Blizzard Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⠈⠉⠛⠶⣄⠀⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠙⠛⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠉⠉⠉⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⣀⣠⣄⣀⣀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠉⠀⠀⠈⠉⠛⣦
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠈⠙⢶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⡁
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣛⣲⠖⣶⠶⢶⢿⣏⢩⣽⠇
⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣇⠀⠀⠀⠀⠀⠀⣀⡼⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣯⠉⠺⣧⠀⠀⠀⢹⡿⠷⣦
⠀⠀⠈⠳⢦⣤⣄⣀⣠⣤⣤⠴⠶⠛⠉⠀⠈⠛⠓⠲⠶⠒⣿⢿⡀⠀⠛⠻⣿⢶⡶⢤⣤⣤⡶⣾⠻⣾⢣⡞⠛⣻⡀⠀⠀⣴⢃⣤⡿⠁⣰⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠻⠂⠙⠶⠶⠶⠿⠂⠻⠶⠿⠈⠳⠾⠇⠀⠟⠒⠚⠉⢛⣓⡚⠁⣛⣛⣛⣛⡃⢘⣛⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣃⡾⠋⣭⣽⢏⡴⠛⠙⠻⣴⢋⣿⢃⣦⡹⣏⣙⣦⡿⠉⠻⣎⢻⡉⠉⠉⠻⣮⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⣷⣀⣸⡅⠀⠀⠐⣿⡉⠁⣿⢨⡷⠈⣹⡏⠀⠀⠀⢹⡆⠙⣿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠟⢷⣤⣤⣤⡾⣡⠷⠛⠙⠻⢿⡜⢧⣤⣄⣠⢿⣷⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⡴⠶⢶⡶⡀⢿⡀⠀⠀⠀⣴⢋⣄⢶⡶⣤⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⡟⣴⢻⡌⠷⣶⡶⠾⢣⡞⠹⣎⢳⣌⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⣛⠋⢸⡇⠻⢶⡴⠟⢿⣠⣶⠟⠀⢙⡇⠉⣭⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣏⡼⣦⡿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠾⣵⣦⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣆⡀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠸⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠠⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠋
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⣤⣴⡄⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⠛⠀⠀⠀⠾⠋
⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠂⠀⠀⢠⣶⠿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶
⠀⠀⠀⢠⣶⣿⠋⠉⣿⣇⣤⣶⠿⠿⣷⡄⠀⠀⠿⢷⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠘⠋
⠀⠀⠀⠀⢸⣿⣤⡶⠟⠋⠉⠀⣀⣀⣸⡇⠀⣴⢶⣦⣄⡀⠀⢹⣧⠀⠀⠀⠀⢠⣿⠃⠹⣧⡀
⢀⣠⣴⡾⠟⠋⠁⢀⣀⠀⠲⠟⠋⠙⢻⡇⠀⣿⡀⠈⠙⠻⠷⣾⣏⡀⠀⠀⢠⡿⠃⣀⣀⠹⣷⡀
⢻⣯⠀⢀⣠⣴⠾⠟⠋⠀⠀⠀⠀⠀⢸⣇⣠⣿⠛⠷⣦⣄⣀⠀⣹⡟⠀⢠⣿⣷⡾⠟⠙⠻⠿⣷⡀
⠀⠻⠿⢻⣿⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠙⠛⠁⠀⠀⠀⢹⡟⠿⠟⠀⠀⠘⢻⡷⠀⠀⠀⠠⣾⡟⠁
⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⣾⠏⠁⠈⠙⣷⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⢙⣷⣄
⣶⠿⠛⠛⠛⠛⠻⢷⣦⣴⠿⠿⠿⠿⠿⢿⣧⣄⠀⠀⢀⣸⣷⣶⠶⠿⠿⠿⠷⣶⣤⣤⡶⠿⠛⠛⠛⠛⢷
⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿
⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣠
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⢀⣴⠟⠋⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢀⣤⡾⠷⠶⢶⡿⠁⠀⠀⠀⠀⠀⠀⢹⣶⠶⠶⠶⣤⣀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢿⣄
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⠟⠉⠉⠉⠙⠻⣦⠀⠀⠀⠀⠹⣧
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠹⡷⠾⠿⠷⢶⣽⡇
⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀
⠹⣧⡀⠀⠠⣄⢰⣆⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⢿
⠀⠈⠛⠶⠶⣾⠿⠿⡷⠶⠶⠶⠶⠶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠠⠚⢳⠚⢦⠀⠀⠀⢦⡀⣸⣷⣀⠔⠀⠀⠀⠀⢦⣀⣸⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡝⠁⠈⣿⠿⠶⠶⠶⠶⠶⡿⠿⠿⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠠⡀⠀⡆⠀⣠⢀⠜⢦⠔⠳⡀⠀⠀⠀⠀⠰⠛⢲⠚⠣⡀
⠀⠀⠀⠀⠀⠀⣀⣈⡖⠙⢺⣁⣀⠀⠘⠀⠀⢀⠀⢠⠀⠀⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢈⠷⡤⠾⣄⠀⠀⠀⠀⠀⠈⣳⠚⠓⣎⣀
⠀⢤⡀⢰⠀⠀⡀⠁⠀⠃⠀⠈⠀⠀⠀⠀⠉⠉⣹⢤⡤⢏⠉
⣀⣀⣹⠊⠙⣎⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠃⠀⠑
⠀⠀⡽⢦⡤⢯⡀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠛⠛⢿⣷⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⠈⠙⢿⣷⣄⣀⡀
⠀⠀⠀⠀⢀⣤⣾⣿⡏⠀⠀⠀⠀⠈⠛⠋⠙⢻⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠿⣿⣷⡀
⠀⠀⠀⣰⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣄
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣧
⠀⠀⠀⢻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠋⠀⠀⠀⠀⣀⡀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⠰⣿⣷⣶⣾⣿⣿⣶⣶⣿⡇⠀⠀⠉⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⢠⣤⣄⣀⣼⣿⣧⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⠈⣿⣿⠁⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⣠⣾⣷⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠟⠋⠻⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⣾⣿⣿⣷⡄⠀⠀⠀⠘⠛⠋
⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⢼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣦⣀⣤⣿⣿⣄⡀⠀⠀⠀⢀⣴⣿⠆⠀⠉⠁⠀⢹⣿⡏⠀⠀⠉⠁
⠀⠀⠛⠋⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠙⢻⣿⡟⠋⠛⠿⠃⠀⠀⠰⣿⠟⠁⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⣀⣀⠀⣀⣿⣿⡀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠛⠻⣿⣷⣄
⠀⠀⠀⠻⢿⣿⡿⠟⠿⣿⣿⠿⠋⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠘⠻⣿⣧
⠀⠀⠀⠀⣸⣿⣇⠀⢀⣿⣿⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⣿⣧⠀⠀⢀⣿⣿
⠀⠀⠀⢿⠿⠛⢿⣿⣿⠟⠻⢿⡷⠀⠀⣀⣤⣶⣶⣦⣄⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⢰⣿⣿⣿⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⣰⣿⡿⠿⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠟⠉⠙⢿⣿⣶⣦⡀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢿⣿⣄⠀⠀⠀⠉⠙⢿⣿⡄⠀⠀⢰⣿⣿⣿⣿⡀⣸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠻⢿⣿⣷⣄⡀⣀⣾⣿⠃⠀⠀⣾⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣠⣤⣴⣿⣿⣤⡀⠀⠀⢸⣿⡇⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣄⠀⠀⠀⢸⣿⣇⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣴⣿⡿⠛⠙⠛⢿⡿⠛⠛⠙⠛⢿⣿⣧⡀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⠟⠛⠙⠻⢿⠿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣴⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠛⣿⣿⡿⠟
⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢸⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣀⣀⠘⠢⡀
⠀⠀⠀⠀⠀⠤⢤⣀⣑⣄⡀⠘⠂⠀⠀⣀⠀⠀⠀⠀⠉⠉⠙⠓⠬⠦⣀⠴⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⣲⣖⠦⠤⠈⠀⠀⡠⢂⣐⣂⣤⢄⡀⠀⠈⣳⠤⣀⣈⠠⢤⡀
⠐⢤⣀⡀⠐⠢⢄⡀⠀⠀⠈⠉⠫⠓⠦⡀⠀⢰⣿⢀⣄⣠⣦⠑⣌⡆⠀⢀⡀⠀⠀⠛⠷⣟⠲⠤⣄⣀
⠀⠀⠈⠛⢷⡦⢄⠀⠀⠀⠲⠤⣤⣀⠀⠚⠃⠸⡘⢌⠙⠃⠤⠄⣿⣧⡀⠀⠈⠉⠲⠦⢬⣉⣉⠓⠶⢶⡉
⠀⠀⠀⠀⠀⠈⠓⠦⣀⠐⠢⢄⡀⠉⢿⠷⡖⠀⡈⠢⢥⣤⣴⣿⣅⣔⣙⣄⠀⠀⠩⢶⣦⣤⣌⣉⣁⣂⣀⣈⣤⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠢⢄⠀⡁⠒⠤⣄⡈⠋⠀⠈⢿⣽⣿⣷⣋⣻⣾⣗⢄⡀⠀⠀⠉⠛⠿⣓⠲⢤⣀
⠀⠀⠀⠀⠀⠈⠉⠒⠲⠤⠀⠀⠀⠈⠁⢢⣄⣀⠀⠀⠀⠈⠛⠋⠉⠹⣿⣿⣿⣶⣵⡀⠀⠈⠉⠉⠙⣛⣳⣶⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠶⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⣿⡏⢹⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣧⠀⢙⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⡀⠄⠀⠀⠀⠐⠂⠀⠀⠒⠀⠀⠐⣦⠚⠹⡀⠀⠀⢈⡔⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡮⠶⢽⡄⠀⠂⠀⠀⢠⣔⣳⡀⠐⠀⢴⣁⡈⢙⡁⠀⢁⡞⣉⠉⢿
⠀⠀⠀⠀⠀⠠⠀⡻⠒⠀⢤⠇⠀⠀⠠⠀⣾⠤⢬⣧⠀⢴⣇⣀⣩⢹⠁⠀⣠⣋⠈⢩⢫⡁⠀⠂
⠀⠀⠀⠀⠐⠀⢘⠗⠒⠠⢤⠷⠀⠀⠀⢐⠗⠒⠢⡷⠴⠧⣀⣀⠈⢫⢁⢀⣞⣁⠀⠉⠻⡁⠀⠐
⠀⠀⠀⠀⠀⠀⠓⠒⡖⡤⠠⠧⠀⠁⠆⠉⠉⣛⠒⣚⣀⣀⣆⣌⣉⡉⠀⠀⠀⢸⢩⢉⣉⣁
⠀⠀⠀⢰⡗⠒⠒⠒⠓⠓⠛⠛⠛⠛⠓⠒⠚⠉⠉⠉⢉⣉⠀⢀⡉⠉⠉⠉⠛⠛⠉⠉⣁⣈⠙⢲⡄
⠀⠀⠀⢸⡇⠀⠑⠒⠀⠐⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠀⠀⠀⠀⠀⠀⠈⢸⡇
⠀⠀⠀⢸⡇⠀⠐⠤⣀⠠⠤⠄⠒⠂⠀⠀⠈⠉⠉⠒⠒⠒⠁⠀⠀⣀⠀⠈⠒⠒⠊⠉⠉⠁⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠤⠔⠒⠒⠀⠒⠒⠒⠢⠤⠀⠀⠀⠀⠉⠀⠉⠒⠤⠤⠤⠒⠀⠀⠀⢸⡇
⠀⠀⠀⠸⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⢀⡁⡀⠀⠁⢒⣀⡀⠀⠀⠐⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠀⠆⠀⠀⠀⠠⠀⠀⡄⠀⠀⢀⠘⠀⠀⡠⠔⠁⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠁⢠⡀⠀⠀⠚⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠤⠥⠤⠀⠤⠤⠬⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⢀⡀⠀⢀⠀⠀⠀⡀⣠⠂⠰⠂⠢⣀⡀⠀⠤⠀⠀⠘⠀⠀⢀⠈⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⠐⠂⠀⠈⠀⠀⠀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⢀⠀⠐⠀⠀⠈⠀⢀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠆⠀⠀⠀⠠⠄⠀⠀⠤⠀⠀⠀⠤⠀⠀⠄⠀⠀⡀⠀⠀⠠⠀⠀⠀⠘⣀⡀⣀⢀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠐⠀⠀⢢⠀⠀⠀⠀⠐⠂⠀⠀⣀⠀⠀⠀⠁⠠⠀⢀⠠⠄⠐⠊⠀⠀⠀⠀⠘⠀⠢⡀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠠⠬⠡⠤⠠⠤⠤⠀⠤⠤⠤⠀⠀⠤⠬⠥⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡀⠀⠒⠀⠀⠀⠀⠰⠆⠀⡀⠀⠤⠀⠔⠈⠉⠐⢄⠐⠂⠀⠀⢀⠀⠀⠉⠀⠀⠀⠰⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⣀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⡀⠐⠘⠀⢀⠦⠀⠘⠄⡀⢀⡀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠰⠾⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⠁⠀⠘⠀⠀⠀⠠⠄⠀⢠⠊⠀⠀⠀⠀⡔⠁⠀⠑⢄⠀⠐⠠⢀⠀⠀⠉⠀⠀⠈⠉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡄⠀⠀⠀⠰⠆⠀⠀⣀⠊⠁⠀⠀⠀⡠⠊⠀⠀⠀⠀⠈⠣⢀⠀⠈⠂⠒⠄⠰⠆⠀⠤⠀⠀⠀⠀⠀⠿⠇⠀⠉
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⡆⠀⠀⠀⠀⣤⠀⠀⠀⠎⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠈⠁⠢⡀⠀⠀⠐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⣄⠀⠀⠄⠀⠀⣀⠔⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⣦⡆⠀⠀⠒⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠁⠈⠁⠀⢸⠀⠄⠀⠠⠀⣀⡀⡀⠠⠄⠀⠄⢸⠀⠀⠈⠐⢉⠀⠀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⣀⣀⣸⢀⡤⠤⠬⣀⠖⠀⠉⠐⢄⣀⡀⠸⠀⠀⠀⠀⠈⢀⣀⠀⠈⣁⠠⠤⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⠂⠉⠁⠢⠔⠒⠂⢤⠀⠴⠁⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠒⠰⠦⠂⠀⠀⠺⠀⠀⠈⠋⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠄⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⡰⠖⠀⠂⢄⡠⠄⠠⢎⠀⠀⠀⠀⠈⠁⠀⠀⠑⠂⠈⠉⠐⠒⠀⠐⢤⠀⠠⡠⠀⠀⠂⢤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠤⠒⠀⠐⡤⠄⠠⢄⡀⡀⢠⠋⠀⠀⠀⠁⠀⠈⠀⠀⠈⠢⠂⠉⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠂⠒⠒⠔⠈⠉⠔⠀⠉⠐⠢⠐⠈⠀⠂⠔⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⢀⢀⡀⢀⣀⡀⠀⡀⠀⢀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢼⠀⡇⠀⠀⠀⡔⠁⢀⡜⠁⣰⢹⡀⣹⢠⠃⡇⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠓⠂⠀⠘⠒⠂⠚⠒⠂⠁⠀⠁⠉⠀⠃⠓⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠛⠛⠒⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⢀⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡀
⠀⠀⠀⣠⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⠶⠶⣤⡈⠉⠙⠳⣀⣤⠤⢤⣀
⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣍⠷⣤⡴⢋⡴⠞⠳⣦⡙⠦⠴⠞⣩⡴⠒⢶⣽⠇⠀⢀⡀
⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠳⠶⠶⠋⠀⠀⠀⠀⠙⠲⠖⠛⣹⠂⠀⠀⢀⣤⣀⣿⣿⣀⣤⡀
⠀⠀⠀⠙⠷⣤⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⡀⠀⣀⡴⢋⣉⣙⠷⣄⠀⢀⣠⠶⢛⣛⠳⣦⢠⡤⠞⠁⠀⠀⠀⠈⢳⣮⠋⠙⣵⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⡛⠚⣋⡴⠋⠀⠙⠷⣌⣛⣋⡥⠞⠋⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠰⣯⠷⣷⣾⠾⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⣀⠈⠉⠉⢀⡤⠶⠶⢤⡀⠀⠀⠀⣀⣤⠤⢤⣀⠀⠀⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡟⡇⢀⣀⠀⢺⣍⠳⣤⡴⢋⡴⠛⠛⢦⡙⠶⠴⠞⣩⡶⠒⠶⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⣛⠇⢟⣫⠿⠀⠀⠙⠳⠶⠖⠋⠀⠀⠀⠀⠙⠓⠖⠛⠁⠀⣠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⣽⡆⣮⣝⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⡲⣿⢸⡶⣛⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⣧⠇⠈⠉⠀⠀⠀⠀⠀⣀⡀⣾⢻⠀⣀⡀⠀⠀⠀⣬⢿⣣⢠⣛⢯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⡛⠘⣫⡽⠋⠀⠀⠈⠛⠋⣿⣸⠏⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣭⣶⢰⣮⣟⡦⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⡾⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠛⠉⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⣠⡤⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠲⢦⡀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⢀⡴⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⡘⠛⠓⠦⣀⣤⣤⣀
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠳⣤⡴⣫⡴⠒⢦⡙⠦⠴⢞⣩⠶⠲⣬⠇⠀⢀⡀
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡈⠓⠶⠚⠉⠀⣀⠀⠙⠓⠚⢋⡿⠀⠀⢀⡤⣄⣿⣿⣤
⠀⠙⠶⠦⠤⠤⠤⠤⠤⠄⣴⢶⣄⢀⡴⢋⡥⢬⡑⢦⣀⣠⠶⣋⣭⣝⣳⠠⠶⠋⠀⠀⠀⠀⣹⡷⡁⣹⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⣭⠶⠋⠀⠀⠙⠶⠭⠴⠚⢁⣀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠓⠛⣿⣿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⢠⡶⣄⠀⣠⡶⣋⣭⣙⢦⣀⢀⣠⠖⣋⣙⠳⡄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢼⣿⡧⣶⡆⠈⠳⣬⣛⣥⠞⠁⠀⠙⠳⣭⣭⠴⠋⠁⣈⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡽⣣⣀⣜⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⡏⣧⡴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠹⣿⠏⠙⠁⠀⠀⠀⠀⣀⠀⡞⡆⢀⡀⠀⠀⢀⣹⢷⡁⣱⢯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣝⠃⢛⣽⠟⠀⠀⠘⠛⠙⣇⡏⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠵⡆⡶⢭⡷⠀⠀⠀⠀⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣴⣶⣶⣶⣶⣶⣾⣾⣿⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣶⣦
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣿⣽⣻⣽⣿⣟⣻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣯⣿
⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣶⣿⢽⣿⢡⣾⣿⡻⣿⣷⣭⣿⣿⣿⠿⠉⠻⢿⣿⣿⣯⣿⣷⣿⣿⣿⡽⣾⣿⣿⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠆⠠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣮⣻⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣯⣛⢿⡟⣺⣿⣿⣿⣿⡿⣿⡿⠯⣼⡗⠂⠉⠘⠆⠍⡃⠤⠀⠾⠥⡿⣉⢙⢿⡿⣿⠿⢿⣿⣿⡿⣿⣿⢟⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⡷⢿⣷⡏⠒⠒⠂⠉⡅⠂⣠⠅⠂⠀⠀⠰⢆⡌⠒⠤⠀⠂⠄⢈⣉⠐⠛⢓⠐⠮⣽⣿⣷⣿⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⠋⣶⣿⣿⡇⠀⠀⠀⠊⠀⡸⠿⠀⠂⠉⠀⠘⠃⠃⠀⠀⠈⠂⢄⡘⠋⠘⠃⠹⠰⢆⠻⣿⣿⣿⡇⣸⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣟⣡⣄⠸⣿⣿⠓⢦⡤⠆⠀⠀⠀⠰⠀⠀⠀⠀⠐⢄⠀⠘⠀⠠⠀⠀⠈⣙⠆⢀⣀⡀⠀⠀⠀⠙⠟⣰⣿⣿⣌⣿⣿⣿⣯⣿⣿⣿⣿
⢸⣿⡿⣿⣿⡇⠀⢠⣾⣮⣀⠂⡆⢀⣀⠀⢀⢠⠄⠀⠀⠀⠀⠀⠂⠀⠀⠻⠛⡟⠛⢻⡃⠐⠿⠷⠟⢲⣷⣶⡄⢿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⡁⠀⠈⣽⣿⡍⠁⡅⢸⢡⣴⡸⠙⠄⠀⠀⡈⠀⠀⠁⠀⠀⠀⠀⠁⠀⠰⡇⠀⠀⣻⡃⠠⡇⢿⡇⠀⣹⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⡇⢀⠸⣿⣿⡇⢱⡄⠈⠘⠛⠃⢘⠈⢈⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠸⡇⠀⡷⠞⠓⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠸⠃⠂⠀⠀⠘⠿⢣⠌⡍⡃⠀⠐⠀⠀⠌⠠⠄⠀⠀⢄⣀⠀⠀⠀⠠⢄⣤⣀⣀⣤⣄⣄⣀⣀⡀⠁⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠒⠀⣘⡠⠠⠀⠐⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠀⠉⢛⣾⡿⣿⣿⣿⣿⣿⣿⡝⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣇⠈⠉⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⣿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣝⠷⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⡶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣄
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⣴⣾⣿⣿⣿⣿⣿⠟⠋⠛⠛⠋
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠋⠉⠉⠉⠋⠁
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷
⣿⣿⣧⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⡦⡀⠘⢤⡇⡄⠀⠓⡃⢣⠀⡇⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡱⡌⢠⡈⢿⡘⡀⠄⠘⣜⡀⡇⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠱⡘⢦⡈⠺⡟⢟⢆⠀⠀⢻⠀⢸⢉
⣠⣶⣴⡗⣶⠀⠂⠠⣸⡄⠀⢄⣠⠀⠀⠀⠀⠀⠀⠀⠀⢨⢉⠐⠒⠂⠰⡄⠑⢄⢹⡘⣆⠱⡀⠺⣆⡞⢸
⣿⣿⣿⣿⢪⠗⠂⠐⠉⠁⠀⠼⣿⡜⠖⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠣⣀⠱⣧⠚⡄⠘⣌⣿⣇⢰
⣿⣿⣿⣿⣿⣿⢈⣷⣾⣷⣷⣿⠑⡯⣀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡀⠸⣄⢸⣿⡀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡶⡿⣽⣷⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⣿⣤⣟⢾⣿⡤⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⢯⣽⣷⣮⡿⠭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣀⡽⣿⣿⣾⣿⠎⣿
⣿⣿⣿⣿⣭⣍⣻⣿⣿⣍⣿⣻⣿⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⣴⣷⣿⣿⣗⣿⣿⣿⣿⣴⣿
⣿⣿⣯⣿⣿⣿⣿⣿⡟⠝⠿⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠛⠙⠁⢿⣿⣿⣿⣿⣿⣿⣹
⠿⠿⠿⠟⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠙⠛⠉⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠰⠀⠀⠈⡀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⡀⠀⠀⠀⠈⢀⠀⠀⠀⠂⣁⡀⠀⠁⠐⠈⣀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡴⡄⠰⠀⢀⠠⠀⠀⠚⠃⡀⠤⠐⠁⠈⢀⠠⠜⣶⠚⠍⢧⠀⢀⠠⠀⢉⡴⠋⢳⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣴⣫⣤⣛⡎⠀⠰⠤⠀⠂⠁⢀⣠⠞⢖⠀⠀⠆⢀⣴⠋⠍⠛⢿⠃⡀⠘⢄⡼⠋⠙⡳⣗⠄⠒⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⣵⣋⣀⠀⠘⢏⠀⠀⠄⠀⠂⠁⡨⠛⢒⠺⡆⠐⠈⣡⢟⠙⠒⠲⡾⠇⢀⠠⢛⠖⡚⠳⠶⡼⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⢀⡴⢫⠈⡍⠙⣏⠁⠘⠂⠈⠅⢚⡟⠋⠛⢲⡷⠐⣈⠟⠒⠦⠬⣇⣻⡀⠤⠰⣯⠤⠥⢼⣇⣱⡄⠀⠈
⠀⠀⠀⠀⠀⠈⠃⠀⢨⠟⣉⠓⠒⠲⡞⠂⠁⠀⠀⠀⡸⠋⢉⠓⠲⡷⠚⠳⠤⣤⣀⡃⠈⣇⢠⡀⣼⣁⣀⡐⠀⠀⢳⡀⢀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⢰⠓⠒⢦⠤⡤⠤⣹⡄⠀⠁⡤⠈⠉⠙⡖⡖⠒⠛⠀⠀⢠⠇⡼⠈⠉⠛⠀⠀⠀⠀⢸⠉⡏⠉⠉⠁⠈
⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣼⣴⣧⡤⠶⠶⠦⠤⣤⣤⣤⡴⠷⠷⠒⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⠶⠶⠶⠾⠶⠷⠛⠛⠛⠳⢦⣀
⠀⠀⠀⠀⢸⡇⠀⢠⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠋⠓⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠰⠶⠦⠤⡄⢹⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠲⢤⣀⣀⣠⠤⠤⠔⠒⠦⠀⠀⠀⠈⠉⠉⠙⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠉⠉⠉⠁⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣄⣀⣀⡠⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠔⠋⠉⠓⠤⣀⠀⠀⣀⡠⢄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣤⣤⣤⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣧⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣤
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠈⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠉
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⣄⠀⠀⠀⠀⢠⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣷⠀⠀⠀⢸⣿⣿⡄
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠙⠋⠀⠀⠀⠀⠙⠋
⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣶⣿⣷⣄
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⣿⣶⡄⠀⠀⠀⠀⢰⣷⣦⡀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⢰⣷⣦⡀⠀⠀⠀⢰⣷⣦⡀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠻⣿⠟⠀⠀⠀⠀⠈⢿⡿⠇⠀⠀⠀⠀⠀⠿⣿⠇⠀⠀⠀⠀⠈⢿⡿⠇⠀⠀⠀⠘⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⢺⣿⣿⣿⣷⠀⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⣶⣤⡀⠀⠀⠀⠀⠈⠻⠟⠛⠁⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠘⢿⡿⠿⠋⠀⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠙⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⡿⠏⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠠⠆⡀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠴⠀⠯⡄⠀⠀⠀⠢⡀⠀⠀⠀⠀⠑⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠠⠀⠘⠆⠠⠂⠀⠘⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠐⠳⠂⠀⠀⠀⠁
⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠃⠋⠀⠀⢀⡀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠐⠐

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⢀⠄⠀⠴⡮⢀⡀⠀⠀⠀⠀⠈⠁
⠠⢴⣆⠀⠀⠀⠐⠀⠀⠀⠀⢰⡄⠉⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠂⢀⡀⠀⠀⠀⡄⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⣸⠀⠀⠀⠀⠸⠁⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎
⠀⠀⠠⠀⠁⠀⠉⠋⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠐⠀⠁
⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⢀⠠⡀⠀⠀⠐⠀⠂
⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣥⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠏⠁⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⢰⣁⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠃⠀⠰⠀⠣⢸⡀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠔⢊⠊⠀⠀⡀⠀⠉⠀⣢⠜⡄⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠩⠢⡀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠃⠈⡆⠀⠀⠀⠀⠘⢯⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠕⠁⠀⠀⠀⠀⠀⢢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢣⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡐⠛⢳⠜⠀⠢⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠢⡀⠀⠀⠀⠈⢆⡀⠀⢀⣀⣀
⠀⠀⠀⠀⢀⡠⠤⠒⠀⡕⠉⠀⠀⠀⠻⡗⢄⠀⠀⠀⠀⠀⠀⠈⠆⠈⠓⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢖⣅⠌⠪⠗⢤⡀
⠀⠀⣀⠖⠁⠐⠃⢠⢀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⡄⠀⠐⠢⢼⡦⢄⡀⢀⡤⠤⡀⠀⠀⢀⠔⠚⠋⠀⠂⠈⠑⠄⠀⠀⠈⠓⠦⣀⡀
⠔⠋⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠂⠀⠀⢀⡤⠦⡟⠁⠙⠆⠀⢑⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠛⠈⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢦⡞⣏⠰⣶⣶⣮⣴⢞⣤⣤⠰⣦⣀⠐⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣿⣾⣿⠖⢤⢀⣀⡨⣀⣀⣦⣗⢰
⢐⡻⡄⠋⢙⠿⣟⣡⠈⢨⢸⡗⣫⠩⡟⠊⡩⡼⢀⣀⣀⢀⣄⠀⣀⣠⣠⠟⣤⢝⡎⢼⠨⣏⣮⠹⣿⠫⡐⢓⢻⠤⢳⠾⣇
⠈⠇⢑⠦⡋⠏⢹⡼⢎⣽⢨⠶⣨⡷⠚⣶⢑⣯⣘⣿⠹⣏⠋⣿⣿⢿⣟⣿⢍⣜⣄⡼⡔⠿⢆⠓⢿⡧⠙⢠⠙⡏⣸⢳⡟
⠐⠀⠾⡖⣩⠓⢞⠋⠂⠶⢊⢌⡽⠋⢔⣠⠋⡐⣬⡱⢏⢀⣀⠈⠗⠞⠣⠊⢄⣿⡸⢆⡲⢌⣆⠛⠶⢦⢘⠀⢅⠱⢗⠊⢍
⠀⠀⣰⠀⡌⡙⠂⣀⠀⠀⠀⠀⠀⠋⠀⠓⠀⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠀⣆⠁⢲⠌⢺⡷⠄⠈⠀⠁⠙⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠁⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢀⣰⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣤⠄⢨⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣶⣶⣶⡄⡿⢿⣙⣇⢻⣿⣆⣿⣿⣿⣿⠇⠀⢀
⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣠⠄⠀⠀⠀⠈⣿⣿⣿⢿⡟⣟⠁⡧⢻⠘⣿⠈⣿⣯⣹⡟⢻⣿⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠐⠉⠛⠀⢀⠠⠀⠀⠠⠟⠃⢸⡁⣾⠁⠁⢰⢈⡿⢀⠸⣿⣿⢄⡠⢿⠋⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠀⠉⠙⠈⢠⡆⠄⠀⠀⠀⠈⠀⠀⠀⢸⡗⠃⠀⡀⢼⣸⢃⣿⡆⢹⣿⣾⡅⣾⠅⡀⠈⢷⠤⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠄⠀⠀⡀⠀⠀⠀⠉⡇⠀⠆⡃⣸⠇⢸⣿⡇⢸⣿⣏⣠⣿⣢⡇⠀⢰⣀⠀⡄⢉⡹⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠃⢄⠂⣼⡿⡇⠀⣤⣤⢉⢙⠛⠲⠧⠈⡡⠃⠀⠠⠘⠛⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠁⠈⣰⣿⣷⢧⠸⣯⣿⣡⣾⣿⡟⢀⣟⡁⠀⠀⠐⠘⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⣸⢠⣿⠏⣿⡺⢞⡇⣌⠛⢣⠀⠀⠂⢀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠰⠀⣿⡿⣿⠠⡃⠸⢁⡴⠟⠀⣿⠇⠀⠘⠀⣧⡴⠂
⠀⠀⢳⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⣏⡿⠃⠁⠘⡡⢖⠀⠄⢩⠆⠀⠀⠀⠇
⠀⠀⠘⠀⡖⠉⠀⠀⣠⢦⣤⣀⣀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡠⡠⢀⡰⠛⡯⢅⠀⠀⠀⠑⠀⠀⠀⠈
⠀⠀⠀⠀⡇⠀⠀⠈⠀⢸⣿⣿⣿⣿⡯⣷⣿⡿⢓⠲⣖⠢⠀⠀⠀⡩⠈⣤⠟⠀⠀⠡⠀⣠⠂⣄⣂⢀⠀⣦⠀⠐⠀⠀⠀⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⣏⢿⣿⢩⢸⣿⣻⢠⠘⠀⣠⠀⣀⡤⠊⡠⠊⠀⠀⠀⠀⠒⠸⠀⣴⣌⠙⢾⡧⢹⣤⡄⠤⠀⠔⠁
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠈⠵⢾⠿⣁⢸⣿⢿⢀⠔⠋⠹⠃⡀⠀⢘⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣹⣿⣆⠙⣯⡇⣡⣷⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠜⣿⠴⠫⢸⠀⠀⠁⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⡹⢟⠹⣧⠈⡟⢿⡇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⢸⠀⠀⠰⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠐⠀⠐⠁⠀⠀⠀⣿⣧⠘⣿⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢪⠹⡄⢻⡏⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢱⢨⡀⠀⠀⠀⠉⠂⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⡀⠁⠀⠀⣠⠔⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠰⡄⢀⡴⠞⠙⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠄⠀⠀⠀⢀⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡀⠀⣻⣤⡲⢀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠄⠂⠀⠀⠠⡼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣿⡀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣌⡆⠀⠀⢠⠟⠞⢃⡾⣹⢧⡹⡏⡜⠛⠁⠀⠀⠀⠀⣀⡤⠒⠋⠘⠁⠠⣶⡀⠀⢸⡞⢻⣀⡀⠀⠀⢠⣷⡄⠀⠀⠀⡩⡀⣥⣾⡀⣠⣿⣄⣾
⢀⣄⢠⣿⠀⣰⡰⡚⠛⣸⣦⣴⣃⣶⣤⣴⣏⠀⠙⠿⠀⠘⠁⢀⡠⢔⣾⡏⠀⠀⠀⠀⠀⢴⣿⣆⠀⠼⣇⣾⡍⠁⠀⠀⣦⢷⣰⢀⠀⢰⡟⢻⣠⡏⢳⣿⣸⣇⢿
⢸⣿⣫⣭⣷⣿⢉⣿⢉⣻⡿⢩⠇⢸⣧⠁⣾⡆⣸⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⣎⣻⢸⡤⣀⣽⣏⠹⠶⠀⣠⣤⣿⡉⢼⠁⠼⣷⣚⣡⣇⣸⣧⣹⠙⡛
⢸⣿⣽⡉⣿⠟⠁⣈⢈⡉⢹⣿⣠⣾⣧⡖⢁⣿⣏⠈⡝⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣷⢿⣌⣥⠈⠾⡟⠳⠇⠀⢈⣡⣯⡛⠆⣉⠰⣾⡿⢋⣍⠁⢹⡻⡦⣿
⢸⣯⣴⣿⡝⠛⠋⠈⣿⡛⠛⣿⣿⣿⡿⣥⣿⢿⣿⣆⣻⣿⣾⣧⣦⣷⣶⣴⣄⣤⣄⡤⠚⣇⣼⣮⣙⣥⡀⡇⠀⣀⣴⡌⢀⣧⢥⠔⢣⡴⢤⣿⣯⣿⣷⣼⣿⣁⣿
⢸⣿⣿⣿⠧⠾⣀⣼⠞⢷⣶⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣯⣛⣧⣿⣿⠖⣉⣿⠈⣧⡙⢯⢻⣿⣟⡣⠾⣙⣿⠅⠞⡔⠢⠗⢤⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⡄⣠⠏⠈⣄⠀⢳⣀⣻⡇⠿⠛⢿⠈⠟⠻⡿⣿⠟⠙⠛⠙⠿⠿⣿⣿⡿⢛⣡⣻⠆⠁⣹⡚⠻⡿⢓⠦⠓⠆⣹⢇⡠⠃⡤⠧⡘⠾⢿⡿⡿⡻⠻⠻⣿
⠈⠋⠻⢯⣀⡴⠦⠤⠊⠓⠛⢿⣄⣀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⣡⠀⣥⠀⢈⣍⠠⡬⠃⠈⠋⠸⡀⠤⣹⠇⡴⢳⠀⡉⠙⡈⢃⠁⠀⠀⠀⠁
⠀⠀⠦⠴⠁⠀⠦⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠀⠐⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠀⠀⠀⠐⠒⠒⠒⠂⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠄⠤⠤⠀⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣈⡉
⠀⠀⣀⠀⢀⡀⢀⠀⡀⠀⠀⠀⠀⣈⢡⢎⣼⣿⣾⣷⣤⡒⢤⡀⠀⠀⠰⠶⠒⠀⢀⣐⠂⣠⡀⠀⣀⠀⠄⢀⡀
⣀⣨⣤⣤⣀⠒⣀⣈⣉⣀⡈⢉⣿⡏⠐⣩⢟⣵⣿⢟⣿⣯⠀⠤⣄⡀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡷⢶⠛⡿⡲⠮
⠈⠙⠉⢉⣁⣈⡉⠛⠙⠛⠋⢉⡭⢒⡠⣸⡽⣛⣵⣿⣿⣿⣦⠀⠈⢝⣆⢠⣰⣠⣀⣀⣈⠉⠛⠛⠛⠻⠿⠾⠞⠛⠒
⠤⢆⣚⠫⠭⣛⣫⣭⠤⣒⡨⠔⣪⠵⣚⣽⣾⣿⡿⣿⣿⣿⡟⣄⡀⠐⠛⠍⡿⢤⡈⣍⣬⠍⣉⠈⠙⢃⡴⣧⡦⢴⡃
⡉⠄⣐⣚⣭⠵⠶⢚⣩⠵⣒⡭⣒⣯⣟⠽⣛⣥⢞⣿⡿⣿⣿⣯⣋⣐⢀⠀⡉⠐⠉⠁⠉⠩⣘⠉⠈⠉⠀⠀⠩⠟⠉
⣫⣭⣽⡥⢴⣒⣫⢽⣾⡿⣗⡿⢟⣫⠥⣐⢭⡾⢟⣽⡾⢟⣽⢿⣿⣿⣶⣤⣬⣥⣤⣬⣴⣮⣵⣍⣱⣀⣒⣵⡶⣾⢣
⠩⠽⠖⣛⠭⢑⣚⢭⣶⠏⣁⡡⢈⣠⡴⠞⣉⡤⠞⣩⠾⣫⣵⠟⣫⣴⠟⣋⢜⣹⠟⡯⢚⣿⣿⣻⣿⣿⠿⣫⠾⢃⣟
⣶⣶⠶⠶⠿⣷⣶⣿⣶⣿⣷⣿⣿⣷⣶⣿⣷⣶⣾⣶⣾⣿⣶⣾⣿⣷⣾⣷⣿⣶⣿⣶⣿⣿⣿⣿⣿⣷⣶⣷⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣉⣤⠒⠒⢲⠒⠠⢌⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡰⠋⠐⣎⢦⠀⠘⡀⠀⣠⠜⣦⡈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢠⠃⣼⣁⠀⡀⠈⣆⠻⠀⡦⢊⠴⠊⠀⠱⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡖⠂⠠⢤⣄⡉⠀⡀⠀⡋⠒⠒⠀⢠⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠲⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣁⠀⠀⣠⣞⡵⠞⣳⡌⢫⠉⠁⠀⢐⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⠻⠙⢫⠋⠁⠈⠀⡇⢿⠉⢦⡱⡀⢀⠎⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠉⠀⡀⠀⢀⡸⠀⢀⡱⠞⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠈⠈⣿⡉⢤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣀⠀⠀⠀⢀⣀⡀⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠁⠀⠉⠉⠉⠁⠀⡀⠄⠂⠙⡗⠲⣤⣀⣀⣀⣤⠔⠚⠉⠀⠀⠀⠀⠀⠙⢆⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡄⠀⠀⠀⢀⠔⠈⠁⠀⡄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⠀⠀⠀⡈⠀⠠⠂⠁⠑⢄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠀⠀⣇⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡔⢃⠀⠀⣀⣀⣀⣀⠀⢦⠀⠀⠀⠀⢸⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠇⠀⠀⠀⠈⢠⡡⣀⠤⠒⠉⠀⡀⠀⠀⡏⠉⠉⠉⠀⠀⢱⠀⠀⠀⠿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠂⠀⠀⠇⠀⠀⠀⠀⠀⢈⠀⠀⢀⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⠀⠀⠀⠀⠀⡠⠉⠀⠉⠓⠴⢦⡂⠀⠀⠀⠀⠀⡕⠸⠀⠀⢸⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⡄⠀⠀⠀⠀⡰⠁⠀⢠⠧⢄⡀⠀⢩⠁⠒⠒⠂⠐⠈⠁⠀⠀⡶⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣁⠀⠰⠃⠀⠀⠁⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢸⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⡀⠀⠀⠀⠈⠢⢀⡀⠀⢀⠄⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⣄⠙⠶⢤⣀⣀⣀⣀⡀⢀⣀⣀⡠⠴⠚⠋⣠⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⠙⠲⠤⣤⣀⣀⣈⣉⣀⣀⣤⠤⠖⠒⠉⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠒⠒⠊⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣻⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣀⡀⢠⠄⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠈⡀⠀⠀⢀⡀⢹⢦⣘⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⠄⠄⠀⠀⡁⠤⠘⣁⠠⠐⠂⢢⣁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠀⠰⠤⠐⠞⢀⣀⡀⠀⠀⠠⠉⠱⠒
⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠶⠵⢆⡠⠀⠠⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠃⡠⠐⠀⠀⠀⠀⠒⢄⠀⠀⠀⠐⡀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠠⠴⠀⠔⢄⡀⠀⡠⢁⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⡀⠘⠀⢰⡆⠀⠰⡦⢠⠁⢘⠅⠕⣨⣀⠀⢀⡄⠀⡇
⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⡀⠀⢨⠀⠂⠀⣤⠀⠀⣀⠁⠁⠀⢀⡔⠁⠈⠑⢀
⠀⠀⠀⣠⠀⠀⠪⡜⠒⠒⡄⠀⠀⠀⠀⠈⠆⠀⠀⠀⠤⠈⠃⠀⡄⡠⢚⠀⠀⠀⡀⣶⢓
⠀⠀⠀⠁⠀⠀⠁⠉⣉⣩⢇⡀⠀⠀⠀⠀⠀⡀⠆⠤⠌⢠⠄⠊⢰⠀⢐⠦⢈⠀⠈⠃
⠀⠀⠀⠀⠀⠄⡀⠤⢤⣤⠺⠂⠀⠀⠀⠀⡀⡘⠉⠁⠐⠉⢄⣧⢀⠓⠂⠉⠁⠒⢘⠀⠀⡄⡀⡌
⠀⠀⠠⡏⠈⠁⢀⠀⠮⠘⠈⢀⠀⠀⠀⠀⠳⡃⠠⠬⠉⠐⠀⢙⠃⠀⠨⠀⣍⡍⢩⠑⠉⠉⠁
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⣴⠊⠁⠀⠀⠀⠀⠑⡒⢒⠒⠊⠀⢠⠀⠀⠀⠐⠈⣣⣼
⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠃⢸⣃⢇⠀⠀⠢⢀⠀⠀⠀⠉⡩⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠄⠈⠀⢀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⡀⠀⠀⠐⡀⢀⣠⠀⠀⠀⠰⡷⡄⠀⡀⢦⡀⠆⠠⠆⢈⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⡄⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠘⠃⢤⠍⢧⣿⣧⠉⢻⡄⠀⠶⣿⡿⠈⢣⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠒⠲⢛⡃⠒⠠⣄⠀⣺⡿⠂⠘⢧⣼⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠘⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣳⣄⠈⠙⣿⣧⠱⣄⠈⣿⣀⠀⢠
⠀⠀⠀⠀⢀⣤⣾⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⢈⠁⠀⣀⡀⠈⠂⠂⠖⠈⠉⠑⢻⣿⣄⣿⡀⢹⡶⢠⡯
⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣌⣑⣈⣃⡀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡙⢷⣈⣿⣼⣧⠖
⠀⠀⠀⢹⣿⡿⠟⠁⠐⠿⢷⣮⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⢀⡽⠛⣶⡶⠾⣿⣿⣄⣿⣿⠁⢀⣿⣿⣿⠗⠂
⠀⠀⠀⢸⡟⠀⢀⠀⠀⠀⢠⣿⣷⡀⢸⣽⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⡄⡩⠴⡞⠋⡀⠀⡀⠀⠈⢹⣿⣧⠈⣿⣿⡟
⠀⠀⠀⠿⠶⠒⣿⣧⣾⣿⣿⣿⠿⠇⠜⠻⡄⠀⠿⣿⠟⢿⡿⠿⣿⠿⢛⠛⠻⠋⠊⠟⠀⠂⠒⢿⡐⠛⣺⡟⢿⢀⡏⠑
⠀⠀⠀⠀⠀⠀⢀⣿⣶⣦⣬⢀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠛⠚⠛⠛⠛⠉⠋⠉⠁⠀⠀⠀⢀⣸⣿⣿⣿⡧⠀⢻⠶
⠀⠀⠀⠀⠀⣀⣄⣤⠛⢉⣈⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣠⣄⣀⣶⣿⣿⣿⠿⠟⣿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠉⣉⢉⢛⠛⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡗⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠠⠲⣤⣤⣀⢀⠀⠀⠀⣀⣠⣦⢠⣶⣀⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡗⡏⣯⣼⡆⢿⣿⡼⣿⣿⣿⠃⠀⠄
⠀⠀⠀⠠⠀⢸⠆⠀⠀⠀⠀⠀⣠⢔⡤⣶⠀⠀⠀⠠⠚⢻⡟⢹⠏⢿⠅⡇⠏⢸⡇⠘⣿⣿⢟⠙⣻⣇
⠀⠀⠀⠈⠀⠀⠀⠀⣀⠠⠄⠀⢸⢠⢈⢁⠀⠀⠁⠀⠀⠉⠁⢨⣶⡿⠀⠆⣧⣾⢣⣆⠹⣧⣯⠔⣹⡇⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢼⠀⠀⠀⠀⠀⠀⠈⠸⡇⠀⡀⡆⣵⡇⣾⣿⠀⣿⡿⠃⣼⡅⡤⡀⢙⠉⢀⠠⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠁⠂⢄⠀⠀⠃⠀⠀⠇⣋⠆⣿⣿⠂⢉⡙⠒⠿⠿⢥⡆⠸⢺⢼⠀⠋⣿⢿⣶
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠐⣰⣿⣽⠀⣸⣯⣟⢰⣶⡦⠈⣶⡃⠠⢀⢀⢨⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⣴⣯⡿⢹⠃⣹⡿⣷⣿⣿⣇⡸⠯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠸⣿⢿⡟⢨⠁⠋⣰⠿⠃⣿⡇⠈⠃⢸⣆⡤
⠀⠈⢦⣀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡻⢋⡟⠈⠀⣀⠥⠀⠠⢙⠄⠀⠀⠸⠋
⠀⠀⠘⢸⡹⠁⠈⢀⢰⣤⣀⡀⣀⣀⣄⡀⠀⠀⠀⠀⠀⢀⠀⠄⣀⠤⢀⡴⢹⡉⠂⠀⠀⠏⠀⠀⠀⠈
⠀⠀⠀⢸⡇⠀⠀⠁⠈⣿⣿⣿⣿⡾⣿⣿⠟⡂⢶⡶⠂⠀⠀⣨⠈⡤⠋⠀⠈⠀⢀⡖⠠⣆⠁⡀⣔⠀⠐
⠀⠀⠀⢨⡀⠀⠀⠂⠀⣿⣿⣻⡩⢺⣿⡏⡆⠑⣈⡄⢀⠰⠊⠠⠊⠀⠀⠀⠈⠂⠍⣠⣦⡉⠻⣧⣸⡤⣶⠇⠠⠊
⠀⠀⠀⠘⡇⠀⠀⠀⠈⠰⠻⠟⣥⢸⡿⣧⠰⠚⡅⡏⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣧⣿⣷⡈⢯⣇⣽⡿⠇
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠊⡿⡚⠁⢉⠀⠀⠄⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⢟⡇⠻⠉⣷⡄⢽⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⣰⠀⠀⠃⠀⠀⣀⠈⡄⠀⠀⠀⠀⠀⠁⠀⠁⠃⢀⠀⡝⣿⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡊⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠅⠘⡇⠸⠃⠁⠁⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡂⢸⠐⠂⠀⠀⠀⣠⠀⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠰⣊⡠⠬⠓⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⡤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⢻⣇⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠺⣿⡁⢰⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⢀⣤⠼⠟⢐⣿⠁⢳⣄⠀⠀⠀⢀⠀⠘⣿⡅⠀⠀⢀⣾⣿⠇⢨⣿⡓⠳⢄⣀
⠀⠀⠀⠀⠀⡠⢀⡼⠁⠘⠉⠀⠀⢀⣽⠏⠀⢸⠟⠛⠦⠂⠀⠀⠴⠛⠁⠐⠈⠉⡠⢖⡚⠛⠛⠁⠀⠀⣹⣦⡀
⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⡀⠀⣤⠈⠀⠀⠠⠕⡋⡀⢰⢠⡄⢀⠀⠀⠀⠀⠀⠨⠒⠈⢻⣶⣤⣄⡀⠈⠉⠈⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⣇⢰⣿⠆⢰⠀⠀⠘⠓⠛⠟⠿⠷⠾⠄⣴⡀⣄⢀⠀⠀⠀⠀⠈⠁⠉⠉⠓
⠀⠀⠀⠀⠀⢠⡇⢰⣿⣾⣿⣿⣿⣧⣿⡆⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠃⠂⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠚⠛⠚⠛⠛⠛⠛⠛⠛⠛⠓⠚⠳⠤⠄⠀⠤⠆⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⣺⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⣀⡀⠀⢀⠀⠈⠊⠀⠀⠀⠀⢀⣀⣇⠀⢠⣿⣿⢀⣿⡄⢸⡄
⠀⠀⠀⠀⠀⠀⠠⠠⠄⠤⠀⠀⠀⠀⠀⠀⢴⡏⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠚⠻⠷⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡷⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⢀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢄⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠈⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⡀⠀⢁⠆⠀⠀⠁⠆⠀⠀⠀⠁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⢑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠑⡠
⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⠀⠀⠀⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠌⠢⡀⠀⠈⠃⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠇⡏⠀⠀⡠⠂⠀⠀⠀⠈⢆⠀⢀⡀⡨⠓⠀⠀⢀⣀⠬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡆⠀⡀⠀⠀⢠⣮⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣰⠀⠀⠀⠀⠈⠸⡁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠈⠉⠀⠸⠀⠠⠀⠀⡀⠀⠀⢀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠀⠀⠠⠀⣀⠀⠀⠰⠀⡠⠀⣀⡠⠜⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠑⢄⠀⢱⡁⠉⠀⢀⣀⡀⠄⠁⠀⣠⠂⠀⠀⡀⢠⠀⠀⡈⢁⡀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠠⠆⠀⠀⠀⡀⠀⢀⠀⢅⠊⠓⠤⣄⣀⣀⡠⠤⢚⠀⠠⠒⠉⠁⣈⢀⠀⠘⢇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠁⠈⠐⠐⠀⠉⢄⡰⠁⠀⠀⠑⠂⠤⠀⠤⠤⠵⠒⣉⠒⠤⠤⠤⠚⢉⠀⠄⠀⠀⠉⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢁⠠⠄⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡣⣀⠐⠁⠎⠐⢀⠂⠈⠀⠀⢠⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠊⡑⠒⠒⠒⠚⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠎⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⠧⢄⡠⠤⠤⢀⣰⡦⢄⣰⡖⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠔⠁⠀⠀⠠⠤⠤⠀⠢⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠐⠂⠙⠂
⠀⠀⠀⠀⠀⠀⠒⠒⠻⠼⡁
⠀⠀⠀⠀⠀⠘⡂⢀⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠻⠤⠄⢶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡨⠆
⠀⠀⠀⡀⠀⣠⠂⠀⠶⢷⡝⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢀⣀⠴⠶⢤
⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣄⣤⣶
⠀⠀⠀⠶⠠⣰⠆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡁⠀⢄
⠀⠀⠀⠀⠔⠁⠀⠒⣀⠀⠶⣀⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠁⢀
⠀⠐⠧⠄⡤⠀⠀⢀⠙⣀⡀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⢀⠤⠚⠐⠾
⠀⠀⠀⠀⠸⠇⠂⠉⡀⢀⡉⠹⠄⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠪⣭⣋⠠⣤⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣤⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣶⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⡤⠶⠒⠚⠛⠛⠒⠒⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠀⠀⠀⠈⢉⣀⡤⠤⠴⠤⣤⣄⡀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡾⠉⠀⣀⡤⠤⠤⢄⡠⠞⠉⠀⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⠈⠉⠉⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠉⠉⢠⠔⠋⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣄⣤⣄⣀⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⣀⡤⠖⠛⠋⠛⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠈⠉⠳⢦⡀⠀⢹⡄
⠀⠀⠀⠀⠀⢀⠇⠀⡠⠊⠁⠀⠀⠀⠀⠀⠢⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡈⠉⠛⢦⡄
⠀⠀⠀⣠⠖⠋⢀⣼⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠈⠉⠳⣄⠀⠹⣆
⠀⢀⡞⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⢰⡄⠀⠀⠀⠀⠈⣧⠀⢹⡄
⠀⡾⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢸⡆⠘⡇
⠰⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠲⠾⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢰⡇
⠀⠻⣄⠀⠳⣄⡀⠀⠀⣀⡴⠞⠉⣭⠗⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡞
⠀⠀⠈⠻⠦⣬⠉⠉⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠛⠉⣹⠶⠤⠤⠴⠚⠉⣠⠟
⠀⠀⠀⠀⠀⣿⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠖⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡋⠀⠀⣀⣠⠴⠋⠀⠀⠐⣶⠶⠛⠁
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠈⠛⠓⠶⠶⠤⣤⣤⠤⠶⠞⠛⠦⣤⣀⣀⣀⣀⣤⣴⠖⠋⠁⢀⡬⣭⣭⣅⣤⣤⣤⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢤⣀⡀⢀⡟⠀⠀⠀⠀⡾⠒⣒⣚⣭⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠶⠚⠋⠁⠀⠀⠈⠉⡿⠁⠀⠀⠀⠘⠛⠋⠉⠁⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣤⠴⠖⠛⠋⡇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠻⠛⢛⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣬⣉⠙⢀⡄⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡧⠥⡬⠀⠥⠬⠼⢿⣄⡀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⠊⠀⠰⠀⠀⠀⠈⠀⠀⠀⠙⢷⣄
⠀⠀⠀⢰⠞⠉⠉⠉⢳⡀⠀⠀⢀⡞⣁⣀⣀⡠⠤⠤⠖⠒⠀⠒⠢⠐⠄⠳⢤⣙⣧
⠀⡴⠖⠛⠂⠀⠀⠀⣸⡃⠀⣴⠛⠏⠠⠀⠀⡆⠀⠈⠀⠀⢘⠀⢰⠀⢠⠀⠘⡀⠉⣧
⢸⡇⠀⠀⠀⠈⢢⠀⠈⢿⡀⡏⢠⠀⢈⠀⠀⠁⠀⠀⠂⠀⠈⠀⠀⡄⠀⠀⠀⡇⠘⣸
⠀⣿⠂⠀⠀⡀⠈⠀⠀⣸⡿⠛⠀⢤⣚⣩⣭⣩⣒⡉⠉⠀⠴⠖⠒⢆⣀⡐⣖⣳⠂⠉⢳⡄
⢀⣸⡇⠀⠀⠁⠀⣤⠞⢹⠃⠀⠀⢰⠀⢀⠊⣴⡿⢷⠀⠀⠀⡴⢷⣦⠑⡄⠈⡇⠀⠀⠈⣷
⡟⠀⠀⠀⣆⠀⠀⡹⠶⠛⠠⡀⢀⡸⢠⣬⣄⣛⣿⠞⣠⣤⣄⢻⣿⠟⡠⣁⢀⡃⠀⠀⠀⣿
⠻⢤⣠⣤⠁⣀⢀⣠⡶⠓⠲⣦⣠⣾⣻⠟⠟⠩⢋⠕⠛⣏⠙⢌⠫⠑⠟⢿⢙⣷⣤⡤⠞⠁
⠀⠀⠀⠈⠉⠉⠉⠁⢀⣴⠞⠋⠉⠙⡇⠀⠀⠀⠀⠀⠚⡍⠂⠀⠀⠀⠀⠀⡋⠉⠉⠙⠦⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠤⠔⠊⠘⠀⠀⠀⠀⠀⠀⠜⠙⢆⠀⠀⠀⠀⠀⡈⠉⠑⠤⢤⡙⣆
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⣀⣀⡀⢳⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⠀⠀⠀⠀⣈⣢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡸⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣦⠄⠊⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢸⠒⠂⢲⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠤⢽⡇⠀⠐⠒⠀⠤⢼⠀⠀⠀⠀⠀⠀⡸⠄⠒⠊⣿⣤⡴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠁⠀⠐⠒⠂⢎⣰⣣⣆⣴⣰⣠⠗⠒⠈⠉⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⡽⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⣛⣦⣤⣀⣀⣀⣤⣐⣿⣾⣓⣠⣄⣀⣀⣠⣴⣞⣯⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠉⠉⠀⠀⠀⠈⠀⣼⣿⡀⠈⠀⠀⠀⠈⠉⠁⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⣀⠴⣿⢷⡳⢄⡀⠀⠀⠀⠀⠀⠀⢀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠤⠒⠶⢤⣀⣀⣀⠀⠀⢀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⢸⠁⠀⢀⡴⠋⠉⠀⠉⠙⢾⡁⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢇⣀⠤⠐⡲⠊⠁⠀⢠⠖⠛⠛⠒⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣸⠁⠀⢠⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡄
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢇⠀⠀⠀⠀⡠⠤⡀⠀⠀⢀⠀⠈⢢⢀⠖⠀⠀⠀⠀⠀⡝
⠀⠀⠀⠀⠀⠀⠘⢦⣀⡔⠁⠀⠀⠀⢸⠁⢄⠀⠀⠀⠀⠹⣄⠀⠀⠀⣴⠁⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠂⡐⠀⠀⠀⣐⠠⣉⡇⢠⢋⡁⠀⠀⠈⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠳⢤⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⢹⡍⠁⠀⠫⡈⠀⠐⢤⠜⠁
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠘⣆⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⡏⠑⠒⠚⠁⠀⠀⠀⡄
⠀⠀⠀⠀⢀⣀⠇⠀⠀⠀⡀⠈⠓⢧⡀⠀⠀⠀⠀⠀⣠⠞⠀⡴⣻⢟⡳⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠓⢤⣀⠈⠑⡏⠁⠀⠀⢇⠉⠆⠙⠲⣉
⠀⠀⠀⠀⠀⢀⢆⠀⢀⣠⠇⠀⠀⠀⠀⠀⠈⢉⠉⠙⢦⡀⠀⠀⢹⠈⡀⠀⠠⡉⠢⢄⡀⠀⠀⣀⠤⣄⡀
⠀⠀⠀⠀⠀⠁⣿⠀⠀⠁⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠁⡇⠠⠀⠀⠈⠲⣄⢈⣑⠊⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢄⣀⠇⠀⠀⠀⠀⠀⠀⡰⠀⠀⠐⠚⠀⠀⡀⠀⠀⢈⠀⢳⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠒⠃⠀⠀⢀⠀⠀⠀⠀⠀⠠⠜⢀⡼⠆⠀⣀⡤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠈⢆
⠀⠚⠁⠀⠘⠀⠀⠠⠁⡸⠀⠀⠀⠀⠀⢠⢪⠀⠀⠤⠆⠀⠀⢀⡏⠀⠀⠀⠁⠀⠀⠀⠀⠈⠳⠀⠀⠒⢄⠀⡜
⠀⠀⠀⠈⢠⠂⠀⢤⣠⠇⠀⠀⠀⠀⢀⠁⢸⠀⠀⠀⠀⠜⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁
⠀⠀⠀⠢⠞⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠲⠊⠀⠀⠀⠀⢸⠀⠀⠻⢦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠲⠊⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⢀⡴⠓⠒⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣒⣛⣉⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡎⢇⠀⠀⢒⠄
⠀⠀⠀⡠⠔⠒⠒⢢⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⡀⠀⠀⢀⠜⠀⠈⢆⠀⠀⠀⣀⠤⣀
⠀⠀⠀⡱⠀⠀⠀⠘⢲⠶⡏⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⢊⠀⠐⢳⠂⠁⠐⠲⡛⠀⠰⠁⠀⠈
⠀⠀⠈⢳⠀⠀⠀⠀⠀⡆⢣⣴⠃⠀⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠀⠀⠐⣷⣖⡁⠀⠀⠀⠀⣑⣤⠀⠁⠒⠈
⠀⢠⠤⠶⠀⠈⠁⠈⠄⠉⠁⠈⡆⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⡡⠤⠀⠄⣀⣀⡤⠋⠀⠀⠀⠀⠀⠈⠢⢄⡀
⠀⢇⠀⢀⡁⠀⠀⠀⠐⠀⠀⢐⡍⡂⠀⠐⠀⣊⠀⠀⠀⠀⠀⢊⠤⠀⠀⠀⠀⢈⠽⠋⠙⠀⠂⠠⠐⠀⠛⢍
⠀⢰⠁⠀⠀⠐⠀⠁⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠒⠀⠀⠀⠒⠁⠀⠀⠠⠀⢌⢑⡶⠀⠀⠀⠀⠀⠀⠀⠴⣖⠉
⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠄⠀⠠⠤⠤⢤⠤⠀⠀⠤⠵⠂
⢹⠀⠀⠒⠒⠒⠁⠀⠈⠉⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠤⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠚⠀⠀⠀⡇⠀⡀⢀
⠀⠀⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⣀⣀⠤⠀⢀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠁
⠀⢧⣀⠄⠀⠀⢣⣀⠄⠀⠀⠀⠳⠤⠂⠘⠦⠄⠀⠘⠦⠔⠀⠈⠳⠤⠤⠂⠈⠳⠤⠤⠔⠊⠀⠳⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠙⠶⢶⣄⣀⠀⠀⠀⠀⣀⡶⠛⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠀⠀⠀⠀⠀⠉⠙⠷⠲⢦⡼⢧⡀⠦⢄⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣧⡀⠀⠀⠀⠔⠲⡤⢄⢀⠀⠀⢀⣈⢥⠀⢈⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠁⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠈⠀⠀⢀⠉⠈⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢠⠒⠃⠀⠀⢠⠀⠀⠀⠀⢀⣄⣼⠃⠰⠚⠁⠁⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⣀⡴⢿⣰⠀⢀⣘⣿⣄⣠⣄⠀⣀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣴⠗⠚⡅⠐⠂⢹⡆⣸⠋⠁⠀⠀⣬⡟⠉⣟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠀⠀⠀⠓⠋⠀⠀⢠⠄⠀⠀⠀⢻⣧⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⠀⠀⠀⠀⠀⠫⠇⠀⠀⠀⠀⠀⠀⡀⢺⡧⠤⢤⡈⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣸⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⡆⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⣿⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠄⣿⡗⠒⠚⢁⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⠒⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡦⣿⡏⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣑⣑⣚⣘⣃⣄⣤⣤⣤⠤⠤⠬⠶⠮⢕⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⣿⣿⣿⠆⠀⢂⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣼⣿⡇⢿⣿⠆⠀⠀⠀⠢⠀⣴⣿⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⢡⣼⣿⠋⢠⣼⣿⣧⡀⠀⠀⠀⢸⣧⣇⡀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣿⣿⠀⠈⠛⣿⣷⡈⣿⢿⣿⣏⠀⠀⠀⠀⢦⣻⡇⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⣙⣿⣄⠀⠀⠸⣿⡁⣿⣧⣿⠛⠁⠀⠀⠀⠈⠻⣿⣄⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⣾⡋⣿⣿⠷⠀⠀⠹⣷⣿⢹⣿⣆⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠻⣿⣷⣿⣧⡀⠀⠀⠀⠈⠻⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁⠀⠀⠀⠈⠉⠁⠙⠿⣷⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦⣤⣦⣄⣴⣀⣀⣴⣀⡀⠈⠓⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠻⠷⠷⠶⠤⠀⢀⣀⣀⣀⡀⠀⢠⡴⠶⠾⠿⠾⠿⠿⠿⠿⠷⠿⠷⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡶⠶⠶⠶⠶⠒⠈
⠀⠀⠀⠀⠐⠒⠉⠉⠉⠉⠛⠛⠛⠿⠿⢿⠶⠶⠶⠖⠂⠀⢉⣙⣻⣿⣿⣿⠶⠄⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣟⣉⣉⡁⠀⠀⠀⠀⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⣈⣉⠛⠛⠻⢿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠃⢀⣠⣤⣤⣶⣶⣶⣶⣶⣶⡶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠋⠉⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉⠉⠉⠉⠉⠉⠉

⠀⠀⣸
⡇⣠⠿⠀⡀⣤⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢹⣿⡉⠀⠺⣳⠀⢸⡟⠀⡄⣸⠀⠀⠀⢸⡄⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⣾⣥⣌⠉⣠⡼⠂⠸⢁⣘⢻⣯⢀⣼⣴⡯⠤⣾⣠⠀⠀⡀⠁⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡿⢿⡶⠂⠠⠤⠀⢀⣬⡍⠼⣥⠀⣿⣿⠛⠂⢹⣿⣄⣼⢁⡀⢀⠁⡀⠀⣰⠀⡀⠀⢠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢀⡀⣀⠀⢠
⡷⠨⣙⣟⡳⠒⠀⢸⡟⣀⣘⠟⡯⣿⠛⡘⣋⡀⣽⣿⠟⣛⣦⣿⣼⡇⢰⡿⢻⣧⣶⡾⠇⣴⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣠⣶⣿⣡⡏⣾⣿⣵
⠀⠀⠀⠀⠈⠈⠀⠘⠛⣷⠍⠂⣼⡻⠂⠠⠤⠀⢐⣿⣧⠆⠰⣿⡗⠭⢿⡥⠄⢿⣿⡷⠼⣿⡿⢲⣾⣆⡀⢀⣄⣤⣿⣿⣿⣿⣿⣿⡿⠥⠽⠿⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⢯⡃⢦⣤⠄⠀⠉⢻⣇⠐⠈⢻⡿⢠⢽⣏⣀⣋⣿⡥⠀⢹⣇⣈⣿⡿⣿⣿⠿⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠶⠾⠿⣯⣘⡛⣷⣀⠊⢿⡧⢴⢺⣄⣐⠈⣷⡆⢸⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠚⠛⠶⠿⠿⠿⠒⠛⠉⠉⠁





⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣿⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠙⡆⣴⠟⣁⣀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣤⡄⠀⠀⠈⢧⡈⠛⠷⠸⠟⢉⡿⠀⠀⠀⢀⡞⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠹⡄⠀⠀⠀⠉⢳⡄⣠⠞⠉⠀⠀⠀⢠⡞⢠⡞⠁
⢀⣠⣄⠀⠀⠀⢀⠀⠀⠀⠀⠘⢧⠀⠹⣄⠀⣾⠳⢼⡇⣾⡴⠒⣦⠀⢠⡟⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣤
⣿⠉⠉⠛⣶⠀⣿⠳⣄⠀⠀⠀⠈⢧⠀⠙⣆⠙⠳⣄⠀⠉⣠⠴⠃⢠⠏⢠⠏⠀⠀⠀⢠⡾⢧⡀⣴⠋⠁⢈⣿
⠈⠳⣤⣤⣬⣛⠻⠀⢷⠀⣶⠓⢤⠈⢧⠀⠘⣆⠀⠈⡇⢸⠁⠀⢠⡏⣠⠏⢰⠞⢳⡄⢸⠀⠸⠟⣩⠴⠶⠛⠁
⠀⠀⠀⣴⠚⠋⢁⣠⣘⡳⠾⠀⢸⡄⠈⠳⢤⣷⡀⠀⣷⢸⠀⢀⣼⡴⠋⠀⣾⠀⢼⠶⣋⣤⣀⠛⠳⣦
⠀⠀⠀⠉⠑⠚⠉⢁⡬⠿⠂⠀⣀⠳⣤⡀⠀⢳⡳⡄⣿⢸⢀⣞⡽⠁⣀⡴⠏⠀⠀⠾⢭⡄⠈⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠿⢤⡴⠖⠛⠉⠙⠶⣍⡳⢦⣷⡹⣿⢸⣾⣿⠴⣛⡥⠖⠋⠙⠓⠲⠤⠗
⠀⣴⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⢤⣤⣤⣭⡷⠬⠙⠋⠈⠉⠴⣾⣥⣴⣶⣶⠖⠒⠚⠒⠛⠛⠛⠛⠛⠛⠛⣳
⠀⠈⠛⠒⠒⠒⠒⠒⠚⠓⠒⠒⠛⠉⠉⠉⣉⡽⣛⣥⠀⢀⣀⡛⢯⣍⡉⠉⠉⠙⢛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣟⠛⠳⢦⣀⣀⣤⢶⣫⠵⠊⢡⢫⣿⢸⣞⣏⠓⢮⣝⠓⠶⠖⠋⠁⣀⣿⠀⢀⡀
⠀⠀⠀⢸⡛⠳⢦⣌⣙⣦⠀⠉⣩⠖⠋⠀⠀⣰⣳⠋⣿⢸⠘⣎⢧⠀⠈⢳⡀⢀⣲⣯⣥⡴⠞⠋⢉⡿
⠀⠀⠀⠀⠉⣳⡄⠈⢩⡴⣶⠀⡟⠀⠀⢀⡖⢳⠃⠀⣿⢸⠀⠘⣮⢧⡄⠈⣇⠘⡏⢻⡄⢀⣰⣾⣋⣀
⢀⡶⠛⠛⢋⡥⣦⠀⣿⠀⠻⣄⡿⠀⢠⡞⢀⡞⢀⣠⠟⠸⣄⠀⠻⡄⠹⡄⠻⣄⡵⠀⣧⠈⣿⠻⣯⠉⠙⢶⡄
⣼⣇⣀⣠⡿⠀⢿⣀⡿⠀⠀⠈⠀⢠⠏⢠⢏⡴⠋⢁⡀⢀⡈⠓⢦⡹⣄⠹⣆⠈⠀⠀⠹⢤⡟⠀⠈⠳⢦⣴⠿
⠀⠈⠉⠁⠀⠀⠀⠙⠁⠀⠀⠀⣠⠏⣠⠏⠾⣤⡴⢋⡿⢸⡙⢦⣬⣧⠙⣆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣰⠏⠀⠀⣀⡴⠋⠀⠀⠙⢦⡀⠀⠀⠘⣆⢘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣸⣇⣀⡴⣧⢻⠳⣄⣙⣧⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢸⠋⠘⣦⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⣿
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢷⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣟⣘⡾⠾⣼⣼⣰⢢⢄⠀⠀⠀⠀⠀⠈⡈⠁⠀⠄⠀⠠⠀⠁⠀⠐⢀
⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⢀⠈⠻⡇⢠⣴⠀⠈⠉⠛⠺⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠷⠶⢤⣄⣑⡆⠙⠂⠕⠚⣣⡰⠟⣠⠋⠀⠀⠀⠀⠰⠁⠀⠄⠀⠀⡀⡐⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠉⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠐⢠⡄⠀⠀⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⢸⠃⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠜⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠘⠆
⠀⠀⠀⠀⠀⢈⠀⠀⠀⡄⠓⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡈
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⡐⠒⠅⠀⠀⡒⠲⡁⠈⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠴⠦⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠒⠶⠶⠶⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⠩⠤⠰⢒⣲⣲⣟⣉⣡⣆⣖⣶⡶⡤⢄⣉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠐⣿⡷⠴⠛⠻⠿⠿⢿⢟⢻⢛⡛⠛⠃⢠⣤⣾⠃⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠃⠂⠈⠑⢾⣿⢿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣶⡤⠊⠀⡠⣿⡟⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠁⠕⠶⣤⣀⡀⠙⠻⣿⣿⣿⣹⣿⣿⣿⣿⠿⠋⠀⣀⣬⣤⢟⢛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⡿⣿⣶⣤⣀⡉⠛⢷⣆⡈⠛⢿⣿⣽⡿⠛⢡⠴⠶⠛⢉⣩⣴⠞⠋⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⣴⣬⡿⠀⠀⠉⠛⠛⠿⢷⣬⣥⡶⢤⣽⢫⣴⢶⣀⣤⡴⠶⠛⠉⠀⠀⠈⠁⠈⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⢀⣞⣱⠅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⣻⡷⠊⠋⠉⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠠⠟⠻⢏⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⢎⢽⡄
⠀⠀⠀⠀⠀⠀⣗⠰⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠻⡀
⠀⠀⠀⠀⠀⢸⣶⠁⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡰⠀⠀⠈⠥⠀⣧
⠀⠀⠀⠀⠀⣿⠘⠄⠄⠈⠳⢘⠲⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⠋⢻⡤⠂⠐⠠⢰⣽
⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠐⢮⢀⣦⢠⡀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠀⣀⢰⣿⣿⠞⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⡿⠃⠁⠀⠀⠀⠀⣴⣆⣿⡜⠇⢠⡐⡠⣠⠀⠘⢁⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢻⣾⡿⠄⡖⡶⠆⠀⠀⠐⣿
⠀⠀⠀⠀⠀⣯⡆⠀⠀⠀⠀⠚⠟⢻⡿⣟⣿⣒⣛⣛⣈⣀⢀⠏⢐⢄⡟⠁⡽⠋⠉⠱⣖⠶⠺⡗⡻⢿⡇⡇⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⢇⡗⠀⠐⠠⠶⢻⣿⡝⠫⠍⠀⢹⠟⠛⠇⡮⠀⠴⠮⠒⠀⠀⠀⠀⠈⠁⠀⠀⠫⠞⢹⡗⠦⠄⠀⠀⠀⠀⢰⡾
⠀⠀⠀⠀⠀⢸⠜⠉⠀⠀⠀⠀⠸⠋⠙⠀⠁⠀⠀⠀⠀⠀⢳⣦⣾⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠐⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⣥⣽⢿⣦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢺
⠀⠀⠀⠀⠀⠀⢻⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡑⢀⡻⣿⠛⣛⠩⣶⢤⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠆
⠀⠀⠀⠀⠀⠀⠀⠣⣄⣠⡄⡀⠀⠀⡀⠄⠀⢨⡴⣟⣫⣻⡿⡖⠱⠘⠈⠁⠹⠃⢽⡠⣢⣠⣔⠀⢀⡀⠀⠀⠀⠀⣧⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣀⡲⡶⣿⡳⠛⠟⡿⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢧⡙⣲⠤⢆⣠⣤⣶⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢩⠏⠁⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠉⠉⢡⢁⣞⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠋⠄⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⠀⠀⠈⣹⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠈⠀⠚⠛⠛⠒⠒⠒⠠⠒⠚⠟⠉⠉⠛⠊⠉⠁⠀⠀⠀⠀⢾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠾⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠶⠄⠄⠖⢦⠐⢶⡶⠶⣶⣠⢶⣶⣶⡶⠲⠹⠟⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠀⣈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⠀⠋⠀⠀⢹⡗⠂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡿⠃⣽⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠛⡘⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⣉⢰⣾⢰⣸⣿⣟⣤⡀⠀⣄⠀⠀⠃⡀⠀⠀⢳⣾⣘⣧⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠘⠓⣪⡇⢸⣿⡿⣷⣿⣿⠸⠇⠀⠈⠀⠐⠌⠛⠖⢄⢼⠻⠳⠁⠈⢳⠄
⠀⠀⠀⠀⠀⠀⣼⡷⢶⡾⠛⠀⠀⢯⣟⢻⣿⣻⡷⠂⠀⠀⢢⠀⣆⢠⠐⠀⣽⡶⣶⣶⣶⡇⠂⢠⠀⠚⣆⡀
⠀⣠⡆⠀⢠⣼⠟⠃⢸⣧⡎⢀⣠⣼⡿⣯⣄⠀⡀⠀⠀⠀⠄⢷⡌⢸⡍⢀⠁⠸⡷⣿⣿⣏⠂⠋⠀⠀⠀⠛⠦
⠰⢾⣇⠀⠀⠀⠀⠀⣠⠉⢀⣨⣧⣿⣾⣿⣿⣇⠐⠲⠄⣠⡌⢆⠀⣯⣧⠀⣤⢀⣼⣿⣿⣿⣷⡄⢦
⠀⠛⣿⡄⠀⢀⣴⣾⠃⠀⠠⢙⠛⠉⠙⠻⢿⣏⣄⠀⠳⠇⠑⢿⡇⠀⠹⠖⢋⣼⡿⣻⣿⣾⣥⡏⢐⡀⠵⢀⡀
⠀⠀⠘⢿⠶⣿⣿⣿⡀⠠⠀⢌⠳⡀⠀⠀⠈⠛⠿⠰⡀⢤⠂⠀⠉⠀⠀⠀⠘⢁⣾⡿⠟⣹⡿⠓⠀⠁⠀⠀⠃
⠀⣀⣴⣿⣏⣴⣷⣿⡟⠀⠀⠀⢁⠐⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⣴⠇⠀⠂
⠘⠿⠋⠋⠿⣿⢒⡼⠋⠈⠁⠐⠈⠛⣄⡀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠲⢹⣟⣷⡇⡀
⠀⠀⠀⠀⠀⠻⠾⠿⠶⠤⢀⡀⠀⠀⠈⠻⠦⠀⠒⠤⠉⠢⠀⠀⢄⡈⠙⠛⠀⠂⠲⠄⠋⠹⠁⠈⠂⠂⠐⠄

⠀⠄⠀⣄⡀⢀⡁⢸⡇⠀⠀⠂⠔⠉⠀⠐⠒⠒⠢⠠⢤⣀⠀⠀⠀⠀⠚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠠
⢡⢊⣹⣿⡛⠄⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⠀⠀⠀⠀⠀⣠⡴⠊
⣩⠘⣛⢟⣛⡳⠦⣦⠔⠀⢀⡀⠀⠀⠀⠀⠀⣀⣦⡭⠴⢒⡠⠂⠀⠀⠀⠈⠀⠩⠄⠀⡠⢄⠋⠉⠀⠀⠀⠀⠐
⠀⠐⢫⣿⣿⣿⠋⡱⠆⠴⠂⠀⠀⠀⣀⠤⢈⡥⣇⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈
⠴⡞⢻⢾⣿⣖⡹⢤⡀⠀⠀⠀⡀⠁⠀⠀⠈⠀⠉⣰⡶⠂⠀⣀⣐⣂⠀⠀⠀⠀⠀⠀⠀⠙⣟⢻⡶⠲⠒⠀⠣
⢬⣭⣟⠛⠋⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠡⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢴⡛⢶⡶⣀⠀⠰⢆
⢰⡿⠛⠋⠀⠀⠀⠀⠀⠐⠲⠖⠀⠀⠁⠀⠘⠁⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢩⣣⢸⣙⣒⡂⠈⠓⠂⠀⢈⠥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⡞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠀⢠⡄⠀⠀⠀⠀⠀⠉⠄⠍⠩⡼⢷⣄⠀⢈⣁⣠⡤⠲
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠠⢤⣤⡾⠀⡀⠀⠀⠈⠑⡀⠀⢐⢄⠉⠀⠀⠀⠀⠀⠠⡖⣆⠀⠐⠺⢒⡠⡙⠊⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡏⣸⠆⠁⠀⠀⠀⣾⠀⠀⠹⠀⡒⠀⠀⠀⠀⠀⣰⠂⣿⡑⠔⠀⠈⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⣌⠀⠙⡶⣂⣀⡀⠀⢀⡿⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣠⡾⢋⡿⡴⠃⡀⠀⠀⠀⠀⠀⠀⠠⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⠵⠎⢰⡿⢡⠅⣀⢀⠠⠔⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣐⣚⠃⡞⣠⣿⠇⣠⡖⠀⠀⠀⡠⢆⡐⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠛⠒⠀⠀⠐⣠⣺⠏⠰⢼⠿⣅⠀⠀⢀⠉⠛⠀⠋⠀⠀⠰
⠀⠀⠀⠀⠀⠀⣤⠤⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠗⢰⣷⡻⠉⡁⠁⠀⠓⠀⠀⠒⢀⡃⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠁⢀⣜⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠏⣰⣻⠤⠤⠂⠀⠀⠀⠀⠀⠕⡂⠠⡰⡀⠠
⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠼⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢘⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠲⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⠛⠀⢀⠰
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⢀⡟⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀⠀⠀⠀⠺⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠆⠀⣴⣶⠋⠁⠀⠀⠉⠀⠀⠐⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡐⠃⠤⡀⠀⠀⠀⠀⣤⣤⡀⢀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡤⢀⠴⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⡾⠛⠉⠠⠤⠤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠳⣤⣤⣤⡤⠴⠚⢁
⠀⠀⠀⢠⠁⠀⠈⠁⠀⠀⢀⣀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠟⠛⠀⠑⠒⠒⠒⠛⠋⠉⡠⣄
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠠⠴⠶⠶⠒⠚⠉⠁⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡤⠶⠶⠖⠒⠒⠒⠒⠶⠤⢬⣽⠓⠦⢤⣤⣀⣀⣀⣀⣀⣤⠴⠶⠛⡏
⠀⠀⠀⢰⠀⠀⠀⠀⠈⠁⠀⣤⠀⠹⠓⠒⠶⠦⠤⠤⠤⠤⠶⠒⠚⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⢠⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠶⠀⠀⠀⠀⠿⠀⠀⠀⠘⠃⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠀⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⠰⠆⠀⠠⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠛⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


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

⣰⣷⡟⠆⠀⡼⠛⣧⣠⣿⣿⠆⠀⠈⣸⢃⠛⡄⠛⠃⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡴⠋⠠⠆⠀⠀⠈⠀⠜⠋⠁⢀⣶⣀⣥⣤⡶⢿⣿
⠿⣿⠠⣀⠀⠏⠀⢹⣿⡿⠃⢀⠀⢀⣿⡿⠀⠀⠀⠀⡼⡋⠀⣠⠘⠘⠃⠀⠀⠀⠀⠄⠀⠠⢠⠮⠃⠈⠏⠇⠀⠀⠀⠀⠀⠘⡇⠀⠘⢿⠿⠿⣳⣶⠿
⠀⢿⣿⣿⢷⣦⣤⣾⡟⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⡸⠁⠉⠃⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠞⠁⠀⠀⠀⠈⠓⡀⠀⠀⠀⢁⣠⣤⡀⠀⢀⣾⣿⡦⢰
⣀⠈⢿⣿⣷⣤⣭⣿⡇⠀⠀⡀⢴⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠐⠀⠀⠀⠀⢀⡄⠘⠂⠀⠀⢀⠀⠀⠈⢠⣗⣄⣰⡴⢾⣿⣿⣧⠀⠘⠟⢿⣷⣿
⣿⣿⣥⣿⡿⡿⣿⣿⠧⣤⡾⡆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠈⠀⠤⠄⠀⠀⠠⣿⠿⠿⠿⠿⣿⣇⠀⠘⢦⡙⣝
⣯⣿⣿⣿⣿⣿⣾⣄⡀⠻⠳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣩⡀⣦⠀⠀⠀⠉⠀⠀⠀⠙⢮
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⠧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⢿⢿⣿⡀
⣿⡏⢻⣿⣿⣿⣿⣿⣿⣿⢏⣅⠀⠈⠻⢎⠉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠉⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠟⡉⡞⠹⣿⣯⡛⠛⣿⠃⠀⠀⠁⠀⣴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠐
⢈⠛⢀⣶⣬⣿⡟⢦⣍⠣⣔⠆⠀⠀⠾⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣼⠁⠀⠀⠀⠀⠀⠀⢠⡆
⢸⡟⣾⣿⣿⣿⣿⣾⣝⣆⠈⣓⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣴⡇⠀⠀⢀⡠⠋⠁⠀⠀⠙⠦
⣻⣸⣿⣿⣿⡿⠛⠛⠻⠿⢻⣿⡃⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⣄⠀⠀⠀⠀⠀⡀⢀⣄
⣿⣿⠛⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡦⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿
⣿⡟⠑⡷⣬⡀⣿⣿⣿⣿⢿⡈⢤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠛⢰⠀⠀⠀⣀⣬⡿⠀⠀⢀⣠⠐⢀⠀⡀⠈⠉
⢸⣤⣠⣻⣾⣿⣹⡿⢿⣛⠛⠉⣁⠾⠉⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⠀⢀⠆⡀⡉⠉⠻⣿⠃⠀⢀⡜⡧⢡⡈⢇⠀⣤⣄
⠹⣷⣿⣿⠻⣿⣟⠧⡄⠹⠷⣷⢿⣦⣤⡀⣀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡀⢀⣿⡯⠀⡘⢠⣸⣇⠀⠀⡟⠀⢀⣴⣿⡇⢻⣷⡈⢻⡄⣛
⡟⣿⣿⣿⢢⡄⢻⡄⣌⠐⠿⣿⣿⣭⣉⡉⣉⠀⠀⡀⠀⢦⡄⠁⠀⠀⠈⠁⠀⠙⡈⠀⠡⠃⠠⣦⣶⣿⠋⠈⠹⣿⣿⠁⢀⣰⡈⠛⢜⢨⣿⡇⣺⣿⠏
⣿⡀⠻⢿⣿⣿⡾⣧⣈⣵⡾⠿⣿⣿⣏⣯⡍⠙⠓⠀⠀⢨⠀⠀⠀⠀⠀⣠⠂⠁⠀⠀⠀⠀⢀⣹⣿⠏⢀⠀⠀⢹⣿⡠⢠⣎⢻⣿⣮⡉⢿⣿⠏⢘⡴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⡤⠀⣀⣀⠀⡀⣤⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢻⡀⣀⠄⢻⡟⡼⠀⠀⢠⢸⠁⠘⠁⢀⠀⠀⠐⠌⠀⣷⠀⡏⢆⠰⡅⣿⠘⠇⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢈⡎⣧⠇⠀⢸⣧⠀⡐⠋⠀⡘⠀⠀⢠⠎⠀⠀⠀⠘⣀⣷⡟⡁⠁⠀⢠⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⢹⠀⠀⢸⣿⠀⠁⠀⠀⣧⡤⠰⠋⠀⠀⠀⠀⠀⠀⣷⠰⠀⠀⠀⠀⢹⠆⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣆⠀⢸⣿⠠⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠘⣋⣠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢽⠀⠀⡀⠀⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⡷⣴⠒⠛⠁⠀⠀⠀⠀⢀⣠⣶⣶⣄⣸⣠⡾⣶⣦⡀⢰⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠇⠀⠀⠀⠀⢀⣠⡶⢿⣿⣿⣿⣿⣿⡛⣅⠉⠙⠃⢸⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡇⠀⠂⢀⣠⡶⠟⠉⠀⠀⠙⠻⣿⣿⣿⡇⢸⣿⣦⡀⠘⡇⢏⣀⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠉⠷⣿⣿⣇⣤⠞⠋⠅⠈⠀⢀⠀⠀⢠⠠⡄⡙⢿⡟⢸⣿⣿⣿⣷⣧⡇⠸⡿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⢀⣠⢼⣿⠛⡇⠀⢀⡶⠒⠲⠓⠐⠁⠀⠀⡗⣱⢾⣏⡼⣿⣿⣿⣿⣿⣿⠦⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⣠⠖⠋⠡⢼⡿⠀⢃⡴⠻⣤⠀⠀⢠⠀⠀⠀⠀⠀⢹⣾⡇⠃⠀⢙⣿⡟⣿⢶⣟⣿⡄⠆
⠀⠀⠀⠀⠀⠀⣤⡴⢞⠋⠀⠠⡄⡀⢸⣷⠓⡟⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⣿⡿⢀⣴⣿⣿⣿⡟⢸⣿⡟⡃⡄
⠀⠀⠀⠀⠀⠀⠈⠀⢻⠀⠂⠐⠛⠙⢾⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⢾⣿⣿⣿⡏⡧⢸⡽⡆⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⢸⣿⠇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡟⢹⣿⣿⣿⡇⣷⢸⠇⣣⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠆⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣠⣾⣿⣷⡺⢿⣿⣿⣧⡏⠘⡇⣏⢸
⠀⠀⣤⣄⠴⣶⣼⣿⣾⠀⠀⠀⠂⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⣾⣿⣿⣿⡟⡁⣾⣿⣿⢿⡇⣠⠃⣿⢸⣦
⠀⢸⣿⣿⡿⣿⣟⣿⣿⠀⠀⠀⠀⠁⢸⣿⣿⣅⠀⠀⠀⠀⠀⡄⠀⣰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢸⡗⣿⠀⡏⢸⡷
⠀⢸⣿⠿⠷⡯⠿⡿⠿⠀⠀⠀⠀⠀⢸⣿⣇⠋⠀⠀⠀⠀⠀⠁⠚⠻⡿⡻⠛⠟⢿⣧⠊⠟⠿⠿⢸⣷⡿⠟⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠘⠛⠁⠀⠀⠀⢸⠋⠁⠀⠀⢰⡇
⠀⢀⠀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣄⡤⠼⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠚⡇
⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠶⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠞⠛⠛⠛⠛⠶⣦⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣤⣤⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡶⠶⠶⠶⢶⣤⡀
⠀⠀⠀⢀⣀⣴⠟⠋⠉⠻⠋⠀⠀⠈⢻⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⣴⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⡀
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⡀
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠙⠛⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⠟⠉⠉⠉⠉⠻⡶⠛⠛⠛⠷⣦⣰⡟
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠛⠷⣦⡀
⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⣽⣿⢭⡇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢤⡆⠀⠀⠀⠀⠀⠀⠀⠈⠾⠽⠶⠁⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡗⣺⣗⢺⠂⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣻⣿⣻⡟⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠃⠀⠀⠀⠀⠀⢾⡷⣽⠆⠀⠀⠀⠀⣴⡖⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠹⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠸⣗⡿⣗⡟⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶⢲⢆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠑⠙⠀⠀⠀⠈⠩⠣⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢟⣺⢿⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢸⠀⠀⠀⠀⠱⡄⠀⠀⠀⣰⠋⠸⡇⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⢿⡇⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⢦⠀⣰⠃⠀⠀⡇⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⣀⣴⠞⠉⠀⠀⠈⢧⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢀⣴⣷⣤⣄⡀⢃⠀⠀⢀⣴⣿⡄⠀⠀⠙⠢⣤⣶⣿⣿⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠑⠤⣀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢀⣴⣿⣿⠋⢹⡇⠙⢮⣀⢠⣾⣿⡏⢳⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉⠓
⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠴⠿⠿⠟⠁⠀⢸⡇⠀⠀⠈⠈⣿⣿⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⣙⣶⡶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣰⣿⡟⠀⠀⠸⡀⠀⢀⢄⣠⣶⡿⠋⠀⡇⠈⠳⢄⠀⠀⠀⣀⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⣠⣶⣿⠿⠋⠀⠀⠀⢧⠀⠀⠀⠙⢦⡀⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠃⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠙⠦⣀⡟
⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠃⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣦⡄⣀⡀⠀⠀⠀⠈
⣿⣿⣆⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠠⡈⠋⠑⠆⠀⢀⣠⣤⣤⣤⣀⣀⡀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡆⠀⠉⠉⠒⠤⢄⣀
⣿⣿⣿⣷⣄⠀⢝⡛⠿⠿⠿⠛⡹⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⣀⣴⣾⣿⣿⠃⠈⢇⠉⠻⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠠⢀
⣿⣿⣿⣿⣿⣷⡄⠉⠛⠲⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠇⣀⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿⣿⣿⣷⣤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⠿⠿⠷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠿⠿⠿⢷⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⣀⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠛⠻⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⠉⠙⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤⣄⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⣠⣾⠿⠛⠉⠉⠉⠙⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠉⠉⠛⠿⣶⡄⢀⣤⣶⣶⠶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⠀⠀⠀⠀⠀⠙⠻⣷⡀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣶⠶⠶⣶⣤⣄⠸⣿
⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠻⣿⣿
⠀⣠⣾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏
⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷
⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠙⠻⠷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠟⠉
⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⢀⣠⣾⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠟
⠀⢠⣾⡿⠋⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠋⠁
⠀⣿⡏⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷
⠀⢿⣧⣀⣀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣷⡀⠀⠀⠀⠀⣀⣴⣾⠟⠉⣿⡆
⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⣿⡇⠀⠀⢀⣾⡿⠋⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡆⠀⠈⢿⣦⣄⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⢹⣿⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⣠⣾⣿⡆⠀⢸⣿⡁⠀⠀⠀⣸⣿⠁⠀⠀⠈⠻⣷⣤⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠁⣿⡇⠀⠀⠻⣷⣦⣤⣾⠿⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠀⠀⠀⣿⡇⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣴⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⡾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠁⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠄⢐⠂⠁⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠠⠠⠸⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠄⣀⠠⠀⠀⠀⠀⠀⡠⠂⠐
⠀⠀⠀⠀⠀⠁⢀⡐⠀⠀⢄⢤⡀⠀⡆⡌⠄⠐⠈⠠⠀⢀⠀⠀⠀⢀⠀⠀⠀⠠⠀⢈⠊⠀⠀⢄⠀⠐⠀⠂⠈⠄⣀⠠⢀⠌⠁⠂
⠀⠀⠀⠀⢀⢀⠀⠁⡀⠀⢈⡓⠈⠈⠁⢂⡀⠊⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⢐⠀⠀⠀⢀⠆⠂⢆⠀⠈⠄⠀⠀⠐⠀⡂⠈
⠀⠀⠀⠀⠀⠀⠆⢀⡂⠀⠂⠄⠀⠀⠈⡀⠎⠁⠂⠑⠈⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢈⠔⠁⠀⠠⠀⠀⠰⠀⠀⠀⠠⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢈⡥⠖⠆⠍⠢⠀⠀⠁⠄⡀⠠⡀⠀⠀⠀⠒⠁⢈⠄⠀⠀⡀⠀⠀⠁⠈⠀⠀⠂⠀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠂⢀⠉⡄⠀⠀⠄⠀⠀⠀⠄⠂⠃⠀⠈⢀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠀⠀⠀⠀⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠠⠈⠀⠄⢀⠀⠑⡠⠂⡄⠤⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠀⠂⠢⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⡀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⢀⠀⠀⠀⠂⠠
⠀⠀⠀⠀⠀⠈⠠⢀⠈⠀⠰⠐⠴⠈⠆⠎⡄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⢀⡠⠀⡀⠀⠈⢀⠘⠁⠀⠀⠀⠀⠘⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡐⠀⠀⠈⠀⠂⠀⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠾⠂⠀⠀⠀⠀⠸⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⡀⠀⡈⠀⠃⠀⠀⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠹⢠⠸⡳⠁⠀⠄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠠⠀⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠋⡠⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢋⠀⠀⠀⠀⠀⠠⠤⠀⠀⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⣽⠃⢴⠛⣃⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠖⢉⡀
⠀⠀⠀⠌⠉⠄⠠⠄⠄⠀⢲⣇⠀⠀⠠⢀⠀⠐⠉⠡⠘⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢫⠄⡍
⠀⠐⡋⠀⠀⠠⢀⡀⡄⠀⠘⡉⢀⠀⠀⠈⠃⠀⡀⠀⠀⠀⠉⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⢠⡈⠂⠀⠀⠀⣠⠚
⠀⠀⠁⠀⠀⠁⠤⠀⢀⡀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⡩⠀⠀⡄⠀⠀⠀⣐⡖⠡⡄
⠀⠀⣿⡀⠘⠂⠁⠀⣼⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⡇⠁⠀⢀⠃⠀⠀⢀⠞⢉⠀⠀⠁
⠀⠀⢸⠀⠀⠀⠂⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢸⠀⠀⠀⡞
⠀⠀⢠⡄⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠘⡅⠀⣸⠀⠀⠀⣀⡀
⠀⠀⠀⣧⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠧⠶⠛⠛⠛⠛⠛⠋
⠉⣩⡍⣹⣾⠻⠓⣾⡗⠙⠒⠉⠙⠛⠛⠿⠿⠻⠋⠉⠉⠛⠛⡉⣛⠛⠉⠉⠛⠛⠋⠙⢋⡁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂
⣴⢱⣿⣿⣷⣇⣶⣾⡗⢠⡀⡀⠐⠒⠀⡀⢀⠀⢀⣀⣀⡀⠈⠉⣤⣾⣯⣠⡀⢀⣠⣄⣠⣴⡤⠤⠐
⣷⣿⣿⣿⣿⣿⣿⣿⡇⣸⣟⣴⣦⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠺⠟⠻⠻⠿⠿⢦⠝⠋⠉⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆
⣿⣿⣿⣿⡿⠿⢿⣿⠂⠿⠿⠿⠋
⠉⠀⠉⠉⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⢅⣀
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠊
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣦⣶⣴⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡲⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢰⠏⠂
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠂⠀⠀⠠⠒⠀⠚⠀⠀⢀⡠⠀⠂⠃⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⢸⡆⣰⣧⣆⠒
⣴⣧⣿⣇⡆⠀⠀⠘⣯⠐⠂⠀⠀⢲⡄⠀⠀⠂⠻⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢰⢷⠀⢠⣾⢷⣭⠌⠛⢶⠒⢠⡆
⣻⡟⢫⣿⣧⣷⣏⡠⠀⠔⠐⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡔⢯⡀⢘⡁⢂⠪⡦⠴⡘⢦⣝⢳
⠚⣯⡶⢹⣿⣿⠋⠂⠀⠂⠐⡈⢺⣶⣆⣤⣀⣤⢀⠀⠀⠀⢀⡀⣤⢀⣠⡊⠃⣴⠞⠃⢜⡺⠤⠉⠱⣿⠀⠈⠀⠙⢿
⢈⠁⠖⢸⣉⡤⠎⣠⠆⠀⠀⠐⠲⣿⣿⡿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⠈⠈⠺⣂⠘⣯⡤⠒⣀⡠⣜⡀⠀⠈⠶⢾
⠸⠄⢠⣟⡉⠠⠠⠶⢀⣰⢿⠑⢠⣙⣯⢓⣹⣭⠟⣋⡁⠀⠀⠀⠙⢿⠀⠈⠙⠳⣎⢢⡟⠒⠉⠈⠣⠌⡂⠀⠠⡀
⠀⠀⢠⡏⠠⢰⠂⢠⠊⠙⢄⣯⡀⠀⠉⠁⠀⢄⣪⣷⣻⣓⣦⣴⡶⠂⠀⡀⠁⣌⠚⢿⣗⠄⣇⠀⢰⡆⠈⠲⡀⡀⠑
⠀⡰⠋⠀⢀⡬⣟⠀⠀⠀⢣⣀⠧⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠉⡋⠀⠀⠉⠐⠉⠄⠀⠁⢿⡁⣀
⠀⠀⠀⠈⠀⠀⠀⠙⠊⠀⠊⠁⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⠘⠉⠀⠄⠐⠤⠦⠀⠽⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡆⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣶⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⢠⣾⣿⣿⡆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠹⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⣀⣀⡀⢀⡀⣀⣀⣀⢀⣀⠀⣀⣀⣀⣀⣀⣀⠀⣀⡀⠀⢀⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣼⣿⣼⣟⠋⣹⣾⣿⠹⢏⣿⣿⣿⡄⣿⡏⠉⣿⠉⠉⢸⣿⣧⠀⣿⢸⣿⣆⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠈⠁⢿⡟⢿⣶⣿⠏⠻⣿⣿⠟⢸⣿⢻⣿⡇⠀⢿⠄⠀⣿⠋⢻⡇⣿⠸⣿⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢀⣀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⠉⠉⠉⠀⣿⣟⠙⣻⣷⠀⠀⢴⣿⣿⣿⡅⠀⠀⢰⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⣼⣿⣧⣿⣷⠀⠀⢸⣿⡄⠀⢘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⣿⡏⠹⣿⣧⠀⢠⣿⡿⠁⠹⣿⣧⠀⢸⣿⡇⠀⢸⣿⣦⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠈⠉⠁⠈⠉⠁⠀⠀⠉⠉⠀⠈⠉⠁⠀⠀⠉⠉⠉⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⢀⣄⡰⠏⠀⠀⠀⠀⠀⠀⠈⢛⣶⡇⢰⠢⣽⠤⠖⣰⡤⠗⠀⠀⠀⠘⢦⣄⡀⣐⣟⣂⠀⣀⡠⠆
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣒⢩⣬⡉⡆⣬⣤⣤⠤⠀⠀⠀⠀⢠⡔⠛⡖⣽⠲⠟⠭⡁⠀⠀⠀⠀⠀⠈⠙⡻⢳⣭⡼⢟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠬⣉⢴⡓⠈⠀⠀⠀⠀⠀⠀⠠⢤⡩⠾⠓⣽⠚⠶⣉⡠⠀⠀⠀⠀⠀⢀⣪⣗⣜⣛⣳⣮⣕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠄⠀⠠⢳⣄⠀⠀⠀⠀⠀⠀⠶⠉⠁⠘⣉⣭⡑⠃⠈⠙⠶⠀⠀⠀⠴⠊⠉⠁⠩⣧⡏⠁⠈⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⣠⠀⡠⢒⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠄⡄⡄⠀⠈⠛⠁⠀⢰⢠⠰⠀⠀⠀⠀⠀⣀⡘⢄⠃⠿⠘⡠⢃⡀⠀⠀⠀⠀⠀⠀⢐⣻⡌⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠲⠤⠛⠀⠲⠈⠂⠀⠀⠀⠀⢀⡠⠬⠝⣃⠟⠉⠙⣌⠩⠐⢒⡠⠀⠀⠀⡀⢄⠀⠄⣨⡨⠄⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠲⠒⠤⠒⠤⢀⡠⠀⠀⠀⠈⠃⠒⠒⣒⡭⣦⣀⣠⡓⠭⣍⠁⠀⠀⠀⠙⠙⠝⠁⠂⢛⠇⠀⠙⠍⠁
⠀⠀⠀⠀⠀⠀⠊⠁⠃⠀⠀⣃⠀⠀⠈⠘⠲⠀⠀⠀⠀⠀⠈⢉⠊⠸⢰⡌⢄⠑⡄⠀⠀⠀⠀⠀⠀⠀⣤⠟⠈⠘⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⠃⠈⠁⠈⠑⠖⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢠⠈⠒⣿⠚⠀⡆⣀⡤⠀⠀⠀⠀⠀⠀⢳⡄⢰⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠡⠓⣤⢀⣹⣀⣤⠶⣛⠀⠀⠀⠀⠀⠀⡹⠿⢤⡀⢿⢠⡴⠿⢉⠀⠀⠀⠀⠀⠀⠲⢄⢡⣜⡴⣁⠤⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠼⣿⠿⣤⢁⡠⠄⠀⠀⠀⠀⠀⢀⡀⣠⠄⢻⢣⣄⢀⣀⠀⠀⠀⠀⠒⠓⠓⢐⠲⣿⡷⡂⠰⠶⡷
⠀⠀⠀⠀⠀⠀⠰⠎⡏⠈⠀⡒⠄⠀⠍⠰⠢⠀⠀⠀⠀⡴⠞⢻⠀⠀⣿⠀⠈⡟⠶⡄⠀⠀⠀⠀⠀⠋⢁⡜⢰⠙⡀⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡏⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠊⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠸⠀⠝⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣗⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠞⢉⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠇⠀⢀⡾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣽⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣿⣿⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢙⡁⣴⢁⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠏⣾⠁⠆⠀⠠⠞⢦⡀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠔⢡⣿⡶⠀⠀⠀⠛⣴⣆⠀⠀⠀⣠⢀⡞⠀⠀⢹⣷⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣷⡿⢃⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢉⣴⣿⠆⠀⠀⠀⠉⠀⠀⣼⢧⣎⣰⣆⠀⠀⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢫⣵⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⢠⡶⠀⠀⠀⠀⣴⠏⣸⣧⣽⣿⣆⣀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣤⡎⠉⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⢾⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣯⣿⣿⠗⣼⠇
⠀⠀⠀⠀⠀⣰⡗⠀⠀⠀⠠⠼⣿⣧⡀⠀⠀⠀⠀⠀⠘⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠘⣿⡿⢟⣵⠟⠁
⠀⠀⠀⠀⠀⡟⢠⣤⣤⠀⠀⠀⠀⠹⢯⠄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⢠⣽⣽⣇⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠁⠋⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣠⡀⠀⠀⠐
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣟⡄⠀⠀⠀⠀⠀⠀⠠⠞⠀⢷⠛⢠⣾⡿⠃⠀⠀⠀⠀⠀⠈⠹⢿⠟⣵⡀⠘⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⣴⠞⣹⠿⠏⠀⠀⠄⠀⠀⠐⠁⠀⠀⠠⢳⢿⣥⢟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⢴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠁⠀⠀⠀⠀⠁⠀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠉⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇
⠀⠀⠀⠀⠀⠀⠀⣠⠶⣹⡾⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⢿⣷⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⣄
⠀⠀⠀⠀⠀⠀⠠⠟⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠣⠤⠄⠀⠀⠀⠀⣠⠀⠀⠘⣩⡟⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠁⠀⠀⣸⡿⠂⠄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢘⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⠄⢀⠀⠀⠀⠀⠀⣠⣴⠾⡁⠀⠀⠀⠀⠠⠟⠃⠀⠀⠈⠀⠙⢃⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠛⠃⠀⠀⠀⠀⠟⣥⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⡵⠎⣠⠖⠀⠀⠳⠄⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠂⠀⠀⠀⠉⠳⠠⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠵⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢩⡀⠀⠀⠀⠀⠀⠀⠀⠛⠇⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠛⠐⠀⠐⠈⠁⠀⠀⠀⠀⠘⠃⠞⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠋⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠲⢦⣄⠀⠀⠀⢀⣠⡤⠶⠶⠒⠒⠲⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠻⣆⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠛⠛⠧⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢀⣀⣀⣀
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠉⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠈⣻⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣀⣀⣀⡴⢾⡀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠿⢫⡟⠛⠛⠻⣤⣞⡃
⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠙⢦⣤⣀⣀⣠⣤⡞⠉⢳⣦⣤⣀⣀⡀⠀⢀⣀⣤⣏⡿⣠⣭⡗⠀⠀⠀⣿⠉⢿⠄⢀⣄
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⠹⣤⣤⣤⣽⡜⢯⣩⣟⢻⣍⣧⠙⣴⣧⣴⠟⣦⣤⡾⠡⣿⡭⠤⠟⠼⠧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣶⢂⡶⢶⣲⡶⣠⠶⠶⣦⡴⢶⡶⣀⠰⡖⢶⣔⡶⠒⣆⢲⡒⠒⠓⢶⣘⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⢾⡉⢰⡇⠀⠀⢸⣗⠛⢰⠋⣷⠙⣻⡏⠀⠀⠘⣧⠛⢶⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⢧⣤⣤⣤⠟⡴⠞⠛⠳⢷⡙⣦⣀⣀⡴⣷⣦⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡴⠒⢲⢆⡘⣇⠀⠀⠀⣰⢃⡄⢶⠶⣄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡞⣷⠙⢲⣶⠚⢡⡏⠹⣎⢧⣍⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⢁⢺⡄⠙⠶⠛⠹⠷⠖⠋⠀⣸⠂⢰⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠟⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠷⠋

⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⢀⣨⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣫⠄
⠀⠀⠀⠀⢠⣄⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣩⢧⠶⠂
⠀⠀⠀⠀⣄⣈⣱⣆⣠⠤⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣤⣩⣿⣦⣶⠛
⠀⠀⠀⢠⡌⠉⢡⣎⣁⣀⡄⠀⣠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣉⣤⣾⣥⡼⠳⠶⠾⠃⢀⠀⣠⠄
⠀⠀⠀⠀⠓⠚⣯⠉⢉⢁⣠⠀⠋⡀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠀⡞⠀⠀⠀⢰⠃⠁⢺⣤⠿⢶⣧⡾⢿⣶⠶⠾⠋⠊⠀⠟
⠀⠦⠐⠶⡴⠾⢛⡓⠟⠉⠁⠀⠀⣧⠀⡀⢀⡀⠀⠈⢧⡄⠠⢠⠆⠀⠐⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣟⣫⡿⠶⢟⡿⠶⠶⠂
⠀⠀⠶⣦⣀⣴⠞⠛⣶⣄⣼⠻⠇⠘⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣳⣫⣿⣭⣿⣟⣻⡷⢶⡾⠇
⠀⢀⣤⣬⣡⣂⣴⣾⣇⠈⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣋⣽⠶⠖⠺⢛⣿⣷⣤⣤⣶⠄
⠀⠉⠉⠉⠙⡉⠉⣹⡋⠛⠋⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠶⠼⠿⠿⣿⣧⣤⣤⡤⠆
⢀⡝⠛⢿⣍⣠⠾⠻⡿⢷⠆⣦⠆
⠈⣿⠏⣉⣈⠈⣀⢾⣧⣀⠀⡾⠟
⠀⠀⠀⠀⠿⠋⠏⠈⠙⠛⠋⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠓⢓⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠈⠀⠠⠀⣶⡶⠀⠀⠀⠠⠀⠀⠀⠀⠐⠖⠓⠶⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣭⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠚⠓⠆⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⢀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠑⠛⠙⠚⠓⠓⡁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠀⢠⠖⠀⠉⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠚⠐⠳⠖⠤⠂
⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠌⣠⠖⠈⠈⣧⣽⠋⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡐⠧⠢⠔⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡯⠀⠈⠐⠉⠈⠒⠚⠀⠙⢆⢀⡠⢀⢀⠀⢠⡄⠤⠒⢲⣴⣧⣶⡜⢚⣒⠘⢀⠀⡀
⠀⠀⠀⠀⠀⡠⠐⡐⠒⠊⠉⠁⢡⣹⣷⢰⠀⣰⣶⡆⠀⡄⣯⡴⣄⢅⠠⡌⡛⣿⣏⣴⠀⠌⠁⢉⡁⡀⣀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⣌⠄⠈⠉⢅⣐⣋⠏⡁⢹⠀⢀⡇⠀⣠⠤⠼⠂⠂⡁⠀⠈⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀⢀⡇⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠋⠉⠁⠉⠐⠄⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠴⣀⠀⡗⢀⡤⠆⠀⠀⠀⠠⠀⢀⠀⢀⠀⠀⠀⠀⢠⣶⡞⣟⢳⣶⡄⠀⠀⠀⠾⣷⣿⣿⣶⡦
⠀⠀⠀⠀⠀⣀⠑⡷⢀⡀⠀⠀⠀⠐⠀⠀⠻⠢⠀⠀⠀⠀⠀⢠⣭⡜⠿⢧⣽⡄⠀⠀⠀⣴⡿⣿⣿⣿⣦
⠀⠀⠀⠀⠛⠁⠀⡧⠀⠑⠂⠀⠀⠀⠈⠀⠠⠀⡀⠁⠀⠀⠀⠈⠙⠱⣿⠎⠙⠁⠀⠀⠀⠀⠀⠻⠟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠠⠀⠀⣅⠀⢀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⡦⠀⠉⠀⣤⡄⠀⠀⠀⢠⠄⠀⡅⠀⢤
⠀⠀⠀⠀⠀⢘⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⢀⣀⠀⠗⠀⣀⡀⠀⠀⠀⢀⡀⠐⠇
⠀⠀⠀⠀⠐⠈⠉⠛⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣦⠀⠉⠁⠀⠀⠀⠈⠁⠀⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⣰⡀⠙⠏⢰⡄⠀⠀⠀⠀⢠⣤⣿⣤⡄⠀⠀⠀⠀⠰⣶⢘⡛⣴⣶
⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⣉⡀⠜⠓⢤⣼⠀⠀⠀⠀⠠⠿⣿⡿⠇⡀⠀⠀⠀⢠⣷⡘⡟⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢤⡦⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠸⡿⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠻⠦⡄⢘⡃⣤⠞⠇⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⠀⠉⠀⠀⢈⠀⠄⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⢀⢀⡄⠳⠜⣤⣀⡀⠀⠀⠀⠀⠀⠣⠼⠃⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠚⠊⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⢰⡷⠂⠀⡀⠀⠀⠀⠀⢦⠀⠀⡰⠁⠀⠀⠀⢀⠀⠀⢻⡇⠀⢀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠰⢫⢤⠖⠛⢦⡞⠹⠂⠀⠀⠀⠀⣱⢤⠁⠀⠀⠀⠀⠛⠳⢦⠹⢣⡴⠟⠃⠀⠀⠑⠂⣤⣦⡀⠰⠂
⠀⠀⠀⠀⣀⣸⣄⢛⣸⢇⢤⡀⠈⠉⠉⠉⡳⠺⡁⠉⠉⠁⠀⣀⣤⠶⢠⡐⠶⣤⡀⠀⠀⣀⠀⠛⡿⠓⢀⡀
⠀⠀⠀⠈⠓⠁⢈⣽⡀⠀⠋⠀⠀⠀⠀⡜⠀⠀⠱⡄⠀⠀⠀⠈⠁⠀⣼⡅⠀⠈⠁⠀⠀⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⠿⠿⠿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⢷⣄⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇⠀⠙⢿⡆⠙⣦⣴⣄⡀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣴⣿⣿⠙⣧⡀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⠀⠈⠁⠈⠻⣦⣄⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⣠⣶⣿⣿⣿⡏⠀⠈⣿⣿⣿⡿⢫⣾⣿⣿⡇⠀⠀⠀⣤⡀⠀⠀⠱⣦⡀⠙⢷⣦⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⣾⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⠟⣱⣿⢏⣿⣿⣷⠀⣄⠀⢹⣿⣦⡀⠀⠘⣿⣦⣄⠈⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢋⣴⡇⠀⢸⡿⢋⣼⣿⠋⣼⣿⣿⣿⠀⢻⣦⡘⣿⣿⣿⣦⡀⠈⢿⣿⣷⣄⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⣡⣾⣿⠃⠀⠛⢠⣾⣿⠃⣼⣿⣿⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⣌⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⣰⣿⡿⠁⣸⣿⣿⣿⣿⠏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏⢀⣼⣿⡟⠀⣰⣿⣿⣿⣿⠏⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣧⣾⣿⠟⠀⢰⣿⣿⣿⣿⡏⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣯⣤⣴⣿⣿⣿⣿⡟⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⠲⠤⢄⡤⠴⠒⠒⠒⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⠉⠉⠉⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⡆⠀⠀⠀⠀⠀⣠⢋⡜⠀⠀⢠⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠀⡴⠒⢄⢀⣠⠗⠉⢀⣀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡄⠑⠒⣺⢡⠃⠀⢀⡎⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠘⢄⣀⡤⠊⠑⠤⠖⠁⠘⠦⠴⠋⠳⠔⠃⠘⠦⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠊⠀⠀⠀⠀⠀⠀⣠⠎
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣀⡀⢰⡟⠀⡠⡄⢠⣤⠀⠀⣠⡉⠀⠀⣠⡦⢦⠀⠈⣿⡔⠒⠆⠀⠀⠀⠀⠈⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⠁⠈⠀⠈⡏⠀⠀⢀⡷⠁⠀⠀⡸⠀⡼⠀⢀⠇⠘⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠱⡀⠀⠀⠀⠀⠀⠘⠤⠚⠀⠣⠔⠂⠀⠣⠤⠴⠊⠳⠴⠚⠐⠃⠀⠘⠒⠊⠀⠀⠉⠂⠀⠀⠀⠀⡸
⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠊⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠦⠤⠤⠤⠤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠤⠤⠔⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠁⡄
⠀⠀⠀⠀⠀⡀⠀⠘⠄⠰⠁⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠖⠚⢃⠐
⠀⠀⠀⠀⠀⠉⠐⠂⣰⣦⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠽⣻⠮⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠠⠂⠉⠠⠀⠄⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠀⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡄⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠌⠁⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠉⠀⠀⠀⠀⠀⠀⠰⣶⠀⡀⠀⠀⠀⡄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠆⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠓⠁⠀⠰⠆⠀⠀⠀⠀⠐⠢⢿⡁⢠⣦⠀⣿⠗⠂
⠀⠀⠀⠀⠀⠀⠙⠷⣄⠿⢠⡾⠋⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣤⠤⠽⡏⠈⡿⠥⢤⡄
⠀⠀⠀⠀⠀⢠⢴⠶⢆⡻⡱⠶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⣄⣷⣤⣬⣧⣤⣽⣾⣥⣤⣯⣤⣴⣭⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋⠀⣴⣃⣠⡞⠙⣦⣀⣳⡄⠈⠃⠀⠀⠀⠀⠀⠐⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠎⢳⣴⠉⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢀⣿⣿⣿⠃⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣩⡟⡇⠀⠀⠀⠾⢻⣍⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⣦⣽⣿⣧⢶⣰⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣷⣧⣼⢿⡷⣾⣿⣏⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡐⢾⣙⣿⣽⣿⣿⣿⣷⣾⣧⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⣿⣟⣿⣽⣏⣻⡙⢿⣿⣾⠂⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠢⠀⡀⢁⢠⠃⢀⡀⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠛⣻⣿⣿⣩⢿⣿⣭⡁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢺⠟⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⠃⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⢀⠃⠈⡀⠀⠉⠪⠃
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠘⠻⠛⠋⠀⠀⠘⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡪⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣬⠐⠂⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠀⠉⠳⣶⠟⠉⠛⢶⡶⠛⠉⠉⠉⠉⠙⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡶⠾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡟⠀⠀⠀⠀⢀⣱⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠠⣴⠿⠛⠀⠀⠀⠀⣀⢀⡝⠀⠀⠀⠀⠀⠀⠛⠛⠛⠓⠶⢦⣄⡀
⠀⠀⠀⣀⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠬⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢦⢠⣀⣔⣬⡺⠛⠁⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠈⢻⡄
⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠢⡄⠮⠓⠋⠁⠀⠀⠀⠀⣠⡌⠁⠀⠀⠀⠀⠀⠀⢈⣀⢀⣠⡴⠎⠀⠀⠀⠀⣀⠠⣴⡍⠀⠀⠀⠀⠀⢀⣿⣀
⠀⢸⡇⠀⠀⠀⠠⡀⢀⡠⢀⠎⠀⠀⠀⠀⠀⠀⡠⠀⠈⠒⠙⠞⠓⢉⠀⠀⢠⣠⡀⣄⣦⣴⣿⣿⡿⠋⠀⠀⠀⠘⠎⠳⠿⠿⠊⠀⠀⠀⠀⠀⢸⠀⠉⠉⠛⢷⡄
⠀⠀⠻⢦⣤⣤⡄⠉⠀⠉⠀⢄⠀⠀⡀⢄⠠⡔⢊⡄⡀⢀⡦⣄⡴⠄⢠⡐⢤⣙⢻⣿⠿⣫⣾⠛⡱⣄⢦⡠⣰⣵⣦⢂⡄⠀⠀⠀⠀⠀⠠⡰⡅⠀⠀⠀⣠⠼⣿
⠀⠀⠀⠀⠀⢸⣇⠀⡀⠀⠀⠀⠀⠁⢈⣤⣤⢾⢯⡳⣝⡲⣝⡲⠭⢃⣼⢯⣷⡿⢋⣡⣾⡿⣷⣷⠙⠮⠻⠟⠛⢉⣥⣿⢭⡇⡄⢐⢦⡪⣕⠿⠃⢀⡠⠖⢉⣼⠏
⠀⠀⠀⠀⠀⠀⠻⣦⣍⡂⠓⠌⣓⣩⡀⣀⡀⣀⠓⠝⠳⠝⢒⣉⣴⣿⣿⠟⠉⠀⠋⠉⣠⡾⣟⢮⣿⡿⢲⣖⠿⡛⣝⣾⡟⣰⣏⣪⣕⠎⢚⢁⣬⣤⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠙⣷⣀⣑⣈⡙⡿⢿⢿⢿⡻⣽⣿⣥⣶⠖⠀⣠⡾⣏⣽⣮⡿⢏⣴⣟⢮⣓⣽⡾⢟⣴⡿⣤⣥⣶⡾⢋⣾⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⢷⣌⠈⢯⣷⣻⣾⡿⠋⠀⣠⣾⢻⣶⣤⣤⣴⣾⣿⣏⣈⣓⣉⣥⡶⣿⢯⡷⠾⠛⣩⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣤⡽⠋⠀⣠⣾⣿⣿⣿⡿⠿⠟⢛⣿⣿⠿⠟⣽⠿⠷⠶⠶⠶⠶⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣤⢦⣄⢀⡰⠋⠀⠀⠔⠛⠛⠉⠁⠀⠀⢀⣴⣟⣋⣤⠴⠋⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠛⠋⠀⠀⣹⠟⠀⢀⣀⣤⣴⣶⣾⠏⠀⢀⣴⠿⠋⠥⠅⠂⠀⢀⣤⣾⣥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠿⠃⠀⠀⠀⠀⣠⣼⣧⣶⡿⢟⣿⠁⣲⠞⠁⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣠⡐⢶⡄⢄⡐⠻⡿⠯⢠⡿⠋⢁⡼⠋⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢶⣤⣥⣴⠞⠛⠛⠋⠀⣠⠟⢁⣴⡿⡫⠂⠀⠀⠀⠀⠀⠀⠀⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⡾⢋⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣤⡴⠆⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣼⠟⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠉⢤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⡾⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⡟⠁
⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⠟
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣷⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡠⠀⡡⠋⣿⣧⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢠⣿⣤⡀⢀⣿⣷⣶⣷⡚⠋⠏⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢿⣿⠖⢼⡿⠋⠀⢾⢿⡿⢿⣿⣿⣶⣄⡿⣿⣿⣿⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢃⠰⠊⣄⠀⣀⣴⡾⢇⣿⣿⣿⠿⠉⠐⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣈⠀⣨⠔⣺⣿⣿⠟⡩⡢⢺⣿⣿⣷⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠳⠤⠻⠿⠾⠿⠟⠟⠛⠋⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⠉⠉⠉⠉⠛⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠋⠉⠉⠉⠛⠓⢲⢤⣄⡀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣀⠀⠀⠀⠀⢠⣦⠰⣿⠇⠀⣭⡓⠦⣄⡀⠀⠀⠀⠉⢳⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠥⠼⠃⠀⢸⣻⣮⠟⠛⠙⠲⢼⡟⠁⠀⡀⠉⠓⢦⡀⢀⡟⣦⣼⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡤⡄⢀⣤⢀⣸⠃⠀⠀⠀⠀⠀⠓⢤⡿⠋⠀⠀⠀⣙⡾⠀⣇⣀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠖⠃⠀⢹⡏⠀⠽⠂⠀⠀⠠⢶⡆⠈⢣⡴⠶⠂⠈⠉⣷⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣯⡿⠁⣠⣄⣠⣄⣀⣠⡀⢀⡀⢸⠀⠀⠀⣄⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠳⡀⠀⠀⠁⠀⠉⠀⠈⠉⠀⢈⡷⠤⠼⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡶⠤⢤⣤⣄⣠⡤⣶⡿⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠋⠙⠲⢶⣶⠶⢾⣋⣉⠀⢸⣧⠳⣄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⣨⣧⣄⣠⣼⣧⣀⣀⣈⣉⣠⣼⡇⢷⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⣿⢻⠀⢠⡄⠀⣄⠀⠀⠸⠀⠀⠀⣴⢃⡜⠉⠛⠒⣶⠶⢭⡉⠁⠀⢸⡇⠀⢳⡀⢘⡆⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣧⡇⠘⡆⣸⢧⢠⢿⡀⠀⠀⠀⣠⠂⣿⢿⡁⠀⠀⢸⠁⠀⠀⠙⠒⠦⣼⡇⠀⠀⠙⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣳⠈⢠⡄⠙⠃⠘⠋⣸⠁⠀⠀⠐⠇⠀⢁⣸⠧⠤⠤⣼⡀⠀⠀⢰⣧⡖⠃⣩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠙⠀⡼⠙⣆⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠙⠒⣾⣲⣶⣏⣙⣛⣻⣛⣲⠭⣟⡷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡾⠁⠀⠘⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠰⣯⣥⣤⠤⣾⠿⠭⢞⡿⠁⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣧⣀⣀⣠⣧⣤⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢡⢾⠉⡏⢇⠙⣍⠪⣝⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠳⣴⠃⣰⠖⢾⡘⡶⠋⣳⠸⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠉⠒⠋⠀⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⡆⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⣈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠟⠛⢉⠉⠉⢉⠻⠇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠀⠀⠘⠛⠀⣀⠘⣃⣠⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠰⢂⡀⠙⠛⠡⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢻⡤⣤⣀⣤⣤⠀⣅⣁⣤⣦⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠓⠦⢤⣀⠀⠀⠀⣸⣿⡿⠿⠿⠿⠿⢷⣿⣾⣿⣦⠀⣀⣤⠶⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣐⠉⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⢻⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡉⠻⠒⠀⠀⠀⠀⠀⠀⠈⠁⢹⣧⢻⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠒⠊⠀⠀⠀⠀⠀⠀⠀⠶⠈⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠄⣀⣠⡀⢀⠀⠀⠀⠀⠛⠀⠈⡟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠭⠛⠋⠉⠉⠉⠉⠈⠋⠙⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠠⣴⣶⣿⠶⣾⣮⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣒⡈⠠⣺⣿⣿⣿⡶⣬⣄⣂⣀⡀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠶⠞⠉⠐⠋


⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣭⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠈⠉⠉⠉⠉⠉⠰⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢁⡄⢶⠋⠉⠉⣙⢻⠋⠑⠶⣤⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⡾⠋⠹⣄⢳⡀⠀⣿⢸⠀⠀⠀⣠⠟⣦⡈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢰⠏⠀⠀⠀⠙⣆⠙⣦⡁⠸⠀⡴⠚⣡⠞⠁⢻⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡤⠄⠀⠲⠶⠒⠒⠒⠒⠒⠒⠒⠲⠂⠀⠀⠄⢠⡏⠀⠷⠠⠤⢤⣤⣤⣬⣧⠘⠁⠘⢁⣀⠊⠁⠀⠀⠀⢳
⢀⣠⠔⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠗⠒⠲⠢⠤⣤⣤⡀⠀⡀⠀⠈⣉⠉⠐⠒⠒⠂⣾
⣿⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢀⣴⣋⣤⡾⢻⣆⠙⣏⠉⠉⠉⠉⠀⢶
⣿⠀⠀⠀⠉⠙⠓⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣵⣤⣵⡦⢲⡶⠛⡩⠛⠉⡄⢸⡟⢶⡈⢷⡀⠀⠀⢰⠇⢰
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⢂⡀⠈⠀⠀⠀⡇⢸⡇⠀⠙⣎⡱⣄⣰⠋⢠⠟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠑⠤⣀⡀⠀⣧⢸⡇⠀⣀⣨⡷⠉⢁⡴⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢈⠉⠁⠘⢻⡟⠈⣉⣁⣤⠖⠉
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⢺⠟⠀⠉⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿
⠀⣷⢠⡞⠙⠛⠦⠴⠦⠤⠖⠛⠛⠉⠉⢉⣛⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠖⠛⠛⠋⠉⠙⠛⠶⣄⠀⢠⡏
⠀⣿⠘⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠚⠁⠀⠈⢣⠉⠛⠳⠶⠶⠶⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡇
⠀⢻⠀⣧⠀⠀⠀⠀⠀⠀⡞⠋⠀⠀⠀⣠⠂⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠇
⠀⢸⡆⢿⠀⠀⠀⠀⠀⣾⠀⢀⣀⠴⠚⠉⢣⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡿
⠀⠀⡇⢸⡄⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡇
⠀⠀⣷⠈⡇⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡹⠶⠖⠒⠐⠀⠒⠀⠶⣄⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇
⠀⠀⢹⠀⣧⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡧⠀⠀⢀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢸⡇⣼
⠀⠀⢸⡇⢻⠀⠀⠀⠀⠀⠈⢷⠘⢦⡀⠀⣀⠴⠞⠁⠀⡧⠀⠀⠀⡟⠉⠉⠉⠁⠀⠀⠈⡇⠀⠀⠀⠀⣼⠁⣿
⠀⠀⠸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠑⠶⠞⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⢠⡏
⠀⠀⠀⣿⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⢟⠀⡀⠀⠁⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⢀⡏⢸⡇
⠀⠀⠀⢻⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠉⠳⢮⣵⣏⠀⠀⠀⠀⠀⠀⠀⢸⠅⡇⠀⠀⠀⢸⠇⡼
⠀⠀⠀⠘⡆⢿⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢐⣇⡀⠀⠀⠀⢹⡗⠶⠠⠤⠤⠀⠀⠀⠶⠁⠀⠀⠀⣼⢠⡇
⠀⠀⠀⠀⣇⠸⡇⠀⠀⠀⠀⠀⢰⠋⠀⠀⢠⠏⠀⠉⠳⢦⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠇
⠀⠀⠀⠀⢻⠀⣇⠀⠀⠀⠀⠀⢃⣦⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿
⠀⠀⠀⠀⢸⡇⢹⠀⠀⠀⠀⠀⠘⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟
⠀⠀⠀⠀⠀⣧⢸⡇⠀⠀⠀⠀⠀⠙⣄⡀⠀⠀⠀⠀⠀⡄⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⠇
⠀⠀⠀⠀⠀⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣄⣀⠖⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡼
⠀⠀⠀⠀⠀⢸⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⡇
⠀⠀⠀⠀⠀⠀⣇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣸⠁
⠀⠀⠀⠀⠀⠀⢻⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣷⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠁
⠀⠀⠀⠀⠀⠀⠀⢙⡆⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠞⠋⢀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠻⢦⣀⠈⠙⠛⠛⠲⠶⠶⠶⠶⠶⠶⠖⠛⠛⠉⠁⣀⡤⠾⠋⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠉⠛⠳⠶⠦⢤⣤⣀⣀⣀⣀⣤⠤⠴⠶⠛⠛⠉⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠦⢀⣀⣀⣀⣀⣀⣀⣀⡤⠶⠶⠛⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⢀⡀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡶⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⡟⠄
⠀⠀⢀⣤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⢴⠋⠀⠀⠀⠀⠠⠠⠎⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣼⠀⢴⢎⡠⢤⡀
⢠⣆⣼⡗⣠⠀⠀⠀⠴⠂⠠⠀⠀⠈⢀⡀⠀⠀⠠⠠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⢀⣼⡆⠛⠛⠿⣤⣠⡄⣀
⣿⣿⡟⣷⣿⣠⣠⠔⢐⠁⡄⣀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠐⣆⠀⠀⣯⠃⠀⡜⢛⠉⣻⡁⣀⠹⣀⠠⣿⣀
⣸⡿⢀⢻⣿⣿⣿⢞⠁⠈⡁⠀⠡⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠕⢀⢘⣤⠓⣄⡔⠀⠶⢌⣯⠈⠣⠈⢳⣮⣿
⢨⡿⢛⢰⣿⠟⠃⠌⠁⡀⠀⠀⢂⢘⣿⣷⣿⣶⣼⣤⣄⣀⡀⣠⣤⣤⣷⣤⣼⠴⠅⣘⣋⠀⣀⡥⠋⣁⠀⠈⢿⠀⠀⠠⡀⠈⣿
⢠⡀⠊⢈⣥⠖⠋⠀⠚⠀⠀⣄⡀⠑⢿⣿⣟⣹⣽⣽⣿⡿⠟⠟⠿⠿⣿⣿⠟⠀⡀⣈⡑⡆⢈⡶⢋⡠⢦⠜⢦⡂⠀⠀⠉⠙⢿
⠘⠋⠀⢯⡥⠀⠁⠚⠁⢤⡜⢳⡀⠱⠦⢷⣀⢼⠷⠛⣡⠤⣄⠀⠀⠀⠈⠻⠀⠀⣀⢉⠻⣄⣾⢉⢁⠀⠀⡁⠂⢄⡀⠀⠢⢀⠠
⠀⠀⢠⡎⠀⠂⣏⡀⠔⠀⠈⠤⠷⠀⣀⢀⠀⠈⠰⣭⡼⠏⢿⣽⠶⠾⠟⠁⣨⠈⢁⣁⣉⣻⣿⡷⢛⣧⣀⣿⣷⢄⣻⣇⣧⠈⢿
⠀⠠⠋⠀⣀⡤⠶⣅⠀⠀⠈⢳⡠⠲⡍⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠤⠀⢩⠉⠛⠙⢦⠠⠉⠻⣏⢠⣼
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠠⠀⠊⠁⠐⠄⠀⠠⠳⠄⠸⠿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠈⠻⣦⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡇⠈⠄⠀⣿⠀⠀⣿⠆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣰⣿⠀⠃⠀⠀⡠⠃⠀⠀⢿⡀⢀⢀⡤⣾⡃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠇⠀⠀⣠⠾⠉⠀⣠⠀⢀⠀⠀⡀⠀⠀⠀⠗⠀⠻⡇⠙⢧⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠀⠀⠀⠜⠁⢀⣀⡾⠇⠀⠀⠀⠀⣹⠆⠀⡔⢃⠀⠀⠈⠂⠈⠁⠀⢸⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⠁⠀⠀⠀⠁⠀⠔⠉⠀⠀⠀⠀⠀⠀⠄⠀⢀⣼⠁⠈⡀⠀⠀⠐⠀⠀⠀⠀⠡⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠉⠀⡰⠃⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡀⠀⢰⡀⠀⠈⠉⠉⠑⠒⠀⠀⠤⢄⣀⡀⢀⡠⠄⠀⠒⠀⠉⠉⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢐⣿⣿⣂⠀⣼⡅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣲⣿⣿⡷⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡗⠀⢠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠠⣽⣿⣿⣷⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⣸⣿⣿⣿⣅⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠚⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣼⣿⣿⣿⡶⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠚⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠠⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⠀⠸⢦⠥⡴⠁⢠⡆⢀
⠀⠀⠀⡀⠀⠀⠀⠠⠾⣖⣠⣐⡾⠆⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣡⠚⠤⣄⠌⡎⢅⡀⠜⢢⣁⣠
⠀⠀⠈⠂⠲⢢⣖⡐⢗⣁⣽⣄⣱⢗⣐⣤⠶⠀⠊⠀⠀⠀⣄⡈⠀⢥⠱⠄⢆⣓⠆⡴⢫⢅⠀⢀⡀
⠀⠀⠀⠀⠀⠈⢡⡧⢴⣟⠩⢙⣷⢤⡧⠁⠀⠀⠀⠀⠀⠠⠌⡗⡪⠥⢬⢱⠡⣷⢹⠸⡤⡭⡒⡏⠤⠄
⠀⠀⠀⡀⢀⡨⣗⢓⣼⠿⢶⠿⢯⣔⢶⡧⣀⠀⡀⠀⠀⠀⠔⠋⠁⣱⢈⡥⡁⡆⡋⣬⡐⡹⠈⠑⠤
⠀⠀⠐⠐⠁⠀⠈⠠⣍⣖⠲⢒⣎⡅⠈⠐⠀⠑⠈⠀⠀⠀⠰⠶⠲⣁⠯⣖⡄⡇⣔⡨⢅⣱⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠠⠎⠉⠀⠈⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣸⠀⢀⡼⠬⢆⠀⢸⡆⠑
⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣤⣀⠀⣦⠀⢹⠁⣠⡆⢀⣠⠄⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⠄⠀⡆⠀⢄⠀⢀⣤
⠀⠀⠀⠀⠀⠘⠱⣦⢰⠓⣈⠀⢳⢠⠶⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⢠⡸⠿⣸⢈⡰⠎
⠀⠀⠀⠀⠈⠻⢴⡒⡵⣯⠻⢻⠷⡔⡲⠜⠋⠀⠀⠀⠀⠀⠀⠐⠉⠠⣭⠔⡡⠨⡉⢨⡥⠄⠕
⠀⠀⠀⠂⠗⠒⢊⠘⡟⣂⠪⢂⡺⡧⡠⠒⠒⠗⠂⠀⠀⠐⠂⠒⠒⠿⣀⠨⡀⠒⡨⢠⡘⠟⠐⠂⠒
⠀⠀⠀⠀⠠⠾⠙⣒⢝⠧⣾⡮⢟⢕⡚⠱⠦⠀⠀⠀⠀⠀⠀⠐⠅⠊⣥⢐⡮⠈⣦⢠⣭⠃⠕
⠀⠀⠀⠀⠀⣰⣞⠋⣘⠎⢲⠈⢞⡈⢻⣶⡀⠀⠀⠀⠀⠀⠀⠀⡄⠟⢀⠊⠘⡟⠸⢠⠘⢳⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⢼⠄⠈⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⡃⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠋⠀⠸⣿⠆⠀⠀⢾⡿⠀⠈⢻⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⣀⣤⣤⡴⣄⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢸⡇⠀⠈⠉⠛⠛⠷⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⡟⠀⠀⠀⠀⢧⠀⠀⠐⠦⠤⣤⡤⠤⠖⠂⠀⢠⠇⠀⠀⠀⠘⡇⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠿⣧⡀⠀⠀⢰⡾⡷⢶⣦⣤⣤⣤⣤⣤⣶⣶⠶⠿⣶⠀⠀⠀⣠⡿⠷⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢸⣯⣭⣭⣭⣇⣀⣀⣀⣀⣮⣭⣭⣭⣿⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠋⣿⣰⣽⡇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿⢹⣼⡇⠀⢠⡶⣦⠀⠀⠀⠀⠀⠈⠁⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣿⣾⣿⡇⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣻⣻⡇⠀⢰⣏⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠉⠉⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠸⣧⡿⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠦⣄⣀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⠟⠁⠀⠀⠀⠀⢀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⢸⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⣠⠖⠀⠺⠁⠀⠀⢀⡀⠔⢂⠋⠀⠀⠀⠀⠀⢤⠀⠀⠀⣄⠀⠀⠀⣿⠀⣚⣡⣔⠲⠄
⢠⣦⠔⡧⢰⡄⠀⠀⠐⢚⡁⢦⠀⠀⠠⢤⡄⠠⠀⠔⠒⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣰⣿⣆⣙⡹⠿⣦⢤⡆⣠
⣿⢗⣍⣰⢾⣧⣤⡶⠂⡉⣰⠄⣁⡀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣸⡄⠀⢸⣼⠇⠠⡟⣱⠈⣹⣄⣤⠘⣇⡈⢻⣆
⣿⣋⢥⡼⡃⢽⣿⠟⣁⠀⣩⣀⡀⢷⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⣀⠀⣰⢿⠒⣀⣡⣌⠳⡄⢉⣠⡷⢤⢿⡏⠱⠄⠙⣷⣿
⠉⡱⢾⣅⣿⠞⠛⡡⠈⢋⣀⣈⡛⢦⣽⣾⣾⣦⣾⣴⣐⣿⣓⣶⣼⣶⡿⣿⣿⣿⡇⣤⢤⣻⡡⢦⣸⠔⠁⣈⠳⡌⢳⣿⡗⠣⣄⠈⣿
⢻⡆⢸⣇⣷⠾⠋⠙⢶⠋⠹⢶⣧⡈⠙⣿⣿⣿⣿⣿⠄⠹⠈⢿⣿⣿⣡⠻⣿⡿⠋⣱⣄⣈⢰⡄⢱⠒⣀⡸⣧⠛⠻⡿⠷⠀⠈⠙⢿
⠁⣼⡟⣿⣥⠔⠋⣸⠋⢠⠠⠋⠁⠙⠲⣽⣿⡟⣾⣗⠕⢱⣀⠞⣿⡫⠡⠒⢻⠇⠂⢈⣠⡈⠻⣷⡏⠉⢁⠀⠸⡗⠢⢽⡀⠈⠣⢀
⣾⣉⣿⣿⠁⠐⢚⡁⣠⠏⠠⡀⠘⢦⠀⡈⣹⢿⡋⠀⢘⠁⡏⠀⠈⡖⠀⠤⡋⢀⣠⡏⢨⣌⠙⢻⣿⠔⢻⡄⠀⡟⢦⣀⠹⣆⡄⠈⢻
⠈⢉⠟⠀⠀⣠⠤⠋⠉⠀⠀⠙⣆⣸⠟⠛⠚⠀⠓⠐⠈⠛⠓⠂⠀⠈⠀⠀⠈⠀⠀⠁⠁⠀⠛⣋⠄⠀⢈⠙⠚⠁⠀⠈⠙⢿⣅⢀⣀
⠀⠀⠀⠀⠈⠀⠀⠀⠙⠂⠀⠀⠈⠛⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠰⠛⠲⠤⠀⠰⠤⠧⠄⠹⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⢠⠀⠠⠀⠀⠀⠀⠐⢤⣘⣀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢋⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣈⣰⢧⡀⠀⠀⠀⠀⠙⡃⠀⠀⠀⡆⢀⡼⢔⣈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠿⠦⣀⠤⠚⠁⢄⡀⠴⠛⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠛⠢⣄⡠⠔⠓⠤⣤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠲⡖⠋⢹⠀⠀⠀⢠⡀⠀⠀⠀⠃⠉⢲⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣂⡸⠁⠀⠁⠀⠀⠀⠀⠀⠉⡟⠢⡀⠀⠀⠀⠈⠆⠀⠋⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠔⠁
⠈⠻⡀⠢⡀⠰⡀⠀⠀⠀⠀⠀⣀⣁⠀⠀⠀⠀⠀⠀⡄⠀⡐⢂⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡛⢲⠀⠀⠀⠀⠀⠀⠐⢄⣸⣀⠔⠀⠀⠀⠀⢠⠀⢀⠖⣻⠟
⠀⠀⠀⠀⢉⣲⣧⠀⠠⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⣸⣷⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣸⣧⡀⠁⠀⠀⠀⠙⠁⠀⠀⠀⡆⣀⣼⣄⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠢⣄⡠⠄⠁⠤⣀⠴⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠭⠾⠄⠀⠀⠘⠂⢄⡀⠘⠿⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠚⠢⢄⣠⠴⠛⠦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢢⣤⠄⠚⠢⣄⡠⠖⠃⢤⣤⠒⠂
⠀⠀⠀⠀⢐⣲⡶⠀⠠⠀⠀⠀⢀⡇⠀⠀⠀⠁⠀⢲⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡖⠋⡹⠀⠀⠀⢈⡀⠀⠀⠀⡎⠙⢶⠂⠈
⠀⣠⠂⠡⠋⠠⠁⠀⠀⠀⠀⠀⠊⠋⠀⠀⠀⠀⠀⠀⠃⠉⢋⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⡹⠀⠘⠀⠀⠁⠀⢀⠔⢹⠛⠦⠀⠀⠀⠀⠘⠀⠐⣍⣙⣄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃
⣶⣶⣶⠶⡶⢶⢶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠛⠛⠻⠿⢶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⠦⢤⣼⡿⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠟⠛⠛⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⣠⣴⠞⠋⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿
⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣿
⠀⠀⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⡟
⠀⠀⠹⣷⣁⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠄⠀⢈⣴⡟
⠀⠀⠀⠙⢿⣦⣁⡂⠀⠀⡀⠄⠀⢀⣀⣠⡾⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣉⡀⠂⠥⣑⢂⣡⣶⠿⠋
⠀⠀⠀⠀⠀⠈⠛⠻⠿⢶⣶⣶⠶⠿⠛⠯⣅⣂⢐⠠⠀⠄⠀⠀⠀⡀⡀⠰⠐⢜⣿⣯⣐⡀⡀⠀⠀⠀⠀⠀⢀⢀⢠⣼⠟⠁⠉⠙⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠾⠶⣷⣷⣷⠶⠶⠟⠛⠉⠀⠉⠛⠷⢾⣦⣵⣤⣬⣬⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠂⢀⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠄⠀⠀⢢⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠀⠀⡀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠄⢠⠠⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠃⣀⠀⠐⢀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⡀⡀⠂⠀⣀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠑⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢐⠀⠂⠁⢁⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢀⠐⠁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠃⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠌⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⡀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠌⠀⢁⠀⠂⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡠⠁⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠅⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠠⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠂⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠤⣄⡀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣰⠉⠉⠓⠲⢤⣱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⡀⠀⠀⠀⢢⠀⠘⢶⡖⠢⢄⣀⠀⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⣰⢿⣦⣠⠤⠬⣃⣀⡜⠀⣔⣉⡴⠷⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣈⣳⠦⠤⠬⣿⡆⠀⠀⠀⣀⠝⠀⢰⣷⣏⣀⣀
⠀⠀⠀⠀⡜⣱⠋⣠⠶⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⠠⡤⠈⠓⠒⠒⠉⠁⠀⠀⡷⢋⣡⡤⡌⢳⠀⡇⢸
⠀⠀⠀⠀⠀⡇⢸⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⢀⡴⠋⠠⢁⠃
⠀⠀⠀⠀⠀⠉⠀⠑⠦⣥⣈⣁⣈⣀⣤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⡆⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡆⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠁⠇⠀⣀⠤⠒⠊⣿⠫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⢹⠛⢲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡠⠖⣉⠀⠄⢀⣀⣸⡯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⡰⠧⠤⢄⣀⣙⣢⣾⣠⣏⣙⣆⣀⣀⣠⣤⠤⠤⠤⠞⣆⠿⢋⡀⠒⠒⠢⢄⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⢙⡇⠠⡄⡈⠑⣄⢀⣴⠿⣦
⠀⠀⠀⠀⡰⢃⠖⣠⠞⣁⣸⠧⠤⠿⠭⠭⠭⠭⢉⣉⡉⢉⡩⠟⠉⠀⠀⠀⣠⠞⡇⠰⠁⠇⠀⠘⢟⠗⠕⠀⠁
⠀⠀⠀⠀⠃⣏⢰⡁⢊⡔⠀⣀⣀⣠⣤⠤⠶⠒⠒⣲⡞⠋⠀⠀⠀⠀⣠⠞⠁⠀⢿⠀⠀⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡏⠉⢹⠀⠈⠓⠦⣀⣰⠁⡇⠀⢀⣠⠴⠋⠁⠀⠀⠀⢸⡀⢰⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠆⡼⣸⠀⠀⢸⠀⠀⠀⠀⠈⠙⠲⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⣜⠀⢇⠻⣄⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠇⢘⡇⢳
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⡿⠿⢷⡶⠒⠒⠒⠒⠲⣶⡶⠶⣶⠟⠋⠉⠉⠁⠀⠈⠉⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠓⠤⢾⠀⠀⠀⠀⠀⠀⣧⡤⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣚⠭⠿⠀⢯⠀⠀⠀⢀⣔⠾⣕⡶⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠁⠀⠀⠛⠒⠩⠥⠤⠬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠰⠀⠀⠐⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡶⠀⠀⠀⠀⠀⠉⡙⠐⠋⠀⠀⠀⠀⠠⠈⢄⡜⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠄⠐⢛⠘⠟⣾⠀⠀⠀⠀⠀⠐⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⠻⡉⠀⠀⢀⠔⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠋⢣⠀⠠⠎⠔⠂⡠⠆⠁⠄⠀⠀⠀⠀⠀⣁⣩⡁
⠀⠀⠀⠀⣠⣀⣠⠀⣤⠤⣤⠄⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠛⠚⠒⢥⣤⣠⣀⡀
⠀⠀⠀⠀⡮⠤⢬⡦⠶⠢⠤⠤⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⢣⣤⠠⣤⡀
⠀⠀⠀⠠⠴⠤⠴⡖⠰⠴⠄⠲⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⣈⣉⢁⡉⠑⢢⡐⠀⠈
⠀⠀⠀⠐⠒⠒⠶⠦⣄⢤⡠⢴⡔⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⡀⠁⠉⢐⡇
⠀⠀⠀⠈⢐⡇⠂⠂⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠈⠃⠀⠀⢐⠂
⠀⠀⠀⠀⢈⡁⠀⠀⠠⠜⠆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢻⡇⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⡇⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣹⣿⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣿⠀⠀⠀⣷⠀⠀⣦⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⣶⠀⠀⢀⣿⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣨⣿⣿⡀⠀⢠⣿⠀⠀⠈⠳⡄⠀⡇⠀⢀⣰⠟⠀⠀⣿⡇⠀⠀⣿⠀⢀⣼⠿⠷⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠻⣄⢸⡇⠀⠀⠀⠀⠙⣦⣧⡴⠋⠀⠀⠀⠀⢻⡇⠀⠀⣿⣴⣟⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠴⠶⠾⢿⣇⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⣾⠃⣀⡴⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣾⣯⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢸⡇⠀⠀⠀⢀⣠⠞⠁⠀⠀⠉⠉⠉⢙⣧
⠀⠀⠀⠀⠀⠲⣦⡀⠀⠳⣄⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣸⡇⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⣠⣴⠖⠀⠀⠀⣠⡴⠆
⠀⠀⢀⣤⣠⣤⣼⣿⣦⣤⣼⣷⣤⣤⣤⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣥⣶⣏⣥⣤⣄⣀⣀⣠⣤⣾⣟⣁⣀⣠⣴⣿⣁⣀⣀⣠⣞⣉⣀⣀⣀⣀⡀
⠀⠀⠈⠉⠉⢉⣼⠟⠁⠀⣠⡾⠃⠀⣠⡿⠋⠀⠈⠉⠉⠉⠉⠉⢉⣥⢿⡟⢧⡀⠀⠀⠀⠀⠈⠉⠙⠻⣍⠉⠀⠙⠿⣍⠉⠉⠉⠻⣯⡉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠠⡾⠋⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢸⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠻⣦⡀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⡀⠀⣀⣀⣀⣀⡴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⠿⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠙⣶⡶⠶⠶⠦⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠶⣶⣾⠋⠀⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢉⡏⠀⢀⡇⠀⠀⠀⠀⣀⣼⣧⡀⠀⠀⠀⠀⠀⣿⠀⠈⠻⣷⡒⠲⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢿⣿⡿⠁⠀⢸⠇⠀⠘⠗⠀⠀⣠⡾⠛⢹⡇⠙⠶⣄⡀⠀⠀⢻⠀⠀⢀⡏⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡇⠀⠀⢸⠀⠀⠀⠀⠀⠸⠏⠀⢀⣼⣧⡀⠀⠀⠙⠃⠀⠀⠀⠀⢸⡇⠀⠘⣿⣟⠛⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⡟⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣏⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⣇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣿⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣿⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠐⡀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠠⠊⠱⡁⠂⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠤⠶⠦⠚⠒⠲⠶⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠢⠀⠀⣁⡤⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠚⠉⠀⠀⠀⠀⣀⣀⡤⠤⠤⠖⠒⠒⠚⠉⠉⠉⠻⡒⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⣠⠤⠒⠊⠩⠥⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢱⡀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣤⠚⠉⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢰⣖⠄⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠸⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡓⠦⠤⣀⣀⣀⡀⣀⣀⣀⡠⠤⠖⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠈⠳⢤⣀⣀⡉⠉⡁⢀⣀⣀⠤⠲⡅⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⡼⢩⣏⡏⠉⠉⠁⠀⠀⠀⠘⡄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⠀⡼⠀⡾⠰⡇⠠⠈⠀⠀⠀⠀⠀⢹⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢸⢠⡇⠀⣧⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠤⠋⢸⣠⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠉⠈⠙⠢⡀⠀⠀⢀⣀⠎⠁⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣄⣀⣀⡤⠏⠉⠉⠉⠙⠦⣤⣀⣠⠤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⣀⠀⠀⢀⣀⣀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠈⠁⠀⠁⠀⠀⠈⠉⠀⣀⣿⣿⣿⣿⡿⠋⠁⠈⢮⠩⠁⠀⠃⠉⠙⠗⠒⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠀⠀⣀⠁⢀⣁⣀⣤⣤⠤⠤
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣯⣽⣠⣖⣀⠀⠀⠀⠀⠀⡄
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠳⢄⢠⣄⡀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠉⠙⢷⡄⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢰⢦⣄⢒⠟⠁⠀⡐⠋⢤⣭⡓⣦⡄⠀⠐⠀⠂⢀⣀⠀⢀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⣸⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⢯⠀⣤⣊⠀⢀⡴⠛⠛⢿⡆⡀⠀⠀⠀⠚⣿⠾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢃⣿⣿
⠀⠀⠀⠀⠀⠀⠠⠲⠻⠁⠀⠙⢵⣿⣧⣎⡀⠀⠠⠊⠀⠀⠀⠀⡀⠌⢱⡄⠀⠉⢓⠤⣀⠀⠀⠀⢀⣼⣿⣷⣿⡿⠁⣠⡆
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢻⡼⣽⠛⠂⠀⠀⠀⠀⠀⠈⠂⣀⢹⣶⣦⣤⣽⣮⣽⣶⣦⡟⠛⣿⣿⠟⡑⣨⣻⠟
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠐⣀⣠⣴⡿⣿⣿⣛⡏⡁⠘⠁⠁⠉⠁⠁⠈⠐⠒⣠⣴⣿⡯⠊⣬
⠀⠠⡀⠀⠀⠀⢀⣀⡀⢀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣿⣶⣿⣿⣿⣿⠿⡿⣶⠤⠂⠒⠒⠺⠟⠛⠛⢯⠵⠛⠠⡚⠁
⠀⣴⣄⣄⠢⠀⠀⠀⠈⠁⠀⠀⠉⠉⠸⠿⣿⣿⡿⠿⠊⢉⠀⠉⠹⡦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡦⠖⠁⡀⢀⡔⢠
⠀⢈⠻⣿⣶⠤⠀⠤⣀⠀⠀⠀⠀⠀⠐⠈⠉⠈⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠋⠁⣠⠆⣪⡀⡊⠄
⠀⠀⠁⠉⣭⣷⣶⣄⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠴⠛⠉⠀⢀⣠⣶⣦⠀⢿⡛⠀⠙⠒
⠀⠀⠀⠀⠨⠙⠛⠿⢿⣇⣄⣴⣏⣿⡇⠀⢈⣦⠀⣀⠀⠀⠀⠀⢒⡂⢠⣴⣾⣷⠶⣿⣷⡤⣿⣿⣿⣿⠗⠀⣝⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠥⠀⠀⠛⠁⢲⣿⡝⠻⢿⡖⠿⡿⠿⢿⣿⠿⠻⢿⣿⠿⠉⠉⠉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⣷⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⢰⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣴⣶⡵⠂⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠻⣿⣿⣿⡧⣄⡠⣤⣷⣶⣃⡀⠀⠀⠀⠀⣠⣴⣿⣧⣾⡆⣿⣿⣆⢈⡁⠀⠀⠀⠀⣼⣷⣿⣶⣶⣿⣿⠇
⠀⠀⠀⠀⠈⠉⠁⠀⢳⣽⡛⠛⠛⢡⡳⣶⣿⣿⣿⣿⣿⣿⣿⡿⢁⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⠟⠟⠋⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⣿⡿⢿⣮⣛⣿⣿⣿⣿⡿⠋⠀⢹⡛⠿⠛⠛⠁⠉⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠧⠀⠀⠻⡄⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠉⠉⠁⢠⣷⣴⣄⠀⠹⡄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⣟⠛⠓⠀⣘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣴⠂⠀⠀⠀⠀⠀⠀⠓⠀⠀⣤⠖⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡾⣟⡿⠈⠁⠉⠀⣄⡀⠀⡀⠀⠀⠀⠀⣻⡏⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⡄⣺⣟⢿⣷⣿⢿⠇⠀⠄⢀⣼⣭⠏⠂⠐⢲⢦⣠⠐⠟⠀⠀⠀⢰⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⢗⠉⡵⢋⡙⠡⠼⠉⠀⠘⣾⣿⠇⠈⠀⠀⢄⢣⠈⠢⠀⠀⠀⢐⣿⣿⡆⣀⢀
⠀⠀⠀⣼⣀⣿⣇⣿⣸⣷⣴⣦⣴⢀⢘⣥⡎⢃⠀⣆⣀⢩⡈⡳⢴⠦⢀⡠⣬⣹⠋⣼⢛⡋⡗⢸⣆⣿⣠⣆
⠀⠀⢰⣿⣿⠛⢿⣿⣿⣿⡿⢿⣿⣿⢿⣿⣿⣾⣷⣿⣿⣾⣿⣷⡷⠼⣾⣧⣿⣿⠆⣿⡾⢿⣿⣿⣿⡿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣯⣭⣭⣭⣭⣤⣶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⠿⠿⠛⠻⠭⠽⠯⠭⠟⠓⠀⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣠⣴⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠿⣦⠀⠀⠀⠀⠀⢰⠟⠛⠣⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⢀⣿⠀⠀⠀⠀⠀⢹⣆⣀⣰⠿⡄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣟⢙⡛⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣷⠀⠀⠀⠸⡀
⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣠⠼⠿⠿⠟⠛⢀⡄⠀⠀⠃⢀⣤
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠋⠀⠀⢀⠋⢀⣶⣠⣇⢀⣀⣀⣶⣴⣷⣶⡶⠟⢻⠏⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⣿⢿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠰⡃
⠀⠀⠈⠛⠛⠛⠛⠋⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⡶⠟⠟⠋⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃⢰⠉⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢣⡀⠀⠀⠀⠀⠙⠛⠷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠟⠋⠀⣠⠏⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⡶⠖⠶⠶⠶⢶⡶⠾⠿⠟⠛⠛⠉⠁⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣦⣤⣄⣀⣠⠀⠀⠀⠀⠀⣯⣤⣤⣤⣶⣶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⣿⠉⠁⢸⣿⣷⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⢸⡿⠿⡿⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡜⠀⠀⠀⠀⠀⢻⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⢰⡶⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⢸⡇⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠈⣇⠰⣿⣿⣷⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⣀⣴⢾⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠙⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⡇⠀⠀⠀⠀⠀⠸⣧⠀⠀⢻⠀⠙⠛⠋⠀⠀⠀⠀⠉⠛⠒⠶⠶⠚⠛⠋⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠉⠛⠛⠻⠶⠶⠶⠶⠞⠛⠉⠀⣿⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠸⣄⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⣴⢿⣿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣿⣧⣽⡾⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⠶⠶⠶⠿⢛⣋⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣀⣀⠀⠀⠀⠀⠀⠈⠻⠟⠿⠟⠿⠟⠛⠛⠁⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⠞⠛⠛⠋⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⡙⣿⠛⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠘⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠌⠒⠒⠒⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣌⢸⡇⢀⣀⠠⠤⠐⠒⠒⠒⠒⠲⠤⢤⣀⠀⣿⡆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣃⡼⠛⠉⠀⠀⢀⣠⠀⠁⠀⠀⠀⢀⣀⠈⠙⢻⣅⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠤⠿⣄⡀⠀⠀⠀⢋⠄⠒⠒⢄⡀⠒⠒⠠⡹⠀⠀⢸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⢤⡀⠀⠀⠀⡞⠀⠀⠀⠈⠷⠤⠘⠐⠁⠀⣤⡀⠀⠀⣠⣄⠀⠐⠰⡦⠏⠻⡀
⣦⣄⡀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠉⠢⡀⢀⡇⠀⠀⠀⠀⡼⠀⠀⠀⠐⢀⠉⢀⠀⠃⠚⢅⡠⠂⠀⠀⠄⠀⡇
⢹⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠙⠦⣀⣠⡴⠧⠙⠢⠄⠀⢀⣀⡀⠀⠀⠀⠀⣇⣠⡴⢦⡀⢀⠇
⢸⡆⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⢛⠛⠛⢿⡀⠀⣀⠤⢾⠁⠀⠀⠐⠠⠀⡈⠙⠻⠶⠶⠖⠊⠀⡀⠠⠀⣻⠁
⠀⣇⠀⣀⡠⣶⡿⠛⠁⡠⠀⠀⠀⠀⠀⣠⠝⠋⠀⠀⣸⣇⠠⠀⡀⠀⠀⠀⠈⠉⠁⠈⠉⠁⢀⠠⠐⠈⣸⠳⢤⡀
⠀⠉⠁⠀⠀⠘⡆⡠⠊⠀⠀⠀⢀⡤⠊⠁⠀⠀⢀⡾⠁⠈⠲⣄⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢧⡀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣠⠞⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⡖⠒⠲⠒⠚⠉⠉⠀⠀⠈⣷⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠶⣿⣷⣄⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣠⡾⠓⠤⣀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⠙⠻⠿⠿⢷⡚⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⣤⣶⠿⠋⠀⠀⠀⠀⠙⢦
⠀⠀⠀⢠⡇⠀⠀⠀⢀⣠⠶⣦⠀⠀⠀⣿⣷⡈⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠋⣷⡞⠉⠀⠀⡶⢤⣀
⠀⠀⠀⠀⠓⠶⠶⠖⠋⠀⠀⢻⡀⢀⣠⠇⠈⢳⣦⣀⡀⠀⠀⠉⠙⠛⠲⠲⠶⠶⠶⠶⠶⠶⠒⠛⠉⠉⠀⠀⣰⠟⢧⠀⠀⢀⡇⠀⠈⠓⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⡇⠈⠙⠲⠦⣤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠚⠋⡇⠀⠈⠙⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠙⡓⠒⠈⠉⠉⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣰⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠓⠄⠀⠀⠀⠀⠀⠀⠀⠠⢳⠆⠀⠀⠀⠀⠠⠞⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠆⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠠⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡘⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠒⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣁⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠃⠂⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠨⠈⠏⠙⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⠀⣀⢌⣳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣀⠴⡁⠈⠀⠠⢗⠎⠱⣄⢀⡤⠤⠔⠒⠦⢴⣁⠀⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠳⣤⡀⠀⠀⠈⢉⣹⡃⠀⠀⠠⡈⠄⡀⢌⠋⠀⠀⠀⢀⠀⢴⠖⠈⣠⢙⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠂⠀⠈⠻⣅⣀⠠⠶⢭⡤⠃⢀⡠⠒⣐⠖⠀⣤⠀⢀⡐⠀⠁⠈⠐⡀⠀⠠⡌⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⡅⠂⠀⠈⠁⢶⣉⣠⡖⠋⠀⠀⣀⣀⣐⢁⠀⠀⣈⠳⢼⣅⡀⠀⢀⣰⠇⠀⢀⡈⠯⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⡴⠀⠀⠀⠰⠉⠁⠀⠡⠐⠂⢄⠀⡈⠙⡁⣀⡀⠈⠁⣻⣾⣉⣉⡅⣬⢧⣀⡄⠀⡒⢶⡏⠤⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠁⡇⡠⠊⠀⠀⠄⢀⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣇⠀⠀⢄
⠀⠀⠀⠀⠠⠒⠀⠀⠀⢂⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⢺⠀⠄⠁⠬⡅⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢹⢰⡂
⠀⠀⠀⠀⠀⠈⣒⠀⠀⠀⢣⠠⠤⠤⠤⠐⠰⠂⠀⠚⠀⠀⠀⢂⡄⠀⠀⠀⠀⠀⠀⢀⣀⡤⡖⠁⠀⠀⠀⢜⡚⠈⠁⠁
⠀⠀⠀⢀⠀⠀⠑⣄⠀⠐⠀⠀⠀⠃⠀⠀⠐⡀⠀⠀⠀⠀⠏⣀⠀⡀⠉⠤⠀⠀⢠⠏⠀⠀⠛⡄⠀⠀⠈⠀⠈⠠
⠀⠀⠀⡆⢀⠐⢄⡤⠤⠀⠀⠀⠀⠰⠰⠀⠀⠀⠢⢄⣀⠤⣄⠁⡩⠈⠓⠈⠀⣠⠃⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢲⠀⢰⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⠉⠀⣠⣀⠠⠚⠁⠀⠀⠀⢰⠀⠀⠀⠠⡀⠀⠀⢀⠃⠀⠀⠀⡀
⠀⠀⢀⣀⠀⠀⠀⠀⠠⢸⣀⠜⠂⢒⣀⡀⣀⣀⣸⣀⠐⠒⠻⣚⠿⠍⠀⠀⠐⠀⢀⢂⣀⣈⢅⠐⢲⢴⡹⠡⣄⣀⡁⡱
⠀⠀⠀⠂⠐⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈