Little baby captain Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⡀⣀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠏⠀⢸⣾⡏⢻⠙⡟⢻⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⢀⣤⣀⡀⣀⣀⣀⡀⢀⣀⠀⢠⣤⠀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠃⢸⣿⡇⢸⣿⠋⠁⣿⣿⣿⡇⣾⣿⠀⣶⣶⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⣼⡷⣿⢸⣿⡇⠀⠉⣿⡏⢁⣿⢾⡇⣿⣿⡇⣿⣿⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠉⠈⠉⠁⠀⠀⠉⠁⠈⠉⠈⠁⠈⠉⠁⠉⠁⠀⠁⠀⠚⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠘⠉⠀⠐⠈⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⣀⡠⠤⣤⣤⣤⣄⣀⣀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣠⣾⣿⣀⢂⣿⣿⣿⠿⠿⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢸⣿⣟⣩⣤⠶⠖⠂⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⡀⠀⠀⠀⠀⠀⠀⠃⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠁⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⣀⣀⣀⣀⣤⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠙⣿⣿⣿⣿⣿⣆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡘⢿⡿⠿⠛⠛⢂⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠃⠰⢀⣤⣶⣶⢈⠄⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⣰⣿⣦⠻⣿⡟⣼⡇⠀⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣬⣍⠰⠀⠻⠿⠿⣷⠙⡃⠿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢸⣿⣿⣿⠷⡘⠟⢠⣏⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠈⠛⣋⣵⣾⡏⣾⣦⢻⡇⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⣃⣌⠀⠛⢿⣿⢡⣿⣿⣷⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣤⣾⣿⣿⣷⣤⣀⠰⠆⠉⠁⣀⣨

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣒⠒⠊⠉⠑⠒⠺⠦⠇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⡡⠖⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⠎⠀⠀⠀⠀⣡⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⡀⡜⠀⠀⢴⣢⡤⠛⠒⠲⡀⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠸⡁⠙⠿⡀⠀⠀⣘⠓⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠁⠀⠈⠉⠉⠹⠒⠋⠉⠉⠀⢀⠤⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⣒⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠘⢳⠌⠱⡀⣷⣄⡀⠀⠉⠐⠒⠂⠒⠈⠑⠔⠃⢀⣀⢄⣀⠙⠚⢓⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⣄⠐⠞⠻⠿⣴⣶⡶⠶⠴⠖⣒⣊⣉⠁⠀⠀⠀⠈⠉⠉⠉⠒⠢⢤⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣠⠔⠾⠤⢤⣀⡀⠀⠈⢦⣙⡐⠿⣷⠲⡀⠈⢫⠉⠉⠒⠒⠤⢄⡀⠀⠀⠀⠈⠙⠓⠦⣄⡀
⠀⢔⠋⠓⠜⠁⠀⠀⡇⠀⠀⠀⠀⠀⠉⠑⠲⢤⣀⠁⠘⡥⠂⠠⠤⠞⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⡆⠀⠀⠀⠙⡆
⠀⠀⠑⢄⣠⠀⠀⠤⣇⠀⠀⠀⠀⠀⠀⠀⢠⠤⢨⠓⣺⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠖⠒⠒⠂⠘⠷⣄⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⣀⠤⠀⠤⠤⡕⠒⡳⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢧⡀⠀⠀⠀⠉⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠄⢲⠀⠀⢘⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠂⠈⠉⠉⠉⠉⠉⠉⠀⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⡠⠊⠡⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⢠⠊⠀⠀⠀⠂⢄⣀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⠂⠈⠉⠀⠀⣀⣈⣑⠄⢠⢀⠔⠂⠐⠤⢀⠀⡀
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⡀⠤⠔⠒⠉⠁⠀⠀⠀⠀⠔⢩⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠤⠒⠀⠒⢄
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⡀⠄⠂⠉⠀⠀⠀⠉⠊⠀⠙⠀⠐⠂⠀⡂⠠⣤⠀⣴⠀⠀⠀⠣⡀⠀⠀⠀⠈⠀⠈⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢀⠠⠚⢄⣤⠀⣠⡀⠀⠀⡀⠀⠀⠀⠀⠰⠂⣜⠁⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⢀⠀⣔⠂⠡
⠇⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡴⡏⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⢨⡗⠀⠀⠀⠐⠀⠁⡤⢤⠀⠀⠀⠂⠀⠁⠀⠀⠰⠀⠀⠀⠁
⠰⡄⠀⠀⠀⠀⠀⠀⡀⡰⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠖⠀⠊⡑⠀⠐⠀⠀⠀⠀⢄⠀⠀⡀⢠
⠀⠡⠀⠀⠀⠀⠀⠈⠃⡴⢊⠣⠀⠀⠀⠀⠐⠟⠀⠀⠄⠀⠀⠀⠘⠀⠀⠀⠜⢣⠠⠈⠂⠀⠀⢀⣠⠆⠺⠈⠂⢀⡄
⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⢸⠊⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠁⢨⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠈⠉⠁⠁⢄⠀⠐⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠒⠠⠀⡀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠇⠀⠀⠀⡀⠀⣘⠈⠀⢘⡀⠀⠀⠀⡠⠋⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠒⠂⠀⠀⠉⣥⠤⠞⠀⠀⠀⠀⠁⡰⠈⠁⠉⠯⠰⠄⠐⠈⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠉⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠃⠀⡀⠀⠐⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠠⠖⠈⡀⠠⡦⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠌⠀⠸⡄⠁⠀⠀⠀⠸⣀⣀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⣀⡀⠶⣔⡈⠀⠀⣀⠠⡐⠓⠂⠐⢤⠚⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠱⢤⡀⠀⠰⠀⠈⠉⢻⡝⢱⢂⡉⢩⡶⢸⠄⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠁⠄⠠⠤⠤⣼⡇⠸⠦⠤⣴⣧⠞⠛⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠀⠀⠀⢀⡴⡘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠎⠀⠠⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢃⠀⠈⠐⠀⠄⢀⡀⠀⠀⢀⡌⠀⠀⠀⣀⡀⠄⠂⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠠⠄⠀⠤⠤⠋⠉⠉⠁⠤⡀⠀⠠⠤⠐⠊⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠀⠀⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠾⠿⠛⠛⠿⠶⠶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠹⣟⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⠷⣬⣙⠛⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⠒⢆⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠶⠶⠤⠤⠄⠀⠀⠀⠀⠈⢳⡄⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠛⠛⠷⣆⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣧⣾⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⢰⡟⢹⣯⡿⣆⠀⠀⠀⠀⣰⣿⠛⣛⢻⣦⠀⠀⠀⠀⠀⠀⢠⠾⢋⣥⡤⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢷⣌⣋⣼⣧⡤⠀⠀⠀⠉⣯⡘⠿⢃⡿⠀⠀⠀⠀⠀⠀⢤⡐⢻⠇⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠉⠉⢽⣇⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⣀⡀⠙⠳⠶⠞⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠉⠉⠛⠳⠶⢶⣦⣤⡶⠶⠛⠉⠃⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⡀⠀⠀⠀⢀⣈⣉⣀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣻⣶⣶⣄⡉⠉⢁⣀⣤⣴⡶⠟⢿⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠉⠇⠘⢿⣟⣛⣛⣉⣵⠟⠁⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⠶⠾⢷⡆⠀⠀⠉⠙⠉⠉⠀⠀⢰⡄⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣼⠏⠀⠙⠛⢷⣄⠀⠀⠀⠀⣀⣠⣀⣼⡟⠋⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢰⡏⠠⣄⣙⢲⡶⠟⠀⠀⠀⣾⣋⣉⠉⠙⣧⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣧⣐⣮⣭⡿⠃⠀⢀⡴⠶⠟⠛⠁⠀⠀⢹⡇⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣠⣤⠿⢿⡅⠀⠀⠀⠘⠷⢶⣟⣀⣀⠀⠀⣸⣧⣀⣴⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠈⢻⡇⠀⠀⢸⡇⠀⠀⠀⢀⣀⣀⣉⣿⠶⠶⠶⠛⠻⢯⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢶⡀⠀⢻⠀⠀⠈⣿⡀⢀⡾⠋⠉⠉⠙⢿⣄⠀⠀⠀⠀⠀⠙⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣷⠀⠀⠀⠀⠀⠘⢷⡿⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠙⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣀⣠⣴⠞⠛⠶⢿⡄⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⢀⣠⣴⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠘⢷⣄⠀⠀⢀⣤⣿⣥⣶⡶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠁


⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣯⡖⢲⣯⣍⣉⣭⣍⣭⣉⣭⣩⣍⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠤⠤⠤⢀⢈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠶⠛⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⣀⠔⠊⠉⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⠎⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣀⠀⢸⠀⠀⠀⠰⣿⣡⡤⠊⠉⠁⠉⠢⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢰⠋⠉⢻⣼⡀⠀⠀⠀⠈⣽⢰⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠣⣠⠀⠀⠙⢦⣀⣀⡤⢿⠀⢀⡀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⣰⠖⠄⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠒⠒⠚⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢆⡰⠦⣄⠈⢳⣄⠀⠀⠀⠑⠢⢤⣀⣀⠀⠀⢀⡀⠠⢔⠊⢙⡆⠀⠀⠀⠀⠀⠀⠶⣐⣲⣤⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠇⠬⢯⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⢀⠀⠄⠒⠦⣤⣀⣀⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⢄⠀⠀⠒⠉⢉⠽⣋⣰⠶⠀⠀⠀⠀⠀⠒⢒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠐⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠑⡄⢀⣴⡤⣭⣍⡉⠁⠑⢖⠐⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⢦⣄⡀
⠀⠀⡀⠀⠀⢀⡤⠖⠒⠒⣶⠂⠀⠀⠈⠁⠒⠂⠤⣀⡀⠀⠀⠑⠢⢼⡀⢉⣳⡧⠂⠱⠂⠀⠀⢳⠀⠀⠀⠀⠀⠀⠁⠒⠠⢀⣀⠀⠀⠀⠀⠈⠀⠀⢨⠉⠳⢦⡀
⣖⠋⠉⠙⡴⠃⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⠀⠀⠈⢳⠶⠒⠢⠤⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⣄⠀⠀⠀⠂⠀⠀⠀⠀⠘
⠀⠑⡀⠀⠀⡀⠀⢀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠦⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣶⣄
⠀⠀⠈⠓⠔⠁⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢈⠑⠣⡄⠸⠃⠀⠀⠠⠤⠄⠤⠔⠒⠒⠛⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⡠⠴⠒⠒⠒⠲⢤⡌⠉⢚⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠴⡀⠀⠀⠀⠀⠀⠀⠓⠊⠉⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⠀⠀⠀⠀⠀⡀⠀⠀⠈⡄⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠈⠙⡆⠀⠀⢠⣵⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠒⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡤⠠⠀⠆⢀⠀⠂⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡠⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠐⠂⣂⠀⠀⠀⠀⠀⠀⠐⡢
⡄⠀⠀⠀⠀⠀⠀⠂⣰⣿⣷⣰⣿⣯⣿⣿⡆⢡⣶⣶⡀⠘⠀⣠⣼⣦⠀⠀⢀⣤⡀⠀⠀⠀⣀⣀⡂⣰⣦⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠐⠀⠀⠀⠠⡤⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡇⠀⢰⡏⣿⢸⡇⠀⣾⣿⣿⣆⣴⣿⣿⡍⠛⠻⣿⣿⠀⠀⠀⠄⠀⠠
⠀⠀⠀⣴⢾⡇⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⢸⡇⠆⣸⣷⣿⣼⠃⠉⣿⢸⡏⣿⣿⣿⣿⡇⠀⡠⡼⣿⡇⡀⢲⣦⡂
⠀⠀⣾⠃⢈⢻⣏⠀⣿⠙⠍⢉⣀⣴⣿⣳⣾⣽⣯⡟⠁⠀⣠⣿⣿⣏⡀⠀⡹⣾⣷⣿⣷⢶⣿⣧⣬⣬⣤⣿⣦⣠⡿⠉⢻⣄
⠀⣸⣧⣤⠶⠟⢙⣿⣇⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁⣟⢙⣿⣿⣿⠛⣦⢡⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⣿⣿⡟⠳⢦⣤⣿⡀
⠀⢻⡆⠀⠁⠀⠀⣼⣟⣋⣉⣛⣛⣯⣿⡿⠿⠛⠛⠛⢳⣿⣿⢟⠙⢿⣾⣿⠿⠟⠿⠿⢿⣿⣏⣛⣛⣋⣛⣻⣟⠅⠁⠀⠈⢸⠇
⠀⢈⢿⣄⠠⠐⢸⡏⠎⠋⠉⠉⠉⠐⢿⡟⠀⠀⠀⡀⠀⣿⠁⠁⠄⠠⢹⡟⠈⠒⠂⠀⠘⣿⠇⠉⢉⡉⢉⠉⢻⡄⠀⠌⣴⠏⠄
⠀⠀⠢⠟⠷⢿⣼⣧⠐⢂⠀⠀⠀⠠⣤⢤⡆⠀⠀⢀⣠⡿⠠⠀⠀⢠⡌⢷⣄⠰⠄⠐⣶⣦⠆⠀⠴⠘⡩⠛⣾⣧⠶⠟⠁
⠀⠀⠀⡀⠀⠁⠦⢜⡷⣦⣬⣤⣤⣤⣽⣿⣥⠶⠞⠛⠁⠀⠄⠔⠀⠈⠁⠂⢉⣛⠳⠶⣿⣿⣤⣤⣭⣤⡶⠟⠁⠤⠐⠂
⠀⠀⠀⠀⣠⠐⠃⠀⢀⡌⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣨⣔⣂⢈⣀⠀⠀⠀⠂⠠⠄⡐⠀⠀⢀⣶⠘⠿⠆⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠢⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠄⢐⠠⠄⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⣠⢼⣄⣈⣀⡼⢤⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡱⢤⣀⣀⣔⣡⣤⣶⠧⢴⣦⢤⣑⣄⣀⡤⢦⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⣌⠙⣿⣿⣿⠏⠀⣿⣿⠘⣿⠟⣡⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠦⠈⠠⠙⠛⠛⠶⠾⠿⠷⠒⠛⠠⡅⠴⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣤⠀⠀⣤⣴⠀⢀⣠⡀⠂⢠⠼⠀⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢷⠀⠠⡀⠀⠉⡹⠀⠸⡉⠀⠀⡠⠀⡼⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢸⠂⢀⡈⡁⠛⣁⣀⣀⡙⢀⢈⡀⠀⢇⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠏⡠⠃⠐⠈⠀⠀⠀⠀⠀⠁⠒⠐⢆⠙⡄⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢸⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡇⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢠⠀⠑⢤⡄⢠⠄⢀⣀⣀⣀⣀⠠⡄⢀⢠⠞⠀⣄⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣼⠁⣄⠘⢁⡄⠗⠈⢻⢲⣈⣉⣧⠧⣁⡖⡳⠋⢠⠀⡄⢙⢀⠄⣏⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⠏⢸⡀⠈⠉⠉⠀⡷⢀⠀⡱⠛⣉⡁⣁⠊⢹⡀⢀⠴⡀⠈⠉⠁⠀⡏⠙⢦⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠀⠸⡇⠀⠀⠀⠀⠙⢶⡍⡰⢷⠑⠋⠚⡼⢆⠉⣗⠟⠀⠀⠀⠀⢀⡇⠀⠘⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠈⢧⡀⣷⠀⠀⠀⣖⣒⣚⠀⣛⣃⣬⡤⣵⣘⣛⡁⣱⣒⣲⠀⠀⠀⣼⠁⠀⢰⠇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡣⡀⠀⠉⠛⠷⠤⢤⣤⣤⠴⠶⠛⠋⠁⠀⠀⠙⠻⢦⣅⣀⣀⣀⣀⣴⡯⠴⠞⠋⣠⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠢⢄⡀⡀⠀⠀⠀⠀⢀⣀⣠⠴⠚⡏⡟⠲⠤⣤⣀⣀⣀⡀⠀⢀⡀⣀⡤⠚⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠦⣄⠈⠉⠉⠉⠉⠉⠉⠁⠀⢀⣠⡇⢷⣄⡀⠀⠀⠈⠉⠉⠉⠉⠉⢀⣠⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⠙⠓⠶⠦⠤⠤⠶⠶⠚⠉⠀⣇⢺⡀⠉⠓⠶⠶⡤⠤⠶⠖⠛⠉⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⠀⠀⠀⠀⠀⣀⣠⡴⠚⢻⢸⠙⠲⢤⣀⣀⣃⠀⠀⣀⣠⣴⠿⠴⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠚⢿⡙⠛⠛⠛⠋⠉⠀⠀⢀⣼⢸⣄⠀⠀⠀⠉⠉⠉⠉⢩⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⣀⣀⣠⡴⠖⠋⣸⢸⡈⠓⠦⣤⣀⣤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠚⠉⠉⠉⠛⠋⠉⠁



⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⣶⣶⣶⣶⣦⣤⣀⣠⣶⣾⣿⣿⠿⠿⠿⣿⣿⣿⣿⣧⣀⣀⣤⣤⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⠿⠿⠿⣿⣿⣿⣶⣤⡀
⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⡋⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠆
⠀⠀⠘⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⣉⣤⣤⣶⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣫⣴⡿⠟⠋⠁⣰⣿⣿⠃
⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⡿⠛⠁⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⢠⣿⣿⣇⣤⣴⣶⣶⣿⣿⣷⡖⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⢀⣤⣴⣿⣿⣟⣭⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆
⠀⠈⠋⠁⣻⣿⣿⣩⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧
⠀⠀⢠⡾⣻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦
⠀⠀⣠⣾⠟⠉⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦
⠀⠈⠛⠁⠀⠀⠀⠙⠻⣿⣿⣶⣤⣄⣀⣀⣀⣀⣤⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣄⣀⣀⣀⣀⣤⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⣛⣛⣉⠩⠤⠤⠭⢭⣛⣛⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⣛⡩⠖⠋⠁⠀⢀⣠⣴⣦⣤⡀⠀⠉⠛⠶⣭⣛⠿⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣛⠭⠒⠉⠁⠀⡀⠄⠀⢠⣾⣿⡱⢎⣿⣿⡄⠀⠀⠀⠀⠈⠉⠒⢬⣙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⠞⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⡿⣯⣅⢨⣽⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡹⣷⡄
⠀⠀⠀⠀⠀⢀⣠⣴⣿⠏⠎⠀⠀⠐⠈⢀⡀⠀⠀⠀⠀⠸⣷⣌⡓⢘⣣⣾⡏⠀⠀⠈⠒⢄⢤⡳⣄⠀⠀⢽⡹⣿⣦⣄⡀
⠀⠀⠀⣠⡶⠛⢁⡼⢋⠜⠀⠀⣀⣴⠞⠁⠀⢀⣀⣀⣀⣠⣽⣿⣿⣿⣿⣿⣤⣴⣒⣶⣦⢤⡨⢻⣾⣷⠀⠀⠳⣿⣷⣌⠻⣷⣄
⠀⠀⣴⡿⠿⠿⠿⠖⠣⣀⣰⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠻⠿⠿⠿⣿⣧
⠀⠀⢿⣧⣀⣀⣤⣴⣾⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣟⣿⣟⡿⣿⣿⢿⣿⣿⣶⣆⣠⣿⡿
⠀⠀⠈⠛⠿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⠿⠛⠛⠛⠛⣿⣿⣿⡏⠉⢹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⢬⣽⢿⣿⣿⣿⡿⠿⠿⠿⠋⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡁
⠀⠀⠀⠀⠀⠈⣿⣻⣿⣿⣿⠿⢿⣶⣶⣦⣤⣤⣤⣤⣤⣉⣉⣉⣀⣀⣠⣬⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⠢⣾⠟⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⡇⠀⠀⢀⣿⣟⣻⡿⣿⣿⢛⣿⣿⠁⠀⡈⢿⣿⣿⡋⣿⡿⣿⣟⣻⣿⣷⣶⠿⣿⣿⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⡇⢀⠀⢀⡀⠈⠙⠛⠻⣿⣿⠗⠘⠀⠀⠀⢸⣿⠻⣿⣿⣿⡿⠟⣿⣻⡟⢢⣳⣿⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠈⢁⣰⣿⣇⠠⠀⠀⠀⠀⠐⠒⠛⠋⠁⠀⠀⠀⠀⠀⢹⣿⠢⠉⠙⠻⠟⠚⠣⣄⣀⡀⢝⣿⣿⣇⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡧⣱⢀⡈⠀⠀⠀⠀⠀⠀⣠⠦⠀⠀⠀⠐⢾⣿⡷⣦⡀⠀⠀⠀⠀⠈⢷⡝⣾⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣘⢯⣀⠀⠀⠀⠀⢠⣔⣯⣀⣄⢀⠀⢀⣶⣷⣤⣻⣿⣄⠀⠀⠀⠠⣄⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣟⣿⣷⣄⢄⣰⣟⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣾⠿⢻⣷⣤⡈⣴⣿⣿⣿⢿⡟⠙⣿⠋⡙⣿⠛⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣴⣿⣝⣿⣿⣿⠟⢻⣧⣼⣷⣶⣿⣿⣿⣿⣿⣿⣷⣼⣿⠿⣿⣿⣿⣿⣿⣷⡼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣾⣿⢿⣿⣯⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣺⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢨⢏⣰⡿⠉⢰⣿⠟⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣮⣿⣿⡿⣿⡜⣿⣼⣿⣻⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣷⠇⣠⡟⠀⣿⢃⣿⡿⣿⠸⢻⣿⣿⣿⡇⣿⢿⣿⣷⣿⣧⢹⣿⡸⣿⣿⣧⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⣿⣿⣸⣿⣇⠀⣿⢸⣿⡇⣿⣄⢸⡇⢸⣿⣿⣿⢸⡇⣿⣯⢻⣾⣿⣿⣿⣷⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣿⡇⣿⣿⣿⡇⣿⣿⣼⡇⣸⣿⣿⣟⢸⣷⣿⣿⣧⠹⣿⣿⣫⣶⣝⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⢻⡇⡟⣿⣧⣿⡇⢿⣧⣿⡏⣿⣿⣿⣿⢹⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣿⣾⣿⣿⣧⢸⣿⣿⣧⢸⣿⣿⡇⣾⣿⣿⣟⣼⣿⣿⣻⣿⣿⣿⣿⠏⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠓⠈⠻⢿⣏⣿⢿⣾⣿⣿⣿⡿⣿⣿⡿⠿⠋⠀⠙⠿⣿⣿⣥⣶⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠀⠙⢿⡿⠋⠀⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣍⣽⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣙⡯⣿⣷⠀⢱⠄⢹⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡿⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⠀⠈⠀⠃⠈⢠⣤⡶⢄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⢸⣿⣝⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢠⠇⠉⠻⠇⠀⠀⢀⣀⣿⡡⠂⠀⢓⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣦⣀⣼⣟⢸⣿
⠀⠀⠀⠀⠀⢀⣿⣷⣶⣦⣤⣶⣾⣿⢟⣇⡝⢻⣾⣿⣿⣯⣱⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⢀⣼⣶⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣹⡏⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡋⣡⣾⣿⣟⠛⠛⠓
⠀⠀⠀⠀⠀⠹⠿⠿⠿⠟⠛⠋⣿⣿⡟⣽⣿⣿⣿⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠺⠿⠿⠿⠿⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣟⣹⣿⠥⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⣀⣀⠀⠐⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣿⣿⡟⠛⠛⠿⢷⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⢀⣀⣀⣀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣽⡭⢵⡄⠠⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⠟⠿⣿⣿⣷⣦⡀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣿⢧⣬⠁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⡾⠻⣽⣿⡿⣻⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⡖⢹⣸⣿⢻⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠝⠛⠁⠀⣹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣠⡿⣿⣯⠈⢧⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡿⠀⠀⠀⢀⡿⠫⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁⣙⠀⠻⢿⣷⣾⣇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣟⣓⣒⠪⠭⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⣙⠿⣇⠈⠙⢀⣸⢏⠞⠹⠏
⠀⠀⠀⠀⠀⠀⠀⣼⠃⣿⠀⠙⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠹⣯⢽⣿⠏
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⢤⣄⣀⣠⠴⠖⠛⠛⠉⠉⠙⠛⠒⠲⠤⣀⢀⡤⠖⠛⠛⠓⢦⣀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠙⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⢀⣀⣀⣀⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⡟⠀⠀⣠⠖⠒⠒⠦⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⠁⠀⠈⢹⡄⠀⠀⣇
⠀⠀⠀⠀⠀⠸⡇⠀⠀⢿⡀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣠⡟⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⢳⣄⠀⠈⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⢡⣬⣧⠀⠀⠀⠀⠀⣴⢫⣍⢳⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⢀⣾⣀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠹⣦⡀⠀⠀⠀⠀⣀⡠⠤⠒⠚⠋⠉⠛⠲⢤⣄⡀⠀⠀⠀⢀⡾⠁⠈⠙⠲⣤⡀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⠻⢦⣀⠀⠀⣧⠀⠀⠀⢰⣾⣿⣶⡆⠀⢈⡿⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣰⠋⠛⠳⢾⣄⠀⠀⠀⠙⡿⠛⠀⢀⡾⠤⠶⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠙⠓⠶⠤⠴⠷⠤⠖⠋⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢰⠇⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣾⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣏⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣸⣧⡤⣤⣀⣀⣀⣀⣀⣴
⢻⣦⡀⠀⢀⣀⣤⠶⣿⠟⠉⠀⠀⠀⠀⠀⠈⠉⠓⢦⡀⠀⠀⠀⠀⣠⠖⠛⠉⠁⠀⠀⠀⠈⠙⠻⣦⠀⠀⠉⠉⠉⠁
⠀⠈⠙⠛⠋⠉⠀⢰⠇⠀⠀⠀⠀⡴⠢⡄⢠⠶⢦⡀⠹⣄⠀⠀⣼⠁⢀⡤⢦⠀⣠⠖⢲⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⡟⠀⡾⠛⠢⡄⢧⠀⢹⠘⣆⠀⣷⠀⢹⣤⣼⡇⠀⣾⠀⢸⠀⣏⠀⡼⣠⠔⠛⢳⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢧⣄⣀⡿⠈⢓⣛⣀⣈⠛⠁⠀⠀⣇⢸⡇⠀⠙⠒⠋⠀⠈⠉⠁⢿⣀⣠⡼⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠉⡴⠚⠉⠀⠀⠈⠙⠲⢤⡀⢹⠸⡇⠀⢠⠖⠚⠉⠉⠉⠲⢄⠉⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢷⣄⠀⠀⠀⠀⠀⠀⣸⠃⢸⠀⢻⡄⠸⣆⠀⠀⠀⠀⠀⢀⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠈⠙⠓⠲⠶⠶⠚⠁⢀⡞⠀⠀⢻⣄⠈⠙⠒⠒⠒⠒⠋⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⡤⠴⠚⠉⠀⠀⠀⠀⠙⠳⠶⣤⣤⣤⣤⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠁⠁⠁⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⡀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠂⡢⠁⠦⠒⠀⠒⠢⡀
⠀⠀⠀⠀⠀⠀⡔⢡⣶⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠈⣢⠀⢰⡲⣄⣽
⠀⠀⠀⠀⠀⠀⠑⢬⣉⡈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠔⡡⢠⣿⢧⣀⣐⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⢼⣼⣿⠇⠀⠀⠀⡫⡈⣾⣽⣶⣡⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡭⠛⠈⣉⣁⣈⡉⠉⠉⠻⣍⢋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⡎⠀⠀⢸⣥⣾⣿⣿⠆⢰⣶⢻⣵⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡀⡇⠀⠀⠀⠉⢻⠛⠉⣠⠗⣟⣹⠊⡢⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣵⢄⡀⠠⣀⣸⣀⡠⢏⣮⣼⣧⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠫⡫⢛⠾⡽⣽⣻⣫⣫⢿⣟⢫⡺⠦⡄
⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⠴⣷⠃⠋⠔⠕⡁⠙⠁⠠⡺⢧⠪⠊⠨⡳⢤⡀
⠀⠀⠀⠀⠀⢀⠎⠀⠀⡰⢢⡿⠁⠀⠀⠀⠀⠈⠲⡡⠊⢔⢽⣇⠀⠀⠀⢲⢝⡄
⠀⠀⠀⠀⡔⠊⠀⠀⡐⠡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⢕⠠⢩⡇⡀⠀⠐⢕⡱⡀
⠀⠀⠀⣰⣦⢤⡄⢈⡠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡡⡪⠊⣻⡄⠀⠀⡀⢉⠾⢆
⢀⠖⠉⠁⠀⠀⠈⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⡪⠈⢜⢷⡵⠉⠀⠀⠀⠐⠹⣦⡀
⡌⢀⠔⠒⠒⠒⠤⣀⢀⠝⣦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢔⢕⢕⢵⠃⠀⠀⢀⠤⠤⢌⡂⢝⣄
⡁⡌⠀⠀⠀⠀⠀⠈⠳⡡⣻⡂⣀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢕⢁⣥⡏⠀⢀⠔⠁⠀⠀⠀⠘⢖⠹⡄
⡇⠃⠀⠀⠀⠀⠅⠈⠂⢹⣺⡏⠀⠄⠀⠀⠀⠀⠀⠀⠀⢕⠕⡅⣻⠀⠀⠎⠀⠀⠀⢠⠉⠀⢸⢸⡇
⢀⠸⡀⠀⠀⠀⢑⡠⠂⠌⣅⡿⠠⠂⠀⡀⠀⢀⢀⢀⠔⢡⣡⣾⡇⠀⠜⠀⠀⠀⣐⠀⠀⠁⡾⣾⣀
⠀⢲⣵⡀⠀⠀⢐⠂⡀⢸⣃⣯⣄⣀⣀⣠⡤⣰⣱⣡⣪⣊⢕⣵⣿⠀⠂⠀⠀⠐⠂⡀⠄⣼⣿⠉⢩⡝⠳⠦⠄
⠀⠀⠙⢿⣦⣀⣀⠭⣢⠾⣾⡧⠭⠭⠭⠟⠻⠟⠉⠙⠛⣉⣛⣛⣿⣸⠀⠀⡠⠀⠤⣠⣾⠿⠓⢀⣐⣒⢙⣉⡛⠟⠂
⠀⠀⠀⠀⠙⠛⠻⠟⢟⠛⣁⡂⠀⡤⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠭⢫⣧⣤⣬⣝⡾⠴⠛⢓⣐⠛⠷⠐⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⡿⢹⣿⡍⠓⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠻⣝⣹⣽⠃⠀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠈⠀⠀⠀⠀⠒⠩⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢶⡞⠛⠛⠛⠛⡓⠒⠢⣝⣿⣿⣿⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣭⣄⠀⡭⠭⠥⠀⠈⣿⡟⡛⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⢀⣉⣉⠉⠂⠀⣤⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⠫⡔⢺⡿⣷⣶⣿⣿⣿⣿⡟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣤⣧⡾⠁⠀⠀⠀⠀⢸⠟⣸⣿⣿⡿⢱⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣅⢧⡀⠀⢀⠀⣴⢰⣿⣿⡿⢣⣿⣿⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⣿⣿⣦⠉⠲⠸⣿⣿⠟⠛⣡⣶⣿⣿⡿⠁⠟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⣿⣿⣿⠀⠀⠀⡈⢀⣴⣾⣿⡿⠟⠫⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢿⣿⣿⠀⢠⠄⣱⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⢈⡼⠟⠅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⡿⠿⠿⠻⢿⠿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠤⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠉⠡⠄⠘⠛⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⡀⠶⠀⠉⠉⠉⠉⠙⠳⢆
⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢄⠀⠀⠀⠀⠀⠀⡌⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠑⢄⠀⠀⢀⠎⠀⣰⠁
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠦⢀⠛⠀⢰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠟⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡆⠀⠀⠀⢀⠀⠁⠀⠀⡀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣘⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⢸
⡇⠀⠀⠀⠈⣄⣠⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠦⣀⣽⣀⣤⣍⣠⠴⠶⠿⠿⢿⣿⣷⣶⣶⣏⠀⠀⠀⢸
⡇⠀⠀⠀⢤⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⡇⠀⠀⢸
⡇⠀⠀⠀⠈⣿⣿⣇⣀⡀⣠⣤⡔⠒⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢒⡒⠒⠀⢤⣤⣄⠀⠀⣿⠃⠀⠀⢸
⡇⠀⠀⠀⠀⠻⣿⣿⠟⢣⠋⠀⠀⠀⣈⠉⢩⣭⡛⠃⢀⡀⠀⠀⠀⠀⠀⠀⣙⣛⣛⡀⠀⠀⢰⠀⣉⠙⡇⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠀⠀⠙⠀⡼⠇⠀⠀⠾⢀⠀⠸⠿⠧⠤⠼⠁⠀⢺⠂⠀⠺⠂⠀⣿⣏⣀⣈⡃⢼⡀⢻⠀⣧
⡇⠀⠀⠀⠀⠀⠀⢸⡦⠀⢀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⡘⠀⠉⠁⠀⠀⠀⡄
⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢳⠟⣠⠃⠀⠀⠀⠛⡀
⠁⣄⠀⠀⢀⣀⠀⠾⠀⢸⡆⠘⣷⡄⠀⠀⠀⠀⢀⣠⣴⡿⠶⠿⠿⢷⣦⣤⣀⠀⠀⠀⠀⣰⠏⣴⠁⢀⡟⠀⣀
⠀⠀⠙⠁⠀⠀⠀⠀⢇⠸⣅⠀⡁⠰⠀⠄⡀⠀⠘⠋⠁⠀⠰⠦⠴⠂⠀⠉⠉⠀⠀⢀⡾⠃⢀⣿⡆⠛⠀⠀⠈⠛⠶⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⡾⢷⣤⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠯⢀⠞⠁⠀⡀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⣧⢀⣤⠐⠂⠁⠀⠀⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠀⠈⠑⣤⡀⠃⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠟⠻⠦⡀⠀⠀⠀⢀⡀⠸⢷⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣸⠃⠹⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⢆⠈⠂⡤⠔⠁⠀⠀⠸⣇⠀⠀⠀⠠⢾⣿⠧⢤⡴⠃⣠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⢻⣇⡀⣀⠃⡼⠃⠀⠀⠀⠀⣿⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⡟⢠⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠁⢸⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⡇⠚⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⡁⠀⠋⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢨⡇⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⡜⠋⠀⠀⠀⠀⠀⡸⠀⠀⠈⠶⠀⠀⠀⠀⠀⠀⠈⣀⠶⢄⠀⠇⠀⠀⠀⠀⡌⠙⣤⡀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡶⠁⠀⠀⠀⠱⣦⠀⠀⢀⣀⡶⠛⣠⠶⡄⠹⣶⡄⢀⣀⣾⠀⢠⠏⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠘⠁⠀⠀⠀⢀⣀⠇⠀⠀⠀⠀⠀⡄⠀⠀⡈⠋⢀⠔⠁⠀⠈⠢⡌⠳⡄⠉⠋⠀⢸⣄⠀⠀⠀⠐⠿
⠀⠀⠀⠀⠀⠛⠁⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⡇⠀⢰⡅⠀⣅⠀⠀⠀⠀⠀⢸⣤⡾⢀⠆⡰⠎⠀⠑⢀⣤⡴⠂
⠀⠀⠀⠀⠀⡁⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣤⡿⠛⠻⢋⠤⠈⠳⡀⠀⡰⠿⣀⢀⣰⣿⣶⠃⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠁⠀⠀⠀⠀⡘⢩⡤⢀⡈⠁⠘⣶⣄⠉⢁⠤⠦⠄⠀⠀⠀⠉⠛⣦⡴⠊
⠀⠀⠀⠀⠀⣧⠄⠤⠤⢼⣀⠀⠀⠀⡈⠀⡄⢠⠞⠻⠗⣤⠙⢧⠘⠛⢷⠆⠀⠀⠀⠀⢀⣠⠉
⠀⠀⠀⠀⠀⠉⣠⡄⠒⠀⠉⠐⢄⠀⢳⠖⠀⡆⠀⢀⣴⣇⠀⢸⡀⠀⠘⠀⠈⢿⠂⠒⠈⠁
⠀⠀⠀⠀⢸⡔⠋⠀⡴⠛⢷⠀⡸⠀⡇⠀⠀⠃⢀⢾⡏⢹⠄⢿⡇⠀⠀⠆⠀⠀⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠘⣷⠀⠀⡇⠀⠈⠟⠀⠐⢧⣰⠟⠀⠉⠀⠁⠛⡀⢸⠁⠀⠀⠀⡄⠀⠈⢆⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠂⠀⠛⠄⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡏⢠⠁⣼⠀⠀⠀⠀⠠⢤⣤⠈⠦⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠘⢧⠀⠀⠀⠈⣡⠉⠀⠟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠱⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⢠⡏⠀⠀⠀⢿⡀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠠⠄⠠⠼⠃
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠾⠁⣠⠇⠀⣿⡀⠀⠀⠀⣾
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠁⡄⠀⣤⣠⡟⠀⠀⣿⡙⠂⠀⠀⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠙⠆⠀⠀⠀⠈⠙⠏⠉⠀⠀⠀⣿⠁⠀⠀⠀⠀⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⡞⠻⠶⠦⠀⠈⠉⠉⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣤⠤⠤⠄⠀⠀⠀⢠⡗⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⣀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠒⠒⠆⠀⠀⠀⠀⢻⡏⠈⠁
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠀⠀⣀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠸⠖⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⣼⢇
⠀⠀⠁⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠐⠢⣄
⠀⠀⠄⠀⠀⢠⡊⠁⠀⠀⠀⠀⣠⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⢶⣶⣄⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⡴⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡤⠀⠠⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠠⠈⠀⠀⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠤⠄⢀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢡⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣠⠄⠀⠀⣀⣠⣠⣤⡶⠊⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣴⣤⣤⣄⣤⣶⣶⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠉⠉⠉⠉⠉⠭⠭⠩⠭⠍⠍⣉⠉⣉⠐⣯⣮⣉⣙⣿⣾⠆⢉⠻⣎⠓⡻⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠊⠉⣉⣉⣉⣩⣥⣶⣤⠌⠙⠿⠛⠛⠿⠒⠈⠀⠈⠉⠉
⠀⠀⠀⠑⠒⠒⠒⠀⠀⠀⠸⠍⢀⣀⣈⡉⠉⠉⠁⠉⠙⠉⠀⠉⠀⠀⠐⠒⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⠋⠉⠀⠀⠈⠉⠻⢿⣿⣦⣤⣤⣤⣤⣤⣤⣄⣠⣾⣿⠟⠋⠉⠉⠉⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠛⠛⠛⠛⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠁⠀⠀⠀⠀⠈⠙⠋⣡⣴⡶⠶⠶⠶⣶⣤⡈⠛⠛⠁⠀⠀⠀⠀⢸⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣰⡿⠋⠁⢠⣶⣶⣦⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢻⣿⣿⣿⠇⠀⠀⠹⣷⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⢿⡇⠀⢶⣄⣀⣴⢿⣄⣀⣠⡦⢀⣿⠃⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠈⢿⣄⠀⠉⠉⠁⠀⠉⠉⠉⢀⣾⠏⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣄⣀⣹⣿⣷⣦⡀⠀⠙⢷⣦⣄⣀⣀⣠⣤⣶⠟⠁⠀⣠⣶⣿⣿⣃⢀⣤⣶⣶⣿⣿⣿⣶⣦⣄⡀
⠀⢀⣴⣿⣿⠟⠛⠋⠉⠛⠻⢿⣿⡿⠛⠁⠉⠻⢷⣦⣤⣀⣉⣉⣉⣉⣁⣠⣤⣶⠿⠋⠁⠙⠻⣿⣿⡿⠛⠉⠉⠁⠉⠉⠛⢿⣿⣦
⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿
⠀⠻⣿⣧⣄⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⡀⠀⠀⠀⢀⣠⣴⣿⡿⠁
⠀⠀⠈⠻⣿⣿⣶⣶⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠉⢹⣿⣇⣤⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⣿⣿⠁
⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠁⠀⠀⠉⠙⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠁⠈⠉⠛⢿⣿⣿⡀
⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⣤⣤⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⢀⣠⣾⣿⡟⠛⠛⠛⠛⢿⣿⣦⣀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣾⣿⣿⣿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⣀⣤⣄⠀⠀⣙⣧⣴⠶⠛⠛⠓⠒⠶⠶⠶⠤⣤⣠⡞⠉⢀⣀⣀⣈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢨⣿⣿⣟⠵⠋⠁⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠈⠙⠾⣿⣿⣦⠍⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠃⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠹⣄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣈⠁⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠠⠴⠟⠛⠓⣤⣾⣿⣿⣻⣆⠿⠿⢥⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⢠⡾⠁⠀⠀⠉⠓⠶⣤⣙⣧⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢀⡇⠀⠀⢀⡄⠀⠀⠀⠀⢀⡼⢁⣠⡤⠶⠖⠒⠒⠲⡄
⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠰⠄⠉⠛⢷⣤⣀⠀⠀⠀⠀⠀⠈⠙⠲⠚⠳⠶⠒⠋⠀⠀⠀⣀⣴⡿⠞⠋⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⢠⠟⠛⠿⣷⡶⢦⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡾⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠉⠙⠒⣶⡿⣿⢻⣏⣽⣏⠻⡻⡅⠀⠀⠈⢷⡀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡜⣽⣱⢃⣾⢻⡜⡿⣄⡇⢹⠀⠀⠀⠈⣷⡀⠩⢷⣢⠄⠀⣀⣤⠟
⠀⠀⠀⠈⠙⠻⠶⢤⣤⣀⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠳⠬⠗⢫⠏⣸⠂⣷⠤⠴⠋⠀⠀⠀⠀⠸⣧⣤⣬⡶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣸⣄⣤⠴⠦⢤⣄⠀⠀⠀⠀⠀⣾⣀⣸⠑⠶⠚⠂⠀⠀⠀⠀⠀⢀⣠⣿⣇⡀
⠀⠀⠀⠀⠀⣰⠋⠁⠈⠉⠲⣌⠛⢦⡀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡴⠋⣠⠋⠀⠙⢷⡄
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⢧⠈⢿⡄⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣼⠁⡼⠁⠀⠀⠀⠀⢹⡆
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢇⠈⣷⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⣸⠃⡸⠁⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢹⡇⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢀⡏⢀⠇⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢸⣿⡄⡆⠠⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢀⡼⠳⠤⣄⣀⡀⢀⣀⣸⣿⠀⠀⣼⠃⢸⠀⠀⠀⠀⠀⡀⠀⠀⣼
⠀⠀⠀⠈⣿⣧⡇⠀⢨⢰⢠⠀⠀⣸⢠⡿⢀⡴⠋⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⣷⡀⣿⠀⢸⠀⣸⠸⣸⢰⠟⠀⢠⡟
⠀⠀⠀⠀⠈⠻⣷⣾⣼⣸⣚⣀⣴⣧⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣧⠸⡀⠉⠃⠉⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⣤⡴⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠹⠒⠉⠉⠑⠔⠒⡲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠒⠒⠒⠲⢄⡀⠀⢀⡠⢘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡞⠉⠉⠉⠓⣆⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠼⡤⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢼⣤⢀⣀⠀⠀⣗⣒⡄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣿⣛⣻⠷⣾⣛⣛⣭⣿⣷⡾⡧⣤⣴⢾⣛⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⢘⡇⠉⠉⠛⠻⠿⣿⠿⠛⠉⠁⣿⠻⠷⢿⠍⠛⠋⣉⣸⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⣶⣾⠿⠿⠛⢻⡇⠷⢀⡀⢠⠄⢸⠀⡀⠀⠀⣹⣤⣤⣼⣶⠟⣛⡥⠖⠛⡇⠀⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⣽⣿⣷⢶⣿⣷⣾⣷⣷⣌⣁⣼⡦⠶⢚⣯⠿⠁⣁⡤⠞⠋⠁⢀⠰⠆⡿⢹⡽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣿⣮⣯⠐⡆⡭⢙⡛⣿⠉⣻⠾⠗⣏⣡⡷⠞⠋⠁⢀⠄⠠⠅⠈⣀⣴⠗⣫⢶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣧⢼⠿⡟⠷⣷⣬⡄⣿⣁⣴⣶⠞⠛⢉⠀⡆⣂⠀⠈⢁⣠⣶⡿⢋⡵⣊⠁⣘⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣤⠴⡞⠛⡇⣿⠴⠛⣧⣌⣠⠋⡛⡟⣿⠁⢸⠀⠘⠘⠀⢏⣸⠴⣚⡽⠛⣡⠞⡉⠂⢐⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⣉⠑⣢⠴⠛⢳⡿⠔⠊⣀⠤⠈⣙⠷⣾⢻⣄⣸⡇⢀⡤⠖⣫⠴⠚⣁⡴⠛⠑⡠⢊⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⡁⠂⣠⠴⠋⣁⠤⠂⢁⠠⠒⢉⠠⠐⡉⠄⣂⠽⣸⡏⠝⣛⡥⠖⠋⢀⡤⠚⡁⠀⠀⢊⡴⠋⡠⠃
⠀⠀⠀⠀⢤⢀⠀⣀⡴⠚⢁⠁⠂⣤⠴⠋⡡⠔⠈⣀⠄⠊⡡⠔⠊⠠⠀⢀⣔⣚⣧⠴⠟⠛⠉⠁⣀⡤⠞⢉⠀⢀⠔⢁⡴⠿⠖⠋
⠀⠀⠀⠀⠘⣧⣞⣁⣈⣒⣢⣔⣋⣀⣔⣈⣀⣤⣊⣠⣴⣥⡤⠴⠶⠖⠚⠋⠉⠁⠀⠀⢀⣠⠴⠚⠉⠰⠀⡠⢀⣤⠞⡛⠠
⠀⠀⠀⠀⠀⠙⢢⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠛⠉⠀⠒⠀⠀⡠⢊⣠⢟⡹⠊
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⡠⠐⢁⡴⠿⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠈⠉⠉⠉⠀⠀⡔⠉⢻⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣠⣴⠏⢔⡩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠈⢧⣶⣾⠎⠀⠀⠀⠀⠀⠐⠈⠠⠔⣲⡞⠑⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⡶⣼⣿⡷⠶⠬⣄⣀⡠⣴⣬⣴⢊⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣿⡿⠿⡒⠾⠛⠙⠋⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢰⠀⠀⠀⠀⠀⠀⠀⠱⣄⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⡀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢠⠃⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠳⡀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠁⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⣀⡀⠠⡯⠣⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢢⠀⠀⠀⢸⠀⠀⠠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣼⣏⣩⣖⢦⣤⣄⣀⣀⠀⢈⡇⠀⠀⠁⡀⢀⣆⣩⣤⡶⠃
⠀⠀⠀⢀⣀⣊⣛⣿⣷⣴⣶⣶⣦⣼⣿⣿⣿⣿⣓⡻⠶⠾⠶⠾⢒⡚⢳⣿⣿⣭⣉⣙⠝⢁
⠀⠒⠀⠀⠿⡉⠹⠿⠶⠟⡉⠽⢯⣭⠋⡐⠿⠿⠧⠽⠿⠟⢀⣽⣿⡋⠙⣛⡂⠘⠛⠯⠐⠛⠀⠀⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠀⠖⠐⠛⠛⠧⠄⠀⠛⠂⠰⠦⠉⠉⠡⠄⠀⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⢛⣉⣛⠓⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠉⠀⠀⠀⠈⠑⠢⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡀⠁⠀⢀⠤⠐⠒⠂⢤⡀⠀⠈⢆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡐⠀⠀⢀⠀⠀⠀⠈⠀⢀⠴⠃⠀⠀⠀⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠋⠐⠀⠀⠀⠂⠀⠀⠀⡁⠈⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠋⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⠐⠀⠀⠀⠀⠀⢠⢸⡆
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢄⠻⠦⣶
⠀⢀⠶⣄⢸⠀⢳⠀⢠⠞⠉⣦⠈⣧⠤⠐⢊⣉⣤⡤⠶⡶⠶⠶⡶⠶⠶⣤⣬⣀⡒⠠⠄⣀⠀⠀⠑⢲⡟
⠀⠘⡄⠈⢮⠆⠘⠀⢸⠀⡜⠁⠀⠓⠒⠛⠉⠉⣥⡄⠀⢇⣰⣿⠇⠀⠀⠀⠀⠉⡟⠻⠶⣤⣍⡐⠦⢼⡇
⢏⠑⠺⣦⡀⡿⠊⣣⠼⠘⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡖⠈⠀⠀⠈⡂⠤⠴⠂⠰⣤⡿⠈⠙⠓⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀
⠈⠑⠤⢈⡋⠀⣰⠁⠀⠀⡴⠄⡀⠀⠀⠀⠀⠤⣼⠀⠀⠀⡛⠶⠶⠶⠞⢁⣤⠀⠀⠸⣯⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⢳⠀⠀⡰⠋⡇
⠀⣀⢀⣀⠤⠀⠉⠀⢠⠎⠀⠀⡼⠀⠀⠀⠀⠀⠘⣇⠀⠀⠹⡀⠀⠀⣈⠭⠃⠀⠀⢰⡿⠤⠵⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢳⡏⢀⡞⡠⠊⣠⠞⡠⠒⢹
⠀⠀⠀⠀⠀⠑⠦⡴⠃⠀⠀⣼⠉⠢⣄⠀⠀⠀⠀⠈⠳⠦⢀⣈⣐⢀⣀⡊⣀⣠⣴⠟⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡎⠀⠀⠀⢸⡇⠈⢧⡀⢣⠀⠁⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠰⡼⠁⠀⠀⠀⠑⠢⠖⡒⠃⠀⢀⠀⡱⠉⡉⠉⠙⠉⠁⠀⢠⠘⢛⠲⢤⠀⠐⠊⠉⠀⠀⢣⠀⠀⠀⠀⢿⠀⠀⠓⠈⡧⠥⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠃⠦⣤⣀⠀⠀⢀⠀⠀⠈⠀⠠⠖⠀⠀⠂⣀⠄⠐⠦⠀⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⠀⠠⢄⠸⣇⠀⢀⣠⡛⢶⡶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢲⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⡶⠤⠤⠤⠤⠴⠶⠚⠛⣌⢈⣁⣠⣽⠋⠉⠀⠙⠦⣩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⠒⠁⠀⠀⠀⠀⢀⠒⠆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⢀⡄⠀⠀⠀⢠⠙⣆⠘⠆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⡀⠘⡄⠘⢦⣇⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⠂⠀⠀⢢⡀⠈⠀⠚⢂⠈⣁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠁⠒⠠⠄⣀⡀⡠⠤⠠⠆⠤⢄⠀⠀⠀⣀⣙⠦⠤⠼⡇⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⠢⠤⢄⣀⡀⠀⡁⡈⠀⠀⠁⢘⠉⠉⠁⠀⣀⣀⡤⠤⠚⠖⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡀⡀⠀⠀⠀⠀⠉⠉⠳⠬⢁⣤⠀⡼⠋⠉⠉⠉⠀⠀⠀⠀⠤⢘⣆⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠒⠒⠀⠤⠤⣤⣀⡀⠀⡇⠰⣤⠂⠀⠀⢄⣀⠤⠔⠚⡍⠀⠀⠣⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⡜⠁⠀⠈⠉⢳⣐⠶⠄⠓⠀⣉⣇⣀⠀⠀⢘⣄⠀⠀⠑⢄⠀⠈⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⣰⡾⠖⠛⣆⠀⠀⠀⠀⠀⠀⠀⣰⢁⡈⠙⠓⠚⠋⠉⣇⠀⠀⠀⠙⢆⡀⠀⢈⡰⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠀⠀⣦⠀⢙⡦⠀⠀⠀⠀⠀⣰⠃⣼⠃⠀⠀⠀⠀⢀⣸⡄⠀⠀⠀⠀⠈⠒⢤⡀⠀⠀⠙⠂⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣀⣀⣤⠏⠛⢹⠀⠀⠀⠀⠀⠀⠈⡻⠃⠛⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠖⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠀⠤⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠋⢃⢆⡀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠓⢦⣄⠰⠃⠈⠀⢀⡄⢸⠀⠀⠀⠀⠀⠀⣷⠀⠦⣈⠐⠣⠀⠘⠋⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣉⠤⠔⠋⠧⡼⠀⠀⠀⠀⠀⠀⠘⠤⠗⠈⠳⠒⠒⠖⠒⠚⠁
⣿⣿⠟⠛⠛⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣀⣀⣀⣿⣤⣯⣴⣷⣿⣦⣿⣧⣶⣯⣾⣧⣿⣿⣴⣧⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣈⣶⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠇⠀⢏⡉⠛⠂⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠑⢄⠀⠀⣸⠀⠀⠈⢳⣄⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡳⠀⠀⠀⠑⢀⡟⠀⠀⠀⣸⠛⠣⡀⠀⡿⠀⠒⡶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⡀⠀⣴⠛⠡⢤⠐⡄⠀⠀⠈⠓⡀⢀⡴⠣⠀⠀⠈⠲⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣽⠁⢄⠀⠈⠙⢃⢠⣤⣴⣟⠋⠶⠖⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣾⠀⠀⠙⠢⡀⠀⢩⣯⠻⣿⣿⣶⡆⠠⢑⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⣿⢠⠀⠀⠀⠈⠱⣾⢀⠷⠈⠻⣿⡧⠀⠀⢹⡦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠠⠐⢤⢆⡜⢤⡀⠀⠀⠀⠀⣬⣿⢸⡆⠀⠀⠑⢄⠀⣾⠁⠀⠐⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣀⣀⠀⠂⣿⠃⣼⡁⡀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠛⢿⠁⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠢⢄⡀⢰⡿⠀⠓⢈⣡⣗⣤⣿⢏⢬⡀⠀⢀⡀⠀⠀⠀⠀⠑⢄⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⢤⣀⣤⠀⢭⡼⠾⠑⠍⢉⢜⣷⠒⡄⣠⡄⠀⠀⠀⠀⠉⠢⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣄⡙⢷⣤⣿⡿⣟⡑⢶⡶⢾⣭⣀⠁⢡⠇⢢⡄⣰⠄⠀⡄⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢡⠀⠈⠙⠿⢾⣿⣄⠀⠉⠳⠶⣄⣻⡟⠈⠉⢢⡄⠁⠉⣿⠀⣼⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⠀⠀⠀⠀⠆⠙⣯⠀⠀⠀⠀⠀⠉⠳⠢⢄⣿⠀⠈⠐⣜⠃⠉⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠀⣼⣷⣠⠀⠀⠀⠈⡎⣿⢀⡖⠁⠀⠀⠀⠀⠀⠀⠉⢲⢶⣀⠘⢗⠢⢽⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡘⠸⠎⣰⣻⣿⠹⢆⡆⢠⡞⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣿⣿⣁⠀⠈⠒⠠⣀⠀⢀⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠔⠀⠨⢻⣿⣽⣏⡋⣶⢿⡟⡡⣿⣿⡇⠀⠘⡆⠈⡀⠀⠀⢀⠀⠠⣴⢀⡝⣿⢿⣆⡄⣳⡀⠀⠉⠛⢅⡀
⠀⠀⠀⠀⠀⠃⠐⠒⠒⠻⡿⣿⡿⢝⣿⡿⠁⣸⣿⣿⣇⣿⡀⣇⢸⣿⢠⠆⡈⠀⠀⣿⣸⠀⣾⣿⡟⠃⡧⢠⢀⣦⠀⠀⠉⠀⢠
⠀⠀⠀⠀⠀⠀⢀⢀⣀⢳⡾⢀⣓⣈⣭⠥⣽⣯⣟⣻⢻⡏⠉⢱⠈⠋⠈⣀⣋⣠⣼⣽⣧⣼⣯⣭⣡⣤⡅⠐⣻⢱⠀⡸⠀⢀⡝
⠀⠀⠀⠀⠀⠀⡿⢿⢿⣿⣿⣽⣿⣄⣀⣠⣌⡛⡈⣝⡤⢶⣶⣿⠿⢛⣩⣭⣤⡭⠽⢿⡿⠿⣿⣿⣿⣿⡀⠀⠀⠀⠢⠰⣴⡿⠁
⠀⠀⠀⠀⠀⣸⠇⠰⣚⠞⠈⠙⢹⣿⣿⣿⣯⡤⡾⢿⡖⣋⠣⠞⠛⠙⠁⠠⠤⠤⠤⠤⣤⣷⣿⣾⠇⣿⣿⡄⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⢿⠀⢒⠃⠈⢥⣀⠒⠠⠽⠛⣽⣯⣿⣿⢿⠿⠂⠀⠀⠀⠀⠒⣀⣀⣀⣀⣒⣻⣿⢏⣾⡉⡽⠓⠀⠀⠂
⠀⠀⠀⠀⠀⢸⡄⠀⠉⣀⠒⠢⠄⠤⠄⢨⢏⣉⢺⠙⣦⣀⠈⠀⠀⠀⠀⠁⠤⠤⣤⣭⣿⡿⣵⡟⢣⠋
⠀⠀⠀⠀⠀⡸⣿⡍⢐⡀⠤⢍⣁⠐⠂⣚⢀⠈⣩⡾⢷⡤⠄⠒⣂⠀⠤⠐⢒⣠⣶⣾⢟⣾⢇⡘⠁
⠀⠀⠀⠀⠀⠷⠞⡛⠘⣿⣷⣒⣲⣒⣀⠩⣇⣀⡴⠾⠛⠓⠛⢟⣣⣴⣶⣭⠴⢶⣿⣟⣾⢁⣮⡄⢀⣀
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠉⠈⠉⠉⠙⠁⠈⠉⠀⠀⠀⠉⠉⠉⠉⠛⠛⠓⠂⠀⠙⠻⠿⠷⠾⠖⠋⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠦⣤⣀⠀⠀⣀⣤⡤⠴⠶⠶⠦⢤⣄⣀⠀⠀⢀⣠⠴⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⠐⠂⠒⠂⣹⠷⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣟⣁⠰⠂⠲⢀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡌⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠈⡥⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠰⠄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣀⠴⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⡟⠀⠀⠀⠀⢀⣤⠀⠀⠀⣀⣀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣷⣥⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⢛⡵⠚⠉⢉⠉⠉⠓⢾⡛⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡞⠀⠀⠸⣿⣿⠆⠀⠀⢷⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠓⠶⠶⠶⠶⠚⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡷⣤⡤⢤⣄⣀⣀⣀⢀⣠⡤⢤⡴⢾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣻⠏⢀⡏⠀⠀⠈⡟⠀⠈⣿⠁⠀⠀⢹⠈⠻⡝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣼⠃⠀⠈⣧⡀⠀⣀⡿⠤⠴⢿⣀⠀⢀⡼⠀⠀⠹⣆⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⠃⠀⠀⠀⠈⠉⠉⠁⠀⡤⠀⠀⠈⠉⠉⠀⠀⠀⠀⠹⡆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢻
⠀⠀⠀⠀⣠⡴⠶⠶⢤⡀⢠⡾⠃⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢳⡄⢀⡴⠒⠒⠶⣄
⠀⠀⠀⣼⠷⠀⣤⠀⠀⠻⡏⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣹⠏⠀⠀⠴⠐⠞⣧
⠀⠀⢰⡇⠀⠀⠀⠳⠀⠀⢹⣤⠶⠖⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠓⠶⢴⠏⠀⢀⡛⠀⠀⠀⢸⡆
⠀⠀⢸⡇⠀⠀⠀⠈⣃⠀⠀⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⢩⡀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⢸⠃
⠀⠀⠀⣷⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⢀⣩⠿⠶⢤⣄⣀⣀⣀⣀⣀⣀⣤⠤⠖⠿⣥⣀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡿
⠀⠀⠀⠸⣆⠀⠀⠀⠰⠆⠀⠀⢀⣀⣤⠶⠚⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣀⡀⠀⠰⠆⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠈⠙⠒⠶⠶⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣟⠻⢿⣯⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠛⠿⣷⣦⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡙⠆⠀⢞⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣶⣾⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⣿⣿⣮⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣤⣄⣀⠀⠀⠀⢠⣔⢾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠛⠛⠛⠛⠻⠿⢿⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣀⣀⠘⣷⡀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠾⠏⠀⡀⠀⡈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣦⣀⣀⢈⠆⢹⣶⣤⣶⣶⣶⣿⣗⣸⣿⢋⣽⠉⠉⠁⠀⠀⠀⠈⠉
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⠟⠿⢻⣿⣿⡿⠉⢿⣿⣿⣿⠃⢨⣿⣿⣿⡆⠁
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⠋⠛⠛⠋⠽⢻⣿⡇⠀⠸⢿⣿⠋⣠⣿⣿⣟⣿⣷⣄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⠲⠿⠛⣹⣿⠿⣿⣿⣷⡶⠄
⠀⠀⠀⣿⣿⣿⣿⣿⠟⠋⢡⡶⣾⣿⣿⣿⣶⣤⡀⣴⣾⣻⠇⠀⠀⠘⢳⣄⢀⣴⣿⣯⡴⣻⣿⣿⣷⣦⣤⣤⡀
⠀⠀⠀⠘⢿⠿⠋⢀⣀⣶⣿⣧⣝⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣆⣴⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⠿⢷⣦⠹⣷
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡆⢹⠠⡟
⠀⠀⠀⠀⢀⣿⢋⡟⢱⣿⡟⣫⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣦⣘⠀⠻⠶⠞⠛⢦
⠀⠀⠀⠀⢸⡏⢸⠀⢸⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⡇⠉⠳
⠀⠀⠀⠲⠞⠁⠈⠀⢀⣿⠏⠛⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢠⡶⠛⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠷⣤⡴⠊
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⠿⣿⣿⣿⡿⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣷⣭⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠈⣿⠈⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⢒⣛⡓⣒⠒⠒⠛⠒⠒⠶⠶⠾⠶⠶⠶⠶⠶⡀⠔⠊⠀⣷⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣙⣿⣿⣿⣿⣿⣿⣿⡟⠿⡷⠶⣶⣾⣷⣶⣶⣶⣶⠿⠶⠶⠶⠼⠶⠶⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠿⠿⠿⠿⡿⠿⠿⣿⡿⢋⣴⣿⣿⣿⡿⠿⠿⠛⢻⡿⠿⠿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠒⠒⣒⣚⣛⣛⣒⣒⣒⣒⣒⣻⣟⠒⠒⢲⣶⠿⠛⠛⠛⠒⠒⠒⠒⠀⣼⡇⠀⠀⠀⠈⠙⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⢛⣛⣓⣒⣒⣒⣒⣒⣒⣲⠈⠓⢲⡶⡶⠶⠶⠶⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠙⠿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠉⠛⢛⡿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⣤⠶⣛⢅⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡏⠀⠀⠀⣠⠾⣫⣵⡿⢣⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣻⡇⠀⠀⠈⠛⢛⣻⣿⣿⣿⣿⣿⡇⣿⣿⣿⡟⠀⢀⣴⢟⣵⣾⣿⡟⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠯⢿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⠟⢀⡴⢋⣵⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⢋⡴⣋⣴⠿⠿⠿⠿⠋⢰⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⢳⣶⠀⠀⢀⣛⣻⣿⣿⣿⣿⣿⣿⡿⢡⣟⡵⢋⣡⠥⢶⣒⡚⣛⠃⠀⠀⣹⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⣽⡇⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⠿⢛⣫⣵⣶⡿⠟⣋⣱⠃⢠⣆⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣛⣿⣥⠾⠟⠋⠉⠁⢸⡟⢀⡤⢖⣫⣵⣾⡿⣟⣫⣵⣾⣿⢋⡟⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣾⡟⠀⠀⠀⠀⠀⢀⡿⣛⣥⣾⣿⣿⣿⣷⣿⣿⣿⣿⣶⡟⣾⠁⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣭⠿⠧⠤⠤⠤⠤⠤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⠇⠀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣋⣭⣴⣶⣿⠛⣛⡛⢛⣟⣳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠏⠀⣰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⣿⣧⣼⢟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠏⠀⢰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⠏⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⡽⠁⢀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠓⠋⠠⠴⠿⠿⠟⠛⠛⠛⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠐⠒⠺⠿⠿⠿⠿⠷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⠽⠿⠿⠿⠿⠿⣿⣿⣶⣶⣶⣶⣶⣶⣾⠿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠉⠒⢄⣀⠤⠔⠒⠒⠒⠒⠒⠒⠤⠄⣀⠤⠒⠉⠉⠉⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠒⠒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⣄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⠃⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠘⠤⠃⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⢠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⠡⠴⠒⠐⠐⠲⠤⢅⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠊⠁⠀⠀⡊⠉⠉⠂⠀⠀⠉⢢⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⡇⠀⠀⠀⠀⠈⢹⠋⠀⠀⡀⠀⠀⡂⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠢⢄⠣⡀⠀⠀⠀⠀⠘⠀⠀⢀⠄⠀⢠⣁⠔⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠉⠛⠦⠄⣀⣁⣀⣀⣀⡠⠤⠞⠋⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡸⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⢇⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⡆⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠰⢧⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡷⠔⠒⠒⠠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠺⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠗⠁⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠤⠠⠄⡀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⠄⠂⠒⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⠀⠀⠀⠀⠈⢂⠀⡗⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢺⠀⡔⠀⠀⠀⠀⠀⢁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢠⠀⠀⠀⠀⠀⠈⢠⠓⠤⢀⣈⠀⠒⠒⠒⠂⢉⡀⠴⠚⡄⠀⠀⠀⠀⠀⠀⡄⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢥⣄⡀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠳⣄⠀⢀⣠⡬⠔⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⢀⠀⡀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠈⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠤⠈⠀⠀⠀⠀⣀⣀⣀⣀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢁⡾⠤⠒⠒⠚⠛⠛⠓⠒⠒⠤⢄⡀⠉
⠀⠀⠠⢤⡀⠀⠀⠀⠐⠢⠄⣸⢀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡐
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠉⠒⠤⠤⠒
⠀⠀⠀⠀⠀⢱⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠠⠐⠈⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⠒⠁
⠀⠐⠓⠲⠄⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠙⢦⡀
⠀⠀⠀⠀⠈⠢⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢤⣀⣀⡄
⠀⠀⠀⠀⡠⠔⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠜
⠀⠀⢠⠊⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣀⠀⠄⠂⠁
⠀⢠⠇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡄
⠀⠸⠈⠁⠉⠐⠠⢀⣀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠔⠂⢙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡈⠀⠈⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣤⡤⠖⠋⠁⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣀⣀⠤⠚⠩⡀⠀⠀⢀⠞⠉⠢⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡴⠋⠁⠀⠀⠀⠀⠑⢄⡀⠏⠀⠀⠀⠈⠑⠒⠠⠵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⣓⢤⣈⡙⠻⢍⡲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣋⣙⡛⠶⢬⣛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⢟⣛⣛⣩⡭⠭⢭⣴⣶⣬⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣍⢩⣶⡶⠀⠀⢿⢿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠏⠀⠚⠂⠀⠀⠀⡿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣖⣉⣁⠀⠀⠀⢠⡶⡧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠒⠈⠀⢀⣀⠀⣠⠄⡿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣳⣾⣿⣿⠷⠞⠋⣸⠃⠈⠻⣟⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢶⣄⠀⠀⣀⡴⣾⠏⢹⣷⣶⡀⢀⣰⠃⠀⣄⣀⣼⠇⠀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡾⠋⠁⠘⣧⡴⢸⣿⡟⠉⣹⠏⠀⠀⠙⣧⡀⠀⠀⠀⠀⢀⡉⢷
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⠇⠀⠀⢰⡋⠀⠈⣿⠃⣰⠃⠀⠀⠀⣀⣼⠗⠀⠀⢀⣴⡟⠁⢸⡆
⠀⠀⠀⠀⠀⠀⣾⡿⣛⡽⠶⣦⡀⠀⠀⠀⠀⢀⣿⡶⢿⣤⣄⣀⠀⠻⣦⡀⢹⣶⡷⢾⣷⡶⠛⠁⠀⠀⠀⣠⣿⠏⢀⡀⠈⣧
⠀⠀⠀⠀⠀⠸⣿⣼⢡⠞⣋⡙⠻⣦⣤⡶⠿⠛⠛⠛⠓⠒⠶⠭⣟⡦⣜⣿⣿⠟⢀⣴⠿⠁⠀⠀⠀⠀⣰⣿⣿⣾⠿⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠨⣿⣿⠘⣯⣿⡾⠋⠁⠀⠀⢀⣀⣀⣀⡀⠀⠀⠈⠙⢾⣿⣧⡴⠛⠁⠀⠀⠀⠀⠀⠀⣿⡿⣫⣥⡶⠆⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣾⠏⠀⠀⣠⣴⣾⡿⢿⡿⢿⡟⠻⢶⣄⠀⠀⠙⣯⢻⡄⠀⣾⠀⠀⠀⠀⢰⠟⣼⠿⠋⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⣴⣿⣿⠻⣄⢸⣇⣸⢃⣴⠟⣯⣷⡄⠀⠈⣧⢻⡀⠀⠀⣀⣀⣀⡀⠚⠁⠀⠀⠀⠀⢠⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣸⣏⣾⠛⢦⣟⣿⣿⢿⣿⣧⡾⠛⠉⣿⡄⠀⠸⡎⣷⢀⡾⢉⡭⣉⡙⢶⡄⢀⣀⣀⣠⣾⠃
⠀⠀⠀⣾⠛⠛⠛⠓⢺⣿⠀⠀⣿⣿⡟⠒⢶⡿⠉⠉⢳⣽⡟⡶⠒⠒⣿⣧⠀⠀⣿⢻⣻⢁⡿⣿⢫⠶⣢⣶⠈⠉⠉⠉
⠀⠀⠀⠙⠓⠶⠶⠞⠛⣿⠀⠀⢻⡿⣟⠛⠛⢿⠀⠀⠸⠏⠓⠻⠶⠖⢻⡿⠀⠀⣿⠛⠻⠎⠋⠁⠀⠸⢛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⣴⡖⢤⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⣦⡀⠀⠀⠀⢸⡆⠀⠀⠸⣦⣄⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡷⠘⣏⠑⢄⡀⢸⡇⠀⠀⠀⣿⡿⠁⠢⡀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠘⠀⠘⡀⠀⠙⢾⣧⠀⠀⠀⡏⠁⠀⠀⠈⢂⣄⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣿⡏⠀⠀⢀⠄⠀⠀⠀⠀⠀⢉⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡆⠀⢸⠀⠀⠀⠀⠀⠀⠋⢹⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢼⡇⢀⠀⡈⠀⠀⠀⠀⠀⠀⠀⢹⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣾⢷⢸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⡿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠃⠀⠀⠀⠀⠀⠁⢈⣷⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢻⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠔⡛⠠⠁⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠈⠢⣿⢿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣼⠀⢣⠀⠀⠀⠀⠀⠀⠈⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡞⠀⠀⠀⠀⠀⠀⠀⠒⠻⣿⠟⣋⠴⣶⠶⠦⠄⠀⠀⠀⠀⠀⠾⢶⡁⠀⠀⠀⠐⠂⢀⣠⣶⡟⠁
⠀⠀⠀⠀⠀⠀⢀⡾⣟⣀⠠⠘⣁⡀⣀⣀⣀⠤⣈⣿⣿⡿⢿⣿⠀⠒⠒⠛⠀⠀⠀⠀⠿⠿⠿⠶⢀⣠⣴⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠐⠛⠐⠊⠤⠤⠤⠄⠀⠀⠀⠀⠉⣻⣻⡿⣾⣿⡆⠀⠀⠀⠀⠀⢠⡤⣟⣭⣴⣾⣿⣿⣿⣿⣿⣿⠁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢒⡃⠀⣸⣿⠏⢀⣀⣤⣶⣾⣿⡿⢿⣿⠿⠛⠃⠀⠈⠙⠃⡠⠎
⣀⣀⣀⣀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣤⣼⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣬⣭⣶⡿⠛⠀⣴⡆⠀⣺⣿⠂⢀⣄
⣿⣿⣿⣿⣿⣖⠀⠑⠪⠄⡀⢀⣤⣀⠀⠛⢿⣿⣿⣶⣶⣶⣿⣿⣿⣿⠿⣟⣻⣿⣭⠉⠁⠉⠉⣴⣶⣾⣿⣿⡇⢸⣿⡿⠗⢸⣿⡷⣄⣀⡀⠀⢀⡠⠀⡀
⠛⠛⠛⠳⠆⡀⠀⠀⠀⢰⣬⣀⠉⠙⠛⢶⣶⣭⣭⣭⣭⣭⣿⣿⣭⣤⣼⣿⣿⣿⣿⣷⣦⣿⢿⣿⣿⣿⣿⣿⡟⠘⢿⠀⠀⢾⣿⣿⣏⠻⢿⣿⣷⣶⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣤⣄⠈⠉⠻⠿⠟⠻⣯⣝⣛⡛⠛⠋⠉⠀⠀⠈⠉⠙⠷⠀⠉⠉⠉⠀⠀⠀⠀⠀⠆⠸⣿⣿⣛⠂⠀⢨⣝⣛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣯⣄⡀⠀⠙⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣄⡀⠀⢀⣠⡴⠶⠚⠛⠛⠛⠛⠛⠓⠲⠶⢤⣄⡀⠀⣀⡴⠖⠚⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠙⠿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣀⣠⣄⣀⡀⠀⠈⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⡴⠖⠛⠛⠓⢦⡀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠉⠀⠀⠉⠙⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢸⡗⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡄⠀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⡟⠁⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⣤⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢸⣄⣿⣷⡿⠀⠀⠀⠀⠀⠀⢸⣇⣶⣦⣿⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠃⠀⠀⠀⠀⠀⢀⣾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠛⠛⠛⠛⠶⣦⣄⡀⠀⠀⠀⠀⠀⢀⣾⠃⠈⠉⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⢸⡉⠀⠀⠀⠀⣤⣶⣶⣤⣤⠀⠈⠙⣷⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⣦⣤⣈⣇⠀⠀⠀⠀⠙⢿⣿⣿⠏⠀⠀⣼⠁⢀⣠⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢰⠉⠉⠛⠻⢦⣀⠀⠀⠀⠈⡏⠀⠀⣠⡾⠋⠉⠉⠙⡞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢈⡄⠀⠀⠀⠀⠈⠉⠓⢲⠚⠛⢲⠚⠉⠀⠀⠀⠀⢸⠃⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⣀⠼⣄⣀⣸⣀⣀⣀⡀⠀⠀⣘⡆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠉⠙⠛⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⣠⡤⠴⠶⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⢶⣿⣿⡓⠶⠶⠤⣤⣤⣤⣤⣾⠟
⠹⣷⣄⣀⣀⣀⣠⣴⡾⠟⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠈⠉⠛⠛⠛⠉⠁⠀⣼⠃⠀⠀⠀⠀⢠⡤⠤⣄⠀⣴⢶⣤⡀⠙⣷⡀⠀⠀⣰⡏⠀⢀⣤⣦⡀⠀⣴⠒⢳⡆⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣴⠶⢦⣀⠈⣇⠀⠸⡆⢻⠀⠈⢷⠀⠘⣧⣀⣠⣿⠀⠀⡞⠁⢸⡇⢸⠃⠀⣼⠂⣠⠴⠶⣦⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠸⣏⠀⠀⠘⡇⠹⣄⣤⠇⠈⠳⣤⡾⠀⠀⢸⡏⢹⡟⠀⠈⣧⣀⡼⠁⠘⠷⠶⠋⢼⠁⠀⠀⣸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠳⠶⠾⠃⣀⡤⠴⠖⠲⠦⣄⡀⠀⠀⠀⣧⢸⡇⠀⠀⠈⠁⣀⣀⣀⣄⣀⡀⠘⠷⠶⠞⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⣿⠘⣿⠀⠀⣼⠋⠉⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣾⠀⢹⣆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠉⠛⠲⠶⢤⣤⠴⠾⠋⠀⢀⡟⠀⠀⠹⣧⡀⠈⠛⠲⠶⠶⠶⠶⠛⠋⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣀⣀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⠀⠘⢿⣦⣄⣀⣀⠀⢀⣀⣠⣴⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠠⠤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⢿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠀⢤⣄⡈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛⢿⢧⠖⠢⣤⠿⠾⣷⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠁⠀⠀⠀⠀⠀⠙⠀⠀⠀⠹⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣴⣶⣶⡞⣠⣾⣅⣀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⣓⣻⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡿⣿⣿⠡⣽⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠀⠨⠀⠍⠀⣽⠉⡇⠈⡉⠨⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣂⡇⣄⠙⠀⠀⠀⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⡖⣋⢹⠛⢀⣥⠤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣭⣿⡛⠛⠛⠻⠟⢃⣻⠞⠛⠻⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣉⣉⣉⣙⣷⢶⣾⣒⣛⠿⠛⠶⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣁⡀⠈⠙⣒⣦⣤⡶⠒⠒⠲⠶⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣝⡛⠛⡟⠛⠃⢐⣒⡂⢀⡠⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⣦⣄⢨⣦⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⣲⠀⠀⠀⠀⠀⠀⢀⣀⣐⣒⣦⠀⠀⠀⠀⠀⠀⠀⡆⠤⡤⢻⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢻
⠀⠀⠀⢿⣤⠿⡇⠀⠀⠀⠀⠀⠀⠀⢩⣤⡤⠜⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⡞⠀⠀⠀⠀⠀⠀⠀⣿⣉⣁⣜⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠟
⠀⠀⠀⢈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⢇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⠀⠀⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀
⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠐⠀⠒⣦⡀⠀⠀⠀⢰⣦⣄⣀⣀⣀⣀⣠⣾⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⣼⠋⠙⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⣄⡀⠀⠝⠀⢡⠀⠀⠀⠳⠒⠾⠟⠛⠲⠲⠋⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄
⠀⡟⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠒⠠⠬⠭⢤⠴⠖⠛⡆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠀⠀⠀⠐⠀⢀
⢀⣇⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠻⠟⠿⠛⠃⠀⢘⠓⠒⠶⠶⠶⠖⠒⠒⡃
⠈⡏⠉⠛⠉⠛⠋⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠄⣀⣀⣀⠠⠤⢴⡇⠀⠀⠁⠀⠀⣀⣀⠀⠀⠺
⠀⢻⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣦⣤⣤⣄⣤⣤⠤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⠙⡄⠀⣾⡇⠀⠀⠀⠀⡂⠀⠈⠆
⠀⠘⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢸⢸⠀⠀⠀⠀⠄⠀⣿⡇⠀⠀⠀⠀⠁⠐⠂⠀⠀⣰
⠀⢀⡇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠖⠀⠐⠒⠛⠃⠀⠀⠀⣸⠈⠓⠆⠀⠀⠀⠀⢻⡇⠀⠀⡀⠀⠀⠀⠀⢀⣄⣿
⢠⣾⠉⠉⠘⠁⠉⠀⣹⠀⠀⠐⠓⠀⠠⠦⠤⠄⠀⠛⠀⠀⠀⠈⢀⠀⠀⠀⠀⢀⣡⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠁⠀⠀⠉⠉⠉⠉⢠
⠀⠻⢟⣳⣒⡲⠆⠞⠃⠀⠀⠀⠠⢄⣀⣀⣀⣠⠤⠒⠀⠀⠀⠀⢀⣈⣙⣿⣿⠿⠃⠀⠀⠙⠶⣤⣀⣀⣀⣀⡤⠴⠃⠀⠀⢆⠘⢦⣀⢀⠼⠀⡨






⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⣋⡭⠭⠤⠶⠶⠤⠭⢭⣙⡓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣫⠴⠚⠉⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠉⠓⠦⣝⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⠋⠁⠀⠀⣀⡴⠚⠉⠀⢴⡆⠀⠉⠓⠦⣄⠀⠀⠈⠙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⣡⠏⠀⠀⠀⠀⡞⠁⠀⠀⣀⣈⣺⣞⣀⡀⠀⠀⠈⢷⠀⠀⠀⠀⠹⣌⢷⡀
⠀⠀⠀⠀⠀⠀⢀⡞⣰⠃⠀⠀⠀⠀⠈⣇⣴⣫⠭⠭⠽⠶⠶⠯⠭⠭⣗⣦⡼⠀⠀⠀⠀⠀⠘⣆⢳⡀
⠀⠀⠀⠀⠀⠀⡼⢰⠃⠀⠀⠀⠀⠀⠀⢨⠏⣹⢓⣲⡤⠤⠤⠴⣖⡚⢯⠙⡇⠀⠀⠀⠀⠀⠀⠘⡆⢷
⠀⠀⠀⠀⠀⢰⡇⡏⠀⠀⠀⠀⠀⠀⠀⢸⣴⡇⠽⡿⢭⡇⠈⠽⣿⠍⢸⣧⡟⠀⠀⠀⠀⠀⠀⠀⢹⢸⡆
⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⣸⣇⠀⠚⢹⡇⠀⠙⠂⠀⣸⣇⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇
⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠯⠴⠖⠛⠓⠚⠛⠲⠤⠽⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇
⠀⠀⠀⠀⠀⠸⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⣤⣤⣤⢾⢷⣤⣤⣤⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠇
⠀⠀⠀⠀⠀⠀⢷⠸⡄⠀⠀⠀⠀⢀⡤⠖⠻⡞⢁⠞⠁⡞⢠⡇⢹⠀⢳⠟⠓⢦⡀⠀⠀⠀⠀⢠⠇⡞
⠀⠀⠀⠀⠀⠀⠈⢧⠹⡄⢀⡠⠖⢻⠀⠀⠀⠹⣾⡀⢸⡁⠈⣇⠈⣳⠞⠀⠀⠀⣿⠲⢤⡀⢠⠏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⣏⠀⠀⣾⡀⠀⠀⠀⢸⡗⠦⠷⠤⠼⢛⡏⠀⠀⠀⢀⣿⠀⠀⣸⢋⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡳⣄⣈⣩⠽⠋⠀⠀⢻⣉⣉⣉⣉⡽⠀⠀⠙⠻⣍⣉⣠⢞⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣝⠲⢤⣀⠀⠀⠈⣧⠤⠤⣼⠃⠀⠀⣀⡤⠖⣫⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠬⣍⣓⣒⠚⠲⠶⠛⣒⣚⣩⠥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⡈⠤⠴⠒⠒⠒⠒⠂⠂⠤⢅⣀⣤⣶⣶⣤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⣈⣉⣉⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠦⡀⠀⠀⢀⠙⠦⣀⠀⡀⠀⣀⠴⠊⠀⠀⠀⢀⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠻⣷⣤⣀⡑⣤⡤⠉⠉⡉⢄⣤⣊⣤⣴⣾⠟⠀⠈⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠻⠿⣿⣿⣶⣶⣾⣿⡟⠛⠉⠁⠀⠁⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠉⠉⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠦⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣠⣬⣉⡑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣁⣤⣤⣤⣌⠲⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣶⣌⠢⠀⠀⠀⠀⠀⠊⣠⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⣿⣿⣿⣿⡿⠀⠤⠤⠤⠀⢿⣿⣿⣿⣿⣿⠟⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣈⡙⠛⠛⣉⠠⠀⠀⠀⠀⠀⠀⣉⠛⢛⣉⠡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠀⣀⣠⣤⣬⣥⣤⣄⣀⠀⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡦⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢴⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠾⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠈⠉⠛⠛⠻⠟⠛⠛⠉⠁⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠛⢾⠗⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠿⣿⢤⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡖⢻⡆⠠⠈
⠀⠀⠀⠀⠀⠀⠙⢗⠒⠒⠶⠼⣧⠤⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠁⠉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠉⠁⣿⡿
⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣸⣿⣴⣿⣛⣻⣿⡿⣿⡾⣦⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⡵⢌⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒⠲⠤⠶⣼⠇
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡀
⠀⠀⠀⠀⠀⠰⠧⠐⠒⠲⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡠⢐⣃⣹⣿⣠⡤⠬⣽⡿⠶⠖⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⢀⣿⣄⣠⣴⣿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣻⡷⣧⣙⠤⣀⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠾⢿⣛⣿⣿⣿⣿⣍⡉⣴⣜⣯⡾⠞⠓⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⠀⢻⣿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⠛⠻⣿⣍⢙⡿⢿⣿⡇⢠⣿⡿⣼⢀
⠀⠀⠀⠀⠀⠀⣨⠿⣿⣿⣿⣯⣮⡀⠛⢛⣤⢀⠈⠛⠲⢿⡟⠓⢿⣇⠳⣄⡀
⠀⠀⠀⠀⢠⣶⣿⠆⠠⠀⠘⠉⠉⠉⠒⠀⠀⠈⠠⠂⠀⠠⠄⠀⢘⠻⠿⢮⣉⠁⢤⣴⣶⣤⡤
⠀⠀⠀⠚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣤⣽⣄⣈⠙⠳⠦⠀⠀⢀⣠⣤⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠟⠛⠋⠉⠐⠀⠈⠙⠛⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣧⣸⣯⣝⣿⣭⣉⣽⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⢀⣴⣾⣿⠿⠛⠋⠉⠉⠛⠻⢿⣿⣦⣀⣴⣶⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣿⣷⣶⣄⣠⣾⣿⠿⠛⠛⠉⠙⠛⠛⢿⣿⣶⣄
⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⢰⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿
⠈⣿⣿⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⢸⣿
⠀⢻⣿⣧⡀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⣠⣿⡿
⠀⠀⠙⢿⣷⣤⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠉⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠟⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⡄⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣼⣿⣿⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣽⡟⠁⠉⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠘⣿⣏⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿
⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⢸
⠙⢿⣿⣶⣶⣶⣿⣿⠿⠟⠛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠛⠻⠿⣿⣿⣶⣶⣾⣿
⠀⠀⠀⠈⠉⠀⠀⠀⢀⣀⣴⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣿⣷⣄⣀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⣉⣉⡉⠉⠻⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠉⣉⣉⡉⠙⠻⢷⣦⡀
⠀⠀⠀⠀⢀⣾⠟⣡⡴⠟⠛⢉⠉⠛⠳⣦⡀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⢀⣤⠾⠛⠋⠉⠙⠛⠷⣤⡙⢿⣆
⠀⠀⠀⠀⣾⠏⣼⠋⣠⠂⠁⠀⠉⠙⠦⡀⠻⣦⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⣰⡟⠁⡤⠞⠁⠀⠉⠑⢦⡈⢻⡌⢿⡆
⠀⠀⠀⢸⣿⢸⡇⡸⠁⠀⠀⡀⠀⠀⠀⠹⡀⢹⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⡟⠀⡜⠁⠀⠀⠀⠀⠀⠀⠹⡀⣿⣸⡇
⠀⠀⠀⢸⣿⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣾⡇
⠀⠀⠀⠀⢿⣿⡁⢷⡀⠀⠀⠀⠀⠀⠀⣰⠃⣼⣇⣼⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣧⡸⣷⠀⣧⠀⠀⠀⠀⠀⠀⢀⣼⢃⣿⣿⠇
⠀⠀⠀⠀⠈⠻⣷⣤⡙⠶⣤⣤⣤⡴⠞⣁⣼⣿⡿⠟⠛⠻⠿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠿⠛⠛⢿⣿⣷⣌⡻⢦⣤⣤⣤⡴⠟⣡⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣶⣶⡾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣿⣷⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡟⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠋⠉⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠆⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠚⠈⠀⠈⠀⠀⠀⠀⠀⠀⠉⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣀⣀⣄⠀⠀⢄⣂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⡴⣿⢻⣏⢙⣁⠀⠈⠈⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠵⠓⠛⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⡠⠀⣸⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣀⣠⣤⡄⠀⠈⣤⡀⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣀⣴⣺⡥⢿⣤⣉⣰⣄⣠⣨⣦⣼⣅⣀⣀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⡴⠞⣛⣩⡤⠷⠞⢻⠚⠛⠁⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⢿⠚⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣃⣢⠘⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡄⣘⡿⣿⣿⣿⣿⣯⣝⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⠞⠁⣹⣁⡟⣻⣔⣻⣿⣿⣿⣷⣮⣟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣀⣦⣤⢿⣻⣮⣷⣿⣿⣿⣿⣿⣿⣿⡏⠈
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⠀⠛⠉⠉⠙⢿⡿⠋⠄
⠀⡂⠀⠀⠀⠀⢤⠤⣤⣤⠤⠶⠦⢤⣤⣬⣿⢿⠿⢁⣤⡀⠀⢀⢢⣼⡇⠀⡄⠖⠠⣤⠄⠀⠀⠀⠠⠶⠦⠠
⠀⠂⠀⠀⠀⠀⠀⠀⠡⢶⣾⢂⣶⢶⣦⣤⡤⠀⠐⢺⣽⡿⠈⣽⣾⣿⣇⣀⠻⢿⣿⣃⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢶⣶⡬⢙⣠⣴⠚⠿⠃⠀⠈⣛⣯⡌⠻⣿⣦⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢳⡀⠀⠀⡇⠀⢸⠃⠀⢀⠞⠁⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠐⢄⠈⢢⠀⡀⢣⠰⠀⡇⠆⢏⠄⣠⠋⠀⣠⠖⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⡑⢄⠑⠌⠀⠂⠀⡇⠘⠌⡔⡡⡢⠞⢁⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⡀⠁⡂⠀⠀⠀⠀⣀⠀⠁⠀⠪⡈⢀⠠⢚⡡⠀⣀⡤⠴⠂
⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⣀⣀⡉⠑⠀⠀⡐⢡⠊⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢉⣀⣠⣄⣠⣤⡴⠒⠦⠤⠴⠒⠶⠄
⠀⣀⣀⣀⣀⡤⠴⠤⠤⠤⢄⡀⠀⠄⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣁⠀⣀⠴⠉⠉
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⢄⣀⣀⠨⠤⠤⠤⠤⠔⠊⠉⠀⠀⣀⠜⢁⡤⠂⠀⠐⠀⢀⠀⠀⠀⠄⠐
⠀⠀⠀⠀⠀⠀⠁⠐⠄⠄⠀⣀⠐⠄⠀⠀⠵⢦⣒⠂⠀⠀⠐⠒⡴⠊⢉⠁⠂⠉⠀⠶⠀⣒⠍⣁⣀
⠀⠀⠒⠐⠒⠐⠀⠐⠂⠐⠒⠀⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⣰⠚⣡⣀⣄⣖⡰⠀⠀⠂⠁⠚⠀⠘⠲⠗⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⢤⣭⠴⠞⠟⠋⣁⣉⠁⣀⣈⠛⠛⠛⠋⠉⠉⠓⠒⠛⠛⠚⠓
⠀⠀⠀⠠⠶⠒⠒⠛⠒⠛⠓⢾⣍⠉⠁⠀⠩⠤⠬⢒⣐⠈⠁⠀⠀⠀⠀⠠⠤⠤⠤⠤⠄⠀⠰⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣶⢀⡁⠀⠀⣨⡄⠀⣼⣿⢷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣦⣿⠟⠉⣹⢻⠟⢰⠿⡯⠊⠀⠀⢀⣠⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠈⠛⠋⢠⣷⠃⠀⠀⠀⢀⠴⠛⠛⠝⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠸⠋⡀⠀⢠⡶⢋⡀⠀⠀⢸⣷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢠⣼⣧⡀⣾⠁⠀⢀⣀⠜⢻⡟⠀⠝⠓⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢀⠀⠉⠉⢉⡳⠦⢶⣿⡀⠄⣈⠓⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢺⡋⠈⠐⠂⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⢦⡄⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣟⠁⠀⠀⢧⡀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣸⠁⠈⠀⠀⠈⠿⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⢐⠃⠀⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠠⠀⠐⠈⠠⡄⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⣿⠀⠀⠀⠀⠐⢘⠉⠢⢄⢳⠀⠀⢀⢀⣀⠀⢠⠄⠨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⠁⢀⡇⠀⠀⠀⢀⡀⠀⠒⠀⠢⠘⢀⣠⣼⡏⠀⠁⠐⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡋⠈⣿⡇⠀⠀⠀⠈⠀⠁⠀⢸⣶⣯⡍⢿⢺⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠀⠀⣾⠇⠀⠀⠀⣀⠀⠀⠀⢸⣿⡞⢁⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁⠀⣸⡿⠀⠀⠀⠀⠉⠀⠀⠀⢸⣿⣧⢨⡄⠀⣀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡯⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⡛⣁⣿⣾⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠯⡍⣛⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣟⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⢿⣟⣿⣿⣗⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⣦⡄
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠟⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⡀
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠈⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣰⣶⣦⡀⠠⠄
⠰⠶⠲⠤⠤⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⡖⠐⠒⠂⠈⠉⠉
⠀⠤⠀⠀⠀⠀⠀⠠⠤⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠢⠽⠿⠟⠁⠀⠀⠀⠀⠀⠠⠤⠮⠤⠄⠀⠀⠀⠀⠀⠀⠤⡤⢤
⣤⣤⣤⣤⣄⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀⡀⢀⠀⠀⣤⣤⡄⠀⣤⣤⣤⣤
⣿⣿⣿⣿⣶⣿⣿⣷⣶⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⠄⠀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⣤⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠹⣷⣤⣾⢿⠯⠿⠛⣿⣯⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠠⢽⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⡒⡺⠟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠴⣚⠶⠿⢦⣶⣮⣽⣿⣿⣿⣿⣿⣛⢛⣿⣶⣦⣌⣛⢷⠶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⢤⣯⣛⣻⠿⣿⣟⣛⡛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠐⠒⠶⠒⠶⢶⣦⣴⡶⢦⣍⠉⢿⣿⣿⣿⡿⣛⢛⠉⣙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣛⣫⣾⣻⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠤⠥⢤⣄⣿⣷⣮⡥⢶⣶⣤⣬⣹⣿⣿⣿⠷⠖⠂⠙⢿⣿⣷⣶⣮⣝⡛⠿⢿⣿⣧⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣀⣀⣀⣤⣤⣍⣙⣛⣛⡛⠛⠀⠀⠀⣊⣉⣙⡛⠛⢛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠿⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⢿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠉⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⣿⣿⣿⣷⣶⣿⡿⠋⠁⠀⠀⠀⠀⠙⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠀⠀⠀⠈⠉⣩⣴⠶⠾⠿⠷⢶⣤⡉⠋⠁⠀⠀⠀⠀⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣾⠏⠁⢠⣾⣿⣶⠀⠈⠻⣦⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⣾⠇⠀⠀⠘⠿⠿⠟⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⣿⠀⢀⡀⠀⢀⣤⠀⠀⢀⡀⢸⡇⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠹⣧⠈⠛⠶⠛⠉⠳⠶⠋⢁⡿⠁⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⢹⣿⣷⣄⠀⠙⠷⣦⣀⣀⣀⣀⣠⣴⠟⠁⢀⣤⣾⣿⡃⢀⣠⣴⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⠛⠿⣿⣿⠟⠋⠙⠻⢶⣤⣌⣉⣙⣛⣋⣉⣠⣴⠾⠛⠉⠙⠿⣿⣿⠟⠋⠉⠉⠉⠛⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣶⣤⣀⣀⣤⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⣤⣴⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣏⣁⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣼⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠋⠉⠉⠉⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠉⠉⠉⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⢀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠿⠿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣶⣶⣶⣶⣿⠿⠃⠀⠀⠀⠀⠘⢿⣿⣶⣶⣴⣶⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⢀
⠀⠀⠀⠀⠀⠴⡯⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠐⠐⠦⡤
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣁⢌⠀⠀⢀⠆⠀⠀⠀⠣⠁⢠⠀⠀⠀⠒⠦⠨⠒⠁
⠀⠀⠠⠆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⢀⣨⢲⣿⠾⢢⣶⡁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠀⠀⣤⣠⡇⠀⠀⠀⠀⠀⠘⠀⠍⠀⠂⠉⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠈⠉⠉⠉
⠀⠀⠀⠊⠒⠀⢀⣦⠀⠼⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠠⠀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠂⠘⠆⠠⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣠⠆⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠰⡘⡤⠒⠈⠁⠀⠀⡖⢈⡆⠀⠀⠀⠀⠀⢠⢆⣄⡀
⠀⠀⠀⠙⠀⠍⠀⠀⡀⡀⠃⣤⢀⡄⠀⠀⠚⠁⠀⠀⠀⣑⠄⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⡈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⢠⣽⠀⠀⠀⠀⢀
⠀⢤⡠⡀⠀⠃⠀⠀⣀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠄
⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠂⠂⠀⢠⠆⠀⢈⠁⢀⠤⣴⠃⠀⠘⠀⢴⣄⠀⠀⠀⠈⠀⠘⠉⠉⠁⡀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⠘⠆⠀⠈⠀⠘⠛⠋⠀⠁⠀⠀⠈⠉⠀⠀⠀⠈⢀⡁⠀⠀⠀⠈⠀⠀⠀⠀⠑⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠿⠓⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠰⠀⠀⠐⡀⠀⠀⠀⢈⠀⠀⠀⡀⠀⠠⠀⠢⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠃⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠘⠆⣠⣞⣧⢀⡀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁
⠀⠀⠀⢀⡆⢀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⠀⡀⢀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠰⠂⡾⠋⣉⠞⠳⡌⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠫⠛⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠦
⠀⠀⠀⣄⠀⠀⢀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠂⠁⠘⠒⠛⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠃⢰⡖⠂⠀⠀⠀⠐
⠀⠀⠀⠎⠁⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⣿⠇⠀⠀⠀⠠
⠀⠀⠀⠒⠀⠠⠄⠀⠈⡀⠀⢢⠶⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠈⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠓⠀⠇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠆⠠⠦⠿⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⣴⠆⠰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡀⠀⠀⣾⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢲⡯⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠋⠉⠀⠂⡀⠉⠀⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⠠⠄⢀⣔⡏⠀⢰⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢿⣇⣀⢸⡇⢰⡶⣄⣀⠐⠀⢀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠈⠙⡛⣸⠃⠀⠉⠙⠻⡾⠧⣤⣛⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠀⣤⠄⠀⠀⢨⣵⡏⠀⠀⠀⠀⠀⢹⡄⠀⠈⢿⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠚⠂⠲⠀⡜⣨⡿⠀⣀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠛⠛⠿⠿⣿⣿⣾⣶⣿⣥⣶⣿⣿⡛⠛⠻⠿⣿⣆⡉⢰⡦⢿⡀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢩⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠯⠿⣿⠃⠀⠀⠀⠀⠀⠉⠙⠳⢾⡧⣤⡀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠚⣇⠀⠀⠀⠀⠀⠀⡠⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⣠⣾⠟⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠀⠀⠈⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣰⣃⢋⢌⣼⣦⣗⣴⣷⣧⣾⣿⠋⠀⠐⠇⠴⠃⠀⠀⠀⠀⠀⢰⣽⠃⠀⣀⣀⠐⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣤⣬⣅⣟⣻⣟⣿⡿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣷⣶⣤⡀⠀⡀⣀⢀⣼⡿⢀⣴⠟⠉⠓⢢⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣉⡉⠛⢻⡿⣿⣿⣷⣮⣿⠋⠰⢟⡿⠿⡿⣿⡿⣿⣷⣦⣤⣤⣽⣿⣿⣷⣿⣧⣦⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣻⠷⢤⢄⣉⠛⠃⠀⠀⢈⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⠆
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣀⣠⣞⣛⢻⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠏⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⣀⣸⠃⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⡅⡟⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣭⡤⣄⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠈⢂⠀⠀⠀⢴⢞⣛⣩⣥⣶⣤⣿⣿⣿⣿⣿⡿⣿⢟⣩⣾⣏⠀⠀⠉⠿⢿⢿⡿⠿⠿⢿⡅⠾⢿⠀⠀⠂⠀⢀⣤⡞
⠀⠀⠀⠀⠀⠈⠳⣤⣀⣐⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣟⣛⠛⠿⣿⡅⠀⠀⠀⠀⢠⠷⣍⠢⣶⣿⣧⣀⢤⣀⣀⣰⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠐⠓⠶⢚⣋⣩⣭⣭⣭⣏⣉⡛⠿⣦⣝⠂⠀⢐⣕⣾⣶⣮⣷⣮⣽⣿⣿⣿⣿⣿⣟⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣄⣀⣁⣐⣨⣽⣿⣿⣿⣿⣿⣿⣿⣄⠈⠛⢷⣄⠀⠉⡛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⣭⣭⣤⣶⣾⣿⣿⣿⣿⢿⡏⠁⢾⣆⠙⠶⣤⣈⣛⠿⠿⠿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⢈⠙⢿⣿⣧⡍⠙⠀⠶⢿⣷⣴⣤⣉⣉⣛⡛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠻⠶⠦⠉⠀⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣾⣏⣰⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣅⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠉⠙⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢿⡿⠁⡀⢹⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⣤⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠆⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⣏⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⢀⣴⣶⣾⣷⣶⣶⣤⣶⡆⠉⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣤⣄
⠀⠀⠀⠀⡾⣥⠀⠀⢘⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⡿⣌⠳⢦⣤⠤⠶⠶⠚⠛⢛⣛⣿⣿⣿⣿⣿⠂⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢰⣷⡌⠙⠒⠦⠀⠀⠠⠖⠿⠛⣉⠝⠛⠛⠿⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⡈⢻⣦⡄⠀⠀⠀⠀⠐⠃⢸⠃⠀⠀⠀⠀⠀⠁⠀⣸⠉⠉⢉⠛⢿⣿⣿⣿⣯⠉⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⣳⣄⡉⠛⠊⠀⠀⠀⠀⠀⠀⣦⣷⣦⣄⣀⢀⣠⣴⡃⠀⠀⠠⠀⠀⠓⠄⠀⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⡇⠈⠻⣟⣃⡀⢠⠤⢤⣤⡀⠀⠉⠛⠿⢿⣿⣿⣿⠃⠀⠈⠓⠦⠂⠀⠀⡠⠀⠁⡀⣿⠟⠻⢿⣿⣿⡇
⠀⠀⠀⠘⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠰⠟⠁⠠⠀⠀⠿⣋⠀⠀⢠⠟⠛⠃
⠀⠀⠀⠀⠀⠉⠛⠦⣤⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣽⠖⠀⠀⢠⡿⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⢿⣍⡉⠙⠛⠻⠿⡷⣶⡤⣤⠾⡿⠟⠠⠂⠀⠈⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣄⡀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢟⡔⢡⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠈⠀⢛⢞⠞⢿⠿⠃⠞⢻⣿⠻⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠟⠘⣿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣷⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠹⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⠉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⡟⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⣀⡴⠞⡻⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⣿⠀⠀⠀⠀⠀⠀⣿⢸⣿⣇⠀⠀⠀⢠⡾⢋⡴⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⢻⣄⠀⠀⠀⠀⠀⣿⢸⡇⣿⡀⠀⠀⣾⠀⡾⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⡀⠀⠀⠀⠀⢹⣄⠻⣄⠉⠛⢶⣤⡀⢸⡇⢸⡇⠸⣇⠀⠀⢻⡄⣷⠈⣷⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠲⣤⡀⠀⠈⠻⢦⣈⠙⠲⣄⠈⢿⣾⠁⢸⡇⠀⢿⡄⢀⣼⠃⣿⠀⢹⡆⠀⠀⣀⡴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡑⢤⡙⠳⢤⣀⠀⠙⣦⠀⢻⣆⣸⣿⣤⣼⣧⣤⣼⣿⡟⠉⣠⠟⢀⣾⣃⣤⠞⢩⡖⣿⠋
⢀⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠉⠓⢶⣿⡶⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠻⢿⣤⣾⠟⠋⣠⡴⢋⡼⠃⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⣶
⠾⠛⠳⢦⡈⣷⣄⠀⠀⠀⠀⢀⣀⣹⣆⠀⠻⣦⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡾⠋⢠⡞⠁⠀⢀⣴⠞⢛⣉⣉⣉⠙⠛⣩⡿
⠀⠀⠀⠈⢷⡹⣍⡛⠿⠿⠛⠋⠉⠙⠻⢷⣴⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣴⣿⣀⣀⣴⠟⣡⠞⢩⡴⠶⠶⠶⠟⠋
⠀⠀⠀⠀⠈⠻⣦⣉⡛⠚⠛⠛⠛⠲⣦⣼⠏⠀⣠⠶⠚⠋⠻⠿⢷⣴⣿⠀⠀⣾⣆⣤⣶⣟⣿⠓⠶⣦⣄⠹⣏⠉⠉⣁⡴⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⣦⣼⠇⠀⣀⠁⢠⣶⣿⣿⣿⣿⣿⣿⠂⠀⢻⣿⣿⣿⣿⢿⣿⣦⠈⠙⣆⢻⡟⠛⠉⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠛⣿⠀⠀⠻⠷⠿⢿⣷⣯⣻⡼⠟⢿⠀⠀⢸⡏⠿⣿⣧⣽⣽⠿⠳⠞⠃⠈⣿⠻⠿⢧⣤⣀⣀
⢀⣀⣠⣤⣶⣒⣚⣛⣉⣀⣀⣀⣀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⢸⣷⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣈⣉⣙⣛⣿⣶⣦⣤⣤
⠈⠙⠛⠛⠻⠿⠧⣤⣤⣀⣀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣏⠀⠀⠀⣿⢙⣦⠀⠀⠀⠀⠀⠀⠀⠀⣟⠁⣀⣀⣤⡤⠴⠶⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡽⠿⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠶⠟⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡶⠚⠛⠛⣷⡀⠀⠀⠀⠀⠀⣠⣀⣀⣠⣴⣤⣤⢶⣤⣄⣤⣄⠀⠀⠀⠀⠀⢠⣿⣄⠀⠻⢤⣤⣤⣤⣄⣀
⠀⠀⠀⣀⣀⣀⣠⣼⠇⣰⠏⣠⡤⠴⣾⠟⠳⣄⠀⠀⠀⠀⠟⠛⠛⢻⣿⠿⠷⠛⢻⡟⠛⠛⠀⠀⠀⠀⣠⣿⡀⠉⠳⠶⠤⠶⠶⠶⢬⣙⠳⣄
⠀⣴⢟⡭⠥⠤⡤⠴⠞⢁⡾⠃⠀⣰⠏⠀⢀⣿⢦⣄⠀⠀⠀⠀⠀⠀⠙⠷⣶⠶⠟⠁⠀⠀⠀⠀⣠⣾⡃⠈⢿⣦⣤⣠⣤⠴⠶⠾⠶⣌⢣⣹⡆
⢸⣷⡶⠟⠛⠓⠶⠶⠟⠋⠀⠀⣰⠏⠀⣴⠟⠁⣀⡽⠷⣤⣀⡀⣂⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣅⠈⠙⢦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠙⢦⣽⣟⣳⣶
⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣠⠞⢁⣴⢾⡟⠀⢠⡟⠉⣙⣿⡿⠿⣶⡶⠶⢾⠟⢻⡇⢀⡟⠉⠻⣦⣀⠙⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣼⣥⠞⠋⠀⠘⣷⠀⣾⠀⣸⠏⠈⣿⠀⢹⠀⠀⣿⡄⠈⢧⠈⢷⣄⠀⠀⠙⠳⢦⣉⢮⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠁⠀⠀⠀⠀⢸⡇⢸⡆⣿⠀⠀⢹⡆⢸⠀⢰⡟⢳⣄⠈⠳⢤⡉⢷⡄⠀⠀⠀⠈⠛⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠀⠀⠀⠀⠀⢀⣼⠃⡼⢀⡿⠀⠀⠘⣧⢸⠀⣾⠁⠀⠉⠛⠷⣦⠹⡄⢿⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⡜⢁⡾⠃⠀⠀⠀⢻⣼⢰⡇⠀⠀⠀⠀⠀⢸⡆⠇⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⣯⡾⠋⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣰⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⢿⣗⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠔⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⠠⠀⠀⠀⠀⠀⠀⠀⠀⣻⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠠⠒⠈⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣀⢴⡤⠴⠓⠀⠀⠀⠀⢸⠀⠀⣀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠤⠐⠛⠉⠀⠀⠀⢀⡀⡀⠀⣈⣺⠼⠓⠚⠉⠙⣦⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣏⠉⠁⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒⠀⠀⠀⠀⠀⠀⢀⡰⠍⠋⠁⠀⢈⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⠉⠀⠀⠀⠀⠀⠀⢺⡇⠀⢈⣤⣤⣶⠶⠓⠒⠚⡂⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠿⠑⠛⠉⠁⠀⠀⠀⠀⠠⡄⣀⣠⣿⠇⠀⠋⠁⠀⠀⠀⠀⠀⠀⢰⣄⠀⠛⢧⣀⣀⣀⡀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣇⡯⠴⠾⣟⡋⠉⠩⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠈⠉⠋⠉⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡬⠉⢒⠈⠁⣥⠟⠷⠛⠁⠀⠀⠀⠀⢀⣀⣀⣤⣤⠾⡾⠿⢿⣀⣀⣀⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠲⠶⠖⢒⡫⠈⠀⠀⠀⢸⡆⠀⡀⡴⢀⡄⠴⠒⠋⢹⡅⠹⣿⣤⣶⣾⣿⣿⣿⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠻⠈⠀⠀⢤⠀⠘⠀⠀⠀⠀⠀⠀⣷⠀⠀⡴⠛⠀⠀⠀⠀⣠⣷⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣫⣠⢴⣶⣶⣿⣿⣿⡿⢻⠿⠿⣿⣿⣿⣵⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣯⣼⣯⣤⣥⣾⣷⣖⡚⠻⢉⣑⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣭⣤⣤⣬⡁⠈⣿⣿⣿⣿⣦⡄
⠀⠀⠀⣶⣶⣤⣀⡀⠀⠀⠙⣶⣶⠒⢀⡤⣤⣶⣶⣶⣿⣿⣟⣛⣛⣛⠻⠿⠿⠟⠻⣂⣽⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣏
⠀⠀⠀⠈⠽⠟⠛⠿⢷⣶⣤⣬⣭⣶⠿⠿⠖⢸⡋⠋⠀⡉⣈⡉⠉⢉⣩⣄⣀⣴⣿⣿⣿⡿⣿⣿⣿⣿⠃⠟⠉⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠁⠀⠀⠀⠓⠂⠈⠉⠁⠀⠈⠉⠉⠉⠉⠉⠈⠻⠛⠿⠛⢫⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡶⢲⣄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠚⠉⠁⠀⠐⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠴⠂⢠⡤⢐⡺⡭⣭⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠸⠓⠲⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢠⣤⣤⢶⣶⢄⠀⠀⠀⣤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⡾⠛⣿⣏⠳⣾⡥⠤⠾⠛⠓⣿⡶⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⠃⢀⣠⠿⠒⠚⠉⠉⢻⠏⠀⠀⠀⠀⠀⠀⠀⣰⣦⡤⢶⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡉⠀⡀⠛⡾⠋⠀⠀⠀⠀⠀⠀⣿⣀⣀⣤⣀⠀⠀⠀⣿⣿⠁⠀⢸⡇
⠀⠀⠀⡀⠀⠀⠀⠀⣾⣏⡉⣉⣤⡟⠀⢠⣦⠴⠶⢳⣶⣶⣜⣩⣭⣭⣿⣿⣶⣤⣹⣿⡄⠀⣼⡀
⠀⠀⠀⠈⠲⢤⡀⠀⢿⣿⣾⣿⠿⢇⣴⠯⠤⠴⠾⠛⠛⢿⣾⣿⠿⠟⠛⠛⠻⠿⣿⣿⡇⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠙⠢⣌⠻⡏⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⢧⣠⣦⣶⣦⣤⣀⡀⠀⣿⣷⣶⣦⣄⠀⠀⠁⣿⣿⣿⣶⣿⣿⣷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣽⣁⣀⣄⡀⣿⡿⣦⡉⠀⠈⢙⣿⠷⣦⡀⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⢿⣿⣿⣿⣿⣧⣬⡙⠦⡄⠀⣿⠀⠹⣿⣷⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣯⢷⡿⢟⡛⠙⣿⣷⣯⣟⣿⢻⠶⠿⡷⣾⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣷⣍⣻⣶⣿⣿⣿⣌⡿⢉⣿⡟⣷⣶⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢬⡘⢪⣿⡏⢉⠛⠻⡟⢻⣿⡿⢿⣿⣿⡿⢻⣿⠿⠟⢻⢿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠀⠈⠉⠁⠀⠀⠐⠃⠀⠉⠙
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠠⠤⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⢀⠄⣴⡆⠄⡊⢶⣦⠂⢁⠀⠀⠀⡀⠀⠰⠄⠀⠤⠀⠀⠀⠀⠈⠓⠀⢀
⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠀⠀⣡⣾⣿⠅⡂⠁⣾⣿⣿⣦⡁⢆⠀⠁⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠑⣌⠐⢄
⠀⢀⠁⠀⠠⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠈⠁⢀⣾⣿⣿⣿⢷⣶⡾⣿⣿⣿⣿⣿⣦⡐⠁⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢈⡘⠀⠀⢀
⠀⢸⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⣿⣿⣿⣿⣿⣻⣦⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⡞⢉⠇⡘⠀⠀⠀⠀⢄
⠀⢸⠀⠀⠀⣄⠠⠀⠀⠀⡀⠀⠂⠀⠀⠀⢀⢸⣿⣿⣿⣿⣉⣵⡎⠹⠎⢩⠛⣿⣿⣿⣿⠆⡀⠀⠀⠀⠀⠂⠠⡀⠰⠲⠁⡾⢀
⠀⠀⡀⠀⠀⢧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢈⠻⢿⣿⣿⣤⣩⡤⢤⣄⣌⣹⣿⣿⣿⠿⠀⡀⠀⠀⠄⠀⠈⠀⠀⢸⠃⡘⠀⢀⠰⠀⠀⠀⠀⢀⠊
⠀⠀⠃⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⡄⣀⣾⣿⣿⣤⣤⣬⣴⣿⣿⣯⠩⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⠁
⠀⠀⢸⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠋⠀⠉⢽⣿⣿⣿⣿⣿⣿⣿⣿⣟⠓⠴⣄⠀⠀⠀⠀⡀⠀⠈⢠⡎⠀⢶
⠀⠀⠘⣇⠀⠀⢷⠀⠀⠀⠀⢀⡤⢀⣲⠋⠉⠁⠀⠀⠈⠛⠿⡿⠛⠿⠿⠛⠛⠁⠀⠀⠾⣆⣾⣿⣷⡄⡠⠤⡞⠁⠐⢺⡅⠀⠀⠀⠀⠀⠀⠀⣾⣶⡆⠁
⠀⠠⠀⠹⡄⠀⠸⣆⠀⠀⠀⠀⢀⠿⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠂⢹⣿⣿⣿⠷⠣⠈⠀⠀⠀⠀⣍⠐⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣦⡄⠃
⠀⠀⠀⠀⢳⡀⠀⢏⠠⣂⡤⠒⠋⠑⠀⠀⠀⠀⢀⡀⠀⠈⢧⠀⠀⠂⠀⣄⠔⠀⠀⠃⠀⠈⣿⠿⠃⠀⠠⠀⠀⢤⣖⣚⣁⣀⡀⠀⠀⠄⢀⣤⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠰⢳⠀⠸⡶⠫⠀⠀⠀⠀⢢⣀⣠⣴⣿⠃⠀⠀⠈⠟⢀⠾⠛⢀⠄⠂⠀⡂⠠⠖⠀⠂⠀⠀⢠⡀⢶⣿⣿⣿⣿⣿⣿⣷⣤⣶⣿⣿⠟⠉
⠀⠇⠀⠀⠌⢠⣧⡀⣀⣤⠁⠀⠀⢀⡀⣿⠟⢺⣿⡇⠀⠀⢀⡴⠛⠃⡸⠋⠀⠀⠀⡃⠘⠀⢀⣿⣄⠀⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠛⠃
⠀⠀⠀⠀⠈⣿⣿⠈⠇⣰⢀⣾⣤⡾⢿⠋⠰⣼⢿⡇⢀⡰⠋⠀⢀⡔⠉⢳⣤⣰⣀⡟⣄⡛⣛⡽⠋⠙⣻⣿⣿⡿⢿⣿⣿⡿⢿⣿⣿⡇
⠀⠀⠀⠃⠀⢹⣿⣧⣀⣝⢨⣿⡷⠻⢋⠀⡡⣟⣁⣨⠍⡭⠁⣀⠼⡇⠈⠏⣡⡝⢿⣧⠈⡙⠫⠀⠀⠀⣿⣿⠁⢀⣸⡿⣿⡃⠀⠉⣿⠇⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠄⠀⠄⠀⢙⠛⠉⡐⠉⠁⢄⠀⠠⢈⠡⣏⣀⣃⠀⣃⣀⠅⠲⠀⢴⠄⠚⣷⠂⠛⢧⠀⠀⠈⠀⠀⢿⣿⣾⣿⣿⣁⣻⣿⣷⣶⣿
⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠃⣐⠏⠉⠙⠛⠛⠿⣶⣾⡶⣶⠾⠿⢿⣷⡀⠘⠳⣤⢀⡰⣢⡤⡂⣽⣿⣿⣿⣿⣿⣿⠙⢃⣤⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣥⣚⣊⠉⠀⠀⠀⢀⠄⠀⠉⠉⢀⣆⠀⠈⢂⠹⣿⣅⠁⠀⠋⠛⠿⢿⡔⠻⠿⢿⠿⡿⡟⠛⠀⢾⣿⣿⣷⣀⣀⣤⣤⡀
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠐⣉⠵⠋⠁⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⢻⡆⠀⠀⠢⡈⠻⣷⣤⡀⠀⠀⡠⠛⢖⠐⠀⠆⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⠆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⣀⣴⠎⠀⠀⠀⠀⠙⣶⣄⡀⠀⠈⣿⢀⡔⠀⠑⠄⠈⢿⣷⡔⠈⠁⢠⠞⣧⠐⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠐⠁⢀⣠⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⢼⣿⣿⣷⣄⣿⠏⠀⠀⠀⠀⢢⠈⢯⡹⣄⡔⠁⢲⣿⣧⣄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠠⠁
⠀⠀⠀⠀⠀⢀⠀⢀⡟⢠⣿⣿⡿⢿⢟⣽⣾⣷⡄⠀⠀⠶⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠁⡈⢣⣷⠀⡰⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⡘⠇⣿⡉⠂⢰⣏⣾⣿⣿⣿⣿⡀⡀⢿⠁⡀⠀⠭⠙⠛⠿⣄⠀⠀⢀⣀⠀⢻⡄⢻⣏⣠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣀⡧⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⣹⢏⡠⠐⠀⠒⠀⠈⢑⣿⠄⠀⠉⢿⣇⡾⣿⡌⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢈⠀⠈⣿⣿⣿⣿⣿⣿⣷⡏⠸⠀⠀⠀⠀⠀⠀⡂⣺⠵⠆⠀⢠⣇⢙⠈⣿⣰⣽⠟⠋⠈⡀⠀⠀⠀⠀⠀⠠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢰⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠄⣻⠀⠒⠠⢭⣍⢹⡆⠐⣏⠉⢶⡀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⣿⣿⣿⡿⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣿⡶⠀⠀⠙⠂⠺⠀⠄⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡟⠁⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠩⠶⣤⣀⣀⣘⣻⡷⠄⠈⢁⠀⠡⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠠⠴⡮⠙⠙⠛⠏⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣈⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣈⣟⡀⠀⠀⠀⢘⣷⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣠⠶⠒⠒⠲⢤⡀⠀⠀⣀⣤⣄⡀⢘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠒⠋⠁⠀⠀⠉⠛⠋⠙⠻⣿⣿⣿⣄⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⢤⣀⡞⠙⢦⡀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⡴⠋⠉⠙⠳⣄⡼⠁⠀⠀⠀⠙⠓⠲⡄⠉⠙⠲⣤⠀⠀⠰⠿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠐⢦⠴⠃⠀⠀⡴⠋⠁⣀⣠⣤⣤⣤⠄⠀⠀⣿⠀⠀⠀⠈⢳⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⣠⠞⠁⣠⠞⠉⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⢧⣠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿
⠿⣍⣛⣉⣁⡴⠊⠀⣀⣀⣀⣀⣀⣤⠖⠋⠁⠀⡴⠚⠲⣄⠀⢀⣽⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣿⡿⠟
⠀⢀⣨⣭⣤⣤⠴⠚⠉⠀⠀⠀⠀⠈⠙⢦⡀⠈⢧⣀⡀⣈⣩⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⣀⡴⠒⠒⠦⣀⠀⠈⠳⢤⣀⣀
⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠙⢄⣀⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⠀⠀⠈⠳⠦⣤⣤⠤⣴
⠀⢀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠿⠟⠛⠛⠶⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣻⣿⣿⣿⣿⣷⣶⣤⣤⣶⣿⣿
⠀⢸⣷⣶⣶⣶⠾⠟⣋⣡⣴⣶⣶⣿⣷⣶⣶⣤⣄⡈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⣿⠿⠛⢉⣡⣤⣤⣤⣤⣤⣌⣉⠙
⠀⠀⠉⣉⣥⣤⣶⣿⣿⣿⣿⣿⣿⣿⢯⣭⣭⣤⣬⣥⣤⣤⣄⡉⠛⠻⠿⠿⠿⠟⠛⠉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠘⠟⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⡿⠿⠿⠿⠿⢿⣿⠷⠶⠛⣣⣴⣿⣿⣿⣿⣿⣿⣦⠤⠤⠶⠿⠿⠟
⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠙⠷⣶⣶⣶⣶⣶⣶⠶⠾⠿⠿⠿⠿⣿⠿⠛⣉⣤⣤⣶⣶⣶⣶⣤
⠀⠀⠀⠀⠙⢿⣿⣿⡿⠟⠛⠛⠻⣿⣿⣿⣿⣷⣦⣄⠀⠰⣶⣶⣶⣶⣶⣶⣶⠶⠟⣁⣤⣶⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢳⣴⠶⠶⠶⢶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⣭⣭⣭⣭⣤⣶⣿⣿⣿⣿⣿⣿⠟⢛⣉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣦⣤⣤⣀⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠛⠳⠦⠄⠉⠛⠻⠿⠿⢿⣿⣿⠿⠿⠟⢛⣉⣤⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣶⣾⣿⣷⣦⣀⠛⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⢀⣠⣶⠾⠿⠿⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⠿⠿⢶⣦⣀
⠀⣠⡿⠋⠁⠀⢀⡀⠀⠀⠈⢿⣆⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⣾⡟⠀⠀⠀⡀⠀⠀⠈⠻⣷⡀
⣰⡿⠁⠀⣴⣾⣿⣿⣿⣾⣦⣼⡿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣄⣾⣿⣿⣿⣿⣷⡄⠀⠘⣿
⣿⠃⠀⣼⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⡀⠀⢹
⢿⣇⠀⢹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠁⢀⣿
⠈⠻⣦⣌⣻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣋⣤⡾⠋
⠀⠀⠈⠙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠉
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡩⠔⠒⠉⣉⡉⠑⠒⠬⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⣾⣿⣿⡇⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣄⣨⣿⣏⢀⡄⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⣧⠀⠀⠀⠙⠋⠁⠉⠋⠀⠀⠀⢰⠇⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣄⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣀⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⢙⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣟⠉⠻⢷⣦⡀
⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠋⠉⠉⠉⠙⠛⢿⣿⣿⣿⣿⡄⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⣿⠁⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⡧
⠀⠀⠀⠻⣧⣀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⢀⣠⡿⠃
⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⣿⣿⣶⣤⣀⣀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠉⠉⠉⢹⠉⠉⠉⠉⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⠀⠀⠀⠀⣀⣴⣿⣦⣄⠀⠀⠀⠀⣀⣴⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡤⠤⠤⠀⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡤⠀⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠘⡆⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠋⠉⠁⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⠈⢯⡆⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠙⢦⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⡇⢀
⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢧⣠⠞⠀⢠⠀⡤⠂⠔
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⡄⠀⠀⠀⠀⠸⠀⠀⣀⣈⠀⠘⠀⠀⣡⡂
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡞⠉⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠒⢉⡽⠀⠀⠀⢠⢃⡠⠞⠀⢃⠀⠀⢀⡠⠒
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣇⠠⠁⢍⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡠⠋⠁⠀⠀⠀⠀⠉⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠈⠦⣀⠀⢀⣠⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠉⠉⠀⠈⠑⠦⣄⣀⣀⣀⣀⣀⣀⣀⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡠⠂⠁⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⡠⠔⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣧⣀⠉⢄⠔⣰⣀⠄⠂⠉⠀⠀⢄⡀⠀⠀⠀⠀⠚⠉⡩⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⠀⠀⡰⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡤⠀⢱⠀⠁⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⣀⣱⠤⠒⠉⠀⠀⠀⣄⠀⠀⠀⠀⠀⡎⠀⠀⢸⠂⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠒⠘⠣⣄⠀⠀⠸⠀⠀⠀⠸⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⣀⣠⠴⠋⠓⢤⣀⠀⢀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⠿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⡠⠄⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡏⠀⠀⣅⣠⠀⠀⢹⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠤⠄⠒⠒⠒⠛⠛⠓⠒⠒⠤⠤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠠⠤⠴⠶⠶⠶⠶⠶⠤⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣄⡀
⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⣰⣿⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠀⠀⠀⠈⠛⠷⢶⣶⠶⠾⠋⠁⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆
⢀⣾⡿⠃⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⣠⣴⡾⠟⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠀⠀⣠⣤⠀⠀⠀⠀⠀⠘⢿⣷
⣼⣿⠃⠀⠀⠀⣠⣶⠿⠋⢁⣤⣶⠿⠋⠁⠀⢀⣠⣶⠿⠛⠁⠀⢀⣠⣴⡿⠛⠁⠀⢀⣤⣶⠟⠋⠁⠀⢀⠀⠀⠀⠀⠘⣿
⣿⣿⠀⠀⠀⠀⠉⣀⣴⡾⠟⠉⠀⠀⣀⣤⡶⠟⠋⠁⠀⣀⣤⣶⠟⠋⠁⠀⣠⣴⡾⠛⠉⠀⠀⣀⣤⡾⠟⠁⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠰⠾⠛⠉⠀⠀⣀⣴⡾⠛⠉⠀⠀⣀⣴⡾⠟⠉⠀⢀⣠⣴⠿⠛⠁⠀⠀⣠⣴⡾⠛⠉⠀⠀⡀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠁⠀⢀⣠⣴⠿⠛⠁⠀⣀⣤⡾⠟⠋⠀⠀⢀⣠⣶⠿⠋⠁⠀⢀⣠⣴⠿⠋⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠠⣾⠟⠋⠀⠀⣀⣤⡾⠟⠋⠀⠀⣠⣴⡿⠛⠉⠀⠀⣀⣴⡾⠟⠉⠀⠀⣀⣤⣾⠟⠋⠀⢀⡀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⢀⣠⣴⡾⠛⠉⠀⢀⣤⣶⠟⠋⠁⠀⢀⣠⣴⠿⠛⠁⠀⢀⣠⣴⡾⠛⠉⠀⣀⣴⡾⠟⠁⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⣶⠟⠋⠁⠀⣀⣴⡾⠟⠉⠀⠀⣀⣤⣶⠟⠋⠁⠀⢀⣠⣶⠿⠋⠁⢀⣠⣴⠿⠋⠁⢀⣠⡄⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⠁⠀⠀⣀⣴⡾⠟⠉⠀⠀⣀⣤⡾⠟⠋⠀⣀⣤⡾⠟⠋⠁⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⣾⠟⠋⠀⠀⢀⣠⣶⠿⠋⠁⠀⢀⣠⣴⡿⠛⠁⠀⣠⣴⡿⠛⠉⠀⣀⣴⡾⠟⠋⠀⣀⣴⡆⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠀⠀⢀⣤⣶⠟⠋⠁⢀⣠⣶⠿⠋⠁⢀⣠⣶⠿⠛⠁⢀⣠⣴⠿⠛⠁⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⣴⡿⠛⠉⠀⠀⣠⣴⡾⠛⠉⠀⣀⣤⡾⠟⠉⠀⣀⣤⣶⠟⠋⠁⣀⣤⣶⠟⠋⠁⣀⣤⣶⠇⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠁⠀⢀⣠⣴⠿⠛⠁⢀⣠⣴⠾⠛⠉⢀⣠⣴⡾⠛⠉⠀⣠⣴⡾⠛⠉⠀⣠⣴⡾⠟⠉⠀⡀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⣤⡾⠟⠋⠁⢀⣤⣾⠟⠋⠁⢀⣠⣶⠿⠛⠁⢀⣠⣶⠿⠛⠁⢀⣠⣶⠿⠛⠁⢀⣠⣶⠿⠃⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠉⠀⣀⣴⡾⠟⠋⠀⣤⣴⣾⠿⠋⠀⣠⣤⣾⠟⠋⠀⣠⣴⣾⠿⠋⢀⣠⣴⣾⠿⠋⠀⣠⣤⠀⠀⠀⠠⣿
⢹⣿⠀⠀⠀⢀⣶⠿⠋⠁⢀⣤⣰⠘⠉⠉⢀⣀⡀⠿⠟⠉⢀⣠⣶⡿⠟⠉⢀⣤⣶⡿⠟⠋⢀⣠⣴⡿⠟⠁⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⠀⠀⣀⣤⣶⠟⠛⠉⢀⣀⡿⠛⠛⠁⠀⣀⠾⠟⠋⠁⠀⣠⡾⠟⠋⠉⣀⣴⣾⠿⠛⠁⣀⣤⡶⠀⠀⠀⢀⣿
⢸⣿⠀⠀⠀⢠⡾⠟⠋⠀⣠⣴⡾⠟⠋⠀⣠⣴⡿⠟⠋⠀⣠⣴⡿⠟⠋⠁⣠⣴⡾⠟⠋⠁⣠⣴⡾⠟⠋⠁⠀⠀⠀⠈⣿
⢸⣿⠀⠀⠀⠀⢀⣠⣶⠿⠛⠁⢀⣠⣴⠿⠛⠁⢀⣠⣴⠿⠛⠁⢀⣠⣶⠿⠛⠁⢀⣠⣴⠿⠛⠁⢀⣠⣶⠇⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⠰⠟⠋⠀⣀⣤⣾⠟⠋⠀⣀⣤⣶⠟⠋⠁⢀⣤⣶⠟⠋⠀⢀⣤⣾⠟⠋⠀⣀⣴⡾⠟⠋⢀⡀⠀⠀⠀⠀⣿
⢸⣿⠀⠀⠀⠀⣠⣴⡾⠛⠉⠀⣠⣴⡾⠛⠉⠀⣠⣴⡾⠛⠉⠀⣠⣴⡾⠛⠉⢀⣠⣴⡾⠛⠁⢀⣤⣶⠟⠃⠀⠀⠀⠀⣿
⢸⣿⡄⠀⠀⠘⠋⠁⢀⣠⣶⠿⠋⠁⢀⣠⣶⠿⠋⠁⢀⣠⣶⠿⠛⠁⣀⣤⣶⠟⠋⠁⣀⣴⡾⠛⠉⣀⣤⡆⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⣤⡾⠟⠋⠀⣀⣤⡾⠟⠋⠀⣀⣤⡾⠟⠋⠁⣀⣴⡾⠟⠉⢀⣠⣶⠿⠛⠁⣀⣴⡾⠟⠉⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠁⠀⣠⣴⠿⠛⠁⠀⣠⣴⡿⠛⠉⢀⣠⣶⠿⠛⠁⣀⣴⡾⠟⠋⢀⣠⣶⠿⠛⠁⣀⣴⡾⠃⠀⠀⠀⢸⣿
⠸⣿⣇⠀⠀⠀⠐⠿⠋⠁⢀⣤⣶⠟⠋⠁⣀⣤⡾⠟⠋⠀⣠⣴⡾⠛⠉⣀⣤⣶⠟⠋⢀⣠⣴⠿⠛⠁⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⡄⠀⠀⠀⠀⠀⠾⠛⠉⢀⣠⣴⡾⠛⠉⢀⣤⣶⠟⠋⢁⣠⣴⡾⠛⠉⣀⣤⡶⠟⠋⢁⣤⠖⠃⠀⠀⠀⠀⢠⣿⣿
⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠐⠿⠋⠁⣀⣴⡾⠟⠋⢀⣠⣶⠿⠋⠁⣠⣴⡾⠛⠉⠀⠤⠞⠋⠁⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠈⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⠉⠀⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠈⠻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣷⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⣶⣾⣿⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⢛⣛⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣖⣯⠭⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⢲⡄⣿⠁⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣖⣾⣿⣧⡿⠀⠀⠀⢀⣀⣸⣧⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⢀⣀⣿⡷⠶⢚⣛⣉⣉⣀⣠⣤⣤⣤⣤⣤⣤⣤⣽⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣰⡏⠉⣟⣋⣉⣭⣭⣥⢤⢤⢶⢶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣬⣭⣉⠙⡇
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠴⠶⠖⠚⡛⠉⠩⢹⡇⠀⡿⠷⠷⠓⣛⣛⣛⣉⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⣉⣛⣛⣤⠇
⠀⠀⠀⠀⠀⠀⢸⣐⣀⣁⣩⣬⠤⠴⢖⣒⣿⢀⠉⡟⢛⣛⣉⣉⣩⣭⣤⢤⡤⣤⢤⡤⡤⡤⣤⢤⢤⣤⣤⣬⣽⡇
⠀⠀⠀⠀⠀⣯⣭⣵⣶⠶⠶⠶⠿⢟⣛⣛⡿⠀⠤⣿⢹⡇⡇⢸⣀⣇⣸⣸⣇⣿⣼⣥⣧⣧⣿⣸⣼⣿⣷⠿⠿⠗⠚⠲⣦⡀
⠀⢀⣤⣴⠚⡓⢒⠒⡉⣉⢉⡉⣉⠁⠄⠠⠀⠆⢀⡟⠛⠛⠋⠉⢉⣁⣀⣤⣤⠤⠶⠶⠚⠛⠋⠉⠉⠀⠀⠀⢀⣀⣀⣀⣟⣿⠆
⠀⠘⠦⣤⠤⠥⠬⠤⠤⠤⠶⠶⠶⠖⠒⠒⠛⠉⠉⠙⠒⠚⠛⠋⠉⠉⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠶⠒⢚⠋⠉⠉⣁⣸⡿⠃
⠀⠀⠀⣇⣐⣀⠀⠀⠀⠀⠰⠐⠐⠂⠂⠂⢀⣀⣁⣈⣀⣠⡤⠤⠤⠶⠖⠒⢛⣉⣉⣡⣤⠤⠴⠶⠒⢾⣿⡟⠉⠉⠉⡿⠁
⠀⣀⣀⢸⡟⠛⠛⠿⠿⠿⠿⠭⠭⠭⠭⠭⠭⠭⠴⠶⠖⠒⠒⠒⠚⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠳⣌⣯⣤⡄⠀⢸⠇
⠈⠉⠉⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡿
⠚⣉⣱⣢⣿⣽⠷⠲⢶⣦⠤⢤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡷⢤⣤⠖⠲
⠚⠁⠀⠈⠑⠦⣀⣀⡞⠙⠻⢷⡲⠶⠋⢈⡽⠿⠭⣭⣽⠛⠻⢷⣒⠒⢒⡖⠶⣖⠒⠲⢲⡶⢶⡒⠒⢒⣿⡿⠭⣿⠛⠳⣤⣀⣀
⠀⠀⣠⢤⣀⡀⠀⠀⠀⠀⠀⠀⣈⡛⠒⠋⠀⠀⠀⠀⢈⣉⡓⠒⠚⠛⠋⢀⣀⠈⠙⠲⠶⠃⠀⠉⠳⢮⣍⡽⠂⠈⡷⠦⢤⡉⠁
⠉⠉⠁⠀⠀⢈⣉⣉⣉⡒⠒⠚⠉⠉⠙⠒⠦⠤⣄⡤⠞⠉⠉⠛⠲⠦⠤⠜⠉⠙⠒⠦⣄⣀⣠⡟⠙⠲⠤⣄⣠⠴⠃⠀⠀⠙⢦
⠀⣀⣠⡴⠞⠋⠁⠀⠀⠉⠙⠒⠤⣄⣀⠀⠀⠀⢀⣀⡤⠖⠋⠉⠉⠒⠒⠤⢤⣀⡀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠉⠓⠒⠤⢄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⠒⠀⠀⠐⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠋⢿⣷⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡏⠹⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⣤⠶⠶⠛⠀⣀⣿⣶⣶⣾⣏⠠⡆⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡅⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣠⠴⢋⣡⣴⣶⣿⣿⣿⣿⣿⣹⣏⣿⣳⣾⣆⠀⢹⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡦⢠⣾⡿⠿⠿⡧
⠀⠀⠀⢠⡿⠃⠀⠀⠀⢀⣜⣡⣾⣿⣿⣿⣿⣿⣿⣯⣛⠿⣿⣿⣻⣿⣿⣿⠆⣸⠀⠀⠀⢀⣤⡔⣾⠀⠻⣿⣿⣿⠿⠛⠋⠁⠁⠀⠀⠀⠀⠷
⠀⠀⠀⣾⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⡻⢛⣋⣉⣉⣉⣟⣻⡷⣯⣀⢴⣾⣿⣿⡿⣿⠀⠀⠚⠉
⠀⠀⢸⡏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣴⣾⣟⣉⡉⠁⠀⠀⠀⠀⠙⣿⣿⣿⣶⠉⣿⣿⡿⠽⡆⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⢸⠃⠀⠀⣴⣿⣿⣿⡿⠟⠛⠋⠉⠐⠛⠉⢉⣉⡙⠻⠀⠀⠀⠐⠚⢷⣇⠀⠀⢠⠄⠉⠁⠀⠀⡇⠀⠀⣠⣴⣶⣿⣿⣿⡆
⠀⠀⣿⠀⠀⠸⢿⣿⣿⣻⠿⡏⠀⠀⠀⠠⡀⠀⠉⠛⠉⠀⠀⠀⢠⣴⣴⣄⡁⠀⠞⠀⠀⠀⠀⠀⠀⢧⣴⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⢸⣆⠀⠀⣿⠉⠂⢻⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠃⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠻⣦⡀⣿⠐⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠄⠀⠐⠀⠀⡄⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠈⠛⠿⣇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⢤⠳⠀⡇⠀⢀⠴⢻⣿⣿⣿⣿⠀⣿⠿⠛⠋
⠀⠀⠀⠀⠀⡀⢀⠙⢦⣠⠀⠀⠀⠀⠀⠐⡄⠀⠀⠐⠶⠌⣉⣉⣐⡶⠄⢰⠃⠔⠁⠀⣼⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⣴⣾⣿⣷⣿⠀⠀⣧⢸⡀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠲⠀⠀⠰⡞⠁⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠋⠉
⢠⣤⡟⣿⠟⠋⠁⠀⠀⣿⠘⢧⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠒⠂⠀⡿⠀⡀⠀⠀⠀⠘⠿⠿⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣶⠚⢉⣀⣀⡴⣦⠤⠐
⠀⠴⠾⠟⣰⠀⠀⠀⢠⣿⡀⠀⠉⠓⠢⢤⣀⣀⣀⢀⣀⠀⠀⠀⠀⣰⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠛⠉⠁⠀⣿⢀⠌⣿⠉⢁⡹
⠀⠀⢰⡿⠿⠀⣠⣤⡿⠀⠙⢦⡀⠀⠀⠀⢉⡟⢁⠌⠋⠛⡒⠲⢯⠁⠀⣠⣶⣦⡄⠀⢠⣀⣠⡤⠐⠋⢡⣤⣾⠓⣄⠐⠈⣯⠀⠀⣾⣃⣼⠇
⠰⠞⢋⣠⣾⣿⣿⣿⣷⢀⠀⠀⠉⠳⢤⣀⣾⠖⢁⠄⠈⠀⠉⠉⣈⠂⡀⣿⣿⣿⣽⣧⣄⡉⢀⣄⠀⠳⣄⠿⡾⢦⠇⠀⠀⣿⠄⠀⠈⠁⠀⣀⡀
⠰⣿⣿⣿⣿⣿⣿⣿⣿⡆⠑⠤⡀⠀⢠⠟⠡⠊⠁⣀⡤⠖⠋⠀⣈⢉⡙⠂⣽⣿⣿⣿⣿⣿⣬⣄⡠⠖⠘⠃⡔⠛⠂⠉⢀⣈⣠⠴⠒⠋⠉⣁⣠⡤
⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠒⡞⡼⠀⠀⠐⠉⠀⢠⣴⣾⣿⣟⠻⣶⣼⣿⣿⣿⠻⢛⣭⣙⢻⡷⣦⡀⠈⢆⠐⠛⢉⣁⣤⠴⠶⠛⠋⠉
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⡿⠁⠀⠀⡀⠀⢀⣾⣿⣿⣿⠟⢃⠭⠁⠱⢯⣤⣿⣿⣿⡿⢋⠁⠐⠘⠓⢾⢀⣺⣯⣿⣄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣼⠃⠀⠀⠠⠁⠀⠈⢙⣿⣿⣏⡔⠁⠀⠀⠀⢱⣽⣿⠿⣿⠁⠆⠀⠀⠀⢰⡄⠟⣿⣿⣿⡿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡏⠀⠀⠀⠀⠀⠀⡀⢸⡀⠙⢿⡇⠀⣠⣤⣶⣿⢿⡇⠘⢷⢀⡄⠰⣶⣶⣾⢃⠃⢹⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢠⣴⣿⡇⠀⢹⣷⣄⡘⠛⠛⣡⡞⠀⠀⠛⠈⣓⠀⠬⠉⠐⣯⠀⢸⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠰⠉⠀⠀⠀⠀⡇⠀⠈⢹⣿⡇
⠀⣿⣿⣿⣿⣿⣟⠻⣿⣿⣿⣿⣿⣧⠀⠀⢀⡞⠀⣿⣿⣿⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⣤⡀⠀⠀⢰⢧⣀⣄⠀⠘⠁
⠀⣿⡿⢿⣿⡘⣿⣆⢻⣿⣿⣿⣿⣿⣧⢀⡎⠀⠀⢻⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠟⠏⣧
⠀⣿⣷⡈⢿⣧⠘⣿⣆⢻⣿⣿⣿⣿⣿⣿⠣⡀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣀⠔⠊⠀⣠⣿⣧
⠀⠹⣿⣷⡈⢿⣧⡘⣿⣆⢻⣿⣿⣿⣿⣿⣷⡑⡀⢈⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⢼⡿⠀⢀⣼⣿⣿⣿⣧
⢠⣄⠹⣿⣷⣌⡛⠁⠿⢿⣆⠹⣿⣿⣿⣿⣿⣷⣡⠀⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⣿⢃⣴⣿⣿⣿⣿⣿⠏⣤
⠸⣿⣆⠹⣿⣿⡇⢰⣷⡆⣹⣦⠹⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢳⣤⣿⣿⣿⣿⣿⣿⡿⢋⣼⢋⡤
⢠⣿⣿⣆⠙⣿⣧⣘⡛⠁⠻⣿⣧⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⣶⣿⣿⣿⣿⣿⣿⠟⢋⣴⠟⣡⠞⣡⡦
⠠⣿⣿⣿⣦⠘⣿⣿⡏⢼⣷⡜⢿⣷⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣥⡾⠟⣡⡾⢃⣼⠟⣱⣶⡀
⠀⣿⣿⣿⣿⣧⡈⢿⣿⡌⢻⣿⣎⢻⣿⣾⣿⣿⣿⡿⠿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣥⡶⠾⢛⣩⣴⠟⣋⣴⠟⣡⣾⣿⣿⣷
⠀⢿⣿⣿⣿⡿⠗⠈⠛⠻⠆⠙⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠿⠿⢧⣴⡶⠾⠛⢩⣴⡾⠟⣡⣾⣿⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠖⠉⣭⠿⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣎⣀⣼⡠⠃⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣛⠯⣭⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢆⠀⠀⠄⠐⢄⠹⡂⢠⠈⢖⣠⠂⢠⠀⡀⣀⡀⠤⢀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠑⠦⣸⡄⢄⠻⣇⡜⢣⣸⢁⢂⣾⠟⠋⠁⣀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⡀⠰⠈⢻⣬⣶⣿⠞⠳⣿⣿⡏⠀⠰⢀⣼⡉⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⠛⠻⣦⣴⣯⠝⠉⠀⠀⠀⠀⠉⢋⣷⡶⣋⠥⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢈⣑⠶⠔⣿⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣥⠶⠿⠒⠉⠉⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠐⠉⠀⠔⠚⢅⣻⣿⠀⠙⠒⠂⠀⠀⠑⠚⠋⢈⣿⢌⡵⠒⢀⣤⠄⠂⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣠⠔⢲⡿⢋⡹⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣒⠻⢍⠑⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠖⠁⢂⣡⡞⠟⢭⣷⣤⣀⣀⣀⣠⣴⣯⠟⠉⠻⣦⡅⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡴⢋⠘⠂⣡⣿⣿⡟⠷⢻⡟⢯⠻⣅⡘⠀⠘⣷⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣀⠄⠉⣀⣠⣴⢾⠏⠌⣸⡏⢶⠋⣿⣄⠣⠹⡏⢦⡀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠉⠁⠀⠀⠐⠀⡔⠁⢧⠀⠀⠸⣄⠑⠄⢩⠀⠌⠢⠑⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⡶⢯⠀⠀⠀⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⠙⠃⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⢾⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠙⠶⠄


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠉⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⡔⠋⠉⠓⣄⢹⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣸⣀⣀⡤⠴⠚⠚⠒⠦⠤⣄⡀⡴⣉⣤⣄⡀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡅⠀⠀⠙⡆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢀⡟⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠭⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣀⡤⠬⣿⣀⣀⡀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⠁⠀⠸⣿⣿⣿⣿⡝⠫⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡇⠀⠀⠀⠈⠙⠋⠉⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢒⡞⠙⠢⣝⠲⠤⢤⣀⣀⣀⠤⠚⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⢀⡞⢀⣀⣀⣀⣉⡓⠲⠤⠤⠤⠤⠤⢤⣶⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢀⡴⠟⠋⠁⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⢀⡎⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⡴⠒⢶⡲⠤⣼⣦⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⣸⠟⢠⣦⣇⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⣷⣿⣷⠀⡏⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢹⡿⠋⡼⠁⠀⠀⠀⠀⠘⢷⠦⣀⠀⠀⢀⠔⠊⢉⠉⠛⢶⡦⡀⠀⢸⢻⡀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠒⠒⠒⠛⠋⠉⠙⠮⣝⢲⢿⣶⠄⠻⠟⣠⣄⢱⠹⣄⡟⠀⠉⠙⡷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⣴⣾⣷⣶⣌⠋⣸⠀⡏⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⠷⠃⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⠭⠭⠤⠴⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠛⠆⠀⠐⡀⡻⣿⣿⣇⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⣯⣿⣿⡇⢰⠀⠀⢠⠀⣹⣿⣿⣿⣷⡀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⣿⣿⣿⡈⠀⣐⢱⣰⡟⡹⢿⣿⣿⣿⣦⣙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠄⠀⠙⢻⢿⣿⣿⣿⣤⣄⣘⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⣀⡤⠀⠐⠛⠻⢿⠿⣿⣿⣷⣦⡉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⡀⠀⠀⠀⠁⠘⠿⣿⣿⣿⣦⣜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⠄⠀⠘⠛⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣷⣬⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣽⣿⡿⠁
⠀⠀⠀⠀⣠⣴⡪⣸⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⠉⢁⡟⠀⡀⠙⣈⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⢠⡾⠋⣧⣴⣿⣿⣿⣿⣿⣿⣟⡛⢿⣿⣿⣿⣿⣿⠿⣿⣿⡇⠠⣿⡿⣿⣿⣿⣾⠌⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⢹⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⣿⣿⠉⠉⠁⠀⢛⠿⠃⠀⠙⠓⠀⠀⠀⠀⢀⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⣀⠀⠀⣠⣴⠀⠀⠀⢤⠀⠀⠀⢀⠾⣟⡝⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⣯⣽⣿⣾⡙⢀⡴⣿⣶⣦⣀⣴⣾⣳⡀⠈⡞⠀⣽⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡴⢿⣿⠃⣾⣿⣿⣿⢿⣿⠿⢿⣿⣧⠈⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⣿⣿⠙⠛⠳⠶⠛⣛⠙⣿⣆⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿


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

⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉
⣏⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦
⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠻⠟⠿⢻⣿⡿⠛⠛⠛⠛⠛⠛⢛⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⢿⣿⣿⣤⣶⣤⣦⣤⣤⣤⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠁⠀⠰⣷⠀⠀⠀⠀⠀⢐⡈⠙⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⢰⣶⣿⣦⣀⠀⠀⠉⣉⣋⣀⠀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠛⠛⢚⣳⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⠗⠀⣀⠴⠒⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢾⠘⣿⠳⣄⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠠⠀⠃⠹⣧⠈⢃⠄⠀⠀⠁⠀⠀⠀⠀⠀⢠⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⣼⡏⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠁⠐⠀⠀⢻⣆⠀⠀⣱⣇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⣶⣶⣦⣰⣤⡠⢤⣤⣌⣿⣿⣷⡄
⠀⠀⠀⠀⡘⠀⠘⡄⢀⣀⣻⣄⣴⠟⣨⠓⢄⠀⠀⠀⠿⠿⢻⣟⣿⣿⢹⣿⠿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣠⣇⠀⠰⢃⣼⣿⣿⣿⣿⣧⢹⣧⣌⠳⣄⠈⠼⡀⣾⣿⣿⣿⣸⣿⡇⠀⠈⠙⠻⠝⡻⢿⣿⣿⣿⣿⣧⠀⠀⠄
⠀⢀⣴⡿⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣳⣆⣥⣿⣿⣿⣿⣿⣿⣷⣶⣴⣦⢤⣀⣉⡳⠿⠿⣿⣿⣿⣧⠀⠰⡄
⠀⣸⡟⠀⠀⠀⣾⠟⢩⣿⠟⠉⠹⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⢸⣿⠀⠈⠉⠙⠛⠿⢾⣿⣿⣿⣧⢰⣿⣦
⠀⣿⠁⢴⠀⣠⣸⣇⣛⣀⣀⣀⣀⣹⣆⣏⣛⣤⣿⣿⣿⣿⣯⣥⣼⣧⣤⣤⣄⣀⣾⣿⣦⣀⣀⣀⣀⣀⣀⣀⣈⣙⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠙⢉⣿⣿⣿⡿⠿⠻⠏⢿⣿⡏⠉⠉⠉⠉⡻⠏⠉⡟⠻⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⢷⡀
⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⢾⣿⡇⠀⠀⠀⡴⠁⠀⠺⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⡏⠋⠉⢉⣉
⣧⣴⣦⣤⣤⣤⣼⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⢿⣿⢦⡤⠤⠴⡦⠶⠤⡶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣌⣾⣇⠀⠀⠀⠁
⢥⠀⠀⠀⠀⠀⢰⡇⢶⡀⠀⠀⠀⠀⠀⠀⢿⣿⡄⢀⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⢰⡗⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠈⣿⣿⡏
⠀⠃⠀⠀⠀⠀⠈⣿⣶⣾⢶⣤⠀⣠⣦⣤⣾⣻⣿⣟⣴⣯⣤⣤⣴⣤⣶⣶⣶⣶⣷⣶⣦⣤⣤⣀⣴⣷⣶⣤⡜⣧⣿⣿⣿⠁
⠀⠀⠀⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠹⣿⣿⠿⠟⠉⣿⡟⠻⠿⣿⠏⢙⣿⣿⣿⠿⠻⢿⣿⣿⠿⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⣿⡇⠀⠀⠀⠀⢀⣿⢹⠗⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣿⣀⣿⣧⡄⠀⢀⡀⢸⣿⠘⡀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢀⣶⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣧⣾⣿⣤⣦⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡖⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣄⣀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠶⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡉⠉⠛⠛⠟⠛⠉⠛⠢⠦⣤⣀⡀
⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣤⣤⣄⣤⣄
⠀⠀⠀⠀⠈⠉⣛⠿⠛⠛⣉⣉⣀⣀⡈⠋⠙⠛⠛⠛⠛⠛⣻⣿⣿⠛⠻⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠻⣿⣋⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠟⠋⠉⠛⠻⠷⢶⣦⣴⡶⠾⠿⠛⠿⠟⠛⠛⠿⠿⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣯⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⣿⣿⡿⠷⢦⣕⠀⣀⣿⣿⢿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣼⠇⠈⡿⠀⠀⠘⠆⢰⠟⢡⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠰⡀⠀⠀⠈⠀⢸⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⣤⣿⡾⠦⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢸⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠟⠉⠓⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣼⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⢀⣀⣄⣀⣻⣤⣴⣶⣿⣿⡿⣿⣷⣯⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣲⣦⣶⣿⣷⣾⣿⣾⣿⣽⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠁⠉⠲⠿⠿⠦⠬⠭⡍⢉⣉⣉⠉⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠔⠒⠀⠀⢀⣠⣤⡴⠂⠄⠀⠀⢀⣀⡠⠭⠄⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡀⠁⠠⠤⠀⣀⣐⣲⣦⣤⣤⣤⣤⣄⣀⣤⣤⣤⣤⣤⣶⠶⠿⠛⠁⣠⢄⠀⠀⠀⠪⠹⠭
⠀⠀⠀⠀⣀⣀⢀⣀⣀⡠⠭⠵⠶⠶⢚⢛⡛⠛⠽⠟⠛⠋⠉⠉⠉⠉⠈⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣳⣷⠶⢦⠀⠀⠐⠄
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣖⣲⡶⡺⠿⠿⠟⠛⠋⠀⢀⡞⠀⠀⠀⠀⠄⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠾⠛⢛⣉⣁⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠞⢫⡀⠀⠀⠀⢀⡠⠔⠋⡀
⠀⠀⠐⠒⢀⣉⣉⣉⣙⣉⣉⣭⠤⠤⠶⠟⠛⠛⠋⠉⠉⠈⠃⠛⣉⣀⢀⣙⣩⠽⠛⠛⠛⠛⢛⣫⠭⠉⠓⠋⠉⠒⠻⠧⠒⣒⠉⠁⠀⢀⣀⣱⠄
⠉⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠴⠖⠒⡋⠉⠅⠐⠊⠉⠀⠀⢉⣠⠴⠒⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⢸⣶⣶⢷⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠒⠀⠀⠀⢀⣠⡤⠤⠒⢈⠄⠙⠂⠀⠀⠀⠀⠀⠀⢀⡤⢮⣱⣎⡿⢟⣓⣿⠉⢀⣉⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠒⠒⠒⠒⠛⠛⠉⠁⠀⣠⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠐⠀⠂⠉⠰⠏⣥⠼⠃⠀⠉⠉⠁⠘⢋⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠐⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠⠐⠂⠐⠂⢄⠈⠢⠄⠂⠀⠈⠉⠉⠁⠀⠐⠠⠆⣀⡠⠐⠂⠐⠂⠄⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠐⠁⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡜⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⠀⠆⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⢰⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠠⠆⠉⠁⠢⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠁⢠⠄⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠘⠀⠀⠀⠀⡔⠀⢡⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠡⡀⠈⠢⢀⠀⠀⠀⢀⠠⠐⠀⢀⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠑⢄⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⢀⠠⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠈⠀⡄⢀⠀⠀⠉⠀⠈⠉⠀⠀⡀⠤⠂⠁⠀⠀⠀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠃⠀⠘⢦⠀⠡⡀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⣀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠂⠉⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⠀⠀⣀⠠⠐⠃⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⠂⢄⡀⠀⠀⣀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⢀⡤⠒⠋⠓⠒⢤⡀⠑⢄⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤⠒⠊⠑⠲⢤⠀⠑⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⢀⡜⠁⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠤⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢂⠀⠀⡌⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠀⢰⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠁⠹⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠌⠀⠀⢢⠈⠳⣄⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠉⠒⠤⠤⠴⠒⠋⡠⠔⠁⠀⠀⠀⠀⠈⠢⢈⠙⠒⠤⠤⠴⠚⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠐⠈

⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣶⠀⠀⠀⡀⢀⣀⡄⠀⢤⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡁⣘⠀⠘⣿⣿⡏⣀⣀⣿⡶⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠇⢾⢿⣇⠙⡀⢸⠏⠙⠁⠉⣿⠟⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠈⠻⣷⣶⣿⡇⠀⠀⠀⡿⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣴⢶⣿⣽⡇⠀⠀⠈⠉⠉⠀⠀⠀⣼⡇⠀⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⣋⠉⠉⠻⣾⣿⣿⣿⣧⡀⢀⣀⠀⠀⠂⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣠⣮⡾⢿⣿⠟⣀⣠⣾⣿⡟⢘⠫⠛⠛⠀⠐⠊
⠀⠀⠀⠀⠀⠀⡰⣿⡏⠟⣫⣿⣾⣿⠉⢻⣿⡇⢸⣶⣄⣀⡀⠀⠀⡄⡠
⠀⠀⠀⠀⠀⣸⣿⠟⠀⠀⠻⣿⣿⡏⠀⣾⣿⠀⢸⣿⣿⣿⣷⣶⣿⣾⢧⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣰⡇⣿⣿⡿⠁⣼⣿⠃⠀⢸⡟⣿⣿⣿⡟⣿⡇⠀⢱
⠀⠀⠀⠀⠸⣹⣿⣿⣿⡆⠈⠛⢁⡄⠙⠃⠀⠀⠀⣷⣼⣟⣿⠀⠹⣇⣠⡾⠀⠂
⠀⠀⠀⠀⢸⡟⠙⣿⠟⠇⢀⣴⣿⡿⠁⠀⠀⠀⠀⢨⣯⣽⡇⠀⠀⢸⣿⠖⠀⡆
⠀⠀⠀⠀⠘⣿⣾⣿⡄⣾⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⢶⡏⠀⠀⠀⠘⣯⣦⣤⡇
⠀⠀⠀⠀⠀⠈⠙⠛⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠒⠉⠁

⠀⠀⠀⢠⣄⣰⣆⣠⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣆⡠⠀⠀⠀⠀⠀⡄⣐⣰⣂⡀
⠀⠀⠀⣤⣿⣿⣿⣿⣤⠀⠀⠀⠠⣿⣿⣿⡧⠀⠀⠀⠀⠬⣿⣿⣿⡎⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⣽⣿⣿⣿⡧⠀⠀⠀⠐⣾⣿⣿⣿⡒
⠀⠀⠀⢠⠿⢿⡿⢯⠀⠀⠀⠀⠀⠹⠿⠟⠃⠀⠀⠀⠀⠈⠽⠿⠿⠓⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠐⢚⠿⡿⢟⠓⠀⠀⠀⠈⠝⢿⠿⠛⠌
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⢀⣴⣶⣶⣦⡀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⣄⣂⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣄⠀⠀⠀⠀⡄⣂⡐⢀⠄
⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⢾⣿⣿⣿⣿⡇⠀⠀⢀⢹⣿⣿⣿⡧⠄⠀⠀⠀⠠⣿⣿⡯⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⢒⢾⣿⣿⢀⡒
⠀⠀⠀⠻⣿⣿⣿⣿⠏⠀⠀⠀⠹⣿⣿⣿⡿⠁⠀⠀⠀⠚⡻⢿⠿⡓⠂⠀⠀⠀⠀⠋⠛⠑⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠁⠀⠀⠁⠆⡉⢁⠲⡌⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⢤⣰⣦⡆⡀⠀⠀⠀⡀⢦⣴⣤⠆⡀⠀⠀⠀⡀⢆⣶⣠⢄⠀⠀⠀⢀⡄⣴⣇⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣂⣅⡂⠄
⠀⠀⠀⣽⣿⣿⣿⣿⡥⠀⠀⠠⣽⣿⣿⣿⣿⠥⠀⠀⢠⢽⣿⣿⣿⡯⡄⠀⠀⣀⣻⠁⠀⠙⡟⠆⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠅⣾⣿⣿⣿⡎⠄
⠀⠀⠀⠚⣻⢿⣿⡟⠂⠀⠀⠀⠊⣻⢿⢿⡛⠂⠀⠀⠀⠊⡻⠿⢿⡓⠂⠀⠀⠈⣙⣷⢤⡞⠻⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠂⠝⠿⠿⠟⡔
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁
⠀⠀⠀⠠⡰⠘⠰⢢⠀⠀⠀⠀⢀⣠⣤⣆⡀⠀⠀⠀⠀⣠⣢⣖⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣷⣶⣄⠀⠀⠀⢀⠰⣀⣆⡐⢀
⠀⠀⠠⠅⢰⣿⣷⡄⠩⠀⠀⠀⢺⡏⠀⠈⣿⡂⠀⠀⢸⣹⠁⠀⠈⣳⡅⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠌⣿⣿⣿⣿⡅
⠀⠀⠀⢫⢌⠙⢋⠠⠑⠀⠀⠀⠙⠷⡦⣶⠟⠀⠀⠀⠘⢭⡷⢤⡴⡿⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠀⠀⠀⠐⢙⠿⠿⢟⠐
⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣵⣭⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣷⣿⣿⣾⣽⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⣾⡿⣿⡿⣻⠟⢿⣿⣽⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣶⡿⠿⢟⠛⢉⢥⣴⣻⡿⠻⢽⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⣿⡟⢡⣲⣾⣿⣮⣿⠟⠉⠁⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⣾⣟⡥⢙⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⣀⢻⣿⣿⣿⣿⣀⣤⡶⡾⠒⠄⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣧⡄
⠀⠀⠀⠀⠀⠀⡠⠂⣀⣤⣿⣿⠿⠀⢐⣾⣿⣿⡿⠟⠟⠉⢁⣀⣴⣀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠐⠉⠀⠀⠛⠉⢋⡀⣄⣶⣾⣿⣿⢯⠙⠐⠊⠉⠛⠿⢿⣿⣦⣀⣀⣠⣴⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢺⣿⣧⣧⣾⣿⣿⣿⣿⣿⡻⠆⠀⠀⣠⣴⣄⣻⣿⣿⣿⣿⠟⠋⠀⠋⠙⢻⠟⡁
⠀⠀⠀⠀⠀⣠⣶⣾⣿⣛⣛⣿⣯⣭⣿⠉⢂⠁⠀⣀⣸⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⢀⡤⣴⣾⠿
⠀⠀⠀⠀⠀⢻⡿⠿⢿⣿⣿⣿⡿⣯⡉⠉⠀⠀⢺⣿⣿⣿⣿⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠈⡁
⠀⠀⠀⢠⣶⣦⣄⡀⠀⠅⠑⠀⠀⢀⣠⡀⣀⣦⣾⣿⣿⡟⠎⠙⠻⠷⠀⠀⠀⠀⢀⣤⣶⡿⠃
⠀⠀⠀⣿⣿⣿⣿⣷⣢⣦⣿⣼⣷⣾⣿⣷⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⣀⣚⣫⠭⠁
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠓⢦⣠⡴⠖⠚⠛⣩⠟⠉⠛⠛⠲⠶⣯⡀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⡼⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣿⣯⣤⣤⣤⡤⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⠞⠁⣏⠀⠀⠀⣹⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢰⠃⠀⠀⠈⠙⠉⠉⠁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠸⡄⣀⠀⠀⢰⡀⠀⠀⢀⡄⠀⢀⡇⠀⠀⠀⢀⣴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⣙⠮⣕⣒⣚⣉⣉⣉⣁⣤⠴⠋⠀⣀⣠⠶⠋⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠉⠙⠒⠓⠲⠶⠶⡶⠶⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠰⣯⠀⠹⠟⢋⠆⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠹⣧⣠⠞⠁⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠶⠶⢶⣤⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠉⠛⢷⣤⡾⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⠶⠚⠛⠉⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⣼⠏⠀⠀⣀⣄⣀⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⣀⣀⡀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⡟⠀⢠⡞⠉⠉⠉⠛⢷⣄⠀⠀⠀⠀⠘⢷⡀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢀⡴⠞⠛⠛⠛⠻⢷⣦⠀⠀⠹⣇
⠀⠀⠀⠀⠀⣇⠀⣾⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠘⣷⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⣿
⠀⠀⠀⠀⠀⢿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣿⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣿⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣇⢻⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢠⡟⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⢿⡄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠙⣮⢷⣄⠀⠀⠀⠀⠀⣠⡟⠀⠀⣠⡿⢁⣰⠦⠤⣄⣀⣀⣘⣦⣀⣠⣤⣤⣾⣷⣼⣆⡀⠀⠀⠀⠀⠀⣀⣴⠟⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣷⣶⡤⠶⠾⠋⢀⣠⡾⠿⠚⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠈⠻⣿⣟⡶⠶⠶⠶⢟⣋⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⣠⣠⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⡁⣛⣀⣈⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠁⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣄⣀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢸⡟⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⡀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣶⣶⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⣿⣿⡟⠛⠻⠿⣿⡛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⣿⠃⢰⣿⡿⠀⠀⠀⠀⠀⠻⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢠⡇⠀⣿⣿⠁⠀⠀⠀⠀⠀⠈⡤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢸⣿⣅⡀⠀⠀⠀⠀⠀⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⢸⣿⣟⠀⠀⠀⠀⠈⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠠⡇⠀⢸⣿⣇⡀⠀⠀⠀⠀⣈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡇⠀⢸⣿⣿⣷⠯⠭⠀⠾⠛⣱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⢸⣿⣿⡆⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡇⠀⢸⣿⣿⡀⠀⠀⠀⠀⠐⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠁⠀⢸⣿⣿⠀⠀⠀⢀⣀⣀⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡆⠀⢸⣿⣧⠀⠀⠀⠈⣽⠋⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡦⠀⠸⣿⡏⠀⠀⠀⢠⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣷⠀⠀⣿⣿⡿⠒⠐⠋⣻⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⠀⠀⣿⣿⣷⡀⠀⠤⣿⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⣿⡆⠀⣿⣿⣿⡇⢤⣖⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠋⠙⠋⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢴⣤⠤⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠰⠐⢀⠄⣄⠄⠀⠘⡂⢻⠐⠀⠀⢸⡟⡗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠒⢢⠇⢀⠡⠀⡖⠀⠀⠐⣦⠀⢧⠀⠀⠀⠀⢹⡄⠛⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡿⣾⣿⣆⢸⣿⡂⠀⠀⡞⠀⢸⡆⠀⠀⠀⠈⢻⡀⠈⢂⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⡇⠀⠀⠀⠀⠘⢧⠀⠑⣷⡀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠉⠙⠛⠛⢛⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⡩⠀⣶⡶⠆⠀⢸⡆⠀⠀⢻⡄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠀⠉⠉⠉⠉⠉⢼⡀⠀⠀⢿⡄⠀⠀⠈⢻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣻⡇⠀⠀⢀⠀⠀⡀⠀⢀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠘⠻⠄⣤⣤⡤⢅⣙⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⢀⣼⡿⠀⡀⢀⠀⠄⠠⠣⢐⣾⡻⡏⠀⢤⡀⠀⠀⠀⠀⠀⠻⡦⠤⢤⠾⠬⠭⣽⣿⣦⡀⣀⡭⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡡⠤⠞⣿⢃⣤⠴⣶⠖⣲⠀⠐⠚⠛⢿⠃⣈⠶⠑⣀⣀⣀⡤⡀⢶⡇⡰⠃⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣄⣀⣀⣀⣿⡁⢀⠐⠼⠀⢸⠀⠀⠁⢀⡎⠠⠔⣞⡏⣿⠼⣻⣀⣀⣿⣾⣤⣶⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠛⣛⠻⠛⠟⠻⠛⠳⠤⠾⠶⠶⠶⠿⠷⠶⠺⣛⣛⠛⠭⢽⡿⠿⠿⠿⢟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣒⣂⣈⠀⠉⠈⠁⠉⠈⠁⠉⠈⠁⠀⠈⠉⡁⡀⠠⣤⣴⣷⣾⣿⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠈⠋⠉⠉⠉⠁