Pill Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠋⠁⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠁⠀⠀⠀⠀⢈⣭⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣶⠹⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣷⠀⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⡠⣾⣿⣿⣿⣿⠀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡈⠛⢿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⣀⠙⢿⣿⣿⡟⣿⡽⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⡽⣿⣟⢿⣿⣿⡇⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣝⢿⣿⣿⣿⣿⣿⣷⣄⠙⢛⣬⠻⣿⣮⣝⣃⡸⠿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣭⣿⣿⣿⣭⣽⣾⠿⠋⠀⠀⠉⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠀⠈⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⣬⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠴⠋⠉⠀⣰⠿⠿⢿⡿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠔⢁⣤⣶⣶⢌⠻⢷⣊⠈⠙⠧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⢠⢣⠀⡀⢀⡠⢂⣉⣤⣾⠻⣿⣿⣿⣿⣿⣿⣦⡝⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣇⣾⣿⣵⢋⠴⠋⠈⢿⡟⠆⠸⣿⣿⣿⣿⣿⣿⡛⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⡈⣱⠊⠀⣀⠀⢈⡇⠀⠀⢹⣿⣿⣿⣿⣿⡇⠏⢹⡀
⠀⠀⠀⢀⣠⡴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣋⠘⠛⠁⠙⠛⠛⠛⠀⣤⣾⣿⣿⣿⣿⣯⠇⢸⣽⠃
⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⣶⠶⠆⠀⠂⠀⠀⠉⠻⣿⣿⣟⣿⡏⠀⣾⡏
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⢻⣿⣄⣀⣀⡀⢀⣀⠀⠀⠀⠙⣿⣿⣿⡶⠁
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡔⠀⠀⠀⠀⠀⠀⠀⠻⢦⡽⡿⠋⠉⠁⠀⠀⠀⢀⠀⠀⠙⣷⠟⠁
⢈⠻⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠈⡀⡺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠻⣦⣬⡉⠛⠛⠛⠛⠛⠛⠛⢉⠉⡤⠀⣾⠀⠈⠀⠀⠀⠀⠀⠀⠸⣤⢀⠀⡀⠀⠀⠀⠀⢶⠀⠀⠀⠈⣧⣄⡠⠒⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⣷⠄
⠀⠀⠈⠙⠲⠼⠄⠀⢀⣃⠈⠈⠄⠐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠁⠀⠀⠀⠀⣸⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢄⣠⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣄⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠦⣤⣤⡄⠀⠀⡀⠀⠀⠀⠙⢦⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠏⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⠀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠪⢒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠐⠒⠶⣶⣄⡀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠉⠻⢷⡂⠤⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢼⡇
⢀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⣦⡀⠀⠀⠀⠀⢀⡠⠛⠲⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡈
⡟⠁⠀⠀⠘⡄⠀⠠⠄⠀⠀⠀⠀⣻⠀⠈⠳⡀⠀⢠⠔⠁⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠁
⢹⡄⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢳⣤⣶⣷⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⢹⡄⢰⣄⢤⣼⡄⠀⠀⠀⠀⠀⣸⣽⡄⠀⣀⢀⠆⡶⣄⡀⢐⡤⠀⣀⣀⣨⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠃⠀⠀⠀⠀⠀⣰⠄
⠀⠀⢻⣿⣷⡈⢿⣿⡆⠀⠀⠀⣠⡿⠻⠃⠚⠉⠉⠈⠐⠋⠻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⢋⣡⣤⣶⠄⠀⢀⣠⡴⠞⠋
⠀⠀⠀⢿⣿⣷⡈⢻⣿⡄⠈⠈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠣⠛⡄⠀⠀⠀⠀⠀⠘⣧⣴⣾⣿⣿⣿⡿⠷⠛⠉
⠀⠀⠀⠈⢿⣿⣷⣼⠛⡇⢀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⢸⡉⠀⠀⠀⠠⡙⣶⣤⡀⠀⠀⠀⣀⣀⡀⣠⡴⠔⠋⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⢢⣼⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣠⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡱⠂⠈⠛⢿⣿⣤⣌⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢆⠀⠙⠻⣿⣧⣄⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⢀⢂⢀
⠀⠀⠀⠀⢺⢆⡀⠀⠀⠀⠀⣀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠢⣍⣿⣷⣏⣍⣇⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣒⠒⠒⠒⠒⠒⠒⠲⠶⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠚⠧⣬⣉⣉⡉⠙⠛⠛⠛⠛⣉⣉⣉⡽⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡿⢶⡶⢦⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⡶⢾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡧⢸⡇⢸⠀⣿⠀⡇⢸⠁⣿⠀⡇⢸⡇⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠾⢷⣼⣤⣿⣤⣧⣼⣥⣿⣤⣷⡾⠷⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢾⣷⣶⣶⣶⣶⣶⣶⣾⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣈⣉⠉⠉⠉⠉⣉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢉⣛⠛⠛⠛⠛⠛⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠀⠀⠀⠀⠀⣠⡾⡛⢳⡄
⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣤⣀⣀⠀⠀⠀⣿⠀⠉⠛⠛⠻⠿⠿⠿⠿⠟⠛⠛⠉⠀⣿⡀⠀⠀⢠⡾⠻⢌⢁⣴⣿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⢈⡇⠯⠝⣧⠀⠀⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⡆⠀⣿⡀⠀⣨⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣶⣶⡾⠋⠀⠀⠙⠻⠿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠿⠛⠁⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠫⠭⢻⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣾⣶⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⣠⠴⠖⠒⠂⣠⣄⠀⠀⠀⠀⢀⡤⠶⠒⠒⠲⢤⡀⠀⠀⠀⢀⣠⠤⢤⡤⡤⢄⡀⠀⠀⠀⠀⣠⠴⠒⢒⡲⠦⣄⠀⠀⠀⠀⠀⢀⠤⠆⣶⠦⣄
⠀⠀⢰⣁⡤⠴⠚⠉⠁⢀⡇⠀⠀⢠⡗⠒⠒⠒⠒⠒⢒⣿⠀⠀⠀⣿⡀⠀⠘⡐⠀⠀⢹⡆⠀⠀⠀⡷⣦⣝⣃⣀⣠⡴⡇⠀⠀⠀⠠⣟⠓⢲⡟⠒⣨⡇
⠀⠀⠘⢝⡓⠲⠶⠖⢚⡻⠁⠀⠀⠘⢏⡓⠒⠒⠒⠚⣉⠜⠀⠀⠀⠳⢌⣙⣛⣓⣒⡨⠝⠀⠀⠀⠀⠳⣄⣀⣀⣀⠤⠔⠃⠀⠀⠀⠀⠳⠅⠛⠻⠿⠋
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣀⣀⡀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⢀⢜⢧⠀⠀⠀⠀⠀⠀⡠⢆⠀⠲⡄⠀⠀⠀⠀⠀⡴⡡⠒⠒⠪⠣⠀⠀⠀⠀⠀⠀⢠⢮⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠕⠁⢸⠇⠀⠀⠀⠀⢸⡀⡨⢶⠁⢸⠀⠀⠀⠀⠀⡗⡀⠀⠀⢀⢆⠂⠀⠀⠀⠀⠀⡇⠀⠙⠦⣄⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡊⠁⢀⣠⠎⠀⠀⠀⠀⠀⠀⠙⠤⠤⠗⠁⠀⠀⠀⠀⠀⠙⠾⣦⣐⡭⠊⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⣀⡠⠄⡀⠈⠉⠉⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⢤⡀
⠀⠀⠀⢀⣴⣊⠁⠀⠀⢈⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⢀⢿⠀⠀⠀⢀⡠⠒⠉⠀⠈⠃⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⣠⡚⠁⠀⠀⢀⠇
⠀⢀⡔⠁⠀⠈⢳⢀⡴⠋⠀⠀⠀⣠⠊⠙⢵⣄⢀⠴⣫⠞⠀⠀⣰⣟⡳⣦⠀⠀⡠⠂⠀⠀⢠⠞⠁⠀⠀⠀⣠⢞⠕⠁⠀⠀⠀⣠⠊⠀⠑⢤⡀⡠⠊
⠀⢸⠀⠀⢀⣠⠞⠋⠀⠀⠀⢀⡜⠁⠀⢀⡠⢟⡵⠊⠁⠀⠀⣜⣿⣺⣽⣽⡧⠚⠁⠀⠀⢠⣇⡀⣀⡀⢔⡫⠚⠁⠀⠀⠀⠀⢰⡃⠀⠀⢀⠔⠋
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠸⢦⣤⠖⠉⠊⠁⠀⠀⠀⠀⠀⠙⠾⠷⠛⠉⠀⠀⠀⠀⠀⠀⠓⠁⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⢀⡤⣔⣒⣒⠢⣄
⠀⠀⠀⡠⠴⠤⠶⠤⠶⠦⣄⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠂⣎⠀⠀⠀⢱⠈⡇⠀⠀⠀⠀⢠⢶⣒⡉⠉⣏⢉⣀⢶⡄
⠀⠀⠀⠳⠤⠄⣀⣀⣠⠶⠞⠀⠀⠀⠀⢯⠲⠤⣤⣤⠤⢶⠃⠀⠀⠀⠀⠘⡧⠬⣭⣃⡭⠥⢊⠇⠀⠀⠀⠀⠘⠦⠤⠤⠥⢤⣤⣤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠐⠚⠁⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠔⠋⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⠁⠀⠀⠁⠢⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠶⠲⠤⣀⠸⣄⣀⣀⣀⣀⣀⡀⠤⡏⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠂⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠠⠀⣀⣑⣅⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠻⡀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣠⠴⠒⠋⣉⠝⢓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣠⠤⠖⠁⠀⢠⠏⠀⢀⠄⢊⠤⠊⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠫⢍⡉⠈⠉⠒⢄⡀⠀⠀⠀⠀⢸⠤⠎⣀⣐⡁⠀⠄⢊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠁⠂⠌⡑⠢⢄⡀⠙⢆⠀⠀⠀⠀⠑⠒⠶⠶⠶⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠐⠠⠀⢀⡀⢁⣢⡬⠑⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⡶⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣦⠀⠀⠀⠀⠀⠙⠓⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡅⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⢻⣄⠀⠀⠢⣤⣀⣀⠛⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⣸⠐⡇⠀⠀⠀⠀⡠⠊
⠀⠀⠈⠛⢷⣆⡀⠀⣿⣿⣷⣦⣌⠙⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⢩⡄⠀⡠⠊⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⢿⣦⣌⣿⣯⣉⠂⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣻⣾⣄⡀⠀⠀⠀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⢏⢿⣿⡉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣱⡏⢸⣙⣦⣺⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣼⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⡤⣛⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠶⠔⠒⠋⠀⢀⣰⠃⠀⠀⠀⠰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⡀⠀⠀⣠⣾⡇
⣼⣤⢀⡀⢀⡀⡀⠀⠀⠐⠊⠁⠀⠀⠀⣀⣤⠾⠛⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠁⠲⠦⠴⣱⣶⣿⣿⡿⠃
⢿⣿⣌⠉⠀⠤⠀⠀⠀⢀⣀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣐⡒⠖⣻⡯⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢹⠽⠟⠋
⠀⠉⠛⠿⠶⠶⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣀⣀
⠀⠀⠀⢀⣶⠾⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⢟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁
⠀⠀⠀⡀⠀⠤⠶⠂⠐⠀⠀⠀⠀⠀⠀⠀⠘⢦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣾⣴⠎
⠀⠀⢸⣧⡤⡴⠒⡶⡀⠀⡄⠀⠀⠀⠀⠀⠀⢻⡨⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⢸⣯⣧⡬⡤⠤⠿⡄⢧⠀⠀⠀⠀⠀⠀⠈⣷⣿⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⣿⡅⣿⠀⠀⠀⠀⠀⠀⢸⣯⣭⠉⠁⠀⠀⠀⠀⠐⠐
⠀⠀⠘⣷⣟⠀⡀⢀⠀⣤⣐⠀⠀⠀⠀⠀⠀⠀⠸⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡇⢿⠀⠀⠀⠀⠀⠀⠸⣿⣿⠄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠹⣿⡴⡿⠿⡣⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⠷⣾⡄⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠙⢶⠖⠛⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣰⣾⣿⠇⠀⠀⠀⠀⠀⠀⠈⢿⡽⠄⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣀⣀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠷⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⡚⠉⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢛⡭⠖⠉⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣋⠴⢚⡩⠀⠀⠀⠀⠀⣀⣤⣶⠾⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠐⣈⡤⠚⠁⠀⠊⢁⡤⢖⡫⠝⠈⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⣀⡴⠚⠁⠀⠀⣀⡴⣞⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⢀⣠⠴⣋⡵⠊⣀⠴⠚⢁⠀⠀⣀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⡀⠈⢧⡀
⠀⠀⠀⠀⣠⠴⢋⠵⠊⠁⠔⠊⠁⠔⠊⣡⣴⣿⠟⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡟⠀⠀⠈⣿⡄⠈⠳⣄
⠀⠀⠀⢯⡁⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣷⣤⣤⠾⣻⠇⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠳⣄⠀⠀⠀⣀⣴⡿⠟⠉⠀⠀⠀⠀⠀⣠⠤⠖⠶⢤⡤⠶⠦⢤⡴⢛⡟⢿⣞⣋⠁⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠈⠳⣤⢞⠕⠋⠀⠀⠀⠀⠀⠀⠀⣼⠓⠒⠲⠤⢬⣷⠀⠀⣿⠀⢰⡇⠀⣿⠀⣩⡶⠶⠶⣦⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣀⣠⡤⢾⡷⣴⠒⢻⣷⣴⣷⣞⡃⣼⠁⠈⢢⣤⠿⡆⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣰⣿⠑⣄⠈⢳⡄⢸⠁⣧⡴⠋⢻⠀⠈⣪⡽⠿⠿⣟⣉⣡⢴⡧⠶⠶⣤⡀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⢹⡹⣄⡈⠳⣸⡇⢘⣧⡘⢷⣤⡾⠀⢰⡟⠶⠴⠤⣼⣧⠀⣸⡀⠀⠀⢈⣷⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠈⠳⣬⣽⡿⠋⣠⢾⠈⠙⣍⢳⣠⡶⠾⣿⣛⣛⣫⠵⠋⠀⠻⣍⣛⣛⣻⠇⠀⠀⢀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠹⣌⠓⠦⣬⣾⠹⣗⢦⡈⠻⣇⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠉⡿⠲⠚⠉⠹⡎⠳⣽⣤⡾⠂⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⢸⡘⢦⣄⣀⣼⠇⠀⠀⠀⠀⠀⢠⠏⠀⠀⢹⡆⠀⠀⠀⢀⢴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠙⠲⠶⠾⠋⠀⢀⣀⣀⠀⠀⢺⣧⡤⠴⣾⠇⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⡴⠉⢹⠉⢳⡄⠀⠉⠛⠉⠁⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⢰⣧⡀⣸⣀⣾⠇⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠈⠻⠿⠯⠽⠋⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⢀⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠠⣤⣀⡀⠀⢀⠀⢀⣼⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢰⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠰⠀⠀⣸⢳⡖⠀⠀⠉⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣀⡤⠚⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⠉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⡀⠓⠋⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠒⣼⠶⠴⠚⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⠀⠀⡿⠇⠀⠀⠱⣈⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⣀⣠⣴⣧⠀⠀⠈⠁
⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠀⠀⠐⠤⣄⢶⡾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢹⣛⣛⣯⡅⠀⢢⠁⣠⠄
⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣌⢻⣋⠙⠻⠿⢿⡄⠂⠈⠚⠁⠀⠀⡀
⠀⠀⠀⠤⠤⠂⠀⠀⠀⡀⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠞⣿⢽⣯⣷⡄⠀⠀⢉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⠁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⣇⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⢀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣠⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠦⡀⠀⠀⠀⠀⠀⠠⠂⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠢⡀⠀⠀⡐⠁⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠑⢄⠀⠈⠒⠈⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡑⣄⠀⠀⠀⠁⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⡘⢬⠆⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠑⠦⡀⠀⠈⢢⠢⣱⠸⠂⠦⠤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠈⠢⡑⠘⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠓⠢⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢡⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠚⠁⠀⠀⠀⢀⣌⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢁⡆⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⢒⠇⠀⠀⠀⠀⢜⠀⠀⠀⠀⠐⢶⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀⠀⠀⠀⠁⠘⠉⠀⠀⠠⣄⠼⣏⢠⡀⠀⠓⡄⠀⠀⢄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠁⠐⢄⠀⠀⡀⠀⢡⡄⠀⠚⠂⠒⢺⠽⡇⠀⠃⠀⡔⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⢄⠈⠳⡤⠵⠦⣄⠀⠀⠘⠇⠉⢙⠦⢤⣤⡤⢊⡴⠏⢤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠑⠀⠠⡄⠒⠀⠀⠀⢹⠂⠀⠉⠓⠔⠛⠋⠭⠀⠀⠴⠽⣶⠠⠈⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠛⠄⠀⠀⡠⠋⠘⡿⢀⣾⣄⠀⢠⠆⡀⢱⠄⠀⢀⡠⠆⢤⣬⡧⣀⠀⢈⡦⡀
⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠐⠒⠒⠒⠚⠛⠁⠀⠰⢄⣄⢠⡞⢀⣠⠔⣳⣏⠀⠈⠑⠢⣄⣸⡾⢀⡔⠋⢀⣀⣼⡥⠔⢋⣠⠏⣀⣼
⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⢼⡦⠤⠤⠴⠎⣥⣤⣤⣤⠀⠀⠀⠑⠚⢻⡧⣤⣭⠥⠞⠓⠶⣋⣉⣉⡥⠞
⠀⠀⠀⠢⠴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠀⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⣀⠴⠋⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠶⠦⠤⣄⣀
⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠟⢦
⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⠈⢧
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⢋⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣤⣀⣀⣀⣤⠤⠖⠚⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠻⠭⢍⣉⣉⡉⠛⠓⠒⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⣞⣋⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⡵⢶⠋⠁⢹
⠀⠀⠀⠀⠀⢀⣤⠤⣤⠶⠿⠥⢤⣤⣤⣀⣀⣈⡉⠉⠑⠒⠒⣢⣴⠞⠋⠁⠀⢸⠀⠀⢸⡀
⠀⠀⠀⠀⠀⣾⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⡴⠛⣿⣿⣻⣿⡟⠳⣼⠀⠀⠀⠀⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⢀⣠⣴⣚⣋⣿⣯⣭⣽⣿⣿⣿⡇⠀⢸⡀⠀⠀⠀⠀⡇⣠⡼⠃
⠀⠀⠀⠀⠀⣿⠀⢠⠿⠚⠉⣾⠭⢍⣉⣹⣯⣟⡛⠛⣻⣿⡇⠀⢸⡇⠀⠀⢀⡴⠟⠁⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⠀⢙⣶⢦⣤⣬⣭⣿⣛⣉⣙⡲⠶⠶⢚⣻⠃⠀⢸⣇⣤⠞⠉⠀⠀⠀⣠⠴⠚⢉⣬⣽⡶⣄⡀
⠀⠀⠀⠀⠀⠸⣶⣋⣁⠀⠛⠻⠭⠽⠋⠻⢭⣭⣭⢟⣩⣽⠀⠀⢸⠋⠀⠀⢀⡤⠖⢋⡥⣤⣾⣭⡿⠛⣃⣤⣙⢦⡀
⠀⠀⠀⠀⢀⣠⠞⠋⠉⠉⠛⠓⠒⠒⠶⠦⠤⠴⠞⠫⢥⣼⣤⡤⠞⢀⡤⠞⢉⣠⣤⣿⡶⠿⠃⣠⣶⣾⣿⠿⢋⣤⠏
⠀⠀⢰⡞⠛⠓⠲⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⡤⢞⣩⣤⣄⣿⣀⣶⣟⣀⣰⣯⣭⣽⠏⣡⠴⠋
⠀⠀⠈⠓⠲⠶⠤⣤⣀⣀⡀⠉⠙⠓⠦⡄⠀⣠⠟⠁⠀⢶⡋⠰⣯⠤⣤⣺⣇⣉⣼⣯⣠⣼⡏⢉⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣭⣝⡓⠲⠦⢿⠞⠁⠀⠀⠀⠈⠛⢦⡉⠉⣽⣋⣉⡩⣿⠉⢉⣡⠞⠉
⠀⠀⠀⠀⠀⠀⢰⢏⣁⣸⣇⣠⠝⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⠒⠛⣁⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠖⠛⢁⣠⠴⡶⡖⠶⣤⡀⠀⠀⠀⠀⠀⠙⠦⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣑⣚⣛⣃⡭⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠲⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠈⢹⠉⠉⣻⠛⠛⠛⡟⠛⠛⢿⠛⠛⢻⠛⠛⢻⠛⠛⢹⡏⠉⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢾⣦⣼⣄⣀⣽⣀⣀⣠⣇⣀⣀⣼⣀⣀⣸⣀⣀⣸⣄⣀⣼⣄⣤⣧⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⢤⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣁⡠⠿⣆
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣼⠷⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⣶⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⠀⠀⠀⠀⣴⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏⠀⣼⠋⠉⠉⠉⡏⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠀⠀⢿⣤⣤⣤⣤⣿⣤⣤⣤⠾⠁
⠀⠀⠀⠀⢀⣤⠶⠶⢶⣤⣤⣭⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡴⠶⢶⣤⡀
⠀⠀⠀⠀⣟⠀⠀⠀⡼⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠁⠈⢹⣧⠀⢀⡼⠛⢶⣄
⠀⠀⠀⠀⠙⢦⣄⣀⣳⡀⠀⠀⢀⣰⠟⢀⣀⠀⠀⣿⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢦⣠⡾⠋⠳⣮⡀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢛⣻⣷⠞⠋⠉⢻⡄⠹⣦⡀⢠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢿⡀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠻⢦⣄⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠈⢧⠀⠀⣠⠟⠀⠈⠻⣧⡀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⣼⠷⠛⠁⠀⠀⠀⠀⠈⠻⢦⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠙⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠀⠀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣾⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠟⠁⠀⠀⠉⠉⠓⠦⣄⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⡾⠁
⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⠁
⠀⣴⠟⠁⠈⠁⠀⠉⠉⠛⠶⣄⡀⢹⣤⣤⣤⣄⣠⣤⣤⣤⠤⠤⠶⠖⠒⠛⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⣼⡏⠀⠈⠳⣄⠀⠲⣄⠀⠀⠈⠙⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⢹⡀⠀⠀⠈⠳⢄⠈⠢⡀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⢻⡀⠳⡄⠀⠀⠀⠀⠑⢤⡈⠢⡀⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⢠⠀⠀⠀⣴⠃
⠈⢷⡀⠘⢦⡀⠈⠰⠀⠀⠙⢦⡈⠦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⢀⡾⠃
⠀⠀⠻⣆⡀⠙⠦⣄⡀⠀⠀⠀⠙⢦⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⠈⠙⢦⣄⡈⠉⠓⠲⠶⠶⢖⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⣀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠶⠞⠛⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠉⠀⢀⣤⠟⠋⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣴⠟⠋⠀⠀⠒⠀⢀⡤⠞⠉⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⣀⣠⡤⠞⠋⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢀⡠⠒⠉⢀⣠⠞⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠒⠒⠲⠶⠶⢤⣄⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠖⠋⠀⣀⠴⠋⠀⠀⠁⠁⢀⡴⢋
⠀⠀⠀⠀⢠⣶⣏⠉⠛⠦⢤⣀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠲⢾⣁⢀⣠⡞⠁⠀⣀⣀⡤⠴⠚⠁⣠⡾
⠀⠀⠀⢰⡏⠀⠈⠛⠶⣤⣀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⠉⠉⠉⠉⢉⣁⣀⣠⣤⠴⠞⠉
⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠉⠛⠢⢄⡀⠈⠙⠲⢤⣀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠸⣇⠙⠦⣄⡀⠀⠐⠀⠀⠀⠉⠛⠶⣤⣀⠈⠙⠲⢤⣤⢿⡇
⠀⠀⠀⠀⠹⣦⠀⠀⠉⠛⠒⠠⠤⣀⣀⣀⣀⣀⣩⡿⠶⠒⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠾⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⠿⢰⣇⠸⠿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣇⣛⢻⡿⢛⣃⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣘⣃⣸⣿⣿⣿⡇⠀⠀⣿⡴⠖⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣡⣴⣾⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⡴⠶⠶⠶⠶⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⠳⠶⠶⠦⠴⢿⣿⣿⣿⡿⠟



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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⣏⠁
⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢿⣿⣿⣿⣿⢩⡍⣿⣿⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⢩⣭⣼⣧⣭⡍⣿⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⣶⣦⢸⡇⣶⣶⣿⣿⡇⠀⠀⣿⡇⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠻⠿⠿⠿⠿⠶⠶⠿⠿⠿⠿⠇⠀⣠⡿⠟⠉⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠞⠛⠙⠛⠛⢻⣿⣿⣷⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠤⠤⠤⠤⠤⠤⠤⢼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⢷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠲⠿⠿⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠛⠛⠛⠿⠿⢿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠻⢿⣦⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣩⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠙⠻⣶⣶⡿⠟⠛⠛⠛⠛⠉⠉⠉⠉⠉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣻⣷⣤⡀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⡛⠛⠛⠛⠛⠛⢿⣶⣤⣀⠀⠀⠙⠛⠿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⢻⣿⠄
⠀⠀⠀⠀⠀⣴⣿⠟⠋⠁⠀⠈⠛⢿⣷⣦⣀⠀⠀⠀⠈⠛⠿⣷⣦⣤⣀⠀⠀⠉⠙⠛⠿⠿⣿⣷⣶⣾⣿⡿
⠀⠀⠀⢠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣄⠀⠀⠀⠀⠉⠛⠻⠿⣶⣦⣄⣀⡀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠉⣹⣿⡟⠛⠛⠛⠛⠉⠁
⠀⠀⠀⢸⣿⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣤⣀⢀⣴⡟⣿⡇
⠀⠀⠀⠘⣿⣧⡈⠛⠿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣩⣿⣿⠟⠋⢠⣿⡇
⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠀⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⠂
⠀⠀⠀⠰⠤⠄⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⡁⠀⠀⠀⠀⠐⠁⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠀⠐⠀⠀⠀⠠⠄⠠⣀⠀⠀⠀⠐⠃⠀⠀⠀⢉⠀⠀⠀⡘⠁⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠒⣀⠀⠀⠛⠀⠘⠀⢈⡀⠀⠴⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⣀⠠⠄⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠈⠦⡀⠚⠀⠀⡀⢈⡁⠐⠃⠀⠀⠀⠐⠀⠀⢀⡀⠒⠈⠀⠀⠀⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠱⡄⢃⠀⢠⠀⡀⠚⠀⡀⠀⡜⠀⡄⠒⠀⠀⠀⠀⢀⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡈⠢⡘⠧⡖⢰⠈⢉⡁⡰⢁⢎⡔⠃⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠠⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠈⠱⣄⡈⢂⠻⡡⣬⣡⡀⣁⠾⣀⠄⢊⡀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢤⡄⢠⠠⠤⠤⠀⢀⠄⠀⠀⠂⠠⠀⠀⡀⠀⠀⠀⠀⠙⠢⣁⢵⣽⡤⣶⠽⠎⠐⢈⠁⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢉⠚⣾⠿⣿⡑⠒⠚⠓⠚⠀⠁⠈⠁⠁⠘⠂⠲⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠒⠂⠀⣸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣂⣡⣠⡠⠓⠐⡟⠸⣌⠑⠉⠳⢒⠰⠠⠆⠤⠠⠄⠠⠠⠄⠀⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠿⠭⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡸⠀⠠⠈⢣⡄⠀⠂⠐⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠁⣸⠈⠁⠄⡀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠄
⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠐⢄⣀⡠⠀⠀⠀⢀⣀⣀⢠⡤⠤⠤⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢯⣠⣾⠏⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡤⠤⠔⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠁⠀⡌⢢⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⢀⠀⠸⠀⡀⠀⠀⠐⠁⠀⢸⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠒⠊⠀⠀⠀⠀⠀⠀⡀⢀⡀⠐⠀⠈⠀⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⢷⠒⠒⠒⠀⠀⠀⠇⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡆⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⠤⠊⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠄
⠙⠒⠚⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤
⠀⠀⠀⠀⠀⣀⠤⠤⠄⠒⠒⠉⠉⡍⠉⠁⠐⠒⠒⠐⠀⠡⣆⠀⠀⠀⠀⢰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣀
⠒⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠿⠀⠀⠀⠀⠈⠐⠀⢳⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⢠⣀⠠⠂⠀⠀⠀⠀⠀⣠⢴⠊⠉⠑⣄⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠶⠚⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⠔⠀⠀⠀⢠⠐
⠀⠀⢀⣀⡠⠤⠔⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠊⠀⠀⠀⠂⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⠀⠀⠁⠀⠀⠀⠀⠐⡄
⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⢀⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⡀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣠⠔⠒⠒⢒⣤⡀⠀⠀⠀⠀⠀⣽⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠈⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠀⠉⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢀⡤⠊⡁⠀⠀⠉⠀⠀⠒⡀
⡀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡠⠼⠇⠤⠀⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈
⢈⢦⡀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⡸⠃⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠐⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠁⠀⠑⠀⠀⠀⠑⢄⠀⢀⣠⠴⠊⠀⠀⠀⠀⠠⡀⠀⠀⠀⡠⠒⠒⠒⠒⠀⠄⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠐⠒⡂⠉⠁⠀⠀⠀⠈⠰⡄⠀⠀⠀⠀⠀⢸⣀⠠⠄
⠀⠀⠀⢃⠀⠀⠀⠀⠓⡉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠇⠈⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⢆⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠈⠢⢄⣀⡀⠤⠊⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠱⣤⣠⠤⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⡀⠤⠀⠄⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠙⠉⠁⠶⠤⣄⢀
⢣⡀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠤⠤⡀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠈⠐⠠
⠀⠁⠀⠀⠈⠀⠀⠀⣠⠞⠙⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠧⠤⢤⡀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⡰⠊⢀⠁⠀⠀⠐⡄⠀⠀⠀⠊⠀⠀⡷⠐⠒⠀⠤⠤⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠈⠆⠀⠀⠀⠀⠀⠀⠠⠀⣀⠋
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⡰⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢤⠄⣀⠀⠀⠀⠀⠤⠄⠀⠀⠀⣀⣀⣀
⠈⠢⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠰⠁⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠆⢀⠁
⠀⠀⠑⣤⡀⠀⢀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢰⠀⡅
⠀⡠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠸⡀⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠘⡂⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠤
⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀
⣆⣀⣀⡀⣀⣀⡀⠈⣀⠀⠀⠀⠀⠐⣏⣀⣀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⣼⣄⠒⠈⠁⠀⠀⠀⠀⠀⣀⠐⠉⠀⠀⠀⠉⠉⣻⠀⠀⠀⠀⠀⠀⣀⠊
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠞⣧⠀⠀⢀⣀⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⣠⠋⠀⠘⠚⠉⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠙⠲⢤⠞⠉⠉⠙⠣⡀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⣧⠀⠀⠀⠀⡰⣋⣞⠉⣱⣄⡀⢸⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠙⣄⠀⠈⠉⠉⠉⠀⠈⠉⠉⠀⠀⢠⡾⣽⠣⣼⠃⢌⣇⡜⡸⠀⢀⡤⠲⡈⠳⣄⠀⠀⠀⠀⠘⠧⠤⠤⢤⣤⣀⣀⣀
⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠒⠲⢧⡦⢴⠛⣬⣶⠁⡰⠛⢢⠰⢇⣠⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⢾⣠⣿⠏⠻⣅⣀⠼⣀⡠⠃⢱⠛⡆⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⣨⠆⠀⠀⢠⡇⠀⠀⠀⠀⠠⠁⠀⣼⠟⠁⠀⠀⠘⠷⣤⢼⠒⠒⡇⢀⠇⠀⠀⠀⠀⠀⠐⠛⠲⠤⣄⣀
⠀⢀⡠⠖⠋⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠽⠗
⠶⣉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉
⠀⠀⠉⠙⠒⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡛⢏⣙⡦⢵⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠉⢫⠈⣇⣸⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⣧⣞⡁⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⣀⣀⣈⣶⡄
⠀⠀⠀⣴⣁⣤⠤⠤⠶⠒⣶⠂⠀⠀⠀⡠⢿⡀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠉⠙⠲⢤⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠔⠋⠀⠀⠙⠓⠒⠚⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠑⠢⢌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡠⠞⠁⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡽⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⢀⡴⠋⠸⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣤⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⣩⣿⣿⣶⣿⡄⠀⣤⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠙⠿⣷⣦⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⢛⡉⠽⣿⣿⣿⣿⣷⣄⠀⢬⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⡠⢂⣤⣤⣾⣿⣿⣿⣿⣿⣧⡀⠀⢼⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢶⣏⠀⣠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣦⡑⠂⠙⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠿⢸⣿⣿⡿⠛⠛⠟⢫⣥⣄⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢸⣿⣟⡁⠀⠘⢣⡬⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣸⠁⢸⣿⡿⠇⣠⡶⠋⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠁⠀⡿⢀⠋⠁⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢫⣹⣿⣿⣧⣿⡏⢿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠠⢼⣿⣿⣶⣶⣶⣤⠀⢠⣶⣿⣿⣯⣿⣿⣿⣿⡿⠈⢳⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⣿⣿⠀⢸⢿⣏⠙⠉⠉⠈⣿⣿⠇⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡿⠀⣤⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠈⡿⠀⠾⠀⠹⣦⣀⠠⢀⣿⡿⠀⠀⣯⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⣯⣽⠃⢀⣿⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⣦⡀⠀⢀⠀⠀⢸⣿⠀⠻⡿⠃⠀⢰⣿⣿⠟⠙⠷⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⡯⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠸⠿⢆⠜⠁⠀⢸⣿⡇⠀⠀⠀⠀⣨⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣠⣾⡇⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⢲⣶⡤⢶⣖⣲⣿⡇⠀⢤⠀⠀⠀⣸⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣈⠉⠀⠀⠈⣹⣿⣿⣶⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡎⠉⣿⣿⣿⢈⣧⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣿⣟⣿⣿⣿⣿⣿⣿⣾⡟⠀⢴⣿⣿⣿⣿⡃⠻⢶⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⣿⣿⣏⠱⡄⠀⠀⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⠆⠈⠀⢻⣿⣧⠀⠀⠀⢸⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡟⠁⠀⠀⠀⢸⣿⣿⡞⣿⣯⣿⣿⣿⢻⡄⠀⠀⠀⢈⡟⣿⡆⠀⠀⠸⡿⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣾⣿⠧⠀⠀⠀⡄⢸⣟⡻⣷⣿⡏⠫⠈⠉⠀⠙⠀⠀⠀⠈⡁⢻⣿⣄⠀⢸⠀⠀⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣹⣿⣿⡏⠀⠀⠀⠀⠃⣼⣿⡁⡿⢻⡇⠀⠀⢫⣿⡆⠀⠀⠀⠀⠓⣼⣿⣿⡄⢸⠀⠀⠈⢻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣹⣿⣿⠇⠀⠀⠀⠠⠀⣿⡿⡇⠀⢠⡄⠂⠀⠀⠉⠻⠀⠀⠀⠀⠘⠻⡿⣿⣧⢸⠀⠀⠀⠈⣿⣿⠻⢆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⠇⡇⠀⠈⠁⠀⠀⠀⠁⠀⢧⠀⠀⠀⠀⠀⡇⠘⠟⢸⠀⠀⠀⠀⠈⠘⣦⠈⢣⡀
⠀⠀⠀⠀⠀⠀⣸⣿⠟⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⣸⠀⠀⠀⠀⠀⠀⠙⠂⠸⠟
⠀⠀⠀⠀⠀⣰⡿⠃⠀⠙⡟⠁⠀⠀⠀⠀⠀⢸⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢟
⠀⠀⠀⠀⢰⣿⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣾⡄
⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢿⣿⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢰⡉⠀⠤⠄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠖⠒⠒⠲⠦⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢾⠒⠦⠤⠤⡤⡤⡤⣤⠤⠴⢾
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠙⢦⡘⡶⠤⠤⣄⣀⣀⣄⣤⡤⢴⢋⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣧⣤⣄⠀⠀⠀⠱⣔⠂⠤⠤⠤⠤⣄⠀⠀⢸⡿⠤⠤⠤⢽⡆
⠀⠀⠀⡜⡏⠀⠈⢫⢳⡀⠀⠀⢻⠀⠀⢰⡱⠀⣿⠀⠀⡸⠋⠓⠒⠊⠙⡦⠤⣀⡀
⠀⠀⠠⠀⡅⠠⣊⣹⡇⡇⠀⠀⢸⠀⠀⠀⠚⠁⢸⠀⠀⡧⢀⣀⣀⢀⣀⣼⠀⠀⠉⢑⠦⡀
⠀⠀⠀⢧⢳⠈⡹⢳⢣⠇⠀⠀⢸⠤⣀⣀⠀⣀⣸⠀⠀⡇⠀⠈⠉⠉⠀⢸⢠⠀⢠⢃⠄⠧⡀
⠀⠀⠀⠈⠓⠛⠓⠻⣁⡀⠀⢀⣨⢆⡀⠈⠉⠁⠀⠀⣀⣇⠀⠀⠀⠀⠀⡸⠼⣄⣺⣸⠤⡼⠷⢤⡀
⠀⠀⢀⣀⣀⣠⠒⠋⣹⠍⠉⠁⠀⠀⣈⢭⣍⡛⠋⠉⠀⠙⠯⢶⡶⠶⠾⠃⠀⢀⣈⣀⣀⠀⠀⠀⠈⠙⠂
⠀⠀⠧⣀⣋⣈⣹⠉⠁⠀⠠⠔⡖⠢⣟⣢⣔⣇⣤⠒⢦⠀⠀⠀⠀⠀⠀⠀⠐⣅⠀⢀⡆⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣐⣓⡺⠃⠀⡜⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠘⠂⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠉⠛⢷⡄⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢿⡄⠀⠀⠀⠀⢠⡿⠙⣧⡀
⠀⠀⠀⠀⣾⠛⠛⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠈⠛⠶⣦⣤⠶⠟⠁⠀⠈⠻⣦
⠀⠀⠀⠀⣿⠀⠀⠀⢹⡇⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣾⠋⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠙⣷
⠀⠀⠀⠀⣿⠀⠀⠀⢹⣧⡶⠟⠛⠉⠉⠛⠻⢶⣄⠀⢿⣄⠀⠙⠻⣦⡀⠀⠀⠀⠀⢀⣴⠿⠋⠀⣠⡿
⠀⠀⠀⠀⢻⠀⠀⢀⡾⠋⠀⠠⠶⠶⠶⠶⠀⠀⠙⢷⡀⠉⠻⣦⡀⠈⢿⡶⣦⣴⢶⡿⠁⢀⣴⠟⠉
⠀⠀⠀⠀⣿⠀⠀⢸⣧⣤⣀⣤⣀⣀⣀⣠⣀⣀⣀⣼⡷⠶⠶⢿⡿⠶⠛⠁⣾⠃⠀⠻⠶⢿⡿⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⢶⡄
⠀⠀⠀⠀⣿⠀⠀⠀⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⣿⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⣿⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⠀⠀⠀⣿⡄⠀⠀⠀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠏
⠀⠀⠀⠀⣿⠀⠀⠀⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⢶⣤⣴⠾⠷⣦⣤⡴⠟⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⢹⡏
⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⣿⡀⣀⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⡀⣸⡇
⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠚⠛⠛⠋⠉⠛⠛⠓⠲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣿⠓⠶⠤⢤⣄⣀⣀⣀⣀⣀⣀⣤⡤⠶⡿
⠀⠀⠀⠀⠀⢀⡤⠖⠋⠙⢦⡀⠸⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠃
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠙⣆⢸⡈⠉⠉⠉⠛⠚⠓⠛⠛⠋⠉⢩⣠⠶⠒⠒⠒⠲⢤⡀
⠀⠀⢀⣠⠷⠶⣖⢦⡀⠀⠀⠀⠈⢿⠀⠉⠑⠒⠒⠒⠒⢶⠀⠀⠀⢸⣏⠙⠒⠒⠒⢚⣹⠇
⠀⣰⢫⠃⠀⠀⠈⢧⠳⡄⠀⠀⠀⠸⡇⠀⠀⠰⣋⠕⠀⢸⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠙⣶⠤⣄⣀
⠀⡇⢸⠀⠀⡴⠒⢺⡇⢻⠀⠀⠀⠀⡇⠀⠀⠀⠩⠛⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⠙⠲⢤⡀
⠀⢧⠸⣄⡠⠗⣲⣋⡇⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡏⠉⠓⠒⠒⠒⠒⠉⢹⠀⠀⠀⠀⡴⠋⢘⡆
⠀⠘⢦⡡⣀⣴⢃⣼⣱⠃⠀⠀⠀⠀⡏⠑⠲⠤⣤⣤⡤⠼⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡀⢰⢁⡎⠉⢙⣦
⠀⠀⠀⠙⠛⠛⠛⠫⢄⣀⠀⠀⣀⣠⡽⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⠀⣼⠲⠦⣇⣿⣀⡷⠤⠿⠛⠦⣤⡀
⠀⠀⠀⠀⢀⠄⠒⠚⠛⡎⠉⠉⠉⠀⠀⠀⠈⣙⣛⡒⠒⠒⠋⠉⠀⠘⢯⣗⣒⣶⣶⣒⡾⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⠲⠄
⡖⠋⠉⠟⠛⠲⣤⠖⠊⠁⠀⠀⢀⣀⣀⣀⢯⣒⣈⣉⡇⠀⣀⣀⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣴⠋⠉⠉⢫⠑⠒⢄
⠉⠓⠒⠦⠤⠴⠃⠀⠀⠀⠀⡎⠀⡜⠀⣹⡗⠦⠬⢴⠗⠛⢅⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⠤⠼⠤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢭⣭⡭⠝⠁⠀⢰⡃⠀⠀⣸⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⢤⣀⣤⠦⠤⠤⠤⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠢⣤⣀⡀⠀⠀⠀⠀⠀⠀⣸⠀⣸⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠞⠉⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠦⠤⣄⡀⠀⠀⡇⠀⠀⠈⠉⠙⠛⠒⠒⠒⠲⣯⣠⡿⠒⠒⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠉⠲⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⡇
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠙⠓⠒⠲⠶⠤⠤⢤⠤⢤⠤⠤⠶⠖⠒⠚⠋⠉⠁⣀⣠⠞⣇
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡦⠤⣤⣤⣀⣀⡿⠀⣿⣀⣠⣤⡤⠤⠴⠖⠚⠋⠁⠀⠀⣿
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠙⢆⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⡾⠿⠛⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣭⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠶⠶⠶⠶⠒⠒⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠚⠉

⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢦⡀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠉
⠀⠀⠀⠀⠀⢀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣀
⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢦⣀
⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠙⣇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢘⣧
⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣠⡴⠞⠋⠙⣧
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣴⠟⠋⠙⠳⣄⠀⠀⠹⣇⠀⠀⠀⠀⠸⡇
⣿⠀⠀⠀⠀⠰⠶⠶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠹⣆⠀⠀⠹⣆⡀⠀⢀⣼⠇
⣿⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡄⠀⢀⣤⡶⠿⣆⠀⠀⠈⠙⠛⠋⠁⠀⢀⣠⡴⠦⣤⡀
⣿⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠰⠶⢶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⡞⠋⠁⠀⠀⠹⣆⠀⠀⠀⢀⣠⡴⣾⡋⠁⠀⠀⠀⢻
⣿⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⣠⡟⠀⠀⠀⠶⠶⣶⠆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢀⡿⠀⢀⡼⠋⠁⠀⠘⣷⡀⠀⠀⠀⣼
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠤⠤⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠙⠶⠤⠶⠋⠁⠀⠸⣇⠀⠀⠀⠀⠘⣷⣤⠶⠛⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠶⠆⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⠶⠛⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠙⠳⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠾⠋⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠂⡆⢰⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣘⣀⣁⣃⣘⣘⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠉⢉⣉⣉⣉⣈⡀⠀⠀⠀⡴⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢨⡇⠀⢀⠎⠈⠢⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠘⣀⠤⡄⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠤⠤⠤⠤⠤⠤⡇⢠⠊⠀⠀⢱⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠣⢀⣀⣀⣀⠠⠔⠊





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

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢰⣿⣟⡑⠐⠒⠒⣩⣴⣶⣴⢾⠷⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⢰⣶⠒⠲⠄⢸⣿⢩⡍⠂⣿⡆⢰⡖⢂⣴⡟⣛⠢⠸⡟⠭⣅⡀
⠀⠀⢺⣿⣿⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠘⢻⣇⣙⠀⠈⣿⢘⠋⠀⢹⡇⢨⡇⠘⣾⣡⣼⣆⠈⠿⣷⣦⡀
⠀⠀⠀⠀⠀⢀⣤⣤⢶⣶⣶⡆⠀⠀⠀⠀⣀⠀⢀⡀⢙⠿⠃⠀⢀⠀⢺⣿⣟⠠⠚⣿⠻⢷⣄⠘⢷⣙⣡⠆⠙⢿⣗⡤⠈⢿⣶⣿⡗
⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠟⠛⠛⠋⠁⠉⡉⠉⡀⠀⠀⠀⠘⢶⠟⠀⠀⠉⠀⠀⠀⠀⠀⣀⡴⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠉⠁
⠀⠀⠹⠜⠁⠀⠀⠀⠀⢀⢀⢄⡀⡀⠀⠀⠹⠿⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⡀⠀⠀⠇⠀⠀⠀⠀⢀⣰⣍⠘⠀⠴⣿⠟
⠀⠀⠐⠐⠓⠊⠁⠊⠁⠛⠛⠂⠀⠁⠀⠀⠀⢠⡟⣿⣿⣟⣿⣿⣿⣷⣐⠒⠘⠳⣴⠀⠈⠀⢀⣤⡄⠀⠈⠉⠁⢴⣀⠴⠋⠀⡤⠤⠒⣸
⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠐⠒⠒⠂⠐⠒⠂⠹⢿⣿⣿⣿⣿⣿⣿⣿⣟⣀⡟⣛⠿⠍⠈⠠⣭⣥⠃⠀⠀⣞⡟⡆⠀⠀⠀⠀⠳⠆
⠀⠀⢀⡀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢤⠐⠂⠀⠀⠀⠀⠀⠀⠉⠉⠯⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠚⠉⠁⠰⠿⠽⠧⠤⠛⠀⠱⡄
⠀⠀⢸⣿⡄⣿⠀⣴⡿⠀⡀⠀⠂⠀⢨⡤⠤⠄⠀⠂⠀⠀⠀⠀⢀⣠⡤⠴⣦⣤⣤⠀⣤⠒⢦⣄⡀⠀⠀⣀⣤⣶⣶⡄⠀⠀⢀⡀⢀⠴⠋⠉⠉
⠀⠰⣶⣿⣾⣿⣾⣿⣾⣿⠃⠀⠀⠁⠀⠀⠒⢁⠀⠀⠀⠀⢠⠶⠋⠀⠀⠀⠀⢈⣁⣤⡙⢷⣄⣬⡁⠀⠸⣿⣿⣿⡿⠃⠀⠰⣿⣣⠁
⠀⠀⢙⣻⣿⣿⣿⣿⣭⣥⡀⠀⠀⠀⢠⣰⣿⢻⣵⣇⠀⣠⡋⠀⠀⡤⣄⣤⢠⣿⣿⣟⣿⣦⠙⠋⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠙⠛⠋⠟⠻⠏⠉⠉⠀⠀⠀⠀⠈⢿⣿⣄⠙⠿⠿⡻⠁⠀⠀⡃⢸⡇⢸⣷⢿⣭⣟⣿⡇⠀⠀⠀⠀⠀⣾⡇⡀⠀⠀⠀⠀⠀⠈⡥⠤⠤⠤
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠛⠁⠀⠀⠀⣧⣼⡇⠘⣿⣿⣶⣿⠟⠀⣠⡶⠀⠀⠀⠈⠉⢣⡀⠀⠀⢀⣄⣼
⠀⠀⠀⠀⠀⠃⠀⠀⣿⣿⠶⣶⠰⣠⡄⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⣿⣿⡇⠀⠁⠁⠈⠀⠰⢿⣏⠃⠀⠀⣠⠀⠀⡠⠋⠉⠁⠻⣿⣬⡄
⠀⠀⠀⢀⡀⠀⢀⣤⣹⣷⣧⣠⣾⠋⠙⠀⠀⢀⣾⡁⠈⠃⠀⠀⠀⣿⣿⠇⠀⠀⢰⠂⠀⠀⠀⠀⠈⠀⠁⠀⠠⣴⠁⠀⠀⠀⠀⠀⠈⠻⣆⣀⣀
⠀⢀⣮⣤⢀⡀⠀⢉⡙⣿⢟⣟⠁⢀⣀⠀⠀⣴⢄⢿⠁⣴⠲⡀⠀⠹⠟⠀⠈⠀⠀⠰⢂⡀⠰⠀⡀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣀⠀⡰⠋
⠀⠈⢷⣿⣶⠖⠀⠙⣿⡃⠀⠈⢻⣾⡿⠀⠈⢻⣦⣼⢴⢽⡆⠀⠀⠀⠀⠀⠀⠀⢤⠰⠈⡇⠡⠸⠇⠀⠀⠀⠀⢼⣷⠀⠦⠦⣾⣷⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢉⠀⣠⣄⣼⣿⣿⣶⣿⡷⠶⠆⣶⠄⠀⠤⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠈⠉⠹⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠐⠚⠀⠘⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣤⠀⠀⣄⠀⢠⡄⠀⢠⡄⠀⣠⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠶⠿⠶⠶⠿⠶⠾⠷⠶⠾⠷⠶⠿⠶⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠦⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⡀⠀⠀⢀⣀⣀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠋⣻⠟⠀⠀⠙⢉⣿⠃⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣴⠏⠀⠀⠀⢀⡾⠃⠀⠀⢸⡇⠀⠀⣀⣼⣧⣤⣤⣿⣄⣀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠼⠿⠶⠦⠀⠀⠿⠷⠶⠆⠀⢸⡇⠀⣼⠋⠀⠀⢹⡇⠀⠈⢹⡇⠀⢸⡏⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣹⣦⣀⣀⣸⣇⣀⣀⣼⣇⣀⣸⣇⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠋⠉⠉⣿⠉⠉⠉⢻⡏⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣿⣀⣀⣀⣼⣧⣀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣤⠒⠀⢉⡀⣀⡉⣉⣀⣒⡀⢁⣁⡐⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⣁⢀⣈⢉⣀⡐⣀⢀⣈⣙⠛⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⡘⠉⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢣⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠙⠉⠉⠁⠙⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠉⢹⣿⣿⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⣷⣶⣶⡶⡶⣶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⢶⣾⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣷⡶⣶⢾⢶⡶⠶⠿⠶⠿⠿⠿⠶⠀⠀⠶⡶⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⡇⣿⢸⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣿⣿
⠀⠀⠀⠀⠀⣇⣿⡿⣇⡭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⣿⣸⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⡇⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣸⣿⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣿⣸⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣽⣷⣷⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠰⠆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠉⠀⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠔⠀⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡸⣧⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⣿⣿⣄⣀⣠⣤⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣇⣀⣀⣤⠄⠈⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣞⠛⠻⢿⣿⣿⣧⣿⣿⣿⡇⠈⣿⣷⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡛⠻⢿⣿⣿⣿⣬⣿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⡿⢿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣹⣿⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⡿⠿⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣟⣻⡿⣿⠿⠿⠿⣿⡿⢿⣟⣻⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠶⢮⣭⣭⣭⣭⣭⣭⣭⣭⡵⠶⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡶⠛⠛⢶⡞⠉⠀⠈⠉⢉⣭⣭⣿⣿⡛⠉⠉⠉⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣼⣷⡀⠀⠀⠹⢦⣤⣤⣤⣴⣿⣿⣿⣿⣇⣀⣀⣤⣿⡿⣿⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠻⢶⣄⣠⣶⣽⣶⡉⠁⢻⣿⣿⣿⡟⠉⠉⠀⣨⣽⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣀⠀⠀⠀⠀⣩⣛⣿⣿⣇⣠⣴⠿⠿⢿⣻⣿⣶⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣙⠻⠶⣦⣤⣿⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣿⠇⠀⠉⣉⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣌⣉⡙⠛⠋⣄⣀⣠⣤⠶⠟⢛⣉⣀⣤⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠿⠁⣾⡿⢫⣴⡿⠃⣰⡿⡛⠀⣀⣠⣴⠟⣰⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⠀⢸⠟⢀⣴⠟⢁⣶⢏⣾⢁⣠⡽⠛⠁⢸⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⢀⡿⢀⣿⠋⢀⠜⢁⣼⣿⡋⠁⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣼⠃⡾⠃⢠⠊⣰⠟⠁⠙⠿⠷⠶⠂⠀⢸⣿⡇⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⡏⢸⠇⠀⠃⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠇⠘⢀⠂⡼⠁⠀⡆⠀⠀⠀⣠⣤⠶⣶⣾⣿⣷⣦⣤⣬⣧⠉⠻⣿⣿⣿⡏⠀⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠎⡸⠁⠀⢰⡇⠀⠀⣾⡏⠀⠀⠀⣿⣿⣶⣭⣿⣿⢿⣷⡀⠈⢻⣿⣿⣿⣯⡶⠋⠀⠀⠀⠀⠀⠀⣰⣿⠟⣽⣿⣿⣿
⠇⡜⣰⠁⠀⢠⣿⠃⠀⢸⣿⡇⠀⠀⠰⢿⡏⠉⠉⠻⣿⣿⣾⢿⣦⡀⠙⣿⣿⡿⠀⠀⠀⣀⣀⣤⠴⣞⣫⡥⠾⢟⣿⣿⣿
⢀⢡⡇⠀⠀⠀⣿⠀⠀⢸⣿⣿⣮⠀⠐⢸⣿⣄⠀⠀⢰⣿⣿⣿⣿⣿⡀⠈⠻⣿⠻⠟⢛⣛⣭⣶⣿⣿⣿⣃⣴⣿⣿⣿⣿
⢏⡾⠀⠀⠀⠀⣿⡀⠀⠈⢻⣿⣿⣧⣀⢸⣿⣏⢳⣶⣼⣿⣿⣿⣿⣿⣷⣀⣴⣿⣿⣿⣿⣿⣿⠟⠛⣛⣛⣛⣻⣿⡿⢿⣿
⡾⠁⠀⠀⠀⠀⢻⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⡀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣙⣋⣛⣁⠀⣀⣰⣿
⠃⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⣀⣤⣴⣾⠿⣿⣿⢿⣿⣿⣿⡿⣿⣯⣽⣶⣿⣵⣾⣿⡿⢿⣟⡻⣿⣿⣿⣿⣿⣿⣯⠛⢛⣻
⠀⠀⠀⠀⠀⠀⡿⠀⢀⣶⠟⢉⣿⣿⠇⠀⣿⣿⠘⢿⣿⣿⣿⣦⣄⣤⣭⣉⣴⣶⣶⣭⣷⣾⣿⣿⣿⡿⠻⣍⣤⣴⣴⣿⣿
⠀⠀⠀⠀⠀⣼⣇⣴⡟⠁⠀⢺⡟⢿⣧⣤⣿⣿⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣴⣿⣿⡿⠀⠀⠀⠈⠀⠀⠉⠉⣴⣿⠀⠀⠀⠀⠀⠉⠉⠙⠻⣿⣿⣿⣿⣍⠛⢻⣿⣦⣍⡙⠻⢿⣿⣿⣿⣿⣿
⠀⠀⠀⣺⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⠉⠳⠆⠻⣿⣿⡧⣄⠀⠉⠛⢿⡻⢦
⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣗⣒⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠙⣫⣵⣾⣆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⣷⡄⠀⠀⠙⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢻⡿⢛⣡⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠘⠛⣿⣷⡶⢠⣿⣿⠿⠿⣿⣿⣿⡇⠀⠀⠀⠀⢺⣿⣿⣿⠀⠀⠀⢀⣤⣄⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⠑⠛⣿⣿⠟⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠰⣿⣿⣿⡆⠻⠛⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣭⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠤⠤⠤⢤⢤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⣀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠉⠉⠉⠈⠹⢿⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠤⠤⠤⠤⠶⠾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠏⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⡌⠐⢲⡶⠲⠂⠒⠒⢒⣾⢻⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⡔⠺⣾⡟⢀⣦⣀⡸⠟⡀⣸⠀⠀⠀⠀⠀⠀⠀⣥⣿⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⢈⣿⡋⢁⣼⡁⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠓⠲⣶⠶⣾⠟⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠃⠀⠀⢤⣧⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢙⡆⠀⠀⣞⠉⣷⠀⠀⣚⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⠋⠁⣀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢸⡇⣼⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⢀⠀⡤⠠⡄⠀⠀⣠⠒⢠⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⠉⠉⠉⠉⠉⠉⢸⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠼⠃⠀⠀⠢⠴⠃⠀⠀⠙⠶⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣋⣸⡇⠀⠀⢨⣀⣵⠀⠀⠺⣤⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠐⠀⠀⢠⣤⣤⣤⣤⣤⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡄⠀⠀⣔⠀⣆⠀⠂⢠⡁⣰⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢹⠙⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠙⠛⠃⠀⠀⠈⠛⠋⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣈⣀⣀⣼⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⣷⠛⠛⣶⢶⡶⣶⠶⠶⣾⠶⢶⠶⠶⣾⠷⠶⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢶⡶⡶⣾⢿⣿⣿⠾⠿⠷⢿

⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿
⣿⡿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿
⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠠⠊⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⣄
⣤⠀⠀⠀⠀⠀⠀⣤⣤⣤⣦⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠑⢄⠀⣠⣾⣿⣷⣄⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⣴⣤⣤⣤
⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣟⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣻
⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢾
⠉⠀⠀⠀⡀⠈⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠰⠊⠈⠐⢄
⠀⠀⠀⠀⠣⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠑⣄
⣤⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣄⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠙⢆⠀⣠⣾⣿⣷⣄⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠘⠄⠀⣠⣾⣿⣷⣄
⠛⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠃

⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀
⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿
⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⠊⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠑⣄
⣦⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣄⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶
⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠔⠋⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⠁⠀⠀⠁⠢⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠶⠲⠤⣀⠸⣄⣀⣀⣀⣀⣀⡀⠤⡏⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠂⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠠⠀⣀⣑⣅⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠻⡀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣠⠴⠒⠋⣉⠝⢓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣠⠤⠖⠁⠀⢠⠏⠀⢀⠄⢊⠤⠊⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠫⢍⡉⠈⠉⠒⢄⡀⠀⠀⠀⠀⢸⠤⠎⣀⣐⡁⠀⠄⢊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠁⠂⠌⡑⠢⢄⡀⠙⢆⠀⠀⠀⠀⠑⠒⠶⠶⠶⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠐⠠⠀⢀⡀⢁⣢⡬⠑⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣖⠚⣋⠩⢬⣓⡶⠤⠄⠤⠀⠀⠈⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠛⠋⠉⠉⠳⢦⡈⠙⠦⣍⣓⠒⠲⠒⠻⠿⠵⣖⠒⠦⢄⡀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⡄⢄⢦⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢠⣤⠀⠀⠀⠀⠳⡝⣌⠢⡳⢄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠈⢳⠀⠀⠀⠀⠙⢎⡓⢌⡒⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢨⣭⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢸⡇⢰⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⡟⠀⠀⠀⠘⢲⠀⠀⠀⠀⣴⣫⣯⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠘⡿⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡀⠀⠀⠀⣾⠃⢀⣀⣀⣤⠿⠛⠛⠛⠿⣟⠛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠜⢁⡞⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣣⠀⢳⡴⣶⡿⠿⠿⠟⠉⢉⢉⣁⠀⠀⠀⠀⠀⠁⠀⣿⡆
⠀⠀⠀⠀⠀⣠⢒⡼⢟⡛⠛⠛⢋⣁⡴⢿⣶⣼⣿⠏⣿⣤⣤⣤⣴⠶⠾⠛⠋⠳⣄⠙⠛⠷⠖⠚⠋⢻⣄⣀⠚⠇⠀⠀⠀⠀⠀⡀⠸⣇
⠀⠀⠀⠀⢸⣷⣿⠟⠋⠉⠋⠉⠉⠁⠀⠀⢈⡽⢋⡼⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠚⢿⣏⡁⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠗⠛⠂
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣤⢖⣺⡯⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⣤⠶⠦⠴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣀⠀⣀⡀⢀⡀⠀⣀⠀⠀⢀⠀⣠⡀⠀⠀⠀⣀⡀⢀⡀⣾⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢹⠀⠸⡇⠀⣯⠀⢸⣹⠈⡇⢀⠀⢸⢀⡏⠇⠀⠀⠀⣿⡷⢸⡃⢿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⠀⢠⣧⠀⣼⡄⢸⡏⠀⡇⢸⡆⢸⢸⢡⡆⠀⠀⠀⢿⠃⢨⡇⢸⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⣇⢸⠀⠀⡇⠀⣸⠀⠸⡇⠀⣇⢸⢻⣸⢸⣄⡇⠀⠀⠀⢸⠀⠈⡇⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡿⠸⠟⠀⠓⠃⠘⠒⠀⡇⠰⠋⠸⠀⢻⡄⠛⡇⠀⠀⠀⢸⠀⠚⠁⠸⠛⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠛⠉⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⢁⣀⣀⣤⣤⣤⣤⣤⣄⣀⡈⢻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠈⢿⣿⣷⡄⠙⢿⣶⣶⣤⣤⣤⣤⣴⣶⣶⡿⠃⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⣀⠙⠻⠿⢿⣿⠿⠿⠛⢉⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣶⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⡿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢰⡇⠀⠀⠀⠀⠉⢳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⡐⡇⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠻⣤⡀⠈⠳⣶⣤⣈⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡥⠀⠀⢀
⠀⠀⠀⠈⠙⠷⣾⣿⣿⣿⣷⣦⣉⣻⣟⠂⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣼⣷⣔⡁⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⣿⠡⣓⣤⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢜⠁⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠉⠁⢀⣤⠏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢷⠀⢀⠀⠀⢀⠀⣀⣴⣿
⣿⣶⠦⠄⠀⠂⠀⠈⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⠀⢠⣄⣀⣀⣀⣤⣆⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢉⣻⣿⣿⡿⠃
⠙⠻⠶⣤⣤⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠄
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠒⠐⠚⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠞⠓⠂⠐
⠀⠀⠀⠉⢁⢤⠁⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣟⡽⠁
⠀⠀⣾⡤⠴⠐⢦⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⡀⢸⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⢳⡴⠀⠚⠇⠰⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠸⡇⢹⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⢹⣿⢀⣄⣄⣰⡶⠀⠀⠀⠀⠀⠀⢹⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠻⣏⡭⠵⢿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⣭⣿⡇⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡠⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⠒⠒⠒⠚⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠿⠿⣲⣦⡶⠿⢻⠿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠟⠛⡿⠳⠖⠉⢫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢂⠠⠀⢀⠀⠀⠤⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⠂⠉⠑⠓⠀⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠶⠶⣤⠠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡐⠁⠀⠀⡿⡆⣳⠒⠦⣄⣠⠤⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠷⣴⣉⡤⠁⠗⠉⢐⡀⠉⠀⣀⣿⣯⣵⢶⣆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢳⣤⣉⡁⠃⠤⣶⡟⠀⠀⠚⠿⣿⢟⣜⣀⣉⢂⠀⠀⠀⢀⣤⣼⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠛⠉⢠⣉⣀⠲⢾⣩⡆⠉⠁⣄⠈⢿⠿⣿⣿⣿⠙⣣⡄⠊⠿⢾⣤⠀⠀⠄
⠀⠀⠀⠀⡶⠿⣿⣿⣮⣛⣫⡉⠹⠾⢛⠻⢦⣾⡘⣿⣧⡀⢼⣏⠀⠀⣿⣿⡻⢿⣂⡴⣁⠔⣻⣿⠄
⠀⠀⠀⠀⠈⢷⣶⣶⣖⣖⣲⣶⡶⡿⠃⠀⠀⠈⠻⡙⢎⣿⠒⢀⡀⠰⡴⢏⡱⠋⢛⡷⣾⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠒⠈⠀⠀⠀⠀⠀⠀⢁⣨⠙⢲⠊⢹⢖⡤⠍⣀⣴⣯⣞⡫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠊⠁⠈⢿⣠⡆⠀⣠⣤⠔⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⣧⠂⢀⣵⡶⠟⢀⣴⣾⣿⣓⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡡⠿⠷⢊⣴⣿⡮⢿⣿⣭⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠋⠁⠀⠀⠉⠀⠀⣰⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣋⣐⠀⠀⠀⠀⠒⠚⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄

⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣀⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣀⡀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⡀
⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⢋⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣡⣴⣾⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣾⣿⣿⣷⡀⠀⠀⠀⠘⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣷⣶⡶⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣿⣿⡷⠀⠀⠀⠀⠈⠛⠛⠋
⣿⣿⣿⣿⣿⡟⢡⣾⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠟⢋⣡⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣄
⣿⣿⣿⣿⡟⠀⠛⠛⢻⣿⣷⣶⠂⣴⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣠⣴⡄⢻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣼⢿⣿⣿⣶⡖⢠⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠋⠀⠀⠀⢰⣿⣿⣿⣿⡄⢻⣿⠿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⠟⠠⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠈⠀⠀⠀⡀⠐⠀⠀⠀⠶⠛⠉⣁⠶⠁⠐⠀⠀⠈⠀⣴⣟⣣⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⢠⠐⢈⠠⠐⠀⠀⠀⠀⠂⠀⠐⠋⡁⠄⠂⢁⣤⣦⣴⡌⠁⠀⠀⣀⣀⣀⣴⣫⣽⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤⡰⠌⠀⠀⠀⠀⡀⠄⠊⠁⢀⠠⠐⠉⠀⠀⠀⠄⡀⠀⣴⣲⣧⡶⣿⣿⣿⣿⣿⢞⣴⣿⣿⡿⣿⣷⣿⡟⣩⣴⣾⠖
⠀⠀⢀⠠⠔⢀⠀⡠⠄⠀⠐⢾⡥⠖⠖⠓⡔⢄⠢⡁⢀⠂⠀⠈⡠⠀⠀⠀⠑⢊⣩⣽⣺⣿⣿⣿⣾⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⢋⣿⣾⣿⣿⣿⣿⣯
⡓⠌⠀⠠⢌⠠⡁⣤⠶⠃⣌⠠⡑⠄⠂⡔⣈⣦⣳⣴⣂⣠⣄⣄⣴⡶⣆⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢩⣾⣿⣿⣿⡟⢹⣿⣿⣿⡿⢿⣥⣿
⠉⠀⠠⡄⠦⠳⢉⣠⣰⣍⢤⠁⣔⡆⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⠋⠉⠈⠉⢙⣿⣿⣯⡟⢧⣾⣿⣿⣿⣿⢃⣿⣿⣿⣿⣷⣿⣷⡝
⠄⠂⠀⠀⠀⣔⣮⣳⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⢀⣴⠟⠉⠈⠻⣇⢸⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣻
⠀⠀⣀⣰⡅⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣀⡀⠀⠀⠘⣼⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⠿⣛⢧
⠒⠝⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠘⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣟⢸⣿⣿⣿⣿⣿⣿⣭⣶⡿
⣑⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⡀⠀⠀⠀⢀⡰⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡽⢞⡋⢅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣶⣶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣥⣶⣾⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣛⡭⠥⠤⣄⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠿⠛⠛⠋⠉⠉⠁⡀⠀⠀⠀⠀⠉⠻⠶⣿⣯⣂⣤⣀⣀⣀⣀⣀⡀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟
⠀⠀⠀⠠⣄⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡉⠻⣿⣿⣷⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⡀⠐
⠃⢀⣄⠀⢀⠈⠐⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⣠⣯⣽⠿⠿⠟⠉⠁⣸⣿⢿⣿⡟⠓⢤⣄⡀⣀⡄⠀⢀⣾⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠛⠀⠀⠄⠀⠀⠁⢂⡤⠤⣖⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⢀⣿⡏⢸⣿⡀⠀⠀⠀⠉⠓⠢⢾⣿⣿⣿⣿⢿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡀⢩⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡾⣿⣄⠀⠀⠀⠀⠀⠀⣀⡼⠿⣿⣿⣿⣛⣛⣛⣻⣤⣬⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠢⡈⠉⠁⠠⠀⠀⠀⠀⠀⠀⠚⠲⣶⣤⣖⣩⣷⠶⠛⠂⣀⠤⠖⠒⣨⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣿⣿⡿⠿⣿⣯⢴⠂⢉⡠⠴⠚⠉⠁⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠄⠰⠐⠂⠛⠛⠺⣉⠙⠻⠟⡻⠋⢛⣻⠿⢿⣛⠉⠀⡀⠴⠞⡉⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡄⠀⠀⠀⠀⠈⣡⡬⠕⠚⠉⢀⣠⠴⠚⠛⣁⣀⣠⣴⣾⣿⠿⠿⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣴⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣄⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⢾⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢉⣿⣿⡿⠃⠀⠀⠀⠀⢉⣿⣿⡿⠃⠀⠀⠀⠀⢉⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⢠⣾⣿⡿⠁⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⣿⣿⣿⣿⣷⠀⠀⢰⣿⣿⣿⣷⣿⣦⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿
⠀⣠⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿
⣼⣿⣿⠋⠉⠙⣿⣿⣧⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢺⣿⣿⠀⠀⢸⣿
⣿⣿⡇⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿
⣿⣿⣿⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠀⠀⢸⣿
⣿⣿⡟⠛⠛⠛⢻⣿⣿⠀⠀⠀⠀⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⢸⣿
⣿⣿⣇⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠹⣿⣿⣷⣶⣾⣿⣿⠏⠀⠀⠀⠀⢻⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿
⣤⣬⣽⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠐⠲⠤⠤⠤⠤⢤⠤⠤⠴⣶⢶⢾⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡽⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣟⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠁⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠛⣛⣿⢿⣿⠑⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣙⡎⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠹⠀⡆⡆⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣱⢳⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠦⠴⠶⠞⠳⠻⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡖⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⢰⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡼⠇⠸⣤⣄⣄⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣮⠉⢧⠀⠀⡎⠘⢿⣿⠉⠉⢏⠉⠉⠉⠉⢩⠉⣴⣦⡶⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣡⡀⣷⠀⣸⣿⡖⠀⢈⢄⠀⠀⠀⣸⢴⡿⠈⢅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⡀⠉⠻⣿⡻⣿⡇⣠⢞⣺⣧⣤⡰⠣⠋⠁⡐⠕⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠈⠻⣾⣿⡿⠋⠁⠀⣨⡧⠁⠀⡰⠋⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣟⣷⠤⣠⣿⣿⣀⡠⣤⣾⢟⣷⣀⣠⣦⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠿⠶⠾⠿⠛⠛⠛⠉


⡿⠿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣉⡉⠀⠀⠀⠀⠀⠀⠀⠉⢉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⡚⠉⣧⠈⠉⠉⠋⠛⠛⠛⠛⠛⠛⠉⣩⠇
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⢦⡈⡏⠛⠒⠒⠶⠶⠴⠶⠖⠒⢻⣁⡤⠤⠤⠤⣄
⠀⠀⠀⠀⢀⣸⠥⣴⢤⡀⠀⠀⠀⠳⡏⠐⠒⠲⠤⠤⠦⡄⠀⠀⢸⣟⠒⠒⠒⠒⣺⠇
⠀⠀⠀⣰⢻⠃⠀⠀⢳⡹⡄⠀⠀⠀⣿⠀⠀⢰⣭⢇⠀⡇⠀⠀⣸⠋⠉⠉⠉⠉⠙⡶⠤⣄⡀
⠀⠀⠀⡇⢸⠀⢠⠒⢺⣇⢹⠀⠀⠀⢸⠀⠀⠀⠘⠛⠀⡇⠀⠀⣧⣀⠀⠀⠀⠀⢀⣽⠀⠀⠈⠑⢢⣄
⠀⠀⠀⢻⡘⡤⠚⣩⢧⡏⡾⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⣷⠀⠀⡇⠀⠉⠉⠉⠉⠁⣾⠀⡀⠀⡰⢁⠨⣇
⠀⠀⠀⠀⠳⣵⣶⣧⣾⠞⠁⠀⠀⠀⢸⡀⠉⠓⠒⠒⠛⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣸⢰⢠⡇⣏⡀⣼⣇⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⢽⡶⠦⠶⠖⠋⠙⠲⠤⢤⣤⣤⠤⠴⠚⢳⡤⢄⣀⣀⣀⣤⡏⠈⠉⠚⠓⠋⠉⠉⠀⠉⠓⠦⣄⡀
⠀⠀⣠⠶⠶⠤⠮⣄⣠⠴⠃⠀⠀⠀⠀⠀⣴⠤⠗⢲⡀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⡤⠒⠒⢶⠤⢤⡀⠀⠀⠀⠀⠈
⠀⠀⠙⠲⠼⠤⠤⠼⠀⠀⠀⢠⡂⢉⠋⢙⡧⠭⠭⣽⠷⢎⠉⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣼⣠⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣭⣭⠽⠃⠀⢰⠁⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⣿⣿⡇⢸⣿⣿⡇⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣇⣸⣿⣿⣇⣸⣿⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉⡉⢉⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⡉⠉⣹⡿⠋⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⡿⠋⣠⣾⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⠖⢀⣴⣿⣤⣤⣤⣤⣼⣿⣿⣿⣿⠟⣋⣥⣤⣶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣁⣀⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠋⣼⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⢀⡴⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠈⠳⣄⢀⡴⠋⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠈⠉⠙⠲⣄⠀⠈⠿⣄⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⣀⣤⠴⠞⣧⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⡤⠶⠚⠛⠉⢁⣀⣤⠴⢾⠄⠀⠀⠀⠙⢶⣤⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡤⠶⠖⠛⠉⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⢶⣶⣶⡶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡷⣿⣿⣿⢸⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⢿⣿⣿⣿⣿⡿⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠓⠒⠒⠒⠒⠒⠒⠒⠒⠚⢷⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⠉⠛⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠐⡄⠀⠈⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠐⠈⠀⠀⠀⢀⡀⠄⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠄⢀⠀⣀⠄⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠟⢶⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⡀⠀⠀⠈⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⠀⣸⠃⡇⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠂⠁⠀⠀⠀⢀⡀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠁⢰⣯⡴⠷⢀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⠀⠀⠀⠂⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⡿⢏⠀⠀⢀⢱⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⢠⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢘⣰⠀⠀⣿⠛⠛⠛⠛⠶⣤⣀⠀⠀⠊⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⡴⠞⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⢠⡖⠂⡖⢲⣰⣄⣶⢰⡂⡴⠲⣴⣖⡆⢶⢀⣶⡀⣖⡆⡆⠀⣶⠂⠠⣖⣰⠀⢰⣆⢰⣖⢰⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠈⠈⠈⠈⠀⠈⠉⠈⠉⠁⠈⠈⠉⠁⠉⠉⠉⠁⠉⠁⠀⠉⠉⠉⠈⠉⠈⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⡇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣸⣿⣀⣀⣸⣇⣀⣀⣿⣇⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣴⠟⠋⠉⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⠀⣿⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠉⠉⠉⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⠶⠶⣶⠀⠀⣶⠶⠶⠿⠀⠀⠀⠀⠀⣿⣷⠀⠀⢀⣀⣀⣤⣤⣴⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠛⠛⠋⠉⠉⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⣿⡀⢶⡄⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⣧⠈⠻⣦⣤⣤⡀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠁⠀⠀⠙⢷⣤⣀⣀⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⡀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢧⢰⢻⡇⣾⣩⠆⣶⠙⡇⢰⢠⡎⠁⢐⣩⡆⢹⠋⢷⢠⠎⢱⡄⡖⠙⡆⢾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠘⠃⠙⠒⠂⠙⠒⠃⠘⠀⠓⠒⠙⠒⠃⠘⠂⠙⠈⠓⠚⠁⠃⠀⠃⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢁⡠⠀⢠⡀⠀⠀⣖⠆⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⣿⠁⠠⠾⡽⠛⠀⠀⠀⣀⣤⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⢱⣟⠀⠀⠀⠉⠀⠀⠐⠋⢡⠇⠀⢘⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠘⣿⠀⠀⠀⢠⣤⠀⠀⠀⠿⠖⠃⠾⠶⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠘⡄⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠹⡄⠈⢦⡈⠻⢶⣤⣀⣀⣀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣹⣉⣿⠀⠀⠀⠀⠈⠲⣄⡈⠑⠒⠒⠛⠛⠉⣀⠀⡶⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠉⠉⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⣝⡼⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠁⠀⠁⠈⠁⠙⠒⢦⡀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⣀⣀⣀⣀⣀⣀⣈⣇⠀⠀⠀⠀⠘⠁⠀⠘⠁
⠀⠀⠀⠀⠀⠀⢸⠉⠩⠭⠭⠭⠭⠭⠭⠭⠭⠍⣿⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣈⣉⣉⣉⣉⣁⣀⣀⣿⠀⠀⠸⢄⣀⣀⣿⠿⢿⣿⠆
⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣿⠀⠀⣰⣶⡦⢄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⢿⡷⠛⠢⣄
⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠏⠀⠀⠀⠀⠀⠈⠒⠄⠼⠁

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⢠⣄⠀⠀⢸⣿⡇⢾⣿⣦⣰⣿⡿⠀⠀⡟⢻
⠀⠀⠀⢀⠀⡘⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⣤⢄⢿⣿⠇⠀⢸⣿⡇⠀⢹⣿⣿⡟⠁⠀⠀⡇⢸
⠀⠀⢀⣾⡞⠀⠀⠀⢀⠔⢲⠀⢀⠠⠶⠂⠀⠀⠸⢿⣿⣶⡄⠀⠀⢸⣿⡇⣰⣿⡿⢿⣿⣦⠀⠀⣧⣼
⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠀⠀⠸⢿⠇⠘⠛⠀⠀⠙⠋⠀⠀⢿⡿
⠀⠀⠁⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣠⣔⣂⠁⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠆⢠⡀⢸⡇
⠀⠀⢠⠤⠤⡄⠀⠁⠀⠀⠀⠀⠀⣴⡾⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠁⠔⠀⢥⡴⢸⠁
⠀⠀⠈⠈⠉⠁⠀⢈⠓⠶⠚⠇⢸⠋⣠⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣄⡄⠐⢃⠠⣴⠌⠁
⠀⠀⠐⠢⠤⠀⡆⠀⠀⢱⣶⠂⠀⠀⠫⠊⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣤⠲⠆⢽⠆⠁
⠀⢀⡅⠀⠀⠀⡇⢈⠀⢘⠦⠀⠀⠀⢰⣶⣤⣤⣤⣴⣾⠀⠠⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⢀⡀⠒⡀
⠀⠈⠢⠶⠒⠚⠁⠀⠒⠺⠕⠀⠀⠀⠈⠻⣿⣿⣿⠿⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳
⠀⡀⠐⢀⠀⡄⠀⠀⠀⠰⢄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠃⠀⠠⠒
⠀⠻⠶⢎⣠⡼⠀⠀⠙⠒⢫⡄⠐⠊⠀⠀⠀⠀⠀⠐⢄⠀⠶⣦⣶⣄⡊⠀⠀⠀⠂⠀⠉⠁⢀⠀⠁⠘⢸
⠀⠰⣤⣤⠁⡀⠀⢀⠀⠘⢒⠀⢤⠄⠀⢀⡘⠛⢀⣿⠈⠀⠐⣫⣿⣿⡿⠀⠀⠀⣀⣤⣴⣦⠀⠀⠀⠅⡇
⠀⠀⠀⠀⠀⠙⠛⠫⣄⠠⠿⡗⠀⠀⠀⠘⠻⠖⠈⠁⢀⡀⠀⠀⠚⠁⠀⠀⠻⣿⣏⣹⣿⡟⠀⠀⢨⣽⠇
⠀⠀⠀⠠⠀⠀⠀⠀⠈⠳⡄⠈⠲⣄⠀⠀⠀⠀⣠⣴⡿⠛⠁⠀⠀⢰⣶⠆⠲⠿⠟⠙⠙⣷⣶⡄⣼⣿
⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠈⢢⡖⠘⢷⣄⠀⡾⠟⠉⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡀⠀⠀⠈⠀⠇⢠⢐⡴⠮⠀⠋⢸⡏⠉⢹⠀⠀⡠⣿⣄⠀⠀⠸⣼⠃
⠀⠀⠀⠀⢄⠀⠀⠀⠀⢸⣏⣿⣹⡇⠀⠀⠰⠬⣕⠻⠦⣵⡚⠣⢾⡇⠀⢸⠀⢰⣵⣿⣿⠀⠀⢠⡏
⠀⠑⠒⠒⠙⠿⠶⠿⠃⠈⠁⠉⠈⠁⠀⠀⠀⠐⠊⠠⠄⠒⠀⠤⠘⠿⠿⠟⠀⠀⠙⠛⠋⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠰⠶⡶⠀⣠⡄⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣞⣁⢀⣞⡀⣠⠃⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⠟⣡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠁⠀⠙⠺⠿⠛⠁





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

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠛⠿⠿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠋⠉⠛⢛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⠀⠀⠀⠀⣤⠀⠐⠒⠂⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⢂⡀⢉⣍⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠰⠶⠀⣀
⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠚⠛⢤⣤⣌⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⢀⡏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠘⠢⠄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤
⣿⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠐⢿⠟⠁⠀⠹⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⡀⠀⠀⠀⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⣀⠀⠒⠒⠒⠒⠒⠶⠶⢤⣤⣄⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⣿⠀⠀⠀⠀⢉⣤⠀⠀⠀⠄⠀⠀⠀⠀⠸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠘⠟⣀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡿
⣿⠀⠀⠀⠀⠀⠸⠯⠀⠂⢀⣀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠛⠁⠤⣤⣤⣤⣤⣤⡤⠤⠿⠿⠷⠼
⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠛⠲⢶⡶⠖⠊⠉⠉
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⣿⠀⠀⠀⠒⠒⠐⠀⠀⠀⠀⢶⡆⠀⠀⠀⣻⣤⣤⡀⠀⠀⠀⠀⠀⠐⠉⣿⣥⣤⣤⣤⣤⣤⣤⣄⢀⡐⠂⠙⢶⣀⣠⣤⣤⠀⠀⠀⣤
⣿⠀⠀⢸⠀⠀⢄⠀⠀⠀⠀⠈⢶⡄⠠⠴⠁⠀⠠⠀⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⢠
⣿⠀⠀⢸⠀⠀⡌⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠐⠋⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⢸⠀⠀⠇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸
⣿⠀⠀⢸⠀⠀⢰⡄⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⢸⠀⠀⠈⢁⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣿⠀⠀⢸⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃
⣿⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⣿⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂
⣿⠀⠀⠀⣿
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⠀⠀⠀⣿⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⣿⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⣿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢸
⣿⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇
⣿⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⣿⠀⠀⠀⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠀⠉⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⡇⠀⠀⠀⠀⠰⠈⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⢸
⣿⠀⠀⠀⡇⠀⢠⠜⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠀⠀⣆
⣿⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⣿⠀⠀⠀⠈⠙⠛⠓⠚⠛⠒⠛⠛⠛⠛⠓⠒⠢⢤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠒⠛⠛⠛⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢦⣤⡴⠛
⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⡿⠿⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠠⣄⣀⡀⠀⢀⠀⢀⣴⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢱⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠱⠀⠀⣸⢳⡖⠀⠀⠈⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢀⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡤⢺⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⢉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⠀⠛⠛⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠐⣾⠶⠴⠛⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⡿⠇⠀⠀⢱⣌⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⢀⣠⣴⢧⠀⠀⠈⠁
⠀⠀⠀⠠⢄⠀⠀⠀⠀⢀⠀⠀⠐⠤⡄⢶⠾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢽⣛⣛⣯⡅⠀⢣⠁⣠
⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻⣋⠙⠻⠿⢿⡄⠀⠈⠒⠁⠀⠀⡀
⠀⠀⠀⠤⠴⠂⠀⠀⠀⡠⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠾⣿⢽⣯⡷⠄⠀⠀⠉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⡁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⡗⠀⠀⢁⡀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⠀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠚⠛⠛⠛⠛⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⢿
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠫⣉⠀⠸⣄⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⠟
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⡄⢸⠙⠛⠒⠒⠶⠦⠴⠤⠶⠶⠖⠚⠛⡃⣠⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⣜⣀⣤⣀⡀⠀⠀⠀⠀⠹⣼⡇⠂⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⢰⣿⠧⠤⠤⠤⠤⠴⢿
⠀⠀⡴⡿⠋⠉⠙⢦⡹⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⡤⠤⡄⠀⣿⠀⠀⠀⢸⡿⠶⠤⠤⠤⠴⠶⣏⣀
⠀⡼⢰⡇⠀⠀⢀⣈⣧⠘⡆⠀⠀⠀⠀⡇⠀⠀⠀⠷⢮⡤⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⡏⠉⠓⠦⢤⣀
⠀⣇⢸⡇⠀⢾⣁⣈⢿⡄⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⢸⠀⠀⠀⣿⠤⣀⣀⠀⠀⢀⣀⡤⡇⠀⠀⠀⠀⠈⣹⠦⡄
⠀⢹⡀⢧⠔⠋⢩⠿⣼⢡⡏⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠉⠉⠉⠉⠁⠀⡧⠀⡀⠀⠀⡞⢁⡀⣿⡀
⠀⠀⠳⣜⡦⢴⣋⣴⣣⠞⠀⠀⠀⠀⠀⢿⠈⠙⠓⠶⠶⠶⠖⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⠁⡄⣸⠀⡏⠀⢀⣽⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠳⢤⣀⣀⣀⣀⡤⠾⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⡀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠲⢧⣿⣤⠽⠳⠾⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠤⠒⠻⠉⢹⡄⠉⠉⠀⠀⠀⠀⠀⣉⣉⣉⡛⠛⠋⠉⠀⠀⠈⠳⣭⣓⣒⣒⣒⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄
⡞⠋⠉⡛⠛⠓⢦⡴⠒⠋⠀⠀⠀⢀⣀⣀⡀⡾⣒⣂⣉⣹⡆⠀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⢹⠉⠓⢦⡀
⠉⠒⠲⠧⠤⠤⠼⠁⠀⠀⠀⢠⡎⠁⡸⠉⢉⡷⠦⠭⠭⣾⠖⠫⡁⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣼⡤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣙⣛⣛⡩⠇⠀⠀⡼⠁⠀⠀⣰⠞⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣹⣟⣿⣿⣿⣿⡿⣏⣿⣿⣿⠀⠀⠀⠖⢠⠀⠀⠀⠀⢨⠸⠃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⡿⠚⠋⠉⠛⠾⣿⣿⣿⣿⠀⠀⠀⠀⣀⣭⣶⣶⣦⣅⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣽⡀⠈⢯⡽⠋⢀⣼⣿⣿⣿⠀⠀⠀⠋⢿⣿⣔⣓⣼⣿⠟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠄⠒⠓⠘⠉⠈⠉⠁⠛⠃⠲⠆⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠉⠁⠀⢀⣀⢀⣤⠀⠤⠄⢤⡄⢀⣀⠀⠀⠀⠘⠓⠀⠀⣠⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠋⠀⠀⣀⠰⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠓⠀⠀⠀⣠⠞⠁⣰⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠋⠀⢀⡴⠈⠁⠀⣀⣤⠶⠒⠛⠛⠋⠛⠛⠀⠀⠀⠀⣀⡤⣤⠞⠁⡀⠀⣏⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⠀⠴⠃⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⢀⡴⢾⠛⠲⣴⠞⠉⠀⣸⠃⠀⠉⢤⡈⠉⠠⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠍⠀⠀⠞⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢀⣴⠻⣆⠈⠳⣄⠈⠳⢤⡾⠁⠀⠀⠀⠈⢡⡀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⢀⡍⠀⠀⠞⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⡴⢯⠙⢧⡈⠷⣄⠈⠳⣄⡀⢳⠀⠀⢰⡄⠀⠀⢡⡀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⣨⠁⠀⠸⠂⠀⣸⠁⠀⠀⠀⠀⢀⣴⡛⢧⡈⠳⣄⠙⠦⠈⠀⠀⠈⢙⡞⠀⠀⠀⢳⠀⠀⠈⣅⠀⠀⣦
⠀⠀⠀⠀⠀⠀⡋⠀⠀⡶⠀⠀⠏⠀⠀⠀⢀⡴⢿⡈⢳⡄⠛⢦⡈⠃⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠸⡇⠀⠀⢉⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡃⠀⠀⡆⠀⠀⠀⣤⢀⡴⢏⠀⠈⠻⣤⡈⠳⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢘⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠇⠀⠀⣦⠀⠀⠀⠈⢿⡀⠈⢧⡀⠲⣌⠁⠀⠀⠀⣠⡾⢃⣤⠖⠛⠋⠉⠛⠲⢦⡀⠁⠀⠀⠚⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠻⠀⠀⠈⠀⠀⠀⠀⣨⠷⣄⠀⠙⢦⣈⢷⡀⣠⠞⠉⣠⠏⢀⡴⠛⠉⠉⠛⢦⡄⠙⣆⠀⠀⠋⠀⢀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠞⢁⣴⠟⢳⣄⡀⠉⣳⠟⠁⠀⢠⡏⠀⡞⠀⠀⠀⠀⠀⠀⢹⡄⢸⡆⠀⠀⠀⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠙⢾⡁⠰⠟⢁⡴⠋⠈⠙⠻⣧⠀⠀⠀⠸⡇⠀⢳⣴⣒⣶⢴⡒⣶⣼⠁⢸⡇⠀⠀⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢦⡴⠋⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⢳⡀⠸⢬⣍⠱⠒⢩⡥⠟⢀⡾⠀⠀⡐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣹⠇⠀⠀⠈⠙⠓⠶⠦⢤⣤⠤⠄⠙⢦⣀⡉⠛⠛⠋⣀⡴⠟⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⢠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⣄⠀⠀⠀⠀⠙⠃⠒⠒⠐⠒⠀⠋⠀⠀⠀⢀⣠⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠦⠄⣤⡀⣀⡀⣀⣄⠠⠤⠐⠛⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⡾⠤⠜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣴⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢸⣿⢠⣶⣶⣶⣶⡄⠙⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆
⠀⠀⠀⠀⢸⣿⣸⣿⣿⣿⣿⣃⣠⣿⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⢿⣿⣿⣛⣻⣿⣿⡿⠿⢿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣤⣤⣤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠛⠛⠛⣿⣿⣿⣿⠛⠛⠛⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⡀⣠⠤⠤⢤⣤⣤⣀⣠⣤⠤⣴⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣰⣇⠀⠙⢥⣀⣀⣀⣿⣿⣿⡀⣀⣸⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠈⠳⢤⣴⣿⣯⠉⢻⣿⣿⣋⡉⢉⣽⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡶⣤⣀⣀⣾⣿⣿⠶⠛⠉⣽⣿⣿⠟⠻⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣬⣍⣛⣛⢋⣀⣤⡴⢞⣛⣉⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠦⢉⡳⢠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣿⠄⠀⣽⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠥⣈⣻⠀⢨⠃⠾⡄
⠀⠀⠀⠀⠀⠀⢀⡤⣄⡀⠰⣾⣗⠉⠉⣡⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣀⠀⣯⢉⣏⠉⣉⡥⣤⡀
⠀⠀⠀⠀⢀⣴⣿⣷⡀⠙⢦⠻⠛⡵⠋⢀⣼⣿⣦⡀⠀⠀⠀⢀⡤⠊⠈⢆⠉⠳⣮⠤⢺⠞⠁⡰⠁⠑⢤⡀
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣌⠇⠸⣠⣴⣿⣿⣿⣿⣿⣆⠀⢠⠊⠀⠀⠀⠀⠙⠢⢽⠄⣯⠴⠊⠀⠀⠀⠀⠑⡄
⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⠻⣿⣿⣿⣿⣿⡟⠀⠘⡄⠀⠀⠀⠀⢀⠔⠁⠀⠈⠲⡄⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠙⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠋⠀⠀⠀⠙⠢⠤⠤⠒⠁⠀⠀⠀⠀⠀⠈⠒⠤⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴⠒⠉⠉⠁⠠⠤⣀⣀⣠⡤⠶⠚⠛⠛⠒⠤⣀⠀⠀⠀⢀⣀⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠑⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢀⠠⢄⠠⡝⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠁⠀⠉⠀⠁⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠦⣄⠈⢓⠔⠁⠀⠀⠀⠀⠀⢀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡴⠟⠁⡀⠀⠀⠘⡆⠀⠀⠀⢂⠒⠀⣀⠔⠫⠊⠁
⠒⠒⠀⠉⠉⠁⠐⠒⠒⠪⠭⠵⠒⠤⠤⣀⣀⣀⣀⣠⡤⠂⠙⣠⠖⠋⠀⠀⠀⠀⠸⣄⠀⠀⠀⠁⠀⢰⠀⠀⢀⠀⣤⡴⠶⠚⠛⠋⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠤⠤⠄⣀⣉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠒⠒⠁⠠⢸⠀⠐⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣄⣀⠀⠈⠉⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠸⠀⠀⠈⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⡀⠀⠀⠈⠣⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠐⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢀⡴⢀⠀⣄⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢣⠀⠀⠀⠀⠐⠁⠀⠀⠑⠮⣆⠀⢸⡇⠀⠀⢀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠙⠶⣭⡉⠁⠀⠐⠒⠒⠀⠈⠑⠘⠁⠀⠀⢸⣤⣼⠂⣨⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀⠈⢢⡉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠀⠐⠊⢀⠀⠘⠓⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠾⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠑⡀⠀⠐⡇⠁⠐⠛⠂⢀⠀⠀⠀⠀⣸⠃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠉⠑⠫⠴⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿