Cartilage Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠴⢲⣄⣤⣤⠀⠀⡀⠀⢠⡶⢒⡒⢶⡄⠀⠀⡤⣴⣹⡇⠀⣺⣉⣽⡠⠜
⠀⠀⠀⠀⠀⠰⣏⣶⣶⠫⢄⡴⠃⠀⡼⢹⠇⠀⠳⠬⠷⠋⠀⠀⢸⢧⣯⡼⠁⠸⣥⠽⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⢸⣉⡿⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋
⠀⠀⠀⢰⣋⣿⣏⣭⠽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢞⢋⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⡀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣶⣼⡧⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣁⣸⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢶⠲⣜⢆⠚⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⢀⣀⠀⠀⠀⠘⢿⣋⡏⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⢉⡿⡍⡽⠀⠀⢰⠏⢓⡴⠁
⢰⡶⣿⣌⠛⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣨⠽⢧⠞⠁⠀⠀⡤⣛⠯⡷
⠀⠙⠧⢬⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⣄⣷⣴⣣⡼⠓⠦⠭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⢛⢶⡬⠵⠇⠀⠀⢾⠒⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠬⢷⢶⠾⠚⠁⠀⠀⠀⠀⠈⠳⣍⡾⠀⠀⠀⠀⠀⢀⡔⣋⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢧⣞⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢼⣭⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠙⢛⡷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠟⠀⠀⢴⠒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠲⢶⢬⡳⢄⡸⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⣘⡆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⠟⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠰⣿⣿⡟⠋
⠀⠀⠀⠀⠀⢀⠨⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠘⠚⠒⠀⠀⠀⠸⠛⠁
⠀⠀⠀⠀⠀⡨⠀⠐⠀⠀⠀⢀⣀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣬⣄⡀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠘⠄⠂⠀⠀⠀⠀⠀⠄⠒⠀⠠
⠀⠀⠀⣸⣿⣿⣿⣧⠀⠰⠽⠋⠀⠀⠈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⠶
⠀⠀⣰⣿⣿⣿⣿⣿⣷⣄⠀⢰⠇⠀⠈⠉⠀⠀⢀⣴⡆⠀⢀⠪⠂⠀⠈⠓⡀⠀⠀⠀⢀⠔⠒⠒⢄⠀⠀⢀
⠀⠀⣿⡿⢿⣿⢿⣿⣿⣿⣧⣤⣄⣀⢠⠤⠠⠤⠦⣿⣇⡀⠀⠀⢀⡬⡶⠀⠀⡐⠀⠀⠂⠀⠀⠤⠄
⠀⠸⠿⠷⠖⠂⠊⠛⠻⠿⠟⠿⠋⠁⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⢀⣴⡟⢠⠀⠤⡈⠁⠐⠀⠀⡄⠀⠃
⠀⠀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠃⠀⠀⠀⠈⣿⣷⣾⣶⣾⣿⣿⠉⠈⠀⠀⠒⠀⠐⠂⠨⠀⠀⢠
⠀⠀⠀⢞⣽⠋⠀⠰⣴⠄⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠈⣿⡟⠟⠿⢿⣿⣦⠀⠀⠁⠰⢗⣻⣷⠀⠀⠀⠈
⠀⠀⠀⠈⠁⠀⠀⠀⠩⠄⠀⠀⠀⠀⣷⢲⡀⠀⠿⠂⠀⠀⡸⠋⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠈
⠀⠀⠀⢭⡄⠀⢠⣴⡄⠀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠀⢀⡄⠃⠀⠐⡀⣲⡀⠀⠀⠘⢿⣤⡀⠀⠀⠁
⠀⠀⠀⠘⠃⠈⠀⠈⠀⠀⠀⣰⣷⣄⡀⠀⠀⠀⣀⣴⠇⠀⠀⠁⠐⠤⠏⠀⠀⠐⠄⠀⠉⠉⠓
⠀⠀⠀⠀⠀⠺⠧⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠰⠒⣠⠀⠀⠀⠐⠿⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⠋⠀⠀⠀⠀⠀⠀⠈⠻⢧⡄⠀⠀⠀⠀⠈⣲⢄⡀
⠀⠀⠀⠀⠐⠶⣴⢆⠛⠀⠀⠀⠀⢀⠄⠐⠐⠀⠀⡀⠀⠙⣷⣄⠀⠘⠺⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠻⣦⣀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡀⠈⠀⠀⠘⠿⢿⣷⣶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠣⠟⠀⠀⠀⠀⠀⠀⡘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠂
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⢀⠴⠋⠉⠉⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⣿⣄⠀⡀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⢠⣸⣛⣋⣹⡧⠀⠀⠀⠀⣿⠛⠋⠙⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤
⠀⠀⠀⠀⠀⠀⠊⠄⠛⠿⠋⠡⠀⠀⠀⣸⡇⠀⠐⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⢻⡀
⠰⢤⡀⠀⠀⠀⠘⠋⠃⠈⡍⠀⣀⠴⠛⠉⠛⠛⠟⠛⠛⠻⡄⠀⠀⠀⢰⡊⡪⣐⡀⠀⠀⠈⠁⠀⠀⢸⠂
⠀⠀⠉⠳⢤⣀⣀⣀⣀⣤⡴⠊⠉⠀⠀⠀⠀⠀⡉⠀⠀⠀⠘⢆⠀⠀⠀⠚⠾⠋⠀⠀⠀⠀⠀⠀⢀⣸⣇
⠀⠀⠀⠀⠀⣿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠒⠉⠉⠈⠒⠲
⠀⠀⠀⠀⠀⢸⡀⢀⣀⣨⣅⠀⠀⠀⡀⠀⠀⠘⠀⡄⠀⠀⠀⠀⢀⡟⠁⠲⡶⠒⠉⠉⢀⡀
⠀⠀⠀⠀⠀⡸⠋⠉⠉⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⠼⣄⣀⣸⠃⠀⢰⣮⣿⣿⠀⠈⠞
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⣀⣠⠤⠒⠊⠀⠀⠀⠀⠈⠉⠣⣀⠈⠛⠛⠁⠀⠄
⠀⠀⡴⠊⡃⠀⠀⠀⣈⣋⠍⡄⠀⠀⠀⠀⠈⡌⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠡⢯⠾⠁⠀⠀⠀⠂⠀⡇⠀⠀⠀⠀⠨⠀⠀⠠⠀⠐⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⠁⠈⠉⠀⠀⠘⣔⣤⠤⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⡟⠁⠀⠀⠀⠀⠀⠉⠢⡆⠀⠀⡀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡘⠀⣄⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡀⠀⠀⠀⠀⠓⠠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡀⢀⡟⠀⠀⠀⣌⠈⠃⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⡇⠀⣿⠃⠀⠀⠀⢉⠀⠆⡄⠀⠀⢾⠀⠁⠀⠀⠀⠀⠀⢔⡤⠷⠀⠒
⠀⠀⠀⠀⠀⠀⠁⡞⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢸⠀⠀⡅⣀⣿⠀⠀⠀⠀⠈⣁⠃⠀⠀⣠⠃⠀⢰⠀⠀⡂⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠠⠀⠀⠀⢀⠂⣀⢠⡏⢫⢿⠀⠀⠀⠀⠈⠁⠀⠀⣰⠋⠀⠀⠀⠌⣼⢀⠋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠚⠲⠷⡶⠶⠿⠟⠛⡉⠀⠀⢀⠂⠁⠀⠀⢠⡿⢣⣿⠈⠈⣾⡀⠀⠀⠀⠀⠀⢀⡼⠣⠀⠀⡀⠀⠠⠃⠆⠀⠀⠀⠒⠻⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⡾⡉⠀⡸⠻⢀⠀⢩⠳⣄⡀⠀⢀⠴⠛⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡁⢃⡔⠀⠀⠀⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡤⡺⢁⠔⡅⢀⠏⣀⡄⡠⢡⡞⠉⠉⠪⣀⠀⠉⠉⡁⠀⠂⠐⠁⡡⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣱⠇
⠀⠀⠀⠀⠀⠠⢖⡤⣭⠥⠶⡾⣾⠛⠋⠁⠀⠼⡜⡏⠄⢊⠊⡵⢋⡴⢃⠔⣀⠀⡀⠠⢀⣲⠌⠁⠈⠒⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣸⢻⡟
⠀⠀⠀⠀⠀⣴⠗⣫⡄⣾⡗⠊⢁⣄⣀⣀⠀⠺⡇⣆⢩⣤⡴⠗⢫⠔⠡⠈⠀⠑⠌⠂⢠⠃⠉⠒⠀⠈⢂⠀⣱⠀⡀⠐⢧⠀⠄⢀⣄⡂⣀⠬⢛⡥⢋
⠀⠀⠀⠀⠀⠇⣰⡥⠚⢁⠼⠛⠊⠉⠁⠀⠀⠠⢧⡞⢋⠡⠒⠂⡶⠀⠀⠀⠰⠀⠀⢡⠆⡴⠊⠑⢦⡀⠆⠀⡧⢰⠀⣼⠀⠈⠁⢌⠉⠉⠁⠂⠁⠐⠉⠁
⠀⠀⠀⠀⢈⡔⣠⣿⠜⠁⠀⢀⠤⠠⡄⠀⠀⠀⢼⠜⠃⠀⡠⠃⡿⠀⠀⠸⠀⠀⠀⡎⡼⠀⠀⠀⠀⠁⣌⠰⠇⠸⠀⠇⠂⠀⠀⠀⠑⠢⢤⡄⢀⠀⡤
⠀⠀⠀⠀⡘⠀⡿⠉⠀⠀⢰⠣⡦⡈⠁⠀⠀⠀⣸⠀⡀⠀⡅⠀⠀⠆⢀⠀⠀⠀⠀⢰⡇⠀⠀⢄⠀⠀⠈⢣⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠘⠁⠀⣷⡇⠀⠀⠘⢦⠴⠁⠀⠀⠀⢠⣯⠜⠀⣼⠂⠀⠀⠈⠏⡇⠀⠀⠀⡼⠀⠀⢀⡀⠑⠄⠀⠀⢧⢂
⠀⠀⠀⠀⠱⡀⣿⡇⠀⠀⠀⠀⠀⢀⣤⡤⢚⡹⠷⠢⢎⡤⠂⠀⢀⠀⠄⢡⠀⠀⣰⡇⠀⠀⢸⠘⠃⡼⠀⠀⢸⡌⡄
⠀⠀⠀⠀⠀⠁⠼⢣⡀⠀⠀⢀⣴⠯⡿⠏⠁⠀⠀⠀⡎⠀⠀⠀⠈⠀⠀⢸⠀⠀⠐⡄⠀⠈⠈⠓⠚⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢠⡇⢺⣻⣿⡿⠡⠞⠋⠀⠀⠀⠄⠠⠞⠀⠀⠀⠀⠈⠀⠸⠀⠐⢀⠄⠙⢄⡀⠀⠀⠀⠀⠀⣠⡟⣠⡧
⠀⠀⠀⠀⠀⠈⠁⠃⠻⠀⠀⠀⠀⢀⡀⠒⢋⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢣⠘⢿⡪⣲⣜⣷⣦⣤⣤⡾⠟⠈⠁⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠳⠌⠙⠳⠦⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⣩⣷⡏⠆⠎⣡⡈⢀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⠀⠠⣶⣄⠀⣠⣤⠀⠀⠀⠀⠀⠘⠀⣉⣻⣯⡌⠏⢿⣿⢺⠀⠰⡠⠄⢠⠀⠀⠀⢠
⠀⠀⠀⠄⠀⠀⠀⠑⠀⠈⠁⠄⠛⠛⠁⠂⠀⠁⠀⠀⠀⠉⢛⠛⠑⠂⠐⡀⢃⠀⠤⠐⡫⣀⡤⠐⠄⠀⠀⠀⠀⣀
⠀⠐⠀⠀⠀⠀⠀⠆⠀⠀⠀⡈⠒⢀⠖⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠖⠂⠈⠻⣿⣿⣶⡃⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠃⢴⠠⠐⠀⠠⠀⠀⠘⡥⣩⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⠦⣐⠲⡛⡉⠽⠁⠠⠄⠀⠈⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠒⠀⠂⠀⠀⠐⠂⠈⡀⠀⢀⣴⣢⣉⠱⠀⠜⠓⠚⠀⣁⠀⠈⠈⠀⡀⠀⠀⠠⠀⢉
⠀⠀⠀⠀⠌⠀⠀⠂⣀⡠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⡻⡟⠠⠁⠀⠀⠀⠒⠀⠸⠀⡀⢠⣹⡆⠁
⠀⠀⠀⠀⠀⠀⠃⡘⢿⡿⠠⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣿⡷⢀⠀⠀⠰⠀⠈⢈⡋⠜⢠⡌⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⣐⠂⡡⠤⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣃⣀⡨⠊⠓⠀⠀⠐⠀⠃
⠀⡀⠀⠀⠀⠈⠐⠀⠁⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⢀⣝⢾⣷⡞⣦⢠⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣾⣿⡷⢌⠠⡑⠀⠀⠀⠀⣄
⠀⢀⠐⠀⠀⠀⠐⠀⠀⠀⣀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡹⠯⣟⡡⠊⠀⠀⠀⠀⠀⠀⢀
⠈⡂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⠀⢉⠠⠀⠈
⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡂⢀⠀⠀⠶⠐⣀⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢾⡇⡻⠿⠗⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⣠⣂⠀⠀⠀⠀⠀⢰⡈⣄
⠀⡀⠀⠁⠀⠀⠀⠄⣰⠈⠂⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡦⠸⣿⠟⠀⡆⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠳⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠠⠁⠠⠄⠊⠁⠀⠀⠀⠲⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠔⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡔⣄⠀⠀⠂⠀⢤⠄⠀⠄⠀⢀⣀⡀⢦⣀⠀⠂⡀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢙⡛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⣡⠯⢁⠠⠤⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⡿⠃⠐⡂⠙⢡⣥⠈⠀⠀⠁⠀⠐⡀⠙⠞⢈⣁⠉⠙⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣺⠗⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂⠐⡇⠃⠀⠀⠀⡀⠈⠄⠀⣀⠸⣟⠁⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠈⠄⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡤⠄⠀⡀⠂⠀⠓⠀⠁⠉⡀⢦⠀⠈
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠛⢈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠼⣘⢇⠀⠀⠀⠀⠈⠀⠙⠆⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠇
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠀⠀⠄⠀⠀⠀⠀⠀⢀⡠⡔⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⡞⠐⠈⠁⠰⠀⠀⠁⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠑⠂⡐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠐⡤⠤⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠔⡐⠀⠐⢠⠈⠄⠀⠀⢀
⠀⠀⠀⡀⢀⠠⠀⢸⠀⡐⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠂⠀⠀⠀⡁⠐⢀⠀⠈⠁
⠀⠀⠀⠀⠀⢉⡠⢆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠁⠰⠁⢀
⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⢀⣠⠔⠀⠀⠐⠠⠈
⠀⠀⠀⠀⠀⠠⢊⢤⠀⢶⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠂⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⣀⠄⣀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠼⢆⠀⡐⠀⠀⡀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠡⠊⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢣⠥⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⢰⠊⠀⠈⠀⠐⡄⠠⠤⢀⡰⠀⠁⠀⠀⠢⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠲⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠣⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠄⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠠⠌⠤⡤⢀⢀⠀⠂⠀⠀⠀⠀⠁⠀⠂⠀⠼⣿⡁⣶⢖⠐⣂⡀⢀⠀⡤⠁⠀⠀⠴⠀⠀⠻⠦⠀⠀⠀⠓⢀
⠠⠤⠀⠀⠁⡄⠀⠀⠀⡀⠀⠤⠴⢤⠀⠀⢣⡄⠀⢁⠀⠘⠈⡭⠙⢃⠘⠉⠁⠈⠁⠾⢀⠆⠀⡔⠋⡀⠀⠀⢈⡀⠀⢀⠀⠰
⠀⠀⠐⠀⡄⣅⠀⠂⠀⡇⠀⠀⠒⠊⠀⠀⠀⣇⣄⢥⠉⠀⠂⠀⠰⢆⠀⠀⠀⠤⠒⠀⡬⠀⠾⠃⠀⠤⠀⠀⠀⠀⢨
⠠⠀⠂⠃⢀⡈⠳⠒⢚⡷⠖⠚⠁⠀⢐⡄⠀⠀⡁⢈⣀⡦⠀⠀⠀⠈⠀⠀⠠⠤⠀⠀⣷⡄⠀⡈⠲⠀⣠⠜⠃⠄⠠⠄⣠⠄⠁
⠀⠀⢀⣍⡀⠃⠀⢀⢺⡀⠀⠀⠀⠀⠈⢀⠀⠠⠀⠋⠈⠂⠀⠀⠀⠀⠰⡀⠈⠉⠀⠠⢟⠂⠀⠧⠖⠀⠐⢄⠀⡗⠀⣤⠀⠀⠇
⠀⠂⠐⠈⠋⠁⢁⠚⠉⠷⢦⣠⡄⠄⠚⠥⠀⠀⠄⠰⡄⠂⠃⠁⠀⠀⠀⠈⣀⡀⢉⡑⣀⠀⢀⠀⠀⠉⠁⠀⣦⠃⠐⢀⠄⠘
⠀⠀⢀⠳⠒⠌⠰⠶⢴⠂⢴⠄⣃⣀⠀⠠⢀⠒⡆⠨⠈⠀⢈⡀⠀⠁⠀⠂⠋⠀⠀⠀⣭⡀⠁⠒⢀⡀⡀⠰⠁⠀⣴⡀
⠀⣀⠁⢥⡔⣠⣤⠴⠒⠘⠋⢁⡀⠀⠉⢦⠒⡀⠀⢐⠤⠈⠀⠙⡒⠀⠇⠠⡆⣀⣀⡠⠋⢀⠂⠠⠀⢹⢅⠠⣠⠀⠀⠀⠶⠁
⢀⡸⢀⠀⣀⣞⠁⠀⠀⢠⠀⠧⣭⠂⠀⠀⢿⠁⢄⣸⠤⡥⠤⠯⣿⡆⢤⡀⠀⠉⠉⡀⠀⠀⠀⠀⡠⢈⠀⠀⠁⣰⠉⠉⠃
⠀⠒⠄⡀⠍⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢸⠋⠀⢀⣤⡀⠹⠦⠁⣀⠙⠀⠈⠀⠐⠑⠀⣒⣉⠀⠀⠁⡀⠀⡟⠀⠒⠀⠈
⠐⡄⠉⠀⠈⠛⠀⠀⡀⣄⣀⡤⠀⢀⣤⣂⠀⢼⡀⠀⠘⠓⠀⠀⠉⠀⠻⠄⢀⠀⠘⠀⠁⠀⠈⠀⢀⠀⠒⠏⠙⠤⠀⠀⠀⢀⠆
⠀⠉⢦⠃⣁⢷⡜⠀⠀⡄⠁⠐⠒⣀⡤⠥⣴⡉⠻⢆⠀⠀⢤⣤⣖⠜⠀⠂⠀⠀⠢⠀⠀⠀⠲⠖⠮⣗⠀⠈⠰⢀⠀⠤⠀⠀⡆
⠀⢠⠠⢂⡌⠨⠓⠀⠀⢀⠐⡽⠂⠀⠀⠀⠀⠉⠦⡀⢁⡀⠼⠟⠛⠶⡀⠂⣃⠱⠀⢠⠀⠘⠀⠠⣄⠈⢷⠀⢥⠘⡄⠀⠀⣸⠃
⠀⢂⡀⡀⠟⢛⣀⣩⠀⠈⡰⠀⠀⠀⢸⡙⠆⠀⠀⢃⡄⠀⠀⣠⡄⠄⠘⡁⠈⣠⠀⠀⠀⢀⠀⠈⠀⠀⢸⠀⣄⢀⠘⠁⠹⠈⡄
⠀⠊⡉⡐⡶⠂⠨⠡⠄⡠⣃⠀⠀⠀⠀⠁⠀⠀⠀⠏⠄⡀⠀⠈⠄⠀⢸⢙⡌⢃⡖⠀⠀⠈⠀⠀⠀⠴⠛⠠⠀⠈⢠
⠠⠀⢄⠒⣺⡶⣦⠠⠤⠄⣁⠰⡠⠀⠀⠤⠀⠠⢎⢀⠓⣜⠒⠰⢶⣤⠁⠀⠠⠘⠁⠀⠀⣁⡀⠀⠀⠐⠀⠐⣰⠀⠀⠆⡠⠀⠀⢀⠄
⠀⢠⠬⠟⠁⢀⣄⠒⠠⠀⠈⠳⣦⠀⠠⡅⠀⠀⢀⡀⢁⡀⠹⠄⠄⠦⠀⢠⡴⠀⢆⠀⠠⠌⠁⠀⠀⠆⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⢀⠁⢠⠠⠇⠀⡀⠀⠀⡠⠩⠀⣀⡨⠗⡀⠐⣀⠂⠈⡳⢀⠀⠀⠄⢁⠀⠀⠀⠀⠀⠨⠐⠀⠀⠄
⠀⠀⠀⡓⡤⣀⣀⡀⣠⡤⠖⣣⢏⠀⠔⠀⠂⡁⣰⠎⠉⠑⢜⡋⡙⢼⠋⠉⠐⠀⠈⠑⣒⢢⡄⠸⠀⠄⡀⠀⠡⢤⡀⠂⠌⢠⠀⠞
⠀⠀⢰⡄⢙⠣⠀⣤⠀⠒⠴⣯⡁⢠⠀⠀⠑⢡⡇⠀⠀⡀⠀⠉⠁⢀⠀⠰⠟⠂⠀⠀⠈⣱⡌⠀⠃⠲⡔⣄⢀⠀⠙⢄⠠⠄⠂⠐
⠀⠷⠚⢧⡠⠀⠙⠹⣓⡀⠀⠈⢹⠀⠰⠀⠀⠈⢤⠀⠀⠀⡀⠀⠀⠋⠑⠀⠀⠀⠀⠀⣠⠉⠀⠀⢀⠐⠠⠈⠀⠀⠀⠀⠀⠀⠋⠀⠁
⠀⠀⠈⠀⠉⠳⡄⠤⡈⠠⠄⠀⠛⢳⣔⠀⠈⢀⠈⠓⡤⠤⣴⡒⠚⠉⡀⠂⠴⣂⣠⠾⠋⢀⠀⣀⠚⠀⢄⠀⠁⠀⢀⠁⠀⡄⠀⠐
⠀⠀⠀⠂⠀⢀⠇⢀⠁⠀⡀⠀⠀⠀⡟⢰⡀⡙⢱⠁⠀⢼⢉⣭⡅⠀⢀⠠⣝⣀⣈⣶⠚⠋⢅⠀⠣⣄⠀⠀⠀⠡⠄⠀⡀⢳⠁⠰⡔
⠀⢒⡲⢤⡴⠊⠛⠸⠆⡀⣈⣁⣠⣼⢡⣶⠠⠀⠸⢆⡀⡀⠈⠁⠀⢀⢿⡛⠉⠀⠈⠊⢙⣍⠢⠈⡈⠚⠁⠰⠀⠀⠀⠀⠈⠂⠑⠀⠉
⠀⠀⠈⠁⠐⠐⠠⠖⠩⠆⠁⠂⡤⣠⡿⣤⡘⢣⠆⠄⢓⣀⢿⢓⣶⣦⡜⠅⠀⠚⠀⠀⠈⢃⢀⢠⡄⠠⠀⡐⠀⠂⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠙⠙⠋⠙⠙⢆⠀⠀⠀⠀⢀⡼⡡⠠⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⣤⣦⠃⠈⣧⣤⡘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣾⣿⠅⠀⠘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢿⣧⣻⠅⠀⢀⠀⢺⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣼⠟⢃⡀⠀⠀⢠⠀⣿⣿⡛⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣀⠀⠀⠈⢠⠌⣰⣿⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠻⢦⡤⠯⢶⣟⡛⢻⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠭⠄⠨⠤⢙⣷⣇⠀⠀⢸⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠈⣿⣷⣺⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠛⠇⠀⠀⠀⠀⠀⠀⠻⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣶⢶⣶⢷⣯⣄⣐
⠀⠀⢀⡀⠀⢀⣠⠈⠉⠐⠛⠿⣦⠂⠉⠉⢠⠶⠾⠿⠛⠛⠋⠉⠉⠛⠿⣿⣿⣤⡄⢀⣂⠀⠀⠀⠀⠈⠁⠀⠀⠑⠀⠂⡒⠂
⠀⠘⠋⠀⢀⢤⡀⠀⠀⠀⠀⠀⠘⢂⣄⠘⣾⣄⠀⠖⢀⣀⡀⢤⡀⠄⠀⠀⠀⠀⠀⠈⠉⠛⢻⣿⣿⣗⣦⠀⠁⠂⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⢀⣨⣽⢶⡶⠶⢾⣭⠤⠶⠶⠳⡿⠷⢿⣿⣯⣥⣀⣀⣡⣤⡎⢁⣠⠔⢨⠷⠞⣛⣨⣽⣭⡽⠿⢿⣷⣶⣤⣤⣤⣀⡀⠀⠀⠯⠶
⠀⠀⠀⠚⠉⠀⠰⠿⠶⣶⣶⣶⣦⣤⣴⡦⠶⠶⠶⠾⠿⠻⣿⣟⣻⢿⣟⠛⠀⠈⠀⢘⣿⣮⡄⠀⠐⠐⠒⠙⠉⠉⠉⠛⠀⠭⢍⣉⡀
⠀⠀⠀⠀⠉⠀⣦⣬⣽⣍⣈⣙⢻⣿⣿⡟⡟⠿⠉⠉⣈⣭⣽⡿⠿⠾⠿⢮⣶⡒⠛⠁⠀⣈⣙⠳⢤⣄⡒⠂⠀⠀⠀⠀⠠⠤
⠀⢒⣛⠛⠞⠛⠻⣿⣿⣿⣿⣛⢉⣥⡞⠀⠁⣀⣄⣀⡉⣉⣤⡤⠆⠐⠀⠰⠁⠀⢄⣀⢀⡿⣿⣿⣦⣍⡛⠷⠂⠠⠤⠀⠠⠄
⠀⠠⠒⠒⠚⠉⠉⠉⠉⠙⠛⠛⠻⠟⠾⡍⠉⠉⣠⣬⠿⢟⠫⠄⠀⠀⠒⠂⢀⡀⠀⠈⠀⠉⠑⠉⠓⠈⠉⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⣘⣫⣬⡤⠖⠚⠁⠀⣀⣰⣶⠾⠟⠛⠛⠉⠉⣭⣤⡳⣢⣤⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⠛⠋⣉⠀⠀⠀⠀⠀⠐⠣⡖⠿⡄⠔⠈⠘⠿⠦⠌⠂⠄
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠒⠀⣀
⠀⠀⠀⡤⠀⠀⠀⣀⡀⠉⠁⠀⠀⣀⣀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠒⠉⠉⠀⠁⠀⠒⠶⠦⠄⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠤⠄⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠤⢴⠦⠄⠠⠀⢀⠈⠉⣁⣀⠀⠲⠤⠀⠀⠀⠀⡀⠠⡀⠉⠓⠀⠀⠈⠶⠤
⠀⠠⠄⠀⠀⠠⠀⢀⡀⠒⣀⣀⡀⠀⡤⠐⠂⢖⣒⢤⠀⠀⠐⠉⣫⠈⢉⣤⡈⠁⠨⠄⣔⣭⡿⠵⣶⠏⣄⠀⣜⠓⡀
⠀⠀⠀⠂⠀⢀⠄⡀⠀⠀⠀⠈⠉⠀⠀⠐⢇⠳⠔⣠⣆⠴⠗⠀⢨⡐⠸⠶⡷⠞⠿⢋⡼⠁⢁⣾⡛⠓⡿⠁⠈⠁
⠀⠀⠀⠘⠂⠀⠐⠐⠃⠀⠀⠀⣀⠀⠈⠢⣀⡙⠉⠀⠴⠀⠀⠀⠉⠉⠀⠾⢖⠂⠀⠀⠙⠀⠹⠯⢙⣻⠛⠈⡀
⠀⠀⠀⠀⢀⣀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠒⣁⡀⠀⠀⢀⠂⠠⠤⠄⣊⠄⢐⣶⣶⡦⢀⠀⠉⠁
⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⢠⠀⠈⣁⣐⠒⢭⠐⣄⢀⡖⢁⣬⠌⠵⢤⣈⠉⢀⠀⢠⡉⠈⢰⢾⣦⣙⣆⣱⣄⣀⡀⣀⣀⠀⠀⠀⠀⠁⠆⠠
⠀⠤⠀⠐⠘⢉⡀⢼⡀⠀⠿⠀⣸⢡⣉⣶⡀⠃⡀⠈⣇⣱⢿⡾⣿⢉⣽⠆⠸⢃⣴⢧⡈⢸⠿⠏⠀⢏⠞⡡⡴⡺⢟⡀
⠀⣰⠁⢰⡛⡉⡄⣦⢡⢦⠀⠀⠈⠉⠨⠍⠋⠜⠉⠈⠒⠅⡀⢰⠾⠓⢀⠀⠀⠸⣭⣿⣜⣩⣽⣟⣃⠥⠾⢰⡀⢻⣩⠆
⠀⠉⠀⢸⣒⡅⠸⠃⢦⣀⡉⢒⣂⡈⠉⠩⠤⠤⠤⠂⠀⠀⣈⠄⢀⣤⡴⣄⠺⣑⠄⢋⣈⠩⠿⢛⣛⣒⡒⢞⠛⠞⠛⠃
⢰⠀⠀⠤⠀⠉⠂⠀⠒⠯⠍⠀⠈⠉⠀⠀⠀⠲⠶⠤⠀⣀⢇⡀⠻⢤⣂⣤⡿⢏⡴⠔⣢⢰⡦⢙⡋⠯⣭⡗⠀⠂⠅⠐⠀⠀⠀⠀⡀
⠈⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠧⣐⠒⠄⠈⠂⠋⠥⣬⡹⠯⠒⠁⢰⠎⡽⠀⢈⠭⡉⠂⢨⡀⠀⡄⣦⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⣀⣖⢀⠢⡄⠀⡀⠀⠞⠑⠋⣉⣉⡉⠉⠉⠁⠒⠀⠰⠿⡚⢟⠲⠄⣢⣄⠠⠠⣀⡀⠸⠗⢂⠉⢉⡽⢩⠍⠉
⠀⠀⠁⠘⠃⠀⠩⢐⡌⠀⠀⠀⢼⠀⠊⣁⡐⠀⠀⢀⡄⠀⠣⠰⡖⣸⣾⣥⠠⠮⠭⢕⢲⣯⣡⡝⠿⠟⢟⡻⠖⡀⢒⡀
⠀⢤⣤⠂⢀⠤⣤⠀⠚⠀⣀⡀⣠⣑⠂⢀⣉⣀⣀⣤⢀⣀⠀⢉⣚⡃⠈⠀⢶⣤⣀⠰⣇⣆⠂⢸⡆⠀⢠⠤⠅⣢⠅⠀⠀⠀⠀⠀⡀⡀⢀
⠀⣇⠒⠤⠤⠀⠀⠀⠀⠀⠖⠒⠒⠂⠀⠈⠩⣀⡭⠅⠀⠀⣀⢀⢀⣀⠈⠁⠐⠂⢈⡃⠉⠛⠛⠁⠄⠞⠀⠀⠠⠁⠛⠁⠀⠀⠀⠀⠁
⠀⠈⠉⠀⠀⠠⠤⠄⠀⣉⣁⠀⢀⣀⡀⠀⠀⠤⠭⠉⠤⠤⠄⠀⠨⠭⠥⢭⣙⣓⡒⠶⠒⠒⠲⢖⣂⣘⠉⠁⣓⠀⠐
⠀⠀⠀⠂⠒⠒⠀⠁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣾⣖⣒
⠀⠀⠀⡠⠐⠀⠀⠛⠭⠉⠛⠿⣯⣸⠆⠉⠉⣤⢴⣶⠶⠾⠟⠛⠛⠛⠻⢿⣯⣭⣭⡥⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒⠒
⠀⠐⠋⠁⠀⣀⠀⠀⠀⠀⠀⠠⡀⠓⢀⠀⢀⣯⡀⣠⠆⠊⠀⣀⣀⣤⡤⡄⢠⠉⠉⠉⠉⠙⠛⠿⢿⣿⣶⣦⣄⠀⠐⠀⠀⠀⠁⠀⠁⠒⠂
⠀⠀⠀⠀⠈⠀⣳⢂⠤⠁⣦⢒⣂⣬⣥⠄⠐⣛⢥⡶⣾⣛⣋⠁⠈⣉⣀⡴⠛⠎⠁⢴⣭⡿⠷⠖⣒⣩⣿⣿⣿⣷⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠤⠀⠉⠀⢔⣣⡤⢬⣤⣀⣐⣀⣠⣤⣤⣤⣥⣥⡿⠽⣿⡻⠿⣥⡴⠜⠃⠒⠈⡡⢶⣪⣍⡉⠥⠀⠀⠰⠃⠉⠝⠛⠛⠭⢉⣀
⠀⠀⠀⠀⠀⠀⢍⢐⣂⠀⠈⠛⠛⣼⣶⡶⠶⠲⡒⠒⠂⠀⣛⣛⣋⣀⣀⠈⡀⢄⠀⠀⠀⠉⠀⠙⠳⣦⣄⠀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠤⠤⠠⣴⣶⠾⣿⣿⣡⡤⠤⠖⠊⢉⠝⠐⠀⠀⠀⠐⠟⠛⠋⣉⡀⠀⠂⢨⡵⠁⡀⠀⠀⢹⣿⣶⣦⣉⠛⠶⣦⣄⢀⣀⠠⠀⡀
⢀⣐⣀⣤⠤⠶⠶⠛⠿⠿⢷⣷⣶⣿⣅⣶⠶⠖⠛⢛⣓⣤⣿⣟⡁⣀⣀⣄⣤⠀⠀⠀⠐⠂⠔⡪⠙⠻⢍⠻⠆⠀⠀⠀⠀⠀⢤⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠤⠤⠒⣠⣤⠼⠛⠉⠉⣘⣭⣥⣦⣴⡤⠶⠖⠚⡀⠦⣰⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠤⠭⠥⠤⠶⠶⠾⠿⠿⣷⣶⣤⣴⠶⠒⠛⠉⠀⠀⠀⢀⡔⢲⠟⡋⢀⡴⠎⣿⣤⣄⠀⡀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣨⣀⣠⣤⣀⣶⣄⣀⣈⣙⣉⣉⣁⣀⣀⣈⣀⣉⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣏⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢠⣄⢀⡀
⠀⠀⠀⠀⠀⣠⣞⣿⣿⣿⣧⣿⣟⣽⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣽⣯⣿⣿⡦⣿⢢⣾⣷⣷⣦⣄
⠀⠀⠀⠀⣴⣿⣿⢿⣿⢿⠷⣿⣿⣿⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⢰⣿⣻⣿⣿⠻⡿⣿⣿⡿⣿⠿⣿⢟⣻⣧⡀
⠀⠀⠀⢰⣿⣿⣷⣿⣿⣿⣿⣿⣽⣻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣿⣻⣿⣿⣯⣿⣽⢿⣿⣿⣻⡿⣿⣿⣿⣿⣧
⠀⠀⠀⢾⣿⣽⣿⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢠⣼⣿⣿⣯⣜⣽⣿⢿⣽⣿⣿⣳⢿⣿⣽⣿⣿
⠀⠀⠀⣿⣿⣾⣿⣯⣿⣿⣿⣻⣿⢿⣧⣿⣿⣿⣿⣿⠇⠀⠀⠸⣿⣹⣿⣳⣿⡎⣷⣿⣷⣿⢿⣟⣿⣿⣼⣿⡟
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡛⣿⣽⠿⣻⣧⣿⠿⣿⡿⠁
⠀⠀⠀⠀⢻⣿⣿⢻⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠹⢾⣚⣙⣿⣿⣿⡿⠿⣿⡟⠛⡿⠟
⠀⠀⠀⠀⠀⠉⠛⠿⣿⢟⣿⣿⠿⣿⣾⠯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣧⣾⣿⣿⠛⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠀⠊⠁⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠀⠀⠀⠀⠀⠈⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠁⢀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠈⠉

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠈⠠⣤⣤⣤⣤⣤⣴⣶⠾⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⣄⡀⠀⠀⠻⣿⣿⡿⠃⣰⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣦⠀⢈⣿⡿⠁⣸⡏⣼⣿⠟⣻⣿⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣽⣿⠀⠈⠛⠀⢰⣿⣦⣿⡃⠈⠻⠈⣿⣆⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⡦⠀⣿⣿⡏⠈⠃⠀⠀⠀⣤⣿⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠃⣸⡇⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠉⠻⡗⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠈⣿⣿⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣏⣹⣿⣿⣿⣾⣿⣿⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡄⠀⣴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⠁⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⡟⠀⠐⠛⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⣰⡶⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡃⠁⠀⠈⠛⢁⣄⣀⣤⠀⠀⠀⢀⡾⠁
⠀⠀⢿⣧⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣤⣤⣾⡿⠁⠀⠀⠀⢀⠄
⠀⠀⣿⡿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢠⣿
⠀⠀⣿⡧⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⠀⠀⣀⣼⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⢢⡀
⠀⢰⣿⡇⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠄⢈⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠹⣦
⠀⣼⣿⠀⣼⡇⠀⠀⢀⣀⣠⣤⣤⡤⣤⣄⡀⠀⠀⠀⢸⣿⣿⠀⢸⣿⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠘
⢠⣿⡇⢰⣿⣀⣴⣾⡿⠛⠛⠛⠉⠀⠀⠈⠙⢦⠀⠀⢸⣿⡏⠀⠘⣿⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⣼⣿⠃⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⢀⣿⡇⠀⠠⡏⠀⠀⠀⢀⢀⣴⣤⠘⡆⢠⡞⠁⠀⠀⠀⠀⢸⣿⣧
⣿⣿⣶⡿⠟⠁⠀⠀⣠⣦⣀⣀⣰⣶⣤⣿⣿⣿⣷⣄⠘⣿⡇⠀⠀⠀⠀⢀⣶⣿⣾⣿⣿⣷⣷⣯⣵⠟⠀⠀⠀⠀⠀⠸⣿
⣿⣿⣄⣀⣀⣤⣶⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠀⣿⣷⡄⠀⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆⠘⡇⠀⠀⠀⠀⠃
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⡄⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠘⣤⣶
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣇⣤⠀⣾⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣴⣿⣿⡖⢁⣼
⠀⠸⣿⣿⣿⣿⣿⣿⣩⡿⢋⡟⢀⢿⡏⢙⣉⣿⣿⣿⣿⣆⠹⢿⠟⠀⠙⠻⠿⣿⣿⠟⠑⠀⠀⠀⠀⠀⠀⠈⠁⡟⢀⣾⠇
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣦⣰⣿⢇⣽⣿⣿⣿⣿⣿⣿⣿⣄⣀⣠⣀⠀⠀⢠⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡾⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿⣿⣷⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠁⠀⠘⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠏
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⠇⠀⠻⣿⣿⣷⡀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠛⠀⠀⠙⠛⠻⠿⣦⡀⣴⣷⣼⣿⠹⠿⠛⢻⡿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⡿⢿⣿⡿⠟⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠙⠋⠁⠈⠃⠀⣠⣶⣿⡇
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣽⣟⣻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣴⣿⣿⣿⠿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⣺⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣴⣦⡏⠉⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠳⠶⣶⣿⣿⣿⢹⡟
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡀
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠛⠋⡀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡏⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠉⠛⠛⠁⠀⠀⠀⠀⠀⡰⠛⣽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⣡⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⡀⢀⣠⣴⣦⣶⠞⠋⣡⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠛⢋⣉⣉⣀⣤⣶⡿⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠚⠻⣿⣿⣿⡟⠛⠋⠁⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠻⠿⠋⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⠻⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣬⣍⣁⣀⠀⠀⠀⢀⣀⣠⣴⣶⡿⠿⠋⢩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠙⠿⠟⠛⠉⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⠟⢋⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⡄⠀⠐⠿⠿⠛⠉⠁⠀⠀⣀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⣙⣁⠀⠀⠀⠀⠀⣀⣤⣴⡿⠟⠋⠉⠛⠋⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⢠⡼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠟⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣥⣾⣶⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⠟⢻⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡄⠀⢦⠀⠀⠁
⠀⠀⣠⠀⠀⣿⣼⣦⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢈⣶⢄⣿⣷⣿⣴⡄⢳⡀⠀⠀⠀⡀⠀⠄⠠⡄
⠀⠀⠀⢹⠿⡙⣿⣿⣿⣍⠀⠀⠈⡇⠈⠀⠀⠀⢀⣿⡀
⠀⠀⠀⢻⣦⣿⣿⣿⣿⣭⢃⠐⠄⢀⠀⠲⠀⠀⢨⣿⣿⢦⠀⡆
⠀⠀⠀⢼⡿⡙⢍⣻⣿⣿⣿⣀⠀⠈⠀⠀⠀⡄⢰⡇⣿⣈
⠀⠀⢠⡼⣿⡏⠸⠛⠉⣛⣛⣛⢧⡀⠀⠀⢰⠘⠀⠑⠚⣋⠄
⠀⠀⠀⢳⣜⢷⡀⢰⡞⣃⣡⣞⣧⠁⠁⠰⠀⠀⠀⠀⢶⣶⡎⡴⠂⠈
⠀⠀⠘⡦⣆⠀⢳⡜⡯⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢀⠮⣙⣒⣦⡙
⠀⠀⠐⠀⢉⠀⣶⢿⣜⡻⠾⢛⠅⠀⠀⠀⠀⠀⠀⢂⠰⠿⠇⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠂⠐⠃
⠀⠀⠀⠀⢈⡒⣦⢻⡁⣽⠶⣖⠚⠀⠀⠀⠀⠀⠀⠈⢙⣲⣌⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒
⠀⠀⠀⠀⠈⡁⣹⡄⢹⠀⠀⢮⠀⠀⢀⠀⠀⠀⠠⠀⠡⠙⠉
⠀⠀⠀⠀⠀⠀⠠⣿⡿⣧⡰⢿⠳⡄⢸⠀⠀⠀⠀⢷⡀⡄⠀⠠⠀⠆⠄
⠀⠀⠀⠀⠀⢱⡄⢈⣍⢻⣭⣦⣰⣮⡎⢀⢸⠢⡄⢀⠱⣴⣦⢀⡤
⠀⠀⠀⠀⠀⣟⠣⠹⣥⣼⣿⡀⣬⣿⠓⣶⠘⠀⠱⠀⠰⠟⠛⣇⠁
⠀⠀⠀⠀⣀⣿⡆⣧⠀⢹⣟⡙⢦⡟⢘⣻⡄⠀⢠⠁⠀⠰⠄⢨⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠸⣿⣷⠉⣷⠈⠈⠻⣛⣋⡀⠙⢻⠹⡈⡄⠀⣀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⣁⢀⣀⢈⢀⣀⠈⠀⠈
⠀⠀⠀⠀⠐⢀⡇⠰⠈⠀⠔⠋⣉⡀⠈⣆⠀⠀⠏⠐⢂⠀⠻⡀⠀⠄⠄⡿
⠀⠀⠀⠀⠀⢿⢻⡇⣳⠀⠆⡙⡿⠟⠴⠀⠀⠤⠀⠆⢾⡀⠀⠻⣀⡀⢈
⠀⠀⠀⠀⠀⠸⣿⠈⣿⢲⡀⠀⢹⣿⠇⡸⠀⣴⠰⡆⠈⠉⠀⠀⠸⢠⣬⡄
⠀⠀⠀⠀⠀⠀⢏⠀⢻⣆⡁⠀⠀⣆⠢⠀⠀⡘⡆⠆⢸⡰⢇⡆⣤⠀⠸⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠙⠇⢠⠁⠉⠀⠀⠙⠃⣀⡄⢰⡃⡴⢠⡷⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠘⠛⠄⠀⠀⠀⢠⡄⠄⠀⢻⣿⣾⠁⣸⣿⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⡆⠂⠈⠿⠛⢰⠀⣿⢠⡄⠺⠟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠺⡀⢀⡰⠄⠀⠁⠘⢄⠈⢲⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠳⢴⡆⠀⠀⠈⢵⢄⠑⢤⡀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⣹⣶⡷⡄⠸⠀⠿⡄⠀⠁⠂⡀⠃⠀⠀⠀⠀⠀⠈⠀⠸⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢿⣻⣶⣿⣆⠀⠀⠘⢆⠀⢠⡀⠂⢀⠀⢐⣄⡠⣀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⣆⠀⠀⠈⠓⠀⠑⠀⠀⠁⠀⠙⢺⡽⣷⡄⠀⡆⠀⠩⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠨⣛⠿⡈⢧⠀⠐⠄⠀⠀⠀⠀⠀⠸⠀⢿⡏⣩⡙⢀⡸⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢧⠀⣷⢸⡇⠀⠀⠀⡀⠀⠀⠀⠀⢱⢸⣧⡘⠓⢸⡄⠶⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣆⠹⢹⣟⡄⠀⠀⠁⡀⠀⠀⠁⠸⠀⠀⠱⢤⡼⡇⠀⠀⢷⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠛⠀⠡⣿⣽⡄⠀⣂⡷⠢⠀⠀⠀⠀⠀⠈⠲⡗⣶⢄⠀⠀⢳⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠱⡆⠠⡽⣽⠓⠈⣱⢗⡀⢀⠐⠂⠀⠢⡀⠌⠻⣷⠀⠀⠈⢧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠐⠽⣅⢀⠸⣆⠂⠠⠠⠀⠀⠀⠉⣄⠰⠐⣄⠀⠀⠈⡆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠘⣇⠘⠂⠈⢑⢠⣥⠀⠀⠀⠀⠘⣧⢡⢩⠂⠀⣀⠙⢆⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠙⡄⠀⠀⠀⢻⡅⢦⠀⠀⠀⠀⢸⡆⢢⢺⣧⣮⡻⠀⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢹⡄⠀⠜⢆⠀⠀⠀⠉⠊⢧⠀⠀⠀⠀⣷⠘⣎⢣⡛⣡⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣿⣦⠀⠀⠣⠀⠀⠀⠀⠈⠆⠀⠀⢄⠸⣇⠹⣎⠉⢱⡌⠠⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢹⠁⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠘⣆⠸⡆⠉⢻⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⠀⠀⢰⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠄⠠⡄⢠⠀⠈⣷⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⣿⡄⠀⠀⠔⠄⠀⠠⠀⠀⢄⡡⣄⠀⣿⡌⠡⣀⢿⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠘⠱⠀⠙⢄⠻⠘⠄⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⢀⠈⠀⠀⠘⣆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠰⡁⠀⠀⠀⠈⡄⢀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠆⢀⣀⡠⡡⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⣋⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⡫⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢀⣤⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠀⣿⣇⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢀⣴⣾⡿⣿⣿⠋
⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⢀⡾⢃⡞⣸⣿⢻⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠉⠀⣀⣦⣽⡿⠛⣡⣶⣿⡏
⠀⠀⣠⣾⣯⣩⣟⣷⣤⣴⣦⣄⣠⣿⣷⡞⣰⣿⣿⡇⡇⠀⢸⡇⠀⢀⠠⠤⠒⠈⠀⠀⢀⣠⣵⡿⠟⠁⠀⠈⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⡻⣿⡻⠛⠾⣿⠿⠡⠤⠀⠒⠚⠁⠁⢸⡆⠀⠀⠀⣒⣴⡿⠟⠋⠀⠀⠀⠐⠂⢸⣿⡏
⠀⢀⣿⣿⣿⣿⣿⣯⣽⣿⣾⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣤⣾⠿⠟⠁⠀⠀⠀⠀⠀⢀⠀⠀⢾⣿⡇
⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣿⣭⣦⣀⡀⣀⣤⣴⣶⣾⣿⣷⣾⣾⠿⠋⠁⠰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⢸⣿⡇
⣿⣽⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣙⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⢿⣿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⢸⣿⣿⣿⡟⢻⡅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⠀⠀⢀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆
⠀⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠻⢿⣿⡆
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⡆⢈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣷⠐
⢸⣿⣿⣿⣿⣿⣿⡏⣿⣿⣟⣉⣿⣿⣿⢿⣿⣧⣀⠈⠀⢀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⠃⠀⡿⠒
⠸⣿⣿⣿⣿⣿⣿⣿⣏⣿⡏⠁⢸⡇⠁⠘⢿⣿⣿⣦⣀⠈⡑⢄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⡏⠀⢰⡇
⠀⣿⣿⣿⣿⣿⣿⡟⣿⣿⣏⠀⠈⠀⠀⠀⠉⠁⠙⢿⡿⣆⠀⠀⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢀⣾⠁
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⠀⠀⠁⠈⠳⣦⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣼⠃
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⣀⣰⠟⠉⠀⢀⣼⠋
⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⡟⣶⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠞⠛⠁⠀⠀⠀⢀⡾⠃
⠀⠀⠠⣿⡄⠙⣯⣉⣉⣋⣙⣛⣋⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣦⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⢻⣿⣿⣿⣿⣿⣿⣻⢿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣠⢸⡇
⠀⠀⠀⠀⠀⠀⠈⣿⢿⣽⣿⣿⣿⣿⣿⡿⣿⠇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡇⣹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠋⣿⣿⣿⣿⣿⣿⣷⣟⣿⡧⡀⢰⡆⢀⡠⣤⣤⣴⣾⣿⣿⣼⡇⠀⠀⠀⣼⢛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡘⡿⠟⠛⢻⡿⣿⣿⣯⣾⣥⣼⣻⣿⣷⣾⠿⢿⣿⣿⣿⣿⠁⠀⠀⢰⡏⣸⣏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣾⣿⣷⣔⢿⣟⣽⣞⣿⣿⣽⢟⡉⣶⣦⣾⣥⣍⣿⣿⠀⠀⠠⣾⢟⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣭⣽⣿⣿⡯⢵⠟⢠⠏⠉⠽⣿⣯⣿⡿⡄⢠⣼⣏⣾⡿⠃
⠀⠀⠀⠀⠀⢸⣷⡆⣟⣛⠛⡛⠛⠻⠿⠿⠿⠿⠿⠿⠃⠀⠀⠛⠀⠜⠂⠀⢿⣿⣿⣿⣿⡟⣨⣿⠁⡀
⠀⠀⠀⠀⠀⠈⠉⠁⢻⣿⣿⣿⣿⣿⣿⡿⣶⣶⣶⣶⣤⣤⢠⡶⢀⣴⡆⣸⣿⣿⣿⡛⢋⣈⡹⠃⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⢻⣽⣶⣶⣦⣴⣍⣙⣃⠻⠿⣿⣶⣿⣼⣧⣽⣿⣿⣿⣿⣿⣿⠏⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡯⠀⠈⠉⠛⠛⠶⠶⠾⠧⢬⣤⣍⡿⢫⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⣝⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣟⣻⣟⠛⠛⠻⠷⠶⢦⡤⣤⣤⣀⣀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢫⣿⣩⣿⣋⣉⣋⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠉⠛⢿⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠿⠿⠿⠿⣿⠌⠲⠀⠶⠠⡆⠀⠤⣄⣀⠀⠀⠀⠐⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⡀⠀⠀⠀⢠⢠⠀⡀⠀⣤⠀⠀⣠⡔⠀⠀⠀⠀⠀⠀⠄⢩⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⣎⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡐⢁⣀⣀⡀⢀⡀⠀⠀⠀⢀⣀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⡀⠄⢁⣼
⠀⠀⠘⣷⣦⣀⠈⠀⠀⠀⠀⠀⠀⠂⠈⠳⠶⠄⠉⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣴⣿⠇
⠀⠀⠀⠈⠙⢿⣿⣶⡶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⠰⣾⠉⠅⢰
⠀⠀⠀⠀⣀⢈⠻⡏⠀⠉⠻⣿⠈⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⡶⡿⠛⠃⡿⠷⢀⠀⡀⠀⣸
⠀⠀⠀⠀⠻⠻⠀⠁⠀⠀⠀⠛⠀⠉⠿⠉⠙⣿⣿⣿⣷⣿⣿⣿⢻⣷⣿⣿⣾⣷⢿⣿⠿⠛⢱⠀⠀⠘⠁⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢠⡀⣀⢠⣀⠀⡄⣠⡀⢉⣁⣉⣉⠁⠈⣯⢏⠉⣁⢈⢠⣾⢀⠂⡀⣤⢤⡦⠤⢤⣶⠴⢖⠇⠛
⠀⠀⠀⠀⢠⠀⠀⠈⠉⠀⠛⠅⠁⠉⡛⠀⠁⠁⠀⠉⠁⡈⠉⠁⠈⠉⠚⠁⠁⠀⠈⡋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⣾⣧
⠀⠀⠀⠀⠆⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠠⠂⠀⣴⣶⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⢹⣿⡄
⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⡼⣯⣠⣿⣿⣿⣶⣀⣀⠀⠲⠀⢀⡄⠀⡙⢷
⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⣀⣠⣾⠋⠉⠀⠈⠉⠛⠿⠿⣿⣦⣭⡸⡢⢙⣶
⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢸⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⣠⣿
⠀⠀⠘⣧⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢳⡀⠀⠀⢀⣞⡅⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠸⣷⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡑⠀⢀⣾⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢻⡞⣆⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⡀⠀⡀⠈⡍⢨⣯⠋⡁⢀⢤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠁⠀⠀⢈⠉⠀⠁⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠐⠁⠀⠰⡉⠰⠴⠀⠊⠠⠁⠂⠰⠃⠞⠇⢸⠏⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣀⢦⣶⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⠖⣤⣀⠀⠀⣀⣤⠀⣾
⠀⠀⠀⠀⠀⠀⢸⠇⠀⡞⢳⣀⣴⡟⠀⣿⣿⣿⣿⣿⣿⡶⣦⣷⣶⣶⣦⣤⣶⣶⣿⣿⣿⣿⡿⢠⣿⣿⣷⡎⠁⣹⣠⡿
⠀⠀⠀⠀⠀⠀⠐⣆⢀⢷⡶⠟⠁⠹⠀⠘⡏⠉⠁⠀⢸⠁⠀⠤⠀⠠⠀⠀⠘⣿⣿⣿⣿⡿⠁⣼⣿⣿⡿⢛⣾⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠈⢢⡰⠆⠛⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠁⡴⠛⢹⣿⡒⣩⣼⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⢁⣠⠞⠁⠀⠀⣿⣿⠟⠁
⢀⢀⠀⠀⡀⢀⠀⠀⡀⠀⡹⣤⠀⠁⠀⠀⠀⠀⡀⠀⢀⡀⣀⢈⡀⣀⡀⣀⣤⠤⠒⠋⠀⠀⠀⠀⢠⣿⠇
⠊⠋⡀⠙⠈⠃⠀⢈⠀⠀⠀⠘⣦⠀⠀⠀⢀⡘⠀⠀⠈⣀⠋⠙⠋⡉⢈⡛⢀⡀⠀⠀⠀⡀⠔⢡⣾⠋
⠀⠘⡀⢀⠀⠀⠀⠘⢀⠀⠀⣀⠈⠳⣤⠀⠐⠀⠛⠈⠁⠁⠀⠀⠀⠁⠸⠂⢉⠀⢀⣐⣼⣃⣴⠞⠁
⠀⠀⠁⠀⠀⠃⠀⠀⠁⠀⠀⠉⠀⠀⠈⠃⠉⠉⠙⠛⠓⠦⣀⣀⣀⣀⣀⣠⠼⠗⠚⠻⠻⡏⠁
⠀⠆⠀⠀⡖⠐⠃⠘⠃⠘⠃⠓⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠁⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⣤⣀⠠⠀⢀⡀⣀⡀⠀⣄⣠⣠⣀⣴⣤⣿⡇
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠙⠙⢁⠘⡇
⠀⠘⠁⠊⠀⠆⠐⠀⠁⠒⠛⠂⠈⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡠⠀⢸⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠦⠴⠄⣤⠀⠠⣤⣄⣠⣴⣦⣤⣿⣶⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠈⠻⠋⠙⠃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢿⣐⣖⣇⡈⠄⠠⠠⠌⠀⠀⢘⠀⠀⠑⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⢠⠀⠈⣁⡂⠀⠀⡆⠀⠀⠀⠁⠘⠈⡀⠀⠀⠀⠀⠁⠀⠀⡒⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠑⢄⢀⣼⣠⠤⠀⠀⠄⠀⠁⡞⠑⢀⠠⠐⠈⠠⠀⠀⢀⠀⠀⣁⠀⠀⢄⠁⡀⠠⢀⠐
⠀⠀⠀⠀⢀⣀⠈⠂⠀⠀⡎⠀⠀⠀⠀⠊⠀⠀⠀⠒⠊⠀⠀⠀⠀⣀⠀⠀⠀⢀⠟⠀⠤⡄⠀⠠⠀⠰⠀⣁⠁⢰
⠀⠀⠀⠀⠀⠈⠒⠁⠀⠋⠱⠦⣀⡀⠀⠀⠀⠠⠄⠀⠀⠂⠂⠀⠀⠈⢁⡀⠈⢁⡀⢀⠀⠀⠘⠀⢠⠐
⠀⠀⠀⠀⢀⠘⠊⠈⠐⠒⠀⣠⡂⠀⠀⡀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠀⠀⠀⡅⠀⠘⠀⣀⠀⠂⠀⠴⠀⢀
⠀⠀⠀⠀⠀⠀⠆⢐⠔⠈⠁⠁⡤⢄⠀⠘⢊⠀⠀⠄⠀⠀⣠⣍⠀⠀⠚⠠⢤⠀⠀⠆⠀⠀⠹⠀⠠⠀⢀⣀⠉
⠀⠀⠀⠀⢀⠀⠲⠇⠀⠀⠐⠂⠉⠋⠀⠀⠘⢀⠄⠚⠛⠉⢡⡟⠀⠲⠄⠀⠀⠠⠀⠀⠠⠂⠠⠀⠀⢸
⠀⠀⠀⠀⠈⠢⠀⠶⠀⠀⠀⠀⠀⠀⢀⡀⠀⢨⠀⠀⠞⠁⠀⠀⠀⡆⠀⠀⠠⠀⠁⠀⠀⠀⠀⠠⠀⢈
⠀⠀⠀⠀⠀⡀⠀⢤⡄⠀⠈⠈⢀⠀⢈⠅⣀⡈⠷⢄⠀⠀⣠⣔⠀⠀⠀⠀⢀⠀⠀⠀⠤⠵⡆⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠠⠈⠂⡀⣐⡐⡹⠂⠀⢀⠀⠈⣷⢚⡗⠴⠛⠛⠶⢐⣞⣃⠃⠠⠄⠃⢀⠄⠘⣏⡴⠈⣄⠀⢀⠎
⠀⠀⠀⠀⢠⡀⠈⠈⢠⠤⠦⠞⠀⠀⠀⠫⠓⠀⠀⡴⠂⠀⠴⠆⠆⢸⠀⣝⠀⠀⠀⠄⠈⠂⠀⡏⠙⠦
⠀⠀⠀⠀⠀⢀⢫⣁⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⣀⠀⠆⠄⠀⠆⠀⠀⠀⠀⠀⡊⠀⠠
⠀⠀⠀⠀⠀⡦⠞⠋⠉⠄⠁⠐⠌⢁⠀⠐⠀⠀⠁⠀⠈⢒⡈⠉⡃⠀⣀⡄⠀⠀⢐⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠠⠑⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠂⠀⠑⠆⡀⠉⠀⠐⠄
⠀⠀⠀⠀⠀⠐⠄⣀⠀⠀⡤⠤⣂⠁⠀⠀⠀⠀⡰⠊⠒⠀⡊⡁⠟⠀⠁⠀⠀⢁⡒⣄⠀⠈⠀⠀⠀⠀⡀⠀⠀⡄⠐
⠀⠀⠀⠀⠀⣆⠈⠑⢀⣄⠀⠐⢦⣄⠀⠀⠀⠂⠃⠀⠀⠀⠈⠀⠀⠀⠛⠑⠀⠀⢠⡆⠀⠀⠲⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠋⠙⠄⡀⠁⠸⠄⠀⠀⣙⠀⠀⠀⠀⢲⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢠⠆⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠐⠀⠁⠀⠀⢹⡆⠀⠠⢄⠈⢁⠘⢫⠄⠂⠀⠀⠔⠚⣁⡠⠄⠐⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠤⠄⣠⠜⠥⣣⠀⠀⠀⢀⡼⢀⠃⠀⢨⡀⠀⠀⠛⠁⠀⠧⠗⠂⠈⠑⢖⠀⠀⠈⠷⠀⠀⠀⠁⠀⠠⠀⠀⠑
⠀⠀⠀⠀⠈⠀⠁⠂⠀⠄⠁⠉⠉⡉⣭⢏⡀⢲⠂⠄⡂⢐⠶⣶⣤⡫⠀⠐⠀⠀⠐⠁⢀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠋⠉⠳⠀⠀⠀⠀⣠⠇⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠠⠤⠠⠤⠠⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⠂⠉⠀⠀⣀⠀⣀⢀⣀⠀⠀⠀⠙⠀⠤⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠀⣀⠠⠆⠉⠁⠁⠀⠀⠀⠀⠈⠉⠐⠆⠀⠀⣠⠞⢁⡾⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⠀⠠⠆⠁⢀⣠⠴⠒⠛⠉⠉⠉⠃⠀⠀⢀⡤⢤⡞⠁⡀⢸⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠚⠀⢀⡴⠋⠀⠀⠀⠀⠀⣠⠚⣏⠙⢲⡉⠀⡴⠃⠀⠐⠦⠀⠐⢆
⠀⠀⠀⠀⠀⠀⠞⠀⢠⠉⠀⣰⠋⠀⠀⠀⠀⠀⣠⢾⡙⢦⡈⠳⣄⠉⢺⡁⠀⢀⠀⠀⠇⠀⠘⣂
⠀⠀⠀⠀⠀⠘⠀⢀⡌⠀⣸⠃⠀⠀⠀⠀⣠⢾⠙⢆⠙⢦⡙⠂⠈⠓⢦⠇⠀⠘⣆⠀⠈⣃⠀⢙⡀
⠀⠀⠀⠀⠀⡋⠀⢰⠀⠀⠇⠀⠀⠀⡠⢎⠹⣄⠳⢄⠙⠂⠀⠀⢀⡴⠋⠀⠀⠀⢹⠀⠀⢙⠀⠈⡅
⠀⠀⠀⠀⠀⡃⠀⢰⠀⠀⠀⣄⡠⢾⠀⠈⠳⣌⠓⠀⠀⠀⢀⠄⠀⠀⢀⡀⠀⠀⢸⠀⠀⢘⠀⠀⡅
⠀⠀⠀⠀⠀⣃⠀⠰⠀⠀⠀⠘⢧⠀⠳⣌⠳⣄⠀⠀⢀⡴⢋⡴⠛⣉⣩⣉⡙⠲⣄⠀⠀⣘⠀⢀⡅
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡠⠚⣳⣄⠈⠳⢬⣧⠴⠋⢠⠏⢠⠋⠁⠀⠀⠙⢦⠘⣆⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢰⠲⣤⠊⣠⠞⢡⠜⠓⠦⣴⠋⠀⠀⢸⠀⢿⣠⢤⣄⡤⣄⣸⠀⢹⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⠳⣄⠜⠁⢠⣀⠀⠈⠁⠀⠀⠸⣆⠸⣭⡛⠵⢙⣫⡗⢀⡏⠀⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣬⡗⠀⠀⠈⠙⠲⠦⠤⠤⠤⠘⠦⣄⣙⠛⢛⣀⡴⠋⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⠠⠄⢀⡀⢀⠀⢀⡀⣀⠀⠉⠉⠉⠀⣀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⢠⣄⢀⠀⠀⠈⠁⠉⠁⠀⠀⢀⡄⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠃⠛⠀⠛⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠸⠦⠀⠀⠀⠀⠀⣀⠴⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠲⠀⢤⠀⢀⡀⢀⡀⠀⠀⠀⠀⢰⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠢⡀⠀⠄⠀⠀⠀⠀⠀⠃⠀⠆⠀⠤⠀⢠⠀⢈⠁⠘⠁⠘⠃⢐⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄⠀⠀⢠⠃⠜⠀⠀⠀⠀⠀⠀⠋⠐⠂⠀⠦⠀⠤⠀⢨⡁⢈⡀⠘⠁⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠐⠊⠹⡖⠀⠀⠀⠀⠀⠠⣂⡀⠀⠀⠀⠀⠶⠂⠀⠀⠀⠀⠀⠈⠁⠠⠀⢀⠶⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠐⠤⠂⣓⣀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠐⠒⢖⠠⠤⠀⣀⠀⠀⠀⣁⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡷⠀⠀⢸⠃⠸⣧⠀⠠⠀⠀⠀⠀⠀⠈⠀⣀⡀⠈⠁⠀⡀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠛⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠚⠀⠄⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠴⠒⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡲⠞⢺⠉⠁⠤⡀
⠀⠀⠀⠀⠀⠀⣔⣮⠇⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠂⠀⠓⠦⡀⠈
⠀⠀⠀⠀⠀⡐⠉⠃⠀⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠂⠀⠀⠂⠀⠀⠀⠈⠓⠂⠉⠉⢢⠄⠍⠉
⠀⠀⠀⠀⠀⠃⢀⣴⣤⢀⠀⠀⠀⠀⠀⢠⡤⢤⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠄⠖⠓⠒⠉
⠀⠀⠀⠀⠀⠃⠘⠩⠞⠂⠀⠀⠀⠀⠀⠈⠙⠊⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠰⣶⣄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠄⠒

⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠠⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⢀⠃⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠚⡆⠀⠀⠄⠓⠁⠑⠀⠐⠀⠠
⠀⠀⠄⠀⠀⠑⠀⠀⠀⠀⠀⡇⠀⠀⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢀⠆⠀⠀⠑⠒⠊⠀⠀⠀⢀⣦⠀⢢⢀⠢⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠎⠀⠺⠇⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡤⣄⡀⢀
⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠬⣁⠰⠄
⠀⠀⢀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠆⠀⠀⠀⠰⠇
⠀⠀⠈⠉⠈⠉⠉⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⢀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠊⠔⠁⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠂⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⡄⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠈⠀⠀⠈⠈⡀⠀⠀⠀⠠⠼
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠘⠀⡃⠈⡀⠄⠀⡀⠁⠐⠀⠀⠠⠀⠀⢃⠀⠀⠀⡄⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠠⠄⠄⠈⠠⠃⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠊⠑⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠄⡰⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠢⣀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢨⠃⠀⠀⢀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⢐⠆⠀⠀⠀⡀⢂⠀⠀⠀⣮⣁⣠⣤⠆⠀⠀⠀⡆
⠀⠀⠀⠀⡄⢘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠃⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠈⠀⠀⠀⠈⢀⠀⠀⠀⠄⠀⠀⠀⠄⠁⠀⠀⠶⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⡉⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠆⠐⠚⠛⠓⠀⠀⠀⢈⡉⠉⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠁⠀⠄⠠⠂⠈⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⡀⠀⢀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⢀⠴⡁
⠀⠀⠀⢦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠐⠀⠀⢠⠀⠀⠀⠤⠴⠂⠀⠀⠉⠉⠉⠉⢹⠁
⠀⠀⠀⠀⠀⠠⠤⠀⠀⠄⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⣦⣤⣀⠀⠀⠀⢀⣠⣤⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢶⣤⣄⡀⠈⠙⢷⣦⣴⠟⠉⠉⠹⣧⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⠀⣼⢏⣤⣄⡀⠀⠉⠛⢷⣄⠀⠈⢿⣄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⣤⡀⠉⣿⡆⠀⢿⡜⣿⡉⢿⡄⢾⡟⢷⣝⢷⣄⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠛⣿⠛⠀⢺⡇⠀⠘⣷⡈⠙⠛⠁⠈⠻⠶⡿⠀⢻⣆⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⠶⠶⠶⠶⢿⡇⠀⠀⠘⢷⣄⠀⠀⠀⣴⢶⣤⡀⠀⣿⡄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⣶⣤⣶⠶⣾⡇⠀⠀⠀⠀⠙⢷⣄⡀⠻⣦⣽⣷⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣦⣀⣀⣀⣴⣟⡁⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣬⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠛⠛⠻⣿⡛⣿⠟⠛⠛⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⣀⣀⠀⠀⢀⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠉⠙⠛⠛⠿⣿⡶⠶⣶⣄⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣀⣀⣀⣀⡀⠀⣿⠀⠀⢠⣭⡛⣷⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠷⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⣛⣉⣛⣻⣿⣦⣤⣤⣤⣤⣤⣤⣄⣀⠀⣾⠋⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡶⠶⠶⠿⠟⠛⣿⠛⠉⠉⠉⠁⠀⢀⣀⣀⡀⠀⠀⠉⠙⢿⣿⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢁⣴⠶⠶⠶⠶⠶⠶⠶⠿⠷⠶⠶⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣿⣧⣄⣀⣀⣤⣾⠿⠟⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡄⣀⣼⣿⡶⠿⠛⠋⠁⠀⠀⣀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠿⠿⠾⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⣀⣤⣴⠶⣿⡃⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠾⠛⠋⠁⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢤⡄⠠⠖⠶⠖⠰⠒⠒⡖⠒⠒⠂⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢴⠀⠉⠁⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⡜⠀⠈⠀⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠀⠀⠘⠖⠀⠀⠀⠀⠀⠀⠁⣲⡄⠀⠀⠀⠀⠀⣸⠃⠀⠀⠐⠀⠀⠀⠰⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣽⢹⡿⠀⠀⠀⠀⡀⣀⢇⡀⠀⠀⠀⣀⣀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⢳⡀⠁⢀⡀⠀⠀⠀⠀⠀⢇⠀⢀⠀⠀⠀⠬⠤⣆⠀⣀⢀⠰⠂⣽⣆⠘⢄⡠⠔⢾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠙⢜⢿⡌⠀⢀⠀⠀⣀⠞⠒⠒⠂⠠⠎⠁⠀⠀⠉⠐⣇⢀⡂⠈⠐⠒⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠛⠒⠒⠞⡌⠜⠀⠀⠱⡀⡁⠄⠀⠀⠀⠀⠓⠄⢃⠀⠀⠀⠈⡦
⠀⠀⠀⠀⠀⠀⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⣠⡋⠀⠀⠀⠀⠀⢱⡀⡄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠁⠠⡒⢀⠀⡀⢴⡖⡦⠀⣜⠀⠀⠀⢰⣦⠀⠜⠁⡇⠀⠀⠀⢀⠁⠈⠠⠀⠀⠀⠀⡰⡸⢌⠤⠤⢚⡗
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠤⣈⡩⠔⠫⠬⠍⠼⠰⠆⢡⣎⠀⣰⠀⠀⠀⠀⠐⢠⠐⢹⡇⠢⡀⠐⠩⠀⠀⠉⠋⠈⠣⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠭⠥⠤⠷⠿⠶⠞⢠⠌⡁⣀⢀⡐⡡⠀⠀⠀⠘⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢖⡆⠀⠀⠀⠈⠈⠁⠀⠹⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠯⢄⡀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠘⠏⢁⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⣠⣯⠣
⠀⠀⡀⠀⣀⠄⠀⠀⠀⠐⡠⠐⠁⠀⠀⠍⠒⠤⣈⢰⣽⣌⣲⠤⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠈⠍⠓⠁
⠀⠀⡃⠈⠙⠟⢡⢚⠐⡎⠀⠀⠀⠀⠀⢰⣫⡦⠈⡹⠋⠉⠀⠀⠀⠀⠑⢄⠁⠀⠀⠀⠀⢀⠄⠃⣄⠀⠀⡀⠀⠀⠘⠀⠀⣀
⠀⠀⡥⠄⠀⠈⢾⡻⠂⢱⠀⠀⠀⠀⠀⠈⠉⢈⠒⠀⠀⠀⠀⠀⢐⠄⡔⣦⠐⢤⣀⡁⠖⠠⠀⠈⠃⠈⠒⠠⣀⡐⠄⠒⠉⠉
⠀⠀⠆⠁⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠠⡁⠰⠀⠀⠀⠀⠀⠈⠁⡐⠙⠄⡀⠀⠀⠐⠂⠀⠃⠀⠀⣈⡀⣐⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢘⠀⠀⠄⠐⡀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠑⠀⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⣈⠩⠀⠀⠀⠀⢀
⠀⠀⢠⣀⠂⠀⠄⠀⢂⠘⠉⠁⠉⠉⠀⠀⠀⠀⠱⠈⡀⠀⠀⠀⠀⢀⡼⠂⡌⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠶⠂⠐⠐⠀⠈⠤⠁
⠀⠀⠀⠀⠁⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠀⠀⠀⣀⣨⠄⠐⢆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠉⠀⠀⠀⠀⠀⠈⠢⣑⠀⠀⠀⡄⢠⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒

⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠒⠒⣒⣛⣒⠒⠒⠶⠦⢭⣍⣓⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢉⣤⣤⣄⡀⠀⢿⣁⣀⣈⡽⠀⢀⣠⣤⣤⡉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠯⣄⣀⣤⠟⠀⣀⡬⠭⠥⣄⠀⠻⣤⣀⣠⠼⢀⡸⠃
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣀⣀⣀⠻⣤⣤⣤⠞⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⢀⡴⠋⠉⠀⠈⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡭⠟⠛⠉⠙⠓⢦⡀
⠀⠀⣼⣄⣀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡀⣠⣷
⠀⠀⢸⣠⠏⠉⠛⠿⣍⡽⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣠⡤⢤⡴⠚⠉⠣⣼
⠀⠀⠠⣏⠀⠀⠀⠲⢦⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡷⠋⠀⠀⠀⠀⡼⠂
⠀⠀⣠⠞⠙⠲⣤⣀⢠⠞⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢈⢳⡀⠀⠀⣠⢞⡓⣄
⠀⢰⠃⡆⠀⡆⢸⠉⠉⠀⣠⢴⡶⠖⠒⠚⠉⠙⢦⠀⠀⠀⢀⣿⡀⠉⠲⣞⢱⡀⠙⣌⣇
⠀⡾⠰⡇⠀⡇⣼⠀⠀⢸⠁⠾⠤⢤⣄⠀⠀⠀⢈⣇⣠⠴⠻⢤⣭⣽⣟⡉⠉⠁⠀⢸⡿⠤⣤⣀
⠀⡇⠀⣇⠀⢹⡇⠀⠀⡿⣆⠀⠀⢀⣈⣷⣤⣠⡼⠋⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠓⢦⠀⠈⠙⢦
⠀⡇⠀⠘⢦⡀⠙⠶⣤⣷⣀⣀⣠⣬⣅⠀⠀⠈⢳⣴⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⡇⠀⠀⠀⢹⡶⢤⣤⣤⣼⠭⠵⠶⠾⠶⠶⠶⠶⠿⠷⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠧⣄
⠀⢻⡛⠛⢛⣛⡇⢿⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣸⠂
⠀⠀⡷⡄⠈⠉⣇⠀⠉⠙⠛⠛⡟⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⢶⡆⠛⠛⠛⠛⡟⠉⠁
⠀⢸⠇⡇⠀⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇
⠀⣼⠀⣿⠀⠀⢸⡀⠀⠀⢀⣀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⣿⠀⠀⢀⣀⣇⣀
⠀⠙⡏⢻⣶⠛⣿⠷⠦⣼⡉⠉⠉⠉⢙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⢿⠛⣷⡟⠙⡏⢀⣾⠉⠉⠉⠉⣹⣄
⠀⢾⣁⣸⣏⣀⣿⣀⣀⣀⣳⠀⠀⠀⣿⣹⡇⠀⠀⠀⠀⠀⠀⣼⣁⣀⣀⣸⣀⣸⣇⣀⣳⣿⣹⡇⠀⠀⠀⣏⣹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠉⠛⢳⠆
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢀⡿⠶⣄
⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠐⣎⢧⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⣀⣼⣾⣇⠀⠀⡾⠁⠀⣠⠞⢳⡀
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⣿⣿⣿⣿⣿⡆⠐⣇⢀⡜⠁⠀⣸⠃
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠘⣿⣿⣿⣿⠇⠀⠈⠻⠤⠤⠖⠃⠀⠀⣀⣀
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠉⢳⡄
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⠞⠉⠉⣹⢦⡀⠀⠀⠀⠀⢀⣤⣾⣿⣦⠀⣠⠴⣰⠃
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡞⠀⠀⣏⠀⢠⠞⠁⠈⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡵⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣸⠁⠀⠀⠙⢶⣋⣀⣠⠼⠁⠀⠀⠀⠀⠻⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣴⣇⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠙⠒⠶⠒⠋⠀⠀⢰⡇⠀⠀⠙⠒⠶⠒⠋⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠲⣤⣀⣠⡴⠂⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡤⣄⣀⣀⣀⣀⣀⣀⣤⢴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣾⣧⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣽⣶⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢄
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠷⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰
⠀⠀⡈⢰⠁⠀⠀⠠⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠓⠄⠀⠀⠀⠀⠀⠀⠂⠦⢀⡀⠀⠀⢀⠀⠤⠄⠠⠀⠄⠀⠄
⠀⠀⣦⠀⠀⠀⠀⢀⠠⢂⠐⠀⠀⠈⠀⢀⠄⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐
⠀⠀⠁⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠠⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠑⠄⠀⠸⠀⠀⠀⠀⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢁⠐
⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄⠄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⢀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠄⠀⠀⠀⠀⢀⡄⡀⠁⢺⠀⠀⠀⠁⠀⠀⠀⠂⠀⠤⡀
⠀⠀⠀⠀⠀⢄⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⢀⠀⠂⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⢀
⠀⠘⠄⠀⠠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠊⠰⠀⠀⠀⠀⠈⠉⠀⠀⢠⢄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠅⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠒
⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⡈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣤⡨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣌⡱⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡂
⣀⣀⣁⣀⣀⣁⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣈⣐⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡈⠻⣦⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⢷⣌⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⣿⠈⠻⣦⣈⣻⣶⡆⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⠀⣷⣄⠙⢷⠌⠉⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠻⣯⡙⠃⣿⡏⠻⠿⠛⠛⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⣄⠰⣶⣾⡄⢻⣤⣤⣤⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡋⠻⣦⡈⠻⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢶⣄⠙⢷⣌⠻⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣦⡈⠻⣦⣨⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣦⡙⢷⣄⠙⠷⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣤⣶⣤⣸⣿⢠⣌⣻⣦⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠛⠛⠛⣧⠘⡿⠿⠆⠙⠃⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠿⣯⡉⠻⣦⡀⣿⡈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣀⡐⢷⣄⠙⢿⠀⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣦⡈⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡙⢷⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⣤⠀⠀⢠⢤⠀⠀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⣄⡀⣄⡀⠀⠀⠀⣼⠁⠀⢸⠁⠀⠀⣸⠆⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⣿⢀⡠⢼⣯⠠⠴⣶⠤⠴⠊⣠⣶⣶⡀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢡⡀⣸⠃⠸⣀⣀⣧⠀⣦⣯⠀⠀⠀⠛⢿⡿⠃⣇⠀⠀⠂⣤⣴⣶⡄⠀⠀⠀⠀⠀⠀⣐⣂⡀
⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⢸⡼⠛⢀⠤⡀⠀⠽⢿⣿⣿⣦⠀⠀⠀⠀⠀⠈⣯⡄⠀⠀⠈⠈⠁⢀⣀⡠⠴⠒⠊⡉⢹⣿
⠀⠀⠀⠀⠀⠀⠙⠲⢄⠘⢦⣾⠁⢀⣑⣤⠼⣼⠄⠚⢿⡏⠈⠛⠃⠀⠀⢀⣈⢉⣤⠔⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢿⡍⠁⠀⠀⠀⣿⠀⠀⠀⠙⣷⣧⣤⣖⠉⠁⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠈⠓⣤⡀⠀⠱⡈⠿⢄⡀⢀⡠⡿⠀⢀⠔⠊⣽⠉⢷⡏⡁⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿
⠀⠁⠀⠀⠀⠒⠦⣌⠻⣦⠀⠱⡄⠈⠙⠯⢘⠵⠊⠁⠀⣰⠏⠀⢸⠿⣏⢤⡀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠙⠛⢷⣄⠈⠢⣀⠖⠁⠀⢀⣴⠞⢁⡠⣶⠉⠀⠈⠳⡙⠦⡀⠀⢳⡀⠀⠀⢀⡀⡴⠊⠈
⠀⠀⠀⠀⠀⠈⠃⠤⣤⡀⠀⢹⣿⣶⠳⡀⠀⣠⠟⠁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠰⢼⣦⠈⣧⠀⣠⠏⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡔⢻⡀⠓⢵⣴⣏⣠⣞⡕⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣙⣷⣏⣠⡞⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⢿⡋⠻⣉⡻⠛⠛⠛⠫⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣤⣿⣟⣿⣍⣉⣑⠒⠒⠒⢲⣶⣒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⣇⠀⠀⠀⢀⣈⣦⣀⣀⣠⠤⠶⠒⠒⣨⡟⠉⠙⣇⠈⢿⡄⠀⠉⠉⠉⠹⠟
⠠⠄⠀⠀⠀⢀⣀⣤⠄⠠⠤⠴⡾⠛⠛⠟⣿⣏⣉⠉⠁⠀⠑⣄⠀⠀⢀⣤⡾⠊⠀⠀⠀⠈⠛⠛⢿⣄⠀⠀⠀⠀⢋
⠀⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠿⠿⠦⠀⠀⠈⠓⣴⣟⢻⡷⡀⠀⠀⠀⠀⠀⠀⠸⣏⠙⠦⣀⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣽⠀⠀⠀⠀⠀⠀⠀⠐⠦⣴⣀⣀⠀⡧⠉⢧⢱⠌⣄⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⣤⠯⠷⣦⣤⠠⠤⠄⠀⢀⣀⣁⣡⣉⣻⠓⠦⣬⣷⣶⣽⣄⠀⢀⠔⠦⠀⠸⡇⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡀⠀⠈⠙⠷⢦⣠⣤⣠⡵⠚⠁⠈⣯⠈⠉⠉⠹⣿⠿⡍⠳⠋⡞⢓⡲⠶⢿⡖⠚⠉⣀⠤⠒
⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⣞⢷⠀⠀⠀⠀⡜⢹⣿⡿⣍⠉⠉⠉⢿⣄⡀⠀⠀⠑⠂⠷⠀⠀⠉⠁⠀⠀⠈⣥⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠰⣶⣧⠀⢀⠀⠰⣸⣮⠇⠈⠛⢦⡄⠈⠳⡝⢄⠀⠀⠀⠀⠀⢀⡠⠶⠒⠒⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⡠⠩⠩⠜⠀⠓⠀⣿⡿⠀⠀⠀⢀⡨⠿⠶⣽⣦⣷⣤⡖⠒⠊⠁⠀⣀⡀⠀⠀⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢾⣮⠜⡇⠀⠀⡜⠁⠀⠀⠀⠀⠉⠙⠺⠿⠿⠟⠻⡿⣿⣿⣿⣶⣤⣀⠀⠈⠛⠂
⠀⣄⡀⡀⠀⠀⠀⣀⣀⣤⣶⣾⡿⠟⠛⠉⠁⠀⡇⠀⠰⡁⢀⡤⠖⣲⠶⣦⡀⠀⠀⠀⠀⠀⢨⣻⣿⡄⠀⠉⠧⢽⣦⣄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢠⡶⣻⡿⠛⠉⠀⢀⡴⠶⠟⡻⠟⠓⠶⣾⣿⣛⡿⠭⠬⢴⣷⠊⣢⡀⠀⠀⠀⠀⠘⢷⠙⠀⠀⠀⠀⠀⠉⠣
⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠘⠁⠀⠞⠁⠀⠀⠰⠁⠈⠁⠀⠀⠀⠀⠀⠉⠙⠮⠖⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠉⠀⠀⠉⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⠀⠀⣴⣶⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣀⣀⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠃⢀⣾⣿⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡀⢀⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠶⠦⣞⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⠃⢸⡇
⠀⠀⠀⠀⠀⢠⣦⠀⠀⣀⡤⠴⠖⠚⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠱⣿⣶⣶⣶⣿⣿⣿⣿⡿⢫⣿⣿⣿⣿⣿⠃⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣿⡿⠋⢠⣿⣿⣿⣿⣿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠉⠻⠿⡿⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠳⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⣿⡆⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢠⡾⠛⣿⡀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠂⣴⡟⠻⣧
⠀⠀⠀⠘⢷⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣴⠟



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠲⢦⠀⠄⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠠⡀⠀⠂⠀⠀⠀⠀⢀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡔⢀⡀⠀⠀⡼⠀⠂⠀⠀⢀⠍⢻⠆
⠀⠀⢸⣿⣶⣤⣤⠀⠀⠟⠀⠀⢀⠔⠊⢶⡴⠋⠝⠀⠀⠀⣷⣦⣤⣤⣴⣾⠀⠀⠀⠪⠙⠆⠃⣰⠃⠀⠀⠀⠀⠀⠁⡞
⠀⠀⠻⣿⣿⣿⡟⠀⠀⠀⠀⠈⡁⢀⡤⠞⠁⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠈⠁⠀⠀⢀⣣⡀⣠⠟⠉⠀⠀⠀⠘⠀⢃⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣮⣀⡀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⢉⡉⠉⠀⠀⠀⠀⢹⣦⡀⠀⠈⠉⠛⠲⠦⣶⡿
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡗⠀⣄⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡄⠀⠀⠐
⠀⠀⠀⠠⠀⠀⠀⠀⠰⣿⣦⡀⠀⠀⠀⠀⠛⠃⠀⠀⠁⠄⠀⠀⠜⠀⠀⠀⠩⠵⠀⠀⠀⠻⠀⠰⠀⢢⠀⠀⠀⣴⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⣾⣿⢿⡆⠀⢠⠀⡈
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡂⠀⢰⢦⠴⣶⠙⢰⠳⡄⡏⡔⠱⢰⡆⠐⠀⠀⠀⢠⡄⠀⡠⠀⢐⡇⠀⠀⠋
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⡞⠂⢸⠀⡇⡇⡇⢠⣸⢼⠀⠀⠀⠀⠰⠀⠁⠽⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠛⠒⠚⠋⠐⠓⠘⠊⠋⠈⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣖⣲⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠁⠀⠐⠈⠁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⢄⡴⠊⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⡜⡖⠤⠤⢤
⠀⠀⡀⠀⢀⡋⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠚⠁⠀⠀⠀⠀⠀⠈⠑⢒⣂⠛
⠀⠀⠈⠒⢭⡰⢂⡌⠰⣀⠄⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⡤⢈⡥⠊⠁
⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠐⠅⠈⠋⠁⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠰⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠁⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⡖⣋⠐⠄
⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⣰⣄⠙⢦⠀⠀⠀⠀⠀⠱⣀⠠⠌⣿⠻⠗
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⢄⣀⡀⠀⠀⠶⠆⠀⠀⠀⠈⠙⠓⠀⡐⠀⠀⠀⠀⠀⠘⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢦⠀⠀⠀⠑⢦⣁⠚⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢀⠀⠘⡐⠓⡀⠀⠀⠀⢻⠻⣄⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠂⠀⠂⠀⠋⠀⠀⠀⠀⠀⢿⠏⠳⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡔⠈⠂⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠠⠀⠀⠀⠁⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢰⣄⠀⠀⠁⠂⠀⡀
⠀⠀⠀⠀⠀⣱⡀⠜⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠓⢀⠀⠀⠈⠉⠰⠆
⠀⠀⠀⠀⠀⠀⢉⠀⢄⠀⠀⠀⠀⠀⠀⠉⢀⡀⠄⠀⠘
⠀⠀⠀⠀⠀⠀⢸⡀⢈⡆⠀⠀⠀⠀⠠⡄⠀⢛⣆⠀⠸⣅⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠇⠈⠁⠀⠀⠀⠀⠈⢠⠄⠘⢀⠱⡀⠀⢰⠄⠀⠀⠀⠀⢐⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠙⣷⠀⠀⠐⠁⠀⠁⠈⠀⠀⠄⠀⠀⠲⣄⠀⠀⢐⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠳⣮⣾⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠙⣆⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣴⠏⠳⣄⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣂⣀⣀⣀⣈⣁⣀⣀⣀⣀⣠⣚⣁⣀⣀⣌⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⢀⣀⢠⣾⠀⠀⢶⣤⠄⠀⣶⣄⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢀⠀⠀⠀⠀⣴
⣤⡄⠀⣠⡀⠀⠶⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⠏⠈⠁⠈⠉⠀⠁⢠⡀⠀⠁⠀⠀⠈⠉⠀⣨⡁⠀⠀⠀⠀⠀⠀⠀⠰⠁⠰⠛⠿⣄⣄⠀⣿
⠿⡇⠈⣿⡁⠻⡟⢠⡈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠀⠀⠀⢀⠀⠀⢀⡀⠈⠀⠉⡀⠀⠺⠀⠀⢄⣙⠁⠀⠀⠀⠀⠀⠀⠀⣿⠂⠦⠄⠀⠿⠏⠀⢾
⠀⢾⣿⠉⣤⠀⠀⠈⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠀⠈⠁⠀⣿⠀⠙⠆⠐⠀⠀⠈⢹⣷⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⢀⠀⠀⠀⠘
⠀⠀⢻⡇⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠆⠀⠀⠃⠀⣾⠃⠀⠂⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣴⡤⠤⠀⢾⠄
⠀⠀⠉⠑⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠐⠶⠀⠀⠀⢀⡿⠃⠀⠀⠀⠀⠀⠁⣠⡄⠀⠀⠀⠀⠀⠀⠀⣉⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢸⡧⠀⠀⣤⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⠀⠧⠀⠐⠀⠀⠘⢁⣄⠀⠀⠀⠀⠠⡄⢈⡁⠀⠀⠀⠀⠀⠀⠀⢿⡧⠀⠠⠀⠀⠀⢰⡶
⠀⠀⠀⠈⣷⠀⠀⠈⠁⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡋⠀⠀⠀⣤⠀⡀⠙⣿⡆⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⡀⢸⡇
⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠘⠃⠀⠀⠀⡀⠀⠟⠀⠀⠀⣀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠘⠃⠀⢷⣼⠁
⠀⠀⠀⠈⢿⡷⠀⠀⠿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠛⠀⠀⠘⣧⢀⡄⠀⠀⠀⠀⠀⠿⠀⢀⡀⠀⠀⣾⡇
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠐⠀⠀⣠⡀⠸⠇⠀⠀⠒⠀⢠⠄⠀⠘⠃⠀⠀⠀⢀⡄⠐⠀⠘⠃⠀⢀⡙⠃
⠀⠀⠀⠀⣻⣧⠀⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⠀⠀⢸⡇⠀⠄⠀⣴⡄⠀⠀⢹⡁⣿⠀⠀⠀⠀⠄⢠⡀⠀⠀⢾⡆⠀⠀⢸⣧⠀⠀⠀⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠻⠟⠀⣀⡀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⣶⠀⠀⣨⠀⢀⡄⢘⡁⢀⣄⠀⠀⠀⠀⠈⠀⠀⢠⡾⠃⠀⠀⠀⠉⠀⣤⠈⠃⢀⡐⠻⡇
⠀⠀⠀⠀⣤⡏⠀⠙⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⢰⣄⡀⢈⡆⢸⡇⢸⣿⠀⠀⠄⢸⡇⢀⠀⠛⠁⢸⠄⠀⢰⣏⠀⠀⠀⠃⢸⠁⢺⡇
⠀⠀⠀⠀⣿⡇⠀⠀⣄⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢸⡇⢾⠀⠸⠋⠁⢈⡇⢸⠇⠈⡟⠀⠀⠀⠀⠁⡼⠀⠀⠀⠘⠀⠀⠀⢉⡀⠀⠐⠆⠈⠀⠈
⠀⠀⠀⠀⣿⡏⢰⠀⣿⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⣄⠀⠀⢠⠘⠃⢸⡇⠀⠁⠀⢀⠀⡁⢰⡇⠀⠀⢸⡄⣠⠀⠀⢸⣇⠀⠀⠸⠀⣠⢀⡀
⠀⠀⠀⢘⣿⢻⣆⠀⣬⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢿⡀⠀⣼⠀⠀⣿⡇⠀⠀⣰⡏⠀⠇⠈⠁⠀⠀⠘⠃⣿⠀⢠⡌⢿⠀⡇⢸⠆⣿⢸⡇
⠀⠀⠀⢺⣏⠹⡏⠀⣿⠀⢽⡇⠀⠀⠀⠀⠀⠀⢰⣿⠛⠀⠈⡟⠀⠻⠀⠀⢻⡇⠀⠀⣸⠃⣰⠀⠀⠀⢀⠀⢠⠀⣿⠀⢸⡇⠘⠀⢇⡈⠀⠻⣄
⠀⠀⠀⢸⣿⠀⡇⠀⣿⠀⣼⡇⠀⠀⠀⠀⠀⠀⢸⡇⠸⣇⠀⡇⠀⢠⡀⠀⠸⠀⠀⠀⣿⠀⣿⠀⢠⠀⣿⠀⠈⠀⢹⡆⠈⠃⠀⣷⠸⡇⢸⢀⡿
⠀⠀⠀⢸⣇⢰⣷⠀⢈⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇⢸⡿⠀⠻⠀⠸⡇⢠⡆⠀⠀⠀⣿⠀⣿⠀⠸⠀⠀⠀⡄⠀⢿⠀⠀⠠⠀⠀⠀⣷⡌⣿⠁
⠀⠀⠀⢸⣿⡀⠋⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⢸⡇⠈⡧⠀⣠⠀⠀⡄⠘⠃⠀⠀⠠⣆⠀⠿⠀⠀⠀⣿⠀⠁⠀⢸⠀⠙⠀⢠⠀⣶⠘⣷⡏
⠀⠀⠀⠈⣿⣿⠂⠀⢠⡄⠘⣧⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣘⠀⠀⢻⡞⠀⠀⠀⠀⣿⡄⠀⠀⢸⠄⣿⠀⡇⠀⣸⠀⢸⡇⢸⠀⢿⡆⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⢸⣧⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⢉⠀⠀⠈⢳⠀⠀⠀⠠⣿⡇⠘⠀⠘⠀⣾⠀⡇⢸⡇⠀⠘⠃⠘⣆⢸⣿⣿
⠀⠀⠀⠀⣿⡇⢰⡆⢸⡿⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇⠸⣇⠀⠛⠀⠀⠀⢸⡆⠀⠀⠀⣿⠁⣤⠀⣴⠀⣡⠀⠃⢠⡀⠀⢰⡀⢸⣟⠘⣿⣇
⠀⠀⠀⠀⣿⡁⢸⠁⠸⡇⠀⣿⠃⠀⠀⠀⠀⠀⣼⡇⠀⢹⠀⠸⠀⠀⠀⢸⠀⠀⠀⠀⣿⡦⠛⠀⢹⡄⢿⠀⠠⣉⡁⠀⢘⡇⢸⣿⣿⣿⡿
⠀⠀⠀⠀⣿⠃⠸⠀⣴⠀⢸⡿⠀⠀⠀⠀⠀⢸⣿⢧⡀⢸⣦⢀⣿⠂⠀⢸⠀⠀⠀⠀⠸⣿⠆⠀⡌⠁⠈⠀⠀⣿⡇⠀⠸⠇⠈⣿⡿⢿⡷
⠀⠀⠀⢀⣿⢰⡆⢀⡿⠀⣼⡇⠀⠀⠀⠀⠀⣸⣿⠀⢿⠀⠻⣮⠉⣦⠀⡿⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⢀⡄⢸⡇⠀⠀⠳⠀⢿⣧⣸⡆
⠀⠀⠀⣸⣿⠈⠃⢸⠃⠀⣿⠇⠀⠀⠀⠀⠀⣿⠉⠀⠘⠷⠀⢹⡀⠀⠀⡇⠀⠀⠀⠀⠀⣿⡄⠃⠸⠃⠀⢸⡇⢸⡇⢸⠀⠘⣦⠈⣿⡿⠃
⠀⠀⠀⣿⣿⠀⠀⡜⠀⠀⣰⡄⠀⠀⠀⠀⠀⣿⠀⡇⠀⢠⠀⠈⠁⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⢀⡄⠀⠀⢸⡇⢸⠆⠸⡇⠀⢿⠀⣹⡄
⠀⠀⠀⠛⠛⠻⠆⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⣿⠀⠹⠀⠸⠁⠀⠙⢬⡟⠀⠀⠀⠀⠀⠀⠘⣷⠀⠃⠀⠀⣠⠇⡀⠀⠀⠒⠀⠀⣧⣸⡇
⠀⠀⠀⠇⠀⠀⠀⠀⣤⠀⠸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⢴⡄⠀⠀⠸⣷⠀⣿⣿⠇
⠀⠀⠀⣾⡆⠀⠀⢀⠉⠀⠀⣿⡄⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣄⠀⠀⢡⠀⠉⣶⢨⣿
⠀⠀⠀⢿⠃⢇⠀⠘⠀⡀⠀⣿⣇⠀⠀⠀⢰⡿⠀⠘⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠈⠀⠹⠃⢠⡾⠆⠀⣿⣸⣿
⠀⠀⠀⠈⣷⡈⠃⠀⢸⡁⠀⠉⣿⠀⠀⠀⣼⡇⠀⠀⢴⠆⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣠⡖⠀⠀⠀⠙⡧⢀⣀⣿⣿⣿
⠀⠀⠀⠀⢻⣷⠀⠀⠀⠃⠀⠀⣿⠀⠀⠀⣿⠁⢼⠂⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠐⢉⡟⠀⠀⢠⠞⠀⢸⣟⠙⣿⣿⡀
⠀⠀⠀⠀⢸⣿⠘⠀⠀⢰⡇⠀⣿⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣠⣽⡆⢠⡄⠐⠀⢸⡏⠀⣿⢻⡇
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠈⠃⢰⣿⠀⠀⢸⡇⠀⡀⠘⢆⠀⠀⢧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠸⠁⠇⠸⠃⠀⠀⣼⠃⠀⣿⢸⣇
⠀⠀⠀⠀⠀⣾⠀⣸⠂⠀⣆⠈⣿⠀⢀⡿⠁⠀⠁⠀⠘⣇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣦⠀⠀⠀⠐⠿⠰⠂⢉⣸⣿
⠀⠀⠀⠀⢸⣿⠀⠁⠀⢠⡅⠀⣿⠀⢸⡇⠀⣀⠀⠆⠀⠉⣀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣃⠀⢸⡂⢈⠀⠀⢠⠀⣤⠀⣖⠋⣸⣧
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⣿⠄⠀⢀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⢺⠃⠘⡇⠀⠀⢀⣁⠀⣈⠀⣹⣿
⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⡀⠀⣿⠀⡏⠀⠀⢀⡄⠀⣸⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡇⢺⡇⠸⣷⠀⠀⠈⡿⠀⠙⣿⢻⣯
⠀⠀⠀⠀⢸⣿⠀⢶⣦⠼⠇⠘⠁⢸⣷⠀⠀⠀⠁⠀⢹⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣸⡇⢸⠁⠀⡷⠀⠉⠠⣷⡄⠸⢿⣸⣿
⠀⠀⠀⠀⢸⣿⠀⠈⠉⢰⡄⠀⠰⢸⡇⠀⣰⠀⠃⠀⢸⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⣈⠀⠀⡇⠀⠘⠀⢸⡇⢀⣼⣿⡟
⠀⠀⠀⠀⠀⢿⡇⢰⠀⠈⠰⣦⡀⢠⣄⠀⣿⠀⢡⡄⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⣈⠀⢸⡇⠀⠀⠀⠸⠇⠸⠛⣿⡇
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⣿⡇⢸⡁⠀⣿⠀⠘⡁⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡈⠀⢸⣿⠀⠀⠀⢠⣄⣿⣾⣿⡁
⠀⠀⠀⠀⠀⠀⢸⠀⢷⠀⠀⢸⣷⣟⠁⢠⡿⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠟⠀⠀⠀⡈⠃⠈⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡴⠀⡀⠀⢽⣇⠿⠀⢸⠇⠀⠀⠀⠀⣶⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⣄⠀⠂⠀⠀⠀⠁⠀⡈⠻⣿
⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠼⡧⠀⢀⡎⠀⠀⡤⠀⠀⣿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡄⠀⠀⣄⠀⠀⣹⣶⣿⡇
⠀⠀⠀⠀⠀⠈⣿⠀⢀⠁⢰⣶⡶⢀⣼⠃⢀⣄⠀⠀⠀⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠖⠃⠀⣤⠀⠐⣿⣀⣄⣽⣿⣿⡇
⠀⠀⠀⠀⠀⢰⡏⢀⡤⠀⢰⣿⡦⡘⠃⠀⢈⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠁⠀⠀⠠⡎⠈⠙⣋⣿⡇
⠀⠀⠀⠀⠀⣨⡁⠈⠁⠀⢃⣿⣷⠋⠀⠀⠙⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⡀⠀⢶⠀⠀⠀⠀⠸⠉⣻⡇
⠀⠀⠀⠀⢀⣿⠀⢰⠀⣐⣿⣇⡿⠀⠀⢰⡇⠀⠀⠀⠀⢀⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣿⠇
⠀⠀⠀⠀⣾⠏⠀⠀⣠⣿⣿⡿⠁⠀⠀⠀⠙⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣤⠀⡄⠀⢀⣽⠆⠀⠀⢸⣿
⠀⠀⠀⢘⡟⠀⠀⠀⣿⣥⣿⠇⠀⠀⠀⢰⠆⠀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⣾⣿⡏
⠀⠀⢠⠿⠃⢰⣆⠀⢿⣿⡟⠀⠀⠀⠀⠈⠀⠀⠀⠸⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⣿⡇
⠀⢠⣾⣦⡀⣼⣿⠀⣼⣿⠇⠀⠀⣀⡆⣸⠃⢠⣶⠸⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⣴⠀⣾⡆⠀⠀⢿⠀⠸⠍⠋⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⣠⡉⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢀⠰⠀⠒⠄⠀⠀⠀⠀⠀⠠⠰⠀⠀⠄⠆⢀
⠀⠀⠀⠀⠀⠀⠸⠤⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⢃⢀⠞⡍⠌⣂⠄⡀⠀⠀⠀⠀⠐⢯⢨⠭⠅⠭⠝⠹⡆
⠀⠀⠀⠀⠀⠓⠖⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⡤⢁⡀⣤⠀⠀⡖⠒⠀⠀⠀⠀⠀⢀⠉⠲⡠⠔⣇⡄⠴⠀⠀⠀⠀⠀⠇⡀⠀⢆⠂⠀⠠⠇
⠀⠀⠀⠀⠀⠰⠉⠈⠉⠡⠀⠀⠀⠀⠀⠀⠀⠨⠀⠨⠤⠄⠅⠀⠑⠀⠀⠀⠀⠀⠀⠈⠚⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠱

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠀⠀⠀⠈⠀⠠⢀⠄⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡉⡈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠛⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⢥⠄⠀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⠊⠀⠀⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠰⣤⠚⡖⣰⠒⠀⠀⠀⠀⠀⠀⢠⣾⠒⢠⡘⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠈⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠁
⠀⠀⠀⠀⠀⠀⡐⠁⠠⡢⠀⣠⠀⡔⠄⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡆⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠐⠀⠀⠈⢬⡱⡀⠰⠹⠀⠀⠀⠀⡔⠁⠀⠈⣤⡀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠰⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⣀⠄⣈⠉⠀⡀⠡⠂⠀⠀⠀⠀⡄⠀⣠⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡠⢀⠁⠐⢄⠀⡠⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⢦⠀⢤⠂⠀⠀⠀⠀⠀⠀⢀⡔⠓⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢇⠠⡆
⠀⠀⠀⠀⣒⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣩⠀⠀⠀⠀⠻⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠑⢸⡀
⠀⠀⠀⠀⢸⢛⣱⡆⣤⡀⠀⠀⠀⠀⠀⢼⣲⡀⣀⠠⢊⣹⡆⠀⠀⠀⠀⠀⠀⢲⣿⡖⠀⠀⠀⠀⠀⠀⠀⠁⠈⣴⣶⠀⢹⡆
⠀⡀⣾⣿⡿⣻⣻⣛⡀⠀⠀⠀⠀⠀⠀⠈⠉⢣⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⢸⠿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⢿⠀⢹⢱
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⣀⠀⠀⠀⠀⠀⢀⠀⣘⢇⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⢀⠞⢿⡿⠀⠀⠀⠀⠀⠀⠋⢿⣿⠙⠃⠀⠀⠀⠀⠀⢀⡀⢞⣻⠇⠵⠒⠂⠀⠀⠀⠀⠀⠀⠀⣼⡃
⠄⠀⢀⠀⡸⠁⢠⠞⠂⣵⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠼⠧⠿⡿⡿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⣷⠈⣀⣠
⢠⣀⣙⣁⣛⣛⣋⣀⣀⣟⣗⡀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡄⠀⠀⣈⣋⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡶⠀⠀⢀⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠠⡖⠒⠊⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡿⠙⠃⠐⠒⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⡀
⠀⠀⣯⣤⠀⢸⢿⠉⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⣾⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⣂⠀⠀⠀⠀⠀⢀⣷⣿⢦⡆
⠀⢿⣿⡟⣇⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠶⠶⠾⢀⡀⠀⠏⡇⠀⠀⠀⠀⣰⣷⣼⣿⣷⣧⣿⣿⡀⠀⠀⠀⠀⠸⣿⣿⠋⡓⠂
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⣤⡄⠀⠀⡂⠀⠸⠀⠉⢀⣼⣯⠏⠀⠀⠡⣶⠂
⠀⠀⠀⠀⠢⠄⠀⠀⠁⠀⠀⠀⠀⠀⠣⠀⠀⠀⢭⠀⠀⠐⠁⠀⣤⠗⣾⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠄⠀⠀⠈⢂⠀⠀⠐⠀⠀⢈⠟⢀⣀⡿⣄⡀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠐⠀⠀⠃⡀⠀⠀⢶⢿⠊⠉⠁⠀⢀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠐⠀⣥⡀
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡀⠀⠄⠀⠠⠂⢤⠦⢰⢶⣲⣌⠀⠀⠀⠀⠀⠢⠄⠠⠀⠀⠀⡀⠀⠒⠀⠀⠀⠈⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠐⠀⠁⣀⠀⠀⡀⠀⣁⠀⠈⠈⠉⠉⠉⢀⠈⠀⠀⠀⢁⠉⠀⠀⡀⠤⠀⠀⡀⠄⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⡄⠀⡈⠀⠀⡐⠀⠀⠀⠀⠙⠄⠀⠂⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠒⠂⠀⡀⠠⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⠀⠢⠂⠀⠀⠀⢀⠑⠄⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠓⡄⠀⠀⡀⠀⠭⠹⡚⠹⠄⠐⠂⠆⠤⠀⠘⠤⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠈⠸⣿⣾⡇⠀⠶⣴⣀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠈⠀⠋⠁⠁⠀⠋⠀⠁⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠄⠉⠁⠀⠀⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⣐⣀⠀⠆⡀⠠⠤⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⣉⢻⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠆⠉⠀⠄⠈⠀⠀⠠⠙⣧⡠⢉⣻⠉⠛⠦⠲⠆⠡⠆⠀⠀⠀⠀⠀⠀⠀⣤⡀⠉⠉⠉
⠀⠀⠀⠒⠀⠀⠂⠀⠂⠠⠐⡏⠀⠀⠀⠀⠃⠀⠠⠈⠛⠫⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠁⠀⠀⠐⠲⠂⠆⠀⠀⠂⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡐⠂⠀⠠⠀⠈⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣧⣿⣷⣭⣯⣬⣵⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⣴⣞⠃⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣠⣤⣄⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣠⡾⠃
⠀⠀⠀⠀⠈⢿⣦⣘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣤⣹⠿⣋⣴⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣹⡿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣰⡟⢿⡆
⠀⠀⠀⠀⠀⠀⠸⠿⠿⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠶⠛⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠈⠛



⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⠇
⠀⠀⠀⠀⠀⣘⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⣴⣾⡆⢈⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⢧⣄⡀
⠀⠀⠀⠀⣾⣿⣿⡄⠔⠑⢢⠀⠀⠀⠀⠀⠀⠀⠺⡿⠿⣿⣿⣿⠿⢿⠗⠀⠀⠀⠀⠀⠈⠋⠻⣷⣬⣭⣵⡿⠃⠀⠀⠀⠀⠀⠀⠀⠤⠤⠯⠬⣩⠤⠭⠭⠄
⠀⠀⠀⠰⠿⠷⠻⣿⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠿⠿⠿⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛


⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⣙⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣏⣀
⠀⠀⠀⠠⠶⠟⣿⣿⡟⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠉⠁
⠀⠀⠀⠀⠀⢀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠍⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⡟⠛⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡟⢿⡇
⠀⠀⠀⠀⠀⢼⠏⠈⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⢸⣥⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣤⣀
⠀⠀⠀⣀⣀⡀⣀⣀⣠⣄⡾⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⣬⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⡁⢾⣿⢇⣴⡟⠛
⠀⠀⠘⠛⠛⠋⣿⡟⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠉⠻⢷⠄⠀⠀⠀⠀⠀⠀⢠⣤⣄⣿⣇⣀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣿⠋
⠀⠀⠀⠀⠾⠿⠿⠃⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠷⠖⠀⠀⠀⠀⠀⠀⠈⠛⠉⠛⠛⠛⠛⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠴⠶⠬⠿⠽⠴⠶⠄

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⢠⣄⠀⠀⢸⣿⡇⢾⣿⣦⣰⣿⡿⠀⠀⡟⢻
⠀⠀⠀⢀⠀⡘⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⣤⢄⢿⣿⠇⠀⢸⣿⡇⠀⢹⣿⣿⡟⠁⠀⠀⡇⢸
⠀⠀⢀⣾⡞⠀⠀⠀⢀⠔⢲⠀⢀⠠⠶⠂⠀⠀⠸⢿⣿⣶⡄⠀⠀⢸⣿⡇⣰⣿⡿⢿⣿⣦⠀⠀⣧⣼
⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠀⠀⠸⢿⠇⠘⠛⠀⠀⠙⠋⠀⠀⢿⡿
⠀⠀⠁⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣠⣔⣂⠁⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠆⢠⡀⢸⡇
⠀⠀⢠⠤⠤⡄⠀⠁⠀⠀⠀⠀⠀⣴⡾⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠁⠔⠀⢥⡴⢸⠁
⠀⠀⠈⠈⠉⠁⠀⢈⠓⠶⠚⠇⢸⠋⣠⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠐⢃⠠⣴⠌⠁
⠀⠀⠐⠢⠤⠀⡆⠀⠀⢱⣶⠂⠀⠀⠫⠊⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣤⠲⠆⢽⠆⠁
⠀⢀⡅⠀⠀⠀⡇⢈⠀⢘⠦⠀⠀⠀⢰⣶⣤⣤⣤⣴⣾⠀⠠⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⢀⡀⠒⡀
⠀⠈⠢⠶⠒⠚⠁⠀⠒⠺⠕⠀⠀⠀⠈⠻⣿⣿⣿⠿⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳
⠀⡀⠐⢀⠀⡄⠀⠀⠀⠰⢄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠃⠀⠠⠒
⠀⠻⠶⢎⣠⡼⠀⠀⠙⠒⢫⡄⠐⠊⠀⠀⠀⠀⠀⠐⢄⠀⠶⣦⣶⣄⡊⠀⠀⠀⠂⠀⠉⠁⢀⠀⠁⠘⢸
⠀⠰⣤⣤⠁⡀⠀⢀⠀⠘⢒⠀⢤⠄⠀⢀⡘⠛⢀⣿⠈⠀⠐⣫⣿⣿⡿⠀⠀⠀⣀⣤⣴⣦⠀⠀⠀⠅⡇
⠀⠀⠀⠀⠀⠙⠛⠫⣄⠠⠿⡗⠀⠀⠀⠘⠻⠖⠈⠁⢀⡀⠀⠀⠚⠁⠀⠀⠻⣿⣏⣹⣿⡟⠀⠀⢨⣽⠇
⠀⠀⠀⠠⠀⠀⠀⠀⠈⠳⡄⠈⠲⣄⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⢰⣶⠆⠲⠿⠟⠙⠙⣷⣶⡄⣼⣿
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⢢⡖⠘⢷⣄⠀⡾⠟⠉⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡀⠀⠀⠈⠀⠇⢠⢐⡴⠮⠀⠋⢸⡏⠉⢹⠀⠀⡠⣿⣄⠀⠀⠸⣼⠃
⠀⠀⠀⠀⢄⠀⠀⠀⠀⢸⣏⣿⣹⡇⠀⠀⠰⠬⣕⠻⠦⣵⡚⠣⢾⡇⠀⢸⠀⢰⣵⣿⣿⠀⠀⢠⡏
⠀⠑⠒⠒⠙⠿⠶⠿⠃⠈⠁⠉⠈⠁⠀⠀⠀⠐⠊⠠⠄⠒⠀⠤⠘⠿⠿⠟⠀⠀⠙⠛⠋⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣪⣤⣤⣈⣁⠀⢀⢈⣉⣤⣬⣁⠢⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡠⢂⡜⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⡳⢉⠳⡙⢦⣤⣤⣤⣤⡤⠖⠊⠁
⠀⠀⠀⠀⠀⡀⠈⠉⠙⠿⠟⢋⠟⣠⠏⣀⣼⣿⣿⠿⠿⠿⠾⢿⣿⣿⣿⣷⣦⡀⠀⠙⢯⠍⠁⠀⠀⠀⡀
⠀⠀⠀⠡⣀⠑⠀⣀⢀⢠⠔⢁⣔⣡⣾⣿⣿⣿⡏⠀⢀⣶⣦⠀⠸⢿⣿⣿⣿⣿⣶⣄⣀⠉⠐⠒⠒⢋⣡⠄
⠀⠀⠀⠀⠈⠛⢲⣀⣠⣤⣼⣿⣿⣿⣿⣿⢯⣹⡷⢀⣾⣿⣿⣧⠀⠈⠛⠗⠹⢿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣿⣯⣻⣿⣿⣿⡷⡅⠑⠻⢿⣿⣿⣿⡆⠀⠘⣿⡀⠈⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢻⠀⠉⠻⣿⡿⠟⠋⢿⣿⣿⡯⢠⡞⠉⠉⠘⠉⢻⡀⠀⠹⡟⠈⠛⠿⣿⣿⠛⠻⣿⠃⠀⠀⠀⣀
⠀⠀⣺⠀⠀⠀⠸⡆⠀⠀⢻⣷⠇⠀⣿⠟⠿⣿⣻⣶⡀⠀⠀⠀⠀⣇⠀⠠⢿⠤⡄⣵⣽⠏⠠⢤⡿⠀⠀⠀⠀⠽
⠀⠀⠀⠀⠀⠀⠀⢹⡇⠉⠉⠙⠫⣠⡏⠈⠀⢸⣿⣿⣿⣶⡀⠀⠀⢸⡀⠀⠡⣆⡰⠞⠁⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠘⠳⡄⠀⣿⣿⣿⣿⣿⣿⣶⣤⣴⡆⠀⣰⠋⠁⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡞⠅⠀⠀⠀⣮⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⠀⠑⢈⠛⠿⠿⠿⠿⠿⢛⣫⠞⠀⠀⣀⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣤⡀⠈⠁⠈⠀⠀⠈⠀⢀⣀⣴⠾⠋⠁⠀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⠵⠖⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠐⠒

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠛⠛⠉⠁⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢮⣀⣀⡀⠀⠀⠐⠈⠉⣀⣀⠤⢀⣀
⠀⠀⠀⠀⠀⡴⡴⠚⠁⢀⣀⣁⠈⠉⠀⢀⡴⠊⢡⣶⣶⠏⠛⢿⣿⣄⡀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠺⢟⢵⣿⠃⠀⠀⠀⣰⠀⢠⠋⠀⣰⢋⡟⢁⣤⠀⣄⢙⠻⠛⠶⢤⣀⡈⢡⣖⠷⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⢠⣿⣳⠃⠀⢀⣴⠃⢠⡏⠀⢰⢃⡞⠁⠀⠁⠠⠧⢸⠀⠀⠀⠀⠀⠉⢛⠓⠳⢶⡤⢤⡶⠋⠀⠀⠛⠛⠛⠲⠤⡀
⠀⠀⠀⠀⠀⡞⣿⡇⠀⢠⡟⠁⢀⡾⠀⢠⠟⡞⢡⠰⠀⠀⠀⠀⠋⠀⠤⠀⠀⢠⢦⠂⠀⡴⢁⡠⠊
⠀⠀⠀⠀⠀⡇⣿⠀⢠⡟⠀⢀⡾⠁⡴⡟⣸⠁⠘⡆⡇⠀⠀⠀⠀⠀⠀⢰⣠⢷⠃⢀⢎⡴⠋
⠀⠀⠀⠀⢰⠗⣿⠀⣸⠀⢠⡞⠀⡼⢱⢣⣇⠀⢀⡟⠀⠂⠀⠀⠀⢀⣠⠴⠁⠃⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠸⡀⣯⠹⢯⣄⡟⠀⣸⠃⣸⡬⢿⣧⠞⠀⠀⠀⠀⠈⠉⠉⠀⠀⠘⡄⡼⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠁⠹⡀⠀⠈⠙⢦⣿⣄⡃⣴⠡⣄⠇⠀⠀⢠⠂⠀⠈⠀⠀⠀⠀⢳⠁⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡦⠖⠒⡖⠂⠺⠗⣿⠀⡇⠀⠀⢠⡏⠀⠀⡆⠀⠀⠇⢀⡼⠀⠀⠀⠀⠀⢀⠘⡄⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡓⠒⠣⠶⡄⠀⢱⣶⠇⠀⢤⠾⠀⠀⣀⣣⠄⣠⡴⠛⠁⠀⠀⠀⠀⠀⣾⠀⢷⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠛⠿⠿⠼⠀⠀⠀⠀⠀⠉⢩⡇⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢸⡄⢼
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⠀⣠⡿⠀⠀⠀⠀⠘⠃⠀⠈⡇⢸⣀
⠀⠀⠀⠀⠀⢰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⡇⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢸⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢰⠞⠋⠁
⠀⠀⠀⠀⢀⣠⢵⣒⠯⠍⠓⠂⠀⠀⠉⠈⣉⠤⠐⠀⠀⢾⠃⠀⢸⠇⠀⠀⡿⠀⠀⢀⣤⣤⣤⡶⠾⠃
⠀⢰⠰⢚⠭⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡀⠀⠀⠒⠂⠀⣸⠀⠀⠀⠁⠀⣴⡶⠧⠀⠀⠀⠀⠀⠠⢤⣀⣀⣀⣀⣀⡀
⠀⠙⠛⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣀⣀⣈⣦⠒⡚⣥⠟⢿⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣉⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⣛⣓⡦⠀⠀⠄⠤⠼⠤⠬⠭⠭⠷⠶⠷⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣠⡀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⣾⣷⠄⣴⣦⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣼⣿⣿⡶⣾⣿⣷⡄⠀⠀⠀⠀⣴⣮⠁⣰⣿⣿⣦⡀⠀⠀⠀⠀⢠⣶⡍⠁⣴⣮⠉
⠀⠀⣾⢻⣿⣿⢻⣿⣿⣿⠃⠀⠀⠀⢰⣿⣧⡴⠟⣿⣿⡏⠙⠳⠖⠀⠀⣾⣿⠻⠶⣿⣿⣄⠀⠀⠀⠀⠀⠀⣠⣴⣦⡄
⠀⠀⠛⢸⣿⣿⠙⣿⣿⣿⠀⠐⢲⠒⠒⣿⣿⠓⠒⣿⣿⡗⠒⠒⢲⠒⠀⠙⣿⡄⠀⢻⣷⡘⠓⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⠀⠀⢸⠀⠀⣼⣿⡆⠀⣿⣿⡇⠀⠀⢸⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠠⠀⠀⠀⢀⡴⣭⣥⢠⡀⠀⣶⣶⠄
⠀⠀⠄⠈⠁⣿⠀⠛⢻⡿⠀⠀⢸⠀⢸⡿⠹⣷⠀⣿⢿⡇⠀⠀⢸⠀⠀⠀⣿⠃⠀⣾⡇⠀⠀⠀⡀⠀⢠⡏⢡⣈⣁⠞⢿⣶⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡀⢠⡄⠘⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣀⣀⡀⢿⣿⣿⡿⠷⣷⣿⢿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢸⣿⣿⡇
⠀⠀⠀⣤⡄⠀⠀⠀⣰⣿⡀⠀⠀⠀⣠⣴⡏⠀⠀⠀⠀⠈⢹⡏⠡⠠⣿⣿⡇⠸⣿⣿⣿⣿⡀⠀⠀⠀⠴⠿⠶⠷⠾⠶⠿⠎⠋⠿⠇
⠀⠀⠀⣿⣗⠀⠀⠀⣿⣿⠛⢦⣄⣀⠴⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⣷
⠀⠀⠀⣿⡟⠉⠉⠉⢹⣿⣏⠉⠉⠀⠀⣿⡇⠀⠀⠀⠀⢀⡼⢧⡀⠀⣿⢿⡇⠀⠸⣿⣿⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣿⡇⠀⠀⢀⣼⡟⣿⡄⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠿⠿
⠀⠀⠀⣿⣇⣀⣀⡻⣋⣀⣻⣃⣀⣀⣀⣿⡇⠀⠀⠀⠀⠀⢘⡡⠛⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣧
⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢿⡿⠃⠀⠀⠀⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣾⡗⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠘⣿⣿⣦⣄⠀⠀⠀⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠋⠙⠟⠙⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣿⣿⢹⡟
⠀⢠⣞⣳⡄⠀⠠⣽⣿⣿⠻⣷⣄⣀⣤⣤⣰⣿⣇⠀⠀⠿⠿⠿⠻⠿⠟⠻⠃⠀⣶⣷⡄
⠀⠸⢿⡿⠇⣀⣀⣀⣿⣀⣀⣈⣩⣭⣟⣋⣻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣆⠀⡐⠿⢷⣶⣦⣤⣤⣤⣤⣤⣤⣠⣴⣄
⠀⠀⠀⢧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⢹⣿⠛⠛⢿⡈⠛⠋
⠀⠀⠀⠘⢦⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣯⢸⣿⠀⠀⠀⠀⢶⣶⣾⡿⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢶⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⢇⠈⢧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣧⠈⢇⠈⢆⠈⢇⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠠⣦⠘⢇⠘⣇⠘⣇⠙⢧⠈⢆⠈⢆⠈⢆⠈⣦⠈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⢿⣈⣿⣿⣿⣿⣿⣿⡙⡇⠘⣄⠈⣆⠘⣆⠈⣆⠸⡧⠸⠇⠸⠇⠸⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠛⠋⠈⠛⠛⠿⣿⣿⣿⣿⣧⠘⡄⠈⡄⠘⡄⠈⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⢋⣬⠐⡄⠘⣄⠸⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿⡷⠞⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡠⠞⠋⠁⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⣀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⢶⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠈⣿⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢿⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠟⠁




⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⢀⣀⣤⣤⣴⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢇⣾⣿⣟⢰⣿⣷⠜⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⣀⣴⡿⣣⣾⣿⣿⣿⣮⡛⣫⣼⣿⣿⠟⣋⣭⣙⡻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠛⣋⣥⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⢟⣵⣾⣿⣿⣿⣿⡌⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢛⣁⠻⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣷⣌⠛⣩⣴⣶⣥⡸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⡏⣾⣿⡿⢋⣼⣷⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠸⠿⢿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⠇⠻⣏⣴⣿⣿⡟⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⣿⣶⣬⡛⠿⣿⣿⠿⢣⣭⣉⣉⣥⣾⣷⣬⣉⣉⣭⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣅⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⢀⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣙⡛⠿⠿⣃⣬⣭⣭⣭⣭⣭⣭⣥⣶⣶⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴
⠀⠀⠀⠀⠘⠋⣡⡀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢈⣤⡀⠈⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡼⠟⠿⣿⡀⠈⠑
⠀⠀⠀⠀⠀⠀⡛⠁⠀⠀⢠⣤⣤⡌⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠁⠈⠀⠢⡀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣈⣥⡦
⠀⠀⠀⠀⢀⡀⡁⠀⠀⠠⠿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣄⠋⠁⠀⠀⠻
⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⡂⠀⠀⠀⠀⠀⠀⠃⠻⠀⠀⠀⠀⠀⢰⣶



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣙⣋⣍⣹⣟⣽⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢴⠀⠀⠀⢀⠀⠀⠀⠆⠰⡄⠀⠐⣄⡄
⠀⠀⠀⠀⠈⠢⣠⠳⢎⡡⡀⠀⠈⢀⡘⢦⡀⠈⢆⡀⠀⠑⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣺⣿⢤⡀⠀⠣⠈⢟⣢⠨⠑⣦⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠘⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣾⣷⡄⠠⡗⠜⣧⣓⡀⠈⠣⠇⣀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⣇⠀⠁⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢻⣭⣥⣿⣦⠀⠈⠀⠉⣧⡀⠀⢈⠈⢡⠀⠂⠀⠀⣦⠀⠀⠀⠀⠀⠀⠉⠄⠀⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣆⠀⠀⠀⢐⣵⣄⠀⢳⣄⠳⠐⢀⡁⠘⣷⣶⡨⣶⡴⡇⢀⠻⡀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢿⣶⣿⡙⢦⡀⠀⠀⠉⠈⢡⠀⠀⠀⠀⠀⠀⠀⠈⢡⣽⣟⣿⣷⠀⠐⢇⠀⠁⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢨⢻⠻⢧⡘⣷⡀⠀⠒⠀⠀⠀⠀⠀⠠⠀⠀⢘⠄⢸⣵⠋⣠⡌⢣⢠⠘⣦⠈⠂⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣧⠛⢻⡗⣹⣧⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠸⢗⡸⣿⡄⠿⣿⠀⣧⢁⢬⣇⠘⠨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠹⡇⢈⣿⡼⣿⣆⠀⠀⢀⠘⠀⠀⠀⠀⠡⠤⢸⡀⠋⢻⣆⠀⠀⣿⠆⠈⠉⢠⣗⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢹⣆⠸⡇⣷⣿⡆⣀⠀⠆⢨⠆⠀⠀⠀⠁⠈⢃⠀⠀⢪⣟⣾⠛⠧⠀⠀⠀⠹⣦⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠻⡀⠈⢾⣧⣿⡄⠄⠰⣠⡷⠛⠀⠀⠀⠀⠀⠠⡀⠠⠸⣿⣿⣿⡦⠀⠀⠀⢹⣆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⢷⡄⠘⣎⢯⣻⣻⠄⢹⣱⡟⢆⠀⡀⠐⠒⠀⠈⢦⡀⢠⠙⢿⣿⠄⠀⠀⠀⢿⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠑⡔⠘⢨⣿⡇⠆⠀⢻⡌⢩⠄⠱⢀⠀⠀⠀⠀⢻⢀⠑⣆⡹⡄⠀⠀⢀⠈⢣⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠽⠀⠀⢩⠿⠲⣆⠈⠻⣌⠒⢃⣷⠊⠇⠈⠀⠀⠹⣦⡹⣵⣼⣇⠀⠈⡀⠫⣧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠤⠂⠠⡉⣿⡀⠈⠂⠀⠘⣿⣻⣿⠆⠈⠀⠀⠀⠀⠈⣧⠹⡜⢎⢡⠀⣀⣀⠙⢧⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⡀⠠⠈⢧⡀⠀⠀⠀⠘⣷⡌⢾⡄⠀⠀⠀⠀⠀⢾⣇⠰⡤⢺⣧⣤⣜⢷⠘⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠈⣷⡀⠐⡈⣷⡄⠀⠀⠀⠰⡻⡎⢳⡄⠀⢀⠠⠀⠈⣿⠀⣷⠙⣏⢿⠟⢻⣄⠃⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠸⣧⡀⠘⢄⠙⠄⠀⠀⠀⠐⠀⠀⣷⠀⠀⠀⠡⠀⢸⣇⠘⣧⠘⡷⠲⡚⠃⠀⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢘⣿⣷⣦⠀⠐⠰⠂⠀⠀⠈⠄⠁⠘⠃⠀⠀⠐⢳⡀⢻⡄⠘⣷⠀⡍⢿⣊⠢⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢻⠀⠠⠓⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⢹⣆⠘⣧⠈⠁⢻⡔⠀⠜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠸⣄⠐⠀⢸⠀⠀⠀⢄⠀⠀⢲⠀⠀⠀⠀⠀⢀⠀⢧⣰⣿⡆⢹⣆⠀⠈⣿⡀⠢⠨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡰⣰⣾⠀⠀⠄⠀⢃⡀⠀⠐⡀⠀⠀⠀⡄⠢⠈⡈⠋⣿⡄⢻⡀⢀⣿⣠⠐⢁⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠹⠿⢦⠀⠀⠀⠁⠙⠀⠀⠈⠠⠀⠈⢴⡄⠿⡶⡈⣟⢿⡀⢛⣶⠘⡇⠘⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠋⠉⠻⠈⠀⠱⢀⠻⡀⢷⠠⠂⠄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠛⡀⡈⢂⠀⠛⠂⠂⠀⠻⣆⢻⡀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡝⢀⠀⠀⠀⠀⠹⠀⢉⡀⢸⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠁⣄⠘⡀⢀⠄⠐⠄⠁⢻⠈⠧⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢡⠀⣄⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣀⣠⠀⠀⢀⣤⣤⡄⡠⠄⠀⠀⠀⠆⠀⠀⠀⠈⠂
⠀⠀⣤⣤⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠈⠙⠉⠀⠀⠸⠿⠿⣿⣷⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢼⣿⠄⠒⠠⠀⠀⠀⡀⠀⠀⠀⠰⠉⠁⠀⠀⠀⠁⠀⠀⡀⠈⠋⠀⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⠀⠶⠤⠆⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⢀⣶⣿⣷⠀⠀⠙⣇⠀⣠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠈⠉⢹⣿⣷⠀⠛⠁⠀⠀⣠⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠋⢁⣤⣄⣀⣀⠀⠹⠤⠾⣧⣜⣷⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠒⠂⠀⠀⠀⢀⣴⣾⣯⠀⠈⠂⠀⡸⣿⡿⢿⣯⣽⠀⠀⠠⠀⢈⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠾⠦⠀⠀⠀⠀⣠⣾⣿⣿⠟⠀⠀⢠⡆⠀⠀⠀⠙⠲⣿⣶⣄⠀⠀⠙⣦⣼⠆⠀⢠⠄
⠀⠀⠀⠀⢠⣾⣿⠂⠀⣀⣄⠀⠉⠀⠀⣁⣀⠠⣾⣿⣿⠿⠛⣀⣤⣀⠀⠈⠁⠐⡀⠀⠸⠿⠟⠋⢀⣠⣾⣿⡅⠀⠀⠈⠀⠀⠀⠀⢀⣠⡤⠶⠆⠈⢻⡆
⠀⠀⠀⠠⠀⠿⡿⠂⠰⢿⣿⠗⠀⠀⠉⠁⠈⠐⠋⠁⢀⠀⠀⢿⣩⣿⡗⠀⠀⠀⠁⠀⣀⠄⠀⠀⠘⠿⢿⡿⠋⠀⠘⠂⠐⠀⠀⢲⡻⠉⣦⡀⢠⣄⠛
⠀⠀⠠⠤⣤⣄⠘⠤⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠾⢹⠃⣌⠑⠋⠬⢄⡀
⠀⠀⠀⠀⠀⠈⠱⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠓⠂⠆⠀⠀⠀⠀⠀⡀⢠⠂⠀⠀⠀⡰⠋⠚⠙⠏⠃⠀⠘⠟
⠀⠀⠀⢀⡀⠛⠀⣀⡀⠀⠉⠀⠘⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⡀⠀⠀⠘⠂⠀⠠⠐⠀⠀⢀⡶⠰⠆⠐⠋⠁
⠀⠀⠀⠀⠀⢀⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⣈⣀⠀⠀⠀⠰⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠐⠀⠁⣀⠀⠈⠀⢀⠀⠉
⠀⠀⢠⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠤⣈⣁⡈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠚⠃⠘⠛⠀⠈⠀⢰⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⠥⠁⣀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡴⠀⠀⢀⣲⣤⣄⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠁⠀⠀⠀⠬⠥⡤⠤⠌⠀⠘⠒⠀⠨⠀⢰⠃⢐⣥⣌⡐⠀⠀⠀⣀⠀⢈⠀⠀⠀⠸⢿⣿⣿⠇⠀⠰
⠀⠀⠀⠀⠀⠐⠆⠀⠸⠀⠀⠀⠐⠆⠀⠗⠈⣀⣠⡀⠀⠀⠀⠀⠀⢠⣶⣾⣶⠀⣿⣷⣼⣿⡿⠃⠤⣄⠀⠐⠀⠉⠁⠆⢶⣤⠀⠈⠀⠀⡀⠀⠀⠉
⠀⠀⠀⣴⣤⡄⠀⢀⡄⢀⣀⠀⠀⣠⣶⣄⣸⣧⣼⣷⡶⢄⠀⠀⢀⠈⠛⠟⢻⡄⢿⣏⡁⢀⡤⡀⠀⠈⠇⠀⠀⠰⠀⠀⠀⠀⠈⠛⢢⣤⣥⣤⣀
⠀⠀⠀⢿⣿⠇⠐⠯⠽⠦⠿⠀⢀⠻⢿⡿⠃⠈⠉⠿⠆⠙⢰⣿⣿⠻⠆⠀⠈⢿⣤⡜⠛⢷⣦⠃⠀⠀⠄⠀⠀⢠⠞⠛⠛⠓⠆⠀⠺⢿⣿⠿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢠⡄⠀⠀⠀⢃⣴⣶⣦⠀⠀⢀⠀⠁⠈⠁⠀⠀⠀⠀⠘⠟⠀⠂⠘⠦⠀⠀⠀⠀⡀⠀⠛⠀⠀⣄⠀⠀⢠⡄⠀⠀⠶⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠘⠛⠛⡁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⣆⣹⡄⠀⠀⠙⢀⠀⠀⠀⠈⠇⠀⠂⠀⠐⢈⡀⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⡈⠑⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠓⠀⠀⠃⠀⠀⠀⠀⠇⠀⠀⢰⣿⣿⣷⣤⣄⠀⠀⠈⣀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠿⣛⣿⣿⠊⠀⠀⠀⠦⠀⠤⠀⠙⢦⡠⠀⠑⠦⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠋⠁⠻⣦⡳⣤⠚⠉⠑⣎⢁⠐⣤⣶⣶⡄
⠀⠀⠐⢁⣀⡦⠀⠀⡻⠟⣁⢀⣀⣀⠀⠄⠀⠀⠀⠀⢋⠀⠀⠀⠀⡠⠀⠠⣀⠀⠀⠀⠀⠇⠀⠀⣴⠋⡉⠀⡀⠂⢄⣀⠈⣏⠰⢿⡿⠟⠃
⠀⠀⠀⡈⠀⠀⠀⠀⠇⣠⠙⠛⠋⠉⠠⠀⠤⠤⠀⠀⢏⠀⠀⠀⠞⠀⠀⠀⠉⠘⠒⠀⠀⢢⠄⠚⠙⠛⣅⡈⠃⡀⢦⠁⠴⠀⠐⢂⣤⢄⡀
⠀⠀⠀⠑⠂⠀⠀⢀⣼⣏⠳⠆⠀⠐⠂⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠐⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⠃⠀⠈⠃⠀⠉
⠀⠀⠀⠀⠀⠆⠀⣿⣿⣿⡇⠂⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⡏⠀⢀⠀⠀⠀⣠⣴⣶⣤⠒⠀⠀⠀⠈⡀⠸⠷⠄⠀⠀⢰⡀⡀
⠀⠀⠀⠇⠀⠀⠀⠀⠙⠁⣠⣤⡀⠀⠀⠀⠀⣀⣴⣿⣤⠀⠀⠈⠉⠀⠀⠀⠈⠁⢀⣀⡀⠻⡟⠿⠃⢠⣶⣶⣦⠀⢰⡄⢰⣆⠀⠀⠈⠛⠉
⠀⠀⠀⡞⠀⠈⠳⠄⠀⠺⣿⣿⡋⠀⠈⠀⠀⠙⠛⠿⠛⠀⣀⣤⠀⠀⢀⠴⠂⠀⢻⣭⣷⠀⣠⠀⠀⠈⠻⣿⢿⣦⣼⣿⣞⢛⠀⠀⠘
⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⢾⣿⣿⣶⠂⠀⠀⠀⠄⠀⠀⢸⣿⣿⡇⠀⢀⣄⢀⠀⠈⠩⠙⣀⣠⣤⣤⠀⠀⠀⢸⣟⣥⡘⠟⠘⣧⠀⠐
⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⢀⡉⣽⣿⣯⠐⠒⠢⣀⠀⠀⠈⣻⠋⠀⠀⠀⠉⠈⢁⣀⠀⠀⠛⣿⠟⢁⣠⡄⠀⣴⣿⣏⠙⣧⣴⡟⠀⠀⠀⢀
⠀⠀⠀⣠⣤⡅⠀⠀⠀⠐⠙⣿⣿⠆⠉⠒⠒⠒⠁⠈⢀⠔⠉⠀⣾⣿⣶⡄⠀⢼⣿⣷⠆⠀⠀⡀⠚⠀⠀⡸⠿⣿⣍⢀⣠⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠏⣤⠈⠁⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⣿⡷⣸⡷⣦⠀⠙⡇⠙⢁⠀⠁⠀⠀⡛⠀⠀⠈⢙⡉⠰⠇
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠐⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠄⢀⠉⠁⠼⡟⠋⠀⠀⠀⠤⠤⠀⢀⠀⠰⠇⣀⠤⣁⡾⠋⢰⡂⠀⠀⠘⣤⢴⣶⣾⡆
⠀⠀⠀⠆⠰⠃⠀⠀⠀⡄⠀⠐⠶⠉⠠⠈⡡⠘⠃⢤⣈⠀⠀⢀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠶⠿⣿⡟⠃⠀⣍⠀⣽⠆⣠⠚⡁⠀⠀⠀⠙⠚⠛⠉⠤
⠀⠀⠀⣶⠀⠒⢠⡀⠀⠀⠁⠀⠀⢀⣀⣌⠣⣄⠀⣄⠋⠈⢉⣥⠀⢶⠞⠋⠀⣠⣤⣀⡀⢠⠒⣮⠁⢀⡴⠛⠻⣿⠗⣙⣲⡇⠘⠀⢀⣴⣶⣦⡀
⠀⠀⠀⠉⠀⠀⠀⠄⠀⢤⢀⡤⠀⠙⢿⣿⠀⣀⠻⠖⠂⡴⠟⠃⠰⠂⠀⠋⡈⢀⣠⠞⣀⠞⢛⡁⠂⡈⣧⡀⡶⠛⢿⣏⠉⠠⠋⠰⠀⣹⠿⠿⡇⢀
⠀⠀⠀⠀⠀⠀⢁⡀⠠⡦⡉⠡⠀⠀⢠⠈⢠⠀⠀⠶⢋⡀⠸⠿⠗⠀⠤⠄⢀⡀⠀⣀⠉⠴⠀⢠⣀⣿⡿⢇⠰⢶⣌⠣⠀⠀⢠⣿⣾⣦⠘⠀⠠⠈
⠀⠀⠀⠀⠰⠀⠈⠁⢰⣦⣴⣄⡀⠘⠀⠘⠿⠗⠠⠄⡤⠴⠚⣾⣀⠀⠀⠐⠊⠒⠀⠉⠀⠀⠀⠹⣿⣿⠞⢦⠴⠀⠉⠄⡉⠁⠈⠛⠻⠋⠄
⠀⠀⠀⠚⠀⢄⠠⠘⣿⠿⢿⡟⢠⠧⢤⠀⠀⠤⠴⠀⠀⢀⠀⣿⡿⠀⠰⡖⠀⠀⠀⢠⠤⠀⡤⠄⢠⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⢾⣷⣶⣦⣼⠆⠀⠀⠀⢀⣤⣉⠀⠀⠀⠀⠠⠋⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣁⠈⣿⣥⡄⢀⠀⠁⠿⣿⠿⠄⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢉⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠛⠁⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⠿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣶⣶⣤⣼⠏
⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⢰⣿⡆⠀⠳⡦⢷⣌⣿⣦⠀⠀⠀⠀⢠⣾⣦⠀⢀⣤⡀
⠀⠀⠀⢀⣙⣛⣃⠀⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⢈⡻⠋⠀⠀⠀⠀⢀⣸⣛⣇⡀⠀⠈⠢⠷⣬⡿⠁⠀⠀⠀⠘⠿⠟⢀⣹⣿⣟⣀
⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⣠⣿⣿⣿⣦⡀⠀⠀⢰⣿⣏⣀⡀⣠⡄⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠙⣧
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢠⡏⣿⣿⣿⡏⣧⠀⠀⢸⣿⡏⠉⠉⣁⣁⣀⣈⣿⣻⣿⣁⡀⣠⣶⡄⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⣿⣿⣿⠐⠛⣦
⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢻⣇⣀⣸⣿⣛⣛⣛⣿⣿⣿⣿⣿⣹⣿⣃⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⣿⡄⠀⣿
⠀⠀⠀⠈⣿⣿⣏⠁⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⢸⡟⠉⠉⣉⣉⣉⣩⣿⣿⣿⣍⣉⣉⣉⡉⠉⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⠀⣿⡇⠀⣿
⠀⠀⠀⠀⠿⠻⠟⠀⠀⠀⠀⠀⠸⠟⠿⠀⠀⠀⠀⠀⠻⠇⠀⠈⠛⠿⠛⠛⠟⠛⠻⠟⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠸⠟⠟⠘⠿⠀⠿⠂⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⢼⣿⡧⣦⣣⣦⠀⠀⠀⠀⠀⣠⣶⡄⠀⣾⣿⡆
⠀⠀⠀⢠⣴⣿⢡⡀⠀⣶⣶⠀⠀⠀⠀⠀⣾⠛⠛⠛⢻⣄⣰⠂⡰⢽⠥⡂⢲⠀⠀⠀⣠⣾⣏⠀⠍⠏⠁⠀⠀⠀⠀⢀⣹⡛⠁⠠⣯⣿⣦⡀
⠀⠀⢠⣿⣿⣿⠶⠶⠶⠈⣷⠀⣀⠀⠀⠀⣿⠈⠈⠉⢸⡇⢘⡄⢘⣸⡸⠀⢸⠀⠀⠘⣿⣿⠉⠛⠶⡗⠀⠀⠀⠀⠀⣾⣿⢷⣶⣾⣻⣿⣿⣷
⠀⠀⣸⣿⣿⣿⠀⢀⣴⣾⡿⢠⡟⠀⠀⠀⢼⣿⣿⣿⣿⠁⠘⠓⣶⣾⣶⠖⠚⠀⠀⠀⢻⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣤⡀⠉⢸⣿⣿⣿
⠀⠀⠻⠿⣿⣿⠇⠸⠓⠛⣾⠛⠃⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡇⠀⠀⠀⠀⣶⠒⣧⠙⣿⠀⠸⣿⣿⠿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣸⡿⠀⠀⡀⡧⣀⠀⠀⠀⣿⠀⣿⠘⠟⠀⠀⢸⣿
⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠁⠈⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⠁

⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢰⣿⡿⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⡀
⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⠐⠿⠷⠾⠿⠇⡀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠿⡏⠛
⠀⠀⢠⣾⣶⠾⣦⠀⠀⠀⠀⠀⢰⣿⣿⣦⣀⡀⠀⠀⠀⣿⣿⢀⡀⠀⠀⠀⠀⢠⣿⣿⣤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠿⣧⡆⠀⠀⡇
⠀⠀⠘⣿⣅⣼⡏⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣶⣾⣿⣷⣠⣿⠏⠀⠀⠀⠀⠸⣿⡏⠛⠛⠃⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣾⠟⠀⠀⠀⡇
⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢹⣇⠀⢤⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⡇
⠀⠀⠈⢹⣿⣿⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⢸⡧⠀⠚⠛⣛⣛⣛⣛⣿⣿⣿⣟⣛⣛⣛⡛⠛⠂⠀⡇
⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⠘⠿⠿⠻⠿⠛⠛⠛⠛⠛⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠛⢿⠟⠛⠛⠛⠛⠛⠛⠿⠟⠃⠀⠀⠆⠟⠲

⠀⣠⣶⡶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆
⣼⣿⣿⣷⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠻⢶⣶⣿
⢿⣿⠏⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠟⢿⠗⠀⠀⠀⠀⠀⠀⣿⣧⠀⣿⣥⡋
⠈⠻⣄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⡶⠟⠃


⠀⣀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣤⡀⠀⣠⡶⠶⡾⣧⠀⠀⠀⠀⠀⠀⣸⡧⠄⢀⣠⣾⣿⡆⠀⠀⠀⠀⠀⠀⢀⣴⡿⣦⡀⣀
⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⡆⢠⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠁⢸⣿⠃⠀⠀⠀⠾⠿⠿⠿⠿⠷⠿⠷⣿
⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⠛⠀⠀⢸⣿


⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣄
⣾⡏⠷⡤⠤⠤⠤⢠⡄⠀⠀⠀⠀⠀⠀⠘⡟⢳⡆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠉⠓⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢛⠓⣄
⣿⡇⠀⡃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⣼⠃⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠛⠀⢩
⠉⠁⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣠⣠⣤⣄⠰⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢰⣖⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃
⠈⠛⠛⢿⣻⣻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡷⠶
⠀⠀⠀⠑⣼⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡾⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠙⠛⠻⣷
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠿⢿⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡤⠞⠈

⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⠀⠀⣀⣤⠴⠀⣀⡀⠀⠀⠀⠀⠀⠠⣶⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢤⣄⡀
⠀⠀⠰⠖⢻⣿⠳⠆⠀⠀⠀⠀⠈⠘⢷⣜⣻⠃⠀⠀⠀⠀⢀⢠⣾⣏⣡⣤⣀⠄⠀⠀⠀⠀⢠⣶⡿⣶⠀⠀⠀⠀⠀⠞⢳⣌⣛⣧⡾⠀⠁
⠀⠀⠀⢀⡿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆⠀⠀⠀⠈⠈⠃⠛⠋⢦⡈⠀⠀⠀⠀⠀⠘⣻⣿⣽⠇⠀⠀⠀⠀⠀⡠⢌⡿⢿⡠⠄
⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⢀⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⣘⣟⢙⣿⣋⣹⡏⠀⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⠈⠽⣦⣻⣟⣤⡾⠅⠀⠀⠀⠀⠀⣘⣿⣃⠀⠀⠀⠀⠀⠀⣠⣴⣟⢣⣿⢷
⠀⢰⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⢰⣟⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠛⠈⢿⣿⡿⠙⠛⠀⠀⠀⠘⠻⢿⣷⣿⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆
⠀⠀⠀⢠⣾⣧⠀⢠⣤⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⠄⠀⠀⠀⠀⠀⣀⢀⣸⣿⣃⡀⣀⠀⠀⠀⠀⠀⡼⣿⠷⣤⡀
⠀⠐⠒⠶⢺⡿⠻⡏⠁⠀⠀⠀⠀⠒⠻⣶⠉⠒⠂⠀⠀⠀⠀⠀⣼⠛⣷⠀⠀⠀⠀⠀⠈⢫⠉⣿⣿⡏⢩⠉⠀⠀⠀⠐⠉⢳⡷⣶⠊⠑
⠀⠀⠀⠛⠛⠃⠀⠃⠀⠀⠀⠀⠀⠀⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣥⣤⠄⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠋⠰⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢀⣴⣶⠻⠃⢻⡂⠀⠀⠀⣠⡔⢠⣶⡄⣹⠓⠆⠀⠀⠀⠀⢠⡄⠀⣴⠀⠀⠀⠀⠀⢀⣶⡶⠶⢶⣦⡀⠀⠀⠀⠀⠀⠀⢿⣿⠇
⠀⠀⢻⣟⢾⠛⣠⣼⣷⠀⠀⠀⠁⠙⢷⣿⣾⠋⠀⠀⠀⠀⣴⣦⣾⣥⣼⣏⣀⣀⠀⠀⠀⢹⣿⣿⢾⣿⣿⠉⠀⠀⠀⠀⡔⠙⢀⣿⣿⡆
⠀⠈⠉⠉⠈⠈⠉⠉⠋⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠐⠛⠛⠋⠛⠃

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢘⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⠄⠀⠀⠀⠀⠰⠾⠷⠆⠀⠀⠀⠀⠀⠀⠔⢉⣬⡙⢦⠀⠀⠀⠀⠀⢀⣴⣾⠛⠁
⠀⠀⡀⠰⠯⠨⠷⠀⡀⠀⠀⠀⠛⠛⢻⡟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⡆⣨⣯⣄⢘⠃⠀⠀⠀⠀⢸⡏⠙⠓⢠
⠀⠀⠁⠋⠆⠀⠎⠃⠁⠀⠀⠀⠀⠙⠛⠋⠀⠙⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠑⠢⠤⠔⠁⠀⠀⠀⠀⠀⠸⠗⠀⠃⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⣋⣉⣩⣤⣤⣾⣿⠿⠟⠛⣻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⡶⢾⣿⠛⠛⣉⣉⣥⡤⠼⠿⠒⠛⢋⣉⣡⣽⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⢉⣩⣤⠤⠶⠾⠟⢛⣉⣉⣤⣤⣴⡶⠶⠿⠛⠛⠋⠉⠁⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⡴⠋⢀⣤⣶⠶⠾⠟⠛⠛⠉⠉⣀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⡇⢠⣿⠋⠀⠀⠀⠀⠀⢀⡴⠛⣩⣤⣤⠀⠈⠳⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⢠⡞⠀⠀⣿⠀⣿⣀⣤⡄⢻⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⣾⢠⡖⠛⠋⠀⢈⣀⣸⡇⣸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⣿⠘⠗⠚⣿⠀⣿⠁⠀⣠⠏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⣿⠀⠀⠀⠀⠀⠘⣦⡀⠀⠻⠶⠛⣀⡴⠋⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠛⠉⠀⢀⣀⣀⣤⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⠶⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠾⠟⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣀⣀⣀⣀⣀⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⢶⣶⡶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠛⠛⠛⢻⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠿⠿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣬⣤⣤⣬⣥⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣉⣉⣩⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣉⣉⣩⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣉⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣶⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⣀⠋⠛⠛⠋⣛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤⣤⣼⣿⣿⡀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⣻⣿⡿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⣿⣿⡅
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣽⣿⡇⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠉⠉⠉⠉⠉⣽⣿⡇⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⢸⣽⠂⠀⠀⠀⠀⠀⣋⠷⣀⣠⣤⣤⡀⠀⠀⠀⠀⢬⡷⣽⢮⡵⣭⠆
⠀⠀⠀⠀⠀⢀⢴⡦⠴⠀⠀⠀⢰⣦⡏⠀⢥⣾⡆⠀⠀⠀⠻⠖⣉⣉⣁⣹⣇⣀⡀⠀⠀⢼⡂⢿⣴⣇⣾⡄⠀⠀⢀⠈⠲⠊⠲⠂⠲⠂⢢
⡄⠀⠀⠀⠐⠎⠺⡷⣄⠀⠀⠀⠨⡇⣀⣀⡠⡏⡇⠀⠀⢸⢩⠂⠐⢦⠗⠾⢾⠆⡇⠀⠀⠀⡠⢤⠡⠀⡀⡤⠀⠀⠀⡿⣏⡹⠍⠹⢉⡹⠉
⡃⢰⠆⠀⠀⢰⣶⠟⠁⠀⠀⠀⠀⣿⣮⣿⣦⡗⡇⠀⠀⠸⠈⠃⠒⠃⠑⢺⣟⣆⡇⠀⠀⠀⠗⠒⢶⠤⡏⣿⠀⠀⠀⢑⣾⣶⣶⡄⡏⠓⠒
⠻⠋⠉⠉⠳⠋⠀⠀⠀⠀⠀⠀⠺⠇⠀⠋⠀⠻⠃⠀⠀⠘⠀⠠⠄⠤⠀⠄⠀⠄⠃⠀⠀⠀⠓⠒⠛⠀⠛⠛⠀⠀⠀⠈⠁⠀⠀⠙⠣
⡔⠢⠰⠲⡤⠒⢆⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠤⣤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀
⠻⡟⠘⣟⠉⢿⠃⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠊⢠⠻⠞⣤⠑⡕⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⢸⢽⠳⠶⠶⠶⢞⠏
⠀⡴⠉⡭⠭⠭⡉⢢⠼⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢫⠢⣌⡾⣳⣩⣜⡝⠀⠀⠀⠫⢧⢥⣮⠉⣤⡼⠓⡄⠀⠈⠀⠥⣁⢉⡉⠭⠚
⠀⠃⠀⠀⠀⠀⡇⠘⠀⠀⠀⠀⢞⠡⠠⠄⢋⠹⣆⠀⠀⢸⡜⣓⠒⡄⠉⠀⠈⡧⡇⠀⣏⣦⡔⡚⡛⠆⣽⣵⣀⠇⠀⠀⠀⠀⢸⠀⡇
⠰⣆⢀⡑⣒⢚⡀⣠⠇⠀⢰⡏⠍⠉⠉⠉⠉⠉⠋⣷⠀⠸⡼⠒⠚⠀⠀⠀⠀⢥⠇⠀⢧⡥⠘⠒⠓⠁⢭⡼⠁⠀⠀⠀⠀⠀⢸⢠⡇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠛⠂⣿⣀⣼⡇⢸⣟⣛⡃⢸⣟⣻⡷⠀⣸⢿⣆⠀⣿⣛⣿⠄⠻⣦⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⣿⠉⢹⡇⢸⣯⣭⡅⢸⡏⢻⣦⣰⡿⠾⣿⡄⣿⠋⠉⠀⠀⣿⡇


⠀⠀⣤⡍⣶⢽⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⡕⠀⠀⠀⠀⠀⠀⠺⣾⠧⠀⣿⠆
⠀⠀⣼⢿⠻⣽⢧⡀⠀⠀⠀⡀⣀⢀⠀⠄⠠⠤⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠉⠉⠶⠀⠀⠀⠀⠀⣨⡛⡧⠈⡧⡦⠄
⠀⠀⠀⢼⡄⠛⠙⠁⠀⠀⠘⠄⡸⠻⣤⠛⡤⠤⣠⡬⠀⢀⣬⠷⣯⠷⣮⠷⠠⠦⡀⠀⠀⠀⠘⣇⣀⣀⡏⠀⠀⠀⠀⠀⠈⢹⡃⢁⢡⠶⠟
⠀⠀⢠⣸⣗⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⢸⠓⡞⡍⡦⠾⡭⠭⠆⡇⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠐⠟⢛⣦⡄⡷
⠀⠀⠛⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠃⠀⠀⠘⠁⠃⠓⠋⠉⠋⠁⠛⠃⠀⠀⠀⠀⠓⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠲⣤⠀⣀⠄⢄
⢠⠦⡄⠀⠀⠀⢀⡴⢄⠀⢀⡄⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡍⣲⣊⡝⣶⣪⣱⠀⠀⠀⠑⠚⠋⣇⢯⠻⣻
⣾⣆⣟⣂⠴⢒⠚⠓⠾⠀⠈⡌⠱⡄⠠⣌⠈⡗⠢⣄⠀⢀⣀⠀⠤⢬⡡⡇⡠⡁⡄⠀⠈⠉⠀⠉⠈⠀⠉⣞⡦⡀⠀⠀⠀⠾⢅⣤⠀⡇
⣿⡋⠒⣙⠀⢸⠀⠀⢸⠀⢰⠷⠶⠷⠦⢬⡑⡗⠒⠀⠀⠈⠛⠒⠒⢲⠣⣏⠗⣇⠇⠀⣯⠋⣭⢫⣽⣽⠀⢻⡗⠁⠀⠀⠀⠀⢀⣹⣄⣇⡀
⣿⡷⠒⠊⠂⠁⠒⠊⣛⠀⢸⣀⣀⣁⣉⣉⣉⣙⣲⣦⠀⠀⠀⠀⠀⠈⢩⣟⣁⣑⡆⠀⢳⡿⠛⠛⢾⣿⠁⠈⠀⠀⠀⠀⠀⠀⣾⠛⣷⠓⢻
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣰⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣶⣦⡀⢠⡾⠋⠁⠀⠀⠀⣿⠀⠀⠀⠈⠛⢷⡄⣸⡟⢃⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⣤⣶⡿⠷⠿⣧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠁⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠗⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣿⣶⣶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣴⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣭⣥⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡄⢀⣤⣤⣤⣤⣤⣤⡀⢰⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠈⠉⠉⠉⠉⠉⠉⠁⠘⢿⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠶⠤⠤⢤⣀⠀⢀⣀⡤⠖⠚⠉⠉⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⢀⣠⣴⠾⣷⣾⡀⠀⠀⠀⠀⠀⠀⢀⣀⣽⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣀⣤⣶⠿⠛⠉⠀⠀⣿⠉⠻⣶⣄⠀⣀⣤⡶⠟⠉⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⠾⠛⣿⠉⠀⠀⠀⠀⠀⠀⡿⠀⠀⠙⣿⣿⡿⠋⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⢀⡴⠚⢩⡟⠉⠉⠉⠛⠲⢤⣿⠀⠀⠀⣀⣤⣶⣿⣿⣦⣀⣾⡏⠀⠀⠀⠀⢀⡠⠾⣄⣀
⠀⠀⠀⠀⠀⡞⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣈⣿⣶⡿⠟⠋⠁⠀⠀⠀⠉⠻⣄⣀⣠⡴⠊⠁⠀⠀⠀⠈⠙⡄
⠀⠀⠀⠀⡸⠀⠀⠀⠈⢧⡀⣀⣤⣴⣶⠿⠟⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⢠⣧⣄⣀⣀⣤⣾⡿⠿⠿⢦⣤⣄⣴⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⡞⠈⠻⣿⣿⠛⠁⠀⠀⠀⠀⢀⣽⣿⡇⢘⣧⣀⠀⠀⠀⣀⣀⣠⣴⣿⣽⣻⣶⣦⣤⣀⣀⣀⣠⠖⠉⢰
⠀⠀⠀⡇⠀⠀⠘⣿⡇⠀⠀⠀⠀⢀⣾⠋⢠⣧⠞⠀⣹⠟⠛⠉⠉⠉⠁⠀⣠⠟⠚⠳⣌⠈⠉⠙⡿⠋⠀⠀⡞
⠀⠀⠀⠳⣄⢀⣠⠼⢿⣟⠉⢉⠟⣛⣾⣶⣟⡙⣷⠞⠁⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠈⠳⢤⣼⡥⠴⠒⠚⠣⡀
⠀⠀⠀⠀⣨⠟⠦⠤⠤⠭⠿⢿⣿⣋⣁⣤⡼⠿⡿⠛⠓⠶⢤⣤⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⡅
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠁⠀⠀⡇⠀⠀⠀⠀⡟⢿⡀⠀⠀⠀⠀⠀⠀⠀⡼⠃⡿⠀⠀⠀⠀⢰⠁
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⡇⠀⠀⠀⠀⢷⢸⣇⠀⠀⠀⠀⠀⠀⣼⠃⢠⡇⠀⠀⠀⢠⠏
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⣼⣿⣷⣤⣤⣤⣤⣼⢋⣴⠋⣧⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⣿⣆⣠⣾⣿⠳⠶⠶⣟⣋⣯⡁⠀⠀⣈⣩⡿⠋⠉⠉⠉⠹⣄⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣀⣤⡴⠟⠉⠀⠀⠙⠳⣶⣄⣀⡈⣙⡿⡿⠋⠁⣿⣷⣤⣤⣤⣤⠴⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⡏⢰⠃⠀⠀⣿⡏⠉⠉⠁⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠘⣧⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⢀⡾⢦⡀⠀⠀⣿⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠋⠀⠀⠙⠦⣄⣻⡀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣘⣃⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢠⣮⣤⠀⠀⠀⠀⠀⠀⠀⠀⣰⣭⠄⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡼⣄⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⡠⢷⡄⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⠀⢸⡃⠀⠄
⠀⠀⠀⠀⠀⢠⣤⣶⣾⠿⡿⡜⠁⠀⠀⠀⠀⠀⠙⠻⡞⠊⢰⠛⠃⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⠀⢸⢣⠀⡆
⠀⠀⠀⠀⠀⠒⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠓⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠘⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣀⠀⠀⠀⠀⠀⠀⢀⡻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡘⢻⡿⠃⠀⠀⠀⠀⠘⠉⣿⠁⠀⠀⠀⠀⠀⠀⣀⡐⣙⠃⢴⠒⠀⠀⠀⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⠠⠀⣀⡀⣎⣀⡞⠉⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠐⠾⠚⣿⡾⠓⠛⠻⠆⠀⠀⠀⠀⠀⣹⡄⠥⠤
⠀⠀⠀⠀⠐⠤⠌⠠⠭⠭⠤⠄⠸⠸⠄⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠐⣇⣀⠔⣶⣶⠀⠀⠀⠀⠀⠀⢸⠂⠀⢘⡥⠤⢰⣂⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠠⣇⡀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠈⠆⠀⢈⡁⠀⠀⣴⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⢠⣷⣆⡀
⠀⠀⠀⠀⠀⣴⣽⡿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡁⣄⣬⠇⠀⠀⡿⡇⠀⠀⠀⠀⣤⣄⣤⣤⣟⣾⣷⠀⠀⠀⠀⠠⣿⣿⡿⠯⠄
⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠁

⠀⠀⠀⠀⠰⠞⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣴⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠟⠛⠛⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⣋⣅⠀⠀⠀⠀⢸⠁⠀⠀⠀⠰⣷⣾⡆⣿
⠀⠀⠀⣀⣤⢀⢁⣄⣠⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⢰⡿⠿⠛⠀⠀⠀⠀⢸⠀⠀⢀⠆⠀⠈⠉⠀⣿
⠀⠀⢸⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡴⣸⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣈⣁⣀⣀⣠⡿
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣀⣠⣴⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⡋⡀⠀⢀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣟⠀⠀⠀⠀⠀⠀⢸⡇⠙⡛⠛⠁⡇⠀⠀⠀⠀⠀⢸⣾⣿⡤⢠⣿⣷⡇
⠀⠀⠸⣿⣬⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢀⡴⡻⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⡇⠉⠑⠉⠀⡇⠀⠀⠀⠀⠈⢿⣿⣿⠇⠈⣿⣿⣷⠃
⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡹⢮⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠉⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣻⣿⠃
⠀⠀⠀⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠁⠀⠀⠀⠀⠀⠀⣿⢩⠉⣷⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠰⣿⣷⡄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣠⠔⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣶⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⢶⡀⡴⣾⣿⣷
⠀⠀⢸⡇⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠈⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⡌⠉⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⣿⢿⣿⡿⠇
⠀⠀⠘⠁⠛⠛⠛⠛⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⣰⣾⣿⣷⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⢐⣿⣿⢫⡝⣿⣿⠄⠀⠀⠀⠀⢀⡠⢤⣀⣿⠴⠖⠋⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⡖⠋⡟⣶⣧⣹⡏⢳⡄
⠀⠀⠈⢿⣿⣷⣾⣿⡿⠁⠀⠀⠀⠀⠻⠤⢾⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠉⠳⠿⣯⣭⡾⠗⠋
⠀⠀⠀⠀⠘⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠺⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠂⠀⢀⠀⠀⠀⠀⠀⠘⢣⣈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠉⠉⠀⠂⠀⠀⠠⢄⣀⠤⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⢤⣀⠡⠄⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡠⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠒⠛⠂⠐⢢⣀⢈⢁⡒⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠭⠀⠀⠀⠀⠄⠐⠀⠒⠐⠶⢶⢎⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⠉⠙⣫⣍⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠔⡦⠄⠠⠠⢠⣄⡀⠀⠀⠀⠀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣔⣤⣀⣩⠥⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠤⠦⠉⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠚⠋⠁⠐⠶⣀⠂⢀⢙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠎⠥⠌⠀⠀⠀⠸⠀⠀⠈⠠⡥⡍⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⡠⠟⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢹⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⣃⣥⡠⠤⠤⠀⠀⢀⡤⠔⠋⢠⠤⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⣔⣓⡶⠒⠒⠀⠀⡄⠄⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠀⠀⢀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠰⣯⡽⠇⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠓⠒⠐⢊⠔⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢉⢣⡀⠀⠀⠀⠀⢀⠈⠒⠄⠠⠀⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠒⢆⠀⠀⠀⠀⠀⠀⠁⠀⠲⢜⡀⡃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣚⡂⣀⣀⢀⣀⡀⠀⠀⠀⢙⡓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠕⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄

⠀⢧⠈⠁⠒⢭⡦⢠⣍⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠢⡈⠓⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡠
⠀⠪⠀⠀⡀⠀⠈⠉⠙⠔⡤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⡝⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠔⢈⢀⣠⡤⠖⠋⠃
⠀⠀⢀⠌⠁⠀⠀⠀⢀⠜⡀⠇⠘⠸⢀⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⠀⢀⠀⡀⠀⠤⠀⢀⠀⠀⡒⠉⠛⠉⠁
⢀⠔⠉⠀⠀⠀⠀⣠⠊⢀⡘⢂⠀⠆⠀⠀⠁⠀⠉⡐⠦⠀⡀⠀⢠⠙⡀⠀⠀⠀⠈⠉⢤⢄⡂⠉⠑⠀⠀⡃⠀⠀⠀⠀⠀⠀⣔
⠀⠀⠘⠖⠀⠂⠤⠅⡰⣉⠄⠤⢡⡁⢀⢀⠀⠉⡉⡁⢓⡂⠈⣁⡘⢣⢰⡤⠄⠀⢺⣆⠦⢶⡉⠀⠠⠤⠄⠇⠂⠐⠀⡀⠚⢩⠏⠤⠉
⠀⠀⠒⢺⢆⠊⢀⠖⠀⠒⠘⠁⠛⠓⠆⠈⢥⢀⠉⠉⠉⠩⡀⠀⠀⠀⠆⢱⠀⠀⠀⠌⠉⠁⠛⠀⠒⠈⠁⠓⠀⠠⠬⣀⡀⡾⠀⡠⢢
⠀⠀⠀⠠⠻⡀⠀⠀⢀⠃⠀⢠⠀⠀⠀⠑⣀⠄⠈⠚⢴⡒⣤⠤⠄⠀⡈⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⢋⠴⠊⠅⢉⠟⠢⢤⣈
⠀⠀⠀⡀⠰⢣⠠⡶⢆⢀⢠⡒⠀⠀⠊⠀⢀⡲⠔⠋⠁⣠⠽⠀⠀⠀⠀⠈⡆⠁⠀⠄⢤⠀⠀⠀⢤⠤⣏⠲⡧⠊⠀⠀⠈⠀⠀⠀⠈
⢀⠀⢠⢀⣦⠑⢃⠈⠟⠀⡈⣄⡶⠼⠚⠉⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢊⠁⣤⣭⣴⣇⢲⡄⣢⣦⣴⣶⠵⠯
⠀⡠⠠⠑⠙⠂⠀⣴⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⠀⡀⠀⠀⠀⢀⢀⠴⠊⠁⢠⠞⠊⠀⢂⠨⠀⠐⠐⠉⢻⡁
⢁⣀⢄⡠⠔⠊⠉⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠠⠀⢀⣼⠚⠅⢀⡤⠔⠁⠀⠀⠀⠀⡆⠀⠀⠀⢸⣷⣀
⠓⠋⠁⠀⠀⠀⠀⠁⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡄⠀⢀⣀⡤⢿⡄⠐⡖⠞⠋⠀⠀⢀⠀⠀⡀⣼⠩⢄⠀⡐⢿⠒⠈⠙⢓⢀
⠀⠀⠀⠈⠀⠈⠰⠀⠀⢵⣀⠀⠄⠀⠀⠀⢠⠟⠀⠀⠀⠀⡄⠂⠀⢀⠘⣷⠄⠡⢄⡌⠆⠐⡜⠀⠄⡶⠃⠀⠨⠆⠀⠟⠀⠀⠀⠺⠛
⠀⠀⠀⠀⠀⠀⠀⠄⠂⠈⠙⡀⠀⠀⣀⣠⠾⠠⢀⠰⠂⠀⢷⡀⠆⢁⣀⠠⠗⢯⡅⣌⠈⠞⠉⠀⠀⠀⠀⠀⣶⠄⢀⡆⠀⡀⠀⠠⣀
⡀⠀⠀⠈⠉⣁⡰⠆⠵⠤⠞⠙⢃⡘⠒⣀⡀⠒⠁⠀⣂⠔⠂⠁⠀⠀⠀⠀⠀⣿⢁⢛⡀⠘⠀⠐⠁⠀⠈⠀⠀⠈⢀⠁⠀⠄⠀⠈⠠
⢴⠘⠉⠉⠉⠈⡔⢒⠒⠉⠉⠹⣩⠩⠛⠡⠤⣀⡀⠊⠁⠀⠀⠄⠒⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠤⠐⡏⠀⠀⠀⡀⠄
⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠐⠠⡪⠊⠁⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠄⠠⠚⠀⣀⣽⢠⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⣴⡄⠀⠃⡤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠐⢂⠀⠆⠖⠐⠒⠻⢤⠴⠯⢥⠾⠀⣡⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠭⠚⠊⠁⠐⠀⠄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⠋
⠂⠈⠣⠀⠐⠂⠀⠄⠈⠶⡤⠧⠤⡤⠤⠦⠄⠭⣁⡈⠀⡀⠂⠀⠀⠀⢠⠴⠧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⣸⠁⣄
⣠⠔⢀⡀⠀⠀⠐⠈⠉⠓⣚⡆⠂⠂⠀⠁⣨⠵⠞⠋⠙⠒⠾⢣⣄⡴⢀⠀⡀⠀⠠⠄⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⡋
⠀⠱⡄⠉⠄⠀⠀⠀⠀⠀⣢⠄⠂⠘⠀⠀⢉⣀⣀⠤⠀⠀⠠⠐⠀⠉⠉⠚⠗⢦⣴⣀⡀⢤⠀⠀⠀⠈⡡⡴⡤⡂⠈⡄⡰⠁⢀⠴⠠
⠁⢀⠘⣀⠀⠀⠄⠀⠈⢀⣼⠤⠄⢒⠛⠉⠉⠽⠀⣀⠀⠀⠄⠀⠀⠀⠀⠐⠃⠀⠀⠈⡉⠟⠶⡾⢌⠠⠠⣀⢘⡃⠈⡟⠂⠠⡀
⢧⠀⠀⠀⠤⠀⠒⠵⠊⠀⣰⠀⠠⠂⠰⠀⠲⠜⡋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠁⠀⠀⠀⠀⠀⢄⠉⠀⠲⠌⣺⢎⡀⠀⠃⠀⠈

⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣫⡭⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⣾⣶⣿⢿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣾⣿⠋⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠈⢿⣿⣿⡞⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⠶⣌⡄⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢿⣿⡗⣾⣽⠷⣾⣿⣟⡇⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⢿⣿⣿⣿⡟⡍⢷⣦⣁⢀⠃⠌⠀⠀⠀⢀⣺⣇⡄⢀⣀⢢⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⢠⣿⣟⣴⣿⣿⣿⣟⣈⣽⣿⡇
⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢰⣾⣿⣿⣟⠁⠤⠀⠉⢉⠫⠉⠀⠀⠀⠀⠸⣷⠀⠊⠀⠉⢽⣿⠀⠀⠀⠀⠀⠠⣄⠀⠉⠁⠙⠿⣿⣿⣿⣿⣷⠙⠻⢿⡇
⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠐⡀⢋⠻⣿⣿⣦⡰⠶⠤⠌⠀⠀⠀⠀⠀⠀⠀⠘⠃⠋⠀⢀⡾⠃⠀⠀⠀⠀⢀⣀⣈⠀⠀⠀⣠⡶⣿⣿⢿⣾⠃⢀⡀⠀⡇
⠀⠀⢸⣿⣿⠟⡇⢁⢢⡀⠀⠀⠀⢙⡈⢠⠈⡛⡻⠝⠁⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⠤⡿⢛⡉⠷⠤⠀⠀⠀⠀⠀⢹⠅⠀⠄⡈⠁⠀⠈⡋⣸⣳⠂⣿⡿⠗⡇
⠀⠀⢸⠛⠤⣸⣻⣾⡀⠳⣄⠀⠀⠘⢿⣶⣨⣴⣁⣠⡆⣼⣠⣀⣼⡎⠀⠀⠄⢤⣤⠖⠀⠀⠀⡠⠀⠀⠀⠀⢀⠀⠘⣦⠀⠀⠀⠀⢳⡄⠈⣿⠃⠀⠀⢀⣴⡇
⠀⠀⢸⡀⠀⢈⠉⠉⠉⠳⢮⠗⠀⠠⠟⠀⠀⠉⠯⡉⠙⠛⠋⠹⢁⡀⠀⠂⣬⣿⣁⠀⠀⢠⣄⠀⠀⣸⡆⠀⠘⡀⠀⣿⡗⠄⢀⠀⢸⣷⠀⡟⡇⠐⠘⠉⢀⡇
⠀⠀⢸⢧⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠙⠋⣉⣱⣁⠛⣶⣿⡏⠈⠀⣴⣿⡇⠀⠀⠁⠀⣼⣿⠀⢘⠀⠈⣿⠠⠠⠟⠀⠀⠀⠸⡇
⠀⠀⢸⠈⢳⡄⠳⡵⣄⠀⠀⢀⣄⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠒⠚⠛⠋⢱⡤⠉⢛⠁⢔⠀⠃⠀⢸⣿⠀⢘⠀⠀⣿⠂⠀⣰⣖⠛⠒⢸⡇
⠀⠀⢸⡀⠀⠀⠀⠉⠈⠙⠈⠛⠿⣷⣤⣄⣀⣀⡀⢻⣷⣄⠰⣤⡠⠀⠀⠀⠀⠺⣆⣠⣅⠀⠤⠀⠀⠀⠰⣿⣂⣓⣀⣘⣋⣀⣘⡀⠀⣟⣐⠋⢩⠟⠒⣻⣿⡇
⠀⠀⢸⣷⣄⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠛⠘⠛⠓⠈⠒⠀⠀⠘⢿⣿⣿⣯⣄⡄⠀⣰⡇⠁⠃⠀⢸⣿⠡⠴⠄⠤⢿⡌⠀⡋⠀⠚⣻⣿⡇
⠀⠀⢸⣿⣿⡔⣰⢼⣿⣶⣦⣰⣆⣦⡀⠀⡄⣄⣆⠀⠀⠠⡄⢠⡀⠀⢠⠀⣀⠀⣤⣄⡈⠉⠻⢿⣿⣟⠛⣧⡀⠄⠀⢹⡇⢸⣿⠏⢀⣀⣿⡶⠀⠀⠚⢙⠛⡇
⠀⠀⠈⠛⠋⠉⠙⠉⠋⠉⠋⠉⠉⠉⠉⠀⠉⠉⠉⠁⠈⠈⠉⠈⠉⠀⠈⠀⠉⠁⠉⠉⠉⠈⠉⠈⠉⠉⠀⠈⠁⠁⠀⠈⠁⠉⠀⠀⠉⠉⠉⠁⠀⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠠⣐⡆⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢽⠽⠳⣠⣄⠁⣆⠀⠰⠀⠀⠀⠀⠀⡄⢸⢸⢿⠀⠀⣀⠄⢠⠀⠀⢠⠀⠀⠀⠠
⠀⠀⠈⠉⠈⢾⢿⣅⠀⠲⣤⣿⠰⡘⠀⠁⢦⡾⢄⢇⠀⠂⠇⠆⠀⣿⠁⠀⡀⠀⠳⢻⡈⠀⠀⢀⡄⠀⢄
⠀⠀⠀⠀⠀⠈⠋⠉⡳⣄⣿⣿⡌⠂⢠⢡⠇⡧⡏⡀⢭⢠⡼⠀⠀⡏⣴⠀⠃⠀⠰⡿⠀⠀⠰⡟⡏⠀⠈
⠀⠀⠀⠀⠀⠀⠠⣴⣷⠈⠙⣧⠨⠀⡌⡻⠈⠤⡽⢘⠘⡬⢀⡇⠸⢱⣞⠉⠠⠂⢂⠄⠀⠀⢰⢅⡆
⠀⠀⠀⠀⠀⠀⠐⠺⢿⣶⡆⡆⠀⠀⡼⡓⠃⠐⠑⠈⠃⠣⡀⠱⡤⢻⣑⠘⠀⠇⡇⠀⢨⠀⠸⣜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⡑⣿⠔⣣⢿⠀⠀⡀⠀⠀⠰⢸⠑⠀⠀⡌⠓⢼⠗⠀⣤⠀⠈⠀⠘⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠎⣾⣿⡟⡟⢿⡘⠐⣣⡇⠰⡷⢾⣦⡀⠀⠈⠁⠠⡎⢤⠊⠀⠀⠀⠄⠃⢴⠖⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⣇⠒⠀⠦⠁⠀⢼⣅⠀⢰⠀⠉⠢⠷⠀⠀⠀⠆⠐⣀⠀⡀⠂⢸⢀⠚⢀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⠀⡈⠕⠱⡘⡄⠀⠀⠀⠈⠀⠘⠃⠀⠀⢀⢃⠀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⢣⠠⠀⠐⡀⣄⢘⡓⠀⢀⡐⢁⠀⠀⠀⠀⢀⠀⠀⢀⠆⠀⠈⠀⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣃⣀⣀⣀⣀⣈⣁⣀⣄⣀⣀⣑⣂⣀⣐⣀⣈⣀⣀⣐⣂⣀⣀⣀⣁⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠯⡄⠀⠀⠀⠀⠀⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠏⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠤⠤⠀⠀⠘⣧⠀⠀⠈⠂⠄⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡶⠀⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠆⠐⠃⠣⡀⠀⠀⠀⠐⠀⠶⠀⠀⠀⠀⠀⠀⠀⡤⢰
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠄⠆⢀⠀⠀⠀⠃⠀⠀⠤⠓⠋⠙⠒⠲⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠀⡈⠆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠨⡀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡴⣶⣦⣤⣤⣖⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠡⠛⠋⣹⣿⣧⣯⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁
⠀⠀⠀⠀⢀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣓⠀⠁⠀⠀⠀⠉⠀⠀⠙⠓⠀⠀⠀⠆
⣿⣿⣿⣿⣷⢶⣾⣿⣿⣷⣶⣿⣿⣿⣶⣶⣾⣶⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣷⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠙⠻⢿⣯⣽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢤⡀⠨⠄⠘⢹⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢧⣂⡄⠀⠘⣿⣾⣾⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠛⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠬⢥⠊⠀⠈⠻⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠠⠀⠀⢠⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢸⡅⢀⠜⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣧⡂⠈⠉⢀⢩⢹⡇⠀⠀⠀⢀⢠⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⡟⠀⠀⠸⣇⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢠⣚⣟⣿⢧⠀⣐⠲⢃⡼⠀⠀⠀⢠⡘⢧⡿⣾⠆⠦⡄⢱⡄⠀⠀⠸⡁⣴⠀⠀⠀⠀⠛⣳⠀⠀⠀⢀⣿
⡄⠀⡤⠐⠒⢺⡉⠙⢁⡞⡀⠀⣷⠻⡤⣄⡀⠀⠀⢳⠈⢠⡏⠀⠀⠀⣸⠃⠀⠀⡄⠀⢸⡇⠀⢠⣷⣵⡿⠤⢤⣤⣼⡟
⣇⠈⣇⠀⣠⠞⣿⠀⢸⡄⣙⣦⢈⡆⠵⠀⠙⢦⡀⢸⠀⢸⡇⠀⠄⢠⡟⠀⠀⢰⠀⠀⣾⠙⢲⣤⣉⠉⣱⠀⠀⢠⡿⣧
⠘⣆⠘⣾⠃⠀⣿⠀⠀⡇⠀⠈⠿⠁⠀⢀⣲⠀⡻⡏⠀⢸⡇⠘⢠⡿⠀⠀⠀⡆⠀⣰⠇⠀⠈⣇⠈⠉⡟⠀⠀⣾⠁⢸⣆
⠀⠘⣆⠘⣦⡤⣿⠀⠀⣿⠀⠀⠀⠀⠀⠈⢻⡎⠀⡇⠀⢠⣿⢀⡿⠁⠀⠀⡸⠀⢀⡟⠀⠀⠀⣙⠦⠊⠀⠀⣼⠃⠤⢚⣿
⠀⠀⠸⣆⠈⢧⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢸⣏⡾⠁⠀⠀⠠⠁⠀⡾⠁⣠⠔⠊⠀⠀⢀⣤⠞⠁⠶⠚⠋⢻⡀
⠀⠀⠀⡏⢧⠈⢻⣄⢀⣿⠄⠠⠤⢒⣢⠴⡟⠁⠐⠦⠤⡟⢹⠇⠀⠀⠀⣤⠄⠚⠓⠉⠀⢀⣠⡴⢞⡫⠤⣔⠂⠀⠀⠀⣸⠃
⠀⠀⠀⣷⠈⢷⡀⢻⣾⠃⠀⠈⢉⣁⣤⣴⣇⠀⠀⠀⠀⣃⠽⠦⠒⢲⣖⣥⡀⢂⣤⠖⠋⠉⢀⡴⠋⠀⠀⠀⠀⠀⢀⡴⠋⠐⡒⠒⠒⢶⡄
⠀⠀⠀⢹⠀⢸⣷⡄⢻⡆⠀⠊⢁⣠⠴⠖⠛⠛⠋⠉⢻⡄⠀⠀⠀⠀⢘⠛⠚⣏⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢀⣴⠟⠓⠒⢲⡈⠳⠶⣉⣉⣑⣢
⠀⠀⠀⢸⡇⢼⠀⢘⣿⣇⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢸⡇⡄⢻⡆⢀⠞⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⢸⣗⣠⡤⠴⠶⠛⠉
⢰⣶⢤⡘⡇⢸⡖⠉⢻⡟⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡇⢿⣇⠈⣾⡄⢸⡇⢁⠘⣿⡀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⣀⣤⠶⠚⠁
⠀⠁⠀⠉⠻⣌⣷⡀⢸⡟⠹⢦⡀⠀⠀⠒⣾⠀⢰⠀⣇⠸⣿⡞⠹⣇⠈⣧⢸⡀⠹⣇⠀⠀⠀⠀⠁⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠁⠢⡈⠻⡇⢸⡇⠢⡈⠳⣄⡴⠞⣿⠀⢸⠀⢻⡀⢻⡇⠀⢿⡀⢻⠈⡆⠀⠙⣶⠒⠀⣦⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠈⠢⣄⠼⢷⣒⠳⣄⠙⣧⡀⢿⠀⢸⠄⠈⠃⢀⡷⣶⠚⠃⣶⠀⣠⠊⡐⣽⠀⢠⡟⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠉⠳⣌⢦⠈⠻⣄⠀⠀⠆⢀⣠⠋⡘⣹⠀⠀⣿⠠⠃⠐⣰⡏⠄⢚⡃⠄⢺⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣈⠛⢷⡄⠙⢷⡀⠔⠩⠃⢰⢠⡟⠐⣼⡣⠔⢒⠩⠅⣐⣬⡴⠶⠛⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠙⢦⣈⣽⠐⣄⢠⠧⠿⢓⠩⠁⣐⣨⣴⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡘⠟⠀⣈⠀⢐⣨⣥⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢼⣿⡿⠋⠁
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡿⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾
⢳⡀⠉⠛⠶⣤⣤⣀⣀⣀⣀⣤⣤⣤⡶⠶⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⢦⣤⣤⣄⣀⣀⣀⣠⣤⡴⠞⠋⠁⣰
⠀⣹⢦⣀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⣀⣠⢾⡁
⠀⠻⣄⠈⠉⠛⠒⠒⠶⠶⠶⠒⠒⠉⠁⠀⠀⠘⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠚⠋⠉⢀⡼⠃
⠀⠀⠈⢻⣶⣤⣤⣤⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⣌⠳⣀⠀⢀⣤⣄⠀⢀⣴⢋⡜⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣠⣤⣤⣴⣾⠋
⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡟⠁⠀⠀⠙⣯⠴⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛
⠀⠀⠀⠀⠀⠈⠛⢷⡶⠤⠤⠤⠒⠊⠉⠀⢀⡠⠀⠀⠀⠈⣇⠀⠀⠀⢀⡏⠀⠀⠀⠀⡀⠀⠈⠁⠒⠒⠤⠤⠴⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣄⣀⣤⡴⠞⠋⠀⣀⡤⠶⠶⠾⢷⡶⣶⠿⠶⠶⠦⣤⣀⠀⠑⠦⣤⣀⣀⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣤⣤⡤⠖⢋⣤⣴⣦⣤⡀⠀⡇⡇⠀⣠⣤⣶⣦⣍⡓⠦⣤⣤⣤⡤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⢿⣾⣿⣆⡇⢇⣾⣿⣾⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣤⡀⠈⠙⠉⡇⡏⠙⠉⠀⣠⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣶⣤⡇⣧⣴⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⠉⡏⡏⠙⠻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⡇⡇⠀⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⡇⡇⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⡏⡛⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠁⠀⡇⡇⠀⢹⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⡇⡇⠀⢀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⣇⣥⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⡆⡏⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⡇⡇⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣤⣇⣧⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⡇⡇⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⡇⡇⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡇⣣⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⡏⡿⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⡇⡇⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⡇⡇⠀⠠⠞
⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣿⣭⣭⣭⣭⣬⣭⣽⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣥⣽⣿⣧⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⢸⣿⣷⣄⡀⣀⣤⣤⣼⣿⠀⠂⢠⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣤⠄⢈⣹⣿⣿⣿⣿⣿⣿⣿⡿⣶⣿⣿⣿⣿⣿⣶⡄⢀⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣼⣿⠇⠀⠈⠈⣿⡟⣿⣿⣿⣿⣿⡇⠀⠙⣩⣈⠙⠛⠻⣿⣾⣿⣿⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⠿⠿⢷⡄⠀⠉⠀⠘⢿⣿⣿⣿⣿⡀⢌⡛⣋⠸⣿⠆⡃⢻⡿⢻⣌⣡⡉
⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⣷⣋⣤⡀⢴⡶⢿⣾⣿⣿⠓⠈⠀⠀⠉⠉⠃⠸⢿⣯⣷⣶⣾⣿⣿⣷⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⢿⣋⣠⣤⣾⣿⠉⢉⡴⢦⣠⠜⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠟⣀⠉⡛⢿⣴⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠈⠿⢟⣿⡍⢸⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠘⠀⠀⢂⣴⣶⣿⣷⣾⣿⣷⠀⠀⠀⢹⣿⡏⠁⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣻⡭⣵⣿⡿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⠛⠙⣿⡿⠙⢀⡀⠀⣿⡏⠑⠂⠀⠒⠁
⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣍⠀⠀⠈⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠠⠄⣹⣷⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠘⠟⠉⠙⢿⣿⡟⠀⢀⣀⣼⣿⣧⠀⠀⣾⣿⠿⢷⣀⡀⠉⠀⠀⠀⠈⡟⣀⠈⢉⢸⡿⣦⣀⣀⡤
⠀⠀⠀⠀⠀⠀⢠⠀⠉⠀⠻⠀⢰⣿⣿⣿⠋⠉⡲⠼⡏⠀⠀⠀⢹⣿⣶⣿⣿⣿⣷⣧⣠⢦⣈⡼⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠀⠐⢾⣿⣿⡟⠐⠀⣙⣛⣉⣁⣀⠉⣈⣿⠀⠀⢹⣿⣿⣿⠟⠿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⣿⡏⠀⢠⣭⣭⣽⣿⣿⣿⣻⣿⣧⡀⠀⢻⡟⠉⠀⠀⠈⠁⠀⠀⠀⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣤⣴⡶⠆⠒⠂⣤⠄⠛⠛⠿⣿⣇⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⣽⡀⢠⣶⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠐⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⢺⠓⡀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡉⢀⢬⠝⠀⠀⠀⠀⠀⠀⠤⠤⡀⣃⠀⢠⠔⢓⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠾⡄⠀⠀⠀⠀⠀⠀⠈⠢⢻⣟⡔⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⡚⣇⠴⠃⠀⠀⠀⠀⠀⠀⢀⣧⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡍⢏⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⣖⣲⠖⢒⣒⡒⠲⣲⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⠲⣆⠀⠘⢆⠹⣤⠤⠤⠤⢤⣤⠋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠿⠃⡸⢀⣠⡈⠓⢌⡻⣦⠼⢛⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡒⠛⢧⡏⡹⠁⠀⡴⢛⡴⢎⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣣⠤⣿⠃⢠⠞⣴⡯⠠⢤⣵⣌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠠⢼⣤⠋⣼⢉⠉⠉⢉⣉⣙⣆⢹⡀⠀⠀⢀⣨⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢨⠓⠛⠛⠒⠒⠒⠚⢻⡄⡗⢦⣀⠜⣡⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⡇⠤⠒⠨⠀⠀⠲⣾⠃⡇⠸⢡⣾⣩⣾⢄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠱⣤⠤⠤⠤⢤⣴⠇⡼⡡⠖⠣⡀⠳⠵⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢬⡙⢮⠽⢋⡤⠞⠊⢱⡂⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡥⢆⠛⢄⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣠⠿⠅⠨⠷⣌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⣓⣲⠖⠒⢲⡾⣆⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣸⠁⠀⠀⠀⠀⠀⠀⠘⡆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⢲⠾⡀⠀⠀⠀⠀⠀⠀⠀⠰⠟⡴⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣌⣦⢧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠊⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⠦⠦⡍⠃⠀⠀⠀⠀⠀⠀⠀⠘⢢⠤⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣂⠓⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⡿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⢀⣀⣀⣀⣀⣀⣀⠀⠀⢸⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⡇
⡏⢉⣉⣉⣉⣉⣉⣉⣉⠹⡶⠖⠒⠛⠒⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⣾⠃⠀⠀⠀⢀⣤⢤⣤⡀
⡇⢸⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⡀⠒⡆⠀⠠⠤⠤⠄⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⢀⣀⡀⣤⡤⠤⠤⠤⠖⠒⠋⠁⠀⠀⠀⠀⣏⢀⣀⢀⢹⡄
⡇⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⢂⠈⠑⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠊⠹⠚⢸⠃⢀⢂⠠
⡇⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⡎⢸⠀⡠⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠐⡄⠂⠒⣃⠀⠀⠀⠀⠠⠀⠨⢀⡀⣈⠶⠕⠚⡞⠳⢦⣄⠁
⡇⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢸⡾⠁⢀⠀⠀⠀⠀⠉⠛⠛⠛⠂⠀⡧⠀⠣⣀⡠⠰⠋⠝⠒⢤⣀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠈⠀⠀⠈⡆
⡇⢸⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡇⢀⣤⣇⣬⡆⡴⢋⠉⠑⢢⠀⠀⢀⣀⣀⣀⣀⡇⠀⠀⠀⡼⠀⠆⠀⠀⢰⠈⢳⡀⢠⠃⢸⠀⠀⠀⠀⢸⠀⠀⠀⣷
⠇⢸⠀⠀⠛⠛⠋⠉⠉⠉⠁⠀⡴⠁⠐⣀⣀⡹⠃⠰⠗⣂⡰⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⢀⡀⢱⠖⠀⢀⡄⠀⠀⢳⠎⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡏⣇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⠚⠋⡉⠁⠀⠈⣆⠀⠫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡠⠚⠀⣴⠋⠤⠀⠀⢅⠀⠄⣁⠀⠠⠀⠀⠀⠀⠀⣸⢇⣿
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣠⠊⠀⠀⠀⠠⡘⠢⡀⠀⠀⠀⣀⠀⠀⢤⠒⠀⠀⠒⠉⢀⣠⠞⠱⡑⡄⠀⠀⠀⠱⡞⠉⡃⠰⠶⢲⠶⣴⠄⢿⠋
⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⡴⠁⠀⠀⠀⠀⡜⠁⠀⠘⠄⠙⠁⢐⡒⢨⣇⣠⡖⠃⢒⠥⠄⠒⠉⠉⠉⠉⠉⠉⠙⠛⠛⡞⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⡀⠘⠘⠕⢄⠀⣀⠄⠂⠀⠀⠉⠀⠄⠀⠀⢀⡠⠔⠒⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣥⣀⡀⠀⠀⠴⠚⡡⠚⠁⠙⠦⢄⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣠⠴⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠀⠙⠉⠉⢉⡤⠞⠐⡲⠆⠀⠀⣀⢾⠩⠥⠄⠀⡛⠉⢙⡦⠄⣀⣀⣀⠐⠒⠉⠉⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠀⠀⠀⢀⣾⡇⠀⠀⠈⠉⠒⠲⠤⡄⠈⠉⠉⢀⣈⡀⠬⠥⠤⠒⠀⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄
⠀⠀⢀⠂⠉⢦⠀⠀⡀⠀⠀⠀⠊⢀⣠⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠠⠀⠄⠠⡀⠀⠀⠀⠂⠂
⠀⠀⢀⠀⠀⠘⣆⠀⡇⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠶⠀⠒⢩⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠄
⠀⠸⠈⠤⠒⠀⠘⡦⠆⠘⠣⠀⠀⢤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠃⠄⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤⢶⣶⠤⠴⠂⠃
⠀⠈⡤⠯⢨⠄⠀⠠⡏⠙⠄⠀⠐⡆⠙⠄⠀⠀⠀⠀⠀⠀⠀⡀⢀⢳⢀⠀⠸⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠮⠿⠂
⠀⠀⡁⠠⠫⠂⠀⠀⠁⠀⠀⠘⠇⠙⠀⣆⠀⠀⠀⠀⠦⡆⠀⡄⠉⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠀⠀⠒
⠀⢠⠁⠀⠀⠀⠀⠀⠃⠀⠀⡇⠀⢰⠀⠁⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠁⠀⠀⠀⠀⠀⡴⢁⠀⠀⠀⡀⡆
⠀⡆⠈⠀⠀⢀⠂⡀⠂⠀⠀⡇⠀⡄⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡰⠂⠘⣆⠀⠀⠀⠀⣼⠀⠀⡷⠤⡎⠀⠱
⠀⠁⠀⠀⠀⡬⠘⠁⠀⠀⠀⠃⠀⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠸⠀⠀⠀⡌⠀⠀⠀⠘⢆⠀⠀⠀⠈⠓⠋⠀⠀⠙⠛
⠀⠄⠀⠁⡆⠀⠀⡀⠀⠀⠀⠀⠠⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠠⠐⠈⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠡⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠨
⠀⠀⡐⠋⠈⠙⢿⣄⡴⠶⠶⢦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠔⢈⠍⢭⡲⠄
⠀⠐⠀⣀⢠⠆⠀⡟⠀⠀⢠⡆⡇⠀⣰⠟⠁⠀⠀⢶⡆⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡶⠖⠚⠚⠒⠒⠒⠚⠛⠒⠒⠆⠀⠀⠀⠀⠀⠀⠖
⠀⠘⠒⠹⠊⡇⢰⣇⣤⡤⢿⡰⠃⠀⡇⠀⠀⠀⠀⢀⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣲⡆⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠤⠤⠖
⠀⠀⠈⢠⡀⠈⢸⠏⠀⢀⠔⠁⠀⠰⡇⠀⠀⠀⠀⣸⠃⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠟⠃⠀⠀⠀⣠
⠀⠀⠀⠀⠁⠀⠀⢀⠔⠁⠀⠀⠀⠀⢿⡀⠀⠀⢰⡏⠀⠀⠀⡀⣒⠍⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠈⠳⣶⠶⠋⠀⠀⠀⠀⢲⡟⠀⠀⢀⠃⠀⠀⠉⠙⠀⠈⠈⠉⠉⠉⠉⠉⠀⠁⠀⠀⠓⠒⠒⠒⠒⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣼⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠄⠄⠀⠀⠂⠃
⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⡴⠃⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⠀⠀⠀⠀⠀⠀⠠⣴⣿⣶⠀⠀⠠
⠀⠀⠀⠀⡠⠇⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠴⠚⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣄⠀⠀⠆⡨⠀⢀⠀⠀⠀⠰⢤⢄⣀⣛⢀⣀⡠⠄
⠀⠀⠀⠰⠇⠀⠀⠀⠀⠘⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⣀⠀⠀⠀⡠⠜⠀⠀⠀⠰⣤⣀⣀⣀⣤⣤⣤⠄
⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⢸⡟⠁⠀⠀⠁⠀⢀
⠀⣠⢔⣊⡀⠠⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⠀⠀⢀⠜⠁⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⢀⠄
⠘⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⠂
⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⣀⣄⣠⣄⣀⣄⣤⣀⣀⣠⣠⣄⣉⣉⣀⣀⣄⣀⣀⣀⣀⣀⣀⣄⣠⣤⣄⣠⣀⣀⣀⣀⣀⣀⣀⣠⣀⣄⣠⣀⣀⣀⣀⣀⣀⣠⣀⣀⣄⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠤⠤⠄⠀⠤⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠁⠁⣀⣀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋
⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠑⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠱⠊⠀⠀⠢⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠁⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠤⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠒⠤⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠀⠀⠀⢀⡀⠀⠀⣠⠖⠀⠈⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤
⠀⢀⠀⢀⠰⠤⠢⠤⠄⠂⡉⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡞⠉⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⢠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠆⠀⢂⡀⠂⠀⠀⠀⠘⡤⡏⠀⠁⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠙⢀⠀⠀⡀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠈⡅⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢩⠀⢀⠀⠀⠀⠀⡈⠀⠀⢀⡁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⢠⠊⠈⠉⠀⠀⠁⠀⠀⠃⠉⠁⠠⠁⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⡀⠤⠄⠀⠀⠀⠀⠉⠐⠄⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡠⠐⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⡀⠤⠒⠋⠉⠉⠉⠉⠙⠒⠀⠠⠀⠀⠀⠀⠈⠀⠀⠁⠁⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠂⠀⢀⡀⠀⠠⠤⠤⠀⠁⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠆⠈⠁⠀⠀⠀⡀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠄⠀⠤⠤⠄⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢠⠆
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠁⢱⣶⣶⠌⠀⠉⠛⠁⢈⢰⣶⣶⠁⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⣿⣿⠀⣼⣿⢋⣐⣂⠀⠀⠀⣐⣂⡻⣿⡇⢸⣿⡇
⠀⠀⠀⢺⠟⠛⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠛⠀⠀⠀⠉⠻⠏⠁⠀⠀⠀⣿⣿⠀⣿⠇⡬⠅⡀⠀⠀⠀⡀⠭⣥⢻⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⠰⢖⡩⠀⣠⣦⡀⠈⣑⠶⠎⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⡇⢚⣫⢎⣴⣿⣿⣿⣌⠪⣛⠇⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣧⣩⣵⣿⣿⣿⣿⣿⣿⣷⣬⣃⡏⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣤⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣧⠀⠀⠀⠀⠀⣿⣇⠀⣿⣿⠛⠛⠛⠿⠿⠟⠛⠛⢻⣿⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⣿⡿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀

⠀⢀⡄⠀⠀⠀⡀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣶⣶
⠀⢸⡇⠀⡄⠀⢸⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠋⠉⠛⠛⠟⠁
⠀⢸⡇⠀⡇⠀⣸⠀⠀⠀⠀⢸⠀⠀⢰⢦⠀⢠⠀⠀⠀⡊⠑⢸⡀⠀⢀⠀⠄⢀
⠀⢸⡇⠀⡇⠀⣿⡆⠀⠀⠀⢸⠀⠀⢸⣿⠀⢦⠀⠀⠀⣵⠀⢸⡇⠀⢾⠂⠂⢸
⠀⢸⡇⠀⡇⠀⣿⡇⠀⠀⠀⢺⠂⠀⣸⢿⡀⠘⣧⠀⢠⠇⠀⢸⡇⠀⣾⠀⠀⢸⡄
⠀⢸⡇⠀⡇⠀⣿⠇⠀⠀⠀⢸⠀⢠⠏⠈⢷⠀⠸⣦⡏⠀⠀⢸⠀⠀⣿⠀⠀⡏⠇
⠀⢸⡇⠀⡇⠀⣿⠀⠀⠀⠀⢸⠀⡟⠀⠀⠈⣇⠀⣿⠀⠀⠀⣸⡀⠀⢿⠀⠀⠇
⠀⢸⡇⠀⡇⠀⣿⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⡙⢰⣻⠀⠀⠀⢹⠁⠀⠀⠀⠘⠃⠘⠂
⠀⠈⠁⠀⠁⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁