Aestetic bio Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⢰⠶⣎⠂⣠⠖⠁⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡊⠈⠑⢄⠀⢀⠀⠠⠤⠴⠶⡄⠀⠀⠀⣀⢀⡀⢃
⠀⠀⣰⢒⡥⠰⡐⠈⠟⠁⠐⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠁⡀⠰⠆⠀⠀⠡⠀⠀⠀⠀⢹⢄⡔⢉⠁⣀⠁
⠀⠀⠈⠿⡉⠿⠃⠀⠤⢀⠢⣤⠀⠀⠀⠐⠂⠠⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠦⠀⠀⡠⠂⢉⣄⠄⢂⡀⣄
⠀⠀⠀⠀⠀⣠⠴⠂⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠐⠋⠾⢀⠞⠀⡰⣊⠀⠀⢂⡟⢉⡶⠄
⠀⠀⠽⠇⠈⠅⠀⠀⢶⢠⣠⡆⠀⠀⠡⠀⢀⠀⢰⠶⢤⠂⠀⠀⠗⠂⠀⠀⠀⠀⠀⣀⢁⣄⠀⠀⠀⠀⠀⠓⠈⠀⠏⠟⠐⠀⢰⡿⠓⠲⠂
⠀⠀⠀⠀⠘⡀⠀⠀⣾⣯⣹⠄⠀⠀⠀⠀⠀⠀⠉⠐⠁⢀⡄⠁⠀⠀⠀⠀⠀⠀⢤⣄⠙⠿⠁⢀⡴⠆⢀⠉⠓⠒⢴⡖⣤⡀⠀⢠
⠀⠀⢀⡘⠒⠀⠀⠀⠉⠻⠏⠁⠀⠀⠀⠀⠀⠈⣛⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⢾⠟⠀⠂⣀⢪⠒⠎⠙⢀⠀⠀⠀⠈⠀⠀⠀⠔
⠀⠀⠀⢬⡀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢚⡁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣍⢀⠛⠙⠀⠀⠓⠂⠘⠀⠀⠀⠠
⠀⠀⢀⡄⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⣘⡬⣄⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠈⠡⠛⠃⠀⠀⠄⢐⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⠄⢠⠀⡀⠀⡄⠠⠀⢐⠄⢁
⠀⠀⡓⡄⠀⣄⠀⠀⢀⣀⡤⠀⢠⡀⠀⠠⡄⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⠁⠀⠁⠂⠐⠈⢡⠀⠤⠐⠀⠀⠤⠀⠄⠀⢀⡊⢲⡄
⠀⠀⡃⠀⢰⣿⣷⣿⣿⣿⡶⠀⠜⢛⣦⠤⠃⠤⡀⠄⢀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠂⠀⠀⠀⠈⠀⠀⢀⡀⠀⡀⠀⠐⡄⢱⣎
⠀⠀⠁⠌⠈⠛⠿⠤⠖⠛⢁⡀⠀⣀⠀⠀⢢⠀⣀⠀⠀⠐⠀⠀⠀⠋⠃⢤⠄⠀⠁⡄⠄⠠⠠⠀⠀⡄⠀⠠⢄⠀⠀⠠⠀⡄⠐⠁⢧⣍⠆
⠀⠀⢀⣀⡀⠀⡀⠀⠐⠀⢐⠄⠀⡔⠃⠰⠃⠾⣉⡇⠠⢢⠄⠀⠆⠂⠀⠀⠐⠀⢀⡤⠲⣦⡀⠀⠀⠈⠉⠉⠀⠀⢤⣦⡾⠆⠀⠀⣰⠧
⠀⠀⠀⠩⠁⠢⡀⠀⠀⠀⠀⠀⠈⠞⠀⡩⢤⣀⡀⢀⣀⠼⠀⠀⣀⣀⡄⢀⠀⠀⢺⡄⠀⢨⡷⠀⠰⢴⢂⡀⢘⠱⠄⢁⣶⠠⠊⡀⠙⣧⠁
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠋⠀⠈⠀⠀⠙⠛⠛⠁⠰⠧⠚⠻⠄⠀⠀⠠⠀⠉⠴⠖⠁⠚
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⡔⠁⠄⠘⠃⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⣩
⠀⠀⠘⠀⠄⠀⠐⠀⢐⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠤⠖⠠⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢀⡁⠀⠀⢰⣿⣿⡆⠀⠀⠀⢀⡈⠃⠘⣔⡀
⠀⠀⠀⠀⡀⡀⠤⠄⠄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠲⠎⠛⠛⠁⠀⠀⠀⠈⡠⠀⠈⠐⠈⣃
⠀⠀⠀⢈⠀⢁⠀⠀⡄⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡁⣀⠰⠗⢤
⠀⠀⠀⠀⠢⡀⠠⠄⢤⡀⠀⠠⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢥⠄⠐
⠀⠀⠀⠀⠀⠀⠁⠐⠀⠄⠐⠀⠰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢒⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠐⠂⠀⡆⠀⠀⠀⠀⠀⠀⠆⠀⠠
⠀⠀⠀⠀⠀⢀⡀⠀⣴⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡐⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣶
⠀⠀⠀⣤⣴⣌⠁⠀⠈⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠻⣿⡿⠀⠤⠀⠐⠿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠦⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡘⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⠆⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⠀⢀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣋⠀⠀⠀⠌⠃⠄
⠒⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡈⢀⠖⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⢋⠈⠂⠦⣆⠘
⠘⠀⠀⠃⠀⠰⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠈⠁
⠁⠠⡁⢠⡄⠀⠄⠀⠁⡀
⠀⠀⠈⠢⡀⠆⠀⡄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠐⠐⠆⢄⡀
⠀⠀⠀⠀⠈⠐⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢘⠃⠀⠁⠃⠇⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣷⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⡟⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠉⠁⠀⣈⣦⣴⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⡄⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣀⣼⣿⣿⠇⠀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⣀⣀⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣽⣿⡿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣭⣷⣾⣿⣿⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣾⡿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠻⣿⣿⣿⣿⠿⠿⠛⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣋⣉⡹⢦⣿⡄⠛⠫⣿⣼⠇⠀⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣾⣿⣿⠽⢿⣿⣿⣶⣆⣀⡁⢀⣼⣿⣿⣿⣷⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣻⣿⣷⡄⠀⠙⠿⣿⣿⣿⣿⣿⢿⣯⣳⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⢋⠘⠹⣿⣿⣦⣠⣀⣠⡉⢉⣉⣿⣏⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠟⠀⠠⠄⠛⣹⡿⣿⣿⣿⣷⣿⣿⣟⣦⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⣿⡝⠿⣿⣿⣯⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⠁⢸⠿⠿⢿⣿⠿⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡃⠀⢤⣨⡄⠰⠛⠁⠀⠈⠠⢀⣠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠎⢈⣿⣿⠶⣶⣿⣷⠀⢄⣀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠲⠀⠀⠀⠂⠀⠀⠀⠈⠁⢿⣿⣿⣷⣤⣬⣿⣿⣾⣿⣿⢧⡄⠀⠀⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⢷⣽⡿⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠀⢸⣿⣿⣿⣿⣿⢿⠟⠊⠁⠀⠙⠰⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢨⣤⣈⡿⠁⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣼⡽⠃⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠼⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣷⠂⠀⢀⡑⠀⠀⠀⠄⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡅⡁⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠖⠛⠋⠘⠒⠶⡤⠆⠀⠘⢻⣾⣥⣿⣆⠠⡀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⢀⣐⣄⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⣶⣤⣀⡀⠚⠓⠲⣄⠠⣿⣾⣿⣿⣿⣆⠡⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣤⠀⠀⠀⣤⡄⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠙⠉⠙⠛⠛⠛⢿⣦⡻⠆⠀⠀⠀⢀⣴⣶⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠤⠀⠾⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣉⣿⠟⢦⡀⠀⠙⢢⠀⠀⠀⣄⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⣦⠽⠋⠒⠠⠻⠶⣆⢠⡘⣶⡐⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⡀⠶⡴⠋⢁⡀⠀⠀⠀⠀⠀⠈⢿⣌⢻⣿⡿⢶⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣰⣿⠆⣰⠏⠙⠉⠀⠐⠒⠀⠴⠒⠂⠀⠀⠙⢻⡛⢿⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢘⣻⣿⣿⡄⠃⠀⠒⢀⡀⠀⠀⠀⣤⡀⠶⠂⠀⠀⠌⠿⣆⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢣⣿⣿⠁⠀⠀⠀⠈⠃⣅⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠁⠰⠇⠹⣦⡰⠶⢤⠀⠄⢠⣤⡄⠠⠴⣐⣛⠰⠂⠀⣤⣭⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇⠀⠀⠀⡀⠀⠉⠥⡀⡀⢀⠀⠀⠀⠀⢢⣽⠟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡀⢷⣠⠈⠁⠈⠁⠒⠙⠂⠈⠦⠠⣾⠛⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡄⠹⣦⣀⠀⠀⠀⠀⢀⣤⡄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠛⠃⠀⠐⠷⣮⡉⠀⠈⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠹⢆⠀⠛⠣⣄⠀⠁⠀⠀⠀⠀⠀⣴⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠾⢿⣦⡀⣤⡀⣤⡄⠀⣆⠀⠀⠈⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠤⣼⠀⣤⡴⢀⣋⣫⠤⠼⢯⡁⠌⠑⠻⣯⡴⢶⣤⡁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡤⠆⠀⠠⠀⣍⣻⠏⢀⠟⠻⣿⡿⠂⠈⡙⠳⠤⡀⠈⠳⠾⣍⣁⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠰⠀⠀⣾⡿⣿⣿⣤⡄⠀⢀⠀⢼⣀⡠⠤⠞⠩⣤⣟⠈⠻⣧⣴⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣔⠟⠁⠀⠈⠙⠛⠉⠉⠉⠀⠚⠀⠀⠒⠛⠓⣦⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⣀⢠⠶⣿⠷⣄⠠⠶⠶⢦⢠⠀⠀⢛⣿⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⠁⠀⣀⡀⠀⠈⠁⠀⠀⠀⣀⠀⠀⠄⣰⡞⢰⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⢰⣶⣾⡿⠃⠀⠂⠛⠀⠚⠉⠀⠀⠘⠛⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣀⡿⠁⠀⠀⠀⠀⠀⢠⡤⣦⣀⡠⣶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢿⡄⠈⢷⠐⢠⡴⠂⢋⣽⣆⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⢰⡞⢀⠰⠉⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣶⠛⠉⢞⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢿⣷⡰⣀⠙⣬⣻⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⡀⠀⠀⣤⣁⣀⡈⠉⢩⣧⣄⠈⠉⠈⢰⣦⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⣠⡟⠰⣿⡏⠴⠊⠁⠙⠑⠸⣍⢣⣌⠑⠄⡀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢲⣦⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⢠⡶⣠⠖⣿⡇⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⡄
⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⣉⠙⠀⢃⠐⣻⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠀⠀⠀⠒⠂
⠀⠀⠀⢀⠐⠊⠀⠀⢀⣴⠾⠃⠀⠀⠈⡟⣵⠻⡦⡀⠀⠀⠀⠀⠄⠠⢀⡀⠀⠀⣠⣤⣾⣿⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠸⠀⠀⠀⠀⠘⡆⠀⠀⠀⠐⢳⣿⡏⠰⢧⡀⠀⠠⠎⠀⠀⠀⣠⠕⠈⠟⠛⣶⠃⡛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡾⠛⣇⠬⠀⠘⣷⠀⡀⠀⠀⠈⠁⠀⠀⠀⠀⣾⠀⠀⠈⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣀⣴⡇⠀⠈⠳⢦⣀⠀⠉⠓⠢⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠟⠱⠌⠉⠀⠀⠀⠀⠀⠀⠉⢻⠆⠀⠀⠘⢧⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⠀⠐⢼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠓⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⢀⠀⠀⢀⣃⣀⡀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠳⢎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠁⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣽⡟⢀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠤⢀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⢹⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢮⠉⠞⠁⠙⠀⠀⠀⢠⠊⠀⠀⢀⠔⠀⠀⠀⠀⠈⠓⠀⠁
⠀⠀⠀⢠⠖⠖⠀⠀⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡲⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠄⠀⠀⢰
⠀⠀⠀⠈⠉⠀⢰⡖⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠑⠄⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠐⠁⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠐⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠐⠈⠀⠖⠀⠀⠀⠀⠀⠁⠀⠌
⠀⠀⠀⠀⠀⠐⠄⠀⢠⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⡀⠈⠁⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⣤⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠂⠀⠠⠀⠀⠀⠀⣀
⠀⠀⠀⣀⠀⠀⢀⠀⠘⠀⠤⠔⢆⡉⠀⠀⠀⠀⡀⠀⡀⠁⠀⠀⠆⠀⠀⠁⠐⠒⢆⡉⠀⠀⠀⠀⠐⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠈⢂⠀⢀⠄
⠀⠀⢰⠉⠀⠀⠈⠠⠄⠁⢰⣿⠇⠐⡑⠆⠀⠀⠁⣤⠉⣤⠀⠀⡴⠀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢠⠀⠀⢉⠀⠀⠐
⠀⠀⠈⠁⠀⠀⠀⠘⠂⠀⠈⠄⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡜
⠀⠀⠀⠀⠀⠀⠄⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠠⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⠀⠀⣘⠀⢀⡴⢢⣰⠇⠀⢠⠆⠀⡤⢠⠄⣠⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠙⠠⠄⠀⠀⠀⠀⠀⠘⣷⡀⡷⠀⢼⠀⠾⠁⠈⢳⡄⠐⠇⠀⠀⠁⡿⠀⠋⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⠀⠀⠀⠈⠁⠠⠄⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⢸⠁⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⣀
⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣯⡽⡇
⠀⠶⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⡿⠁⠀⠀⠒
⠀⠀⣀⠀⠀⠀⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠃
⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⠠⠈⠣⠀⠿⠀⠈⠀⠈⠀⠉⠀⠀⠀⠒
⠀⢠⡄⠷⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠈
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠰⠀⠉
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⢀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠺⡟⠋⠁⠄⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞
⠀⠀⠀⢀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠑⠀⠀⠚⠦⢀⠀⠠⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡄⠀⣠⡴⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⢢⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠓⠶⣤⣀
⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠉⠲⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠛⠁⠀⠀⠀⠈⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⢦⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⣦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠆⠰⠂⠀⠀⠀⠘⢆⡀⠀⠓⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⠏⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⢠⠀⢰⠀⠀⠀⠀⠀⠀⠉⠐⠀⡇⠀⠀⢆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⠀⠀⠀⠣⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢠⡄⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⢀⠀⠈⠁⠂⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣴⠶⣶⣾⠟⠋
⠀⠀⠈

⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⡇⠠⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⢼⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⢢⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠠⠀⠄⣘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⢀⠀⠐
⠀⠀⠠⠀⠀⠄⣿⠆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠀⠀⠀⠀⠠⠀⠠⠄⠤⠀⠠⠤⠤⠄⠀⠈⠀⠀⠀⠀⠚⠁⠄
⠀⠀⠀⠑⠄⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠒⠤⠔⠃⠀⠀⠐⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⢠⣄⣀⣀⣠⣀⣤⡄
⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠉⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡑⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡆⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠
⠀⠀⠀⠀⠀⠀⡀⠈⢆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⣦⠀⠘⣿⣦⣼⡗
⠀⠀⠀⠀⠀⠀⠉⢳⡎⢁⣀⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⣀⠀⠀⠀⢀⡀⠀⠀⣀⠀⡄⢠⠀⠀⠀⠠⠀⠀⠅⠀⠀⠀⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⠁⠁⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⡡⠇⠀⡇⢸⠀⠀⡆⠀⠇⠀⡇⡎⡈⠁⠡⠘⡁⠀⠀⣀⣠⣤⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⠇⡇⢘⣀⠈⢇⡀⠆⡀⠁⢣⡸⠂⣀⡠⠇⠀⠀⣿⡿⢋⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢳⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠈⠡
⠀⢀⠀⠀⠀⠀⠆⠀⠡⡀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⢀⠀⠀⠀⠁⠀⢀⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⢀⣾⠟⠙⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠃⠀⠄⠸⠀⠀⠀⠀⠀⠀⠰⠛⠁⠈⠁⠀⢄⠀⠀⢸⡅⠀⠀⢀⣇⠀⠀⠀⠀⠠⠀⠄⠀⢆⣀⡀⠀⠀⠀⠁⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⡀⠀⡀⠀⠺⠗⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⢀⣀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⡠⢈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⠞⠃⠀⠀⠄⠀⠀⡀⢀⠀⠀⠀⠀⠃⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⠀⠈⠀⠇⠀⠀⠀⠀⠀⠀⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⡦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⣷⣲⢱⠃⠀⠀⠀⠀⠀⡀⢀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠘⠡⠖⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠈⠡⠏⠰⠆⠂⣰⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣏⣷⠀⡄⣀⢸⠀⡀⢀⡀⡁⠀⠃⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣨⠗⡿⣉⢿⢾⣹⢾⣿⢧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢒⣢⡌⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢴⡟⢀⡜⠀⠀⠀⠀⣠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠻⢆⠀⠰⠀⠀⠀⠀⠘⢲⠺⡗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠤⠬⠵

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⢁⠈⠢⠀⠐⠀⠀⠀⠀⢘⣻⣇⣾⡿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⡿⠋⠀⠀⠀⠀⣆⠀⢰⡟⢀⡴⠁⠀⠀⠀⠁⠳⣆⡄⠀⠀⠀⠀⠻⢿⣟⢫⣾⡿
⠀⠀⣠⣀⡀⠈⢻⡟⢀⣤⣴⠆⠀⠀⠀⠘⠻⢿⠷⣿⡇⠀⠀⠀⣿⡀⢈⣠⠞⢁⠀⠀⠀⠀⠂⠀⠘⡄⠀⢀⠀⠀⠀⠻⢿⠟⢏⣴⣶⠄
⠀⠀⠘⠿⣿⣷⣄⣧⣿⡿⠋⠀⠀⠀⠸⢿⣷⣾⣶⣿⡆⠀⠀⢦⠘⢧⡍⠀⣰⠏⠀⠀⠀⠀⠀⠀⠓⢧⠀⠀⠀⠀⠀⠀⠿⠿⢿⡛⣩⣄
⠀⠀⢤⣤⣀⡉⠉⡍⢠⣴⣶⠇⠀⠀⣴⣶⣦⣇⣤⣥⡄⠀⠀⢸⣆⠀⣤⠾⠋⡠⠀⠀⠀⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠀⢾⣿⣷⡿⠟⠋
⠀⠀⠈⠻⢿⣿⣦⣵⡿⠟⠋⠀⠀⠀⢈⣉⡉⡏⠙⠛⠁⠀⠈⣦⠙⢦⠀⢠⡾⢁⠀⠀⠀⠀⠈⠠⢤⣸⠀⠀⢀⠀⠀⠀⢰⣶⣶⣷⣿⠿
⠀⠀⢤⣶⣤⣄⡀⡇⣠⣴⣶⣶⠂⠀⢿⣿⡿⢷⣿⣿⡷⠀⠀⠘⢧⣀⠚⠋⣴⠋⠀⠀⠀⠀⠀⠀⠀⢸⣠⠀⠀⠀⠀⠀⣤⣦⣤⣧⣶⣷
⠀⠀⠀⠙⠛⠛⠛⠻⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠉⡤⠞⠁⠀⠀⠀⠀⠀⠈⠀⣤⡘⠁⠀⠀⠀⠀⠀⣨⣭⣉⣥⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠛⢻⡍⠉⠁



⠀⠀⠀⠀⠀⠀⢰⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢷⢸⡇⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⡰⢩⢪⠀⠀⠀⠀⠀⢸⠁⡰⠛⠀⠀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢦⢸⣿⣷⣋⣤⠶⠂⠀⠀⠀⣓⣖⢢⢣⣧⣎⣀⠀⠀⢲⠆⠈⡞⢁⣦⠀⠀⠀⠀⡈⢿⣿⠂⣠⣶⠀⠀⠀⠉⠀⠀⠀⢀⠈⠁
⠀⠀⠀⢲⡘⣿⣿⢛⣫⣥⠶⠂⠀⠀⣀⢈⡢⠹⠿⣒⠪⠟⠁⠀⢸⡀⡸⠖⠋⠀⠀⠀⠀⠀⣿⣦⣹⣾⡿⠃⠀⠀⠀⠳⢀⠈⡇⠂⠀⠊
⠀⠀⠐⣦⡻⣟⣮⣽⠿⣷⣚⡀⠀⠀⠹⡗⠮⣷⣖⠩⢗⠆⠀⠀⠀⠱⡇⠀⣰⠟⠀⠀⠀⣤⡈⠻⢿⣠⣴⡾⠀⠀⠀⣄⠀⠈⠟⠀⠀⡤
⠀⠀⠲⣬⡻⣎⠳⢚⣛⣋⣭⠀⠀⢴⢖⡒⢬⣈⡡⠯⣥⣄⠐⢷⠀⢸⠤⠚⠁⠀⠀⠀⠀⠹⣿⣷⡼⠿⣛⣥⠀⠀⠀⠈⠀⠰⣾⠄
⠀⠀⠓⢮⣟⢮⣉⣩⣭⡷⠶⠂⠀⢈⣓⣭⠵⡿⢖⡭⠕⠁⠀⠈⠣⣼⠀⠀⣤⠀⠀⠀⠀⢷⣦⣍⣷⣾⡿⠃⠀⠀⠈⠇⡀⢀⣠⣀⠖⠃
⠀⠀⠙⢶⣽⡳⠤⠴⢶⣟⣛⡁⠀⠹⣓⠬⣳⣷⡫⠭⣿⠇⠘⢇⠀⢸⠤⠚⠁⠀⠀⠀⠀⣌⡛⠛⣧⣴⣶⡿⠁⠀⠀⠀⠀⠄⢛
⠀⠀⠀⠀⠈⠉⠓⠛⠋⠉⠁⠀⠀⠀⠈⠉⠈⡏⠈⠉⠀⠀⠀⠀⠑⢾⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⠀⠆⠀⠀⠁⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⣤⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⣄
⣠⡷⠀⠀⠀⠋⠁⢀⡤⠀⠀⢸⠁⠀⠀⠾⢥⠙⡄⠀⠀⠈⡀⠀⠀⠀⠠⠀⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡿⠇⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠤⠘⢀⡆⠁⠀⠀⣼⡇⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠛⠀⠀⠀⠀⠀⠀⢠⣔⠷⠀⡖⠀⠀⠀⠀⠀⠑⠀⠀⣼⣿⠁⠠⡇⠀⡠⢄⠀⠀⠀⠀⠁⠁⠄
⡄⠀⠀⠀⠀⠐⠺⢦⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⢠⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡹⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠘⠀⡀⡀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠡⢆⠽⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠸⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⡀⠀⠔
⢹⣽⡲⠤⠀⠀⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠃
⠁⠓⠁⠀⠠⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠰⠀⠀⢤⠀⠀⠈⠁
⠀⠄⣤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢀⡀⠀⠀⠀⠀⠘⠂⢠⠆⠘⢆⡀⠈⠓⢀⢰⠀⢀⠀⢀⠀⢀⣰⣦⢄⣀⠃
⢁⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⠀⠀⡠⠀⠀⠀⠀⠈⠃⠀⠸⠑⠦⡀⠀⢸⠀⠉⠀⠀⠀⠀⡼⠁⠀⠀⠧
⠀⠀⣀⢰⠀⠀⠤⠤⠒⠀⠀⠀⠀⠈⠀⢀⡐⡾⠆⠒⠀⠀⠀⠑⠄⠀⠀⠈⢢⠇⠀⠀⠀⠀⠁⠀⠙⠆⠀⠄
⠀⠀⠀⡟⠐⠒⠲⡄⠀⠐⠦⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⡠⠀⠱⣀⠀⠀⣹⠀⠀⠀⠉⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢁⠐⠀⠀⠀⠀⠙⡀⢀⡀
⢠⠃⠀⠀⠈⠉⢒⡟⠒⠲⡄⠀⠀⠈⠇⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢆⣏⡏
⠈⠀⠀⢀⠄⠀⠈⢧⣀⣀⡆⠀⠀⠀⠈⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢠⡖⠲⠼⣾⡇⠀⠀⠀⡽⠉⠛⡆⠀⠀⠀⠆⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣆
⠈⠀⠀⠀⢨⠑⠀⠀⠀⠙⠤⣀⡇⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏
⠘⠀⠀⠢⠞⠀⠀⢐⡀⠀⠀⠀⢯⣹⠀⠀⠀⠶⣶⣶⣦⣀⡀⠀⠀⠈⠁⠐⠒⠂⠤⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠙⠓⠀⠀⠀⠀⠀⢄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡅⠀⠀⠀⢤
⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣠⣀⣅⣀⣀⣈⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠤⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠏⡠⠈⠀⠀⠖⠛⠛⠉⠀⠀⠀⠀⠀⡄⡀⠆⠀⠠⠘⠀⢀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠆
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠤⠤⠀⠈⠈⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠤⠤⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠁⢀⠎⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠼⡇⠀⠀⠀⠀⠀⠺⠆⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⢐⠂⠀⠀⠀⢈⠠⠀⠀⠀⠀⠀⠀⠀⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢠⠆
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠴⠆⠉⢀⠀⠁⠀⢀⡐⣶⠁⡠⠊⡁⠀⠐⠀⠀⠀⠄⠠⠍⠀⠃⠰⠀⠀⢀⣴⠂⢻⡾
⠀⠀⡏⠀⠀⠠⠂⡀⠒⠀⠀⠀⠜⠁⠀⠀⠠⠓⣈⡉⢀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠬⠛⣜⣃⡟
⠀⢰⠂⠀⢶⠄⠀⠀⠀⡀⠇⠀⠀⠀⠀⠀⢀⡔⠁⣤⠀⠁⡀⠀⢠⠮⠓⠄⠀⢀⠀⠈⠀⠀⠃⠀⠐⠛⣿⠿
⠀⢸⠀⠀⠀⡀⡀⠐⠂⠀⠀⠈⠀⣀⠠⢐⡦⠀⣸⠆⢦⠈⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠛⠀⢤⣄⠀⠀⠀⢀⠒⠀⠦⠀⢨⢠⠘⠂⣱⢿⡠⡸⠀⠀⠀⢀⠀⠠⣶⠀⠀⠀⠀⠄⠀⠁⠀⠀⠙⠀⠡⠆
⠀⠉⠀⣬⠁⠄⠀⠀⠰⠀⠈⠀⠀⠈⢣⡀⣱⠣⠃⢱⠃⠀⡆⣢⣮⠅⠀⠹⠀⡄⠀⠀⢤⣀⣀⡀⢠⠀⠉⠘
⠀⠻⠇⠙⣫⡶⠀⠀⠀⠉⢁⣀⡀⠐⠀⠙⠇⠰⡈⠁⠀⠀⠀⠙⠙⠈⠀⠀⠀⣠⣤⡄⠀⢀⡤⠤⢼⡏⠁
⠀⠀⠀⢀⡤⠀⠀⠠⠴⣘⠣⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠛⠉⠀⠀⡏⠀⢀⣰⠃⣠
⢘⡢⡰⠏⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠾⠀⠁⠐⠏⠀⠀⢠⠶⠶⢷⠚⠋⠀⠀⠘⣇
⠸⣟⣧⠞⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰⢄⠀⠀⠀⠀⠀⠻⠀⠀⠀⣸⣄⣠⠟⠀⠀⢄⠀⠀⠁
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⢀⠀⡍⠀⢀⠠⠀⠄⡄⠒⡁⠀⢰⡏⠉⣷⠀⠀⡀⣿⠿⠚⠻⣦
⠀⢠⣦⠀⡄⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⣈⡒⠀⠀⠐⠦⠀⠀⠀⠂⠀⢀⣼⡷⠚⠁⢠⡀⠈⢰⠂⠀⠀⣨⠁
⠀⠀⠇⠀⠘⢆⠀⠀⠘⠄⠐⠂⠋⠉⠉⠁⠉⠀⠀⣀⡤⣶⠾⠿⠒⠀⢀⣼⠞⠁⠀⠐⠺⡅⠀⠀⠙⠧⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢰⡀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠆⠀⠀⠀⠀⠄⢠⠀⡀⠀⡄⢸⢀⢏⣾⢇⢻⣼⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷
⠀⠀⢠⣼⣧⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⢂⠀⠘⠸⢹⠇⡀⠚⠀⠈⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣄⠀⠸⣿⣯⢆⠙⠹⣄⠀⢀⠀⢀⠀⠀⠀⠀⢰⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⢀⠀⠏⠃⠁⠀⠀⠀⠁⠀⠀⢰⣿⠿⠶⠄⠴⠖⣶⠀⠀⢀⠃⠀⠀⣴
⣿⠐⠆⡹⣿⣾⣇⢣⠸⣂⣄⡿⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢿⣦⠀⠀⠀⠀⠀⢤⣶⣦⣄⣧⠀⣀⡀⣀⠞⠁⠀⠀⠈⢧⡠⣼⣿
⣿⡆⠣⡄⠙⣿⣿⡞⣧⡘⣌⠴⢖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⠀⠀⠀⠀⠀⠀⣿⠄⠀⣹⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⢳⣸⣿
⣿⣿⣦⡈⢦⡈⢿⣿⣦⡄⣿⣏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣏⠀⢀⣱⣿⡴⢀⡴⣊⠀⠀⠀⡌⠀⢀⡿⠀⠀⠀⠀⣄⠀⠀⢀⡆⠀⠀⠙⣿
⣿⣿⣿⣷⣎⢿⣷⣿⡷⢾⣿⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠆⠈⠁⠃⠀⠀⠀⢸⣥⠞⠋⠀⠀⠈⠁⠶⠟⠉⠀⠘⠛⠏⠁⢀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣤⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⣤⡶⠤⢼⣆⠖⠀⠾⡍
⢷⣿⣿⣿⣿⣿⣿⣿⣿⢿⣫⡅⣾⣣⠂⣀⢠⣾⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠒⠻⢆⠠⠙⠛
⠸⣯⡻⣿⣿⣿⣿⡻⢿⣿⣟⡁⢳⡝⠂⠽⢿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣦⣤⣤⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠛⠀⢀⠀⠀⠀⠀⢀⡀
⠜⠘⢿⣮⣻⣿⣽⡿⣴⠊⢿⣷⢿⡏⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠹⡿⠉⣿⠟⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀
⠀⠀⠀⢙⣿⣿⣿⣁⡈⠆⠘⡿⢘⣷⡀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⡰⢇⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠠⠿
⠂⠀⠐⠉⠀⠘⢿⣧⡙⣿⢿⢆⣼⣿⠇⢠⡟⠁⠀⠀⠀⠀⠠⠄⢸⣟⣿⡋⠒⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣷⠀⠀⠠
⠀⠀⠀⠴⣣⠀⠀⠙⢻⣦⢳⡚⣶⣿⣿⣁⡴⢞⠉⠀⠀⠀⠀⢠⢋⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣯⠻⣿⣿⣯⠞⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣀⠶⡀⡀⣄⣀⠀⠙⢷⡝⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⡴⠀⠀⣿⣦⡀⠀⠀⠠⠖⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⣄⡠⠄
⠀⠀⠀⠈⣿⣷⡄⠺⠋⠉⠀⠀⠀⠻⠉⠀⠈⠇⣴⣄⡆⣠⣶⠞⠀⠀⢸⠿⠟⢁⠠⠆⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⡏⠀⣀⠀⢠
⠀⠀⠀⠀⢻⣷⡘⢿⣆⠀⠀⠈⢀⣀⠀⢠⠴⢗⣿⣾⡿⢡⣿⣤⡀⢀⣼⡤⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢨⣿⣡⡠⢟⣀⡤⠤⠤⠆
⠀⢠⣤⠀⠘⠿⠆⠀⠘⠳⠀⠰⣯⣿⣿⣿⣿⣯⣷⡜⠃⣀⣄⣼⡟⠚⠁⣡⠤⣄⡙⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠘⢿⣿⠯⡽⡆⠀⡆
⢀⡘⠙⠀⠀⠀⠀⠀⣀⣴⣦⣼⣿⣿⣿⡏⣹⡏⢸⣧⣸⡿⣷⣤⡽⠶⢾⡱⠷⣄⡁⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢀⠀⢈⣶⣤⣷⡄
⢺⣿⠗⠀⠀⠀⡀⢀⡹⣿⣿⢿⣾⣿⣧⠠⣾⣷⣯⣽⣿⣳⣿⣿⣧⣾⣿⣷⡶⡟⠇⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠸⣆⡞⠛⠏⠰⣷
⠀⠈⠀⠀⠀⠀⠉⢰⡾⠛⠳⠿⣏⣿⣥⡔⠛⣿⣦⣾⡛⣷⠂⣿⣿⣿⣿⠯⣷⡀⢠⡃⠀⠸⣶⠴⠂⠀⠰⠷⠐⠃⠁⠐⠃⠆⠀⠀⠁⠀⠀⢣⡅⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣘⢿⣯⠳⣾⣍⣭⣤⣿⣿⣷⢬⣙⠟⢻⣽⣿⣁⠀⡿⠤⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⠀⣴⣿
⠀⢀⠀⠄⠀⠀⠰⠤⣤⣀⣀⠀⠉⠀⠻⣄⢉⣹⣿⡟⣻⣛⣋⣤⣙⣦⡀⠙⠋⠈⠀⠀⠀⠀⠀⠀⣠⣴⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣯⡀⠙⠋⠁
⠀⠀⠀⠀⠀⠄⠀⢀⡀⠉⠍⠻⡓⠈⣠⠼⣟⣿⡿⣿⣿⣿⣿⣿⣿⣻⣿⠏⠀⠀⠀⢀⣤⣤⣦⠘⠙⠻⡾⠋⠀⠀⠀⠀⠘⠶⣦⣶⣾⣶⣤⡀⣿⠀⠀⣂⡖
⡠⡇⠀⠠⢀⡄⠀⠀⠀⢀⣰⡿⠋⠀⣡⠞⠉⠀⡴⢿⠟⠉⠉⠉⠉⠉⠈⠂⠀⢀⡐⣿⣿⣿⣿⣇⠀⠀⠀⣦⣤⡤⠄⠀⠀⠀⠈⠻⣿⣿⣿⣷⣿⡀⠀⡇
⠀⠀⠀⠀⠚⠐⠀⠀⣠⣿⠟⠀⠀⠐⠁⠀⠀⠞⠁⠉⠀⣔⠀⠀⠀⠀⠀⠠⠀⠀⣁⣸⣿⡟⣿⡟⠀⠀⣼⣿⣭⣤⣄⣀⡀⠀⠀⠀⠈⠻⣿⣿⣿⣷⢦⠁
⠀⠨⠀⠂⠀⠀⢀⣰⠟⣱⡇⠀⠀⠀⠀⡀⠀⢄⣀⡀⡰⠏⠀⠀⣁⠀⠀⠀⠀⠀⠉⠻⠁⢸⡏⠁⠀⡿⡀⠀⠉⠉⠉⠉⠉⠉⠒⠀⠀⠀⠘⢏⠁⠱⣼
⠀⠀⠀⠀⠀⠀⠀⠟⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢍⡹⠁⠀⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⡌⠀⠀⠀⢷⣌⡱⠀⠂⠀⠀⡁⠀⠀⠀⠀⠀⠀⠈⢂⠀⢹⣄
⠀⠀⠀⠀⠀⣤⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠟⠀⢠⣾⡔⢠⣾⢻⡌⢷⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⠠⢲⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣯⣷⡄⢠⡩⠻⠃⠀⠀⠀⣠⠔⠚⠉⠀⠀⠙⠬⠱⠊
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠿⢥⣆⡀⠀⠀⢀⢴⣞⠉⢠⣐⡀⠀⣿⠉⢺⣤⠏⣀⠀⢀⡠⠋
⠀⠀⠀⠀⠈⡳⠉⠀⣢⡄⠀⠀⠸⡀⠀⡈⠀⡇⢷⠳⡄⣰⠿⠟⠅⢀⣄⡙⠙⣶⣿⡠⣾⠏⠘⠁⠀⠀⠁⠀⠤⠀⠲⠲⡽⠈
⠀⠀⠀⠀⠀⠙⠁⠀⡉⢉⢢⠀⠀⢣⠀⣧⠀⡇⢸⠀⢸⣿⡀⣀⠤⢴⡛⢿⣷⣿⣿⣿⣿⠴⢃⣠⠊⠀⠀⠀⠀⢰⠢⠦⡶⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉⣹⡃⠀⡈⣧⣼⣀⠧⣾⠄⣯⡟⠓⠋⠹⠭⣭⣭⣨⣿⣿⣿⣇⡀⠈⠀⠀⠀⠀⠀⢈⠼⠷⣿⣻⣿⡿⠿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠙⡄⠀⢀⣨⣍⢶⣬⣾⣯⠟⠲⢿⡏⠋⠀⡄⠐⣀⠀⠲⣶⢾⠿⣿⣿⢻⣓⣋⠩⠂⠀⠀⠘⠋⢍⡿⠋⠉⠀⠀⠈⠂⣶⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠙⣽⣽⠋⠙⢳⡀⢸⣷⢸⡆⢣⠀⠘⠁⠐⢹⡯⢶⡟⠋⠙⢉⠉⣠⠀⠀⠀⠀⡆⡸⡇⠁⢀⣤⢊⠠⠎⡍⡽⢀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣘⠿⠶⡒⠻⣿⣿⣽⣿⡔⢻⣦⡀⣀⠀⠀⠱⣸⢷⣄⣶⡏⠐⣁⠀⠃⠌⢀⣼⣰⣿⣤⠞⠛⣍⡠⠞⣼⠃⠈⢾⡇
⠀⠀⠀⠀⠀⠀⡶⡦⢀⣠⣄⣾⡃⢀⠶⠶⣿⣿⣿⣿⣿⡿⠛⠀⠀⠌⣭⠎⣹⣼⢿⣷⣿⣎⢚⡡⠂⠀⠀⠀⠀⠙⢯⣠⣤⣼⣯⢶⡿⠃⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢘⣤⠴⠻⠛⠻⠉⠀⠀⡱⢒⣫⠿⣿⣿⢧⣀⡀⠀⠠⠦⣄⣠⣿⣿⣿⣿⢿⡟⠁⠀⠀⠀⢀⣠⣾⠿⣡⠭⠄⠚⠟⠀⠀⢀⣀⠀⠀⠀⣌⠃
⠀⠀⠀⠀⠀⢀⡟⠱⠂⠀⠀⠰⢤⣰⡛⠙⠋⠁⠚⠫⢨⠜⠁⠀⠀⠀⠀⠒⠭⣙⡿⣻⡿⠿⠃⠤⣤⣶⣶⢻⢿⡆⠀⠠⠖⠀⠀⠀⠂⠀⠸⠋⠀⠀⠀⠊
⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠐⠀⢀⡅⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠁⠀⠁⣀⡘⠁⠁⠙⠀⠀⠀⠀⠙⢷⠀⢤⢳⠄⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⣁⠀⠦⣀⣀⠀⠦⠀⠀⡀⠀⠀⠀⠀⡔⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠄⠈⠀⠐⠀⠀⠂⠀⠀⠦⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠉⠡⠀⣀⠨⢧⣜⣿⣄⣀⠀⠀⠀⠤⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⠲⠄⠘⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢉⠓⢂⣈⣉⣼⣿⣿⣿⣿⢵⡤⠠⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⣑⠦⣀⠀⠀⠀⠘⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⢄⠿⣏⠈⠙⢛⡿⣿⣿⡿⣿⣆⡅⠈⠁⠀⠀⠀⠐⠀⠀⠂⢤⣄⣤⢴⣾⣧⣤⡴⠾⠥⠈⣆⣀⠑⠢⠀⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡱⠀⠀⠀⠈⠰⣾⣷⡯⠏⣝⢀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠘⠰⠈⠉⠺⡿⣿⡿⠙⠋⠁⠀⠀⠙⣌⠑⠲⠤⣬⠭⢄⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⠌⠀⢈⡍⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠙⠚⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⡀⠈⣷⣀⡀⠀⡈⠐⢲⠖⠒⢲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡿⡀⡼⠛⢏⣿⣾⡇⠈⡿⠈⠀⡾⢡⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡮⢞⠵⠋⠀⠀⠈⢻⣿⡇⢠⠇⠀⡴⠛⢀⠠⡀⠀⠀⠀⠀⢀⠔⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠁⠀⠀⠀⠀⠀⠀⢹⠀⣾⣀⡼⣣⣤⡤⠰⠆⠀⠂⠠⠐⠉⠀⠦⢶⠑⠒
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡅⣫⠞⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠈
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠁
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡎⠀⠰⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠇⢠⠁⠀⠀⠀⠀⠀⠘⠿⣷⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠒⠀⠀⠀⡄⠀⠀⠀⡠⡋⠀⢠⣁⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣠⠋⠀⠀⠀⡀⠀⠀⠀⢠⣮⡄⠛⣀⠀⢠⣷⠞⠁⠈⠪⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡶⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣿⣦⣄⣈⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⢀⣀⠀⣀⠠⠚⠟⠁⠀⠋⠉⠛⠉⠛⠿⠦⠌⠉⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⡐⠁⢸⡇⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⡠⣥⣄⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⠀⠀⣼⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢿⣻⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠇⠀⠀⢰⡏⠀⢠⡇⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⣿⡇⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡀⠀⢸⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣿⠃⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠇⠀⣿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠈⣦⠀⡏⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⠃⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠙⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠠⣸⠃⠀⠀⢀⢀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠈⡄⠀⣿⢦⠀⠀⠀⠀⠀⠀⠀⠈⢇⠜⠁⠀⠀⠀⢀⡌⢀⡀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢹⡜⠳⣀⡀⢀⡠⠀⠀⠘⠁⠀⠀⠀⠀⠀⢿⡿⠫⢔⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀⡴⡸⣼⠃⠀⣇⣴⣉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⢆⠗⣎⢀⣄⣿⡉⡁⠈⠧⠜⣀⠀⠀⢀⣤⣠⡶⣺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⢮⠔⢹⣟⣟⢁⠈⠈⢋⣑⠟⣁⠽⠭⠩⠤⠿⠾⠻⠙⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢇⡄⠞⢻⠀⠃⠀⠀⠈⠁⠈⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠁⠛⠃

⠀⠀⡇⠘⣦⠈⡇⠀⠀⣿⠀⢀⡄⡇⠀⣶⠛⣿⠀⠀⢸⠀⠛⢣⣿⠣⡆⢸⠀⠀⡶⣾⡏⢻⡇⣼⠃⣸⡏⠀⠠⡗⠀⠀⠀⣿⡾⠈⢿
⠀⠠⣇⠀⢘⢧⢻⠛⠛⣟⢛⡛⠛⣟⠛⣛⣛⡿⢛⢛⢻⠟⠛⠛⡇⢸⠀⠸⠀⠀⡇⢸⠀⣼⢱⢏⠀⣿⡗⠒⠺⡿⠒⠒⢲⡗⠒⠒⣾
⠀⠀⣿⣀⣾⢾⢿⡇⠀⣿⠙⠃⠀⠁⠀⢀⠀⠀⠀⠀⠈⠓⢆⠀⡇⢸⡀⠀⢰⡄⠇⢸⠀⣿⡿⢸⠀⣏⣇⣰⠷⡇⠀⠀⠀⡇⠸⡿⢹
⠀⠀⣿⠻⠃⢸⣈⣃⣀⣿⣠⠃⢀⣈⡓⠀⠀⠀⠀⠀⡄⢀⢈⣆⡇⢸⣅⣤⠟⢿⡇⢘⠀⣿⠁⢸⡆⡇⡏⣛⣀⣇⣴⣶⣾⣷⣶⣦⣼
⠀⠀⣿⠀⢀⢸⢤⠀⠀⣿⢸⠽⠛⣓⠛⠀⠀⠀⠀⠀⠀⠉⢸⠁⡆⢸⠉⢟⣀⡾⠃⢸⠀⠁⣠⣼⡷⠆⣧⡀⠀⣿⡏⠛⠿⠛⠙⣿⣿
⠀⠀⣿⣿⣿⣿⡄⢁⡀⣿⠀⢄⠠⠇⠐⢚⣳⠦⠄⠀⢀⣀⣼⣦⡇⠈⠀⠈⠻⠃⠀⢘⠀⡀⠛⠛⠂⠀⡇⠘⠀⠻⣧⡀⠀⣀⠈⣿⢿
⠀⠀⣿⣿⣿⡿⢀⢂⢉⣿⡄⠆⠀⠀⠀⠈⠉⠁⠀⠀⠛⢲⣛⣻⣿⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣶⣤⡀⠧⠀⠠⠀⠈⡆⠠⠀⠀⣉⢸
⠀⠀⣿⢗⡓⣦⠒⡼⢘⣿⡾⠂⠀⠀⠀⠀⠀⠀⠀⢠⠀⣼⣿⡿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⠀⠄⠈⢫⠀⣀⠔⢹⣿
⠀⠀⣿⠀⠀⠉⠛⠷⣾⡟⠁⠀⢀⠀⠀⠀⠀⣀⣀⠀⣰⡋⠄⣼⣿⠿⡟⣵⣿⣿⣿⣿⢾⣯⣽⣭⡻⣿⣿⡄⢠⠄⠸⢾⣩⣄⠀⣾⣿
⡀⣀⣟⣀⣤⣤⣶⣿⣿⡀⠀⢢⠘⣷⣄⠀⠀⠀⠁⡼⡅⠀⢸⣿⣿⣾⣿⣿⡟⠛⠋⠁⠀⠙⢿⣿⣿⣿⣿⣇⡀⡴⣆⠟⣸⡇⢸⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠑⠾⣿⣿⡿⠟⣯⡐⢃⠀⢸⣿⡟⡿⠋⠁⠀⠠⠤⣄⡀⠀⠀⠈⠉⣿⣿⠇⠀⠉⡹⢲⠟⢷⣾⣿⣿
⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣤⣥⣄⠀⣿⣿⣦⢨⣈⠿⣷⡅⠀⠀⠀⠦⢥⡀⢁⠀⣠⠴⢶⡟⢁⠀⠀⡼⢡⡇⠀⠈⢻⣿⣿
⣎⠂⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡴⠋⢹⣿⠙⠧⣿⣿⣿⠿⠟⢳⠏⡆⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⢳⡇⠈⠀⡼⠁⠸⡇⠀⠀⠀⠹⣿
⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣾⡿⠖⠒⣩⣽⣟⣦⡀⠀⠛⡄⠻⣄⠀⠀⠠⣤⣴⠃⡄⢸⠀⢿⡄⡼⠁⠀⠀⠙⠐⣄⠀⠀⠘
⣎⠛⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡜⠉⠀⠀⠉⠀⢀⣀⣉⡛⠀⠀⠘⠱⢹⣶⣤⣀⣀⠏⠀⠀⠀⠀⠘⡟⡅⠀⠀⠀⢠⣴⣿⣷⣄⡀
⡙⠳⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡎⠀⣠⠊⠀⠀⠀⠐⠀⢈⣿⠿⣶⣄⡀⠈⠘⠙⠹⡟⠀⠀⠀⠀⠁⠀⠙⡘⡄⠀⠀⢠⣿⣿⣿⣿⣿
⣿⡷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣟⢀⡔⠁⠀⠀⠀⠀⢀⡀⢸⣯⣿⢬⣿⣿⣿⡗⣶⡾⠁⠀⠀⠀⠀⠀⠀⠀⢑⡞⠀⣠⣿⣿⣿⣿⣿⣿
⣿⣦⣸⣿⠿⠿⣿⣟⣿⣿⡟⠀⣼⠀⠀⠀⢀⡴⠊⣷⡞⣻⣿⣿⣾⡿⣾⣿⣷⣾⣷⢶⢺⣵⡦⣄⣠⣴⣾⠁⣠⠄⢿⣿⣿⣿⣿⣿⣿
⣵⣿⣷⣶⣴⣿⣿⣿⣿⣿⡇⠀⢻⣤⡖⠉⠁⠀⢰⣿⣿⣏⣿⣽⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠉⠉⠉⢆⠀⠀⠈⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣠⣴⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠸⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣄⠀⠈⠙⢿⣿⣿⣆⠈⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢀⠝⠛⠳⠦⣀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠟⠋⠁⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡔⠁⠀⠀⡘⠀⠀⠀⡄⠀⢠⠀⠀⠀⠈⠀⠈⢢⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢃⠀⠀⠑⡀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡘⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠈⡄⠀⠀⠈⢆⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠐⢤⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢆⠀⡠⠒⠘⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇⠀⣀⢀⣘⡀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠐⢠⡀⠀⠀⠀⠀⠀⠀⠰⡎⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠫⠀⠄⠓⡂⠄⠟⠘⠃⠀⠁⠘⠁⠂⠀⠀⢀⣤⣀⡤⠀⠀⢀⠾⣄⠀⢠⠊⠀⠀⠀⠀⣠⠀⣠⡐
⠀⠀⢦⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣫⣆⠝⠁⠀⠀⠀⠉⠀⠈⠁⢱⠀⠀⠀⢀⡠⠃⢠⢋⠟
⠀⢀⠀⢣⡆⠀⠀⢠⠦⡠⠂⠀⠀⠓⠦⠠⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡴⠂⠒⠀⠒⠳⡌⠉⠁⠀⠀⠘⡘⢄⣠⠔⢾⡁
⠀⠈⠑⣜⡇⠀⠰⡇⠀⠘⡇⠀⠀⠀⠀⣠⠜⠋⠉⠉⠐⠛⠂⠛⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⠤⠤⠖⠁
⠀⠀⠀⠘⡇⠀⠐⠹⠦⢞⠃⠀⠀⠛⠀⠀⢀⠀⠀⠀⠀⢀⣴⠀⢀⣀⣀⣱⣄⡀⣀⣠⠴⠋⣴⠟⠛⢠⢲⢀⡀
⠀⠀⠀⠀⢃⡰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡴⠟⠁⡼⠉⠀⠀⠀⠈⠣⡀⠀⠀⢸⠘⢠⣤⠃⠒⢊⠇⢰⣶⡆
⠀⠀⠘⢣⢸⠇⠀⡤⠲⠠⣤⡖⠉⠃⠀⠀⢀⣠⠤⠤⠠⠤⢤⣘⣆⣀⣀⣀⣀⡠⠇⠀⠀⠀⠉⠁⠘⠊⣆⠎⠀⠈⠛⠁
⠀⠀⠀⠀⢻⠀⠀⢣⡀⡼⢡⡌⢑⢇⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣯⠉⡇
⠀⠀⠀⠀⢸⠀⢠⠄⡝⠢⣀⣀⠟⠀⢣⠀⠀⠀⠀⠀⠀⠤⠤⠴⠊⠀⠀⠀⠀⢹⣻⠀⣟⡋⠀⣿⡃⠀⠀⡟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠧⡠⠖⠉⠁⠈⠁⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢸⣿⠀⣿⡇⠀⣏⡇⠀⠀⡏
⠀⠀⠀⠀⠀⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣀⡇⠅⠀⠀⡎⢤⢇⠀⢸⣿⠀⢿⡇⠀⣿⡇⠀⠀⡇⠘
⠀⠀⠀⠈⠀⣿⠀⠂⠀⠀⠀⠀⠀⣤⣄⣠⠀⠀⢸⢠⠤⢄⠀⢀⡀⡏⠞⡜⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⣉⠈⠈⠁
⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠸⠀⠸⡀⠀⠈⠼⠀⠘⠇⠰⠃⠈⠉⠀⠀⠀⣴⠁⠀⢀⡠⠶⢦⣀⠔⠉⠢⣀⡀
⠀⠀⠀⠀⢀⠿⡀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢣⠀⠀⠀⣠⢀⡀⠀⠤⠤⠤⠀⠀⠀⠀⠈⠛⢅⠀⠀⠀⠛⠀⠀⠀⠈⠁
⠀⠀⠀⢠⠧⣢⣵⠀⠀⠀⠀⢀⣎⣠⣦⣤⣬⣆⠀⠀⠁⢸⠁⠀⠀⣖⠀⠒⠒⢂⠐⠀⢤⠈⠁
⠀⠀⠀⢇⠀⠀⠀⠄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⡀⣸⠀⠀⠀⣿⠀⣿⠀⢸⡁⠀⣈⠉⠁⢐⡒⠒⣓⠀⠀⠛
⠀⠀⠀⠈⠑⠒⠋⠀⠀⡀⠸⠿⣿⣿⣿⣿⡿⠿⠗⠀⠀⢸⠀⠀⠀⣿⠀⣿⠀⢸⠁⠀⣿⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠰⣲⣄⡠⠿⡦⡤⠚⣶⠖⠂⠀⠀⠀⠀⠐⢸⠂⠀⠀⡇⠀⡇⠀⢸⡇⠀⡏⠀⠀⢸⡇⠀⣻⠀⡀⢲
⠀⠀⠀⠶⠖⠉⠀⠛⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠰⡆⠀⠘⠃⠉⠉⠉⠉⠉⠉⢉⠉⠉⠭⠍⠉⠎⠉⠉⠉⠉⠋⠈

⠀⠀⠀⠂⠀⠀⠀⠀⢠⣄⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⣤⣤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣴⣾⠋⠇⠳⢠⠏⢭⢿⣄⠄⠒⣀⠀⠦⠀⠀⢀⠀⠀⡀⠀⢠⠄⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣤⠜⠛⠻⢒⡖⠲⠻⢷⣀⠒
⠀⠀⠀⢠⡐⢄⣶⠉⠙⠷⣼⣜⡅⠀⠈⠙⡦⣌⡠⠖⢫⡡⠀⠁⠔⠀⣀⠀⢸⢴⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣯⠛⠛⠶⣼⣜⠄⠀⠀⢠⣉⠅
⠀⠀⠀⡀⢹⣷⣈⢆⠀⠀⠈⣙⣣⣀⠄⢘⡱⠉⠀⢰⣾⣁⠠⡀⠁⡀⣥⡀⢨⢰⣿⠁⠠⠀⠀⠁⠄⠀⡘⢷⣞⡙⣄⠀⠀⠀⣩⣶⣤⣒⢨⢎⡄
⠀⠀⠀⠠⠀⢿⣿⣿⣓⡁⣞⠭⠼⢛⣳⠎⠁⠙⠲⣜⣝⣦⣶⢷⠀⠰⣿⡇⠈⣼⣿⠀⠀⠀⠀⠀⣀⡤⢓⠈⣿⣷⣮⢓⣃⣾⠫⠔⢛⣽⠃
⠀⠀⠀⢢⡄⠘⡼⠔⠋⢻⣷⣄⡠⣪⠃⠀⠀⠀⠀⡘⠩⢒⣲⣼⣧⠀⢻⠀⠀⣿⠋⣰⣶⣶⠂⠘⡁⠐⢤⡂⠸⡉⠀⠝⢻⣷⣤⡐⠹⠁
⠀⠀⠀⢴⣿⣄⠸⢌⣠⣔⡽⣿⣿⣷⣄⡀⠀⠀⢀⣁⢉⣀⠉⣼⣿⡆⠀⠀⠀⠁⠐⢋⡩⠽⠗⠿⠿⣤⣬⣿⣄⡡⣔⣀⣄⡙⣿⣿⡷⣤⡄
⠀⠀⠀⢠⡟⢷⣀⡨⠍⢁⡈⠬⢿⢀⠈⠃⠀⡍⢈⢉⣯⣭⣛⣍⠻⣷⠀⠈⠁⠹⢆⡞⠛⢦⣄⠀⠀⠀⢈⡿⢷⣀⣈⠏⢀⠀⠬⢿⢅⢀⣂
⠀⠀⠀⠘⠀⠂⠁⠀⠈⠀⢀⠀⢰⠀⠁⡀⠀⠃⠘⠙⣻⣿⣿⣿⡷⠈⠁⠀⢢⠠⢀⣬⣀⣀⣬⠟⣠⢀⠼⠁⠘⠉⠀⠈⠀⢀⠀⠠⠀⠁⡀⠀⡇
⠀⠀⠀⢀⠀⡐⢀⠀⠀⠀⠁⠀⠀⠀⠀⢀⢠⠀⠟⠛⠛⠛⠻⠛⠁⠀⠀⠓⢈⡴⡯⠼⡏⠉⠀⢁⡈⣵⡄⠂⠀⠂⠀⠀⠀⠁⠀⠀⠃⠀⢠⠠
⠀⠀⠀⠘⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠤⠤⠄⠀⠠⠀⡀⠀⠔⠧⠄⠠⠀⢈⣦⣊⣥⠞⢋⠞⠑⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠘⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠰⢰⠀⠁⡠⠁⠀⡠⠡⠊⣀⠀⠂⠀⠐⢦⡰⠿⠿⢿⡧⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⢈⠀⢀⠠⠀⢀⠔⣤⢇⣔⠠⣄⣀⢠⢬⢏⠒⠦⣄⡊⠀⠈⢃⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠂⠀⠀⢻
⠀⠀⠀⠐⣄⡤⢀⠀⠀⠐⢀⠀⠀⠈⢆⢻⠸⠈⠰⠄⢁⠄⡈⠸⣿⡆⠀⠙⡆⠀⠀⢀⡀⠀⠁⠀⠀⠀⠑⢄⡤⠀⠀⠀⠀⢀⠀⠀⠈⢄⢸⠸
⠀⠀⠀⢸⡟⠘⢦⡀⠀⠐⠁⠀⠐⠀⢘⢻⡇⠀⣶⢀⠂⢰⣶⣦⣝⡧⠤⠚⠋⠲⣴⡶⢶⣤⣀⠐⠀⣠⣶⡿⠰⢧⡀⠔⠀⠀⠀⠀⠄⠸⢻⣷
⠀⠀⠀⢘⠁⠀⠀⡈⠒⠄⣀⠀⠐⠀⢸⡌⣇⠀⣿⠇⢀⣶⣮⠍⠉⢁⠀⠀⠀⠀⠘⡏⠀⠙⣤⣷⠞⣿⢟⠃⠀⠀⣈⠒⠄⣀⠀⠐⠀⢰⡄⣿
⠀⠀⠀⠀⣠⣠⡞⠀⢻⣶⣏⠩⠙⠛⠠⢄⣿⠀⠏⠀⣼⣧⣈⠋⠁⠚⠀⠀⠀⠀⢀⣸⣴⣾⠟⠈⠁⢀⠃⣠⣠⡞⠁⢺⣶⣞⠋⠉⠛⠀⢤⣿
⠀⠀⠀⢰⣿⣿⣿⡟⢻⣒⣫⣧⡢⢎⢠⠖⠈⠀⠀⢰⣿⣏⣛⣭⡭⠉⠃⢃⠀⠈⠉⠉⡿⠑⠲⠶⡤⠃⢰⣿⣿⣿⡿⢻⣄⣫⣧⡂⢞⣀⠞
⠀⠀⠀⣾⡿⠛⠀⢷⢈⢂⠀⠐⠚⣠⡑⢄⣠⠀⠓⣾⠏⣴⣿⣟⣛⠛⠓⠀⠀⠀⠀⠁⠙⠒⠀⠠⠒⠦⣾⣿⠿⠁⢻⠰⣂⠀⠒⠚⣢⡁⢤⠠⠄
⠀⠀⠀⠟⠀⠅⠀⡈⢈⢽⡋⠓⡭⣉⣹⣦⡑⠴⠃⠀⠘⠻⠿⠿⠷⠶⢾⠈⡄⠐⠁⢀⠀⠀⠄⠀⠀⣼⠟⠁⠄⠀⠈⢃⠽⡏⠓⡭⢍⣍⡦⡙⠔
⠀⠀⠀⢀⠀⠐⠀⣜⠷⣔⠺⣄⠀⢀⢀⣀⣩⣄⠐⡀⠀⠄⠈⢀⣉⡀⢀⠀⠗⠃⠀⠀⢀⠀⠀⠀⡼⠋⠀⠀⠀⢀⣔⢿⣗⡻⢦⠀⠀⣀⣠⣬⠦
⠀⠀⠀⠁⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠁⠀⠁

⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡴⢶⣶⡄⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠾⠿⠷⡄⠀⠀⠀⠠⠀⠀⡀⠀⠀⢰⣷⣶
⠀⡄⢀⡄⠀⠀⠀⠀⠀⠠⣶⣎⡉⡇⡓⢒⠷⣄⠐⢀⢤⣆⠐⠱⠀⡀⠀⣠⢀⡴⠀⠀⠀⠀⠀⠀⠰⣿⣭⡄⣫⡍⠻⠻⢦⡀⡡⢴⣣⠀⢀⠂⣠⢸⣿⣿
⢈⢱⡏⠀⠀⠀⠀⠀⣄⡠⠇⠨⠛⠿⠃⠀⢁⢄⠙⠁⣼⠃⢀⠐⠈⣅⠀⢣⣿⠀⠀⠀⠀⠀⠰⣤⠼⡁⠀⠙⠛⢃⢀⠀⡢⠋⠀⣼⠃⢠⠀⠀⣬⢸⣿⣿
⠈⣾⡇⠀⠀⠀⠀⡰⠘⣷⣌⡤⠀⡴⢚⡷⡤⠃⠲⢄⣫⣢⣼⡄⢰⣿⠀⢸⣧⠀⠀⠀⠀⣠⠇⢸⣷⣴⠤⢠⠞⠫⠗⠜⠁⠒⠤⣽⣶⡾⣇⠀⣿⢸⣿⣿
⠀⡿⢁⣦⡆⠐⠉⢄⡀⠩⠛⠱⣷⣅⠀⡼⠃⠀⠀⠌⢉⠨⡱⣷⠀⠿⠀⣿⠃⣴⣶⠒⠉⠠⣄⠀⢝⠭⠺⣷⣅⡀⡞⠁⠀⠀⢠⡍⢒⣞⣿⡄⠹⠸⣿⣿
⠀⡠⠚⡻⠷⠶⢧⣤⣷⡀⢠⠀⡈⢿⣷⣦⡀⠀⠀⢘⡁⣋⢢⣿⡇⠀⠀⡀⠘⡉⠽⠲⠿⢦⣬⣧⠀⠄⣀⡜⢿⣿⣦⡀⠀⢀⢀⣉⣩⡀⣿⣧⠀⢰⣿⣿
⠀⠣⣘⠛⢦⡀⠆⠈⡿⢧⣀⠛⢁⠀⢿⠅⠉⠀⠄⢈⣙⣙⣭⡙⢷⠀⠀⠘⢦⠋⠳⣄⢈⠀⢨⠿⣄⡈⠋⠀⠈⢿⠀⠁⡀⠅⣈⣽⣯⣍⣍⠻⡀⢸⣿⣿
⢀⠀⣰⣀⣤⡞⢑⠤⠁⠈⠁⠀⠀⠀⠀⠀⢀⠠⠀⢉⣉⣿⣿⣿⠈⢁⠀⠔⡠⣇⣤⠴⠃⡢⠘⠀⠉⠀⠈⢀⠀⠀⠈⢀⠀⠁⠏⣉⣽⣿⣿⠂⢉⣸⣿⣿
⠀⠚⠓⢇⠀⠀⢈⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⡤⠀⠉⠉⠉⠉⠁⠀⠈⠁⠼⠳⠺⡀⢀⡤⣼⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⠀⠋⠉⠉⠉⠁⠀⠀⢹⣿⣿
⠐⠂⠀⣠⣦⡴⠋⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡠⠛⠒⠀⢀⣶⣤⠞⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢺⣿⣿
⠀⢨⣞⡛⠛⠗⢺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠁⠀⠄⠃⠀⠀⠀⠀⣶⡛⠛⠛⠒⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠅⢸⣿⣿
⠐⠚⠀⠉⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⡀⠠⠀⠚⢾⡉⠲⡤⠒⢁⠉⠒⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⢠⠂⠞⢶⡅⠒⣼⣿⣿
⠤⡄⣀⣂⠀⠀⠀⢀⣴⢪⠀⠀⠀⢂⠀⠀⢦⣇⠀⡃⠐⢀⣀⡺⡇⢀⡴⢤⢀⡂⠀⠀⠀⠀⣀⡶⢁⠀⠀⠀⠀⠀⠀⢤⣇⠀⡋⠠⢀⢀⠘⢇⠀⣸⣿⣿
⠀⠘⡷⠉⠟⣤⣤⣿⠏⠀⠑⠄⠀⠀⠀⠀⡀⣿⢸⣷⠁⣸⠻⠛⠎⠁⠀⠈⢿⠌⢻⢂⣄⣴⣿⠁⠈⠂⢁⠀⠀⠀⠀⡈⣿⢸⣷⠁⣘⣛⠿⠶⠉⢸⣿⣿
⠀⠀⢨⣠⣾⠋⠒⠱⢀⢀⡞⢠⣤⡲⠶⠦⠉⢸⠸⠏⢰⣏⠿⠆⠤⠀⠀⠀⠈⣄⣴⡿⠣⠊⠇⠀⣠⠖⢤⣐⢦⠤⢄⠃⣹⠘⡏⢠⡟⠷⠤⠠⠀⢸⣿⣿
⠀⠘⠋⣿⠣⢤⡴⠀⣼⣿⣷⠾⣛⣳⡂⡄⢠⠋⠀⠀⣾⡟⢂⠰⠲⠀⠀⠠⠞⢻⡟⠠⣄⠈⢠⣿⣿⣶⢿⢛⣦⢀⠄⣨⠛⠀⠀⣼⡿⢶⡴⠶⠂⢸⣿⣿
⠀⠀⠋⠐⠀⠀⠐⢴⣿⠿⠹⡐⡉⠀⠥⣈⠡⡀⠀⢰⡟⣹⣿⣷⠶⠆⠀⠀⠐⠉⠂⠀⠈⢤⣼⣿⡏⢷⠘⠉⠨⠥⠈⢋⠀⠀⢤⡿⢫⣿⣶⡶⠦⢸⣿⣿
⡀⠂⠀⠂⠀⠀⢀⡾⠁⠀⠀⢁⠽⠘⠪⠉⡵⡈⠰⠂⠈⠻⠿⠿⠶⠆⠀⠀⠀⠀⠀⠄⠀⢰⡟⠁⠀⠈⢊⢗⠒⢙⣛⣦⠁⠴⠊⠀⠿⡿⠷⠶⡄⢸⣿⣿
⢉⠁⠀⠀⠀⢀⠞⠀⠀⠀⢰⡻⢤⠳⠀⠀⠠⠮⢄⠀⠀⠀⠀⢬⠄⠀⢈⠅⠀⠀⠀⠀⣠⠏⠀⠀⠀⢔⢷⡂⢦⠀⠉⣊⣅⡄⠂⠀⠀⠀⢀⡁⠐⢘⣿⣿
⠘⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠻⠌⠳⠾⠆⠔⠂⠀⠄⠀⠐⠀⠀⠀⠀⠈⠄⠀⠀⠀⠰⠃⠀⠀⠀⠀⠈⢧⠙⢦⣶⡄⠤⠄⠌⠄⠀⠰⠀⠀⢀⠀⠸⣿⠿

⠀⠀⢀⢠⢀⠀⢀⠀⢀⠀⠀⣀⣀⠀⠀⡤⡀⠀⡀⢀⣀⢀⢀⢀⣀⣀⣀⠀⠀⠠⠄⠀⠀⠀⠀⢀⣤⡀⠠
⠀⠊⠄⣜⠀⠁⠘⠁⠘⠢⠀⣉⣉⡇⢂⠀⠈⠀⢢⡊⣓⢻⡌⠀⢿⠿⡿⢠⡈⢰⣿⣦⣶⠀⢰⣿⢸⣿⡆
⠀⠀⢀⠀⠀⠀⡀⠀⢀⠀⠀⠉⠉⠀⠐⠈⠁⠀⠶⠺⠜⠺⠧⠀⣤⠀⡤⠀⠀⠀⠈⠙⠋⠀⣈⣻⣿⣟⣙
⠀⢒⡚⢀⣁⠀⠀⠀⠀⡀⠀⠀⣤⣆⡀⡳⠇⠖⠀⠂⠀⠀⠀⠄⢀⣤⣀⠀⠂⡀⠀⣠⠀⠀⣿⣿⣿⣿⣿
⠀⢇⣼⣷⣠⢀⠀⠁⠀⠠⠀⠀⠀⠈⠁⡁⡄⡇⣾⣿⣿⣷⠄⠀⣾⠶⢿⠄⢠⣿⠛⣿⣧⠀⠀⠂⠀⠒
⠀⠀⡙⡋⠁⠀⠀⠀⠠⠀⢀⣀⠀⠀⣀⣀⣀⢑⠐⠭⠭⠕⠊⠀⡯⠤⢼⡀⠤⠀⠀⠡⠄⠀⠀⠀⡄
⠀⠐⢀⠄⢒⠂⠄⠀⣤⡄⠀⠋⠀⣊⠉⠉⢹⠈⠀⠁⡀⠉⠄⠀⠂⠀⠀⠀⠀⠘⠛⠏⠀⠀⠀⠐⡇⠀⠘
⠀⠀⠈⠁⠙⠀⠀⠀⠀⢀⣼⠈⠁⠈⡀⠤⠘⠀⠡⠚⠁⠐⠀⠁⠁⢸⡇⠈⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⢸⠆⢾⠭⢿⠀⠀⠈⢿⣇⠀⠀⡀⢀⠀⠀⠤⠴⠒⠂⠄⠂⠄⣤⣤⡄⢻⠓⣶⣀⡀⠓⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⡘⠋⡀⠀⠀⠈⠀⠀⢀⣠⣤⣀⣤⡀⠀⡃⠉⡇⠀⠀⠠⠦⠀⠀⠀⠀⢸⣿⡇
⠀⣠⣤⣶⣤⣄⠐⣠⣴⣶⣶⡀⠀⠀⠀⠈⠀⢰⠉⠹⠿⠇⠉⠹⠀⠋⠉⠃⠓⠆⢀⣶⣦⣤⠀⠀⢸⣿⡇
⠀⡷⣄⠀⠀⢸⠐⠻⣿⣿⣿⣷⢦⢰⣄⣀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⠀⠀⠀⠸⢿⣿⡟⠀⠀⣸⣿⡇
⠀⡇⠀⠀⡀⣸⠀⠀⠨⠈⠄⠀⢀⡈⢿⠋⠉⠓⠀⠀⢠⣒⠀⠐⢄⡂⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⡛⠛⡃
⠀⢧⡀⠀⠈⠵⡀⢬⠇⠁⠀⠐⣬⡓⠐⠰⠟⠋⠀⠠⣟⣛⣉⣂⣘⡋⠀⠀⠀⠘⠀⠀⠀⣶⣀⡄
⠀⣤⣤⣤⣤⢠⠀⠈⠀⠀⠀⠀⠙⠃⠀⡀⠀⢉⡉⠀⢽⣯⣭⣩⣿⠀⠀⠀⠀⡀⠀⠄⠀⢉⠙⠓
⠀⠿⠻⠿⠿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠴⡧⠶⢦⡀⠋⣉⢉⠂⣠⠤⣤⠤⣤⠀⠀⠀⡠⠀⠀⠀⡠
⠀⣬⣤⣤⣤⠄⠉⠁⠈⠁⠀⠀⠀⠀⠐⣿⢹⣟⣿⣻⠿⠄⢐⡨⠀⣙⣛⢃⢐⡁⠀⢀⠐⠄⠐⠨⠄⠐
⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢸⠀⢀⣿⠀⠀⢀⠤⠀⣀⠔⢃⠤⠀⠆⡀⠂⠂⠸⠐⠀⠀⠐
⠀⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⢸⠀⠀⣿⠀⢠⠄⠈⠀⣠⠄⠛⠂⠀⠄⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠤⠀⠄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⢦⡀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⣿⡇⣸⠇⠀⠀⠀⠀⣾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠻⣍⠁⢀⡴⠚⣛⢦⡼⠛⢹⣧⠖⢓⢦⡴⠋⠛⠛⠳⡄⣠⠶⠲⣄⡴⠚⠲⣄
⠀⠀⠀⠀⠀⠀⢀⡴⣆⠙⢦⠈⢳⣼⠁⣼⣿⣿⡇⠀⣼⡏⠀⣾⢸⡇⠀⣾⠇⢀⣿⠃⢰⣿⣿⠃⢠⡗⣿
⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⢸⡇⠀⡇⠀⢿⣿⡿⠁⢰⣿⡇⠀⢣⣿⠃⠀⣿⠀⣸⣿⠀⢸⣿⡿⠀⣨⠾⠁
⠀⠀⠀⠀⠀⠀⠹⣌⠳⠶⠋⠀⣠⣿⣄⣀⣤⣾⠀⢸⣿⠇⠀⣿⢏⣤⣾⡇⠀⣿⡏⣤⣤⣬⡆⠀⣿⡟⡧
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢶⣟⡽⠶⠶⠯⣭⣛⠧⣈⣵⣧⣄⣭⡾⠃⡿⠳⣄⣋⡼⠃⠀⠀⠻⣤⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠛⠦⣌⣉⣉⣁⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⡀⣴⡻⠇⠀⠀⠀⠀⣤⡤⡄
⠀⠀⠀⠀⠀⠐⢯⣶⣲⣞⣿⣿⣿⣿⠀⢀⠀⠀⠀⠀⠀⣠⢾⡉⠀⣠⣤⣤⢿⡗⢄⠀⠀⠀⠀⠻⣟⡼⠁⠀⠀⠀⠘⠂⣁⣥⣨⣀⣀⣀⣤⡬⠤⠚
⠀⠀⠀⣴⠀⠀⠀⣷⡌⠉⠀⢀⡻⣿⠀⠈⠀⠀⠀⠀⣞⡕⢏⠀⠈⣿⣿⠿⠻⠧⣄⢳⠐⢄⡀⠀⠈⠀⠀⠀⠀⢀⡔⠛⠉⠝⢦⡀⠀⣴⠂⢠⡄
⠀⠀⠀⠀⠀⠀⢠⢃⠀⠀⠀⠀⣔⢹⠀⠀⠀⠀⠀⢸⣉⣤⠼⠀⠀⠛⠲⢤⣁⡤⠏⠈⡇⠀⠋⠀⠀⠀⢠⣤⢠⣌⢣⡀⠀⠀⠀⠈⠢⡈⠃⠈⠀⠓
⠀⠀⠀⠀⠀⢠⠇⠈⡒⠀⢀⣀⣉⢸⡅⠀⠀⠀⠀⢸⡀⢠⡶⠟⠲⣄⠀⠀⠀⢠⣶⣶⠃⠀⠀⠀⠀⠀⠀⣈⠬⠧⠤⣝⣦⡀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣼⣶⣿⣿⣿⣿⣿⣿⣷⣇⠀⠀⠀⠀⡆⠳⡘⢦⣴⢗⡿⠀⣠⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠠⠄⠈⠙⢶⠶⠶⠛⠘⠂
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢀⡀⠁⠀⠈⠓⠭⣭⣅⣤⠿⠟⠋⠀⠀⠀⠀⠀⣦⡄⢶⣠⣷⣤⣀⣀⣀⣀⣀⣀⠇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡞⡝⢍⢢⠀⠀⡤⢤⡀⠀⠀⠀⢠⡋⣲⠀⠀⣀⠀⠀⣠⠞⠋⠡⠀⠈⠓⣄⠀⠀⠁⢀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠙⠺⠭⠭⠿⠿⠟⠛⠛⠉⠘⠛⣝⣋⡜⠀⠀⠓⠚⠁⠀⠀⠀⠀⠉⠁⠀⠸⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠈⠉⠀⠋⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⣤⠤⠄⠀⠀⠀⠀⢀⠀⢀⡤⠤⠀⢤⡤⠄⡴⠲⡌⠰⣄⡠⠂⠀⣀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡤⡄⠀⡞⠁⠀⠀⡷⠰⢾⠀⣿⠰⠀⡼⣦⠟⡄⠘⡁⠈⠳⡄⠀⠀⡇⠀⡷⠮⠄⠀⢨⠀⠀⠀⠀⠘⣿⡿⠃
⠀⠀⠀⠀⢸⠶⡆⡾⢰⡇⣤⠠⢤⣄⡆⣠⠀⠳⠤⠤⠀⠁⠀⠈⠀⠈⠉⠀⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠈⠀⠈⠀⠀⠀⠀⠀⠃⠃⠛⠰⠀⠀⠀⠀⠀⣠⠀⣠⣤⣄⠀⠀⢀⣤⣄⢀⡀⠀⣠⣤⣤⠀⡄⠀⠀⠀⠀⡀⢀⣠⣴⣶⣶⣶⣶⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠒⠲⠲⢤⡀⣀⣀⡀⠀⠀⠀⠀⡇⠀⢹⠀⠀⢸⠈⢹⠀⠀⠀⢯⠀⢸⠀⠀⠀⠀⠀⠈⠁⢸⠧⡏⠉⠉⠉⠜⢹⠀⠉
⠀⠀⠀⠀⠀⡄⡄⢀⡜⠁⠀⠀⠀⠀⠠⠀⡹⣇⡰⠃⠀⠀⢠⠀⣷⣤⣾⠀⠀⢸⠀⢸⠀⠀⠀⢸⣻⣿⠀⢸⠀⠀⠀⠀⠀⢸⠀⢃⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠁⠀⡼⠀⠀⠀⠀⡀⠀⢀⣯⠾⣻⠀⠀⠀⣤⣼⣤⣷⣿⣿⣤⣤⣼⣷⣾⣤⡴⠶⢾⣿⣿⡶⣾⠆⠀⢿⡿⠀⢸⠛⡀⢀⣀⣀⣏⣸⡀
⠀⠀⠀⠀⠀⢠⡞⣇⠀⢄⣀⠥⠖⠋⠁⢠⠈⡟⠀⠀⠀⠀⢸⠀⢹⣿⣿⠀⠀⠘⣿⣿⠀⠀⠀⢸⣿⣿⠀⣇⠀⠀⠈⠁⠀⢸⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠳⠼⠛⢯⡁⠀⠀⠀⠀⢀⣴⠞⢀⣀⠀⠀⣀⣼⣀⣼⣿⣿⣤⣤⠤⠽⠿⠴⠤⠛⠛⠛⠛⠛⠟⠃⠀⣀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠊⠉⠀⢰⢹⡽⣷⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢶⠀⠀⠀⠠⠼⠿⢤⠀⠀⠀⠀⢀⣀⣔⡀⠄
⠀⠀⠀⠀⠀⠬⠀⠀⣀⣀⣸⡿⠿⢿⠄⠲⠌⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢢⠀⠀⠀⠙⢃⣤⡶⠚⡙⡢⠀⡎⠀⠀⠈⡴⠋⠀⠠⢉⢶⣉
⠀⠀⠀⠀⠈⠁⢀⣨⣥⣶⣮⠭⡝⠋⢀⠘⡃⠀⠀⢠⠆⢀⣠⢀⡀⣀⣀⣠⠋⠉⢳⠎⠀⠆⠆⡴⠋⢀⡠⠔⡞⠁⢺⠁⠀⠀⣸⠇⢜⠓⢛⣆⣊⣇
⠀⠀⠀⠀⠀⠀⡇⠹⠤⠴⠂⠀⡇⠀⠀⠀⡇⠀⠀⠘⠦⣇⠀⠀⡿⠛⠋⠉⠓⠒⠋⠀⠀⠀⡼⠁⡰⠋⠀⢠⡇⢰⡟⠀⠀⠀⠌⢇⠘⣿⣸⣸⡿⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠐⠀⠀⡇⠘⢆⣤⠀⠈⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡇⢰⠁⠀⠸⣾⠀⣾⢷⠖⠀⠀⠀⠈⠛⣾⣹⠟⠡
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠈⠀⢣⠀⠘⠁⠀⣠⣶⡖⠀⢀⣴⡆⠀⣀⣀⠀⠀⢸⡂⠘⢦⣀⣀⡉⡶⠛⠉⠀⠀⠀⠀⠀⢸⣧⣿⡄
⠀⠀⠀⠀⠞⠀⡇⠀⠀⠀⠀⠀⢸⠠⠤⠔⠚⠀⠀⣀⣰⠿⠿⠥⠤⣾⡿⢡⣾⣗⡼⠀⠀⠸⡇⢸⣟⠆⠈⠉⢙⠉⢱⠀⠀⠀⠀⢰⢸⣿⣿⡇⠄⢄
⠀⠀⠀⠀⠀⠀⣇⡤⠔⠒⠒⠒⠚⠀⠀⠀⠀⠀⠈⠙⣿⣷⡄⠀⠀⢿⣷⡄⠀⠀⠀⠀⠀⠀⠙⠶⣦⣤⣤⣤⣤⡷⠋⠀⠀⠀⠈⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣫⣭⣶⣶⣶⣦⣤⣀
⠀⠉⣵⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⢟⣵⣿⣿⡿⠿⠿⠿⢿⣿⣿⣷⣄
⠀⠀⠙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⣶⣾⣿⣿⣿⠿⢋⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡆
⠀⠀⠀⠈⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣭⠽⠟⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⠛⠛⠿⢶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣃⣀⠀⠀⠀⠀⠉⠙⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠞⠁⠈⠉⠉⠛⠲⠦⣤⡀⠀⠀⠙⢿
⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠈⠓⠤⣀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⠀⠀⣸
⠀⠀⠀⠀⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣾⣫⣥⠴⠞⠉
⠀⣠⣤⡀⠀⠘⢿⣿⣿⠆⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠿⠻⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁
⠀⠹⣿⣿⣄⠀⣴⣿⣥⣄⠈⠻⣿⣄
⠀⠀⠈⠛⠋⠀⠈⣻⣿⠿⠛⠊⠉⠹⣆
⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⢀⣴⣿⠇⠘⢧⡀
⠀⠀⣴⠟⠁⠀⠀⠀⠀⠐⠿⠟⠋⣀⣄⠈⠻⣄
⢀⣾⠋⠀⠀⠀⠀⢀⣀⡀⠀⢠⣾⡿⠋⠀⠀⠈⠳⣄
⣼⡇⠀⠀⠀⠀⠀⠘⠿⢿⠿⠈⢹⣶⣦⣄⠀⠀⠀⠈⠳⣄
⣿⣇⠀⠀⠀⠀⠀⠰⣿⣦⣄⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠁
⢹⣿⣆⠀⠀⠀⠀⠀⠈⠻⠿⠇⣰⣿⣷⠄
⠀⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏
⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠈⠙⠿⣿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣷⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠶⠶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠴⠖⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠏⣂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⠯⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣯⠋⠻⢿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣁⣔⢀⠓⠈⣤⣀⡀
⠀⠀⠀⠀⠀⣤⣿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣬⣰⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢐⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣹⣿⣿⣿⣅⠀⠁⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠤⠼⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣀⠦⡈⡀⣿⡗⢰⣼⡀⢰⣦⣶⣶⡀⢉⣡⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠻⢳⣿⣿⣿⠿⡇⠐⢻⢟⡛⠁⠹⣿⣁⡀
⠀⠀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣿⡇⠐⠃⠘⣻⣿⣿⣿⣿⡟⢡⣽⠁⢀⡘⠀⠀⢀⢧⠀⠚⠂⠀⠰⡎⠃⢀⣤⣀⣀⣠⡄
⠀⡀⢀⢀⣸⣿⣿⣿⣿⣟⣿⣿⣿⣿⣟⣳⠁⡐⠛⠀⠀⠀⢾⣿⣿⣿⣿⡏⢀⣸⣿⣄⡉⠄⢸⡆⡈⢰⡀⢿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠀⠈⢳⡀⠀⠀⠹⣿⣿⣿⠁⢸⣿⣿⣿⣿⣶⣿⣿⣵⣿⠀⠈⡄⢀⣀⣵⣞⣸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢈⣀⠀⠀⠘⢷⣤⠀⠐⠿⢿⠋⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠀⠇⠸⢻⣿⡖⡘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣇⠀⠀⠰⣏⢀⣤⣀⡘⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣤⣄⡆⢹⣿⡟⠀⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠐⠂⠀⡼⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢭⠃⠀⠀⠀⠀⢱⣐⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⠀⠀⠀⠀⠀⠽⠿⠿⠿⠛⠋⠉⠠⠞⠋⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡞
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣲⠆⠀⠀⢀⡀⠀⠀⠀⠀⠙⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠉
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣠⡄⠴⠞⠀⠀⠀⡰⠏⠀⠀⠀⠀⣦⠐⢯⣤⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣥⣄⠀⠀⠀⠀⠛⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⡍⠙⠻⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢟⢿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣿⠟⠟⢋⠉⠉⠀⠀⠀⠻⣄⠀⠉⠉⠉⠉⣏⣙⣇⠀⠂⠀⠀⠀⠀⠀⠀⢺⣯⢻⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣀⠠⠄⠀⠉⠻⣀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠀⠀⠈⠛⠛⠓⠢⠄⢀⡴⠟⠋⠉


⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠬⡗⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⣾⡿⠾⠼⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣴⣦⡀⠀⠀⠐⢆⡀⠁⣀⡐⣹⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⢯⡓⣿⡄⠀⠀⠀⠀⠈⠊⢥⣿⡏⡉⠀⠙⣿⣧⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢠⢾⣿⣷⣠⣏⢠⣀⡀⡀⠀⢀⣿⠿⣿⣷⠋⠙⢷⣿⣿⣿⡟⢿⡄⠀⠀⠀⠀⠀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⡖⠘⠛⠋⢸⡟⢤⣹⠀⠻⠈⠀⠘⠛⢿⠀⠀⣿⡏⠋⠱⢿⡄⣿⡄⠀⠀⠀⠀⠀⢆⠸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠓⠀⠀⡀⢰⠖⠻⠿⠚⠏⢈⡈⣿⡤⠀⠀⡀⠀⠸⠁⠀⠀⢀⣭⣤⣬⣽⣿
⠀⢀⣀⣴⡶⢚⣁⠀⠄⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠂⠒⠤⠠⡠⠐⠁⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠉⠉⠉
⢀⡩⠤⣞⠟⡉⠀⠄⠀⢢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠠⢦⡀⠻⠁⢀⡀⢠⠔⠀⠀⠀⠀⠴⠀⠀⠀⠈⠀⠀⣠⣼⣿⢤⣤⣤⣴
⠨⡁⠀⡷⠰⡅⠀⡨⠄⣠⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⠄⡘⠢⡿⠃⠀⠀⠀⠀⠀⣀⡐⡀⢀⠀⠆⠀⠀⢸⡇
⠀⢳⣰⢵⡀⠨⠁⠺⣿⠄⠀⠀⠀⠀⠈⠃⠀⠤⡆⢠⠀⡾⠠⠴⠄⠑⢤⠎⠀⠀⠀⠀⡀⡴⢚⡾⢿⠗⠶⡌⠀⠀⠀⡾
⢀⣹⡋⠛⠓⠂⣀⣴⢻⣇⡀⠀⠀⣤⠈⠛⠠⠏⠻⠈⠋⠀⠣⠀⡴⠂⢸⡀⠀⠀⠀⠹⠇⣠⠟⠁⠁⠀⠀⣨⣵⠙⣺⡓⠦⢴⡷⣴⡦
⠠⣟⡷⢈⠓⠖⠛⠛⠷⠼⠃⠀⠉⠁⢠⣎⠐⠀⠸⣼⡄⠀⠀⠀⠀⠀⠀⠧⠤⠶⠤⠤⠬⠴⠾⠆⠀⠠⠞⢿⣿⠂⠙⠓⠒⠈⠁






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠈⠠⠠⠊⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⢄⠠⠀⣂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣀⣀⣈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠔⢈⠇⠀⠀⠀⢘⡆⠀⢸⣄⠀⠀⠀⠀⡁⠢⡀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣉⠳⣌⡠⠔⠁⠀⠀⠀⡔⠁⠙⠋⠉⠀⢱⠀⠀⠀⠀⠤⡀⣊⠴⠓⣄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⠀⠂⠀⠀⠠⣄⣀⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⢑⠎⠀⠀⠀⠀⠀⢘⠉⠉⠁⠉⠉⠉⠉⡂⠀⠀⠀⠀⠈⠡⢔⠩⠈⠀⠀⠠⠀⠀⠰⠂⠠⠀⠀⠂⠀⠀⠀⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢉⡉⠉⠉⠉⠉⡉⡅⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠀⠤⠀⠂⠀⡆⠐⠀⠀⠀⠀⠀⠈⢠⡌⠀⠘⠁⠌⠃⠀⠀⠀⠀⠀⢀⠂⠀⠀⠖⠀⠀⠀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠈⢷⠀⠀⠀⠠⠤⠥⠤⠁⠤⠀⠼⠄⠂⠀⠀⠀⡇⠘⠀⢀⡇⠨⠅⢈
⠀⠀⠀⠀⠀⠀⠀⠤⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠣⠄⠄⠀⠒⠚⠒⠒⠒⠂⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠶⠀⠀⠌⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⠔⠉⡄⠀⠀⠀⠀⠠⠈⠂⠈⠀⠀⢰⠅⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⢰⠠⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠟⡠⠔⠊⣁⠴⠀⠀⠀⠐⠁⠈⠀⡤⣃⠀⡀⢀⡀⣀⢀⡀⢀⠀⡀⠀⡁⠀⠀⠀⠀⡀⠠⠄⠘⠀⠐⡀
⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠱⠖⠂⠉⠂⠀⠀⡐⠀⢀⠀⠠⠄⠁⠉⠀⠀⠀⠀⠁⠈⠈⠉⠈⠁⠈⠁⠉⠉⠁⠁⠀⠆⠰⡀⠀⠐⡀
⠀⠀⠀⠀⠀⢭⣩⣉⣉⡁⠀⠀⠁⠀⠀⠀⠀⡜⢠⠀⠞⠁⠀⢠⢄⡀⠀⠄⠤⠤⠤⠠⠄⠤⠠⠀⠤⠠⢄⠤⠠⢄⠀⠀⠀⠹⠄⠤⠐⡄
⠀⠀⠀⠀⠀⠲⠤⢤⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠄⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢠⠂⠀⠀⠤⠁⢀⡆⠀⠠⠆⠀⠀⠀⠀⠈⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠘⢤⠀⠡⠀⠀⠘⢂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠈⠀⠀⠀⢀⠔⠁⠂⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠈⠤⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⡠⠊⠀⠀⠀⠀⠀⣀⠀⠀⠸⠁⠀⠀⠀⢰⠀⠀⠀⢼⠀⠀⠀⡀⠀⠀⠈⠣⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡔⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⠀⣀⠀⠇⠀⠀⠀⠀⠐⡄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⡜⠀⠀⠀⠀⠀⠰⠒⠀⠒⠐⠀⠂⠀⠂⠐⠄⠢⠤⠄⢄⠠⢄⢤⣠⠀⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⡡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡀⢀⡜⠀⠀⠀⠀⠀⠀⢠⠤⠠⠤⠤⠠⠠⠤⠄⠀⠀⠄⠤⠠⠄⢤⢠⡤⡘⠀⠀⠀⠀⠀⠀⠀⠐⡤⢀⠉⠐⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢁⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡎⠀⠅⡠⠂⠀⠐⠃⢀⠀⡆⠈⠠⠁⠘⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠐⠀⠂⡀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⣀⡀⠀⢠⠆⠂⠀⠀⠠⠄⣀⠌⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠸⡆⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠁
⠀⠀⠀⠀⡀⠐⠄⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⡀⠠⠂⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⠑⡄⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⢀⠀⢀⠜
⠀⠀⠀⠠⠀⠀⠸⠀⠀⠀⠠⠀⠆⠀⠄⠀⠀⠀⠉⠖⡁⢤⠖⠊⠀⡏⡆⠒⡁⠀⢠⢰⠀⡖⠚⠒⢞⠁⠀⢸⠀⠀⠄⡄⠀⢤⠆
⠀⢀⡄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⠟⠈⠢⠄⠚⠅⠂⠡⠄⠼⠃⠜⠐⠁⠶⠩⠥⠄⠀⢸⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⣤⢤⠀⠀⠠⢤⡤⠄⣤⡤⠤⡤⡤⣤⠤⢤⢤⠤⠀⠠⣤⣤⢠⣮⠀⠠⠆⠀⣀⠀⣈⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠈⠈⠉⠁⡁⠉⠉⠉⠉⠀⠀⠀⡀⠑⠀⠘⠀⠈⠀⠈⠀⠁
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡅⠀⡀⠀⡆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⢇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⢀⠔⠀⠈⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠁⠀⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠄⠢

⠀⠀⠀⠀⠀⣠⣀⣠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⡠⠞⢉⣤⣴⣶⣾⣿⣶⣬⡓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⢀⡀
⠀⣼⣯⣾⣯⣹⡿⡿⣿⣿⣿⣿⣿⣝⡆⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠟⠸⡣⠔⠀⠀⠀⠀⠤⠉⢷⡀
⠀⢸⣿⣿⣿⣾⣶⣿⣾⣾⣷⣿⣿⣿⣷⠀⠀⠀⠀⢀⣠⢴⡿⠷⠶⠀⠘⠀⠀⠀⠀⠀⣰⠀⡀⣴⣧
⠀⢸⣿⣿⣿⡿⢿⣿⣿⢫⢾⣿⣿⣿⡟⠀⠀⢀⡴⢩⡞⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⣸⣿⣦⡀
⠀⠀⠹⣯⡻⢿⣿⣿⣿⣾⣿⡿⠟⠿⠃⠀⣴⠃⠈⣸⠧⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠶⠖⠀⠉⠀⠉⢇⡀⠔
⠀⠀⠀⠈⠛⠖⢒⠛⣻⣭⠥⠐⠁⠀⢀⠚⢁⣷⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣅⣀⣴⠃⠀⠀⢀⣀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣾⠿⠏⠛⠛⠋⠀⡉⠉⢩⣀⡀⠀⢀⡀⠀⠀⠀⠚⠑⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠋⠁⠀⠰⠂⠀⠒⠀⠙⠓⠀⠉⠉⠀⠠⡔⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⡏
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⢶⣿⡇
⠠⣠⡄⢀⠀⠸⠟⠁⠀⠀⠀⠀⠀⢀⣠⣦⣾⠋⠀⠀⠀⠀⠀⠀⠙⢢⠉⠀⠀⠈⠳⣄⠀⠀⠀⠀⠸⡿⣥
⠀⡵⣕⠘⠄⠀⠀⠀⠀⠀⠀⢀⠸⣞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⣷⣤⣀⠀⠀⠃⣿⡆
⠀⠉⡄⠁⠀⠀⢀⠀⠀⠀⠐⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⣿⡛⠿⣧⠀⠰⢻⢸
⠀⠢⣑⠀⠀⠀⠀⠀⠀⠀⡇⣠⠜⠂⠀⠀⣀⣀⠀⠀⠠⠐⠀⠀⠀⠀⠀⣧⡀⠀⠀⡠⠋⢷⡀⠈⠇⠀⠨⠀⠄
⠀⠐⡄⠀⢀⡀⠀⠀⠁⠀⣷⠇⠠⠁⠀⠀⡏⡯⠀⠁⠀⠀⠀⠀⠀⠀⠀⢣⠉⠀⠀⠀⠀⠈⠻⡄⢀⠀⠀⠣⣸⡄
⠀⠀⠉⣖⣒⡀⠁⠀⠀⠴⠁⠀⢀⠈⣄⠀⠐⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣼
⠀⠀⠀⠀⠙⠋⢁⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠠⠀⠠⢄⡈⣷⣤⣀⣀⣀⣿⡏
⠀⠀⠀⠒⢒⡿⠁⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⣿⡟⠛⠛⣿⣛⣋⡀⠂⡀
⠀⠀⠀⠀⠀⠃⠤⠄⠀⠶⠒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠿⠻⠛⠉⠃⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⡀⠀⠀⠘⢳⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠘⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠓⠒⠒⠚⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⢀⢾⠓⢻⣆⡠⠄⠤⣀⡾⠋⠘⣆⠀⠀⠀⠀⠀⢴⣉⣀⡀⠀⠀⠀⠉⢑⡆
⠀⠀⠀⠀⠀⠀⢀⡀⠤⠠⠄⠊⡥⠀⠂⠐⢶⠯⣕⢄⠀⠀⠀⠀⠀⢸⣇⡤⠒⠉⠀⠀⠀⠀⠑⠢⣄⡼⠀⠀⡠⢤⡀⠘⡆⠀⠉⠉⠉⠉⠉⢩⠃
⠀⠀⠀⠀⣴⢊⠅⠐⠈⠁⣶⠱⣆⠀⠀⢀⡼⠀⠀⠑⡕⡄⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣴⡢⣄⡏⠀⣧⡧⠲⠆⠀⠠⠀⡸
⠀⠀⠀⠰⠹⢻⣄⠀⠀⣠⡟⠀⠈⠛⠙⠋⠁⠀⠀⠀⠐⠃⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⢀⡼⢛⠟⢀⠏⠀⠈⠹⡇⠀⢾⠉⠉⠀⠀⠀⠀⡏
⠀⠀⠀⢣⠃⠀⠉⠛⠛⠉⠀⢀⡠⠶⠶⠶⠶⠶⢤⡤⢤⠄⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣨⠶⠋⠀⡎⠀⢀⢔⡚⢄⠀⢻⠆⠀⠀⠀⠀⠀⡇
⠀⠀⠐⡜⡄⠀⠀⠀⠀⣠⠔⠋⠒⠀⠐⠀⠤⠤⣊⠴⢿⡀⣀⣀⣠⡤⠤⢤⣤⠤⣄⠀⠀⠀⠀⠀⢸⠁⠀⢠⡘⠜⡸⡀⠉⠓⠦⠤⠤⠤⠔⠃
⠀⠀⠀⠈⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⣤⠞⠉⡗⠁⠙⠓⠒⠒⠚⠁⢸⠀⠀⠀⠀⠀⢇⠀⠀⠀⡏⢻⠄⠱⡄⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢠⠊⠑⠒⠒⠀⠀⠉⠉⠉⠙⠁⢀⣴⠟⠁⠀⢀⡇⠘⠁⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⢱⠭⣰⠎⠀⠈⡇⠀⢷⠀⠀⢸⠰⠶⢿
⠀⠀⠀⠀⠸⣼⠌⣍⣀⣤⣤⣤⣤⣤⣴⣿⠟⠁⠀⠀⠀⢸⣇⠈⠁⠀⠀⠀⠀⢸⠙⠀⠀⠀⠀⠀⠇⢠⠃⠀⠀⠀⡇⠀⢸⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠓⠁⣀⡀⠀⠀⠀⡤⠒⡦⠒⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⠈⠲⠃⠀⠀⠀⠀⡇⠀⢸⠀⠀⢸⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⡆⠀⢸⠁⢠⠃⢰⠗⢲⠀⠀⢸⣻⢀⠀⠀⠁⠀⠁⡄⡇⠀⠘⠢⢄⣉⠑⠒⢦⠀⠀⣸⠁⠀⣸⠀⠀⢸⠿⠑⢾
⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⢁⡠⠃⠀⡜⠀⡜⠀⡯⢤⠀⠸⣍⠂⠤⠄⠀⠀⠒⣁⠇⣠⡤⠤⣈⠒⠻⢅⠛⢄⣰⢃⠂⢀⠏⠀⡤⢸⠀⠀⢸⠧⡄
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠉⠀⠠⠊⢀⠜⢁⡜⢀⡞⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠑⢤⣐⠂⢱⠦⣀⡗⢊⣍⠳⣄⡞⠀⠀⠑⠒⠈⠉⠓⠒⠁
⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠁⠔⢁⡤⠎⠀⠀⠀⢰⠩⠭⡗⠀⠀⠀⣠⠤⠤⠤⠒⣛⣉⠵⠞⠀⠘⠚⠁⠸⣦⢄⡀
⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⡾⠀⠀⢰⠀⠀⢰⠏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⢰⠒⠒⠒⠒⠒⢲
⠀⠀⠀⠀⠈⢯⡢⣄⣀⣀⣀⡤⠖⠋⠐⡆⠀⠀⠀⠀⠀⣰⡗⠀⠀⠸⢇⠀⠀⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢚⠛⠛⠋⢸⠀⠀⠚⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠉⠚⠁⠀⠀⠀⢀⠤⠄⠧⣀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠑⡄⠀⢸⠀⢀⡇⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠈⢧⠀⢠⠇⠁⠀⠀⠀⠀⠀⠘⡆⠀⢀⠤⠤⡀⠀⠀⡠⠤⠤⣀⢜⠷⣀⡴⠁⠀⢸⠀⢸⡇⡇⠀⢸
⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠶⣗⠤⣀⡀⠀⠀⡸⠀⠀⠳⢤⣀⣀⣀⣀⡠⠞⠁⠀⠸⡀⢀⠿⠲⡞⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢸⠀⠸⡇⡇⠀⢸
⠀⠀⠀⠀⠀⠸⡁⡀⠀⠀⠀⠈⠑⠲⠦⠭⠽⠧⣀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠤⣄⠀⣀⠀⠀⢣⡀⠀⢠⡶⣇⠀⠀⠀⠀⠀⢸⠀⠘⠛⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠳⡄⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⡜⠅⠀⠀⠀⢀⣈⢦⠉⢷⠀⠀⠉⠉⠉⠙⢾⠛⠉⠑⢆⠀⢸⠀⠈⠁⡇⠀⢸
⠀⠀⠀⠀⠀⠀⣠⡸⣦⣀⠀⠀⠉⠓⠒⠦⠤⠤⠄⠄⢘⠆⠀⠀⠳⠤⠭⠭⠤⠄⠴⠚⠉⠉⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⡼⠀⢸⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠐⠏⠀⠈⠑⢲⣤⠤⣤⣤⣤⣤⠴⠒⠁⠀⢀⡄⣠⣄⡠⠤⣤⡤⠤⡤⠤⡤⠤⠤⠤⡤⠤⡀⠀⠉⠒⠉⠀⠀⢸⠀⢎⠀⣳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⠀⠀⠀⢠⣞⡦⠀⠀⠀⠣⠤⠦⠤⠧⠴⠷⠗⠒⠚⠒⠚⠒⠙⠓⠓⠘⠈⠀⠀⠀⠀⠀⠀⠘⠤⠤⠩⠡⡤⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢖⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⢀⣠⣤⣉⡛⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠉⠹⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠷⠦⠤⠾⠋⢹⡆⠀⠀⢀⣠⠶⢻⡟⠀⠈⠉⢉⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠲⠦⣄⣹⡎⠙⠶⣤⣀⣤⣤⣴⠶⣾⠁⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠉⠁⠀⣾⠁⠀⠀⣠⡟⠁⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⣀⣀⣠⣿⠾⠛⠀⠀⠀⠀⠀⢸⠻⡇⠀⠀⠀⢸⡇⠀⠀⣰⠏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣇⠉⠛⠛⠋⠉⠉⠀⣿⠀⠀⠀⠀⠀⠀⢀⡿⠀⣷⠀⠀⠀⣾⣀⣤⠾⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⣸⠷⠶⢿⡶⠚⢻⡏⠉⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡇⢻⣄⠀⠀⠀⣠⡏⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⡇⠀⠙⣶⡀⠀⠟⠀⠀⠀⢨⣧⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢹⣇⣠⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢀⣀⣀⣤⣤⣿⠀⠀⠀⠀⠈⢷⣤⣀⣀⣀⣀⣠⣤⣤⠤⠶⠋⠀⠀⢸⡇⠀⠀⠉⠉⠉⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢶⡟⠛⠋⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠉⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠄⣸⠏⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⡀
⠀⠀⠀⠀⠀⠉⠐⢿⣤⡀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⠀⣿⡀⠀⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠙⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠙⠿⠆⠀⠰⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣦⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠄⠰⢂⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢳⣼⣿⣿⣧⣶⣀⣶⣢⣀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⣳⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣦⣤⣶⣾⣿⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣴⣾⣆⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⠀⠀⣸⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠈⢀⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⡖⠐⠀⠀⠀⠀⣀⣴⣦⠝⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⢻⡿⠿⠿⣿⣿⣟⠛⡿⠋⠉⠀⠈⠳⠶⠍⠉⠁⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⢈⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢸⣷⣀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⣿⣿⡗⢶⣾⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢹⣿⣿⣯⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⣿⣧⠀⢈⠁⠀⠀⠀⠈⣾⣄⠰⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⠈⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣷⡿⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣧⣴⣶⣼⣿⣄⣶⣿⣿⣿⠸⣦⠀⠀⠀⠀⠀⣿⣿⠏⢀⡞⢠⢯⣿⣿⣿⣿⣿⣿⣿⢟⡡⠀⠀⠀⠠⠔⢤⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣷⣤⣀⣠⣶⣿⣿⣷⣞⣷⣏⡾⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣠⣄⣲⣥⣙⣿⣿⣿⣿⣿⣿⣿⡾⡻⠂⠈⢻⣿⣿⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡋⠀⠀⠊⠁⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡿⠚⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡇⠐⣄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⠄⠀⠀⠊⠹⢿⣿⣿⣿⣿⣿⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣆⠉⠑⢀⡀⠀⠀⠀⠀⠀⠈⠛⢿⡃⠀⠀⣀⣀⣤⠾⢿⣶⣿⠿⠍⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⢿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣾⡿⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢰⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣬⡸⠏⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠀⢀⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⢞⢀⣵⠎⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣭⣝⠂⣿⢃⣶⣀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠇⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠐⣖⣸⣅⢤⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠷⣦⡾⣻⣿⠆⠀⠀⠀⠀⠀⠀⢠⣌⡁⠆⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡶⠐⡃⠿⣥⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡦⣵⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣈⠟⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣧⢈⠳⠒⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⡿⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⢀⡰⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢻⣦⣷⠟
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣦⠈⢣⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⣴⠉⠀⣿⣠⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠄⠈⠃⣰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣬⣿⡟⠀⠘⣿⢟⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠠⠄⡜⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠔⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠰⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡄⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⣨⠓⡆⣼⡇⠞⣫⡆⢀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢠⡄⢴⡙⡿⣿⠟⣁⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠦⠠⠆
⠀⠀⠀⠀⠀⠀⠶⣠⠰⠄⠘⠁⣸⠟⢠⣟⣠⣤⡤⠀⠀⠀⠀⠈⠻⢷⡼⠇⢸⣇⠐⠠⢾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡄⠹⣆⠂
⠀⠀⠀⠀⠀⠀⠛⣡⠈⠁⠀⢢⠁⠀⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⣤⣀⡈⠂⠀⣻⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠉⡴⢃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠄⠲⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠆⢀⠁⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠒⢰⡑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠶⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣛⣟⣜⢳⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡞⠋⣩⠉⠙⢿⣧⣽⣻⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠻⠻⣦⡀⠠⠀⠀⠈⠡⢘⡁⠄⠙⠻⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣦⡀⢀⡔⠒⠰⠂⠀⡠⢾⣿⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠟⠿⣿⣿⡋⠀⡀⢴⣼⠿⠛⠋⠉⠹⣿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡆⢈⠟⠈⠀⢀⠻⣤⠃⠀⢀⠀⣄⢘⠁⠆⡜⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠁⡺⠀⢸⠛⣄⠸⣏⢸⣎⢺⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠠⡄⢿⠑⢿⡕⠬⣿⣽⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠈⢀⡘⠳⡄⣻⣄⣻⣮⣽⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠴⡶⠹⣦⡀⠻⣿⣏⣺⣿⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣤⣄⣠⣴⣷⣄⣿⢻⣶⣿⠙⣿⣻⢟⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡍⣿⡿⠿⣥⡾⠹⣷⣴⣿⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣲⣷⠟⠛⢾⣼⠷⣎⠻⢽⣿⣾⣼⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣼⢟⣄⣀⣾⢻⠛⠿⢿⣵⣶⣭⣻⣿⣟⠻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⢹⡟⠛⠠⢄⠀⠉⠛⢿⣿⣷⣬⣵⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣿⡻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢻⣯⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣶⣂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡼⠛⣿⣛⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⢢⣧⢸⣿⣇⣿⣏⣿⢻⣿⡗⠯⡂⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠡⢹⡿⠋⠉⠁⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠐⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣰⡦⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠁⠀⠏⢀⣴⠞⠋⠉⠁⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠲⠶⠦⣄⡉⠀⠀⠀⢛⠃⠠⠀⠀⠈⠀⠀⠀⠀⠀⣤⣶⣾⢿⣦⡀
⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⢵⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢿⣇
⠀⠀⣾⡏⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡆⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⠀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⢀⣄⣠⣀⣤⣶⣶⣿⣿⣿⣿⣿⡿⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣼⡟
⠀⠸⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣾⠟⠁
⠀⠀⢻⣷⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠙⠿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠿⠏
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⠏

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠤⠤⣄⡀⠀⢰⡃⠡⠀⠀⠀⠀⠐⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⠋⠐⠑⠁⠈⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠒⢀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠐⠚⡄⠀⠈⢀⠆⠀⠀⠀⠅⠂⠀⠦⡀⠀⠀⠠⠐⠀⠀⡀⠴⠳⣱⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠞⣁⠀⠈⠁⠀⣠⠆⠀⠀⠀⡀⠐⣒⠖⢲⢫⠀⠀⠀⢀⡱⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠈⠃⠉⡀⠙⠐⠒⠒⠉⠀⠀⠀⠀⢸⢸⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠤⠤⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠤⢃⡀
⠀⠀⠀⠀⠀⠰⠂⠐⠎⠁⠀⠀⢸⣀⣠⢀⠅⠀⠀⠀⠀⠀⠉⠛⡛⠐⠒⠔⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠡⡀⠀⢀⠜⠀⠀⠀⡄⠀⠀⣄⡀⠀⠀⠀⠀⢀⣀⡇⢸⡀⠀⠀⠀⢂⠖⠉⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠘⠁⢠⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⡀⢠⡦⠂⠀⠊
⠀⠀⠀⠀⠨⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⢈⠵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠠⣤⣀⠀⠐⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠂⠃⠀⠀⠀⠻⠗⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠉
⠀⢸⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⣄⠀⠀⠀⠀⠀⠂
⠀⡆⠀⠀⠀⠀⠁⢀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠤⠄⠀⠀⠀⠨⡀⠀⠀⣸⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⢸
⠠⠀⠀⠀⠀⠀⠀⢈⠁⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡬⣉⠉⡵⠢⢄⠀⠀⢇⣀⡎⠀⠀⠀⢃
⠁⠀⠀⠀⠀⠀⠀⣨⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠼⠀⠓⠤⠊⠀⠀⠀⢨⠖⠂⡀
⢰⠁⢱⡀⢀⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⠁
⣀⡉⠉⠟⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⡀⠀⢀⠢
⡀⡸⠎⢇⣀⡠⠃⠀⠀⢐⠐⡆⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠠⣦⠀⡀⠀⠀⠐⠀⠀⣠
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⡀⠈⠀⠀⠀⢀⠋
⠴⠊⠠⠀⠀⢠⠒⢄⣀⣀⠜⠢⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠚
⠀⠀⠀⠀⡀⠈⠑⠁⠀⠙⢄⣀⠼⣀⠀⢄⠀⠀⢀⢀⠀⠀⢀⠤⠴⣢
⠀⠁⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⢇⠀⢀⡗⠀⠣⠠⠃⠀⠀⡆⠀⠘⠀⠀⠀⠀⠀⠀⠁⣤
⠀⠀⠂⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠙⡉⠀⠀⠀⠀⠀⠀⠀⢡⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠈⠀⡀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠠⠋⠢⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⢀⠠⠤⣀⠀⠀⠀⠀⠀⢠⡀⠜
⠀⠀⠢⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠓⠀⠀⡆⠀⠀⢀⡇⠀⠀⢠⠈⢹
⠀⠀⠀⠈⠐⠂⠐⠂⠀⠀⠀⠀⠀⡔⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢈⣖⠒⢫⠦⢄⠀⠀⠁⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠂⠐⠞⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⢈⠇⠸⠤⠴
⠀⠀⠀⠰⠁⢈⠀⠀⠀⠈⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⣠⢠⣾⢀⡄
⠀⠀⠀⠀⠀⢠⡦⠀⡀⠀⡜⠛⠀⠀⠀⢰⡇⢿⣇⡞⢀
⠀⠀⠀⠀⠀⠋⢤⠀⠛⣾⡟⠆⠀⠀⠀⢸⣃⣇⢸⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠠⠀⠀⠀⠀⢠⣿⡧⠀⠀⠀⠀⠘⡋⠉⠻⣣⣾⣀⡀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢘⡇⠀⠀⠀⠀⠀⠁⠀⢠⠈⠹⠿⠃⠀⠀⠀⠀⡠⠊⠁⣀⠴⠂
⠀⠀⠀⡤⢀⡀⣿⠀⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⠀⢀⣼⠋
⠀⠀⠀⠀⣀⠙⡷⣴⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣄⣤⡐⠀⠀⢠⣼⠉
⠀⠀⠀⢱⠋⣼⣿⢁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠝⠛⠙⠀⠀⠈⠊⢅⣀⣀⣠⠤⠐⠀⠀⠂
⠀⠀⠀⠘⣰⡟⢻⡏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄⡵⠂⠀⠀⠀⢤⣤⣤⣬⣿⣿⣧⣀⠀⠀⠀⠈
⠀⠀⠀⢰⡏⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣏⣹⠛⢿⠷⠤⠄⠀⠀⢀⠠
⠀⠀⠀⢸⢷⣾⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠖⡠⠐⠂⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡇⠀⡜⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠢⣀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⡃⠀⡃⡾⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⣙⣽⠾⠧⠇⠀⠀⠀⠀⠀⠀⣶⣥⡒⠂⡐⢾⣶⢄⣀
⠀⠀⠀⠀⢸⡼⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠛⠛⣁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡄⠀⢸⠀⠀⠛⡀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠁⠉⣴⣯⡆⠀⠀⠀⠀⠀⠰⣀⠿⣿⣦⡟⡂⢴⠈⠖
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠂⠋⠈⠁⠀⠄⠱⠈⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠤⡀⠈⠁⠀⠀⠀⣠⠱⢦
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠁⠀⠀⠀⠀⠀⠸⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢳⡀⠀⠀⠀⠀⢠⠏⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠲⡄⠀⠀⠀⠀⠀⢸⡀⠀⣧⠀⠀⠀⠀⢸⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠹⡄⠀⠀⠀⠀⠈⣇⠀⡟⠀⠀⠀⠀⣿⢀⡞⠀⠀⠀⠀⠀⢀⡴⠚⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢤⡀⠀⠀⠀⠱⣄⠀⢳⡀⠀⠀⠀⠀⠸⣀⡇⠀⠀⠀⠀⢹⡞⠀⠀⠀⠀⢀⡴⠋⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⢆⠀⠀⠀⠈⢦⡀⢇⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⣴⣫⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⢧⡀⠀⠀⠀⠙⠾⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⣳⡀⠀⠀⠀⢀⡠⠖⠋⠉⠁⠀⠀⠀⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⣠⠖⠉⣀⣀⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠲⠤⢤⣀⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⣤⡖⠒⠒⠓⠒⠚⠓⠲⡄
⠀⠀⠀⠀⠀⠈⠓⠲⠶⠶⠒⠒⠒⠋⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡄⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠠⣶⠶⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠀⣀⠴⠋⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⠶⠶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣰⠃⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡶⡀⠀⠀⠀⠀⠀⢧⠀⠈⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡴⠁⠀⠀⠀⢠⠏⢸⠀⠀⠀⠀⢸⠃⠙⡄⠀⠀⠀⠀⠈⢳⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣠⠞⠀⠀⠀⠀⢀⡎⠀⢸⠀⠀⠀⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⠀⠙⠦⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⠀⠀⠀⣼⠀⠀⡞⠀⠀⠀⠀⢸⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡼⠁⠀⠀⠀⠀⠀⢧⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠞⠁

⠀⠀⠀⠀⠀⠀⣩⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⡁⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁
⡌⠛⠛⢲⠄⠀⠈⠁⠀⠀⠀⠀⠀⠔⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠠
⠀⠀⠀⡇⠀⠀⠀⠀⣀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀
⠀⠐⢸⠀⠀⠀⡔⠈⠿⠗⠂⠴⠄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⡄⠀⠀⠀⠡⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢐
⠀⢠⠁⠀⠀⠀⠀⠑⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⡜⠀⠀⡐⠁⠀⠀⠈⠠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢆⠘⠛⠃⡈⠀⠀⠀⠀⠣⣄⡀⣀⡴⠇⠀⠀⠀⠀⠀⡔⠂⠢⡀⠀⠀⠀⢀⠇
⢠⠃⠀⠀⢄⠀⠀⠀⠀⢐⠀⠁⠢⣤⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⣠⠮⣅⠀⢸⠚⠒⢦⠀⠀⠀⢦⣀⡼⠀⠀⠀⠀⠸⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣄⢀⡸⠀⠑⢤⡤⠊⠀⠀⠀⠀⠀⡶⠂⠤
⢀⡔⠒⢆⠀⠀⠀⠀⠀⠿⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢠⠃
⠘⢆⣀⠾⣢⠤⠲⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁
⠤⠤⡀⢠⠇⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠠⠀⠀⠀⠀⡀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠿⠸⢆⠀⢀⡴⠁⠀⠀⠀⡔⠉⢢⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⣴⡆⢠⠀⠀⠀⠠⠐⠀⠀⢀⣀
⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠘⠛
⠀⣀⠄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠇⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠂
⠚⠁⠀⠑⡀⠀⠀⣇⠀⡱⠤⢄⡶⠉⠀⠹⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠰⡀⠀⠀⠐⠄⠀⠈⠉⠀⠀⠀⠙⢄⣀⡴⢇⣤⠤⠤⡀⠀⠀⢀⠄⢄⠀⠀⠀⡤⠶⠶⢒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠐⠄⠀⠀⠈⠢⠄⠠⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⢸⠦⠄⠇⣀⡰⠁⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⢈⠢⡀⠀⠀⠀⠀⠉⠒⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⡄
⠀⠀⠀⠀⡄⠀⠐⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣅⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡀⠀⠀⠀⡄⠲⠶⠦⡀⠀⠀⠀⠀⠀⠀⠰⠤⠴⠃
⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⣸⠀⠀⠀⠀⡌⠉⢹
⠀⠀⠀⠀⠑⠢⠤⠄⠤⠔⠊⠀⠀⠀⠀⠀⢀⠤⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⡁⠀⠀⠈⡳⡤⠤⠲⣃⣀⠀⠀⠀⠈⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣀⡼⢄⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠁⠀⠀⡔⠛⠳⡄⢰⠁⠈⢙⡆
⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠀⠀⢸⠀⠀⢈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠔⠁⠀⠑⠒⠋
⠀⠀⠀⠀⠘⡀⠀⡘⠀⠀⠀⠀⠈⠑⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢿⠏⢉⠀⡈⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡄⠀⠂⠀⠀⡍
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⢇⠳⣀⢦⡤⡎⠑⠒⠲⢤⡀
⠀⠀⠀⠀⠀⣠⢋⡀⠀⠀⠈⠦⢎⣹⠒⠁⠀⠀⠀⣀⣨⣦⣤⣀
⠀⠀⠀⠀⠀⡇⠀⠈⠂⠀⠀⠀⣸⠙⡄⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⢸⠀⣷⠀⠀⣿⣿⣿⠿⣋⣌⠻⡏⢹⣧⣀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⢸⠀⢸⠀⢠⢋⠋⡾⣪⠞⡩⡇⠀⠈⢁⠛⣍⠉⠓⠒⢦
⠀⠀⠀⠀⢰⡧⠖⠒⢤⡇⠀⠀⢸⠀⢸⠀⢸⢸⠀⠀⠀⢜⡾⠃⣠⠃⡸⠀⠟⠤⣷⣯⣿⠗⢄
⠀⠀⠀⠀⠸⠤⠒⠒⠢⣵⢀⣀⣸⠀⢸⣤⡼⡍⠀⡴⠒⠉⠈⡏⣉⣦⠁⣤⡄⠀⠀⠈⠋⠀⠀⠳⡀
⠀⠀⠀⠀⠀⣴⠀⠀⢸⠈⠀⠐⠺⣄⢸⠃⣷⡇⠀⡇⠀⠀⠀⠘⠏⢻⢶⠏⠀⠀⠀⠀⢀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡟⠀⠀⠸⠀⠀⠀⠀⠈⠁⠀⣿⠀⠀⡇⠀⡀⠀⠀⠀⡜⠉⡆⠀⠠⠄⠀⠈⡄⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡇⡇⠀⡇⠀⠀⠀⢠⠀⠀⠀⣿⠀⠀⢳⠀⣱⡀⠀⢰⠇⠀⣧⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢱
⠀⠀⢀⣀⣰⡇⡃⢀⡁⠀⠀⠀⡄⠀⠀⠀⡏⠀⠀⢸⢠⠇⠙⡄⡼⠀⢀⣿⡄⠀⠀⠀⠀⠀⣴⠒⣛⡓⠺⡆
⠀⠀⠀⣈⣭⠋⢀⠈⡟⠛⠓⠒⠓⠒⠲⠶⣇⠀⠀⢸⢻⣀⣀⣸⢃⡤⠾⢌⣁⣀⣠⠤⠴⠒⠋⠉⠉⠉⢣⢹
⠀⠀⠰⠿⠓⠊⢩⡔⠁⠀⠀⠀⠀⠀⠀⠀⠘⣄⣠⣯⠏⢠⠞⠁⢼⣿⡆⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⡤⠾⠯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠓⠒⠒⠋⠙⠂⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠢⣀⠀⠀⠀⠀⢈⡁⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⢢⣰⠈⠂⠀⠀⠀⣈⣁⣀⣛⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣰⣤⠀⠀⢀⠀⡀⠀⠀⠀⢠⢇⠔⠀⠀⠀⠀⠀⠀⡄⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠆⠀⢀⡀⠚⠄⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠠⠤⡀⠀⠀⠀⠀⠡⢤⠀⠀⠀⠁⠄⢀⣄⠀⠀⠠⠸⡀⠀⢀⡄⠀⠀⠰⣿⠀⢐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠈⠀⢀⠄⠀⠙⡄⠀⠀⠀⠀⠀⠈⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢢⠀⠀⠰⠞⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠤⠁⢀⠀⠀⡀⠀⢤⡀⠀⠀⠃⡀⣆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⢈⡅⠉⠁⠀⠀⠀⠀⠀⠀⠐⠻⡷⠄⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣐⠀⣴⡀⣀⣀⠀⠀⠡⡀⠀⠀⠀⠀⠢⢠⡄⠄⠁⠀⠀⠀⠀⠀⠁⠂⠙⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢤⠄⠙⠉⠑⡀⠀⠀⠀⠀⠴⠖⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠐⠄⠀⢒⠘⠉⠉⠉⠀⠀⠂⣤⠄⠀⠐⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠉⠉⠉⠈⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⢄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⠭⠗⠲⠄⠶⠆⠆⠄⠰⠀⡄⢀⡵⠲⠴⠦⠆⠀⠀⠀⠀⠀⠀⠓⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⡂⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠀⠀⠀⢠⠀⠘⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠈⠁⠙⠁⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⠀⠀⢠⠀⠀⡄⡇⣀⡀⢀⢀⡀⠀⢀⣄⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠓⠃⠀⠀⠆⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡜⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⠀⡄⠁⢀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠞⠀⠀⡈⢦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢸⣿⣿⠀⠇⠉⠘⠀⠀⠃⠃⠀⣆⣠⠰⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠺⠃⠙⠚⠀⠀⠉⠁⠀⠀⠛⠁⠀⠈⠋⠀⠀⠙⠋⠘⠓⠀⠀⠀⠑⠲⠅⠀⠠⠒⠁

⠀⠀⠀⡀⡀⠀⠀⣀⣀⣀⡔⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠂⡀
⠠⠉⠀⠀⠀⡐⠁⠀⢀⠃⠀⡀⠀⠀⡷⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦
⠀⠐⠈⠁⠍⠁⠈⠈⠀⢀⣤⣟⣉⣿⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⡄⠀⠀⠀⠊⠀⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠈⠙⢻⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢈⡉⠙⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄⣤⣤⠀⠀⠘⠃⠀⠀⣀⡄⠀⠀⠀⠀⢃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠿⠇⠐⠂⠀⣸⠉⠀⠀⠀⠐⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠇⠀⢠⡶⠶⢦⡀⠀⡀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠖⠀⠀⣏⢉⡷⠀⠀⠀⠈⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣾⣇⠀⣍⢀⣠⡀⢸⡇⣠⣄⠀⢀⣤⡀⡄⠀⡄⠀⠁⠀⠀⠀⠀⠀⣈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⠀⠀⣸⡇⣿⣾⠁⣻⣼⣷⡏⢸⡧⡿⢸⡇⣧⢸⣿
⠀⠀⠀⠀⢀⡀⠀⠠⡦⣀⢄⠘⠷⠚⠛⠉⠀⠟⠘⠷⠋⠘⠋⠻⠟⠁⠛⣻⡇⠙⠛⣿
⠀⠀⠂⡠⢊⣈⣡⣦⡀⠘⠤⠃⠀⣀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡽⠃⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢙⣤⠖⠋
⠀⠠⠞⣡⡿⠋⠁⠀⠁⠀⠀⠀⠀⠀⠉⡗⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⠚⠋⠁
⠀⢠⣾⠋⠀⠀⢰⠦⠀⠀⠀⠀⠀⠀⠀⠑⠮⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣉⣆⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⡟⠓⡖⠿⣿⡟⠰⠶
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠡⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣀⠀⠈⣧
⠀⠀⠀⠀⡴⠃⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢀⡏
⠀⠔⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠀⠈⠀⢠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣶⣤⣤⣤⣭⣭⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⣀⣴⣞⣡⡄
⠀⠀⠀⠀⠀⠀⡔⣿⣿⣮⢞⡵⣫⠝⠁
⠀⠀⠀⠀⢠⢖⡣⣞⡿⠁⢀⣜⣡
⠀⠀⠀⠀⣎⣿⣿⣿⣷⣠⠜⠻⡀⠀⠀⢀⡀⠀⠀⠀⠈⠁⢀⣀⡀
⠀⠀⠀⠀⠙⠿⣿⣿⠿⣇⠀⠀⠱⣄⠀⢉⡤⢤⣀⠀⢀⠞⠁⠀⢸⠂
⠀⠀⠀⠀⠙⠓⣼⣅⠀⠀⠑⢢⡄⠀⠙⠺⣆⠀⠈⠳⣼⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢠⡎⢻⣷⣄⠀⢀⣭⡓⢤⡀⠈⢣⡀⠀⠈⢳⡭⠥⠤⠤⠤⠤⠔⠒⠚⠉⠁⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠳⢿⡈⢮⣑⢮⡀⠈⠙⢿⣦⡀⠙⠲⢤⠤⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⢀⡤⢔⡛⠿⠆⠀⠀⠀⠃⠀⠀⢹⡉⠁⠐⠒⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⠋⣉⠴⠚⢇⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠉⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈⢆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠻⠻⡖⠚⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⢣⠀⠀⠙⠛⠓⠿⣶⡄⢀⣤⣶⠿⠛⣁⣸⠾⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠹⡭⠞⠋⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⣄⠀⠀⣾⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠷⢖⠤⣈⣋⢿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠸⡁⢠⡼⠂⠀⠙⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠔⣊⡥⠄⠒⠂⠀⠀⢲⡀⢱⠀⠁⠀⠱⢬⡑⢤⡀⠀⠀⠀⠀⠀⣈⡦⡇⠀⠀⠈⠳⡞⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣈⠳⢄⡠⢊⡵⠊⠁⠀⠀⠀⠀⠀⢰⡣⠷⠞⠀⠀⠀⠀⠈⢯⠓⢬⡒⠒⣒⡩⠥⠒⠊⠹⣤⣀⡀⠠⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠑⣒⣻⡀⠀⣀⠉⣉⣉⡹⠂⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠕⠊⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣤⣀⣀⣀⣀⣀⣀⢤⠤⣴⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣻⠧⡔⠈⢋⠫⠏⠉⢖⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣍⠋⢀⢿⣾⣿⡛⠺⣧⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣷⣶⠷⠞⠿⢳⣾⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⡴⢩⠃⠀⠀⣠⠎⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⡀⠈⣛⣦⣀⡀⣀⣨⠇⣴⡉⠀⠀⢉⣑⣾⣖⠒⣒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣏⡫⢟⣽⡩⠊⠀⠀⠉⠒⠭⣓⠿⣏⡩⣟⣿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠽⠷⠟⠉

⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣠⠖⠋⠉⠁⠉⠉⠒⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠀⠀⠉⠙⠶⣄
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠋⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡋⠀⠀⠀⠀⠀⠀⠀⣠⠅⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠈⠙⠒⠦⠤⢤⣤⡤⠴⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⣀⣀⡠⠤⠔⠁⠀⠀⠀⠀⣀⣀⣀⠀⣠⠞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⠉⠙⣦⠀⠀⠀⠀⠀⠀⢀⣀⠛⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠉⢷⡈⠉⠙⢄⣀⡀⠀⣀⣀⣠⠤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⠉⠀⡴⠋⠉⠙⣆⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⣼⠃⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⣒⡚⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⢀⣿⡀⠀⠀⠀⠀⢀⣠⣬⣙⣛⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠁⠙⣷⣤⡀⠀⠀⠀⠀⠀⣸⠃⠙⠲⠶⠛⠉⣷⣀⣀⣤⠖⢫⡏⠀⠀⢉⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠙⠲⢾⣄⠙⠓⠒⠒⠛⠛⣿⣠⡄⠀⠀⠀⠀⣿⡏⠁⠀⠀⣾⠀⠀⣠⠏⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠓⠶⠶⠖⠒⠛⣿⠁⠀⠀⠀⠀⢰⡇⣷⠀⠀⢰⠇⣀⡴⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⣾⠶⢾⡶⠶⣾⠋⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡏⢷⡀⠀⠀⣼⠃⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⢸⡇⠀⠙⠆⠀⠃⠀⠀⠀⣇⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢀⣀⣠⣿⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣠⡤⠟⠀⠙⡟⠙⠛⠛⠛⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡶⠛⠋⠉⢹⠁⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⢹⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣼⠋⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⣻⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠆⠀⠀⠀⠀⢿⣤⡀⠀⠀⠀⠀⠀⠀⠰⠟⠃⠀⠀⠸⢷⡄⠀⣠⣶⠟⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠉⠉⠉⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠈⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⢀⣀⣛⣛⡛⠻⠿⢯⣛⠿⢦⠀⢦⣼
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⢁⣀⠀⠀⠚⠋⣉⣩⣭⣟⠛⠶⠀⠈⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢠⣿⣡⠴⠀⠀⠸⠟⣦⣀⣀⣠⣴⣶⡄⠀⠀⠀⠀⣠⡶⠶⣤⠀⣿
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⡟⣡⠾⠋⠀⠀⠀⠀⢉⣩⢴⣿⡽⠂⠀⠀⠠⡾⠋⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢸⠃⣠⠆⠀⠀⣀⣾⣯⣶⣯⡵⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⢻⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣴⠶⣠⣾⠃⠀⠀⠀⣉⡵⢞⣽⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⡶⠿⠦⠀⠙⢷⣄⠀⠀⣠⣄
⠀⠀⠀⣀⡴⠿⠀⠀⣠⢴⡟⠀⢸⠇⡿⠀⠀⠀⠀⠉⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⡟⠉⠻⢶⣤⡶⢶⣄⣀
⠀⠀⣾⠋⣰⠟⢡⣾⡟⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠀⠀⠀⠀⠙⠷⢾⣧⣽⡿⣦⠀⠀⣠⠶⡆
⠀⠸⣏⠀⠿⠀⡿⠘⠇⠀⠀⠰⣄⡀⠀⠀⠀⠲⣦⣀⣀⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢿⣶⣞⣡⠞
⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣦⣤⣴⢿⣯⣩⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣄
⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣙⠶⢤⣤⣤⠶⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢧⣤⣤⣤⡤⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡖⢀⡟
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠙⠻⠶⠖⠂⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠿⣤⡌⠻⠓⢶⣦⣤⣀⡀⠀⠀⠀⢠⡏⢀⡾
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⣴⠏⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⠀⠀⠈⢻⡄⠀⠀⠓⠀⠈⣹⠟⠲⠦⣼⣁⡾⠁
⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⣶⣶⠶⠛⠁⠀⣀⣼⣄⣠⣄⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⣿⠆⠀⠀⢀⡾⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⠉⠛⠉⠈⠙⢷⣶⣶⣤⣴⣟⠉⠙⠛⠓⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠄⠶⢦⣤⣄⣀⠀⠀⠙⠿⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠉⠙⠻⠶⣤⡀⠀⠸⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢃⣴⠶⠛⠂⠀⠀⣀⠀⠀⠈⠙⢦⠀⣤⣿⣧⡀⠀⣀⡠⣄⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠴⠋⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⢶⣶⡉⣿⠟⢋⣡⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠗⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠈⢻⣽⡏⠀⡈⢻⡿⠳⠶⢦⣤⣤⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⣿⠛⠁⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⠛⣅⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⣼⠂⠀⠀⠀⠀⢿⣿⣋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣗⠀⠈⠙⠷⣦⡀⠀⠀⢀⣴⣿⠋⠀⠚⠁⠀⠀⠀⠀⠀⠈⢿⡉⠉⠛⠛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠛⣷⠀⠈⠙⠆⣴⡟⠉⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⠳⢶⡶⣦⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⣰⠿⡅⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⣼⠃⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢿⣀⡞⠁⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠀⠀⠁⠀⠈⠁⠀⠉⠀⠀⠀⠀⠠⠰⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣀⠴⠋⠉⡆⠰⢷⣴⠿⠄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠐⣶⣲⣶⣮⣯⣷⡄⠀⠀⠀⠀⠀⠄⠀⠀⠐⠄⣀⠀⠊⠀⠀⠀⠠⣷⠄⠀⢀⠤⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠰⠐
⠀⡄⠁⠀⠀⠀⢋⡢⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠐⠃⠀⠀⠘⠠⠆⠀⠀⠀⠀⢠⠀⠀⠈
⠀⠀⠀⠀⠀⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄
⢀⡀⠀⣀⡀⢧⣂⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠉⢉⣇⠀⠀⠀⠀⠀⡀⢀⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠂⠀⠀⠀⠀⠈⠰⠂⣅⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣀⡏⠀⠠⠀⠀⠀⠀⠀⢠⠖⠒⠲⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⢀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⠓⠲⣦⡴⠀⣼⢠⣶⢠⣄⡄⢀⡶⢀⡴⡆⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠒⠀⠛⠂⠛⠙⠛⠚⠛⠟⠈⠓⠊⠛⠚⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢠⠀⣠⢄⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⢤⠀⢀⠄⠀⠀⠀⢀⡇
⠀⠢⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢉⠉⠉⠈⠀⠈⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠀⠉⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃
⠀⠀⠆⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡸⠀⠀⠀⠀⢎⠀⣀⠇⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⡘⠠⠀⠀⠊⠀⠀⠀⠀⠠⣊⠀⠀⠀⠀⠀⠀⠜⠁⠀⣐⠆⠀⠒⠢⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠦⠀⠀⠠⠠
⠀⡀⢁⠄⠀⠀⠀⠀⢀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⢰⣏⡹⢷⡀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠀⠉⠀⠀⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠞⠀⠀⠀⠀⠀⠀⠉⠒⡷⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠈⠀⠀⠀⠀⢀⣀⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠂⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠂⣀⠀⢰⠶⠒⠒⠲⠶⠎⠀⢤⢀⡆⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⢀⠤⠚⠂⠀⠀⠁⠀⠈⠭⠀⠩⠉⠹⠅⠀⠀⢀⡜⢀⠢⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉

⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠂⠠⠀⠀⠀⠀⠀⢀⠀⢤⠄⠂⢀⢀⣄⡀⠀⠂⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⠀⢀⠠⣔⣈⠰⠶⠆⡙⠙⠉⠐⠊⠁⠁⠀⠀⠀⠀⢀⠈⠠⠆⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⡀⠀⠀⢉⠀⠐⠉⠀⠔⡫⠅⠈⢀⠠⠆⠀⠈⠉⠀⠀⠉⠀⠀⠓⠠⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⠀⠀⠉⠀⠀⠁⠐⠂⠈⠀⠄⡠⠔⠉⠉⠀⠀⠀⠀⠀⢀⡀⠀⢀⡐⠂⠁⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠
⠀⠀⠛⢀⠀⠈⠁⠀⠄⠀⡀⡠⠚⠁⠀⠀⠀⠀⠀⠐⣀⣠⣄⣠⠀⠀⠈⠑⢄⠂⠀⠀⠑⠀⠀⠀⠁⠃
⠀⠀⠀⠈⠀⠀⠀⠊⠀⡀⠊⠀⠀⠀⣠⠔⠀⠀⠐⠈⠀⣠⠉⠉⣛⡾⣄⠄⠀⠑⡀⠀⠀⠠⢀⠀⠀⠀⠀⠘
⠀⠀⠀⠰⡄⠀⡆⠀⡜⠁⠀⠀⠀⠊⠀⣀⠀⢚⠓⠁⠀⢃⢀⠀⣦⠑⢚⠃⡀⠀⠀⠀⠀⠘⠀⠀⠈⠈⠀⠀⠆
⠀⠀⠀⠀⡀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠠⡅⠀⠂⠀⡄⢀⢀⡀⠀⠈⢢⠀⠡⠀⠀⠀⢠⣳⠄⡃⠀⠀⠈⡀
⠀⠀⢱⠀⡁⠀⠱⢸⠀⠀⠀⠒⠀⠀⠀⠁⢸⠀⠠⠥⠀⣐⠘⠈⠀⠀⠞⠁⠁⠀⠀⠀⠙⠁⡇⠀⠀⠒⠀⠀⠜
⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⡀⠀⢀⠀⠐⠃⠜⢄⠀⠀⠁⠉⠀⠀⢀⠔⠤⠀⡤⠀⡀⠀⠀⠀⠩⢀⠂⠸
⠀⠀⠀⠀⠀⠀⠁⠀⠐⢄⠀⢀⢄⢀⠆⠀⠈⠓⠁⡂⡠⢀⠠⡈⠴⠀⠀⠠⠁⠀⠂⠬⠀⠀⠘
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⠈⢧⡅⣄⠠⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠑⡐⠈⡳⣶⣁⠆⠠⠄⠂⠀⠄⠀⠀⠀⠀⠀⠀⡠⠁⠀⠁⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⣤⠁⡀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠙⠗⠀⠌⠀⠀⠀⠀⠀⠀⠀⡄⠈⠑⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⢂⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠃⠠⠀⠀⢀⡁⡄⠀⠀⠀⡀⠠⠆⢂⡀⠁⠀⠀⠀⠀⠀⠀⢀⠐⠁⠒⠀⠄
⠀⠀⠁⠀⠀⠀⢀⡤⠑⠄⠀⠀⠀⠰⠀⠀⢀⠀⠠⢀⡀⣀⣤⡜⠶⠒⠉⣠⠀⡐⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠉⠁⠀⢂⠀⡡⠔⠋⠀⠀⠀⠀⠀⠀⠐⠀⠃⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠘⠁⠀⠻⠄⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠁

⡟⠉⣿⣛⣻⣛⣻⣛⣟⣛⡟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣟⣻⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡎⠀⠀⠀⠀⡤⢀⣀⡀
⠀⠈⣈⣤⣤⣄⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣨⡝⢆⢀⡀⠀⠀⢠⡆⠀⠀⢈⣄⡀
⠀⠀⠉⠀⠰⠷⠄⠀⠀⠀⠈⠙⡏⢀⡅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⣀⡈⠩⢓⡏⡈⠀⠀⠀⢠⡀⠀⠕
⠀⠀⠀⢈⣵⡆⠀⠀⠀⠀⠀⠀⠘⣾⡇⠀⠀⠀⠀⠀⠡⠀⡀⠀⠈⠐⢩⢠⣶⠀⠉⠁⠀⠀⠀⠘⠃⠂⠒
⠀⠀⢈⡧⠄⣠⡔⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⡎⡔⠀⠀⣁⣤⠄⢅⠉⠁⠀⠀⠀⠀⠰⢢⠀⡀⠙⠷
⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⡀⠀⡿⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠈⣽⣶⠃⠀⠀⠀⠀⣾⡗⠀⠀⠀⠀⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨
⠀⠀⢀⠱⢟⣛⠀⠀⠀⠀⠈⣱⡀⠀⠀⠀⠀⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⢈⣻⡩⢊⠁⠄⠀⠀⠀⠠⡀⠠⠒
⠀⠀⠈⣇⠀⠉⡤⠀⢀⣶⣿⡿⠅⠀⠀⠉⠉⢀⠀⠰⠀⠆⡂⠀⠀⡰⠀⠾⢿⡿⠀⠀⠀⠀⠀⠉⠂⠀⢀⠈
⠀⠀⠀⢹⣶⡟⠁⠀⠘⢛⣿⣿⡆⠀⠀⠀⠀⠃⠀⠀⠀⠀⢳⠀⠀⠀⢰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣌⡤⢀
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⡄⠀⠀⠀⠀⠀⢱⡁⠀⠀⠀⠀⠀⠀⠀⠉⡃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⣸⣤⡾⠻⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⢀⣴⣏⡾⠁⠀⡀⠀⠀⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⢦⣤⠶⠛⠉⠘⠷⣤⣤⡤⠖⠋⣡⣏⣀⡀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⣤⡀⠙⢦⣄⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⢾⡏⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠙⢷⣄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠛⠻⣾⣧⣀⣀⣀⣠⣶⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠙⣧⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠈⣿⠀⠀⠀⠙⣦⡉⠉⢩⡿⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣿⡀⠀⠀⠀⣼⣇⣰⡟⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⠋⣿⣏⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢋⣾⣧⣤⠤⠤⠴⠶⢶⣶⡶⠶⠶⢼⡇
⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⣧⡾⠉⢿⣆⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⣠⡿⠁⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⡟⠀⠀⠀⠻⣆⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣾⣿⠟⠀⠀⠀⣠⡶⠛⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢹⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠛⠁⠀⣠⡴⠛⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣠⣄⣠⡾⠋⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣩⠟⢿⣄⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⣀⣴⢟⣡⡾⠟⠁⠀⠀⠹⣷⡄⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠘⣧⠀⠀⢀⣠⣾⣯⡶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠙⣷⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠈⠻⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⣶⡄⠉⠀⠀⠀⠀⠀⣠⣤⣬⣿⡀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⣀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠓



⠀⠀⣀⡀⠀⠀⢀⠀⠀⡀
⣿⡟⣉⣻⠿⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⡠⠀⠀⠀⠀⡀⢤
⠀⠀⢀⢀⠀⠀⠀⠈⠀⠂⠠⠈⠁⠄⢀⡂⠀⠀⡀⠀⠀⠀⠈⠂⠀⡈⠀⠀⠀⠀⠄⠕⠃⠄⠈⠀⠁⠀⠀⢠⠀⠄
⠀⠀⡈⢉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠤⠠⠀⠀⠂⠉⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠈⠀⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠈⠠⠠⡁⠁⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠠⠄⠂⠀⠀⠀⠀⠀⠂⠐⡄⠁⠁⠀⠀⠀⠀⠙⢷⠀⢄⣰
⠀⠀⢠⡀⠂⠐⠀⠀⠀⠠⠄⠀⠀⠐⠂⠀⠤⡆⣤⡀⠠⠠⠀⠐⠀⠀⠀⠀⠀⠀⢰⡥⢾⠷⠶⠆⠀⡐⠀⠀⡀
⠀⠀⠀⢈⡀⣀⠁⠀⠀⠀⠀⠀⢒⢠⠀⠀⠳⢌⠴⠀⠠⠠⠀⠂⠻⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⡀⠂⠀⢠⠀⠁⠀⢀⠀⠀⠀⠐⡅⠀⡃⠂⠠⠀⠈⠅⠄⠁⠠⠀⠀⠀⠀⠀⠀⠀⢠⡆⢰⣶⠸⠂⠀⠠⠀⣠⠀⡉
⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠠⠄⠈⠀⠀⢀⡀⠀⠀⢀⡐⠀⢠⠀⢀⡀⠀⣀⡈⢉⡩⠔⣉⠀⠀⠔⠂⠈⢄⠀⠂
⠀⠀⡈⠀⠀⠀⢤⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⠂⠁⠈⠀⠀⠀⠀⠰⡶⢀⠀⠀⠀⠚⠂
⠀⠐⣋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐
⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠠⠀⡀⠀⠀⠀⢀⠤⠰⣲⣤⠂⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⡰⠀⠀⠁⠀⠀⠈
⠐⠊⠎⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡀⠀⢀⠀⢄⡂⠠⠀⠀⠁⡀
⠀⠐⠄⠁⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠠⠀⠀⠾⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⢀⠀⡀⠠⢀⠀⠀⠀⠈⠀⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠿⠿⢟⣛⣛⣭⣭⣭⣭⣝⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢗⡲⣶⣿⣿⣿⣿⠫⣵⡤⣶⠝⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⣵⣿⣿⡿⠿⢿⣿⣮⡃⠫⠾⠇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣛⣫⢍⢠⣚⠿⢸⣿⣿⣿⣮⡻⢏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝⡋⠾⠇⢟⣣⣿⣿⣿⠿⠿⣿⣿⣿⣀⠀⣤⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⢟⣼⣿⣿⣿⡤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣿⣿⢰⣭⡝⠻⠿⣿⣿⣿⣿⠛⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣮⣣⣿⣿⣌⢵⡞⣴⡹⣶⢎⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣭⣥⣶⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠻⣦⡶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⢹⣇⠀⠛⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⢾⡇⠈⣷⠀⠀⠀⠀⠙⣷⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⣀⣴⡏⠀⠀⠀⠀⢀⡿⢸⠇⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢧⠹⡄⠀⠀⠀⢸⡇⣿⠀⢀⣴⣾⣿⣏⣻⣝⣿⠿⣛⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢻⡄⠀⠀⣿⢱⡇⢰⣟⣿⣿⣿⢧⢻⣽⡾⣿⣚⣿⣯⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢻⡄⢠⣿⣼⢁⣿⣷⣿⣿⣿⡞⢯⢷⣛⢩⣭⣷⣾⡖⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣿⡾⠻⣿⢛⡿⣿⣮⣿⠛⣧⢘⣼⣿⣿⣿⠿⣿⣿⠿⣿⣄⡀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣞⣿⡿⢫⣿⣁⠢⠩⣟⢳⠞⣵⡿⣹⣿⣷⡿⢟⡿⣩⡞⣫⢶⡝⢯⠶⣩⠿⡛⣿⣭⣛⣵⣾⡍⢟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡳⣟⣭⣿⢁⣿⢣⣥⢉⣿⢂⠇⣼⠏⣽⣫⣿⢋⡜⣧⠞⣥⢚⡴⢫⠝⣥⠿⣡⡜⢯⣩⣿⣟⣽⡴⡾⡟⣮⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡼⣱⣟⣾⡧⣜⡏⣗⡮⡙⡙⠾⠽⡟⣼⣳⣿⣋⣏⡸⡏⡶⣹⢎⡸⢇⢿⠙⡤⠹⣧⠚⣇⠴⢻⣿⣷⣻⣿⣱⢾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣯⣽⣿⣗⣿⣗⣶⣽⡃⢯⣿⣳⣲⢦⣆⣿⣿⣸⠇⣸⣀⢇⡘⢢⡜⢆⣗⠈⡆⠹⡖⢫⣨⣼⡿⣿⣭⣿⣬⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⡷⠟⠛⠛⠛⠛⠻⠷⣧⣽⡒⣬⡼⠟⠉⠉⠉⠻⢶⣦⡟⡴⠣⡜⠳⡜⢻⡆⢡⠜⣧⣾⣥⣾⡷⠿⠷⠷⣷⣯⣀
⠀⠀⠀⠀⢀⣀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⣤⣑⣮⣉⣮⣽⡾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⢠⡾⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠷⣦⡀⠀⠀⠀⠀⣠⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣆⣤⣤⣴⡏⠀⠀⢈⡷⠀⠀⠀⢀⣀⣤⣤⢶⡶⠶⠶⢶⣤⣤⣀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠙⣦⣀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠙⢷⣄⣀⣏⠀⢀⣿⣥⣤⡴⠞⢁⣤⡶⠟⠋⠉⠠⠀⠈⠀⠀⠀⠀⢀⠈⠙⣻⣶⣤⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠉⠻⡟⠛⠛⠉⢉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣶⡾⠛⢹⣿⣿⡙⢷⣤⣶⠞⠋⡁⠀⠀⠃⠀⢀⠀⢠⠄⠀⠂⠀⠁⠀⢐⡟
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠂⠀⠀⠀⠀⢁⠀⠀⠈⠀⠀⣿⠋⠀⢀⣾⠋⠙⣷⠀⠻⣧⣀⠀⠄⠀⠐⠂⠀⠈⠀⠀⠀⢀⠄⠀⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠉⠈⣿⣤⣀⣼⠏⠁⠀⢻⣦⠶⠟⠃⠀⠀⠀⢀⡀⠀⠰⠀⠘⠁⠀⡀⢠⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠨⠙⠫⠀⠀⠀⠰⠀⠂⠂⠀⢈⠁⠀⠠⠤⠀⠄⠐⠐⠁⠀⠁⣀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢈⡀⠈⡀⠀⠰⠀⠀⠀⠀⠀⠆⠀⠂⠘⠁⠘⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠄⠀⠒⠀⠘⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣡⣀⠀⡀⠀⠁⠀⠈⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠓⠲⠷⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠖⠛⠛⠉⠁


⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠑⠢⡄⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣠⠃⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣀⡀⣀⡀⠀⠀⡠⠒⠂⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⠎⡄⠩⣑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡠⠋⠀⠀⠀⠈⢠⠔⠢⠤⣈⠀⠀⢀⣀⣀⠼⠀⠀⠀⠀⠀⠀⠸⢠⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠢⠘⢰⠁⠀⠀⠀⠀⠀⠰⠀⠀⡠⠂⡠⠊⠀⠀⢠⠀⠀⠑⠆⠀⠀⠀⡆⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⣠⠔⠒⠒⠚⢦⠀⠀⠀⠀⠀⠀⢀⣼⢀⡜⠀⠀⠀⠀⡇⣠⠀⠀⠸⠇⠀⠘⣱⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠖⡠⠚⠁⢀⣀⣠⠎⠀⠀⠀⠀⠀⢀⡇⠀⠀⠠⢀⠜⠁⠀⠈⠀⠀⠀⣀⠀⣶⠁⠀⠀⣸⠋⠀⠀⢣
⠀⠀⠀⠀⢀⠖⢁⠔⠉⠀⠀⡜⡩⠋⠀⢄⣀⣠⠤⠤⠐⠁⢀⡓⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⢠⡏⠀⠀⠀⣿⢈⡀⢨⠀⠘
⠀⠀⠀⠀⡆⠀⣼⣦⡤⠚⡁⠐⠁⠀⠀⠀⠀⠀⣀⣠⣗⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠧⠄⠀⡾⠁⡀⣠⢲⡿⠈⠄⠀⠂
⠈⠀⡄⠀⠐⠀⠻⠽⠐⠠⠄⠀⠀⢁⣈⣩⣽⣛⡋⠍⠁⠀⠀⣓⣂⠀⠀⠀⠒⠈⠈⠉⢡⠀⠀⠀⠀⠀⣰⠃⡼⢋⡵⠏
⠀⠀⠄⠀⣀⣀⡀⠀⠀⣀⡀⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⢂⡀⠀⣠⠔⠰⠤⢼⡤⠤⠲⢖⣪⣥⣾⣿⣋⣀⣀⣀⣀
⠀⠀⠀⢀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⠫⠊⠀⠀⣀⣠⡀⡼⠀⠀⠀⢐⠀⠀⠘⠋⠉⠉⠉⠙⠛⠿⣟⡲⢤⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡥⠤⠴⠛⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⣀⠠⢄⡽⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣶⠇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣤⠤⠶⠶⠦⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠉⠛⠒⠲⠶⠶⠶⠒⠚⠛⠋⠉⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣀⣠⣀⡀⠀⠀⠀⢀⣀⠀⠀⢀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⠀⢨⠛⣦⣤⣴⠛⣍⠳⢴⡏⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⡾⠀⢸⡀⡇⠀⢸⠀⢸⠀⢸⡇⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⠀⢧⡇⠀⠀⡇⡇⠀⠈⡇⢸⠀⢸⡷⠋⠉⠙⣆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⠞⠁⠀⣿⠀⠀⢸⡇⠀⠀⣧⡇⠀⠀⣧⢸⠀⠠⣧⠀⠀⠀⠈⠉⠈⠉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⢻⠀⠀⢿⣷⠀⠀⢸⢸⡄⠀⣶⠀⠀⠀⠀⠀⠀⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⠸⡀⠀⢸⣿⠀⠀⢸⡀⣇⣀⣽⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄
⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⣿⠟⡗⢲⠾⢶⠷⣶⠾⠿⡶⢲⡟⠛⣯⢉⣧⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠹⢦⡄⠀⠀⠀⠀⠀⠀⠈⠻⠷⢼⣤⣼⣤⣼⣤⣤⣷⠴⠷⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⡴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠛⠉⠉⠳⣄⠀⠀⢀⣠⠖⠚⠓⠶⣄⡀⠀⢀⡴⠋⠁⠀⠉⠙⠲⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣤⠀⢰⢖⠠⢄⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣠⣶⣾⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⣁⡴⠋⠀⢸⢸⠀⡠⠛⠛⠋⠉⠉⠉⠉⠀⠀⢠⠚⠛⠛⠛⠉⠉⠉⠍⢹⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠠⠆⠀⣠⠔⠋⢀⡦⠚⠁⠀⠀⠀⠈⠛⠋⠀⡰⣶⡄⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⡡⢠⠃⠀⠀⡰⠄
⠀⠀⠀⠀⠄⠆⢰⣖⠋⢀⡤⠞⠉⠀⠀⠀⠀⠀⢠⠀⣐⡄⠀⠑⠭⠔⠀⠀⠛⠁⢰⠀⠀⠈⠢⢄⣀⣀⣠⡔⠁⠀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢷⠏⠀⠀⢀⡀⠙⠃⠀⢠⡇⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢂⣀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢰⢤
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⢳⡾⠶⠲⢦⠀⠀⠣⠐⠺⠠⢰⠁⠀⠈⠉⠒⠤⢄⡀⠤⢄⡀⠀⠀⠈⢻⠖⡲
⠀⠀⠀⠀⠀⠀⠁⠀⡿⣮⣍⣢⡀⠐⠀⢂⠀⠀⢼⣤⡤⣶⠾⣄⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠉⠃⡰⣄⡾⠊
⠀⠀⠀⠀⠀⠀⢀⣼⠁⢀⡝⠁⢠⠀⠁⠀⠀⠀⠀⠀⠀⣇⣤⣾⣁⣀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢣⡿⢀
⠀⠀⠀⢀⣔⡊⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣸⠇⠀⠀⠀⠑⢄⠀⣀⡀⠤⠃⠀⠀⠀⢰⡆⣰⣏⠭⠃
⠀⠀⠀⢺⣿⣿⣿⣶⣄⠈⡆⠀⢸⠤⡇⢤⠰⠗⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⡠⣀⠀⠈⡿⠁
⠀⠀⠀⠈⠻⣿⣿⣿⣿⡷⠃⠀⠘⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠘⣤⡜⠀⠈⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⣠⢤⣲⣶⣶⣑⣲⠀⢸⠙⠦⠸⠃⠀⠀⠀⢹⡄⠀⠀⣠⡺⢦⡞
⠀⠀⠀⠀⠀⣰⠲⡆⠀⠀⠀⠀⣴⠉⠀⣀⣀⡴⠀⠀⠀⠑⢻⢿⠟⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡧⢤⡞⠉⠀⢸⡇
⠀⠀⠀⠀⠁⠈⣞⠁⠀⠠⣡⠖⠚⢻⣍⠍⠁⠀⠀⠀⠀⠀⠘⡼⣶⡎⢹⡆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠬⠟⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⡠⢿⡀⠀⠀⠹⠶⣄⡀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠇⣿⣷⠸⣷⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠑⠔⠃⠀⠀⣴⠚⠋⢿⠉⠀⠀⠖⠂⠤⠀⠀⠀⠸⢸⣿⡄⢿⡄⠰⠖⠢⣴⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⢎⠋⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠼⠿⣶⠾⠀⠀⠀⠀⠀⢀⠀⠄⢀⠀⡇⣿⣧⢸⡇⠀⠀⠀⠈⢢⡎⠀⠀⠀⠐⠐⠠⠀⠀⠀⠉
⠀⠀⠀⠐⠿⠀⠀⠀⣟⠀⠀⠀⠈⡆⠀⠀⠀⠘⠉⠈⠁⠀⠀⠀⠱⣸⡿⣊⠏⠀⠀⠀⣴⠁⠑⣄⠀⠀⢀⡀⠤⠤⠤⣀
⠀⠀⠀⠀⡔⣢⠀⣤⡄⠀⠀⠰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡀⢀⢠⠀⠀⠀⣠⠜⠃⠀⠈⢻⠿⠿⢿⠃
⠀⠀⠀⠀⠈⣁⣤⣭⣄⣀⣤⣀⡀⠀⠀⠀⠈⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠐⠠⡶⠉⠀⠀⡖⣦⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠘⡅⠀⠀⠀⢻⠀⠀⠇⠀⠀⢀⣀⣀⣀⣠⣴⠒⠛⠛⠛⠓⠒⣦⣤⡤⠤⠴⠶⠶⠂⠀⠈⠀⡴⠊⣀⣀⣈⣢⡀
⠀⠀⠀⠀⠀⢳⣀⣀⣀⡸⠀⠀⢸⠀⡀⠈⠉⠉⠁⠀⠉⠓⠒⠲⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⢿⣿⣿⣿⣿⡿⠳⡄
⠀⠀⠀⠠⠀⠀⠀⠀⠳⠖⠒⠒⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠈⠉⠉⠁⠒⢒⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢒⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡜⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠜⢇⡀⠀⠀⠀⣦⠰⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⢀⣀⣀⠠⠤⢄⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠀⠀⠀⠀⠈⠑⣯⠤⡃⠀⠀⠀⠀⠀⠀⠨⠛⠲⠖⣚⡱⠢⣀⡠⠂⡂⢸⢘
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠾⠍⣱⢊⠯⢭⡁⠢⡏⠀⠹⣖⡠⠄⢀⡀⠤⢞⢢⠀⠀⠀⠀⠀⠀⡤⠐⠙⠚⢿⡖⢄⡀
⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⢋⠼⢮⡉⠂⠀⠀⢱⠀⠀⢡⠈⠓⢦⢄⠀⠀⢇⣢⣀⣀⠀⠤⠊⠀⠀⠀⠀⡰⠁⠀⠈⠑⡄
⠀⠀⠀⠀⠀⢰⠁⢸⠀⠀⢸⢀⡝⢻⡄⠀⠀⢸⠀⠀⠈⡆⠀⠈⠶⢄⢘⡀⠀⠀⠱⡀⠀⠀⠀⠀⣠⠞⢀⡤⠶⠚⠋⡁
⠀⠀⠀⠀⠀⠠⣀⣾⠀⠀⡔⠋⠀⠈⠙⡄⠀⠀⡆⠀⡀⡇⠀⠀⡀⠀⠉⡇⠀⠀⠀⠑⠤⠤⠔⠊⠀⠀⠉⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠱⠀⣧⠃⠀⠀⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⡆⠀⠀⠀⠀⠈⡀⠀⠀⢣⡟⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢷⡀⠀⡸⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠷⡠⠃⠀⠀⠀⠀⠀⠀⠉⠗⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⠴⠂⠀⠀⠀⠀⡰⠁
⠀⠀⠀⢠⡄⣀⠼⣦⣀⢴⠗⠁⠒⠒⠠⠤⠤⢼⣤⡀⠤⠇⣀⠀⣀⡀⠤⠐⠒⠂⠉⠁⠀⠀⠀⠀⣀⠠⠞
⠀⠀⠈⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⣞⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠑⠀⠒⠂⠀⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠀⣿⡟⣥⠶⣬⠹⣿⠀⢲⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣍⡻⠇⠀⠀⠀⠀⠀⠸⣿⡿⠁⠀⠈⠷⣴⣶⣦⠾⠃⠀⠈⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣯⣙⠻⢿⣿⣷⣦⣀⠀⠀⠀⢀⣀⣠⣤⠶⣀⣤⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣶⠉⠛⢿⣿⣿⣶⣿⣿⣿⠟⣡⣾⢿⣿⣿⣿⣿⣿⡿⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠙⠛⠉⠁⢀⣾⠟⠀⢸⣿⣿⣿⣿⣿⡇⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⢸⣿⣿⣿⣿⣿⡇⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⡆⠀⠀⠛⠟⠁⠀⢸⣿⣿⣿⣿⣿⣧⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡏⠁⠉⠉⠉⠉⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠛⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⢿⣿⣿⡀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣷⡀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⠿⠁⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⢿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢴⠓⣦⢤⡀⠀⠀⠀⠀⠀⠀⣴⣦⠀⢀⡤⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠀⠀⢸⡌⠛⣘⠃⠀⠀⠀⠀⠀⠀⠉⠁⡴⠋⣶⢾⠄
⠀⢀⣠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠺⣇⣸
⠀⠸⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡠⠤⢈⡁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠁⠀⠀⠀⠀⣤⣶⡆⠀⠀⠀⠀⠀⠀⡀
⠀⡱⠶⠛⣃⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢀⡀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⢂⠀⠘⠀⠀⢰⣦
⠀⠈⠉⠉⠀⢀⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠲⢤⣀⡑⢄
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⣾⣋⣡⠬⠃⢀⣀⠀⠀⠀⣴⣿⣿⡇⠐⠂⠀⠀⠤⠡⠄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⢀⡖⠲⣏⢹⡆⠀⠀⠉⠛⠿⠇⠀⠀⠀⢤⠶⣖⡒⢓
⠀⠰⡻⢦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣝⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⣙⡯
⠀⠐⡇⢠⣤⣌⣙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠹⣤⣄⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⢄⠰⢤⣀⠉⠀⠀⠀⠀⢠⠊⣼⠇⡟⠀⠀⢠⡖⢛⣻⡷⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⡀⠢⠀⠈⢛⠂⠀⠀⠀⠀⠉⠓⠜⠁⠀⠀⠀⠙⣛⣁⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⣀⢤⡀
⠀⠛⠃⠀⠘⠀⠠⠂⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠈⠉⣠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⡴⠶⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⠀⠀⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢁⡐⠒⠚
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⡏⢹⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁
⠀⠀⠀⠀⠀⡷⠿⣠⠞⢀⡀⠀⠀⠀⠀⠀⠀⢀⡊⢤⡘⣇⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠷⠚⠁⠀⠘⠛⠀⠀⠀⠀⠀⠀⠈⠳⠾⢧⡟⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⣠⢤⣄
⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣼⠶⢦
⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠟⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠿⢃⣴⠟
⠀⢀⣀⡈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠞⠋
⠀⠘⡤⠬⠽⢒⡞⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄
⠀⠀⠃⠐⠂⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⠀⠀⠀⣤⣶⡆
⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⢌⠉⠁⢄⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⢄⣀⠑⠄
⠀⠀⢀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣶⣟⣁⡼⠃⠀⠀⠀⠀⠀⣴⣾⣿⡆⠐⠠⠤⠀⠈⠁⠀⠐
⠀⠀⠻⣅⠷⠶⣤⠓⠀⠀⠀⠀⠀⠀⠀⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠇
⠀⠟⠃⢈⠓⠦⠟⠀⠀⠀⠀⣠⠖⠒⠒⠶⠤⣀
⠀⠀⠀⣸⢳⠀⠀⠀⠀⠀⠀⠻⣤⡾⢃⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣠⠞⣷⠀⡇⠀⠀⠀⠀⠀⠀⠿⣠⠞⠁⠀⠀⠀⠀⣠⠒⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟
⢸⡁⣸⠏⢀⠇⠀⠀⠀⢠⣿⣿⣶⡄⠀⠀⠀⠀⠀⢰⣁⣞⣋⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⢒⡤⡀
⠀⠉⠈⠓⠊⠀⠀⠀⠀⠈⢿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⡹⠗⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢉⡰⠤⠒⢤
⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣰⣿⣿⣷⣴⣶⣾⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⡠⠒⣏⠈⠉⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠘⣷⣠⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠃⠀⠰⡶⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠟⠛⠛⠉⣠⣿⠟⠉⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆⢠⡄⠀⠀⠀⠀⠀⠀⡍⠒⠄⠀⠀⠀⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠻⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠖⠀⠀⠀⠀⠀⠈⠂⠐⠂⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠃⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠎⠘⠃⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⢀⣤⣶⣶⡀⢰⣶⣶⣶⡄⢰⣶⣶⣶⣦⠀⣴⣦⠀⢠⣦⠀⢀⣤⣴⣶⡆⠠⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠈⠉⠀⢰⣿⠟⠛⠛⠁⠀⢹⣿⣿⠁⢸⣿⣏⣀⡀⠀⣿⣿⣧⣸⣿⢀⣿⡿⠛⠛⠃⠀⣿⣯⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⡙⠻⣶⡄⢹⣿⡀⢀⣀⡀⠀⢸⣿⣿⠀⢸⣿⣟⠛⠃⠀⣿⡟⣿⣿⣿⠸⣿⣇⠀⣀⣄⠀⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠃⠀⠙⠿⠿⠿⠃⠐⠿⠿⠿⠦⠘⠿⠿⠿⠿⠈⠿⠃⠈⠻⠟⠀⠙⠻⠿⠿⠟⠐⠿⠿⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⣿⣿⣷⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡱⠆⠛⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁⠀⠀⠀⠀⠸⠿⠿⠿⠿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠂⠀⠀⠀⠀⠀⠀⠀⡰⢭⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⣠⡀⣀⡀⣚⠲⠶⠆
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠓⠠⡇⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠛⠃⠛⠃⠿⠇
⠀⠀⠀⠀⠀⠀⢸⠃⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⡤⠃⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠰⠷⠰⣷⢠⣶
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠤⣔⠒⡋⠁⠀⠀⠀⠀⠀⠼⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠸⠷⢰⡶⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢤⢠⣚⠣⣄⡉⠒⣤⠝⠀⠀⠀⠀⠀⠀⣠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠏⠾⡇⢶⡆⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠇⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠓⠛⠛⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⠓⠛⠛⡛⣄
⠀⢠⡞⠀⠀⠀⠀⠀⡀⠀⠉⠒⠠⠄⠀⠀⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⡀⠀⡙⠒⠠⠄⠀⠀⠉⠀⠀⠀⣡
⠀⣿⡃⠀⠀⠀⠀⢀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⠀⢸⡇⠀⣿⡇⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⣀⠀⢰
⢀⡿⢡⣤⡄⠀⠀⢀⡀⠉⠙⠱⣦⣀⠀⠀⠀⠀⠀⠀⠈⠉⢰⣇⠘⡇⠀⡿⢡⣤⡄⠀⠀⢀⡀⠉⠛⠰⣦⣀⠀⠀⠀⠀⠀⠀⠉⠉⢰⣇⠘
⠀⠀⠉⡉⠁⠚⠣⢤⣷⡄⠀⡀⠈⢻⣷⢦⡀⠀⠀⢀⠀⣄⢰⣿⡀⠀⠀⠀⢉⡉⠁⠚⠣⢤⣿⡀⠀⢀⠈⢻⣿⣦⡀⠀⠀⢀⠀⣄⢰⣿⡀
⠀⠀⠀⠈⠒⠀⠀⠀⡟⠣⠤⠀⠀⠀⠛⠀⠀⠀⠀⠠⣤⣤⣴⡌⠧⠀⠀⠁⠀⠈⠂⠀⠀⠀⡟⠣⠤⠀⠀⠀⠛⠀⠀⠀⠀⠤⣬⣤⣴⡌⠧
⠀⠀⠚⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠿⠋⠀⠀⠀⠀⠚⠒⠚⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠿⠋
⠀⠀⠀⢀⡄⣀⠔⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⠔⣨
⠀⠀⡰⠟⠛⠧⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠟⠛⠇⠼⠃
⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠐⠠⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⢀⠀⠀⠀⠀⠀⢀⡴⠁⡀⠀⠀⠀⠀⠀⠢⣆⢀⡄⠀⢀⣀⠘⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⡴⠁⡀⠀⠀⠀⠀⠀⠰⡆⢀⡄⠀⢀⣀⠘
⠀⠀⠂⠀⢠⡶⠒⠛⠃⠀⢀⠀⠀⠀⠀⠀⠄⣿⢸⡗⢀⡌⠀⠉⠀⠀⠀⠀⠀⠀⢠⣶⠖⠛⠃⠀⢀⠀⠀⠀⠀⠀⡄⣷⢸⡇⢀⡮⠈⠁
⠀⢀⠴⣾⠟⠀⠀⠀⣠⣴⣅⣸⠶⡍⠉⠁⠀⠿⠘⠁⣼⡧⠀⣀⢀⠀⠀⢀⡴⣾⠟⠀⠀⠀⣠⣴⣅⣸⠶⠈⠉⠁⠀⠿⠘⠁⣼⡦⠀⡀⢀
⠀⠀⠀⠉⠀⠈⠁⣠⣿⡿⢻⠁⠀⠐⠀⠀⠂⠀⠀⢠⡿⣣⣤⡤⠤⠀⠀⠀⠀⠋⠀⠈⠁⣀⣿⡿⢻⠁⠀⠐⠀⠀⠀⠀⠀⢠⡟⣣⣤⡤⠤
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠁⠃⠐⠀⠉⠀⠀⠀⠈⠘⠿⠷⠶⠤⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠁⠲⠐⠂⠈⠀⠀⠀⠈⠘⠿⠷⠶⠤
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⡐⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠠⡑⢄⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⣿⠀⠀⣄⠀⠀⢰⣿⣧⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠚⠛⠋⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣶⡄⠀⠀⠉⠀⠀⢀⣠⠴⠶⠚⠛⠛⠛⠉⠛⠛⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⣀⠀⠀⠀⡄⠀⠀⠀⢣⣤⣶⣄⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠘⣷⣄⢸⣿⡇⢀⡞⠀⠀⠀⠀⠈⣿⣻⣛⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⡠⠤⡿⢿⡀⠀⠀⠀⠈⣮⠺⠋⠙⣿⠀⠀⠀⠀⠀⠀⣹⠈⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠆⠀⠀⢳⠀⠀⠀⠀⢸⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⡇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢸⡁⠀⠀⠀⣇⠀⠀⠀⠀⣰⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡀⢁⠀⡇⠀⠀⢠⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠻⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡷⢷⡟⠁⠀⠀⠀⠙⢶⣤⣤⣖⣸⡇⠀⠀⠀⠀⢻⠟⠲⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣧⠀⠀⠀⠀⠀⢸⠟⠀⠹⣯⠀⠀⠀⠀⠀⠘⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣲
⠀⠠⠤⠠⣤⣤⣬⣤⣤⠤⠤⢤⣤⣬⡶⠶⣿⡦⠒⠀⠀⣤⣬⡤⠤⢨⣼⡤⠤⠤⠤⠤⣷⡦⣤⣤⣤⣄⣤⣀⣐⣀⣀⣀⣤⣿⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣴⣿⡏⠀⠀⠀⠙⣿⣿⣶⣿⣿⣤⡄⠀⠀⠘⣿⣦⣼⣿⣦⡍⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠆⠀⠀⠂⠂⠀⠂⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠐⠀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⠲⠦⢤⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣀⣀⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠀⠀⠀⢠⣶⡄⠀⠀⡉⠳⣄
⠀⠀⠀⠀⡼⠁⠀⢀⣴⡎⠁⠛⠋⠈⢹⣦⡀⠀⠹⡄⠀⠀⠀⠀⣰⠋⠀⣠⣀⠀⠀⠀⠈⠁⢰⣶⡄⠀⠘⣆
⠀⠀⠀⢰⠃⠀⢀⠏⠉⠁⠀⠀⠀⠀⠈⠉⠱⡀⠀⢹⠀⠀⠀⢀⡏⠀⠀⠛⠋⠀⠰⣿⡦⠀⠀⠉⣀⠀⠀⠸⡆
⠀⠀⠀⢸⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⢸⠀⠀⠀⢸⡇⠀⠸⣷⠄⠀⠀⢁⣀⠀⠐⠸⠿⠃⠀⠀⡇
⠀⠀⠀⠸⡆⠀⠈⢇⣀⡀⠀⠀⠀⠀⣀⣀⡸⠀⠀⡼⠀⠀⠀⠀⣇⠀⠀⣤⣄⠀⠀⠸⠿⠃⠀⢀⣀⠀⠀⢸⠃
⠀⠀⠀⠀⠹⣄⠀⠈⠹⢇⣀⣴⣦⣀⠽⠋⠀⠀⡼⠁⠀⠀⠀⠀⠘⢆⠀⠉⠉⠀⢀⣀⠀⠀⠀⠻⡿⠂⣠⠋
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠁⠈⠀⠀⣀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠻⠿⠂⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠛⠉

⠀⠀⠀⠀⢀⣀⣀⣀⣠⣒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣭⣭⣭⡦
⠀⠀⠀⠀⢰⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣶⣖⢒⡇
⠀⠀⠀⠀⢸⠀⣴⡜⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠿⠯⢼
⠀⠀⠀⠀⠘⠒⠒⠂⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂


⠀⠀⠀⠀⠀⣀⣀⣀⣖⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣄⢠
⠀⠀⠀⠀⢰⠁⠀⠨⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠸⠘⠄
⠀⠀⠀⠀⢇⠀⠀⠇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡹⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⢹⠓⡆
⠀⠀⠀⠀⠀⠁⠒⡖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣸⠋⠁
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠂


⠀⠀⠀⠀⠀⣀⢠⡄⣀
⠀⠀⠀⠀⣰⣁⣰⣀⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒⠄
⠀⠀⠀⠀⢸⠀⠙⠀⠀⡇⠀⠀⠀⠀⠀⠀⢫⠱⠋⠉⠉⠉⠉⠙⡗⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠘⡀⡄⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡷⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃
⠀⠀⠀⠀⠀⣇⡇⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠺⡿⠿⠿⡿⠂⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣦⣄⣀⣀⣤⣾⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠛⠛⠿⣿⣿⡟⠉⠙⣿⣿⠿⠟⠛⠛⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⣿⣆⠈⠻⣧⣤⣴⡿⠁⢀⣾⡇⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠘⣿⣦⠀⣿⣿⣿⡇⢠⣾⠟⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣿⣿⣿⣧⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⢀⣀⣴⣿⡿⠟⠻⣿⣷⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠒⠈⠉⠉⠁⠒⢲⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢒⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡼⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠜⢇⡀⠀⠀⠀⣦⠰⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⢀⣀⣀⠠⠤⢄⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⠀⠀⠀⠀⠀⠈⠑⣯⠤⣃⠀⠀⠀⠀⠀⠀⡨⠛⠲⠖⣒⠹⠢⣀⡠⠂⡂⢸⢘
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠾⠉⣱⢊⠯⢭⡁⠲⡟⠀⢹⣖⡠⠄⢀⣀⠤⢞⢢⠀⠀⠀⠀⠀⠀⡤⠐⠙⠛⢿⡖⢄⡀
⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⢋⠼⣮⡉⠂⠀⠀⢱⠀⠀⢡⠈⠓⢦⢄⠀⠀⢏⣢⣀⣀⠠⠤⠊⠀⠀⠀⠀⡰⠁⠀⠈⠑⡄
⠀⠀⠀⠀⠀⢰⠁⢸⠀⠀⢸⢀⡝⢿⡄⠀⠀⢸⠀⠀⠈⡆⠀⠈⠶⢄⢘⡀⠀⠁⠹⡀⠀⠀⠀⠀⣠⠞⢀⡤⠶⠛⠋⡁
⠀⠀⠀⠀⠀⠰⣀⣾⠀⠀⡜⠋⠀⠈⠙⡄⠀⠀⡆⠀⡀⡇⠀⠀⡀⠀⠉⡇⠀⠀⠀⠑⠤⠤⠔⠊⠀⠀⠉⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⢰⡀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠱⠀⣧⠃⠀⠀⡇⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⡆⠀⠀⠀⠀⠈⡀⠀⠀⢣⡟⠀⠀⢀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡀⠀⡸⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⡷⡠⠃⠀⠀⠀⠀⠀⠀⠉⠗⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣤⠴⠂⠀⠀⠀⠀⡰⠁
⠀⠀⠀⢠⡄⣀⠼⣦⠀⢴⠗⠉⠒⠒⠠⠤⠤⢼⣤⡠⠤⠇⣀⠀⣀⡀⠤⠐⠒⠊⠉⠁⠀⠀⠀⠀⣀⠠⠞
⠀⠀⠈⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣰⣞⠁⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣄⢠⣾⣶⡄⢀⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠶⠾⣟⡛⣿⣿⣷⣿⣿⣿⣾⣿⣿⣷⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⠡⠀⠠⢴⡾⢶⣿⣿⣿⠛⠡⠤⢤⣙⢿⣿⣿⣿⡆⣿⣿⠑⢦
⠀⠀⠀⠀⠀⠀⠠⠦⡌⡀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠒⠉⢀⡚⠒⠛⠳⢝⢿⣿⠰⠻⣡⡀⣘⡇
⠀⠀⠀⠀⠀⣰⠀⠘⣇⠹⣿⢿⢷⣶⣄⡀⢀⠀⠀⣰⡇⠰⠂⠈⠙⢦⣄⣀⣐⣄⣄⠀⢣⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠙⢷⣤⣌⣳⣶⣤⠦⣉⠻⣿⣮⡟⠛⠟⠀⠀⠀⠀⢶⣄⣬⠉⠉⣿⣿⡄⠞⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠢⠌⠳⣦⣴⠾⢃⡀⠀⠀⠀⠀⠛⠯⠀⡀⢀⣿⣿⣧⠈⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⡇⣠⣀⠀⠀⠀⠀⠁⠀⢤⡶⠟⠛⠶⠀⠀⠀⠤⠶⠾⠋⡼⢻⣿⣿⠀⣿⣿⡀⣧⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⡞⠁⣼⢿⡏⢠⡘⠿⡿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡾⢳⡄⠀⠀⠀⠀⢠⠞⣷⣦⡀⠀⠀⠀⠀⠀⢡⡌⢻⣁⣾⠧⣄⣙⠳⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠿⣧⠀⠀⠀⠀⠀⢤⠿⠛⠁⠀⠀⠀⠀⠀⢲⡄⢸⣿⠏⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⡁⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠀⠙⠂⠉⠀⠁⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠒⢫⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠉⠠⣴⠶⠶⠦⠤⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠸⣦⣀⣠⣾⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⠛⠛⠁⠀⠀⠀⣴⣊⠉⠁⠀⠀⠀⣀⡨⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣽⠀⠉⠉⠉⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠾⣅⢘⠀⠀⠀⠀⠀⢀⡀⣀⠜⠚⢻⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠈⢿⡅⣀⣙⠀⠏⢉⡽⢁⠄⣠⠞⠉⢈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢩⡆⢀⣒⠚⠇⢹⣿⡗⠀⠉⢚⣿⠋⣠⠔⣡⠾⡄⠀⢀⡴⠞⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣠⡟⠀⠀⠈⠙⣿⣾⣿⣿⣧⠰⢻⣷⡞⣡⠞⢁⣴⡷⠖⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⢠⡟⢰⡟⠀⠀⠀⠀⠀⢈⣿⣿⣋⠁⢀⠈⠹⣿⢧⠾⠋⣡⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣦⡟⠠⣾⣃⠀⠀⠀⠀⠀⠘⡿⠿⠟⠃⠘⠳⠟⠛⠃⢰⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⠏⠀⠀⣈⣛⡛⣦⠀⠀⠀⠐⣿⣿⣽⣧⣿⣴⣷⣿⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠈⣍⡉⠙⢧⠀⠀⠀⢻⣿⣄⣤⣤⣤⡶⠟
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⣄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣰⠟⠛⠿⢃⣠⠟
⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⣰⡟⠀⠀⠚⠋⠁
⠀⠀⢀⣀⣿⠃⠀⠀⣀⣤⡾⠋
⠀⠀⠛⣩⣿⣄⠀⠀⠈⣿
⠀⠀⠈⢧⠼⢿⣷⣤⣀⠁⣼⢿
⠀⠀⠀⠀⢶⣼⡟⢳⡇⢲⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠺⠿

⣹⡏⢻⣀⠈⣟⣿⠀⠀⠀⠀⣠⣶⣶⠆⣤⢤⢥⠀⣼⠄⠀⢸⠀⠀⢸⢅⢤⣤⠀⠀⣤⢀⣠⠿⣦⣄⠤⠶⠀⢶⣶⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⢉⣀⣄⣠⣶⡾⠋⠉⣁⠀⠀⠀⡆⠀⢸⢀⣀⢸⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⢻⡄⢀⣽⡀⠀⢠⣾⣿⡄⠀⣿⣿⡿
⠀⠀⢲⣶⡶⠿⠿⢋⡉⣍⣤⠀⠀⢿⠆⠀⠀⠀⠀⣰⣿⣹⡧⠀⠀⠘⣃⣤⣶⡆⢀⣴⣦⣉⠉⣛⠁⠉⣛⣈⠻⣿⡟⠀⢿⣿⡁
⠀⠀⠉⠉⠀⢀⠀⠘⠊⠁⠘⠁⠀⢀⣤⣴⡶⠿⠛⠋⠙⠛⠁⣀⣀⣾⣿⡿⢋⣴⡿⢛⡛⢿⣷⠉⣿⠉⠻⠛⢛⣏⠙⠀⠈⢻⣷
⠀⠀⢀⡀⠔⠿⡗⠀⠀⢠⡼⠃⠀⠀⠉⠀⠀⣤⠀⠀⠀⠀⢈⣾⡻⣶⣄⠀⠸⣏⣇⠘⠃⣸⣿⠃⣿⣀⣀⣀⣈⣟⠀⠀⠀⢸⠟
⠀⠀⠋⠀⠀⠀⢻⣀⡴⠋⠀⠀⢠⣤⣤⠀⠀⣿⠀⠀⠀⣀⣾⣿⣿⣮⠋⠀⠀⠙⢾⣿⡿⠿⠋⠀⠉⡙⠛⠉⠉⣠⣴⣤⣤⣤⣤
⠀⠀⠀⠀⠀⢀⠪⠟⠀⠀⢠⣜⣿⢿⡄⠀⠀⣿⠀⢀⣞⣭⡾⣿⠋⣴⡶⢶⣄⠀⠀⠀⢀⣠⡴⢖⣻⡽⠂⠀⠀⣿⡿⢟⣿⣿⣿
⠸⣿⡆⠤⡀⢯⣗⠀⠀⢰⣬⣿⣝⣷⣿⠀⠀⠉⣤⡾⡽⠿⡷⠃⢸⣿⠇⣼⣿⣦⣖⣻⠽⠖⠛⠉⠁⣀⣀⣠⠄⠘⣿⣿⣿⣼⣿
⠀⠸⣕⣂⠁⠀⢉⡀⢀⢀⡛⢛⣛⣛⠛⠂⢀⠀⠀⠐⢢⣄⠀⠀⠀⢬⣦⣻⠟⠁⢉⣠⣤⡶⠖⣋⡙⢿⣿⠏⠀⢠⢯⣽⣿⡿⠛
⠀⠀⠀⠀⠋⠓⠎⠳⠙⠎⠳⠈⠠⠬⣶⣴⣿⣇⣀⠀⠀⠰⠛⠁⠀⠀⠀⣤⠀⠀⢙⡟⠁⠀⠸⢯⠟⣠⡟⠀⠐⠿⠿⠿⠿⠟⣀
⠀⠲⠂⠀⡀⠒⢲⢶⡶⣶⢆⡀⢠⣶⣿⣿⣿⡿⠋⠀⠠⡋⠻⣆⡠⠐⣦⠀⢀⣀⣼⣷⡞⠋⣀⣴⣾⠏⠀⢻⣧⡤⣶⣲⣦⣀⣿
⠀⠀⢀⡄⠀⣀⣤⣼⡟⠁⠉⠁⢰⠏⠹⠿⠩⣤⠆⠀⣶⣳⡖⡛⣧⡼⣁⣾⡿⢛⣿⢿⡟⠛⣿⡿⠃⠀⣼⣿⣿⢦⣴⡄⣮⣿⡄
⠀⠰⠿⠚⠋⢉⠀⠚⠁⡀⠀⢤⠿⠄⠀⠀⠀⢰⠀⠀⡌⠉⣹⡟⠛⣷⠺⠿⠿⠟⠁⢸⣧⠀⣾⠀⢀⣤⣙⣿⣵⣾⣤⣦⣽⣽⣷
⢠⣤⣤⣤⣤⣄⠀⠀⢤⣿⡆⠈⠀⠀⡴⢢⡄⠘⡄⠀⠙⠋⠁⠘⠆⠋⠀⠀⠀⠰⡧⠈⢿⠀⢠⣼⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢠⠋⢧⠀⠀⢀⣠⣶⠉⠁⠀⠀⠀⢳⡄⠀⠊⠛⠀⣶⠀⣤⣤⠀⢀⠀⣀⢠⣴⡄⢠⣤⣴⠆⠙⠿⢻⣿⣾⢿⣿⣿⣿⣿⣿⣿
⢀⠇⠀⠈⢧⠀⢸⣷⣿⡄⢼⠃⢀⠀⠀⢹⡄⣾⠋⠀⣿⠀⣯⡄⠀⣾⣼⠉⡟⠀⠁⣿⣀⣤⠀⣤⠄⠘⠉⡿⠻⡿⠉⡿⣿⣿⡽
⣾⠀⠘⠀⢸⣷⢸⣿⣿⡇⠀⠀⠻⣧⣠⡼⠚⣯⣠⠀⣿⠀⣯⣀⠀⣿⠻⠀⢻⣤⠀⣿⣍⢁⡀⣿⠀⠀⠀⠋⠀⠁⠰⠃⢻⠏
⠀⢀⣠⡀⠀⠀⠈⠛⠿⡇⠀⠀⢀⣠⣤⣄⣀⣈⣀⣀⣉⣀⠈⠉⠀⠁⠀⠀⠀⠁⢀⣌⠉⠛⠁⢸⡆⠀⠀⠀⠀⠀⠀⠐⣋⣀⣠
⢰⣦⢿⣦⠐⡆⠀⠀⠀⠀⢀⣀⡌⣡⠖⢂⣤⣍⠉⠉⠉⠉⣍⠛⠛⠛⠛⣿⡟⠛⠛⠋⠘⠿⠀⣠⣤⣶⣞⣛⣀⣤⣤⡶⣼⣿⣯
⢱⣿⡧⢸⣗⠇⠀⢀⠀⠀⣼⢰⠃⣹⣂⣿⣯⠁⠀⠀⠀⣰⣿⣦⠀⠀⠈⣿⣷⠀⠀⣰⣿⠆⢀⠻⣿⡿⠙⢿⣽⠉⣠⣤⣮⣁⡁
⠀⠙⠚⠛⢋⢠⡶⠃⢀⡸⣿⢁⣼⣿⣽⡶⠀⢰⡆⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⠂⢸⣿⡟⠦⣼⣁⣾⣆⠁⡐⠀⣾⣿⣿⣿⣿⡿
⠀⢀⣠⡄⠘⢋⣠⣴⣿⣤⠀⠀⣿⠟⠛⣠⣤⠤⡑⠀⠀⠉⠛⢁⣀⡀⠀⠺⣿⡆⠸⣿⠃⢿⣾⣿⣿⣧⡄⠀⠘⠿⣿⣿⡿⠟⠃
⣀⣾⣿⠇⠀⠛⢿⣿⣿⡿⠀⠀⠀⣀⢷⡝⠻⣱⣺⡄⠀⠀⢸⣿⣿⣿⠆⠀⢀⣤⡾⠛⢶⣄⠘⠿⠛⠋⠁⠀⠀⢀⡀⠀⠐⠀⣤
⠙⣛⠀⠀⢀⡄⠀⠈⠛⠇⠀⠀⢠⣠⣾⣳⣾⣿⣿⣵⡀⠀⠈⠻⠿⠟⠀⠀⣾⣿⣶⣶⣶⣿⡇⠀⠀⢰⣾⣇⣀⠻⣿⣦⣬⣄⡨
⢹⣿⠃⢔⣣⠀⠀⡶⣦⠀⠀⠀⠀⢹⣿⡛⠛⣻⣿⠈⠀⠀⢰⣆⠸⡾⠀⠀⠹⢿⣿⣿⣿⡟⠁⠀⠀⢺⣿⠿⣿⣷⡜⢿⣿⣿⣿
⢸⣿⠀⠀⠀⢰⣾⣇⠻⣶⠀⠀⠀⠀⠹⢿⡿⠯⠋⠀⠀⠀⣠⣇⢠⣄⠀⠀⠀⣠⣀⣉⣤⣶⣤⠀⠀⠀⠀⠄⢸⣯⣿⡉⢻⣿⣿
⢸⣿⠆⠀⠀⠈⠉⣯⣿⣏⡀⠀⣠⣶⠟⠻⣦⡀⠀⠀⠀⣸⣇⣽⣇⣨⣇⠀⠀⠉⠉⠉⠁⢼⡏⠀⡚⣿⣷⣴⣾⣿⠟⢸⣿⣿⣿
⠈⠋⠀⠀⠀⠀⣠⣤⣶⠘⣿⡀⣿⠈⣇⠀⢻⣷⠀⠰⡞⠁⣹⡁⠸⠿⠈⣷⢶⡦⠀⠀⠰⣿⣿⣆⡤⠛⢻⣾⣿⣿⠬⣿⣿⣿⣿
⢠⣤⠀⠃⢶⣿⣿⣿⣿⠗⠘⣷⡟⢿⣤⣤⡾⠋⢀⠀⠀⠀⢻⠋⠀⠀⣀⣤⣴⡾⠳⣦⣤⣽⡛⠯⣠⣭⣿⣿⣿⣿⡧⣿⣿⣿⣿
⣸⠿⡄⠀⢎⠛⠋⠉⠀⠀⠀⠈⢿⡄⠀⠀⠀⠞⢻⣄⠀⣷⣿⣀⣀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣣⣾⣿⣿⣾⣿⣔⣧⣿⣿⣿⣿⣿
⠈⠀⠁⠀⠈⠄⢀⡤⠔⣂⣠⣴⠾⢛⣠⣤⣤⣄⡀⠙⣷⣿⡿⣛⣽⣧⣤⡿⢿⡿⠿⠿⠿⢧⠙⠛⣿⣿⣿⣿⡿⢿⢻⣿⣿⣿⣿
⠀⠀⠰⠂⠀⠘⠾⠾⠟⢋⣩⣤⠀⢿⣿⣿⣿⣩⡿⢠⣾⣿⣿⣿⣿⣿⣿⣿⣶⡀⣠⡶⠶⢦⡝⢒⣜⣻⣟⣯⣷⣿⣿⣿⣿⣿⣿
⢠⠶⣶⠵⡆⠀⢀⡴⠞⠛⠋⠁⢀⣄⣉⢹⡟⣉⢀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⢇⡞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣷⠛⢶⣇⣠⣶⣷⣤⣄⠠⢴⣾⣿⣿⣾⣿⣿⠀⢻⣿⣏⢉⠁⣿⣿⡿⠿⠟⠋⢀⢻⣿⣿⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿