Fruity Emojis & Symbols

⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢴⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡴
⠀⠀⠀⠀⠀⡴⢋⣀⠄⢀⡞⣷⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⡼⠁
⠀⠀⠀⠀⠈⠀⠉⣀⡴⠟⠁⣿⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠀⠤⠒⠋⠉⠀⠀⠀⣿⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢳⣶⠟⠛⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠉⠙⠋⠉⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣸⠃⠀⠀⠀⡔⠘⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠉⠉⠙⢻⡄⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣸⠇⠘⠢⢤⣠⠤⠞⠁⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⡽⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠷⢂⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣰⢟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡆⠀⢀⣴⠶⠾⠲⠶⣤⡀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⢀⣱⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠈⠻⠿⣶⣶⡶⠿⠋
⠀⠀⠀⠀⠀⠀⢠⠖⣦⡰⠀⢤⢀⣤⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠘⢆⠸⣷⢁⣾⣥⣾⣤⣀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⢴⡚⢲⡤⣄
⠀⠀⠀⠀⣠⠖⠒⠚⢂⣽⠾⠋⠁⠀⠉⠻⣧⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⢘⡥⢤⡿⠛⠦⣤⠷⢤
⠀⠀⠀⠀⠈⠓⣶⡾⠋⠁⡀⠀⠀⠆⠀⠀⢹⣇⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣧⣸⠀⢀⣧⡀⠀⠘⠣⠚⢷⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠁⠀⠀⡄⠀⠠⠈⣿⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⣰⢸⡏⠙⣇⠀⠈⡷⠒⢺⠙⢻⡅
⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠰⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠹⣮⡳⠶⢾⡓⠛⢷⣤⡴⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠠⠀⠰⠀⣿⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣤⣤⣤⣤⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⣤⣬⣿⠶⠚⣹⠶⠋
⠀⠀⣀⡀⠀⠀⠀⠀⠉⠲⢤⡁⠀⠠⡀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⠶⠟⠶⠶⠋
⣴⠋⢹⣷⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠘⢆⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢻⣿⣿⠆⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠐⠶⣤⣄⡀
⠀⠈⠂⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠈⢀⡟⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⣀⠀⠉⠻⣦⡀
⠀⠀⠀⢀⠘⠛⠙⠛⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣰⡟⠁⠀⢀⠀⠀⠀⠀⢀⡟⠲⣄⠈⢻⣆
⠀⠀⠀⣿⡇⠀⢄⡀⠀⠀⠀⠈⠙⠛⠷⠶⢶⣤⣤⣤⣤⣤⡤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⣿⠀⢀⠀⠀⠑⢄⠀⠀⠌⠀⠀⠘⣆⠀⢿
⠀⠀⠀⠸⣷⡀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⢀⣾⠏⠀⠀⠀⠀⢸⣿⠀⣼⠀⢀⣀⡤⢽⡿⠂⠐⠒⠒⢻⠀⢸
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠈⠙⠛⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠟⠋⠁⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠘⣿⡀⠸⡏⠉⠀⣠⠏⢠⠈⠢⣄⠀⣼⠀⢸
⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠹⣄⡰⠃⠀⠀⣇⠀⠈⣻⠃⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡈⠛⠶⠦⠤⠾⠶⠛⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣤⣤⣶⠾⠟⠁

⠀⠀⠀⣀⣄⡀
⠀⢠⣾⣿⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⢀⣀⣀⣴⣷⣦⣤⡀⠀⢠⣤⣆⣶⣿⡄⠀⠀⠀⣄⡀
⠀⣸⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⢃⣤⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⡧⠄
⠀⢻⣿⣿⠿⠋⠁⠀⠀⠀⠈⢿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠙⢿⣿⡿⠁⠀⠀⠀⢨⠁
⠀⠀⠈⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⢉
⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⢠⣾⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠸⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡶⠀⠀⠀⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠁⣀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⡀⢈⣀⣠⣤⣤⣀⠀⠀⢀⣠⣀⣾⣿⣿⣧⣠⣄⡀⠀⣾⣿⣿⣶⡀⠀⣴⠿⣿⣿⡃⠀⠰⣶⣾⣿⣿⠆
⠀⢸⣗⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠛⠛⠛⠛⠓⠀⢻⣶⣴⣿⠗⠀⠈⠉⠛
⠀⠈⠻⣿⣽⣿⣿⠿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⢠⣤⣤⡦⠀⠀⠈⠿⠿⠇
⠀⠀⢀⣠⣤⣆⣤⡀⠀⠀⠀⠀⢀⣀⢈⡙⠛⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣤⣤⣄⡀
⠀⠀⣽⣿⣿⣿⣿⣯⡀⠀⠀⣺⣿⣿⣿⣿⡀⠀⠀⣶⣦⣶⣶⣦⠀⢀⣾⡹⣼⣏⢿⣷⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠛⠉⠋⠋⠋⠛⠃⠀⠸⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⡇⠘⣿⣷⣽⠿⣸⣿
⠀⠀⢠⣤⣤⣤⣤⡤⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⠟⠁⠀⠈⠻⠿⣿⡿⠇
⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠙⠛⠋⠀⡀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⡤⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⣿⣿⣧⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⣁⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠉⠉⠁⠀⠀⠀⠈⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡴⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣄⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠉⠄⠛⠉⢉⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠤⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠
⠀⠀⠀⠀⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣀⠀⢀⡞⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⡀⠀⠘⠀⠙⠿⢷⣶⡶⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠂

⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢀⠀⢰⠂⣈⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡆⠈⠀⠈⢳⡞⢤⡴⠎⠀⠀⠹⣧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣫⡷⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠠⠆⠀⠐⣮⠛⢉⣁⡛⠞⠓⠧⠾⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠈⠢⡀⠀⠀⠀⠀⢘⡀⡄⢀⣄⢐⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⣀⣠⣤⣼⠁⠀⡈⠛⢿⢠⡎⠀⠀⠀⠀⣧⡔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⣰⣠⡿⢳⡀⠀⡁⡁⠈
⠀⠀⠀⠀⠀⠒⠒⢀⡌⠁⠀⠉⠓⡄⡌⠋⠀⠁⠀⠲⠐⠒⠂⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⢀⣀⡥⠞⠋⠉⠓⠋⠀⠀⣀⠇⢠
⠀⠀⠀⠀⠀⠀⠀⠼⠃⢄⣀⠀⠐⠻⢀⡇⠀⡀⠀⠀⠀⣀⠀⠀⢠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⡋⠀⠀⡀⠀⠀⡀⠤⡀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣠⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠤⣀⡉⠒⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠌⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠦⢞⠖⣲⣆⠁⡈⠴⠂⢒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢰⣃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠋⠙⠁⠀⠀⠀⠈⢿⣯⠦⣨⣿⡋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⢿⡂⠀⢠⠶⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⣈⠀⢘⣹⣷⢯⠁⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠐⣄⣀⣐⡦⢄⠞⠉⠀⡛⢢⣠⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⣤⠀⠀⡙⠉⣲⣉⠹⠞
⠀⠀⠀⠀⠀⠈⠀⠀⠶⡏⠀⠀⠙⡋⠙⣤⡄⠏⠉⠉⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⡡⠃⢤⡄⠀⡴⠿⠑⠋⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠲⠀⠀⢠⢤⠄⠞⠁⠀⠈⠉⠈⠀⠎⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠱⣆⠂⣽⢧⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⠁⠘⠛⠃⢄⣀⠀⠀⠀⣁⠜⠂⠀⠀⠁⠀⠀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠒⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠑⠒⣤⡀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡰⣠⠄⠳⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣹⡿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⡠⣀⠀⢨⡿⠒⠛⠁
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⠙⠗⠃⠀⢱⠀⠀⠀⠀⠸⣅⠠⣙⠢⠄⠀⠠⠤⣒⠾⢁⡜⢉⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡩⠷⠤⡜⠓⢦⡗⠻⡅
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⢜⠷⢄⣉⡐⠒⢈⣉⡤⢖⠩⣢⢞⠏⢸⠀⠀⠀⠀⠀⠀⢀⢠⠎⢉⠖⠀⠲⣏⠟⠉⠉⡖⢧
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠫⣀⣒⡤⣭⣭⡥⢄⣒⠥⠚⡡⠋⢀⠆⠀⠀⠀⠀⡔⢊⣇⢈⠖⠳⣀⣀⣠⣏⣐⠤⠚⣷⠼⡀
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢿⠀⠭⠍⣉⣉⠡⠤⠖⠋⠀⢀⠎⠀⠀⠀⠀⠀⠓⠾⡀⢩⠣⢤⠼⠤⡆⠀⠈⡷⠚⣷⡴⠃
⠀⠀⠈⠲⢄⡀⠀⠀⠀⢂⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠓⠒⠋⠒⠊⠉⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠆⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡲⠖⢶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡈⣇⠙⠈⡞⡿⡆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠘⢦⡈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⡠⠊⢠⠌⢙⠳⣄⠋⠀⡗⢀⡢⠄⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⣠⢟⣀⡀⡀⠀⠀⠀⠀⠀⢠⠏⡄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠸⡄
⠀⢀⠜⠃⠠⠄⠀⢉⡁⠘⠳⡄⠉⣙⣆⠀⠀⠐⠥⡀⠀⠀⠀⠀⠀⠀⠀⠚⢡⣾⡷⡅⠀⠙⡮⠙⣦⡀⠀⠀⢸⡀⢇⣀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇
⢀⡾⠈⠃⢀⢄⠀⠑⠁⠦⠆⠹⡑⢿⡌⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⣀⡴⢻⠥⢷⡦⢵⡪⠔⢒⢼⠹⡄⠀⠀⠳⣄⠘⠦⠤⠀⠀⠀⣠⠏⠀⣀⡴⠃
⡸⠤⠰⠆⠀⠈⠀⠘⠀⠠⣢⢀⡇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⢹⡤⣚⢧⡦⣝⠲⠞⡼⠀⠙⡄⠀⠀⠀⠉⠓⠒⠒⠒⠉⠉⠉⠉⠁
⡷⠂⠰⠀⠀⠃⠀⠐⠓⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣸⢀⣀⢗⡔⢁⡴⠚⠁
⠙⢤⣷⣀⣛⣠⠴⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡆⣿⣶⣿⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⣠⠖⠒⣓⡲⢶⡶⠀⠀⠀⠀⠀⠀⠀⠛⠻⡗⠦⣿⢹⡟⡷⠟⢫⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡘⣾⠔⠂⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠳⡈⡧⠛⢈⣩⠽⠟⠒
⠀⠀⠀⠀⠀⢀⣤⢄⣀⢀⡦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⢷⡹⠲⠤⠤⠤⠾⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣯⠿⣰⣶⠗⠺⣿⢦⡌⠶⡄
⠀⠀⢀⡤⢚⡩⠝⠦⢠⣙⡦⠘⠖⠲⣌⠙⠢⡀⠀⠀⠀⠀⢰⢡⢊⠀⠀⠒⠾⠗⠂⠀⠀⠀⢀⢹⠀⠀⠀⠀⠀⢀⡤⢚⣩⣉⠉⣄⣚⡞⢿⠢⢸⠚⠇
⠀⢠⠏⠰⠟⠒⢸⡣⢶⢰⠦⢬⣯⠉⠉⠀⠀⢹⠀⠀⠀⠀⠘⣆⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⣰⠋⢉⠀⠀⢃⠀⢰⠀⠘⠉⡇⠸⠂
⠀⢼⢀⠀⠀⠀⠈⠀⠘⠇⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡟⠀⠀⠀⢰⢧⠀⠸⠒⠒⢺⠀⠘⠓⠒⣷⠇
⠀⠸⣜⢄⡠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠁⠀⠀⠀⣇⢠⣀⣀⣇⣀⣸⠀⢤⠆⢰⠏
⠀⠀⠈⠳⠤⣤⣅⣈⣉⣡⣠⣤⣤⡤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣠⠤⢄⣀⠀⢀⡴⠃⠀⠀⠀⠀⠸⡼⡄⣀⣇⠀⣘⣀⣸⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣇⣸⠥⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣰⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣐⠤⣀⠀⠀⠀⠘⠁⡤⠞⠓⠄⢀⠠⠂⠀⠀⢀⣘⣷⣻⢆
⠀⠈⠒⠦⠘⠄⠀⢀⡰⠀⠀⠘⡆⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣄⠀⠀⠀⠀⠀⠘⠛⠮⠻⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠈⠐⠃⠀⠡⠖⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢠⠀⢄⡀⠀⠀⠙⠄⠀⠀⠀⠀⠒⡵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠈⠈⡀⢁⠀⠑⠀⠀⠸⣄⠴⠋⠱⡀⠀⠀⠂⠀⠀⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠑⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢁⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠤⠙⠂
⠀⠉⠃⠀⠈⠉⠒⠠⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⣀⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠴⠒⠂⠀⠀⠀⠠⠀⡠⠃⠂

⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀⣀⡀⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠉⠁⢉⠀⠈⢸⢳⠂⠀⢀⠴⠋⢠⠄⠀⠀⠈
⠀⠀⠀⠘⠀⠀⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂

⠀⠀⠀⠀⣀⠄⠒⠂⠒⠐⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣒⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡉⠓⢢⣄
⠀⠀⡴⠋⠀⠀⠀⠀⠀⣸⣢⡄⠑⡄⠀⠀⠀⠀⢠⡦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣾⣽⡿⡛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⡤⢄⠀⢸⡏⠉⠉
⠀⠜⠀⠀⠀⠀⠀⠀⠀⡈⠗⠉⠀⠘⡀⠀⠀⠀⠸⣄⠠⢍⡢⠤⠤⣀⣲⠽⢂⠜⢀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⣎⡩⠛⠒⣎⣉⣲⡏⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡺⠓⠤⢬⣉⣁⠤⠔⡚⢕⡠⣫⠃⡇⠀⠀⠀⠀⠀⣀⠄⡎⢠⠛⠀⠙⣧⠋⠀⢸⡋⢧
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢳⡴⠥⣶⣖⣶⡮⠭⠒⣉⠔⠁⠠⠁⠀⠀⠀⢰⠉⡼⢤⣌⠈⢢⠤⠴⠇⠬⡛⢉⡗⢳
⠀⠘⢆⡀⠀⠀⠀⠀⢀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠈⢣⡈⠒⠒⠂⠐⠒⠉⠁⠀⡰⠃⠀⠀⠀⠀⠀⠉⠳⠤⢎⡑⣎⠓⣧⣀⣠⢏⡡⠗⠊
⠀⠀⠀⠙⠒⠠⠤⠤⠄⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⣀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⢲⠰⠏⣦⢿⡆⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠊⠁⠸⢅⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠠⠐⣈⠒⠳⣄⠰⠊⠰⠀⢠⡀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢱⠀⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢧
⠀⢀⠔⠃⢠⠀⠀⠃⠘⠷⣄⠙⡚⢅⠀⠀⠰⣁⠀⠀⠀⠀⠀⠀⠀⠰⠊⣴⣯⡎⠉⠓⣝⠲⣄⠀⠀⠀⡇⢸⣀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢸
⢀⡾⠸⠂⢀⡀⠘⠛⠠⠂⠘⡗⢿⡍⠁⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⣠⢞⡯⢷⣤⢤⠊⠔⢢⢩⢣⠀⠀⠘⢄⡉⠦⣤⠀⠀⠀⣠⠏⠀⣀⡼
⡘⠤⠰⠄⠈⠁⠀⠆⠀⣤⠄⡇⠀⠳⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠉⠀⠸⡧⢔⢧⡦⣑⠢⠞⡎⠈⢣⡀⠀⠀⠉⠓⠒⠒⠒⠊⠉⠙⠉⠁
⡷⠂⠲⠀⡘⠀⠀⠚⠀⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣧⣸⢀⡠⢇⠜⣠⠔⠋
⠙⠶⣧⣬⡭⠤⠞⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠓⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠠⣆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⣿⣆⣿⡾⣗⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⢦⢀⡤⠚⡉⠭⠟⢻⠛⠀⠀⠀⠀⠀⠀⠉⠙⢯⠓⣿⢹⡏⣗⣋⣽⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣆⢻⡊⠁⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣉⣙⠄⣖⣉⣠⠶⢋⠉
⠀⠀⠀⠀⣀⠶⣖⠲⢤⡟⠲⡔⠦⠤⢄⡀⠀⠀⠀⠀⠀⣠⢞⠉⠀⣀⢸⣼⡉⠓⠒⠊⠙⡆⠀⠀⠀⠀⠀⠀⢀⣤⠴⢶⡛⣚⣿⣉⡙⢟⣷⠐⠛
⠀⠀⡴⢋⣔⣂⣉⠁⠛⠙⠀⣭⠭⠷⠀⠙⢆⠀⠀⠀⠀⣇⠪⢤⠀⠀⠉⠉⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢀⠴⠁⠐⢢⠀⠲⠐⢯⢽⡄⢼⠈
⠀⡸⠀⠉⠁⠀⠗⠉⣧⠋⠙⠺⠆⠀⠀⠀⢸⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡟⠀⠀⠀⣰⠃⠀⣆⣀⢠⡄⢨⣄⣠⣀⠇⠈
⠀⢳⢢⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠰⣱⠃⠀⠀⢀⠏⠅⠀⢁⠀⠀⠀⠀⣄⣠⡟
⠀⠈⠳⣝⣉⠓⠛⠲⠖⠀⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠈⡇⣗⠀⢺⠀⢸⠃⢹⣁⠞
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠉⠉⠙⠒⠚⠁⠀⠀⠀⠀⠀⠈⠻⣍⣙⢀⣞⡠⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡽⣛⣻⣮⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣽⡷⣿⣿⣿⣧⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠻⠿⠿⠿⡄⢠⠊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡎⠙⠶⠾⠿⠟⢣⣤⠄⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣦⣄⣀⣰⣾⡯⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡧⡄⣤⣶⣾⣧⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⡉⣠⡆⠀⠛⢻⣾⣾⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⣿⣿⣿⣿⣿⡝⠇⠃⠁⠀⠀⠀⠀⠈⠏⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⢴⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣮⣠⢀⣠⣀⣠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣛⣛⣛⣛⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠋⠙⠛⠙⠛⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣾⣿⡿⠿⠿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⢟⣻⣯⣟⠻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣋⣭⣭⣶⡿⢷⣿⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣭⣭⣿⣶⣿⣿⣿⣼⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⣭⣷⣾⣿⣿⣿⣿⣿⠀⠀⢀⡴⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡙⣉⢉⠙⠻⣧⣀⡟⣀⡤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⠊⠉⠳⠶⣾⣿⠿⠿⠛⣠⣤⣠⠄⠀⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣦⣀⡀⡀⠀⠠⢀⣤⣾⣿⠁⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣾⣯⣽⠛⠀⠀⠀⠀⠀⠀⣠⠄⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡧⣵⢀⣴⣾⣶⣾⣿⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠽⡏⢿⢸⣉⡁⠘⠀⣿⢿⣋⣸⣭⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⢀⣠⡇⡾⢸⠿⠇⠀⠀⠃⠎⠿⢿⣿⡌⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣌⠫⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠋⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣿⣿⣿⣿⣿⣿⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⢿⣿⣿⣿⣿⣿⣿⣮⡀⡆⡀⠀⡀⠁⡀⢀⣆⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣾⣿⣷⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣾⣿⣿⣷⣿⣿⣟⣁⣈⣬⣬⣤⣭⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠻⠷⠎⠛⠙⠻⠛⠛⠛⠿⠛⠋





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠙⠀⠀⡀⠀⢉⣵⣆⠀⠀⡀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠄⠀⠀⠀⠠⠀⠘⠋⠀⠐⢁⡴⠞⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣤⡔⠁⠀⠀⠀⢀⣴⠞⠉⢀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠛⠶⣄⠀⠈⠛⠷⣦⣴⡶⠓⠈⠁⣨⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢈⠂⠰⠦⢤⡙⣿⡄⠀⠀⠞⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣀⣷⡄⠀⠀⠀⠙⠧⠀⠔⠂⢋⡤⠦⠈⡣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⠉⠛⠻⡦⠐⠿⠿⠶⠁⠀⠀⠞⠁⠚⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⣶⣤⠾⠶⣶⠮⠐⢶⡾⠂⢠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢰⠆⣀⣁⣤⡶⠦⢶⣦⣾⡷⡄⠀⣄⡈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣇⣨⢉⢹⣿⣯⣀⣾⠋⠸⣿⡿⢶⣼⣿⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢻⣿⠃⣿⡟⢠⠀⠈⣿⡡⠄⠸⢧⠀⠙⡎⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠸⣷⢴⣿⡇⠉⠀⠀⣹⠀⠀⣄⠀⢃⡿⠀⠉⢠⡔⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⣤⡘⢷⠃⠙⣇⣠⠴⠚⠹⣆⠀⠉⠀⢈⢷⡶⢄⣤⠀⣄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢿⣷⠋⠀⠀⠈⠁⠐⠶⡄⠈⣷⣀⠔⠁⠀⠛⣄⢀⡄⠁⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠁⣄⡈⠻⡴⠚⡉⠙⢇⠀⠋⠀⢀⣼⠿⡠⠴⠶⠄⠘⡟⠀⠸⡇⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢠⠀⣀⣾⡅⢻⣓⡀⢘⣧⣠⠔⠉⠀⠀⠻⣆⢀⠤⠂⢻⡂⠀⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢾⡟⣉⠉⢏⠉⠀⢉⣠⠴⢏⡒⠶⠿⠦⠄⡟⠧⢤⣄⡀⣷⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⡇⠧⡄⠈⢣⡴⠋⢀⡀⠀⠹⣀⣀⠤⠐⢿⣄⠘⠩⠉⠈⠉⠒⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣤⣧⡀⣤⠖⠘⢧⠲⠟⠧⢄⠠⣿⠀⢠⣆⠀⢘⣇⠀⠀⣠⡸⡇⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢙⢻⡇⣴⠃⠀⢀⡘⢀⣤⠄⢾⣀⠤⠟⠉⣉⠸⢷⡴⠋⠁⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡈⠻⣦⠁⠀⠈⣿⠉⠀⣀⠀⠙⣆⢠⠞⠁⠀⠀⠻⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠈⢡⣼⣿⣶⠶⠾⠟⣢⡴⠿⡄⠀⠙⣟⠀⠠⠞⠣⠀⠧⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣇⣶⣄⠀⢱⡄⢠⡶⠒⠉⠉⠳⣀⡄⠀⠘⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣆⠛⠽⢡⡼⢉⡛⠀⠠⣄⡀⠠⠥⢄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠘⢄⡙⣦⠀⠀⠀⠀⠀⠀⠀⠓⣤⣇⠀⠀⠀⠀⠀⠀⠫⣉⣲⡴⢊⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠲⣄
⠀⠀⠀⠀⠀⢠⢖⠉⠛⠓⠂⠒⢄⠀⠀⠀⢀⡎⠀⠈⢇⠀⠀⠀⠀⢠⢋⠀⠌⡉⣉⡆⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢘⡄
⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⢸⠀⠀⢀⠞⠀⠀⠀⠘⢆⠀⠀⠀⠸⡠⠀⠄⠄⢠⠃⠀⠀⠀⠀⢀⡠⠞⠁⣠⠀⢨⠃
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡜⠀⠀⡎⢰⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢄⠂⣂⠎⠀⠀⡴⠖⠍⠡⠤⠴⠚⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠘⢆⣀⡤⡠⠞⠀⠀⠀⠘⢼⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠓⠒⠐⠒⡒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢹⡀⠀⠀⠀⠀⠀⡠⣒⠒⠚⢖⠳⢄
⠀⠀⠀⠀⠀⠀⣴⠿⠂⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⣠⠒⢾⡽⠓⠻⣼⠒⠒⢤⠀⠀⢸⢱⠁⠀⠀⠈⡇⠀⢳
⠀⠀⠀⠀⠀⢼⠉⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡞⡳⣤⠼⣇⠀⣠⡿⠷⢖⠉⠀⠀⠸⡘⠀⠀⠀⠐⠁⠀⡜
⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⣸⣛⠼⠣⡄⠀⡏⠉⣣⣀⠜⠀⠀⠀⠀⠑⠤⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⡠⠔⠃⠀⠀⠀⠐⢇⡸⠦⠤⠚⠒⠋⠚⠁⠀⠀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢇⠒⠀⠂⠀⡀⠁⠀⠁⠀⠢⠀⠂⡇⡬
⠀⠀⠀⠀⠀⠀⠀⣦⡀⡼⢳⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢦⡈⢠⠄⡀⠘⠀⠈⠠⡀⢉⡜⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡴⣌⢣⠔⢉⢼⡀⠀⠀⠀⠀⡠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⡲⠤⣁⣈⣀⣉⡠⠴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢱⡤⣿⡴⠥⣜⠀⠀⠀⠀⠮⣤⡤⢾⠟⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⢀⡜⢇⢀⡼⠳⣄⡏⢦⠀⠀⠀⠀⠀⢠⢣⠂⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⢸⣤⡴⠻⢄⣠⠊⠉⡿⠀⠀⠀⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡔⠉⠒⠊⠁⠒⠂⠉⢉⠆
⠀⠀⠀⠀⠀⢻⡀⢑⣤⣞⠉⢲⠾⣸⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣀⠴⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⢟⠻⢤⣈⡽⠛⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⡀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠫⠥⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠳⣾⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⢤⣤⣤⣴⣶⡶⠾⠶⣶⣤⣀⠸⠃⠈⣷⡀⣀⣤⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠃⠀⠀⣀⣀⣀⣀⣀⣀⠈⠙⢷⡄⢠⣿⠟⠋⠀⠀⠀⠀⠈⢉⣷⣦⣀⣠
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠚⠉⠉⠉⠀⠀⠀⠀⠉⠙⢦⣼⠿⣿⠁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠨⠽⠧⠤⣴⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⢠⣤⡤⠖⣂⣤⠴⠖⣲⡿⣿⠇⣺⣿⠟⠉⠉⠉⠉⠉⠛⠳⠶⠤⠤⠴⠶⢺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣶⣛⣭⣶⣶⠟⢁⣴⠏⣼⣿⣿⢠⣤⣂⣤⡀⠀⠀⣤⣤⣤⡤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢉⡽⠋⢁⣴⠿⡟⢸⡏⠘⠻⣷⣭⣭⣭⣤⣤⣶⠶⠶⠾⠿⠆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⠟⠁⠀⢠⡟⢁⣴⠟⠁⢸⡇⢸⠁⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⣠⣶⠿⠛⡉⢉⡿⠿⠿⠷⣶⠏⢠⡞⠁⠀⠀⠸⡇⢸
⠀⢠⣾⠏⠀⠀⠀⠳⢮⡶⠂⠀⢀⡏⢠⣿⡄⠀⠀⢀⣠⣧⢸⣤⣤⣤⣤⣀
⠀⣾⡇⢠⡆⠀⠀⠀⠀⠀⠀⠀⣸⢠⡏⢸⣿⣀⣶⡿⠟⠻⡄⢫⣉⠉⠛⠛⠿⣦⡀
⠀⣿⡇⠸⣇⠀⠀⠀⣀⣠⣤⣤⡇⣼⣀⣼⣿⣿⠏⠀⠀⠀⠚⠾⠋⠀⠀⠀⠀⠈⠻⣦
⠀⠘⣿⣆⠉⢀⣴⡿⠟⠉⢁⠘⡇⡏⠉⠉⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠈⠻⣷⡿⠁⠀⠀⠀⠈⠻⣷⡷⠏⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⡇
⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣿⠇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⡴⠾⠋⣠⣾⠟
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⢰⣿⣤⣄⣀⣀⣀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠙⣷⣄⠀⠀⣀⣀⣀⣀⣤⡾⠏⢀⣴⣿⠋⠈⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠈⠙⢿⣶⣦⣭⣭⣭⣭⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉

⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢠⣿⣿⣿⣿⣦⠀⠀⣴⣿⣿⣿⣿⣆⠀⢀⣠⣄⣴⣿⣦⣶⣀⠀⢰⣴⣦⣶⣷⡄⠀⠀⠀⣤⡀
⠀⣼⣿⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⠏⣤⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⣿⡿⠶⠂
⠀⠻⣿⠿⠛⠉⠀⠀⠀⠀⠙⠿⡿⠋⠀⠙⠿⢿⣿⡿⠿⠟⠋⠀⠀⠀⠘⠿⣿⠟⠀⠀⠀⠀⠤
⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣤⣀⡀
⠀⠀⢀⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⢠⣿⣿⣿⣿⣿⣦
⠀⠀⢸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠘⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠁⠀⠀⠸⠿⠿⠿⠛⠁
⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⢀⣤⣦⣤⠀⠀⢀⣀⣰⣠⣄
⠀⢠⣄⣶⢶⣾⣿⣶⣦⠀⠀⣴⣶⣾⣿⣿⣿⣶⣶⣦⠀⣿⣿⣿⣿⣆⠀⣿⡉⢻⣿⡆⠀⠩⠿⡿⠻⠏
⠀⠸⣯⣿⣿⣿⣿⣿⡿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢀⢀⡀⠀⠀⠹⣿⣿⡟⠁
⠀⠀⠈⠛⢛⡛⠋⠁⠀⠀⠀⠀⠙⠛⠿⢿⠿⠋⠁⠀⠀⠈⠻⠿⠋⠀⠀⠀⠉⠉⠁
⠀⠀⢶⣾⣿⣿⣿⡆⠀⠀⠠⣤⣶⣷⣶⡄⠀⠀⢀⣀⣀⣤⣄⠀⠀⣰⢶⣻⡻⣿⡆⠀⠀⠀⠀⠄
⠀⠰⠿⠿⠿⠿⠿⠿⠀⠀⢰⣿⣿⣿⣿⣷⠀⢠⣾⣿⣿⣿⣿⡆⠰⣿⣏⢻⣷⢽⡷⠀⠀⠀⠀⠀⠀⠐
⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠸⣿⣿⣿⣿⡏⠀⠘⢿⣿⣿⣿⣿⠃⠀⠙⢿⣷⣭⣿⠇
⠀⠀⠈⠻⣿⣿⡟⠁⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠈⠛⠿⠛⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠠⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⢀⣄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠀⣿⣾⣤⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋
⣿⣟⣛⣟⣛⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠄⠀⡀⠀⠌⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠡⡰⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⢀⣀⠀⠀⠠⠀⣒⠂⠒⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠉⠁⣵⠂⠻⡐⠂⠠⣀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠊⠉⠀⠆⠀⠀⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⡀⢸⠃⠀⠀⠈⢲⡄⠀⠀⠀⠀⠀⣠⣾⣿⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠭⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠘⠢⣤⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠉⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠂⠀⠀⠠⠞⠉⠀⠤⡀⠀⠀⢀⠤⠤⠤⠦⠸⢿⣿⣿⣿⡿⢀⠀⠀⠀⠀⢀⣤⣶⣦
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠓⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠯⠉⢉⠔⠉⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠤⠊⠀⠐⠆⠀⠀⠀⠀⠀⠈⠉⠀⠁⠑⠀⠀⠀⠀⠀⠴⠈⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄⣠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠆⠀⠀⠀⢚⣏⠀⠀⠀⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠄⠀⠀⠠⠀⠚⠉⠀⣀⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠙⠷⢶⣶⠂⠀⢀⠀⡴⢊⣁⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠓⡄⢀⡈⢻⣾⠋⠁⢀⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⣣⡀⠈⠁⠻⡇⠀⠤⠄⣀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠛⠻⡄⠲⠶⠖⠀⠀⠞⠁⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠳⠶⠛⠲⠖⠐⣳⠃⠰⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠶⢶⣾⡟⢻⡟⣿⣷⣄⢲⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡿⢲⡟⠉⠑⢿⡀⠈⢿⠉⢻⠋⠉⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠯⢸⡶⣾⡇⠁⠀⣸⠀⢠⡀⢃⡏⠉⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣶⣙⠏⠈⢧⠔⢋⠙⢦⡀⠀⠀⢻⡒⠰⠀⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠛⠹⣏⡠⠤⢤⡀⠩⠃⠀⣷⡎⣀⣀⠙⣤⠂⣤⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡁⡈⢀⣼⠱⡦⠀⢳⣀⡠⠚⠁⠹⣅⠀⡤⢰⠄⠈⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⡟⡉⠹⡍⠁⣉⠤⠿⡐⠒⠗⠄⢛⠣⢤⡀⢳⣀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡏⣷⠓⠄⠘⡞⣁⣠⠀⠘⣤⠔⠂⠙⢦⡀⠈⠀⢀⠉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢶⡏⡠⠈⠈⠍⠑⡀⡇⠀⣻⠦⠜⣧⣀⠾⠚⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠘⢷⡁⠀⢸⡖⠉⢀⠈⢣⡀⡔⠁⠀⠳⠄⠀⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣡⣾⣷⠶⠾⢣⠤⠿⠄⠈⣻⡀⠰⠛⢀⠓⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡛⢾⢦⠀⡦⣰⠋⠁⠀⠙⠖⠀⡈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠛⠐⠂⠀⠘⠂⠈⠉⠘⠁

⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣤⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢿⣾⣿⣿⣿⣿⣿⠏⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⢿⣿⣿⣿⣿⣯⢰⣿⡿⢡⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⡻⣟⡛⠛⣷⣝⣿⡟⠅⠀⢿⢹⢰⡟⠁⢀⣼⢳⡾⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠻⠟⠻⣿⣜⣷⣎⠀⠈⠈⡿⠁⠀⣾⠟⠋⣴⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣧⣌⠻⣟⢿⡀⢄⠀⠁⠀⠀⠋⠀⢠⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠿⣿⣿⡻⡛⣦⠘⢾⣃⠀⡴⠉⠀⠀⠀⢀⣿⣿⣿⡿⢛⡿⢻⣿⣿⣭⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢉⣹⡿⢷⣾⣩⠻⠶⣍⣧⡀⠹⡄⠀⠐⠀⠀⠀⠀⠈⠛⣣⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣶⣍⡙⢿⣾⣆⠘⢷⠀⠘⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣬⡿⢷⣮⣙⢿⡆⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⣠⣿⡿⠿⠟⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣋⣉⠺⡉⠃⠹⣆⠀⠀⢀⠀⣀⠀⠉⠀⣉⣤⣆⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⡛⠻⣿⢐⣦⣙⡇⠀⠀⠀⢈⣤⠂⡼⠉⠛⢛⣁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡅⠐⠿⠿⣖⣊⣻⠷⠌⢭⡛⢷⣶⠷⠞⠁⠀⠠⣠⡶⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠒⢾⡷⢏⣙⠲⣇⠀⢙⡾⠧⠤⢀⣾⡷⠃⢴⣉⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡉⠀⣈⣿⡷⠠⣭⡿⠶⠶⢀⡼⠟⢠⣼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢏⣉⠩⣝⣦⣤⡯⠓⣣⠾⠦⢴⡟⣲⢏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠇⠐⢠⠶⡦⣾⣋⣉⣁⣄⣈⣃⣹⣦⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢿⠿⠋⠁⠐⠃⠀⠰⣿⠓⣼⣿⣿⣿⣏⡘⢿⣧⠀⠙⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⢀⠄⠐⠆⣀⠠⠛⡿⠁⠈⠹⣦⠉⠉⠛⣇⠀⠀⢃⠀⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⢻⡏⠀⠀⠀⠀⠁⠀⡃⠐⠢⣧⣤⡔⠂⠀⠠⣤⣰⠁⠀⠰⡾⠁⣰⣽⣷⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣲⣄⡜⠓⢶⡃⠀⠀⣏⣀⢀⡸⠃⠈⢣⣤⣤⡤⠀⡈⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠢⣴⠇⢬⣽⡋⠈⠉⣿⣂⣀⣼⠋⠀⢱⠖⠁⠀⠛⢼⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣭⠓⠐⣧⠀⣀⣹⣋⢀⣚⡟⠉⠉⢻⣄⣀⣼⠖⡇⠀⢖⠤⡀⠀⠀⠀⠀⠀⠈⠉⠚⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡀⢲⣿⣤⣵⣎⣁⠉⢹⣗⠚⣀⣿⢁⡍⣿⠊⢳⠶⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢛⣿⣿⣿⣿⣿⣿⣏⡉⠙⣿⣉⣤⣿⣂⣿⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣽⣿⣿⣿⣿⣿⣿⣹⣿⣿⣄⣨⣿⡧⢀⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⣉⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣠⣴⣾⢟⣻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⣰⣾⣤⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⣼⣿⡟⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠋⢙⣿⣿⣿⣿⡿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⠋
⠀⠀⠀⢿⣿⣿⣿⣿⣯⠀⠀⠈⠙⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⢁⡼⠃
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣤⣀⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣉⣁⣀⡀⢺⣇
⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⡿⠿⠷⢄⠀⠀⠀⠀⠀⢀⣶⣾⣿⣉⣙⠲⣇⣀⠉⠉⠛⣿⣳⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⢀⣾⣟⣉⡡⣤⢬⣹⠟⠛⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⣿⣿⣟⣻⠏⠀⠀⠠⠀⣱⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⣿⣧⣼⢿⣶⠖⢛⣾⣾⢁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣿⣿⣿⣿⡿⣿⣋⣿⡿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠍⠉⠉⠳⢦⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣀⣤⣤⣤⣤⣶⣾⣶⣤⣄⡀⠈⠟⠀⢻⡆⢀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⠟⠓⠂⠀⠀⠀⠀⣀⣀⡀⠀⠉⠛⢷⣄⠀⣼⣿⠟⠋⠀⠀⠀⠀⠉⢛⣦⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠻⣍⠁⠀⠀⠐⠒⠒⠛⠋⠉⠉⠉⠉⠙⠓⢦⣈⣿⣾⡟⠁⠀⢀⣀⠀⠀⠀⠀⠈⠉⠉⣿⣏⣀⣤⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⢀⣀⣀⡤⠄⢀⣀⣤⢤⣶⣾⣟⠡⣾⡷⠞⠛⠛⠛⠛⠻⠶⣦⣄⣀⣀⣠⣤⠴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣭⣭⣥⠶⣛⣭⣤⡶⠛⢉⡾⢡⣾⣿⠇⣀⣀⠀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⠿⠟⣻⡿⠋⢀⣴⣿⠁⣿⠛⢿⣧⣝⡶⠿⠒⣀⣀⣈⣉⣉⣛⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⢀⡾⠋⢀⣼⠟⢡⡟⢰⡇⠀⠀⠉⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⣀⣤⣶⠶⠿⢷⣾⣿⣤⣄⣀⡞⠁⣴⠟⠁⠀⠸⡇⢸⡇
⠀⠀⣠⣾⠟⠉⠀⢶⣀⢞⣩⠀⠈⢉⡟⢀⣾⠁⠀⠀⠀⠀⣧⢸⡇
⠀⣰⡿⠁⣀⠀⠀⠀⠙⠛⠁⠀⠀⣼⢁⡾⢿⣧⠀⢀⣴⣾⣿⡀⢿⠿⠿⣿⣶⣦⣄
⠀⣿⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⢀⡇⣼⠁⢸⣿⣴⡿⠛⠁⠀⢳⣈⣦⠆⠀⠀⠉⠙⢿⣆
⠀⢻⣧⠈⢿⡀⠀⣀⣤⣶⡶⠿⢿⢁⡿⠶⣿⣿⣿⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⢻⣷⣄⣠⣾⠟⠋⠁⠀⢦⣸⣸⣁⣠⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠙⣿⡟⠁⠀⠀⠀⠀⠈⠛⠿⠛⠁⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⣿⠇
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⣰⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠴⠟⠋⣀⣴⡿⠁
⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⣸⣿⣧⣤⣤⣤⣤⣤⣤⣶⣾⠿⠋
⠀⠀⠀⠀⠈⢿⣦⣀⠀⠠⣤⣤⣤⣤⣴⡿⠃⢀⣴⣿⠃⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣦⣭⣭⣭⣥⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠞⢉⣠⣴⣶⣦⣶⣶⢶⣶⣨⣭⣝⡒⠤⣄⡀
⠀⠀⠀⠀⠀⣴⠃⣴⣷⢿⣿⣯⣿⣿⣾⣻⣿⣿⣿⣟⣷⣞⢦⣭⡒⢤⡀
⠀⠀⠀⠀⢰⣿⡀⢿⣿⣿⣿⣿⣯⣿⣾⣿⡃⠉⢘⣻⡟⣻⣿⣿⣷⡶⡌⢢⡀
⠀⠀⠀⠀⣿⣿⣷⡄⠰⣾⣿⣷⣿⢿⣿⣿⣿⣶⣻⣿⣿⠾⢷⢾⣽⣟⣳⠆⢱
⠀⠀⠀⠀⣿⣿⣿⣿⣶⣌⠻⠿⠿⣫⣿⣿⣿⣟⡛⢃⢶⣷⡄⠂⠀⠝⠻⣗⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣷⣆⣰⣾⣿⣿⠁⠀⠀⠀⠈⢻⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⠀⠀⠀⠁⣠⣶⣾⣿⣿⣛⣉⡍⠛⢷⣦⣤
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣣⡄⠰⠀⢀⣾⣿⣿⣿⣿⣿⣿⣮⠀⢸⣶⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⢟⣔⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣝⠿⣿⣿⣿⣿⡟⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠦⠀⢴⣶⠆⠆⠹⣿⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡗⠀⠀⠀⠀⠆⡀⠸⠅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣶⣄⣤⡤⣾⢆⡄⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⡟⠙⠂⠈⠙⠻⣿⣿⣿⠇⡠⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⢻⣷⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⠁⢁⠐⠠⠀⠀⡉⠉⠻⣿⣿⣤⣠⣄⣤⡈⢻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠄⠄⠀⢀⣴⣦⠙⢿⣿⣿⣟⣤⣉⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣶⣿⣿⣧⣸⣗⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⢀⣠⠴⠶⢴⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⣴
⠀⠀⠀⠀⠠⢋⡠⠄⣠⡏⡇⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠰⠃
⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⡿⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢯⣁
⠀⠀⠀⠐⠉⠁⠀⠀⠀⢀⡇⠀⠀⠈⢦⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢦⣤⣴⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⡄⡿⠁⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⡴⠋⠉⠚⠶⠶⣄⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣽⠈⠦⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⢠⡶⠾⠛⣳⠋⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣤⠾⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢦⣻⠔⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠇⠀⢀⣤⠶⠶⠶⢦⣄⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⣩⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠀⢀⣴⠟⠁⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠉⠛⠷⠶⠶⠟⠋
⠀⠀⠀⠀⠀⠀⡞⢳⣴⠀⣧⡠⡤⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⣀⣱⡀⢿⣠⣿⠾⠷⣶⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠖⢯⣉⡗⠲⣄
⠀⠀⠀⠐⢯⣉⣀⡭⠞⠋⠀⢀⠀⠀⠻⣆⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢠⡆⡴⠛⢺⠁⠙⠺⡏⣳⡀
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠂⠀⠀⠀⠀⡀⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⢳⠷⣤⠚⠓⢄⠀⣨⠤⣽
⠀⠀⠀⠀⠀⢿⠀⠄⠀⢀⠀⠈⠁⠀⠀⣼⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⢺⡸⣤⣨⡦⠤⣾⣀⣨⠀⣸⠂
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⣀⠀⠄⣿⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣀⣀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⣍⣥⣀⣻⢤⠴⢻⡥⠟⠁
⠀⠀⣀⡀⠀⠀⠀⠙⠢⣄⠂⠀⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⡽⠷⠴⠞
⣴⠋⢿⡇⠀⠀⠀⠀⠀⠀⠑⢄⡀⢤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠘⢆⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⡿⣿⡇⠀⠀⠀⠀⢀⣠⡴⠒⠚⠀⠲⠶⣤⡀
⠀⠀⠀⠈⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⣼⠁⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠠⣀⠈⠙⢷⡄
⠀⠀⠀⣤⠉⠀⠀⠉⠙⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⣼⠏⢀⠀⢀⡀⠀⠀⢠⠏⠙⢦⠀⢻
⠀⠀⠀⣿⡄⠀⠢⣄⠀⠀⠀⠀⠈⠉⠛⠛⠛⠓⠒⠛⠛⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⣴⠏⠀⠀⠀⢀⣿⠀⡆⠀⠀⠈⢢⣤⡀⢀⣀⣈⡇
⠀⠀⠀⠸⣷⡀⠀⠀⠙⠓⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠖⠉⠀⠀⢀⣼⠏⠀⠀⠀⠀⠈⣿⠀⢣⡤⠒⠊⣩⠛⠀⢄⠀⠀⣿
⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⢻⣇⠘⢧⠀⡴⠁⠀⣇⠈⠑⣦⠇⢠
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡈⠛⠧⣤⣤⣼⡤⠖⢁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣤⣀⣀⣀⣀⣠⣤⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⡶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡁
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠱⠋⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣤⣼⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠁⠀⠀⠙⣇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠈⠉⠓⠀⠀⠐⠈⠁⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠳⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠒
⠀⠀⠀⠐⠀⠀⠈⠱⣄⠀⠀⠀⠠⠒⢶⣾⣀⣤⣀⣤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠈⠁⠀⢳⡶⣤⠴⠉⠉⠙⢾⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣷⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡆⠀⠴⠀⠀⣮⠛⢉⣐⡳⠚⠲⠴⠋⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠈⠂⡀⠀⠀⠀⠀⣃⠠⠀⣤⡐⡀⢀
⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⣼⠁⢀⡈⠛⠇⠴⠁⠀⠀⠀⢴⣖⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠈⠀⠀⢀⣆⣼⠛⡆⠀⠁⡁⠈
⠀⠀⠀⠀⠈⠉⠀⣤⠀⠀⠀⠑⣤⠎⠁⠀⠀⠐⠒⠚⠋⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠑⠀⢄⣀⣀⣀⣤⠷⠋⠁⠈⠉⠀⠀⢀⠃⠠
⠀⠀⠀⠀⠀⠀⠐⠋⠀⠤⠀⠈⠛⢸⠅⠠⠀⠀⠀⣠⠀⠀⠠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠻⡅⠀⠠⢀⡀⢀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⠖⠞⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠲⠤⠈⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣀⣄⡀⠈⢇⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⠀⠈⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠎⠁⠙⠀⢻⣷⢖⡈⣡⡤⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠒⠺⣶⠀⠀⢠⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠐⠀⠟⢷⣽⡿⠃⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠰⣄⡀⠼⠂⠰⠯⡀⡐⠂⠁⠀⠀⠀⠀⠀⠀⠀⡖⠁⠀⠀⣀⡀⠀⠲⠓⠤⢚⣯⠧⠁
⠀⠀⠀⠀⠀⠁⠀⢤⡾⠁⠉⠱⠋⠲⣄⠠⠒⠉⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⡐⢠⣠⠉⣠⠾⠓⠚⠋⠁
⠀⠀⠀⠀⠀⠒⠆⠀⢀⢄⡀⠜⠁⠀⠉⠃⠀⠠⠙⠣⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⢦⠁⣼⣧⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠁⠈⠛⠃⠄⣀⠀⠀⢈⠨⠓⠀⠀⠈⠀⠀⠁⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢩⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣧⣾⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢿⣾⣿⣿⣿⣿⡟⢹⣿⡿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣦⣿⣾⡟⢿⣿⡿⢿⣿⠐⠾⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣍⣉⣿⣮⢿⡕⡄⠈⠧⣇⣿⠁⢀⣾⣻⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣯⡈⢻⣯⣿⡗⠀⠀⠸⠃⠀⢸⠏⠀⢺⣿⣿⣿⣿⣿⣿⣿⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣏⣉⣻⣿⣿⣿⣿⣿⣦⡈⢯⢻⠀⠆⢀⠄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠿⣿⣯⣛⠿⣯⣃⠿⡈⠱⡆⠐⠁⡀⠀⠀⠀⠛⢿⡟⢋⣴⣭⣽⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣤⣶⢯⣍⡛⢿⣶⣭⡛⢻⡄⠘⠇⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣷⣬⡝⢷⣦⠘⠀⠀⠀⠀⠀⠀⠀⣠⠿⠋⣽⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠷⠚⢽⠓⠌⢳⡀⠀⠀⠀⠀⠀⠘⠁⠐⣋⡍⠁⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣅⣰⣿⣿⡟⠶⣷⢡⣌⣳⠀⠀⠁⠈⣡⡄⢰⠚⠿⠛⢃⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⢿⠿⣶⡛⢻⢦⠉⡑⢶⣤⡶⠶⠃⠀⠀⣐⡬⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⠐⢶⡷⢟⣛⢶⡀⠈⢳⠿⠤⠀⣴⡶⠃⢤⣉⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢀⣈⣻⡖⠠⣭⡗⠶⠂⣴⠟⢀⣴⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢏⣩⠩⣽⠶⢼⣟⣋⡼⠓⠰⣟⣳⠎⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡃⠈⠴⣲⡶⣯⣭⣥⣴⣤⣥⡬⠶⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠟⠋⠀⠈⠁⠂⠸⣯⣩⠿⣿⡿⣿⣄⣻⡷⠀⠉⡷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠌⠃⡤⠂⢹⠇⠀⢀⠻⠂⠀⠈⡳⠀⢀⣡⠀⠹⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠿⠀⠀⠠⣀⠀⢀⣄⢈⠝⠛⢶⠅⠀⠀⣷⠺⡅⠀⠘⠋⠀⢿⡿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠷⠇⡀⢹⠀⠠⣬⠖⠤⢾⡄⠀⢨⡷⠛⢏⣠⠂⢹⡟⣿⣿⣿⣿⣿⣿⣿⡏⢹⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢒⠧⢨⡏⠉⠛⣷⠄⠠⣼⠶⠶⢾⠀⠀⣸⡡⡀⢠⣈⠙⠛⠛⠛⠛⠛⠛⠧⢤⡈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠠⣤⣗⣀⣪⠛⠲⠶⣯⡤⠀⢼⠛⠛⣿⠴⣇⡄⠁⠄⠀⡀⠀⠀⠀⠀⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⢿⣿⣿⣷⣶⣶⣿⠒⠚⣿⠒⣁⣿⠀⡇⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⣿⣿⣿⣿⡟⣿⣿⣇⣀⣿⣯⠉⣻⡿⠃⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣻⣷⡾⠏⠁⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢀⣠⣶⡿⣛⣶⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⢀⣴⣿⡴⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⣾⣿⣋⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⢸⣿⣿⣿⣿⣟⠛⠋⠉⣿⣿⣿⡿⠟⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⡿⠁
⠀⠀⠘⢿⣿⣿⣿⣿⡄⠀⠀⠈⡻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⣠⠏
⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⣴⣾⣇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠶⠤⣤⣤⣿⣧⡀⣀
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⢧⣄⠀⠀⠀⠀⣼⣿⡽⠶⠶⠭⣿⣶⠀⠀⠉⢿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣶⣿⣏⣶⠉⠁⠀⠀⢄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣸⣟⣹⣶⣇⣠⠴⣬⣤⠊⡀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⣿⣿⣽⣿⣷⣶⠿⣯⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⢛⣛⡛⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠈⠿⣿⡶⠶⣤⣤⣤⣤⣤⣤⣤⡴⠶⠛⠋⠁⠐⢒⣤⣤⣾⠿⠛⠛⠛⠲⠿⣶⣄⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⣀⠀⠀⠀⠠⣀⢀⣈⣭⠿⢺⠏⠁⣰⠋⠀⢀⣠⡴⠚⠛⠚⠿⢷⣆⣰⠟⠂⠀⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣌⡉⠙⠛⠛⢋⠝⠋⠀⠰⠋⠀⠐⢁⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣀⣤⣤⣴⣾⣛⣥⣤⣤⣶⣶⣶⣶⣶⣤⣤⡿⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⣭⣶⣿⣿⠿⠿⠛⠛⠛⠋⠙⠛⠛⠛⣿⠃⢠⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠾⠿⠶⣿⣄⠉⠛⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⣤⣄⣀⣀⡀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⢲⣦⣤⣀⣀⣀⣀⣀⣀⣤⠴⠞⠫⢁⣐⣶⡤⠭⢵⣦⣄⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠻⣮⣍⣉⣉⠉⣁⣀⣠⠴⡺⠋⡱⠃⢀⡤⠖⠒⠛⠷⣤⡞⠃⢉⡢
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣌⣉⠉⠊⠀⠀⠁⣀⡤⠞⢉⣀⣀⣀⣀⢀⡾⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢛⣻⣿⣿⡿⠿⠟⠛⠛⠛⠻⣿⠃⣰⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠐⠚⠛⠺⠧⠈⠛⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣶⣶⣤⣤⣤⣤⣤⣶⣶⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠘⢄⡙⣦⠀⠀⠀⠀⠀⠀⠀⠓⣤⣇⠀⠀⠀⠀⠀⠀⠫⣉⣲⡴⢊⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠲⣄
⠀⠀⠀⠀⠀⢠⢖⠉⠛⠓⠂⠒⢄⠀⠀⠀⢀⡎⠀⠈⢇⠀⠀⠀⠀⢠⢋⠀⠌⡉⣉⡆⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢘⡄
⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⢸⠀⠀⢀⠞⠀⠀⠀⠘⢆⠀⠀⠀⠸⡠⠀⠄⠄⢠⠃⠀⠀⠀⠀⢀⡠⠞⠁⣠⠀⢨⠃
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡜⠀⠀⡎⢰⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢄⠂⣂⠎⠀⠀⡴⠖⠍⠡⠤⠴⠚⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠘⢆⣀⡤⡠⠞⠀⠀⠀⠘⢼⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠓⠒⠐⠒⡒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢹⡀⠀⠀⠀⠀⠀⡠⣒⠒⠚⢖⠳⢄
⠀⠀⠀⠀⠀⠀⣴⠿⠂⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⣠⠒⢾⡽⠓⠻⣼⠒⠒⢤⠀⠀⢸⢱⠁⠀⠀⠈⡇⠀⢳
⠀⠀⠀⠀⠀⢼⠉⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡞⡳⣤⠼⣇⠀⣠⡿⠷⢖⠉⠀⠀⠸⡘⠀⠀⠀⠐⠁⠀⡜
⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⣸⣛⠼⠣⡄⠀⡏⠉⣣⣀⠜⠀⠀⠀⠀⠑⠤⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⡠⠔⠃⠀⠀⠀⠐⢇⡸⠦⠤⠚⠒⠋⠚⠁⠀⠀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢇⠒⠀⠂⠀⡀⠁⠀⠁⠀⠢⠀⠂⡇⡬
⠀⠀⠀⠀⠀⠀⠀⣦⡀⡼⢳⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢦⡈⢠⠄⡀⠘⠀⠈⠠⡀⢉⡜⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡴⣌⢣⠔⢉⢼⡀⠀⠀⠀⠀⡠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⡲⠤⣁⣈⣀⣉⡠⠴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢱⡤⣿⡴⠥⣜⠀⠀⠀⠀⠮⣤⡤⢾⠟⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⢀⡜⢇⢀⡼⠳⣄⡏⢦⠀⠀⠀⠀⠀⢠⢣⠂⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⢸⣤⡴⠻⢄⣠⠊⠉⡿⠀⠀⠀⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡔⠉⠒⠊⠁⠒⠂⠉⢉⠆
⠀⠀⠀⠀⠀⢻⡀⢑⣤⣞⠉⢲⠾⣸⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣀⠴⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⢟⠻⢤⣈⡽⠛⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⡀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠫⠥⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠊⣉⣤⣶⣶⣴⣶⣶⣶⣎⢉⣙⣒⠦⢤⣀
⠀⠀⠀⠀⠀⢠⡏⢠⣶⣿⣯⣿⣻⣿⣷⣿⢾⣿⣻⣻⡿⣣⡶⣮⣙⠢⣄⡀
⠀⠀⠀⠀⢀⣿⡄⢹⣿⣿⣿⣿⣿⣻⣿⣻⣿⠝⠋⢙⢿⡷⢿⣿⣟⣿⣤⡙⢦⡀
⠀⠀⠀⠀⣼⣿⣷⡀⢩⣽⣿⣿⣽⣿⣿⣿⣟⣴⣄⣾⣿⣾⣽⣯⣽⣛⡷⢯⡦⠹⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣦⡘⠻⣿⣿⡷⣫⣿⣿⣿⡿⠿⠋⣵⣦⡈⠈⠉⡻⠿⣧⠀⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣄⣘⣿⣿⣿⣿⣯⡁⢠⣽⣿⣷⠂⠀⠐⠀⠉⢾⡃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠋⠀⠀⠄⠀⣨⣤⣷⣾⡿⠿⠿⠷⣦⣄⠀⡀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⠋⠀⣤⣽⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡷⡿⢣⢦⠄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⡐⢿⣏⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠙⣃⣩⢛⠻⣿⣿⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡉⠁⠈⠛⢋⠈⠀⢸⠏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢏⡀⠀⠀⢀⣌⠸⠀⠘⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡛⠛⠿⣿⣾⣿⣽⣟⠼⠂⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠈⠙⢿⣿⣟⣤⣣⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⡿⠛⠿⠻⠿⢿⡿⣿⣿⣦⠄⠀⠀⠀⠀⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣯⠀⠀⠈⠀⠀⠀⠄⠀⠈⢿⣿⣷⣶⣶⡶⢦⡈⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⢂⠂⠀⣀⣶⡷⠂⡻⣿⣿⣿⣴⣆⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣬⣟⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⡿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠤⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⢄⡀⠀⠀⠀⠀⠀⠀⠴⠫⠐⢀⡴⣤⠀⠀⠀⠀⡀⠀⠀⠀⠘⠠⣦⠬⠿⡀
⠀⠘⢄⠀⠀⠸⡇⠀⠀⠀⠀⢠⠀⠀⠀⣜⠀⢀⠀⢀⡈⠲⠍⠓⠒⠀⠀⠀⠀⠈⠐⠙⠉⠁⠀⠓⠀⠒⠊⠀⠀⠀⠀⢠⣒⡆⢯⡼⣭⣆
⠀⠀⠈⠙⠓⠂⠑⠀⠀⢀⡤⠞⠀⠀⠀⠹⡀⠀⠀⠀⠉⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠁⠘⠶⠹⠠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⣀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠤⡀
⠀⠀⠀⠀⠐⠓⠄⢈⠤⠴⠆⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠐⡄⡀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠘⠓⡩⠷
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⢂⠜⠀⢊⠉⠁⠢⠀⠀⠀⢸⡀⠁⣖⠎⢻⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡔⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢣⠐⠀⡀⠀⠀⠀⠙⠯⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢦⣄⡠⣇⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⣧⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠳⣄
⠀⣤⣄⡁⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡹⠆⠐⠁⢡
⠀⠀⠉⠁⠀⠀⠀⠨⠉⠐⠦⢤⡀⠀⠀⠀⡉⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠆⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠴⣦⣀⣤⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠍⠉⠤⠤⠶⠀⠂⠀⠀⠀⢀⠀⠀⣨⠃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠘⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢂⣰⣤⡀⠀⢀⠀⣀⡆⠊⠀⠀⠀⠀⠀⣀⠄⠀⠀⡀⠀⠀⡀
⠀⠐⠀⠃⠀⠰⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡘⠀⠀⠁⣿⢳⠃⠀⠀⢀⡴⠋⠀⣠⠄⠀⠀⠀⠉⠀⠐⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠢⠑⡄⠀⠀⠘⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠃⠃⠀⠀⠀⡈⠀⠀⠀⠀⢀⡠⠆⠠⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠑⠸⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠁⡀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠂⢸⠀⡈⠀⠀⠀⡀⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠊⠉⠀⠐⢁⠀⢈⣁⣀⣀⣀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢀⡀⢁⡤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⣴⠏⠀⠓⢌⠉⠐⠤⣀⠀⠀⠀⠀⠀⠀⣠⣌⠢⡀⠈⠀⠀⠀⠓⠀⠀⠈⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠄⠀⠀⠠⠀⡏⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠋⢭⠁⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⢇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠂⠘⡀⠀⠀⠀⠀⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⡣⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⢀⠛⠃⠁⠀⣰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠣⠀⠀⠀⢀⠀⠀⠓⠀⠀⠀⠙⠒⠀⠀⠀⠐⠊⠐⠚⠛⠂⠙⢿⣿⣿⡿⠟⢠⠀⠀⠀⠀⢀⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠁⠁⠈⢄⣀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠈⠙⠂⠀⣠⠖⠀⠁⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠰⠒⠁⠀⠐⠇⠀⠁⠀⠀⠀⠀⠀⠉⠁⠉⠀⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⠁
⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣀⣤⣤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠅

⠀⠀⠀⠀⢀⡀⠠⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠤⠒⠀⠄
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠡⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠂⠀⠀⠊⠀⠀⠁⢀⠀⠀⠈⠆⠀⠂⠀⠀⠀⠁⢀⠂⠀⠀⠀⡔⠁⠀⠑⠄
⢀⠀⠀⠐⡄⠀⠀⠀⠀⠀⢁⠀⠹⠐⠀⠀⠀⠀⠀⠀⠒⠈⢀⠁⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠢⣀⡠⠃⠀⠀⠁⠄⠈⠄⠈⢀⠀⠀⠸⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠑⠀⠑⢄⡀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⢀⠂⠐⡀⠀⠀⠈⠀⠈⠁⠀⢀⠀⠀⠀⠀⠃⠄⠀⣄⠡⡄⠀⠑⠤⠤⠐
⠀⡀⡀⠀⠀⠀⢌⠀⠀⠀⠀⠊⠀⠀⠀⠈⠁⠀⠈⠈⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠅⠀⠀⠀⠀⠈⠀⠠⠀⠐⠀⠁⠀⣀⠀⠠⡀
⠀⢸⡀⠈⠀⠀⠀⠈⠐⠠⡀⠀⠀⠒⠋⠑⠀⠀⢀⣤⣀⡀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡄⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⠀⠀⡌⢃⠀⠀⡀
⠀⠀⠣⡀⠀⠀⠀⠀⠀⢠⠌⠀⠀⠂⠀⠐⠀⠀⢹⣿⣿⣿⣷⣿⡄⠈⠢⠄⠀⠀⠀⠇⠀⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⣀⡩⠞⠁
⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⡀⠀⠀⠈⠐⠀⠐
⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⢢⡢⠀⢀⡀⠀⠀⡠⠀⠀⣀⣀⠠⠐⠁⠀⠀⠠⠀⠠⠄⠂⡀⠀⠀⡀⠤⠀⠀⠀⡠⠂⠁⠈⠉⠙⢂⠐⠒
⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡀⠐⢄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠐⠀⠐⠁⠀⢊⠠⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠠⠀⠀⠐⠀⠀⠉⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⡀⠀⠀⠀⠀⢀⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡂⡄⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠑⠄⡀⠀⠀⢀⠄⠁
⠀⠀⠀⠈⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠈⢉⡃⠀⠀⢠⠀⢂⠀⠀⠀⢨⠀⠀⠑⠠⠆⡀⠀⠀⠀⠀⠀⡠⠒⠂⠐⠠⡀⠀⠈⠁⠉
⠐⠂⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢘⠁⠀⠀⡅⠃⠀⠸⡄⠀⡄⠀⠀⠀⠁⠐⠃⣀⠠⠀⠀⠀⠄⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠁⠀⠉⠀⠀⠀⢁⠀⠀⠰⡀⠀⠆⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⡀⠀⠐⠌⠐⠡⠄
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠀⢈⣉⢐⠀⠀⠐
⠀⠀⠀⠐⡁⠉⠒⠄⠐⠀⠐⢄⠀⠀⢀⡀⡠⠃⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣀⣴⣆⣀⡀⡀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠉⠉⠁⠢
⠀⠀⠀⡀⠀⠁⢂⡀⠊⢀⠀⢀⡁⠈⠁⠀⠀⢠⠊⠁⠀⠹⠓⠤⡀⠀⣠⣾⣿⣿⡟⣿⣿⣿⣿⡿⣿⢿⣟⠀⠀⠀⢇⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢘⡤⠤⢠⣀⠀⠀⠘⠄⡀⢈⡀⣀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡇⢸⣿⣿⣿⣿⡇⠉⠋⠁⠈⠁⠉⢉⠉⠀⠀⠀⠀⠁⠂⠀⠀⠀⡆
⠀⢀⣭⣦⣴⣿⣿⣿⣦⠀⠐⠀⠀⠀⠀⠀⠀⠱⡠⢄⣀⡀⠔⢋⠀⠀⠙⠿⢿⡿⠁⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠄⠐⠁
⠀⠙⣿⣿⣿⣿⣿⣯⡟⠀⠀⠀⡀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠠⠊⠀⠑⠆
⠀⠀⠀⠙⠛⠛⠛⠛⠁⠀⢀⠊⠀⠀⠳⢄⠀⠀⠉⠀⠀⡀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⠀⠀⠀⠐
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠂⠀⢀⠠⠀⠁⠀⠈⠀⠉⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠑⡀⠀⠀⠀⡠⠀⠐⠒⠂⠀⡀
⠀⢀⣴⠃⠀⠉⠀⠀⠀⠀⠃⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠚⠈⠉⠁⠢⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⡈⠀⠀⠀⠀⠀⠀⠰
⠀⢸⣿⣆⠀⠀⠀⢠⠆⠸⠀⠀⠀⠀⠀⠘⠀⠀⠸⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠻⣿⣦⣄⣀⡥⠀⠀⠢⡀⠀⡀⠔⡡⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀⠀⢀⠠⠊
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⣀⠠⠤⢀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠀⠤⠀⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠰⠁⠀⠀⠀⠑⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠑⠀⠀⠁⠀⠀⠀⡀⠀⠈⠀⠀⢁⠈⠀⡀⢠⡁⠀⠀⠠⠀⠀⠈⠂
⠠⠀⠀⠐⠀⠀⠀⠀⠀⠠⡀⢣⠁⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠠⠆⠀⠀⠠⠀⠀⠦⠐⠀⠀⠀⠀⣀⠒⡀⠠⠀⠀⢠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠁⠂⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⡘⠢⠀⠁⠒⠈
⠀⠰⠀⠀⠀⠀⠂⠀⡀⠀⠀⢀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⡤⠈⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⢴⠂⠀⠂
⠀⠘⠀⠀⠀⠀⠀⠀⠈⡀⠀⠠⠀⠀⠀⠀⢸⣿⣷⣶⣤⡄⠀⢁⠀⠀⠀⢐⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠨⡀⠃⣠⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠿⠿⠃⠀⠀⠀⠀⠀⠀⠠⠊⠅⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡠⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠄⠂⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠲⡀
⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠈⢂⠀⠢⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠂⠀⠀⠐⠁⠔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠐⠀⠀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠬⠠⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠢⠄⠀⠀⠐⠁
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠀⠠⠁⡀⠀⡆⠀⠀⠀⠀⠰⠀⢀⠁⠉⠀⠀⠀⠀⠀⡀⠊⠁⠀⠀⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⢀⠳⡀⠁⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⠠⠂⠐⠄⠀⠂⡁⠄
⠀⠀⠀⠐⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡣⠔⠒⠒
⠀⠀⠀⠀⠁⠐⠀⠔⢀⠀⠀⠀⠀⠁⠀⢀⠔⠊⠐⠾⠦⡀⠀⢀⣴⣿⣿⢸⣿⣿⣿⣿⣿⢿⡇⠀⠀⠐⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢃
⠀⠀⢨⠤⢄⣄⡀⠀⠘⠄⠀⣀⠀⠀⠀⡎⠀⠀⠀⠀⠀⣸⠀⣿⣿⣿⣿⠘⠙⠉⠈⠃⠉⢋⠉⠀⠀⠀⠈⠒⠀⠀⠀⡀
⠀⣠⣾⣤⣾⣿⣿⣷⡀⠒⠀⠀⠀⠀⠀⠸⠖⠆⠠⠤⢊⠄⠀⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁
⠀⠘⠿⣿⣿⣿⣿⠏⠀⠀⡠⠀⢄⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠁
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠀⠀⠁⠄⠀⠀⠀⠀⠂⠐⠄⠠⠜⠀⠀⢀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠄⠀⠀⠐⠀⠀⠀⢈⡀
⠀⠀⣠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠐⢀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⢸⣷⠀⠀⠀⠀⡄⢰⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠇
⠀⠘⢿⣷⣄⣀⣈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠄⠀⠀⠀⠀⠔
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⣼⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠠⠆⠀⠀⠀⣀⠠⠐⠂⢩⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣥
⠀⠀⠀⠀⠈⢳⠀⣠⡾⠀⠀⠻⢦⡀⠀⡀⠀⠀⠈⠲⢤⣤⠤⠂⠉⠀⠀⠀⠈⣿⠈⢳⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣤⠜⠛⠸⡟⠁
⠀⠀⠢⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⢾⣅⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢤⣴⡿⢀⢸⣿⣦⡀⠀⠠⠋⠉⠀⡾⠿⣿⣇⡀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣨⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⢠⠀⠁⢠⠀⢀⣀⣼⣿⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠈⠳⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢸⡁⢀⡀⠀⠀⠀⢠⡀⠀⠀⢀⣼⣿⡟⠀⠀⠠⠃⠀⠀⠘⠀⠈⠻⢿⣿⡀⠀⠀⢸⡿⠛⠀⠀⠀⠄⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠺⣦
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣿⢿⣧⣾⣿⡏⠀⠀⠰⠁⠀⢠⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠰⠀⠀⠘⠉⠀⠀⢀⠠⠾⠗⠀⠈⠷⠀⠀⠹⡆
⠀⠀⢀⡆⢀⣠⠄⠀⠀⠘⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠘⠉⠀⠘⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠈⡳⠚⣻⠶⡖⠠⣾⣤⡀⠀⠀⠈⠁⠀⠀⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠺⣿⡶⠀⠀⠀⠀⠀⡀⠤⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⣤⡯⠀⠉⠀⢻⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢘⠀⠀⣶⣿⠓⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣾⣶⠀⠤⡤
⠀⠀⠀⠛⠘⠃⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢁⣻⣧⣆⣀⠀⠀⠀⠻⠆⠀⠀⠹⣇⠀⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⣰
⠀⠀⠀⠀⣀⡀⠀⠀⠀⣸⣷⠸⡇⠀⠀⠷⠔⡇⣤⣽⡿⢿⣯⠳⡄⠀⠀⠀⠀⠤⠠⣿⣷⡄⠀⠀⠀⠀⣠⣄⡈⣀⡀⠉⠀⠀⠀⣀⣀⠀⢀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⣿⡁⠀⠀⠀⠘⠿⠄⠀⠀⠀⠠⠄⠙⡁⠁⠀⠀⠙⣷⢹⡄⠀⠀⠈⠀⠀⢸⣿⣿⡄⠀⠀⣠⣻⣿⢹⣿⣿⠀⠀⠀⠀⠈⠻⠷⠎⢘⠿⠚⠃
⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢀⣲⠔⠀⣴⠂⠁⠀⠀⠀⠀⣿⡞⠁⠀⠀⠀⠀⠀⢸⠿⠟⠀⢀⡀⠘⠿⣿⡆⢿⡿⠀⣀⣀⠀⠀⠀⢀⠰⠃⣴⡶⣶⣶⣆
⠀⠀⠀⠀⠉⠀⠀⢀⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣰⠉⡷⡈⢿⡀⠀⢿⣷⣤⢡⣇⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠠⠀⣤⣠⣤⡴⠀⠀⠀⣀⣀⣀⣀⣤⠀⠀⣀⡄⠀⠀⠘⣧⣑⢼⡾⠁⢰⣮⣿⣿⡗⠙⠉⠛⠁
⠀⠀⢀⣀⣤⡴⠖⡁⠀⠀⠀⠻⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢠⡀⠈⠉⠉⠀⠀⠀⠀⢹⡟⡶⠭⠛⣚⣟⣿⡄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠻⠟⠀⠀⢀⡄
⠀⠀⠀⠀⠉⠀⣠⣡⡶⠠⢤⡤⠦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⡆⠀⠀⠀⣐⣦⠀⠈⠐⠫⠔⠃⠉⠉⢿⠓⣀⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢠⣽⡿⢿⡔⠋⠁⠀⠀⢠⣀⡀⠀⠀⠈⣷⠀⠀⠈⠋⢀⣤⣾⣫⠏⠀⠀⠀⣠⠇⠀⠀⠄⠈⠸⠏⠀⠀⠀⠀⠀⢠⠀⠀⠈⢀⠇⠀⠀⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠨⠿⠿⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠈⠉⠙
⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠸⣿⣾⣅⠀⠀⠀⠀⠀⠀⢀⣉⣁⣉⢀⣰⠏⠀⠀⢠⣴⣾⢿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⠆⠉⠀⠀⠀⠉⠙⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠠⡦⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠉⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣡⠴⠦⢦⡐⠄⠀⢠⣄⣠⢤⠀⠀⠀⢀⣑⠢⡀⠀⠀⣠⡆⠀⣸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⠆⢸⠇⠀⠀⢃⣼⢁⡈⡤⡠⠀⠀⠈⠀⢿⡄⣰⣿⣿⠟⢻⠁⠈⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⢤⡶⣤⣄⠀⠀⠶⠶⠴⠿⠓⠛⠛⠛⠧⠀⠀⠀⠀⠀⢳⡛⠋⠀⠀⡸⠀⠀⠀⣈⣷⠲⡼⣡⠄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀⠹⣿⣿⣿⣿⡕⣶⣴⣿⣦⡤⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠁⠐⢓⣺⢇⠋⢀⣴⣤⠄
⠀⠀⠀⠀⠀⠀⣿⡛⠷⣬⣀⡘⣿⣿⣷⣿⣿⣿⣻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⠞⠀⠀⠀⠈⣽⣎⣥⠀⢹
⠀⠀⠀⠀⠀⠀⢽⣿⡓⠢⢍⣉⣃⡙⢿⣿⣿⣿⣿⠶⠿⠚⠒⠀⠀⠀⣰⠇⠀⢠⡟⡀⠄⠀⠀⠀⠀⠀⠀⠁⠛⢿⣷⣤⠤
⠀⠀⠀⠀⠀⠀⠘⢻⣿⡧⢀⣀⣩⣿⣎⠻⣾⢿⣿⣿⣿⠓⠂⢤⣠⡄⠻⡄⣠⡿⠻⠖⠢⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣦⣙⣛⣿⣻⣧⣅⣤⣿⣿⡟⠀⠀⠀⠉⠙⢦⡅⠻⠗⠉⠀⠀⠆⠀⠀⠀⢸⣿⣿⣿⣿⣷⢶⣦⣤⠄
⠀⠀⠀⢀⣼⣿⡟⠩⠛⢛⣭⣝⣩⢹⣿⣿⡿⢾⣿⣶⣤⣄⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⢸⠀⢀⣰⣿⣿⣿⡿⣫⠖⣫⠿⠛⣥⠄
⠀⠀⠀⣼⠟⣉⠤⢂⡨⠞⢃⣾⣿⠘⠇⠉⢀⣰⣿⣿⣿⣿⣶⡀⠀⣼⠃⢠⡀⠀⣀⠀⣶⣿⣴⣿⣿⣿⣿⡿⠋⠁⠞⠀⠀⠀⠀⠀⢫
⠀⠀⠘⣿⣏⠀⣈⠄⣀⣴⣾⠁⣿⡀⣠⠀⣾⢛⣿⣿⡟⠛⠿⠇⢠⡏⠀⢸⣅⢾⢃⣠⠿⣿⣟⣿⣿⣿⠿⣿⣿⣿⣿⠛⠛⠓⣶⣤⣤⣦
⠀⠀⠀⠙⣿⣿⠗⢩⣿⣷⣉⣧⣽⣿⣿⣿⠻⠿⣿⣀⠉⠙⠢⠀⠈⠃⠀⢀⣻⣾⢷⣿⣆⣿⣿⣿⣿⢷⣤⡀⠀⠀⢈⠙⠳⢄⡉⠙⠟⠁
⠀⠀⠀⠀⠙⠋⠃⠘⠋⠾⢿⣿⣿⡿⠻⠷⠾⠟⠷⢶⣶⣴⣶⣿⣷⡆⠀⠁⠀⠈⠈⠉⠉⠉⠉⠙⣷⣾⣷⣮⣴⡦⣄⠀⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠥⣤⡤⡴⡶⣶⣴⣖⣪⣽⠿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠏⠋⠻⠿⢿⣿⣷⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣾⣿⣿⣷⣾⣿⣿⠟⣁⢰⣿⣿⣿⣿⣿⣶⣀⠀⠀⠀⠀⢠⣼⣿⣦⣄⠐⠀⠀⠙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠙⠀⣿⣿⣿⣏⠧⣿⡍⠀⠀⠀⠀⢻⠟⣿⣿⡿⢧⡀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠟⢉⡀⠄⠉⠀⠀⠀⣀⣸⣶⣿⢿⡿⠿⣤⡙⣿⢇⠀⠀⣠⣷⠌⣿⣿⡇⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣟⠃⢀⣀⣤⣷⣴⣿⡿⠿⠏⣹⡏⠀⢸⣿⣿⣿⣾⣶⣿⡟⡹⠋⢿⣿⠛⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠾⠿⠋⠉⠉⠃⠀⠀⣶⡎⣿⠃⠀⣾⠏⠈⢿⣿⣿⣿⣿⣵⠳⠼⣿⣶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢿⠀⢰⡟⠀⠀⠀⠛⠻⢿⣿⣿⣶⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣾⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢻⡽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠹⣜⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢠⡄
⠀⠀⠀⠀⢀⠀⣶⣄⡠⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⢾⣿⣧⣽⡿⣾⡇⣄
⠀⠀⠀⣀⣸⡆⣿⣿⣿⣿⠿⣛⣙⣦⡸⢍⠄⡀⠀⠀⠀⠀⠀⢠⣾⠿⢉⠘⣻⢷⣯⠿⣷⣿⣿⣧⡴
⠀⠀⡀⠈⠻⣿⣿⣿⡟⣽⣿⣾⣿⣿⣿⣾⡇⡒⠤⠀⠀⠀⢠⣟⡓⠆⠖⣰⣶⣿⣿⣛⡿⣿⣿⣿⣆⣀
⠀⠀⢹⣿⣿⣿⣿⣯⢩⣿⣿⣿⣿⣿⣽⡇⠲⠨⢁⣀⠀⠀⡓⠠⢀⢸⡏⣻⣿⣿⣿⣿⣻⣿⣿⣿⣇
⠀⠀⠀⣹⣿⣿⡿⠥⡜⣿⣿⣿⣿⣿⣿⣷⣻⢒⣐⠠⠄⠀⠳⣇⣖⣰⣠⣷⣿⣬⣿⣥⣾⢹⣟⠃
⠀⠀⠚⢩⡿⠿⢻⡠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣋⠀⠀⠈⠛⠿⢿⣿⣿⣿⣯⣿⣷⠿⠋
⠀⠀⠀⠉⠁⡜⢀⠗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠑⡈⣯⠛⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠈⠈⠷⣾⣷⣾⣯⣯⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⠶⠆⠀⠀⠀⠀⠀⠀⢀⣸⡧⠤⠀⠀⠀⠀⠀⠀⡠⠤⠀⠠⠤⢄
⠀⠀⠀⠀⡠⠂⠀⠲⡆⡀⠀⠀⠀⠀⠀⠀⢀⣠⣧⣄⢠⣤⣄⢠⡀⣀⠀⣅⠀⢸⡇⠀⣴⡦⠀⠀⠈⢻⠂⠀⠀⠀⠀⠀⠉⢢
⠀⠀⠀⠐⠀⠀⠀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣼⠁⢸⠀⣿⢀⣿⣀⣼⣧⢴⡛⣷⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠠⡀⠐⠈⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠘⠛⠙⠛⠉⠋⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡠⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠈⠓⠤⣀⢀⠀⠀⢀⠇
⠀⠀⠀⠀⢀⡠⠤⣀⠀⠀⠀⠀⢈⠆⢟⣘⣜⠀⠀⠀⠀⠀⠀⢔⠂⠉⠉⠉⠉⠁⢈⣀⠠⠤⠤⠬⣶⡶⠂
⠀⠀⠀⣾⣗⣺⠭⠿⣷⠆⠀⢀⠬⠾⡎⠀⠄⢱⠀⠀⠀⠀⠐⢎⠉⣉⣉⠉⠉⢉⣁⣀⠤⠖⠊⢁⠜⠀⠀⠀⢆⣔⡿⣫⠃
⠀⠀⠞⠻⣥⣤⣒⡩⠃⠀⠀⢇⠐⠂⡸⠖⠲⡯⠵⠢⡀⠀⠀⠺⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠈⣟⡪⠥⢤⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠰⠉⣿⣿⡁⠰⠀⡘⠉⠉⠁⠀⠀⠀⠈⠑⡒⠠⠤⠤⠤⠤⠒⠉⠀⠀⠀⠀⢰⠋⠉⠋⠀⠀⠀⣡
⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⢰⢁⠕⠑⠒⠊⠀⠀⠀⢀⡀⠀⠘⢢⠔⠉⠀⠀⠀⠀⠀⠀⣀⣠⠆⡠⠀⢸⠀⠀⠀⠀⠀⠀⡺
⠀⠀⡊⠉⠉⠉⡂⠀⠀⠀⠀⠈⠁⠀⠀⡀⣀⡀⠀⠀⠀⢋⢢⡄⠸⠄⠊⣁⠄⠓⠀⠀⠀⠇⠀⠈⠀⠀⠀⢣⡀⠀⠀⠀⢀⠇
⠀⠀⠱⡀⠀⡠⠃⠀⠀⢀⡆⢐⡊⢑⡼⡓⢅⣣⡀⠀⠀⠈⠀⡅⣰⠀⠴⠤⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠒⠶⠖⠁
⠀⠀⠀⠈⠉⠀⠀⣰⡨⠦⡨⡥⠳⣁⠀⡨⠀⠁⠀⡠⠄⠲⡤⢟⡁⠄⠂⠉⠀⠀⠀⠈⠟⠀⠐⠦⠁
⠀⠀⠀⢀⣀⣔⡝⢤⠓⠤⢧⢧⠠⡎⠈⡃⠀⣠⠉⠠⡄⠀⠸⠌⢃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠁⠀⡠⠒⠉⠉⠉⠑⠢⣄
⠀⠀⠀⠐⢞⢢⠃⣚⠁⠙⡁⣠⣀⠜⠈⢀⠌⠁⠀⠀⢃⠀⠀⣣⠠⠄⠀⠀⠀⠀⠀⢀⣄⠠⡀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⢈⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡞⠒⠘⡀⠁⠉⠅⠀⠈⣤⠀⠀⠀⡠⠐⠒⢻⢖⠉⠀⠀⠀⠀⠀⠑⠢⠤⠀⠤⠔⠊
⠀⠀⠀⡔⠂⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⡏⡄⠀⠑⣀⡀⠨⡤⠂⠏⠀⠀⠀⠁⠀⠀⢸⠀⡇⠀⠀⠀⠀⠰⣄⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠉⠀⢉⠴⢦⠀⠀⠀⠀⠀⠀⠀⠩⠙⡉⠁⠙⡀⠀⢸⠎⠀⠀⠀⠀⡆⠀⠠⠃⣠⠃⠀⠀⢠⣶⡟⣿⣏⠛⣷⣮⡙⢿⣷⣄
⠀⠀⠀⠀⠀⡘⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠑⠶⠖⠂⠹⠚⠁⠀⠀⠀⠀⠀⠈⠒⠀⠊⠁⠀⡠⢠⣿⡟⠀⣿⣿⡆⠈⢿⣷⡄⢻⣿⡆
⠀⠀⠀⢀⠔⠁⠀⠀⠣⠀⠐⠌⠙⠻⠐⣄⠤⠤⢀⠀⠀⠀⠀⠀⡠⠄⠓⠉⠊⠠⢀⠀⠀⠀⠁⢸⣿⣇⠀⠸⣿⣿⠀⠸⣿⡇⢸⣿⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠱⡀⠀⠀⠐⠁⠁⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣿⣿⡄⠀⢻⣿⡇⠀⣿⡇⢸⡿⠃
⠀⠀⠀⠐⢄⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⡀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠘⢄⠙⣿⣿⣄⠈⢿⣿⣸⠟⣠⠟⠁
⠀⠀⠀⠀⠀⠁⠶⠆⠂⠁⠀⠀⠀⠈⠢⡀⠀⠀⠀⠔⠀⠀⠀⠀⠑⠄⣀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠑⠊⠙⠿⠿⠶⠿⠛⠊⠁

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⡔⡞⠓⣶⡄⠀⠀⠀⠀⠀⢀⠎⠀⢱⠀⠀⠀⠀⠀⠀⠀⡴⠉⠙⡄⠀⠀⠀⠀⠀⢀⣔⣲⠛⠛⣷⡀
⠀⢰⠁⠈⠈⠉⠁⠘⡄⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠃⠀⠀⠱⡀⠀⠀⠀⠀⡏⠀⠉⠉⠉⠀⢱
⠀⠘⡄⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠣⡀⠀⢀⠆⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⢸⠀⠀⠀⠀⢇⠀⠀⠀⠀⢀⡜
⠀⠀⠈⠢⠤⠤⠴⠁⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠈⠚⠙⠚⠉⠁⠀⠀⠀⠀⠀⠉⠒⠒⠒⠋
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤
⠀⠀⢀⣴⠾⠷⢢⡄⠀⠀⠀⠀⡠⠊⠉⠾⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⡨⠛⢦⡀⠀⠀⠀⠀⣶⣿⣿⣿⡅
⠀⠀⣞⡂⡅⢘⠹⣸⡅⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢱⠀⠀⡇⠀⠀⠀⠀⣠⡾⡿⣷⣄
⠀⠈⣖⠅⡁⢀⢒⢼⠆⠀⠀⠘⣄⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⣀⢀⠤⠊⠀⢀⠇⠀⠀⠀⠀⣟⣝⢾⡳⣿
⠀⠀⠛⡯⣄⣀⡧⠋⠀⠀⠀⠀⠈⠑⠲⠤⠴⠊⠀⠀⠀⠀⠘⣅⣀⣀⣨⠴⠋⠀⠀⠀⠀⠀⠹⣵⣳⣻⠏
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⡰⠋⠙⠉⠉⢆⠀⠀⠀⠀⠀⢀⡠⢤⣀⡀⠀⠀⠀⠀⠀⢀⡠⠦⣧⣤⡀⠀⠀⠀⠀⡴⢋⠁⠈⢉⢙⢦
⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠋⠀⠀⠀⠈⡆⠀⠀⠀⢀⡞⠃⡐⠀⠁⢹⡀⠀⠀⠸⠐⠀⠀⠀⢀⠐⠈⡇
⠀⠀⠱⡀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡀⠀⠀⠀⢀⠇⠀⠀⠀⢸⡇⠉⠁⠀⠸⢸⠁⠀⠀⢠⠀⠠⠀⠀⠀⠠⢠⡇
⠀⠀⠀⡇⠀⢀⡰⠃⠀⠀⠀⠀⠀⠈⠓⠒⠒⠁⠀⠀⠀⠀⠈⠻⣴⣀⣀⣠⠎⠀⠀⠀⠈⠢⣁⡀⢀⣀⡴⠏
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠸⠃⢢⠀⠀⠀⠀⠀⠀⠀⠻⣶⠶⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣄⢴⣶⠀⠀⠀⠀⠀⠀⢀⣀⣸⡀
⠀⠀⠀⠀⠈⡂⠈⠆⠀⠀⠀⠀⡠⠚⢉⠃⣭⠷⣄⠀⠀⠀⣀⡴⠹⠁⠐⢁⠤⡏⠀⠀⠀⠀⢠⣖⣟⣲⣋⡇
⠀⠀⠀⠀⢀⡎⠀⡁⠀⠀⠀⢸⠷⠓⢀⠗⠀⠐⢮⡆⠀⠀⠇⣁⠤⢲⠀⠀⡾⠁⠀⠀⠀⡤⢯⠒⢯⠤⣧⢼
⠀⠀⡠⠒⠁⢀⠔⠁⠀⠀⠀⠈⢄⢛⠨⠆⢠⡉⡴⠀⠀⠀⢇⠀⠀⠎⢒⠞⠋⠀⠀⠀⠀⢳⠞⡶⢻⣲⠏⠁
⠀⠀⠘⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠒⠉⠀⠀⠀⠀⠀⠉⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⢠⠟⢡⡀⠀⠀⡀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⢀⠀⠀⠀⢀⣾⡄⠀⣰⠇⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣜⠀⠀⢀⠹⣿⣁⠀⣿⠀⢀⣼⠁⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠸⢿⡄⠱⡄⠀⣿⣿⢠⡟⢀⣾⠇⣸⣏⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠛⣿⣦⠀⠀⢿⣿⡇⢠⠟⢠⠚⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣆⠻⡇⠀⠀⢰⣿⡰⠇⠀⣠⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣄⡲⣦⣈⣑⠉⢿⣄⠂⠀⣸⣿⡇⢀⣴⡿⠁⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⢳⣌⠛⣷⣤⡟⠀⠠⠋⣸⣷⣾⠟⣣⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣤⣄⣈⣻⠿⣿⣮⡛⠀⠀⢠⣿⡟⠁⣾⡏⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣭⣿⣆⠸⠉⢿⣆⠀⣹⠏⢀⣴⣃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣽⣿⣇⠀⠘⠛⣿⣁⣰⡝⠛⠉⣡⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⠀⠀⠛⣿⡁⣠⠾⣿⣧⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡛⣿⣷⣀⠰⠛⣿⣤⢎⣹⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣻⣧⣉⣫⣿⣦⣾⣿⡛⠾⠛⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣿⣯⣭⢉⣿⠉⣿⣷⣄⣹⣷⣶⢢⣽⣏⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣴⠋⢻⡄⣼⡟⠙⢷⣿⠁⢈⡿⠟⢿⣀⢈⡿⠻⡝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⣿⠃⠁⣸⠷⣿⠀⠁⢰⡿⠤⣾⡇⠘⠀⣿⣬⣇⠈⢘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠈⣧⣼⡇⠠⢸⣇⣠⡟⠀⠀⠈⣷⣀⣶⠁⠀⢻⣄⣸⠃⠜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠹⡇⣶⢃⠘⣷⠀⣼⠃⡉⢳⡄⠀⢠⡟⠉⠹⣧⠀⣸⠏⢹⡆⢰⠟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡍⣠⠿⢿⠀⢰⡿⠾⣿⠀⠁⢺⠷⠶⣿⠀⠘⠐⣿⠴⣷⠀⠀⣿⣿⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣷⡏⠂⣼⣤⣿⠀⠂⢹⣦⣤⡿⠀⠂⢸⣧⣤⣾⡃⠠⢸⣇⣸⡇⢸⣇⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣢⡟⡀⢹⡄⢠⣞⠁⠈⣷⣀⣀⣼⠃⠀⠙⣵⠂⡼⠋⠹⢇⢰⡉⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢀⡿⠙⣇⠀⣼⠛⠛⣯⠀⠀⣾⠋⠉⠿⠀⠀⢀⡿⠲⣷⠀⢀⡾⢷⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⣼⡇⠃⣽⣴⣏⠐⠂⢸⣦⣼⣏⠈⠁⢸⣧⣤⣾⠀⠀⢸⣇⣸⠇⢸⣇⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣻⣱⡏⡄⢹⣂⣠⡏⢠⠀⢿⣅⣠⣾⠃⡀⢹⡆⠀⡜⢉⢹⡆⡸⢋⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⣿⠙⣇⠀⣼⠋⠙⣧⠀⠀⣾⠋⠉⢿⣀⠀⢰⠟⠺⣧⠀⢸⡿⣷⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣏⠁⣿⡤⣿⠀⠀⢸⣧⣼⡇⠀⠀⢸⣧⣤⡿⠀⠀⣿⣤⣿⠐⣽⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢸⣂⡛⠄⢸⣆⣐⡟⠀⠀⢹⡄⣰⡎⠡⠈⢷⡀⣰⠏⠀⢿⡀⢏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⠉⣿⠄⣨⠋⡉⢿⡀⠀⣼⠋⠙⣧⠀⢠⡟⠉⢻⡄⢀⡞⠻⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣬⠗⠻⣆⠁⣸⠗⠚⢧⠀⢐⡿⠒⢿⡆⠀⣼⠷⣾⢈⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⡻⠖⢿⡀⠁⣸⠷⣿⡀⠀⣸⡷⢴⡏⠀⣨⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣷⣀⢈⣿⠴⣯⠀⣨⣷⣼⣇⠀⣠⣷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⠿⣿⡿⢿⣿⣿⠿⠿⠿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦
⠀⠀⠀⠀⠀⡤⠊⠁⠠⠊⠁⠀⠀⢄⠀⠀⠀⠀⡀⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠔⠋⠀⠀⠁
⠀⠀⠀⠀⠈⠀⠀⣠⡀⠀⣾⡀⠀⠀⡆⠀⢀⠄⣿⡖⢡⣶⠇⡀⠁⡀⠀⠀⠀⣾⡏⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠹⠗⠀⠉⠁⠀⠀⡀⠀⠀⠀⢉⠙⢊⠛⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠴⠶⠟⠀⠠⠃⠀⠰⡀⠘⠿⠟⠠⠈⠠⢀⠂⠀⠀⠀⠙⠿⠓
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠁⠂⠀⠀⠀⠐⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⢀⠄⠠⠠⠄⠐⠐⠀⠀⠀⡀⠀⠐⠀⠀⠀⣀⠈⠀⠠
⠀⠀⠀⠐⠀⠀⠀⠘⣤⡄⠘⢻⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⡀⠀⠀⠀⢀⣦⡄⢀⣀
⠀⠀⠀⠰⠀⠀⠀⠀⣿⠿⠀⠈⠉⠀⠀⠀⢠⠀⠀⠀⠀⠐⣿⡆⠀⣿⠇⠀⠀⠀⠀⠀⠾⠿⠁⣼⡿
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢤⣶⠆⠀⠀⠀⠸⠀⠀⠀⠀⠀⠛⠁⠀⠁⠀⠀⡄⢰⠀⠀⣀⣀⣀⠈⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠴⠾⠛⢀⠜⠀⠀⡄⠀⠈⠛⠉⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠁⠀⠀⠀⠈⠂⡀⠀⠠⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⠀⠀⠀⠈⠐⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢦⡊⠀⠀⠀⠀⠀⠈⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡘⡢⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠴⠔⠀⠉⠀⠀⠀⠀⠀⠀⠀⠔⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠛⠛⡂⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⡀⠀⠠⠠⠌⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠰⠴⠄⠀⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠍⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢠⣴⡀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠉⠁⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣜⣀⠾⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢆⠠⢅⠸⢤⠘⢠⠇
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠠⠖⠀⠠⠀⠉⠉⠡⠀⢀⠀⠀⣰⠆⠀⠀⣠⠚⢀⠶⣄⠼⣀⠜⢤⠚⣄⠃⣄
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠡⠘⣦⠀⠐⢡⠀⢈⡀⢀⠃⠀⢁⡴⠣⠀⠀⠀⢙⣀⠠⡤⠢⣠⠒⠤⠘⢴⢁⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⠄⠂⠡⡈⠛⠄⡀⡀⠀⠀⣀⡡⠴⢋⠔⠁⠐⠀⠈⠀⠐⢅⠄⡀⠛⠀⣓⣤⡮⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⢀⣀⣀⣀⠀⠤⠒⠁⠀⠐⠲⡄⠀⠀⠀⠀⠀⠉⡉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠅⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⡄⠨⡙⣶⠃⡀⠱⡄⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠛⠛⠒⠾⢾⡄⣇⠀⢹⣀⡴⢃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⣄⠀⠀⢰⡆⠀⠀⠈⠛⢄⠸⠯⠶⢧⣤⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⠁⠀⣀⠀⠀⠀⣀⠀⠀⠈⠳⡄⠀⠀⠀⣀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⣰⡄⠀⠘⠛⠀⠀⠈⠑⠁⠠⢆⠀⢹⡋⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠁⠀⠈⠀⠀⠀⣀⠀⠀⠀⣀⠄⠀⠀⠀⠀⣧⡈⠢⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣰⠃⠐⠃⠀⠐⠣⠂⠈⠁⠂⠀⠀⠑⠊⠀⣰⡀⠂⣿⠹⡗⠂⠀⠑⠀⠀⠀⠀⠀⠀⠀⣸⢰⢀⡤
⠀⠀⠀⠀⠀⢠⣯⠀⢀⣄⠀⢀⡄⠀⠀⢠⣶⠀⠀⣠⡄⠀⠀⠀⢠⠏⠂⠁⠀⠀⢀⣠⠖⠚⠉⠉⠛⠲⣿⠘⡟⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠈⠂⣠⡄⠀⠀⠀⠀⠀⣊⡤⣂⡴⠋⠀⠀⠀⠀⡴⠋⠀⠀⠀⢄⡀⠀⠀⠈⢧⡸⣸
⠀⠀⠀⠀⠀⠘⢦⠀⠀⠚⠄⠀⠀⠐⡊⢤⣒⣲⡯⠽⠖⠛⠉⠀⠀⠀⠀⣠⠞⠀⠀⢀⣡⠶⠚⠉⠀⠀⠀⠈⠻⣭⢍⡑⠒⠂⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⠶⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢀⠶⠋⣀⡠⢀⣠⠖⠁⡀⠀⠀⠘⡆⠉⠲⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⠀⠜⣡⠴⣊⣥⠖⢋⡡⢴⠊⠳⠀⠠⣰⡟⠒⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡀⠀⠾⠷⠻⠭⡖⠋⠹⠀⠈⠀⠀⣀⡴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠐⣀⣊⣀⣀⣡⣤⣤⣶⣖⠻⠍⠁⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣭⣭⣉⣀⣀⣀⣀⣀⣀⣀⡤⠽⠛⠁


⣤⣤⣴⣶⣶⣤⣴⣶⣦⣴⣦⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣦⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠠⠦⠒⠂⠀⠐⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⣠⡇⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⢀⠀⡀⠀⠀⠠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣢⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠐⠀⠁⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠒⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠁⠀⠀⢸⠂⠀⢀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠊⠀⠁⠀⠀⠀⠀⠰⠤⠀⠔⠃⠀⠐⢄⠀⣀⡀⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀
⣿⣟⣙⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠤⠐⠂⠤⠤⠄⠀⠀⠀⠀⠓⠤⠦⣄⡀⢀⡠⠃⠀⢀⡤⡄⠘⠦⣄⡀⢀⣢⠞⠁
⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⣸⠁⠀⠀⠀⠉⠉⢀⡠⠖⠔⣇⣠
⠀⢘⠀⣀⠀⡀⣀⠔⠀⠀⠹⡄⠈⠉⠢⣄⠀⠀⠀⣠⠞⠀⢠⢿⡄⠀⠀⠀⠀⠐⠿⠁⡂⢰⠀⢽⠒
⣀⣤⠤⢤⣤⣍⡀⠀⠀⠀⠀⢸⠢⡀⠀⠀⠈⠉⠉⠀⠀⢠⠟⣸⡇⠀⠀⠀⠀⠀⡿⠤⢅⢍⡙⡚
⠀⠀⠐⠂⠀⠀⠉⢷⡀⠀⠀⠀⠳⣄⠀⠈⠁⠀⠀⠒⠊⠁⡰⢁⠇⠀⠀⠀⠀⠀⠱⣅⡇⣐⡞⠀⢀⣴⠚
⠂⠈⠀⠠⠀⠈⠁⠀⢷⠀⠀⠀⠀⠈⠙⠓⠲⠤⣤⣄⣒⣊⠤⠊⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢠⠋⠀⠁
⠀⠀⠁⠀⠀⡀⠐⠀⣸⠀⠀⠀⠀⣀⠤⠤⡀⠀⠀⠀⠀⠀⠀⡠⠄⠂⢄⣼⣭⠄⠀⠐⢒⠂⠀⣇⡀⠢⠠
⠀⠄⠀⢁⠀⢀⢀⡰⠃⠀⠀⡴⠋⠀⠀⠀⡙⣆⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠉⠉⠳⡄⠁⠀⠀⢧⡀⠂
⠀⠐⠀⣀⣠⠴⠋⠀⠀⠀⢸⠁⠀⠀⠀⠔⠀⣿⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠳⣄⣆
⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠢⣤⣴⣎⣒⡼⠏⠀⠀⠀⠀⠀⠑⢤⣀⡀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣀⣀⢀⡄⠀⠀⠀⠀⠀⠈⠉⠁
⠶⡄⠀⠀⠀⠠⡤⠀⡠⠤⠤⣤⡀⣤⠀⠀⡐⠁⠀⠀⡐⣄⠀⠀⢠⡀⡰⣀⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔
⠠⠈⡄⠀⠀⠀⢹⣶⡀⠀⠄⠀⢰⠃⠀⠀⡗⠀⠀⠀⠀⠜⠀⠐⡾⠈⠁⡁⢸⡇⠀⠀⠀⠀⠀⡔⢩⣤⠶
⠀⢠⠁⢀⠴⠒⠺⠛⠳⠠⡴⠐⠋⠀⠀⠀⢇⠀⠀⡀⠁⠀⠀⣐⡷⠄⠀⠀⠈⠟⡇⠀⠀⠀⢸⣑⠈
⠒⠁⠀⡏⠀⠀⢈⠀⡁⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⣢⡀⠀⠀⠐⢸⡄⠀⠀⠀⠀⠈⠓⠦⠤
⠀⠀⠀⠈⠣⡀⢀⠘⢄⢹⠁⠀⠀⣴⡄⠀⢀⡂⣀⠀⣠⡄⠀⠀⠙⢧⠀⠀⠀⢰⠁
⠦⡀⠀⠀⠀⠙⠯⣔⠤⡿⠀⠑⠈⡽⠷⢄⠀⢑⡬⢿⠁⠀⠀⠀⠀⡜⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⡠⠔⠒
⠀⠘⠛⠲⣄⠀⠀⠈⠉⠀⠀⠀⠀⡇⠀⠈⣦⠇⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡜⠀⠈
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⠀⠸⡀⠀⠀⠀⢸⡀⠈⠀⢀⠀⠀⠀⣇⠀⠀⢣
⠚⠤⠤⠤⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠈⣇⠀⠠⠀⠀⠀⢀⡟⠀⠀⠀⠑⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⠏⠀⠀⢀⣠⣤⠶⠚⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⠀⠀⠀⠀⣠⠞⠋⣰⠏⣠⡴⠞⠋⠁⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⠀⠀⢀⡞⠁⠀⢰⣿⠞⠉⠀⠀⠀⢀⣠⡶⠟⠳⠶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡇⣿⠀⠀⡞⠀⠀⣠⠞⣡⠔⠂⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠈⣹⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⠷⣾⣿⡸⣆⡼⠁⠀⡼⠃⡴⠃⣠⣾⠿⠶⠛⠛⠛⠛⠛⠛⠒⠒⢒⣻⠟⣦⡀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⣧⠹⣇⠀⣸⠁⣼⠁⢀⣤⠶⠒⠒⠀⠀⠀⣀⣀⣤⣤⡶⠟⠉⠀⠈⠃⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠿⠛⠋⠹⣧⠙⢧⡁⣼⣧⡾⠋⢁⣠⣤⠶⠾⠛⠛⠋⣉⠉⠀⠀⣠⡀⠀⠀⠀⣀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⣴⠟⠉⢀⡤⠶⠖⠛⠛⡛⢷⣼⡿⣸⠋⠀⠘⣯⠁⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠘⠟⠀⠀⠀⢿⡇⠀⠸⣷
⠀⠀⠀⢀⡾⠁⠀⠘⢁⣀⣤⣴⡶⠛⣵⠟⠁⡄⠀⠀⠀⠀⣿⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⡆
⠀⠀⠀⡼⢁⣠⡶⢿⡟⠁⣴⠏⢀⠞⠁⠀⣼⡇⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣿⡇
⠀⠀⣼⣵⠟⠉⢀⡿⠀⣼⠏⠀⡏⠀⢠⠞⢸⣇⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠸⣿⠆⠀⠀⠀⢴⣄⠀⠀⠹⠇⠀⣿⡇
⢀⡾⠛⠁⠀⠀⣼⠃⢰⡿⠀⠀⠀⣰⠏⠀⠀⢻⣦⡀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⣿⡇
⠉⠀⠀⠀⠀⢠⡟⠀⠸⣇⠀⠀⣼⠏⠀⠀⣤⡀⠈⠻⣦⡀⠸⡇⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⡀⢰⡟⠀⠀⠀⠙⠷⠀⠀⠈⠻⣦⣧⠀⠀⠘⠿⠃⠀⠀⠀⠠⣶⡄⠀⠀⠀⠀⠀⣿⣆⠀⠘⣿⡀
⠀⠀⠀⠀⠀⢸⡇⢀⡀⠈⣧⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠘⠋⠀⠀⢹⣧
⠀⠀⠀⠀⠀⢸⣿⠘⣷⠀⢹⡟⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⢿⣧⠈⠀⠈⡇⠀⠠⣤⡀⠀⠀⠈⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢾⣦⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠀⢀⡀⠸⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠁⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠸⣿⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⢀⣀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠁⢸
⡉⠏⠁⠉⠁⠁⠁⠁⠁⠉⠛⠿⢷⣀⢈⠛⠛⠈⡢⢘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠧⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⢸
⡐⠠⠀⠠⠀⠤⠤⠤⠖⠀⠀⠠⠈⠛⠿⢷⣶⣶⣬⣤⡂⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⢀⣾
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠨⣙⠛⠿⠿⢿⣶⣤⣤⣀⠀⠀⠉⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⣄⡀⠀⠀⠀⠀⠀⠻⢷⡄⠀⠀⠻⣷⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣉⣉⣐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⣧
⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⢸⡟⠷⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣸⢷⣄⠀⣸⠇⠀⠸⣇⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠘⣇⠀⠀⠉⠛⠳⠶⣤⠶⠋⠁⠀⢠⣄⣀⠙⡏⠀⠈⠙⠛⠲⠶⢦⣽⣴⡟⠁⠀⠀⠀⢀⡤⠂⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⢰⠷⠶⢦⣄⠀⠀⠀⠉⠛⢷⡀⠀⠐⢤⡀⠀⠀⠈⠻⣄⠀⠀⢀⡴⠋⠀⢀⣴⠋⠻⢦⣀⣀⣀⣀⣀⣤⣴
⢀⣀⣀⣀⣀⣈⣻⣶⣤⣤⡤⠤⠤⠖⢘⣿⣦⣀⠀⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠀⠙⣷⠞⠋⠀⣀⣴⣏⣉⣓⡲⠀⠈⢉⣉⣩⡽⠟⠁
⠈⠻⣯⣉⡉⠉⠉⠁⠀⠀⠤⠶⠖⠛⢉⣉⣭⠟⠻⠶⢶⣶⠾⣷⡀⠀⠀⢿⡄⠀⢀⣸⠷⠖⠛⠉⠈⠉⠉⠉⠙⠛⠻⢿⡉⠁
⠀⠀⠀⠉⢙⡿⠶⠶⠶⠶⠶⠶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠾⠷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠙⣦
⠀⢀⡾⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠸⣧
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠁⠀⠀⠀⢠⠀⠀⢻
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⣠⠂⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠘⣡⠀⠸
⣾⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠
⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢰
⢿⠀⠀⠑⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠐⠄⠀⠁⠀⣾
⢸⣇⠀⠈⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⣾⢱⡄⠀⢀⠀⡀⠀⠐⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠸⠀⠃⣰⡟
⠀⢻⡄⢂⠀⠀⠀⠻⠀⠀⣂⡄⠀⠀⠀⢧⠗⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠙⠊⢀⠤⠀⢠⡿⠁
⠀⠀⢿⡄⠀⠀⢄⠀⠀⠄⡉⠀⠀⢀⠀⠀⠀⠀⠀⠖⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠁⠀⡐⠃⠀⢀⣿⠁
⠀⠀⠀⢻⣆⠀⠒⠀⠀⠸⣙⠀⠀⠀⡜⢦⠀⠀⠀⠰⣇⣳⠀⠀⠀⠀⠀⠀⠀⢀⠐⡄⠀⠀⠀⡆⡑⠀⢠⡞⠀⠀⡠⠈⢀⣾⠃
⠀⠀⠀⠀⠹⣧⡀⠀⠀⣄⠀⠀⠀⠀⠈⠚⠀⠀⢤⣀⠈⠁⠀⠀⠀⠉⠅⠤⠀⠈⠧⠟⠀⣀⡀⠀⠀⠀⠀⣠⠄⠀⢢⢊⡿⠃
⠀⠀⠀⠀⠀⠈⢷⡄⠀⠰⠆⠀⠀⢰⢄⠀⠀⠀⠐⢼⠂⠀⢠⣀⡀⠀⠀⠀⢀⠤⠤⠀⠋⠄⠀⠀⠈⠀⠀⢀⡀⠀⣱⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠖⠀⠀⠠⠤⡀⠀⠀⠀⠐⠙⠂⠀⠸⠋⠐⠀⢠⠴⠀⠀⢀⠰⠀⠀⠊⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠰⠀⠀⢀⠀⠀⡀⠑⠚⠀⠀⠶⢠⡀⠀⡄⠴⠀⠀⠀⠈⠈⠀⠀⠈⠉⡄⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠠⡀⠁⠀⠀⠃⠀⠀⠀⡀⠀⠁⠀⠀⠁⠀⠠⠂⠀⠀⠀⠀⠀⢉⡀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⠀⠀⢀⠀⠀⢀⠀⠋⠀⠀⠐⠐⠦⠀⠀⠀⠀⠀⠀⠀⡐⠁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠁⠀⠁⠚⠀⠠⠔⠄⠀⠀⠀⠂⠟⠀⡴⠂⡀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠁⠐⢀⡀⠀⠀⢀⡀⠐⠀⠀⣀⡄⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⡀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣀⡈⠓⠀⣀⣨⣴⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠁⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠁⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠄⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⢠⣯⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠂⠀⠠⠄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⢰⠀⠄⠀⠀⠀⠋⠉⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠒⠚⠉⠁⠀⠀⠀⠀⠋⠀⠀⠀⠠⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠸
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠂⠂⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡇
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠁⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠰⠀⡀⢠⢧⠨
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠀⠈⠀⠀⠀⠀⢀⡄⠀⠀⠐⠢⠄⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢌⠀⡡⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠣⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡑⠉⢊⠢⡁
⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠘⠀⠀⠹⠀⠀⠠⠀⠀⠀⠈⠐⠑⠁
⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠑⠦⣤⣤⠴⠀⠀⠀⠀⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠔⠢⠏⠀⠢⠀⠀⢀⠚⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠌⣡
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠔⠐⠀⠀⠀⠀⠀⠀⠀⢠⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢋⣡⡴⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠒⠐⠀⠀⠀⠀⠀⠀⠘⢎⡠⣀⠀⠀⠀⠀⠀⢧⡤⠞⣋⣥⠶⢟⣡⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⣂⣤⣇⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡠⠖⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡴⣡⡄⢺⣿⠛⡈⠀⠈⢟⣳⠄⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠠⠆⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⡁⠠⡨⣒⢽⠂⠀⠀⠀⣩⠉
⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠠⠂⠀⠙⢆⠀⠀⠀⠀⠀⠀⢚⢐⠀⣀⠶
⠀⠀⠀⠀⠀⠈⠀⡀⠀⠔⠠⢀⠐⠀⠁⠎⡤⠀⡀⠀⠀⠀⠈⠘⠀⠁⠀⠀⡀⠈⣰⠀⢀⠄
⠀⠀⠀⠀⠀⠃⠀⢁⠄⠀⢠⠄⠀⠀⡘⢠⡣⡀⠀⠀⢠⣀⡀⡐⠠⢄⡤⠰⠊⢉⠉⠛⠓⡖⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠎⠀⠀⠐⢀⠄⠀⠐⠁⠐⠀⠁⠀⠀⠦⡀⣨⠓⠯⠖⠀⡄⠀⢀⠈⠀⠰⠀⠰⠨⠁
⠀⠀⠀⠀⠘⡀⠐⠁⠀⠠⠄⠀⠁⠀⠀⠀⠀⠀⢠⠈⢀⢃⢈⣾⠰⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠃⡤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡀⠄⠜⠀⠀⠁⠀⠀⠠⠀⢠⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⢠⠀⠀⠀⡄⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣺⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠃
⠀⠀⠀⡀⠀⠀⣀⠀⣀⣄⣬⡡⣄⠀⠀⠀⠍⠀⠂⠀⠈⠊⠂⠀⠀⠐⠀⠤⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠨⠘⡿⠗⠢⠀⢄⠀⠀⠈⠙⠾⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠼⣴⣖⠀⠀⠈⣋⠀⠘⠀⠁⡀⡀⠃⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠆⠀⢩⠛⣈⠳⡄⣇⢃⢉⠂⠠⠁⢄⡙⠀⢀⣀⣄⣠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣃⢠⠐⠇⠀⢉⢠⠐⢩⠉⠀⠤⠰⠠⠈⠁⠸⠍⠉⠝⢿⢳⠀⠜⡿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢍⠠⠈⡀⠂⡀⢀⠈⡀⠀⠀⠀⠐⠃⠀⢘⢉⢙⣁⠀⡛⣼⢇⠠⣅⠘⡱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢁⠠⠁⡌⠄⠀⠀⠀⠀⠀⠀⠀⢸⡄⠰⢀⠂⠚⠱⠘⠀⠄⡄⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠉⠀⠀⠀⠁⢉⡔⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣽⠿⠋⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠬⠋⠐⢂⡀⠀⣀⣠⣆⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣰⠋⠁⠀⠀⣤⣤⣤⣤⣶⣿⣦⠀⠀⠀⠀⢀⡀⠀⠙⢻⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⣿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠄⠀⠀⣼⣇⠀⠀⠀⠙⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⠊⣿⣶⡾⣿⣿⠿⣿⠽⠯⠅⢠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⣿⣗⣀⣈⣀⡄⠀⠁
⠀⠀⠀⠀⠀⢀⠒⠛⣻⣷⣶⣿⡏⠑⠛⠙⠙⠉⡉⡀⣴⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⠿⣿⣿⣿⡉⣽⣏⣁⣤⡀
⠀⠀⠀⠀⠀⠐⣤⣴⣿⣻⣿⣿⣷⡀⠀⣤⠶⠾⢻⣿⣿⣶⣤⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣸⣿⡙⠗⠿⣿⣿⣯⡗⠂⣀
⠀⠀⠀⠀⠀⠀⠘⢧⠚⢧⣾⠟⢻⣙⣶⣯⢻⣼⣿⣿⣿⣿⢷⣄⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠈⠹⡍⠀⣄⣉⣹⣿⣿⣿⣶⣿⡷⠄
⠀⠀⠀⠀⢨⣵⣾⣾⣶⣿⣿⣿⢙⣿⣿⣿⣿⣿⣿⣿⡋⢀⣤⣭⡟⠻⣿⣷⣄⣀⣀⣴⡄⠀⢁⣀⣥⣤⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠙⠿⣿⣿⠿⠿⠟⠛⠛⠿⣿⣿⣿⣿⣾⠿⠿⠛⠛⠛⠛⠛⠒⠻⠿⠿⠿⠟⠻⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⢴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠲⠃⠉⢲⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠰⠶⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⡎⠐⢄⣀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠐⢤⣄
⠀⠀⠀⠀⠀⠀⢀⡀⡴⠋⠀⠘⠒⠫⡀⠀⠀⠀⠀⠀⡴⠁⠡⠄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⡠⠚⠀⠀⠗⠒⠒⠠⡀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⡧⢀⣸⡃⠀⠅⠄⢀⠛⢦⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢱⠆⠸⡄⠀⢀⡁⠉⣀⠼⠀⠀⠀⠀⢧⠀⢠⣄⠀⠀⠀⣤⡀⢀⠆⠀⠀⠀⢀⠀⣠⣄⠀⠀⢀⣤⡀⢠⠀⠀⢁⢀⣀⠀⠀⠀⣀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠣⡌⠁⠐⡈⠉⡖⠁⠀⠀⠀⠀⠀⠀⠓⠬⣉⣀⢀⣀⣩⠔⠋⠀⠀⠀⠀⠀⠁⠌⢁⠀⠀⣈⡉⠔⠁⠀⠀⠀⠢⢉⡁⠀⠀⣉⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠈⠉⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⢀⠖⠉⠉⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠠⠂⠉⠁⠱⠀⠀⠀⠀⠀⠠⡊⠒⠒⠤⡀⠀⠀⢰⠁⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠠⠂⠈⠁⠛⠶⠤⡀
⠀⠀⠀⡇⡄⠀⠀⠀⠑⠀⠀⡠⡔⢂⡩⢗⡖⣠⠋⠀⠀⠞⠀⣤⡄⢀⡀⢠⣤⠀⡇⠀⠀⠀⠀⡜⠀⠛⠀⠂⠘⠃⠘⡄⠀⠀⠁⡖⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠑⢄⣀⡛⠔⠁⣠⠊⢀⠜⠁⡴⠁⡄⠘⢧⠀⠀⠑⠦⡉⠀⠀⠀⠈⣡⠞⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢀⠎⠀⢰⠁⠀⠀⢸⢹⠀⠀⠀⠀⠈⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡀⠄⠀⢠⡄⠀⠠⡸
⠀⠀⠀⠀⣀⡠⠔⠉⠀⢀⠞⠀⠀⡼⠆⠀⢠⢜⡘⠀⠀⠀⢀⡴⠒⠛⠓⠲⡄⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠈⠒⠤⠤⠤⠤⠚⠁
⠀⠀⠀⢿⣀⠀⠀⢀⡠⠊⠀⠀⢠⠇⠀⠀⠀⠆⠇⠀⠀⠀⣼⠁⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠉⠹⣿⠉⠀⠀⢀⣠⠊⠀⠀⢀⢎⠎⠀⠀⢀⡞⠁⠀⣀⢛⠠⢀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣠⡰⢢⡠⡀⠀⠀⠀⠀⠀⠡⡀⠈⠖⣂
⠀⠀⠀⠀⠀⠀⠉⠛⠒⠻⣾⡁⣀⡠⣔⠕⠁⠀⠀⢀⡟⠀⠀⢠⡅⢩⠱⢦⡀⠀⠘⣆⠀⠀⠀⠀⡠⠕⠀⠀⠐⢅⡀⠀⠀⠀⠀⠀⡜⠀⠀⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⢸⠀⠀⠈⢃⡜⡘⢣⡕⡃⠀⠀⣿⠀⠀⢠⠊⠀⠤⠀⠀⠀⠀⠘⢆⠀⠀⠀⢠⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⢀⣠⠤⣀⠀⠀⠀⣀⡤⠤⣀⠀⠀⠀⠀⢻⠀⠀⢨⡽⢦⡅⢛⢨⡉⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⢰⠋⠀⠀⠈⠇⠀⢸⠀⠀⠀⠈⠑⠀⠀⠀⢸⡀⠀⠀⠙⣀⠂⢰⠄⠁⠀⠀⣼⠀⠀⢸⡀⢠⣄⠀⠀⢠⣤⠀⡸⠀⠀⠁⢀⣤⠀⣀⠀⣤⡄⢨
⠀⠀⠀⠸⡛⠤⢠⡀⡄⠀⠀⡀⣀⠀⠘⢣⠀⠀⠀⠈⢧⠀⢀⢀⠉⠘⠁⢀⢀⠀⣠⠇⠀⠀⠀⠙⠢⢅⣀⣀⣀⠥⠚⠁⠀⠀⠈⠢⠍⣀⡉⣀⠉⠔⠁
⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠁⠊⠀⠐⠁⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⣀⣤⠞⠃
⠀⠀⢠⠒⠲⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠤⣀
⠀⠀⢈⠀⠀⠠⡄⠀⠈⠉⠁⠐⡒⠂⠈⠉⠉⢱⠀⠀⠀⠀⠀⠀⡐⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⠊⠀⡠⠃⠀⠀⠀⠀⠀⠀⢠⠶⣀⠀⠄⠃
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢠⣤⠀⠀⢈⠀⠀⠀⢀⠔⠉⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠹⡄
⠀⠀⠀⢣⠀⠀⠀⠐⠀⠀⢶⠆⠀⠀⠁⠀⢀⡌⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠈⣄⡠⠤⣲⠀⠀⠀⡠⠒⠫⠒⢄⠀⠀⠀⠠⠂⠁⠉⠢⠀⡠⠺⠁⠐⢄
⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠘⡀⢤⣤⠀⡀⢠⣤⢀⠂⠀⢀⠇⠀⠀⠀⡁⡀⠀⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠀⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠈⠙⠂⠐⠐⠀⠚⠋⠒⠊⠉⠀⠀⠀⠀⠈⠃⠀⠘⠁⠀⠀⠀⠀⠁⠒⠒⠉⠀⠉⠂⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⡉⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠉⢩⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡄
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢰⣦⡀⠀⠀⢠⡿⠀⠈⣿⡀⠀⠀⢀⣠⣶⠿⠛⠋⠉⠉⠉⠛⠻⢶⣄⡀
⠀⠀⠀⠀⢻⡄⠉⠛⠷⣤⣤⣀⡀⠀⠀⣠⣴⠾⠛⠛⠛⠛⠻⢦⣼⠉⠻⢦⣤⣾⣁⣀⠀⠹⣧⠀⣴⡿⠋⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢙⣷⡄
⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⠉⠙⣷⠟⠉⠀⠀⠐⠒⠒⠤⣄⣀⣿⠀⠀⢀⠀⠈⠉⠙⠛⠶⣿⣾⠏⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⣾⠋⠁
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠸⠿⠛⠳⢶⣄⡀⠀⠀⠀⠈⠙⢻⣄⠀⠀⠐⠦⣀⠀⠀⠀⠈⠻⣦⡀⠀⠀⣠⡴⠋⠀⢀⣴⡿⠋⠙⠷⣤⣀⣀⣀⣀⣀⣤⣤⡾
⢀⣀⡀⠀⠀⠀⠈⠻⣷⣦⣄⣀⣀⠤⠤⠤⠤⠘⢿⣦⣀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠙⢳⣄⠀⠀⠀⠈⢷⡶⠟⠉⠀⢀⣴⣿⣋⡙⠓⠶⠦⠀⠉⠉⠉⣉⣥⠾⠋
⠈⠻⣿⡛⠛⠛⠛⠛⠋⠉⠉⠀⣀⣤⡤⠶⠞⠛⠛⣋⣿⡿⣶⣦⣤⣤⣤⣿⣆⠀⠀⠀⢹⣦⠀⠀⠀⢈⣷⣤⠶⠾⠛⠉⠙⠛⠛⠛⠛⠿⠿⣿⡟⠛⠋⠁
⠀⠀⠈⠙⠻⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠟⠋⠁⠀⠀⠀⠉⠉⠉⠈⠻⣦⣤⣄⣠⣿⣤⣤⡶⠟⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⢀⣴⠏⠁⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠹⣦
⠀⠀⣼⠏⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠂⠀⢻⣧
⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⠈⣿
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⡄⢠⠆⠀⠀⠀⠀⠀⠀⠀⠰⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⢹
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⡀⠀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⢸
⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡀⠀⠀⠀⠀⠀⠁⠀⠀⢤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠲⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠀⠀⣼
⢻⡇⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⣆⠀⢠⣿
⠸⣷⠀⠀⠘⠇⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢰⡉⢾⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⢀⠄⠒⢀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠂⠀⠀⠀⠋⢀⣾⡏
⠀⢻⣇⠐⠄⠀⠀⠀⠰⡇⠀⢀⠚⡄⠀⠀⠀⠀⣇⡹⠀⠀⠀⠀⠀⠘⠷⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠠⠆⠀⠞⠀⠃⢀⡠⠀⠀⣼⡟
⠀⠀⢻⣆⠰⠀⠀⢀⠀⠀⠀⡀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠏⠀⠀⣰⡿
⠀⠀⠀⢻⣦⠀⠀⣈⠀⠀⠀⠰⠆⡀⠀⠀⠉⢠⠀⠀⠀⠀⠀⢠⠖⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⠀⠀⣤⠀⠀⠰⠀⠔⠀⢠⡿⠁
⠀⠀⠀⠀⠹⣷⡀⠈⠀⠀⠀⠈⠲⠃⠀⠀⠀⣤⢹⠄⠀⠀⠀⠈⢧⣼⠃⠀⠀⠀⡄⢠⠀⠀⠀⢠⡆⢲⡀⠀⠀⠀⡿⠐⠁⠀⠘⠃⠀⠀⢠⠁⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠘⢷⣄⠀⠈⠁⢄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠰⠖⢄⠀⠀⠀⠀⠀⠀⠐⠆⠘⠀⠀⠈⠓⠞⠁⣠⣤⠀⠀⠀⠀⠀⢠⠶⠂⠀⠐⠞⣱⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠢⠀⠀⠀⠈⡵⢄⠀⠀⠀⠀⠠⠼⠃⠀⠀⢤⢄⡀⠀⠀⠀⠀⣠⠤⠒⠠⠈⠠⠀⠀⠀⠀⠀⠀⠃⠀⣀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⢐⡶⠃⠀⠀⡤⢀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⢶⠉⠠⠂⠀⡠⠤⠀⠀⠀⠀⡤⠀⠀⠊⠁⢠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⢀⡄⡀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠃⠄⠀⠀⠀⠧⠂⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠐⠆⠀⠁⢠⠀⠀⠀⠀⠀⠡⣘⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠊⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠑⣄⠀⠀⠀⠀⡀⠀⠈⠃⠰⡀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠐⠂⠀⠀⣠⠶⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⠂⠀⠀⢀⠀⠀⣀⠀⠈⠀⠀⠀⠉⠉⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠁⠀⠁⠘⠃⠀⠰⠖⠦⠀⠀⠀⠐⠊⠙⠁⢠⠞⠁⡀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡈⠂⠐⠠⠀⠀⠀⠀⠀⡀⠀⠐⠂⠀⢀⡀⠀⠀⠘⢁⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠳⠀⠀⠀⠊⠉⠀⠀⠀⠀⠈⠉⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠠⢤⡀⠀⠐⠛⢃⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣤⣤⣤⣤⣶⡾⠿⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⣿⡿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⣀⣤⣴⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡀⠀⠀⠀⠀⠀⠀⣿⣷⣤⠋⡀
⠀⠀⠀⠀⣼⣯⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣿⣿⡇⠀⠀⠀⠀⠀⡼⠉⠉⠉⠉⠈⢳
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣥⣾⣿⡿⠁⠀⠀⠀⠀⠀⢳⠀⠐⠂⠂⠀⡸
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠞⠁


⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡇⠀⢀⡀⠀⠀⠀⠀⠀⢰⣦⣀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣤⠂⠁⠀⠀⠀⠀⠀⣴⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⠛⣆⣽⡆
⠀⠀⠀⢼⣿⣿⡟⡻⠿⠿⠇⠀⠀⠀⠀⠀⢾⣿⣿⡿⠿⡿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⢋⣁⠐⢢⠀⠀⠀⠀⠀⢐⠻⣤⣺⣾⣿⡿
⠀⠀⠀⠀⠙⠻⠿⢷⡟⣶⠲⣯⠆⠀⠀⠀⠘⢿⣿⣿⣶⠖⡴⣦⣠⠆⠀⠀⠀⠀⠙⠻⠟⢦⣤⣭⣴⡿⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠈⠙⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢻⣿⣷⠏⣀⡀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢼⣿⣿⡿⣟⣿⣿⣀⣤⡀⠀⠀⠀⠀⠀⣾⣿⠛⢿⣿⡄⠀⠀⠀⠀⠀⢀⣤⣀⣀⣀⣠⣠⣿⡇
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣿⣿⠛⠁⠀⠀⠀⠀⠀⣿⣧⣀⣰⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣙⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⢾⣿⣿⣷⣿⣿⣿⡷⠀⠀⠀⠀⠀⢀⣾⢟⣽⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢧
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣿⣇⣿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⣼⣾⣦
⠀⠀⠀⠀⠀⠀⠻⣟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠿⠽⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⣀⠀⠗⡀⠈⠀⠀⠀⠀⠀⠠⣠⣤⣤⢦⡠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡤⡄
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢐⠓⠊⠨⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠠⠀⠀⠀⠀⢎⠰⠈⡟⠉⡵⡄⠀⠀⠀⠀⠀⠀⠀⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⡔⠀⠀⠀⠀⠀⠈⠢⣤⠤⠔⠉⠀⡀⠀⠀⠀⠂⠟⢳⡋⠛⣲⣾⠁⠀⠀⠀⢠⠊⠵⠇⢪⠓⠂⢑
⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠎⠀⠀⠀⠀⠀⠀⠑⠂⠤⣀⡀⠤⠊⠀⠀⠀⠀⠀⠲⠦⠉⠙⠀⠁⠀⠀⠀⠀⠈⠂⠤⠠⠛⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⢀⠀⠀⠀⠀⠀⠀⠀⣁⢓⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠉⠀⠐⢄⠀⠀⠀⠀⠈⠤⠀⢀⡦
⠀⠀⠀⠀⠀⠈⡸⠶⡇⠀⠀⠀⠀⠀⠀⠢⠜⠫⠙⣉⣃⠖⠀⠀⠀⠀⠀⠀⠘⢃⡀⣄⣀⠀⠀⠀⠀⠦⠊⠀⠉⡉⢢⣀⡠⠀⠀⠀⠰⠃⠀⠀⠈⣄⡀
⠀⠀⠀⠀⠓⢺⠀⠀⠐⠂⠀⠀⠀⠀⠈⢈⠃⡉⢰⡈⡐⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠂⣸⠉⠀⠀⠀⠀⢠⡀⠀⣠⡟⡠⢤⡱
⠀⠀⠀⠀⠀⠀⠁⠐⢀⡠⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠬⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⠿⠃⠀⠀⠀⠈⠓⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠣⡊⣉⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⢀⡜⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⣿⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠐⠶⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⣀
⠀⠀⠀⠐⠁⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⡡⠀⠀⠀⠀⢺⠮⣿⢿⠆⠀⠀⠀⠀⠀⠀⣢⣄⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⢛⣬⣇⣐⣨⣻
⠀⠀⠀⠠⡀⠀⣠⠶⠲⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢜⢎⣷⡦⠀⠠⠀⠀⠀⠀⢰⣿⣿⣳⣦⣀⠴⠋⠀⠀⠀⡈⣿⢫⠞⢁⠏⡠⡅
⠀⠀⠀⠀⠈⠉⠛⢄⡑⠖⠊⠀⠀⠀⠀⠀⢀⣦⣄⡀⡠⠃⠀⠀⠀⠀⠀⠣⣳⢟⡅⠨⠀⡀⠀⠀⠀⠀⠑⢿⣿⣿⠿⠒⠀⠀⠀⠀⠀⠈⠻⠴⠚⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠜⢂⠍⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⠾⣷⣶⣤⠀⠀⠀⠈⢢⡀⠀⠀⠀⣤
⠀⠀⠀⠀⢆⣤⣶⣶⣆⡘⠂⠀⠀⠀⢠⡄⢠⣀⣀⣠⣿⣀⡀⠀⠀⠀⠀⢘⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣬⡻⣿⣇⠀⠀⢀⡀⠃⠐⢓⠚⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⡿⠁⠀⠀⠀⢀⠄⠀⠀⠹⡀⠀⠀⠀⠀⢀⣀⣀⣠⡬⣿⠿⣿⡾⠏⠀⠀⠘⡀⠀⠁⣴⠋⠉⠲
⠀⠀⠀⠻⣿⡿⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠠⣠⣀⣠⣀⠇⠀⠀⠀⠀⠈⠈⢷⣼⣀⣼⡷⠃⠀⠀⠀⠀⠀⠀⠒⠚⠻⣄⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⠿⣿⠿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣦⣶⣶⣶⣷⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠈⠉⠁⠒⠂⠀⣀⠀⠀⠀⠠⠏⠀⣜⣂⠀⡸⠆⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾
⠀⠈⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⠉⠁⣳⠀⠀⢱⠄⠀⣸⢁⠀⠑⠚⠳⠴⠃⠨⠧⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢳
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⢲⠆⠈⠉⡗⠀⠆⠁⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠄⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⢹⠈
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠂⠀⠉⠀⠀⠢⡰⠃⠂⠀⠀⠀⠀⠀⠀⠈⠛⡆⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⣧
⠀⠔⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡠⠂⠀⠀⠀⠀⠰⣽
⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⢀⣸⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢦⡤⠿⠀⠀⠒⠄⢀
⠒⠛⠻⣔⢢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣘⣳⣮⣷⡿⠟⠂⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⡻⠇⠀⠀⣀⠥⣮⠭
⠀⠀⠀⠀⠀⣧⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⢀⡠⠔⠂⠁⠀⠀⠀⠔⡰⠀⠀⠀⡼⠁⠊
⣸⡆⠀⠀⠀⣿⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠇⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⡇
⠤⠀⠀⢀⠀⡏⠀⠀⠰⠤⠤⠀⠤⠤⠤⠀⠐⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡜⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢹⡀⣆
⢀⣀⡠⢞⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣀⣀⣀⡂⠥⠖⠋⠀⠀⠀⠳⡐⠃⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠳⣌⢦⡀
⠉⠉⠉⠁⠀⠀⠀⢀⡐⠆⢉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⣀⣀⣀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⠂⠀⠀⠀⠠⠀⢀⡀
⠀⠀⠀⠀⠉⠢⡀⠀⠈⠖⢄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠀⠀⢀⠀⢀⡴⠖⠲⠲⢅⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⡲⠀⠀⠀⠀⠉
⠀⠀⢀⠀⠀⠐⣥⠀⠀⠀⠢⡁⠭⢓⠀⠘⠏⠡⣄⠀⠀⠀⠀⠀⢱⠃⠐⠄⠀⠀⠨⢳⠀⠀⠀⠀⠱⣄⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⡴⠁⠀⠰⠁
⠐⠒⠊⠉⠙⠒⠋⢠⠀⠀⠀⠈⠀⠀⠐⠢⠤⠀⠃⠒⠀⠀⠀⠀⣸⠠⡀⠀⡡⠎⠀⢸⠁⠀⠀⠀⠀⠈⠓⢄⡀⠀⠄⠀⠀⠀⠠⠊⠀⠀⢈⡑⠄⠀⠐
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⣊⡀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠤⠤⠤⠤⠐⠁⠀⠀⠀⠹⣿⡷⠀⢀⡿⢅⠀⠀⢙⠃⠀⠀⠀⠀⠀⠀⠈⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠑⠄⠎⠀⠀⠃⠊⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠴⠂⠈
⠴⠤⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⣀⠤⠀⠘⠋⢑⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠠⠉⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴
⠃⠀⠀⠀⠱⠀⠀⠀⠰⠀⠀⠀⡄⠀⠀⠀⠇⡀⠀⠀⡆⠀⠀⠀⡞⠁⢀⣠⡀⠆⠀⠈⠀⢄⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⡔⡁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠁⠀⠀⢰⠀⠀⠀⠀⠃⠀⠀⢸⠀⢠⡐⣹⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣧⠉⠄
⠀⠀⠀⠀⢰⠃⠀⠀⠀⢃⠀⡈⠀⠈⠀⠘⠀⠐⠀⠈⠀⠀⠀⢸⠀⠇⢃⡹⢾⠁⠀⠀⠀⠀⡀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢀⠀⢣⠀⠀⠀⠀⠱⡈
⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⢣⡈⢤⣧⡚⠀⠀⡄⠠⣲⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠡⡐
⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⠭⠌⠤⠤⠒⠁⠀⠀⠀⠀⠱⢤⣀⣀⣀⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠒⡤⠇⠁⢀⠌⡁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠖⡒⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⡈⡆⠍⠁⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠂⠉⠁⠀⠄⠐⡀⠀⠀⠀⠀⢀⡊⠐⠁⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠄⠀⠸⠀⠀⠀⠠⠈⡉⠰⠃⠰⠆⠘⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⠘⠁⢰⠂⠀⠱⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⣀⣀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠘
⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠂⠀⠀⣁⣀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣯⡀⢋⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡘⢱⡖⠂⢀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⢰⠀⠙⣄⠁⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠰⠙⢘⡠⢇⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠈⠅⠘⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠀⠀⠈⠷⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡄⠠⢀⠹⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠁⠝⠀⠒⠂⢈⡉⠀⠀⠈⠀⠀⠠
⠀⠀⠀⠀⡀⢒⣾⠀⢤⡀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠠⠐⠂⠌⡐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠸⠀⠀⠀⠀⢀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⡉⠤⠈⡁⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⣀⡀⠄⢀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠐⠂⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠓⠠⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢼⡤⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠉⠄⠡⣄⡗⠋⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡐⠀⠛⠛⠈⠀⠐⡽⠦⣀⣀⡀⠀⡀⠈⣃⢀⠊⢉⢧⡀⢁⠨⠧⡀⠀⡀⠈⠀⠀⠀⠀⢀⠀⠀⣾⠛⠂⢤⡠⢴⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠉⣈⠀⠀⠿⠀⠀⠐⠲⠀⢀⠀⠐⢌⠂⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠂⡂⢀⡍⠀⠠⠋⠈⢠⠠⡂⠌⠐⠀⠀⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⢐⠡⠀⠐⠁⠄⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡜⠀⠀⠀⠀⠂⢀⣀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡠⠒⢒⡄⠈⡄⠀⠀⠀⠀⠀⠴⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠓⠒⠉⢀⠄⢰⠀⠀⠀⠀⠀⠠⠀⠀⠅⡀⠀⡀⠀⠀⠀⡀⠀⢊⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢅⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠡⡑⠀⡀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠀⣀⣀⡀⠄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠃⡰⠀⡄⡐⣀⠠⠀⢰⠁⠤⡂⢀⠂⠰⠂⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣬⣁⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⣶⣿⢚⠟⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⣼⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡃⠚⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠄⠀⣀⠔⠀⠀⠀⠀⠀⠀⠈⠀⢈⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⣠⡔⠉⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣤⡺⣦⣾⠇⠉⠉⠒⠆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢠⠐⠁⠀⠀⠈⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠅
⠀⠀⠀⠀⠀⡂⠐⠉⠀⠙⡏⠀⠀⢸⠏⠀⠀⠠⠀⠀⡺⢀⠃⢀⣆⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣷⠀⢰⠟⠀⢀⡠⠞⠉⣽⣱⡬⠶⡋⠉⠾⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡼⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠐⡀⠀⠀⠀⢉⡛⠂⠾⠶⣂⣾⣡⣴⣾⣿⠃⠀⠀⠈⠈⡇⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⢾⡧⢂⣽⣷⠂⠛⠛⣿⠀⠀⠀⠀⠜⠀⠀⠻⣯⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠞⠀⠀⠀⠀⠀⠀⠸⠋⠀⠁
⠀⠀⠀⡀⠀⠀⣦⢠⡒⠄⠡⠀⠐⠚⢻⠷⢎⡄⠀⠘⢧⣀⠀⠄⠀⠈⠄⠰⣿
⠀⠀⠐⠀⠀⠄⠻⣷⣿⡎⠉⠒⢦⣶⢼⡄⠘⢛⢸⠓⠒⠉⠐⠢⣄⡀⠂⣰⠍
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠇⠀⠓⠾⠮⡳⣽⠁⣀⣴⠲⡄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⠀⠠⢄⡀
⠀⠀⠦⡀⣀⣀⡀⠀⠂⠀⠀⢀⠀⠔⠀⠸⡟⣱⠃⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠁⢠⡀⠀⠂⠘⠆⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠿⠄⠀⢡⣦⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⢱⡄⠀⢀⠀⣰⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠁⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠘⣷⡰⣨⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⣠⣄⣺⣽⣇⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠉⠛⠟⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠠⠤⠐⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣀⠐⠂⢉⠀⢙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠒⢤⠁⡀⢰⠋⢤⠁⠀⠂⠁⢠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⠀⠁⢠⢀⠐⢁⣀⠀⢠⠞⠙⠂⠉⠈⠁⠙⠀⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠂⠉⢉⠙⠓⠦⣘⣏⢀⡀⠜⣠⠀⠀⠠⢀⢀⣀⣀⢀⡀⣀⠑⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡀⠀⠤⠀⠀⠀⡀⠈⢳⡋⠀⠠⣍⠀⡀⠀⢉⢀⡀⠀⠀⠀⠀⠀⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠁⠀⣀⠂⠀⠖⠈⠛⠄⠓⠀⣐⣿⣿⢉⡐⠃⠔⠁⡀⡠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣠⠁⠀⠁⠀⠀⠀⡀⠀⡀⠈⠃⢙⡿⣋⠓⠀⠀⢿⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠠⠄⢀⡀⠀⠀⡠⠐⠀⠁⠴⠸⠀⠉⠀⣙⠐⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠦⠄⠀⠀⡀⠰⠅⠀⠒⠐⠀⠀⠁⠐⠠⠀⠈⠁⠀⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⡎⠀⠒⠀⢀⡆⠀⠄⠂⠂⠀⢸⡄⠀⠤⠠⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⣀⠀⠴⠁⠀⢱⠀⠠⠀⠀⠀⠀⢻⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⠈⡅⠰⠖⠰⠂⠀⠑⠀⠀⠄⠀⠀⠀⢣⠀⡀⠒⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠂⠁⠌⠁⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠘⡤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢐⡉⠁⢀⡀⠀⣀⠀⠀⣬⠷⣇⡍⠰⠀⠀⠀⢀⡄⠀⠀⠀⢀⡀⣠⠔⠈⠉⠀⠉⠐
⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⢘⡄⠀⢲⠀⠉⠉⠓⠲⣖⣛⣵⣄⣤⣤⠴⠋⠀⠀⡠⢄⠘⣿⣏⣭⡀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⣀⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⡗⠀⡰⢿⠀⠸⠀⠌⢀⡎⡀⠀⣄⠦⠋⠡⡲⡒⠃⠀⠀⠀⠀⠀⠀⠀⡌⢡⠀⠀⠀⠀⠀⠀⠀⢀⡋⢀⡠⢟⠉⡜⠀⠈⢠⡄
⠀⠀⠀⠀⠀⠸⣀⡀⠄⠌⠀⠆⢈⡣⠖⠈⡹⢎⡉⠐⠝⢡⣡⠙⢆⡀⠀⠀⠀⠀⢁⠂⡀⠀⠂⠂⠀⠀⠀⡀⠀⣼⣿⠀⠀⠂⠸⠃⠤⠀⡆⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⢐⣔⠁⠀⠀⠈⠀⢌⡄⠀⣏⡼⠧⡙⠆⠀⠀⠀⠀⠀⠘⠀⢡⠀⡀⠃⠀⠀⠾⠀⢊⡅⠙⠷⠐⠀⠗⣸⠓⠀⠃
⠀⠀⠀⠀⠀⠀⠞⠀⠻⢇⣼⡷⣯⡿⠀⠠⡀⣦⣦⣠⢬⡤⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠆⣃⠈⢠⠇⡔⠂⡦⠔⠄⣴⠜⠁
⠀⠀⠀⠀⠀⠀⠄⢈⠠⢐⠀⡀⣿⣤⣮⡴⢏⠛⠋⢉⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡠⠄⠀⠀⠌⠁⢀⡾⠂
⠀⠀⠀⠀⠀⠂⢀⠁⠆⠈⢀⠀⠆⠃⠤⠐⠂⠐⠄⡌⢀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠈⠁⠒⠐⠀⣬⠐⠃
⠀⠀⠀⠀⠀⠃⠈⠄⢠⠀⡀⢀⡀⠆⠄⠒⠠⠄⠦⠠⢈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠆⢘⣴⣤⠄
⠀⠀⠀⠀⠐⠀⡁⠆⠠⠂⠆⠠⠀⡄⢠⠐⠀⡀⠂⠰⢠⠐⡆⠀⠀⠀⠀⠀⠀⠄⡐⠀⠄⠛⠻⠯⡍⠀⠠
⠀⠀⠀⠀⠀⠐⠁⠪⠀⠀⠀⠀⠠⡁⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠃⡈⢈⠐⠀⠖⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠤⠀⢀⠀⡈⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⣣⣟⣦
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀⠒⠉⠖⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠂⠈⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠋⠀⠀⠔⡉⢹⡕
⠀⠀⠀⠠⠒⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⣄⠀⠀⠃⢠⠀⠀⠀⠄⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠀⠈⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣶⣰⣦⡿⠇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢀⡉⠀⠀⠀⠀⡨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡄⠀⠀⠀⡤⠚⠛⢋⠠⠀⠑⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡴⢃⣤⠤⢤⣴⠬⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠊⣀⢀⠞⠉⡀⠈⠀⠀⠀⠃⠀⠦⠠⠄⠙⠈⢠⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠙⠛⠻⠿⠓⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢛⠚⡋⢳⠛⠿⠯⠈⠀⠘⠂⠲⠀⠀⠆⠉⡈⠂⠁⡀⠀⠀⠀⠀⠀⢲⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠆⣈⠀⠃⣠⠰⠘⢁⠀⠀⠀⠔⠀⠀⠆⠰⠀⡄⢈⠠⠀⠀⠀⠀⠀⠀⡀⠀⢼⣿⡧⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⡁⠈⡀⠁⠀⡦⢈⡀⠀⠀⠀⠀⠈⠂⠳⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⡈⠐⢀⠠⠀⡀⠡⠋⠁⠉⠛⣟⢷
⠀⠀⠀⠀⠀⠀⠀⢀⠁⢠⠁⠘⠁⠀⡈⠀⠀⠀⠀⠀⠀⠈⠠⠒⠈⠐⠀⠀⠀⠀⠀⠀⠀⡀⠂⠠⠐⠀⠀⠀⠒⠀⢴⠞⠹⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠃⠘⠃⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠁⠀⠀⠁⡧⠠⠈⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠘⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⢀⠀⠀⠈⠁⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡠⢀⣦⣴⡶⢀⣄
⠀⠀⠀⠀⢐⣤⡶⠋⡉⢰⡌⠱⣋⣠⢤
⠀⠀⠀⠀⢨⣝⡃⠀⢿⣿⣿⡄⠨⣦⣼
⠀⠀⠀⠀⠈⣭⡶⣆⠈⢿⣿⣿⡀⣷⠆
⠀⠀⠀⠀⠀⠈⢴⣯⣿⣤⠉⠿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠚⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡜⠂⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠖⠃⠈⡰⠀⠈⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢦⡠⡈⣧⣰⡎⠀⠀⠀⠀⠌⢀⠀⠠⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠄⠅⡤⢻⠿⡟⢿⡅⠀⡀⣀⣄⣤⡑⡌⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠠⠼⠾⡯⢸⡇⠦⠹⡶⠂⠄⠀⠀⠀⠙⠲⡴⡂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⡈⣸⡃⠀⡿⠀⠀⠀⠀⠀⠀⠊⠀⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠘⠠⢀⠃⡁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⡄⠰⠀⡄⢰⡮⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠐⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⡾⠋⠉⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣼⠛⠭⠀⡀⠀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣾⣤⡀⣠⠞⠃⠀⠉⣉⣉⣉⣀⣤⣿⣦⠀⠀⠀⠀⠠⠀⠀⠙⠿⣎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⣠⠀⠀⢠⣿⠀⠀⠀⠙⠷⠌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣿⣦⣤⣾⣿⣿⣿⣟⣻⣟⠂⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣾⣿⣷⠤⢀⠆⢀⠀⠸
⠀⠀⠀⠀⠀⠀⢠⠴⣶⣿⣤⣤⣾⠛⣻⠿⠿⠧⠞⠛⠈⣥⡤⠾⠷⠶⠿⠿⠿⠿⠿⠿⣿⣿⣷⣶⣾⣿⣿⣿⡶⠛⣶⡟⠀⡀
⠀⠀⠀⠀⠀⠸⡄⢀⣾⣿⣿⣿⣿⡄⠀⠀⣀⣀⣴⣶⣾⣿⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠛⣿⠟⣷⣸⣷⣿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⢻⡟⢫⣷⢩⣿⣿⡿⣦⣸⢿⣍⣭⣽⣿⣿⣿⣏⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠗⠒⠒⠿⣿⣿⣿⣤⣠⣶⣄
⠀⠀⠀⠀⠀⡄⣠⣽⣧⣼⣿⣯⡥⣿⣾⣿⣧⣿⣿⣿⣿⠟⠛⠟⢷⣶⣤⣶⣶⠂⠀⠀⢀⠀⠀⠲⠀⠠⠙⢀⣸⣶⣶⣿⣿⣿⡛⠛⠛⠛
⠀⠀⠀⠀⠘⢿⡿⠿⠛⠿⠿⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣧⣸⣿⣿⣿⣶⣶⣿⣷⣄⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠉⠙⠻⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠉

⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠋⠀⠀⠀⠀⣀⣠⣤⠶⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⢀⣠⠾⠋⣼⠃⠀⣀⣴⠶⠛⠋⠁⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⠃⠀⠀⠀⣰⠟⠁⠀⣼⣏⣴⠟⠋⠁⠀⠀⠀⠀⣠⣾⣋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⠀⠀⠀⡼⠃⠀⠀⢠⡿⠋⠁⠀⠀⠀⢀⣠⣴⠿⠋⠉⠉⠉⠛⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⠀⠀⢸⣇⢹⡄⠀⣸⠃⠀⠀⣴⠋⣠⠞⠋⢀⣴⠾⠛⢉⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣼⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠛⠿⣾⣿⡘⣧⣰⠏⠀⢀⡾⠁⣴⠋⢀⣴⡿⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣫⣿⠻⣶⡀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢹⣧⠸⣧⡀⠀⣾⠁⣼⠃⠀⣀⣤⠶⠒⠒⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠛⠁⠀⠙⠋⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣶⠾⠛⠻⣧⠘⢷⡜⠃⣼⣏⣤⠾⠋⠁⣀⣀⣤⣶⠶⠿⠟⠛⠛⠋⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⣀⣤⣤⣤⣶⠿⣧⣈⣻⡆⢹⠟⠁⠀⣴⠟⠋⠉⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠸⣿⡄⠀⠀⠀⣿⣦⠀⠀⢿⡆
⠀⠀⠀⠀⠀⣴⠟⠁⢀⠴⠛⠉⠁⢀⣀⣤⠔⣨⡿⠛⠁⠋⠀⠀⠀⢸⡇⠀⢠⣄⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠈⠀⠀⠀⠀⠘⠿⠀⠀⢸⣿
⠀⠀⠀⠀⣼⠃⠀⠀⣀⣤⣴⠶⢻⣿⠟⢁⡾⠋⠀⣰⠂⠀⠀⠀⠀⣼⠇⠀⠈⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⣰⠃⣠⣶⠟⢻⡿⠁⣰⡿⠁⣠⠏⠀⠀⣰⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠈⣿⡇
⠀⠀⣰⣧⡿⠋⠁⢀⣿⠁⢰⡿⠁⠀⠏⠀⢀⡼⠁⢿⡄⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠆⠀⠀⠀⠀⣶⡄⠀⠀⠘⠿⠀⠀⣿⡇
⢀⣴⠿⠋⠀⠀⠀⣼⡇⠀⣿⡇⠀⠀⠀⣠⡟⠀⠀⠘⢿⣦⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⣿⡇
⠚⠁⠀⠀⠀⠀⢠⣿⠀⠀⣿⠀⠀⠀⣰⡟⠀⠀⢠⣀⠈⠙⢿⣦⡀⠀⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡇⠀⢠⡿⠀⠀⠀⠘⣿⡆⠀⠀⠙⢿⣦⢸⡇⠀⠀⠘⣿⡧⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢷⠀⣾⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣷⢰⣦⠀⠸⣧⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡄⢻⡇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠁⠀⢸⡇⠀⠐⣶⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⢀⡀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠁⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⢸⣿⡀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⢻⣦⡀⠀⠀⠙⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣌⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⢿⠇⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣶⣦⣤⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠈⠻⣷⠄⠀⠀⠘⢿⡧⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢶⣶⣶⣴⣶⠶⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡞⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣕⠢⣄⢠⠎⢸⡠⢚⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠬⣦⠈⣏⠔⠛⢤⡾⠔⠒⣲⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢉⡱⢤⡈⢣⡏⠀⠀⠀⣱⣶⣉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣤⠤⠗⠈⠳⢄⣀⣸⣀⠞⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⢊⣭⣵⣔⡭⠑⡄⡐⣩⣭⣦⣪⠍⢢⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⢽⣾⣿⠟⢋⣴⣯⣇⣥⣿⡿⠛⣡⣾⣯⠕⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠙⣥⣾⣿⣿⠏⠁⠈⢫⣴⣿⣿⡿⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⠻⠟⠁⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢦⠞⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠂⠴⠶⠒⠒⠃⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⡈⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⢀⣴⣿⠇⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢰⣿⣿⡿⠀⠀⢰⠂⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣿⣿⣿⡇⠀⠀⠸⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⣀⣀⣱⠀⠀⡈⢿⣿⣿⡽⣄⠀⢰⠛⠀⠀⣰⣾⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠗⠙⢿⣿⣿⣇⠄⠳⣼⣿⡿⢷⣿⡄⠁⢔⣤⣎⣭⣄⣀⣀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢋⣉⣀⣀⣤⣀⣈⣛⣿⡋⠙⠉⠉⢀⣿⣿⡧⣾⣧⣄⠛⠿⣉⣉⠛⠿⣿⣿⣿⠷⠦⠄
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠃⠸⡿⣿⠟⠿⠿⣿⣇⠀⢨⡿⠀⠏⠁⠉⠉⠒⣶⣄
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡄⢸⠇⠻⠂⠀⢠⣌⠉⢷⣠⣿⠁⠀⠈⠻⣦⠀⠠⣾⣷⣄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠗⠈⠋⣀⠀⠀⠠⣿⠛⠀⠀⢽⡶⣷⠀⢀⠀⠀⣴⡆⠿⢿⣿⣦
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣄⢀⡾⣧⡿⠀⠈⠋⢀⣠⡀⠘⠿⠃⠀⢸⣽⡄⠙⢧⣀⣈⠋⣽⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣲⣿⣻⠄⠛⡋⠀⠀⠀⠀⢬⡿⠹⠄⠀⢠⣤⡸⢦⠀⠀⠀⠿⣿⣀⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡹⠋⢠⣟⡇⠀⢴⣾⡄⠀⠻⡄⠀⢀⣨⡵⠅⠀⠀⠀⠘⢦⠃⣩⡿⢻⡃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⢉⣅⡀⢹⡟⠃⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⢸⣶⡄⠀⢉⣼⣾⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣦⡀⣾⡿⣷⡀⢀⡤⢶⡄⢠⡚⣧⡀⠀⠀⠀⠀⣿⡿⠁⠀⢸⣿⣿
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠐⠋⠗⠻⠀⠠⣿⡻⠁⠘⠻⠌⠀⢀⣶⣷⠀⠀⣤⡄⠀⠀⣉⣿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣷⣶⠀⠀⢀⠀⠈⠙⢀⠀⠀⣠⣄⠘⠾⠛⠀⢰⣿⠇⢰⣿⣿⠃
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡸⣷⡟⠀⣰⣋⡿⢀⡴⢟⡆⢘⣷⣿⠀⠀⠀⣤⡀⠁⠀⠘⢉⡇
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⡟⢋⣀⠀⡙⣿⡟⠋⠹⠋⠀⠀⠙⠃⠀⠀⢸⡿⠃⢠⣿⣆⣿
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣫⣽⣷⡄⠋⠀⠀⣠⠆⠄⠀⢀⡤⣄⠀⠀⢀⠀⠻⢟⣼⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣼⠿⠀⢀⣀⡼⢱⢷⣆⣀⢿⣞⠛⠀⢰⣟⡷⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⡷⣦⣴⣿⠿⣧⡈⠋⠀⠈⢤⠍⢀⣠⠀⠋⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣟⣿⣿⠛⠗⠈⠉⢠⣴⣶⡆⢠⣿⣿⢦⣶⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣽⠏⠀⠀⢀⣶⣶⠊⠿⠈⢁⣀⣩⢽⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡇⣿⣄⠀⢸⣿⣿⠀⠀⢸⣿⣿⡿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣷⣿⣿⠆⡈⢛⣹⠘⣶⣮⢹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣯⣿⣽⣿⠹⡟⣿⣵⣾⣿⣾⢹⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣯⣟⢰⣿⡟⣿⣿⣿⣯⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠱⠿⠿⠛⠋

⠀⠀⠀⠀⢄⡀⢤⠄⡀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠠⠄⢀⠀⠀⠀⠀⡠⠀⠤⢄⠀⠀⠠⡴⠒⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠀⢠⠋⠀⠀⠀⠈⢂⠀⢠⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠑⠀⠒⠁⠀⠈⠀⠇⠀⠀⠰⠀⠈⢃⠘⠁⠉⠠⡘⠀⠀⠀⡔⠉⠀⠙⠆
⢠⠀⠀⠘⡀⠀⠀⠀⠀⠈⢄⠀⢏⠑⠀⠒⠒⠒⠂⠈⠁⢀⠆⠀⠀⠀⠀⢀⠄⠀⠀⠢⡀⠈⢢⣄⠜⠀⠀⠈⠀⠀⠥⠈⢁⣀⠀⠀⡇⠀⠀⠀⡅
⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⡃⠈⠢⠄⡀⠀⠀⣀⣀⠠⠊⠀⠀⠀⠀⠠⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠈⡠⡉⠡⡀⠦⡀⠙⠢⠤⠚
⠀⢄⠄⠒⠒⠂⠌⡁⠒⠀⠂⠁⠀⢀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢀⠨⡀⠽⠂⠠⠀⠀⠀⠠⠀⠀⠘⠂⠁⠀⣠⠤⠠⠄
⠀⠸⡀⠀⠀⠀⠀⠤⠁⠢⡀⠀⠀⠉⠀⠁⠀⢀⣴⣤⣄⣀⢀⠀⢰⠃⡀⠀⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡱⠌⠐⠀⠀⡎⠡⣀⢀⡌
⠀⠀⠑⠄⡀⠀⠀⠀⢀⠔⠁⠀⠈⠐⠂⠁⠀⠘⢿⣿⢿⣿⣿⠇⠀⠑⠂⠁⠬⠀⠃⢀⠶⠀⠀⠢⡀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠑⠤⠄⠋
⠀⠀⠀⠀⣀⠨⠤⠬⠀⢀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡂
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠃⢠⠤⡀⠀⢔⠒⠂⠤⠤⠐⠈⠀⠀⠀⡔⠀⢐⠀⢱⠀⠀⡤⠀⡃⠀⠀⠰⠉⠀⠀⠀⠂⠹⣌⠉
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠀⠀⠰⠀⠈⢆⠀⠀⠤⢀⡀⢀⣀⠀⠄⠊⠀⠀⠈⠀⠁⠀⠈⠀⠊⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⡆
⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠂⠁⠀⠀⠀⠂⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠑⠠⣀⣀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⠀⠰⠇⠣⡀⠀⠀⠀⢠⠂⠆⢄⠀⠀⠀⠀⠀⠀⠐⠊⢀⣀⣀⡀⠀⠑⠲⠄⠠⠄⠊
⢀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠐⠎⢦⠀⢸⡆⠐⠀⠀⠀⠘⠄⢀⡌⠈⢁⠄⠀⠀⠄⠀⡔⠋⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠣⠜⠀⠀⠀⠀⡠⠀⠲⠆⠁⠐⢄⠀⠀⢀⠈⠀⢀⢣⠀⡇⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠐⠀⢀⣀⢄⠄⠀⠁⠂
⠀⠀⠠⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠱⡠⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡠⠄⠀⠤⠅⡔⠊⣃
⠀⠀⠀⠀⠀⠠⣀⡀⢀⠈⠄⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠦⠼⠦⢀
⠀⠀⠀⠀⠑⠠⠄⢃⠜⠀⠈⠂⠤⠔⠒⠒⠁⣠⠄⠒⢦⣼⣁⠀⠀⠀⣠⣾⣿⡳⣷⣶⣶⣶⣶⣾⣶⡄⠀⠀⢠⠀⢄⠀⠀⠀⡎⠀⠀⠀⠀⠈⠆
⠀⠀⠰⢢⣀⡀⠐⠀⠀⢞⠉⠑⠄⠀⠀⠀⣸⠁⠀⠀⠈⠀⠈⣣⢠⣾⣿⣿⣿⡗⠟⠿⠋⠿⠹⠿⠿⠇⠀⠀⠀⠓⠤⠀⠀⠀⠅⠀⠀⠀⠀⠀⠸
⠀⠀⣺⣉⣱⣿⣷⣦⡀⠀⠍⠀⠙⠈⠁⠀⠹⣄⣀⠀⠀⣀⠔⡋⠈⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠘
⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠍⠉⠠⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⢀⣀⡀⡠⠊
⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠲⡄
⠀⠀⠙⠛⠿⠿⠟⠟⠀⠀⢠⠊⠁⠱⣄⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⠀⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢂⠱⠀⠀⣐⡀⠎⠀⠈⠂⠒⠁⠀⠀⠲⠒⠁⠀⠀⠀⠈⠁⠀⠀⠀⠠⠒⠑⢄⠀⠀⠀⢀⠀⠂⠢⠦⢄
⠀⠀⣴⠂⠉⠁⠀⠀⠀⠘⠀⠁⠀⠀⠈⡄⢃⠀⡇⠀⠀⠐⠀⠀⠀⠀⢀⠄⠒⠂⠈⠑⢄⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⠀⢠⠁⠀⠀⠀⠀⠀⠱
⠀⢸⣿⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠇⡘⠀⠄⠀⠀⠀⠀⢡⠀⠀⠁⠀⠀⠀⠠⠀⠈⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⡄⠀⠘
⠀⠈⢿⣿⣦⣂⣀⠕⠀⠐⢄⠀⢀⡠⢊⠐⠀⠀⠣⡀⠀⠀⠀⠸⠀⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠑⢄⡀⠀⠀⡀⠈
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠑⠄⠀⠀⠔⠁⠀⠀⠀⠀⠀⠑⠠⠠⠀⠊

⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⠀⢀
⠀⠀⠉⠀⠀⠐⠶⠀⠀⠀⠙⠻⠆⠀⠈⠀⢸⡀⠀⠀⠀⠀⠀⠛⠦⡤⠀⠀⠀⢿⣆⣿⢠⣿⢀⣤⠀⠀⠀⠀⢀
⠀⢀⣀⣀⣤⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠘⣧⡀⠀⠂⠀⢀⠀⠀⠀⡼⠁⠀⠘⣿⣿⣿⣷⡿⠃⠀⠀⡏⣾⣿
⠀⠰⠟⠻⡟⣃⣠⡀⠀⠻⠿⠃⣾⣿⡆⠀⠀⠈⠻⣦⣤⣄⣀⣠⣴⠟⠁⠀⠀⡰⠋⠀⢁⠙⢀⠀⠀⠀⠁
⠀⡞⠉⠲⣼⠁⠀⡿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠉⠉⠉⠉⠀⠀⠀⢰⠶⠳⠦⣤⣤⡤⠬⣄⡀⠀⡇⣶⢸
⠀⠳⠤⡴⠀⠓⠚⠁⠀⢲⣶⡦⠄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⢧⣅⠽⠃⢧⣃⣀⡟⠀⠀⠁⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⢤⠀⣀⣀⠀⠀⠀⠰⢠⡄⠀⢀⡀⠀⠀⣀⠐⠃⠄⢀⡤⠀⠀⠀⡄⣤⣠
⠀⠀⠶⠂⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⢸⠀⢿⠀⢸⠴⡇⢸⢸⡅⠀⠈⠗⠀⠀⠀⠉⠑⠀⠁⠀⠀⠀⠀⠇⠚⠸
⠀⠀⠀⠀⢀⣠⠄⠀⠁⠀⠀⠁⠀⢀⢀⡀⢀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠇⠑⠙⠋⠙⠘⠃⠋⠃⠹⠀⣜⠉⠦⠂⠳⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣿
⠀⠀⣀⣀⢀⠴⢤⠀⠀⢠⠄⠀⠀⠀⠀⠀⢰⠀⣲⣶⡖⠀⠀⠀⠀⠈⠋⠀⠙⠁⠀⠀⢀⡟⠛⠋
⠀⢸⣀⡸⠙⢤⡼⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠒⢦⠔⠒⢳⠄⠀⣰⣿⣿
⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⠀⠈⠀⠀⠀⠀⣤⡄⠘⠢⠄⠊⠓⠄⠘⠀⠀⠉⠁⠉
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠶⠶⢤⣄⠀⣠⠞⠉⢻⡄⠀⠀⠀⣠⣴⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢿⣇⠀⠀⠀⠈⠙⢿⡀⠀⠀⢿⢀⡤⠞⣋⣡⣼⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠙⢦⡀⠀⠀⠁⠢⣳⡀⡀⣸⣫⣶⣛⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢰⣁⡽⠀⠀⠉⣳⣶⡶⠶⢾⣿⣿⣿⡍⠩⠉⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡠⢄⠀⠀⠉⠀⣀⣴⡾⠛⠁⠀⠈⢀⣽⡟⠻⢉⠢⣄⠀⠀⢀⣙⣿⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⡧⠞⠀⠀⠀⠙⠻⢷⣦⣤⣤⣴⡾⠟⠙⣷⣄⠀⠁⠈⢿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢠⠞⣱⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠻⣷⣦⣄⣘⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⠤⡄⠀⠀⠀⠘⠛⠁⠀⠀⣰⠋⣷⠀⠀⠀⣴⢙⡆⠀⠈⠉⢉⡭⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠸⡾⠃⠀⠀⠀⢠⠒⡆⠀⠀⠘⠛⠃⠀⠀⠀⠻⠟⠁⠀⠀⠀⢸⣇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣀⠀⠀⢻⡶⠃⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢠⠖⢢⠀⠈⠉⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣏⣸⠇⠀⠀⠀⠀⠀⠀⠀⢸⣧⡴⠃⠀⠀⠀⠸⡶⠋⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠉⠀⠀⠀⢠⠖⢢⠀⠀⠀⠁⠀⠀⠀⠀⣀⡀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⡔⢆⠀⠀⠀⠀⠸⠶⠋⠀⠀⣴⠚⣲⠀⠀⣾⡤⢆⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢥⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⡞⢩⠆⠀⢠⣞⣩⠆⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣙⣉⣀⣀⣀⣩⣥⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣟⣩⣍⣹⣏⣿⣻⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡐⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠲⡄
⠀⠀⠈⢠⡄⢀⠀⠀⠀⠀⠔⠀⡀⠀⠈⠁⢀⢀⠀⠀⢀⠄⠒⠂⡼⠶⠃⠀⠓⠆⢀⠂⠀⠀⠀⠀⠀⠤⠮⠁⠀⡄⠀⠀⠘⢄
⠀⠀⠰⠈⠁⠄⡄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠊⠀⠀⠀⢀⠄⠌⠁⠐⠔⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠁⡔⠂⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⡀⠀⠠⡀⠀⠀⠀⡀⠀⠀⠈⡄⠜⠁⠡⠀⠀⠀⠀⠞⠂⠤⠤⠤⠔⠚⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⡤⠀⠄⠀⠀⠘⠀⠀⠀⠈⠐⠐⠈⠀⠀⠀⠀⠀⠀⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⢝⡒⠤⠐⠊
⠀⠄⠀⠀⠉⠈⠀⠀⠀⠀⠐⠉⠑⠀⠀⠀⠲⠢⠀⠀⠀⠀⠀⠀⠀⠋⠁⡀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠤⠔⠁⠀⢀⠃⠀⠀⢐⠀⠀⠀⠀⠈⠂⠀⠀⠂⠠⠐⠀⠀⠰⠜⠂
⠀⠀⡀⠀⠀⠀⡀⠁⠀⠌⠀⠀⠀⠀⢣⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠉⢲⠁⠀⠁⠀⢴⠦⡤⠀⠀⠀⠀⠀⢀⣀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⡃⠀⠠⢖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠂⠉⠀⠀⠀⠀⠀⠀⠘⠀⡙⢬⡀
⠀⠀⡄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢀⠇⠀⠀⠛⠀⣀⠀⠀⠀⠮⢀⠀⠀⠔⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠠⠁
⠀⠀⠘⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠒⠉⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠰⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔
⠀⠀⠀⢀⠀⠠⠀⠘⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢈⠀⠀⠀⠘⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠄⠐⡀⠀⠀⠀⢀⠃⠂⠄⡠⠠
⠀⠀⠀⠀⣁⠀⠀⠀⠁⠀⠀⠄⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⢀⠄⠀⠀⢀⠀⢠⠀⠀⡆⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠳⠄⡀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠐⠠⠀⠁⠀⠀⠐⠁⢤⣠⠰⠇⢀⡠⠄⠀⡀⠀⠀⠀⠀⠈⡀⠀⠂⠀⢀⢀
⠀⡀⠀⠀⠀⠀⠈⠀⠀⠢⠀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⢈⣠⠀⠀⠀⠉⠁⠐⠒⠀⠉⠉⠀⠀⠀⠎⠙
⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠉⢀⠠⠈⠉⠀⢀⠁⠁⠀⠀⣌⠂⡑⢊⡱⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⠀⠀⠀⢸⣤⠂⡔⢢⡔⢠⡇⠀⠐⠒⠀⠀⠐⠄⠀⠀⠔⠀⠐⠒
⠀⠀⠀⠀⠀⠀⢀⠠⠰⠈⢣⠀⠀⠀⠀⠂⡀⠀⠀⡤⠀⠀⢀⠠⢄⠀⠘⠤⠃⢜⠡⠜⠠⡇⠀⠀⠀⠄⠠⠄⠀⡀⠀⠰⠄⠄
⠀⠀⠀⠀⢀⠈⠉⠑⡀⠀⠀⠑⢤⣀⠀⠀⠀⡀⠀⠞⠀⢀⠁⠀⠈⢆⠀⠐⠡⠎⠱⠎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠄⠀⠀⠀⢈⠀⠐⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠞⢀⠠⠀⠀⠳⡀⠀⠀⠀⠀⠀⣀⡈⣅⣀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡄⡀⠀⡐⠒⠀⠀⠘⡀⠀⠀⠀⠀⢀⠇⣄⣠⠀⠄⠉⡡⠘⡋⡃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠘⠁⠠⢀⡀⠂⢤⠀⠙⠦⢀⡀⠤⠊⠀⠀⠈⠁⠜⠈⢠⠠⠈⠉⠀⠈⠀⡀⠀⠉⠁⢀⡈
⠀⠀⠀⠀⠀⠀⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠡⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠈

⠀⠀⠀⠀⠀⢠⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⢤⢄⡀
⠀⠀⠀⢀⣢⣄⣿⣤⣼⡃⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⡐⠈⢸⣸⠿⣇⠀⠀⣐⣿⡿⠇⠀⠀⠀⠦⣷⢿⣿⣿⣧
⠀⠀⣴⡃⡜⢈⢹⣻⣿⡳⠶⠆⠘⠢⣾⣾⣼⠠⣠⠀⣰⠇⣆⡿⠗⢚⡿⠀⠀⠳⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢉⣵⣿⣶⣄
⠀⢠⠋⡁⠱⣸⣭⣿⣿⣿⠀⠀⠠⣌⡉⠽⢿⣧⡇⢀⣿⣼⣟⣣⠍⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠈⠁⠀⣪⣿⣿⢾⡇
⠀⢸⣁⠠⢸⣽⣿⣿⣿⠟⠀⠀⠀⠈⠓⠊⠉⠉⠳⠘⠛⠛⠁⠀⠀⠀⠀⢀⢴⣴⣷⣀⡴⣄⡈⠀⠀⠀⠀⠀⢈⡵⣿⣿⠃
⠀⠈⢤⣭⣾⣿⣯⠏⠉⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣒⣀⡀⠀⠐⠿⢿⣿⣁⡤⣿⣿⣭⣶⣟⣅⠀⠈⠀⣿⡉
⠀⠀⠈⠙⠋⠁⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⠹⣿⣷⢖⣫⠀⠀⠀⡟⠠⡸⣵⠿⣼⡿⣏⠛⣿⣷⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠠⣦⡰⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠃⠛⡇⠈⠀⠀⠀⢗⣰⣿⣿⡠⠉⠷⠋⣻⣿⣿⠇⠀⠀⣄⠠⠶
⠀⠀⢀⣭⢿⡶⣿⣿⡷⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⢿⡿⠿⠗⠈⠄⣼⣿⣿⡟⠀⠀⣾⣏⡗⢀
⠀⢰⡿⠐⠆⠹⠆⣿⣿⣦⠀⣤⢢⣙⠀⠀⠀⠀⠀⠀⣄⣀⣠⣧⠴⠀⠀⠀⠀⠀⠀⣴⣡⣄⣀⠀⠚⠿⠋⠀⠀⠀⠉⠉⠁⠉
⠀⢺⣦⢉⡘⣧⣿⣿⣿⣿⠀⢲⡈⢿⣷⡀⣂⠀⠐⢲⣿⣿⣿⠟⡶⢦⡀⢀⣲⢶⣶⠟⡐⠀⠜⢳⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⣿⡤⠹⣿⣿⣿⣿⠏⠀⠀⠁⠽⣿⣷⠃⠀⢰⠋⣁⠈⣉⡀⠐⠊⢻⠀⡅⠀⠖⠈⠛⠂⠀⡀⢣⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠻⣿⣿⡿⠟⠁⠀⠀⠀⢀⣀⣤⠽⠀⠀⠸⡄⠀⠄⠙⠇⢘⠀⢸⠀⠻⢦⣄⣁⡈⡁⣁⣀⣨⠀⢀⣤⣄⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⠉⠃⠀⠀⠀⠀⠙⢦⡀⠂⠀⠀⢰⠃⠀⠀⠙⠤⠿⣟⠿⠟⠋⠀⠈⢿⣼⣯⡿⢋⣤⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⠛⠁⠙⠼⠿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⣄⣀⢀⡀
⠀⠀⠀⠀⠀⠔⠘⠛⠋⠙⢂⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⠤⠀⠀⢠⢢⠆⢻⢏⠀⠀⠻⣦
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠋⠁⠉⠈⠀⠀⠄⠀⠀⠀⠀⠁⠛⢹⠄⡀⠀⠀⠀⢈⠌⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠉⠐⠚⠢⠄⠀⠀⢀⠀⠀⠈⠁⠀⠀⣀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠄⠀⡀⠲⢦⣤⠓⠁⠁⠀⠈⠈⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠄⠀⠀⠈⠘⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠄⠀⠀⠐⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡄⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠐⣩⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠐⠀⠔⠣⣌⠀⠀⢤⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⣑⣤⣀⠀⠄⠀⠀⠀⠀⠀⡀⢤⡶⠾⢀
⠀⠀⠀⡁⠵⠀⠀⠈⠛⠈⠉⠱⡟⠁⠈⠀⠄⠀⠀⠀⠀⢻⠉⠄⠀⢨⠛⣎⠁⡀⠀⠀⠀⠀⠉⠑⢀⡇⠈⠣⠐
⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⣠⢈⠠⠈⠄⠆⡉⡀⢈⢀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠄⢂⠀⠑⢀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⡐
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠚⠲⠂⠨⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀⢁⠘⠂⠀⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠈⠋⡀⠠⠄⠀⠀⠆⠁⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡖⠀⠀⠃⠀⠄⠀⠀⠀⠀⠀⠰⠀⡄⠁⠀⡀⠃⠄⠰⠀⠀⠀⠀⡰⢼⡧⠄⡀⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠔⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠰⠀⠀⠂⠸⠃⠀⠀⠀⠈⠀⠘⠃⠀⠀⠐⠠⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠈⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡁⠲⠀⠀⠀⠀⠈⠃⢀⠂⠀⠀⠂⢁⠐⠐
⠀⠀⠀⠀⢀⠀⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⢀⠠⠀⣁⠠⠀⡐
⠀⠈⠁⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠡

⠀⠀⠀⠀⢀⠠⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣀⡤⠶⠢⡀
⠀⠀⠀⡐⠁⢄⢸⠀⠙⢦⠀⢀⠤⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⢚⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠘⠄
⠀⠀⢰⠁⡀⠀⡰⠀⠀⠀⠷⠁⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡘⠀⡄⠀⠀⠀⠀⠀⠀⠰⢁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠸⠀⠀⡐⠁⠠⠊⠀⠀⠀⠀⠀⠐⠀⠀⠾⠂⢣⠀⠀⠀⠹⡄⠀⠀⠒⠀⠀⠀⠀⠁⣠⠀⡰⠁⢀⠇⠀⠀⢀⠊⠀⠀⠀⠀⠡⠀⠀⠀⠀⠂⡀
⠀⠀⠀⣆⠌⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⣦⡘⠃⠀⠄⣀⠔⠀⣠⠞⠀⣀⠎⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠔
⠀⠀⠀⠉⠀⠀⠀⠐⡀⠶⠀⠀⢄⠀⠀⡠⠃⠀⠀⡰⠁⠀⠀⠀⠀⠈⠛⠦⣤⣤⣤⠔⣊⡡⠴⠊⠁⠀⠀⡠⠃⠀⢀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢀⣠⣤⡤⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡰⠁⠶⠀⠀⠀⠀⠀⠁⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠄⠘⠛⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠒⠀⣀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠐⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠛⠣⠐⠊⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠶⣦⠤⠄⠀⠐
⠀⠀⠐⠒⠒⠉⠀⠀⠈⠁⢀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠐⠁⠘⠕⠈⠒⠀⠑⠀⠉⠀⠉⠂
⠀⠀⠀⠀⢈⠀⠀⠀⠀⠰⠀⠀⠀⠁⠰⠾⠀⠀⠀⢀⠀⠀⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣦⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠈⡀⠀⠀⠶⠀⠀⡀⠀⠠⠀⢀⠇⠀⠀⠀⣁⠆⠪⠀⠐⠐⠀⠀⠀⠀⣠⡲⠦⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⣼⣤⡀⠂⠂⣀
⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠉⠀⠀⠢⠀⠀⠀⠀⠀⣓⠢⠐⢸⠁⣇⡜⢁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠤⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠉⡳⡄⣻⣀⣹⠁⠜⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣿⠏⠑⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢿⠋⢉⠄⣋⠝⠳⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⡀⣠⠖⠁⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠎⠀⠘⠉⢡⡄⠥⠀⠨⠇⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠰⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⢄⠀⠈⠀⠀⠁⠀⡀⠐⠀⠀⠀⠘⠀⠉⠀⠀⠁⠀⠀⠀⠄⠁⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠡⠀⠈⠇⠀⠀⠀⠀⠀⠀⣀⡀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡆⠠⠀⠀⠆⠀⠀⠀⠀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠳⣤⠴⠶⣒⠒⠢⣄⠀⠀⠀⡀⠀⠲⠂⠀⠀⠀⠀⠀⠀⢠⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢄⡀⠀⠀⠀⠀⢀⠨⠦⠒⠒⠒⢄⠀⠀⠀⠀⠀⠁⡌⡤⠭⠀⠀⠀⠈⠂⠀⠀⠘⡀⠀⠀⠈⠒⠤⠔⠊⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢢⠀⠀⢠⠁⠀⠀⠀⠀⠄⡀⠆⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⢀⠴⠁
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠁⢴⢸⠀⠀⠘⡀⢀⡀⠀⠀⡄⠉⠆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠉⠑⠶⠰⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠁⢝⠀⠐⠒⢁⠤⠃⠀⠀⠀⠐⠌⣀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠳⡀⠲⠀⠀⠤⠊⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠁
⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⠿⠻⣿⠛⡿⢿⡿⢻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⢿⣦⡀⠀⠘⣿⣶⣄⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⢻⣿⣿⣿⣆⠀⢹⡿⢹⡇⠀⠀⠀⣠⣾⣇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⠟⢦⠘⡏⠀⡇⠀⣠⣾⡿⢫⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⣀⣀⣀⠀⠀⠀⠻⣯⠻⣿⣿⣷⣾⣧⡆⢀⣧⣾⡟⢉⠀⠈⢀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣻⣿⣿⠷⠶⣾⢿⣾⣿⣵⠾⣶⡬⡭⢻⣿⣿⣛⣡⣶⣚⠅⠶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⠖⠛⠍⠙⢱⣆⣴⡇⠺⠃⢛⣥⣼⣿⡟⣰⣿⣀⣤⣬⣝⡧⠉⣉⡛⠻⣟⠛⠻⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡀⠀⡤⢸⢨⣷⣿⠞⣷⣇⢸⣿⡌⣿⡿⣿⣍⣿⣷⣿⣿⠻⣆⠻⢷⣿⣉⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠁⠸⣧⢏⡈⣿⠟⣠⣵⣿⣨⣿⡿⣿⣧⣽⣿⣿⣿⡛⣿⣾⣿⢸⣶⢿⣯⣟⢦⡽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠥⠀⣴⡄⣤⠛⣿⣅⣴⣎⠻⣿⣛⣿⣷⣽⣿⣿⣿⢫⣿⣷⣿⣿⡿⢦⡠⣦⣷⢼⡆⡯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡀⠀⣦⠀⠁⢯⣹⢰⣿⣮⣼⣧⣿⣿⣷⣿⣿⣿⣩⣿⣮⣿⣿⣿⡋⣷⣿⣷⡿⢻⣿⣿⣄⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠈⠷⢂⠘⣦⠉⢼⡉⢳⡜⣯⣬⣻⣿⣩⣿⣿⣿⣿⢟⣿⣏⣿⣷⣿⣿⣿⣧⡻⣿⣶⡿⢘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣄⢿⣧⠝⢳⠶⡍⢿⠚⣻⣿⠛⢿⣿⣿⡿⢿⣿⣽⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⣄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢋⣶⣍⠀⣌⠛⠃⣾⣷⠸⢿⣿⣷⡿⣿⣾⣾⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⢿⡛⠰⣇⣋⡇⠹⢡⡶⣬⢹⣿⣷⣾⣿⡟⢻⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢆⡘⢻⡆⣬⣉⠛⠀⣌⡻⣾⣟⣙⢻⣿⣿⣧⣷⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⡀⡂⠻⠿⢠⣦⣿⡗⣸⣿⣿⣷⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡑⠿⣖⢿⣲⡍⢙⠻⣿⣿⢏⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣾⣏⣿⣇⠸⣿⣻⠽⣼⣾⣿⣛⣿⣿⣶⣽⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡍⠻⣧⣽⠿⠈⠉⣾⣷⣿⣿⣿⣾⣻⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⢮⡕⢈⡻⠷⢠⣿⣯⢭⢻⣿⣿⣿⣿⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠻⠎⠻⢀⠻⣦⡹⣿⠿⢿⡿⣦⣹⣿⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣦⠹⢛⣿⢿⣧⣼⣻⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡟⠿⣽⣿⣝⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠛⠉

⠀⠀⠀⡀⠀⠄⠂⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠈⠤⢀⠐⡌⠓⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡁⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠
⠀⢀⠉⠀⠐⠂⠀⠀⠀⠀⡂⡠⠄⣅⢁⡄⡀⠀⠀⠓⠐⠤⠂⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠠⡀⠀⠀⠀⠀⠀⣀⣴⡀⠀⠁⠀⠐⢂⡀
⠀⠈⡀⠀⠆⠀⠀⠀⠁⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⢀⢌⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠎⢀⡀⢀⠄⢠⣭⠁
⠀⠀⠈⠢⣀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠔⠀⠀⠰⡃⠀⠄⣀⠀⠀⠀⠀⢀⡉⠄⠀⡣⠀⡘⠀⡤⠐⠈⠄⠛⠀⠽⠃⠠⠄⠣
⠀⠀⠀⠀⠀⠁⠂⠂⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⠁⠂⠀⠀⠈⠁⠀⠀⠀⠂⠁⠀⠀⠁⡄⠆⡀⠀⠄⠀⡀⠄⡀⠠⢤
⠀⠀⠀⠀⡤⠤⠀⣀⠀⠀⠀⢀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠶⡤⢼⠙⣁⠦⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠔⡩⠂⠀⡀⠀⢈⠀⠀⢨⠀⢀⡄
⠀⠀⠀⠀⠈⣾⠧⠄⠜⠀⠁⢀⠱⠀⠀⠀⠀⢀⠀⠀⠀⢖⠂⠼⡄⢱⡁⡰⠅⢒⠶⠀⠀⠀⠀⠀⠀⢈⡬⠄⠀⢤⠀⠉⠀⠈⢃⠀⢀⠁⠀⠁
⠀⠀⠀⡠⠊⠉⠙⢢⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈⠀⠀⠀⢱⠖⠉⠉⠈⠓⢠⠂⠀⠀⠀⡠⠂⠀⠐⠛⠤⠀⠄⠣⡀⠀⠀⠘⢀⠀⡨⠃⠀⠀⢀⡀
⠀⠀⢠⠃⠀⠀⠀⠀⢇⠀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢱⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠒⠀⠀⠚⠓⠀⠀⠁
⠀⢠⠃⠘⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠀⠀⠘⠀⠀⠀⠀⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡞⠀⠀⠀⠉⠑⠄⠀⠸⠀⠀⠀⠀⠀⢀⣠⡆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⢀⡄
⠀⢃⠀⠀⠀⠀⢀⠌⠀⢠⠀⠀⠀⡠⠊⠁⠀⠈⠱⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠑⠢⠤⠀⠠⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠦⡀⠀⠀⠀⠀⡠⠂⠀⠀⡘⠀⡀⠀⠀⠀⠀⠁⠀⠱⡄⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⢀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⡇⠈⠁⠀⠀⠈⠀⡀⠀⠀⠈⠉⠉⠉⠉⠁⠉⠀⠠⠀⠚⠊⠙⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⠀⡀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⡠⠐⠡⠁⠀⠀⠀⠀⠀⠀⠄⢈⠢⢄⠀⠀⠀⠑⠀⢀⣠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂
⠀⠘⠀⠀⢠⠀⠀⠀⠀⠐⠈⠴⠉⠀⠗⠀⠈⠁⠒⠈⠘⠠⡌⢳⡇⢄⠀⠀⠀⠀⠂⢀⠀⠀⡠⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⢸⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠉⡀⠤⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡎⣄
⠀⠀⠀⠀⠈⡀⠀⠄⠀⠃⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠘⢄⠀⠀⠀⠔⠈⠀⠀⠈⠑⢄⠀⠀⠀⢀⣠⣸⠰⠀⡀⠀⠀⠀⡠⠂⠁⠈⠙⠲⡁
⠀⡀⠀⠀⠀⠐⡀⠈⢄⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠐⠀⢀⡀⠀⠀⠀⡀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠐⢄⠀⠀⠀⠈⠢⣀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠈⠀⠀⠀⠀⠁⠀⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠂⠈⠁⠀⠀⠀⠃
⠀⠀⠀⠑⠤⡀⠀⠀⠀⠑⠂⢠⡄⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠈⢆⠀⠀⠀⠀⢀⠔⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠐⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁

⠀⠀⡼⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡶⣶⣶⣶⠀⣶⣲⣶⣶⣶⣶⣶⣶
⠀⢀⣡⣿⣅⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣛⣛⣛⣛⢛⠛⣃⣛⣛⠛⢛⣛⣛⠘⠛
⠈⠀⢙⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠠⠛⠻⠿⠆⠸⠟⠷⠐