Sick Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣭⣛⡛⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⣿⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠷⢣⡖⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣏⠏⠉⠈⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠘⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡍⠿⣶⣅⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠈⢢⡀⠁⠈⠉⠻⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⢢⡀⠉⢲⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⠃⠀⠀⠈⣇⠙⢦⡀⠰⠧⡀
⠀⠀⠀⠀⠀⠀⠀⡰⢱⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠰⠁⣿⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡇⢯⠸⡀
⠀⠀⠀⠀⠀⢠⠃⢸⣿⠀⠀⠀⠀⠀⣸⣠⣀⣤⠖⡀⠈⡇⡇
⠀⠀⠀⠀⠀⡜⢠⣿⣿⠀⠀⠀⠀⢠⣭⣽⡧⠔⣹⠇⣠⡇⢇
⠀⠀⠀⠀⢀⡇⠘⢻⣿⠃⠀⠀⠀⠀⡿⠛⣞⣿⣵⡿⠁⢿⣾
⠀⠀⠀⠀⠘⡇⣦⢸⣿⡀⠀⠀⠀⢠⣇⠀⠀⣼⡯⠃⠀⢸⢻
⠀⠀⠀⠀⠀⣷⣿⡄⣿⠗⣉⡑⠛⢦⣹⠀⢠⣿⣷⡀⢀⣼⠆
⠀⠀⠀⠀⠀⡘⢻⣿⣿⣾⣯⠍⠙⢦⡻⠀⢸⡈⠓⠞⠒
⠀⠀⠀⠀⢀⡇⠀⠹⣿⣿⢹⡆⠀⠈⠁⠀⠈⡇
⠀⠀⠀⠀⠈⢧⣳⣤⣹⣿⣆⣇⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠄⠀⣶⣾⡆
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢂⠈⠻⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡇⠁⠀⠐⣦
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⠆⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⡻⢿⣿⣿⣧⣤⡙⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡳⣍⠀⠉⠙⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠋⠀⠀⠀⠀⠠⣤⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠟⠉⠈⠳⣄⠀⠀⠀⣠⠞⠛⠻⢿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⣷⣠⡾⠃⠀⠀⠀⠀⠈⠙⠛⠿⣷⣦⣄⣀
⠀⠀⠀⢀⣠⣤⣶⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢻⣶⠶⠤
⠀⠀⠋⠉⠉⢸⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⠤⠤⣿⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡷⠖⠒⠛⠉⠉⠹⣏⠉⣹⣍⣿⠟⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⣤⣼⣭⠿⠁⠀⠉⠉⠉⠉⠒⠒⣿
⠀⠀⠀⠀⠀⠸⣿⠀⢀⡠⠄⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⢹⣷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣿⣷⠀⠁⠀⠀⢠⠀⠀⠀⠀⠐⠲⣄⡀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⢀⣹⠀⠀⠀⠀⠀⠀⠀⢽⣠⡾⠁⠘⠷⣄⡀⠀⣮⠁⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣬⠇⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠈⠙⠛⠧⠤⠤⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠋⠉⠙⠻⣿⣿⣓⠾⣯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣈⣷⣮⣝⣷⢯⣝⡳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠉⠛⠻⢧⣍⣷⠮⣝⣓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣯⣙⢲⣭⣛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣮⣿⡒⢬⣝⡲⢤⣄⣀⣤⠶⠶⠶⢤⡀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢧⣽⣗⠮⣭⣀⣤⣶⠦⡄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠀⢿⣿⣷⢤⣿⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠻⠿⠿⠋⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠸⠀⠐⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⠠⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠋⠀⠀⠢⣦⡀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⠀⠀⠉⠢⡈⠲⣌⣦⡖⠠⢥⡒⠷⠠⠀⠀⠈⣶⠏⠀⠀⠀⠀⢁⠀⠁⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠡⠀⠀⠀⠀⣻⣋⠐⠓⢠⣐⠁⠈⠆⠀⠂⠀⡀⠻⠀⠀⠀⠀⠀⠘⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⢸⡁⠑⢌⡀⣈⠬⠘⠂⢬⠀⢀⡼⠀⠐⣇⠀⠀⠀⢸⡔⡀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠀⠌⢀⠄⡞⠀⠒⠀⠠⠤⠂⠀⠀⠊⠉⢀⠛⠀⠀⣤⠆⢀⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠤⠈⡔⢀⡀⠛⠀⠀⠀⠀⠀⠀⢀⠒⠂⠐⠁⠀⠡⡐⠈⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢷⠊⠉⠁⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠈⠐⠒⠒⣲⠚⣯⡀⠁⠱⠒⠁⠁⠺⠀⠂⠀⠀⠠⠠⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡔⠓⠒⠭⠧⡐⠀⠀⢃⣘⡀⢬⠈⠀⠀⠀⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⢀⣀⢪⠁⠀⠔⠢⠤⠅⠀⠈⠙⡛⠁⢘⣀⠤⡐⠐⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⠒⠚⠦⠤⠄⠓⠶⠤⣲⡄⢠⠄⠀⠄⠠⡤⣀⡉⠀⣀⣡⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠈⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠄⣰⡃⠠⠀⠉⠐⠺⡁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄⡀⠀⠀⠈⠸⡁⠈⠈⠀⠤⠆
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠈⢄⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠶⠖⠒⠒⠒⠛⠛⠛⠉⠉⠛⠛⠛⠓⠒⠒⠶⠤⢄⡀⢠⠞⠙⠲⣄
⠀⠀⠀⠀⠀⠀⢠⠏⠁⠉⢷⣠⠤⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⣀⠤⠒⡶⠀⢀⣀⡤⠶⠒⠛⠉⠉⠉⠉⣑⣲⠦⠈⠉⠀⣀⣀⡸⠇
⠀⠀⠀⠀⠀⠀⠸⠤⣀⠀⠈⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀⡴⠋⠁⠀⣼⠤⠚⠉⠀⠀⠀⠀⠀⢀⣤⣖⡋⠭⠄⣀⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢠⠃⣰⡀⠀⠀⠀⠀⢠⠋⠰⢃⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢀⠏⡘⠁⡇⠀⠀⡀⠀⡆⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠄⠀⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⡈⠰⠿⠿⢧⠀⠀⡁⠠⠁⠀⠀⠀⠀⠀⡠⠴⠒⠋⠉⠉⠉⠉⠁⠊⠁⠀⠀⠢⡀⠀⠁⠄⠀⠁⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣼⠀⠀⣘⡄⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡠⠔⠒⠒⢮⡓⠀⠰⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⢻⡆⡞⢁⢤⠀⠀⠀⠀⠠⡓⠀⠀⠀⠀⢠⠞⠁⠀⢀⠎⠀⠀⠀⠀⠀⠹⡄⠀⠱⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⡀⣿⣶⣾⣿⣿⡇⠙⠁⡏⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⠂⠀⠢⡎⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢧⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠇⣅⣠⣤⣤⣼⡇⠀⠘⠷⠒⠒⣚⢳⡀⢀⡇⠀⠀⠀⠀⠀⠀⣤⠚⡖⢤⣤⣀⡀⠀⠀⡟⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⡇⠀⢠⠖⠉⣉⣄⣈⡉⠉⠀⠀⠀⠀⠅⠀⠀⠈⣰⡇⠉⠁⠀⠈⢉⡾⠁⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⣦⣤⣶⣶⣶⡇⠀⣿⠀⠈⠙⠒⠚⠉⢀⠀⠀⠀⠀⠀⠀⠀⡾⠏⠙⠿⠶⠶⠚⣋⣀⡀⠀⠀⣸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡄⡏⠉⠉⠉⢉⡇⠀⠘⠳⠦⠤⠶⠒⠛⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⡀⠉⠀⠀⣹⠀⢀⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡁⣿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠉⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢳⣡⣤⣤⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠘⢀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠂⠦⠄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠸⣸⡏⢉⣉⣉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⠲⢄⡀⣀⣀⣤⡄⠀⠀⠒⠈⠁⠈⠒⠁⠀⠀⠀⠀⠐⠿⣿⣷⡖⠢⡄
⠀⠀⠀⠀⠀⠀⢣⢻⡿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠳⣄⠔⠀⢻⡠⠊⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠋⢳⣶⣿⠁⠀⠀⠀⠀⢀⡴⢢⠞⡿⢲⡆⣀⠀⠀⠘⠛⠀⡄⢣⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⣀⡤⠂⠉⠉⠈⠉⠉⢭⠉⠉⠓⠘⠢⠓⠊⠀⠁⠉⠉⠉⠉⠙⠛⠛⢆⣸⠀⡏⢳⣄⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⡀⠔⠋⠁⠀⠰⣖⠒⠀⡔⠁⢸⣤⠄⠤⠐⣦⡤⠤⠤⠤⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢆
⠀⠐⠉⠀⠀⠀⠰⠚⠉⠉⠣⠀⡀⠀⠰⠊⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠂⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠉⠑⠒⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡉⡆⠀⠀⠀⠀⠀⠚⠃⢂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⢴⡥⠤⢀⣀⠉⠀⠒⠒⠚⠋⡠⠒⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠄⡁⠒⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠉⠁⠉⢐⠉⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⣤⣀⣈⠤⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠿⠿⣿⣷⣤⢃⣔⣥⡶⠶⢄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢈⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⢦⡀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣴⣿⣿⣿⡟⣩⡦⠀⠈⣿⣿⣿⡏⢛⣿⣿⣦⡙⠂
⠐⡀⠂⠠⠀⠂⠉⠀⠀⢸⢫⣾⣿⢃⠹⠠⢁⣀⠀⢸⡟⢸⠇⣀⠛⡜⢿⣿⡍⠒⠢⢄⡀
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠈⠀⠴⣟⠫⠥⡀⠀⠀⠘⠿⣷⠀⠈⣿⣿⡄⠀⠀⠈⠑⠢⢄
⠀⠀⠙⡦⠀⠀⠀⠀⢀⠀⣿⣿⡇⠀⠀⢰⠁⠠⠀⡀⠀⢀⡀⠘⠈⠀⢠⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⣸⠃⠀⠀⠀⢊⢊⠴⡿⢿⠃⠀⠀⠸⡀⠀⠈⠁⣀⠈⢀⡜⠀⠀⣼⣿⣏⠈⡀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⢠⡏⠀⠀⠀⠀⢠⠏⠀⢢⣄⠀⠀⠀⠀⠒⠛⠁⢤⡠⠟⠛⠈⠀⠀⢻⣭⢌⢧⢙⠀⠀⠀⠀⣰⠀⠀⣷
⠀⣸⠁⠀⠀⠀⠀⠘⣆⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡼⠋⢊⡞⠀⠀⠀⠀⢠⡏⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠈⠲⠶⠾⢧⣀⣀⠀⡴⠖⠒⠒⠚⢁⣀⡤⠖⠿⠤⠶⠋⠀⠀⠀⠀⢀⣿⠁⠀⢀⡇
⠀⣷⠀⠀⠀⠀⠀⠀⢀⣠⣐⠤⠑⣂⡥⠾⢶⣶⠂⢠⠞⠛⢿⣿⠀⠐⠢⢄⡀⠀⠀⠀⠀⢌⠆⠀⠀⢸⠃
⠀⣿⠀⠀⠀⠀⠀⠸⠶⡋⠄⠂⠁⡳⠂⣸⣦⡁⢠⣮⣶⠒⠒⢃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢀⡟
⠀⢻⡀⠀⠀⠀⠀⠀⣁⠀⠀⡠⢊⠝⣼⣿⠃⣿⡟⠸⣿⡆⠠⡀⠳⡀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⡾⠁
⠀⠘⣇⠀⢀⠂⢁⡎⠀⠈⠈⣀⡏⣼⣿⡏⢠⣿⣧⠀⢻⣿⡀⢱⡀⠘⣦⠀⠀⠀⠀⢠⠁⠀⢀⡾⠁
⠀⣀⠿⠶⠺⡀⠈⣇⠀⣆⠀⡏⠉⠉⠉⠓⠺⠿⢟⠒⠉⠉⠉⠉⠉⠑⠚⠢⢤⣀⠀⠘⠀⢠⡟⠁
⠈⠀⠀⠀⠀⠉⠒⠉⠐⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣴⠏
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⡀⠀⠀⢀⠀⠀⢀⣀⣀⠀⡀⡀⠀⡀⠀⠀⠀⣀⣀⡠⠤⠤⠴⠖⠒⠒⠒⠒⠛⠛⠋⠉⠙⠛⠛⠒⠒⠒⢶⠤⣤⣀⣀⣤⠞⠉⣲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⢳⣀⡠⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⣀⡤⠔⡶⠀⠀⢀⣠⠤⠶⠒⠚⠛⠉⠉⠛⢒⣢⣤⠈⠉⠀⡀⣀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⡴⠚⠁⠀⣼⡡⠖⠛⠉⠀⠀⠀⠀⠀⢀⣤⣖⣛⣉⣁⣀⠀⠀⠀⢫⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⡀⠀⠀⠀⠀⠀⡴⠋⡽⢀⡴⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⣴⠚⠋⠁⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⠋⣇⠀⠀⠀⠀⢸⠃⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⡠⠽⠆⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⣿⣶⣿⠀⠀⡗⢄⣿⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠒⠒⠒⠢⠤⠞⠉⠉⢤⣀⠁⠙⣇⡠⠜⠃⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠇⡏⣈⣉⣹⡆⠀⠹⣄⠁⠀⠀⠀⢀⠄⠊⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣤⡤⣍⡳⢄⠈⢂⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣸⣿⠿⠿⢿⡇⢰⠖⢉⡀⠀⠀⠀⠉⣐⡄⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁⠀⠀⠀⠙⣆⠀⠈⢆⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⡏⣯⣤⣤⣤⣼⡇⢸⡴⢹⠃⠀⠀⠀⠀⠙⣦⠀⠀⠀⠠⠚⣡⢤⣄⣰⠃⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⡆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠛⠛⠛⠛⡇⠀⠀⣿⣀⣀⣀⣤⡀⠀⢸⡇⠀⠀⠀⡞⠁⠀⠈⢻⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢷⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⢼⣿⣿⣿⣿⣿⡇⠀⠀⢈⣩⠤⠤⠤⠷⠤⣼⠁⠀⠀⠰⡧⠖⠚⠿⠁⡏⠹⡿⠒⠶⠤⣄⣸⠃⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣸⡁⠀⠀⣀⢀⣧⠀⢠⠏⠀⡠⣖⣒⣦⠄⠀⠀⠀⠀⠀⠳⣄⠀⣀⣴⢷⣄⣀⣀⣀⣠⡼⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⡿⠿⣿⠀⢸⣄⠀⠀⠈⠉⣀⣀⢤⡀⠀⠀⠀⠀⠘⠛⠛⠉⠀⢉⠙⠉⡉⠥⠤⠦⣄⠀⠀⡟⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⢸⣼⣇⣀⣀⣄⣀⣿⠀⠀⠉⠙⠛⠛⠉⠉⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢁⣝⠐⣠⡀⠀⣀⣠⠟⠀⢰⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡏⡿⠟⠿⠟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⡇⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⢷⢿⣶⣶⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠐⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠾⣿⣿⡶⣶⣤⣤⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡼⣏⣉⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠈⠓⢦⣀⣀⠤⢤⣴⠒⠚⠋⠉⠁⠀⠉⠉⠁⠀⠈⠈⠉⠛⠻⢿⣿⣟⡛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢳⢻⡿⠿⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠈⠳⣤⠖⠁⢹⣤⠊⠉⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢳⣾⣿⡇⠀⠀⣀⣀⣀⣠⠖⣶⢻⠗⣲⣇⣀⣀⣀⠈⠛⠃⢰⢸⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⠉⠉⠉⠉⢉⠽⡍⠉⠙⠒⠓⠼⠲⠋⠀⠀⠀⠉⠉⠉⠉⠛⠛⢶⣀⣇⣸⣉⣦⣀⣀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠰⣦⠒⡒⡤⠊⠀⣧⡤⢤⠤⢲⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣞
⠀⠀⠀⠐⠉⠀⠀⣀⠤⠖⠛⠉⠣⡙⡄⠀⠈⠖⠁⠂⠀⢀⡥⠄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠓⠒⠦⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠙⢃⠈⠀⠈⠀⠀⡠⠚⠁⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⣀⡀⠀⠀⢀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣊⣀⠀⠉⠘⠒⠀⠤⠦⠚⠒⡠⠖⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠤⣈⠒⠠⢽⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠉⠉⠉⠓⠒⠒⠢⡔⠋⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⣄⣀⡀⠀⠀⠃⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠐⠂⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⠶⣦
⠀⠚⠛⠛⠙⠋⠛⠛⠒⠲⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡒⠒⠲⠦⣄
⠀⠀⠀⠀⠲⣄⠀⠀⠀⢀⣀⣠⡤⣤⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⢊⣁⣀⣀⣀⡀⠈⣷
⠀⠀⠀⣀⡀⠈⠳⣀⡔⢉⡥⠾⠁⠉⠳⡄⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠈⠩⡝⠷⠖⢛⠲⡘⣧
⠀⠉⠙⠲⠭⣷⡀⣿⣶⢩⡀⠀⠄⠀⢨⣿⡀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢠⣤⠐⠻⠴⠚⡆⣹⠃⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣯⣴⠗⠀⠉⠁⢀⣃⢱⠀⠹⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠉⠀⠀⢀⡴⢣⢿⡇⠀⢸⣇
⠀⠀⠀⠀⠀⢠⣾⣿⣏⣿⣄⡀⠀⠀⠙⢛⣼⣷⡆⠘⠊⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠂⣀⣼⡁⢺⣿⣷⠿⠛⣀⣙⠲⣄
⠀⠀⠀⠀⠀⠘⠛⣿⣿⣟⣷⢦⡀⠀⠀⢾⣿⣿⣖⣦⡀⣠⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣻⠁⢸⠙⡾⠀⠀⡴⠋⠁⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠉⡽⠟⠋⢍⡳⠤⣀⠀⠀⠶⢿⣿⠗⠒⠒⠛⡓⠲⢤⣀⠀⠀⠀⠀⢀⡇⢹⡀⠸⣴⠃⠀⣼⣁⣀⣤⠭⠥⠄⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠖⠿⠦⠙⠦⠜⠛⠛⣛⡿⠚⠛⠋⠋⠉⠉⠓⢤⡈⠑⠲⠤⣠⡏⠀⠘⡇⢀⡩⠖⠻⢄⡀⠀⠀⠀⢀⡴⠃⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢦⣤⣄⢀⡔⠋⠉⠉⠁⠴⠒⠒⠛⠛⠒⠋⠉⠁⠈⠲⣄⠀⠀⠉⠙⠒⠿⠉⠀⠀⠀⢀⣉⠦⡀⢀⡾⠁⠀⠀⠀⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣤⠤⠖⠚⠉⠈⠙⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠠⣤⣤⣼⡟⠛⠛⠉⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⠈⠉⣿⠠⠤⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇⠀⠤⢤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠻⢂⡀⠀⠀⠀⠀⠒⠢⠄⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠋⠁⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠈⠀⠁⠐⠀⠀⠀⣤⡄⠀⠀⠿⠋⢙⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡄⠀⠀⢰⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢋⣁⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⣶⡦⠀⠀⠻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠂⠀⠠⠶⠀⠀⢀⣼⠃⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠉⠛⠻⣿⣿⣿
⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣒⠭⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣫⠕⡊⠁⠀⠀⠀⣀⣤⡼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⢀⡩⠖⠉⠀⢈⡠⣔⠿⠋⠁⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⡚⠉⢀⡤⠞⠉⠀⢀⣤⡾⠝⠊⠁⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⣀⠴⣊⠵⢊⠤⠚⡉⠔⣀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⢠⠖⠛⢲⡄⠘⢦
⠀⠀⢠⡊⠁⠈⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡴⡿⠀⠈⠳⣄
⠀⠀⠀⠱⣄⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⢀⠤⠤⠤⣤⠤⠤⣤⠖⣾⠻⣗⡋⠁⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠈⠳⣖⠕⠉⠀⠀⠀⠀⠀⠀⡏⠐⠒⠲⢼⠆⠀⣯⠀⢿⢀⡿⢀⠵⡒⠒⣦⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢀⡴⡟⠶⣶⠚⡿⢻⢉⡹⡗⠛⡿⢥⣯⣀⣬⠖⣻⣀⣀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢾⢧⠈⢦⢸⡇⢷⠘⣯⣀⡿⠀⡼⣋⣉⣙⣶⠊⣹⠉⠉⠙⡆⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠘⢮⣛⣶⠟⣡⡎⠛⢞⢯⣠⠶⣷⣶⣖⣻⠟⠀⢿⣒⣖⣺⠇⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⢳⣙⠲⢤⣞⠻⡶⣄⠻⣍⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⡸⡋⠉⠀⣹⠈⠺⠶⠋⠀⢠⠤⠤⣄⠀⠀⠀⠀⢀⣄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠱⣌⣓⣲⠟⠀⠀⠀⠀⢠⣇⣀⣀⣼⠀⠀⠀⣪⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⢀⡔⢻⠓⣆⠀⠛⠻⠛⠃⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢸⣄⣸⣠⣾⠀⠀⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠈⠛⠛⠛⠁⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⢃⣤⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡴⢁⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⢸⠅⠘⡻⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⣉⣧
⠀⠀⠀⠀⠀⠀⡔⠁⣴⠋⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠂⠀⠝⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⢣⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠐⣠⠞⠡⠂⠁⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⢠⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠐⠢⠜⠋
⠀⠀⠀⠀⣠⣾⡫⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⡠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⡛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣡⠄⠊⣀⡀
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠙⠘⠁⣟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⢿⣷⡴
⠀⠀⠀⠈⣆⡀⠸⢰⠄⢸⠂⣃⡈⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡀⣠⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⠿⠀⠀⣼⢧⡀
⠀⠀⠀⠀⠀⠑⠀⠍⠀⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠁⣟⡄⠀⠀⠀⠀⠀⠀⠰⡇⠠⠈⠓⢬⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢤⠀⠒⢀⡧⠄⠀⠀⠀⠀⠀⠀⠀⠁⢢⣠⠇⠐⣾⠿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣀⡠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣀⢠⠀⠀⠀⠐⠄
⠀⠀⠀⠠⡄⠄⠽⠞⠛⠒⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⣷⢉⣹⣿⣄⣌⢠⣤⡇⠀⠀⠀⠀⠀⣴⠁⠀⠄⠂⠀⠐⠂⠀⠠
⠀⠀⠀⠀⠁⢠⡖⣤⣀⢢⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⣟⠃⠀⢽⡄⠀⠈⠁⠀⠀⠀⠀⠀⠁⢴⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠆⠈⠈⢙⣏⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠔⠐⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢤⡄⣁⡀⠀⠂⠃⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡧⠤⢤⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣤
⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⣂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣾⡅
⠀⠀⠈⠀⠀⠸⡇⠄⢀⠰⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣆⢰⡌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣴⠿⢿⣤
⠀⠀⠀⠀⠀⢠⡇⠀⠨⠄⢻⠄⠀⠀⠃⠀⠀⠀⠀⠀⠀⡸⠛⢠⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⠁⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⢥⣝⣀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⢰⣶⣛⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⢤⡤⠾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠄⢀
⠀⠀⠀⠀⡠⠈⠁⠁⣀⣠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡄⠀⠀⠐⢢
⠀⠀⠀⠀⣇⣈⡤⠞⠋⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣾⣿⣦⣤⣦⣼⣤⣶⢴⡆
⠀⠀⠀⠀⣿⠃⠀⠐⠀⠠⣶⡏⠀⠀⠀⠀⠀⠀⠀⢈⠛⠀⠊⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠤⠲⣦⣀⡟⠒⠒⠿⣶⣦⠉
⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠆⠀⠐⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠉⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⣷⣶⣟⡛⣿⣿⣿⣇⠀⢰⣤⣴⡶⢠⣤⣤⡄
⠀⠀⠀⠀⣿⣿⣿⡿⠿⣿⣿⡿⠀⠘⠉⣿⠁⣿⣚⣿⠃⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣿⣿⣿⣤⡖⣟⣟⠋⠀⠀⠀⠏⠘⠱⠿⠏⠀⡿⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⣦⣦⣵⣦⡀
⠀⠀⠀⠀⣿⣿⣿⣿⡉⢸⣿⡁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠉⢹⠟⣿⣾⣿⣟⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣧⣸⣿⣗⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣱⣘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣼⣿⣷⡇⣿⢢⣿⣿⣿⣿⡗
⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⠀⢸⠇⠀⠀⠀⠀⢺⡗⢰⢿⡅⣋⠀⠸⣿⡄⣀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡆⠀⠀⠀⠈⢹⣿⣿⣿⣗⠈⢻⣿⣿⣿⣿⣿⣷⠀⠀⣿⣍⠀⠀⠀⠀⠀⠈⠙⠿⠟⢀⡀⠙⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⢁⡀⠀⠀⢰⠛⠻⠿⠿⠛⠀⢠⡏⠈⣿⣿⣿⣿⡆⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⡘⠛⠂⣀⠀⡀⠀⠀⢰⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣷⡄⢸⣼⣿⣦⣶⣾⣶⣬⣅⡴⢻⣿⣿⣿⣿⠟⠛⠛⠂⠀⠀⠀⠀⠀⠀⠁⠀⣇⣄⠚⠁⠻⣿⡆⠀⣼⣧
⠀⠀⠀⠐⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣾⣿⣿⣿⣿⣿⣿⣯⠀⣴⣁⡽⢛⣩⣠⡠⠆⠀⢢⠀⠀⠀⢰⡆⠀⠐⠉⢉⣭⣤⣶⣿⡿⠇⢰⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣇⣤⡄⠀⠀⠉⠙⠛⠿⣯⡇⣿⣙⣯⠘⢃⣴⣶⣤⡐⠒⢦⠀⡁⣀⢀⠀⠈⢥⠀⢻⣿⠁⢠⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⠃⠒⣽⣼⣿⣿⣿⡿⠀⠀⣀⣀⣀⣶⣿⠛⠉⠉⠈⡃⣿⣿⣿⡟⢀⡀⠀⠀⣧⠙⣿⣦⣾⡏⠀⣾⠃⢀⣾⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠋⠉⢰⣵⣿⣻⣿⣿⣿⣇⢠⣿⣿⣿⣿⣧⣤⣷⣶⣾⡿⢿⠍⠛⠋⠉⠛⠀⣀⣤⣿⣼⣿⣿⣿⠃⣸⣃⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠿⠿⠿⢿⣿⣟⠀⣦⡀⣼⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⢧⣿⠃⣠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣲⣶⣶⣶⣶⠆⠀⠀⠏⠐⣿⣿⣿⣿⣿⡿⣿⣿⣿⡄⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠈⠿⣿⣿⣿⣿⣾⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠋⢉⣩⣥⠀⠀⠀⠀⣶⣤⣽⣿⢿⣿⣿⡇⣿⣿⣿⣿⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣴⣿⡿⢿⠿⢿⣿⣿⣿⣿⣿
⠀⣤⣿⣿⡇⠀⠀⠀⠀⠹⣿⣧⠁⢾⣿⣿⡇⣿⣿⣿⣿⣿⣄⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠟⠟⠿⠿⢫⣿⡟⠰⢞⣿⣿⣿⣿⡿
⢸⣿⢿⣿⣷⣶⣶⣴⣶⣶⣿⣿⣦⣾⡿⠛⢁⣿⣇⣼⣿⣿⠅⣿⠀⢻⣯⢹⣿⣿⡿⠿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣧⣤⠶⠶⠶⣿⡟⢳⣾⣿⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠉⠉⠀⠘⠙⠛⠛⠁⠀⠀⠁⠉⠛⠛⠓⢾⣿⣿⣿⣧⣾⣷⣄⠙⣿⣿⣿⣿⣿⣿⣿⠷⠆⠐⣉⡤⠞⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠿⠿⠿⠷⠼⠟⠉⠁⠀⠀⠀⠀⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠔⡃⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠉⡱⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰
⠀⠀⠀⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠖⠀⠀⠀⠀⠀⠄⢢⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⡁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⣿⣿⣿⣿⡇⢀⣀⣀⣀⠀⠀⣀⣀⣄⠀⠉
⠀⠀⠀⠀⠀⣠⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⣿⠀⠀⢰⣿⣿⣿⣿⢠⣿⣿⡿⡿⠀⠀⠀⢀⣴⠿⠂
⠀⠀⠀⠀⠀⣿⠿⠀⢿⣿⣿⣤⣤⣀⠀⠀⣿⣿⡇⢸⣿⣿⣶⣿⣿⣿⠇⣿⣿⣷⠆⢻⣿⣿⡁⠀⠈⢿⣿⣶⣤⣄⡀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⢀⠈⠉⢹⣿⣿⣷⡀⣿⣿⡇⢸⣿⣿⢿⣿⡏⠁⠀⣿⣿⡇⠀⠀⠙⢿⣿⣶⡄⠀⠉⠉⠛⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⣿⣿⣿⠃⣿⣿⡇⢸⣿⣿⠘⣿⣿⡄⠀⣿⣿⣷⣶⣶⡄⠈⢿⣿⣿⣠⣶⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁⠀⠙⢿⡇⢸⣿⣿⠀⠸⣿⣿⣦⣈⣉⣉⣉⣉⣁⣤⣿⣿⣿⢻⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠦⣤
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠘⠙⡀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣶⣶⡶⠀⠀⢀⠄⠀⡤⠀⠀⠀⠀⠀⠀⠀⣸⣤⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠁⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⣽⡿⠇⠀⠀⠀⠀⡀⠀⠀⠔⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣸⡏⢹⡛⠛⠻⡟⠶⠶⢶⠶⠶⠶⡶⠶⠶⣶⠶⠶⢲⡖⠞⠻⡟⠋⢻⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣇⣀⣇⠀⢘⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⠀⢸⡇⠀⢘⡇⠀⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⣙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠈⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣸⠇⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠛⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠟⠀⠀⠀⠀⢸⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⡀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡍⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢹⡟⠀⢸⡏⠀⠀⠀⢸⡀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⠸⠷⣤⣤⠶⠾⠷⠶⠶⠶⠋
⠀⠀⠀⠀⢠⡴⠶⠶⠶⣶⠶⣤⣤⣈⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣴⠶⠲⢶⣄⡀
⠀⠀⠀⠀⣿⠀⠀⠀⢰⠃⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉⠀⠈⣿⣄⠀⣠⠞⠛⢶⣄
⠀⠀⠀⠀⠙⢷⣄⣀⣸⣄⠀⠀⠀⣀⡾⠃⢀⡀⠀⢰⡟⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠉⠳⣄⣴⠟⠙⢷⣇⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣛⣯⡶⠛⠋⠙⢷⡈⠻⣄⠀⣠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢸⡅⠀⠀⢀⣴⠟⠁⠀⠀⠀⠙⠷⣤⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠳⡄⠀⢀⣼⠇⠀⠈⠻⣧⡀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⠶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⣀⣿⠶⠟⠁⠀⠀⠀⠀⠈⠻⣦⣀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠈

⠀⠀⠀⣶⡶⠀⠀⠀⠀⣰⣶⢄⠀⠀⠀⢠⣶⡀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⣠⣶⢆⡀⠀⠀⠀⣴⣦⡀
⠀⠀⢰⣿⣿⡆⠀⠀⢰⣿⣿⠚⠂⠀⠀⣿⣿⠛⠂⠀⠀⣾⣿⡟⠃⠀⠀⢺⣿⣿⠓⠀⠀⠀⠿⣿⡿⠃⠀⠀⢸⣿⣿⠛
⠀⠀⢻⣿⣿⡗⠀⠀⢀⣿⣿⡄⠀⠀⢸⣿⣿⡆⠀⠀⠀⣿⣿⣇⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⣸⣿⣧⠀⠀⠀⢼⣿⣿⡀
⠀⠀⠈⣿⣿⠁⠀⠀⠈⣿⣿⠁⠀⠀⠀⢹⣿⠁⠀⠀⠀⢹⣿⡏⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠩⣿⡏⠀⠀⠀⠈⣿⣿⠁
⠀⠀⠀⠛⠛⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣤⡀
⠀⠀⠀⣴⣯⡿⠃⠀⠀⣿⣯⡀⠀⠀⠀⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣯⡀⠀⠀⠀⣼⣿⡅⠀⠀⢸⣿⣧
⠀⠀⢀⣿⣿⢧⡀⠀⠀⢳⣿⠁⠀⠀⣠⣾⣿⡀⠀⠀⢀⣤⣤⣾⣿⣶⠀⠀⣸⣿⡏⠙⠦⠀⠀⣿⣿⡇⠀⠀⢸⣿⣟
⠀⠀⠛⢻⡇⠀⠀⠀⠀⢿⡿⣆⠀⠠⡿⠿⢿⡇⠀⠀⠺⠿⠿⣿⠁⠀⠀⠀⢻⡿⡇⠀⠀⠀⠘⣿⣿⠃⠀⠀⠺⣿⡿
⠀⠀⠀⠸⡇⠀⠀⠀⠠⡞⠁⢻⠄⠀⠃⠐⠌⡧⠀⠀⠘⠀⠐⠻⠀⠀⠀⠀⢸⠇⡷⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⡿⡇

⠀⠀⠀⣶⣦⠀⠀⠀⠀⣠⣴⣆⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⣴⡦⠀⠀⠀⠀⢀⣠⣶⠀⠀⠀⢀⣴⣦⠀⠀⠀⢀⣾⣇
⠀⠀⢰⣿⣿⠇⠀⠀⢰⣿⡿⡇⠀⠀⠀⣼⣿⣿⠀⠀⠀⣞⣿⣿⣳⠄⠀⠀⣻⣿⣷⠀⠀⠀⠸⣿⣿⠇⠀⠀⠈⣿⣟
⠀⠀⢸⣿⣿⡄⠀⠀⢸⣿⣧⡙⠂⠀⠀⣿⣿⣏⠀⠀⠀⢨⣿⣿⡅⠀⠀⠈⣿⣿⡄⠀⠀⠀⢠⣿⣿⡄⠀⠀⢰⣿⣿⡄
⠀⠀⠀⣿⣿⠀⠀⠀⢈⡏⢹⡅⠀⠀⠀⢩⡏⣿⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣾⠈⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠉⠉⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣖⢲⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡐⠟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣎⣭⡛⠫⠭⠙⠉⠒⢄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠹⣆⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠉⠛⠢⢄⠠⣴⣵⡄
⠀⠀⠀⠀⠀⢸⡷⠲⠶⢶⠒⣿⠀⠀⠀⣀⣹⣄⠀⠀⠘⡿⠿⠿⠿⠶⣶⡶⠶⣤⣧⣀⡏⠉⠁⠒⢲⠀⠈⡆⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣧⣀⣠⣸⠀⢋⡄⠀⣾⡟⠙⠻⣇⣀⣴⠗⣤⠀⠀⢀⣀⣈⣲⡀⠈⣿⣿⠀⠀⠀⢸⠀⠀⡇⣿⣿⡇
⠀⠀⠀⢠⡞⠉⠛⠾⠭⠭⠷⣿⠙⠓⠛⢻⡷⢾⠿⠿⣥⣾⣷⣤⡤⠴⠿⠿⠿⣿⣿⡿⠋⠀⠀⠀⢸⠀⠀⣟⣿⣿⡇
⠀⠀⠀⢸⠉⠓⠒⠒⠀⠐⢺⣿⣿⠛⠉⢹⡇⣧⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡇⢀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇
⠀⠀⠀⢸⠀⡖⠲⠤⠤⠤⠞⣿⣻⡶⠶⣾⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠈⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣤⣿⡛⣉⣃⡨⡳⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣃⡉⠉⠀⢀⣲⡄⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⣼⣽⣿⣷⣿⣿⣯⠨⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⠁⡇⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡟⠻⠿⠿⠿⠿⠿⠂⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⡓⣒⣒⣛⣩⡵⡀⠀⠀⢸⢿⣿⣇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⠀⠰⢤⡰⡶⠶⠀⢸⣷⢄⣀⠀⠀⠀⠀⠀⢀⣷⢤⣄⣈⣉⣉⣁⣤⢴⡟⠋⠉⠙⠛⠻⠷⢤⣄⣀⡀
⠀⠀⠀⢸⠀⠧⢄⣀⣀⡇⠀⣴⠋⠀⠈⢲⠄⠀⣿⣿⠟⠻⠿⠿⠿⠿⠓⡏⠙⠓⠒⠶⠒⠒⠊⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢓
⠀⠀⠀⠘⠦⣄⣀⣀⣀⡇⠀⣈⡳⣤⡔⣁⠀⠀⣿⡟⠀⠠⡤⠒⠚⢿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠈⠉⠉⠉⠉⢀⣠⡟⠧⢤⣀⣷⣷⡶⡟⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣤⡴⠊⠁⠀⢀⡤
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣿⠿⠿⣿⣿⣿⠇⢿⠇⡀⠀⣠⣯⣧⠤⠂⡼⣿⠢⢤⣄⣀⣀⣠⠤⠖⢻⠿⣿⣿⣿⣿⣿⠀⢀⡤⠞⠉
⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠒⠊⠁⠘⠿⠾⠉⠉⡟⠒⠚⠋⢻⡀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠉⠉⠛⠻⠖⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠼⣧⣤⠴⠠⡄⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠚⠋⠁
⠀⠀⠀⣿⠤⠤⠤⠀⠐⠒⠒⠒⠒⠂⠉⢻⠀⠘⠶⠒⠊⠉⠁
⠀⠀⠀⠹⠴⠶⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠉⠉⠙⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣶⣶⣖⣒⣻⣭⣝⣒⡲⢽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢼⠉⠙⠛⠓⠒⠒⠒⠒⠒⣯⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡜⠀⡠⠞⠀⠀⠀⠳⠤⠀⢣⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣿⠁⢀⡤⠤⡄⠀⢠⠤⢤⡀⠈⣿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠸⣀⣂⡽⠀⢯⣐⣀⠇⠀⣿⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⡇⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠀⢸⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢳⣀⡼⠁⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⡜⠀⢳⡀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⣀⡠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠉⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡤⠀⠤⠖⠀⠀⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⢀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡐⠀⠑⠄⡀⠉⢉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠤⠤⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠤⠀⠠⠤⠤⠤⠤⠀⢀
⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠠⠄⠐⠂⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⡆⠀⠀⠀⠀⠈⢀⡀⠠⠀⢂⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠐⠂⠆⡓⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠠⠼⠤⠄⠀⠒⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⢄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠄⠀⠀⠀⠀⠀⡀⠼⠄⠈⠁⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⢊⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠒⠈⠀⠀⠠⠀⠀⠁⠀⠄⠀⣀⠀⠀⠀⠐⠆⠤⠀⠀⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠤⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠢
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⠒⠤⢤⡀⠀⣀⣀⣰⡿⢯⡙⠃⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠞⠀⠀⠀⠁⠀⡀⠀⠈⠜⢇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠉⡆⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⢀⠃⠀⢠⡇⡟⠁⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⡴⠫⣤⣤⡀⠀⠀⠀⡎⠀⠀⣸⠁⠩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠩⠀⠀⠈⠁⠂⢀⣀⣼⡄⠀⠒⠋⠀⠀⠈⠁⡄⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠑⠀⠀⠀⠁⠀⢀⡰⣄⠀⣀⡔⣇⠀⠀⠀⠈⠀⡐
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡤⠈⠁⢏⠲⢶⡶⠸⢇⠀⣀⡀⠀⠸⠋⠙⠉⠀⡞⠓⠀⠣⠔⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡁⠀⢀⣨⡷⡾⠀⠀⠀⢢⡿⠿⠶⣾⣦⣶⠖⠛⠛⠂⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠢⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠧⣤⠼⠷⣶⣿⡏⠀⠈⢤⠞
⠀⠀⠀⡀⣠⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣾⣶⣿⢶⡄⠀⠈⠓⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⢻⠀⠒⠀⠄⠤⠄⠑⠒⠊⠘⠉⡉⠹⣭⣠⡦⠴⠉⠒⠈⠓⠀⠈⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡨⠀⣠⡆⠀⠀⠂⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠖
⠀⠀⠀⡠⠄⠀⠀⠐⢾⣆⠀⠀⠀⠀⠀⠀⡘⠁⠀⠃⠁⠀⠀⠈⣀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠠⠊⠀⢄⠀⠈
⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠜⠋⠔⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⣸⠶⠞⠋⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢧⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⠧⠔⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⣀⣀⠀⠀⠀⢈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢉⠒⠶⢤⣄⠀⢠⣀⣤⡼⠟⠿⣄⡉⠇⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠿⢷⣶⡾⠀⠀⠀⠀⠁⠈⠂⠀⠀⠘⡄⢯⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠒⣄⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⠀⣿⢱⡖⠁⠀⠀⠁⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡏⠘⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⣠⠞⠑⠒⢻⡷⠆⠀⠀⠀⠀⡼⠀⠀⢀⣼⠇⠀⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠛⠋⠀⠃⠀⠁⡀⢀⠈⠀⢢⣤⡾⣧⠀⠈⠉⠁⠀⢀⠐⠀⠀⣾⠀⠁⠀⠀⢀⣤⠆⢤
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣤⠄⠀⠀⠈⠦⠀⠀⢀⠁⡀⠀⠀⠑⣔⡁⠀⣀⡔⣇⠀⠀⠀⠀⠈⠁⠀⡐
⠀⠀⠀⠐⠀⠤⠀⠀⣶⠀⠀⠀⠀⠀⣔⢀⠐⠛⢹⡗⢤⣤⣤⡅⣳⡆⠀⡀⠀⠀⠀⢸⡟⠛⠛⠉⠁⣤⠿⠦⡀⢇⣤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢽⠋⠀⠀⠀⢹⣀⣬⠋⠀⠀⠙⡄⢸⣿⣦⣀⢰⣅⣀⣀⣠⣴⡿⣌⠑⠂
⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⢀⡀⠀⠀⠘⢦⣄⣡⣤⡾⠟⠛⠀⠀⠀⠀⠨⣿⠋⠉⠉⢿⣿⣿⣯⣁⠀⠘⡌⠑⢀⡀
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡙⢲⡖⠚⠛⢿⣿⣿⡇⠄⠀⠑⠼⡁⠀⠀⠢
⠀⠈⠀⠀⢀⢠⠭⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⢴⠀⠀⠀⣀⣾⣷⢚⡿⢶⣄⠀⠀⠈⠓⡄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⠁⠀⠘⢿⠀⠲⠆⢀⣀⣀⣠⠑⠦⠤⠜⢰⠛⢙⠛⢻⣹⢀⣠⣤⣤⠛⠠⠄⠙⠦⠤⠐⢁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⡀⠘⠀⠀⠀⠀⠀⠈⢡⠀⠀⢠⡄⠀⠀⢸⠀⠰⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠀⠤⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢠⠞⡇⠀⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢑⡤⠋⠁⠀⠀⡀⠐
⠀⠀⠀⣀⠜⠂⠀⠀⠀⠈⠿⠷⡀⠀⠀⠀⠀⠀⠀⢀⠜⠰⠀⢈⠀⠀⠀⠀⠀⢠⣤⠎⠀⠀⡀⠐⠊⠉⠀⠀⠀⠀⠐⠉⠀⠀⢦⡀
⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠛⠡⠖⠁⠀⢀⡀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣦⣀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣏⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠙⣫⣥⣶⠟⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠶⠚⠉⠁⠀⠀⣿⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⡀⣀⢀⠀⢀⠀⣠⡀⣠⠀⣀⠀⣀⢀⢀⡀⡠⢀⡀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠋⠃⠁⠋⠛⠀⠘⠀⠋⠃⠋⠀⠛⠃⠃⠘⠛⠃⠋⠐⠙⠃⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡠⠎⠣⣄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠁⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠉⢦⡔⢩⠔⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣀⣶⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠘⠬⠵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠻⠶⠟
⠀⠀⠀⠀⠀⠀⡉⠉⢉⡉⠉⢉⡉⠉⢉⡉⠉⢉⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⣉⡉⠉⣉⡉⠉⣉⠉⠉⡁
⠀⠀⠀⠀⠀⠀⡈⠉⣁⠈⢉⠁⢈⡉⠁⡈⠉⢁⠀⠀⠀⠀⠀⠀⠀⢀⡉⢉⡀⠉⣉⠀⣉⠉⢀⡉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠀⠠⠄⠠⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠀⠤⠀⠠⠄⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣺⢻⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢎⡵⣻⣣⡏⣩⢻⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⢳⣿⡟⣿⣿⣾⣿⣿⣿⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠉⢿⢸⣿⠷⠛⠿⠿⠛⠙⣿⠇⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠜⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠟⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠉⠉⠉⠉⠉⠉⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠿⠳⠄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⢤⡆⠠⠒⠋⠀⠀⡌⢧⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠐⠦⢤⣄⣀⣀⠀⠀⡀⠀⣀⠴⠃
⠀⠀⣀⠀⠠⠶⣯⡀⠃⠀⠀⠀⠀⠀⢳⠀⠀⢀⣀⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⡤⠞⠁
⢠⠏⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠉
⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠐⣄⠀⠠⠚⠈⢷⡀⡆⠀⠠⠤⠒⠚⠉⠁
⣷⠀⠀⠀⠀⠀⠀⠀⠐⣾⣷⡇⠀⠀⠀⢳⠀⠀⠀⠀⠀⢻⡁
⠘⣆⠀⠀⠀⠀⠀⠀⠀⢹⡜⡇⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⣷⡀
⠀⢹⢧⡀⠀⠀⠀⠀⠀⠀⢳⡇⠀⠀⠀⠀⢻⣀⣀⣀⣠⡴⠋⢷⡀
⠀⠈⠃⠱⣄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⡏⠉⠉⠁⠀⠀⠈⣷
⠀⠀⣾⠛⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹
⣀⣀⣘⣂⣑⣈⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣔⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣇⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠯⢭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣭⣭⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⠙⠳⠦⢤⣤⣄⣀⣀⣀⣀⣉⣁⣀⣠⣤⡤⠾⠛⢳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢻⡶⢶⣶⣦⣤⣤⣭⣭⣭⣥⣤⣤⣴⣶⡶⢿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣼⣧⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣼⣧⣾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢾⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⠆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⠷⢶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⣿⡇⠀⠀⠀⠀⢀⣴⠟⡽⠊⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣶⣦⣤⣄⡀⠀⠀⢸⣿⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⣿⣇⠀⠀⠀⣰⡿⠛⠳⣄⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣸⠒⠲⠍⣿⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠄⠀⣿⡀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣶⣦⣶⠟⠀⠀⠀⠙⠿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠟⠋⠀⠀⠈⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢿⡟⠛⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠈⠉⢹⡇⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⣶⠀⠀⠿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣛⢉⣿⣿⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣿⣟⡽⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣨⣮⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡔⣯⣾⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣯⡺⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡙⢅⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢦⡴⠋⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⢋⣴⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣧⠀⠈⠺⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣀⣦⣀⣀⠁⡀⠀⢿⣿⣰⣇⣶⣿⣿⣫⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠄⠠⠢⣀⠀⠀⠘⠉⠰⣧⡦⡄⢀⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡄⣦⡏⠒
⠀⠀⠀⠀⠀⠀⠀⠐⠥⣦⠀⢀⠀⠀⠀⠱⣀⡂⡄⢾⠻⡟⣬⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⣿⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡉⡐⠀⠀⠆⡹⣤⠉⣪⣼⣶⣺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⣚⣟⢁⣠⡃⠀⠀⠠⢿⣍⡗⣶⣿⡿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠹⣮⣀⣀⣀⣮⢻⣛⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠹⠝⡁⠹⣿⣸⣿⣿⣿⡿⣿⣷⣿⣛⢽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣍⣭⡀
⠀⠀⠸⠍⣿⣷⣤⠀⠀⠀⠀⢀⣀⠠⣀⠈⠉⠀⢀⡿⣠⣽⠿⣻⣿⢿⣿⣶⣚⣻⢺⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘⠁
⠀⢀⣀⠀⢠⣾⣻⠀⣠⣤⣠⡾⣿⣻⣿⡑⣶⢒⣿⣷⠏⠙⠁⠈⠈⡏⠻⡿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⡦
⠀⣶⣾⣿⣾⣽⣿⣾⡿⣿⡿⣧⣽⠿⢻⣷⣡⣿⣽⠟⢠⠀⠈⠁⠤⠴⠊⢄⣸⣋⣽⣿⣿⣿⣏⣽⣿⣿⣿⠶⠃
⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡧⣂⢸⠸⣷⣿⣿⡦⠀⠻⠶⣤⡄⠀⠈⠈⠻⠟⠡⠴⠏⣰⠻⢿⠏
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡟⢷⡈⠀⠈⢻⠿⡦⢁⣠⠀⢠⠄⠀⠀⠠⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣿⡾⣿⠎⠀⠀⣰⡞⠀⠈⡧⣼⣳⡜⣷⠇
⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⡟⠁⠉⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡄⠀⠀⠀⡀⣐⠣⠔⠻⠟⠀⢠⣤
⠀⠀⠉⠿⣻⣿⣿⣿⣿⣍⠉⠀⣠⣴⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣬⡇⠀⠰⣼⡿⢉⢧⣠⣤⠀⠀⢘⣣⡤
⠀⠀⠀⠀⠉⣿⣿⣿⡿⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣟⣿⣿⣿⣟⡿⠀⠀⠰⠏⠑⠈⣾⣟⣥⢠⠀⢟
⠀⠀⠀⠀⠀⠁⠻⡿⠃⠀⠀⠀⢻⣿⣧⣽⣿⣿⣟⠳⠀⠀⠙⣿⠿⠟⣉⠀⠀⢠⣶⣀⣤⡼⣯⣤⣿⣧⠀⠛⠡⠂⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⡿⣯⣿⣿⣿⡘⠝⠶⣤⢀⡘⢯⣃⣭⣥⡷⢯⣽⣿⣿⣶⣿⣾⣞⠀⠐⠳⠐⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣸⣠⡝⠂⠘⣿⢱⣎⡦⣬⡆⠹⣧⣄⠠⠉⢿⡚⣃⣀⠛⢷⡌⠻⣟⣌⠁⣾⡵⠀⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡿⠲⢈⣆⣄⣿⣿⣷⡋⣁⣶⣧⠿⣷⡤⢑⣦⡉⢳⣶⠾⡿⢤⣤⣾⠿⠿⠧⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⠒⠺⣿⠛⠩⣿⣾⣑⣿⢁⣿⣟⣽⣿⣽⡳⣷⣆⡤⣠⣴⡎⠉⠻⠇⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⠤⠀⠻⠳⢦⣅⣾⣿⡏⠽⣌⡙⣿⠧⠜⢻⡀⠚⠅⠉⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠆⠀⠹⢧⠸⣷⢴⠛⠓⠀⠘⠻⢤⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠔⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠂⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡇⠀⠀⠉⠙⠳⢶⣤⡀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⡄⠀⠀⠀⠀⠀⠉⠻⣇⡒⠉⡁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠐⡿
⣰⡂⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢨⡄⠿⣦⠀⠀⠀⠀⣀⠔⠀⠙⠦⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠠
⣏⠀⠀⠀⠈⢆⠀⠋⠉⠀⠁⠀⠰⠇⠀⠈⠳⡀⠀⠊⠀⠀⠀⠀⠀⠈⠣⡠⣀⠀⠀⡆⠀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄
⠘⣆⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡡⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⡹⢾⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣀⣤⠖⠉⠁⠀⠀⠀⡀
⠀⠸⣧⣼⡖⢺⣿⣦⠀⠀⠀⠀⢰⣷⣿⢀⣰⢦⠟⢜⣳⣤⣤⣵⣦⣴⣦⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⢛⡁⠀⠀⠀⠀⣀⣴⠇
⠀⠀⠹⣿⣿⡄⢹⣿⣆⠀⢀⠠⠿⠁⠃⠀⠀⠀⠀⠀⠀⠈⡟⠛⠿⠿⠿⡟⣤⠀⠀⠀⠀⠀⠀⢰⠉⣋⣡⣴⣾⣿⣯⣀⡤⠶⠛⠉
⠀⠀⠀⠹⣷⣿⡄⢻⣿⡄⠀⠈⠐⢤⣀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⢡⡇⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠹⣿⣿⡏⠘⠁⡤⠄⠀⠀⠉⠳⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⢀⠑⣼⣿⣷⣀⠀⠀⠒⠒⠂⠚⠉⠁⠀⠀⠠⢾⡿⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⣄⠙⠳⣶⣿⡆⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠛⠐⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠷⢤⣤⣤⠄⠠⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢢⠈⠛⢿⣿⣦⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠙⠻⠿⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡀
⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠘⣝⠶⣴⡧⠒⢲⢋⣽⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣾⣦⣤⣤⣾⣤⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⡟⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣵⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠾⠿⠯⡿⠟⠛⠻⠿⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠧⢤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣯⣯⣿⣭⣿⣿⠉⠁⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣶⡀⣠⣾⣿⣿⡿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢸⡿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢸⣿⣿⣿⣾⣽⣯⣿⣾⣿⣿⣿⣾⣽⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠦⠬⠻⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠿⠛⠁

⠀⠀⠀⠀⠀⢀⠀⣴⢦⣰⢷⣦⣟⣆⣀⣀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢯⣧
⠀⠀⠀⢠⠴⢿⡟⣿⣹⣟⣶⣯⠿⢿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⣁⠀⣈
⠀⠀⣆⣡⡁⠹⢿⠟⠿⠋⢛⣦⢑⠲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⣨⡞⠋
⠀⠠⠽⠏⠖⠻⠦⠀⠻⠦⡴⠦⠈⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⢰⠀⠶⠓⠂⠀⢠⡶⣿⣿⣆⠀⠀⠀⠀⡂⢀
⠀⣀⡐⢲⣶⠒⣲⣶⣶⠶⡿⣷⣶⣖⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣰⡃⠢⡀⠀⡚⠈⠀⠀⠀⠄⠀⠀⣿⢻⡟⣿⣿⡄⠀⠀⠀⢻⣄⣀
⠀⠈⠛⡛⢛⡰⢮⣝⣀⠀⣇⣊⣈⣉⠀⠈⠈⠀⠀⠀⠀⠀⠀⣨⡽⣯⡟⠸⡄⣈⡀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠸⡟⣠⡀⠀⠀⠀⢻⣷⠄
⠠⣿⣿⣿⣿⠁⠸⣿⡙⠦⡘⠀⢭⣿⠀⠛⠃⠀⠀⠀⠀⠀⢐⠋⠉⡙⢿⠀⠷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣿⠋⢡⡜⠀⢀⡀⢀⣀⣀
⠀⢸⣿⣿⡿⠀⢰⣿⣷⡀⠈⠂⣄⣋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⣶⠖⢽⣶⣶⠾⢿⣆⠀⠀⠀⠀⠀⠀⢹⢣⡼⢿⠿⠟⠁⣬⣿⣟
⢸⣿⣿⣿⣯⣀⢸⣿⣿⣧⣾⣿⣾⠛⠛⢻⡀⠀⠀⠀⠀⡀⠀⠀⠀⢻⣦⣤⠀⠉⠈⢿⣦⣾⡟⠀⠀⠀⠀⠀⠀⠙⣹⡧⠁⢀⡀⣠⣬⣿⣟
⢨⣿⢻⣾⢿⣿⣿⣿⡿⠟⢋⠿⠻⡷⣦⡈⣧⠀⠀⠀⢠⠎⠀⠀⢀⠀⠈⣿⣷⣀⣶⣿⣯⡍⣿⠀⠀⠀⠀⠀⠀⠀⣿⣡⡀⠈⠉⠉⠉⠉⠁
⢸⣿⣿⣷⣿⡷⠛⡏⣤⣠⣿⣉⠀⣾⠻⣇⣿⣶⣴⣶⣧⢃⣤⣬⣿⡄⠀⠉⠉⠉⠛⠛⠛⠛⠿⢦⡀⠀⠀⠀⠀⠀⢿⡩⠽⠆
⠙⣿⣿⣯⣿⣃⡾⢹⣿⣿⡿⣿⣳⡿⢰⣿⡏⠉⠙⢯⠕⠉⠀⠈⠛⡇⠀⠐⢰⡖⠒⠻⠟⠛⢻⡏⠀⠀⠀⠀⠀⠀⠸⠙⣆
⠀⣿⣽⣽⣿⡿⢉⠈⠀⠀⠀⢈⢹⣷⣾⣿⠀⠀⢀⣤⣿⡀⠀⠀⠀⣷⠀⠈⠈⣿⡀⠀⠀⠀⣼⣧⡀⠀⢀⣀⣀⠀⣀⡆⠘⣷
⠀⠛⢿⡟⣿⡃⣴⣄⠀⠀⠀⠀⣿⣿⣿⠗⠀⢠⣿⣿⣿⣷⣦⣄⠀⠘⣇⣀⣰⣿⣷⣟⣿⣶⣿⡌⠷⠀⡀⠈⠉⠙⠛⠓⠄⠈⠣⡀
⠀⠀⢛⣾⣯⡇⣿⣿⣿⣄⣴⢷⣿⣿⡇⠀⠀⣾⣿⣿⠯⠍⠉⠙⡄⠀⠙⠃⠈⠃⠀⠙⠁⠈⠹⣧⠀⠀⠀⠉⠙⠛⠛⠛⠿⠿⠷⠒
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⣾⣿⠟⠀⠀⢀⣿⣿⣿⣶⠂⠀⠀⠈⣶⣦⣲⡶⠂⣤⣄⣀⣀⢰⡿
⠠⣾⡷⣶⣿⡿⠛⠛⠋⣰⣶⡿⠇⢀⣤⣾⣿⣿⣿⣿⣿⠀⠀⠀⢸⡿⠿⠲⣤⣤⠈⢉⡉⠙⠛⠛⠓
⠀⠈⠙⠛⠉⠑⠓⣿⣾⠿⠛⢳⠘⠟⠿⠟⠻⣟⣿⣿⣿⡀⢀⠖⠋⠀⠀⣠⡼⠁⠉⠀⠸⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠸⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣧⡀⣀⣦⣶⣿⣡⡴⠾⠓⠒⠛⠒⠛⠚⠶⠆⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⠶⡶⠶⠶⠶⢶⡴⠶⠶⠦⣤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣀⣀⣀⣛⣀⣀⣀⣘⣃⣀⣀⣀⣋⣀⣀⣀⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢀⡀⠀⠀⢸⡇⠀⠀⢀⡀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢙⡴⠋⠉⠉⠙⢶⡋⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣀⡀⡟⠀⠀⠀⠀⠀⠀⢻⣀⣀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⠀⢧⠀⠀⠀⠀⠀⠀⣼⠀⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡬⠳⢤⣄⣠⡤⠞⢥⡀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠀⠀⠀⢰⡆⠀⠀⠀⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠶⠶⠶⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠈⠻⣿⣦⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠻⣿⣦⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⠙⢿⣿⡋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠘⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣿⣦⡀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠙⢿⣦⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢿⣦⡀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⢠⣾⠿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣷⣄⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⣠⣾⠟⠁⠙⢿⣷⣤⣾⠟⠁
⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⣠⣾⠟⠁⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⣠⣾⠟⠁⠀⠙⠿⠟⠁
⠀⣠⣾⠟⠁
⣾⡟⠁
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠒⠒⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⠶⠋⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣦⡀
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣫⠞⠋⠹⣆
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⠀⠀⠸⣆
⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣫⠞⠁⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⣀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢋⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⢃⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠛⠛⠋⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⣴⣶⣶⣿⣿⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢸⣿⣿⠟⣋⣛⢿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⣿⣿⣿⠸⣿⡿⢨⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣤⣤⡾⢛⣵⣿⣿⣿⣿⣷⡆⣶⣿⣿⢟⣥⣶⣶⣦⡝⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣭⠍⣴⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⠟⣵⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣵⣶⣝⢿⣿⠿⣛⡻⠏⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⡟⣱⣿⣿⣿⣿⡇⣴⣿⣿⠿⣳⡌⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡅⣿⡿⣩⣾⣿⡗⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣤⣬⣭⡛⢿⣿⣿⣿⣷⠌⠻⠿⠿⢛⣵⣌⠻⠿⠿⢛⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣙⠛⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣛⠻⠿⣿⣿⠇⣘⣛⣛⣛⣛⣛⣛⣋⣥⣴⣶⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉⠁

⠀⠀⠀⢀⣤⣴⣤⣄⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣾⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠞⠿⠿⠟⢿⡿⣦⣠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⡄
⠀⠀⠸⣋⠈⢉⠀⣿⣿⡏⢀⠀⠀⣻⢿⣿⣿⠀⠀⠀⠀⠀⠀⢖⠂⠐⠦⢸⣿⣿⣿⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⣶⣶⣬⡋⠁⠘⣿⢿⣿⡧
⠀⠀⠀⠎⠂⠘⠄⣠⠜⠁⠸⠃⠐⡁⢼⡿⠃⠀⠀⠀⠀⠀⠀⡏⠓⠈⠃⠘⣩⠏⠀⠠⡀⠙⣹⣿⣿⡇⠀⠀⠀⢰⡿⣿⢿⣿⣿⣿⡶⠠⠉⠸⡿⠃
⠀⠀⠀⠐⠀⡴⠛⢅⠀⠀⣀⣠⡰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠎⠁⠀⢈⡀⢀⣂⣽⠛⠋⠀⠀⠀⠀⠈⢃⡉⢀⡁⢻⢿⡄⢀⢬⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣑⠂⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢱⠒⠉⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⣱⠐⠈⢀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⢈⠃⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠻⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣳⣧⡚⠁⠀⠁
⠀⠀⢀⡤⠆⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡎⠀⠈⠀⡀
⠀⠀⠀⠜⠁⡴⡈⠧⠀⠀⠀⠀⢠⠢⡀⢀⡀⠁⠄⠀⠀⠀⢸⣿⣿⣿⡋⠣⠀⠀⠐⠈⡤⢤⠤⣀⠈⠠⠀⠀⠀⠀⠋⠇⣴⠚⠏⠀⠀⠀⢠⠢⡄⢀⡀⠁
⠀⣀⣔⣦⢠⠤⠄⠀⠀⠀⠀⣀⣸⠶⣆⣠⣀⠀⠀⠀⠀⣀⣼⣿⣿⠧⠤⠀⠀⠀⠀⢀⣌⠔⣄⣀⡀⠀⠀⠀⠀⠀⣼⡷⢧⠄⡀⠀⠀⢀⣈⠶⢆⣸⣀
⠀⠉⠙⠂⠉⠀⠀⠁⠀⠀⠂⠀⠉⠘⠃⠙⠋⠛⠀⠀⠀⠉⠙⠋⠉⠁⠀⠈⠀⠀⠀⠀⠉⠙⠉⠛⠁⠃⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠉⠈⠛⠘⠋⠙⠃
⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣶⣦⣄⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⣝⠛⠋⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣆
⠀⠀⣿⢠⠈⢹⡛⣿⣿⣿⠙⠋⠻⡿⣿⣿⣿⠀⠀⠀⠀⠘⠇⡀⠀⣉⢈⣿⣿⡿⣦⠄⡸⠋⣿⣿⠃⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⠻⠟⢿⡿⣿⣿⣿
⠀⠀⠙⡈⠁⠈⣴⣿⣿⠟⠅⠲⢀⢰⣿⣿⠟⠀⠀⠀⠀⠀⠐⠓⠀⠩⠈⠛⠋⠀⠉⠀⡰⠈⢟⠁⠀⠀⠀⠀⠀⢸⡏⠸⡏⠈⢻⣿⣆⠀⠄⠠⣾⠿⠟
⠀⠀⠀⠀⡰⠎⠙⣢⣀⢀⣶⣤⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣵⣤⣀⣠⣶⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠰⢆⠈⡹⠃⠀⠸⠄⠛⢀
⠀⠀⠀⠀⡇⠀⠀⣤⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣯⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣄⡄⠺⠿⠃⡀
⠀⠀⠀⢀⡁⠀⠀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⠛⠂
⠀⠀⠀⠁⠀⠀⠠⡁⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠩⠋⡉⢹⡃⠀⠀⠀⠂⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠴⣿⣿⣿⣧⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⢤⡠⢳⠀⠁⠀⠀⠀⠘⠉⡋⢹⠂⠀⠀⠀⠀⠀⠀⠀⣸⢸⢒⠀⠁⠀⠀⠀⠀⡍⢀⢰⠀⠀⠀⠀⠀⠀⠀⣰⡦⢹⠀⠁⠀⠀⠀⠘⠉⡋⢱⠂
⠀⠀⠰⡜⠾⠛⠀⠄⠀⠀⠀⠲⢌⡽⢶⡶⢤⠀⠀⠀⠀⠀⠾⡿⠽⠚⠀⠄⠀⢀⠐⠶⢯⡭⢾⡦⣤⠀⠀⠀⠀⠘⠻⠟⠙⠀⠄⠀⠀⠀⠲⣮⣽⢾⡶⢤

⠻⣦⡀
⠀⠈⠻⣦⡀
⠀⠀⠀⠈⠻⣦⣤⡀
⠀⠀⠀⠀⠀⠻⣄⠙⠷⣄⡀⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⣨⠟⢁⣽⠟⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣨⠟⠁⣴⠟⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣷⠟⠁⠀⠀⢀⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⢁⡴⠀⢀⡴⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡴⠋⣀⠀⠀⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⣠⠖⢀⣴⠗⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⠟⢁⡄⠀⢀⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡾⠃⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡴⠋⣠⠞⠁⠀⠀⠈⠻⣦⢀⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀⠀⠀⠀⢀⣼⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠈⠻⣦⡀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣞⣋⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢀⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⣹⣿⣦⣄⠀⠀⠀⠀⠊⠀⠀⠀⢐⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⣠⣾⠟⠁⠉⠻⣷⡄⠀⠀⠀⠀⠀⠔⠋⠁
⠀⠀⠺⢷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⣠⣾⠟⠁⢀⣀⣀⡀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣆
⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⣦⣄⣀⣴⣾⠟⠋⣠⣴⡿⠛⠁⠀⣴⡿⠛⠛⢿⣆⠀⢻⣇⠀⠀⠀⠀⠒⠒⠚⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣯⣤⣶⠿⠛⠉⠀⠀⠀⠀⣿⣇⠀⢀⣼⡿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣤⣄⡀⠀⠀⠈⠛⠿⠿⠛⠁⠀⢸⣿⠀⠀⠀⠲⢤⣀⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠈⠋⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣦⣬⣍⣉⣙⣛⣛⣛⣉⣩⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠈⠉⠙⠛⠛⠛⠛⠛⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣄⡀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡀
⠀⠀⠀⠀⠀⣠⣤⣰⡯⣿⣿⣙⣿⠷⣿⣶⡶⠒⠛⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠛⠏
⠀⠀⠀⢈⣫⢙⣿⣼⣿⣿⣵⣿⠷⢟⠛⢿⠛⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠰⠄⣠⡦
⠀⠀⢷⣴⢇⢐⡚⠟⠈⣛⠀⢩⠿⠢⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠥⠀⠀⠀⢰⣾⡅
⠀⠐⠶⠋⠸⠉⠟⠂⠈⠛⠓⣟⡗⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠆⠛⠘⠚⠁⠃⠀⢠⡿⣿⣿⣿⣄⠀⠀⠀⠀⡅
⠀⢠⣍⣉⣿⡟⠉⣟⣿⡿⠿⡟⣿⣿⣯⣯⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⡤⣇⡙⣄⠈⠉⡉⠈⠁⠂⠀⠀⠀⠀⢸⣟⣿⢻⣿⣿⠂⠀⠀⠀⠹⣆⣠⡄
⠀⠈⠛⣛⠛⣓⠲⢶⣗⣀⠈⣇⣉⣀⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣯⣿⠁⢧⢀⣭⠬⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢻⣋⡄⡀⢀⠀⠀⠹⣷⡇
⠠⣿⣽⣿⣿⡏⠀⢿⣏⠻⢄⡙⠀⣍⣿⡇⠙⠻⠀⠀⠀⠀⠀⠀⢰⠏⠉⡉⢿⡅⠹⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢘⡟⡉⢥⠝⠀⠀⡀⠀⢀⢀
⠀⠨⣿⣿⣿⠇⠀⣷⣿⣇⠀⠙⠢⣀⠚⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡤⢶⡶⠬⣷⣤⣴⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⣿⣡⣿⢶⢿⠟⠉⣀⣽⡿
⠸⣿⣿⣿⣯⡀⠀⣻⣿⣿⣦⣼⣷⣥⠿⠿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣧⣨⡂⠐⠃⠙⣿⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠗⣿⡏⠃⠀⠀⣀⣈⣻⣿
⠘⣿⣿⣏⣿⢿⣷⣿⣿⣿⡿⠟⣿⢿⣦⣤⡀⢿⡀⠀⠀⠀⢈⡗⠀⠀⠀⠀⠙⢻⣷⡄⢠⣤⣿⣏⡛⣷⠀⠀⠀⠀⠀⠀⢀⢸⣿⣀⠀⠘⠓⠛⠟⠛⠛
⢸⣻⣶⣛⣐⣟⣻⣿⠛⡁⢀⣾⠖⠀⣩⣾⣿⢸⣗⣀⣤⣤⠎⠄⢀⣐⣶⡆⠀⠹⠿⠿⠿⠿⠿⢿⣷⣿⣀⠀⠀⠀⠀⠀⠀⠸⣿⢳⣲⡄
⠼⣿⣿⡿⢿⡿⢁⡴⣯⣿⣿⣿⣷⣄⣺⠇⣽⣿⠟⠻⢿⠿⣋⠞⠛⠛⢿⣧⠀⠀⠀⣀⣤⣤⣤⣤⣤⣬⡭⠆⠀⠀⠀⠀⠀⠀⠻⢯⠁⠈
⠀⣿⢿⡿⣿⣷⡾⡡⠛⠛⠙⠋⠻⢾⣿⢰⣿⡏⡀⠀⠀⠙⡀⠀⠀⠀⠀⣯⠀⠠⠄⣿⡔⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠈⢷⣄
⠀⣿⣾⣿⣿⣿⡁⢂⠀⠀⠀⠀⠠⣼⣿⣹⣿⠋⠀⢀⣶⣿⣿⣄⠀⠀⠀⢹⣄⠀⠀⢸⣿⣆⣠⣄⠀⣿⠿⡆⠀⠀⠶⠶⣦⣴⣾⠃⠀⢳⡄
⠀⠀⣩⢭⣾⣶⢰⣿⣦⣀⠀⠀⡀⣿⣿⣿⠏⠀⠀⣿⣿⣿⣿⣿⣷⣦⠀⠀⣿⣤⠤⣿⠟⠻⣴⡿⢿⣿⡧⠙⠂⠶⢤⣤⣤⣀⣈⣉⣁⣠⡏⠂
⠀⠠⣨⣿⣿⣾⣈⣿⣿⣿⣤⣿⢻⣿⣿⠗⠀⠀⢸⣿⣿⡟⠓⠂⠀⠈⢦⡀⠀⠉⠀⠈⠀⠀⠈⠀⠀⠘⣷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠉
⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⠟⠀⠀⣀⣸⣿⣿⣿⣾⠁⠀⠀⢀⣷⣷⡮⣽⡛⠰⣤⣤⣤⣄⣰⣿
⠠⣾⣶⣷⣿⣿⠛⠛⠛⢉⣶⣶⡟⠇⠀⣴⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⠿⠗⢦⣤⢄⣀⡀⡈⢉⠙⠛⠛
⠀⠈⠝⠛⠋⠙⠚⢼⣷⡾⠿⠟⢳⡌⠟⠿⠿⠛⣿⣻⣿⣿⣿⠀⢀⠖⠋⠀⠀⢀⣤⡍⠈⠁⠀⢱⠈⣦⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⡀⠠⣦⣴⣾⣏⣡⣴⠶⠶⠒⠓⠒⠛⠾⠦⡦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠿⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠔⠋⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⠁⠀⠀⠁⠢⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠶⠲⠤⣀⠸⣄⣀⣀⣀⣀⣀⡀⠤⡏⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠂⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠠⠀⣀⣑⣅⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠻⡀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣠⠴⠒⠋⣉⠝⢓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣠⠤⠖⠁⠀⢠⠏⠀⢀⠄⢊⠤⠊⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠫⢍⡉⠈⠉⠒⢄⡀⠀⠀⠀⠀⢸⠤⠎⣀⣐⡁⠀⠄⢊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠁⠂⠌⡑⠢⢄⡀⠙⢆⠀⠀⠀⠀⠑⠒⠶⠶⠶⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠐⠠⠀⢀⡀⢁⣢⡬⠑⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⣶⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣄
⠀⠀⢀⣴⣶⣶⣮⠁⠀⠀⠀⠀⠀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⢰⣿⣿⡆⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⢸⣷⣿⣿⠿⣦⡤⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠀⠙⠋⠀⠀⠀⠀⠀⣠⡸⢿⡿⠃
⢀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠂⠀⡉⠀⠀⠀⠀⣿⣿⣷⣶⣦
⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⡟⢸⣿⠀⠀⠀⠀⠀⠀⢀⣻⣿⣇⣽⣿⠀⠀⠁
⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⠟⠀⠀⠀⠀⠀⠀⠛⠋⠀⠙⠟⠀⠀⠀⠀⠀⠀⠻⠿⠛⠋⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠀⠀⠀⠀⢠⡶⢸⣿⣿⠄
⠀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣭⣤⠀⠀⠀⠀⠀⠀⣠⣬⣭⣥⡀⠀⠀⠀⠀⢸⣧⣤⣭⣥⡄
⠀⠀⢠⣴⣮⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠛⣿⣿⣿⡇
⠀⢰⣿⣿⣿⣀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠠⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢀⣠⣰⣿⣿⣿⣿⣷⣠⣀⠀⠀⠀⠀⠀⢸⣿⣻⣿⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⡇
⢠⣬⣭⣭⡙⣿⡆⠉⠋⠀⠀⠀⠀⠀⣾⣿⢹⣿⡟⠛⣻⣿⠛⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⣼⣿⣿⣿⣇⢻⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣷⢠⣿⡏⠀⣿⡇⠀⠀⠀⠀⢸⣿⢾⣿⠀⠀⠀⠀⠀⠀⢸⣿⢼⣿⠀⠀⠀⠀⠀⠀⠀⣿⡷⣿⡇
⠀⠀⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢃⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣀
⠀⢀⣼⣿⣿⣥⡀⠀⠀⠀⠀⠀⢾⣥⣾⣿⣷⣬⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠸⣷⣦⣿⣶⡿⠀⠀⠀⠀⠀⠀⢻⣿⣿⣾⡿
⠀⢸⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢩⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡅
⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠇
⠀⠀⣿⡟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿
⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⢸⡿⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⢋⡴⣫⡼⠛⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⢿⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⡥⠤⣤⠄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢰⡏⣠⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣭⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⣷⣝⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⠶⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣭⡅⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢸⡇⣒⡂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⣦⠀⠀⠀⠀⣸⠀⣧⠀⠀⠀⠀⢸⡇⠭⠥⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣼⠀⠀⠀⠀⡟⠀⢹⡀⠀⠀⠀⢸⡇⣛⡃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠳⡄⠀⠀⠐⣇⠀⢸⠇⠀⠀⠀⢸⡇⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠈⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⣤⡄⣿⠀⠀⣴⠋⠀⠈⢷⠀⠀⠀⢸⡇⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠳⠴⠃⡞⢹⠄⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣾⠛⢻⠀⠀⣠⡼⣧⣤⣤⣤⣼⣧⣤
⠀⠀⠀⠀⣰⠻⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣿⠀⢸⠀⠀⠙⠛⠻⡟⣿⢻⡟⠛⠋
⠀⠀⠀⠀⠳⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⢿⠀⢸⠀⠀⠀⠀⢰⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣤⣤⣤⣤⠇⣿⠀⠀⣿⠀⠘⠒⢾⠀⠀⠀⠀⣸⣇⣿⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠞⠃⠀⠀⠙⠶⠶⠶⠋⠀⠀⠀⠘⠷⠿⠿⠿⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠁⠐⣤⡀⠀⠐⡆⠀⢰⣧⠠⠤⠄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⢰⣶⣶⠚⠀⠀⠁⠀⠸⣿⣆⢀⠂⠠⠈⢃⡀⠀⠀⠀⠀⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⡀⢰⣿⣿⣀⠀⡠⠋⠀⡀⠀⣿⣿⠀⡀⠰⡇⠈⣅⠀⠀⠀⢦⣄⣤⣿⡿⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⣄⢘⣿⣿⣿⣿⡟⢹⠃⢀⡶⠀⠀⣿⣿⡄⠀⠊⣿⠀⠸⠀⠀⠀⣼⣿⣿⣯⠀⢠⣿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢰⣿⣿⣿⣿⣿⡿⠅⣸⠀⡆⢶⠀⠀⣿⣿⡌⠀⠀⣿⠀⢠⠠⡆⠸⣿⣿⣿⣷⣠⣿⡟⢐⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡏⠈⠉⢟⠋⢻⣿⣿⣷⡾⠁⠘⡇⢸⡆⢸⣿⣟⡟⠃⠈⣷⠀⠼⢠⡇⠀⣿⣿⣿⣿⣿⣿⠃⣾⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠓⠀⠀⠀⣠⠄⠸⠷⣌⡇⠀⠀⣁⣸⡄⣼⣿⣿⡇⠃⠀⢿⡀⠘⢺⠁⠀⡿⠟⠻⣿⣿⣿⣷⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣄⡴⠶⠞⠁⠲⢲⣀⠈⠳⣤⡀⠰⣾⡇⢹⣿⣯⣇⠀⠀⡿⠀⠀⠃⠀⡘⠁⠀⣹⣿⣁⣉⢛⣻⢿⣾⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣦⣀⠑⠀⣯⣇⣼⣿⣿⣿⣥⣀⡇⠀⠀⡇⠠⠁⢀⡴⠋⠁⠀⠙⠟⠛⠛⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠉⢳⣀⡗⢿⣿⡟⢯⡟⢿⣽⣷⡀⠀⡇⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⡾⠧⣀⠀⠀⡠⣠⡄⠀⣸⣿⣇⣬⠅⠻⢿⣥⣿⢟⣯⢟⡀⣷⡏⠀⢠⠀⠀⠀⠰⠃⠀⠀⢀⠀⠀⠛⣷⣄
⠀⠀⠀⠀⠀⢰⠂⠀⠸⣁⠀⠋⠀⠀⠀⠐⠆⠀⠀⠀⢀⣾⣿⡏⠠⠀⣹⣲⣿⣿⡒⡳⣾⣿⣾⡇⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⠁⢄⡠⢾⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠆⠀⡀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⢺⣿⣿⠃⡠⢾⡟⠉⠉⣉⠛⠿⢄⠙⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡙⣧
⠀⠀⠀⠀⡀⠀⠀⠀⠔⠻⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⣿⣿⣿⠊⠀⠌⣷⡇⡟⠶⣶⡣⠄⠡⠈⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⢿⣿
⠀⠀⠖⠀⠡⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⣀⠙⢶⣤⠐⢬⣅⡀⠀⠀⣸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣟⡫⣧
⠀⢐⠃⠀⠀⠀⠁⠀⠀⠆⠀⠀⠐⠀⠀⠀⡆⠀⠀⣾⣿⣵⣿⡤⣿⣯⠀⠠⣿⠀⠀⣸⣿⣼⢶⣽⣿⡗⢄⠀⠀⠐⠀⣀⠀⠀⠀⡇⠀⠈⠈⢰⠹⡇
⠀⠒⠰⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢠⠁⠀⣸⠗⢿⡧⠘⢰⠏⠀⠀⠀⣿⠀⠒⢈⣿⡿⠀⠈⠛⠀⠀⠀⢀⡀⢀⣼⠂⠀⠘⠣⠀⠀⠀⣾⠁⠻⡄
⠀⠂⠀⡄⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⠴⠃⣠⠴⢡⣴⡿⠏⡤⠊⠀⠄⢠⠀⣿⠀⠀⠀⣄⡙⢄⣸⣧⣤⡗⢐⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡟⠆⠀⡿
⠀⡉⠀⠀⠀⠀⡆⠀⠀⣠⠖⠁⠀⠀⠀⠀⣴⠞⠋⠁⠐⠊⡁⠀⠀⠀⡿⠀⢛⠀⠀⢠⣿⡿⣾⣿⣿⣌⡛⠿⣄⢰⡀⠀⠀⠠⣶⠀⠀⢸⡿⢃⠀⣹⠇
⠀⠀⠀⠇⠀⠀⢹⡀⠀⠀⠀⠀⢀⣤⣾⠛⣉⣀⡁⣀⣰⣯⡊⣠⠴⢶⠎⡉⡛⠁⠑⠾⣗⠙⠃⣈⣷⡙⠣⠁⠋⠻⣷⣄⠀⠀⠀⢨⣘⠿⣯⣧⣽⣿
⠀⠀⠀⠈⢄⠀⣸⠃⠀⣠⣶⣿⡿⡟⡽⡟⡏⢹⢿⡿⣿⣍⠻⠇⣠⣤⡇⠀⠦⠀⢤⣀⣿⡷⠊⠁⢨⣿⣶⠈⢱⢴⢮⣍⣷⣄⠀⠀⠈⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠘⡗⠁⢀⣴⢿⣿⡟⠁⠀⠠⡏⠇⠀⠀⠐⡘⡮⡁⢤⡩⣤⣼⠀⠁⠀⣌⣀⣿⡥⢒⣥⣾⠏⡞⢠⠀⠀⠀⡜⠁⠋⠻⣷⣾⣿⢟⣽⣿⠁
⠀⠀⠀⠀⠀⠹⣦⣾⣳⣿⣿⠁⠀⠆⠄⠈⠊⢄⠀⢶⣲⣑⣿⣆⠳⡉⠙⠀⡅⢐⢋⣿⡟⣰⣿⡿⠋⣠⠁⠎⡃⡄⡀⣅⠀⠀⡧⢹⣭⣽⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠄⠀⡴⣤⠀⠠⠘⣦⣀⣽⣿⣿⣿⣇⢥⠀⠀⢇⠨⣸⡿⣼⣟⣛⣥⣾⣯⠈⡰⡹⠃⢇⢅⠀⢀⡟⢸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣍⣿⣿⡆⡄⢷⡘⢗⡀⠄⢀⠈⢻⣟⣿⣿⣿⣠⡄⠀⡀⢠⣿⣿⣿⣿⡿⠿⠟⢁⣸⡟⠁⢠⡾⡀⠀⣾⣧⣘⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⡌⠿⣟⢿⣿⣷⣦⣆⣠⢬⣙⠿⢿⣿⡇⢀⣲⠺⣿⣿⣿⣿⣿⠷⠛⣫⡏⣠⣠⠞⠁⡁⣰⣿⢳⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣟⡳⢮⣽⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣴⣶⣿⡿⣿⣿⣿⣷⡾⠷⠾⠟⡉⣠⢠⣷⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣬⣍⣛⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⢁⠀⣠⢂⣔⣴⣧⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣝⡛⣿⣿⣿⣿⣿⣿⣿⠟⠘⣿⣿⠻⢿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠛⠉⠀⠀⠈⠛⠷⠿⠿⠿⠿⠿⠛⠛⠉

⠀⠾⠿⠆⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢶⣼⡴⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠰⣯⣧⣤
⠠⣾⣷⡄⠀⠀⠀⠀⠐⠟⠻⠟⠟⠀⠀⠀⠀⠈⡽⢳⢫⡍⠀⠀⠀⠀⠀⠐⢳⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⢠⣾⣆⠀⠀⠀⠀⠀⠀⠲⣶⡶⠂⠀⠀⠀⠀⠀⢶⣄⣽⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⢿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠸⣦⢸⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎
⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈


⠀⠀⠀⠀⠠⣦⣿⣧⡦⠀⠀⠀⠀⠀⢀⣄⠘⠃⠀⠀⠀⠀⢀⣾⣿⣆⡀⠀⠀⠀⠀⠀⣸⣃⡀
⠀⠀⠀⠀⠐⠾⣿⡿⠗⠀⠀⠀⠀⠀⡛⠛⡃⠀⠀⠀⠀⠀⢨⡉⠉⢩⠀⠀⠀⠀⠀⠸⡀⢓⠆
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠈⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣀⡤⢄⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠈⢁⠄⣊⣭⡙⣯⡟⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠠⣀⡀⡀⢈⣩⣼⠻⣿⣿⣿⣷⣿⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠟⢿⠔⠁⠈⠟⠁⢹⣿⣿⣿⣿⣱⢦
⠀⠀⢀⣠⠴⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡚⠂⠙⠖⠛⢀⣴⣿⣿⣿⡿⢀⣾
⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⣿⡗⠂⠀⠀⠀⠈⠻⢿⣿⣇⡸⠃
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⢎⣿⠗⠚⠀⠀⠀⠀⠘⢿⠟
⢨⡳⢤⣄⣀⣀⣀⣀⣀⡠⠄⢀⠀⠜⠀⠀⠀⢀⠀⠀⠈⠛⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠙⠷⢤⡄⠀⠀⠀⠀⠠⠀⠋⠀⠀⠀⠀⠀⠀⠁⣦⡀⠀⠀⠀⡅⠀⠀⠸⠂⠀⠀⠀⠀⠳⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⢤⡂⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠈⠒⠒⠀⠀⠀⠀⠀⠙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣤
⠀⠀⠀⣄⣠⣿⣧⣴⡄⠀⠀⠀⠀⠀⣤⡾⢛⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⡴⣻⠟⠁⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⡿
⠀⠀⢰⣿⠿⠿⠟⢿⠇⠀⠀⠀⠀⠀⠙⠛⣧⣿⣿⡏⣿⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡇
⠀⠀⢸⡇⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠃⠃⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠃
⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐
⠀⠀⠀⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣟⣸⣿⣇⣻⣆⠀⠀⠀⠀⠀⠀⠀⣾⠿⣷
⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⢠⣾⣯⣤⣽⣶⣆
⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⡇⣿⠂
⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋

⠀⠀⠀⠀⣺⣿⡦⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠺⣿⡿⣻⡇⠀⠀⠀⠀⠀⠀⡰⠋⢠⣶⡄⠉⢦⠀⠀⠀⠀⠀⠀⢀⣬⣿⠋⠀⠀⣿⡇⠀⠀⠀⣠⣶⣞⣿⡿⢶⣄⡀
⠀⠀⠀⠀⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⡇⠸⢿⣿⡿⠇⢸⠀⠀⠀⠀⠀⠰⣿⣟⠛⠓⠶⢓⠻⠃⠀⠀⠀⠛⠿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠙⢄⡈⠛⢃⡠⠋⠀⠀⠀⠀⠶⠾⠿⠿⠇⠀⠩⠿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠻⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠄
⠀⠀⠀⠀⢾⣷⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠢⡿⠂⢲⣄⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣷⣿⠛⠋⠀⠀⠀⠀⠀⡴⠻⣠⡷⢄⠀⠀⠀⠀⠀⠀⣶⢠⣄⣤⣄⣀⣀
⠀⠀⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢶⡋⣣⡾⠓⣄⠀⠀⠀⠀⢛⣾⣸⣿⣿⣿⣿⣿⣶
⠀⠀⠐⢥⡏⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣨⠾⠋⠀⠀⠀⠀⠈⠏⠉⠉⠉⠉⠉⠉⠏
⠀⠀⠀⠈⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠓⡆⠀⠀⠜⣀⣠⠤⣤⠶⠒⠋⠉⠉⠉⠉⠓⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠛⠤⡄⢀⡸⠔⠒⢉⣡⠖⠛⠒⠒⠒⠒⠒⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⡠⠗⠛⢤⠴⠚⠉⡏⠀⢐⣁⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡮⠀⠀⠀⠙⣅⠀⠀⢻⣰⠋⠈⠹⣄⠀⠈⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠸⣀⡶⢀⣠⣄⣵⠀⠀⠀⣿⠀⠀⠀⢹⡶⠋⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠙⠀⢋⣀⣸⣿⡆⠀⠀⣿⠀⠀⠀⠀⡷⠖⠉⠉⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣠⠞⣩⠥⣌⢻⠃⠀⠀⢹⡀⠀⠀⢀⡟⠒⠶⣏⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠙⠀⠉⠃⠀⠀⣿⣿⣿⠁⠙⢿⣿⣿⣷⣄⠀⠀⠀⠙⠒⠤⣤⠙⠈⠀⠀⠀⠀⢙⠲⣾⡟⢡⡄⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠒⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⠀⣠⠔⠲⠤⠼⢿⣿⡟⠀⠀⠈⠻⣿⣿⣿⣷⣶⣤⣦⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠦⣄⡀⠀⠀⠀⡀⠀⠀⢀⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⠔⢛⣥⣤⠄⢀⣈⣶⠤⠴⠒⠏⠛⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣠⠴⡖⠲⣤⡀⠀⠀⠀⠀⠀⠀⠉⢹⠖⠶⠦⠤⠥⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠳⠤⠋⠸⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⣠⢺⠇⢸⠁⣠⡃⠉⠢⣄⠀⠄⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠳⠾⠔⠛⠉⠁⠈⠀⠀⠈⠋⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⢤⣴⣶⡞⠛⠉⠉⠁
⠀⠀⠀⠀⢀⣀⣀⣀⡆⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡏
⠀⢀⡴⡺⢷⣛⡟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡦⢄⡀⠀⠀⠀⠀⠀⠀⣴⠋⠁⢸⣿⣿⠁
⣠⢋⠊⠠⣶⣼⡇⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⠏⠈⠉⠒⠢⠤⣄⣠⠞⠀⠀⣾⣿⣿
⡇⡞⠉⠉⠳⡽⡇⠇⠃⠀⢀⢀⠀⠀⠀⢀⡴⢋⡴⠁⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⢹⣿⣿
⠳⣧⡀⠀⣰⠇⠙⢄⠀⠀⠀⢉⣹⠖⠒⠿⡴⢏⣀⡀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠸⣿⢿⣣⠤⡄
⠀⠀⠉⠉⠁⠀⠀⠀⠙⠒⠚⠉⠀⠀⢀⡞⠁⠀⠙⠩⠙⠂⠀⡝⠀⠀⠀⠀⠀⠀⠀⢠⢛⠊⠱⠯⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣗⡒⢦⣤⡤⣤⡶⢳⠞⠛⠓⣄⠀⠀⡠⠚⢹⠃⢠⣼⢮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠻⠿⢿⣶⡫⠤⠧⣤⣤⣖⡟⠀⠸⣀⠄⠧⣀⣈⣉⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠻⣤⣠⡋⠉⣉⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠹⠿⠃⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣼⣿⣷⠀⠀⣠⣄⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣷⣾⣿⣿⣧⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠀⣀⠀⠘⢿⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠉⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠈⠄⢨⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⠊⠁⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠠⢸⣿⣿⠀⠀⠈⠙⠿⣿⠗⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡿⠀⣴⣶⣶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢴⣿⣿⠀⠀⠀⠀⠀⠖⠀⠀⣠⣶⡄⠹⣧
⠀⠀⠀⠀⢀⠞⢤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⣿⡆
⠀⠀⠀⠀⠰⣤⣶⣇⠘⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢿⡇
⠀⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⣿⣷⡄⠀⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⢻⣿⣿⣿⣿⡄⠀⠀⢀⣿⣿⠃⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠙⢿⣿⣿⡇⠀⠀⢸⣿⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⡠⠙⣿⣿⣄⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⠛⣿⣿⣿⣿⡇⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠈⠛⣿⠆⠸⡿⢷⡄⠀⠀⠀⢸⣿⣿⡏⠀⠘⣿⣿⣿⡇⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⣾⣿⡟⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣧⣠⣄⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⢰⣿⣿⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠙⠿⣿⡿⢄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣾⣿⡟⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⣄⣙⣠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⡆⢠⣿⣿⡇⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡇⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠿⠿⠾⠿⠶⠶⠶⠶⠶⠶⠿⠵⠿⠽⠿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢄⣿⣾⣿⣶⣦⣶⣴⣿⣷⣮⡄⢀⠀⢠⡀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣰⣿⣿⣿⣯⣿⣿⣿⡟⠁⠀⠀⠀⠈⠛⢴⡦⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⣿⣿⣿⣿⠟⢉⣅⣀⣀⡀⠀⠤⠀⣁⣀⠀⠀⢀⢠⡶⠧⠀⠀⠀⢰⣿⣯⠐⠋⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠉⠉⠉⠹⠖⠂⠀⠀⠀⠈⠉⠙⠻⠿⠿⠷⠓⠋⠀⢀⣰⡆⠀⠀⣮⡿⠁⠀⠀⠀⠀⠀⠀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⡿⠗⠋⠉⠀⠀⠀⠀⠀⢁⣴⣿⠛
⠀⠀⠀⠐⠂⠀⠀⠀⢀⡞⣿⣿⢁⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣿⣿⣿⣿⡟⣁⣴⣄⡀⠀⠀⢠⣀⣠⣤⣼⣿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣚⠓⠐⠚⠺⠟⠛⠛⠛⠛⠛⠛⠓⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠃⠠
⠀⠀⠀⠈⠑⠉⠂⠉⠉⠈⠀⠀⠀⠈⠙⠛⠋⠉⠙⠓⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠋⠉⠉
⠀⠈⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠲⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠂⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣸⣿⢰⣟⣛⢸⡟⠻⣆⣿⢠⡞⠛⠂⢰⡿⣆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⠏⠿⠸⠷⠶⠸⠷⠾⠃⠻⠈⠳⠶⠂⠿⠛⠻⠸⠷⠆
⠀⠀⠀⠀⠀⢠⣤⣤⢠⣤⣤⡀⣤⣤⠀⢠⣤⠀⣤⣤⡄⣤⡀⣠⡄⢠⣤⡄⣠⡄⢠⡀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢸⠀⢸⡷⣾⠁⣿⣒⢀⣿⣽⣇⢸⡇⠀⣿⢷⠟⡇⢸⣗⡂⣿⠻⣾⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈⠁⠉⠉⠉⠁⠀⠉⠈⠁⠀⠉⠈⠀⠁⠈⠉⠉⠈⠀⠈⠁⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣧⡀⠀⣀⣀⣤⣤⣴⣄⣠⠀⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠤⢘⡇⠶⠛⠉⠁⠀⠀⣈⣉⣛⠂⣾⠁⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢸⠀⠒⢸⡇⠀⠀⣾⢻⣶⠟⠉⢉⣽⠿⣿⠀⠀⠀⣿⠀⣀
⠀⠀⠀⢀⣀⣶⠶⠟⠛⠉⢸⣀⣛⣸⡇⠀⢠⡟⠘⣧⢀⣴⠟⣡⡞⠹⡟⠛⠛⣿⠈⠛⠳⢶⣆⣀⡀
⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣼⣏⣿⣹⣇⠀⢸⡇⠀⣿⠞⣠⡾⠋⠀⣸⠇⠀⠀⣿⠀⠀⠀⠀⠈⠙⣧⡀
⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⢩⣭⣿⣭⡅⠀⠸⣧⣤⡿⠿⠯⢠⡄⠚⠻⢦⣤⡴⠋⠀⠀⠀⠀⠀⠀⠘⣯
⠀⢀⣿⠀⠀⠀⣀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠈⣹⣆⢀⡾⠋⢀⣿⡀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠲⠶⣤⣀⣤⠶⠖⠶⢦⡀⠀⠀⣰⠷
⠀⠀⠉⠙⠸⡷⠶⠛⠉⠛⠶⠶⣿⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢀⡈⠛⠁⠀⠀⠀⠀⢹⡆⠼⠋
⠀⠀⠀⠀⠀⣷⠶⠶⠶⠶⠶⢶⡏⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⡾⣧⠀⠀⣠⣄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠹⣷⠂⠀⠀⢲⡿⠁⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⠛⠛⠁⢿⣴⠟⠋⠙⢛⣿⠟⠛
⠀⠀⠀⠀⠀⣀⣽⣟⣛⣛⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠸⠏⠀⢀⣴⠟⠁
⠀⣠⡶⠚⠛⠹⢧⣍⡿⣯⣡⠿⠙⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣴⠟⠁
⢰⡏⠀⠀⠀⠀⠀⠹⣧⡿⠁⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⣠⠶⠶⠶⠦⠤⣾⡟⠛⠛
⣼⠁⠀⣄⠀⠀⠀⠀⢹⠁⢸⡏⠉⢹⡇⠀⢨⡀⠀⠀⣾⠛⢷⣄⣤⠦⠦⠴⠞⠁⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⢸⠀⠈⠛⠛⠛⡁⠀⢠⡄⠀⠀⠈⠳⣄⠙⠷⠶⠶⠶⠶⠀⠀⠀⠀⢀⣠⣼⡇
⠋⠀⠀⠋⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠃⠀⠈⠃⣤⣀⣀⣤⡙⠳⠶⠶⠶⠶⠶⠶⠶⠶⠞⠋⠁⠹⠧⠶⠶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣥⣽⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⢹⣿⣿⠉⠉⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡀⠀⠀⠑⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡷⠀⠀⠀⠙⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⣠⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⣿⠀⣿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣤
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣿⠀⣿⣶⣶⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠟⠀⠻⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠛⠓⠒⠀⠀⠘⠓⠒⠒⠀⠀⠀⠒⠒⠚⠀⠀⠘⠓⠒⠛⠀⠀⠘⠛⠓⠛




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⢀⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢀⠀⠀⠀⠶⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⡰⠀⠀⠀⠀⠀⢀⠀⢀⣠⣀⠀⢠⣤⣤⣌⠀⠀⠀⠀⠄⠀⠀⠀⠰⠀⠀⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⠀⣤⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠀⠈⠉⠸⢻⣿⠄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣉⠀⠀⠀⠜⠀⠀⠀⠀⠀⠂⠀⠊⠀⠁⠀⠐⠶⠀⠀⢠⡄⠀⠀⠀⡀⠈⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡆⠈⠇⠄⠀⢯⠀⠀⠀⠁⠀⠀⣆⣀⡠⠀⠀⠀⠀⠀⠀⠙⢉⠀⠀⠀⢁⠸⠀⠀⢀⡀⠵
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠠⠄⠀⣗⠘⠀⠀⠣⠀⠀⠹⣾⡇⢀⠀⠀⠀⣰⠇⢀⢀⠀⠀⣼⠉⠀⠈⡀⢀⡄⢡⠶
⠀⠀⠀⠀⠀⠀⠀⠘⠙⡆⢠⠄⣗⢠⠙⠀⠀⠐⠀⡀⢿⣰⣻⠀⠈⠅⠁⠀⣼⢋⠦⠙⣏⠁⠀⠂⠈⣦⠘⠋⢰
⠀⠀⠀⠀⠀⠀⠀⢀⡶⡌⢨⠄⡺⢿⡆⡀⢠⠀⠀⠸⠘⠡⠴⠀⠀⡖⢠⣼⡗⡯⢠⣾⡟⣷⡄⠀⠀⠀⠹⢂⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣠⣾⡇⣼⣿⡋⠀⠀⣀⡇⣦⠀⢠⠀⢈⠳⠺⣍⡻⢷⡘⠜⣷⡈⢷⣴⠂⢀⣐⠜⠲
⠀⠀⠀⠀⠀⠀⠀⡄⠘⢿⢿⠥⡿⠜⢻⣷⡄⡈⢸⠃⠹⢦⣦⠀⠸⢁⠀⠈⢙⣿⣿⣀⡄⢧⣾⢽⣦⠮⢬⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣬⣿⠿⣷⠞⢺⡏⣿⢱⣿⠄⠴⣿⣿⠀⢰⡟⠛⣠⠆⢿⣯⣈⠁⣘⣁⣼⡎⠓⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠈⣥⣘⣿⣿⣿⠐⢪⣁⡼⢿⡎⢸⠗⡇⡨⠀⢰⣇⣤⠟⣿⣾⢻⢗⡆⡹⠋⠟⠑⢮⣷⣰⣬
⠀⠀⠀⠀⠀⠀⠀⢏⣿⣿⣯⣝⣿⣁⢌⢧⣿⣿⣿⣿⡶⠡⠴⠀⢸⣻⣿⣿⣿⣼⣌⠩⢫⣷⡆⢰⣄⡾⢁⡟⢻⠂
⠀⠀⠀⠀⠀⠀⠀⡛⣿⣿⢿⣿⣁⣀⢾⣼⣿⣿⣛⣿⠈⢳⡂⠀⢸⣿⣻⢸⣿⡿⢋⣼⢉⣹⣿⣾⣿⣷⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠀⠉⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠒⠒⠷⣿⡖⠐⠢⠀⠀⠀⢀⠀⢀⣀⣀⠀⠀⠀⠀⡠⠒⢒⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⠙⠲⣶⣶⣦⣀⢈⡿⠶⠴⠁⠀⠀⢻⣦⣤⣤⣄⣍⣑⠖⠀⣠⣤⡿⠋⠁⣠⡑⣀⢀⡀
⠀⠀⠀⠀⠀⡠⠊⠉⠉⠛⠲⢶⣿⣀⠀⠈⢻⣿⢿⠟⠁⠀⠀⠀⠀⠀⠘⠿⢿⠿⠟⠻⡇⠀⣸⡿⠋⢀⣼⣿⡟⠋⢉⣁⣌⠃
⠀⠀⠀⢀⠊⢀⣼⣿⣶⣤⣤⣾⣿⣿⣷⣶⠾⢱⢺⠀⠀⠀⠀⠀⠀⠀⣴⣤⣾⣦⣼⠘⠀⣠⣿⠇⠀⣸⣿⠏⠀⣰⣿⣿⣿⡀⠆
⠀⠀⠀⢘⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⡧⣼⡦⠤⣄⠀⠀⠀⠀⡖⠒⠀⠀⢺⠘⠶⠋⢰⠀⣰⣿⣿⣤⣾⣿⣿⣿⣟⣳⠈
⠀⠀⠀⢸⠈⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⠄⣰⠊⠀⠀⣠⠞⠀⠀⠀⠀⡆⠀⠁⠀⠙⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢡
⠀⠀⠀⢘⠈⠋⠹⢛⣿⣿⣿⣿⣿⢿⣿⣶⣯⣤⣴⡿⠁⠀⠀⠀⠀⠀⢷⣶⣶⣶⣾⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⡆
⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⢻⠃⠀⠀⠀⠀⠀⠀⢾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢱
⠀⠀⠀⠠⠀⢿⣿⣿⣿⡟⣿⠁⣿⣿⣿⣿⡟⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠛⠛⠛⠿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠸⡆
⠀⠄⠀⠘⣣⣉⣿⣿⣿⣇⢻⡄⠻⡟⠋⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡘⡻⣿⣿⣿⣿⣿⣿⣯⣤⡈⡇
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⢾⣿⣿⣿⣿⣿⣿⣷⣿

⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⢿⡿⠃⠀⠀⠀⠀⣾⣿⡆⠀⠀⠰⣞⣿⣻⡇⠀⠀⠀⠀⣸⣿⣿⣂⠀⠀⠀⢠⣾⢷⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣰⣶⣦
⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⣸⣿⣿⣿⡀⠀⠀⠈⣿⣿⣿⡆⠀⠀⢨⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⢀⣴⣦⠿⣿⡟⠀⠀⠀⠘⠛⠋⣶⣦
⠀⠀⢸⢻⣿⣿⡏⣷⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⡏⠀⠀⠈⢻⣿⣿⡏⠁⠀⠀⢠⣿⣿⡇⠀⢠⡄⠀⠀⠀⠀⠀⢀⣿⣿⡇⢀⣤⣤
⠀⠀⠈⢸⣿⣿⡇⠁⠀⠀⢹⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⡿⢿⡇⠀⠀⠀⠈⠻⢿⣿⠆⠀⣿⠀⠀⠀⠀⢸⣿⣿⣿⣃⣸⣿⣿
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⣼⡟⠀⠀⣻⣆⠀⠀⠀⠈⣿⠟⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠋⠙⠁⠀⠀⠀⡈⠛⠘⠃⠀⠀⠀⠀⠛⠙⠃⠀⠀⠀⠀⠈⠋⠙⠁⠀⠀⠀⠙⠁⠈⠋⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣄
⠀⠀⠀⠀⠀⢰⣶⣦⠀⠁⠀⠤⠀⠀⠀⠸⣯⣿⠀⠀⠀⠀⢸⣿⣿⠈⠀⠀⠀⠀⣶⣷⡆⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡆
⠀⠀⠀⢠⣾⣿⣷⣯⣤⠀⠀⠀⠀⢀⣴⣿⣿⣶⠀⠀⠀⣤⣶⣿⣶⡄⠀⠀⠀⣠⣿⣿⣷⠀⠀⢰⡄⠘⣿⣿⣃⡀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠈⣿⣿⣿⠻⠇⠀⠀⠀⠴⠟⢹⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⠀⢀⡼⠋⢿⣿⣿⠀⠀⠸⡇⣾⣿⣿⡿⠙⣛⣻⣃⣐⣶⣖⣀⣀⣀
⠀⠀⠀⠰⣿⣿⣯⡀⠀⠀⠀⠀⠀⢠⣿⢿⣿⠈⠓⠀⠀⠀⣾⣿⣿⠟⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⣿⣿⣿⣿⣧⠀⠙⣟⠛⠛⠛⠛⠛⣻⠋
⠀⠀⠀⢀⣿⡇⢹⡿⠀⠀⠀⠀⢀⣿⠏⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢠⡟⠛⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠐⠿⠋⠀⠻⠇⠀⠀⠀⠀⠘⠋⠀⠈⠿⠀⠀⠀⠀⠀⠻⠟⠿⠀⠀⠀⠀⠀⠻⠟⠿⠀⠀⠸⠋⠘⠿⠻⠟⠀⠀⠿⠀⠀⠀⠀⠀⠿⠀⠀⣾⣿⣷
⠀⠀⠀⢀⣤⣄⠀⢤⠀⠀⠀⠀⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢋⣤⣄
⠀⠀⠀⠹⢿⣟⠀⠀⠀⠀⠀⠸⣟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠏⠀⠀⠀⠀⠀⠀⠀⣶⣷⡆⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⢶⣤⣿⢿⣿⣧
⠀⠀⠈⣿⣿⣧⢰⡄⠀⠀⣰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⢠⣤⣝⣛⣁⣀⣀⣼⣿⣷⡄⠀⠀⠀⣠⣾⣿⣶⢤⣤⣴⡾⠛⠁⠈⢻⣿⡇
⠀⠀⠀⢻⣿⣿⡀⠀⠀⠀⠈⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿⣿⡅⠉⠉⠛⠋⣷⣹⣿⣿⡄⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⠟
⠀⠀⠀⠈⣿⡟⣷⡄⠀⠀⠀⣿⡿⣿⡇⠀⠀⣀⣤⣤⣶⡀⠉⣿⣿⣿⠁⠀⠀⠀⢈⣿⣿⢿⣿⠀⢘⣙⠛⠛⠛⡛⠃⠀⢀⣸⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡏
⠀⠀⠀⣼⡟⠁⣿⡇⠀⠀⠀⣿⡇⣿⡇⠀⠀⢹⣿⢿⡿⠃⠀⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⢸⣿⣛⣻⣿⣏⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠋⠀⠀⢛⡀⠀⠀⠀⠛⠁⠙⠃⠀⠀⠀⠀⠀⠁⠀⣀⣛⣉⣋⣀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠈⠛⠉⠛⠙⠋⠀⠀⠈⠉⠉⠉⠀⠀⢠⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣼⢲⡆
⠀⠀⠀⢀⣤⣄⠉⢩⣶⣶⣄⠀⠀⠀⠀⠀⢠⣶⣦⠀⢠⣤⡀⠀⣴⣶⡄⢀⣤⣄⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢹⢀⡀
⠀⠀⠀⣸⣿⣿⡀⢈⣿⣿⣿⣧⠀⠀⠀⠀⣈⣿⣏⡀⠻⣿⠏⢀⣻⣿⣁⠘⢿⡟⢀⣘⣿⣏⡀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⣿⣿⣿⣿⡾⣿⣿⣿⣿⣧⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣄⢀⣸⣿⣿⣡⠀⠀⠀⠀⠀⠐⢸
⠀⠀⢸⣿⣿⣿⣿⠐⠿⣿⠿⠟⠋⠀⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠇⠀⠀⣷⣼⣿⣿⣿⣿⡄⠀⠀⠀⣀⣀⣸⠀⠀⠀⢰⣶⡄⡇
⠀⠀⠈⢹⣿⣿⠉⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡾⣿⣿⡿⢷⣿⣿⡿⢿⣿⣿⠿⣾⣿⣿⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⠿⠇⡇
⠀⠀⠀⢸⣿⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⣿⣿⡷⢸⣿⣿⡇⢸⡇⣿⠀⣿⣿⣿⠀⠀⠀⠀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⢄⡀⠀⠀⠀⢠⡷⣄
⠀⠀⠀⠈⠁⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠈⠀⠁⠀⠉⠈⠁⠀⠁⠉⠀⠈⠀⠉⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠋⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠈⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣼⠧⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡾⠁⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡞⠁
⠀⢀⣤⠶⠶⠶⠶⠶⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟
⢠⡟⠉⠢⡀⠈⠠⡀⠀⠈⠙⠶⣄⣿⠛⠒⠒⠒⠓⠛⠛⠋⠉⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⣿⢧⠀⠀⠈⠳⣄⠈⢦⡀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⠘⣆⠀⠀⠀⠈⠳⣄⠙⢦⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠸⣆⠈⢢⡀⠀⠄⣀⠈⠳⢄⠙⢦⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠁⠀⢀⡾⠁
⠀⠘⢦⡀⠙⢦⡀⠀⠀⠀⠀⠑⢄⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠙⢦⣀⠈⠓⠶⢤⣤⣀⣤⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣤⠶⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠉⢉⣽⠟⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣠⠾⠋⠁⠠⠄⠀⢀⡤⠞⠉⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⠀⢀⣀⣠⠴⠛⠁⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⡠⠚⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⠦⠤⢤⣄⣀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⡃⠀⠀⣠⠖⠁⠀⣠⠖⠉⠀⠐⠀⠀⣠⠎
⠀⠀⠀⠀⣠⣴⡛⠛⠲⢤⣀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⢴⣟⡁⢀⣠⠞⠁⠀⣀⣀⡤⠖⠋⢁⡼
⠀⠀⠀⣰⠏⠈⠙⠲⢦⣀⡈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠈⠉⠉⠉⠉⠉⢉⣀⣠⡤⠶⠋
⠀⠀⠀⣿⣄⠀⠀⠀⠀⠈⠙⠲⢤⣀⠈⠙⠲⢤⣀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⢹⣏⠑⠦⣄⡀⠀⠂⠀⠀⠈⠙⠲⢤⣀⠈⠙⠲⢦⣤⢿⡆
⠀⠀⠀⠀⠻⣆⠀⠀⠉⠓⠒⠤⠤⣀⣀⣀⣀⣬⠽⠶⠒⠉⠀⢀⡿
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⣀⠀⠀⣀⣀⣀⣤⡴⠞⠋
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⣶⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣼⠀⠀⠀⠀⠀⠉⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠈⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⢻⣄⠀⠀⠢⣠⣀⣀⠘⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⣼⠘⡇⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠈⠻⢶⣆⡀⠀⢹⣿⢷⣦⣄⠙⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⢛⡄⠀⢀⠔⠁⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠉⠻⢾⣿⣿⣿⣿⣿⣿⣶⣄⣙⣿⣍⡑⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣾⣻⣶⣁⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣳⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⢫⡟⢱⠒⣤⡽⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣾⣌⣹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠾⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⢠⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠒⠊⢡⠆⠀⠀⠀⢀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾
⢰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠉⠀⠀⢀⣠⣶⠟⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠹⡇⠀⠄⣀⡀⢀⢇⣀⣠⣶⣿⡿
⣿⣿⡰⠦⠐⠂⠒⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠰⣤⣀⢀⣀⣀⣠⣶⢔⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⣉⢾⣿⣿⣿⠟⠁
⠙⢿⣷⣤⣀⣈⣡⣤⣤⡤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣦⣭⠼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠘⠋⠉
⠀⠀⠈⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡀⠂⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣡⡤⠶
⠀⠀⠀⢠⠞⠟⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢿⠏
⠀⠀⠀⣇⠀⠰⠚⠋⠀⠡⠀⠀⠀⠀⠀⠀⠀⠘⣧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⣿⣴⠇
⠀⠀⢸⣯⡖⢾⠉⠹⣧⡀⢡⠀⠀⠀⠀⠀⠀⠀⢿⡼⡀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⢀⣀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⡀
⠀⠀⢸⡿⢶⡤⠦⠐⠛⠯⠸⠆⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠈⣿⠈⣷⠀⠀⠀⠀⠀⠀⢸⣷⣶⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠈⣿⣿⠁⣀⢀⡀⢱⣤⡁⠀⠀⠀⠀⠀⠀⠀⢻⠎⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆
⠀⠀⠀⠘⣿⡶⠿⠿⡛⢽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠽⢶⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠈⠷⡖⠋⠙⡩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⠧⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀⣀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠲⠞⠉

⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⢦⣄⠀⠀⠀⠀⢀⣀
⠀⠀⣀⣤⣴⣾⣿⡅⠀⠀⠀⠀⠀⢀⣴⣾⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡷⠶⠟⠃⠀⠀⢀⣿⣿⣇
⠀⠈⢿⣄⣿⣿⣿⢿⡀⠀⠀⠀⠐⢿⣽⣿⣿⣏⣿⠆⠀⠀⠀⢠⣾⣿⣿⣆⠀⠀⠀⢀⣴⠟⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣟⣷⡀
⠀⠀⠀⠉⣿⣿⣿⡈⢿⠄⠀⠀⠀⠀⢹⡿⣿⡏⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠈⠁⠀⣿⡿⣿⠀⠀⠀⠀⠀⠈⠙⣿⣿⡏⠉
⠀⠀⠀⠀⢸⣷⠹⣷⡀⠀⠀⠀⠀⠀⣿⠇⢹⣧⠀⠀⠀⠀⠀⢘⣿⠃⢻⡟⠀⠀⠀⠀⠀⠀⣿⡇⢿⡇⠀⠀⠀⠀⠀⢨⣿⣿⡇
⠀⠀⠀⢀⣾⠏⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣆⣿⠇⠀⠀⠀⠀⠀⣴⡟⠁⢸⣧⠀⠀⠀⠀⢀⣾⠏⠘⣿⡄
⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢀⣠⣴⢦⣤⡴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣋⡀⠀⠀⠀⠘⠻⣦⣘⣿⣣⣴⠟⠁⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⢀⠀⠀⢀⣹⣿⣁
⠀⠀⢀⣼⣿⣯⡀⠀⠀⠀⠀⣀⣤⡾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⡅⠀⠀⠀⠘⢷⣶⣿⣿⣿⡏
⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⠈⠉⠁⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠉⣿⣿⡇
⠀⠀⠹⣿⡟⣿⡟⠀⠀⠀⠀⠀⠀⢀⣿⢻⣿⠀⠀⠀⠀⠀⠀⢠⣿⠉⣿⡄⠀⠀⠀⠀⠀⣿⡟⣿⣾⠃⠀⠀⠀⠀⠀⠀⢸⡿⢸⡇
⠀⠀⢠⣿⠃⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡇⠀⠀⠀⠀⢠⣿⠇⢹⡇⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⣷
⠀⠀⠿⠃⠀⠹⠇⠀⠀⠀⠀⠀⠀⠘⠟⠘⠿⠀⠀⠀⠀⠀⠀⠸⠇⠀⠸⠇⠀⠀⠀⠀⠿⠃⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠿⠂

⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⣿⣿⣩⡿⠇⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢴⣿⡆⠀⠀⠀⠀⠀⠀⠐⣿⡿⢠⣄⠀⠀⠀⠀⠀⠀⠘⣿⡟
⠀⠀⣰⣿⣿⣟⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⢷⣄⠀⠀⠀⠀⠀⣰⣿⣿⣿⣄⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠷⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠈⠻⢿⣿⣿⠀⠀⠀⠀⠀⣾⠃⣿⣿⣿⣠⡿⠂⠀⠀⠀⠘⣯⣿⣿⣿⣿⠂⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⠟
⠀⠀⠀⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⢘⣿⢻⣿⠁⠀⠀⠀⠀⠀⠸⢻⡿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠂
⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⢀⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⣿⠁⢻⠇⠀⠀⠀⠀⠀⢸⠏⠸⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⠼⡿⠀⠀⠀⠀⠀⠀⠀⢿⠇⢿⠇⠀⠀⠀⠀⠀⠠⡿⠃⠹⡷

⠀⠀⠀⢀⣠⣈⣶⣦⣠⣀⠀⠀⠀⠀⠀⢠⣶⢆⣠⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠸⣯⣤⣿⣯⣬⡿⠇⠀⠀⠀⠀⠿⣧⣤⣽⣧⣤⠀⠀⠀⠀⠀⠀⠀⣘⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄
⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⢿⣿⡿⣇⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⢸⣿⣇⣻⠀⠀⠀⠀⠀⠼⢫⣿⣿⣿⣿⠹⠇
⠀⠀⠀⠀⠀⢸⣏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⡇⠀⠀⠀⠀⠀⠀⠁⢸⠀⣿⠈⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣿⡟
⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⢀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤
⠀⠀⠀⠀⠀⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢠⣦⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠃⠀⠀⠀⠀⠀⢀⠀⣼⠛⣿⣶⡀
⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠻⠿⢿⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢸⡿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿


⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⢠⣶⣿⡿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠟⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⢠⣿⡁
⠀⠀⠀⠀⣿⣯⣿⡄⣷⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣷⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣀⡀
⠀⠀⠀⠀⠀⢸⣿⠁⣹⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀⣹⡿⢉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⡄
⠀⠀⠀⠀⠀⠘⠃⠀⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠈⠋⠀⠀⠀⠀⠀⠀⠛⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠒⠲⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⣀⣤⠤⠀⠀⠀⢀⡄⠀⢀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢠⠖⠃⠀⠀⢸⠀⠀⠀⠀⠀⢳⠴⠃⡔⠉⢢⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠤⣄⠸⡖⠁⡀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠸⣄⣠⢎⡞⠀⢀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢰⠁⢀⡤⡄⠳⠊⠀⣀⡤⠴⠒⠒⠒⠒⠦⢤⣀⠀⠀⠸⣤⠴⢋⡴⢦⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠸⣄⣀⡴⠃⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠰⢛⠗⠉⠀⠀⢳⡀
⠀⠀⠀⠀⠀⣼⠀⠀⢀⠄⠀⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠸⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢀⡇⠀⠀⡼⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡶⠋⢶⡄⠀⢱⡀⠀⠀⠘⡆⠀⠀⢸⡀
⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠴⢏⣀⠜⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠀⠀⠈⡇
⠀⠀⠀⠀⢸⡀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⠀⣴⠚⢁⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⡇
⠀⠀⠀⠀⠈⡇⠀⠀⠘⡆⠀⠀⠈⢇⠀⠐⣶⣾⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡞⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⠆⠀⠀⠘⢦⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⡄⠐⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢀⡐⠛⢦⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⢨⠷⠄⠀⠉⠑⠲⠤⠤⠤⠤⠖⠊⠉⠀⢀⢰⡃⠙⡆⠈⠃⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⡰⠓⠂⣠⠏⠀⢠⠀⠀⡀⠀⢀⡤⠆⠀⣆⡸⣆⠳⠤⠃⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠰⣅⡄⠀⡇⠀⡸⠁⠀⠘⠒⠒⣦⠘⠄⠈⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠓⠚⠁⠀⠀⠐⠒⠋⠁⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⠤⠤⠴⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⢀⡴⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠈⠳⣄⢀⡴⠋⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠈⠉⠙⠲⣄⠀⠈⠿⣄⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⣀⣤⠴⠞⣧⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⡤⠶⠚⠛⠉⢁⣀⣤⠴⢾⠄⠀⠀⠀⠙⢶⣤⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡤⠶⠖⠛⠉⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⣀⠀⠀⠀⠀⠀⠀⠐⠂⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣾⠇⣸⡣⠀⢨⠆⠀⠀⠀⢰⣤⣴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢛⢻⣿⠾⢹⣏⣄⣸⣇⢤⠀⠀⠀⢙⣿⣿⣿⣧⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠴⢿⣿⣿⣿⣷⣾⣯⣤⠤⠤⡍⠀⠤⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢀⡄⣶⣿⣿⣧⣨⠟⠛⠉⠏⠋⠒⠲⠒⠡⠞⣁⢾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢛⡙⠺⣫⣬⣿⣯⡀⠤⠾⣿⢷⣶⡦⠖⠒⠚⣿⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢿⢲⣖⣚⡯⡀⣼⠛⠁⡄⠀⠈⣎⣹⢃⣀⣠⡔⠋⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣷⢘⣿⠍⡉⢀⡰⢿⡇⢶⣿⠀⠀⡿⠛⠉⠁⠀⠱⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⣼⣇⢹⡟⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⣿⠞⡀⠰⠖⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⢛⣛⣛⣛⣛⡛⠛⢛⣛⣛⣛⣛⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣏⠀⢠⣿⣿⣿⠠⡏⠀⢠⣿⣿⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠈⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⡔⠚⢛⣒⣳⣦⢀⡖⠛⢛⣚⣲⣦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠳⠦⠼⠿⠿⠛⠀⠳⠤⠾⠿⠿⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⣠⠤⠤⠤⢤⣄⠀⣠⠤⠤⠤⢤⣄⢸
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣼⣤⣡⣀⣀⣛⣛⣛⠘⢇⣀⣸⣿⣿⡿⢸
⠀⠀⠀⠀⠀⢰⣿⡿⠿⢿⣿⣿⡿⠿⢿⣿⣿⡿⠿⢿⣿⣿⣿⠿⢿⣿⣇⣀⣀⣀⣀⣀⠀⢸
⠀⠀⠀⠀⠀⢸⣿⣠⠞⢁⣿⣿⣠⠔⠉⣿⣿⣁⠔⠋⣿⣿⣇⠴⠋⣿⣿⣿⣿⣭⣭⣽⣷⢸
⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣶⣾⣿⢸⣿⣿⡟⠛⠛⠁⢸
⠀⠀⠀⠀⠀⢸⣿⠟⢉⡿⣿⣿⠟⢉⡿⣿⣿⠟⢉⡻⣿⣿⡟⠋⣹⡟⠘⠛⣛⣷⣶⣖⣦⣸⣀⡀
⠀⠀⠀⠀⠀⢸⣿⣖⣉⣠⣿⣿⣶⣋⣠⣿⣿⣶⣋⣀⣿⣿⣷⣊⣠⡇⠀⡞⠉⠀⠀⢸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠈⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦⣷⣀⣀⣀⣈⣭⣭⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⣋⣭⣤⣶⣦⣤⣭⣭⣭⣭⣭⣥⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⠿⠿⠿⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣀⡀⠀⣀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⠿⠷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⣀⣀⣀⣠⣴⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠸⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣤⣄⣀⢀⡆⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡏⣾⡇⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣦⡀⠙⠻⣿⣿⣿⣿⣿⡇⣿⣧⢻⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⡀⠈⠻⣿⣿⣿⣷⢹⣿⣎⢿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠻⣿⣿⣧⠻⣿⣧⡙⢿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠻⢿⣷⠙⢿⣿⣦⣝⠻⢿⡇⠀⢸⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣮⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⣀⣵⣿⠇⠙⠻⢿⣿⣷⣦⣤⣬⣭⣭⡭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣭⣭⣭⣭⣭⣭⣵⣶⣿⣿⠟⠁⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣪⠭⠭⠭⢑⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡸⢇⠸⢄⣀⣀⡠⠜⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠀⠒⠒⠈⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠒⠒⠒⠒⠊⠉⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠉⠒⢬⡑⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠴⢒⢤⠀⠱⡘
⠀⠀⠀⠀⠀⠀⡗⢦⡀⠀⠀⠀⠀⠀⢀⣀⠤⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣠⣾⡵⢻⠇⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠂⢬⡉⠉⠉⠉⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⣀⠀⡠⠚⣡⣴⡿⠟⣋⠴⣁⣀⣠⠗
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢉⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠉⠉⠲⡝⢦⣾⠟⢋⡤⠊⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣗⠠⣀⠇⠀⠀⠀⠀⠠⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠧⠚⠉⠉⠉⠑⢄⠘⡞⣧⠔⠁
⠀⠀⠀⠀⠀⠀⠙⠢⣀⡀⠀⠀⠀⠀⢀⣀⠴⣪⠃⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠈⡆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠢⢍⣉⣉⣉⣉⡡⠤⠊⠁⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠈⠉⠢⡀⠀⠀⢀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡠⠐⠒⢄⠀⠀⢱⠀⠀⣨⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡍⠢⣀⠜⠀⠀⣸⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣫⠖⠛⠊⠁⠀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⢀⡠⣞⠵⠊
⠀⠀⠀⠀⡠⢖⡽⠊
⠀⣀⢔⡫⠖⠁
⣾⠕⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠛⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡙⠀⠖⠂⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠊⡁⢉⡇⠀⠀⠀⠀⠀⠀⠀⡞⠁⠉⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⢻⢌⡟⣄⠉⠁⠴⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡻⠄⠴⢴⡇⠀⠀⠀⠀⠀⠀⠨⡗⠂⠐⣿⡇⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠾⢥⡤⠲⠞⣸⠋⠀⢸⠀⣠⡶⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢙⡇⢣⡤⠚⠃⠀⠀⠀⡀⠀⠀⠀⠙⢀⡎⢘⢁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣧⢾⠆⢳⣴⣻⣟⢋⣴⠞⠁⠈⡆⠀⠀⠀⠀⢀⡞⠙⣅⣤⣾⠑⢄⠀⠀⠘⢏⢺⠀⡴⢋⣹⣦⣾⠛⢿
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⡞⠑⢠⣯⠀⢸⠟⠁⠀⣠⠈⣷⠀⠀⠀⠀⢸⠀⢰⣯⣛⠅⣧⢸⠀⠀⠀⠀⡟⠷⢁⣜⣿⡾⣿⣧⠀⡇
⠀⠀⠀⠀⣤⠒⢆⢛⡿⢤⡀⢰⠃⠀⣾⠸⡇⠚⠃⣠⡾⠁⠀⣿⠀⠀⠀⠀⠸⠀⢸⡏⣄⠄⣿⠀⡆⠀⠀⠀⠙⠖⢁⠏⢠⠰⡽⢯⡀⠇
⠀⠀⠀⠀⡇⠙⠲⣭⠕⢺⠀⠘⠒⠚⣏⠀⠻⠶⠞⠋⠀⠀⠀⣻⠀⠀⠀⠀⠀⡃⠰⣇⣈⢸⣿⠀⡇⠀⠀⠀⠀⠀⢸⣀⣁⣑⣚⢘⡄
⠀⠀⠀⠀⡇⠀⠀⣿⠀⢸⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠣⠀⠱⠼⠶⠿⠰⠇⠀⠀⠀⠀⠀⠀⡇⠈⡅⠉⢹⡁
⠀⠀⠀⠀⠉⠓⠶⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡵⠻⠟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠂⣱⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠠⡷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠤⠤⣄⠀⠀⡌⡿⡉⢖⢡⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⠒⠒⢲⣶⢾⡂⢸⣄⣹⠎⢳⡀
⠀⠀⠀⠀⠀⡔⢻⢸⠆⠠⠤⣼⢀⠜⠂⣿⢛⢻⣧⠡⣌⣱⣦⣀⣄⡀⠀⠀⠀⠀⣾⣍⣥⠶⢶⣟⠉⢻⡇⢸⣇⡴⠦⠴⢧⠀⡀
⠀⠀⠀⠀⠀⡇⢸⠈⠑⠒⠒⢲⣎⡠⢊⣟⣰⡢⠝⠂⣇⠉⢹⣈⣀⠉⠀⠀⠀⠈⢓⣾⡇⠀⢀⣽⡶⠼⣅⣸⠻⠆⢸⣶⣮⣏⠟
⠀⠀⠀⠀⠀⠿⠟⠀⠀⡐⠂⠃⠲⠤⡀⠀⠉⠉⠉⠛⠓⠒⠾⠤⠤⡄⠀⠀⠀⠀⠓⢢⡿⡺⣿⠿⢿⣦⣌⡉⠛⠲⢤⣝⣲⠈⠳⡄
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠉⠀⠉⠀⢀⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠼⠻⣽⡛⠓⢦⣄⡈⠛⠶⠄⠀⠀⠉⠁⠀⢹⡀
⠀⠀⠀⠀⠒⠲⢭⣭⣽⣒⣒⠦⠤⢤⣀⣸⠀⠈⠉⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢡⡶⠿⣷⣦⣄⡙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠠⠻⠌⣆⣿⣿⡩⠛⠛⠓⡶⠾⡆⠀⠀⠀⢸⣧⠠⠤⠄⠀⠀⠀⠀⠀⠀⠙⣶⠈⠳⣤⡀⠉⠛
⠀⠀⠀⠀⠸⣵⣞⣍⣿⡿⢙⣿⡿⠝⠊⠀⡏⠉⡐⠖⠺⣯⢉⣉⡒⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⣴⠉⠙⠒⠛⠲⠶⠶⠶⠶⠚⠶⢤⡀
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⣿⣯⡤⣀⣀⣿⣠⡾⢿⠀⠀⠀⠀⠀⠀⠰⠴⠆⠀⢷⣀⠀⣠⣆⠀⠀⣤⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠓⠒⠃⠀⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣤⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⣿⢷⡄⠀⣾⣿⣿⣟⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣆⣩⣿⣅⢼⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⡯⣻⣿⠃⠀⠙⣿⣿⣿⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⣿⣿⣿⣿⣾⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣠⣬⡄⠀⢈⣵⢶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣾⣿⣿⣿⣽⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⡿⠀⢘⣻⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⡈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⣭⣍⠁⠀⠸⣿⣟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡛⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣾⣿⣿⣿⣷⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠆⣴⡦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⢿⠿⠋⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣄⠀⠀⠀⠀⢾⣽⣿⠆
⠀⠀⠀⠀⠀⠀⠀⣦⡀⣠⢶⢹⣿⣿⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣿⡿⣿⠀⠀⠀⠀⢿⣟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠉⢁⣘⢸⣿⣿⣿⣿⣿⣿⣿⣷⡴⠀⠀⠀⠀⠀⠀⠀⠀⣺⢷⢿⣇⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠰⡇⠀⢸⣀⡏⢛⣿⣿⣻⣯⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡏⠀⠀⠀⠶⣾⣿⣹⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡇⠀⠉⠻⠿⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠾⠇⠀⠀⠀⠻⠛⠉⠙⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⡻⢿⣿⣿⣿⣿⣿⣿⣿⢟⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢟⣼⣷⣮⣭⣭⣍⡩⣵⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⡍⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⢩⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠿⠿⢛⠿⣿⣿⣿⣿⠿⡛⠿⠿⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣴⣿⣿⢟⡛⢡⡌⠿⣿⣿⣿⣦⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣸⡇⣿⢱⡗⢼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⣿⢃⣿⢸⡏⣾⢃⡆⣽⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠻⣸⣧⣿⣱⡟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣿⡟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡄⣿⣿⣿⣿⣿⣿⣿⢣⡿⢟⣴⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⢹⣿⣿⣿⣿⣿⡟⣨⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⢀⠊⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠑⢄⠀⠀⡠⠁⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠢⡀⠀⠑⠈⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠳⡄⠀⠀⠈⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢢⠑⡞⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠈⠢⣄⠠⡈⣂⢢⠇⠋⠐⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡈⠳⣄⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠉⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣣⠎⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠑⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠊⡤⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣨⡇⠀⠀⠀⠀⡸⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠈⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⠠⠔⠁⠀⢀⠀⣰⠗⡀⠀⠐⠄⡀⠃⢀⠀⠀⠀⠀⠠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠑⠀⣄⠀⠀⡀⠀⢀⡀⠀⠽⠀⠥⣜⣳⠆⠀⠁⠀⡄⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠈⠲⣄⣡⣄⡈⠁⠀⠰⡆⠒⢺⣄⣀⣀⣠⠞⣰⢇⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢉⠓⠀⠁⣄⠠⠉⠀⠀⢲⠄⠀⠛⠦⠼⠿⢖⡋⠀⢀⣌⣦⡄⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠒⢇⠀⠀⢉⠖⠐⡶⢀⣾⡀⠀⢠⢄⠀⢤⠀⠀⢀⡠⠄⣀⣷⣀⠀⠈⣦⡀
⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠒⠒⠺⠛⠄⠀⣄⣀⢀⡔⠁⣀⡴⣳⣞⠉⠉⠒⢄⣀⣱⡎⣀⠔⠋⠀⣀⣟⡩⠞⢁⡼⠁⣸⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣨⡯⠅⠠⠤⢖⣁⣀⣈⣤⠀⠉⠉⠓⠚⢻⣈⣉⣩⠴⠛⠶⣞⣛⣒⣩⡼⠁
⠀⠀⠀⠢⠴⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⡤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢢⣈⠋⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠻⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⣴⠟⢡⣾⠟⣹⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⢷⡀⢠⡟⠁⣴⠟⢁⡶⢋⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢳⡿⢤⣼⠃⣰⠟⣠⠟⣱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢿⡀⠈⠙⢦⡉⠛⢧⣴⠏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⡇⠀⠀⠀⢱⡞⠳⣝⣾⠃⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢸⡇⠀⠀⠀⠸⣇⠀⢻⡄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢘⡇⣤⡀⠀⠀⠹⣆⠀⢷⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠈⠙⠛⠶⠆⣿⠀⠀⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡎⢷⡀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⡟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⡟⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⣿⣷⣿⣿⡿⠿⠿⣿⣿⣿⣿⡆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⡿⠿⠇⣿⠀⠿⠿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣇⠛⠛⣿⠟⠛⢂⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣇⠛⢀⣿⣿⣿⣿⡇⠀⠀⣿⣧⡴⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢃⣠⣶⠟⠉⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⣀⣠⣤⣤⣄⣀⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠈⠉⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⣄⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⢿⣿⣿⣛⣻⣿⣿⡿⠿⢿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣤⣤⣤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠛⠛⠛⣿⣿⣿⣿⠛⠛⠛⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⡀⣠⠤⠤⢤⣤⣤⣀⣠⣤⠤⣴⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣰⣇⠀⠙⢥⣀⣀⣀⣿⣿⣿⡀⣀⣸⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠈⠳⢤⣴⣿⣯⠉⢻⣿⣿⣋⡉⢉⣽⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡶⣤⣀⣀⣾⣿⣿⠶⠛⠉⣽⣿⣿⠟⠻⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣬⣍⣛⣛⢋⣀⣤⡴⢞⣛⣉⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡤⠴⠖⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⣀⡠⠀⠀⠀⠰⠄⠈⠳⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠀⢠⠀⢈⠊⠀⡀⠀⠀⠀⠀⠀⠀⠰⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣳⣶⡊⠀⠈⠀⡀⢦⠀⠃⢠⣶⣿⡍⠧⠰
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⢀⠘⡅⢿⡿⣿⡗⡀⠀⡑⠀⠀⠀⠻⠜⠛⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⣱⡀⠀⠀⠀⠀⡇⠀⣦⠎⠈⡒⠈⠙⠋⣄⣀⣈⠀⠀⢀⡄⠀⠠⢤⠄⣀⡠⣧⣧
⠀⠀⠀⠀⠠⡋⠋⠹⡀⠀⠀⠛⠃⢿⡿⠁⠉⠉⠉⠉⠉⠉⠩⣛⠍⠁⠀⠀⠀⠀⠀⠀⠩⢍⠨⡙⠄
⠀⠀⠀⠀⠀⠡⠀⠀⢣⠀⠀⠀⢸⠘⣧⡀⠀⠀⠀⢀⣀⣀⡀⡅⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⡋⣧
⠀⠀⠀⠀⠀⠀⢣⠀⡀⢧⣀⠴⡐⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢗⡓⡎⢏⠆⠱⣸⢹⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠼⡶⠄⠘⢾⡀⠀⠀⠀⠀⠉⠙⠓⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⢺⣥⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⣜⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⠢⢄⡀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠚⠛⠛⠋⠙⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢼⡗⠶⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⠾⡇
⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⢧⡀⠘⢧⣀⡀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠙⢦⠀⡏⠉⠙⠛⠒⠒⠒⠒⠒⠚⠛⠉⢹⣠⠤⠶⠶⠶⠦⣄
⠀⠀⠀⣀⣧⣤⡤⢤⡀⠀⠀⠀⠈⢳⡏⠁⠒⠲⠤⠤⠤⠤⡄⠀⠀⠀⢸⡟⠒⠒⠀⠒⠒⢻⡇
⠀⢠⢞⡏⠀⠀⠈⢦⠱⡄⠀⠀⠀⠀⣧⠀⠀⠀⢐⢒⠆⠀⡇⠀⠀⠀⣸⠟⠓⠒⠒⠒⠋⠻⣤⣄⣀
⠀⡏⢸⠀⠀⣠⠤⠬⣇⢹⡀⠀⠀⠀⢹⠀⠀⠀⠘⣳⠆⠀⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⠙⠒⠤⣀
⠀⣧⠸⡄⢀⡧⢤⡞⣿⢸⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡏⠒⠦⠤⠤⠤⠤⠖⢻⠀⠀⠀⠀⢠⠞⠙⡆
⠀⠸⣆⢓⠁⣀⠞⢱⢇⡞⠀⠀⠀⠀⢸⠲⢤⣀⣀⠀⢀⣀⣼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡔⠀⢀⠇⡠⠒⠳⣤
⠀⠀⠈⠳⠭⠿⠶⢿⡋⠀⠀⠀⠀⠀⢸⣄⠀⠀⠉⠉⠉⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⢤⣇⡇⢸⠀⢧⣀⣰⡾⣤⣀
⠀⠀⠀⠀⠀⢀⣠⡤⠭⣗⠒⠶⠒⠛⠉⠉⠙⠲⠤⠤⠤⠤⠤⠴⠒⠉⢷⡢⢤⣀⣀⣀⣠⢴⠏⠀⠈⠉⠛⠛⠉⠈⠉⠀⠀⠉⠛⠲⢤⣀
⣠⠤⠤⡤⢴⣅⡀⣠⡤⠏⠀⠀⠀⠀⠀⠀⢠⣒⠲⠶⢦⡀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠚⠁⠀⠀⢠⠤⠶⠒⢤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠁
⠳⢤⣀⣁⣀⣀⡿⠀⠀⠀⠀⢠⠔⢒⠒⠲⣮⣑⣒⣒⣻⣡⣴⠚⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⢨⠀⢀⣸⠆
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢟⠢⠼⠤⢖⡿⠀⠉⣡⠋⠀⠈⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠳⣄⣠⠴⠋

⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡀⢶
⠀⠀⠀⠐⣳⢓⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠰⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠺⣿⠇⢈⠇
⠀⠀⣀⣀⣟⣥⣷⠰⠆⠀⠀⠀⠀⠀⣯⣦⡠⠄⢪⣼⡇⠀⠀⠀⠀⠀⠈⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿⡆⢸⣇
⢠⢴⣿⣿⣯⣿⡯⢥⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢈⠨⠄

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⠀⠀⠀⠀⠀⠠⢴⣶⡆⠄⠀⠀⠀⠀⠀⠀⢀⢶⣶⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠁
⡀⠀⠀⠀⡔⠀⡠⠧⢒⣧⠀⠀⠀⠀⠀⠀⠨⣿⡅⠀⠀⠀⠀⠀⢀⣺⣲⣷⣷⣎⣶⣶⣀⠀⠀⠀⠀⠀⢸⡝⠄⢀
⢠⡀⠛⠰⠷⠾⢁⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠇⠈⠉
⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡄⠀⢀⣝⣄⠀⠀⠀⠀⠀⠀⢰⡆⠀⠰⠆⠀⢀⣜⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⢰⡖⠒⠀⣿⣿⠀⠀⠀⠀⠀⠀⠸⡃⠀⠸⠋⠉⠈⣚⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀
⠀⣸⣷⣦⠀⡿⡏⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰⡆⠀⠀⣿⡇⠀⠀⠀⠀⢀⠀⣀⡀⣴⣻⣥⠀⠀⠀⠀⠀⣼⣿⣗⡷
⣀⣻⣿⣩⣄⣇⣇⣀⣀⣀⣀⣀⣀⣐⣒⣛⣛⣒⣆⣀⣇⣇⣀⣀⣀⣠⣾⣷⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣻⣿⣃⣤⣁
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⣉⡠⠔⠛⠂⠀⠀⡴⠩⠡⠤⠉⣦⠀⠀⣰⠚⠉⠛⠃⠲⡄⠀⠀⣎⣭⠔⠈⣑⡄⠀⠀⢠⠮⢥⡏⢑⡆
⠀⠀⢟⣒⠶⠶⡒⠃⠀⠀⠇⡒⠒⠒⢒⠉⠀⠀⠸⠅⢒⣒⠂⠜⠁⠀⠀⠣⢌⠉⠉⠥⠃⠀⠀⠘⠣⠘⠳⠞⠁
⠀⠀⠀⠀⠉⠁⠀⡠⠄⠠⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⡠⣀⡀⠄⠀⠀⠀⠀⠀⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠀⠀⠀⠀⡎⡱⡄⢱⠀⠀⠀⢰⡋⠀⠀⡄⠀⠀⠀⠀⢐⠙⠢⣀⢸
⠀⠀⠀⠀⠀⠀⠘⢇⣁⡠⠎⠀⠀⠀⠀⠙⠂⠘⠂⠀⠀⠀⠀⠻⠦⠮⠊⠀⠀⠀⠀⠘⠦⠤⠬⠃
⠀⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠀⡠⠒⠀⢢⠀⠀⠀⢀⠠⠐⢠⠀⠀⠀⠀⡠⠔⠊⠉⡦⠀⠀⠀⠀⢀⠔⠈⠑⡆
⠀⠠⠊⠉⢢⢀⡴⠁⠀⢀⠔⠻⣄⢀⢔⡝⠀⢀⣴⣧⡀⠀⡀⠀⠀⡠⠊⠀⠀⣀⠜⠀⠀⠀⢀⠔⠑⢄⣀⠔⠁
⠀⢇⣀⠤⠘⠁⠀⠀⢠⠃⢀⡠⡺⠕⠁⠀⠀⣿⣿⣿⠿⠊⠀⠀⠰⡤⢠⣄⠾⠋⠀⠀⠀⠀⢇⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⢀⣀⣀⡀⠀⠈⠉⠀⠀⢀⠀⠀⢀
⠀⠀⠠⠤⠄⠀⠠⢤⠀⠀⠀⡞⠁⠀⠀⠈⡂⠀⠀⠀⠀⢆⠁⠈⠠⢱⠀⠀⠀⢠⠄⣀⣐⣆⡀⢦
⠀⠀⠈⠒⠀⠀⠚⠋⠀⠀⠀⠫⢑⠒⢒⠾⠁⠀⠀⠀⠹⣐⣛⡒⠀⠝⠀⠀⠀⠈⠒⠒⠒⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⣼⠉⠀⠀⡘⠄⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡄⢸⣿⠋⡀⣿⢴⡀⡀⠐⠅⠀⠀⠀⠀⠀⠀⢻⢶⣾⣦⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢉⠻⣼⣿⣸⡇⢸⣧⢱⠁⢀⣓⠀⠀⠀⠀⠀⠀⠀⠱⡴⢹⣽⣿⣿⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡧⣹⡏⣴⣶⣬⣥⡥⠞⠉⣄⣁⣈⠐⠂⠀⠀⠀⠹⠷⠿⢿⢾⣿⣿⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠛⢷⢻⢸⡿⠛⢻⢦⣖⣿⣿⣹⣉⣁⠨⠄⠠⠙⢛⠿⠛⠿⠟⢻⡼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⣰⠰⣾⣟⠸⢬⢳⣄⣤⡾⠋⠉⠀⠹⠄⠋⠉⠉⠱⠒⠃⢲⠚⢁⡠⢛⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⠾⠛⠮⣭⡅⠌⢘⣷⣿⡙⠀⠀⢀⣴⣾⣷⣦⣤⣤⣀⣨⡤⠤⠴⢿⣇⠀⢡⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡖⢻⡇⠐⠒⠀⢘⣵⠟⠛⠉⣹⣭⡔⠈⠉⠈⠙⢿⠹⣿⢻⡁⠀⠀⠀⠀⣨⣿⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⢸⡷⠘⣿⢙⣝⢉⣉⡿⢄⠀⢸⣟⠀⠀⢰⡆⠀⠀⠘⣇⠠⠋⣀⣀⣄⣤⡞⠁⠈⠓⠅
⠀⠀⠀⠀⠀⠀⠀⠈⣶⠀⢹⢿⡋⠉⠉⠀⠀⢰⡿⣿⡄⣶⣼⡇⠀⠀⠀⣿⠶⠚⠋⠉⠁⠉⠹⣄
⠀⠀⠀⠀⠀⠀⠈⠀⠹⠧⠾⠋⠢⠉⠁⠀⠒⠉⠀⣿⠇⢠⠿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣠⠨⢰⠇⠀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⣃⠿⡀⠈⢶⠶⢀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⣼⠇⠐⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠶⣤⣀⠀⠀⠀⠀⠀⠀⠻⣕⠶⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⡠⠂⠁⠀⠈⠈⢵⠄⠀⠀⠀⡀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣴⣾⣿⣤⣶⡖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠐⠶⡾⠶⠦⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⣩⢿⣿⠿⠛⢋⣉⣥⠀⠀⠀⠀⠀⣀⣰⢇⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣧⣀⣠⣠⡌⢿⣤⣶⣶⣿⣿⣿⣿⣤⣤⠤⠶⠛⠋⡁⠈⠀⣴⣶⣶⠆⠀⠀⢀
⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢀⣹⢿⣇⢢⣀⣀⡀⠀⢀⢀⣠⣤⣤⣤⣾⣿⣿⣿⣿⣿⠿⠟⠁⠈⠛⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⢀⠀⠀⠈⠛⠋⠁⠀⣀⡴⠁
⠀⠀⠀⠀⠀⢻⣀⠀⠀⠐⠈⠀⠀⠀⠙⢿⡛⠛⠛⠉⠉⠩⠉⠛⠋⠛⠏⠉⠙⠙⠛⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠛⠁
⢠⠴⢾⣶⣦⣄⡹⣧⡄⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠉⠀⠑⠢⢄
⣿⣿⣦⣌⡙⠻⣿⠟⠿⣦⡀⠀⠀⠀⠀⢀⡼⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠙⢿⣿⣿⣿⡷⠀⠀⠀⠀⠙⠳⢤⣠⣈⣽⡾⠻⠾⢿⣶⢦⣤⣤⣤⣤⣐⣐⣒⣻⣿⡿⠟⠋⠀⠀⠀⠀⢣⡀⠀⢀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠉⠛⢿⣧⣀⠀⠀⠀⠀⠀⠀⡀⠻⡇⢀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠛⠛⠷⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⡙⠴⠀⠀⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⢀⡄⠀⠀⠱⣀⣀⣀⠀⢀⠀⠂⢸⣿⣿⣷⣶⣶⣦⣶⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢅⡀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠜⠀⠀⠀⠀⠈⠛⠛⠛⠛⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠛⣷⡄⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠈⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢠⠊⠀⠀⠀⠀⢀⣿⣫⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⠐⠁⠀⠀⠀⠀⠀⣪⣵⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⢶⣴⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⠿⣿⢿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⠛⠳⣶⣄
⠀⠀⠀⠀⢠⣾⣿⠉⢲⣶⣶⣾⡝⣿⣿⣷⡄⠀⠀⠀⠀⢠⣾⢫⣿⢟⣼⣿⣿⣷⡝⣿⣷⡀⠀⠀⠀⠀⢠⣾⠻⠿⢋⠊⡀⠧⢤⣻⣿⣷⡀
⠀⠀⠀⢀⣿⣿⣿⣔⣚⣛⣛⣛⣵⣿⣿⣿⠇⠀⠀⠀⢀⣿⣿⣿⣻⣶⠉⣽⣭⣿⣾⣿⣿⠇⠀⠀⠀⢀⣿⣿⢋⡀⣢⢚⣵⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⢰⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠉⢰⠀⠀⠀⠀⢸⣿⣷⣍⣴⣶⣿⡿⠛⠛⠉⠉⢸
⠀⠀⠀⠀⣿⣿⣿⠋⠉⠛⠃⠀⠀⢤⠄⠀⢇⠀⠀⠀⠀⣿⣿⣿⠋⠉⠛⠃⠀⠀⢤⠄⠀⢇⠀⠀⠀⠀⣿⣿⣿⠋⠉⠛⠃⠀⠀⠤⠄⠀⣆
⠀⠀⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠘⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠈⢻⠛⠁⠀⠀⡀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠈⢻⠛⠁⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠈⢻⠛⠁⠀⠀⠀⠀⠀⢈⠏
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠉⠉⠉⠉
⠀⠀⠀⢀⣤⣶⣿⣤⣤⣤⣼⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣤⣤⣤⣼⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣤⣤⣤⣼⣷⣤⡀
⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⣿⣿⣿⡿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⢸⣿⣷⣾⣿⠀⠀⢸⣿⣯⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⢀⣄⠀⠸⠟⠁⠸⡏⠀⠀⠿⠛⠉⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⡿⣿⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠁⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⣴⣶⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠘⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣤⣴⣾⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃



⣿⣿⠿⠿⡿⢻⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿