Healthy food Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠒⠀⢀⡴⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠫⢭⡽⣆
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠰⠀⠖⠀⠀⠇⠀⠀⠀⢀⠀⠀⠀⠀⢠⣟⠀⡺⣀⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠁⢉⡆⢘⣿⡀⠀⠀⠈⠀⡠⠛⠃
⠀⠀⠀⠀⠀⢀⠀⠃⠣⣄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡹⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠼⠒⠹⠐⠨⣇⠀⠀⠀⡜⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⢦⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⢠⡞⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠏⡃⠏⡁⠾⡄⠀⢰⠇⠰⣶⣤⢴⣤⣿⣥⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⠀⢸⠇⠀⠀⠀⠀⠰⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣃⣙⣢⣙⣻⠃⠀⢸⠀⠀⣠⣿⣶⣿⢿⢋⡄
⠀⠀⠀⠀⠀⠀⠢⣀⣤⠶⠊⠁⠀⠀⡼⠀⠇⡾⠀⠀⠀⠀⠀⠀⠈⠛⢦⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡟⡟⠯⠀⠀⠆⠀⠰⡿⣿⣟⢻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⠞⢀⣼⡾⠁⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⢀⠀⠀⠀⠈⣿⣿⣿⣿⣛⡁
⠀⠀⠀⠀⣤⣤⠤⠤⠴⠶⠶⠛⣁⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⢹⣾⣿⠉
⠀⠀⠀⠀⠀⠈⠉⠀⠒⠒⠒⠉⠉⠀⠀⣀⣀⣀⣀⣤⣤⣤⡴⠶⠶⠖⠚⠟⠛⠉⠉⠉⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣤⡀
⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⢰⠋⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠞⠁⠀⠀⠀⠀⠀⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣬⣥⠜⢻
⠀⠀⠀⠀⡴⢋⡴⠂⠀⠈⠑⠄⠀⠈⠓⠦⣄⣀⣀⣐⣀⣀⣀⣀⣠⣤⡤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢙⠳⢄⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⢄⢘⡉⠺⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⢻
⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣀⣀⣐⣠⣄⡶⠦⣄⠀⠀⠀⠈⠀⠀⠀⠈⠋⠀⢹⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠚⣿
⠀⠀⠀⢸⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡞⠁⠀⠙⡇⠀⢹⡆⢹⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⡇⠀⢀⡀⠀⡻
⠀⠀⠀⠀⢳⣜⠦⠀⠀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠁⠀⠀⠀⡇⠀⣸⢃⣿⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠠⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⢀⠃⠠⣯⠞⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢢⠈⠀⠀⠁⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢠⡟⡇⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⢰⢣⡇⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠉⢉⠁⠂⠤⠀⠀⠀⠄⠀⠀⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠤⠔⣣⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠃⠀⠀⠃⣠⠖⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡄⠀⠀⠀⠉⠛⠛⠓⠋⠁⢀⠠⡔⠒⢤⢀⣤⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣠⡤⠶⢤⣄⣀⣠⠼⠃⠀⠀⠀⠀⢠⠁⠀⠀⠀⠤⠤⢍⡉⢩⡄⣾⣹⠀⣠⠖⠀⠀⠀⠀⠀⡰⡄⣨⢃⠫⣜⣻⣍⠛⢞⣷⣦⡀
⠀⠀⠀⡄⠁⠀⠀⠀⣿⠮⣤⣄⠀⢀⣀⣀⣀⡀⣀⣀⠀⠀⣀⠀⠀⠀⠀⢀⣠⡶⠛⠑⣤⠶⠿⣷⠶⠶⣤⡀⠀⠀⠀⠀⢽⣤⡁⠋⡐⡛⢉⣿⣾⣻⡙⢹⡇
⠀⠀⠀⣱⠄⠀⠀⠀⢿⡀⠁⢉⠓⠋⣀⣹⡅⠘⠋⠹⠓⢾⡏⠸⠀⠀⢠⣾⠟⠀⠀⠜⠁⠀⠀⠈⠃⠀⠈⠻⡆⠀⠀⠀⠐⠛⠑⠆⠈⠒⠲⢿⣷⣤⣅⣾⠇
⠀⠀⠘⠇⢶⠀⠀⠀⠘⣧⡀⠀⠀⠸⡏⠉⠐⠀⠀⠁⢈⡼⠁⠆⠀⠀⢸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡼⢂⡼⠋⠉⠁
⠀⠀⠀⠀⡃⠀⠀⠀⠀⠈⠻⣦⣴⡋⠁⠀⠀⠀⣀⡴⠋⠀⠎⠀⠀⠀⢸⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡜⢰⢃⠊
⠀⠀⠀⠀⠉⠒⠤⢤⡀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠁⠀⠀⡴⠃⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⢰⠃⡜⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠃⠀⠀⠀⠀⠐⠒⠂⠐⠢⠒⠁⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⣀⢀⣀⣀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠮⢤⣧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣷⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠳⡀
⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⢰⡴⣰⠁⠀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⢈⣇⡄⠀⠀⠀⠀⣀⡀⡼⠟⣹⠀⠘⡍⢡⠔⠁⢈⠇
⠀⠀⢀⡄⣻⡄⠀⠀⠀⠀⢣⡘⢰⠋⡁⠐⡛⢻⣾⠛⠚⡷
⠀⠀⠙⠢⠬⠷⡏⢳⣀⠸⣍⣻⢸⠎⣹⠀⡜⡱⡙⠢⡉
⠀⠀⢀⡤⠴⡞⢔⢾⡉⣧⣄⠹⠀⡋⠀⢸⢀⠧⣨⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠎⠢⡀
⠀⠀⠀⠢⡰⣜⣚⣦⡑⢧⢠⠀⠣⡰⡀⢰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠂⠁⠈⠉⠁⠄⠀⠘⣄
⠀⠀⠀⠀⠈⢙⣿⡢⣈⡉⡗⢢⣄⣈⢺⠮⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠀⠸⠀⠀⠀⢸⠑⠢⠀⡀
⠀⠀⠀⠀⠀⠯⠤⠕⣢⣍⡛⠰⠧⠭⣍⠀⠀⡈⠦⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⡠⠤⠥⠤⢇⣀⠴⠉⢾⠀⠀⠀⢨⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠰⠧⠔⠋⠉⠉⠉⠙⡔⠁⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⡄⢰⠀⠀⠀⡀⠀⢀⠏⠀⠀⣆⢀⠔⠁⠀⠀⠉⠱⣀⣀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢘⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡐⠐⠊⢀⣂⡆⠀⠀⡰⠁⢠⠏⠀⠀⠀⡟⠛⠤⣀⢀⠄⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣾⣿⠁⢠⣀⣤⡶⠋⠀⠀⠀⠀⢀⡷⡀⠀⠀⢠⠦⠔⣁⠀⢠⠋⡴⠀⠀⡴⠁⠠⠋⠀⠀⠀⠰⠃⠀⠀⠀⢃⢀⠤⠊⠀⠀⠀⡆
⠀⠀⠀⠤⢤⣦⣭⣔⡲⠦⢌⣿⣿⠔⣠⠲⡎⠀⠀⠀⢀⣀⡤⠞⠁⢣⠀⠀⣸⡀⡨⠀⠉⠁⡴⠁⡠⠊⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⡰⢣
⠀⠀⡠⠚⠧⢄⠢⠥⡂⠐⢦⠹⢋⡤⠖⡉⠛⠷⠒⠢⡀⠀⠀⠀⠀⠀⢣⣀⡇⠈⠀⠀⠀⠜⠁⠀⠀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠊⠀⠀⠱
⠀⡔⠁⠀⡄⠀⠀⠀⠈⠑⠒⠚⠃⠐⠊⠀⠀⠀⠀⠀⠈⢢⡴⠂⠀⠀⠈⠟⠀⠀⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠂⠁
⠘⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⣠⠴⠊⣄⣤⣶⠾⠛⠉⠀⠀⠒⠒⠒⠛⠛⠒⠖⠂⠤⠄⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⡄⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠸⡥⠴⠒⠒⠒⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⣈⠒⢄⠀⠀⠀⢀⣀⠀⢸
⢃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⢷⣄⢀⡤⠂⢡⡰⠂⠈⢉⣒⠒⠒⠒⠂⠉⠀⠈⠑⠂⠐⠂⡕⠋⠀⠈⠣⢄⠜⠁⠀⠉⠁
⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢏⠀⠀⢀⣑⣄⠀⠀⢇⠀⠀⠀⠀⠉⠑⢂⣄⡀⠀⠀⢀⠤⢄⣀⠇
⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠑⠒⠁⠀⠀⠑⢄⠈⣄⡀⠀⢀⡠⠂⠁⠀⠉⠢⠠⠊
⣀⣀⣀⣀⣈⣁⣂⣶⣤⣤⣤⣤⣤⣤⣤⣶⣒⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣧⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠄⠀⣀⡀⠀⢀⠀⢀⢾⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⢻⡶⣿⣿⠟⠁⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡤⢿⣏⡀⠀⣿⣧⠀⢸⠀⣼⠀⢠⠅⢀⣴⣶⣶⣄⠺⠿⠿⢋⣿⡆⠀⠀⠘⠄⠀⠀⠈⠃⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡹⠧⣿⡆⠀⣿⢸⠀⢺⢀⡟⢀⡞⢰⣾⣿⣿⣿⣿⣷⣤⢠⣽⡧⣴⣷⠈⠐⠀⠈⠁⠀⢠⡸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣶⡁⠀⠀⣿⣼⣶⣿⣾⢃⡞⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⡿⠈⡟⣡⡾⠃⠀⠀⠀⠀⢼⣿⠄⢸⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠂⢠⣿⣿⣽⣿⣿⡿⠀⠀⠘⢿⣿⣿⣿⡿⠟⠁⠀⠇⠀⠘⢉⣵⣿⣿⣶⣶⣦⡈⠁⢠⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⣿⣿⠀⢀⠀⢀⢀⠀⠀⢸⣿⣿⡿⢿⣿⣿⣿⣷⠈⠉⣡⣄⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⣿⣿⢀⡀⠈⡉⠛⠛⠋⠀⢀⠇⠀⢀⠀⢉⢉⢀⡏⢠⠏⡜⠀⢀⢀⠋⢻⣷⡾⢛⣿⣿⣿⣆⣸⣿⠙⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣍⡈⣧⠀⡇⢠⠀⣧⠀⢸⠀⠄⠇⠀⠇⠸⠘⠀⠘⠀⠇⠇⠾⢸⠀⢸⣿⣷⠟⠉⠺⠿⠋⠋⠰⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡗⠈⠿⠿⠷⠸⣆⢷⠘⣧⠸⣆⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⢀⢀⠖⢀⡟⢠⣿⣿⠁⠀⠀⡀⠠⠀⠂⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣤⣤⠀⢠⡀⢹⣾⣧⠸⣇⢻⡄⠀⢠⡁⢠⠀⣠⠀⢀⢀⡏⠈⠀⢊⣤⣜⠛⠏⠀⠀⠄⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢋⣴⡆⠉⠚⣿⣿⣇⢻⣎⣷⡀⠸⡃⠻⠀⠓⠀⠳⠘⠀⠀⢰⣿⣿⣿⣿⣷⠀⢀⡀⠀⠀⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸⡇⠀⣀⡘⣷⢻⡞⣿⡹⣧⠀⠁⢠⣷⡄⣠⣴⣷⠀⠀⢺⣿⣿⣿⣿⣿⠑⠿⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⢿⡟⢿⣞⣿⣿⣧⠹⣧⢀⣸⣿⣿⣿⣿⣿⢴⡆⣾⣿⣿⣿⠟⣁⣀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠇⠀⣶⡄⠸⠿⠻⠛⠛⠀⣀⣿⣿⣿⡿⣿⣿⣿⣾⡇⢿⣿⠟⣡⣾⣿⣿⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣷⣿⣿⡿⠛⣤⣶⣦⠐⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⠀⠈⢿⡿⠛⠁⣀⣘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣦⡀⠞⢠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⡀⠀⣀⠴⠚⠓⠒⠦⣄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⡏⠑⠄
⢠⡪⠃⠉⠓⣀⠀⠁⠠⠀⠉⠓⢄⠀⠀⢂⠀⡁⢠⠀⠀⠀⣀⠀⠀⠀⣄⣅⡄⡀⡈⢂⠀⢀⠀⠀⡀⠠⠄⠀⠀⠤⠔⠒⣀⠀⠈
⣼⢀⠀⠀⠀⠈⠴⣀⠀⠀⢀⠀⠌⢆⠀⠀⡄⠀⠀⠀⠠⠀⡉⠢⠤⢀⣀⣆⣀⡤⠤⠚⠀⠀⠰⠎⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⡀⢤
⣿⡞⠀⠀⠀⠀⠀⠻⢼⡾⠀⠀⠀⠀⠧⣀⠁⢀⡀⠚⢀⡀⠃⢀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣠⠖⠚⠋⠋⠈⠀⠀⠨⠀⠖⠀⠁
⠇⠙⢴⡄⠀⡀⠀⠈⠀⠀⠉⠻⠢⡄⠀⠉⠳⡄⠀⠘⠋⠊⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠈⣷⠁⠀⠀⣎⠈⠁⣀⡀⠠⠂⠀⠐⢐⣺
⠸⣄⠀⠈⠢⣬⣀⣀⣀⣀⡀⠒⠘⢌⡓⠆⣤⡛⣦⠀⠀⢈⢅⠢⡤⠯⢢⠔⠃⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⠀⠂⢁⣀⠤⠒⠂
⠀⠈⠑⠦⣄⣁⠉⠉⠁⠈⠉⠙⠒⣤⣌⡓⠤⣉⠛⢳⠀⠀⠈⠈⠀⠈⠀⠀⠀⣀⠼⠀⠀⠀⠃⡰⠃⣠⠤⠒⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣌⠉⡅⠀⠀⠀⢀⣀⡁⠈⠉⢉⢉⡦⠾⢀⣄⠀⢰⡀⠐⠉⠁⣀⣀⢀⠀⠀⠀⠀⠁⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⢠⠒⠏⠙⠲⢼⠰⠀⡴⢠⠄⠈⠉⠛⠛⠋⠁⠀⢘⣿⣥⣤⢅⠀⠈⠣⡌⠀⠈⠀⠀⠀⢀⠀⠐⠉⠀⠀⠀⠀⢀⡀⡄⠂⢉⡁⠔
⠀⠀⢀⣀⣀⡄⠀⠀⠆⠀⠀⣀⠀⠀⣀⣀⣀⣀⣀⠀⠉⠉⠈⠙⠁⠃⠈⠁⠀⠀⠃⠂⠀⠀⠉⠀⠀⢀⣀⡤⠖⠒⠈⡀⠠⠀⠁
⠀⠘⢈⡙⠙⠈⣤⠉⠀⣱⣾⣗⣻⢿⣽⣿⣿⣏⣭⣯⣽⣯⣯⣩⣷⣦⣦⠤⣄⡀⠀⠀⠀⠀⠀⠀⢰⠋⠁⢀⠀⠔⠂⠀⠀⠀⠀⢀
⠀⠰⢊⡁⠺⠁⢀⣠⠾⠟⠛⠑⠛⠋⠉⠉⠉⠀⠀⠀⠀⠐⠀⠀⠉⠈⠉⠙⠛⠛⠠⠀⠀⠀⡀⠈⠳⠴⠘⠀⠀⠀⢀⣤⣴⣶⣯⣿⡇
⠀⠘⠟⠁⡰⠋⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠒⠤⢄⣀⣠⣾⣿⡿⠉⠛⢛⡿⠁
⠀⢀⡠⠊⢠⡄⠀⠀⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣶⣨⣿⡇
⠐⢯⣄⠀⢀⡀⠀⠀⠼⠀⠀⢠⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠄⠔⠶⣿⣿⣧⣬⣉⣽⣷
⠀⠉⠓⠤⣄⡀⠀⠀⠀⠀⠠⠾⠎⣯⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣶⣶⡛⠉⠁⠀⠀⠀⠀⠈⠳⣜⡻⠿⢿⣿⡆
⠀⠀⠀⠀⠀⠈⠉⠈⠂⠀⠀⠀⠋⠓⠀⠀⠀⠐⠂⠀⠘⠐⠒⠒⠒⠛⠉⠋⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠁

⠀⠑⠶⠕⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⢠⡅
⠁⠓⠁⠐⠁⠀⠀⠀⠰⠈⠀⠄⠀⠀⠀⢠⠊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚

⣰⣖⠀⣺⡂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠰⢀⡁⠀⠀⠀⠀⠀⢀⠄
⢨⠇⠀⢹⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⢡⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡤⣀⠀⡄⠀⠀⠀⠄⢘⠀⠢⠀⠀⠀⠀⡁⠀⠀⡀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠉⠉⠃⠀⠀⠀⠀⠦⢀⡁⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠈⠀⠀⠀⠆⠀⠀⠀⠘⠙⢐⠂⡀⠀⠀⠀⠀⡬⢁⡃⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⢀⣤⣦⢄⡀⠀⠀⠀⢈⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⢵⡅⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠋⠃⠃⠀⠀⠀⠀⠀⢐⡀
⣿⣿⠿⠿⠻⠿⡿⣻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣼⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠠⠆⠀⠀⠀⣀⠠⠐⠂⢩⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣥
⠀⠀⠀⠀⠈⢳⠀⣠⡾⠀⠀⠻⢦⡀⠀⡀⠀⠀⠈⠲⢤⣤⠤⠂⠉⠀⠀⠀⠈⣿⠈⢳⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣤⠜⠛⠸⡟⠁
⠀⠀⠢⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⢾⣅⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢤⣴⡿⢀⢸⣿⣦⡀⠀⠠⠋⠉⠀⡾⠿⣿⣇⡀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣨⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⢠⠀⠁⢠⠀⢀⣀⣼⣿⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠈⠳⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢸⡁⢀⡀⠀⠀⠀⢠⡀⠀⠀⢀⣼⣿⡟⠀⠀⠠⠃⠀⠀⠘⠀⠈⠻⢿⣿⡀⠀⠀⢸⡿⠛⠀⠀⠀⠄⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠺⣦
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣿⢿⣧⣾⣿⡏⠀⠀⠰⠁⠀⢠⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠰⠀⠀⠘⠉⠀⠀⢀⠠⠾⠗⠀⠈⠷⠀⠀⠹⡆
⠀⠀⢀⡆⢀⣠⠄⠀⠀⠘⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠘⠉⠀⠘⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠈⡳⠚⣻⠶⡖⠠⣾⣤⡀⠀⠀⠈⠁⠀⠀⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠺⣿⡶⠀⠀⠀⠀⠀⡀⠤⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⣤⡯⠀⠉⠀⢻⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢘⠀⠀⣶⣿⠓⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣾⣶⠀⠤⡤
⠀⠀⠀⠛⠘⠃⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢁⣻⣧⣆⣀⠀⠀⠀⠻⠆⠀⠀⠹⣇⠀⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⣰
⠀⠀⠀⠀⣀⡀⠀⠀⠀⣸⣷⠸⡇⠀⠀⠷⠔⡇⣤⣽⡿⢿⣯⠳⡄⠀⠀⠀⠀⠤⠠⣿⣷⡄⠀⠀⠀⠀⣠⣄⡈⣀⡀⠉⠀⠀⠀⣀⣀⠀⢀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⣿⡁⠀⠀⠀⠘⠿⠄⠀⠀⠀⠠⠄⠙⡁⠁⠀⠀⠙⣷⢹⡄⠀⠀⠈⠀⠀⢸⣿⣿⡄⠀⠀⣠⣻⣿⢹⣿⣿⠀⠀⠀⠀⠈⠻⠷⠎⢘⠿⠚⠃
⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢀⣲⠔⠀⣴⠂⠁⠀⠀⠀⠀⣿⡞⠁⠀⠀⠀⠀⠀⢸⠿⠟⠀⢀⡀⠘⠿⣿⡆⢿⡿⠀⣀⣀⠀⠀⠀⢀⠰⠃⣴⡶⣶⣶⣆
⠀⠀⠀⠀⠉⠀⠀⢀⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣰⠉⡷⡈⢿⡀⠀⢿⣷⣤⢡⣇⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠠⠀⣤⣠⣤⡴⠀⠀⠀⣀⣀⣀⣀⣤⠀⠀⣀⡄⠀⠀⠘⣧⣑⢼⡾⠁⢰⣮⣿⣿⡗⠙⠉⠛⠁
⠀⠀⢀⣀⣤⡴⠖⡁⠀⠀⠀⠻⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢠⡀⠈⠉⠉⠀⠀⠀⠀⢹⡟⡶⠭⠛⣚⣟⣿⡄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠻⠟⠀⠀⢀⡄
⠀⠀⠀⠀⠉⠀⣠⣡⡶⠠⢤⡤⠦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⡆⠀⠀⠀⣐⣦⠀⠈⠐⠫⠔⠃⠉⠉⢿⠓⣀⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢠⣽⡿⢿⡔⠋⠁⠀⠀⢠⣀⡀⠀⠀⠈⣷⠀⠀⠈⠋⢀⣤⣾⣫⠏⠀⠀⠀⣠⠇⠀⠀⠄⠈⠸⠏⠀⠀⠀⠀⠀⢠⠀⠀⠈⢀⠇⠀⠀⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠤⠄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢇⣀⣬⠗⠒⠐⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠂⠈⠀⠀⠀⢀⠀⠀⡁⠠⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠈⠉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⢠⡀⠀⠐⠄⠀⠇⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠋⠁⣀⣠⢰⠚⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡀⠀⠀⠀⠂⠀⠁
⠀⠀⠒⠁⠦⢀⢀⡀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠎⠋⠉⢁⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⡠⣄⢠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠐⠂⠀⠀⣀⠄⠐⠆⠁⠀⠉⢁⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠈
⠀⠀⠀⠀⡀⠀⢄⡤⠴⠀⠐⠚⠁⣀⠀⠤⠀⠒⠀⠛⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⣀⣀⠀⠃
⠀⣀⠀⠀⠀⠐⠀⠀⠀⠐⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⢀⠀⠀⢐⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠂⢈⠃⠀⠀⢀⠆⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠔⠉⢀⡂⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⡤⢀⠀⠄⠈⠁
⠀⠀⠃⠀⠑⠀⠐⠒⢐⡋⠁⠀⠀⠆⠤⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠁⠀⠶⠈⠁⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠀⡀⠀⠐
⠀⠀⠀⠈⠉⠂⠀⠠⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠂⢀⠆⠁⠔⠁⠀⢸⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠈⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠥⢭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠈⠁⠀⠀⠀⠀⠀⢰⠀⠸⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠰⠀⠀⠘⠀⠐⠚⠉⠂⠀⠀⠤⠤⠄⠂⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⡄⠐⠾⠒⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢣⡄⠀⠀⢀⢰⠘⠀⣅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠐⠠⠀⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠂⠀⠐⠒⠀⠈⠒⠀⠛⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠉⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⣌⢀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡀
⠀⠀⠜⠁⠉⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢤⠀⠂⠀⠉⠁⠀⠀⠀⠂⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢃⠀⠀⠀⠰⡄⢈⢉⠉⠁⠀⠀⢀⠈⠠⠦
⠀⠈⠀⠀⠀⠀⢒⠀⠀⠀⠀⢸⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⡀⠈⢁⠀⠀⠈⠠⡀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⢲⣄⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⣀⡀⡀⣰⣆⡈⢠
⠀⠀⠻⠀⠘⠉⠉⠈⢡⠃⠀⢸⠀⠀⠀⠀⠐⠤⠄⢩⣈⣁⣭⡥⠤⠶⢦⠀⠀⠀⠀⠀⠀⡄⠀⡀⠁⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠂⠐⠒⠤⠄⡀
⠀⠀⠀⠈⠁⢀⠀⡉⠁⠀⠀⠈⠀⠀⠀⠘⡇⠠⠀⠀⣄⠰⡆⠠⠄⠀⢸⠀⠀⠀⠀⠀⠀⡧⢠⠂⠁⠑⠦⠆⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠂⠘⠐⠁⠀⢀⠈⢤
⠀⠀⠀⠀⠐⣶⢄⡀⠀⠀⠀⢨⠀⠀⠀⠀⠳⡀⠉⠈⠉⠀⠂⠐⠈⠀⠟⠀⠀⠀⠀⠀⠀⠂⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠔⢘⣋⠉⢀⠘⠃⠙⠈⠀⡼
⠀⢰⠀⠀⠀⠄⠀⠀⢄⠀⠂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠤⣀⡈⠉⣉⡈⣀⡤⠊
⠀⠀⢄⡀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠚⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠈⠀⠈⠉⠁⠀⠀⡀⠂⠀⠀⠀⠀⠰⣤⡀⡀⠉⠉⠉⠉⠀⣀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠉⠲⡄⠀⠀⢰⡷⠂⠁⠀⠀⠀⠀⠀⠀⠚⠈⡀⠀⠀⠀⠀⠀⢰⠒⢦⣤⣤⡴⠖⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⢠⠀⠀⠀⢀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⠲⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡒⠀⢠⠀⠀⠀⡠⠘⢩⢃⠀⠀⠀⠀⠀⠄⠀⠈⠉⠂⠀⠀⠀⠀⠀⠔⠇⢘⢁⠀⠀⠘⠢⠰⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠘⠠⠸⠁⠀⠀⠱⠀⢐⠄⠀⠀⠀⠀⠀⢄⠀⠀⣁⠎⠀⠀⠀⠀⠠⢆⢨⡉⠡⠀⠀⠀⠘⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠰⢦⣤⣤⡶⠂⠂⠀⠀⠀⠀⠉⡙⠃⠀⢠⠊⠀⡰⠀⠀⠀⠀⣠⣤⣄⠀⠀⠘⠣⣄⣀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠶⠛⠀⠀⠀⠀⠀⠀⢀⠀⢠⠇⠰⠋⠀⠀⠀⠀⢼⠁⡠⢸⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⡄⠀⠀⠀⠁⠈⠀⠀⢠⡀⢈⣶⠀⠈⠃⠒⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠰⢀⠇⠀⠐⠂⠀⠀⠀⠀⠀⢡⡸⠀⠀⠀⠀⠀⠀⢼⡀⠀⠀⢀⣠⣶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡠⠀⡟⠀⠀⠰⣵⣷⢿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠉⠁⡀⠀⠀⠀⡂⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⠆⠀⠀⠁⠴⠊⠀⠀⠀⢸⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣂⠀⠀⣠⠃⠀⠀⠀⢃⡀⢺⠀⠀⠈⠻⠷⠴⠞⠋⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠉⢡⠆⠩⠄⠀⠀⠀⠀⠀⠀⠀⠓⠂⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡠⠤⣀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡾⡆⢀⣲⢺⡿⣦⠀⠀⠀⠀⠀⢀⡀⡀⠀⡀⠀⢶⡁⠀⠀⠀⡙⠆⠀⢀⠀⠈⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣵⣿⣿⣿⠋⠀⠀⠠⣶⣶⡶⠀⠀⠙⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⢀⡠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢤⡤⠠⠤⠠⡀⠐⠴⣔⡶⠤⠴

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⢡⡠⠀⠀⠂⠑⠀⢀⠀⠀⠀⠹⣆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠅⣀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠈⠃⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠧⡃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠁⠀⠈⠂⠀⠀⠉⠁⡀⠆⢰⠁⠀⠀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢠⡤⠓⠈⠀⢀⠀⠀⠀⠀⢸⡽⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⢠⣀⠘⠒⠀⠀⠐⢄⢀⡁
⠀⠀⠀⠀⡀⠀⠀⠊⠀⠀⠀⢀⠆⠀⠀⠀⠀⠸⣟⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠄⠀⠀⠀⠉⣉⠈⠁⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠤⠤⠄⠓⠐⠒
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡴⠆⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢹⡖⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠻⢇⡀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⢰⠀⠈⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠈⢷⣆⠀⣀⡤⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢘⡁⠀⠠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠀⢹⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⢠
⠀⠀⠀⠀⠱⣄⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⡄⠀⠀⠀⠀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠔⠈⠀⠢⡀
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⢠⢀⠆⠀⠀⠀⠀⠀⢀⠄⠁⡌⠈⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡀⠀⠀⢀⢀⡼⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⡌⡀⣣⠀⢁⠀⠊⢘⣀⢠⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠘⣆⠠⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠸⢧⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠀⠀⠀⣜⠀⢀⠆⠀⠀⠀⠀⠀⡐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠁⠐⠉⣦⠠⠊
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠚⠙⠛⠚⠉⠀⠀⢀⠀⡀⠀⠀⠈⠓⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠦⢀⠀⠀⢀⠄
⠀⠀⠀⠀⡆⠀⠈⠉⠀⠀⠀⢠⡀⠀⠀⠀⠐⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠆⠀⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡐⠁⠉⠚⢐⠈⠁⡂⠙⢄
⠀⠀⠀⠀⠉⠐⠦⠄⠀⠀⠀⠠⡇⠀⠀⠀⠀⡇⢀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠰⠀⠀⢁⠀⢠⠀⠀⠄⠆⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠁⠈⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠑⢾⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠆⠀⠈⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠢⣤⡀⠀⢀⡀⠀⢀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠀⠠⠀⠤⠀⠀⠈⠂⠀⠀⠀⠀⠀⢰⣿⠅⡚⠁⡈⠁⠉⠉⠉
⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢰⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠃⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠉⢉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠱⣥⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠸⣟⠀⠇⠸⠀⡀⡘
⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠄⢀⣀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⠀⢀⠀⠄⠉⠒⠒⠒⠒⠃⠁
⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠐⠂⠁⠀⣀⢀⡀⠀⠈⠛⠂⠂⠀⢤⠀⠀⠀⠀⢠⠂⠀⠓⠌⢀⠉⢀⣀⠀⠄⠀⠀⢀⠄⠠
⠀⠀⠀⠂⢙⠓⣦⠤⣀⣀⡀⠀⢀⣠⠀⠀⠀⠈⠀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠤⡄⠐⠀⠀⡉⠁⠀⠀⠈⠶⠂⠉⠁⠀⠉⠛⠣⠤⠀⠄⣰⡀⠠⠤⠤⠤⡀
⠀⠀⠀⢰⠑⢖⡙⢆⠀⠐⢙⠀⠠⠀⠄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠀⠇⢠⠀⠁⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐
⠀⠀⠀⠈⢇⠀⠈⠁⠀⣐⠁⠋⠈⠒⠀⠀⠀⠀⠧⣄⣀⠠⡇⠀⡀⢠⠀⠁⠠⠈⠀⡄⠘⠆⠴⠃⡇⠀⠀⠀⠀⠣⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠑⠂⠤⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠢⠤⣨⡀⠈⠀⣁⡀⠷⠄⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⣀⠀⠀⠀⣀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠛⠛⠛⠶⣦⡘⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⠻⣿⠉⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠲⠶⠶⣶⣶⠿⠿⠿⠿⠿⠿⠿⣷⣦⣄⠀⠋⠀⠀⣿⣇⣀⣤⣶⠶⠶⠶⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠛⠒⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠙⣿⣆⠀⢠⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⢙⣷⡦⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡉⠁⠀⠀⠤⠤⠤⠶⠒⠛⠛⠉⠉⠉⠉⠉⠛⠳⢦⣄⢘⣿⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣛⣿⣃⣀⣀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣽⡿⠋⣍⣿⣤⣴⡶⠾⠿⠿⠶⣶⣤⣄⡀⠀⠀⠀⠉⠉⢉⣩⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣄⡐⠼⠶⠶⠛⣋⣡⡴⠶⠛⢋⣩⡿⠟⣿⠗⣨⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⣩⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⢟⣋⣥⣶⣶⣿⠟⠁⢀⣾⠃⣰⣿⣿⣯⢠⣤⠤⣂⡤⠄⠀⠀⢀⣠⣤⣤⣤⣤⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠛⣻⡿⠛⠁⣠⣶⣿⡏⢰⣿⠉⠻⣿⣦⣝⡛⠛⠛⢉⣀⣀⣠⣤⣤⣭⣝⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⢀⣼⠟⠀⣠⣾⠟⠉⣾⠃⢸⡇⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣾⣏⡀⠀⠀⢠⡾⠁⢀⣼⠟⠁⠀⠀⣿⠀⢸⠁
⠀⠀⠀⠀⣠⣾⡿⠟⠋⡉⠉⢩⡿⠟⠛⠿⠿⣶⡿⠁⣠⡟⠁⠀⠀⠀⠀⣿⠀⢸
⠀⠀⢠⣾⡿⠋⠀⠀⠀⠻⣦⣈⣤⠆⠀⠀⠀⡿⠁⣰⣿⡀⠀⠀⠀⠀⠀⣹⡄⢸⣄⣀⣀⣀⡀
⠀⢠⣿⠏⠀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣸⠃⣰⡏⢿⣷⠀⠀⣠⣶⣿⣿⣧⠈⣿⠿⠿⠿⣿⣿⣷⣤⡀
⠀⢸⣿⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡟⠀⢸⣿⣧⣾⣿⠟⠉⠀⠘⣦⠘⣦⡴⠀⠀⠀⠉⠙⢿⣷⡄
⠀⢸⣿⡀⠸⣿⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⡇⣼⣥⣤⣾⣿⣿⡿⠁⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⢿⣷⣄⠈⠃⢀⣴⣾⡿⠟⠋⠉⠉⢹⡃⡏⠉⠉⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠈⠻⣿⣦⣴⣿⠟⠉⠀⠀⠀⠈⢷⣼⣅⣧⣤⠞⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⣸⣿⠃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⢀⣴⣿⠏
⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢠⣿⡿⠻⢿⣶⣶⣶⣶⣶⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠠⢤⣤⣤⣤⣤⣶⣿⠟⠁⢀⣴⣿⡿⠁⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣤⣬⣍⣉⣉⣉⣤⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠓⠚⠉⠀⠠⠔⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰
⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢀⣀⡄⠖⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠀⠑⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠂⠈⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⡀⣀⢀
⠀⠀⠀⠀⠐⠒⠂⣀⡩⠀⠀⠂⠀⠀⠉⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡀⡀⡀
⠀⠘⢀⡃⠀⠀⠰⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⢉⡀⠉⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠐⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⢙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠂⠀⠀⠀⠋⠉⠀⠀⠀⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠂⠠⠄⠧⠄⣶
⠀⠀⢀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠆
⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠐⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⢠
⠀⠁⢀⠀⢐⣀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠈
⠀⢠⠀⠴⠠⠠⠀⠀⠀⠀⠀⠀⡀⠀⠞⠉⠱⠆⢀⡀⠀⠀⠀⠀⠀⠖⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠑⠂⠀⠐⠁⠀⠀⠀⠀⢰⠈⠁⢉⠉⡉⢉⠀⢱⠀⠀⠀⠀⢀⣠⠀⠨⡤⠀⠀⠂⠀⠀⠀⠐⠈⠁⠰⠐⠈⠙⢢
⠀⠀⠀⠐⠆⠀⠀⠀⠠⠀⠀⠈⠂⠈⠉⠁⠀⠀⠁⠊⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⣀⡉⠈⠈⡰
⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⡈⠑⠢⠤⠤⠔⠊⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠠⠦⠒⠂⠀⠐⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⣠⡇⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⢀⠀⡀⠀⠀⠠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣢⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠐⠀⠁⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠒⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠁⠀⠀⢸⠂⠀⢀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠊⠀⠁⠀⠀⠀⠀⠰⠤⠀⠔⠃⠀⠐⢄⠀⣀⡀⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀
⣿⣟⣙⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡸
⠀⠀⠀⠀⠀⣀⡠⠤⠤⡇⡧⠤⠤⢄⣀
⢀⠴⠊⠉⠉⠑⢢⡤⠒⠉⠉⠐⢤⡠⠒⠉⠉⠑⠢⡄
⡎⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⡆⢀⣀⣀
⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠔⠉⠁⠀⠀⠉⠢⡀
⢰⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡠⠒⢩⣿⢿⠀⠀⢠⡀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⢢
⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠎⠀⠀⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡼⠉⠉
⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠓⠀⠀⠀⠘⠃⠀⠰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠏⢈⡾⢥⣠⠎
⠀⢃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⢆⠀⠙⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⡠⠧⠤⣀⠀⠀⣰⠏⢀⠞⢠⠾⡅
⠀⠘⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠈⢢⡀⠀⠓⠀⠀⡀⢀⡠⠤⠒⠉⠸⣆⠀⠈⢣⡾⠁⠀⠀⢀⡵⡞⠓⡄
⠀⠘⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠀⣰⣉⠦⠤⠒⠚⣯⠁⠀⠀⢀⡀⠀⠹⠆⠀⠀⣧⣤⣤⡬⠵⠖⠓⠉
⠀⠀⠱⣄⠀⠀⠱⣄⠀⠀⠀⡠⠒⠉⠉⠳⠀⠀⢀⠀⠀⠘⣧⠀⠀⠈⢷⡀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠉⠒⠊⠉⠉⠒⠺⣀⡀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⣀⣘⣃⠠⠤⠒⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢀⡤⠶⠶⠶⠤⣀⠀⠀⠀⠀⢀⣀⣼⣁⡀⠀⠀⠀⠀⠀⡟⢻⠀⠀⠀⠀⠀⣀⠤⣶⣆⣷⠯⡳⡄
⠀⠀⠠⣏⣀⣀⣀⣀⣀⣸⡆⠀⠀⠀⣟⣓⣛⣛⣻⠆⠀⠀⠀⢠⡗⠺⡆⠀⠀⠀⡼⣱⣋⢩⣿⣿⢿⣻⡁
⠀⠀⠀⣗⣒⣒⣒⣒⣒⣺⡇⠀⠀⠀⢸⡀⠀⠀⡏⠀⠀⠀⠀⢸⣉⡆⡗⠀⠀⠀⡇⡏⢳⠻⠖⣫⣍⡇⡇
⠀⠀⠀⠻⠽⢦⡀⡠⠯⠝⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⢸⠁⠀⡇⠀⠀⠀⠳⡙⢟⣣⣴⣭⢞⡜
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠚⠁⠀⠀⠀⠀⠸⠶⠶⠇⠀⠀⠀⠀⠈⠓⠒⠒⠚⠉
⠀⠀⠀⣠⡴⣾⢳⢦⣄⠀⠀⠀⠀⠀⠀⢰⣰⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶⢤
⠀⠀⠰⡗⠷⠾⠾⠾⠚⡇⠀⠀⠀⠀⡤⠬⠭⠥⣄⣀⠀⠀⠀⡴⠋⠅⠀⠈⠑⢦⠀⠀⠀⠀⡞⠁⠀⠈⣻⠃
⠀⠀⠀⣇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣇⠀⠀⠀⣯⡼⠀⠀⠀⠹⡍⢻⠉⣿⢩⠏⠀⠀⠀⡸⢦⣂⣠⠖⠁
⠀⠀⠀⢸⣀⣀⣀⣀⡞⠀⠀⠀⢰⣒⠛⠒⡒⠚⢓⣲⠆⠀⠀⠀⢣⣸⣀⣇⡞⠀⠀⠰⣏⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣚⣲⡄
⠀⠀⠀⢀⡤⠴⠊⢧⡀⠀⠀⠀⢀⡤⠤⡤⠤⣤⠤⠤⡀⠀⠀⠀⠀⠀⠀⢀⣾⣙⡄⠀⠀⣾⣤⣼⣷⣼⡆
⠀⠀⠀⣞⣉⣉⣉⣉⣳⠀⠀⢀⣯⣤⣤⣥⣀⣈⣤⣤⣽⡀⠀⠀⠀⠀⡠⠻⣄⠈⡷⠀⠀⠘⣧⠴⢊⡽
⠀⠀⠀⢻⠈⡇⢸⠁⡾⠀⠀⠸⡯⣕⣻⣿⣉⣾⣿⣪⢽⠇⠀⢀⣠⡚⠳⡄⠀⢙⠇⠀⠀⠀⢹⣊⣽⠃
⠀⠀⠀⠈⣇⣧⣸⣰⠃⠀⠀⠀⠉⠉⠛⠒⠒⠒⠛⠉⠉⠀⠀⠙⠦⠷⣤⠼⠒⠋⠀⠀⠀⠀⠈⢧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢀⡴⣏⣯⣙⣇⠀⠀⢀⠜⡙⢄⡔⡙⢆⠀⠀⠀⢻⠛⡟⢴⣉⡦⠀⠀⠀⠀⠀⣠⣯⢯⠟⠲⡄
⠀⠀⠀⢀⡴⠋⠀⣿⠬⣿⠟⠀⠀⣾⢀⡟⠈⡇⡝⠈⡇⠀⠀⣸⠀⣧⠞⠀⠳⡄⠀⢀⡤⣞⣵⡷⠋⠀⢠⠇
⠀⠀⢰⡋⠀⢀⠔⢁⠔⠁⠀⠀⠀⠘⢌⢃⡼⢇⢃⡜⠁⠀⢰⠃⠀⢸⠀⠀⠀⡇⠀⠸⣯⠗⠉⠀⢀⡴⠃
⠀⠀⠀⠙⢶⣁⠔⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠸⣅⣀⣸⣄⣀⣠⡇⠀⠀⠈⠢⠤⠖⠉

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

⠀⠀⠀⣀⣄⡀
⠀⢠⣾⣿⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⢀⣀⣀⣴⣷⣦⣤⡀⠀⢠⣤⣆⣶⣿⡄⠀⠀⠀⣄⡀
⠀⣸⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⢃⣤⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⡧⠄
⠀⢻⣿⣿⠿⠋⠁⠀⠀⠀⠈⢿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠙⢿⣿⡿⠁⠀⠀⠀⢨⠁
⠀⠀⠈⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⢉
⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⢠⣾⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠸⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡶⠀⠀⠀⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠁⣀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⡀⢈⣀⣠⣤⣤⣀⠀⠀⢀⣠⣀⣾⣿⣿⣧⣠⣄⡀⠀⣾⣿⣿⣶⡀⠀⣴⠿⣿⣿⡃⠀⠰⣶⣾⣿⣿⠆
⠀⢸⣗⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠛⠛⠛⠛⠓⠀⢻⣶⣴⣿⠗⠀⠈⠉⠛
⠀⠈⠻⣿⣽⣿⣿⠿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⢠⣤⣤⡦⠀⠀⠈⠿⠿⠇
⠀⠀⢀⣠⣤⣆⣤⡀⠀⠀⠀⠀⢀⣀⢈⡙⠛⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣤⣤⣄⡀
⠀⠀⣽⣿⣿⣿⣿⣯⡀⠀⠀⣺⣿⣿⣿⣿⡀⠀⠀⣶⣦⣶⣶⣦⠀⢀⣾⡹⣼⣏⢿⣷⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠛⠉⠋⠋⠋⠛⠃⠀⠸⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⡇⠘⣿⣷⣽⠿⣸⣿
⠀⠀⢠⣤⣤⣤⣤⡤⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⠟⠁⠀⠈⠻⠿⣿⡿⠇
⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠙⠛⠋⠀⡀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⡤⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⣿⣿⣧⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⣁⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠒⢄⠀⠀⠀⠀⠀⠀⠀⡔⠈⠁⠀⠈⠁⠈⠈⠑⡂
⠀⠀⠀⠀⠀⠀⠀⡖⢤⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠔⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠢⡎⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠌⠀⣀⠀⠀⠤⠘⠒⠀⠈⠒⡄
⠀⠀⠀⠀⠀⡠⠄⠒⠚⢂⠤⠒⠉⠉⠉⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠆
⠀⠀⠀⠀⠀⢀⠀⠀⡴⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢀⠄⡒⠂⠈⠉⠀⢐⠪⣄⠤⠄⠈
⠀⠀⠀⠀⠀⠀⡣⣼⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠣⡀
⠀⠀⠀⠀⠀⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠈⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠡⠜⠀⠀⠀⠀⠠⠀⡟
⠀⠀⠀⠀⠀⢠⠀⠚⠗⡒⢄⠀⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⣌⠀⠂⠐⠈⠀⠷⠤⠠⠀⠤⠤⠂⠙⡄⠐⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⡇⠐⠀⠈⠀⠀⢀⠀⢠⠒⠐⠢⠀⠠⡘⠢⡀⠀⠀⠀⠀⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠈⠂⠤⠤⠤⠤⢊⡠⠼⠀⠀⠄⠀⠀⢸⣄⠈⠙⡒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠸⠀⠀⠒⠀⠀⠘⣀⡀⠀⡠⠤⠀⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠂⢠⠔⠁⠄⡀⠐⠀⢀⡰⠀⢁⡰⠁⠀⠀⠀⠀⠈⠑⢄⠉⠲⢄
⠀⠀⠀⠀⠀⠀⢀⡊⠀⢈⠀⠀⠠⠄⠀⠀⢧⠀⠀⠸⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠄⠁⠁⠆⠀⠀⣶⠁⠀⠀⠇⠀⠀⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠢⠀⠐⠄⡀⡄⠀⠀⣒⠀⢈⠖⠊⠁⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠉⠁⠉⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⣀⠄⠀⠀⠀⣀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉⠁⠢⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠉⠁⣲⠐⢎⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠃⠀⠀⠱⠄⠀⠀⠀⠀⢠⣾⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠻⣿⡿⠏⠀⣀⣀⣤

⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⡄
⠀⠀⠀⠀⠀⠀⢠⠄⠈⢄⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠛⠫
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠐⠀⠀⠴⠋⠀⠠⠀⠀⠀⠠⠄⠤⠄⠻⣿⣿⣿⡇⡀⠀⠀⠀⣀⣤⣶
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠑⠀⢄⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠉⠡⠂⠁⠀⠀⢰⣿⣿⣿⠃
⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢒⣈⠉⠉⠀⠀⠈⠉⠉⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠤⠤⠤⠤⠤⢤⣤⣤⣀⣀⠀⠀⠀⠀⡠⠒⠒⢦⡂⠶⠉⣲⢸
⠀⠀⠀⠀⠀⢀⣾⡟⠛⠉⠉⠉⠳⡖⠦⣴⠒⠤⠴⢚⣁⠼⠛⣻⣦⠀⠐⠰⡆⢱⠋⠉⡀⠹⠀⠋
⠀⠀⠀⠀⢀⣤⡙⢷⣄⠀⢀⠤⠤⠽⠛⠸⣣⢾⠉⠉⠀⣠⡴⠟⠁⠀⠀⠀⠈⠡⠝⣙⢇⡙⣆
⠀⠀⠀⢰⣿⠉⠁⠀⠉⠛⠾⣦⣄⣀⣀⣀⣀⣤⡽⠶⠛⣉⡄⠀⠔⢉⡉⠳⡄⢀⡀⠇⡄⠏⡞
⠀⠀⠀⠀⠙⠷⣤⡀⢰⠒⠒⠀⠀⠉⠉⢉⡀⠀⣠⡴⠟⠁⠀⠀⠸⢇⡨⢇⡟⣁⠤⡀⢶
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢤⣤⣤⣤⠤⠶⠟⠋⠉⠀⠀⠀⠀⠀⢹⠟⠛⣮⣄⠷⣄⠟⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣾⡇⡿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠁



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠀⠗⡀⠈⠀⠀⠀⠀⠀⠠⣠⣤⣤⢦⡠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡤⡄
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢐⠓⠊⠨⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠠⠀⠀⠀⠀⢎⠰⠈⡟⠉⡵⡄⠀⠀⠀⠀⠀⠀⠀⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⡔⠀⠀⠀⠀⠀⠈⠢⣤⠤⠔⠉⠀⡀⠀⠀⠀⠂⠟⢳⡋⠛⣲⣾⠁⠀⠀⠀⢠⠊⠵⠇⢪⠓⠂⢑
⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠎⠀⠀⠀⠀⠀⠀⠑⠂⠤⣀⡀⠤⠊⠀⠀⠀⠀⠀⠲⠦⠉⠙⠀⠁⠀⠀⠀⠀⠈⠂⠤⠠⠛⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⢀⠀⠀⠀⠀⠀⠀⠀⣁⢓⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠉⠀⠐⢄⠀⠀⠀⠀⠈⠤⠀⢀⡦
⠀⠀⠀⠀⠀⠈⡸⠶⡇⠀⠀⠀⠀⠀⠀⠢⠜⠫⠙⣉⣃⠖⠀⠀⠀⠀⠀⠀⠘⢃⡀⣄⣀⠀⠀⠀⠀⠦⠊⠀⠉⡉⢢⣀⡠⠀⠀⠀⠰⠃⠀⠀⠈⣄⡀
⠀⠀⠀⠀⠓⢺⠀⠀⠐⠂⠀⠀⠀⠀⠈⢈⠃⡉⢰⡈⡐⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠂⣸⠉⠀⠀⠀⠀⢠⡀⠀⣠⡟⡠⢤⡱
⠀⠀⠀⠀⠀⠀⠁⠐⢀⡠⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠬⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⠿⠃⠀⠀⠀⠈⠓⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠣⡊⣉⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⢀⡜⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⣿⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠐⠶⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⣀
⠀⠀⠀⠐⠁⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⡡⠀⠀⠀⠀⢺⠮⣿⢿⠆⠀⠀⠀⠀⠀⠀⣢⣄⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⢛⣬⣇⣐⣨⣻
⠀⠀⠀⠠⡀⠀⣠⠶⠲⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢜⢎⣷⡦⠀⠠⠀⠀⠀⠀⢰⣿⣿⣳⣦⣀⠴⠋⠀⠀⠀⡈⣿⢫⠞⢁⠏⡠⡅
⠀⠀⠀⠀⠈⠉⠛⢄⡑⠖⠊⠀⠀⠀⠀⠀⢀⣦⣄⡀⡠⠃⠀⠀⠀⠀⠀⠣⣳⢟⡅⠨⠀⡀⠀⠀⠀⠀⠑⢿⣿⣿⠿⠒⠀⠀⠀⠀⠀⠈⠻⠴⠚⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠜⢂⠍⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⠾⣷⣶⣤⠀⠀⠀⠈⢢⡀⠀⠀⠀⣤
⠀⠀⠀⠀⢆⣤⣶⣶⣆⡘⠂⠀⠀⠀⢠⡄⢠⣀⣀⣠⣿⣀⡀⠀⠀⠀⠀⢘⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣬⡻⣿⣇⠀⠀⢀⡀⠃⠐⢓⠚⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⡿⠁⠀⠀⠀⢀⠄⠀⠀⠹⡀⠀⠀⠀⠀⢀⣀⣀⣠⡬⣿⠿⣿⡾⠏⠀⠀⠘⡀⠀⠁⣴⠋⠉⠲
⠀⠀⠀⠻⣿⡿⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠠⣠⣀⣠⣀⠇⠀⠀⠀⠀⠈⠈⢷⣼⣀⣼⡷⠃⠀⠀⠀⠀⠀⠀⠒⠚⠻⣄⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⠿⣿⠿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣦⣶⣶⣶⣷⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠖⡒⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⡈⡆⠍⠁⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠂⠉⠁⠀⠄⠐⡀⠀⠀⠀⠀⢀⡊⠐⠁⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠄⠀⠸⠀⠀⠀⠠⠈⡉⠰⠃⠰⠆⠘⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⠘⠁⢰⠂⠀⠱⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⣀⣀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠘
⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠂⠀⠀⣁⣀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣯⡀⢋⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡘⢱⡖⠂⢀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⢰⠀⠙⣄⠁⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠰⠙⢘⡠⢇⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠈⠅⠘⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠀⠀⠈⠷⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡄⠠⢀⠹⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠁⠝⠀⠒⠂⢈⡉⠀⠀⠈⠀⠀⠠
⠀⠀⠀⠀⡀⢒⣾⠀⢤⡀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠠⠐⠂⠌⡐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠸⠀⠀⠀⠀⢀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⡉⠤⠈⡁⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⣀⡀⠄⢀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠐⠂⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠓⠠⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢼⡤⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠉⠄⠡⣄⡗⠋⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡐⠀⠛⠛⠈⠀⠐⡽⠦⣀⣀⡀⠀⡀⠈⣃⢀⠊⢉⢧⡀⢁⠨⠧⡀⠀⡀⠈⠀⠀⠀⠀⢀⠀⠀⣾⠛⠂⢤⡠⢴⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠉⣈⠀⠀⠿⠀⠀⠐⠲⠀⢀⠀⠐⢌⠂⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠂⡂⢀⡍⠀⠠⠋⠈⢠⠠⡂⠌⠐⠀⠀⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⢐⠡⠀⠐⠁⠄⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡜⠀⠀⠀⠀⠂⢀⣀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡠⠒⢒⡄⠈⡄⠀⠀⠀⠀⠀⠴⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠓⠒⠉⢀⠄⢰⠀⠀⠀⠀⠀⠠⠀⠀⠅⡀⠀⡀⠀⠀⠀⡀⠀⢊⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢅⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠡⡑⠀⡀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠀⣀⣀⡀⠄⠀⠈

⠀⠀⠀⢠⠄⡐⢀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⢀⠤⢒⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿
⠀⢀⢢⢠⣸⢀⢸⣴⠀⠀⠀⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢸⠖⠀⠀⢀⠜⡡⢆⠈⠀⠷⠀⠀⠀⠀⢠⡤⠴⠤⠾⠿⢷⣄
⠀⠘⠈⠉⠉⠉⠁⢠⠀⠀⠀⠃⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠸⠆⠀⠀⠀⠀⠘⠷⣎⣁⠀⢀⡆⠀⠀⠀⢙⠀⠀⠀⡀⠤⠀⠅
⠀⠀⢂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⢠⢶⠁⣀⠀⠀⠀⠀⢤⠁⠀⣠⠄⠂⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⢠⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡖⠀⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⡀⠀⠀⠸⠀⠀⠠⠤⠤⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠰⠉⠠⡀⠀⠀⠀⠀⠀⢞⣁⠁⣐⡆⠀⠀⠀⠀⠀⠀⠀⢄⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢠⡖
⠀⠀⠀⡄⠀⠀⢄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠸⠀⠺⣅⡰⢴⠀⠀⠀⠀⢄⠡⡄⠰⠀⠠⠀⠐⠀⢄⢁⠁⠀⠀⠀⡐⠀⡇
⠀⠀⠈⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠮⡵⠂⠀⠀⠀⠑⠌⡀⠧⠀⣂⠈⠄⠀⠀⠀⠀⠄⠐⠅⠀⡠
⠀⠀⠢⢀⠠⠤⢀⡀⠃⠀⠀⠀⠀⠈⠂⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠡⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠂⠀⠂⠀⠁⠄


⠀⣀⠄⠲⠂⠐⠒⠢⠄⠀⠀⠀⢤⣠⡄⠐⣆⣸⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠘⠁⢀⠤⠖⣶⡶⠤⣀⠀⠀⠀⠐⡟⠓⠀⡼⣼⡁⠀⠀⠀⠀⠀⠤⠴⡉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠃⢃⢠
⠈⠀⠁⠀⠼⡩⠗⠀⠀⠀⠀⠀⠀⢡⠀⠀⡇⢀⠁⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⢀⠈⠄⠀⠀⠀⠀⠈⠆⣡⣶⣴⠦⠃
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠃⡆⠀⠀⠀⠀⠀⠀⠘⠂⠉⠀⠈⠲⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢡⡁⣴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠈⠁

⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡤⢄⠀⠀⠀⠀⠀⢀⣠⠄⣠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠠⠄⢀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢠⠢⢀⠂⠘⠀⠀⠀⠀⢀⡎⠅⠁⠀⠀⠈⢣⠀⠀⠀⠀⠠⠐⠒⠂⠀⡀⢀⠠⠀⠀⢀⠤⢆⠀⠀⡈⠢
⠠⣀⠀⠠⠐⠒⠚⠛⠢⠼⠀⠀⠀⡀⠁⠁⠣⠂⠀⠁⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠨⡀⠀⠀⠀⠀⠈⠁⢘⠀⠀⠒⣄⠴⠀⠐⠇⣀⠓
⠀⠈⠂⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠱⣁⡀⢁⠔⠀⠀⠀⠀⠀⠘⣆⡀⠠⠤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠊⠀⠀⠀⠀⠀⠀⠑


⢀⠉⠃⣶⣶⣶⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣤⣀⡀
⠈⠀⠀⠻⣿⠃⠐⠌⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⡁⠀⠀⠡⡀⠀⠀⠀⣴⣿⣿⠇
⠀⠀⠃⠀⢻⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⡽⠛⠋⠀⠀⠀⠀⡖⠀⠀⠀⠀⣀⡀
⠀⠀⣿⠀⠸⡆⠀⡾⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠹⡃⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢠⣭⡽
⠀⠀⠐⠀⢠⠃⠀⠀⠀⠀⠞⠒⠒⠲⠶⠶⠶⠶⠖⠶⠾⠶⠀⠀⠀⢠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⡚⠁⠀⠀⠄⠀⠀⠀⠀⠔⡒⠂⠀⠆⡀
⠀⠀⠀⠁⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠦⢰

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠄⠀⠐⠚⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠁⢀⡀⠓⠒⠒⠒⠒⠒⠒⢀⡀⠀⠀⠀⣶⡷⣿⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡠⢺⢀⣁⠆⠁⠀⡂⡾⡀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡟⣰⠋⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⢠⡌
⠀⠀⠀⠀⠰⣀⠀⠇⢐⠈⠼⠀⠀⢻⡥⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠤⠲⠶⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢨⣉⢿⡇⠄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠙⠚⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠰⠒⠀⠀⢸⠀⠆
⠀⠀⠀⡠⠀⠰⢂⠛⢺⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠡⠄⠄
⠀⠀⠀⢉⣀⠀⠀⠌⠀⠨⠌⢻⠍⠀⠀⠀⠠⠄⠐⠀⠀⠁⠀⠀⠀⠈⠀⠀⢣⠀⠀⠀⢀⢀⠀⠠⠄⠤⣀⠀⠀⠐⠀⠀⠀⠀⣀
⠀⠀⠀⠁⠰⢤⢀⠀⠈⠓⠂⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠂⠐⠂⠀⠰⡁⠀⠒⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠭⠙⢲⡄⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⠊⠀⠰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂
⠀⠀⠀⠀⢀⣀⣄⣀⣀⡀⡀⣴⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠄⠀⠀⠠⠶⠀⠀⢂⠀⠀⠠⠄⠀⠀⠈⢀⠠⢀⣀⠀⠒⣤⡀
⠀⠀⠀⠀⠨⡉⠁⠙⠀⠛⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣰⠆⠀⢀⡀⠀⠀⠀⢀⠀⡡⠀⣁⢀⡴⠎⠁⡱
⠀⠀⠀⠀⠀⠱⡒⠲⠲⠒⠒⢚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⣀⢠⠴⠙⠘⠀⠀⠀⡀⠋⢸⠅⠀⡀⡤⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⡀⠀⠀⢀⠉⠃⠀⠀⢒⠈⢡⠀⠠⠇⠀⠘⠀⠂⠁⠑⠀⠀⠀⢀⠀⠈⠀⠀⡀⡁⠀⠄⠊
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠐⠈⠀⠈⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⢠⠀⢀⣄⠀⠀⠀⠉⠁⠀⢀⠐⢉⡀⠀⠀⠀⠀⢀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⠀⠀⡘⠀⠀⠠⠀⠈⠂⠀⠉⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⢀⣠⠰⠃⣀⢶⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡘⡷⠀⢠⣄⠀⠀⠀⠀⢀⠨⠁⠀⠄⠄⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠾⣯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢂⢀⣔⢴⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠈⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠁⠀⠛⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠒⢀⠀⠩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠈⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠋⠀⠉⠀⠀⠀⠈⠀⠀⠄⠀⠠⠠⠔⠲⢖⠒⠀⠥⠀⠀⠀⢢⢢⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠿⠛⠛⠛⠻⠿⠁⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⣠⡄⠀⠀⠀⢠⣄⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠠⠀⠈⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⠃⠀⠀⠀⠤⠆⠀⠀⡏⠲⠂⠀⠀⣷⠀⠀⠀⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢰⡙⣿⡆⠀⠀⠀⠀⢀⣀⠀⡇⠀⠀⠀⠀⣿⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣷⡀⠀⠀⢀⣸⡇⠀⠈⠙⠁⠀⠀⠀⠀⡿⠀⠀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⣈⣧⠀⠀⠀⠀⠙⠢⠤⠤⠤⠖⠁⠀⢸⠇⠀⠀⠀⢸⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢉⡱⠦⣄⣀⡿⣷⣄⠀⠀⠀⠀⡀⢀⢀⠀⠀⣠⠟⠀⠀⠀⡠⣼⣷⣹
⠀⠀⠀⠀⠀⠀⠀⠰⠟⠠⣤⣼⠛⠀⡇⠘⠳⢦⣄⣀⣁⣈⣬⣴⠾⣧⡄⠀⠀⠀⢁⣿⣋⠛⢆⡔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣏⣨⣘⠀⠇⠀⠀⣼⠃⢹⠈⠹⡄⠈⠃⢻⡝⢦⡀⠀⠘⣌⠳⢃⣩⠞
⠀⠀⠀⠀⠀⠀⠀⢀⡾⡝⡏⡉⢹⠛⣧⢀⣼⠋⠀⠃⠀⠀⢃⢠⡠⣄⢻⣈⢓⡄⠀⢸⠀⡎
⠀⠀⠀⠀⠀⠀⢀⣾⢹⠀⡇⡇⢸⠀⡏⢻⡃⠀⠀⢰⡱⡀⡜⠸⢣⣸⠀⠻⣟⠁⠀⣸⠀⣇
⠀⠀⠀⠀⠀⠀⣶⢻⢸⡄⡇⡇⢸⠀⠇⣘⣧⠀⠀⡀⢧⠉⠀⠀⠀⣛⡼⠀⢸⡆⢠⠇⠀⢸
⠀⠀⠀⠀⠀⢠⡇⢸⠈⣷⡇⠀⢸⣤⠿⢛⡁⠀⢰⡇⢸⠀⣠⠖⠋⣡⣀⣀⡼⢣⣼⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣇⢸⠀⡏⣷⣾⣏⠁⠀⠈⣷⠶⢾⣹⠃⡸⡷⡴⢟⡿⠙⢯⡀⠀⢁⡀⢠⢧⣀⡀
⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⡇⢸⠹⣦⠀⠀⠹⣧⠜⠁⢠⠃⡇⡇⣿⠃⠀⠀⢱⠖⣉⣀⣀⠀⢈⠉⢐⢢⣀⣀
⠀⠀⠀⠀⠀⢸⣧⣬⣄⡇⡇⠘⠐⠙⣧⡀⠀⠉⠀⠀⡿⠀⡇⣳⡿⠀⢀⣠⣶⠲⠤⠤⠔⠒⠒⠉⠀⡸⢿⣿⣿⣿⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢸⡏⠉⠙⠛⠛⠿⠾⠷⠿⢷⣄⠀⢀⣼⢶⣶⣿⣿⣿⣿⣿⡟⠈⠳⣀⠀⠀⠀⢀⣠⠴⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣉⣉⣉⣁⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣿⠇
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠒⠛⠛⠛⠶⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⢿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠈⠻⣆⠈⠹⣿⠿⣿⣿⣿⣿⡿⠟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠶⢦⣤⣤⣤⣤⣼⣿⣤⣀⠀⠀⠀⠘⢧⡀⣿⣀⣬⣿⣿⠉⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠉⠻⣦⠀⠀⠈⣷⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⢷⣀⣾⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣿⡿⢛⡛⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠻⣿⣯⣶⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿

⠀⠀⠀⡀⡤⠀⠰⢀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡀⠀⠀⠀⠀⢀⠤⠒⡠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠇
⠀⢀⠠⡈⡁⡎⠁⢊⣴⠀⠀⠀⠘⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢠⡶⠄⠀⠀⢀⠔⠁⢆⠈⠁⢸⡆⠀⠀⠀⠀⢀⣀⣤⣤⣴⣿⡿⣤⡀
⠀⠸⠚⠃⠛⠓⠛⠉⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠀⢀⡎⠁⠀⠀⠀⠉⠰⣧⡜⠃⠈⠆⢠⠀⠀⠀⠀⠻⡀⠀⠀⠀⢀⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⣬⠆⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠈⠛⢉⡀⠀⠛⡀⠀⠀⠀⢸⠀⠀⠁⠉⠀⠀⢠
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠑⢄⠐⣀⠄⠀⠀⠰⠿⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣀⢇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉


⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⢀⢄⡠⠄
⠀⠀⠀⠀⠂⠉⢢⠀⠀⠀⠀⠀⠀⢸⡉⡀⠀⣙⠆⠀⠀⠀⠀⠀⠀⠀⠠⢠⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣴⠂
⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠯⠐⢻⣁⣰⠴⠂⠀⠀⠀⠸⡈⢣⡄⠰⠀⠀⠄⠀⠂⠠⡀⢀⠁⠀⠀⠀⢀⠃⢸
⠀⠀⠐⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢏⡦⣙⠆⡀⠀⠀⠈⠢⠀⠀⠮⠀⠐⠀⠁⠄⠀⠈⠀⠀⡠⠀⠌⠀⠀⣤
⠀⠀⠠⡀⠀⣀⡀⠀⠀⠇⠀⠀⠀⠀⠈⠢⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠼⠒⡀⠀⠀⠀⠀⠀⠁⠐⠒⠉⠠⠐⠊⠀⠀⠀⠀⠣⠀⠄⠀⠘⢀
⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⢀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⢀⠴⠂⠀⠁⣀⡀⠀⠘⠁⠀⠀⠀⠘⢶⣷⡁⠈⣷⢫⡴⠂⠀⠀⠀⠀⠀⠀⢐⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠂
⠈⡀⣠⠐⠋⣩⣿⡛⠒⠤⠐⠀⠀⠀⢩⠉⠉⢀⡛⠳⡆⠀⠀⠀⠀⠀⡄⠒⠋⠄⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠡⠈⣴⠅⠂⠀⢀
⠀⠀⠀⠀⠐⢣⡔⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢠⠄⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠛⠤⠾⣷⠞⠊
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠃⠆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠈⣉⡃⢱⡀⠀⠀⠀⠀⢀⡴⡛⠕⠚⠉⠳⣤⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⠐⢄⡀
⠀⠀⠉⠐⠂⢀⣀⣀⣀⠐⢣⠀⠀⠀⠀⢠⠢⢀⡔⡀⠁⡀⠀⠀⠀⠀⣾⠂⠁⠀⠀⠀⠀⠈⢧⠀⠀⠀⠠⠊⢀⠀⠀⠀⠒⠤⠀⠁⠀⠀⢰⠉⠁⡀⠀⢰⠀⠁⡀
⠀⠤⠀⠈⠉⠉⠉⢉⠉⠉⡟⠁⠀⠀⢠⠀⠀⢊⠜⢀⠄⠀⠀⠀⠀⠀⣟⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⠄⢀⠀⠀⠀⡀⠐⠀⣤⠀⠠⢀⠶⠘⠁⠀⠉⠲⢆⣀
⠀⠀⠈⠂⠠⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠣⠤⠆⠠⠊⠀⠀⠀⠀⠀⠀⠸⠦⠄⠐⠒⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠉⠃⢰⣦⣶⡆⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢠⣄⣀⡀
⠈⠀⠀⠸⢟⡿⠈⠠⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⢀⣿⣿⣿⠃
⠀⠀⢰⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⢹⡿⠿⠃⠀⠀⠀⠀⡤⠠
⠀⠀⢸⠀⠀⣷⠀⠀⡷⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢰⣏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠛⣦
⠀⠀⢸⠀⠀⢸⠀⠀⡇⠀⠀⢠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⡀⠀⠀⠀⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣰⠎⠁⠀⠀⠀⠀⠀⠀⠀⢘⣀⣀⠀⢀⠛⠋⠁
⠀⠀⠀⣄⠀⠻⠀⠀⠠⠄⠀⠁⠀⠀⠀⠉⠉⠉⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠘⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⣈⠊⠀⠀⠀⠪⢂⠀⠀⠀⠀⠃⠂⠀⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⡠⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠕⠆
⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠒⠀⠀⠚⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠀⠀⠣⣄⠀⠀⠐⠠⣾⣡⣀⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠈⠀⢳⣦⡵⡈⠉⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠷
⠀⠀⠀⠀⠐⠀⠃⣀⠗⠁⢤⡍⡉⠋⠁⢀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⢰⣄⠐⠠⠄
⠀⠀⠀⠀⠀⣈⠋⠉⠢⣨⠂⠁⠁⠤⠐⠈⠑⠐⠀⠀⠀⠀⠀⠃⢀⡀⢀⣀⡤⠚⠙⠚⠀⢀⠃
⠀⠀⠀⠀⠀⠋⠀⠀⠈⠁⠇⠀⠀⢀⣴⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠉⠙⠇⠀⠀⢀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠤⢤⡀⠘⡤⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠁⠀⠀⠈⣿⣗⣼⠏⠉
⠀⠀⠀⠀⠀⠀⢀⢈⣄⠨⠇⠠⢏⡀⠕⠀⠀⠀⠀⠀⢠⠂⠀⠀⡀⠀⠖⢤⢐⡯⠁
⠀⠀⠀⠀⠀⠐⠏⠀⢙⠉⢢⡌⠈⢱⡄⠀⠀⠀⠀⠀⠈⠁⠀⠄⣠⠚⠁⠉
⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠴⠛⠦⠀⠀⠀⠀⠐⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣋⠉⢹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣃⣥⠍⣽⠇⢸⣿⠟⠉⣤⠄⠀⠀⣰⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡁⢰⣷⣦⠀⠁⠀⠀⠀⢀⣠⡈⠛⣠⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣿⣿⠙⠀⠀⠀⠀⠀⠀⠨⣻⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣈⠘⠻⢿⣿⡷
⠀⠀⠀⠀⠀⢸⠑⠒⠒⠒⠒⡇⣿⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⡻⢿⣿⣷⣞⢟⡄
⠀⠀⠀⠀⠀⠘⠂⠀⡀⠀⠐⡇⡏⠛⢧⣀⡶⢄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣿⣉⡿⠇
⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠐⡇⠇⠀⠠⠋⠃⠀⢳⣄⡀⠀⠀⠀⡉⠉⠙⠛⢿⣿⣿⠜⡄
⠀⠀⠀⣀⠀⠀⡇⠀⡀⠀⢸⣇⡄⠀⠀⠄⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⠫⠖⠁
⠀⠀⠀⠃⠀⠀⠓⠐⠀⠀⠈⠁⠀⠀⠈⢀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡀⠐⠂⡓
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⡾⠋⠉⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣼⠛⠭⠀⡀⠀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣾⣤⡀⣠⠞⠃⠀⠉⣉⣉⣉⣀⣤⣿⣦⠀⠀⠀⠀⠠⠀⠀⠙⠿⣎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⣠⠀⠀⢠⣿⠀⠀⠀⠙⠷⠌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣿⣦⣤⣾⣿⣿⣿⣟⣻⣟⠂⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣾⣿⣷⠤⢀⠆⢀⠀⠸
⠀⠀⠀⠀⠀⠀⢠⠴⣶⣿⣤⣤⣾⠛⣻⠿⠿⠧⠞⠛⠈⣥⡤⠾⠷⠶⠿⠿⠿⠿⠿⠿⣿⣿⣷⣶⣾⣿⣿⣿⡶⠛⣶⡟⠀⡀
⠀⠀⠀⠀⠀⠸⡄⢀⣾⣿⣿⣿⣿⡄⠀⠀⣀⣀⣴⣶⣾⣿⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠛⣿⠟⣷⣸⣷⣿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⢻⡟⢫⣷⢩⣿⣿⡿⣦⣸⢿⣍⣭⣽⣿⣿⣿⣏⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠗⠒⠒⠿⣿⣿⣿⣤⣠⣶⣄
⠀⠀⠀⠀⠀⡄⣠⣽⣧⣼⣿⣯⡥⣿⣾⣿⣧⣿⣿⣿⣿⠟⠛⠟⢷⣶⣤⣶⣶⠂⠀⠀⢀⠀⠀⠲⠀⠠⠙⢀⣸⣶⣶⣿⣿⣿⡛⠛⠛⠛
⠀⠀⠀⠀⠘⢿⡿⠿⠛⠿⠿⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣧⣸⣿⣿⣿⣶⣶⣿⣷⣄⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠉⠙⠻⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠉

⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⢉⣭⣍⢩⣭⣭⣭⣝⠓⠲⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⣐⣿⢷⣿⣿⣿⣟⣿⣽⣿⡧⣿⣿⣶⢆⣉⡓⠦⣄⡀
⠀⠀⠀⠀⠀⢀⣾⠁⣼⣿⣟⣿⣿⣷⣾⣿⡿⣿⣼⡿⣷⢷⣿⣿⣞⣯⣻⣷⣦⠍⠲⣄
⠀⠀⠀⠀⠀⣼⣿⡆⠸⣿⣿⢿⣿⣿⣷⣾⣿⣾⣿⡋⠀⠀⢭⣻⣋⣽⣿⡷⣿⣿⡷⣈⠱⣄
⠀⠀⠀⠀⢠⣿⣿⣿⣄⠀⢶⣿⣿⡷⣿⣿⣿⣿⣿⣾⣷⣞⣿⣯⡿⠾⢷⣾⣭⣽⣚⣲⠷⠘⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠙⠿⣿⣿⢟⣽⣾⣿⣿⣿⢿⠿⢁⣼⣮⣄⠱⠀⢉⠝⢿⣷⠀⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣘⣽⣿⣿⣿⣿⣍⠀⣥⣽⣿⣿⠆⠀⠀⠂⠀⠉⢾⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⡟⠁⠀⠡⠄⠀⢀⣠⣷⣶⣾⣿⠿⠷⢶⣦⣄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡵⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⠶⡒⠀⣉⣻⣷⣾⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣷⣭⠲⠆⣘⡃⠂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⡿⣽⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢏⣌⣭⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢶⡝⠷⣿⣿⣿⣿⣿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡦⠀⢠⣴⣶⠒⡄⠙⣿⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡦⠀⠀⠀⠈⢠⠀⠀⠀⡏⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣄⡀⠀⡀⣠⢾⠈⠃⠀⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⣙⠙⠻⢿⣿⣿⣿⣽⣿⡴⠃⠀⢀⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠉⠻⣿⣿⢟⣣⣞⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿⢟⢿⠿⢿⣿⣿⢿⣿⣾⣤⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡋⠀⡁⠐⠀⠄⢀⢀⡉⠁⠙⣿⣿⣧⣄⣤⣤⣠⣀⠙⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠠⠈⡀⢈⠠⠀⢀⣤⣤⡘⢿⣿⣿⣿⡿⢥⡉⣃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣰⣆⣤⣴⣾⣿⣏⠠⣶⢽⣿⣿⣿⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⡎⠻⡆⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⣴⢛⡴⢦⡄⠀⠀⠀⠀⠀⠉
⠀⢀⣄⣤⣄⠀⡄⢠⢀⡄⠀⠘⠠⠤⠤⠀⡀⠀⠀⠀⢸⡇⢸⣷⠀⠛⡄⠀⠐⠉⠂⠀⠀⠀⠀⠀⠀⣀⢚⡷⣭⢟⡷⠁⠀⠀⠀⠀⠀⢀⡤⠖⣦
⠀⠀⠀⠁⠈⠀⠱⠜⠘⠃⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠈⣟⠀⠠⠀⣰⠃⠀⠀⠂⠘⠓⠀⠂⠀⠀⠀⠣⠾⣡⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣏⡰⠟
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠚⠃
⠀⠀⠀⣠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣠⣀⣤⣀⠀⠀⠀⠀⠀⢤⠀⠊⠁⠀⠀⠀⠀⢀⡀⣀⣀⣄
⠀⠀⠀⢩⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⢤⡀⠀⠀⠀⢀⡐⠿⠈⠁⣰⠀⠀⠀⠉⠛⠿⠟⠉⠀⠀⠀⠈⢀⡤⠈⠑⢴⣆⠀⠀⠀⠿⠿⣿⡿⠛⠂
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⡐⠅⠰⠟⠀⠀⠀⠀⠀⠈⠛⢀⡠⠞⠁⠀⠀⠀⠂⠀⠀⠀⠀⢄⡀⠀⣰⠾⠁⠶⠆⠀⠉⠀⠀⠀⠀⠰⠎⠁
⠀⠀⠀⢠⣄⡉⠀⠀⠀⠀⠈⠃⠀⠲⠶⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠁⠀⠠⠴⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠨⠟⠛⠢⡄⠀⠀⠀⡀⠉⠰⢶⡄⠀⠀⠀⠀⠐⠞⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⢠⡞⠠⠀⠀⠀⠀⣰⠀⠀⠙⠧⠈⠀⠄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡴⠖⠛
⠀⠀⠀⠀⠀⣽⣟⢟⠀⠀⠈⠁⠀⢠⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠶⠾⠿⠃⠀⠀⠀⠀⠀⡞⣶
⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⡀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣦⠀⠀⠀⠀⠀⢀⠀⢂⠀⢂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠐⠛⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⡇⠀⠀⠀⠄⠘⢀⢨⠖⠉⠀⠰⠀⠀⠈⠀⠀⠃⠀⠀⠐⡛⠛⠛⠛⢋⣙⡦
⠀⠀⡀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠄⠀⠠⡦⠀⠀⠀⠀⠠⠦⠀⠤⠶⠤⠃⠀⠈⠛⠃⠛⠋⠀⠀⠀⠀⠘⠀⠓⠀⠠⠤⠄⠀⠀⠀⠉⠢⠄⠀⢊⠉
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⡄⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠂⠀⠨⠿⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠀⠀⠀⠰⠀⠛⡟⠁⠀⠀⠀⠀⠤
⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⣰⠇⣸⡄⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠵⡄⠀⠢⠤⠀⠀⠈⠄⠀⠀⣀⢊⡀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠴⠌⠀⠀⠀⢹⠿⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣸⠇
⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢠⣤⡀⠀⠀⠠⡀⠀⠿⠀⠀⠀⠀⠀⠀⣀⣤⣀⣠⠀⣤
⠀⢣⣤⣄⡀⣀⣠⣤⠆⠀⠀⠿⣧⣰⣦⣬⣯⠀⠀⠀⠀⠞⠙⠆⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⡶⢁⢴⣷⠧⣴⠒⢤⡀⢾⣯⣍⣹⠇
⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠘⢶⣤⣤⡤⠞⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠀⠄⠈⣼⣃⣠⠿⠦⠚⠁⠀⠀⠈⠉

⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⢺⡆
⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡤⢤⡤⠀⠀⠀⠀⠘⠿⣿⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⡆⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢠⡀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⠧⠀⠀⠀⠀⠰⢀⡴⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⢱⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠃⠀⠀⠄⠀⠀⠀⠻⠶⠶⠶⠟⠁
⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠀⠰⠀⠀⡑⠀⠀⠀⠀⠀⢀⣤⡀⠐⠀⠀⠀⠠⣦⡍⠓⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠴⢷⡆
⠀⠀⠀⠚⢁⡴⠾⢃⠀⠀⠐⠓⠒⠂⠀⠐⠀⠀⠀⢰⣧⣿⡿⡶⡄⠀⠀⠀⠀⠀⣼⠀⣉⡿⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠶⠊⠛⠒⠛⠁⠀⠁
⠀⠀⠈⠒⠀⠑⠤⠘⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠰⠦⠏⠰⠆⠱⠟⠂⠀⠀⢀⣁⠉⢀⡏⠀⠀⠀⠀⠈⠋⣤⡤⠸⠷⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠃⠤⠴⠦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣶⠄⠀⠀⢀⣀⡀
⠀⠀⠈⠁⣤⣤⡀⠀⠀⠀⢠⠀⠀⠀⢷⠀⠀⠀⠀⣠⣶⡾⠛⠋⠁⠠⠀⠀⠂⠀⠐⣄⡉⠁⠀⠀⠀⠀⠉⠉⡉⠀⠰⠀⠀⠀⠀⠈⠠⠀⠘⣽⢀⡿
⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢉⡿⠏⠀⠀⠀⢲⣶⣤⣤⣷⡬⠃⠀⠀⠀⠀⢀⠦⠀⠀⠠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠀⠀⠀⠀⠐⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠠⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⡿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣆⣥⣤⣿⣄⣴⣇⣄⣷⣬⣴⣾⣁⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠊⠀⠈⠑⢄⡠⠊⠀⠈⢢⠀⠀⢀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠠⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢥⠀⠀⠀⠋⠀⠀⠀⢀⠃⠀⠀⠀⠔⠂⢀⠀⠊⠀⠀⠀⠀⠀⢄⠀⡄⠀⠀⢀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠠⠄⠀⠠⠀⠂⠀⠀⠈⢀⠁⣠⢠⠀⡞⢠⠄⡀
⠀⠀⠀⠀⠀⠈⠢⠀⠀⠱⠀⣀⡀⠔⠁⠀⠀⠀⠀⠁⠐⡀⠀⠀⣠⠀⡠⠀⠀⠁⠀⡀⢠⠄⢤⢀⠀⠀⠀⠀⠐⠀⣀⠀⠀⡄⠀⠁⡈⠄⣔⠁⢁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⡄⠠⠀⠀⠀⠠⠆⢁⡀⠐⠀⠀⠉⠀⢤⢠⠆⠁⢀⡐⠂⠀⠀⠀⠀⠀⠋⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⠀⠀⠀⠰⣿⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠠
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠔⠐⠊⠀⠀⠀⠀⠠⠀⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠤
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠊⡀⠀⠈⢀⢀⠄⢄⠀⠀⠄⠈⢢⠀⠀⠀⡀⢀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⠄⠀⠔⠲⠁⠀⠀⡀⢈⠆⠀⠄⠊⠀⠀⠀⢁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⣤⡀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠐⠀⠀⠀⠀⠀⡠⡊⠀⠀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠒⠒⠒⠂⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⠌⠀⠀⠀⠠⠪⠊⠀⠀⠀⠀⠀⠈⢱⡄
⠀⠀⠀⢸⠁⠈⠢⢀⠠⠂⠀⠁⢀⠀⡀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⡉⠛⣦⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠈⡆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⡞⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⣧
⠀⠀⠀⢸⠀⠀⠠⠐⠠⠀⠀⠀⠑⠀⠂⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠂⢠⡴⠋⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⢂⠀⠐⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠀⠀⠑⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠖⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠤⡀⢀⠀⠀⠀⡿
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⠁⠀⢠⠇
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠌⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠸⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠸⠤⠔⠢⠤⠠⠤⠤⠤⠤⠤⠌⠀⠀⠱⠴⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠤⠤⠤⠄⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠔⠁⠀⠈⠂⠄⠋

⠀⠀⠀⠀⢄⡀⢤⠄⡀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠠⠄⢀⠀⠀⠀⠀⡠⠀⠤⢄⠀⠀⠠⡴⠒⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠀⢠⠋⠀⠀⠀⠈⢂⠀⢠⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠑⠀⠒⠁⠀⠈⠀⠇⠀⠀⠰⠀⠈⢃⠘⠁⠉⠠⡘⠀⠀⠀⡔⠉⠀⠙⠆
⢠⠀⠀⠘⡀⠀⠀⠀⠀⠈⢄⠀⢏⠑⠀⠒⠒⠒⠂⠈⠁⢀⠆⠀⠀⠀⠀⢀⠄⠀⠀⠢⡀⠈⢢⣄⠜⠀⠀⠈⠀⠀⠥⠈⢁⣀⠀⠀⡇⠀⠀⠀⡅
⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⡃⠈⠢⠄⡀⠀⠀⣀⣀⠠⠊⠀⠀⠀⠀⠠⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠈⡠⡉⠡⡀⠦⡀⠙⠢⠤⠚
⠀⢄⠄⠒⠒⠂⠌⡁⠒⠀⠂⠁⠀⢀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢀⠨⡀⠽⠂⠠⠀⠀⠀⠠⠀⠀⠘⠂⠁⠀⣠⠤⠠⠄
⠀⠸⡀⠀⠀⠀⠀⠤⠁⠢⡀⠀⠀⠉⠀⠁⠀⢀⣴⣤⣄⣀⢀⠀⢰⠃⡀⠀⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡱⠌⠐⠀⠀⡎⠡⣀⢀⡌
⠀⠀⠑⠄⡀⠀⠀⠀⢀⠔⠁⠀⠈⠐⠂⠁⠀⠘⢿⣿⢿⣿⣿⠇⠀⠑⠂⠁⠬⠀⠃⢀⠶⠀⠀⠢⡀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠑⠤⠄⠋
⠀⠀⠀⠀⣀⠨⠤⠬⠀⢀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡂
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠃⢠⠤⡀⠀⢔⠒⠂⠤⠤⠐⠈⠀⠀⠀⡔⠀⢐⠀⢱⠀⠀⡤⠀⡃⠀⠀⠰⠉⠀⠀⠀⠂⠹⣌⠉
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠀⠀⠰⠀⠈⢆⠀⠀⠤⢀⡀⢀⣀⠀⠄⠊⠀⠀⠈⠀⠁⠀⠈⠀⠊⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⡆
⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠂⠁⠀⠀⠀⠂⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠑⠠⣀⣀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⠀⠰⠇⠣⡀⠀⠀⠀⢠⠂⠆⢄⠀⠀⠀⠀⠀⠀⠐⠊⢀⣀⣀⡀⠀⠑⠲⠄⠠⠄⠊
⢀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠐⠎⢦⠀⢸⡆⠐⠀⠀⠀⠘⠄⢀⡌⠈⢁⠄⠀⠀⠄⠀⡔⠋⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠣⠜⠀⠀⠀⠀⡠⠀⠲⠆⠁⠐⢄⠀⠀⢀⠈⠀⢀⢣⠀⡇⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠐⠀⢀⣀⢄⠄⠀⠁⠂
⠀⠀⠠⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠱⡠⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡠⠄⠀⠤⠅⡔⠊⣃
⠀⠀⠀⠀⠀⠠⣀⡀⢀⠈⠄⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠦⠼⠦⢀
⠀⠀⠀⠀⠑⠠⠄⢃⠜⠀⠈⠂⠤⠔⠒⠒⠁⣠⠄⠒⢦⣼⣁⠀⠀⠀⣠⣾⣿⡳⣷⣶⣶⣶⣶⣾⣶⡄⠀⠀⢠⠀⢄⠀⠀⠀⡎⠀⠀⠀⠀⠈⠆
⠀⠀⠰⢢⣀⡀⠐⠀⠀⢞⠉⠑⠄⠀⠀⠀⣸⠁⠀⠀⠈⠀⠈⣣⢠⣾⣿⣿⣿⡗⠟⠿⠋⠿⠹⠿⠿⠇⠀⠀⠀⠓⠤⠀⠀⠀⠅⠀⠀⠀⠀⠀⠸
⠀⠀⣺⣉⣱⣿⣷⣦⡀⠀⠍⠀⠙⠈⠁⠀⠹⣄⣀⠀⠀⣀⠔⡋⠈⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠘
⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠍⠉⠠⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⢀⣀⡀⡠⠊
⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠲⡄
⠀⠀⠙⠛⠿⠿⠟⠟⠀⠀⢠⠊⠁⠱⣄⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⠀⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢂⠱⠀⠀⣐⡀⠎⠀⠈⠂⠒⠁⠀⠀⠲⠒⠁⠀⠀⠀⠈⠁⠀⠀⠀⠠⠒⠑⢄⠀⠀⠀⢀⠀⠂⠢⠦⢄
⠀⠀⣴⠂⠉⠁⠀⠀⠀⠘⠀⠁⠀⠀⠈⡄⢃⠀⡇⠀⠀⠐⠀⠀⠀⠀⢀⠄⠒⠂⠈⠑⢄⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⠀⢠⠁⠀⠀⠀⠀⠀⠱
⠀⢸⣿⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠇⡘⠀⠄⠀⠀⠀⠀⢡⠀⠀⠁⠀⠀⠀⠠⠀⠈⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⡄⠀⠘
⠀⠈⢿⣿⣦⣂⣀⠕⠀⠐⢄⠀⢀⡠⢊⠐⠀⠀⠣⡀⠀⠀⠀⠸⠀⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠑⢄⡀⠀⠀⡀⠈
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠑⠄⠀⠀⠔⠁⠀⠀⠀⠀⠀⠑⠠⠠⠀⠊

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣖⣈⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣁⣲⠄⠀⠀⢀⡀
⠀⠀⠀⠀⣿⠈⠉⠙⠛⠛⠛⠛⠛⡛⠛⠛⣛⣋⣉⠩⣿⠀⢠⠚⣁⠨⠆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⡏⢠⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⡀
⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⡀⢸⣧⢋⡈⠰⠶⠤⡔⠊⠉⠑⠚⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠶⠀⠀⠀⢀⡤⠀⠀⠀⠀⣻⣾⣏⣀⡀⠠⠤⠰⡀⠀⠀⠀⠠⣀⠀⣀⠄⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢠⣚⠝⢡⠆⠰⢄⡀⠒⢄⡎⠀⠀⠀⠀⠀⢈⡝⠁⠀⠀⠀⢀⡕
⠀⠀⠀⠀⠀⢸⡀⠀⠰⠆⠀⠀⠀⠀⠀⢠⠟⢁⠔⠁⠇⠀⠃⠉⠢⢄⣗⠦⣤⠤⣢⢭⢭⢺⢳⣤⠢⠴⢊⡴
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢾⣿⠀⠀⠀⠐⠓⢪⠀⠀⠀⢰⠀⡄⠀⠀⠀⠉⠑⠒⢘⠧⣓⠵⠇⠘⡇⠈⠈⠁
⠀⠀⠀⠀⠀⠀⡕⢄⡀⠀⠀⠀⠀⠀⠀⠀⢈⣦⠀⠀⠀⠦⠁⠀⠀⠀⠀⠀⢠⠃⠀⠀⠑⡄⢀⢳
⠀⠀⠀⠀⠀⠀⠈⠢⢌⣀⣁⣀⣀⣀⣀⣀⡡⠔⠓⠤⣀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⣄⡞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉





⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⢀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠐⣩⣶⢠⡁⠀⠐⢈⠀⠈⠀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣬⢒⣢⡀⠀⠀⠀⠉⠁⢺⡆⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠
⠀⠠⢁⡄⠡⠃⡿⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠂⢀⡀⡄⠀⠀⠀⠀⠀⠈⠀⠑⢎⡁⠤⠒⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⢀⡄⢀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠛⠈⠡⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⣖⠁⠆⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⣾⣟⣿⠑⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠇⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠐⠀⠀⠀⠀⠻⢠⣌⢀⢀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠋⠀⠀⠀⠰⢀⠀⠀⠐⠈⠈⢂⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠁⠀⠀⠀⠀⠀⡠⠀⠀⠀⢰⡖⠒
⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⣀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠁⠠⠄⠀⠀⠀⠀⠀⢂⡘⠀⠀⠀⢠⡆⠀⠈⠀⠀⠀⢀⡀
⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠰⠀⠀⠀⠀⢐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠃⠑⠠⠀⠀⠀⠀⠀⠀⠀⠈⠠⠦⠀⠃
⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⡀⢠⣆⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠢⠤⠀⠀⠀⠀⢀⢐⡦
⠀⠀⠀⢰⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣴⣾⣬⣻⢵⠂⡀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠅⡀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠶⠟⣻⣈⢵⣚⡜⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠂⢐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣠⣒⡟⢛⣶⡀⠀⠀⠀⠀⠀⡜⠀⠘⡀⠀⠀⠀⠀⠀⠀⡜⠉⠱⡀⠀⠀⠀⠀⠀⣰⣚⡛⠛⡳⡀
⠀⢸⠁⠀⠈⠁⠀⢱⠀⠀⠀⠀⢰⠁⠀⠀⢣⠀⠀⠀⠀⠀⡸⠀⠀⠀⠣⡀⠀⠀⠀⠘⠀⠀⠉⠉⠀⢸
⠀⠘⣄⠀⠀⠀⢀⡜⠀⠀⠀⠀⠘⢄⠀⢀⠎⠀⠀⠀⠀⠀⡅⢀⡀⢀⣀⡅⠀⠀⠀⠘⢄⠀⠀⠀⢀⠜
⠀⠀⠈⠑⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⢴⡂⠀⠀⠀⠀⠀⠀⠀⣀⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⣠⣤⣶⡀
⠀⠀⢠⡛⡛⢫⡵⣀⠀⠀⠀⡰⠋⠀⠙⠁⠈⠳⡀⠀⠀⠀⠀⠀⠀⡎⠉⢢⠀⠀⠀⠀⠸⢿⣿⣿⠆
⠀⢨⣓⠁⠄⠰⡈⡕⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⠇⠀⠀⠀⢰⢏⡟⡽⣷
⠀⠐⣟⣄⠀⢠⢮⠟⠀⠀⠀⠙⢄⣀⠀⠀⣀⠜⠀⠀⠀⢠⠖⠒⠊⠀⢀⠞⠀⠀⠀⠀⢻⣽⣜⣾⣾
⠀⠀⠈⠛⠓⠚⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠓⠲⠒⠚⠁⠀⠀⠀⠀⠀⠀⠙⠓⠛⠁
⠀⠀⢀⠤⠶⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢤⡀
⠀⠀⡇⠀⠀⠀⠀⢃⠀⠀⠀⠀⡠⠊⠉⠑⠲⡄⠀⠀⠀⠀⣴⠋⠉⠋⠛⡄⠀⠀⠀⡎⡀⠃⠀⠀⠀⠘⡆
⠀⠀⢇⠀⠀⠀⠀⡘⠀⠀⠀⠀⡇⠀⠀⠀⠀⡘⠀⠀⠀⢸⡅⠐⠂⠀⠀⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡆
⠀⠀⢘⠆⠀⠀⡠⠃⠀⠀⠀⠀⠘⠦⠤⠤⠞⠁⠀⠀⠀⠸⣦⢀⠀⠀⢠⠇⠀⠀⠀⢣⡡⠀⠀⠀⣠⡴⠁
⠀⠀⠈⠒⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠛⠁⠀⠀⠀⠀⠀⠉⠛⠚⠚⠋
⠀⠀⠀⠀⡲⠂⡄⠀⠀⠀⠀⠀⠀⠴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⡂
⠀⠀⠀⠀⢱⠀⠐⠀⠀⠀⠀⢀⡔⠂⠋⣗⡦⢄⠀⠀⠀⢀⡰⢻⠈⠙⢁⣸⠇⠀⠀⠀⠀⣤⡾⢣⠟⣣
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⣾⡖⠈⡱⠌⠁⢮⡆⠀⢀⠏⢁⡨⠶⠀⠁⡞⠀⠀⠀⢀⢼⡥⢿⣡⣏⣽
⠀⠀⡠⠐⠁⢀⠞⠀⠀⠀⠀⢣⠐⡂⡅⠀⡉⡤⠁⠀⠈⢆⠁⠠⠃⢒⠞⠁⠀⠀⠀⠑⡞⢲⠚⣦⡞⠊
⠀⠀⠑⠒⠈⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠒⠋⠀⠀⠀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠉⠉⠊⠁

⠀⠀⠀⠀⠀⠠⠆⠀⠀⠠⠤⢄⣔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠄⣀⡴⢶
⠀⠀⠀⠀⠀⠈⠀⠀⠸⠃⠒⠓⠚⠂⠀⠀⠀⠀⠀⠀⢐⠣⢰⡁⠀⠀⠀⠀⠀⠀⢀⣤⠒⠘⠃⠰⠉⣁⡼⠶⠒⢁⢅⡴⡋
⠀⣴⣢⣴⡀⠀⣤⣲⣼⠇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢚⢀⡒⠈⡓⠀⠀⠀⠀⢀⠊⣶⣄⡤⣚⡛⠋⢀⣆⡄⣤⣚⣡⢼⠏
⠘⠠⠴⠓⠐⠒⠀⠒⠋⠒⠒⠂⡬⠄⠃⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠳⣌⠛⠻⠴⣇⣼⡥⠖⣪⠯⠥⠚⢁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠬⢤⣬⣭⠤⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠
⠀⠀⢀⣴⢶⣀⡔⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⡸⢁
⠀⠀⠀⢹⡟⠁⡄⢁⠀⠉⠑⡄⠀⠀⠀⠀⠀⣀⠀⢰⡦⣴⣉⡉⡳⠛⡅⠀⢀⡀⠀⠀⠀⠀⠀⡼⠙⠓⠚⠃⢆
⠀⠀⠀⢾⣓⣒⣒⣲⣖⣓⣒⣷⠆⠀⠀⠘⣁⢹⡽⣛⡛⠀⠀⢈⢷⠱⠟⣾⣞⡐⠀⠀⠀⠀⠀⢧⢤⠤⠤⢤⡿
⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢰⣹⣕⣸⡫⢓⢲⣬⢵⡛⠊⢑⣥⢟⡇⠀⠀⠀⠀⠀⢸⡉⠉⠉⠉⠁
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠘⡟⠮⣍⣉⣙⣄⠁⠀⣩⣟⣫⠴⣺⠃⠀⠀⠀⠀⠀⠀⡅⠀⠀⣀
⠀⠀⠀⠀⠙⣶⠤⠴⠤⢶⠏⠀⠀⠀⠀⠀⠈⠲⢤⣌⣉⣙⢦⡴⣋⣩⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⠤⠇
⠀⠀⡠⠖⡍⠙⠉⣻⣷⠏⣠⡻⣋⣵⠀⠀⠀⠀⠀⠉⠓⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢰⠁⣠⣓⣶⠟⠉⡄⣬⠉⠐⡏⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠚⠓⠢⡀
⠀⣿⡜⡻⣯⣏⠀⢮⣀⡨⠀⢠⣿⠀⠀⠀⠀⠀⠀⡞⡞⠲⠖⠒⢺⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⢙
⠀⣟⠮⣿⣷⣮⣶⣶⣶⣶⣿⠿⢻⠀⠀⠀⠀⠀⠀⡇⢧⠀⠀⠀⡸⢸⠀⠀⠀⢀⡀⡔⢉⡉⠉⠉⠉⠉⠉⠉⠙⠁⠈⢣⡀
⠀⠙⣷⠤⣀⣉⡉⠉⠉⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠑⠤⢽⣶⡯⠤⠊⠀⠀⠀⠀⠁⢂⢰⣿⣶⡦⠀⠀⠀⠀⢀⡅⠀⠐
⠀⠀⠈⠙⠲⠤⣤⣤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣤⣷⠄⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠦⠤⠤⠤⠤⠤⠤⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡜⠀⠀⠀⡼
⠘⠣⣀⠀⠀⠀⠠⠋⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⡞⠀⠀⠀⣰⣧⠤⠴⠦⠤⠤⣄⣀⡀⠀⠀⠀⢀⡀
⡏⠀⠈⠙⠢⢤⠃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⡋⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⡹⠁
⡇⠀⠀⢀⠀⢸⢀⠀⢰⢀⡀⠸⠀⠀⡀⢀⣀⠀⠀⣀⣀⣀⠘⣷⡽⣠⡞⠁⠀⠀⠀⠀⡀⢀⣀⣠⠤⣐⢂⠁⣀⣀⡜⠁⠀⣀
⣇⠀⠀⠀⣢⣸⠹⠀⠀⣟⠇⠀⣄⠇⠀⠀⠀⠀⢾⠀⠀⠀⢾⣭⠀⠀⢠⡞⡉⠉⠉⠉⢹⡏⠀⠀⡎⡇⠀⠋⠁⠀⠑⣴⠏
⠸⡄⠀⠀⠀⢭⢐⠀⠀⣷⡀⠀⣗⡀⠀⡴⠞⢐⡼⠀⢰⠀⠛⡯⠄⠀⠨⢿⣣⠤⠀⢠⠾⢧⠀⠀⡇⡇⠀⠶⠀⢄⠀⠈⠀⢠
⠀⠹⡄⠀⠀⢸⢨⠀⠀⠛⠁⠀⣇⠄⠀⠀⠠⢸⠚⠀⠸⠀⢸⣗⠅⠀⢠⣄⣰⠩⠀⢠⣠⣩⠀⠀⣇⡇⠀⠀⢱⡈⣆⠀⢀⠃
⠀⠀⠙⢦⠀⢸⣺⠀⢀⣀⠀⠀⣇⠂⠀⢀⣀⢼⡆⠀⣠⠀⠀⡄⡀⠀⠀⠈⢙⡢⠀⠈⠀⣻⠀⠀⠀⠀⠀⠀⠀⢳⠁⠀⢸
⠀⠀⠀⠈⠓⢾⢘⠀⢰⡟⠀⠀⣷⠆⠀⠋⠁⣸⠃⠀⡏⡆⢀⣗⣇⣀⣐⠀⢼⢈⠀⠀⠀⢚⠀⠀⣖⠆⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⢸⢴⠀⢸⡇⠀⠀⣇⡄⠀⠀⠀⣿⠀⣀⠷⠛⠉⠁⠀⠀⠀⠉⠙⠲⢄⢠⣼⢹⠀⠀⣿⠄⠀⠸⠀⢸⡅⠀⢸
⠀⠀⠀⠀⠀⠸⡴⠲⠞⣧⣗⡶⢿⡓⣐⣖⣶⠟⠋⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⢻⣸⣝⣒⡖⢸⡽⠶⢾⡀⠸⠼⠴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠈⠉⠀⠁⠐⠂⠀⠐⠒⢺⠍⠭⣔⠢⢤⣀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⣀⡠⠤⠭⠗⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣏⠀⠀⠀⠀⠉⠓⠄⠀⠀⠀⢳
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠉⠋⠛⢻⠉⠉⠉⠘⡆⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠘⠋⠉⠉⠓⠒⠦⢤⣀⣀⠀⠀⢀⣀⣠⠤⠖⠻⡄⠀⠀⠈⢣⠀⠀⠀⣷⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⢠⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣑⣄⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣒⣶⡿⠋⠙⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⠶⢛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⣴⣍⡀⠀⣠⠮⠀⠐⠛⠛⠓⠒⠀⣈⣷⣄⠀⠀⠀⠀⠀⡈⠀⠐⢶⣦⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡾⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡆⠀⡀⠀⠀⢰⡆⠀⠀⠈⢷⣆⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣀⢀⣠⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣷⡞⠀⠀⢠⣿⣿⣀⠀⠀⡀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠉⢉⣿⣿⢿⣛⣯⣟⣓⣿⠚⠛⠂⠀⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣾⣿⣿⣯⣤⣥⣠⣶⠀⠈
⠀⠀⠀⠀⠀⠀⡌⠉⢙⣿⣿⣿⣿⣏⠀⠛⠉⠉⠉⢀⣀⡀⣼⠏⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⣿⣿⢛⣻⣿⣿⡁⣴⣽⣄⣠⣦
⠀⠀⠀⠀⠀⠀⢳⣤⣶⢿⣹⢿⣿⣿⣆⠀⢠⣄⠶⠾⢻⣿⣿⣷⣦⡤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣼⣿⣘⠛⠺⢿⣿⣿⣿⠓⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⣤⠺⢧⣾⡿⠻⡏⢳⣾⡵⣷⣽⣿⣿⣿⣿⣿⣔⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠩⠽⡉⠁⢄⣉⢉⣿⣿⣿⣾⣶⣿⣷⡄
⠀⠀⠀⠀⠀⣚⣤⣷⣷⣭⣾⣿⣿⡛⣿⣿⣿⣿⣿⣯⣿⣿⡏⠁⣐⣍⣽⠷⢿⣿⣯⡄⠀⠀⣠⣄⠀⠈⠁⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠇⠈⠉
⠀⠀⠀⠀⠀⠙⠟⠋⠉⠉⠉⠉⠻⢶⣿⣿⣿⣿⣿⣿⠿⠿⣷⣶⣿⣿⣿⣧⣾⣿⣿⠿⠿⠿⠿⠿⢦⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⢠⠤⢄⠀⠀⠀⠀⠀⠀⠸⡉⢢⠀⠀⠀⠀⠀⠀⡤⢄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡶⡀
⠀⠀⠀⠀⠀⢀⠱⢤⣗⢀⡀⠀⠀⠀⠀⡨⠛⢣⠀⠀⠀⠀⢀⡽⠂⠿⠥⡎⠀⠀⠀⠀⠀⠀⠀⡇⠈⢢
⠀⠀⠀⠀⢰⡱⠀⠀⠀⠀⠈⡆⠀⠀⡰⠁⠀⠀⢇⠀⠀⠀⢸⢐⢈⢀⠀⡏⠀⠀⠀⠀⠀⣀⠜⠀⡀⢸
⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⢀⠇⠀⠰⢡⠀⠀⠀⠈⢆⠀⠀⠈⢢⡨⠠⡰⠁⠀⣠⠄⣒⣊⣁⠤⠊⢀⠞
⠀⠀⠀⠀⠀⠘⢆⢀⣀⡠⠎⠀⠀⠘⢼⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠉⠁⠀⠀⠙⠢⠤⠤⠄⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢉⠆
⠀⠀⠀⠀⠀⠀⢀⠖⠚⠺⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⡇⢱⠀⠀⠀⠀⠀⡔⡮⠉⠛⡏⠢⡄
⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠈⠑⡄⠀⠀⠀⠀⣠⡎⠙⡞⠉⠙⣾⣉⣑⠆⠀⢸⢸⠀⠀⠀⡸⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⡤⣵⠊⠑⡤⠾⡏⠉⡆⠀⠀⠈⢎⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⡠⠃⠀⠀⢠⠛⢞⠁⣱⠄⠧⠤⠋⠈⠀⠀⠀⠀⠀⡉⣒⢒⣈⣁⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠈⠁⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⢸⢹⠠⠀⠄⠀⠀⠀⠐⠀⢄⠀⢄⠏⡇
⠀⠀⠀⠀⠀⠀⣤⡀⡜⢆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣦⡐⢀⠈⠀⠂⠀⠂⡀⠀⡜⡰⠁
⠀⠀⠀⠀⠀⠀⡼⣝⣧⠜⡡⡇⠀⠀⠀⢀⡤⠤⢤⠀⢀⠀⠀⠀⠀⠀⠀⠙⠿⣢⠤⣀⣀⣈⣀⠤⡪⠞
⠀⠀⠀⠀⠀⠀⣹⠤⢷⠞⢴⡃⠀⠀⠀⠪⠤⢔⡟⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠊⠉
⠀⠀⠀⠀⠀⡞⠣⣠⠎⠑⡼⣙⡄⠀⠀⠀⠀⡎⡎⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⡠⠔⣒⡂⠤⢄⣀
⠀⠀⠀⠀⢸⠷⢎⠉⡢⢎⡀⡜⡇⠀⠀⠀⠀⠳⡁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡰⠋⠀⠁⠀⠈⠁⠀⡔⠁
⠀⠀⠀⠀⠈⣦⢴⡛⠣⣤⣏⡱⠁⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠁⠀⠀⠀⠀⠰⣁⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠈⠢⣝⣛⡧⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠔⠊

⠀⠡⠀⠀⠀⠀⡠⠒⠉⠀⠀⠉⠀⠢⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠣⡀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠂⠑⠀⠁⠀⠇⠀⠀⠠⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠹⢦⣀⠀⢀⣀⡴⠂⠀⠀⡀⠀⢁
⠀⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠢⢀⠀⠀⠁⠢⠤⢀⣁⠀⠀⠔⡡⠒⠒⠒⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡄⢀⡠⠊⠃⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠔⢢⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸
⠰⡉⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢄⠀⠐⠠⠄⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢤⡀⠀⡠⠒
⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠔⠁⠀⠀⠈⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠶⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⣱⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠦⢠⡴⠶⣦⡀⣠⡶⠶⣤⠀⣶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠂⢿⡀⠀⢸⡇⣿⠀⠀⣸⡇⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠛⠛⠋⠀⠈⠛⠛⠋⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣾⡄⢠⠞⠓⠀⣦⠞⢠⠞⣓⡂⣾⣳⢠⡞⠓⡆⢲⢰⡆⡷⣀⡆⣾⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠘⠉⠙⠈⠓⠚⠀⠋⠓⠈⠓⠚⠁⠋⠓⠈⠓⠚⠁⠘⠚⠀⠃⠘⠃⠛⠚⠁

⠀⢀⣀⣀⡀
⠑⡈⠦⠆⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⠖
⠄⠰⠸⠀⠸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠚⠁⠀⠀⢄
⠀⠐⡠⠀⠀⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠒⠢⡄⣀⡉⠢⠀⢰⠁⠀⠀⠀⠀⢀⢀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⣀
⠒⠉⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠈⠀⠀⠀⠨⡤⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠢⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠄⣀⠠⢔⡥⠒⠀⠀⠁⠒⠠⢄⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⡀
⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠒⠀⠀⣠⠖⠛⠛⠛⠶⣄⠀⠀⡴⠂⠀⠀⠀⢀⠀⠄⠀⠄⠀⠀⠈⠰⠀⠀⠀⠀⢰⡆⠐⠂⠀⠀⡅⠀⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢷⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⡄⠘⡀⠈⠂⠄⣀⠀⠀⢀⡠⠔⠁⠀⠀⠂⠙