Fleur de lis Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢀⣤⠴⠖⠚⠛⠓⠒⠶⣤⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⡤⠶⠒⠛⠛⠒⠶⢤⣀
⠀⠀⠀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣃⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⢠⠞⠁⠀⠀⢀⣠⣶⣾⣿⣿⣿⣷⣦⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⣠⣶⣾⣿⣿⣿⣶⣦⣀⠀⠀⠀⠙⣦
⢠⡏⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣼⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣧
⣼⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⢿⣿⣿⣆⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⠁⠀⢀⣾⣿⣿⠟⠛⠛⠛⠻⢿⣿⣿⣿⣿⣷⡀⠀⠀⢸
⡏⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⣰⠃⠀⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀⠀⠈
⣷⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⠀⠀⢿⣿⣿⣿⠀⠀⢰⠇⠀⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⢠
⠘⣆⠀⠀⠘⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣤⣬⣿⣿⣿⣤⣤⣯⣤⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠀⠀⢀⡾
⠀⠈⠳⢤⣀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⢀⣠⠴⠋
⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡤⢤⣤⣤⣼⡦⢤⣤⠤⣤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣼⣿⣿⣿⠀⠀⠹⡄⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣾⣿⣿⣿⣿⠀⠀⠀⠙⢦⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠳⣄⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⢠⣾⣿⣿⣿⠿⢿⣿⣿⣿⠀⠀⢸⠷⣤⣀⣀⣹⣦⠀⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣈⠳⣄⠀⠀⠀⠈⢿⣿⣿⠀⢠⡟⠀⠀⠀⢀⡴⢃⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠆⠀⠀⠈⠻⣿⡴⠋⠀⠀⠀⠶⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⡿⢿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠁⠈⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⣿
⠀⢀⣠⣤⣄⡀⢻⣿⣿⣿⡟⢀⣠⣤⣄⡀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠿⠿⣿⡀⠀⠀⠀⣿⠿⠿⢿⣿⣿⣿⣇⠀⠀⠀⠀⢀⡀⠤⢄⡀⢻⡀⠀⣾⡟⢀⣤⠤⢄⡀
⣴⣿⣿⣿⣿⣿⣆⢿⣿⡟⣰⣿⣿⣿⣿⣿⣦⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⠈⢧⠀⠀⡼⠁⠀⠀⠀⠈⢻⣿⣿⠀⠀⠀⡴⢁⣴⣶⣶⣬⡂⢷⣸⡿⣰⣡⣶⣶⣶⣌
⢿⣿⣿⠋⠉⠛⢿⡜⣿⢣⡿⠛⠉⠙⣿⣿⡿⠀⠀⠀⣿⣿⣇⠀⠀⣶⣶⣦⡈⡇⢸⢃⣴⣶⣶⠀⠀⣸⣿⣿⠀⠀⠀⢃⢾⣿⠋⠉⠛⢿⡜⣿⢣⡿⠛⠉⠙⣿⣿
⠈⠛⠛⠋⠀⠀⢈⣇⣿⣸⡁⠀⠀⠙⠛⠋⠁⠀⠀⠀⢹⣿⣿⣷⣶⣾⣿⡿⠷⠷⠾⠾⢿⣿⣷⣶⣾⣿⣿⡏⠀⠀⠀⠈⠛⠛⠋⠀⠀⢈⠇⠿⢸⡁⠀⠀⠙⠛⠋
⠀⠀⠀⠀⣤⠀⠛⡛⣛⣛⠛⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠙⠿⠖⠖⢲⠲⠿⠋⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠛⣐⣂⢚⠛⠀⣤
⠀⠀⠀⠀⠻⢷⡾⢻⣿⡞⢷⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣤⣾⡁⢈⣷⣤⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⡾⢋⢻⡞⠷⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣷⣾⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠞⠀⠽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠊⠀⡄⢠⡼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠷⣋⡘⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢠⠀⠀⢀⣈⣉⣀⣀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣴⠷⠚⠟⠛⠋⠁⢺⠋⠟⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣷⡶⢰⢶⠢⠦⣾⠀⣿⠐⠗⠃⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⣚⠉⠀⢨⢀⡄⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⣠⡄⣠⠤⣉⡀⠠⠷⠛⠰⠋⣿⠁
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡀⠀⣠⣶⠂⠐⣤⡀⠀⠀⠀⢠⠚⠁⠀⠀⣿⡏⠀⠒⣢⠀⠀⣼⠃⠀⠀⠀⠀⢀⠄⠀⣀⣀⡀⢀⠤⠄⠀⠠⣄
⠀⠀⠀⠀⠀⣍⠔⠀⢀⣤⣶⣶⠿⠇⠀⠀⠐⣿⠱⣄⠀⠈⢷⡊⢀⣈⠋⠀⠀⣰⡏⠀⣼⠃⠀⠀⠀⡀⠶⢛⣴⣿⠟⠋⠰⠃⣞⡉⠀⡠⠌⢷⡀
⠀⠀⠀⣐⣶⢏⢯⠀⡈⡤⢀⡀⠀⠀⠀⠞⢻⢃⣀⣉⢷⣄⠀⢁⠈⠉⠉⠘⠀⠛⠁⣼⠃⠀⠀⡀⠐⠂⣰⣿⠋⠀⠀⠀⠠⠀⠀⠐⠃⠂⠀⠘⢷
⠀⠀⠘⣉⠔⢡⠄⠀⠈⢀⣊⣁⡀⣠⢳⠖⠋⠁⠐⢁⣀⣻⣆⠀⢠⣶⠠⠶⣶⣧⣼⠏⠀⠀⡾⠏⡦⠸⠟⠋⠄⠀⣤⠤⢰⣴⣶⠟⡷⠀⡗⠄⣿⡇
⠀⠀⠀⠁⠀⣠⠒⠿⠛⣛⢻⠟⢀⣅⣈⣄⣠⣤⠟⠋⠉⢉⣹⣆⠀⠀⢀⣾⠏⢠⡏⠀⠀⢁⡤⠚⠁⠀⣞⣀⣀⣮⡤⣤⠘⠛⠃⡀⣀⠐⠟⡘⢹⡇
⠀⠀⠀⠠⠘⣛⠉⢐⠋⢀⣤⠶⠛⠋⠉⠉⠉⠛⠳⢶⣀⣠⠄⢿⡀⠠⠴⠃⣸⣿⠀⠀⠀⠘⣁⣴⠟⠛⠉⠉⠉⠙⠛⠲⢤⣈⠋⢀⣀⠰⠏⠀⣾⠁
⠀⠀⠀⢀⢀⠉⠘⡛⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⢸⡇⠀⠘⢐⢻⡇⠀⢠⡟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⣁⠀⣠⣼⠏
⠀⠀⠀⠈⢯⢀⡘⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠐⣋⢼⡇⠀⠈⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠐⣼⠏
⠀⠀⠀⠀⠈⠻⣅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡴⢼⣧⣤⡴⠇⢨⣴⣦⠟⢨⣧⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣸⡇⠀⠀⠉⣸⡅⠀⠀⢸⡇⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣠⡿⠀⠀⢀⣤⣿⡇⠀⠀⣚⣷⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⡛⡇⠀⣔⣽⠃⠀⠀⣾⠑⠋⢱⡀⠀⢩⠈⠷⡄⠀⠈⠁⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⣭⣀⢀⣨⡿⠁⠀⠀⠀⠁⠀⠔⢺⡇⠀⠀⠳⣆⠀⠐⠀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠟⠉⠀⠀⠀⠀⠀⠰⡆⢠⣿⠀⠀⠀⠀⠈⠛⠿⠶⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⡟⢻⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢦
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⣤⣶⣦⡜⣿⣿⢣⣴⣶⣤⠀⠀⢰⣿⡿⠛⠛⢷⠀⠀⡼⠛⠛⢿⣿⡆⠀⠀⠄⣀⣀⠸⡄⣼⢃⢔⣀⠠
⠀⢸⣿⡟⠛⢿⣽⣯⡿⠛⢻⣿⡇⠀⢸⣿⡀⠀⣤⣄⢃⠘⣠⣤⠀⢀⣿⡇⠀⠈⣼⡟⠛⢷⣽⣯⡾⠛⢻⣿⡇
⠀⠀⠉⠉⠀⢠⣭⣭⡄⠀⠉⠉⠀⠀⠈⣿⣿⣶⡿⣟⣋⣛⣻⢿⣶⣿⣿⠁⠀⠀⠉⠉⠀⢠⣛⣫⡄⠀⠉⠉
⠀⠀⠀⠀⠳⠶⢻⡟⠶⠞⠀⠀⠀⠀⠀⠈⠻⣿⣷⣭⡆⢰⣭⣾⣿⠟⠁⠀⠀⠀⠀⠀⠳⠴⠛⡿⠦⠞
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙
⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐
⠀⠀⠀⣀⡸⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⡀
⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃
⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠
⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸
⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙
⠟⠂⠀⠀⢀⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢀⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐
⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀
⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃
⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠
⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸
⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙
⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐
⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢃⣀⠀⠀⠀⠀⠀⠀⢀⡸⣿⣿⢃⣀
⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃
⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠
⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸
⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙
⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐
⠀⠀⠀⣀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡘⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⣀
⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⡀⠀⠘⠋⠙⣿⣿⠋⠙⠃⠀⢀⠀⠀⠘⠋⠙⣿⣿⠋⠙⠃
⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠⣾⣷⡄⠀⠀⠐⠻⠟⠂⠀⠀⢠
⣿⢇⡀⠀⠀⠀⠀⠀⠀⢀⡸⣿⣿⢇⣀⠀⠀⠀⠀⠀⠀⣀⡸⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⢀⡸⣿⣿⢇⡀⠀⠀⠀⠀⠀⠀⢀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⢀⡤⠒⠉⠉⠑⠢⣄⠸⡀⠀⠀⢀⡇⣠⠔⠊⠉⠉⠒⢦⡀⠀⠀⣠⣶⣾⣿⣿⣶⣤⡀⣿⣿⣿⣿⡿⢀⣴⣶⣿⣿⣷⣦⡄
⡞⠀⠀⠀⠀⠀⠀⠈⢣⢣⠀⠀⡼⡴⠁⠀⡀⠀⠀⠀⠀⢱⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⡼⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿
⢧⠀⠀⠀⢸⠉⠉⠳⡄⣿⡆⢠⣿⢡⠞⠉⠉⣧⠀⠀⠀⡸⠀⠸⣿⣿⣿⣿⠋⠉⠙⢿⣿⣿⣿⣿⣿⡟⠉⠉⢹⣿⣿⣿⣿
⠀⠑⠦⠤⠼⠆⠀⢀⣹⢸⡇⢸⡇⣏⡀⠀⠐⠧⠤⠴⠊⠁⠀⠀⠙⠻⠿⠿⠗⠀⠀⣈⣿⣿⣿⣿⣿⡀⠀⠀⠾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢧⢠⡄⢠⣄⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⡎⢧⣠⢎⣿⠃⠘⣿⡹⣄⡼⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⣼⡿⣾⣿⣿⣿⣦⣠⣿⡆
⠀⠀⠀⠀⠀⠑⠦⠴⠊⢸⠀⠀⡇⠑⠦⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠟⠱⣿⣿⣿⠈⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏

⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠛⠲⢦⣀⠀⠀⣧⠀⠀⠀⠀⣸⠀⠀⣀⡴⠖⠛⠛⠛⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣀⣄⣀⠀⠈⢷⡀⢸⡄⠀⠀⢠⡇⢀⡾⠁⠀⣀⣠⣀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣾⣡⣄⡈⠙⢦⡀⠹⡄⣷⠀⠀⣾⢠⠟⢀⡴⠋⢁⣠⣌⡷⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢳⡀⢳⢸⡆⢠⡇⡞⢀⡞⠀⢰⠏⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣰⠃⠀⠀⢷⣸⣿⣇⣸⣻⣇⡾⠀⠀⠘⣆⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠒⠋⠁⠀⠀⣠⠬⠭⠤⠭⠭⠤⠭⠥⣄⠀⠀⠈⠙⠒⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⣤⡈⠉⣭⡉⣩⣍⢉⣭⠉⢁⣤⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⡀⣨⡇⣰⢻⠃⡟⢻⠘⡟⣆⢸⣅⢀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⠿⠭⠞⣡⠏⢸⠃⠘⡇⠹⣌⠳⠭⠿⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠶⠚⠁⠀⡟⠀⠀⢻⠀⠈⠓⠶⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣴⡄⠀⣿⣿⣿⣿⣿⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣀⣀⠀⠙⣆⢻⣿⣿⣿⡏⡰⠋⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠸⣿⣿⣿⣿⣿⠃⢀⣀⣤⣤⣀
⠀⢰⣿⣿⣿⣿⣷⣌⢿⣿⣿⣿⡿⣡⣾⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡹⣿⣿⣿⢃⣾⣿⣿⣿⣿⣿⣷⡄
⠀⢸⣿⣿⣿⡛⠛⢿⣮⣿⣿⣿⣵⡿⠛⢛⣿⣿⣿⠇⠀⠀⢸⣿⣿⡟⠋⠉⠛⢿⣿⣿⣿⣿⣿⡿⠛⠉⠙⢻⣿⣿⡇
⠀⠀⠉⠉⠉⠻⠂⠀⢹⣿⣿⣿⠏⠀⠰⠟⠉⠉⠉⠀⠀⠀⠀⠙⠻⠀⢀⣠⡄⣤⣿⣿⣿⣿⣿⣄⢠⣄⠀⠠⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣦⣠⣿⢿⣿⣻⣧⣄⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠩⢿⣿⡷⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣜⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣸⣿⣧⣀⠨⠑⣄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⡎⡀⠐⠈⢀⣿⣅⡁⠀⠀⡹⣇⠀⠀⠀⠀⠀⠀⢢⣤⡀
⠀⠀⠀⠀⢰⡯⢉⡤⣀⠘⠀⠀⠀⠸⢀⠀⠀⢀⣼⣿⣿⣄⠀⠀⢠⣹⡄⠀⠀⠈⠠⠀⢄⠐⢳
⠀⠀⠀⠀⠈⠁⠈⡄⠀⢦⠀⠀⠀⢆⠂⠀⠀⠀⢀⣿⣇⠀⠈⠃⠀⢳⠇⠀⠀⢁⡁⠠⠦
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠃⠀⠀⠀⣸⠀⡄⠀⢀⣼⣿⣿⡀⠀⠀⠚⣸⠁⠀⠀⠂⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⡟⡄⠀⢀⠛⠋⣿⡏⠙⠂⠀⢀⡟⠃⠀⢁
⠀⠀⠀⢀⢀⠴⠒⠂⠀⠀⠶⢉⠙⠃⠘⣤⠉⠀⢈⣿⡏⠀⠀⣼⡜⢀⠏⠉⠵⠛⠁⣉⠉⠩⠉⠲⣤⡀
⠀⢀⡔⢱⠁⡆⢀⠘⠁⠀⠀⠀⠑⢤⠀⠹⣀⠀⠾⢻⠿⠄⢀⡿⠠⢃⡖⠁⠠⠤⡀⠈⢣⡀⡄⠀⠀⢻⡆
⢠⡟⡀⠁⠀⢳⡏⠀⠀⠀⡀⠀⣀⣭⡳⡄⢻⠀⠄⣸⡀⡆⣿⠡⡐⠋⢤⡀⠀⠀⠈⠀⠀⣿⠁⠁⠀⣦⣿
⣼⠃⠇⠀⠀⠘⣇⠀⢀⣀⣿⡟⠉⠀⠉⠘⡌⣇⢰⡻⡇⣸⣧⡏⡚⠀⠀⢆⡻⣯⣀⠐⣰⣟⢀⠸⢠⣽⢿
⢻⡄⢌⡐⠂⢀⣟⡗⢾⣟⠿⣟⠳⣤⢄⠠⠸⠘⠀⠀⠀⡿⣿⠞⣀⣴⠶⣻⠿⠛⠿⣿⣾⡷⢔⡞⠛⢁⡾
⠀⠳⡠⢄⢀⡲⠛⣾⣧⠀⢲⡼⠀⠀⠑⣷⠄⢦⣧⠀⢰⣽⡋⢾⡟⠁⠀⠑⣐⠹⣰⢽⡞⠃⠀⢒⢠⡟⠁
⠀⠀⠈⠢⣄⡀⡤⢼⣿⣣⠊⠀⠀⠀⠀⠈⢦⠈⣿⡀⢸⣿⢰⠏⠀⠀⠀⠀⠀⠑⣽⠿⢶⣦⡴⠖⠁
⠀⠀⠀⠀⠀⠉⠙⠒⠂⠈⣁⠀⠀⠀⠀⠀⢘⣷⣿⠇⢾⣿⣿⠀⠀⠀⠀⠀⠀⠄⡠⠚⠉⠀⠀⢠
⠀⠀⠀⣸⣀⡀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⢦⠹⠀⠀⠍⡖⠀⠀⠀⠀⠀⢸⣀⡅⣤⠀⠀⠬⢼⣧⡀
⠀⠀⢾⣿⡦⠌⠴⠦⣉⣩⠟⠀⠀⠀⠀⠀⠀⠈⣶⡘⣦⣮⠀⠀⠀⠀⠀⠀⠀⠓⠄⠁⠘⠃⢄⡻⠛⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⢐⠂⢠⠄⠀⠜⡙⢙⠣⡤⡴⠂⠰⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⠀⠀⠀⣀⠜⢁⠈⠃⣀⠄⢰⠀⣶⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠑⡾⡥⠠⠻⠘⡄⠸⠗⢫⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠁⠉⠑⢄⡠⠋⠁⠐⠚⠷⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⢘⡃⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡐⠁⠸⠇⠈⢂⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠜⠁⢀⡇⢸⡀⠈⢣⡀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⢊⡄⠄⠸⣿⣿⠇⠠⢠⡑⣄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡄⡰⣡⠋⠀⠀⣠⣿⣿⣄⠀⠀⠙⣌⢆⢠⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡀⡧⣍⣦⡶⣲⠟⡽⢏⠻⣄⢶⣴⣩⢼⢠⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⠁⠹⣿⠋⡔⠸⠀⠀⠇⢤⠙⣿⠏⠌⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⣧⠀⣼⠀⡇⢸⡄⠠⡇⠸⠀⣧⠀⣼⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢎⢧⠸⣆⠀⠸⣧⣼⠇⠀⣰⠏⡾⡱⠋
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠈⠳⡣⡹⡄⠀⢻⡟⠀⢠⢏⢜⠞⠁⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⡠⢒⡭⠀⠀⠠⠤⠀⠈⠉⠒⢤⡙⣆⠘⡄⣸⣇⢠⢃⣲⢋⡤⠒⠉⠁⠀⠠⠄⠀⠀⢭⡒⢄
⠀⠠⠊⣠⠎⠀⠀⠀⠠⠔⠒⠒⠲⢤⣄⠈⠻⣧⢘⣨⣄⠁⣼⠟⠁⣈⡤⠖⠒⠒⠢⠄⡀⠀⠀⠹⣄⠑⠄
⠀⠂⠌⣾⠶⠆⠀⠀⠀⠀⠀⡠⣤⣤⣤⡙⢦⡘⣿⣿⣿⣿⠃⡴⢋⣤⣤⣤⢄⠀⠀⠀⠈⠀⠰⡶⣿⠱⠐
⣰⠸⢸⡧⣼⠆⢀⠀⠁⠀⠂⠀⠀⠙⠳⣍⢢⡱⡘⣿⣿⢃⢎⡔⣩⠞⠋⠀⠀⠐⠀⠈⠀⡀⠰⣧⢼⡇⠇
⣧⠀⢂⢷⣻⡀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠙⠆⢳⢷⢹⡏⣞⡞⠰⠋⠀⠀⠀⠀⠀⡀⠀⠀⠈⢀⣟⡾⠐
⠁⠀⠠⣐⠉⠉⠉⠑⡄⠓⠐⠄⠀⠀⠀⠀⠘⣸⣿⢾⣷⣿⡇⠁⠀⠀⠀⠀⡠⠂⠚⢀⠉⠉⠉⠉⣈⠄
⠀⠠⠀⠀⠑⠀⠀⠈⠉⢁⣠⠏⠀⠀⠀⠀⢀⣄⣿⣸⡇⣿⣤⠀⠀⠀⠀⠀⠹⣄⠈⠉⠁⠀⠀⠈⠀⢀⠐
⠀⠀⠀⠐⠀⠤⠴⠮⠍⠛⠃⠀⠀⠀⠀⠀⣾⡽⠿⡼⢧⠿⢯⣷⠀⠀⠀⠀⠀⠘⠂⠤⠶⠦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣴⣶⣶⣶⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⡄⠀⠃⠀⠀⣸⠃⣿⣿⠘⣆⠀⠀⠘⠈⢢⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠙⠒⠒⠒⣺⠏⣰⣇⡸⣆⠹⣓⠒⠒⠒⠋⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠂⠀⢀⣈⣵⠾⡿⣾⣧⢿⠷⣬⣁⡀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠍⠀⠀⣠⡏⢻⣄⠀⠀⠩⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡋⠁⠁⠉⠈⢙⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⡤⠞⠉⠁⠀⠀⠀⠉⠙⠲⢄⡀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡤⠖⠋⠉⠀⠀⠀⠈⠉⠳⢤⡀
⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⡆⠀⠀⠀⠀⢀⡴⠋⠉⠉⠉⠉⠓⢦⣀⠀⠀⢳⠀⠀⠀⢀⡟⠀⠀⣠⠴⠚⠉⠉⠉⠉⠙⢦⡀⠀⠀⠀⠀⢰⠃
⠀⠀⠹⣄⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⡇⠀⠀⣸⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⠏
⠀⠀⠀⠈⠳⣄⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠦⠿⠤⠤⠿⠴⠚⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠀⠀⠀⠀⣠⡆⠀⠀⢻⣀⡀⠀⠀⠀⠀⢀⣠⠏⠀⠀⢱⣄⠀⠀⠀⠀⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⣇⠀⠀⢠⠏⠉⣿⠛⠛⣟⠉⠹⣄⠀⠀⡼⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⠙⠚⠁⠀⢠⡟⠀⠀⢻⡀⠀⠈⠙⠋⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⢀⣀⣤⠟⠀⠀⠀⠀⢻⣦⣀⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣡⠞⢀⡀⠀⠀⢀⠀⢳⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⠙⡇⠀⠀⣸⠙⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⡠⠈⢠⠈⠢⡀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡀⠀⠀⠀⠀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠤⠆⠀⠀⠀⠀⠀⠈⠦⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠱⠄⠔⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⠍
⠀⠀⠀⠀⠀⠠⠀⠐⠒⠂⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠐⠒⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢲⠁⠀⠀⠀⠀⠀⠀⢱⠆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠀⠉⢀⠀⠀⠀⠤⠠⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⡀⡠⠄⠀⠀⢀⠘⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠑⠓⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⣀⠀⠄⠀⠠⠀⠀⠀⠀⠄⢀⣀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢⣤⢄⢄⡤⠊⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⢠⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠘⠀⠀⢀⠀⠀⠘⠀⠀⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⠒⠁⠈⠀⠑⠢⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿⣿⣿⣿⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠿⠛⠋⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠀⠀⠀⢀⣾⡀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⡛⠀⠀⠀⣸⣆⠀⠀⠀⠀⠸⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣤⣶⣿⡿⣹⣿⣿⡸⣿⣷⣦⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⢡⣿⣿⣿⣧⠹⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣼⣿⣿⣿⣿⡄⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣶⣶⣤⣀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣠⣤⣶⣶⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿⣿⣿⣿⣿⣿⠏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣇⢻⣿⣿⡟⣸⣿⣿⣿⠿⠟⠻⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠻⣿⣿⠸⣿⣿⠇⣿⣿⠟⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠃⠀⠀⠀⠀⠀⠀⣘⣛⣁⣛⣛⣈⣛⣁⠀⠀⠀⠀⠀⠀⠘⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⢉⣭⡉⣭⣭⢉⣭⡉⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣤⣶⣿⡿⢰⣿⣿⡇⢿⣿⣶⣤⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠁⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠸⣿⣿⣿⣿⠇⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⠶⣤⠶⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣋⡛⣋⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣇⠀⠀⠀⢼⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⣿⣿⣿⡿⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢠⢹⠀⣤⢀⡏⠄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢻⡟⣿⢣⣿⡏
⠀⠀⠀⠀⠀⠀⠀⡞⢁⣬⣱⣼⡇⣿⢸⣠⣎⣤⡈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⢮⢻⢸⡇⣿⢸⢫⢾⠿⣦
⠀⠀⠀⠀⠀⠀⡀⣧⡘⢤⣝⡻⡅⠉⢬⠛⣯⡤⢃⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣘⠺⣼⣺⣷⣿⣲⣼⢚⣱⠟
⠀⠀⣠⠖⠊⠉⠁⡈⡉⢂⢬⡙⢫⣩⡝⣋⠥⠒⢉⣁⠈⠉⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣶⣿⣟⠶⣼⠷⢿⡴⢞⣿⣷⣾⢿⣷⣶⣤⡀
⢀⣾⠃⡠⠖⠀⠐⠷⡄⠓⣿⢝⢦⣟⡼⡷⣿⠒⢤⠾⠂⠀⠢⡄⠸⣷⡀⠀⠀⠀⠀⣸⣿⣻⣿⣿⣯⣻⣯⡇⡵⣼⠇⢿⡵⣅⣯⣿⣏⣿⣿⣿⣻⣿⡀
⡾⣿⢠⣥⠞⠋⠉⠉⠓⠾⣝⠘⣿⠙⣿⢁⣫⠷⠚⠉⠉⠙⠲⣼⡄⣿⢷⠀⠀⠀⡆⣿⠻⠋⠁⠀⠈⠉⠉⠱⣿⡞⣴⡜⣻⡿⠋⠉⠉⠀⠀⠉⠻⢿⡇
⣇⠹⣾⡇⠀⠀⠶⣄⠀⠘⢟⢧⡇⠀⢸⡼⡿⠃⠀⡠⠖⠀⠀⢸⣷⠏⣸⠀⠀⠘⣷⡹⠀⠀⠀⠀⡄⠀⠀⠐⣜⢳⣿⣷⢛⡔⠀⠀⠀⡄⠀⠀⠀⠰⢱
⠘⢆⡈⠳⠤⠴⠋⣸⠀⠀⢸⠈⠃⣀⠘⢹⡇⠀⠀⣇⠙⠦⠤⠞⢁⡴⠃⠀⠀⠀⠘⢷⣦⣀⣀⣠⡟⠀⠀⠀⢸⣾⡿⢿⣾⠀⠀⠀⠘⣷⣄⣀⣠⣶⠟
⠀⠀⠙⠲⠶⠖⠚⠁⠀⢠⣾⡿⠼⠛⠷⢿⣳⡄⠀⠈⠓⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠠⢌⣙⣬⣌⣉⠤⠀⠀⠀⠈⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣷⢐⣾⡁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⢏
⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠺⣥⣤⣤⣬⡬⠗⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠸⢛⣛⣟⠻⠂⠀⠀⡀⡀
⠀⠀⠀⠀⢀⡞⡽⠛⠁⠀⠀⢈⣿⠟⣿⡁⠀⠀⠈⠛⣮⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠠⣤⡤⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⢸⡅⠙⢦⣀⣀⢤⠊⡌⣤⢣⢑⣤⣀⣀⡴⠋⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⡀⠀⣀⢴⣧⡟⣧⣷⢄⡀⠀⢀⣰⣿
⠀⠀⠀⠀⠈⢧⣐⠀⠠⠆⢸⠏⠜⣿⠣⢹⡣⠰⠄⠀⣂⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣻⣿⢦⣿⡆⣼⣧⢸⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠈⢹⠀⡆⣿⢰⢀⡏⠑⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢾⣿⡇⣿⣿⠆⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⣇⠉⣸⠾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣷⡿⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣟⣫⣛⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣭⣯⣿⣯⣿⣿⣽⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⢠⣤⡀⢸⣿⣿⡀⣠⣤⡀⠀⠀⠀⢀⣤⣄⣾⣿⢄⣤⣄⠀⠀⠀⠀⣀⣤⣤⡰⣼⢀⣤⣤⡀⠀⠀⠀⠀⢀⣀⣀⡀⣿⡇⣀⣀⣀
⠀⠀⠀⠀⣿⡿⠻⣞⣿⣟⡾⠛⣿⡇⠀⠀⠀⣿⠛⢿⣿⣿⡿⠛⢻⡇⠀⠀⣼⠛⠉⠻⣿⣿⡿⠛⠙⠻⣆⠀⠀⡼⠋⠉⠙⢿⡎⣿⠟⠋⠉⠛⠆
⠀⠀⠀⠀⠉⠀⠀⠈⣿⡏⠀⠀⠈⠁⠀⠀⠀⠹⠃⠀⢹⣿⠁⠀⠻⠀⠀⠀⢷⡴⠀⠀⢻⣿⠇⠀⠀⣦⡟⠀⠀⠀⠀⠀⠀⠸⡷⣿
⠀⠀⠀⠀⠀⠀⢀⣄⣿⣇⣤⠀⠀⠀⠀⠀⠀⠀⠠⣄⣸⣿⣀⠤⠀⠀⠀⠀⠀⠀⣄⣄⠼⠛⢆⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠁⠈
⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀
⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⢳⡄⠀⠀⠀⠀⠀⠀⢠⢿⠀⢸⢧⡀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠑⡄
⠀⢀⣤⣤⡹⣿⠠⣡⣤⣄⠀⠀⣠⣤⡻⢰⣿⡄⣟⣤⣀⠀⠀⢠⡶⠾⣿⣇⣾⡿⠶⣦⠀⠀⣴⢛⣙⢺⣿⠞⣋⡛⣆⠀⢀⣤⣄⡏⠀⣠⣶⣯⣤⣄
⠀⠘⠒⠁⣱⣿⣼⡁⠑⠊⠀⠀⠻⡔⠈⠻⣿⠟⠁⢢⠟⠀⠀⠈⠃⠀⢈⣟⣏⡀⠀⠋⠀⠀⠘⠚⠋⢰⣿⠀⠙⠛⠁⠀⠋⠻⠗⠉⢂⣟⠋⠐⠿⠉⠂
⠀⠀⢀⣌⣻⣿⢿⣃⡄⠀⠀⠀⠀⠀⠠⣤⣿⣠⠀⠀⠀⠀⠀⠀⠀⣤⣹⡿⣿⣡⡄⠀⠀⠀⠀⠀⠠⡾⣿⢷⠄⠀⠀⠀⠀⠀⠀⠀⢾⣿⡆
⠀⠀⠀⠀⠙⠿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢇⠝⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇
⠀⠀⠀⠀⠀⢀⡤⠤⣄⣿⣇⡤⠤⣄⠀⠀⢀⣤⣄⡀⣾⣿⡄⣀⣤⣄⠀⠀⠀⢀⣤⣤⣏⢹⡟⣹⣧⣤⣄⠀⠀⠀⣠⣤⣤⡘⣿⠇⣠⣤⣄
⠀⠀⠀⠀⠀⠸⣐⡷⠈⣿⡏⠰⣗⡸⠃⠀⢿⣿⠟⢿⣜⣟⣾⠟⢿⣿⠇⠀⠀⣿⠋⠈⠙⣿⣿⠟⠁⠉⣿⡇⠀⠸⣿⡟⠙⣷⣿⣾⠛⢙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⣿⠁⠀⠀⠉⠀⠀⠀⠈⠁⠀⣿⣿⣿⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢤⠞⢻⠛⢦⠄⠀⠀⠀⠀⠀⠀⠼⠃⠇⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⡏⠣⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⢿⠟⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⢀⣼⣿⠟⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⢠⣿⣿⠃⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠃⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⢀⣠⣴⣾⡿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⣿⣏⢻⣿⣷⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⣿⣿⠟⠉⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠙⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠃⠸⣿⣄⡀⠀⠀⠀⠀⠀⣸⣿⡿⠋⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣿⣿⢿⣷⣦⣤⡀⠀⠀⠀⠸⣿⣷⣄⣀⣀⣼⣿⠇⠀⠀⠀⣀⣴⣿⣿⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⢀⣿⡟⠀⠉⣿⣿⠁⠀⠀⠀⠀⠘⠻⣿⣿⣿⠿⠋⠀⠀⢠⣿⡟⠋⢻⣿⡀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠺⣿⣷⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣼⣿⣷⡄⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠭⠉⠉⠉⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣬⣭⣽⣿⣿⣿⣶⣾⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣽⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠛⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⠀⣠⣄⢡⣄⡀⢀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠚⢳⠀⠀⠀⢹⣿⢸⡟⠀⠀⠀⢰⠟⠐⠶⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠉⠀⠀⠀⢀⣀⣼⣧⣶⡾⠎⠁⠈⠉⠷⣶⣦⣿⡴⣀⠀⠀⠀⠈⢉⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢰⣿⠛⠉⠉⡀⢀⡀⠃⠈⢃⡀⢀⡉⠉⠘⢻⣧⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⣷⠀⠀⠀⠙⠓⠖⠢⡔⠲⠶⠟⠀⠀⠀⢸⣿⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⣿⠀⠀⠴⡄⡀⠀⠸⠇⠀⠀⠀⡄⡀⠀⢸⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣿⠀⠀⠀⠻⣄⡀⠀⠀⠀⣡⠞⠀⠀⠄⣾⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠑⠀⠄⠀⠈⡈⠳⡁⡱⠞⠉⠢⠀⠀⠀⠙⠇⠀⢸⠁⠀⠀⠀⠀⠀⠀⡠⣴⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡴⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢀⣀⣠⣄⣤⡄⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠀⠀⢀⡀⠀⠀⣿⡇⠀⠀⠘⠛⠿⣿⣿⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⡀⠈⠀⢠⡾⠃⠀⠀⠿⠃⠀⠀⠀⠠⠀⣸⣿⣿⣀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣿⣶⡶⢉⡤⠦⣄⠀⠀⠀⢠⠔⠒⠀⠸⣿⣿⣏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣠⣤⣤⣤⣤⣤⣤⡀⣬⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠙⠛⠛⠛⠛⠛⠋⠀⠙⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠁⠀⠀⣠⡆⠀⠀⠰⢦⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠙⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠙⢦⣠⣴⣧
⠀⠀⠀⢀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀
⠀⠀⠀⠀⠉⣀⠄⠀⠉⠉⡽⠂⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⢾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠈⠁⠈⠂⠒⠠⢈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⢷⠀⠈⠹⣿⡿⠿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠄⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠠⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⠀⢠⣀⡄⠀⠀⠀⠀⢀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠺⠿⠁⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀⠀⠀⠀⠀⠄⠒⠀⠐⠐⠀⠢⠀⢄⠀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢴⡾⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠒⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣍⠶⢆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⡿⡟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⡇⠠⠤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⢻⠃
⠀⠀⠀⠀⠀⠀⠀⡄⠛⠛⠁⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡣
⠀⠀⠀⠀⠀⠔⡀⠀⠀⠀⠀⠀⡀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠀⣦⣤⡔⢀⢴⠦⢀⡀
⠀⠀⠀⡠⠆⢀⠀⡶⠀⡄⠀⠄⠀⠄⠄⠲⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⡇⠈⠁⢠⣳⣏⠞⠉⠙⠂
⠀⠀⠀⣥⣘⡀⠠⠀⢁⠀⠂⡀⠀⠠⠀⢐⡠⠀⣀⡰⠀⠀⠠⢄⠀⠹⠇⠀⢠⢳⢧⣟⠀⠀⠀⠀⠂
⠀⠀⢰⣿⣿⣿⣿⣿⣶⣶⠖⡂⠀⠁⠹⣿⣿⣤⡤⠫⠁⠰⡦⡀⠑⢌⡄⢀⡏⣿⣼⡫⠄⠀⠀⠀⠰⡀
⠀⠀⣼⣿⣿⣿⣿⣿⡿⣿⠀⠁⠀⠀⢣⠘⣿⣿⣶⠶⠆⠀⠇⠈⠦⣾⣿⣼⣟⣽⣿⣯⠅⠐⠶⣤⣬⡅
⠀⠀⢿⣿⣿⠁⢰⠁⠀⡾⠘⠿⠿⠿⠿⣧⠈⣰⣤⠘⠀⠀⠠⠀⣾⣿⣏⣹⣾⣿⡿⠋⠀⣀⠔⠉⠁
⠀⠀⠘⣿⣇⠀⢾⢈⣿⡇⠀⠀⠀⠀⠀⢻⡇⠹⡇⠂⠀⠀⢠⠀⢻⣿⣿⣿⡿⠟⠁⣠⣾⣿⣆
⠀⠀⢸⣿⣿⣄⣀⣼⡿⠁⠀⠀⠀⠐⠀⠘⣿⠈⠉⠀⠀⢀⣶⡆⢠⣿⣿⡟⠁⢀⣺⣿⣿⣿⣿⡆
⠀⠀⠿⠿⠿⠿⠿⠿⠁⠦⠤⠤⠠⠤⠤⠴⠿⠇⠀⠀⠀⠼⠿⠿⠿⠿⠿⠷⠶⠿⠿⠿⠿⠿⠿⠿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⣇⢠⡿⣦⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⣧⠀⢰⠆
⠀⠀⠀⠀⠀⢸⠚⣿⠉⣛⡏⢻⡟⠞⠀⠀⠀⠀⠀⠀⠀⣆⢸⣇⢰⣇⢰⡇⣰⠀⠀⠀⠀⠀⠀⠘⢧⣼⣷⠟⡙⢷⣾⣤⠟
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣷⣾⣷⡇⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⡟⢻⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣶⣷⣶⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠇⠠⠿⠾⠸⠣⠷⠈⠳⠀⠀⠀⠀⠀⢤⣼⣿⣿⣉⣿⣽⣽⣿⣹⣧⡤⠀⠀⠀⠀⠐⠌⠸⠦⠆⠟⠞⠆⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠆⠄⠀⠐⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠀⢀⡀
⠀⠀⠀⠀⠀⢶⡄⢀⣹⢤⢾⡁⠀⣴⠂⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣷⡠⠀⠀⠀⠀⠀⠀⠀⠰⡀⣸⣄⢼⢄⣼⡀⡰
⠀⠀⠀⠀⠀⢘⣾⣁⣹⣿⣿⣁⣹⡟⠀⠀⠀⠀⠀⠀⠀⣴⣩⣍⣯⣼⣭⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣤⠶⣢⣬⣽⡇
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣉⣉⣉⣉⣁
⠀⠀⠀⠀⠠⡆⢸⠿⠾⠸⠩⠿⠈⢳⡄⠀⠀⠀⠀⠀⠐⠏⠹⠷⠆⠞⠾⠌⠳⠄⠀⠀⠀⠀⠀⢶⡿⠽⠯⠽⠿⠯⠽⠯⠿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠀⠀⠀⠘⠀⠀⠀⠘⠉⠃

⠀⠀⠀⠀⠀⠀⢀⣀⡀⢼⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⡿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⣿⣧⣼⡄⡀
⠀⠀⠀⠀⠀⠀⢻⣇⣀⣿⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⣿⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣽⣅⣿⣇⣽⣭⠁
⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣾⣯⣷⡿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⠛⠛⠛
⠀⠀⠀⠀⢀⡄⢠⣤⣤⢠⢄⣄⠤⣄⠄⠀⠀⠀⠀⢀⣰⣶⣶⣒⣶⣲⣲⣶⢲⣆⣀⠀⠀⠀⠀⠀⡠⢠⣠⣠⢠⣤⣤⠠⣄
⠀⠀⠀⠀⠀⠁⠈⠉⣉⠈⢈⠈⠀⠈⠁⠀⠀⠀⠀⠼⠿⠍⠉⢉⠉⡍⡉⠉⠩⠿⠧⠀⠀⠀⠀⠀⠓⠈⠉⠉⢈⠈⡉⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁

⣿⠿⢿⢷⢿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⡿⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⢴⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡶⣠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠬⢇⡠⠁⢦⣀⠘⣦⡀⠀⣰⣧⠀⠀⣠⠖⠀⣀⡌⢠⡸⡯⠘
⠀⠀⠀⠀⠀⠀⠀⢰⡤⠶⣟⢃⡄⠀⠙⣷⣿⣿⣶⣿⣿⣷⣿⣿⣴⠟⠁⢠⡘⣛⠷⠦⣖
⠀⠀⠀⠀⠀⢀⡀⠋⠰⣦⣉⠌⣿⡶⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣶⣿⠃⣌⣱⠆⠸⢀⡀
⠀⠀⠀⢀⡀⠬⣻⠎⠲⠀⣼⣏⡺⣿⣿⣇⠘⠛⠉⠉⠉⠉⠛⠃⢨⣿⣻⡷⣙⣯⡀⠔⠱⢟⠥⠀⡀
⠀⠀⢴⡻⣿⣾⣇⡚⢷⣌⣀⡝⠁⣿⣏⣙⠦⣄⡀⠀⠀⢀⣀⡴⢋⣙⣿⠀⢻⣄⣈⡴⢛⣸⣷⣿⠟⡷
⠀⠀⠀⠈⠋⢿⡨⠅⠈⢿⢌⣁⣽⣠⡽⡉⠿⢁⡉⠀⠀⢈⣁⢿⠉⢹⣥⣻⣈⡡⣾⠃⠀⣍⡾⠏⠃
⠀⠀⠀⠀⠀⠉⠓⠀⠐⠚⠘⠂⢀⢮⡄⢹⡦⣾⣣⡄⢠⣌⣳⢴⡞⠀⣭⠄⠀⠂⠙⠂⠀⠺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠿⠏⠙⠃⠀⠉⠁⠈⠉⠁⠈⠋⠹⠿⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⣦⡈⢧⢰⠏⣠⠶⠶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⢀⣹⡜⣏⣞⣁⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⢿⣿⡶⠶⠛⠉⠀⣤⣤⡄⠈⠛⠶⢶⣿⡿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢠⡟⢀⣐⣾⣷⣦⡌⡭⣴⣶⣿⣆⡀⢻⡇⠀⠈⢻⡆
⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀⠀⠻⣄⢀⡞⠀⠸⣿⣿⠉⠉⣼⣿⡌⠉⣿⣿⡇⠀⢻⡄⢀⡾⠁⢀⣠⣤⣤⣀⡀
⠀⠀⠀⣤⣾⡿⠋⠉⠉⠉⠛⠲⣬⣝⠃⣶⡆⢛⣥⣶⣶⣿⣿⣷⣦⣬⡻⢰⣶⠘⣛⣭⠴⠚⠋⠉⠉⠙⢿⣿⣦
⠀⠀⠀⠈⠻⣿⣶⣤⣤⡶⠖⢋⡥⢲⡇⠙⠃⣶⣮⠙⠛⣿⣿⠛⠛⣩⣶⡘⠛⢐⡖⢬⡙⠲⢶⣤⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣿⠀⠀⢻⡄⢸⣿⣿⣶⣤⢻⣟⣤⣶⣿⣿⡇⢀⡾⠁⠀⢻⡄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣀⣀⣿⣀⠘⠛⠛⢉⣥⣬⡉⠛⠛⢃⣀⣼⡇⣀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⠛⠛⠳⢤⣤⡍⢩⣤⡤⠞⠛⠛⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⣠⠞⣸⢧⠳⣄⡀⢀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⣰⠇⠘⣆⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⢠⡦⣄⠐⡇⣽⣄⣴⣶⡄⠀⠀⠀⣴⣶⣦⣿⣿⣴⣶⣦⠀⠀⠀⢀⡤⢤⣤⢠⣤⣴⣶⣶⣄⠀⠀⠀⣠⣤⣤⣤⡰⡄⣀⡠⠤⢀
⠀⠀⠀⠀⠸⠃⠀⠀⣼⣿⠏⠉⠿⠇⠀⠀⠐⢿⡉⠹⣿⣿⠏⢉⡿⠃⠀⠀⠋⠀⠀⢸⣿⣿⠋⠀⠈⢻⡄⠀⠘⠁⠀⠀⠙⣿⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⡟⠀⠀⠁⠀⠀⠀⠑⠀⠀⠀⣿⣏⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠶⢺⡷⠖⠀⠀⠀⠀⠀⠀⠀⠘⠲⢾⡷⠶⠃⠀⠀⠀⠀⠀⠀⠰⠖⢥⡌⠲⠶⠂⠀⠀⠀⠀⠀⠀⠀⠜⢷⡿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣄⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⡀⠀⠀⠀⣠⣤⣄⣻⣇⣤⢤⣄⠀⠀⠀⠀⠰⠛⠃
⠀⠰⣟⡇⠀⠁⠀⠀⠀⠀⠀⠀⠾⠛⢪⣽⣿⣧⠓⠛⠆⠀⠀⠐⠁⠈⠠⢀⡞⠉⠉⠂⠀⠀⠁⠲⠆⢻⡏⢰⣶⡽⠀⠀⠚⡇⠀⠀⢠⠀⠀⣰⡶⡄
⠀⠀⠀⠀⢶⣄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡶⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠛⢶⣿⠐⠄⠁⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⠉⡿⠿⠂⠀⠀⠀⠀⠀⠈⠸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣿⡧⢀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠶⣿⡶⣦⣀⡀⠀⠀⠀⠀⢀⡀⠐⣿⡿⠀⢀
⠀⠀⠀⠀⠀⠐⠉⠄⠑⣿⡗⢩⡤⠹⠀⠀⣾⣿⢷⣦⢻⡿⣴⡾⣿⣷⠀⠀⢰⣿⠟⠻⣷⣿⣴⠟⠛⢿⣦⠀⠀⣾⡿⠿⢷⠹⢣⡾⠿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠁⠀⠀⠉⠉⠀⢹⢿⣿⡏⠀⠙⠉⠀⠀⠈⠛⠀⠀⠸⡿⠿⠀⠀⠘⠋⠀⠀⠉⠂⠀⢰⣶⣮⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣰⢿⡇⡀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⢶⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⣤⣖⢻⡟⣲⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣀⡀⠀⠀⠀⠀⣷⣿⣿⣯⣻⣿⣿⣿⣟⣟⣼⣿⣗⡿⡀⠀⠀⠀⢀⡀⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣈⠀⢠⡀⠀⢿⣿⣿⣦⣶⣶⣶⣾⣷⣶⣶⣶⣼⣿⣿⡿⠀⢀⡄⠀⣀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⡉⣛⠓⢢⢹⡆⠀⢻⣟⣿⣭⣽⣧⣼⣧⣼⣯⣽⣿⣻⡟⠀⢰⡏⠰⠚⣛⡉⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣟⠁⠠⡿⢿⣃⡼⢁⣤⣻⠿⠿⣿⠋⢻⠙⠁⡋⠙⣿⡿⠿⣟⣤⡘⢇⣛⡿⢿⠄⠈⣛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡳⣶⣞⣼⣿⣷⣿⣛⠅⣐⣰⣤⣤⣰⣴⣷⣦⣤⣤⣆⣂⠘⡋⣿⣮⣿⣧⣳⣶⢞⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⢂⣾⣿⡍⡿⣯⣿⣿⣿⣿⣳⣾⣿⣿⠋⠉⠁⣙⣋⠀⠉⠙⢿⣿⣿⣗⣿⣿⣿⣿⣽⢿⠩⣿⣷⡐⡦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⣸⡁⠋⡶⢱⣿⣿⣿⠟⠋⣍⣉⣾⣧⣀⣠⣀⠈⠁⢀⣄⣀⣼⣷⣉⣭⠹⠻⣿⣿⣿⠞⢿⠙⢘⣇⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣯⣷⠀⠀⢸⣿⣿⣟⣰⡿⢉⣿⣷⡄⠘⡛⡇⠀⠀⢸⢛⠋⢠⣾⣿⡙⢿⣦⣻⣿⢻⡇⠀⠀⣾⣽⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣧⣿⡀⣤⣼⣧⣿⣟⣏⣁⣩⣴⣿⣽⣾⠃⣀⠀⢀⣀⠘⣵⣯⣿⣮⣉⣉⣹⣻⣿⣿⣧⣦⢀⣿⣼⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣬⡁⠸⣇⣿⣿⡝⢻⣿⠀⢸⣿⣿⣿⠀⠙⠳⠞⠋⠀⣿⣿⣿⡏⠀⣿⠿⢩⣿⣿⣸⠇⣨⣥⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⢲⣤⣹⠿⡄⠙⣧⣿⣿⡴⢲⣦⡼⡟⢻⣿⣶⠤⢾⣷⠦⣴⣿⡟⠻⠧⣴⡶⢦⣾⣿⣼⠋⢠⠟⣏⣤⡞⠁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣙⣷⣦⣿⣀⣿⣿⣻⣧⢺⠋⠀⢁⡾⡿⣿⣦⣤⣠⣴⣿⠿⢳⡀⠀⠹⡇⣸⣟⣿⣿⢀⣿⣵⣿⣋⣡⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⡼⠟⢻⣿⣿⣿⣿⣽⡌⣿⣏⠘⣧⡀⢻⡿⢿⡿⢿⡟⢀⣾⠃⣹⣿⢡⣯⣿⣿⣿⣿⠟⠻⢧⣤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠉⠻⠿⡿⣿⣿⣿⣿⣿⣿⣬⣄⣢⡹⠟⢳⣤⣴⠞⠹⢏⡜⣰⣥⣿⣿⣿⣿⣿⣿⢿⠿⠟⠉⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣾⣅⡈⢁⣨⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣦⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠘⣿⣿⣿⣟⣿⣿⢹⡿⣿⣿⣿⣿⣾⣿⣿⣿⢿⡏⣻⣿⣻⣿⣿⡿⠁⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⢴⣤⣸⣿⣿⣿⣯⣻⣿⣷⣿⣿⣿⡇⢸⣿⣿⣿⣾⣿⣏⣿⣿⣿⣿⣃⣤⡦⠀⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣃⣶⢿⣟⣿⣿⣿⣶⣿⣾⣿⣟⠻⠃⡘⠿⣻⣿⣷⣿⣾⣿⣿⣿⣻⠿⣶⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣿⣾⣿⣿⣿⣿⣯⡄⢉⡏⢀⣿⣿⣿⣿⣿⡿⣿⣤⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠋⠁⠈⠻⢿⣿⣷⣼⣦⣴⣧⣾⣿⡿⠟⠁⠈⠙⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⡿⠋⠛⣧⠀⠀⠀⠀⣿⠋⠀⠀⠙⣷⠀⠀⣾⡏⠉⠙⣷⠀⠀⢰⡿⠋⠉⢿⡄⠀⠀⣴⡿⠛⠻⣦⠀⠀⠀⠀⠀⣠⣴⠶⠶⣶⡄
⠀⠀⠀⠀⠀⢿⣇⠀⢀⣿⠀⠀⠀⠀⠻⣧⣤⣤⣼⠟⠀⠀⢿⣧⣠⣴⡿⠀⠀⢸⣧⡀⠀⣸⡇⠀⠀⢿⣄⡀⢀⣿⠀⠀⠀⠀⠀⣿⡁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠈⠻⢿⣿⡁⠀⠀⠀⠀⠀⢸⡿⢿⣄⠀⠀⠀⢠⡿⠛⣿⡀⠀⠀⠀⢹⣿⣿⣏⠀⠀⠀⢈⣿⠿⣿⠁⠀⠀⠀⠀⢀⣽⣿⣶⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣦⡀⠀⠀⢀⣿⠁⠈⢻⣦⠀⢠⡿⠁⠀⠘⣷⡄⠀⣠⡿⠁⠈⠻⣧⠀⢠⡿⠃⠀⠹⣷⡀⠀⠀⣴⡟⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢿⣦⢀⣾⠃⠀⠀⠀⠹⣷⡿⠁⠀⠀⠀⠘⣿⣴⡟⠀⠀⠀⠀⢹⣷⣿⠃⠀⠀⠀⠹⣷⣤⡾⠃⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢿⠃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠉⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⣷⠀⠀⠀⠀⠀⠀⣰⠞⢋⡿⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣷⠶⣿⣇
⠀⠀⠀⠀⠀⣸⡏⠀⠰⣄⣿⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠟⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢹⡆⠀⠀⠀⠀⢀⡟⠀⠈⠁⠐⠃⢹⡇
⠀⠀⠀⠀⠀⢻⣧⣀⣳⣼⠏⠀⠀⠀⠀⠀⠘⣷⡀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿⡴⢀⡄⠀⣼⠃⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠙⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠷⠛⠃⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⢿⣇
⠀⠀⠀⠀⠀⢠⣾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣦
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠷⠶⠶⠶⠶⣶⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣴⠶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠆⠀⠓⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣴⢫⠀⠀⢀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣠⠞⠑⠁⠀⠀⢸⡀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢰⢃⠎⡀⠀⠀⠀⢺⡁⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡟⡼⠰⠀⠀⠀⠀⣿⢀⠂⠄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡇⠃⠦⠀⠀⠀⠀⢿⠃⠄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣷⠁⠠⠀⠀⠀⠀⣼⠌⠐⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⡆⠰⠀⠀⠀⠀⣝⡐⠀⠁⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠹⡐⡀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⢳⡄⠀⠀⠀⣿⢁⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠻⡂⠀⠀⣿⠂⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⣀⠀⠀⠈⢷⡀⠻⠀⠀⣿⠀⠀⢀⣾⠃⠀⢀⣠⡴⠶⠶⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠛⢦⣄⠀⢻⡄⠀⠀⡏⠀⠀⣼⠃⣠⡶⠋⠀⠀⠀⡀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⣴⠟⠀⠀⠀⣤⢶⠿⠛⠛⠓⠂⠀⠀⠙⢧⡀⢷⠀⠀⠇⠀⢰⠇⣴⠋⠀⠠⠶⠛⠉⠉⠛⠲⣶⣄⠀⠀⠘⣷⡀
⠀⠀⠀⣸⠇⠄⠀⢀⣼⡇⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⡆⠀⠇⢀⡏⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⢸⣧
⠀⠀⠀⣿⡶⠀⠀⢸⣿⠅⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢹⠀⡆⢸⢣⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠠⠀⠚⣿
⠀⠀⠀⠸⣷⠀⠀⠸⣿⣆⠈⠀⢀⣴⠿⠟⠛⠷⣦⣄⠀⢸⠘⡀⣇⢸⣾⠀⢀⡴⠟⠛⠛⠶⣄⡀⠀⠀⠀⣾⡿⠀⢀⣾⡿
⠀⠀⠀⠀⢻⣆⠀⠀⠙⣮⡢⠀⢸⡇⠀⠀⠀⠀⠀⠻⣦⠘⣯⡇⣿⢸⡇⢠⡏⠀⠀⠀⠀⠀⠸⣧⠀⢀⣾⠛⠁⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠉⠓⣈⣿⡄⠀⠀⠀⠀⠀⢻⡀⠇⡇⡄⠲⡇⣿⠀⠀⠀⠀⠀⠠⣾⣃⠀⠀⢀⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈⡥⣇⡇⣁⣽⣇⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣼⣧⣿⣧⣤⣿⣯⣿⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣤⣄⣀⣄⣀⣀⣤⣀⢀⢀⢀⣀⣀⣠⣤⡶⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣉⣉⣩⠏⢹⢻⠋⣯⢻⣏⠹⣏⣉⣉⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠉⢁⣠⢇⡞⠀⢹⠈⡞⣆⠈⠉⠛⣝⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣮⣴⣿⠏⢸⡀⠀⠈⠀⣹⡎⠷⣤⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⠛⠚⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠻⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠕⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠰⠆⣤⢠⡄⣠⣶⣯⣤⢀⡄⢠⢠⡄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒⣲⣇⡀
⠀⠀⣀⠠⠤⠠⡀⣀⡤⣾⠃⡀⠀⠠⣤⠤⣄⠀⠀⠤⠁⠊⠉⣐⣀⣀⡂⡇⣻⣹⠓⣒⣒⣒⠐⠢⢳⡦⠀⠀⠀⣀⣴⠾⠛⠉⡏⣿⡋⠛⠷⣦⡀
⢨⠃⠀⠀⠀⠀⠀⠒⢹⣿⡜⠑⠂⣁⡀⠉⠢⢂⠀⢒⢀⠀⠀⠛⣿⠁⠀⠁⢐⠀⢰⣿⠟⠻⣶⠀⢸⠓⠀⢠⡾⠛⠁⠀⠀⠀⡇⡗⡇⠀⠀⠈⠻⣆⡀
⠺⢠⠚⣏⢹⣤⣻⣿⣟⣫⠾⡅⡜⠿⢻⣦⣔⡼⠂⠘⢈⢇⠀⢸⣟⣦⣂⢧⢨⣶⣴⢠⠈⣿⡿⠇⠚⠁⠀⡼⠡⠀⢰⠄⣄⠀⡀⣰⠋⠄⣀⢰⡀⠝⢿
⠀⢣⣽⣾⢼⣿⣿⣷⣶⣿⣶⣿⣿⣧⣼⣿⣵⠁⠀⠀⢿⣴⣿⣦⣿⣿⣿⣶⣿⣦⣷⣿⣺⣯⣭⣽⡧⠀⠀⢷⡀⠋⣽⡏⠃⠞⣺⣷⠀⠖⢩⡼⠁⠈⡿
⠀⠸⢟⠛⢻⣿⣉⠛⡉⣿⡛⣿⣿⣿⣿⢿⠇⠀⠀⠀⢼⣫⣭⣭⣭⣥⠽⠿⡿⠿⢶⣿⣿⣯⣭⣿⡇⠀⠀⢸⠽⢼⣽⣯⣤⣼⢫⣨⣯⡐⢹⡽⣅⢌⡥
⠀⠨⣿⣭⣭⣽⣬⣦⣾⠿⡷⠿⠿⢿⣿⣿⠁⠀⠀⠀⢤⠶⡥⠤⠶⠸⠄⢤⠴⠶⠸⢿⣤⣿⣿⣿⡇⠀⠀⡼⠁⠉⠛⢈⡀⠃⢘⠋⠘⣃⠹⢿⡿⢿⡧
⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠣⣤⣥⣤⣬⣤⣤⣥⣤⣬⣶⡥⠼⠶⠼⢭⡷⠀⠀⠉⠛⠐⠒⠒⠐⠀⠀⠀⠐⠒⠐⠒⠑⠊
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠾⠿⢶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡝⣷⠦⠀⠀⠀⠀⠀⠀⣤⠤⠻⣶⢱⣶⣄⡤⢀⣀⣠⣴⣾⣿⢶⡾⠅
⠀⠀⢠⣄⠀⠀⠀⠀⢧⣿⠁⠀⠀⠀⠀⠀⠀⣤⣿⣿⡇⠀⢿⣿⣿⣏⣴⣿⣿⣿⡟⢿⠿⠁
⠀⠀⠀⠀⠘⢦⠀⠀⣼⣯⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣷⣄⣼⣿⡏⠙⠛⠉⠙⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣬⣿⣦⠲⠀⠀⠀⠉⢋⣉⡔⠀⠀⠀⠀⠀⠀⣴⣶⣦⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⡛⠿⠟⠟⠠⠄⠀⠀⠀⠀⠀⠉⠉⠒⠒⠶⠠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐




⠀⠀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢿⠇⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⢹⡿⣿⠁⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⢿
⣿⡆⠈⢿⣇⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⣿⠟⠀⢾⣿⣿⠆⠸⢿⡇⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⢠⣿⠏⠀⣾
⣾⡄⣶⠀⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⢀⣦⣰⣷⣷⣠⣆⠀⠀⠀⠀⠀⢰⣿⣿⡧⠀⠀⠀⠀⠀⢰⡆⣼
⣿⠉⠛⠃⠀⠀⣀⣀⠀⢿⣿⡏⠀⣀⣀⠀⠀⠘⠛⢹⣿⣿⠙⠛⠀⠀⢀⣀⡀⠈⣿⣿⠇⢀⣀⡀⠀⠀⠛⠋⢹
⠁⠀⠀⠀⢰⣾⣿⣿⣷⣸⣿⢣⣾⣿⣿⣷⠄⠀⠀⠀⠈⠀⠀⠀⠀⢴⣿⣿⣿⣦⢻⣿⣰⣿⣿⣿⣶
⠀⠀⠀⠀⠀⢻⣿⣧⠘⣿⣿⡿⢁⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣄⠹⣿⣿⡏⣠⣿⣿⠃
⡄⠀⠀⠀⠀⢀⣿⡏⢠⣾⣾⣧⠈⢿⣿⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢸⣿⠏⢠⣿⣾⣦⠈⣿⣇
⣿⡆⠀⠀⠀⠈⠁⢠⡄⣽⣽⡇⣠⡀⠉⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠈⠁⣠⡀⣿⣿⡅⣤⠀⠉⠀⠀⠀⠀⣾
⣿⠇⠀⠀⠀⠀⠀⠻⠟⣹⣿⡟⠻⠗⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠐⠿⠚⣿⣿⡙⠿⠃⠀⠀⠀⠀⠀⣿
⣿⣠⣾⣿⣷⣄⠀⠀⠀⠈⠋⠁⠀⠀⠀⣴⣿⣿⣷⡘⣿⡟⣰⣿⣿⣷⡄⠀⠀⠀⠉⠋⠀⠀⠀⢀⣴⣿⣿⣦⢸
⣷⡟⢉⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⡙⢷⣹⢹⠏⣩⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣏⠙⣷
⣽⡅⠙⣿⡏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⣿⠃⣸⣯⣿⡀⢻⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣿⡟⠁⣽
⣿⠁⣀⠉⠋⠀⠀⠀⠀⣴⣿⣆⠀⠀⠀⠀⠋⠁⣀⢹⣟⣿⢁⡀⠉⠃⠀⠀⠀⢀⣾⣷⡄⠀⠀⠀⠈⠋⢁⡀⢹
⣿⠳⣿⠄⠀⠀⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⢰⡿⢾⣿⣿⠾⣷⠀⠀⠀⠀⠀⠸⣿⣿⡏⠀⠀⠀⠀⠀⢾⡷⢻
⠛⠀⠀⠀⢀⣴⣶⣶⣄⢹⣿⠇⣤⣶⣶⣄⠀⠀⠀⠘⠛⠋⠀⠀⠀⢀⣴⣶⣦⡄⣿⣿⢁⣴⣶⣶⣄⠀⠀⠀⠘
⠀⠀⠀⠀⠘⣿⣿⡛⠻⣾⣿⣼⠟⣻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡛⢿⣼⣿⡾⠛⣻⣿⡟
⠀⠀⠀⠀⠀⠘⣿⡿⠀⣻⣻⡇⠸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠈⣿⣻⡃⠺⣿⡟
⣧⡀⠀⠀⠀⠐⠛⠁⠈⢿⣿⡟⠀⠙⠻⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠸⠛⠀⠘⣿⣿⠋⠀⠙⠓⠀⠀⠀⠀⣠
⣿⡇⠀⠀⠀⠀⠀⣼⣧⢿⣿⣧⣾⣆⠀⠀⠀⠀⠀⢿⣿⣿⠇⠀⠀⠀⠀⢀⣾⣦⣿⣿⢧⣿⡄⠀⠀⠀⠀⠀⣿
⣿⠁⣠⣤⣤⠀⠀⠈⠀⠻⠿⠇⠈⠁⠀⢀⣤⣤⣄⢸⣿⡿⢀⣤⣤⣄⠀⠀⠉⠀⠿⠿⠃⠈⠀⠀⢠⣤⣤⡀⢹
⠟⣾⠿⢿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⠿⡧⠿⢧⡿⠿⢿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⠿⢿⡞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠩⠋⡄⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢄⠀⡠⠀⣠⡾⠧⠄⡀⠀⠀⠀⠀⠀⠀⢦⡀⠸⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠋⢉⣀⠀⠀⠀⢠⡝⠀⠀⠀⠈⢢⢠⣤⣤⠀⠀⠀⠉⠛⠉⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠙⣧⣴⠋⠈⠙⡆⠀⣼⣿⣿⣿⣷⣦⡾⠈⠛⠃⠀⠒⠒⠂⠀⠀⠀⠙⢿⡄⢰⡶⠀⠀⠀⠀⠺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⣤⠴⠃⠘⠦⣤⠾⡅⠀⢹⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⠑⢦⣄⠀⠀⣴⠀⡤⢠⠀⡀⠀⠀⠀⢀⣴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣤⣄⢠⡀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⡀⡆⠉⢦⡆⠉⡦⠈⠻⣦⠉⠀⠀⠈⠀⠀⠀⠰⠖⠁⠀⠀⠉⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⣈⣭⠉⠉⠉⠉⠉⠀⠈⠉⠁⣀⡀⠙⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣒⣂⠙⣆⠀⠀⠿⠃⠀⠀⢱⣞⣇⠀⠀⠀⠀⠀⠀⢤⣴⣏⠁⠀⠸⣧⠀⣤⡄⠀⣠⡾⠛⢡⣴⡆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠘⣦⣉⣉⠀⠀⢼⣿⣿⣿⣿⣿⠞⣿⣿⡄⠀⠀⠀⠀⠘⣿⣿⡿⠀⠀⠀⣿⡄⠉⢡⡾⠋⠀⠀⠸⠿⠇⡤⠶⠚⠑⠂
⠀⠀⠀⠀⠀⠀⠘⠟⠀⢀⡾⠉⠉⢷⡀⠀⣽⣿⣿⣿⣿⣷⢻⣿⣇⠀⢷⡖⠀⠀⠈⣭⠁⣤⠀⠀⣿⡇⢠⣿⠁⢠⣤⣠⠀⠀⠀⠀⠾⠗⠒⠐⠿⠂
⠀⠀⠀⠀⠀⢀⣤⡀⠀⠈⠀⠉⠉⠈⠁⠀⠉⠉⠉⠉⠉⠉⠈⠉⣉⣀⡀⠀⠀⠀⡆⠀⠀⠀⢰⠀⣿⡇⣼⡏⠀⢸⣿⣿⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⣦
⠀⢀⡴⠀⠀⠸⣿⠇⠀⠀⡀⠀⡀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⣀⠀⣤⠀⢤⠀⢰⣿⢀⣿⠁⠀⠸⣿⡿⠀⣤⡉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠚⠻⢶⣦⠀⠠⣄⠙⠀⠁⠘⢁⡤⠀⠀⠈⡇⠀⠀⠇⠀⠀⠀⠀⠀⡀⠀⠀⠹⣷⡀⠀⠀⠀⣾⡏⣼⡟⠀⠀⠀⣶⣶⣶⣻⣇⠀⢵⠆⠀⠠⡾
⠀⠀⠀⡾⠁⠀⠶⠌⠀⠀⠀⠀⠠⠶⠂⠀⠀⡷⢰⣿⣿⣿⡆⠀⠀⠀⠄⠀⠀⠀⢸⣿⡄⢀⣼⡿⢡⣿⠇⣠⡀⠀⠻⠿⠿⠛⠟⠀⣀⣤⣄⣀⣀⣀
⠀⠀⠘⠁⠀⠀⠒⠂⠁⠀⠀⠀⠀⢒⣂⠀⢰⡇⠙⠛⠛⠛⠋⠀⠀⠂⠀⠁⠀⠀⠀⣿⣷⣾⣿⣣⣿⡿⢠⡿⢶⣖⡂⠀⠀⠴⠶⠿⢿⣿⣿⠿⠛⢉
⠀⢀⣴⡶⠂⣀⢀⡀⠀⣶⣶⡆⠀⠋⣽⠂⢸⡇⢠⣴⡶⣿⣿⣿⣷⣦⣄⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠁⡀⠀⣠⡟⣰⠀⠀⠐⠀⠀⠀⠀⠀⠔⠈
⠀⡘⠋⠀⠀⠻⣿⡇⠀⠈⠋⠀⢀⡀⠃⠀⢸⣇⠀⠈⠹⣿⣿⣿⡿⠈⠁⠀⠀⢀⣾⣿⣿⣿⠿⠋⠀⠀⢉⣿⣯⡈⠛⢳⠆⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢶⣶⣤⠀⠿⠃⠀⠀⠀⢀⣾⣧⡴⢄⠘⣿⣄⠀⠀⠀⠉⢡⣴⡇⠀⠀⢀⣾⣿⣿⠟⢁⣠⠄⠀⠀⠀⠉⢈⠀⠀⠃⠀⢀⡄⠘⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠈⠉⠀⠀⢈⠁⠈⠀⠈⠁⢀⡿⠁⠀⠘⢿⣷⣦⣄⡀⠹⠿⠃⠀⣠⣿⣿⠟⠁⠀⠉⠀⠀⠀⠀⢀⣶⣿⠀⠀⠀⠀⠀⠄⠘⠁⠤
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠘⣳⣞⠁⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣄⣴⣿⣿⠃⡀⠂⢒⡐⠀⢠⠏⠀⠀⠙⠋⢀⣄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠉⠉⠁⣠⡀⠘⠀⣀⠀⠀⠙⢿⣿⣿⣿⣿⣇⠰⠩⠡⣭⠄⠽⠁⠀⢰⡇⠀⠀⢀⣅⠀⠀⠀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⢀⣲⣶⣶⡀⠀⠀⢰⡆⠀⢀⣼⣿⣿⣿⣿⣿⣦⡀⠠⠯⠄⠀⠀⢀⣼⠇⢤⠆⠈⠉⠑⣦⠈⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠀⠀⠀⠀⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢠⣾⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣀⣤⣤⠤⠶⠶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠉⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⣠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⢛⡛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⢀⣾⡧⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⢦⣄⢸⡇⠀⢀⣠⡤⠶⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠓⠶⢦⣼⣦
⠀⠀⠀⠀⣾⠟⠒⠛⠛⠛⠛⠉⠙⠛⠙⠛⠛⠛⠛⠛⠓⠒⠶⠶⠶⠤⣬⣿⣷⡿⠿⠶⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⢻⡅
⠀⠀⢠⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⢠⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⡆
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣛⣛⣻⣛⣉⣛⣻⣛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣿⣭⣭⣽⣿⣿⣭⣉⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⠏⠀⣼⡇⠈⢻⠈⢹⡆
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠲⠤⢤⣀⡤⠂⠀⣀⣀⣤⡀⠀⠘⢣⣞⣦⣥⣿⣧⣧⣞⣦⠚⠀⠀⣠⣄⣀⡀⠀⠢⣄⣠⠤⠴⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠒⠲⣄⠀⡎⠉⢳⠮⠤⠠⠏⠉⠛⠋⠉⣿⣿⣻⣻⣛⣻⣛⡏⠉⠛⠋⠉⠧⠤⠬⢶⠊⠉⡇⢀⡴⠒⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⠀⠈⢄⠀⠀⣎⡗⠀⠀⣀⣤⡤⠴⠦⠶⠤⣤⣄⣀⠀⠀⢏⡆⠀⢀⠈⠀⢠⠇⢸⡀
⠀⠀⠀⠀⠀⠀⠲⠤⣀⡀⠠⠔⠃⠀⠈⠓⠦⣤⣤⣬⣧⡶⠚⠋⠉⠀⠀⠀⢐⠀⠀⠀⠈⠉⠛⠲⣦⣯⣤⣥⡤⠖⠋⠀⠀⠑⠤⣀⠀⡀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠈⠉⠉⠑⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⣴⡿⣷⡄⢀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣅⣀⣹⣿⣿⣁⣀⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⠉⠓⠲⠤⣄⠀⠀⠀⠀⠀⢩⢭⣭⣭⣯⣽⣽⣭⢯⠁⠀⠀⠀⠀⢀⡤⠴⠒⠋⠉⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠂⠂⠀⠐⠲⡄⠀⠀⠈⠳⣤⠖⠋⠉⠒⠒⠒⢒⡖⣖⠓⠒⠒⠊⠉⠓⢦⡴⠋⠀⠀⠀⡴⠒⠀⠀⠂⠒⠲⣄⡀
⠀⠀⠀⠀⠀⢠⠎⠀⠘⢦⣐⢠⡀⢀⡴⠃⠀⠀⠀⣼⠉⠳⣀⠀⠀⠀⠐⠈⠁⠉⠐⠀⠀⠀⢀⡰⠋⢹⡀⠀⠀⠀⠳⣄⡀⣠⢐⣠⠞⠀⠈⢦
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⢉⡏⠁⠀⠀⠀⠀⠀⠸⣄⠀⠈⠓⠤⣆⡀⣦⠀⢠⡆⣀⡤⠔⠋⠀⢀⡼⠁⠀⠀⠀⠀⠈⠉⣏⠉⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠉⠒⠦⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠄⣀⠠⠶⠃⠀⠀⠳⠦⢀⡀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣀⡀⠀⠀⠀⠀⠀⠰⢱
⠀⠀⠀⡄⠀⠐⠀⠀⠂⠛⢷⡄⠀⠀⡟⠛⠿⣿⣷⡾⠛⠻⠆⠀⠀⠁⠈⠠⣰⣿⡾⠋⠉⠟⠀⠀⢰⠟⠳⣄⠀⠀⠀⠂
⠀⠀⠀⠁⠀⠀⢀⡶⠀⠀⠉⠁⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⢿⣦
⠀⠀⠀⠀⠀⠀⢸⡿⢤⠆⠀⠀⠀⠀⠀⠀⠀⠾⡿⠄⠀⠀⠀⠀⠀⠀⢠⣠⠿⡿⢇⡤⠀⠀⠀⠀⠀⠀⠶⠻⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⣀⣸⣷⣀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⡀⠀⠀⠀⠀⠀⢠⣷
⠀⣠⣄⡀⢻⠃⣀⣀⠀⠀⣠⠖⠶⣽⣟⡵⠲⢦⠀⢠⡖⠒⠄⠘⠠⠚⢿⡀⠀⣾⡟⠳⣾⣷⠞⢻⣷⠀⢠⡴⠂⠈⠟⠀⠀⣤
⠀⠈⠁⢈⣄⣈⠀⠉⠀⠀⠙⠾⠇⢿⣿⠀⠿⠚⠀⠀⠙⠀⢀⣀⣥⠀⠋⠁⠀⠙⠋⠀⣿⣿⠀⠙⠋⠀⠈⠂⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠜⢴⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⡀⠀⠀⠀⠀⠀⠔⠀⠈⠢⠀⠀⠀⠀⠀⠀⠂⣤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⣠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣦
⠀⠀⢀⠤⠤⠬⢻⣏⡤⠤⢤⡀⠀⠀⢀⣤⣜⣿⣿⣣⣤⣀⠀⠀⢀⣤⣤⣬⣻⣿⣫⣤⣤⣄⠀⠀⠀⠰⠿⢿⣿⡿⢿⠆
⠀⠀⠈⠀⠀⢤⣤⣿⠆⠀⠀⠁⠀⠀⠛⠁⢈⣿⣿⡏⠀⠙⠀⠀⠸⠇⠀⠀⣿⣿⡧⠀⠀⠻⠀⠀⠀⠀⣄⣀⠙⢃⣠
⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢌⠁⠀⠀⠀⠀⠀⠀⠀⢀⠴⣴⢦⠀⠀⠀⠀⠀⠀⠘⢻⣿⣷⠘⠛
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣿⣿⡿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡂⠁⢉⠉⢙⣥⡤⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⡆⣷⣿⠋⠀⠀⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⣿⡉⡷⣇⣀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⢙⠷⡀⡷⣬⣼⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡶⢚⣾⠃⢳⠶⠾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⡼⡠⣶⣿⣰⡿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣤⣶⡶⢶⣾⠟⣻⠯⠈⢡⠷⣿⡅⠉⠲⠿⠻⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠛⣋⡵⠤⠒⢞⣻⠶⢚⣩⠐⠊⠀⠀⠀⠃⢀⡏⢻⠀⠀⠀⠀⠈⠙⠻⢭⢻⣯⠻⠹⢿⣿⢿⣿⣰⣤⣀
⠀⠀⠀⠀⠀⠀⠦⠞⠃⠀⠚⠁⠀⠀⠀⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⡀⠀⣊⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⠙⢪⡽⠀⠀⠀⠁⠈⠛⢿⣿⣷⣄⡀
⠀⠀⠀⠀⡶⠎⠁⠐⠀⠀⠀⠀⠀⢀⣰⠏⠰⣰⣶⣶⣶⣿⣿⠟⢁⠃⠀⣀⣽⡆⢻⠽⠻⡟⠓⣶⣶⣄⠀⠀⠛⣉⡇⡀⠀⠀⠀⠀⠙⢿⣿⢧⡄
⠀⠀⠀⠶⠃⠀⠀⠀⠀⠀⢀⣤⠀⢤⡁⢠⢁⣿⣿⣿⠟⠉⠀⠀⠈⠀⠀⡀⣈⡁⠸⡆⢀⣠⣶⣯⣏⣹⡇⢀⠀⡁⢾⡤⣄⠀⠀⠀⠀⠀⢻⣟⣷⡄
⠀⢀⠐⠂⢠⠀⠀⠀⣠⣶⠟⠀⠀⢼⡆⠈⢸⣿⣿⠃⠀⠀⠀⠀⠀⢀⡜⠁⠘⢷⠀⣼⣾⣿⣿⣿⣿⣿⣿⢠⠄⠀⢼⡇⣿⣷⣦⡀⠀⠀⠈⣿⣽⣦
⠀⣘⢺⢀⠈⠀⢀⣜⣿⠂⠀⠐⠢⢶⡇⠀⢸⣿⡧⠀⠆⢀⡀⠀⢨⠃⠀⠀⠀⠀⠰⣿⣿⣿⡿⠏⠉⣄⢭⢸⡃⡠⠶⠗⢻⣿⣿⣷⣄⠀⠠⣽⣿⣷
⠀⢈⡻⢈⠈⠀⣾⣉⠋⠀⠀⠀⠀⠀⠀⢰⠸⣿⣦⣀⠆⠈⢡⠔⠘⠄⣀⠀⠀⢄⡴⠻⢿⣿⣃⢹⣯⡿⡖⣸⠃⠀⠀⢠⡸⣿⣿⣿⣿⡆⠀⣼⣾⣿⠄
⠀⣈⣽⣽⡄⣾⣷⡟⠂⠀⠀⠀⠀⠀⠀⡦⠃⡠⠀⠑⣧⣀⡎⢠⡴⠀⠈⢀⠉⠂⣴⠒⠀⢸⣭⡥⢋⡤⠄⠙⣴⣶⣠⡟⣳⣿⣿⣿⣿⡇⠤⣿⣿⡷
⠀⠉⠉⠛⠻⡹⠷⠿⠦⢤⠀⡤⠀⠠⠘⠃⢸⢘⣦⠀⣾⠗⠁⢻⡀⢻⠀⠠⠀⣸⣯⡷⢀⡬⠻⡇⢺⣶⣦⠀⡿⣳⢏⣵⣦⢸⣿⡿⠿⠫⣼⠟⠛⢃⡼
⠀⠀⠀⢤⡀⡁⣰⢲⠀⡺⢌⠧⣴⡆⡄⠠⠈⠇⢻⣶⡟⠒⠀⣾⣿⣉⣁⢀⣀⣈⢹⣿⣿⠃⠐⢿⣾⠇⢻⣀⠁⢁⣾⡏⣸⣿⡿⢡⣶⣇⣿⣾⡿⠟
⠀⠀⠀⠀⠉⢁⡘⡩⠣⡧⢰⠛⣾⣧⡤⠖⠖⠻⠞⣿⣿⠏⠻⠿⡿⠇⣡⡈⣧⡈⠻⠿⠿⠋⠻⣿⣏⠰⡿⢻⠷⣾⣿⣟⣿⠠⣧⣸⡾⢳⠟⠁
⠀⠀⠀⠀⠀⠀⠩⣘⣤⣵⡾⢉⡛⢙⡁⠖⠒⠋⠒⠠⠰⠊⠙⠲⠆⠈⠐⠸⠇⠈⠄⠐⠆⠿⠶⠤⡄⣨⣷⣼⣷⣿⡟⣛⢹⣿⠯⣤⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡵⠃⣀⢀⠤⠤⠀⠄⠒⠂⠂⠀⠀⠀⠀⠀⠒⠒⠖⢲⡲⢚⢒⣢⣤⣤⣴⢖⠰⣟⣿⣿⣿⣼⣿⣯⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠞⠉⣀⣀⠀⠀⢪⣭⢽⡆⠘⢣⣶⣜⠀⠠⢠⡴⠾⠒⣿⣰⢮⡵⣷⣿⠛⢠⡾⠉⣿⣟⠿⣿⢿⡟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠈⢿⡁⡂⠀⠾⠷⠶⠃⠀⠚⠁⠘⠀⠀⢽⢭⠛⠫⠓⠸⠾⠶⣦⢿⣀⣾⣤⣠⣿⣟⣾⡽⣿⠃⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⢁⣀⢀⣀⠤⠄⠄⢀⡄⠠⠄⠀⠀⠐⠀⠂⠀⠐⠀⠄⠀⠀⠂⠐⠧⠤⠠⠭⣿⣯⣿⣿⣿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⣿⣁⠀⢨⡦⠄⢠⣨⢇⡰⠀⠐⠢⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠉⠊⠛⠛⠛⠛⠛⠙⠂⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣤⣄⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⣼⣿⣿⣷⣦⣄⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣄⣠⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣍⣉⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠈⣿⣿⣿⠛⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⡿⢿⣿⠁⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⠃⠛⢿⣿⡿⣿⣷⣸⠏
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠉⠢⡀⣼⣾⣿⣹⣿⣿⠇⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢀⢀⡀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⢀⣸⣾⣷⡆⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⢀⣀⣾⣿⣿⣿⠉⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣠⣾⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣻⣿⣿⣿⠏
⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡟⢷⣮⣸⠇
⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣨⡿⣶⣶⣄
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣀⢀
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠋⢷⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⡭⠄⢨⣴⣬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡯⠒⢲⠀⠠⣟⡛⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡴⠛⣻⠀⠀⢛⣛⠳⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠁⠀⠀⣐⢻⣿⡅⣿
⠀⠀⠀⠀⠀⠀⢀⣠⢄⡖⣒⣶⡦⠤⠈⣿⣷⢋⣉⡆⠀⣭⣍⢿⣿⣟⡠⣤⣤⣤⡤⡤⢄⡀
⠀⠀⠀⠀⣠⢾⡟⣷⡾⢛⣉⣉⣛⠛⠿⣯⣿⣿⣩⠆⠀⢈⣹⠿⡻⠛⠿⢒⣛⡛⠷⢿⡆⣻⣷⡄
⠀⠀⠀⢰⣣⡿⠋⢠⣾⣿⠿⠟⠻⠿⢷⣤⡘⢿⡇⠀⠀⢨⡿⡀⣠⣾⣿⡟⠛⢿⣿⣦⣍⠻⣿⢻⣆
⠀⠀⠀⢸⣻⡇⠀⡿⠿⡁⠀⠀⠀⠀⠀⣹⣿⡎⠿⠴⠴⠽⠷⠿⡿⠋⠀⠀⠀⠈⠪⢿⣿⡆⢠⣼⣿
⠀⠀⠀⠘⣿⠷⣌⣷⣟⠛⠒⠒⠒⠒⠒⠛⣾⣿⢿⡷⣿⣾⣿⢶⡿⠧⠤⠤⠤⠤⠤⣀⣿⡇⢰⣿⣿
⠀⠀⠀⠀⠘⢷⣿⣜⣻⣦⣀⠀⠀⠀⠀⠀⣿⣟⣷⣴⣍⣷⣺⣖⡁⠀⠀⠀⠀⢀⣴⣿⣟⣠⣿⡽⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⣿⣭⣭⣭⣉⣉⣭⣽⣧⠀⠀⠀⠀⠉⠛⠫⠽⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⠀⠀⠀⠀⣹⠟⢿⠟⠛⢿⡛⢿⡁⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⠹⣷⣤⣤⣾⠏⢀⡞⣄⠀⡼⣿⡌⢿⣄⡠⢔⣿⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣴⣦⣭⣅⣶⣶⣿⢧⡿⠀⣇⣾⣷⠦⠉⣛⡋⣡⣴⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣾⣿⢾⣿⢿⡲⠀⠀⢈⢘⣿⠻⢯⣛⣯⣽⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠉⠀⠀⠀⡽⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣍⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⢻⣿⣿⣿⣿⢶⣾⡿⠍⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠺⣭⣙⣧⠘⠟⢟⠿⣙⡇⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣣⣾⣿⣞⣶⣿⣿⣦⣤⡈⠙⠛⠀⢠⣾⣿⣿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⠈⢹⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣻⠿⡿⠍⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡀⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⣿⣿⣿⣿⠾⣿⣿⣿⣄⠀⠈⠙⠻⠿⣿⣿⣿⡏⢿⣧⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠉⠀⠀⢹⣿⣿⣷⣶⣶⣶⡄⣠⣶⣾⡇⢾⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠁⠀⠋⠈⢡⣾⠟⣿⣿⡿⣿⣿⣿⣟⣾⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣷⡟⢛⣿⣿⣷⣿⣿⡿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⢸⠏⠛⢻⣿⡟⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⢤⣼⡤⡰⠛⠁⠀⠀⠁⠠⣀⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠰⠁⢸⣿⣿⢶⣶⣿⣷⠁⣄⣀⡀⠀⠀⠀⠀⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠋⠸⣿⣿⣿⣲⣬⣭⣾⣿⣶⣿⣿⡷⣄⠀⠀⠀⠘⣏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣔⣿⣧⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠅⠀⣼⣿⣿⣿⣿⣿⣿⡿⡽⠋⠁⠰⠏⡌⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠋⡙⢛⣿⠋⠉⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣿⣷⠎⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣭⣙⠃⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⣸⣯⣿⡏⣀⣠⡤⢀⣈⣀⠀⠁⠀⢀⣀⡀⠬⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣋⡉⠉⠀⠈⠉⢙⡖⠋⠀⠀⣬⡿⣷⣿⣿⣆⠘⡄⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢤⣵⣦⡀⠀⠀⠀⠀⠀⢸⠿⠿⢿⣿⣿⣷⣶⣤⣀⠉⠉⢈⣧⣄⣿⣿⣿⣿⣿⣿⣆⢰⣄⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⣀⠀⢀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠙⠻⣧⣙⠂⠀⠀⠀⢀⣰⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠀⠚⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡽⠿⠿⣅⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡴⣦⣴⢞⡿⢋⡙⠛⢧⣼⡀⠻⠃⣸⣤⠟⠛⣉⠻⣟⢶⣤⡶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠁⢀⣯⣬⡿⠛⠋⠉⠉⠀⣿⡃⣿⡇⣿⡇⠈⠉⠙⠛⠻⣯⣬⣇⠀⢹⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⢸⣤⣥⡇⠀⠀⠀⠀⠀⡟⢳⣶⣶⠞⡇⠀⠀⠀⠀⠀⣧⣥⣼⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⡀⢸⣬⣅⡇⠀⠀⠀⠀⠀⢧⠈⣩⡉⢰⠃⠀⠀⠀⠀⠀⣇⣭⣼⠀⢸⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠃⠈⢉⣅⠡⠀⣰⣷⣄⠀⣠⡜⢿⠿⣤⡀⢀⣴⡷⡀⠀⢀⣍⠈⠀⢛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⣾⡿⡷⢾⡷⡿⢿⠟⢿⣟⢯⢟⣿⠟⢿⢻⡷⣿⠶⡿⣯⣧⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣬⣤⣵⣯⣤⣤⡷⢿⠶⢶⣾⢿⣾⣶⢿⣶⠶⢾⠷⣽⣦⣬⣧⣧⣬⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠟⡹⢂⣿⣐⣷⣾⣠⣷⣜⣡⣙⣴⣧⣸⣶⣗⣸⣇⠺⡙⠇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠟⠛⠣





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⣿⡇⣠⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠛⣿⣿⣿⡟⢛⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠀⠁⠀⣸⣿⣿⡆⠀⢀⠤⣒⢦⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⢹⣿⣷⣶⣤⣿⣿⣿⣷⣾⣵⣿⣿⡏⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠹⣶⣄⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⢟⣿⣿⣿⣿⡇⢻⣿⣿⣷⡟⡟⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⢀⣴⣾⠋
⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⢀⣎⢮⣹⣿⣿⡀⣠⣿⡿⣩⡔⣠⣀⣠⣿⣿⡿⠀⣀⡀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⢠⠊⡷⠀⣿⡟⢻⣟⢿⣿⣯⢟⢿⣿⣿⣿⢟⡞⣝⣼⣿⣯⡿⠋⣿⡇⠘⠃⢸⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣀⠓⣤⣔⠻⣧⡀⣿⣼⣿⣿⣷⡣⣯⢿⣏⣎⢮⣾⣿⣿⣿⣀⣼⠏⣽⣶⣮⢁⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣯⣾⣟⢿⣿⣹⣿⣿⣿⣿⣟⠎⡸⣳⣿⣿⣿⣦⡽⣟⣻⣷⢽⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣭⡽⣿⣞⣻⣿⣿⣭⣭⣭⠎⠰⡹⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢿⣛⣫⣭⣵⠶⣶⣿⣿⣛⡧⣴⣹⣟⣛⣶⠾⣯⣽⣟⡷⢿⣽⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣟⣿⣽⠿⠞⠛⠛⠉⠉⠉⠉⢞⡟⠉⠉⠉⠉⠛⠛⠶⢿⣽⣻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠘⠓⢄⡀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣧⡀⠀⠀⠀⠀⠈⠁⠀⠀⢤⡄⠈⠀⢀⣉⡀⠀⠁⠈⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠲⠿⠇⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣿⣿⡕⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣷⣤⣀⡀⣤⣀⢤⣤⡄⢴⡖⣶⣤⣤⣈⠂⠀⢸⠀⠂⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡯⢩⣕⠰⣶⡉⠛⠢⣹⡁⣼⣄⣾⠵⠿⢿⣧⡀⠠⠆⠈⠀⡄⠀⠀⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡙⡗⢄⣩⠳⣤⣈⠿⠆⣟⡁⠈⠃⠀⠀⠀⠀⠙⡇⠀⠀⠸⠀⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠊⣭⣭⣤⣤⣴⣾⡯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣷⠿⡛⠿⠿⢿⣿⣿⣷⣿⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣠⠞⣫⣾⣷⣦⡭⠳⣦⣀⡲⠾⠿⢿⣿⣿⣶⣦⣤⣤⢤⣀⣴⣾⣿⣿⣿⣷⣶⣠⢄⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢊⡴⣫⡵⠟⠉⠁⠀⠀⠀⠈⠉⠛⠛⠛⠓⠲⣆⡩⣭⣥⣤⣶⣿⣿⣿⣿⣿⠟⠟⠛⠿⢝⣿⣺⢶⣄⡀⡀⠂
⠀⠀⠀⠀⠀⡠⣢⣶⡿⠟⠋⢀⣀⡀⠠⠄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠪⢍⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠨⠉⠋⠒⠯⣄⡀
⠀⠀⠀⢀⣴⡼⠟⠉⠀⠀⠁⠀⠀⠀⠀⠀⢄⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡌⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠢⢤⡄
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠂⠄⡀⠀⠀⠀⡀⠀⠠⢿⠸⣿⣿⣿⣧⡄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠀⠀⠈⠓⠀⠀⠀⣦⠔⠘⣰⣿⣿⢹⡿⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠈⠀⢀⣴⢿⣿⡇⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢴⠀⢀⣀⣠⠼⠛⠛⠏⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢨⣿⣟⠋⠁⠀⠀⠀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠒⠈⠉⢹
⠀⠀⠀⠀⠀⠀⠙⡝⠒⠦⠤⠔⠒⠂⠉⠀⠀⠀⠀⠀⢈⡢⠀⠀⡠⠔⠂⠉⣀⠀⢶⠆⢪⠁⠀⢸⡇
⠀⠀⠀⠀⣰⢻⡉⠙⠄⠈⢄⣤⣤⠀⠐⠈⠀⠈⠁⠀⠈⠅⣥⣾⣧⢢⠾⠌⠋⡁⠠⠄⠀⠁⠀⢸⣧
⠀⠀⢠⡶⣯⣨⢳⠀⢰⡀⠘⣿⣿⣇⠀⠀⠐⠀⠀⠀⠀⠀⣿⣿⣿⣯⠀⢀⠄⠀⣠⠈⠁⠀⠀⢸⣯⢆
⠀⠀⠀⣧⢹⣼⣎⡆⠈⣧⡀⠙⠙⡻⠀⠀⣀⠀⠠⠰⡄⠀⢹⣿⠟⣩⣇⢀⡀⠀⠀⠀⠠⠀⢠⡈⣿⡆⢆
⠀⠀⠀⢹⡈⢿⣿⡾⡄⢸⣧⠈⢁⡄⠁⢀⡁⠀⠀⠀⠀⠀⠈⣿⣷⠄⢿⠈⠀⠀⠀⠀⠀⠀⠠⠀⠘⣿⡼⡀
⠀⠀⠀⠈⣇⠸⣿⢿⣷⠀⢿⣇⠈⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣾⡇⢀⠄⠀⠀⠉⠙⠒⠄⠀⢸⡇⣇
⠀⠀⠀⠀⢸⡇⢻⣏⣿⣄⠈⢹⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣃⣠⣶⣿⣛⣛⣛⡳⠶⢶⣾⣿⣺⢢
⠀⠀⠀⠀⠀⢷⠀⢿⣾⢹⠀⢸⣋⠒⢄⢀⣦⣀⢀⣠⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡻⠿⣷⡿⣿⣭⣷⡱⡀
⠀⠀⠀⠀⠀⠘⡃⠈⣧⡘⡀⠀⠀⠁⠈⣺⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣻⡿⠿⠿⣿⣿⣿⠿⢿⣶⣿⣿⣶⣿⠥⣘
⠀⠀⠀⠀⠀⠀⠳⠀⢻⣧⠣⠠⣶⣾⣿⣿⣿⣿⣿⡿⠟⠉⠈⠷⣭⣽⣿⣿⠇⠀⠀⠀⠀⠉⠉⠛⠲⠯⣭⣽⣛⠻⢿⡁
⠀⠀⠀⠀⠀⠀⠀⡆⠘⠽⠿⣿⣿⣻⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠶⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⡀⡀⡀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠠⢠⣤⣤⡄⡆⠐⡀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣶⣁⡆⠅⠀⠀⠀⠀⠙⠛⠛
⠀⠀⠀⠀⠀⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⣁⠡⠆⠀⠐⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⣠
⠀⠀⠀⠀⠀⡁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠠⠋⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠇⠀⠀⠤⡤⠄⠀⠀⠸⢰⡀⠁⠀⣿
⠀⠀⠀⠀⠀⡁⠀⠁⠀⡁⠀⠀⠀⠀⠀⢀⣀⡀⠀⢐⠧⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡏⠐⡖⢈⠀⠀⠀⠀⠀⠓⣶⠂⠃⠀⠀⠛
⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⣇⠀⠀⠀⡟⠀⠀⠀⠀⠇
⠀⠀⠀⠐⠒⠆⠒⠂⠒⠒⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⠂⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠀⠀⠀⠀⠀⠀⢰⣀⡄
⠀⠀⠀⠀⠀⡁⢸⠀⠀⠁⠀⠀⠀⢤⡧⠁⠀⠀⠀⠀⠀⠈⠜⢥
⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠬⠀⠀⠀⡏⣿⢸⡇⠀⠀⠀⠀⠃⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠃⠿⠸⠇⠀⠀⠀⠀⠀⠿⠹
⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣖⠒⠂⠀⠀⠀⠲⠟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣦⢴⠀⠐⠀⠀⠀⠀⣶⢰⡄
⠀⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠄⠴⠖⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡈⠉⠈⠀⠀⢀⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠐⠄⠀⠀⡐⠙⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠀⠀⠡⠀⠀⠃⠀⠹⠁⠀⠀⠀⠀⢀⢠⣄⠐⠀⢰⣶⠀⠂⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠓⠀⠀⠘⠛⠀⠀⠚⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⢀⡠⣿⣏⣹⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⣠⣿⣯⢿⣿⣶⡤⢤⣄⠐⣿⡿⢽⣧⣿⡭⢿⣿⠒⣤⡤⢠⣶⣿⡿⣴⣿⣄⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠙⣷⣶⢤⡄⣤⡎⢿⡏⢹⣿⣏⠙⠿⣾⣿⣶⡝⠆⢨⣿⣿⡁⠸⢯⣶⣿⢧⢿⠋⣽⣿⡟⢹⡿⣰⣆⢤⣤⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣞⣿⣿⣍⣴⣿⣿⣷⣶⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣾⣿⣿⣿⣶⣾⣿⣿⣦⣬⣿⣿⣳⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣟⣳⡿⣟⢻⢹⣟⣛⣻⡽⠯⣿⡿⢭⢩⣿⣛⣻⡟⡝⣻⢿⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣾⠷⠖⠛⠓⠚⣚⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣓⣒⠚⠛⠾⠿⢷⣶⣿⣯⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠟⣋⣭⣥⣶⣶⠟⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠳⣶⣶⣬⣭⣛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠿⣿⣿⣿⣿⠶⠶⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⣿⣿⣿⣿⠿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⡄⠀⠀⠀⣠⣿⣶⣤⣤⣤⣾⣿⢿⣷⣤⣤⣤⣴⣿⣄⠀⠀⠀⢀
⠀⠈⢀⣤⡀⠀⠈⠃⠈⠀⠠⠀⠈⠁⠀⠄⠀⠀⠘⠁⠀⠀⣠⣄⠁⠀⠀⠘⠷⠲⣾⣿⣿⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣿⣿⣷⠖⢾⠃
⠀⠀⢨⡿⢉⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⡉⠻⡇⠀⠀⠀⠀⠘⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠃
⠀⠀⠐⠋⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣭⡝⠃⠀⠀⠀⠀⢠⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⡟⢆⠀⠀⠀⠀⢀⣤
⣠⢀⣀⠀⠀⡇⠀⠳⡀⡠⠖⢉⠂
⠈⠲⣌⠉⠓⠓⠀⠀⠉⠀⠀⣯⣤⣄⣀⣀
⠀⠀⠈⠢⡀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⢀⡀
⠀⢀⡠⠖⠉⠀⠀⠀⠸⡓⢄⠀⠺⢤⣀⠀⠀⠀⠀⠀⢀⣸⠹⣤⢤⡄
⠀⠉⠉⠛⠛⠛⣻⠀⠀⣱⡀⠙⢶⡉⠉⠀⠀⠀⠀⠻⠭⣅⠀⠀⢯⡀
⠀⠀⠀⠀⠀⠀⣏⡴⠊⠁⢳⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⣼⠖⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢣⡀⠀⠀⡈⠳⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠈⠢⡈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠳⢄⠙⢦⡀
⠀⠀⠀⠀⢀⣀⢀⡞⠸⡄⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠑⠀⠉⠳⢄
⠀⠀⠀⠀⠈⠻⣍⠀⠀⠉⣳⡦⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⠢⣄⠙⢦⡀
⠀⠀⠀⠀⢀⣴⡧⠶⢤⣸⡁⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠈⠑⢄⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡰⠀⢀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⢀⡔⠁⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⡴⠛⢦⡀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣶⣦⣶
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢀⡴⠞⠛⠃⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⣀⠀⠀⠀⠀⠈⠙⠡⠶⠶⠂⠀⠀⠉⠀⠀⠀⠀⠁
⠀⢀⡀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡀⠀⠄
⠊⢀⠀⡀⡁⠢⠔⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⡠⢄⣠⢂⡠⢊⡥⢚⡥⠄⣀
⣨⠔⠫⠀⠊⣠⠊⠐⣩⠒⠋⠥⠒⣡⠤⠀⢀⣀
⢁⡤⢋⠵⣊⡤⠞⣩⠖⠊⣥⠞⣋⠁⣾⠋⣩⡴⢊⡥⢀⡦⠀⣀⠀⡀
⣋⣔⣵⣚⣵⣒⣭⣗⣫⣚⣵⣚⣡⣞⣡⣔⣋⣴⣋⣴⣛⣡⣞⣡⣊⣵⣋⣠⣖⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢤⣤⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⣤⡀⠀⠀⠀⠰⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⡄
⠀⢀⠀⠀⠀⢰⠾⠛⠻⠰⠄⠀⠀⠀⠀⠘⢂⠉⠁⠀⠀⠀⠀⠀⠠⠦⣄⠀⠘⣿⠀⠀⠀⠴⣿⡽⣿⣤⠀⠀⠈⣾⣧⡀⠀⠀⣰⣿⣿⣿⠗⠀⠀⠀⢈⣿⣶⡄
⠀⠚⢃⠀⠀⠀⠀⠀⢀⣤⠄⡁⠦⠀⠀⠀⠈⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣷⣷⡀⠀⠀⠈⣿⠃⠀⠀⠿⣿⡟⠉⠀⠀⠀⠀⠩⠿⠞⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⡄⠀⠀⠀⠀⠈⠑⠆⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠠⠀⠘⢶⢶⣤
⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡽⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠸⡦⠀⠀⢈⡄⠬⠒⠒⠀⠀⠀⠘⠛⣯⣥⡂
⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠐⣂⠐⢾⣾⠆⠀⠀⠀⠀⠀⠀⢦⣤⠀⠀⣠⠆⠒⠻⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠜⣨⠀⠀⠀⡄
⠀⠀⠠⣶⠃⠀⠀⠀⠀⢠⠂⠆⠀⠀⣀⠀⠀⢐⣾⡽⣷⡄⠀⠐⢀⢑⣠⣤⡤⠀⢤⣄⡀⠀⠈⠿⢟⣶⢺⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⠀⢠⠄⣀⠜
⠀⠀⠀⣿⠀⠀⠀⠀⡰⢋⠃⠀⠀⠀⠔⡞⠂⠴⠽⢿⡟⡿⢀⡀⠀⠀⠘⢿⠗⠰⢺⣯⢿⣦⠀⣰⣮⣤⣬⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣟⡿⡈⢺⠀⣬
⠀⠀⠀⠃⠀⠀⣠⠞⢡⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣽⡁⠶⠄⡖⠠⣀⠰⣀⠀⠈⠛⠿⢿⡟⠋⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣬⣿⡎
⢀⣀⣀⣀⣴⣋⡠⠄⠉⠀⠀⠀⠄⠀⠀⠀⠀⠐⠙⠛⠁⢡⣶⡾⣾⡷⢤⡀⠙⢄⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡿⣽⡇
⠀⠉⢣⣠⠌⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⡷⡿⠟⠉⠀⠙⢆⠘⣆⣰⠏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⣤
⠀⠀⠀⠙⢤⡀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⢉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠱⡄⠂⠀⠀⠈⠓⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠖⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠈⣗⠂⡀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠈⠀⠤⠠⡄⠀⠀⣀⠀⠀⠟⠀⠀⠀⠂⠀⠀⠀⠀⢰⡞⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⢴⠂⢄⠀⠀⠐⠀⠀⠀⠀⡼⠋⠀⠀⠀⡀⠂⢀⡤⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠄⡂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠁⠣⡀⠀⢀⡞⠁⠀⠀⢀⣆⡱⠂⠁⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⢣⣠⠞⠀⠀⢈⣠⠚⠁⠀⠀⠀⣨⠄⠀⠀⠀⠀⠀⢀⢀⠆⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢐⠀⠀⠀⡀⠀⠀⠀⠀⠙⢾⠋⣆⣀⣜⠁⠎⠀⡄⠀⣄⢀⣸⣤⡀⠠⣤⡴⠂⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠁⠸⡉⠘⠇⣄⠀⠀⢸⡦⠞⢉⣤⠼⠐⢲⠆⠙⢿⣤⢿⡄⢀⡴⠁⠀⠀⠀⠀⢀

⣿⣿⠟⠋
⣟⣀
⣿⣿⡷
⣿⣁⡀
⣿⣿⡿⠄
⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣾⣿⣿⣤⡀
⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣼⣿⣄⣀⣀⣤⣾⣿⣿⣁⣠⣤⣠⣤⣤⣤⣄⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠤⠤⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⣀⣠⣴⣿⣽⣿⣿⡿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠀⠀⠀⢲⡄⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠻⠋⠨⡳⣝⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⢠⠠⠌⠁⠀⠀⠀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡝⢎⣡⠶⢂⣤⣤⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣶⢸⣶⡶⢒⡶⢮⣝⣛⠶⠆⠤⠶⣖⣒⡰⠾⠿⠶⠏⣙⣛⠻⣿⣷⣌⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣰⣮⢰⢸⣿⣇⢛⣛⡿⣛⣛⣫⡭⢉⠶⣾⠿⡛⣴⣿⣿⡇⣶⣝⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣿⢰⡌⣿⣿⡎⣭⣝⣫⣭⠶⢟⣫⣵⡶⠮⠁⠈⣭⣏⢶⣜⢿⡆⡹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⠧⢻⡜⣿⡇⣯⡭⢩⡶⠟⠛⠉⠀⠀⠀⠀⠀⣿⣿⢇⡻⣆⢷⢹⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠱⢹⣧⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣾⠇⠈⠘⣠⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠇⠀⠀⠀⠛⢧⠻⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠀⠀⠀⠀⠀⠀⠀⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠊⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠐
⠀⠀⠀⠀⠂⣠⠈⠛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡝⠀⣄
⠀⠀⠀⠀⠙⢟⢁⠀⢳⠑⢄⠘⢉⡆⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⡐⠢⠀⠀⠀⣠⣾⣿⣿⡀⠀⠀⠀⢐⣈⠃⡠⢾⣿⠀⠀⡛⠋
⠀⠀⠀⠀⠀⠀⢣⣣⠸⡇⠈⣦⣻⣧⡀⠀⢠⣿⣿⣿⣿⣿⢦⡀⠀⢛⡆⠀⠀⠈⠛⠻⢿⣿⢷⡀⠀⢀⣼⣯⠜⠀⣼⣇⣀⠌
⠀⠀⠀⠀⠀⠀⠀⢻⣿⢧⠀⣿⣿⣿⣿⣴⢟⣼⣿⣿⣿⣿⣷⣝⡷⡉⠉⠁⠀⠀⠀⠀⢸⣿⣯⠻⣴⣘⣭⡆⠀⣴⠘⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢁⡘⠀⢹⣿⣿⠿⠺⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣾⣽⡞⠀⢸⣿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢼⣟⣛⡤⢤⣌⣩⣭⣿⣭⣭⣭⣭⣍⣁⣀⣀⣀⣀⠉⠉⢉⣙⡛⠿⣿⠿⠃⢠⣾⠇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡙⢩⣽⣿⠉⠉⠀⢾⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣾⣿⣽⠛⠒⣚⡛⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣸⣿⣷⣄⡀⣠⣾⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠻⢿⠿⠿⢿⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠙⠲⠾⣿⣿⣿⣿⣿⣿⣛⣛⣛⣋⣓⠂⠀⠀⣴⣤⣤⣤⣤⣤⣬⣟⣩⣅⣉⣉⣉⣥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠻⣿⣟⣛⠛⠛⠿⠏⠉⠉⠉⠉⠉⠀⠠⠿⠿⠿⠿⢿⣿⣿⣟⣿⣿⣯⣭⡷⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠓⠒⠚⠚⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉








⣿⢿⢿⠿⢿⡻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠹⠀⠴⠄⡄
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠋⠀⠀⠁⣶⠂
⠿⠓⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⢠⠔⠁
⣾⣶⣖⢸⡟⣳⣶⣤⣄⣀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠌⠀⢀⠉
⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠛⠿⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⢰⡴⠁⠀⠄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣴⣶⣶⣿⢯⣭⣤⡤⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣾⣁⣈⠀⢀⣤⣤⠀⢘⡿⣷⢽⣻⣿⣿⣿⣿⣿⣿⣶⣶⣾⣧⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣤⣤⣤⣤⣤⣤⣄⣀⣀⣰⣿⣉⣀⣀⣀⣀⡙⢒⣾⣒⣺⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⣉⡁⠈⠉⠈⣿⣿⡉⠁⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣉⣉⡈⠁⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢲⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢁⡀⢀⡀⢀⡀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠆⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠉⠛⠶⣤⣠⣀⢻⡖⠐⠂⢲⣖⣁⣠⣤⠖⠛⠉⠉⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⣠⣤⣶⣦⣤⣤⣄⣀⣉⣹⡇⣿⣿⢸⣏⣉⣀⣤⣤⣤⣴⣦⣄⡀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡘⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢿⢇⠛⠛⠸⠿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢹⣿⡿⢶⣾⣿⣿⣿⡏⢿⣦⡀⠶⠶⢀⣴⠟⢹⣿⣿⣿⢱⣦⣿⣿⡟⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢾⠟⠔⠜⣥⣄⢹⡇⢠⡌⠁⣴⣦⠉⢡⡄⢸⠏⣶⡌⠣⠦⢻⡿⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡀⢨⡮⢸⡇⢈⣡⡦⠙⠋⣴⣌⠀⢸⡆⣶⡄⣀⣀⡿⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣐⣋⣀⡀⠘⢧⣿⣷⠿⠋⠀⠛⠓⠈⠛⠷⣼⣷⡼⠁⢀⢀⣛⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠩⠿⢟⠛⠲⠶⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠖⠖⠛⠻⠯⠍⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠐⠟⣢⠀⡌⢵⡌⡀⠀⢰⣿⣷⠀⠀⡀⣴⡍⠄⠀⠐⡻⠀⢸
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠚⠿⠤⠤⣤⣜⣈⣀⣀⣘⣻⣛⣀⣀⣈⣐⣣⣤⡤⠴⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⡄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠋⠉⠉⠉⠉⠉⠛⠛⠉⠉⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄
⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⣠⣴⣦⣄⡸⣿⣿⢀⣤⣶⣦⣄⠀⠀⠀⣠⢤⣤⡀⢿⣿⣰⢃⣠⣤⢤⡀⠀⠀⢀⣤⣤⣀⢿⣿⡟⣠⣤⣄⡀
⠘⠋⠉⠉⢻⣷⣿⣿⣿⠟⠉⠉⠙⠇⠀⠰⣷⡏⠉⠻⣎⣿⣧⡟⠉⠙⣧⡇⠀⠀⡿⠛⠛⢿⣎⣿⣼⡿⠛⠻⢷
⠀⠀⠀⠀⠐⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣐⡿⣿⣻⣇⣀⠈⠉⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⠀⠀⠀⣀⡼⢿⣿⣿⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠾⣿⡷⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠈⠁
⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣿⣿⣷⠀⠀⣀⣀
⣠⣶⣿⣷⣦⣸⣿⣿⣠⣴⣾⣿⣶⡄⠀⠀⠀⢰⣶⣦⡘⣿⣟⣴⣶⣦⠀⠀⠀⢸⣿⣿⣷⣄⢿⣿⡟⣠⣾⣿⣿
⠿⠋⠀⠀⠉⢻⣿⣿⠟⠉⠀⠈⠙⠟⠀⠀⠀⠘⠀⠈⢻⣼⡾⠁⠀⠙⠀⠀⠀⠈⠿⣿⠉⠻⣾⣿⣿⠋⢉⣿⠟
⠀⠀⠀⠀⠀⠰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢼⣿⣷⠄⣀⠀⠀⠀⠀⠀⠀⠸⠇⠀⢸⣿⡇⠀⠸⡅
⠀⠀⠀⠰⣦⣴⣿⡿⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢼⣿⡳⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⣄⡼⣿⢦⣠
⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡿⠀⠁
⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣬⣿⣿⣿⣧⣴⣶⣄⠀⠀⠀⢰⣾⠷⣦⢸⣿⢃⣴⢿⣷⡄
⠀⠀⣼⣿⣿⣷⣿⣿⣾⣿⣿⡆⠀⠀⠀⠀⠸⣿⠛⠻⣿⣿⣿⠟⠛⣿⠟⠀⠀⠀⠸⢿⡤⠈⢧⣿⡞⠁⣤⠿⠁
⠀⠀⠈⠛⠻⠏⣿⣏⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⢇⠀⢺⣿⡇⢀⡻⠄
⠀⠀⠀⠀⢠⣀⣿⣧⣀⡄⠀⠀⠀⠀⠀⠀⠀⢰⣦⣤⣾⣿⣿⣤⣤⣷⠀⠀⠀⠀⠀⠀⠻⠶⣫⣿⡝⠶⠃
⠀⠀⠀⠀⠈⠉⢿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⢿⠏⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣠⣾⣻⣶⣄⠀⠀⠀⠀⢀⣀⣀⣀⣠⣿⠦⠀⣶⣴⣄⠀⠀⠀⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣾⣿⣍⣹⣿⣿⣷⠀⠠⠞⣿⠟⠛⠿⢿⠇⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿⡟⠛⠛⣿⢿⣿⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⣻⠞⢻⡆⠀⠀⠀⠃⠀⠀⠴⠏⢸⠇⠀⠀⡼⠓⣿⠄
⠀⠀⣿⡿⠿⠿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠿⠀⠈⠇⠀⠀⠀⠀⣀⣤⣼⡇⠀⠀⠀⠀⣀⡀
⠀⠀⣀⡠⣄⠀⠉⠁⠀⠀⠀⠀⢀⣀⣴⣶⠟⠀⠰⣶⠦⠀⠀⠀⡴⠶⣌⠉⠛⠿⠟⠋⠁⣴⣦⡀⠀⠉⠁
⠀⠀⣾⢣⠛⣛⣒⡄⠀⠠⣂⢦⡭⠿⠻⠃⠀⠀⣾⣿⣿⣦⠀⠀⠀⡰⠃⢀⣀⡀⠀⠀⠈⠉⢹⣷⣦⣄
⠀⠀⡳⣷⣃⣏⣕⣦⣨⠱⠟⠋⠀⠀⠈⢀⠀⠀⠈⠻⣿⣿⡀⠀⠘⢧⣴⣿⣿⣿⣷⣄⠀⠀⢸⡿⢿⣿⣇⣀
⠀⠀⠈⠈⠉⠉⠀⠁⢀⡤⠀⠀⠀⠀⠈⢉⣧⠀⠀⠀⠊⠉⠁⢠⣶⡀⠈⠉⠛⠛⢍⠁⠀⠀⠚⠀⠃⠸⠿⠟⠂
⠀⠀⠀⠀⣿⣿⠀⢠⣾⣥⡀⠀⠀⠀⠀⣻⡟⠀⠀⠤⣶⣾⣿⣿⣿⠗⠀⢀⠰⠀⠈⠀⢀⣠⣶⡆⠀⣈⣷⡄
⠀⠀⢠⣾⣿⣿⠀⠈⢻⣿⣿⡆⠀⢦⣾⣿⣿⠀⠀⠀⠘⠛⠻⠍⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣀⣰⣜⣿⣿
⠀⠀⣿⣿⣿⠃⠀⠀⠚⠛⠛⠀⠀⠘⢿⠿⠇⢀⣤⣴⣦⣆⠀⠀⢀⣴⣶⣶⣌⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⣿⣿⣿⡄⠀⠰⠶⣿⣷⡆⠀⠂⠀⠀⢀⣿⣿⣿⣿⣿⠗⠀⠼⠿⠿⢿⣿⡿⠃⠀⠈⠻⠿⠿⣿⣿⡿⠋
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣌⢿⣿⡌⠻⣯⢷⠀⠙⠌⠄⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠻⣄⠀⠀⠀⠙⣆⠻⣄⠀⡣⡀⠀⢄⢻⣧⠳⡈⢿⣧⡠⡹⡄⢌⢻⣷⡹⣷
⢿⣿⣎⠻⣧⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢢⡀⠀⠀⠀⠙⣦⡀⠀⠀⠈⢷⣽⣧⡙⣷⡄⠈⢢⡹⣷⡔⡄⢻⣷⡕⡜⢎⢢⠹⣿⣜
⡄⠻⠻⣆⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡱⡄⠀⠀⠀⠈⢷⣤⢀⠀⠈⢻⣾⣷⡜⢿⣆⠀⠱⡜⢿⣎⢆⠹⣿⣌⢮⢣⡱⡘⢿
⠙⣆⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠱⡵⡜⢆⠀⠀⡀⠀⢻⣧⣳⡄⠀⠻⣿⣿⣎⢿⣷⡀⠘⢎⠻⣧⡣⡘⢿⣦⠣⡱⡜⢌
⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⢆⠠⠀⠀⠀⢀⢢⡀⠙⣿⣎⢣⡀⠀⠄⢦⡹⣿⣿⣆⠀⠹⣿⣿⣧⡻⣿⣄⢈⢧⡙⣷⡕⠌⢻⣷⡑⡜⢎
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢷⡑⡀⠀⠀⠠⡻⣄⠘⢿⣷⡱⡄⠀⢪⢳⡜⢿⣿⣧⡀⠘⢿⣿⣷⡝⢿⣆⠀⠳⡌⢿⣎⢂⠹⣿⣌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⡀⠀⠀⠀⠱⡄⠀⠀⠀⠈⢧⡀⡻⣌⢆⢢⠀⠱⡝⣧⡘⣿⣿⣜⢆⠀⠡⡻⣮⢻⣿⣷⡄⠈⢻⣿⣿⣎⠻⣷⡀⠙⢆⠻⣧⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⢢⠀⠹⣜⢆⠀⠀⠀⠙⣆⠀⠀⡀⠀⢳⡔⢽⣦⡣⡱⡀⠘⢾⣷⡌⢿⣿⣮⣣⡠⡘⢽⣷⡹⣿⣿⣆⠀⠹⣿⣿⣧⡙⠟⣄⠈⢣⡘⢷⡄⠀⠹
⠀⢦⠀⠀⠀⠈⢄⠀⠱⡀⠘⢯⣣⡀⠠⠀⠈⢷⡠⠘⢄⠀⢻⣎⢿⣷⡕⡜⢆⠈⢻⣿⣎⢻⣿⣷⡵⡄⠈⢫⢿⡜⢿⣿⢆⠀⠈⢿⣟⢷⡄⠈⢢⠀⠱⡄⠻⣄
⠀⠀⠳⣤⠀⠀⠀⠣⡀⠙⣄⠈⢿⣷⡄⠑⡄⠈⢻⣶⡈⢣⡀⠹⣧⡻⣿⣎⢎⢣⡀⠹⣽⣧⡹⣿⣿⣞⢆⠀⠱⡹⣎⠻⣷⡀⠀⠀⠙⢦⠻⣆⠀⠡⡀⠘⢆⠈⠢
⠀⠀⠀⠹⣷⡄⢀⠀⠹⣄⠈⢧⡀⠻⣿⣆⢪⢆⠀⠹⣿⣆⠱⡄⠘⣷⡝⣿⣧⡣⡳⡄⠘⢮⢷⡘⢽⣿⣯⡣⠀⠘⠌⠆⠙⣷⡀⠀⠀⠈⠣⠙⣦⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠘⢿⣦⠢⠀⠘⢦⠀⠳⡄⠙⣿⣧⡹⣦⡀⠘⢿⣧⡘⢆⠈⢿⣎⢿⣷⡔⠘⣆⠈⢳⡹⡌⢪⢻⣷⡄⠀⠈⢂⠀⠈⢷⡄⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠑
⡄⠀⠐⡀⠀⠈⢻⣷⡵⡈⢮⢳⡀⠙⣆⢈⢿⣷⡜⣷⡄⠈⢻⣷⡌⢣⡀⠹⣧⠻⣿⣎⠈⢧⡀⠹⣌⠀⠡⡹⣿⣄⠀⠀⠁⠀⠀⠹⣄⠀⠀⠀⠀⠀⠹⡄
⢻⣆⠰⣄⢄⠀⠠⡻⣿⣞⣌⢳⡽⣄⠈⢧⡡⡻⣿⣎⢿⣆⠀⠹⣿⣆⠱⡄⠙⢷⡙⣿⣧⡀⠳⡄⠘⢦⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠈
⠀⠻⣷⡘⣮⡢⠀⠘⣝⣿⣿⣦⠻⣾⣦⠀⠳⡕⡝⣿⣧⡻⣧⡀⠘⢿⣧⠘⢆⠈⢂⠈⢿⣷⡄⠙⢆⠀⠳⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠹⣿⣌⢷⣵⡀⢈⢮⢿⣿⣷⡙⣿⣷⡁⠙⣌⢎⢿⣷⡝⣷⡄⠈⢻⣇⡀⠂⠀⠡⠀⠻⡿⣄⠈⢣⡀⠑⠄⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣄⠀⠐⣜⢿⣮⢻⣾⢄⠀⠳⡿⣿⣿⣌⢿⣿⣄⠈⢦⠳⡹⣿⢎⢷⡀⠀⠙⣦⠀⠀⠀⠐⠀⠙⠝⢦⠀⠑⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢌⢷
⢚⣦⠠⠈⢮⣻⣷⡹⣿⣢⠁⠙⣜⢿⣿⣦⠻⣾⢦⠀⠱⡐⡜⢷⡂⠳⡄⠀⠈⢧⡀⠀⠀⠀⠀⠈⠊⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⢦⠑⣽⣄⠈⢿
⣧⡹⣷⡐⠀⠳⣽⣿⣌⢷⡕⡀⠈⢯⢻⣿⣧⡙⢧⡣⠀⠀⠈⢊⢳⡄⠙⣆⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠈⢳⡀⠀⢳⡌⢿⣦⠈
⠘⢷⡜⢿⣄⠀⠙⣞⢿⣦⠻⡌⢄⠀⠳⡙⣿⣆⠈⢳⡐⠀⠀⠀⠡⠙⣆⠈⢧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⢳⣄⢠⡀⠻⣶⡀⠹⣎⢻⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡑⡾⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠂⢹⠟⠉⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠺⡟⠙⢮⠤⢔⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣆⠤⠀⠀⠠⠖⣤⠤⢹⡤⢸⠋⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠄⠀⠰⣇⣐⢺⣀⣮⠧⠀⢉⡿⠒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠂⠀⠀⢐⠀⠀⠀⠲⠀⠀⠀⠵⠂⣈⣩⣼⣾⣚⣇⢤⣤⣌⠁⠒⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠩⠀⠀⢀⡀⡆⡐⠷⣤⣷⣴⣿⣿⣿⣿⣿⣀⢙⡿⣤⢖⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢴⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⢈⠇⢀⣛⣾⡿⢿⣿⣽⢻⣿⣵⣟⣿⣥⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢀⢀⡀⢈⡷⣍⢹⡏⠀⠘⢿⣿⣍⣻⣟⣿⣿⣟⡻⡶⠒⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⠣⠌⣁⠈⢷⢞⣾⣧⡄⠀⠙⢿⣿⣟⣿⣟⣻⣿⣽⣭⠉⢀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠴⠋⢤⠀⡄⠀⠀⢰⣿⡶⢂⣉⣸⣇⣽⣸⡿⠋⠄⠀⠀⠻⣭⣿⣿⣿⣿⣷⣦⡤⠐⢀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠑⢞⠀⠀⡀⠀⠇⢠⣸⣤⢬⣗⣸⣾⣿⣿⣿⡿⠀⠀⠀⡠⠐⠀⠙⣿⣿⣻⣿⣿⣟⡝⣠⡌⠀⠞⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢄⠰⠀⠠⢘⠀⢀⣵⣼⣌⠁⠐⠋⠁⠙⠻⠿⠿⠛⠁⠀⠀⠀⡐⠁⡀⠁⡃⢸⣿⣿⣿⣿⣿⢷⠟⠋⣔⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠁⢹⢤⡟⢶⣵⡿⠂⡀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⡀⠑⢠⡿⣿⣿⣿⣷⡾⣵⠄⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣿⣿⣴⣆⢯⣯⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡔⢪⠀⠀⠈⠻⣰⠆⢸⣿⣿⣿⣿⣿⣧⡷⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠲⡖⢢⣸⣟⣟⣫⢾⣷⣮⡟⠁⠀⠀⠀⠨⠄⠈⢑⠀⠀⠀⠀⠁⡄⠀⠀⠀⣹⣯⠖⣾⣿⣿⣿⣿⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡻⣷⣿⣿⣯⠿⣿⣛⢿⡿⠃⠀⠈⠀⢀⡀⠄⠀⠀⠄⢃⢀⠀⠁⠀⠐⡤⠀⢨⣿⢻⣟⣛⣿⡋⠙⢷⣾⡇
⠀⠀⠀⠀⠀⠀⢡⠀⣹⣿⣿⣿⣿⣶⣿⣽⠟⠀⠀⣠⣾⣷⡌⠴⣎⠰⢀⠘⡄⠈⠆⣠⠐⢀⢺⢠⡌⣿⢿⣿⠿⠿⣻⣦⣴⢻⡷
⠀⠀⠀⠀⠀⠀⠈⣠⣼⣿⣿⣿⣿⣿⠿⠀⠀⠀⣾⣿⣿⡷⣷⠀⠁⠰⢠⡀⠀⠀⠡⠄⡁⠰⡊⣼⣿⠡⣾⣿⣿⣿⣿⣿⣼⣾⣏⠢
⠀⠀⠀⠀⠀⠀⢲⡟⢻⡉⣿⣯⣬⣧⣴⣶⣶⣶⣿⣿⣿⡷⢿⡷⣶⡆⠠⠘⠈⠰⠠⠰⠄⣳⣿⣿⣧⣿⣿⣿⣿⡿⢿⡿⢩⣯⣿⣍⠦⣄
⠀⠀⠀⠀⠀⠈⠀⠀⠘⠉⠉⠉⠉⠿⠿⠿⢉⡻⡏⢹⣿⣿⢿⡟⢻⣿⣷⣶⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⢿⡿⢿⣗⠈⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠚⠻⢇⡉⢈⣿⢿⣿⣋⠻⣿⢿⡿⠋⠙⠛⠻⠋⠁⠀⠀⠁⠀⠈⢹⣽⠏⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⡉⠑⠸⣿⠗⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣀⣶⣾⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⣿⣿⣿⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠛⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣘⠿⣿⣿⣿⡿⢇⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⣀⣠⣾⣿⣿⣷⡼⣿⣏⣾⣿⣿⣷⣄⣀⠀⠀⠀⢿⣷⣄⡀⠈⢻⣿⠏⠀⣀⣴⣿⡇⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀
⠀⠀⠀⠀⠙⠻⠿⠟⠉⠙⢻⣿⡞⠋⠉⢻⠿⠟⠋⠀⠀⠀⠘⢿⣿⠿⣷⣄⢟⣴⡾⢿⣿⠟⠁⠀⠙⠁⠴⠄⠀⠀⠠⠐⠀⠀⠀⢀⠦⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⣈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣫⣿⡻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣿⣿⣿⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣮⣿⣿⣿⣿⣵⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⡑⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢰⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡀⠀⢁⠀⠀⠐⠀⠀⡜
⠀⠀⠀⠀⠀⠀⡠⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣄⠀⠑⡄⠈⡆⢠⡇⢀⠞⠀⢀⡄⢀
⠀⠀⠀⠀⠀⡞⠀⠠⠈⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠄⠈⢣⠀⠀⠀⠀⠀⠀⠀⠞⠁⠠⠈⠐⢄⠈⠄⢳⣸⢀⠊⢀⠔⠙⠀⠀⠱⠀⠠⡀
⠀⠀⠀⢀⣴⣷⣶⣶⣾⣦⣄⡙⠻⠋⠙⠟⢋⣠⣴⣶⣶⣶⣶⣤⡀⠀⠀⠀⢀⠄⠳⠠⠤⢠⣄⠀⠀⠰⠘⠁⠄⠀⠀⣀⣄⠠⠤⠞⠠⣄
⠀⠀⠀⣿⠟⠋⠙⠃⠀⠀⡟⠃⠀⠀⠀⠀⠘⢻⠀⠀⠙⠋⠛⠿⣿⡄⠀⣰⠃⡤⠒⠀⠋⠀⠈⠟⠃⠀⠀⠀⠀⠐⠻⠁⠀⠘⠂⠒⠠⡈⢆
⠀⠀⢀⠿⠀⠀⠀⠀⠀⠀⠈⠀⣴⣶⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠁⢠⠀⠀⠀⠀⠀⠀⠈⠀⠄⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⣙⡛⠙⣙⡀⠀⠀⠀⠀⠀⠐⠒⠈⠀⠀⠀⠐⠲⠄⠀⠀⠀⠀⠀⠀⡐⡠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠠⢤⣷⣠⣧⠄⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠁⠀⠀⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⡟⣼⣿⡝⣦⣄⡄⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢿⣿⣿⣿⠁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣮⢿⣿⣣⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠠⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣡⡄⠀⢹⣾⣷⡯⠀⢀⣄⣿⣿⣿⠇⠀⠀⣀⡘⠘⢿⣿⣿⡿⠃⠀⣀
⠀⠀⠀⠀⠀⢀⣥⣤⣄⡈⢻⡿⠁⣀⣤⣤⣀⠀⠀⠈⠻⠿⠟⠁⠀⢸⣿⣿⡟⠀⠈⠻⠿⠟⠋⢀⣴⠟⠛⠙⠓⢤⢻⡟⡠⠚⠋⠙⠻⣦⡀
⠀⠀⠀⠀⢰⣿⡟⡉⠉⠛⣨⣥⡛⠉⢉⢹⣿⡆⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠸⣿⠀⠀⣄⠀⠨⠟⠻⠅⠀⣠⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠘⢿⡿⠇⠀⠈⠛⠋⠀⠀⠀⠀⠘⠿⠿⠛⣿⣿⣿⣿⡛⠿⠿⠃⠀⠀⠀⠙⠛⠒⠃⠀⢡⣄⣠⡌⠀⠘⠓⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⡰⣦⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⢿⡿⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⡘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣷⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⣶⣶⣿⣶⣾⣿⣿⣿⣿⣶⣦⣤⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣤⣼⣿⣿⠟⠛⠋⠛⠂⡏⠘⠁⠀⠉⣋⠉⢻⣿⣾⣤⣖⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⣄⣠⣿⡿⠛⠊⡷⢂⠀⠀⠀⣠⡇⠐⠰⢣⠄⠀⠀⠉⠈⠉⠛⢿⣯⡅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⣿⣿⠟⠣⢄⠀⠀⠀⣀⠂⢀⣼⣿⣿⡅⣹⢠⠀⠀⠀⠀⠀⠀⠀⢚⢹⣧⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠛⠉⠁⠁⠀⠀⠌⠀⠀⠸⣇⣸⡿⠛⣉⠙⠻⣷⣴⣀⡶⠂⠀⢀⠀⠀⢀⠀⠃⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⣠⣿⡏⣀⣾⣿⣷⠀⠙⣿⣿⡿⢇⣔⠁⠀⠀⠈⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠑⠒⢆⠀⠈⣻⣿⣿⣀⣻⣏⣩⣿⣧⣼⠿⡻⣦⣺⠁⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣾⣿⣿⣿⣿⣿⣯⣿⣿⠟⢣⠄⠓⠈⢻⠷⠂⠀⠀⠈⢀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡻⢿⣿⣿⣿⣿⢿⣿⣿⠃⠀⣴⣶⣄⠀⠈⠀⠀⠀⠀⠀⠀⠗⠀⣼⣶⣾⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣹⣿⣿⣿⣿⣿⣿⠻⣷⠀⢸⣿⣿⣿⠄⠠⣾⣤⣤⣴⠂⠚⢀⠀⠀⠗⠉⠙⡿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣺⣿⠉⣿⣿⣿⣿⣿⣇⣸⣿⣿⣾⣿⣅⡶⠀⠁⠀⣠⣾⡿⠛⠉⢡⠉⠉⠃⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠙⠨⠥⠿⠛⠛⠛⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠈⠉⠙⢿⣿⡿⠉⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⢽⣧⠀⠈⣿⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡌⢻⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣠⡄⢿⣟⣹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠱⠆⢀⣾⠇⡰⠰⠀⣾⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡾⣠⣴⣿⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⣤⣤⣨⣤⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⣶⣝⣿⣿⣿⣿⣿⣿⣧⣴⣄⣀⣀⣤⡀⣀
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠿⠿⣾⡿⠿⢷⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣮⣿⣿⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠛⠉⠁⠨⠇⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠋⢉⣉⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⣤⣤⣤⣤⣦⣶⣦⡦⠒⠈⠀⠆⠀⠈⠀⠁
⠀⠀⠀⠀⣲⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠛⠛⠛⠿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡟⣁⣀⣀⣠⣠⣀⣀⡀⠀⠉⢻⣷⣦⡀
⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣻⣿⣿⣿⣿⣿⣷⣦⣄⠈⢻⣿⣦⡀
⠀⠀⠀⠀⠘⠿⣿⡿⠟⠋⠿⢿⣿⠋⠀⠀⢸⣿⣿⣿⣿⣿⡟⢛⣻⠙⠳⣦⡙⢿⣿⣧⣤⣴⣶⡆⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣻⣿⣿⣿⠄⠀⢼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠈⠉⠒⠬⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣶⣿⣿⠷⣤⣈⠻⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⣦⣭⣉⣈⠉⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⢿⣟⠛⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠏⠹⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⠀⠀⠸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣿
⠀⠀⠀⣀⣤⣄⡀⢿⣿⣿⡿⢀⣠⣤⣀⠀⠀⠀⠀⣾⣿⣿⡿⠿⢿⡆⠀⠀⢠⡿⠿⠿⣿⣿⣿⡀⠀⠀⠀⣀⠀⠠⡀⢧⠀⣸⡿⢀⡤⠤⣀
⠀⠀⣾⣿⣿⣿⣿⣎⣿⣿⣱⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⠁⠀⠀⠀⠹⡀⢀⠏⠀⠀⠀⠈⢿⣿⡇⠀⠀⠎⣴⣾⣷⣮⡈⣇⣿⢱⣵⣶⣶⣦⣵
⠀⠀⢻⣿⣇⠀⠈⢻⣸⣇⡟⠉⠀⣸⣿⡟⠀⠀⠸⣿⣿⣄⠀⣻⣿⣆⠃⠘⣰⣿⣟⠀⣠⣿⣿⠇⠀⠀⠢⣿⣇⠀⠈⢻⣸⣇⡟⠁⠀⣸⣿⡟
⠀⠀⠀⠀⠀⢀⠠⣴⣾⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣿⣍⣉⣉⣩⣿⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⠠⣄⣉⣱⣦⠄⡀
⠀⠀⠀⠀⠀⢻⣦⡴⣲⣖⢦⣴⡟⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣌⣡⡆⢰⣌⣡⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠻⣀⣴⠾⣷⢦⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣷⣾⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣭⣯⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⠠⣀⡀⠀⠄⠈⠀⠉⠀⠄⠠⣀⡠⠀⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⣀⢀⠀⠤⠀⠀⠀⠀⠀⠠⠄⢀⢀⣀⠖⠊
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠁⠂⠒⢁
⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠐⠀⠀⠀⠂⠀⠐⠀⠀⠒⠀⠀⠀⠀⢀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠆⠀⠼⠀⠀⠀⡒⠐⠒⠊⡸⡆⠾⣌⠒⠒⠒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡐⠀⠀⠈⠲⠤⠱⣺⠖⠡⠃⠸⠝⢾⣲⠁⠰⠚⠁⢀⠐⢀⠐
⠀⠀⠐⠐⠁⠁⠀⠀⠂⠀⠂⠀⠀⠈⠂⠂⠀⠀⠉⠑⠶⠤⠦⠄⠒⠒⠉⠀⠀⠀⠀⠑⠒⠒⠠⠦⠴⠖⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣹⡟⣏⠐⠁⠀⣸⠑⣄⠀⠀⡿⡆⠀⠀⡾⡇⠀⠀⡴⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢳⠃⡟⠞⠀⠀⡅⠣⡈⢂⠀⣿⣟⣠⣌⣿⡇⠀⠌⢠⠋⣸
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⡎⠀⠀⠸⡌⠢⢁⣢⣠⣌⡙⠁⠙⢉⣤⣠⢆⠁⠊⡸
⠀⠀⠀⣐⠻⣦⣀⠀⢀⢈⣠⠼⢓⡀⠀⠀⠀⠀⠀⠀⡩⡒⢻⢄⠀⠫⣑⣒⣾⠌⢡⠙⣆⡜⢁⠎⢥⣖⣒⡫⠃
⠀⠀⠀⠉⠳⢼⡹⠃⠀⠻⣫⡴⠋⠁⠀⠀⠀⠀⠐⣊⠼⠁⠨⡣⣍⡁⠑⠴⣂⠑⠤⣠⠃⢳⡴⠔⢉⡒⠔⠃
⠀⠀⡎⠑⠲⠤⡇⠀⠀⠀⠮⠴⠒⠉⡇⠀⠀⣀⠈⢁⡼⠀⠀⠳⢄⣀⣲⡀⠈⠈⠓⠚⠀⠈⠒⠋⠉
⠀⠀⠧⣠⣄⣐⠇⠀⠀⠀⢿⣀⣤⡀⠗⠀⠀⠛⠈⠁⠀⠀⡠⠚⣉⡂⢈⠤⠠⢄⠐⡊⡙⢦⡀
⠀⠀⠄⠀⣰⠀⠀⠀⠀⠀⠀⢠⣀⠀⡂⠀⠀⠀⠀⠀⠀⠎⠀⠪⡔⠀⢋⡁⠀⣈⠁⠒⡬⡂⠉⠆
⠀⠀⢠⣏⣷⠀⠀⠀⠀⠀⠀⢰⣧⣧⠀⠀⠀⠀⠀⠀⠐⠔⠄⠳⠁⠁⠤⠀⠀⠠⠌⠁⠱⠁⠕⠔⠀⡀
⠀⠀⠈⢯⡱⡄⠀⠀⠀⠀⠀⡴⣨⠏⠀⢀⠄⢒⣡⠴⣫⠄⣠⢀⠤⡴⠀⠀⠀⠀⠰⡰⢄⢠⡀⢬⡳⢤⣑⠢⢄
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠙⠐⠚⠗⠊⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠒⠟⠒⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣴⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⡘⠻⠟⠀⠀⠀⠀⠄⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣀⣀⠒⠦⠀⠊⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠢⡀⠀⠀⣀⡤⠀⠄⠀⠀⠀⠠⠀⢣⣡⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡁⠻⠀⠀⠣⠄⢠⣶⡦⠀⠀⠀⣿⠈⠛⠀⢰⡈⠃⠐⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠘⡇⠀⠀⠺⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡿⡀⠠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⡇⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⢸⡃⢀⠀⠀⠀⢸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠠⠄⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠛⠀⠀⢠⢀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠛⣆⡀⠀⠀⣀⡤⠐⠚⠉⢀⡄⠀⢀⣤⣶⣿⠏⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠐⠾⠋⠀⠀⠛⣋⡵⠃⢄⣿⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠱⠚⠁⠀⠐⠿⠋⣘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⠀⠄⠂⠀⠀⠀⠀⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣾⣧⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢦⡀⣠⣦⠀⡠⣨⣾⣿⣷⣍⢤⡀⣰⣦⠀⡤⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⡷⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣼⣿⣿⣯⣴⣿⣿⣿⣿⣿⣧⣼⣿⣿⣯⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣿⣿⡿⠿⠋⢉⣉⣠⣤⣤⣤⣤⣤⣤⣈⡉⠙⠻⢿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣛⣉⣭⣭⣭⣭⣭⣭⣉⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⣈⣩⣭⣭⣭⣭⣭⣍⣙⣓
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣭⢯⣿⣻⠽⠟⣛⣫⣭⡶⣃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⡳⣭⣝⣛⡻⠯⣟⡿⡽⣭⣽⣶⣄
⠀⠀⠀⠀⠀⣀⡀⣻⣿⣿⣿⠘⠩⣶⣿⣿⣯⢭⣡⣾⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣷⣤⡩⣭⣿⣻⣷⡎⠋⢾⣿⣿⣿⠀⣀
⠀⠀⠤⣦⣬⣿⣿⠿⠿⣿⣿⠿⣷⣶⣬⢍⠐⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⣿⣿⠓⡉⢥⣶⣾⠿⢿⣿⠿⠿⢿⣿⣧⣴⡤⠄
⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣯⣴⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣷⣝⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷
⠀⠘⢸⠩⣿⣿⣿⣿⣿⣿⣿⡇⣿⣭⣿⠿⠟⠛⠻⢿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣿⡿⠟⠛⠻⠿⢿⣯⣿⠁⣿⣿⣿⣿⣿⣿⣿⡏⠗⠙
⠀⠀⠀⠀⠙⣽⣿⣿⣿⣿⣿⣇⣿⢩⣴⣿⣿⣿⡿⣦⡙⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠋⣴⠿⣿⣿⣿⣶⡌⢻⣆⣿⣿⣿⣿⣿⣧⡻
⠀⠀⠀⣠⣾⠟⣿⣿⣿⡿⠟⣻⣿⢸⣿⣿⠟⠛⢿⡌⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⢣⣾⠛⠛⣿⣿⡇⣼⣟⠻⢿⣿⣿⣿⡿⣷⣦
⠀⠀⠀⠙⣯⣾⡿⠀⠀⠈⠛⢿⣿⡌⣿⡏⣸⣷⠈⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⠇⣾⣷⢸⣿⠇⣿⣿⠟⠉⠀⠀⢸⣷⣾⠛
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠻⣧⢹⣧⢻⣿⠀⣿⢰⣌⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣩⣄⢻⡀⣿⣿⢸⡿⣸⡟⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢻⡜⣿⠐⠃⠛⠻⠷⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠾⠟⠛⠊⠃⣿⣏⡿⡱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠹⣿⠿⠿⠟⠛⠆⠈⠙⠻⢿⣿⣿⣿⡿⠟⠛⠁⠰⠚⠛⠿⠿⣿⡟⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⣿⣿⣿⣁⣀⣀⣉⣿⣋⣀⣀⣀⣿⣿⣷⡷⠟⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⣿⡟⣡⣿⣆⠙⣿⣯⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠒⠀⠈⠄
⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠄⠀⠇

⠀⠠⠄⠀⠀⠀⠀⠀⠀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⢤⠀⠀⠀⡀⢠⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠰⠆
⠀⠀⠀⠀⠃⠀⠀⣷⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠠⠋
⡀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣤⠂⠀⠀⠀⠙⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠰⠶⠠⠠⣄⡀⠀⢀⣀⣀⡀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀
⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠤
⠤⢄⠉⠑⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⡦⢠⡴⣀⣤⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈
⡇⡼⠃⡯⠿⣿⣿⡾⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠁⢸⠶⠟⠋⠉⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣀⠁⠄⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠁⠀⠠
⣴⣤⡄⠒⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠂
⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿