Vitamin c Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠋⢻⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡦⠤⠶⣏⠛⢦
⠀⠀⠀⠀⠀⠀⠀⣠⠊⢰⢧⡀⠀⠘⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⢠⠗⠺⢅⣀⣠⡞⠋⠙⢯⠙⢦
⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⠀⠉⠢⡀⣡⣀⠞⠈⢧⠀⠀⠀⠀⠀⢻⡀⠀⠈⠀⠀⠈⠀⠀⠈⠉⠻⣄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠦⠤⠀⠸⡇⠙⡖⠒⠺⡆⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⢄⠀⣠⡇⣷
⠀⠀⠀⠀⠀⠀⢇⠀⡇⠈⣇⠀⠀⡰⠛⢶⠓⢄⠀⡇⠀⠀⠀⠀⠀⠉⡟⠠⠦⠂⠀⠀⠀⢈⣏⠁⢸⡁
⠀⠀⠀⠀⠀⠀⠘⣄⠘⠄⠘⢦⡜⠁⠀⠈⡄⠀⠑⡇⠀⠀⠀⠀⣠⠜⠁⡀⠀⠶⠅⠀⠀⠈⠀⢱⠋⡷
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠈⠳⣄⠀⠀⢳⢀⡼⠁⠀⠀⢰⠙⠣⡀⠈⣡⠔⠲⡆⠀⠀⣀⣠⠞⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠤⠿⠓⠚⠉⠀⠀⠀⠀⠈⠳⣄⣹⠞⠁⠀⠀⠈⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⢀⡔⠋⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠉⠓⢌⠙⠢⡄⠀⠀⠀⠘⡄⠑⡶⠚⠢⣄⠀⠀⣈⠳⣄
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⣠⠤⡄⠀⠀⢳⠀⠘⣆⠀⠀⠀⠈⣺⠁⠀⠀⠀⠑⠦⡈⠁⠈⠳⡄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠏⠀⠈⠁⠀⠀⠈⡇⠀⢸⠀⠀⠀⡼⠉⠢⡀⠑⢤⡀⠀⠈⠢⣄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢿⡀⢀⡀⠀⠀⠀⢠⠇⠀⣸⠀⠀⠀⠳⡀⠀⢈⠓⢄⡀⠀⠀⠀⠈⠳⣄⡼
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠉⠉⠀⠀⠀⣠⠎⠀⡰⠃⠀⠀⠀⠀⠈⠲⢌⡑⠂⠈⠑⠢⢤⣀⡀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⣤⣤⣞⡥⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⢄⣀⡠⠏⠁

⠀⠀⠀⠀⢀⣠⣴⠖⠛⠛⣟⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣦⡤⠤⣶⡛⠛⠓⢦
⠀⠀⢀⠴⠋⣼⠁⠀⠀⠀⢹⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣰⠋⠀⠀⠀⢹⡶⠶⠾⣷⠶⢦⣄
⠀⣰⠃⠀⢸⡏⠳⣄⠀⠀⠈⡇⠀⠀⢠⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⢱⠴⠒⠲⢧⡀⠀⠀⠈⣧⣀⣹⡆
⢰⠃⠀⠀⢸⠀⠀⠈⠑⢄⠀⣹⡀⣰⠋⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠙⢧⣀
⡟⠀⠀⠀⢸⣆⣠⣤⣤⣤⣽⡃⠈⢣⠤⠤⠤⢿⡀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈
⡇⠀⢰⠀⠈⣧⠀⠀⠀⠀⢘⣧⣀⣸⡀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈⢧⣀⡇⠀⡆⠀⡀⠀⠀⠀⠀⠈⢳⡤⠞⠙⣦
⢳⠀⠸⡆⠀⠸⡆⠀⠀⢠⠎⠀⠉⡇⠈⠲⣄⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠟⠋⠀⣀⠀⠀⠀⠀⣸⢤⡀⠀⣽
⠈⢆⠀⠹⡄⠀⠹⣆⣰⠃⠀⠀⠀⢸⡀⠀⠈⢳⡇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠠⠾⠥⠄⠀⠀⠀⠁⠀⠹⡟⠁
⠀⠈⢣⡀⠈⠀⠀⠘⢣⡀⠀⠀⠀⠈⣇⠀⠀⣼⠁⠀⠀⠀⢠⠴⢾⡉⠀⠀⠴⠋⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⣰⣧⠾
⠀⠀⠀⠉⠲⢄⣀⠀⠀⠙⠶⣤⣀⣀⣹⣤⠞⠁⠀⠀⠀⠀⠘⣆⠀⠈⢣⡀⣠⠞⠉⠀⠀⠳⣄⣀⣀⡴⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡷⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⢤⣤⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠳⣄⠀⠀⠀⡞⠁⠀⠀⠈⠙⢦⡀
⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⠙⢦⡀⠀⠀⠀⠀⠀⠱⡀⠈⢳⡶⠛⠛⢦⣀⠀⠀⢠⣀⠙⠢⡀
⠀⡔⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⢷⡀⠀⠙⣆⠀⠀⠀⠀⠀⠙⢦⡞⠀⠀⠀⠀⠈⠐⢤⡀⠈⠃⠀⠙⢦⡀
⡼⠀⠀⠀⠀⠀⠀⣠⠞⠉⢹⡇⠀⠀⠀⠈⣷⠀⠀⠘⡆⠀⠀⠀⠀⢀⡼⣇⠀⠀⢤⡀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠙⣆
⡇⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡧⠀⠀⠀⠀⡟⠀⠈⠳⣄⠀⠙⠲⣄⠀⠀⠀⠈⠳⣄⠀⠀⠘
⢧⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⠀⠀⢀⡇⠀⠀⠀⠀⢳⡀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠘⣆⠀⠀⠀⠀⠙⠒⠚⠋⠀⠀⠀⠀⠀⣰⠃⠀⢀⡼⠁⠀⠀⠀⠀⠀⠙⢦⣀⠘⠲⢄⠈⠙⠢⢤⣀⠀⠀⠀⠀⠀⢹
⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠈⠙⠒⠦⣤⣤⠞
⠀⠀⠀⠈⠓⠦⠤⣀⣀⣠⣤⣴⣞⣥⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠀⣀⣀⡤⠞
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⢉⡙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠦⡄⣼⠁⣰⢫⡭⠭⠇⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠋⣧⠀⣇⢿⣀⣀⡀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡈⠳⠬⠵⠃⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠉⠉⠉⠉⠛⠒⠦⣝⡒⠶⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣀⡤⠴⠖⠒⠒⠒⠶⠤⣄⡀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠈⠳⡄⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⡆⡆⣶⢰⠀⠀⡞⠁⢀⡴⠃⣠⢴⣲⣿⣷⣲⠦⣀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠙⣆⠀⠀⢀⡏⢸
⠀⠀⠀⠀⠀⠀⡇⡇⣿⢸⠀⡾⠀⢀⡞⢀⣞⡵⢏⡀⢸⡇⢈⡽⢮⢦⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠸⡆⠀⣼⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠁⠉⢸⢸⠇⠀⣸⠀⣼⣼⣀⣀⣹⡾⢷⣋⣀⡼⣛⣿⣿⣟⣲⢤⡀⠀⠀⢹⡀⠀⢷⢀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠙⡖⢲⠋⢸⠀⠀⡟⠀⢹⣻⡀⢀⡼⢳⡟⣼⣫⠞⠙⣆⠀⡾⠉⠳⡽⡄⠀⢸⡇⠀⢸⢸⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⠀⠀⣷⠀⠈⠳⣳⢏⣀⢸⣇⣧⡟⠓⠶⣼⠾⡥⠖⠋⢹⢻⠀⢸⡇⠀⣸⠈⠛⣷⢸
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠘⡇⠀⠸⡄⠀⠀⠈⠓⠿⠭⠽⠏⢧⠶⠚⣹⠻⡏⠓⠶⡾⡿⠀⡼⠀⢀⡟⠀⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠹⡄⠀⠹⡄⠀⠀⠀⠀⠀⠀⠘⢮⡶⣤⣏⣀⣹⣤⢞⡽⢁⡼⠁⠀⡼⠁⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⢰⡇⢸⠀⠀⠀⠹⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⠓⠿⠿⠷⠚⠉⣠⠞⠁⢀⡼⠁⠀⠀⢠⡇⢸
⠀⠀⠀⠀⠀⠀⠘⢧⡼⠀⠀⠀⠀⠈⠣⣄⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⢀⡤⠋⠀⠀⠀⠀⠘⠧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠉⠉⠛⠛⠋⠉⠁⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠶⠶⠶⠒⠋⠉




⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠧⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⢠⠄⢀⠤⢀⢀⡀⢤⠄⢀⠀⢀⠄⡀⡀⠀⡠⠄⠀⢀⠄⠠⣤⠀⡠⣀⢀⠤⡀⢀⢀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠸⠂⢸⠀⢨⢸⡇⢸⢀⠎⢇⢸⠒⡅⡇⠀⡗⠂⠀⠈⢢⠀⡇⠀⡇⢎⢯⠀⡸⢸⠣⡀⡗
⣶⣶⠶⠶⠶⠶⣶⣾⣿⣾⣿⣷⣾⣷⣿⣾⣶⣾⣾⣿⣶⣿⣿⣿⣿⣶⣿⣿⣶⣿⣾⣷⣾⣾⣿⣷⣾⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⣧⡏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣃⡙⠋⠀⠀⠀⠀⠀⢰⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠸⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠍⠀⠀⠀⠀⠀⢸⠉⡇
⣧⣼⢰⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡴⠆⠈⠉⠁⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⠓
⠃⠘⠈⠓⠃⠰⣤⣀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠈⠉⠛⠲⠤⣄⣀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣤⠴⠖⢛⣉⣥⠄⠙⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠤⠤⠤⠤⠤⠤⠤⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠛⠛⠛⠛⠛⠛⠛⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⢼⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢲⣰⣄⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠞⠙⠃⠓





⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⢰⡄⢀⡖⢦⢠⡖⠦⢠⠶⣆⢰⠶⡄⢰⢦⡄⣤⢠⡖⠦⠀⠀⣶⠀⢠⠶⡄⣤⢠⡶⣤
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⡟⣧⠈⠧⣄⢸⡇⠀⢸⠀⣿⢸⣤⠇⢸⢴⡃⣿⢸⡇⠀⠀⢰⠟⡇⢸⠀⠀⣿⢸⡇⢸
⠀⠀⠀⠀⠀⢸⣅⡀⠀⠀⠀⢰⠏⢹⠐⣆⡽⠸⣇⡴⠸⣀⡟⢸⠘⡇⢸⣠⠇⠿⠸⣇⡤⠀⢸⠉⢧⢸⣀⠆⣿⠸⣇⡾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢲⠲⣞⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠤⣀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢿⡩⠞⠁⠀⠀⠹⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⣀⡠⠞⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠈⠉⡙⡛⣛⣉⡁⠀⠀⠀⠀⠀⠀⠀⠓⠒⠀⠀⠐⠋⠁
⠀⠀⢀⠔⠒⠒⠷⠒⠒⠒⢦⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⠀⢠⡄
⠀⢀⡇⠀⠀⠈⠙⠁⠀⠀⠀⢱⠰⠂⠀⢲⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⢢⣀⣡⡀
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆⢀⢸⡦⡎⠐⠲⢉⠂⢸⠃⠉⠘⡃⡝⣉⠀⠀⠰⠀⠀⠀⠀⠈⠄
⠀⠀⢣⠀⢄⡠⠀⠀⠄⠀⠀⡎⠀⠘⡈⢰⠑⠈⢸⢰⡏⡀⠀⣎⠾⢀⠇⡇⠑⢆⠀⠸⠀⠀⠀⠀⡈
⠀⠀⠀⢣⡀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠳⠂⠂⠀⠂⠉⠈⠙⠈⠈⠀⠉⠁⠉⠀⠈⠀⠀⢢⠀⡠⠊
⠀⠀⠀⠀⠈⡁⠉⢉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⡉⡉⠑⡄⠀⠀⠀⠀⠀⠤⠀⡄⠤⠄⡄
⠀⠀⠀⠀⠀⠈⠉⠁⡁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠰⡇⡎⠀⠈⠉⠀⠀⠀⠀⢠⢀⢠⡀
⠀⠀⠀⠀⡰⠒⠊⣉⠀⠀⠘⠑⠲⡀⠀⠀⠀⠀⠀⡇⢣⡀⢀⡖⢢⠀⠀⠀⠴⢦⡼⣀⠡⠡⡀
⠀⠀⠀⢨⢃⣀⣀⡀⠑⠆⠀⠀⠀⠸⠀⢂⠀⠀⠀⠘⠦⣉⠉⣀⠜⠀⠀⠀⢑⠯⣈⣻⠫⠰⠡⢦
⠀⠀⠀⡌⠉⠈⡘⠁⠀⠀⠀⠀⡠⠂⡀⠀⢅⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⡯⣶⢲⢿⠛⣧⡶⠒⠸⢙⠁
⠀⠀⢈⡆⠀⡄⠣⡀⠄⠀⡀⠊⡀⣈⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣨⠒⣿⣄⠙⡛⢆⢉⡃
⠀⠀⠀⡗⠀⠈⠀⠀⠒⠈⢀⡠⡍⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡯⣴⢋⣷⠒
⠀⠀⠀⠈⠉⠛⠑⠒⠓⢮⠙⣤⡀⢹⡀⠀⠀⠀⠀⠀⠀⣰⢟⣿⡵⢋⣴⠟⠁
⠀⠀⠀⠀⡤⠀⠀⠀⠠⠀⢧⠈⠃⠀⠑⡄⠀⠀⠀⠀⠨⣀⣺⢁⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠊⠀⠀⠀⠀⠀⠀⠻⠘⠛⠁⠀⠀⠈⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⠛⠛⠛⠛⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⣀⣀⣤⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⣀⣠⣤⣶⣾⣿⠿⠟⠛⠉⠉⣹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⢀⣀⣤⣴⣶⣿⡿⠿⠛⠋⠉⠀⣀⣠⣤⣴⣶⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⠿⢿⣿⣿⣏⢀⣀⣤⣤⣶⣾⡿⠿⠟⠛⠉⠁⣀⣠⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⣀⡀⠈⢻⣿⡿⠟⠛⠋⠉⢀⣀⣠⣤⣶⣾⣿⠿⠟⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢻⣿⣶⣿⣿⣧⣤⣴⣶⣿⡿⠿⠛⠋⠉⠀⣀⣠⣤⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠈⣿⡏⠀⢹⣿⡟⠉⠉⢀⣀⣤⣤⣶⣾⡿⠿⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⠈⠁⣠⣾⣿⣿⣶⣿⠿⠟⠛⠋⠉⠀⣀⣠⣤⣶⣾⠟⠁⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⠃⠀⣴⠟⢿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠋⠉⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣷⣤⡀⠈⠙⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⣿⣿⣿⣷⣦⣀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⡿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠈⠛⠿⠿⠿⠟⠋



⣿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣴⣿⣦⣤⣾⣦⣤⣾⣧⣤⣾⣷⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄⠀⣶⣶⣶⣶⣶⣶⠄⠙⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⠿⠿⠛⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⠿⠟⠛⠉⠁⣀⣀⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄⢀⣀⣤⣴⣶⣾⡿⠿⠛⠋⠉⢀⣀⣤⣤⣶⣾⡿⠿⠛⠃⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠟⠛⠉⠉⠀⠀⣤⣴⣶⣿⠿⠟⠛⠋⠉⠀⢀⣤⣤⡄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⣠⣶⣶⣶⡄⠀⠉⠉⠁⡀⠀⢠⣴⣶⡷⠀⠈⠛⠉⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣏⠀⠙⠟⠀⠀⢾⡿⠿⠀⠀⠉⠁⢀⡀⠀⢰⣶⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢹⣿⡄⠀⣠⣤⠀⠀⣀⡀⠀⣶⡦⠀⠙⠛⠀⠀⢀⣀⣠⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢿⣷⣤⣿⡟⠀⠀⠛⠃⠀⠀⣀⣀⣤⣴⣶⣿⠿⠿⠛⢋⣽⣿⣿⡿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠉⠉⠉⢀⣀⣠⣤⣶⣾⡿⠿⠟⠛⠉⠁⠀⠀⠀⣰⣿⠟⣁⠀⠀⠀⠈⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣀⣤⣴⣶⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠘⠿⣷⣦⣄⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠈⠙⠿⣿⡆⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣄⠀⠀⠀⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠿⠿⠛⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢸⠔⠚⠁⠀⠐⠫⣉⠏⠀⠀⠐⢤⡀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠀⠀⠒⠁⠀⠀⠤⡉⠂⠀⠀⠠⡀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣶⣄⠈⠃⠀⢄⣀⣀⡤⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠁⠀⠀⠉⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠳⢦⡀⠀⠀⠀⠀⣯⣤⣀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣠⣄⠛⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠻⠶⠶⠟⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⣴⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⣀⣤⣤⡤⠶⠖⠛⢻⣄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣼⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠁⢠⣤⡤⠶⠆⠀⠀⠰⠶⢤⣤⡄⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⣠⠀⠀⣀⣀⣠⠄⠀⠀⢠⣄⣀⣀⠀⢠⡍⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣸⡀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠠⢦⠶⠀⠀⠀⠀⢀⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠹⣦⡀⠀⢀⣀⣀⣀⡀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⣧⠀⢸⡟⢦⣈⠉⠙⠻⣿⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⣸⠃⠀⠙⠳⠶⠶⠛⠙⣯⡉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠉⠳⣆⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⠛⠉⠉⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠳⠶⠋⠉⠙⠛⠓⢶⣄
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠋⠩⠉⠉⠙⠻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣤⡀⢸⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡇⢸⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣙⠛⠶⠶⠶⠶⠶⠛⣩⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡇⢸⠀⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⡇⢸⠀⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⣸⡇⢸⣿⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀⡾⠉⣠⣼⣿⣧⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣾⠀⣼⣿⣿⣿⣿⣿⣇⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢿⠀⢻⣿⣿⣿⣿⣿⡏⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢷⣀⠙⠛⠿⠛⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠉⠓⠲⠶⠖⠛⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣻⣛⣛⣿⣻⣽⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣭⣭⣭⣭⣿⣯⣭⣯⣽⣍⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡆⠀⠀⠒⠀⠈⠉⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠂⠤⠐⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠠⠒⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠚⢀⠀⠁⠀⠈⡃⠒⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⢀⠓⠄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠛⢒⣄⠀⠀⠀⠀⠀⠐⠒⠢⠤⠔⠀⠀⠑⠰⠄⠄
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢨⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡌⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⡟⠀⠀⠀⠀⠀⠀⢀⢀⡠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠰⠁⠈⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂
⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⠔⠀⠀⠀⠀⠀⢉⡀⠂⠠⠤⠤⠤⠀⠲⠂⠉⠀⠀⠀⠒⠒⠲⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠠⠄⠤⠄⠀⠉⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠠⠤⠤⠀⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠁⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣟⣛⣻⣛⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣯⣭⣿⣿⣽⣿⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠒⠀⠀⠔⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠰⠁⠀⠀⠀⠀⠀⠀⠈⠰⠒⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⠤⠀⠀⠒⠀⠀⠐⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢠⠆⠀⠀⠀⣠⣾⠇⢰⣴⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡤⡀⠀⠸⠀⠀⠀⠚⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡌⠆⢀⠁⠀⠀⠀⢀⣠⠀⢰⠴
⠀⠀⠀⣀⡤⠤⠤⠤⢀⡀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠝⠋⠀⠀⠢⡀⠀⠀⠀⠀⠀⡀⠤⠐⣠⡙⠆
⡞⠙⠛⠁⠀⠀⠀⠀⠀⠈⢩⠒⠂⠀⠀⠀⠀⠀⠀⠸⣇⡴⢷⡴⠃⠀⢠⢐⣠⠥⠔⠂⠈⠭⠐⠁⠀⠀⠈
⠘⠦⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢼⣶⠾⠏⠃⠁⠈⠁
⠺⡄⠀⠀⠀⠀⠀⠀⢐⣺⣿⡇⠀⢀⣀⣀⠀⠀⠀⠋⠁⠰⠆⢠⠊
⠼⠁⠀⠀⠀⠀⠀⠀⠶⠟⠏⠀⠀⠀⠀⠈⠑⢦⡀⠀⢀⣀⡤⠾⡀
⢠⠀⠀⠄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢆⢀⡤⠼⠖⠒⠶⠤⠤⣀⡀
⢸⠆⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢢⡀⠀⠀⠀⠀⠳⣴⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣀
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⡴⠚⠂⠀⢀⡀⠀⠀⠀⠈⠙⠓⠶⢤⣄⣀
⠳⠀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⢤⣄⣀
⠠⡄⠙⠀⠀⠀⠀⠀⠀⠴⢺⣇⠀⠀⢀⡼⠃⠈⠓⠢⠤⢤⣤⡤⠶⠛⠉⠒⢈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⣄⡀
⠀⢳⠈⠆⠀⠀⠀⠀⢀⣴⣿⣿⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦
⠀⠀⠒⠒⠒⠂⠈⠉⠀⠀⡀⠝⠋⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠶⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣶⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣐⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣀⣀⣀⣐⣒⣒⣒⣶⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣒⣚⣉⣁⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⠴⠶⠚⠻⣦⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢧⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡾⠃⢀⣤⣤⠶⠆⠀⠀⠰⠶⢤⣤⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢡⡀⠀⣀⣀⣠⡄⠀⠀⠠⣄⣀⣀⠀⠀⣌⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣸⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⢰⣇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠀⢦⡴⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢧⡀⠀⠀⣀⣀⣀⡀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣷⠀⢸⡟⢦⣄⠉⠉⠻⣿⣷⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⢸⡇⠀⠉⠳⠦⠴⠞⠙⢷⡉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠈⠛⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠋⠉⠁⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠶⠟⠉⠙⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⡐⠀⠀⠀⠐⡃⠄⠀⠀⠀⠠⢰⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠘⠀⠀⠀⢀⠘⠐⠀⠀⠀⠀⠀⠠⡑⠀⠒⡐⢊⠄⠀⠀⠀⠀⠈⠉⠌⠈⠁⡁⢁
⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠩⠐⠁⠀⠀⠀⠀⠀⠀⠀⡈⠑
⠀⠀⠀⠀⢀⡈⠁⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠴⠠⠤⠔⠆⠂⠀⠀⠀⠀⠀⠀⡄⠁
⠀⠀⠀⠀⡈⢂⠁⠀⠀⠈⡂⠀⠀⠀⠀⠀⢘⣐⣐⣒⣒⣒⡃⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠘⠈
⠀⠀⠀⠀⢁⠄⡀⠀⠀⢀⠥⠀⠀⠀⠀⠀⢨⠤⠤⠤⠤⠤⠅⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⢀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠂⡱⠒⠒⠲⢎⠄⠀⠀⠀⠀⠀⠈⠐⠀⠀⡄
⠀⠀⠀⠀⠀⢀⠄⠊⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⣩⠰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁
⠀⠀⠀⠀⢠⠂⠄⠀⠈⢠⠂⠀⠀⠀⠀⠀⠔⠴⠤⠤⠤⠌⠂⠀⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡖⠠⠀⠀⠀⠀⡔⠂⠀⠀⠀⠀⠘⠒⠒⠒⠒⠚⠂⠀⠀⠀⠀⣐⠈⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠈




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡄⠀⠀⢠⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣤⣿⣿⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⠿⣿⣿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⢿⣷⣄⣠⣾⡿⠟⠋⠉⠀⠀⠀⠻⠛⠀⠀⠀⠉⠙⠻⢿⣷⣄⣠⣾⡿⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣏⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⣹⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠙⠋⠀⠀⠀⠀⠀⢠⣿⡟⠛⢻⣿⡄⠀⠀⠀⠀⠙⠋⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⡀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢀⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⡟⠛⣿⣧⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⠉⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠻⣿⣾⡿⠃⠀⠀⠀⣼⣿⠛⠉⠉⠻⣿⣦⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠉⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣀⣀⣠⣿⡟⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠋⠀⣠⣄⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣾⡿⠋⠙⢿⣷⣦⣄⡀⠀⠀⠀⣴⣦⠀⠀⠀⣀⣠⣴⣾⡿⠋⠙⢿⣷⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠛⣿⣿⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣿⣿⣶⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⣿⣿⠛⠛⠛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠃⠀⠀⠘⢿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠙⢦⡈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠳⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢦⡈⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⣾⠿⠿⣿⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠻⣄⠘⢦⡈⠳⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣄⠙⢦⡈⠱⣄⠙⢦⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠢⡈⠳⣄⠉⢦⡈⠱⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠑⢄⠉⠢⡈⠳⣄⠙⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠢⡀⠑⣄⠈⣦⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣾⣷⠶⠿⠶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⢟⠉⠣⡀⠑⢄⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢏⠉⠢⡀⠑⢄⠈⠢⣀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠣⡀⠑⢄⠈⠢⡀⠑⢄⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠑⢄⠈⠢⡀⠑⢄⠈⢢⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠢⡀⠑⢄⠈⠢⣀⣱⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢄⠈⢢⣀⣵⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⣶⠶⢾⡿⠾⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠻⣅⠙⢦⡈⠣⣼⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣄⠙⢦⡈⠳⣄⠙⢦⣼⡇
⠀⠀⠀⠀⠀⠀⢀⣿⠛⢦⡈⠳⣄⠙⢦⡈⠳⣤⡿
⠀⠀⠀⠀⠀⠀⢸⡏⠳⣄⠙⢦⡈⠳⣄⠙⣦⡿⠁
⠀⠀⠀⠀⠀⠀⣿⡟⢦⡈⠳⣄⠙⣦⣼⡿⠋
⢀⣀⣠⣤⣤⣤⣿⣧⣶⣿⡶⠾⠟⠛⠉
⣟⠙⢯⡈⠳⣄⣿
⡈⠳⣄⠙⢦⣨⣿
⠙⢦⡈⠳⣄⣽⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣶⣶⣤⣄⠀⠀⠀⢹⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣿⣾⣿⣿⣿⣿⣿⣆⠀⠀⢳⡀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡇⠀⠀⠀⠀⢠⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢏⣵⣭⣛⡇⣩⣭⣭⣭⡹⡇⠀⡞⠁⠀⠀⠀⠀⢸⡇⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡅⠘⠇⠀⠤⠤⠤⠤⣼⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⢀⣸⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣭⣝⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢺⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⢸⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⢀⣴⣿⠇⣟⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⣿⡧⣻⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠘⢿⣷⣬⣭⣵⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⠛⠛⠛⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⡀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠸⠇⠹⠇⠿⠸⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⠾⠟⠋⠉⠛⠻⠷⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠀⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡾⠿⠛⠋⠉⠀⠉⠙⠛⠿⢷⡆⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢀⣀⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⢹⣿⠁⠀⠰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠘⠋⢿⣶⡟⢛⣿⣿⡷⣶⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢿⣆⠀⠀⠀⠀⠀⣤⡀⢠⣿⣿⣿⣿⣿⣿⣦⣼⣧⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⠻⣦⡀⠀⠀⠀⢿⠟⢻⣧⣿⣿⣁⣹⣿⣿⢿⣿⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠉⠻⣶⣤⡶⠀⠀⠀⣻⣿⣿⠿⣿⣿⣧⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠘⢿⣏⠉⠛⢻⣿⠛⠋⢉⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⠾⠛⠀⠀⠉⠀⠰⠾⠿⠶⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢄⣣⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠟⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣶⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠷⢶⣤⣄⣀⠀⠀⠀⢤⣍⣙⠛⠿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣴⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠉⠙⠻⠶⣦⣼⣿⣿⣿⡆⠀⠈⠉⠛⠛⠿⠛⠿⠿⠻⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⠛⠻⠶⠦⢄⣀⡀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠛⠶⠦⠄⢀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⣀⣀⣀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠁⠐⣦⣾⠇
⠀⠠⠒⠉⠐⠀⠁⠐⠠⢜⣿⣿⣿⣿⣿⣿⣷⣶⣤⣬⣉⡛⠃⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠉⠉⠉⣙⣋⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡷⢟⡋⠉⠙⠓⢦⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⡵⠶⠃⠘⢯⣒⡾⠟⠐⡿⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠐⢶⣄⠀⠉⣀⣠⣬⢙⡶⠷⠄⠀⠀⠀⠀⠀⠘⣯⢭⣸⠟⠉⡀⠉⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠀⢸⡼⠃⠘⣥⠋⠇⣸⠃⠀⠀⠀⠀⠀⠀⢀⠞⢩⢁⡀⠀⠀⡿⢤⣀⣀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡛⣀⣕⢀⠛⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃⠲⡶⣄⠀⠀⠙⠊⠉⠁⠀⢚⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢥⣘⣏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢹⣸⠃⠀⣠⢤⣀⡀⠀⢹⣄⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠛⠁⠠⠀⣧⠞⠉⠁⠀⢸⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣟⠤⣄⠀⠩⠀⢀⣠⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠳⢄⢿⠓⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⡴⠚⠋⠉⠉⠩⠙⠶⢤⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣭⠼⠏⠀⠀⢰⣄⣈⣠⠄⠀⠈⣿⡾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡁⠀⠀⠀⠀⠳⠔⠉⠀⠀⢢⢀⣳⡾⠵⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⢠⣤⣄⡀⠀⠀⠀⠀⠀⢠⠀⠀⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⡄⠈⣆⡝⠀⠀⠀⡖⢒⣲⣦⠀⢂⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣀⠐⠛⠀⣀⠈⠀⣷⠁⠀⠀⠘⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣱⡀⣠⣤⣤⠀⢀⣈⡩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡯⠥⣜⡶⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⠾⠛⠻⢶⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠛⠉⠉⠁⠀⣀⣀⣀⠀⠀⠉⠉⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⡶⠾⠟⠛⠉⠙⠛⠷⠶⣶⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⣀⣬⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⢈⣹⣏⡁⠀⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠛⠙⣷⡾⠟⢉⡙⠛⢷⣿⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠸⣧⡀⠀⠀⠀⠀⣶⣀⣸⡟⡀⠿⢈⡐⠿⡀⢻⣆⣀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠘⢷⣄⠀⠀⠀⣿⠛⢻⣇⢙⡤⠙⢃⣤⠋⣼⡟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠙⠻⢶⠶⠀⣀⢈⣿⣦⣀⠰⠂⣄⣴⣟⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⣀⠀⢀⣀⠙⢿⡇⠈⠙⢻⡟⠋⠁⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠘⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⠷⠶⠀⠀⠀⠀⠙⠛⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⠛⠻⠟⠋⡡⠤⠀⠉⠀⣴⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢄⠀⠈⣧
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠰⠀⠀⠀⠀⠀⠀⡀⠁⠀⠠⠀⣼⣿⣶⠀⠀⠀⢀⠀⠀⠀⠀⡂⠀⠸⡆
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣄⠀⡠⠊⠀⠀⠀⠐⠀⠀⠀⢷
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣇⠀⠀⠀⣀⣀⡀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⣷⣄⠈⠉⠉⠁⣀⣴⣿⡿⢿⣿⣿⠓⣇⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠀⠀⠀⠀⠉⠋⢉⡀⠄⠁⠀⠀⠹⣆⢀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠆⠀⠀⠀⠀⠁⠉⡽⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠙⢦⣀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⢉⢡⠐⠀⠀⠀⠀⡄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⢷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡁⠈⠙⠛⠁⠀⠀⠀⠁⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⢠⠤⠤⢠⡀⢀⡄⣤⠤⠄⣠⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠂⢸⠓⠒⠈⢧⡼⠀⣿⠒⠂⣾⠲⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠀⠈⠁⠀⠉⠉⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⡤⠶⠛⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠏⢀⣀⣀⣀⡼⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠘⠋⠩⠔⣚⣿⣿⣿⣿⣿⠟⠋⢻⣿⣿⣿⣿⣿⣧⠀⠐⠋⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠡⢖⣻⠿⠛⠉⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⣰⠁⠀⠀⠴⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⠤⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢨⣿⡆⠀⠀⢠⠤⠀⠀⡆⠀⠉⠁⠀⡀⡠⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣾⣿⣧⠀⢀⢀⠀⠀⠈⠃⠀⠀⠀⠈⠐⠁⣹⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠘⢿⣿⣿⡗⠁⠂⠀⠀⢔⣉⠭⠵⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠉⠻⣿⢿⣿⢷⡀⠀⠀⢸⠛⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠈⢶⠲⠔⠃⠀⠀⠀⠙⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠙⢶⣶⣶⡶⠖⠋⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⡿⠟⠛⠻⢿⣿⣿⣷⣶⣤⣄⣀⡀
⣠⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣄
⣿⣿⡿⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⢿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⠿⠟⠛⠻⠿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿
⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠸⣿⡿
⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⣀⣤⣤⣤⣄⣀
⣿⣿⡇⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠆⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣾⣿⣶⣄
⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣁⠀⠀⠀⣀⣤⣤⣾⣿⣿⣦⣤⣄⡀⠀⠀⢈⣽⣿⣿⣷⣄
⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡟⠙⣿⣿⣷⣴⣿⣿⣿⠿⠟⠛⠛⠻⣿⣿⣿⣷⣴⣿⣿⠟⠛⣿⣿⠆
⢹⣿⣿⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡿⠛⠉⠉⠀⢠⣶⣦⠀⠈⠉⠙⠻⣿⣿⣇
⠘⣿⣿⡆⠀⠀⠀⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⣿⣿⡟⠀⠀⣴⣶⡄⠈⠛⠋⢀⣴⣶⡄⠀⢙⣿⣿⣧⠀⠀⠀⠀⣀
⠀⢹⣿⣿⡀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⣾⣿⡟⠋⠀⠀⠻⠿⠃⠀⣀⡀⠈⠻⠿⠃⠀⠈⠙⣿⣿⡆⠀⠀⢺⣿
⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⣷⡄⠀⠀⣾⣿⣿⡆⠀⠀⣴⣷⡆⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠉⠙⠙⣿⣿⡇⠀⠉⠉⢀⣀⠀⠙⠛⠛⠁⢀⣀⠈⠉⠁⢀⣿⣿⡟⠉⠋⢻⣿
⠀⠀⠀⠀⢿⣿⣷⡄⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⢹⣿⣿⡷⠀⠀⣿⣿⡇⠀⠀⠀⠰⣿⣿⡇⠀⠐⣿⣿⡿⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⣤⣶⣿⣷⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠈⠉⠀⢰⣿⣷⠀⠈⠁⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠋⠁⠀⠀⣠⣤⡄⢀⣴⣿⣿⣿⣿⣶⣶⣄⡀⠉⠀⣀⣴⣷⣾⣿⣿⣿⣷⣄⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠟⠁⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠛⢿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠈⠻⣿⣿⣶⡄⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣶⣤⣶⣿⣿⣿⠿⠂⠀⠀⠈⠙⠛⠁⠀⠀⠀⣠⣤⣼⣿⣿⣤⣤⡀⠀⠀⠀⠙⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣻⣿⣟⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⢛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠻⠿⠿⠿⠿⠟⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠶⠶⠶⠶⠶⠶⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣉⣉⣉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⣀⣀⣀⣀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⡉⠉⣹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣉⣉⣹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠷⠶⠶⠾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣉⣹⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣤⣤⣤⣤⣼⣿⣿⣇⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⢛⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣤⣤⣤⣤⣽⣿⣿⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣉⣉⣉⣉⣉⣉⣹⣿⣿⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠶⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢉⣉⣉⣉⣉⢉⢹⣿⣿⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠛⠛⠛⠛⠛⢻⣿⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠸⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣀⣙⠁⣼⡟⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⣈⠁⢰⣿⡀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁⠀⣾⠏⠙⠶⣄⡀⠀⠀⠙⠳⢦⡀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠙⠳⣤⡀⠀⣠⡿⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠈⠙⢶⡟⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡿⠲⣤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣤⣸⠇⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⣧⡀⠀⠉⠛⠳⢤⣀⠀⠀⠀⣠⡾⠋⣄⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠈⣿⠙⠳⢤⣀⠀⠀⠉⠓⢶⡿⠋⠀⠃⠈⢀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢿⡄⠀⠀⢉⣻⣦⣤⣀⣀⣹⠄⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣧⠀⠀⢸⣷⠶⠟⠛⠉⠁⠀⠈⢉⣡⣴⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠟⠛⠉⠉⠘⣿⠀⠀⠘⣿⠀⠀⢀⣀⣤⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠟⠛⠉⠁⠀⠀⠀⣀⣠⣤⣾⣿⠀⠀⠀⣿⡶⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⢀⣤⣤⣴⣶⠟⠛⠋⠉⠁⢠⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⣿⡃⠀⢀⣼⠷⣄⡀⠉⠛⠳⢦⣄⠀⢸⡟⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠰⠆⠀⣴⠟⠁⠀⠀⠙⠳⢦⣄⡀⠈⠙⣿⠃⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢀⣤⣼⣏⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣾⡟⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣅⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡟⠶⣤⣀⠀⠉⠛⠦⣄⣀⣴⠟⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⣧⠀⠀⠉⠛⠶⣄⣀⣬⡿⠋⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢿⡄⠀⢀⣀⣤⡾⢟⡉⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣀⣠⣼⣿⠾⠛⠋⣁⢲⡘⢧⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠈⠁⢀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⡶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⢀⣠⣴⠶⠿⢿⣟⠉⠉⠀⠹⣷⡀
⠀⠀⠀⠀⢠⡾⢋⡲⡝⢀⣴⣾⣟⣉⠀⠀⠀⠀⠻⣧⡀⠀⠀⠘⢿⡄
⠀⠀⠀⣰⡟⠁⠈⢁⣴⣿⣁⠀⠀⠉⠛⠲⢦⣄⡀⠹⣷⡀⠀⠀⠘⣿⡀
⠀⠀⣼⠟⠀⠀⣠⡾⠋⠀⠉⠙⠲⢤⣄⡀⠀⠈⠙⠳⠿⣇⡀⠀⠀⢹⡇
⠀⣾⠏⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣀⡀⠈⠙⣦⠀⠸⣿
⣼⠏⠀⠀⣰⡟⠙⠲⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠒⠋⠀⠰⣿
⢿⣦⣠⣼⠟⠙⠳⢦⣤⣀⠈⠉⠛⠲⠦⣤⣀⠀⠀⠀⢀⣿⠀⠀⠀⢸⣿
⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠛⠶⢤⣀⡀⠀⠈⠙⠓⠦⣼⡏⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣄⣀⠈⢹⡆⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠋⠁⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠻⠿⠛⠀⠀⠀⢀⡦⢶⢖⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⢐⠷⢈⠤⡓⢌⢻⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠑⢀⢡⠀⠀⠀⠀⠈⡖⣈⠶⣁⠎⡑⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣀⡲⠁⠀⢀⠀⠀⠀⠉⠄⢖⡤⡞⠋
⠀⠀⠀⠀⠀⠠⠀⠀⠉⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠁⠢⠤⠓⠀⠰⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣾⡇⠀⠀⠀⠀⠀⢀⣀⠴⠃⠀⠀⠀⠀⠀⠙⠈⠙⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣴⠫⡩⢜⠴⡄⠀⠀⠀⠒⠀⢙⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡥⠐⡍⢢⠃⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠥⢦⢵⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠋⠙⠻⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠿⠿⠟⠛⢉⣠⣴⡾⢷⣦⣄⡉⠛⠻⠿⢿⣷⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣠⣤⣤⣤⣤⣤⣤⣶⣶⠿⠟⠋⠁⠀⠀⠈⠙⠻⠿⣶⣶⣤⣤⣤⣤⣤⣤⣄⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢹⡿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣇⠀⠀⠀⠈⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠁⠀⠀⠀⣸⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠻⣷⣤⡀⠀⠀⢀⣤⣾⠟⠁⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠙⠻⢷⣾⠟⠋⢀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⣀⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠋⠁




⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠴⠘⡘⢃⡄⣀⠠⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣏⣻⣿⣬⠿⡿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⡏⠀⢠⣆⠀⢈⣍⠈⠑⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⡿⣿⣿⠋⢿⣿⠶⣿⣿⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠊⠁⠈⠁⠉⣿⣿⣌⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣾⣷⡄⠀⠹⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠈⠛⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣦⡌⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⣗⠁⠀⠀⠀⡸⠗⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⡏⢿⣿⣿⣿⣿⣨⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⡠⠑⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠠⡛⠿⣦⣜⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡘⠛⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣡⠓⠀⠀⠈⠹⣇⡔⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣯⣿⣿⣿⣦⡈⢟⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⢀⢀⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢾⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢁⠙⠿⣶⣤⡘⠒⠀⠆⣠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⠈⠛⠻⣭⣿⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⡠⢀⡔⠟⠙⠻⣷⣔⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣧⣶⣤⡈⠛⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣇⠃⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣀⠀⢠⡾⡆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡈⠙⠿⣿⣿⠟⢼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠋⠊⡟⢻⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢷⣿⡦⣤⡀⠉⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⠤⠙⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣟⣶⡌⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠑⠤⡀⣼⠁⠀⠀⠀⢻⡠⠆⠔⠂⠀⠀⠀⣿⣿⣿⣿⣿⣝⣿⡏⣿⣿⣿⣿⣧⢼⣽⣿⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⣿⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡅⢿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀⠀⠀⠀⠰⢿⣇⢸⡇⣸⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⢐⣷⣤⣽⣿⣿⣧⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⡀⠻⣿⣿⣿⣿⡿⠃⣀⠀⠀⢡⣤⡞⢻⡟⢷⣤⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣰⣿⣿⣦⣌⣉⣉⣉⣤⣾⣿⣿⣦⠀⠙⠁⠾⠷⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁⠀⣿⣿⣿⠻⣿⣿⣿⣿⣿⡋⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣿⣿⣿⠀⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⣿⣿⣿⣶⣿⣿⢠⣄⡉⠛⠿⠿⠟⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠿⠿⠿⠿⠿⢸⣿⣿⣷⣦⠀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠰⣶⠆⣠⡀⠀⠀⠀⣶⣶⣶⣾⣿⣿⣿⣿⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⢀⠛⠻⣦⣿⣤⡿⠛⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠰⣿⡁
⠀⠀⠀⠀⠀⠀⢸⠿⠟⣿⣿⣿⡿⠻⡯⠀⠀⣼⣿⣿⣿⠿⣿⣿⣿⡆⠀⠐⣿⡅
⠀⠀⠀⠀⠀⠀⠀⢶⣾⠋⣿⠉⣿⡶⠀⠀⢀⣿⣿⣿⣿⠀⢿⣿⣿⣷⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⠃⠈⠀⠀⠀⢸⣿⣿⣿⡇⠀⠘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢹⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠶⠒⠒⠛⠋⠁⠀⠀⠀⣀⣀⣀⡠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⠤⠤⠒⠒⠒⠛⠋⠉⠉⠉⢁⣀⣀⣀⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⠦⠤⠶⠒⠒⠒⠛⠉⠉⠉⠉⠉⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠒⠲⠖⠒⠒⠒⠋⠉⠉⢉⡽⠋⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡒⠓⠒⠚⠛⠊⠟⠉⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠲⠋⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⡠⠂⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⢀⡤⠞⠓⠒⠓⠶⠒⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡠⠾⠿⠶⠶⠶⠶⠶⠶⠶⠲⠶⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠶⠓⠲⠒⠒⠲⠦⠦⠦⠤⠤⠤⠤⠦⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⢤⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠦⢤⠤⠤⠤⢤⣤⣤⣤⣤⣤⠤⠊⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠤⠴⠤⡤⠤⠤⣄⡤⠖⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⣤⠦⠐⠉⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⡀⠴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⣤⣆⣉⣄⣀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣀⣴⢮⣅⣀⣀⣀⣀⠉⣌⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠾⠥⢄⣀⣀⣀⣀⣀⠀⠈⠉⠙⠉⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠤⠤⣤⣀⣀⣀⣀⣀⣉⡉⠉⠉⠉⠉⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⠄⢀⣀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⢷⠞⠚⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠇⠀⠂⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢠⣦⠀⢠⣆⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣘⠋⠀⣘⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⣀⣀⠀⢀⡀⠀⢀⡀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠁⠀⠈⠉⠁⠉⠉⠀⠉⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠒⠀⠠⠀⠤⠤⠤⠤⠶⣅⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠢⣀⠀⠀⠤⠀⠀⢰⠊⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣊⢢⠠⡈⠠⠈⢂⣀⡠⠜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢀⠅⢠⠈⠋⠐⠠⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⣨⠉⠉⠀⠀⠈⠉⢳⢠⠄⢤⡀⠈⢦⡀⠀⠀⠀⠀⢀⠗⠊
⠀⡀⢀⡀⠀⣦⠀⠂⣠⣚⡥⠤⠐⠒⢻⣉⢳⡀⠀⠀⠀⠀⠀⢸⡀⣀⠗⠢⢤⣙⣆⠀⡀⠀⣸⠶⠒⡆⣀
⠀⡯⢩⠁⣄⣉⣁⡈⡄⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠸⠑⠉⠀⠀⠀⠀⠀⠉⠃⠀⠀⢈⡀⣀⠃
⠀⣏⣹⠀⣟⣁⣀⠊⠇⠀⠀⠀⠀⠀⢀⠸⣀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠠⡄⠀⡀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠉⠒⠒⢀⣠⣤⠴⠖⠀⡉⢁⠀⠀⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣦⣬⣥⣥⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠹⣤⠼⠇⣼⠁⢀⣀⠀⠀⣀⣠⡤⠶⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⣴⠶⣤⠟⠀⢀⡀⠀⠈⠳⢋⣹⠟⠋⠉⠀⢀⣀⣤⣀⡀⠀⠉⠙⠳⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠛⠲⡆⠀⠀⠈⠁⢀⠀⠀⣿⣁⣤⡴⠖⠛⠉⠁⠀⠈⠙⠛⠲⢦⣤⣀⡀⠈⠉⠻⡆
⠀⠀⠀⠀⠀⢠⡴⠗⡀⠀⠀⠀⠀⠀⢀⣬⣉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣿
⠀⠀⠀⠀⠀⠘⠶⠛⠛⣦⢀⣀⣤⡰⣯⠀⠉⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⣼⡇⠘⠧⠾⠁⠀⠀⣠⠴⠛⠉⠉⠉⠉⠉⠛⢦⣄⠀⠀⠀⠀⠀⢸⡍⠷⠾⠡⣏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣰⠲⡆⠀⠀⠀⠙⢧⡀⠀⢼⣛⡛⠁⠠⠄⠀⠈⣥⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣻⠀⡗⠀⠀⠀⠀⠈⣧⠀⢀⣹⡇⠀⠀⠀⠂⠀⣘⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡇⠀⠰⣏⣉⣉⣉⠀⣉⣉⣉⣻⠀⠀⣿⠀⠘⠷⢾⣦⢄⣀⣄⢾⡉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢿⠀⠀⠈⠉⠉⣿⠀⡏⠉⠉⠁⠀⢀⡟⠀⠀⠀⣼⠻⠼⠃⠙⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠈⢷⡀⠀⠀⠀⠻⣤⠏⠀⠀⠀⢀⡾⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠙⠶⣄⣀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⢀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣌⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠓⠒⠢⠤⠀⠀⠀⢠⠀⠀⢄⣀⠹⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⡿⠃⠀⠠⠀⠀⣀⡀⠀⠀⠉⠒⠈⠁⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⡽⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⣀⡄⠐⠚⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠐⠊⠉⠉⠁⠛⠰⡄⠀⠤⠭⠱⠲⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡜⠄⠀⠀⠀⠀⠤⠈⠐⠒⠒⠒⠲⠶⣶⡁⠀⠈⠃⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠂⠒⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠓⠂⠒⢆⡈⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠐⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⡀⣎⠉⡁⠀⠀⢀⠀⠀⠐⡀⠀⠀⠀⣀⡠⠔⠁⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠨⡀⠁⡁⠚⠛⠲⠄⢀⡠⠄⠈⢁⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⣗⠶⠒⠉⠁⠀⠀⢀⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠒⠛⠁⠈⠛⠖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⣀⠀⠀⠉⠉⠈⠉⠙⢣⣄⣁⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠒⠑⠐⠒⠂⠀⠀⠀⠃⠀⠀⠀⠢⡤⣤⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠀⠀⠀⠀⠠⠤⠄⠠⠤⠀⠀⠀⠠⠀⠀⢠⠟⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⢲⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⡉⠛⠀⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡴⠎⡃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠤⠄⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢌⠈⢛⣍⣉⣉⣉⡁⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣲⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⣀⣀⣤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠒⠀⠿⠦⠾⠉⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⡀⠈⠁⠁⠉⠉⠎⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⣃⡀⠀⠀⠀⠀⠀⠀⠉⠒⣤⠀⡀⠈⡓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢧⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⢌⡚⠘⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⠧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⠧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢾⠚⣲⠆⠂⠒⠂⠃⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠁

⠀⠀⠐⠄⠤⢶⡠⡀⠀⠀⠀⠀⢀⣤⠶⠶⣄⠀⠀⠀⠀⠀⢀⠤⣒⡂⠒⡀⠀⠀⠀⠀⠀⠴⣂⢄⠢⡀⠀⠀⠀⠀⠀⣔⡦⢅⠢⡀
⠀⠀⠐⢆⠀⠠⡷⠃⠀⠀⠀⠀⢸⡇⠀⡀⣬⠃⠀⠀⠀⠀⢸⠀⣅⠀⡀⡅⠀⠀⠀⠀⢸⠠⠀⢀⠅⡅⠀⠀⠀⠀⠰⣀⡡⢅⡨⡓
⠀⠀⠘⠔⠉⠉⠄⠀⠀⠀⠀⠀⠈⠙⠾⠛⠛⠁⠀⠀⠀⠀⠀⠓⠜⠣⠐⠁⠀⠀⠀⠀⠀⠑⠢⠤⠚⠀⠀⠀⠀⠀⠀⠑⠫⠡⠐⠁


⠀⠀⢀⣰⠴⠴⣀⠀⠀⠀⠀⠀⠀⢀⠲⣀⢠⠀⠀⠀⠀⠀⠀⢀⠴⠤⣠⡀⠀⠀⠀⠀⠀⢠⠶⠶⡆⠀⠀⠀⠀⠀⠀⡠⢤⢒⣢
⠀⠀⢐⡇⢎⡑⣹⠀⠀⠀⠀⠀⠈⣣⠂⢐⡭⡄⠀⠀⠀⠀⠐⡇⠀⠀⢹⠁⠀⠀⠀⠀⢀⠀⡼⢪⠀⡀⠀⠀⠀⠀⠰⠀⠈⠛⠃⠡
⠀⠀⠀⠚⠊⠚⠋⠀⠀⠀⠀⠀⠈⠊⠀⠿⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠛⠀⠀⠀⠀⠀⠀⠁⠹⠋⠉⠀⠀⠀⠀⠀⠀⠑⠂⠀⠐⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⡆⠀⠀⠀⠀⠀⠠⡦⠀⠠⡀⠀⠀⠀⠀⠀⠀⡠⠔⠂⢄⠀⠀⠀⠀⠀⠀⣠⠴⡶⣤
⠀⠀⠀⠠⣶⡦⡀⠀⠀⠀⠀⠀⢰⣋⡆⢻⣹⠆⠀⠀⠀⠀⠀⠒⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⢧⡞⠆⡇⠀⠀⠀⠀⠀⡇⠐⡇⢀⡇
⠀⠀⠀⠀⠀⠉⠪⠆⠀⠀⠀⠀⠀⠳⠞⠀⠀⠀⠀⠀⠀⠀⠐⠷⠘⠂⠛⠂⠀⠀⠀⠀⠀⠑⠢⠅⠊⠀⠀⠀⠀⠀⠀⠙⠲⠷⠛


⠀⠀⠀⢠⠴⠤⡄⠀⠀⠀⠀⠀⠰⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⢐⡂⢀⠀⠀⠀⠀⠀⠀⡠⣄⡢⢄⡀⠀⠀⠀⠀⠀⡠⠒⠒⠤⡀
⠀⠀⢐⡇⡈⠱⣸⠀⠀⠀⠀⠀⠀⣌⡉⠰⠄⠀⠀⠀⠀⠀⠀⣹⡏⢹⡏⠀⠀⠀⠀⠀⢰⢁⠀⠂⠀⡁⠀⠀⠀⠀⠐⠁⠍⠏⠕⡁
⠀⠀⠨⠗⠄⠶⠑⠀⠀⠀⠀⠀⠰⠖⠀⠐⠒⠀⠀⠀⠀⠀⠀⠁⠹⠇⠈⠀⠀⠀⠀⠀⠀⠓⠥⠥⠒⠁⠀⠀⠀⠀⠀⠓⠤⠤⠔⠁


⠀⠀⠀⢄⢄⢄⢄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠀⡠⡀⢄⡄⠀⠀⠀⠀⢀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⢄
⠀⠀⢘⣂⠢⢂⠌⡀⠀⠀⠀⠀⢰⢃⡳⣼⠑⡄⠀⠀⠀⠀⠘⢤⠒⡀⢉⠁⠀⠀⠀⠀⠈⠚⢵⢵⢄⡀⠀⠀⠀⠀⠀⡁⣀⡈⢆⠇
⠀⠀⠐⠤⠀⠒⠜⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠧⠉⠮⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⠯⠃⠀⠀⠀⠀⠐⠐⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⣰⣿⠟⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣰⣿⠃⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⡇⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣿
⣤⣄⠀⠀⠠⣤⡄⠀⠀⢠⣤⡀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⣤⣤⣾⡿
⢘⣿⡆⠀⠀⢹⣿⠀⠀⠈⣿⣷⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠉⠉⠉⠁
⣾⡟⠁⠀⢠⣿⡏⠀⠀⢰⣿⠃⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣀⣀⡀
⢻⣿⡄⠀⠀⢿⣷⠀⠀⠘⣿⣆⠀⣿⡇⠀⠀⠀⠀⠀⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠷⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄
⣼⣿⠃⠀⢀⣾⡿⠀⠀⢠⣿⠏⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣽⣿⡿⠗⠀⠀⠀⠐⠿⣿⣿⣭⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠉⠁⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⣿⡇⠀⠀⠀⠀⠐⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⣠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠿⢿⣷⣶⣶⣶⣶⣾⠿⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠙⢦⡀⠀⠀⠀⠀⣠⠞⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠙⣤⡀⠱⣄⠀⢀⡴⠁⣠⡞⠁⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⣄⠈⠛⠉⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⡟⠉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠀⠀⢀⣠⡤⠴⠶⢾⠀⢸⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⢼⠋⠛⠛⠛⠛⠛⠁⠀⢿⡀⣠⡴⠛⠉⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠈⠙⠳⣤⡀⢀⡟⠀⠙⠲⠶⠒⠒⠒⢲⡄
⠀⠀⠀⠀⠈⠛⠛⠛⠒⠒⠲⢦⣄⠈⢻⡅⠀⠀⠀⠀⠀⠀⠀⠸⢦⠾⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠀⣀⡤⠶⠶⠶⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢣⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⣠⠞⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠙⠶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠋⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⣾⠋⢳⣄⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢀⡴⢦
⠈⠳⡀⠙⢦⡀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⡴⠋⢀⡼
⠀⠀⠙⢦⡀⠙⠲⠤⢧⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣇⣠⠴⠋⢀⡴⠋
⠀⠀⠀⣰⠇⠀⣀⣀⣤⣤⣤⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣉⣉⣉⠁⠀⠀⠀⣟
⠀⣠⠞⠁⣠⠞⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡏⠙⠲⣄⠈⠳⡀
⣾⠁⣠⠞⠁⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⢷⡄⠙⢦
⠈⠛⠁⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠙⠦⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢠⠞⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠳⣄⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡷⠋⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠘⢶⣏
⠀⠀⠀⠀⣴⠛⠛⠛⠛⠛⠋⠁⠀⣴⠿⣄⡀⠀⠀⠀⠀⠀⠀⢸⠋⢻⠀⠀⠀⠀⠀⠀⠀⣀⡽⣦⠀⠉⠛⠒⠒⠲⠶⠶⢦
⠀⠀⠀⠀⠙⠒⠒⠒⠛⠛⢲⡀⢰⡇⠀⠈⠙⠶⣤⣀⡀⠀⠀⢸⠀⢸⠀⠀⠀⣀⣠⠴⠞⠉⠀⢸⡇⠀⡴⠶⠶⠶⠶⠦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⠀⢸⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣴⠇⠀⠀⠀⠀⠀⠀⣠⡾⠁⣠⠶⢤⡀⠻⣦⠀⠀⠀⠀⠀⠀⠸⣇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⠜⠁⠀⠀⠙⣄⠈⠳⡄⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣦⡞⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⢀⡾⠁
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⢠⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢾⡉⠻⣦⡀⠀⠀⠀⠀⠀⢀⣠⣼⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢹⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⠟⢉⡷
⠀⠀⠀⠀⠀⠙⢦⡈⠻⣦⡀⢀⣴⣾⣿⣿⣿⣀⣈⣉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⣉⣁⣀⣿⣿⣿⣷⣦⡀⢀⣴⠟⣁⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣿⠟⢹⣿⣿⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⢿⣿⣿⣿⡏⠻⣿⣿⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡄⠛⢁⡄⢸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⡇⢠⡈⠛⢠⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣴⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣦⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⡄
⢀⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⠉⢻⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡟⠉⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤
⢿⣅⣤⣠⣤⣄⣤⣄⠙⣿⠇⣰⡄⢻⣿⣿⣿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣿⡟⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣆⠸⣿⠋⣠⣤⣤⣤⣤⣤⣨
⠀⠀⠀⠀⠀⠀⣿⣿⣧⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⣼⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⡿⠟⠁⢀⣤⠀⠘⠿⠛⠁⠀⠀⠀⠀⠀⣤⣀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⢿⠛⠉⠉⠀⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠂⠀⠀⢨⡿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠀⣺⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⢸⡧⠀⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⣼⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⡇⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⠗⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣄⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣤⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠶⠾⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⣀⣤⡾⠛⠉⠉⠉⠉⠉⠉⠉⣉⢉⣟⡷⠋⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⣤⣾⡟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡿⠋⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡎⡏⣾⣁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠋⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠸⣿⡀⢻⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢦⡓⣄⣀⠤⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉⠀⠀⢀⣠⡶⠂⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡤⠶⡟⠥⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⣠⡶⠛⠙⢦⣄⠁⢾⠿⣿⣿⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⢀⣤⣶⠟⠉⠀⠀⠀⠀⠘⠉⠉⠛⠉⠉⢙⠛⢿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣔⡝⣽⣁⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⠀⡀⢡⡈⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⣾⠠⡛⠒⠒⠀⠒⠐⠒⠒⠒⠒⠒⠒⠒⠒⢒⣶⢀⢧⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣵⠇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣷⣠⣄⣤⠠⣄⠀⣤⡀⠀⠀⣠⡶⠿⠋⠉⠁⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⡷⠈⠁⢯⣭⡷⠟⠉⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠁⠀⢀⡠⠴⠻⢿⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⠀⠠⡄⠐⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⢀⣠⡴⠿⠩⠅⠀⠀⠀⠀⠀⠐⣿⠀⢁⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢀⣤⣶⠟⠡⠤⠄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣮⠜⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡠⣺⣿⠯⠥⠤⠬⠤⠤⠌⠒⠒⠒⠒⣲⣶⠿⠛⠛⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠁⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠁⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⡘⡀⠹⣄⠀⠀⠀⣀⣤⠾⠛⢉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡤⠈⡷⠖⠊⠉⠀⠠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⣠⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠻⣯⠾⣷⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣤⡶⠟⠉⠈⠙⠶⠄⠳⠌⠛⠾⠟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⣠⣾⡿⠉⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⡌⢻⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⢮⢫⡟⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⢤⡤⠴⠄⡷⡇⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢸⢿⠘⠛⠛⠛⠛⠛⠛⠛⠛⠐⠒⠒⠒⠒⠒⠒⣾⡰⡵⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠾⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠘⢦⠙⠋⡴⠃⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⢿⠀⠀⣀⣠⣬⡇⢸⣥⣄⣀⠀⠀⡿⢸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣭⣍⣁⠘⢶⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⡶⠃⣈⣉⣭⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣄⣹⣿⣿⣿⡟⠛⢿⣿⣿⣏⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⠓⠦⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠴⠚⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡤⠖⣶⣶⣾⣿⣿⣤⣿⣿⣿⣿⠛⠛⠻⣿⣿⣷⣶⣶⠲⢤⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⣿⣿⣿⣿⡟⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⣹⣿⣿⣿⣿⣿⣿⣶⣿⣏⠙⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣛⣋⡉⢠⠾⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⠷⡄⢉⣙⣛⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⣾⠀⠀⠉⠛⢛⡇⢸⡛⠛⠉⠀⠀⣷⢸⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢠⠞⣠⣄⠳⣄⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠈⠓⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⣀⡀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⠁⣀⣤⠶⠛⠉⠙⠳⢦⣄⡀⠉⠛⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⡄⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢠⡶⠶⠶⡆⠀⠀⠀⠀⠀⠀⡇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢠⡶⠶⠶⠾⠇⠀⠀⠷⠶⠶⠶⡆⠀⠀⠀⠀⠀⢴⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣠⡀⣴⣲⠈⡇⠀⡴⠀⢀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠈⠉⠉⠉⢹⡇⠀⠀⡟⠉⠉⠉⠁⠈⠓⢳⡤⢻⡘⠛⠓⢦⡴⠋⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⢷⡀⠀⠀⠀⠀⢸⡇⠀⢀⡇⠀⠀⢀⠀⠀⢃⡞⠀⣀⠁⡀⠰⠆⡽⡖⠓⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠳⣄⠀⠀⠀⠈⠉⠉⠉⠁⠀⠘⠯⠗⠒⣚⣃⣠⠄⠻⠽⢀⡀⠀⡟⠒⠺⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠳⢦⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠻⢛⣄⠀⠠⠆⡄⢁⣼⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠉⠓⠦⣤⡴⠞⠋⢀⡀⠀⣤⢴⠋⢈⡝⠲⡆⣝⣦⠈⢦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⣀⣤⠖⠋⠁⠀⠉⠋⠀⠘⠀⣠⢧⠈⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⣶⠖⠢⣀⣀⣶⠲⠼⢷⡾⠥⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⣤⡾⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⣒⡄⠀⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⢀⡴⢩⠏⠀⠀⢰⢀⡼⢇⡄⠀⠀⠀⠀⠀⠈⢾⠁⠘⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠼⢀⡴⠴⠻⠊⠀⡟⢡⡷⣠⡄⠀⠀⠀⢾⠀⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢸⢳⡀⠀⢀⣤⡖⠀⠀⢀⠀⠈⠑⢤⡄⠀⡾⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣟⣲⣾⣾⡇⠀⠀⠀⣔⡀⠀⠺⠣⠄⠀⠀⠘⠦⠧⡄⠀⠀⠉⠳⡆⠀⠀⢀⣤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠷⣄⣈⠉⠙⡿⢷⡶⠶⠾⣥⠀⠀⠀⠘⠷⠀⣠⠀⣰⠃⢀⡴⠋⢱⠇⠀⠀⣶⠘⠛⠛⢹⠃⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢉⡟⣋⠉⠛⠶⣄⠀⠉⠙⠒⠷⡀⠀⠀⠀⠀⠓⠀⠀⢀⣠⠞⠛⠋⠁⡴⠋⠀⣰⠋⠀⠀⠀⢻⠀⠀⠀⢸⠀⠀⡟⠛⢻
⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠘⢧⣏⣧⣄⡶⠼⣶⣶⣒⠦⣤⠞⠲⢤⣤⣀⣤⠴⢾⡋⠀⠀⠀⠀⡼⠁⢀⠞⠁⠀⠀⠀⠀⢸⡀⠀⠀⡟⠀⣈⡗⠒⢾
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠠⢯⡀⠀⠀⠉⠓⠦⣤⣘⡡⠖⠉⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⢰⠃
⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠴⣿⠋⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⢦⡀⠸⣄⠀⠀⣀
⠞⠁⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢾⣿⡴⢀⡟⠒⠒⠒⠲⠦⣄⠀⠀⠀⢀⡘⢟⣦⣖⠽⠃⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠋⠀⠀⠀⠀⣠⠀⠘⣦⠀⠀⠾⠱⠆⠹⠷
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠘⣇
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣲⣼⢀⠃⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡴⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⣃⠈⠡⠭⠬⠂⠈⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⣀⠀⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠠⢆⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢳⠀⠀⠊⠀⠀⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠄⠘⠉⠻⣤⢞⣡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠠⢄⠣⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠈⢱⡋⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡽⠀⠀⢁⠀⢧⠀⠀⠀⣤⣤⣤⣀⣀⣀⣀⢠⡤⠀⠠⠤⢀⣀⣀⣀⣀⣤⣤⡄⠰⣏⡅⠀⡆⡤⠀⣼⠛
⠀⠀⠀⠀⠀⠀⢺⠁⢀⣀⠀⢀⣀⡀⡣⠀⠀⢻⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⡀⢠⡇⠀⠀⠈⠲⠭⠵⠷⢮⣓⢶⡄⠀⠀⠐⠼
⠀⠀⠀⠀⡤⡄⠀⠑⠉⠈⠓⠉⠀⠈⠀⠀⠀⢸⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⠀⠀⣀⡀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠠⠀⢠⣤⣤⠀⠀⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⢧⠸⡀⠀⢀⠤⠒⢢⠀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣛⠳⣧⡀⠀⠀⠘⡇⢸⠀⠀⠀⠁⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⠁⣾⠀⠀⠀⣀⣀⡹⠓⢖⣁⣠⡤⠊⠀⠁
⠀⠀⠀⠀⠀⠀⢰⡀⠧⡇⢆⢀⠅⣽⡧⠀⠀⠀⡇⠸⡄⠀⣶⣶⣶⣾⣿⣿⣶⣶⣶⡆⠀⢸⠀⡿⠀⢠⣸⣁⡴⠲⣀⣄⢡⠀⠀⠀⠀⠀⠀⠰⡏⣱
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢻⣢⡴⣞⡇⠀⠀⠀⠀⣿⠀⡇⠀⠟⠛⠛⢻⣿⣿⠛⠛⠛⠃⠀⣸⠀⡇⠀⠠⠁⠀⠀⢀⢿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢹⠀⡇⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⡇⢰⡇⠀⠀⠀⠀⠀⠸⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡢⡀⠀⢀⠄⡇⢼⡀⠀⢸⡀⢷⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⡇⢸⠇⠀⠀⠀⠀⠀⠀⣠⢀⡶⢤⠦⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠸⣤⠜⣦⠜⠀⢸⡇⠸⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠃⢸⠀⠀⠀⠐⠃⠇⢴⡓⠀⠆⠀⣠⠡⣧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⡴⠃⠀⠀⠀⠳⢤⣀⣀⠉⠙⠲⢄⡴⠖⠋⢉⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠘⣧⠠⡀⢀⠀⠀⠨⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢦⣄⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠧⣀⡈⢀⣠⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠋⠉