Classical Music Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢴⣯⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⢀⠰⣌⣷⢿⣷⡀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠆⠈⣺⣿⣦⡄⢿⣷⡀
⠀⣼⣷⣏⠆⠀⠀⠀⠀⠈⠛⠻⠿⠷⠗⠀⠀⠀⠀⠀⠀⢰⣾⣥⡇⣴⢀⡄⣤⢠⠄⣄⢠⠀⡄⢲⣸⡆⠁⡈⠸⣿⡆⠸⣿⣿⣿⠰⠎⢿⣧
⢠⡿⠱⣾⣯⡐⣴⡠⠠⢀⢀⠀⠀⠀⠀⠀⡀⡀⣄⣦⠀⢸⣿⠋⣩⣾⡏⣿⡄⠀⣿⡏⣷⣦⣕⡜⣿⣷⢸⡀⠃⢿⣿⡐⢷⣼⣿⣟⡷⠘⣿
⣼⢏⣹⣿⢻⣡⣿⠰⢆⣼⡖⣙⣡⣶⡖⢡⣷⣟⠛⣿⡄⢸⣿⠁⠻⣿⡇⣻⡆⠀⣿⣇⣿⣿⡿⠍⢻⣿⡎⣖⠘⠸⣿⣧⠘⡿⢿⣿⡐⠒⢹
⣿⣬⣿⣿⡇⣼⡿⢤⣵⣿⡗⣯⣽⣿⡇⢨⡟⣿⠇⢻⡇⢸⡏⠖⠀⣿⡇⣿⡆⠀⣿⣯⠹⣿⠯⠁⠸⣿⣿⠀⢈⠀⣿⣿⡌⣵⡞⣿⡇⡷⠊
⡇⣤⣿⣧⡗⣿⡇⠊⢹⣿⠁⠽⣟⣻⡇⠰⣏⣿⠐⢺⡇⠸⣇⠀⣶⣿⣧⢉⡖⠀⣿⣿⢨⣦⣬⣢⠀⣿⣿⡦⡯⠰⢹⣿⡇⣙⡃⣿⡇⠀⠤
⢠⠄⣿⢛⣁⣿⡇⢱⣼⣿⢠⣄⣾⣿⡇⢸⣤⣿⠗⢸⠃⠀⠇⠀⠈⢹⣿⣸⡿⠀⢹⣿⣎⡬⣿⡿⠆⢸⣿⡇⣓⡴⠸⣿⣷⢩⣷⢿⡇⣤⡐
⠀⣤⣿⣺⣽⣿⢓⠯⣿⡟⠸⣿⣿⣿⡇⣸⢻⡿⠀⠌⠀⠀⠀⡉⠀⣸⣿⣧⢸⡃⠸⣿⣯⠻⣿⡷⠁⢸⣿⣿⠀⡈⡀⣿⣿⣘⠟⣿⡇⡯⠁
⠀⢹⣻⡟⠿⣿⢠⣄⣿⡇⢈⣻⢡⣿⠣⣾⣿⡿⢀⠀⠀⠀⠀⠀⢆⠙⠿⣿⣿⣿⠀⢻⣿⣮⣷⣬⣴⡀⣿⣿⢸⠅⡇⣿⣿⣼⣆⣿⡷⠁
⠀⠀⠹⣿⡿⣿⡼⣜⣿⣷⣿⣿⣿⣿⣰⣿⡿⠤⠀⠀⠀⠀⠀⠀⠀⠐⢞⠹⣿⣿⣧⣌⢿⣿⣿⣿⣿⢭⣿⣿⠼⠅⢃⣿⡯⣝⣿⡿
⠀⠠⠄⠹⠯⣿⣧⠈⣿⡟⢻⣻⣿⣽⣿⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠻⠛⠻⢿⠿⠎⢿⣿⣽⡟⣉⣿⣿⡆⢈⣼⣿⠧⠞⡋⠀⢐⠓⠂
⠀⠀⡃⠀⡃⠈⡉⠉⡍⠉⡍⠀⠭⠀⠩⠀⠨⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣭⠀⠀⢩⠀⠀⢨⡅⠀⢨⡍⠉⢉⡍⠀⠀⡍⠀⢈⡅⠀⢨⡁⢀
⠀⠀⠆⠀⠆⠀⡆⠀⡂⠀⢒⠀⢒⠀⢘⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠶⠀⠀⠰⠀⠀⠰⠀⠀⠰⠆⠀⠰⠆⠀⠀⠆⠀⠰⠆⠀⠰⠠
⠀⠀⠈⠀⠁⠀⠥⠄⠥⠀⠼⠀⠴⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⡛⣀⠀⣘⠀⠀⢘⠀⠀⢘⡃⠀⢈⡃⠀⠘⠇⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣶⠔⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠸⣟⠹⢿⡠⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⡄⢹⣧⠀⠛⣦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢟⠋⡄⠀⢀⣡⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡞⢫⣽⣸⠃⠵⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣖⢤⢸⡇⢿⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⢺⡍⣦⢹⢸⢿⠇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢲⡝⣧⢹⣮⡇⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣤⡖⠛⠙⠓⠢⢄⡀⠀⠀⣀⠴⠚⣧⢹⡄⣷⣿⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢡⣾⡟⠀⠀⠀⠀⠀⠈⠓⠖⠋⠁⠈⡇⢸⣸⡷⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣾⣿⠁⠀⠀⢠⡄⡆⢿⡀⠀⠀⠀⢀⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⣿⡇⠀⠀⢸⡿⣏⢿⡈⠃⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⢹⣇⠀⠀⠘⠷⠉⠁⠀⠀⠀⢀⡴⠀⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⢠⡾⢃⠠⢔⡠⠤⠐⠀⠀⠠⡙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠈⠀⢀⡀⠀⠀⢀⣴⠟⣿⠧⠀⠀⠒⠀⣶⠀⠀⢀⣹⣤⣙⣄⣀⣀
⠀⠀⠀⠀⠀⢀⡠⠴⠖⠛⠉⠛⣓⣶⣶⣤⣽⣟⣛⣋⡁⠀⠿⠀⠀⠀⠀⠀⢸⡄⡴⢿⣤⣀⣉⣓⠒⠈⠉⠁⠀⡄
⠀⢠⣄⠀⠀⠀⠀⠀⠑⠒⣒⣤⣭⣍⣉⣙⠉⠋⠷⠻⠿⣫⣿⣶⣶⣶⠤⠄⠀⠛⠀⢀⠏⠉⢹⠏⠉⠹⡇⠀⠀⢻⡀
⠀⠀⢻⣟⠳⠶⠤⣤⣀⣀⠀⠈⠁⠀⠉⠉⠉⠛⠛⠓⠒⠀⠠⠤⣭⣄⣀⣀⣀⠂⠀⣀⠀⠀⠀⠄⠀⠀⣇⠀⠀⠘⡇
⠀⠀⠀⢻⣶⣶⡦⠤⣤⣍⣉⣛⡒⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠋⠉⣼⡗⠲⢶⠤⠤⠤⣿⠀⠀⢀⡥
⠀⠀⠀⠈⣧⠈⠁⠀⠀⢰⡆⣴⡀⣬⠁⠀⠠⣤⠤⠤⠀⢶⡛⠋⣉⡤⠤⠀⠀⠀⠀⣿⡇⠀⡾⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢶⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢰⣄⣀⣤⠤⠀⠀⢹⣇⢸⠃⠀⠀⠀⠀⢀⡞
⠀⠀⠀⢀⡈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠉⠁⠀⠀⠀⠀⠘⣿⣟⣒⢒⡒⠐⠀⣸⠄⠤⣄⣀⣀⣀⣀
⠀⠒⠋⠉⠓⠉⠛⠛⠿⠿⢶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠈⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠲⠦⠤⠀⠀⣷⠀⣀⣠⡤⠶⠿⠿⠛⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣥⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⡴⠚⠉⠉⠉⠉⠁⠒⠒⠂⠤⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⣴⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⡎⠐⠒⠊⠁⠀⠀⠀⠈⠑⢦⡀
⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠠⣟⡃⠀⠈⠉⠀⠒⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⢰
⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⣠⣄
⢿⣿⣿⣿⣿⣿⠃⣀⣤⣴⣶⣶⡀⠀⠀⠀⠀⢲⡄⠈⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡿⠟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⣿⠉⣿⠈⠙⠋
⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠃⠀⠀⠀⠀⠙⠁⠀⢲⡄⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⠿⠇
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠛⠛⠛⠛⢉⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⡠⠒⠉⠉⠀⠀⠀⢳⢀⡠⠀⣀⣀⠀⠀⣀⡠⠔⠁
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡅⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠
⠀⠀⡀⢰⡆⢀⡄⠀⣼⣿⣿⣿⡇⠀⠀⠀⠙⢦⣤⡴⠶⠶⠖⠚⠋⠁⢀⣿⣿⣶⣶⣤⣀⣀⡀⠀⢰⣿⡟
⠀⠀⢁⣾⠃⠸⠃⠀⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢅⣀⣿⣿⢻⠻⢻⡆⠸⣿⣧⡀⠀⠀⡶
⠀⠀⠉⠁⠀⡇⠀⢠⣿⣿⣿⣿⣿⣿⠀⠘⠓⡖⠀⠀⠀⠀⠀⠘⢳⠄⠀⠀⠀⢠⣌⡉⠙⠛⠋⠀⠀⠈⠉⠁⠀⠰
⠀⠀⠀⢀⣴⣷⣄⠀⠁⠉⠉⠉⠙⠋⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⣼⠿⣿⣦⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠘⣦⡀⠀⠀⠀⡖⢺⢠⡀⣀⣤⡴⡴⡾⠀⡀⠀⡿⠀⠘⣿⠀⠀⣀
⠀⠀⠀⣸⣿⣿⣿⡁⠀⠀⢀⣴⠿⠻⠆⠀⠡⠁⣉⣉⣉⣁⡰⣀⣅⠦⠈⠁⢀⡇⠀⠀⠹⠷⣿⡟
⠀⠀⣼⣿⠻⣿⣿⣿⡀⢀⡞⣻⣼⢷⡀⠀⠀⠀⠟⠟⠛⠛⢒⠋⠉⠀⠀⠀⢸⠃⠀⠀⣠⣾⠟
⠀⠀⠻⣿⣾⣿⣿⡿⠀⠈⢧⣿⠿⣴⠃⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⣼⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⡰⠆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⣴⣿⣿⠃⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⣦⣦⣤⠤⠤⠤⠠⠦⠀⠲⠒⠶⠶⠆⠀⣿⣿⣏⣿⣿⡿⠃⠀⠀⣼⣿⣿⡟⠁⠐⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠋⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠈⠁
⣶⣶⢶⣶⢶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣠⡀⡈⠢⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣡⣤⠀⠁⢄⠉⢠⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡾⠁⠀⠀⠀⢈⣠⠺⢷⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⢳⡶⠆⠙⢋⣳⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣋⣀⣀⠀⠉⣷⠿⢓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠿⢿⣭⠙⠇⠻⡄⠀⢺⢽⣻⣄⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⣄⠐⠩⢗⡻⣦⢿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣉⣤⣶⣆⠀⠀⠀⡙⣆⠀⠹⣾⠽⣦⣰⣯⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⢡⣶⠘⣿⡎⠀⠀⢒⡫⢞⣯⡙⢠⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣵⣿⣿⣤⡟⠁⠀⠀⠀⢐⡽⣞⣽⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠨⠵⣪⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢟⣭⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠶⠶⢦⣤⣄⠀⠀⠀⠀⠀⠀⠘⣫⢷⣾⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡇⠀⠀⠀⠀⠀⠀⠘⠭⢺⣭⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⢀⣤⣶⡒⣐⣦⠀⠀⠀⠀⠀⣀⣴⠿⣿⣆⠀⠀⠀⠀⠀⠀⠈⢵⣺⡿⣳⡄
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠘⠻⠿⠿⠛⠋⠀⠀⣀⣠⣴⡞⠛⣿⡄⠈⢻⣆⠀⠀⠀⠀⠀⠀⠈⢶⡿⣟⡿⡄
⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣀⣀⣀⣀⣀⣀⣤⣤⠶⣾⣿⠉⠉⢿⣧⠀⠘⣿⡄⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⢪⢽⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⠁⢹⣿⠉⢹⣿⠉⠀⣿⣇⠀⢻⣿⡇⠀⠘⣿⡆⠀⠘⣿⡄⠀⠀⠀⢀⣀⡀⣀⡀⠀⠀⠱⣚⣯⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⣿⡀⢸⣿⡇⠀⢸⣿⠀⠈⣿⣿⠀⠀⢹⣿⣀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠈⣹⡇⠀⠀⠁⠀⣀⣠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡇⠀⠸⣿⡄⠀⠸⣿⡇⠀⣴⠏⠁⠠⣶⣿⠶⠇⠀⠀⣀⡤⢾⡋⠻⣶⠀⠀⠙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⢿⣇⠀⠀⢿⣷⠈⣿⢦⣤⣄⣠⠤⣤⠲⣶⡏⠹⣷⠈⢿⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⣧⡀⠀⠸⣿⡄⠀⠘⣿⡆⠃⠀⣇⢸⣷⠀⣿⠀⢹⣧⠀⢹⣇⣼⣿⠁⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢷⣄⠀⠘⣿⡄⠀⢻⡇⠀⠀⣿⠀⣿⠀⢹⡇⠀⣿⡄⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣦⡀⠙⢷⣄⠘⢿⡄⠸⡇⠀⠀⣿⠀⣿⡀⠈⣷⠀⠸⣧⣾⢳⣻⡇⠀⠀⠀⠀⠀⠀⠀⣴⣶⠿⣟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⣤⠿⠦⣤⣈⠳⣤⡙⣆⢃⣠⣀⠈⠳⡌⠳⣄⠘⣧⠀⢿⣿⡜⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡏⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⡇⠀⢰⠇⠀⢨⠁⠉⣿⠀⠀⠙⡇⡤⢛⡶⣌⠓⣌⢳⣸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠈⢄⠀⢘⡀⠀⣈⢀⡀⠐⠃⠀⢾⡀⣼⠁⠈⠉⠃⠙⢿⣿⣿⣟⡿⢷⣤⣄⣀⣀⣀⣀⣀⣼⡷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣾⣻⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡿⢿⡿⠻⡿⣿⢿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣾⣶⣾⣷⣾⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢀⣘⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣦⣤⡀⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣁⢹⣁⣏⣿⣶⣶⣤⣶⣶⣗⣠⣄⡿⣿⣿⣿⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣤⣾⣿⣿⣿⡟⣉⣿⣿⣿⣿⣿⣿⣷⣶⣬⣝⠻⠷⡈⠁⠙⠚⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⡟⣽⣿⡿⢿⣿⣿⣿⢿⣿⣿⠦⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣗⣿⣿⣿⣿⣿⣿⣷⣼⣎⣥⣿⣿⣿⡧⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠛⠉⠉⢿⣛⣯⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⠄⢀⡀⢸⣴⣿⡋⠉⠉⠙⣏⠏⢥⣿⣟⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣮⣴⣶⣴⣾⣿⣿⠿⠀⠀⠀⠀⢸⡄⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢿⠋⠛⠻⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠉⠻⠙⣧⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠹
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣭⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⢼⢹⡍⡳⣄⠀⣈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⣠⡤⢒⡡⠻⡌⠓⢴⡘⣮⡌⠳⢬⣑⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⢋⣴⠞⠋⠀⠀⢳⡀⠀⢳⡈⢷⣄⣀⡤⠒⠈⢓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣰⣿⣿⡐⠄⠀⠠⢒⣳⣄⣀⠙⠾⢶⣢⣀⣀⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⣿⡟⠛⠁⠀⠀⠁⠛⠛⢿⣿⣿⣿⣯⡫⢻⣿⡿⣦⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡿⢫⣧⠀⠐⠀⠀⠀⠀⠀⠈⡿⢷⡿⢹⢟⣤⣥⣯⣻⡟⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣆⢰⡶⠶⠄⠀⠀⡠⣣⠞⢡⠎⣾⣿⣿⢞⡙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼⢉⡟⢿⣿⣆⠈⠀⢀⣠⣾⠟⣡⠖⡡⠂⢻⠿⣿⣿⢡⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⡇⢯⣻⣿⣿⡿⣿⢟⣡⣞⠕⣩⣶⣩⡵⣛⣭⣶⣿⣣⣖⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡟⢄⠹⡀⠉⢻⡿⢡⢇⣾⡕⣡⠖⢡⣼⢟⣼⣿⣿⣿⣯⠮⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⢡⣿⡆⢹⡀⢋⣴⣿⣾⡿⣴⣣⡖⣺⣿⣾⣿⡟⠁⢳⠰⡝⢮⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢸⠘⡟⣀⡷⢛⠏⣾⣿⣧⣿⣡⡞⢰⣿⣿⡟⠀⠀⠀⢣⠙⢦⣙⢦⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣨⠶⠛⠉⠀⡰⣰⣿⡏⣿⣿⡿⢁⣾⣿⠉⠀⠀⠀⠀⠈⣧⡈⠫⡓⠽⣎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠵⣒⣊⣥⣾⣼⡟⣿⢳⣻⡿⠃⣼⠇⡟⠀⠀⠀⠀⠀⠀⢹⣿⢦⣈⠲⢬⡸
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣥⣶⣿⣻⣟⣛⡿⢏⣼⡏⢎⡟⠁⣰⣿⢠⡇⠀⠀⠀⠀⠀⡄⠀⣿⡷⣌⢻⠍⠁
⠀⠀⠀⠀⠀⠀⠀⣴⠻⢡⣿⡟⢥⡰⣿⢻⣿⣋⣤⡿⠁⢠⣿⡇⣼⠀⠀⠀⠀⢀⣼⣠⡶⠋⢛⡾⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠙⢬⣂⢿⣧⣞⠧⣀⡿⠿⣿⡾⠀⣠⡾⣻⡏⢭⣒⢒⣒⣉⣀⣀⡩⠤⣠⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣮⠍⡛⠒⠛⠫⠥⢶⡿⣋⣴⢯⡟⠋⠉⠉⠁⢠⠿⡋⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣟⠓⣲⣾⠷⠛⢇⢜⣮⣁⠤⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉
⣶⣶⣶⣶⡶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⠶⢶⣶⣶⠶⢶⡶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣯⠸⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠲⠾⠟⠉⠉⠉⢻⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠿⠂⢒⡛⢡⡀⠀⢀⡆⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠐⢐⣩⠊⠐⠟⠁⠘⠁⣄⣀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡇⠀⠀⡀⢀⣢⣵⠾⢛⣴⠄⠀⠐⠢⣈⠘⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡗⠀⠀⢀⢠⣂⣰⣾⣿⣋⣁⣀⣈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠾⡗⠀⠀⢀⢠⣰⣼⣾⣿⢿⣯⣽⢿⢿⣿⡯⠌⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠛⠟⠀⠀⠠⡐⣄⣾⣿⡿⠟⠋⣰⠟⣊⠻⠿⠿⣋⠰⠂⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣔⠀⠈⠋⠀⡠⠔⢊⣣⣿⣿⡿⠛⠉⠀⠀⠀⣿⣄⠉⠀⠛⠂⠉⢀⣤⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠂⠀⠀⢀⠤⢒⣡⣴⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣶⣶⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⡤⡤⠤⠤⠀⠀⠀⡠⠐⣈⣤⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠛⠋
⠀⠀⠀⢀⡤⠒⠉⠁⢀⣀⠀⣠⣶⣾⡶⠀⠁⣤⣿⣿⠿⠋⠁
⠀⠀⡴⠋⠀⠀⢀⠀⠩⠛⠀⠛⠛⠋⢁⣄⣿⣿⣿⠋
⠀⡼⠁⠀⠀⠀⠀⢳⡀⠀⣀⡀⠀⢠⣦⣿⣿⣿⡏
⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⢠⣦⣾⣿⣿⣿⡇
⣼⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⠃
⠈⢾⡓⣤⡀⢀⠀⢀⡀⢰⣶⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠻⣿⣶⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣍⣮⣭⣤⣬⣩⣏⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠔⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠺⠛⠳⡀⠀⠆⠠⠔⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢹⠃⣠⠎⠀⠀⣹⣆⡛⠁⣠⠘⡏⠙⠆
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⡀⠀⠀⢰⡿⠲⣄⠀⢴⡴⠋⠀⠀⠀⠉⠨⡁⠈⠀⡸
⠀⠀⢰⡞⣩⠟⡆⠀⣀⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠙⠶⣄⠿⣅⠀⠈⢳⣄⣀⣄⠀⠀⠀⠀⠃⠀⠀⡐⠀⡠
⠀⠀⠈⠳⣤⣾⡏⣶⢀⠿⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⠂⠀⠘⢷⡈⠳⣄⠘⠿⠁⡀⠀⢀⡷⣄⠀⢀⠀⡀⠂
⠀⠀⠀⢀⣴⢙⡁⣇⢰⡦⠶⠀⠀⠀⠀⠀⡇⢠⡟⠀⠀⠀⠀⠀⢹⣄⢸⣷⠀⠀⠀⠀⠈⠁⠈⢶⡀
⠀⠀⠦⠼⠃⡟⠛⠘⢇⠀⠀⠀⠀⠀⠀⢠⠇⠈⠀⠀⠀⠀⠀⠀⠀⠹⣎⠉⠀⠀⠀⠀⠀⠀⠀⢼⠗
⠀⠀⠀⣀⣤⠾⣤⠖⢇⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠻⡆
⠀⠀⠀⠉⠁⠀⠱⡀⠈⢧⠀⠀⣠⠞⠁⢀⡤⠞⠋⠉⠁⠀⢀⣀⣀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⣷⠞⢁⠄⠊⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⠷⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣨⣧⠀⠘⣇⠁⠀⠀⠀⠀⣀⣀⣀⡀⠀⠠⣤⡀⠀⠀⠀⣧⠰⠄
⠀⠀⠀⠀⠀⣠⠞⠁⠘⣇⠀⠘⣦⠆⢠⡴⠛⠉⠈⠉⠛⠷⣶⣄⡀⢀⡀⠀⡷
⠀⠀⠀⢠⠞⣡⣄⠠⢌⣹⡆⠀⠈⣦⢟⣛⣛⡻⠷⣦⣄⡀⠀⠙⠷⣮⣤⡴⠃
⠀⠀⡰⢫⠞⠉⠀⡰⣡⡶⣻⡄⠀⠘⡄⠀⠀⠈⠑⢮⡻⣿⣄
⠀⡼⣥⡃⠈⠁⠀⢲⢯⠞⠀⢱⡀⠀⠸⡀⠀⠀⠀⠀⠙⡌⢿⣆
⢠⠁⣿⠀⠀⠀⢀⡀⠇⠀⠀⠀⢣⠀⠀⠹⡀⠀⠀⠀⠀⢹⠘⣿⡀
⡎⢠⠋⠀⠄⢐⠄⠁⡆⠀⠀⠀⠈⢇⠀⠀⢻⡄⠀⠀⠀⠀⠆⢿⣷⡀
⡇⠈⠇⠀⣀⠶⠂⢸⣣⠀⠀⠀⠀⠘⡆⠀⠀⢻⡀⠀⠀⢀⠌⣶⠏
⡇⠸⠴⣂⠠⢐⡖⣅⡷⣳⡄⠀⠀⠀⠸⡆⠀⠀⢳⡀⠀⢸⠈⣿⡀
⢹⡈⢰⡙⠁⠏⠀⠔⠥⠹⢿⣄⡀⠀⠀⢻⡄⣠⡴⠗⢠⡄⢣⠹⣷⡄
⠀⠳⡄⠹⣇⠠⡌⠸⠂⡄⢻⠶⠊⡳⡄⠀⣛⠁⠀⠀⠈⠀⠀⠳⣌⠻⣶⣤⣤⢖⣶
⠀⠀⠙⢦⡈⠣⠙⣀⠖⠀⠈⠂⠀⠸⡱⠀⠉⠀⢀⣤⣴⣶⡀⠰⡌⢹⡆⠉⠛⣎⢻⣷⡀
⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⠐⠿⡏⠁⠉⠁⠀⠈⠒⠋⠀⠀⠈⠳⣝⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠦⠄⠀⡰⣸⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⡌⠳⠃⠀⠀⠀⢠⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⠈⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡷⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠴⢣⠕⠊⠉⠊⠷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠀⣀⣀⣤⣤⠄⠀⣼⣿⣷⣄⠀⡀⣴⡞⡁⠀⣽⠀⠀⠀⠀⠄⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠿⢛⣩⣥⣶⣾⣷⠦⠉⣹⠛⠉⢹⠸⣧⣴⠀⢰⡇⠀⡀⠀⠀⠀⠀⠠⣙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢱⡌⣶⣦⠉⡁⠉⡥⠀⠀⠀⠀⠀⢐⢸⡇⢻⢿⡆⠀⣸⠃⠈⣱⠄⠀⢀⣤⣬⣼⣧⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡿⡼⣿⣯⡿⡻⡀⣶⠘⠀⠀⠀⠀⠘⢸⣿⡌⡿⣿⣆⠀⢇⠀⢉⣀⠀⢛⡛⠛⠛⠛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⣾⠱⢱⣿⣿⣃⢧⢱⣿⢰⠃⠀⢀⠀⠀⠀⠘⣧⠙⢉⣬⣧⡘⢦⣌⣻⣿⣿⣶⣶⣤⣤⡿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣍⠸⡿⠃⡟⣼⢿⣿⣿⣸⡏⢸⡇⠀⠘⢠⠀⠀⣀⠙⢿⣿⣿⣿⣿⣦⣝⢛⢿⣿⣿⣿⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⢠⣌⢋⡁⠋⠃⠘⢧⡔⣶⡠⡁⢦⡘⢿⣦⡙⠿⣿⣿⣿⣿⣷⣄⠉⠻⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣿⣿⡽⣄⠀⢦⣈⡻⣎⠻⢞⢿⣟⣦⡙⢿⡦⡈⠻⣿⣿⡿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠻⣷⡹⣷⣌⢻⣿⣮⢧⡑⠁⠙⠷⣻⣆⣹⡎⠞⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⡀⠀⠣⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠠⠀⠀⣠⠀⡟⢡⠐⡄⠀⠀⢀⠀⠀⠀⠀⠀⡗⢨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⠂
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⡀⠈⠁⠀⡀⠀⡆⠈⠀⠟⢥⠀⢀⠀⡰⠃⠀⠀⠙⠠⢶⣀⠀⣆⠀⢱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⠛⠁
⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠁⠀⠀⠀⠀⠚⡧⢼⡠⠀⠀⢀⠀⡀⠠⡄⠀⠶⣤⠀⠀⠂⠈⢓⡅⠀⠱⣬⠿⠀⢰⠙⢆⠀⠀⠀⠀⠀⠀⠀⢠⡼⠤⠄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣈⡠⠂⢀⠀⢠⠋⠉⠀⠀⠀⣇⢀⣇⡀⠀⠸⢿⡦⠀⠀⠘⠫⣞⡏⠈⢧⢰⡄⠱⣀⡕⠀⠀⠀⢀⠔⠲⢿⢠⠓⠐
⠀⠀⠀⠀⠀⠀⠠⠇⢀⠀⠀⢻⠀⠀⢰⠁⢛⠃⠀⢱⡖⠂⡖⢹⡞⠈⢳⡀⢰⠀⠤⠤⢤⡰⠏⢳⡈⠀⡼⢠⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠆⠈⡠⠀⡏⡧⠤⠃⠘⠁⣴⠀⠉⠘⠀⠀⠀⣈⡡⣠⢎⠉⠊⠀⡏⠀⠀⠀⠀⢀⡜⠣⠀⣔⡠⠊⠁⣄⢀⠰
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⣼⡙⠗⠀⠐⡇⢁⡄⠀⡀⢴⠁⢼⠀⠀⡀⠀⠀⠈⠃⠈⢸⡄⠀⢀⠟⡀⠐⠃⠀⠺⠿⢧⡴⢻⢡⡞⢧⡀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣤⠀⡈⣴⠀⡠⠴⠁⠈⢐⡶⠊⠈⣀⣾⠃⠉⢿⠍⢀⠇⢀⠄⠈⢃⠛⠋⠚⡇⠀⠁⠐⠁⢀⡞⢀⡞⢸⠛⣤⣹⣿
⠀⠀⠀⠀⠀⠀⠀⢄⡤⠂⠀⠀⠈⠄⣇⢸⠀⡗⡂⠐⠀⠏⠁⠀⠀⣬⢼⣶⡂⠀⢠⡁⣴⡇⠀⠀⢸⠀⠀⢸⡣⢄⡁⠨⢷⠯⠠⠞⠳⠏⠈⢉⠀⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠸⠔⡇⠃⠀⢇⢰⢀⢠⡀⠀⠈⠈⠉⠁⠈⠁⠀⠀⠀⠀⠘⠀⠀⠘⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⠀⠚⢤⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⣠⠀⠀⠀⠉⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠬⠤⠤⠈⠀⠛⠒⠁⠀⠀⠀⠤⢿⣀⠀⣤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠈⠑⠠⠀⠆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣆⣴⠀⣀⣔⣀⠃⠰⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡉⠉⠀⠾⠀⠀⠁⠉⠉⠉⠓⡶⠀⠀⠀⠐⠦⠇⣈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠊⠀⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⠀⠰⡀⠠⡤⠀⢀⣀⣀⣀⡀⠀⡀⠐⠠⣤⡆⠠⠀⠀⢀⠀⠀⢠⣄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣍⡘⢛⡋⢤⢛⣇⠈⠉⣼⡖⣀⡂⠠⢠⡀⣀⣄⠀⢒⣒⠶⠒⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠉⠹⠿⠶⠾⢯⣄⣉⡁⠉⠀⠂⠀⠨⠁⠨⠀⠀⠀⢀⣄⠀⠀⠈⠁⠀⢠⡄⠀⠀⠚⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠊⠀⢰⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠘⠛⠲⠶⢾⣶⣤⣄⣅⣀⠀⣼⠀⣒⢲⣶⣂⡻⠤⠀⣾⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⢀⠷⢰⢀⣠⡤⠄⢸⠟⠀⢀⣄⣥⣥⣾⠀⠀⠀⠀⠐⠉⠍⣽⠛⠓⠒⠶⠤⣤⡛⠛⡁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⢐⠸⠿⢾⠉⠉⢀⣺⣁⠥⠮⠐⠒⣶⡆⠋⠽⠏⠉⠁⣀⠁⠀⠀⠰⠎⠠⠀⠀⠀⠀⠤⠀⠸⡃⠀⣰
⠀⠀⠀⠀⠀⢀⡀⠀⠈⡀⠐⢊⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠹⠶⢶⣦⣄⣀⣅⠀⠀⢘⠋⠀⠀⠀⣤⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⡀⠙
⠀⠀⠀⠀⠐⠀⠁⠀⠊⠅⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠶⠶⠶⢧⣤⣤⣀⠆⠀⠀⠀⠀⠶⠶⠶⠖⠂
⠀⡀⠀⢂⠄⠀⠈⠡⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠁⠀⠀⠈⣀⠂
⠰⠃⡄⠈⠔⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⣿⡏⠟⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡳⢔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣹⡿⢏⣼⡇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⣠⣴⢞⣫⣵⣾⣿⣿⣡⣞⣵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⣱⣿⣿⣿⣿⣟⡀⢩⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣯⣤⠀⠀⠀⠀⣴⢒⡴⢠⣿⡿⣼⣿⣿⡿⠛⠉⠉⢡⡬⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⠛⢻⠠⣦⢴⡆⠀⠀⠙⢩⣧⠞⣻⣿⣿⣿⡟⠀⠀⠀⣦⣬⡆⢸⠛⣢⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠺⣳⣧⢢⡾⠘⣇⠀⠀⢠⣿⠇⣰⣿⣿⣿⡿⠀⠀⠀⢠⡇⢸⡆⢨⣶⠻⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠶⠘⠻⣿⣿⣶⣠⡿⠋⢰⣿⠟⠛⠛⠁⠀⠀⣴⣿⣻⡿⢋⠰⠞⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠙⠖⠺⣞⣚⢿⣿⡟⠓⢶⡿⠟⠀⠀⠠⣤⠖⠛⣿⡿⢛⣘⡾⠲⠛⠁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢶⠗⡁⠈⠉⣯⢀⡛⢛⣋⠹⠇⢶⣆⣶⠂⠟⢙⣟⢻⣃⢸⡉⠱⢈⡁⢱⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣿⣈⡉⠻⣯⡉⠠⠿⢟⡃⠙⣿⠛⠛⠛⣻⡛⢁⣛⠾⠥⠉⣹⠿⠉⣍⣼⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠍⠷⠿⣌⡄⠀⠠⠗⠑⠀⣨⣻⣮⠉⠀⠀⠀⠉⠸⣞⣩⠀⠐⠐⠇⠀⠰⣨⡾⠻⠏⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣿⣿⢟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡤⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠿⣿⣿⡇⣇⢈⡇⠀⠀⠀⡾⢤⣾⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⣣⡔⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣳⣤⣤⣤⣤⣼⣿⠿⣡⡾⠁⡀⠀⠀⢑⣬⡓⠋
⠀⠀⠀⠀⠀⠀⠀⣼⠞⠛⣯⢡⣆⠀⣼⠀⠀⠀⣾⣍⡥⢄⣤⣾⡿⢛⣭⣶⣶⣷⣶⣾⣾⠟⠀⠀⣹⠀⢰⡎⢩⡟⡓⢾⡀
⠀⠀⠀⠀⠀⢠⣄⢁⠘⠧⢤⣂⢻⣿⣿⡄⠀⠀⣠⣼⠤⠲⣿⣫⣾⣿⣷⣿⣿⣿⣿⠛⠹⣾⣯⣵⣿⣿⣿⢁⣢⠴⠏⣀⢡⡄
⠀⠀⢀⣀⣄⣘⡿⣃⡉⠀⠺⣧⠝⣿⣿⣧⣴⡾⠛⢁⣴⣿⣿⣿⣿⡿⠋⠁⠀⠀⠙⠃⠀⠀⠀⣠⢿⣿⡟⢤⡟⢂⠈⣈⠹⣟⣀⣄⡀
⠀⠀⠘⢍⡟⣽⢧⡌⢹⡶⢴⡎⣀⠿⢷⣬⣻⠦⣴⣿⠿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡤⣾⣡⣴⠿⢇⡈⡶⢴⡾⠉⣤⢿⡿⡏⠟
⠀⠀⠀⠀⠀⢻⣖⠂⠀⣻⢂⠰⠿⠶⠆⣄⠛⢠⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠘⢃⡔⠷⠾⠦⢐⢿⠁⠀⣲⣾⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠈⠁⣐⣿⣄⣼⡟⠿⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠾⠛⣿⢄⣾⣳⡀⠉⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣿⣿⣿⣟⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⣿⣿⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⢻⡿⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠀⣿⣿⣿⡇⢸⣿⣷⣦⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⣿⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⣀⡀⢀⣸⣇⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⠟⠀⠀⠀⠀⣿⣠⣾⠟⢋⣉⣉⣉⡙⠻⣷⣄⠀⣿⡏⢸⣿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⣿⣿⣿⡇⢸⣿⡏⠀⠀⠀⠀⠀⣿⡿⢁⣾⣿⣿⣿⣿⣿⣷⡌⢻⣧⠘⠇⠸⣿⣿⠇⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣿⣿⣿⡇⢸⣿⣷⠀⠀⠀⠀⢠⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣷⠈⣿⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⣤⣤⣤⣤⣾⣿⣿⣷⡄⠀⠀⠈⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠿⠛⣛⣛⠻⢿⣿⣿⣿⣿⣆⠀⠀⠹⣷⣌⠻⣿⣿⣿⣿⣿⠟⣡⣾⠟⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠃⣴⣿⣿⣿⣷⣄⢹⣿⣿⣿⣿⡆⠀⠀⠈⠻⣷⣤⣬⣉⣥⣤⣾⠿⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣿⠀⣠⣤⣤⣼⣧⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣄⠹⢿⣿⣿⠿⢃⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠙⠛⠛⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠶⠶⠶⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠈⠉⠀⠀⠀⠀⠀⠀⣰⢲⠀⠀⠀⠀⢠⡖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡼⠀⠀⠀⠀⢸⡀⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⢠⠄⠀⢀⣤⠀⣴⠋⡟⠀⣿⡇⡼⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⠇⡿⢰⣿⢸⣷⡼⠙⠿⠃⠀⢀⣀⣀⡤⣄⠀⠀⠈⢦⢠⡏
⠀⠀⠀⢀⡤⠀⣠⢶⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⣶⠀⠀⣿⢀⣿⡄⣠⠟⠿⠃⠉⠀⠀⠀⠀⢀⡼⣻⣿⠸⠻⠆⠀⠀⢠⡟
⠀⠀⢀⣾⠁⡴⢣⠏⠀⣰⠇⡟⠀⠀⠀⢰⡀⢠⢿⡇⣸⢿⠞⠉⠋⠁⠀⣀⣀⣤⣤⣀⣠⡖⢋⣴⠋⠀⠀⠀⠀⠀⣠⠏⢱
⠀⠀⣼⣏⣼⡷⠋⠀⢰⡟⢰⢇⡴⣶⠀⣿⣧⠎⢸⡟⠃⠀⠀⠀⣠⡶⠛⠉⠁⣠⣴⢟⠁⢩⡿⢧⣀⠀⠀⠀⠀⣴⠏⠀⣸
⠀⠀⠘⣿⠟⢁⣄⠀⣾⢃⡞⣼⢃⣿⣸⢹⡏⠀⠉⠀⠀⠀⢀⡼⠋⠀⢀⣴⡾⢏⢕⠅⣴⠋⠀⠀⠙⣧⠀⠀⢰⡏⠀⢠⡇
⠀⠀⢸⡿⢠⡏⢈⢳⣿⠞⢰⣿⡾⠉⠁⠀⠀⠀⠀⠀⠀⢸⢧⠀⣠⠖⣹⢿⣴⣡⢪⡞⠁⠀⠀⠀⢀⣿⠀⠀⢸⣇⣠⡞
⠀⠀⣿⡇⢸⡇⡜⢸⣿⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⢞⡷⢾⣔⢻⣿⠿⠋⠀⠀⠀⠀⣠⠞⡿⠀⠀⠀⠉⠁
⠀⠀⣿⡇⢸⣿⠁⡎⠙⠋⠀⠀⠀⠀⠀⠀⣠⠤⠤⢖⡿⢾⣿⡞⣡⢏⡬⣻⢄⡀⠀⠀⣀⣠⣴⡯⠊⠁
⠀⠀⠈⠓⠋⠻⠖⠁⠀⠀⠀⠀⢀⣠⠴⠚⠁⠛⠓⠉⣠⣿⣏⣞⡵⣻⡖⠋⢈⡿⢠⡞⣋⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠛⠠⣄⡀⠀⠀⠀⣰⠋⠈⣻⠿⠂⠈⠁⢀⡞⠀⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣄⢸⣿⣆⠄
⠀⠀⢧⠀⢠⠞⡆⠀⢀⡏⠀⠀⠀⠀⠀⢹⡆⢀⡼⢃⣴⣿⠟⠀⠀⠀⠀⠘⢧⠄⢑⡄⠀⠀⢀⢀⡆⢀⢸⣆⣿⡞⠛
⠀⠀⠈⠣⣿⡴⠇⠀⠈⣇⣄⠀⠀⠀⢀⡞⣠⢞⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡇⠀⠀⣿⣸⠃⣼⣼⠿⠁
⠀⠀⠀⠀⢿⡀⠀⠀⠀⣿⣿⠦⣀⠀⣿⠕⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠊⠀⠀⢸⣿⣿⣀⡏⠉
⠀⠀⠀⠀⠸⣇⠀⠀⠀⡇⠙⢷⣄⡀⠈⠛⠅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⠀⢸⢸⠀⠈⠛
⠀⠀⠀⠀⠀⢻⣆⠀⠀⠳⣄⠀⠙⠻⢶⣤⣀⢈⣧⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡇⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠙⢷⣄⠀⠀⠈⠙⠻⠯⣤⣄⣀⣀⣀⣤⡶⠟⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠛⠶⣤⣀⣀⣀⠀⠈⠉⠉⠉⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠉

⠀⠙⣄⠀⠀⠠⡄⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣇⠀⠀⠀⠀⠀⠀⠀⠸⠥⣽⢧⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠉⠢⠀⢀⣤⣄⡀⣻⣆⣀⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⣰
⢀⡀⠀⠀⠀⠀⠀⠀⡠⣤⣅⣄⣼⠀⠀⡀⠀⠈⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢀⠉⠁⠀⠙⠉⠀⠀⠀⠀⠀⠂⠀⠀⣠⠟⠶⢘
⡞⣂⠀⣀⠀⠀⠸⠬⠄⠀⢏⠙⢿⣧⣄⡇⠀⠀⠀⠀⠀⢀⣗⣫⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢠⠀⠀⠀⠀⠀⡌⠄⢱⣿
⠑⠉⠀⠛⢯⠂⠀⠀⠀⠀⠀⠨⢤⣿⣿⠇⡆⢀⠀⢠⠀⠀⠈⠙⠁⠀⠀⠰⣿⣷⠀⠀⠀⠘⠆⠀⠙⠉⠀⠀⡦⠀⠀⠀⠀⠃⠰⠎⠓
⠀⠀⠀⠀⠁⠀⠄⠀⢀⡀⠀⠀⠀⠿⣿⡖⡱⠏⠀⠘⠃⠀⠀⠀⠀⠈⠀⠀⠙⠉⠀⢀⠀⠀⠑⢀⠄⠀⠀⡀⠀⠀⠀⠰⠦⡀⠀⠈⢢
⣴⣶⡷⠀⣀⣄⠀⠀⠘⠓⠀⠀⠀⠚⠉⠀⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⢀⠀⠀⠑⡀⠈⢻
⢿⣇⠀⠈⠉⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢰⠌⠁⠀⠀⠀⣾⣥⠀⠀⠀⠀⠘⠄⠀⣄⡀⣧⡄⠈⠑⡄⠁⠠⠔⠀⠀⠻⠇⠀⠀⠉⢲⡀
⡄⠈⠀⠀⢀⡀⠈⠁⠀⠀⢷⡄⢀⠀⠀⡰⠀⠀⠀⠀⠀⠹⣼⠃⠀⢀⡠⠀⠐⣦⣿⣿⣿⣷⠀⠀⠀⠐⠁⠀⢀⠀⠀⠀⠀⠀⠀⣸⠉
⠠⠄⠂⠐⠋⠍⠀⠀⠀⢤⠀⠐⠊⢀⡜⠁⠀⠀⢀⣀⠀⠈⠁⠀⠀⠏⠀⠐⠲⠾⣿⠟⢽⣻⡇⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⠃
⣀⠀⠀⡀⠁⢒⣤⠀⠀⠀⠤⠄⠠⠚⠀⠀⠀⠈⠰⣩⡭⡖⣢⣀⠀⠈⠀⢰⠀⡀⠀⠛⠛⠋⠀⠀⠀⠀⢰⡏
⠲⠍⢻⣻⠿⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡘⢹⠃⢵⣿⠷⣬⠀⠀⠈⠁⠰⠇⠀⠀⠠⡀⠀⠀⠀⠀⠸⠇⠀⠀⡃⡀⠐
⠀⠀⡜⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⠀⠎⣹⣉⡘⠅⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠸⠀⢀⡗⠁⠀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠊⠋⠁⠾⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⡄⢀⣴⠀⠀⠀⠀⠀⠀⡈
⠈⠀⠀⠀⡄⢀⣤⠀⠀⢳⠀⣰⣿⣟⠀⣼⠂⠀⠀⠀⠀⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠛⠁⠀⠀⠀⠀⢀⠀⠀⠂⢀⡀
⠀⠀⠀⠀⢰⡘⠻⠂⠀⠀⠀⢻⣿⠿⠛⠃⠀⠀⢤⡄⠀⠀⠀⢁⣀⠀⠀⠀⢠⠀⠀⠀⢀⣓⠀⠹⠀⠀⠀⠀⢌⠸⠃⡾⣿⠓⠀⠈
⠀⠀⠀⠀⠀⢠⠆⠀⠈⠀⠀⠀⠁⠀⢀⠆⠀⠀⠀⠀⠀⠓⠀⠀⣀⡀⡀⠀⠈⠃⠀⠀⠉⠁⠀⠀⠀⠀⠀⢿⠄⣞⠙⣋⠁⣗⣲
⠐⠀⠄⠰⠂⠀⠀⠀⠀⠀⡐⡞⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠰⣿⣡⡷⠂⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣔⢿⣹⣁⣿⣹⠇
⠀⡇⠀⠀⠀⢰⣶⣾⠁⠀⠌⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⣠⣶⡄⠀⠀⢸⣇⠀⠈⠉⠑⠓⠁
⣼⡗⠂⠀⣻⠾⠟⢿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠀⣱⢶⡃⠀⠀⢸⣿⡀⡀⠀⠀⡀⠀⠀⠈⠐⠲
⠘⠛⢄⠀⢉⡀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠙⠷⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣦⠈⢿⢧⣤⣿⣼⣿⠷⠶⠂
⠀⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⢤⡀⠦⢀⡐⣄⠀⠀⠀⠀⠀⡀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣼⠞⠙⠉⠉⠉⠀⠀⠀⠀⢀
⠀⡇⠀⠀⠘⣧⡄⠀⠀⠀⠀⠀⠘⢁⣄⡏⣥⣭⠀⠀⠀⠀⠀⢰⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⣀⠀⠀⠀⢠⠖
⢠⡶⣃⠀⠀⠙⢿⠀⠀⠀⠀⠀⣞⠻⠭⠟⢢⡄⡅⠀⠀⠀⠀⠈⠁⠀⣤⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠁
⠀⠇⠉⠀⠀⠀⠈⢆⠀⠀⠒⠂⡩⠀⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣄⢠⣄⠀⠀⠀⠀⠖⠀⠀⠀⢀⣀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣤⣴⣞⣋⠁⠒⡶⠴⣶⠠⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠶⣞⣉⣒⣒⣛⣫⣽⠷⢀⣸⣷⣾⡝⠛⠚⣶⠓⠺⠄⣀⣶⡶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⣴⡶⠻⡟⢉⢴⡾⠻⢤⣴⡴⣷⣿⣿⣿⡊⢦⣽⣭⣭⣥⣤⣤⣹⣍⣓⠾⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⡀⠈⢷⣤⡿⢾⢿⡷⢷⢞⣫⣾⢏⣇⣀⣌⡹⠢⣿⡟⠛⡣⡘⣿⣿⠟⠲⡿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡿⣧⠉⢭⣶⡾⣿⣄⠊⣨⣃⣀⣼⣽⣠⣽⣿⣥⡏⢀⣴⣿⣶⣶⣿⠿⢯⣓⣲⡶⠷⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠛⣿⣃⣼⡇⡜⠿⣿⠿⣿⣿⣟⠋⠠⠭⣽⣷⣾⣧⣾⠋⣿⠿⢿⣼⣦⣾⣿⡿⢟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠁⣰⣿⣿⡮⠍⠳⡶⣏⢀⡡⢏⣿⠇⠨⠛⡿⢿⡳⣅⡉⢝⡿⠀⠈⠛⢉⣻⣿⣷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡝⠋⡟⠠⠙⣋⣿⣧⣡⣿⣦⣴⣾⣤⢿⣶⡾⡶⣬⠇⠀⠤⠴⠾⣿⣶⣶⡴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠱⢤⣭⠛⣿⢋⣾⣿⣿⣿⣍⠐⠒⣣⣿⠞⠃⠀⠀⠀⣀⣤⣬⣽⠧⢸⠟⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠴⢟⢹⣿⣷⡞⡟⣹⣿⣿⣿⣠⣹⣿⣁⣾⠀⠀⠀⠀⠘⢯⡉⢸⡿⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡮⣤⣹⡱⡈⢻⡣⡙⠿⠞⣿⣽⠷⣤⢿⣍⠀⠀⠀⠀⠀⠀⠉⠉⠁⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠞⣿⣷⣧⡜⠑⡦⣍⣁⣼⡟⢾⣁⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡾⢁⠢⣉⣺⡾⡃⠌⠉⠁⠠⣤⡝⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⣶⣭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⣿⣶⢿⣧⢰⠟⠀⠀⡦⠀⡈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣶⣶⣉⣶⣿⠋⠀⣴⠀⣇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡿⠆⣠⣴⣿⠆⠀⠀⠀⠈⠦⣀⡀⠉⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⣆⢸⡟⠃⣢⠃⠀⠀⠀⠀⠈⠹⡛⠶⣦⣖⣈⠉⠁⠀⠀⠀⢀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⡙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⡀⢈⠉⠿⢷⠟⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠂⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⣀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣀⠁⢙⢹⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⢘⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠓⢌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⢀⣈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢀⣤⠉⠀⣬⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠾⠦⣤⣀⡀⡆⠴⡊⠀⠀⠀⠀⠀⠀⠀⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⣄⠀⠠⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠖⠋


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⡴⠒⠒⠒⠒⠜⠉⠈⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠛⠳⢤⡤⠀⠀⠠⠀⠠⠇⠀⠀⠠⠤⠤⢀⡴⠒⠒⢂⣺
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣀⠀⠉⠀⠀⣠⠴⢿⣯⡄⠀⠀⢠⠉⣦⠀⠀⠀⠀⠀⠀⠀⢀⠀⡻⠶⣤⣤⣤⡄⠀⢠⣤⠤⡀
⠀⠀⠀⠀⠀⠀⢀⢠⣽⠃⠀⢹⣷⠀⠀⠀⠁⠐⠀⣟⣇⣠⢤⣔⣛⣓⢶⣤⣀⠀⠀⠀⢀⠃⠀⣸⣿⣾⡄⠉⡉⠉⠉⢙⢿⣇
⠀⠀⠀⣀⣴⣾⣷⣿⣿⣆⣂⣼⣿⡆⠀⠀⢧⣠⣤⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⣄⡀⣿⠀⢠⣷⣿⡧⣻⠀⡂⠀⣸⠉⢸⣿⣧
⠀⠀⢠⡿⠿⣰⣿⣿⡈⣿⣿⣿⣿⡇⠀⠀⢾⣿⣧⣿⣋⣠⣼⠟⠋⠉⣉⣙⢿⣿⣿⣿⣿⠀⣼⢿⣿⠋⢺⠀⠁⠀⣷⡀⣹⣿⣿
⠀⠀⠀⠀⠘⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⣶⣾⣿⣿⣿⣿⡟⠁⠀⠠⠜⣓⣮⡅⢹⣿⣿⣿⣧⣻⣷⡈⢠⣿⣾⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⠀⠀⢠⣷⢿⣫⢞⢿⠀⣿⡿⠿⢿⣿⣯⣿⣾⠿⢛⣉⠩⠔⣶⣿⣼⠁
⠀⠀⠀⠇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⠀⠀⠠⢷⣿⡿⢻⠼⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠠⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣷⡿
⠀⠀⠀⠀⠑⢄⡱⠈⢛⣛⣿⠟⠁⠀⠈⠉⠉⠉⠉⠉⢃⠀⠀⢀⣧⡎⠃⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠈⢎⠋⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠭⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣶⣛⠋⠙⢟⣿⣶⡄⠀⠈⠁⠈⣀⢀⢀⡀
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠠⢄⢄⣼⣿⡏⠁⠀⠀⠈⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⠃⠀⠁⣤⣿⣿⡏⠁⣿⣷⡄⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠦⠤⠎⠹⣿⣿⡇⢸⣿⣿⡗⠀⠀⠀⠀⡄
⠀⠀⠀⠒⠂⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠒⠂⢀⠒⠒⠐⠒⠈⡃⠀⠀⠈⢀⠙⣿⢡⡼⢿⢿⡛⢺⣅⠘⠉⡃
⠀⠀⠀⣄⠀⠤⠤⣤⡤⣀⣀⣤⣤⠤⡤⠀⠀⢣⡤⠄⠤⣤⣤⣜⣦⣠⣴⠦⢾⠁⠀⣷⡀⠀⠈⣻⣿⣢⣴⡇
⠀⠀⠀⢩⠀⠀⠀⠀⡶⢈⠉⣡⡀⡾⠇⠀⢀⣤⣿⡎⢶⣰⣤⣿⣦⢟⠉⠀⠀⠀⠀⡟⠻⣆⠀⢹⡟⢿⣿⣿⡟⡉⠉⠛⠉⠍⠛
⠀⠀⠀⡾⠀⠀⠀⠀⠘⠃⢀⡴⠛⠀⠀⠀⢨⡟⣛⡶⢿⣾⣯⣿⠷⡈⠁⠀⠀⠀⠔⠁⠀⢟⡀⠀⠂⣿⣿⣿⡦⠕⠒⠀⠀⠀⠒
⠀⠀⠀⠷⠶⠶⠷⠶⠦⠶⠏⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢶⣄⠀⠀⠀⠿⠧⠂⠈⢻⣿⣿⠧⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⢰⠘⡇⠀⠈⡱⠊⠁⠀⠀⠀⠀⢀⣠⣾⣿⡤⠄⠀⠀⠀⠀⠀⢴⣷⣿⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⣼⣂⠷⣌⡀⣿⡀⠀⢀⣀⣠⣶⣿⣿⣿⣯⣉⠢⢀⠀⠀⠀⠀⠀⣸⣿⣿⡦⠢
⠀⠀⠀⣶⣴⣦⣴⣶⣤⣤⣤⣤⣴⣤⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣥⣤⣨⣲⣶⣴⣾⣿⣿⡟⡛⠣⠄⣀⡀⠠
⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣾⡿⣿⣿⣿⣿⣷⣦⣤⡀⠙⢚
⠀⠀⠀⣟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡝⢯⢉⣨⠇⠁⠀⠸⠀⢘⡛⣿⣿⣿⣤⣿⣿⣓⣈
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⣡⡿⠟⠋⠠⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠁⣿⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠅⠀⠰⠞⠋⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣿⡏⢻⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⠶⠋⣿⣿⣿⣿⡿⠿⣧⡝⠿⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡇⣸⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⠛⠀⢀⠉⠀⠀⣠⣿⠇⠀⠂⠀⡀⠀⠘⠃⠰⢀⣀⠀⢀⡀⠈⡄⠐⠀⠀⣠⡼⠁⣿⡝⣿⣿⣿⣿
⠀⠀⠀⣭⣴⢿⣿⣿⣿⣾⠛⢤⡖⠊⠀⠀⠀⣺⡙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠩⣿⠾⠋⠡⠀⠀⢀⣾⣿⣇⢠⣼⣼⣿⣿⣷⣿
⠀⠀⠈⣿⣿⣿⢧⣬⠝⠻⣷⣎⠓⣦⣴⣶⣌⣿⡿⢄⡀⠀⢀⠀⠀⠀⠀⠀⣠⡼⢿⢛⡢⠠⢤⣾⣿⡷⣾⣿⣿⡟⠹⢿⡿⠩⢈
⠀⠀⢸⣿⣿⡏⠀⠈⠷⡄⠈⢻⣿⣿⣿⣷⣼⣿⣽⣿⡗⣲⠮⣟⣛⣋⣋⣒⣳⣤⣤⣴⣅⣰⣿⣿⡿⢷⣿⣷⣿⣽⣷⣿⣿⠀⠸
⠀⠀⠘⣿⣸⠇⠀⠀⢀⡅⠀⠀⠙⡿⢛⣽⣫⢽⣿⡻⢿⣤⡿⡿⡟⠛⠿⠿⣿⣿⣿⣯⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⡋⣿⣄⣠
⠀⠀⢰⡿⠁⠀⠄⣠⣿⣷⠞⠛⠛⣷⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⢻⣡⣿⣿⣿
⠀⠀⠀⠣⣴⣤⣾⣿⣿⠧⠴⠤⢦⠽⠶⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉
⠀⠀⠰⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢴⣶⣤⠀⠀⠀⠀⣀⠻⠀⠀⠀⠀⠀⣤⣾⣿⣷⣦⡀
⠀⠀⠀⠀⢂⣽⠄⠀⠀⠀⠀⠀⠈⠲⣯⢆⠀⠀⠀⠀⠀⣴⣿⣿⡆⠀⠀⢻⣽⠏⠀⠀⠀⠀⠴⠎⣔⠀⠀⠀⠈⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢰⠇⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠀⠀⠀⠀⠀⠀⠴⠀⠀⠐⠂⠀⢭⡄⠀⠀⠀⠙⠛⠿⠛⠋
⠀⠀⠀⢰⢯⢟⡈⢇⠀⠀⠐⠀⠀⢀⡔⢀⡀⢴⣴⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡎⢀⢀⠀⠀⠀⡀⠙⠂⠴⢂
⠀⠀⠀⠸⠀⡘⠿⠞⠁⠀⠀⠀⠀⡸⠀⠀⣀⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢤⠰⣅⠈⠗⠀⠀⠀⠹⣧⠀⣶⣿⡟⠂
⠀⠀⠀⡀⡄⢀⢠⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠤⢙⣤⣥⣀⠀⠀⠀⠀⠀⠰⠈⠋
⠀⠀⠀⠀⠂⠘⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠿
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣔⡷⣿⣄⠀⠀⠀⠢⠤⠂⠀⠀⠀⠀⠀⠀⠀⣦⢢⣄⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠲⠀⠀⢹⡍⠆⠀⠀⠸⠿⡿⠋⠀⠀⠀⢣⡠⠀⠀⠰⣿⠇⠀⠀⠀⠀⠁⠀⠀⠀⠪⡽⠿⢿⠃⠀⠀⠤⡀⠀⠈⠀⠁⠐
⠀⠂⠀⠀⠀⢠⣾⣗⠀⠀⠀⠀⣦⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠶⠉⠀⠀⢀⣀⣄⠀⠀⠈⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠢⢹⣧⡞⠀⠀⠀⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣟⣷⣆⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠃

⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣤⣤⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠉⠈⣿⣿⣿⣿⣿⣿⣦⠙⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣷⣽⠋⠙⠿⣿⣿
⠀⠀⠀⠀⠀⣿⠟⠋⠀⣻⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢰⣿⠟⠏⠉⠛⠁⠘⣿⣿⣿⣿⢻⣿⠄⠀⠀⢹⡟
⠀⠀⠀⠀⠀⡿⠀⠀⠀⣿⣿⠟⠉⢀⣰⡄⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⢠⠈⠻⣿⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⣾⣿⣿⣿⣷⠀⠀⠀⠀⠛⣿⠠⠀⣰⣾⣿⣶⣧⡸⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⣿⣿⣿⡏⠀⠀⠀⠀⡀⠉⠻⠀⢿⣧⣛⣿⡟⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢰⡄⠲⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠉⠋⠂⢠⠏⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠠⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⣼⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣿⠇⠀⠀⠀⠀⠀⢀⠀⡁⠀⢰⠀⠈⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣊⡞⠀⢀⡶⢀⣰⡿⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⣀⢠⡿⢁⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣧⡀⠀⠀⢀⣼⣿⠟⣻⠇⠙⠉⠈⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠁⠚⠛⠛⠁⠐⠠⣴⣾⣿⣿⣿⣤⣴⣿⠿⠻⠞⠁⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠿⣿⣿⣿⣥⠀⠁⠀⠀⠀⢀⣾⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠿⠆⠀⠀⠀⠀⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⣠⡆⢲⣶⣷⣤⠦⣤⡀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⡎⣼⣿⣽⠀⠈⠇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣿⣿⡿⢿⣦⡀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣟⡀⠈⢉⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣿⡤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢄⣷⣆⣠⠏⠀⠙⢷⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⢶⡶⠶⣶⣾⣿⣿⡏
⠀⠀⠀⠀⠸⠶⠄⢶⡯⠁⠀⠶⣿⣶⣹⣷⡏⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⣠⢄⣠⣤⣤⠤⣾⣿⣷⣶⡤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠳⣾⣿⣿⣿⣿⣿⢧⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⣴⠟⠉⣀⣠⣶⠛⠟⣿⣿⣿⣓⣀⣼⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⢋⣿⣿⣿⡏⢨⠛⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⣼⠿⠞⡫⠟⣯⡷⠟⠛⠛⢿⢿⡏⠉⠙⠿⢿⣷⡖⠚
⠀⠀⠀⠀⢀⠀⣠⡴⠂⠀⠀⠸⣏⣿⣿⡟⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⢀⠐⠀⠀⠀⠉⠀⠀⠀⠀⢨⢸⣧⠀⢰⡄⠤⣿⣿⠃
⠀⠀⠀⠈⠁⠀⠀⣤⣀⢠⡀⢠⣼⣿⣿⡇⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠷⠄⠀⠀⠀⠀⠀⠀⠀⠻⠀⣿⠀⠀⡷⠀⠿⠟
⠀⢀⠀⠀⢀⡴⢷⣻⡿⣿⣿⣿⣹⣽⣿⡟⢮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠘⣇⣿⠗⠶⢷⣤⡀
⠀⢀⣠⣾⣟⣿⡂⣹⣿⣿⡟⠋⣠⣿⣿⡟⠀⡷⠀⣀⢀⠀⠀⠀⠀⢶⡀⠈⠀⠀⠀⢠⡀⣀⠤⠒⠊⠀⠘⠉⠀⢸⣧⣷⡄⠀⢸⡌⣻⣆
⠀⠈⢿⣟⣻⣿⣧⣿⣿⠋⣹⣿⣯⣽⣿⣷⡀⢢⠀⠈⠉⢠⣤⣴⠖⠂⠁⠀⠀⠀⠉⠹⡗⠀⠀⠰⠦⠶⠖⠒⠒⢺⣿⠿⠷⠶⢼⠄⠘⠛
⠀⠀⢿⢯⣹⣥⣿⡿⠃⠀⣧⣸⣿⣿⣿⣏⡀⠠⣷⣾⠖⣤⣉⡙⠋⠀⠁⠀⠀⠀⠀⠀⢆⣀⠤⠀⠀⢘⣀⣤⠀⣨⣿⣀⠀⠀⠰⡆
⠀⠀⠙⠉⣠⣿⣍⡁⠀⢺⣥⣿⣿⣿⣿⡟⢹⣤⣿⣿⣶⡤⠈⠀⠀⠤⠀⠀⠀⠐⠶⠒⢿⠃⠀⢠⠾⢟⣉⣀⡀⢹⣿⠉⠉⠐⠤⠀⠂
⠀⠀⢀⡾⠋⠀⠨⠿⠛⢿⣽⣿⣠⣿⣿⣷⠿⣻⣿⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢂⡀⢶⣴⡟⣿⠛⣁⣿⣿⠀⠀⠀⠀⠀⠈⢲⡀
⠀⡠⠞⠃⣀⡴⠖⠒⠒⠒⢰⡟⠘⢻⣿⣧⡀⣹⡇⠀⠀⠹⠷⢤⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣧⣶⣶⣼⡿⠘⠛⣿⣿⠀⠀⠀⠀⠀⠀⠈⠃
⢀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⣷⠀⢻⣿⣧⠼⠟⠛⠻⠶⣤⣄⣀⣀⣤⣀⣤⠀⠀⢈⠹⢟⣻⠿⣟⢻⣟⠁⠀⠀⣿⣿
⠀⠰⣦⣤⠤⠶⠅⠐⢤⣀⠀⡿⢀⣽⣿⡇⠀⠀⠀⣠⣶⣿⣿⠋⠉⠉⣹⢟⡙⣏⠙⠟⠋⠻⣄⠘⡿⣏⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠈⠛⠋⠈⠛⠀⠈⠉⠁⡿⢸⣿⣿⠓⢀⣾⠿⠛⠓⠛⠁⠀⠀⠰⢃⣈⣙⣛⣦⣀⠀⢰⣈⡟⠀⣿⠀⠀⢠⣿⡇⠀⠀⠀⢀⣠⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⣿⣿⡔⡋⠀⠀⠀⡀⠀⠀⠀⠀⠰⣿⠿⠛⠙⠿⣿⠃⠈⢿⣿⣤⡟⠀⣀⣺⣿⡇⢀⣤⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⣉⣿⡟⠁⠀⠀⠀⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⣿⠀⠀⠘⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠀⣀⠻⣦⣶⣾⣿⡏⠀⠀⠀⠀⠀⠈⢛⣠⣤⠴⠶⠶⠶⠶⣤⣄⡀⠀⠀⠈⣿⣿⣤⣶⣿⢿⣿⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⢝⣻⣿⡿⠛⠻⠇⠀⠀⠀⣤⣤⠶⠋⢩⣄⢀⠀⠀⠲⠄⠀⠈⠛⢶⣤⣼⣿⣿⣿⠛⠁⠀⠋⠀⣤⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡅⠀⠀⣀⡀⠀⣾⠟⠁⠀⠀⠀⠘⠻⠇⠀⠀⢀⣀⣀⣴⣾⣿⣿⠿⣯⠀⠀⠀⠀⠀⠀⢸⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⢿⡃⢰⠾⢿⢿⣿⡏⠀⣧⠀⠀⠀⢀⡀⠀⠀⢀⣼⣿⣿⡿⠟⠋⠀⠀⢹⡄⠀⠀⠀⠀⠀⢈⡼⠃
⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⣿⣿⠀⠀⢸⣿⡏⠀⠀⢹⡇⠀⠀⠹⠿⣠⣾⣿⡿⠟⠉⠀⠀⢀⡀⠀⠀⣷⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢻⠿⣧⡀⠀⢹⣿⡇⢀⣀⣾⣿⣿⣯⣄⠀⣀⣀⡀⣘⣿⣆⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⡇⠀⠈⠻⣦⣠⣾⣾⣿⠟⠋⠉⠉⠉⠛⣶⠛⠋⠉⠙⠛⠻⣷⣤⡀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⠁⠀⠀⣀⣼⣿⣿⢟⡁⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢸⠀⣠⣾⣿⠿⠋⠁⠀⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⡟⠁⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠶⠖⠛⠙⠛⠋⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⡀⠀⢀⣀⡀⡀⣀⣀⡀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⡠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣤
⠀⠀⣸⢣⣶⣿⣯⣙⣧⣶⡦⣬⣍⣛⠲⢤⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠟⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⠶
⠀⠀⣧⣿⣿⣏⣽⣿⣿⣿⡿⢷⣦⣽⣿⣿⢶⣽⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻⡄⠀⠀⠀⠀⠀⠀⣠⣰⡄⠛⠐⠛⠛
⠀⠀⠀⢿⣿⣿⣿⢿⣿⣿⣷⣿⣿⣿⣿⣻⣿⣿⣯⡞⠀⠀⠀⠀⠀⠀⠐⠲⣄⡀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⢀⢄⡀
⠀⠀⠀⠀⠻⠿⠻⡿⠿⠿⣿⣿⣿⣍⣿⣿⣿⣿⣿⠀⠄⠀⠀⠀⣤⣌⣵⣦⠀⣽⣄⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠙⢯⣽⠇⢸⣾⣍⡁
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⠼⢯⣭⣉⣙⣿⣻⣏⣧⡼⠀⠀⠀⠀⠙⠷⠛⠋⣼⣶⣾⣿⠀⠀⠀⢸⣧⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢸⣿⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣅
⠀⠀⠀⠀⠀⣠⡶⠟⠋⢏⣘⣻⣿⣿⡿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡷
⠀⠀⢀⡴⠞⠋⢀⠄⠀⢼⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠇⠒⠻⣴⣷⣾⣯⣭⣭⣍⠛⠛⠿⣿⣿⣿⣿⣿⣿⡄⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠳⠶⠦⠤⣬⡍⠃⠀⢀⣉⣹⣶⠲⠤⠀⠀⠀⠀⢠⣔⣸⣿⣛⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣿⣿⠶⡤⠀⠀⠀⢰⣿⣿⣿⣿⢻⡏⠘⣿⡆⠀⠀⠀⠠⠀⠀⠹⢾⣿
⠀⠀⢀⣀⣤⣴⣶⣟⣯⣿⣒⣋⣭⣥⢽⣿⣶⡀⣄⠀⠀⠀⠀⠈⢩⣿⡿⢦⡄⠀⠀⠀⢻⡟⠋⢀⣉⡟⠩⢀⣿⠇⠀⠀⠀⠀⠀⡴⠀⢸⡎⢳⡀
⠀⢠⣯⣿⣄⣀⣈⣭⣽⠛⠛⠛⠓⠓⠚⣿⣟⣾⣿⠀⠀⠀⠀⠀⠘⠻⠇⠀⠀⠀⠀⠀⠀⠓⠦⣤⣤⣤⠴⠛⠁⠀⠀⢀⣴⣿⡞⣀⠀⢸⡇⠦⡙⢦
⠀⠀⠙⣿⣿⣿⣿⣿⣿⢭⠭⠍⠀⠀⠀⣿⠯⢽⡟⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡟⢰⣿⣷⡾⢽⡦⢸⢘⡇
⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⠭⠀⠀⠀⢀⣯⡼⠟⠋⠀⠀⠀⠀⠀⡄⣇⡶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡍⢧⣹⣿⣿⣿⡶⠞⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠖⠚⡉⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣯⡷⠦⠀⠀⠀⠀⠀⠀⢀⡤⠶⠤⠀⠀⠀⠀⠀⠀⠙⠾⠽⣿⠿⠿⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣷⡦⠀⠀⠀⠀⠀⣴⣯⠀⠀⢰⣶⣦⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣴⣤⣀⠰⣄⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⣿⣯⠀⠀⠀⠀⢸⣟⣿⣷⣦⣀⣉⣉⣁⡤⠀⣿⣿⣿⣷⣷⡆
⠀⠀⣰⡟⣿⣿⣿⡿⠏⠘⣛⣛⣋⡡⠀⡌⠃⠀⠀⠀⠀⠀⡾⠀⣿⣿⣿⣧⠀⠀⠀⠀⠸⣿⢡⡿⠛⢻⡿⢿⡏⣴⠀⢿⣿⣿⣟⣯⣿⣷
⠀⠀⠋⣿⡭⢿⡷⠞⠛⣛⣉⡥⠤⠒⠀⠀⢰⠇⠀⠀⠀⠀⠁⠰⣿⣿⠏⠉⠀⠀⠀⠀⠀⢹⣾⣧⣀⡾⢁⣾⠀⠁⢠⣾⣿⣿⣿⣿⣿⠿
⠀⠀⢿⣿⣴⡾⠛⠛⠋⠁⣀⣀⣴⣶⣦⠠⡤⡆⠀⠀⠀⠲⠞⢸⣿⡟⠶⡄⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠗⠀⠀⠘⣏⣿⣿⣿⣛⣡⡀
⠀⠀⢻⣿⡿⢁⣀⣾⣿⡿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠿⠟⠁
⠀⠀⠀⠻⣿⠛⠿⣋⣤⣤⠶⠖⠋⠁⠀⠀⠠⠄⠀⠀⠀⠀⠘⣿⣿⠀⢠⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⣴⣶⣶⠄
⠀⠀⠀⠀⠙⠛⠛⠉⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣿⣯⠴⠋⠀⠀⠀⠀⠰⠶⠶⠶⠤⠦⠶⠶⠶⠶⠒⠚⠒⠚⠛⠛⠛⠋⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣿⣫⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠒⠒⣲⢲⡶⠚⠓⠛⠒⠂⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢷⣾⣷⣶⣿⠿⢿⣿⣷⣶⣶⡦⠹⢉⣤⣤⡔⣂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⢸⣿⠀⢹⣷⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠉⣷⢹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⢠⣝⣧⣤⡼⣧⣤⢌⣫⢽⣿⣥⣴⣶⣤⡖⠀⠶⣠⠦⠸⠈⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠋⠁⣤⡀⠀⢀⡆⠛⠁⠀⠀⠈⠁⢀⠀⠀⠀⠠⠷⠄⠀⢀⡀⠂⢄⣀
⠀⠀⠀⠀⠀⠀⠀⣰⠾⡃⠙⠀⠀⠀⠒⠁⠐⣺⡅⠀⠀⢀⡴⠾⣿⡏⠙⠒⣤⡀⠀⣀⣀⠀⢁⡄⠀⢈⣵⣄
⠀⠀⠀⠀⠀⠀⢰⢱⡆⢘⠄⠆⠀⠀⠀⢱⠇⣿⠁⠀⠀⠡⣦⠀⢺⠇⠀⣼⣿⣿⣿⠣⠤⣿⣿⠁⠀⢰⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣌⣓⠠⠬⡄⠤⢄⣀⣠⣼⣤⣿⠠⠤⢤⡔⣀⣒⡁⠀⢰⣿⠋⢿⣿⡖⢲⣿⡿⠀⠀⢸⡿⢻⡇
⠀⠀⠀⠀⠀⠷⣿⣿⢧⡾⠿⠿⠿⠿⠿⠿⠿⡿⠿⣴⠿⠹⢶⡾⠷⡶⢻⣟⠀⣿⣿⣿⣿⣿⣇⣀⠀⣼⠃⢸⠃
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⠶⣶⡶⠦⠚⠾⣷⣶⣶⣿⣿⣿⣿⣿⡗⢸⡏⢠⣿⣿⣽⣿⣿⠟⣿⡿⢿⡄⡸
⠀⠀⠀⠀⠠⠤⠽⠿⠿⠿⠷⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣾⣿⣾⣿⣾⣶⣶⣶⣶⡶⠶⠾⠿⠿⠿⠧⠤






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

⠀⠀⠀⠀⠐⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⢄⠢⢣⠄⠀⠀⠀⢒⡿⡴⠰
⠀⠀⠀⢀⡠⠖⡲⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⣠⣮⠷⡘⠝⠀⠀⠀⠀⢀⠀⢩⡃⢠
⠀⠀⠀⠁⡀⠀⠀⠀⢆⠀⡀⠀⠀⠀⠀⣀⠉⠀⢁⡠⠚⡱⠔⠋⠀⠀⠀⠀⠀⠌⠀⠀⣁⢈⠀⠈
⠀⠰⡓⢆⡁⠀⣀⣀⡋⠈⠁⠀⠀⡰⠒⠃⠔⢐⣥⡐⢠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡀
⠀⠀⣀⣾⣷⣾⣼⣿⣾⡦⠀⠀⠀⠱⡌⠀⠀⢎⠀⠀⠐⠈⢀⡀⠀⠀⠀⠀⠠⠀⠄⠢⠀⠁⠀⠄⡄
⠀⠀⢹⠿⠞⠻⣝⡏⠫⠗⠁⠀⠀⢒⣒⣒⣚⠒⠛⠒⠂⠂⠋⢂⡐⠒⠀⠀⠀⠀⠀⠀⢐⠂⠈⠆⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠁
⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏
⠀⠀⠀⡠⠐⠰⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠲⡄
⠀⠀⢀⣠⠠⠄⢠⢴⣄⠀⠀⠀⢀⣤⣤⠚⠬⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡰⠃⠀⠀⠱
⠀⠀⡨⠥⠀⠠⢠⣎⡷⠇⠀⠈⠁⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡤⢴⡧⡭⡖⣀
⠀⠀⠘⢀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠈⡄⠀⠈⣀⣫⣀⣀⡸⢇⡀⠀⠄⠉⠀⢲
⠀⠀⠐⠀⠀⠑⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠳⠤⠤⠀⠀⠐⠣⠄⠐⠙⠊⠁⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⢀⣰⣶⣷⣷⣦⡀⢀⣴⢄⡿⠛⠢
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣿⣡⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣧⡾⣡⡾⠁
⠀⠀⠀⠀⠀⢠⡾⣋⣭⣡⡌⠙⠿⣧⠀⠀⠀⠀⠀⣼⡿⠁⠩⠈⠀⠀⠀⠀⠀⠀⠙⣿⣿⠟⠋⢈⡿⠁
⠀⠀⠀⠀⢀⡿⠁⣹⣿⣿⣿⡇⠀⢹⡆⠀⠀⠀⢰⣿⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⣈⣴⠟⠁
⠀⠀⠀⠀⠸⡇⠀⢿⣿⣿⡿⠏⢀⣿⠀⠀⠀⠀⠸⣿⣿⣿⡖⠂⠀⠀⠀⠀⠀⠀⠘⢍⡾⠋⠁
⠀⠀⠀⠀⠀⠹⣦⣤⣈⣀⣀⣤⠞⠃⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣤⠤⠀⠊⡡⣤⡀⠀⠀⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⢀⡒⠂⠝⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⣆⠀⠀⠨⢁⠞⢀⣤⣶⠂⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠛⣿⡀⠀⠐⢁⣴⠋⠂⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠡⠀⠀⠀⡁⢸⣿⠦⠐⣹⠃⠀⠀⠀⡄⠀⠀⠀⠀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⠀⢀⡄⠀⠀⠀⠀⢿⡄⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠸⣾⣿⣆⠀⠀⠀⠘⣿⡟⠀⠀⢀⣀⡀⠄⠀⠀⡀⠀⠀⠈⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠁⠀⠀⠈⠻⣿⣦⣀⡾⠚⠛⠉⠉⠉⠁⠀⠀⠠⠈⠀⠇⠀⠀⠀⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⢁⣴⣾⣿⣷⣦⣉⣻⣿⣷⣶⣶⣶⣶⣿⣶⡶⠀⠀⠀⢀⠀⠀⠀⠀⠈⣻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⡼⠛⡛⠉⠛⠛⠛⠛⠉⠉⠉⣩⣤⣤⣌⣩⠁⡘⠀⠐⠀⠀⠀⠀⠀⠀⢺⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⣰⣦⡄⠈⠀⠀⠀⠠⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⠀⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢾⡿⠁⣠⣶⣿⡿⠀⠀⠀⠀⡀⠁⠀⡄⢀⠀⢸⣿⣿⣿⣿⣿⣆⠀⠠⠀⠀⠀⠀⠀⢾⣿⣷⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠠⠿⠀⣰⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠹⠿⠿⠿⠿⠟⠲⠁⠀⠠⠀⠀⠠⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠈⣍⠉⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠿⢂⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡠⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⣴⣿⣿⡿⢋⠅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⢟⠛⢤⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡆⠀⠀⠁⣶⣶⣤⣴⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣿⣿⣧⣠⣴⣤⣄⣀⣠⣄⣀⣀⣤⡤⠶⠾⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣀⠀⢠⢀⣒⠓⣤⡞⠋⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢸⣶⣾⣾⣿⣿⣦⣽⣶⣁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠐⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣀⣿⣶⣿⡧⢿⣿⣿⣿⣿⡿⢚⣇⡠⡤⣄⠾⠂⠀⠀⠀⢲⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⡗⢠⢻⣿⠀⣿⡿⣿⣧⢼⣿⣿⢿⡿⠲⢺⣾⠭⠁⠍⠀⠀⢀⠄⠀⣸⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣤⡅⠀⠰⠄⠰⠐⢠⠄⠄⢻⠄⣸⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢻⡹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢀⣤⣤⡀⠄⠀⠀⢸⠉⢹⣿⣷⡀⠄
⠀⠀⠀⠀⠀⠀⢰⢸⡇⠀⣸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡗⢀⣼⣿⣿⣇⠀⠀⢂⣾⠤⣾⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠘⣾⣷⠀⢻⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⢵⣾⣿⣿⣟⣿⣦⡄⠀⢸⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⣹⣿⣶⣶⣶⢻⣿⣿⣿⣿⣿⢻⣬⠟⣯⣿⣿⣾⣿⣿⣿⣛⣋⣉⣉⣠⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⢀⣀⣶⣿⣿⣿⣿⡏⠀⣿⣿⣿⣻⣿⢸⣽⣧⢿⣷⣿⣿⣿⣿⣿⣹⣹⣛⣟⣻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠐⢤⣿⣿⣿⢹⡟⠚⠛⠶⠾⠹⠿⠺⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠁⢠⣿⣿⣿⣟⣼⣿⣄⠐⢶⣒⢲⠤⡀⢁⠀⠀⠀⠀⠀⠀⠚⠒⣾⣿⣿⣿⣾⠄
⠀⣄⣻⣿⣿⣿⣿⣿⣿⠃⢰⣾⣿⢿⣿⣿⣿⣟⣿⣦⠀⢻⣿⣆⢹⣆⠁⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣄
⢀⣿⣿⣿⣿⣿⣿⣿⢋⣶⣿⣿⣿⣾⠋⠡⣼⣿⣿⡿⣷⡀⠙⣿⣠⣿⣧⡀⠄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣆
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⢿⣿⣿⣷⣿⣷⡄⠈⠛⠛⠛⠿⠄⠡⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠿⠿⣟⢧⣼⢿⣿⣶⣶⣶⣶⣶⣶⣶⣼⣤⣶⣶⣶⣶⣶⣾⠿⠿⠿⠿⠿⠂
⠀⠀⠀⠐⠲⠤⠄⣀⠉⠉⠉⠉⠙⠻⠛⠚⠿⣦⣠⣶⣷⣾⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⠿⠛⠿⠿⠿⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣡⣀⣀⣀⠀⠀⠀⠀⣠⣤⣭⣶⣶⣤⡀⢰⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠓⠀⠙⠻⣿⣿⢿⠃⠉⠉⠉⠁⠀⠀⠀⠀⠀⠒⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠐⢄⠀⣀⡀⡠⠀⠐⣄⠀⢀⠰⡤⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢀⣀⠂⡀⠁⡤⠀⡀⠀⡈⢀⠀⢤⠁⠀⠈⠙⠀⠀⢀⣤⣤⠀⠀⠀⣷⣾⣶⡇⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⠤⠀⠆⠉⠡⠆⢁⡀⠁⠈⢁⠀⢘⠉⠀⢀⡹⠆⣩⣒⠀⢴⢻⣿⠟⠀⠀⠀⣏⣩⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠉⠻⠿⢈⡰⡷⢔⣠⢉⠆⠀⠹⣾⣿⣿⡌⢫⠄⠀⢷⡄⠈⠋⠁⢀⡐⠀⠀⠀⠄⠆⠀⢀
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⣄⠘⠏⠀⠀⠀⠁⡀⠠⠦⡄⡶⠿⣀⠀⢀⠀⠉⠛⢧⡤⠀⠀⠀⠘⠿⢁⢳⠁⣀⡀⠋⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⢠⣄⠠⢈⠑⠒⠁⠀⡀⣴⢠⠒⣀⡁⠀⠀⠀⠄⣰⠦⠂⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⡾⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠛⢨⣵⠀⣤⡐⢆⡀⠀⠀⣨⠇⡰⠂⢐⣾⣽⠲⠤⣴⣟⠁⢀⠐⠀⠀⣼⠣⣌⠂⠀⠐⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢫⣹⢄⣿⣯⣾⣶⠧⠀⠘⠀⠃⠈⢸⡟⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⣙⠓⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠁⠀⠘⠛⠛⠣⠀⠀⠀⠀⠀⠀⡬⠁⠠⡐⠃⠀⠁⢀⠀⠀⡄⠙⣿⡄⠘⠖
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠱⠀⠀⠁⠢⠿⠄⠀⠒⠀⠀⠀⠀⠀⡄⢄⠀⠄⠀⠢⢤⡀⢈⡐⠃⠀⠀⠉⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⣷⡀⠀⠀⠈⠁⠬⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⠳⠇
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠅

⠀⠀⠀⠀⠀⠄⠀⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣦⣄⡀⠀⠀⣠⡤⣤⣤⣤⣀⣀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠩⢶⣶⣤⣽⣿⣿⣿⡿⠏⣳⣾⣿⣿⡞⣿⣿⣿⡟⢈⡿⢛⡛⣿⣿⣿⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠤⢤⣭⣭⣿⣿⣿⠿⣉⣴⣿⣿⣿⣿⣿⡇⣯⣿⣿⡷⠘⣇⠻⢆⡟⠁⠀⣌⠿⠋
⠀⠀⠀⠀⠀⠀⣀⣉⣭⣭⣽⣿⠟⢡⣼⣿⣿⣿⣿⣿⣿⢟⣲⠽⠟⠀⠑⢄⠈⠉⠁⠀⠀⠘⠑⠶⢴⠄
⠀⠀⠀⠀⠀⠀⠊⣉⣩⣾⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠲⠄⠀⠀⠀⠉⠦⠀⠀⢠⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠚⠍⢿⣿⡟⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⠄⠀⠀⢀⠰⢄⣀⢀⡠⠞⠁
⠀⠀⠀⠀⢀⢴⢾⣿⠏⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢙⣄⠀⠀⠐⠍⠉⠲⣦⠼⠋⠁
⠀⠀⠀⠀⠀⢀⣼⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠈⠖⠀⠠
⠀⠀⠀⠀⠐⠹⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⠄
⠀⠀⠀⠀⠠⢾⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣄⣤⠖⠒
⠀⠀⠀⠀⢀⣴⡇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⡿⡆⢠⣖⣰⣶⣿⡿⠃
⠀⠀⠀⠀⠉⢙⡇⢸⣿⣿⣿⣿⣿⣿⣿⡿⡽⡼⣾⣟⠯⢮⣰⣼⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠋⢣⢸⣿⣿⣿⣿⣿⣿⣿⣯⠘⠆⠘⠷⠻⠶⠽⠋
⠀⠀⠀⠀⠐⠀⢿⡀⣿⣿⣿⣿⣿⣿⣿⡷⢁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠘⠃⠀⠷⠹⣿⣿⣿⣿⣿⣿⣜⢠⠌⠀⠀⠀⠀⠀⠀⣰⠾⠛⠋⠉⠉⠛⠻⢮⡳⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃
⠀⠀⠀⠀⠀⠘⣏⡐⢇⣹⣿⣿⣿⣿⣿⣿⢫⣖⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⠫⠻⣽⣆⡀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠸⣧⡘⢁⢻⣿⣿⣿⣿⣿⣿⣎⠄⠀⠀⠀⣠⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠏⣧⣇⠀⠀⠀⠀⠀⢠⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠉⣷⣸⣯⠙⢿⣿⣿⣿⣿⣿⣳⡂⠰⣾⣟⣟⣡⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣿⣿⠀⠀⢀⢀⣴⡏⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡸⡯⠸⣧⠹⢿⣿⣿⣿⣿⣟⣄⠀⠉⠀⠀⠙⠛⠚⠀⠀⠀⠀⠀⠀⠀⠂⠀⢋⣌⣿⣶⣶⣿⣫⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⡻⢳⢪⣭⠻⢿⣿⣿⣿⣦⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣼⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠙⠪⣟⠃⡀⠉⠻⠿⢿⣿⣿⣿⣶⣤⣤⣄⣀⣀⣤⣶⣥⣤⣠⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⠶⠦⣭⣩⣭⣿⣻⣿⣟⣿⡿⠿⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢠⣶⣦⣌⠛⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁⠀⣿⣿⢏⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣓⡀⠀⠀⠀⣿⣥⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⣰⣶⣿⣿⢙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣻⣿⣿⣿⣿⣿⢿⣟⡛⢦⢰⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠠⠿⣿⣿⣿⠟⠻⠿⠿⠟⠀⢰⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣴⡿⢛⣡⣤⣴⡶⠶⠖⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢷⣼⣽⢯⡾⠁⠈⠉⠀⣀⣀⣤⣤⣤⣤⣦⣤⣤⣀⣀⡀⠀⠈⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣷⣶⣦⢄⠀⣀⣤⡴⠀⢠⣷⣽⣿⣿⣿⣿⠿⢿⢶⣾⣿⣿⣿⣿⠿⠿⣿⡿⠛⠛⠛⠿⢿⣷⣦⣶⣿⢷⣾⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣟⡿⠿⠟⠋⢉⣥⣶⣿⣿⣿⣿⣷⣰⠾⣿⣿⣿⣯⣥⣴⣾⣿⣿⣿⣿⡟⠛⣤⣴⣾⣿⡇⡦⢄⠀⠀⠀⠙⣿⣿⣿⣿⡟⠷⡤
⠀⠀⠀⠀⠀⣠⣤⣴⣶⣾⣿⣏⣠⣴⣶⣾⣿⣿⣿⠿⢿⣛⣫⣽⣝⣿⣿⣿⣿⠿⢿⣿⣿⣤⠿⣿⣿⠇⣰⣿⣟⣿⡿⢷⣦⣦⣌⡀⠀⠸⣿⣿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣫⣭⣶⣶⣿⣿⣿⡿⠟⢻⣿⣿⣯⣅⣀⣿⣿⣿⣿⣴⣿⣷⣿⣿⣿⣿⣿⣷⣿⣟⠙⣛⣿⣿⣶⡏⠿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣨⣿⣿⠟⢛⠟⠋⠀⠀⠀⠀⠹⣿⣿⣿⣻⣿⣶⡏⣰⣬⣿⡿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣧⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉
⠀⠀⠀⢀⣿⣿⣧⠖⠁⠀⢀⠀⠀⠀⢠⣸⣿⣿⣿⣿⣿⡏⠉⠉⠉⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣧⠛⢫⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠐⠿⠟⠋⠀⠀⣠⣾⣿⣷⡄⠀⠀⣿⢿⣿⣿⣿⣿⠇⠀⠀⠀⡀⣀⣤⣿⣿⣿⣿⠛⢿⣿⣏⠋⠐⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠛⢿⣿⣶⣤⡈⠑⣿⣿⣿⣿⣿⣿⡟⠀⣼⡿⠺⣿⣔⢓⣾⣟⠀⢉⣭⣿⣿⣿⣿⢿⡗
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠿⠿⢿⣿⣿⣿⣷⣪⡼⠃⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠸⢿⢧⡀
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⢿⣿⡏⢻⣿⣷⡀⢠⢨⡁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠌⣿⣿⣿⣶⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠻⢶⣤⣤⣤⣸⣿⠀⠀⢠⣿⣷⣄⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⡀⢿⣴⠙⢻⣿⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣷⣦⣤⡀⠈⠙⠻⠿⠿⣷⠀⡌⠹⣇⡙⠻⠿⠿⠿⠄⠠⢤⣄⠀⢲⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⠿⣿⣦⣤⣤⣀⡀⠀⠇⠀⠻⠟⠂⠀⠀⢀⠤⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃
⣶⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣷⣾⣶⣶⣶⣶⣦⣤⣦⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣈⣈⣀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣤⣤⡀⠀⠀⠀⣀⣴⣶⣦⣄⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠇⣀⣴⣿⣿⣿⣿⣿⣿⣦⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠛⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠟⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣋⣭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠉⠉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⣶⣶⣿⡿⠛⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⣾⡿⠛⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠟⠛⠉⠀⠀⠀⠀⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠛⠀⠀⠈⠙⠁⠀⠀⠀⠀⢘⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣽⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣍⡉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣦⣀⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡵⠤⣟⣛⠛⣛⣛⣛⠛⣋⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠿⢋⣀⣤⣤⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣠⣷⣾⣶⣿⣿⡿⣃⣤⣾⣶⢀
⣿⣿⢷⡖⣿⣛⣍⡉⠉⠉⢙⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇⠀⠀⠀⠀⠀⣤⣿⣿⣿⢿⣿⡿⠿⠿⠿⣿⣿⣿⣧⣦
⠏⠁⢸⠀⣻⣿⣿⣿⣟⠳⢦⣌⠻⣿⣿⠄⠀⠀⠀⠀⠀⠀⡸⠟⠀⠀⠀⠀⠀⠠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄
⠀⠀⢨⠀⠀⠈⢿⣿⡿⠀⠘⠿⣷⠟⠁⠀⣠⣤⣶⣶⣶⣶⣧⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁
⠀⠀⢠⠀⠀⠀⠀⠀⠈⢉⡠⠀⠀⠀⠀⠀⣿⣿⡿⢯⣍⢤⠏⠀⠀⠀⠀⠀⠀⠘⣿⠀⣠⡤⣀⡀⠀⠀⢀⣤⡤⢤⠀⢹⠃
⠀⠀⠘⡆⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢠⠚⠻⡿⢀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠻⠳⡟⢿⣶⣤⡶⢻⡟⠿⡷⣾⠆
⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠰⣌⣳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣠⡏⠈⢅⠂⠀⠠⢠⠏
⣧⠀⠀⠀⢳⡀⠀⠀⠀⣔⠁⠈⠀⠀⠀⢁⠀⠉⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡵⡇⠀⠈⡉⠛⠉⠁
⣿⠃⠀⠤⣄⡳⣄⠀⠀⠻⢿⣿⣷⣤⣤⡴⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣀⠀⡙
⡏⠀⠀⠀⠈⠙⢿⣿⣤⣤⡘⣿⣿⣿⣏⣴⡿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠂⠋⠉⠉⠻⡆⠀⢀
⣿⣤⡴⠆⠈⠉⣙⠿⣿⣿⣟⣻⣿⣿⣼⡟⣁⣀⣤⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⠀⢸⢀⢸⠇⠀⠀⢠⠀⠀⣿⣿⣷⣦
⣿⣿⣧⡀⠀⠠⣼⣦⣀⡉⠛⠛⣿⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠈⠃⠀⠀⠀⠀⠀⠀⢰⠟⠋⠉⠁
⣿⣿⣇⠀⠀⠀⠀⠀⠉⢻⣿⣿⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠋

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡤⠖⠈⠀⢁⡖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⢦⡤⠲⣳⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣯⣤⣄⠹⣟⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠈⢀⠙⣿⣷⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣵⣾⡄⣀⣬⡧⠘⢿⣿⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣵⣿⣼⠃⠀⠈⢿⣿⣾⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋⠁⠀⠀⠀⠈⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⢤⣤⣀⠀⠀⠀⠀⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⣀⣀⠀⠀⠀⠀⢀⣽⡆⠀⠀⠀⠀⢹⣿⣷⡀
⠀⠀⠀⠀⢀⡶⠋⠀⠀⠰⠿⠷⠚⠁⢀⣠⡴⢿⡍⠻⣄⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠘⡿⢦⡤⣤⡤⢤⣶⠲⣿⡍⠹⣧⠈⢿⡄⠙⠀⠀⠀⠀⠀⠙⣿⣿⣄
⠀⠀⠀⠀⠀⠃⢸⡇⢸⡇⠀⣿⠀⢻⣧⠀⢻⣆⠈⠟⠀⠀⠀⠈⠙⣶⠀⠘⠉⣁⡠
⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⢿⡆⠈⣿⡄⣼⠁⠐⠾⠛⣁⡠⣴⠺⡍⣿⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠘⣧⠀⣿⡀⠘⣷⠀⢸⡇⠋⢻⢹⡏⣿⠹⣇⠸⣆⣿⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣈⠳⣄⠘⣧⠀⣿⠀⢸⠸⡇⢸⡄⢻⣀⣿⡿⠀⠀⠀⠀⠀⢀⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡖⣉⡶⢌⡓⣌⣳⡸⣀⡘⢦⡳⣄⢳⡈⣿⣿⣿⡀⠀⠀⠀⠀⠋⠹⡗⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠯⡀⡎⠀⡇⠈⡇⠀⣻⢐⡵⢪⠳⢵⡿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠒⠁⠀⠀⠀⠁⠐⠀⠀⠀⠙⠻⢿⣿⣿⣷⣶⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⢻⣶⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣉⣷⢰⡋⣹⣷⡾⠞⠻⡗⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠻⣯⢿⠿⠆⠀⣴⡗⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣽⣀⡴⣧⣜⠦⠴⡾⢋⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⡴⣫⢊⢞⣽⣷⣞⡵⣋⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣨⢟⢔⡕⣡⣿⡟⣡⠛⠳⡧⠘⣦⡈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣦⢞⡵⡣⢪⣾⡿⣫⢾⠿⣆⣴⠃⣴⠋⢡⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⢀⡴⡣⢊⢞⣕⣿⢿⡜⠁⣿⢦⣄⣠⠤⣿⡴⢋⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡷⢫⠞⡔⣡⣻⣿⡵⠋⠀⠀⢿⣤⡿⠧⠖⣋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣇⣠⢞⠔⡡⢊⣾⣿⣿⠏⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⣠⠟⡱⢋⢞⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢉⡷⣫⢊⡴⡡⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⡴⢋⠜⡡⢊⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⣠⢟⡵⢁⠞⣰⣵⢟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⠞⡡⠋⡴⣡⣾⡾⣱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣫⠎⡠⢊⣔⣽⢋⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⡯⢁⠔⢁⠜⣰⡿⢹⣷⠋
⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⠋⠉⠀⠀⠀⠰⢮⡴⠟⣺⣧⣾⣯⠄⡟⣷
⠀⠀⠀⠀⠀⠀⢰⣏⡏⠀⠀⠀⠀⢀⣄⣠⡾⣤⢊⣼⡟⢹⠀⣧⣧⢸⡄
⠀⠀⠀⠀⠀⠀⢸⡘⣇⠀⠀⠀⠀⢯⡌⢙⠶⣬⣿⠋⠹⠾⠀⢹⣿⡀⣧
⠀⠀⠀⠀⠀⠀⠘⣧⢨⠃⠀⠀⠀⠈⣉⢷⣾⡏⣹⠆⠀⠀⠀⠘⣿⡇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣤⣤⡤⠔⢻⠟⠋⠉⠁⠀⠀⠀⠀⢠⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡛⠳⢦⣄⠸⡀⠀⠀⠀⣠⠀⠀⠀⣼⣿⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠉⢷⣽⣦⣠⡴⠋⠳⠶⣚⡽⠃⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣈⠛⠓⠲⠶⠒⠛⠉⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⡀
⠀⢰⡷⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣧⣨⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⣽⣿⣿⣿⣿⡿⠋
⠀⠀⢀⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣥⣤⣀⠀⠀⠈⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣻⡟⠀⠀⠈⠉⠉⠉⠋
⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠘⠛⠛⠻⠀⠀⠘⠻⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⣏⣛⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣿⣿⣿⡗⠀⣴⣿⣿⣿⣧⣄⣀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣀⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⢹⡿⠛⠛⠛⢿⣿⣿⣿⣿⠋⠙⢿⣿⣿⣿⣧⠈⠙⢿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠘⠀⠀⠀⠀⢸⡏⢉⣩⡉⠀⣠⣿⣿⣿⣿⣿⣿⠁⠙⠛⠋⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢻⠇⣠⣤⣾⣆
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡟⢰⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣙⣷⣿⣿⣿⠇⣾⢡⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢡⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠿⠹⣿⣿⣿⠟⠛⠋⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣸⣿⡿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⣿⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣿⡿⡛⣻⡿⣿⣿⣿⡿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣭⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠐⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢰⠴⠓⠠⠒⣔⠋⣁⣒⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠆⡆⡿⢻⣿⠆⠀⡜⠐⣂⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣀⡗⣙⠛⠿⠒⠋⠀⢉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⠴⢏⣉⠑⠢⠍⠀⠉⠓⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠁⠁⠀⠀⢉⠒⠂
⣾⡋⢎⢾⡑⢼⠁⠻⠿⠀⠀⠘⠿⠟⠀⠀⠻⠿⠇⣾⣿⣍⣛⡿⣠⣾⠃⠃⣿⣷⣾⣳⣁⢄⣴⣿⣦⣠⣆⣶⣶⣶⣶⣶⣶⣶⣦
⠻⠮⢶⠄⠓⠚⠶⠶⠶⠶⠤⠢⠔⠤⠶⠴⠦⠶⡖⢿⣷⡌⠾⢧⣧⠹⡄⠀⢿⣀⣨⣌⣀⣀⣜⣕⣜⡽⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⡈⠆
⠀⢠⠁⢰⣀
⢠⣾⡆⠻⣽⣧
⢸⠏⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠜⠒⠠⠐⠁⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡈⠈⡁⠀⠄⣲⡆⢀⠀⠀⢠⣆⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠁⠀⠰⠀⠀⠀⠀⠀⢀⡀⠀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡌⠀⢀⡄⠀⠀⠀⠀⠀⠂⠄⠀⢸⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⢳⡖⠁⠀⠀⢀⠀⢀⣠⠔⠂⢄⣸⠁⠒⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢨⡄⡐⢁⠀⠘⠤⠀⠀⡀⣀⣤⢁⢠⣐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢴⠀⠙⣄⡇⠀⠀⠀⠈⠑⠒⠉⠁⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣮⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡏⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠑⠀⠁⠀⠑⢾⠀⠀⢦⠀⠀⠀⠀⢠⣠⠟⢠⡔
⠀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡀⠀⠀⢀⠀⠀⠢⠀⠠⣄⠈⢠⣘⢛⡕⠀⣴
⠀⠀⠀⠀⡇⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢤⣄⠀⢡⣤⣀⡀⠀⠈⠇⡀⠈⠻⣷⣵
⠀⠀⢀⢀⠃⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⢆⣃⠀⠀⠀⠈⠀⠀⠀⠾⠶⠤⣽⣯⡠⢠⠂
⠀⠀⠈⠓⣺⢧⡀⠀⢡⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢌⠉⠐⠀⠀⠠⠄⣀
⠀⢀⠠⠲⠄⡀⠀⠀⠺⠃⣀⢀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠤⠖⠛⠻⠶⠤⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⣄⠀⠂⠣⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠤⠤⣤⣤⠤⠤⠒⠒⠒⠒⠀⠀⠚⠂⠘⠉⠉⠉⠋⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢙⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣥⣶⠆⠀⠀⠈⡦⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠻⣶⣀⠒⠆⠀⠉⠉⠙⠛⠛⠛⠙⠛⠛⢛⣋⣁⣤⡤⠖⠋⣀⡄⢨⡟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⣿⡝⠉⠛⠓⢲⠦⣄⢸⡽⠁⣴⠆⠈⣭⢙⣓⣒⠒⠛⣛⣛⠛⣛⡛⣉⣫⡭⠉⢰⡶⠀⢡⡟⠀⣸⢇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡆⢻⣿⡷⣶⢶⣾⣶⣿⣾⣷⠾⣇⣀⣾⠃⢀⡾⠁⠀⣼⠏⠀⣰⠏⠀⢰⡟⠀⢀⣿⠁⠀⣿⢁⣠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢸⣿⣎⠄⠣⠔⢬⢛⣿⡏⡟⣲⣯⣽⣓⡻⠷⠤⠾⢯⣤⣴⣯⣀⣠⣿⣠⣤⠾⠧⢶⣚⣫⢭⡖⠟⠿⣇
⠀⠀⠀⠀⠀⠀⡼⠋⠀⠹⣿⢸⣿⠏⠈⠉⡍⡃⠚⣿⡇⠀⠀⠉⠀⠽⠉⠻⠟⢻⣶⠒⣶⠒⢶⡖⢶⡖⢲⡾⠉⠻⠈⠕⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠐⠁⠠⣶⠀⢿⢸⣿⣍⡓⣒⣓⣂⢒⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⡆
⠀⠀⠀⠀⠀⢰⡇⠀⠏⠀⢸⣼⣿⡏⣣⠮⢤⡷⡄⣿⡇⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠜⠠⡀⠀⠀⠀⠐⡀⠘⡇
⠀⠀⠀⠀⠀⠛⠁⠀⠀⣤⠸⣿⣿⢽⣛⣀⣙⣲⣸⣿⡇⠀⠀⢀⠔⣡⣾⡄⠠⡀⠀⠠⢨⣷⡄⠠⡀⠀⢠⠂⣼⣦⠈⠂⠀⠊⣰⡿⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣿⣧⣜⣆⣘⢉⡛⣾⡿⡁⢀⠔⣡⠞⡡⢻⣿⡀⠀⣠⢡⣟⡿⣻⣄⠀⣠⠁⣼⢯⡎⢷⠀⠆⢰⣏⡟⢼⡇
⠀⠀⠀⣠⠀⠀⠀⠀⠈⠁⢸⣿⡍⠑⠻⠉⠙⣻⢿⡇⣷⠁⡞⡵⢋⣴⣆⣻⡇⠀⢃⣿⡜⣤⠘⣿⡆⠈⢠⡏⡞⠙⢞⡇⠀⣿⡜⣴⣌⡇
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣸⣃⣜⣠⠀⠀⠤⠋⣿⠀⣿⣾⡷⢧⣿⣿⣿⣿⡇⠀⠸⣿⣾⣿⡇⣛⡇⠀⠘⣿⣷⣿⣼⣇⣀⣿⣷⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⡿⠕⠒⢬⡳⡄⠀⢠⡏⢰⡟⠟⣽⣷⣶⠀⠉⠉⢉⣛⣛⣛⣛⢿⠿⠿⠷⠶⣶⣛⣛⣿⡟⢉⡽⡏⡈⣿⣙⣻
⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⣿⣄⡀⢁⣹⡜⢦⣼⠁⣸⢗⣶⣿⢹⠅⢊⢳⠀⠰⠂⣼⣿⣯⣽⡇⠨⣧⡤⣿⣿⡟⡟⠇⣮⠎⡇⣿⣿⡛⣿⣇
⠀⠁⣄⠀⠀⠀⠀⠈⠀⡟⠈⠳⢭⠍⠀⠈⣹⡟⢀⣿⣦⡅⢿⣿⡧⣱⠋⠀⠀⠀⡞⢛⡿⠾⣿⣿⣸⡴⢼⡉⠁⠀⠀⠈⣶⡇⠛⢻⣹⠹⢿
⠀⢰⡇⠀⠀⠀⠀⠀⢸⣃⠠⠈⠀⢂⠀⠀⣿⠁⢸⣧⣵⠻⣿⠻⡷⡑⢶⠀⢤⢠⣇⣨⡷⠺⣿⠛⢻⡶⠾⢴⣾⢸⣈⠳⣻⡇⣶⣾⢚⡷⣺
⠀⠘⠁⠀⠀⣴⠆⠀⣿⣭⣄⣐⠆⠀⠶⣾⠇⠀⣼⣨⣽⠶⣼⣴⣧⢩⡉⡀⠀⠈⣿⣿⢳⠾⢻⣶⣶⣷⢛⢺⠿⢘⢺⠋⢱⠲⢿⡟⢛⣶⣙
⠀⡆⢰⡇⠀⠟⠀⣼⣤⣅⡉⠛⠟⠟⣹⡏⠀⠀⡿⢈⣹⣦⡴⣿⠿⡂⠀⡼⢀⢠⡏⠉⣟⡛⡛⡿⠻⣹⣛⡇⠀⣸⢀⠱⣼⣀⢠⡿⢿⡋⣿
⠀⡇⠘⠋⠀⠀⢰⡧⣭⣙⠻⠧⣶⣴⡟⠀⠀⠀⠹⣞⢳⣏⣉⡻⠀⢷⣼⡱⡂⠀⣷⣶⢛⣋⣋⣷⣤⣞⣍⣹⣿⣷⡉⢘⣧⡿⣬⡶⢺⣷⠏
⠀⣷⠀⠀⢀⣾⣟⣥⠵⡾⢊⡑⣴⡿⠀⠀⠀⠀⠀⠈⢿⡙⢥⢶⣷⣧⢶⠭⣤⣀⡿⠿⢹⣭⣽⢽⣿⣯⣧⣿⠉⡹⣾⣿⠈⣽⣫⢷⡼⠁
⠀⣿⣦⣴⣟⡞⠢⠭⣛⡲⢯⣜⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⣼⣿⡿⣧⣛⣤⠱⡀⡨⡶⠦⢺⡄⢸⠷⢤⣤⢷⣾⡿⡱⣧⡾⠋
⠀⠻⡿⢫⣏⣀⠀⢀⠀⣩⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣧⣬⣿⣭⣤⣿⣷⣿⣽⣽⣿⣿⣿⣿⣧⣤⣿⡿⠞⠁
⠐⠧⣖⣉⠔⡫⠕⣶⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠧⠭⠭⣥⣥⣭⣭⣬⠬⠼⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠾⠇⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣭⡴⢶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠳⡜⠁⠀⠀⠀⣴⣗⣦⡀⠀⠀⢠⡀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠟⠃⠀⠀⠸⣵⠀⢀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⢀⡀⠳⡖⢀⣫⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⢄⣶⠠⡀⠀⠀⠀⠀⠀⠈⣷⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡈⠑⢃⡇⠀⠓⠰⡔⣤⣠⣤⡼⠁⡶⠋⠀⠀⢀⡴⠶⠄
⠀⠀⠀⠀⠀⠀⣀⡀⠈⠀⠀⠠⡶⠛⠐⠢⣽⠀⠀⠀⠐⢒⣻⣿⣿⣿⣿⡷⠄⡠⠈⠁⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠉⠀⠀⢢⢀⡀⣘⠏⠉⠻⠿⠿⠁⠙⡞⠀⠀⠀⡄⠀⡀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣷⣦⡋⢣⣽⣷⣆⢣⡆⢀⡄⠐⢀⡁⠀⣾⡆⢡⡆⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⢧⡀⠹⣿⡟⠒⢰⣾⠗⢠⣼⣷⣀⡉⠀⠻⠆⠙⠋⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠿⠿⡏⣳⣿⠆⠀⢀⡄⠀⢡⡄⣄⢹⡿⠁⣾⣡⡄⠸⣿⡶⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠁⠈⠣⠀⠀⠐⢠⣿⡎⠉⣥⣿⡏⠩⡞⠹⢭⠛⠶⣤⡁⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣤⡈⠀⠀⠀⠀⠠⣤⣿⣿⣦⣿⣋⣷⣧⡌⡁⠸⠿⢛⣡⣴⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣿⣿⡀⠀⠀⠀⠘⢫⣿⣿⣯⣿⢭⣭⣷⣦⢄⢳⣶⣯⢷⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣿⣿⣿⣿⣿⣿⠀⠁⠀⠈⣻⣿⢷⣿⣯⣿⣻⡿⢖⠛⠻⣿⣽⢿⣷⣾⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠉⢀⠈⢻⡿⠆⠀⠀⠀⠀⠽⡏⢼⡾⡿⠃⠀⠐⡆⢰⠄⢡⣿⣛⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠿⣿⠗⠀⠀⢠⢇⣠⠀⠀⠀⠀⠀⡁⣠⣼⣿⣷⣦⣤⣍⠻⠃⢸⣋⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢾⣶⡏⠀⣀⣼⣷⣿⠼⣶⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠈⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣇⣸⡏⢉⣟⣵⢿⢹⣿⣿⣿⣿⣿⣿⣏⣻⣋⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⠁⢾⣉⡟⠉⠂⠻⠛⠿⠿⠟⣻⣿⣿⣿⣷⣯⣿⠀⡈⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠹⠀⠀⠀⣾⣿⡄⢠⣆⠸⣿⣿⣿⣿⣿⡟⠁⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣄⡀⠀⡈⠁⠀⢙⣿⡿⠿⠉⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⢰⡶⠈⠁⢀⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⠀⢸⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠴⠒⠒⠀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠁⠀⠀⣠⣤⣤⣤⣀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⠄⠀⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⡇⠀⠀⠘⢿⣿⣿⣿⣿⣷⠀⠀⠹⡄⠀⣰⡀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣀⢰⣿⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡷⢀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⢀⣿⠀⡟⣵⣦⡀⣄⡀⢀⣀⣀⢀⡀⣠⣤⣤⢰⣾⣿⣿⡇⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣿⣧⢀⡄⠀⢀⠀⠀⠀⢀⡠⣾⠟⠀⣷⣿⣿⡞⣿⣷⣿⣿⢸⣾⣿⣿⣿⣿⡸⣿⣿⣿⣿⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⢫⣿⡟⣾⣿⣿⡏⣿⣿⣯⣿⣧⣿⡄⠀⢸⣿⣿⡇⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡎⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢧⣿⡿⣸⣿⣿⡿⣸⣿⣿⢿⣿⣏⣿⣇⠀⢸⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣧⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢣⣿⣿⣧⣿⣿⣿⢳⡏⣿⣿⢸⣿⣿⢹⣧⠀⣾⣿⣿⣷⢹⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⣿⣿⣾⣿⣿⡿⠟⠀⠹⣿⣿⣿⢸⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣧⡿
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⣿⣿⣾⣯⣭⣽⣯⣅⣭⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠮⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢦⡀⠀⠀⡴⣣⠴⠣⠀⢠⡏⠂⠀⢀⢀
⠀⠀⠀⠀⠀⠀⡴⠉⠀⢸⠀⠀⠈⠒⢼⣿⣅⠀⡼⠀⢸⢀⢃⠔⠉⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡞⠀⠀⣠⢼⣲⠂⠀⠀⢸⣍⠻⠛⣦⡀⡎⢸⣷⠖⠲⣠⠤⢄⠘⣄⠀⠀⠀⢰⢆
⠀⠀⠀⠀⠠⡇⠀⠀⠀⢸⣷⡡⠀⠀⡘⢇⠀⢀⠉⠙⡿⠋⠁⠀⢀⠏⠀⠀⠻⣄⠱⡀⠀⠈⠀⡗⢄
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠸⢿⣿⠖⢩⣷⡮⠭⠉⢷⣦⣇⠀⠀⠀⡏⠛⠁⠀⠀⠈⡶⠃⢐⠀⢸⣷⡬⠖⠋⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠃⠀⠊⠉⢻⣷⣶⠳⠤⢍⠳⡄⢾⠀⡄⢀⣠⣶⠟⠓⠤⢄⣆⢸⠋⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠀⢀⠄⠚⡝⢻⡠⠀⠀⠓⠛⢻⣿⣿⡿⠋⢻⠀⠀⠀⠀⢿⣬⡝⠛⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⡀⠀⠉⢸⠇⠀⢀⡄⢠⠞⠍⡞⠀⠀⢸⣖⣄⣀⣴⠋⠉⠓⢦⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠔⠉⠉⣽⠁⠀⠈⠛⠚⡇⠀⠀⢘⣟⠛⣿⢸⣤⠢⠈⣢⡇⠀⠀⠀⢤⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠬⠷⣄⡀⣀⣧⣸⣄⠀⣾⣷⢰⣿⢸⣤⣟⠻⡁⠀⣀⡄⠀⠀⣧⠴⠂⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⠲⢿⡟⠳⡌⢙⠟⠀⠘⣿⠿⣷⢦⣿⣦⡃⣸⣿⣄⣠⡼⠯⠥⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁⠱⣄⣼⠸⠀⠀⡼⡇⢠⠃⢀⡿⠀⢻⢷⡄⣀⣀⡔⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠷⣹⠙⠻⣿⡁⠀⠾⠞⢿⣟⣉⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⠇⠀⠀⠀⠈⢧⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⡴⠃⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏

⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⣿⠿⠛⠛⠛⡿⠛⠛⠛⠛⠛⠛⢻⠃
⠀⠀⠀⠀⠀⢸⡿⠀⠰⠤⣤⣿⣤⣤⣶⣤⣠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠚⡷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡒⠒⠒⠒⠒⠚⠆⠀⠀⡆
⠀⠀⢠⣄⣺⣦⣣⠀⠀⠉⢨⣿⠉⠉⠉⢙⢛⡛⣟⣛⡻⠷⠶⠦⣤⣤⣼⣿⣶⣦⡄⠀⢀⣀⣶
⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⣰⣿⣏⡵⠉⠉⢉⣿⣿⣽⡏⣿⣿⡇⢠⡟⢣⢘
⠀⠀⣿⣿⣯⣿⠙⣦⣀⠀⠀⠀⠀⠀⠀⢀⡸⠻⠏⠿⣧⣈⢀⢸⣿⣿⣾⡇⣾⣿⣿⡿⢷⣷⣶⣾⣿⡆⡀
⠀⠀⢸⣿⢿⣿⠆⢿⣿⡁⡆⠴⠆⢀⣴⣿⣿⣿⣿⣿⠛⠛⣿⢸⣿⣿⣶⣧⣿⣿⡟⠻⣿⣿⢿⣿⣿⡇
⠀⠀⠘⣿⣏⣼⡿⠫⡙⠛⠿⣀⣢⣾⣿⣿⡿⠿⣿⣿⣗⠖⣹⣼⣿⣿⣿⣿⣿⣿⣄⠖⢠⣇⠀⠘⣿⣿⡀
⠀⠀⠀⠙⠿⠿⠁⠀⠀⠐⠀⢠⣿⠿⢿⡿⠙⢠⠘⣿⣿⣿⣿⣟⣿⢉⣉⣭⣥⣴⣿⣿⣿⣿⣿⡄⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠄⣐⠳⢽⣼⣿⣿⣿⢿⣿⡿⣟⣛⣉⣩⣥⣵⡾⠟⠀⡌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣗⠘⢿⡯⢹⣿⣿⣿⡟⠚⠛⠓⠋⠉⠁⠀⠹⣿⣿⣶⣾⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⡄⠁⢸⢟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⣠⠎⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠉⠉⠉⠩⠭⠥⢀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠈⠀⠀⢀⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⡡⠂⠀⠀⢀⣴⣻⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠠⡐⢷⢼⣿⣆
⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⣀⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠃⠀⠀⠀⠀⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⢀⠀⠄⠀⡌⠐⣤⣿⣙⡃⣻⣿⣆
⠀⢀⣶⣡⢀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣲⡄⠀⠀⠀⠀⠀⠀⠀⣈⣷⢠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡅⠰⡀⠶⣬⣶⠈⢠⣾⣿⣿⠟⣀⢻⣿⡄
⠀⣼⣏⣓⣯⡔⢀⢀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠠⠀⠀⣿⣿⠹⡷⢿⣤⣧⡘⠀⢻⣴⣧⠝⠀⣗⠸⣶⣿⠁⣴⣴⡸⣿⣧⠈⣻⠻⣿⣯⣍⣀⢻⣷
⢰⣿⣁⣻⣿⣷⢀⣾⠞⠐⢰⣠⢀⢀⠀⡀⡄⡄⡄⣄⣦⣿⡆⠀⣿⡟⡄⣶⣿⡇⣿⡇⠀⢸⣿⣸⣿⣿⣮⣦⢿⣿⡇⠷⡂⣇⢿⣿⡎⢩⣿⣿⣿⡞⡇⡈⣿
⣾⢧⣤⣿⣟⣧⣼⣿⠸⣇⣼⣿⣸⣠⣾⣿⡇⢰⣿⣯⣏⣿⡇⠀⣿⡇⠁⡛⣿⡇⣹⡷⠀⢸⣿⣿⣿⣿⣟⡒⠸⣿⣿⠸⣽⢉⢸⣿⣿⢀⣻⠋⣿⣷⠉⠁⢸
⣿⠤⢹⣿⣿⢆⣿⡧⢶⣭⣿⡏⢿⣿⣿⣿⡇⢼⡛⣿⠋⢸⣿⠀⣿⠗⠃⠄⣿⡇⣿⡷⠀⢸⣿⡏⣹⣿⡗⠂⠀⣿⣿⡇⠀⣈⡄⣿⣿⡇⢹⣿⢹⣿⠸⠇⠋
⡿⣠⢸⣿⣜⢺⣿⡗⠈⢹⣿⡇⠹⣿⢛⣿⡇⢸⡇⣿⡇⠚⣿⠀⢿⡃⠀⣾⣿⣷⢈⣷⠀⢸⣿⣧⣬⣶⣬⣲⡀⢸⣿⣷⢼⡯⣧⢹⣿⣧⢈⣛⢸⣿⡆⡢⢤
⢁⡀⢸⡿⣟⣸⣿⢨⣷⣼⣿⠀⣦⣴⣯⣿⡇⢺⣵⣿⣷⠀⡏⠀⠸⠁⠀⠙⢻⣿⡜⣿⠆⠈⣿⣿⢻⣿⣿⡿⠅⠘⣿⣿⠘⣞⡾⢸⣿⣿⢉⣿⣼⣿⡇⣅⡐
⠀⣠⢸⣧⣏⣿⣿⠶⣞⣿⣿⢐⣿⣿⣿⣿⠃⣻⢿⣿⠀⣀⠃⠀⠀⢀⠃⠀⢹⣿⣧⠹⡶⠀⢿⣿⡟⢿⣿⣯⡅⠀⣿⣿⡇⠉⠐⠀⣿⣿⠘⣿⢳⣿⢁⡿⠁
⠀⢹⢸⡏⣟⣽⣿⣋⠀⣿⣿⠐⡻⡟⣻⣿⢈⣯⣾⣷⡄⠀⠀⠀⠀⠀⢢⡀⠿⣽⣿⣎⣿⡆⠸⣿⣿⣐⣯⣑⣦⠀⣿⣿⡇⣴⣓⡇⣿⣿⣛⣧⢸⣿⡸⠃
⠀⠀⢻⣿⣾⣼⣿⣯⣷⣿⣯⣼⣶⣷⣿⡏⣸⣿⣿⡋⠐⠁⠀⠀⠀⠀⠀⠑⢄⣰⢻⣿⣿⣷⡂⢻⣿⣯⣿⣿⣿⠯⢼⣿⣷⣭⢄⡇⣿⣿⢿⣏⣿⡿⠁
⠀⠀⠀⢻⣿⢽⣿⠙⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢨⣽⣿⣿⣿⡧⢻⣿⣿⢿⣿⡭⢿⣿⣿⠙⣁⢰⣿⡟⢳⣾⠟⠁⢢⣀
⠀⠀⣃⠀⣙⠓⢿⣯⣀⣿⣿⣬⠷⢿⡗⠛⡟⠉⢩⠀⠡⠀⠀⠀⠀⠀⠀⢠⠁⠀⢨⡅⠉⠙⣿⠛⠓⢿⡟⠶⠧⡥⠼⠿⢿⡤⠤⠿⣿⠃⠉⣭⠀⠀⣬⠀⢡
⠀⠄⠤⠀⠴⠀⠰⠀⠀⠆⠀⠲⠀⠐⠂⠀⡒⠀⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠶⠀⠀⠰⠆⠀⠀⠶⠀⠀⠰⠄⠀⠀⠶⠀⠀⠶⠀⠀⠶⠀⡐
⠀⠀⢚⠀⢘⡀⢘⡁⠀⣏⠀⢨⡀⠈⡅⠀⢭⠀⢨⡄⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⢚⠀⠀⠐⡃⠀⠀⢚⠀⠀⠐⠓⠀⠀⢚⠀⠀⠐⡓⠀⠀⡛⠀⠀⢓⠐
⠀⠀⠀⠁⠘⠀⠠⠤⠄⠶⠀⠰⠆⠠⠶⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠠⠀⣈⣁⣀⡀⣩⠀⠀⢈⡃⠀⠀⣩⠁⠀⣈⣋⠀⠀⠯⠄⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠇⠀⡄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠷⣦⡀⠀⢀⣼⣿⣿⠗⣀⣀⣀⣀⠀⠀⠀⠰⠷⡞⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡅⠀⠀⠀⠈⢻⡄⣾⢟⣩⠖⠛⠉⠉⠉⠉⣹⡷⠂⠀⠐⡿⢀⣠⠞⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣿⡇⣦⠀⠀⠀⠀⡧⢫⠞⠁⠀⣀⣤⠄⠀⣼⠏⣤⠀⠀⢀⡗⣉⠀⠀⣼⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣇⣿⣧⢰⠀⠀⠃⠀⢀⢦⣾⣫⣤⡄⣴⠋⢠⣿⡆⢀⢈⡾⠃⠀⡰⢃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠝⠻⣿⡆⣇⠀⠀⣄⣾⣾⡿⠟⠁⠊⠀⠀⢸⣿⣿⣼⣨⣾⠁⠈⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠂⠀⠈⢃⡿⠴⠚⣿⡏⠉⠀⠀⠀⠈⠙⠓⢮⣻⠇⣻⣿⣷⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⡴⠦⣬⣶⣏⣀⣤⣾⡿⢁⡶⠒⠈⠡⢤⣀⣀⢰⣽⣾⡿⠀⠀⣴⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣤⣀⠤⣬⣽⡿⢿⠟⢃⣤⣭⣍⠉⠉⢠⣛⡳⠦⣤⣤⣶⣾⣿⣿⣷⠟⣠⣤⣤⠸⣷⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣻⣿⣱⢟⣵⢸⠁⠀⠀⢸⣿⣿⡷⠀⠀⢈⣩⣤⢶⣿⡽⣿⡻⣿⣧⡿⠀⠀⢀⣿⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣿⡿⣿⡈⠀⠀⣸⠘⠿⣟⣥⠀⠀⢉⠛⠧⣽⣦⡀⠀⠈⠊⣿⡇⠀⡄⣾⢏⣴⡿⠿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡏⢏⣿⣬⣁⣀⣠⠏⠀⣀⣭⠷⠾⢿⡜⣷⡀⠀⠙⠿⣧⠱⡄⡏⢠⣾⠱⠏⢚⣵⡾⠿⠟⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⣀⣉⣉⠁⠈⠳⢿⣿⣵⢋⡴⠞⢩⣶⠾⠿⢸⡇⣿⣷⠀⠀⢀⣈⠃⠚⣵⠛⣇⣀⣚⡛⠛⠛⠉⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣍⠉⠉⠉⠙⠓⢦⡀⠈⢀⡞⣴⣧⡞⠁⠀⠀⢸⡇⣿⣿⠀⣴⣿⣿⠇⡀⠻⣤⣿⡟⢷⣤⣴⣆⣀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠸⣇⣿⡀⣤⡠⣀⠀⢀⠁⠀⠀⣸⣿⢋⠔⠀⠀⠀⣼⢇⣿⢃⣠⣿⠟⢡⣾⡇⣷⢬⡙⠛⠶⡀⠉⠉⠻⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡻⡸⣷⣿⣷⣌⢳⡌⣆⠀⠀⠿⣵⡿⠀⠀⢀⣼⣫⡾⣣⣿⡿⠉⡏⡿⠛⠈⠁⢀⡇⢸⣷⡍⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣙⢮⣟⣻⣿⣳⡿⢋⡴⠖⠶⣦⡙⣦⠖⠋⠚⢩⣌⣛⠋⠀⠀⣧⠀⠀⠀⣠⡞⣷⢈⢷⣍⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⢯⡀⢌⣉⣛⡛⠃⣿⡀⠀⠀⢸⣧⢐⠚⠛⠻⠿⢓⣮⣝⢶⣄⠹⠷⠾⠟⠉⢸⣿⣯⡳⣮⣳⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢤⣴⣾⣿⣿⣿⢟⡿⣫⣶⣿⣿⡟⣡⣆⠹⣿⣶⣶⣿⠇⣼⣿⠶⠦⠬⠭⠍⠙⠓⠹⣆⠀⠀⠀⠀⠀⠙⢿⣿⡎⠙⢦⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢫⡿⣁⣠⣤⠞⠩⠞⠁⣸⡷⢠⣭⣭⢡⡈⠻⢦⣄⡀⠀⠀⠀⠀⣀⡴⣛⣤⣶⡟⠀⠀⠀⢀⠙⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡿⠋⠁⠀⠀⠀⣰⡿⢁⡿⠉⣿⢸⣿⣆⢀⢯⣝⣛⣛⣿⠍⠀⠾⠿⣟⣻⣃⣀⣀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⠻⠇⠀⠀⢀⣠⡾⣟⣵⢺⡇⠀⠸⠸⡿⣿⡌⡇⠿⠿⠛⠁⠀⠂⠉⠉⠉⢛⣿⡟⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠁⢸⣿⣿⡸⣇⠀⠀⠀⠃⢹⢧⡇⠐⢶⣤⣤⣤⣤⣴⣶⣾⠟⠋⠀⣠⡟⣴⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠙⢆⠀⠀⠀⠞⣾⠁⠀⠀⠛⠿⣦⣉⠉⠉⠀⠀⣀⡴⠋⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠈⠳⣦⣠⣾⠃⠀⠀⠀⠀⠁⠒⠤⠤⠴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃

⠀⠉⠉⠉
⠀⠑⠒⠃

⠀⠀⠀⠀⣴⣄⡀⠀⠀⢀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢹⡟⢷⣄⣠⡾⣿⡇⠀⠀⠀⢻⡟⠒⢄⢀⣠⠖⠚⣿⠀⠀⠈⣷⡞⣤⡀⠀⢀⡔⣳⣹⠀⠀⠸⣿⣷⣦⠀⠀⣠⣶⣿⡟
⠀⠀⠀⠀⢠⡟⢈⢿⣟⡁⢯⡀⠀⠀⠀⠈⣡⣖⣾⣿⣷⣖⣮⡉⠀⠀⠀⠙⣻⣟⡾⣿⢷⣿⣛⠉⠀⠀⠀⢛⣿⡻⣷⣾⡟⣿⣟⠁
⠀⠀⠀⠀⢸⣧⡏⠈⠀⢩⣼⡇⠀⠀⠀⠀⢿⣭⠞⠁⠹⢯⣽⠇⠀⠀⠀⠘⣿⣿⠇⠋⠺⣿⣿⠁⠀⠀⠀⠸⣿⣷⠎⠈⢶⣿⡟
⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉

⠀⠀⠀⢰⣦⣤⡀⠀⠀⢀⡤⣴⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⣄⠀⠀⠀⣤⠲⣶
⠀⠀⠀⠀⢿⣿⣾⣶⣴⣷⣿⠿⠀⠀⠀⠈⠀⠀⠀⣴⠄⠠⠀⠀⠀⠀⠀⠿⢀⡀⣱⣶⣆⢀⠠⠟⠀⠀⢠⠂⠉⠛⢲⣶⠾⠛⠀⢄
⠀⠀⠀⠀⢼⣿⣷⠻⠟⣾⣿⡇⠀⠀⠀⠀⢰⠂⠀⢿⠁⠀⢢⠀⠀⠀⠀⢰⣏⢡⣿⢿⣿⡌⣻⠆⠀⠀⠈⠙⣶⠿⢿⣿⠷⢶⠞⠃
⠀⠀⠀⠀⠈⠛⠉⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠘⠻⠟⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉


⠀⠀⠀⢰⡶⠲⣤⣀⣀⣤⠲⢶⠀⠀⠠⣖⠖⠒⢦⣤⣤⠖⠲⢲⡤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⣴⣦⣀⣀⣠⣶⡄⠆
⠀⠀⠀⠀⢻⣄⡈⣿⣿⣁⣠⠏⠀⠀⠀⠈⠑⣦⣀⡿⣄⣠⠖⠉⠀⠀⠀⠀⠀⠀⡈⠛⢁⠀⠀⠀⠀⠀⠀⠘⣿⡻⣿⣿⡽⣿⡇
⠀⠀⠀⠀⠈⠓⠏⠈⠀⠫⠚⠀⠀⠀⠀⠀⠀⠸⠋⠀⠙⠫⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠻⠇⠀⠀⠀⠀⠀⠀⠹⠿⠾⠻⠾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠄⠉⠆⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣰⠞⠛⠷⣆⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢿⣀⣠⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠉⠀⠀⢀⡟⣠⡴⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⣏⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⡛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢶⣄⡀⢠⡟⠀⠠⣄⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠊⢳⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣾⠟⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⣧⣀⠀⡄⢻⡄⠀⠀⠀⢀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣱⢠⡅⡐⠁⣸⠁⢀⡤⢞⣫⣥⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠂⠀⢠⡟⣰⣟⡔⡩⡦⣾⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠙⠏⠈⠀⢣⣿⡟
⠀⠀⠀⢀⣀⣤⠤⠴⠶⠴⢤⣄⡀⠀⠀⠙⢶⣤⣴⠇⠀⠀⠀⣘⣠⡾⠋⠀⠈⠲⡄
⠀⠀⠀⠈⠻⣦⠸⣏⣽⠿⢷⣮⣥⡀⢀⡀⢼⣿⣿⠓⣶⠖⠚⠉⠙⣧⡀⠀⠀⢀⡆⣀⢀
⠀⠀⠀⠀⠀⠈⠳⣌⠨⠳⣄⡀⠩⠃⠀⠀⠀⠹⣇⠸⠇⠀⠀⠈⠀⣿⣷⣶⣶⣟⡃⠉⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡌⠛⢧⡀⠀⠀⠀⣴⠋⠀⠀⠀⠟⠻⢿⣿⣿⣶⣿⣏⠀⠀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⣦⣶⣾⣧⠀⢀⣀⣀⠂⠀⠔⠒⠉⠛⣟⠛⠳⣄⣠⠾⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣺⣷⣾⣟⡏⠀⠀⠀⠑⢼⠀⠀⠀⠀⠀⠁⠀⠹⠛⠻⢶⣍⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠹⣬⠀⠀⠀⠈⠀⣸⣧⠀⠀⣀⡄⠀⠠⣎⠤⠄⠴⢒⣙⣤⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⡿⢃⣤⠠⠶⠶⣾⣿⣟⣿⠇⠀⠀⠀⠈⠶⣤⢤⣤⢤⣤⢤⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢋⣽⣤⢄⣀⠐⡛⠁⠀⠀⠀⠀⢻⣿⢿⣿⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣰⢟⢟⣀⣠⡴⣪⡇⠀⠀⠀⠀⢀⡼⠁⠀⠏⠛⡦⢤⣤⣮⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⣏⡼⠭⠍⠒⣈⡴⠿⠁⠂⠄⠀⠚⠀⠀⠀⠀⠀⠐⡂⠻⢿⡿⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣤⡴⠶⠞⠛⠋⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⣀⣴⡳⣄⣃⢳⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢷⣝⢮⣝⣸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣮⣍⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶⡆⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠐⣿⠂⢿⣅⢼⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣄⠘⣷⠀⠙⣶⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⠒⣡⠀⠀⢈⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢊⣹⣄⡇⢩⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⣇⢸⣈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⠋⣆⢻⢸⣧⡏⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⠺⡅⢺⣘⡇⡿⠸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠖⠒⠶⠤⣀⠀⠀⠀⠀⢀⡠⠖⡉⢶⠈⡇⣿⢸⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣱⣿⠏⠀⠀⠀⠀⠀⠻⢦⡤⠒⠉⢰⡀⢻⢸⣀⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢰⣿⡏⠀⠀⠀⢀⢀⠰⣆⠀⠀⠀⠀⠀⡠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⢸⣿⠁⠀⠀⡆⢿⢸⡆⠻⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⢿⡘⠷⠙⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠈⢿⡆⠀⠀⠀⠁⠀⠀⠀⠀⢀⣾⠁⢀⠀⠀⢀⡀⠄⠀⠀⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⣠⡿⣥⣂⡈⣉⣉⠤⣤⠀⠀⠈⢦⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⠷⠤⣤⣀⣀⡀⠲⢦⣤⣤⠾⠋⢰⡏⠀⠀⠠⠀⠀⢹⠀⣠⣶⠚⠛⠳⣗⣒⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣀⣀⠴⠛⠿⠻⠿⢿⠶⣲⣶⣤⢬⣥⣀⣀⣀⠀⠀⠘⡶⠋⠙⡻⠳⢶⡶⠦⠤⡤⠤⠀⢿⡀
⠀⠐⣷⣤⣤⣀⡀⠀⠀⠀⠒⠈⠉⠭⠦⠒⠶⠤⠤⣁⣉⠁⠋⠛⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠘⣇
⠀⠀⠘⣷⣈⢉⠉⠛⠒⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⢒⣦⡤⠄⢠⣄⡀⠀⠁⠀⠀⠻⠀⠀⠀⠻
⠀⠀⠀⠸⣷⠭⠍⠙⠋⠒⡒⠒⠀⠠⠨⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⠉⠀⠀⠀⣿⡇⠈⣹⠉⠉⠁⠛⠀⠀⢀⡞
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠘⠓⡘⠇⠸⠇⠀⠀⠘⠓⠚⠀⠀⣿⡄⠐⠒⠂⠉⠀⠀⠀⠀⢿⡇⢀⡏⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠻⠶⠶⠒⠁⠀⠀⢸⣧⣼⣀⣀⣀⠀⠀⠀⠋
⠀⢀⣀⣤⠄⢠⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠪⠭⠭⠭⠄⠀⠼⠃⠐⠒⠒⠂⠠⠤
⠈⠉⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠶⢶⣤⣤⣀⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢀⣀⣤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠀⠀⠈⣇⣠⠤⠶⠚⠛⠋⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶