Fascinated Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢦⡀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⡴⠛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⢻⣷⣄⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡇⠀⠻⣿⣿⠀⠀⠀⠀⣀⠀⠀⢠⡇⠀⠘⢿⣿⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⡇⠀⣾⣿⣿⠀⠀⢀⣠⡿⠀⠀⢸⡇⠀⢸⣿⣿⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠾⠷⠶⠿⠿⠿⠆⠀⢾⡀⠀⠀⠀⠾⠷⠶⠾⠿⠿⠆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣿⣿⣿⠿⠿⠿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⣿⣉⣀⣀⣀⣀⣀⣈⣿⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⡠⠄⠒⠠⢄⠀⠀⠀⠀⠀⣀⠤⠒⠢⢄⡀⠀⠀⠀⠀⢀⠤⠐⠂⠤⡀⠀⠀⠀⠀⢀⡤⠔⠒⠤⣀⠀⠀⠀⠀⠀⡠⠄⠒⠠⢄
⠀⠀⠀⡎⢠⡄⠀⢠⡄⠱⠀⠀⠀⡜⢁⣄⠀⠀⣄⠙⡄⠀⠀⣰⠁⣤⠀⠀⣤⠈⡆⠀⠀⢠⠋⣠⠀⠀⣠⠈⢣⠀⠀⠀⠎⢠⡆⠀⢢⡄⢳
⠀⠀⠀⡄⢀⠀⠀⠀⡀⢀⠃⠀⠀⠇⠀⢀⡀⣀⠀⠀⡇⠀⠀⢠⠀⠀⠀⠀⡠⠀⡟⠀⠀⢸⠀⡤⠤⠤⢤⡄⠸⠀⠀⠘⡀⠀⡠⠤⢀⠀⢰
⠀⠀⠀⠙⠤⣉⠒⣉⡠⠊⠀⠀⠀⠈⠢⣁⡀⣀⡡⠎⠀⠀⠀⠈⠢⣌⡒⢉⡠⠜⠁⠀⠀⠀⠱⢌⡒⢐⣊⠔⠁⠀⠀⠀⠑⢌⣀⠀⣀⠵⠃

⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠀⠀⠀⢀⠤⠤⠤⢄⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⡠⠤⠤⠤⡀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀
⠀⠀⠀⡜⢁⡀⠀⢀⡀⢳⠀⠀⠀⡰⠁⣆⠀⢀⡆⠱⡀⠀⠀⢰⠃⣀⠀⠀⣀⠙⡄⠀⠀⢠⠊⢀⠀⠀⢀⠈⢆⠀⠀⠀⠎⣠⡄⠀⣠⡌⢣
⠀⠀⠀⡄⠈⠁⠀⠀⠁⢀⠂⠀⠀⡇⠀⠈⣀⡈⠰⠗⡇⠀⠀⢥⠀⠉⠀⠀⢀⠀⡯⠀⠀⢸⠀⠈⡀⢄⡈⠀⢸⠀⠀⠸⡀⢈⣁⣀⣈⡁⢸
⠀⠀⠀⠑⢄⡈⠉⢁⡠⠊⠀⠀⠀⠘⢤⡉⠀⠈⣁⠜⠀⠀⠀⠈⠢⣐⠂⠐⣉⠔⠁⠀⠀⠀⠣⣈⠒⠒⢋⡤⠃⠀⠀⠀⠱⢌⡢⠤⢐⡡⠊
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⢀⡠⠤⢄⡀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⠀⢀⡤⠤⢄⡀
⠀⠀⠀⡔⢁⡀⠀⢀⡈⢣⠀⠀⠀⡰⠉⡀⠀⠀⡈⠱⡀⠀⠀⢠⠊⣀⡀⢀⣀⠑⡄⠀⠀⢀⠎⢀⠀⠀⢀⠙⢆⠀⠀⠀⡜⠅⡀⠀⣀⠌⢢
⠀⠀⠀⡁⠈⠁⠀⠈⠁⢀⠆⠀⠀⡇⠀⠁⠀⠀⠁⠀⡇⠀⠀⣟⡆⠀⠀⠀⠀⢐⡻⠀⠀⢸⠀⠘⠀⠀⠈⠀⢸⠀⠀⠸⠀⠀⡡⠤⣉⠀⢨
⠀⠀⠀⠱⣄⠀⠛⠀⣀⠞⠀⠀⠀⠘⢜⠉⠋⠋⢙⠔⠀⠀⠀⠘⢆⡙⠭⠭⢋⡰⠁⠀⠀⠈⠢⡚⠓⠑⠑⡢⠃⠀⠀⠀⠣⣐⢄⣀⠼⣠⠎
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⡴⢉⠀⠀⠀⡈⢢⠀⠀⠀⠠⠋⣀⠀⢀⡈⠢⡀⠀⠀⢠⠊⣁⠀⠀⣈⠱⡄⠀⠀⢀⠜⢁⠀⠀⢀⠑⠄⠀⠀⠀⡔⠁⡄⠀⢤⠙⢆
⠀⠀⠀⡁⠈⠁⠀⠈⠋⠀⠆⠀⠀⣇⠶⡈⠀⠈⣱⢆⡇⠀⠀⣈⠀⠉⢠⢠⠤⡀⣷⠀⠀⢸⠀⠉⠀⠀⠉⠀⢸⠀⠀⢰⠀⢈⣁⣀⣈⡁⢸
⠀⠀⠀⠣⡀⠐⠤⠀⢀⠜⠀⠀⠀⠹⣍⠀⠈⠀⢈⡽⠁⠀⠀⠘⢄⠀⠘⠈⠊⡠⠃⠀⠀⠈⢦⡈⠱⡲⠉⣠⠎⠀⠀⠀⠣⡈⠢⠤⠜⢁⠞
⠀⠀⠀⠀⠈⠁⠒⠈⠁⠀⠀⠀⠀⠀⠈⠉⠐⠊⠉⠀⠀⠀⠀⠀⠀⠉⠐⠂⠉⠀⠀⠀⠀⠀⠀⠉⠑⠒⠉⠁⠀⠀⠀⠀⠀⠈⠁⠒⠈⠁

⠀⢀⡤⠖⠛⠉⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢤⡀
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹
⡟⠀⢠⠞⠳⠄⠠⠞⠳⠄⠀⢻⠀⠀⠀⠀⡏⠀⠀⢾⠆⠀⠀⢾⡇⠀⠀⢷⠀⠀⠀⠀⡏⠀⠀⢾⡷⠀⠀⢼⡷⠀⠀⢻⠀⠀⠀⠀⡟⠀⠀⠺⠗⠀⠀⠺⠗
⣧⠀⠀⢠⡀⠀⠀⢀⡄⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⢀⡀⠀⠀⢀⡄⠀⠀⡾⠀⠀⠀⠀⣇⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⣼⠀⠀⠀⠀⣧⠀⠀⢤⠤⠤⠤⠤⡄
⠘⣆⠀⠀⠉⠓⠛⠉⠀⠀⣰⠃⠀⠀⠀⠀⠙⣆⠀⠀⠙⠓⠚⠉⠀⢀⡴⠃⠀⠀⠀⠀⠘⣆⠀⠘⠁⠀⠀⠈⠃⠀⡰⠃⠀⠀⠀⠀⠘⣆⠀⠘⠦⣄⣠⠴⠃⠀⣰
⠀⠈⠓⠦⣤⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠚⠁


⠀⢀⡤⠖⠛⠉⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢄⡀
⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢠⠏⠀⠰⣄⠀⠀⣰⠆⠀⠱⡄⠀⠀⠀⠀⢠⠏⢀⡀⠀⠀⠀⠀⢀⡀⠱
⡟⠀⠀⢾⡷⠀⠀⢾⡷⠀⠀⢻⠀⠀⠀⠀⡏⠀⠰⣤⡴⠀⠐⢦⡴⠂⠀⢷⠀⠀⠀⠀⡏⠀⣀⣙⣋⣀⣀⣛⣋⣀⠀⢻⠀⠀⠀⠀⡏⠀⠀⣉⠶⠀⠀⠶⣉
⣧⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⠀⣠⡤⢤⣀⠀⠀⠀⡾⠀⠀⠀⠀⣇⠀⣏⠉⠉⠉⠉⠉⠉⣹⠀⣼⠀⠀⠀⠀⣧⠀⠀⠀⣀⣤⢤⣀
⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠙⣆⠀⠚⠁⠀⠀⠈⠃⢀⡴⠁⠀⠀⠀⠀⠘⣆⠈⠳⣤⣀⣀⣤⠞⠁⡰⠃⠀⠀⠀⠀⠘⣆⠀⠘⠁⠀⠀⠈⠃⠀⡰
⠀⠈⠓⠦⣄⣀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣈⣁⣤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣠⠴⠚⠁


⠀⢀⡤⠖⠋⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠙⠲⢤⡀
⢠⠏⠀⠐⠛⠀⠀⠛⠂⠀⠹⡄⠀⠀⠀⠀⣰⠏⢀⠀⠀⠀⠀⠀⢀⠈⠳⡄⠀⠀⠀⠀⢠⠏⢀⡀⢀⡀⢀⡀⢀⡀⠱⡄⠀⠀⠀⠀⢠⠏⠀⡀⠀⠀⠀⠀⠀⠀⠹
⡟⠀⠀⠺⠗⠀⠀⢺⡗⠀⠀⢻⠀⠀⠀⠀⡏⠀⢀⣹⠶⠀⠠⢾⣉⠀⠀⢳⠀⠀⠀⠀⡏⠀⢀⡵⢏⡀⢀⡽⢯⡀⠀⢻⠀⠀⠀⠀⡟⠀⠀⣉⡷⠄⠀⠰⡷
⣧⠀⠀⠀⣀⣤⢤⣈⠁⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⢀⡀⠀⠀⢀⡌⠀⠀⡾⠀⠀⠀⠀⣇⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣼⠀⠀⠀⠀⣧⠀⠀⢡⡀⠀⠀⢀⡄
⠘⢆⠀⠘⠁⠀⠀⠈⠃⠀⡰⠃⠀⠀⠀⠀⠹⣆⠀⠀⠙⠛⠛⠉⠀⢀⡴⠃⠀⠀⠀⠀⠘⣆⠀⠉⠉⠉⠉⠉⠉⠀⡰⠃⠀⠀⠀⠀⠘⣆⠀⠀⠙⠛⠛⠉⠀⠀⡴
⠀⠈⠓⠦⣤⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠊⠁


⠀⢀⡤⠖⠛⠉⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢤⡀
⢠⠏⠀⠠⠴⠂⠀⠦⠄⠀⠹⡄⠀⠀⠀⠀⣰⠋⠀⠠⠖⠀⠐⠲⠄⠀⠱⡄⠀⠀⠀⠀⢠⠏⠀⠰⢤⡀⢀⡤⠄⠀⠱⡄⠀⠀⠀⠀⢠⠏⠀⠠⣄⠀⠀⣠⠄⠀⠹
⡟⠀⠰⣄⣠⠄⠠⣄⣠⠆⠀⢻⠀⠀⠀⠀⡏⠀⠀⣠⠞⠉⠙⠳⡀⠀⠀⢳⠀⠀⠀⠀⡏⠀⠀⣴⣆⠀⠀⣰⣦⠀⠀⢻⠀⠀⠀⠀⡟⠀⠀⢾⡿⠀⠀⢿⡷
⣧⠀⠀⢨⡀⠀⠀⢀⡄⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⣯⣠⡤⢤⣀⡇⠀⠀⡾⠀⠀⠀⠀⣇⠀⠀⠈⣁⣤⣤⣈⠁⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⢠⣤⣤⣤⣤⣄
⠘⣆⠀⠀⠉⠓⠛⠉⠀⠀⣰⠃⠀⠀⠀⠀⠘⢆⠀⠈⠳⠤⠤⠟⠁⢀⡼⠁⠀⠀⠀⠀⠘⣆⠀⠘⠁⠀⠀⠈⠃⠀⡰⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠈⠓⠦⣤⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠚⠁

⠀⠀⠀⠀⠀⣀⠤⠴⠲⠦⢤⣀⠀⠀⠀⢠⣤⠀⠀⠀⢀⣠⠤⠖⠲⠤⣄⡀⠀⠀⣰⣶⡄⠀⠀⠀⣀⡤⠴⠒⠦⠤⣀
⠀⠀⠀⡤⠊⠁⣀⠀⠀⢀⡀⠈⠳⣄⠄⠀⠁⢀⢀⠔⠉⣠⣄⠀⠀⣠⣄⠉⢪⡀⡈⠉⠁⠠⣢⠞⠁⣀⠀⠀⠀⢀⠈⠑⢦
⠀⢀⡞⠁⠀⣾⣿⡅⠀⢸⣿⡇⠀⠈⢧⠀⠀⢢⠏⠀⠸⠁⠸⠀⠀⠇⠈⠇⠀⠹⡔⠀⠀⡼⠁⠀⢸⣩⡇⠀⢰⣏⣷⠀⠀⢳⡀
⠀⣼⠁⠀⠀⠈⠉⠀⠀⠈⠉⠁⠀⠀⢸⡇⠀⡟⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⢹⠀⢸⡇⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠈⣧
⠀⠹⡄⠀⠀⠴⠻⣴⠳⣴⠳⠄⠀⠀⣸⠃⠀⢷⠀⠀⠀⠸⣦⣀⣀⡤⠇⠀⠀⠀⡞⠀⠘⣇⠀⠀⠀⠛⠟⠛⠻⠟⠁⠀⠀⢠⠏
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠉⠓⠶⠦⠤⠶⠖⠚⠁⢀⣀⠀⠀⠀⠀⠈⠙⠲⠶⠤⠴⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠤⠶⠶⠚⠍
⠀⠀⠀⠿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠘⠛⠀⢰⣿⣧⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⣶⡆⠀⠐⠿⠂⠀⠀⠀⣀⡀⠀⠀⠐⠟
⠀⠀⠀⠀⡠⠖⠉⠉⠉⠉⠙⠢⣄⠀⠀⠀⠀⠉⠁⢄⡴⠚⠉⠉⠉⠉⠓⢦⡠⠀⠉⠀⠀⠀⠀⣠⠔⠋⠉⠉⠉⠉⠲⢄
⠀⠀⣢⠎⠀⣄⠀⡄⠀⣀⠀⣤⠈⠳⡤⠀⠀⡐⡴⠃⠀⣀⣀⠀⠀⣀⣀⠀⠘⢦⠂⠀⠀⢠⠞⠁⣠⢶⡄⠀⢠⣖⢦⠀⠹⣔
⠀⢰⠇⠀⠀⠙⠛⠁⠀⠈⠛⠁⠀⠀⢹⡄⠀⣼⠁⠀⠀⠉⠉⠀⠀⠉⠉⠀⠀⠈⣧⠀⢠⡏⠀⠀⠷⠿⠇⠀⠸⠿⠾⠂⠀⠸⡆
⠀⢺⠀⠀⠀⢰⣀⠀⠀⠀⣠⠆⠀⠀⢸⡇⠀⣇⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⠀⣸⠀⢸⡇⠀⠀⠀⠀⣤⠶⢦⠀⠀⠀⠀⠀⡿
⠀⠈⢧⡀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢀⡞⠂⠀⠘⣄⠀⠀⠀⠛⠀⠀⠓⠀⠀⠀⣠⠋⠀⠀⢳⡀⠀⠀⠀⠙⠶⠚⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠑⠦⣄⣀⡀⠀⢀⣀⣠⠴⠋⠀⠀⠀⠀⠈⠳⢤⣀⣀⠀⠀⣀⣀⡤⠞⠁⠀⣠⣤⠀⠙⠦⣄⣀⡀⠀⢀⣀⣠⠴⠊
⠀⠀⢠⡄⠀⠀⠉⠉⠉⠉⠁⠈⠀⢀⣀⠀⢠⣶⡄⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠁⠊⠉⠉⠉⠙⠀⣴⣦
⠀⠀⠀⠁⠀⣠⠤⠒⠒⠢⠤⣀⠀⠈⠋⠀⠀⠈⠀⠀⢀⡤⠤⠒⠒⠦⢤⡀⠀⠀⢠⣤⠀⠀⠀⠀⣠⠤⠖⠒⠲⠤⣄⠈⠁
⠀⠀⢔⡴⠋⠀⠀⠀⠀⠀⠀⠈⠑⢄⠄⠀⠀⠀⢢⠖⠁⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠁⠀⠠⣠⠊⢁⡀⠀⠀⠀⢀⡀⠙⢮⡂
⠀⢀⡞⠀⠀⢴⣤⠄⠀⢠⣤⡆⠀⠈⢧⠂⠀⣰⠋⠀⠈⢳⣄⠀⠀⣠⡞⠁⠀⠙⡆⠀⠀⡼⠁⠀⠀⣩⠷⠀⠲⣯⡁⠀⠀⢳⡀
⠀⣼⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⠈⣉⠀⠀⣉⠁⠀⠀⠀⢹⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠸⡄⠀⠀⠀⠳⣤⣀⣤⠞⠀⠀⠀⣸⠃⠀⢻⡀⠀⠀⠞⠹⡞⢳⠏⠳⠀⠀⢀⡟⠀⠈⣇⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⢠⠏
⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⣠⣤⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⣤⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠒⠋⠑⠀⠀⠈⠁⠀⠀⠐⠉⠓⠲⠶⠶⠖⠚⠋⠂⠀⠀⠀⠀⠀⠀⠊⠙⠒⠶⠶⠶⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣷⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠿⠛⠛⠛⠛⠛⠿⢿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁⠸⠄⢠⣿⣿⠄⠀⠀⢠⣶⣦⠀⠉⡏⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⣿⣿⡟⠀⠀⢀⣾⣿⡟⠀⠀⢀⡈⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠘⠿⢿⠁⠀⣰⣿⣿⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣾⣿⣿⡿⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄⠀⢻⣿⣦⡀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠈⠓⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄⠀⠹⣿⣿⣶⣴⣶⣿⣿⡿⠟⠁⠀⢀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠈⠛⠿⠿⠟⠋⠁⠀⠀⢀⣤⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣴⣾⣿⣿⡿⠛⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⠿⠿⣿⣿⣿⣿⢿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⡰⠊⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⢄
⠀⠀⠀⠀⠀⣸⠀⠠⡄⠀⢠⠄⠀⠀⠀⠀⠀⢰⠃⠀⡦⠀⠠⡄⠀⠀⠀⠀⠀⠀⡟⠀⢴⠀⠀⠤⠀⠈⡆
⠀⠀⠀⠀⠀⢻⠀⢄⣀⣀⣠⠴⠃⡔⠀⠀⠀⢸⡀⠀⠀⠠⠤⠀⠀⣰⠀⠀⠀⠀⣇⠀⠠⠖⠂⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣀⣠⠞⠁⠀⠀⠀⠀⠹⢤⣀⠀⢀⣠⡼⠃⠀⠀⠀⠀⠘⠧⣄⣀⣀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠠⡀⠀⠀⠀⠀⢠⠖⠋⠉⠁⠉⢳⡄⠀⠀⠀⠀⢀⡔⠋
⠀⠀⠀⠀⠀⣼⠁⠀⠠⠀⢠⠀⠀⢱⠀⠀⠀⢠⡏⠀⢠⠀⠀⡄⠀⢻⠀⠀⠀⠀⣼⠀⠘⠃⠀⠛⠃
⠀⠀⠀⠀⠀⢹⡀⠀⣴⣶⣦⠀⠀⡾⠀⠀⠀⠘⣇⠀⠠⠤⡠⠄⠀⣼⠀⠀⠀⠀⢹⡀⠰⣿⣷⣶⠆⢀⡖
⠀⠀⠀⠀⠀⠀⠙⢦⣄⣉⣁⡤⠞⠁⠀⠀⠀⠀⠘⠷⣄⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠑⢦⣀⣉⣀⡤⠚

⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠈⠙⢦⡀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⡏⠀⠐⠂⠀⠒⠂⠀⣷⠀⠀⠀⣾⠀⠘⢃⣠⡘⠃⠀⢻⠀⠀⠀⠀⡏⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⢳⡀⠀⠊⠉⠀⠀⢀⡟⠀⠀⠀⠹⡄⠀⢸⣿⡷⠀⠀⡼⠀⠀⠀⠀⢧⠀⠢⠤⠤⠴⠚⣠⠇
⠀⠀⠀⠀⠀⠀⠑⢦⣄⣀⣠⡴⠋⠀⠀⠀⠀⠀⠉⠀⠀⢈⣀⡠⠞⠁⠀⠀⠀⠀⠈⠳⢤⣄⣀⣤⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⡔⠉⡀⢀⠑⢄⠀⠀⢠⠞⢁⠀⡈⠲⡀⠀⠀⡰⠊⡀⢀⠉⢆⠀⠀⢀⠔⢁⠀⣈⠱⡄⠀⠀⠠⢊⡀⢀⡉⢢
⠀⠀⠀⠀⠀⠐⡀⢀⠁⠈⡀⢸⠀⠀⢨⠀⣈⠀⡁⠀⡀⠀⠀⡇⢀⠀⠈⡀⢸⠀⠀⢈⠀⠀⠀⢀⠀⡀⠀⠀⡇⢰⠤⠤⠤⠀⠇
⠀⠀⠀⠀⠀⠀⠑⠤⣁⣉⠴⠃⠀⠀⠈⠢⢄⣀⡨⠔⠀⠀⠀⠘⠤⣉⣉⠤⠊⠀⠀⠀⠣⢄⣀⡁⠔⠁⠀⠀⠈⠢⢑⣒⠡⠊


⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⣀⠀⠀⠀⠀⢀⠠⠤⢄⡀⠀⠀⠀⠀⣀⠤⠤⢀⠀⠀⠀⠀⢀⡠⠤⠄⡀⠀⠀⠀⠀⣀⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠎⣖⡆⢔⡢⢣⠀⠀⢰⠁⢂⠀⢐⠈⠄⠀⠀⡜⠐⡂⢈⠀⢱⠀⠀⢠⠃⢰⠀⡖⠈⠆⠀⠀⡜⢡⣂⢀⡦⠑⡀
⠀⠀⠀⠀⠀⠈⡄⠨⡄⡰⠀⡸⠀⠀⠰⡀⠀⢰⡄⡖⢛⠄⠀⢇⠀⠤⠤⡀⠸⠀⠀⠸⡀⢀⠠⠘⠃⡄⠀⠀⢃⢨⠂⠐⡅⢠⠃
⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⠊⠁⠀⠀⠀⠙⠢⠤⠐⠉⠁⠀⠀⠀⠑⠠⠄⠒⠁⠀⠀⠀⠈⠂⠤⠔⠊⠀⠀⠀⠀⠑⠫⠌⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⠔⠂⠒⠦⡀⠀⠀⠀⡠⠒⠂⠒⢄⠀⠀⠀⢀⠔⡒⠒⠢⡀⠀⠀⠀⡠⠐⠐⠒⢌⢁⡄⠀⢀⡤⠒⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠃⠐⠒⠐⠀⠱⠀⠀⢘⠀⠩⠀⠅⠀⠃⠀⠀⡇⠈⠆⡰⠁⢸⠀⠀⠰⠁⠠⠀⠠⠀⠃⠀⠀⡎⠀⠒⠐⠂⠈⡄
⠀⠀⠀⠀⠀⠀⢢⡈⢶⠖⢁⠜⠀⠀⠘⣄⠐⠉⠂⡠⠃⠀⠀⠣⡀⠏⠹⢀⠜⠀⠀⠘⢄⠓⠤⠐⣡⠃⠀⠀⠱⡀⠼⠻⢀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠁⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠁


⠀⠀⠀⠀⠀⠀⣰⣊⣁⣈⣑⡄⠀⠀⢀⠔⠉⠀⡉⠢⡀⠀⠀⡠⠊⠁⠈⠑⢄⠀⠀⢀⠔⡩⠀⢉⠢⡀⠀⠀⠠⠊⠁⠀⠉⢢
⠀⠀⠀⠀⠀⠰⠓⠄⠚⠃⠐⢻⠀⠀⢈⠀⢈⠀⡁⠀⡁⠀⠀⡇⢤⠅⠨⡤⢸⠀⠀⢸⠀⠐⠀⢒⠀⡁⠀⠀⡇⠀⠉⠈⡁⠀⠇
⠀⠀⠀⠀⠀⠀⠱⢄⡀⢊⡡⠂⠀⠀⠈⠢⣀⠁⣈⠔⠁⠀⠀⠑⢌⡒⢒⡡⠊⠀⠀⠈⠢⣈⠒⣉⠴⠁⠀⠀⠘⠦⣈⣁⡠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣿⣿⢿⣷⡀⠀⠀⠀⠀⠀⢘⣷⢿⣿⣿⡿⣾⡃⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣾⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⣼⣿⣶⣿⣿⣶⣿⣧⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⢿⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⣍⡉⢉⣩⣿⠇⠀⠀⠀⠀⠀⠘⣿⣿⡉⠉⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⣥⣿⣿⣬⣿⣷⠀⠀⠀⠀⠀⢸⣿⣯⣿⣿⣯⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠿⠿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣏⢿⣿⡟⠀⠀⠀⠀⠀⠸⣿⡟⢻⣿⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⠿⡿⠿⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⣾⣶⣾⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣙⣿⣟⣹⣿⡆⠀⠀⠀⠀⠀⣼⣿⣋⣿⣿⣙⣿⣧⠀⠀⠀⠀⠀⢰⣿⣏⣻⣿⣋⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⢿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠻⢷⣾⣿⣶⠿⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠻⣿⡿⢻⣿⡄⠀⠀⠀⠀⠀⣰⡟⠛⠛⠛⠛⢻⣆⠀⠀⠀⠀⠀⢠⣿⡟⣻⣿⡟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣤⣾⣷⣴⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣷⣿⡿⠁⠀⠀⠀⠀⠀⠘⢿⣿⣭⣭⣿⡿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣾⣿⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⡐⠀⢀⠀⢀⠈⠢⠀⠀⠈⠀⡀⢀⡀⠀⠄⠀⠠⠀⢠⠀⢠⠀⠠⠀⠀⠔⠁⡀⠀⡀⠈⠄⠀⠠⠂⢀⡀⢀⠀⠑⡀
⠀⠀⠀⠀⡀⠀⠈⠀⠉⠀⠀⠀⢸⠀⠀⢁⣀⠁⠀⠀⠀⠄⠠⠤⠀⠠⠤⠀⠂⠈⠀⠀⠁⠀⠁⠀⢸⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⠜⠀⠀⠢⡀⠀⠀⠀⡠⠃⠀⠀⢄⠐⠤⠄⢁⠔⠀⠀⠢⡀⠀⠀⠀⡀⠂⠀⠈⢄⠀⠈⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⢀⠀⠉⠀⠈⠀⢄⠀⠀⡀⠈⠁⠀⠉⠢⡀⠀⢀⠄⠉⠀⠈⠑⢄⠀⠀⡠⠊⠁⠀⠍⠀⡀⠀⢀⠔⠈⠀⠈⠁⢀
⠀⠀⠀⠀⠁⠀⠰⠀⠐⠀⠈⠀⢰⠀⠀⠁⠀⠃⠀⠐⠀⠀⠀⠘⠀⠐⢀⠀⠀⠐⠀⠀⠒⠀⠂⠀⢰⠀⠈⠀⠀⠀⠐⠂⠀⠁
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⡠⠀⠈⠄⠀⢖⢶⠂⢀⠄⠀⠠⡀⠀⠀⠀⠘⠠⠀⠈⢄⠀⠀⠀⠀⠀⠌⠀⠠⡀⠀⠀⠠⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠐⠊⠀⠀⠀⠀⠑⠀⠀⠒⠁⠀⠀⠀⠈⠂⠀⠀⠊⠀⠀⠀⠀⠑⠀⠀⠒⠀⠀⠀⠀⠈⠒⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠂⠀⠐⠠⡀⠀⠀⠀⠄⠀⠀⠀⢄⠀⠀⠀⡠⠐⠀⠐⠠⡁⡤⠀⢀⠄⠀⠀⠀⢄⠀⠀⠀⡠⠐⠀⠀⠠⡀
⠀⠀⠀⠀⠎⠀⠰⠀⠰⠀⠀⠀⢠⠁⠀⠄⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃⠀⠀⠀⠀⠀⢡⠀⠐⠀⢠⡀⢀⡀⠈⠂
⠀⠀⠀⠀⠄⠀⠀⢤⠀⠀⢀⠀⠘⠀⠀⠔⠒⡀⠀⡐⠀⢀⠀⠀⣀⣀⠀⢀⠀⠀⡀⠀⠀⢀⠠⡒⠚⡂⢀⠀⠠⠒⠂⡀⠀⠄
⠀⠀⠀⠀⠈⠂⠄⠀⠀⠐⠀⠀⠀⠐⠀⠁⠀⠡⠀⠀⠀⠀⠂⠄⠀⠀⠄⠂⠀⠀⠀⠠⠀⠀⠀⠐⠊⠀⠀⠀⠌⠐⠂⠤⠂

⠀⠀⠀⠀⠀⢀⠀⠤⠄⡀⠀⠀⠀⠀⣀⠠⠤⢀⠀⠀⠀⠀⠀⡀⠤⠄⣀⠀⠀⠀⠀⢀⠠⠤⢀⡀⠀⠀⠀⠀⡀⠤⠄⢀
⠀⠀⠀⠀⡐⠡⠄⠀⡤⠠⠠⠀⢀⠀⠀⠀⠀⠀⠈⠄⠀⣰⠁⠀⢀⠀⠀⢠⡀⠀⠌⠀⠀⠀⠀⠈⢂⠀⠠⠀⢀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⡀⠈⢊⣀⢈⠁⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠍⠂⠐⠈⠐⠀⠊⠅⠠⠀⠤⠀⠀⠤⠄⢸
⠀⠀⠀⠀⠑⢄⠈⠀⠈⠀⠌⠀⠀⠢⡀⠀⠂⠀⡠⠁⠀⠈⢄⠀⠀⠀⢀⠔⠀⠀⠡⠈⠂⠀⠊⡠⠂⠀⠈⠄⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠈⠁⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀

⠀⠀⠠⠀⠠⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⢥⣤⣥⡀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠤⠀⠤
⠀⠀⠐⠒⠚⠀⠀⠀⠀⠀⠠⠊⠂⠀⠀⢐⠒⠚⠀⠀⠀⠜⠋⠁⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃

⠀⡔⠀⣴⢀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠉⠉⠀⠉⠉⠀⠀⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛
⠀⠀⠠⠀⠠⠀⠀⣁⠀⡀⠀⡀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⣀⡀⠀⠀⢿⠀⠀⠀⠀⠸⠇⠀⠀⣀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠈⠀⠈⢀⠀⠀⣠⠉⣉⠑⡀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠤⢀
⠀⠀⠐⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡂⠀⠀⠀⠻⠃⠻⠃⠀⠀⠐⠃⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⣒⠀⠀⠀⣐⠀⢀⡂⠀⠀⢄
⠀⠀⠠⠀⠠⠀⠀⠀⠀⡄⠠⡄⠀⠀⠺⣷⠖⢶⡿⠀⠀⠀⠄⠀⠄⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡄⠀⡄
⠀⠀⠀⠒⠐⠀⠀⠀⠀⠁⠆⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠲⠶⠂
⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠉⡀⠀⠐⡐⠆⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠄⠀⠀⠐⠛⠻⠟⠓⠀⠀⠐⡄⠀⡠⠠
⠀⠘⢗⡂⣚⠇⠀⠀⠀⠀⠀⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠠⣬⣴⣤⣥⠀⠀⢆⠴⠀⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⢀⠀⢀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⣀⡈⢢⠀⠀⡐⡀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢀⣀⠀⢀⣀⠀⡄
⠀⠀⠨⠀⠀⠶⠀⠶⠀⠀⠀⠀⠀⠀⠰⡆⠀⢴⠀⠀⡇⠀⠀⠀⠶⠀⠈⠁⢀⢨⠀⠀⡀⠁⡐⠂⠰⡂⠀⢰⠀⠸⠀⠀⠈⠀⠉
⠀⠀⠀⠢⡀⠀⠀⠀⠀⡠⠁⠀⠀⢄⠀⠀⠀⠀⢀⠜⠀⠀⠐⠄⠤⠴⢖⣿⢇⠞⠀⠀⠠⡐⠂⠘⠐⠒⣠⠂⠀⠀⠢⡀⠐⠀⠐⠀⡠⠁
⠀⠀⠀⠀⠈⠐⠀⠒⠈⠀⠀⠀⠀⠀⠁⠂⠀⠂⠁⠀⠀⠀⠀⠀⠁⠂⠐⠊⠁⠀⠀⠀⠀⠈⠑⠂⠐⠊⠀⠀⠀⠀⠀⠈⠀⠀⠐⠉
⠀⠀⠀⠀⣄⠀⠀⠀⢠⡀⠀⠀⠀⣀⡄⠀⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢀⠂⠈⠣⠀⠰⠃⠈⠄⠀⢀⠀⠀⢀⠀⠀⠀⡠⠀⠀⠀⠀⢀⣀⢄⡀⠀⢱⠀⠀⠞⠉⠀⠀⠀⠈⠉⠃⠀⢀⠢⠖⠁⠀⠀⠓⠌⠆
⠀⠀⠰⠀⠄⠛⠀⠚⡀⠀⡄⠀⢀⠀⢀⣀⣀⣠⠄⠀⠃⠀⠀⠈⠀⠁⠈⠀⠀⢰⠀⠀⠄⠀⠙⠃⠘⠁⠀⠀⠀⠸⠀⠀⠷⠀⠲⠂⠀⡐
⠀⠀⠀⠁⢸⡇⠀⠀⣿⠔⠁⠀⠀⠢⢀⠈⠵⠶⡢⠎⠀⠀⠈⠢⣀⠁⠁⢀⡠⠂⠀⠀⠐⠤⣀⠐⠂⣀⠔⠁⠀⠀⠱⢄⠐⠛⠃⣀⠔⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠠⣀⣀⠀⢀⣐⢀⠀⠀⠀⡠⠂⠀⠀⠀⠰⡄⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⡀⢢⡀⠀⠀⢀⠄⠀⠀⠀⠠⣄
⠀⠀⢠⠁⢀⣈⣀⢉⣉⠀⠂⠀⠈⠀⠘⠃⠀⠘⠀⠈⡄⠀⠂⠀⢾⠗⠀⣤⡄⠀⠀⠀⠎⠀⠛⠀⠸⠛⠀⢀⠀⢠⠀⠀⠶⠀⠰⠆⠀⠂
⠀⠀⠘⡀⠀⠉⣛⣫⣅⡀⡄⠀⠠⠀⢀⣴⣶⣦⡀⢀⠁⠀⢀⠀⠀⢀⣀⡉⠁⠀⠀⠀⢇⠀⣴⠒⠲⣆⠀⡘⠀⠘⡀⠀⠢⣤⡤⠂⠀⠄
⠀⠀⠀⠐⠦⣚⣿⣟⡫⠊⠀⠀⠀⠑⠼⡣⠀⠜⠕⠁⠀⠀⠀⠓⠄⡈⠉⡁⠔⠁⠀⠀⠈⠳⠬⣀⣀⠥⠊⠀⠀⠀⠐⠤⡀⣾⢟⠡⠊
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡠⠂⠀⠀⠀⠐⢦⠀⠀⠀⠔⠁⠀⠀⠀⠙⢄⠀⠀⢠⠀⡁⠀⠀⠀⠐⠄⠀⠀⢰⠞⠄⠀⠀⠜⠳⠄⠀⠀⠔⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⠀⠀⠺⠂⠀⠃⠀⠁⠀⠀⠀⠀⠗⣀⠾⠀⠀⡆⠀⠀⠈⢁⡀⠀⣀⠀⠀⠀⠀⠀⡀⢴⠄⢠⠄⠀⠀⠀⢠⠀⠀⡦⠀⢠⡄
⠀⠀⠈⡄⠀⣴⠚⢲⠀⢀⠂⠀⠐⡀⠀⣞⡛⡇⠀⡀⠀⠀⢠⠀⠈⠁⠀⠉⠀⡰⠀⠀⠠⠀⢠⣴⣦⡍⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠈⠒⠤⠀⠤⠐⠁⠀⠀⠀⠈⠐⠠⠤⠄⠊⠀⠀⠀⠀⠑⠢⠄⠀⠤⠊⠀⠀⠀⠀⠈⠐⠀⠀⠂⠁⠀⠀⠀⠀⠁⠂⠀⠐⠊
⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠤⢄⠀⠀⠀⠀⢀⠤⠀⠀⠤⡀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⣀
⠀⠀⠀⡔⠁⠀⠀⢀⡀⠀⡀⠀⢠⠊⠀⠄⠀⠠⠀⠱⡀⠀⠐⠁⠠⠄⠀⠄⠀⢢⠀⠀⠐⡁⢤⠀⠀⡄⢈⠂⠀⠀⠼⠉⡁⠀⠈⡍⠳⡀
⠀⠀⢸⠀⠈⠟⠀⠀⠁⢀⡀⠀⠀⠀⠰⡦⠀⢴⠀⠀⠇⠀⠀⢀⢰⠄⠀⡶⠀⢀⠀⠀⠀⣷⠂⣁⣈⠒⣯⠐⠀⢰⠀⠀⠀⣀⠀⠁⠀⠠
⠀⠀⠈⢆⠀⠀⠀⠠⠄⡀⠀⠀⠈⢀⠀⠈⠀⠀⠀⠐⠀⠀⠐⠈⠆⠀⠀⠀⢀⠄⠀⠀⠘⢇⠸⠉⠙⠂⡹⠃⠀⠀⢂⠀⢸⠿⠷⠀⡠⠃
⠀⠀⠀⠀⠉⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠉⠒⠀⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣷⡄
⠀⣰⣶⣶⣤⣴⣦⡀⣿⣿⣿⣿⣿⣦⣀⢶⣾⣿⡷
⠀⢿⣿⣿⣿⣿⣿⣿⣞⣿⣿⠻⣿⣿⢉⣿⡃⠈⠁⠀⠀⠀⣀⣀⣀⡀
⠀⣼⣿⣿⣿⡀⠈⢻⣿⣿⠇⢠⣿⣣⣟⣀⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀
⠀⠹⠿⣿⣿⣿⣷⣄⠿⢟⣰⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⢿⣿⣿⣦⣄⡀
⢀⣤⣶⣶⣶⡶⠿⠛⠐⠿⣛⣭⣥⣤⣀⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣄
⢿⣿⣿⣿⠃⠀⢀⣴⣿⣷⡉⢿⣯⡛⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄
⣸⣿⣿⣿⣷⣾⣿⣿⣻⣿⣇⠀⣿⣿⣆⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⢻⣿⣿⣿⣿⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄
⠀⠉⠁⣾⣿⡟⠀⢸⣿⣿⣿⣿⣿⡏⠁⢀⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⣼⣿⡟⠀⠀⠀⠛⠛⠛⠿⠋⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄
⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢿⣿⣇⠀⠀⠀⠀⣠⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠸⣿⣿⡀⠀⠀⠀⠀⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠙⠃⠀⠀⠀⠀⠀⣾⣿⡿
⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃
⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣤⣤⣤⣤⣤⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠁⢀⠀⠀⠠⠂⠁⠀⢈⠀⡀⠀⠀⠀⠈⠀⡀⠁⠄⠀⠀⠠⠈⠁⠀⠈⠀⠀⠀⠀⠐⢁⠀⢀⠑⠄⠀⠀⡀⠈⠀⢀⠁⢂
⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠐⠀⠁⠀⠀⡀⠀⠄⠀⠠⠀⠀⠀⠸⢀⠌⠁⠈⢄⠠⠀⠀⠀⠐⠀⠀⡠
⠀⠀⠀⠀⠁⠈⠙⢉⠀⠊⠀⠀⠀⠄⡈⠛⠀⠐⠁⠀⠀⠢⢘⠛⠛⠡⠂⠀⠀⠀⠄⡀⠐⡁⠔⠀⠀⠀⠢⢀⠀⠀⠠⠂⠀⠀⠁⠌⡋⠘⡋⠈

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠑⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⡐⠁⠀⠀⠀⠑⠀⠀⢀⠈⠀⠀⠀⠈⠂⠀⠀⠰⠁⠈⠀⠈⠡
⠀⠀⠀⠀⡀⢈⣁⢈⡁⢀⠀⠀⠀⠐⠂⠀⠐⠀⡀⠀⠀⠀⠈⠀⡈⠁⢀⠀⠀⡤⢰⣅⣀⣰⠂⠆⠀⠸⠀⠒⠀⡔⠂⡸⠀⠀⡀⠘⠃⠀⠂⢀⠂
⠀⠀⠀⠀⠐⠈⡇⢸⠅⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠀⠀⠁⠔⠁⠀⠀⠀⠪⠙⠛⠉⠓⠀⠀⠀⠐⠀⠉⠉⠄⠀⠀⠀⠀⠀⠈⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠠⠂⠈⠁⠒⠄⠀⠀⢀⠔⡀⠉⡀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⠀⠀⠀⠔⠀⠉⠀⠀⠀⠀⠀⠀⠂⠉⠁⠂⡀⠀⠀⠠⠀⠈⠉⠐⢄
⠀⠀⠀⠠⠀⠴⠀⠠⠤⠀⠀⠀⠀⠀⠛⠀⠃⠀⠁⠀⠀⠀⠐⠂⠐⠂⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⠀⢰⠀⠤⠀⠀⠄⠰⠀⠀⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠢⠀⠿⢾⢠⠌⠀⠀⠀⠘⠻⠿⠟⡁⠁⠀⠀⠂⡙⠿⠿⠋⠀⠀⠀⠀⠄⠀⠆⠀⠀⠀⠀⠀⠀⡀⠒⠂⡀⠄⠀⠀⠡⡈⠠⠄⢁
⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠁⢀⡀⢀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠠⠀⢠⡄⣤⠀⢠⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⢄⠨⠤⠤⠄⠐⠀⠀⠀⡀⠀⠸⠠⠀⠆⠀⠀⢄⠈⠤⠌⠁⠀⠀⠀⠠⡀⠡⠤⠁⠀⠀⠀⠈⢀⠐⠴⠄⠀⠌⠀⠀⢂⠀⠡⠄⠁⠰
⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⡠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠡⠀⠀⠀⢁⡀⠀⣀⠈⠄⠀⠀⠁⠀⠀⢀⠀⠁⠀⠀⠌⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠈⠐⠀⠠⠂⠐
⠀⠀⠀⠀⠄⠈⢁⡘⠀⠠⠀⠀⠀⠀⢁⣀⠉⠀⠄⠀⠀⠔⠜⣁⡘⠀⠠⠀⠀⢀⠨⡅⠀⣭⠀⠀⠀⠐⡀⠀⣤⡄⠀⡘⠀⠀⠀⠀⢂⡁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⢄⢀⠔⠀⠀⠀⠀⠈⠂⠈

⢀⡴⠚⠛⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠙⠓⠦⡄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠙⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠋⠉⠛⠓⢦⡀
⡾⠀⣤⠄⠀⠀⢴⠀⠹⡄⠀⠀⠀⠀⢰⠃⢤⡄⠀⠀⢰⠆⠘⣆⠀⠀⠀⠀⠀⣸⠁⠠⠄⠀⠀⠤⠄⠙⡆⠀⠀⠀⠀⠀⡼⠁⠐⣦⠀⢠⣖⠀⠹
⣇⠀⠰⣤⣀⣀⠴⠃⢠⡇⠀⠀⠀⠀⢻⠀⠀⡴⠚⠛⠓⠦⠀⡿⠀⠀⠀⠀⠀⢻⠀⠀⠢⣤⡤⠖⠀⠀⡇⠀⠀⠀⠀⠀⢇⠠⣌⣁⣀⣀⣈⡴⢀
⠈⠢⣄⡀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⢀⣀⠜⠁⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠢⣝⡚⠉⠉⢀⣠⠞
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⣷⣆
⠀⣠⠴⠒⠒⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⠒⠦⣄⠹⣿⡂⠈⠉⠀⠀⠀⣠⠴⠖⠒⠲⠦⣄
⡼⠁⣠⡄⠀⠀⣤⡈⢳⡀⠀⠀⠀⠀⢰⢯⣦⣴⡄⢴⣶⣶⠝⡄⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⡀⠀⠱⡄⠀⠀⠀⠀⠀⣼⣧⣤⣤⣤⣴⣶⣾⣷
⡇⠠⣤⠤⠤⠤⠤⡶⢈⡇⠀⠀⠀⠀⢻⠀⠻⠟⣁⣈⡻⠋⠀⣿⠀⠀⠀⠀⠀⢿⠀⠘⠛⠁⠀⠙⠁⠀⡇⠀⠀⠀⠀⠀⣿⢿⣿⣿⠟⢻⣿⣿⠿
⠙⢄⡘⠦⠤⠤⠞⣁⡞⠀⠀⠀⠀⠀⠈⢧⣀⠀⠈⠉⠀⢀⡴⠃⠀⠀⠀⠀⠀⠘⢦⣀⠘⠒⠂⠀⢀⡼⠃⠀⠀⠀⠀⠀⠘⢦⡉⠀⠤⠔⠋⢁⡼
⠀⠀⠉⠙⠓⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⣤⣀
⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣶⣤⠶⠛⠁
⢠⠞⠋⠉⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⡴⢋⡍⠀⠉⠭⡓⢦⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠁⠈⠉⠳⣄
⡟⠀⠳⡦⠀⠰⡞⠁⠸⡆⠀⠀⠀⠀⣸⠁⢰⣴⠀⠀⡶⡆⠈⣧⠀⠀⠀⠀⠀⣼⠀⠠⠤⠀⠀⠤⠄⠈⡇⠀⠀⠀⠀⠀⡞⠀⠀⠒⠀⠀⠖⠀⠘
⢧⠀⠀⢠⡤⠤⠄⠀⢰⠇⠀⠀⠀⠀⠸⡀⠈⠀⡴⢶⡄⠀⢀⡟⠀⠀⠀⠀⠀⢹⡀⠀⢀⡤⠤⠰⡷⢀⡇⠀⠀⠀⠀⠀⢣⠀⠀⢧⣀⣀⠀⠀⢠
⠀⠓⠦⣄⣀⣀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠙⠦⢄⣉⣋⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣈⣀⣠⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀
⠀⢀⡤⠴⠶⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⢰⠋⢧⣤⠴⠶⠦⢤⣼⢈⡆⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠤⢤⡀
⣰⠋⣀⣀⠀⢀⣠⡉⢧⠀⠀⠀⠀⠀⢠⠏⠀⣀⠀⠀⢀⡈⠳⡄⠀⠀⠀⠀⠀⢱⠏⣀⠀⠀⠀⢀⡈⢻⡀⠀⠀⠀⠀⠀⣰⠋⣀⠉⠲⣤⣤⡉⢣
⡇⠐⣷⣻⠇⠸⣔⡽⠈⡇⠀⠀⠀⠀⢺⠀⠈⠉⠀⢀⢉⣁⡀⣷⠀⠀⠀⠀⠀⣿⠀⣈⣛⣀⣘⣛⣠⠄⡇⠀⠀⠀⠀⠀⡏⠀⠘⠛⠀⠻⠿⠿⢤
⠹⣄⠀⠴⣿⣷⠆⢀⡼⠁⠀⠀⠀⠀⠘⢆⠀⠀⠀⠸⠙⠿⣣⠇⠀⠀⠀⠀⠀⠘⣄⠹⢄⣉⣀⣠⠇⣰⠃⠀⠀⠀⠀⠀⠹⣄⠀⠦⣄⣀⡴⢂⡼
⠀⠈⠙⠒⠒⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠶⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠺⠿⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠒⠒⠋


⠀⠀⠀⠀⢸⣿⡏⣾⣿⣧⣾⣻⡏⣻⡏⢹⡷⣿⣛⣲⣟⣿⣾⣿⣿⣿⣿⡁⠀⢸⣿⣷⣿⡇⣰⣿⣦⣿⣟⣳⣿⣾⠀⠀⠛⠛⠛⢺⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⡀⢀⡀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠄⠀⠠⠀⠀⠀⢀⠀⠀⠀⠀⡈
⠀⠀⠀⠉⠀⠀⠋⠀⠀⠀⠀⠁⠘⠁⠀⠙⠀⡀⠀⠀⠀⠙⠃⡀⠙⠃⠀⠀⠀⠀⢠⣶⣶⣶⣦⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠐⠀⡀⠀⠀⠄⠀⠀⠈⠢⢈⠀⢈⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠
⠀⠀⢀⡀⠀⠀⢀⡁⠀⠀⠀⠀⣀⠀⠀⢀⡁⠀⠀⠀⠀⣀⡀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⡀⠀⠀⠀⠀⢀⡀⠀⠠⡤
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⠈⠁⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀
⠀⠀⠂⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡈⠀⡀⠔⠀⠀⠀⠡⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠐⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⣄⣄⣠⣠⡄⠀⠀⠀⠀⡌⣤⣤⣈⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢁⠀⠀⠀⠀⠀⠃⠀⠘⠃
⠀⠀⠂⡀⠀⠀⢀⠔⠀⠀⠀⠀⠙⠛⠟⠛⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠈⠁
⠀⠀⣄⡄⠄⠀⡤⣤⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⡀⣄⢀⢨⡀⠀⠀⢀⣀⣀⡀⢀⣀⣀⡀⠀⠀⠀⢀
⠀⠈⠑⠄⠊⠁⠠⠂⠀⠀⠀⠀⠘⠀⠘⠃⠀⠀⠀⠀⠀⢻⠏⠈⠿⠃⡀⠀⠘⠿⠿⠟⠹⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠂
⠀⠀⠂⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⠛⠛⢃⠐⠀⠀⠀⠢⡘⠶⠶⢋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠐⠾⡞⠒⢲⣶⢶⢶⡆⠀⢠⠡⠤⠄⠄⠤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠋⠀⠘⠁⠀⠀⠀⠈⡛⠛⣛⡛⠛⠛⠃⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠛⠉⠉⠉⠉⠛⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⢀⣠⠴⠒⠋⠉⠉⠁⠉⠉⠙⠒⠦⣄⠀⠀⠀⠀⡷⢦⡀⠀⠀⠀⠐⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡤⠞⠉⠀⠀⢀⣀⣤⠤⠤⠤⠴⠤⠤⠤⢬⣙⣦⡀⣰⡃⠀⠹⡄⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⢰⡷⠋⠀⢀⡤⠖⠊⠉⠀⣀⣠⡤⠤⠶⠒⠒⠛⠛⠛⠛⠛⢧⠈⠳⡄⢹⡄⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⢠⠟⠀⡠⠚⠁⣀⠠⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠘⡄⡇⠀⠀⣦
⠀⠀⠀⠀⠀⢀⠏⡠⠋⣠⠖⠋⠁⣀⣀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠣⣀⡀⠀⠀⠀⠀⠹⡄⢰⣿⠀⠀⠁
⠀⠀⠀⠀⠀⣾⠞⡵⠋⠀⠀⣀⣬⠶⠒⠒⠒⠦⣄⠀⠀⠀⠀⣀⠤⠤⠬⢭⣕⡀⠀⠀⢷⢸⡇
⠀⠀⠀⠀⣸⣿⠞⡇⠀⠀⠀⠻⡏⠀⢠⣿⣿⣤⠘⡆⠀⠀⢰⠁⣶⣿⣄⡀⠘⣿⠂⠀⢸⣿⠁
⠀⠀⠀⢀⡟⢹⡀⡇⠀⠀⠀⠀⠃⣀⣈⡻⠟⠋⢰⠁⠀⠀⢸⠀⠻⠿⠟⠁⣠⠁⠀⠀⢸⢉⡇
⠀⠀⠀⠈⠁⠀⠙⢷⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠓⠋⠉⠉⠉⠁⠀⠀⠀⣼⠞
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⢾⡙⠦⣄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⣰⡏⣀⠴⢋⡷
⢀⣀⡠⠤⠤⠝⠂⡀⠙⢦⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣠⣼⡿⠋⠀⠐⠯⠤⠤⢤⣄
⣞⡭⠭⠭⠀⠀⠈⠉⢳⢸⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢺⠟⠙⡇⡞⠉⠁⠀⠀⠭⠭⣝
⢣⡤⠤⠤⠴⠶⠖⣶⠋⠘⣇⠀⠀⠀⡰⢫⡿⡓⠒⢒⣶⡒⠒⣿⠙⣄⠘⠮⠷⣾⠁⠑⣶⠶⠤⠤⠤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⠶⠶⠊⠁⣸⠁⠈⠒⠻⣤⠋⠒⠘⡇⠈⠓⠶⠟⠃⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⡤⠞⢹⠀⠀⠀⠀⠀⠀⠀⠀⢽⠢⢤⣀⣀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣄⣀⣀⣀⣀⣤⡤⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣞⠦⣤⣤⣤⡤⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣠⠞⠘⠧⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡘⠳⣄⠀⣠⠜⢃⣹

⠀⠀⠀⠈⠉⠀⠐⢄⠀⠀⠀⠀⠀⠠⠀⠈⠉⠁⠐⢄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠀⠀⠀⠀⠀⡠⠂⠈⠉⠁⠀⠄⠀⠀⠀⠀⠀⡠⠀⠀⠉⠁
⡀⠀⣴⡄⠀⢴⡦⠀⠂⠀⠀⠀⠀⠀⠔⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢤⠀⠀⠀⠀⠀⠐⠀⢤⠀⠀⠀⢠⠀⢀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠘
⠀⠄⠁⠄⠀⠄⢊⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠊⠀⠁⠀⠀⠀⠈⠀⠐⠄⠀⠀⢂⠀⠀⠀⠀⠀⠈⠀⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⡈⠀⠀⠀⠁⡠
⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢄
⡀⠀⣤⡄⠀⣠⣄⠈⠄⠀⠀⠀⠀⠀⣤⡄⠀⢠⣄⠈⢂⠀⠀⠀⠐⠀⣤⡄⠀⢠⣤⠀⠂⠀⠀⠀⠐⠀⣠⡄⠀⢠⣤⠀⠀⠀⠀⠀⠀⠁⣠⣄⠀⢠⣤
⠇⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠸
⠀⠀⠐⠒⠒⠒⠂⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠐⠀⠀⠢⠤⠔⠀⠠⠂⠀⠀⠀⠀⢄⠑⠤⠀⠤⠊⠀⠀⠀⠀⠀⠈⢄⠑⠤⠀⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⢿⡏⠛⠿⠉⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣀⠤⠒⠈⠁⠀⠀⠀⠀⠉⠉⠒⠤⣀⠀⣀⡾⠇⠒⠂⠀⠀⠀⠒⠢⠌⣹⣆⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠰⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠖⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠁⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠁⣠⡤⠶⠖⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠁⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣀⣤⣤⠀⠙⣦⠀⠀⠀⠀⠀⣠⠞⢉⣀⣀⠀⠈⠳⣆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⣽⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⣿⣿⣿⣤⣄⢸⡇⠀⠀⠀⢠⡏⢰⣿⣿⣯⣀⡀⠀⢈⡆⠀⠀⠀⠀⠀⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⢿⣿⣿⡿⠃⢸⠇⠀⠀⠀⠘⣇⠸⣿⣿⣿⣿⠇⠀⢨⡇⠀⠀⠀⠀⠀⣽⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣼⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠙⠆⢈⠉⣭⠡⠤⠤⠟⠀⠀⠀⠀⠀⠀⡿⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣾⠋⠻⢦⣀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⣀⡴⠞⠙⣷
⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠉⠳⢦⣄⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠶⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⡴⠞⠋⢀⣤⠞⠁
⠀⣠⠶⠖⢒⡛⠛⠛⠋⢉⣀⣀⠀⠘⣧⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⣴⠟⣽⠋⠀⢀⣀⡉⠙⠛⠛⢛⣒⣶⠶⣤
⣼⢛⣉⣉⣬⣅⠀⠀⠀⠈⠉⠉⢻⡀⣞⠀⠀⠀⠉⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠁⠀⣿⠀⡖⠁⠉⠀⠀⠀⠀⢨⣭⣭⣁⡉
⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠃⢻⡀⠀⠀⠀⠀⠀⢙⡷⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡞⠋⠁⠀⠀⠀⢀⡿⠈⢧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠘⠷⠶⠚⠛⠛⠛⠛⠛⠋⠹⡏⠀⠀⠘⣧⠀⠀⠀⠀⣠⡞⠁⠀⣿⣌⠉⠙⢛⣻⢿⣿⣟⠋⠉⢿⡄⠈⢳⣄⠀⠀⠀⠀⣸⠃⠀⠀⢩⡏⠙⠛⠛⠛⠛⠛⠓⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠘⠷⣤⡴⠞⠋⠀⠀⢠⣿⠈⠦⠒⠉⢻⡿⡿⠉⠑⠎⠸⣇⠀⠀⠙⠳⠦⠤⠾⠃⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣿⠀⠀⠀⠀⢠⣴⣷⠀⠀⠀⠀⣿⢦⣀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠤⡤⠤⠤⠶⠚⠋⠀⠀⢛⠀⠀⠀⠀⠘⠙⠻⡇⠀⠀⠀⢸⡀⠉⠛⠶⠤⢤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣶⣶⣿⣧⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿⣿⣿⢿⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠻⢿⣿⠟⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠓⠒⢲⡆⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢨⡄⠀⣸⠁⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⣸⠇⠀⢿⡀⠀⠀⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⣴⠟⠁⠀⠀⠀⠻⣦⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⢀⡀⣀⣀⣀⠀⠀⣸⣧⣤⣤⣤⣬⣷⡄⣀⣀⣠⣾⣥⣤⣤⣤⣤⣿⡀⠀⠀⠀⣀⣀⡀⠀⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠖⠒⠒⠒⠒⠒⠒⠶⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠿⠿⠿⠿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⢿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠐⠿⠛⠉⠀⠀⠀⠀⠀⠉⠙⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⢀⡜⠀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣦⣄⠀⢣
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣦
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⡇⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢹
⠀⠀⠀⠀⢸⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠦⠤⠤⠤⠤⠤⠤⠴⠒⠒⠋⠁

⠀⠀⠀⠀⠀⡀⠠⠤⠀⡀⠀⠀⠀⠀⠀⠀⡀⠠⠤⢀⡀⠀⠀⠀⠀⠀⢀⠀⠤⠤⢀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⣀
⠀⠀⠀⠠⠊⢀⠀⠀⢀⣈⠠⡀⠀⠀⠐⠁⠀⠀⠀⠀⠈⢢⠀⠀⠀⡐⠁⠀⠀⠀⠀⠈⢆⠀⠀⢀⠈⡀⣀⠀⢀⠀⠑⠄⠀⠀⠠⠊⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⡁⢠⡴⢐⣤⠀⠆⢁⠀⠀⠀⠀⣀⡁⢈⣀⠀⠀⡇⠀⢠⠀⢠⡄⠀⠰⠛⠁⠘⡇⠀⡈⠀⠀⣤⠂⣤⠄⡀⢸⠀⠀⡆⠀⠉⠳⠀⠞⠋⠀⢸
⠀⠀⠀⢂⠀⠀⠁⠀⠁⢀⢀⡆⠀⠀⠀⠁⠉⠤⠤⢋⠀⢠⠃⠀⠠⡀⠠⢀⣀⣠⣤⡖⣸⠃⠀⠰⠀⠠⠃⢠⠠⢩⠀⡰⠀⠀⢁⠀⠀⣀⡀⣀⠀⠀⡜
⠀⠀⠀⠈⠂⢌⣀⣂⣈⠥⠊⠀⠀⠀⠈⠢⢀⡀⢀⡀⠔⠃⠀⠀⠀⠈⠪⢅⣉⣴⡫⠗⠁⠀⠀⠀⠑⠤⣉⣉⣉⡡⠞⠁⠀⠀⠀⠑⠤⠀⠀⢀⠤⠊

⠀⠀⠀⢀⠴⣅⠀⠀⢀⡵⢆⠀⠀⠀⠠⠴⠂⠀⡀⠘⠳⢀⠀⠀⠀⡠⠈⠄⡀⠀⠤⠑⣄⠀⠀⠀⣴⣦⠀⠀⠀⣬⣦⡀⠀⠀⠀⠔⢁⠀⠀⠀⡁⠢
⠀⠀⠀⠂⠁⠙⢃⢀⣚⠁⠙⠆⠀⠰⠄⠀⠀⡘⠐⢀⠀⠐⡆⠀⠀⢈⠀⢠⡼⣤⡄⠀⠘⡄⠀⠸⠋⠀⣈⡄⣈⡀⠀⠑⠀⠀⡌⠞⠋⠐⠀⠂⠙⠒⢳
⠀⠀⠀⡄⠁⠈⠛⠈⢫⡀⠂⡌⠀⠰⠀⠄⢭⣤⣤⡤⢤⠀⠃⠀⠈⠐⢁⠈⠀⠈⢀⠁⢠⠇⠀⢠⠐⠠⠛⠀⠙⠁⠈⢠⠀⠀⠇⠁⠸⠗⠀⠻⠃⠈⡸
⠀⠀⠀⠘⢤⣿⠀⠀⠈⣿⠜⠀⠀⠀⠑⠌⢀⣠⡶⠾⡣⠎⠀⠀⠀⠑⢄⡈⠐⠈⣁⡠⠋⠀⠀⠀⠣⣄⠀⠐⠀⣀⡴⠁⠀⠀⠈⠦⡀⠘⠛⠃⣀⡴⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⡠⠀⠀⠀⠀⢤⡀⠀⠀⠀⢀⠄⠀⡀⠀⠀⠄⠀⠀⠀⠀⣠⠔⢀⠈⠀⠂⢄⠀⠀⠀⠀⣀⠤⠀⠀⠀⠤⡀
⠀⠀⠀⠌⠉⠉⠃⠀⠚⠓⠀⠄⠀⢀⠺⠀⠴⠀⠄⠶⠀⠹⡀⠀⢠⢃⢠⣶⡄⠀⣀⡀⠀⠀⠀⠰⠃⠰⡶⠀⢰⡷⠈⠃⠀⠀⡐⠁⢠⡌⠀⢡⡄⢹⢂
⠀⠀⠀⣰⠈⠛⠶⠶⠶⠂⠠⡀⠀⢠⠀⠀⠀⣀⣄⡀⠀⠀⡇⠀⢸⠀⠀⠉⠀⠀⠿⠃⠀⠀⠀⢁⠀⠀⣠⣤⣤⡐⠀⢰⠀⠀⡇⠀⢀⠘⠀⢁⡀⠂⢸
⠀⠀⠀⠡⣀⢀⣴⣾⣿⡷⡣⠃⠀⠀⠢⡀⣾⠛⠛⢻⢄⡴⠀⠀⠈⢦⡀⠀⠶⠶⠆⢀⠌⠀⠀⠈⢦⡘⠏⠀⠈⠓⣠⠊⠀⠀⠐⣄⠀⠉⣻⣥⠄⣠⠂
⠀⠀⠀⠀⠈⠑⠻⠿⠓⠊⠀⠀⠀⠀⠀⠈⠙⠛⠋⠛⠉⠀⠀⠀⠀⠀⠉⠒⠂⠒⠊⠁⠀⠀⠀⠀⠀⠉⠓⠒⠒⠋⠀⠀⠀⠀⠀⠈⠑⠺⠿⠓⠊⠁
⠀⠀⠀⠀⢀⡀⠄⠀⠄⣀⠀⠀⠀⠀⠀⣀⠄⠐⠀⠠⣀⠀⠀⠀⠀⠀⢢⠠⠀⠠⠄⡀⠀⠀⠀⠀⢀⡄⠒⠀⠐⠠⣀⠀⠀⠀⠀⢀⠄⠀⠂⠂⠠⡀
⠀⠀⠀⡰⠏⠀⢰⠀⠀⡈⢳⠀⠀⠀⢼⠁⠀⠁⡄⠁⠈⠳⠀⠀⢀⡄⣀⠀⠀⠀⢀⠈⢂⠀⠀⢠⠿⠋⠠⠀⠀⠙⠛⠆⠀⠀⠐⠁⠀⠀⠀⠄⠀⠈⢂
⠀⠀⠀⠀⠢⠈⠟⠀⠘⠣⠂⠀⠀⠈⠀⠢⠽⢃⣘⠻⠄⠀⡇⠀⠤⠈⠁⣤⠀⢀⡄⠈⠀⠀⠀⠀⠀⠀⠶⠁⠶⠆⠠⠀⠀⠀⡇⠁⠰⠦⠀⠶⠆⠀⢨
⠀⠀⠀⢂⠀⠠⡞⠛⣶⠀⢀⠃⠀⠈⢄⠀⢰⡏⢙⡇⠀⠠⠁⠀⠐⡄⢀⠉⠀⠐⠁⠀⡸⠁⠀⠘⡀⠀⣠⡶⣶⡏⠀⠎⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠑⠤⢀⣀⡠⠔⠁⠀⠀⠀⠀⠑⠠⠤⠠⠤⠊⠀⠀⠀⠀⠈⠢⢄⣀⣀⠤⠚⠁⠀⠀⠀⠈⠑⠠⠤⠄⠒⠉⠀⠀⠀⠀⠈⠒⠩⠭⠍⠚⠁
⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⠀⢀⡀⠤⠤⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡾⠁⠄⠠⠂⠓⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠈⢢⠀⠀⠀⡔⠁⠀⠀⠀⠀⠉⢆⠀⠀⢀⡜⢉⣁⢄⢈⡉⠙⡆⠀⠀⢀⡾⠋⠢⠀⠜⠛⢧⡀
⠀⠀⢀⠻⡀⢶⡆⠁⠘⠗⠀⠀⠀⠰⢀⠀⣀⡀⢀⣀⠀⠂⡇⠀⠈⠀⠀⣀⠀⢀⣀⠀⠈⡀⠀⠈⢹⣤⠕⠁⠨⢥⡼⠐⠄⠀⡎⢀⠘⡡⠁⢜⠃⡘⢱
⠀⠀⠀⡆⠈⠈⠀⠀⡆⠊⠑⢢⠀⠈⡄⠐⡘⠥⠤⢏⠀⢀⠃⠀⠀⡤⢂⡙⠤⠨⠃⠀⢰⠀⠀⠰⣾⠃⣴⠶⢶⡀⢻⡔⠀⠀⢃⠀⠀⣰⣶⣆⠀⠀⡸
⠀⠀⠀⠘⠦⣀⠀⠀⢊⡰⠖⠁⠀⠀⠈⠢⠀⣀⢀⡀⠐⠀⠀⠀⠀⠀⠨⣀⣀⣀⡀⠐⠁⠀⠀⠀⠉⠢⠍⠀⠈⠤⠊⠀⠀⠀⠈⠢⣄⡙⠩⢋⣠⠞
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢀⠀⠀⡀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⠀⠉⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣶⣶⣶⣦⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆
⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⢀⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⣸⣿⡟⠀⠀⠀⠀⢀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠘⠋⠀⠀⠀⣀⣀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⡀⠀⠛⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⣀⣤⡴⠶⠿⠛⠛⠿⠶⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣁⢀⣈⣉⡿⣶⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠩⡓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠃⠀⠁⠀⠀⠉⠀⠙⣅⠀⢀⡤⠄⠒⠒⠒⠒⠒⠠⠄⡀⠀⠈⠢⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⢀⡀⢀⣀⡀⠀⠉⢠⠋⠀⡀⠠⠶⠄⠀⠤⠄⣀⠀⠑⢄⠀⠙⢆⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠁⠀⠀⣠⣤⣌⠑⠄⠀⣴⣀⡐⠂⠈⠉⠐⠲⢤⡀⠑⢄⠈⢆⠀⠈⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢠⠃⠀⣠⠊⢁⡠⠤⠤⠽⣶⠴⠟⠉⠁⠀⠈⠉⠑⠢⣄⠉⢂⠀⠡⠈⣁⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠠⠆⠀⡠⢁⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠄⠀⠈⠣⡀⠢⠀⠆⠙⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡷⠀⠀⡄⠂⣤⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠦⢀⡀⠀⠀⠡⠀⠃⠀⡀⠀⠀⠘⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢸⡇⠈⣁⡄⠀⠀⣄⠀⠀⠀⠀⠀⡜⠀⢀⠀⠀⠈⠦⠀⠀⠀⣼⠀⣧⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡇⠀⣾⠀⠸⠁⠀⣠⣤⠀⢱⠀⠀⠀⠀⡇⠐⠿⠃⠀⠀⠐⠂⠀⠀⢧⡞⠁⠀⠀⡘⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠰⡆⢸⡄⢠⠀⠀⠈⠁⠀⡸⠀⠀⠀⠀⠐⢄⣀⠀⣀⡠⠃⠀⠀⢀⣀⠇⠀⠀⣰⠃⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠙⣇⠀⠀⠓⢄⣀⡀⠖⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢰⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠇⠀⠀⢹⣶⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠙⡀⠀⠀⠀⠀⢀⡴⠂⠖⠂⠲⡄⠀⠀⠀⠀⠀⣠⣾⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡏
⠀⠀⠀⠀⠀⢀⡴⠶⠶⠦⣾⡇⠀⠀⠀⠱⣄⠀⠀⠀⡟⠀⠀⠻⠂⠀⡀⠀⣀⣤⡶⠟⠋⢻⡄⠀⠐⠀⠀⠃⠀⠜⢡⣴⡟
⠀⠀⠀⠀⣰⠏⡠⢦⠀⠀⢸⠃⠀⠀⠁⠀⣾⠳⠶⣶⣧⣀⢀⣀⣠⠶⢻⣿⠋⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⢀⣠⣾⠏
⠀⠀⠀⠀⢿⣆⠀⠊⢠⠄⠁⠀⠀⠀⣠⡾⠃⠀⠀⠀⠈⢉⡽⣿⡀⠀⣠⠟⢷⣤⣤⣀⡀⠀⠀⠈⠙⠛⠾⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⣀⣤⡴⠞⠋⠀⠀⢀⡴⠚⠛⠻⣗⣈⣉⢉⣁⡠⠏⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀⣰⡏⠀⠀⠀⠀⠉⠀⠉⠈⠁⠀⠀⠀⠤⡀⠀⣹⠿⣦⠀⠀⠀⠀⠀⣠⡶⠟⠛⠻⠷⠶⣤
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠹⢄⡰⠃⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⢸⠈⢁⢠⣿⡀⣠⡴⠞⠛⠉⠀⠛⠃⣀⠰⢎⣻
⠀⣠⣤⣶⠿⠈⠳⢦⣤⣄⣀⣀⣀⠀⣴⠟⢣⣄⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⢶⣏⠀⠈⡿⠋⠀⠀⢀⣤⠞⠛⠿⠿⠷⠾⠋
⣸⠟⢀⠍⢠⢈⣓⣀⠀⠈⠉⠉⠉⠛⠋⠀⣸⡿⠉⢻⡗⠀⠀⠀⠴⡆⠀⠀⠀⣸⡇⠀⠀⠹⣦⡀⠁⢀⣤⠾⠋⠁
⠛⢿⡷⠶⣶⠟⠉⠉⠛⠛⠛⠷⠶⠶⣦⣴⠿⠁⠀⠈⣿⠀⠀⠀⢀⡀⠀⠀⠀⣿⠇⠀⠀⠀⠘⠷⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠻⣤⡀⠀⠈⠁⠀⠀⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⡰⠃⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⢐⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠰⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⡆⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⣰⡟⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢰⠀⠀⠀⢹⡇
⠀⠀⠀⠀⢰⣟⠀⠆⠻⠷⠏⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠈⠻⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠉⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⠁⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣆⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠾⠛⢿⡉⠂⣀⡀⣠⣴⣄⠀⠀⠀⠁⠀⠀⢀⣤⣤⣀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⠺⣿⠉⠈⣿⠟⠳⣶⠶⠾⠛⠋⠁⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣿⠀⠀⣿⠀⡀⢿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠛⠛⠛⠁⠀⣿⡀⠀⢻⡄⠀⠀⠉⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣭⣭⣴⢦⣭⣿⠃⠀⢸⣧⣶⣉⢉⣉⣿⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠏⠀⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⣤⣴⠖⠋⠁⠉⠉⠛⠦⣉⠓⢄⡀⢀⣀⣿⡇
⠀⠀⠀⢸⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⣏⣿⣇
⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⢀⣤⣶⣾⠛⢻⡟⣛⡿⡛⡶⢾⣳⠾⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⣄
⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⡿⠋⠀⠻⣼⣿⣿⠛⣮⣯⣿⣧⣵⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⢻⣿⣷⠀⠀⢀⣞⣀⢀⡀⣠⣦⣀⣰⢦⣀⡀⡶⣶⣦⣀⡀⢀⣀⠀⣀⡀
⠀⠀⠀⠀⠈⢿⣿⡆⢠⣿⢿⡭⠫⣿⢹⢹⢯⣭⢸⢫⣹⡇⡟⣿⢩⢽⠋⣍⣿⡩⣿
⠀⠀⠀⠀⠀⠘⣿⣷⠏⢸⡿⢧⡿⠮⠾⠞⠳⠷⠞⠾⠿⠷⠷⠿⠟⠾⠷⠿⠿⠷⠟
⠀⠀⠀⠀⠀⠀⢈⠁⠀⠈⠉⠉


⠀⠀⠀⡀
⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠻
⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⠏⠀⣀⡙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠉⢠⣄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣆⠀⠙⠁⢠⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣤⣤⣤⣴⣾⣶⣶⣶⣤⣄⡀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⠀⠀⠀⠀⣿⣿⣄⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⡀⢸⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣧⢠⣤⣩⣭⣭⣭⣭⡉⣹⣿⣿⣿⡿⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡻⢿⣯⣉⣁⣠⣾⡿⢋⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡉⠉⠙⠋⣁⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣾⠿⠟⠋

⠀⠀⠀⠀⢀⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠠⣄
⠀⠀⠀⢀⠔⠈⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⡠⠂⠁⠀⠀⠈⠐⢄⠀⠀⠀⠀⢀⠄⣠⡁⠀⠀⣉⠀⢄⠀⢀
⠀⠀⠀⠁⡐⢉⠂⠀⠠⢊⠑⡀⢂⠀⠀⠈⠀⢀⡀⠀⠀⣀⡀⠀⠡⠀⠀⢀⠂⠠⠐⢄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠧⢘⠀⠀⠀⢙⠠⠇⠀⠀⢐⠂⣀⠉⠉⠀⠀⠉⠍⢀⠐⣢⠀⠀⠀⢇⠸⠂⠀⠐⠋⠉
⠀⠀⠈⡀⠰⣦⣀⣀⣐⣰⣿⠂⠌⠀⠈⠄⢻⣶⣶⣶⣶⣶⣶⠟⡰⠀⠀⠀⡀⢀⠁⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠈⠢⢈⠁⠉⠁⢀⠡⠊⠀⠀⠀⠈⠢⢁⠂⠉⠉⠑⡀⠔⠀⠀⠀⠀⠈⠢⠁⠀⠀⠀⠀⡡⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⡀⢀⡀⠠⠄⠀⠀⠀⠀⠀⠠⠂⡀⠀⡀⠢
⠀⠀⠀⠀⠀⠥⠀⠀⠀⠤⠑⢄⠀⠀⠀⢀⠔⠈⠀⠀⠀⡀⡁⡢⢀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠠⠁⡐⠒⠂⠀⠠⠒⠢⠀⢁⠀⢰⠁⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⡌⢰⢁⣤⡀⠀⣠⣄⢱⠈⠄
⠀⠀⠀⠀⢇⠘⠀⠀⠀⠛⢀⠃⠀⠀⠈⠑⠤⢀⠜⠀⠀⠀⠠⠔⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢂⠰⣶⣶⣀⣒⣬⣿⠇⡐⠀⠀⠡⠘⢿⢿⣶⣶⣶⢿⡟⠠⠁
⠀⠀⠀⠈⠢⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠑⠄⡁⠈⠁⢀⠡⠊⠀⠀⠀⠀⠑⠀⢁⠒⠒⢂⠁⠐⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣒⠒⠉⠙⠉⠉⠉⠒⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠁⠀⠀⠈⠉⠓⠦⡀⠀⠀⡌⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢢⣼⠆⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠉⢢⡿⠋⠀⠀⠀⠁⠀⠀⠈⢷⡀⠀⠀⠻⠛⠛⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⣀⠤⠔⠒⠛⠉⠉⠉⠉⠉⢧⡀⠀⠀⠀⢀⠀⠐⠄⠈⢧⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠈⠀⠘⡆⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣠⠎⠁⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣀⡤⠔⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⣀⣀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⢸⠀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⡆⣶⡟⢋⣥⣆⠀⠀⠀⠀⠠⢖⣾⣟⢶⣦⠀⠀⠀⡇⠁⠀⠄⠀⠀⠀⢸⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠃⠈⠀⠈⠽⠋⠀⠀⠀⠐⠀⠈⠹⠟⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠂⠀⠀⠀⠀⠀⡼⠀⢺⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠧⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠚⠛⡽⢳⠀⠀⠀⠀⠀⣠⠠⠦⠀⢠⡀⠀⠀⠀⠀⠀⠀⣠⢎⡀⠀⢠⠀⠀⢠⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠺⡄⠈⢣⡀⠀⠀⢰⠛⠀⠀⠀⠀⠛⣆⠀⠀⠀⠰⠛⣻⠟⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⢀⠤⡀⠀⠈⠓⠦⢬⣦⣄⣀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣠⣴⣟⣁⣀⡠⠖⠊⠁⡠⠒⠄
⠀⠀⢀⣠⢤⠬⠧⠌⠢⡄⠀⠀⠀⠀⠀⠉⠙⠓⠒⣶⠒⠒⡞⠋⠉⠀⠈⠉⠉⠀⠀⠀⢠⠊⠀⠖⠒⠶⠶⢦
⠀⠀⠋⠉⠉⠀⠀⠀⢲⢼⡀⠀⠀⠀⠀⠀⣀⡴⠖⣩⡀⠈⠘⢉⡓⢀⡀⠀⠀⠀⠀⢀⡥⠐⠉⠀⠀⢈⣉⣉⠃
⠀⠀⠉⠈⠉⠀⠐⠂⠛⢶⠉⠒⢦⣀⡠⢞⡝⠴⣫⣿⡛⠤⠆⢸⣄⠀⠙⠦⣀⡴⠚⠁⣰⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠹⠀⣸⠀⠀⢻⡏⠀⠀⢠⠟⠈⠳⢄⡀⠘⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊⠁⠑⣄⠘⡇⠀⢂⠏⠀⠀⠀⠀⠉⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠚⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⡶⣀⣀⡠⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠀⠈⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢹⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠰⡆⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣿⣀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⢹⡵⠋⠉⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⣴⢶⣾⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢻⣿⡯⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣨⣿⣾⡸⣿⡿⣫⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⢳⣷⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣷⣿⣿⣿⡿⣛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⢷⣾⣩⣗⣻⠿⡛⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣦⠿⣭⢛⣑⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⣴⣾⠈⣃⢿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⢮⡿⠀⢠⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠇⠀⠰⢯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡁⠀⠀⣸⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠒⠄⢰⠐⠂⣦⠀⢰⢰⢢⢰⠀⠐⠂⣤⢰⡂⢰⡆⡆⡆⠀⡆⠀⣶⢶⡆⡆⢰⡔⠀⡆⢰⣶
⠀⠀⠀⠀⠀⠁⠁⠈⠈⠁⠁⠀⠀⠈⠉⠈⠀⠀⠀⠀⠈⠀⠀⠀⠉⠈⠀⠁⠀⠁⠈⠀⠁⠈⠃⠀⠁⠈⠉

⠀⠀⠀⠀⡠⠒⠉⠉⠓⢄⠀⠀⠀⠀⡠⠚⠉⠉⠓⢄⠀⠀⠀⠀⡠⠚⠉⠉⠓⢄⠀⠀⠀⢀⡴⠚⠉⠙⠲⣄
⠀⠀⠀⢰⠁⠘⠃⠘⠃⠀⡇⠀⠀⢸⠁⠘⠃⠘⠃⠈⡇⠀⠀⠸⠀⠘⠃⠘⠃⠈⡆⠀⠀⡌⠀⠐⠀⠺⠃⠘⠄
⠀⠀⠀⠈⢆⠰⣀⣀⠔⣠⠃⠀⠀⠘⢄⠠⠄⠀⠄⡠⠃⠀⠀⠘⣄⠢⠀⢠⠖⡰⠁⠀⠀⠰⡄⢦⣀⡠⠆⡴
⠀⠀⠀⠀⠀⠙⠒⠒⠊⠁⠀⠀⠀⠀⠀⠑⠒⠒⠊⠀⠀⠀⠀⠀⠈⠑⠒⠒⠋⠀⠀⠀⠀⠀⠈⠑⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⡠⠚⠉⠉⠑⢦⠀⠀⠀⠀⡠⡞⠉⠉⠷⢄⠀⠀⠀⠀⡴⠋⠉⠉⠓⢄⠀⠀⠀⢀⠖⠉⠁⠉⠙⢆
⠀⠀⠀⢰⠁⠘⠃⠘⠃⠀⡇⠀⠀⢸⠀⠘⠃⠘⠃⠀⡇⠀⠀⢘⠀⠘⠃⠘⠃⠈⡆⠀⠀⠎⠀⠘⠀⠘⠀⠈⠆
⠀⠀⠀⠈⢆⡠⠂⠀⠂⣠⠃⠀⠀⠘⢄⠀⠰⠆⠀⡰⠃⠀⠀⠘⣄⠻⣶⡾⢇⡰⠁⠀⠀⠘⢄⢢⣤⣤⢃⠜
⠀⠀⠀⠀⠀⠉⠒⠒⠈⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉⠀⠀⠀⠀⠀⠀⠉⠚⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡠⠊⡉⠉⡙⢢⡀⠀⠀⠀⡴⢊⡁⢉⡑⢦⠀⠀⠀⢀⡔⢋⡁⢉⡑⢄⠀⠀⠀⡠⠊⠉⠈⠉⢢⡀
⠀⠀⠀⢰⠀⠘⢃⡘⠃⠀⡇⠀⠀⢸⠀⠘⠃⠘⠃⠀⡇⠀⠀⢘⠀⠘⠃⠙⠃⠀⡆⠀⢰⡃⠘⠃⠈⠓⠀⡇
⠀⠀⠀⠈⢦⡴⠿⠻⠷⡠⠃⠀⠀⠈⢆⡰⠿⠿⠆⡰⠁⠀⠀⠘⢄⠰⠚⠲⢂⡴⠁⠀⠈⢧⡘⢿⡿⠟⡠⠃
⠀⠀⠀⠀⠀⠉⠐⠒⠉⠀⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠉⠒⠂⠉⠀⠀⠀⠀⠀⠉⠐⠒⠉
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡔⠀⠈⠈⠑⢦⡀⠀⠀⢠⠎⢀⠀⠀⠉⠢⡀⠀⠀⢀⠔⠊⠁⠈⠑⢦⡀⠀⠀⢠⠄⠀⠀⠀⠈⢢⡀
⠀⠀⠀⢰⡇⠘⠀⠘⠀⠀⡇⠀⠀⣏⠀⡘⠀⠘⢁⡀⣿⠀⠀⡏⠀⠈⠀⠈⠂⠀⣷⠀⠀⡇⠀⠘⠀⠘⠀⠀⡇
⠀⠀⠀⠈⢧⡐⠦⠔⠃⡠⠃⠀⠀⠹⣄⠉⢶⠒⡻⣠⠏⠀⠀⠳⣄⠻⣁⠀⠟⡠⠃⠀⠀⠳⣄⠐⠀⠈⠂⡔⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠉⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡔⢉⣀⢀⣙⣦⡀⠀⠀⢀⠔⠕⠀⠀⠝⢢⡀⠀⠀⢀⠔⢀⠀⠀⡑⢦⡀⠀⠀⢀⡄⠈⠀⠈⠑⢆
⠀⠀⠀⢸⠀⠣⠜⠈⠓⠁⣷⠀⠀⣿⠀⠈⠁⠈⠀⠀⣷⠀⠀⣾⠀⠘⠃⠘⠁⠀⡇⠀⠀⢼⠀⠙⠀⠘⠀⢸⠆
⠀⠀⠀⠘⢦⡀⠐⠐⠀⡰⠃⠀⠀⠙⢆⡐⠉⠉⠂⠠⠃⠀⠀⠙⢆⡈⠁⠁⢀⠜⠁⠀⠀⠘⢦⡀⠀⠷⠠⠊
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⡠⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠉⠉⠉⠉⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢤
⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⢀⡤⠤⢤⡀⠀⠀⠀⠀⣀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠱⣀⠀⠀⠣⡀⠀⠀⠀⠀⠀⢀⠜⠁⠀⢰⠋⠀⣀⠀⠙⣆⠀⡴⠋⠉⠉⠳⡄⠀⠙⣄⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⡰⠁
⠀⠀⠈⠣⡀⠀⠈⠀⠀⡀⠀⢀⠎⠀⠀⠀⡇⠀⣶⣿⣷⠀⢸⠀⠁⢰⣿⣷⠀⢸⠀⠀⠈⣆⠀⠀⣀⠄⠈⠁⠀⢠⠛⠁
⠀⡠⠔⠚⠁⠀⠀⠀⠀⠘⡄⡸⠀⠀⠀⠀⠱⡀⠈⠛⠁⠀⡸⠀⢄⠀⠉⠀⠀⡼⢀⠀⠀⢸⡀⡜⠁⠀⠀⠀⠀⠛⠢⢄⡀
⡎⠀⠀⠐⠁⠈⢳⠀⠀⠀⢸⡇⠰⢶⣀⠀⠀⠈⠒⠒⠒⠊⠁⠀⠀⠑⠒⠒⢋⣠⡴⠛⠆⠀⣯⠀⠀⠀⢠⠊⠉⠒⠀⠀⠈
⠳⣄⠀⠀⠀⣠⠞⢦⠀⠀⠊⣇⠀⠀⠉⠻⣖⠤⢤⣀⣀⣀⣀⣀⣤⡤⠶⠚⢉⡜⠀⠀⠀⢀⡏⠆⠀⣀⠜⢄⡀⠀⠀⢀⡠
⠀⢣⡈⠉⠉⠀⣀⠜⣣⡀⡄⠸⡀⠀⠀⠀⠈⢳⣶⣤⣄⣉⣉⣀⣀⣠⣴⣾⡿⠀⠀⠀⠀⡸⠀⡀⢠⠛⣄⠀⠉⠉⠉⢉⠇
⠀⠀⢏⠁⠀⠉⢁⡴⢃⡏⠀⠀⢳⡀⠀⠀⠀⠀⠙⢏⠉⠀⠀⠀⠀⠈⢙⡿⠀⠀⠀⠀⣰⠃⠀⠈⡇⠣⡀⠉⠒⠒⢘⠇
⠀⠀⠀⠉⠻⠭⠥⠔⠋⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠻⢆⣀⠀⣀⡽⠛⠀⠀⠀⢀⠜⠁⠀⠀⠀⠈⠲⠬⢍⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⣠⠖⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣒⣶⣦⣤⣤⣶⣖⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡤⠖⠚⠉⢩⣟⣥⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠻⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣀⡤⢶⡦⣄⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠇⠀⢠⠀⠀⢀⠀⠀⠀⠤⠤⠒⢀⡾⠋⠀⠀⠘⢦⠀⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠠⡀⢌⣆⣱⢄⣉⠙⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠈⡇⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣬⠽⢛⣥⣶⣯⠉⠉⠉⠁⠀⠀⠀⣠⣤⣀⣀⠀⣷⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢸⣴⡿⠛⣉⣁⡀⠀⠀⠀⠀⠀⠀⢙⣛⡿⢿⡇⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠈⡇⣠⠊⠉⠉⠉⠳⡄⠀⠀⠀⡼⠉⠉⠙⢣⡀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠻⣤⣷⠇⠀⠀⠀⠰⠆⢻⠀⠀⢸⡇⠀⠘⠃⠀⣧⡿⠀⣇⣀
⠀⠀⠀⠀⠀⠀⠀⡇⠈⢢⡀⠈⢹⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡅⠀⠀⠀⠀⣾⣧⠞⢉⡉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢷⢰⡇⠇⠀⠘⣆⠀⠀⠀⠀⢀⡼⢀⣀⡀⠳⢄⣀⣀⡴⠃⠀⡼⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⡂⣠⠀⠈⠛⠲⠶⠒⠋⠀⠉⠐⠛⠀⠀⠀⠀⠀⠀⠘⢀⠇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢾⡿⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⢤⣤⣤⣤⣤⡤⠴⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⢙⠿⠷⣿⣿⣗⢀⡀⢔⣲⣶⠞⠛⠋⠙⠛⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⡎⠋⠁⠀⠀⠀⠘⣧⣤⣕⣮⣻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠈⢹⣿⣿⣾⣬⣯⣞⣿⣬⣿⣿⣿⣿⣿⣿⣷⣦⣔⢀⠶⠀⠀⠀⢀⣼⣿⢏⡟
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠁⢀⣀⣤⠾⠛⠉⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⠛⢷⣿⣿⣿⡶⠔⠀⠠⠶⠾⠿⢻⣻⡄
⠀⣤⣤⣶⣖⣚⣉⣁⣤⣤⣶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣀⣠⣿⠟
⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣹⢶⢰⣦⣤⢦⠀⣰⡆⢸⢲⣰⣦⡖⣤⣒⡆⠀⣴⣿⣿⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢀⣀⡁⠀⠀⠙⣛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠲⠾⣿⣿⡿⣿⣶⣶⣷⣿⣿⠏⠁⠀⢶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⢀⣠⡴⠟⢡⡜⠋⠈⢿⣿⣧⣀⣀⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠤⠚⠋⠉

⠀⠀⠀⠔⠈⣀⠈⠐⠄⠀⠀⠔⢈⠀⢉⠂⡄⠀⢀⠔⠉⣀⠉⠢⡀⠀⢀⠔⠈⠀⠉⠢⡀⠀⢀⠐⠁⠀⠁⠢⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠈⠀⢘⠀⡄⠀⠀⠉⠀⠀⠠⠀⠄⢀⠀⠁⠁⡄⠀⠀⡆⠀⠀⠛⠀⠀⠡
⠀⠀⠘⢄⠀⠀⠀⢀⠜⠀⠐⢄⠀⠀⠀⢀⠄⠀⠐⡀⠀⠀⠀⢀⠄⠀⠠⡈⠛⠈⠛⢁⠂⠀⠠⡀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⢀⠄⠀⠀⢄⠀⠀⠀⠀⠄⠀⠀⢄⠀⠀⠀⡠⠄⠀⠠⢄⠀⠀⠀⡠⠄⠀⠠⢄⠀⠀⠀⡠⠀⠀⠠⢀
⠀⠀⠰⠁⡀⠂⠂⡀⠱⠀⠐⠀⠰⠀⠴⠀⢡⠀⠈⢀⣀⣒⣄⣀⠁⠀⡈⠀⠀⠒⠀⠀⠃⠀⡌⠀⠀⠠⠀⠀⠂
⠀⠀⠰⠀⠻⠒⠺⠋⠀⠀⠠⠀⠀⠀⠀⠀⡸⠀⢀⠘⠿⣿⠿⠋⡈⠀⢀⠘⠒⠒⠂⠊⡀⠀⢃⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠑⠢⠄⠠⠂⠁⠀⠀⠑⠠⠀⠄⠊⠀⠀⠀⠑⠠⠀⠄⠊⠀⠀⠀⠑⠠⠀⠄⠊⠀⠀⠀⠑⠠⠀⠄⠊
⠀⠀⠀⢀⠤⠀⠠⢄⠀⠀⠀⢀⠤⠀⠤⢀⠀⠀⠀⣀⠤⠀⠤⢀⠀⠀⠀⡀⠤⠀⠤⣀⠀⠀⠀⡀⠤⠀⠤⡀
⠀⠀⢰⠁⠀⠀⠀⠀⠱⠀⠰⠁⠀⣤⡄⠀⢡⠀⡐⠀⠀⣠⠀⠀⠃⠀⠘⠀⠀⣀⠀⠀⠂⠀⡌⠀⠀⣀⠀⠈⠂
⠀⠀⠰⠀⠀⠈⠁⠀⠠⠀⢠⠀⠾⠛⠻⠆⡀⠀⢀⠠⠄⠀⠀⠦⡈⠀⢁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠴⠀⠀⡌
⠀⠀⠀⠑⠠⠀⠠⠐⠁⠀⠀⠑⠤⠀⠠⠐⠁⠀⠀⠑⠤⠀⠤⠂⠀⠀⠀⠐⠄⠀⠤⠊⠀⠀⠈⠂⠤⠀⠄⠊
⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⢀⠊⠀⢀⡀⠈⢂⠀⢠⠊⠀⠀⠀⠉⢆⠀⠠⠊⠀⣀⠀⠑⠄⠀⠠⢊⠀⠠⠄⢑⡄⠀⠠⠈⠀⠤⠀⠑⡄
⠀⠀⢸⠀⣄⡀⣀⡰⠀⠀⠀⠀⠀⠚⠂⠀⢸⠀⠄⢠⣶⣶⣿⡶⠐⠀⠀⢸⣿⣿⣷⡮⠐⠀⡇⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠢⣈⠁⢉⡡⠊⠀⠈⠢⡀⠀⢀⡠⠂⠀⠈⠌⡉⠉⢙⠡⠂⠀⠘⠄⡀⠈⢋⠁⠁⠀⠐⢄⡀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⣶⣶⢶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⢶⣶⣶⢶⣶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠀⠉⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⣸⣭⠏⠉⠉⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠈⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢖⡰⠀⠰⣱⠄⠸⠀⠀⠀⠀⠀⠀⢰⠁⢰⣲⠄⠠⣞⡆⠈⡆⠀⠀⠀⠀⠀⠀⠁⠀⢆⠆⠀⢔⡂⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣀⡀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠂⢠⡀⠒⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡤⣄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠐⠛⠃⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠘⠋⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠡⡀⠙⠚⠙⠒⠃⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠂⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠐⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠉⠁⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠉⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠈⠉⠑⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠢⠀⢀⢢⠀⠐⠀⠀⠀⠀⠀⠀⢐⠁⡖⠒⢒⡒⠒⢢⠈⠀⠀⠀⠀⠀⠀⢀⠂⠀⡖⡄⠀⢔⡂⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠑⠒⠋⠑⠒⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠗⠒⠒⠅⠀⡰⠀⠀⠀⠀⠀⠀⠐⢄⠀⠢⠄⠀⠔⠀⡀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠞⠉⠉⠙⠢⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠤⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠤⠄⠂⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢠⡠⠀⠠⣠⠀⢣⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠞⠀⣒⠀⠀⢰⡢⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠊⠙⠀⠘⠉⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠙⠊⠀⠀⠑⠋⡀⡇⠀⠀⠀⠀⠀⠈⠀⠈⠛⠁⠀⠙⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⡔⠒⡒⣄⠀⡰⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣎⣱⠀⠂⢀⠇⠀⠀⠀⠀⠀⠈⢄⠀⠲⣶⣶⡶⠂⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⡀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⣀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢀⣀⠠⠄⠊


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣠⣤⠄⣄⣤⡨⣆⠀⠀⠀⠀⠀⠀⢀⠎⢀⠤⠀⠀⠠⣀⠡⡀⠀⠀⠀⠀⠀⠀⡐⢁⡀⠀⠀⠀⣀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣦⣝⣀⣘⣤⣗⣨⡄⠀⠀⠀⠀⠀⠰⠀⠲⠲⠀⠀⠖⠶⠀⠆⠀⠀⠀⠀⠀⠀⡇⠫⣈⡇⠀⣏⡠⠇⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢀⣄⣠⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢣⠀⢀⡀⠀⡀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠑⠤⣈⠀⠀⣁⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣙⢊⡡⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡶⠶⠿⠿⠿⠛⠻⠿⠿⠷⠶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠟⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠙⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⣰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠿⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣻⣿⣿⣿⣶⣾⣿⣿⣿⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠉⡉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊⢠⣴⠿⠛⠛⠷⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡂⠀⠀⠐⠒⢀
⠀⠀⠀⠀⠈⠉⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠟⠁⠀⠀⢀⠄⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠷⣦⡀⠰⣄
⠀⡄⠀⣴⡿⠿⣦⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠈⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢈⡿⠀⣿
⡀⠁⣼⡏⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢺⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠉⠀⠀⠉⣀⣴⠋
⣇⡀⣹⡇⠀⢀⡘⠀⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣠⡿⠛⠿⠿⠟⠋⠁
⠘⠟⠛⠁⠀⠈⠛⢷⣄⡈⢡⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡇⢀⣴⠆⠀⠀⠀⠀⠀⠈⠳⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣀⣤⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀
⢀⣤⣴⡌⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⣿⣦
⣾⣿⣿⣇⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⠻⠿⠛
⠀⠉⠉⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⢀⡄⠻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⢛⣀
⣴⣿⣧⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⢣⣤⣾⣿⣷
⠿⣿⠿⠋⠁⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄⠀⠀⠀⠸⣿⣿⡇⠀⠈⠛⠿⠛
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠙⡆⠀⠀⠀⠀⠀⠀⡐⠋⠉⢿⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠉⣠⠇⠀⠀⠀⠀⠀⠀⢃⡘⠁⣼⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⢀⠀⠀⠙⠊⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⢀⣄⣀
⠀⡞⠉⠉⠉⠙⢡⠀⠀⠀⠀⠀⠀⠀⣀⠿⠿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⣃⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⠉⠳
⡆⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⣀⠚⠉⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⢿⣆⠈⠓⣤⠀⠀⠀⠀⣠⠃
⠀⠉⠉⠁⠰⢦⡀⠈⢷⡀⠀⢀⣿⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣼⡅⠀⢀⡴⠉⢀⡰⠆⠈⠉⠉
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠹⣦⠛⠙⢳⡔⣤⡾⠁⠀⠀⠀⠀⢀⡤⠤⡤⢀⣠⠄⠐⢤⡄⠀⠀⢹⣿⡼⠋⠙⣴⠎⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠛⣄⠀⠀⢀⡴⠎⠁⣿⠇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠉⠁⠀⠀⠀⡇⠀⠀⠀⣿⡿⢦⡀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠔⠛⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⢹⣇⠀⠙⠢⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⢀⡠⠞⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣄⣤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠛⠛⠛⠛⠛⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣴⣷⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⣿⠀⠀⠀⣿⡇⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠀⢹⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⠀⠀⠀⢸⡇⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⣿⠀⠀⠀⢸⣇⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⢘⣿⠀⠀⠀⢸⣟⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣷⣄
⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣀
⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠍⠀⠈⠁⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠠⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠆⠀⠀⢠⣤⡄⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⡀⠀⠀⢰⠃⠤⠤
⠀⠀⠀⠀⠉⠀⠀⠀⢰⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢤⡤⠀⠀⠀⠐⡀⠂⠀⠀⠀⠂⠂⠀⠀⠀⠀⠤⢐⠇⠀⠀⢴⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠁⠀⠀⠀⠀⠰⠷⢶⠗⠀⠀⠀⠀⠀⠀⠚⠰⠄⢠⠌⠣⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠠⠠

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⢀⠀⡐⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠃⠀⠀⠀⠤⠍⠀⠀⠀⠈⠈⠁⠀⠀⠈⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⢱⠉⠀⠀⠀⠈⠀⠁⠀⠀⠀⢠⠠⡤⠄⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⢠⣀⠀⣢⡄⠀⠄⢀⡀⢦⠀⣠⡀⢀⣠⡀⢀⣀⠀⣀⠄⠀⠀⠈⠁⠀⠀⢠⠀⠉⠁⡄⢀⣾⣻⣟⣿
⠀⠀⠀⠀⠤⢅⠀⠀⠺⠾⢿⠖⠀⠁⠠⠽⡀⠀⠀⡶⠬⡷⠾⠀⢌⠁⠌⢀⠃⢢⡉⡴⢃⠄⠀⠀⠀⠀⡠⠀⢀⠈⠝⢣⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠁⠈⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠘⠀⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡰⢾⣿⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠆⠁⠀⠀⠄⠀⠀⠀⠠⢤⠅⠊⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢧⣷⣬⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣀⡄⠀⠀⠂⠓⠶
⠀⠀⠀⠈⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⠀⠀⠀⠈⠁⠐⠰⠀⠀⠠⠀⠡⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣄⣀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⢀⢀⡀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⢠⠁⠀⠀⠀⢀⠄⠀⠰⠾⢷⡆⠀⠀⠸⠭⠛⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠧⠀⠀⠿⠛⠛⠇⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠠⠒⠀⠀⠀⠀⡀⠀⠀⢀⡀⢀⠐⡀⠀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡰⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⡠
⠀⠀⠀⠾⡷⡷⠀⠀⠐⠶⠦⣄⠀⠀⠩⡄⠀⠃⠀⠈⠉⠛⠁⠀⠀⠀⠈⠀⠀⠀⠲⣆⠄⠀⠀⠀⠂⠒⠀⠀⠀⠰⠀⠶⠀⠀⠚⠇⠖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠳⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣶⣶⣶⣜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠏⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⡟⢦⣸⣦⡘⠀⠀⠀⢀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⣿⡸⡏⠛⡇⠀⣴⠺⣆⠀⠈⢀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠙⣯⡻⣿⣶⡙⠄⠀⠈⣟⡻⠃⠀⠀⣛⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣀⣠⡴⠾⠛⠚⠙⠛⠐⠺⢟⣛⠛⠀⠀⠀⠀⠈⠠⠔⠊⠁⣡⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢀⠔⠁⠀⠀⠀⠈⠉⠓⠒⠠⢤⡐⢂⣤⠄⠀⠀⠉⠓⣤⢤⡀⠀⠀⠀⢀⡄⠀⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⣿⠀⠀⠀⢸⣘⡷⠋⡆⠀⢠⣾⠧⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣰⠁⠀⠀⠀⣾⡅⠀⠀⠀⠀⣧⠁⢀⡄⠀⠐⠀⣀⠀⠂
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠸⠀⠀⢾⡁⠸⠄⠀⣼⠆⠀⠁⠄⠸⢁⠛⠂⠉⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠘⠀⠀⠀⠠⣸⡇⠐⡆⠀⢿⣦⠈⠳⡆⢠⣆⣀⣀
⠀⠀⠀⠀⠀⠘⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢰⡀⢧⢡⠀⢱⠀⢻⠊⠃⠀⢀⠀⡉⠉⠛⠇⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡀⠀⠀⠀⢀⠌⠀⠀⠀⠐⡀⠀⠀⡀⣷⢸⡄⠀⢤⡆⠀⠤⡀⠀⠀⠉⠑⠀⠢⠶⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢷⠸⣄⢱⡙⣆⢻⡄⠘⣷⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠢⡘⢶⢇⠙⡎⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠀⠓⠈⠈⢇⠃⠀⠀⣄⣀⣀⣀⠀⠀⠀⠀⢠⣤⣶⠶⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡭⠴⠾⠟⠀⠀⡛⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⣦⣴⣿⡷⠶⠆⢰⡶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠦⠼⣭⣏⣁⣁⣤⠠⠀⣤⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠤⢄⡀⠀⠀⠀⠀⠹⡉⠙⠉⠛⢠⢰⣧⣀⣴⠃⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠴⢦⣀⣷⣄⠀⣤⣼⠦⡙⠯⣁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠀⠀⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄
⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆
⠀⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆
⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆
⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⢿⣿⣿⡄⠀⠀⠀⠀⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⢠⣿⣿⡿
⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠏⠀⠀⠀⠀⢀⣼⣿⣿⠏
⠀⠀⠀⠀⠹⣿⣿⣷⡄⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⠃⠀⠀⠀⠀⢠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢂⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠀⠠⢖⢀⡒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢐⡲⡄⠀⠀⠀⢜⣳⠀⠀⠀⠀⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠄⠡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢄⠀⠀⠀⢀⠐⣤⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⡄⠀⢀⡼⣀⣁⣼⣀⠀⠀⠣⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⠁⣠⣇⠠⢈⡁⠤⢈⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⢙⠎⡴⢃⣀⣠⣅⣀⡜⢢⡻⣈⡽⠟⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠴⠾⢤⡗⠉⠀⠀⠀⠀⠉⠲⡧⠿⠀⠶⣄⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠓⢳⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣉⣉⣑⠢⣄⡼⠁⠈⠉⠓⠒⠒⠒⠒⠒⠒⠒⠉⢁⠀⠀⠀⠀⢀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⠋⠀⡀⠀⠱⣼⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⢇⣀⠠⠏⠀⠀⣸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠄⠒⠄⠐⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢬⣓⠆⠀⠀⣠⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠰⣄⣄⣿⡎⠁⠉⠀⠀⠀⠀⠀⠀⠈⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣉⡀⠹⣷⡀⠀⠀⢸⠉⠉⣹⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⣍⠇⠠⢁⠉⠀⠀⠀⠃⠠⠃⠀⠐⠈

⠀⠀⠀⢀⣤⠖⠚⠛⠒⠦⣄⠀⠀⠀⠀⠀⣀⡴⠒⠛⠓⠲⢤⡀⠀⠀⠀⠀⢀⣠⠶⠚⠛⠒⠦⣄⠀⠀⠀⠀⠀⣀⡴⠖⠛⠓⠲⢤⡀
⠀⠀⢠⡞⠁⢀⡀⠀⣀⡀⠈⢧⠀⠀⠀⣴⠋⠀⣀⠀⢀⣀⠀⠹⡄⠀⠀⢀⡞⠁⢀⡀⠀⣀⡀⠈⢧⠀⠀⠀⣰⠋⠀⣀⠀⠀⣀⠀⠹⡄
⠀⠀⢸⠀⠀⠘⠁⠀⠙⠁⠀⢸⡇⠀⠀⡇⠀⠈⠋⠀⠈⠋⠀⠀⣿⠀⠀⢸⠀⠀⠘⠁⠀⠙⠁⠀⢸⡇⠀⠀⡇⠀⠀⠋⢀⠈⠋⠀⠀⣿
⠀⠀⠘⣆⠐⢦⣀⣀⣠⠖⢀⡾⠀⠀⠀⢻⡀⠲⣶⣶⣶⡶⠂⣠⠇⠀⠀⠘⣇⠀⠀⠤⠤⠤⠀⢀⡼⠀⠀⠀⢻⡀⠴⠛⠉⠉⠳⠄⣠⠇
⠀⠀⠀⠈⠳⢤⣈⣉⣠⡴⠛⠁⠀⠀⠀⠀⠙⠦⣄⣉⣁⣤⠞⠋⠀⠀⠀⠀⠈⠳⢤⣀⣀⣠⡴⠛⠁⠀⠀⠀⠀⠙⠦⣄⣀⣀⣤⠖⠋

⠀⠀⠀⠀⢀⣤⠴⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠦⢤⣀
⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⣠⠞⣡⠖⠦⠶⠶⡌⢳⡀
⠀⠀⢸⠁⠀⠚⠓⠀⠻⠃⠀⢸⡆⠀⠀⡏⠀⠐⠛⠀⠈⠓⠀⠀⣷⠀⠀⢸⠁⠀⠻⠟⠈⠻⠟⠀⢸⡆⠀⠀⡏⠀⢧⣘⣠⣘⣁⡟⠀⣷
⠀⠀⠸⡄⠠⣄⠀⠀⢀⡤⠀⣸⠁⠀⠀⢷⠀⣠⠶⠚⠒⢦⡀⢀⡏⠀⠀⠸⡆⠠⣄⠀⠀⢀⡤⠀⣸⠁⠀⠀⢷⠀⠀⢩⣥⣬⡁⠀⢀⡟
⠀⠀⠀⠙⢦⣈⠙⠛⢋⣠⡾⠃⠀⠀⠀⠈⠳⣄⡀⠀⠀⣀⣤⠟⠀⠀⠀⠀⠙⢦⣈⠙⠛⢉⣠⡼⠃⠀⠀⠀⠈⠳⣄⡘⠛⠛⣁⣴⠟
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⠀⠀⣰⠞⠉⠀⠀⠀⠉⠳⡄⠀⠀⠀⢀⡶⠋⠁⠀⠀⠈⠙⢦⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠉⠳⡄⠀⠀⠀⢀⡴⠋⠁⠀⠀⠈⠙⢦
⠀⠀⢸⠃⠀⣷⣟⠀⣷⡇⠀⢹⡄⠀⠀⡟⠀⢰⣷⠄⢰⣷⠆⠈⣇⠀⠀⢰⠃⠀⠴⠦⠠⠶⠦⠀⢹⡄⠀⠀⡾⠀⠀⡶⠀⠠⡶⠀⠈⣧
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣇⠀⣀⠀⠀⠀⢀⡀⢀⡟⠀⠀⢸⡄⢀⡀⠀⠀⠀⢠⠀⣸⠇⠀⠀⣧⠀⠀⣀⣀⣠⡀⠀⢀⡿
⠀⠀⠀⠳⣄⠀⠉⠉⠉⢀⣰⠏⠀⠀⠀⠘⢦⡈⠓⠶⠖⠋⣀⡾⠁⠀⠀⠀⠳⣄⠙⠳⠶⠖⠀⡴⠟⠀⠀⠀⠙⣧⡀⠉⠉⠉⠁⣠⡾⠃
⠀⠀⠀⠀⠈⠛⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠒⠚⠛⠉
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢠⡴⠛⠉⠉⠉⠳⢦⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⣠⠞⠋⠉⠉⠙⠲⣄
⠀⠀⢠⡿⢶⣴⣶⢶⣴⣶⡶⢷⡀⠀⠀⡾⠉⠉⣭⠉⢉⣭⠉⠙⡆⠀⠀⢠⠏⠀⣲⡄⠀⣴⣆⠀⢳⡀⠀⠀⡼⠁⢠⣀⡄⢠⣠⠀⠘⣆
⠀⠀⢸⠀⠘⠛⠋⠀⠛⠛⠀⢸⠇⠀⠀⣧⣤⣤⣥⣤⣤⣥⣤⣤⡿⠀⠀⢸⡀⠀⠚⠁⠀⠈⠃⠀⢸⠇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⢧⡈⠳⢤⣤⡴⠋⣠⡞⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⢧⡀⠀⠒⠒⠒⠀⢠⡞⠀⠀⠀⠹⣄⠙⠦⣤⣤⠞⠃⣴⠃
⠀⠀⠀⠀⠙⠶⠤⠤⠴⠞⠋⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠙⠲⠤⠤⠴⠞⠋⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠚⠛⠛⠉⠉⠉⠉⠉⠙⠛⠒⠒⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠤⠤⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠴⠶⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠇⠀⠀⠀⠀⠈⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠛⡋⡙⠁⠀⠀⠐⠶⣤⡀
⠀⠀⠀⠀⠀⠀⡴⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡋⠀⠀⢀⡄⢸⠀⠀⢠⡄⠀⢸⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦
⠀⠀⠀⠀⠀⢀⡡⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢣⠀⠀⠘⠇⢸⠀⠀⠹⠇⠀⠸⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⡀⠀⡂
⡤⠖⠉⠀⠉⠈⠀⠀⠈⢢⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠓⠀⠀⠀⠊⠡⢀⡀⢀⠔⠁⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠔⠁⠀⠉⠉⠁⠈⠰⠆
⠑⢄⠀⠀⠀⠀⠀⠀⠀⣨⡀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠈⠁⠀⠀⠉⠁⠀⠈⢻⣦⠀⢀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⢤⠀⠀⠀⠀⠀⣿⣄⡀⠀⣠⡾⠋⠐⠀⠐⠒⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠙⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠁

⠀⠀⠀⣀⡤⠤⣄⡀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⣀⡤⠤⢤⣀⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⣀⡤⠤⣄⡀
⠀⣠⠋⠀⠀⠀⠀⠙⢦⠀⡔⠁⠀⠀⠀⠈⠳⡄⢀⡞⠁⠀⠀⠀⠈⠳⡀⠀⡴⠉⠀⠀⠀⠀⠑⡄⢠⠞⠁⠀⠀⠀⠈⢣⡀
⠀⡇⠀⠚⠀⠀⠛⠀⢸⣾⠀⠐⠃⠀⠐⠃⠀⣷⢸⠀⠐⠃⠀⠘⠃⠀⡇⢸⡃⠀⠓⠀⠀⠃⠀⢹⢼⠀⠘⠃⠀⠘⠂⠀⡇
⠀⠱⡀⠐⠄⡠⠆⢀⡜⠈⢆⠀⠀⠠⠐⠀⣠⠇⠘⢆⠀⠐⠒⠒⠀⣠⠃⠈⢧⡀⠐⠀⠐⠀⢠⠏⠘⣄⠀⠔⠀⠢⠀⡰⠃
⠀⠀⠉⠒⠦⠤⠒⠋⠀⠀⠀⠙⠲⠤⠴⠚⠁⠀⠀⠈⠑⠲⠤⠖⠊⠁⠀⠀⠀⠙⠲⠤⠴⠚⠁⠀⠀⠈⠓⠢⠤⠖⠊⠁





⣶⣶⡶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣤⠶⢚⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣖⡲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡞⢁⣾⣿⡟⠛⠻⣇⠀⠀⠀⠀⠀⢀⡿⠋⠙⢿⣿⣆⠹⣆⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣇⢼⣿⣿⣦⣀⣠⡿⠀⠀⠀⠀⠀⠸⣷⣤⣤⣿⣿⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⢀⣤⣶⣶⣦⣄⠀⢀⣴⣶⣶⣦⡀⠀⣀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⠛⠙⠻⣿⣿⣿⡿⠋⠙⠿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⢀⣀⣰⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⡀⠀⣀⢀⣀
⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣶⡀⠂⠀⠐⠰⠀⡃⠐⢚⡂⡀⠉⢉⣤⣠⣀⣁⢠⠀⠀⠀⠀⢀
⠀⠀⠀⣏⣀⡈⠉⢀⣈⠙⠻⣧⢉⠀⣈⣉⣉⢈⠀⠀⠉⠀⡀⠀⢠⠤⠄⠀⠦⠄⡄⠐⠒⠚
⢠⣄⠾⣿⢻⡷⣦⠨⠏⣀⠀⣿⣤⡀⠀⢀⣠⠂⠠⠤⠤⡀⠂⠤⠶⠖⠒⠒⢦⠀⠓⠀⠘⠛⠙⢀
⠀⢹⡇⣿⢸⠇⣟⢀⠁⠁⢀⡟⠠⠄⠐⠄⠔⠀⠔⠆⠠⠖⠐⠲⠀⠈⠃⠁⠀⣈⣀⡀⡉⠉⠉⠉
⠀⣄⢧⢻⠸⢁⡿⣿⡆⢐⡽⠀⣋⣛⣙⣘⡀⡀⠈⢁⡀⠀⢈⢉⣀⡀⠀⠠⠄⠀⢁⠴⣤⠤⠤⠠⠄
⠀⠈⠈⠘⠀⠀⢃⣬⡴⠛⣧⡀⠠⠌⡥⠄⠁⠤⠴⠤⠀⠀⠘⠷⠖⠆⠀⠀⠰⠶⠁⠐⠃⠂
⠀⠀⢰⠀⠀⢠⣎⣏⣀⣠⠞⠁⠑⠀⡐⠒⠰⠋⠒⠊⡰⠀⠀⠙⠁⠀⠈⠑⠃⠀⢉⡉⠁⠙⠁⠁⠁
⠀⡀⢉⠀⠀⠘⡌⠉⠉⠀⠀⠀⠀⠀⠈⢂⠛⠘⠊⠀⠀⣜⠉⠉⠁⠀⠈⢈⣁⡀⣀⠀⣀⢀⣀⣬
⢠⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠈⢈⣉⣁⣀⣀⣠⡤⢀⠀⢄⠄⣤⠈⠀⠀⠀⢤⠤⠠⠄⠁
⠀⢶⠄⠭⠀⠀⣬⠄⡀⠈⠀⠀⣈⡀⠉⠁⠠⠤⠤⠸⠤⢦⡤⠈⠀⠐⠀⠀⠤⠄⠀⠄⠀⢤⠤
⠀⠷⠒⠶⠖⠲⠦⠴⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⢀⠠⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⡀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢀
⠀⠀⠀⠠⠈⠀⠀⠀⠀⠈⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⡄⢠⣀⠀⣠⠀⠀⢰⠀⠀⠠⠀⣀⠀⠀⣀⠀⠀⢡⠀⢠⠐⠀⣄⠀⠠⠞⠉⠀⠃⠀⢰⠀⠁⢠⡄⢨⡄⠀⠀⠇⠀⠘⠀⠈⠛⠄⠰⠛⠁⠀⡆
⠀⠀⠀⢂⠀⠀⠁⠀⠉⠀⠀⡌⠀⠀⠄⠁⠈⠁⠀⠉⠀⢁⡎⠀⠈⡈⠀⠀⢀⣀⣤⣴⢂⠆⠀⠐⡀⠀⠦⠀⠄⠄⠀⢀⠆⠀⠐⡀⠢⢀⠀⣀⠀⠐⢀⠃
⠀⠀⠀⠀⠢⢀⠂⠀⢂⡠⠊⠀⠀⠀⠀⠢⢀⠀⠀⢀⡠⠊⠀⠀⠀⠈⠢⣁⠉⠱⢟⠫⠊⠀⠀⠀⠘⠦⣉⠀⠀⣁⠴⠃⠀⠀⠀⠀⠤⡀⠈⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠴⡀⠀⠀⠈⡰⢄⠀⠀⠀⠀⠤⠊⠀⠀⠘⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⢠⣤⡁⠀⠀⢀⣤⡄⠀⠀⠀⠀⠐⠈⠀⠀⠁⠠⡀
⠀⠀⠀⠊⠀⠙⠂⠀⠘⠁⢠⢃⠀⠀⠄⠀⠀⠠⠀⠄⠀⡠⠇⠀⢀⠁⠀⢠⣴⢀⡄⠀⠀⠆⠀⢠⠛⠀⢀⠂⠐⡀⠀⠉⠄⠀⠰⠰⠛⠁⠄⠀⠘⠓⠈⡄
⠀⠀⠀⡀⠀⠘⠛⠀⢛⣀⠀⠸⠀⠀⠀⠀⢀⣀⣀⣠⡄⠀⡀⠀⠘⠀⠄⠀⠁⠈⠀⠀⠀⡄⠀⠸⠈⠀⠙⠃⠘⠋⠀⠀⠄⠀⢠⠐⠀⠷⠀⠐⠗⠠⠀⡇
⠀⠀⠀⠐⢄⢿⠀⠀⠈⣿⡤⠁⠀⠀⠑⢄⠀⢉⣭⡷⢂⠔⠁⠀⠀⠑⢄⡀⠀⠀⢃⢀⠜⠀⠀⠀⠱⣀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠢⡀⠀⠺⠗⠀⣀⠎
⠀⠀⠀⠀⠀⠁⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠉⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠄⠂⠀⠂⠄⡀⠀⠀⠀⠀⣀⠐⠀⠀⠐⣠⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⡠⢂⠀⠀⠀⣀⠀⠀⠀⠀⠀⡠⠐⠀⠐⠀⡀
⠀⠀⠀⡐⠑⠛⠆⠀⠴⠲⠀⠄⠀⠀⠜⠁⢠⠀⠀⢠⠀⠑⠄⠀⢀⠎⠀⣤⣄⠀⢀⡀⠀⠀⠀⢀⠊⠀⣴⠁⢈⣶⠀⠑⡀⠀⢀⢊⠁⣄⠀⠀⣄⠈⠡
⠀⠀⠀⠀⠈⠲⣶⣤⣤⠖⠂⢸⠀⠰⠀⠀⠀⢂⣀⠂⠀⠀⠰⠀⢸⠀⠀⠙⠁⠀⢾⠇⠀⠀⠀⢸⠀⠀⠀⣀⣈⡀⠀⠀⡀⠀⠀⠀⢀⡉⠂⠐⣉⡀⠀⡇
⠀⠀⠀⢣⡂⠀⣠⣶⣶⣶⢆⠆⠀⠀⠢⠀⣴⠿⠻⢿⡄⡠⠃⠀⠀⢂⠀⠀⢠⣤⡄⠀⡠⠁⠀⠈⢦⠀⠾⠉⠉⠿⠀⡰⠁⠀⠘⢄⠀⠘⢛⣛⣀⠀⡰
⠀⠀⠀⠀⠙⠪⠝⠻⠭⠐⠁⠀⠀⠀⠀⠁⠊⠥⠤⠍⠂⠁⠀⠀⠀⠀⠑⠂⠤⠤⠄⠊⠀⠀⠀⠀⠀⠙⠒⠤⠤⠒⠋⠀⠀⠀⠀⠈⠑⠤⠚⠫⠅⠊
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄
⠀⠀⠀⠠⠞⠀⠢⠀⠀⠘⠦⡀⠀⠀⡠⠊⠁⠂⠀⠀⠈⠦⡀⠀⠀⡈⠀⡀⠀⠀⠀⠀⢂⠀⠀⠀⣴⠟⠀⠀⠀⠐⠛⠦⠀⠀⢀⠀⠀⠀⡀⠀⠀⠈⠂
⠀⠀⠀⠁⢀⠐⠷⠀⢐⠃⠀⢠⠀⠠⠀⠀⠰⠆⠀⠶⡀⠀⠀⠀⢰⠠⠉⣁⠀⠀⣀⠀⠀⠃⠀⠘⠀⠀⢤⡄⢠⡤⠀⠁⠁⠀⠈⠀⠀⣤⠄⢠⣤⠀⠀⡂
⠀⠀⠀⠄⠀⢀⡴⠶⣤⠀⠀⡈⠀⠀⠄⠀⠀⡾⠻⣆⠀⠀⠄⠀⠘⡀⠀⠙⠁⠀⠋⠀⠁⠆⠀⠈⡄⠁⢀⣤⣤⡔⠂⢠⠃⠀⠘⡀⠀⠄⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠈⠢⣀⠁⠀⢈⡠⠊⠀⠀⠀⠀⠢⢌⣉⢀⣉⠄⠀⠀⠀⠀⠈⠦⣀⠀⠀⢀⡡⠊⠀⠀⠀⠈⠂⠌⣁⣈⠡⠒⠈⠀⠀⠀⠈⠂⠄⣀⣀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉
⠀⠀⠀⢀⡤⠊⠁⢀⠀⠄⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠑⢄⠀⠀⠀⢀⠔⠁⠀⠀⠀⠑⢄⠀⠀⠀⡠⠎⠒⠄⠠⠐⠒⢄⠀⠀⠀⢠⠶⠆⡀⠀⠶⢶⡀
⠀⠀⠀⠎⠀⣠⣠⠀⠰⣆⠀⢀⠀⠀⠂⠀⠀⠀⢀⠀⠀⢀⢁⠀⢀⢁⠀⠀⠀⠀⠀⠀⠀⠂⠀⢰⠸⣄⣛⠀⠠⡛⣠⠆⠂⠀⠠⢉⠀⠆⡀⢀⠶⠀⠛⡄
⠀⠀⠀⡀⠁⠈⠁⠀⠄⠀⠢⢈⠀⠀⡀⠠⠘⠂⠀⠻⠀⠀⡘⠀⠈⠀⠀⠻⠂⠀⠟⠠⠀⡄⠀⠘⣠⡟⢁⣤⣤⡀⢻⣆⠆⠀⢠⠀⠁⠈⣠⣄⠀⠀⠀⠇
⠀⠀⠀⠱⣄⠀⠀⠀⠕⠂⡄⠀⠀⠀⠐⢄⠀⠀⠀⠀⢀⠔⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⢇⡘⠂⠀⢋⡸⠋⠀⠀⠀⠢⡀⠸⠛⠛⠂⣀⠞
⠀⠀⠀⠀⠀⠁⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠊⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣽⣭⣽⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⡟⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣍⢻⣷⣿⣿⡿⢟⣉⣼⣿⣿⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢟⣟⣻⣿⣿⣶⣿⣿⣧⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⢿⣟⣩⣿⣧⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣤⣤⣀⣄⡀⠀⠀⠀⢀⠀⣰⣦⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣦⣦⣬⣶⣿⣿⣿⣿⣿⣿⡟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣴⡟⣧
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢲⡟⣿⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣍⣿⣿⣿⡾⣷⠉⠛⣉⣿⣿⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣄⣿⣿⡆
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠋⢹⣿⣿⡇⢸⡟⠀⠀⣾⣿⣿⣿⣿⡟
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿⣿⣧⣼⣧⠀⣰⣿⣿⣿⣿⣧⣅
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠻⠿⠿⠝⠃⠀⠻⣿⣿⣿⣿⣻⣿⣟⣻⣿⣿⢿⣿⣿⣦
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣯⣽⣿⣿⣶⣾⡿⠿⠟⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠙⡄⠈⠛⠻⣿⡿⢧⣀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡧⠀⢸⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠖⠒⠒⠛⠀⠀⠀⠀⠀⠀⢻⠇⠀⠉⠙⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠶⠶⠶⠶⢶⣦⣤⣄⣀⡀⠀⢀⣠⣼⠏⠀⠀⠈⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠛⠿⣶⣄⠀⠀⠀⠘⣿
⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠶⠶⠶⣶⣦⣤⣄⡀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠹⣧
⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⢿⣷⡀⠈⢿⣤⡿⠀⠀⢀⣴⣿⠿⣦⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣼⣿⣧⠀⠘⣿⡇⠀⢠⣿⣿⣿⣤⣼⡇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠃⠀⠀⣿⡇⠀⠈⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣼⠟⣷⡄⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⢾⡄⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⣾
⠀⠀⠀⠀⠀⢠⡈⢿⣆⡀⠈⠻⢷⣤⣀⣀⡀⠀⣀⣀⣠⣴⡾⠟⠉⠀⠀⠀⠀⠀⠈⠙⠿⢶⣶⣦⣶⡶⠟⠋⢀⣼⠏⣤
⠀⠀⠀⠀⠀⠈⢿⣄⠙⠻⣶⣤⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢫⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣦⡀⠀⠀⠀⠸⠟⠛⠛⠿⠿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠟⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠂⠄⣀⠀⡴⠋⠁⠀⠀⠀⠉⠑⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⣰⣶⡀⠀⠀⠀⣿⠀⠀⠀⢠⣶⣆⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⣿⣿⠂⠀⠀⣿⠀⠀⠀⢸⣿⣿⡗⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⢸⡀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠙⣦⡀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣤⠖⠋⠀⠀⠀⠀⠈⠛⠶⣶⣶⠾⠛⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠶⠒⠒⠚⠛⠉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠁⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⢠⣿⡟⠙⠿⣿⣷⣶⣶⣶⣾⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣷⠀⠀⢀⣤⣾⣿⠿⠟⠛⠛⠛⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠋⠀⠀⢀⣤⣤⣄⡀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⢰⣿⠟⠛⢻⣿⡄⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠁⢀⣀⣼⣿⠇⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢰⣿⡿⠛⠉⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣷⣦⡀⠀⢿⣿⡀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⣾⡿⠋⠁⠀⠈⠙⠻⢿⣷⣦⣤⣤⣶⣿⡿⠛⠉⠀⠀⠈⠻⣿⣦⠈⢿⣷⣄⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠙⣿⣷⣤⣀⡀⠀⠀⢀⣀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢰⣿⠏⢛⣿⣿⠃⣠⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣸⣿⠇⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣠⣤⡀⠀⢸⣿⣀⣿⡿⠀⣾⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⠀⠀⠘⠛⠋⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠀⠀⢸⣿⣿⣿⣷⣦⡈⠉⠁
⠀⠀⠀⠀⠀⠀⣼⣿⠋⠉⢿⣿⣿⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⡏⠉⠻⣿⣆
⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣠⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠿⢿⣷⡄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠋⠁⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⡀⢀⣠⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣒⣲⡿⠿⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣫⡴⢟⡫⠵⢒⣋⠁⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢡⡾⣫⢞⣩⠔⠚⠉⣁⣀⣀⠉⠉⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⡇⣴⣿⡾⠛⠉⣀⣤⣖⣫⠭⠶⠛⠀⠀⢶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⢸⢡⠞⠁⣷⣠⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠐⢸⡿⡄
⠀⠀⠀⠀⠀⣠⣾⢦⡀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡼⡀
⠀⠀⠀⠀⠀⣿⣿⡜⣇⣼⡨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠿⣽⢳
⠀⠀⠀⠀⠀⣿⢻⠃⣿⢿⡻⡗⢦⡀⢀⡴⠒⠒⢦⣀⢠⡴⠋⠉⡏⣰⢿⢮⠗
⠀⠀⠀⠀⢠⡟⣼⠀⣿⠀⡇⣧⠀⠙⠻⠦⣤⣤⡤⠼⢿⡟⢶⡖⢿⡥⠂⡾
⠀⠀⠀⠀⠀⠀⣿⠛⠚⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⢠⣀⡇⢸⣇⣰⡧⠞
⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠤⢻⠳⣄⠀⠀⠀⠀⠀⣀⠙⠷⢨⡼⢿⣿⣯⣝⡓⠲⢦⡀
⠀⠀⠀⣀⣤⠤⠴⣦⣄⡈⠐⠋⠀⠈⠳⢤⡀⠀⠀⢈⡙⣷⣼⡇⢸⢧⡀⠙⠿⣦⣄⠘⣆
⢀⡔⠋⣁⠀⢀⣤⣞⠛⢿⣧⣀⣀⣀⣀⣀⠉⠓⢤⡻⢿⣿⣯⠙⢶⣷⠻⢶⣤⣈⠻⣷⡘⡆
⢸⠀⢠⣿⡄⠿⣧⠈⢳⡀⠙⣿⣑⠤⣌⣉⣙⣛⣻⣿⡖⠓⠿⢦⣀⡽⠀⠀⠈⠙⢷⡈⢷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⢸⡀⠸⡟⢻⣧⠘⣧⡀⠹⡄⠸⡝⠻⢿⣟⡛⣭⣩⠏⢀⣀⣠⡤⠬⠤⠤⠤⠤⠤⠼⡿⢼⡏⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⢱⡄
⠈⡇⠀⣇⠈⢿⣧⡘⡷⡄⠹⣄⢻⢦⡀⣽⢈⡼⢃⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⢻⠀⢻⡄⠈⢿⡗⣄⠹⣆⠘⡄⢙⡟⣡⠎⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠘⡄⠀⠁⠀⠈⢻⡜⢦⠘⣆⠙⢉⡼⢱⡆⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⡇⠀⠀⢰⡖⠢⣿⣼⣇⠈⣣⠋⢠⠞⣱⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡀⠀⠈⣇⠀⠈⢿⡼⣾⠁⡴⠋⣠⠟⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣘⣆
⠀⠀⠀⣇⠀⠀⢹⡀⠀⠘⣷⣨⢿⣴⠟⠁⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣼⢉⡏
⠀⠀⠀⢸⠀⠀⠀⣧⠀⢠⡞⠷⠋⠙⣆⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢹⠈⢻
⠀⠀⠀⠘⣆⠀⠀⠸⣦⠏⠀⠀⠀⠀⠘⣆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢸⡄⠘⡆
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡿⢸⢇⠀⡇
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣠⠞⠁⢾⣍⣉⣉⣉⣙⣛⣉⣉⣩⣭⣭⣭⣭⡭⠽⠿⠿⠿⠿⠛⠛⠛⠛⠻⠭⣍⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡇⢸⢸⠀⡇
⠀⣀⣀⡀⠀⠀⠘⢆⣀⣠⠴⠋⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣃⣀⣀⣀⠀⠀⠀⠀⠀⣸⠀⢸⠘⡆⣷
⠀⠀⠉⠉⠙⠛⠛⠛⠛⠒⠲⠶⠶⠶⠶⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠛⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢈⣉⣉⡑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡾⠋⠉⠈⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢈⣠⠟
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠒⠠⢀
⠠⠊⣠⠶⢦⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠶⣄⠲⡀
⡇⢸⠇⠀⢸⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠠⡄⠋⣠⠇
⢧⡼⠇⠀⢶⣄⠙⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠳⣄⠀⠀⠀⠀⠀⠀⣴⠃⡴⠶⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠈⠛⠾⠃⢀⡄⠀⣼⠛⠳⣦⡀⠀⠀⢠⡏⠀⠀⠿⣄⠀⠀⠀⢠⡀⣛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⣻⡄⠀⠀⠙⣦⠴⣾⡄⠀⢀⣀⣽⠂⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣀⣤⠿⠚⠛⠛⠻⠟⠛⠛⠛⠳⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡶⢦⣤⡀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⡟⢀⣀⣤⠾⠋⠀⠀⠈⠙⢷⣄⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣀⣀⣤⣴⠾⠛⠁⠸⣿⠛⠋⠉⠀⠀⠀⠀⢠⡄⠀⠀⠹⣷⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⢉⣿⠉⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠖⠤⠀⠀⠀⠀⠀⢀⠤⢦⠀⠀⠀⣼⠿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢨⠃⢀⠃⠀⠀⠀⠀⢿⠒⢸⠀⠀⠀⣿⠀⣷
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠰⠀⠀⠙⠁⠀⠀⢠⡿⠀⢹⡆
⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠻⣦⣀
⠀⠀⠀⠀⣾⡋⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⣻⠆
⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⣈⣉⠛⠛⠶⠿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠟⠛⠋⠉⣠⣀⡀
⠀⠀⠀⠀⣠⠉⠉⠁⠀⡄⠀⠀⠀⠀⣠⠝⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢾⡿⣄⠀⠀⠀⠀⢠⠈⠀⠉⠈
⠀⠀⠀⠀⠑⠀⠀⢠⡀⠘⣄⠀⠀⡾⠁⠀⠀⠀⣭⠙⠛⢷⠶⠶⠶⠞⠛⡿⠀⢸⡇⠈⢳⠀⠀⣠⠇⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠣⠔⠙⣦⣠⡔⢁⠞⠀⠀⠈⠓⠤⠀⠤⠞⠀⠀⠸⣧⣤⠋⠳⠔⠁⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⣀⠞⠁⠀⡟⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⢸⡏⠈⠳⣄⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⡇⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⠆⠀⢸⡇⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠣⢄⣀⠤⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠲⠲⡶⠒⢶⠖⠶⢶⡶⠲⣶⠒⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣼⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢸⡇⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣁⣿⠀⠀⢸⣏⣉⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡄⠀⢸⣿⣿⣿⣿⣶⡀

⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⢸⣧⠉⢑⣦⡀⠀⠀⠀⠀⠀⣀⡠⠤⠄⠒⠒⠒⡐⣒⣒⣒⠂⠤⠤⣀⡀⠀⠀⠀⠀⠀⢀⣴⠊⢉⣾⡇
⢸⣹⣇⣾⠇⢈⣦⣠⠄⠒⠉⢶⣦⡀⠀⠀⡰⠚⣭⠙⠛⣫⡅⠀⠀⠀⠀⣽⠒⢤⣀⣔⠁⠸⣷⣼⣋⡇
⢸⠀⠸⠻⠆⡾⢻⡟⢿⣦⡀⠀⠙⠻⡞⣼⣧⠀⠀⢀⢰⡿⠃⢶⣦⡀⠀⣿⣾⡿⢻⠿⣧⠰⢟⠇⠀⡇
⢸⡄⢀⣷⣸⢣⣼⡇⠀⠛⠳⢀⣴⠀⡘⠈⢿⠀⠀⡨⠛⠁⠀⠈⠙⢷⢶⠋⠀⠀⢸⠀⣻⢀⣾⡀⢠⡇
⠀⡇⠻⣿⣯⠀⢸⡇⠻⣶⣄⢻⡟⣴⠁⠀⠈⡏⠀⢀⡀⠀⣤⣄⠀⠀⠇⣠⣤⠄⢸⡀⠀⣾⣿⠟⢹⠇
⠀⡇⠀⠋⠻⣰⡿⡇⠀⠰⡟⢿⣈⣿⣾⠟⠀⠐⢀⠸⣿⠀⠈⠛⢷⣾⡼⣛⠉⠀⣿⢿⡆⡟⠻⠂⢸
⠀⡇⣀⡀⠸⡯⠄⣧⠀⠘⠁⢸⠞⠁⠀⣠⣴⡶⡖⠑⠻⣆⠐⠠⠀⠹⠀⠉⠀⠀⣿⠰⢿⠃⢀⡀⢸
⠀⣇⠘⢿⡄⠀⠀⣿⠀⢤⣤⣌⡆⢀⠀⠛⠉⠀⠀⠀⢀⡀⠑⣤⡄⣆⠀⣀⡀⠀⣿⠀⢸⢠⡿⠃⢸⠠⠄⠠⠄
⠀⢹⠀⠘⢹⡤⠒⣿⠀⠀⠉⠉⠙⢌⠀⠀⢠⣿⢶⣦⣾⡇⠀⣿⢿⣽⣿⣛⠁⠀⣿⠀⢄⡎⠒⠀⣸
⠀⢸⣷⠀⡜⢀⠕⣿⠀⠀⠻⢿⣶⣤⠳⢴⢾⠋⠀⠙⢿⣑⣜⡷⠀⠀⠙⠻⠗⠀⡿⢆⡈⢣⠀⣾⡿
⠀⢸⣿⣴⣴⣯⡄⣿⠀⠀⠰⠿⠋⠉⠓⠀⠙⢄⠀⢀⠔⠁⠈⠙⢿⣦⡀⠀⠀⠀⡇⠈⣻⣆⣆⣿⡇
⠀⢸⣸⠃⢴⣯⣵⢿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⢢⠃⠀⠀⠀⣄⣠⣶⠂⠀⠀⠀⡷⣾⢻⣭⠉⡇⡇
⠀⠸⡏⠀⠤⡼⠁⢸⠀⠀⠶⠿⠿⠒⠰⢀⠀⡀⠎⢄⡀⣀⠴⠶⠿⢷⣶⠄⠀⢸⡇⠈⢧⡠⠀⢸⡇
⠀⠀⣇⠀⣰⡡⠔⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⠓⠤⣄⣇⠀⣸⡇
⠀⠀⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢾⡇
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁