Mario bros. Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⣠⢤⠀⢀⡀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⡳⠦⣄⠀⠀⡴⢹⠞⠁⠀⣧⠎⡇⡠⠖⠛⠉⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⡠⠋⣀⣀⡼⠖⠊⢁⠀⠀⠀⠀⠀⢠⠟⠧⣄⣀⡑⠄⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠷⢤⠧⠔⠀⠀⠀⠀⠑⢦⣀⣠⡴⠋⠀⠀⠰⠴⣥⠴⠧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⡔⠋⠳⢄⣀⠀⠀⠀⠉⠁⠀⠀⡀⢀⡤⠶⣼⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡽⠀⢙⡶⢤⣀⠙⠉⠲⠀⠀⠠⠖⠩⠛⠁⣀⣠⠜⢯⠑⢦⡀
⠀⠀⠀⠀⠀⠀⣰⠋⢀⣀⠃⠀⢸⠁⢸⣛⣿⣶⢴⣤⣠⣼⣤⢶⣶⣏⠁⣿⠀⢸⠀⠀⠱⣄
⠀⠀⠀⠀⠀⣰⠃⠀⢢⢈⡳⠤⣌⢆⣈⡻⠿⠧⣌⡀⠀⣈⣼⠿⣿⣃⢠⢃⠤⣼⠒⡆⠀⠘⡆
⠀⠀⠀⠀⢠⣇⠄⠀⢸⠏⠀⠀⠀⠙⠁⢀⣤⣤⡀⠈⠉⠀⣠⣤⡄⠈⠙⠁⠀⠈⢳⠃⠀⠀⢻
⠀⠀⠀⠀⢸⠃⠀⠀⢸⡀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠈⢺
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢳⡀⣒⠒⠂⣸⠛⢿⣷⠒⣢⡤⠤⠤⣀⣀⣀⣀⣀⣀⠤⣤⣤⣴⡾⢻⠀⠀⠄⠂⢀⠇
⠀⠀⠀⠀⠀⠈⠋⠛⢻⡏⠀⠀⠈⠛⠤⣘⣦⠚⠋⠓⢄⠜⠉⣓⣴⠷⠋⠁⠀⠈⢻⡿⠖⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠠⣀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⣠⠂⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣤⣀⣀⣈⠛⢶⠶⠦⠤⠤⠴⢶⡖⠛⣡⣀⣠⣤⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣎⡀⣸⠀⠀⣇⣈⠇⠀⠀⠀⠀⢸⣀⣌⠀⢈⡆⢈⣆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠛⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⢦⡜⢦⢈⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢈⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠉⣼⣿⡿⠻⣿⣿⣿⣿⠿⠋⠉⠀⠉⠙⠛⢦
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⠟⠛⢧⠀⠀⣿⠉⠙⢦⢻⡏⣹⡏⠀⠀⠀⠀⠀⠀⠛⢾⡇
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠀⢰⠃⠀⣤⣴⡆⠀⣿⣿⣆⢸⡿⣿⣍⣉⡉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⢸⡀⠸⣿⣿⡇⠀⢿⣿⣿⠼⠶⠿⢿⣿⣿⣷⡀⢀⠀⢀⣷⣶⠋
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠓⠒⠿⠛⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠻⣿⣇⣸⣷⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠻⣿⡟⢡⣀⡀⠈⢿⣿⣿⣿⡿⠃⠸⣿⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡤⠽⢦⠈⠛⠿⠟⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⣀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⣤⣤⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⠿⠿⢿⣿⠟⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣶⣤⣤⣤⣄⣀⣀⣀⣻⣿⣿⣿⣥⡴⠶⠛⠉⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠛⠋⠀⠀⠀⠀⢤⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣐⠲⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⣀⡴⣺⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⣤⡈⠁⠀⠀⠠⢄⡀⠀⠀⠹⣆
⠀⠀⠀⣠⢞⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢦⠀⠀⢸⡇
⠀⣠⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣷⣄⣀⠀⠀⣦⠀⠈⢳⡀⠀⠈⢷⣤⡼⠃
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣴⣿⣿⣿⣿⡀⠀⣸⣆⠀⢀⡿⢦⣤⠾⠁
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠿⣿⣷⣄
⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠻⠿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣆⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⣛⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠶⣦⣭⣍⣉⣛⣋⣉⣭⡽⠟⠁

⠀⠀⠈⠀⢠⡀⠀⠠⡀⢀⢀⡀⠀⠀⠀⠀⠀⣄⠠⡀⠀⢀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠳⠀⣄⢡⡄⠀⠁⡁⠃⠀⠀⠠⠀⣤⠑⡄⠀⠇⠀⠀⢠⠀⠀⢈⡨⠀⠖⢈⡀⠀⢀⠁⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⢶⣶⣄⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⣀⣀⣴⠋⠁⠀⠂⠠⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⡾⠛⠋⠉⠉⠉⠙⠲⢤⣀⠃⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠞⠛⠛⠉⠉⡛⠻⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⠔⠒⠈⠉⠐⠒⠢⢄⠈⠑⢦⡀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⡔⠈⠁⠀⠉⠀⡙⢷⡀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢀⠄⠤⠤⠤⠒⠻⡦⡀⠙⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⣀⣤⡴⠶⠶⠶⠶⣤⣤⡘⣧⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⡟⢀⠀⠀⡀⠠⠈⠃⠸⣦⠈⡆⠸⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⣠⠞⠋⠁⢀⣤⡤⠄⠀⠤⢄⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢠⡄⠐⠀⠀⣠⠀⠀⡘⢷⣨⣄⡀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠇⡠⠊⢠⡴⠚⠹⠛⠀⠰⠂⠂⢄⡠⢈⠲⡄⠈⢿⡄⠀⠀⠀⠀⠀⠀⣴⢩⡷⠞⠃⠤⣄⡾⠃⠰⠀⠀⠀⢁⠄⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⣀⣰⠁⠊⠰⠁⠀⡀⣁⠑⡀⠀⠀⠀⠁⢾⠀⠈⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠗⠀⣼⠁
⠀⠀⠀⠀⢀⡶⠛⢦⡀⡿⠁⡀⢹⠁⠀⠃⠀⢸⣿⣀⣦⠃⠀⢠⡌⢙⠀⣷⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⢠⠛⠦⢄⣀⠠⠄⠉⠉⣹⠃⣠⣦⡤⠞⠁
⢠⡴⠶⣤⣸⠃⠀⢸⡷⣇⠀⢷⢠⣀⡤⠏⠀⠈⡻⠛⠉⠁⠒⢿⣥⡟⡀⡸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣤⠚⠢⢤⠴⠞⠁⡼⠁⢸⡆
⣿⠀⠀⠀⢻⡇⠀⢸⡇⠙⢦⣀⠤⠀⠀⡋⠀⢠⡄⠀⠀⠀⠀⠀⡏⢀⣸⠃⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣁⡀⠀⢀⣼⣷⣿⣯⣁
⠈⠳⣄⠀⠀⠳⣄⡼⠋⠙⢶⣧⣀⠆⠀⠈⢇⠀⠈⠢⣤⣀⣤⠞⠋⡤⢻⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡟⠁⡴⠟⡏⡰⠁⡠⠛⢳⠴⠶⢶⡀
⠀⠀⢨⡟⠛⠛⣿⠀⠀⢠⠘⣧⣽⣞⣢⣀⠀⠙⣉⢢⣀⣀⡔⠀⣈⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣾⡀⢀⠞⠀⢱⠧⣠⡇⢀⡄⢀⣤⠾⠁
⠀⠀⢸⠋⠁⠒⢼⡦⠔⠋⠰⠁⡇⠀⠈⠉⠙⣆⢈⡐⠒⡉⢔⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⢨⣴⠅⣸⠋⠀⢀⠞⢦⠄⠀⠀⠀⢻⡇
⠀⠀⠈⢷⣄⠢⠾⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⠸⡆⠀⠙⣄⠤⢧⠘⣎⠓⣦⡀⠀⠀⣀⣠⣤⡀⢀⣴⠏⢨⣗⢊⡟⠀⠁⠠⡴⢿⠀⣎⠳⠤⠤⠖⠋⣷
⠀⠀⠀⠀⠈⠙⠓⠛⠷⠚⠋⠁⠈⢙⡇⠀⠀⢠⡷⣠⠖⢳⠀⠀⢣⠄⠱⠈⣧⣖⠛⢌⡓⠁⠈⡏⢣⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣷⣄⡀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢧⣀⡴⠋⢹⡿⣄⣠⠀⠀⠀⠣⣻⡴⠁⠹⣄⡀⠁⠀⠀⠁⠈⠲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠉⠀⠀⠀⠓⠖⠋⠀⠀⠀⠀⢸⠄⠀⠀⠀⠉⠛⢦⡄⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⠁⠀⣿⠉⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠈⠻⡆⠠⢄⣀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡄⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣇⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢻⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠤⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡡⠤⢄⣀⠀⠀⢸⣿⠁⠀⠀⠀⣀⠤⠽⠷⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠒⠤⣄⡀⢸⠃⠀⠀⠀⣀⡤⠤⠿⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠉⠓⠦⣿⣄⡠⠖⠉⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠉⢻⠦⠤⠶⠛⠉⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣅⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⣂⡀⠐⢒⣒⣒⣫⡵⠋⠙⠶⠶⢶⣶⣶⠶⠾⠟⠛⠀⠀⠀⠀⠀⠀⠈⠳⢾⣥⣤⣶⣾⠿⠟⠛⠳⢮⣽⣓⣒⣒⣒⣒⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⢦⣼⣋⠔⠉⠉⠉⠢⡀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⣦⡀⠀⠀⠀⢀⣠⣴⡏⠀⠀⠀⠀⡈⠙⢦⣄⠀⠀⠀⣣⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⢀⡶⠻⣆⠀⠀⠘⢷⡀⣠⡶⠛⠁⢸⡇⠀⠀⢀⠀⠈⢢⡀⠉⠳⣄⢀⠏⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢠⡾⠻⣇⣠⡽⠧⠤⠄⠈⢿⡏⠀⠀⠀⠀⢻⣄⣼⠿⢿⡖⠒⠻⣦⣠⣜⣧⡀⠀⠀⠀⠀⢿⣦⡀
⠀⠀⠀⠀⣸⣇⠀⣿⠁⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡀⣹⢣⠖⢢⠁⠀⣘⡭⣿⡟⠇⠹⣄⠀⠀⠀⢸⡏⢻⣄
⠀⠀⠀⢸⡃⠙⢦⣽⣷⠶⡆⠀⠀⠀⠀⣼⢦⣴⠟⠉⠉⠙⠻⣾⡟⠀⡰⠁⣠⣸⠙⠦⣤⣽⡄⠀⠀⠀⣷⠀⢻⡆
⠀⠀⠀⠈⠻⢦⣤⡼⠃⠀⠈⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠈⠛⠀⢧⠠⣷⡟⠀⠀⠀⢀⣿⡀⠀⠀⡿⠻⣄⢿⡀
⠀⠀⠀⠀⠀⠀⠙⢦⣤⣀⣤⠀⠀⠀⢀⡴⠻⣧⡀⠀⠀⠀⠀⠀⣠⣆⣈⣉⣭⣴⡆⡶⠛⠉⠈⣧⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⣤⠾⠋⠀⠀⢻⡿⣶⣶⣤⣶⣾⣿⣿⣿⣿⢿⠿⢳⡋⢀⡤⠖⠛⠛⢦⡀⣀⡼⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠻⣦⡀⠀⠀⠈⢧⡙⠋⢽⣿⣿⣭⠽⣿⠁⠀⠀⠈⠛⠉⣠⣖⠀⠀⢈⡟⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠈⠻⣦⡀⠀⠈⠳⣄⠀⢳⡖⠚⢉⡟⠀⠀⠀⠀⠀⠀⠋⠀⠀⣠⡾⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠈⢻⣦⡶⠛⣹⣧⣀⠉⠛⠉⣀⣤⣤⣤⣤⣶⡓⠲⠲⣟⠉⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⣤⡴⣿⠁⣠⣾⣥⠤⠭⠿⣿⣟⠁⣰⣋⠀⠀⠈⠙⢿⣟⠁⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣅⠄⡾⣸⠷⠀⠀⠀⠐⠶⠉⠈⠛⠏⠙⣷⠶⠦⠄⠀⠙⢷⡄⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣼⡃⢀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣤⣤⣴⣞⣀⡼⠷⠦⢤⣤⡴⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠷⠲⠄⣤⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⢀⠖⠀⠀⠀⠀⠀⠀⠙⠁⠀⢸⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣂⠛⠃⠀⠀⠀⠀⡠⠄⣀⣀⡀⠘⠷⠘⠃⠀⠀⡾⠁⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠀⠀⣾⠀⣀⠀⠀⣰⡄⣠⣎⠀⠀⢠⡟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⢇⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠿⠆⠀⢀⠒⢀⣵⠘⠋⠀⠀⠛⠀⣤⠏⠀⠀⠀⢷⡀⠀⠀⠀⠁⠀⠀⠋⠀⠀⠉⠀⢀⣠⣾⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣶⠀⠀⠀⠀⡨⢯⠀⣰⡦⠎⠀⠀⠘⠇⠀⠀⠀⠈⠻⣤⣀⣀⣠⡀⠀⠀⠀⠀⠀⣀⠾⠁⠚⡻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠘⠳⠖⡚⢃⡤⠰⠦⠙⠋⠁⠘⡆⢤⠄⠀⠂⠹⡖⠁⣸⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠶⠚⠁⡆⠀⠀⠀⡶⠀⠀⠀⠀⣷⠄⢠⠆⠀⠁⠀⠸⣇⠀⣤⡀⠰⠶⠎⠀⢘⠀⠀⠀⡀⢷⢠⡶⠞⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠀⠀⠘⠦⡄⢾⡀⠀⠀⠀⣴⠘⠄⡘⠀⠀⠀⠀⠀⠈⠁⠈⢻⡖⠒⠒⠐⠇⠀⠀⠀⠀⣼⠋⠁
⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⣏⣄⠀⠀⠒⠀⠻⣭⠅⠤⠀⢶⡄⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⡸⢧⠀⣰⠇⠀⠀⠸⣀⠘⠃⠀⠀⢴⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠉⠀⠀⡤⠓⢀⠀⠢⣀⠀⢀⠛⠦⣤⡹⣆⠀⠀⠂⠀⠀⠀⣁⠀⠁⡟⠀⠀⠤⠼⠉⠙⠂⣀⣠⠖⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡘⠀⠀⠀⠐⢂⠀⣟⠁⠀⠀⠀⠉⠉⠉⠉⠲⣄⠀⠀⠀⠈⠀⠃⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣤⡇⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠂⠀⠀⠀⢀⡆⠸⣇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡺⢷⡀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠠⠊⠀⠀⡿⠀⠀⠀⠃⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⢋⠶⢉⣿⠙⢦⣄⠤⠶⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣼⠋⠀⠀⠀⠂⢀⡀⠀⠀⠀⡀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠠⠈⠀⠈⠁⢈⣡⠞⠁⠀⠀⠀⠄⠙⣄⠀⢀⡀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⣀⡴⠂⠐⠀⠛⠁⠀⡍⠀⠁⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣀⡶⠛⠉⠈⠋⣠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠸⠏⢀⠀⠀⠛⠐⠀⠀⠀⢀⠀⠼⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠇⠀⠀⠀⠀⣠⣾⡿⠿⠶⢛⡛⠋⣡⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⢀⣤⠋⠀⠉⠀⠀⣴⠀⠟⠉⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠔⠲⣿⣿⣄⣠⡆⠚⠉⠉⠀⠀⠀⠀⠀⡸⠀⠀⣀⠀⢰⡦⠤⠀⠁⠄⠰⠀⠠⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⠁⠤⡤⠙⠿⠿⠟⣠⣶⣄⣀⣼⡿⠿⠖⣈⠀⠀⠀⠝⣁⣳⣖⣒⡐⠂⠀⢀⣤⢥⣤⣤⣴⡖⣛⣉⣴⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⣠⠶⣄⠀⠹⢿⣿⣿⠛⢁⡀⠀⠉⠆⠀⢀⠛⠀⠀⠉⠉⠹⣿⡉⠶⣶⢫⣹⡿⠷⠶⠏⠁⠈⡟⠿⡶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠙⣦⠀⠀⠞⠀⠀⠀⠀⠐⠉⡆⠀⠞⠁⠀⠀⠀⡇⢈⡿⢧⣼⠇⢫⣿⣤⣀⣴⡆⠀⠀⠀⠈⠟⢚⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠛⠒⠿⣖⣒⠀⠤⠔⠊⠁⠿⠀⠨⠧⠄⢴⠓⣾⠁⡘⠛⠷⠷⢆⣈⣉⣁⠒⠙⢃⡀⠄⢶⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⠼⠏⠠⠀⠀⠈⠛⠖⠀⠤⠼⠤⠄⢚⡀⣀⠄⠛⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠟⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠙⢷⡶⠶⠋⠸⡇⠀⠠⠀⠀⠀⠈⠀⡤⠀⠠⠰⠆⠈⠀⠸⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠉⠲⠶⠤⣤⣤⠶⠞⠛⠲⢄⡀⠱⡄⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠈⠄⠀⠈
⠀⠀⠀⠀⠀⡠⠀⠠⠄⣀⠠⠒⠒⠒⡄⠀⡇⠀⠀⠀⠀⠀⢠⡖⠋⠀⠀⠀⠀⠀⠀⠹⣆⢱⣄⠀⣀⣀⠘⠂⠀⠀⠠⢦⣀
⠀⠀⠀⠀⠀⠀⣀⣐⣀⢉⣷⡀⢀⡤⠃⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠁⠀⠈⠉⢣⣀⡀⠄⠴⢀⠠⠘⠣⣀⣀⡀⠀⠀⠒⠂
⠀⠀⠀⠀⣀⠠⠈⠙⠋⣉⣡⣤⠋⠀⠄⠙⡾⣄⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡰⠟⠉⠁⠱⣦⡿⠁⠀⠂⣠⣽⠐⠂⡋⠉⣠⣈⠀⠀⠸⢇⠀⣼
⠀⠀⠀⠐⠛⡌⠀⠒⡖⠲⡏⢸⡁⡐⠒⠈⠔⠈⠳⣤⡼⢳⣀⣀⡦⠰⣏⣀⣠⡤⠔⠛⠀⠀⠀⠀⠀⣼⣄⡰⠋⠉⠠⢨⣼⠃⠁⠈⠛⣍⠁⢶⡀⠈⢀⠁
⠀⠀⠀⠀⠀⠸⣀⠜⣑⠲⡇⢸⠏⣁⠄⠁⢸⢂⡴⠊⠀⢸⢉⡹⢣⡀⠏⢹⠇⢀⣀⣀⣀⣀⣀⣀⣦⡴⢹⡇⠀⣠⠄⠂⠹⠂⡀⠤⣴⠏⠐⠀⠙⢢⡘
⠀⠀⠀⠀⠀⠀⣽⠀⢁⠰⡆⢸⡷⠏⠀⠀⢰⡏⠀⠀⠀⢸⡎⠀⢲⠃⠀⢃⣘⠋⣌⣡⢄⡍⠈⢏⡐⠁⠈⣣⠘⠀⠰⢡⠘⡇⢁⠔⠁⢰⠀⡄⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠈⠋⠀⠀⠀⠘⠀⠀⠀⠀⠉⠁⠀⠉⠀⠀⠘⠁⠀⠘⠁⠈⠁⠀⠘⠁⠀⠀⠉⠀⠀⠀⠈⠈⠁⠉⠀⠀⠈⠈⠃⠀⠉

⠀⢸⡇⠠⠀⠀⠀⠀⢸⡏⣠⣤⣤⣤⣼⣟⡓⠶⣿⡄⠀⠀⠀⠻⣌⠛⠋⠀⢰⡟⣸⣥⣾⣧⣶⣾⣝⣿⣄⠈⢷⡄⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡯⠠⠬⠠⠌⠁⢹⣷⣿⣿⣿⡿⠛⣻⣿⠿⣿⣿⣦⡀⠀⠀⠈⠛⠷⣄⢸⣿⣿⣿⣿⣿⠟⡹⢏⠙⡝⢿⣦⣻⣾⣾⠀⠀⣰⡧⠌⠌⠡⠀⠈⠭⠁⢸⡇
⠀⢸⣧⠠⠄⠁⠀⠀⠀⠙⣿⣿⣿⡟⡆⣼⠿⠓⠈⠻⠈⠻⣦⡀⠀⠀⠀⢹⡇⠻⣿⣿⣿⢳⣁⡑⢂⣘⣵⣬⣹⣟⣿⡿⢀⣴⠟⠅⠤⠁⠄⠀⠠⢄⠀⢸⡇
⠀⠀⣿⠀⠀⠀⡀⠀⠀⢸⡏⠀⠀⠉⠳⣿⠞⠀⠀⠀⠀⢠⣿⠿⠒⢦⣤⣾⠃⠀⠘⠿⣿⣿⣿⡿⢿⣿⡿⢿⡿⢿⣿⣿⣟⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⢐⢒⠀⡂⢃⠀⠀⢻⣦⣀⣄⠀⠀⠰⢶⠟⠙⠀⠈⢡⠶⡇⠀⡟⠁⠀⠀⢀⣶⣼⣿⣌⡇⢸⢏⡇⡜⠀⣾⣏⡍⢻⣶⡿⢖⢦⡀⣱⠞⢲⡄⠀⢸⡇
⠀⠀⣿⢸⣿⡧⡟⡯⠆⣠⣟⡹⢿⣿⠿⡲⢊⠷⠂⠀⠀⠀⣉⠀⣠⣾⠁⠀⠀⠀⢸⣇⠉⠀⠈⣡⣴⣿⡿⠂⣰⠿⠋⠇⣸⣿⡗⡭⢩⣿⣇⠀⠄⣿⠃⢸⡇
⠀⠀⣿⠁⠈⡽⠉⢛⠸⡟⠛⠙⡦⣤⣀⣂⡝⠂⠀⢀⡀⠀⣿⡟⠋⠁⠀⠀⠀⠀⠈⢿⣭⣘⣋⢁⣌⡀⣡⢐⡤⢂⣾⣾⣿⠿⢶⣴⣴⣿⠥⠤⡼⣿⣇⢹⡇
⠀⠀⣿⡤⣿⠏⡿⢧⣾⠳⠋⠀⣀⣼⢿⣭⣥⣴⣾⣯⣙⢦⢹⣧⣤⣤⣀⠀⠀⠀⠀⠐⣿⡟⠚⠿⠧⠟⠿⢀⣴⣿⣿⣿⣇⡀⠀⠀⢨⠁⠀⣀⣴⠃⠱⢹⡇
⠀⠀⣿⢃⣠⣥⠙⠙⣯⣻⠽⣶⠏⢁⡾⣹⠟⠉⠀⠀⠙⣆⢧⢻⡄⠈⠙⢷⣄⣠⣴⣶⣿⣿⣮⣍⣐⣠⠜⠉⣹⣇⠹⣏⠙⠻⢶⣶⣻⡶⢦⣿⠿⡗⠚⢻⡇
⠀⠀⣿⢉⣿⣷⢤⣷⣰⡏⠀⢿⣴⠟⣰⣣⣶⣶⡀⠀⠀⢹⡈⣇⢻⣦⣄⢠⡟⠋⠁⠀⠀⢘⡏⠽⡍⠓⠦⣤⠃⠹⡆⠹⡆⠀⠀⠛⢷⣷⣔⡷⡆⠀⠀⢸⡇
⠀⠀⣿⡿⠋⡏⠀⠉⠀⣇⠀⢠⣯⣺⠟⠉⠀⠀⠙⣦⣆⡼⠁⠙⢶⣿⣿⠿⠦⠀⢸⣷⡄⢸⡇⣀⣥⣤⣤⡤⠤⠦⢿⠄⣿⣿⣄⢀⡴⠛⠙⢷⣿⣏⡉⢸⡇
⠀⠀⣿⠁⢠⠷⣶⡶⠦⡷⠀⣾⣯⣥⣤⡀⠀⣠⣤⣿⠏⠀⠀⠀⠀⠈⠹⡆⠀⠀⣨⣿⣿⣾⠡⡀⢈⠇⠀⠀⠀⠀⠈⠷⢿⣿⣿⡟⠁⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⣿⠉⠀⠀⡟⠀⠀⣷⡾⠋⠁⠀⠈⠙⢷⣿⣿⣿⠞⢀⡀⠀⣠⠀⢠⣏⣤⢾⣿⣿⣿⡿⠀⠉⠁⠴⢖⣒⣒⣲⣭⣥⣭⣹⣿⣦⣄⠀⠀⠀⠀⠻⠿⣿⡇
⠀⠀⣿⠉⢀⣴⡧⣦⣾⠋⠀⠀⠀⠀⠀⣠⣾⣻⣿⣿⣷⣿⣥⣾⣧⣴⣿⣿⣕⣦⣼⡟⢓⠶⠉⠈⠉⣁⣀⣀⣀⣠⣤⡤⢤⡼⣿⡉⢿⣷⣴⠆⠀⠀⠀⢸⡇
⠀⠀⣿⡀⢈⡱⠞⣿⡇⠀⠀⠀⠀⣠⣾⣿⡧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣚⣛⣉⣉⣭⠝⠛⠳⠶⡖⠉⣀⡺⢿⡇⢸⣿⠇⠀⠀⠀⠀⢸⡇
⠀⠀⣿⠀⢀⣴⠟⠋⠀⠀⠀⢠⣾⣿⣿⣳⣶⣶⣾⡟⢛⡻⢋⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣶⡒⠶⠶⢳⣶⣶⣶⠚⠁⠤⠋⠀⣻⣿⡼⣿⣀⢺⣧⣄⡀⢸⡇
⠀⠀⣿⠀⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⡉⢻⣿⣿⣿⣟⡥⢚⣡⠞⠉⠀⠀⢿⣿⣿⣿⣏⠀⢀⣥⣤⣤⣸⣿⣿⡿⠀⠶⠒⣛⣭⢟⣿⣿⠌⠛⠻⣿⣅⣀⣸⡇
⠀⠀⣿⣄⣹⡇⠀⠀⠀⠀⢀⣴⠄⣿⡇⠀⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠸⣿⣿⣿⠻⡛⠲⠶⠶⠤⢤⣤⠤⠶⠶⠟⠋⠁⣀⣬⠞⠻⣷⡀⠀⠈⠛⠛⢻⡇
⠀⠀⣿⠀⠀⢿⣃⠘⡆⠀⠙⣹⣿⢿⣇⠀⠀⡏⠋⣿⡟⣿⣿⡧⡀⠀⠀⠀⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⢶⣾⣿⡉⠀⠀⠀⠘⣿⡀⠐⠂⠀⢸⡇
⠀⠀⣿⠀⠀⠈⠿⠷⠿⣶⣾⠋⠀⠀⢿⡄⠀⠇⢰⡿⠀⠈⠻⣷⣄⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢜⣿⠟⠁⠀⠈⣿⠿⢟⡻⠀⢰⡿⠀⠀⠀⠀⢸⡇
⠀⠀⢿⣤⣤⣤⣤⣤⣴⣶⡄⠀⠀⠀⠘⣷⠀⠀⢸⣧⡀⣠⣤⡈⠻⣇⠀⠀⠈⢻⣿⣿⣿⠄⠀⠀⠀⣴⡿⠋⠀⠀⠀⣸⡏⣠⠟⣀⣀⣾⠃⠀⠀⠀⠀⢸⡇
⠀⠀⢸⡯⠍⠉⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢿⡷⠀⠀⠀⢠⣿⡀⠀⠀⠸⣿⡿⠿⡤⠤⣄⠀⣿⡇⠀⠀⠀⣠⣿⣤⢖⣟⠯⠟⠛⠛⠿⢶⣄⠀⢸⡇
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣷⣀⣀⣠⣾⠁⠀⠀⠀⠈⢿⣄⣀⣀⣤⣿⣿⣥⣰⣿⣭⠷⣿⣇⢀⠀⢠⣏⣯⣿⠞⠁⠀⢀⣀⣠⣤⣤⣜⣷⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡏⢹⣦⡀⠀⠀⠀⠀⢹⠟⢻⠁⢄⡀⢀⡄⠠⣧⠈⠉⢻⡿⠿⢿⣿⣅⣤⢐⣴⣾⣿⣿⣿⣿⣿⣿⡿⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⢶⣾⣿⣶⣬⣭⣛⣛⡛⠿⠿⠿⣻⣥⣤⣤⣤⣤⣿⡶⠈⠚⠋⠱⠞⠑⠋⠁⢈⢦⡾⣿⣶⣾⣿⣯⡳⢾⣿⣿⣿⣿⣿⣿⠿⢛⡅⢸⡇
⠀⠀⢸⡇⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡁⠛⠒⠛⠉⠉⠉⣉⠉⣁⠬⣰⠿⠿⣿⣿⣿⣿⣷⣮⣭⣅⣀⣠⣶⣿⠿⠃⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣻⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣠⣤⣾⡏⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠘⡷⠶⣶⢶⡶⠶⢶⠶⠶⠶⢶⣶⠶⠶⠶⢶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣚⠭⠅⡉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⣴⠞⢷⡘⡆⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⠉⠍⣉⠙⠳⢥⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢠⣤⡴⠒⢻⠿⢿⡏⠳⣄⠀⠈⣧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠉⣇⠀⠐⢙⣦⠉⠓⢛⣧⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠛⠛⠿⠀⢡⣸⡿⠀⢰⠋⢠⠗⠲⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣤⣤⣿⣿⠇⠘⠶⢣⡮⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡶⣾⡿⣿⠟⣻⠅⠀⠀⠀⣀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⣦⣀⠈⠩⠄⢀⣠⢤⡾⢥⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠊⠁⠀⠀⢈⡉⣲⠆⠙⠍⠖⠁⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠄⠀⠀⡴⠁⠀⠘⠂⠼⠊⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠛⣀⣣⣄⡀⠀⠀⠀⠀⢀⡔⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠾⠟⠀⠀⠀⢿⣶⡶⣶⠖⠛⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠤⣄⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣀⡀⠀⢘⡇⠀⠀⠀⣀⣀⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠉⠛⢻⡤⢶⠞⠋⠁⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣍⣉⣉⡭⠭⠭⢿⠲⡤⠤⠤⠤⠤⠤⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠚⠛⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠈⠀⠔⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿
⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠂⢶⠒⡄⠀⠚⣅⠀⠐⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠁⠀⣠⣴⠆⠈⠁⠀⠀⢀⠠⠐⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⢋⠁⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠁⠆⠀⡀⠐⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠀⠘⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠀⠀⠀⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢀⠴⠊⡹⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⡠⢞⡷⢺⣷⣷⢾⣷⣧⠴⠚⠉⢃⣤⢸⠱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡹⠋⠀⢈⠀⣾⢛⠁⢸⣏⣤⣤⡀⣸⣯⡼⠃⠀⡇⢠⠚⡆
⠀⠀⠀⢠⡄⠀⠀⢠⣾⣿⢅⣶⣄⣾⡷⣼⢿⣧⡾⠛⣿⠿⣴⠟⠋⠀⢠⢻⡶⠁⠀⣷⠀⠀⢀⡀
⠀⠀⠀⢈⡑⢦⣀⡟⠛⠙⣿⣿⠟⢹⠟⠁⠘⣋⠀⣸⠁⠀⠀⠀⢀⣴⢯⡿⠁⠀⠰⢿⣤⣾⠥⣧⣀⠀⠀⠀⡀⠂⡆
⠀⠀⠀⠈⢧⡀⢩⣷⣶⣠⣹⠏⠀⠀⣶⡇⣼⣿⣼⣿⠀⠀⣤⣴⣿⣵⣿⣤⡀⠀⠀⣠⡟⠁⠀⠀⠈⣧⠴⠊⠀⣰⠇
⠀⠀⠀⠀⠘⢿⡎⠹⣿⣿⡿⢸⡿⠆⣿⣵⣿⣿⣿⡟⣷⣤⣀⣩⣴⡇⠈⠻⣿⣶⣾⡟⡀⠂⢙⣦⢰⡏⠀⠀⠈⢿⠂
⠀⠀⠀⠀⠀⠈⢧⣠⡈⢿⣷⠿⣿⣾⢟⣵⣿⣿⣿⣾⠿⠛⠋⠉⠙⠛⢦⠀⠀⠉⣻⠀⢣⠀⣼⠗⡉⠀⠀⠀⠀⢠⣅
⠀⠀⠀⠀⠀⠀⢘⣿⣿⡦⠈⠛⢋⣄⣿⣿⢿⠟⣸⡇⠀⠀⠀⠀⠀⠐⡄⢳⡀⣰⡇⠀⠈⠘⣱⡾⠁⠀⠀⠀⠶⡜⠙⣇⠐⠦
⠀⠀⠀⠀⠀⠀⢸⢫⣭⡿⠀⠀⠙⢻⣽⠷⠶⠚⠛⠓⠂⠀⠀⠀⠀⡠⠛⠚⠛⠉⠀⠀⠀⠀⢹⡠⠒⠒⢀⢰⡰⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⠂⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢠⡼⠃⣠⣴⣿⠜⠁⢀⣼⣿⠀⡧⠤⠀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣄⢀⡤⠀⠀⠀⠀⠀⠀⢠⡾⠿⠁⠀⣼⣇⠰⠟⠛⠉⠠⣦⣿⣿⣤⣶⡟⠉⠃⢂⡄⢸⡟⢡⠀⡅⠀⠀⣀⡴⠓
⠀⠀⠀⠀⠀⠀⠀⠷⣠⣤⣘⣶⣎⣁⣂⣀⣢⣴⢻⡾⠟⠀⢀⣤⣾⣿⣗⣠⠈⣻⣦⣤⣬⣤⣤⣌⠋⣀⣴⣾⣵⣿⢁⡞⣴⠳⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠙⠃⠷⠛⠛⠂⠛⠋⠁⠀⠀⢰⣿⡀⠈⡿⡍⠻⣿⣿⣿⠛⢻⣿⣿⣟⠛⣿⣿⣿⣿⡿⣣⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⡰⠛⠛⣇⠀⠀⢀⣀⣀⣀⠀⠀⠠⣰⡅⠛⠉⠉⠀⠁⡀⣧⡝⠂⠘⢤⠛⠛⡿⣿⣷⣿⣿⣿⣣⣾⣿⣿⡿⢻⠦⣄
⠀⠀⠀⠀⠀⢠⠣⠛⠃⢸⡷⠿⠿⣿⠋⠙⠛⠓⠒⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠈⡟⢡⣿⣿⣿⣇⣸⠒⠋
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠉⠀⠀⢲⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠬⠀⠀⠀⢠⠿⣿⣿⠀⠀⠀⢸⣿⡿⠀⡈⣯
⠀⠀⠀⠀⠺⡀⢤⣤⡀⠀⠀⣠⠌⢹⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢉⢹⡄⠀⠀⢸⣿⠃⠰⠁⠘⠢⣄
⠀⠀⠀⠀⠀⠘⠚⠏⢡⡤⠚⠁⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠑⣸⣠⣼⣾⡇⠀⠀⢸⣿⣿⡇⠀⡀⠀⠈⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⣦⣘⡻⣦⣾⣭⠏⡗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠿⠟⣿⣿⠀⠀⣾⣿⣿⣿⠖⣹⠟⠛⡛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢰⠷⠿⠻⠶⢿⣿⣷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡾⠋⠀⠀⠀⠘⠛⣽⣇⣸⣻⣿⣿⣿⠋⢡⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠹⣿⣿⣿⣇⠀⠤⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣾⢀⣿⡙⢦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠠⠄⢠⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⢀⣀⣹⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠋⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠠⠄⠉⠉⠛⢿⣿⣿⣿⣄⡁⠀⠀⣀⣠⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢿⣿⣿⠁⠶⠇⢀⡀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣄⠐⠒⠀⠀⣼⣿⣿⣿⡟⣿⣶⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢸⣿⣿⣷⣄⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠠⠤⠒⠾⠻⠿⣿⣿⣿⡤⣿⢈⡛⢿⣿⣿⠄⣆⠀⠀⠀⠀⠀⠀⠀⢈⡘⣿⣿⣿⣿⣿⠿⠿⣛⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠤⠠⠆⠀⠐⠉⠉⠛⠛⢻⣿⢸⡇⠁⠀⠈⠙⣖⣷⣦⣀⠀⢀⣀⣀⠐⣱⣾⣿⡼⠒⠒⠒⠉⢁
⠀⠀⠀⠀⠀⠀⢢⣀⡄⠀⠐⢶⣄⣰⣁⣠⣤⣤⣶⣶⡿⢹⠇⠸⠷⠀⠀⠟⣈⠉⠻⣷⣾⣿⣿⣿⠿⢿⣙⡇⠀⢠⣤⣰⣆⣀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡋⣤⣾⣿⣿⡛⠿⠖⠉⠋⠉⠉⠛⠁⠀⠀⠀⠀⢠⠖⠉⠁⠠⣤⠦⠠⠄⠵⠂⠞⠛⢧⠀⠸⠍⠻⠉⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⢀⡀⠀⡀⢠⣤⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠀⢠⣿⡇⠀⠀⢸⡿⣾⡇⠈⢻⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢀⡽⠿⠯⣧⡀⢨⣧⠿⠿⢦⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⢶⠒⠶⠶⠖⠒⢲⠖⡐⣊⢵⡶⠒⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠢⣑⣤⣗⠸⡄⠘⡓⢧⡽⠓⠳⣄⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣥⠌⡁⠙⠣⡈⢾⠀⠀⠀⠀⠀⠈⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣄⣀⣀⡽⢜⡧⣈⣑⣦⡤⠊⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠹⣤⠎⢡⣝⠏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⢊⣡⠚⣇⠘⡃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⣰⢚⡿⠛⠯⣀⠗⣻⠀⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠴⠐⠋⠉⠁⠀⠀⠈⠉⠢⡀⠀⠀⢸⡀⡇⠀⡶⠁⠀⠨⠕⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠉⠙⠤⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⣀⣠⢖⣲⣄⣀⣀⣤⣤⣄⠠⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⢨⠃⠐⡿⠆⠀⡇⠀⣘⣿⠒⠒⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣔⠛⡏⠈⣦⡈⠀⠳⠋⠁⣰⣵⡟⠒⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡤⡔⠛⠉⠛⣅⠀⠈⠉⠻⢶⡃⠀⠀⠀⠀⠀⢏⢫⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢺⢁⠀⡀⠁⠀⠀⣹⣇⡴⠀⠀⠀⠙⢳⣦⡀⠀⠀⣼⣸⣀⡀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣇⠈⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣸⡅⢰⡆⢀⡏⢙⢟⡲⠄⠀⠀⠀⣷⣱⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠁⠀⠘⢦⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⢋⣷⣉⡤⠺⡗⢹⠀⠙⠒⠒⠒⠊⠀⢷⣼⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡀⠀⠰⣶⠀⠈⢧⣀⠀⠀⠀⢳⣀⠽
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣶⣝⣦⡄⣸⠃⡞⠀⠀⠀⠀⠀⣠⠤⠒⠛⠉⠑⠢⡀⠀⠀⠀⠹⣿⡟⣻⠟⠀⠀⠉⠀⠀⠈⢹⣇⡤⠚⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠓⠚⠁⢸⡃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠋⠙⠲⠤⠤⢠⡴⠒⢳⠀⠀⠀⠀⣠⠞⠁⠀⠀⠙⣾⠇⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢀⠎⠀⠀⠈⣤⠤⠖⡋⡁⠀⢀⠀⣀⣠⠇⠀⠀⣤⣤⠈⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢣⣀⣄⣿⠿⠚⣏⠟⠉⠀⠀⠀⠀⠀⠁⠀⠀⣠⢤⣤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠧⣀⡀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⣸⣿⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣯⡀⠀⠉⠛⠒⠛⠋⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⢴⠄⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠙⠳⠦⣄⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠈⠁⢸⠄⠀⠀⠀⠀⠀⠀⠀⡴⣦⡴⢦⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠓⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠲⠾⠧⠼⠈⠁⠀⠀⠀⠀⢼⡿⠿⣿⣷⠄⠀⠀⠀⡀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⡆⢹⣿⣤⣤⣴⣿⣿⣷⣄
⠀⠀⠀⠀⠈⠀⢀⣠⣶⣶⣦⣄⡀⠀⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⢿⣿⡿⠁⢸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣇⠀⠹⣿⣿⣿⣆⣠⠄⠀⠴⠃⠀⠀⠐⠙⠂⠒⠀⠀⠈⠀⠀⢴⣿⣿⡿⣿⡇⢻⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡿⢛⣃⡀⡈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣤⣾⣿⣿⣿⣿⣧⣤⡀
⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⣿⣴⣿⣿⣿⡿⠶⠞⠁⠀⠀⠀⠸⣿⡄⠀⠀⠿⣁⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⢟⣥⡶⠂⠀⠀⠀⡄⡀⠀⠸⠀⠀⠀⠰⠌⢀⠌⠀⠀⡀⠀⠹⣶⡀⠀⢹⣦⡙⣿⣿⣿⣿⣿⠋
⣶⣦⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⠀⣸⣿⣿⢹⣿⣿⣿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆⠙⢈⣿⣿⣟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠃⠀⣼⣿⣿⣿⣧⡀⣠⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠂⠈⠉⠛⠀⠖⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⢱⣿⣿⣿⣿⠟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⣰⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠖⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣾⣏⠙⢻⣿
⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄⠀⣿
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠟⠀⢀⣿
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠑⠚⣾⠇⠀⢀⣄⠀⠀⠀⢀⠀⠀⣼⡾⠴⠛⢇⠀⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⣀⣴⡾⠋
⣿⠟⠋⣩⣾⣷⣧⡀⠀⠈⠂⢢⣤⠄⠀⠀⠀⠀⣠⠃⠀⠀⠀⠈⠀⠀⠃⠀⠀⠈⠙⠇⠀⠀⠈⠃⢠⣤⠆⠉⡐⠀⠀⠀⠈⠛⠿⠿⠁⢀
⣿⠀⢸⣿⣿⠿⠋⠀⠀⡠⠐⠊⠁⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠉⠁⠐⠀⠀⠀⠀⠀⠀⣴⣿
⠿⠦⠸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠈⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⡠⠊
⠀⠀⢀⡴⠋
⣀⡴⠋
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡚⠭⠅⡈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣰⣼⠞⢳⡘⡆⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⠀⠍⣉⠙⠓⢥⡀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢠⣤⡴⠒⢻⠿⢿⡏⠳⣄⠀⠈⣧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠉⣅⠀⡐⢘⣦⠉⠓⢛⢧⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠛⠿⠀⠁⣸⡿⠀⢰⠉⢠⠗⠲⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⣤⣤⣿⣿⠇⠘⠶⠡⡎⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡶⣾⠿⣿⢟⣻⠄⠀⠀⠀⣀⣠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⢦⣀⡈⠩⠄⢀⣠⠤⡾⢥⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠁⠀⢈⣙⣲⠾⡙⣎⡶⠃⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠛⣆⢀⠀⡴⠁⠀⠙⠢⠜⠋⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠈⢻⣄⣳⣤⡀⠀⠀⠀⠀⢀⡜⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⠟⠉⠁⠀⢿⣷⠶⡶⠚⠉⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠦⣄⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢻⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⣄⣀⠀⢈⡇⠀⠀⢀⣀⣀⣼⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠈⠛⢻⡤⢶⠞⠋⠀⠀⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣭⣭⣭⠭⠥⠤⢿⡒⡢⠤⠤⠤⠤⠴⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣻⣛⢳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣯⣿⣿⣿⣿⣷⣄⠀⠀⠀⢀⣿⣿⠟⢋⡋⠀⢉⡙⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣧⠀⠀⠸⣿⣇⠀⠀⣶⠀⣶⠈⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⡩⢿⠀⠀⣟⠢⠉⢻⣿⡇⠀⢸⢉⣿⣄⣰⠉⠀⠙⣂⣠⣿⠉⡇⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⡸⣿⣧⡀⠇⡾⠓⠒⢿⠀⢀⢸⡿⢧⠀⠘⢮⣿⣿⣿⣶⣶⣾⣿⣿⣿⠖⠁⣸⢁⠏⡜⢳
⠀⢠⣴⣦⣰⠋⠈⡇⠀⠀⣇⣿⡿⣿⣿⣧⣀⣠⣼⣿⣿⠛⣿⡼⠀⠀⠀⠈⠹⡋⠉⠀⠉⠉⡟⢟⠙⢦⡟⠘⠀⡔⢻
⠀⢿⡀⠀⢻⡆⢀⣧⣤⡀⠈⠛⢧⡈⠙⠻⠟⠻⠟⠉⣡⠜⠉⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢠⠃⠘⡀⠀⠀⠀⠀⢀⡞
⠀⠀⠹⣶⠶⢿⠋⠀⡜⣧⡀⠀⢀⣽⣷⡶⠶⠶⢶⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠒⠚⢻⣦⡀⣷⣆⣤⣄⡤⢾
⠀⠀⢰⡋⠛⢾⡗⠛⠑⢻⣇⣠⢋⠟⢿⣦⣶⣶⣼⡟⠳⡘⣆⠀⠀⠀⠀⢠⡾⢿⣧⣤⣤⣼⡿⣿⣾⠗⠮⠤⡶⠃
⠀⠀⠀⠻⠿⣯⣤⣤⠶⠋⠈⠁⣎⢀⣼⣿⣿⣿⣿⣧⣀⣧⠘⡄⠀⠀⢀⢣⠁⢸⣿⣿⣿⣿⡇⠘⡆⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠈⠋⠙⠉⠉⠉⠉⠉⠙⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡿⠿⣿⣷⣄⡀⢰⣿⣿⠟⣉⠉⠛⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠉⣴⣟⣛⣉⣿⣿⣿⣿⡇⣼⢿⣾⣿⠀⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠰⠶⠞⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠀⠀⠀⠈⠉⢻⣿⣧⣦⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣏⠛⢉⣴⡶⠶⠿⠿⣿⡏⠀⠀⠀⣼⣿⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠋⠀⠀⠀⠀⠈⠑⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⠀⠀⣴⣾⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⢀⣤⣤⣴⣾⣿⣿⡇⠀⢻⣿⣿⡿⠃⠀⠀⠀⡀⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠉⠁⠀⠀⠀⣴⠏⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠳⣤⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣍⢻⣿⣿⣿⠃⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠈⢿⣿⣿⣷⣽⣿⣋⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠚⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢠⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣶⡀⠀⢰⡄⠈⢿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣀⣈⣿⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⠿⠿⠿⠿⠛⠁⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡏⠀⠌⢹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⠿⣿⣻⣶⣶⣿⣿⣿⣿⡆⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⢙⣿⣿⠛⠛⣻⣿⣿⢯⣀⣤⣾⣿⡟⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣭⠁⠀⣭⡈⠙⣾⡟⢿⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⠉⠀⠀⠙⠃⠀⠈⢡⣄⠙⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣦⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣍⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣷⣿⣿⣿⣷⠀⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡆⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⣼⡏⠉⠁⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢠⡶⣶⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣴⣿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣥⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜
⠀⠀⠀⠀⠀⠀⠂⠀⣀⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⡠⠂⠀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢹⣿⣿⣿⡿⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠐⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠆⠒⠛⠛⠛⢿⣧⠀⠀⠠⠟⠛⠁⠘⠛⠿⢿⣿⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡶⠶⠖⠚⠛⠻⠿⡏⠀⠀⠀⠲⠖⠛⠒⠛⠻⢿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣶⣤⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣥⣄⣸⣆⣄⣀⣜⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣭⣯⡭⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠄⠐⡄⠀⠀⠀⠀⠀⠀⡠⠆⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠄⠱⣶⠒⠄⠀⠀⠠⠁⠀⠻⠆⠀⠀⠰⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠊⠀⠀⠄⠘⠁⡔⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠐⠀⠀⠈⠂⠀⠀⠁⠀⠀⠈⢀⣀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⢠⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⡀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠃⠄⠁⠀⠙⡖⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠨⡀⠠⣀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⡔⠀⣂⣀⠤⠧⠴⠁⠀⠀⠀⠀⠀⢑⠄⠤⠒⠀⠀⠁⠀⠀⠀⠀⠀⠀⡈⠂⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑
⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢄⡠
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⡀⠌⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠄
⠀⠀⠀⠀⠀⡀⢀⠀⠀⠈⠀⠀⠀⠃⢀⠀⡀⢀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚
⠀⠀⠀⠀⢀⠀⠀⠠⠐
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⡆⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢴⠀⠠⠒⠢⠀⠀⠀⠀⠀⠠⡄⠀⠰⢤
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⢺⡗⠲⡗⠚⠓⠖⠲⠖⠂⠀⠀⠀⠠⢀⠆⠀⠀⠆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡤⠀⢀⡁⠀⢈⠁⡇⢠⠀⠓⣠⠀⠀⠀⢀⢀⡠⣴⠆⠚⠕⠀⠀⠀⠀⡉⣀⣤⠤⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠈⠋⠉⠈⠙⠋⠉⠙⠁⠙⠛⠁⠀⠀⠀⠀⠀⠐⠀⠚⠉⠀⠀⠀⠀⠀⠀⠐⠀⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀⠀⠄⠠⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠂⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠉⠀⠈⠀⠀⠁⠀⠀⠀⠂⠃⠃
⠀⢀⡠⠄⠡⠴⢤⢤⡠⢤⡀⠀⠘⠀⠀⠀⠀⠀⠠
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢹⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠉⢉⠑⠄⠀⠀⠀⢆⠀⠀⡄⢀⠀⢀⠂⠀⠀⠠
⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⡐⠁⠀⠀⠆⠐⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢾⠀⠀⢆⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠠⠐⠈⠐⠠⠀⠀⠀⠀⠀⠃⠂
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠙⠲⠶⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠑⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣰⣧⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣄⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡉⣤⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⣀⡀⠀⠀⠁⠀⠀⠀⠀⣾⣦⠘⢣⣾⡆⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠧⠛⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠋⠉⠁⠀⠘⠀⠀⠀⠀⠀⢿⠟⢠⡘⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⢀⠀⠀⠀⠀⠀⢀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⢀⠔⠁⢸⡇
⡆⠒⠂⢰⠂⠒⠐⢻⠛⠛⠛⠟⠃⠒⠒⠆⠂⡆⠂⡖⠂⠖⠂⢲⠐⢰⠒⠲⠒⠐⠖⠒⠖⠀⠶⠒⢰⠒⢳⠐⠂⠚⠗⠐⠒⠒⡆⠒⠒⢰⠒⠀⠒⠰⠒⠒⠂
⡗⢲⠖⠚⠒⠲⠒⠚⠒⠖⠒⠓⠒⠒⠒⠀⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠒⢲⠒⠓⠒⠒⠒⠓⠒⠖⠚⠒⠲⠒⠚⠒⢶⠒
⡇⠈⠁⢰⠀⠈⠀⢲⠀⠁⠀⠆⠀⠁⠐⠆⠀⠇⠀⠇⠀⠦⠀⠼⠀⠸⠀⠰⠄⠠⠆⠀⠆⠀⠤⠀⠸⠀⢸⠂⠈⠀⠒⠀⠁⠀⡆⠀⠁⢰⠂⠈⠀⠰⠀⠉
⡇⢰⠂⠈⠀⠐⠀⠈⠀⠒⠀⠁⠐⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢲⠀⠉⠀⠒⠀⠁⠐⠂⠈⠁⠐⠂⠈⠀⢲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠿⠿⠿⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⢁⣠⡤⣦⣴⢤⣄⡀⠀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣴⠛⠁⠀⢀⠀⠀⠈⠙⢷⡀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢀⣠⣤⡿⠶⠟⠛⠛⠛⠿⠿⢶⣶⣄⣽⠃⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣠⡶⠟⣩⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⢀⣉⣙⠻⣦⣄⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⠏⠀⣾⣿⠿⢿⣿⡉⠉⠉⠉⠉⢙⣿⣿⣿⣿⣷⡌⠙⣷⡀⠀⠀⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣇⣠⡾⠋⢠⡴⠶⣌⠃⠀⠀⠀⠀⢛⣩⣥⣈⠙⢿⣿⣄⠈⢿⡆⠀⠀⠘⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⣛⣿⠁⢰⠏⠠⠔⣘⣧⠀⠀⠀⣴⠋⠀⠄⠙⣷⠀⠛⠻⣦⣸⣿⡀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⡿⣿⠀⣿⠀⣆⣼⣯⣿⣤⣀⣰⡇⠰⢀⣶⣷⣿⠄⠀⠀⠈⠛⠻⣧⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⣈⣵⡟⠀⣻⡶⠋⠁⠀⠀⠀⠈⠙⢷⣆⢸⣷⣼⣿⠀⠀⠀⢀⣠⡾⢻⡄⢀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣄⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣎⣻⡿⠃⠀⣀⡀⣿⡁⠀⣸⠟⠛⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣁⣠⣴⣾⣿⣿⢼⣇⣸⢋⣠⠤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠏⠀⠛⢁⣾⡧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠁⠀⠀⠀⠸⡇⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⣰⡾⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠉⠙⣿⠿⠼⠿⠿⠿⢿⡖⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢁⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠻⣦⣄⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠸⣿⠟⠛⠛⠛⣻⠁⠀⠀⠀⠀⠀⣠⡾⠟⢿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢽⠟⠁⢠⣬⣿⣤⣶⠶⠶⠾⠿⠟⢻⣿⠿⢻⣷⡀⠀⠙⢦⣄⣠⠞⠁⠀⠀⢀⣠⣴⣾⣿⣷⠶⠟⠁
⠀⠀⠀⠀⣠⡶⠟⢻⡇⠀⠀⠀⠀⠈⠀⢠⡟⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⣾⠃⠙⢶⣤⣀⣈⣀⣀⣠⣴⡾⠟⠉⠀⣿⠉⠙⠻⢶⣤⣀
⠀⢀⣴⠟⠋⣀⡀⠀⠃⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⢀⣾⠃⠀⠀⠀⠈⠉⣙⡛⣽⠟⠁⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⠛⢷⣤⡀
⢠⣾⣫⡶⠟⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣀⣤⣾⠷⠶⣄⠀⣸⣇⣠⣤⣤⣀⣀⣀⠀⣸⠏⠀⣀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⣸⡿⠃⣠⡴⠚⢿⡀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠛⣻⡟⢉⡿⠁⢸⡆⣿⢀⡿⠉⠉⠉⠉⠉⠉⠉⣻⣏⡴⠛⠉⠙⢦⡀⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⢹
⣿⣧⡾⠋⢀⣤⠞⠃⠀⠀⠀⠀⢀⣠⡿⠿⠶⠾⠟⠁⢸⣇⠀⠜⣡⠏⣼⠇⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠀⣴⠘⡇⣿⡀⠙⢷⣄⠀⠀⠀⠀⠀⡘⢸
⠈⠻⣷⣴⣿⠉⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⣼⣿⣳⢚⣫⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⣦⡀⠐⣁⡞⣹⡟⢿⣤⣾⡟⠛⠀⠀⠀⠴⣱⡿
⠀⠀⠀⠈⠛⠷⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣉⣉⣡⡶⠋⠀⠈⢿⠛⣷⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢰⠀⣿⣦⡿⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⢄⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸⡇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⣿⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠈⠉⠛⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠜⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⠛⠛⠛⠻⢶⣤⣀⠀⠀⠀⠀⣸⡟⠀⠀⣀⣤⣴⠶⠾⠛⠛⢻⡿⠿⢷⣬⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣿⣧⡴⠟⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣼⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠉⠉⠛⠛⠛⠛⠛⠉⠉⣉⣩⣉⣀⣸⣿⠛⠳⠶⠦⣤⣤⣤⣤⣤⣤⣶⣶⡶⠾⠿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠛⠿⠷⣦⣄⣀⣀⣀⠀⠀⠀⣀⣀⣀⣠⣴⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠌⠀⢁⣤⠑⡂⠑⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⢠⠀⠁⠀⠀⠀⠀⠈⢠⠀⡇⠀⢾⠲⣄⠀⠀⡠⠊⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⣉⡞⠀⠀⠸⠁⠀⠸⠋⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡀⠀⠁⠹⡄⠀⠀⡀⠀⠀⠀⠀⠰⠁⠀⠙⢦⢀⠦⢀⠈⠀⡁⠀⠠⠤⠛⠐⢢⡀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢦⡀⠹⠦⠀⠀⠀⠀⠀⠠⠁⢀⠀⡼⠋⡈⠀⠀⠈⠀⡀⠁⠒⠒⠈⠔⠈⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠐⠄⠀⠀⢃⣠⣦⠀⡰⠀⠘⠀⠐⠂⡀⠈⠢⠤⠊⠀⠀⠀⠀⠀⣠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠁⠀⠜⠱⠚⠁⠐⣦⣤⣄⡀⠬⠯⣋⠅⠐⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠜⠁⡤⢄⠀⠃⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠶⠀⠀⠀⣰⠀⡀⠂⡈⡠⢊⡀⠀⠴⠀⠀⠀⠀⠀⡖⠀⠀⠀⠰⠀⠀⠀⠀⠀⠠⢆⠐⡡⠀⠀⠶⢠⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠄⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⡴⡤⠀⠐⠂⠃⢀⠃⠈⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠈⠀⠀⡎⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠄⠀⡄⠒⠁⣌⡐⠀⠘⢤⠃⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⣦
⠀⠀⠀⠀⢀⡮⠀⠤⡀⠀⠀⠀⡀⠀⠀⠘⡀⠀⠀⠀⢓⡶⠤⠀⡖⠀⠀⠀⠀⠈⠂⠀⠲⠀⢘⡂⠋⡄⠐⠀⠂⠰⢰⠀⠀⡀⠁⠀⠀⡤⠀⢄⡀⠈⠁⠁
⠀⠀⠀⢀⠉⠔⢪⣀⣈⠋⠀⠂⠀⡀⠐⡀⠀⠦⢀⠁⠐⠎⡀⠐⢁⠀⠀⠀⠀⠀⠁⢠⡇⠀⠈⠑⠀⠉⠂⠤⠀⠀⠀⠐⠒⠓⠅⠀⠀⠢⠀⠬⠀⠑⠄
⠀⡠⠠⡏⡠⠀⡀⠤⠀⠀⠥⢀⡀⣍⠀⠙⠀⠑⠀⠉⢀⠀⠉⠠⡀⠐⣀⠠⠀⠒⠂⠐⠂⠀⢆⡠⠛⠀⢢⢀⠀⢠⠈⠀⣤⡆⠄⠀⠀⠀⠀⠠⠤⢀⡠⢃⡀
⠀⢀⣰⡣⠀⠁⠀⠀⠀⠠⠀⠀⠀⠙⣖⡧⠀⠦⠤⠄⣈⠓⠂⠀⠘⠊⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠠⠈⠂⡈⠙⠓⠘⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⢀⠙
⠀⠠⡟⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡀⠀⠀⠀⠀⠀⡛⢀⠀⠀⢀⠠⠚⠚⠉⠉⠁⠀⣀⠔⠀⠀⣁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠡⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢠⡀⣀⣀⣀⣀⣀⠀⠠⠀⠀⠈⠀⠀⡀⠀⢹⢃⠀⡠⠄⠀⡀⠀⠀⠀⠀⢠⠁⠀⣀⠀⠤
⠀⠈⠀⠃⠀⠀⠁⠰⣄⠀⠇⣠⣤⠀⠀⠀⠀⢈⠀⠀⠀⡠⠐⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠴⠀⠚⢄⠀⠋⠉⢁⠀⠀⠀⠈⡒⠋⠀⠀⠀⠀⢀
⠀⠀⠀⢃⠀⠀⠀⠀⢰⠛⢁⠃⠀⢻⠀⡠⠂⠂⠀⠠⠊⠀⠀⠀⠃⡀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠠⠂⢀⠂⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠠⠋⠐⠄⠀⠀⢼⠀⡒
⠀⠀⠀⠀⢁⡄⠠⢤⡉⡆⠀⠀⠀⠈⠂⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡃⠀⠒⠂⠄⠚
⠀⠀⠈⠉⠠⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⡤⠀⠀⠀⠀⠀⠀⠑⠒⠦⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⣀⠀⣀⠔⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠓⠀⢀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⢄⠐⢤⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠒⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⠅⠀⠤⠀⠀⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⠀⠀⠀⠀⡠⠀⢦⠀⠘⡖⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢈⡄⠀⡑

⣿⣿
⣿⣿
⣿⣿⡆
⣿⣿⡇
⣿⣿⠁
⣿⣿
⣿⣿
⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣦⣄⣠⣶⣿⣿⣶⣦⠀⢠⣄⣀⣨⠃
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢽⣿⣿⣿⣿⣛⣿⣿⠟⣿⣷⣾⣧⣼⡧⢣⣄⡀⡀⠀⣀
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⢣⣴⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠰⣿⣿⣿⣷⣍⠑⠀⣘⣿⠇⠀⠀⢲⡄
⣿⣿⣿⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⣿⣿⣍⣉⡳⣦⡜⢏⠀⡀⠀⠀⣧⡀
⣿⣿⣿⣿⣿⣖⢳⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢇⠀⣀⢀⣼⣿⣿⡿⣿⣿⠿⢼⣿⣿⣶⡿⢿⣷⠠⡄
⣿⣿⣧⣽⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⢉⣉⣉⣤⣴⣿⣿⣾⣿⣿⣿⣿⣾⡿⠏⠃⡈⠙⠿⣶⡄⠀⢸
⣿⣿⣿⣾⣋⣤⡙⣿⣿⣿⣿⣿⡟⢁⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣶⣾⠟⢻⣷⣦⣰⣦⣿⡄⣀⣰⡶⣇
⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠟⣁⣴⣿⣿⣿⣿⣋⡩⠥⠀⣈⣻⣿⣿⠿⠻⠟⠛⠀⠉⠃⢤⣻⣧⡉⠉⣻⣿⣛⡉⠉⠛⠋
⣿⣿⣿⣇⣤⠙⣿⣿⣿⠏⣴⣿⣙⣿⣿⣿⣿⣿⣷⣌⡇⡀⢰⢋⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠛⠉⠉⠁
⣿⣿⣿⣿⣟⢦⣼⣿⢟⣶⣿⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣶⣿⣿⣿⣿⡀⠀⠀⠀⣠⡀
⣿⣿⣿⣿⣿⣸⣿⣻⣿⣿⣿⣿⣻⣟⠻⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⡀⢻⣿⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠁⠘⣿⣹⣿⣆⠀⠘⣿⡿⢿⣤⣀⠀⠀⠀⠀⠀⢀⣔⣂⠐⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣯⣁⣫⠀⠀⠘⢿⣿⣿⣦⡀⠈⠳⡟⢿⣿⢛⣿⣿⣧⣶⡀⢻⣿⣄⣀⠔
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣿⣛⣏⣽⣿⣿⣥⡀⠒⠀⢠⣙⡿⣹⣷⠀⠀⠈⠛⠧⠶⠟⠛⠉⠉⠀⠈⡿⠟⠉⠀⢀⣀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡏⢙⣿⣿⣿⡿⠿⢧⣀⠁⠚⢞⣻⣿⣿⣈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⣠⣮⣉⠚⢿⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣶⣶⡾⢿⣿⣿⣿⠿⠿⣿⣿⡟⠳⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⣼⠟⡛⠋⠁⠈⠙⠋⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⢇⣸⣿⣿⣿⣆⣰⠪⢸⡿⠿⣿⣦⠀⠀⠀⢹⠶⠃⠀⠀⠀⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣼⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣤⣆⠀⠀⠀⠀⠀⣀⣈⠁⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠙⠉⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣦⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⡿⠛⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠒⠂⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠘⠛⠛⠁⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢠⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣄⡀⠀⣠⡾⣇
⠀⠀⠀⠀⠀⠀⢰⣦⣀⡀⣀⣀⣴⠶⠛⠳⢶⣌⣯⠙⣦⠀⠀⠀⢻⡌⠙⢶⡟⠀⢻⡄
⠀⠀⠀⠀⠀⢠⡘⣇⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⣿⠀⠸⣧⠀⠀⢸⡇⠀⠈⢷⠀⠘⣇
⠀⢀⣀⠀⠀⣾⢳⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡿⠀⢀⡾⠁⠀⠀⢸⣧⣀⣿
⢠⠏⢹⡀⠀⢿⡀⠙⠿⠦⠀⠀⠀⠀⣀⣠⣤⡤⠴⠤⣼⣿⣿⣿⡷⢤⡀⠀⢸⣇⣀⠙⢷⡀
⣿⠀⠘⣧⢀⣼⠷⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⢰⠏⠀⠈⠙⢲⡙⢦⡿⠁⠉⠛⢿⣅⣤⡶⠶⣦⣄
⣿⠀⠀⠈⠛⠷⢤⡴⣾⠷⠿⢥⣄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⣬⡿⢷⡈⣷⢦⣄⢀⣴⠋⠁⠀⠀⠀⠙⣷
⠸⣆⠀⠀⠀⢠⠏⣸⠗⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣀⣼⠀⢀⡟⠈⢷⠀⢻⡇⠀⠉⢿⠁⠀⠀⠀⢀⣀⣀⣹⠇
⠀⠘⢷⣄⠀⡾⠀⣧⡄⢀⣤⡤⣤⡀⠈⢻⡇⠀⠀⠘⡇⢀⣼⠁⠀⣸⢀⣠⡽⠿⠶⣦⡀⠀⢀⡾⠋⠉⡭⢿⣄
⠀⠀⠀⢨⡿⣇⠀⢸⠳⢿⡇⠀⠀⢙⣶⣤⣧⠀⠀⠀⣿⣟⣛⡵⠚⢩⡟⠁⠀⠀⠀⠈⠻⣆⢸⡇⠀⠸⡇⠀⢈⡷
⠀⠀⢠⡟⠁⠙⢷⡾⠀⠈⢧⠀⠀⠘⠿⢋⣏⣷⠾⠛⠛⠛⠿⣴⠞⠛⠀⠀⠀⠀⠀⠀⠀⢹⡌⢷⣄⣀⣙⣾⣏
⠀⢀⡿⠁⣠⡶⠛⠛⠛⠳⢾⣛⣉⣭⣭⣭⡟⢁⣀⠀⠀⠰⠳⠈⠀⠀⠀⠀⠀⠀⢸⡄⠀⠘⡷⣿⠋⠉⠉⡞⠉⠙⢦
⠀⣼⠃⢰⡏⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⢠⡇⢹⡄⠀⠀⠳⣤⡴⠋
⢀⣿⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⣴⣿⣸⡇⠀⣸⢧⢀⡿⠶⠶⠶⣿⣧
⢸⡇⠀⠸⡇⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡁⢸⣿⡟⠁⢰⡏⣸⢻⡇⠀⠀⢼⠀⠈⢻
⢸⡇⠀⠀⢻⣄⠀⠀⠀⢿⣿⡶⢦⣤⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⡿⠟⠛⠻⣾⣹⠁⠀⠀⡟⠁⠈⠻⣦⣀⣘⣶⡞⠋
⠈⣿⣤⣴⣿⣻⢦⣄⠀⠈⠉⠳⢾⣿⣧⡀⢸⠟⠋⠉⠙⠛⠿⠁⠀⠀⠀⠀⠈⣿⠀⠀⢸⣷⡄⡤⠶⠦⣍⠉⣿
⠀⢻⡄⠈⢷⣟⠀⠉⢻⠳⣆⠀⠀⠹⣍⣿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⠀⠀⣾⠁⠙⣧⠀⢀⣸⢶⡏
⠀⠘⣷⣀⣸⣏⣻⣏⡋⠀⠙⣦⡀⠀⠘⢿⣰⢦⡀⠀⠀⠀⠀⠀⣀⣀⣰⣇⣀⣸⡆⠀⠻⣆⠀⠸⠖⠛⢷⣿⠁
⠀⠀⢸⡿⠂⠀⠉⠻⣟⠦⣄⣸⡟⢦⡀⠈⣿⠀⢙⣦⡴⠾⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠸⣇⠀⠀⢀⣾⠃
⠀⠀⣿⣀⣀⠀⠀⠀⣿⣴⣋⠉⠳⣿⠀⠀⣹⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢠⡾⠃
⠀⠀⢻⠏⠈⠙⡄⣰⠏⠀⠙⣧⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢤⣄⣀⣀⣀⣀⣀⣠⡾⢃⣽⠟⠁
⠀⠀⠘⠦⠶⠚⡿⠻⢦⡀⠀⣸⠁⢻⣆⡀⠀⠀⢀⣀⣤⠾⠋⢁⣀⣀⡤⠽⠟⠋⠉⠉⢀⣴⠟⠁
⠀⠀⠀⠀⠀⢸⡇⣀⣀⣧⣠⡿⣄⠀⠉⣿⠛⠛⠛⠙⠛⠉⠉⠉⠁⠀⠀⠀⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⡟⠀⠀⣳⣠⣿⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠋⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⢠⣠⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠼⣿⣧⠀⠀⠀⠀⠀⠀⠈⡅
⠀⠀⠀⠘⠿⠡⣷⡀⠀⠀⠀⡀⠀⠀⠀⠀⢁⠀⠀⠤⠉⠁⠀⠀⠀⠘⣅⠀⣴⡟⠀⠀⠰⠀⠀⠰⣸⣿
⠀⠀⠀⠘⠀⠀⠘⣿⣶⠶⢚⣅⠀⠀⠀⠀⠁⠀⢀⠀⣀⣀⠄⠀⠀⠀⠀⠻⠿⠁⠀⠀⠀⠈⠒⠚⠛⠁
⠀⠀⠀⠀⠙⠒⠶⠚⠉⣀⣸⣋⠟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡴⠀⠄⢤⣟⢷⣄⡀⣤⠆
⠀⣆⣀⡀⠨⣿⠆⡀⠀⠈⠋⠀⠀⠀⣠⠒⠉⠉⠒⢤⠀⠀⠶⢦⡤⠞⠀⣤⣶⣿⡇⠀⠀⠉⠁⡀
⠀⠈⠉⠁⣶⣯⢀⡀⢀⡀⠀⠀⠀⠀⣧⡀⠃⠈⠀⣸⠇⠀⠀⠀⠀⠀⢠⣾⠃⣼⠁⠀⠄⠀⠀⠅
⠀⠀⠀⠀⠈⣿⣿⣧⢺⣄⣠⡶⠀⠀⠈⠙⠓⠞⠋⠁⠀⠀⠀⠀⠀⠀⠘⣿⠀⢿⡄⠀⢀⡃⢀⠀⡀
⠀⠀⠀⠀⠀⣽⠟⠛⠶⠟⠋⠀⠀⠀⠀⠀⠰⠰⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠶⠞⠁⠀⠀⡺⣌⣁⣃⡼⠂
⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠉⠁
⠀⠀⠀⠀⢀⠀⠀⠠⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠
⠀⢀⠀⣶⢾⡀⢺⠶⣾⣿⠎⣧⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⢰⠰⠀⠈⠁⣉⠶⡄
⠀⠀⠀⠰⣟⢷⣠⣧⣰⡟⣷⣿⠇⠀⣼⣄⣀⠀⠀⠀⠀⠀⠀⠄⠀⢸⠏⡷⠀⣼⠄⠀⣴⡬⠶⢛⢻⡀
⠀⠀⠀⠀⠈⠆⡻⠿⢛⣼⡿⠟⠀⠘⢿⠟⠛⠛⠛⢿⠗⠀⠀⠀⠀⠘⠀⠀⠀⡇⠀⢸⡧⢐⣇⡈⠉
⠀⠀⠀⠀⠠⠈⢉⣹⡟⣟⡳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠘⢤⡼⠧⠈⣙⠛⣿⠄
⠀⠀⠀⠀⢠⠀⠾⣿⣾⠏⡵⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⢆⠀⠀⠀⠐⠁⠀⠀⣀⠈⠻⠥⡀
⠀⠀⠀⠀⠀⠀⣤⡙⣧⣘⡇⠀⠀⠀⢶⠷⣾⣿⣷⡆⠀⢿⡏⢀⣴⣿⠗⢠⡇⠀⠀⠀⠀⣸⣷⣤⠴⣛
⠀⠀⠀⠀⠀⠀⣿⣷⡸⣧⢧⠀⠀⠀⠺⠦⠶⠛⢻⠃⠀⠀⠈⠻⠿⠯⠤⠾⣇⠀⢀⣀⣀⡛⠉⠻⣿⣿⣷
⠀⠀⠀⠀⠀⡀⢼⣿⣇⡙⢻⢄⠀⠀⠀⢟⠙⠻⢆⣻⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣷⣦⣭⣾⠋
⠀⠀⠀⠀⠉⠙⠛⠻⠛⠋⠙⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣺⠧⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⣀⣀⣠⢤⠒⠉⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⡀⢀⠴⠚⠅⠀⠀⢈⣖⣋⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣰⠀⠀⠠⡀⡴⠀⠐⠺⢉⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢮⠀⠢⣀⡀⠀⠀⠀⠀⠈⢀⣁⠤⠞⢁⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠉⠑⠒⠢
⠀⠀⠀⠀⠀⠀⢀⠤⠶⠒⠒⠚⠋⠒⠒⠒⢢⡇⣠⣀⣧⡠⠤⠤⠤⠴⠟⢳⠋⠛⠉⠀⠀⠘⠓⠢⡄⠉⠓⠪⢂⣠⡮⠁⠀⠀⠀⠀⠀⠘⠒⡄
⠀⠀⠀⠀⠀⠀⣜⡀⠄⠀⠠⠤⠀⢀⣀⣠⠞⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀⢲⡞⠀⠀⠀⠀⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠻⡤⢂⣤⡄⢀⡼⢋⡭⠟⠀⠀⠘⠀⠀⢀⡠⡤⠒⠚⠛⠛⠳⠷⠤⣤⠀⣦⣹⠋⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⢀⡴⠛⠛⣜⠤⠏⣴⠋⠀⠀⠀⠀⠘⠤⣤⢴⠃⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠀⢀⠴⠟⠀⡠⠊⠈⠳⣤⠯⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠤⠔⠒⠉
⠀⠀⡰⠃⠀⠀⠰⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣀
⠀⠀⢻⣀⠀⢀⣼⣤⡀⠀⠀⠁⠀⠀⢀⣠⢴⣀⠰⠞⠁⠀⠙⢷
⠀⠀⠀⠉⠛⠋⠁⠀⠈⠳⢦⠤⠶⠚⠉⠀⠀⠈⠳⡄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁⠀⣂⡀⣀⢀⢀⠀⣀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⡼⠛⠋⠻⣆⠀⠀⠀⠀⠐⠆⠚⠞⠓⢃⣾⠄⢸⠀⣀⢠⣼⠐⢽⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⠀⠉⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠚⠳⠖⠺⠛⠻⠻⠟⢻⡟⠛⠟⠛⠿⠛⠿⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠛⠛⠛⠉⠀⠀⠀⠀⠠⢸⠀⠀⠐⢀⢈⠸⠀⠸⢸⡇⠀⠂⠁⡇⡇⠰⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣶⣶⣶⣶⣾⣶⣾⣶⣾⡷⣶⣷⣶⣶⣶⣷⢶⣷⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠤⠤⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠉⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⢀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⢄⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢠⠖⠉⠀⠀⠀⠀⣀⣀⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠉⠢⡀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣯⣭⣭⣕
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡴⠁⠀⠀⠀⣠⠖⢋⣁⠀⠀⠀⠀⠀⠀⣈⠙⠢⡄⠀⠀⠀⠈⢆⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⡱⣢⡒⡸
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠸⠀⠀⠀⠀⡼⠁⠀⣼⢸⡀⠀⠀⠀⠀⢸⠯⡇⠀⠈⢆⠀⠀⠀⠈⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣼⣀⣈⣢
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇⠀⠁⠀⠀⠀⠀⢸⠀⡇⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠻⠔⠃⠶
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠀⠡⣀⠀⠘⠞⠀⠀⠀⠀⠀⠈⠒⠃⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠡⡀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⢀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠛⢻⣭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢤⣠⣤⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠺⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠱⠆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠒⢶⣅
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠉⠉⠉⠙⠲⢤⡀⠀⠉⠉⡇⠀⠀⢸⠉⠉⠀⢀⡤⠒⠉⠉⠉⠉⠉⠉⠒⠤⣀⠀⠀⠀⠀⠀⡱⢻⡍⡀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⡇⠀⠀⢸⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡬⡭⠵⢧
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⡇⠀⠀⢸⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢿⡹⠏⠯
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠇⠀⠀⢸⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢫⠍⠥⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠑⠉⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠲⠦⠤⠤⠤⠤⠴⡄⠀⠀⢠⠶⠤⠤⠤⠤⠤⠖⠒⠚⠉⠁⠀⠀⡀⣀⡀⣀⣀⡀⣀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⢀⡀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣹⠇⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⢃⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠸⣿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⢋⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢱⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢀⡸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢠⣿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣤⣴⣾⣿⡄
⠀⢀⣼⠏⡀⠁⡈⠁⡀⢀⡀⢀⡈⢓⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣸⠋⡄⠁⡄⠁⡄⠁⡄⠁⡄⠁⡄⢁⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢀⠃⠄⠀⠄⠀⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⢸⠂⠀⠂⠀⠂⠀⠂⠐⠂⠐⠂⠐⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠚⣷⡃⡀⠃⣀⣧⣄⠃⡐⠃⡀⠃⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠈⠙⠷⣶⠟⠁⠉⠿⣅⡀⢁⡀⢁⣈⣥⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠇⠈⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡕⢶⣶⣤⣀
⠀⠀⠀⠀⣤⡀⡶⢄⡀⠀⠀⠀⠀⢠⣋⣀⣀⣀⢻⠀⠀⠀⠀⠀⡠⠞⢛⡷⣟⠸⡝⢦⡈⢏⣲⣄⠀⠀⢀
⣈⡙⠲⣤⠁⠙⡇⠀⠙⠦⡀⢀⣠⣟⣉⣉⡉⠉⠻⡆⠀⠀⢀⡞⠀⠀⢸⡀⡙⠳⣬⢠⠩⢗⢠⠉⠣⣠⠋⡖⢱
⠀⠈⠀⢸⣠⠤⠃⠀⠀⣠⠼⠛⡶⠤⡀⢉⣉⣉⡹⢓⣦⠦⡞⠀⠀⠀⠰⡱⣌⣢⡌⡑⠦⠄⡀⠆⡄⢹⠀⢀⡼
⠀⢸⠀⢻⡡⢺⣃⠈⢉⣠⡴⢎⣀⣀⣷⠋⠀⢀⡽⠋⠁⠀⢃⠀⠀⠀⠀⢸⠛⡿⢿⣄⠻⡐⠌⢣⠀⡜⠀⠈⣇
⠶⠃⠀⠀⢃⠀⠉⣩⠟⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢸⣆⠀⠀⢀⠜⢠⠇⢸⡿⠙⠛⠾⡀⣷⣇⣀⣀⡿⠆⠀⢀⣄⠀⣀
⠀⠀⠀⠀⠈⠇⠞⠁⠀⡴⠙⢆⠀⠀⢀⣀⡀⠀⠀⠀⢀⣠⣿⣿⠤⠒⣁⠴⠋⠀⠀⢹⣦⡀⠀⠹⣌⠉⠀⡸⢃⠌⡰⠁⠘⡆⠹
⠀⡠⠀⠀⠀⢠⠾⣿⣿⣤⣤⣬⣷⣯⡉⠀⠈⠓⠲⣾⣟⠛⠻⣿⢋⡬⠓⠂⠀⠰⢆⠸⣑⠭⠓⡶⠌⣃⣤⣷⣏⣘⠉⠒⠒⡇
⠀⠀⠀⠀⠀⣀⠱⣷⡙⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⢿⣦⣼⣿⠋⠀⠀⠀⠀⠀⠀⠁⠉⠙⠢⠤⠒⠋⠉⣀⠀⠀⢩⠲⡜
⠠⠖⠒⠒⡏⠁⠀⠘⣇⠀⠹⣿⣿⠉⠙⣻⡇⠀⠀⠀⠈⣿⠿⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠱⠄⠈⠀⡏⠙⠚
⢢⣀⠀⢀⡇⠀⠀⣸⡏⠳⡄⢹⣿⣦⣼⣿⣧⠀⠀⠀⠀⣧⣀⣧⡀⠀⠀⢰⡋⣐⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁
⣶⣿⣿⣿⣿⣿⣿⠃⠀⠀⠁⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⣿⡃⠀⠈⢿⢊⢴⠋⡙⠲⠦⡤⢴⣶⣤⣄⣠⣤⣾⣿⣿⣦⡀
⢿⣿⣧⣄⠜⠛⣁⣠⠔⠁⢀⣾⡿⠋⢻⡿⠁⠀⠀⠀⢀⡜⢹⢃⣹⣇⠀⢠⡤⠓⠀⠚⠓⠳⠾⠇⠀⢻⠀⠉⠛⢿⣿⣇⠀⢸⣿
⣼⠇⠈⠉⡿⠉⠉⠹⣶⠿⢿⠛⠧⠤⢌⡧⠤⠴⠖⢡⡞⠁⠀⠈⠛⠿⢧⣌⡀⠀⠀⠀⠀⠀⢀⣀⣰⠏⡀⠀⠀⠀⠉⠻⢿⣿⣿
⣿⠀⠀⢸⠁⠀⠀⠀⠈⠲⠃⠀⠀⠀⠀⠀⠀⠀⢠⢼⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣶⣶⣶⣶⣿⠉⠀⠀⠨⡝⠢⢄⡀⠀⠀⢉⣿
⡇⠀⠀⣼⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠉⠲⣄⡀⠀⠀⠀⠀⣰⠛⢻⣿⢉⣿⣿⠀⠀⠀⠀⠈⠂⠀⢈⣀⡴⠿⠃
⡇⠀⢀⠋⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠙⢆⠀⠀⠀⠀⠉⠉⠉⠙⠉⢸⣇⠀⠚⠉⠛⠛⠐⢶⠶⣦⣤⣀⠞⠁
⠇⢀⡞⠀⠈⠉⠙⠲⢤⡀⠀⠀⠀⢀⠔⢃⠀⠀⠀⠙⠲⠦⠤⠤⠤⣤⣀⡀⢸⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠄
⢹⣘⠀⠀⠀⠀⠀⠀⠀⠙⢦⡄⢠⠋⠀⠀⠛⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠉⠙⠻⣦⠀⢀⣴⣎⣦⢤⠔⠉⠁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⠢⣄⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠲⢲⠏⠀⠀⠀⠀⠀⠀⠀⢻⡦⠊⢹⢞⠇
⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠉⠙⠓⠒⠒⠲⠦⠤⠤⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣰⠟⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠶⠶⣶⣶⣤⣤⣄⣀⣀⣤⢞⡁⢀⣤⠞⠋⠀⠀⠀⠀⢀⣼⡇⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⡠⢤⡀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⣶⠳⢿⣆⡀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⣚⠻⠿⠿⣿⣿⢿⣶⣤⣄⣀⠀⠙⠟⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠴⢪⣷⣦⣀⠀⠘⣿⡏⡤⢸⠏⠙⠺⢟⡢⣄⡀⠀⠀⠈⣳⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠻⣆⠀⢸⡇⡜⠡⣀⠀⠘⢹⠀⠀⣿⡆⠀⠀⠈⠑⣭⡲⣤⡴⠋⠀⠈⢷
⠀⠀⠀⠀⠀⠀⢀⡴⠚⢅⡀⠀⠈⠳⣄⠹⣇⣀⣽⠷⠀⠘⡀⠀⠻⣿⠀⣀⢀⣼⣿⣿⣿⠃⠀⢾⠃⢸
⠀⠀⠀⠀⠀⣰⠟⣀⣀⡀⠙⣶⠴⠲⢬⡷⠋⠁⠀⠀⠀⠀⠑⢄⣡⠞⣠⣿⡾⠿⣿⣿⡟⠀⠀⠘⢀⣾⠶⠖⠛⠛⠛⠛⠓⠶⣄
⠀⠀⠀⠀⢸⡇⠀⠈⠉⠙⡟⠁⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠼⠷⢤⣀
⠀⠀⠀⠀⢸⡇⠀⠴⠒⢺⠀⠀⠀⣦⣿⡄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⢹⣆⡀
⠀⠀⠀⠀⠸⡇⠀⠀⠀⢸⡀⠀⠀⣸⠿⣿⣦⣤⣤⣤⣾⣿⣿⡿⠛⡹⠀⡿⢆⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⢀⠴⠖⠋⠀⠀⢈⠙⢦⡀
⠀⠀⠀⠀⠀⠙⢦⠀⡀⠀⠙⣳⠛⢁⡜⠙⣿⢿⠉⠛⠛⠋⠀⢠⣞⣡⠞⠀⣼⢰⣧⠞⣇⠀⠀⠀⠀⠀⣠⡞⠉⣿⡀⠀⠀⠀⠀⢠⡄⢷⠈⠁⠈⣧
⠀⠀⠀⠀⠀⠀⠸⣤⣙⣶⠞⠁⠴⠋⢀⡼⠃⠀⠳⢄⣀⣀⣲⣄⠈⠛⠦⠤⢋⣾⠁⠀⢸⡀⠀⠀⠀⠺⠃⢿⠀⡿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣤⣶⠋⠀⠀⠀⠀⢠⡏⠉⢹⡏⠛⠶⠶⠶⠋⢸⡆⠀⠀⢳⠀⠀⠀⢀⠀⢸⡇⢷⣼⡆⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⢸⡇⠀⠀⢧⠀⠀⠀⢀⡀⣼⡇⢀⠤⡈⢧⣀⣀⡜⠀⢸⡇⢠⡟⠁⠀⣤⠀⠀⠀⣤⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣸⣇⢀⠤⢌⠳⡂⠀⠀⠀⢸⢡⡏⠀⣸⡼⡆⠀⠀⠀⢸⣇⣈⣧⣀⣴⡛⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡜⡀⢠⢱⠹⡆⠀⠀⢸⡆⢧⣤⡿⢁⡇⠀⠀⠀⢸⣏⣁⣀⢀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⢿⣷⠚⠚⠳⠿⣄⡀⠀⠳⣤⣤⣤⠾⠁⠀⠀⢀⣾⣅⣀⠀⠀⠈⠓⢤⡀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣋⣉⡉⠛⠓⠶⢤⣈⠙⠂⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠉⢳⡄⠀⠀⠀⠙⣆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡀⠀⠈⣉⠒⠤⢀⠈⠓⢦⡀⠠⡀⠀⢀⡇⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⢰⠇⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠈⠐⠀⢙⠢⣄⠙⣆⣿⠀⡼⠁⠀⣀⣠⣴⠿⠋⠀⠀⠀⢀⡤⠿⠤⠤⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⣀⠀⠀⠀⣠⠑⢌⠣⡈⣿⣾⣷⣟⣛⣛⣛⣛⡒⠲⠶⠒⠛⠉⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠛⠷⠶⣇⡀⠀⢣⢱⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠀⠉⠷⠾⠾⠧⠤⠄⠀⠊⠉⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣀⣶⣶⣶⣶⣶⣦⣄⣀⡀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⣿⣦⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡗⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣞⠙⣆⠀⠀⠀⠈⢎⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠁⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣖⣶⣶⣖⣰⣦⣤⣄⣄⡀
⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣆⣀
⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉
⠈⣿⣿⣏⡉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⢀⣼⣿⣿⣿⣿⡟⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠟⡋⠁⢴⣆⣦
⠀⠘⣿⣿⣿⣿⣿⣿⡻⡿⠿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠙⢿⣿⣆⠀⢸⣿⣿⣿⣿⣿⣿⠀⢠⣾⣿⣿⣿⣿⣿⣇⣠⣴⣿⣿⣿⣿⣿⣿⡄⠀⢀⣀⣴⣿⣿⡟
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢈⣿⣿⣆⢸⣿⣿⣿⣿⣿⣿⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣤⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⣰⣶⢤⣽⡆⣿⢿⡙⠑⡦⢄⡀
⠠⢤⣀⠀⣼⠳⣼⡏⠑⠦⡀⠀⠀⠀⢠⣾⠶⠾⠷⠶⢬⡇⠀⠀⠀⠀⣠⠊⠁⢀⡞⠨⣧⡘⠧⠙⠦⣵⢒⠻⣦⠀⢀⠴⣀⢄
⠒⠦⡈⠻⡇⠀⢸⠇⠀⠀⠉⠲⣤⡔⠿⠷⠶⠤⢤⣤⣌⣿⡀⠀⠀⣴⠃⠀⠀⢸⢣⠱⣄⠙⠶⣙⠈⠚⠈⠃⡈⠳⣞⠀⡇⢸⠄
⠀⠀⡄⢸⣧⠖⢺⠀⣀⣀⠤⠚⠉⡹⠋⢲⠄⡤⠤⠤⢴⣊⣽⡿⠓⡇⠀⠀⠀⠈⢣⣳⡦⣴⡆⠌⢛⡒⠤⣙⠘⠀⡏⢀⢰⡾
⠀⢠⠥⠘⣦⠖⢻⣉⣁⣀⣤⠶⠿⠥⠤⣰⣞⣁⣀⣀⡼⠋⠀⠀⠀⣇⠀⠀⠀⠀⠀⡏⢙⠛⢿⣤⡸⣎⠢⡙⣆⢀⡇⠀⠀⣧
⠶⠃⠀⡀⠘⣄⠀⢁⣭⠟⠁⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⣸⣆⠀⠀⢀⡰⠃⣼⠀⢺⡿⠉⢛⠳⣇⢸⣾⣀⣀⣀⡿⢇⠀⢀⡠⡄⠀⣀
⠀⠀⠀⠀⠀⠸⠠⠞⠀⠀⣰⠋⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠄⠔⢉⣠⠞⠁⠀⠀⢱⣮⡐⠀⠈⢦⡉⠉⠀⣼⢏⡼⢠⠎⠀⢸⠀⢻
⠀⢀⠤⠀⠀⠀⣠⡶⣿⣿⣁⣀⣀⣳⣶⣎⠉⠉⠉⠳⠦⣴⣾⠿⠿⢿⣿⠓⢐⡭⠶⠒⠒⢠⡀⢸⠳⣝⡷⢤⣄⡹⢀⣀⣷⡿⢠⠛⠒⠶⢾
⠐⠁⠀⠀⠀⠁⠘⢾⣏⠻⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⢿⣷⣀⣼⣿⡞⠁⠀⠀⠀⠀⠀⠉⠂⠙⠲⢦⣉⣠⠼⠛⠛⠉⠉⠉⠓⣦⣀⠞
⠀⣀⣤⠤⣤⠶⠂⠈⢻⡇⠀⢻⣿⣿⡿⠻⠿⣿⡆⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠓⢦⡀⠀⠃⢹⠦⠤⢴
⡈⠁⠀⠀⢸⠀⠀⠀⢰⡷⣄⠀⠻⣿⣇⠀⣠⣾⣇⠀⠀⠀⠀⢸⡏⠉⡇⠀⠀⠀⠀⣠⠔⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡹
⣙⣦⣄⣠⣞⣀⣀⣠⡾⠃⠈⢳⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣷⣶⣿⣄⣀⠀⠀⣷⡤⡌⠈⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣀
⣿⣿⡿⠿⠿⣿⣿⠟⠁⠀⡀⠀⢀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢻⣿⡿⣿⡇⠀⠀⠘⢏⠔⠙⢀⠄⡍⠛⣳⠛⢿⡿⠶⣶⣶⣾⣿⣿⠿⠿⣷⣄
⢻⡿⣿⢦⡰⠋⣁⣤⡤⠞⠁⣀⣾⣿⠟⠉⢻⠟⠀⠀⠀⠀⠀⣰⠏⠸⣁⣼⣧⡀⠀⣴⠎⠓⠂⠉⠉⠙⠛⠚⠀⠈⡧⠀⠀⠙⠻⣿⣧⣀⣀⣸⣿
⣸⡇⠀⠉⢹⠏⠉⠀⠹⣿⠿⢻⠟⠛⠲⠤⣬⡷⠦⠴⠚⠋⣼⠋⠀⠀⠀⠙⠿⠷⣬⣁⠀⠀⠀⠀⠀⠀⢀⣄⣠⡾⢡⡀⠀⠀⠀⠈⠙⠿⣿⣿⣿
⣿⠀⠀⠀⡟⠀⠀⠀⠀⠈⠣⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣶⣶⣤⣤⣶⣾⠋⠁⠀⠀⢨⡓⠢⢄⡀⠀⠀⠈⢙⣿
⡟⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⣼⠲⢿⣿⠛⣻⣿⡀⠀⠀⠀⠀⠙⠄⠀⠉⠁⣀⣴⡿⠉
⡇⠀⠀⢸⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣇⠀⠀⠀⠀⠉⠓⠒⠒⠲⠖⠊⣿⠀⠈⠽⠺⠿⠿⠇⣤⣤⣤⣄⡀⠀⣠⠞⠉⠉
⡇⠀⢰⠃⠀⠒⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⣀⡏⠀⠀⠈⠳⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⡘⠳⣦⣀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠁
⢥⢀⠏⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⢀⠞⠁⠱⣤⡀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠒⢠⡇⠀⠈⠙⠿⣦⣴⣄⠀⠀⠀⢀⡠⡀⠀⠀⡠⠤⠊⠁
⠘⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢾⠀⠀⠀⠀⠙⠲⠶⢤⣀⣀⣀⣀⡀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠈⣿⣆⢀⡴⣟⣦⡗⠻⠋
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡏⠒⢦⣀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠊⠁⣸⢫⠃
⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠉⠉⠙⠛⠛⠒⠒⠒⡶⠚⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⠶⠶⣶⣶⣶⣦⣤⣀⣀⣠⡴⢞⣁⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⣴⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣄⣶⡐⠨⠁⠈⠑⠄⠁⡤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡒⠃⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢠⢈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠐⠀⠀⡠⠄⠀⠈⡆⠀⠀⢀⠈⠈⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⠠⠪⠀⠀⠀⣠⡁⠀⠀⠈⢑⠀⡀⠠⡇⢀⠔⠁⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣐⡄⢰⣦⠀⠀⠘⣿⠀⠀⠀⢀⠢⠀⠆⠘⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠈⠿⠃⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠃⠐⠀⢠⠊⢀⠰⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠀⢉⠠⣥⠒⢁⠌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠃⢠⠀⠀⢀⣀⠀⠤⠄⠒⠂⠉⠄⣦⣤⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡕⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠈⠉⠉⠉⡙⠀⠀⠘⠋⠉⢹⠤⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⢸⠷⠿⠿⢿⠀⡀⢀⠄⠂⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢠⣷⢶⣤⣤⣼⡆⡀⠌⠳⠤⢔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠙⠿⢿⠠⢍⣯⣽⣌⢁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠈⠋⠉⠉⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠁⠚⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠁⢢⣀⡀⠀⠀⢡⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡔⠁⠑⣼⠄⠀⠈⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡶⠃⢀⡇⢀⠥⠀⠊⣡⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⣠⠶⠋⠀⠰⠀⡀⠊⠁⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠉⠀⠀⠀⠀⠀⠁⠈⠈⠀⠉⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠱⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢦⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣀⣆⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⢠⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟⡰⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⡰⠃⠀⠀⠀⡌⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠀⠈⠂⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠛⠛⠻⠛⠛⠿⠿⠿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⣩⠔⠁⠀⢈⣀⣀⣀⣀⣉⣐⢢⡀⠀⠈⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠠⠈⣀⣤⠶⠿⠟⢉⣉⠉⠉⠉⠉⠉⠛⠻⣶⡔⠠⠤⠉⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣁⠀⢴⣡⠞⠉⣀⠠⣀⣤⣶⠶⠿⠶⠶⢶⣤⣮⡀⠈⠙⢷⣄⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠅⢠⣾⠃⡀⠉⣠⡾⢋⢥⠀⠀⠀⠀⡀⢠⢤⠙⢿⣆⠀⡀⠙⣦⠀⠀⡙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢠⠀⣾⡏⠀⠀⢰⠇⠀⢸⣴⡇⠔⠀⠐⡀⢺⣼⠂⠀⢿⡆⡇⠀⢸⡏⠹⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠘⡀⣿⡀⠀⠀⢼⡀⡐⢺⣿⠁⠀⠀⠄⠀⠹⣿⠀⠀⣾⠇⢠⠀⢸⡇⠠⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠙⣧⠀⠀⡈⢷⣤⡀⡁⠐⠉⠀⠀⠀⠀⠀⣠⣾⠟⠁⠂⢠⡟⠀⡰⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠙⢧⡀⢘⠄⠉⠛⠷⢦⣤⣤⣤⣤⡶⠿⠋⠁⢀⣁⣴⠟⠀⡰⢡⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣇⡀⠀⠉⠻⢶⣤⣄⡀⠒⠉⠀⠀⠀⠀⣐⣠⣴⡿⢏⡁⠀⢀⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣀⠒⠒⠪⠭⠛⠟⠛⠿⠛⠛⠛⠋⡉⠔⠊⣀⣼⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣙⡛⠿⣷⣶⣤⣤⣄⣀⣰⣤⣤⣴⣤⣤⣶⠿⢟⣋⣁⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⡿⠟⠛⠛⠛⠻⢿⣶⣄⡉⠉⢹⡏⠛⠛⣿⡏⠉⣠⣴⡾⠟⠛⠛⠙⠛⠛⠛⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣏⠁⠀⡆⢀⣀⣀⣀⠀⠀⠈⠻⣿⣦⢸⣿⠂⠀⣿⣇⣼⡿⠛⠀⠀⠀⢒⣠⣤⠑⢆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠣⢄⡩⠛⠛⠶⣤⣀⠄⠈⢿⣿⣿⢸⠀⢸⣿⣿⡁⢀⣠⣴⠞⠋⠩⠀⠀⠀⢇⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠉⡀⠀⠀⡼⠛⠿⣦⡈⣿⣿⡄⣄⣼⡿⣠⣾⠟⠛⠒⠀⣀⡘⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣧⣤⣸⡀⠀⠀⠈⢻⣿⣿⠋⠀⣿⣿⣟⣁⣀⣀⣀⣠⣬⣷⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⢻⣿⣦⣶⣿⡟⠛⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠘⠔⢄⢀⡎⠀⠀⠀⠣⠢⡀⢰⠉⠀⠀⠘⠖⢄
⠀⠀⠀⠀⠀⡠⠦⠊⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠘⢆⡤⡀
⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅
⠀⠀⠀⠀⠀⠈⠒⠢⣀⠀⡠⣀⠀⠀⣀⢄⡀⢀⠤⣀⠀⢀⡠⣀⠀⡠⢄⡀⠀⣀⢄⡠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠉⠀⠀⠈⠉⠀⣀⠄⠂⡀
⠀⠀⠀⠀⠀⠀⡀⠤⢄⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠜⠀⠀⠀⠁⣤⠂⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢠
⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡀⢀⡀⡀⠀⠀⠀⠂
⠀⠈⢠⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠔⠐⠤⠔⠐⠈⠁
⠀⠀⠀⠉⠁⠠⠤⠀⠌⠄⠐⠤⠅⠢⠨⠡⠀⠐⠁⠀⠀⠀⢀⠠⠂⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠎⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⠀⠂⠒⠀⢀⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉

⠀⠀⠀⠀⡆⠰⣤⠀⠀⠀⣿⠀⠄⢸⠉⠲⠤⠤⠶⢊⡴⠋⠁⠀⣀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠙⠳⢶⡚⠁
⠀⠀⠀⠀⠧⠀⢤⢤⠤⢤⣥⡀⢀⠸⠀⠀⠀⠀⣰⠋⠀⠀⠀⣰⠋⠳⣄⣠⠞⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⢤⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠶⢤⡾⠁⠀⠀⠀⢠⠇⣠⣄⠈⠁⣠⣆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠈⠉⠉⠉⠙⠲⠤⣤⣤⣤⠤⠖⠋⠀⢀⡞⠀⠀⠀⠀⠀⣟⣠⠏⠈⠳⠾⠁⠸⠦⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠳⠦⣤⣠⣤⠤⠶⢤⣤⣤⡤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⣀⣬⠥⠶⠒⠚⠛⠛⠛⠛⠒⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡴⠚⠉⠁⣀⣤⠤⠴⠶⠶⠶⠶⠶⠤⢤⣄⣀⡀⠉⠙⠶⣄⡀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⢀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⠉⠛⠶⣤⣀⠙⢦⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⡴⣿⢀⣴⣶⣶⣶⣄⠀⠀⠀⠀⢀⣴⣿⣿⠿⣿⣷⡄⠀⢼⡉⠛⠾⣇⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡤⠤⡖⠒⠲⣄⠀⠀⠀⢈⡟⢰⡏⣾⡟⢉⠝⢿⣿⡇⠀⠀⠀⡿⠿⢋⠔⠀⠢⡙⢿⠀⠀⠻⣄⠀⠈⠙⢦⣀⣸⣇⣤⣀⠀⡀
⠀⢀⡴⠛⠛⢋⠀⠀⠈⢂⠀⠘⡆⠀⢀⡾⠛⣿⠀⠋⢠⠁⢰⣶⡀⠀⠀⠀⠀⠀⠀⡌⢀⣾⣦⠰⠈⠀⠀⠀⢹⡆⢀⡼⠋⠉⡽⠁⠀⡨⠋⠉⠳⣤⣤⡀
⣰⠛⠢⡀⠀⠀⠑⡀⠀⣴⠛⠋⠉⠛⠻⣄⠀⡟⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠃⠀⠀⠀⠀⣇⣾⣥⠶⠚⠓⠶⢴⡁⠀⠀⡐⠀⠀⠙⢦
⡟⠀⠀⠐⠄⠀⠀⠐⠀⢸⡆⠀⠀⠀⠀⢸⣂⡇⠀⠀⠠⢸⣿⣯⠷⠶⠶⠶⢤⡀⠀⡄⣿⣿⣿⣷⣇⠀⠀⠀⠀⠿⣿⠁⠀⠀⠀⠀⢨⠇⠀⡐⠀⠀⠀⠔⠉
⠻⣄⠀⠀⠈⣀⣠⠴⠓⠁⠙⠶⠖⠁⣠⠏⡿⠀⢠⣦⢘⡾⠋⠀⠀⠀⠀⠀⠀⠙⢦⢐⣹⡿⠟⠁⣿⠀⠀⠀⠀⠀⢹⡄⠀⢦⣀⡴⠛⠦⣴⡀⠀⠀⠊⠀⢀
⠀⢹⡉⠉⠉⠀⠀⠀⠀⠀⠈⢀⣠⠞⠁⢰⣇⠀⣼⠝⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠀⠀⢘⣿⠀⣀⠀⠀⠀⠀⢹⣦⡀⠀⠐⠄⠀⠀⠈⠑⠒⠶⢲⡏
⠀⠀⠳⣤⡀⠀⠀⠀⠀⠐⠈⢹⡇⠀⠀⠈⣏⠙⢾⡇⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠰⣿⠟⠋⠁⠀⠀⠀⢀⡟⣀⣽⡗⠤⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⣇⠀⠀⢀⣀⣠⠤⠶⠺⢧⣀⡀⠀⠹⡄⠀⠻⣆⠻⢦⣀⡀⠀⢀⣀⣠⠞⠃⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⡞⠛⣁⡼⢤⣄⣀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠙⠻⡏⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠓⠻⣄⠀⠈⠛⠶⡾⠿⠟⠛⠛⠳⠶⠶⠚⠋⡗⠀⠀⠀⠀⠀⠀⣠⠞⠛⠉⠁⠀⠀⠀⠉⠙⠓⠲⣶⠶⠃
⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠹⠒⠲⠶⠶⠶⠒⠚⠙⠚⠁⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⣷⢤⡀⠀⠀⠠⣄⣀⡤⠀⠀⠀⢠⠄⣀⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⢦⢄⡀⠀⠀⣰⠀⠈⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⡿⠀⣿⠀⠙⣦⣀⠀⠀⠀⠀⠀⣀⡴⠿⡟⠁⢰⡇⠀⠀⠀⢠⡦⠤⠶⠒⠛⠉⠁
⠀⠘⢆⠉⠓⠞⢁⣖⣒⣒⠒⠒⠉⣩⠛⠛⠓⠒⠲⡇⠀⢿⠀⠀⡇⠉⢙⣛⣛⣛⣋⣉⣀⣘⡇⠀⢸⡇⠀⣠⠴⠞⠓⠒⠲⢤⣄
⢀⡠⠚⠀⠀⠀⢿⡷⠞⠉⠀⠀⠀⠑⢤⡀⠀⠀⠀⡇⠀⢸⠀⣠⠿⠚⠋⠉⠉⠁⠀⠀⠉⠉⠛⢒⣼⣤⠞⠁⢀⠤⠤⣀⡀⠀⠈⢳⡀
⠯⠀⢰⠞⠓⢄⣘⣳⠶⢾⠀⣴⠗⢶⡆⠽⠂⠀⠀⣧⡤⢾⠟⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢹⠀⡔⠁⠂⠄⡀⠙⢦⠀⠀⢳
⠀⢠⣋⣴⠞⠟⠁⣰⡒⠚⢟⠷⢤⡀⢹⡀⠀⠀⠀⣿⠀⠸⣄⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣴⠇⡼⠁⠒⠤⢀⠀⠑⠺⡆⠀⣸
⢀⡼⠁⢠⠟⠒⠚⠁⣅⠀⠀⡸⠂⠛⢮⡀⠀⠀⠀⢹⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠒⠠⢀⡀⠈⠐⢰⠃⢠⡟⠉⠉⠉⡏⠉⠉⠉⡋
⠟⠒⠒⣡⠤⢄⠀⢀⣀⣉⠉⠀⠀⠀⡞⠙⣆⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡏⠑⠢⢄⣀⠈⠑⠢⣞⡴⠋⠉⠉⠋⠉⠉⠉⠋⠉⠉
⢱⡄⢸⠁⠀⠈⣷⠋⠀⠈⢣⢴⠂⠐⠷⣂⣼⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢸⡃⠂⢄⡀⠈⠉⠒⣼⠋⠀⠀⠐⠒⠓⠒⠖⠒⠓⠒⠖
⠻⢤⣌⣦⣀⣴⣋⣦⣄⣤⣋⣦⣠⣤⠴⠞⠁⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠳⣄⡀⠈⠁⢂⡴⠏⠠⡄⠀⠆⠀⡤⠀⠒⠀⠤⠀⠂
⠀⠀⠀⠀⣨⡏⠀⠙⢦⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡬⠉⠛⠛⠉⠛⠛⠉⠀⠀⠀⣇⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣦⡤⣀⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⢀⠀⠀⢤⡤⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠉⠳⣤⣀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡃⢽⡶⣄⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡀⠀⠀⠀⠀⠰⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⢯⡛⠶⣿⣯⣌⣲⣤⣄⠲⣴⡆⣀⡀⢤⣤⠤⠀⣀⡀⠀⡠⠀⠀⠈⣊⣤⠎⠳⠠⠄⠀⠙⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠓⠊⢤⣴⡒⠦⣛⣴⣤⣤⣄⡀⠀⠈⠓⣤⣤⣀⠞⠀⠀⡀⠚⢩⡼⠂⠀⠁⠀⣀⠴⢚⠤⣴⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠁⠀⠀⡐⠦⣤⣀⡀⠀⠈⠛⠷⠾⠇⣻⢿⣤⣿⣿⣟⡷⣮⣞⠉⠉⠒⠊⠀⠀⣀⣀⠠⠀⠂⠩⠐⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠠⠄⣸⠍⠙⠻⠻⢏⣹⠷⢋⣙⠛⠛⠁⠀⠀⠠⠖⠋⠉⠀⠀⠀⠒⠀⠁⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠤⡀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠀⠈⠉⠉⠴⠶⠾⠀⠀⠉⠀⠀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠓⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠊⠳⡈⠳⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠤⠤⠀⠀⠀⠒⠂⠈⠉⠉⠉⠉⠐⣀⠤⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡀⠸⡄⠀⡀⠐⠠⣄⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣖⠴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠁⠀⣧⣄⣈⣓⠒⠀⠉⠉⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠤⠄⠉⠉⠉⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠼⠴⢦
⠀⠀⠀⠀⠀⠀⠀⡴⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⢉⡁⠁⣦⣄⠶⡄
⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠠⣀⠋
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠁⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣝⡛⣋⡙⢻⡟⣫⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⣤⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣀⣠⠞⠁⣀⣀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⡾⠉⠻⠶⠟⠁⠈⠻⣦⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡃⠀⠤⠀⢴⠄⠀⠀⣽⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠈⢳⡄⡄⠉⠳⢤⡤⠾⠋⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣡⣶⣿⣿⣿⣦⠁⣴⣾⣿⣷⡄⠀⠀⠀⠰⣿⣼⣿⠁⣤⠀⠀⠀⢀⡴⡏
⠀⠀⠀⠀⠀⠀⠀⢰⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢻⡗⢶⣿⣿⡿⠿⠋⢠⠃⢀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣿⡖⠓⠀⠀⠀⡠⠃⠈⠉⣧⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢹⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣟⡅⠀⠀⠀⠀⠸⡧⠤⠤⠑⠦⣄⠀⠀⠀⠀⣠⠿⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⣿⣾⣿⣿⣿⠷⠋⢀⣀⡀⠀⠀⣠⣷⡒⠒⠀⠀⠀⠀⣠⠴⠚⠛⠓⠲⠤⣼
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠉⠙⠻⠿⠦⡤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣤⣶⣿⣿⣿⣿⣟⣛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⣼⣿⣿⢿⣿⠁⠙⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠛⣿⠇⠀⠋⠀⢰⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠻⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⠃⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠸⣆⠙⠆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠙⢷⣄⡀⢀⣠⡾⠃⠉⠛⠛⠻⠿⠛⠋⠁⠀⠘⢿⣟⠀⠀⠀⠰⣄⣀⣀⣀⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠈⠙⠛⠛⠉⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⢀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⡀⠀⠀⢙⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠶⠂⠦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠒⠷⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣿⠖⣤⡜⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣟⢦⣽⣎⣒⢠⣈⡉⢄⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠫⠆⡠⢄⣀⠀⠈⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠓⠪⠋⣙⡯⣭⡹⣠⣉⣀⡉⠉⠉⠣⣀⣁⠀⠔⠁⠄⠠⠞⣡⠅⠀⠀⠀⠀⡮⢄⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠑⠀⠀⠐⢤⣄⡀⠀⠈⠛⠷⠼⡏⣻⣯⣽⣿⣷⣶⣼⡭⠙⠂⠒⠀⠀⠀⢁⡀⠀⠐⠃⠅⠂⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣄⠀⠀⠀⠀⠀⡀⠈⣙⠳⢂⣦⣜⣎⡙⠛⠻⣛⣿⢾⣍⢛⡛⠁⠀⠀⠠⠚⠉⠁⠀⠀⠂⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢤⣀⠀⠀⠀⠀⠀⠙⠒⠀⠈⠀⠀⢈⠐⡓⠺⠛⠃⠙⠁⠠⠤⠀⣀⣤⣅⡀⠀⠈⠀⡘⠋⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢧⠈⢷⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂⣀⠈⠉⠉⠀⠀⠈⠀⠀⣤⡐⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢧⠀⡇⠀⢠⣈⠒⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⡗⠃⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠓⠲⠤⠭⠀⠀⠀⠈⠶⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢄⡀⣀⡈⠁⠉
⠀⠀⠀⠀⠀⠀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠍⠉⠀⡈⠝⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠈⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢯⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⢀⣠⡤⠴⠖⠒⠒⠒⠒⠒⠒⠶⠦⣤⣀⠀⠈⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣒⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠩⣅⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⢀⡴⠋⠀⠀⠀⠀⣀⡤⠶⠒⠛⠛⠛⠛⠒⠦⣤⣀⠀⠀⠀⠈⠑⣄⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣬⣤⣉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⡞⠀⠀⠀⠀⣠⠞⠁⣴⣤⠀⠀⠀⠀⠀⢀⣴⣄⠉⠳⣄⠀⠀⠀⠈⢧⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠹⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣼⠁⠀⠀⠀⢸⠃⠀⠀⡟⢻⠀⠀⠀⠀⠀⢸⡟⢿⠀⠀⠹⡆⠀⠀⠀⠘⡆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢻⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡇⣾⠀⠀⢠⠇⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠳⢷⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠸⡄⠀⠀⠀⠘⢦⡀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠛⠋⠀⣠⠏⠀⠀⠀⠀⣸⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⢺⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠹⣄⠀⠀⠀⠀⠉⠳⢤⣀⣀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⡴⠃⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣩⢄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠱⢌⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠙⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠞⠉⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢪⢾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⣛⠷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠱⠷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠒⠒⠒⠒⠲⢦⣄⡉⠉⠛⠒⢲⡦⠤⠤⢴⠒⠚⠛⠉⢁⣠⠴⠖⠒⠒⠒⠲⠦⢤⣀⠀⠀⠀⠀⠀⠀⢫⡍⠭⡇
⠀⠀⠀⠀⠀⢠⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⢸⡇⠀⠀⢸⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠄⠀⠀⠀⠉⠈⠉
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡇⠀⠀⢸⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣄⠠
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⡇⠀⠀⢸⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠈⣁⠀⢈⡙
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠺⣿⡛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠻⣆⣀⣀⣸⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠈⠌⠌⠅⠨⠉⠀⠤⠠⠠⠄⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠛⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡖⣺⣿⣯⢻⠒⠢⢤⡀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⢦⣀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⡿⣿⣿⣿⣿⢿⣾⠟⠀⠀⠀⣿⣷⡀⠀⠀⣾⡟⠉⢠⡌⣭⠓⢊⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠙⠻⠷⠾⠚⠋⠁⠀⠀⠀⠀⢻⣋⢿⠀⠀⠻⣷⢤⣈⢀⢁⣀⣼⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠉⢻⠀⢀⣀⢈⣿⣿⣟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⢳⡀⠀⠀⠀⢀⡔⠋⣉⠁⠀⣯⡉⠢⣄⢀⡞⠀⠛⢾⣿⣿⠿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢋⡇⡇⠀⠀⠀⡏⠠⠀⠻⡧⠀⠈⠁⡀⠚⢻⡀⠀⠀⢏⠤⣟⡭⢽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣹⠃⠀⠀⢠⡇⠀⢻⠶⠶⠶⢾⣿⡇⠀⢈⡧⠴⠚⠉⠀⣛⣒⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠠⠴⢷⡀⠈⠳⣄⣁⣤⠟⠀⣠⠞⠀⢀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦⣀⡤⠞⠛⢦⣤⣤⣭⠤⣶⣾⣁⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡃⢀⣀⣠⣴⣾⣿⠏⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⣹⡿⣿⡿⠓⠤⠴⠖⠚⠻⣇⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣤⡀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠒⠒⠒⠿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠈⠈⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠘⠀⠈⠈⠉⠀⠉⠀⠀⠈⣧⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⡀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⣀⣀⠀⠀⠀⣿⠒⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠴⠇⠂⠀⠀⠈⠀⠀⠀⢠⡦⠀⠰⣄⠂⠀⠋⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠀⠀⠀⠀⢀⣠⡤⣶⣤⡟⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠿⠻⠃⠀⠀⣀⢀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡀⠀⠀⠉⠿⢧⣶⣄⣶⠀⠀⠀⠑⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⢠⠍⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢻⣦⡀⠂⠀⠈⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠛⠿⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⢈⣥⣷⣤⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠈⠀⠈⠋⠽⣷⠲⡞⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⣀⣠⣴⡶
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠋⠀⣿⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠪⣿⣿⣽⣿⠿⠶⢻⠁⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣠⡄⡿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⢹⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠨⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠣⡀⠀⣀⡴⠂⠉⠀⠀⠀⠀⠈⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⡾⠁⠉⢆⢸⠀⠀⠀⠀⠀⢴⡇⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠄⢂⠵⣤⡌⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠈⠂⠆⠀⠀⠀⣶⡾⠃⠰⠋⠀⠀⠀⠀⢂
⠀⠀⠀⡖⢀⠐⠀⢠⠊⠀⠛⡇⠀⠀⠀⠀⠀⠀⠰⢦⣦⣄⣀⣀⣈⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠎⠢⢄⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠐⢆⣁⡀⠀⠀⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⠀⢄⠀⠀⠀⣀⠐
⠀⠀⠀⠉⠙⠻⣿⣷⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠉⠓⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠉⠙⠂⠀⠀⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣴⣋⣀⡀⠀⠀⠀⢠⣤⣽⣟⠁⠠⠄⣀⣀⣀⠀⠰⠀⠑⠄
⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⡀
⠀⠀⠐⠓⠐⢲⣾⣀⣤⣤⠀⢈⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠿⠿⠿⠶⠶⣤⣄⣀⣤⡤⠄⠤⠤⠷⠄⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢚⣻⠿⠿⠿⠿⣳⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⢀⠖⠉⠀⠀⠀⠀⠀⠀⠙⢦⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣀⡷⠖⠒⠚⠛⠛⠛⠛⠓⠒⠲⠮⣀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡟⠒⣶⣿⣿⣯⡉⠉⠉⠉⠉⠉⠉⢉⣽⣿⣷⡖⢲⢯⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⡼⠁⡇⠀⠀⠀⣾⠉⣷⠀⠀⠀⠀⠀⠀⣾⠉⣧⠀⠁⢸⠀⢧⢀⣠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠈⡇⠀⢳⡀⠀⠀⣿⣀⣿⠀⠀⠀⠀⠀⢰⣿⣀⣿⠀⢀⠎⠀⣸⠉⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠤⠜⢦⡀⠇⠀⠀⣿⣿⣿⣀⣀⣀⣀⣀⣘⣿⣿⡿⠀⡎⢀⣠⠣⡤⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠈⠃⡆⠉⠃⠀⠀⠛⡿⠋⠁⠀⠀⠀⠀⠈⠻⡿⠃⠀⠓⠉⠘⡄⠁⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢾⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢀⡷⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⣀⠀⠈⠳⢤⣀⣀⣀⣠⠴⠊⠀⢀⣀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢨⠏⠉⢻⠒⠒⠒⠒⠒⢺⠋⠉⣯⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣟⠀⠀⡎⣄⠤⣼⠀⠀⠀⠀⠀⡘⡀⢄⠉⡆⠀⢘⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⣤⣉⣹⠁⠳⣽⠟⠁⠀⠀⠀⠀⠙⢻⡾⠋⢹⡈⠡⠔⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣖⠆⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⢦⡱⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⣦⡏⠉⠒⠒⠲⠤⣤⡤⠤⠒⠒⠚⠉⣧⡆⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⠶⠿⠷⢦⣤⣀⡀⢰⡏⣷⠀⣀⣠⣬⠶⠿⠿⢾⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠈⠈⠉⠉⣿⡏⠉⠉⠉⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣧⢀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⢥⣴⣶⣦⠶⠿⠛⠋⠁⠉⠛⠻⠿⢶⣶⣶⣦⡽⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣶⡆⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣶⠀⠀⠀⠈⢻⣿⠿⣿⣿⡟⣱⣷⣶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⡿⣿⣿⣿⡄⠀⠀⠀⠀⢁⣤⣻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⣶⣿⡇⠋⠀⢸⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⣨⣍⡛⢧⡹⣿⣿⣿⣿⣇⡇⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠐⠻⢿⣿⢿⡏⢸⣿⣿⣿⣷⣄⣸⣿⣿⣿⢹⡇⠀⣸⣦⣽⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣯⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⢻⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣷⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣯⣥⣷⣾⣧⣀⠀⣠⢽⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡽⠖⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣍⠳⣜⠿⣿⠿⣟⣛⣛⡿⣿⣿⡿⣫⡵⢋⣥⣶⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣍⡛⢛⣋⣭⣭⣭⣙⠲⠶⠚⣫⣴⣿⡿⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣠⣤⣴⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡄
⠀⢺⣿⣿⠟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⢠⣾⡿⠋⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⡿⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿
⠘⣿⠇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⡇⠈⠟⠛⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠟⠉⠁

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠖⢩⠭⡉⠲⡄⠀⠀⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⢀⣥⠁⠀⠀⠀⠀⢰⡥⣚⣩⣭⣍⡒⣼⡆⠀⠀⠀⣴⡇⠐⡳⡄⠀⠀⠀⠀⠀⠀⡐⠊⠅⠀⠀⠀⢀⠉⣠⠐⡂⠠
⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⡼⢿⠉⣍⣀⣩⠉⡿⡇⠀⠀⢆⣀⣡⣿⠄⠈⠀⠌⠀⠀⠀⡀⠙⠒⠃⠀⠀⠀⠈⠀⠈⢳⣤⠧⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⢶⣧⣀⣼⡖⡧⠃⠀⠀⠈⠉⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠲⣠⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⠭⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢉⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠻⣄⣨⠄⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀⠈⠐⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⠂⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡒⠀⢐⡄⠀⠀⠀⠀⠀⡀⠀⢀⡴⠠⠄⠀⠀⠀⠀⠀⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠩⠶⠎⠈⢄⠀⠀⠀⠀⢀⡍⢩⠅⡉⡰
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠰⢧⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠄⠴⠀⠀⠀⠀⠀⠙⠚⠅⠀⢈⡅⢄⠀⠀⠀⠀⠀⠉⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠊⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡀⠀⠐⠄⠀⠀⠀⢀⠴⡋⠀⠴⣽⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠁⠀⠂⠀⠀⠀⠀⠀⡍⠤⠔⢀⠀⡀⡞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠃⠸⠀⠈⠡⠈⠀⠈⠡⡀⠀⠈⠁⠓⠁⢠
⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠄⠀⠀⠀⠀⠀⠐⢀⣀⠠⠀⠀⠀⠈⠀⠈⠠⠘⠂⠀⠊⠁⠄
⠀⠀⣠⠈⢧⠟⠁⠈⠢⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⢀⠂⠀⠀⠀⠀⠀⢀⠆⠀⡠⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠄
⠀⠘⢆⠀⠀⠐⠀⠒⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣙⡤⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⢿⠀⠉⠙⢿⡆
⠀⠀⠀⠸⣿⡇⣿⣿⡟⠘⠋⠋⠅⠀⠀⠀⠉⠀⠈⡇⠀⠀⢀
⠀⡀⠀⢀⣿⣧⣸⣿⡇⠀⠀⠀⡆⠀⠀⠀⠂⠁⠀⡇⠀⠀⡄⠂⡄
⢆⠀⣠⣾⣿⣿⠏⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⢧
⠈⠛⠛⠛⠛⠁⠀⠀⢹⣄⢀⠀⠀⢸⣶⣶⡇⠀⠀⡸⠀⢀⠁⠇
⠀⠀⠀⠨⠐⠄⠀⠀⠘⠮⣅⡀⠀⠈⠁⠁⠀⣀⡜⠓⠆⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄
⠀⠀⠀⠐⠂⠨⡢⠀⠀⡀⡔⠉⠑⠒⠒⠒⠋⠁⠘⡆⠁⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠂⠉⢲⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠶⠎⠀⠀⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⠤⠤⠶⢲⠾⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠲⣶⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢀⣀⣴⣏⣀⣾⠄⡼⠀⠀⠀⠀⢸⣿⣭⣭⣍⣉⣹⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢑⢦⠞⠉⠉⠁⠀⠀⣠⢣⠎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣵
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢶⣤⣷⣼⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠟⠛⠿⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣥⣐⣊⣤⣤⣤⣍⡲⣝⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠙⠋⠀⠀⠀⠈⢻⡎⢧⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣤⠀⠀⢠⣦⠀⠀⢸⣿⣿⡟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⣀⣉⣴⣦⣈⣉⣀⣠⡾⣻⣷⣿⡽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢍⡉⡹⢧⣼⠭⣉⢩⣥⣞⣿⣿⣿⢇⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⠷⣮⡹⣝⢯⣤⡶⠿⢎⢋⣻⣯⣽⣟⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠂⠡⣷⢘⡷⣥⣑⣚⣀⣤⠴⡾⠉⣴⣦⡙⣯⡉⠛⠛⠛⣷⡄
⠀⠀⠀⠀⠀⠀⣰⡿⠛⢦⣼⣧⠾⠛⠁⠀⠉⠛⠋⠀⠀⢧⣾⡀⣞⠒⣿⠙⠲⣶⣶⣿⣁
⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠁⠀⠀⠀⠈⠉⠛⢿⣦⡀
⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟
⠀⠀⠀⠀⠙⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣤⣤⣤⣤⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠉⠙⠛⠻⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣌⡉⠛⠻⠿⠿⣿⣿⣿⡿⠿⠿⠛⠋⣉⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⣿⡇⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠘⠐⠒⠐⠒⠒⠒⠒⠒⠠⠂⠂⠂⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠋⢿⣿⣿⠏⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⢀⠀⣾⣄⠀⠀⢀⣴⠁⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⡟⠹⣦⣜⠁⠀⠀⢹⣷⣾⠋⠀⠀⠀⠀⠀⠀⡀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣾⡿⡟⢾⢿⣸⡷⣶⢠⡨⢿⣥⡀⠀⠀⠀⠀⠀⡜⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⡘⢏⡇⢻⠞⠄⠠⣷⡇⡦⠁⠀⠀⢈⠀⠰⣇⣀⢸⡁⠛⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢤⡄⠉⠈⢻⣤⣷⠚⣆⡆⠇⠃⠚⣤⡤⠊⠃⠀⠱⡀⢲⣤⠤⢏⡠⣤⣿⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠻⣶⣇⠀⢻⡿⠃⠸⣇⡹⡷⢈⣼⣥⣥⡴⠁⠀⠀⠀⠀⠈⢡⡀⠈⢳⣦⢀⣠⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣩⢽⣷⣦⠘⣶⡧⢸⣷⢸⣇⠉⠉⠙⠉⢸⠴⢃⣀⣁⣦⡐⢤⠇⢀⠈⡷⠋⠀⣿⠏⢿⣃⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢏⠃⠎⠙⠋⠾⠿⣇⠛⢻⢯⣿⣟⣳⣶⣶⢃⠀⠾⡟⠙⠙⠪⣾⢿⡌⣀⠒⢤⣾⠏⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⣼⡐⠿⠿⢹⣿⣻⣿⣷⣶⣷⢤⡀⠀⠘⠙⠻⣿⣤⣀⣉⣉⣁⣀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣀⡀⠻⣿⣿⣷⡟⠉⢁⣤⠍⠀⠀⠙⣿⡖⣄⠀⢀⠩⠙⠿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⢦⣹⣧⠀⠀⢶⡿⠁⢠⠖⠀⠀⣼⣧⣿⣆⠀⠁⢀⣦⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⠔⠋⡁⣸⣿⡿⠀⠀⠟⠀⠈⠀⡠⠈⠉⠉⠈⠛⠿⢿⣿⣾⠟⠃⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢷⠀⠀⠧⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠘⠁⠘⢄⠜⠀⠀⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⠂⢠⣤⣤⣄⣀⠀⠀⣰⣧⣬⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣽⣿⣶⣿⣿⣿⣿⣿⣆⡀⣿⣯⣄⢠⣀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠹⠇⠹⢿⣿⣿⣿⣷⠸⡅⣩⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡉⠀⣘⠃⠸⣿⣿⣿⣿⠤⣧⡙⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣦⣁⡴⠀⠻⣿⣿⣿⣶⠟⣿⠟⢀⣾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠻⢻⠯⣤⡟⠀⠀⣀⣈⣋⠀⠀⠀⠘⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⣌⢠⢠⠀⢈⠄⠀⠐⠙⠿⠈⠳⡆⠀⠀⢻⣿⣿⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡾⠃⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢇⠀⠀⢸⣿⣿⡆⠀⢌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣰⣤⣞⠰⣧⠚⣷⣄⣄⠀⠀⠃⠀⢀⣲⡏⢳⣿⠀⢸⢸⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠈⢿⡟⠁⢠⣿⣿⡿⠀⢰⠄⠀⣨⢷⡅⢈⣻⠀⢸⣾⣿⣿⡇⢠⣟⠃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣠⠟⠈⢻⡀⣰⠃⠀⣴⠋⣾⣯⣨⣿⠀⢘⣿⣿⣿⡇⠀⠈⢁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠶⢀⠈⠃⠋⠐⠈⣧⠚⠉⠛⢿⡿⢀⣾⠛⠉⢹⡇⠐⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠧⣀⣠⡀⡇⠀⢀⠄⠈⡠⠊⠃⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡛⣡⣤⣴⡾⠁⠀⠀⢀⣴⡟⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢠⣤⣴⠋⠀⠀⠀⠀⠠⠽⠋⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣰⡏⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⢠⠀⠀⠀⠀⠱⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣀⢀⡀⠉⠀⣀⠴⠦⠀⠀⠀⠀⠀⠀⠕⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠠⣻⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠇⠀⡟⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣭⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⣗⡆⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣿⣧⡀⢫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⡛⢃⣺⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⢠⡤⢠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠻⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⣶⠄⢠⣴⡄⠀⣀⣠⣶⣿⣶⣤⣶⣶⣦⣿⣄⣀⢸⡟⡁⢀⣸⣿⣿⣿⣿⠛⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠆⠀⠘⣻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⣘⣿⣿⣿⠏⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠛⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣀⠀⣿⣿⡟⠀⢀⣠⣿⣿
⠀⠀⠀⠀⠀⣶⣴⡄⠀⠀⠀⠀⠀⠀⠀⣠⣈⡋⠀⢀⠀⠀⠀⢀⣤⣶⣦⡕⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⢀⣤⣹⣏⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣦⣶⣶⣶⣶⣦⣾⡿⠟⠁⠀⠀⠀⣴⣾⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⡿⠋⠀⡀⢠⣶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠿⠋⠀⠀⠸⡅⡽⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢷⠇⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠃⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣥⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⢀⣀⣤⣤⣄⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠚⠛⠓⠿⢅⣀⣀⣀⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣤⣀⠀⠹⠿⢛⡿⠅⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠳⣤⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⠖⠉⠈⠑⢌⣷⡶⠚⠋⠉⠙⡆
⠀⠀⠀⠀⠀⣰⠏⠀⠀⢸⠀⠀⢀⡴⠛⠁⣀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠈⢣⡴⠋⢀⡴⠊⢀⡀⠀⣠⡟⠙⠛⠶⣤⣀⠀⠀⠀⠀⢀⡴⠛⢹⡆
⠀⠀⠀⠀⡿⠀⠀⠀⠀⣰⢏⣀⣠⠾⠶⢲⠟⠻⢶⠏⠀⠀⠀⠀⣠⣭⣷⣦⡀⣴⠏⠀⠀⣼⡥⠖⠚⢶⡄
⠀⠀⠀⢰⡇⠀⠀⠀⡼⠃⡿⠋⣉⣁⠀⠀⡔⠒⢜⣇⠀⠀⠀⠀⣯⠀⠀⠙⣿⡃⠀⠐⠾⡋⢀⡤⠖⠛⢻⡄
⠀⠀⣴⠛⠀⠀⠀⣼⠛⠛⠃⢸⠁⠈⢣⠀⢻⣦⡼⠟⠒⠶⣄⠀⠈⢳⡄⠀⠀⠉⠣⠀⠀⠈⢯⣀⡴⠖⠛⣷
⠀⠀⣿⠀⠀⠀⢰⠿⡄⠀⠀⠸⣯⣧⠈⡇⠚⠃⠀⠀⠀⠀⠸⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡴⠋
⠀⠀⢸⣧⣄⣤⣿⡄⠉⠓⣆⠀⡈⠓⠚⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣟⠙⠆⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⢸⡇⡟⢀⡤⣜⠦⣤⠏⢰⣿⣷⣦⣤⣶⣦⣤⣤⣤⣾⣿⠀⣴⠻⣦⡀⠀⠀⠀⣀⣀⣤⠾⠋
⠀⠀⢸⡄⢷⡀⠀⠚⠳⠀⠀⠸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢏⡞⠁⠀⠈⠛⢦⣤⣀⣼⣿
⠀⠀⢸⡇⠀⠛⢦⣄⣀⣤⢤⠀⠈⠛⢿⣟⣛⣓⣲⠎⢩⣷⠋⠀⠀⠀⠀⠀⣰⠏⠁⢀⡟
⠀⠀⠀⢷⠀⠀⠀⠀⢀⡗⠈⢳⡀⠀⠈⢇⠉⢉⡟⢀⡾⠁⠀⠀⠀⠀⢠⡾⠁⠀⠀⣸⠃
⠀⠀⠀⠘⣧⠀⠀⠀⠸⣤⣴⡤⢷⠀⠀⠈⠉⣉⣠⠾⣅⠀⠀⠀⠀⣴⠏⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⣴⡞⠛⢷⡤⠤⠤⠥⠞⣆⠈⢷⡀⢀⡾⠁⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠙⢾⡋⠙⢧⣽⡄⠀⠳⡄⠀⠀⠀⠙⡄⠀⠹⣿⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⣸⠂⢻⡙⢷⠛⢲⣀⣀⣠⣼⣄⡶⢻⣦⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⣤⣼⠀⣸⠃⠀⣿⠭⠴⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠓⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠱⡀⠀⠀⡀⠀⠂⠐⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⠌⠀⠀⠀⢉⠐⠂⠈⢀⠀⠀⠄⠀⢀⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠘⠀⠀⠀⠀⠠⠠⠓⠈⠁⢈⠀⠀⠒⣀⠀⠈⠀⠰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⢀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⢀⠂⠀⠀⠀⠈⢸⣀⣸⡞⠀⠀⠀⠀⠀⠀⠁⠀⠒⠠⠆⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠁⠀⡌⠀⢀⠈⢁⠀⠊⠉⠉⠿⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠄⠀⠀⠀⠈⢻⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠤⣤⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠀⢸⡆⠀⠀⡠⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠨⡙
⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⡰⢾⡇⠀⠠⠁⠀⠘⡄⠀⠀⠀⠀⠀⠈⠁⠀⠐⠶⢆⠀⠀⡘⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⡇⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⠐⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⣀⣀⡠⠤⠆⠴⡊⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠐⡼⠀⢣⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⢀⠤⠠⡀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠋⢀⣀⡠⠤⠐⠊⠁⠀⠀⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠚⠛⠛⠉⠉⠉⠛⠛⠛⠒⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⣀⣠⣤⠴⠶⠶⠶⠶⠶⠤⢤⣄⣀⡀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⠀⠀⠉⠳⣄
⠀⠀⠀⢀⡴⠋⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⢤⣤⣀⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⢳⡄
⠀⠀⢀⡾⠁⠀⠀⣴⠋⠀⠀⠀⠀⣠⠶⠋⣁⠀⠀⠀⠀⠀⠀⠀⢈⡙⠳⢦⡀⠀⠀⠀⠈⢳⡀⠀⠀⠹⡆
⠀⠀⣾⠁⠀⠀⣼⠃⠀⠀⠀⢀⡾⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠻⡄⠀⠀⠀⠀⢳⠀⠀⠀⢹⡄
⠀⢠⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⠁⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⢸⡇⢹⠀⠀⠀⢿⠀⠀⠀⠀⠸⡇⠀⠀⠈⣇
⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠸⡄⠀⠀⢹⣠⡇⠀⠀⠀⠀⠀⠘⣇⣼⠀⠀⢠⠎⠀⠀⠀⠀⢸⠇⠀⠀⠀⣿
⠀⠘⡇⠀⠀⠀⠸⣆⠀⠀⠀⠀⠙⢦⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡴⠋⠀⠀⠀⠀⢀⡞⠀⠀⠀⢠⡇
⠀⠀⢻⡄⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⣀⣀⣀⣠⠤⠖⠋⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠻⣄⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠋⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉
⠀⠀⠀⣀⣤⠴⠶⠶⠶⠶⠦⣤⣀⠉⠙⠛⠲⠶⣦⠤⠤⠤⢤⠶⠖⠚⠛⠉⢉⣠⡤⠶⠶⠶⠶⠦⢤⣄⡀
⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⣿⠀⠀⠀⢸⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⠀⠀⠀⢸⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢸⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⢤⣤⣤⣀⣀⣀⣀⣠⣿⠀⠀⠀⢈⣥⣄⣀⣀⣀⣀⣠⣤⡤⠴⠖⠛⠉

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠠⡄⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠐⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠸⠀⠀⠀⠀⠀⢀⣀⠀⠄⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⣠⡀⠰⠀⠀⢀⠘⠁⠀⢈⠍⢿⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡟⠀⠂⡰⠈⠉⢁⠕⠠⠤⣴⠈⠃⢀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠃⡀⠀⠁⠀⠀⠀⠈⠉⠒⠘⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠠⠀⠀⠠⢀⡄⡀⠀⢀⡀⠁⠀⠒⠒⠂⣄⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠂⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣇⡠⠾⠀⡀⠂⠀⠀⣠⠐⡂⠀⠀⠘⠁⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⠀⠀⠀⠀⠁⡖⠂⠀⠀⡈⡀⢀⠃⠀⡈⠀⠈⠐⠠⠀⠀⠑⠬
⠀⠀⠀⠑⠀⠈⡈⠀⠄⠀⠀⠀⠂⠀⠀⠐⠃⠀⢑⡄⠑⠃⠀⠀⠀⠉⠉⠁⢀⠇⡀⠀⠄⠋⠀⢀⠀⠒⢉⠠⣤⠄
⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠳⠀⠀⢀⡄⠠⠤⠤⠔⠒⠀⠀⠀⠀⠀⠄⠁⠀⣠⠒⢂⡛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠂⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⢀⠜⠁⠀⠀⠁⣄⣀⠀⢀⠠⠀⠒⠂⢀
⠀⠀⠀⠀⠀⠀⢀⡠⠠⢄⠀⠀⣀⡀⠀⠄⠁⠒⠇⠀⠄⠀⠀⠀⠉⠀⠀⠀⠈⠈⢡⠀⢻⠀⣠⠊⠀⠀⠀⠈⢀⠔⠁⠀⠨⠲⡤⠀⢀
⠀⠀⠀⠀⢀⡰⢁⡐⢀⠀⠈⢀⠀⣀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠠⠀⠀⠀⠀⠤⠀⢀⠀⠈⠡⠅⠀⠀⠀⠀⠐⠁⠀⠸⠁⠀⠀⠀⠉⠁⡄
⠀⠀⠀⠞⠤⠶⢠⠉⠀⠀⠀⡀⠂⠈⠁⠀⠀⠀⠀⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢄⠀⣰⠀⣀⠄⠙⠀⠀⠀⠀⠃⠁⠚⢢
⠀⠀⠀⠐⠠⠂⣠⠀⠠⠀⠈⠀⠁⠀⠀⠀⠀⣠⠀⠠⠄⠀⠐⠀⠀⠈⠉⠀⠀⠐⠒⡆⠀⠀⠀⠤⠤⠷⡍⠀⠁⠀⠀⠀⠀⠠⣈⡟⠂
⠀⠀⠀⠀⢀⠀⣈⠞⠄⠓⠀⠀⣀⢠⡰⢃⠡⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⡂⢷⠈⠀⢠⠞⢄⠘
⠀⠀⠀⠀⠀⠀⠀⠢⠤⠔⠂⠈⠀⡩⠀⠁⠀⠀⠀⠀⠀⢂⠀⠈⠉⠁⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠒⠒⠒⢐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⠁⠈⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⣂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠁⠀⢄⠀⠀⠁⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⠂⠀⠀⠀⠀⠀⠀⠀⠐⠈⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⢰⠤⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠂⡄⣀⢐⡤⠴
⠀⠀⠀⠀⠀⠀⠈⠣⢤⣉⣉⣆⣀⣀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠊⠀⠀⠻⠀⠀⠱⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠒⠚⠀⠐⠒⠂⠉⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠈⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⡄
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠀⠀⠀⠀⠉⠐⠒⠒⠒⠒⠚⠛⠋⠉⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⣿⣿⣿⣿⣷⣦⡀⠀⠀⠰⢶⠾⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⣤⣀⠠⠀⣤⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⢀⣼⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠒⠂⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣛⠶⠟⣋⣙⣤⣴⣶⣾⣷⣶⣤⣔⣐⣓⠖⣋⣉⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⠛⠛⠛⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⠛⠛⠛⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛⠛⠀⠀⠀⠀⠀⠀⢸⡇⢠⡄⠀⠀⠀⠀⣤⠟⠛⠀⠀⠀⠀⠀⠀⢸⡇⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢀⠀⠈⠱⠎⠱⢦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡈⠹⠏⠹⢆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠶⠉⠀⣀⠶⠖⠀⠀⠈⠰⠀⠀⠀⠀⢸⣧⣰⠶⠉⠀⣀⠲⠶⠀⠀⠀⠈⠰⠂⠀⠀⢸⡯
⠀⠀⠀⠀⠀⠀⢀⡰⠶⠶⠎⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣶⠀⣀⠶⣀
⠀⠀⠀⠀⠀⢴⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⠉⠀⣿⠀⣀
⠀⠀⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⠛⣥⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠛⣦⡄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠛⠁
⠀⠀⠀⠀⠛⣣⡀⠐⢂⣀⣠⣇⡀⠀⠀⠀⣀⣀⣀⣼⣄⠀⠀⠀⠀⢀⡀⠀⣀⣦⣀⠀⠀⠀⣀⣀⣀⣰⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⣦⡀
⠀⠀⠀⠀⠀⠺⢇⣀⣀⣀⡀⠈⠓⠲⣶⣶⠛⠛⠛⠀⠘⢷⣶⣶⡖⠂⠀⠀⠀⠀⠛⠒⣶⣶⠛⠛⠛⠀⠘⢳⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⣀⣀⡈
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠱⢦⣀⣀⠀⠀⠀⣀⠶⣄⣀⡈⠀⠀⠀⢀⣀⡰⢶⣀⣀⠀⠀⠀⣀⠶⣄⣀⡀⠀⠀⠀⢀⣀⡰⢶⣀⣠⠶⠶⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠶⠶⠶⠉⠀⠉⠉⠷⠶⠶⠶⠎⠉⠁⠀⠉⠉⠶⠶⠶⠉⠀⠉⠉⠱⠶⠶⠶⠎⠉⠁⠀⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡞⠃⠀⠀⠀⠘⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣴⠓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠿⠀⠀⢀⣀⡀⠀⠀⠐⠂⡀⠁⠀⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠶⠉⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠿⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠾⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣀⠶⠉⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢿⣇⡰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡄⠀⠃⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⠛⠛⠛⣿⣄⣀⣀⣴⣿⣷⡟⢻⣧⣀⣀⣀⣀⠓⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠷⣄⠀⠀⠀⠙⠛⠀⢀⡀⠀⠀⠀⠛⠛⠋⠀⠀⣀⠀⠀⣠⣀⡾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠶⣀⣀⣀⡰⠎⠱⠶⢆⣀⣀⣀⣀⠶⠶⠉⠶⠶⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⣼⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣶⡄⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢱⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣶⠟⠋⠁⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠈⢿⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⣸⣿
⠀⠀⠀⠀⠀⢿⣏⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠙⢶⣤⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢴⡟⠿⠿⣷⡄⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠲⡄⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣷⡤⠜⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⠤⠶⠒⠒⢤⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠠⣤⣀⠀⠀⠀⣰⠏⠀⠀⢀⠊⠀⠀⠀⠀⠀⡴⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠢⠚⠋⠀⠀⠀⠀⠂⠁⠀⠀⠀⣰⣃⣄⣠⠖⠛⢇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠿⣆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠄⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⣤⣤⣽⡧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡏⠉⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⠶⠶⠾⠿⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘⣍⣧⡲⡄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡄⠀⢀⡀⡈⢋⣡⣷⡈⠤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⣣⣴⣡⢀⡴⠜⢦⣤⠤⠴⣖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠗⠁⠘⠀⠉⠁⠀⠀⢠⡏⠀⠀⠈⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢽⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠖⠳⣀⠃⠀⠀⡴⠀⠀⡠⠞⠀⡿⠉⠀⢒⠂⡻⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⡇⠈⠹⠸⡏⠀⢛⡆⠀⠀⠀⠀⠈⠀⠀⢨⡠⠐⠂⠀⠀⠀⠰⠁⣼⡁⣀⣴⣿⠈⠁⠐⢳⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠀⢰⣦⣄⣼⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠔⠁⠀⠚⠁⠀⢠⡾⣽⡄⠀⢀⡾⠛
⠀⠀⠀⠀⠀⠰⠀⠄⠀⡀⢀⢰⡤⡜⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⡀⠀⢀⣤⠟⠙⠁⢻⣆
⠀⠀⠀⠀⠀⠀⠘⠈⠹⠃⠀⠙⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠛⠘⠉⠁⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⢏⡽⠀⠀⠀⠀⠀⠀⠚⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⠄⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⣾⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠚⠛⠉⠉⠉⠉⠉⠙⠛⠒⠲⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣰⠃⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠙⠒⢤⡀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠳⡀
⠀⠀⣰⠃⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣰⢷⡆⠀⠀⠀⠀⠀⠀⣶⢷⡀⠈⠳⡀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢱⡀
⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣇
⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠸⠃⠀⠀⠀⠀⡿⠀⠀⠀⠀⣿
⠀⠸⡇⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃⠀⠀⠀⠀⠀⠀⠻⠿⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡿
⠀⠀⢧⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢠⠇
⠀⠀⠘⣆⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣀⣀⣀⣀⣀⣠⡤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉
⠀⠀⢀⣠⠴⠒⠛⠋⠉⠙⠛⠒⠦⣄⡉⠉⠙⠓⠒⣶⠶⠶⠶⢶⡖⠒⠛⠉⠉⣁⡤⠖⠚⠛⠉⠉⠛⠓⠲⢤⣀
⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲
⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⣿⠀⠀⠀⢸⡇⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣿⠀⠀⠀⢸⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢘⡧⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠋⠉⠉⢿⣀⣀⣀⣰⠏⠉⠙⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⡀⢀⠀⠀⠀⠜⠿⠿⠿⡟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢈⣠⠤⢤⣌⠑⢦⠀⠀⠀⣿⠀⠀⢠⠏⠠⠘⡇⠀⢸⡇⠘⢦⡄⠠⣤⠀⢸⠀⢰⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠁⡉⢩⠀⠀⠀⢹⡷⢾⡇⠀⠀⠹⠀⠀⠤⠀⠻⠤⠤⠰⠆⠧⠀⠸⢥⠀⠻⢦⣤⣀⣾⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠛⠛⠅⠀⢒⡖⠚⠋⠀⠈⢹⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣐⠲⣾⡿⠏⢀⣀⣤⠴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡠⠶⢒⠛⣾⣗⠶⡶⢞⣋⡭⠾⠓⣽⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⠦⠧⠿⠴⠋⠉⠓⠞⠋⠙⠴⢥⣞⣹⡿⣿⣏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠈⠉⠁⠸⢿⣍⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⡞⠁⠀⠀⠀⢀⠀⢸⡟⠀⢸⡏⢀⠄⠀⠀⠀⠀⠀⢈⣿⡄⢰⣿⣿⣿⡗⣿⣿⣿⣿⣯⣝⡇⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⣸⡿⢀⣼⣿⣿⣯⣵⣿⣿⣿⣿⣷⣾⣇⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠳⣤⣄⠀⠈⠁⠈⠙⠒⠒⠋⠉⠈⠁⠀⠀⣠⣴⣿⠋⠀⣾⣿⣿⣿⣿⣿⣧⣶⢎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⢀⣠⣼⣿⣏⠀⢸⣿⡿⣿⣿⣿⣿⣿⣰⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠖⠒⠒⠒⠒⠒⠒⠲⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⢀⣀⠤⠤⠔⠂⠐⠦⠤⠤⣀⡀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡠⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⢆⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢰⠃⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠘⡆⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣰⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠈⠒⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠁⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣙⡒⠤⢄⣀⣀⡀⠀⠀⢀⣀⣀⡠⠤⢖⣊⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠉⠓⢄⠀⠀⡏⠀⠉⢩⠀⠀⡠⠚⠉⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⡇⠀⠀⢸⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⠤⠤⠤⠤⠄⣇⠀⠀⢸⠠⠤⠤⠤⠤⠤⠒⠒⠉⠁