Horse racing Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢘⣿⡄⡀
⠀⠀⠀⠀⠀⠀⢠⣄⣀⡀⢀⠀⠀⠀⠀⣀⣤⠀⢠⣀⠀⡄⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⢿⣿⠟⠇⠟⣦⣀
⠀⠀⠀⠀⠀⠀⢘⠛⠛⢰⣿⣿⣷⣦⡀⠉⠁⢠⣾⡛⠊⡀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡋⠀⠟⠃⠀⠀⢀⣸⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠁⣤⢼⣿⠟⠀⠉⠻⢿⣷⡤⠸⣿⣧⣾⠏⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⢀⣹⠶⡗⢫⡉⢿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⣦⡀⠤⠐⠊⠉⠀⠠⢠⣥⣤⣤⠰⣞⡂⠀⠀⣀⣀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠰⠃⠻⠟⢠⣾⠃⠈⣇⠈⠋⢻⣿⣧
⠀⠀⠀⠀⠀⠀⣭⡻⠟⠋⠸⣷⣌⠳⣄⠀⠀⢀⠎⠀⠈⢛⣶⡘⢿⣟⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠸⡀⠀⠈⠛⢿⣧
⠀⠀⠀⢆⣛⣴⠟⠀⠀⠀⠀⠘⢿⣧⠹⣆⢀⠸⠤⠖⠊⠁⠀⠀⢀⣿⣷⡄⠈⣯⣍⡙⠲⣄⠀⠀⠀⢀⠀⠀⠀⢀⣤⢤⣶⡟⡁⠀⠀⠀⠀⣧⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣿⣤⣶⡇⠀⢀⣾⣀⣀⣀⣀⣘⣩⣭⣤⣶⣿⣿⣿⣷⡈⠃⠀⠀⠂⠀⠀⠔⢋⣤⡾⢋⣮⣤⣤⠶⢁⣼⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣠⡄⠀⠚⠩⢯⡘⢿⠿⠖⠒⣸⣿⣿⡷⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡘⢛⠁⠀⠛⠢⠰⣇⠀⠀⢀⡼⠹⣿⢟⣾⡀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠴⣾⠏⠀⠀⠈⠳⣤⠏⠀⠀⢵⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠿⠙⠁⣴⣿⣿⢿⠿⠇⠙⠁⢀⣀⣤⡄⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣅⣀⣀⠐⠿⠂⠀⠀⣤⣌⠲⠾⠿⠟⠁⣰⢺⡆
⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⠀⠠⠤⢠⡶⠊⠉⠉⠁⢀⡠⠀⡠⣶⡌⢣⡀⠸⣿⣷⡿⠛⠻⠦⣀⠠
⢠⣤⣤⣶⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠈⢠⣮⣾⣿⣿⣿⣿⣐⡼⠋⠀⠀⠀⠀⠈⠉⠁
⠈⠿⠛⠛⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠸⣳⠋⣹⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠉⡁⣀⢀⠠⢤⣄
⠀⠀⠀⢀⣦⠀⣠⣤⣤⡶⠛⠉⠙⠓⠶⣶⢦⣷⠀⠰⠞⠳⡄⠙⣻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣀⠀⠠⣤⣤⠆⠀⠤⠼⠟
⢀⣀⣴⠋⣠⠞⠉⠉⠁⠀⠀⠀⠀⠀⠀⢹⡌⡏⠐⠀⠀⠀⠀⣰⠌⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⠀⠘⣤⣴⣤⣴⡄⣀⠷⠆⢀⡄⠀⠀⠀⠀⡀
⠈⠽⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⢰⡆⠀⢀⣸⠟⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠘⠿⠯⠁⣴⠿⠛⠇⠀⠘⢡⣾⣌⡙⠓⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠠⠴⠾⠧⠦⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣴⣶⠖⠀⠀⠀⠀⠀⠚⠂⠀⠀⣿⡟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠒⠛⠓⠲⠒⠂⠀⠀⠀⠀⠀⠀⠀⣀⣰⣼⣿⡿⠂⢰⡾⠟⣀⣶⡽⠋⠀⠀⠀⠀⠑⣆⠀⠐⠆⠀⢻⣿⣄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢾⣿⡿⠿⠛⠉⠀⠀⢋⠀⣸⡟⠁⢀⠀⠀⠀⠀⢰⢠⣿⣿⣷⡆⢻⣶⡿⠛⢧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠎⠀⢠⡏⠀⠀⣿⣄⡟⢛⣷⢸⣿⣿⣾⣏⠀⠀⠀⠳⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⠀⠀⠀⠀⠀⣀⣴⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣻⠚⠇⠀⠀⢠⣾⣿⠿⠛⠉⢠⠷⡄⠴
⠀⠀⠀⠀⠀⠤⢒⣲⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⢤⣤⣤⣴⣟⢣⠀⣀⢀⣤⠟⠉⠢⢤⣾⣿⣤⣈⣢⣄⠀⢂
⠀⠀⠀⠠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡿⢛⡿⠀⠉⠁⠈⠉⡷⠖⠒⡾⣆⣀⠀⣀⣀⣉⠳⠄⠈⠀⠀⠀⢀⣾⣿⠋⠀⠉⠉⠙⢿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠁⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣻⣿⣷⠄⠀⠺⠦⠀⠀⠀⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢠⣴⣤⣶⣶⡲⠄⠀⠾⠿⣥⠀⠀⢀⡀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠀⠀⠀⣠⠾⠛⠛⠛⠛⠻⢷⣤⣄⣀⠀⠀⠀⢠⣷⡀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣲⣾⣿⠟⠉⢀⣠⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣶⣾⣿⣷⠀⠀⠀⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢉⣦⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡗⠒⠶⣦⣌⠳
⠀⠀⠀⠀⣀⣤⣐⣢⠞⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠉⠉⠁⠀⠀⡰⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡓⠀⠀⠀⠀⠀⠀⠀⠈⢲⣄⣄⡀
⠀⠀⠀⠀⣀⣄⡀⠀⡀⣿⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿
⠀⠀⠀⠚⠛⠛⠟⠿⠛⠿⠛⠿⠟⠛⠛⠋⠝⠛⠛⠋⠉⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠠⠤⣶⠄⢠⢄⠽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣟⠟⠉⣳⠀⡄⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠛⠓⢤⡿⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠙⢷⣄⣻⡟⠷⠀⢢⠄⠀⠀⢉⠉⠙⠡⠄⠶⣄⠀⠀⠀⢷⣄⡀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠀⠀⠀⠤⠉⢿⣤⠄⠈⠀⢰⣧⠾⠃⢠⡇⢸⡦⠋⠐⠾⣭⡦⣿⣍⣧⣀⡀
⠀⠀⠀⠀⠀⠀⡷⠶⠾⠧⣤⡀⠀⠠⠈⠁⠀⠤⠀⠄⠒⠀⢸⡟⠀⢀⡾⣩⣿⡽⡦⠾⠿⣷⣶⣚⠣⡀⠁⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠿⡄⡀⠀⢀⣠⡔⠁⠀⠀⠀⢀⡞⠀⠀⣸⣧⣿⢽⡄⡼⣷⢼⣿⣏⠉⠛⣤⣬⣾⣟⢻⡛
⠀⠀⠀⠀⠀⣼⠋⠀⠀⡀⣰⡇⢤⣴⣟⡉⠰⣾⡗⢀⣀⣺⡔⠃⣤⠙⣿⣻⡾⣷⡍⠘⠀⠙⠻⣶⣦⣼⣿⣿⣿⣧⠱⣄⠀⣄
⠀⠀⠀⠀⠀⢁⠂⢠⣶⣹⡏⢷⢠⡉⢻⣿⣿⣿⣿⣶⣯⡙⠓⢊⠁⡀⣿⣿⣧⣿⣷⣶⡦⠀⠀⠈⠻⢤⡈⣿⣿⣿⡟⠻⠂⠻
⠀⠀⠀⠀⢠⡆⡦⢸⠁⣶⣿⡜⣧⢳⣀⡝⠉⢻⣿⢿⣧⣷⠂⠈⢳⡉⣿⣿⣿⢿⣿⣿⠃⠀⠀⠀⠀⠀⢿⣻⡼⠃⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠓⠀⠀⠀⢹⣷⣿⡈⠂⠻⡇⠀⠘⢻⣷⣙⣯⠅⢠⣤⣿⣿⣿⣯⡘⣿⣿⠀⠀⠀⠀⠀⠠⡆⢻⣃⠀⠀⣰⡷⠂⠀⣰⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠃⠀⢀⠀⠀⠀⠀⠹⣿⣥⣶⢰⢿⣿⣿⣿⢻⡆⢿⡟⠀⠀⠀⠀⠀⠀⠃⡼⠁⠀⠰⣿⣄⡀⠀⠹⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣶⡖⠁⠀⠀⠀⠀⠀⣿⣿⡟⣼⢿⣿⣿⡟⠻⣿⡈⣿⣄⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠇⠀⢰⠋⣧⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⡇⢲⣦⣀⠀⠀⠀⢻⣿⠞⠁⠈⡛⠘⣷⣤⣬⣁⡉⣻⣆⠀⠀⠘⣶⠃⠀⠀⠀⠀⠀⣸⠇⠀⠈⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣀⢣⡀⠙⣿⣷⠀⠀⠘⠁⢲⣄⣾⣷⠠⢤⣿⢿⠛⠿⢿⠿⣿⠀⠀⠁⠀⠀⠀⠀⠀⢀⣿⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠦⢼⡋⠀⠈⠙⠢⣼⣿⣿⠁⠀⠀⣿⣈⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⣼⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⣀⡄⠀⠀⢺⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⣴⡀⠀⠀⠈⣿⠇⠀⠀⠸⡇⠀⠀⠀⣼⠛⣿⣹⠛⠀⠀⣶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⣿⣷⡀⠀⠀⢸⣷⣇⠀⢸⣿⠀⠀⣤⣿⠷⠛⠋⠀⠀⠀⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠙⠿⡷⠤⢶⣀⠙⢿⣷⠜⣿⣶⣜⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛


⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠻⠿⠛⠿⢿⠿⢻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣦⣤⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠹⣯⣩⠟⡀⠀⠀⠀⠀⡀⣀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠰⡀⠀⣅⡰⢀⡠⡷⠐⠚⠛⠋⢉⡀⠙⠟⣦⣄
⠀⠀⠀⢀⢀⣀⣀⣀⠀⠀⠀⣀⠄⠀⢀⡴⠤⠀⠠⣠⠊⠀⢀⣷⡄⠘⢾⣌⢙⣒⡬⠟⠛⠿⠾⠷⠔⠴⠾⣟
⠀⠀⠀⠀⢿⡉⠻⠏⢛⡻⠟⣵⡿⠟⠁⠀⠀⠀⠀⣸⣦⠀⠈⢳⠛⠁⡤⣽⡯⠁⣄⡀⠀⠀⠀⣴⠀⣠⡄⠈⡧
⠀⠀⠀⠀⠻⣭⡛⠛⢉⣤⠞⡩⡜⠀⠀⠀⠀⠀⠐⠃⠉⢣⡀⠀⠂⠀⠙⠠⠝⠋⠀⠀⠐⠤⠘⣏⢣⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⠁⡇⡇⠀⠀⠀⠀⠀⢁⡶⠖⠉⢁⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠢⠰⣶⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠘⠃⠀⠀⠀⠀⢠⣙⣰⠆⠸⡙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢙⠀⠀⠀⠈⢂⣉⡠
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⢸⣦⡀⠀⠀⡠⠊⠑⠷⣌⡄⠀⢣⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠡⠼⠃⠉⠂⠈⠀⠀⠀⠀⠀⠁⠐⠒⠒⠷⢄⣀⢢⡀⠀⠀⠀⠲⣯⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠢⣀⠀⠀⠑⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠐⡧⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠈⠀⡑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢷⡈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡄⢉⣢⣈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠈


⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣼⣷⣬⣿⣶⣥⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⣄⠐⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡮⠁⣴⠠⢹⡅⠀⠀⢠⣤⣤⣴⣿⣾⣷⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠂⠒⠨⣛⣇⣀⠀⣿⡿⠿⢛⣥⣾⣿⣿⣿⣗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡗⢿⡿⠿⠛⠛⣷⣴⣵⣾⠿⠿⠿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⣟⠀⠸⠀⠀⠀⠘⣿⣿⡿⠃⠀⠀⠀⠀⠉⠑⠛
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⢀⣀⠀⢀⠀⢰⠂⠀⠀⠀⠈⠶⣿⠖⢠⡆⠠⣤⣀⣸⡿⠁
⠀⠀⠀⠀⢀⣾⣿⣿⢿⣆⠰⣦⣿⣷⣮⣻⣿⣿⡀⠀⠀⠀⠀⣿⠖⠚⠀⠑⢮⣿⣿⠇
⠀⠀⠀⢀⣿⣿⡿⠛⠚⠉⠀⢸⣽⣜⠯⡁⣿⡟⠿⣷⣦⣤⣤⣽⣇⠰⠇⠀⣠⣿⠿
⠀⠀⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠻⡓⠀⣿⠇⠀⠀⠈⠉⠉⠉⠛⠛⠛⢼⣷⣟⣶⣤⣀⡀
⢀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⠉⠻⣿
⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠐⠂⡀⠀⠀⠴⠶⠾⠟⠁⠀⠀⠀⠀⠘⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⣀⡀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⢸⣿⠀⠉⢁⠀⠛⡹⢾⠍⠀⠀⠀⢀⣀⣀⡠⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢶⣿⡆⠀⢹⣤⠈⠁⠀⢀⣀⣴⣾⡿⠟⠋⠻⡌⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠙⠂⢀⣿⠁⠀⣠⣴⣿⡿⠟⠁⠀⠀⠀⠀⠘⣿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⠤⠤⡤⠀⠠⣄⣀⡀⠀⠐⠉⣠⡖⢀⣀⡉⠛⠻⠟⠉⠀⠀⣠⠆⢀⣤⣀⡀⠹⣿⣄⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠿⠿⠶⠀⠀⠀⡏⠀⠀⠀⠈⣿⡟⣀⣾⣿⠇⣠⣬⣭⣷⡶⠋⠑⣰⠞⠓⢒⣾⠋⠙⠶⠞⣷⡟⣿
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣴⣶⣿⡿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢲⠧⠄⠀⠀⠀⢈⠘⠻⣿⠋⢠⠀⠀⠀⠀⠀⠠⡾⠃⠀⢠⣾⠃⠀⠀⠀⠀⠈⠻⣿⠄
⠀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠠⣿⣃⠀⠀⠀⠀⠀⠀⠀⢮⠳⠒⠲⠤⣄⡀⠉⡖⠼⠂⠀⠀⠀⠀⠀⣤⡀⠁⢀⣴⠟⠁
⠀⢘⣿⣿⣿⣿⣿⣿⣿⡟⣽⠏⠀⠀⠀⠀⢿⣿⣷⣤⣤⣤⣤⠄⠀⢸⢀⡀⠀⠀⠀⠀⠈⢁⠘⠂⣀⣀⠀⠀⠀⠸⣿⣶⣿⡇
⠀⠀⠈⠒⠛⠋⠁⠐⠋⠉⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⠻⠿⠅⡀⠀⢸⠘⢿⣶⣄⡀⠀⠀⣿⠀⠸⡇⠀⠀⠀⣀⠔⢹⡟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢀⠀⠀⠈⢸⣷⠚⠽⣿⣿⣶⣿⣀⠀⡧⣠⠏⢀⣠⣀⣼⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⡄⠀⠀⠉⠙⠿⠿⠿⣇⣿⠂⠀⠙⣿⣏⣀⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡀⠈⠋⠉⠉⠉⠉⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢀⣀⣉⢀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣧⣸⠆⠀⠈⠻⢿⣤⣤⣤⣤⡘⠷⠀⠀⠀⠀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣤⣀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠒⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡆⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⢯⡛⠉⠻⣤⣴⠞⠉⢀⢀⣀⡁⢔⣺⣿⠿⣯⣄⡀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⢄⠘⠛⣿⣤⠞⣽⡿⣇⣠
⠀⠀⠀⠀⠠⢶⣶⡿⠟⠉⠉⠀⠀⠀⠀⣶⣟⣤⣌⠁⠀⠀⢺⡇⣸⣿⣯⠻⠛⠁⠀⠀⠈⠁⠲⠾⠿⠋⣾⠀⠸⣋⣠⣿⠜⣦⣄⠀⠀⣰⠋⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⢿⣪⣿⡿⠀⠀⣴⣿⣿⣿⣝⣏⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣋⡴⠞⠉⠙⠻⠿⢟⣛⡶⢼⠇
⠀⠀⠀⠀⠀⠀⠀⣤⠴⠀⠀⠀⢀⡤⢿⣗⠟⠓⠒⢦⣤⠁⠉⠉⠉⠙⣯⠓⠦⣄⠀⠀⠀⠀⠀⠸⠈⠁⠀⠀⠀⠀⠀⠀⢀⡞⠁⠐⢄
⠀⠀⠀⠀⠀⣠⢎⠐⠋⠁⠐⠚⡡⠊⠉⠀⠀⠀⠀⠀⠈⠂⠀⠀⠉⠂⣜⣆⠀⠀⠈⠃⠀⠻⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠈⠉⢡⠁⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⠂⢀⣀⢀⣀⣀⢈⡀
⡀⠀⠀⠤⢤⣤⣤⣤⠤⠬⠭⠭⠭⠯⠽⠽⠿⠿⠿⠿⠧⠛⠓⠉⠉⠁⠀⠁⠁⠀⠈⠀⠉⠉⠀⠈⠙⠋⠍⠸⠿⠭⠿⠉⠉⠉⠙⠁⠉⠉⠁⠉⠁⠈


⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣤⡴⠆⢀⠀⠀⠀⢠⣴⡶⢂⡀⠀⠀⣀⣤⠖⣠⣤⡴⢀⡀⠀⠀⠀⠀⠀⣠⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤
⠀⠀⣀⣠⣤⣤⣽⣷⣾⡟⣷⣤⣤⣼⣿⣷⣿⣿⣤⣤⣹⣿⣴⣿⣿⣶⡿⢿⣄⣀⣀⣀⣀⣹⣽⣶⣿⢿⡄⠀⠀⣀⣤⣤⣿⣿⣶⣿⣆
⠐⠛⠉⠙⣿⠿⠿⢿⣿⡿⠛⣿⠿⠿⣿⣿⢋⣽⠿⠿⠿⣿⣿⣿⣿⣿⣇⠉⠉⣩⢿⡿⠿⠿⣿⣿⣇⡀⠐⠛⠛⠻⣿⡿⣿⣿⣟
⠀⠀⠀⠀⠙⣆⠀⠀⠃⠁⠀⠈⠦⠤⠼⠬⠞⠁⠀⠀⠠⠇⠘⠧⠄⠈⠳⠤⠊⠁⠏⠀⠀⠀⠀⠘⠄⠑⠀⠀⠀⠀⠹⣦⠀⠘⢊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠟⢙⣿⣿⣿⣿⡿⠛⠋⣹⣿⣿⣿⠿⠟⢙⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⣿⣿
⣿⣿⣿⡿⠿⠷⠄⠘⠉⠀⠈⠟⠛⠃⠀⠈⠁⠈⠻⠯⠀⠀⠋⠀⠀⠈⠀⠈⠻⣿⣿⠿⡿⠄⠀⠋⠉⠈⢻⣿⣿⡿⠿⠯⠀⠀⠊⠉⢻
⣝⣁⣠⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⢰⣷⣎⣉⣁⡀⠀⠀⠀⠀⢀⣶⣤
⣿⣿⣿⣿⣄⠻⣿⢓⣠⢸⣿⣤⠚⠿⠆⠂⠁⣰⣿⡿⠿⢰⣄⠐⢖⠂⠀⠿⣣⣔⢡⣾⣿⣷⣶⣆⢲⡌⢿⣿⣿⣿⡀⠚⢖⠆⡠⣸⣿
⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣦⣼⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⣿⣿⣦⣾⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠡⢴⣿⣴⣤⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢴⡆⠹⠆⠋⠉⠈⠘⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢀⣤⣾⣤⡂⠉⠀⠀⠀⠀⠰⣾⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⡀⣼⡿⠿⠛⠻⢿⠟⠿⠿⣦⡀⠀⢨⡹⣯⠱⣿⡇⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⢀⣤⠿⣇⣸⠂⠀⠀⡠⠃⠀⠀⠀⠀⠉⣳⣮⣠⠚⠋⠉⠋⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠙⠃⢭⣷⠱⣀⣄⡴⡁⠀⠀⠀⠆⠀⠀⠘⣿⣿⣿⣙⡿⢈⠁⠈⠛⢏⠀⠈⠉⠉⠉⠙⠉⠙⠛⠉
⠀⠠⠬⡥⢦⣼⡋⣹⣴⠟⠋⢸⣿⠃⢰⣿⠂⠒⠀⠀⠧⣽⣿⣥⡽⠋⢁⠀⠀⠀⠡
⠀⠀⠐⠀⠀⠈⠉⠁⠀⠀⠀⠀⠹⡤⢈⠛⠢⡀⠀⣀⡴⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣧⣄⠈⠙⣿⣄⣀⣀⣀⡤⠔⠒⢠⡀⠀⠀⠀⡔⠂⠄⠛⢿⠲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠀⠀⠀⠀⠈⠀⠈⠀⠈⠒⠀⠊⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⣴⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀⢠⡄⠀⠀⠀⠀⠀⠀⢠⣾⠏⡜⣦⠛⢽⣉⣷⣤⠀⠄
⠀⠀⣠⣴⡾⠿⣶⣶⣡⠞⢭⡧⠀⠃⠀⠀⠀⠀⠀⣴⢯⣵⡄⣽⠘⢷⣄⣘⡁⠀⢡⣐
⠀⣴⣿⣿⣿⣇⡀⢘⣻⢷⣶⣦⣠⣦⡀⠀⢀⣀⠀⠙⠊⠁⠘⣿⡆⠀⠙⡿⣏⡙⢿⢾⣦⡒⠀⠀⠀⡀
⣰⢿⣿⠯⠟⠻⣿⣶⣬⣛⠿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣆⣤⣄⣹⣿⣄⠀⠁⠙⠿⣼⣾⣿⢃⣷⠀⠀⠘⠿⣷⣦
⠙⠛⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⣉⣿⣿⣿⣿⣿⣿⡟⠉⠋⢹⣿⣿⡀⠀⠀⢂⠀⣠⣾⢿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣿⡟⣷⣿⠿⠛⢿⣿⣿⣿⠃⠀⠀⠈⢿⣿⣷⣤⠀⠛⠻⣏⣉⡲⣿⢀
⠀⠀⠀⠀⠀⢀⠘⣡⠞⠛⠙⠋⠉⠉⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠀⠀⠻⠜⠃
⠀⠀⠀⠀⡀⢈⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣧⠀⠀⠀⠀⢸⡵⠧⡘⠇⠀⠰⡆
⠀⠀⢀⡴⠙⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠘⢧⣤⡄⠀⠀⠁⠈⠳⡀⠀⠛⠼
⠀⠀⠀⠀⣰⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠁⠀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄⠀⣿⣿⡟⠉⣼⣿⠿⠛⠛⠛⠿⠿⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢤⣀⡒⠻⣿⣷⣄⠈⠛⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠶⢂⠞⢻⣀⡤⠀⠙⢯⣽⣶⢤⡟⠀⠀⠀⠀⢒⡫⠽⠟⠂⠀⠀⢠⡄
⠀⠀⠺⣷⣀⡴⣫⠴⢋⠁⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⡆⠀⠀⠀⠀⠀⣀⣠⣤⡾⠁
⣾⠁⠀⢿⡟⠋⣁⣤⠿⣧⠀⠀⠀⠀⠀⠈⠛⠿⠿⠗⠘⣶⣶⣶⡿⠿⠛⠛⠉⠀⠀⠀⠒⠒⠒⠚⠛⠛⠓⠢⣄
⠻⣦⡴⠈⠳⠆⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠐⢶⣶⣶⣾⣿⡇⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢿⣿⣷⣄⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠿⠛⢉⣀⣴⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠸⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠿⠛⠻⣿⣿⣿⣿⣿⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⣠⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠿⣦⡀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣤⠴⠚⠉⠀⣼⡄⠀⠀⣾⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡁⠀⣀⠀⠁⠀⠀⠀⠀⣼⠟⠛⠛⠉⠀⠀⠀⠀⢰⣿⣷⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠿⠛⠋⠉⠉⠀⡴⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⢀⣼⡇⠀⠔⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠿⠛⠁⢀⣤⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢀⣀⣸⣿⡿⠃⠀⢀⡴⠂⠀⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⢿⠟⠁⠀⠀⢀⡞⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂⠕⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⢤⣶⢰⣿⠆⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠶⠋⠁⢤⣾⣿⢼⣿⣧⣤⡖⠀⠀⢤⠀⠀⠀⠀⣠⡆⣀⣧⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⡀⠀⣤⣠⣴⣫⣿⣿⣏⢻⡍⣠⣀⣤⣤⠈⠀⠀⠀⠘⢿⣿⣿⣿⣷⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀⢻⣷⡀⣼⣼⣿⣿⣿⣿⣿⣆⠀⠙⣉⣹⠁⠀⠀⣠⣾⣦⡀⠉⠀⠁⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⠷⠎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣿⣿⡆⢀⣠⣿⡿⠛⢡⡎⠀⠀⠀⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠿⠿⣿⠃⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⣾⣿⡟⠁⣰⣸⣿⣠⡾⠀⠀⠃⠀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠰⡄⢀⠔⠀⠂⠊⠉⠀⠀⠀⠉⢻⣿⣿⠟⣉⡘⣷⣽⣿⡟⠀⢰⣟⡘⣿⡛⠃⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠂⠄⠀⢀⠀⠀⠸⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣽⣿⠏⠀⠀⡴⠺⣷⡼⣿⡿⡄⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠘⠀⠉⢄⡀⣴⣿⣿⣦⣾⣿⡿⢋⣩⣵⣿⡿⠉⠀⠀⠀⢀⢁⣿⣿⣹⡷⠄⢀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⡀⠚⣿⣿⣿⣿⡋⡩⠁⣠⡿⣻⠿⡻⠁⠀⠀⠈⢠⡟⠼⢿⣽⢷⡑⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⣿⡟⢡⠞⠁⠀⠀⡰⠀⠀⠀⠀⠀⣾⠁⣸⣿⣾⣿⣿⣋⡗⢶⣦⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠋⠀⣠⡎⠀⠀⠀⠀⠀⡸⠀⣸⣿⣿⢏⣼⣏⡐⠁⠀⠀⠀⠀⢇⠀⠀⠀⠀⢰⡏⠀⣿⣿⣿⣿⡏⠉⠑⠠⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⣿⠇⠀⠀⠀⠀⢠⣧⣴⣿⣯⢱⣿⠋⠁⠙⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣾⡇⢸⣿⣿⣿⣿⠃⠀⠀⠴⠿⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠙⠀⢀⢀⠀⣾⣿⣿⠀⠀⠈⡼⠃⠀⠀⠀⠀⢀⠀⠀⢀⠈⡀⠀⠀⣸⣿⠃⣾⣿⣿⣿⣿
⠀⠀⠀⢠⣤⣄⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣇⠸⢿⣿⣿⣿⢶⣤⡃⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠁⠀⣰⣿⡏⣴⣿⣿⣿⣿⣿⡆
⠀⢀⣠⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡈⣿⣿⣦⣌⢻⣏⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⣦⣤⣈⣉⣉⣩⣩⣿⣿⣿⡇
⠀⢏⣩⣿⣯⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣷⡄⠀⣉⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠈⠁⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⡀⠀⠀⢠⠘⣿⣿⣿⣿⣿⣿⣄⣿⣿⣸⠀⢸⡆⠀⠀⠀⠀⡀⠀⠀⣿⣿⣿⣿⡿⠋⣸⣿⣿⣿⣿
⠀⠀⠀⠴⣿⣿⣿⣿⠿⠿⠿⠿⠛⠁⠀⠀⠘⣧⠀⠀⠘⣷⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⠀⠸⣿⣦⣀⣄⠀⠁⠀⢀⣿⣿⣿⠏⢀⣾⠿⢿⣿⣿⡇
⠀⠀⠀⢬⠽⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣿⣿⠇⠀⠙⢿⣿⣷⣿⣿⠀⠀⠻⠿⢻⡏⢸⡆⣄⣼⣿⣿⣿⠀⠞⠁⢀⣾⣿⣿
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢸⣿⣿⠀⠀⠀⠀⠉⠛⢿⣿⢠⣶⠀⠀⠋⢠⣿⣿⣿⣿⡿⣀⠀⠀⢀⣴⣿⣿⣿⠿⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣔⣾⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⡄⣿⠃⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣶⡀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢻⣷⡆⠀⠀⠀⠰⡄⢻⣿⡿⢿⣿⠿⠛⢿⣿⣿⣃⠀⣄⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠹⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠶⣽⣶⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠙⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡄⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⢀⠀⠀⠀⠀⠘⢿⣿⡼⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⣶⠋⠀⠀⣠⡄⠀⠠⠻⣧⣷⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠀⠐⠾⣿⣿⣠⢀⣄⠉⣉⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⢠⠈⠉⠙⢾⡿⠿⠿⢿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡁⠠⠂⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⣄⣸⡒⠃⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⣻⡽⣿⠁⠀⠀⣠⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠱⣿⣄⡻⠦⣀⡴⣻⣿⣿⡿⠿⢿⣿⡄
⠀⠀⠀⣀⣠⣴⣶⣦⣄⠀⠀⠀⠀⡠⠴⢶⣶⣄⣀⣀⣀⣀⣀⣠⢌⠋⢁⣤⣶⣷⣿⣿⣿⠇
⠀⠀⠘⢿⣿⡿⠿⠿⢿⣷⣤⣤⡾⠃⠀⠈⠛⠿⡿⣩⢙⣵⡿⠛⣤⣴⡿⡿⠁⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⣦⣶⣾⣉⡆⠘⠿⠗⢺⣿⣿⣿⣿⣷⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣦⣿⡿⣿⣿⣿⡗⣦⣤⣼⣿⡿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠃⣿⡿⠋⠃⠽⢿⣿⡿⣽⣦⣨⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⢀⣾⡟⠁⠀⠀⠀⠀⠀⣾⡿⠁⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠉⠙⠲⢤⣀⠀⠀⣸⠏⠀⠀⠀⣈⣿⠇
⠀⠀⠀⠀⠉⠁⠲⠀⠄⠀⠀⠀⠀⠀⠘⣷⠀⢀⣀⣀⣉⣶⠞⠉⠘⠻⠶⠋⠁
⠀⠀⠀⠀⠀⠀⢂⢢⡄⢠⠀⠀⠑⠀⢈⠀⠸⢭⠉⠉⠉⠀⠀⠀⢀⣰⣄⢀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠙⠙⠻⠿⠛⠛⠻⠿⠟⠛⠒⠛⠛⠘⠒⠂⠋⠑⠛⠻⠉⠋⠛⠙⠃⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⢶⣆⠀⠀⠀⣀⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⢘⠁⠀⠈⠏⠀⠀⠀⠉⠁⠉⠁⠀⣸⣷⣤⣷⣾⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠉⠘⡛⣿⣿⠀⠰⣴⣷⣶⣾⡇⣠⠠⣶⣿⣿⡿⠟⠛⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠊⣩⣿⣄⣰⣛⠋⠀⣹⢧⣭⣇⠉⠉⠉⠀⠀⣠⡀⠘⠻⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠁⠋⠈⢉⣿⡿⠿⠃⢸⠃⠈⠃⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣶⡦⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠿⠿⠲⠶⣶⣶⣾⡿⠃⣤⣠⡿⠋⠀⠀⣀⠀⠀⡼⠀⠀⠀⢀⠐⢤⣀⠀⣈⣷⣄⡀⠀⣀⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠁⢀⠤⢺⡿⢁⣠⣿⠟⣡⣴⣾⣿⣿⣏⣴⠇⠀⠀⠀⣾⣠⣾⡿⠋⠉⠉⠛⢇⠘⠛⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠠⣦⠀⠀⢠⠀⠀⠀⣠⠟⣀⣴⠟⠁⣼⣿⣿⡿⠃⠸⣿⡏⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠰⡿⠀⢰⣧⣖⡀⢀⢡⣴⣟⠁⠀⠸⢻⡇⠈⠁⠀⠀⢿⣧⠀⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠧⠀⠀⠀⣽⡄⠋⠉⠻⣄⡀⠙⠿⠛⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠙⠷⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣇⠀⠀⠀⠀⣿⡄⠀⠀⠀⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢋⡿⢷
⠠⣄⣀⣀⠀⢀⣠⣴⣿⣿⣧⠈⠆⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠙⡿⠚⠁⡿
⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⡀⠀⠀⢸⣿⣷⣄⡀⠀⠀⢹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠸⠿⠟⠛⡿⠟⠁⠀⠀⠀⠀⠹⣦⡄⢸⡏⠻⣿⣿⣦⣄⡈⢿⣿⣧⡔⠀⣀⠀⡀⠀⠀⠐⠢⣿⣾⣁⣠⠆⠀⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠌⡇⠀⠈⠻⣿⣿⣿⣿⡟⢿⣷⠾⡁⠀⠙⢶⡲⠤⠶⢿⣿⣿⠁⠀⠀⠲⣤⣌⣙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢇⠀⠀⠀⠘⣿⣿⣿⠀⠘⠿⢦⣀⠀⠀⢄⠙⢄⠀⠀⠙⠿⠿⠖⠚⠋⠉⠉⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣠⠘⣦⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠈⠉⠓⠾⣷⣌⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣄⡜⢷⣄⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣍⠙⠮⠻⣿⣿⠀⠀⢠⣤⣴⣦⣀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡆⠀⠙⢿⣇⠀⠀⠙⠿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣎⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣦⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣻⣛⣟⣙⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣾⣿⡿⠃⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠁⣠⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣶⣶⣶⣦⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⢿⡿
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⢀⣚⣿⣿⣿⣿⣿⠇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠉⠉⠉⠙⠋⠉⠁⠀⠀⠀⠈⠙⠿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⠉⠉⠻⣿⡟⠛⠛⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⣶⣀⣤⣀⠀⢙⣿⠄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣈⠙⠉⠉⠉⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢶⢾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⡞⣴⣋⠟⢋⠀⠀⠈⠂⠾⠉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣦⣡⣶⠞⣿⢰⠊⢗⠄⠀⢺⡄⠀⢀⡏⢀⣦⠖⠃
⠀⠀⠀⠀⠀⠀⠄⣼⡏⠄⠐⠾⠛⠛⠷⢿⡞⠆⠀⠘⣧⡀⠀⠀⢮⠄⣼⣵⡾⠏
⠀⠀⠀⠀⠀⠠⣘⣏⣙⣶⡢⣄⠀⠀⠀⠀⢰⡖⠂⠀⢬⣷⣀⠃⣿⣳⠟⠇⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢆⣼⣏⡿⠛⠛⠾⢂⣀⠤⠄⠀⣇⡆⠀⢨⣻⣿⣷⣾⠇⠀⠀⣀⣀⣀⣨⣭⣭⣾⣷⣶⣦⣤⣀⠠⠀⠄
⠀⠀⠀⢀⢈⣼⡿⠏⠀⠀⠀⠈⠉⠳⣴⠾⠁⠸⣿⡾⠘⠋⢿⡿⠋⢀⣠⡪⠍⣵⡿⢹⡟⢹⡿⠉⠁⠀⠉⠙⠛⠷⣦⣄⡀⢠⣴⠤⣤
⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠒⠀⣿⣎⠀⡸⢋⡖⠀⠀⠛⠀⡾⣉⣽⣶⠆⠋⢀⣌⢰⡏⢿⣷⡠⠀⠀⠀⠀⠀⠙⣿⢿⣶⣄⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⠘⣗⢿⣠⢐⣰⡆⣼⡇⣿⣿⠁⠳⠀⣀⠻⢦⡻⠎⣿⣿⣄⠀⡀⠀⢰⡀⣿⡃⠹⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠈⠛⣦⣿⣿⣿⢿⣃⣾⣿⣿⣿⣯⣤⣤⣶⢌⣛⣣⣴⡾⠺⣿⣿⡃⠀⠀⣾⣿⣿⡇⡄⠙⢿⣿⣟⡰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢾⣿⣿⠿⠛⠋⠉⢀⣠⢙⠛⣱⣮⣶⡿⠿⠿⠿⠿⠿⠛⠛⠉⠁⠀⠁⠊⠹⣿⡻⠆⠠⡿⣿⣿⣧⣱⡀⠀⠈⠛⠿⠿⠃
⠀⠀⢀⡀⣀⠶⠚⣩⡴⠛⢉⣄⣀⣤⠤⠬⠯⠖⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠻⣅⣤⣀⣁⣠⣤⣾⣸⣶⣶⣶⢀⡀
⠀⠀⠀⢀⠡⣶⣟⣁⣀⣤⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠡⣤⡄⠀⠈⣭⠉⠀⠀⢹⣇⠉⠛⠼⣷⡀
⠀⠀⠀⠐⠛⠛⠉⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣠⣀⡀⠀⠏⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠑⠒⠀⠐⠐⠛⠀⠀⠀⠂⠰⠴⠲⠴⠦⠶⠐⠶⠐⠒⠂⠐⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠴⣤⣤⣄⠈⢋⣠⡀
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠓⠶⠠⠀⠶⠒⠶⠂⠴⣦⣤⣤⠤⢤⠦⣤⣤⣤⠤⠤⠀⠀⠀⠀⠀⠀⣠⣀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⠓⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣿⣟⠾⣥⣀⣤⣴⣾⣷⣒⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣖⠀⠸⣿⡴⢟⠉⠿⠡⢀⣸⣿⡗⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠾⣿⣦⡀⠁⣠⢾⠁⢠⠎⢠⣿⣵⠫⣷⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠄⠀⠀⣤⣄⣶⢶⣀⠀⣀⣀⣠⣠⡦⠀⠉⣠⠖⢁⠇⠀⡟⠀⣿⡿⠉⠳⠾⠿⢿⣿⡎⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⢉⡻⣷⣶⣿⣿⡸⠟⠁⣌⣢⠖⠁⠀⡎⠀⡸⠁⣸⡿⠁⠀⠀⠀⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣿⠃⠀⠀⡠⠀⠀⠀⠀⠀⢠⣏⠀⢨⣛⢿⣿⣿⠋⢀⣴⡾⠛⠁⠀⢀⡼⠀⢴⣄⠸⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⠏⠀⡇⠀⠀⢸⠃⠀⠀⠀⠀⠱⣄⠀⠈⠑⠛⠿⠿⣅⣀⠻⣿⡇⠀⠀⠀⠘⠁⠀⠈⣿⣶⠇
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡟⠀⠀⢿⡀⠀⠈⠷⣄⠀⠀⠀⡄⠙⢦⡀⠀⠀⠀⠀⠀⠈⠑⠒⡇⠀⠀⢄⠀⠀⠀⢀⢻⣿
⠀⠀⠀⠀⢀⣾⣿⣿⡿⠻⢿⡿⠛⡟⠀⠀⠀⠈⢷⣄⣻⣄⠈⠃⠀⢄⣳⠀⠈⣿⣷⣤⣀⣀⣀⠀⠀⡇⠇⣾⠀⠈⠀⠀⠀⠀⠶⣯⡀
⠀⠀⢀⣴⣿⠿⡟⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣼⣦⡀⠹⠄⠀⢸⣿⠋⠉⠛⠻⠿⠷⢷⣾⣿⣆⣀⠠⣦⣀⣒⡒
⢀⡴⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣶⣶⡛⠛⠛⠒⠰⢦⣈⠁
⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠈⠛⠻⢿⣦⡀⠀⠀⠀⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠻⣤⣄⣀⣀⠀⠀⠀⠈⠛⢷⣤⣤⣤⣤⣤⣾⣿⡟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠦⣌⡙⠛⠛⠻⠿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⠘⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢢⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣿⣿⡲⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣷⠿⣿⣿⣿⣏⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠘⣿⣿⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣤⣤⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠛⡛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣹⡟⣛⠻⣿⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣴⣿⣶⣶⣤⣠⣠⣴⣼⣿⣿⣿⣿⡏⠉⠙⠛⣛⠛⠉⢉⠈⠉⢿⣿⣿⣿⣿⡿⢹⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣁⡈⢙⣿⣿⣿⣿⣿⣿⣇⣀⣙⠉⣭⣭⡍⣛⠁⠀⠀⢿⣿⡏⢿⣿⡘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣷⣦⣀⠈⣿⣿⡈⣿⣷⠹⡿⠁
⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠛⢻⡟⠻⡿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠿⣿⣿⣓⢺⡧
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⠤⣿⠁⠀⢈⣏⠉
⠀⠀⠀⠀⠀⠀⠀⢶⡶⠿⠿⢭⣿⢿⣟⠛⠻⠿⣯⡿⠿⠿⠟⠉⠉⠙⠛⠻⠿⣿⣿⣟⡻⡟⢿⣤⣄⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠶⠋⠋⠀⠈⠁⠀⠀⠀⠀⠠⠿⠤⠒⠂⠐⠀⠀⠀⠀⠠⠍⠛⠫⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⢘⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⢀⠀⠀⠀⠀⢀⣤⠀⢀⣀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢿⣿⠿⠇⡟⣦⣀
⠀⠀⠀⠀⠀⠀⢘⠛⠛⢰⣿⣿⣷⣤⠀⠉⠉⢠⣼⡛⠎⡀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠟⠋⠀⠀⢀⣹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠉⣀⢼⣿⠟⠀⠙⠻⢿⣦⡤⢸⣿⣧⣾⠏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⣹⠶⡇⢫⠉⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⣡⣾⣿⣦⣀⠠⠔⠒⠉⠁⠠⢨⣭⣤⣤⢴⡾⡆⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠰⠂⠿⠟⢠⣾⠃⠈⣇⠈⠋⢻⣿⣧
⠀⠀⠀⠀⠀⠀⣨⣻⠟⠏⠺⣷⣌⢲⡀⠀⠀⠀⠌⠀⠈⠛⣦⡘⢿⣶⡀⠉⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠸⡀⠀⠈⠻⢿
⠀⠀⠀⢄⢒⣴⠞⠁⠀⠀⠀⠙⣿⣆⠹⣆⠀⡸⡤⠔⠚⠉⠀⠀⢀⣿⣧⡄⠈⣭⣙⡛⠶⣄⠀⠀⠀⠀⠂⠀⠀⠀⣠⣤⣴⡿⡁⠀⠀⠀⠀⣧
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⣿⣤⣷⡆⠀⢀⣶⡀⠀⠀⣀⣘⣋⣩⣥⣴⣿⣿⣿⣦⡈⠆⠀⠀⠂⠀⠀⠔⢋⣡⡾⠛⣾⣀⣠⡴⢂⣴⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣠⡀⠀⠐⢫⣭⠱⣿⠿⠧⠀⢰⣿⣿⡧⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠘⠟⠁⠀⠒⢦⠨⣇⠀⠀⢀⡴⠛⣿⢟⣵⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣤⣶⡇⠀⠀⠈⢧⣀⠜⠀⠀⢥⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⠃⣤⣾⣿⣿⣿⡎⠻⠀⠀⠀⣤⡄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⡀⠀⠀⠠⣿⠍⠀⠀⣄⡁⠤⡴⡿⠟⠉⣀⢴⡆
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠤⠤⠀⢀⡤⢀⣶⠘⠋⠉⠉⠀⢀⠀⢠⢦⡉⢉⠀⠲⣶⣶⡾⠻⢿⣄⡀⢀
⢀⣀⣠⣴⣾⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠘⢁⣜⣷⣿⣿⣾⣷⣐⣼⠛⠀⠀⠀⠀⠈⠃
⠘⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠟⣻⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⣤⠀⢀⣀⣠⣴⠞⠛⠳⠶⢤⣤⣆⣧⠀⢠⡶⢯⡀⠹⢿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⢠⣤⣀⡄⠀⢀⡰⡷
⠀⢀⣠⠞⢁⡴⠛⠛⠉⠀⠀⠀⠀⠀⠀⢻⡈⡟⠠⠀⠀⠀⠀⣠⡉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠹⣀⣠⣉⣉⡀⠀⢦⡄⠀⡀
⠘⣻⣥⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⡆⠀⠀⣰⡶⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠉⠠⠰⢿⣟⠋⣨⣷⠿⡇⠀⠘⢃⣴⡄⠲⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⢁⣠⣼⣏⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣠⣤⡤⠀⠀⠉⠀⠀⠴⠄⠀⠈⣿⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠿⠦⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠄⢠⣴⡶⠠⣴⣻⠟⠀⠀⠀⠀⠠⡀⠀⠠⡆⠀⢿⣷⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣴⣶⣿⣿⠿⠛⠁⠀⠚⠁⢰⣿⠋⠁⠀⠀⠀⠀⢠⢠⣿⣶⣦⡀⢶⣬⣿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣤⣄⣜⠁⢀⡞⠀⠀⣢⡀⡾⠾⣿⢹⣿⣷⣼⡟⠁⠀⠈⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡽⢿⡷⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣾⠇⣀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⣋⣡⣿⣱⣴⡄⠀⠀⢠⠐⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠸⠿⠿⢿⣿⣶⣷⣤⣤⡤⠀⠀⣿⣿⣿⣿⣿⣧⣦⢀⠸⣶⣡⠀⡀⡆
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣢⡏⣹⣶⣽⣷⣦⣍⠻⢿⣿⣿⡆⠀⣿⣿⠋⠙⠻⠿⣿⡯⠀⢿⣿⣯⣜⠳
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣳⣿⣷⡹⣿⣿⣿⣷⣄⠫⠻⣿⣿⣥⡟⠀⣀⣶⣀⣤⣌⣀⠎⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢰⡻⠿⣿⡟⣡⣿⡿⠻⣿⣮⣿⣿⣿⣿⣿⣦⡭⣷⣾⣿⡟⢋⡭⢋⣽⠏⠁
⠀⠀⠀⠀⡐⣴⣫⣾⣦⡾⠿⠟⠓⠒⠘⣿⣿⣿⣿⣿⣿⣿⡇⢽⣿⣿⣿⡀⣿⣿⡇⠀⠀⣐⡋
⠀⠀⠀⠀⠹⣏⣿⡿⠋⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣠⡞⢉⣿⣿⡇⠙⢿⣷⣶⠀⠻⠋⠻⣿⣿⣻⣤⡁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠿⣛⣯⡷⢛⣵⣿⣧⠀⠀⢹⣿⡟⠀⠀⠀⠸⡿⣿⢹⢁⣧⣐⣶⣿⣏⡑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⡁⠉⣴⣿⣿⣷⣄⣿⣿⣂⠰⠀⠀⠀⣿⣾⠀⢾⣿⣿⡜⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⢞⣡⣾⣿⡿⣫⣿⣏⣌⡿⡇⣂⡀⠄⠀⣿⡿⢸⣸⣿⣿⡇⣿⣿⣿⣿⣿⠷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣻⡄⢹⣿⣿⣷⣿⣧⣿⣿⢯⣿⠃⠹⡿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⠭⣶⣿⣿⣿⣾⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣻⣿⣿⡿⠋⠀⠀⠀⠈⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⠻⠿⠿⠟⠛⢻⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣧⡼⠁⠉⠉⣹⣿⣿⣿⢟⣿⣿⣿⡿⣋⠝⠁⠀⠀⠀⠀⢀⠄⡐⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣠⡖⣫⣾⠿⠛⠋⠁⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⡿⡷⠊⠀⠀⠀⠀⠀⠀⡰⣡⠎⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠏⠊⠀⠀⠀⠀⠀⠀⠠⢊⠔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠙⢿⣦⡀⠠⢶⣤⡀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⠔⣠⠞⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠻⠿⠗⠚⠛⠁⢸⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⡠⢂⡵⠚⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠃⠀⣀⠴⠊⠀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⠀⣠⣤⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⡀⠈⠙⠛⠻⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠋⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠈⠛⣛⣿⣿⣿⣿⣿⣿⡿⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠐⠛⠛⠛⠛⠿⡿⠻⠟⠋⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠁⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠈⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣶⣦⢀⣠⡀⠀⠀⠈⢻⣧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡎⠉⠛⠿⠟⠛⠛⠁⠀⠀⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠿⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣻⣟⣝⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢠⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠀⠀⣠⣴⣾⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡉⠉⠛⣿⣿⣿⣿⣤⣄⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠉⠉⠉⠋
⢠⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠚⢿⣶⣦⣜⣷⣾⣿⣿⣿⡿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠛⠛⣿⠿⠿⠟⠋⠉⠀⠀⠀⠙⣿⣿⣿⣿⣿⠇⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣏⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠙⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⠙⣿⣶⣄⠀⠀⠀⠀⣸⣿⣯⠀⣀⣠⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⡆⠉⠛⢻⣷⣶⠶⠶⠿⠋⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⠀⠀⠀⠛⠃