Boom boom mushroom Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣤⡤⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⠿⠂⠀⠀⠀⡀⠀⠀⠀⠉⠁⠀⠀⢤⣀⣠⡼⠋⠉⠹⠁⠈⠒
⠀⠀⠀⠀⠀⠀⠰⠀⠀⢄⣀⠀⠠⠄⠀⠀⣰⢞⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢀⠛⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣯⡄⠀⢀⠀⣰⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠻⣏⠈⠉⠀⠈⠋⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⢀⣽⣏⠀⠀⠀⢙⡀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠉⣶⠂⠀⠂⠀⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⠀⠁⣿⠂⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄⠈⠀⣀⡀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠀⠀⠀⣩⡰⠆⠀⣴⢦⠴⠄⠀⠀⠀⠀⠀⠀⡸⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⠀⠀⠀⠠⠀⠈⢳⠀⠚⠀⠂⠀⠀⠀⠀⣀⠀⣀⣠⠤⠤⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣷⣖⢀⣀⡀⣠⡞⡅⢸⡖⢀⡀⢰⣄⣀⣨⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⡟⢹⣿⡾⠿⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠛⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣤⢦⡔⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣤⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀⠀⠀⠀⠀⢸⣿⡟⠰⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡃⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⣾⠃⠁⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⠏⠑⣠⡆⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣺⣿⣿⠀⠀⣸⠂⣤⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⣀⡀⠀⠠⠈⠁⠠⠄⠀⠀⠐⠦⠬⣽⡿⢦⣄⡀⢹⠀⠘⠂⠀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⣸⣟⣿⣷⣶⣄⣐⣆⣀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠀⢲⠀⠀⠀⠀⠀⡈⠋⠀⠀⠐
⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣄⠊⠲⠶⣤⢤⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠒⠂
⠀⠀⠘⠛⠛⠛⠉⠉⠉⠉⢩⠯⠭⠍⣩⣭⣤⣤⣤⣤⣤⣤⣤⡤⠉⠙⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⣭⡭⠍⠍⠹⠿⠛⠛⠓
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣟⣉⣻⣋⣙⣛⣟⣋⣿⢻⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⠉⠉⠙⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠈⠉⠲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠈⠁⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⠳
⠀⠀⠀⠀⠀⠀⠀⢠⠔⢃⡀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡷⢠⡠⠓⢄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠁⠈⠳⠄⠀⠀⠀⠀⢀⠀⠉⠉⢛⣧⣄⣀⣀⣀⣉⣬⡝⠋⠉⠁⠀⠀⠀⠀⠀⠠⠔⠁⠀⠃⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⣠⠀⠀⠀⠀⠈⠢⠴⠶⠋⠙⣛⣏⠀⠀⠀⠀⠀⠀⠀⢨⢏⡉⠙⠲⠤⠖⠀⠀⠀⠀⠀⡄⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠋⠒⠲⠦⠰⢶⠒⠀⠀⠠⣀⣀⢸⡀⠀⠀⠀⠀⡀⠀⡎⠀⠀⠀⠀⠀⠐⡦⠄⠤⠒⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⠛⠃⠰⣇⢰⢰⠀⢠⢃⣿⠇⠘⠛⠒⠒⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣾⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣴⡟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠠⠄⠻⠟⠛⠓⠟⠠⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⡀⠀⠠⠤⣴⠦⠀⠄⢦⠤⠄⠀⢀⣙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠐⠒⢾⣷⣴⡆⡿⠒⠂⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⣸⡬⠤⠥⢇⣀⣀⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠦⣤⡠⣤⣄⣁⠀⠀⠐⠋⠀⠀⠀⠀⠀⢨⠦⠀⠀⣈⣓⣠⠄⣤⠔⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⣎⠄⠀⠀⠉⠁⠀⠒⠁⠀⠠⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠐⠁⠀⠀⠐⢩⣄⡀
⠀⠀⣀⣀⣤⡐⠀⠋⠲⠒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠈⠀⠢⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠈⠀⠁⠈⠈⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠚⠛⠛⠓⠒⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⡼⠖⢒⣫⣭⣭⣽⣭⣽⣭⣭⢼⣥⠯⣽⣽⣉⣟⡓⠒⠶⠤⣄⡈⢧
⠀⠀⠀⠀⠀⠸⡇⠰⣏⠁⠂⡄⠀⠀⢀⠀⡇⠀⠀⠀⠀⢠⡏⠉⠙⠛⠳⠶⢦⣍⠻⣇
⠀⠀⠀⠀⠀⠀⠙⠦⣌⡛⠲⠦⣤⣄⣈⣸⡇⠀⠀⠀⠀⣸⠳⠀⠆⢐⣀⣀⣠⠟⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⠦⠬⡽⠀⠀⠀⠀⠀⣿⣛⣛⣛⣉⣭⠭⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣰⠛⠉⠙⠉⢣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡇⠀⠀⠀⠀⠀⢸⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠻⢤⣀⣀⣠⠴⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⢀⣠⡤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡁⠀⠀⠀⠀⠀⠩⠿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠓⠐⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⣀⣤⢶⠶⢾⡟⠛⢿⡟⢟⣟⣶⣶⣄⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⣾⣯⡴⣷⢳⢹⣗⠀⢸⣷⣻⡼⡿⣿⣿⢂⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣘⠻⠿⣾⣧⣤⡇⠀⠀⣿⠷⠿⢛⣫⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠚⠛⢦⡀⠀⠀⠀⠀⠉⠛⠒⠲⠶⢾⡇⠀⠀⡿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠁⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⡇⠀⠀⠀⠀⢀⣤⠶⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠋⠁⠀⠀⠀⠀⠀⠐⠿⣦⡀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣼⠁⠀⣠⡶⠾⠛⠁⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣴⣶⣲⣲⡶⠒⣶⣶⢦⣄⠈⢻⡄⠀⠀⠀⢀⡾⠀⠀⢠⡏⠀⣾⠙⠐⠄⠀⠀⠀⠀⠀⠈⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣙⣛⣳⠇⠰⡿⠿⠾⢛⣡⠞⠁⠀⠀⠀⣼⠁⠀⠀⣼⠁⠀⠹⣎⡂⠀⠀⠀⠀⠀⠀⠀⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠀⠀⡟⠛⠉⠉⠁⠀⠀⠀⠀⣸⠃⠀⠀⣸⠃⠀⠀⠀⠀⠙⢲⣤⣄⣀⣀⣀⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠃⢲⡏⠉⠉⠉⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⡾⠁⢀⡞⠀⢀⣀⣤⡶⠛⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢳⡄⠀⠀⠀⠀⢸⡇⠀⠀⢠⡇⠀⠀⠀⠀⢠⠟⠀⢀⡾⠁⣴⠋⣉⣀⡀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢤⣀⠀⠈⢧⠀⠀⠻⣄⠀⠀⠀⣾⠀⠀⠀⢸⠁⠀⠀⠀⢠⠏⠀⢀⡾⠁⠀⠙⣦⡻⢭⣽⠗⣶⣤⡀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠙⠳⣦⡈⢷⡀⠀⠙⣦⠀⠀⣿⡀⠀⠀⣼⠀⠀⠀⢠⡟⠀⠀⣼⠁⠀⠀⠀⠀⠙⡷⠃⢰⣟⡾⠟⣂⡼
⠀⠀⠀⠀⠀⠀⠀⣾⡫⠃⠀⠀⠀⠀⠀⠨⣻⠌⢷⡀⠀⠈⢳⣸⡇⡅⠀⡄⣿⠀⠀⠀⣾⠃⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁⣠⠏⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣠⣤⠴⠚⠁⠀⠈⢷⡀⠀⠀⢻⡇⡇⢀⢷⢿⡆⠀⢰⡿⡔⡄⣿⠀⠀⣀⡴⠛⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠹⡄⠀⠀⠀⠀⠈⣧⢎⠂⠹⣿⢷⢸⢺⢿⣧⠀⢸⣇⣇⡇⣿⣠⠞⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠙⢦⣤⣀⣀⣀⠸⡎⡆⠠⢹⣟⡌⡎⡏⢿⡆⢾⣏⡏⡇⣹⣿⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠭⢛⣛⣛⣷⢿⣠⠗⢃⢿⡜⢜⢌⢬⡇⢸⡏⠇⠇⢻⣷⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠿⠶⠟⠃⠸⣧⢸⠘⣸⡟⠳⠶⠛⠁⠈⢿⣜⣙⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠶⠟⠁⠀⠀⠀⠀⠀⠀⠙⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⢠⣤⠀⠀⠀⠐⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠑⠠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠛⠛⠋⠁⠀⠀⠀⢀⡤⠀⠀⠀⠀⣴⡧⠀⠀⠀⢠⡤⠀⠀⠉⠉⠁⠐⠒⠂⠠⠄⣀
⠀⠀⠀⠀⣴⡞⠋⠁⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠈⠻⣷⣤⣀⠀⠀⠀⠈⠀⠀⠀⠙⠁⠀⠀⠀⠀⠘⠁⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠼⢓⡺⠟
⠀⠀⠀⠀⠀⠈⠙⠿⣿⡷⢶⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠐⠖⠋⣩⠭⠕⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣽⣯⣭⣉⡙⣯⡉⠉⠉⠉⢻⠙⡉⣉⣔⣤⣴⡥⠶⠖⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⢻⣿⡾⠛⠃⠘⡋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⣯⣄⡀⡀⣀⠴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⣨⢉⣅⡱⢦⡟⠀⠀⠀⡰⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡄⢰⠀⢸⣿⠟⠉⠁⠀⠀⢷⠀⠀⢰⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢆⠹⣼⠀⢸⡿⠀⠀⠀⠀⠀⠘⡇⠀⡿⠀⡔⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢧⢱⡟⢦⣾⠅⠀⠀⠀⠀⠀⠀⠸⠀⡇⡜⢀⡇⠀⢀⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢸⣸⢿⡄⣿⣧⠀⠀⠀⢀⠁⠀⠀⢸⣧⡃⣸⠞⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡟⣾⣽⡟⣹⠀⣀⠀⡌⠀⠀⠂⠸⣿⠃⡏⢠⠏⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢁⡇⣾⡇⣽⠇⡇⢠⠀⠀⠀⠀⢸⣟⣸⢁⣞⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣧⣿⣯⢻⣴⠄⢸⠀⡇⠀⣇⢸⣿⣷⣾⣋⡥⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣿⣿⣆⣸⡄⣇⣶⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠿⠿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣦⣵⣦⠀⣀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣓⣿⣿⣿⣿⢿⣿⣿⣿⣿⣜⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡍⢻⡿⣿⣶⣭⢿⡦⢾⢻⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⠟⠃⡀⠀⣀⣈⡑⠲⣄⠀⣾⣿⢿⣿⣿⣿⣿⠀⠀⠠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⣿⡿⣧⡍⢷⣟⢾⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠏⠀⠀⠚⠧⢓⢿⣾⣿⣷⣿⣤⣿⣯⣿⣿⣿⣿⠟⣹⣶⣾⣶⣤⣄⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠙⣿⣾⡇⢭⣵⣶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠙⢼⣷⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡉⠏⣙⣁⣛⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣀⣀⣀⠀⠀⠀⢠⣿⣿⡿⠏⣰⣿⣿⣿⣿⣿⠋⣼⣿⣿⠟⠇⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⢬⣽
⠀⠀⠀⠄⣤⠶⠖⠈⠙⠛⠛⠿⠿⣷⣶⣶⣿⣿⣿⠅⣰⣿⣿⣿⣿⡿⠃⣼⣿⡿⠋⠀⠀⢹⣿⡿⢻⣿⣿⠿⣛⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣥⣲
⠀⠀⢤⡾⠋⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⢿⠆⣴⣿⣿⣿⣿⣿⠀⣼⣿⠋⠀⠀⠀⠀⢺⣿⣿⣟⣩⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠃⢀⣼⠿⣿⣿⣿⡿⢃⣾⣿⣿⣦⣤⣄⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠀⣠⠞⠁⠀⠈⠛⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣾⠟⠛⣩⣭⣯⡛⠛⢻⣿⣿⣿⣿⣡⡆⣸⣦⡀
⠀⠀⢻⣿⡀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⠀⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢀⣿⣿⣿⡗⠀⠀⠈⢹⣿⣿⣿⣧⣿⡿⠿⠆
⠀⠀⠀⡼⣿⡆⠀⠀⠀⣾⣿⣫⣴⣶⣀⣀⣀⣀⣠⣶⣶⣄⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣾⣇⣾⣿⣿⣿⣧⡀⠀⡠⠈⠉⢹⣟⣡⣴⣴⣶⣶⣶⡀
⠀⠀⠀⠱⣈⠁⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢂⡀
⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠐⣄⡀⠈⠁⠀⠀⠀⣷⣶⢀⢀⣀⣀⠀⣾⣿⣿⡟⢻⢿⣵⠟⠁⢻⣿⡿⢋⡸⣷⣠⣶⣿⣿⣿⣿⣿⡿⠏⢡⣿⠀⣸⠷
⠀⠀⠀⠠⣇⣼⣿⣆⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠹⡍⡘⢸⣿⣿⢿⣿⣿⣿⣿⣷⣾⡏⠀⠀⣸⣿⣡⣿⣿⠛⣿⣿⣿⣿⣿⣿⡟⠀⡠⣿⣿⣿⣯⣀
⠀⠀⠀⠀⢾⣿⣿⠃⠀⠀⠀⠀⠊⣿⣇⡀⠀⠀⠀⠀⠀⠁⢾⣿⠑⠻⣿⣿⣿⣯⣾⣿⣧⣶⣿⣿⣿⣿⣿⣿⣦⠘⣿⡿⢻⣿⠹⠃⣼⠇⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠈⠻⣷⡤⠀⠀⠀⠀⠀⠈⢿⣟⢳⣤⣤⣄⡀⠀⠘⡄⠀⠀⠛⠛⠛⠿⠏⠉⠀⠀⠀⠉⠛⢿⣿⣿⣿⣧⣿⠁⠀⢻⣄⣼⣏⢀⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠀⠀⠙⢷⣌⢹⣿⣟⠆⠀⠈⠲⣄⡀⠀⢀⣤⡀⠀⣀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣦
⣶⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⣿⠀⠀⠀⠀⠘⢿⡻⢿⣿⣿⡆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠐⣿⣿⣿⣿⢿⣿⢿⣿⣿⠿⠛⣿⣿⡟⠁

⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢀⣽⣿⢛⣿⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡀⠀⠀⠀⡷
⠀⢸⣅⣹⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⣀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠸⠇⢀⣀⣴⠎⠁
⠀⠀⢹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢶⣿⡄⠀⣿⡄⠀⠀⠀⠀⠀⠀⠁⠛⠛⠚⠿⠁⠀⠀⠈⠋
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠏⣠⣄⠘⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣦⣅⡈⠛⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⢀⣀⠘⠛⠶⠶⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢆⠙⠋⣠⠿⠛⠁⠀⠀⠀⡖⠻⠿⠿⠈⠛⠁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⢠⢰⠙⢶⣤⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡄⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⢤⣼⣄⡀⠀⢸⡇⢸⡌⢷⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠞⠁⠐⠀⢁⠀⡞⠁⠐⠀⠀⠀⠀⠘⠃⠈⠁⠉⠻⠆⠸⠇⠈⠃⠀⠀⠀⠀⢺⠇⠀⠀⣀⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣙⠟⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣤⠄⠀⠙⠦⠄⠀⠀⠙⠟⠁⠐⠈⠹⣿⣿⣿⣿⣧⠀⠀⠀⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠙⠂⠀⠀⠀⠀⠔⣉⣙⣢⡀⠀⠀⠀⣿⣿⣿⣿⡟⠀⢠⣤⣀⠹⠿⠋
⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠉⠙⢿⣿⣿⡆⠀⠀⠀⠀⠀⢲⣿⣿⡿⠃⢠⣤⡜⡻⠿⠿⠋⠀⠀⠸⠿⠟
⠀⠀⠀⠀⢸⣯⡄⠀⠀⠀⢺⣴⡃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣼⣿⣾⡄⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢁⡴⣢⣼⣿⣧⡙⣄⡀⠀⠀⡜⡶⡄
⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⢸⠈⠻⠆⠀⠀⠼⢆⣀⡄⠀⣽⡟⠁⣼⠋⣇⢹⣆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠇⠈⠙⠛⠛⠻⠬⠇⠀⠘⠾⠜
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡀⢀⣈⠀⠀⠉⠀⣼⡏⠀⣿⠀⢻⣷⡄⠀⠀⠀⣀⣀⠀⠀⠀⣠⣦⣤⣤⣦⡀⠀⠀⠀⠀⠀⢀⣶⣄
⠀⠀⠸⠷⠸⢯⣴⡄⠀⠀⣤⡀⠀⠀⠀⣸⠋⠀⠉⠁⠀⠀⣼⣿⠁⠀⣿⡇⠀⢿⡇⠀⠀⢈⣉⡉⠛⣦⡀⠙⠿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦
⠀⠰⠶⠒⣄⢰⣤⠀⠀⠀⢿⣷⣄⣠⣾⡟⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⣿⣿⠀⠈⠇⠀⠀⠈⠉⠹⣇⠸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠘⠛⠀⠩⣴⣤⣤⡾⠋⠁⠉⠙⣧⣄⣀⣀⠀⠀⠻⠟⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⠀⠀⠀⣸⡿⣃⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡁⠀⠀⠀⠀⢸⠟⠛⠋⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢠⢰⣿⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣄⣀⣀⣤⣿⣦⠀⠀⡀⠀⠀⣿⢉⡟⠀⠀⢰⡟⢹⡇⠀⠀⠀⠀⠀⠉⠀⠁⣴⡸⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⣿⡟⠀⠉⠛⠓⣈⢁⠀⠀⠙⠾⠋⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣾⣿⣿⠇⠀⠀⣀⢀⠤⠄⣚⣍⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⣉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⡄⠐⠃⡄⠀⠀⠀⢉⣽⣿⣧⣄⠀⢀⣿⢆⣾⣉⠁⢈⣧⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⠀⠀⠃⠋⡒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⠉⠁⠀⠀⠠⢠⣿⢏⣤⣌⢻⣧⢸⡉⢼⡃⠀⠀⣀⢘⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⣠⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⢸⣿⣿⣿⣿⢸⣿⢸⣿⠘⣇⠐⢿⣿⢿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡜⠀⢀⣤⣤⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢸⣿⢿⣿⣿⢸⣿⠀⣿⢀⣻⣿⣿⠁⣾⣿⣧
⠀⠀⠀⣦⣴⠂⠀⢲⣶⠂⠀⢤⣄⠀⠾⠟⠀⠀⠀⣰⠀⠀⢸⠀⠀⢸⣿⣯⣀⠀⠀⠀⢸⡏⠙⣿⡀⠀⠀⠀⠈⠉⢉⣉⠉⣨⡍⠀⢸⣿⣿⣿⣿⣷⣿⣾⡄
⠀⠐⠛⢿⡟⠂⠀⠈⠀⠀⠀⠲⠦⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⣤⣴⣿⣿⡿⠿⢟⡿⠂⢸⣿⢿⣟⠀⠀⠀⠀⠀⠀⢸⣿⣤⣿⡇⠀⢿⣿⠟⠛⠿⠿⠿⠿⠇
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠻⣿⣿⣿⡏⠉⠉⠉⠀⠀⠸⢧⡴⠟⠀⠀⠀⠀⠀⠀⠸⠟⠿⠻⠇⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⠀⠀⠘⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡴⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⢄⣀⡀⠀⣀⡀⠀⠀⠀⢀⣀⡤⠔⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢸⠀⠀⢸⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣒⡒⠒⠒⠒⠒⠒⠚⠀⠐⠒⠛⠒⠒⠒⠒⠒⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢹⠂⠀⠀⠈⡏⠉⠙⠒⠒⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣠⠤⠤⠒⠖⠚⠋⠀⠀⠀⠀⠀⠀⠓⠦⠤⢶⣤⣤⣄⣀⣀
⠀⠀⡀⠀⠘⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠙⠓⢲⡀
⠀⠀⠀⢀⠉⣀⣤⠤⣄⣠⣀⣀⡀⢀⣀⣀⣀⣤⣀⠀⣀⣠⣄⣠⠴⠶⠤⣤⣀⡀⠀⢢⣤⣄⣀⣠⠄
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣖⣀⣀⣀⣠⣆⣄⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢰⠖⠒⠒⠒⠒⠒⠒⠒⣲⠶⣦⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣛⢋⣿⠿⢿⣯⠙⠻⣄⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢶⡖⢲⣶⣶⣾⡟⢀⠀⣸⣿⡗⠀⠀⠀⠀⠀⠀⠀⢺⣿⣍⠸⣿⣄⣴⡿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠲⣄⡦
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠙⠛⣩⣥⣭⣥⣿⣿⣿⣿⣿⣧⠀⠀⢀⣶⣶⣦⡀⠈⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠇
⠀⠀⠀⠀⠀⠀⢨⢿⡾⠩⣭⣭⣭⣭⣭⣭⣭⣭⣯⠛⠁⠀⠀⠀⠻⢿⡿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣴⣷⠀⠀⠀⣉⣋⡀
⠀⠀⠀⠀⠀⢰⣾⠟⠳⠄⠛⠛⠛⠛⠛⠛⠛⠛⠁⢠⣿⡦⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠟⠁⠀⠀⠀⢬⡽⠇⠀⠀⠀⠀⣀
⠀⠠⣶⡦⠀⠀⠉⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⣇
⠀⠀⠋⠙⠀⠀⠀⠀⢠⣤⣄⠛⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⣼⣇⣿⢿⢿⣶⣦⣄⠀⠀⡀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠾⠋
⠀⠀⢀⣤⣴⣤⣄⠀⠈⠛⠃⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣹⡟⡛⢀⠀⠀⠈⢿⣧⢹⠿⠁⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⢸⣿⠉⠙⣿⣇⠀⠀⠀⠀⠀⣀⣀⠀⢀⡄⠀⢀⣴⣦⠀⠘⠉⠋⠑⠿⢿⣧⠀⠀⠘⣿⡄⠀⠀⢨⡇⢠⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⡰
⠀⣴⠮⢥⣴⣾⣿⠋⠀⠀⠀⢠⣾⠟⢿⣶⣼⣷⣆⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⠀⢁⣾⠻⡇⠀⠀⢀⡀⠠⠄⠀⠀⠛⢦⣄⡧
⠀⠀⢀⣶⠉⠙⣿⡄⠀⠀⠀⠸⣿⣀⣼⣿⣿⣿⣿⡟⠀⠈⣷⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⡇⠀⠀⠀⠀⠙⣶⢶⣦⠀⠈⢁⡀⠲⠀⠼⣃⡄⠈⠁
⠀⠀⠈⠙⠿⠿⠛⠁⠀⠀⠀⠀⠙⠛⠛⠃⠸⠟⠙⠃⠀⠀⠁⣀⡀⠀⠀⠀⠀⢸⣿⡦⠀⢹⡇⢲⡦⠀⠀⠈⢷⣤⣿⠃⢀⡘⠃⢠⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠸⠉⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠇⢰⣿⣿⣿⠛⠃
⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⠀⠸⠃⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠁
⠀⢴⣤⡈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢰⣄⣀⡀⠀⠀⠀⠀⢀⠀⣠⠀⠀⡀⠀⠀⠀⠀⣀
⠀⠙⠛⠁⠈⢧⡀⢀⣠⣴⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣻⠀⢾⡿⠿⠿⣷⡄⢀⣾⣿⠿⠿⣿⣆⠀⠀⠀⢿⣿⠟⠀⢈⠷⠀⠀⠐⠿⡷
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡌⢁⣀⣠⣿⡏⠁⣿⢧⡀⣀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠈⠷⠛⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⢚⡍⠿⠋⠀⠀⠙⠷⠿⠿⠟⠁⢀⣤⡄⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⢳⡄⠀⣧⠈⠀⠀⠀⢠⡶⣦⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⣀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡄⣠⣶⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠈⠀⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠻⣦⠀⠠⢸⣇⣨⡿⣿⠁⣹⡇⠘⠬⠂⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠾⠟⠈⠀⠈⠛⠛⣵⡟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⣿⡏⠉⠉⠀⠀⠀⢸⣏⠉⠉⠙⠛⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⢀⣴⣿⡟⠉⠀⠀⠈⣿⡄⠀⠀⠀⠀⠈⠻⢷⣦⣶⠾⠋⠀⣨⣿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠙⣷⣄⣀⣀⣴⡿⠀⠀⢠⣴⠿⠛⢷⣦⡀⠀⠀⠀⢰⡿⠁⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⡀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⣿⠁⠀⠀⠀⢹⣷⠀⠀⠀⠘⣿⣄⡀⠀⣠⣿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠉⢻⡆⠀⠀⣀⣀⣀⣤⣤⣤⣤⣿⣦⣤⣤⣤⣾⣯⣤⣀⣀⣀⠈⠙⠛⠛⠋⠁⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⣀⣤⣾⣿⠿⢿⡛⠛⣿⡋⠉⢹⡇⠀⠀⢿⠁⠀⠀⢹⡏⠉⠉⣿⠛⠻⢷⣶⣤⣄⡀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠋⠙⢧⡀⠈⠳⠀⠘⠃⠀⠀⠃⠀⠀⠘⠀⠀⠀⠛⠀⠀⠠⠋⠀⢀⡾⠁⠈⣹⡿⢷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣤⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⣹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣀⣀⡴⠀⠀⠀⣠⠀⠀⢸⣿⠀⠀⠀⠀⠀⢾⣧⠀⠀⢀⠀⠀⢤⡀⢀⣹⣶⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣶⣴⣯⣤⣄⣼⣿⠀⠀⠀⠀⠀⢸⣿⣀⣤⣼⣦⣶⣾⣿⡿⠿⠛⠉
⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⣿⡏⠀⠀⠀⠀⢰⠘⣿⡟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⢸⡆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⢸⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⢠⢣⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⢠⠏⣸⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⡞⠀⠃⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⣸⠃⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠘⠁⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⣀⣀⣀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⣁⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⡿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⢿⣾⠿⡇⠀⢠⣄⠀⢠⢀⣴⣤⡶⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠿⠛⠉⠁⠘⡄⠀⠁⠁⠈⠙⠛⠈⡎⠉⢘⠋⣤⠀⢰⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⡄⠁⠀⠀⡈⠈⠀⠘⣿⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⡄⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⢿⣇⢠⣷⣏⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠻⠿⣿⡳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⣹⡄⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠤⠆⠶⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠰⠀⠀⠨⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠀⠏⠀⡀⠀⠀⠀⠀⠀⠀⢀⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⢰⢧⢰⡄
⠀⠀⠀⠀⠀⠀⢰⣆⡆⠘⠃⢠⠀⠀⠿⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠘⠀⠀⠀⠀⠀⠀⠀⠃⠘⣾⠉
⠀⠀⠀⠀⠀⠀⢠⣿⣅⠠⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠈⠣⠄⠀⠀⠀⠀⠀⡆⡆⠀⣿⣶⡄
⠀⠀⠀⠀⠀⢰⣾⣿⠈⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠐⠆⠀⠀⣀⣤⣾⣿⣿⣿⠟⠛⠃⡀⣲⠀⢳⠰⢀⣿⣿⣿
⠀⠀⠀⠀⠀⣼⡿⡏⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⣶⣦⠶⠆⠀⠀⣀⡀⣀⣀⣤⣤⡶⣶⣾⣿⣟⡻⢯⣖⠯⠙⠀⠀⠀⠀⡠⠁⠀⢸⡆⠀⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣷⡇⠀⡁⠀⠀⠀⠀⠀⠀⢀⣴⡃⠛⢀⣠⠶⣿⣿⣭⡙⢄⣸⣼⣷⣿⣿⣿⡥⠚⣉⠅⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⣄⠀⢻⣿⣿⠇
⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣴⣖⠛⣉⣠⣽⣿⣿⣿⣿⣿⣿⣿⠿⠛⠰⣶⣿⣿⣿⡿⣶⣾⠶⠁⠀⠀⠀⠀⠀⠸⢰⣼⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⠀⡀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⠛⠋⠉⠵⠒⢫⡿⢛⣁⣤⣀⣀⣠⣾⣿⣿⣿⠿⠛⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿
⠀⠀⠀⠀⠀⠘⣿⣿⡄⠛⠀⠀⠀⠸⢿⣿⣿⣿⣾⣦⠄⠀⢀⢀⢔⣾⣷⣿⣿⣿⠛⠹⠏⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠒⡟⠋⠉⠉⠉⠉⢻⣡⠀⠀⠀⠀⠠⢀⠂⠀⠄⠀⠀⢀⠀⠀⡀⠀⢀⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣀⢀⠀⠞⠄⠀⠀⠀⠀⠀⠀⠆⠀⠈⠄⠀⠀⡀⠀⠘⡟⠀⠀⠀⠀⠀⣈⠣⠠⠇⠀⠀⠈⠀⠂⠀⠀⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡉⠳⣄⠈⠐⢢⡀⠠⡀⠀⠀⠀⠀⠒⠂⠀⠀⡘⠀⡷⠀⠀⠄⣰⣿⠉⠀⠀⠀⠀⠀⠀⢄⣡⠞⣵⡏⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣴⠄⠀⢢⡀⠈⠀⠹⣰⣂⠀⠀⠀⠀⠀⠘⡇⡀⣿⡆⠘⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⢠⣛⡉⠰⣤⠀⣿⣿⣖⣀⣤⣤⠀⠂⡁⠀⠘⣿⠆⠀⠹⣿⠿⣷⣶⣦⣀⣀⣀⡀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡏⣹⣴⣦⣿⡞⢿⣿⣿⠟⢻⣿⣟⣴⠁⠀⢀⡿⠂⠠⡅⠠⣰⡟⠻⣧⠋⢉⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢾⣿⣽⣷⣯⠛⠿⣾⡁⠀⢤⣿⣦⣄⢈⡤⠔⡑⠀⢠⣿⠀⢲⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢇⣃⡀⢠⣾⣿⣿⣿⣿⣏⣷⡆⣰⣶⣿⡿⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠒⠛⠛⠲⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⣼⣿⣶⣶⣿⣿⣿⣿⣿⣶⣶⣦⣤⣴⣶⣶⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⢿⣿⣿⣿⣿⡿⠋⢠⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡉⠻⣿⣿⣿⣿⣿⣿⡿⢃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣌⣉⣉⣡⡤⠆⣀⣙⠳⢦⣬⣍⣉⣉⣙⣋⣉⣉⣭⣤⠶⢚⣁⣀⠠⣭⣉⣉⣉⣡⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣏⢡⣶⣿⣿⣿⣷⢰⡄⠈⠉⠉⢉⠉⠉⠉⠀⢠⢰⣿⣿⣿⣷⡶⢈⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⣛⡛⠛⠛⣀⣇⠀⠀⠀⢸⡄⢀⡄⠀⣿⣌⠛⠛⣛⣩⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⠀⣤⠀⢸⡇⢸⡇⠀⣿⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⣤⣿⣤⡿⠷⠾⢷⣤⣿⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⢛⣩⣥⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣬⣍⡙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣼⣟⠙⠯⣅⣽⠀⣿⠀⢹⡟⢹⡏⠀⣧⠤⠟⢉⣿⣆⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠲⠶⢿⠀⢹⠀⢸⡇⢸⡇⠀⡿⠶⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢸⡇⠈⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⢚⡯⠟⠛⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣖⣾⣻⣷⣿⣿⣿⠿⢿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣠⠤⠤⠀⡠⠄⠊⢟⡰⠊⠁⠀⠀⠤⡤⣀⠀⠘⠄
⠀⠀⢀⣴⣾⣿⣭⣿⣱⣿⣿⣿⣾⢿⣿⣿⣿⣿⣿⣿⣾⣻⡇⠀⠀⠀⢠⠞⠉⠀⠘⠃⠼⠓⢁⠔⠉⠠⠀⠀⠀⠀⠀⠀⠀⡳
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠔⠁⠐⠄⠀⢤⠄⢀⡀⠀⠈⠀⢠⠂
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣍⣻⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠘⡃⠀⣀⠀⠀⠀⠀⡠⢤⠀⠘⠿⠂⢈⠉⠀⠠
⠀⠀⠀⠙⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠊⠁⠀⠀⠀⠀⠈⠆⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣉⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢀⠠⠘⠒⠲⣦⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⣿⣿⢿⣿⣿⣇⣶⣿⣷⣤⣤⣠⠴⣦⣀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠄⠤⢠⣀⠀⠙⠋⠁⠈⠙⢷⣻⣿⠿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⣿⣾⣯⣽⡿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠘⠀⠛⠢⣄⠀⠀⠀⠉⠉⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣿⣿⣟⣻⢿⣿⣻⠿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⠤⢰⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠟⣻⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⠂⠀⢀⠰⠀⠠⠐⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⠀⠀⠉⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⣿⣿⣿⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⣆⠀⠀⠀⠀⠀⠠⠁⠀⢀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣾⣿⣿⣿⣿⣿⣿⡁⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⡆⠀⠀⠀⠆⠀⢀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏⢿⢿⣿⣿⣿⣿⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠘⠳⣷⡀⢧⣠⡆⡀⠀⢱⣧⠷⠖⠢⠤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠉⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠲⠽⠿⠟⠿⣷⠤⠏⠁⠀⠨⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⣀⠀⠀⠀⢀⣀⠀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠎⡀⠀⠈⢋⢲⠞⠋⠈⠉⠋⠉⠛⠁⠈⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⡞⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣢⠖⢢⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡉⠡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠢⠀⢀⠆⠀⠀⠀⠀⠀⠀⠘⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⣁⠀⠀⣨⠀⠀⠀⠀⠀⠠⠀⢤⡠⠞⡀⠀⡀⢀⠖⠓⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⣗⠀⠐⠠⠀⠀⠀⠀⢠⣾⡶⣿⣆⠀⠀⠀⠀⠀⠀⠈⢹⣿⣧⣦⣤⡄⠀⠀⠀⠀⠀⠩⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠃⠀⠠⠀⣀⡀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠠⠘⠋⠻⠟⠁⡀⣀⠀⣄⣀⡀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢇⠆⢀⣤⠂⠀⠀⢀⡇⠂⠀⠀⠀⠀⠀⡄⠀⢀⣀⡵⣅⣩⠴⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠓⠋⠛⠉⢷⠀⠀⠀⠀⠀⢸⠛⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⣄⡴⠊⣿⡁⠀⠀⠀⠀⣿⠦⢤⡤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠀⠀⠀⠐⡂⢹⡤⢄⡀⠤⣀⣿⢐⠤⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⠆⢀⠀⣀⣄⠁⠐⠀⠀⣀⣀⣀⡿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠙⡏⠈⠛⠦⢾⡶⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⢧⡀⠀⢀⣠⠊⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠐⠒⢴⡉⠉⠋⡇⠀⣀⢀⣿⡁⠈⠉⠡⠀⠀⠀⠳⢦⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠀⢀⠐⠋⠁⢀⠀⠊⠙⠞⢄⠁⠀⠁⠀⠁⠀⠀⠀⠈⠁⢀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡃⠆⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠰⢎
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⠛⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠐⠀⠀⠉⠑⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠙⠛⠃⠉⠀⠀⠀⠀⠁⠀⠐⠐⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠁⠈⠉⠙⠓⠊⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣶⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠫⠙⠉⠉⠀⠀⠀⠈⠀⠀⠀⠈⠙⠿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⠛⠳⠁⠀⠀⠀⠀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⣶⣃⣀⠀⠀⣀⣠⣎⠀⠀⠀⠀⡱⠄⠀⠤⡀⠀⠠⡀⠀⠉⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⠟⠈⢛⠟⠣⡴⠊⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠒⠂⡐⢀⣘⠈⠙⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣻⠀⢀⡎⠀⠀⢸⡇⠀⠀⠀⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠈⠢⡮⠛⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣽⣉⣄⠘⣇⡀⠰⣾⣿⣦⣀⣳⣄⢈⣿⣆⡀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⠀⠅⠀⢈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⢶⣶⣶⣅⣄⣀⣀⡀⠘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⡻⣿⡿⠻⣯⣽⣟⣻⣿⣿⣿⣿⠁⠀⠀⠀⠀⣛⣿⣿⣿⣿⣯⣭⣭⣿⡿⣛⣴⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠟⠁⠹⣿⣿⣿⣮⣹⣿⠿⢿⣿⣿⣿⡖⢤⠴⠒⠢⣼⡟⣻⣿⠿⢿⣯⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠀⠀⠀⠀⠋⠙⡿⢿⣿⣿⣆⠀⠹⠉⣿⡇⠀⠀⠀⢠⠉⢠⡿⠁⣠⣾⣿⡿⣋⣵⠟⠛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⡿⢷⣝⠳⡈⠻⣦⠀⢀⣿⡇⠀⠀⠀⢸⡀⠘⠁⣴⣿⠟⣡⠞⡛⠛⠀⠀⠈⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⠿⣷⣬⡑⠮⡂⠈⠷⢸⣿⡇⠀⠀⠀⠈⡇⢀⡼⠋⠠⣪⠥⠬⣡⣤⣤⣤⣤⣤⣭⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣈⠁⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⢹⡄⠀⠀⠈⠁⢀⣈⣭⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⣾⣭⣭⣁⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠈⣉⣩⣭⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠀⠀⡀⢰⣿⣿⣿⣿⣄⠋⠁⡤⠄⠊⠃⠄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⠀⠠⣀⣀⡀⠀⠻⠟⠉⠉⠙⢿⣷⣿⣤⣄⢀⣀⣄⣡⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢾⣥⣤⣤⣤⣤⣤⡽⠿⠿⠧⣤⣤⣤⡄⠈⠉⠀⠉⡙⢻⣿⣤⣬⣭⣽⣿⣶⣶⣶⣾⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣛⣟⣹⢛⣟⢋⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⢀⠠⠤⢄⣀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣀⣀⣀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢹⣂⣴⣷⢖⡟⡛⠾⣙⠲⣖⣶⡿⣛⣾⠿⠦⣼⡿⠤⠙⠋⠁⠀⠀⠈⠀⢐⡴⠒⢂⣀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⣶⡿⣫⡾⠁⣾⣀⣱⡀⢉⢴⣬⡉⠉⢁⡠⠖⠒⠒⠢⠦⣤⣀⣀⣀⣀⡠⠔⠃⣴⣾⠭⠟⢉⡀
⠀⠀⠀⠀⠀⠀⢀⡛⢿⣉⠈⢦⠟⠉⠛⣧⡄⠀⠀⢱⠞⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠳⠶⠤⢤⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠠⣈⢳⡆⢀⣶⡄⠈⢇⢀⡐⠁⠀⣠⣴⣿⣭⣭⣍⡙⠲⠦⣤⣤⠴⢾⠳⢓⡯⢷⣿⣭⣴⠏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣷⣿⣿⣻⣦⠔⠋⢀⡴⠚⣉⣥⣶⣿⢣⢒⠈⢦⣤⣤⣤⣦⣵⣾⠭⠴⣬⣿⣿⡿⢰⠁
⠀⠀⠀⠀⠀⠀⠈⠿⣝⡲⣄⣝⣮⣉⣉⣁⣤⠴⣋⡴⠛⠁⠀⠀⢦⠔⢩⡵⡀⠙⠉⠉⠉⢉⣵⣞⣿⣿⣿⣿⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⠷⠶⣶⣿⣿⣿⡶⠟⠩⠴⠶⢤⣤⣴⣮⣂⣢⠜⣜⢄⠀⣀⣤⢟⡵⣫⡹⣾⣿⠏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣱⡟⠓⠆⢶⢦⣤⣄⣀⣀⣠⣴⠯⠖⢚⣽⣟⡿⢯⠭⣟⣾⣷⣟⡹⣴⣿⣛⣹⡿⠟⠁⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣟⠿⡔⠦⡀⠈⠲⢬⢉⠉⢀⣠⣔⢾⣟⢋⣭⣽⡆⣠⣾⠟⣳⠿⢛⣋⣉⣭⣥⣤⣴⣾⣻⡟⣮⣻
⠀⠀⠀⠀⠀⠀⠀⠦⠀⢵⠀⠀⣶⣴⡞⡉⠙⠛⠳⣤⡉⢿⠔⠈⠋⠙⡿⢡⣾⡷⠚⠋⠛⠙⠒⣶⣾⢟⡗⠟⣻⡿⢹
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠸⡄⠀⡎⢿⣿⣶⣿⣷⡾⣿⣿⣦⢫⠜⢠⢠⠀⣾⠿⡿⡓⣣⢚⡼⠞⣋⣭⢽⢿⠟⡻⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠀⡟⠆⡛⠛⠾⢾⣞⠽⠫⣿⡟⣰⢣⠃⣰⠏⣿⡿⡇⣰⠟⣠⡞⢻⡶⣶⣮⣔⣁⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢧⠐⣷⠤⠬⢭⣿⣦⢹⣞⡳⣼⣇⣧⡏⣰⡿⣥⢈⣶⡿⠋⣰⡿⣫⢚⠷⣾⡿⡋⢙⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⢦⣜⣿⣅⣚⣟⣛⣻⡵⠜⣛⡉⠥⠬⢬⣩⡟⣛⣋⣠⡶⠋⣈⣠⣍⡛⠰⠴⡞⣫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⠻⡙⠛⣻⠿⠶⣦⣽⣤⡶⠐⠒⠚⣼⣷⣯⣬⣥⡶⣟⠉⢺⣼⣯⣿⠻⢛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⣳⣦⣬⣮⢤⢤⣄⠈⣟⠻⠰⡥⣀⢉⣽⠟⡞⠹⢹⢟⢺⡳⢦⣭⡾⣹⣷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⠀⣶⣿⡄⣺⣶⠋⢀⠜⡠⠋⠨⠃⠜⡡⠁⠎⠼⠀⠛⣧⠀⡧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠼⠾⢱⣿⢁⣄⣰⣛⡋⢳⡒⣂⣋⢉⣲⣤⣾⡂⠈⠩⡆⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣮⣿⠁⣵⣬⡙⠮⣝⢀⣀⣉⡉⠍⠚⠉⣻⠽⠇⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣈⣁⣟⠀⠀⢈⡼⢉⠔⣡⠄⡠⠈⣳⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠭⣴⠶⢋⡠⠋⡴⢁⡞⡰⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠁⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠖⠒⠈⠀⠒⠛⢃⡀⠀⠀⠀⠀⣠⣴⠶⠔⣇
⠀⠀⠀⢀⡶⠦⣦⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡀⠀⠠⠄⠤⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⢀⠘⡄⢀
⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣇⣃⣀⣧⣤⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠖⠚⠛⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠡⠉⠠⠀⠀⠀⠀⠀⠀⣄⠀⠘⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠘⣃⣤⣠⣤⣄⠀⠐⠲⠎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣤
⠀⠀⠀⢀⠀⠀⠠⠠⠀⠀⠀⠀⠀⣴⢀⠖⠉⢀⠀⠀⢡⠈⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡤⣄⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠈⠈⠀⢀⠀⠀⠀⢀⡀⠀⠀⣸⢛⡁⠶⠈⠀⠰⠆⢤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣤⠟
⠀⠀⣤⠴⠂⠛⣡⡴⠦⣭⡁⢰⣿⠇⠀⢹⡄⠀⣠⠀⣴⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠠⣾⠏⠀⠀⠘⠿⠟⠻⣄⣀⣀⣈⠇⠀⠀⠀⡄⠀⠀⠀⢰⡞⢁⡴⢲⡄⠀⠀⠀⠺⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣤⠴⢮⣻⣼⡏
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⠃⠀⠀⠈⠁⠑⠀⣀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠀⠐⠀⠒
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡂⠄⠨⠀⠠⠅⠸⠀⠀⠓⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣭⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠵
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⣀⣠⡤⠠⠀⠀⠀⠆⠰⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠶⠂⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡚⡒⠀⠀⠀⡀⠉⠵⠆⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠁⣈⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠐⠆⠀⢨⣍⡥⠀⠁⠀⢁⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⢀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡤⠤⠀⠈⢙⠉⠀⠋⠀⠀⠤⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠻⠚⠴⢇
⠀⠀⠀⠀⠐⠶⠲⠶⠶⠶⠒⠂⠀⠀⠀⠰⠞⠀⠀⠀⠀⠴⠦⠄⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⢀
⠃⠓⠢⣤⠀⢰⣶⣀⠀⠉⢉⣴⠒⠀⠀⠀⠀⠀⡀⠂⡔⠀⠀⠀⠀⠀⠀⢀⠀⡔⢄⠀⠀⢤⣀⣀⠀⠀⠀⠀⢠⠾⠿⠋⠀⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠁⠀⠀⠀⠀⠰⠶⠀⠐⠈⠔⠂⠀⠀⠀⢀⡀⠹⠋⠠⠄⠀⠀⠀⠀⢠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣟⠉⠀⠿⠋⠀⠀⠙⠻⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⠁⠀⢠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠹⠏⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠐⠇⠀⠀⠀⠸⠃⠀⠀⣴⠃⠀⠀⠘⢷⠂⠀⠀⠸⡟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁⠀⡄⠀⠀⠀⠀⠀⠀⢀⣦⣹⣷⣤⣤⣀⢨⡀⠀⠀⠀⠁⢼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡖⡀⢙⡋⠀⠠⢴⡿⠛⠛⠋⠉⢀⠁⣼⡛⠿⣧⡄⢾⡃⠀⡀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠈⠁⠒⠀⠉⢛⠦⣧⠀⡆⡼⣸⣿⠧⠐⠋⠁⠀⣤⡠⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠙⠉⠛⢻⡇⣧⣿⡿⣗⠒⠶⠶⠛⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⣻⣽⣷⠈⢹⢀⡯⣭⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢀⡉⠻⣥⣿⣼⣮⣽⡷⠻⡄⠘⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⢷⣄⣤⡌⠀⣁⣠⣄⢀⣀⣰⣤⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣿⡟⣩⢹⡍⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠟⣿⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡿⠟⠁⠀⠸⠇⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣟⡿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⢻⣿⣿⣿⣸⣿⢿⣿⢣⣿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣥⣶⣾⣆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠈⢿⡿⠿⠇⡿⠋⠉⠙⠻⣿⣿⡿⠟⣋⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣍⣛⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠈⣿⣶⣿⠿⠿⢛⣛⣭⣭⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠶⢦⡿⢿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠁⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣧⣄⣀⠀⠀⠀⠀⢹⣆⣀⣀⣤⣄⣀⣴⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣴⣦⣤⣤⣽⣿⣿⣶⣤⣤⣴⣿⣿⡿⠿⠛⣿⡟⠛⢉⣠⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⣽⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣻⣿⣿⣿⣦⣤⣾⣿⢹⠉⢹⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⡁⠀⠀⠀⠀⠀⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⣻⣿⣿⣿⠃⠀⠀⠀⢰⡇⣿⣿⣿⣿⣿⣿⣿⣟⣉⡉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⣭⣭⣭⣭⣭⡿⠀⠀⠀⠀⢸⡇⣿⣿⣯⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡆⢸⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣦⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣆⣀⣤⣄⣀⡀
⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣤⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⣠⣦⣀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠁⠀⠀⠸⠇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠙⢦⣄⠀⠀⣼⠀⠀⠀⠈⠈⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⢤⣠⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢠⣿⣵⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢂⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⣀⠀⠀⠀⢀⠐⠢⣄⠀⠠⠈⠠⣄⠀⠀⠀⠊⠁⣾⡏⠀⠀⠀⠀⢠⡄⢀⣀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣈⡀⠀⠈⠙⠀⠀⠀⠙⠃⡀⠀⠀⣸⡿⠂⠀⠴⠃⠀⠹⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⠤⠂⠂⠉⠉⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣰⣿⣿⠋
⠀⠀⠀⠀⠠⠶⣎⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠉⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣼⠃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⢀⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠉⠉⠁⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡉⠉⠁⠀⠀⠀⠀⠀⠙⢿⣅
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⠶⢶⣯⡴⠇⠀⠀⠤⠤⣿⣟⣠⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠒⢄⡈⠳⣌⢀⠠⣼⠓⠀⢀⣿⠃⠀⠀⠀⠘⣧⡀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠈⢳⡄⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠈⠓⠀⠀⢹⣿⡟⠛⠛⠛⠓⠒⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣿⡀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣷⣿⠿⠆⠀⠀⠀⣴⣿⡷⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⣿⡟⠁⠀⠈⡄⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⣾⣿⠇⠀⠀⠀⠹⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣾⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉


⣿⠿⠿⠿⡿⠟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣻⣟⣻⣟⣿⣿⣿⣿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⡃⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⢤⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⠀⠐⠃⡀
⠀⢀⣀⠀⠐⣬⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠐⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⣠⠏⠀⠀⠀⢀⠴⠀⠀⣁⠈⠀⠀⠀⢀⠀⠀⡴⠋
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⣠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⢀⣀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠠⠆⢀⢀⡈⢉⠀⠀⠉⡠⠆⠀⠃
⠀⠀⠀⣀⠀⠀⠀⠋⠀⠈⠛⠂⠴⠓⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠃⠀⠀⡄
⠀⠀⠂⠌⠀⠀⣀⢀⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠀⠀⠀⠀⠐⠐⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠛⡒⠤⠀⠀⢸⠀⠀⠀⠀⠂⢀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⠀⡀⢀⡠⠚⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⠀⠀⠀⠄⠄⠀⠀⠀⠀⡀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢡⠀⠀⠀⡇⠀⠀⠀⢀⠌⠀⠠⠒⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠱⠄⠀⠣⡀⠐⠁⠿⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠐⠀⣀⠀⡀⠀⠀⠀⠀⠋⠒⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⡴⠒⠀⠀⠀⠀⠀⠐⡌⠓⠀⠃⠀⠀⠀⠀⠀⠁⠂⠀⠀⠐⢢⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠐⣀⣀⡄⠐⠀⣠⠞
⠀⠀⠤⠀⠀⠓⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣴⢟⣉⡁⢀⠀⡀⠀⠀⠀⠀⣉⡡⠤⠔⠋
⠀⣀⠀⠀⠀⠀⠀⠀⢠⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠷⠀⠀⠀⢀⡤⠀⡆⠀⠔⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠒⠋⠁⠐⢀⣡⣌⠢⣀⡤⠟
⠀⠉⠀⠀⠀⠀⠀⢠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⠋⠉⠉⠈⠉⠈⡧⣈⠂
⠀⠀⠀⠀⠀⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⣠⡄⠀⠹⡀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⡰⠃⠀⠀⠀⠄⠚⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⡀⠀⠈⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠋⠀⠀⠀⠀⠀⠀⠀⡀⢠⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠢⢌⠙⢤⠀⠀⠀⠀⠀⠁⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⢇⠀⠀⠀⠀⢤⣀⠀⠀⠀⣠⠂⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠒⠒⠀⠀⠀⠀⠀⠐⢄⠀⠈⠀⠀⠀⠀⠀⢀⠀⡸⠁⠀⠀⠀⠀⠈⠗⢠⡎⠀⠀⠀⡀⠀⠀⠀⠀⠈⡦⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡤⠒⢀⠀⠄⢀⠀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠤⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⢀⠤⠀⠀⠀⠀⠃⠀⠀⠠⠀⠸
⠀⠀⠀⠀⠁⠊⠀⠀⠀⠈⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣀⠀⢀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠐⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⡀⠀⠈⣄⠀⠄⠀⠀⡶⣄⡀⣀⡼⠃⠀⠀⠀⠀⠀⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⣦⡀⢻⠀⠀⠓⠴⠃⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢻⡄⠙⠛⠀⠀⠀⠀⢀⣤⣴⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠉⠙⠲⠾⠃⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠘⠧⠤⠴⢞⡿⠁⠀⠀⠀⢀⣀⡤⢖⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢾⣄⣠⡤⠶⠚⠋⣡⡴⠋
⠀⠀⠠⠒⠀⠀⠀⠰⠟⠉⠁⢀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣀⣀⣀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠻⣶⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⣠⣤⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠳⢦⣄⠀⠀⠀⠀⠘⠛⠛⣋⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⡓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢠⡞⠁
⠀⠀⢀⠀⠠⢀⡀⠀⠀⠀⢀⣈⣙⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠙⢆
⠀⠀⢾⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠳⠤⣄⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⣀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇
⠀⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠴⠶⠃⠈⠛⠛⠉⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠈⠛⠒⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠤⣤⣤⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡄⠀⠀⣠⡿⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠑⠛⠋⠀⠀⠀⠀⠀⠹⣄⠀⢈⠉⠳⡄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡵⠆⠁⠀⣿⠀⡆⢀⣴⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠸⡆⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠁⠰⢠⠟⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⢢⠹⡄⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠗⠚⠛⠉⠀⠀⢦⢰⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⠛⠶⠒⠛⠳⠶⠶⠞⠛⠶⠞⠋⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⡔⣍⣁⣀⣀⣈⣹⡵⣄⣤⣤⣤⣤⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠓⢸⣿⣿⣿⡟⣳⣾⣤⣠⡈⢀⠀⠀⣀⣱⣧⣼⢻⣿⣿⣿⡆⠈⠘⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣿⣿⢠⡟⠀⣹⢟⣣⣹⣏⣘⣿⣯⡉⢹⡄⣿⣿⣿⣧⠀⠀⠀⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⢧⡀⢤⣿⣿⣿⣿⡶⣟⣽⣿⡿⠟⢛⡛⠿⢿⣿⣿⣿⣇⣿⣿⣿⣿⡄⠠⢀⣯⣉⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢸⣿⣿⣿⡇⢠⣿⡟⠁⠐⠀⢸⠃⠀⠂⠉⢿⣷⡌⢸⣿⣿⣿⡇⠀⠀⠀⠸⡗⢻⣿⣷⣾⣤⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢸⣿⣿⣿⡇⣿⡟⠀⠛⠀⠀⢸⡀⠀⠀⠚⠈⢿⣷⢸⣿⣿⣿⡇⠀⠀⠀⢀⠟⣫⡿⠿⢿⡃⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠱⢤⠤⢼⣿⣿⣿⡿⣿⡇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣾⣿⣿⣿⡷⢤⡤⣤⣼⡼⡿⠁⠰⣟⣙⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⡇⢻⣿⡄⠿⠀⡀⠀⠀⢀⡀⠚⣰⣿⠇⣿⣿⣿⣿⠀⠀⠀⢸⣩⠼⠃⠠⣖⠻⣏⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢹⣿⣿⣿⡄⠻⣿⣶⣄⣁⠐⠂⣀⣥⣾⣿⠋⣸⣿⣿⣿⠇⠀⠀⠀⡘⠁⠀⣴⠲⣎⠛⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠋⠹⠅⠛⠻⢿⡿⠿⠿⣛⡫⣹⠙⠛⠛⠛⠛⠉⠉⢉⡉⠁⣴⠶⡜⠓⢾⡗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣾⣽⢷⡞⣷⢠⡶⣦⢠⢶⡄⣿⢹⡆⠹⢦⣿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠼⣿⡁⢸⣧⠟⠸⣠⡇⢙⣿⣇⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠚⠋⠉⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡷⠀⠀⠀⡄⠀⠀⠀⠀⠀⢴⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⣏⡀⢶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⢀⡿⠀⢠⡞⢁⡴⠆
⠀⠀⠀⠀⠀⢀⠴⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⣇⠘⠀⡸⠃⡰⢋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠈⢠⠀⠀⠂
⠀⠀⠀⠀⠀⢡⡘⢗⠤⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⡙⡄⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⢀⠀⡴⢰⠂⠀⢀⠀⠀⠀⠶⢶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠑⠈⠀⠀⠀⠀⠀⠀⠤⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢄⢠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠘⠧⠠⢤⣀⣤⡀⣀⡔⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⡿⠇⠀⠀⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠤⠊⠰⠐⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠙⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠇⠈⠉⠑⠀⠀⠀⠀⠀⡄⠀⠈⠁⠀⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡁⠙⠃⠀⠁⠀⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠢⠀⠤⢀⠀⠄⠛⠁
⠀⠀⠀⠀⠀⠀⢀⡞⣠⣄⡄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠸⠻⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠦⠤⡄⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⣄⣹⣶⡀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁⠀⠂⠀⢠⠄⠀⠈⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠙⠢⠝⢀⣀⠀⠐⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠠⡿⠶⠶⠶⠀⠀⠀⣿⣴⢷⣤⠐⠀⠛⠙⠀⠀⠀⠀⠠⡶⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠤⠀⡄⠸⠛⠃⠘⠀⠘⠙⠣⡁
⠀⠀⢰⡶⠐⡒⠈⠁⠐⡂⠀⠿⠈⠀⠀⠀⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠑⠄⣡⡙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠶⠁⠀⠈⠂⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠈⠉⢉⣠⠖⠀⠴⠦⠐⠀⠒⠻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢀⠀⣠⡄
⠀⠀⠈⠁⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠈⠉⠂⠈⠤⠉⠁
⠀⠀⠀⢀⣀⡀⢆⡠⠄⠆⠐⠒⠢⡀⠤⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡠⠚⠃⠀⣤⣀⠀⠀⠀⢀⡀⠀⠊⡀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠇⠀⠀⠀⠙⠋⠀⠀⠀⠈⠁⠀⢀⠇⠀⠀⠀⠀⠶⠀⠀⠀⢀⡀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠆
⠀⠀⠀⠀⠀⢦⣀⣀⡀⠀⢄⠠⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⢀⠄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡈⠉⢁⠀⠏⢠⣋⣀⣀⣀⣤⣶⠊
⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⠛⢻⣕⣶⣢⣧⣶⣷⣶⣶⣿⣿⡿⠋⠉⠉⠁⡀
⠀⢨⡉⠓⠒⣲⣌⣀⣔⣄⣁⠀⡄⠀⠀⠀⣠⣬⢤⣍⣛⣃⣬⣽⣷⣿⣿⣻⣩⣙⣻⣟⣿⡿⠁⠀⠀⠈⠉
⠀⠈⣯⣫⣭⡶⠟⢓⣺⡟⣏⠀⠀⠒⠶⠾⠋⠉⠳⣬⣭⣯⡭⢴⣶⣶⣾⣿⣽⡯⢷⡿⠋⠀⠀⢀⠄⡘
⠀⠀⢛⣫⣟⣽⣟⣑⢎⣽⣮⢳⠂⠤⠤⠤⠦⣤⠀⠀⢨⣿⣿⣿⣿⢷⣶⣾⣽⣿⣋⣤⣄⣤⣶⣅⡠⠓
⠀⠀⠀⠉⠉⢙⣻⣖⣻⣯⢺⢆⠀⠀⠀⢀⣀⣌⡇⠀⢸⣿⡟⠁⣤⡀⠨⣙⣫⣽⣷⢮⡉⠍⠛⢦⣄
⠀⢰⣄⣛⣲⣤⣤⣷⠳⣗⡷⡘⣟⡝⣏⣽⣛⢟⠇⠀⠈⠛⠛⠮⣭⣤⣭⡶⣶⣄⠁⠠⠉⣰⠀⢸⡯⠛⠴⢤
⠀⠈⢮⡋⢓⡙⠘⢻⣧⠈⣿⢿⣓⣋⣩⢥⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⢷⣿⣧⡴⠮⣄⣀⣀⣤⣱⡖
⠀⢀⣄⠈⠀⠈⢻⠧⣿⣷⣌⡳⠭⡭⢶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣛⣻⡵⣋⣝⣪⣉⡉⠙⠛⣃
⠀⠘⢧⣄⠀⢊⣍⣙⣾⣿⣿⣻⣿⣿⣿⣿⣾⣶⠊⠁⠀⠀⠀⠀⠠⢀⣧⣬⣉⣫⣽⣿⣶⣿⠿⠛⠛⠿⠥⠞⠉⣀
⠀⠀⠦⠜⢉⠀⣿⣟⡭⣿⣿⡿⠿⣿⣿⣍⣿⣿⣿⣷⣦⣤⡄⣠⠀⣿⠿⠷⣷⡞⣶⣾⢷⡾⣒⣚⡳⢄⡀⠀⢸⠃
⠀⠀⠉⠙⣶⣿⣻⢏⠞⠛⢙⠯⣁⣲⣬⢭⣿⣻⡿⠛⠛⠋⠀⣿⠂⠙⡟⠷⣿⣟⠿⠿⣿⡿⠭⢍⢻⣤⣥⠄⠁
⠀⠀⠀⣨⠝⠋⠁⠀⠀⠊⠉⠳⠖⢶⣽⣷⣽⣽⡇⠀⠀⠀⠀⣾⣄⠀⣇⣤⣼⡳⣭⣽⠏⠀⠁⠀⣧⣨⣥⠛⠛⠁
⠀⠀⠀⠹⠰⠄⠈⠀⡄⠐⠀⠀⢀⣁⣉⠿⠿⠾⣧⣀⣀⣠⣴⣿⣥⣾⠿⠋⠉⠑⠦⠜⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣨⢱⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠑⣴⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⢀⠄⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠈⠁⠐⣻⡿⠻⠾⣾⡟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠚⠋⣀⠀⠠⠼⠇⢻⠷⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠉⠀⠉⠀⠀⠀⠀⠛⠉⠠⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐


⠀⣆⣂⡀⣄⠀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠑
⣿⣿⣿⣿⣿⣶⣷⣿⣶⣷⣴⣿⣷⣶⣎⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠘
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠂⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣓⣐⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠃⠄⢀⣴⣿⣿⣿⣿⣿⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠰⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢛⠋⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⠟⠛⠙⠛⢉⠉⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⣤⣄⣴⣿⣿⣿⣿⣿⣿⣷⣶⣤⣶⣶⣶⣦⣤⡀⠀⠀⠀⡀
⠀⠀⠀⡄⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣅⡀⠄
⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠈⠿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃

⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠉⠙⠳⡤⠶⠠⠀⡀⠀⠀⢀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠠⣼⣿⣓⠦⣄⡀⠀⢀⣀⡀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠳⣄⠉⠉⠀⠀⠉⠻⠋⠉⠩⠋⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠴⣚⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣾⠷⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢋⣥⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⡀⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠳⢦⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠁⠀⠀⠀⠀⠁⢐⡟⠀⠀⢀⣀⣠⡴⠖⠋⠁⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠈⠛⠻⢯⣍⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⣻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⣀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠷⠶⠤⠄⠀⠀⠀⠀⠀⠀⢾⡛⠉⠋⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠃⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⢰⣴⣮⡀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡼⠃⢿⠹⣿⡏⠇⠙⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣠⢤⡖⠒⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠛⠉⠁⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣆⠀⡤⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⢀⠀⠀⠈⠉⠁⠀⠀⠀⠙⠲⣝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡏⢸⡄⠀⠀⠀⠀⢀⣄⠀⠀⠀⢘⡆⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⠀⠀⠙⠶⣤⣤⠶⠋⠹⣄⣀⣠⡾⠁⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠛⠟⠺⠟⠲⠆⣀⠰⠦⠄⣤⡏⡾⣶⣶⣿⣶⣄⡿⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⣋⣀⠀⢀⣶⣤⣴⣤⣀⣿⣤⡄⣼⣿⠿⠋⠿⠛⠉⣿⢷⣾⣿⢉⣿⢤⣆⡀⠙⢷⡄⠀⣜⣋⣉⣨⣥⡁⢀⠂
⠀⠀⠀⠀⣾⣿⣯⣹⣿⣿⣿⣏⣙⣶⣭⢿⣿⣿⡿⣠⡁⣴⣦⣤⡄⠀⢠⣾⣿⣿⣿⣿⣤⣼⣷⣀⠀⠀⠀⣉⠛⠈⡹⢿⣿⣿⣿⣄⠒⠀⠤
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣍⠀⠀⢰⡶⠟⠛⣟⡿⠿⣦⡄⠀⢀
⠀⠀⠀⢨⣽⡿⠿⢛⣿⣿⣿⣿⣿⣿⡏⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣟⠛⣿⣿⣿⣷⣶⣿⣄⣾
⠀⠀⢠⣜⣤⣴⣾⣿⣿⣿⣿⣿⣟⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠠⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠈⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⠻⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠻⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠛⠋⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠟⠋⠉⠉⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣛⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⠻⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣴⣿⣽⠟⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠈⣿⠃⢀⠐⣿⢻⡿⢻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣠⣶⣶⣴⠦⣀⡀⢠⢤⢾⣷⣶⣅⢻⣿⣿⣆⡙⢾⣷⣿⣿⣿⣿⣐⣿⣶⣤⡤⠤⣤⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣷⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠻⠿⠿⠻⠿⠿⠟⠛⠿⠿⠛⠿⠛⠛⠿⣿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢨⡀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠄⠀⠊⠀⠀⠀⠀⠀⠀⠙⠙⠂⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠒⠋⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⡀⠈⠀⠐⣂⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⡖⠀⠀⠀⠀⠀⣼⡆⠀⠀⠰⡀⠁⠋⠀⢹⡵⠋⠀⠰⢀⠀⢀⡁⢀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡭⠁⠀⠃⠀⠈⠓⠀⠀⠉⠠⠄⠀⠀⠀⠀⠀⠊⠰⠄⠀⠀⠀⠀⠊⣭⢤⡼⢃⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠠⠄⠀⠀⠀⠸⣦⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠛⠒⠒⢿⡣⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢴⡾⠛⠓⠀⢀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⡄⢸⣷⠀⣿⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠀⠀⣀⡏⠉⠁⠐⠘⠀⠀⠀⣤⠠⠞⠃⠰⠆⢠⣤⣌⡶⡚⠀⡆⠀⢩⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⣼⠃⠁⠀⢰⠆⡴⠃⠰⠦⠐⠤⠄⠀⠃⠀⣀⣀⣤⢅⡆⠇⢴⡀⢈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣾⠗⠀⢠⡖⠐⠺⢦⡀⡦⠤⢿⣷⣶⣶⣦⣭⣥⣴⣾⣿⣷⣆⣀⠘⣿⣯⡴⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⠻⣦⣒⠲⣽⣮⣻⣯⣙⣭⢙⠉⢻⣭⣿⣤⣯⣛⣛⡛⠨⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠚⠛⠉⠀⣯⣽⠙⣈⣁⢉⡞⠂⠨⣻⣿⡃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢊⠉⠹⠻⡇⠳⢷⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠉⡛⣻⡆⢀⠤⡆⢄⢟⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣿⢸⠀⣘⡇⠸⡀⣴⣿⣨⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⣼⣿⡏⠗⢀⣀⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠃⠿⠿⠁⠶⠌⠁⠀⠙⠋⢹⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠰⠀⣀⠀⠀⠉⠙⠃⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣐⣲⣿⣠⣄⢲⣴⣤⣤⣦⣬⣿⣟⡾⣠⣤⣀⣰⣽⣿⣵⣆⣀⠀⠠⠤⠶⡤⣦⣤⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠠⠤⠤⠬⠿⠿⠶⠌⠐⠂⠒⠚⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠑⠀⠈⢠⣀⣿⠛⢾⠃⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⡀⢀⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠐⢂⣤⠀⢀⡴⠁
⢀⣶⣗⠌⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠈⠉⠀⡀⠀⠀⠀⠰⢠⠀⠀⠀⠘⠁⠀⠊⠀⠳⣀
⣏⠀⠉⢠⠶⠈⠂⠀⠀⡰⠖⠛⠞⠇⠀⠀⠀⠖⠀⠃⢀⠀⠀⠁⠀⠀⠀⠀⠀⠔⠆⠀⠀⠀⠀⠆
⠈⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣴⡉⠓⠀⠀⠀⡠⠊⠑⡄⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡰⠐⠂⠁⣀⢀⣀⠀⠀⠀⠱⠀⡀⠀⠀⠀⠀⠏⠉⡀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠠⠚⠁
⠀⠠⣆⠀⠂⢘⠀⠀⠀⠘⠇⠈⠀⠀⠆⠀⠀⠰⠁⠃⠀⠀⠀⠟⠁⠡⠀⠁⠈⢱⠘⢂⠀⠠⡄
⣌⠀⠀⠀⠀⠠⠛⠉⠁⣚⠀⠋⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠘⠄⠀⠠⠆⠀⠀⢀
⡉⠁⠀⠀⢀⠤⠂⠰⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠃⠠⠈⠀⠀⠭⠔
⠛⠠⠄⠀⠆⢀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀
⠀⠐⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠤

⣀⣀⣀
⣉⣅⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣩⡤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤
⣹⣤⠶⢚⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⢽⡶⠟⡋⠄⠀⢀⡠⠂⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡈⠻⢿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣀⢀⣴⣿⠿⠛⠛⠿⠿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠉⠉⠉⠛⠿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⠀⠉⠉⠀⠀⢀⣀⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠈⠉⠉⠉⠙⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⠀⠀⣀⠀⠀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠻⢿⣤⡀⠀⠀⠀⢰⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⠏⠁⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⡄⠀⣿⣿⡗
⠀⠀⠀⠀⠀⢸⣿⣯⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣹⣿⠇⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⣠⣴⠗⠀⠀⠀⢀⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣀⠀⠙⠀⠀⠀⢀⡀⠀⠀⠓⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡉⠉⣀⠀⠀⠃⠀⢸⣿⡉
⠀⠀⠀⠀⠀⠀⠘⠻⣿⡆⠀⠠⡄⠀⢰⠆⠘⠛⢷⣶⠚⠀⠀⠰⠀⠀⠀⠀⢀⡀⠀⠁⠀⠙⠀⠐⠂⢠⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⠀⠀⠀⠀⠀⣠⠀⠀⠉⠃⠀⢠⠀⠀⣀⠀⠀⠀⠀⣠⢀⣤⣀⣷⣀⣷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣤⣦⣤⣷⣾⢿⣷⣴⣆⢠⡄⢈⣠⣾⣿⣷⣤⣶⣤⣿⣿⠿⢿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠙⠻⠿⢿⣿⣿⣿⠋⡄⢸⡟⡛⣿⣏⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠶⠿⢟⣻⣿⠀⡇⢘⠁⡇⣿⣟⣛⣛⡻⠿⣶⣦⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣼⣿⠋⠁⢠⣾⠛⠉⣽⡿⢰⡇⢸⠀⡇⢹⣯⠉⢙⣿⡷⠈⢻⣿⡆⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⣿⣷⡀⠀⠀⠙⠛⠛⠛⠛⠛⠷⠿⠷⠟⠛⠛⠛⠛⠉⢀⣠⣾⡿⢃⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣌⠛⠿⣿⣷⣴⣤⣤⣤⣤⣀⣴⣀⣀⣤⣠⣤⣤⣴⣿⡾⠟⠋⢐⣋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⣹⡿⠋⠉⣿⠉⢻⠉⠉⢉⡉⢿⣧⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢁⡀⣸⡇⠀⢸⠀⡆⠀⢷⡀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠋⢀⡾⢀⡉⠁⡀⠀⠀⢷⠸⡌⢷⡀⢙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣿⣧⣼⣇⣀⣀⣸⣦⣽⣶⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡆⢰⡆⠀⠀⠀⢠⡜⢳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⡀⠀⠀⠀⣷⡄⠀⠀⠀⠀⢸⠇⢸⠀⠀⠀⠀⠀⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢞⡀⡐⡁⠀⠀⠀⣿⣿⣦⡀⠀⠀⢸⠀⠛⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣿⡇⠙⢿⣷⣤⣬⣀⣀⣴⣿⣄⡀⢀⣀⣤⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠈⠙⠛⠛⠋⠁⠙⠛⠿⠛⠛⣿⡟⠀⢠⡤⠤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢷⣶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠿⢧⣀⢘⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠛⣦⣞⠁⢀⣀⣀⡀⢈⡿⢻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢉⣀⣠⡾⠷⠤⢤⣄⣾⣻⢧⡀⠀⢠⡇⠀⠸⣧⣼⠟⣭⠿⠛⠛⠙⣿⡇⠀⢿⣀⡀
⠀⠀⣀⣀⡄⠀⠀⠀⠉⠛⣿⡟⠁⠀⣀⣀⠀⠈⠙⣿⠅⠙⣆⣸⠀⠀⠀⢹⣿⣄⢹⣤⡤⠀⠀⡿⡷⠒⠺⣄
⠀⠀⣽⣀⡡⠀⠀⠀⠀⠀⣿⣿⢴⡾⠛⠛⠳⡄⠀⠘⣷⣀⠈⠛⠀⢰⡄⠀⢻⡉⠉⠉⠀⣀⡼⣡⣿⣤⣤⡟⠛⠛⠓
⠀⠀⠀⠀⠁⠀⠀⠀⣠⣾⣿⣿⣿⡀⠀⠀⠀⣻⠀⠀⣿⣿⣦⡀⠀⡾⢷⣀⣈⣿⠶⠶⠟⠋⣼⠁⠈
⠀⠀⠀⢀⣠⡤⠶⠿⠿⠿⣿⣿⣿⡳⢦⡤⠔⠃⠀⣰⣿⣿⡌⢳⡶⠇⠈⠛⠉⠁⢀⢠⣀⣀⣘⣦⡀⠀⠀⠠⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠿⢿⣿⣀⣀⣀⣠⣴⣿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠜⠳⡘⢦⡀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠊⢁⡴⠃⠀⠀⠟⠛⠛⠋⠉⠀⠉⢿⡄⠀⠀⣠⠖⠋⠉⠓⠦⡆⠀⠙⠦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣷⢀⡾⠁⣠⠖⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⠃⠐⠆⠀⠀⠀⠀⢹⡾⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠲⡼⠀⠀⠀⠀⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣶⣄⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠒⠒⣦⣀⠀⢀⡖⠉⠉⠉⠙⢿⡻⣦⡀
⠀⠀⠀⠀⡴⠋⣠⠴⠒⠒⠒⠒⠶⢤⣄⠀⠀⠀⠀⠀⠀⢀⠇⠈⠉⠉⠀⠀⠀⠀⠀⠀⡹⣆⠻⡟⢾⡛⠙⠛⠓⢦⣀⡀
⠀⠀⠀⡼⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣆⠹⡄⠹⡄⠀⠀⠀⣏⠙⠳⢦⡀
⠀⠀⢸⣷⠷⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢳⠀⠀⠀⠀⠀⢻⠀⠀⠀⠹⣦
⠀⠀⣿⠃⠀⠀⣿⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣇⠸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠳⣄
⠀⢸⠙⢄⣀⣴⣿⣿⣿⣿⣿⣿⣷⠀⠀⠱⡃⠆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣶⠏⠀⠘⣿⠀⠀⡄⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⢹⢷⡀
⠀⡎⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⣸⠁⠠⠀⠀⢀⣎⠀⠀⠀⠀⢳⠘⠀⢻⡀
⠀⣧⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠀⡄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢰⡏⢠⣧⠤⠤⣤⠞⠉⠉⠳⣤⠤⠀⢸⠀⠃⠈⡇
⠀⢸⡀⠀⠀⠹⣿⣿⣿⣿⣧⣾⢃⣄⣄⡀⢀⡄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⣼⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⠀⠀⠀⡇
⠀⠈⢷⡀⠀⠀⡈⠛⠿⠟⠋⠁⠉⣿⠿⢣⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⠀⢀⢠⡇
⠀⠀⠘⣷⢄⡪⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡞⠠⠃⡾
⠀⠀⠀⠈⢷⡍⠒⠦⠤⠤⠴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠊⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠈⣠⡴⠋⢀⣤⠤⢤⣄⡀⠀⠀⠀⠀⣀⣠⡤⠚⠀⠀⢀⣠⠞
⠀⠁⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠑⠠⠀⠀⠀⠠⢀⠤⠷⠤⠒⠤⣀⣀⣤⠾⠋⢀⡔⠉⠀⡀⠀⠀⠉⠙⠛⠿⠭⠭⠀⠀⠠⣊⡵⠛⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣀⣀⣀⣀⣠⣤⡴⠶⠛⠉⠀⠀⠀⡞⠀⣠⠿⠶⠦⢤⣔⣂⣀⡠⠤⠴⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⠲⢤⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⡠⠼⡆⢀⡤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⢀⠀⠛⠘⠉⠑⠀⠈⠐⢄⡠⠁
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠸⠀⢢⠀⣸⡁⠀⠀⠀⠀⠀⠀⣀⡈⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⢄⠀⠀⠀⠀⣇⠀⠳⠇⠀⠀⢀⠚⠀⢀⠜⡱⠁⠀⠀⠸⣀
⠀⠀⠀⠀⠙⠲⣒⠤⢤⣀⣈⣻⠢⣄⠀⢸⠀⠀⠀⠀⠔⠁⠸⠔⠁⡴⠁⠀⠀⠀⠀⠺⡄
⠀⠀⠀⠀⡖⠁⠀⠑⠢⣀⠈⠉⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠐⠧⠤⠤⠤⠤⠤⠴⡧⠤⠄
⠀⣠⠒⠀⠃⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⡠⠐⠠⠀⠀⠐⠢⡀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⢢
⠰⡇⠀⢠⠂⠀⠀⠀⢀⣠⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⠀⠀⠙⠒⠶⠤⣄⣀⠀⠀⠈
⢀⠕⠀⠘⠀⠀⠀⠈⠉⠉⠉⠉⠉⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡖⠒⠀⠈⠉⠉⢠⠃
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠀⠀⢠⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⠌⠲⠤⠀⠀⠀⠀⡆
⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠉⣩⠜⠁⡀⠀⠀⠀⠘⠲⠖⠁⠀⠀⢶⠤⢤⣀⡐⢤⡀⠀⠀⠀⠀⠀⢱⡀
⠀⠸⡄⠀⠀⣀⠀⠀⣀⣴⠭⠖⠚⡹⣃⣤⠀⢀⠀⠀⡀⠀⠀⣀⠈⠆⠀⠀⠉⠑⠛⠦⠀⠀⠀⠀⠁⠈⢣
⠀⠀⠉⠐⡎⠠⠔⠛⠁⠀⠀⣠⡾⠚⢁⢃⠔⠉⣧⠊⢹⡀⢰⠋⠙⢌⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠙⠒⠲⠀⠀⢀⠔⠉⠀⢀⡿⠃⠀⠀⠁⠀⠈⡇⡎⠀⠀⠀⠹⣆⠀⠀⠀⠠⠀⣀⣠⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠱⣄⣀⣤⣀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⡠⠤⠴⠊⢗⠊⠀⠁⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣁⣀⣄⠀⢀⠴⣄⡠⠊⢻⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣴⡿⠟⠛⠛⠛⠛⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠛⠉⣻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⠏⠀⠀⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣄⣀
⠀⠀⠀⠀⠀⣰⡟⠉⠀⠸⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠋⠙⠻⣿⣆
⠀⠀⠀⠀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢸⣿⣦⣄
⠀⠀⠀⣼⠃⠁⠁⠀⠀⢠⡀⠀⠀⠀⢀⡇⠀⢀⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣰⠀⢀⠘⣹⠋⣿⡇
⠀⠀⠀⠹⣧⣀⣀⣿⣶⣾⣧⣀⣠⣴⣾⣧⣤⣤⣿⣿⣿⣷⣦⣤⣤⣶⣶⣿⣃⣤⣾⣯⣤⣿⣦⣭⣴⡿⠃
⠀⠀⠀⠀⠈⠉⠋⠁⠀⠈⠻⣿⡿⠟⠋⠛⢻⡿⠉⠉⠙⠛⠛⢛⣿⣏⠙⠻⠿⠛⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⠑⢲⠼⢓⠙⠹⠟⠻⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣦⣠⣷⠾⣷⣴⣾⣊⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣾⠏⠈⠉⠁⠀⠬⢟⣿⣛⠻⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣠⣾⠻⠟⠛⠃⠈⠙⠙⠆⠀⠀⠰⠲⠾⠍⠉⠉⠙⠁⠛⠈⠙⠟⠻⠿⣦⣤⣤⡀
⣤⣤⣴⣶⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⣀⢀⡀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⡖⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠠⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠠⠄⠴
⠀⠀⠀⠀⡂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⡴
⠀⠀⠀⠀⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢧⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⠻⣦⣀⣤⠀⠀⣀⠀⢀
⠀⠀⢀⣦⡀⢠⣼⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣱⡀⠀⢹⣶⣶⣆⣒⣛⣒⣲⣂⡀⠀⢀⣧⠀⠀⠀⠀⡀
⠀⣤⣾⣿⣿⣿⣿⡿⠛⠛⠛⠛⠻⠛⠛⠛⠟⠛⠻⠳⣦⣶⣿⣻⣿⡟⣿⣿⣿⠿⠃⢴⠀⡏⠀⠀⠀⠐⡇
⣰⣿⣯⣿⣿⣿⣷⣄⣀⣀⣀⣀⣠⣀⣀⣀⣠⣀⣀⣠⣘⣾⣿⣶⣿⣶⣿⣿⣿⣭⣀⣘⣀⣰⣿⣶⣶⣤⣅

⠦⡜⢲⠀⠀⠀⢀⡀⠀⠀⠠⡄⠈⠣⡀⠘⡄⠈⠀⠓⠊⠁⡀⠠⠀⠀⠠⡀⣀⠀⠀⣼⢗⠞⢕⠟⠁⠹⣼⠀⢁⣀⢧
⠀⠁⠀⠐⢂⣀⠀⠀⠀⠰⠆⠀⠀⡀⠈⠢⡘⠀⠀⠀⠖⢨⠅⠖⠈⠁⠠⡄⠰⠶⠸⢈⣇⡸⡘⠀⠀⠁⠀⡄⠀⠁⠠
⠀⠈⢿⣿⣿⣿⠁⠀⠀⠀⠄⠁⠀⠐⠃⠀⠈⠻⠆⠀⠁⠄⠐⠀⠀⠀⠀⠁⠀⠀⠀⠙⠖⠊⠃⠀⠀⣄⡤⢀⡁⠀⡄
⠀⠀⠀⢿⣿⠃⠀⢀⣧⠀⠀⠀⢀⠠⠀⠀⠐⣀⠀⠀⠁⠀⠀⠀⢴⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣸⢋⡉⢛⣓⣓⠿
⠀⠀⢴⡎⠁⠀⠀⠘⠋⣀⣀⣀⣀⣀⡀⠃⠀⡄⠀⠀⠀⠀⠸⢄⠀⠐⠃⠀⠤⠀⣶⠄⢬⠿⢆⡹⠧⠿⠧⣬⣩⡕⠿
⠎⠀⠀⣔⢕⣚⠶⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠴⠚⢡⡆⢰⡇⢠⡀⠀⠀⠀⠐⠛⠀⠀⠀⠛⢋⠈⠛
⠀⠄⠀⢋⢜⠈⡎⡆⠘⣿⣿⣿⣿⣿⡇⠨⠂⠉⣁⡂⠀⠀⢠⠄⠀⢠⡆⢀⠈⢁⠘⠃⠀⠀⠁⠀⠰⠆⠈⠱⠓⣴⡔
⢀⡂⠛⢀⢋⠸⠳⡁⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠰⡇⠈⠁⢺⠇⠙⠀⣤⠀⠀⢀⠀⣠⡀⠀⠀⠀⠁
⠘⢌⣭⠫⡆⣤⠞⠘⠀⠋⠉⠉⠙⠋⣁⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠸⠀⡄⠀⣶⠀⠛⠀⣀⠀⠀⠈⣥⠀⠀⢂⠀⠳
⠀⠀⠁⠀⠈⢀⠀⢠⣆⡃⢠⡄⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⡀⣠⢠⠄⠀⠁⠀⠀⠀⡤⠐⠀⠆⠀⠀⠀⠀⠀⠈⠐⠂
⠀⠀⠀⢰⣆⣠⣶⣿⣿⣿⣿⣿⣾⣥⠆⠀⠀⣶⠄⠀⠀⠤⠯⠑⡖⢙⡖⠀⠀⢀⠀⠀⡀⠈⠌⠠
⠀⠀⠔⠀⣹⣿⣿⣿⣷⡿⣿⣿⣿⣿⢀⡁⠀⠘⠀⠀⠐⠑⡎⣹⣉⠍⠅⢠⣦⠀⠀⠀⠀⠀⠀⠰⠂⢱⠄⡀
⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠃⠀⠀⠀⠀⠀⠈⠨⠁⠘⠀⢀⡀⣀⡀⠠⠆⠘⢄⠐⠀⠀⠘⠒⢉⡁⠄⡀
⡀⠀⠀⣀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠀⠀⣤⡀⣤⠶⣆⠀⠀⠂⠀⢀⡮⠳⠔⠛⠺⠀⠀⠀⢀⠀⠀⣀⠀⢨⠰⠈⠁
⠀⠀⠄⠉⠀⠀⠰⠀⠀⠀⡄⠀⡆⠀⠸⡯⣚⣇⣸⢮⢞⣠⣆⠀⢀⢸⢧⢢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀
⠀⠀⢻⣿⣿⡿⠀⢀⡀⠀⢀⠀⠀⠀⠶⠀⠛⡘⠓⠀⠈⠓⠀⠀⠈⢗⢆⡩⡆⢀⡀⠀⠁⠀⠒⠀⡀⠀⠀⠀⢠⡀⠡
⠂⠀⠀⢻⡿⠙⠛⠟⠀⠀⠸⢷⣄⠀⠀⠙⠏⠁⠀⠛⠀⠀⠀⠀⠛⠈⠈⠉⠠⣿⡿⣠⣾⡧⠀⠀⡀⠀⠀⠀⠄⠃⠐
⢰⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡀⠀⠀⢀⡀⠀⠠⠆⠀⠜⠃⠀⣠⣄⢟⣽⣿⣧⠀⣤⠈⠁⠂⠐⡀
⡿⠧⠠⠠⠸⠂⠀⠀⠀⠀⠀⠀⠀⡌⢡⡀⠀⠀⢈⠁⠠⠁⠜⠂⢤⠀⡄⢿⢿⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡂⢐⡀⠀⠀⢀⠀⠀⠦⠀⠀⠶⠂⠀⠆⠰⠈⠀⠁⠠⠁⠀⠀⠀⠀⡠⠁⠈⠿⣿⣭⡄⠀⢠⡄
⣁⡽⢼⣠⠀⠛⠃⠰⠀⠄⠀⠀⠒⠀⢈⢃⠚⠀⢠⡀⠄⠀⠠⠁⡠⢁⠠⠀⠀⡠⢉⠀⠀⠈⡃⠀⢀⠀⢀⠀⢠⠀⡳
⡼⢤⠼⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠔⠁⠀⡘⢃⠀⡷⠀⣀⢀⡀⠀⠈⠏⠀⠀⠐⠈⠀⡴⠾⠍⡻⢏⢩⡢⠀⣀⡍⢨
⠀⠁⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⠾⠷⠶⠶⠞⠛⠛⠶⢦⣤⣤⣤⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣀⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣤⣦⣄⣠⣆⣀⣤⣴⣄⣀⣠⣄⣀⣰⣄⣀⣄⠀⢀⣴⣶⣾⣿⣶⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠋⠉⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⣀⣿⠀⠀⠀⠀⠀⣿⣄⣠⠴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣉⣀⡀⢀⣉⡉⠉⣀⡀⠀⣀⢀⡀⢀⡀⠀⢀⠈⢻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⢹⡟⠛⠿⠟⠛⠛⢿⠋⠉⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⢷⣤⣄⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⡀⢀⣠⡶⠟⠻⡶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠯⠟⠀⠀⠈⠁⠉⠉⠻⠾⠧⠔⠂⢀⡀⠀⡠⠜⠏⠻⠋⠁⠁⠀⠀⠀⠈⣉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣦⣴⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣀⣀⣀⣠⣄⣴⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣶⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⣳⣤⠄⢀⣠⣴⡾⠛⠚⠛⢶⣶⣤⡀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢕⢶⣿⡿⠟⢻⠿⠒⠣⠀⠀⠀⢉⠙⢿⣤⡄⠲⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣷⠋⠀⠃⠁⠀⠀⣀⣄⡀⠀⠀⠽⣿⠿⣾⣷⠀⠀⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡿⠖⠀⠀⠀⠔⠉⠀⠀⠈⠁⠀⠀⠈⠀⠈⢻⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⡿⠻⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⢿⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠼⡇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣇⠀⠀⠀⠙⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣼⡢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣫⣷⡁⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⢾⡿⠉⠛⠦⣌⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢫⡻⢿⣿⣷⡷⣄⠙⠚⠳⢤⣤⠒⠅⠀⣀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁⠀⠉⠛⠚⠛⠛⠋⠙⠿⠿⠿⠿⠛⠓⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠓⠒⠒⠊⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⣤⣤⣤⣄⠀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀
⠀⢀⣿⣿⣿⣯⠀⠀⠀⣸⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣾⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⣸⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⣠⣄⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⡀⠀⠀⠀⢀⣿⣿⣿⣿⣇
⢠⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢀⣾⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠻⠿⠶⠷⠿⠿⠻⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⡆⢰⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⠀⠀⣿⣿⣿⡁⠀⠀⢸⣿⣿⡟⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣾⣶⣶⣿⣿⣿⣿⣷⣶⠀⠀⠀⢸⣇⣸⡇⢸⡇⠀⢰⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⠀⠀⢰⣿⣿⣿⡇
⠀⣶⡄⠀⣤⣼⣿⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿
⠚⠛⠛⠛⠛⠛⠛⠃⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣸⣿⣿⣿⣿⡆⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⣧⣼⡇⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢰⣿⣿⣿⣿⣿⣧⡀⢀⣾⣿⣿⣿⣿⣿⡄⠀⠀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣆⣀⣾⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡇
⣤⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣴⣶⣤⣴⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠐⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠂
⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⣄⣤⣴⣦⣀⣴⣤⣤⠘⠀⠀⢸⣿⣿⣿⠀⠀⢠⣿⣿⣿⡇
⢀⣤⢀⣿⣿⣿⣿⣧⠀⢀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣩⣿⣿⣿⣬⣿⣿⣿⣀⡀⢠⣿⣿⣿⣿⣇⠀⣼⣿⣿⣿⣷
⠸⠿⠟⠻⠿⠟⠟⠙⠓⠻⠛⠻⠛⠻⠛⠿⠛⠛⠿⠿⠻⠿⠻⠟⠻⠟⠟⠟⠿⠿⠻⠟⠻⠛⠿⠸⠛⠟⠟⠛⠋⠾⠻⠛⠟⠿⠛
⣤⣤⡄⢴⣶⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣬⢿⣤⣼⣿⣿⣯⣍⣿⣿⣿⣻⣿⣛⣻⣿⣻⣿⣿⣟⣿⣛⣿⣿⣿⣛⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠋⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⣿⣿⠿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠞⠋⠉⠀⠀⠀⠀⠉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣠⣿⣶⣶⣿⣿⣿⣷⣶⣶⣤⣶⣶⣾⣿⣿⣿⣦⣀⡀⠀⠀⢀⡘⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡐⣶⣶⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⡛⠛⠛⢋⡁⠙⢮⣝⣛⠻⠿⠿⠿⠿⠟⣛⣩⠴⠈⢙⡻⠿⠿⢛⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡋⣭⣶⣿⣷⡀⡍⠙⠛⠛⠛⠛⠉⢩⢰⣿⣿⣶⡍⣹⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣽⣛⣛⣡⣇⠀⠀⢸⡀⢠⠀⣸⣌⣛⣫⡭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢰⡆⣸⣇⣿⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣒⣛⣋⣩⣭⣭⣭⣭⣭⣍⣛⣒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣟⠻⢭⣽⠹⡏⢹⡟⣿⠉⣯⠽⠋⣻⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⢻⠀⡇⢸⡇⢻⠀⡟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⢸⡇⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣶⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⣤⣶
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⢈⡏⠁⣠⣆⣠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣿⠁⠃⣨⠙⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠶⠀⠸⠇⢀⡾⢡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣱⠄⠀⠀⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⡱⣦⠀⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠧⠀⠀⠋⠠⠋⠔⠁⠀⠀⠀⠀⠀⠀⢀⡀⡠⠀⠃⠀⠀⠀⢠⣄⣂⣀⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠰⡄⠇⠀⠀⠁⠀⠀⠀⠉⠙⠛⠻⠷⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⣀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠒⠶⠲⢀⣤⠄⣠⠴⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⠟⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠰⠀⠐⠂⠘⠢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠂⠙⢻⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⡠⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠆⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠞⠢⠄⠀⠤⠊⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢄⡀⣀⡀⠠⢀⠐⠃
⠀⠀⠀⠀⠀⠀⡬⢀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣷⡾⠷⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⣈⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠀⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠠⢛⠀⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⠀⠀⡄⠐⠃⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⢤⡀⢤⠈⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟
⠀⣠⠀⠀⠀⠀⠈⠀⣀⠒⣀⠀⠂⡐⢂⣤⡄⠀⠀⠀⠀⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡀⣀⠀⡀⣀⡠⠆
⠘⢋⡙⠉⠉⠁⡀⠀⠻⠿⣃⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠁⠀⠀⠁⠂⠀⢀⠀⠀⠀⠀⠀⠀⠚⠃⠰⠂⠉⠀⠀⠀⠀⠀⠀⠁⠒
⠀⠼⢇⡨⠍⠀⠀⢀⠄⠀⠛⠀⠀⠠⠀⠐⢢⡤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡃⠐⢀⠀⠀⡁⢠⡤⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠛⠂⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡼⠃⠀⠚⠃⠀⠀⠀⠁⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤
⡄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠋⠁
⠁⠀⠀⢠⡀⢃⡰⠐⠶⠀⠑⠲⢄⣠⡄⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡰⠚⠎⠀⣠⣀⠀⠀⠀⠀⣀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀
⠀⠀⠐⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠉⠀⠀⡰⠀⠀⠀⠀⠠⠤⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀
⣀⣀⣀⣀⣈⣉⣉⣁⣀⣘⣢⣄⣀⣀⣐⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡶⣻⣽⣏⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠚⠉⠁⠀⠀⠀⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣇
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⢀⣀⠀⣀⣴⣄⣀⠀⠀⠀⠀⠀⣀⣴⣾⡄⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⡟⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⣠⣤⢻
⠀⠀⠀⠀⠀⠀⠀⢻⡘⢿⣿⣿⣿⡿⢉⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⣿⣿⣿⡿⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣬⣭⡥⢖⣠⣝⠲⠦⣭⣭⣍⣭⣭⡭⠴⢚⣥⣄⡪⢭⣭⡭⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⠿⣿⣿⡇⣇⠀⠀⢠⠀⠀⠀⣆⢺⣿⡿⢟⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⢻⠀⡀⢸⡆⣾⠀⡟⠓⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠼⠶⠷⠾⠷⠿⠶⠧⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣵⢶⡶⢿⠻⡟⢻⡿⣿⠛⡟⢷⡶⣬⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⠭⢿⠀⡇⢸⡇⣿⠀⡯⠵⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡟⢲⣾⣾⣶⡄⣶⣶⣶⡆⣶⣶⣶⣶⢶⣦⢰⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⠉⠁⢸⣿⣁⣿⢷⣿⡇⣿⣧⠁⢠⣿⠇⠸⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢸⣿⢿⡇⠀⣿⠶⢿⡇⠀⣼⠇⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣠⡇⢀⣿⣼⣿⣶⣿⣿⣿⣷⣾⣯⣀⡀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠮⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠤⠭⠭⠍⠁⠀⠀⠀⠀⠀⠀⠁⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀⢀⣠⣀⡀⠀⠀⠀⠀⣠⣶⡆⢄⠲⡄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⣴⠀⠿⣿⠏⣆⠀⢀⡀⠙⠛⠁⢸⡇⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⣄⣀⣀⣠⠿⠚⠊⠳⣤⣤⣴⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢹⣿⠿⠛⠁⣴⣰⣆⡄⠈⠻⠿⠿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⡠⠀⠘⠋⠙⠃⠀⠀⣤⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢼⣧⡤⢤⣤⠄⠠⠤⠶⣿⠃⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⣿⣶⠀⠀⠈⠀⠀⢸⣿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢏⠻⠶⢶⢶⢶⠞⠋⠌⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆⠉⠐⠀⠐⠐⠈⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠐⠂⠐⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠓⠚⠉⠁⠉⠉⠓⠓⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀
⠀⠀⠀⠀⠀⠀⣠⡶⠚⠃⠀⠀⠀⠒⠤⠂⠐⠤⠒⠀⠀⠀⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧
⠀⠀⠀⠀⣰⡟⠙⠀⠀⠉⠉⠉⠁⠂⠀⠀⠀⠀⠐⠉⠉⠉⠁⠀⠘⠙⢿⡄⠀⠀⠀⠀⠀⣿⡇⣿⡀
⠀⠀⢠⢾⡿⠃⠀⠀⡄⠀⠀⠀⠀⡠⠀⠀⠀⠀⡄⠀⠀⠀⠀⣄⠀⠀⠛⣿⣶⡀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠘⢾⣿⣦⣤⣤⣷⣄⣀⢀⣀⣧⣀⠀⠀⣀⣧⣀⡀⣀⣠⣿⣤⣤⣴⣿⠿⠁⠀⠀⣠⡟⣧⠟⣧⡀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⠟⠀⠀⣴⣾⣿⡇⣿⠀⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣻⣛⣭⣿⣿⡿⠯⠽⢿⣿⣿⣭⣻⣛⠋⠀⠀⠀⠀⠀⠀⠉⠉⠀⡇⢹⠀⡏⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠰⢿⣯⡁⠀⢁⣠⡈⠀⠀⠀⠈⢁⣄⡁⠀⣈⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⡟⠟⣿⣿⠛⣿⠏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣿⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⡄⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⠀⣿⡇⠀⣧⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢳⣼⣧⡞⠛⠿
⠀⠀⠀⠀⠀⠀⣀⡴⠒⢊⣀⠄⠀⣿⠀⣿⣿⠸⣿⠀⢀⣈⠓⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠎⠁⠀⠊⠉⢁⣀⣸⣿⢸⣿⣿⡄⣿⣄⣀⡈⠉⠁⠀⠈⠃⠀⠀⠀⠀⠀⢰⠠⡄⢀⠀⡄
⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⠟⠋⠉⠻⠁⠈⠁⠹⠏⠉⠛⢻⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⢸⡆⣇⡸⢰⠇
⠀⠀⠀⠀⠀⢸⣿⣿⣯⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢧⡈⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠺⠿⢷⣤⣴⣄⣠⣦⣤⠿⠿⠖⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠞⠁⠒⠁⠀⠁⠰⡄⠢⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⣀⡌⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠗⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠾⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠄
⠀⠀⠀⠀⠀⢀⣠⡀⠀⠠⣀⠀⣠⡄⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡂
⠀⠀⠀⠀⠀⠀⢠⡄⠐⢀⠀⠀⠈⠐⢛⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠑⡀⠂⣀⠄⠈⠉⠉⢂
⠀⠀⠀⠀⢀⣄⢤⣷⣶⣀⣄⠀⢠⠀⠺⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⣾
⠀⠀⠀⠀⠀⡁⠀⠀⢀⡀⠀⠁⠀⠇⢀⣀⡈⠀⠂⠀⠀⠀⠀⣤⠀⡀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⣀⣠⠄⠉⠁⠀⣥
⠀⠀⠀⠀⠀⠛⢻⠳⠛⠛⠐⠲⡖⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⢄⣀⣛⠀⡄⠀⠉⢤⠀⠀⣰⡼⠃
⠀⠀⠀⠀⠀⠐⠭⠷⠦⢾⡆⠐⠛⣶⢿⣧⣀⡠⠠⢦⣤⠞⠂⠀⠀⠀⠀⢀⡀⠀⠀⢉⣥⣨⣄⣄⣀⣸⣷⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣿⣦⣴⣿⣦⣭⣭⣶⣤⣶⣌⣲⡶⣿⡶⣶⢤⣬⠟⢒⣠⣤⣉⣴⣬⣭⡼⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠙⠻⡝⡟⡿⡇⡿⠀⠛⠀⣿⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠁⠋⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡆⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⡇⡦⠀⠓⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠶⠉⢛⠗⠒⠂⠓⣹⠖⠳⠞⢓⣣⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠂⠠⣄⡄⠈⠀⠀⠀⠐⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠄⠰⠄⣤⠤⠀⡤⠤⠰⠂⠙⠋⠁

⡀⠀⢀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⣿⣿⣿⣻⣛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣿⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣿⠿⣿⣿⣿⣋⡀⢀⣶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣀⡀⢀⣠⣦⣿⡿⠿⢿⣿⣿⡉⠙⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣷⣶⣾⡏⠉⠁⠰⣦⣿⣯⣁⣶⡀⣼⡿⠇
⠀⠀⠀⠀⠀⠀⣠⣤⣠⡄⣠⡶⢁⠁⠹⢹⣟⣋⣡⣿⣿⡇⣤⣤⣿⣏⣿⣿⣏⠁⢺⣿⣯⠻⢶⣆
⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⣿⣿⣌⢳⡆⢀⣿⣿⠋⢴⣦⢙⣺⣿⡿⠿⣷⠉⠙⢿⣯⣈⣁⣠⢼⡟
⠀⠀⠀⠀⠀⠀⢈⠛⠻⠁⢸⣿⣷⣤⡁⣬⣻⣷⣶⠞⠛⢞⡛⠛⠻⠷⠦⣾⣿⣶⣿⡿⠿⢟⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣈⣛⠻⣿⡟⣿⣿⣯⣡⠆⣦⡬⡻⢹⣷⠀⢬⣿⣿⣯⣉⣡⠀⠉⠋⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⢿⣿⣷⡶⣂⣼⣿⠇⡈⢸⣏⡸⠁⣯⠃⣠⠘⠛⠛⢿⣯⣅⣠⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠠⠈⠛⠉⠉⠁⠀⣻⡖⢹⡇⢠⡿⢀⡁⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⣿⣷⣾⡷⡿⠶⣾⡷⢶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠶⠀⠘⡇⢸⠃⠀⣾⠋⠀⡀⠶⠶⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⢀⠀⢀⣤⣤⡀⣾⠀⡁⡄⢀⡀⠈⢠⡀⣶⠀⠀⠀⢀⣤⣄⢴⣶⣄⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⣿⣿⣿⣦⣶⣦⣤⣇⣿⣧⣽⣤⣜⣵⣾⣴⣿⣿⣮⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠟⠛⠟⠛⠻⠛⠛⠻⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠛⠛⠉



⣿⣿⠛⠿⢻⠿⡿⢻⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠒⠛⠛⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡞⠉⠀⠀⠀⠀⠀⠈⠉⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠃⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣆⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠴⠦⢄⣠⣄⠀⢀⣠⡀⠀⠀⡀⠀⠀⣀⣤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢸⠁⠀⠀⢻⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣤⡤⠾⠀⠀⠤⠸⠧⢤⣤⣤⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣥⠤⠶⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⢀⣤⣄⣀⣀⡀⠀⣀⣤⡤⠤⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠇⠀⠀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡴⡖⠲⠶⠞⠛⠛⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠷⠶⠶⠶⣤⣤⣄⣀⣀⡀
⠀⠀⢀⠠⠀⠀⠋⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⠛⢲⡄
⠀⠀⠁⠀⠀⠊⠁⠀⣀⣠⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣴⣄⣀⣀⡀⠀⠀⠀⢤⣀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠑⠶⠶⠛⠉⠉⠉⠛⠋⠛⠛⠛⠶⠶⠒⠒⠶⠶⠛⠛⠒⠶⠒⠛⠉⠉⠉⠉⠀⠀⠈⠉⠛⠓⠶⣤⠴⠋⠉⠛⠓⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⠀⠐⠈⠉⠉⠒⠄⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠈⠓⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⠀⠀⠠⠄⠀⠀⢄⠀⢀⠀⠑⠒⠊⣤⡤⠀⢀⣀⡠⢄⠄⠀⠀⠀⠁⠀⠀⢄
⠀⠀⠀⠀⠀⠀⣠⠤⠌⠀⠀⠀⠀⢈⢀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣀
⠀⠀⠀⠀⣀⡈⠀⠀⠀⠀⡀⠀⣀⣌⠹⣄⡀⠀⠀⠈⠒⠒⠂⠤⡠⠀⠈⠒⠒⠉⠉⠉⢀⣠⢦⠆⠀⠀⢰⠀⠀⠀⠈⠳
⠀⠀⠀⠘⠁⠀⣄⡄⠀⠠⠹⠦⠀⠄⠀⠀⠉⠛⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠉⠀⠀⡀⠀⣠⠞⠤⠀⠀⡄⠀⠀⢱
⠀⡠⠊⢀⠀⠉⠀⠙⠤⡀⠄⠀⢀⢀⡀⠀⠐⠚⠁⣀⠄⠀⠄⣀⡤⠃⣀⡠⠀⠀⠑⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⣠⠇⠀⠀⠀⠘⢦
⠀⠁⠀⠀⠉⢆⡀⠀⢶⠀⠀⡄⠀⠁⢆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠓⠂⠀⠑⠀⠉⠀⠉⠉⢀⣀⠴⠓⠙⠀⠘
⡎⣀⠀⠀⠳⠤⠀⠀⠱⠀⠀⠑⠤⠄⠀⠀⠐⢤⠌⠓⠐⠀⠤⡤⠂⠀⠀⠳⢤⠀⠤⠂⠀⠀⠀⠀⠀⠒⠌⠋⠁⠀⠠⢠⠔⠀⢀⡠
⠣⡈⠒⠀⠀⠦⠀⡆⠀⠠⡀⠀⢄⠤⢀⡀⡠⠀⣀⣀⠤⠀⠐⠂⠢⠴⠊⠂⠀⠐⠤⠤⠈⠒⠒⢢⣄⠀⠐⠒⠀⢀⣀⡠⠀⠊⠭⢴⡲
⠀⠈⠐⢆⠂⠀⠀⠑⠄⠀⣉⠁⠀⠐⠺⣄⠤⠤⠄⣤⠀⠁⠈⢀⢠⠀⡀⠀⠀⠀⠀⡴⠄⠀⠐⠒⠀⠀⠀⠀⠀⠉⠀⠀⠐⢁⡴
⠀⠀⠀⠀⠐⢤⣈⠑⢈⠠⠤⠄⠀⡠⢄⣀⠀⠀⣀⣿⠀⠀⡄⢸⠘⢂⠇⡀⠀⠀⣼⢁⣠⣀⡀⠀⠀⠤⠠⠔⠀⢁⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠂⠐⠤⢤⡀⠀⣫⠀⠀⢀⢸⠀⣽⢠⢠⢀⢡⣇⡀⣀⠀⡠⠄⣀⠤⠂⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⠘⢸⠀⡀⡀⡜⡘⣸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡏⡌⠀⢣⣇⠇⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣔⣻⡇⢀⣸⣹⢰⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⠚⠋⠁⠙⠁⠀⠙⠘⠾⠢⡄⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⠀⠀⢀⣠⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⢩⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠢⠀⢈⣿⡆⣯⠀⡏⠉⡖⣄⠤⣀⡠⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡟⢠⡇⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠁⣸⡇⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢹⢀⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⢈⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠠⠴⢦⠀⠀⡠⠤⢄⡠⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠳⠀⠀⠀⠀⠉⢲⡀⠀⠀⠁⠀⢈⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠞⠀⠀⠔⠲⡤⡈⠃⢀⡀⠠⠔⠒⠤⢤⠈⠁⠀⡓⠦⢄⢀
⣀⢀⠀⣀⠀⣀⣀⠀⠀⠀⣀⠐⡉⡁⠐⠂⢀⢢⣄⢀⠀⠀⠀⡀⠈⢀⡘⢀⢀⠀⢈⡆⢀⡉⠀⠈⡀⣉⠃⣀⠀⣀⠀⡀⡀⡀⢀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣬⠒⠂⡀⠁⠀⠀⠁⠠⡀⠀⠀⠄⠀⠀⢄⠀⠈⠲⡀⠀⢀⠀⠈⠀⠀⠈⢇⠀⢹⡏⢻⣮⠹⣿⣴⣧⡿⠏⢉⡏⠀⡱⢋⠡⠂⢴⢁⠼⠋⠟⠀⣡⠞⠃
⣈⡀⠀⠀⠈⠠⠀⠀⠐⠀⠐⣄⣀⣀⣀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠶⢾⣎⡀⢣⡎⣼⠶⡏⠅⠀⢻⣆⡜⠀⡀⠁⠘⠀⠀⠀⠈⠀⢀⠠⠊⠀⠀⠀⠀⠀⢀⡴
⣍⡉⠓⠠⡀⠀⠀⠀⠄⠀⠀⣾⠛⠀⠈⠉⠉⢻⡶⢦⣤⡀⠀⣀⣸⡍⠂⠀⠛⠙⢠⣵⣁⡀⠁⠀⠠⢼⠻⠔⠿⠉⠛⠙⢳⠞⠋⠙⡟⠛⢳⣦⠀⠀⢀⠤⠚⠙⠋
⠾⠈⠀⠀⠈⠀⠄⠀⠀⠀⠀⣷⡚⠀⠑⣞⠉⠛⠁⠈⠀⠈⠘⠙⢹⡦⣤⡀⠀⠀⠈⠀⠽⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠛⠀⠀⢰⠇⠀⡁⢿⠠⠚⠁⠀⠀⢀⠨
⣍⡀⠀⠚⠒⠤⠄⠀⠀⠀⠀⣯⠁⡀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥⣄⣀⣀⡀⠀⠀⠀⠀⢤⡼⠋⠀⠀⠀⠀⢀⠀⣰
⠉⠉⠓⠠⢀⠀⠀⠀⠀⠀⠀⠈⠻⡷⠂⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠐⢠⠈⠀⠒⣿⠉⠀⢹⠆⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠈⠉⠉
⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⠷⣤⣄⠀⠀⠀⠈⠀⠈⠃⠰⠀⠄⠀⡀⠀⠀⢢⡔⢉⠠⠚⠁⠀⠉⠀⠀⠀⠀⠀⠘⠿⠀⠀⣤⠖⢓⡡⠀⠀⠀⠀⠀⠀⠀⠐
⣠⣤⣤⣀⡀⠈⠀⣢⠶⠛⠷⠂⠸⡄⠻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠹⠗⠛⠓⣦⣠⣤⡀⠈
⣀⣀⣀⡈⠉⠀⢠⡿⢖⠀⠀⣀⣠⠄⠀⢧⡀⠀⠀⠀⢀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠁⠙⠀⢹⡶⣖
⣤⣈⡐⠀⣉⣡⣾⠃⠀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⡀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠠⠶
⢉⣁⡶⠻⠀⠀⠙⠄⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠐⠂⠐⠀⠀⠠⠜⠛
⠀⢺⡁⣀⠀⠀⢀⡀⠀⣀⠀⠀⢀⡀⠐⠒⠀⠀⠀⠀⠀⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠄⠀⢀⠀⠲⣶⣦
⠲⠒⠻⣭⡴⣥⡟⠂⠀⠻⠦⢠⡎⢁⡀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⡀⢰⠀⠀⠀⠀⢀⠀⠀⠤⢀⠈⠂⠁⠀⠀⠀⠀⠀⠈⠁⢐⡀⠀⡤⠀⠀⠀⣀
⠡⠀⠀⠀⠀⠀⠙⢧⣀⢀⠀⠀⠉⠉⠀⠀⠀⠀⠔⠀⠀⢀⠁⠈⠀⠀⠨⠀⠀⠀⠀⠈⠃⠀⠀⠀⠁⠂⠄⢄⠀⠀⠀⠀⠀⠀⠀⣠⣰⡇⠀⠠⠴⠿⠛⠅⢒⠒⠦
⣴⡶⠓⠀⠀⠀⠀⠀⠉⠛⠿⠚⢤⡀⠀⠀⠀⠀⠘⠤⡤⠶⠤⠂⠀⠀⠀⠀⠘⡄⠀⡀⠀⠀⠀⠠⠄⠀⠀⠠⠽⠀⠀⢀⠀⠀⠀⣸⡽⠀⠈⡇⠀⠠⢀⣀⠀⠉⠙
⡩⡁⠐⠀⠀⠀⠀⡠⠄⠈⠁⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠰⣀⣠⠆⠀⠀⠲⣤⠤⡀⠘⢆⠀⠀⠀⣠⡀⠀⢀⠀⠑⠒⠉⢙⣷⢛⠉⢀⣤⣾⠁⠀⢀⠀⠀⠁⠀⠈
⠔⠀⠀⢀⡠⠔⠁⠀⠀⢀⣴⡿⠚⠷⣴⣤⡴⠞⣆⣀⣀⣾⡍⢩⣁⡀⡀⢀⣿⡆⠡⠸⠾⣤⡴⣶⠋⠙⠖⠞⢧⣤⣤⡽⠟⠀⠉⠙⠛⠉⠀⠀⠀⠀⠈⠓⠄⠈⠂
⣞⡭⠊⠁⠀⠀⣠⠴⠛⡁⠊⠁⠀⠀⠀⠀⢀⠀⠈⠉⢁⡾⠀⡸⣏⣠⣤⣞⠙⢶⡆⠀⠀⠀⣴⠇⠀⠀⠀⠈⠂⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠈⠛
⠁⠀⠄⢀⡴⠋⣠⡔⠋⢀⠀⣀⠔⣠⠄⡠⠛⣠⠂⠀⡞⢀⣶⡠⣎⢿⣜⡼⣼⣇⢙⠧⢹⣛⠁⠀⠀⠀⠨⡂⠀⢴⡀⠀⠢⠀⠀⠠⠀⠀⠀⠄⠁⠀⠀⠁⠢⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢦⠶⡴⣆⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢛⣛⡛⢲⡄⠀⠀⠀⠀⠀⠀⠀⢀⡰⠊⠉⢲⡐⠤⢤
⠀⠀⣀⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⡎⣾⢱⣭⣦⠀⠀⠀⠀⠀⠀⢸⡇⢰⣾⣹⡶⠀⡇⠀⠀⠀⠀⠀⢀⡴⠉⠀⢠⠔⠁⠈⠉⠒
⢤⣬⣭⣭⣭⣭⣭⣤⡾⣋⠩⢀⠀⠀⠀⠀⠀⣿⢸⡇⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⣾⡿⠿⣿⡶⡇⠀⠀⠀⠀⠀⠀⣶⣶⡆⢰⣶⣶⡆⠉⠉
⠈⢩⣭⣟⣛⠻⡿⢯⡾⣿⡶⣾⡆⠀⠀⠀⠀⣿⢸⡇⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⣿⢛⡞⣹⣇⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⡇
⠀⠸⢳⣯⡟⣿⠿⠏⣾⣭⢿⡞⠁⠀⠀⠀⠀⣿⢸⡇⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⢿⣿⣿⣿⠋⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⢸⣿⣿⡇
⠀⠀⠈⠛⠛⠃⠀⠀⠙⠓⠛⠀⠀⠀⠀⠀⠀⠛⠘⠃⠛⠘⠓⠃⠀⠀⠀⠀⠀⠀⠸⠷⠞⠷⠷⠷⠶⠗⠀⠀⠀⠀⠶⠾⠟⠿⠟⠾⠻⠟⠿⠶⠆

⠀⠀⠀⣀⢤⣀⢀⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣦⣶
⠀⠀⠀⠇⠀⡴⠻⣄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠈⢉⢸⣿⣏⠉⠁⠀⠀⠀⠀⠀⢠⡞⣵⣦⠀⠀⣠⣶⡝⣆⠀⠀⠀⠀⠀⠀⠀⢫⣞⣲⡝
⠀⡰⠊⢁⡞⣡⣦⡌⢧⠉⠒⠄⠀⠀⠀⠀⠀⠈⠉⣸⣿⣇⠙⠀⠀⠀⠀⠀⠀⣾⠸⠿⠿⢣⣤⠻⠿⠿⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠑⢤⣞⣀⣙⢛⣁⣘⣇⠴⠃⠀⠀⠀⠀⠀⠘⠛⣾⠛⣗⠛⠂⠀⠀⠀⠀⠀⢹⡀⠀⠀⣬⣧⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡧
⠀⠀⠀⡇⠉⢙⢍⠉⠁⡹⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠻⡈⢆⠀⠀⠀⠀⠀⠀⠀⠻⢤⣘⠿⠿⢗⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷
⠀⠀⠀⠈⠀⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢠⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⢉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⣭⣴⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⣿⠉⢉⣍⠉⢹⣷⠀⠀⠀⠀⠀⠀⠀⢸⢦⢤⣤⢤⢼⡇⠀⠀⠀⠀⠀⡴⠤⡤⠔⠊⠁⣰⠻⣬⠻⠁⠀⠀⢰⣶⣷⣿⣿⡛⢛⣿⡏⣾⣶
⠀⠀⠀⠻⣶⣟⢛⣳⣾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡇⠀⠅⠀⠀⠀⢿⣡⠏⣿⠀⠀⠀⢸⣿⣿⣿⡉⢱⡏⢹⡇⣿⣿
⠀⠀⠀⢶⣿⣉⣮⣡⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣠⣽⣿⡇⠀⠀⠀⠀⠀⠧⠴⠳⠦⠤⠄⠄⣘⠲⡿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⢀⡤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⣠⣤⡴⣚⣛⡲⣤⣤⡀
⠀⠀⠀⠖⠉⠀⠀⣀⡬⠜⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⣱⢉⣿⣿⣷⡆⠀⠀⠀⣋⣶⣷⣾⣿⣿⣿⣶⣶⣝⡂⠀⠀⠀⠀⣀⠀⠀⡄⢀⠆⡀
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠛⡛⠛⡛⠛⡛⠛⠁⠀⠀⠘⠿⠻⠿⡛⠿⡿⢟⡻⠿⠿⠟⠀⠀⠀⠀⢀⣿⡀⣸⢃⣾⣀⠠
⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣴⣶⠌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⡙⢿⣿⠉
⠀⠀⢀⣿⣏⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⣀⣿⣏⣐⣀
⠀⢻⣿⣿⣧⣽⣿⣿⣿⣿⡿⠃⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠈⠛⠻⠿⠟⠛⠉⠐⠁

⠒⠒⠒⠂⠀⠤⠐⢐⣬⣥⣥⣀⠖⠛⠓⠀⠀⠜⡜⠑⡷⡋⢹⠸⡉⡋⠙⡛⠻⢯⣟⣶⣶⣻⣯⠿⠟⠻⠢⠙⢧⣎⠒⠸⠓⠴⠦⢑⠊⠈⢳⡄⠠⠀⢤⡑⡈⢂⡼
⠳⣤⡀⠀⢀⡠⠆⢹⠋⠉⠁⣨⠟⣮⠛⠒⠚⠎⠀⠀⠘⡉⠢⢑⡬⠦⠴⢶⠟⠋⣡⠤⠭⠭⣭⣭⣍⡀⢣⢱⡄⡈⠉⠙⠙⠛⠛⠒⡒⠬⡊⣧⡀⠀⢀⣇⠟⣪⡗
⠀⠘⢷⡒⠭⣖⠖⠪⡓⠆⠈⠁⠁⢸⣧⠾⠛⠒⠒⠢⠜⡢⠄⣺⠀⠀⡴⠃⠀⡪⠖⠲⢶⣚⠥⠤⡈⠻⣜⢄⠳⠤⢀⣀⠀⠀⠀⠀⠈⠑⠌⢺⠟⠓⣛⣼⣤⢾⣇
⢤⠀⠀⠻⣦⡤⠉⠢⠀⠀⠄⢤⡴⠋⠁⠀⣀⡀⠀⢀⣀⣀⠑⠛⠀⢂⢄⣤⣾⠕⠀⢑⡢⠗⢒⣠⢌⣚⡮⠳⣧⣄⣀⡀⠙⠲⣀⠀⠀⠀⢸⠀⡇⢤⣀⢏⠁⠈⢙
⠢⡑⢄⠀⠈⠙⠲⠦⠤⠤⠞⠋⢀⣤⠆⣁⠎⠠⣢⠔⠂⠉⣉⡁⡒⢢⡟⣡⢁⠄⣤⣤⣀⡩⣔⠾⠾⠤⠠⠀⣤⢂⢭⡛⠓⢄⠙⣦⠔⡠⠈⢀⡿⡪⠥⠬⢧⡠⡄
⢀⢸⡎⣷⢤⡀⠀⠀⠀⣀⡤⣾⠋⢀⠞⠁⠔⢸⠡⢉⣈⠁⢠⡈⠀⠑⠪⣕⢒⣫⠍⢉⠖⢉⠧⡖⠀⠒⡄⠀⢸⠘⠱⢌⢢⠊⢳⡛⣧⠀⡄⢰⣾⠁⣐⠀⠀⢻⢟
⣌⢸⡇⣿⠈⠄⠉⠁⠉⠀⣵⡏⠀⢸⠀⠀⠀⠸⣄⠂⠉⠻⠍⡀⠀⠀⠀⡄⠀⠠⢠⠏⠀⠀⠀⠠⠶⠦⡅⠀⠋⢰⠀⠘⠂⠀⣿⠇⡿⣆⣦⡼⠛⠲⣟⠓⡲⣯⡷
⠜⣺⡁⠎⢢⡈⠳⢤⢤⡴⠿⠁⠀⣼⠳⢄⠠⠀⠉⠛⠟⣿⠶⣦⠑⠄⠀⢂⡀⡂⢹⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠰⠑⢮⣿⣠⡟⢰⠁⠏⠉⠀⠈⠠⠈⠳⣌⠈⣿
⠜⠏⢇⢠⠀⠙⠢⢄⣀⣀⢀⣠⡤⢬⣄⢺⡀⠀⠈⠠⡼⢃⠀⢈⢣⠈⠀⢎⣃⠁⠙⢄⠀⠀⠀⠀⠀⢁⠀⣀⣾⠇⡤⣤⠍⡜⠝⠸⣦⡀⠀⠀⠀⠀⠰⠀⡈⠙⠛
⡰⠛⠢⠢⣍⡒⠂⠒⠄⠉⠀⠁⢠⠁⠀⢢⡹⣄⠠⣼⢃⠘⠀⠀⠊⡆⠠⠈⠁⠀⠔⠂⡐⢀⡤⡀⢀⡴⢹⢮⡙⢸⡏⢠⢞⠀⣖⠚⠓⠣⠐⠀⠀⠀⠀⠃⠈
⠁⠄⠀⠀⠀⠩⣁⠀⠈⠉⠉⠀⢺⠀⡀⠀⠙⢾⠃⢽⢼⠀⠀⠁⠀⡕⣀⠀⢀⠀⠀⣀⣈⣡⠔⢁⠟⠠⠘⣚⣠⡾⣱⣿⣛⡛⠻⣄⠐⠒⢣⡆⠀⡀⠠⡃
⡀⠀⠀⣀⣄⡀⠨⠀⢠⠞⡛⠛⢺⠀⠀⠀⠀⠸⡄⢸⡈⡇⡖⠒⠀⠐⢁⡔⡉⠉⠔⢁⢤⡖⠚⠁⠀⣴⠛⢯⣼⠿⠋⠁⡜⠀⠀⢈⣷⣦⣄⢁⠆⠀⠀⠐⢀⠀⢀
⠈⢠⣠⠀⠠⠩⠿⢄⣘⣄⣀⡠⠂⠀⠀⠀⠤⢤⣽⣄⠳⣿⠀⠀⡤⠀⣻⠀⠀⠀⠀⢶⠊⠀⠀⢀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣈⣿⠀⢲⠀⠈⠂⠀⢀⠛
⣶⠛⠙⢄⣀⡸⠀⠒⠀⠩⡍⢢⣀⡀⠈⠀⣀⣤⣌⡻⢷⣍⢷⣦⣧⣤⣺⡂⠀⢤⡀⠈⠳⢤⣴⠵⠯⠲⠚⢛⠉⣉⣉⣳⡄⠀⠀⠀⠀⠀⠑⡖⠋⠀⡀⠀⠀⠈⣆
⠀⠉⠀⠁⠈⠉⠢⠀⠀⢤⣀⣀⡀⣠⡴⠋⠁⠀⠀⠀⠀⢈⡘⣁⠙⠷⣄⠉⠦⣄⠈⠶⠠⠈⢧⢡⡀⠄⠉⠐⠀⠀⢀⣼⡁⣈⠈⠑⠀⠄⠀⡀⢀⠀⠀⠀⡬⢰⢄
⠀⠀⠀⠄⠔⠂⠐⠓⢐⠈⠠⠀⢌⠩⠀⠤⢀⠀⠀⢀⡠⠊⡄⢿⡣⡑⠨⣑⡒⠦⣬⣍⣁⡁⠐⠡⡚⢤⡀⣰⠶⠊⡉⢄⡀⠀⠀⡀⠁⢀⠀⠰⣌⠐⠢⠀⢰⣧⠜
⠠⠀⠀⢀⠠⡄⠀⠀⢤⠀⠁⣉⠁⢌⡀⠀⠀⠀⠉⠉⠀⠀⠈⢦⣙⡚⠷⠦⢄⡟⠉⢐⠦⠻⣶⡀⠘⡄⢹⠁⠀⠀⠀⠠⠄⡘⠦⡁⠀⠀⢣⠀⢙⣯⠇⠀⠀⢧
⢲⠒⠚⠯⡑⠜⢆⠀⠀⠳⢄⡀⠀⠀⠉⠀⠠⢄⣀⣀⠀⡤⠴⠒⠏⠉⠉⠉⠻⡇⠠⡌⠻⡆⢛⣃⠀⢁⠘⠀⠀⠒⠧⠦⠤⠁⠀⠀⠀⢀⢸⠀⢘⢸⡼⠢⠄⡜⡄
⠈⢦⡲⠀⠐⠈⠂⠀⡄⠀⡴⢛⠛⣒⠖⠒⡫⠅⠁⢀⠀⠄⠒⣰⠃⠀⡀⠀⢄⢣⠘⣸⡀⠀⠌⠹⣧⠈⣄⢧⠀⠀⠀⠄⡐⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⡀⠀⠉
⠀⠀⠉⠦⢴⡰⡙⠈⡰⠚⠄⢀⣼⠥⢤⠴⠠⢐⡞⢁⣴⠛⣋⠅⠀⠤⣈⠈⠄⠄⠑⣄⠑⠄⠐⠀⠹⣧⡈⢮⣣⡀⠀⠀⠀⠬⢦⡀⡼⢡⣾⠀⢀⠸⠇⠑⠤⢄
⠉⠤⣐⠀⠀⡙⠻⣛⢁⡗⠊⡾⠁⣊⠉⠩⠙⢣⡗⣩⠃⠨⢔⣀⣤⣀⠠⠍⣚⣦⣀⣀⣑⣦⣄⣀⡄⠈⠻⣦⣝⠻⣶⣄⡀⠀⣠⠜⡔⠁⢸⠀⠘⣆⠡⡀⠀⠀⣧
⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠃⠈⠐⠂⠀⠉⠁⠀⠉⠀⠁⠀⠚⠁⠈⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠀⠈⠙⠛⠈⠉⠙⠚⠁⠀⠁⠀⠈⠃⠀⠈⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⡟⠉⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠿⣿⣿⣶⠞⢛⡿⠛⠋⠙⠛⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣏⠙⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣤⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠛⠋⠉⠀⠀⠀⠉⠛⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢻⣿⣿⠟⠛⠛⠻⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⢹⣿⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⣿⠛⠙⢷⡄
⠀⠀⠀⠀⠀⢰⣿⣧⣀⣀⣾⠟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠿⢦⣤⣾⣿
⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄
⠀⠀⠀⠀⠀⢯⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣡⡿⠁
⠀⠀⠀⠀⠀⠈⢷⣾⣦⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠟⠛⠛⠿⠿⠿⢿⣿⣿⣷⣦⣤⣤⣤⣴⣾⣿⣶⣶⣶⣾⣿⣷⣶⣶⣶⣾⣿⡿⠿⠿⠿⠛⠓⠾⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠹⠛⡁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠛⡧


⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠒⠃⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⠀⠀⠀⠀⠀⠈⢥⣣⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⣀⡤⣤⣤⡤⠾⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠻⠛⢺⡟⠁⠀⠀⠀⠀⠀⠀⡾⠼⡿⠗⠛⠿⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠁⢛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠆⣸⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⠠⠋⠀⠀⠀⠀⢀⡀⠾⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⠀⢠⠀⠀⠀⠀⠀⠀⠐⡀⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣱⠞⠣⠜⠁⠀⠀⠀⠀⠀⠀⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠢⠤⠄⠀⡈⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣼⣷⣶⣿⣿⣶⣴⣿⣶⣾⣿⣷⣦⣄⣸⣿⣦⣠⣾⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣦⣤⣤⣴⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣶⣶⣦⣀⣀⣀
⠀⠀⠀⠀⠠⣶⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣤
⠀⠀⣀⣤⣤⣾⣿⣿⣷⣿⣶⣭⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣏⣵⣶⣿⣿⣿⣿⣧⣤⣄

⠑⠀⠈⢠⡀⣧⠛⠾⡓⠀⠀⠀⠀⠀⠀⢀⠸⡃⠀⢀⠀⡀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠐⣠⠄⠀⣠⠊
⢀⣶⣕⠌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠠⠂⡄⠀⠀⠀⠁⠀⠐⠁⠘⢆
⡉⠀⠁⢠⠶⠈⠀⠀⠀⡀⠆⠘⠖⠒⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠈
⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⠓⠀⠀⠀⢀⠐⠑⠆⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⠐⠂⠁⢀⠀⣀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠀⠘⠉⠁⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠔⠋
⠀⢀⡄⠀⠂⢘⠀⠀⠀⠀⠏⠈⠀⠀⠢⠀⠀⠀⠁⠐⠀⠀⠀⠸⠂⢈⠄⠋⠈⠁⡆⠓⡀⠀⢄⠀⠀⠀⠐
⡈⠀⠀⠀⠀⠠⠛⠈⠁⢐⠀⠊⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠥⠀⠀⠰
⠉⠁⠀⠀⢀⠤⠆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠂⠠⡄⠀⠀⢨⠥
⠓⠠⠄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰


⣉⣉⣀⠤
⣉⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⣉⣤⡴⠖⡊
⠉⣥⠶⢃⠁⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠛⢿⣶
⣈⣴⣮⣅⣤⣴⣎⣠⣠⣄⣤⣄⣠⣇⣤⣄⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣀⣤⣤⣈⣤⣌⣵⣦⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠉⠉⠉⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠐⠤
⠀⠀⠀⠀⠀⠀⠀⡠⠔⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠒⢤
⠀⠀⠀⠀⠀⠀⠀⢅⠀⡁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠳⡄
⠀⠀⠀⠀⠀⡎⠀⠈⠀⠑⠀⠀⠀⠀⢀⣈⣉⣙⠦⠤⠤⠤⠤⠽⣉⣉⡀⠀⠀⠀⠀⠚⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠘⠢⠄⠆⣀⡀⣀⡈⠉⠉⠀⠀⢣⠀⠀⠀⠀⠀⢰⠃⠀⠉⠉⠁⣀⠀⣀⡰⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠴⠦⠨⡆⡄⡄⢰⢠⡎⠰⠦⠠⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⡷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⡁⣁⠀⢈⣀⡑⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠠⠬⣷⣤⣄⠧⠆⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠠⠐⠒⢢⠤⠒⠀⠑⠂⢔⠒⠂⠄⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣂⠁⠀⠚⠉⠩⠃⠀⠤⠒⠀⠀⠀⠀⠀⠉⠀⠀⠐⠛⠉⠁⠀⠀⠙⣀⣀
⠀⢀⣀⣤⣀⣘⣓⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣐⣤⣀⣀⣀

⠀⠲⡄⠀⡴⠂⡄⠄⢤⠄⡀⡄⠐⠠⡦⠄⠀⠰⣦⣤⡤⠤⠆⢤⣄⠠⠀⠄⡠⠄⣤⡤⠀⠀⣤⠤⠠⠠⡄⠀⠀⠠⠄⠀⠆⠀⠀⠀⠀⡀⢀
⠀⠤⠊⠁⠅⠦⢀⡀⠈⠁⠈⠳⠀⠶⠓⠀⠀⠀⢠⣨⡍⠀⠀⠈⠐⠇⠀⠀⣀⠒⠉⣍⣁⠀⠺⠂⠚⠊⠑⠖⠠⡄⠀⠈⡀⠀⠀⢂⠖⠁
⠀⠀⠂⠉⠀⢰⡿⠛⠻⡗⠰⡀⠀⢠⡐⠂⠂⠀⠘⣋⣀⣀⠀⠈⠀⠠⠇⠀⠈⣠⠈⠁⠀⣀⠠⡤⠤⢤⠀⠀⠀⠂⠈⠰⠄⣀⠘⠁⠀⠀⠨
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠁⠖⠳⢳⡞⠀⠈⠉⠀⢰⠆⠀⠀⠀⠸⠀⠀⢠⡊⠀⠀⡂⠊⠀⢁⠀⠢⠄⠈⠀⠀⠀⠲⢟⡄⠒⠒⠂
⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡰⣹⠋⢀⡀⠀⣤⠭⠿⠆⠀⠀⠃⠀⠀⠉⠒⠀⠀⠉⠀⠖⠀⠀⠀⠀⡀⠀⠀⠇
⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⢇⡇⢘⣣⣤⣤⠌⠀⠀⠀⠀⠸⣇⢀⠀⣆⠠⠀⠀⠠⠀⠰⢂⡀⠀⠀⠹⣶⠀⠀⢸⣥⡀⠀⠀⠤⡀
⠀⡀⠁⠀⠀⢈⣁⣠⠆⢠⠀⠀⠿⢀⣀⠋⠊⣉⣘⡉⠐⠒⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠆⠀⠤⠄⠀⠀⠀⠔⠂⠀⣠⠀⠸⢿⣯⣅⠀⠀⠀⠐⣼
⠀⡇⠀⠀⢠⡔⢡⡀⠀⠈⠁⠀⠀⠉⠀⠠⠊⠉⠁⠉⠀⠠⣄⠉⢦⣤⡇⠀⠀⠀⠀⠀⠜⡀⠁⠀⠀⠀⠀⠡⠀⠀⠀⠀⢴⠒⣉⠛⠂⠀⠀⠀⠁
⠀⡇⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⣠⣤⣄⡀⠀⠉⠉⠁⠀⠀⠀⠀⠂⠄⠸⠆⠀⠀⠀⠀⡀⠶⠀⠘⠂⠀⡦⠀⠈⠁⠀⢤⠀⠄⢘
⠀⢵⡆⠰⠆⠽⠀⠀⠀⠀⢢⠀⣇⠰⠈⢄⠀⡼⢟⠧⠁⠈⣐⠆⢄⡄⢰⡏⢊⠔⠁⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠤⠀⠘⡶⢠⠴
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠖⠈⠀⠉⠀⠀⠜⠂⠃⠀⡱⢘⣓⠀⠀⠀⣛⡆⣵⠘⢤⠄⡀⢀⣀⠀⠁⠦⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠒
⠀⠀⠈⠀⠀⢀⠐⠀⠐⠻⠀⠀⢀⠀⠁⠀⠙⠃⠀⠁⠀⠉⠀⢂⠩⠃⠉⠁⠰⠶⠀⡀⠀⠁⠀⠸⠆⠀⠀⠀⢀⠀⠀⠀⢨⡀⡰
⠀⠀⠀⠂⠰⠈⢍⣲⣄⡀⠀⠁⡀⠁⠀⢀⠠⠐⠀⠀⠀⠆⠀⠈⠗⠀⠀⠈⠀⠀⠀⡁⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠚⠒⠪⡍⠃⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠄⠀⢢⠀⠀⠀⠀⠀⠀⢀⢲⠈⠀⠀⣀⠈⠀⡀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢀⠀⠢⢀⡄⠂⠀⠀⠀⠀⠀⠀⠀⣂⣀⣐⠊⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⢀⡀⠀⠀⠀⣈⣀⠁⠀⠀⠀⠠⠰⠸⠄⠘⠿⢂⡆⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⠐⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⢘⡃⠐⠃⢀⡆⠀⢈⡤⠆⡀⠤⠄⠐⠂⠀⠉⠉⠀⠀⠀⠀⠀⠄⠀⢠⠶⠀⠀⠁⠀⠀⠠⠂⡂
⠀⡠⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠘⠂⠈⡠⠄⠌⠓⠂⠀⡀⠀⠀⠀⢃⣂⠀⠀⠠⠀⠀⠀⠀⠐⠡⠀⠀⢊⠀⡀⠀⠀⠁⣀
⠀⣁⠠⠴⠖⠢⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠈⠀⠐⠀⠀⠈⡝⠁⢠⡄⠀⣴⠀⠀⡀⠀⠀⠀⢹⠀⠄⠀⠀⠈⣁
⠀⠈⠉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠀⠀⠠⡄⠀⠀⠄⠂⠀⠀⢀⠀⠀⠂⠀⠈⠃⠐⠈⠀⠀⠳⠀⠀⠀⠠⢀⠂⠺⠆⠀⠉
⠀⡐⠃⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⢈⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠴⠰⠀⠀⠀⠐⠁⠀⠀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⢤⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠌⠘⢷⡄⠠⠄⠔⢠⡄⠁⠀⢸⠇⠀⢶⠀⠀⠀⠶⠿⠀⠈⠁⠀⠉⢻
⠀⡀⠀⠀⠀⠀⠀⣸⣧⠀⠠⠾⠗⠒⠂⠠⠘⠀⠀⠀⠀⠀⠈⠈⠃⣀⣤⠀⠀⠨⠅⠀⠀⠐⠁⠀⠈⠉⡠⠁⠀⢠⡰⠀⠀⠀⠀⠘
⠀⠇⠐⠀⠀⠀⠀⣤⢸⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠀⠠⢼⠗⠂⠀⢀⠐⠀⠀⠀⠁⠀⢺
⠀⠛⠂⠔⠉⠃⠀⠆⢠⠀⠈⠀⠠⠄⠄⠀⠀⠀⠊⠸⠇⠀⠀⠁⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠶⠾⠃⠀⠀⠈⠀⠀⠀⢰⠶⠶⠛
⠀⠀⢀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠷⠛⠛⠛⡁⢻⡤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢶⠶⡶⠂⠀⣀⠀⠀⠀⠐⠀⢻⡄⠀⠠
⠀⠀⠀⠐⢈⡀⠀⡀⠀⠀⠀⠀⢀⠶⡀⠀⠀⠀⡘⠈⠀⠁⠀⠡⡞⠰⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠿⠛⠀⠀⠘⠃⠀⠀⢠⠀⠀⢸⡧
⠀⠶⠶⠶⠶⠃⠀⠀⠲⠶⠶⠶⠂⠀⠈⠒⠒⠚⠁⠐⠂⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠰⠛⠻⠒⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠄⣀⣀⢀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⡄⠰⠋⠟⠿⠷⠿⠟⠻⠖⠀⡤⠀⠀⠀⠀⠀⠐⠀⠀⠔⠀⠀⠀⠀⠀⡴
⠀⣠⠴⠶⡆⠀⠖⠈⠐⠲⢄⠰⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⣶⠀⠄⠠⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⡄⢀⡀
⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⠘⠚⠉⠀⠀⠐⠈⠿⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠰⠢⠖⠂⠖⠦⠀⠂⠭
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣓⣀⡈⠀⠀⠀⠀⠀⠀⠀⡀⠵⠓
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠁⠉⠀⠀⡀⠀⢀⠀⠀⠘⡀⠀⡀⢨⣄⡄⠀⠄
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠀⣀⠁⠄⢠⠁⠀⠀⠁⠂⠁⣤⠀⠀⠂⠐
⠀⠀⠀⢙⡀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠘⣿⣶⣙⣷⣴⣖⠒⡀⠀⠀⠀⠘⡄⠄⠀⠀⠀⠀⠀⢀⣄⣠⣄⡀⠀⠀⠀⠀⠁⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠁
⠀⠀⠀⠒⠘⢋⠠⣀⢀⠙⠏⠁⠀⠀⠀⠐⠐⠀⠀⠀⡀⠸⣿⡿⠾⠳⠿⢹⡿⠒⠀⠀⠀⠀⣰⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⡁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⡏⠀⠀⠀⠀⠀⠀⠤⠄⢀⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⡆⢀⢀⠀⢀⡠⠂⠀⠈⠀⠀⠀⠈⠀⠈⣸⠣⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⣁⡠⠀⠈⠀⠠⠀⠀⠀⠂⢀⣀⣤⡞⠁⠀⠀⠀⢠⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠛⠦⠠⣦⣤⣤⠟⠻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠠⣄⡀⠀⠀⠀⢀⣀⡀⢀⠀⢀⠀⠒⣀⢄⣀⣠⣐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠹⡟⠧⠿⠶⠟
⠀⠀⠀⠉⠲⠶⠖⠀⠀⠉⠉⠉⠁⠀⠀⠋⠀⠋⠙⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢦⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠓⠋⠉⠀⠀⠉⠉⠋⠁⠈⠛⠓⠀⠰⢤⣀

⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣼⣷⣼⣼⣷⣷⣼⣼⣭⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣷⣶⣿⣿⣿⣶⣶⣶⣿⣷⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⣠⣤⠿⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⢷⡀⣈⣠⣼⠀⣧⣀⣀⡀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡢⣀⠀⠀⣀⡀⣸⣿⣿⣿⠿⠤⠋⠉⠉⠙⢷⡀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡳⣿⠟⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⡋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡏⡄⠀⠀⠀⠀⠀⠀⠒⣲⡦⢤⣄⡀⠉⢻⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡀⠉⠛⢿⣿⡦⠤⢐⡒⠦⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣷⣶⡏⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣰⣀⡞⠀⠀⠘⠄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠹⡙⢧⠀⡀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣾⡀⠀⠀⢹⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢸⣆⠀⣸⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⠀⠀⠀⣼⢋⡴⠋⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⡶⢤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⣋⣴⣿⣿⣦⣀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠜⣰⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠊⠓⠀⠉⠉⠁⠉⠻⢿⣿⣿⣶⠤⠤⠤⠶⠛⠣⡙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠐⠋⠉⠉⠠⠙⠢⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡋⠀⠀⠀⠀⠓⠀⠀⠀⠐⠁⢠⠉⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⢀⡀⢀⣀⡀⠀⠁⠀⢠⠈⠀⡀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⠋⠀⠌⠀⠁⠈⠉⠀⠀⠀⠉⠉⠚⠂⠀⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠢⣄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⣠⠤⣴⠋
⠀⠀⣸⡿⠿⠋⠀⠙⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠁⠒⣄⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⣀⡤⠤⠤⠶⠇⠀⠀⠀⠀⠹
⠀⠘⠁⠀⠀⠀⢄⠀⠉⠲⠶⢄⣠⠤⠴⠲⠞⠁⠡⠆⠄⠀⠀⠀⠀⠁⠀⡁⠀⠀⠀⠀⠀⠀⠹⠋⠀⠈⠠⠠⠀⠠⠀⠀⠀⠀⠄

⠀⠀⠉⠻⣷⣄⢻⣿⠀⢀⣀⣈⣉⣀⣀⣄⡀⠘⣷⣄⡀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠘⣿⣷⠀⠘⠿⠁⢰⣿⡇⢸⡇
⡄⣄⣠⣽⠿⠃⣸⡿⠀⠛⠙⠉⠉⠉⣙⣻⣿⡆⢻⣿⣿⣦⡀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠿⣿⣦⣤⣤⣿⡟⣠⢼⠃
⣇⠙⢋⢸⠂⠈⢿⣿⣦⣄⡀⠙⠻⢭⣭⣥⣀⣀⠀⢻⣿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠛⠁⣰⢃⣸⣶
⡽⠞⠛⢹⣦⡄⠀⠙⠿⣿⣧⠀⣀⣀⣀⣉⡙⠻⣿⠶⣤⣸⠟⠁⠀⠀⣠⣿⠀⠀⠠⢤⣤⣤⣤⣤⡴⠖⡿⣿⢹⡟⡛
⡄⢰⣄⣸⣿⣧⠀⠀⠤⠾⠋⠀⠀⠀⠈⠙⢻⣦⣿⡹⣎⢻⣷⡄⠀⢸⠟⠁⠰⢸⡇⠀⣀⣀⣈⣄⣤⢎⣴⠏⣀⢭⣭
⠀⠘⠛⠿⢿⣿⣀⣴⡾⡋⠀⠀⠀⢀⡀⠀⠀⢹⣿⠳⠈⡇⣯⢻⣦⣀⠀⠀⣰⣿⠇⢸⣿⣏⠉⠀⢀⣼⣿⣞⠁⠀⢠
⠀⢠⣀⠀⠘⠿⠛⠋⠀⠀⠀⢀⣴⠋⠀⠀⠀⡀⣿⡇⢠⡇⢸⡗⠉⠛⠛⢛⣿⠏⠀⠀⣿⡍⠻⠿⠟⣫⡾⠋⣤⠀⢸
⠀⢻⣿⣧⣷⡇⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⣀⣿⣿⠌⣧⠀⣷⠰⠖⣰⢛⣵⡇⠀⠀⠨⣏⠀⢤⡾⠉⠀⢠⡟⠀⣾
⡀⣸⡟⣿⣿⠇⠀⠀⠀⠀⠘⠀⠀⢀⣴⣿⣟⠉⠁⠀⠀⢿⡆⢻⡀⣸⠣⢟⣭⠹⣦⡶⠀⢻⡟⡟⢿⣷⣤⣟⡄⢸⣿
⣧⣿⠇⣿⣿⣶⣶⣶⡶⠶⣶⣦⡀⠈⠿⠛⢿⣶⣄⠀⠀⠀⠛⢮⢳⡟⢠⣾⡏⠀⢀⠀⠀⢸⡿⠄⠀⠛⢈⡿⠁⢻⠋
⣿⡿⣀⡀⠀⠁⠀⠀⢀⣤⣼⣿⣿⠶⠤⠾⠗⠻⣿⡄⠀⠀⠀⢸⠀⠀⢸⡌⠁⣴⡿⠆⢀⡿⣱⡇⠀⢈⡞⠁⢀⠈⣠
⣯⠞⣽⠀⠀⠀⠀⣤⣾⡿⠋⣀⣴⣤⡀⠀⠀⠀⠙⣿⡀⠀⢀⠈⣄⠀⠈⠳⣾⣯⣤⡶⠟⡵⠏⣴⢁⡿⢁⣶⣏⠀⣿
⠃⢰⡟⠀⠀⠀⣾⡿⠋⠱⢟⣋⣥⡶⠿⣶⠆⣤⣀⡈⠁⠀⢸⡇⢹⣷⣤⣀⠀⠀⠀⢀⣤⣤⣼⢧⡟⢠⣿⠇⡇⠀⢿
⠀⣾⡇⠀⢀⣾⡿⣣⣴⠾⠛⠉⠁⠘⠛⠉⠀⠘⢿⣿⠀⠀⢸⡇⣿⡇⢿⣍⣻⣶⣶⣤⡤⠾⢋⣾⢳⣿⠇⠀⣷⠀⠈
⣼⣿⠀⠀⢸⣿⡃⠁⢀⡀⢀⣈⢤⣤⣤⣤⣴⣄⠈⢻⣧⠀⠘⣷⣸⣇⠀⠀⣀⡀⠈⠉⠁⢠⣿⢃⡼⠋⠈⠀⢹⡄
⠿⠃⠀⠸⣾⣿⠃⠀⣾⢠⡟⣿⡆⢀⣤⣤⣭⣭⣤⡽⣿⡆⠀⠈⢹⣿⣦⠀⠉⠙⣋⡟⠛⣫⡵⠛⠁⠀⠀⠀⠀⠃⢴
⣠⡆⢠⡞⣼⠏⠀⢰⣷⣿⣇⣹⡏⠀⠈⠀⠀⠀⠙⠃⣻⡷⠰⢿⣿⣿⣿⡇⠀⣼⣟⠚⡛⠉⠀⢀⣠⣴⠶⢿⣣⣤⡼
⣿⠀⣸⢷⣿⠀⠀⡼⢿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⣰⣾⠇⠀⠀⠈⠉⠉⠀⢀⣙⣛⠉⠁⢠⣾⣟⣍⣠⡄⠈⠉⢀⡴
⡟⢀⡿⡏⣿⠀⠀⢷⠈⢱⣄⠀⠀⠀⠀⠀⠠⢶⡾⠟⠁⠀⠀⠀⠀⠀⣰⠞⣫⡽⣻⠅⠀⠸⣿⣿⣿⠟⠀⢠⡾⠉
⠁⣸⢸⡇⣿⠀⠀⠈⠀⢸⣿⣦⠀⠀⠀⠀⢀⡀⠀⢠⣤⣤⣄⠀⣤⣚⣿⠿⣫⠿⣷⣄⠀⠈⣿⡟⠀⠀⣰⢟⣿⢇⣼
⣴⡎⢸⣇⣸⣆⠀⠀⠀⠈⠻⣿⣷⣶⣶⣿⣿⡟⣢⣴⡤⣤⣬⣍⠙⢉⢀⡼⠃⠀⠘⣿⣷⡄⠉⠁⢀⣴⣫⣾⠃⢸⣿
⢿⣷⣤⣭⢙⢿⣷⡀⠀⠀⠀⢈⣥⣤⣴⠞⠋⢾⠛⠻⠿⠶⠎⠻⠷⠟⣡⣶⠶⠛⠿⣿⣯⠁⠀⢠⣿⣿⠟⣱⡇⢾⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠐⠦⠤⣀⠶⠀⠀⢠⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠇⢀⣤⠑⠒⠒⣯⣤⣄⠘⠀⠠⢄⡄⠀⠀⢄⢠⣵⣖⢟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰⠖⡀⠖⠈⢩⡤⠴⠃⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠣⡄⠉⠁⠀⣵⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢓⡎⠍⢸⠇⠀⠀⣿⣁⡀⢄⡀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⢀⠘⣿⡅⠠⠄⠿⣀
⠀⠀⠀⠀⠀⠀⠀⣶⠈⠀⢸⡎⠠⡀⣷⣄⢀⡀⢡⡝⠋⡈⠑⢶⣴⠟⢠⣥⣤⣶⡶⢛⣛⠛⠿⠳⣶⡃⢀⠀⠡⡈⢻⡎⢄⣄
⠀⠀⠀⠀⠀⢠⣎⢉⣷⡞⠈⠷⣤⣾⠯⠉⠀⣩⣀⣽⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⣻⡤⣿⢦⣀⠹⡏⢠⠤⠙⢳
⠀⠀⠀⠀⠀⢘⡥⣴⢦⡞⡁⠀⠛⡛⢤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣔⣤⡴⣾⡥⢆⠐⣯⣙⡆
⠀⠀⠀⠀⠀⠚⡀⢸⡈⠳⣤⣀⠾⣒⣿⣿⣿⣿⣿⣿⣿⢿⣿⡼⠟⡏⠺⠀⢿⣿⢿⢿⣻⣿⣿⡻⣾⣿⣿⣿⣿⣾⣿⣋⣵⣯⡝
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡑⠀⠀⠀⠀⠀⠹⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠉⠙⠋⠙⠛⠉⠉⠉⣷⠄⠀⠀⠀⠀⠀⣸⠋⠙⠛⠁⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠸⠗⠰⠀⠀⠦⠖⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣶⣁⣷⣶⣾⣷⣶⣶⣷⣶⣶⣾⣥⣤⡨⣤⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⡿⠟⡟⠀⠟⠿⣿⠯⣽⠷⠶⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⣿⣶⠀⣾⡄⡀⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣾⡿⣿⣾⡏⣿⡾⢿⡄⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣐⣋⣾⣟⠁⢿⢿⡇⢻⣯⠈⢧⣰⠌⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢮⣼⡟⣿⡿⣤⣤⡬⠛⣖⡲⠁⠏⠱⢒⣿⡷⢿⡿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣷⢦⣾⡉⢬⠁⠮⡀⣙⡡⣛⠛⣋⡝⠱⠋⠾⠋⠄⠲⠒⠋⠟⠽⠿⣿⣇⣢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠁⠀⠀⠀⠐⠀⠈⠵⠋⠀⠌⠀⠀⠀⠰⠆⠀⠐⠀⠠⠀⠀⠰⠂⠀⠀⠈⠐⠛⠛⠂