Nut Emojis & Symbols

⠀⠀⡸⡀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⡤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠁⠀⢀⠧⢀
⠐⠁⠈⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠈⠂⠀⠀⢀⡈⠃⢀⠤
⠄⠐⠠⢀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠉⠀⠹⡀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠴⣄⠀⠀⠀⠀⢠⡈⠀⠀⠀⢤⡀
⢆⠀⠀⠀⠁⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠈⠀⠀⣶⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⣁
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⡔⣋⠄⠀⠀⠀⠙⢦⡆⠀⠀⠀⠀⠈⠂⠀⠀⠘⠃⠀⠀⠳⢄⡀⠀⠀⠀⠘
⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠻⠈⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⡀⡀⠀⠀⠀⠚⠒⠀⠀⠀⠀⠽⠥⠤⠀⠁
⠀⣀⠦⠠⢀⣀⡀⠀⠀⠀⠀⠻⠃⠀⣀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⢀
⡾⠋⠀⠀⠀⠈⣿⣧⠀⠀⣠⡴⠖⠋⠉⠀⠈⡟⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠰⡀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠁
⣇⠀⠀⠀⠀⣰⡿⠉⢀⡜⠉⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⠀⠀⠁⠀⡀⠈⠂⠀⠀⢀⠀⠀⠨⠀⠀⠀⠠⠀⠀⠀⢠
⠛⠿⠶⠶⠚⠙⠀⣀⣼⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⣠⣀⣀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠰⠀⠀⢱⠐⠄⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⡶⠟⠉⠁⠀⠀⠀⡀⠀⡴⠊⠉⠀⠀⠀⢀⠀⠀⢰⠟⠛⠉⢉⠉⠒⠈⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠟⠀⠰⣀⠀⠀⠀⠀⠁⠀⠀⠈⠁
⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠐⠁⠐⠇⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠀⠃⠠⠀⠀⠐⠂⠀⠀⠀⠀⠘⠀⠀⠐⠀⠀⠀⠀⡠
⠀⠀⠀⢧⡀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⢠⣞⠇⠀⠀⠈⠂⢄⡀⠀⠀⡠⠊⠀⠀⠀⠀⠠⠀⠀⠀⡌⠒⠀⠀⠀⠀⠀⠀⠢⠀⠠⠁
⡀⠀⠀⠈⢉⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠃
⠉⠉⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠢⢀⠄⠀⠀⠀⠀⠀⠰⡄⠀⠀⢠⡞⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⡀⠀⠀⠀⠀⠈⠀⢀⡀⠀⢠⠶⢦⣀⠀⠀⠀⢠⠁
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠑⠈⢑⡂⠀⢈⣶⠟⠀⠀⠟⠀⠀⣀⣤⠞⠔⠁⠀⠀⠀⠈⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡏⠀⠀⠉⠀⠐⠄⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⡢⠖⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⢀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠻⣆
⠐⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠐⠠⠂⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⡆⠀⠀⢹⠏⠀⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣔⣴⠿⠛⠻⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⣇
⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠸⣇⠀⠀⠀⠀⠈⣷⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢷⣀
⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⣽⣇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠈⠳⢤
⢉⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⢀⡀⠼⠀⠠⠉⠁⠒⠒⠟⠻⠋⠀⠀⠀⠀⠈⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠄⠒⠂⠀⠀⠀⠠⠐⠈⠀⠀⠀⠢⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠂⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠅⠀⠰⠀⠀⢀⠴⠀⠊
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠠⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀
⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⣀⠄
⠀⠀⢱⡄⠐⠀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡫⠂⠀⠀⠀⠉⣦⣀⡀⠀⠀⣀⡤⠤⠤⡀⠀⠀⣠⠤⣄⣼⠀⠀⠀⢧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠏⠀⠀⠀⢀⣠⡎⠁⠀⠉⠉⠉⢁⣀⣀⡀⢈⣀⡴⠃⠀⢈⣿⠀⠀⠀⠀⠉⠉⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⣿⠀⠀⠀⠀⢋⣤⠷⠒⠒⠒⣦⡾⠃⠀⠈⠙⠋⠉⠀⠀⠀⣼⠃⠱⣤⡀⢀⡠⠤⡄⢠⠗⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠒⠉⠙⠐⠲⢄⣴⠏⠁⠀⠀⢠⠞⠅⢻⡀⠀⠀⠀⠀⠀⠀⡠⢞⠡⣤⣀⣀⡰⠋⠀⠀⡟⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⣴⣶⣏⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡏⠀⠀⠀⠉⡳⠒⠒⠒⠲⣧⣠⡏⠁⠀⠉⠉⠀⠀⠀⣰⠇⠀⣠⡄
⠀⠀⠀⠀⠀⠀⢹⡄⠈⠙⠻⢿⣷⣀⠀⠈⣇⠀⠀⠀⢸⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢻⢧⣀⠀⠀⠀⠀⣀⣴⡥⠖⠋⢸⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠈⠉⠓⠛⠶⠤⣴⣿⣧⣀⠀⠀⢀⣧⡤⠤⣀⢀⣀⣨⣄⣬⠽⠿⠛⠛⠉⠁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣟⣛⣲⠶⠶⢶⣶⣶⣶⣶⣶⣶⡶⠶⠶⡖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⢀⡴⠚⠋⠉⢀⡼⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⠴⠂⠀⠀⠀⠀⢳
⠀⢠⠏⠀⠀⢠⡴⠃⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡤⠖⠋⠁⠀⠐⢒⠀⠀⢠⡟
⠀⠁⣀⡰⠋⠁⠀⠀⠀⠀⠀⠀⢀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣧⣀⠈⠀⠠⠄⠂⣁⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⣈⣱⣄
⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠠⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⢹
⠀⠘⢌⠢⡀⠀⠀⠀⠀⠑⢄⡀⠀⠱⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠓⢤⣀⡀⠀⠀⠄⣀⣉⣶⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠀⠀⠉⠉⠉⠙⠓⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⢰⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⢀⡀⠀⠀⠉⠉⠁⠀⠀⠀⠐⠄⠙⠷⣦⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡌⠰⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⠶⠋⠁⠀⠀⡠⠤⠶⠄⠒⠒⠒⠦⠄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠁⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠀⢹⡀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣁⣀⠀⠒⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠁⠀⢀⣀⡀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠖⠂⣀⡴⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⠒⠶⢦⣤⣤⣌⣁⡀⠀⠀⠀⠀⠐⠛⢀⣁⡤⠴⠖⠛⠉⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠋⠉⠉⠀⠠⠄⣠⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠉⠛⠲⠤⢤⣑⠒⠒⠶⠤⠔⢂⣉⣉⣠⣤⠾⠋
⠀⠀⠀⠀⠀⠀⣠⡔⠢⣍⠛⠉⠙⢛⡉⠉⠗⢦⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠛⠉⠉⠉⠉⠀⠀⠀⢀⡓⢦⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠰⣁⠁⠀⢿⣤⠟⢦⣄⠙⢶⠄⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡆⢀⣀⣀⠠⡄⠀⠀⠀⢠⠂⠁
⠀⠀⠀⢀⠖⢦⡈⢦⡤⠦⡄⠀⠀⢹⡇⠘⠆⢀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⡤⠘⠲⣄
⠀⠀⠀⠀⠀⢀⡽⠇⢴⠉⠁⠀⠴⠋⣼⠟⠓⠞⢤⠳⡈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⣼⠃⠀⠀⢸⣆
⠀⠀⠀⢀⣤⠆⠀⡴⠋⠀⢈⠓⠦⢄⡈⠳⡀⠀⠀⠀⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣦⡆⣸⣴⠏⡀⠀⠀⣾⠻⣆
⠀⠀⠀⠙⣎⠁⠀⠣⣀⣠⠋⢙⡂⠀⠱⢤⣑⠂⠠⡠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣷⢿⠋⠀⠑⣿⢸⣿⠀⠈⠁
⠀⠀⠀⠀⠫⡀⠤⣄⡀⢠⡒⠋⠈⠙⠳⡄⠈⠳⢤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡇⠉⠀⢀⠀⠘⢿
⠀⠀⠀⠀⠀⠈⠃⢀⢀⠀⢈⠂⠀⣤⡴⠻⣶⡄⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⡀⠔⣉⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣈⣀⣠⣄⣀⣤⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠦⢤⣤⣤⠤⠶⠚⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠒⠒⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠠⠗⡾⠋⣥⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⢦⣀⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡡⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠐⠢⢨⡷⠈⠴⢻⣦⣸⠆⣒⣿⣀⣠⣆⣀⡀⠀⠀⣇⣀⣀⣀⣠⠜⠋⠁⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⣈⣳⣦⡀⠀⠀⢈⢖⣀⡴⢻⡁
⠀⠀⠀⠀⠀⠘⣠⢡⡟⢑⣸⠖⣾⣽⠛⢠⠯⣍⠿⢷⣌⢻⣥⡀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⢀⣀⠔⠀⠟⠈⣻⣿⣷⣤⣴⣿⡿⠝⠉⠁
⠀⠀⠀⠀⠀⢀⢃⡟⣰⣿⣿⣿⣿⠟⢳⡄⢻⢡⡶⠶⣧⣤⣿⣷⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠛⠃⠀⠀⠏⠀⠀⠀⠀⣷⡾⠃⠀⠈⠻⠷
⠀⠀⠀⠀⠀⢤⡿⠤⣼⡿⠿⠛⠉⢀⠺⣿⠾⠷⣶⣦⣿⣿⣿⣿⠇⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡄⠀⠀⠀⠐⠀⠐⠋⠉⠀⠀⠀⢆⣀⡄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠈⠛⢭⣯⠤⠿⠟⢃⣠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⡤⠀⠀⠀⠀⠓⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠁⠀⣆
⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠀⢻⣿⣿⣷⡄⠀⠀⡀⢀⠀⠀⠀⢀⠀⠀⠒⠐⠒⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⠀⠀⣰⢟
⠀⠀⠀⠀⠀⠀⠨⠔⢉⣭⣔⠿⢻⠁⠂⠆⠀⠀⢻⣦⡇⣀⠤⡷⡀⠀⠀⠀⠀⢀⣽⡀⠀⠀⠀⠀⠐⣆⠀⠀⠐⠌⢉⣩⠭⠁⠀⠀⡔⠉⠐⠂⠀⠴
⠀⠀⠀⠀⢀⢁⣴⣶⣻⡟⠩⠄⠋⣠⠎⠀⠀⠀⠀⠙⠓⠒⠊⠉⡐⠠⠀⠀⠒⠀⠘⠓⠂⠀⢀⣠⣼⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⠀⡶⣾
⠀⠀⠀⠀⠈⠙⠿⠿⣧⠠⢀⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠑⠲⠤⠥⠾⠾⠞⠁⠀⢀⣤⡶⠶⠆⠀⠀⠀⠀⠻⣿⣿⣷⣿⣷⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠞⠩⢀⡈⠛⢃⣤⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡔⣒⣶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⢧⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣶⣼⠷⠛⣍⠁⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡿⣽⣤⣴⣧⣼⣿⡁⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠄⣘⡻⠶⠋⠵⠿⠷⠐⠉⠀⠐⠀⠀⢀⡄⠀⠢⢴⡶⣸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣦⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠢⠴⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠴⣲⣤⣦⠒⢈⡠⠂⠀⠀⢀⡾⠀⠀⠲⣧⡘⠁⠈⠳⣄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠍⠒⣢⣄⣤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⣇⢀⡤⠀⠀⢿⣦⣤⣀⠜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠷⢤⣬⣉⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⣀⣴⣄⣫⢋⣋⡁⢠⣜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠋⠀⠀⠄
⠀⠀⠀⢀⠈⠀⢀⣉⣺⣿⡭⣠⡝⠿⠟⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣴⣦⡀
⠀⠀⠀⣌⣀⢠⢾⣿⣿⣿⣷⣿⣽⣟⣉⢶⣶⡟⠀⠀⣀⠤⠀⠀⠀⠈⠁⠀⠀⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⡓
⠀⠀⠀⠙⠛⣱⣿⡿⠛⠁⣨⣼⣿⣿⡋⣷⡾⠃⠀⢰⣏⡄⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣤⣦⣷⣿⣿⡟
⠀⠀⠀⠀⠀⠛⣿⣵⣿⣿⣿⣽⠿⢊⠷⠞⠀⠀⠀⠘⢿⣇⣀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠀⠀⠱⣄⣤⣼⠆⠀⠀⠀⠀⠉⠛⠉⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠘⠻⠶⠿⠥⠟⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠰⣶⣆⠙⠶⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⢷⣤⠛⡋⢰⣠⡀⠀⠀⠀⠀⠔⠀⠁⠀⡶⠾⣁⣀
⠀⠀⠀⠀⢣⣄⡤⠛⠷⠤⣌⡙⠿⠃⠀⠀⠀⣠⡖⢀⠀⠐⠛⠡⠒⠒⠚⢻⣧⠀⠀⣠⠀⢀⡔⢨⣉⣴⠋⠀⢠⡦
⠀⠀⠀⠀⠈⠋⠃⣀⠠⣦⣀⡉⢛⠁⠀⠀⠘⢍⡣⢤⣄⡀⢀⣴⠄⠶⢛⣣⡞⠀⠀⢁⠀⠈⣡⣤⠞⠁⣀⣏⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠺⠏⠉⠁⠀⠀⠀⠀⠀⠛⢄⣰⠠⣴⣶⣶⣿⠿⠋⠀⠀⠀⠀⠒⢛⢉⠁⣰⠶⠏⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠉⣉⣵⣤⡀⠀⠀⠀⠀⣀⢀⣴⠒⠄⣀⡄⠀⠀⠀⠀⠀⡀⢿⠀⣹⡀
⠀⠀⠀⠀⢠⠋⠀⠀⣀⣤⠶⠏⡍⠩⣿⣿⡄⠀⢀⠞⣧⣮⡀⢿⣧⠙⠤⡀⢷⢄⠀⠀⠱⠀⠁⠈⡍⠀⠀⢀
⠀⠀⠀⠀⠸⣼⡶⠋⠁⠀⠀⠀⣀⣸⣿⣿⠇⠀⠘⠾⣦⠀⡏⠈⠙⠀⠀⠀⣘⡷⠀⠀⠀⠀⠀⠒⠁⠀⠐⠈⡷
⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⡀⢠⣴⣿⣿⡿⠀⠀⠀⠲⣤⣉⣛⡶⠦⠦⠤⠔⢋⡼⠃⠀⠀⠀⠀⢀⡀⠈⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠳⣶⣤⣴⣶⣷⣾⡿⠟⠁⠀⠀⠀⠀⠈⠻⢧⣜⣥⣝⣩⡍⠀⠁⠀⠀⠀⠀⠀⠀⠁⢊⡹⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠛⠉⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡿⠋⠁⠀⢀⠀⠂⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢛⡡⠊⠀⢀⠠⠂⠁⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣫⠔⠉⢀⠤⡚⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⢀⡠⠊⠁⡔⠀⠀⠀⡠⠂⢠⡟
⠀⠀⠀⠀⠀⢸⠇⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⡰⠋⠀⢀⠎⠀⢀⠔⠊⢀⣰⡟
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢹⣇⡜⠀⠀⡴⠁⠀⡴⠁⢀⢔⣿⠏
⠀⠀⠀⠀⠀⢻⠀⠀⠈⠀⠀⠀⠄⠙⢷⡀⠀⠀⠀⠈⢻⣦⡠⠊⠀⢠⠎⠀⣰⣷⠟⠁
⠀⠀⠀⠀⠀⢸⣇⠀⠀⡄⠀⠀⠈⠆⠈⢻⣆⠀⠀⠀⠀⠙⠻⢶⣶⣧⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠸⣇⠄⠀⢰⢀⠀⠀⠘⡄⠀⡽⣧
⠀⠀⠀⠀⠀⠀⣿⠘⡀⠘⡀⠡⡀⠀⠰⡀⠘⢿⣧⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣇⢡⠀⢣⠀⠘⢄⠀⠱⡄⠈⢿⡆⠀⠀⠀⢠⣾⠟⠙⠢⢄⠀⠉⢻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢻⣌⡆⠈⢆⠀⠈⢆⠀⠘⢆⣼⡇⠀⠀⢠⣿⠁⠑⢄⡀⠀⠑⢄⠀⠱⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠈⢦⡀⠈⢆⢀⣼⠟⠀⠀⠀⢸⣟⠢⣄⠀⠙⠢⡀⠀⠱⡄⠈⢆⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣷⣶⠾⠟⠉⠀⠀⠀⠀⠈⢿⣄⠀⠑⢤⡀⠀⠑⠠⠈⢆⠀⠑⢝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡦⡀⠙⢆⠀⠀⠀⠈⢂⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣆⠀⠑⢄⠀⠀⠀⠡⡀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡁⠠⠀⠀⠀⠄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣄⣀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠈⠁⠢⡀⠀⠀⠀⡰⠊⠉⠉⠑⠢⠤⠀⠄⠀⠒⠠⡀⠀⠀⠀⢀⢴⡶⠟⠛⠉⠁⠉⠉⠙⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⣅⠠⠀⠀⠀⠀⠀⠀⡀⢡⠀⠀⠸⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠂⠀⠀⠘⢶⡤⠭⠀⢀⣀⠀⢀⡤⠴⠶⠟⢠
⠀⠀⢀⠔⡈⠤⠀⠔⠒⠤⢍⡛⡶⡤⠤⣀⣒⣚⣛⡻⠀⠀⠘⢮⣝⡀⠂⠀⢋⣠⠄⢙⣲⢲⣤⣿⡁⠀⠀⠀⠀⠙⠛⠛⣻⠖⢀⠀⠀⠀⠀⠐⢫
⠀⠸⡍⡒⠒⠒⠠⠦⠤⠀⠰⢒⢃⡎⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠉⢉⣉⠭⣭⠴⠋⢊⠟⠁⠉⠹⡾⡂⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠱⡀⠈⠉⠉⠉⠉⠉⠀⠀⡼⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡄⠈⠀⠀⡠⢗⣒⡒⢢⠭⢒⡇⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⣀⡤⠞
⠀⠀⠀⠙⠢⢅⣠⡀⣀⡠⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡛⣀⣄⠒⠮⠔⠃⢠⡔⠴⠦⠞⠀⠀⠀⠀⠀⠀⠙⠶⠤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣁⡊⢀⢂⠸⠟⠁
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡤⢤⢄
⠀⠀⠀⠀⣀⡔⠁⠀⠑⣤⣀⠔⠛⠫⡉⠉⠉⠐⣄⠀⠀⠀⠀⠀⣠⠶⠒⠀⠀⠐⠂⠀⠀⠈⠙⠁⣀⠀⠀⠀⣠⠋⢠⡞⢠⠇⠈⠃
⠀⠀⠀⡼⠻⣿⣠⡖⠉⠉⠛⣆⠀⠀⠈⠆⠀⠀⠈⡡⠀⠀⠀⠀⣷⣀⠀⠀⠐⠀⢀⡀⠀⠠⠄⢴⡌⠀⠀⢸⠁⢠⡞⢀⡞⠀⢸⣂⡤⠔⢒⠢⢤⡀
⠀⠀⠀⣄⠀⠀⠁⠀⠀⠀⢠⣿⠃⠀⠀⡐⡀⠀⡰⠃⠀⠀⢠⢎⠁⠘⠉⠉⠁⠤⠒⠁⠀⠈⢉⣆⡃⠀⠀⠘⡄⢿⠀⡞⠁⡴⠋⣡⠔⣊⡴⠚⠉⣤
⠀⠀⠀⠹⣷⡀⠀⠀⢀⣠⡿⠧⡀⣀⣴⡋⠤⠚⠁⠀⠀⠀⠸⣦⣁⣄⠀⠀⠀⠠⠄⢀⣀⣀⣉⣴⠇⠀⠀⠀⠀⠀⠀⠀⡎⠠⢊⣴⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠛⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠉⠁⠉⠁⠀⠈⠁⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⢥⣚⢀⡤⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⣖⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⠀⣄⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⣠⣾⠤⠤⠤⣄⢠⡾⠁⠀⠀⠀⠀⢾⠀⠑⢒⣀⣠⡏⠀⠀⠀⠀⠀⠘⡄⠀⠀⠠⠀⠀⠀⠓⠂⣠⠄⠀⠠⠵⢀⡀
⠀⠀⠀⢸⡀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠈⠢⢊⠁⠀⣠⠈⠑⣔⠚⠊⠀⠠⠂⠀⠀⠡⠀⠀⡠⠐⠉⠉⠉⠉⠐⣀⠀⢸
⠀⠀⠀⠀⠉⠁⢛⠀⠀⠀⢀⠠⣒⣀⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠈⠁⠀⠀⠓⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠡⣀⡀⠠⠄⠀⠂⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣶⡤⠕⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⣠⠴⢒⠊⢛⡛⢒⡲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣤⡤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⠈⠳⡄⠀⠀⡜⠡⢴⠤⠤⣀⠉⠁⣂⠀⢢⡍⠢⡀⠀⢀⠀⠠⠤⠤⣀⡀
⠀⠀⠀⠀⡰⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡇⢀⠲⣄⡀⠒⠑⠢⡀⠀⠭⠀⠀⠈⠀⢀⡤⠒⠒⠒⠲⠬⣍⡒⢄
⠀⠀⠀⣸⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⢣⡀⣠⣄⡈⢦⣄⠀⠉⠒⠄⠀⠀⠀⠀⢱⡤⠖⠚⠛⠛⠛⠛⠛⠲⠧⣄⡀
⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠚⠋⠀⠀⠀⠀⠱⡀⢎⡑⠮⣀⠱⠠⢀⣀⠀⠀⠀⠄⠘⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠈⠳⠦⣤⣀⣀⣤⡤⠤⠒⠈⠉⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠘⣆⢈⢦⣈⠓⠢⢈⠩⠁⠀⠀⢠⣀⠣⢥⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠒⠉⠁⠐⠂⠈⠙⢢⡀⠀⠀⠀⠈⠳⢄⡈⠓⠤⣉⣀⡀⡒⠀⡘⠤⣕⠦⢄⣘⡛⠲⣄⠀⠀⠀⠀⠀⣀⡤⠞⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠛⠦⢤⣬⣁⡽⠴⠛⠢⣀⠁⠢⢉⡀⠀⠈⠉⠛⡋⠉⢠⠀⠈⢅⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡈⠈⠓⠀⠐⡤⠀⠀⠒⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⠤⠴⠐⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⣀⡠⠴⠚⢉⣀⡤⣤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠁⣠⠴⠚⠋⢀⣀⠤⠤⢤⠄⠈⡛⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠋⠉⠉⠙⠉⢉⠁⠂⠰⣊⣁⣀⣤⣤⠄⠠⣄⠀⢠⠀⠑⢄⠀⠀⠀⠀⠀⠀⡠⠖⠒⠀⠉⠉⠉⠩⠉⠙⠓⠒⠦⣄
⠀⠀⠀⠀⠀⣠⠞⣫⣤⠤⠖⠒⠂⠀⠀⠀⠀⠐⠒⠋⠉⠁⠐⢀⠁⠠⠂⠉⠉⠉⠀⠀⢩⠃⠀⠀⠀⢠⠎⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⣸⠁⢋⠀⣠⠦⠤⠈⠁⢘⣂⣠⢤⠦⠖⣒⣠⠦⠀⠒⠀⠀⠉⢉⣁⡤⠀⢠⠏⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⢧⣀⣩⠩⠥⡄⠐⠛⠉⢉⣁⡤⠆⠀⠀⠀⠐⡐⠈⢀⠀⠁⢊⠀⡠⢉⡴⠃⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁
⠀⠀⠀⠀⠘⣆⠀⠀⠤⠤⠖⠚⠉⠁⡀⠀⠀⠀⣀⠐⢀⣀⣀⣀⣀⣀⣠⡤⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⠤⠤⠄⠀⣀⣤⠤⠞⠁
⠀⠀⠀⠀⠀⠈⠓⢄⡀⠤⠢⠒⠈⠄⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣤⡤⣀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠠⠀⣛⡁⢄⣛⠂
⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⡚⣿⣷⠀⠀⢠⠀⠀⠀⠀⢀⣾⣃⣩⠿⠐⢊⠁⠭⠛⠐⢿⠀⠀⠀⣀⠴⠒⠒⠒⢦
⠀⠀⠀⢿⣿⣧⡀⣀⡈⠀⠀⠀⠀⠸⡞⣿⣷⡀⢐⡆⠀⠀⠀⠈⡿⢃⡤⠀⣀⡀⠀⠒⢠⡾⠂⠀⢀⠞⠁⠀⠀⢠
⠀⠀⠀⠈⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠙⢿⣿⣷⡿⠃⠀⠀⠀⠀⠘⢿⣇⡀⣀⠠⠔⠂⠁⠀⠀⠀⡎⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠎⠠⠆⠐⠒⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣾⡀⠑⢐⣄⣄⣠⣧⡿⠀⠀⠀⠀⠀⠀⠀⣠⣞⣛⡻⢷⣶⡀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⣾⠟
⠀⠀⠀⠀⠀⠀⢠⡈⠭⠷⠿⣅⣠⣄⣤⢅⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⣮⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⢻⡈⣁⣀⣈⣽⡉⢁⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⢀⣤⠤⠰⠖⠒⠐⠲⢤⡀
⠀⠀⣠⠒⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⣰⣍⠀⠀⠂⠀⠐⠒⠀⣺⣿⡀
⠀⢰⣿⡂⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡴⢶⣄⠀⠀⠀⠀⠀⣃⡒⡒⢬⣌⢡⠄⣤⣀⣤⣶⡇
⠀⠀⠹⣆⠀⠀⠀⢈⡇⠀⠀⡈⠀⠀⠀⠀⢀⣦⠀⠀⠀⢻⣺⡭⣟⡇⠀⠀⠀⠀⠸⢥⡴⣶⡀⠀⠈⣁⣂⡾⠟
⠀⠀⠀⢸⠀⠀⠀⣨⠀⠀⢰⣷⣄⣠⣤⣥⣾⣿⠀⠀⠀⠈⣿⠤⢹⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠂⠀⠀⡰⠃⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣡⠥⠆⢹⢧
⠀⠀⠲⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡦⢆⠘⣠⠾⡆⠀⠀⠀⠀⠀⢀⣤⢶⣫⣵⣿⣾⠄
⠀⠀⠀⠀⠀⠀⣠⣶⢶⣶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⣛⣿⣺⡇⠀⠀⠀⠀⠀⣾⣿⣿⠟⠛⠁⠀⠌
⠀⠀⠀⠀⠀⢠⣟⢯⣬⠓⠞⢉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠻⣯⣅⡀⡠
⠀⠀⠀⠀⠀⠈⠻⣯⣷⢜⡃⠼⠐⡷⣢⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⢲⠲⣄⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⣴⡥⣼⢡⢻⡇⠀⠀⠀⢀⠼⠁⢊⠀⢀⣊⠷⢿⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠠⠂⠋⠽⣷⣄⠀⠀⠈⠛⠿⠿⠟⠁⠀⠀⠀⠸⣆⣉⠓⣿⠋⢀⣤⡾⡲⡆⠀⠀⠀⠀⢰⡗⠾⠶⣍⣻⣷
⠀⠀⡐⠀⢀⣀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠩⢑⡋⠉⠉⣏⣁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿
⠀⠀⢰⣶⣿⠿⣻⡽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣅⠠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠠⠾⠛⠁
⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠖⢲⣦⣄⡀⠀⠀⠀⣀⣴⡾⠻⠋⠟⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⢿⠋⡰⢠⠇⡏⡏⡟⣦⢀⠞⠉⠈⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠲⣖⠒⠒⠒⠒⠲⠦⠤⣼⢏⡎⠏⣰⠁⠘⡘⣸⢃⢃⠙⣏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠠⡀⣸⢹⢸⢸⠰⠁⡀⢠⡗⡸⢀⡎⠘⢹⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢱⡇⠞⡀⣼⠇⢰⠇⡘⢠⠃⡞⣠⠆⣿⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⠀⠀⠀⢹⢀⢀⡔⢀⡇⠀⡘⠉⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠒⠚⠋⣿⡄⢀⡆⢋⠎⡜⠀⡜⣠⠎⡴⣱⠓⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⢸
⢀⣤⠴⠒⠋⠉⠀⠀⣀⠀⠐⠠⣄⣿⠉⠈⠀⡸⢠⠇⠐⡫⣇⢎⡴⠁⠐⠀⠹⣄⠢⠁⠀⠈⠀⠀⠀⠀⠀⠀⡀⣾
⠀⠈⠙⠲⢤⣀⠀⠀⠈⠓⡠⠄⠨⣿⢡⠃⡰⡱⠋⣠⠆⢠⣷⠟⢧⡀⠀⠈⠑⢌⠳⡑⢄⠀⠀⠀⠈⠀⢀⠀⢀⡏
⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⡀⠀⠀⢿⠈⠀⡠⢀⠜⢁⣴⠟⠉⠉⣉⡩⠝⠉⠉⠉⣉⠽⠳⣅⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠾⣷⣴⣡⣮⠶⠋⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢀⣀⡤⠟⠲⢤⣄⣀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣶⠶⢤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⡿⠙⠛⠉⠁⢒⡀⠬⠅⠀⠤⠀⠉⠉⠛⠿⠟⠛⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⢐⡩⠔⡠⠔⢊⣭⠅⠀⠀⠀⠀⠈⠐⠂⠀⠀⠥⢐⠒⢌⠠⡙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⣁⠴⠟⣋⠉⠁⠤⠾⠛⢉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⢀⠀⠑⠬⣒⠺⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⠄⠊⢁⠔⠉⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠉⠒⠶⠄⠈⠐⠀⢌⠂⠀⠈⠳⠌⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⠋⢒⡴⠋⠀⠀⣠⡤⠖⠒⢂⡉⠁⠀⠀⠀⢀⣀⣀⣄⣀⣀⣀⠀⠀⠄⡀⠁⠂⠑⠀⠈⠘⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⣫⠀⢡⠋⠐⢁⢔⡟⠡⠀⠀⠀⠀⣀⠀⠀⠈⠉⠑⡂⠀⠒⠀⠤⢀⠀⠤⢀⠀⠉⠂⠄⠢⢄⠀⢁⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠏⡆⠁⢈⠔⡁⠁⠠⠀⠀⠀⠉⠀⠀⠀⠐⠂⠨⠤⠤⠤⠤⠌⠀⠀⠈⠀⠂⠈⠁⠒⠐⠲⠀⠳⣄⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠃⡅⠀⠸⠈⠀⡀⠄⠐⠒⠀⠀⠀⠀⢀⠲⠟⠛⠒⠲⠀⠐⣀⡀⠀⠀⠀⢀⣤⣬⣤⡀⠀⠀⠀⠌⠑⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⣧⢀⠃⠀⣈⠠⠀⠀⠀⠀⠀⠉⠁⠀⠂⠠⠀⠀⠄⠠⠀⣀⠀⠒⠒⠈⠉⠐⠂⠈⠉⢉⣉⡐⣒⣚⣶⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢰⡗⢬⣉⣛⡚⠒⠚⠀⠀⠉⠉⠉⢉⣐⣀⣀⡠⠄⢒⡀⠁⠀⠀⢀⣤⠤⠤⠒⠦⣤⣤⣬⣭⠴⠖⠚⠛⠉⣁⣄⡠⠨⢽⡦
⠀⠀⠀⠀⠀⠀⢸⡟⣶⣤⣤⣉⣛⠒⠲⠶⠶⠶⢶⣦⣤⣌⣉⣉⡛⠛⠓⠒⣀⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⠤⠤⠔⠒⠒⢉⣉⣤⠶⡶⠋
⠀⠀⠀⠀⠀⠀⠘⣧⡁⡟⠓⢝⠫⡙⠻⢗⡒⠢⠤⢀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠤⠤⠀⢀⠰⠞⠛⠍⢉⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠃⢡⠀⠀⠑⢌⡢⠄⠠⠁⢀⡀⠠⠀⠀⠀⠒⠒⠲⢚⡉⠉⠉⠉⠀⠀⠀⠁⠀⠀⠬⠁⠀⣀⠠⢐⡴⣫⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠠⡳⣷⡄⠀⢈⠒⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠀⣰⠟⢨⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡐⢌⡻⢦⡄⢉⠒⠄⠤⠤⠀⠉⠁⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠒⠒⠀⠀⢉⠀⠀⣀⠼⢁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣬⣒⠤⣀⠠⠀⠀⠀⢒⠒⠲⠦⠤⠤⠤⠤⠀⠠⠤⠤⠄⠀⡂⠔⣨⠤⠒⠈⢁⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⢅⠢⢤⣀⣀⣀⣉⡐⠒⣀⡂⠀⠀⠀⠀⣒⣈⡥⠖⠛⣉⣭⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣄⣀⣀⣀⠀⣀⣠⣤⡴⠞⠀⠀⠀⠀⣀⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡇⠀⡇⠀⠀⠀⠐⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡃⢧⠀⢹⡰⡄⠀⠀⠀⠀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢊⠋⠉⣹⣿⣿⠿⠿⠟⢛⣛⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⠘⣷⡹⡀⠀⠰⡀⠢⠂⣈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢉⣴⠿⠀⠉⡠⠄⠂⣀⡀⣠⣶⣶⡛⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡆⢻⡀⠱⣷⡑⠀⢐⠄⠡⡀⢸⣇⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠋⡳⣄⡿⣿⣿⣟⡆⠀⠀⠀⠀⠀⣴⣆⣻⣿⣇⠀⢧⠀⠹⣟⠀⠀⠀⣀⣀⡀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠠⠞⢋⣾⣽⣿⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣌⢣⡀⠙⠧⢦⣦⡙⣿⣧⣈⣿⡄
⠀⠀⠀⠀⠀⠀⡔⠀⠀⡰⠁⠀⠀⠀⠀⠀⢀⠄⠂⣡⣿⣿⣿⣿⣿⡏⠀⠀⠁⠀⠀⠀⠉⢹⣿⡻⣿⣿⣷⣌⠳⣄⠀⠻⣟⣿⣿⣿⡏
⠀⠀⠀⠀⠠⢘⣴⠂⡔⠁⠀⠀⠀⢀⠀⢐⠀⠀⢸⣿⣿⣿⣿⠛⠁⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣌⡑⠦⢌⡙⠻⣿⡅
⠀⠀⠀⠀⠀⠞⠡⠊⠀⠀⠀⠀⢀⠁⢀⣾⣥⣶⣿⡿⠋⠀⠁⡀⠀⢀⠈⢛⣋⣿⣯⣭⣾⣍⠀⠁⣽⣾⠁⣿⣿⣿⣿⣷⣶⣭⡓⢮⡇
⠀⠀⠀⠀⠀⠀⣧⠀⢀⡤⢔⣲⠍⠐⣫⣾⣿⣿⠋⠀⠀⣰⠋⠀⠀⠀⢐⡼⠋⠀⠀⠀⠙⢻⣶⢾⠟⢁⣼⣿⠟⠛⠛⠋⠉⠉⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠲⢽⣖⡻⢶⣂⣴⣽⣿⣿⣿⡦⣶⠞⠁⣀⣀⣠⣴⡿⠃⠀⠀⢀⣤⣴⠟⠁⣀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠛⠋⠁⠀⣯⠀⠊⠉⠉⠉⢋⣁⣀⣀⡠⠟⠉⣀⣴⣾⣿⡿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠛⠳⠤⣀⡤⠞⠉⠀⢉⣁⣤⠶⠛⣹⠵⣿⣟⣷⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⣶⣶⡶⠾⢿⣿⠟⠀⠰⠂⠀⣩⢵⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠿⣿⠥⠾⠁⠀⠀⠀⣠⠴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢯⣧⣴⣶⣤⡤⠶⠛⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠢⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢏⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⢁⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣀⣀⣀⣀⣀⡴⠁⠀⠀⠀⠀⠈⠀⠀⠈⠑⣄⠀⠀⠀⠙⠒⠋
⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡘⡀
⠀⠀⡠⠉⠀⠀⠁⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠜⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⢤⣤⡤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡔⠉⠀⠀⠈⠓⣄
⣸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢣
⡇⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠃
⠃⠀⠀⠀⠀⠀⠈⠒⠦⣄⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⡀⢀⡀⣀⣀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⡄
⠈⢧⠀⠀⠢⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠑⠤⣤⣀⣤⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⣤⠄⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠉⠉⠉⠉⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣀⣤⠤⣄⠀⠀⠀⠀⢀⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⠶⠖⠋⠁⠀⠀⠈⠳⣄⠀⠀⠻⠁⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠶⠶⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡦⠄⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢀⠁⣄⠀⠳⢤⢸⠃⡇⣶⠘⠡⣀⣆⡰⠀⠐⡎⢹⠸⡀⣸⠀⠠⠀⣙⡆

⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠔⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡔⠉⠡⠀⠀⠠⣄
⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡜⠁⣠⠀⠀⠀⠆⠀⠑⡄⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠯⠀⢄⣀⠀⠀⠀⠀⠀⠀⢸⠅⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠄⠀⢄⡀⠱⣆⠀⠀⠀⠀⢸⡆⠀⢇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⣀⣀⣀⡴⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠹⡶⣠⠀⠀⢠⠞⠀⠀⠀⠀⠀⢀⠃⢀⣿⣆⠀⠀⠀⠘⣿⣄⠈⠦⣀⣀⠀⠀⠁⢰⠇⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠌⢀⠞⣿⠟⠀⠀⠀⠀⠈⠻⣦⣄⣀⡀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡅⠰⣠⠤⠤⠊⢁⡤⠊⣸⢦⠃⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣧⣤⣤⡄⠀⠚⢩⣄⣴⠟⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⠦⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠙⠷⠦⢄⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠄⢁⣀⣉⡀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣾⢦⡈⢫⠁⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⣿⢹⡇⠀⠧⠄⡀⠀⠀⢀⡆⠀⡆⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷
⠀⠀⠀⠀⠀⢹⡀⠁⠀⠀⠄⡀⠀⠀⢉⣀⣴⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡏
⠀⠀⠀⠀⠀⠀⠙⢤⣀⡀⠀⢀⢀⣉⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⡀⠀⠀⢀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉

⣿⣿⠿⠿⡿⠛⠿⢿⠿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢂⡿⣿⣿⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⠿⢹⡿⢃⠾⣋⣿⠋⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣯⡿⠁⣿⣵⣫⣒⣁⡠⢤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⣄⣿⣿⣋⣿⡅⠊⠀⠘⠛⠉⠉⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠈⢳⣨⢹⣿⢟⡉⠌⠻⣶⡶⡶⠾⠖⢚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⡿⣿⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⣡⡿⢵⣶⣯⣓⢶⣶⣦⣤⠴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠿⣄⡘⢮⣀⠀⠀⠀⣂⣤⣦⠴⢏⣆⠀⠀⠀⠈⢉⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⠀⠀⠀⠀⣝⣶⣼⣿⣿⠛⠋⠉⠂⢰⣍⣿⠿⠾⠛⣻⣏⣴⣆⣄⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⢿⣉⠛⠛⢋⣁⠀⠿⢽⣿⣷⣆⣀
⠀⠀⠀⠀⠀⣀⣤⣴⣄⢙⣓⣧⣿⠶⣬⣁⠀⠀⡀⣀⣜⠁⠦⡔⠁⠀⢀⡄⠙⠁⠀⠀⢃⢝⣬⠂⠈⠙⠛⠁
⠀⠀⠀⢠⠚⣓⣢⠔⣫⠽⢣⣿⠏⢠⣾⣉⣽⠟⠛⠉⢿⠃⠘⠃⠃⠘⠋⠀⠀⠀⣀⢔⡼⠋⠼
⠀⠀⠀⠘⠡⠿⢱⠾⠿⠴⠛⠓⠈⠉⠉⠁⠀⠀⠀⠀⠈⠳⣦⡀⣄⣀⣀⣤⣤⠿⠟⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠠⠤⠤⠠
⠀⠀⠀⠘⢷⣛⠓⣂⠔⠀⠀⢀⡼⣿⠀⠀⢐⠀⠀⠔⠉⠛⠁⠀⠁⠀⡠⠀⠀⠀⢾⡀⠐⢀⢂⣀⡔⢰⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⠟⠐⠁⠀⠀⠘⠦⠤⠂⠐⠢⠀⠀⠐⠊⠀⠀⠀⠀⠈⠉⠓⠊⠉
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢢⡑⠂⠀⠀⠧⠥⠤⢤⠂
⠀⠀⠀⠹⠶⠄⠀⠄⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣨⠇⠀⡄⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠧⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⣨⣿⣀⠀⠀⠀⠈⠂⠄⢀⣈⠭⠋⠀⠀⠠⠤⣤⣤⣾⠟⠁⠀⠀⠀⠀⠀⠈⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠈⠑⡀⡀⣦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠠⣄⣀
⠀⠀⠀⢦⣤⠤⠴⠆⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠁⠀⠈⠀⠀⢸⠀⠀⠂⠀⠐⡊⠀⠔⠀⠈⠻⢦⡀⣀⣠⠾⠃⠀⠘⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠰⠀⠀⠀⢀⡠⠄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣴⠖⠁
⠀⠀⢠⠂⢠⣷⠤⣀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⢀⡤⠀⢤⠀⠁⡐⠒⠲⢦⠀⠀⠀⠀⠀⠙⠛⠀⠁
⠀⠀⠘⢶⣿⣁⣠⣻⠇⣄⢰⣿⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡀⠀⠀⡀⠘⡀⠀⣀⡾⠀⠀⠤⣤⣴⣶⣶⣶⣶⣶⢀⣀
⠀⠀⠀⠀⠀⠙⠛⠋⠀⣈⡛⠋⠀⠀⠀⠈⠓⢄⣀⣀⠄⠀⠀⠀⠀⢙⠚⠋⠀⢀⠈⣈⠉⠁⠀⢶⣾⣿⣿⣼⣿⣿⣿⣿⣿⡿⠄
⠀⠀⠀⣀⣀⣴⡇⠀⠒⠛⠃⠀⢧⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣾⣅⠀⢐⠀⠀⠀⡌⡇⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠊⠀⠐⠒⠛⠁⠀⠀⠋⠉⠉⠉⠉⠉⠉⠙⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⣿⡿⠿⠭⢟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠹⠄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣦⠄⠀⠀⠀⢰⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠼⠃⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣴⡀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠀⠀⣸⣟⣦⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⢠⣸⣿⡇⠀⠀⠀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⢠⣷⡿⠉⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠛⢳⣿⢀⣤⣾⣿⣿⣿⣿⣶⡤⠄⠚⠀⠰⠶⣾⣿⣿⣿⣿⣿⣾⡀⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢠⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⣾⣿⣖⣾⣿⣿⣿⣿⣿⣿⣿⡆⢸⡆⠀⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡜⠛⠀⢻⣿⣿⣿⣿⠿⠿⠣⢎⣼⣿⣿⣾⡜⢿⣿⣿⣿⣿⣿⡿⠁⠸⣷⣶⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠉⠉⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣉⣄⠀⣀⡀⠉⠀⠄⠀⠀⢸⣍⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣯⠏⠃⠁⠀⠠⠀⠀⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⠀⠉⠺⡿⠁⠁⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⡌⢿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣠⣤⣠⣤⣽⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣆⠈⠻⣿⡏⣌⠃⡏⢸⡃⡏⣏⣙⣩⣿⣿⠿⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠀⠈⠑⠓⠦⠶⠸⠿⣹⡤⣭⣴⠿⠃⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠈⠃⠀⠀⠀⠀⠈⠋⠉⠙⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠃⠀⠀⠠⢈⣿⠇⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠋⠉⠉⠓⢲⠏⠀⠀⠀⠀⢀⡴⠷⠿⠦⣤⠴⠃⠀⠙⣆⣀⣀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣏⠀⠀⠀⠀⠉⠀⠈⡇⠀⢀⡴⠀⠀⢀⡴⠓⠒⠒⠠⠤⠄
⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⢀⠗⠂⠄⠀⣿⣆⢀⡆⠀⠀⠀⢀⣷⠞⠛⠉⢳⣖⡭⠠⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣼⣧⡀⠀⢀⣠⡏⠀⠀⠀⢠⡼⠛⠛⢧⡀⠀⠀⠈⢷⣀⣀⣀⣼⣧⣤⣀⢀⠀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠊⠉⠉⢢⣀⣘⣿⡷⠞⡽⠁⠀⠀⠀⣾⠀⠀⠀⠀⠙⣆⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⠷⠶⠶⠛⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⣄⣀⡠⠤⠒⠒⠒⠒⠒⠲⢾⡀⠀⠀⡴⠋⠉⠑⠄
⠀⠤⠤⠤⠤⣄⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣠⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢠⠁⠀⠀⠀⡄
⢣⡄⠀⠀⠀⠈⠙⢦⡀⠸⡄⠀⠀⠀⢰⠃⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⠀⠀⠀⠀⣸⡇⡆⠀⠀⠸⢧⣄⡀⠠⠄⣄
⠀⠉⠐⠢⣄⠀⠀⠀⠹⡄⠈⠢⣄⣀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⠉⠀⠀⠀⠈⠙⠶⢤⣤⡴⠛⠀⠙⣄⡀
⠀⠀⠀⣠⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠁⠄⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⣇⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⣀⣀⣤⡴
⠀⢀⡎⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠉⠉⠁⠀⠘⢦⣀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠈⠣⣄⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠁⠀⠄⠀⠐⢀⠀⠀⡀⠄

⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠠⡇⠑⠦⠀⣀⡀⣠⡀
⠀⠀⠀⠀⠀⠀⣴⡃⠙⢦⡄⠀⠀⠉⠙⠶⠶⠦⣄⣀⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⢷⣄⢀⠃⠀⠀⢀⡄⠈⠙⠱⣦⠼⢷⡀
⠀⠀⠀⢠⡾⢟⠁⠀⠄⢠⠤⠽⣦⡀⠀⢀⣈⠤⠄⠀⠀⠀⠀⠈⢷⣦
⠀⠀⢀⡸⠃⠀⠡⢀⠀⠀⠀⠀⠙⢿⣦⡟⠀⠀⠀⠀⠀⡰⠥⠄⠀⠙⢶⡀
⢀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⢿⣷⡀⠀⢀⠄⠁⠀⠀⠀⠀⢀⠈⢷⣄
⠈⣏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠉⣷⡴⠋⠐⠐⠰⣔⠃⢀⠦⠄⠈⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⢀⣀⠀⠀⢀⡀
⢰⣿⠂⠀⠀⠉⠁⢂⡠⠤⠀⢄⣀⡀⡀⠱⣿⣷⠀⠀⠀⠀⣠⡴⣥⣀⡀⠀⢿⠄⠀⠀⣠⠶⠶⠖⠟⠃⠀⠉⠉⠙⠋⠉⠉⠹⠓⠂⠴⠢⠄⡰⠂
⢸⣇⠀⠀⠀⠂⠞⠀⠀⠀⡠⠄⠉⠉⠉⠻⣿⣿⡀⢀⡴⠋⢀⢴⣿⢏⡁⠖⢸⠆⣤⠞⠉⠀⡁⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⣀⣀⡤⠖⠁⢠⠃
⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢈⣿⡷⠋⡾⠋⢀⣾⣵⣾⡇⣿⣯⡼⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣦⣴⠟⠋⠅⠀⠀⠀⡀
⠈⢧⣄⠀⠀⠀⠐⠂⠚⡙⣿⣆⡂⠠⠀⡂⢨⣿⣧⠞⣁⠴⠛⣱⡟⠉⣟⠻⢏⠀⣀⠀⠀⠀⠀⠀⠈⠑⡀⣀⣶⠿⠟⠛⠂⠀⠀⠀⠀⢰⡇
⠀⠈⢧⡀⠀⠀⢸⡶⢾⡿⠻⣌⠛⢓⢦⣼⡟⠉⠀⠈⠀⠀⣴⣿⡄⢠⠌⠀⢰⡆⠀⠀⢀⠀⠀⠀⠀⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠁⠠⠈⠁⠀⠈⠀⠋⡙⣲⣤⣽⣿⣿⠀⠀⠀⠀⠐⠁⠀⣴⡇⣰⣆⣸⣀⠀⠀⠀⢑⠄⣠⣾⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢘⡷
⠀⠀⠀⠀⣤⠀⡄⠀⠀⣀⣠⠿⠗⠀⠀⢻⡟⡀⠀⠀⠀⠀⣠⣾⣿⣶⣿⢿⣿⡿⣀⣴⠾⣛⣿⣿⣿⡦⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢛⠊⠑⢀⡀⠀⢹⣆⣀⡀⠠⣼⣷⣆⠀⠀⠀⣈⣩⣭⣭⡿⢷⣾⣿⣿⢋⣴⠛⠉⠉⠀⠉⠁⠘⢿⡶⣤⠀⠀⠀⠀⠀⠀⢀⡷
⠠⠄⣀⠐⢼⣄⣷⣿⣟⣛⣛⢛⡛⣻⠿⣿⣟⢛⠛⣿⣿⠋⢀⡾⠋⠈⠀⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⡛⠳⠆⠀⠀⠀⣠⡏
⠀⠀⠀⠋⠀⠹⢿⣿⠻⠿⢿⣿⣿⠁⢀⡟⠋⠙⢻⣿⣯⡖⠁⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⢀⡠⠖⠛
⠀⠀⠀⠠⠚⠀⠜⠋⠁⠲⢿⣿⣷⢀⡾⠓⠀⢀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣤⣤⣠⣴⣿⣿⣿⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣇⠀⢀⣤⣿⡿⣿⣿⣼⣄⠀⠀⠀⢀⡔⡺⢿⣿⣿⣿⣿⡿⣫⣿⣿⡿⠏⠀⠈⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⢑⣿⠟⠛⠁⠈⠑⠉⢻⣿⣦⣤⠾⠒⣀⣀⡉⠉⠛⠛⣟⢿⣿⡇⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡶⢛⠋⠁⠀⠂⣀⠀⠀⠀⢿⢉⡴⠛⠛⠛⠻⣍⢢⡀⠀⣿⡗⢸⣷⠄⠀⠀⠀⠀⣴⣿⣠⠀⠀⡐⠀⢀⣠⣶⡿⠋⠀⠀⠸
⠀⠀⠀⠀⣀⠄⠒⠂⠀⠈⠉⠒⢝⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠆⠀⠀⠀⠀⠈⠇⢹⡀⠸⣧⣾⣿⣶⣦⣤⣤⣼⣿⣾⣧⠅⠀⠁⠀⠈⠉⠀⠀⠀⠀⣰⣿
⠀⠈⡍⠁⢤⣴⣶⣶⣤⠤⠀⣀⣼⣾⣿⣿⣯⡀⠀⠀⢀⣀⣀⣤⣿⣿⣄⠀⠀⠀⠀⢄⠘⣺⡇⠀⠙⠿⣿⣿⣿⣭⣭⣿⠿⠋⠀⠀⠈⠠⡀⠀⠀⢀⣀⠔⣺⣿⠏
⠀⠀⠷⣀⠀⠀⠀⢀⣀⣤⣶⣿⠟⡇⠻⣿⣿⣿⣷⣿⣿⣿⡿⠛⠙⢿⣿⡄⠀⠀⣀⠀⣀⣿⠃⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠶⠞⠚⠉
⠀⠀⠐⡀⠈⠉⠉⠉⠻⠋⣹⣿⡾⠁⠀⠀⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠙⠻⠿⠦⠼⠿⠛⠒
⠀⠀⠀⠈⠒⣶⣤⣦⣴⡞⠉⠉
⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢋⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⣽⣽⡇⠂⠀⠀⠀⠀⠀⢠⡿
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠤⠀⠀⠀⠠⣄⣀⠀⠀⡁⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢤⡀⠀⠀⠀⠄⠠⠀⠀⢠⠀⠀⠀⠀⠀⣀⠠⡶⠆⠀⢆⠿⡁⡅⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠠⠇⠀⠀⠀⠀⠀⡠⠆⠀⠈⠁⣀⠀⠀⠐⠒⠹⠁
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⡀⠀⠀⠀⣄⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡄⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⢀⠶⣭⠙⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⠀⠀⠴







⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠶⠏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈
⠀⠀⠀⡠⡖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣖⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠
⠐⠀⠐⣴⠔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣮⣯⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠤⠼⠂⠀⠀⠀⢤⣤⠂⠀⠀⣰⡿⠀⠠⠼
⠀⠀⠀⠈⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⣀⣄⠀⠀⣀⠀⡀⠀⠀⣀⣀⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣴⡓⢀⣲⣀⣄⠀⠀⠀⠀⡀⠀⢀⣀
⣿⡯⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡤⣀⣤⣄⡀⡏⢂⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠄⠀⠤⢤⡀⠀⠀⠀⠀⢰⣧⣟⡤⠌⡗⠙⢚⠔⢲⡀⠀⠈⢀⠀⠀⠀⠠⠖⠐⡂⡀⢀⡀
⠀⠀⠀⠀⠄⡀⠀⠐⢦⠀⢀⡉⠀⠀⠀⠀⠀⠈⣻⡦⠼⠀⢮⠴⠞⠁⠀⢠⡆⠀⠀⠀⡀⠐⢀⠀⠀⢡⠭
⠀⠀⢄⠀⠀⢁⠺⠀⠘⠏⠀⠀⣀⠄⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⡘⠶⣄⢀⣀⡠⣤⢟
⠀⠀⠀⠉⠉⠁⢤⡤⠎⠀⠀⠈⠁⠀⠀⠀⣠⠶⠠⢀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠈⠑⠲⠎⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠤⠀⠀⠀⠀⠈⠐⠆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠴⠖⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠜⠀⠀⠀⣀⣀⡠⠔⠀⠀⠀⠐⡄⠁⣀⣰⡁
⠀⢀⠤⠚⠋⢀⣤⣆⣈⠁⠈⠉⠀⠀⡀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⢀⡉
⠀⠨⡰⠀⢰⠁⠀⠀⠉⠓⠲⠶⣀⡀⠁⠀⠘⡿⣾⡤⡄⡟⢰⡀⠀⠀⠀⠀⠀⠀⠀⠒⣀⣀⡴⠏⠉⡀
⠀⠀⠈⠈⠉⠁⠛⠼⠷⠦⣤⠔⠉⠀⠀⠀⠈⠁⡁⢁⢡⢡⢈⠁⢀⣄⠀⡀⣀⠀⠈⠲⠬⠉⠲⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠇⠻⠛⠛⠻⠘⠺⠺⠚⠛⠀⠀⠀⡤⠄
⠀⠀⠀⣠⠀⠀⠘⢦⠀⣀⡀⠀⠀⠀⢀⠄⢀⡀⠀⢄⠀⠀⠀⠀⠀⠀⣀⠀⠤⢦⠀⢠⡃⠐⢩
⠀⠀⠀⠧⣀⠀⢀⡠⠛⠉⠉⠓⡄⢰⡁⠐⠉⠁⢁⡼⠀⠀⠀⠀⠀⠾⡁⠀⠀⡀⠀⠞⠁⢠⠏⣀⣀⡀
⠀⠀⠀⠀⠈⠉⠉⣧⠀⠀⡀⢰⣄⠀⠉⠄⠀⢨⠝⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠑⠊⠀⠐⠣⠀⠈⠡⠒
⠀⠀⠀⠀⠈⠐⠊⠛⠦⢤⣀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠔⠂⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣭⣤⡭⣐⢾⡗⠁⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡇⢸⠋⠀⠀⠀⠀⢹⡄⡀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠳⠀⢤⡤⠖⠒⢿⡀⠀⠀⠀⣠⠞⠀⠀⠀⠈⣏⢀⡀⠀⠀⠀⠀⡘⠛⠧⠤⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡝⠒⠒⠉⠀⠀⠀⠀⠀⠀⠈⠀⢈⣀⣤⣶⠞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠁
⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠉⠈⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦
⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠋⠙⠛⠓⠦⣄⡀
⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣠⡟⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣰⡏⠀⢀⡎⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⣿⡇⠀⣸⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠀⣰⡟⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣼⠏⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠤⠤⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠉⠀⠒⠒⠦⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⣠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸⠁⠀⢀⠤⠐⠒⠊⠁⠀⠀⠀⠀⡔⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠒⠁⠀⡰⠁⠀⠀⠀⢀⠀⠀⠀⠀⡴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢀⠎⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡄⠀⠀⠜⠀⠀⠀⠀⠈⠀⢀⠖⠉⢁⠀⠈⢀⠎⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠒⠁⢀⠞⠁⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠛⠤⠀⠀⠁⣠⠊⠐⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⣠⠤⠐⠒⠊⠀⠀⠀⡀⠀⠀⠀⠘⠁⠢⠀⠀⠀⠀⡠⠒⠈⠁⡀⠀⢀⡼⠀⠀⠀⠀⠐⠀⠀⠤⢀⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⢀⠔⠁⠀⠀⠀⠀⡀⠀⠀⢈⡤⠀⠠⡄⠀⠀⡠⠄⠀⠈⠀⠀⠠⠀⠈⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⡀
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⣀⠤⠒⠁⢀⠀⠀⠀⣀⠜⡀⠀⠀⠦⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⣀⠀⠀⠀⠈⠢⡀
⠀⠀⢰⠁⠀⢀⡰⠃⠀⡠⠀⣠⠁⠀⠀⡔⠁⢀⡀⠀⠈⠁⠐⢊⠑⠄⠈⢀⣀⡠⠴⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄⠀⠱⡀
⠀⠀⡆⠀⠰⠁⠀⡠⠎⡰⠋⠀⡠⠶⡊⠀⠀⠀⡠⠄⠀⠀⠀⢀⠔⠂⠉⠁⠀⠀⠀⢃⣀⣀⠤⠤⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠃
⠀⢠⠁⢀⠆⠀⠘⠀⢀⡀⠤⠊⠀⠀⠀⡠⠔⠊⠀⠂⡰⠀⢡⠃⠀⠀⢀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠁
⠀⠸⡀⡜⠀⠀⠁⠀⡏⡀⠀⠐⠀⢀⢎⡀⠈⠂⡠⠊⠉⢠⠂⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⢤⣀⡀⠑⣄⠀⡀⠠⠄⢒⡡⠊
⠀⠀⢣⡱⡀⠀⡔⠋⠀⠈⠂⠀⣀⠜⠀⢀⣠⠎⠑⢀⡴⠁⡜⠁⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢮⡆⠀⠐⠈⠁
⠀⠀⠀⠱⣁⠘⠀⢀⣀⡀⣠⠎⠀⣀⠴⠁⢀⡠⠖⠁⢀⡞⠀⢀⡀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸
⠀⠀⠀⠀⠈⠓⠦⠥⢀⣈⣀⣒⡊⠤⠤⠒⠉⠀⠀⠀⣎⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⡀⠀⠈⠛⠋⣉⣁⡤⠤⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠂⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡀⠀⢀⠀⠀⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⠆⢠⠸⡄⠠⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⣿⠀⠀⢸⠀⠀⠀⢱⠀⠀⡀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⠙⠉⠁⠞⠓⠲⡶⠧⢤⡾⠗⠋⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣉⣉⣉⠛⠛⠛⠒⠒⠒⠲⠶⠖⠚⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠞⣋⡡⠔⠒⠚⠿⠓⠲⢄⡀⠀⠀⠀⠀⢰⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠰⠚⠉⠁⠔⠂⠀⠀⠀⠀⡄⠈⠻⣄⠀⡆⢀⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠥⠚⠁⠀⠀⠀⠀⠴⠊⠉⠑⠒⠒⠊⠀⢀⡄⢹⡞⣠⠏⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⢀⣾⠿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡉⠛⠒⠂⠀⠀⣀⡤⠔⠈⠉⠉⠙⠒⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣦⣤⣤⣤⡴⠶⠛⠛⠛⠛⠛⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠤⢶⡶⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠟⠿⠿⢿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠉⠀⠀⠀⠀⠉⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⡀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠛⠛⠛⠛⠓⠶⣤⡀
⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⣰⡟⠁⠀⣠⠒⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⡟⠀⠀⢠⣧⣠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⢹⣿⣿⡆⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⠇⠀⣼⡟⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀⣼⡟⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣾⠏⠀⠀⠀⠀⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣤⣤⣴⣶⠾⠟⠋
⣿⣿⠿⠿⡿⠿⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⡔⠚⠉⡡⠋⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡠⠂⠀⠀⠈⡇
⠀⠀⠀⠈⠀⠤⠊⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠸⣷⡋⠁⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢣⣹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⡀
⠀⠀⠀⢀⠀⠀⠀⠈⠢⡀⠀⢂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠑⠦⢄⣀⣀⣬⠵⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⢀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢄⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠤⠀⣧⠀⠀⠀⠀⠑⠢⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⣿⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡒⠲⠤⢤⣅⣀⣀⣀⣐⣂⣠⠄⠒⠋⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣀⣀⠄⢀⣉⠁⠄⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢠⡄⢤⠊⡙⢒⡉⠒⣄⠀⠀⠈⠙⠒⠒⠚⠉⠉⠉⠀⠀⣐⠶⠂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣀⡐⠀⣘⡚⠙⢲⠙⡇⠘⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠂⠀⡀⢄⡀
⠀⠀⠀⠀⠀⠀⠹⠆⡆⠁⠠⠊⡖⠒⠣⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣱⡀
⠀⠀⠀⠀⠠⡲⠀⠋⠀⡴⠍⠒⣌⠂⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⣧⣿⠋⢠⢠⡏⠓
⠀⠀⠀⠀⠀⠃⡀⢄⠉⡔⠋⠒⢆⠙⠢⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠏⠃⠀⠀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠒⠉⣻⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄⣀⣀⣀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⣠⠴⠖⠚⢉⡟⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢀⡜⠁⠀⢀⡰⠋⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠤⠒⠉⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⡀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣯⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣹⣦
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⢄⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠀⠈⡆
⠀⠀⠀⠀⠈⢢⡁⠀⠀⠀⠀⠈⠳⢄⠀⠘⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢱
⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣀⣀⣠⣤⠽⠶⠟⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⠀⠉⠙⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠈⠻⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢠⠞⠋⠀⠀⠀⠔⠂⠉⠉⠉⠉⠉⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠔⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠒⠒⠀⣷⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠠⠊⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣥⣄⣀⣀⣀⠀⠐⠀⠀⠀⠀⠀⠠⣤⠄⠀⠀⣀⣤⡴⠞⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⡉⠉⠙⠛⠶⠶⠶⠶⠶⠶⠶⠶⠞⠉⠀⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⢤⣀⡀⠢⠤⢤⡄⠠⠄⠒⠂⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡒⠚⠙⠶⡚⠛⠦⣄⠀⠀⠀⠀⠉⠓⠶⠤⠴⠶⠚⠋⠛⠋⠉⠀⠀⠐⠤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠁⠠⣇⣴⠶⣄⠙⢦⡄⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠀⠀⣀⣀⣀⠀⠀⠄⢠⠂
⠀⠀⠀⠀⠀⠀⢀⠴⢦⠙⢄⡤⢬⠁⠀⠉⡷⠀⠧⢀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⡄⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⠂⡎⠉⠀⠠⠎⢱⡟⠓⠚⢦⠣⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣻⡀
⠀⠀⠀⠀⠀⠀⢀⢤⡂⢠⠞⠁⠀⣈⠒⠦⣌⠳⡄⠀⠀⠀⢁⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡴⡆⣸⣶⠇⡀⡀⢀⡟⢷⣄
⠀⠀⠀⠀⠀⠀⠈⣦⠁⠀⠣⣠⠜⢀⣉⣀⡈⠲⢬⡁⠂⡤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣿⢻⠃⠀⠘⣧⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠲⠤⠆⠰⡉⠀⠈⠙⣇⡀⠙⢲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠇⠈⠀⡠⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⠀⡌⠀⠒⠒⠉⢻⡆⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠐⣊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠒⠤⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠒⠛⠋⠁


⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⣶⣶⠶⠶⢶⢶

⠀⠀⠀⢤⣤⡀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢶⡶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠛⠛⠓⠦⣄
⠀⠀⠀⠀⢀⡽⠟⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⠀⠙⣦⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⢠⡟⠳⢦⣤⣀⠈⢳⡄
⠀⠀⠀⢠⠏⢀⣠⢖⣥⠞⠁⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡉⣦⣎⡘⢯⣀⡙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣰⠟⠀⠀⠀⠢⡙⢷⡀⣷
⠀⠀⠀⠸⣤⠽⠞⠋⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣌⣹⢦⡉⠛⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⣯⠀⢰⡏⠀⠀⠀⠀⠀⣹⣼⠇⡟
⠀⠀⠀⠀⠘⢆⠳⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠱⠦⣄⠹⣧⡀⣳⣞⠀⠁⣼⡇⠀⠀⠀⠀⠀⠀⢸⣆⠈⢷⣄⣀⣀⣀⣠⡾⠋⣼⠃
⠀⠀⠀⠀⠀⠈⠳⣍⡳⠦⣤⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⢊⢷⠘⢿⣤⣟⣷⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⠶⢭⣉⣉⣭⡥⢔⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡤⠟⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⠤⠴⠖⠋


⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡤⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣠⠾⠧⡈⡷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⢼⡏⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣯⠴⠻⣄⠀⢀⡼⠓⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⠙⠻⣟⢿⣌⡈⣎⢷⡀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⣤⡀⠀⠀⣠⣿⠀⠀⠉⢸⣷
⠀⠀⠀⠀⠀⡜⠱⣄⣀⡬⠿⢯⣀⢀⡾⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢧⡀⠈⠳⣌⠻⣾⡜⣷⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⢻⣻⣿⢟⠜⠀⠀⢸⢸⣿
⠀⠀⠀⠀⠀⣼⠖⠋⠳⣄⠀⢀⡼⠛⠓⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠳⡄⠀⠘⢧⡘⣷⣿⡆⠀⠀⠀⠀⠀⠀⠘⢷⣁⣾⠛⠉⠉⠁⠀⠀⠠⢋⣾⠇
⠀⠀⠀⠀⠀⢻⣧⣀⣀⠼⠛⠷⣤⣀⣸⢋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣜⢦⡀⠀⢳⡘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠣⣍⠳⢦⣄⣀⡴⢚⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⡀⠀⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠹⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠏⡇⡿⠁⠀⢹⡴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢉⡒⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠙⢶⣄
⠀⠀⠀⠀⠀⢀⣾⠃⠀⡇⡇⢠⢁⡾⠁⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡸⠈⠳⣝⢲⡄⠀⣀⠴⠊⠉⠀⢱⠀⠀⠀⠀⠀⢀⡴⡟⣹⣠⢦⡰⢄⢻⠙⢳⣄
⠀⠀⠀⠀⠀⣸⠇⠀⠀⠇⣇⢀⡾⣱⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠊⢷⣙⡎⡹⢤⡀⠀⠀⠘⡇⠀⠀⠀⠀⡞⣰⠁⠟⠁⠘⠇⠀⠙⠆⠀⢹⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⡟⡰⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡟⡼⠀⠀⠻⠦⢤⣼⠃⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢿⡀⠀⠈⣹⢏⠜⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢳⡀⠀⠀⢨⡇⡇⠀⠀⠀⠀⣴⢻⠆⠀⠀⠀⠈⢷⡘⣀⠀⢀⣀⣀⣀⡀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠓⠦⣤⡤⢷⠳⣄⣀⣀⡼⢣⠏⠀⠀⠀⠀⠀⠈⠻⣶⣋⠉⠉⠉⠉⣉⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠘⠷⣶⣒⣒⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠒⠋⠙⠒⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⢱⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠾⡄⠉⠆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢳⢧⠄⢰⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡞⡞⡄⢌⣆⠀⠀⠡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⡑⡑⡀⣍⠂⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣹⡱⡔⣌⢦⡀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠋⣀⡠⠀⠠⣄⡀⠀⠀⠸⢧
⠀⣠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⣮⡣⣝⠶⣌⡂⠀⠀⠀⢀⣀⠂⢈⠈⠤⠀⠀⠀⠀⠀⠠⠀⠀⠘
⢀⠁⡠⣐⡪⢥⣐⣒⣒⣒⡆⠤⠄⡀⠀⠀⠀⠀⠀⠀⠐⢌⠳⣮⣕⢮⣍⣛⠒⠤⠤⠤⠤⠤⠄⠐
⠀⠀⠈⠒⠍⢯⠙⠤⠣⠬⠭⣏⡒⠀⠑⠄⠀⠀⠀⠀⠀⠀⠁⠈⢛⣻⢾⣭⣛⡓⠒⠲⠒⠒⠒⠃⡉⡠⠀⠂⡀⠀⠀⠀⢀
⢠⠆⠡⠤⠄⠌⠉⠉⠉⣉⠁⠚⢼⡑⠄⠀⠀⠀⠀⠀⠀⠀⡆⣇⢢⢹⣿⣦⣯⣉⣉⡉⠋⠉⠉⣉⡀⠄⠒⢀⡀⢀⠀⡰⠂
⠀⣦⠀⠀⠀⢀⣒⢒⠤⠤⢈⠑⠤⠉⠀⣠⠖⠂⠀⠀⠀⠀⡇⢸⢸⠀⣏⡓⠺⠭⢭⣉⣉⣉⢉⡁⠤⠄⠒⣀⠔⠁⠊
⠀⠈⠳⠀⠀⠒⠒⠬⠉⠀⠀⠀⠁⠀⡠⠃⠈⠀⠀⡄⡐⢠⠃⠆⠸⢠⡷⠦⠍⣒⠒⠢⠤⠠⠤⠀⠄⢐⣂⡤⠖⠁
⠀⠀⠀⠀⠀⠐⠒⢲⣦⣤⣀⡀⠀⠀⠀⠀⠀⠡⠈⠐⠁⠀⠀⠠⠃⢆⡇⠀⠈⠉⠛⠛⠿⠶⠾⠓⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠄⣀⠤⣀⡴⣢⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢋⢞⠵⣫⣔⡎⢗⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢯⠞⠓⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠶⠧⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⡔⣀
⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⡂⠡⡇⢀
⠀⠀⠀⠀⠀⠛⠂⠀⠦⠀⠀⢀⠀⠀⠠⣄⠳⠿⣆⣣⣠⣤⡄⡀⠚⠳⠈⢱⡦⣀
⠀⠀⠀⠀⠀⠀⠋⠀⢀⢐⡟⣨⡀⠖⠲⠆⠖⠲⡄⠠⢭⠈⠄⠶⠊⡠⣥⠚⣽⣆⣳
⠀⠀⠀⠀⠀⠀⠀⠂⠊⡟⡬⡷⢑⣛⡻⠚⠛⢿⣆⡶⠶⢦⡒⢋⣻⣠⣴⢛⣴⢿⣿⣷⡄⠠⠌⠤⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⢿⣟⣓⢀⣹⣠⣷⠉⢐⣀⡉⢥⡟⡻⣿⣿⣼⣿⣳⣾⣿⠧⠖⡶⢒⣦⠶⣶⣦⡄
⠀⠀⠀⠀⠀⣠⣤⠶⠖⠒⠒⠲⢭⣭⣭⣿⣿⢠⣯⣬⣷⣶⣶⣇⢹⣿⣿⣿⣿⣿⣿⣿⣾⣯⣰⣭⣴⡿⠟
⠀⠀⠀⠰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣈⡩⠽⠟⠛⠛⠥⢄
⠀⠀⠀⢱⣬⣲⢤⣤⣀⣀⣤⣴⣤⣴⣾⢟⣿⣿⣿⣿⣾⣿⡿⠿⠿⣦⣄⠀⠀⠀⢀⣠⣷⠆
⠀⠀⠀⠈⢛⣻⣿⣿⣿⣿⣻⠿⢖⡻⠟⠛⠙⠛⢻⠟⠉⠀⠀⠀⠀⠀⠉⠻⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠉⠙⠺⠷⠈⠐⠈⠉⠀⠀⠀⠀⠀⢸⣤⣤⣀⠀⠀⠀⠀⠀⢀⡹⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣠⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⡀
⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠓⠄
⠀⠀⠀⠀⡀⠈⠓⠄⠀⠀⠀⠀⠀⠈⠒⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⡲⠀⠀⠀⠀⠀⠀⠀⢁⡀⡀⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢠⡒⠊⢉⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⢀⡴⠉⢉⣣⠤⡊
⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⣃⡀⠀⠁
⠀⠀⠠⡁⠉⠒⢄⠀⠀⠀⠀⠀⠊⠁⠐⡄⠀⠈⠀⠀⠀⠀⢀⣀⠀⠀⡇⠁⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠤⠤⡀
⠀⠀⡇⠀⠀⡤⠊⠈⠢⠀⠀⠀⠣⡀⠀⠓⠀⠀⠀⠀⠀⠀⠫⡀⠀⠀⠈⡰⢃⡗⠀⠀⠀⠀⠀⠀⠀⢰⢃⢄⠀⡇
⠀⠀⠈⠒⠾⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠐⠄⠀⡄⣬⠊⡐
⠀⠀⠀⠀⠘⠲⠤⠴⠔⠁⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⡀⠀⡀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠐⠄⠳⣅⢁⠀⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠈⠀⠀⠘⠀⠁⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠐⣂⣤⠀⢀⡀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠸⠈⠆⢀⡇⠀⠂
⠀⠀⠀⠘⠄⣠⢉⠃⠸⠂⠀⠀⠑⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⣆⠑⠄
⠀⠀⠀⢎⠂⠢⠠⠄⡍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠸⡄⡠⠒⠶⡄
⠀⠀⠀⠈⠀⠍⣐⣐⢠⠁⠀⠀⠀⢄⣀⠀⢀⠄⠀⡄⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠊⠀⠄⡠⠋⠀⢄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⣀⣀⠔⠁⠀⠀⠀⠀⠤⠂⢠⠒⢢⠀⠀⠀⠀⠀⠀⢏⠀⠐⠁⠡⠁
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠃⠄
⠀⠀⠀⠀⠀⠰⠀⠋⠉⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀
⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡾⠋⠭⣙⢇⠀⠀⠀⠀⠀⢀⠄⠤⠤⠠⣄⡀⠀⠀⡐⠁⠀⠁
⠀⠀⠀⠈⠠⡁⠀⣀⢀⠄⣒⠞⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⡻⠀⠀⠀⠀⠀⠀⢄⠠⠀⠀⠀⢹⡄⢸
⠀⠀⠀⠀⠀⠊⠶⠶⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠜⠁⠘⠦⠴⠊

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣀⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠔⠉⠲⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠐⠉⠑⠦⡀⠀⠀⠐⠤⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠶⠒⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⡄
⠀⠀⡠⠚⠉⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠁
⠀⡔⠁⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠉⠉⠓⢄
⣸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡀⠀⠀⠈⠀⠀⠱⡀
⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⢡
⠃⠀⠀⠀⠀⠀⠑⠲⢤⡀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⣠⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡘
⠈⢣⡀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠙⠒⠶⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠖⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣤⠴⠚⠉⠁⠈⠢⡀⠀⠀⠞⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠤⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⢀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠠⠶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠈⢠⡄⠘⠒⡄⠇⠙⢺⣚⠡⣠⣇⠆⠀⢸⠀⡇⢇⡸⠀⠐⠠⢙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠀⠄⠀⠗⠂⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡈⠀⠄⠀⠐⠂⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠄⠀⠒⠀⠈⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢒⠀⠠⠌⠉⠁⠒⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠱⠆⠚⠉⠁⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣁⠀⠠⡀⠀⠔⠀⠀⠀⠔⠁⣀⡼⠁⠀⠀⠀⠀⡀⢀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣖⠀⠀⠀⠀⡀⠀⠀⣁⣠⠜⠉⠀⠀⠀⢀⠔⠺⠀⠛⠀⠉⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠲⠖⠒⠊⠉⠀⠀⠀⠀⠀⣰⠛⠀⠀⡔⢁⡀⠀⠴⢊⡤⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠃⠘⢀⠄⠀⠈⢰⣯⠴⠁⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠑⠘⠅⠀⠀⠈⢀⠀⡀⠊⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⡜⢠⡀⠀⠀⠀⠀⠀⠀⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠒⢠⠐⠀⠰⠖⠂
⠀⠀⠀⠀⠀⢤⡀⢀⡀⢠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠄⠤⠍⠉
⠀⠀⠀⠀⠘⠈⣧⣸⣇⡘⢰⢲⡄⣿⢰⡖⣦⢰⡄⡦⢸⡇
⠀⠀⠀⠀⠀⠀⠙⠃⠛⠁⠻⠘⠃⠛⠘⠃⠏⠘⠓⠛⠘⠃


⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠋⠀⡈⢿⣄
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠃⠀⠀⡇⢸⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣤⣀⡠⢤⣀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠀⣷⠀⠁⠈⣿⡄⠹⡀⠀⠀⠀⠀⠀⢀⣾⡿⣋⠀⠤⠴⣦⡀⠉⠉⠓⢶⣭⣂
⠀⠀⠀⠀⢿⣿⣇⢻⣿⡿⣄⠘⢧⡀⠀⠘⢷⣄⠀⠁⠀⠀⢀⣀⣿⣿⡆⠻⠤⣄⠀⠀⠉⠁⠀⠀⠀⣙⠻⣷⡐⡀
⠀⠀⠀⠀⠸⣿⡿⣆⠻⡷⣝⡲⣄⠁⠀⠀⠀⠉⠓⠶⠾⠯⠽⣿⣿⣿⣝⣶⣶⡤⢅⡀⠀⠀⠀⠀⠀⠈⢳⡈⢻⣜⣆
⠀⠀⠀⠀⠀⠹⣿⣝⢦⡈⠻⣿⣿⣷⣶⣶⡶⣶⣦⣄⠀⠒⠄⠸⣿⣿⣿⣿⣿⣟⡿⢶⣄⠀⠀⠀⠀⠀⠀⠱⡀⠹⣎⢦
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠛⣩⣅⣴⠶⠂⠈⣿⣷⣀⣀⠀⠙⠿⣿⣿⣿⣿⣷⣒⡬⣷⣄⠀⠀⠀⠀⢀⠓⢣⢻⣌
⠀⠀⠀⠀⠀⣠⣴⡿⢟⠋⣁⣴⣻⣵⠏⢀⡄⣰⢠⣿⣿⠙⠛⠿⣷⣦⣾⢿⠏⠉⠉⠉⠛⢿⣿⣧⠀⡀⠀⠀⢧⠸⠈⣿⡄
⠀⠀⠀⣠⣾⠟⣫⠾⣿⣿⣿⣿⠟⢁⠔⠋⠰⢣⣿⣿⡿⠀⠓⠦⣄⠙⢿⣎⠀⠀⠀⠰⣔⠀⠙⣿⣇⢹⠀⠀⠸⠂⠀⢿⡇
⠀⢀⣾⣿⣷⢟⣷⣿⡿⠟⢉⡄⠀⠀⠀⡀⠀⣾⣿⣿⡏⢰⡀⠀⠉⠁⠈⢿⣆⠀⠀⠀⠸⠀⠀⣿⣿⠠⣦⣤⢦⡆⠀⣸⣷
⢀⣾⣿⢿⣷⣿⣿⣁⢄⡼⠋⢀⡄⠀⡴⠁⣼⣿⣿⣿⢿⡄⢳⡄⠀⣆⠹⠌⣿⡆⠀⠀⠀⠀⠀⣿⣿⡳⣌⣛⣋⣠⠞⣿⡟
⢸⣿⣯⣿⣿⢟⡵⡵⠋⠀⣰⠋⢀⡾⠁⣼⣿⣿⣿⣿⣄⠹⣦⠻⣄⠙⣄⠀⢸⣿⡀⠀⠀⠀⠀⠹⣷⣝⣛⣒⣫⣤⣾⡿⠁
⢘⣿⣿⣿⠏⣾⠞⣁⠄⠀⠀⣴⡟⢡⣾⣿⣿⣿⣿⣟⢯⡳⣌⢳⡝⠧⠙⣦⡀⣿⣇⠀⠀⠀⠀⠀⠈⠙⠛⢛⣛⡛⠉
⠘⣯⣿⣿⡈⢁⠞⠁⣠⣴⡾⢋⣴⣿⠃⠈⢿⣿⣟⢮⡳⡙⢿⢦⡹⣦⠀⠘⣷⣿⣿
⠀⠈⠙⠻⢷⣬⣹⣿⣿⣿⠾⠛⠉⠀⠀⠀⠀⠙⠻⣷⣽⣺⣄⠁⠑⠝⢷⣵⣦⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣖⣛⡿⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣶⣾⣿⣿⣿⠟⠉⠀⠀⠀⣠⣴⣿⣿⢿⡿⠉⠀⣀⣤⣴⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⣿⠿⢷⣄⠀⣀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢀⣼⣿⢕⡫⠊⢁⣠⣶⣟⡿⠿⠟⠒⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⠍⠀⢀⣾⡏⣼⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣾⣿⡷⠋⣠⣴⡟⢹⣿⣁⣠⣴⠾⠛⠉⠉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣥⣤⣶⠿⠋⠀⣿⣿⣥⢹⣷⠀⠀⠀⠀⠀⠀⣿⣿⣎⣾⣿⢋⣤⣾⠿⡋⢉⡤⠖⠉⠀⣡⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⣀⡀⠀⢻⣟⣟⣆⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⢋⠴⣫⢞⡭⢂⡴⣠⠞⣡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⣿⣆⠀⠹⢿⡿⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣵⢐⡵⣫⠖⣉⣤⡴⣞⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣻⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠷⢯⣿⣥⣤⣽⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣙⠃⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡟⠈
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿