡁⠘⣹⠃⣸⣇⡼⠃⠈⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢺⡆
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣶⠆⠀⠀⠀⠘⢻⣟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠆⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⢐⣠⣖⡀⠀⠀⠀⠀⠀⣤⡀⠀⢀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⢠⠐⡂⠈⢤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠹⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀
⠀⠀⠀⠦⠀⣠⡖⠀⠀⠠⠤⠤⠈⠛⠀⠀⠀⢠⣘⣿⣦⡈⠂⠀⠀⠀⠀⣄⠀⢳⡄⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⣤⠤⡤⠤⠆
⠀⠀⠀⠄⠙⢄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠏⣹⠙⣽⠆⠀⠀⠀⠂⠛⢰⠊⠀⠀⠀⠸⠛⣀⡀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠢⣤⣤⡤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠠⣶⠄⠀⠀⣀⡀
⠀⠀⢉⣡⣤⡄⠀⠀⠀⢠⠀⠀⠘⠆⠀⠀⢀⣤⠶⠟⠋⠉⠀⠀⠀⠂⠀⢰⣌⡉⠀⠀⠀⠀⠉⢉⡁⣀⢃⠀⠀⠀⠀⠄⠀⠩⠃⠼⠂
⠀⠀⠈⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠟⠀⠀⠀⣱⣷⠶⠶⠷⠊⠀⠀⠀⠀⢠⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠛⡙⢻⡏⢉⡟⢛⣏⠋⣹⡿⣻⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠔⠓⢆⡀⢐⣦⣠⠼⠷⡖⠀⠀⢀⠠⡾⠀⣤⣤⣤⣭⣥⣀⣀⡀⠀⠀⠘⠿⠃
⠶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⢶⣮⣷⢶⡚⠙⢯⣀⣈⣶⣤⠀⠀⠀⠀⠀⢱⠀⢒⣒⣒⣿⣿⣿⠿⠇
⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣧⠟⢾⡉⠉⢳⣄⡈⠀⠀⠠⠄⠀⠀⠀⢴⠚⠛⠩⠉
⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠺⠗⠀⠀⠀⠀⠀⣿⠶⠖⠛⠛⠩⡈⠀⠐⡀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣶⢆⣶⠁⢀⣀⠄
⠀⠀⠀⠀⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠰⠷⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⢸⣿⡆⢰⣿⢸⠇⣴⣿⣿⣿⣦⢠⡀
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡭⠋⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⣾⡄⢿⣿⣿⣿⡿⢰⡿
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣾⢿⣁⠀⠀⠙⠿⢦⣽⡿⣿⡁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠈⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⣤⣤⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⣠⣄⣠⡀⠀⠀⢀⡀⠂⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤
⠀⠀⠸⣆⠁⠠⠃⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣶⣿⡂⠀⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠘⠃⠀⠀⠀⢰⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⢸⡭⢽⡗⠒⠒⠂⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⡗⠐⠒⠀⠀⠀⠀⣰⣟⣻⣿⣿⣳⡄⠀⠀⠀⣠⣄⠀⢀⣤⡀
⠀⠀⠀⠀⠀⣄⢀⢠⠀⠀⢀⡴⢳⡄⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢫⣿⠿⣧⡿⢿⠇⠀⠀⠀⠛⠛⠀⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⣧⠀⠀⠀⠁⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢻⡀
⠀⠀⠀⠰⠶⠶⠶⠖⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠏⡳⠿⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⢿⣿⣿⡿⠰⠁⠀⠀⠀⠀⢠⣀⣤⣀⣤⣀⣤⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠻⠆⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠛⠉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣿⣿⣿⣿⢀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠛⠒⠿⠿⠿⠿⠿⠿⠿⠗⠛⠓
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⡄⠀⠀⠀⢀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⢠⣤⣤⡀⣀⣀⣀⣀⣀⣠⣤⡀⠀⠀⠀⢸⣿⣿⡇⠸⠿⠿⠿⠀⠀⠀⠀⣿⣷⣶⣦⣤⣶⣶⡆⠀⠀⠀⠀⢠⡶⡄
⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⡿⠀⢿⡀
⠀⠀⠘⠟⠿⠃⠻⠟⠻⠛⠟⠛⠿⠃⠀⠀⠀⠘⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠈⠀⠀⠦⠀⠀⢘⣺⣄⡠⢀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠄⣠⡁⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠀⠋⠀⠀⠐⠀⠀⠀⠀⠀⢀⠘⠛⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⢀⠀⠀⡆⠀⠠⠘⢥⠽⠀⠀⠀⡀
⠀⡀⠀⠐⠀⢠⠀⠒⠈⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠠⠄⠀⠀⠀⠀⢀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠰⣷⢄⠀⠀⠂⠀⠁⠀⢠⡇
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣊⢄⠀⠀⠀⠐⢜⢃⡀⢀⣀⣐⣤⡤⢊
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠑⠈⠉⣓⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠈⠀⠀⠀⠈⠆⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠄⠀⠀⢀⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⡀⢊⠀⠀⠀⠀⡊
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢈⡠⠀⠀⠀⠉⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⠀⠀⠀⠀⠐⠊⠀⠀⠐⡀⠀⠀⡰⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠠⡀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡉⢉⡒⡄⠀⠀⠀⠐⠠⠀⠀⠀⠀⣄⡠⠉
⠀⠀⠀⠀⠀⠤⢤⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⡄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠺⠀⠀⠈⢶⠀⠀⠈⢱⠂⠐⠒⠒⠋⠁⠄⠀⡇
⠀⠀⠀⠀⠀⢠⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠢⣄⡀⠐⢆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠃⠀⠘⠀⠀⡠⡧⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠉⠘⣆⡀⠀⢀⠀⠲⡄⠀⠐⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠄⠼⠀⠀⠀⠀⠀⠀⠀⢌⠢⣄⠐⠀⢀⡴⠤⢛⢽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠛⠐⠒⠂⠈⡼⠀⠀⠀⠀⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⣀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⣠⠀⠑⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣠⠞⠁
⠀⠃⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠛⠫⠄⠀⠀⠁⠀⠐⠤⢀⣀⣀⡠⠴⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠘⠀⠀⠘⠋⠀⠠⠀⠐⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⣰⠀⠀⠀⠀⣠⠄
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠦⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣛⡛⠛⠓⠒⣀⣈⣭⡷⠤⠤⠤⠶⠶⠤⠤⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⣉⡭⠶⠛⠩⡭⠀⠰⠖⠀⣤⠀⠛⢁⠀⠀⡀⠀⠀⢀⠈⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠚⣁⠀⠘⠀⢤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣞⠷⢽⠆⠀⠀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢒⡀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⣁⣤⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠴⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠈⢧⠀⠀⠀⠀⠛⠛⠛⠊⣩⠇
⠀⠀⠀⠀⠀⢀⡴⢻⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠤⠒⠂⠀⠈⠁⠀⠀⠈⠃⠀⠀⠀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⣾⠄⣸⠀⢀⡴⡒⠂⠀⠀⣀⡤⠴⠖⠒⠛⠳⣉⣄⣀⡴⠶⠶⠶⠶⠖⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠹⣮⣿⠀⠸⣥⣢⠔⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢰⠋⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⠇⠀⣌⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⡠⠔⠃⠀⢦⣈⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢄⠀⢦⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠈⣆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠦⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠠⣶⡄⠀⠀⣧⠶⠛⠛⠉⠉⠉⠙⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⢀⣀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣀⣀⣀⣀⣀⣠⣴⡾⠛⡅⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢿⢻⠛⡟⢻⢻⠛⠙⢹⡇⢀⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⡶⡟⣿⢷⣤⡾⣿⠀⡇⢸⠘⡀⡇⢸⣈⣀⣠⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⣴⢿⠉⡏⢻⡇⣧⢸⢸⡈⡇⢸⣀⣷⡾⠟⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠶⠾⠿⠟⠛⠁⠀⠀⠀⠘⠃⠀⠀⢠⣴⣿⣾⡄⢇⢸⣧⣼⣼⣤⣇⣧⡾⠛⠁
⠀⠀⢠⡶⠋⠁⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢳⢸⣿⣧⣼⣼⣿⠁⠈⠙⠛⠋
⠀⢰⡟⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠙⢿⡜⢿⡏⠀⠈⠉
⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⣠⢾⣷⠟⠋
⠀⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⣼⣷⢸⣿
⠀⢸⣷⢹⠛⡿⢿⡿⡷⢶⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣼⡿
⠀⠀⠻⣿⣄⣧⠘⡇⡇⢸⢼⣧⠀⠀⠀⠻⠇⠀⠀⠀⠀⢀⣾⣿⠋
⠀⠀⠀⠈⠙⠛⠿⠿⠿⠾⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⡿⣶⣤⣤⣀⣤⣴⡿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡇⠀⡏⢹⠉⢻⠈⡇⢣⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣷⣬⣦⣼⣤⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⢀⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡀⠀⢀⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠢⢤⠀⢠⡠⠀⠀⣠⢀⡲⠶⠔⡉⢅⠉⠀⠀⢭⡉⠐⠦⡀⠀⠀⠀⠀⠨⠤⢉⡀⠄⠠
⠀⠀⠀⠀⠀⠠⠔⠀⠐⠀⠼⡋⠉⢹⠈⠑⠐⣀⠤⣶⣧⠴⠄⠊⢠⡦⢆⡷⠀⠽⠀⠀⡔⣩⣉⢀⡀⠴⣾⠇⣐⠀⠀⠀⠀⠤⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢄⠙⠟⠛⣆⣉⡔⣀⡠⣔⣎⠰⠤⠚⠁⠀⠀⠀⡂⠉⣁⠉⣠⣤⣀⠅⠉⣠⠒⠷⠦⠊⡶⠀⠒⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⢆⠤⣄⡀⢌⡨⢵⠀⠌⢰⡀⢠⠰⠞⠁⠠⢁⣄⡘⠿⠈⡃⣠⠈⡛⢲⣋⡴⢣⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⠈⠔⠂⡀⠰⣄⣈⠐⠀⡤⠃⠤⣈⣧⡀⠧⠭⠀⣀⣤⠃⠀⠉⠉⢉⠔⠁⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠀⠢⢄⡄⠀⠐⠃⠀⠎⠙⠛⠛⣛⠉⡑⣲⠐⢀⣣⠀⠀⠀⡀⡄⡀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⠐⢠⡠⠖⠀⠴⠆⣤⣤⣠⣤⠅⡥⢨⠟⠀⠀⠀⡆⣆⡗⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣄⠒⠒⠂⡠⢀⣐⡐⠲⠔⠒⠚⢖⠦⠚⠃⠀⠀⠀⠃⠓⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⢀⠀⠀⠀⠀⠀⠈⠒⠀⠄⠀⠀⠀⠀⠀⠐⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠍⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡀⠀⠀⠀⠀⠈⣀⠤⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠐⢉⠁⠀⠀⠀⠈⡒⠰⢂⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠁⠀⠀⠂⠄⢀⠀⠀⠀⡀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠻⣺⡷⠲⠦⣄⠀⠀⣴⠞⣉⡀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡶⠻⠋⠁⠀⠀⠈⣧⠀⢷⣻⣭⣽⣳⣎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢈⡿⠁⢸⡟⠋⣠⠴⠚⠛⠛⠛⠓⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⢧⠀⡀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠓⠒⠛⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠙⠛⢛⠲⣌⠛⠦⣤⣤⡤⠖⠋⠀⢀⣠⣤⠶⠶⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⠐⡀⠁⢸⡆⠀⠀⠀⢀⣀⠀⣴⠛⠁⠀⠀⠀⢹⡆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⠞⠀⠀⠀⢀⣿⣽⠀⢿⡀⠀⠀⠀⣀⡼⠃⢸⡇⠀⠀⠀⠀⠀⢀⣠⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢺⠟⠟⠀⠀⢀⣰⠏⢀⢸⠇⠈⠳⢦⣴⢾⢿⠁⠀⣼⠁⠀⠀⠀⣠⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠶⠒⠚⠋⠡⣐⡵⠋⠀⠀⠀⠀⢾⣤⡼⠇⢸⡃⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⣲⣶⣶⠿⠭⠶⠶⠶⠶⠶⠶⠶⠶⢶⣦⡼⢋⣿⣾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠉⠁⠀⠀⢀⣀⣀⣠⠴⠛⣧⠀⠀⠐⣏⣉⡀⢻⡅⠀⠉⠙⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠐⠀⠀⠺⣥⡉⣀⣀⣸⠏⠀⠀⠀⠈⠙⠷⠾⠃⠀⠀⠀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠉⠛⠲⠶⠭⣤⣬⣉⣙⣉⣁⣀⣀⣀⣈⣁⣠⣤⡤⠤⠶⠒⠋⠉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠶⠷⠼⠾⠶⠶⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠠⣠⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⠀⢀⡀⠀⠘⣧⡄⢠⢰⠒⠒⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢣⠀⣧⠀⠈⠁⠀⠀⠸⡿⠜⠚⠓⢤⡄⠀⠀⡄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⡀⠘⢧⡀⠠⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⣸⡿⠆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⢀⣀⠈⠙⠓⠘⠂⠛⠐⠚⠛⠛⠋⠈⠁⣀⠠⣀⠀⠀⠀⠈⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⣸⠤⠀⡰⢧⠀⣏⡁⣰⠋⠳⣤⡏⠉⢣⢹⠀⢘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠓⠂⠰⠉⠹⠀⠇⠀⠹⠤⠴⠃⠳⠤⠊⠈⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠛⠛⠛⠒⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀
⠀⠀⠀⣀⣴⣬⡽⠿⠲⣷⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢂⠀⠀⡠⣄⠀⠀⣀⢀⢀⠀⠀⠀⢠⣤⣤⡀
⠀⠀⢨⣏⠙⠒⠂⠉⢁⢹⡆⠀⢀⠞⠁⠀⠀⠀⠀⠀⠢⡑⠄⠀⠀⠀⡠⢤⠤⡀⠀⠀⢨⠀⣯⠀⡎⠀⠹⡇⠀⢟⣏⡮⠁⠀⠀⢸⠁⢩
⠀⠀⠀⣾⠐⢒⣈⡉⠤⠄⣿⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠇⡘⠀⢀⠎⠀⠀⠱⣑⡀⠀⠈⠄⢸⠀⠘⠢⡔⠁⠀⢣⢠⠚⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢹⡁⠤⠤⠐⢒⡀⢸⡀⠀⠘⠢⠤⠤⢤⠤⡤⠤⠊⠀⢠⠃⠀⠱⠓⠀⠈⢷⡀⠀⠇⣨⡇⠀⠆⡇⠀⠀⡆⡈⠀⠀⠀⡠⠃⠀⠀⣷⡄
⠀⠀⠀⠀⡷⠖⠬⠵⢂⣒⠭⠇⠀⠀⠀⣇⣂⣈⣀⣁⣀⠀⠀⠧⢤⣦⣤⣤⣤⡤⠬⠇⠀⠀⢐⣠⠀⢁⡇⠀⠀⢇⠇⠀⠀⠀⠧⠤⠤⠤⠬⠬
⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀⠀⢸⠀⠠⡤⡂⠀⠈
⠀⠀⠀⠀⠀⣀⠤⠄⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠉⡉⣿⣻⣉⢉⣉⢉⣏⣟⣉⡉⠉⠉⠀⠀⢸⠄⢈⣀⣀⡀⢤
⠀⠀⠀⡠⢊⡤⠊⠉⠉⠁⠢⡑⢄⠀⠀⠀⠀⣠⣖⠉⡄⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠉⢁⣴⠞⠛⢶⡌⠉⢳⡇⠀⠀⠀⠀⠈⣄⣀⠀⠀⣀⡄
⠀⠀⢰⢁⢋⠔⢲⡄⣀⢀⢀⠘⡘⡄⠀⠀⡐⠕⠁⣼⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢸⣵⣶⢠⣤⣯⠀⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⠘⣇⠀⢸⠅⣋⣿⣸⢀⢃⠃⢀⠤⠥⠤⠤⡤⠤⠶⠶⠶⠶⠶⠼⠤⡀⠀⠀⠀⠀⢻⡧⠤⣿⠃⠀⢸⡇⠀⡆⡶⡆⣖⢆⡶⡠⡆⢒⡞⡄
⠀⠀⠀⠣⣩⢲⠉⠀⠳⡄⡵⢋⠜⠀⠈⠋⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠁⠀⠂⠓⠒⠀⠁⠀⠈⠀⠒⠃⠇⠀⠥⠥⠥⠭⠭⠤⠥⠥⠭⠗⠃
⠀⠀⠀⠀⡄⡸⠭⠉⠘⠃⡆⠁⣠⡎⣙⢢⠀⠀⠀⢀⣀⣀⣀⠠⠤⢒⠒⡄⠀⠀⢠⠒⠒⠂⢐⣒⡦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠳⠁⠀⠀⠀⣄⠃⠀⢟⢲⠲⢽⠂⠀⠐⠁⡜⡐⢠⢰⠀⠓⢁⡿⠀⠀⢨⣠⡤⠤⣤⣤⡄⠀⠀⣠⣴⣡⣤⣤⣤⣤⣤⣤⣤⣼⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠈⠀⡌⠀⠀⢻⣄⣀⠃⠘⣀⡡⢴⡩⠎⠀⠀⠘⡇⢀⣰⣿⢷⡇⠀⠀⠇⠊⣠⠤⣄⡤⣤⡤⢠⣄⡌⢱⠈
⠀⠀⠀⣀⠤⠤⠤⠠⣄⠀⠀⠈⠙⠋⠙⠁⠀⠀⠈⠑⠣⠷⠾⠐⠋⠉⠀⠀⠀⠀⠀⣷⠻⠿⠀⣸⡃⠀⠀⡏⢇⢙⠖⢋⢋⡘⠧⠘⠘⢃⡼⢋
⠀⠀⠀⡗⠒⢀⡀⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠋⠉⠙⠋⠀⠀⠀⠁⠂⠐⠀⠂⠀⠂⠀⠀⠒⠀⠒⠁
⠀⠀⢠⢸⠟⠂⢒⠘⡇⡀⠀⠀⡏⡇⠤⠤⠤⠤⠴⠥⠭⠽⠥⠵⠤⠤⠤⠤⢄⢈⢸⠀⠀⠠⠒⠊⣑⣒⣉⣓⠒⠤⢦⡠⡀⠀⠀⠀⣀⣀⡀
⠀⠀⠈⢌⢆⡀⢀⠰⡱⠁⠀⠀⡇⡇⠉⠉⠉⠉⠉⠉⠛⠙⡏⠉⠉⠉⢉⠉⠁⡀⢸⠀⠀⡸⢊⠉⡇⢂⢠⢠⠈⡑⠤⣰⠗⡂⠀⠮⠄⠄⠽⡀
⠀⠀⠀⠀⠑⠲⡖⠈⠀⠀⠀⠀⡇⡤⠤⠤⠈⡆⠀⠀⠀⠀⡇⠀⠀⢸⢠⠀⠀⠄⢸⠀⠀⡣⣀⠀⡇⠸⠸⠸⠀⣃⡴⠳⡀⠅⠀⡟⢻⠙⠋⡅
⠀⠀⠀⠀⠀⣨⣇⡀⠀⠀⠀⠀⡇⡇⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠀⠀⢸⠀⠀⠉⠢⠽⢓⡒⣒⡲⠩⠔⠁⠀⠈⠁⠀⣆⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠈⠈⠁⠀⡴⢌⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠊
⠀⠀⢠⢰⠰⣠⠤⠤⢤⡴⠖⠚⠛⠉⠀⠀⢀⠤⣒⠒⠀⡰⠖⠉⢳⠁⠀⠀⠀⠀⠀⠀⠀⢴⣶⡖⢲⠮⠅⠒⠀⠀⠀⠀⠀⠀⣀⢴⣂
⠀⠀⡬⠤⠤⠤⠥⠬⠭⠤⢤⠀⠀⠀⠀⡴⢁⠞⡝⠀⠀⡁⠀⣁⠎⢡⠀⠀⠀⠀⠀⠀⠀⠨⣿⠗⠃⠀⠀⠀⠀⠀⠀⠀⢀⠏⠙⠒⢋⣉⢶
⠀⠀⢇⢆⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⡇⠘⡄⠙⢦⠀⠈⢉⠡⢂⠜⠀⠀⠀⠀⡠⣺⣟⣻⣻⣿⣛⢷⢦⠀⠀⠀⠀⠀⡼⠔⢚⣉⡡⠤⠚
⠀⠀⢠⡓⠕⠀⠀⠠⠤⢺⡄⠀⠀⠐⢄⣉⣀⣈⣉⣉⣀⣀⣁⣈⣉⡰⠂⠠⡆⠐⠓⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⡤⠀⠀⣇⣐⣁⠬⠤⠒⠋
⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡰⠃⡤⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡼⢡⠞⡤⢊⡴⣉⠖⡢⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢡⢮⡀⣇⢼⠤⢋⠜⢡⢊⢔⡥⣢⢭⡢⡄⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⠻⣿⣿⣿⡫⠻⣟⣟⣿⡿⡾⢾⣷⣦⣔⡃⠀⣠⣦⣢⢀⠌⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⣀⣤⣾⡿⣻⢫⠂⢌⢯⣿⣿⠑⡁⢞⣿⣿⡥⡁⣡⣿⣿⣿⣿⡿⡻⣶⣿⣵⣫⣪⣶⡏⡂⠀⠀⠀⠀⠀⠀⢀⣤⢞⠤
⠀⠀⣀⡔⣺⢋⣠⡀⠀⠉⠑⠪⠦⠲⡻⢿⠙⢈⢜⣿⣿⣽⢉⠱⢻⣿⢿⣷⣜⡜⡹⣿⣿⡯⣹⣻⣦⣤⡤⣄⣤⣤⡤⣴⢻⡷⢓⡀
⣴⠞⢅⠐⠧⣩⠌⢀⠀⠆⠰⣤⡁⡀⡁⡀⠎⢎⢌⢾⣿⣧⢆⢄⠑⣿⣿⡿⡈⢬⢹⣿⣿⢟⠿⠿⣿⡿⠴⢿⣾⢿⢷⢽⢩⣿⠳⠔⠺
⠉⠲⡃⠙⣶⠘⠇⡻⠀⠀⠱⠒⡀⠈⢲⣴⡟⠂⠀⠂⡛⠔⡥⢣⢎⣼⣿⡱⠵⡱⡸⡿⡯⠪⢣⡣⣋⣥⡮⠵⠒⠘⠒⠦⣽⣿⣟⡑⠂
⠰⠤⢽⣟⣏⡫⠘⠱⢖⡋⠀⠀⠼⡐⣿⣍⡉⠀⠀⡰⣝⡬⡺⣔⢵⢟⣃⡌⡬⡪⠨⠈⣎⣶⡵⣾⠾⠻⢦⠔⠀⠀⠀⠀⠈⠳⠦⣳⣔
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⣂⣄⣨⢚⡥⢂⢙⠣⢑⠡⢰⢡⢊⡊⣗⣬⣮⣬⠧⠿⠒⠋⠉⠋⢉⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠛⣛⣩⠍⣉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣻⣞⢿⠣⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘⡲⠀⠙⠉⠛⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠘⣂⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠓⢂⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜⠀⡄⠀⡷⢶⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⠀⠀⠀⢐⡖⠀⠋⢉⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠀⠁⣈⠐⠀⢀⣠
⠀⠀⠀⠀⠀⠛⠋⠁⠖⢠⡻⡄⠹⠁⠀⣠⣤⣤⣬⣠⣬⢇⣾⡤⣏⣀⣤⣀⢠⣆⠁⠀⠀⡼⠃⡤⠴⠛⢉
⠀⠀⠀⠀⠀⠘⠂⠀⠈⠀⠐⠳⠠⠀⡀⣈⢳⣿⡾⢫⡇⠉⣻⣿⡀⠘⠀⢇⣸⣿⣿⡿⢰⣣⣄⠄
⠀⠀⠀⠒⠉⠁⠉⠡⠦⠀⢠⡀⠀⣾⠑⠟⢈⣣⡆⣼⡟⠛⠻⣤⡠⠾⠟⠃⠙⡟⠒⢴⢿⣏⣥⣖⣴⢂⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠙⣴⣯⣰⢷⡴⡄⠀⠈⢢⣼⠾⠿⣷⣼⠦⣤⣴⣾⣶⣶⣾⣿⠛⠛⣿⣿⣋⣀⣤⢀⡖⠁
⠀⠀⠀⠀⣀⡀⢈⠀⠀⠠⢀⢀⠁⢼⣿⣿⣿⠽⣦⡰⣮⣄⢀⣄⠩⣿⠐⢋⣴⣿⣿⡿⢿⡿⣿⢿⣿⣷⣿⣿⠷⠲⠄
⠀⠀⣴⣾⣿⣿⠂⠀⣤⡀⠀⣈⣳⣂⣸⣿⡇⠀⣙⠀⠀⠰⣿⣿⣿⣃⡴⠿⠛⠉⣿⣧⣿⠁⢻⣦⢿⣿⣿⣶⣶⣙⣆⠂
⠀⠈⣟⣤⣌⠉⣶⡀⠋⢙⡿⠉⠉⢩⣿⣿⣇⠀⢩⠀⠐⠘⢌⠉⠷⢛⣷⣦⣴⣾⠃⠀⠀⠲⣾⠏⣉⣉⣨⢉⠛⡁⢫
⠀⠀⠙⠛⠁⠀⢲⡄⣴⣾⣿⠆⠀⠀⢁⡀⠈⠳⣦⠀⠀⠀⠈⢰⡶⠋⣹⣥⣿⣿⣄⠀⠀⣽⢧⣼⣏⣩⣿⠇⠈⣁⣠⡄
⠀⠀⠀⠄⠀⡀⢼⠗⠰⢾⣁⠊⠀⠀⠀⣋⡙⠆⢠⡀⠠⢤⡈⠁⠀⣠⠋⠉⠀⠉⢻⠿⢿⣿⣤⠍⠙⠉⠉⢈⣠⣛⠛⠀⡀
⠀⠀⠈⠀⠘⣋⣴⣷⠀⣾⡟⣿⢥⣠⠎⣹⣿⠐⢀⢳⣤⣴⡏⢡⠋⠈⠖⢒⣿⣿⠛⠲⠊⣹⣿⣿⣶⣗⣲⣿⣟⣛⡉
⠀⠀⠀⠀⠀⠁⠘⢋⢰⣿⡣⠙⢛⠃⠾⡿⠃⣴⢿⠟⠛⢿⣧⡀⠠⠞⠃⠈⠉⠈⠁⠛⠉⠺⣽⣿⣯⣼⣿⣿⣿⣿⡅⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠋⣨⡛⠳⢊⡡⠾⢿⡯⣤⡄⠀⠋⠀⠀⠀⠀⣀⢠⣤⣀⣀⣤⣤⣤⣙⣿⣿⣿⣿⠋⡿⠑
⠀⠀⠀⠀⠀⠀⠀⣘⣤⣜⠀⠀⣽⢻⡏⣰⣧⣮⢀⣀⣤⡆⠀⣀⣤⣶⣯⠉⠀⢀⡁⠈⠘⣿⣿⢏⣽⣿⠿⠿⣦⣄⠀⢨
⠀⠀⠀⠀⠀⢀⣸⠿⣿⣧⠀⣰⣿⡓⠻⡿⠋⠀⠀⠈⢉⣵⣶⢿⡯⠙⡟⠓⣶⣿⣿⣦⣤⣿⣷⣾⣷⡦⠂⠈⡟⠿⠷⠾⢅⠠
⠀⠀⠀⠀⠒⣻⠟⡦⠸⢷⣠⠛⣿⡨⠂⠀⠀⠀⢀⡴⠟⣿⡟⠸⣧⣼⣿⣦⣹⣿⣿⣿⣿⣿⣿⠏⠙⣿⢾⣿⣷⣖⢃⣠⡀⡼
⠀⠀⠀⠀⠀⡰⣦⡀⠤⠀⣩⠆⠉⠀⠀⠀⣠⣾⣿⡠⠾⠛⢿⣿⡿⠛⠙⣛⣿⣿⡟⠉⠁⠀⣽⡄⣤⡿⢀⣿⣿⣿⡛⣿⣆⢰
⠀⠀⠀⢀⣴⢂⣅⣰⠤⠛⠁⠀⠀⢀⣤⣾⢿⠯⣭⣄⡈⣈⡀⠓⡇⠀⠉⢉⣿⠡⡤⣴⠆⢼⠋⠀⢨⡷⢿⡃⣼⣿⣿⣤⣿⢈⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠶⢶⡤⠰⢾⠟⠉⣅⡀⠘⠷⠦⣀⠉⢭⣙⣹⠿⠿⢿⣿⣾⣀⣤⣀⣼⡗⠚⢻⣅⡼⢿⣿⣿⣿⣿⣿⣬
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠲⠀⡀⠀⠀⢾⡏⠟⠀⠀⠀⣸⣷⣿⠋⠀⣠⠀⠀⠀⠀⢹⣧⡀⣠⣀⣠⣼⠏⠀⣠⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠶⠒⠓⠈⠵⠆⠈⠆⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃⢰⣿⡇⠀⠀⠀⢀⣾⣿⢻⣇⣀⣀⡀⠀⢸⠏⢻⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⡀⠀⠀⠀⣀⠀⢀⣾⣿⣷⣧⣀⣻⡆⠰⢢⣤⣴⣿⣿⣏⡁⣾⣿⣷⣶⠿⠲⣿⠁⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣶⣿⣿⣥⣾⣿⡿⠿⠿⠋⢿⠉⠑⠲⠶⠿⣻⢋⣽⣿⣿⡟⡙⠦⣹⣷⠎⠉⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡉⠂⡄⣤⣀⣈⡀⣠⣵⢾⠾⠃⠀⠛⠛⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠋⠐⠻⠚⠫⣽⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠁⠀⢰⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⡉⠐⠒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠦⣙⣤⠀⠀⠀⠀⠀⠀⠀⢮⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⣦⣫⡶⠋⠀⠀⠀⠀⠈⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠿⣷⣋⡦⠀⠀⠈⢻⢲⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⡲⠆⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⡾⠀⠑⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡔⠁⠀⢀⠄⣢⡆⠀⠀⠀⠀⠀⠀⠘⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣻⡦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⢀⡈⢧⠀⠀⠀⡇
⠀⠀⠀⢀⠊⢠⠃⠰⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣾⡇⠀⠀⠀⢠⣿⡟⠀⢳⠀⠀⡇
⠀⠀⠀⠊⠀⠁⠀⠀⠀⢠⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠘⠛⢁⠀⠀⡇⠀⡇
⠀⠀⠶⢀⡵⠀⠀⠀⠀⢨⣼⠁⠀⠀⠀⠀⠀⠀⢀⣠⣖⣮⣽⣦⣤⣴⣦⣤⣇⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⢄⡀⠸⡄⡇
⠀⢘⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠛⠷⠟⠀⢻⡇
⠀⢨⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠿⣿⣿⠟⠛⠉⠉⠉⠉⠉⠉⠙⠻⣅⣀⠤⢊⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠁⠀⠀⠀⠰⠀⣠⡇⣸⡃
⠀⣈⡀⠠⠀⠀⠀⣸⡿⢳⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠒⠈⠙⠲⠤⠤⠤⡤⠤⠤⠔⠒⠚⡉⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⣶⣤⣾⣿⡷⠀⢀⡴⠏⢀⣼⣿⢠⠟⡇
⠀⡍⡄⠰⣴⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠐⠀⠀⠉⠀⠀⠀⠀⠂⠀⢀⣀⠀⠀⠀⠀⠀⠈⠉⠉⢀⡤⠖⠋⢀⣤⣿⣿⢿⣿⢘⡇
⠀⠳⡙⡄⠈⢿⣷⣤⡀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠤⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣠⣒⠋⠀⢀⣠⣴⣿⣿⣟⣵⣿⡇⢨⡇
⠀⠀⢹⣿⣷⣦⡙⢿⣿⣷⣤⣘⢮⣭⡹⠳⠂⠀⢀⢾⣷⠀⠀⠀⠀⠀⠀⠸⠶⠾⠿⠋⠀⠀⠀⠀⠀⠿⠏⠀⠀⠀⠚⠀⢀⣴⣦⣴⣿⣿⣿⡅⣴⣿⣿⣿⠇⠰⡇
⠀⠀⠈⡄⠙⠿⣿⣜⠿⠿⠀⠙⢻⢞⡂⢀⡀⠀⠻⠞⣡⣶⡦⠀⠀⠀⠀⠀⠄⠀⣀⠠⠤⠤⠀⠀⠀⠀⠀⣀⣀⣠⣤⢰⣿⣿⣿⣿⡿⠟⠃⣼⣿⣿⣿⠏⠀⢸⡇
⠀⠀⠀⠱⡀⠀⠈⠿⢿⣶⣦⡀⠈⠛⢿⡿⣷⠿⠷⣾⣿⣯⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⣛⣯⣤⣴⣾⣿⣿⣿⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠛⠿⣿⣦⣤⣤⣤⣤⣀⣀⡀⠈⠛⢿⣿⣿⣿⣿⣿⠿⠟⠻⠛⢛⣿⣋⣽⣷⣶⣬⣟⣛⣉⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠈⠉⠉⠛⠟⠿⢿⣿⣿⣦⣄⡀⠉⠛⠛⢉⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⣴⠀⠀⠀⠀⠉⠈⠛⠿⣿⣷⣦⣤⣶⣿⠿⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⣤⣤⣀⠀⠀⠑⠛⠛⢿⣯⣶⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠾⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢆⣼⠀⠀⠀⢸⡟⣗⣿⣿⣺⣄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡆⢚⠀⡄⣿⣉⣹⣿⣿⣯⣿⣧⣤⠶⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⡘⣿⣿⡧⢾⡶⢧⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⠐
⠀⠀⠀⠀⠀⠀⠀⢰⢇⣿⣿⣿⣟⢻⣿⠟⠛⠃⠀⠀⠈⠙⠋⡭⠿⣟⣗⣺⣿⡎⣉⠘⠿⣿⣗⢀
⠀⠀⠀⠀⠀⡀⠀⠚⠛⠿⠥⡈⢈⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣿⣸⠟⠟⠛⠏⠙⠻⢿⣯
⠀⠀⠀⠀⡄⠀⠀⣀⡄⠀⠀⢸⣘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣛⣵⡃⡄⠠⣰⠀⠀⣰⢻⣿⣿⡆
⠀⠀⠀⡄⣾⣄⡀⣀⣀⣀⣠⣿⣩⣭⣽⣿⣷⠄⠀⠀⢠⣿⣿⣿⣿⣿⣙⠓⠴⠿⠷⠄⣚⣿⣿⣿⡇
⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠷⠾⠶⢾⡶⢶⠾⠿⠿⠾⠷⠿⠿⠿⠾⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣘⡻⢝⠻⡙⣌⠦⠰⠒⠋⠋⡇⠉⠉⢉⣀⣂⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠒⠦⢈⠓⢓⡙⠁⢠⣇⠀⠀⠀⠁⠀⠀⡟⢟⢉⡇⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠷⠭⢍⣢⣄⣀⠴⠋⣢⠔⠃⢹⡄⠀⢀⣄⠀⠀⠙⠒⠛⠁⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠠⣞⣭⣍⣑⡶⠋⢀⣤⣶⠛⠁⠀⠀⢰⡇⢠⠞⠉⠳⣄⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⡯⠖⠒⣲⠏⠀⠀⠐⠋⠛⢷⡀⠀⢀⡾⡿⡧⡀⠀⠀⠈⣇⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢠⠟⠒⠒⠶⣤⣄⡀⠀⠿⡤⠋⠈⠀⠁⢳⣠⠖⠀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⣏⠢⡄⢻⠀⠀⣀⡤⢺⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⠶⣾⠲⠒⠢⢜⡄⠘⣼⣠⠚⠁⠀⢸⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡀⠀⠀⢡⢀⡟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⣤⠦⣧⣄⡀⣼⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⣾⣿⣦⣑⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⢻⢿⢿⡺⣷⣤⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠟⡇⠃⠈⢫⡳⡑⠢⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡇⠘⠀⣀⣳⡈⠢⣈⠂⠌⣢⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡜⠀⠀⡸⠀⠈⠑⠤⠤⠌⠭⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢻⠜⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⣏⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠤⠤⠤⢤⣤⣤⣤⠤⠔⠒⠒⠚⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠖⠊⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠑⠺⢧⣄
⠀⠀⠀⠀⠐⠀⢠⠞⡝⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢣⠹⡄
⠀⠀⠂⠀⠀⠀⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⢷⠀⡇⠀⠀⢈⠎⠀⠀⠀⠀⢨⢀⠀⡁⡁⠀⣁⠀⠁⠀⠡⠀⠑⠀⢸⠀⠏⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢸⣠⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠁⠀⠃⠀⠀⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠰⣿⣶⣿⢰⣷⢰⣷⢰⣶⣀⣾⡆⣶⣦⣠⣾⡆⢿⣶⣾⠆⢸⣼
⠀⠀⠀⠀⠀⠀⠀⡏⡇⠰⠿⠛⠁⠈⠻⠾⠟⠸⠟⠛⠻⠇⠻⠟⠛⠿⠇⠿⠟⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠇⡇⠀⠄⡀⢤⠀⠄⠀⠀⠠⠄⠀⡠⠄⠠⠄⠀⠤⠀⠄⠀⢤⠀⢸⠋⡆
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡀⠀⠁⠀⠀⠀⠀⠐⠰⠀⠆⠄⠀⠢⠰⠄⠀⡀⠠⠊⠀⢸⠀⢇
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⢢⣱⡀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣎⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠈⠻⡢⠤⠤⠤⠤⠤⢤⣤⣤⣬⣥⠤⠤⠤⠤⠤⠤⠤⠤⢔⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠴⠲⠒⠚⠉⠉⠉⠉⠛⠓⠒⠒⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠓⠚⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢀⣠⡰⠊⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠈
⠀⠀⠀⠀⠀⠀⡀⢀⡠⠠⠄⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠄
⠀⡀⠀⠀⠈⠉⠠⠤⠂⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠
⠀⢁⠀⡀⠀⠀⡀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⠀⠈⠀⢠⡀⠤⠄⠄
⠀⠈⠀⠂⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⡀⠀⠀⠀⠀⣠⡆⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⢀⢀⠀⠀⠀⢠⠠⠀⠀⠀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠈⠁⠉
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁
⠀⠀⠁⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠈⣠⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⢒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠴
⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⢁⠐⠒⣒⢂⠉⢱⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠠⠁⠐⢀
⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠱⠐⠐⠁⠀⠀⠀⠚⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⢂⡐⠐⠊⢠
⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢀⠑⠠⠤⠤⠤⠒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢸⠏⠷⣄⠀⣾⡛⠛⠻⠟⠛⠷⣶⣿⣟⢋⣷⠶⠶⢯⡿⢁⠷⢒⢍⣷⡴⠶⣶⡶⣤⣀
⠀⠀⠀⠀⠀⢠⡟⠐⣴⠉⠷⠿⡇⠀⠐⢲⣍⣉⡉⠉⠉⣻⡁⠀⣀⠀⢠⠘⠤⠍⢢⣾⣧⡀⢸⣿⣷⣿⣷⡄
⠀⠀⠀⠀⢠⠟⡀⣒⠠⠶⠂⡈⢤⠀⢝⡩⠙⠓⠚⠿⠛⢛⡀⢈⣁⣤⣪⣿⣲⠶⠻⢯⣹⣿⡿⠿⢻⡴⡀⡿⠹⡆
⠀⠀⢠⡟⢿⣦⡀⠤⠄⠁⠈⣁⠘⣤⠜⠴⠀⠀⠀⠀⠀⠾⠉⠁⠂⡌⠠⠛⣿⡇⣇⣨⡽⢟⣃⠂⣸⢱⡗⠃⢀⣿
⠀⠀⠈⢻⡿⢛⡁⠀⠆⠀⠀⠀⢀⣃⠀⠂⠀⠙⠐⠀⢃⡄⠐⠗⢤⣤⢀⡄⠀⢣⣿⣉⢀⠆⠈⠳⣅⣟⣀⢀⣾⣧⡀
⠀⠀⢰⡏⢠⠈⠘⢆⠀⢒⣀⡴⡤⠽⠂⠀⠀⣄⢀⣠⡴⢷⣤⣄⣀⡀⠀⣀⣀⢺⡿⢆⡤⠀⠀⠀⠀⠠⠀⣨⣟⣾⠁
⠀⠀⣸⠃⣈⠸⠀⡙⠁⠜⡏⠁⡂⡀⢄⡀⠠⣸⣍⡿⠛⠈⠙⠛⠙⠛⠛⠛⣭⣿⣷⣾⢃⡁⠀⠀⠀⠀⢀⣾⢾⣅
⠀⠀⢸⡄⠁⠦⢈⡃⠄⠘⣾⠁⠀⠀⠀⠀⡰⢸⡟⠁⠀⠀⠀⠡⢰⠆⠐⠋⡭⠛⡋⠉⠀⢀⣀⡀⠱⠠⢾⣷⣤⡏
⠀⠀⠈⣷⣤⣥⡈⣅⢀⠞⠂⠑⠁⢀⠀⠀⠲⣼⡄⡀⠀⠀⠀⠀⠂⠁⢠⣎⠀⣀⣤⣶⠿⠛⠉⠀⠀⣿⠆⣿⢯⡄
⠀⠀⢰⣿⣟⢰⣶⠈⠡⡐⠐⡆⢠⠄⣦⠴⠿⣟⠛⠗⠲⠄⣴⠆⣿⣄⠀⠈⡆⠂⢀⡀⠀⠄⠘⠀⠀⢄⣾⣿⣼⣇
⠀⠀⠈⢿⣿⣼⣿⣧⡴⠄⡄⠀⠂⠐⢛⠦⢀⠄⢀⡶⠠⣠⡤⠔⠋⠋⠉⠀⠀⠀⠤⢀⣀⠠⠐⢈⠐⠃⠻⡿⠷⠛
⠀⠀⢠⣻⣿⣷⣧⣀⣷⣄⠢⠐⠆⣸⠂⠀⢀⢈⣿⣇⡔⠹⠲⠂⠀⣠⠄⣀⠴⠆⠀⠮⣄⢀⣶⠿⣤⠀⣱⣷
⠀⠀⠘⣿⠿⠿⠏⠙⠈⣿⡟⠆⢠⣼⣤⠊⠉⠛⢷⠿⠲⢂⡽⠄⠀⠄⠀⠉⠀⠀⡏⢠⣦⠈⣠⡙⢩⠉⣿⣹⡇
⠀⠀⢼⠃⠀⠀⠧⠀⣚⢹⠇⠁⢀⣹⠇⠀⠀⢀⠲⢀⣄⠐⠂⣠⣄⠀⠈⣿⣙⣯⣀⡿⢇⢠⣿⠁⣼⠼⠅⠈⣷
⠀⠀⣸⣧⡠⢀⠬⣀⠠⠤⡧⠂⣾⠅⠙⢦⠯⡏⠀⢻⣿⣦⣴⣿⡿⠀⣰⢿⡟⠓⠀⠰⠠⠤⢥⢀⣧⡀⢐⣠⣿
⠀⢠⡿⠟⣿⠀⠀⠈⠃⠀⢹⠊⡑⢦⢭⣁⠠⣟⣤⡀⠉⠛⠛⠋⢀⡆⠰⠠⠆⠰⠀⣷⣤⠄⢨⣴⡄⠋⠙⣿⠃
⠀⠈⣛⣾⣿⣦⣄⣀⣉⡀⢈⡠⠀⠐⠀⣹⠰⢋⡍⠁⢰⡿⠿⢿⣿⣤⠀⢄⡤⠄⣐⣭⣴⣮⠶⠃⠀⣀⢀⣾⣧
⠀⠘⢧⠄⠚⠁⠈⠟⢁⣴⡿⣩⡾⠒⣃⢹⣶⣋⣴⡿⢼⡧⠦⠀⠰⣦⣾⠟⡿⠿⠿⠛⠛⣡⠀⠿⢂⣽⣿⣿⣟
⠀⠀⠸⣦⣀⡀⠀⣰⣿⣷⠿⡋⠰⠆⠀⢨⣟⠻⠀⠣⣬⡀⠠⠔⡂⠰⣿⡆⠀⠀⠀⠾⠂⠁⢀⡿⢯⠝⢿⣿⣿⡆
⠀⠀⠀⢸⣿⣧⡄⠛⠉⢠⠀⠙⠀⠈⢀⡼⢿⣾⣍⠀⣤⠹⠀⠀⠀⢀⣯⡽⠟⡚⠷⣶⠞⢴⠉⠀⠀⢠⡼⣿⣿⣧
⠀⠀⠀⠀⣿⢟⣡⡌⣃⡀⠀⠈⡠⠈⠁⠀⠈⢳⣹⡄⠘⡐⠁⢠⣿⡿⣽⡧⠄⠀⠠⡇⢈⠘⣶⢛⡊⠍⢓⣛⣩⠿
⠀⠀⠀⠀⣟⠈⠻⣧⠈⣻⡿⠋⠰⠿⣤⣀⣤⠈⣏⠶⣶⡅⠈⢸⣝⣦⡹⠰⠢⠐⠄⣿⡶⣫⢕⠢⡴⢾⣟⣿⣽⠆
⠀⠀⠀⢠⣿⣄⠸⣿⠇⠛⠀⠀⠰⠀⠀⢀⠁⠀⢸⡨⣿⣿⢾⣿⣻⣫⢷⣦⣀⢄⣴⣫⣞⠿⠶⣻⠟⠁⠀⠈⢻⡀
⠀⠀⠀⠸⣭⡿⠗⠒⢯⣄⡀⠀⠀⠀⠀⠈⠀⠀⠈⣇⣿⣿⡐⠗⠦⠚⣂⣿⣿⣷⡟⠁⠈⠇⠀⡡⠳⠘⠢⠀⢸⠇
⠀⠀⠀⠀⠈⠓⢶⣄⡂⠀⠈⠛⠶⠤⣤⣠⣴⠐⠶⠖⠒⢾⡛⣿⣻⣿⣟⣿⣿⣿⣿⣟⣇⣀⣰⢿⣦⣤⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⢤⡴⠶⠛⠋⠉⠳⠶⠤⠴⠶⠚⠁⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠁

⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠒⠂⠉⠉⢻⡉⠉⠁⠒⠢⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⣀⣄
⠀⠀⠀⠀⣯⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⣀⣴⠤⠶⠿⢶⡿⠼⢷⣤⣤⣤⣀⡀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⢤⢽⡋
⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⢁⢀⣴⣾⣿⠏⡰⣾⡿⢀⣴⡑⣶⣶⣼⣷⣼⠟⢉⠛⠦⣄⡀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⣐⣾⠿⠛⣼⣿⢠⣄⣤⠀⣈⠛⠃⣼⠋⠛⠁⡸⡀⠀⠀⠐⢈⢿⣦⠰⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⢀⢒⣼⢙⣄⠿⠁⠺⠿⢷⣼⣅⢀⣜⣘⡦⢿⣄⠀⠀⡘⠰⢣⣷⣆⠈⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢠⣿⡟⠂⣟⣯⣬⣿⡆⢿⡷⡶⢶⣾⣏⣥⣿⠀⠙⢿⣧⣾⠛⠻⢦⣤⡶⢿⣥⡙⣦⠀⠉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢐⠋⠀⢷⣝⣻⣴⠿⣸⣘⣿⠠⠀⠀⠰⠄⢀⣽⣾⣂⣽⣮⢻⡧⢤⣴⣯⣽⣿⡿⠟⣙⣃⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⣭⡄⠻⢧⣹⣮⣹⡬⢷⣟⣿⣿⠚⣉⠁⠲⢻⠏⠉⢹⣿⣷⢼⡿⢛⡿⢿⣿⣿⠁⠀⣤⢤⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢸⠿⡁⠀⠀⠀⠀⠀⠚⢿⠿⣿⡀⠀⠀⠀⠘⣻⡆⠑⢶⣯⡿⠣⢿⡏⠀⢧⡸⣧⠈⠀⠀⣸⡏⠀⠐⡄
⢰⡿⣧⡄⠀⠀⠀⠀⡇⠀⠀⠠⣋⣁⣀⣀⡀⠀⠀⠉⣴⣿⡃⠀⢀⡀⠀⢻⣿⠛⡻⣯⣀⣀⣈⣿⣠⠜⣓⢿⡄⢀⣀⣴⣷⠂⢀⡁
⣮⡆⣿⠇⠀⠀⠀⠀⠓⠀⠡⡦⠯⣿⠋⡍⠍⢮⡷⣿⠚⠈⠛⠶⢻⣦⣴⠖⣿⣶⣎⣻⠁⢈⠻⣿⡟⠋⢫⣤⣍⠿⣶⡿⣾⡗⠈⡇
⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠨⠀⠆⢹⣤⠇⠃⠀⠁⢾⡶⢦⣤⠔⣛⣓⣞⣩⡿⠑⡛⠋⢿⣭⡼⡏⠰⣦⡈⠛⠡⣦⢸⣷⣌⠃⠀⠇
⠹⣇⣻⠀⠀⠀⠀⠀⠘⠀⠀⢀⣶⣮⣾⣷⣀⡀⠀⣠⡶⡼⠱⣊⣹⠿⡉⠃⢿⡄⠁⠐⠊⠉⡸⣧⣸⡿⣡⣦⣦⠋⣼⣹⣏⠁⠈⠀⠀⠀⠀⣀⠤⠊⠁⣡
⠀⠿⣹⡄⠀⠀⠀⠀⠀⢁⠀⠘⣿⣿⣿⣷⣼⠛⠉⢉⡱⢟⣵⣨⣯⣿⣷⡈⢻⣧⢀⢂⣠⣾⣿⣌⣷⣤⣽⣯⣵⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠝⠃⠀⠐⢁
⠀⠀⠻⢷⡄⠀⠀⠀⠀⠀⢇⠀⠈⢻⠟⠷⣿⡀⠀⢸⡃⣛⣛⣉⣭⣭⠻⢇⣼⣿⣿⣟⢡⣀⣿⢻⣯⢀⣐⠷⣿⡈⢿⡀⢐⠂⠀⠀⠀⠀⠀⠘⠄⠀⢂⡀⠀⠁
⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠈⠣⡄⠈⠀⠀⠈⠻⣾⣿⣧⠛⠿⠇⢿⣿⡿⠷⠾⢿⣿⡯⢝⣽⣛⠓⠌⣭⡽⠞⣩⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢖⠊⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠉⢦⡀⠀⠀⠀⠙⠲⡄⠈⠀⠰⣏⣬⣿⡹⡷⠶⡺⢧⡀⠀⠀⠈⠑⣶⡄⠰⠟⠾⡹⣿⣿⠿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠈⠙⠋⣉⣛⣤⠘⣅⣽⡿⢶⣶⣶⣾⠿⠵⠮⢁⡄⠼⠃⠀⠸⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠙⠛⠯⠧⠄⢈⠿⠴⠶⠃⠚⠉⠁⣀⡠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⣤⠤⠤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣆⣱⢄
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣲⠿⣋⣥⣴⣮⣿⣿⣧⠸⡂
⠀⠀⠀⠀⢀⣥⢞⢉⠵⣟⣾⣿⣿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣾⣻⣏⣫⣾⢋⢻⣿⣻⣿⣥⢿⣦⡙
⠀⠀⠀⢰⣓⠳⣎⣿⢱⡾⠚⣽⣶⡗⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣷⣶⣿⠿⣩⣿⣯⣭⣤⠿⠿⣧⢀⣿⣿⠆
⠀⠀⢠⣿⠼⣯⡛⡏⢻⠏⢞⢿⣻⣽⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢾⢩⣗⣶⣶⣝⣯⣿⠛⡙⠲⣿⣏⠰⣷⣶⣾⡝⣿⣿⡇⡆
⠀⠀⠈⣽⠶⠥⡞⠻⢧⣿⡟⢯⡻⣟⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠎⣿⣟⣿⣿⣿⣭⣿⣿⣿⣿⣧⣏⣤⡹⢟⣿⠷⡇⢹⣿⣼⣿⣿⡇⠃
⠀⠀⠀⠹⣧⡝⣟⢞⣷⣩⠅⣟⣻⣜⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⣾⢿⣾⣏⣙⢿⣿⣿⣿⢿⣟⣴⣿⣿⣁⡨⠙⠿⢾⣾⣫⡟⣿⣛⢁⡆
⠀⠀⠀⠀⠈⠛⢮⣾⣭⣱⢷⡁⣤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠓⠛⠿⠍⠿⠶⢿⣮⣶⡮⠿⣿⣡⣶⣿⠋⡸⠁
⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣥⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣥⣭⣷⣥⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠈⠉⠉⠀⠀⠁⠀⠒⠂⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠃⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⣀⣀⣠⡶⠾⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣉⣀⣀⣀⣠⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠉⠉⠝⢻⡇⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠙⠛⢶⣄⠀⠀⠈⠑⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⡇⠀⠀⠠⠙⠿⠷⢶⣄⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⠶⠃⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠾⠶⠶⣶⣶⡶⠶⠶⠟⠛⠉⠉⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠁⠀⠁⢰⣿
⠀⠀⠀⠀⠀⠀⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠤⡦
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣖⣤⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠦⠀⠀⠀⡄⠀⠀⢀⡎⠀⠁⢀⡖⠀⠀⠀⠀⢸⠃
⠀⠀⢸⣶⣤⡀⠀⠀⠀⠀⠀⠉⠛⠒⠳⠶⢢⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠄⠀⠉⠀⠀⠀⣀⡤⠖⠉⠀⢀⣤⢸⡂⠀⠀⡘⠋⠀⠀⠀⠐⣿
⠀⢀⠉⠉⠛⠛⠽⠆⣶⣶⠀⢸⡗⠒⠛⡿⠟⠁⠀⠀⠀⢀⣀⣀⠈⠉⠑⠂⠀⠀⠀⢀⣀⠦⠚⠉⠀⠀⠀⠀⢰⠃⠉⠀⡻⢣⡞⠁⠀⠀⠀⠀⠜⠁
⠀⠈⠻⢿⣶⣤⡄⢀⣀⠀⠀⣾⠂⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠈⠉⠀⠀⣀⡠⠴⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⣸⡀⠀⠀⢁⡌⠁⠀⠀⠀⢶⣾
⠀⠀⠀⠀⠀⠉⠁⠉⠛⠛⠀⠁⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⢀⠠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠛⣇⡄⣴⠉⠀⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⣀⣤⡤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢀⣿⣤⠍⠀⠀⢀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⠄⠂⠈⠀⠉⠉⠓⠶⠤⣀⠀⠀⠀⠀⠀⠀⡾⣿⡁⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠛⠒⠒⠚⠛⠋
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⡄⡀⠀⠀⠀⠸⣿⣿⣿⢷⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠤⠦⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠉⠛⠿⣿⣮⣭⡙⠳⢦⣤⠔⠒⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠠⡶⠋⠉⠋⠉⠓⣆
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠉⠙⠟⢿⣷⣀⣠⡦⠔⠋⠉⠀⠀⠀⠀⠠⠎⠈⠐⢦⣄⣀⣀⠀⠀⣸⠷⣦⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠰⠛⠙⢸⡟⢛⣏⠀⠀⠘⡇
⠀⠀⠀⠑⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠁⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⣠⠀⠀⠀⠀⠈⡿⠁⠀⠀⢰⠇
⠀⠀⠀⠀⠈⠙⠿⠿⢿⣏⣀⣚⢛⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⡀⠑⢤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠲⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠠⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠰⠚⠀⠀⠀⠀⠀⠄⢤⣄⣀⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢠⠀⠀⢀⡀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠆⡈⢁⠀⠀⢀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠜⠢⠀⡂⠀⠀⢆⠀⠒⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡀⠡⠴⡂⠀⠀⢩⡸
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠒⠐⠁⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡄⠀⠀⢀⠀⠖⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠶⠶⠚⡠⠁⠀⠀⠀⠀⠁⠀⡐⢁⠐⠁⠀⠀⡠⠖⢦⠀⠀⠑⠦⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣀⠀⠀⠀⠂⠰⠁⠁⠀⠀⣀⠀⠧⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠄⠇⠀⠀⠀⠀⠀⠀⢑⣰⠉⠀⠀⠀⠀⢔⠀⠀⢀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠁⠈⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠎⠀⠐⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⡆⠀⡀⠀⢷⣀⡀⢀⡠⠂⠀⠀⠐⠋⠀⠀⠈⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⠒⠀⠀⠀⠄⡂⠇⠀⠀⠉⠉⠉⠀⢄⢠⠷⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⣀⣴⣾⣥⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠁⠀⢀⡰⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠋⠀⠀⠶⠶⠖⠀⠈⠀⠀⠀⠙⠋⠉⠀⠀⠀⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣀⡤⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠈⠀⡀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⡀⠈⠀⠀⠀⠑⠦⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⡥⠤⠠⠤⢠⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠠⠤⠠⠤⡅
⠀⡰⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⠃⠠⣀⡠⠐⠀⠀⠂⠀⠀⠀⠀⠒⠀⠐⠀⣀⡀⠀⠳⠀⠀⣠⠄
⠀⢀⠀⠀⢀⠀⠀⠀⠀⢰⠂⠁⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠀⠀⠀⢲⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠩⡉⠀⠀⠀⠀⠀⠈⢀⡀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⣀⠈⠀⠀⠀⠀⠈⠈⡩⠁
⠀⠀⠀⠈⠀⠀⠠⠀⠄⠀⠀⠈⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢍⠀⠀⠀⠄⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠢⣀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⣀⡠⠒
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠉⣀⠢⡀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡠⢂⡈⠉⠉⠀⠀⢀⡀
⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⣀⠀⠐⠂⠳⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡴⠓⠒⠀⢀⡀⠀⠀⠀⠀⣠
⠰⠂⠈⠋⠀⠀⠀⠈⠉⠉⠀⠀⢀⡉⠆⠛⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠃⠎⢁⠀⠀⠈⠉⠉⠀⠀⠀⠈⠋⠀⠲
⠀⢀⠀⠀⠀⠈⠣⠐⠀⠀⠀⢀⠁⠀⠤⠊⠁⡈⠒⠀⠤⠤⠤⠔⠐⠊⡄⠈⠢⠄⠀⠁⠀⠀⠀⠐⠠⠋⠀⠀⠀⢀
⠓⠉⠀⠀⡀⠔⠃⠀⠀⠀⠤⢀⣀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠀⠀⠀⠓⠄⡀⠀⠈⠑
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⡀⠀⢀⠸⠀⠀⠀⠀⠀⣄⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⡄⠀⠀⠀⠀⠸⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠄⣦⢲⠆⠀⠀⠀⠀⠁⠀⠀⠂⠄⠀⠀⠀⠀⠀⢤⡄⡀⠀⠀⠙⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⢄⣀⣓⣠⢂⣘⣀⠂⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠘⢧⡀⠀⠰⠄⠀⠀⠀⢥⠁⡔⠊⢀⠄⠀⠀⠀⠘⣣⡔⠀⠀⣀⢄⡟⠂⣄⠀⠈⠁⠀⢹⡋⠀⠀⡈⠉⠁⠀⢙⡇
⠀⠀⠀⠀⢘⠃⠀⠀⠀⠘⠂⢀⣀⣴⡀⢀⠈⠖⢀⠞⠁⢀⡄⠊⠀⠀⠀⠀⠀⠠⣡⠜⢧⢗⡫⠂⡀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⣼⠁⣀
⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⢀⠌⠈⠈⠁⠀⠀⠐⠦⠀⢀⠎⢠⠞⠆⠀⠀⠀⠠⣔⣄⣶⠨⠍⡠⠖⡧⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠀⠐⢤⡆⠀⢧⠀⠂⠀⠀⠄⠀⡅⢤⣥⠔⠚⢀⡠⠆⠀⠀⠀⠙⠠⠤⠄⠠⠤⠤⠂
⠀⠀⠀⠀⠀⣀⣰⡄⠀⠀⠀⢤⠀⠀⣀⡀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠸⢗⣸⢩⡍⢮⡛⠀⠀⣄⢶⠆⠀⠀⣀⠀⠀⢦⣆⡄⠈
⠀⠀⠀⠀⡶⠚⠁⢃⣀⣀⠀⣀⠀⠀⠘⢡⠾⣼⠀⠀⠀⠀⢀⡀⠀⠀⠀⠦⠀⠀⠈⠉⠛⠃⠉⠀⠀⠷⡉⠀⠀⠀⠀⠁⠀⠀⠀⢊⢱⡆
⠀⠀⠀⠀⠀⠀⡞⠋⢀⡠⠴⠬⢤⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⡦⡀
⠀⠀⠀⠀⠀⠀⠻⣶⠃⠁⠀⠀⠀⠈⠆⠀⠀⣥⠀⡆⡄⢐⢰⠀⡄⢀⠇⠀⠂⢰⠀⠰⣀⠂⡦⢀⠀⠀⠀⠀⠀⠘⢼⣁⠄⡓⣧⢂
⠀⠀⠀⠀⠋⠀⠀⠘⠀⠁⠀⠀⠀⢀⠀⠉⠀⠤⠐⠳⠁⠬⠸⠄⠇⠨⠤⠀⠀⠇⠱⠐⠻⠀⠗⠀⠇⠁⠀⢲⡦⡄⢩⢽⣶⠲⠨⠇⡰⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠠⠀⠀⡈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠉⠹⢾⣤⡜⠿⢭⠘⣧
⠀⠀⠀⠀⣠⠀⠀⠢⡇⡀⣀⠀⣠⠅⠀⠀⠙⣣⡆⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠎⠃⠀⠀⣄⠀⠀⠀⠀⠘⠳⠴
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠂⠀⠀⠚⠃⠀⢀⠀⠀⡠⠠⠎⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡠⠀⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⣄⣀⣄⣀⡀⠀⠀⢠⡄
⠀⠀⠀⢠⠀⡈⠀⠀⠀⢠⡀⢠⠔⠀⠀⠀⢄⠀⠀⠁⠀⠀⠁⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⢻⣿⣧
⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠉⠲⠀⠀⠀⠀⠘⠀⣴⡀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠁⠀⢰⠇⠀⠀⠀⠀⠻⡿⢤⠂⠀⢠⣿⣿⠃⢠
⠀⠀⠀⠀⠀⠘⡀⢀⠄⠎⠁⡀⠀⠰⠄⠀⢡⣹⠓⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣦⣟⠁⠀⠀⠂⠀⡜⠀⠀⠀⠀⠾⠋⠐⠀⡀
⠀⠀⠀⠀⠀⠲⠈⠈⢀⢀⠉⠈⠀⠙⠀⠀⠈⠁⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠉⠒⢦⣀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡤⢄⠐⠀⡀⠈⣆⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠖⠀⢀⡆⠀⠐⠒⠂⠰⠦⠂⠀⠀⢸⡶⣌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢺⣀⠐⣯⠂⠾⠋⠀⡀⠲⣀⣤⠀⠀⠀⠀⢀⣼⢡⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠈⠀⠈⢄⠉⢰⡞⠀⡾⢛⠛⠁⢀⣤⣤⣾⡿⠃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠰⠉⠀⠀⣷⣾⣶⣶⣿⣿⡿⠟⠁⠀⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⠀⠀⠀⡦⠒⡂⢶⢤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⠊⠢⡀⠀⠀⠀⠀⠀⠡⠀⢓⢈⠈⡆⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠀⣀⠔⠉⠁⠂⠀⠀⠑⣀⡀⠰⠋⠢⡘⠀⠣⠁⠀⠀⡌⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠖⠘⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠅⠀⠢⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠚⡁⠀⠀⠀⢰⡆⠀⠀⠀⠀⠁⠘⡆⠀⠀⠀⠀⠀⠀⠀⡠⣴⣶⡶⠧⠶⠓⠒⠒⠛⠒⠒⠷⠴⠂⠀⠀⣀
⠀⠀⠀⠀⠀⡠⠃⠀⡇⠀⠀⠀⠜⡄⠀⠀⡲⣤⡀⠀⠺⡄⠀⠈⠀⠀⠀⠀⠁⠒⠻⢧⡤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠤⣤⠶⠞⠃
⠀⠀⠀⠀⡰⠁⠀⠀⢡⠀⠀⡄⠀⢱⠀⠀⠙⣈⠻⣶⣄⡉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡷⡒⢲⠶⠒⠒⡒⠂⠢
⠀⠀⠀⡰⠁⠀⠀⠀⢸⠀⡐⠀⢰⠸⡄⠀⢄⠈⠓⠀⠙⠻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢱⠈⠢⠌⠀⣰⡇⠀⠀⢁
⠀⠀⠀⡇⠀⠀⠀⠀⠘⠴⠁⠀⠞⠀⠈⡲⢈⠏⢀⠀⠀⠀⠈⢃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢢⡀⠈⡁⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⢶⡖⠒⣋⡵⢲⠀⠀⠙⢶⣄⠀⠈⠓⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠐
⠀⢀⡜⣀⣀⣀⠤⣤⠒⠉⠀⠞⢁⡔⠁⠀⡎⠀⠸⡄⠀⠈⠻⢦⣀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠠⡄⠀⠀⠈⢠⡐⠂⠀⠀⠀⡀
⠀⠀⠀⠈⡁⠀⠀⠉⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠊⠈⠑⠒
⠀⠀⠀⠀⠑⠲⠄⠤⠤⠚⠁

⠀⠀⠀⠀⠀⠛⠛⠓⠶⣦⡄⢀⡤⠀⠀⠀⠀⠀⢠⣂⣴⣶⣶⣲⣀⢠⡆⠀⠀⠀⠀⠀⢀⣀⣤⣔⣆⣄⠀⣠⡀
⠀⠀⢀⠀⠀⠀⣀⣀⠰⠄⡀⢸⡇⠀⠀⠀⠀⣶⣿⣿⢿⣛⡽⠏⠁⠻⠀⠀⠀⠀⣠⣠⠀⢠⣤⠤⠒⣚⠄⢵⠇
⠀⠀⠈⠀⠀⢀⣌⠉⠐⠛⠁⠀⠙⠀⠀⠀⠂⠈⠉⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡁⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣄⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠈⠐⠂⠈⠻⠀⣠⠀⠀⠀⠀⠀⠀⠔⠎⣿⣿⣿⣿⡿⠷⣺⡇⠀⠀⠀⠀⠀⢀⠈⠙⣿⣿⣿⡆⣀⡄
⠀⠀⠀⠀⠀⠐⠓⠉⣠⠈⣿⠀⠀⠀⠀⠀⠘⠒⠈⠀⢽⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⢾⣿⣿⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠇
⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⡄
⠀⠀⠀⠀⢾⡛⡟⣿⢹⠀⢀⡄⠀⠀⠀⠀⠀⣠⡞⢩⣍⢹⢇⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠠⣄⡀
⠀⠀⠀⢳⠸⡧⣿⣸⢸⠆⢽⡇⠀⠀⠀⠀⠀⣽⣧⣼⣼⣾⣼⠉⠳⠀⠀⠀⠀⠀⠀⠈⠃⠰⠻⠉⡿⣛⠓⢲⡿
⠀⠀⠉⠚⠪⣿⡃⠚⠻⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠻⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣶⣶⣦⣤⣄⠀⣠⠄⠀⠀⠀⠀⠀⢀⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣶⣴⣶⡄⢀⡀
⠀⠀⠀⢀⠨⢿⣿⡟⣛⠉⠉⠿⠀⠀⠀⠀⠀⠀⠘⢀⠀⠐⠈⠑⠀⣤⡀⠀⠀⠀⠀⡴⠿⠈⠏⣯⣿⣿⠷⢿⡗
⠀⠀⠢⠀⠀⣬⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠠⣀⡟⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡑⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠈⠀⠀⣠⡧⢱⠍⠲⣾⠄⠀⠀⠀⠀⠀⠀⠀⡭⢽⣿⣿⠗⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⠙⠻⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⢀⣀⣰⣶⣶⣶⣦⣄⠀⠀⠀⠀⠔⠀⠰⡀⠀⠀⠀⠀⢀⣀⣠⣤⣠⣀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⡴⠆⠀⢀⡴⠂⠀⢀⡰⠆⠀⣀
⠀⠀⠐⠛⠿⠿⡿⠟⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠈⠠⢈⡯⢻⣷⣧⠀⠀⠀⠈⠉⣷⠀⠀⠀⣀⡀⠀⢁⣀⠀⠀⣀⠀⢀⣈⠀⢀⡈⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠇⠀⠀⠀⠈⠀⠁⠀⠈⣟⣻⣾⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣷⢺⣾⢟⣷⠒⣿⠻⠶⣖⠛⠛⠷⠲⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠁⠀⠀⠀⠈⢀⡿⠀⠀⠀⠈⠉⠀⠒⠒⠚⠂⠀⠘⠓⠛⠒⠛⠓⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠁⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⢀⢔⣡⣶⣾⠿⠿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣻⣳⣴⣾⣿⣷⣿⣿⡷⠀⠈⠒⠒⠉⢹
⠀⠀⠀⠀⣀⠂⠄⢀⠀⠠⢀⣐⠢⠀⠀⠀⠀⠀⠀⢤⣵⠿⠋⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⡿⠿⠛⠛⠀⠈⠁⠀⠀⠀⠀⠀⠨⡄
⠀⠀⠀⠢⠤⣉⠐⠀⠈⣁⠀⢈⠔⠃⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢸⠀⢠⠁⠀⢀⡀
⠀⠀⣶⠤⢄⣀⠈⠑⠂⢈⠐⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠋⠀⠀⠀⠀⢘⠀⠄⠀⢰⠁⣿
⠀⠀⠙⠛⠛⢻⣌⣹⠶⠋⠀⠀⠀⠀⠀⣰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣀⢄⣄⠀⠀⠐⠒⠀⠂⠀⠀⠐⠁⠀⠀⢈⡜⠀⢀⠘⠓⠛⣴
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⢨⡷⠈⠀⠀⢀⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡇⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠶⢶⣶⡶⣶⠶⢚⠂⠀⠀⠀⠰⡀⠁⠀⠀⣾⣿⡏⢀⣮⠀⠀⠀⠀⠀⠀⠞⠀⠀⠘⡁⡛⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⢀⡿⠿⠾⠿⠾⡿⠿⢿⠀⠀⠀⠀⠀⡈⣴⠂⠀⠘⠿⠷⠄⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡆⠃⠀⡇
⠀⠀⠀⠀⠀⢤⠦⠄⠀⡄⣠⡀⠀⠀⡠⠾⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠁⠀⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠄⠀⡇⡄⠠⡇
⠀⠀⡀⠀⠀⠀⣰⠏⠀⡔⠉⢧⠙⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢸⡇⠀⠀⡀⣀⣴⣴⣶⡆⠀⢀⣀⠀⠿⠆⠀⠀⢣⡅⢸⡇
⠀⠀⠀⠀⠀⠀⠁⢰⠞⠀⠀⠈⠇⠘⣁⠤⠀⠀⠀⠀⠀⣠⣴⢆⡜⢉⠝⠗⠦⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡛⠋⠋⠉⠙⠇⠀⠀⠉⠁⠀⠀⠀⠀⠸⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣴⣽⢿⣶⣭⣏⣷⣄⣬⣵⣤⠀⠰⠀⠀⣠⠋⠀⠀⠘⡧⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣯⣟⡻⢶⣤⡀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⢀⡴⠊⢁⠶⠀⠀⠀⢲⡈⠀⠰⠀⢀⠀⠉⢻⡀⠀⠸⣧⣤⣤⣉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣶⣤⡙⡿⣿⠟⢱⡶⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠂⢀⡎⠀⢠⡾⠁⠀⠑⠦⠈⡻⢟⣁⡿
⠀⠀⠀⠀⠠⣤⣤⡀⠀⠈⠙⢿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠃⢀⡾⡀⢰⡿⠁
⠀⠀⣼⠀⠀⢸⡏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠤⠀⠂⠀⠀⠀⣰⣶⣺⠟⠀⠀⠀⠀⠀⠌⠀⢠⡿⠁⠀⠀⠀⠀⢤⡂
⠀⠀⣹⠀⠀⢈⡁⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡷⠎⠁⠀⠀⠀⠀⠀⠀⠠⢤⡾⠁⠀⠀⠀⠀⡆⠸⢁⡐⡇
⠀⠀⣿⠀⠀⠈⣿⠄⡄⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⢀⡴⣾⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡄⠀⠀⠀⠀⠀⢀⠃⠸⠀⡇⡇⢄⠔
⠀⠀⣿⠀⠀⠀⠡⡆⠁⠀⠀⠀⠀⠀⠒⠀⠒⠐⠒⠀⠒⠒⠀⠐⠀⠀⠀⢐⣿⡷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠈⠀⠀⠀⠀⠘⠀⠂⠚⣛⣽⡌
⠀⠀⢿⠀⠀⠸⣷⠀⠈⠀⠀⠀⠀⠀⠠⣀⣤⠀⣄⣀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⡀⢂⠐⡀⣂⠀⠀⠀⠀⠀⠀⠀⢸⣶⠆
⠀⠀⠸⡀⠀⣸⢡⠄⡄⠀⢀⡀⠢⠄⣻⣾⠏⣹⣁⡼⣤⣾⡚⣩⣤⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⡟⡌⠁⠉⡀⢆⠰⡐⢂⠀⠀⠀⠀⠀⠀⠈⣿⡶
⠀⠀⠀⠈⠰⢯⠎⠉⠀⠀⠈⠡⠤⠈⠭⠭⠬⠩⠍⠠⠭⠌⠭⠉⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠉⠁⠉⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠄⠒⠂⠀⠀⠀⠀⠀⠀⠄⠀⢐⢤⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⣀⣀⠀⠚⠀⠀⠀⢁⡤⠠⡀⠀⠻
⠀⢀⠉⠀⡄⡁⢀⠀⠠⢄⡀⠈⢀⠄⠀⠀⢂⠠⣆⠄⠀⠀⠀⢀⠀⠀⠀⠀⢸⣅⡈⠙⠁⠋⠋⠐⠀⠀⠢⡀⠀⠂
⠀⠁⠀⠀⠄⠂⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⡀⠙⠐⠅⠀⡀⠀⠀⠀⠀⣎⠙⠻⣷⣦⡇⠁⠀⠀⠀⣀⠈⠀⠊⠠
⠀⠘⣆⠀⠈⠲⠀⢀⠀⠀⠄⠒⠀⠡⠀⠀⠀⢀⠀⢀⣀⣦⠀⠀⠀⠀⠀⠀⠻⣷⣂⢄⡉⢁⠀⠀⠀⠀⠉⠀⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⠐⠆⠀⠀⠐⠀⠀⠀⠀⠈⠙⢛⠀⠀⡄⡀⠀⣠⣄⠈⠙⠷⠃⠄⠀⠀⠀⠈⠠⠄⠂
⠀⠀⠀⠀⠄⠀⠀⠁⠈⠀⠀⠀⢀⠀⠀⠀⠠⢄⠂⣈⠄⠀⠈⠁⠀⠉⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠐
⠀⠰⡦⠀⠀⠔⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠁⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠖⠠⠀⠀⠀⠀⠀⢀⢀⣴⣤
⠀⠀⠀⠀⠋⠁⠁⠢⣄⡀⠢⠀⠀⠀⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠃⢘⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠠⠔⠀⠀⠀⠀⣠⣴⣦⣤⣄⢤⠤⡖⠲⣶⣿⣿⣷⣄⠀⠀⠁⠀⠀⠀⠀⠀⡀⣼⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠱⡄⠀⠀⢸⠋⣽⣿⣿⣿⢺⣾⡗⣺⣿⣿⢿⣿⢸⠀⠀⠈⠀⠀⠀⠀⠺⡀⠙⠂⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠸⡇⣞⠊⣆⣻⠸⣿⣇⣯⣒⣤⣧⣝⡸⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠈⡀⠂
⠀⠠⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢘⣷⣢⠤⠈⠛⠛⠛⡛⣋⠉⠉⠉⠉⠉⢉⠉⠐⠆⡀⠀⠉⠂⠀⡄⠁⠀⠀⢈⡈⠂
⢠⠁⠀⠀⠀⠀⢁⠀⠀⠀⠑⠰⡉⠀⢅⠀⡀⠀⠀⠀⠀⠔⠂⠉⠀⠀⠀⠀⠀⢊⠄⠄⠀⠀⠀⠀⠀⣐⣛⣏⡿⢟⣦
⠘⠀⠠⢀⡀⠠⠂⠀⢰⠂⡁⠀⠏⠉⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⢀⠀⣀⠑⠂⠈⠀⠀⠀⠀⠀⠈⠁⠴⣦⢴⠚⠉
⠀⠁⠀⠀⠀⠀⢀⠤⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⢠⠀⠀⠰⠃⠼⠉⠀⠸⠄⠀⠀⠀⠀⠀⠀⡤⣀⣀⠤⡤⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠣⠀⠰⠂⠀⠀⡶⠝⡦⢀⠀⠓⢤⡧⣤⣀⣀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠒⠁⠈⠀⠀⠆⠀⠈⠉⠁⠀⠤
⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠸⠇⠀⡀⠀⠄⠀⠀⠐⠄⠀⢀⠀⠀⠀⡀⠀⠠⠌⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠀⢀⡆⠈⠀⠀⠀⠀⠁⠄⠀⠀⠆⠀⠐⠀⠀⠠⠁⢀⠀⠀⡀
⠀⠀⠀⠀⣠⣀⠉⠹⢦⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠟⠯⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⣤⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⡤⡄
⠀⠀⠀⠈⠳⠄⣀⡀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠁⠀⠀⠀⠀⠈⠳⠄⣀⡀⣀⡴⠂⠀⠀⠀⠀⠀⠈⠈⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡿⠇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⢽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⢿⠟
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠻⠋⠀⠀⠀⠀⢀⡠⠐⢊⣱⡀⠀⠀⠀⠀⣀⡾⠤⣄⠀⠀⠻⠋⠀⠀⠀⠀⠀⣠⠖⠈⣱⡀⠀⠀⠀⢀⣠⡾⠤⣄
⠀⠀⠀⠀⠀⢀⡛⠀⠤⠊⠉⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠠⠂⠉⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠾

⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⣤⡄⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠀⡤⡄
⠀⠀⠀⠈⠳⠄⣀⡀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠈⠳⠄⣀⡀⣀⡤⠂⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠸⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡿⠇⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆
⠻⠋⠀⠀⠀⠀⠀⡠⠴⣚⣵⡀⠀⠀⠀⢀⣠⡾⠤⣄⠀⠀⠳⠏⠀⠀⠀⠀⠀⣠⠔⢘⣱⡀⠀⠀⠀⢀⣠⡾⠤⣄
⠀⠀⠀⠀⠀⢀⠛⡁⠐⠂⠉⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠁⠤⠊⠉⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣰⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠍
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⣿⣷⣷⣶⣶⣾⣿⡿⢿⣿⣿⡿⠿⠿⠛⠋⠀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⣛⠶⠶⠦⠤⠅⠀⠀⠀⠠⠄⠤⠤⠤⠄⠒⠒⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⠊⡁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠿⢿⠿⠿⠟⠛⠻⠶⠓⠚⠲⡶⠚⠿⠋⠁⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣖⣄⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣻⡛⠽⠛⠿⢷⣤⣀⣀⣀⣀⣀⣠⠤⠖⠒⠚⠋⠉⠁⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣠⣤⣀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⣀⣤⣤⡴⠚⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⢶⢶⣶⢿⡿⠉⠁⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠿⣿⣿⣿⣿⣉⣈⠉⠀⢀⠀⡈⣉⣉⢀⣀⣠⣴⡤⠶⢚⡉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⡁⠪⠽⢛⡛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠄⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⣄⣀⣀⠀⠀⠀⠈⠀⠀⣀⣀⡤⠴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⠠⠤⠤⠤⠠⠤⣤
⠀⠀⠀⣰⣖⠀⣶⢈⠁⠀⠾⠋⠉⠙⣀⠀⠠⠄⢲⠂⢀⡀⢡⠀⡠⠊⠀⠀⠀⠐⡀⠀⠀⠀⠐⠒⢤⡀⠘⢦⡀⠀⠀⠀⡠⠃
⠀⠀⢀⡈⣇⣘⡏⠀⠀⠱⡌⠛⠛⠩⢵⠂⠀⠢⣉⣛⣻⠄⠁⠀⠅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠉⠀⠀⢈⡁⠐⠉
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠔⡲⠃⠀⢣⡀⠀⠀⠀⢠⡜⠀⠠⠖⠇⢰⠀⠠⠄⠀⠠⠄⠀⠰⠰⠆⡀
⠀⠀⣠⢻⡀⠀⠀⠔⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⣘⠁⠊⠀⠀⠀⠀⠉⠒⠒⠒⠁⣀⠊⣤⠀⡰⠀⠀⠠⠄⠀⠀⠠⠀⠀⣀⢀⠋
⠀⠀⠁⠰⡇⠀⢸⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠳⢤⣀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠩⣤⡔⠈⠀⠐⠂⠀⠰⠃⠠⠠⠀⢀
⠀⠀⠒⠀⠇⠀⠀⠀⠀⠄⠀⡐⠂⠀⠁⠀⢠⠂⠙⠢⠇⠀⠀⠀⠄⠀⡠⠴⠒⠒⠀⠒⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠁
⠀⠀⠈⡄⠜⢄⠀⠀⠀⠒⠤⠄⠂⠀⠀⠀⡇⠀⠈⠀⠈⠂⠤⠐⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⡠⠐⢠⣼⣯⢧⡜⠁⠢
⠀⠀⠀⠈⠂⢀⠂⣀⠀⠐⣆⠀⣠⡀⠀⠀⠈⠒⠂⠀⠀⠀⠤⣚⠒⢌⠁⠀⣄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠐⠁⠀⠀⠀⠈
⠀⠐⢦⣻⠇⡀⠉⠂⠙⠒⢃⡴⠋⠱⢄⠀⠀⠀⠀⠀⡀⠀⠑⢌⠐⠤⢽⣦⣄⠌⠐⠐⠀⠂⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡐⢿⣴⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⢠⠊⠁⠀⠀⠀⠈⡀⠀⠈⡉⠀⠀⠀⠀⠀⠀⢀⠷⠀⡆⠐⡀
⠀⠀⡙⠢⣹⣇⡆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣀⠀⢀⣹⡲⢞⠣⡀⠀⠀⠀⠀⠀⢘⠛⠆⠑⠄⣡⠀⠀⢠
⠀⠀⠈⠑⠐⠼⢷⠀⠀⠁⢀⣀⠀⠀⠀⢀⠔⠀⠀⠉⠒⠒⠁⠀⠏⠀⣿⠈⠛⠃⠀⢀⠤⠀⢀⠇⢸⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠤⠥⢀⡀⠀⠉⠳⠟⠈⠀⠀⠀⢀⢀⡀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠠⡎⠠⠁⡁⢀⠋⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⡄⣶⠖⣰⣶⣮⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⢈⣐⡒⠚⠁⠀⠀⢀⠀⠔⠁⠀⢄
⠀⠀⠀⠀⢼⣏⡙⢣⡼⠛⠈⠀⠀⡄⠀⢀⢤⠀⢁⠌⠀⡠⠆⠁⠀⠀⠀⠀⠄⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠂
⠀⠀⠀⠀⠌⢠⣠⣍⣡⣃⡽⠀⠀⠀⡨⢾⣿⣊⡷⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠀⠘⢉⣭⠖⠊⠀⠀⠀⠎⠀⠀⠰⠈⠉⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⣸⠀⠀⠀⠀⠀⠈⠒⠄⠀⠠⠀⠠⠂
⠀⠀⠀⠀⠀⢶⣤⣂⣠⣆⠀⠀⠀⣄⣐⠔⠁⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⠀⠀⢀⣠⠄⠀⣠⠄⣠⠤⠄⣀
⠀⠀⠀⠐⠙⠛⠋⠉⠉⠄⠈⠑⢄⠈⠀⠀⣀⣀⠀⣤⢤⡀⠈⠉⠉⠉⠉⠑⠒⠒⠒⠒⠚⠀⡜⢩⠫⡭⠉⠁⠉⢩⠍⢓⢤⢑⡄
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡼⠀⠈⠛⠀⠀⣻⠀⠀⣀⠤⠒⠘⠓⠒⠢⣄⠀⠀⣏⠂⡀⠁⠈⢠⠀⠑⠄⠚⣸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⠀⠀⡒⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢧⠀⢹⡀⠠⠤⡁⠀⢣⠤⠒⠈⣼⠀⠆
⠀⠀⠐⠄⣈⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠈⠲⠠⠔⠁⠀⠀⠘⢧⠀⠔⠃⠀⠀⠀⠀⣸⠀⠀⠣⣄⣀⡀⢘⡀⠀⠄⢀⡿
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠐⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⡞⠁⠀⠀⠀⠀⠀⠀⢃⢠⡴⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢂⣁⡗⠢⠤⡀⠄⠒⢢⠤⠒⠧⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣠⣎⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠂⢁⡨⠀⢠⠤⠀⠈⠀⠠⠖⢂⠀⢸⡀⠀⡏⠢⠄⠀⠀⢀⢎⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠡⠄⠀⣠⡤⣀⠀⠀⣀⠀⠀⠑⠈⠁⠀⠐⠛⠉⠉⠀⠈⢱⡔⡑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢒⡞⡀⢤⡬⢤⣄⡇⠐⠉⠀⠀⠐⠀⠀⠤⣀⣀⡤⠀⠀⠀⣀⢄⡦⠪⢊⡘⣖⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢾⡓⠐⠒⠒⠒⠀⢘⢣⠀⣰⣓⣱⠀⠀⠀⠀⣄⠀⠀⠠⠾⡠⠥⠤⠖⠐⠁⣈⠆⢀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠈⠢⠄⣀⡀⠴⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠥⠤⠐⠒⠊⠉⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠲⢆⠠⠤⠤⠄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠤⠤⠄⡴⠖⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠐⠈


⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣶⣿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⠁⣀⡀⡱⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢹⡧⣟⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣷⠋⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⡚⢛⡛⠻⠟⠛⢓⠔⢻⠀⢸⣿⣿⠿⢟⢃⣤⣾⣿⣿⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠰⣇⠎⡠⡀⢃⡄⠀⠈⠀⠈⣃⠈⠅⠀⠀⠠⡏⠁⠀⠀⣤⣴⣶⡶⠷⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠂⠀⡀⠐⢻⠀⠏⠦⠬⠤⠿⠧⠶⠉⠁⣦⡏⠦⠤⠦⣠⣤⣥⣤⣄⠐⣨⠒⠠⠦⢠⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣾⠑⠀⣠⣶⣿⣿⣿⣷⣦⠀⠀⢀⣀⣀⡷⣧⣀⠔⡿⠚⣿⢄⠀⠊⡗⠐⠒⠀⠠⣼⠐⣅⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⣿⠀⣠⣵⣿⣿⣿⣷⡜⣿⣴⣾⣿⣿⣿⣿⢩⠏⢰⠁⠀⠈⣿⡂⣤⢣⠶⠿⠄⠀⣿⣏⢉⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⡛⠛⠉⠻⢿⣿⣿⡿⣿⠀⠀⠁⢸⣿⣿⠿⠘⢄⣿⡀⠀⠀⣼⣇⣏⣨⠃⠒⠒⢰⡿⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⣀⣀⠀⠘⠒⠒⠒⠛⠛⠀⠀⠀⠀⠈⠉⠉⠉⢉⣀⣈⠩⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣺⣿⣿⡏⢻⠿⣶⣶⡖⣶⣖⣶⡾⢿⢻⣿⣷⣿⣶⣶⠶⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⡟⢹⠀⠈⠉⢓⢺⡀⠀⢹⣯⣿⣿⣃⡒⠠⢸⡇⠀⠉⠙⢏⣾⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠚⠓⢺⡒⠦⠠⠾⠎⠉⠁⠈⠀⣌⡇⠀⠉⣉⣉⣑⠒⠠⠸⠟⠛⠿⠋⢩⣉⣉⣭⣽⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠇⠀⠉⢘⠛⢛⣀⠀⠀⠄⢀⣀⡈⠓⢛⡿⣿⣿⣿⣿⠛⢷⣶⠛⠻⠿⣿⠿⠟⢻⣷⣾⠧⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠠⡀⠀⠀⢨⡾⠥⣀⣀⠀⠀⢀⣀⣨⡆⣸⣼⣿⣿⣿⣿⣷⠈⣿⡃⠀⠀⠠⠀⣀⣇⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠭⢍⣛⣉⠓⠤⢀⣀⠈⢉⣁⣀⡽⠿⠛⢿⣿⣿⣿⣿⣿⣾⣋⡈⣁⣂⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠒⠲⠶⠶⠶⣦⣤⠦⠤⠉⠑⠒⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠭⠽⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡾⠵⠥⠤⠴⢲⡎⢳⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡛⠿⣤⣤⣤⣤⣤⣀⠢⠭⢛⣩⣿⣷⣦⣄⣀⡀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠂⠀⠐⠒⠒⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠃⢀⣀⡀⡀⠀⠀⠀⠀⠈⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢀⣀⡀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢰⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠈⠁⠲⣄⠀⠀⠈⣄⠀⠀⠈⠁⠸⠄⠀⠀⠀⠀⠀⡈⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣠⣤⠀⠀⣠⣤⣤⣤⡉⠢⢀⠘⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⣼⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠍⢠⡄⠀⢈⣤⠀⠀⠉⠂⠀⢷⡄⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠁⠘⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠃⠀⠀⠉⠂⠀⠀⠀⠀⢸⣧⠀⠀⠀⠸⠐⠢⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠁⠈⠄⠁⠤⠀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢄⠀⠀⠀⢀⣠⣤⣴⣆⣀⡀⠀⠀⠀⠀⢸⣤⠀⣈⠆⠀⠀⠈⠂⠀⠀⠀⠆⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⠂⠠⠄⠀⡀⠂⠀⠈⠙⠻⠯⣭⠍⠿⠛⠋⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⠴⠋⠀⢰⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠦⠤⠶⠒⠁⠀⠀⡰⠋⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⢲⣿⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠉⠓⠦⠤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠒⠁⢠⠋⠀⠈⠸⣖⣤⣤⣤⠠⠄⡐⡅⠀⢀⣠⠂⣠⡊⠀⠀⠈⡉⣲⠶⢄⠀⢰⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠞⡵⠃⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⢉⠀⠐⡎⠃⢰⡟⠀⣦⠀⡾⢰⠃⠀⠀⠑⢬⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠔⡀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠀⢰⠀⣤⣼⠁⠀⠁⢸⠃⢀⡔⡀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢿⠁⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣿⡏⡜⠀⡠⡿⢸⣿⡧⠊⠀⣀⣈⢢⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡟⢹⢹⡇⣼⢡⠇⡾⡏⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠶⠀⢸⠚⠀⠀⢸⣿⠃⠸⠈⢱⡇⠀⠁⡀⠀⡂⠀⠰⡀⠀⠀⡰⠀⠦
⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠄⢰⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡏⠀⠆⠀⠀⢧⡀⠋⣀⣾⡗⠄⠀⢈⠉⠉⠀⢀⢰⠂
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠙⡀⣿⢣⠐⣄⠀⠻⣆⠀⠀⠈⠈
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡏⠀⡀⠀⠀⠀⠀⠀⠇⠹⡈⡄⠈⢗⠀⠙⠂⠀⠀⡐
⠀⠠⠇⠀⠀⠀⠀⠀⠀⢀⢮⠀⢈⡇⠘⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⡇⠀⠀⠈⠀⢰⠁⠀⠀⠀⠀⡞⠀⠀⠀⠛⠒⠠⠀⠀⠀⠐⠈
⠀⡧⠘⠀⠀⠀⠀⢀⡔⠁⠰⠰⠊⡅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡏⠀⠀⠀⠀⣽
⠀⠸⡀⠃⠀⠀⡠⠋⠀⠠⠃⡦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠃
⠀⠀⠑⣦⠤⠐⠁⢀⡴⠕⠊⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠈⠒⠶⠒⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠌⠉⠐⠒⠂⠁⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠂⠀⡄⠀⠀⠀⠂⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠄⠂⠀⠀⠀⠀⠀⠀⢠⢄⡄⠀⠠⠤⠄
⠀⠀⠉⠋⠀⠀⣀⣤⠊⠀⠀⠀⠀⠀⠀⠂⠀⣀⣀⡤⠀⠠⣴⡒⠒⢂⣏⠀⠇⢷⡀⡀⠀⠀⠀⠀⠀⠀⠀⡱⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡞
⠀⠀⠀⠀⠀⠈⠣⡠⠤⠤⠐⣲⡖⠀⣨⣥⣶⣀⠀⠠⠈⠉⠙⠚⠉⠁⠠⠀⠙⠻⣛⢕⠂⢀⣁⡠⠤⠖⠉⠀⠀⡎⠀⠀⠀⠀⠀⠈⠰⢶⡿⢖⣠⣤⡤⠤⠤⠀⢸
⠁⠀⠀⠀⢀⠀⠀⠑⠲⠶⠛⠉⠀⣈⣁⠤⠄⠀⠀⠀⠒⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠀⠧⠤⢄⣒⠉⠉⠥⣤⣏⡀⠄⠒⠁⠀⠀⡀⠀⢸
⠀⠀⠀⢄⠀⠀⠂⠀⠁⠀⢉⡩⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠶⠨⠤⠄⠀⠂⠀⠈⠁⠀⡌
⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⣠⠒⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇
⠉⠂⠀⠀⠇⠀⠀⢀⠀⠀⠀⢀⠀⣙⡦⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢲⣦⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡃
⠢⠀⠀⠐⠁⢀⡞⠊⠀⠀⠒⠀⠈⠀⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣿⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠔⠒⠈⠓⠒⡂⠀⠀⠀⠀⠀⠠⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣿⣦⠀⠀⠀⠀⢀⠠⠐⠀⢀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢀⡠⠘⠁⡠
⠀⠀⢹⢿⠃⠀⠀⠀⠀⠀⠁⠀⠈⠄⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠠⠃
⠀⠀⡈⠓⠲⣦⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠈⢇⣦⠤
⠀⠚⠁⠀⢷⣏⡄⢀⣀⣤⠤⠄⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠡⠐⢋⣤⠄⠈⠀⠖⠀⢀⣀⠀⠁
⠀⢄⠀⠀⠘⣦⢿⡧⠄⠀⠀⠀⠀⠀⣠⠴⠞⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠠⠇⢀⠀⠀⡨⠋⡠⠐⠃⣀⡤⠊⢩⡇⠸⡅
⡀⢀⡠⠀⠀⠘⣮⢤⠀⣈⡄⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠓⠒⢄⠀⢀⢎⠀⠀⣀⠄⠈⣹⣥⠀⡼
⡀⠀⡸⠀⠄⠀⠘⡭⣦⣬⠴⠒⠀⠐⠀⠀⠀⠀⡄⠀⢀⠴⠀⠚⠃⠈⠈⠁⠐⠠⡀⠀⠀⡀⢀⡰⠀⠁⠈⣰⠶⠒⠂⠲⣄⢀⣠⠔⠊⣧⡆⠀⣿⠟⠋
⠁⠈⠀⠀⠀⠠⠀⠘⡎⠀⠀⠀⠀⠀⡃⠀⢀⡠⠃⡴⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠻⣿⡉⠐⠶⠒⠧⢤⣀⣀⣦⠚⠉⣇⡄⠀⡿⠗⠈⠀⠀⠀⠄⡠⠤
⠀⢠⡀⠀⠐⠀⠃⡀⠙⠤⣀⣀⣀⢠⡅⠂⠁⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⢧⡀⣲⣦⡀⢘⣿⡀⢼⣣⠀⣯⠟⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢠⠇⠀⡄⠀⣀⠔⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⠿⣵⢆⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢀⠀⠀⠀⠈⠁⠒⠛⠷⠼⠿⠊⠁⢀⠔⠁⠀⠃⢡⠀⠀⡠⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⠒⠒⠦⣀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡀⣀⠠⡀⠇⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢤⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠐⣳⡟⠛⣼⠃⠀⠀⢂⠀⠈⢆⠀⠀⠀⠀⢰⠉⠁⠀⠀⠀⡈⢂⢸⡠
⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⠁⡐⢬⠯⢦⠈⠁⠀⠘⣿⡄⠀⢸⠀⠀⠀⠀⠄⠀⠀⠀⠀⢺⢀⠜⡏⠃⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⣤⠟⠀⠀⠻⣔⣟⡡⠁⡼⠀⠀⠀⡘⠀⠁⠀⠀⠀⠀⠁⠉⢅⡸⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠐⡀⠀⢰⠀⠀⠀⠀⠈⢧⠀⢷⣻⢦⠜⡤⠀⠄⠀⠀⡴⠁⠀⠀⢀⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠢⢑⡚⣆⠈⡐⠀⠀⠀⠀⠈⠳⠤⣬⣙⣉⣀⣀⣠⠴⠋⠁⠀⠀⠀⡘⠀⠃⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣑⣂⣀⠠⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡗⠆⢀⠁⠀⠀⠀⠀⠀⠌⠀⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠄⠀⠀⠀⢀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⣈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠀⣠⣪⠤⠚⠁⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢀⣐⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠑⢤⣀
⠀⠀⠀⠠⠀⠰⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠄⠡⠼⠁⠀⠀⠀⠀⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢔⢤⣤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠸⣌⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⢀⠔
⠀⠀⠀⠀⠀⠤⠤⠐⠲⠁⠀⠀⠀⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡐⠀⠀⠀⠾⠦⠄⠠⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠑⠢⡀⠀⠀⠀⠀⠀⠙⣄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠂
⠀⠀⠀⡐⠁⠀⠀⠄⡀⡠⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⢄⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⠀⡴⠊⠀⠀⢀⠠⡄⡀⠀⠀⠐⡀
⠀⠀⢠⡁⠀⠀⠀⡸⠢⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠳⢵⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠐⣠⠀⠀⡌⠀⢜⡅⠂⠀⠀⠀⡴⠀⠀⠡⠰
⠀⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠆⢔⠏⡀⠘⠋⡁⠈⣀⠘⡔⠀⠀⡇
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣀⣠⠞⢁⡞⠁⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢆⠘⠣⣉⠅⠀⡀⢣⢽⣟⡠⢀⢠⠃
⠀⠀⠀⠀⠈⠓⠦⣤⣀⣈⣋⡥⠖⠋⠀⠀⡆⠸⠆⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠸⠀⠀⠀⠀⠈⢢⡑⠄⡀⠙⣄⠮⠞⠀⠀⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡍⠉⢉⣀⠤⠚⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠢⠀⣀⣀⣀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠰⠦⠤⠴⠇⠄⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠃⠉⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠴⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⠔⡂⠄⠈⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⠀⠠⠊⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⡐⢁⠄⠀⠀⠐⠈⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⣮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠿⣾⣶⠶⠶⣵⣾⣥⣴⣎⠀⠀⠀⠀⠀⠛⠂⡀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢞⣩⠃⠂⠀⢈⠹⢁⡬⢬⢻⠋⣍⢙⣛⢶⡞⣀⠀⠀⡀⠀⠀⠀⢀⡾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⣀⡀⠀⠀⢰⣿⣾⠶⢟⣱⠀⠀⠀⢃⠀⠐⠀⠓⠘⢄⠖⠀⢘⠏⠫⣻⢋⠀⠀⠀⢠⣟⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠈⠉⠀⣠⣴⣿⣛⣬⣤⡟⠁⣸⣿⡡⠀⠇⠀⠀⠀⠀⢊⡀⢀⢀⡈⠂⠠⠀⠈⣲⣾⣿⣿⣏⠕⠀⠀⠀⠀⠀⠀⢀⠜
⠀⢸⡶⠁⣀⠾⡿⠿⣻⡭⠉⠙⠛⠒⠋⢈⠛⠀⠀⢰⣠⡠⡃⠀⢷⢱⡋⠀⠀⠀⠀⠀⠛⠄⣿⣿⣿⡄⠀⠀⠀⢀⡴⠊⠁
⢠⠋⠀⠈⡔⣩⡍⠑⡌⠃⠀⣨⠟⠀⠀⠄⠀⠀⠲⠈⢐⢃⠒⠀⠑⡚⠃⠄⠀⠀⠀⠂⠢⣴⣿⣿⠅⠀⠀⠀⠀⠸⡅
⡏⢳⡀⠀⢇⡛⠓⣠⠇⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠬⠂⠀⢕⣐⠡⣠⢀⡴⠞⠛⠳⣾⣿⡿⣧⡀⠀⠀⠀⠀⠀⠙⡄
⠐⠀⠙⠀⠀⣉⣉⠥⠀⠀⠀⠀⠀⢀⠐⢁⠆⠀⠀⣠⠄⡞⣠⣜⣧⣠⣴⡏⠙⡀⠀⠀⢿⣿⡿⠌⠓⠄⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠑⢆⠀⠀⡄⢀⠀⠀⠀⠠⠘⠁⣴⡟⢄⠀⠄⢀⠆⢢⣾⣿⣿⣿⡟⠀⠀⠈⠐⠒⢺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠉⠓⠦⠀⠀⣀⣤⣒⣀⢴⣿⣧⡀⠃⠀⠀⣰⢾⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⢿⣽⣿⣿⣿⣿⡽⣿⣾⣿⣿⡷⠀⠀⠀⠀⠄⠀⣸⠁⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠳⣽⠿⠿⠿⠿⢿⡿⢯⣁⠀⠀⠀⠐⠊⠀⠀⡇⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠙⠲⣤⡀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡀⠀⠀⠀⠟⠦⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢤⣰⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠐⠄⠀⠀⠅⠀⠀⠉⠑⠀⠀⠀⠀⠀⢘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣠⡄

⠀⠀⠀⠀⠀⠠⣒⣺⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠁⠘⡦⠀⠦⣤⣔⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡆⠛⠫⣿⢹⣼⣿⠅⠀⠀⠀⠀⠀⡓⠀⠘⢦⣀⡄⢫⠙⠒⠶⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⣐⣀⣦⣤⣈⣡⢿⣬⡀⠀⠀⠀⠀⠃⢐⠛⠘⣿⠋⠙⣳⣤⣿⡥⠐⠚⡆⠀⠀⠀⢤⣀⣀⠔⢞⠀⠁⠀⢙⡆
⠀⠀⠀⠀⠀⠩⡀⠁⠀⠁⡡⠄⠀⠁⠀⠀⠀⠈⠓⠤⢆⣴⣛⠶⠖⠃⠉⠀⠀⠀⠀⡇⠀⠀⢠⢲⠊⡁⠐⠀⣠⡀⢢⣼⡷⣀
⠀⠀⠀⠀⢺⡀⣀⡍⣠⣄⣁⣽⡀⠁⠀⠀⠸⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⣨⣛⡁⠀⠈⠋⠀⢁⣈⣤⡴⠿⠂
⠀⠀⠀⠀⠀⣏⠉⠁⠉⠀⠉⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠋⠀⠀⠀⢠⠀⠀⠉⠉⠁⠀⠈⠀⠀⢀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣣⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠉⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢰⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⣶⣄⣀⣀⣀⣀⣤⣼
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢛⣛⡛⠻⢟⣛⠕
⠀⠀⠀⠀⠀⠀⠀⣥⠀⠁⠀⠀⠀⠀⠀⢀⠆⠀⠀⢀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠢⣌⢣⣀⢸⡀⢠⣴⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢙⠀⠀⠉⠉⠁⠉⠉⠙⠧⣀⡠⠊⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⢀⡀⠀⠤⠒⠂⠐⠀⠠⠤⢄⠀⠈⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⢒⢶⣧⠀⠀⠀⡀
⠀⠀⠀⠠⠀⠀⠀⠠⡄⠀⢀⡄⢠⡄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠄⣥⣮⣽⣿⠿⢀⠞⠋⠔⠡
⠀⠀⠀⡆⠠⠀⠚⠄⣸⣦⣾⢤⠖⢀⠆⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠂⠀⣄⡈⠛⠛⠋⠉⢉⡉⠙⣁⣔⣀⣀⣀⡀
⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠀⠉⠙⠋⠁⠉⠉
⠀⠀⠀⠂⠉⠢⠖⠐⠂⠄⠒⠀⠤⣄⠏⡴⠀⠀⠀⠐⠒⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⣀⠀⢀⣠⡄
⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⢀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⠀⠀⠀⠈⠛⠿⠛⠺⠽⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠒⠐⠃⠐⠒⠒⠂⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠓⢦⡟⠀⣸⠃
⠀⠀⠀⠀⠀⣠⣞⡱⠶⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣤⠤⠖⢺⡥⣤⡿⣄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠦⣄⣤⠴⠛⠉⢹⡄
⠀⠀⠀⣴⢷⣀⣈⣇⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠇⣰⣞⣙⣦⣭⣹⠛⡆⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣀⡤⠤⣄⡀⠈⣇
⠀⠀⠾⠷⡞⠁⠀⠙⢷⣄⡀⠀⠀⠉⠙⠓⡞⡇⠀⠀⠀⡿⠿⣾⣽⣉⣈⣹⡾⠁⠀⢻⡀⠀⠀⠀⠀⠀⠈⢳⡄⢰⠃⠀⠀⠀⢳⠀⠈⠙⢦
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠳⠶⢶⣶⡚⢙⠃⠀⠀⠀⢹⡄⠀⠠⠈⢁⡟⠠⠀⠀⠈⣧⠀⠀⠀⠀⢀⡴⠋⠀⠸⣆⠀⠀⢀⡼⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⢀⡿⢹⠃⠀⠀⠀⠀⢳⡄⠀⢠⠞⠀⠀⢠⠀⠀⠸⡄⠀⠀⠀⣾⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠙⠾⠀⠀⠀⠀⠀⠀⠙⢦⠏⠀⠀⠀⠀⠀⠈⠀⢳⡀⠀⠀⠙⢦⣤⣤⠴⠚⠛⠛⠛⠲⠦⢤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠰⠀⠀⠄⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠁⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⢰⣛⣧⠀⠀⠙⠲⠶⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⡴⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⣆⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢾⡉⣷⣿⣉⣷⡴⢧⣠⣄
⠀⠀⠀⠀⣀⣀⣀⣀⣸⣷⣇⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⣤⣾⣤⣽⣦⡄⠀⢸⡇⣞⠀⠀⠀⢀⣴⡿⠂⠀⠀⡤⣤⣽⡁⣠⢿⠇⣷⡀⠳⡟
⠀⠀⠀⢾⣭⠭⠥⠤⠤⠤⠤⠤⠴⢦⡼⠇⠀⠀⠀⠀⢀⡷⠶⠶⠶⠶⣇⡀⠀⣷⠘⢰⠛⠓⢿⡏⠀⠀⠀⠀⠓⠒⣦⡉⠳⣼⢠⡏⢳⡀⠹⣄
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢹⠀⣩⠶⢾⣷⣄⣸⠇⠀⠀⠀⠀⠐⣶⠷⠷⣤⣼⣿⡤⠿⠗⠚⡿
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣀⣧⡀⠀⣹⠊⠁⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠰⡏⠉⠝⣯⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⢛⠲⣿⡾⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣹
⠀⠀⠀⠀⠀⠀⢷⣤⣤⣤⣤⣤⡼⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣘⣆⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣽⡿⠋⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⣠⢖⣶⣒⡦⠴⢦⡤⢦⡄⠀⠀⠀⠀⠀⠀⠘⠏⠁⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⠀⠀⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⡴⠛⠉⠁⠈⠉⠳⢼⡛⣻⠿⣟⠲⣄⠀⠀⠀⠀⠀⢀⡴⠛⣍⠀⣀⠓⢍⡙⠲⣄⠀⠀⠀⠀⠀⠀⠰⣟⡛⠲⠦⣾⡁⠀⠀⠈⠙⢦⡀
⠀⠀⠀⢸⠁⠀⠀⠀⠐⠃⠀⡀⠹⣍⠳⡿⢲⡌⣧⠀⠀⠀⠀⡏⠰⠂⠈⠀⠉⣀⠈⠡⡴⠎⣧⠀⠀⠀⠀⠀⢸⡏⠛⡆⠀⠠⠉⠛⢧⣀⣠⠀⠙⣆
⠀⠀⠀⠘⢦⡉⠀⠰⠀⠀⠀⠀⢠⠜⣦⠙⣿⡧⣻⠀⠀⠀⠀⢹⠶⠶⠶⠶⠾⠷⢶⡶⠶⠶⣾⠀⠀⠀⠀⠀⢸⣏⡴⠃⡴⣚⡛⣽⡲⣌⣳⡤⠶⠛
⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠒⠀⠀⠀⠸⣆⣏⣿⡏⠀⠀⠀⠀⢾⡓⠛⣙⣓⣶⣚⣉⣙⣓⣚⣩⠇⠀⠀⠀⠀⢸⣁⠀⢸⡗⣯⣷⠷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣄⡈⠀⠀⣿⢩⡟⠀⠀⠀⠀⠀⠈⢿⡉⠉⠉⠉⠙⠻⣍⡉⢁⡽⠀⠀⠀⠀⠀⢸⢉⣷⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠠⡄⠀⠀⡇⡠⠀⠀⠀⢀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⡆⣿⠀⢰⠁⡇⠀⡠⢖⣵⠥⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣿⠀⡎⣸⡡⣪⠔⠉⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⢀⠇⢀⢧⢿⡾⣰⡿⠋⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠱⣦⠀⠀⠀⣼⠀⣸⡞⡾⠕⢻⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠏⢧⠀⢠⠇⣰⡿⢁⣠⣴⣿⣟⣖⣒⣒⡒⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⡇⡸⣸⣀⠎⣴⠟⠩⢉⣛⠿⠉⠁⠀⠀⠈⠙⠳⣄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡈⢂⢰⢡⡵⢛⣛⠛⠲⢾⣯⣉⣉⠙⠓⠢⢤⡀⠀⠀⠀⠈⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣚⣷⡼⣠⡴⠶⣭⠙⠉⠙⠳⢽⡄⠀⠉⠑⠢⣀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⢟⣵⢿⣝⠢⡀⠈⣷⠈⢆⣀⣀⡀⠀⠀⠀⠀⠈⠳⡄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣚⡽⠑⣹⡟⢸⠈⠳⠃⣀⡼⠗⠋⢁⠔⠁⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣖⣫⠵⠚⠁⣇⣴⡟⣠⢃⡤⠖⠋⠁⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⡀⠀⠀⠀⡀⠀⠈⠀⣴⡄⠀⣨⠟⠴⠋⠁⣀⣤⡶⠯⠥⠐⣲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⡈⢢⠀⢰⠃⠀⣠⢾⢃⣷⣞⣁⣤⣴⠚⠉⠁⢀⡠⠤⠖⣛⡛⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠱⠈⣇⡟⢸⢞⣡⣫⣞⣉⠀⣤⣔⣛⠻⠿⢿⣯⣉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣑⣀⡴⠠⢟⣴⡿⢭⣍⡉⠙⠛⠿⢷⣮⣝⡫⣙⠒⠤⣍⡛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠴⣋⣭⡤⠤⣛⠫⢭⡙⠗⠚⠛⠿⠶⢤⣄⡈⠙⢿⡻⢷⡄⠀⠉⠲⠬⣻⣄
⠀⠀⠀⠀⣠⢞⣭⠖⣻⢫⢷⡈⢢⠀⠙⠢⡈⠢⣀⠀⠀⠀⠀⠀⠉⠒⢤⡉⢦⡙
⠀⠀⠀⠀⠈⠉⠀⠀⠘⠊⠈⢧⡜⠀⠀⠀⠘⢆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠒⠲⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⣀⡘⢻⣿⣿⣷⣦⢤⣠⣶⣟⣿⣿⣷⡶⢰⣶⢶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣉⣛⣿⣿⣿⡿⢋⣥⣾⣿⣿⣿⢸⣿⣿⡇⢸⡱⣆⠹⠛⠋⣻⠿⠃
⠀⠀⠀⠀⠀⠀⣉⣛⣻⣿⡿⢉⣴⣿⣿⣿⣿⣿⠟⢼⠿⠉⠃⡈⠛⠚⠁⠀⠘⠧⢤⡄
⠀⠀⠀⠀⠀⢈⣉⣵⡿⠋⣴⣿⣿⣿⣿⣿⣿⣷⡄⠑⠆⠀⠀⠀⠰⠀⠀⠠⠀⢀⠔
⠀⠀⠀⠀⠈⢁⣺⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⡀⣄⠢⠄⣠⠖⠉
⠀⠀⠀⠀⠚⢙⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠷⠤⣀⠀⠂⠈⠛⠋⠁
⠀⠀⠀⠀⠴⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠁⠀⠁
⠀⠀⠀⢀⣴⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣀⡠⠤⠄
⠀⠀⠀⠀⣰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠀⣴⣤⣶⣿⠟
⠀⠀⠀⠈⢨⡇⢸⣿⣿⣿⣿⣿⣿⣻⠯⢿⡯⢚⢤⣮⡿⠛⠋⠁
⠀⠀⠀⠀⠉⣵⢸⣿⣿⣿⣿⣿⣿⠆⢙⠈⠉⠙⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡄⠙⡌⣿⣿⣿⣿⣿⣿⠅⡀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠿⢿⣿⣻⣗⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠐⡖⠰⡘⣿⣿⣿⣿⣿⡟⡡⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠉⢯⡻⠿⣗⣄⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠹⣇⠛⡸⣿⣿⣿⣿⣷⡿⡁⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣫⡇⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠹⠆⣿⢈⡻⣿⣿⣿⣿⣽⡂⠰⢯⠯⠥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡯⠀⢀⣀⣴⡏⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠿⡈⢷⣝⠿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡀⠀⢠⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠋⢌⣱⡮⠙⠿⢿⣿⣶⣷⣤⣀⠀⠀⠀⠀⠀⣀⠐⠀⢀⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⣤⣬⣙⢛⡛⣿⢿⣿⣿⣿⣿⡿⠿⠷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀
⠀⠀⠀⢀⣠⣄⠶⠮⠉⠓⠀⡁⢨⠀⠀⠘⠀⣐⠀⠄⠢⠀⠀⠀⠀⡊⠄⠄⡀⠀⠐⠰⢱⠀⠀⢀⠉⢈⠂
⠀⠀⠀⡁⠀⣀⣀⠀⣤⠤⠌⠂⠀⠀⠠⢳⠘⠐⡁⢄⢴⢂⠀⢀⠀⠡⠐⢂⣀⡀⠐⠠⠙⠀⠀⢨⣦⠆
⠀⠀⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⣠⡳⠑⠉⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⣠⢒⠂⡉⢙⣢
⠀⠀⠀⠀⠘⠐⢲⠀⡠⢢⠄⠀⠀⠰⠍⠃⠋⠁⠀⠀⣆⣀⣀⣀⣐⡇⠀⠀⣔⡒⢄⠀⢧⠀⠀⠀⠀⠨
⠀⠀⠀⠀⡘⠀⡼⢋⡴⠋⠀⠀⢀⠄⠀⠠⡀⠀⠀⠀⣟⢋⣉⣒⠋⡃⠀⡔⠈⠀⠀⠀⠀⠗⠒⠒⠲⠁
⠀⠀⠀⢸⣧⢊⣔⣗⠀⠀⠀⠀⠂⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡢⠀⠀⠌⠀⠀⣀
⠀⠀⠀⠀⠈⠉⠐⠚⠀⢖⢳⡀⠴⠀⠀⠀⠂⠀⠀⣠⠁⠐⡀⠀⠀⣀⣬⠀⠀⠊⠀⡴⠻⡉⠉⠢
⠀⠀⢀⡄⢀⠀⡀⣀⣀⠀⠁⠀⠀⠀⠀⠀⡠⠐⠁⠀⣁⠈⠀⣑⡀⠈⠉⠁⠀⢀⠞⢑⠌⠀⠀⠀⠑⡀
⠀⠀⢺⠀⢱⠀⡁⠘⠻⠠⠀⢂⠈⠀⢄⠀⣅⣈⣀⣀⣭⣥⣤⣤⠁⠀⠀⠀⠀⣾⠪⠂⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠈⠲⠊⠀⠈⠐⠁⠄⠰⢁⣠⠃⡠⠀⠩⠭⠉⠉⠭⠉⠀⠐⠀⠀⢀⠦⡀⠀⠉⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⠠⢀⢀⠄⠀⠀⠀⡄⠀⠂⠠⢀⠀⠀⠀⢀⡃⠉⠨⠄⠀⠀⠀⡄⠡⠐⡄
⠀⠀⠀⠠⠄⠀⠀⠤⠀⠀⠀⢀⣀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠈⣢⠀⠸⠀⠐⠀⠲⠀⠀⣚⠀⠀⠁⣀⠆
⠀⠀⠀⠀⠀⠀⠄⠐⠀⠁⠀⠀⠀⢈⠄⠀⡀⠀⠀⠀⠀⠀⠮⠁⠀⠈⣳⡴⡻⠃⠀⠀⠀⠀⠀⠀⠐
⠀⠠⠔⠄⠐⠣⠀⠀⠀⠀⠄⠐⠈⠀⠀⠀⠡⠆⢄⢀⠀⡀⠂⠀⠀⠀⠘⣵⡞⠀⠀⠀⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⣀⠀⡴⠋⢳⡀
⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠉⣻⠇⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀
⠀⠀⢀⠀⣴⣧⡟⠛⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣰⠶⠞⣉⣻⠶⣴⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠛⠓⠦⠴⠖⠋⠀⠀⢹
⠀⣠⠟⣧⣤⣼⣇⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡟⣀⣾⣩⣹⡦⢦⡽⠋⣇⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⢀⡤⠶⠦⣄⠀⠘⣆⡀
⠾⠷⢶⠋⠀⠀⠙⠷⣄⡀⠀⠀⠀⠉⠙⢳⡟⡇⠀⠀⠀⣾⠿⣾⣵⣏⣀⣈⣳⡞⠁⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⢳⠀⢰⡏⠀⠀⠀⠈⣇⠀⠈⠙⢦
⠀⠀⠘⢧⠀⠀⠀⠀⠈⠛⠷⢶⣶⣶⡖⠊⠙⠇⠀⠀⠀⠸⡆⠀⠀⡍⠉⢩⡟⢠⠀⠀⠀⢷⠀⠀⠀⠀⠀⢀⡴⠏⠀⠸⣇⠀⠀⠀⢀⠏⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⢙⡟⣻⠀⠀⠀⠀⠀⠹⡄⠀⠀⢠⠏⠀⠀⢀⠀⠀⠘⡇⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠶⠒⠋⢷⡿⠀⠀⠀⠀⠀⠀⠙⣦⣰⠏⠀⠀⠀⠈⠀⠀⠀⢹⡄⠀⠀⠀⢧⣀⠀⢀⣠⡤⠶⠶⠶⠤⣤⣀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⢠⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠄⠀⠈⠀⠀⠈⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠈⠳⣄⡀⠀⣀⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢩⠗⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣼⡇⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄⠀⡤⣠⡋⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡏⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⡄⠀⠀⠀⢀⡾⢀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠙⣦⡼⠿⢧⣸⢷⡞⢳⡶⢦
⠀⠀⣀⣀⣠⣤⣤⣼⣵⣧⡤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⣴⠿⠤⠦⠿⢶⠀⠀⢸⡇⢿⠀⢀⡀⠀⣠⣯⠟⠀⠀⠀⡶⠶⢼⣇⣠⡞⣿⢠⣷⡀⠹⣏
⠀⠰⢧⡤⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠿⠀⠀⠀⠀⠀⢀⡿⠖⠒⠒⠒⠺⣄⠀⠀⡷⠘⢰⡏⠹⠻⣿⠁⠀⠀⠀⠀⠛⠛⣶⡌⠙⢶⡇⢸⠏⣷⠀⠘⣆⡀
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⣷⠀⣡⠴⢮⣷⣄⣈⡿⠀⠀⠀⠀⠀⠀⣷⠿⠽⢤⣤⣽⣯⡴⠿⠗⠛⣿⠁
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⡀⠀⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⡟⠛⠻⣟⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⢦⣼⣧⣴⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣏⠀⠂⠈⠹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠒⠒⠚⠛⠛⠒⠛
⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⣶⣿⠷⣼⣤⠾⠁
⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠓⠲⠦⢤⣄⣀
⠀⠀⠀⢀⣾⣭⠿⢭⣝⡛⢻⣞⣛⣷⣀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣠⡤⠶⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣰⡀⠀⠀⣤⠀⠉⠛⠦⣄
⠀⠀⣠⠞⠁⠀⠃⠀⠀⠉⠳⣍⢹⣟⠻⡍⠓⣦⠀⠀⠀⠀⠀⢀⡴⠋⠱⣤⠀⣄⠉⢂⡤⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣯⣍⠉⠛⠺⢧⣀⢀⡀⠀⠈⠳⣄
⠀⠰⡇⠀⠀⠀⠀⠈⠃⠀⡀⠈⢳⡉⢳⡟⣳⠌⣧⠀⠀⠀⠀⣾⠀⠟⠀⠀⠀⢁⣠⠀⠀⠶⠂⢹⡆⠀⠀⠀⠀⠀⠠⣇⠚⢷⠀⠀⠆⠈⠙⠦⣄⡴⠄⠈⢷
⠀⠀⠻⣄⠁⠀⠰⠀⠀⠀⠀⠀⡤⢻⡌⠙⣏⡧⣿⠀⠀⠀⠀⠈⡿⠲⠶⠶⠶⠶⠶⢶⡶⠶⠶⢶⡇⠀⠀⠀⠀⠀⢸⣯⡵⠏⣠⠖⣋⢩⣽⡲⣌⣳⣤⠶⠚
⠀⠀⠀⠈⠳⢦⣀⠀⠀⠲⠀⠀⠀⠀⢳⢰⣏⣷⡏⠀⠀⠀⠀⢸⡟⠚⠛⢛⣳⣶⣚⣋⣙⠓⢒⣋⣽⠀⠀⠀⠀⠀⢸⡇⠀⠀⣏⢾⣹⣯⠷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠃⠀⠸⡟⢉⡟⠀⠀⠀⠀⠀⠀⢻⡛⠛⠉⠉⠙⠻⢯⣍⠉⠉⢩⡇⠀⠀⠀⠀⠀⢸⠉⣳⣤⠿⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⣤⣤⡼⠷⠖⠋⠀⠀⠀⠀⠀⠀⠺⠚⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⠶⠶⣟⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⢴⡶⠖⠋⢝⡃⠠⠠⠀⢸⢠⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⣾⢟⣫⠛⠋⠄⢀⠀⣀⢱⣔⢸⡇⣼⠈⠙⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⣀⢀⣠⣄⣀⢼⣵⠒⠻⠿⣿⡁⠀⠀⠠⢀⣠⣶⣾⣧⠃⣴⣧⡴⢾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠾⢋⡎⠀⠀⢀⣨⣿⣿⠟⠁⠀⣠⡴⣛⣽⣄⣬⣷⣿⠿⣉⣥⣾⠿⠿⡿⣤⣬⡇
⠀⠀⠀⠀⢀⣠⡖⠋⠈⢸⣿⡄⣼⣴⣾⠧⠞⠛⣿⡟⠀⠀⠞⢧⣦⣿⣿⣿⢿⡍⣧⣷⣿⣿⠉⠉⠉⡛⣯⣿
⠀⠀⢀⣴⡿⠋⠀⠀⣰⣿⠟⢃⠋⠉⠀⠀⠀⣬⠟⠁⣰⠂⣼⣿⣯⠿⣿⣿⣾⡿⠛⠛⠿⡋⣉⡙⢻⠁⣼⠋
⠀⣰⣛⠿⢅⣀⣴⠛⢻⡿⠀⠈⠀⠀⠀⠀⢠⠟⢂⠰⠷⠀⣸⣥⠴⣶⣿⣿⡫⠛⣷⡄⠀⠀⣸⡧⠚⢲⠏
⣰⣿⡟⢠⣾⡿⢿⢀⣼⡇⠀⠈⠇⡀⠀⣀⡍⣱⢦⣤⣾⠏⠁⠀⠀⠸⣿⣦⠀⠀⣨⣿⣠⣦⠾⣥⠤⠏
⣿⣿⣧⣿⠃⠀⠸⣼⠟⠀⠀⠀⠀⢉⡽⣿⢾⡟⠁⠈⠀⠀⠀⠀⠀⠀⠈⢻⣧⣀⣺⣾⠉⠁
⢻⣿⣿⡟⠀⠠⠚⠁⠀⠀⠀⠀⡰⠋⡼⠁⠻⡇⠀⠀⠀⠀⢀⡀⠠⣴⣦⣴⣿⠟⣿⣿⡴⠒⠒⠒
⠈⠻⣽⠇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠐⡇⠀⠀⣈⣒⣶⣾⣿⣋⣭⠟⠋⠉⠁⠁⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣫⣭⣥⣬⣉⣽⠏⠁⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠉⠉⢉⠉⠭⠟⢱⡀⠀⢢⣾⣾⡿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⣄⠀⠀⠠⠠⠒⠉⠀⠉⠂⣬⣽⡟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠵⣤⣶⣶⣦⡴⣶⠾⠟⠋⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⣿⣻⠿⣿⣻⢿⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣾⣾⣿⣾⣾⣾⣾⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⢠⠛⠂⢲⠀⠀⢀⣶⣤⣼⡀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠚⠛⠒⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗⠚⠛⠃
⠈⢷⡄⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⢰⠿⢿⡄
⠀⠀⠀⠀⠀⣠⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣀⡀⠀⠀⠀⠀⣴⢶⣶⣶⢦⡀
⠀⠀⠀⡀⠠⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣻⣾⣟⣿⣿⡇⠀⠀⠐⢿⠇⠀⠿⠿
⠀⠀⠀⠁⠀⠁⠀⢀⡿⠀⢿⠀⠀⠀⠂⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠙⠓⠛⠛⠊⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⡀
⠀⠶⠶⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡽⣳⠿⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠀⠀⠀⢸⣿⣿⣿⣷⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⣘⠿⣿⣿⠏⠊⠀⠀⠀⠀⠐⣤⣴⣤⣶⣤⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠉⠀⠁
⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠤⠼⠿⠿⠿⠧⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⠛⠛⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣶⣶⣶⣦⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡀
⢸⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠈⠉⠉⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠃⠀⠀⠀⢰⡏⢹⡆
⠸⠿⠿⠸⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠸⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢿⡀
⣿⣿⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⡂⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠠⠐⠠⠴⠃⠆
⠀⠄⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠪⠄⢲⣂⡘⠂
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢀⠂⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⢂
⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠙⠀⠠⠂⠀⠆⠂
⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠈⠈⠈⠐⠀⠀⠄⠀⠀⠀⢄⠀⠀⠀⠀⠻⣙⠒⠊⠀⠀⠁
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠄⢠⣤⡀
⠀⠀⠀⣀⢀⡀⠈⠻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠠⢊⠐⠲⠧⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣀
⠀⠀⡌⣗⠶⡃⠹⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⢀⠎⠀⢤⢠⠀⠑⡀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠉⠂⠒⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠀⠀⠰⠛⢀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⠀⠀⠀⠑⠄⣀⡀⠠⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠘⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣁⠀⠌⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠁⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠞⠰⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⣠⣶⣿⠄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠐⠒⠋⠀⠙⠟⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠠⠠⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⠤⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠂⠀⠀⠂⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⢀⣀⣀⣐⣒⣒⣂⣀⣀⣠⣠⣤⣤⣤⣀⡄⡀⢠⣤⠤⠤⠤⠤⠐⠒⠉
⠀⠀⠀⠀⠠⠔⢶⠀⠀⠀⠈⠙⢲⣤⢀⣀⣀⣤⣤⠶⠛⠉⠉⠁⠀⣀⣴⡀⠀⠀⠀⠀⠐⠉⠈⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠶⢍⡉⠁⠀⠉⠉⠀⠀⢀⣀⣤⣤⣖⣋⣁⡀⡁⠂⢐⠀⣋⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⡎⢭⠀⠀⠒⠬⠍⠉⠓⠒⠒⠊⢉⡀⠤⠛⠉⠉⠩⠉⠉⠻⠄⠀⡠⠂⠀⠹⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠀⠀⢀⣠⣴⠶⡋⠉⠉⠉⢀⠀⢀⠀⠀⠀⢀⣀⣀⠰⠀⢠⠀⠀⢀⡀⠄⠁⢀⣀⣀
⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⠴⢋⠉⠙⠂⠈⠛⠛⠒⠀⠀⠘⠁⠤⠄⠈⠀⠀⠂⠀⠐⠶⠚⠉⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠔⠛⠇⠀⠀⢠⠶⠶⣿⡆⠀⠀⠀⢀⠴⠖⠶⠄⠀⢀⠞⠳⠄⠀⠟⡟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢾⠀⠀⠀⠐⠤⠐⠁⠀⠀⠈⠃⠐⠂⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⢀⣀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡏⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⢄⣠⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠
⠀⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠚⠻⢸⠾⢡⠻⢓⠀⠀⠀⢀⡀⠔⠒⠋⠱⠤⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⢠
⠀⠧⣄⣀⣀⣀⡠⠜⠀⠀⠀⠀⠀⠀⠘⠈⠈⠁⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠠⠑⠀⠀⠀⠆⠀⠀⠀⡀⠞⠚⠁⣸⠜⠉⠀⡀⣴⠀⠠
⠀⠿⢦⣤⡄⠽⡤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠘⠚⠀⠈⠓
⠀⠀⠀⠬⠩⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢀⣀⠀⠠⠄⢀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣶⣿⠟⠳⠶⠦⢦⡄⠀⠀⠀⠀⠀⠁⠀⠀⠁
⡔⠀⠁⠄⠄⠀⠒⠀⠲⠂⠀⣈⠁⢂⡠⠀⠀⠀⠰⠒⠀⠲⠶⠛⠉⠉⠂⠀⠀⠀⠈⠉⠻⠥⢀⣀⢤⡤⠴⠂⠀⠀⠀⠀⠀⠄⡀
⠈⠲⠤⠤⢑⣁⣂⠀⡀⠈⠛⢀⠀⠀⠀⠔⠂⠀⠀⠴⢤⣄⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠿⠾⠶⠶⠿⠑⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂
⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⣤
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠐⠀⠀⠀⠀⠁⡀
⠀⠱⢬⣽⣿⣿⡫⠅⠀⠀⠀⠀⠁⠀⡇⢠⠀⡄⠁⠀⠀⠖⠄⠐⢠⠤⠀⡄⠀⠀⡄⡀⠀⠀⢏⠀⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠔⠁⠸⢄⠀⠀⠠⠀⠢⠀⠰⠘⠠⠃⠡⠠⠠⠁⠃⠀⠀⠈⣉⠃⠀⠀⢠⣷⡈⣧⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠾⠋⠁
⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠱⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠁⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⡀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠄⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠈⠂⣐⠂⠀⠀⠉⠓⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⢄⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⣀⠄⠀⠀⠍⠄⠠⣝⠅⠀⠀⣦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠷⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠠⠀⢀⡐⡁⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⡏⣼⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢂⣄⠀⠀⠀⠀⠀⠀⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠆⠀⠀⠋⡋⠉⣠⣤⣴⣿⠃⠸⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⢿⣷⣾⣿⠿⠟⠃⠀⢸⢇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⡔⠁⠀⠢⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠋⠀⠀⢠⠄⠀⠐⡂⡘⠀⠘⠧⠤⠤⣀⣰⡀⢀⠄⣠⠀⠀⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢀⠴⠃⠀⠀⣠⢆⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡀⠀⠜⠁⠀⠐⠀⠀⠀⠀⠰⠀⠁⣰⠇⠘⢰⠁⠀⠀⠀⠀⠙⠂⠠⢶⣎⡁⠀⣤⡶⠿⠿⠉
⠀⠀⠀⠀⠀⢀⠀⠀⢀⣿⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⣠⡏⡄⠀⠀⠀⢰⣿⣦⣡⣾⢿⡇⠀⣸⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣿⠀⠀⠀⠤⠀⠀⠀⠀⢠⠀⠰⠃⠉⣷⠁⠙⠁⠀⠀⠀⣿⢏⣿⣿⡿⠀⠙⠔⢁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⠀⠀⠸⢇⠀⠈⣿⣿⣿⣿⣧⢀⡄
⠀⠀⠀⠀⠀⢀⠔⠟⠁⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠠⠁⠀⠹⣿⡷⠿⠿⠞
⠀⠑⠄⣀⣤⣶⣊⡤⠖⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠒⠀⠀⠀⠀⡜⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⣿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⣠⠊⣠⠖⢉⡤⠝⣷⣤⣀⠀⠀⢀⣴⠟⡹⠋⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣱⣱⣃⡞⣡⠞⣁⠔⢋⣡⣬⡿⠃⢀⡾⢃⡞⠀⣰⠋⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠉⠩⠭⢝⣛⡻⢾⣥⣖⣉⢤⣿⠀⢀⣾⢁⡞⠀⣰⠃⣠⠎⡴⣿⠏
⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠉⠑⠮⡙⢷⣾⠃⠀⣼⢇⡞⢀⣼⠃⣰⠇⢀⡾⠃
⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⠣⡙⢷⣤⣿⣟⣤⠟⣡⡾⢃⢠⡿⠁
⠀⠀⠀⣤⣿⠀⠀⠀⠀⢼⣟⣹⡄⠘⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣛⠭⠖⢁⡿⠁
⠀⠀⠀⣿⡙⠶⠂⠀⠀⠈⠛⠋⠀⠀⡇⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣒⣒⡂⢸⡇
⠀⠀⠀⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⣸⠃⠀⢀⣿⣄⠀⠀⠀⠀⠀⠀⢠⣴⠶⣦⣤⡑⠢⣄⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⣤⠄⠐⠁⠀⣠⡾⣿⠮⣛⢶⣄⠀⣀⣴⣿⢧⣄⠈⢿⣿⡳⣦⡙⠢⡹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢶⣶⣿⣋⣀⣈⣿⣮⣿⣿⣾⣏⠑⢬⡓⣭⣿⠌⢿⡻⣆⠙⢦⡀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢏⣿⣯⡙⢮⡑⢝⢷⣹⡶⠟⠋⠁⠀⠈⣷⡘⢷⡈⠻⡄⢈⡲⢝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣿⣷⡙⢦⡙⢮⣻⣿⠀⠀⠀⠀⠀⠀⠘⣷⡈⢳⡀⠙⣆⢹⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢮⣿⣦⡙⢦⡙⣿⡄⠀⠀⠀⠀⠀⠀⠘⢷⡄⠳⡄⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⡿⣯⡢⣱⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣽⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⢠⠤⠤⢤⣄⡀⢐⠋⠒⠐⢆⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡔⢱⠤⣀⡴⡁⠈⠀⠒⡦⠉⠙⢎⣢⠇⠠⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠆⣰⠚⢍⢍⠙⡉⠉⡝⣧⡷⠉⡝
⠀⡹⠐⠉⠉⠐⣼⡦⠀⠉⢠⠀⢺⢻⣅⠄⠒⢊⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠘⠒⢆⡀⢸⡜⠀⣇⠀⡁⣿⡦⣀⠸
⡎⠀⢀⣤⠒⠪⢀⣁⠤⠀⠄⢁⢁⡼⢏⠙⢀⠇⠉⠀⠀⠀⣀⡀⠀⡀⢀⣀⡀⠀⠀⠸⠴⡆⣜⠷⠎⠢⠼⠴⠤⠿⠔⠓⠃⠘⠃
⠈⠐⠉⠀⠱⠤⠜⠣⢇⣒⣱⡥⠚⠀⠀⠉⠉⠀⠀⢀⡒⠃⠄⢈⡶⡶⠭⣄⠬⣙⡆⠀⠘⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠑⠒⠂⠀⠖⠀⠒⠗⠊⢻
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⡇⠀⠀⡇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⡠⠤⣀
⠀⠀⠀⠀⢀⢠⠔⠁⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠈⠠⢀⡇⣀⣀⣇⣀⣀⡧⠔⠃⠀⠀⠀⠀⠀⠀⠀⢀⠞⠅⠀⠀⢰⣉⡈⠣
⠀⠀⠀⠀⣀⠈⢆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠠⠂⠠⣈⠆⠀⠀⢆⠃
⠀⠀⠀⠀⢘⠢⡀⠑⠤⣀⠀⠀⠀⣠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠂⠄⣀⡀⠀⠀⠀⠀⠀⠀⢣⠠⡀⠀⠠⠀⣀⠹⢀⠁
⠀⠀⠀⠀⠈⢦⡈⠑⠂⠤⢈⣉⣉⡤⠊⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⣠⠖⠂⠈⠁⠒⢢⡄⠀⠀⠑⠆⡈⣉⢀⣤⠴⡃⢤⡀
⠀⠀⠀⠀⠀⠀⡝⠒⡤⠤⠠⠴⠊⠀⠀⠀⠀⠀⢀⠤⢦⣊⠀⠀⠈⠀⠱⠂⠀⣀⣀⠀⢀⠄⠂⠁⢰⠀⠀⠀⠀⠀⢠⠩⠤⡰⠹⡉
⠀⠀⠀⠀⠀⢠⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⣀⠄⠓⠒⠂⠬⢲⡤⡀⠀⠀⠀⢀⠀⡠⠊⡄⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠱⡀
⠀⠀⠀⠀⢠⠏⡰⠁⠀⠀⠀⠀⠀⣠⠖⢉⠀⠀⠀⠀⢀⠔⠀⠊⠉⠑⠒⡶⡉⠓⡄⠀⡧⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠱
⠀⠀⠀⢠⠏⢠⠃⠀⠀⠀⠀⠀⠀⢈⠑⠢⢅⠂⠠⢴⠐⠓⢢⠤⠀⠴⡄⠀⠉⠀⡶⠈⠀⠀⠀⢀⡠⠖⠋⠉⠙⠙⠢⡄⠀⠀⠀⠈⠉
⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢸⠄⠄⣠⠀⠀⢼⡠⠄⠤⣇⠠⠂⠉⠁⠀⠀⠀⣠⠋⠀⠀⢀⡤⢤⣀⣀⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢐⣀⡜⢁⡤⠄⣻⠀⠊⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢰⣧⠈⠦⡀⠀⠀⠀⠀⠀⠈⣆⠀⠸⡀⢀⡦⠔⢋⢆⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠚⢍⠡⠀⠉⣧⡤⠀⡆⠀⠀⠀⠀⠀⠀⠈⠣⣌⡙⢧⣀⣀⣼⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⠒⠘⠃⢉⠢⠀⠀⠀⢃⢁⡠⠛⠳⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠠⡈⢆
⠀⠀⠀⠠⠠⣤⣀⠀⡔⠉⠭⡉⠢⡐⡀⠀⠀⣂⣣⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠳⡀
⠀⠀⠀⢠⢄⡘⢄⣉⡉⡠⠀⠁⠀⣸⠼⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⡆
⠀⠀⠀⣼⠀⢠⢦⠤⠋⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⢀⣤⣔⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠉⠀⠀⠀⡀⡀⠛⠀⠠⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠒⠦
⠀⠀⠀⢠⡶⠋⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡄⠀⠀⠀⠀⠀⠀⣠⠞⠂⠀⠐⠋⠀⠀⠀⠘⠋⠉⠀⡀⢀⠄⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡜⠁⠀⢀⣤⢀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⡀⠀⠀⢀⠀⠀⠘⡻⠋⠀⠀⡔⠁⠀⣾⠖⠀⠀⠀⠀⣀⡀⠉⠁
⠀⠀⢸⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣀⠴⠂⠀⠀⠀⠀⡛⠁⠀⣤⣄⣀⠤⠚⠁⠀⠀⢰⡗⠃⠀⠀⠀⠀⠀⠀⠀⠹⠏
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣀⡀⣠⣆⢒⣈⣀⣤⡤⠟⠉⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⡅⠀⠀⠀⠀⠀⠘⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢃⠀⠀⠀⠀⠚⠛⠃⠀⠀⠰⡿
⠀⠀⠘⠻⠀⠀⠀⣠⡀⠀⠀⠀⠀⢀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠂⠀⠉⠁⠀⠀⠀⠀⠞⠀⠘⠟⠀⠀⠀⣠⣤⣄⠀⠀⣠⣤⣤⣤⣀⡀⢀⣾⢃⣼⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠘⠲⣿⠆⠀⠀⠈⡁⠀⠐⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⣠⣿⠃⠘⠟⠛⠙⠛⠛⠛⣿⡟⣛⡁⣘⠁⣤⢤⢿⣼⠀⠀⠀⠀⠀⠀⠀⠉⠀⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢸⣿⠇⢀⣶⠲⡄⣼⡏⢹⢠⣿⣏⣼⢣⡿⢸⡧⢊⣔⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠛⢂⣾⣯⣠⣧⣿⠣⡼⢻⡟⢿⣄⠘⢓⣉⣙⡉⢸⣇⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⣠⠞⠻⣧⠟⠁⠙⠚⢁⣀⣥⣼⠿⢿⣍⣁⣈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠈⠿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠞⠃⠀⠈⠉⠁⢀⡀
⠀⠀⠀⠀⣴⠆⠀⠀⣤⠀⠀⠀⠈⠙⠁⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠒⠓⠚⠃⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⡾⠖⠋⠉⠁⠙⠒⠀⠀⠀⠰⠒
⠀⠀⠀⢠⠀⠘⠷⠀⠀⠀⠀⠀⣴⡶⠂⠀⠀⠉⠉⠀⠄⠀⠀⠀⡠⠂⠛⠁⠀⠐⠟⢃⡀⠀⢀⣤⡀⢀⣀⠀⠀⠀⠀⠘⢿⠁⣠⣤⠀⣀⣘⣀⣀⠠⣤⠀⠀⢤
⠀⠀⠀⣿⣧⠀⠀⣠⣄⢠⣴⣦⠀⠀⢠⣶⣤⠀⠔⢠⠆⠀⠀⣼⠃⠀⢛⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡄⢦⡤⠒⠉⠉⣉⠉⠉⠉⠓⢄⢀⡀⠁
⠀⠀⢰⣿⣿⣿⣧⣤⣤⣄⡀⢤⣄⣀⣀⣀⣀⣀⣴⡏⠀⠀⢀⡴⠀⠀⠙⠁⠀⠀⠀⠤⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⣀⠀⠀⠋⠀⠀⢀⡀⠀⠈⠡
⠀⠀⠘⢿⣽⣋⡉⣉⡉⠹⠿⠟⠛⠉⠉⢉⣽⡷⣀⣶⠀⠀⠈⠳⠀⠀⠦⢀⠐⠀⠈⠀⠁⠚⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⣏⠀⠀⠋⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠃
⠀⠀⠀⢰⣿⣿⣿⣭⢤⣦⣦⣤⣤⣴⡷⠾⠿⠛⠙⠋⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠉⠀⣀⠀⠀⠤⠀⠀⣀⡀⠀⠀⢸⡇⣴⠄⠀⠀⠀⠀⢴⣆⠀⠀⠀⡀
⠀⠀⠀⢨⣥⣌⣉⠀⠀⣀⣀⣀⢠⠾⠆⠀⣀⣠⣤⣴⡛⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠉⠀⠀⠈⣿⠀⠀⣤⡀⠀⠀⠀⠀⠀⢠⡄⠛
⠀⠀⠀⢉⠾⠋⠉⢭⡉⠉⠋⢹⠟⢻⡏⠉⠉⠉⢈⣉⣤⠀⠀⠀⠀⠀⣀⣀⠀⠰⠖⠒⠒⠀⠉⠈⠁⠀⢠⡀⠀⠀⠀⠀⠘⣇⠀⠈⠁⠀⠶⠂
⠀⠀⢠⣿⡟⢛⡶⠶⣤⣤⣤⣤⡶⠶⠶⠞⠛⢋⡉⠡⢄⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢴⣦⡄⠀⠀⠀⠙⠁⢠⡆⠀⠀⠀⠈⠳⣄⣀⡀⠀⠀⢶⠆⣀⠤⠔⠁
⠀⠀⠀⠨⣷⣿⣿⣄⣀⠺⠷⠀⠀⠀⣀⡀⠀⣛⣣⠴⠊⠀⠀⠀⠀⠀⠀⠈⠁⣀⡀⠀⠀⠉⠁⠀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠃⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣠⠖⡿⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡤⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡿⠁⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠘⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠔⠀⠀⡠⠊⢀⣄⠀⠀⠀⠀⠀⠰⠦
⠀⠀⢸⠀⠀⠠⡿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠈⠀⠀⠴⠂⠀⣀⠀⢀⡠⠊⠀⠀⣰⡥⠀⠘⠁⠀⠀⠀⠐⢶⠆
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠀⢀⡀⠤⠐⠀⣀⣸⠟⠂⠁⠀⠀⠀⠀⠙⡁
⠀⠀⢸⠀⠀⠀⠀⠀⠰⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠐⠓⠂⠀⠀⢴⠆⠀⠈
⠀⠀⠙⠇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⠋⠀⠛⠁⠀⢀⣠⡤⣄⠀⢀⣤⣤⣤⣄⣀⢠⣟⣡⠇⡀⠀⠀⣠⢤⠀⠀⠀⠀⠓⢿⡆⠀⠀⢈⠀⠄⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢃⣴⡿⠀⠛⠋⠉⣉⣉⠛⣿⣛⣅⢠⡍⣴⢶⠻⣾⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠁⣼⠏⢳⢸⡏⢸⣼⣿⡵⠟⣾⣃⣿⡨⢾⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠉⣸⣿⢦⡟⢻⣉⡟⠹⠏⢻⣦⡬⠵⠶⣄⠘⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣠⠞⠁⠙⠊⣤⣤⣤⣴⣶⠿⠋⠉⠛⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣠⠤⠀⠰⠿⠃
⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⠀⠚⠷⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠀⠛⠦⠀⠀⠀⠀⠀⠀⠀⢠⠞⣤⣤⠔⠒⠒⠢⠄⠈⠀⢀⡤
⠀⠀⠀⡈⠁⠶⠄⠉⠀⠀⠀⣤⡤⠀⠀⠙⠛⠀⠀⠀⠀⠀⡀⠒⠋⠀⠰⠶⠆⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⢻⡟⢁⣤⠀⠀⠒⠀⠀⣀⡀⠀⢀
⠀⠀⠰⣿⡀⠀⢀⣄⢀⣴⣤⠀⠀⣴⣦⡄⠠⢢⠆⠀⠀⡾⠀⠚⠂⠀⠀⠀⠈⠃⠀⠉⠁⠀⠙⠀⠀⠀⠀⢀⢱⣬⠕⠊⠉⡉⠉⠉⠐⠢⡀⣀⠃
⠀⠀⢸⣿⣿⣷⣴⣦⣤⣠⣤⣄⣀⣀⣀⣀⣤⡏⠀⠀⢠⠆⠀⠈⠁⠀⠀⠀⠄⠀⣦⡀⠀⠀⠐⠀⠀⠀⠀⢸⡟⠁⣀⡀⠀⠋⠀⠀⣀⡀⠀⠉
⠀⠀⠘⢫⣭⣌⣡⡄⠘⠛⠋⠉⢉⠉⣽⣷⣠⣾⠀⠀⠈⠃⠀⠐⢂⠐⠀⠀⡀⠀⠉⠀⠀⠘⠀⠀⠀⠀⠀⢨⠄⠀⠉⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢾⠿⢿⠷⠒⠷⠶⠶⠶⡾⠛⠛⠋⠉⠁⣀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠠⠄⠀⠐⠀⢀⠤⣄⠀⠀⢿⡴⠃⠀⠀⠀⠀⠺⠆⠀⠀⢠⡀
⠀⠀⠀⠾⣶⠶⠤⣤⣤⣤⣤⣼⣍⣤⣤⡴⢾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠄⠤⠀⠀⠀⠀⠀⠀⠘⣇⠀⠺⠆⠀⣀⠀⠀⠀⠓⠈⠁
⠀⠀⢠⣾⣥⣄⣚⡃⠀⠀⣙⣁⣛⣀⣤⡤⠴⠖⠒⠀⠀⠀⠀⠐⠒⠀⠈⠁⠀⣀⠀⠀⠀⠀⢸⠆⠀⡀⠀⠀⠘⢄⡀⠀⠀⠉⢀⣀⠀⠀⣀
⠀⠀⠈⣻⣡⡾⡍⠛⣻⣏⠛⠉⠉⠉⠀⠰⠦⣈⠜⠁⠀⠀⠀⠀⠐⠆⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠉⠀⠲⠤⣤⠉⠐⠋⠁
⠀⠀⠀⠈⠉⠉⠙⠛⠂⠠⠶⠴⠖⠚⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠢⠀⠺⠂⠀⠀⠀⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂