Frisbee Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠴⠶⣶⣶⣶⡤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣖⠟⠭⠁⠂⠈⠁⠉⠉⠉⠉⠉⠉⠛⠻⢿⣿⣛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⣛⠕⠊⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⡀⠀⠀⠀⠀⠀⠈⠻⣷⣌⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀⠀⠀⠀⠀⠀⢹⣿⡄⠈⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢁⣴⠏⠀⠀⠀⠀⣠⠂⠀⠀⣴⣿⡿⠂⠀⠀⢀⠀⢀⡇⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⡾⡆
⠀⠀⠀⠀⠀⠀⢀⢞⣵⢁⣾⡇⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⣀⡤⠖⠁⡠⠊⠀⠀⠀⢀⠀⠀⣼⠟⠀⢀⠂⡇⣴
⠀⠀⠀⠀⠀⢀⢏⣾⡇⢸⣿⡆⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠈⠀⠀⠀⣠⠔⠁⢀⡾⠋⠀⢀⠌⡰⠀⡍
⠀⠀⠀⠀⠀⡜⢸⣿⡧⠘⢿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⣀⡴⠋⠀⠀⡠⢃⡜⠀⣼⠁
⠀⠀⠀⠀⠀⣧⠘⠉⠀⠀⠀⠙⠿⢿⣶⣦⣤⣤⣤⣤⣤⣤⣤⡤⠶⠞⠋⠉⠀⣀⠴⠚⠁⠀⢀⠔⢋⡰⠋⢀⡾⠃
⠀⠀⠀⠀⠀⢻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠄⠊⣁⠔⠉⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠈⢎⠳⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⢁⡠⠔⠊⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠢⡈⠑⠫⢄⡐⠂⠀⠤⠤⠤⠤⠄⠀⠒⠒⠀⠈⣁⠠⠄⠒⠈⠁⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠲⠶⠬⠁⠀⠒⠒⠂⠀⠉⠉⠁⠁⠀⠀⣠⣤⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⠄⣀⣀⣀⣀⣀⡀⠠⠤⠴⠚⠛⠉





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠒⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⡾⠿⠋⠁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠉⠛⠻⠿⠿⢷⣶⣶⣶⣶⣾⠿⠿⠿⠟⠛⠋⠉⢁⣀⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠙⠿⣿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣿⠿⠟⠛⠉
⠀⣤⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠃⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⢰⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠛⠉⠀⠀⠀⣀⣤⣾⣿⡷
⣿⡇⠘⢿⣦⣄⣀⣀⣀⣤⣤⣴⡶⠿⠟⠛⠉⠀⠀⢀⣠⣴⣾⣿⡿⠟⠋⠁
⢻⣿⣄⡀⠈⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣤⣴⣶⣿⡿⠿⠛⠋⠁
⠀⠉⠛⠿⠿⣷⣶⣶⣶⣾⣿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⢋⣽⠥⠴⠶⠒⠲⠶⠦⢤⣀⡀
⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛
⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⢤⡞⠃
⠀⢼⠁⠀⠀⠀⠀⠀⢀⣸⣏⡉⠉⠉⠀⠀⢒⣒⡉⠢⡀
⢀⡨⠦⠀⢀⡠⠔⠂⠁⢸⠋⠁⠲⢄⢀⠔⠉⠀⠈⢦⠈⠢⡀
⠟⡶⠀⠀⠀⠑⣄⠀⠀⢸⠀⠀⠀⠀⢻⡤⣤⠀⠀⡸⠀⠀⡹⠒⢄
⠀⡇⠀⠀⠀⠈⢧⡀⠀⠈⢇⠀⠀⠀⠶⣏⣉⡠⠔⠁⠀⠐⠁⢀⣜⠀⠀⠀⠂⠄⡀
⠀⠻⢇⠀⠀⠀⠀⠱⡀⠀⠈⠓⠒⠒⠲⠇⠀⠀⠀⠀⠀⠀⠈⠁⠈⡆⠀⠀⠐⠢⢌⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⠀⡤⠒⠒⠒⠲⢆⡀⠀⠀⣀⡀
⠀⠀⠈⠑⡤⠖⠒⠲⠧⡄⠀⢔⢢⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣤⠀⢠⠦⡄⠀⠀⠀⠐⠒⠊⠉⠉⠁⠘⠀⠁⠀⠉⠚⠷⢦⡤⠄⣈⠉⠒⠒⠈⠛⠒⢄⡀
⠀⠀⠀⠀⢇⡀⠉⠉⣀⣠⣤⣀⡉⠚⠤⠃⠀⠀⠀⠀⣀⣠⠴⠋⠀⢸⠛⠃⠚⠃⠱⡆⢄⠀⠀⠀⠀⠀⠐⠒⠀⠀⠒⠒⠒⠒⠀⠠⠄⠉⠐⠒⠋⠠⠤⠀⣠⣀⣈
⠀⠀⠀⠀⠀⠉⠉⠉⢩⡅⠀⠀⢉⠉⠙⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⢸⣲⠒⠊⢲⠘⣬⠏
⠀⠀⠀⠀⠀⠀⡀⡠⠊⠱⣄⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⠂⠀⠀⠉⠁
⠀⠀⠀⠀⢸⠇⡀⠁⠀⠾⡄⠉⠁⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠻⣯⡺⢵⣦⡀⡀
⠀⠀⠀⠀⠈⠫⠤⠖⠉⠉⠁⠀⠀⠘⠢⡤⠤⠤⠴⠶⡖⢏⠁⠀⠀⠀⠀⠀⠈⡷⠧⢬⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠸⣬⣷⡔⠀⠀⠀⢀⡰⠓⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⢄⣈⣀⣀⣨⣭⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠮⠹⠿⡾⠕⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⢴⠶⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣚⣉⡭⠤⠤⠬⣿
⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠠⣤⣀⣍⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣋⡥⠖⠋⣉⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠹⡄⠳⡀⠀⣝⡀⠘⢄⡈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⡡⠚⠁⠀⠀⣀⡏⣗⣶⢯⣤
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠢⣄⠈⠲⠏⠁⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠛⠋⠉⠁⣸⡸⡜⡜⡎⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⢗⡯⢖⣒⣠⣐⠃⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠛⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠆


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢁⣀⠤⢄⡀⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢖⣒⣒⣛⣛⣒⣒⣒⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⠋⣀⡔⢀⡀⠢⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣮⠖⠋⠉⠁⠀⠀⠀⠀⠀⠈⠉⠑⠺⡆⠀⠀⠀⠀⠀⠀⣿⠀⢀⠈⠃⢀⢠⠋⢀⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⠀⠀⠀⠀⣀⣀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠢⢈⣀⣈⠥⠊⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣀⣀⣀⣠⡶⠛




⣿⣿⠛⢿⠛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⠤⠤⠤⠤⣀⣀
⠀⠀⠀⠀⢀⠠⠐⢚⠉⠀⠀⠐⠂⠒⠀⠩⠉⠉⠉⠩⠋⠗⠶⠦⣄⠀⠀⡀⡄⢀
⠀⠀⣀⠀⠂⠀⠀⣀⣀⠤⠤⠄⠐⠒⠒⠂⠉⠋⡻⠛⠁⠓⠳⠒⠒⣷⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠾⣁⢴⠖⠋⠉⠑⠤⠀⠄⠠⠤⠀⠀⠀⠀⠈⠀⠀⠠⠐⠀⣀⡴⠋⢀⡀⠀⣀⠀⠀⠠
⠁⠐⢦⣌⣙⢓⢒⠒⡒⡒⢒⠊⠀⣀⣈⣁⣠⣤⠤⠤⠶⠚⠉⠑⠘⠉⠁⠀⠁
⠀⠀⠀⠉⠫⠍⠉⠉⠉⠉⠉⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⣀⠀⠀⠈⠀⠀⣀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄
⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀

⢀⣴⠒⠒⠒⠒⠒⠲⡄⠖⠛⠉⠉⠙⠓⢦⡀⠀⠔⡏⠉⠉⡇⠀⢀⡤⠖⠚⠉⠙⠒⠂⠀⢀⠴⠒⠒⠚⠛⠓⠲⣄⠀⣠⠖⠒⠒⠶⠶⢦⢠⡖⠚⠉⠉⢛⡀
⡎⢸⠀⠀⠀⠀⠀⢀⡇⡃⠀⠀⡤⣄⠀⠀⠙⡤⠎⡇⠀⠀⡇⡴⣿⠁⠀⢀⡴⠲⢤⡔⠀⡠⢺⠀⠀⢀⣀⡀⠀⠈⣆⠑⡇⠀⠀⠀⠀⢸⡆⡇⠀⠀⠀⢸⡄
⡇⢹⠀⠀⢰⣛⣻⠛⡀⡇⠀⠀⣧⣘⡆⠀⠀⣽⢃⡇⠀⠀⣿⠀⡇⠀⠀⢏⠉⠉⠁⠀⠀⡖⣹⠀⠀⠘⢢⡷⠀⠀⣿⠈⡇⠀⠀⡖⠖⣞⣧⣯⣠⢤⡬⠟
⡇⢨⠀⠀⠸⣁⣀⠀⡅⡇⠀⠀⡇⣧⠃⠀⠀⡿⠁⡇⠀⠀⣿⠀⠻⡀⠀⠈⠓⠤⣄⠀⠀⡧⢼⠀⠀⠐⢚⣁⣠⣤⠿⠖⡗⠒⠙⣏⣉⡉⡅⣻⠀⣀⣓⢲⡄
⡇⢸⠆⠀⠀⠀⢸⠀⠆⡇⠀⠀⠗⠁⠀⠀⣼⢩⡁⡇⠀⠀⡏⠣⡀⠈⠳⢦⣀⠀⠀⣱⣤⡴⡿⠒⠚⠉⠉⠀⠠⣏⣀⣇⡇⠤⠤⠐⠒⡟⠟⣻⠀⠀⠀⠀⣇
⠓⢨⡀⠀⢠⢖⡞⠀⡂⡇⠀⠀⠀⠀⠰⢾⡁⠘⡅⡇⠀⠀⡇⠀⠈⣙⠦⣴⠾⣿⠉⠀⢣⣂⣭⠠⠄⢀⡒⠈⠉⠈⢳⡇⡇⠀⠀⡤⢴⠗⡋⣽⠀⣀⣶⡾⠃
⢚⢠⡇⠀⢸⠉⠀⠐⡁⡇⠀⠀⢀⣀⠀⠀⠙⣄⠖⡇⢀⠠⡗⠚⠉⠀⠀⠈⣇⡽⠀⠀⡿⡅⡇⠀⠀⠸⠌⡆⠀⠀⠈⡇⡇⠀⠀⡷⠊⠀⣧⣾⠊⢁⡧⠞⠁
⠘⢰⡇⠀⢸⠀⠀⠐⡁⡇⠀⠀⢿⠀⢳⠀⡀⣿⢚⡏⠀⠀⡇⢀⣴⠶⠒⠚⠋⠀⠀⣰⠃⣆⡧⠀⠀⠘⠚⠁⠀⡀⢰⡇⡇⠀⠀⣉⠿⡏⡇⣺⠴⠋⠑⠒⢳
⢛⢰⡇⠀⣸⡂⠀⠨⡆⣧⠀⠀⣸⡷⢻⡁⣀⣹⡄⡇⢀⣠⡇⡏⢰⣀⢀⣀⣀⡤⣾⠧⢚⡇⣇⣀⣀⣀⣀⣤⣮⢴⠟⡇⣇⣤⣊⣁⣀⣸⡟⢻⣀⣀⣀⣀⣸
⠸⠎⠉⠭⠋⠀⠀⠘⢥⣫⣭⡯⠋⠫⠌⠍⠽⠉⣶⣿⢩⠝⠁⠳⠡⠤⠤⣤⠔⠋⠁⠀⠀⠲⠴⢡⠬⠏⠴⠤⠒⠉⡠⠟⠥⠴⠥⣤⠞⠁⠳⠽⠽⠡⠭⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠶⠶⠶⠦⠤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠔⠁⠀⠀⡴⠁
⠀⠀⢀⡴⠋⠀⡀⡄⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⢙⠳⢦⣀⠀⠀⠀⠀⠈⠀⠠⠊⠀⠀⢀⠞
⠀⣰⠋⠘⠀⠌⡜⡀⡘⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠙⠳⣄⡀⠀⠀⠀⠁⠀⠀⢀⠏
⢰⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡎⠀⠀⠀⠀⡖⠒⠒⠦⣄⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⢀⠏
⣾⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⢄⡀⠀⠀⠈⠓⠒⠒⠋⠀⠀⠀⠀⡷⠀⢰⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠌
⢻⠀⡀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠉⠒⠤⣄⣀⡀⠀⠀⠀⢀⣀⡴⠃⣠⠎⠀⠀⢀⠀⠀⠀⠈⣧⠀⠈
⠘⣏⢳⡀⠀⠀⠀⢀⠀⠐⢕⠭⡢⣄⡀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠁⠘⠉⠁⠀⠀⣠⠊⠐⠈⠀⠀⣿
⠀⠹⣎⠱⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠙⢦⡉⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠙⢧⡌⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣻⠏
⠀⠀⠀⠀⠀⠀⠙⠳⢤⣈⠙⠛⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⣩⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣤⣀⣉⠉⠏⠛⠃⠀⠀⠀⠀⠒⠖⠛⢋⣉⣥⠴⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣒⣶⣶⣶⣶⣶⣶⣖⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠿⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡤⢶⣞⠥⣄⣈⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣀⠈⠘⠋⠘⠺⠛
⠀⠀⢀⠀⠀⠀⠠⠄⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄
⠀⡔⢠⠀⠋⠀⠀⠀⠀⠀⠀⠁⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⡀⠀⠀⠈⢢⠄⠈
⡄⡇⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠤⣀⠀⠀⠄⣌⣀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⡄
⠑⡘⣄⠀⠀⡀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠊⠀⠀⠢⣤⡷⠀⠀⠀⠀⢠⠎⠀⡀
⠀⠀⠈⠢⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⢀⣿⡯⠀⠀⠀⡴⢡
⠀⠀⠀⠀⠈⠢⣀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠐⠠⠄⠀⠃⠀⠀⠀⠑⠘⠛⠗⠀⠀⠠⠀⠸⠰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠⢙⠢⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠆⡂⠀⠀⡈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠭⡂⠤⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⢰⠀⠈⠢⠵⠆⠀⠀⠀⠠⠀⠦⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠡⢖⠂⢤⡤⠤⠤⣥⣤⣶⣿⣿⣶⣤⣀⠀⠀⠠⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⣿⣿⣿⣿⡉⠛⡿⠗⠐⠀⠀⠐⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⢓⠀⠚⡛⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠂⠀⠀⠀⠀⢠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠈⡐⢄⠀⠀⠒⠠⢀⡄⠀⡆
⠀⠀⢀⣠⣤⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⡈⠈⠁⠨⣾⣿⣶⠄⠀⠈⢷⡆⠐⠨
⠀⠀⠘⠻⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠁⠄⢀⣀⣿⡿⠿⠚⠀⠀⠘⠷⣄⣀⠈
⠀⠀⠀⠀⠻⢿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣗⣠⣀⢀⣀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡔⢆
⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⡇⣿⠇⠐⠒⠒⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠾⢿⣿⣿⣿⣿⣿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢻⣿⣿⣿⣿⣰⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠛⠈⠻⣷⣔⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣄⠀⠀⣤⠋⢀⣼⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠦⣄⠀⠀⠀⠀⣿⣿⣿⣿⡇⠈⠁⠐⠋⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣌⡂⢰⣤⣠⣿⣿⣿⣿⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣹⣿⣿⣿⣧⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣒⠈⠙⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⡿⣋⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠛⠛⠛⠛⠛⠋⢉⣼⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⢶⣄
⠀⠀⠀⠀⠀⠀⣾⣻⣭⣥⠴⠶⣦⣹⣦⣄
⠀⠀⠀⠀⠀⢰⡿⢃⡀⠠⠤⠶⠾⣿⠇⣹⡀
⠀⠀⠀⠀⠀⣸⠃⢏⣀⠀⠤⠤⣤⣾⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠶⠒⠒⠒⠒⠀⠀⣀⡤
⠀⠀⠀⠀⠀⣿⠀⠈⠁⠐⣦⣤⡤⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋⠁⠀⠀⠐⠦⣤⣤⣤⠶⠟⠉
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠈⠙⣧⣴⢟⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠀⠀⣷⠀⣶⠀⠀⠀⢸⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⣿⠀⠛⠶⠶⠶⢋⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⡴⢒⡦⠖⣻⠓⠆
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠙⠻⡻⣌⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣿⣤⣘⣵⣋⡉⠉
⠀⠀⠀⠀⠀⠀⢻⡀⢢⡀⠀⠀⠙⣦⠙⣧⡀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠛⢿⣟⢷⣄⠐⢶⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢷⡀⠀⠀⠈⠃⠈⢷⣄⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠹⣆⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢷⠀⠀⠀⠀⠀⠀⠙⢷⣄⣾⠃⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⣧⣄⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣸⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠉⠛⠦⣌⠙⠻⠷⢶⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⢠⡿⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⢸⠀⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⠸⣄⠀⣿⣿⢧⣀⣀⡀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⢸⡇⣸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢹⡎⠒⠀⢹⡄⠑⠚⠒⠊⠀⠀⠀⠀⠀⣿⣿⢯⠐⠦⣤⣤⣤⣴⠾⠋⠀⡠⣞⠄⠀⢸⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⣤⠾⠃⢹⡄⠀⠀⠀⠀⠀⠀⢄⠀⡼⡼⠁⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠛⠷⠶⢶⣤⡤⠤⠄⠀⠀⠸⠃⢰⡄⠀⠀⠀⠉⠢⣭⣥⣷⠄⠀⢀⣾⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣾⠋⠀⠙⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠙⠦⣤⣤⠤⠀⠈⠁⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠉⠛⠛⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⡀⣀⣠⣴⠾⠛⠛⠋⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠁⠀⠀⢠⠿⠟⠉⠉⠙⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⢠⡀⠀⣻⣶⡆⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀
⠀⠀⠀⠀⣤⣾⣧⡄⠈⠉⠁⠀⠀⠀⠀⠚⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠼⠁⠸⠧⠀⠀⠀⠀⠀⠐⠦⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⢀⣾⠿⠿⠿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠀⣠⡀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⡄⠠⡀⣤⣦⡀⠀⢾⡶⠀⠀⠀⠀⠀⠀⢀⠀⣾⡄⠀⠛⠀⣀⡩⣷⠀⠀⡇
⠀⠀⠀⠀⠠⠤⠀⢠⠍⠻⡿⠟⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⣻⠋⢻⡃⠀⠛⠿⢷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠊⠉⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠛⣡⡦⣖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣗⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⢀⡤⢠⣶⡐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢤⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣸⣿⡇⠈⣷⠀⠀⠀⠀⠀⠀⢀⣘⣙⣀⠀⠀⠀⠀⠀⠀⡰⢫⡴⠛⠛⠛⠲⣌⢣⡀
⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⢲⣿⡇⠀⠀⠀⠸⣧⠀⢻⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣉⣉⡁⠀⠀⠀⠀⠀⢰⢡⡏⠀⠸⣦⡀⠀⠸⡆⣷
⠀⠀⠀⠀⠈⠿⠛⠀⠀⠀⠀⠀⠚⠻⠇⠀⠀⠀⠀⠘⢦⣸⣿⣁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⢸⡘⣇⠀⠀⠙⣇⠀⣰⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠷⠀⠀⠀⠀⠀⠀⠳⣜⠳⢤⣤⣤⠶⣫⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠿⠛⠻⠷⠂⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⢿⣧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⢠⣄⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⣸⣿⠀⠀⠀⠀⢰⡏⠃⠀⠀⠀⠀⠀⠈⢱⡀⠀⠀⠀⠀⢀⣸⣿⣦⣤⣴⡶⠂
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠏⠀⠀⠀⠀⣿⠶⠴⠤⢤⣤⡄⠴⠤⠾⡇⠀⠈⠛⠿⢿⣯⢯⡷⣿⡋
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠻⣿⣿⠏⠀⠀⠀⠀⠀⠘⢄⣀⣀⠜⠈⢤⣀⣀⠜⠀⠀⠀⠀⠀⢠⣿⡿⠙⠿⣷⡄
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣿⣦⣴⣿⣷⣂⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⠀⣀⣀⣀⠀⠀⠀⠰⠛⣩⡿⠻⡛⢿⣯⡙⠓⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀
⠀⠀⠀⠀⢸⣿⢻⡏⢱⣿⠿⣷⡌⢹⣿⠀⠀⠀⠀⠀⣿⠁⠀⢘⠈⢿⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃
⠀⠀⠀⠀⢸⣿⣿⣧⣜⢿⣿⠿⣣⣼⣿⠀⠀⠀⠀⠀⠙⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠀⠙⠉⠉⠙⠀⠀⠀⠀⠀⠀⣠⣤⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣛⣋⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣶⡄⢿⠦⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢳⡀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠋⠀⠀⠀⢹⣷⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣤⣤⣄⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸⣧⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⣸⣿⣿⠆⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡏⢷⣄
⠀⠀⠀⠀⠀⠀⡐⠀⣴⡈⣿⣧⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⢿⣷⣤
⠀⠀⠀⠰⠀⠴⠶⠶⠿⠷⠿⠿⠷⠀⠲⠀⠀⠀⠀⠀⠀⣤⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠹⠿⠛⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡇⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢰⠋⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢱
⠀⢠⠒⢺⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡗⠒
⠀⢼⠀⠸⡇⠀⢸⠀⠀⠀⠀⠀⢀⣠⢤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢤⢄⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡶
⣤⢸⡀⠀⡇⠀⠸⣒⡒⢒⣒⣒⣇⢠⡠⠀⢗⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠂⡤⢠⡁⠀⠀⠀⢈⡇⠀⢸⡇⠀⡇
⠛⠀⡇⠀⡇⠀⠀⠁⠀⠀⠀⠀⠙⣆⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⣴⠋⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⡇
⠀⠒⡇⠀⡇⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⣀⡤⢤⣤⡄⠀⢀⢤⡖⠲⠤⣀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠘⡇⠀⠉
⠀⠀⠣⠤⡇⠀⠀⡇⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠘⠉⠀⠈⢑⠈⠉⠀⠀⠈⠳⣼⠃⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⠒
⠀⠀⠀⠀⠣⠄⠤⠃⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠀⠀⣀⠀⠎⣤⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠓⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠈⠀⠀⠀⡄⠘⠛⠀⡆⠉⠁⢀⠃⠀⠀⠈⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠂⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⠀⡠⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡀⠀⠀⠀⠑⠠⣀⡀⠀⠀⠀⡀⡀⠐⠀⠀⠀⠀⠀⡀⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⠀⠀⠀⠀⠀⠀⠖⠂⠀⠃⠠⠃⠀⠔⠀⠀⠀⠀⠀⠀⠼⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⣀⡉⠦⠀⠀⠀⠐⠤⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⣀⢀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⡤⡀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠑⠒⠒⠒⠉⣿⠀⢹⡏⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⠀⢸⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⢂⠀⢀⡹⠂⢎⡀⠈⡐⠉⠈⠲⡀

⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⠀⣤⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⠺⢿⣷⣿⣞⣋⡀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣯⡀⠀⠀⢀⣙⣿⣷⣿⣃⣀⠀⠀⣠⣤⣾⣿⣷⣿⠗
⠀⠀⡴⢛⡿⣿⣿⣿⡍⠉⠀⠀⠀⣸⣿⣿⣿⣷⠀⠀⠀⠀⠐⠿⢿⣿⣿⡿⠿⠃⠀⠀⠿⢻⣿⣿⣿⠟⠃⠀⠀⠈⣻⣿⣿⣿⣷
⠀⠀⠀⠈⢀⡟⠯⠃⠛⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⡟⠀⠀⠀⠀⠀⠀⠘⠿⠙⠛⠓⠀⠀⠀⠀⠘⠿⣿⠉⠉
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⢸⡏⣿⢹⡏⡇⠀⠀⠀⠀⣠⣤⣄⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣰⣿⡄
⠀⠀⢸⣟⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⢠⣿⣿⣿⡇⠀⠀⢀⣴⣶⣿⣿⣶⣤⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⡄⠀⢰⣿⣿⣿⡀
⠀⠀⢸⣯⣿⣽⣯⡇⠀⠀⠀⠸⣿⣿⣿⡄⢸⣿⣿⣿⠃⠀⠀⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣟⡇⠀⠀⠀⠀⢿⣿⣿⠃⢹⣿⣿⠏⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠆⣿⣿⡿⠀⠀⠀⠀⠀⠙⠿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠿⢿⣿⡿⠟⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⡤⠀⠠⢄⣀⡤⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⣴⣮⣽⣭⣭⣭⣭⣭⣭⣯⣦⡄⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⢃⠀⠀⠘⠙⡀⠀⢀⠀⠀⠀⠀⠀⢯⡆⠀⠀⠘⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠁⢹⠁⠉⠀⠀⠀⠀⠀⣤⣴⣶⣶⣦⣤⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠈⠙⠘⠉⠁⠀⠂⠀⠀⠀⠀⠀⣼⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢉⠛⣡⠇⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⡴⠐⠠⢄⣀⡠⠐⠒⣶⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣠⣀⣄⣄⡀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠘⠉⠂⢀⡠⠃
⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠇
⠀⠈⣿⡟⡿⡿⡄⠀⠀⠀⠀⠀⠀⠘⠻⠷⠶⠶⠶⠟⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⢹⣷⣳⣷⡟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣶⣧⡀⠀⣴⣶⠀⠀⠀⣠⣾⣿⣦⡀
⠀⠀⣸⠣⣿⣿⣷⠾⣆⠂⠀⠀⠀⠀⠀⠶⠶⠶⠶⠀⠀⠀⠀⠀⢿⣷⣦⣀⣀⣴⣾⣿⠀⠀⠀⣿⣾⣧⣼⣿⣿⠀⠀⠰⣿⣿⣿⣿⡇
⠀⠀⠛⠋⠉⢻⡄⠀⠘⣆⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢳⣿⣿⣷⣿⡽⠀⠀⠀⣿⠋⠉⢻⡇
⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠻⠻⠿⢿⠇⠀⠀⠀⢿⣶⣶⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠋⠈
⠀⠀⠀⠀⠈⠒⠐⠀⠂⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⠶⠖⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠈
⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⣹⠳⡀
⠀⠀⠀⠀⠀⢀⡞⠁⡟⠀⢠⠃⠀⡇
⠀⠀⠀⠀⠀⡼⠀⢸⠃⠀⡎⠀⠀⠃
⠀⠀⠀⠀⢰⠇⠀⡟⠀⢰⠃⢀⢰
⠀⠀⠀⠀⣸⠀⢰⡇⠀⡾⠀⣾⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⠤⣀
⠀⠘⠀⠠⡿⠀⣸⠀⢀⡇⢠⡿⠧⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡸⠀⢸
⠀⠀⠀⠀⡇⠀⡿⠀⢸⠁⢸⣿⠃⠐⠂⠀⠨⢍⠋⣰⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢠⡇⠀⣸⠑⣆
⠀⠀⠀⠀⡇⠀⡟⠀⢸⠀⢸⢋⠀⠀⠀⠀⠀⢐⠀⠀⠀⠉⠐⠚⠀⠬⢐⡂⠀⠄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠜⡤⠀⡼⠀⢠⡇⠀⡏
⠀⠀⠀⠀⡇⠀⡇⠀⣾⠀⠀⠆⠀⠀⠀⠀⠀⠸⡄⠀⠀⠤⣤⡉⣿⠆⠀⠀⠀⠁⠒⠇⡀⡐⠀⠄⠀⠀⡜⣼⠇⢰⠃⠀⡾⠀⢰⠃
⠀⠀⠀⠀⢃⠀⡇⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢄⡉⠈⠛⠑⠀⠈⠑⡄⠀⠀⢀⡴⠀⠀⠈⠑⠂⠨⣙⡟⢀⠏⠀⣸⠃⢀⡟
⠀⠀⠀⠀⠈⠉⢧⠀⢧⢠⠃⠀⠀⠀⠀⠀⠠⡀⠀⠀⠙⢄⠀⠀⠀⠀⠠⣼⡤⠔⠋⠀⠀⠀⠀⠀⢀⢱⡿⢀⡞⠀⢰⠏⠀⡼⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠙⢶⠢⢲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠞⠁⡜⠀⢠⠏⠀⡼⠁⠂⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠖⠉⠉⣽⣦⣄⣀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡼⠁⢠⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡈⠻⠿⣿⣿⠿⡇⠑⣄⠀⠀⡀⠈⠀⡎⠀⡜⠀⣠⠋⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡿⣿⣦⣤⣀⣀⣴⡇⠀⠈⡠⠊⠀⠀⠀⣇⠎⢀⡴⢇⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡈⠙⠻⠿⢻⠏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⠷⠶⠞⠁⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠁⠀⠀⠀⠀⠀⠁⠀⠐⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀

⠀⠀⠀⠀⣠⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⣴⣴⠀⠀⠀⠀⢠⣤⣄
⠀⠀⣠⣿⣿⣄⣄⣼⣿⣧⡄⠀⠀⠀⣰⠛⢻⣷⣶⣾⡇⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠿⣿⠁⠀⢸⡿⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣶⣄⣀⣀⣰⣶⠀⠀⠀⠀⡷⠶⠶⠶⠶⠶⡇⠀⠀⠀⠀⠀⠀⢠⣥⡄⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⣤⡄⠿⠏⢉⣯⡹⠿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⢀⣹⣏⣀⣀⣀⣀⣀⣀
⠀⠀⣿⡟⠛⠛⠻⣿⠅⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠈⢹⡏⠉⠉⠉⠉⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠘⢷⠂⠀⠀⢠⡾⠏⠀⠀⠀⠀⣀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣀⠄⢀⠤⣀⢰⣄
⠀⠀⣤⣾⣶⣶⣶⠾⢧⡀⠀⠀⠀⠈⣿⠀⠉⠉⠍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⢿⣯⣼⣿⣿⣄⣠⠇⠀⠀⠀⠸⠿⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⡇⠀⠀⠙⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠙⠋
⠀⠀⠀⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢠⣄⢀⣤⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⣤⣤⣤⣤⣿⣇⠀⠀⠀⠀⣿⣿⣤⣄⣾⣿⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠙⢻⠉⢹⣿⡍⠉⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣄⣅⣸⣿⠀⠀⠀⠀⠀⢸⠀⢸⣿⡇⠀⡇
⠀⠀⢶⣶⣶⡶⡶⣶⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣍⠀⠀⠀⠀⠀⠼⠄⠨⠿⠄⠤⠧

⠀⠀⠀⠀⠀⣀⣠⢀⣆⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⣰⣀⣀⣀⣀⣀⣶⡀
⠀⠀⠀⠀⠀⠙⠶⣾⣷⡶⠞⠁⠀⠀⠀⠀⠀⢰⣿⠻⠦⠄⣴⠂⠀⠀⠀⠀⠀⠠⠞⣿⢦⣠⢀⡿⠀⠀⠀⠀⠘⠐⣆⡶⣠⠆⠛
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣄⡀⠀⠀⠀⠀⠀⠀⢶⣭⣷⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣸⠟⢶⡀⣸⠇⠀⠀⠀⠀⠀⠀⢘⣿⡏
⠀⠀⠀⠀⠀⠀⢻⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢹⠶⠿⠻⣗⠀⠀⠀⠀⠀⠀⢠⣭⣥⣴⣾⣶⡿⠀⠀⠀⠀⠀⠀⠀⣼⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢉⡳⢄⠀⠀⠀⠀⠀⠀⠀⠐⢲⡂⢶⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣸⣃⣀⡽⠂⠀⠀⠀⠀⠀⠀⠀⠹⣶⣦⡄⠀⠀⠀⠀⠀⠀⢈⣭⣀⣠⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣥⡀
⠀⠀⠀⠀⠀⠀⢹⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠟⠂⠀⠀⠀⠀⠀⠀⠻⣿⣥⣄⠈⣻⡇⠀⠀⠀⠀⠀⣠⠿⣿⣿⢷⣄
⠀⠀⠀⠀⠀⣤⣬⣿⣏⣿⣤⣄⠀⠀⠀⠀⠀⠀⣾⠁⢻⡀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣷⡟⣷⣿⡇⠀⠀⠀⠀⠀⠘⣿⠿⢿⣿⠃
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⢠⡴⣿⣿⠦⡄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣷⣆⠀⠀⠀⠀⠀⠀⠠⡾⣿⢧⡀⢀⡾⠃⠀⠀⠀⠀⢶⠎⣷⣦⣤⣄
⠀⠀⠀⠀⠀⢰⠀⣿⣿⠀⡰⠀⠀⠀⠀⠀⠀⠀⠘⣼⣿⣮⡅⠀⠀⠀⠀⠀⠀⢹⡟⢳⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣮⡙⣷
⠀⠀⠀⠀⠀⠈⠢⡌⣿⠴⠁⠀⠀⠀⠀⠀⠠⠴⠚⠉⠀⠸⠁⠀⠀⠀⠀⠀⠀⢸⠃⠼⢤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠹⣄⡀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⡇⠀⠀⠀⠀⠀⠀⠰⡶⣻⠄⢀⣄⡀⠀⠀⠀⠀⠀⠀⠈⢉⣹⣷⡘⠟
⠀⠀⠀⠀⠀⠀⠸⢿⣟⢻⠆⠀⠀⠀⠀⠀⠀⠀⠸⡶⢛⡇⠀⠀⠀⠀⠀⠀⠀⠐⠿⣷⣾⡿⢻⡄⠀⠀⠀⠀⠠⣔⣛⡯⠽⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠒⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⣀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠰⠇⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠐⣬⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠘
⠀⠀⠀⠀⠀⣀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣉⠙⠣⡀⠀⠀⢂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣦⣀⣈⠀⢬⠉⠠⣠⡀
⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠻⣏⠏⠉⢳⡄⠀⠀⢸⡝⠆⠈⠂⠒⠆
⠈⠛⠡⢀⣀⣤⠀⠀⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⣀⢿⡆⠈⢳⣲⣾⡧⠀⠂⠀⣻⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠉⠀⠐⠂⠐⠉⠉⠁⠀⠀⠀⠀⡈⠚⠛⠻⠇⠀⠉⢿⡏⠀⠀⠀⢰⡋⠹⠀⠀⠀⠀⠀⠀⡲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⣼⣦⣤⡄⠀⠈⠁⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠈
⣷⡆⠀⢀⣠⡔⠀⠀⠀⠀⠀⠈⢦⡂⠰⣟⠻⣿⡿⠻⣿⠐⣶⣾⠀⠀⣇⠀⠘⠁⠀⠀⠀⣦⢠
⢤⣀⣠⡼⠇⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢁⡮⠁⠀⠈⠙⢿⡏⢿⣿⣷⠀⠀⢠⠀⠀⠀⣿⠀⠀⠈⠉
⠀⠉⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣿⢁⡿⢁⣀⣀⠀⠀⠀⠛⠆⠙⡿⠂⠀⠀⣧⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣍⠀⠀⣸⠛⢻⠿⣿⣿⣿⠿⣿⣿⣆⠀⠀⣄⡀⢠⠀⠸⡄⠀⠀⣻⠀⡠
⠴⢦⣤⡴⢾⢿⡟⠻⠮⠏⠁⠀⠀⣿⡀⠀⣻⠶⡄⠉⠚⣽⠇⠘⠻⣤⡏⢱⣿⠃⣤⢹⡄⣴⡿⠉⢀⡀
⠀⠉⠀⠀⠈⠀⡀⠀⠀⠀⠀⢀⣴⣯⣴⣶⣏⡀⢱⡀⠀⠙⡷⢦⡀⠘⢷⢸⣿⣧⢸⣆⣷⣿⠟⠂⠀⢳⡀
⠀⠀⠀⠤⣀⡀⢳⠀⠀⠀⠀⢸⡷⣾⣿⡿⣿⣷⣾⣷⡀⠀⢄⠀⠑⠠⣈⣼⡏⣸⡇⣸⣿⠟⠀⠀⣤⣈⠁
⠀⠀⠀⠀⣈⡳⢃⠀⠀⠀⠀⣿⢁⣸⣿⣿⣦⣼⢻⣿⣧⠀⣻⣆⠀⢀⢸⡏⡇⣿⣿⣿⠋⠀⠀⠀⣠⠟
⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⣶⡠⢴⣿⣿⣏⡾⢋⡟⣿⣿⣿⣿⣿⣷⣿⣾⣷⣧⣿⣿⠉⠀⠈⠁
⠀⠀⠄⠀⠘⠶⠀⠈⠁⠈⠻⢻⣷⣾⣽⡿⣷⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣴⣿⣿⠿⠟⠉⣉⣉⣁⣤⣽⣷⣶⣿⣿⣿⣿⣿⣏⠃⠘⣂⣀⣀⣀⣀⣀⣤⣤
⠀⠀⠀⢀⣀⣰⡟⠋⠕⣛⣯⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿
⣴⣶⣿⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⠯⣾⣯⣤⣶⣾⣿⣿⣿⣿
⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣴⣷⣶⣶⣦⣬⣵⣶⣤⣬⣤⣵⣤⣭⣙⣯⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣛⠿⠿⠿⠿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣶⣦⣴⣶⣶⣶⣶⣯⣿⣿⣿⣿⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⢶⣶⣶⣶⣶⣶⡦
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣬⣿⣦⣀⣄⠀⠀⠀⠀⠀⢀⣦⣴⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⠏⠀⠙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠰⣿⣿⡟⠋⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠛⠛⠉⠋⠀⠀⠀⠀⠀⠸⢿⣿⣿⡟⠛⡗⠀⠀⠀⠀⠀⠀⠳⠾⢻⣿⣧⠀⠀⠿⣿⣿⣿⣇
⠀⠀⣴⠛⠛⠻⡍⢻⡗⣰⠞⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠻⣶⠀⠈⢹⣿⣏
⠀⠀⣇⠀⠀⢀⡿⣾⠃⢿⡀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢸⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠻⠃⠀⠀⠉⠋
⠀⠀⠈⠛⠚⠋⠀⠉⠀⠈⠙⠚⠛⠁⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠛⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛


⠀⠀⠀⠘⢷⣄⣻⣇⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⣼⣤⠀⠀⠀⠀⠀⠀⠀⢻⣧⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⡆
⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣿⣯⣽⣽⣯⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⣿⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠠⣄⠿⣠⡀
⠀⠀⠀⠀⠀⣿⣀⣸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠉⢧⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⠿⣿⣆⠀⠀⠀⠀⠈⠳⣍⠻⣷⣤⡶⠷⣦⣄
⠀⠀⠀⣤⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠐⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠚⠻⠿⠿⢿⣿⠇⠀⠀⠙⠛⠂⠀⠀⠀⠀⠀⠈⠳⠾⠷⠶⠶⠶⢶⠶


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⣠⡀⠀⠀⠩⠟⡛⠍⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⢩⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣤⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⠀⡀⢸
⠀⠀⠳⣝⢳⣦⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢂⣿⣿⡀⠀⠀⠀⠀⠀⢰⣿⣷⣠⣾⣿⠟⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⢏⡸
⠀⠀⠀⠈⠳⣝⠻⣷⠾⠛⠻⠷⠆⠀⠀⠀⠀⢴⣬⣭⣭⣤⣭⣭⣥⣴⠀⠀⠀⠀⣻⣿⣎⣿⡿⠋⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠛⠻⠛⠛⠛⠛⠟⠃⠀⠀⠀⠴⠿⠿⢿⣿⣿⣿⣿⠇⠀⠀⠀⠈⠉⠻⠷⠿⠶⠶⠶⠿⠿⠿⠿⠷⠄⠀⠀⠀⠈⠻⠋⠀⠈⠉⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠻⢿⡿⠿⠟⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠠⠾⢛⣻⣦⣴⣿⠆⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣼⣧⣤⣤⣼⣿⣿⡎⠉⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣇
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⠷⠶⠤⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣠⣿⣿⢉⣛⣛⢁⣀⡄
⠀⠀⠀⠲⣤⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣟⣻⠿⣟⣛⡿⠿⠿⠿⠿⠿⢿⣟⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢀⣀⡤⠖⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢿⣛⣿⢩⣶⣫⣵⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢟⣫⣷⣾⣿⠿⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⣾⣿⣿⣯⣹⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⣫⣾⣿⣿⣿⣿⡋⠙⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠉⣛⠿⢷⣤⣄⣀
⠀⠀⠀⠀⠀⢀⣾⢟⣾⣷⣾⠟⢿⣾⠇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⢷⡄⠈⠉⠉⠛⠛⠋⠉
⠀⠀⠀⠀⢀⣾⢫⣯⣿⣿⣿⣶⣿⡿⠷⠐⡈⠀⠙⠻⣿⣿⣌⡻⠿⣿⣿⣯⣉⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⠆
⠀⠀⠀⠀⣾⢯⣷⣾⣿⣯⣼⣷⣿⣷⠀⡁⠁⠀⠀⠀⠙⢜⣿⣄⡀⠀⠀⠉⢉⠉⣘⠿⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢦⣄⡀
⠀⠀⠀⣸⡟⡾⢿⣷⣿⣿⣿⣧⣤⢿⡆⠀⠀⠀⠀⠀⠀⣾⠱⠸⢏⠄⠀⠀⠀⠀⠀⠀⠀⣀⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠉
⠀⠀⠀⣿⢻⣿⡾⠻⣿⣿⣿⣿⣿⡾⡁⠀⠀⠀⠄⠀⢰⣏⠁⠉⠀⠀⠀⠀⠀⣀⠀⠀⣠⣿⣷⣟⡿⣿⣿⣿⣿⣿⣎⠻⣿⡆
⠀⠀⢠⣿⣘⠉⣻⣿⣿⣋⣿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⡀⠀⠀⠚⠟⠃⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣆⠹⣿
⠀⠀⢸⣿⢾⣿⣿⣻⣿⣿⣿⠦⣿⣆⠀⠀⠀⠈⠂⠀⡀⢤⣿⣿⣿⣿⣶⠂⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⣿⣿⡆⡏
⠀⠀⠀⣿⢸⣿⡿⢿⣿⡿⣧⣀⣼⣿⣷⡀⠀⠀⠀⠈⠿⠎⣿⣿⣿⣿⣿⣦⣤⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣇⢈⢿⣿⠁
⠀⠀⠀⢿⡟⣿⣦⣼⢿⣿⡿⣼⣿⣿⡿⢿⠄⠀⠀⢴⠀⠀⠉⠁⠈⠉⠙⠛⠛⠶⢤⡀⠀⢿⡍⠛⠻⢿⣏⠻⣿⣿⢸⡎⢿
⠀⠀⠀⠘⣿⣻⣶⣿⣴⣿⡶⣿⣽⣟⡿⢛⡄⢀⣤⣿⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠙⠄⠘⠃⠀⠀⠀⠈⠀⠘⣿⡆⣿⢸
⠀⠀⠀⠀⠹⣷⢻⣻⣧⣼⣿⣿⣤⣿⡑⢿⡷⠟⠉⠀⠀⣠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⢰⡟
⠀⠀⠀⠀⠀⠹⣧⣻⣴⣿⣿⣿⣇⣨⠃⢀⡄⠀⠀⠀⢴⣿⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⣥⡟
⠀⠀⠀⠀⠀⠀⠙⢿⣝⢏⣩⡟⢿⠏⠀⣼⡇⠀⣰⡦⠀⠀⠀⣾⣿⡦⠀⠀⠀⣴⣶⡆⠀⠀⠀⣿⡀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣝⢿⡏⠀⠀⠈⠁⠀⠉⠀⣶⣶⡆⠈⠉⠁⣶⣾⣆⠈⠉⠀⣶⣶⡦⠈⠁⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠠⣤⡀⠙⠛⢁⣤⣦⡀⠹⠛⠁⣤⣦⡀⠙⠛⢁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⣀⡘⠇⢀⣀⠀⠻⠿⠋⠘⠄⠀⠿⣟⣣⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠷⣾⣶⣶⣶⣶⣶⠶⠿⠟⠛⠉⠁

⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣶⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇
⠀⠀⣿⡇⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⣿⡇⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢸⣿
⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⢸⣿
⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠰⠿⠿⠇⠀⠿⠿⠇⠀⠿⠿⠿⠿⠿⠿⠗⠀⢸⣿
⠀⣾⡇⠀⢀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠀⣿⡇⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⣿⡆
⠀⣿⡇⠀⠀⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠀⠀⣿⡇⠀⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⡀⠀⣿⡇
⠀⣿⡇⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⣿⡇⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢿⡇
⢰⣿⠀⠀⣶⣶⣶⣶⣶⡆⠀⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⣿⡇⠀⢰⣶⣶⣶⣶⣶⣶⠆⢰⣶⣶⠆⢰⣶⣶⡆⠀⢸⣷
⢸⣿⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⣿⡇⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⣿⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿⡇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣾⡇⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⣿
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠛⠛⢻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡟⠛⢻⣟⠛⠛⠛⠛
⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⣿⡇⠀⣼⡏
⠀⠀⣼⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣧⣾⣿⣥⣤⣤⣤⠄
⠀⠀⢩⣿⠟⠉⣿⡏⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣽⡟
⠀⠀⣾⡏⠀⠀⣿⡇⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇
⠀⠀⢻⣧⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇
⠀⠀⠀⠻⣷⣦⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷

⣀⣀⣀⣀⣀⣀⣀⣠⣾⣟⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣏⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠁⠈⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣤⣤⣶⠖⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠰⣤⣤⣴⣦⣤⣤⣴⣦⣦⣶⣿⣿⣿⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠈⠒⠒⠢⢄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣈⠀⣸⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠻⣏⠉⢳⡄⠀⠀⢿⡆⠀⠀⠐⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠃⡤⠤⠀⠀⢀⣤⡀⠀⠀⠀⠀⢀⣠⣻⠀⢘⣵⣿⠧⠘⠆⢸⣧⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣠⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⣠⠈⢉⠙⠀⠀⠸⡏⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⣤⢿⣴⣿⣿⡞⣀⣠⠀⠀⡀⠀⡿⠀⠀⠀⡀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿
⠛⠛⠛⠛⠋⠋⠉⠉⠙⠛⡋⠀⣠⠞⠃⠀⠀⠀⠀⠀⠉⢀⣾⠆⣙⠃⠈⠓⢼⣿⢶⣶⡇⠀⠀⠀⠀⠠⣿⠁⠀⠒⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣼⢇⣀⣀⠀⠀⠹⠆⠹⡿⠀⠀⢱⠀⠀⠙⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠿⠿⠿⠿⠿⣿⣿⠿⣿⡟⠀⠀⠀⠀⢀⣀⣠⣤⣆⠀⢀⡟⠛⡟⢿⢿⣿⢻⣿⣧⣀⠀⣆⡀⡀⠘⣆⠀⠈⣇⡀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠛⠛⠛⠛⠛⠛⠋⠉⢹⡷⢲⠶⠖⠛⠻⠟⠋⠉⠁⠈⢈⡧⠀⢸⠛⡆⠈⢫⣟⠀⠙⢶⡇⢹⣗⢰⡘⣆⣾⡏⠀⣄⠀⠀⠉⠙⠛⠀⠘⠛⠛⠛⠛
⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⠀⠀⠀⠀⠰⡀⠀⠀⠀⢠⣿⣾⣿⣿⣄⣸⡄⠀⠉⠙⢆⠈⢃⣸⠿⣾⢳⣿⡿⠁⠀⠈⠆⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠿⠿⠿⠿⠿⠟⠛⠛⠻⠟⠀⠀⠈⠐⣦⠃⠀⠀⠀⣼⠋⣿⣿⣍⢹⣿⣷⡄⠘⣆⠀⠀⢶⢿⢰⣷⣼⡟⠁⠀⠈⣳⠀⠘⠛⠛⠛⠛⠿⠿⠿⠿⠿
⣀⣀⠀⠀⢀⡀⣀⡀⢀⣀⡀⠀⠀⡉⠁⠁⠀⠀⣠⠁⣸⣿⡿⣹⠟⡾⣿⣷⣾⣿⣦⣶⣿⣿⣽⣿⡟⠀⠀⠀⠈⠁⠀⠀⠀⢀⣤⣤⣄⡀⢀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠰⠄⠀⠀⠀⠻⢷⣮⣿⣿⣷⣮⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⡏⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠀⠀⠀⠀⠀⠀⣠⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠋⠉⠉⠉⠛⠛⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⣀⣿⡿⣿⣿⣿⣿⡿⠿⠿⠿⣿⠛⣛⣻⣿⣿⣿⡿⠷⡀⠀⠀⠀⢀⣤⣠⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢠⡾⢟⣻⡿⢟⣋⣩⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣦⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡏⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠋
⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣤⣭⣯⣥⣤⣍⣭⣭⣭⣭⣩⣭⣙⣻⣏⣭⣷⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶
⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣮⣵⣶⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠿⢿⠿⠿⠿⠿⠿⠿⠿⣯⣭⣿⣿⣏⣭⣭⣭⣭⣩⣍⣉⣽⣿⣯⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⢰⠚⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢲
⠀⠀⠀⠀⠀⠀⠀⠈⣟⠙⣆⠀⠀⠀⢠⠴⠲⢤⡀⠀⠀⠀⠀⣰⠋⢹⠏⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⣆⠀⠀⣿⠞⠉⠉⡇⠀⢀⣠⠞⠁⢠⠏⠀⠀⠀⣴⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠈⠙⠲⢼⣦⡤⣾⡥⠞⠉⠀⣀⡴⠋⠀⠀⠀⣠⣿⢾⡽⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠈⢻⡅⠀⢰⡖⠋⠁⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢠⣖⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠈⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⢻⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠓⠒⠒⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⡗⠒⠛⠛⠉⢷⠀⠀⠀⠀⠀⠀⣉⠀⢠⠏⠉⠳⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠁⠀⠀⠀⣧⠀⠀⣠⠀⠈⣧⠀⠀⠀⠀⠀⠻⠀⠘⠦⣤⠼⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠏⠀⠀⠀⠀⡿⠀⠀⡿⡄⠀⠘⡆⠀⠀⣀⡀⣾⠀⣠⠖⠒⠶⣄⠀⡇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠇⠹⡄⠀⢹⡄⠠⠤⠅⣿⢰⡇⢰⣲⡆⢸⡆⡇⠨⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣼⠀⠀⠹⡄⠀⢷⠀⠖⠃⣿⠈⠳⣄⣉⣠⠞⠀⡇⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⠆⢀⡟⠀⣰⠃⠰⠶⠀⢳⠀⢸⡄⠀⠰⠿⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⠃⠀⠀⠀⠀⠘⡇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠠⣤⣼⣧⣴⣧⣤⣤⣤⠀⠀⠰⠿⠶⠿⠶⠦

⣿⣿⣿⣯⣭⢽⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⣿⣭⣿⡿⣓⣀⡀⠀⢀⡴⢋⣀⣀⣀⠀⠀⠀⢳⣀⠃⣠⡴⠒
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⠀⠉⠛⣦⣼⣟⡋⠉⠁⠀⠀⢀⣀⣈⣷⣾⣋⣀⣀
⣿⣿⣿⣿⣿⡿⢿⣿⣇⣠⡴⣶⣿⡟⢹⣆⢻⡄⠀⠠⠚⠉⢀⡼⠻⡅⠀⠈⠙⢇
⣿⣿⣿⣿⣿⣿⢿⣷⣾⣿⣿⣿⣿⣷⣾⣿⣶⣿⡀⠀⠀⣴⠟⠁⠀⢿⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣤⣤⣤⣼⣤⣀⣀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠙⢉⠏⠈⠉⠋⠁⠁
⣿⣿⣿⣿⣿⣿⣿⠟⠀⠉⠁⢀⠎⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⡰⠃
⣿⣿⣿⣿⣿⠿⢅⠀⣠⡾⠁⠀⠀⠀⣀⠴⠊
⣿⣿⣿⣿⣿⣶⣶⡿⠋⢠⣤⣶⣾⠇
⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠊
⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣷⣶⣾⣷⣿⣷⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⢐⣀⣤⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⢴⣾⣿⣿⠫⠏⡿⢫⢳⡖⣶⢶⠞⡛⢿⣿⣿⣤⠄⠀⢀⣤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢠⣾⠋⠀⢸⣇⠀⣼⠿⠿⠶⠶⠿⠦⠾⢬⣿⣬⣧⡤⠿⠟⠋⢁⠀⣴⡿⢁⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣿⡇⠀⠁⣾⡇⠀⠀⣀⣀⠀⠒⢀⣤⣤⡄⠀⠀⡀⠀⠐⠶⠤⣤⡼⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠈⣼⡿⠀⢠⣾⠋⣸⡇⢠⣿⠏⠠⢇⣶⠀⢀⣴⠟⣹⠆⢠⣻⡇⢀⣀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⠾⠋⠀⠀⣾⣿⠾⠛⠀⣼⣿⠀⢠⣿⢹⠀⣾⡟⠰⠋⢀⣾⣿⡾⠋⢠⣿⡇⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⠀⢀⡴⠒⣦⢹⣽⡄⠀⢠⡿⣿⣤⠟⠀⢿⣇⢻⣧⠀⣠⠞⣿⣿⠁⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⡾⠁⣰⣿⠀⠙⠿⠶⠟⠀⢠⣄⠀⠀⣀⠙⠉⠛⠛⠁⠀⢹⣿⠀⠀⣿⡏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣾⠟⠁⣶⣶⣶⣄⠀⠀⣿⣿⣆⠀⢿⣇⢀⣾⣧⣴⣶⣌⠁⠀⡀⠘⢷⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢹⣷⠈⢻⣷⢸⣿⠉⣿⡆⠈⣿⣾⡟⢹⣷⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⣿⡄⣼⡟⢸⣿⡶⢿⣿⡀⣼⡟⢀⠀⢿⣧⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢻⣿⠟⠀⠘⠛⢀⣤⠉⠘⠟⠀⢻⣧⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣤⣾⣿⠀⠀⠄⠀⠀⠈⠁⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠈⣿⣿⢿⣻⣿⣶⠶⠆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⣿⠿⠻⣾⣿⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠈⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢀⣤⢤⡖⣶⣦⡶⠦⠂⠀⠀⠀⠀⠀⠐⠦⢤⣤⣤⣀⣀⣀⡀⠂⠀⠀⠀⠀⣀⣀⣤⣄⣀⣤⣤⣠⡀⠀⣰⣏⣫⡀⠈⣡⣄⢠⣠⢀⣀⡂⠀⠀⠀⡀⢀⠄⠀⠀⠰
⡛⢙⣻⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢽⣷⣿⠖⢶⣤⠰⣿⣿⣾⣿⣯⣿⣿⣉⢻⠛⢛⣼⣿⣛⣿⣿⣟⢡⣮⡛⢿⠻⣿⣿⣻⣿⣾⡍⠁⠀⠀⢀
⡿⣿⡹⠿⢿⣟⢡⢦⡤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣿⠛⣛⣉⠼⣏⠉⣿⠏⠙⣹⣭⠿⣹⣆⣬⢙⣿⣟⣿⢭⣗⣾⣛⣶⣿⣟⡓⢟⡻⡿⠁⠀⠀⠀⠀⠈
⠶⠰⠦⠀⡎⠁⠀⠀⡀⠠⢈⡹⠷⠱⠖⠂⠀⠀⠀⠀⠀⠁⠁⠚⠃⠛⠐⠽⠿⠵⠦⠼⠿⠿⠿⣷⡏⣻⠻⣿⠼⠏⠀⢰⣿⠩⢭⣵⣿⣉⢿⠟⠀⠀⠂⠀⠀⠄⡀
⠀⠠⠖⠐⠂⠂⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢿⡐⠀⠀⡸⠦⠉⡷⠝⠓⠛⠣⠤⠄⠈⠀⠀⠀⠀⠘
⠁⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⢚⡀⠂
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠀⠤⠊⣗⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠂⠀⠄⠘⠿⠖⠀⡐⠀⠀⠌
⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠂⡐⠀⠄

⡠⠒⠲⡴⠒⢢⡔⠒⢦⠖⠒⣤⠒⠢⡴⠒⢦⡴⠒⢦⠖⠲⡤⠒⠲⡴⠒⢦⠔⠒⢦⠖⠲⡤⠒⠢⡴⠒⢦⠔⠒⢦⠖⠲⡤⠒⠲
⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠛⣴⠂⣤⣢⣠⣶⠐⡶⢠⠀⡆⢸⠃⢣⡖⢀⣔⡆⣤⣦⢐⠆⣠⣲⢠⣦
⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠈⠈⠈⠁⠘⠿⠃⠈⠁⠁⠁⠀⠉⠁⠈⠉⠉⠀⠉⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣹⠆⠀⠀⠀⣀⣀⡀⢀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠲⠠⠀⠰⠂⠀⠀⠀⣠
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠀⠀⠀⠀⠀⠀⠈
⡜⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠐⠒⠀⠀⠀⠙
⣹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠰
⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡜⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣲⠦⡟⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣱⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⢧⡀⠀⢀⣀⣀⣀⣀⢀⡀⢤⣤⣤⣤⡤⢄⣠⣤⡠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣎⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡼⠃⠀⠨⠤⠄⠠⠄⠤⠤⠄⠁⠀⠖⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡱⠄⠀⠀⠀⠀⠀⢠⣀⣀⠀⣀⠀⠀⠐⠂⢀⢀⣀⣀⢠⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤
⢿⡀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀
⡾⠀⢀⠀⠀⠀⠀⢠⠀⣤⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠀⠠⠀⠀⠀⠀⠁⢀⠀⠉
⡼⢃⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠻⠤
⢟⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣼⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠸⠿⡿⡁⠀⠀⠒⠀⠒⠀⠀⠀⠀⠈⠛
⢳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⢶⣂⠀⢀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡤
⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠉⡍⠉⠉⠉⠋⠙⠛⠛⣛⡿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡾⠁⠐⠂⠀⠀⠀⠐⠢⠀⢀⠀⠀⠀⢀⣇⣀⠀⢀⣀⣀⡀⠐⠈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣼⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⡄⠀⠀⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⢳⠄⠀⠖⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⢷⡀⠀⡀⠈⠀⠈⠀⠀⠀⡀⠈⠀⠁⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡾⠁⢀⡧⠀⠀⡀⠠⢀⡀⠀⠀⠀⠀⣀⠀⠀⢀⠀⢄⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡉⠀⢀⡀
⠘⠒⠚⠓⠒⠊⠓⠒⠊⠓⠂⠀⠰⠒⠛⠒⠒⠄⠄⠚⠓⠖⠄⠐⠛⠓⠒⠊⠓⠒⠊⠒⠒⠛⠲⠚⠓⠒⠚⠒⠒⠚⠳⠒⠂⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⣖⣶⣿⣭⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣫⣶⣿⣿⠫⡦⢤⡀⠀⠀⢩⡙⠛⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⢰⣿⣿⢾⠀⣶⡇⢸⣇⡔⡀⢸⠃⡄⣤⣨⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠀⠈⢿⣿⣾⣬⢸⡗⠉⢸⣃⣇⣼⣠⡿⢸⢿⡇⠈⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣿⠿⠛⠒⠛⠿⠄⣠⠤⣤⠤⠴⠆⠁⠀⠀⠁⠀⠀⠀⠀⠀⢀⡁⠀⠀⠹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⡁⣶⣿⢰⣴⢠⢤⢀⡴⡀⠀⠀⢺⡀⠃⡀⢹⡶⠶⠆⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡟⣻⣿⣿⣿⠻⣦⠈⠙⢿⡆⠀⠀⠉⡁⣿⢸⠀⢸⡉⢸⡋⠀⠀⣴⢫⠔⣞⠁⠀⠀⣀⣀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⣿⣿⠀⠹⣧⠀⠀⠁⢠⡏⡄⢢⢉⣠⠀⣀⠉⣠⡈⢀⢀⡘⠎⣁⠞⠀⢠⡞⢉⣠⣍⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠙⢿⣄⠀⢻⡆⠀⠀⢸⡇⡇⢸⢿⠁⣸⠟⢹⡇⡗⣸⡏⡇⠀⠈⢳⣄⡘⢧⣸⡄⢸⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠀⠘⣿⠀⠀⠀⠙⠒⠋⢈⡷⢬⡷⣌⠋⠙⠉⠀⠉⠀⠀⠀⠀⠙⠀⠉⠁⣸⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡄⠀⣿⡇⠈⢷⢀⡀⠀⡟⢰⢸⣇⡸⢦⣤⢀⢤⢀⡤⠀⡤⢤⠄⡤⡀⢠⠏⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⣿⡇⠐⠛⠋⠉⠀⠙⢈⢸⡏⣳⣾⠉⢹⠚⢸⡟⠀⣰⠋⣸⡗⣱⢏⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡄⠀⠻⣿⣷⠛⠃⠀⠀⠀⢀⣤⣶⠾⠿⣷⣭⡈⠀⠈⠉⠀⠉⣈⣉⣉⣠⡟⣡⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⣤⡈⠻⢷⣄⡀⠀⢠⣿⠋⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⣸⠏⠉⠈⠉⠻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠒⠬⣙⠒⠘⣿⣄⣀⡀⢀⣀⣠⡶⢦⣄⠈⠙⠻⠶⣦⣀⣀⣀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣴⣦⣤⠁⠐⢚⣿⠟⢻⡿⠛⠛⠛⠲⣬⡛⢦⣀⠀⠈⠉⠉⠉⠳⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠀⠐⠚⠉⠀⠀⣻⣄⣀⠀⣀⣀⠀⠙⠢⣍⠛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠉⠉⠉⠛⠉⠁⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⠀⡄⡀⡀⢀
⠀⠀⠀⠘⢲⢡⣤⣤⣤⣤⣮⣤⣴⠃⠀⠀⢀⡤⡄⡀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⡿⢏⣬⡆⣃⡃⡋⣚⢀
⠀⠀⠀⠘⠧⢨⣭⣭⠹⠋⣩⣭⡉⠀⠀⠀⠈⠳⣅⡄⣥⡥⠠⣄⡬⣼⠁⠀⠀⠀⠀⣯⢿⢼⠽⡵⣧⡧⢻⠄
⠀⠀⠀⢰⢱⢄⢠⠆⢲⠀⢿⣿⠇⠀⠀⠀⢙⣾⣭⡏⣉⣉⡀⣩⣍⠉⠀⠀⠀⠀⢋⣂⣃⣓⣛⣃⣛⣸⣚
⠀⠀⠀⢠⡞⠂⢰⣆⠐⣶⡆⢰⡖⠂⠀⠀⠙⡾⠢⣲⣠⢠⠄⠉⣬⡒⠀⠀⠀⠀⢪⣼⣼⣤⣦⣤⣵⣤⡧⠂
⠀⠀⠀⠈⠛⠃⠋⠛⠚⠃⠛⠚⠛⠃⠀⠀⠀⠁⠀⠉⠉⠉⠁⠈⠌⠉⠀⠀⠀⠀⠸⠿⠾⠧⠿⠤⠧⠼⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⢰⡏⡽⠀⣰⣽⣷⣧⣆⠀⠀⠀⢀⡀⣀⠀⠀⣀⣀⠙⠛⢿⢷⠀⠀⠀⢺⡙⢀⣋⢉⡩⢙⣰⡀⡀
⠀⠀⠀⡀⠹⣦⣰⠗⣴⣳⠇⣞⠂⠀⢰⣇⣟⡼⣧⢘⣟⡛⣢⣸⣇⠀⠀⠀⠀⢦⠽⣿⣿⣟⣷⣟⡷⣿⠇
⠀⠀⠈⠳⣶⠋⣙⠚⣛⢙⢋⣘⠃⠀⠀⢸⡴⢃⠯⢺⢚⠞⠧⡟⢻⠂⠀⠀⠀⠘⢾⣇⣇⣮⣰⣌⡿⠹⠏
⠀⠀⠀⠈⠕⠶⢿⡁⡟⢹⢺⣙⠀⠀⠀⠘⠵⠿⡜⢹⢸⠩⢻⡉⢳⡅⠀⠀⠀⠦⠤⠷⠶⠴⢨⠸⠴⠸⠆
⠀⠀⠀⢸⡟⣶⠀⣿⡇⠘⢷⡞⠀⠀⠀⠀⢰⣻⣶⣷⡇⣇⣀⢳⠃⠀⠀⠀⠀⠀⣿⣿⢾⡷⣿⢬⣯⠄
⠀⠀⠀⠸⠿⠟⠲⠏⠿⠆⠾⠇⠀⠀⠀⠀⠀⠉⠈⠉⠁⠉⠁⠈
⠀⠀⢀⣀⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⡀⠀⣀⡀⣀⣀⣀⡀⡀⠀⠀⣠⣤⣤⢄⢀⣀⢀
⠀⠀⠾⣟⡋⠋⢀⣤⣤⡀⠀⢶⣶⡆⠀⢨⠆⠣⠂⠟⠃⠟⠘⠊⠇⠧⠀⠈⢣⣏⡤⡤⡤⡠⢥⣯⣄⡤⢰⡄
⠀⠀⠀⢯⣁⣀⣿⣻⣻⣿⣀⠄⡌⠀⠀⢰⣿⣟⢿⡟⢿⡟⡟⢟⢻⣿⠀⠀⠘⣬⡊⣫⣍⢛⣽⠈⠋⣫⣌⡃
⠀⠀⢬⠎⣭⣩⡍⢸⡅⢡⢩⡦⡅⠀⠀⢘⡛⡛⣛⢛⣛⢛⡛⢛⡛⡿⠀⠀⠸⣇⡜⣿⠀⣿⠂⢠⡴⢋⠛⠇
⠀⠀⠈⠈⠛⠛⠓⠋⠓⠚⠚⠛⠃⠀⠀⠙⡾⡷⡧⠿⢹⠜⡧⣯⠼⡇⠀⠀⢐⣷⢶⣰⢲⠚⡖⠠⠶⠾⠦
⠀⠀⠀⠀⠘⠀⠀⠧⠀⠐⠀⠁⠀⠀⠀⠒⠼⠧⠿⠼⠳⠧⠼⠌⠇⠔⠀⠀⠀⠈⠀⠴⠌⠤⠥⠭⠦⠅⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣀⣿⢀⣾⠛⠻⣦⠰⣿⣛⡷⠀⣿⣛⣿⠆⠻⣦⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⣿⠈⢿⣄⣰⡿⢀⣿⣉⣿⠆⣿⣉⣹⡇⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠉⠁⠀⠀⠉⠉⠁⠀⠈⠉⠁⠀⠀⠈⠁

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⡠⠀⡇⠀⠀⠠⠀⢄⠀⠀⢠⠀⠂⢀⣄⢄⣀⠂⢰⠀⠀⠀⠀⠀⢴⠪⢔⠉⠣⠀⠀⠀⠀⢀⣴⣀⢀
⡇⠀⠀⠁⠈⠀⠀⢀⠀⠀⠀⠀⣂⡈⠙⢀⣁⠈⢰⠀⠀⢸⡀⠸⠉⠓⠚⠿⠀⣺⠀⠀⠀⢀⢰⠌⢗⠀⠀⠀⠁⠀⠀⠀⣸⠛⠢⠐⠌⢂
⠃⠂⠐⡐⠄⠀⠂⠒⠀⠀⠀⠠⠤⠤⠀⠠⡤⠤⠀⠀⠀⠀⠁⠁⠈⠀⠀⠁⠀⠁⠀⠀⢐⠋⠁⠈⠚⠂⡀⠀⠀⠀⠀⠀⠑⠈⡄⠀⠀⠈
⠀⠀⠀⠁⠀⠆⠀⠀⠀⠀⠐⠦⠢⠲⠴⠦⠤⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠐⠄⠀⠀⠁

⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⣀⣠⡄⠠⠄⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢖⠔⠢⠀⠀⠀⠀⠀⢀⠠⠤⠀⣀⢄⠀⠀⠀⠀⠀⠀⡀⡄⢀
⠀⡐⢠⢦⡄⠀⡠⠊⠀⠀⠀⠈⠉⠐⡾⠂⠰⢮⡀⠀⠀⠀⢀⣴⢦⠀⢀⢎⠄⠀⠀⠀⠀⡐⠁⠀⠀⠈⡵⠃⠀⠀⠀⠀⠀⡰⣷⡗⡽
⠀⠀⣣⠍⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡷⠀⠀⠀⠀⠀⠨⠋⠀⠈⡂⠀⠀⠀⠀⠀⠀⠁⣀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢺⡧⣿⢙⡍
⠀⢸⣻⠁⠤⢤⠢⠀⠀⠀⠀⠀⠀⠀⠀⠉⠖⠀⠀⠀⠀⠀⠀⢪⡀⠀⠰⠀⠀⠀⠀⠀⠀⠜⠵⠊⠀⠂⠀⠊⠀⠀⠀⠀⠀⢘⠀⠀⢘
⠀⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡄
⠀⢀⡀⣀⢀⡀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡘⠀⠘⡀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠐⠂⠐⢀⢂⡀⠀⠓
⠀⠉⠑⡀⢀⡴⠉⠀⠀⠀⠀⣤⢀⠊⠫⡀⢄⡀⠀⠀⠀⢰⠁⠀⠀⠍⠁⠀⠀⣰⠀⠀⠀⡀⠂⠁⡨⠈⠁⠀⠄⠀⠀⠀⠀⡀⠀⢂⠀⠀⡄
⠇⠀⠰⠂⠀⠃⠈⠈⠀⠀⠀⠙⠺⢦⠀⠔⠀⠀⠁⠀⠀⢸⢴⡆⠈⠁⠀⠐⣶⢾⠀⠀⠀⣠⣊⠡⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠘⠛⠧⠀⠀⠀⠀⠟⠋⠀⠀⠐⠋⠋⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⢀⡌⡅⠀⠀⢰⡱⠀⠀⠀⠀⠀⠀⠀⡞⢡⠄⠀⠀⠀⠀⠀⡠⠒⠉⠉⡂⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⡤⠒⢉⣑⢦⡀
⠀⠐⢀⢀⡀⡪⠊⠀⠀⠀⠀⠀⠀⢐⢺⣀⠹⠀⠀⠀⠀⠀⠀⠣⡀⠄⢀⠁⡰⠂⠀⠀⠀⢰⡆⠀⠀⠰⡀⠀⠀⠀⠀⠘⠔⠁⢀⠀⡑⢱
⡀⠂⠁⡰⠻⠀⠀⠀⠀⠀⠀⠀⠀⡃⣸⠁⡀⠀⠀⠀⠀⠀⠀⠢⡄⢠⠟⠀⢴⠀⠀⠀⠀⢸⡆⠀⠀⠲⠀⠀⠀⠀⠀⠘⣄⠀⠢⠠⡁⡎
⠃⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⡭⡁⠀⡃⠀⠀⠀⠀⠀⢀⠊⠉⠃⠜⠁⠁⠀⠀⠀⠀⠈⠁⠲⡀⠃⠀⠄⠀⠀⠀⠀⠀⠉⠒⠉⠈⠢⡀
⣶⣾⡿⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⢰⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣆⣀⡆⠃⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠐⢻⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⣦⡀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢾⡷⡴⠂
⠀⠀⠀⠀⠀⣞⡷⠀⠀⠀⠀⠀⢀⣯⣍⠁⠀⣻⣇⠀⠀⠀⠀⠀⢰⢿⠀⠀⠀⠀⠀⠀⢀⣀⡿⣇⢣
⠀⠀⠀⠀⡀⠘⠃⢀⠀⠀⠀⠀⠘⢿⡿⠃⠀⢏⠉⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⢠⡄⢠⣼⣼⣦⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣻⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡟⠀⠀⠀⠀⠀⠀⡞⣿⡦⠓⠀⠀⠀⠀⠀⠀⣠⡾⣷⡄
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⣰⠿⣬⠁⠀⠀⠀⠀⠀⠀⠓⣿⡄⠀⠀⠀⠀⠀⢀⡼⢻⡄⠸⣿⡀
⠀⠀⠀⠀⠰⠁⢸⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠳⡄⠀⠀⠀⠀⠀⠰⠁⡇⠀⠀⠀⠀⠀⠏⠀⠞⠀⠀⠻⠇

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢈⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠐⣿⠂⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⣤⣾⣿⡇⠀⠀⠀⠀⠀⣀⣤⠟⠻⢿⠀⠀⠀⠀⠀⠀⠼⣿⠄⠀⠀⠀⠀⠀⣶⣾⣷⣶⣶⣦
⠀⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠀⠾⠉⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢶⠠⢠⡄⡄⡦⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠙⢾⡗⠋⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠀⠀⠁
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⠀⡎⠋⡇
⠀⠀⠀⠀⠀⡃⠃⠀⠀⠀⠀⠀⠀⣸⠀⠀⠓⠂⡄⠀⠀⠀⠀⠀⡞⠀⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡂
⠀⠀⠀⠐⠀⠂⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣦⣤⣤⣶⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠠⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀
⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠶⠀⠸⣟⣿⠀⣴⣿⣷⠀⠀⠄⠀⠀⠀⠈⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠉⢰⡉⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⡏⢸⢀⢀⠄⠀⠀⠀⠆⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇⡁⢸⠸⣈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠁⠀⠠⢀⡤⠀⣀⠀⠀⠈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⣿⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⡱⢿⠀⠀⣸⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣠⣴⣾⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠿⠿⠟⣿⣿⣿⡿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⣡⢠⠀⠀⠀⠈⠛⢿⣷⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⠀⡆⢀⡂⠸⠅⠀⠀⠈⠀⣼⣏⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⣦⠸⡇⢹⡀⠓⠉⠀⠀⠀⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠓⠀⠀⠀⣼⠀⢠⠀⠀⡀⢀⣠⣾⣿⣿⣿⣿⣿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢀⣀⡀⠉⢀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⢊⣁⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠕⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢐⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⢡⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡁⠀⠀⠀⠌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢁⣀⣀⣂⣩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⡿⠿⠿⣿⣿⣶⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠴⠚⠋⠁⠀⠀⡀⠀⠀⠉⠉⢁⢠⢀⡘⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡉⠉⠉⠀⠀⢀⣠⣄⠠⠰⡃⣅⠀⠀⠀⠘⠘⠀⣥⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣅⠟⢠⡦⣄⢤⠄⣤⠰⡞⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠌⣿⣧⣿⢠⣯⣼⡆⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠛⠀⣏⣼⠇⢸⣇⠾⠀⠛⠉


⣿⠿⠿⠿⠿⡟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣻⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤
⠀⠀⣶⢖⣫⣭⣭⣓⢶⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⣻⠁⠀⠈⣿⠠⠄⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠈⢿⡇
⠐⢶⢣⣿⣿⣿⣿⣿⣧⢳⠦⠀⠀⠀⠀⠀⠀⢸⠀⢸⢻⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⢀⣼⠁
⢀⣼⡸⣿⣿⣿⣿⣿⡿⣸⣄⠀⠀⠀⠀⠀⠀⢸⠀⢸⣺⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⢤⡆⠈⠒⠁⢠⡤⣀⠀⠀⠀⠀⠀⠀⢀⡿⠉⠀⠘⢿⣀
⠀⠀⣷⣝⡻⠿⠿⣛⣵⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠙⣆⢸⠀⠀⠀⠀⠀⠀⡌⠀⢸⣧⣀⣀⣀⣼⡇⠀⢡⠀⠀⠀⢠⠋⣨⣄⡀⠀⢀⣠⣇⠙
⠀⠀⠀⠀⠛⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣙⣒⣃⣸⠀⠀⠀⠀⠀⠀⠇⠀⣾⣿⣿⣿⣿⣿⣧⠀⠸⠀⠀⠀⠸⠀⠿⣿⡿⠖⢿⣿⡿

⠀⠀⠀⠀⣰⣄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⡀
⠀⢀⡄⣬⣹⠰⣆⢷⣍⢷⣄⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢠⣿⢸⣧⢿⠇⠿⠎⠛⠈⠋⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠒⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡆
⠈⠉⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⣆⣠⣶⣠⣴⣀⣴⣀⡇⠀⠀⠀⠀⠀⠀⢸⠳⠚⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠒⠒⠒⠒⠛⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⣀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⢤⣠⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢐⣁⣀⡁⣀⣈⡀⠀⠀⠀⠀⠀⠀⣀⣀⣒⣋⣈⣙⣂⣀⣀⠀⠀⠀⠀⠀⠀⢤⣬⣥⣤⣬⣥⢀⠯
⢹⣿⣿⣿⠟⠿⠻⣿⡟⠛⠛⣇⠀⠀⠀⠀⠀⠈⣿⣿⣇⢿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⡏⠀⣹⣿⣿⠈⠁
⢸⣿⣿⣿⣀⣀⣀⣿⣷⣶⣶⣾⣦⡄⠀⠀⠀⠀⠘⣿⣿⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢠⡇
⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣧⠀⠀⠀⠀⠀⢹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠉⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣀⣿⡇
⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⣠⢔⣯⣭⣭⣖⠖⡦⠄⠀⠀⠀⢠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣦
⠀⠠⣀⠴⠯⠼⣛⣛⣿⣻⠕⠋⠀⠀⠀⠀⢠⣿⣿⣿⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣴⣶⣆⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠴⣶⣝⡋
⣀⣎⠙⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⢿⠘⢫⣿⣿⡿⠀⠀⠀⠀⠀⠀⠻⣿⡿⠀⣏⣩⣥⠀⠀⠀⠀⠀⠀⠀⠼⢯⣽⠆⠀⠀⠉⠁
⠀⠑⡤⠀⢀⣆⣀⣰⣀⡀⡀⠀⠀⠀⠀⠀⠘⠿⣿⣧⠀⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⣷⡆⡆⠛⡇⠙⠋⠀⠀⠀⠀⠀⠀⠰⣦⣌⢹⣠⣴
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠘⠙⢆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠒⠚⠒⠓⠒⠒⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠒⠓⠒⠂⠀⠀⠀⠀⠀⠀⠒⠒⠒⠛⠒⠒⠒⠂

⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⣿⠀⠐⠋⠀⠠⠀⠀⠀⠀⠀⠀⠂⣠⡤⢶⡥⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠀⠔⠘⣫⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢂⡀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⡀⠀⠀⠀⠈⠊⠉⠄⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⢀⡠⣤⡶⠂⠀⠈⠢⣄⡀⠀⠀⠀⠐⠂⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠤⠿⠷⠂⠉⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠤⠀⠀⠀⢸⣿⣿⡀
⣀⣀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣇⣀
⣿⣿⣿⡿⠋⣩⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⢩⣿⣿⡿⡟⠋⠉⠋⠉⡉⠋⢉⠉⠙⠋⠋⠉⠉⠙⠋⠉⠉⢩⠉⠛⣿⣅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⢀⡀⠀⠀⡀⠀⢀⡀⣀⣤⣴⡄
⠀⠀⡀⡀⠀⡄⠀⡀⠄⢄⣦⡵⠊⠉⠉⠉⠁⠒⢄⠒⢠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⣀⠈⠰⣷⡅⢈⣁⣠⢀⡀⢀⠈⠀⠠⡀
⠀⠀⠃⣹⣾⠗⠀⠀⠀⣠⠟⣶⢖⡴⢿⡢⠐⠀⠀⠀⠐⠓⢀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣠⣿⣶⣲⣿⣏⠀⢀⠉⠚⠅⠛⠁⢠⠀⠉
⠀⠀⢰⡝⡏⠀⣀⢄⠘⠻⠉⢿⡀⠻⡾⠀⠉⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠟⠚⠁⢙⡵⠻⡏⢻⣁⡤⠀⠈⠀⠀⠀⠒⠠⡀
⠀⠀⠸⠉⠁⠀⠉⠆⠀⠀⢀⣿⡏⠀⠀⢀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⡟⠁⠀⣿⡭⢹⣋⠀⠂⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠘⠷⠗⠚⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠀⠀⠨⠁⠀⠀⡽⠓⠴⠋⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢠⣠⣦⡴⠀⠀⠘⠀⠀⠐⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠠⠄⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠞⠃⠐⠣⠈⠁⠀⠀⠀⠄⠀⠀⠄⠀⠀⠄⠀⠀⠀⣀⣠⣡⠀⠘⣆⠀⠀⠀⠀⠀⠁⠒⠀⢀⡃
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⠀⠀⠁⠀⠈⠟⡇⠈⠙⡛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⠀⠀⠦⠔⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣎⠘⢻
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠔⠃⠀⠀⠀⠀⠠⣴⣤⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠂⠀⠀⠀⠉⠁⠒⠂⠀⠀⠀⠀⠀⡀⠀⠀⣀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠖⠊⣡⡴⠂⠀⢀⠐⣠⡴⠛⠔⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠈⠁⠀⢀⠀⠴⠊⠀⠀⠀⠀⢀⡾⠃⡔⠂⢀⡠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠁⠀⠀⠄⠠⠆⠘⠁⠀⠀⠀⠀⠀⠀⣰⠏⠶⠃⢤⡶⣫⠾⠛⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠁⠀⠀⠀⠤⠀⠀⠈⡄⠀⠀⠀⠀⠀⢰⠀⠀⣰⠇⠊⣠⣴⠂⠉⠐⠢⠌⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡤⠖⠈⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠘⣄⠀⢠⠃⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢹⡆⢸⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠒⣂⠀⠀⠀⢀⠀⢷⠘⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠈⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠂⢀⠄⠀⠀⠀⠀⠀⠀⡏⠀⠈⠄⠀⠀⠀⠃⠀⣠⠀⠀⠀⠀⢀⡙⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠤⠤⠤⣄⠀⠘⠁⠀⠀⠀⠸⠀⠀⢀⡠⠄⠀⠀⠐⢠⡏⠀⠀⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠈⠱⡄⠈⠀⠀⠀⢀⡀⠖⠁⠀⠀⠀⠀⠀⣼⠁⠙⢠⠤⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠠⠔⠚⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⢐⠉⠀⠀⠀⠀⠉⠉⠀⠘⠛⠑⠋⠀⠈⠀⠀⠀⠒⠂⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⣀⠀⠀⠀⠔⠁⠀⠀⠀⠂⠠⢔⠎⢑⠋⠀⠀⣀⠄⢀⡠⢄⡀⠀⠀⠀⠀⠀⠉⠑⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠠⠔⠁⢐⣨⢔⣪⡴⠞⣉⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠐⢉⡠⠄⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡨⠞⠋⠁⠔⠋⠡⠔⠒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⣰⠂⠀⢤⡀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠄⠀⠒⠂⠁⣄⠀⠀⠀⢀⡖⠀⣡⠚⠤⠤⠀⠀⠙⠦⠀⣤⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡆⣤⣩⣤⣀⡀⠀⣁⣤⠶⠋⠀⠀⠀⣸⠀⠀⢸⠐⡀⠀⠠⠆⠉⠉⠙⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣠⠾⠛⢋⡽⠀⠄⠂⠠⠀⢀⡽⣇⠀⠸⠀⠈⠂⠀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⡋⢀⡀⠀⡀⢀⡤⠀⠀⠈⠓⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠤⠞⠋⠀⠀⠀⠐⠂⠀⠉⠉⠉⠁⠀⠀⠀⠐⠀⠀⠀⠀⠉⠁



⣿⣿⣿⠿⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡛⢶⣄
⠀⠀⠀⢠⡾⣿⣿⣿⣿⣿⣿⣆⢻⣧⡀
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣄
⢶⣆⣚⠛⠛⠻⠉⠙⢻⣿⣿⣿⡇⢸⣿⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣷⡌⣷⡄
⠀⠀⢸⣿⣿⣿⣤⣾⣼⣿⣿⣿⡇⢸⣿⠀⢠⠋⠻⠿⠿⠿⠶⢶⣶⣶⣶⣤⣤⣤⣤⣀⣤⠚⢿⣿⣿⣿⣿⣿⣷⠸⣿
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣧⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⡁⠀⢯⣀⣈⣿⣿⣿⢀⣿⣦⣤
⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⣡⣿⠏⠀⡇⠀⢳⡀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⠀⠀⠀⠀⢷⠀⠘⣿⣿⣿⣿⡿⣸⡟⠉⠁
⠀⠀⠀⠀⠈⠛⠿⣿⣯⣵⣾⠟⠁⠀⠀⢸⠀⠀⢳⡄⠀⠀⠀⣾⣿⡟⠁⡤⠙⡄⠀⠀⠀⠸⠁⠀⣿⣿⣿⢟⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠻⣄⡀⠀⣿⠋⠁⠀⠁⠈⣧⠀⠀⢀⣇⡀⠀⡝⠻⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠱⣄⣘⡇⠀⣀⡀⢈⣧⣠⡔⠁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⣀⡀⠉⠑⠲⣤⡙⠛⢷⣄⠁⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠛⠛⠆⠀⠀⠸⣷⡀⠀⠙⣦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢠⡀⠀⣿⣿⣿⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⣿⣿⣿⣿⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⡿⠟⠉⠀⠀⠀⠙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠀⠀⠀⠀⠀⢰⠂⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⣠⣾⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡦⠰⣤⣀⣀⡀⠀⢠⠛⠙⠒⠉⠉⠀⢸⡀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢧⡸⣇⠀⠀⠉⠗⠁⠀⠀⠀⠀⢀⡴⠻⣓⢀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⡏⠉⠉⠳⢤⡀⠀⠀⠀⠀⣠⠖⠉⠀⠀⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⠿⠿⠟⠉⠉⠉⠉⠉⠓⠶⠶⠊⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⢠⣃⣀⠀⢠⣀⣻⣄⠀⠀⠀⠀⠀⢸⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠰⣄⠔
⠀⠀⠘⣯⠀⠀⠀⢀⣿⣌⠀⠀⠀⠀⠀⢸⣿⠀⡀⠀⠀⣠⣄⠀⠀⠀⠀⢐⣿⣤⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡋
⠀⠀⠀⠘⢇⠀⠀⠞⠁⠘⠆⠀⠀⠀⠀⠸⡟⠀⠸⠛⠛⢯⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠠⢾⡟⠚⠀⠀⠀⠀⠀⠀⠀⠀⡬⣿⡶⠤⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡷⠒⠲⠀⠀⠀⠀⠀⠀⠀⢸⣇⣬⣯⡄
⠀⠀⠀⠀⢀⠾⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⢸⣿⠙⠆
⠀⠀⣤⣴⣾⡶⢿⠟⠛⠀⠀⠀⠀⠀⠀⠀⢸⡅⠳⢤⣄⠀⠀⠀⠀⠀⠀⠀⡼⠃⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠈⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠃⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢻
⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⢀⡀
⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢯⡀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⠶⡏⠀⠀⠀⠀⠀⠀⢰⣀⣶⣤⣄
⠀⠀⢢⣖⠈⣿⣿⣷⡄⠀⠀⠀⠀⢠⣶⣿⣾⡛⡦⣴⣿⣶⣄⠀⠀⠀⠀⢴⣦⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿
⠀⠀⠀⠙⠋⣿⡿⠋⠉⠀⠀⠀⠀⠘⢿⣿⡿⠱⠃⠻⣿⣿⠏⠀⠀⠀⠀⠈⠉⢸⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⢸⠏⢹⣦
⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠇⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠦⡄⣠⡾⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢠⣿⢁⡼⣤⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣾⡿⠊⣴⠄⢠⣿⠁⠀⣴⡿⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢠⡿⢀⣾⡏⠀⣰⣿⠧⠊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⣄⣀⣿⣇⡀⠘⠷⢺⣿⣇⠔⠙⠿⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡯⠿⠋⡉⠛⠿⣦⣼⡏⠉⡆⣀⠀⢠⠀⡶⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⢑⡛⢓⠀⣿⡇⡆⠯⢿⠀⠿⢯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⢐⠂⡜⣺⠃⣾⢠⠻⠷⢁⡤⠄⢠⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⣿⠜⠸⡅⣯⠸⠇⡯⠀⠀⢾⠰⡧⢾⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⡆⠸⡽⠶⢴⠴⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡿⢠⣿⡎⡾⠡⣞⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠀⠀⠀⠀⠀⡠⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⠋⣽⢻⢋⢛⡭⣿⣿⣿⢩⡙⡟⢋⡏⢽⣿⣿⡟⠉⡛⠻⠻⢋⡽⣿⣿⣿⠋⢿⢻⣿⣿⡟⠩⡏⠝⡛⢽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣭⣼⣦⣼⣮⣥⣿⣶⣿⣬⣵⣥⣮⣧⣿⣿⣾⣧⣾⣧⣷⣼⣬⣥⣿⣾⣯⣴⣼⣼⣷⣾⣧⣬⣧⣿⣯⣤⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠛⠛⠳⢦⡄
⠀⠀⠀⢀⣠⡶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣿⡆
⣼⠃⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠛⠛⠋⠉⠉⠀⠸⣇
⣿⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢿⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣤⠀⠀⠀⢸⡆⢸⡆
⢸⡇⠀⠀⠀⣀⣤⣤⠿⠀⠀⠀⠀⠹⠂⠀⠀⠈⠁⠘⣧
⠀⢷⡀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢿⡀⠀⠀⠀⢀⣠⡴⠶⠞⠛⠶⠶⣤⡀
⠀⠘⢷⡀⠈⠷⣤⣄⠀⠀⠀⠀⢀⣤⡴⠞⠛⢉⣿⠀⢸⡇⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠙⠢⣤⣤⣿⡀⠀⠀⠀⠀⠹⢦⣤⣤⠞⠃⠀⣿⠀⠀⣼⠃⠀⠀⢀⣤⠶⠶⢦⣄⠀⠀⠈⢿⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢀⡟⠀⠀⠀⣾⠁⠀⠀⠀⢻⡆⠀⠀⢸⡇
⠀⠀⣠⠀⠀⠀⠀⠀⣠⠿⠳⢦⣤⣤⣤⣤⡴⠾⢯⡀⠀⠀⠀⣿⠀⠀⠀⢻⣄⠀⠀⣀⡾⠁⠀⠀⢸⡇
⠀⣼⠋⠀⠀⠀⢠⡾⠁⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠙⣦⡀⠀⠹⣆⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⣠⡟⠀⠀⠀⣸
⢰⡏⠀⠀⠀⢠⡟⠀⠀⠀⣠⡾⠛⠉⠉⠉⠙⠷⣤⡀⠘⣧⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠉
⣼⠁⠀⠀⠀⢸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣿⡀⠀⠀⠀⠈⢹⡟⠛⠛⠛⢻⡍
⣿⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⣨⣿⣄⣀⡀⠀⢸⡇⠀⠀⠀⠸⣇
⠉⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧⡀⠀⠀⠀⢀⣴⠏⠀⠀⣴⠏⠁⠈⠉⠙⢷⣼⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⢦⣄⣠⡾⠁⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⣰⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠈⠙⢷⣶⣤⣀⠀⠀⠀⢰⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡇⠈⠉⠛⠳⠶⣼⣧⣀⣤⠾⠃
⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠶⠶⠶⢾⡃
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⣄⠎⠈⠀⠈⡆
⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠋⠀⠀⠀⠠⢾
⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠈⠀⠄⠀⢸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁⢸
⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠄⠐⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⢰⠀⠀⠀⠀⠆⢠⠀⡈⠀⠀⠀⠀⠇⡀⡄⠀⠀⠀⢸⠂⠁⢀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢠⣲⠀⢇⠸⡄⠀⢠⣲⠀⡏⠀⠀⠈⠃⢸⠈⡆⡎⠀⠀⢸⠚⠁⡎⠀⣐⡆⢘⠀⢷⠈⠆⠀⢸⠆⠀⠘⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⢄⡰⠀⠀⠀⠀⠀⠓⠀⠀⠀⠆⠈⠀⠃⠈⠁⠀⠈⠓⠁⠈⠁⠀⠀⡌⠁⠀⠸⠀⠀⢸⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣅⣀⣀⡀⠀⠀⠈⠀⠄⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠅⢀⠃⠠⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⢓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢲⢰⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⡏⠇⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠘⠀⠀⠀⢰⠸⠀⠀⠀⠀⢨⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⠠⠄
⠠⠀⠀⠀⠀⠐⠁⠀⠀⠀⠠⠀⠀⠀⠀⠐⠄⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠆
⠀⠀⢠⠀⠀⣀⠃⡈⠀⠀⡀⠤⢄⠀⢀⡀⠀⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⢛⣷⣦⣴⣶⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⣨⣿⣿⡋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⢾⣿⠙⠿⠟⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠎⠉⠁⠀⠈⠉⠉⠉⠙⠛⠿⢷⣶⣾⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠀⠀⠀⢀⣠⣤⢶⡆⢸⡟⣿⠛⣿⠷⣶⡄⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⠀⠀⣴⡞⠻⠅⠛⠈⠁⠈⠀⠀⠀⠉⢀⣿⠀⠟⢀⣷⣄⡀⠀⠀⠐⢿⣷⠶⠮⣽⣿⣄
⠀⠀⠀⠀⣴⢋⣾⡿⠁⠀⠀⢀⣴⣶⣬⠛⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⣾⡟⠀⠀⠉⢀⡼⣷⣄⠀⠀⠈⢻⡟⠶⢤⣌⠙⣦
⠀⠀⠀⢠⠀⣾⡿⠁⠀⠀⢠⡾⣯⠉⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣼⣿⠧⠀⠀⠀⠀⠘⠋⣹⣷⡀⠀⠀⢿⣟⠲⢦⣄⣸⣧
⠀⠀⢀⡟⣸⡿⠁⠀⠀⢠⡿⢦⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠈⠡⠞⣿⡀⠀⠀⢿⣿⣿⣿⣿⣿⣇
⠀⠀⢸⠇⣯⠀⠀⠀⠀⠾⣦⡄⠀⠀⠀⠀⠉⠳⠆⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣿⠀⠀⠘⣿⣿⣿⣧⣼⣿
⠀⠀⣾⢰⣿⠀⠀⠀⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⠃⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠛⣿⡇⠀⠀⢀⣘⣿⠁⠀⢿⡆
⠀⠀⣿⠸⣿⠀⠀⠀⢸⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢨⣿⣿⡇⠀⣸⠇
⠀⠀⢻⠀⣿⡀⠀⠀⢸⡏⠳⠆⠀⠀⣤⠶⠋⠀⠀⠀⢀⣿⣡⡟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⣼⣿⠀⠀⠀⣾⠰⢧⠀⢰⣿
⠀⠀⢸⡇⢻⡇⠀⠀⠀⢷⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⢰⣾⡏⠀⠀⢀⡟⠀⠀⢀⣿⡏
⠀⠀⠀⢻⡌⢿⡀⠀⠀⠘⢃⣤⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⢠⡄⠀⠀⠀⠀⠀⠈⠛⠀⠀⣤⣽⡟⠀⠀⠀⣼⠁⠀⢀⣼⣿⠁
⠀⠀⠀⠀⢳⡘⣷⡀⠀⠀⠈⢷⣤⡄⠀⠀⠀⠀⢠⣿⠏⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢀⣤⣻⡟⠀⠀⠀⣴⡃⢚⣛⣿⣿⠇
⠀⠀⠀⠀⠀⠳⣼⣷⠀⠀⠀⠀⠹⣶⡖⠀⣀⠀⣾⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀⣤⣸⡿⠋⠀⠀⠀⣼⣯⣽⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠙⢧⡀⢤⣄⠀⠀⠈⠙⠿⣯⣼⡃⣴⠆⢠⡄⣠⡀⣤⠀⣄⠰⣶⡿⠟⠋⠀⠀⠀⢀⣠⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠙⠳⣤⡀⠀⠀⠀⠈⠁⠙⠳⠾⠷⠿⠧⡾⠷⠟⠀⠁⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣷⣶⣦⣤⣤⣤⣦⣤⣴⣶⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⡃⠀⠐⠂⠀⢸
⠀⠀⠀⡃⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⡄⢄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⣀⠠⢤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⠀⠃
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤
⠀⠀⠈⠐⠀⠀⠀⠀⠑⠠⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣄⣤⣤⣤⣤⣀⣤⣄⣀⣀⣄⣀⣀⣀⣠⣄⣀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣀⣀⢀⣀⢀⡀⣀⡀⣀⢀⣀⢀⡀⢀⣀⣀⠀⡀⢀⠀⢀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠰
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣾⣿⣿⡇
⠀⠘⢿⣿⣿⡟⠻⣏⡉⠉⠉⣉⠉⠉⢉⣩⡟⠹⣿⣿⣿⠏⠁⠈⢻⣿⣿⣿⠙⣯⣉⠉⠉⣉⡉⠉⠉⣩⡿⠉⣿⣿⣿⡏⠁
⠀⠀⠈⠛⠛⠁⠀⠙⢿⣦⣸⣿⣆⣴⡿⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠈⢻⣷⣤⣿⣧⣤⣾⠋⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⠃⠀⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠈⠛

⠀⠀⠀⡠⠒⠒⠒⠒⠒⠢⡄⠀⠀⢀⡴⠒⠒⠒⠒⠒⢢⡀⠀⠀⢠⠖⠒⠒⠒⠒⠒⢄⠀⠀⠀⡰⠒⠒⠒⠒⠒⠢⡄
⠀⠀⠀⡇⢠⣲⣿⣷⣶⡄⣿⠀⠀⢸⡆⣿⣿⣿⣷⣠⠀⡇⠀⠀⣸⢰⣿⣿⣿⣿⣷⢸⠀⠀⠀⡇⢲⣶⡆⠤⠀⠀⣷
⠀⠀⠀⡇⣿⣿⣿⣿⣿⡇⣿⠀⠀⢸⡇⣿⣾⣷⣿⠁⢸⡇⠀⠀⣿⢸⣿⣿⣿⣿⣿⢸⠀⠀⠀⡇⣸⣿⡇⠀⠀⠀⣿
⠀⠀⠀⢷⣙⣛⣛⣛⣛⣡⠏⠀⠀⠘⣧⣉⣉⣉⣉⣀⡸⠃⠀⠀⠸⣌⣉⣉⣉⣉⣁⡼⠀⠀⠀⢷⣈⣉⣀⣀⣀⣠⠏
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⡎⠠⣀⣀⢄⡀⠈⣧⠀⠀⢰⡃⣤⣤⣤⣤⣤⠈⡆⠀⠀⢸⠁⠀⣴⣶⠄⠀⢹⠀⠀⠀⡏⢀⣠⣤⣄⠀⡈⡇
⠀⠀⠀⡇⢰⠿⢷⡘⠣⠀⣿⠀⠀⢸⡇⣿⣿⣟⣤⣿⠀⡇⠀⠀⣿⠀⣤⣸⣟⢠⠀⢸⠀⠀⠀⡇⣾⣿⠿⢿⡞⠁⣿
⠀⠀⠀⣇⢁⡿⢧⠂⠀⠀⡏⠀⠀⢸⡇⠛⢻⣿⡟⠛⢨⡇⠀⠀⢻⠀⠘⢻⣿⠟⠀⢸⠀⠀⠀⣇⠘⠿⠦⠟⠀⠀⡿
⠀⠀⠀⠙⠓⠶⠶⠒⠒⠚⠁⠀⠀⠀⠙⠒⠖⠒⠒⠒⠋⠀⠀⠀⠈⠓⠖⠶⠒⠒⠒⠋⠀⠀⠀⠙⠒⠒⠶⠒⠒⠚⠁

⠀⠀⠀⡰⠒⠒⠒⠒⣒⡒⡄⠀⠀⢀⡔⠒⠒⠒⠒⠒⠢⡀⠀⠀⢠⠖⠒⠒⠒⠒⠒⢦⠀⠀⠀⡴⠒⠒⠒⠒⠒⠲⡄
⠀⠀⠀⡇⣴⣶⣶⣿⣤⡇⣭⠀⠀⢸⡄⣿⣾⡿⢿⡇⠀⡇⠀⠀⣸⠀⣤⣴⣤⣶⡄⢸⠀⠀⠀⡇⢀⣠⢴⣚⢷⡀⣧
⠀⠀⠀⡇⣿⠷⡟⣹⡇⠀⣿⠀⠀⢸⣷⣿⣾⣧⢸⣷⠰⡇⠀⠀⣿⢠⣿⣿⣿⣿⡇⢸⠀⠀⠀⡇⠸⣋⣶⠟⠋⠁⣿
⠀⠀⠀⢳⣌⣉⣉⣉⣀⣠⠏⠀⠀⠘⢧⣉⣈⣁⣀⣁⡴⠃⠀⠀⠸⣄⣀⣀⣀⣀⣠⡾⠀⠀⠀⢷⣀⣉⣀⣀⣀⣠⠏

⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⢀⣠⣤⣤⣄⢀⡀⠀⠀⠀⠀⣀⡤⢤⣤⣄⣀⡀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⡏⠀⠀⠐⠂⠀⠀⣃⠀⠀⢰⡇⠀⣀⣴⣦⠀⠈⡆⠀⠀⢸⠁⠀⢠⣆⠀⠀⢹⠀⠀⠀⡏⠀⠀⢐⠂⠀⠀⡇
⠀⠀⠀⡇⠀⣄⠁⣤⡀⠀⣿⠀⠀⢸⡇⠈⣫⣿⡟⠀⢀⡇⠀⠀⣿⢠⣶⢾⣿⢶⣄⢸⠀⠀⠀⡇⠀⠋⣿⡞⠃⠀⣿
⠀⠀⠀⣇⠀⠙⣀⣈⣰⠆⡿⠀⠀⢸⡇⠈⣿⣿⣯⡀⢸⡇⠀⠀⢿⠀⠀⠺⠿⠆⠀⣸⠀⠀⠀⣇⠀⢿⣿⣿⠃⠀⡿
⠀⠀⠀⠈⠓⠒⠒⠒⠒⠚⠁⠀⠀⠀⠙⠒⠒⠒⠒⠒⠋⠀⠀⠀⠈⠓⠒⠒⠒⠒⠚⠉⠀⠀⠀⠙⠓⠒⠛⠓⠒⠚⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠄⠀⠨⠀⠀⢀⠀⠀⠀⢀⠇⠀⠀⠀⠘⡆⡰⠁⡁⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠁⢄⢁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⠁⠉⠀⠀⡠⣷
⠀⡀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠘⠀⠢⢀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡀⢸
⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠠⠀⣀⠀⠀⠀⠡⠀⠀⠈⠀⢀⠃⠀⠀⠀⠀⠀⠐⡇⠢⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⠘⠀⠑⠨⠀⠀⠀⠀⢸⠁⠀⡀⠀⠀⠀⠀⣇⠠⠀⠀⠀⢸
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇⠈⡆⢀⡀⢠⠀⢠⠀⠀⠀⢀⡀⢸⡅⠀⠀⢰⡇⢸⠀⢄⢀⢤⠈⠀⢸⣠⠇⣠⠄⠀⣀⠈⡴⠀⡇⠠⡀⠀⠀⡇⠀⠀⠐⠉⢹
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣧⣰⠃⠧⢿⠘⠇⢸⠀⠀⠸⠝⡇⢸⠀⠀⠀⢸⠀⠸⠁⡜⠸⣀⠀⠀⢸⡉⡆⢯⡀⠪⠺⡀⣇⡀⠟⢠⠇⠀⢀⡏⠆⠀⠘⠤⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠞⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠃⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠄⠀⠀⠘⠀⠀⢸⠆⠁⢀⡀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠤⡀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠲⣆⣀⣀⡀⠀⠀⠘⠀⠠⠇⠀⡯⠤
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⢀⠸⠅⢀⠓⠠⡖⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠒⠉⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠐⠁⠀⠠⠉⢢⣰⠁⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠆⠀⠘⡇⣗⠤⣀⠀⠈⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠁⠀⠀⠀⠄⠀⢀⠐⠀⠀⠈⠀⠀⠾⡀⠀⢠⢱⠸⡄⠀⠉⠁⠀⢸⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢸⠀⠀⢀⠀⠀⠀⠈⠂⠀⠀⡀⠀⡀
⣀⠀⠀⠀⠀⠀⡠⠃⠀⠈⠀⠀⠀⠀⡀⠀⠀⢃⢀⠂⢸⠀⣥⠀⠀⠀⠀⠚⠀⠀⠀⢠⡇⠀⠀⠀⠀⢸⠅⠈⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠁
⠈⠁⠂⠐⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⢸⠀⢸⡀⡀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⢰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠂⠀⠘⠀⠀⠀⠀⠀⠀⠈⠁⡀
⠀⢀⠠⣅⣀⡠⠤⡑⠄⠀⢀⣥⢚⡗⠦⡀⠠⠂⠀⠀⠼⠀⢸⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠄⠀⠀⠀⠂⠠⠄⠀⠀⠀⠊
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣠⣀⡀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⢤⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⣄
⠀⠀⠀⣴⣮⣿⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⢿⣯⣶⡄
⠀⠀⢸⠉⡇⢸⠀⣿⣿⣿⣿⣷⡀⠤⠤⠤⠐⠒⠒⠒⠒⠒⠒⠠⠤⠤⠄⣰⣿⣿⣿⣿⠇⢸⠀⡏⢹
⠀⠀⣸⠀⡇⢸⠀⢸⣿⡟⣧⣴⣶⠶⠿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠷⢶⣶⣤⡟⣿⣿⠀⢸⠀⡇⢸⡀
⠀⠀⢳⡆⢡⠀⡆⠈⣿⣿⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⡏⠀⡆⢠⠁⣾⠃
⠀⠀⠀⠱⡈⣆⣰⣠⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣤⣰⣀⡎⡰⠁
⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠋⠁