Seashell Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣠⣶⣿⡟⠳⣶⣶⣿⣿⡿⢿⣶⣶⣶⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠉⣿⣿⣿⣿⠃⢱⠟⣻⣿⣿⠁⠈⢻⣷⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⢸⡏⣿⣿⡇⠀⡀⢸⣿⡇⠀⠀⠀⣿⣿⠃⠀⠀⠀⣼⣿⡿⠀⢨⣿⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⢿⣿⣿⣿⡉⠈⡇⢿⣿⡇⠀⠃⢸⣿⡁⠀⠀⢰⣿⡿⠀⠀⠀⣸⣿⡟⠀⠀⠈⣿⣿⠟⠉⢹⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣏⡄⠁⢿⣿⣧⡀⠀⢸⣿⡿⠀⠀⢸⣿⠛⢶⠀⢸⣿⠇⡄⠀⢠⣿⡏⠀⠀⠀⣼⣿⠃⠀⠀⢾⣿⣦⣤⡀
⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⢿⣹⣿⣿⣄⠀⠘⣿⣿⣇⠁⠘⣿⡇⠀⡆⢸⣿⠀⣢⠀⣿⣿⠀⠐⠀⣼⡿⠛⡄⠀⣸⡿⠃⠀⠀⢀⡞⠛⠛⠉⣿⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣵⣷⠈⢻⣿⣟⡁⠀⢿⣿⠉⠙⠀⣿⡇⠀⡇⢸⡿⠀⣧⠀⣿⡿⣄⠀⢰⣿⡇⠀⠇⣰⣿⡇⠀⠀⣰⣿⡿⠂⠀⠀⡿⣇⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢻⣿⣿⠧⡀⢿⣿⡁⢀⠸⣿⡿⠻⣧⣿⣇⠀⣿⣾⣿⠀⡿⢸⣿⠁⢹⡇⣼⣿⣦⡄⢰⠟⠃⡁⠀⣴⣿⡟⠀⠀⠀⠀⠀⣿⡿⢷⡄
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣀⣹⣿⣶⠿⣾⣿⣿⠛⢷⣿⡷⠀⠅⢹⣿⠀⡗⢸⣯⢀⡇⢸⡿⠀⠀⢱⣿⠁⢹⠃⠀⠀⠀⢡⣾⡿⠋⠁⠀⠀⠀⣠⡶⠋⠁⠀⣷
⠀⠀⣿⣿⣿⣿⣟⠻⣿⣿⣿⣍⣻⣿⣿⣿⣿⣿⠀⠀⢹⣿⠀⣤⢸⣿⠀⢧⣼⡏⢸⡇⣾⡇⠀⠀⣼⡏⢠⡍⣶⠶⠀⠀⣼⣿⠂⠀⠀⢀⠀⠿⠃⠀⠀⠀⠨⣟
⢀⣴⣿⣿⣿⣿⣟⣧⣼⣿⣿⣿⣷⣿⣿⠀⠹⣿⣷⠀⢾⣿⡆⠘⢿⣿⠀⠈⣿⡇⠸⠁⣿⠁⢰⣷⣿⠁⢶⣴⡟⢀⠙⣾⡟⢻⡆⠀⣠⡿⠗⠀⠀⠀⢀⠀⠒⡿⢷
⢸⣷⣿⣿⣿⣿⠿⣿⣿⣴⣿⣿⣷⡿⢿⣶⠖⢿⣿⡆⠘⣿⡇⠀⠸⣿⠀⠀⣿⡇⠰⢠⣿⠀⠘⣿⡏⠀⣹⣿⠁⣾⣾⡏⠀⠞⢠⣶⡏⠀⠀⠀⢀⡀⠙⠆⠀⠀⢸
⢸⣿⣿⣿⣿⣷⣿⣿⢿⣿⣿⣿⣿⡶⠘⢿⣿⠺⣿⣇⠀⢹⣿⠀⠀⣿⠀⠀⣿⠃⠀⢸⡇⠀⢰⣿⠃⠀⣿⠃⢰⣿⡏⢀⠎⣠⡟⠁⠠⠀⣀⡲⠟⠁⠀⠀⠀⠀⢿
⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⣿⡗⢺⣿⡀⠘⣿⠀⠀⣿⡀⠀⣿⡀⠀⣼⡇⠀⣸⡇⠀⢸⡟⠀⣺⡏⠀⣜⣾⠋⠀⠐⣡⣶⠛⠁⠀⠀⠀⠀⣀⣤⢼
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⣿⣇⠀⢿⣇⠀⣿⡆⠀⢿⡇⠀⣿⡇⠀⣿⠁⠀⣿⠁⢀⣿⠀⣸⡟⠀⠂⡝⠁⠀⢀⠶⠁⠀⠉⠀⠀⡀⠆⠀⠋⠀⢈
⢹⣿⣿⡿⢿⣿⣿⣿⡿⣿⣿⣻⣿⣏⠻⣧⠀⣿⡇⠘⣿⡀⢹⣧⠀⢾⡇⠀⣿⡇⢰⣿⠀⢾⣿⠀⣼⠃⢰⡿⠀⢄⠁⠀⠐⣤⠉⠀⠂⠀⣦⠀⠈⠁⠀⠀⠀⢀⣳
⠘⢿⣿⣿⡿⣿⣟⣿⣿⣯⠻⣿⣟⢿⣦⢿⣷⣘⣿⡟⢿⣇⠘⣿⡀⢸⣧⠀⣿⡄⢸⣿⠀⢸⡇⢸⡟⢀⣿⠁⡜⠂⠀⠀⠘⢃⡄⠀⠨⠓⠎⠀⠀⢀⡄⠀⠘⣫⠏
⠀⠀⠙⠿⣿⣿⣿⣿⣿⣛⢿⣯⣿⣦⣻⣯⣿⣿⢻⣷⠘⣿⡄⣿⡇⢰⣿⠃⣾⡇⢸⡇⠀⣿⠁⣾⠃⣸⠇⡸⠁⢀⠀⠠⠀⠀⠀⠀⢀⠀⢿⠀⠉⠀⠀⠤⠾⠋
⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣝⣷⣜⢿⡿⣯⣿⣏⣿⡆⢻⣧⠸⣇⠀⣿⠀⢼⠃⣸⡇⢰⡿⢰⠋⣸⠏⢸⠁⠀⠂⠀⠀⠀⠀⠘⠀⣈⡴⠇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣇⠙⠿⣿⣿⣿⣿⡿⢿⡌⣿⡀⣿⡄⣿⡄⣼⡇⣿⡄⣸⠃⣾⢀⡟⢰⠂⠀⠤⢀⠰⠀⠀⣀⡾⠿⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⡙⢹⣿⣿⣿⡼⣿⣿⣧⢹⡇⢿⣄⣿⡇⣿⠀⣿⢰⡏⣸⢡⡁⠀⠀⣠⠋⠀⢁⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⠘⣧⢸⣿⣽⣿⡟⢸⡏⣿⣿⡟⣾⡡⣾⡖⢀⣤⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢏⣿⣿⣿⣿⣿⣿⣿⣿⣸⣦⢿⣨⡏⢹⣿⣧⣼⡿⣿⣿⠰⠣⡿⢋⣴⣿⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣈⢻⣇⣼⣟⠘⠟⠁⢀⣠⣾⡿⡧⠀⢚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣷⣠⣿⣿⣿⣟⢿⣿⣿⢻⣿⢿⠋⣧⣿⡶⠀⣶⡟⠁⢈⣷⣿⣀⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠈⠻⢧⡼⣿⡶⢤⠿⠃⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠐⡲⠤⢄⣀
⠀⠀⠀⠀⠀⢀⠄⢰⡎⠉⠉⢳⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⢠⠎⠀⠀⠀⠈⠓⡀
⠀⠀⠀⠠⠂⡇⠀⠈⡇⠀⠀⡸⠀⠀⡟⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣎⣁⣀⣠⠿⠒⢶⠢⣄⣀⠀⠀⠀⡜⠰⡆⠀⠀⡜⠀⣀⣀⣤⠒⠈⠁
⠀⠀⢠⡆⠀⢰⠀⠀⠇⠀⠀⡇⠀⢀⠃⠀⣧⠀⠀⠀⠀⡠⠖⠲⢧⣀⣀⣀⣀⣀⣀⣠⠞⠀⢈⠈⣆⠀⢠⠃⠀⠙⢄⠀⣽⠋⡩⢀⡤⠛⠢⡄
⠀⠀⡀⠈⢄⠀⢧⠀⢸⠀⠰⠃⢀⠎⠀⡔⠁⠁⠀⢰⡛⠓⠦⢤⣀⣀⣀⠈⢉⣀⣀⣀⣤⠴⠃⣠⠛⡄⠘⣄⠀⠀⠀⠈⣇⠹⣝⡇⢱⠒⠒⢣
⠀⠀⣹⢄⡈⠣⡈⢢⠀⡄⢰⠀⠌⠠⠊⢀⡴⡇⠀⠸⢟⠲⠤⢤⣀⣉⣉⡉⠉⠉⢁⣀⣠⡤⠞⠁⡼⠀⠀⢻⡁⠀⠀⠀⠙⡧⠤⡵⠛⢢⠀⡸
⠀⠀⠘⠢⣍⠂⢌⣊⣣⡀⠀⡎⠜⠁⢂⡡⠒⠁⠀⠀⠀⠙⠲⠤⣄⣀⡉⠉⠉⠉⠉⠁⣀⣀⡤⠞⠁⠀⠀⠀⠑⠤⡤⠀⠊⠀⠀⡅⠀⢀⠷⠁
⠀⠀⠀⠀⠘⢄⣹⠿⣟⠓⢛⡹⢿⣁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠄⠚⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠄⠀⢒⠀⢠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡞⠀⠈⠂⣤⢲⣀⠀⠀⠀⠀⠀⠀⣠⠊⠑⢄⡨⠲⡂⠃⢠⠇⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢹⣦⠀⡶⠲⣢⠆
⠀⠀⠀⠀⠀⠀⣰⠋⢅⡠⢿⠦⣀⣀⡿⢠⣏⣱⢤⠔⡆⠀⣌⠀⠐⡶⠛⠀⣄⡨⠄⣠⠀⢹⡀⠘⠆⠀⠀⠀⠀⠀⡠⠂⣻⡀⢸⢹⠀⠧⠀⢸
⠀⠀⠀⠀⠀⢰⢇⢀⡾⠀⢸⠀⠀⠉⡁⠠⣆⠸⣤⠔⠁⣌⠀⠁⢸⠂⠀⠾⠁⡤⢢⠀⡳⠈⡇⠀⢄⠀⠀⠀⠀⢠⡇⡏⠀⠳⡈⠦⡓⠄⠀⣎
⢀⣀⣀⣀⡴⣋⡤⠏⢰⠀⢸⡀⢀⡴⡷⠉⢱⠜⠁⠀⢠⠉⠐⠂⢹⡤⠂⢣⡀⠳⠄⡴⠋⣸⠅⢀⡌⠀⠀⠀⠀⡼⡸⠁⠀⠀⠈⢦⣀⠀⠀⠈⣣
⠘⠿⣿⣿⡿⠿⣗⡻⠦⢷⡤⢷⡋⠀⢘⣄⡏⠀⠀⠀⡏⠑⠂⠐⠊⠳⣤⠇⠱⠠⢦⠀⠛⠁⣀⡼⠀⡀⠀⣀⣨⣡⡴⠦⣤⠀⠐⠋⡠⠟⣰⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠒⠚⠳⣄⣼⠀⠀⠀⠀⠀⠣⣀⣠⠴⠖⠦⠌⠶⠴⢄⣀⠰⠄⠒⠁⠀⠀⠉⠉⠉⠉⠀⠀⠉⠚⠭⢄⣉⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⢸⡄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢳⣷⡿⢞⠛⠛⠲⢾⣥⡴⠀⠀⠀⠀⠀⠀⢀⣐⡦⠚⠚⠓⠓⠴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢔⠀⢲⡋⢳⠖⠦⡄
⠀⠀⠀⠀⠀⠀⡾⠐⠀⢠⠡⠀⠀⣀⠿⣤⢤⡄⠀⠀⠀⠀⣠⠏⡔⠀⠀⠀⠈⠲⡈⢷⡄⠀⠀⠀⠀⠀⠀⠀⡔⠳⢄⠈⢧⠀⡇⢸⡇⠀⢹⢦
⠀⠀⠀⠀⢀⣠⢿⡁⠀⠘⢶⢶⣁⠀⠀⢻⢃⡄⠀⠀⣀⣴⠛⠛⢯⠉⠙⢦⡤⢤⣷⠀⠻⣄⡀⢀⣤⠀⠀⡜⠒⢄⠈⢣⠸⡆⣿⢸⠇⠀⡏⢸⣆
⠀⠀⢠⠏⠀⠀⠀⢙⠦⠤⡄⠊⠓⣄⢀⡿⣅⠀⠀⠱⡏⢉⢦⠀⠘⣆⠀⠈⢳⡀⠈⠳⡦⠛⠻⣭⡇⠀⠈⡧⣄⠈⢣⠈⡇⡇⡿⢸⠀⡼⠀⡞⢸
⠀⠀⠘⠗⠲⣄⡴⠉⠀⠀⡼⠀⠀⣈⠿⠓⠪⠷⠀⠀⣇⠀⠬⣇⠈⠻⡄⠀⠌⠷⡀⠀⠙⣦⠀⠘⠁⠀⠀⢇⠀⠱⡌⣇⢹⣧⣇⢇⠜⡀⠊⣠⠋
⠀⠀⠀⠀⠀⢀⡿⢶⢦⣤⣷⡖⣿⠭⠉⠃⠀⠀⠀⠀⠈⢦⡐⢾⡄⠉⢻⣆⡀⢠⡿⠦⠈⠁⠀⠀⠀⠀⠀⠀⠁⠈⠹⣾⣿⣿⣿⡇⢈⠠⠊⠁
⠀⠀⠀⠀⠀⠈⠀⢠⡼⠀⠁⠙⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠈⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠉⠉⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠀⠀⢀⡀⠒⢠⠀⠀⠘⢻⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠈⠁⠘⢆⠀⠀⠀⠀⢀⠊⠑⠀⠀⣁⣁⣀⠎⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣂⡖⢁⠀⢀⠈⢦⠞⡩⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠰⠀⠀⠀⠀⠨⠀⠙⢌⣁⠨⠤⣸⠅⡾⡋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠈⠁⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢀⣎⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⡀⠔⠁⠀⠈
⠀⠀⠀⠀⠀⠀⢘⣀⠀⠀⠄⠀⠈⠁⢰⠀⠀⠀⠠⠝⢂⡀⣤⣶⠑⠀⠀⠀⠀⠀⠀⠐⠀⠐⢡⢺⠕
⠀⠀⠀⠀⡀⣀⠈⠀⠀⠐⠀⠀⠀⠄⣰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠀⠀⠀⠀⢄⠄⠀⠐⠀⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠉⠑⠁⠄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⣠⡎⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠓⢓⠂⠈⠙⢀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡞⢀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⣮⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠆⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢤⠌⣐⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠉⠉⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠡⡀⠀⠀⠀⠠⠂⠀⠘⡩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠡⠀⠀⠀⠈⡀⠀⢀⠃⠆⠀⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣳⠀⠀⠀⠀⠘⠀⠀⠤⠐⠉⠀⢀⠀⠀⠀⢡⠀⠘⠀⡴⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣈⢁⠉⠥⡤⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠈⠀⢸⡀⡴⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠤⠦⡜⢡⠀⠀⠀⢘⠀⠀⠀⠀⠐⠒⠩⠀⠀⠂⠀⠀⠘⠧⠶⢀⡦⠀⠀⠀⠐⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡳⢀⠀⠈⠀⠀⠀⢀⢀⠀⠀⠤⠀⠂⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⡼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣭⡿⠿⡟⠙⡛⠟⣦⡐⡇⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠠⠤⠀⠀⠀⢈⢡⡈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔
⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠁⠀⠀⢉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⠂⣠⠏⠀⠑⣤⠀⠀⠀⠀⠀⠘⠀⠐⠒⠒⠘⠒⢆
⠀⠀⠀⠀⡀⢀⠗⠀⠂⠐⠀⠀⠀⠀⠐⠀⢂⠑⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡀⠀⠀⠄⢁⠜⠁⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢸⡵⢉⡶⠃⣤⡀⡀⠀⠀⢐⠀⢀⡀⢒⡀⢶⡙⠦⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢠⡞⠀⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠄⢰
⠀⠀⠀⠈⢁⠟⠀⠐⠀⠨⠉⢙⠉⠉⡅⠀⢀⠀⠱⣄⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡆⢔⢸⠀⠀⠀⠀⡄⢀⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠌⡠⠂
⠀⠀⠀⠀⠩⣄⣸⠃⠀⡐⠀⢸⠀⠀⡀⠀⠈⣆⠀⠻⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⣦⡆⠀⠀⠚⢤⠂⠀⠀⠀⠀⠀⠣⡀⠀⣀⡠⠄⠌
⠀⠀⠀⠀⠀⠈⠙⢦⣈⡇⠀⢼⠀⠀⢽⠀⡠⠿⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣰⠆⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⡒⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⡤⢤⣠⡤⠶⠤⠤⠤⣤⣀⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠋⠉⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡏⠋⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣾⡟⠃⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣷⣲⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⢸⣿⠇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸⠋⠀⠀⠈⠉⣧
⠀⠀⠀⠀⠀⠀⢀⣀⣴⡏⠀⠀⢸⠻⠀⠀⠀⠀⠀⠀⡏⠀⠶⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⣯⣿⡳⢦⡀
⠀⠀⠀⠀⠀⣴⠋⠙⣿⡄⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢣⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⣸⠈⠤⠀⠀⢀⡾⠉⠁⠀⠈⢻⡄
⠀⠀⠀⠀⢰⠗⠀⠀⠹⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⢸⡄⠀⠀⠀⠀⣿⠀⠀⠀⢀⣧⠀⠀⠀⣠⣟⡈⠀⠀⠀⠀⣼⣅
⠀⠀⠀⣠⡿⡤⠀⠀⠀⢣⡀⠀⠀⠆⠸⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⡸⡏⠀⠀⢈⡿⠉⠀⠀⠀⠀⣼⡿⠛⢧
⠀⠀⠀⡿⠀⠘⡆⠀⠀⠀⢡⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡆⠀⠀⠀⢰⠃⠀⠀⢠⣇⠀⠀⠀⡼⠀⠀⠀⠀⠀⡜⠁⠀⠀⣸⡁
⠀⠀⢠⡧⠀⠀⠈⢷⣄⠀⢈⢧⡀⠀⠀⠘⡄⠀⠀⠀⡀⢠⣆⠀⠀⠀⣷⠀⠀⡀⣸⡄⠀⠀⡜⠀⠀⠀⢰⠁⠀⠀⠀⠀⡜⠀⠀⠀⣰⢿⢿⡀
⠀⠀⢠⡿⢄⠐⠀⠫⣻⣄⠀⠈⢧⡀⠀⠀⢹⣼⠀⠀⠀⢸⠸⠀⠀⠀⡿⠀⠀⢠⡿⠇⠀⢰⠛⠁⠀⣠⠧⠀⠀⠀⢀⡜⠀⠀⢀⠜⠁⠀⣠⠇
⠀⠀⠘⣧⠀⠳⡠⠀⠙⢿⡆⠀⠀⢻⡧⠀⠈⢿⠇⠀⠀⠐⡎⠃⠀⠀⠀⠀⠀⢸⡏⠀⢀⣿⠀⠀⢀⡏⠆⠀⠂⢀⣾⠀⠀⢠⠎⠀⢀⡶⢹⡆
⠀⠀⠀⢿⠻⣶⡿⣦⠀⠀⠙⢶⣄⠀⣿⡀⠀⠘⡄⠀⠀⠀⢣⠀⠀⠀⡀⠀⠀⣸⠀⠀⣸⠏⠀⢀⣾⠂⠀⠠⣠⡃⠄⢀⡔⠁⢀⣞⡩⠒⡏
⠀⠀⠀⠈⢳⣌⢻⣌⠳⡄⠀⠈⢿⡄⠀⢳⡀⠀⢹⡀⠀⠀⠸⠀⠀⠀⠁⠀⠀⡟⠀⢀⡇⠀⠀⣾⠃⠀⢠⡞⠁⠀⣠⡊⢊⢔⣵⢋⡥⣴⠃
⠀⠀⠀⠀⠘⢮⡻⣍⠢⡝⢦⣀⠈⢻⡆⠀⠹⣄⠀⢣⠀⠀⠀⡇⣄⠀⢠⡤⣠⢇⠀⣼⠀⠀⡼⡕⠀⢀⡏⠀⢀⡾⢫⢞⡵⣫⢟⣫⡵⠋
⠀⠀⠀⠀⠀⠀⠙⡮⢷⣍⡲⡙⢄⡀⠙⣦⡀⠹⡆⣸⡞⠀⠂⢻⠋⢸⠈⠁⣸⠉⢱⠿⠦⣴⡷⠀⣠⠋⢀⡴⣡⢞⡵⢛⣫⡶⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣍⣻⣿⣦⡙⢄⡈⢿⣦⠙⡅⢹⡀⠀⢸⡀⢸⠈⠀⡎⠀⣞⠁⢠⡿⠛⣳⣅⣠⡫⢚⢕⠫⣖⣫⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣭⣝⡳⢷⣦⡙⢧⡘⣄⢣⠀⠈⡇⢸⡄⢰⠁⢰⡏⣠⡏⢁⡼⣩⣻⣿⣾⡿⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣛⢷⣯⣿⣅⠹⣜⢆⢇⠀⣧⢸⡇⡼⠐⣾⢧⡿⢡⣾⣿⣿⣽⠟⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣈⠉⣽⡍⠉⠛⣷⣽⣮⢻⣧⢸⠸⢷⣧⢲⢏⡿⣱⣿⡿⠿⠟⣫⠴⠞⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡘⠛⢳⣴⣶⣄⣸⡻⠟⢷⣿⣄⡆⣼⢇⣯⢎⣾⡿⢿⠁⣀⢶⣿⣧⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⢉⣒⠀⠀⠀⣨⡙⠓⢚⣿⣿⣧⣿⣾⣿⣿⣟⣂⣿⣏⠩⣭⡯⠶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠙⠛⠛⠉⠉⠉⠀⠈⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠁
⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠳⣄⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠘⡆⠀⠀⣗⠀⠀⠷⣤⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠈⣓⠲⠤⠄⠀⠀⠀⠃⠀⠀⠀⠑⠀⣀⣀⣡⢰⡦⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣀⢸⣿⣿⠋⠀⡄⠀⠠⣄⠀⠲⠦⡀⠀⠀⣿⡏⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⢻⣿⣿⡇⠀⡀⠹⣄⠀⠀⣿⠀⢀⣷⡾⣸⣿⣯⠤⠂
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⡴⠀⢸⡇⠐⣿⡆⣾⣿⣧⡌⠛
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣼⣿⣿⠃⠘⣷⡀⠀⢳⠄⠹⣿⠙⢿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⢠⣤⣿⣿⠟⠁⠲⢰⣿⠃⠀⣼⠃⢠⡿⠐⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡇⣰⠟⠋⣉⢡⠄⡼⠘⣧⢸⡟⡆⢸⡇⠀⣿⠀⣾⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠰⠰⠁⠀⡆⢻⣘⣆⡿⣠⠿⠴⠿⣄⣼⡿⢀⣽⡝⣧⣀⡀
⠀⠀⠀⠀⢀⠊⠀⢀⣄⡧⠷⠊⠉⠁⠀⠀⠀⠀⠒⠂⠉⠿⢿⡿⠶⠞⠛⠋
⠀⠀⠀⠀⠳⡴⠾⠞⠛⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠖⠓
⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⡀⠋⠁⠀⠀⠀⣠⠰⠚⠋⠉⠹⠱⢦⢄
⠀⠀⠀⠠⡀⠀⠷⠇⠉⡆⠀⠀⠀⠀⠀⠀⠀⠠⠖⠒⠂⠈⠀⠀⠀⠀⠀⡼⡙⡄⠁⠃⠀⠀⠀⠂⠞⣡
⠀⠀⠀⠀⠀⡤⣀⠠⠾⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠗⠀⠀⠀⠀⠀⠀⠀⠈⠘⢼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠉⠂⠀⢀⣀⠀⠃⠀⠀⠀⠀⠓⢤⣖⠀⢀⣀⣀⠀⣀⠴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣼⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⡆⠐⡇⠀⢸⠉⢱⠔⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢒⠁⠁⠀⠇⠀⠇⠀⢸⠀⡸⠀⠘⠀⠘⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⡅⠘⡀⠘⠀⢰⠀⠀⠀⠀⠀⡇⠀⠄⢀⠀⠀⠈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⡀⢱⠀⢣⠀⠆⠀⡄⢸⠀⡆⠀⠃⠀⠀⡌⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠡⠀⠆⠀⠄⢀⠀⢁⠘⠀⡇⢠⠀⡀⠀⠀⠠⠀⡐⢀⠊⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠂⠀⢀⠘⡀⠐⠀⡄⠀⠀⡆⡇⠘⠀⠁⠀⢠⠁⡐⠠⠃⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⢆⠀⠀⠱⡀⠂⢠⠀⠄⡇⠁⠀⠐⢰⠀⠆⡐⡠⠃⡔⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢂⠀⠀⢣⠘⡀⡀⡃⠀⠀⠀⠀⡆⡈⡰⡰⢁⠎⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠄⢂⢁⠀⢰⠠⠀⠇⢠⠰⠡⡑⡡⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠱⡈⠌⠆⠀⠀⠀⠀⠀⠀⠂⠚⡐⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣔⠜⠌⡄⠀⢀⣠⡆⠀⠀⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣀⣑⣼⣞⣸⣼⣿⣧⣮⠚⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢺⣇⠀⠀⣼⠀⠀⠀⣴⠀⠠⣄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡏⠀⠀⡿⠀⠀⣸⠃⠀⠀⢈⡳
⠀⠀⠀⠀⠀⡦⠭⠀⠀⠀⠀⠀⠀⢀⣠⠊⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡇⠀⢠⠇⠀⣰⠏⠀⢀⡴⠋⠀⠈⢳⡀
⠀⠀⠀⠀⠀⢳⡈⠀⠀⠠⣤⣿⣿⣾⣿⡶⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠁⠀⡞⠀⡰⠃⢀⠔⠉⠀⠀⠀⣀⣀⢗
⠀⠀⠀⠀⠀⠈⢣⣀⣈⣙⣟⣛⣿⣿⣿⣥⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣶⣞⣧⠜⠁⠀⠁⣀⠤⠔⠚⠋⠉⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠟⠋⠋⠙⠋⠉⠀⠀⠀⠀⡀⠀⠀⣤⣶⣾⣿⣿⣿⣿⣵⣿⢧⠒⠉⣀⣀⣀⣀⠤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢿⡛⠻⠻⢿⣿⣿⣿⣿⣁⣁⣀⣀⣀⣀⡀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⠻⠆⠀⠀⠀⠁⠐⡀⠀⠀⠘⣦⣀⠀⢸⣿⣿⣿⣿⣆⣀⡀⠈⠉⠉⠙⠛⢷⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠂⠀⠀⠈⠻⠿⡿⣿⣿⠛⣿⣿⣿⣭⣟⡓⠶⣤⣄⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣖⡛⢙⣮⡿⣇⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠉⠁⡴⠟⠉⠉⠙⠙⠛⠳⣤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣿⣿⡇⠐⠲⠊⢉⢴⢿⣶⠀⣀⡀⠀⠀⠀⡔⠒⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢫⣿⣯⣔⠁⠀⠀⡠⠀⠎⠡⠁⡏⣷⠀⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣃⡾⣿⣿⡆⠀⠀⢀⠌⡀⠀⠀⣴⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⡼⠹⢟⣾⣿⣴⣮⣰⣀⠀⣀⣿⣾⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡈⢀⡟⠻⣿⣿⣿⣿⢿⡏⢿⠛⢁⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣾⣤⣸⠀⣌⠀⠁⢀⡇⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⢿⣿⣷⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠁

⣶⣶⡶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣦⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠰⠄⠀⠂⣠⠖⠢⡀
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠄⠀⠈⠉⠑⠀⠀⠀⠀⠚⠁⠀⠀⠑⠂⠀⠀⠐⣶⢶⠂⠊⠑⠠⢀
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠂⠀⠀⠀⠀⡄⠀⠁⠀⠀⢻⣿⣿⡾⣀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⢸⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣵⣟⣤⡴⣀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣾⣇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⡀⠉⠺⢿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⡄⠃⢹⠳⣍⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⡦⢡⠀⢀⠀⠀⠀⣀⠀⠀⢠⡀⢀⢱⡶⠦⠴⣾⣤⣨⣃⡟⣄⢊⠳⢮⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠛⠓⠳⠾⣿⣦⡵⡴⠯⠷⠦⠮⠛⠉⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⢷⣌⡛⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠀⠑⠀⠐⠄⣀⠀⠀⠈⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠰⠝
⣤⣄⣤⣀⣴⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠈⠙⠒⠂⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠒
⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀
⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠓⠲⢦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡂⣠⠉⠙⠛⠷⣤⣠⢋⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢐⢠⡅⢀⠀⡈⢷⡄⠹⣿⣿⣡⡤⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣷⣴⠀⠀⠀⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⣴⣾⡷⣿⢸⣿⢰⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠘⢿⣿⣋⣁⣀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⣿⣣⡾⢃⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣌⣧⣀⣼⣷⣤⣤⣿⣿⣿⣯⣥⣤⡶⠋⠁
⠐⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠉⠉⠁⠈⠛⠋⠛⠋
⠀⢡⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⡀
⠀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣼⣷⠄⣀
⠀⠹⠿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠀⠀⠀⠀⠀⡟⠁⠀⣾⠷⢤⡀
⠀⠀⣄⣜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠿⣾⡄⠀⠀⠀⢀⡄⠀⠀⢹⠀⢈⣈⣓⡤
⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⣼⡷⠀⣠⡼⠷⠛⠉
⠀⠒⠒⠒⢾⣷⡀⠀⣀⡴⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣾⣿⡟⠁⠈⠁
⠀⠀⠀⠀⠈⠻⣿⣿⡏⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠟⠁⠀⠀⠀⠀⠀⠀⢀⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠃⠊⠔
⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡁⠀⠀⠀⣠⣆⣀⣀⠀⠀⠀⠀⠀⡀⢠
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⡳⠂⠀⣄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⢿⣿⣖⣂⣀⣀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⢀⡜⠉⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠤⠔⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣧⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢯⢷⢌⠑⠄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⢻⡋⠀⠂⠂⠉⣿⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠆⠀⠀⢸⠀⠀⠠⠀⠀⡟⠀⠀⠀⠁⢸⡷⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡇⠀⠈⡀⠀⠸⡆⠀⠈⠀⠀⠇⠀⠀⠀⠀⢹⠃⠁⢊⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡀⠀⠀⣇⠀⠀⠀⠀⠀⡁⠀⢀⠀⠀⠂⠀⠀⠄⠀⠎⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣇⠀⠁⠀⠸⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡈⠀⣰⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠹⣆⠀⢂⠀⠄⠀⠐⠀⠀⠆⠀⠀⠀⠨⠀⠀⠀⠀⡈⠀⠀⠀⢠⠃⠀⠀⠼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠠⠀⠘⣆⠀⠀⠘⡀⠀⠁⠀⡆⠀⠐⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡀⠁⠄⠘⡆⠀⠀⢂⠀⢀⠀⢒⠀⢈⠀⠅⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠜⡃⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⢆⠀⠀⠠⠀⠠⠀⡆⠀⠀⠨⠀⢈⠀⠁⠀⠀⡀⠀⠠⢀⠀⡀⢀⡴⠋⢐⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡁⠄⠳⣄⠠⠐⠀⠄⠀⠀⠀⠀⡁⠀⠀⠃⠀⠠⠀⠀⠀⠂⠄⠀⠋⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡈⠄⠀⠐⠀⠀⠀⠐⠀⠡⠀⠀⠁⠀⠀⠀⠀⠀⡀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠡⠀⠀⠂⠀⠐⠀⠀⠀⢀⠀⠐⠀⢂⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣽⣦⡀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⣴⣣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠛⢦⡀⠀⠀⠀⠐⠀⠀⣰⠿⠷⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣅⠂⠄⣠⣃⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁




⣶⣶⢶⢶⠶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⣶⠶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠒⠋⠻⡇⠀⠀⠉⣿⠉⠙⠒⠦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠉⠉⢻⡄⠀⠀⠀⢹⡀⠀⠀⢸⡄⠀⠀⠀⡿⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⢳⡀⠀⠀⢻⡄⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⢰⠇⠀⠀⠀⣼⠗⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⡀⠈⢷⠀⠀⠀⢿⡀⠀⠀⢹⠀⠀⠀⡇⠀⠀⣾⠀⠀⠀⡼⠁⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢷⠀⠸⣇⠀⠀⠘⣇⠀⠀⢸⠀⠀⢠⡇⠀⢰⡇⠀⢀⡾⠁⠀⠀⠀⢀⣴⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⣇⠀⢿⠀⠀⠀⣿⠀⠀⣸⠀⠀⡼⠀⠀⡾⠀⢀⡾⠁⠀⠀⣠⡶⠋⠁⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠸⡆⢸⡆⠀⠀⣿⠀⢀⡇⠀⣰⠃⠀⡼⠁⢀⡞⠀⠀⢀⡼⠋⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢹⠈⡇⠀⠀⡏⠀⣸⠀⣰⠃⠀⡼⠁⢠⡞⠀⢀⡴⠋⠀⠀⠀⢀⡤⠞⠋⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⡇⡇⠀⢸⠇⢠⠇⢰⠃⢀⡞⠁⢠⡟⠀⣠⠞⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢻⡇⠀⣼⠀⡜⢠⠏⢀⡞⠀⣰⠏⠀⡴⠃⠀⢀⡴⠟⠁⠀⢀⣀⣤⠶⠞⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢸⡇⢀⡇⢰⢣⠏⣠⠋⠀⣰⠋⢀⡞⠀⢀⡴⠋⠀⣀⡤⠞⠋⠁⠀⠀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⣿⡇⢸⢃⢇⠎⡴⠃⢀⡼⠃⣰⠋⢀⡴⠋⢀⡤⠚⠁⣀⣤⠴⠖⠛⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⢸⣇⢸⣼⢎⡜⠁⣠⠞⢠⡞⠁⣠⠞⣡⠔⢉⣠⠶⠛⠉⣀⣀⣠⣤⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⣿⣸⣿⡞⢀⡴⢁⡴⠋⡠⢞⡡⢚⡥⣚⡩⠤⠒⠚⠉⠉⠁⠀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣡⡫⠖⣉⠴⣫⣴⣏⣾⣷⠭⠴⠶⠒⠒⠒⠚⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⣶⣭⠷⠿⠛⠋⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠲⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣤⣀⣠⣤⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣾⠟⠉⠀⠀⠀⠉⣿⠛⠁⠀⠀⠉⢻⣷⡶⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⢿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠾⢿⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡈⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⠁⠀⠀⠀⠸⠷⣦⡄
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⣼⠀⠀⠀⢀⠀⠀⠈⢿
⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀⠘⠷⣄
⠀⠀⢀⣴⠟⠁⢹⡀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⡀⠀⠀⢰⡇⠀⠀⡼⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣿⠃⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠸⡇⠀⠀⢸⠁⠀⢠⠇⠀⠀⠀⠀⠀⢠⣟
⠀⢸⣿⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣇⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠈⣿⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢷⠀⠀⠀⢹⠀⠀⢸⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣼
⢀⣾⠏⢳⡀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⢇⠀⠀⠈⣇⠀⠀⡇⠀⠃⠀⠀⠀⠀⠀⢠⠞⠁
⢸⡟⠀⠀⠙⣆⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠈⠄⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⡰⠋
⠘⣿⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠙⣷⣄⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⢦⡀⠀⠀⢀⠀⠀⢀⠀⠄⠀⠀⠀⡜
⠀⢰⡟⠙⠳⣄⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠑⢄⠀⠀⠱⡄⠀⢂⠈⠄⠀⠰
⠀⠈⣿⠀⠀⠈⠑⢤⡀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠑⢦⡀⠈⠀⠀⠠
⠀⠀⠙⢦⡀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠈⠙⠢⣤⣀⠀⠀⠀⠉⠲⠦⣀⠀⠀⠀⠀⠈⠒⠄⡀⠀⠈⠀⡀⠑⢄
⠀⠀⠀⠈⠻⡦⢄⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠉⠓⠲⢤⣀⡀⠀⠀⠉⠓⠢⢤⣀⡀⠀⠀⠑⠂⠀⠀⠀⠀⠁⠀⢠
⠀⠀⠀⠀⠀⢷⡀⠈⠒⠦⣤⣀⠀⠀⠀⠉⠒⠦⢤⣀⡀⠀⠀⠉⠑⠒⠶⠤⢄⣀⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠻⢦⣀⡀⠀⠈⠙⠓⠶⢤⣄⣀⠀⠈⠉⠛⠒⠶⠤⢤⣄⣀⣀⣀⣀⠈⠉⢁⣀⢀⠀⠀⠀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣏⠉⠓⠒⠒⠒⠂⠉⠙⠛⠒⠲⠤⠤⠤⣤⣤⣀⣀⣀⣤⣤⠤⠤⠤⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠤⠤⠄⠀⠀⠐⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠖⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⢀⠀⣀⡄⡀
⠀⠀⠀⠀⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⡂⣶⢢⣴⠢⣀⡀
⠀⠀⠠⠁⢀⣶⠟⣩⣥⣅⠀⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣧⣿⡇⣿⢸⡏⣼⢏⣼⢢⡀
⠀⠀⣰⠀⢸⣏⣼⣽⣿⣿⣗⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣷⣿⣷⣿⣾⣇⣿⣿⢱⢏⡾⣱⢟⣥
⠀⠀⢀⣅⣼⣿⠻⠘⠛⠛⠕⠁⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡏⡟⡼⣽⡵⣫⢴⡆
⠀⠀⠀⠁⠀⠀⠁⠤⠀⡄⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⢵⡟⣽⣿⣾⡿⠟⠁
⠀⠀⠀⠀⢠⣤⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡎⢀⣿⡏⠁
⠀⠀⠈⠿⣿⠿⠿⠿⠿⠻⠟⢛⡻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣻⣿⣿⣿⣷⣿⣿⣧
⠀⠀⠀⠀⠈⠛⠶⣓⠒⠓⡓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡀
⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⡍⢠⣧⠀⠀⠒⠶⣦⣤⣤⣀⣿⣧⣠⣤⣤⡄⠖⠀⠀⢸⣿⣽⣷⣦
⠀⠀⠀⠀⣸⣿⣬⢆⠀⠀⠀⠀⠀⠸⠃⡉⢻⡄⠀⠀⠀⠀⠉⠛⣿⣿⣿⡟⠛⠁⠀⠀⠀⢀⣾⣿⣟⠿⣿⣧
⠀⠀⠀⢀⣿⣿⣿⡯⡆⠀⠀⠀⠀⣶⡀⢏⢾⣇⠀⠀⠀⠀⠀⣸⡿⠋⠙⣿⣆⠀⠀⠀⠀⢸⣿⣿⠴⡈⠞⣿
⠀⠀⠀⣸⣿⡿⢯⣝⣩⡀⠀⠀⠸⠁⢀⢠⡼⢻⠀⠀⠀⠀⡼⠋⠀⠀⠀⠈⠻⣆⠀⠀⠀⠈⣿⣿⣯⠴⢫⣿
⠀⠀⢰⣿⣿⡿⠣⣌⠛⣷⠀⠀⠠⠐⡨⡼⡥⣾⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⡪⠦⡇
⠀⢰⣾⣿⣿⣷⠚⣠⡟⢫⡀⠀⠰⠃⠅⣰⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣧⠁
⠀⢸⣿⣿⣿⠭⠑⠲⣹⢽⡆⠀⠀⢀⢷⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠆
⠀⠘⠻⢽⣿⣶⡠⢷⡄⠦⠃⠀⠀⠀⣼⣿⠟
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠟⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡐⡄⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣴⠟⠻⠇⠀⠀⠀⠀⠉⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠁⠔⣁⢊⠄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠠⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⠀⠄⠂⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⢀⠀⠀⠉
⠀⢠⣄⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢡⠆⠀⠀⠀⠁⠀⠀⠀⠀⠈⠂⠀⠂⠀⠀⠊⣡⣆⢡⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠
⠀⢘⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠛⠉⠊⠠⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⢀⠉⠀⠀⠀⠀⠀⣀⠀⠙⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠴⠶⢴⡀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠿⠁⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠙⠄⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢀⠀⠀⠀⠀⠀⠀⠐⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠎⠑
⠀⡄⢀⠀⠀⠒⢀⡀⠀⠡⠀⢱⠂⠀⠠⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠲⢾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢂⠀⠡⠄⠀⠀⠀⠈⠐⠁⠀⠀⠈⠀⠄⠀⢀⠠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠠⠄⠀⠐⠀⠀⢹⡦⡀⠉⠄⠐⠆⠀⠀⠌⠂⠁⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠆⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠄⠂⠀⠀⠠⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⡂⠀⢀⡤
⠀⠀⠄⣀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⡠⠂⠀⠀⠂⠰⠠⢤⠀⠀⠀⢀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠡⣄⢉⡀
⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠓⠨⠑⠈⠀⠀⠠⠀⠂⠁⡀⢀⣈⠛⠋⠀⠀⢀⡀⠄⠀⠀⢲⡒⢦⡀⠠⠄⣈⠁⠀⠀⡆⠀⠈⠁
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠛⠒⠒⠐⠙⠀⠀⠁

⠀⠀⢀⣾⡶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⣞⠉⠙⠲⢍⠙⠶⢶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣽⣿⡟⣿⣏⣿⣿⣿⡟⣿⣿⣿⣷⣦⣄⡀
⠀⣸⠏⠙⠲⢄⡀⠙⠶⣀⠈⠉⠛⠷⣶⣤⣀⠀⠀⠀⢠⣶⣿⣿⣿⠿⣿⠥⣿⠻⠙⢻⡇⣿⢱⣿⣿⡿⢻⡿⣾⢿⣿⣿⣿⣿⣦⣄
⠀⣿⠓⠦⡄⠀⠁⠂⡀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣤⣴⣿⣿⣿⢿⡝⡇⠻⠈⡇⠀⠀⠀⢀⣿⣿⣿⣟⡠⢋⠞⠀⢈⡿⢿⣿⣿⡿⣻⢷⡀
⢸⡟⡶⢤⣀⠁⠲⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣻⣿⣿⡌⠃⠀⠁⠀⠀⠁⠀⠀⠀⠸⠋⢀⣿⠿⠁⠊⠀⠀⣡⣴⣾⣿⣟⣽⢟⣿⡿⣆
⣼⠷⡆⣄⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⣼⣿⣿⣿⡟⢭⣶⠂⢡⡄⠚⣧
⣿⣶⣤⣄⣈⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⡗⡀⠀⠀⠀⠰⣤⢶⠦⢶⣄⣀⠄⠀⠀⠀⠈⠀⠀⢙⣿⣯⠱⢃⡩⠴⠷⠚⡿⠇
⣷⣤⣤⡍⢉⠙⠠⠆⣄⣀⠀⣀⣀⢀⠀⠀⢀⠀⠀⠀⠲⣾⣿⢆⡇⠀⣦⣿⡶⠛⠋⠈⠉⠹⢿⡀⠄⠀⠀⣀⠠⠴⠛⠋⠈⠉⠀⠀⢀⣔⣋⣦⣼
⣿⣭⣄⡁⠀⠀⠀⠂⠀⠠⠀⠁⠉⠉⠉⠿⢿⠟⠵⣦⣤⣾⣏⢸⠇⠀⢸⣿⠀⣼⠟⠏⢳⣄⠐⢻⡤⡷⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠉⠩⢦⡶
⣿⣛⠉⠉⠉⠉⠁⠓⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠭⠸⣧⠀⢺⣿⣆⡻⠷⠟⢡⣿⠄⡀⡇⣿⠆⠀⠀⠀⠀⠀⢺⣿⣛⠛⠒⠶⠶⠾⠟
⢻⡟⢃⢈⣉⡁⣉⣨⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠄⠀⢻⡆⠀⠙⠻⢷⣶⣶⠿⠋⢠⡼⢘⠃⠀⠀⠀⠀⠀⠘⠛⠻⣷⠦⢄⣀⡒⠒⠛
⠸⣿⠟⠋⣉⢁⢀⡤⠄⠢⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠈⠙⠷⢤⣄⡀⣀⣀⣄⡵⠛⣴⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠲⠬⣉⡻⠿
⠀⢻⣿⠿⠛⣀⣠⠤⠀⠄⠂⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⡞⠿⠆⡈⠉⣉⠉⠑⠺⠏⠀⠀⠙⠶⣦⣄⠀⠀⠀⠀⡀⠀⠈⠑⠦⣌⣛⣿
⠀⠀⢿⣿⠟⠉⣀⣠⠰⠐⣀⡠⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣦⡀⢠⡌⠓⣦⣝⣶⣬⣿⡿
⠀⠀⠈⢿⡷⠋⠉⠠⠶⢋⣠⡴⠚⢉⡠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠈⠲⣿⡝⠿⣍⠳⣮⡑⣦⡙⠳⣾⣿⠃
⠀⠀⠀⠈⢻⣞⣁⣤⠖⠉⣀⡠⠖⢋⡡⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠠⡉⠂⠈⢷⣌⠻⣦⡹⣷⣾⠃
⠀⠀⠀⠀⠀⠻⣿⣤⡶⠟⣉⡤⠞⣋⡥⠚⣁⠀⡀⢀⡞⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠙⢷⣌⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣶⡾⢋⡤⠞⢁⡴⠚⣠⠊⣴⠏⣠⠐⠀⢠⡏⢀⣇⠀⠀⠀⣾⣿⣿⡆⠄⠀⣀⠰⠀⠀⠀⢣⠀⢢⡀⠙⣦⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣡⣾⢋⣴⠋⣠⠞⣡⡶⢁⠀⢠⡟⢀⡇⡃⢐⡆⣰⡟⣻⣿⡇⠈⠆⢨⡄⢣⠀⢢⠈⣷⣄⣹⣶⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣿⣧⣾⣏⣴⠟⢡⠟⣀⡟⢠⡞⠠⡅⣸⠁⣼⡁⣿⠈⣇⢤⠐⡚⣿⡤⣷⣘⣷⣩⣿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣯⣸⡟⣰⡿⢀⣿⠁⣰⠀⣼⠀⣰⡇⣾⠐⣿⡈⣆⢿⣾⣿⣏⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢾⣿⣼⣿⣴⣿⣶⣿⣧⣾⣦⣿⣷⠾⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠹⠿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡋⠀⠀⢀⣠⣤⣤⡽⠻⣷⣾⡷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠚⠍⠉⠉⠁⠉⡉⠉⠁⠲⣀⣀⡉⡉⣽⣿⣿⣿⣄⣤⣠⣀
⠀⠀⠀⠀⠀⠀⡰⠚⠃⠈⢙⠉⠁⠉⠉⠀⡋⠉⠉⡀⣛⣉⣉⣩⣽⣿⣿⣿⣿⣷⡷⠾⡛⢳⣖⣄⡀
⠀⠀⠀⠀⠀⣜⠁⠀⠂⠒⠜⠓⠒⠓⠒⠂⠶⠋⠿⠿⠾⠿⠛⠛⠛⣻⣿⣻⣿⢿⣿⣿⣶⣤⣉⠉⠻⣦⣄
⠀⠀⠀⠀⡎⠀⢀⣒⠲⠦⣥⠤⠬⠬⠦⢔⣿⣐⣒⣖⣲⣿⠿⠿⠿⢛⢛⣿⡿⢻⣿⣿⣿⣿⣿⡷⠦⠈⠙⢶⡄
⠀⠀⠀⠰⠀⢈⡀⠀⠠⠖⢶⡄⢀⡀⡀⠤⠴⡧⠤⠠⠴⢤⣶⣖⣛⣿⣿⣿⣟⣹⣿⣿⣽⣿⣿⣿⣀⠀⠀⠸⣿⣦
⠀⠀⠀⣒⠀⠐⢆⣉⣉⡀⢭⣭⢤⡤⡥⢬⢌⣭⢉⣉⣉⣩⣭⣤⣤⣾⣾⣿⠥⣾⣿⣉⣩⣹⣿⣛⡉⠀⠀⠈⠀⠹⣄
⠀⠀⠀⠀⠀⡪⣭⠴⠒⠒⠒⣶⠒⠚⠓⠒⠒⢲⠒⠒⠒⣒⣛⣉⣭⣽⣾⣒⣻⣿⣿⣿⣷⣿⣿⣯⠍⣁⠀⠀⠁⠀⠙⡆
⠀⠀⠀⠰⠀⠀⠨⣵⠒⠂⠀⠐⠆⠀⠀⠈⠉⣩⠁⠀⠤⢭⠵⢷⣞⣛⣩⣿⣿⣿⣿⣿⣿⣿⣿⡶⠂⠆⠀⠁⠂⠤⣀⠆
⠀⠀⠀⠐⠸⠆⡠⠝⠤⠒⠂⣁⠰⡄⠀⠠⠤⠔⠒⠒⣒⣻⣿⣯⣣⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⣄⣂⠤⣀⠈⠒⠤⢤
⠀⠀⠀⠀⠢⠀⡄⡀⠛⣏⡠⠤⠔⠒⠒⣀⣉⣭⢿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠀⠌⣉⠓⠦⣄⡂⠄⠀⠁
⠀⠀⠀⠀⠘⢆⡠⠔⢊⣡⡤⠐⣒⣩⠭⠔⣒⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠶⣤⣈⠀⠬⡙⠳⢴⠆
⠀⠀⠀⠀⠀⠈⢇⡶⠋⣠⠔⢋⡥⢖⣪⣽⣿⣿⡿⠟⢛⠝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢀⠢⢄⡀⠉⠛⢷⣬⡑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠓⢞⢁⡔⣩⢞⡹⡫⠟⠋⡡⠀⣴⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢲⣬⣑⠦⣄⡉⠛⢦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣡⣞⠜⠱⢀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠲⣦⣄⡀⠈⠛⠷⣬⡙⠶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡀⠀⠀⠡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢲⡤⠀⠈⠹⠿⣶⣄⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣸⡄⠹⣿⢸⣿⣿⣿⣿⣶⣾⣭⡋⠁⠀⠀⠀⠈⠑⠦⣀⠈⠙⠿⣶⣄⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢀⢿⣿⡄⠿⣼⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⢦⡀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡈⢸⣿⣿⢠⣿⣿⣿⣿⣿⣿⠆⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣀⠙⡳⢌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿⣿⣼⣿⣿⣿⣿⣝⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢦⡀⠙⡷⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠻⣿⣿⣿⣿⡿⣿⢮⡑⢄⠀⠐⣄⠀⠀⣀⠀⠑⣄⠀⠸⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⣿⣿⣧⡹⣎⢣⡱⡀⠱⡄⠈⢷⡀⠘⣦⡀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠏⠉⠙⢷⡘⡇⢷⠘⡄⠸⡆⠀⣿⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠑⢸⣌⡇⠹⠄⡿⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠃⢷⡀⣀⡤⢤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠦⣞⡁⠀⡟⢷⣬⡙⠳⡄
⠰⣖⣒⡶⠚⢠⣧⠍⢠⠞⠉⠀⠀⠀⡜⣷⡒⠲⢤⣌⡒⢦⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⢿⣼⣟⠀⠴⠿⠁⢀⠆⣽⣿⣖⠀⢿
⠀⠀⠈⠉⡆⢘⣉⠂⢿⡀⠀⠀⠀⢾⣷⢹⣭⠭⠭⠤⠬⣻⣿⠟⠁⠀⠀⣠⣔⣚⠛⢯⠉⠹⡗⠢⡀⠙⠳⣾⡇⠀⣭⡝⠀⢸⠉⠋⢻⣿⣦⣘⣇
⠀⠀⠀⣞⡴⠋⠀⠙⢦⣹⡄⠀⠀⠀⠙⢶⢶⣒⣒⠤⠗⠋⠀⠀⠀⠀⡴⣭⣦⣭⣑⢮⣷⢠⠇⢀⡼⡆⠀⠘⢷⡤⣼⠎⠀⢚⢘⠇⠀⢈⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⢿⣿⣿⠟⣿⣾⣔⠚⣁⣤⠀⠀⠀⠀⠈⣿⣤⣿⣼⡴⠟⠉⠉⠉⠛⠛⠃
⠀⠀⢀⣤⡖⠞⢻⠙⠋⠟⣶⢤⣀⠀⠀⠀⠀⠀⢀⡠⠔⢶⠐⠒⡖⠒⡀⠀⠀⠀⠹⡊⢅⠹⣌⡉⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⢝⢦⡀
⠀⣴⡝⡇⠇⠰⢸⠀⠀⢀⠃⡜⢩⢷⡄⠀⢀⡔⠉⠑⣄⢘⣄⣀⡇⢸⠁⠀⠀⠀⠀⠙⠼⠆⠀⠝⠋⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⡰⢿⡧⡉⠄⢆⢻⡀
⠀⣧⠑⡈⡘⠀⠀⢠⠀⠈⡰⠠⢃⠜⡹⠀⡌⠉⠲⣤⠞⡉⢹⠉⡿⣇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢠⣟⡇⠀⠀⠀⡟⡘⠘⢰⠘⠘⠈⡇
⠀⠈⢦⡐⡐⡴⣠⢸⠀⠀⡱⠡⢊⡜⠁⠀⡗⠤⠤⡿⠒⣰⣾⢾⣥⣼⡆⠀⠀⢠⠮⢐⡡⢂⠔⠁⠨⠳⡄⠀⠀⢸⠥⢾⡀⠀⠀⢹⠃⡀⡁⠀⡀⡇⣿
⠀⠀⠀⠓⣜⢜⣷⣯⣖⠜⢀⡴⠋⠀⠀⠀⢳⣤⠴⠻⣏⣬⣣⡽⢧⣠⠇⠀⠀⣋⡴⠋⣰⢃⡜⢠⠁⡃⣧⠀⢀⠗⠒⠈⡅⠀⠀⠘⣤⢃⢀⠀⠇⡇⡿
⠀⠀⠀⠀⠿⠷⢿⣿⣿⣶⣿⠆⠀⠀⠀⠀⠀⠙⠲⣾⣁⣼⣁⡧⠖⠃⠀⠀⠀⢻⢀⡼⢁⡞⠀⡟⠀⡇⣿⠀⢸⡋⡡⣴⣿⡄⠀⠀⢷⢞⡼⣰⠀⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣼⣇⣰⣧⣠⠗⠋⠀⠀⠙⣳⣿⡽⠃⠀⠀⠘⢿⣞⣫⢎⡞
⠀⠀⠀⣀⠜⠻⡍⠋⠹⠍⡙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣤⣀⣀⣄⣀⡈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⢀⡞⠀⠀⠀⢳⣄⣐⢠⠇⠀⠙⣦⡀⠀⠀⠀⢀⣴⣾⡳⣷⣤⠀⠀⠙⠻⢬⡀⠀⠀⠉⠹⡖⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤
⠀⣾⠤⢤⣤⠶⣁⣴⠉⢙⣠⠐⢀⣈⣿⣆⠀⠀⣟⠭⢕⣴⡈⣸⣿⡆⠀⠀⠀⠙⣄⠀⠄⢀⠁⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⢻⣿⣿⡿⡛⢶⣄⡀
⠀⢸⠃⠐⢸⣤⠿⣿⣏⢁⣸⠟⠋⠉⢠⡇⠀⠀⡇⣾⣿⣿⣿⣼⣯⣟⣦⠀⠀⠀⠀⠉⠛⣉⡉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣴⠻⢿⣣⣻⢼⠎⠁⣹⠢⡀
⠀⠀⣷⡚⠉⠋⢹⡋⠉⠛⡾⢠⠀⢰⡐⣿⠀⠀⢧⡻⣿⣿⣿⣿⣿⡿⠋⠀⣀⡤⠤⡞⡋⠉⠙⡟⠛⠶⣤⣄⠀⠀⡴⣋⠘⡄⡀⠀⠀⠀⢂⢢⠣⡐⣿
⠀⠀⠈⠉⠓⠦⢼⡤⠶⠶⠶⠾⠶⠖⠛⠛⠀⠀⠀⠙⠓⠛⠛⠛⠉⠀⠀⢰⡣⠒⠀⠠⡀⠀⠀⢹⡀⠳⡈⣹⠃⠀⣿⠜⣀⢀⠁⠃⠓⠃⠋⢀⢠⠙⣼
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⡤⠶⠒⠲⢕⠄⡀⡀⠙⢦⠟⠁⠀⠀⠈⠲⣇⣸⠠⡇⠆⢸⠘⡈⣆⣷⠋
⠀⠀⠀⢀⣰⣿⡿⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡻⠿⣿⣷⣦⣷⣌⣀⣴⠏⠀⠀⠀⠀⠀⠀⠈⠉⠚⠧⠷⠼⠶⠛⠉
⠀⠀⣠⢟⡟⠋⠑⠟⣩⣧⡀⠀⣴⡶⢶⠶⠛⣳⡏⠙⠲⠒⢋⣉⠛⢲⣄⠀⠛⠛⠶⠚⠓⠞⠉⠉⠁⢀⣀⣀⢤⡤⢶⡤⠒⢦⣀⠤⢤⣀
⠀⣰⢱⢣⠖⡥⢤⣶⣿⣧⡇⠀⣿⠖⡁⣸⡏⠉⠻⣶⡀⠀⢿⣿⣿⣦⠹⡆⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠲⡏⡸⠁⠘⠀⠀⠘⠁⠀⡠⡉⠻⣆
⠀⢻⡘⢌⣧⣱⣿⡿⣫⡞⠀⠰⡇⣂⣯⡉⠻⣦⡀⠈⢿⡄⠘⣿⣿⣿⡁⣿⠀⠀⠀⠀⣾⠁⠡⠉⠷⣄⠀⠙⣇⣀⠀⠀⠀⠁⠀⠰⠀⠀⠀⠎⡇
⠀⠀⠉⠓⠶⣿⣯⡴⠋⠀⠀⢀⣿⣧⡉⠻⢦⣈⡛⠦⣄⠻⣌⢿⣿⣿⡇⣿⠀⠀⣠⠴⡑⠀⠂⠀⠐⠁⣷⡀⠀⢹⣄⢀⡜⠀⠀⠆⡇⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠳⣄⠙⠳⠤⣬⣙⠲⣼⡦⣙⢆⢿⣿⣱⠃⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠉⠙⣆⢀⠊⠀⡇⠀⠀⠀⢸⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⣭⣽⣆⣁⣯⡀⢹⣿⡏⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠘⢾⣤⡀⠇⠀⡀⠆⠈⣇⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠓⠓⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⡄⢠⡀
⠀⠀⡞⠂⠐⠂⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢢⡈
⠀⢼⡙⠁⠀⣀⣴⡇⠀⠀⠀⠀⠀⣠⠔⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠑⠀⠀⢰
⠀⠘⠉⠙⠛⢻⠋⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠑⢄⠸⡆⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠈⢣⡇⠀⠀⠀⢠⣀⠀⠀⠄⠐⠈⠀⠀⡀⠈⠄⠠⠖⠂⠁⠈⠓⠒⠄⢀⡀
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⠰⡴⣒⣷⡤⢤⣀⣀⡀⠢⠠⠂⠀⠀⠀⠀⠀⠀⠀⡤⠂⡄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⣀⣿⣿⣇⠀⠀⣿⣿⣭⣁⣐⣦⠀⠀⠀⠀⠀⠀⠀⢣⡴⠃⣾⠈⢟⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⡖⠬⢉⠉⣻⢷⡾⢛⣉⠀⠤⢀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠳⡴⠃⠀⢸⢷⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣧⣀⢀⢀⠀⠀⠀⢠⢐⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠁
⠀⠀⠀⠀⡄⠀⠀⡆⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠿⠖⠒⠛⠉
⠀⠀⠀⠀⠀⠀⢰⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀⣆⠀⠀⠀⢀⡀⠀⠈⠉⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠐⢀⠄
⠀⠀⠀⠀⠀⠐⢵⣽⣶⣄⣀⠉⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠐⠀⠀⠀⠀⡀
⠀⠄⠀⠡⠄⢤⠤⠤⠤⠄⠀⠈⠒⠀⠀⠀⠀⠀⠀⢄⡀⢠⣐⡝⠀⠀⠁⠀⠀⠀⠀⠀⠀⢴⣀⡸⠶⢦⣤⣤⣤⣀⡀⠃⢤⣤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⠛⠶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠛⠛⠛⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠀⢿⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣿⠀⠘⣇⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣿⠀⠀⢻⡀⢻⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⠀⠀⠸⡇⠈⢧⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣿⠀⠀⠀⣧⠀⠸⡆⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢻⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠈⡇⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣧⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡏⠀⠀⠀⣿⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠇⠀⠀⠀⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡆⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⡇⣿⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣀⣀⣠⠄⠀⢀⣀⣧⣿⣿⠴⠶⠶⢤⣤⣀⣀⠀⠀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣯⠭⢷⣶⣾⣿⠯⠽⠶⠿⠚⠛⠛⠛⠉⠉⠉⣉⣹⣿⣿⣿⣿⡿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡥⠶⠒⠋⠉⠁⠀⣀⣀⣀⣀⣤⣤⣤⣶⣶⣾⣿⣿⣿⠿⠟⠛⠉⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣶⣶⣶⣾⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠀⣀⣀⣀⣤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠉⠉⠉⠉⠉⢀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠴⠶⠶⠒⠚⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⡇⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠈⠃⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⢀⡼⣃⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠇⢀⠀⠀⣠⣾⠿⠋⠁⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⢠⡟⣠⡾⠋⠁⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⡟⣹⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣼⡟⢀⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⠜⡿⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⡼⠁⠈⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⡼⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⡾⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢀⡾⠁⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢀⡾⠁⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢟⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠛⢉⣴⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠉⠁⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢠⡀⣰⠏⠀⠀⠀⠀⠀⢀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⣀⣴⣋⣡⡤⠀⠀⠀⢀⣀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠘⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⣠⣾⣿⣿⣿⡷⠶⠶⠚⠛⣹⠿⣷⣶⣶⣦⣤⣤⣤⣤⣴⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠁
⠀⠀⠚⠛⠋⠡⠤⠤⢤⣤⣤⣤⣾⣥⣤⣤⡤⠤⠤⢶⠒⠒⡆⢿⣋⠛⠒⠒⠒⠀⠀⠠⠤⠤⠤⢤⣤⣴⣶⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡹⠯⠛⠻⣷⣦⣤⣅⣈⣁⠘⠳⠦⠬⢥⣤⣀⣀⣀⣀⣀⣐⠺⠗⠀⣀⡵⠀⠀⡈⠉⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⡟⠋⡉⠙⠛⠿⣿⣟⡛⠛⠲⠶⢶⣶⣶⣶⣶⣶⣶⣖⣚⣋⣉⣠⣤⠞⠀⠤⢒⣋⣭⣤⠶⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠈⠻⣿⣦⣄⡀⠋⢀⡀⠈⠹⣿⢿⣿⣿⣛⣛⣉⣁⣤⣴⠾⠛⠉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠀⠀⠀⠀⠈⠙⠿⣯⣍⣉⣀⣠⣴⠟⠀⠉⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠶⠶⠶⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢋⡩⠄⠒⠚⠋⠉⠉⠁⠒⠀⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡤⠚⠁⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠐⠈⠙⣦⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡴⠋⠀⠀⠁⣀⠤⠐⠉⠁⠀⠀⠀⠀⠈⠑⠒⠄⠀⠐⠀⣲⣟⠭⠭⠭⠭⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⠏⡠⠀⢀⠤⠊⠁⠀⠀⠀⠐⠈⠁⠀⠀⠀⠐⠀⠀⢀⠐⣼⣋⠤⠀⠒⠀⠀⠀⠈⠺⣻⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣿⣡⠊⢀⠔⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠥⠒⠉⠀⠀⠀⠄⠀⢀⣿⠋⠉⠉⢩⣷⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣳⣿⠞⣡⡞⢁⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⡧⠂⢀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⢸⣿⢘⣯⡿
⠀⠀⠀⠀⠀⢀⡠⠖⠚⠛⠛⠉⠉⠉⠉⠉⠳⢆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠋⠁⠀⠀⠀⠀⠀⠀⢐⣿⣆⢀⠀⣨⣿⡿⠛
⠀⠀⢠⠖⠋⠁⣠⣴⣶⣾⣷⣶⣶⣤⣴⣦⣄⣈⠠⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡎⠀⠀⠀⠀⠀⠀⠀⢈⠀⣻⣿⣿⡯⠞⠁
⠀⠀⣟⠀⠀⢸⠁⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡐⠊⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠸⣯⡤⠀⠀⠀⣀⠠⢂⠤⣺⣿⣿⠃
⠀⠀⢿⠀⠀⠸⡄⠀⠀⠀⠀⠉⠝⠿⣿⡿⢿⣿⣿⣿⣿⣶⣄⣀⠰⠀⠀⠀⢀⡀⠤⠐⠂⠉⠠⠖⣩⣷⣖⣚⡩⠔⣊⡵⠪⣿⠟⠁
⠀⠀⠘⣆⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠉⠳⣿⣻⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⢉⠤⠒⢊⣡⠴⣻⢷⣶⣭⡤⠖⠋⠁
⠀⠀⠀⠘⢦⡀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⣻⠋⠑⣫⣷⣦⣀⡈⠡⠤⠀⠒⣉⣡⠴⣚⣥⣾⠟⠁
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠈⠑⠒⠶⠦⠴⠷⠿⢛⣩⣴⡊⠁⣐⣨⣴⣾⠿⠻⢿⣧⣭⣭⣬⣥⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠦⠤⠶⣶⣶⣾⣯⣅⣤⣦⣵⠿⠟⠋⠁⠀⠀⠀⠀⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣷⣶⣤⡀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡉⠉⠉⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠟⠛⠛⢁⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡟⢻⣿⣿⣿⣦⠀⠘⠻⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠋⣿⣿⡿⠋⠀⢸⣿⣷⠀⠙⣿⣿⣿⣧⠀⠀⠀⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⣿⡿⠀⠀⠀⠘⣿⣿⠀⠀⠈⢽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⢀⣿⣥⣄⣀⠀⠀⣿⣿⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣤⣤⣠⣾⣿⣿⣿⣿⡿⠿⣤⣿⣿⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⠈⢿⣆⠙⠻⣿⣷⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⣿⡏⠀⠀⠘⣿⡆⠀⠈⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠻⠀⠀⠀⠀⢹⣿⡀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢾⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢸⡏⢹⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⢸⡇⣰⠌⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢸⡏⠁⠨⠶⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣾⠇⠀⠀⢸⡇⠀⠀⢐⣨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢠⣿⠀⠀⠀⢸⣿⢶⣞⣯⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⣿⠀⠀⠀⢸⡇⢻⡅⠞⠃⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⢸⣿⡀⠀⠀⢸⡇⠀⢂⣠⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢸⣿⠁⠀⠀⢸⣗⡀⠈⣿⡯⠖⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡇⠀⠀⠈⡶⣒⣈⠄⠀⠈⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠸⣟⢿⡄⠀⢸⣯⣀⣤⠀⠺⡿⠂⠁⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⠄⠀⠀⠀⠀⠀⠀⣿⢘⣷⡀⢸⣿⣫⣥⡀⠀⠸⠀⠀⠀⠀⠀⢀⣱⡀⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠡⠀⠀⠀⠀⠀⠀⠠⠈⢿⣿⣷⣸⣿⣿⣿⡁⠀⠀⣡⣤⣶⠾⠛⠋⠙⠉⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⣀⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⡷⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠐⢒⣖⠠⣤⢠⣿⣿⣤⣶⠾⠿⠟⠛⠛⠛⠛⠉⠉⡉⠉⢻⣿⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀⠀⠀⢀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⢿⠾⠶⠶⠶⠶⠶⠶⠷⠾⣿⠿⠿⠿⠿⠿⠶⠶⠷⠟⠿⠿⡟⠿⠷⠶⢶⡶⠶⣿⠷⣦⠔⠃
⠀⠀⠀⠀⠀⠠⠤⢤⣤⣵⣤⠈⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋⠛⠒⠒⠀⠀⠙⠛⠋⠀⠀⠛⠛⠓⠈⠛⠛⠛⠾⠟⠛⢋⣷⣤⣤⣤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣷⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⠤⠤⠴⠶⡾⠿⠯⠥⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⠬⠉⠙⠛⠖⢛⣻⣿⣟⣙⠛⢻⣯⣭⣄⣉⡙⢛⣯⣭⣥⣭⣭⣥⠶⠾⠟⠛⠛⠛⠛⠒⠶⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢉⡙⣛⣉⣉⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣄⣘⡛⠻⠿⢿⣿⣛⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⢉⣉⠁⠀⠤⠖⠒⠒⠛⠒⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⣤⣤⣶⣶⣶⣾⣻⣂⣀⣀⣀⠀⠄⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠉⠉⠉⠉⠉⠉⠥⠤⣤⡀⠉⠑⠓⠲⣶⢶⣶⣶⡶⣶⣶⣶⣦⠐⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⠖⢛⣩⠤⠀⠀⠐⠀⠐⠛⠛⠛⠛⠛⠛⠉⠁⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠉⣀⡀⢀⣀⠈⠃⣀⡉⠀⠀⠀⠀⠒⠒⠂⢠

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⠱⣆⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠻⠄⢠⠀⡀⠈⡼⣋⠄⠀⠂⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣉⣉⣉⡛⠷⢦⡈⣵⠲⣮⢢⣞⡼⠋⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡒⢼⣋⣬⢿⣾⣲⠅⠒⣝⢾⣷⢳⣿⣋⣴⣆⣽⣥⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⡴⠄⣶⣤⣠⠆⡀⠀⠀⠉⠒⠾⣾⣷⢿⣭⣭⣍⡤⢀⣀⣈⠁⢀⠙⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠛⠓⠒⡯⠔⢊⢹⡇⠡⠀⡀⠈⠉⠒⠶⣤⡛⠘⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⣠⡾⣫⣿⠁⠀⠏⠙⠑⠴⠄⣀⠀⠉⠢⡀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢁⡼⢋⡴⣇⡟⡧⠀⢸⠈⡓⠀⠀⠁⠘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠰⢋⣴⡟⢰⢸⠇⣶⠀⠘⢀⡋⠀⠀⠀⠀⠀⠘⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣠⡟⠉⠀⠆⣿⠀⢹⡀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣤⠋⠀⠀⠀⠘⡿⠀⠋⠷⢀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢰⢰⣷⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠻⣷⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣄⠻⣿⡆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡇⢰⡿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠉⠉⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣇⢀⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣸⣿⣿⣟⣛⣉⣭⣤⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠾⠟⠛⠛⣛⠒⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠿⠿⠿⠿⠟⠛⠉⠀⠒⠒⠒⠉




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣬⣍⣤⣬⣽⣏⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠂⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣀⡀⠀⠀⠀⠂⠂⡄
⠀⠒⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠐⣧⠂⠀⠀⠀⠉⠲⣶⣤⣀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠕⠆⠀⠀⠀⠠⠾⢣⠀⠀⠀⠀⠀⠈⠣⠄⠠⠀⢠⠠⠂⠀⡀⠀⠀⣨⠙⠻⠷⠶⣄⡀
⠀⠀⠀⠐⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠋⠀⠉⠀⢀⠀⢀⣄⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠑⢀⠐⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⣠⣴⢀⣠⠴⠊⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⢲⠐⡆⠸⠋⠀⠉⠀⠒⠷⠦⠄⠀⠀⠀⠀⠀⠉⠉⢁⡤⢄⡦⠀⣀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠂⠳⠀⢦⣀⠀⠀⣀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠷⡄
⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠠⠀⠀⣀⣄⣌⡀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⡀⠠⣄⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉
⠀⠀⠐⠀⣰⠞⢋⣉⠉⠃⠀⠀⠀⠀⠀⠀⢸⠀⣰⢆⡎⣱⠐⡖⠂⠤⣄⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠐⠀⠐⠀⣿⡰⣯⠍⣷⠀⢠⠀⠀⠀⠀⠀⠘⢰⠇⢸⠁⡏⢰⠃⣷⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡠⠌⠁
⠀⠂⠈⠀⠘⢻⢶⠶⠃⠀⠼⣄⠀⠀⠀⠀⠀⠀⢀⠸⡄⡇⠀⠸⡞⣔⠏⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠂⠇⠀⣢⠞⠁
⠀⠀⠀⠀⠀⣀⠀⠰⠀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⢀⡄⠨⠀⠁⠀⠁⠀⠀⢶⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⢀⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡃⠀⠀⠀⠀⠀⢠
⠀⠈⠀⠀⣠⣴⠖⠷⠶⣤⠀⣀⠀⠀⠂⠀⢶⠐⠆⠀⠀⢨
⠀⠀⠀⠐⠫⣄⣦⡠⡀⢈⡏⠁⠀⠀⠤⠀⢀⡆⠀⠀⠠⠆
⠀⠘⠁⠒⠀⠁⡁⠹⢆⠀⣼⣋⡁⢀⡀⠀⠈⢁
⠀⠀⠐⠆⠐⠈⡄⠠⠁⣠⠭⠥⠄⠀⠀⠀⣰⠏

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠐
⠀⠀⠀⠀⡠⣤⡄⠀⠀⠤⡖⠀⠒⠀⠀⠀⠀⡀⠤⠂⠁⠀⠀⠀⢀⠠⠄⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠉⠂⡀⠀⠀⠀⠀⢀⡤⠔⠋⠁⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠙⠒⠂⠀⠀⠚⠁
⠀⠀⠀⠀⠲⠄⡀⠀⠀⣢⠀⠠⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠒⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⢄⡈⠁⠉⠉
⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⢠⠊⠀⠀⠀⠀⠋⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠘⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠄
⠀⠀⠀⠙⠒⠒⠒⠉⠉⠀⠀⠉⠙⠛⠟⠀⠀⠉⡘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠂⢁⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠠⢴⡂⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠥
⠀⠀⠀⠀⠀⠁⣀⡀⠀⢀⣀⡾⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠅⡀⠀⠘⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠘⠆⠘⠉⠀⠂⠒⠚⠁⠀⠀⠀⠀⠀⠈⠉⠒⠐⠃⠉
⠀⠀⠀⠀⠀⡄⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠄⠐⠀⠀⠅⠐⠆⠀⠂⠀⠸⠀⠂⠏⠰⠐⠨⠐⠀⠴⠀⠀⢰⠐⠏⠰⠄⠀⠂⠂⠆

⠀⠀⠀⠀⠀⣇⡴⠪⡀⣨⡶⢋⡵⠊
⠀⠀⠀⠀⠀⣿⠗⣠⢟⡡⢞⠍⢀⠂⠀⠀⢈⠤⠀⢀⣤⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢺⣷⢷⣷
⠀⠀⠀⠀⠀⣿⣾⡫⠋⠈⣀⣤⡶⠞⢁⠆⢀⣤⠔⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢾⣿
⠀⠀⠀⠀⠀⣿⣿⣴⠞⢛⣉⣵⣶⣤⠾⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⣿⣺⣿
⠀⠀⠀⠀⠀⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠀⠀⢻⣿⣼⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⠀⢹⣿⢺⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢸⣿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⣿
⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡏⢣⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣽⣦⠀⣿⣡⣴⣿⡿⠿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣟⣥⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⢿⣿⣿⣿⣿⣟⠛⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣴⠏⠀⣀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠁⣼⣿⠿⡿⠙⣿⡆⠀⠈⠋
⠀⠀⢀⣤⣶⣾⣿⣿⣶⣿⣾⣿⣾⣟⠿⢿⣆⠀⠀⠀⠀⣿⠁⠀⣰⣿⠇⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⢀⣴⠶⠿⣿⣿⣿⡉⠛⢷⡀⠈⠀⠀⠀⠀⠃⢀⡼⢹⠏⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⢰⡟⠁⠀⣼⠛⢿⣿⣷⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠁⠈
⠀⠀⠀⠀⠈⠁⠀⠀⢿⡆⠈⢷⡙⡇⠀⠁⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣾⣷⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣼⣿⣿⣿⣼⣿⣷⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠲⠦⠤⠤⠤⠤⢴⡶⢀⣀⣀⡏⠉⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢦⡀⢀⣧⣀⣤⣤⣶⣾⣿⣿⠇
⠀⠀⠠⠄⡀⠀⠀⠀⠐⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣯⠀⠀⠀⠀⠀⠀⢄⠀⢀⣀⡀
⠀⠠⠌⠀⣀⣛⣒⣶⣤⣤⣽⣟⣿⣿⣽⣿⠿⣿⣿⢿⣿⣿⣟⣫⣭⣥⣶⣿⣿⣿⣿⣶⣄⠀⠀⠤⠤⠬⠭
⠀⢀⣬⣭⣍⣉⣙⣿⣷⣶⣾⣿⣿⣿⣿⡳⠾⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣯⣭⡤⠤⠄⠒⠒
⠉⠉⣍⣉⣛⣋⠋⠛⠦⣤⣀⣨⡍⠉⢿⣿⣏⣉⢾⣿⣿⠗⠛⠛⠀⠀⠀⠛⣟⣛⣻⣿⣇
⠀⠀⠀⠀⠉⠀⠀⠙⠓⠲⠦⠤⠤⠀⣀⣀⣀⠒⠒⢺⣿⠂⠀⠈⣉⡉⠉⠭⠤⠴⠒⣀⣀⡀⠉⣉⣉⡉⠑⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⣀⣀⣀⣛⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢚⡻⠃⠉⠉⠙⠋⠉⠙⠋⠟⠛⠳⠿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠒⠒⠛⠐⠒⠂⠀⠸⠇⠉⠀⠠⠶⠿⡿⠘⢿⣿⣿⣯⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣒⠂⠀⠰⠆⠀⣀⣀⣀⠀⠠⠤⠤⠤⢤⡤⣤⣶⣶⣾⣿⣿⠷⣻⡶⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠈⠀⠈⠉⠉⠉⢉⣉⣽⢁⣴⢋⣿⣿⣶⣤⣀⠀⠙⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠂⠀⠀⠀⠠⠤⠈⠄⠉⠃⠁⠸⠛⠿⠻⠃⣌⣍⢸⣿⣿⣿⣿⣿⣷⣤⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠂⠀⠚⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⠤⣤⡴⣶⣾⣿⣯⠄⢨⣿⣿⣿⣿⢿⣿⡆⠂⠀⠀⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠥⠒⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⣩⣽⡤⠒⣸⣿⣿⣿⣿⣿⣿⡶⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⣚⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠅⠉⠈⠉⠿⠿⠿⠿⣿⠃⣠⣿⣽⡷⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠤⠤⠀⠤⠤⠲⠶⣾⣿⡯⣤⣽⣿⣿⣿⣿⣿⣷⢿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢊⣩⣭⠽⢣⣶⣿⣽⣿⣭⣬⣹⣿⡿⡛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣥⡬⣥⢲⣬⣻⣿⣻⣟⡿⣿⡿⢿⣾⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⣈⣁⣀⣠⣤⡤⣴⣶⡾⢟⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣽⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡤⠖⠂⢉⣉⠠⠄⢐⠚⣋⡻⣿⡟⡉⢸⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣠⠶⠛⣁⠴⠞⣻⣿⣵⣿⠿⠋⠀⠀⣼⣿⣿⣷⣾⣷⣿⣯⣭⣟⡿⠷⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⡵⢎⡭⡰⠏⠉⠁⠀⠀⢀⣴⣿⣭⣭⣿⣿⣻⡿⢿⣭⣛⡻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⠡⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣾⣿⡁⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠓⣿⣿⣿⣻⣿⣿⣿⣿⣿⣭⠋⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢿⠅⠀⣿⣿⣿⣿⣿⣾⣯⣿⠟⠋⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⢠⣿⣿⣻⡿⣿⣿⣭⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⣾⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⢿⣿⣟⡿⠷⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⢸⣿⣿⣿⣿⠿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⡙⢌⢣⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣧⠑⠈⢧⠡⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠈⠃⠹⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢣⠀⡁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠑⠢⣼⣆⣀⣀⣀⠀⠀⠀⠀⠀⣄⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠉⠒⠤⢀⠀⠀⠁⠲⠢⠬⣦⡀⠘⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠐⠀⠑⠐⠒⠓⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣱⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⣠⠴⠖⠛⠉⣉⣉⣉⣉⣙⣛⡲⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣈⣦⠖⠋
⠀⠀⠀⠀⠀⠉⠀⠀⠔⠚⠉⣉⡠⠤⠤⠤⠬⠭⣽⣓⡻⠽⣟⣓⡶⠶⠶⠶⠶⠶⠛⣋⣩⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠪⠭⢭⣙⣛⣛⣋⣉⣡⠤⠔⠂


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢴⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠠⢶⣾⠿⢿⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠖⠶⠦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠑⠾⢟⠛⠛⠃
⠀⠀⠀⢀⣴⣞⡭⢴⣟⣠⠤⢤⡶⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⡜⠰⠿⡛⠛⠃
⠀⠀⠐⠋⠿⠋⠀⠛⠁⠀⡴⠟⠒⠒⣲⠶⠂⠀⠑⣄⠀⠀⢰⠳⢾⣟⠋⠀⢀⣠⠤⠐⠒⠒⠒⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⣉⣷⠶⠌⢣⡀⡆⢠⠞⢁⠴⠊⠁⠠⣤⣄⣀⠘⣶⠦⣄⣰⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣉⡓⠦⡳⣵⢃⠞⠁⣐⣶⣖⠒⠺⢷⡀⠉⠺⠇⠀⠙⣧⠙⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢉⠀⢀⣤⠎⢉⣷⣼⡏⣹⢾⡿⠷⠮⠭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣶⣰⢻⡴⢩⠗⠊⢹⠋⠻⣩⠩⡷⣅⢰⣧⢠⡆⢉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣤⡜⠸⠇⠘⠁⠀⠀⠀⠈⣻⠁⡟⠒⠁⠈⠻⢹⡼⢻⢸⡇⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠈⠀⢸⡎⣧⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣇⠀⠀⠀⠀⠀⠀⠈⠀⢸⢿⣾⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠈⠁⢀⣸⣆⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⢻⠀⠈⠉⠀⠘⣆⠀⡾⡔⣇⠔⠡⢝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢆⣣⠈⡧⠴⠖⠚⠁⠈⢣⣧⠃⠻⢰⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠙⠀⣸⠄⠀⠀⠀⠀⣠⠭⠷⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣯⣀⣽⣭⣭⣭⣭⣿⣽⣭⣭⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣯⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣫⣾⡿⠛⣽⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢡⣾⡿⢋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢋⣴⣿⠋⣠⣾⣿⡿⠿⢋⠉⢉⠈⠉⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠻⠻⢿⢿⣿⢿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣡⣾⡿⢁⣾⣿⠟⠉⠀⢀⣐⣤⣤⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣦⡀⠀⠈⠠⠓⣿⣿⣿⡟⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣴⣿⡟⢠⣿⠟⠁⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣿⣿⠉⠻⢿⣿⣿⣿⣿⣦⡀⠀⠀⡺⣿⣿⣧⢹⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⣴⣿⢏⣾⣿⡟⣰⠟⢁⣴⣾⡿⠿⠛⠛⠛⠙⠉⠉⠛⠟⠿⣿
⠀⠀⠀⣠⣿⣿⣿⣿⣄⠀⠉⠹⢿⣿⣿⣿⣷⡀⠀⠀⣿⣿⣿⣄⢿⡟⣿⡞⢿⣿⣷⡀⢀⡾⣿⢫⣿⣿⣏⡼⣣⡶⠟⠉⠀⠀⠀⠀⠀⣀⣀⣤⣤⣦⣼⣬⣌
⠀⠀⣰⣿⠁⠻⣿⣿⣿⣷⣤⣀⠀⠘⣿⣿⣿⣿⡀⠀⡾⣿⣿⣿⣦⠹⣎⠛⠶⠭⠽⣷⢟⡾⣱⣿⣿⡿⠫⠞⠁⠀⠀⣀⣠⣤⣶⣾⣿⣿⣯⣿⣽⣯⣿⣻⣿
⠀⢰⣿⣿⡆⠀⠙⠛⠙⠋⠉⠙⠛⠲⠄⠙⣿⣿⣳⡀⠀⠺⣿⣿⣿⣷⡘⢿⣶⣶⣿⢫⣟⣽⣿⣿⠟⠊⠀⣀⡤⠶⠛⠋⠉⠉⠉⠀⠀⠉⠉⠉⠛⠿⣿⣿⣿
⢀⣿⡏⠻⣿⣦⣀⣀⣀⣀⣀⣀⣤⣀⠀⠀⠉⢿⡷⣷⡄⠀⠘⣻⣿⣿⣷⣼⣿⡿⣡⣯⣾⣿⣟⠅⠪⢒⡩⠅⠂⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣇⠻⣿
⢸⣿⣧⠀⠈⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣶⣤⣀⣹⣿⡟⣹⡿⣱⣿⣿⣿⢟⣩⣴⣬⣥⣶⣾⠿⠿⠿⠿⠿⠿⠿⠿⢷⣷⣿⣽⣿⣿⣿⣿⣿
⣾⣿⣿⣷⣄⣀⣀⣠⣤⠖⠂⢀⠄⠀⠀⠀⠂⠈⠩⣿⣿⣿⣟⣛⣛⣡⣴⢟⣼⣿⣿⣿⡿⠿⠟⢛⣉⡉⠥⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⡏
⣿⣿⡌⠛⠻⠿⠟⠋⠀⠀⣠⡟⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠵⢖⣊⣩⣤⣴⣶⣶⣶⣾⣛⣟⣿⣻⡿⣷⣶⣶⣦⣤⣤⣸⢿⣿⡿
⢿⣿⣿⡀⠀⠀⠀⢀⣠⣾⠏⠀⠀⠀⡴⠀⢠⡞⣼⡇⣿⣿⣿⣿⣿⣿⣿⣯⣶⣶⣶⡿⠿⠿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⣾⣯⣿⣿⣿⣿⣾⡿⠁
⢸⣿⡻⣿⣧⣤⣠⣾⠿⠃⠀⠀⢀⣼⠁⠀⡾⣸⠘⡇⢻⢻⣿⢿⣻⠿⣯⣍⣉⠡⠄⠠⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠿⣿⣿⣿⡿⠁
⠀⣿⣿⣦⡉⠉⠉⠁⠀⠀⠀⢀⣿⠇⠀⠰⠇⡏⠀⠄⠀⢀⠹⣷⡝⠅⡢⢍⡈⠓⠲⠤⣤⣍⣉⡉⠙⠛⠛⠻⠿⣿⣶⣶⣶⣤⣄⣀⡄⠔⠹⣿⡿⠁
⠀⠘⣿⣿⣿⣶⣤⣠⣆⣠⣴⡾⠋⠀⢠⢡⣿⠃⠀⠀⠀⢸⡗⠘⢮⡀⠀⠀⠉⠑⠦⣄⡀⠉⠛⠿⣷⣦⣀⠀⠀⠀⠈⠉⠻⣿⣿⢻⣿⣷⣶⠟
⠀⠀⠹⣿⡛⠿⠿⢿⡿⡿⠋⠀⠀⠀⢁⣾⡟⠀⠀⢸⠄⠀⣿⡈⠀⠙⣦⡀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠙⠿⣷⣤⡀⠀⠀⠀⠈⢿⣿⣿⡿⠋
⠀⠀⠀⠙⣿⣷⣶⣶⣄⡈⠀⣀⣠⢴⣯⠏⠀⠀⢀⣿⠀⠀⡇⣷⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠘⢿⣿⣷⣶⣤⡀⢸⣿⠟⠁
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣯⣽⠶⠛⠁⠀⣀⣠⣿⠏⠀⢰⡇⢹⡇⠀⠀⠈⣿⣿⡄⠀⠀⠀⠈⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣭⣤⣤⣤⣠⣶⣿⡿⠃⢀⣀⣾⠁⣼⣿⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⣿⣿⣧⣄⠈⣴⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⢟⣛⣡⣤⣶⣿⡿⠃⣀⣼⣿⡄⠠⠀⣾⣿⣿⣷⡀⣂⣼⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⡿⢛⣡⣾⣿⣿⣿⡏⢖⣼⣿⣿⣿⣿⣿⣽⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠈⢣⡄⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⡰⠁⠠
⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠈⠀⠀⡂⢀⠢⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠂⠀⠀⠁⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠑⠠⢐⠠⠂⢁⠠⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡤⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠔⡀⠀⠈⠀⠀⠀⡐⠀⠀⢀⠔⠁
⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠂⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠠⠀⠀⡀⠐⠀⠀⢀⠔⠁
⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠌⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠐⠠⠀⠑⠈⠀⢀⠔⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢎⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠐⠀⠈⠀⡠⠊⠀⠀⠀⠀⠀⠁⠐⠀⢀⠠⠐⠈
⠀⠀⠁⠂⢀⠀⠀⠀⠠⠀⠀⠁⢄⠀⠀⠀⠀⠡⡂⠀⠁⠀⠀⠁⠀⠘⠀⡄⠀⡈⠀⠀⢀⠇⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠘⢆⠠⠄⠀⠄⠠⠠⠄⠁⠠⠀⠀⣠⠃⠀⠀⠀⡠⠈⠀⠀⠀⠀⠂⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⢠⠄⣑⢄⠠⠀⠈⠁⠀⢀⠀⠁⠀⠀⠉⠀⠒⠤⢄⠀⠜⡢⠈⠀⠀⠠⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠐⠀⠀⠤⢀⠀⠀⠂⠀⠀⠀⠀⠂⢄⠈⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡢⡀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠤
⠀⠄⠀⠀⠀⠀⠈⠐⠠⠄⣈⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⢀⣀⠀⠀⠀⠐
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠂⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡄
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠠⠠⠤⠤⠠⠠⠤⠄⢄⢤⢠⢀⢠⢠⠠⣠⠀⡄⣤⣦⠧⠤⠤⠤⠤⠤⠤⠸⠠⠠⠤⠤⠤⠦⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠒⠒⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠈⠁
⢀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀
⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠂⠁⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⢠⠾⣗⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠫⢅⡀⢠⣞⣀⡀⣈⣢⣠⠼⢿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠐⠀⠀⠀⠈⠁⠈⢹⡍⠉⠡⣄⣀⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⣀⣀⣴⣄⣰⣶⣀⣠⣘⣷⣀⣄⣿⡿⠗⠛⡛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠞⠁⠀⠀⢀⠐⠀⠀⠩⢉⣉⣉⣥⡐⡀⣤⣶⣧⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣐⣆⣀⣸⣦⣵⡠⠄⣢⣿⣿⠿⠶⠶⣿⡿⠋⡾⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠤⠞⠋⠉⠀⠀⠀⠀⣷⠀⠀⠀⢀⣦⡀⡀⣽⠏⠠⢸⣇⣃⠈⠙⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣄⠰⣄⣹⣐⣀⣀⠽⠿⠧⣿⠇⡠⣰⣿⣟⠄⠀⠀⠄⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣈⠀⢠⠤⠞⠋⠉⠉⠉⠉⣯⢀⢰⡴⠊⠁⠀⣰⡟⠀⠢⠀⠀⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢡⣀⡀⠀⢠⣼⣧⠊⠀⡀⢡⣾⣿⣭⣉⠃⠀⠠⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢠⠀⣠⣯⡿⠶⠞⡿⠁⠀⠐⢡⣿⣻⣷⡤⠅⡉⠓⠲⠤⣀⡠⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠛⠉⠀⠀⢰⡟⠀⠀⠀⣾⡿⠿⠿⡏⠀⠀⠀⠀⢀⠤⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⣠⠖⣿⠀⠀⠀⠀⢹⡏⠛⠀⠀⠀⠀⠀⠀⠀⠹⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠀⣦⣿⡄⠀⠀⠀⣾⣿⣭⣄⠀⠀⠀⠀⠀⠐⠚⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡶⠛⣽⠃⠀⠐⢰⣿⠶⢖⡢⠍⢌⠝⠋⠄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⡇⠀⢀⣲⣿⣓⠻⠕⠌⠲⡰⠃⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣀⡗⣴⣻⠿⠿⠚⠭⠔⠒⢈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡏⢼⡿⠟⠋⣁⠴⠛⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⡖⠛⠛⠛⠳⢶⣦⡤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠊⠉⠀⠀⠀⠙⣧⠀⠀⠀⠀⠘⣿⠀⠀⠀⠈⠉⢳⣶⠶⢦⣄⡀
⠀⠀⠀⠀⠀⢀⣠⠎⠁⠀⠈⠻⣆⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢸⡏⠀⠀⠉⠻⣦⡀
⠀⠀⠀⢠⠞⠉⠹⣆⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⢸⣷⣤⣀
⠀⠀⢀⠿⣆⠀⠀⠹⣆⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⢠⡿⠀⠀⠀⠀⢀⡾⠋⠀⠈⠻⣦⡀
⠀⠀⣾⠀⠹⣆⠀⠀⢻⡆⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⠀⠀⠀⣼⡇⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠈⠻⣆
⠀⠀⢻⠀⠀⢻⡆⠀⠈⣿⡀⠀⠀⠀⠸⣷⠀⠀⠀⠀⣿⠀⠀⠀⢠⡇⠀⠀⢠⣿⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⣠⣿⣆
⠀⠀⢸⡆⠀⠀⢿⡀⠀⢹⣇⠀⠀⠀⠀⣿⡄⠀⠀⠀⡟⠀⠀⠀⣼⠃⠀⠀⣼⠇⠀⠀⢠⡟⠁⠀⠀⠀⠀⢀⣴⡿⠛⠉⠙⢦⡀
⠀⠀⠀⢷⠀⠀⠘⣧⠀⠈⣿⠀⠀⠀⠀⢹⡇⠀⠀⢰⡇⠀⠀⢰⡏⠀⠀⢰⡟⠀⠀⣠⡟⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠘⣧⠀⠀⠸⣇⠀⢻⡆⠀⠀⠀⢸⡇⠀⠀⣼⠀⠀⢀⡟⠀⠀⢠⡟⠀⠀⣰⡟⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠸⣆⠀⠀⢻⡄⢸⡇⠀⠀⠀⣾⠁⠀⢠⡇⠀⢀⡞⠀⠀⢠⡟⠀⠀⣰⡟⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⢀⣠⡴⠟⠛⢷⡀
⠀⠀⠀⠀⠀⠹⡆⠀⠈⣧⢸⡇⠀⠀⠀⡟⠀⠀⣾⠀⢀⡾⠁⠀⣠⠟⠀⠀⣴⡟⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⢸⡇⠀⠀⢸⡇⠀⢰⠇⠀⡾⠁⠀⣰⠏⠀⠀⣼⠏⠀⠀⣴⠏⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠸⣿⡇⠀⠀⣾⠀⠀⡟⠀⣼⠁⠀⣰⠏⠀⢀⣾⠏⠀⢀⡾⠁⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⢀⣠⣤⡶⠿⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣿⡇⠀⢀⡏⠀⣸⠁⣼⠃⢀⡼⠃⠀⢀⣾⠃⠀⣠⠟⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣤⡶⠟⠛⠉⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢀⣠⠾⣇⢻⡇⠀⢸⠇⢠⠏⣸⠃⢠⡞⠁⠀⢠⡿⠁⠀⣴⠋⠀⠀⣠⡾⠋⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⢀⣀⣤⣴⣾⠃
⠀⠀⠀⠀⠀⢴⠛⠁⠀⢸⣼⡇⠀⣿⠀⡞⣰⠃⣰⠏⠀⠀⣰⡟⠀⣠⡞⠁⠀⣠⡾⠋⠀⢀⡴⠚⠉⠀⢀⣀⣤⡶⠾⠛⠋⠉⠉⠀⣿
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⣿⣇⠀⡟⣸⢡⠏⡼⠃⠀⢀⣼⠋⢀⣼⠋⠀⢀⡴⠋⠀⣠⠞⠉⠀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⣀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⢹⣿⠀⣷⣏⡏⡼⠁⠀⣠⠟⠁⣠⡟⠁⢀⣴⠟⢁⡴⠊⢁⣤⠶⠛⠉⢀⣀⣠⣤⣴⠶⠾⠿⠛⠛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⣿⡆⣿⣿⣼⠁⢀⡾⠋⣠⡾⠋⢀⡴⠋⣠⡴⢋⡤⠞⣋⡤⠴⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢃⡴⢋⣤⠞⠉⣠⠶⢋⣤⣞⠥⣚⣵⣒⣉⣡⣤⣤⡤⠴⠶⠶⠶⠶⠚⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠞⣉⣤⠶⣋⣥⣾⣿⣭⠶⠟⣿⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⠟⡛⠋⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠦⣼⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⢤⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡔⠉⠉⠀⠀⠀⠀⠌⠀⢠⠉⠉⡳⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡏⠀⠃⠀⠀⠀⠀⠀⠄⠀⠠⠁⠀⡰⠁⢀⠊⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠁⠀⠐⠁⡰⠁⡠⠊⠀⡠⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⠀⠀⠊⠀⠊⠀⠠⠊⠀⢀⠼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠸⠈⡄⠀⠀⡇⢠⠃⠀⠀⠠⠁⡠⠀⠐⠁⠀⢀⠔⠁⠀⠄⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠁⠃⠀⠈⠀⠁⡞⠀⠀⡰⠁⠄⡠⢊⠔⠁⠄⠀⠄⠈⠀⠀⠀⠠⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⢠⠰⠀⠀⠀⠐⠀⠀⡐⢀⠊⠔⡀⠀⢐⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠊⠀⠠⠀⡄⠀⠀⡔⡠⠡⠂⠈⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⢠⡀⢰⠇⠀⠘⠐⠐⣁⢐⠕⢀⠄⠊⠀⠀⠀⠀⠀⡀⠤⠀⠂⠈⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡸⠃⡞⡀⡐⠈⢀⠔⠑⠡⠂⠠⠀⠈⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⢠⢠⢃⡏⣰⢂⡜⠁⠀⡀⠀⡀⠄⠂⠁⠀⠄⠐⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢀⡞⢾⡇⣸⡎⣼⡭⣡⠏⣀⠀⡠⠐⠉⠀⢀⡀⠤⠐⠊⠈⠉⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠸⡁⢸⣷⣿⢮⣾⡵⡫⢛⠕⣈⠤⠶⠐⠉⠁⣁⣀⠠⠤⠤⢀⣒⣀⣀⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⢾⡿⢈⢀⠴⠊⠁⠄⠐⢒⣈⣉⣁⣀⣄⣀⣀⡀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣕⡃⣁⡤⠥⠖⢚⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⣄⣠⠞⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣾⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣶⣾⣿⣆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠙⢿⣿⣿⣿⣦⠀⣰⣿⣿⣿⠿⢁⣠⣤⣶⣶⣶⣶⣶⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠋⠛⠛⠛⠻⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⠀⣡⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣿⡇⠀⠙⣿⣿⣿⣟⠻⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠃⢀⣿⣿⣿⠉⠀⢸⣿⣿⣏⣿⣷⠀⠀⠙⢿⣿⣿⡄⠀⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⢸⣿⣿⠃⣿⣿⠀⠀⠀⠀⠙⠟⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠋⠁⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡫⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠐⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢠⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⣠⠖⠚⠈⠉⠉⠉⠂⠳⡀⢅⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿
⠀⠀⠀⠀⠀⠀⠀⠤⠤⠌⠝⣡⡄⠰⢚⡋⠀⠋⡓⠆⣀⡉⠉⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢸
⠀⠀⠀⢀⠀⠠⠖⠋⠉⣰⡌⠋⠓⠀⠈⠁⠀⠀⠀⠀⠙⠛⢀⡀⠁⢆⠀⠀⠀⠀⢠⠀⠀⠀⠘⢄⡞⠉⠆
⠀⠀⢸⠀⣄⣀⣠⠐⣠⠈⠏⠀⢀⠀⠀⠐⠠⠄⠀⠀⢠⡴⠐⢃⠀⠀⠁⠀⠀⠀⠀⣆⠶⣸⠆⠀⠈⠀⠈⡀
⠀⠀⠀⢻⣿⡡⠃⠀⢿⠚⣤⠀⠀⠀⠉⠑⢦⣀⡦⠰⡄⠀⠖⠿⠀⠘⡀⠀⠀⠠⠚⡰⠃⡾
⠀⠀⠀⠀⣿⡅⠀⠀⢸⣷⡟⠆⠀⠂⠳⠀⢿⣆⣴⢸⠃⠀⠀⣠⣄⣠⡿⠀⠀⡀⠎⠀⠀⠀⠀⠀⢠⡐⡄⠰
⠀⠀⠀⠀⠘⠙⢂⣴⠁⠙⠛⣿⣷⢶⡶⢞⣿⣣⠷⠂⠠⠤⠀⠚⢻⠞⠁⠀⠀⠀⠀⠀⠀⣀⢀⢠⣾⣷⠟⠁
⠀⠀⠀⠀⠀⠀⢺⡗⠃⠀⠀⠈⠛⠛⠻⠿⠋⠁⣠⢤⠄⣠⠄⣀⡏⢀⣀⠀⣀⣠⡼⣥⣴⣼⣿⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⠢⢬⡀⠀⠈⣶⣦⠄⢈⠱⠛⠛⠒⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀⠒⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⣄⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⣻⠀⠀⠀⠀⣸⠇⠀⠀⠀⢠⡴⠚⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠠⠔⠃⠀⠀⢀⠴⠋⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡆⠀⠀⠀⠉⠉⠛⠛⠛⠶⠀⠀⠈⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠚⠛⠛⠛⠳⠀⢀⡤⠶⠛⠋⠉⠉⠉⠉⠙⠛⠷⣦⣀⠀⠘⠉⠀⢀⡴⠋⠀⠙⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⠀⠀⢠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠰⠋⢀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⠀⠀⣠⠞⠁⠀⠰⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡴⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠛⠒⠒⠒⠲⠶⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠚⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⣀⣤⣤⠤⠶⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⢛⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠦⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢


⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠠⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡤⠤⠤⠓⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠰⣀⣀⣤⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠄⡷⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢼⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⢸⠁⠀⢀⣀⣠⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣠⡤⠴⡟⠛⠉⠉⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⠉⠁⠀⠀⢰⠇⠀⠀⠀⠀⡁⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡾⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⣤⠔⠛⢲⠏⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣆⡠⠤⠔⢺⠉⠉⣀⣡⣥⡛⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠁⠒⠉⠹⡀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣚⣨⣤⣾⣿⣿⡿⠻⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠈⣛⢛⠛⢛⣻⣭⢛⣻⣷⠆⣟⣿⡍⢻⣿⣿⡟⠳⢶⣶⣷⣶⣋⣀
⠀⠀⠀⠈⠉⠀⠀⣄⣉⣉⣼⠯⣬⣿⣿⣞⣛⣯⣴⣾⣿⣿⠛⢋⣭⣶⠉⠨⣽⣋⣉⠛⠿⡿⠷⠾⢿⣿⡏⠁⠤
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠴⠶⠀⠽⠯⠍⠀⠐⠊⣉⣉⣁⡒⠁⠴⣟⡏⠀⠘⢶⣼⣷⠤⠒⠲⣿⣷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⠀⠀⢠⡄⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠘⣆⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠐⢆⠀⠈⠳⡀⠀⠀⠘⣆⠀⡄⢸⡇⡆⢰⠇⡤⠀⣠⠋⠀⠀⢀⡴⠆⠀⠀⢀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⠀⠀⠀⠑⢤⡀⠙⢄⠘⣆⠘⡄⡇⢸⠀⠃⡏⡼⢁⡴⢁⡔⢀⡴⠋⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⢠⡙⢮⠢⠣⡈⠂⠁⠀⢸⠀⠀⠐⢡⠎⡠⢋⠔⠋⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠀⢉⠲⢌⠢⠀⠀⢈⠀⠂⣀⣈⣈⠀⠐⢅⠈⠀⢁⡤⠞⢁⡠⠀⠀⣀⣠⠴⠖
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠈⠉⠙⠲⠤⣉⠂⠍⢢⠔⢁⠔⠉⠀⠀⠀⠈⠒⢄⠡⡒⠁⠐⢊⠡⠤⠒⠉⠁⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠒⠶⠦⠬⠥⣀⣀⡀⠂⢠⠇⠀⠀⠀⠀⠀⠀⠀⠈⡆⠠⠀⢈⣀⠀⠤⠴⠖⣒⠿⠥⠖⠚⠓⠋⠀⠀⠉⠉⠉⠁⠀⠈⠉⠁
⠀⣀⣀⣀⣀⣄⣤⠴⠒⠒⠒⠒⠒⠶⢤⡀⠀⠀⠒⠀⠀⠀⠉⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⡒⢀⣠⠼⠃
⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⡀⠀⠀⠈⠀⢣⣀⣤⣤⣄⣀⡤⠴⠚⠉⠉⠉⠉⠉⢠⡞⠁⣀⠴⠀⠐⠂⠖⠂⠀⠀⠀⠀⠀⢠⡄⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠙⠚⠫⣉⢀⣀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠤⠴⠚⢉⠰⠲⠁⢀⣀⠀⢀⡤⠴⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠒⠂⠠⠤⠄⢈⡓⠁⠐⠀⠓⡻⣲⣭⣀⠉⠉⠉⠉⠉⢩⠟⢁⠀⠀⠀⠀⠉⠀⠀⠈⠓⡂⢮⠖⠲⣤⠤⢤
⠀⠀⠐⠒⠀⠛⠃⠈⠃⠀⠐⠂⠈⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣰⡟⠉⡴⡀⢰⣐⣋⡂⠆⠀⠀⠐⢉⠀⠜⠅⠀⠐⠳⠶⠎⠡⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠚⣁⣀⣜⣫⡶⠛⠉⠙⠋⠁⠉⠉⠳⠶⠶⠶⠦⠖⠛⠒⠲⠦⠶⠶⠶⠶⠧⠿⢦
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡠⠤⠴⠶⠶⠚⠭⠍⠭⠽⡟⠉⠉⢰⡄⠒⠐⠒⠒⠋⠉⠒⠒⠊⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠰⠾⠋⠉⠉⠁⠀⠀⠀⠀⠉⠹⠦⢤⠀⠀⠀⠀⠐⠶⠞⠻⠭⠥⠥⠄⠠⠀⠀⠀⠀⠀⠀⠘⠛⠓⠒⠒⠒⠛⠋⠀⠀⠙⠛⠛⠛

⠀⠀⠀⠀⣀⢰⣤⡀⣠⣴⠀⡀⠀⠀⠀⠀⠀⠀⢐⣳⣶⡄⢀⣤⡤⠀⠀⠀⠐⠲⣶⣠⣶⣖⠀⠀⢀⣀⣀⣻⣆⠀⣀⣄⣀
⠀⠀⠀⠀⠘⢻⣿⣷⣿⣿⣿⣥⡀⠀⢀⠀⠀⣰⣯⡿⠛⣿⠿⣿⡻⣆⠀⠠⠾⢿⣿⣿⣿⡿⠷⠄⢴⣿⣿⠟⣯⢼⡿⠿⣿⠂
⠀⠀⠀⠀⠒⠛⡿⠁⠙⣿⣍⠁⠀⢠⣾⡿⢶⠿⣟⠣⣼⠃⠀⣸⠇⠋⠀⠀⠐⠛⠁⣿⠙⠀⠀⠀⠘⠹⡏⠀⡇⠈⢿⡆⠈
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠉⠀⠀⠈⠸⡇⠀⢧⠈⢰⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠃
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⠀⠀⠀⠀⠀⢠⣤⣤⡀⣠⣶⣖⣀⠀⠀⢀⣤⣶⣦⣀⣠⣴⡦⠀⠀⠀⠀⠀⡀⢠⣶⣦⠄
⠀⠀⠀⠀⣀⠀⣴⢠⣬⣿⣿⣶⣞⣀⡀⠐⣻⣿⣿⣿⡿⠿⣯⡅⠀⠀⣴⢿⣿⣿⣿⣿⣿⣷⡄⠀⢠⢶⣿⣿⣿⣿⣿⠯
⠀⠀⠀⠤⣿⣷⣿⠛⠛⡠⢻⣏⠛⠿⡄⠀⣟⠰⡏⠀⢆⠀⠀⠙⠀⠀⠀⢸⡟⣸⠃⢻⡿⠛⠀⠀⠰⠛⣿⠀⠱⡀⠈⠃
⠀⠀⠀⠸⠋⣿⠀⢳⡾⠁⢰⠟⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠈⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⠿⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⡛⠹⣦⡀⠈⠀⠀⣀⣠⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⢿⣿⠿⠲⠇⡆⠀⠀⠙⠓⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠠⣞⡿⠟⠛⢩⠟⠉⠀⠀⢼⡇⢸⡌⠻⣿⡶⣠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠙⠀⡑⢼⣿⡄⠈⠰⢽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢸⡇⠈⣿⣇⠀⠀⠈⠙⠉
⣀⣀⣀⣀⣀⣀⣀⣀⡼⠀⢀⣀⡀⣀⠘⣀⣈⢇⣀⣿⣷⠀⢀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀
⠉⠉⠉⠉⠉⠉⠙⠉⠇⠀⠺⠛⢋⠦⠉⠙⠷⠶⠇⠸⡿⠀⠈⠉⠉⠉⠛⠛⠛⠛⠟⠋⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣀⣀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠐
⠒⠠⠤⠤⠤⠤⠀⠀⠀⠀⡔⠈⠈⠉⠀⠀⠘⠓⠒⠀⠀⠀⠀⠀⣀⣀⣉⣘⡋⠢⠤⠤⠄⠀⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠓⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣦⠈
⠀⠀⠀⠠⡀
⠀⠀⠉⠀⠴⠦⠤⠲⠒⠐⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⢶⡟⠉⠉⠉⠛⣷⠖⠒⠶⢤⣄⡀
⠀⠀⠀⠀⠀⢀⡤⠒⠛⢿⡁⠀⠀⠀⠀⢻⡄⠀⠀⠀⢹⡀⠀⠀⠀⠈⣿⠛⠛⢦⣄
⠀⠀⠀⣠⠖⢿⡀⠀⠀⠀⢻⡄⠀⠀⠀⠈⣧⠀⠀⠀⠈⣇⠀⠀⠀⢰⡇⠀⠀⠀⠙⣧⣀
⠀⠀⣰⣇⠀⠀⢳⡀⠀⠀⠈⢿⡄⠀⠀⠀⢸⡄⠀⠀⠀⣿⠀⠀⠀⣼⠃⠀⠀⠀⣠⠟⠉⠙⢦⡀
⠀⠀⡇⠘⣆⠀⠈⣷⠀⠀⠀⠘⣿⠀⠀⠀⠘⡇⠀⠀⠀⣿⠀⠀⢠⡟⠀⠀⠀⣰⠏⠀⠀⠀⠀⠙⢦
⠀⠀⡇⠀⠸⣆⠀⠸⣇⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⢀⡏⠀⠀⣸⠃⠀⠀⣴⠏⠀⠀⠀⠀⠀⣠⣾⣧
⠀⠀⢻⠀⠀⢹⡄⠀⢿⠀⠀⠀⠈⣷⠀⠀⢰⡇⠀⠀⣼⠁⠀⢠⡟⠀⠀⣸⠃⠀⠀⠀⢀⣤⠞⠋⠀⠀⠳⡄
⠀⠀⠈⣇⠀⠀⢷⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⠁⠀⢠⠇⠀⢀⡞⠀⠀⣼⠃⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠘⣆⠀⠘⣇⠀⣧⠀⠀⠀⡟⠀⢀⡏⠀⢠⠏⠀⢀⡾⠁⠀⣼⠃⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⣠⡴⠿⣆
⠀⠀⠀⠀⠹⡄⠀⢸⡀⣿⠀⠀⢸⠇⠀⣸⠁⢀⡎⠀⢀⡞⠁⢀⣾⠃⠀⢀⡼⠃⠀⠀⠀⢀⣠⡶⠋⠁⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢹⡄⠀⡇⣿⠀⠀⣼⠀⢠⡏⢀⡞⠀⢠⡟⠀⢀⡾⠁⠀⣰⠋⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⢳⡀⢻⣿⠀⠀⡏⠀⡼⢀⡞⠀⣠⠏⠀⢠⡿⠁⢀⡼⠁⠀⠀⣠⡾⠋⠀⠀⠀⢀⣠⣤⠶⠛⠛⢻
⠀⠀⠀⠀⠀⠀⢀⣧⢸⣿⠀⢸⠃⢰⠃⡜⠀⣰⠃⠀⣠⡟⠀⣠⠟⠀⠀⣠⡾⠋⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⢀⣼
⠀⠀⠀⠀⢠⡴⠋⠉⣞⣿⠀⣾⢀⡏⡼⢀⡼⠁⠀⣰⠏⢀⡴⠋⠀⣠⡾⠋⠀⣠⠴⠋⠁⠀⣀⣠⡤⠶⠶⠛⢻⡇
⠀⠀⠀⠀⠘⢆⠀⠀⢹⣿⠀⡟⡸⡸⢡⠞⠀⢀⡼⠃⣠⠞⠁⢀⡴⠋⢀⡴⠋⠁⣀⡤⠶⠛⠉⠁⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠳⣄⠸⣿⠀⣷⣷⢣⠏⠀⣠⠟⢁⡼⠋⢀⡴⠋⣠⠖⢁⡤⠶⠋⠁⣀⣠⣤⠴⠶⠶⠿⠛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⣇⣿⣯⠏⢀⡞⢁⡴⠋⢀⡴⢋⡤⢞⡥⢚⡩⠴⠒⠋⠉⠉⠀⠀⠀⣀⣀⣠⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⣴⣫⠖⢋⡠⠖⣩⣴⢿⣪⣷⡯⠥⠶⠶⠒⠚⠛⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣭⣴⣚⣭⡶⠿⠿⠛⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠢⠤⣄⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠿⢿⢻⠿⡿⢻⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠃⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⠉⠙⢻⣿⣿⣿⡏⠙⠟⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⢿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠿⠽⠿⠛⠿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣸⠟⣿⡿⠋⠘⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠾⠃⠀⠀⠀⠀⠀⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣬⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⠉⠉⢀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣧⣬⣜⣓⠤⡦⠶⠶⠤⣄⣚⣶⠈⠹⠹
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡤⠈⠙⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣷⣦⣄⣀⡀
⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⡿⣶⣶⣿⣿⣿⠿⠿⠿⠿⣯⣍⠫⠭⠍⠹⠯⠽⠿⠿⠿⠿⠛⠟⠶⠶⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢢⣿⣿⣿⣦⡠⠤⠒⠀⠀⢀⣀⣀
⠰⠶⠴⠤⠤⠤⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠨⣿⢿⣿⣶⡖⠒⠒⠚⠂⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢐⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠺⢿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠂⠀⠀⠉⠁⠀⠀⠨⠥⠀⠀⢀⢀⣈⣉
⠐⠛⠋⠉⠉⠉⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠐⠃⠙⠛⠛⠛
⢶⣶⡶⠶⢶⠦⢤⣤⣤⡤⠤⠤⠤⠤⠤⢤⣤⣀⣀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⢠⣤⣤⣄⡀⢄⣀⣐⣲⢶⣶⣖⡀⢰⣶⣶⣶⣶⡶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⢀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⣿⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⠿⠛⣛⣛⠻⠿⢿⣿⣽⣿⣿⣭⣿⡂⠀⠈⠉⠻⢿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠿⠿⠿⠿⠻⠟⠛⠋⠁⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣀⠀⠙⠋⡿⠟⠿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣤⠴⢶⣦⣶⣄⣠⣤⣝⣻⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣯⣥⣤⣀⠘⠾⣽⣬⣤⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠁⠀⠈⠐⠉⠙⠛⣿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣾⣯⣭⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠶⣶⣭⣭⣟⣻⣯⣵⣶⣤⣻⣝⢿⣿⣿⣿⣿⡻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠐⠒⠒⠒⠚⠲⠚⣿⣶⣦⣽⠷⢶⣤⡈⠙⢽⣿⣿⣿⣿⣿⢟⣉⠉⠀⢈⡛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣾⣋⣉⣡⣾⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣚⣁⣀⡀⣾⣿⣦⣌⣉⣤⣤⣤⣀⣀⡉⢿⣿⣿⣿⣿⣷⣦⠤⠭⠹⢿⣿⣿⣯⣤⣤⣌⡛⠿⢿⣿⣾⣿⣿⣥⣤⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠛⠛⠋⠋⠀⠙⠛⠉⠻⡿⢿⣿⣿⣿⣿⣶⠤⠤⠀⠀⡤⠿⠿⠿⣿⣿⣿⣿⣷⣶⣶⣾⣭⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⢦⣶⣶⡿⣿⣿⣶⣤⣮⣥⣤⣤⣀⠀⠀⠀⢠⣤⣶⣶⣦⣬⣤⣤⣤⣭⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠶⠶⠶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⣉⠤⠔⠒⠒⠒⠐⠒⠒⠀⠈⢉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢋⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢁⠔⠉⠀⠔⠀⠀⣀⠤⠒⠊⠉⠉⠀⠀⠐⠂⠤⢄⠀⠀⠤⡁⢭⡷⣚⣛⣓⣒⡢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⡴⠋⡄⠀⠀⡠⠔⠉⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⢀⡀⠀⠀⢄⣰⠟⢉⡁⠤⠤⠀⠈⠀⠨⣝⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⣡⠊⢀⠴⠋⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡿⢊⣡⠤⠂⠀⠀⠀⠀⠈⢐⣿⠟⠛⠻⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⣵⣻⠞⢀⡴⠋⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⡗⡉⠀⠀⠀⠀⠀⠉⠀⠤⣸⡟⠀⠀⠀⢨⣿⢌⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣿⡿⠥⠾⠯⣴⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢺⡏⣠⠄⠀⠀⠀⠀⠀⠀⠀⣺⣗⠀⠀⠀⠸⣿⣤⣿⡟⠁
⠀⠀⠀⢀⣀⡤⠔⠋⢉⣉⣀⣀⡀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢻⣦⣤⣠⡼⢟⡿⠁
⠀⠀⢰⠋⠀⠀⣴⢾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣤⣄⠑⠄⡀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠄⣪⣿⣿⡿⠖⠋
⠀⠀⣿⠀⠀⠀⡇⠀⠈⠙⢻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠘⣷⡖⠂⠀⣀⡠⠄⢊⠤⣪⢟⣿⡟⠁
⠀⠀⢸⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠚⠟⢽⣿⢙⣿⣿⣿⣿⣿⣷⣤⣀⢐⡂⠀⠀⠀⠤⠄⠒⠊⣁⠀⠔⢋⣡⠿⣟⣩⠥⢒⣋⠥⠊⣑⡿⠋
⠀⠀⠀⢷⡀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠈⠸⢻⣏⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⡁⠠⠔⠚⣉⡠⠖⣫⠿⣿⣭⡴⠶⠛⠁
⠀⠀⠀⠈⠳⡄⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⣻⠋⠑⣫⣿⣶⣀⣀⠩⠤⠄⠀⢚⣉⣠⠴⣚⣥⣾⡿⠋
⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠉⠓⠲⠤⠤⠤⠶⠾⠟⢛⣩⣴⡋⠁⢐⣈⣵⣾⡿⠿⢿⣷⣌⣠⣥⣬⣤⣶⣿⡽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⣤⣤⣤⣤⣶⣶⣾⣭⣩⣀⣈⣤⣽⠿⠛⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉