Saltwater Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣄⢶⣾⠻⣿⢻⣿⢿⡶⣾⣭⣛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⢿⣿⣿⡌⣿⡿⣿⡾⣿⣾⣧⣿⣼⡟⣿⣷⣤⡀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣜⢗⣽⣿⣇⣿⣷⣿⣷⣿⣼⣿⣻⣼⡿⣿⣿⢾⣿⣷⣤⣤⡶⠛⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣹⣯⣏⣿⣻⣧⣿⣿⣿⣿⡿⠿⠛⠛⢷⣄⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣏⣿⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣍⣙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠿⠿⠿⢿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣟⢿⣿⣿⡟⢷⣶⣭⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣾⣿⢈⣿⣾⡏⣻⣹⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡏⣶⢹⣿⣿⣿⣇⣿⠿⣿⣸⡟⢿⣝⣷⣿⢻⣦⡀⠀⣠⡶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣿⣿⣿⣿⡟⣿⣡⣿⢙⣷⣾⣿⣧⣿⣿⣿⣿⣿⡁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠈⠻⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣏⣹⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣍⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⣛⣛⠿⠿⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡉⠉⠛⠛⠛⠶⢭⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣏⣉⣉⣛⠛⠲⠦⣌⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡏⣶⢹⣿⣿⣿⣟⢉⣉⣉⣙⣛⠓⠲⠭⣗⣿⣦⡀⢀⣠⡶⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣿⣿⣿⣿⣟⣉⣉⣉⣉⣉⣭⣭⣭⣿⣿⣿⣿⣿⡁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠈⠻⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠻⣯⡽⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣍⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⣠⢾⣧⣤⣀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣷⣦⣤⣄⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣤⣄⣴⣆⠀⠀⠀⣠
⠀⠀⠀⠀⠀⡀⠂⢀⡺⠿⣻⣾⡧⠶⢛⠷⢾⡅⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠛⢋⣩⠟⠉⠻⠆⠀⠀⠀⠀⠀⠀⣠⡶⠟⠿⠛⠿⢋⠿⣟⡿⠗⠺⣏
⠀⠀⠀⠀⠰⠠⠀⠈⠀⣴⠛⠉⣠⠖⠁⠀⠀⠑⠀⠀⠀⠀⢰⣿⠟⠋⢩⢀⣩⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠙⠀⠀⣐⡋⠵⠞⠋⠋⠀⠀⠀⠈
⠀⠀⠀⠀⢦⡀⢠⠄⢦⣆⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠟⠃⠚⠛⠦⣄⡀⢀⡴⠂⠀⠀⠀⠀⠀⠀⢀⡤⠀⠻⣿⣿⣿⣿⣷⡄⠀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣿⣶⣶⣤⣄⣴⡟
⠀⠀⠀⠀⢀⠖⠁⠀⠘⢓⣈⢉⠄⢈⡷⢺⡄⠀⠀⠀⠀⠀⠀⢠⠋⠤⢀⡄⠟⢻⡟⣻⣿⠓⣨⣿⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⢿⣿⠟⠉⣩⠟⠁⠙⠳⡄
⠀⠀⠀⣠⠃⠲⠀⠀⠼⠟⠉⢡⠞⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⣤⡀⠀⣸⢃⣺⣿⠿⢿⠟⠀⠀⠙⠆⠀⠀⠀⠀⠀⠻⠟⠋⡡⢤⣤⡃
⠀⠀⠀⠈⠛⠀⠘⠁⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣷⣦⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⢿⣿⣦⣾⣧⡄⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⢙⣷⣿⣶⣄⣀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⠆⠀⠀⠀⠀⢠⡄⠑⣀⠶⢀⣙⣯⡽⢿⡗⠂⣉⣿⡅⠀⠀⠀⠀⢀⠂⠐⢪⣿⠛⣽⡿⢯⠿⢿⣷⠀⣀⣤
⠀⠀⠀⠐⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠋⠀⠀⠀⠀⠀⠛⠻⠤⠤⢾⣼⣿⠂⠘⠿⠅⠀⠈⠛⠃⠀⠀⠀⠀⠘⠏⠈⣍⠁⠀⣾⠿⣋⡶⢛⡛⠾⣹⢏
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣿⡟⠉⠹⡿⠃⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠷⠐⠛⠶⠶⣤⡀⣠⡖⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣷⣶⣾⡶⢤⣄⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⡶⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠄⠀⠀⠔⠊⢉⡁⣈⠿⠛⠉⠙⠧⠀⠀⠀⠀⠀⢀⠖⣥⠈⠈⠹⠟⠁⢀⡠⠂⠀⠀⠙⠆⠀⠀⠀⠀⣀⡀⢀⣴⣿⣿⣷⣮⣷⣈⡽⢂⠈⢧⡄
⠀⠀⠀⠀⣶⣈⠁⢀⣰⠞⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠐⢦⣴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⣭⣶⣛⣿⣋⣷⣟⣡⡤⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⠿⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢦⢤⣆⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣖⣃⣔⣿⣋⣉⡜⣿⡯⣓⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠾⣛⠋⠉⠉⢭⡉⢹⡍⠉⠛⠿⢶⣤⣈⢵⣗⣢⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠴⠞⠉⢵⠔⡀⠀⠀⣇⠀⠀⠀⢧⣹⣿⠀⠀⢸⡷⣦⠈⠙⢿⣆⠈⢩⣶⡦⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⣠⣆⣴⠆⠀⢀⠀⢫⡎⠀⠀⠑⡄⠀⠀⠈⢾⣿⠄⠀⠀⣗⣄⠀⠀⢰⣯⠳⣾⡟⠁⠁⠀⠀⢀⡠⣺⣽⡞
⠀⠀⠠⣾⡷⠉⠀⠀⠀⠘⢀⡄⡇⠀⠀⢠⠇⠀⠀⠀⢸⡿⠀⠀⠀⢸⣾⠀⠀⢯⣯⠀⠈⡹⠓⠂⢶⠖⠉⣿⣟⡿
⠀⠀⢢⠤⠝⠀⠀⠀⠀⠀⠈⡏⠁⠀⣴⣾⠷⠾⠷⠚⣻⠋⠀⠀⠀⢈⡇⠀⠀⣸⡇⠀⠀⡉⠀⠀⠸⠀⠀⢩⠷⣧
⠀⠀⠈⠒⢄⡀⠀⠀⠀⢀⡴⠃⠀⠀⠉⢻⠆⠀⠒⠂⡹⠀⠀⠀⠀⡷⠀⠀⠀⣸⠁⠀⠀⡠⠔⠂⠒⢦⡠⣾⣳⢿⡄
⠀⠀⠀⠀⠀⠉⠓⢤⣈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣴⣿⣗⡶⠀⠀⠀⠙⠦⣝⢳⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣿⣿⣿⣿⠗⠁⠀⠀⠀⠀⠀⠈⠙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣟⠄⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⢠⡄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⡀
⠀⠀⠀⠀⢠⡎⠶⣆⠉⢙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠱⣿⣿⣌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⣿⣬⣷⡀⠄
⠀⠀⠀⠀⠀⠙⢮⡅⣂⡉⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣽⣿⣛⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣟⣫⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣴⣻⣷⣌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠃⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣏⠳⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⠦⣦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠙
⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣾⣦⣤⣴⣇⠀⠀⢠⠄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣦⣤⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠼⣦⣀⠀⠀⠀⢀
⠀⠀⠀⢀⣴⠿⠛⠛⣉⡤⠀⢉⠙⠒⢯⠀⠀⠀⠀⠀⠐⠈⠀⠀⡀⠀⢀⡠⠤⠀⠦⡀⠀⠀⠀⠀⠀⠀⡔⠈⡀⠀⣀⠠⠍⠑⠦⢰⡋
⠀⠀⠀⣿⠍⠁⢀⣀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢀⡈⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠤⠐⠡⠔⠀⡤⠊⠁⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠀⠰⠦

⠀⠀⠀⠐⠂⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣴⣦⠙⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⢿⠛⠀⢀⢼⣯⡀⠀⠀⠀⠀⠀⠀⠐⠲⡦⠔⠚⠶⠧⣼⣿⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠶⠶⠦⢴⣟
⠀⠀⠀⠀⠀⠊⠀⠲⠿⣬⣋⣙⠓⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡙⠋⠉⢘⠃⠦⠠⡇⠀⠀⠀⠀⠀⣀⣼⠛⠁⠀⡤⠄⢠⡆⠈⠀⠀⠹⡄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠙⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠱⡀⠀⠀⠐⠈⠁⠉⠃⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣄
⠀⠀⠀⠀⠉⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠲⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠁⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣠⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⣦⡀⠀⠀⣀⣤⣴⡿⠿⠿⢿⡿⠿⠿⠷⣶⣤⡀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣧⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀⣤⡾⠋
⠀⠀⣿⡁⠀⠉⠉⠀⠀⠀⠀⠈⠙⠛⠇⠀⠀⠀⠁⠈⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠛⠇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠉⠉⠛⢦
⠀⠰⠋⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠉⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⢲⡀⣠⠤⠀⡀
⠀⠀⣀⣤⣤⣴⣿⣷⣴⣿⣷⣄⣀⣤⡀⢀⣠⡤⠀⠀⠸⣷⣄⠀⢀⣄⣠⣤⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀⣀⡀⠀⠀⢀⡴⠛⢦⡀⢸⠆⡇⠀⢀⡱⠀⣠⡀
⠀⠋⠉⠀⠁⢳⡿⠗⠊⠉⠙⠛⠉⠉⠋⠩⣿⣧⠀⠀⢀⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠋⠀⠀⠰⢋⣤⣄⣀⠳⣼⣶⣿⣷⣏⣱⠞⠁⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠼⠟⠁⠀⠘⠟⠓⠀⠀⡤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠉⠉⠻⣿⣿⣿⡿⠤⠶⠶⠶⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠀⠀⠈⠉⠉⠙⠲⣦⡀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠴⠖⠋⠸
⠀⢀⣠⣤⣴⣦⣤⣄⡀⠀⢠⣦⣤⣤⣄⣀
⢰⣿⠟⠉⠀⠀⠈⠙⠻⢷⣤⡉⠉⠉⠉⢙⡇⠀⠀⠀⠀⠀⣀⣀⣴⣦⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⣀⣀
⢻⣿⣦⡀⠀⢀⠀⠀⠀⠀⠙⠻⢷⣶⡶⠟⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠶⢾⣟⠁⠀⠀⢀⣠⣴⣶⣶⣟⣿⣿⣶⣶⣤⣽⣆⣀⣀⠘⢆⠀⠀⢀⣤
⠈⠛⠿⣿⣿⣿⣿⠿⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⠉⠁⠐⠋⠁⠀⠀⠙⠂⠀⠻⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⠿⠗⠒⢻⣿
⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⠉⠉⠩⠥⠴⠂⠀⠀⠐⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀
⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⡤⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⣀⡠⠄⢀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⣠
⠀⣶⠆⠀⢀⣁⣠⣤⣼⣿⣾⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠅⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿
⠀⢿⡄⠀⠚⠻⢿⣿⣿⡏⠀⠈⢹⣿⣿⣿⣿⣟⠂⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠆⠀⠀⠀⠈⠉⠉⠉⠁⠻⠟⠉⠉⠁⣤⣶⠀⠀⠘⠿
⠀⠀⠀⠀⠀⣦⡠⠤⠙⠛⠒⢒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣷⣶⣤⣤⡄
⠠⣤⣀⠀⢀⣄⣀⣰⣶⣿⣿⣶⣿⣿⣦⣤⣀⠀⠀⠀⠀⢠⣤⣴⣶⣾⣶⣷⣧⣤⣀⡀⠀⣀⣤⣤⠄⠀⠀⠀⠀⠀⠀⢴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣤⣴
⠀⣿⣿⠷⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠻⢶⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡶⠶⣶⣿⣿⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿
⠀⠉⠁⠀⠀⠈⠀⠘⢿⣿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⣷⠄⠀⠀⠀⠙⠛⠿⠄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠻⣏⠉⠉⠛⠛⠛⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⢿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣂⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣩⣱⠏
⣀⣤⡶⣶⣿⣿⠿⠿⠯⣻⡟⠃⣰⡇⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⣷⣶⣦⣤⣴⣶⣿⣿⣿⡶⠋
⠹⣝⡗⠈⠯⣉⣀⡐⠒⠛⢣⡿⣿⣇⠀⠤⠦⠢⠠⠩⠉⠁⠸⠈⠠⠑⠤⠨⠅⠁⠉⠩⠭⠌⠈⠄⠁⣈⡚⢁⡒⠤⠄⡨⠭⠥⣭⣤⣿⣿⡏
⠀⠈⠻⢤⣀⢈⣡⠥⢤⣶⣤⡉⡸⢌⡄⢀⡀⠀⠀⠀⠀⠄⠢⠐⠒⠐⠐⠄⠀⠀⠀⠀⠀⠢⠔⠄⠐⠂⠂⠒⠒⣂⣠⣴⠶⠶⠶⣬⣿⣿⣿⣄
⠀⠀⠀⠀⠈⠑⠒⠦⢤⣭⣿⣶⠀⣀⢠⡤⠀⠉⠁⠀⠂⠀⠒⠂⠐⠒⠒⡈⠉⠁⠉⠁⠐⠂⠀⣀⣀⣠⡤⠖⢋⣭⠞⠁⠀⠀⠀⠈⠳⣟⠻⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⣿⣿⣿⠷⠿⠿⠾⠶⠒⠚⢿⣿⣿⡟⠛⠛⠛⠉⠉⠉⠛⠿⣯⡦⣲⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⡶⠎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢿⣧

⠀⠀⠀⣀⣀
⠀⢀⣀⠀⠀⠈⠙⠒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⣀⡄
⠀⣀⣀⠀⠀⠘⠲⡠⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠁⠀⠀⣀⣠⣠⠤
⠀⠁⠉⠀⠷⣄⡀⠀⠘⢦⡈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠧⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⡀⡘⠀⠀⠀⢠⡀⠈⠁
⠀⠀⠤⠤⠀⢀⣀⠘⠓⢄⠅⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣴⠉⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠉⠀⠀⠐⠗⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⢖⢤⡙⣯⡧⠀⠀⠀⠀⠀⠀⢳⠸⠄⢻⣇⡆⡜⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⡈⠃⠀⢐⠕⠀⠀⢀⣤⠀⠙⠋⠁
⠀⠐⠛⠻⠀⠰⠖⠦⠀⢀⠁⡑⢃⣳⡄⠀⠀⠀⢀⠀⠈⡆⡦⣎⣯⣳⢠⠔⣶⣢⠀⠀⠀⠀⠸⠃⠀⠉⠁⡀⡈⠋⢀⠀⠘⠋⠁
⠀⠀⢤⢀⠀⠀⠀⠀⠀⠙⠵⠌⡊⢿⣷⠀⠀⠀⢸⡀⠀⣹⣿⡟⣑⠁⢈⡌⠋⠀⠀⠀⠀⡤⢀⣀⠟⠠⡠⠊⠠⣠⠕⠁⠀⠀⠀⣰⡄⠐⠖
⠀⠀⠀⠀⠀⠀⠉⠛⠃⠠⣤⡐⢾⣏⢿⠃⠀⠀⠀⢳⠴⠋⡿⢿⡹⣗⣟⠀⠀⠀⠀⠀⠼⡁⡀⢡⣀⣠⡰⠄⠀⢀⣀⣠⠄⠀⠀⢀⡀⢠⡤
⠀⠀⠀⠀⢠⣤⠀⠀⣀⡀⠈⠋⣠⢀⣌⠚⠀⠀⠰⢛⣶⠃⣴⣦⢻⣾⣾⠀⠀⢀⠤⢤⡓⠻⣶⠭⠐⣃⠤⠦⠀⠀⢈⡀⠀⠐⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠤⠄⢨⣘⠊⢀⣜⣙⣦⣙⣶⡲⣦⣾⢻⢸⠈⡎⡆⣗⢹⣃⣠⣟⡵⣋⢥⣥⡵⠒⠁⠶⠒⠒⠂⠈⠛⠉⠀⠀⠀⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⣿⣽⣷⣿⣍⡽⠟⡜⢼⢠⡇⣧⢛⡌⣇⠰⡒⣚⣭⡱⠾⠗⠶⠶⠛⠛⠛⠻⠦⠶⠶⠶⠶⠴⠶⠚
⠀⠀⠀⠀⠀⠀⠀⢤⡄⠤⠖⠲⣶⢿⣿⣿⢿⠖⠈⢑⣊⠀⣁⠘⡟⠋⢺⡾⣾⣾⣿⣟⢒⡋⢙⣋⣘⠚⠿⠴⣤⣤⡀⣀⣀⣀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠗⣨⠓⡋⣫⠃⠈⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢾⢮⢉⠄⢆⡙⠔⢀⠈⠁⢠⡄⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠐⠚⠀⠀⡼⢀⠚⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢦⡋⢈⠠⣆⠑⢂⣄⠀⠈⠃⠤⢆⡄⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⠀⠦⠉⠃⠶⠤⠄

⠀⠀⠀⠀⠐⠋⠙⠓⠶⣤⠀⣠⠆⠀⠀⠀⠀⢀⣺⣼⣶⣶⣶⣄⢰⠂⠀⠀⠀⠀⠀⣤⡤⢴⣦⣤⡀⣠⡄
⠀⠀⢀⠀⠂⠀⣀⡠⠒⣀⠀⣿⡀⠀⠀⠀⢴⣿⡿⣿⠟⠽⠋⠀⠛⠀⠀⠀⠀⡄⠄⠀⣤⠴⢒⣲⠄⠹⠇
⠀⠀⠈⠀⠀⢤⣌⠁⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣀⠦⠤⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⢈⣀⠀⠻⢠⣆⠀⠀⠀⠀⠀⡊⠁⠹⣿⣿⢿⣿⠉⠻⠇⠀⠀⠀⠀⠀⠄⠀⠿⣿⣿⣯⣤⣦
⠀⠀⠀⠀⠀⠈⠉⡠⠆⠘⠇⠀⠀⠀⠀⠀⠉⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣘⠓⠿⠇⠈⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⣠⣶⣤⡄⡴⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢶⣴⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣄⢹⡄⡇⡇⡧⠠⣼⠀⠀⠀⠀⠀⠰⣟⢰⢷⣼⢱⠶⣇⠀⠀⠀⠀⠀⠀⢤⠀⣸⡷⢮⣵⣦⣀⣤
⠀⠀⠤⣾⡘⣧⠗⣧⣏⠈⠻⠀⠀⠀⠀⠀⠙⠿⢿⡟⠛⠻⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠥⠇⠰⠗⠂⠈⠋
⠀⠀⠀⠀⠈⠛⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣀⣄⡀
⠀⠀⠀⠀⢨⣿⣿⠿⠿⠓⢺⡇⠀⠀⠀⠀⢀⠠⠃⢀⠩⠙⠦⠀⡀⠀⠀⠀⠀⢀⣴⡟⢻⢻⣿⣿⣧⣶⣦
⠀⠀⠄⠈⠀⣙⠋⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡴⠀⠀⠉⠀⠀⠀⠀⠸⠆⠀⡀⣸⠯⠿⠆⠈⠉
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⣿⠀⡝⠣⣴⡆⠀⠀⠀⠀⠀⠀⠀⡩⡮⣿⣿⠂⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡉⠺⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠔⡣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⢤⡴⠾⠷⣧⣾⣮⣼⣦⣀⣀⣶⠗⢲⣦⣄⣀⣀
⠀⠀⠀⠀⠀⣀⠠⠒⠋⠉⠥⣄⡀⠀⠀⡀⠀⠀⠀⠂⠀⠈⠀⢋⢉⠙⠛⠛⢶⣮⣄⣩⠙⠒⡒⠤⣀
⠀⠀⣠⠔⠋⡶⠀⠀⠀⡄⠀⠀⠁⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠉⡙⠶⢦⣄⣀⡓⠀⠀⠀⠀⠀⠀⣀⡤⠔⣆
⠀⢮⣀⣀⠀⠀⠀⠀⠀⡇⠀⠠⠀⢾⣻⣿⣿⣿⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠉⠙⠳⠦⣤⣤⠔⢫⢵⠆⠀⠸⡀
⠀⠀⢱⡦⣄⣀⠐⠂⠔⠀⠀⠀⠀⠀⠀⠉⠙⠛⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⡀⠬⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠿⡻⣟⡻⡛⠲⠶⠶⠶⠤⢤⠤⠤⠤⠤⠤⠤⠴⣶⡶⣶⣶⠶⠶⠒⠒⠂⠉⠉⠉⠉⠓⠲⢤⣉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⡤⠶⢚⡛⠉⠉⠉⠙⠉⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢦⡀
⠀⠀⠀⠀⢀⡞⠁⣀⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⡞⣋⣁⣀⣀⣹⣆⣀⡀
⠀⠀⠀⠀⠘⣇⠰⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠈⢉⣭⠞⠋⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⢀⣀⣬⠶⠞⠋⠉⠋⠀⠀⠀⠘⠉⡟⠙⡳⢦⣄⡀
⠀⡤⣄⣀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠁⠀⣠⠏⢀⠔⢂⣤⣶⠶⣦⣤⣄⣼⣣⠴⠞⠋⠁⠀⠀⢢⡶⠶⢦⡀⠀⠀⡇⢀⠃⠛⠃⠀⠈⢳
⠀⣧⠀⠀⡍⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⣰⠋⠀⡆⢠⣿⠃⠀⠀⠈⢆⠈⠉⠉⠆⠀⠀⠀⠀⠀⣿⠁⠀⠀⠙⣦⠀⢃⠀⠣⡀⠀⠀⣴⡿
⠀⢸⡀⠀⠀⣹⢦⡀⣀⠀⠀⠠⠀⠀⠀⠀⣠⣮⢁⡴⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⢆⠀⠀⠐⠀⠀⠀⠀⠀⢿⡀⠀⠀⠈⡗⠀⠈⠢⣀⣈⣴⠞⠉
⠀⠀⠱⣄⡞⠁⠈⡇⠀⠑⡄⠀⠀⢀⡀⡿⢁⡾⠋⠀⠀⠀⠀⢃⠘⣿⣆⠀⠀⠀⠀⠘⣤⠶⡶⣤⣀⡀⠀⠈⢄⠻⢶⣦⣶⠶⣠⡤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠁⣀⣥⠞⢃⠌⠀⠀⠀⠀⠀⠀⠀⠣⢌⠻⢷⣶⣤⣤⡾⠋⠀⠳⣄⣈⣉⣉⣹⠟⠛⣯⣀⣠⡼⠃⢀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠁⠀⢠⠏⠀⢻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⣀⡀⠠⣤⢯⠀⠈⠀⠙⠛⠛⢛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢁⡞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⣖⡶⠿⠟⠛⠛⠋⢉⠉⠉⠠⠀⠐⠀⠀⠸⣄⣀⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣠⠏⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⠋⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡜⠁
⠀⠀⠀⠀⢸⢱⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠘⡀⠀⠀⠀⢀⡜⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⡠⢂⣴⣿⠇
⠀⠀⠀⠀⡾⡘⢇⠀⠀⠀⣠⣞⠁⠀⠀⠀⠀⠀⣇⠀⠀⢀⡞⢄⡈⠛⠁⠀⠀⠀⠀⠸⡄⠀⣠⢤⣶⠞⣩⠞⠁⠀⣠⣴⡿⠋⠁
⠀⠀⠀⣸⢗⢔⣌⣳⡶⣴⣿⡎⠀⠀⠀⠀⠀⠀⡸⡆⠀⣸⣤⣤⢬⣢⠀⠀⠀⠀⠀⢰⠇⠀⠓⠛⠛⠛⣋⣤⣴⡯⠟⠋⠀⠀⠀⣤⣤⡤⣀⡀
⠀⣴⠞⢯⣑⠠⡈⣻⠇⣏⠟⠁⠀⠀⠀⠀⠀⢠⣿⡟⠀⠹⣤⣒⣂⣿⠃⠀⠀⠀⢀⣞⣀⡠⠤⠖⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠈⠙⠳⢭⡢⡀
⠀⠉⠺⠦⣬⣙⣻⠏⢸⠃⠀⠀⠀⠀⠀⠀⠀⠘⣽⠃⠀⠀⠀⠉⠉⠉⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠦⢤⡼⠛⠛⢲⡈⢳⣷
⠀⠀⠀⠀⠀⠀⠙⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⠀⠀⠀⢀⣀⣠⠴⡮⠥⠤⠤⠴⠶⠖⠛⠁⠀⠀⢸⡇⢸⣿
⠀⠀⢤⠶⠛⠁⢴⣾⠀⠀⠀⡠⠄⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡤⢖⣚⢩⡅⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⢾⠛⠓⠺⠛
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣧⡀⢀⠀⠀⠀⣸⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢫⠡⣄⡎⣭⠺⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀⠘⣇⢈⣹⠀⠀⢠⠏⠋⡀⠳⢄⠀⠀⠀⠀⣠⠞⠙⠒⠀⠀⠘⠇⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣠⠋⠸⡄⠆⣠⠊⠀⠀⠀⠀⠈⠀⠀⠀⡰⢧⣦⠀⠀⠀⠀⠀⠀⠀⣤⣴⠚⠙⡄⠀⠀⠀⠄⠀⢠⡟⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣇⠀⢰⢃⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠁⠐⠀⠀⠀⠀⠀⠀⠿⣭⡀⢀⡇⠰⠀⢀⠀⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⣶⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠲⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠉⠀⠀⠂⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠃⢿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⢦⠀⠀⠀⠀⠀⠡⠄⢠⠀⣐⣈⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠛⠊⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⠤⠤⠤⠤⠤⠄⢄⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠐⣵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠑⠄⠠⠔⠈
⠀⠀⠀⠀⢄⠀⣠⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠈⡉⠳⡉⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠄⡀⠐⠀⡄
⠀⠀⠀⠀⠈⠑⢄⡀⠀⠂⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠴⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢉⣉⠉⠛⠛⠓⠒⠒⠛⠉⠉⠁⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠂


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡷⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢠⣿⣯⣼⣕⠓⠊⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡦⠤⠤⣄⡀⠀⠀⢄
⠀⠀⠀⠈⠛⢿⣗⡛⢿⠿⢿⣿⣷⣦⢾⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⢠⣄⣠⡀⠀⠀⠈⣼⡇⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⢤⡄⠀⠀⣠⠈⠒⠲⠊⣀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠢⢭⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⢆⠈⠈⠀⡻⠇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠈⢹⠀⠘⠤⠀⠀⣠⠤⠾⠆⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠙⡶⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⣀⠀⡀⠀⡴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡠⣴⠟⠀⠀⠀⠀⠈⠹⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠖⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⠀⠀⠀⠀⠈⠐⠐⠀⠀⠀⠀⠠⢮⣾⣯⣟⣫⠗⡦⢀⢀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠳⣦⣤⣤⣀⣀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠎⠀⠀⠀⡀⠌⠑⠂⠀⠀⠀⠀⠀⢀⡀⠊⠄⡟⢿⡟⣛⢿⡟⠛⠛⠻⠿⡧⣤⣬⡞⠁⠀⠀⠀⠀⡀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⡀⠀⠈⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠯⠉⠙⠋⡝⠛⠓⠋⠉⠀⠈⠁⠙⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠐⠄⠈⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⡿⣿⠟⠛⡟
⠀⠀⠀⠀⠢⠄⠨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡓⡋⠣⠆
⣶⣶⡶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⡀⠀⠀⠀⠀⣶⢀⣀⣤⣴⣦⣤⣤⣤⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠁
⠀⠘⢦⡤⣤⣴⠷⠿⠟⢩⣉⣥⣠⣤⡿⠋⠀⠀⠀⢠⣤⣤⣠⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣦⣤⣤⠀⣠⡴⠂
⠀⠸⠁⠀⢨⡭⣀⣀⣠⣀⣈⣉⠋⠀⠀⠀⠀⢦⣄⣙⢿⣿⢻⠥⡆⠀⠀⠀⠀⡠⠾⢻⣅⡀⠈⠑⠲⣒⣿⠟
⠀⠀⠠⠘⠁⠀⠀⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⢀⣎⣻⣿⣷⡟⣁⡀⠀⠀⠊⠁⠀⠀⠀⠉⠙⠿⣿⠀⠘⣿⡆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⢀⠔⠋⠟⠉⠙⠛⠉⠉⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠈⠁⢸⡇
⠀⠠⣄⠀⠀⠀⠀⠀⠀⣿⣷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⢄⡀⠀⠀⠀⣠⡆⠀⠘⠁⠀⠀⠀⢞⣻⡀
⠀⠀⢸⣧⡀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠘⣷⢳⣬⣧⣿⣦⣄⠉⠁⣀⣠⣤⣤⡾⠋⠀⠙⠛⠦
⠀⠀⢠⡿⠋⠛⠛⣻⣿⣿⣿⡿⠏⠉⠁⠐⠒⠂⠀⠀⠀⠀⠀⠀⠸⠥⢤⣟⡙⠛⢛⣿⣿⣮⣿⣿⠿⠉
⠀⠀⠊⠀⠀⢀⠤⠒⠋⠉⠁⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡄⠙⠻⠿⠯⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⣀⣠⣽⣀⣀⢀⣴⡏⠀⠀⠀⢠⡀⠀⠀⠀⣀⣈⣅⡀⠀⠀⠀⠀⠀⠘⡦⠉⠛⠻⣤⣀⡀⣶
⠀⠀⠀⢀⠿⣿⣿⣯⣿⡿⠉⢺⡇⠀⠀⠀⠈⢿⣄⢀⣾⠿⠿⠛⠃⠄⣀⡒⠂⠀⠀⢀⣠⣴⣶⡮⠛⢿⣿⡀⡔
⠀⠀⠀⠉⢀⣈⣩⡄⠿⣇⡀⠀⠁⠀⠀⠀⠀⢸⣿⢍⣗⠉⢀⠀⠀⠠⠤⢤⡀⠀⠀⠀⠹⣋⣁⣀⣀⠄⠀⣹⣧⡀
⠀⠀⠴⠓⠀⠉⠀⠀⠀⠀⠈⠁⠒⠂⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠉⠛⡿⠀⠀⠈⠁⠀⠉⠉⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣽⣭⣤⣭⣯⣽⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠂
⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠴⠓⠁⠀⠀⠀⠀⣀⡤⢴⠒⡖⣲⢦⣀
⠀⠀⠀⠀⠀⠀⢠⣞⡍⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣀⡀⠤⠊⠀⠀⠀⠀⠀⢠⠺⡅⠃⢰⠀⠀⠁⠈⡘⢹⢦
⠀⠀⠀⠀⠐⠀⠈⠙⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠂⠱⠀⠀⠀⠀⠀⠐⢀⠊⡼⡇
⠀⠀⠀⠀⠀⠘⠒⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡢⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⠠⢤⠄⠁⠀⠀⠀⠀⠀⠙⠦⣬⠁⢀⡠⣤⢄⡀⣤⠔⠛
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⡍⠀⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⣤⣶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⠟
⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣴⣃⣾⠏
⠀⠀⠒⠞⠿⠿⢿⠛⠿⢿⣟⣿⡿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠈⠓⠻⠿⢿⡛⠛⠼⣿⡟⠿⠿⢿⡿⠷⠶⠶⠶⠶⠿⠍⠛⠉⠉⠀⠀⠠⠤⠄⠀⠀⠀⠐⠉⢷⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⣾⣆⠤⢽⡶⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⢡⠀⠀⠀⠀⠠⠂⠄⠈⠀⠀⠜⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣐⣰⢁⠀⡈⠡⠔⠩⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠘⠈⠁⠒⢠⠃⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠳⣄⠀⠀⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⣓⡔⠀⠀⠀⠀⠀⠀⠒⠤⠀⠒⠁
⠀⠀⠀⠀⠀⠒⠂⠀⠁⠀⠀⠀⡅⠀⠀⠈⠠⠆⠙⠛⠁⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠋⠇⡀
⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠓⠒⠀⠑⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠈⠀⠀⢀⢷⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠪⠥⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠀⠀⠂⠀⠀⠄⠀⠀⠰⡙
⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⡆⠀⠀⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠈⠡⠤⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡀⡇⠰⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠎⡄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠙⠒⠂⠂⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⢀⢤⣤⣤⢤⣤⣀⢀⡀⠀⠀⠠⠌⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡀
⠀⠀⠀⠀⠀⠀⠸⠟⠁⠁⠀⠀⠈⠓⠇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⢀⠀⡰⠊⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸
⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠠⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢁⠜⠁⠀⠀⠁
⠀⠀⠐⡵⢋⠞⠡⠄⣀⢀⠀⣀⠀⡄⢢⡘⢮⡳⠀⠀⠀⠀⠀⠀⠀⡀⠀⠼⠠⠇⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢡⠏⢀⠉⠐⠃⢈⠀⠸⠀⢠⠀⢱⣌⡇⠀⠀⠀⠀⠀⠀⠀⠈⠘⢸⠸⠀⠀⢀⠄⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠳⢾⡀⢼⠀⢸⠀⠠⡄⠀⣧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⡇⠀⣀⠔⠁⠀⠀⠀⠀⠈⠀⢔⠢
⠀⠀⠀⠀⠀⠀⠑⠚⠐⠚⠀⠐⠃⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠆

⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿
⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠄⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⣴⡮⠉
⠀⠠⡄⠀⠈⢡⣿⣿⠿⣦⣤⣤⣀⠀⠀⠀⠀⠀⢤⠔⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⢦⠀⣷⣿⠟⠁
⠀⠀⠀⠀⣠⡼⣿⡻⣷⣒⣿⣿⣿⣿⣦⣀⠀⠀⠀⠰⣀⣀⠀⠀⠦⠀⠀⠀⠀⠴⠂⢠⠐⣾⡧⠹⠋
⠀⠀⠀⢠⡿⣏⠋⠀⠙⢛⣟⡉⢻⡿⠟⠙⠆⠀⠀⠀⠈⠁⠀⠀⢀⣠⡖⠻⡄⡀⡁⢸⣿⡿⠃
⠀⠀⠀⠸⠁⡉⠀⠀⠀⠀⠈⠀⠈⠋⠚⠀⠘⢤⣄⣀⡀⢀⣀⣴⡏⠁⢄⠀⢀⣧⣧⡼⠋
⠀⠀⠀⣄⢀⣛⣀⠂⠀⢰⡄⠀⠀⠀⠀⣰⡆⠀⢉⣀⠈⢩⠟⣀⢅⢰⣄⢸⣼⣿⠏
⠀⠀⠀⠙⠿⣿⣿⣿⣆⠈⣅⡀⣀⣠⣴⣾⣷⣤⣿⣿⣧⣶⣾⣿⣾⣿⣿⣿⠟⠁
⠀⠀⢀⣶⠤⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣍⠁⠉⢻⣿⣿⣿⣿⡏
⠀⠀⠈⠁⠀⢸⣿⠟⠋⠉⠉⠉⠙⠢⠈⠛⢹⠀⢀⣈⠳⢄⠀⠙⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠊⠀⠰⠦⠀⡝⠀⠀⠹⢿⣿⣿⡄
⠀⠀⠀⠠⠖⠰⠀⠀⠀⠀⣴⣾⣷⣶⣶⣦⠄⠀⣔⣠⢠⡤⣷⣄⠀⠀⠀⠙⠻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠛⢻⣿⠟⣿⠿⠟⠛⠋⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠄⡀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠦⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠂⠀⠠⢦⣀⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠈⠛⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⡨⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⢀⠀⠀⢀⣀⣄⣾⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⠀⠀⢀⣤⡤
⠀⠀⠀⠀⠀⡀⠄⠂⠉⠀⠀⠀⠀⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⢠⣾⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣿⣧⣾⡞⠁⡠⠀⠀⠀⠠⠄⠠⠄⢀⣀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣠⠐⣂⣠⣴⢀⡀⠀⣴⣶⣿⣧⣾⣿⣿⣷⣿⣇⣀⣀⣴⣶⣶⣿⣿⣶⣿⣿⣿⣷⣶⣾⣀⣀⣉⡐⠒⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠐⠓⣂⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣷⣼⣆
⠀⠀⠀⠀⢂⣠⣴⣾⡿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠛⠛⠛⠙⠛⢏⣻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢹⡏⣠⣄⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡟⠇⠈⠙⠛⠿⣿⡿⠟⠛⠉⠁⢁⡠⠶⢶⠶⣶⣦⣤⣴⣶⣾⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠘⠿⣿⠿⠿⠿⠿⢿⣿⣿⣯⣽⣿⣿⣶⣾⣾⡿⠟⢋⣡⣶⣼⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⢿⢻⡿⡟⣛⠇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠤⠞⠛⠉⠉⠉⠉⠛⢉⣠⣴⠾⡛⠋⠉⠀⣤⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠴⠆⣿⣾⣶⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⢛⣉⠀⠀⠀⠉⠙⠛⠚⠻⠶⠾⠶⢶⢶⡴⣶⣦⣤⣀⣀⣲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠋⠉⠀⠀⢈⡩⠉⠁⠲⣦⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠙⠿⠉⠉⠉⢻⣷⡀
⠀⠀⠀⠒⠒⠒⠒⠋⠉⠁⡀⠀⠀⠀⡇⠀⠂⡿⠿⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⣀⣸⣇⣀⢀⣀⡀⠀⢰⠀⠀⠀⠀⣀⣠⣄⣤⣤⣶⣞⣦⣄⡀⠀⠀⠐⠀⠀⠘⢠⣄⣀⣄⣀⡀⠀⠈⢦⡀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢿⡏⠉⣯⣁⣽⣦⣼⣅⣧⣀⣘⣛⣿⣿⢿⣽⣯⢿⣾⣿⣷⣄⣄⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⠀⠀⠙⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠈⠙⠓⠻⢷⣽⣿⣿⡟⢹⣿⣿⣶⡟⣻⠿⢿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠭⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⣡⣤⣼⣿⣶⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢤⣤⡶⠯⠷⠆⠈⠁
⠀⠀⠀⠀⠀⣠⡴⢞⣫⡥⠀⠀⣀⣀⡈⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⢀⠏⣤⡤⠤⣵⠄
⠀⠀⠀⣠⢾⣿⠞⢉⡿⠗⠋⢉⣽⣋⣀⣀⣀⣀⠈⠲⣄⠀⠀⠀⠀⣎⣀⣬⣽⡄⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠁⠀⢀⣴⠯⠭⣄⣀⠈⠳⡀⠀⢰⠀⢉⡻⠂⢀⣠⠴⠒⠉⠁⠀⠀⣀⡀⠈⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢯⣍⡀⠙⡄⠘⣠⠎⣠⠖⠉⣀⣀⡐⠿⣖⠢⢄⣙⣍⠓⢦⣽⡷⣝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⢤⣌⡓⢌⣾⣣⠞⣁⣤⢭⣿⣬⠉⠉⠻⠆⠀⠈⠛⠀⠀⠈⠇⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢀⡄⢀⣠⡶⢂⣀⣿⣶⣇⣨⣟⢿⠛⢒⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣾⣠⠋⣧⠎⠶⠚⠉⢰⠉⢹⢨⠀⢿⠳⣄⢸⡇⢰⡆⢈⡓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣴⣼⠈⠟⠀⠋⠀⠀⠀⠀⠈⣹⠅⣾⠓⠋⠀⠘⠟⢻⡞⣿⢸⡇⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣀⣿⠀⠀⠀⠀⠀⠈⠀⢽⡜⢷⣿⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢿⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡿⣷⡞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣿⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠤⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⠴⠻⡄⠀⠀⣀⢀⡾⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡄⢹⡀⠀⠀⠀⣀⠙⣆⢰⣿⡎⣧⠊⠔⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢦⣣⠀⢷⠒⠚⠋⠁⠀⠈⢷⣇⠁⠹⠸⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠙⠀⣸⠦⠀⠀⠀⠀⢀⡤⠬⠿⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠁

⣏⠉⣹⣋⣛⣛⣛⣛⣏⣛⣛⣛⣟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠀⣴⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⠄⣠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⢀⡤⠊⢀⣴⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣄⣤⣤⠋⣀⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⠀⠀⠀⠀⠂⠁⠠⣻⠀⠀⠠⣬⣿⣿⣿⣿⣿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡓⣪⡟⠀⠀⠀⠈⣹⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢬⡭⣿⠇⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠠⠃⠀⠃⠀⠀⠀⢰⣶⣿⠃⠀⠀⠀⠀⣿⠿⠟⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡗⠒⠲⠀⠑⠀⠀⠀⠀⡀⢬⡟⠁⠀⠀⢀⢀⣒⣿⣷⣶⣿⣿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠋⢻⣿⣷⣷⣮⣀⣀⣐⡾⠏⠀⠀⢀⠠⠤⣼⣿⣿⣿⣿⣿⡟⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⡀⣈⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⢠⣼⣿⣿⣿⣿⣿⣿⢧⡧⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠈⢿⣻⣿⡟⠃⠀⠀⠀⢀⠀⢄⣧⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠒⠒⠊⠄⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣾⣷⡄⠀⢈⡿⠁⠀⠀⠀⠀⡈⣼⣸⣿⣿⣿⣿⣿⣿⡿⢋⣵⠏⠀⠀⠀⠀⣀⠐⠀⡀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⢸⡇⠀⠀⠀⣠⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠋⠀⡀⠀⠈⠁⡀⠀⠌⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠠⡇⠋⠀⠀⠸⢇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠖⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢋⣵⣶⣮⢹⡇⠀⢠⣿⣿⡇⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⡸⠟⢁⣀⡀⠻⡏⣨⣶⣽⣷⣾⡇⠀⢸⠛⣉⡉⠆⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠨⢂⡀⣤⣵⠀⣾⣿⡷⠀⣧⠈⣾⣻⣿⡿⠷⠀⠈⠀⠻⠃⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣄⣄⠘⢾⣿⣿⣆⠈⠂⠀⣄⣮⣷⡝⠛⣭⠖⠀⠀⠀⠠⣀⡀⣄⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢤⠈⠈⠻⣷⣦⣽⣿⣿⣷⣦⣤⣈⡛⠻⢃⣀⣤⢴⣶⣶⣶⣤⣙⢿⣿⣿⣿⣿⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠶⢬⣿⣿⣿⣿⣿⣽⣿⣿⣿⡟⠋⢉⣀⣠⣶⣾⣿⣿⣿⣿⠉⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠲⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠚⠛⠛⠛⠿⠿⠍⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⢀
⠀⠀⠊⠉⠳⢄⠈⠙⠋⠉⠉⠀⠁⠀⣁⠨⠜⠋⠁⠀⠀⠀⠀⣠⠀⠤⠈⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⡀⠴⠒⠋⠁⠀⢀⠐⠊⠈⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⢃⣀⣀⣀⡴⠏
⠀⠀⠀⠈⠐⠠⠖⠋⠀⠉⠀⢀⡀⣀⠀⠀⠀⠈⠁⠀⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠚⠁
⠀⠠⢀⣀⠠⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠂⠛⠂⠃
⠀⠀⠀⠀⡠⠴⡄⠤⠠⢨⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠸⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⢅⠀⠀⡄⠀⠀⠀⡤⢀⡄⡄⡄⡀⠀⠀⠀⠀⠀⠘⠦⠀⠠⣔⣰
⠀⠀⠰⡀⠠⠆⠠⠤⠴⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠋⠁⠉⠀⠁⠉⠙⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⠀⠐⠒⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⢀⡞
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢆⠀⠀⢠⠅
⠀⠀⠀⠀⢀⠐⠒⠂⠄⠀⠀⠀⠈⡄⠀⠄⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠐⠀⠀⠀⠈⡀⠀⠀⠀⠐⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠐⠄⠀⠀⠀⠀⠔⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⢀⡴⠞⠁⢠⣀⣀⣠⠤⠖⠒⠲⠶⠶⠶⠄⠀⠉⡑
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⠉⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠽⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣀⣀⣀⣤⡙⢛⣷⣶⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠒⠂⠋⠉⠑⢒⡒⠒⠓⣶⠀⢂⡒⠘⢽⣿⣿⣿⣆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠻⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠞⠛⢓⣛⣫⣽⣿⣿⣿⣿⣽⣭⡿⠷⣦⢤⡀
⠀⠀⠀⠀⠀⢠⠖⠀⠄⠠⢄⠽⠠⠦⠤⠼⠬⣥⠬⣿⣿⣽⣿⠭⠿⠿⢿⣿⣟⣽⣿⣿⣷⣮⣄⣙⠋⠙⢷⣄⡀
⠀⠀⠀⠀⣰⠋⠁⠠⢤⣤⣀⣆⣀⣐⣀⣄⢤⣤⠠⠤⠤⢤⣴⣶⣶⣶⣿⠿⣾⣿⡷⣿⣿⣿⣿⣿⣷⣦⣄⠙⠻⣤⡀
⠀⠀⠀⢀⠎⠀⠂⠉⢁⣈⣈⣁⣀⣉⣁⣈⣉⣙⣏⣉⣉⣉⣉⣭⡤⠤⢶⣶⣿⡿⠗⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢸⣷⣄
⠀⠀⠀⢠⠀⠀⢌⠐⠒⠂⠐⠳⠒⠒⠒⠒⠒⠲⠗⠒⠒⠒⠖⠛⢛⣋⣉⣯⣿⢷⣫⣿⣿⠛⠛⢿⣿⣻⠓⠂⠀⠐⠉⢻⡆
⠀⠀⠀⠘⢀⡠⢼⣒⣒⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⢭⣭⡭⢽⠿⠿⢿⣟⣯⡥⣶⣿⣷⣦⣛⣿⣿⣖⠲⠤⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢀⠀⠂⠹⢯⣀⡠⠤⠌⣃⠀⠀⠀⠠⠠⠟⠂⠀⠀⠒⢒⣚⣻⣿⠿⢷⣾⣿⣿⡿⣿⣿⣿⣿⣉⠄⣒⠀⠄⣀⠀⠘⡙
⠀⠀⠀⢨⠀⡄⠈⠻⡄⠀⣀⡠⠄⠀⠀⠀⠀⠀⣚⣉⣀⣉⣭⣥⣼⣗⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠈⣀⠀⠀⠀⢈⡓⢱
⠀⠀⠀⠀⣅⠋⠘⠑⢨⡥⠤⠐⠂⣐⣀⣀⠈⠭⠭⣥⣀⣖⣾⣿⣯⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡛⠛⠷⢮⣍⡒⠀⡀⠉⠹
⠀⠀⠀⠀⢨⡀⠼⠂⣀⠴⠒⠈⣉⣠⡤⠤⠶⣒⣺⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣈⡁⠂⠤⡙⠳⢬⣑⠀⠂
⠀⠀⠀⠀⠀⠉⡼⠋⣠⡴⠚⣁⣭⠴⢒⡻⠭⣵⣶⣿⣿⣿⢿⣿⣿⣿⣿⣽⣭⣿⣿⣟⣿⣿⣿⡍⠉⠉⠛⠛⠶⣤⡑⠢⣙⠻⠃
⠀⠀⠀⠀⠀⠀⠐⢾⠁⡠⠚⣁⠴⣚⡽⣶⣿⣿⠿⠛⠉⣱⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠤⢈⡒⠤⣀⠉⠛⢷⣄⡑⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢅⡼⣡⠞⣡⣮⢞⠁⢀⠀⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⠀⠈⠹⢷⣮⡛⠦⣄⡉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣼⢵⠁⠈⠔⡁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⠋⠙⣶⣤⣀⠠⢉⠛⣷⣬⡙⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡀⠀⢐⢿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣟⠋⠉⢷⠦⣄⠀⠙⠛⢿⣦⣁⠀⠈⠻⢦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣾⡄⠹⣿⢸⣿⣿⣿⣿⣻⣿⣶⠬⠉⠁⠀⠀⠀⠀⠙⢶⣄⠀⠉⠛⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠄⡀⢿⣿⡆⠟⣾⣿⣿⣿⣿⣿⡿⠗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡅⢸⣿⣿⢠⣿⣿⣿⣿⣿⣿⡗⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠊⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡃⢸⣿⣿⣼⣿⣿⣿⣿⣯⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠛⡷⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⠻⣿⣿⣿⣿⡿⣿⡧⡉⠢⡀⠀⢢⡀⠀⢠⡀⠀⠳⣄⠀⠸⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⣿⣿⣷⡙⣮⠳⡙⠄⠈⢆⠀⠹⣆⠀⢹⣄⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠏⠉⠛⢿⡜⣧⢹⡈⢆⠈⢧⠀⠸⣧⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠱⢸⣎⡇⠘⣇⢸⡇⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡐⢦⡀⠀⣸⡇⢀⣤⣤⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠿⢿⣿⣿⣄⣿⣷⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⣿⣿⣿⣿⣾⣿⣾⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⢻⣿⣿⣿⣿⣿⣍⠉⠛⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢠⣾⠃⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⣾⣿⠟⠿⠁⢻⣿⡄⠀⠀⠉
⠀⠀⠀⣀⣴⣾⣿⣿⣿⣷⣿⣷⣿⣷⣿⣟⠻⢿⣷⡄⠀⠀⠀⠀⣸⠏⠀⢀⣼⣿⡗⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠁⠀⠀⢀⣠⣴⡿⢿⣿⣿⣟⠙⠛⢷⡄⠈⠁⠀⠀⠀⠀⠟⠀⢠⡾⢹⡏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣠⡿⠉⠀⢠⡿⣿⣿⣿⣆⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈
⠀⠀⠀⠀⠀⠻⠀⠀⠀⣿⡇⠀⢻⡝⢿⡄⠀⠸⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠻⣎⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣿⣿⠀⣿⣷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣾⣿⣿⣾⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠻⠿⠿⠟⠛⠛⠃
⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣛⣿⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣟⣷⡄
⠀⠀⠀⠀⠀⠸⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣬⣬⣅⣭⣑⡀⠁⠉⠉⠙⠛⠷⠶⣦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⢦⡀⡄⢰⢀⠒⠒⠊⢭⣝⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣭⡭⠍⠋⠉⠉⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣈⣿⣿⣿⢃⣿⣊⣠⣤⣦⣬⠽⠽⢿⡿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠐⠶⢿⣛⠃⠀⠁⠉⠉⠛⠉⠛⠛⠛⠛⠿⣯⣿⣿⣿⣿⣿⠟⠉⠙⠉⠁⠈⠉⠀⠀⠀⠀⠙⢿⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⢠⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣤⣦⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⣄⠀⠹⣿⣿⣇⠀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⣐⣺⣿⣿⢀⣿⡿⢂⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣅⣘⠿⣿⣷⣼⣿⣿⣾⣏⣴⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣫⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⣠⣶⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠙⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣯⣾⡿⠛⣵⣿⡟⠀⣿⣿⢻⣿⣿⣿⣿⠋
⠀⠀⠀⠀⢀⣀⡀⢀⢱⡇⣰⣴⣶⠦⠀⠀⢠⠟⢁⣾⡿⠛⣡⣾⣿⡿⠀⠀⣿⣿⠈⠘⢻⣿⣿⡄
⠀⠀⠠⢄⣛⣿⣿⣿⣆⣿⣿⣿⠁⠀⠀⢀⠀⠀⠸⠉⠠⣾⣿⣿⡿⠁⠀⠠⣿⣿⠀⠀⠀⣿⡿
⠀⠀⠀⠀⢈⣹⣾⣿⣿⣿⣿⡗⠀⣠⣿⣿⣿⣷⠄⠀⠀⠉⠉⣿⠃⠀⠀⠚⣿⣿⠀⠀⠀⠉
⠀⣠⣤⣴⣾⣿⣻⣿⣿⣿⣿⢇⣼⡿⠟⠉⠉⠉⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠁
⠀⠈⠉⣉⣭⣭⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⡿⠇⠀⠀⢰⡟
⠀⠀⠺⠟⢋⣻⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣷⣧⡀⠀⢀⣿⠁
⠀⠀⢀⣴⠿⠻⢫⣿⣿⣿⣿⠈⣿⠿⣿⣦⡉⠻⠻⡀⣼⡇
⠀⢀⡾⠁⢀⣴⡿⣹⣿⢻⣿⣇⠘⣇⠘⣿⡏⠀⠀⢰⡿
⠀⠈⠀⠀⢸⡿⠱⣿⡿⠈⣿⣿⠄⠘⣆⠉⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠈⠉⠀⠀⢹⡄⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣿⣾⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⣴⣟⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣼⣿⣿⣿⣿⣿⣿⣿⣯⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠈⠀⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⣀⣒⣒⣀⣨⡐⣎⣤⢶⡶⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠻⢿⣿⣿⣿⣷⣶⣶⣬⡍⠶⠒⠊⣩⣷⣶⣶⣾⣿⣿⣿⣿⠿⠟⠻⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠙⢾⣵⠿⢛⣩⣥⣤⣶⣶⣶⣿⢿⣿⣿⣿⡿⠋⠛⠋⣀⣀⣤⣤⣤⣤⣄⡀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢩⣴⣾⣿⣿⣿⣿⣿⣿⢻⣿⢻⡋⣫⠉⠀⠀⠔⠚⠙⠃⠀⠀⠩⡙⢿⣇⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⢨⡅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⣿⣷⣶⣶⣴⣶⣤⠤⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣿⣿⣿⣟⡷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⡎⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⡠⠐⠈⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠂⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢄⢻⣿⣿⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢆⢻⡟⠀⠀⠀⠀⠀⠀⠢⢀⣀⠀⣀⣤⣾⠏⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢐⣀⣀⡀⠀⠀⠀⠈⠉⠉⠉⠁⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠊⠉⠛⠛⠿⠿⠿⢿⠀⡰⠶⣶⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⢿⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄
⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡕⡄
⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⡠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡼
⠀⠀⠀⢀⣴⡿⠛⠁⠀⡜⣷⡄⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⣄⡼⠋⠁⠀⠀⠀⡇⠈⠀⠀⠀⠠⠘⠶⢦⣄⠀⠀⠠⠄⠿⠿⠟⢰
⣤⣾⡏⠀⠀⠀⢠⣤⣴⡏⠀⠒⠁⠀⠀⠀⠀⠀⠾⣧⣀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣞⠠⣂⡤⠤⠤⠤⠄⡀⠀⠀⠈⠈⠓⠤⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣴⣶⣿⣾⣴⣴⣤⠲⠄⠀⠀⠀⠀⠀⠙⠳⣤⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠰⡀⠀⠀⠀⠈⠂⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⢿⣿⣿⣿⠋⢿⣿⣿⡧⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣼⣿⣿⣿⣾⣯⡿⡟⠁⠀⠀⠀⠀⠈⠑⠂⠰⣲⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠻⣍⣿⣽⠭⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠚⠉⠑⠲⣤⣤⣤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⡠⣢⠞⠁⠀⠀⠀⠀⠀⠈⠿⢿⣷⣦⣤⣤⣴⡶⠾⠟⠛⠉⠁⠀⠉⠛⠶⣌⡢⢄
⠀⠀⠀⠀⠠⡪⠞⠁⢀⠠⠀⠒⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣕⡀
⠀⠀⢀⣪⣾⣄⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄
⣤⣼⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⣤⡤⣀⡀
⠀⠀⠀⠀⡈⠘⢄⠠⢔⡲⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡞⠓⢺⣅⠀⠏⣷⣰⠉⢲
⠘⠯⠭⣉⠁⡷⡆⣰⠋⠀⠀⠀⣰⢹⣭⡭⠷⠦⢙⣶⣶⣶⠆⠀⠀⠀⣀⣀⠠⢤⣀⠀⠘⢯⡿⣿⠇⢰⢻⡁⠠⣁⣿⣿⣆⠘⡇
⠀⠀⠀⡜⣠⠖⠢⡘⣆⠀⠀⠈⠻⣇⣛⣛⣋⠉⣈⠿⠋⠀⠀⢀⠴⠿⠤⣍⢢⡀⣿⠈⢢⡀⠉⢿⡇⠘⣗⠀⢘⢠⡅⠙⢿⣶⣿⣄
⠀⠀⠈⠚⠁⠀⠀⠙⠚⠃⠀⠀⠀⠘⠛⠒⠂⠉⠀⠀⠀⠀⠀⢮⣿⣿⣷⣮⣿⣧⣇⡠⠏⠁⠀⠈⠋⠙⣯⠀⣰⣰⣀⡴⠶⠻⠿⣿⡧
⠀⠀⠀⣀⢤⠴⠶⡶⡤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠤⢤⠠⠀⠀⠉⠙⢫⠞⠻⣟⠒⠒⡏⠀⠀⠀⠀⠈⠋⠉⠉⠁⢠⡴⠶⢤⡀
⠀⣴⠻⠹⠀⠀⡄⠀⢀⠃⠞⣳⣄⠀⠀⡠⠊⠣⡀⢣⡀⣹⠀⠇⠀⠀⠀⠘⠣⣧⠈⠹⠞⠀⠀⠀⠀⢀⡄⠀⠀⠀⡠⣿⢏⠢⠡⢹⡄
⠈⡎⢂⠁⠃⠀⢀⠀⠈⠈⡰⠡⢋⠆⡐⠙⠢⣤⠟⠉⡏⢻⢆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣸⣷⠀⠀⠀⡇⡈⠘⡄⡂⠆⣧
⠀⠘⢆⢢⢠⣠⢘⠀⠀⠐⠐⡡⠋⠀⡗⠲⠴⡟⢒⣶⡷⣯⠤⡇⠀⠀⣰⠇⡢⠀⠄⡁⠨⢳⡄⠀⠀⡯⠰⡄⠀⠀⢻⢁⠀⠀⠀⠀⢻
⠀⠀⠀⠳⣕⢷⣿⣾⠌⣠⠊⠀⠀⠀⠘⢦⠒⢛⠥⣮⢶⠛⣤⠇⠀⠀⣥⠊⣠⠎⡔⢠⠁⡅⡇⠀⣘⣋⠉⢵⠀⠀⠸⡼⡠⡀⠀⠀⡿
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠈⠙⠻⠤⠧⠜⠛⠁⠀⠀⠀⠋⣴⠃⣼⠁⣾⠀⣇⡿⠀⠫⣤⣺⣿⡷⠀⠀⢿⡵⣣⢇⢢⡇
⠀⠀⠀⠀⣠⡤⣀⢤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠒⠛⠴⠟⠒⠉⠁⠀⠀⠸⠿⠋⠁⠀⠀⠈⠻⣵⣯⠞
⠀⠀⡄⠊⠀⢳⡀⠈⢁⡆⠙⢦⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠻⣟⠛⠒⠚⠳⠲⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⣼⣀⣀⣠⡜⢋⠓⠺⢀⠠⠈⢳⣄⠀⠀⡼⣛⣫⡈⠛⣷⣄⠀⠀⠉⢢⡀⢀⠀⠃⠈⠙⠦⣄⠀⠀⠀⠀⠀⢴⣾⣿⣿⢧⣄
⠀⢱⠀⠏⣇⡼⣟⡖⠈⢹⠶⠛⠉⣿⠀⠀⡏⣴⣾⣿⣮⡟⣿⣆⠀⠀⠀⠙⠒⠒⠓⠒⠒⠒⠚⠓⠀⠀⠀⣠⡾⣿⣛⣫⣤⠛⠙⡦⡀
⠀⠘⣦⠚⠙⠑⡎⠉⠺⡇⢠⠀⣆⢺⠀⠀⢣⡻⣿⣿⣿⣿⡿⠛⠀⣀⠤⢤⠞⠛⠙⣟⠓⠦⣄⣀⠀⢠⢞⡙⠀⠈⠀⠀⠀⠐⡜⡄⢽
⠀⠀⠈⠙⠲⠶⠧⠖⠲⠶⠚⠒⠛⠛⠁⠀⠀⠙⠚⠛⠋⠉⠀⠀⢰⡡⠊⠀⢂⠀⠀⠘⣄⠳⣈⡟⠀⠸⡕⢡⢀⠁⠃⡛⡈⡁⡐⡜⣼
⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣔⣚⠉⠓⢔⠄⡄⠈⣳⠋⠀⠀⠀⠘⠧⣼⢐⡃⡃⡇⢡⣱⡴⠋
⠀⠀⠀⣴⣿⣿⣛⡷⡄⠀⠀⢀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⠈⠳⣝⣛⢛⣿⣚⣷⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠉⠁
⠀⢠⢚⢝⡉⠀⢉⣶⡿⡆⠀⡟⡩⠋⡥⠼⣧⡈⠉⢀⣴⣦⡌⢷⡀⠈⠈⠉⠀⠉⠀⠀⠀⠰⡒⡖⡲⠉⡟⠉⢹⠖⠘⠳⢦⣄
⠀⣇⢏⢮⠸⣼⣿⡿⣿⠁⢠⡋⢰⠺⢷⡄⠈⠻⣦⠈⢿⣿⣿⡎⣧⠀⠀⠀⢀⡖⠒⠦⣄⠀⠘⢶⠃⢀⠀⠀⠀⠀⢐⠈⠀⢘⢆
⠀⠈⠲⢽⣽⣿⣫⡞⠁⠀⢈⣶⡛⠳⣆⠙⠷⣄⠙⣦⢸⣿⣿⣧⣽⠀⠀⣀⡼⠅⠀⠀⠠⠛⣄⠈⠛⣇⠀⢠⠀⠀⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠘⢏⠙⠶⢌⣙⡓⢮⣿⣌⢣⣻⣿⣯⠏⠀⢸⠙⠌⠀⠀⠀⠀⠄⢹⠀⠀⠈⠛⣇⠀⠐⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣭⣭⣴⣍⣰⣇⠉⣿⡟⠀⠀⠈⠣⣀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠘⢶⣄⡀⠀⠀⠠⠀⢛⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠓⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⢠⣼⣦⣠⣾⣥⡄⠀⠀⠀⠀⢀⣭⣿⣦⣴⣶⣂⠀⠀⣈⣿⣧⣾⣯⡄⠀⢤⣶⣿⡆⣠⣴⣤⡀
⠀⠀⠀⢀⣼⣿⠛⣿⡿⠗⠂⢀⣦⣄⣾⣾⠉⡟⠉⣿⢹⠀⠈⢩⡿⢻⣿⠏⠋⠀⠿⣿⠁⡆⢿⡍⠻
⠀⠀⠀⠀⢰⠃⠀⠈⠛⠀⠀⠛⣟⠙⡏⠃⣼⠁⠀⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠁⠀⡇⠀⠛
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣀⠀⠀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠐⣦⣼⣀⡤⠀⠀⡼⣿⣷⣴⣿⣿⠂⠀⢐⣶⣿⣷⣴⣿⣏⠀⠀⢀⣠⣤⣾⣿⣯
⠀⠀⢀⣰⣦⡿⠿⢍⣿⡿⢿⣗⠀⣾⢹⡏⢩⠉⠙⠃⠀⠈⢹⡟⣹⠻⣿⠿⠁⠀⠽⢿⠛⢋⠙⠣
⠀⠀⠠⠟⣿⠙⢦⠏⠀⡟⠀⠈⠀⠈⠀⠁⠘⡆⠀⠀⠀⠀⠈⢁⡇⠀⠉⠀⠀⠀⠀⠈⠀⠘⡄
⠀⠀⠀⠀⠈⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⣴⣼⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠈⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠛⠋⠕⠁⠀⠀⠀⠀⣸⣷⣾⣿⢋⡉⠀⠀⠀⠀⢴⣿⣷⣶⣤⣴⠞⠋
⠀⠀⠉⢿⣷⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠴⠿⢯⡧⠍⡠⢟⣀⠀⢀⡈⠹⣿⣿⣿⡷⠊
⠀⠀⠀⠈⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣯⣦⣶⣏⣹⣿⠷⣾⣟⣁⠈⣉⣰⣾⢿⠿⠃
⠀⠀⠀⠀⠘⣿⣿⣯⣿⣿⣄⡀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⣿⣷⣮⣽⣿⣿⣿⣿⡆⠼⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠛⣨⣬⣛⣻⣿⣿⣷⣿⣥⣧⡍⠹⠿
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠋⠉⠙⣿⣿⣿⣯⣉⣼⣯⠁⠀⠳⣈⡙⣯⣿⣿⣿⣷⠎⠁⠀⠀⢀⣦⡀
⠀⠀⠀⠀⢀⣿⣿⣿⡿⠁⠀⠀⠰⠿⠻⢿⣿⣥⣿⣿⣷⣄⠀⠉⣻⣿⣿⣿⣿⣿⣿⣿⡄⢀⣾⣿⢿⣿⣶⣄⡀
⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣍⣀⡸⣾⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠉⠻⢶⣝⢿⣿⣷⡄
⠀⠀⠀⣼⣿⠟⠋⠀⠀⠀⣠⣴⣿⣿⣿⣿⠋⢺⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣿⡄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠡⠒⣻⣿⠿⠟⠉⠉⠉⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁⠀⠀⠊⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣄⣤⠀⠀⠀⠀⠀⠈⠻⣿⣧
⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠣⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠬⠍⠉⠩⡩⠉
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠁
⠀⢀⣀⣀⡖⠀⠀⠀⠠
⠀⣾⡿⠿⢿⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⣾⠏⠀⡠⡾⠛⢋⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇
⣧⣄⡔⠉⠀⠀⠈⠀⢧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿
⡿⣿⣶⣤⣠⣀⡀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠃
⠀⢸⣿⣿⣿⠟⢻⣦⡀⠈⢿⣾⣾⣷⡤⣼⣤⣄⣀⠀⠀⠙⠃
⠀⠸⣎⣻⣏⠀⣿⣿⣿⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡒⠰⣖⡂⠃
⠀⠀⢹⡏⣿⢄⣿⣿⣿⣷⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡤⢄⣄
⠀⠀⣞⡡⣿⣮⡿⢿⡿⠁⠀⠀⠈⢉⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⢇⣀⡄⢈⠷⡀⠀⠀⠀⠀⣀⣀⣤⣤
⠀⠀⠻⢷⣾⠷⠗⣋⣤⣴⣶⣷⣟⣤⣤⣾⠯⢚⣽⣿⣿⣿⡏⠡⠐⢲⠦⠤⠠⢤⣙⣶⣤⣶⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠒⠚⠛⠛⠻⣦⠰⡄⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣾⣿⣿⣿⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣷⣿⣯⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⣩⣽⣿⣿⣿⣿⣿⣍⡁
⠀⠀⠀⠀⠀⠉⠉⣛⣿⣿⣿⣿⣿⣿⡛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⣾⠿⢛⡽⣿⣿⣿⣿⠻⣿⣦
⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣿⣿⣿⡻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣴⠋⣸⣿⠏⢿⣿⡄⠀⠙⠇
⠀⠀⠀⠀⠀⠟⠁⠀⣿⣿⠹⣿⣏⠻⣄⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡴⠟⠁⠀⢘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⠛⠦⠘⢦⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⣿⣿⣴⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣟⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠻⣍⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣶⣶⣶⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡇⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠏⠸⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⡛⠻⢿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣿⣶⣮⣍⣛⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣟⣛⠻⠶⠶⠶⠶⠶⠶⠶⠶⠒⠂⠀⠀⠀⠉⠻⣷⣾⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠿⢿⣿⡿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠘⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢀⡿⣰⣿⣿⠏⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣸⣷⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⠖⠒⠲⢜⡆
⠀⠀⠀⢀⣸⣿⣿⣿⣿⣇⣤⣄⡀⠀⠹⡄
⠀⠀⠀⣸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣷⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⢠⠊⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣶⣶⣶⣾⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠈⠉⠀⠀⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠙⠛⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣾⣿⣶⣶⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣶⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠧⠤⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⣀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢚⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠟⠉⠉⠀⠀⠀⢁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠁⠐⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢀⢀⠠⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠐⠀⠀⠑⠈⢀⠀⠠⠀⠀⡤⢘⠢⠀⠀⠰
⠀⡘⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢟⠃⠃⡀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠙⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠂⠀⠀⠀⠀⠀⠀⠑⠀⠄⠀⠀⠄
⠀⠴⠦⣖⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠚⠿⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠈⠣⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⡀⠀⠈⠀⠈⠀⠂⠁
⠀⡆⢐⠀⠈⠀⠤⠀⠐⠀⠋⠀⡄⠂⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠂⡀⠀⢠⡀⠀⡄⠐⢀⠀⠀⠀⡐⠌⢿⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⠀⠀⠀⠈⠏⢂⡈⠀⠀⡠⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠠⡀⠀⠀⡀
⠀⢀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⢀⠄⠁⠐⠄⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠊⠁
⠀⠀⡈⠉⠀⠀⠀⠀⠑⣄⠀⠀⠰⠀⡋⠀⠀⠀⡀⠐⠐⠁⠀⣐⠾⠛⠁⠀⢀⡀⠄⠀⢦⠢⣄⠀⣠⢀⠈⠈⠀⡄⠈⠓
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠑⠚⠓⠒⠂⠛⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⡠⢀⣤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣧⡅⠢⡀⠐⣿⣦⡀⠀⠠⢊⣶⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣻⣧⠬⠢⡙⣿⡰⠠⢁⣾⠛⢁⢄⣤⡶⠦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠺⠿⡷⣶⣤⣐⠺⣗⡑⣘⣧⡇⣽⣭⣯⣴⠟⠛⢉⣁⠠⣄⢤⡨⣤⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣈⠍⣉⠁⡛⠻⠿⣵⠢⡘⣯⣅⠟⡵⢋⣰⣦⡙⠧⠙⠳⠙⠃⠙⠈⠑⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣵⢟⡾⣻⠇⡾⢃⡾⣱⡾⡄⠨⣙⢺⣼⣿⠏⠔⢃⣨⣍⣭⣭⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠀⢠⣂⣥⡦⣶⡶⠖⠐⣾⣡⠛⡏⢙⡭⠥⠬⣍⢩⡉⠛⠫⢛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢛⠝⠃⢡⣠⢞⣩⠿⣀⣸⢈⡿⠫⡐⢦⣦⣼⣳⡗⢰⡄⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⡄⠿⢈⣧⣾⢃⡈⠀⡇⡁⢨⡌⢦⡄⠩⠙⠋⠇⠘⢱⣷⡲⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣴⣆⠻⠀⠘⠇⡇⢬⡏⠀⠁⠁⠐⣯⡈⡼⡂⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠸⠉⠀⠀⠀⠀⠡⡸⠍⢀⡄⣀⠠⠞⠀⠘⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠦⠘⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⠒⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡤⡶⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠏⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣇⠀⡀⠢⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⢦⣌⠢⣄⡐⠈⠀⢌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡄⠴⠈⠀⠀⠀⠉⠓⠶⣭⣑⢮⠀⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⢫⠿⢹⠁⠀⡀⠀⠡⠀⠀⠀⠀⠀⠙⢾⣇⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣋⣠⠏⠀⠀⠀⠀⠱⡐⠀⠀⠀⣀⡴⠯⢭⠽⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡟⠀⡴⣫⠭⣕⣦⡀⠀⣠⣿⡻⠛⠷⣦⠀⢤⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠁⢸⢱⠃⠀⣀⢻⠹⡝⣧⠁⢠⣦⠈⢊⢷⠆⠂⣲⠹⡄
⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠦⠼⠾⠷⣏⡈⡏⠳⠛⠭⢳⣌⠉⠀⠀⢊⠇⠀⢻⠀⡷
⠀⠀⢏⠈⢉⣙⣒⣒⣋⡥⠴⣶⠿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠼⠧⢤⣤⣤⠴⠒⠉⠉⢳⢳⢳⡥⠀⠠⣹⡄⢿⠇⠈⢠⠁⠁⣰⠃
⠀⠀⡼⠀⡄⠀⠠⡏⠀⠀⣸⡄⠀⠈⠳⣄⠀⠀⠀⢀⣠⡞⢳⡚⠉⠁⠀⠀⢀⡨⠗⠻⣄⣳⣍⠓⢎⡹⣜⢀⡀⣰⣞⣠⠶⠃
⠀⠀⢇⣀⣁⠒⡄⢳⡶⠋⠀⠹⡄⠀⠀⠈⠲⠖⠋⠉⠀⢣⠀⢣⠠⠄⠒⠈⠁⢀⠒⢄⠀⡷⣬⠗⠢⠤⠜⠋⠙⠓⠙
⠀⠀⠀⠀⠈⡇⢷⠟⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢢⠀⠀⠀⠀⠀⣁⣥⣞⠁⠈⠳⣄⣀⣀⣠⡴⣻⣤⣤
⠀⠀⠀⠀⠀⠥⠋⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠤⠤⢴⡤⠀⠀⢳⡀⠳⣤⠤⢖⡯⠟⠉⠈⠳⣄⠀⠀⠀⠀⠀⢹⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡟⡟⠉⠙⠒⠒⠒⠒⠉⠀⠀⠀⣠⠟⠙⠓⠚⠁⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠉⠉⠒⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠜⡡⡟⠀⣇⡀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⢀⡤⢚⠥⠊⡼⠀⢀⡏⠉⠉⠙⠛⠒⠒⠚⠉
⠀⠀⠀⠀⠻⣄⠓⠒⡂⢇⣀⡜
⠀⠀⠀⠀⠀⢸⠀⣔⠥⠆⣽⠃
⠀⠀⠀⠀⠀⠀⠓⠛⠲⡴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣦⡀⢀⣴⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠻⠿⠿⣷⣬⣿⣾⣷⣶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠿⣿⣿⣿⣿⣿⣿⣷⣿⠿⠿⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠶⣤⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣟⣻⣿⣿⣿⣿⠏⣿⣿⣿⣿⡿⣿⣷⣌⠛⢿⣦⣀⣀⡀⠀⠀⠀⠀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⣾⢩⡾⢋⣿⣉⣸⣿⠇⢰⣿⣿⣿⣿⣧⡈⠙⠻⣆⠀⠙⢿⣍⡙⠻⣶⣤⣼⣯⣶⠶⠺⠲⢤
⠀⠀⠀⠀⢲⣴⣿⣿⣿⣟⣁⣤⣼⣧⣄⣸⣿⡟⠉⣿⣿⣷⠀⠀⣠⠶⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⡛⠓⠦⡀
⠀⣠⠖⠟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣉⠉⢿⡇⠀⠀⠙⣿⡆⠐⠋⠀⠀⢀⣤⣶⣿⣿⣿⣿⣹⣿⣽⣷⣤⡀
⠀⠀⣴⡾⣻⣿⣿⣿⣿⣿⣿⠿⣿⣦⡈⠀⠘⠃⠀⠠⠀⠈⠃⠀⠀⣠⣴⠿⣫⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣆
⠀⣼⠏⡼⢻⣿⣿⣿⣿⣿⣿⣷⣄⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣴⠟⠛⣿⣿⣿⣿⡇⠸⣿⠈⠻⠀⠉
⠀⠇⠀⠀⣸⡏⣼⡟⢸⣿⡇⠙⢿⣇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⣿⡇⠀⠸
⠀⠀⠀⠀⣿⠁⠹⠀⠀⢿⡇⠀⠀⠉⠣⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠿⠁
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢸⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠨⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣇⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⢀⣷⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠧⠿⠛⠾⠿⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣠⣀⠀⠐⠋⣀⣀⣀⣀⣀⣠⣤⣤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣾⣿⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠻⣦⡀⠀⠀⠀⣰⢶⣶⣶⡄⠀⠀⣾⣷⣿⣿⣿⣿⡿⠇⠀⢀⣀⣀⣠⣀⡀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣈⣻⣶⣾⣿⣿⠿⠿⣏⠀⠀⠀⠉⠙⢿⣿⣿⡿⡿⢿⠿⠿⠟⠛⠷⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀⠀⠀⠤⠶⠛⠛⠃⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⢸⣿⣿⣷⡄⠀⢀⣿⣿⣿⠁⠀⠀⢀⣠⡤⡖⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⢧⠀⠠⢾⣿⣿⢻⣿⡀⠸⣿⣿⡿⠀⠀⠈⠉⠉⠀⠀⣀⡀⠀⠀⢰⣧⡴⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠉⠀⠈⢀⣠⣾⣿⠿⠋⠿⠃⠀⢻⣿⣇⠀⠀⠀⠀⠰⠾⠿⠋⢀⣠⣴⡾⠃⠀⠀⠈⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠙⣷⠀⠀⠀⠀⠀⢸⠀⠹⣄⠀⠀⢠⣀⠀⢀⣠⣿⡟⠋⠀⣠⣴⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠹⣦⠀⠀⠀⢀⡞⠀⠀⣿⡀⠀⣸⢿⣿⣿⠿⢻⡀⠀⠚⠉⠩⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠁⠀⠀⢀⣿⡄⠀⠀⠸⡇⠀⠀⣿⠃⠀⠘⢾⠁⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢷⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢶⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠈⠳⣄⡈⢷⡀⠀⠙⠛⠛⠁⠀⣢⠆⠀⠀⢸⡏⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢿⣿⣷⣽⣤⠀⠀⠀⠀⠀⠀⠈⢧⡀⣷⣄⠀⠀⠀⠤⠴⣿⣶⡶⠆⠘⡇⢨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⡌⠙⠳⠶⠦⣤⣤⣀⠀⠀⠈⠛⢻⣿⣿⣷⣦⡀⠀⠈⠉⠀⠀⠀⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠲⣦⣄⡀⠈⠛⠿⡿⠀⠀⠀⠉⣿⣉⡁⠙⠀⠀⠀⠀⠀⠀⣿⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⡄⠀⠀⢠⡆⠀⠀⢷⣀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⠳⢄⣀⣀⣀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢧⠀⠀⠀⠓⠒⢠⡄⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⢠⣦⣤⣭⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠒⢶⣾⡿⣼⣿⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢀⣤⣽⣿⣿⠋⠀⠠⡇⠀⠘⠲⣄⡀⠉⠓⣆⠀⡀⣠⣿⡇⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠠⡌⣿⣿⣿⣿⠀⢤⠀⠑⣄⠀⠀⢸⡇⠀⢠⣿⣿⢡⣿⣿⡧⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢹⣮⣿⣿⣿⠀⢠⡆⠀⢸⡇⠀⢿⣷⡆⣿⣿⣿⣤⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⠇⠀⣾⣇⠀⠈⢷⡄⠘⣿⣇⠻⣿⣿⣽⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢼⣿⣿⡿⠋⢠⡀⣼⣿⠂⠀⢠⡇⠀⢸⡿⢠⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣶⣼⡿⠿⠟⠋⡴⢀⡜⠠⣿⣏⠀⢀⣾⠁⢠⡿⠁⣠⣾⣿⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⡟⠋⠀⢠⠄⡗⠰⡃⠀⢸⠀⣿⠹⠀⢸⣧⡀⢸⣇⢠⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠋⠀⠀⣇⢸⣆⣻⣢⠟⡤⠿⠶⠿⠧⣤⣾⡿⢃⣤⣿⠸⣧⣤⣤
⠀⠀⠀⠀⠀⢀⠊⠀⠀⢠⢸⣧⠿⠊⠉⠉⠀⠀⠀⠀⠀⠒⠒⠒⠈⠽⢿⣿⣿⠶⠿⠛⠛⠁
⠀⠀⠀⠀⠀⣧⣤⣴⣶⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠉

⣿⣧⡄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠈⠀⠐⠀⣀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠐⠝
⣤⣤⣤⣴⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠈⠉⠐⠂⠀⠌⠳⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⣀⣄
⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⢤⣄⡀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠚⠀⠠⣌⠹⣷⣧⡞⠁⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣄⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⡘⢋⣴⣬⣦⢹⡆⣹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⢻⣿⣦⠄⠂⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠛⣿⢏⡾⠃⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣄⢢⡀⣹⣦⣀⣠⣿⣿⣾⣛⣁⣠⡴⠏
⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠉⠛⠿⠛⠛⠉
⠀⢇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠄
⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⣾⡧⢀⡀
⠀⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠈⠀⠀⠀⠀⠸⠏⠀⢸⡿⢦⣄
⠀⠘⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣧⠀⠀⠀⢰⡀⠀⠈⡄⢈⣄⡽⠶
⠀⠀⠘⢟⣀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢀⣀⣿⡗⠠⠖⠛⠋
⠀⠈⠉⠉⢿⣧⣤⣴⠞⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⠿⠃
⠀⠀⠀⠀⠈⠙⠛⣿⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡴⠀⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠁⠀⠁⢀⡀
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⣦⠤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠦⠴⠾⢿⣷⣦⡤⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡎⠀⣠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣍⡉⠝⠉⠁
⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⣿⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡿⠌⠑⠄⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣾⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠒⠀⠉⣙⣻⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣴⣧⣾⣷⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡹⢿⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⡩⠿⣿⣿⣄⠀⠀⣠⣾⣿⣟⠻⠿⠟⢛⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠑⣞⣿⣿⣦⣴⣿⡿⠯⠝⠋⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣟⣻⣷⡶⣶⣶⣾⣿⣟⢿⡷⡶⣖⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⡿⣿⢿⣟⡿⣿⣿⢒⣿⣿⣟⣽⣿⣿⣿⣿⣯⣿⡷⣿⡉⠛⠟⠚⠓⠁⠙⠈⠎⢿⠛⡏⢻⢶⣄
⠀⠀⠀⣀⣴⣿⢿⣿⡿⢫⢞⠞⡡⠋⠊⠐⠋⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠙⡷
⠀⢀⣼⣿⣿⢫⡾⠋⠐⠁⠈⠈⠀⠀⠀⢀⣾⣿⣿⣿⡿⢱⠏⢻⣿⠻⠟⢻⣿⣿⣿⣿⣆⡀
⢰⣿⡟⣹⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡏⠙⠀⠀⠀⣸⣿⠀⠀⠠⠘⢸⠘⢿⣿⣿⣦
⠨⡟⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠀⠘⣿⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡝⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠁⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢻⡿⣄⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⠈⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣚⣩⣵⣶⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⠋⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣊⣥⣶⡿⠿⡿⠟⣛⣉⣭⣤⣴⣶⣶⣶⠾⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠉⠀⣰⣿⣿⣿⡿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⣀⠴⠛⠉⠀⠀⠴⠞⠛⠉⠁⠈
⠀⠀⠀⠀⠐⠈

⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠈⢿⣿⣷⡄⠀⠀⡀⠀⠀⠀⠀⠀⠞⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⠷⠖⠒⢶⠶⢶⣶⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⡼⠛⠁⠀⠀⠀⠀⠰⠾⠿⣿⣿⣿⣦⣤⣀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⣛⣿⣿⣿⣾⣿⠿⠿⣷⣤⣄⣀⣤⣀⣀⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣶⠜⠛⠒⠂⠨⠭⠭⠙⠙⠿⠟⠛⠛⠋⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣶⣦⣀⢀⠀⠀⡀⠀⢀⠀⠀⣠⣾⣿⡏⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⢿⣿⣿⡟⢁⡤⣄⣦⣁⢨⣷⢠⣾⣿⣿⠅⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠉⠀⠛⠛⠋⢠⣿⣵⣶⣯⢽⣷⣿⣾⣻⣿⠟⠀⠀⠀⢘⠂⢈⠃⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣯⣿⣿⠟⣻⢇⣠⣂⠀⠀⠈⠀⠐⠅⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢠⡴⣿⣿⣿⣿⣷⣶⣿⣿⣿⣟⣿⠟⣡⣾⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣈⣀⣉⣉⣻⣿⣿⣿⣿⣾⣿⢟⣀⡀⡠⣄⣤⡤⠄⢀⣀⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⢿⣿⢸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠘⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⡿⡯⠊⣿⢶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠃⠁⣀⡾⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⡨⢿⣯⡙⢿⣿⣯⢿⣿⣆⠀⠢⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀⢀⣼⡿⢈⣼⣿⢿⡷⠙⢰⣿⡇⢿⣻⣿⣷⣾⣧⣀⠻⣿⣿⡟⣿⣅
⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⢀⣾⠟⠀⣾⠏⠟⠏⠁⠀⢸⣿⠇⠀⠻⡟⣿⣿⣿⢯⡀⠉⠹⠻⠹⢿⣦
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣸⠃⠀⠈⣿⠊⠀⠀⠀⠀⢸⣿⠀⠀⠀⠁⠊⣷⣯⣟⠆⠀⠀⠀⠀⠸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠃⠀⠀⠀⠀⠀⠸⡽⠀⠀⠀⠀⠀⠉⢹⣾⡇⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⢦⡴⠶⣤⡴⠲⠲⠶⠶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠉⠹⣿⠇⠀⠀⠀⣿⠇⠀⠀⠀⠀⢹⠍⠁⠈⠁⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢲⣿⡏⠁⠀⠀⠀⣿⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠿⠟⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⣿⠁⠀⠀⠀⠀⢸⡆⢀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣧⣄⡀
⠀⠀⠀⠀⠀⣠⠴⣾⡇⠀⠀⠘⡌⠀⠀⠀⠀⠀⢸⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠇⠂⠀⠀⠀⣸⠿⠿⠉⢷⡀
⠀⠀⠀⠀⢰⡇⠀⠹⣧⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠈⡧⠀⠀⠀⣸⡀⠈⠀⠀⡼⠃⠀⠀⠀⠀⡟
⠀⠀⠀⢀⣯⠀⠀⠀⢱⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⣧⠄⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⡿⠁⠀⠐⣾⠓⠀⠀⠀⠀⣼⡿⢦
⠀⠀⢠⣟⠉⢦⠀⠀⠀⢣⠀⠀⠀⠘⡂⠀⠀⠀⠀⢸⡄⠀⠀⠀⡅⠀⠀⠀⢸⠀⠀⠀⣰⠀⠀⠀⢰⠉⠀⠀⠀⠀⠼⠋⠀⢈⡇
⠀⠀⢸⡇⠀⠈⢲⣄⠀⠠⢦⠀⠀⠀⠱⡀⠀⠀⠀⠈⣡⠀⠀⠀⣧⠀⠀⠀⣾⠀⠀⢀⠏⠀⠀⢠⠇⠀⠀⠀⢀⡜⠀⠀⢀⣼⣷⡄
⠀⠀⢨⢧⡀⠄⠲⡿⣆⠀⠉⢧⠀⠀⠀⢷⣖⠀⠀⠀⡏⡆⠀⠀⡿⠀⠀⢀⢿⠀⠀⡜⠂⠀⢀⣞⠀⠀⠀⢀⡜⠀⠀⢠⠎⠀⢀⡇
⠀⠀⠸⡆⠘⢄⠄⠈⠻⡆⠀⠀⢳⡆⠀⠘⣿⠀⠀⠀⢇⠃⠀⠀⠁⠀⠀⢸⠂⠀⣠⡇⠀⠀⡟⠄⠀⠂⢀⡞⠀⠀⡴⠃⠀⡠⠎⡇
⠀⠀⠀⣿⠳⣾⢷⡀⠀⠙⢶⣄⠀⢿⠀⠀⢹⠀⠀⠀⠸⡀⠀⠀⡀⠀⠀⣿⠀⠀⡿⠁⠀⣼⠇⠀⠀⡠⡣⠄⢀⠞⠀⣰⣯⠕⣾⠁
⠀⠀⠀⠘⣷⣈⣷⡙⢦⠀⠀⢿⣆⠀⢣⡀⠀⢧⠀⠀⠀⡇⠀⠀⠁⠀⠀⡏⠀⣸⠁⠀⣰⠏⠀⢠⡞⠁⢀⡴⢅⡠⣪⣞⣵⢴⠋
⠀⠀⠀⠀⠙⢮⡻⣝⢮⡳⣤⠀⠹⣆⠀⠹⡄⠈⡆⠀⠀⢣⣠⢀⢠⡤⢴⣁⢀⡧⠀⢰⠹⠀⢀⡏⠀⣠⢞⡱⣫⣺⠖⣫⡷⠋
⠀⠀⠀⠀⠀⠀⢹⣚⢷⣝⣮⡣⣄⠘⢷⡄⢹⣤⢿⠁⠁⠸⡅⠸⣂⠀⡾⠀⡼⠛⢲⣿⣀⣠⠋⢠⢞⡕⣫⢞⣩⢶⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡿⠿⣮⣢⣌⠿⣦⠙⡄⢣⠀⠀⡇⠰⠁⢠⠇⢠⡇⢀⡾⠉⡵⢷⣶⣗⣡⣎⣪⠭⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡶⣭⣻⢷⣬⠳⡘⣌⢇⠀⢿⢸⡇⢸⢀⣾⢀⣾⢀⣼⣵⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⠷⢽⠿⢿⣦⡹⣞⢞⣆⢹⠸⣇⡏⢈⡟⣾⣫⣾⣿⣿⣿⠇⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢲⣮⡟⣁⡀⠀⡿⣿⣯⣿⡌⡄⣹⡟⣾⡼⣱⣿⡟⠉⢡⣴⡏⢁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⠤⠽⠋⠉⠙⠳⠦⢌⣿⣿⣇⣿⣴⣿⣾⡟⢡⣷⠖⢚⣿⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠷⠖⠶⠾⠗⠒⠒⠋⠉⠻⠿⠿⠟⠓⠛⠛⠛⠒⠿⠿⠶⠚

⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠛⠛⠛⠓⠒⠦⣄⢰⠋⣳⠀⢀⣀⡀⠀⠀⠀⠘⢦⣀⣀⣠⠞
⠀⠀⠀⠀⢠⡏⠁⠈⢳⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⡠⡀⠀⠀⠈⢻⡍⠁⢰⡋⠀⠙⡆⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠈⠧⣄⣠⠞⠀⠀⠀⢸⡯⠴⢎⣀⣀⠄⡊⠀⠈⠱⡀⠀⣀⣷⡎⡢⠓⠒⠚⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢠⠖⠒⢆⠀⠀⠀⠀⢀⣼⣷⣶⡶⠖⠚⣛⣻⢟⢿⣦⠗⠉⠁⣿⡉⣁⠀⠀⠀⠀⠀⠀⣾⠀⢸⠆
⠀⠀⠀⠘⠦⠤⠎⠀⠀⠀⠀⢸⣿⣿⠉⡔⠊⠀⠀⢐⣲⢱⢻⣇⠴⠚⣿⠟⠛⢿⣦⠀⠀⠀⠀⠈⣉⡉⠀⣠⢤
⠀⢀⡔⠒⡄⢀⣀⠀⠀⠀⠀⠀⢿⣿⣆⣱⣩⡿⢿⣦⣤⣾⡿⠁⠀⣰⣿⣶⣶⣾⣻⠶⢤⡀⠀⠘⠧⠞⠀⡈⠁
⠀⠀⠓⠖⠁⢯⣀⡇⠀⠀⠀⠀⠀⠙⠻⣟⢋⣠⣤⣍⠉⠁⢀⡠⠾⠗⠛⡖⠲⢤⡀⠀⠀⠙⢦⠀⠀⢰⠋⠉⢱
⠀⠀⠀⡠⢤⠀⢠⢄⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠶⠞⠉⠀⠀⠀⢠⠁⠀⠀⢳⡄⠀⠀⢸⡆⠀⠈⠳⠤⠞
⠀⠀⠀⠈⢊⣀⣨⣥⣀⣀⠤⣄⡀⣼⣿⣿⡿⡿⠭⠭⠥⠵⠶⠶⡄⠀⢸⠀⠀⠀⠀⣷⠠⠤⢸⡇⠀⠀⠀⢠⠖⠲⡄
⠀⠀⣠⣾⣿⠿⠾⠷⣿⣋⡓⠦⣝⠳⢿⣿⠃⡄⠀⠀⠀⠀⠀⠀⡿⠀⢸⠀⠀⠀⠀⣿⢠⣬⢼⡇⠀⠀⠀⠹⣄⣠⠎
⣀⠾⣷⣿⢶⠀⠀⠸⣟⠦⣭⣙⡂⠀⠀⠛⢄⢉⡉⠉⠉⠉⠉⠉⠀⠀⢸⠀⠀⠀⠀⣿⢚⣻⣻⡇⠀⢠⢤
⠣⠋⠛⡅⢸⡀⠀⠀⠈⣹⠖⠂⠤⢄⣀⠀⠸⠀⠈⡋⠐⠂⠠⠤⢀⣀⣘⠀⠀⠀⠀⣯⢭⡉⠉⡇⠀⠈⠊
⢚⡉⣈⣦⠀⠙⢛⡛⢯⡉⠀⠀⠀⢠⣿⣿⡿⢃⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣱⠀⡇⠀⢠⠤⡀
⠀⠹⣿⣷⣤⣀⠼⠃⢀⡇⠀⠀⣰⠋⣿⣿⣇⠀⠀⠈⠐⠂⠤⢀⣀⠀⠀⠀⠀⠀⣠⣯⠔⠁⠀⡇⠀⠈⠚⠁
⠀⠀⠈⠙⠻⠿⠶⠶⠾⠓⠒⠋⠁⠀⢻⣿⣿⡂⠀⠄⠠⠠⣤⣤⢤⡾⢛⠷⣶⣿⣿⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⡴⠒⢦⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿⣷⣶⣟⠥⣬⢽⠀⠀⠀⣿⠿⡩⢻⡉⠉⠁⣿⠀⠀⠀⠀⢀⣠⠞⠛⠨⡙⣆
⠀⠀⠀⠀⠀⠳⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠭⣉⠙⠒⠀⠚⠳⠶⠞⡣⠊⠀⠘⡇⠀⠀⣿⠀⠀⢀⡴⢏⠉⠑⡄⠀⢁⣽⡄
⠀⠀⠀⠀⠀⠠⡦⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆⠀⠉⠒⠤⣀⠀⠀⠌⠀⠀⠀⠀⢷⠀⠀⣿⢀⡴⠋⠀⠀⢈⣿⣤⣤⣾⡇⢻⡀
⠀⠀⠀⠀⠀⠀⠰⡇⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣆⠀⠀⠀⠀⠉⢚⠀⠀⠀⠀⠀⢸⡦⣠⡾⠋⠀⠀⢀⡴⠉⡏⢸⢩⠁⢰⠈⣧
⠀⠀⠀⠀⣞⢹⠀⠉⢉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣆⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢿⠋⠀⠀⢀⡴⠋⠀⢠⡇⢸⠈⣦⠈⡀⠸
⠀⠀⠀⠀⠈⠁⠀⢈⣿⣧⡤⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠈⠀⠀⣠⠏⠀⠀⠀⢸⡇⡘⠀⢿⠀⢃
⠀⠀⠀⠀⠀⣦⠀⠘⣿⢞⣃⠀⠀⢀⣀⣬⣾⣵⠆⠀⠀⠀⠈⢳⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢸⠁⡃⠀⢸⡆⠸
⠀⠀⠀⠀⠀⠀⠚⣧⣾⣵⡮⠁⠀⢺⣯⡤⠛⠋⠁⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⠑⢤⡤⠴⠊⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⢸⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠈⠛⣧⣽⡇⠀⢰⣿⡿⠀⠀⣿⣶⡿⡆⠀⠀⠀⠀⠈⠷⣄⣀⣀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣁⡀⢸⡇⠀⢃
⠀⠀⠀⠀⠀⣤⢤⠀⠉⠿⣷⣄⣿⢷⣳⢐⢾⠻⣞⠻⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠙⣾⡟⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠆
⠀⠀⠀⠀⣀⠤⠤⠐⠒⠈⠉⠉⠉⠁⠀⠤⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠂⠠⠤⢀⡀⠀⠀⠀⢀⠠⠄⠂⠁⠀⠀⠀⠀⡠⠂
⠀⠀⠰⡏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠮⣁⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠙⢄⡀⠁⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠲⣖⠁
⠀⠀⠀⠀⠀⠻⣶⣤⣀⣀⣀⣀⠤⡤⢤⡤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠈
⠀⠀⠀⠀⠀⠀⠈⠪⡿⡻⡇⠉⠀⠀⠀⡀⢁⢈⣉⣳⣦⡀⠈⠀⠀⠄⠀⣸⠀⡇⢸⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⣂⣦⣻⠊⠉⠉⠀⠁⠁⠉⠉⠀⠀⠀⠀⠐⠁⡜⢁⡞⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠾⠀⠀⠖⠒⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡹⠛⠿⠶⣶⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⣄⣀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⣀⣵⣾⣻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣄⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⣿⣿⠏⠊⠁⠉⠛⠟⠷⢶⣤⣤⣄⣀⠀⠀⠀⠉⠳⢯⣷⣤⡀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣽⣞⠽⠮⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠙⠢⡀⠀⠀⠀⠹⣿⣮⣶⣤⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⢖⠟⠊⠈⠳⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⡀⠀⠀⢰⣿⣿⠋⠙⠹⣦⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⡮⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠐⣉⠍⠉⠀⡰⠀⠀⣠⣿⠟⠁⠀⠀⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠒⢠⡤⠂⠁⠀⠀⠀⠀⣀⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠊⠁⠠⠀⠀⣀⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢳⣶⡶⠖⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁

⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⡄⣤
⠀⠀⠀⠉⠻⢿⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣶⣿⣷⣿⣦⡀⢐⣤⣀⠀⠀⠀⠰⢿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⢀⣨⣿⣙⠻⢿⣤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠂⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦
⠀⢀⡠⠤⠖⠛⠉⠉⠛⢿⣶⣿⣿⣿⣦⣀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣶⣦⡀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠁⠀⠛⠃⠀⠀⢸⣿⡿⠻⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣼⡟⠹⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠛⣿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣤⣬⡿⢿⣿⣿⣿⣿⣿⣷⣾⣿⠁⠀⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠙⠻⢿⣿⣉⡉⠙⠉⠀⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣤⣠⣴⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⠂⠀⠀⠈⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠱⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠏⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⡿⠟⠙⣿⣿⣿⠛⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣴⣶⡿⠟⠛⠉⠉⠁⠀⠀⠀⢘⣿⣿⠆⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡀
⠀⠀⣼⣿⠋⠀⠀⠀⠀⢀⣴⣿⣷⣾⣿⡿⠿⢿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣏⡀
⠀⣾⣿⠏⠀⠀⠀⠤⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦
⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⡿⠉⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧
⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠉
⠀⠀⠀⠀⠀⢰⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠟⠁⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢿⣿⣿
⠀⡀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡟⠿⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⢸⣿⣿
⠳⣾⣷⣄⣸⣿⢿⣿⣿⣿⣿⣿⣿⣤⣈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⢸⣿⡿
⠀⠀⠀⠙⠿⠏⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠋⠙⠛⠿⣿⣷⣤⣄⣠⣤⣾⠟⠁⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠏⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣴⡖⠛⠛⠛⠛⢶⣶⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⣶⡞⠉⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⢻⣶⠶⢦⣄
⠀⠀⠀⠀⢀⣠⣴⠁⠀⠀⠈⢿⡄⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸⡇⠀⠀⠉⠳⣦
⠀⠀⠀⣰⠋⠀⠹⣆⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡷⢦⣄
⠀⠀⣰⠛⣆⠀⠀⢹⣆⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠏⠀⠀⠈⠻⣄
⠀⠀⣿⠀⠸⣆⠀⠀⢿⡄⠀⠀⠀⠸⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⡿⠀⠀⠀⣿⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢿⠀⠀⢻⡄⠀⠘⣷⠀⠀⠀⠀⢻⡆⠀⠀⠀⣿⠀⠀⠀⢰⡇⠀⠀⢰⡏⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⢀⣴⣿⢷⡀
⠀⠀⠸⡆⠀⠀⢿⡀⠀⢻⡆⠀⠀⠀⢸⣇⠀⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⣿⠁⠀⢀⣼⠃⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠙⣆
⠀⠀⠀⢳⡀⠀⠈⣧⠀⠸⣇⠀⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⣸⠃⠀⠀⣼⠃⠀⢀⣾⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⢧⠀⠀⠸⡆⠀⣿⠀⠀⠀⢀⡇⠀⠀⣼⠁⠀⢰⠏⠀⠀⣼⠃⠀⢀⡾⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣠⣾⣇
⠀⠀⠀⠀⠘⣧⠀⠀⢻⡀⢿⠀⠀⠀⢸⠇⠀⢠⡇⠀⢠⠏⠀⠀⣼⠃⠀⢠⡿⠁⠀⠀⣠⠟⠁⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠘⣦
⠀⠀⠀⠀⠀⠸⣆⠀⠈⡇⢸⠀⠀⠀⣾⠀⠀⡾⠀⢠⠏⠀⢀⡼⠃⠀⢠⡿⠁⠀⢠⡾⠁⠀⠀⠀⢀⣠⣶⠟⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠹⡆⠀⢿⢸⠀⠀⢀⡏⠀⢰⠇⢀⡞⠀⢀⡼⠁⠀⣰⡟⠁⠀⣰⠏⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⣾⠀⠀⢸⠃⠀⡟⢀⡞⠀⢠⡞⠁⠀⣰⡟⠀⢀⡼⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⣀⣤⡴⠾⠛⠋⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣷⠘⣿⠀⠀⡿⠀⣸⢁⡞⠀⣠⠏⠀⠀⣼⠏⠀⢠⠟⠀⠀⢀⣴⠟⠁⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⣀⣠⡏
⠀⠀⠀⠀⠀⣠⠞⠋⠈⣇⣿⠀⢰⡇⢠⠇⡼⠀⡴⠃⠀⢀⣼⠃⢀⣴⠋⠀⢀⣴⠟⠁⠀⣠⠶⠋⠁⠀⠀⣀⣤⡴⠶⠞⠛⠛⣿⠁
⠀⠀⠀⠀⠀⠻⡀⠀⠀⢸⣽⠀⢸⠇⡞⡼⢁⡾⠁⠀⣠⡾⠁⣠⡞⠁⠀⣠⠟⠁⢀⡴⠋⠁⢀⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⣿⡇⢸⣼⣱⢣⡞⠀⢀⣴⠋⢀⣼⠋⠀⣠⠞⠁⣠⠖⠉⣀⡴⠞⠋⠁⠀⣀⣀⣤⣤⣶⡶⠶⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣷⢸⣿⣧⡟⠀⣠⠞⢁⣴⠟⠁⣠⠞⢁⡤⠚⣡⠴⢛⣁⡤⠴⠖⠛⠋⠉⠉⠁⠀⠀⠀⢀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣿⡿⢀⡜⣁⡴⠛⢁⡤⠞⣡⣴⣫⢔⡫⠔⣚⣉⣀⣀⣤⣤⣤⣤⡤⠶⠶⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⠿⠚⣉⡤⠖⣫⣴⣞⣻⡽⠾⣿⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⢿⣵⠶⠟⠛⠋⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠤⣼⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡛⣽⢳⣴⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣗⡹⣿⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⡿⠟⢯⣿⣿⣿⣿⣿⣿⣿⣧⠇⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣤⡴⣚⢻⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣷⢍⣜⢿⣿⣿⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⠇⣵⠀⢀⣿⠃⠈⠙⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠘⠋⢀⣼⣿⠀⠀⠀⠀⠈⠉⠀⠉⠙⢷⣄
⠀⠀⠀⠀⠀⣼⣿⡟⠀⢀⡀⠀⣀⣴⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⢀⣴⡿⠋⠀⣰⣾⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⣠⣴⠿⠋⠀⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠈⠁⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⢿⠟⠿⠙⠯⠹⠯⠻⢟⡻⢶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠏⠣⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠋⡝⠷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠟⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡽⢳⣄
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⡀
⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⢀⣠⣴⣶⡶⡾⣶⢶⣶⣤⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⢀⣿⠉⠁⠀⠀⣠⣾⡟⠿⠙⠀⠀⠀⠈⠉⠘⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⢸⡏⠁⠀⢀⣼⠿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⣾⠒⠀⠀⣾⡯⠁⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⢿⡄⠀⢰⣿⠄⢠⣾⠟⠋⠉⠉⠘⠙⢻⣧⡄⠀⠀⠀⠀⠀⢈⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⡇
⠀⠀⠀⠀⢸⣟⠀⢸⣿⢠⣿⣡⡶⣶⠶⣶⡄⠄⠀⠙⣿⡄⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠈⢿⡆⠀⣿⣼⣿⣿⣿⣿⣦⣽⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠈⢷⣄⠘⣿⣿⣿⣿⣿⣟⣰⡿⠀⠀⢠⣿⠁⠀⠀⠀⠀⣘⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣌⡻⢿⣿⣿⡛⢉⣀⣤⣼⡿⠁⠀⠀⠀⠠⢠⣼⠟⠛⠻⠶⠶⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣍⠙⠛⠛⠛⠋⠁⠀⠀⢠⡀⣠⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣷⣦⣤⣦⣶⣦⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⠁⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡬⠿⢿⣿⣶⣦⡀⠛⣸⡇⢀⠖⣁⠀⢈⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠙⠿⣷⠀⣼⣣⠏⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣭⣭⣶⣦⣬⣵⣟⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣡⣤⣜⣿⣿⣾⣶⡭⢙⣷⣶⡶⠦⣝⣣⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠿⢿⣿⣿⣯⣾⣟⡟⢩⣿⣿⣦⡘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠸⣿⠋⣿⢛⣿⣿⢸⠈⠉⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢻⠋⡰⠈⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣤⣏⠀⠀⠀⠀⢀⠀⣀⡀⡀
⠀⠀⠀⠀⣠⣤⡤⣤⣤⣤⣤⣤⡉⣭⣭⣽⡿⠿⠩⠈⣿⠤⢬⣕⣛⠚⢻⠉⠉⠩⠁
⠀⠀⢠⣤⡴⠦⣴⣿⣿⣿⣽⠻⠷⠛⠉⠁⠀⠀⠀⢀⣹⣧⠀⠉⠙⠻⢛⣛⣛⠓⢲⣖⣀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠠⢶⡶⢶⣶⣦⣭⣙⢂⣀⡀⡀⠀⠀⠀⠀⠈⠉⠳⣄⠐⠀⠀⠙⠻⢿⣷⠍⠉⡉⠈⠉⠉⠛⠛
⠀⠀⠀⠀⣤⣤⣶⣿⣶⣬⣭⣾⣶⣿⣿⣿⣧⣈⠓⠒⠓⠈⠀⠈⠳⠄⠀⠀⠀⠴⠾⠒⠿⠿⠶⠆⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠤⠒⠶⠶⣾⣯⣤⣀⡈⠛⠋⠀⠲⠾⠿⠿⠿⠻⠒⠒⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠖⠒⠒⢛⠉⠉⠉⠉⠉⠉⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⢉⡩⠄⠀⠀⢪⣗⢂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢁⣠⠤⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡤⠔⢃⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⡆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡀⠊⣠⠿⠛⠛⠁⠃⠘⠃⠓⠚⠳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⢤⡀⠀⠀⠀⢀⡴⠋⠁⡀⢸⠀⡇⠀⠀⠀⠀⠀⠘⡃⠀⠀⢀⣠⠞⠁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⠒⡶⠋⡀⢰⠘⡇⠸⠀⠃⠀⠀⠀⠀⠀⢀⠉⡩⠔⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣠⠞⠀⠀⢹⡈⢇⢹⠀⠆⠈⠀⠀⢀⡠⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡴⠃⠀⠀⠀⠀⢇⠈⠀⠆⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡞⠁⠀⠀⠀⠀⠀⠈⡄⠀⠈⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⡤⠈⡄⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⠹⣘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠣⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠔⣫⠟⡀⠔⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠠⣁⠞⡡⠊⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⡞⠀⠀⢐⣃⠔⡡⢊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⡇⠀⢀⠞⡡⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠙⠒⠒⠂⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⣇⡴⢫⠎⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⣠⢏⡔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠇
⠀⠀⠀⢀⡔⣡⢊⡄⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢀⠔⠈⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⡌
⠀⠀⢠⠎⡔⡡⠊⢻⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣴⠃⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡴⠃
⠀⣰⢃⡾⠊⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡼⠁⠎⠀⣾
⣰⡷⠋⠀⠀⠀⠀⠀⡸⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⢦⣤⠼⠁⠀⠀⡀⣼
⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠊⠑⢄⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠀⠀⠀⠉⠓⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠐⠠⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢌⡑⠓⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠉⠉⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⢄⠀⠈⠓⢿⡦⢔⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⡀⠠⠤⠤⠀⠐⠒⠐⠒⠒⠒⠒⠛⠚⠢⢄⡀⣂⠌⠀⠀⠘⢣⢋⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢗⡀⡠⠀⠀⠀⠀⠀⠀⠀⠐⡤⠄⣀⠀⠀⠀⠀⠀⡰⠙⡁⠀⠀⠀⠰⡀⢉⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡠⡔⠉⠀⠀⡠⠊⠉⠒⠒⠉⠀⠀⠰⣠⠐⠉⠒⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣜⣄⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠒⡩⠋⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠁
⠀⢀⣀⠠⠤⠤⠤⠤⠤⠀⠀⠠⠤⠀⠀⠠⡄⠠⠤⠀⠒⠂⠀⠉⠐⠒⠂⠩⠁⠀⠀⠀⡰⠁⠀⠀⠰⡀⠀⠀⠀⠀⢀⣀⠤⠐⡢⠂
⡎⠁⡠⠤⠄⠐⠒⠒⠒⠂⠀⠐⠄⠀⠀⣈⠤⠄⠀⢀⣀⣀⣀⣀⣀⣀⠀⢠⠀⠀⡠⠊⠀⠀⠀⠀⠀⣱⠄⠒⠈⢁⠔⢁⡠⠊
⠱⡀⠢⠀⠀⠀⠀⠀⠀⠀⣀⣴⠮⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⡠⠚⢡⡄⠀⠐⡁⠔⠁
⠀⠸⠀⠇⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠠⢀⣀⠔⠉⠀⠀⣞⣷⡠⠜
⠀⠘⣀⣑⡠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢀⡠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⡁⣀⠤⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⡉⠔⠉⠉⣂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢁⡠⠊⠀⠀⠀⣰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢀⠔⠁⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⠤⢀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠄⠡⣀⢌⠎
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣢⣤⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠐⠶⣦⣄⣀
⠀⠀⠀⠈⠉⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠉⣻⣷⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣀⣠⡄
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣯⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣦
⢀⣀⣤⣴⣾⣿⠟⠋⠉⠉⠉⠙⠿⢿⣿⣿⣿⣷⣤⡀⠀⠀⢀⣀⣀⣀⣿⣿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠈⠙⠛⠛⠻⠿⣿⢿⣿⠋⠉⠉⠛⠋⠉⠛⠻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠁⠀⠀⠸⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠗






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢶⣄⠀⠀⠄⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣥⣤⣤⣤⣋⣶⢀⠀⠀⢠⢴⣟⠿⠿⢿⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⡽⠟⠋⠉⡁⠺⣀⣀⣠⣂⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢰⠯⠿⠋⠈⢁⡴⠋⠀⠀⣀⠘⣷⠈⣷⡄⠻⢟⠟⣤⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠈⡐⡘⠲⣿⣷⠀⠈⠰⢼⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠑⣿⠀⢹⣿⡆⠀⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⠘⣿⡇
⠛⠛⠛⠛⠛⠛⠛⠿⠟⡏⠀⣠⣿⠿⠋⡙⠂⠿⣿⣤⣽⠉⣿⡇⠀⠙⠛⠻⠛⠻⠿⠿⠿⢿⣿⡟⠻⠛⠻⠿⠿⠯⠟⠛⠛⠛⠚⠛⠛⠻⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠉⠉⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠋⡀⠥⠠⠄⠀⢀⣀⣀⣀⡀⠀⠁⠀⠀⠀⠀⠒⠶⠦⣠⣄⡋⠁⠁
⠁⠉⠉⠉⠐⠛⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠤⠤⠤⢶⡤⢄⡈⠛⠓⠀⠀⠐⠒⠲⠶⠆⠀⠀⠀⢀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠉⠛
⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢴⡆⠀⠀⡀
⠀⠀⠀⠀⢄
⠀⠀⠈⠁⢈⡤⣬⠤⠤⠴⠀⠦

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠤⠜⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣴⠂⣶⠆⣤⠤⢀
⠀⠀⢀⠀⠀⢠⣶⡶⢐⣀⡀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⣿⡜⣿⡄⣿⢰⣿⢠⡾⢉⡶⡄
⠀⠀⠀⡅⠀⣿⠋⡾⣽⣿⣿⡦⡇⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡽⣿⣽⣷⣿⡇⣿⣼⠇⣾⢡⡟⣱⠿⡆
⠀⠀⠉⠇⠈⣿⣾⣗⢿⣿⡿⢣⠃⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢸⢣⢟⡾⣡⢞⣩
⠀⠀⠐⠶⠛⠛⠳⢉⠀⠀⠀⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⢇⣏⢏⣮⣞⣵⣯⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣹⠏⣜⣻⠿⠛⠋⠁
⠀⠀⠠⣠⣤⣶⣦⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣠⣿⣯
⠀⠀⠀⠙⢿⣟⠛⠛⠛⠛⠙⡋⢩⣙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⠽⠿⠿⠿⠿⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠈⠙⠿⣩⠩⠉⡭⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣢⣄
⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⣈⠁⣽⡄⠀⠀⠲⢦⣤⣤⣀⣀⣸⣿⣄⣀⣤⣤⣀⠔⠂⠀⢠⣿⣯⣿⣶⡄
⠀⠀⠀⠀⠀⣾⣏⣻⡀⠀⠀⠀⠀⠀⢠⡿⠘⠙⣷⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⣸⣿⣿⢿⡻⣿⡆
⠀⠀⠀⠀⣸⣿⣿⣧⣧⡀⠀⠀⠀⠀⣠⠀⣼⢢⣿⡆⠀⠀⠀⠀⠀⢀⣾⡿⠻⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣏⡅⢎⡿⣿
⠀⠀⠀⢀⣿⣿⣿⠛⠼⣳⠀⠀⠀⢠⡿⠑⠈⢂⣿⡇⠀⠀⠀⠀⢠⡿⠛⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⣿⣿⡷⠜⡡⢞⡿
⠀⠀⠀⣼⣿⣿⣷⠛⡲⣿⡆⠀⠀⠨⠀⡀⠆⡿⢁⣷⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⢹⣿⣿⣣⢑⢹⡇
⠀⠀⣰⣿⣿⣿⣁⣼⠳⣄⣿⠀⠀⢈⣀⠦⠻⣹⡯⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣬⠹
⠀⢠⣿⣿⣿⣿⣧⡄⠻⣀⢽⠆⠀⠈⠄⣘⢴⣿⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⡷
⠀⢸⣿⣿⣿⡗⠒⢉⠗⠜⠺⡄⠀⠀⠠⠟⣿⣿⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛
⠀⠀⠙⠋⠿⣿⡷⠺⡷⠚⠓⠁⠀⠀⠀⢰⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣆⠀⠀⠀⣠⢠⣼⣾⣿⣿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣀⣄⣀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡆⢀⣾⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⣿⣿⣿⣶⣤⣆⠀⠀⢿⣿⣿⣿⣷⣾⣿⣟⣯⣿⣇⣰⣶⣴⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣿⣿⣿⣷⣦⣼⣿⣽⣿⣿⣿⣿⣿⣡⣾⣷⣿⣯⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠈⠙⠿⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣥⣤⣴⣴⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠿⣟⣿⠟⢿⠿⢿⣶⣾⣿⣝⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠻⢿⣯⢻⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⣀⠐⠋⣽⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠁⠈⠛⡙⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡏⠀⢈⣵⣿⡿⢿⡟⣿⣿⣿⣿⢿⢿⣿⡟⢿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣷⣦⡀⠀⠀⠀⣰⣿⣿⠋⢀⣴⣿⣿⡿⡝⣿⠀⣿⣿⣿⣿⣎⠟⠹⠋⡌⡿⢻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⢀⣼⣿⣿⠀⢠⣿⣿⢻⡝⠣⠉⠀⠀⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠘⠉⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢿⣿⣷⣾⣿⣿⣋⣰⣿⣿⣹⣧⣵⣶⣶⣶⣤⣿⣏⢸⣟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢣
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⡿⣿⣿⣷⣶⣀⡀⢨⣿⣿⣿⣿⡟⢉⣿⣿⣿⣿⣿⠟⠋⠉⠈⠉⣿⣿⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠁⠀⢲⣿⣿⣿⣾⣿⣿⣿⣿⣵⣾⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⣿⣟⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣸⣿⣿⣯⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⣿⡯⠀⠀⠁⠃
⠀⠀⠀⠀⠀⣴⣿⢿⠛⠉⠈⠁⠀⠛⠛⢛⣩⣿⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠉⠛⠀⢠⣿⡇
⠀⠀⠀⠀⠰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢹⣿⡟⣿⡿⣿⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⣿⣿⠀⣿⡇⣿⡇⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⢹⡇⠀⢻⣇⢹⣧⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠈⠁⠀⢸⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⢰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⢀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆

⠀⣴⣶⣶⣶⣶⣶⣦⣶⣶⡤⢄⣤⣄
⠀⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣄⣹⣿⣷⡀
⢠⣿⣿⣿⣿⣿⣻⣿⣿⣿⣏⢻⣿⣿⣿⣗⣀
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣝⠺⣿⣷⣤⣶⣄
⠀⣌⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣌⣻⣿⣧⣀
⠐⠛⠿⣷⢹⣿⣿⣿⣗⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⣿⣿⡅
⢀⣄⣠⣿⣶⣤⣝⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⡃
⠀⠙⠿⣿⣍⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠳⣀⡀⠀⣀⠀⠀⠀⠀⣶⣿⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴
⠐⣾⡷⡎⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣦⣶⣦⡰⣄⣿⣿⣿⣿⣶⠀⠀⣀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠈⠠⢀⣬⣿⣿⣿⣿⣿⣿⣻⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣤⣬⣿⠿⡿⢯⣽⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⡼⢾⣿⣿⣤⣿⣿⣿⣿⣿⣟⣽⡾⣷⣿⣆⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣶⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠸⢀⣠⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢢⠀⠀⠀⠀⠀⠀⠈⠄⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⣠⣤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣾⡿⣿⣶⣄⠀⠀⠀⠀⠀⢠
⠀⢻⣿⠀⢀⣾⣿⣿⣿⣦⠀⠀⣴⣿⣿⣷⣦⠀⠀⣿⣦⡀⠀⢀⣿⡟⠻⣇⡿⠛⣿⡆⠀⢤⣀⣀⡜⣇⡀⣀⡀
⠀⢸⡇⠀⠘⣿⣿⣿⢿⣿⠂⠀⠛⠛⠉⠛⠛⠀⠀⠻⣿⣿⠀⠘⣿⣿⠟⣹⡙⢿⣿⡇⠀⠀⠈⢳⣺⣓⡋⠁
⠀⠀⠃⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠿⣿⣧⣿⡿⠟⠁⠀⠀⢠⠓⠁⠙⠣⡀

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⣾⣿⠂⠀⣠⣤⣤⣤⡀⠀⠀⢀⣤⣤⣄⡀⠀⠀⣷⡀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣸⡆
⠀⢿⣿⠀⢸⣿⣿⣿⣿⣿⡄⢰⣿⣿⣿⣿⣿⡀⢀⣿⣿⣦⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠓⠶⣶⣿⣷⣶⠶⠒
⠀⠸⡏⠀⠈⠿⣿⡿⠛⠿⠇⠀⠉⠻⣿⠟⠉⠀⠀⠙⠻⡿⠀⠈⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⠿⢿⣇
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠉⠀⠀⠀⠚⠁⠀⠀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣷⣦⡀⠀⠀⢰⣽⡇⠀⠀⠀⠀⠀⣤⣾⡿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⣀⡸⢿⣿⣷⣄⠘⣿⣧⠀⠀⢠⣠⣾⡿⢃⣤⣾⣿⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠞⠛⠛⢉⠛⠉⣉⣩⣿⣿⣿⣷⣿⣝⢷⣿⣏⢀⣼⣿⣿⣟⣡⠿⢻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢛⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟⠉⣀⣀⣀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠿⢯⣉⠹⣿⣄⣀⠙⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠈⠁⠀⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡍⠻⠿⣿⣶⣄⠀⠉⢻⣿⡙⠂⢀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣳⣿⠆⠀⠀⠙⠓⣠⡀⠀⠈⠙⠀⠸⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠻⠁⠁⣼⣿⣿⣿⢿⣇⠉⢻⣟⣻⢦⠀⠀⠀⠀⠸⡿⣶⡆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣰⣿⣿⠂⣯⢻⡅⠀⢸⣯⢹⣷⠀⠀⠀⠀⠀⠈⢏⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⣇⣾⠁⠀⠀⢿⡗⣿⠀⠀⠀⠀⠀⠀⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠁⠀⠀⢻⡇⠀⠀⠀⠸⣿⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠘⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣤⣶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⣤⣀
⢀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣁⡿⢤⡙⢿⣿⣿⣿⣿⣿⠿⠟⠉⠉⠑
⠀⠈⠉⠙⠳⢶⣤⣀⡀⠀⠀⠘⡿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠈⢉⡉⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣾⠃⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡳⢤⡀⠀⣸⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣈⣻⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡴⠚⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠿⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷⣦⣀⣀⣤⣤⣶⣶⣶⡶⠾⠛⠛⠛⠛⠻⠿⠿⣿⣿⣛⠛⠛⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠻⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠻⣦⡀⡱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⣴⣾⠟⠛⠉⠉⠙⠛⢿⡿⠟⠛⠉⠙⠻⢿⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠉⠛⠛⢿⠟⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡟⠋⠉⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠹⠿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠋⢻⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡇⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠟⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡗⠀⠀⠀⠀⡄⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⢀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢰⡇⠀⠀⠀⠐⠀⠀⠀⠀⠸⢷⣄
⠀⠀⠀⢀⣴⠿⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠁⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢹
⠀⠀⣰⡿⠁⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠀⠀⠀⡞⠀⠀⠀⡐⠀⠀⠀⣼
⠀⠀⣿⡇⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣇⠀⠀⠀⣿⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢻⠀⠀⠀⢿⠀⠀⣸
⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠸⡇⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⣾⡟⠙⢧⡀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢻⠀⠀⢸⡆⠀⠃⠀⠀⠀⠀⠀⠀⢠⡞⠁
⢸⣿⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠘⡀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠘⣿⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠹⣷⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠈⢄⠀⠀⠑⠀⠀⡀⠀⠰⠀⠀⡜
⠀⠀⣿⠿⢦⡀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢦⡀⠀⢳⠀⢡⠀⠀⠀⡌
⠀⠀⣿⠀⠀⠙⠦⣀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠈⠳⣄⠀⠀⠑⡄⠀⠃⠀⠃⠀⠠
⠀⠀⢻⡇⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠈⠓⠦⡀⠀⠀⠈⠑⢄⠀⠀⠠⡀⠰⡀
⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠙⠳⢄⣀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠈⠓⠦⢄⡀⠀⠀⠀⠀⠈⠓⠂⢀⡀⠀⠀⠠⡀⠑⢄
⠀⠀⠀⠀⠈⢳⡦⣄⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠉⠓⠲⢤⣀⡀⠀⠀⠀⠉⠛⠂⠤⣄⣀⠀⠀⠀⠉⠒⠄⠀⠀⠑⠀⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠈⣧⠀⠉⠒⠦⣄⡀⠀⠀⠀⠈⠉⠓⠶⣤⣀⠀⠀⠀⠀⠉⠑⠲⠦⢤⣄⣀⡀⠀⠈⠉⠀⠀⠀⠤⠀⣀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠉⠛⠲⢦⣄⣀⠀⠀⠀⠈⠙⠓⠶⠦⣤⣄⣀⡀⠀⠀⠀⠉⠉⠉⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⠦⠤⢤⣤⣀⣉⣉⣓⠲⢦⣤⣄⣀⣀⡀⠀⠈⠉⠉⠉⠛⠒⠒⠒⠒⠒⠒⢂⣉⣉⡠⠤⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠍⠉⠛⠛⠛⠛⠛⠓⠒⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠐⠂⠀⠀⠀⠂⠀⠂⠂⠀⠂⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⣤⡔⠒⠓⢦⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠉⠀⢀⡔⠉⠀⠀⠉⠓⢄
⠀⠀⠀⠀⡠⢰⠃⠀⢸⡇⠀⠀⢸⠃⠀⠹⡆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⢲⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⡞⣹⠀⠀⠀⡸⠀⠀⠀⠀⣀⠤⠼
⠀⠀⠀⢠⠁⠘⡄⠀⠀⡇⠀⠀⢸⠀⠀⢠⠁⠈⡄⠀⠀⠀⠀⠀⢀⣀⣠⠞⠛⠛⠓⠚⠋⠉⠀⢀⡇⠈⠟⠲⡄⠀⠀⡾⠀⠘⡄⠀⠀⣧⡤⢲⠒⠛⢢⣄⡀
⠀⠀⠠⠻⡄⠀⢱⡀⠀⢡⠀⠀⡎⠀⢀⠎⠀⢠⠛⠄⠀⠀⣠⣾⡉⠀⠉⠛⠒⠶⠶⠶⠶⠶⠒⠋⠀⢀⡆⠀⣷⠀⠀⡇⠀⠀⠈⠒⢠⡟⢤⢾⣄⢺⡀⣀⣙⡄
⠀⠀⢠⠀⠘⢄⠀⢷⠀⠸⠀⠀⠃⠀⠞⠀⡰⠁⠀⡄⠀⢐⣇⡀⠉⠓⠲⠦⢤⣤⣤⣤⣤⠤⠴⠶⠚⠉⢀⡼⢁⡇⠀⢳⣄⠀⣀⣀⠠⣧⣈⠆⢾⢀⡏⠀⠈⢣
⠀⠀⢸⡳⢄⡈⠳⡀⢣⠀⠇⠸⠀⡜⣀⠎⢀⡠⢚⡇⠀⠈⠣⣍⠛⠒⠦⠤⢤⣤⣄⣀⣀⣀⣤⡤⠴⠚⠉⢀⡾⠀⠀⠈⢧⠀⠀⠀⠀⢈⠿⠂⠾⠋⠘⢦⢀⠇
⠀⠀⠀⠙⢢⡍⠒⢌⣂⣣⡀⢀⣈⠐⡁⠀⢡⠔⠋⠀⠀⠀⠀⠀⠙⠓⠢⢤⣀⣀⡀⠀⠀⠀⢀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠑⢢⠒⠀⠁⠀⠀⡐⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠳⣌⡹⠿⣍⡛⠋⡩⠿⣏⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠔⠚⠁⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄⠀⠰⠂⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⠃⠈⠢⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠃⡀⢘⣤⡄⠷⢀⣰⠀⠱⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠲⣆⡀⢠⡤⣤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠾⡋⠀⣹⣄⠀⠀⢨⡇⢸⠒⢄⡀⢀⣀⠀⠀⠆⠁⢄⣠⠾⡁⠀⠑⡀⠀⠉⠑⠆⠀⢰⡀⠀⠀⠀⠀⠀⠀⢀⡠⢾⠀⢸⢿⠀⢸⡀⠉⣹
⠀⠀⠀⠀⠀⠀⢰⡇⠀⣵⠋⢸⠀⠉⠒⠾⠁⢸⠃⢻⠙⢁⡜⢀⠞⠢⠄⣴⡁⠀⣠⠟⠛⡉⠙⠣⡀⠼⠃⠀⠙⠀⠀⠀⠀⠀⢰⠏⡔⠙⣧⠘⣏⢧⡀⠉⠀⡇
⠀⠀⠀⠀⠀⢠⡏⢰⡼⢋⠀⢸⠀⠀⠀⢸⣀⠸⡆⢨⠟⠁⠀⠼⢄⣀⠀⡇⠀⡀⡜⠀⣞⠁⠃⢠⠇⣠⠇⠀⢱⠀⠀⠀⠀⠀⣼⢸⠀⠀⠈⢣⡈⠓⠍⠀⠈⠷⡀
⢠⣶⣖⣶⣾⣩⣶⡋⡇⠸⡄⠈⣇⣠⠖⠙⡇⠀⡼⠉⠀⠀⢠⣆⠀⠀⠀⢸⡊⠀⡴⢆⠈⠗⠚⠁⣀⠞⠂⢠⠏⠀⠀⠀⠀⣰⠣⠃⠀⠀⠀⠀⢹⠦⢄⣀⠀⣀⡟
⠀⠙⠿⠿⠿⠟⠻⢯⣍⠓⠻⠶⠚⣇⠀⠀⣹⠤⠇⠀⠀⠀⣿⠀⠁⠀⠉⠀⠑⢶⠃⠈⠁⠛⢆⠀⠉⢀⡤⠎⠀⣤⣀⣀⣤⣶⠶⢟⣻⢶⣀⠈⢁⡠⠊⣡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠢⣤⡇⠀⠀⠀⠀⠀⠹⠤⠤⠶⠒⠒⠒⠀⠵⠚⠧⠤⠄⠗⠒⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠲⠤⠥⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠈⣆⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣞⣦⣷⡼⠳⠛⠶⢦⣝⣁⡄⠀⠀⠀⠀⠀⠀⠀⠀⢲⡤⠶⠖⠣⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⢲⡒⠲⣤⠤⣄
⠀⠀⠀⠀⠀⠀⢀⣞⠡⠁⠈⡖⠀⠀⠀⢸⣏⣀⣀⡀⠀⠀⠀⠀⠀⣹⠋⡀⠀⠀⠀⠑⢢⡉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢇⠀⠘⣆⠀⣇⠀⡇⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣷⠂⠀⠸⣄⣁⡄⠚⠁⠘⣷⠊⠁⠀⠀⠀⠀⣸⠷⣾⡶⠲⢦⡄⠀⡀⢹⡀⠻⣦⡀⠀⠀⠀⠀⠀⠀⡎⣀⠀⠱⡄⢹⡄⢸⠀⡇⠀⢠⡇⢹⡀
⠀⠀⠀⣠⠤⠒⠃⠹⣦⡀⠀⠘⡹⢷⡂⠀⢀⣿⠘⠁⠀⢦⣲⠿⢇⠀⠀⢳⠀⠀⠹⣏⠉⠙⢷⣀⢙⣷⣦⠶⣝⠀⠀⣾⠀⠈⢳⡀⢹⡌⡇⢸⢀⡇⠀⡼⠀⡜⢳
⠀⠀⠀⣇⠁⠂⠀⢀⠜⠉⠉⢫⠄⠀⠘⢤⣼⣋⠳⡀⠀⠀⣿⠀⠪⣧⠀⢈⣧⠀⠠⠸⢧⠈⠀⠹⣇⠀⠈⢻⡇⠀⠀⡜⠙⢦⡀⢳⡀⣧⣧⡸⣸⠁⡼⠁⡴⠁⡞
⠀⠀⠀⠉⠉⠙⢶⣏⠀⠀⠀⣎⠁⢀⣠⡞⣁⡈⠉⠉⠀⠀⠹⡀⠈⠺⡇⠀⢌⣆⠀⠀⠈⣧⡀⠀⢸⠗⠀⠈⠀⠀⠀⠙⠤⠄⢹⡄⢧⣿⣿⣇⣏⠞⡠⠊⣠⠞
⠀⠀⠀⠀⠀⠀⣴⠝⡛⢳⠶⡿⢿⢹⡓⠇⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⣿⡀⠠⣹⣷⣄⣠⠞⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣈⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠜⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⢤⠀⠓⠲⠤⠀⢈⡀⠠⠄
⠁⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠈⠁⠀⠐⠀⠙⣴⡀⠀⢶⠼⣇⣀⣀⡀⠰⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢐⡀⠄⠞⡩⢷⡂⠘⡆⢨⣀⡀⠙⠟⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠡⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠈⠀⠂⠠⠐⠀⠈⡲⡷⣴⠼⡉⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢂⢀⠀⢀⡤⠒⠉⠉⠝⠢⠀⠀⠀⠀⠸⠀⠀⢠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⢀⠠⠉⠂⠀⠊⠀⠀⠀⠀⡶⡀⠀⠀⠠⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠆⠴⠀⠀⠐⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⠠⠊⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡰⠋
⠀⠀⠀⢀⠀⠄⢂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⡙⠻⣶⣌⣷⣶⣿⣶⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⠀⠻⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣶⣽⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⠛⠟⠋⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣴⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⡿⡿⠿⢸⣿⣽⣿⣿⠇⣻⣿⡛⠹⢾⣿⣿⣿⣶⣶⣤⣴⣤
⠀⠀⠀⠀⠀⠠⣄⠻⣷⣼⡇⣠⡄⠀⠀⠀⣠⣶⣿⠿⠟⠋⢁⣾⣿⣿⣧⡀⠀⢾⣿⢻⣿⣿⣿⣿⣇⢀⣀⣀
⠀⠀⠀⣰⣿⡿⣿⣷⣿⣿⣿⡿⢀⣀⡀⣸⠿⠋⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⡿⢿⣿⣬⢻⣿⣿⣿⡿⣟⣻⣿⠟
⠀⠀⠘⠛⠛⡛⣿⣍⠻⣿⣿⣿⣋⡉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⢻⡿⡷⢀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣿⣯⣭⣭⣿⡟⠛⠛⣯⠙⠲⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣿⠀⠀⠀⠿⠛⢿⣿⣯⡿⢻⣿⣿⣯⣝⣛⣿
⠀⠀⠀⣸⡟⠉⠁⠿⠿⠁⠹⣶⣝⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⢞⣵⣿⣿⣇⢨⣿⣭⡉⠛⢿⣿⡄
⠀⠀⠀⠉⠀⠀⠀⠀⢀⣶⠀⠀⠙⣷⣄⠀⢹⣇⣽⣿⣰⡏⠀⠀⠀⣿⠀⠀⢰⣿⠈⣿⣿⡇⢿⣾⣿⣿⢿⣷⣶⣯⣃
⠀⠀⢸⣷⣶⣦⣴⢟⣿⣷⣄⠀⣀⣈⡙⢿⣄⢿⣿⣿⡿⣢⣤⣤⠀⣿⠀⠀⠸⣏⠀⠛⢹⡇⠈⠘⣿⣿⠀⢹⣇⠉⠉
⠀⢐⣶⣾⣿⣿⣿⣾⣿⣿⣿⡶⠦⣬⣙⢿⣿⣾⡿⢿⣿⣿⣙⣛⠇⣿⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠘⠿⠀⠀⠃
⠀⣿⣛⣉⡙⠛⣿⠁⠴⣿⣷⣦⣴⣾⣿⣿⠿⣿⣧⠸⣏⣉⡉⠛⠓⣿⠀⠀⠀⠀⠀⠀⣿
⠀⣼⠿⠛⣿⣿⢻⣧⡶⢾⡇⠹⠇⠉⠁⢠⣾⣿⠛⢻⣿⡙⠻⢿⠆⣿⠀⠀⠀⠀⠀⢀⣿
⠈⠁⠀⠀⣿⣿⢾⠙⢧⢸⣷⡀⠀⠀⠞⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠛⠁⢸⡄⠈⢹⡈⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠂⠘⠛⠛⢻⠷⠶⠶⠶⠶⣶⣶⣾⣿⣶⣦⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣼⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄
⣀⣀⣠⣀⣀⣀⣀⣀⣀⣉⣉⣻⣿⣿⣉⣉⣉⣉⣈⣉⣉⣙⣻⣿⣿⣿⣿⣋⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⡍⢽⡟⠛⠛⠛⠛⠛⢛⠻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣀⣤⣤⣄⣀⣀⣼⣇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣥⣤⣭⣭⣿⣿⣧⣶⠾⠶⢷⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠙⢿⣿⣿⡿⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⡿⠿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⣠⣾⡟⠁⠀⢀⣠⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣼⢻⣿⣿⣿⣿⣿⡿⠟⠀⠀⢀⣾⠋⢀⣾⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣏⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⣹⣿⣿⣿⠿⠿⠛⠻⠿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠟⠉⠁⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡿⠋
⠀⢶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋
⣀⡈⠙⠛⠛⠻⣿⣇⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⡒⡆⣠⣤⣀
⠈⠻⢦⣄⣀⣀⣀⠹⣿⣦⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠉⠛⠿⣶⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠿⠿⠿⠟⣿⣿⣿⣿⣿⣟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⣿⣿⡋⠹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣾⣢⣹⣧⠤⢬⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⢸⠻⣥⠛⠓⠈⢯⣿⣤⣤⣄⡈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣝⠧⣾⣤⠀⠀⠀⡀⣀⠘⣿⠀⠉⠉⠓⠺⠻⢻⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣾⣿⣷⣾⡿⠩⠈⢻⣇⣤⠤⣀⣀⣀⠀⠀⠀⢁⣟⣷⠟
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⣿⣛⣷⣶⣤⠤⡉⡛⠛⣷⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠋⠩⣿⣿⣿⣿⠿⠿⣿⣿⣿⡏⠉⠉⠉⢩⡓⣾⡙⢿⣤⢘⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠛⠫⠟⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠤⢼⠼⠷⠿⠷⠾⠿⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠉⠁⢢
⠀⠀⠀⢀⠔⠒⢄⠀⠀⠀⠀⠀⠀⠀⠈⢍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⣀⠄⡐⠂⢨⡥⠀⠚⠠
⠀⠀⠠⠁⠀⠀⠀⠉⠒⠤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⣁⣀⢠⠀⠀⠀⠤⠀⢰⠔⠦⡀
⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠉⠐⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠁⠁⠀⢄⢄⠀⠒⣠⠏⠀⠀⡨
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⡁⢀⠔⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠁⠑⢉⣡⢖⠀⠉
⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠉⠀⠆⠀⠀⠗⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⢤⠀⢄⢘⠩⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡄⠀⠢⢠⠞⠳⠂⠐⠀⠀⠀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢆⠀⠑⣄⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠠⠊⡂⢠⠀⠀⠈⡄⠀⠀⠀⠀⠠⠡⠊⠄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢀⠊⠀⠀⠀⠀⠀⠀⠀⠠⡠⠀⠄⣀⠬⠃⡀⠀⠀⠀⠃⠀⠐⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠈⡤⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⠦⠀⠨⠐⠀⢣⠄⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢄⠀⠀⠑⠦⣀⠀⠀⠀⠀⠠⠃⠀⠣⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⠀⡁⠀⠀⠀⢈⠵⠶⢤⣄⣈⣹⡈⠙⢄⠀⠀⠀⠀⠀⠀⠉⢓⡶⠶⠶⠒⠂⠁⠀⠠⠠⠂⠈⡂
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠠⠁⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⢉⠟⠉⠀⠀⠁⠐⠀⠀⠀⠲⢾⠉⠀⠀⠀⠀⠁⠀⢒⠁⠀⠚⠭⠁
⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠑⠢⢀⡀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⠤⠔⠛⡀⠈⠀⠄
⡠⠐⠉⠀⢀⠔⠀⠀⡠⠊⠀⠀⠀⠈⠉⠐⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢁⠀⠀⠊⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠢⡀⠀⠀⠀⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠀⠈⠉
⠀⠀⠀⠀⠀⢀⠤⣖⡒⠒⠒⠒⠢⢶⠁⠀⠈⠁⠀⠁⠀⠀⠀⣀⠴⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠒⢶⣄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⠁⠀⠀⠉⠓⢄⠀⠀⠀⠑⠀⠀⠀⠀⢄⡀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢤⣄⡀⠀⠰⠛
⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠑⡄⠀⠀⠀⢀⠄⠚⠋⠀⠀⠀⠀⢀⣠⠄⠂
⠀⠀⠀⠀⠀⠈⠉⠓⠤⣀⢀⣀⣸⠗⠀⠘⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠐⠉⠐⠀⠀⠀⠉⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠈⠉⠐⠒⠊⠉
⠀⠀⠀⠀⠀⢄⣀⣀⡀⣀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⢀⠟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢠⠀⠈⣆⠀⠀⠀⠀⠀⡜⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⢀⡘⠁⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⠢⢄⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⢀⠀⠀⢀⣀⣵⡖⠊⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠙⠒⠒⠒⠒⠉⠉⠀⢀⠀⠀⠉⠉⠙⠻⠟⠂⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠂⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠖⢶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢞⠀⣀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣘⠃
⠀⠀⠀⠀⢠⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠚⠉⠀⠀⠁⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣔⡞⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢂⠀⠀⠀⢠⠃⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠠⠤⢤⠴⠞⠋⠀⠀⠀⢸⡀⠀⢀⣰⠀⢀⠀⠀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠡⢴⡀⡀⠁⡠⢀⡧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⠀⠀⠈⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠁⢤⠀⢄⠀⡖⡠⢄⡠⠄⢀⢀⠄⡀⡄⠀⢄⢸⢢⢀⠀⡇⡹⢠⠀⠀⠠⡠⠀⢠⢠⢠⣸⠤⣀⠀⠀⠠⡀⡠⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠁⠁⠀⠁⠀⠀⠉⠀⠁⠁⠀⠈⠈⠈⠈⠀⠁⠁⠀⠁⡈⠃⠁⠈⠈⡙⠀⠉⠈⠉⠁⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣷⣶⣦⣄⣀⣴⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⣯⠉⠻⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠉⣿⡿⠋⠀⢸⣿⠀⠙⣿⣿⣇⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠸⣿⠃⠀⠀⢸⣿⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣁⣀⣠⣾⣿⣿⣷⣦⣸⣿⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⣿⠿⣿⣿⡙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⣿⠏⠀⢹⣧⠈⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠿⠀⠀⠀⣿⡆⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣿⣿⣿⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⡟⣶⣿⡿⢻⣶⣾⡟⢷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⠀⠉⣿⡇⠈⢸⡿⠁⠈⣽⡿⠉⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⠛⢻⣿⡀⠛⣿⡄⠀⣿⢦⠀⣿⣇⠀⢸⡟⠀⢀⣿⠋⠀⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠻⣿⣧⠀⣿⡯⡀⣿⡇⡀⣿⢀⢀⣿⠀⢀⡿⠃⢀⣾⠃⠀⣰⡛⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⡧⠘⣿⣀⢸⣷⢶⣿⡁⡧⣿⢸⢸⡟⢣⣸⣧⡀⠾⠉⢀⣼⠟⠀⠀⠩⡶⢤
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣷⡾⣿⣽⣿⡏⠙⣿⠀⢸⡇⣇⣿⢸⣸⠃⢀⣿⠨⣡⡀⢀⣿⠉⠀⢀⡄⠋⠀⢸
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣼⢿⣿⣿⣿⠙⣿⡆⣿⡂⢹⡇⢸⡿⠈⣿⠀⣾⠇⣶⡏⣐⡾⢻⠀⡴⠃⠀⢀⡀⠺⢧
⠀⠀⠀⠀⠀⢈⣿⣿⣿⣽⣿⣿⣿⣯⠹⣧⢿⣇⢸⡇⠸⡇⢸⡇⠠⡇⢀⡿⢀⡟⢠⡿⠁⢠⠟⠃⢀⠴⠂⠀⠀⣌
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⡎⢿⠀⣧⠀⣧⢸⡇⢰⡇⢸⠇⣸⠁⡾⠀⡵⠋⢀⠴⠏⠀⠀⠀⠴⠾
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢻⡌⣷⣸⣇⢿⠀⣿⢸⡇⢸⠃⣾⢠⡏⡼⢁⠀⠀⡤⠁⠀⠤⠀⠃⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣏⢿⣸⡇⢹⠀⡇⣸⢀⡏⡼⢰⢃⠏⠀⠀⠐⠀⠈⢧⠠⠐⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⠯⣿⣿⣿⣿⡸⡇⣷⢸⠀⡇⣿⢸⢣⢃⠏⠌⠀⢀⠀⠀⣠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣌⣻⣿⣿⣷⣿⣽⢸⣿⣧⡏⣾⣼⡸⡈⠀⡀⠀⣠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⣇⡿⣿⣇⣷⣿⢻⣷⢏⡴⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣿⢿⣿⣿⣿⣿⣷⣛⡿⣏⠛⣀⡤⢿⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠛⠛⠛⠙⠿⢹⣯⠰⠏⠑⠛⠲⠾⠿⠿⠁