Broccoli Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠖⠐⠢⠄⣠⠔⡲⠂⠟⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠁⠀⠀⠀⠀⠀⠿⠈⠀⠀⠀⠀⠀⠀⠙⢆⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠼⠀⣄⠄⠀⠀⠀⠀⠀⠀⠀⠁⣂⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠉⠒⠄
⠀⠀⢀⡴⠚⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣀⣄⡢⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⠎⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠢⣀⢀⡠⠠⠠⣀⣀⡴⠞⠧⡀
⠀⢸⠂⡐⠤⠀⠁⠀⠀⠀⣝⡠⠤⣤⣦⡴⠴⣤⣯⠂⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⡃⠀⠀⠙
⡰⠋⠁⢀⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢱⡎
⡯⠀⠀⠈⡀⠀⠀⡀⠤⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⡆⠀⠀⠀⣠⣜⣡⠋⠀⠀⠀⠉⠉⠛⠀⠀⠃⣴
⠑⣢⠔⠒⠉⡐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡄⠠⢀⡽⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠑⢤⠵⠊⠈
⠸⡄⠀⡀⠀⣄⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⣀⢈⢂⡤⠞⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡎⣠⠏
⠀⠸⢤⣀⣨⣇⠀⠀⠀⠀⠀⢀⣏⠀⢀⣤⣩⠟⠉⣷⣄⣤⣂⣀⣴⣦⣀⡀⠀⣀⣀⣂⡡⠎⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠈⠓⠦⣤⠤⠟⠙⣪⡹⠯⠁⠙⣧⠀⢹⡇⠙⣇⠀⠘⡟⠈⢙⡷⠖⡶⠏⠀⠀⣀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⠦⡤⠾⡆⠘⡄⠈⡇⠀⠸⠀⠀⡇⡾⢭⠴⠞⠁⠈⠓⠦⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠠⢀⣧⠀⠀⡄⠀⠁⠀⣎⡴⠔⡲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⠇⠈⠀⠈⠁⠘⠀⠀⠁⠀⠀⢠⠟⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⣨⠻⡀⢱⠀⠀⠀⠀⠀⠀⠀⠠⣠⠆⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣨⠁⢸⠁⠘⡀⠀⠀⠀⠀⠟⠁⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡔⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠊⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⠀⠀⡄⠀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⢶⡴⠒⠛⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠀⠀⠀⢸⡀⢀⡀⠀⣸⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠉⠀⠀⢀⠀⠈⠀⠀⠀⠈⠉⠉⠀⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⡠⠜⠡⣾⠑⣶⡦⢆⠀⣤⠞⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠏⠸⢋⣠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠋⠀⠀⡤⠀⠀⠀⠀⢀⠴⠊⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠔⠀⠰⠈⠀⠀⣐⠐⠀⠋⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⡀⠐⣀⠀⠀⠈⢧⠰⡌⠳⣖⠉⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠧⠂⠈⠙⠁⣆⣀⣉⣉⠁⠀⠀⠛⠀⠀⠇⠀⣿⡟⠉⠀⡊⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠘⣦⣴⣄⠀⠀⠨⠿⡏⣡⡞⠠⠁⠀⠀⢀⣠⠉⠁⠀⠀⡘⠉⢲⡴⠏
⠀⠀⠀⠀⠀⠀⠀⢏⡀⠀⠹⠀⣀⠀⠙⠉⡄⠠⢄⠀⠀⠄⢻⠀⠀⣠⠁⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⣀⣠⠋⠈⠑⠀⠀⠀⠀⠱⡀⠐⠬⠧⣀⡿⠶⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣀⢀⡠⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠒⡂⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⡔⠁⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠋⠉⢰⠁⠀⠀⠀⠘⠲⣀⠀⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠒⠉⠀⠁⠐⠉⠑⠢⠀⠈⣄⣀⣠⣿⠀⡀⠘⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠁⠀⠒⠀⠀⠀⠀⠀⢘⠦⣔⢈⡇⡼⣿⠉⠑⢠⠀⠀⠀⠊⠑⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⢘⠄⠀⡈⠀⠀⠀⠀⠀⠀⣤⠶⡍⢷⡀⠱⡝⠃⠉⡁⠀⢰⠃⠀⣠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠇⡐⠀⠱⢄⠀⠐⠀⠀⠀⡈⢠⠙⡌⢿⡄⢡⠀⢰⠁⢀⠜⣠⠖⡽⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠀⢹⡀⠀⢀⠜⠫⡝⠂⢆⠐⠈⢇⢈⠀⢋⡿⠃⡔⠁⠀⠉⠈⡄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠉⢁⡤⠀⠈⢦⠘⡄⠀⠘⠸⠀⠘⢀⠎⢀⠔⠀⢄⠀⠀⠀⠀⠠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠒⠒⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠁⠁⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⠀⠀⠖⠋⠂
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢤⡀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄
⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡸⠶⠲⡶⠶⠒⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠠⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⢼⡗⢠⡀⠀⠀⠃⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠚⠁⡤⢇⠀⠀⠀⠀⠈⠂⠀⡀
⠀⠀⡰⢠⠐⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠨⠒⠀⡀⠀⠀⠀⠀⠘
⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠾⠞⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠓⠀⠀⡶⠦⠀⠀⠉⠡⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⣀⠳⠀⠠⠀⠀⠀⠀⠀⠀⢾⠀⠀⠔⠈⠀⠂⠀⠀⣶⠋⠙⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⠠⠄⠉⢠⡀⠀⠀⠀⢀⡤⢌⣁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣀⠤⠒⠂⠀⠨⣆⠈⠀⡆⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠞⠁⠀⠀⠀⠀⠘⠢⠐⢆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⡀⡀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠠⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⡹⠛⠉⠉⠁⠉⠝⠋⠀⠀⠀⠈⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡌⠀⠀⠀⠀⡠⠊⠁⠀⠀⠉⠐⢄⠀⠀⠙⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠒⠚⠓⠐⢠⠔⠂⠉⠁⠲⡀⣀⡀⡀⣀⠇⠀⡰⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⣤⡇⠀⠀⠀⢀⡤⠋⠝⠋⠟⢩⣉⢯⠀⠀⠀⡸⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡴⠡⢐⠑⠰⡖⠺⡻⠐⡀⠀⠀⠀⠋⣀⣫⣤⡄⠒⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢾⠀⠀⠄⣀⠀⠈⠀⡘⠄⠐⠆⠀⠀⠀⠁⠈⠰⠹⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⡟⠙⢄⡤⠐⠚⢦⣉⠁⠀⣀⠀⠀⠈⠚⠄⠈⠢⡀⠀⢱⠁⠀⢾⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠸⡇⢀⠊⠀⠀⠀⠀⣱⠠⠤⠤⠀⠘⠒⠠⢀⠀⠀⠈⠂⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⡷⠘⠀⠀⠀⠀⢀⠇⣉⠀⠒⠀⠀⠀⠐⠂⠁⠂⠀⠀⠀⠀⠀⠀⠘⠢⣄⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠡⣄⡠⠠⢯⠁⠀⡀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⡁⠀⠀⢹⡀⠀⠖⠒⠀⣀⠠⠀⢤⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠱⣀⠀⠀⠳⠤⠯⠴⣁⠀⣠⡴⠏⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣅⣼⣥⣀⣀⣴⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠙⠾⣏⣉⡙⠲⣤⡤⠖⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠚⣁⣀⣀⣤⣤⡀⠀⠀⠀⠙⢦⠀⠀⠔⠲⠤⡄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⡾⠉⠉⠋⠀⠀⠹⢤⡀⠀⠀⢸⣀⠀⠀⠀⠀⠈⠀⠘⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢳⣀⣤⣤⣀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⣀⣀⣹⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠉⠳⢤⠴⠶⢧⡀
⠀⠀⠀⠀⢠⠞⠉⡼⠃⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⠴⢤⡀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢸⡀⢸⡇⠀⠀⠀⢀⡴⠾⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠃⠀⠈⠉⢳⡄⠀⠘⣧⡀
⠀⠀⠀⠀⠀⡷⠈⠳⣄⣀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣼⠁⠀⠀⠈⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⢧⡀⠀⢀⣀⡴⠒⠲⡦⠤⢶⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠁
⠀⠀⠀⠀⠀⠳⢤⣀⣀⣀⡀⠀⠉⠉⢉⣥⣤⡤⣾⡇⠀⠀⢷⣄⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣤⠞⠙⢦⡀⠈⠃⠀⠀⠘⠃⠉⠉⡟⠙⢦⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠉⠁⠉⠂⢤⡠⣀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠙⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠄⠒⠊⠑⠂⠒⠊⠉⠙⠂⠀⠐⣄⠀⠀⠀⠀⠘⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⢢⠀⠀⠀⠀⠀⠀⢬⣀
⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠰⣀⠀⠀⣀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠋⠑⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠞⠁⠈⠉⠉⠑⠒⠀⠢⠄⢄⢀⡅
⠀⠀⡠⠄⠀⠀⠀⠀⠀⡴⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄
⠀⡈⠁⠀⠀⠀⠀⠠⠜⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠛⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠏⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠈⠛⠤⣄⣀⡀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⡄⠀⠀⠀⠀⠀⠀⠀⡸⠘⠑⠀⠀⠀⠀⠀⠀⠾⡌⠲⡒⠀⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⢄
⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⠀⠘⢦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢶⡀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⠀⠸
⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠒⠒⠁⠈⢦⠀⠀⠙⡇⠀⠀⠤⠀⠀⠀⠀⠀⣀⠔⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠉⠲⠤⡀⠀⠀⠀⠀⡤⠃⠀⠑⣄⠀⠀⠈⢣⡀⠀⢷⠀⠀⠀⠙⠖⠒⠴⠒⣁⡤⢲⠀⢳⡀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⡔⠚
⠀⠀⠀⠀⠀⠈⠣⠦⠜⠊⠀⠀⠀⠀⠈⢦⠀⠀⠀⠱⡀⢸⠀⠀⠀⠀⠅⡠⠛⠉⣠⡰⠃⠀⡔⡹⠓⣤⠶⠖⠉⠒⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠹⣼⠀⠐⠀⠀⢰⠁⠀⣰⠃⠁⠀⢨⠞⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⡀⢹⡆⠀⠇⠀⢨⠀⠀⠈⢀⠀⠀⠏⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠸⡌⡇⠀⠀⠀⠘⣀⠀⠀⠌⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢣⡇⠀⠀⠀⡀⡷⠄⠊⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⡇⠀⠀⡈⠉⡀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⡇⠸⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⣀⣀⣀⡀⠀⠀⠀⠀⢻⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⣵⢂⣀⢀⣶⣀⣶⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠈⠀⠻⡿⠛⠉⠉⠉⠛⠛⠂⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣰⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠤⠠⢒⡒⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⣴⠾⠋⠀⠀⠀⠀⠀⠀⠠⠀⣠⢀⡼⠄⢁⢀⡈⠀⡀⠀⠀⠀⠀⠠⠀⠀⢫⡴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢘⣷⠟⠀⠀⠀⠀⠀⠀⠀⠲⠀⢥⣼⣻⣷⡼⢨⣜⠷⡞⠧⣠⠀⢀⣤⠀⠀⠀⠈⠷⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡙⠉⠠⠀⠀⡀⠳⡤⢶⣄⣆⣩⣴⣾⣻⣾⣿⣾⣿⣧⢹⣏⣿⣬⣻⣯⢿⣁⣄⣳⣄⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠀⢀⠆⠀⠀⠀⠶⠀⣴⠆⠀⡀⡉⣁⢶⣶⣿⣯⠿⣷⣿⣿⣿⡰⢹⠋⠋⣽⡟⣾⣷⣿⣬⣿⣹⣧⢾⣿⣛⠈⢃⣴⡀⣰⠄⡀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠀⢾⣫⡀⠠⣽⣩⣏⣸⣷⡟⢾⣏⣯⡕⠛⠃⠉⠀⢠⡏⠈⣞⢻⠛⣾⡟⣷⣶⣦⣼⠟⣧⣾⣯⣿⣥⠖⢡⡄⢥⢲⣄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢠⣖⣤⣶⢿⡿⣧⠐⡾⢧⡾⠯⣞⣹⡿⠇⠹⣷⠐⠀⠀⠀⠸⠁⢠⠛⠲⢶⣿⣷⣿⣿⣹⣿⣏⣿⣶⡟⢳⣿⣻⣾⡝⠶⣦⠘⣦⠠⠾⠃
⠀⠀⠀⠃⠀⣀⡄⡤⠞⣥⣻⠞⣿⡿⣄⣿⣯⠻⢻⣿⣷⣄⠀⠀⢻⣇⠀⠀⠈⠁⠀⡿⠀⠀⢸⣿⢠⡿⣾⠇⣽⣷⣿⣿⡟⢻⣿⣷⣤⡶⣶⡛⣲⣯⣗⡎
⠀⠀⠀⡇⠀⠀⣀⡧⣺⣾⡽⣏⡀⠻⣟⠛⠻⢿⣇⠀⠹⣿⣇⠀⠈⠁⠀⠀⠀⠀⢰⡇⠀⠀⠈⣿⡿⠸⢟⡴⢳⠟⠟⣹⣿⣿⣯⣿⡟⣶⣾⣻⡟⠙⠋
⠀⠀⠀⠙⠀⡀⠰⣤⠇⢿⣵⡏⠀⠀⠙⠀⠀⠀⠙⢆⠀⠘⡟⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠃⠔⠉⠀⠀⠀⠀⠽⡷⣿⣏⣼⡿⠷⠋⠉
⠀⠀⠀⠀⠀⠈⠓⠛⠃⢘⣧⡀⠾⠿⠶⣄⠀⠀⠀⠀⠣⡀⠙⠻⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠣⠉⢡⢦⣾⡿⠁⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡾⠁⠀⠀⠀⠀⠀⠀⢠⣿⣴⠶⠿⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣌⣷⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⣠⣶⣯⣤⡀⠈⠻⣿⣦⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠛⠛⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠟⠉⠁⠀⠈⠢⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⡟⠀⠀⠀⠀⠀⠀⠇⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠛⣧⠀⠀⠀⠀⠀⠀⠀⠄⠈⠳⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠌⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠿⠷⠖⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠶⠤⠢⢤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠁⠀⠀⠀⠀⠀⠀⠐⢳⣀⣠⠖⠆⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠉⠋⢟⡀⠀⠀⠀⠀⠀⠀⠈⢠⡯⠁⠁⠐⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠁⠀⠈⠄⠀⢸⣄⡄⡐⠀⠀⢀⣀⣀⣿⠃⠀⠀⠀⠀⠈⠀⠄⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠁⠀⠀⠀⠘⠴⣖⣶⠲⠋⠁⠀⡀⠛⣶⣠⠀⠀⠀⠀⠀⣰⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠁⠀⠀⠀⠀⣻⠀⠀⠀⡠⠀⠀⠄⠀⠈⠳⢄⢀⡀⡼⠃⠀⠀⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣁⡥⠦⣄⣼⣋⣰⡧⡄⠀⠀⢀⠀⠀⠀⠀⡀⠀⢺⡉⠁⠀⠀⠀⠐⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⠀⠈⣧⣦⣄⠀⠄⠀⠀⠀⠀⠀⢰⣟⣀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢠⠫⠀⢻⣤⡾⠄⠀⠀⣁⣀⠞⠉⠙⠒⢮⡡⢤⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡼⠀⠀⠀⠀⡿⠋⠙⠶⣦⢿⣞⣉⠀⠀⠐⠂⠀⠁⠀⠋⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⣼⠷⢀⠇⠀⠈⠀⠀⠰⠺⠧⢾⣨⠀⠀⠀⠀⠀⠀⠈⢀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠟⣄⠀⠀⠀⠀⠀⠀⣀⣠⣅⣠⣬⣿⠀⢀⡀⠀⠀⠀⠀⠂⣈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡼⠁⠀⠀⠁⠀⠀⣀⣀⣴⣿⠉⠁⠀⠀⠀⠈⢻⡙⠖⠀⠀⠂⢈⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣧⠞⠀⠀⢀⡠⣴⢂⢾⣀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⠼⠬⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢻⡀⡴⠋⠉⠳⡥⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠈⠚⠇⠀⠀⢰⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠸⡆⠀⢀⣀⣄⣁⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡎⠐⠋⠀⢲⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠃⠠⡀⢰⢠⢀⣠⠀⡄⠀⡄⣄⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠈⠈⠈⠉⠀⠁⠈⠀⠈⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠔⠍⢏⠕⠉⡰⠐⠠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣭⣿⣣⣥⣎⡤⣆⣏⠙⠧⣠⣌⢻⣯⣍⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣽⣛⠟⢿⣿⣿⣿⡿⣬⣧⣼⣷⡾⢶⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢻⣾⣶⣷⣿⡾⢙⣿⣿⣮⣻⣛⣿⣾⣿⣿⣯⣿⣿⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡟⠊⡍⣝⣿⢿⣿⣽⣿⣧⣽⣿⣿⣷⣯⡟⢿⣿⣿⣿⣿⣿⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡮⡑⠎⣾⣿⣿⣿⡿⣿⠋⢹⢿⡹⠉⢫⠄⠀⠛⢿⣿⣿⡿⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣢⣿⣿⣿⣿⡛⠀⠀⠈⠀⠁⢠⠿⣼⡆⠀⢣⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠧⢛⣿⣿⣿⡏⠂⠀⠹⢦⠀⠀⠀⠀⠈⡰⠿⠃⡠⢾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⣴⡚⣻⣿⣿⠉⠀⠀⠀⠀⢣⠀⠀⠀⠀⠃⠀⢸⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣴⣿⣿⡿⠃⠐⠘⢿⣧⢀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣴⣀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡄⠀⠀⠀⠀⠀⠈⡆⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⢁⠼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⡀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉

⣀⣀⣀⣀⣀
⣿⣿⢿⣿⡟
⠷⠿⠾⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣯⠞⠛⣶⣏⣽⡂⠄⠳⠃⠉⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣥⣾⣿⣿⣿⢿⣭⡀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⣿⣿⣍⣁⣤⣻⠿⠛⠏⠰⣇⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⡟⢸⣿⠻⣿⢿⣿⣿⣦⣃⡀⠀⢈⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢼⠃⢰⠃⠞⠉⣙⣿⡿⠷⠓⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢫⠆⡠⠂⢠⠀⠀⠐⠛⠛⠻⣷⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⣀⠔⠀⠄⠁⠀⣤⠄⠀⠀⠀⠹⣶⣷⣄⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡁⠀⠀⠀⠀⠀⣀⢠⣤⣶⣾⡿⣿⣿⡇⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡀⠀⢠⣾⠿⠟⠋⠉⢉⣀⢀⣰⣿⠋⠂⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠳⡀⠀⠀⠀⠀⠀⠀⢻⣿⣙⣿⣏⠀⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠀⠀⠀⠉⠉⠙⠻⣶⡶⠟⠋⠉⠁⠀⠀⠈⠉⠉⠛⠻⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⢶⣦⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠀⠀⠈⣿⡀
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⣸⡇
⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⣿⠳⢤⣄⣀⣀⣀⣠⡴⠖⠀⠀⠀⠀⠀⢶⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠙⣟⠛⠒⠚⠋⢹⡇⠀⠀⠀⢰⠇⠀⡴⠋⣿⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠹⡄⠀⠀⠀⠘⡇⠀⠀⣠⠏⢀⡾⠁⠀⢹⡴⠋⢹⣤⣀⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣤⣾⡁⠀⠀⠀⢿⠀⠀⠀⠀⠻⣤⡴⠃⠀⡼⠀⣀⡴⠋⢠⡖⠋⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠉⠙⠉⣻⣤⡀⠙⢦⡀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡷⠚⠁⠀⣴⡟⠻⣦⣄⡀⠀⢀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣀⣤⣴⠾⠋⠙⢿⣄⠀⠙⠲⣄⡇⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⣼⠏⠀⠀⠀⠉⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠹⣧⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣴⠀⢀⠀⠀⠀⠀⠀⣤⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢆⠀⠀⠀⠁⠀⠈⠀⠀⢉⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢠⠂⠐⠒⢠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⢀⠀⠀⠈⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠌⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠄⠒⠒⠀⠀⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣤⣄⣀⣀⣤⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠉⠀⠀⠀⡄⠘⠋⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⣿⠟⠉⣨⣾⣿⣿⡿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠄⠀⠀⠆⠀⠄⠀⠀⠀⣈⠤⠂⠀⠘⣆⡀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠿⣿⣿⣶⣾⣏⣩⣿⣿⡷⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠋⡄⠀⠀⠀⠀⡀⠀⠂⠀⠉⠀⠀⠀⠀⠠⠀⠀⢻⡄⠀⠀⠀⠀⣾⣿⠘⢿⣿⣿⣿⣷⣿⣷⣿⣿⢩⣶⣭⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣸⠈⢣⡀⠠⠛⡰⣮⣥⢤⣉⠀⠀⠀⠀⠀⠁⠀⠀⡝⢺⠀⠀⠀⢸⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡧⢼⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠇⠀⠘⢋⠤⣴⠣⡘⠋⢿⣿⠉⡶⢆⣐⣦⣿⣤⣾⣧⠞⠀⠀⠀⢸⣽⣿⣿⣿⣿⠻⣟⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠘⠲⢘⣧⡀⠹⣧⠙⡄⢸⡇⠀⣷⠀⢹⡟⠛⠉⠈⠁⠀⠀⠀⠀⠘⠻⢿⣿⣝⣿⣷⡘⣿⣿⣿⢻⣿⡾⣿⡟⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠘⣧⣳⠀⡇⠀⠇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣷⣹⣼⣿⣿⣿⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⡿⠀⢀⡆⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⣿⣧⣿⣿⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⠊⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣿⣿⣿⣇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠠⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡌⠉⣿⡟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠁⠀⠄⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣠⣿⢁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⢤⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣖⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠄⠼⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠒⠶⠒⠒⠒⣋⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡰⠟⠈⣀⡤⠤⠶⠿⠋⠁⠈⠙⢿⣿⠟⠃⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⣠⡋⠀⣠⣼⠿⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠆
⠀⠀⠀⢀⣼⠟⠛⢛⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣤⣀⢠⡶⢶⣾⠆⣶⠈⣡⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢴⡟⠀⠀⠀⠀⠀⠀⠀⢀⣄⣇⡼⣿⣿⣿⠀⠁⠈⠁⢢⠿⠿⠿⠟⠃
⠀⠀⡠⠀⠀⠀⢴⣶⣿⣀⣀⠀⠀⠀⣴⣾⠁⢹⡇⣾⣿⣿⠋⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡿⠟⠿⠶⢟⠻⠆⠀⠃⠹⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣤⣴⠞⠛⠉⠉⠙⠙⠷⣦⣀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣶⣶⣤⣤⣤⣶⣿⣿⡏
⠀⠀⠀⡄⠀⣶⣿⣧⣤⠄⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠋⠁⠈⠉⠛⠻⠿⢿⣦⡀
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠐⢊⠙⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢀⣀⣄⢀⣼⣿⠆⠃⡤⠀⠀⠀⠀⠀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠄⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣧⡀⢀⣴⢶⡎⠉⢿⠋⢹⣿⣿⢎⣀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠿⣅⠀⠁⠀⠀⢀⣿⡇⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⢠⣧⣤⣶⠶⠿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠛⢧⡈⠀⠀⠈⠻⠿⠃⠉⠝⠡⣄⣄⢀⣀⠀⠀⡿⠋⣛⢿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⢁⡀⠀⠀⠀⠂⢀⠀⠀⠀⠀⢀⣾⡿⢶⡾⠀⠈⠁⢘⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣿⡀⣿⣧⠀⠀⠀⠀⠁⠀⠀⠀⢠⡿⠁⡴⠋⠀⠀⣠⡀⠛⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⡰⠏⠛⠀⠀⠀⠀⠀⠈⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠅⠁⠀⠀⠠⣿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣡⢆⡔⣦⡴⢠⢆⡔⣦⣼⢃⡅⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⠉⠀⠉⠀⠉⠈⠁⠉⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠛⠆⡿⠤⠀⠈⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠛⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠖⠲⠢⣀⣀⣠⠦⠖⠊⠟⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠀⠀⠀⠀⣀⠀⢸⠃⠋⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⠀⠀⠄⠂⠀⠀⠀⠀⠀⠈⠐⢀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠚⠙⠛⠉⠉⠙⠲⢄⡀
⠀⠀⠀⠀⠀⣀⣤⡤⠞⠉⠁⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⢀⠀⣨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢆
⠀⠀⠀⡴⠋⠁⡔⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⠀⠠⠶⠤⠫⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢺⡀
⠀⠀⡼⠁⠀⠀⠁⠀⡀⢠⠬⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⣀⠤⠤⠠⣅⣀⣤⠶⠛⠳⣄
⠀⢸⠧⠀⢢⠀⠄⠃⠀⠀⠀⠀⡽⢠⣄⣀⣰⣤⣰⣥⣦⢼⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡃⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⣧
⢀⡞⠓⠈⠐⠂⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠈⠈⠀⠀⠉⠉⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡏⠀⠀⠀⠀⠀⠘⢤⡇⠀⠀⠀⣻
⡿⠀⠀⠀⠺⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢤⡀⠀⠀⠀⠀⠀⢠⠖⡰⠃⠀⠀⠠⠤⠶⠯⠏⠀⠀⡄⢀⣿
⢟⣀⠀⣀⢈⡄⢀⣴⠐⠈⠋⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢧⢄⣄⡤⠴⠿⠵⠚⠁⠀⠀⠀⠀⠀⠀⠨⠀⠠⠔⣡⠿⣄
⢀⡽⠛⠉⠀⢀⠌⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⢀⠜⠀⠘⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡝⠶⠚⠁⠀⢸
⠘⢆⠀⣀⠀⠀⣦⠂⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠠⣀⣁⡜⣠⠶⢋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢥⢠⠞⠀⠀⠀⠀⠀⢨
⠀⠘⠤⣀⡀⣨⣇⠁⠀⠀⠀⠀⠀⠌⣾⠀⠀⣁⣀⣩⡽⠋⢹⣷⣆⣄⣂⣀⣠⣴⣆⡀⡀⠀⢀⣀⣀⠂⣁⠞⠁⠀⠀⠀⣀⠀⣼
⠀⠀⠀⠈⠉⠉⠈⠲⣤⣄⣀⣈⡟⠛⢍⠓⢶⡚⠉⠻⣧⠀⠀⣿⠈⠙⣯⠉⠁⢹⡟⠙⠛⢶⣦⠤⣶⡏⠁⠀⠀⠐⠀⢈⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⡞⣉⡁⢀⣤⡄⠘⡆⠀⢹⡄⠀⢹⡀⠀⢸⠇⣠⠖⢛⣀⡼⠁⠱⢄⣀⣨⣥⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡏⠈⢧⠀⠙⠀⠈⡇⠀⠀⡁⠀⢸⠐⠋⢙⠋⠀⠀⣀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠸⡄⠀⣂⠴⢇⠀⠀⡇⠀⠈⠀⠀⢮⡜⠙⣩⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣒⣢⠇⠀⠀⠀⢁⠀⠘⠀⠀⠀⠀⠀⠀⢠⠏⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⢁⡟⢧⠈⢱⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⣰⠆⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢘⡏⠀⡞⠀⢸⡀⠀⠀⠀⠀⠀⡿⠂⠒⠉⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⢀⡴⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠞⠠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⡀⠀⠀⠀⠀⣶⠀⣀⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠈⠉⠉⠉⠒⣄⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⣀⡀
⠀⠀⠀⠀⢀⣀⣀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠑⠦⡀
⠀⠀⢠⠞⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⡞⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠈⠀⠀⠀⠀⠠⠄⠠⠔⠢⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄
⢇⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠳⡤⠀⠀⠀⠀⠄⠠⠐⠁⠈⢱⡾⢀⡤⠓⠢⠴⠒⢤⣄⣄⠀⠀⠀⠀⠙⡆⠀⠀⠀⠐⠢⡀
⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠣⡀⠈⡆⠀⠀⠸⡀⡀⠀⠀⠑⠖⠲⡀⢀⣣⣀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⢀
⢠⠀⠀⠀⠀⠀⠂⠀⠀⢀⡈⠀⠀⠀⠢⣐⠀⠀⠀⠇⠡⠀⠀⠀⠁⠀⠙⠁⠀⢈⠝⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏
⠀⢑⡆⠀⠀⠀⠀⠈⠉⠈⢷⡀⠀⠀⠀⠈⢂⠀⠀⢸⢰⠀⠀⢠⠀⡀⠀⠀⢠⠋⠀⠀⠐⠤⠄⠀⠀⠀⠀⠀⠀⠀⣡
⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⢦⡀⠀⠀⠀⠡⡀⠀⣿⠀⠀⠀⢠⠁⠀⢀⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⢢⡀⠀⠀⠀⠀⠈⠙⢄⠀⠀⠙⢦⡀⠀⠀⠑⡀⢿⠀⠀⡀⠂⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠁
⠀⠀⠀⠈⠙⠛⠙⡆⠀⠀⠀⠑⣄⠀⠀⠙⢄⠀⠀⠀⣸⠀⠀⣿⠀⠀⠰⠀⠀⠀⠀⠀⠀⡰⠓⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠴⠚⠉⢣⡀⠀⠈⠢⠀⠀⠹⠀⠀⠃⠀⠀⡧⢄⣀⣀⣀⡠⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠂⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢀⡇
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢀⣀⣉⣿⣤⡀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠈⠀⠢⡠⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢯⡌⠉⠙⠉⠁⠀⠀⠀⠁⣲⣄⣤⠶⠿⣷⣿⣿⣿⠃⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⣾⣿⣷⣦⣷⣄⠀⠀⠀⠀⠀⡀⠭⣽⠟⠁⠀⠀⠀⣽⡿⢿⣆⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢸⣿⣿⣻⠛⠡⠱⡄⡠⢀⢀⡤⠔⠋⠀⠀⠀⠀⡄⠛⢈⣴⣿⡇⠀⡀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⣿⣤⣤⣤⣎⠴⠐⠋⠁⠀⠀⠀⠀⠀⠀⢦⣤⣄⣸⣷⣆⣬⠾⠃⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠽⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡑⣜⣿⣿⡟⠁⣀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢜⠛⢏⡟⢠⣿⠇⣴⣾⣿⣦
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣂⣼⡷⣿⡏⡾⠛⡹⣽⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠈⠢⠀⠀⣀⡯⢙⢫⣿⡿⠁⠊⠀⠉⠁⠀⠱⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⣀⢄⡡⠘⠉⢀⣾⠟⠄⠀⠀⠀⠀⠀⠀⠀⢰
⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄⠄⠊⠏⠀⠀⣠⣿⡿⠊⠠⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡦⠏⠉⠁⠀⢠⣾⠟⠁⠄
⢼⣤⢤⢀⡄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢅⠃⠀⠀⠀⣀⣴⣿⣧⣀⠄⠀⠀⠀⠀⠔⢀⠄
⠈⢿⣷⡆⣈⡀⠀⢀⠀⠄⠀⠀⠀⠀⠈⠀⠀⡀⣄⠀⠀⡐⠘⠌⠃⠀⠈⢀⣠⣾⢿⣿⣿⣿⠟⣋⡐⠁⠀⠀⠀⣠⠔⠀⠀⠀⠂
⠀⠀⠻⣿⣿⠼⢦⡁⡄⣌⡔⠤⠈⠦⠹⠀⠗⠅⠘⣀⠃⠀⠀⠀⢀⣤⣶⠟⠋⠀⠀⠙⢿⣿⣶⢂⠏⠖⠘⠐⡀⠠⢞⠴⢀⢀⣾
⠀⠀⠀⠈⠻⢷⣤⣈⡀⠃⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣮⣼⣩⡛⣵⠠⣂⣺⣽⠟⠁
⣀⣀⣀⣀⣀⣀⣉⣙⣛⣿⣿⣿⣿⣶⣿⣿⣿⣛⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣿⣿⣿⣿⣟⣋⣁⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⣀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠉⠙⠀⠁⠀⠁⠀⠉⠈⠖⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⠙⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣨⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠂⠑⠁⠀⠁⠀⠉⠹⠦⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣀⡤⠲⠉⠁⠈⠁⠈⠀⠙⠐⠄⠀⠀⠀⠀⣀⣀⡀⣀⠀⣆
⠀⠀⠀⠀⠀⠀⡔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠀⠈⠁⠙⠢⡄
⠀⠀⠀⠀⠀⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡀
⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁
⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠈⠒⠒⠢⠴⡦⠔⠢⠔⠦⠖⠤⠛⢎⠈⢢⠰⣀⣀⢀⡀⢀⠀⢀⠀⢀⡀⢠⡤⢒⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠈⢆⠈⠄⡇⠀⠉⠉⠉⠁⠉⠁⠉⢙⠁⡠⠃⠀⠈⠑⠣⣤⢀⣀⣠⣀⡤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⢀⡀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⣿⢲⡷⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢯⣨⣀⣸⣿⣤⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠙⢿⣿⠿⣶⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣿⣿⣿⡆⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢾⠿⠿⠟⠛⣛⣛⣻⣍⣩⣿⣼⡗⡼⢀⣦⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠗⣉⣀⣀⡒⠀⠀⠀⠤⠤⣿⣿⣿⣿⣟⣡⣿⣿⡿⢟⣿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠐⠂⠉⠁⠈⠁⠀⠀⠀⠐⠚⠿⠋⠙⠋⢉⡋⠙⢛⣽⡧⠄⢀⠀⠀⢉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⢀⣼⣿⡿⠂⠀⠀⠀⣀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠁⠈⠙⠁⠀⠀⠀⠙⠲⢌⠳⣤⣙⡏⠻⣷⣄
⠀⠀⠀⠀⣰⣿⡻⠋⠀⠀⠀⠀⠊⠁⠀⠈⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠶⣌⠻⢷⣤⡀
⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢻⣷⡄
⠀⢀⣿⣏⡎⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠹⣿⡄
⠀⣾⡟⡉⠀⠂⠀⠀⠀⠀⠀⡾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠂⠻⣿⡄
⢸⣿⡏⠁⢠⠁⠀⠀⠀⠀⠌⠰⠁⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣧⠘⡆⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢰⡹⣷
⣿⣿⢿⠀⡦⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⣿⣿⣿⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⢸⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿
⣿⣿⠁⠀⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠂⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⣸⣿
⢸⣿⡜⡰⡄⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⣸⣿
⠘⣿⣿⣷⣿⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠹⣿⣿⣝⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠹⣿⡟⣎⢿⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠔⠀⡀⣿⡟
⠀⠀⠀⠙⣿⣮⢳⢿⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠠⠂⠁⢀⠄⢠⡿⠁
⠀⠀⠀⠀⠈⢿⣿⣆⢻⣷⡐⣤⣤⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⠖⡡⣪⣊⣤⠉⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣧⣹⣿⠹⣿⣷⡀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣿⡷⣡⣾⢟⣭⠟⣡⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣿⣿⣷⡘⣷⣶⣴⣅⣀⣀⣀⣀⠀⠀⡠⠄⠀⠀⠀⠀⠀⣰⡽⠖⣫⢏⣴⣯⣴⣿⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣤⣭⣝⣻⡶⠤⣤⠤⠤⠴⠤⠶⠖⠚⠒⠀⢰⣋⣴⣾⣿⣿⣟⣫⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⣝⣿⣿⣿⣿⣿⣿⡼⠿⣿⣿⣶⣶⣶⣶⣾⣷⣖⣲⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣫⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⡉⠙⠛⠛⠙⢿⡍⠉⠉⠁
⣿⣿⡿⠻⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡴⠒⠒⠋⠰⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠶⣾⣿⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢀⠀⠀⠀⠀⠀⢀⠄⠉⢣⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣯⣤⣾⠻⣿⣿⣯⣿⣿⡆
⠀⠀⠀⠀⠀⠼⠁⠈⠀⠀⠀⠀⠄⢀⠂⠉⠀⠀⠀⠈⠳⡆⠀⠀⠀⢀⣾⡟⢿⣶⣿⣿⣽⣯⣿⣿⢛⣽⣻⣿⣿⣷⡄
⠀⠀⠀⠀⢠⠐⢧⠀⠴⢦⢦⣤⢄⡁⠀⠀⠀⠀⠀⠀⢈⢻⡆⠀⠀⣸⣿⣷⣾⣿⣿⣿⣿⣿⣿⡯⢼⣾⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⠀⢘⠩⢰⡞⢌⠉⢿⡏⢱⢲⣀⣶⣧⣤⣿⡼⠁⠀⠀⣿⣿⣿⣿⣿⡻⣟⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠈⠑⠨⠶⡌⠻⡌⠆⢸⡇⢸⠆⢨⠏⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣷⡸⡿⣿⣿⣿⢿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠹⣾⠀⠃⠈⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣿⢿⣿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠇⠀⠺⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠛⢻⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠃⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣾⡇⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠦⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣵⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠖⠎⡀⠂⡂⠠⣛⡈⠹⢿⣶⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣿⣷⣮⣗⡗⣠⣅⣹⣂⣿⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣞⣽⣇⣦⣌⣿⣛⠿⣿⣿⡟⣿⢿⣌⣳⣿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠝⢓⡻⣿⣿⣿⣿⣦⣻⣿⣿⣾⣺⡿⣿⣿⣿⣿⣽⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡔⠠⡇⢿⣿⣿⣿⣿⠟⢻⣿⢻⠙⢛⠀⠹⠿⣿⣿⣿⣿⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣶⢸⣿⣿⣿⣟⠋⠁⠀⠀⠁⣠⠿⣶⠀⠘⣽⣿⣷⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⢛⣿⣿⣿⠋⠄⠈⠧⡀⠀⠀⠀⠋⡴⠟⢀⠴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⠘⣿⣿⣏⠁⢀⡀⠀⠢⠀⠀⠀⠀⠀⠀⡄⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⡿⠟⠀⠀⠻⢷⠄⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢧⠀⠀⠀⠀⠀⠸⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣌⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠁⠀⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣀⡤⠤⠄⠀⠀⠄⠄⠀⠀⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⢴⣞⣿⣩⣭⣿⣿⣭⣀⣀⣠⣤⡤⠦⠒⠶⠶⠶⠖⠤⠤⣶⣾⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣖⣚⣩⠅⢰⡾⠗⣫⡵⢛⣩⣤⣶⣾⡏⢉⣁⡄⠈⠅⠀⠀⠀⠀⡚⠀⠀⣸⠟⠁
⠀⠀⠀⠀⠀⠀⣀⡤⡔⠀⣰⡛⢋⣉⠉⠀⢿⣿⠏⢉⣽⣶⡾⠿⢟⣛⣋⣭⣥⢶⠾⠟⣩⣾⣿⣿⣿⣿⡿⣞⣋⠥⠖⠋⠉⠉⠉⠁
⠀⠀⠀⠀⡠⣢⣅⣾⣽⠦⣻⢟⣍⣁⣐⠿⠛⠋⡴⠾⢿⡽⣿⣋⣉⢩⠁⠺⣡⡤⣲⣾⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⡐⢰⣓⣈⢿⠋⣶⡸⢆⢉⣭⠿⠴⠶⠚⠃⠋⣟⠓⠶⠤⠶⠿⢮⡐⠟⢱⣿⣿⣿⣿⣿⣿⡏
⠀⠀⢰⠁⣏⣼⣿⣎⣳⣝⣇⣘⣉⢠⡋⠀⢀⠊⠀⠸⡄⠀⠏⠈⡃⣽⠈⡿⡆⣿⣿⢿⢿⣿⣿⣿
⠀⠀⠘⣠⣿⣾⣻⠁⣽⢉⢳⠀⡀⢐⠠⠀⠸⠀⣤⢓⢰⠃⠀⢰⠁⠸⢸⣬⢫⡿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⡇⠈⡟⢧⣴⢣⠫⣺⣴⡿⠛⡉⠉⠳⣄⣘⠪⠈⠂⢐⣀⣳⣱⡞⢁⣿⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢠⠄⡀
⠀⠀⠀⢙⠲⣌⢿⣇⣾⣿⣯⡞⠁⡄⢀⢤⡇⢨⠻⡛⣭⣭⠭⢍⡄⠁⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣻⠀⣹⠀⣀⠀⣀⢠⡏⡔⠁
⠀⠀⠀⠈⠀⠈⢧⠻⣿⣿⣿⣵⠘⢅⣀⢾⣀⠰⠵⡁⣢⡬⠞⣉⣴⣿⣏⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣧⣾⠙⣿⠉⣾⢣⡀
⠀⠀⠀⠸⡀⠀⠈⢦⡈⠻⠿⣏⣠⣰⡾⠾⠜⣂⣉⣥⣴⣶⣯⣿⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢉⠒⠁⠈⠀⠉⠀⠘⠔⠁
⠀⠀⠀⠀⠑⢄⠀⠀⠈⠒⠂⠬⠉⢥⣴⢚⠹⠃⣼⢈⡟⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠠⢣⡆⡄⠀⠒⠛⠀⢰⡆⣀
⠀⠀⠀⠀⠀⠀⠱⣆⢀⡤⠀⢠⠀⠮⠋⢘⠀⣾⣷⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠴⢾⠋⣿⠉⣶⢃⡏⣿⡞⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠯⣿⣤⣸⣴⣀⣾⣽⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠾⠀⠘⠆⠳⠀⠻⠚⠇⠻⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣠⠞⠋⠉⠉⠙⢲⣶⠋⠉⠉⠳⣄⡤⠖⠛⠓⢦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠉⠛⠀⠀⠀⢀⠀⠀⠇⠀⢀⡴⢦⡙⠀⠀⠀⠀⢸⠋⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠻⠀⠀⡀⠀⠀⠀⢸⡏⠙⠆⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⠀⠀⠀⠀⢠⡄⢀⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠈⣿⠁⣀⠀⠳⣄⣀⡼⠧⠴⠏⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⢀⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠈⢁⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠙⣦⡄⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⣠⠏⠀⠀⠀⠈⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢧⣀⣴⣇⠀⠀⢠⡄⠀⠀⠀⠀⠈⠦⣀⣀⠜⠉⠉⠀⠀⠀⠀⠀⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡇⠀⠀⡀⠀⠉⢀⠙⠿⠿⠟⠁⠀⠀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⣰⣤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠙⠦⠤⠞⠀⠀⠀⠀⠀⠀⠙⠻⠛⠁⠀⠀⣠⣀⣀⣠⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠶⣀⠀⠀⠀⣰⣆⠀⠀⢀⣼⠷⣤⣤⣤⡾⠋⠈⣿⠃⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡛⠉⢻⠀⠉⠛⣟⠁⠀⠀⠀⣿⠀⠀⢸⡏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢇⠀⠀⠈⣇⠀⠀⠀⡿⠀⠀⣼⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠘⡄⠀⠀⢸⡤⠤⠀⡇⢀⣼⠏⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢳⡀⠀⢸⡆⠀⠀⣿⠟⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠳⣶⣾⠇⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠁⢀⣀⣀⡀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠒⢦⠀⠀⢠⠋⠀⠀⠙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠘⠀⠀⠈⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⣀⡠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡷⢿⣿⣿⣷⣶⣶⣦⡿⠏⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠦⢾⣫⢻⡇⠸⡿⡿⠿⠻⡆⠈⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣡⣶⣶⠶⣬⣿⣿⣄⣄⠘⠛⠟⠁⢀⣼⣿⣿⣷⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡭⠙⢻⣿⣿⣿⣷⣦⣤⣴⣾⣿⣿⣿⣿⣿⣍⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣄⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡄⠀⣺⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣽⣿⣿⣷⡀⠀⠘⠻⣿⣿⣿⣿⣿⡟⣿⣮⣹⣶⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⢃⠘⠙⣿⣿⣿⣤⣤⣤⣤⡈⢉⣩⣽⣿⢸⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⠿⠗⠀⠠⠄⠛⢋⣿⣿⣿⣿⣿⣷⣿⣿⣿⣻⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣴⣯⡽⣯⣿⣿⣛⣵⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠃⢰⣿⣿⣿⣿⣿⡯⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⢸⠁⢀⣴⠟⠃⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢠⠚⢿⣿⣄⣈⣙⣿⣏⠎⠀⠀⠀⠀⠀⠈⠐⠻⢷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⡀⠀⠀⠂⠀⠐⠀⠀⠀⠀⡎⢠⣿⣿⣿⡘⠿⠿⣻⣤⣓⣶⣦⣄⡀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠘⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠟⣷⡆⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢟⠷⣿⠟⡄⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⡿⠿⠟⠛⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣅⡄⣹⠿⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⣯⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣰⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣶⡌⠁⠀⠀⠧⢀⠀⠀⡀⠀⠀⠀⠀⢼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣁⣤⣴⠖⢢⣤⣤⠀⣀⠀⠀⢤⣅⡰⢟⣷⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣯⣅⣀⠀⠀⠀⠀⣩⡏⢁⡀⠀⢠⡟⣿⣿⣿⣷⡀⠅⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠰⣶⣷⣄⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⢷⣦⠄⠀⠈⢈⣷⣄⣽⣿⣿⣿⣿⣿⣷⡀⢦⡀⠀⠀⠀⠀⠀⢸⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣄⣀⡀⣰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣎⣛⠀⠀⠀⠀⢠⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠐⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠛⠲⠶⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠉⠉⠉⠛⠛⢒⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠈⠉⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⢀⣀⣀⣠⠶⠛⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠚⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠴⢶⡟⠋⠉⠀⠀⠀⠀⠀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⢠
⠀⠀⠀⠀⠀⣼⠟⠛⠉⠁⠀⠀⠀⠀⠀⡠⠋⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⢀⡾
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢠
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢸
⠀⠀⢰⡏⠀⠀⠀⠀⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⣿
⠀⠀⣿⡴⠖⠚⠛⠚⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣀⣴⠞⠉⠀⠀⠀⠀⢰⡏
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⣀⣠⣤⠤⠶⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⣀⡴⠊⠀⠀⠀⣰⠏
⢠⡿⢶⣄⠀⠀⠀⠀⠀⠈⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡧⠶⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁⠀⠀⢀⣤⠾⠋
⣼⠃⠀⠈⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣤⠶⠋⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁
⢿⡀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠶⠶⠞⠛⠉⠁
⠈⠻⣦⣀⠀⠀⠉⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠉⠉
⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⢀⡇⠀⣀⣠⣤⠶⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠄⠠⣤⣒⡸⢗⣶⣟⣱⣶⣶⣥⣲⡦⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡝⣳⣞⣽⡶⣵⣯⣿⣿⣯⡝⠷⢡⡿⣯⣿⡿⡿⣻⣾⣿⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⣯⣭⣽⣟⣿⣛⢿⢿⣿⣼⣿⣏⣿⡷⣎⣾⣤⣭⣿⣽⣿⣏⣿⣷⣿⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢷⣂⣶⣿⣻⣿⢿⣯⣿⢿⣷⡾⣞⠹⣋⡶⣮⡿⣳⠶⣾⣽⣿⣭⣽⡿⣿⣿⣿⣻⣶⣴⡶⣶⣶⢤
⠀⠀⠀⠀⠀⠀⠀⢀⣼⢛⣿⣾⣯⣿⣷⢽⣿⣬⣟⢿⣿⢿⡧⣹⣾⣻⣿⣯⣿⣏⣿⣿⢫⣿⣹⣷⣿⣫⣻⣾⣿⡿⣿⣶⣟⣿⣷⣷⡶⡄
⠀⠀⠀⠀⠀⠀⢰⢷⣲⣿⣿⣩⣿⣿⢿⣼⣿⣻⣿⢿⣯⣹⡿⣿⢾⣧⣿⡿⢽⣷⣿⡷⠿⣽⣿⡾⠿⢯⣿⣿⠿⣷⣷⣉⣿⡵⣿⣿⣷⡷⣤⡀
⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣿⣿⣿⡷⣿⣿⣿⡽⣿⣿⣦⣼⣦⣽⢻⣿⣿⢿⡿⣿⣟⣽⣕⣻⡟⣾⣿⣿⣶⣏⣁⠿⣿⣯⡳⣿⣿⣿⣿⣿⣿⣼⡄
⠀⠀⠀⠀⠀⠀⠘⣭⣵⣶⣿⢽⣛⣿⣤⣿⣿⣻⣿⣿⢼⣿⣿⣿⣿⣟⣶⡾⣿⣿⢿⣻⣾⣿⣽⣿⡿⣿⣷⠿⣿⣗⣝⢹⣿⣟⣿⣿⣿⣿⣿⣿⣿⡷⡀
⠀⠀⠀⠀⠀⡠⣶⢯⣿⣿⣿⣿⡿⣟⠻⡟⠹⣯⢿⣷⣿⣵⡯⢮⣟⣥⡿⣿⣿⣷⣾⡿⠿⢟⣾⣿⣿⡟⢻⣿⣻⣿⡾⢦⡜⢿⣿⢿⣿⣿⣿⣟⣻⠿⢷
⠀⠀⠀⡠⣾⢻⣿⢿⡵⠛⣝⣣⣶⣽⣿⢿⣮⣿⣿⣯⣽⣿⣿⣿⣿⣼⣿⣾⣟⣿⣿⣻⣿⣿⣟⣳⣿⣛⣿⣯⣻⣿⣿⣷⣴⣼⣿⣷⡿⣮⣿⣿⣿⢿⣯⣿⢦
⠀⢠⠯⢨⣑⣿⣯⡟⡵⢷⣿⢿⣾⣿⣙⠿⣿⣿⣻⣛⡾⣿⢻⢟⣵⣿⣳⣿⣼⣷⣿⣷⣼⣿⣯⣽⣿⣿⣾⣿⣿⣿⣿⣿⡿⣻⣿⣿⢷⣿⣏⣽⣿⣟⣻⣿⣽⣳⡄
⢰⠋⢲⣾⣋⣿⣿⡇⡸⡿⣿⢟⣿⣮⣟⣳⣿⣭⣾⢫⣷⣿⣿⣿⡷⣿⣽⣿⣿⣾⣿⣽⡵⣿⡞⣻⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⡿⣾⠟⣿⣷⡹⢿⣯⣿⣾⢯⡼
⡊⣲⣽⢋⣫⣹⣿⣇⢌⣥⣾⣿⣧⣿⢿⢻⣿⣏⣿⣷⣼⢿⣿⣿⣟⣷⣿⣟⣿⣿⣿⣷⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣾⣥⣄⢤⣤⣿⣿⣿⣿⣭
⡇⣴⣟⣠⡻⣶⣿⡇⠿⣷⣼⣿⣿⣛⣮⣿⣿⣿⣯⣷⣿⣿⣿⣿⣷⠞⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿
⡏⠱⣼⣯⣽⣯⣿⡟⠛⢯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡛⢿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣥⣿⣿⣿⣿⣿⣿⣿⣿⣽⠟
⠘⢄⡘⣮⠿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣌⢿⡄⣷⣄⠻⡄⠹⣨⣿⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆
⠀⠘⣆⠬⢷⡿⢿⣿⣷⣾⣿⣿⣿⣿⣿⡿⣿⣿⣟⣳⣆⠉⢃⢹⡿⣆⠹⡀⠻⣿⠀⣿⢟⡿⠻⢿⣿⠏⠝⢁⣴⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠈⠲⣏⠋⣽⣿⣿⣿⣿⣿⣿⣿⠟⠿⠿⠍⢛⣛⢿⣓⠮⠀⢻⡿⡆⢹⠀⢹⡇⠙⣸⠃⣰⢻⡟⠀⠔⣫⢷⡾⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠕⠁
⠀⠀⠀⠀⠀⠉⠒⠪⠿⡿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠪⡷⣄⠠⡳⣜⢀⣇⠈⣇⠀⡏⡼⢁⡜⠀⡴⢫⠞⠁⠀⠀⠀⠀⠈⠻⣿⣿⠿⠿⠿⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⢳⡘⢞⠣⣿⠀⡇⢰⡽⢡⡎⢀⠞⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⡄⢧⣻⣣⡇⢈⣷⡏⠀⡞⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢳⡈⣿⣇⠀⠉⣿⠀⢸⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⣧⠸⡿⠀⠃⡏⠀⡞⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⡔⣇⠀⠀⡇⠀⠁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⣿⣟⠀⠀⣧⡚⠠⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢻⣧⠀⢰⠏⢙⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣙⣋⣭⣹⡄⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠈⠇⠀⠀⠈⣂⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡅⠀⠀⠀⠀⠀⠀⢸⡆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⠀⠀⠀⠀⣺⣧⠟
⣦⣶⣴⣶⣦⣦⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣦⣴⣴⣶⣾⣶⣶⣶⣶⣦⣤⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣤⣴
⣿⣿⣏⣀⣁⣠⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⣀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣉⣴⡾⠿⠛⠛⠉⠉⠉⠙⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡄⠘⠟⠉⣰⣿⣷⣄⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣸⡷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣉⣉⡛⠻⢿⣷⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣌⠻⣿⣷⡦⠈⣀⣤⣶⡶⠛⡷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣿⣷⣿⠟⣠⣾⣿⡇⠋⣠⣾⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠻⣿⡏⢰⣿⡿⠋⣠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣇⠸⠋⣠⣤⣤⡼⠛
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣌⣉⠉⠁⠀⠀⠀⢀⣴⣿⣿⠆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣉⣭⣭⣭⣭⣭⣭⣤⣄⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣠⣿⣿⣿⣿⠛⠛⠛⠛⠛⢛⣠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠡⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

⠀⢙⠛⠓⠀⠀⠀⠀⢠⠄⠀⠀⠀⠰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠘⣻⣿⣦⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡟
⠿⠿⠗⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠿⠛⠉
⣶⡦⠈⠀⣄⣀
⣥⡄⣾⡇⠈⠁
⠟⠃⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣶⣾⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿
⡏⣹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⣿⣀
⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘
⠀⢀⣤⣤⣤⡀⡀
⣶⣿⣿⣿⣿⣽⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣶⣆⡀
⣿⣿⣿⣽⡟⡿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣿⣯⣻⡆⠀⠉⠟⠋⠁
⣿⣿⣿⣿⣤⣿⣿⡞⣿⣿⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣤⡀⠀⠀⣚⣿⣿⣿
⣽⣿⣿⣿⢿⡿⣿⣿⣾⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣿⣿⣿⠛⢻⣿⣷⠀⠀⠈⠟⠛⠉⠀⠀⠀⠀⠀⠀⠈

⠀⢻⣿⣿⠀⠀⠀⠀⠉⠙⣿⣿⣧⠀⢰⣿⣿⠉⠉⠛⠛⠀⠘⠿⠿⠿⠟⠁⠀⣨⣿⣿⠀⠀⣿⣿⠁⢸⣿⣿⡏
⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⣼⣿⡿⠀⢹⣿⣿⣄⠀⠀⠀⠀⣠⣴⣶⣤⡀⠐⠿⠿⠟⠁⠀⠀⣿⣿⡇⠘⢿⣿⠇
⡀⠘⣿⣿⣧⣄⠀⠀⠀⢰⣿⡿⠃⠀⠈⠻⢿⣿⣷⣦⡀⠰⠿⠿⢿⣿⣿⡄⢀⣄⣀⠀⢀⣠⣿⣿⠀⠀⠀⣠⣤
⣷⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⢀⡄⠀⠀⠈⠛⣿⣿⡆⠀⠀⢸⣿⣿⠁⠈⠻⠿⠿⠿⠿⠛⠁⠀⣰⣿⡿⣿
⠏⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢿⣷⣀⠀⠀⣠⣾⣿⡏⠀⠀⢿⣿⣿⣄⣀⣤⣄⡀⠀⠀⠀⢀⠀⠙⠿⣴⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠘⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣦⣀⣤⣿⣇⠀⠘⣿⣿
⣿⣿⣷⣆⠀⣼⣿⣿⠟⠛⢿⣿⣷⡀⠀⠀⠉⣁⣀⠀⠀⢀⣠⣤⣄⡀⠉⠉⠁⠀⠙⢿⣿⡿⠛⠻⠋⠀⠀⠸⢿
⠀⣸⣿⡟⠀⣿⣿⣿⣀⢀⣼⣿⣿⠇⠀⢰⣿⣿⣿⣷⠀⠘⠛⢿⣿⣿⡄⠀⠀⠀⠀⢀⣀
⣰⣿⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣠⣿⣿⡟⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣄⠀⢰⣿⣿⣷⣆
⠈⠻⣿⣷⡄⠀⠀⠈⠉⠉⠉⠀⠀⠀⢠⣾⣿⣿⠏⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠘⣿⠈⠻⣿⣿⣿⡏⠉⢿⣿
⠀⠀⠀⣿⡇⠀⢀⣤⡄⠀⢰⣦⣤⡀⢸⣿⣿⣷⣶⣄⠀⠀⠘⣿⣿⣿⣀⡀⠀⠀⠐⠺⠇⠀⢉⠻⠿⠃⠀⢸⣿
⠀⠀⠀⢸⣿⣾⣿⡿⠃⠀⠀⣿⡿⠃⠀⠉⢻⣿⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⠀⠀⣾⣿⣿⣷⣦⣴⣿⡟
⣀⡀⠀⠀⠉⠉⢀⣤⣶⣶⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠉⠉⠛⠻⣿⣿⡇⠀⠿⠏⠙⠛⠛⠛⠋⠁
⣿⣿⣷⣤⡀⠀⣾⣿⣿⠿⠛⠛⠁⣠⣴⣦⣄⠘⠻⣿⣿⣷⣶⣿⣿⠇⠀⠀⢀⣿⣿⠀⠀⠀⠀⢀⣤⣄⡀⢀⣾
⠋⠛⢿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣾⣿⠿⢿⣿⣷⡀⠀⠉⠛⠛⠛⠉⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⣸⣿⣿⡷⠸⣿
⢀⣤⡀⠉⠛⠛⠛⠉⠀⠀⠀⣿⣿⡇⠀⠀⠁⢹⣷⠀⠀⠀⠀⢀⣠⣤⣀⠀⠘⢻⣿⣿⣷⣶⣾⣿⣿⠟⠁⠀⠉
⣹⣿⣿⠀⢠⣶⣿⣿⣦⣄⠀⢸⣿⣷⣄⠀⠀⠈⢿⣧⠀⠀⣼⣿⡿⠿⣿⣷⠀⠀⠈⠙⠿⠿⠟⠛⠁⢠⣴⣤⣄
⣿⣿⠏⠀⣿⣿⡏⠀⣸⣿⠀⠀⠙⣿⣿⣧⠀⠀⠻⣿⣷⣾⣿⡿⠀⠀⠘⠛⠀⠀⢀⣀⠀⠀⠀⠀⠀⢻⣿⠛⠿
⠀⠀⠀⠀⠸⢿⣿⣟⠋⠁⠀⠀⠀⣸⣿⣿⠀⠀⠀⠈⠛⠛⠋⣠⣤⣶⣄⠀⠀⢰⣿⠿⢿⣷⣤⣤⣴⣿⡿
⣶⣤⣀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠘⢿⡫⠃⠀⠀⠀⠀⠀⠀⣼⡿⠛⠻⣿⣷⠀⢿⣿⡀⠀⠀⠈⠙⠛⠉⠀⣠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣶⣶⢠⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢌⣿⣿⡈⢿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣾⣿⢟⣭⣶⣷⣶⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠙⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣶⣤⣌⣉⠉⠉⢁⣤⣾⣿⠇⠀⠀⠀⠀⠈⠙⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⢤⣶⣿⣿⣿⣿⣿⣿⣟⣫⣭⣝⣛⣣⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠉⠙⠛⠻⠿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧
⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣅⣾⣤⠉⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠄⠘⣿⣿⣿⡟⠁⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡆⠀⣷⠀⢸⠀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠪⣄⣀⠀⠀⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⣿⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣟⣀⣸⣃⣀⣟⣀⠸⠀⢹⣿⣿⡿⠁
⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠘⠛⠀⢁⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠉⠉⠉⠙⠉⢀⣠⣴⡎⢻⡿⠃⣦⣤⣀
⢀⣠⣴⣾⣿⣿⣿⣿⡿⠿⠿⠶⢦⠄⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢨⣧⢸⣿⣿⣿
⠙⢿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠶⣶⣶⣶⣤⣤⣶⣶⣶⠶⠿⠟⠛⠉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠚⠓⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠘⡋⠙⠉⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡰⠒⠒⠢⣄⣠⠅⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⢱⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢸⠉⠲⢦⣀⠀⠀⣠⠼⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⢱⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠈⠙⡤⣀⣀⠼⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠁⠀⠀⠰⠖⠁⠁⢀⣹⠀⠀⠀⠀⣠⠎⠀⠀⠀⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⠤⡺⢫⣥⢤⠄⠀⠀⠀⠴⢮⣁⢀⠞⠓⠤⠤⠒⠧⣀⣀⡤⠎⠀⣹
⠀⠀⠀⠀⠀⣀⡤⠞⠡⠁⠀⠀⠀⠐⠀⠀⠀⢀⣀⣀⣀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⢠⠆
⠀⠀⠀⠀⠀⡇⠀⠀⠠⠤⢤⡤⠀⠀⠤⣤⠔⠋⠉⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠞
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠚⠩⣤⡤⠔⠓⠛⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⢧⠀⣀⡤⠔⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⣀⡴⠚
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⢯⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠓⠘⠀⣦⡀
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠰⠏⢩⣿⡿⣭⠁⠀⢀⣴⣦⡤⣀⠀⠀⠀⣿⣿⣦⣤⣶⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢰⡷⢶⢀⠙⠁⠀⠄⣤⡄⠀⠀⠙⠞⠉⠁⠀⢰⣯⢞⣻⠿⠞⠁⠀⣀⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣦⣸⣿⠦
⠈⠀⠀⠶⠀⠀⡀⠀⠀⠄⣴⣦⣦⠀⠀⠀⠀⠈⢁⣼⣷⠀⠀⠀⠀⠙⣏⠙⠛⠛⠛⠋⠙⢢⣶⡔⠁⢀⡔⠆⠀⠀⠀⠘⠛⠓⠂
⠀⠀⠀⠀⠀⢸⡿⠀⠲⠖⠀⠈⠛⠀⠀⠀⠀⢠⣟⡵⢫⣦⣵⠂⠀⠐⠁⠀⣤⠀⢶⡀⠰⢟⡟⠻⢄⢾⡷⠤⡀
⠀⠀⠀⠀⠀⠠⢆⡆⠀⠀⣠⣶⡆⠀⠿⠿⠆⣼⠅⠀⢸⡿⡟⠀⠀⠀⢀⢤⣽⣶⠀⡿⠠⠈⣟⠀⣿⣎⠀⠀⣻⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣤⣾⣿⣟⣡⠀⠑⠃⠒⡋⡅⡠⢋⢁⠛⣤⠀⠘⡄⡙⠂⣹⠯⠀⠀⠈⠀⣤⣄
⠀⠀⠀⠀⠋⠿⠀⠀⠀⢸⣦⡀⠀⠈⠻⣿⣿⣿⡿⠋⠀⢀⠤⣨⡖⢫⢣⣡⠀⢇⡅⢣⣴⠇⢿⡾⠛⢷⠀⠀⠺⣄⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠉⠁⢰⣦⣤⠈⢯⣟⡛⠀⠀⠈⠚⠋⠪⣵⣦⣬⡁⠀⠡⠵⢰⠀⠀⠰⣦⠟⠀⠀⢠⡄⡦⠀⠉⡉⠀⠘
⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⣲⣂⣔⡏⠛⢁⠂⣹⣿⠀⢀⡄⢠⡆⢺⣿⣿⣻⡟⣆⡀⠀⣀⠀⠀⠀⣎⢝⡉⢢⣤⠈⡡⢾⠛⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢸⠢⡤⠜⠪⡿⠏⠁⠀⣈⣄⣻⣿⠵⠛⣇⢸⡇⣸⠉⢉⠟⠉⢹⠙⠯⣾⣷⡶⠀⠉⠀⠉⣹⠲⠤⢥⡤⣀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠘⢧⡝⣈⢄⠐⠀⢁⣴⣿⣿⡜⣱⢦⡄⢸⡸⡇⡇⡴⢁⡤⢞⣵⣿⣿⣍⠛⠉⠀⠀⠀⠀⢸⠂⠀⠈⢽⣭⣷⠄⣸
⠀⠀⠀⠀⠀⠀⠀⡈⣧⣬⠀⢀⠿⢿⢉⣿⣿⣿⣻⠀⣌⢢⢟⡉⡉⠳⡫⠴⢾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⡀⠀⣰⣾⡿⣷⡰⠁
⠀⠀⠀⠀⡈⠂⠀⠀⠀⠊⠀⠸⡆⢸⠎⡼⠁⠐⢙⡀⠀⠉⠈⣶⠈⠂⠟⠿⡍⡫⢯⠉⠀⠀⣰⣶⣤⡀⠀⠀⠁⠀⠉⠺⣿⠛⠝⠟
⠀⠐⢄⠀⠑⠀⠀⠀⠀⠀⠀⠀⣏⢨⡴⡇⠀⣰⠟⣿⣇⠀⠀⠋⠀⠀⠀⠁⠊⣵⢋⣀⡀⢰⡿⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⠃⠁⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢙⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⡶⡄⠒⠢⢶⡀⣹⡒⡀⠁⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣲⡑⠂⠈⠠⠈⢠⠁⢠⠈⣷⣿⢱⣌⠁⡖⠸⣂⠀⡵⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠔⣈⠁⠀⠁⡌⠀⠱⠒⣂⢀⡤⣬⠀⠀⠥⠠⠁⠤⣀⠀⠁⠀⢈⠄⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡈⠚⠨⠅⢦⠀⠨⢀⠈⠃⡠⢾⠑⢋⠐⡠⠈⢌⠀⠠⠁⡴⠰⢚⡤⡐⠒⢀⠀⠇⡄⠘⠆
⠀⠀⠀⠀⠀⠀⢚⡈⡀⢠⠁⠀⣨⠆⠠⠂⣁⠠⡧⠉⢐⠘⠃⠀⡄⠒⠀⣚⣠⠈⢃⣀⠂⠂⢀⡘⡁⢤⠀⠂⠀⠘⢃
⠀⠀⠀⠀⠀⢀⠗⢀⡐⠀⠀⠩⠀⠀⢒⡀⠀⡟⠓⠲⠠⡀⢀⡉⢄⠀⢰⠘⡕⢠⢁⠀⠙⡓⠾⢗⠀⠶⣌⠁⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠈⡞⠈⠥⠱⠒⠀⠋⠠⠜⢀⢐⡇⡠⢉⠀⢀⡏⠅⠀⢀⠠⢈⠀⡃⠀⡤⠐⠡⡀⠐⡳⣆⡀⠀⠀⠀⠀⠈⠈⠑⠄
⠀⠀⠀⠀⢠⣠⢇⡀⢀⠠⣰⡒⠯⠻⡍⠛⢲⡌⠁⠵⠐⢊⡡⣤⠠⠈⠠⠦⡔⠃⠀⠂⠳⢀⠐⠀⠱⠎⣳⡄⠰⠀⠋⠁⢘⠠⢤⡀
⠀⢀⣠⡛⠂⡐⢤⡵⠏⠊⠄⠀⡀⠂⠀⠈⠉⠀⠠⠀⢠⠅⠀⠀⡰⣄⠀⢥⠀⢐⡂⠈⠣⠀⠁⠀⠀⠀⠐⠈⠉⢐⠆⢀⠂⠼⠀⠉⣢⡀
⢀⣶⢏⣩⡤⠀⣾⠳⠀⠊⡀⣮⢑⡷⣀⡴⢨⠼⠐⠁⠉⠂⢁⠒⠀⠂⡡⢠⠄⢴⡀⠦⠀⠁⠀⠀⠂⠀⢊⠀⠀⠚⠀⠨⢠⡄⢉⡀⢠⢉⣄
⣜⡏⣠⣬⠄⠄⢐⠀⠀⠀⠶⠀⢈⠃⢀⡀⠑⠆⠀⠀⠀⡖⠂⢄⠀⠀⠀⠒⠣⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢄⠀⠦⠀⠀⠣⠼
⣿⡂⡽⢆⠒⠀⣮⡃⠓⠁⠀⠬⠇⠀⠠⠠⠈⠈⠁⠀⠀⢑⡔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⠈⠁⠀⠀⠀⠀⣀
⢿⡛⡰⠪⠂⠀⢱⣅⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⣄⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠘⠁⠈⠀⠀⠀⠀⠀⠂⡼
⠘⣾⡎⣤⠀⠀⠘⣦⠐⠀⠀⠀⠀⠀⠀⠀⢨⣳⡌⣇⠘⢷⡹⣧⠆⢀⡄⠀⠀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠈⢯⢧⢰⠆⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠙⣷⣿⡌⢌⢷⣹⣧⠸⣷⢰⢢⣶⠖⢀⣾⡾⣋⡤⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠙⠻⠴⡅⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠪⢕⠿⣿⡴⣌⣧⢿⡇⣿⡏⡾⢣⣗⣾⣿⡪⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠒⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢾⣮⣻⠸⣿⣽⠷⣡⢏⣾⢯⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢻⡿⡄⡟⣿⡄⢋⣾⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣎⢷⠀⣡⣿⡇⣾⡏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡘⣧⢼⣿⡇⣿⢡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠻⢸⣿⣇⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡧⣛⢾⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣸⣿⣷⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢉⣴⡅⣿⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣿⣿⣿⣿⣿⡯⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢺⣿⣿⣿⣿⣿⡏⠘⠁
⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡄⠀⠀⢠⠀⠀⠀⠀⠀⠘⠢⢌⣉⡙⠒⠣⣄⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⢘⣷⡂⠀⢻⠀⣇⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡇⠀⡇⠀⠀⠠⡒⡉
⠀⠀⢀⠎⠀⠀⠀⠀⠀⣤⣀⡀⠠⢈⠑⠀⠀⠀⢀⠘⠀⠀⠃⠄⠀⣠⣑⣒⡮⣧⠠⠀⠀⠏⣸⠀⠸⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠸⣄⠀⠀⠄⣂⡱⠭⠖
⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠁⠀⢄⠀⠀⠈⢀⠀⢉⠉⠿⣷⣐⠀⠐⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠑⠂⠠⠔⠒⣂⢀
⠉⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠈⠈⠰⢀⠄⠀⠀⠀⠀⠀⠀⠡⠈⠀⡀⠀⠀⠤⡀⠣⠴⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⠐⣆⠐⠈⠉⠈
⠄⠀⠀⠄⣀⠤⠴⠶⠌⠀⡢⢂⡤⢖⣠⠴⠤⠀⠑⠀⠠⠀⠀⠨⡐⠀⠀⠀⠀⠄⠄⠔⠉⣤⠶⠖⠛⠐⢤⡤⢊⠔⣝⡲⢤⣄⡀⠀⠀⠀⠐⠀⢀⠀⠈⢦⠀⢀
⠁⠀⢀⡀⠀⠀⠀⠀⠀⢀⡰⠋⡴⠫⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢸⠀⠸⠀⢀⠴⠶⡋⠡⣴⡁⡢⣄⣙⠛⠲⣍⠳⠄⠀⠀⠀⠈⢣⡀⠀⠀⠀⠑
⠁⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠜⡠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⢀⠈⠀⠀⠀⠁⠀⠈⠘⠉⠈⡁⠀⡈⠆⠆⠀⠂⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠀⠀⠰⠀⠀⠠⠀⢁⡘⢦⠢⡠⡀⢦⣄⡤⠴⠶⡷⢶⡳⣶⣴⠖⠂⡀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠀⠀⠈⠀⠠⠂⠀⣀⠤⠶⣤⡀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠈⢿⠀⠂⠙⢦⠤⠠⠤⠀⡊⠠⢫⡾⠃⡀⠐⠄⡀⠀⠀⠀⡀⠀⠀⠀⠠⢀
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠀⠀⠔⠀⡠⠋⠀⠀⣀⡈⠙⠧⠊⡑⢀⠈⠀⠀⠀⠀⠂⠲⣆⠀⠀⠀⠀⠀⠀⠀⠠⠐⠹⠉⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⡌⢰⢃⠀⠀⠀⠀⠙⠲⢄⠀⢀⢘⡤⠠⠀⠀⠀⠀⠀⢀⡉⠳⠲⠄⠀⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠤⠀⠀⠀⠀⢀⡀⠀⡀⠠⠤⠤⡊⠀⠈⣸⢡⠐⠄⠀⠀⠀⠀⠔⠡⢂⢚⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠀⠀⠑⡀⠀⡀⠀⠀⠀⠀⣤⠔⠊⠑
⣀⣒⠒⠢⣄⡈⠂⠁⠀⠀⠀⣿⠀⠀⠀⡧⠈⠸⣆⠀⠀⠀⣟⣠⡇⢸⣸⡅⠀⠈⠉⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⢠⠔⠁⠊⠀⣀
⡁⠅⠀⠀⠀⠑⣄⠀⠎⠀⠁⣈⢧⠀⠀⠈⠀⠀⠌⠙⢦⡄⠈⠸⠳⠈⢳⢳⡒⠂⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⢀⠂⠈⠀⠂⠤⠀⠀⠀⠐⠊⡀
⠀⠀⢀⣸⠀⢠⡏⡀⠀⢄⠈⠁⠀⠣⡀⠀⠀⠀⠀⢀⣒⣛⡷⡀⠄⠀⢸⢀⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠄⠀⠊⠀⠀⠀⢠⠀⠐⡀⡀⢰⠏
⠀⢌⢢⠇⠀⠞⠀⢁⠔⠀⠀⠀⠀⠀⠈⠀⠄⠠⢒⣀⠦⢤⠮⢯⣅⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢠⠆⢀⡎⣐⠋⠂⠀⢀⣀⠈⣆⢣⠀⢠⡞
⠫⠔⠇⣂⠊⡁⠑⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠜⠁⠀⠀⠀⠀⠋⠉⢀⠔⠈⠀⠀⠀⠀⠆⠀⠠⠁⠀⠀⠂⠀⢠⠏⠀⡚⢀⠁⠠⠀⠀⠀⠍⠈⢿⡌⣦⠟⢁⣰
⡥⠬⡂⡈⠺⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠄⠀⢀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃⠀⠠⠞
⠖⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⢠⠀⢀⣚⡀⠀⡃⠰⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠤⠤⢖
⠉⠀⠀⡀⠀⠀⣆⠀⠀⠀⠀⠐⠀⠀⣠⡤⢤⢀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡴⠋⠉⠙⠳⣥⣾⡀⠀⠀⠀⡄⠀⠀⠈⠁⠀⠰⠚⠉
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⣠⣾⠗⠋⠱⣸⡇⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠐⡇⣾⡠⠐⢉⣛⢶⣤⢫⡟⣦⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣶⣯⢟⣭⣾⠧⣴⣿⣗⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⡞⠠⢫⢷⣎⠂⠀⠛⢿⣻⡝⡞⡅⠀⠁⠀⠰⠄⠀⡀
⠠⠄⠀⠀⠀⠀⠀⠀⠀⣻⠿⣽⣿⠿⠋⢰⡿⡜⢞⡷⠂⠀⠠⠀⠀⠀⠀⠀⠀⢈⠀⠐⠀⡀⠀⢹⡀⠃⠸⣎⡘⠦⣄⡀⠸⠿⣧⢳⣷⡀⠀⠄⡀
⠀⠀⠀⠀⠁⠐⠠⢄⡀⣿⠁⣿⠉⠀⠀⣾⠀⢃⡘⠇⡁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠈⢱⣄⠀⠈⠈⠂⠈⠻⣦⡀⠙⠀⡽⢻⡀⣀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠀⢀⠱⣏⠀⠫⣀⢚⣿⣃⡼⠡⠑⡌⠈⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠁⡀⠒⢀⣂⠐⣛⣷⡾⢿⣦⡈⢀⠂⠀⠀⠀⠁⠀⠀⢁⣀⣀
⣲⠀⠄⡀⠀⠀⠄⠀⠁⠈⢓⠶⠤⠽⠷⢁⠐⢀⠾⣍⠀⠄⠀⠀⢀⡠⠖⠐⠚⢶⣄⠄⠈⠀⠀⠀⠈⠀⠀⠈⠀⠈⠀⠁⠠⠈⠀⠉⠁⠀⠀⠀⠀⠀⢀⡜⣩⠄⠂
⣿⡄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠋⠉⠙⠉⠛⠉⠀⠋⠱⢀⡜⢡⢟⠀⠀⠄⢤⡁⠙⢷⡐⢂⠀⠰⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣪⠞⢀⡀
⢣⢳⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠞⠀⡔⠋⠀⢁⡶⣀⠀⠀⠀⠙⠢⠀⠕⡡⢀⠂⠀⠀⠀⠀⠀⠀⠌⠀⢀⠀⠀⠀⠀⠀⠀⠒⡩⠚⡁⣴⣏⠀⢐
⠀⠃⠋⠱⠀⠀⠀⠓⠆⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠰⡇⠀⠀⢞⠐⠈⡆⠀⠀⢠⡄⢡⡎⠀⡟⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠈⠀⢠⠴⡑⢌⠠⡁⡈⠉⠀⣼
⠘⠘⠀⠀⡇⠀⠀⢀⠀⡈⠢⣀⠀⠀⠁⠀⠀⠀⢱⠀⠡⠀⠀⠈⠂⠈⠳⣄⠀⢨⡅⣧⠁⡆⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢠⡎⠀⡇⠘⠀⠀⠀⣾

⣴⣦⣀⡟⠀⢸⣿⣧⡀⠀⠀⣠⣶⣷⡀⠘⣿⣷⣶⣤⡀⠙⣿⣿⣶⣤⣄⠀⢻⣿⡄⢰⡿⠛⠻⠿⠏⠀⠿⠿⠿⣦
⡟⠉⠉⠳⠶⠟⠉⢹⣟⣿⣿⣿⠁⠉⣿⠏⠁⠀⠀⠙⣿⣿⠟⠉⠙⣿⡟⠀⠀⠙⣷⣾⡄⠀⠀⠀⢀⣤⣄⡀⢀⣏⣸
⠿⣦⣶⣶⡆⢠⡎⠙⣟⣿⣬⣿⠀⣴⡏⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢸⣧⠀⠀⢀⣿⡿⠛⠒⠲⢾⣿⠀⢈⣛⠉⠉⠙
⣠⣿⠟⣨⣤⣴⣿⠀⣿⠉⣠⠟⠀⢿⣿⣦⣀⠀⠀⠀⣿⣿⣦⣄⣀⣀⡛⠿⠿⢛⣡⣀⠀⠀⠀⠀⢻⣿⡿⠛⠛⠶⣾
⢿⣧⣴⡟⠉⣿⠏⠀⠈⣿⠏⠀⠀⠀⠉⢻⣿⣷⠀⣠⡀⠈⠉⠉⠙⢿⣿⡿⠂⣿⠟⠛⢧⠀⠀⠀⢠⡟⠀⠀⢠⣄⠙
⠀⠹⣿⡇⣸⣿⣄⣀⣠⣿⡀⠀⠀⠀⢀⣴⡿⠁⠀⣿⣿⣄⡀⠀⢀⣾⡏⠀⠀⢸⣷⣤⠈⣷⣦⡶⠟⠁⢀⣴⣿⣿⣿
⣀⣴⣿⠇⠈⠉⠉⠉⠉⠙⣧⠀⠀⢰⣿⣿⣧⣀⣠⠟⠉⣹⣿⠟⢋⣿⣷⣤⣴⣿⣁⣿⣷⠋⠀⡾⣿⠇⠘⠋⠀⠈⣿
⠛⠉⠁⢠⡾⠷⣄⠀⠀⠀⣿⠳⣤⣀⠈⠉⣻⡟⣡⣶⣾⠟⠛⠒⣿⡅⣸⡟⠁⠀⠀⠙⣧⡀⣠⣧⡼⣷⣴⣶⣄⢸⣿
⡀⠀⣠⣿⡇⢀⣽⣶⣤⣾⠿⠟⠳⠿⢿⣟⣉⣿⡿⠟⠁⠀⠀⠀⢸⣧⣿⡅⠀⠀⠀⠀⠘⢿⣿⣏⣀⣠⣌⡉⠛⣾⣿
⠿⠛⢿⣿⠋⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣠⣿⣿⡝⣿⡿⠛⠛⢿⡄⠀⠈⠉⠉⠛⣿⡉⢻⣻⡿
⠀⠀⠈⣿⣦⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣾⡿⠋⠉⠉⠙⢿⣷⠠⣤⣾⡇⠀⠀⠀⠀⠀⣼⣧⣾⣿
⠀⠀⠀⣿⣀⣻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠈⠻⣿⣄⠀⠀⠀⣠⣿⠃⠈⠙⢷⣀⠀⠀⢀⣴⣿⠁⠀⢻⣿
⣀⣤⣤⣀⠉⣻⣿⣦⣄⣀⣀⣀⣠⠴⣿⣿⡇⠀⠀⠀⠀⢠⠛⠉⢀⣴⣾⡿⣇⠀⠀⠀⣸⣿⣋⣻⠿⠿⣿⢧⣴⠋
⠻⣿⡟⠉⠙⣿⠉⣿⡏⠉⠉⣫⣥⣴⣾⣿⣿⣤⣀⠀⠀⣿⣦⣤⠞⠛⠛⢦⣀⠙⣶⣿⡟⠙⢿⡁⠀⣠⣿⡾⠋
⣾⡿⠃⠀⣼⣿⡇⠈⠑⢲⣾⡿⣿⠋⠀⠀⠀⠙⢻⣿⣦⡍⠋⠁⠀⠀⠀⠀⠹⣿⣮⠻⠿⠿⣿⣿⡄⠻⣿⠀⠀⣶⣶
⠋⠤⠄⠀⠘⠛⠓⠀⠀⠀⠛⠀⠘⠀⠀⠒⠒⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠐⠛⠛⠂⠀⠀⠀⠛⠁⠀⠙⠂⠀⠘⠂
⠀⠢⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⣤⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣿⠿⣿⣷⣿⣿⣞⣿⣻⣿⣿⣿⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡟⠛⠘⢉⣴⡶⡛⠋⠋⡙⠯⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣄⣳⣦⣾⣿⠺⠑⠀⠂⠌⣔⢹⣷⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢛⠹⣫⣽⣿⣛⡧⣀⣤⡔⣴⡤⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⣴⣿⡿⢿⣿⣿⣿⣾⣽⣿⣷⣿⣿⣿⣿⣿⣿⣷⣦⣟⣺⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢐⣿⣻⣿⣯⣿⣧⡀⠘⢿⣿⡸⠟⣿⡿⠟⢏⣿⣿⡿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢻⠿⢿⡲⣄⠉⢷⠀⢸⠁⠀⢸⡿⠙⣺⠏⠀⠚⠛⠻⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠃⠈⠁⠀⠈⠀⡄⠀⠁⠘⠀⠀⠘⡿⠀⠏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣹⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢠⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢦⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠐⣎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡒⠀⠠⡀⠀⠀⠀⠠⣠⠀⠃⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⢠⢖⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠘⢼⠶⠀⠀⠀⠀⠠⠄⠆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠁⠀⠀⠀⠀⠀⠀⢿⠐⠒⠄
⠀⠋⣸⠲⠀⠁⢶⠀⠀⠀⠀⠐⠁⢀⠀⠀⠀⠄⠀⠀⢳⣀⠀⠀⠀⣀⣀⣀⣀⣀⣅⠀⠀⠊⢻⢿⣿⠄⠀⠀⢰⠦⣃⢴⢀⡀⠈⠣⠄⢢
⣤⣤⣴⣶⢄⢐⡚⠀⠀⠀⠀⠀⠨⠼⢄⠀⠁⠈⠄⠀⠰⢿⡆⠀⢐⡟⠉⠘⠉⠉⠈⠉⠫⠀⠘⢳⠀⠃⠳⠆⢀⠀⢉⡂⣄⢀
⠀⠉⠓⠚⠃⠛⠀⠐⢄⡀⠀⡀⠀⠀⠂⢀⠀⠀⠈⡘⠳⠞⠁⠀⢾⠥⠧⠦⠤⡤⠤⠤⠀⠄⢀⠋⠃⠀⠀⠐⢁⠔⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⠟⠤⣔⢦⠒⠄⠓⡀⠀⠙⣀⠀⠃⠀⠰⠀⢸⠀⢠⠁⠀⠀⡌⠀⠖⢀⡠⢎⡡⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡶⡶⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⢖⠀⠀⠛⠢⢀⠀⠈⠂⠀⠛⠀⠗⠀⠶⠀⠰⠀⠾⠀⠀⠺⠀⠘⠃⠈⠁⠈⠁⠀⠠⡦⠄⠀⢗⠂⠀⠀⠀⢲⠀⠁⢀
⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠩⢤⠤⠤⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⢱⠀⠀⠀⠀⠀⢀⡀⠄
⠀⠀⢀⠀⠀⢨⣭⡳⠀⠀⠀⠀⠲⠒⠒⠒⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⡶⠚⠋⠀⠈⠋⠉⢹⣿⣽⡏⠉⢻⣿⣭⣽⣾⣿
⠀⠀⠒⠀⠀⠈⠞⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠘⡗⠀⠀⠀⠀⡐⠂⣠⣦⣆⠀⡀⠄⠀⠠⣿⡇⣿⡇⠀⠀⠙⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡴⠆⠀⠀⠀⠉⢢⣀⡄⠀⠀⠀⢰⡇⢀⡠⣤⣤⣠⣄⣠⡤⣤⣤⣠⠀⢀⠸⡟⢠⣿⡇⠀⠀⣠⣶⣤
⠀⠀⠀⠐⠀⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠂⢆⠀⠀⠀⡿⣖⠒⠀⠀⢸⠃⠒⠂⠛⠉⠁⠀⠀⡇⠈⠻⣷⣤⡙⢋⠏⢹⡟⡏⠀⠀⠈
⠀⠀⠀⠀⢠⣆⡤⠤⠔⠒⠀⠀⢀⢠⡀⠀⠀⢀⢴⠶⠴⠀⠈⠠⡀⠀⠸⠀⠀⠈⠀⠀⢈⣥⡶⠦⣠⡀⠀⢼⠋⠂⢀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠⠄⠂⠁⠀⠀⠇⢀⢀⡀⠀⠈⠀⠀⠐⣀⡀⠀⠀⠀⠓⠒⠤⡰⠆⠀⢰⠀⠀⡘⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡏⠎⠀⠀⡀⢀⡀⣘⣻⠇⠀⠀⠀⠀⠀⠀⠀⠠⠭⢃⣐⡶⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠾⠿⠿⠿⠿⠿⠿⠶⢶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⢁⠀⠠⠠⠐⠐⠐⠀⠀⠀⠀⠄⠀⡉⠙⠻⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁⡠⠔⠈⠀⣤⡰⠒⣄⡎⢹⠄⣤⠀⠀⠀⠀⠀⠁⠢⢀⠈⠛⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢀⠀⠁⠀⠀⠀⢠⠇⣇⣰⠛⠦⠞⠀⠉⠁⠀⠀⠀⢀⣾⡇⠀⠈⠀⡀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠄⠀⠀⠀⠀⡀⠀⠈⠀⢠⡄⠀⠀⠀⣤⣠⠀⣠⠶⡶⢸⠟⠀⠀⠀⠀⠀⠠⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⠈⠀⠀⣼⡇⢸⠇⡤⣴⠌⡟⢡⡇⣸⠃⣯⡟⢰⡏⣼⣃⠿⠤⠃⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣿⣿
⠀⠀⠀⠀⠀⢀⣿⠃⢀⠂⠀⠀⢰⡏⣷⡟⣾⢁⡟⣸⣇⠼⠵⠻⠞⠀⠑⢉⣉⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠸⠀⠙⠃⠙⠋⣉⣀⣠⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⣹⡏⠀⣠⡄⢘⣿⡇
⠀⠀⠀⠀⠠⠿⠀⠐⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣟⣉⠉⠈⢣⡄⠀⣾⣿⡄⠘⣿⡇⠀⣿⣿⠋⢻⣷⡀
⢠⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠟⠉⣉⠉⢻⣿⣿⠀⢠⠀⢻⣿⣿⡀⢰⡄⠙⠀⢻⣿⠇⠀⠛⢻⣄⣈⣁⣠⣾⣿⣿⡄
⠀⠻⣿⣿⣿⡿⠛⠛⠻⣿⣉⡁⢠⣤⠀⢸⣿⠀⢸⡟⠒⠚⢻⡟⠀⣠⡤⠀⠻⠟⠃⢈⣙⣦⣠⣼⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠹⣿⡟⠀⣼⣿⡄⠈⣿⡇⠀⣠⡀⠉⢿⡄⠈⠛⠃⠀⣿⠁⢠⣤⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⣭
⠀⠀⠀⢹⣿⡀⠸⠿⠇⢀⣿⠋⣀⣈⣵⣤⣤⣿⣷⣶⣿⣿⣿⡆⣶⣬⡛⢿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⠁⢰⡿
⠀⠀⠀⣼⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠁⣾⣿⣿⣦⡀⠀⠀⢀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠂⢀⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⣿⢟⣩⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⠂⢀⣾⠏
⠀⠀⠀⠉⠉⠉⠀⠐⣶⡄⠀⠄⠀⠀⠀⠀⠀⠀⠤⣶⣶⣿⣿⣿⣿⣿⣶⣌⡻⣿⡿⣿⣿⣿⠀⠀⠀⠀⠠⠂⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠐⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣻⡿⠿⠿⠿⣿⡔⣿⣿⣿⠇⠀⠀⠀⠂⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠁⠢⠄⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⣅⡛⠛⠁⠀⠐⠈⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⡈⠐⠠⠠⢀⢀⢉⠉⠉⠉⠉⠀⠄⠙⠒⠁⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣶⠾⠟⠋⠁
⣶⣶⡶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⣛⣿⣿⣿⣻⣿⣿⣷⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⠏⣥⣬⣙⣿⣟⣻⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⡞⠻⣿⣽⠿⠿⠛⢿⣿⢛⣿⠋⣩⣥⣤⣽⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣼⣿⣿⡿⣿⡿⢶⣿⠛⣃⣼⣿⣿⣾⣋⣴⡞⢋⣽⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣿⣿⣿⣷⢿⣻⣿⡿⠋⠻⢿⣍⣹⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⣭⣽⣌⠙⢿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡘⣿⣿⣿⡿⠁⣀⣯⣷⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⠻⣿⢃⡾⢻⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⢸⡇⢸⠀⣿⣿⡟⠋⠉⣹⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⡟⠛⢻⣿⣿⣿⣧⣾⣰⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡅⠉⠻⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡀⠀⣰⣿⣾⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠞⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠉⠁⠉⠒⢤⡠⡀⣀⡠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠒⢄⡀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢂⡀
⠀⠀⠀⠀⠀⢀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠤⠤⠒⠦⠒⠤⠖⠉⠒⠄⠤⠤⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⡰⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠀⠈⠉⠦⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠓⠂⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠉⢱⠄
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠂⠔⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⠞⠉⠣⠔⠒⠦⢄⣀⡀⡀⡀⠈⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢄⡀
⠀⠀⠊⠀⠀⠀⠀⠀⢀⡞⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢤⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠁⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⢨⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠘⠦⡄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠛⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠀⠀⠀⠀⠈⠉⡖⢲⣀⣀⡠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⢦
⢃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠙⢆⠙⣤⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢳
⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠒⢧⠀⠀⠑⢾⡀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⡘⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠘
⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⢯⡁⠀⠀⠈⢧⡀⠀⠈⡇⠀⠀⠙⢄⠀⣀⠀⣀⡰⠊⢀⡀⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠋
⠀⠀⠀⠉⠒⢂⡄⠀⢀⣀⡔⠀⠀⠀⠙⢆⠀⠀⠀⠳⡄⠀⣿⠀⠀⠀⠀⠉⠉⢹⣁⡤⠒⣡⠁⠈⣧⣀⡀⢀⠀⣠⣄⣠⣄⡴⢦⡠⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠚⠉⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠹⡄⢸⠀⠀⠀⠀⠇⡔⠉⠀⣴⢲⠃⠀⡔⡱⠋⣱⠞⠛⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠘⣼⠀⠀⡀⠀⢸⠁⠀⢰⠃⡆⠀⠠⡟⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠐⡄⢹⡀⠀⠃⠀⢸⠀⢠⠁⢠⠀⠀⠌⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠸⡘⡇⠀⠀⠀⠈⡄⠃⢀⡄⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢳⡇⠀⠀⠀⡤⡵⠃⠋⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⢘⡜⢘⡀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠇⠀⠀⡇⢸⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢹⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡶⠋⠉⠉⠉⠳⣾⠋⠉⠉⠳⣤⡴⠚⠉⠑⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠙⠀⠀⠀⣀⣀⠀⠋⠀⢠⠖⢢⡉⠀⠀⠀⠀⡟⠁⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠃⠀⡀⠀⠀⠀⠸⡏⠉⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠰⠋⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠸⣄⣀⠀⠀⠀⠀⠀⢠⡀⠀⣾⠀⠀⠀⠀⢴⡀⣰⠂⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠸⣇⡠⠀⠘⠦⠤⠞⠓⠚⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣴⠿⣦
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠴⢿
⠀⠀⠀⠀⠀⠀⠀⣸⠗⠂⠀⠀⠀⣼⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣻⢤⡠⠞⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⠀⠀⠀⠘⠶⠶⢿⣄⣀⣠⡗⠀⠀⠀⠀⡀⠓⠒⠒⠁⠀⠀⠀⡀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠰⡄⠀⢀⠄⠉⠉⠉⠀⠀⢤⣀⣼⠇⠀⠀⠀⠀⠀⠀⣠⣿⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⣀⠉⠛⠁⠀⠀⡀⠀⠀⠀⢠⣍⠁⠀⠀⣠⠶⢦⣶⠾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣤⠤⢴⠛⠦⣤⣤⠞⠙⠛⠚⣿⠁⠀⢸⡏⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⠆⠀⠀⠹⡄⠀⠀⠀⡇⠀⠀⣿⠁⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠘⡀⠀⠀⢻⣀⡀⢀⡇⠀⣰⡏⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢣⠀⠀⢸⡋⠈⢸⣧⡾⠋⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢧⣄⣼⡇⠀⠀⠉⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠋⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⢤⠀⠀⢀⠞⠉⠉⢳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠸⠃⠀⠘⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣤⣶⠟⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣄⡀⠀⠀⠀⠇⣴⠛⢋⣀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡝⠻⣷⣄⠀⠈⠥⠾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣷⣦⡙⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢀⡀

⠀⠀⢠⠤⢠⡄⣤⢠⠤⠠⣤⠄⣤⡀⣤⢠⡄⡄⢠⣤⠀⡤⡄⢠⠀⢠⠤⠀⢠⠤⣄⣤⠤⢤⢀⡄⣤⠄⣤⠀⣠⠤⡄⡤⣤⢠⡄⣤⢀⡤⠄⣤⢠⡤⣤⠄
⠀⠀⠨⡽⠘⢧⠟⠨⠽⠀⠿⠸⠛⠧⠿⠸⠙⠇⠾⠻⠄⠯⠗⠿⠤⠸⠯⠀⠸⠤⠟⠿⠭⠈⠿⠁⠿⠅⠿⠄⠷⡤⠇⠟⠉⠸⠻⠹⠗⠯⠅⠏⠻⠇⠿

⠀⠀⠀⠀⠀⠀⠹⡇⢳⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢚⣋⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠹⡆⠀⠀⠀⠀⠀⠀⢀⡴
⢠⡄⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⢀⣠⡤⢞⣥⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠙⠀⠁⠀⠀⠀⣀⡤⢶⣫⣴
⠋⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⣡⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⡁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢁⡼⠛⠋⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⣧⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣡⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⣤⡻⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⢦⡀⠀⠀⠀⠀⠀⣠⢞⣏⡾⠟⠀⠀⠀⠀⠀⠀⢤⣙⠶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠈⠉⠓⠂⣦⣍⡳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣿⠀⠀⠀⠀⠸⢁⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢦⣬⣙⢦⣄⣀
⠀⣀⡤⢀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢾⡙⢣⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⢧⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣰⠄⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣍⠳⠄
⣛⡭⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣇⠀⠀⠀⠀⠀⠀⢀⡴⠚⣛⣩⠵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⠴⡺⣯⣾⠟⠁
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢛⡡⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡼⠋⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⠀⠻⡜⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣥⡾⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣡⣶
⠀⠀⠀⠙⣮⠹⣆⠀⠀⠀⠀⠀⣠⢞⣷⡿⠋⠀⠀⠀⠀⠀⠀⠰⣮⡛⠶⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡙⢶⡀⠀⠀⠀⠀⢠⠞⢭⡿⠟⠁
⠀⠀⠀⠀⢸⣷⣸⡆⠀⠀⠀⠐⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢶⣮⣳⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⣇⠀⠀⠀⠀⠋⢠⠋
⠀⠀⠀⠀⠀⠙⣷⠝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⢆⡄⠀⠀⠀⠀⠀⠀⠉⠛⠛⢧⡉⠗⠀⠀⠀⠀⠀⠀⠀⠘⢿⡪⢧⡀
⠀⠀⠀⠀⠀⠀⠘⡇⠹⠀⠀⠀⠀⠀⠀⣠⡶⢋⣩⡭⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⠇⠀⠀⠀⠀⠀⢀⡴⢛
⣴⢆⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠖⢯⣹⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣤⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠴⢺⣭⣶⠿
⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡜⠉⠀⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢛⡥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡰⠋⠁
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣣⣾⠋⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠳⢬⣛⣓⠲⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠹⣆⠀⠀⠀⠀⢀⠞⢑⡿⠛⠁⠀⠀⠀⠀⠀⠀⠸⠮⣙⣛⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣬⡷⡶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣻⡀⠀⠀⠀⠈⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣮⡿⢶⢦⣄
⣤⡴⢟⣤⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⣆⠙⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠹⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠞⣡⠄⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⡈⠃
⠶⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠓⠀⠀⠀⠀⠀⣀⡴⢋⣥⡴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢫⣧⡴⠟⠋
⠀⠀⣤⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⡵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⢠⡠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢋
⠀⠀⠙⢎⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⡴⢣⣾⠏⠀⠀⠀⠀⠀⠀⠰⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣼⡟
⠀⠀⠀⠀⢳⡌⢷⠀⠀⠀⠀⢀⡞⢱⡷⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⠮⢭⣉⡛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠹⡄⠀⠀⠀⠀⡴⠋⡾⠛⠁
⠀⠀⠀⠀⠘⣿⣜⣧⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⢷⣮⣻⠗⢦⡀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣷⡀⠀⠀⠀⠀⠸⠁
⣀⣀⣀⣀⣀⣈⣋⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣚⣡⣆⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣆⣉⣀⣀⣀⣀⣀⣀⣀⣀⣙⣇⣙⣀⣀⣀⣀⣀⣀⣀⣀⣠
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢬⠂⡔⢂⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡇⣠⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠉
⠀⠀⠀⠀⢀⢶⡀⠀⡴⣺⣫⣟⣗⢦⠀⠀⡶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡰⠰⠰⠔⢆⠀⠀⢠⡄
⠀⠀⠀⠀⡜⣸⠀⢸⠥⣯⢬⡧⢼⠤⡇⠀⣇⣳⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣚⡃⣛⢘⣓⢛⡃⠀⠘⣷
⠀⠀⠀⠀⡇⢧⠣⡈⢦⣷⠲⡗⡾⡴⢃⡜⡹⢹⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠘⣃⢩⢨⣏⡛⠃⢀⣾⣿
⠀⠀⠀⠀⠙⣄⠳⠙⢆⠉⠛⠛⠉⣰⠋⠜⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠈⠀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠈⢧⠀⡜⠀⠀⠀⠀⢣⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠸⠴⠃⠀⠀⠀⠀⠘⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠋⠙⣛⣿⣦⣴⣿⣛⠋⠙⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣤⡾⠛⠉⠉⠉⠉⠉⠉⠛⢷⡄⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠋⠙⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠛⠋⠉⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠃⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠘⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡀⠸⣦⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⣰⠟⢀⣾⢷⣄
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠈⠻⣦⡘⠳⣦⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⣴⠾⢋⣤⡿⠁⠀⠹⣧
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⢀⣀⣴⡞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⣿⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡋⢹⡟⠛⠻⠟⠛⢻⡏⢙⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⡋⠉⠀⠘⢷⣸⡇⠀⠀⠀⠀⢸⣇⣾⠃⠀⠉⢛⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⣿
⠀⠀⠀⠀⠀⢹⣇⠀⣶⡀⠀⠀⠀⠀⠀⣰⡟⠈⢿⡄⠀⠀⠘⣿⣿⠀⠀⠀⠀⣾⣿⠃⠀⠀⢀⡾⠁⢻⣄⠀⠀⠀⠀⠀⢀⣴⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠻⣆⠈⠻⣦⡀⠀⡀⠈⠋⠀⠀⠈⣷⡀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡏⠀⠀⢀⣾⠃⠀⠀⠙⠀⠀⠀⢀⣤⠾⠁⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡈⠁⠀⣿⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣿⠀⠀⠀⠀⣿⠁⠀⠀⣼⠇⠀⠀⠀⠀⠀⣿⠀⠈⢁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⣿⣧⠀⠀⠀⠀⠀⢻⡆⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⢠⡟⠀⠀⠀⠀⠀⣼⣷⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⠀⢘⣧⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⣼⡇⠀⣀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠸⠃⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡿⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣃⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⠿⠃⢀⣄⡸⠆⠀⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠝⠟⣣⠀⢐⣿⣾⣿⣵⣐⣿⣷⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣶⡆⠀⢰⠟⠿⠏⢲⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢠⠛⣿⠀⠋⠈⣴⣤⣾⣿⣦⣾⣿⣵⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⢀⠸⠁⠀⡀⣾⣿⣿⠟⢙⡻⣿⣿⠝⠿⢛⠛⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⡴⠉⠀⠿⢋⢛⣿⣿⠋⣰⣿⣦⣝⣿⣶⣾⣿⡖⠀⠰⠖⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠚⠿⣿⠿⢛⠀⠠⢿⣬⣻⣿⣡⣿⣿⣿⡿⣿⣿⣿⢋⡠⠤⠀⠀⠁⠀⠘⠛⠀⢀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠈⡻⣶⣄⡠⣄⡄⠀⣠⠔⠃⢁⡀⣹⣿⣶⣿⣇⠀⢉⡋⠙⠛⠛⠛⠚⠳⠍⠀⠀⠄⠀⠀⠀⠀⠀⠐⠊
⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⢀⡔⣿⣿⣼⣿⡼⠿⠝⠉⠀⠀⢹⣿⣿⣿⣿⣿⢛⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⡀⠀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡄⢀⣀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⣿⣿⣷⣴⣶⣷⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠊⠀⠉⠈⠀⠈⠻⣿⣿⣿⣿⣟⣻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⡔⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠛⠛⠉⠛⣿⠉⠙⠛⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⢻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⢀⣤⠴⠶⠾⠋⠀⠀⠀⠀⣰⡟⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⢿⡀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⣠⣴⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⢰⡟⠀⠀⠀⠀⢰⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⢧⡀⢀⣾⠁⠀⠀⠀⠀⢺⡇⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠾⠇⠀⠀⠀⠀⠀⣸⠇⠀⠻⠶⠟⠙⣷⡀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢿⣤⣀⡀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠈⢙⣦⢠⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢾⣷⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢧⣽⢷⣦⡀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣀⡴⢿⣩⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠛⠀⠉⠻⢷⣦⣤⣄⣀⣀⣀⣠⣤⣴⣾⡟⠉⠠⣿⡟⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠙⣧⠉⠉⠉⠉⠉⠁⢠⡟⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣻
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖
⠀⠀⠀⣀⡴⢶⠋⣙⡿⣻⣯⣼⣧⠀⠀⠀⠀⠀⣀⣤⡄⠀⣀⠤⠒⠉⠀⢀⡀⠤⠀⠀⠀⠊⠉⠉⠉⠉⠁⠒⠀⣀⡔⠉⢸⣦
⠀⠀⠀⠹⠦⣤⡬⠽⡿⢿⠶⣿⠟⠀⢀⣤⡶⠛⢡⣴⡶⠋⠀⠀⡠⢐⡉⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⡶⠋⢁⣴⢟⣽⡟⠀⠀⢀⣶⠞⣿⣿⠏⣡⡿⢃⣷⢦⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⢾⠟⠛⣷⣿⣣⣾⠏⠀⠀⠀⣼⠋⠄⠛⠁⣾⣻⣿⣿⡧⡻⣿⠏⠀⠀⠀⠀⠠⣰⠋⡀
⠀⠀⠀⠀⣠⢴⡾⠛⠉⠁⠀⠁⠀⢘⣿⣧⣿⠃⠀⠉⠀⠀⡒⠀⠀⠀⠈⢹⣯⣿⡜⠓⠶⣿⠆⠹⠄⣄⢀⣼⠃⣀⠃
⠀⠀⠀⣨⡷⢋⡆⠀⠀⠀⠀⠀⢾⣎⣾⡟⣿⠀⡝⠀⠀⠀⠉⢯⣀⣊⣟⡙⠛⣿⣧⣄⣈⡿⢿⣷⠂⣽⡾⠃⡠⠀⠀⢻⠱⠄
⠀⠀⠀⢻⡃⢸⠀⡄⠀⢠⡤⢠⣿⣿⡾⢃⡇⠀⠂⠀⠀⠀⠀⠀⠈⠉⠻⢶⣚⣿⣛⠾⣧⣲⣿⣿⡾⠟⡁⠄⠁⠀⠀⠀⡇
⠀⠀⠀⢸⣿⢼⣇⣹⡀⠀⠶⣿⣿⣡⣤⡾⠃⠀⠀⠀⣀⣀⢀⣠⡄⣀⣀⡀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠙⢿⣿⣌⣙⣳⣿⠟⠛⠛⠋⠀⠀⢰⣿⣿⣿⣶⣾⣟⡘⢡⣿⠏⠀⠀⢀⣠⣴⣶⢦⣄⠀⢄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠙⠻⠩⠍⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⠭⠷⠧⠽⠚⠋⠀⠀⣠⣶⣿⠿⣿⡷⠐⣟⢻⣦⠱⠄⠀⠀⠀⢰
⠀⠀⠀⣜⠁⢰⠀⢰⠀⣔⠀⣆⠀⡇⣼⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⣠⡴⣾⠿⠁⢻⣧⣿⣍⠀⢸⣦⡿⠃⠀⠀⠀⢀⡾⣴
⠀⠀⠀⡛⠀⢬⠀⣾⠀⢍⠀⢯⠙⣧⠼⠖⠃⠀⠈⢁⣀⠀⢠⣴⣿⠧⣿⣤⢀⡀⢀⡀⢈⣵⣤⣺⡿⠃⢼⠀⠀⠀⠀⣛⢻⡄
⠀⠀⠀⠳⢦⡘⣇⣈⣦⣹⠦⠜⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⢼⣷⠥⠰⠻⠏⢛⠛⠛⠛⠀⠉⠉⠀⠀⠀⠁⢀⣀⣀⢺⣿⢸⡇
⠀⠀⠀⠀⢀⠛⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠂⠒⠒⠒⠒⠈⣀⣀⣤⣶⣟⠻⡿⣶⣥⣿⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⠊⠀⠀⣠⣀⣴⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⣠⣬⣿⣯⣿⣿⣿⢷⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠐⠂⠁⠀⠀⠀⠀⣠⡼⣿⣿⠋⢁⣼⣿⢿⣿⣿⣷⣄⠀⢠⣿⣟⠉⢹⠁⠇⣁⡀⣀⡌⣿⡟
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⢄⡀⠀⠀⠸⣯⣷⣿⢀⣰⣯⣝⣷⡿⣿⣿⣿⣿⠀⢸⣏⡝⣻⠇⠈⣦⣡⣾⣿⣱⣿⠃
⠀⠀⠀⠀⢀⣺⣯⢽⡷⠈⠽⠽⣿⡆⠈⠁⠦⠀⠙⠻⣿⣿⡹⣭⣿⣣⣿⣿⣿⠟⠋⠀⠸⣿⡟⣜⡂⣿⡟⠦⣯⢻⣿⠃⠘⠁
⠀⠀⠀⢠⣽⣅⠀⠩⠀⠂⠠⠚⠻⠓⠛⣿⣦⠈⠁⠀⠀⠀⠀⠀⠄⠠⠀⠅⠄⠀⠀⠀⠀⠈⣿⣽⣿⣍⣷⡖⣱⣿⠃⡠⠂
⠀⠀⠀⠈⠳⣄⣀⣤⠦⣤⣴⣆⣀⣠⣼⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠀⠀⠀⠀⠀⠉⠻⠿⠟⣋⣼⣿⠃⠀⠁
⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⢛⣿⡿⠛⠁⠀⢸⣿⠀⠀⠉⠻⣿⣿⡻⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⣴⣿⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠻⣷⣄⠈⠛⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⢙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣿⠟⠛⠻⠿⣷⣾⣿⣧⣤⣄⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣠⣤⣿⣿⣶⡿⠿⠛⠻⣿⣆
⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢠⣿⠏⠉⠛⠛⠛⠛⠻⠿⢿⣿⠿⠿⠛⠛⠛⠛⠋⠉⢻⣿⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⣤⣤⣤⣤⣄⡀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⢀⣿⡇⠀⠀⠀⢰⣿⠋⠉⠉⠛⠁⠀⣿⣟⠉⠉⢻⣿⡄⠀⣿⡟⠋⠙⠿⠷⠀⠀⢀⣀⣀⣀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⢸⣿⣷⣶⣦⠀⠘⢿⣿⣶⣦⣤⡀⠀⣿⡿⠀⠀⢸⣿⡇⢸⣿⡇⠀⣤⣤⣤⠀⢸⣿⣛⠛⠛⠁⢠⣶⣶⣿⡇
⠀⠀⠀⠸⣿⡏⠉⠁⠀⢀⡀⠀⠈⠉⣿⡧⠀⣿⣇⠀⠀⣸⣿⠇⠸⣿⣇⠀⠉⣽⣿⠀⠈⠛⠛⠿⣿⡆⠀⠉⠉⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠚⠿⣿⣿⡿⠟⠁⠀⢿⢿⣿⡿⠿⠋⠀⠀⠙⠿⣿⣿⠿⠃⠀⠸⠿⣷⣾⠿⠃⠀⠀⢸⣿⠃
⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀⣀⣀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⣀⣠⣴⣿⣷⣶⣿⠿⠿⠿⠿⠿⢿⣿⠟⠻⠻⠿⠿⠿⣿⣶⣿⣿⣤⣄⡀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⠛⠉⠙⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⡿⠉⠙⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠘⢿⣧⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣾⡟⠀⢀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣈⠻⣷⣄⠀⠀⠀⢸⣿⠀⠀⠀⢀⣴⣿⢏⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣶⣤⣼⣿⣤⣤⣶⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⠿⠿⠿⠿⣿⣿⣶⣤⣄⡀
⣴⣿⡿⠿⢿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣤⣦⣤⣀
⢿⣿⣤⣀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣶⣶⣤⣤⣀⣰⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠛⠻⢿⣿
⠈⠙⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠺⠇⣼⣿
⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⣾⣿⠏⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⡿⠿⠛⠛⠛⠿⣿⣿⡏⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣶⣶⣾⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣷⣶⣿⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣯⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⣉⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⢀
⠀⠛⠟⠀⠀⠈⠉⢀⣶⣦⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢉⣙⣾⠛⢦
⠀⠀⠀⠀⡀⠀⠀⠈⠛⠋⢀⡀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⣤⣀⠀⠀⠀⠘⠉⣻⣿⠰⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⣤⣌⣉⣹⣷⣦⣤⣏⣹⣿⢡⢰⡇
⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠁⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠶⣠⣞⣛⢿⠟⣩⣿⣿⣿⣿⠟⣿⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠶⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⡀⠀⠀⠀⠀⢀⡀⠀⠀⠴⠟⠉⠁⢰⣾⠗⣫⣷⠟⣿⣡⣴⣿⠇⠁⡿⠁
⠀⠀⠀⢀⣾⣷⡄⠀⠀⠀⠠⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢳⣶⢦⣀⡏⠷⠀⡀⠀⢀⣠⠖⢂⣴⣾⠟⠇⠘⣿⡿⠿⢃⣴⠞⠁
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠐⠂⠀⠀⠀⠀⣮⣿⡀⠝⠡⠀⢤⠀⠐⠋⠀⠰⡯⠞⠁⠊⠀⠀⠛⠿⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢠⡐⠑⡄⠐⡀⠀⠁⠀⠀⠆⠠⠀⠀⠁⠘⠀⢀⣂⠀⣠⠾⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠂⠀⠀⠀⢄⠀⣄⢀⣿⣼⣷⣿⡇⠈⠙⠀⠇⠈⠀⠀⠀⠀⠲⣦⠀⠉⠉⠀⢀⣠⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⠂⠆⠀⡿⢿⣿⠟⡠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠾⣂⠀⠀⣠⡾⠟⣽⠟⡟⢷⣦⡀⠀⠀⣰⢦⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⢀⠀⠈⠶⠁⠘⠿⠀⢠⠀⡷⡀⠀⠀⠀⠀⠠⠎⣡⠄⠉⠷⢶⣄⢀⣾⡟⠰⣿⠀⠙⣣⢀⣴⡾⢋⣌⢇⣼⣥⡤⡀
⠀⠀⣀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⠘⠀⠈⠃⡴⡆⠁⢸⢆⡀⠳⠦⣉⡜⣿⣦⣴⣃⣀⡄⠀⡀⢿⠈⣿⠤⠴⢛⣧⢠⢿⡟⣉⣿⣜⡿⣈⣷⡆⣺⣧⣀
⠀⠀⠁⠀⠑⠈⠀⠀⢠⠀⠀⠀⠀⠀⠰⡁⠀⠓⠀⠠⠋⠄⠊⡀⣃⣼⡁⢀⣼⡟⢋⣥⠌⢿⣶⠋⠦⠖⢀⣿⡄⠀⢸⡏⢤⣄⡀⡻⣿⡶⣥⡙⠦⠀⣹⡅⢏⠁
⠀⠀⠀⠀⠀⠰⠄⣄⢀⠋⠀⠠⠀⠘⠀⢁⠀⣠⠄⡀⠈⠤⠀⠀⠁⠆⢁⣿⣿⠀⠟⢤⣤⡰⢮⡴⡦⢠⣾⡿⠀⠢⡈⠳⠟⣹⣿⣷⡌⣴⣻⣙⣧⣀⣤⡴⠎
⠀⠀⠀⠂⠀⠀⣠⠁⣬⣿⡞⠁⠀⠀⠀⠀⠐⠋⠐⠃⢻⡄⠀⠀⣤⠟⣻⣿⣇⠀⠘⠂⠃⣬⡎⠹⠾⠿⠋⠀⠀⣠⣾⣶⣾⠟⠀⠀⠉⠁⢸⣦⢙⣙⡋⠃
⠀⠀⠀⠀⠀⠀⠀⠤⠰⠟⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⡘⣧⠀⠀⢀⡁⠙⣿⣿⠀⡴⣦⠐⣧⠔⠃⠌⢱⡟⠻⠟⡿⠛⡉⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠁⢀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⡀⣤⢦⣄⠀⠀⠀⠀⢀⠀⠐⢁⡀⠀⢸⡶⠓⣦⣿⣤⣿⡿⠀⠰⡞⢠⡉⡀⠀⠄⣼⠇⠆⠈⣷⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⢀⠀⠠⠀⢣⡀⠀⠈⠀⣄⠀⣠⣿⣧⣤⣾⡇⠀⢾⣇⠤⣿⡿⣿⣿⣿⣤⢴⣿⠰⢱⣏⣁⣴⠏⢀⠃⣀⠁⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⢀⣼⣿⣿⠟
⠀⠀⠀⠊⢀⡤⠊⠀⠀⠀⢁⡶⠂⠀⠈⠻⣷⠴⢿⣧⠴⠚⣿⡶⠿⣧⠀⢠⠃⢀⡼⣏⠀⢀⣬⣩⡀⠶⠉⣹⠿⠃⢋⠠⢘⣯⠹⠎⠛⢛⠶⠶⣾⠿⠿⠛⠁
⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠙⣷⠛⠻⣷⡞⠙⣷⠶⣿⡇⣸⡀⣼⢀⠉⠃⠀⠈⠿⣁⣴⠛⠛⢠⠢⡌⠀⣸⠃⠀⢬
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢍⠁⢦⠀⠀⠀⠀⣿⠋⠛⣿⡶⢿⡿⢛⣿⠃⠉⠈⢳⣼⠀⠀⠀⡈⢀⠈⠁⠀⠀⠀⡤⡌⠀⢸⡆⡅⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠹⢦⡀⢸⡀⢻⡶⠋⠀⠀⠀⠀⣿⡛⠺⣿⡗⢿⣧⣼⣏⢠⣅⡀⠀⠀⣱⠄⢺⣄⣨⠟⠀⠀⡐⠴⠀⠀⠀⣼⡇⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢼⡗⠀⠀⠔⠲⠉⢉⢿⡏⠻⣧⡀⢻⡿⣧⡌⢤⡙⢀⢢⡙⠶⠛⢡⡀⠀⠀⠀⠈⠆⡄⠁⢀⣿⡟⢀⠁⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠀⢀⠤⢷⡁⠀⢨⢀⡈⢑⠄⣱⡟⠳⡄⣇⠼⣣⡝⠃⠚⠁⠀⠀⠀⠀⠀⠆⠤⢀⣼⡿⠁⠀⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢐⠇⠀⠀⠀⠀⠀⠀⠃⣸⣏⠁⠈⠁⠰⣤⣼⠁⣈⠃⠀⠖⠉⠁⣀⠀⠀⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡘⠓⠀⠀⠀⢀⠈⠀⠘⠻⡿⠓⠀⠄⠀⠀⠁⠀⠉⠀⠀⠀⠘⠃⠉⠤⠀⠀⠁⠀⠀⠈⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⢀⠀⢀⣉⠉⠐⣭⡀⢀⠁⠀⢰⠄⠀⠰⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢀⠤⠼⠗⠂⠀⠀⠀⠢⡞⠋⢰⡟⡹⠟⠉⠀⠀⠓⣀⠀⠀⢈⡄⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⣽⣉⡿⣿⣿⡄⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢽⡖⠒⠳⡄⠁⠀⠀⠰⢀⣀⠀⠀⠀⣧⠥⣼⠿⣴⠂⠀⠀⠈⠀⠈⠀⠀⠀⠀⣀⠀⠀⠘⠀⠀⠈⠃⠀⢠⣼⣿⢨⣷⠿⠇⠀⢀⣼⣿⡿⠃
⠀⠀⠀⠀⠠⠀⠈⠃⠀⠀⠈⢢⠀⠀⢠⠘⢃⠀⠀⣠⠀⡀⢶⠂⠀⣤⠀⠀⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠚⠀⠀⠀⠀⠀⠸⣿⣼⣿⣤⡄⣄⣴⣿⣿⡃
⠀⠀⠀⠀⠀⢷⣄⠀⠀⠀⠀⠀⢣⡔⠂⠀⠀⠉⠾⣽⣔⡷⠛⠓⣡⣟⣦⠤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⢀⡼⡏⠁⠙⠛⠙⠁
⠀⠀⠀⠀⠀⠀⠉⠣⠀⠀⠀⠀⠀⠱⣄⠀⠀⢈⡁⠈⠋⠿⠾⠾⠷⠋⠀⠀⠀⠈⣁⠀⠀⠀⠀⠠⠶⠀⠀⠀⠰⠆⠀⢀⣴⠛⣬⡇⠈⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⣆⠀⠀⠑⠀⣾⢀⡀⢀⠀⠀⠤⠒⠊⠉⠉⠁⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠝⠛⢋⢸⣧
⠀⠀⠀⠀⠀⣠⠶⢦⣄⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠻⠦⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡉⠉⠛⠛⣻⠷⠀⠀⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⡇⣀⡴⠛⠁⠀⠀⠀⣀⠶⡄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢼⠾⠋⠀⠀⠀⠀⠀⡜⢁⢰⠇⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⡀⠀⠀⣠⠄⠓⠛⠁⠀⠀⢀⣄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠘⣯⠙⠲⡌⢳⣄⡼⠛⠛⠋⠀⣀⠀⡴⠋⢸⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢦⣑⡿⠀⠻⣅⠀⠀⠀⠀⣿⠸⣥⡥⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢦⣽⣆⠀⠀⣠⡿⠤⠤⠄⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣠⠴⠒⣓⣦⡀⣿⡴⠛⠉⠀⠀⠀⣀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠙⠛⠲⠶⠞⠁⣿⠀⠀⠀⠀⣠⠞⣿⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠛⠀⠀⣠⠞⠁⠀⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⠀⢠⣾⣥⣤⣤⣤⣬⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⣛⣻⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣶⣄⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣧⣴⣿⣿⣿⠿⠻⠳⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⢿⣿⣿⣿⣿⡟⡀⣦⣤⣤⣄⠀⣿⣾⡛⣌⣹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⢟⢻⣿⣿⣿⣿⣿⣷⣿⢿⣷⣦⣽⣿⣿⠿⠿⠿⢋⠁⡙⢛⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣿⣯⣽⣾⣿⣿⣿⡿⠋⠉⠛⠉⡈⢙⣷⠾⣧⣠⣹⡿⠣⣄⣴⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⡟⣿⣶⣶⣾⣿⡍⣿⣁⢀⣼⢿⣿⣿⣷⣿⠏⠀⣠⣤⠞⠛⠋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣻⣿⣿⣏⣸⣿⣿⠉⣉⢹⣷⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⢧⣿⣶⣿⠶⢧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣻⣿⣿⡿⠋⠉⠛⠿⣿⣡⣄⠀⣿⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣹⣿⣶⣿⣿⣿⣿⡇⣤⣶⣤⡀⢀⣹⣿⣷⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣼⣻⣦⣿⡆⢢⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⠿⢟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣸⣾⣇⠹⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⣿⠿⣛⣙⠛⣺⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣾⣿⡀⣿⣿⣿⣿⣿⣿⡏⠀⢀⡴⣩⣶⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠫⣿⣷⢸⣿⠿⣿⣿⣿⠀⣠⢏⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣉⢿⢾⣿⡀⢿⣿⡇⢸⡇⠚⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣬⡛⢾⣿⢷⢸⣧⠀⢸⡇⠀⣿⣿⣿⣿⣿⠟⠛⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢸⣿⠀⣼⡇⢀⣿⣿⣿⣿⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠛⢿⣿⣿⣿⣿⢸⣿⣤⣿⡇⣾⣿⣿⣿⡇⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⠿⠛⠙⠉⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡟⠿⠿⠿⠿⠿⢿⣿⠿⢻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⣾⣿⣷⣝⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠻⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣧⡀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡟⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠋⠉⠉⠉⠉⠉⠉⠉⠝⠢⣀⣀
⠀⠀⢀⣀⣠⠤⢔⢋⣠⠄⠀⢠⡀⠀⡀⠘⢀⣀⠄⢀⠀⠀⣢⠀⠈⢳
⠀⣾⠉⠀⢂⡠⠞⠙⢄⡀⠀⠀⢙⢞⠀⠠⠀⠁⠀⢀⠑⠊⠀⣈⣠⡏
⠀⠸⡦⣤⣁⡙⠢⡔⠋⠉⠢⠀⠀⠀⣁⡤⠴⠒⠒⠒⠒⠒⢋⣩⠞⠁⠀⣀⣀⠴⣪⣿⣒⣦⠤⠤⢤⡀
⠀⠀⠙⢦⣈⠉⠉⠙⠛⠚⠛⠛⠛⠉⣁⡠⠖⠛⠉⠉⠉⠉⠁⠀⢀⢖⣿⣿⣿⣿⣿⣿⣿⣿⠟⠪⢷⣮⡳⣄
⠀⠀⠀⠀⠉⠉⠓⠚⠒⠒⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⣀⡠⣴⣺⣥⣬⣽⠿⣍⢉⣯⣽⣯⣴⣿⣿⢰⣿⣿⡞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣥⣞⠻⣽⣿⣿⣗⣟⣻⡷⣻⡿⠿⠿⣿⡿⢰⡿⢛⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣦⠀⣿⠈⣿⡏⠉⢹⣿⣯⠀⠉⠉⠙⣿⣏⠉⠁⠋⢉⣿⠃
⠀⠀⢀⡴⣲⣟⠓⡲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠒⠳⠾⠿⠧⠤⠼⠿⢿⣄⣀⣀⣠⣿⠿⠧⠒⠒⠋
⠀⢰⢏⣼⣿⣿⡆⣿⣦⣬⣭⣿⠛⣛⣛⣛⣓⠒⠶⣤⡀
⠀⡟⣾⣿⣿⣿⡇⠙⠿⠿⢋⣡⣾⣿⣿⣿⣿⠿⠷⠶⠉⢢⡀
⠀⡇⢿⣿⣿⣿⣿⡄⢻⣷⣦⣭⣭⣭⣭⣥⣤⣶⣶⣿⠟⢠⡇
⠀⢷⡘⢿⣿⣿⣿⠃⣹⣿⣿⣿⣿⣿⣿⡿⢛⣩⠤⠶⠾⣿⠇
⠀⠘⣿⠦⢭⣉⠁⠸⣿⣿⣿⣿⠿⢟⣩⣶⠋⢁⣠⠴⠚⠁⣀⠤⠒⠒⠒⠲⠤⣀⣀⣀⣀⣀⣀⠤⠤⢄⡀
⠀⠀⠹⡇⠀⠈⠉⠑⠒⠖⠶⢶⣾⣿⣿⣿⡶⠋⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⣘⣿⠿⠛⠁⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⠢⢄⣀⠀⠀⠀⢀⣀⣀⡠⠤⠖⠒⢉⣁⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠉⠉⠉⠁⠀⣀⣀⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠤⠔⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⡤⠤⣄⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡖⠋⠀⢀⠤⠀⠠⠄⡼⠁⠈⠠⠈⠉⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⡀⣼⠉⠐⠂⠀⠀⢀⡀⠀⢀⢧⣀⣀⠒⡀⠀⠀⠂⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠃⠀⠀⠀⡇⠀⠀⠀⠃⠀⢀⠴⠊⠁⠈⠁⢠⠉⠉⠳⢤⡀⠤⠀⠙⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠉⠀⡤⣷⠀⢀⣩⢤⡴⠋⠀⠈⠁⠀⠤⠀⠀⠀⣠⡀⠙⠲⢦⠀⠦⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢧⠀⠰⠀⠀⠀⢨⠗⠋⠀⣀⡧⠀⠰⠆⠀⠀⠀⢀⡀⠀⠀⠀⠤⠀⢸⠰⠒⠒⠧⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢈⡓⠲⠶⠊⢻⠏⠀⡠⠀⠀⣇⠀⠀⠀⠠⡄⠀⠀⢀⣀⠀⠀⣄⠀⢸⠀⠀⢀⡀⠀⠘⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠉⠀⠀⠀⠀⠘⡄⠀⠀⢠⠄⠘⢦⣀⣀⢀⣀⣀⠴⠚⠓⠦⠀⢠⠴⠾⢄⣀⡀⠀⠀⢀⡀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⠘⠁⠀⠀⠀⠀⡷⣄⠀⣀⣤⠴⠚⡇⣿⠉⡜⠁⠀⠀⠒⠀⢴⠀⠀⠀⠀⣤⠉⢣⠀⠀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢤⡠⡴⠋⠀⠈⡏⠉⣧⠀⠀⡇⡝⠠⠃⠀⠈⠁⠀⢀⠈⡦⠀⠠⠄⠀⠀⠘⡌⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢠⠀⢹⠀⠀⣧⠇⠀⢑⡶⣄⡀⢀⣈⡀⠱⠄⠀⠀⣀⠀⢰⡃⠤⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣾⠀⢸⠀⠀⡏⠀⠀⠘⡰⠁⠉⣽⣇⠀⠀⠀⣀⠀⠀⠀⠀⠱⣄⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠇⠀⠀⠀⠀⠇⠀⠀⡴⠁⠀⠘⠁⠘⠦⣤⠤⣤⡄⠀⠆⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣀⡤⠤⠶⠖⠒⢇⣠⣄⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢄⣿⣟⡤⠀⠀⠀⠀⢀⡀⠂⠠⠈⠠
⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠾⢿⣿⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣹⣿⡟⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⡀⢀
⠀⠀⠀⠀⠹⢻⣦⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣄⣷⠏
⠀⠀⠀⠀⠀⠈⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠲⡄
⠀⠀⠀⠀⠀⠰⣶⣶⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⣠⢲⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠉⡀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠠⣦⣼⣇⣤⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⣶
⠀⠀⠀⠀⢛⣿⣯⣿⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠘⠩⣿⠙⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠿

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⣾⠒⢲⡾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣴⡞⠛⠓⢢⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⣼⣇
⠀⠀⠀⠀⣿⠤⢼⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣶⢿⡟⣥⠹⡟⠀⠀⠀⠀⠀⠀⠀⣿⡗⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣅⣽⣤⡇⠀⠀⠀⠀⠀⠀⠀⠻⢧⣤⣤⠜⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⠿



⠀⠀⠀⢀⣀⠖⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣆
⠀⠀⠀⠀⢸⣆⠀⢸⠛⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⢙⣵⣷⠀⠀⠀⠀⠀⢠⣖⡿⣿⣯⣿⢿⣳⡄⠀⠀⠀⠀⠀⢠⡟⢩⡙⣿
⠀⠀⠀⠀⠘⣿⣷⡘⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⣼⠟⠁⠀⠀⠀⠀⠀⠈⠙⠻⣿⣽⡿⠟⠋⠀⠀⠀⠀⠀⠀⠘⣿⣦⡴⠛⠢⡄
⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠀⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⣺⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⣤⣴⣿⠱⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢾⣿⣽⣿⠆
⠀⠀⠀⢸⢟⠛⠛⢻⠟⣿⠆⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣉⣁⣀⣀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠸
⠀⠀⠀⠘⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠞⠘⠦⠑⠤



⠀⠀⠀⠀⣠⣶⠶⠠⡀⠀⠀⠀⠀⠀⠀⠀⠰⢂⡠⠤⠄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣄⠀⠀⣀
⠀⠀⠀⢰⣿⠃⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⢦⣀⣀⣀⣀⡖⠀⠀⠀⠀⠀⠀⣀⣴⣾⣻⡿⢟⣧⠀⠀⠀⠀⠀⠀⢀⣴⠞⡻⢦⣿⣿
⠀⠀⠀⠘⢿⣆⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠸⣗⡶⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⠮⣽⣽⣾⠿⠛⠀⠀⠀⠀⠀⠀⠛⠁⠖⣱⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⠀⣶⣶⣶⡄⢰⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⢸⣿⣿⣿⣧⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠁⠸⠿⠿⠿⠿⠿⠇⠀⠿⠿⠿⠿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⢸⣿⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠻⣿⣿
⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢸⣿⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⣛⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠘⢃⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣦⣄⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⣾⣿⠿⠛⠛⠛⢿⣿⣿⣿⣿⣷⣦⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⢠⣾⣿⣿⠁⣠⣶⣿⣦⠀⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⣿⣿⣿⣿⣄⠈⠛⠛⠿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣿⣷⡀⢹⣿⣿⣷⣄⡈⠛⠿⠿⠿⠿⠟⠁⣴⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣆⡈⠛⠿⣿⣿⣿⠟⠀⣼⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛