Hi Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⢶⡶⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⢠⡞⠁⠀⢸⡇⠀⠙⢷⡀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⢠⡟⠀⠀⠀⢸⡇⠀⠀⠈⢷⡀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠛⠶⣤⣀⣾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠇⢀⣀⣤⡤⠶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢸⡏⠙⠃⠀⠀⢈⣀⣤⡴⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠸⠀⣀⣀⡀⠀⠀⠉⠛⠓⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⠀⠀⣠⠶⠛⠉⠉⠉⠛⠳⣄⠀⠀⠀⢸⡇⠈⠉⠛⠳⠶⠞⠛⠉⠁⠀⡧
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠀⣼⠋⠀⣀⠀⢀⡀⠤⠀⠈⢧⠀⠀⣸⠷⠤⢤⣤⢤⣤⠤⠤⠤⠤⠴⠟
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢠⡇⠀⠀⣿⣤⣼⡇⣷⠀⠀⢸⡄⢠⡇⠀⣠⠟⠁⠀⠉⠛⠒⠒⠶⠄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣷⠀⠀⠿⠀⠸⠇⠿⠀⠀⣼⠃⢸⡇⢀⣿⠀⠚⠃⠀⠘⠛⠀⣶⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠶⠘⢷⣄⠀⠀⠀⠀⠀⣀⣀⣙⣦⡄⣷⢸⡟⣧⡀⠶⣤⠶⢀⡼⢷⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠛⠲⠶⠖⠛⠉⠉⠉⠁⢠⡟⢸⣇⡈⠛⠶⠶⠶⠛⢁⠘⡇⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇⠙⢦⣤⣀⣤⡴⠋⢰⡇⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⠀⣰⢿⡇⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠻⢦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠟⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⢦⠀⠀⣼⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⡇⠀⢸⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡞⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢡⠀⠘⡇⠄⠀⠀⠸⡀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠘⡄⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⣼⠀⠀⠀⠀⡇
⠀⣠⠖⠶⣄⠀⠀⠀⠈⡇⠀⠀⠀⢣⠀⢳⠀⠀⠀⠀⢻⠀⠀⠀⠀⡏⠐⠀⠀⠀⡇
⠀⡇⠀⠀⠘⡆⠀⠀⠀⡇⠀⠀⠀⠘⡆⢸⢀⠀⠀⠀⠈⡇⠀⠀⢀⠃⠀⠀⠀⠀⡇
⠀⢳⠀⠀⠀⠹⡀⠀⠀⢳⠀⠀⠀⠀⢳⢸⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⢸⠃
⠀⠈⡇⢀⠀⠀⢱⠀⠀⠈⡀⠁⠀⠀⠘⡏⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢸
⠀⠀⠘⡄⠀⠀⠀⢣⡀⠀⡇⠀⠀⠀⠀⡇⢃⠀⠀⠀⠀⡇⠀⢠⠇⠀⠀⠀⠀⡄
⠀⠀⠀⠹⡀⠀⠀⠀⠧⠀⢹⠀⠀⠀⠀⢣⣼⠂⠀⠀⠀⠿⠤⠜⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠹⡀⠀⠀⠘⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠂⠉⠉⠉⠲⡀
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠿⠶⠋⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⡀⣀⡀⣀⡀⣀⡀⢀⡀⣿⣄⣄⣀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⢢⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠁⠀⠈⠉⠉⠉⢙⠳⠆⠀⠀⠀⠀⣤⠞⠁
⠃⠀⠀⠐⠀⠂⠐⠀⠁⢺⠋⠀⠀⠀⠀⢲⡆⡠⠈⠀⠀⠀⠀⠀⣿
⠒⠚⠒⠛⠒⠒⠚⠐⠁⣿⠓⠓⠊⠒⠙⠘⠓⠒⠚⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠛⠛⠛⠛⠛⠛⠲⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⢴⠟⠁⠀⢀⡤⠖⠋⠉⠀⠉⠀⠀⠉⠉⠛⠲⢤⡀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⢰⣦⣴⣾⣭⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠹⣦
⠀⠀⠀⢀⡴⠛⠳⣦⡞⠉⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⣠⠞⠋⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠘⣆
⢠⡴⠖⢾⡇⠀⠀⢸⡇⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣻⣆
⣿⠀⠀⠘⣧⠀⠀⠀⣷⠀⠀⠀⢷⣤⡤⣤⡀⠀⠀⠀⢸⠇⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⢀⣾⠀⢀⡀⢰⣦⢀⣿⠹⣆
⢸⡆⠀⠀⢻⡄⠀⠀⢹⡆⠀⠀⠘⡇⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣞⣁⣀⣠⠞⢻⣀⡾⣧⣸⡏⠛⢻⡆⢹⡄
⠈⣧⠀⠀⠈⣧⠀⠀⠈⣃⠀⠀⠀⢹⠀⠈⡅⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡾⠛⠁⠀⠀⠀⠀⠀⠉⢩⣍⡁⠒⠛⠉⠀⠙⠋⠀⠀⠀⣿⠈⣷
⠀⢻⡀⠀⠀⠿⠀⠀⠀⠈⠀⠀⠀⠈⣧⠀⢹⡆⠀⢘⡇⣀⡴⠟⠁⠀⠀⠠⠶⢟⣛⣻⣭⣍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⡆⢿
⠀⠘⡇⠀⠀⢀⣀⣤⣤⠶⠶⣶⠟⠀⠀⠀⠀⢻⡞⢻⡟⠉⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣙⠻⣦⣄⠀⠀⠀⠀⢸⡇⢸
⠀⠀⢿⡀⠀⠉⠉⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⡾⠀⠀⢀⣴⣿⣿⡇⠀⠸⡆⠀⠀⠀⠀⢀⡴⠋⢁⡀⠀⠉⠙⢦⠉⠀⠀⠀⠀⣸⠀⣿
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⣧⣸⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠸⣿⣿⣿⣿⣾⠀⡇⠀⠀⠀⠀⡟⢀⣾⣿⣿⡇⠀⠀⠈⣷⠀⠀⠀⠀⠛⢶⣏
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣸⠇⢹⡇⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣙⠛⠿⠛⢁⡼⠁⠀⠀⠀⠘⡇⠸⣿⣿⣿⣿⡟⠀⠀⣿⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠈⣆⠀⠀⠀⠀⢀⣀⣽⡶⠶⠒⢲⣏⠁⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⣤⣈⣛⣛⣋⣀⣀⡴⠃⠀⠀⠀⠀⠀⣾⢀
⠀⠀⠀⠀⠘⠳⠶⠚⠻⣏⠉⠀⠀⠀⠀⠀⠙⢷⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⢡⣤⡀⠀⠀⠀⠀⣰⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠙⢦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠦⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠙⢦⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣠⡴⠞⠋⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣀⣀⠀⠙⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⢼⡟⠛⠷⣶⠦⢤⣤⣤⡤⣶⡶⠖⢻⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠳⠦⣤⠴⠞⠋⠀⠀⠸⡏⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢶⢾⣿⣿⣿⣿⠀⠀⠀⢹⡆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⠉⠁⠘⠋⠉⠀⠀⠀⠸⡇⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣾⣇⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⣿⡄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣧⣤⣀⣀⣀⢀⡼⠋⠉⠉⠈⢻⣄⣀⣀⣀⣀⣬⣿⣤⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠉⠉⢹⠂⠀⠀⠀⢸⡉⠉⠉⠉⠀⠀⠀⠘⡯⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣤⣤⣤⣄⣀⣀⡿⠀⠀⠀⠀⠈⣧⣀⣠⣤⣤⣤⣤⡴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢰⡏⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⢧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠶⠛⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠷⢶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠄⠀⠀⠠⢀⠀⠀⠀⢀⠄⠀⠀⣀⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⢼⣿⣿⠃⠀⠀⡐
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⣉⠥⠥⠒⠉⠁
⠀⠀⠀⠐⠀⠀⠀⣾⡇⣠⣿⠏⠶⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡄⠀⠀⠀⣽⣿⠛⣿⣰⡆⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠇⠀⠀⠀⢻⡇⢀⣿⢻⡇⠀⠀⡔
⠀⠀⠀⠐⠀⠀⠀⠘⠃⠈⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⣴⡆⠀⣶⣦⠀⠀⢀⡇⣸⠁⡀⠀⠀⠀⢰⣂
⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⡏⣷⣴⣆⣸⠃⠉⢾⡟⢸⣾⣇⣿⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠤⠤⠤⠄⡆⠀⠀⠀⠀⠀⣿⡏⢻⡇⠇⠟⠉⠙⠟⠁⠘⠃⠘⠋⠉⣿⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⠾⣿⢰⡆⣰⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⡄⠀⣠⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢷⠾⠷⠋⢡⣾⠛⠻⠆⠀⠀⠀⠀⠀⣼⣧⡾⣡⡀⣿⢿⠇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⡏⣏⣠⢯⡾⣠⠧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠰⡀⢀⠂⠀⠀⠰⠀⠀⠀⠂⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⣵⠁⢸⠀⠀⢸⠀⠀⠀⢇⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⠀⠀⠀⠀⣀
⠀⠁⠠⠇⠀⠀⠀⠟⠀⠘⠀⠀⢸⠀⠀⡇⢸⠁⢸⠀⠀⠀⢸⠀⠃⢀⠆⠀⡀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠃
⠀⠀⠐⡡⠄⠀⠀⠀⡀⠀⡆⠀⢸⡀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⢠⠀⠰⢦⠈⠀⠀⢀⣀
⠀⠀⠀⠈⠀⠀⠀⠐⡅⠀⠿⠀⢸⠁⠀⡇⠀⠀⠘⠀⠀⠀⢸⠀⠀⠈⠀⡂⠀⠀⢼⠀⠀⠀⡀
⠀⠀⠀⢽⡀⠀⠀⠀⠸⠀⠀⠀⠜⠀⢀⠇⠀⡀⢀⠀⠀⠀⠘⠀⠀⠀⢠⠁⠰⡀⡀⠀⠀⠀⠃
⠀⠀⠀⠈⠪⠒⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠚⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠁⠀⠀⠀⢠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡀⠀⠂⠋⡀⠀⠀⠐⠂⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠈⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠤⠀⢀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠤⠀⡀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠒⠒⠠⢄
⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠊⠀⣠⣦⣼⡧⠀⠀⠀⢨
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠸⠟⠻⢋⡠⠤⠔⠁
⠀⠀⠀⠀⡐⠀⠀⠀⣀⣀⠀⢠⣾⡇⣀⠀⠀⠀⠀⠀⡆⠀⠘⢀⠤⠐⠊⠉⢁⡀⠀⠀⠀⠀⠤⠄⢀⣀
⠀⠀⠀⠀⠁⠀⠀⠀⢻⣿⣠⣾⣿⠘⠛⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⢸⠀⠀⠀⠀⢸⣿⠋⣽⡇⣾⡇⠀⠀⠀⡠⠃⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠸⠀⠀⠀⠀⢸⣿⠀⣿⡇⣿⠇⠀⠀⡔⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢃⠀⠀⠀⠘⠋⠀⠛⠁⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⣤⡆⠀⢰⣶⡄⠀⠀⢀⡏⢸⡇⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣦⣿⢸⣤⣠⡄⣸⠇⠘⢱⣟⠧⣶⣸⡇⣾⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠄⣀⡀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠠⣿⡿⢻⡟⢸⢹⡿⠳⢻⣶⠆⠀⣿⠀⢹⠏⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡈⠁⠉⠀⠀⠀⠀⠀⠀⠛⠁⠘⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠾⣿⡇⣶⠆⣴⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡀⠀⢀⡄
⠀⠀⠀⠀⠂⠀⠀⢸⡿⠀⣿⣤⣿⡴⠟⢫⣼⠟⠻⣦⠀⠀⠀⠀⠀⠀⢸⣿⣠⡟⢀⠀⣿⣷⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠁⠀⠀⠀⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢹⣷⡟⢀⣟⢸⡇⣿⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⢠⠀⠀⠀⠀⠀⠀⠸⠃⠘⠀⠓⠋⠙⠉⠛⠉⠉⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠓⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⢲⡀⠀⣿⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢹⠀⠀⠀⠘⡆⠀⠀⠀⠀⢠⠏⠁⠉⢦
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢰⠀⠈⡔⠀⠀⠀⢣⠀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⣀⡀⠀⠀⠀⠈⡆⠀⠀⠀⡆⠀⡇⠀⠀⠀⢸⡀⠀⠀⠀⡠⠀⠀⠀⢸
⠠⡎⠉⠙⣆⠀⠀⠀⡇⠀⠀⠀⢰⠀⠁⠀⠀⠀⠈⡇⠀⠀⠀⡇⠀⠀⠀⢸
⠈⡇⠀⠀⠘⡆⠀⠀⢹⠀⠀⠀⠀⡇⠇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸
⠀⠸⠀⠀⠀⠙⡀⠀⠈⡆⠀⠀⠀⢰⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡜
⠀⠀⢣⠀⠀⠀⠱⡀⠀⢇⠀⠀⠀⠈⡌⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠇
⠀⠀⠀⢧⠀⠀⠀⢡⠀⢸⡀⠀⠀⠀⣇⣷⠀⠀⠀⠸⡄⡼⠀⠀⠀⠀⢠
⠀⠀⠀⠈⢆⠀⠀⠀⢄⠈⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠘⡆⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠉⠉⢦
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢼⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⡠⠊⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠇⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⣾⠁⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠹⡆⠀⠀⣿⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡄⠀⠘⡇⠤⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⢇⠀⠀⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡇
⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⢸⠀⠀⢻⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡇⣀⠀⠀⠀⢸⡇
⠀⣾⠉⠉⠉⢳⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⢳⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢸⡄⢸⠠⠤⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⡇
⠀⠸⡆⠀⠀⠀⠈⢦⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⢻⠀⠀⠀⠀⠘⣇⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡆⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠇⠐⠀⠀⠀⠀⡜
⠀⠀⠀⢇⠈⠀⠀⠀⠙⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⢃⠀⠀⠀⠀⠀⢸⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠘⡆⠀⠸⡇⠀⠀⠀⠀⠀⢳⢸⡂⠀⠀⠀⠀⢐⡄⠀⢀⠇⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠹⡆⢀⠀⠀⠀⢱⠀⠀⢳⠀⠀⠀⠀⠀⠸⣴⠟⠀⠀⠀⠀⠘⠓⠰⠛⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢆⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⢷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⡠⠖⠉⠂⠀⠀⠀⠀⠀⠀⣰⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡀⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣢⣷⣤⡴⠚⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠤⠤⠶⠶⠶⠦⠶⠶⠤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣤⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠶⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟

⣶⣶⠶⡶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡤⠒⠈⠉⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣜⠁⠀⠀⠩⢐⠤⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⠈⠒⣀⡴⠤⡀⣀⠀⠀⠀⠙⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡀⢖⠠⠀⠃⠀⠈⢈⠆⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⡈⠀⢇⠀⡠⠀⣛⢠⡀⢰⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠳⣄⠂⠸⠀⣠⡇⣠⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡺⡽⡏⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⢓⣋⣷⠒⠊⠙⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢷⡱⠱⢠⠞⠇⠀⠀⠀⠀⠀⠀⠀⡠⠄⠲⢡⠋⢌⠀⠀⠀⣸⡗⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠁⠀⡸⠀⡆⠀⠀⠀⠀⠀⡠⠋⢀⡔⠓⠋⢵⣮⡯⠉⢉⠍⢠⠃⠈⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠁⠀⡇⠀⠀⠀⠀⡰⠁⢀⡎⠀⠀⣼⣷⡟⠃⠀⠎⢀⡎⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡠⠔⠛⢄⠀⠀⡐⠁⢸⣿⣇⠀⡐⢿⣿⣧⠀⡜⢲⡉⠅⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⢆⡸⠁⠀⠀⢻⣿⠉⠀⠀⠻⣿⣶⢡⢎⠍⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠈⡇⠀⠀⠈⠈⢿⡆⠀⠀⠀⢻⣿⣇⠎⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠸⠀⠀⡟⠀⠘⣷⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣼⠇⠀⢀⠛⣧⠀⠀⠀⠀⠁⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⣀⠜⠁⡄⠀⢸⠀⠹⣧⡀⠀⠀⠀⠀⣀⡴⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⡰⠁⠀⣶⠦⠄⠁⠬⡗⠶⠶⠞⠋⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠲⣤⡇⠀⠀⠀⠀⢇⣀⣠⣤⣶⣶⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠉⢿⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢰⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠸⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡔⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠁⠿⠿⠇⠀⠀⠀⠀⠀⠀⠳⠀⠀⠈⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⢋⡽⠋⠁⢹⠁⠉⠻⣏⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⢠⡟⠁⠀⠀⢸⠀⠀⠀⠘⣧⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣏⡀⠀⠀⢀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⠙⠳⠶⣾⣧⣄⠀⠀⠀⠼⠀⠀⠀⠀⢀⣉⣠⣤⠶⠖⠛⠛⠳⠶⢦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⣤⣶⡞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠘⢃⣀⣀⣤⣀⡀⠀⠀⠉⠙⠛⠲⣶⣤⣄⣀⡀⠀⠀⠀⣀⣀⣤⡴⣶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⠀⠀⣠⡾⠋⠉⠀⠀⠉⠙⠳⣦⠀⠀⠀⠀⣿⠀⠀⠉⠙⠛⠞⠛⠉⠉⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠏⠀⢀⡀⠀⣀⠠⠄⠀⠈⢷⠀⠀⢠⡿⠶⠶⣦⡴⢶⣶⠶⠶⠶⠶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⡟⠀⠀⢸⣧⣤⣿⢰⡇⠀⠀⢸⡇⠀⣜⠀⠀⣴⠋⠀⠀⠙⠓⠶⠶⠶⡄⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣷⠀⠀⢸⡇⠀⢿⠸⡇⠀⠀⣸⠇⠀⣧⠀⣸⡇⠀⠶⠂⠀⠰⠶⠀⣰⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣤⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⢿⡀⣿⢷⡀⠀⣄⣀⣤⠀⣠⣿⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠙⠷⢦⣤⣤⣤⠶⠛⠛⠛⠋⠁⣼⠃⣿⠀⠛⢦⣬⣩⣤⠾⠋⠈⣧⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⠺⣦⡀⠀⠀⠀⣀⡾⠀⣿⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣀⣀⣀⠀⠀⣴⡏⠀⠀⣿⠀⠈⠙⠛⠛⠛⠉⠀⠀⡏⠀⠀⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣾⠙⣧⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⣠⡿⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠈⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⠋⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠔⠉⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠤⠀⠀⠀⠄⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠂⠀⠀⠀⠀⡸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡇⠀⠉⠀⠀⠁⠀⣇⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠠⣤⡤⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠄⠠⢺⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠣⢀⣀⠠⠊⠁⠐⠂⡤⡀⠀⠀⠀⠹⡁⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢆⠀⠀⠀⡘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠐⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠡⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⡀⠄⠊⠉⠉⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⢀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⡠⠔⠉⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡒⠹⠀⠀⢰
⠀⣀⣀⠨⠋⠐⡆⡁⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡆⠀⠀⡄
⠤⢔⣯⣅⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊
⠐⠉⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢶⣖⣒⠒⠒⠒⠒⠶⠶⠤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠦⢤⣀⡀⠀⠉⠉⠙⠛⠒⠶⠤⠤⣤⣀⣉⡉⠛⠲⠮⢭⣭⣙⣒⠒⠲⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢤⣀⠈⢉⡿⠶⠶⠖⠒⠒⠒⠒⠒⠲⠶⠮⠭⠿⠷⣶⣦⣤⣈⠉⠙⠛⠶⠶⢬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⣀⣈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⡶⠤⢤⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣯⣄⣀⢉⡇⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣄⠀⠀⠀⡄⠀⠀⠀⠹⡖⠦⢤⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⡉⢹⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠀⠀⢠⣇⠀⠀⠀⠀⢳⠒⠦⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠉⢻⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡓⠶⠤⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣏⠉⠓⣿⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⡇⠒⠲⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡉⠙⠓⣿⠀⠀⠀⠀⠈⣿⣿⣷⣶⣿⣿⡇⠀⢀⣿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⡏⠉⠓⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡋⠓⠲⢿⠀⠀⠀⠀⠀⣿⣿⡿⠛⠛⣿⣿⠀⢸⣿⡿⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⣏⣉⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡟⠒⠶⢼⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⢸⡟⠀⢸⣿⠇⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡇⣈⣙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡗⠲⠦⠬⣇⠀⠀⠀⠀⢸⣿⠁⠀⠀⠘⡇⠀⢸⡿⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⣸⣀⣀⡀⠉⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠲⠤⣤⣘⣢⣀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⣀⡉⠉⠙⠛⠒⠶⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠤⣄⣈⡉⠙⠛⠷⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⢾⣅⣀⣈⡉⠉⠛⠓⠒⠶⠦⠼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣌⣉⣙⠓⠲⠦⢤⣌⣉⡛⠓⠶⢤⣌⣉⡉⠉⠉⠙⠓⠲⠤⣤⣀⣀⠈⢉⣉⠛⠛⠒⠶⠦⣤⣄⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠫⠿⠿⠶⢶⣤⣬⣉⣙⡓⠒⠦⢤⣀⣀⢀⣉⡹⠇⠀⠙⢦⠤⢄⣀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⣦⣄⣈⠉⠙⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠉⠙⢲⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⢳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⣳⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢠⠀⠀⣀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⢀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⢆⢀⠀⣰⠀⠂⠀⡇⠈⠀⠀⢹⡄⢀⠃⠀⠀⠀⠀⠃⠀⠈⠀⠀⠐⠀⠐⠆⠐⠀⠠⢀⡀⠤⠀⠀⢀
⠀⠀⠄⠀⢀⠀⠀⠀⠈⣞⡇⠀⢸⠀⠀⠀⢇⠀⠀⢀⠀⣇⡈⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠀⠀⠀⠔⠀⠀⠀⠀⠙⠆⠃⠀⠂⠀⠕⢤⡀
⠀⠈⠀⢰⡇⠀⠀⠀⢀⠸⠁⠀⢸⠁⠀⠀⢸⠀⠀⢸⠀⢹⡇⠀⡇⠀⠀⠀⠀⢸⠀⢸⠀⢰⠀⠀⡂⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⢀⢣⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⠀⠀⢸⠀⠈⠀⠀⡇⠀⠀⠀⠀⢸⠀⠈⠀⣼⠀⢀⡃⠀⢠⣄⠐⠃⠀⠀⠀⠀⠀⠑⠀⠀⠈
⠀⠀⠀⠈⠶⠍⠀⠀⠀⣀⠰⠀⠀⣧⠀⠀⢸⠆⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⠀⠀⠀⡇⠀⢸⠁⠀⠀⢈⡇⠀⠀⠀⠀⠒⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⡀⠀⠻⠀⠀⣸⠀⠀⢸⠀⠀⠀⠀⠇⠀⠀⠆⠀⣿⠀⠀⠀⠀⠀⡌⠀⠀⠀⢺⠁⠀⠀⠀⣠
⠀⠀⠄⠂⠼⡆⠀⠀⠀⠀⠀⡧⠀⠀⠀⢠⠃⠀⠀⢸⠀⠀⠀⠀⡄⢀⠀⡀⠀⢉⠀⢰⠀⠀⢰⠇⠀⣧⡀⡀⠀⠀⠀⠠⠹⠀⠀⠠
⠀⠀⠀⠀⠘⢌⣂⠄⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠉⠀⠀⠀⠉⠀⠑⠂⠘⢄⠼⡀⠀⠀⠀⡅
⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠌⠣⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡁⠐⠳⠒⠀⢐⣠⠔⠂⠀⠈⠀⠀⡘⢦⣀⣸⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠐⢀⠀⣋⣐⠀⠐⠂⠈⣀⡀⠀⠀⠒⠊⠉⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡡⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠘⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢋⡉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠅⠰⠤⡤⢀⠀⠄⠀⠀⠄⠀⠀⠀⠌⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠤⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⡴⠶⠒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡼⠒⠒⠓⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡄⡼⠠⠤⠤⢄⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⠁⠰⡄⢀⠸⠇⠸⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡧⠀⠀⠀⠀⠂⠀⠐⡅⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⡆⠀⠐⠒⠂⠁⡸⡀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⠀⠘⣦⣤⣤⡤⠚⠀⢻⡤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⡇⠀⠀⠀⢸⡖⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰⡹⠩⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⢥⠃⠀⠀⠀⠀⢢⡄⠏⠉⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⢠⠙⡴⠁⠂⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢨⠀⠑⠠⠤⠤⣴⡋⠐⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⠃⠀⡅⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠘⠀⣶⡦⠀⠀⠛⠏⠐⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠈⠆⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⡔⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⠠⡇⠀⠀⡀⠀⠀⣀⡀⠀⢀⠃⠀⠀⠀⢀⡠⠖⠋⢇⠀⠀⠜⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡇⠀⠀⠇⠀⠀⠛⠏⠀⢸⠀⠀⠀⢸⠋⠀⠀⠀⠘⣆⠎⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠘⠀⠀⠀⠀⢠⠋⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⢸⢠⣤⠀⠀⠀⡇⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡄⠀⠀⠀⢠⠀⠁⠀⠀⢸⡇⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡇⠀⢀⠆⠘⡀⠀⠀⣀⣼⡇⠀⠀⠑⣀⠀⠐⡀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠄⡠⠊⠀⠀⣏⢀⠀⠀⠀⡇⠀⠀⠀⠈⠳⢤⣸⢄⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡔⠋⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣧⠀⠀⠀⠀⠀⢸⠀⠲⡇⠀⢸⠀⠀⠀⠀⠀⠀⠠⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⡇⠀⠁⠀⠘⡄⠀⠀⢀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠞⠋⠉⠉⠙⠛⠀⠀⢰⠀⠀⠉⠉⠉⠉⠙⠻⣷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⢲⡶⠒⠒⠛⠻⠷⠻⠿⠟⠛⠛⠛⠛⠁⠹⠗⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡄⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠠⣿⣀⣀⣀⣸⡟⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣽⠀⠈⠉⠉⡏⠀⠀⣿⡀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠁⠀⠀⠈⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠲⣶⣤⣤⣤⣤⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠙⠉⠛⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⡀⣀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠀⠀⢀⣤⡦⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣃⣠⡴⠴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠒⠀⠀⠐⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠈⢉⠁⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠨⠿⢄⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⡀⠠⠀⠂⠐⠒⠂⠠⢀⠁⡀⠀⠀⠀⠀⠀⠰⠀⠴⠀⠒⠠⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠠⠀⠀⠈⠢⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠃⠀⣠⡄⠀⠀⠀⠀⠀⠀⠁⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⢀⡂⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢠⣿⡆⠀⠐⠐⠀⠀⠀⠀⠈⠀⠀⢿⡟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⢀⠂⠀⠀⠀⠘⠢
⠀⠀⠀⡠⠀⠀⠃⠀⠀⠈⠀⠀⠠⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠉⠀⠀⢠⡐⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠇⠄
⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠤⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⡠⠶⡆⠡⠀⠀⠀⠀⠒⠂⠠⢤⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⡠⠁
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠐⠏⢣⠅⠀⢆⠀⠀⡀⠀⠀⠐⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⡀⠀⠀⠀⠀⣀⡠⠀⠒⠉⢈⠠⠐⠀⠘⢨⠄⠊⠕⠠⣀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠠
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠉⡀⠤⠄⠐⠀⠊⠀⠀⡠⠐⠀⠀⠐⢅⠀⠀⠀⠀⢐⡖⠁⠁⢰⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡐⠁⠘⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠈⠂⠠⡴⠃⠀⠁⠀⡃⠀⠉⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠐⠂⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠸⠁⠺⣄⡀⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢤⠀⠀⡇⠈⠳⣯⠞⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⢀⠂⠀⠀⠀⠀⠀⠀⡐⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡄⠀⢰⠀⠀⠚⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠰⠫⢤⣹⠗⠚⠄⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢦⣀⠀⠀⠀⠀⣂⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠀⠉⠐⠀⠠⠀⠠⠤⡈⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠈⠉⠉⡘⢁⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⡠⠊⠉⠀⢸⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠊⡑⠀⠀⠀⠀⠀⣠⣀⣅⡀⠂⡠⠊⠁⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⠀⠡⠈⢀⠜⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢂⠖⠁⢀⡈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠚⢀⠀⣀⠑⠉⠀⠈⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢠⣀⠹⠄⠑⠒⠄⠀⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⡌⠀⠀⢀⠄⢘⢠⠀⣦⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣙⣤⡀⠃⣠⣇⠼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⣿⡠⣀⡄⠀⠀⠀⠀⠀⠀⠘⢊⡩⡵⠏⠁⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⠀⠀⠇⡅⠀⠀⠀⠀⢀⠔⢈⡴⠼⢤⣧⡤⠄⠺⢁⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⠀⡇⠀⠀⠀⠠⠃⢀⠊⠀⢰⣿⠟⠀⠰⠁⡎⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠄⠚⠄⠀⠠⠁⢸⣿⣀⡀⢿⣿⡆⠠⠓⣌⠅⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣤⠁⠀⠀⢻⣇⠀⠀⠹⣿⣆⢎⠊⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠘⠀⠀⣀⠈⢿⡀⠀⠀⠹⣿⠎⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢠⡇⠀⠸⣧⠀⠀⠀⠙⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⡰⠋⡀⠀⡆⠘⣧⡀⠀⠀⠀⢀⡴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡰⠁⢀⡶⠂⠀⠸⡓⠲⠞⠋⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⡀⢸⡇⠀⠀⠀⡁⠀⠀⠀⣀⣠⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠛⠁⠀⠀⠀⠓⠖⠚⢿⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢰⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠈⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⢰⣿⡇⠀⠀⠀⠀⠀⡄⠀⠘⠄

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠛⠉⠉⠛⠛⠒⠶⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⡀⠤⠤⠤⠤⢄⣀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠛⢛⠁⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠈⠣⡀
⠀⠀⠀⢀⣤⣤⣀⡤⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣠⠾⠛⠛⠛⠛⠛⠓⠶⠦⣤⡀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠹⡆
⢀⣠⢤⡟⠀⠀⢻⡁⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⡄
⣯⠀⠀⢿⠀⠀⠘⡇⠀⠀⢹⣄⣤⣄⠀⠀⠀⢰⠇⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣼⠀⢀⠀⣤⡀⣸⠻⡄
⢹⡀⠀⠸⡇⠀⠀⢻⠀⠀⠈⣧⠀⢻⠀⠀⠀⣾⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⣴⣟⣀⣠⡼⢻⣀⠾⣆⡿⠛⠻⡆⢻⡀
⠘⣇⠀⠀⢷⠀⠀⠈⡅⠀⠀⢸⡀⠨⡄⠀⠀⣏⠀⠀⣾⠀⠀⠀⠀⣀⣀⣤⣴⡶⠟⠋⠀⠀⠀⠀⠀⠀⢹⣄⡐⠉⠁⠀⠉⠀⠀⠀⢿⠘⡇
⠀⢻⠀⠀⠘⠀⠀⠀⠀⣀⣀⡀⠧⠀⢻⣄⣤⣧⡴⠛⠁⠀⠀⠐⢛⡭⠝⠒⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⠀⠀⠀⠀⠀⢸⡄⣿
⠀⢸⡇⠀⠴⠶⠚⠛⠉⡽⠁⠀⠀⠀⠀⣿⢠⡏⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⣤⡄⠈⢧⠀⠀⠀⠀⠀⣠⠴⠒⠒⠲⢭⡛⠆⠀⠀⠀⢸⠁⡷
⠀⠀⢿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣸⡇⠀⠀⠀⠀⠀⣏⠀⠀⢸⣿⣿⣷⣤⢸⠆⠀⠀⠀⡼⢁⣴⣶⡆⠀⠀⠹⡄⠀⠀⠀⠾⣤⡇
⠀⠀⠸⡆⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⡿⠙⡇⠀⠀⠀⠀⠀⠙⠦⣄⣈⠻⠿⠿⢃⡼⠀⠀⠀⠀⡇⢸⣿⣿⣿⡶⠀⠀⡇⠀⠀⠀⠀⢸⠷
⠀⠀⠀⢡⡀⠀⠀⠀⣀⣨⡷⠶⠒⢲⡋⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠋⠀⠀⠀⠀⠀⠰⣄⣙⣛⣛⣁⣀⠜⠁⠀⠀⠀⠀⡿⢠
⠀⠀⠀⠈⠛⠛⠛⠻⣍⠀⠀⠀⠀⠀⠙⢦⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⠀⠀⠀⣸⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠻⣦⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠃⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠙⠾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦⠤⢤⡤⠤⠴⠶⠚⠉⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠦⣄⣀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⠬⣿⠓⠶⣦⠤⢤⣤⡤⣤⡴⠖⢾⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠳⠶⠶⠞⠋⠀⠀⢸⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣶⣶⣶⣄⠀⠀⠘⡇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠛⠿⠻⣿⠿⠀⠀⠀⣿⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢸⡄⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣸⣇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⢿⡄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠸⣏⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠶⠤⢤⣤⣠⡟⠀⠀⠀⢹⣦⣤⣤⡤⠤⠿⢦⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢈⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠛⣻⠖⠒⠶⠃⠀⠀⠀⠀⠻⠒⠚⢿⠛⢻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢧⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠈⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠤⠴⠉⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀⠀⠀⠀⢀⣀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡉⠉⠉⢀⠈⢂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⡅⠀⣤⠀⠀⢠⠀⢸⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⡄⠀⠀⠀⠠⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠐⢶⡶⠂⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣨⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠂⢄⡠⠔⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠋⠛⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⢇⠀⠀⣀⠔⠉⠐⠂⠤⣄⠀⠀⠀⠀⠈⢫⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⠑⢄⠀⠀⠀⠀⠑⠐⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⢢⠀⠀⢀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠘⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⡘⢄⡠⠄⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⣀⠤⠒⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⡸⠀⠀⢠
⠀⠀⠀⠀⣀⠀⠀⠀⢀⡠⠔⠉⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⢆⠉⠇⠀⠀⢸
⠀⢀⢀⡀⠽⠉⠐⡖⢁⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⡄
⣀⣭⢴⣧⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠑⠠⠒⠁
⠠⠖⢛⡽⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢠⠞⠑⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢀⣀⣀⣀⣀⡀⡀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⠉⠉⠈⠀⠘⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⠆⠀⠄⠀⠀⠄⠀⠿⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠘⠛⠋⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠑⠒⠒⢋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡌⠉⠉⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠒⠂⠉⠣⠤⠤⠒⠁⠀⠈⠐⡲⢤⡀⠀⠀⠀⠘⢄⣀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠑⣀⠀⠀⠀⡌⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⢆⠀⢀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠚⠁⢣⡀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⢦⡘⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⣀⡄⠂⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡀⠀⠀⠀⢨⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⣀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠢⣤⠐⠞⠀⠀⢀
⠀⠀⠀⠘⣷⠠⣄⠤⠚⣉⠠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡇⠀⠀⣠
⢀⣺⣿⣧⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠳⣀⠰⠋
⢋⡽⢿⣿⠦⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⡆⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣇⢈⣅⠀⢀⣿⣛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠶⣿⡿⠀⠀⠀⢸⡆⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡴⣦⠴⠶⠶⠶⠶⠾⠀⡏⠁⠀⢈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢂⡀⠺⠅
⣾⣷⣾⣶⣾⣷⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣾⣿⣷⣾⣿⣿⣶⣿⣾⣷⣶
⣿⣿⣿⡇⠀⠋⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⠞⠂⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡋⠁⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⠃⣩⠉⠉⡥⠢⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣎⠀⠈⠀⠣⠁⠠⠆⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠰⡄⠀⠐⠤⠀⠠⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠹⣦⣤⣤⠴⠁⢻⡄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢐⡇⠀⠀⠀⡇⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡰⡹⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠈⢳⡀⠀⠀⠀⢐⠆⠋⠉⠉⠒⣄⠀⠀⠀⠀⠀⢀⠆⠶⠁⠃⢛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠐⠀⣉⠐⠒⢺⣧⠈⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢈⠀⠡⡀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⠻⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡘⠀⠀⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣀⠤⡞⠀⠀⡔⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⠀⠀⠀⠰⢿⠂⢠⠀⠀⠀⡶⠊⠀⠀⠘⡀⠜⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠇⢠⡄⠀⠀⣿⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠀⠀⠀⢠⠀⠀⠀⠀⡏⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠸⠀⢀⠃⢸⡄⠀⠠⠼⡇⠀⠀⠑⢄⠀⢡⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣠⠔⠁⠀⠀⡇⠠⠀⠀⠐⠀⠀⠀⠀⠙⠶⢷⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢸⠁⠀⠀⠀⠀⣷⢀⣀⠀⢠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢹⠀⠸⠀⠘⡀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠖⠒⠒⠲⠞⠀⠀⠀⠀⠓⠒⠒⠒⠶⣶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠸⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠥⣄⣀⠉⠉⠓⠒⠲⠤⠤⢬⣉⣙⠛⠻⠭⢥⣒⣒⠒⠤⠤⡀
⠀⠀⠀⠀⠀⠀⢠⠓⠢⢄⡨⠟⠓⠒⠀⠉⠉⠀⠒⠒⠚⠛⠛⠶⠶⢤⣉⣉⠛⠒⠾⢆
⠀⠀⠀⠀⠀⠀⢸⠑⠒⢾⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⢫⣉⣒⠺⡄
⠀⠀⠀⠀⠀⠀⣬⡉⠒⡇⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⢾⣿⡗⠀⠀⣇⠀⠀⠀⢧⠬⢍⡇
⠀⠀⠀⠀⠀⠀⣇⣈⠉⡇⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣿⠀⠀⠀⢸⠒⠦⢇
⠀⠀⠀⠀⠀⠀⡧⣌⣙⠇⠀⠀⠀⣿⣿⡀⣀⣤⡀⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⠀⡭⣉⡃
⠀⠀⠀⠀⠀⠀⡧⢤⣨⡇⠀⠀⠀⢹⣿⡿⠿⣿⡇⠀⣿⣿⠀⠀⠀⡟⠀⠀⠀⠀⡦⠤⡇
⠀⠀⠀⠀⠀⠀⡷⠦⠤⡇⠀⠀⠀⢸⣿⠁⠀⢸⡇⠀⣿⡏⠀⠀⠀⣀⠀⠀⠀⢠⣍⣑⢇⡀
⠀⠀⠀⠀⠀⠀⢻⠒⠲⢶⡀⠀⠀⠈⣿⠀⠀⠀⠇⠀⠿⠁⠀⠀⠈⠋⠀⠀⠀⡸⢤⣀⣉⡉⠲⣄
⠀⠀⠀⠀⠀⠀⠸⡍⠓⠲⠵⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⠦⠤⣄⣉⣉⣙⢣
⠀⠀⠀⠀⠀⠀⠀⠙⢍⣑⠒⠦⠤⣍⣙⡛⠳⠶⣖⣒⡒⠒⠒⠒⠶⢬⣉⣉⠉⠓⠒⠲⠦⠤⣄⣉⡉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠉⠽⠷⠶⢤⣭⣉⣒⣒⢤⣤⣀⣈⣉⡹⠃⠙⢦⠤⢀⣀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⣄⡉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⢤⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠒⢆⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⣦⠀⠀⠁⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠔⠒⠈⠉⠀⠒⠠⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠻⠿⠟⠛⠛⣧⠀⠀⠀⠀⢠⢀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠙⡄
⠀⠀⠀⠀⠀⣾⣿⣿⡟⠠⠒⠂⠀⠀⠀⢁⠀⠀⠀⡀⠢⡌⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠒⠲⠤⠀⠀⠸
⠀⠀⠀⠀⠀⢿⡿⠻⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠐⡀⢰⠤⡀⢀⠀⠀⠠⠉⠀⠀⠀⠈⠁⠀⠁⢀⠘⡀
⠀⠀⠀⠀⠀⠈⡀⠉⠀⠠⠤⠀⠀⠀⠴⠀⠈⠀⢀⠈⣠⠃⠀⢱⠈⠆⠀⠀⠀⢀⠀⠀⠀⠒⠀⠀⠠⠂⠘⡄
⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⠈⠁⠀⠌⠀⠀⠁⡰⠁⠀⠀⠈⠆⠘⡄⠀⠰⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⡀⠀⠀⣀⡠⠀⢀⠴⠁⠀⠀⠀⠀⠘⡄⠘⢦⡀⠈⠉⢀⠀⠀⠀⡤⠀⠀⠀⠇
⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠁⠀⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠉⠉⠀⠀⠀⠀⠈⠀⠀⢀⡌
⠀⠀⠀⢀⠃⠀⠀⠀⠀⠡⠄⠀⢀⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠀⡀⠀⠆
⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠱⠀⠸
⠀⠀⠀⡏⠀⠲⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢀⠀⢰⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⠀⠂
⠀⠀⠈⠄⠀⠂⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡇⠘
⠀⠀⠀⠘⡄⠀⡀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠁⠀⠀⠀⢨⠁⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⠠⠀⠸⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡰⠀⡀⡗⠀⡄⠀⠀⠀⠀⢆⠠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠓⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⡀⠀⠀⠢⡶⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⡠⢧⣀
⠀⠀⠀⠄⠀⠀⠜⠃⠏⠠⡀⡠⠀⠀⠀⠀⠀⠐⠉⠁⠉⠻⣍⣀⡀⡀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠱⡀⢠⠀⠂⠸⠀⠈⢀⡀⠀⢀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡘⢲⠒⡀
⠀⠀⠀⠀⠀⠀⢀⠺⡔⠀⡄⠀⠀⠀⠹⠄⠐⠤⡄⠈⠃⠠⠀⠀⠀⠀⠀⠀⠈⠉⠑⠊⠐
⠀⠀⠀⠀⠀⠀⠌⠁⠁⠀⡑⠆⢈⢑⡀⢀⡍⢀⠁⢀⡈⠉⢲⠀⠂
⠀⠀⠀⠀⠀⠀⢑⠁⣰⠀⡁⠀⠠⠀⠁⠀⠒⠻⠔⠰⠁⢀⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⡜⠲⠀⠀⠀⠀⠘⠂⠀⠐⠀⠘⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠮⠀⠀⣀⡀⠄⡠⠀⢀⠐⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠐⠢⠅⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⡇⡐⣿⠁⢸⠀⣇⢰⢁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⣷⠐⠋⢩⢿⠋⢸⡀⣿⠘⠞
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣴⢆⡇⠀⠀⠀⠀⠀⠈⣠⡛⠁⠀⣀⠀⠀⠀⢀⣀⠀⠀⣠⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠻⣼⣀⡀⢀⣶⡆⢀⣄⢫⣄⠀⢀⣾⠀⣾⣷⢾⣿⢀⣾⣿⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠟⢁⣿⡏⣿⣧⠏⣿⡏⣾⣇⣾⣿⣸⠻⠏⢸⣿⡾⣿⠞⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⠁⣿⡏⣼⡿⠀⠙⠛⠈⠻⠋⠀⠀⠸⡿⠁⢀⡴⣾⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣾⠏⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⡀⠀⣼⣿⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠉⣇⢠⣿⣿⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡟⢸⣿⣧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⠃⠀⡀⠀⠀⠀⣠⣴⣦⣄⠀⣾⣿⡇⢀⡇⢸⣿⣷⠀⡎⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠇⢀⠞⣷⠀⠀⣼⣿⡏⠀⢸⠇⢿⣿⡇⡸⠁⢸⣿⣿⠀⠀⠀⠀⣄⢾⣏⣹⣧⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣼⠀⣿⡀⠀⣿⣿⡃⣠⠏⠀⢺⣿⣷⠁⠀⠘⣿⣿⡌⠀⠀⢸⣿⠀⠉⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣇⡇⠀⣿⡇⠀⢻⣿⣏⠀⠀⠀⢘⣿⣿⡄⠀⠀⢿⣿⣇⠀⠀⣼⣿⡄⠀⢀⣿⠃
⠀⠀⠀⠀⠠⠴⠚⠁⠀⢻⣿⣿⡇⠀⣿⣇⢀⡞⠹⢿⣶⣦⠶⠋⠹⣿⣷⣤⣤⠞⠻⣿⣷⠞⠁⠻⣿⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠟⠀⠘⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡴⠶⠶⠶⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠉⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣖⣲⡒⠒⠒⢒⡒⠒⠒⠒⢲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣖⣖⠒⠒⠒⢒⡒⠒⠒⠒⣲
⠀⢸⡃⠈⣦⡠⠏⠈⠓⢄⠄⢸⠀⢀⡤⠤⠤⠤⠤⠤⠤⡀⠀⠀⢀⠤⠤⠤⠤⠤⠤⢤⡀⠀⣟⠀⢹⣄⡼⠅⠉⠢⡠⠀⡇
⠀⢸⠫⣄⡍⠈⣢⠀⡨⠓⡆⢸⠀⡼⠓⠛⠛⠛⠛⠛⠛⢣⠀⢀⡜⠛⠛⠛⠛⠛⠛⠛⢧⠀⡟⢥⣈⠉⠑⡄⢀⠜⠣⠀⡇
⠀⠸⡇⠃⠉⠍⠸⢏⠐⠀⡘⡏⠀⡇⢀⠖⠡⢶⣌⠑⡄⢸⡇⢸⡇⠀⡞⠢⡀⠀⠀⠀⢸⠀⢹⠸⠉⠩⠁⡾⡉⠂⢀⢱⠇
⠀⠀⡏⢑⠖⠠⣇⠎⠉⠚⢡⡇⠀⡇⠃⠀⠰⣾⡟⠀⠈⣼⡇⢸⡇⠀⡄⠀⠿⠦⡀⠀⢸⠀⢸⠈⡲⠂⢴⡠⠁⠁⠛⣽
⠀⠀⡿⡀⠌⠀⢨⣀⡀⢀⢺⠇⠀⡿⠠⠶⠲⠾⠶⠖⠄⢸⡃⠸⡇⠀⠈⠲⠥⠦⠚⠀⢸⠀⠸⣏⠀⠁⠀⣧⣀⠀⡰⢹
⠀⠀⢻⠈⠢⡞⠋⠁⡸⡁⢸⠀⠀⡇⠔⠲⠶⠒⠶⠶⢠⢻⡆⢸⡇⣖⣲⢶⣰⠀⡶⡆⢸⠀⠀⡇⠑⢴⠚⠁⢀⢫⠁⡟
⠀⠀⢸⠀⠀⠸⡀⢀⠠⠇⢸⠀⠀⡇⠈⠢⣀⡛⣀⠔⠁⢸⡇⢸⡇⠀⠀⠐⠒⠒⠀⠀⢸⠀⠀⡇⠁⠀⢧⠀⡀⠤⠂⡇
⠀⠀⢸⡃⠉⠀⠉⠉⠀⠁⡟⠀⠀⢣⠤⠤⠤⠤⠤⠤⠤⡜⠁⠈⢣⠤⠤⠤⠤⠤⠤⢤⡞⠀⠀⢻⠈⠀⠈⠉⠁⠈⢘⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠅⠍⠩⠉⠙⠈⢽⢿⡒⠒⠶⢤⡀⢀⣀⣀⣀⣀⣀⣤⠤⠴⠚⠛⠛⡒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⡇⠀⠀⠀⡟⠉⠁⠩⢉⠟⠡⠌⠀⠀⡀⣤⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠂⠀⠀⠀⠀⠀⠂⠄⣇⠀⠀⡄⢃⠀⠀⢴⡧⠀⠀⠀⢼⠀⠀⠀⡁⣩⢰⠞⠀⠀⠀⠀⠀⡙⢦
⠀⠀⠀⠒⠒⠛⠛⠙⠉⠊⠁⠀⠀⠀⠀⠀⠀⠀⠰⢰⡟⢆⠀⠁⢨⠖⠀⠀⣣⣄⣀⠀⢘⡀⢀⠐⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢈⡳⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠀⠁⠒⠈⠀⣠⠊⠀⠀⠀⠀⢸⡇⠀⠀⢀⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠚⣄⠀⠀⠀⠀⠈⠣⡄⠴⣿⢷⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠒⠀⠀⠀⠠⢄⣴⠟⠉⠁⠐⠀⠀⠀⠀⣸⢿⢮⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠇⣿⢻⡅
⠀⠀⠀⢀⣀⣠⣬⡥⠽⠶⣄⣀⠀⠀⠀⠀⠄⠀⣀⣀⠀⠣⣍⣀⣠⡤⠋⣹⠆⠀⠀⠀⠀⢀⣺⠁⠀⠓
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢿⡂⠠⠄⠀⣀⣤⡞⠀⡀⠠⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠦⠥⠤⢤⣤⣥⣤⣄⣤⣤⠤⠶⠒⠛⠓⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⡜⠀⠀⠀⣿⠀⠀⢰⡇⠀⢠⡖⠒⠶⠆⠀⣾⠀⠀⠀⢰⠀⠀⠀⢀⡴⠒⢦⡀⠀⠀⠀⠀⢷⡀
⠀⠀⣸⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢸⣇⣀⣀⡀⠀⢹⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⠀⢻⡀⠀⠀⠀⠘⣇
⠀⠀⡇⠀⠀⠀⠀⣿⠒⠒⢺⡇⠀⢰⡏⠉⠉⠁⠀⢸⠀⠀⠀⢸⡀⠀⠀⢸⡀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠘⣇⠀⠀⣸⠇⠀⠀⠀⢸⢿
⠀⠀⡇⠀⠀⠀⠀⠛⠀⠀⠘⠃⠀⠀⠓⠒⠚⠀⠀⠘⠒⠒⠂⠘⠓⠒⠒⠂⠈⠓⠚⠋⠀⠀⠀⠀⡜⡞
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣰⠃
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⡰⠃
⠀⠀⠀⠀⠀⠙⢶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⢊⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠺⡄⠀⠀⢠⠚⣖⣒⣒⣒⣒⣒⣒⣒⣘⣙⣍⡭⠴⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡔⢣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠶⠾⠂⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡋⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠃⣩⠈⠉⡥⠒⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣆⠀⠈⠀⠁⠁⠀⡆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠰⡄⠀⠂⠄⠂⢀⡁⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠱⣦⣤⣤⠴⠁⢹⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢒⡃⠀⠀⠀⡖⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡐⠹⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠠⠀⠀⠀⠀⢁⠆⠅⠉⠑⠒⣄⠀⠀⠀⠀⠀⢀⠋⡶⠁⠁⠛⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢈⠐⠒⢪⣧⠰⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⠀⠡⡀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⠛⠁⠀⠈⠁⡄⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡈⠀⠀⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠤⡞⠀⠀⡐⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠰⣿⠂⢠⠀⠀⠀⡶⠊⠁⠀⠸⡄⠜⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡆⠀⠀⠀⠀⢸⠀⠀⠀⢁⠀⠀⠀⢀⠏⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇⠀⠀⠃⢠⡄⠀⠀⣿⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢸⠀⠁⠀⠀⡏⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢸⠀⢀⠂⢨⡀⠀⠠⠼⡇⠀⠀⠑⢄⠀⢁⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡤⠁⠀⠈⡇⠀⠀⠀⢠⠀⠀⠀⠀⠑⠾⡵⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠉⠀⠀⠀⠀⣧⢐⡀⠀⠸⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠃⠀⠀⠀⠀⢸⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠴⠖⠒⠶⠾⠀⠘⠀⠀⠓⠒⠒⠲⠶⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠘⣿⠀⠀⢀⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠈⠛⢷⠀⠀⠉⠀⠀⠸⠋⠀⠀⣀⣄⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⡾⠛⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⣴⣿⣿⣿⣿⡟⠀⣰⣿⣦⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠏⠀⠀⢀⣴⣾⣿⣿⣿⣿⠟⠀⣰⣿⣿⣿⣿⣦⣀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⣉⣀⣤⣴⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣦⡀⠈⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣿⣿⣿⣿⣧
⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣇
⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠛⠛⠛⠛⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣯⡿⠿⠿⢟⣛⠛⠛⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⡛⢋⣠⣾⣻⣶⣶⣶⣿⣿⣿⣿⣶⣿⣡⣴⣛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣉⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⢃⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢦⣬⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠧⣘⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⡿⠃⣸⡿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣘⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⢉⣼⣿⣿⣿⣿⡟⠀⡿⣿⣿⠿⢿⡇⢸⣿⠁⢸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⡸⢿⣿⣿⣿⣿⣿⡇⢰⡇⢸⡏⢠⣿⡇⢸⣿⠀⢿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣽⣿⣿⣿
⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣧⣼⡇⠸⣧⣀⣿⣧⡈⢻⣆⠘⣿⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠛⣿⣿⣿⣿
⣿⣿⣿⣿⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣧⣿⢧⣼⣻⣿⣿
⣿⣿⣿⣿⣧⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢁⣴⣿⣿⣿⣿⣿⡟⠁⣶⣾⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿
⣿⣿⣿⡟⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣤⡿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⣸⡟⠉⣽⡟⢻⣿⠀⣸⣿⣿⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣦⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⡇⢸⣿⠁⢸⣿⠀⢿⣿⣯⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣇⣈⣹⣆⠘⣿⡀⠸⣿⣿⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣌⠻⡾⣿⣿⣿⣿⣿⣿⣿⠏⢀⣿⣿⣿⣿⣿⣿⣶⣿⣷⣦⣼⣿⣷⣦⣴⣿⣿⣿⣿⣿⡟⣷⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⠛⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡛⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣻⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣹⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢾⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣭⣤⣽⠿⣿⣽⣿⣿⣿⣿⣿⠿⠛⣿⣿⣶⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣯⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢀⣤⣀⠐⠂⠀⠀⣤⣄⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠴⠶⠄⠤⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⢀⡼⠃⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⣀⠀⢸⡇⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⡆⢰⡟⠀⢹⡇⠀⣿⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⡇⠘⠻⠀⠸⢷⠄⠻⣧⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆
⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⣾⠉⠀⠀⠀⠀⠀⢠⣾⠋⠁⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⠿
⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⣄
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢀⣶⠆⢠⣄⠀⣿⡇⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠘⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣼⡇⠀⣼⣿⠈⣿⡄⠀⠘⣿⡀
⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠹⣷⠆⢹⣿⠀⢿⣇⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠉⠶⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⠃⠀⠈⠛⠂⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢠⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢆⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠒⠀⠠⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠘⠋⠀⠈⠛⠣⠄⠉⠉

⠀⠀⠀⡀⠔⠈⠻⣷⣦⣄
⠀⢀⠎⠀⠀⠀⠀⠀⠙⠳⣝⡦⡀
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡢⡀
⡆⠀⣀⣠⡤⡆⢔⠀⠀⠒⡢⠀⠈⢻⣝⣄
⡷⢄⣓⠈⡪⡰⠅⠄⠠⡊⠊⠀⢨⢆⠹⣎⢆
⢱⠀⠀⢉⠘⠢⣕⡡⡠⠂⠀⡑⡣⡪⡂⠹⣏⢆
⠀⡇⠀⢘⣰⠚⠒⠾⣶⣌⠚⠪⡪⢊⠌⠄⢻⣟⢆
⠀⠸⠀⡒⢹⠀⠀⠀⠈⢫⣳⡈⢐⠅⠑⢑⡄⢿⣜⢆
⠀⠀⡆⠙⢺⠀⠀⠀⠀⠀⠹⡿⡄⢡⡅⡠⠟⠌⣷⣙⣄
⠀⠀⢁⢠⢸⠀⠀⠀⠀⠀⠀⠙⡿⡄⠺⢶⡣⡢⡸⣧⣎⠢⡀
⠀⠀⢸⠠⢼⠀⠀⠀⠀⠀⠀⠀⢹⣽⡀⠀⠈⠘⠶⠙⣧⡇⣌⠲⠤⣀
⠀⠀⢸⢨⢾⠀⠀⠀⠀⠀⠀⠀⠈⢏⣧⢑⠄⢄⡠⠪⠈⠙⠲⢯⣵⣀⡭⣉⣒⡦⢤⣀⡀
⠀⠀⢀⢘⣻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⡆⣀⣉⢄⢔⢕⠁⣲⢒⣄⢌⢉⣉⠛⠻⠦⠦⠞⠁⠐⠢⢄⡀
⠀⠀⠸⢈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢷⡨⣐⢕⢕⣡⡀⠁⢈⠁⢀⣀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⢠⠠⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⢣⡩⣑⡝⢗⢕⢅⣀⣵⠕⡕⠀⠄⠀⡰⡀⡀⡁⡑⡡⡐⡐⡐⣤⣡
⠀⠀⢘⠰⣾⠀⠀⠀⣀⡀⠀⣀⠀⠀⠄⢹⣗⢙⠪⢔⣕⡕⠽⠗⡡⠞⢕⠄⢴⠀⠊⣎⣊⣈⣊⣂⡐⢎⣴⢛⣿⠀⢠⣠⣤⠠⡠⣀
⠀⠈⠙⠛⠏⠀⠭⠉⠅⠤⡈⠀⠄⡠⢀⠥⣿⢷⣕⣤⣤⢌⢉⢝⢍⣄⣈⣝⣝⣍⣴⣔⣔⣔⣔⣔⣔⣝⣭⣿⣿⠶⡣⠢⠵⠜⠚⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡟⣽⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡏⣿⣿⣿⡇⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣿⣿⣿⢿⣿⣿⣿⣇⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣠⣤⣤⣿⠁⠈⢻⡿⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⠀⠘⣿⠀⠀⢸⡇⠀⠀⢻⡶⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⠀⠀⢹⡇⠀⠘⣇⠀⠀⢸⠁⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣀⣤⣶⣶⣶⡄
⠀⠀⠀⠀⣿⡄⠀⠈⣷⠀⠀⢿⠀⠀⢸⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⣇⠀⠀⢻⡀⠀⢸⠀⠀⢸⡇⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣭⣭⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇⠀⠘⠀⠀⠀⡇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣭⣭⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⣀⣀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠘⣯⡈⠉⠛⢦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠈⢷⡀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣃
⠀⠀⠈⢷⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣫⣾⣿⣆
⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠋
⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠁
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃

⠀⠀⠀⠀⠀⣀⡠⠤⠶⠖⠒⠲⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⢄⣀⣀
⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄
⠀⢠⠏⢀⣀⠀⢀⠀⣀⣀⣀⢠⣄⠀⣀⠤⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠒⠂⡤⢆⠴⠌⠏⠀⢀⣟⠐⣧⠀⠈⢳
⠀⡎⠀⢾⠀⡄⢇⡽⣀⠿⡼⢫⠇⠘⢸⡁⢀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠃⠀⠀⠀⣀⠀⡄⢀⠀⠀⠀⠀⠀⢸
⠀⢡⡀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠜⠉⠃⠓⠘⠒⠐⠂⠀⠀⡜
⠀⠀⠑⡄⢀⠄⠀⠀⠀⠀⠀⠠⠤⠄⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠢⠤⠤⠤⠤⠄⠠⠀⠤⡄⠀⠎
⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⢶⡶⠖⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣄⠀⢀⠇⡰
⠀⠀⠀⠀⠈⠃⠀⠰⠋⢀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠛⠛⢻⣿⡇⠉
⠀⠀⠀⠀⠀⠀⠀⢲⡸⢿⠀⠀⠠⠂⢀⠃⠀⠀⠀⠀⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠤⠀⠀⢿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣎⠁⠀⠀⠀⠬⠂⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢸⠀⠀⠀⠀⣠⣞⡎⡙⠉⠀⠃⠀⠀⡴⠃
⠀⠀⠀⠀⠀⢀⣀⠘⡟⠉⢑⣄⣉⡛⢁⠃⠀⠀⠀⠀⠈⠀⠠⡀⠀⡀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡅⠀⢸⠀⠀⠀⠀⣫⠚⣏⢦⠀⠤⠂⢀⣼⠃⡶⠄⡀
⠀⠀⢀⣤⡶⠋⢀⠤⠁⡠⠾⣿⣿⠏⠑⠀⠀⠀⠀⠀⢀⡆⠀⠀⠐⠃⠀⠰⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢹⡀⣇⠆⣢⢤⠖⡿⢇⡸⠁⠀⠀⠙⣽
⠀⣰⣿⠋⠀⡔⠁⠀⢀⡗⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡎⠀⠀⠀⠀⠀⡼⠈⠍⠀⠀⠘⡟⠀⠀⠀⠀⠀⠀⠀⢹
⠀⣿⡧⠀⠸⢤⢀⢀⠞⠀⠀⠀⠀⠀⢂⡴⠏⠀⢠⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⣸⢃⡼⢳⠇⠀⢸⠇⠀⠀⠀⠀⡄⠀⠀⢸
⠀⠘⣧⡀⢀⡶⣾⠋⠀⠀⠀⠀⢀⡴⣃⣐⣁⣘⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢀⡀⡟⠁⠀⠸⡇⠀⠸⡆⠀⠀⢀⡰⠇⠀⠀⢨⡆
⣀⣀⣈⣉⣉⣁⣉⣁⢀⣀⠀⠀⢀⣀⣈⡀⣈⣁⣁⣀⣀⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣰⣧⠒⠚⠛⣟⢄⠀⠀⠀⠀⠀⡸
⠀⣇⡅⠀⡇⠀⠀⠀⢢⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠎⣁⡰⠟⠚⠲⡴⢊⠙⢿⣠⡤⠖⢲⠋⡇
⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⡾⠛⠻⣤⡖⠄⠀⠈⢆⠀⠀⠀⠱⡀⢸⠇⠃
⠀⣿⠃⢴⣿⠀⠀⠀⢰⣿⣿⣷⣦⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣇⣠⠤⠞⠂⠀⠀⠀⡧⠞⢸
⠀⣿⠀⠀⡟⠀⠀⠀⢸⣿⡏⠉⠙⢷⠀⠀⠀⠀⠙⢦⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠉⢩⠁⠀⢃⠀⠀⠀⠀⡗⢰⢸
⠀⣿⡇⠀⡇⠀⠀⠀⣸⠿⠷⠤⣄⠈⠳⡀⠀⢀⠔⡉⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⡄⠀⠈⡀⣀⡀⠀⠁⠸⢸
⠀⣿⡇⢀⣟⠉⣙⡖⠟⠀⠀⠀⠻⠃⠀⠈⠲⢃⡂⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠛⠋⠀⠈⣣⠀⠘⠟⠻⠐⡆⠁⠀⠼
⠀⠉⠁⠈⠐⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠣⠀⠴⠃⠁⠀⠐⠉⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠁⣶⡈⣿⣿⣻⣷⢾⢿⡿⠻⣫⣿⠋⣩⠻⣿⡿⢋⣍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣇⢸⣿⢃⣿⣷⣾⣿⣿⣿⣫⣾⣿⡏⢰⣿⡇⣿⡇⣼⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠸⡏⣼⣿⣿⣿⣿⣿⣿⣵⣿⣿⡇⢸⣿⠀⣿⠀⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⠿⢿⣿⣿⣿⣿⠿⢿⣿⣿⡇⢸⠇⣸⣿⠀⣿⠁⣾⣿⣿⡿⢿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣷
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⣤⠀⢀⣴⣾⣿⣿⣿⠁⣴⣿⡿⣿⡇⠘⢠⣿⣿⠀⠃⣸⣿⣿⣿⣷⣼⣷⠉⣛⣯⣴⣿⣿⣿⣿⣿
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⢸⣿⡏⢸⣿⠟⢀⣿⠇⢠⣿⣿⡿⠀⢰⣿⣿⡿⢛⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⢸⣿⡇⢸⣥⣴⣾⠏⠀⢸⣿⣿⠇⠀⣾⣿⣿⠁⢸⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣟⢸⣿⣿⡇⢸⣿⡇⢈⠻⠟⣡⣴⣧⡸⡿⢋⣴⣆⠻⡿⣁⣶⡘⢿⡿⢋⣼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣍⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⡿⣿⣿⡿⠿⠿⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⢉⢠
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠊⢹⣦⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⢁⣄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣏⣥⣽⠄⢤⡄⣀⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠿⠛⠛⠉⠁⣀⣤⣤⣦⣤⡀⢈⠻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣡⣶⡟⢀⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣦⣤⣤⣤⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⣟⡥
⠀⠀⠀⠀⢈⠓⠶⠶⠾⠿⠿⠭⠭⠭⣭⣭⣭⣉⣙⣛⣛⣛⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣛⣛⣻⣿⣿⠿⠿⠿⠗⠛⠉⠔⠃
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⣶⣤⣄⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡴⡿⢹⣿⣕⡄⢀⣴⣟⣿⢿⣿⡟⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠿⠿⣝⣧⣿⣷⣿⡿⣿⡿⠭⠿⣿⣽⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠉⠪⣿⢿⠟⠁⠀⠀⠀⠀⠉⠺⣽⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣟⠆⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⡇⠀⠀⠀⡜⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣠⠴⡄⠤⡀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠂⠀⠀⠉⡏⠉⠉⠉⡟⠁⠀⡴⠋⢉⡇⠀⡇⠀⠀⢸⠀⠀⡰⢁⡔⠁⠀⠸⡄⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢰⠗⠚⠉⠀⠀⡇⠀⠀⢸⠀⠀⡗⠉⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠘⣆⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢧⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⠇⠀⠀⠘⠀⠀⠀⠙⠒⠤⠴⠊⠀⠀⣎⣱⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠣⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣦⡀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣴⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⢸⣿⡇⠀⢀⣴⡿⠋⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣿⡇⠀⠸⣿⠇⠀⠘⠛⠁⣠⣶⣾⡿⠛⢻⣷
⠀⠀⠀⠀⠀⠀⣰⣿⠛⣿⣷⣤⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣾⡟⢹⣿⠁⢀⣼⣿⣶⣄
⠀⠀⠀⠀⠀⣾⡿⣿⡄⣿⡏⠙⣿⡆⠀⠀⠀⠀⠀⠀⣠⣴⣿⠁⢸⣿⠀⣼⡟⠀⠘⣿⡀
⠀⠀⠀⠀⠀⣿⡇⢿⣧⣿⣧⠀⢸⣿⣦⣄⠀⠀⠀⣼⡿⢹⣿⠀⢸⣿⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⣇⠸⣿⡜⣿⡄⢸⣿⠉⢿⣧⠀⢠⣿⠇⢸⣿⠀⣸⣿⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⢸⣿⠀⢿⣇⢹⣷⠘⣿⡆⠈⣿⡇⢸⣿⠀⣼⡟⠀⣿⡇⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠈⣿⡇⢸⣿⠈⣿⡇⢻⣷⠀⠸⣿⣼⣿⠀⣿⡇⠀⣿⠇⠀⣿⡇⠀⢸⣿
⠀⠀⣴⣶⣶⣤⣹⣿⠘⣿⡆⢿⡷⠸⣿⡄⠀⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣤⣾⠿⠿⢿⣦
⠀⠀⢻⣧⡈⠛⢿⣿⡆⠛⠃⠀⠀⠀⠉⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠁⠀⢀⣼⡿
⠀⠀⠀⠻⣷⣄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠏⠀⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠘⣿⣆⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢾⡿⠛⠉⠁⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠑⠎⠡⠔⣋⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢖⠂⢠⡄⠀⠀⡀⠐⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⢠⣿⡿⠀⠺⠄⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢉⠸⠿⢿⠰⠀⠀⠀⠀⠀⠀⡾⠟⠛⠻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠐⢉⠃⠀⠀⠀⠀⠀⠀⣄⠁⣀⠀⠈⠻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠟⡁⠀⠀⠀⠀⠀⢀⠋⠀⡇⢰⠂⢳⠀⠀⠀⠀⠀⠀⠀⡁⠀⠈⠤⠄⢠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡟⠁⠀⠒⠈⢂⠀⠀⠀⠀⡈⠀⢀⠁⢸⠀⠠⠀⠀⠀⠀⠀⡀⠀⢢⡠⠤⠊⠀⠀⠛⠁⢙⠁
⠀⠀⠀⠀⠀⠀⠸⣿⡇⢈⠀⠀⢖⠒⠒⢈⠀⠀⠀⢠⠁⠀⡈⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⠈⠂⠄⠀⠀⠀⡶⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋⠀⠀⠈⢓⠠⠂⢀⡀⠀⡄⠀⢀⠁⠀⠀⡆⠀⡇⠀⠀⠀⠀⠀⣀⡠⠤⠐⡞⠀⠀⡠⡏⠐⠂⢄⣀
⠀⠀⠀⠀⠀⠀⢀⠊⠙⢅⡂⢤⠊⠀⠀⣀⡀⠠⠴⠀⠀⠰⠀⠀⠀⡇⠀⢠⣀⠠⠄⠂⠉⠀⠀⠀⢰⡇⠀⡰⢁⣷⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⢀⠊⠀⠄⠒⠚⠈⠁⠉⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠴⡴⠅⠞⢹⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠄⠀⠸⡀⢃⡀⠌⡠⠊⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⣀⣠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠺⣿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠉⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂
⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⢸⣿⠀⠀⠀⣰⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠹⣿⣆⠀⢸⣿⠀⠀⣼⡿⠃⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠘⠛⠀⠀⠉⠀⠈⠛⠁⢀⣠⣾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠸⣿⣿⣧⠀⣴⣶⣆⢰⣶⣦⠀⣼⣿⣿⠇⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠸⣿⣿⣧⢹⣿⣿⣇⢻⣿⣿⣎⢿⡟⣸⣿⣿⠏⣼⣿⣿⠏⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠹⣿⣿⣆⢻⣿⣿⡆⢻⣿⣿⡌⢰⣿⣿⡟⣸⣿⣿⡏⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⢻⣿⣿⡆⢿⣿⣿⡌⢿⣿⣿⡸⣿⡿⢰⣿⣿⡟⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⢿⣿⣿⡌⢿⣿⣿⣾⣿⣿⣷⡙⢡⣿⣿⡿⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣡⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⡿⠀⢀⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⢁⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⠿⠟⣭⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⣿⣿⣿⣿⡶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣐⡞⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠈
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢆⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠈⠀⠀⢀⣄⢄⠄⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠡⠀⠀⢀⣨⠄⠒⢀⣈⠅⠻⠄⠀⠀⠄⠹⠭⠀⠈⢉⡷⠀⠤⠤⡀⠀⠀⠀⠠⠺⠷⠯⡀⠀⣠⠞
⠀⠀⠀⠀⢀⡠⡴⠁⡨⠄⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠻⠓⠚⠃⠐⠒⠚⠚⠛⠛⠁
⠀⠀⠀⠀⠔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⢿⣿⣿⡿⠉⢻⣿⣿⠟⢻⣿⣿⡟⠛⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣧⠀⢸⣿⣿⠀⢸⣿⣿⡇⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠉⠉⠀⢸⣿⣿⠀⢸⣿⣿⡇⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⠀⢸⣿⣿⣷⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇⣠⣿⣿⣿⣧⣴⣿⣿⣤⣼⣿⣿⣏⢈⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠤⠄⠀⠀⣰⡷⠀⠀⠀⢠⣄⠀⠀⢠⣾⠿⠛⢿⡄⠀⠀⠀⠂⠀⠀⢸⣿⠗⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠸⠏⠀⠀⠈⠀⠃⠐⠃⠁⠀⠀⠀⠑⡀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣴⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⠿⢿⣷⠀⠀⠀⠲⠀⠀⠀⠋⠭⠩⡛⠇
⠀⠀⠀⠋⠉⠉⠀⠀⠀⣾⣽⡆⠀⠀⠀⠒⠚⠒⠀⠀⣾⣇⠂⠀⠈⢸⣿⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⣁⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡛⠻⣿⣷⠀⠀⠀⡆⠀⢠⡾⠿⣿⡆
⠀⠀⠀⠐⠤⠢⠀⠀⢾⣿⠁⠀⠀⢈⣿⡄⠀⠠⠠⠂⠀⠀⠐⠋⠙⠛⢠⣿⣿⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣄⠀⠘⣿⣿⣆⠀⠀⢀⣤⠀⠀⠀⣿⣿⡇⠀⣰⣿⣿⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⣿⣿⣦⡀⠘⣿⣿⣆⠀⢸⣿⣧⠀⢸⣿⣿⠁⢀⣿⣿⡟⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⡀⠘⢿⣿⣷⡄⠹⣿⣿⣆⠘⣿⣿⡆⣾⣿⣿⠀⣼⣿⣿⠁⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠈⢿⣿⣿⣆⢻⣿⣿⣦⣿⣿⣷⡸⣿⡇⣸⣿⣿⡇⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣤⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣯⣀⣠⣴⣾⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣱⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠛⠉⠐⠿⠿⠿⠿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠶⠞⠛⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠿⠿⣶⣄⠀⠀⣀⣀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠿⢷⣶⣤⣀⡀⣀⣀⣀⣤⣤⣤⣼⠟⠁⠀⠀⠀⠈⠻⣷⡿⠟⠛⠉⠉⠉⠹⣷
⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠈⠙⠛⠿⠛⠛⠋⠉⠉⣹⡟⠀⠀⠀⢀⣤⣤⣄⣿⣇⣀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢾⡁⣼⡟⠋⠉⠛⢿⣶⣶⠿⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⣿⣄⡀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠾⠛⢿⣦⡀⠀⣀⣼⡏⣹⡇⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⠉⠉⠉⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣦⣤⡶⠟⠉⢿⣧
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⢀⣀⣀⣼⣿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⣿⡿⠿⠻⠟
⠀⠈⠛⠋⠉⢹⣿⡉⠉⠁⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⢀⣿⣧⣴⡦⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠘⠛⣿⡿⠿⠷⠶⠄
⠀⠀⠀⠀⠛⠛⠛⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠿⠻⢷⣦⣄
⠀⠀⠀⠀⠀⣴⠿⠋⠁⠈⠛⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠟⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠳⣦⣀⣠⣤⠤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠉⠛⠷⠶⠶⠞⢻⡿⠁⠀⣀⣈⣿⣁⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣧⡟⠉⠉⢳⡟⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠞⢧⣀⣀⣾⣻⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣄⣀⣴⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⢿⡓⠂⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠈⠉⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⣷⠂⠀⠀⠙⠁⠀⠀⠀⢰⡒⣦⠀⠀⠀⠈⠁⠀⠀⠀⣹⡟⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢷⣖⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣽⠟⠷⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠈⠛⠷⢶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣤⡴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⡤⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡟⠛⠛⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠳⡄
⠀⠀⣧⢤⣤⣼⠁⠀⠀⠀⠀⠀⠀⡧⠤⠤⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣯
⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣇⣀⣀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⠀⠀⠀⠀⠀⢸⡀⠀⢠⠇
⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠉⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣴⡆⠀⠈⠀⠀⠀⠀⢀⠀⠀⣿⠗⠀⠀⠀⠀⢀⡀⠁⠀⠑⠀⠰⠀⠀⠀⠐⠠
⠀⠀⢀⠀⠀⠊⠀⠀⠈⠀⠀⠀⠀⠈⠿⠃⠀⠀⠁⠀⠈⠁⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠔⠀⠐⠀⠀⠀⠀⠀⣀⠀⠔⠳⠀⠀⠀⠀⠀⠒⠀⠠⠄⠀⠀⠀⠀⠀⠀⠄⣀⠀⡀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠃⠹⠀⠐⠄⠈⠢⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠢⠀⡀⠀⠀⠀⠀⡀⠚⠀⠀⠀⠤⠀⢐⠀⢀⢀⠀⠀⠀⠀⠂⢘⡀⠀⠁⠀⠀⢀⡠⠄⠀⡀⢀⡀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠔⠀⠂⠉⠀⠀⠈⡀⠀⠂⠀⠀⠀⠀⠀⢀⠀⢀⠔⠃⠀⢠⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠘⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠆⠀⠈⠀⠠⣀⠵⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠠⠂⠀⠀⠀⠀⠀⡐⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠐⠋
⠀⠀⠀⠀⠀⠰⠯⠦⣽⠓⠁⢀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢢⣀⠀⠀⠀⢀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠒⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠉⡠⡁⢬⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠈⠀⠀⠠⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⠒⠛⢲⣄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡇⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣠⠖⣄⢰⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣿⣇⣀⠀⠀⠀⠀⣿⠀⣿⢸⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠉⠉⢸⣿⠋⠉⠛⣀⣀⠀⣿⠀⡏⢸⣿⢰⠃⢰⣿⢵⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⣼⣿⠛⡇⣿⡾⠁⠈⣿⡏⠀⢿⣇⠘⠳⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠸⣿⠀⠀⣿⡇⡰⠁⣿⡇⠀⠀⣿⡇⠀⢘⢿⣦⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠊⠙⠿⡤⠞⠙⠷⡤⠊⠈⠛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠒⠀⠀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢻⣥⣄⢠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟

⣀⣠⣄⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣗⣿⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⣴⡾⢛⠋⠉⡉⠉⠛⠷⣤⡀⠀⠀⣠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣘⠇⠃⢠⡿⠃⠀⠈⣁⠀⠀⠀⠀⣀⡈⠻⡄⣰⠟⣡⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣁⡀⠸⠁⠀⠗⠇⠧⠀⠄⠸⠄⠧⠜⠀⠉⠀⠈⠥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣋⣉⠙⠀⢐⣠⣤⣤⣤⣄⣀⠀⢰⣶⠀⠀⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢹⣿⣷⠀⣿⣟⢉⡉⠉⠛⠻⢷⡀⣀⣤⠀⣠⣦⡀⠈⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⠀⠀⣹⢿⣿⠒⣲⣶⢛⣏⣿⡏⢠⣿⣿⡇⠀⠰⠆⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢿⣿⢀⡜⠁⣾⣿⢺⣿⡟⡼⢹⣿⢠⡿⣿⣿⣷⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⡈⠙⠉⢀⣴⣿⣿⠘⠿⠟⠁⠈⠛⠋⠀⠘⢿⣿⣷⣤⡄⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣼⠃⠀⣴⡟⢱⣿⣿⠀⠀⢠⣦⣤⠶⠚⣧⠀⠀⠉⠛⠛⠁⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⡟⠀⣼⣿⡏⠀⢠⡿⠀⠀⣠⠀⠙⠿⣶⣤⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⢿⣶⡿⠟⠀⣰⡟⠁⠀⣴⡟⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣀⣠⡴⠟⠉⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⠢⣀⠀⠀⠀⠀⣠⠴⠒⠒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡠⠞⠋⠉⠉⠛⠳⣄⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠈⢧⠲⠀⠀⠀⠀⠀⠸⠂⢀⡇⠀⢸⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣠⠊⠀⢀⡏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⢧⠀⠀⠀⠀⠀⢸⠁⠀⠀⡼⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡝⠢⣼⡀⠀⠀⠀⣠⣾⣀⣠⠞⠁⡇⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠋⢉⢉⠉⠉⠉⠉⠉⠉⠉⠙⣾⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢾⢠⣤⢸⠀⠇⡴⢦⠀⡏⠀⡴⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠈⠈⠓⠈⠈⠀⠑⠋⠀⡇⣸⠁⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⡔⠋⠙⠲⡄⠀⠀⠀⡇⡇⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢹⠀⠀⠀⣇⢦⣠⢆⡟⠀⠀⠀⣷⠇⠀⠀⠀⠉⣶⢶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢉⣟⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⣎⢸⣀⣀⣀⣀⣴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡇⠘⡶⠒⠋⠸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⢤⢧⢤⣇⣀⣀⣀⡗⠒⠋

⠀⠀⠀⠀⠀⠀⠤⠤⠃⠐⣬⣪⣐⣠⣞⣈⣌⣀⣓⣠⣦⢰⣴⣑⣉⣑⣋⣒⣐⡨⣮⣀⣎⣒⣐⣐⢄⠠⠤
⠀⠀⠀⠀⠒⠒⣶⣶⣇⠀⢯⡿⢧⠿⢿⡿⢯⢿⡽⣯⡇⠸⠿⠏⡿⣯⣿⣿⠯⠀⡿⠯⠿⠽⠿⠹⠉⣲⠖⢲⣶⣶⠆⡰⢐
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠠⡇⠀⠀⢹⠀⣠⠔⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⢱⢈⡇⠀⠀⢸⠀⡇⠀⠀⢸⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡌⡇⠀⠀⢸⢸⠀⠀⠀⡸⡸⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⣷⡇⠀⠀⢸⣼⠀⠀⠀⣷⠇⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹⡇⠀⠀⢸⡇⠀⠀⢰⡟⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠉⠲⡀⠈⡇⠀⠀⢸⡇⠀⠀⢸⠃⠀⠀⢸⠃⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠱⡀⡇⠀⠀⠈⠁⠀⠀⠘⠀⠀⠀⠉⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⡀⠀⠀⠀⣀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⣀⡀⠀⣀⡀⢀⣀⠆⣠⠀⢀⣆⡀⢀⣀⠀⠀⣔⡀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠸⠗⠧⠐⠃⠃⠿⠚⠆⠩⠆⠞⠁⠃⠯⠺⠄⠞⠛⠀⠿⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⢀⢤⠇⢹⠛⣷⠢⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢸⠀⡬⠀⡟⢦⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠃⢸⠀⠟⠀⡇⢸⢸⡄⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠁⠀⠀⠀⠀⠇⢸⡀⣇⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⠀⠄⠀⠀⢸⣇⢻⠀⡇⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠆⢀⡞⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⣠⡟⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠉⢠⣟⠦⠂⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢀⠏⠈⢆⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢰⠀⠀⣿⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⢹⡀⠀⠘⡇⠀⣿⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⣠⠞⠁
⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠄
⠀⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡆⢰⢉⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⣀⡀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣇⡇⢸⡿⢹⣶⢦
⠀⠀⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣿⠁⣾⠃⢸⣹⠸⡆⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠃⢸⡇⢀⡟⠀⣯⠟⡆⣧⠀⠀⠀⠀⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡟⠀⠈⠀⠸⠁⢰⡏⢠⠇⢻⠀⢀⣤⡀
⠀⠀⠉⠙⠛⠛⠛⠀⠀⠀⠀⠀⡏⢸⠁⠀⠀⠀⠀⠀⠘⠀⡞⠀⢸⢀⡞⢰⡇
⠀⢀⣠⠤⠤⠤⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⠾⠀⢸⠀⠀⠀⠐⠒⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠆⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡴⠁⠀⠀⠲⢤⡀⠀⠀⠒⠲⠤⣀
⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠀⡀⠘⡆⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠈⠓⢤
⢀⡤⠚⠉⠀⠀⠀⠀⠀⣠⠞⠁⣰⠃⠀⠀⠀⠀⠀⡴⣎⠀⠀⠀⠀⢳⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⣰⠃⠀⠀⠀⠀⠀⢸⠁⠸⡄⠀⠀⠀⠀⢳⡀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠓⠲⠤⢤⣀⣀⡏⠀⠀⢣⣀⣠⡤⠴⠒⠛⣆⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠸⡅⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⢧
⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿