Curved arrows Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⠀⣤⣤⣤⣀⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⣠⣤⣄⠀⠀⣴⣶⣆⢠⣶⠶⠿⠿⠟⠛⣿⡿⠋⠀⠀⠀⠀⠈⠉⢉⣽⡿⠿⠀⠀⣀⣤⣤⣄⣀⣀⣀⣀⣀⣬⣽⣿⡿⠋
⠀⠀⢀⣼⠏⠀⢻⣄⣾⠏⠀⠻⡿⠃⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠉⠉⠛⠛⠛⠋⠉⢽⡟⠁
⠀⠀⠾⠁⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⣀⣤⡴⠶⠶⠒⠆
⠀⠀⠀⠀⠀⠀⠀⣤⡾⠟⠛⠉⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⣸⣿⡾⢋⣁⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣴⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣾⢏⡀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⢰⣿⣿⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡀⠀⣀⣀⠀⠉⠙⠿⣶⡀
⠀⠀⠀⠀⢶⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠘⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠛⠛⠉⠛⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠙⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⣀⣀⠀⠀⠀⠀⠉⠛⠳⢶⣤⡀⠀⠀⠀⢿⡄⠀⣿⠀⢀⡀⠀⠹⣧⣄⣀⣀⣀⣀⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠴⡶⠶⠶⠾⠿⠿⢿⣿⡿⠋⠀⠀⠀⣠⠴⠶⠶⠶⠞⠁⠀⠀⢿⣼⡇⠀⣿⣠⡿⠃⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠋⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⣹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⢀⠀⠀⣀⣤⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⢀⣾⢿⣦⡀⣼⣿⣦⢀⣼⢿⣆⣰⡿⣷⡄⢉⣿⠟⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⢷⣄⠀⣰⡟⠀⠀⠀⠀⣀⣰⣶⣤⡀
⠀⠀⠀⠀⢠⡾⠁⠀⠙⢿⠟⠀⠻⡿⠋⠀⠻⠟⠁⠘⢿⡿⠁⠀⠙⠁⠀⠀⠀⠀⠀⠀⠿⠈⣿⡄⠉⣰⡟⠀⠀⠀⠀⣾⣛⠉⢹⡿⠁
⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣷⣰⡿⠁⠀⠀⠀⠀⢈⣛⣻⣷⣄
⠀⠀⠀⠀⣾⠿⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠷⣦⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⢻⡿⠁⠀⠀⠀⢰⣿⠛⠛⠉⠉⠉⠁
⠀⢰⡀⠀⠈⠳⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣶⣤⡀
⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⢾⣿⣥⣀⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣌⡉⠉⠉
⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠈⢉⣻⡆⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡶⠿⠿⠿⠗
⠀⠀⠀⠀⠙⢦⣀⠀⠘⣆⠀⠀⠸⡇⠀⠀⠀⣾⣵⡾⠟⠋⠀⠀⠀⠀⠀⠙⠷⣦⣤⣤⣤⣽⣿⣿⡷⠀⠀⠀⠈⠛⠿⢶⡄
⠀⠀⠀⠀⠀⠀⢉⣿⣶⣼⣷⡄⠀⠀⠀⠀⠈⠛⠛⠛⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠿⠋⠀⠀⠀⠀⠒⠒⠚⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⢀⡴⠋⠉⠉⠛⣦⣠⠀⠀⢀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠀⠀⢀⡴⠞⠛⠻⠿⠗⠀⠀⠀⠀⠀⣀⣤⣼⣦⣄
⠀⣾⠀⠀⠀⠀⠈⠻⠿⠀⠀⠈⠓⠲⠤⠴⠖⠋⠹⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠉⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⡤⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠰⢻⠿⠄⠀⠀⠀⢀⡞⠀⠀⢸⡆⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⣾⣇⠀⠀⠀⠀⠀⠀⠰⢿⠛⠂
⠀⠀⠀⠀⢀⣰⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⢦⣧⡄⠀⠀⠀⠘⠦⣄⣀⣠⡴⠋⠈⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣤⢤⣼⣄⠀⠀⠀⠀⠈⠑⢦⡀⢀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠠⢴⣾⠁⠀⠀⠀⠀⠀⢀⣼⣧
⠀⣀⣠⠴⠋⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠠⣿⣾⠀⠀⠀⠀⠈⠳⢤⣄⣤⠴⠋⠘⠀⠀⠀⣀⣀⣤⠽⠟⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠺⢿⡷⠶⠦⣤⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⢿⡀
⠀⠀⠀⠀⠀⠐⢾⣷⠂⠀⠀⠀⠀⠀⠁⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⠛⠲⠮⣷⡦⠀⠀⣀⡀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁







⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⢀⣿⣿⡿⠂⠀⠀⠀⣀⣤⣶⣾⣿⣷⡤⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⡀
⠀⠀⢻⣿⣿⠀⠀⠀⠀⣴⣿⠟⠻⠁⠀⠀⢀⣼⣿⠟⠉⠙⠋⠁⠀⠀⠀⣴⣿⠟⠉⠉⠉⠙⢿⣿⣦⡄
⠀⠀⣿⡿⠈⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠘⠿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠉⠀⠈⠉⠙⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⣠
⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿
⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣿⣿⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠉⠃⠀⠀⠀⠘⢷⣄
⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣤⣤⣤⣤⣄⣀⣀⣠⣽⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⢻⣿⣿⠟⠋
⠀⠠⠤⢤⣤⣤⣤⠶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠉⠉⠉⠉⠙⠛⠻⢿⣿⣿⣷⣦⣤⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠉⠉⠉⠛⠻⢿⣷⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣷⣶⣄⠀⡄
⠀⠀⢀⡀⠀⣀⣀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠉⠉⠉⠙⠻⣿⣿⣿⣷
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣼⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⣦⣄⣀
⠀⠠⣀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⡉⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠈⠙⠓⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⢿⣿⣿⣷⣶⣶⣶⡿⠟⠁

⠀⠀⣠⡀⠀⠀⠀⢠⣀⠀⠀⣀⣄⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⣤⣴⣶⣄⡀
⠀⠈⠿⢿⡆⠀⣴⡿⠟⠀⠈⠙⠛⠳⣄⠀⣠⠞⠛⠋⠁⠀⠀⠀⠀⠈⠀⠠⠒⠋⠉⠀⡠⠞⠛⠉⠙⠋⢀⣴⠿⠟⠛⠛⠻⡿⠛⠉
⠀⠀⠀⠀⢿⠠⡏⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢾⠁
⠀⠀⣠⡀⠀⠀⠀⣀⡄⠀⠀⢠⣤⣀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠈⠙⡆⠀⡼⠉⠀⠀⠀⠀⠀⠈⠣⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣷⣶⣶⣾⠿⠋⠀⢴⣦⡤⠶⠞⠁⠀⠤⠴⠒⠁⠀⠄
⠀⠀⠘⠂⠀⠀⠀⠚⠀⠀⠀⠀⠓⠂⠀⠀⠀⠔⠚⠀⠀⠀⠀⠈⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⣼⡿⠀⠀⠀⢀
⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢰⡯⠀⠀⠀⣤⡀⠈⢿⠏⠀⠀⠠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠈⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠐⠒⠋⠀⠀⠀⠀⠉⠛⠛⠉
⠀⠀⣠⠖⠲⣆⠀⠀⠀⠔⠒⠠⠀⠀⠀⠀⠐⢦⡀⠀⠀⡰⠖⠲⣄⠀⠀⡠⠒⠢⡄⠀⢀⡴⠶⣤⠀⠀⣠⠖⠲⡄⠀⠀⡀⠀⠲⣦
⠀⠀⢻⣀⠀⠙⠁⠀⠘⡀⠀⢘⠃⠀⠘⣇⠀⠘⠃⠀⠈⢧⣀⣠⡟⠀⠀⢄⠀⢀⠄⠀⠸⡀⠀⠈⠀⠀⢿⣀⣀⡶⠀⠀⢻⣀⣀⡼

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⡷⠖⠀⠀⠀⠀⣠⡾⠛⠉⠁⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣦⣄⠀⠀⠀⠀⠀⠴⠋⠉⠉⠛⠃
⠀⠀⠀⠀⣰⠋⠀⠈⠁⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣷⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡟⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⢳⣀⠀⢀
⠀⠀⠀⠀⠀⠱⣄⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠓⠀⠀⠀⠙⢷⣄⣀⣀⠀⡠⠏⠀⠀⠀⠀⠀⠙⠻⢾⣿⡶⠤
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢤⣶⣾⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠛⠛⠛⢦
⠀⠀⠀⠀⠀⠀⠈⠙⠈⠙⢳⡀⠀⠀⠀⠀⣠⡶⠋⠉⠉⠠⣄⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⣰⣿⡀⠀⠀⠀⠀⢸⣧⠀⠀⣼⣿⢦⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⠆⠁⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⣸⡿⠀⠀⠀⢻⣆⠀⠀⠀⠀⡰⠋⠀⠀⠀⢀⣤⣶⣿⣴⠞⠃
⠀⠀⠀⠀⠀⠛⠛⠟⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠓⠲⠖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⣤⣀⣴⠾⠛⠛⠛⠷⣦⡀⠀⠀⠀⠀⠀⠀⠻⠏⢿⡄⠀⠀⠀⠀⢀⣾⠋⠟⠁
⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⣙⣿⠿⣧⠀⠀⠀⠀⢹⣿⡿⠃⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀



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

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠰⡄⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⠫⠀⠀⠈⠀⠁⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠐⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠂⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠙⠒⠒⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⡀⠀⠀⢀⣀⠀⠀⢀⡄⡤⣄⣠⡀⠀⢠⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢀⠠⠶⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠴⠃⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠢⠀⠀⠰
⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠊⠉⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣄⡀⠀⠀⠀⣀⣤⡦⣤⡀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⣠⣾⣿⡿⠃⠀⢰⡟⠁⠀⢀⠇⠐⠻⢿⢿⣦⠀⠀⠀⠀⣾⣿⠀⠀⠀⣠⣠⣿⡇⠀⢀⡴⠛⠛⠋
⠀⠀⡟⠁⠈⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⢠⣀⣠⡿⠀⠐⠶⠾⠟⠁⠀⠀⠰⠿⢿⠉⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⣀⣀
⠀⢸⣷⣆⠀⠀⠀⠀⠀⣠⣤⣾⠿⠀⠘⣦⣤⣀⠀⠀⢠⣿⠛⣿⣷⠆⠀⠀⢀⣰⣿⡇⠀⠹⠛⠛⠛⢹⠇
⠀⠀⠈⠛⠛⠒⠂⠀⠀⢹⠉⠁⠀⠀⠀⠀⠹⢿⡟⠀⠈⢿⡀⠀⠉⠀⠀⣼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠏
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠉⢳⣦⠀⠀⣸⠋⠙⠛⠿⠂⠀⣠⣶⣷⠄⠀⠀⣠⣤⣼⣶⡄⠀⣴⣦⡀⠀⠀⠀⢶⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣿⣇⠀⡏⠀⠀⠀⠀⠀⠰⣟⠀⠀⠀⠀⢸⠋⠉⠘⠁⠀⠀⢹⣿⡶⠋⠁⠀⠀⠉⠀⠈⢻
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠿⠛⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠈⠻⣿⠀⠀⠀⣠⣴⣿⣿⠿⠛⠉⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠎⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠎⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣀⣤⡶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠃⠀⢀⣠⠴⠚⠋⠁
⠀⠀⠀⠀⡠⠖⠉

⠀⠀⠀⠀⠀⣀⣀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀
⠀⠀⣠⣶⠿⠟⠛⣿⠿⠓⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⣿⠟⠂
⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠘⠋⠉⠉⠀⠀⠀⠀⠀⣾⣿⠟⠛⠉⠹⠟⠁⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠈
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⢀⣤⣶⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣿⡿⠋⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣦⡄
⠀⢀⣼⠿⠛⢉⡿⠟⠋⠁⠀⠀⠀⠀⠀⢀⡿⠋⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠋⠀⠀⠀⠀⠀⢰⡿⠛⠉⠩⠟⠋⠁
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠈⠉⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠉⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣀⣴
⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⡏
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢿⣿⣿⣿⡇⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠛⠇⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣤⣄⣀⣀⣀⣀⣸⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠤⠶⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣄⡀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣷⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠛⠛⠛⠿⢿⣶⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⠀⡀
⠀⠀⠀⠀⡀⠀⠀⣀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢠⡾⠟⠛⠉⠙⠛⢿⣿⣷⣷
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣤⡄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠐⠤⣄⣀⣤⣴⠿⠛⠉⠁⠀⠀⠀⠉⠉⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⣿⣷⣤⣀⣀⣀⣠⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⠛⠿⠿⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣹⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣠⡼⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠴⠌⠓⠉⠀⠁⠙⠰⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠁⠉⠀⠚⢄⡐⢎⠉⡉⢽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠁⢠⣤⣼⣿⣿⣿⣿⣧⣠⢠⠤⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠤⣹⣿⣿⣿
⠀⠀⠀⠀⠀⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠀⠀⠀⠀⣿⣿⣿⣿⡅⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠄⡹⣿⡿⠋
⠀⠀⠀⠀⠀⢤⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡅⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠡⠄⠟⠉⣠⣾
⠀⠀⠀⠀⠀⠀⠠⣼⠀⡀⠀⠀⠀⠀⠀⠤⢤⠆⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⠈⠛⣿⣿⣿⣿⣿⣿⣿⠿⠀⢀⢠⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⣳⠤⢉⡷⠂⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⢋⣴⣀⠀⠉⠛⠙⠛⠋⠉⢀⣄⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣥⣴⣿⣿⣿⣿⣷⣶⣤⣾⣔⣳⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢟⠿⣟⠻⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠐⠒⠺⠗⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠨⠷

⠀⠀⠀⠀⠀⢰⠠⠀⠀⠀⠀⠀⠤⠤⢶⠦⠀⠀⠀⠳⠤⠤⠤⢼⡦⠀⠀⠀⠤⠤⠤⠤⢾⠆⠀⠀⠀⠤⠤⠤⠤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣦⠤⠀⠀⠀⠠⠤⠤⠤⠤⡦⠀⠀⠀⠤⠤⠤⠤⢼⡦⠀⠀⠀⠤⠤⠤⠤⢴⡄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣀⣀⣠⣀⣠⡄⠀⠀⠀⠀⠀⣀⣀⣦⡀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⣀⣀⣀⣀⣄⡀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠀⠉⠟⠀⠀⠀⠈⠉⠉⠉⠙⠛⠀⠀⠀⠉⠉⠉⠙⠁⠀⠀⠀⠀⠛⠛⠉⠹⠛⠁⠀⠀⠀⠉⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠐⠒⠛⠂⠀⠀⠰⠚⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠒⡺⠃⠀⠀⠀⠒⠒⠒⠒⠛

⠀⠐⠒⠒⠒⢾⠖⠀⠀⠀⠐⠒⠒⠒⣿⠶⠀⠀⠀⠐⠒⠒⠒⢚⠗⠀⠀⠀⠀⠀⠐⠒⠾⠆⠀⠀⠀⠒⠒⠒⠺⠷

⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠠⠤⠤⠤⡂⠤⠀⠀⠀⠤⠤⠤⠤⠤⡦⠀⠀⠀⠤⠤⠤⠤⣽⠆⠀⠀⠠⠤⠤⠤⢴⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠺⡟⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠈⠃⢻⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢻⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⣶⣦⣤⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⢸⡟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⠿⠶⠶⢶⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢇⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉




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

⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠘⢹⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⡻⠁⠀⠀⠀⢱
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢀⠔⠊⠁⠀⠀⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠀⣇
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢀⠤⢤⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢰⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠘⣆⠀⠀⠀⡎⠀⠙⡆⠀⠀⠀⣠⠞⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡠⠃⠀⡠⢤⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁
⠀⠀⠀⠈⠓⠤⠤⢧⣔⣊⣀⡤⠔⠋⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠔⠊⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠻⠷⢤⣀⣀⣀⣀⡤⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⣦⣤⣴⣤⣤⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢜⣿⣦⠀⠈⠫⡻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠑⣝⢿⣿⣄
⠀⢠⣀⣖⣂⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣀⣤⣨⣿⡆⠀⠀⠈⠳⣿⣿⣷⣄
⠀⠀⣸⣿⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠄⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡄
⠀⠸⣛⣧⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⠀⣠⡾⡫⠟⠁
⠀⠈⠉⢻⠛⠿⠿⠿⠿⠿⠿⠛⠛⠙⠉⠉⠋⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠛⠛⠛⠛⣿⢿⣿⠅⠀⠀⣠⣾⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡛⠁⠀⢀⣴⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⣾⣿⣿⡿⠿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢲⣶⣶⣦⠀⠀⢠⣤⣤⣤⣧⣄⠀⠀⢠⣤⢠⣠⣼⣿⣧⡀⠀⠀⢸⣷⣦⣄⡀⠀⠀⠘⣿⣶⣤⣀⠀⠀⠀⣠⣤⣿⣷⣦
⠀⠀⠀⠼⠿⠿⠟⠀⠀⠘⠛⠛⠛⡟⠋⠀⠀⠘⠙⠘⠛⢻⣿⠟⠁⠀⠀⢸⡿⠟⠋⠁⠀⠀⢠⡿⠟⠋⠁⠀⠀⠈⠁⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠁
⠀⠀⠀⢶⣶⣶⣆⠀⠀⠄⠄⠤⠸⠤⠀⠀⢀⢠⢠⣤⣼⣿⣦⡀⠀⠀⠻⣶⣤⣀⠀⠀⠀⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣶⣤⣀
⠀⠀⠀⠼⠿⣿⠟⠀⠀⠐⠃⠓⢘⠒⠁⠀⠘⠘⠘⠛⢻⣿⡿⠃⠀⠀⣰⠿⠛⠉⠀⠀⠀⣰⠿⠛⠉⠀⠀⠀⠠⠚⠛⠋⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⢶⣔⢦⡀⠀⠀⠀⢦⣦⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⢀⣰⣦⣄
⠀⠀⠀⢀⣿⣿⣿⠇⠀⠀⢀⣽⢇⡽⠂⠀⠀⢀⣽⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠒⠒⢺⡿⠂⠀⠀⡰⠛⠙⠛⠁
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠛⠑⠋⠀⠀⠀⠀⠋⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⣠⠴⠲⢤⠀⠀⠀⢀⠴⠲⢤⡀⠀⠀⢀⡤⠖⠤⣀⠀⠀⠀⡠⠔⠢⢄⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢸⠁⣾⣶⠄⡇⠀⠀⡇⢘⣿⡦⢹⠀⠀⣎⠠⠬⡦⢸⠄⠀⢸⣶⣶⣶⠌⡇⠀⠠⣶⣶⣶⣿⣿⣶⠄⠀⠀⠀⣠⠶⢿⣿⠗
⠀⠀⠀⠳⢬⡤⠔⠁⠀⠀⠑⠬⣬⠴⠋⠀⠀⠘⠦⣬⡤⠞⠀⠀⠈⠢⢤⡤⠞⠁⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣤⣤⣤⣼⣶⣄⠀⠀⠀⣀⣀⣠⣤⣷⣤⡀⠀⠀⣠⣤⣤⣼⣷⣄⡀⠀⠀⣠⣤⣤⣤⣷⣦⣄⡀⠀⠀⠀⠀⣀⣤⣼⣿⣦
⠀⠀⠀⠉⠉⠉⢻⠟⠋⠀⠀⠀⠉⠉⠉⠛⡿⠛⠁⠀⠀⠙⠛⠛⢻⡿⠋⠁⠀⠀⠙⠛⠛⠛⡿⠟⠋⠁⠀⠀⠀⠋⠉⠀⠸⠋⠁
⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤
⣯⣽⣽⣽⣭⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣿⣿⣿⣯

⢷⡄
⢘⣷⡀
⠘⢷⡙⠢⣀
⠀⠈⣿⣄⠀⠉⠀⠀⣄
⠀⠀⠨⡆⠐⠄⡀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠸⣀⠀⠀⠁⠒⢤⣀⠀⠈⠳⡄
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠈⠑⢄⠀⠈⢆
⠀⠀⠀⠀⠈⣴⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠴⠒⡄⠀⣠⠞
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠉⣀⠴⣆⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢁⣠⡴⠖⠉⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢁⣀⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⣀⡤⠖⠉⣀⡤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⢋⣡⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡤⠖⠛⠲⣄⣀⡠⠴⢛⣩⡴⠚⠙⢇
⠀⠀⠀⠀⠀⠀⠀⢾⣯⣅⣀⡀⢢⠴⠊⢩⡴⠚⠁⠀⠀⠀⠀⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣹⡷⡖⠇⢸⠇⠀⠀⠀⠀⠀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⢀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⡄⠀⠀⠰⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣀⠀⡆⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡄⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠈⠳⣄
⣶⠖⠒⠒⠒⠒⠒⠒⠖⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣙⣆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣡⣿⢇⣺
⣿⣤⣤⣤⣶⢶⠴⢶⣤⣤⣤⣤⣤⡤⡤⡤⠤⠤⠤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠒⠁⢋⡶⠋
⠈⠙⢷⡕⡡⡪⡪⡪⢊⠕⠑⡠⠪⡪⢚⠅⠀⢂⠔⠁⠊⠈⢀⠔⡡⣢⡟⠀⠀⠀⠀⠀⠀⠀⣠⢟⡄⠁⠀⣤⠎
⠀⠀⠈⢿⣮⣬⣬⣤⣡⣣⣎⣎⣴⣁⣁⣀⣐⡀⠀⠀⢀⠔⠡⠊⠎⢵⡇⠀⠀⠀⠀⠀⣠⡞⠁⠄⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⢺⡇⠀⠀⠀⣠⡞⡉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡼⢫⠞⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣴⠏⠂⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠋⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣰⠏

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣤⣾⣿⣶⠄⠀⠀⣰⣿⠋⠉⠈⠙⣧⠀⢤⣾⣿⣷⣦⡄⠀⠀⠀⠀⠀⣠⣴⣿⠀⠀⠀⠀⢀⡀⢙⣿⡆⠀⠀⠀⣠⣴⠶⣿⠷
⠀⠀⢠⣿⡿⠛⠟⠁⠀⠀⣀⣿⣧⠀⠀⠀⠐⠃⠀⠀⠈⠙⠋⢻⣿⠀⠀⠀⠀⢀⣽⣿⠿⠄⠀⠀⢀⣾⣷⣿⡿⠁⠀⢀⡾⠋
⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠳⣤⣠⣾⠟⠀⠀⠙⠻⠿⠛⠁⠀⠀⠀⠀⠛⠛⠿⠅⠀⠀⠀⠘
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⢦⣀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⣆⡄⠀⠀⠀⠀⠀⣴⣾⡇⠀⠻⣿⣷⣶⠿⠿⢻⡇
⠀⠀⠛⠿⣷⣤⣀⣀⡀⠀⠀⠀⣿⠿⠿⠋⠈⠀⠀⠈⠻⢿⣿⣦⡤⠀⠀⢻⡏⠀⠙⠻⡿⠀⠀⠀⣠⣴⣾⡿⠛⠃⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠇⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠰⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠉⠙⢷⣦⡀⠀⠀⠀⣼⠟⠛⠻⠿⣿⠄⠀⠀⢀⣤⣿⣦⡀⠀⠀⠀⢀⣀⣤⣷⣄⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⢠⣴⣾⣥⣄⡀
⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠟⠉⠀⠀⠀⣾⠿⠟⠛⡿⠟⠁⠀⠘⣿⣿⢁⣤⠤⠄⠀⠀⠙⠿⠙⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠐⣿⡷⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⢀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⢰⡶⠶⠂⡀⠀⠀⣤⡶⠶⣤⠀⠀⣠⠀⠀⠀⠀⢦⡀⠀⠀⢀⣤⡄⠀⠀⢀⡴⠶⠀⠀⠀⠀⣠⣴⡦⠀⠀⠀⣠⡶⠶⣀⠀⠀⣾⠛⣷
⠀⠀⠀⣤⡀⠀⢸⡟⠀⠰⣆⠀⠀⢸⡇⠀⢿⣤⣄⠀⠀⣼⠇⠀⠀⢿⣀⣠⠀⠀⠸⣇⣀⣶⡶⠀⠰⣇⠀⢀⡤⠀⠀⢿⡄⠀⣹⡇⠘⡿⠃⣿
⠀⠀⠀⠈⠛⠃⠈⠀⠀⠀⠙⠓⠚⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠉⣀⣀⣀⡀⠈⢉⣉⣁⣀⣀⠈⠛⣋⣁⣀⣀⡀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⡤⠆⠀⠀⠀⡀⠀⠈⠉⡉⠙⠁⠀⠀⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠀⠈⠉⠉⠉⠙⠋⠀⠀⠀⠀⠀⢠⣾⣦
⠀⠀⠀⢦⣀⣸⠃⠀⣇⡀⣰⠂⠈⠀⠀⣰⠂⠺⠟⠛⠛⠻⠟⠀⠐⠛⠛⠛⠿⠂⠐⠛⠛⠛⠛⠂⠐⠛⠛⠛⠓⠀⠛⠓⠀⠛⠿⠂⠀⢸⡿⣿⡀
⠀⠀⠀⢀⣈⡀⢀⡀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣠⣄⠀⠀⠀⢸⣿⣿⡄
⠀⠀⢼⠋⠉⠁⠈⠙⡆⠀⠙⣦⢻⣮⢻⡞⣳⡄⠀⠘⣷⡝⣦⠙⣷⠈⢻⡄⠀⠘⣿⣿⣿⣦⠀⠈⢻⣿⣿⣷⡄⠀⢙⣿⣿⣿⣷⠀⠀⢸⣿⣿⡇
⠀⠀⠈⠳⠀⠶⠶⠚⠁⠀⠚⠁⠛⠑⠋⠘⠋⠀⠀⠘⠋⠚⠁⠚⠁⠐⠋⠀⠀⠘⠛⠛⠛⠁⠀⠐⠛⠛⠛⠋⠀⠀⠛⠛⠻⠟⠁⠀⠀⠘⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣀⣀⡀⠀⢀⣀⣀⣀⡀⠀⠀⣤⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⠀⠀⡀⣀⣀⣴⣤⣀
⠀⠀⠀⣤⠀⠈⠉⠉⠉⠉⠉⣿⠠⣬⣭⣭⣭⡭⠁⠀⠈⠉⠉⠉⠁⠀⠈⠉⠉⠉⠁⠀⠀⠛⠛⠋⠉⠋⠀⠀⠀⠙⠛⠛⠀⠀⠃⠛⠛⠻⠟⠋
⠀⠀⠀⠻⠶⠶⠶⠶⠶⠀⠖⠛⠀⠐⠛⠛⠛⠛⠃⠀⢠⣤⣤⣤⣤⡀⠀⣤⣤⣄⣀⣤⣀⠀⠀⢀⣀⣀⣤⣴⣤⡀⠀⠀⠀⢀⣀⣀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠁⠉⠙⠉⠀⠀⠀⠀⠐⠛⠛⠛⠻⠟⠋⠁
⠀⠀⠀⠤⣤⣤⣤⣤⣦⣄⡀⠀⣤⣤⣄⣀⣤⣄⠀⣀⣀⣲⣤⣀⠀⠀⣤⣤⣤⣤⣦⣄⡀⠀⢀⣀⣀⣤⣀⡀⠀⢠⣤⣤⣤⣄⡀⠀⣀⣀⣘⣳⣄
⠀⠀⠀⠘⠛⠛⠛⠉⠟⠋⠀⠀⠛⠛⠉⠉⠛⠉⠀⠉⠉⠝⠋⠉⠀⠀⠉⠉⠉⠉⠛⠉⠀⠀⠈⠁⠉⠉⠁⠀⠀⠈⠈⠀⠉⠁⠀⠀⠀⠀⠠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⢨⣿⡿⠂⠀⠀⠿⠶⠂⠀⠰⠶⡿⠂⠀⣩⡿⠆⠀⠲⢾⡷⠆⠀⠰⠆⡷⠆⠀⢸⠷⠂⠀⢸⡿⠖⠀⠀⢿⢞⠵⠀⠀⣿⠷⠂⠀⢨⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⢠⡴⠶⠆⠀⠀⣠⡄⢰⡆⠀⠀⢴⡆⠀⠀⠀⠀⢀⡶⠛⢶⣄⠀⠀⠀⣠⣤⣦⠀⠀⣠⣤⣄⠀⢀⠀⠀⢀⡀⣀⡀⠀⠀⢀⣀⣸⣇⣀⣀
⠀⠀⢰⡏⠀⠀⠀⠀⠀⢸⡇⢼⡧⠀⠀⢸⣧⣤⣦⠀⠀⢼⠇⠀⠀⠿⠀⠀⠀⣟⠀⠀⠀⠀⠉⠀⢿⣄⣿⠃⠀⠙⠛⠛⠛⠀⠀⠙⠋⢹⡏⠉⠋
⠀⠀⠈⢷⣄⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠈⠙⠁⠀⠀⢰⠀⠀⠀⣀⣄⡀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢠⡀⠀⠀⠀⢀⣤⡀⣠⡀⠀⠀⠀⢀⣄
⠀⠀⠈⠛⢦⡀⢀⣤⣀⣼⣄⣠⣀⠉⠋⢹⡇⠀⠶⠶⠿⠶⠆⠀⢾⠶⠶⠇⠀⠺⠾⠿⠷⠀⢠⡖⢺⡗⢒⡿⠂⠐⢻⣾⣿⣿⡿⣧⣤⡀⠀⠉⡏
⠀⠀⠀⠀⣸⣧⠀⠙⠉⠀⠈⠉⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠁⠈⠀⠀⠀⠈⠻⠋⠻⠃⠀⠉⠀⠰⡤⠇
⠀⠀⠀⡀⠘⠃⢀⣀⠀⠀⢀⣤⣤⣤⡀⠀⠀⣠⣤⣤⡄⠀⠀⢀⣤⣦⣄⠀⠀⢀⣤⣤⣤⡀⠀⠀⣠⣴⣤⣄⠀⠀⢀⣤⣦⣤⡀⠀⠀⣠⣴⣤⡄
⠀⠀⠈⠉⣳⡞⠉⠋⠀⠀⣾⣿⢈⣻⡷⠀⢸⡟⣭⣬⣿⠀⠀⣿⡧⠈⣹⡇⠀⢾⣿⠆⣹⣿⠀⢰⣿⢌⢌⣿⡆⠀⣿⣏⡉⣹⡷⠀⢸⣟⡁⢙⣿
⠀⠀⠘⠛⠁⠘⠛⠛⠀⠀⠈⠻⠿⠟⠁⠀⠀⠛⠿⠿⠋⠀⠀⠙⠷⠿⠟⠁⠀⠈⠻⠾⠟⠃⠀⠀⠙⠿⠿⠋⠀⠀⠘⠻⠿⠟⠁⠀⠈⠻⠿⠿⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣟⣿⣯⣛⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣯⣭⣭⣿⣿⣭⣽⣿⣭⣿⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠐⠒⠙⠓⠲⢄⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠒⢤⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠖⠊⠉⠙⠃⢀
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢣
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠱⢄⡀⠀⠀⣀⠜⠁⠀⠀⠀⠀⠀⠘⠦⣀⡀⢀⣀⠀⠉⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⢠⡤⠃⠀⠀⠀⠀⠀⠀⠓⢀⣀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⡀⠖⠒⠲⢦⣄⠀⠀⠀⠀⠀⠀⢀⠐⠖⠛⠛⠲⢤⡀⠀⠀⠀⠀⠀⢠⡴⠛⠉⠙⠾⠇⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠉⠹⠟⢀⡀
⠀⠀⢰⠟⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢀⡟⠂⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⢀⡍⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢺⠷⠀⠀⠀⠀⠀⠈⣷
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠙⣏⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠈⢳⣄⠀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠙⢦⣀⠀⢀⣀⠘⠛⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠓⢠⣤⣀⣀⣠⠌⠉
⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⣴⠶⠿⠶⢦⣄⠀⠀⠀⠀⠀⠀⢀⢴⠶⠛⠛⠶⣤⡀⠀⠀⠀⠀⠀⢀⣴⠾⠛⢻⡿⢆⡀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠉⠛⠛⢦⡀
⠀⠀⢶⣿⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢲⣿⠄⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠐⢾⠧⠀⠀⠀⠀⠀⠈⣷
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢠⣼⡇⠀⠀⠀⣸⣷⠄⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠰⣿⠄
⠀⠀⠘⢿⣄⡀⠀⠀⣀⣼⠏⠀⠀⠀⠀⠀⠻⣦⣀⠀⢀⣀⡜⠟⠁⠀⠀⠀⠀⠹⢧⣄⣀⣀⢠⣷⡟⠀⠀⠀⠀⠀⠀⠻⢦⣤⣀⣀⣤⠖⠁
⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⡄⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢸⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣅⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⢀⠔⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⡠⠋
⠀⠀⠀⠀⣀⠀⠀⠀⡠⠔⢁⢼⡄⠁⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡠⠞⠁
⠀⠀⠀⠀⠸⠀⢀⠎⢀⡜⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⢧⠞⢠⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠈⢐⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠲⠭⢢⣤⣤⣤⣤⣤⣤⠤⠴⠖⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣤⣶⡗⠀⠀⢠⣄⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⡄⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⢢
⠀⠀⠀⠀⢈⣽⢻⡿⠀⠀⢀⣿⣿⢦⠀⠀⡼⣿⢿⣄⠀⠀⠀⡇⠀⠀⠀⡼⣿⣿⡀⠀⠀⢺⡟⣿⠃⠀⠀⠀⠸⡇
⠀⠀⠀⢠⡟⠁⠀⠁⠀⠀⠘⢩⣿⠀⠀⠈⠀⣿⡀⠁⠀⠀⠀⣧⠀⠀⠈⠁⣿⠈⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠸⣇⠀⠀⠸⣦⣿⡴⠀⠀⠀⣿⠀⠀⠀⠸⣧⣞⣻⠆⠀⠀⠀⢰⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠘⠚⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⢹⣿⠃⠀⠀⠀⢹⡇⠀⠀⠀⠹⡏⠁⠀⠀⠀⢿⣾⣷⠆
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙⠄⠀⠀⠀⠺⠟⠁
⠀⠀⠀⠀⠀⣴⣿⣿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⣴⣿⠃⠀⠀⣠⠆⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠚⢡⡟⠹⠇⠀⠀⢠⡟⠀⠀⠀⠀⣈⣽⠟⣿⠀⢀⡾⠁⠀⠀⠀⠀⣰⣿⡇⠀⢰⠀⢀⣾⠛⢉⡧
⠀⠀⠀⠀⢠⡿⠁⠀⠀⢰⣠⡿⠁⠀⠀⠀⣾⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠚⣱⡟⠿⠀⠈⠳⣼⣧⠶⠟⠁
⠀⠀⠀⢠⡟⠁⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠓⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⣧⡀
⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⣈⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠂
⠀⠀⠀⠀⡤⢾⣿⡟⠀⠀⠀⠀⠀⠈⠁⠀⣸⡆⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠤⠒⠒⠛⠓⠶⢶⣤⣀
⠀⠀⠀⠀⣴⠟⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠒⣻⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⣦
⠀⠀⢀⡾⠁⢠⠴⢦⠀⠀⠀⠀⣠⢀⣼⠟⠀⠀⠀⣼⡟⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣲⣶⣶⠶⠀⠀⢀⣙⣿⣿⡆
⠀⠀⠸⡇⠀⠈⣠⡿⠀⠀⢀⣼⣿⣿⡷⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠟⠁⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⢈⡉⠉⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⠄⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⠀⢐⠀⠀⠀⠀⠙⠶⠖⠁⠀⠀⠁⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢤⣶⣶⡟
⠀⠀⠀⣴⠛⣷⡀⠀⣠⡿⠙⠁⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠠⠤⣶⣿⡟⠀⠀⡠⠒⠉⠉⢻⡇⠀⠀⣠⡴⠛⠟
⠀⠀⡼⠃⠀⣿⣇⣴⠟⠀⠀⠀⠀⠀⠀⠈⠙⠶⢦⣤⣤⣤⣶⠾⠛⠿⠀⠀⠈⠀⠀⠀⠀⠈⠻⠶⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⡽⠁
⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⣾⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀
⠀⠀⠺⢭⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡿
⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠻⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣽⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢤⣢⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣠⠤⠔⠒⠒⠒⠀⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⡀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⣦⠀⠀⣠⠊⡐⠃⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠘⢎⠌⢱⠮⣑⠲⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠠⢇⢀⡾⠉⠓⠤⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠃⣀⡿⠁⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡊⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⢉⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⢀⠀⠀⠀⠀⡀⢣
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢼⠳⢄⡐⠾⣸⣦⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣮⣿⣷⣾⣿⡿⠟⠂
⠀⠀⠀⠨⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣥⣭⡿⠟⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠊⠉⠁⠀⠀⠁
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠖⠒⠉⠉
⠀⠀⠀⢀⣸⠀⠀⣀⣠⠤⠤⠔⠒⠚⠉⠁
⠀⠀⢀⠼⡟⠉⠉
⠀⠦⠕⠋
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⢰⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⠀⣿⡆⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁⠀⠀⠀⠀⢸⣥⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠠⢔⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⢀⠀⠀⢀⢿
⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⢀⠌⠀⠀⠀⠀⢀⡤⠚⣏⠑⠺⣿⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢠⢿⣉⣉⣉⣧⠀⢀⠊⠀⠀⠀⠀⡠⢊⠔⠉⠀⠀⣁⠉⠤⠐⠀⠀⠀⣰⢹
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢠⢃⠎⠀⠀⠀⠀⡠⠁⠀⠀⠀⡠⠊⡰⠁⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢰⠊⠎⠀⠀⠀⠀⡐⠀⠀⠀⢀⠜⣠⠊⠀⠀⠀⠀⡨⠂⠀⠀⠀⠀⠀⠀⣰⢱
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠎⡜⠀⠀⠀⠀⡜⠀⠀⠀⡰⢁⠔⠁⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣀⡀⠀⡙⡈
⠀⠀⠀⠀⠀⠀⢠⠀⢀⡊⡔⠀⠀⠀⠀⠌⠀⠀⢀⠞⡠⠋⠀⠀⠀⡠⠊⠀⠀⠀⢀⡠⠞⣁⠤⡈⠒⣷⠁
⠀⠀⠀⠀⠀⠀⠈⠀⡸⡱⠁⠀⠀⠀⠌⠀⠀⣠⢊⠜⠁⠀⠀⢀⠔⠀⠀⢀⡠⠒⣁⠔⠊⠀⠀⠈⠑⠛
⠀⠀⠀⠀⠀⠀⠄⢀⣧⠃⠀⠀⠀⠘⠀⠀⡰⣣⠊⠀⠀⠀⡠⠁⢀⡠⠞⢁⠔⠊⠀⠀⠀⠀⠒⠂⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠄⢼⠇⠀⠀⠀⠠⠁⠀⡴⡱⠁⠀⠀⢀⠎⢀⡔⢊⠤⠊⠁⠀⠀⠀⠀⢀⠀⠬⠀⠀⠀⠀⠀⠉⠀⠐⣠
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⡄⠀⣜⡜⠀⠀⠀⡐⢁⠔⡣⠚⠁⠀⠀⠀⡀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠝
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠠⠀⣼⠏⠀⠀⢀⢚⣴⠗⠋⠀⠀⣀⠄⠒⠁⠀⠀⠀⡀⢀⣀⣀⢠⡄⠀⠀⢠⢞⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣼⠃⠀⠀⢀⡾⠚⠁⠀⡠⠔⠉⣀⡀⠤⠴⣒⣊⣩⠭⠭⠤⠤⡎⢱⣀⠔⡵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠃⠀⠀⠀⠋⠀⢀⣠⣾⡔⠾⠍⠑⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⢤⡵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠰
⠀⠀⠀⠀⡠⠃⠀⠀⡠⠐⠀⠀⠐⢄⡀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡇⠈⠒⠀⠐⠁⠀⠀⠀⢁
⠀⠀⡠⠊⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠘⠀⠀⠀⠔⠢⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⡅⠀⠀⠠⠤⢄⠀⠀⠀⢀⠀⠀⠀⡅⠀⠀⠀⠀⡰⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠘⠤⠀⢥⡠⠊⣀⠤⠒⠁⠀⠀⠀⠐⠤⠀⠠⠐⠁⠀⠅⠉⠁⠀⠀⠠⡤⣀⠀⠀⣀⠀⠔⠊

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⣠⣶⠟⠛⠙⠻⢶⣄⠀⠀⠀⠀⠀⣠⡾⠛⠛⠉⠛⢷⣄⠀⠀⠀⠀⠀⢠⣶⠟⠛⠋⠻⢷⣄⠀⠀⠀⠀⠀⢀⣴⠟⠛⠋⠙⠻⣦⡀
⠀⠀⢰⡿⠁⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢘⣷⡀
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠸⣗⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠻⣧⣄⣀⣀⣠⣼⠟⠀⠀⠀⠀⠀⠙⢷⣤⣀⣄⣤⡾⠏⠀⠀⠀⠀⠀⠻⣷⣄⣀⣀⣠⣴⠛⠁⠀⠀⠀⠀⠈⠻⣦⣄⣠⣠⣴⠿⠁
⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠉⠁
⠀⠀⠀⠀⢀⣠⠤⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠠⣄
⠀⠀⠀⡴⠋⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠱⡄
⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠙⠦⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠲⠄⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠆⠰⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠀⠋⠀⠠⡀⠀⠀⠀⠀⠀⢀⠐⠈⠉⠀⠀⠢⡀⠀⠀⠀⠀⠀⢀⠄⠀⠘⠁⠐⠠⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠉⠀⠑⢄
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⡙
⠀⠀⠀⠐⢄⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠐⠄⡀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠀⠀⠀⠀⡀⠛⠀⠀⠀⠀⠀⠀⠢⢀⠀⣀⠀⡀⠔
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡉⢳
⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⡞⡿⣡
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⡰⠱⣼⢡⣣
⢹⣿⣿⠟⣻⢟⡟⣛⢛⠛⣻⢟⡿⢻⠟⡻⢛⠿⣛⢛⡛⢛⠛⠚⠓⣲⠖⡒⢒⡶⢲⠶⡶⠶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡴⠱⢡⠡⢀⡾⠁
⠀⠈⠻⣾⡴⣫⢎⠵⡫⢊⠕⡩⠞⡡⢊⠔⡡⢚⠕⢋⠔⠁⠐⡠⠊⡠⠊⡠⠪⠘⡡⢊⡴⣣⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⣡⠊⠠⠁⢆⡷⠋
⠀⠀⠀⠈⢿⣱⣋⣎⣔⣁⡔⠠⠎⡴⢡⠎⣰⠃⠐⢁⠄⢀⠊⠠⠋⠠⠊⠀⡠⠊⡠⢋⠔⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⡙⢀⠀⠁⠇⣰⠟
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠓⠒⠒⠒⠶⠶⠶⠾⠶⠾⠤⠤⢤⣥⣿⠀⠀⠀⠀⠀⠀⣠⡾⠛⠑⠐⠁⠆⣨⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢠⡾⢋⡴⠁⠠⡀⣨⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⣴⠋⢰⢋⢠⠁⢁⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣴⡏⡔⠄⠃⠂⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⡱⡘⡀⡜⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠡⠐⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠳⣄
⠀⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠈⠳⣄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⢸⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠈⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⠁

⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠤⠤⢄⡀
⠀⠈⠙⠦⡀⠀⠠⢻⠂⠀⠀⠀⠉⠀⠈⠋⠁⠀⠉⠉⠋⠀⠀⠀⡀⠀⠀⠀⠀⡖⢂⠆⠀⢾⣀⣄⡀⠈⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⢀⡈⠳⢄⠀⠇⠀⠀⠀⠐⠢⠴⠒⠤⠚⠢⠜⠏⠀⠀⠐⠓⢒⡖⠀⢸⠀⣏⠀⠀⠀⠈⠋⠁⠀⠀⢠⠀⡴⠀⡆⠀⠀⠉
⠀⠀⠐⠟⠀⠄⠀⠑⠀⠀⠀⣤⠀⢀⢄⠀⠠⠦⡀⢀⠄⠀⠀⠀⢠⠎⠀⠀⠈⠚⠁⠀⡀⠀⠀⣾⡄⠀⠀⢰⣴⡡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣀⠇⠈⢆⠇⠀⠣⠄⠀⠀⠀⠰⠿⠂⠀⠀⠀⠀⠀⠘⡏⠀⠀⢸⠀⠀⠀⠀⢀⣠⣤⠴⠔⠊
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⢠⣤⣀⠀⠀⠀⢰⡆⠀⢀⣤⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠉
⠀⠀⡌⠀⢰⣖⡒⠒⢦⠀⠀⡔⠉⠀⠀⠀⠉⠲⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠉⠀⠰⠷⠀⠀⢸⠀⠀⡔⠁
⠀⠀⢣⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣄⠀⠀⠐⠋⠛⠛⠀⠀⠈⣆⠀⠀⠀⠀⠀⢸⠀⠀⠈⠒⠒⠒⠒⠒⠒⠢⡀
⠀⠀⠀⠑⠢⠤⠴⠚⢡⡄⠀⠀⠀⠈⡏⠉⠹⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⡜⠀⠀⡀⠀⢀⡎⠀⠀⠀⣤⣤⣀⣀⡀⢀⣠⠇
⠀⢀⡤⠤⠤⠤⠤⠀⠀⠑⠤⠔⠃⣀⣱⠀⣇⡀⠙⠢⢤⣀⠀⠀⢠⠋⠀⠀⢀⡀⡀⠀⠈⠉⠁⢠⣄⠀⠀⠈⠁⠀⠀⠉⠉
⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣄⠀⠀⠘⢦⢀⠜⠁⠀⠀⠀⠈⠙⠀⡸⠀⠠⠌⠀⠀⠀⠉⣂⡄⠀⠀⢱⠀⢠⠂⠀⠠⡖⢢⣀⠴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠉⠀⠀⠀⠀⠈⠑⠒⠊⠁⠀⢐⠀⠀⠀⠀⠀⠀⠀⠰⣠⠎⠀⠀⠢⡀⠀⢈⡽⠁
⠀⠀⠀⣀⣤⣔⠋⡟⡏⠉⢲⠀⠀⠀⠱⡀⠀⠀⡴⠃⠀⠀⡔⡄⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉
⠀⠀⡞⠀⠸⠼⠀⠈⠁⠀⠀⢀⣀⠀⠀⠙⡄⣰⠁⠀⠀⢀⠜⠣⢀⠀⠀⠀⠀⢁⠉⠀⠀⠀⡠⠒⠒⠂⢀⣤⠴⠒⠒⠒⢦⡀
⠀⡀⡇⠀⠀⠀⠀⣠⠔⠚⠉⢀⣀⠀⠀⠀⠈⠃⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢠⡋⣱⠄⠀⠀⠑⠤⠴⠚⠉⠀⠀⠀⠲⠦⠴⠃
⠀⠙⠛⠀⠀⣠⠞⠁⠀⠀⠊⠀⢀⡅⠀⠀⠠⢄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠰⠃⠀⠀⠀⣀⡤⠔⠉⠀⠀⢠⡄⠀⢳⠀⠀⠀⠑⠒⠊⢱⡀⠀⠀⠘⠉⠉⠀⠠⠀⠄⠀⢀⡟⠀⡴⢋⠄⢌⠱⡄
⠀⢰⠉⡉⠉⡇⠀⠀⠚⠁⠀⠀⠀⠀⠀⠈⢧⡀⠈⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢠⠒⠒⠃⠀⠀⢀⠞⠀⠐⡇⠸⢔⣊⠴⠁
⠀⢸⠀⠦⠤⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠋⠀⠀⠀⢀⡜⠉⠉⠀⠀⡰⢤⡖⠋⠀⠀⠀⠱⢄⣀⠀⢀⡠⠄
⠀⠈⠉⠉⠉⠉⠉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠘⣦⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠈⠟⡀⠀⠀⠘⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⢰⡅⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⡠⠁⠀⠀⠀⠀⡠⢲⠂⠤⣦⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⢾⠀⠑⢻⡄⠀⠐⠀⠀⠀⠀⡠⢊⠔⠉⠀⠉⠘⠀⠀⠀⠀⠀⡈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠎⠀⠀⠀⢀⠌⠀⠀⠀⡠⠊⠔⠁⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠂⠎⠀⠀⠀⢀⠂⠀⠀⢀⠜⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡌⠀⠀⠀⠠⠀⠀⠀⠠⢃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢀⠀⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡌⡈⠀⠀⠀⠀⠁⠀⠀⠜⡠⠃⠀⠀⢀⠔⠁⠀⠀⢀⠄⢊⡡⠒⠄⡉⡬
⠀⠀⠀⠀⠀⠀⠀⡰⡸⠀⠀⠀⢀⠁⠀⢠⢎⠜⠀⠀⠀⡠⠀⠀⢀⠄⠊⡠⠐⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⢀⣷⠁⠀⠀⠀⠀⠀⠠⠢⠂⠀⠀⢀⠄⠀⡠⠂⡡⠐⠁⠀⠀⠀⠀⠨⠀⠁⠐⠀⠠
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⡠⡡⠁⠀⠀⡀⢁⠴⡊⠔⠁⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠜⡇
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⠀⡰⠔⠀⠀⠀⢎⢔⠥⠊⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡩⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠏⠀⠀⢀⡦⠞⠁⠀⡀⠀⠀⠀⣀⡀⠤⠤⠒⢒⣊⣉⡹⢃⠀⡤⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠋⠀⠀⠰⠋⠀⢀⣄⡂⣔⠂⠩⠅⠐⠂⠉⠉⠁⠀⠀⠀⠑⣈⣫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠢⡐⠂⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⢢⠀⠀⠀⠉⠐⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢑⡄⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠄⢖⡶⠀⠀⠀⠀⠀⠠⠊⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢴⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠀⢀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠔⢁⠔⠁
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⢀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠔⠁
⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⢀⠈⠀⠀⢀⡠⠂⠁
⠀⠀⢠⠃⠀⣠⠔⠁
⠀⠠⠁⡠⠊
⢀⠁
⣷⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠛⣦⡀
⠀⢠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⣦⡀
⠀⠀⣿⠈⠉⠛⠻⢿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣶⣦⣄⣀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣦⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡛⣧⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⢋⣤⠇⡏⣳⡄
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⡄⣸⣿⢸⣵⠋
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡴⢰⠇⡏⣣⠞⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⠛⢩⣼⠃⠀⠀⠀⠀⠀⢀⣴⠟⢱⠀⡇⡞⢀⡼⠃
⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣤⣴⣶⢿⡿⣻⠋⣽⣡⡷⠖⢛⡟⠀⠀⠀⠀⢀⣴⡟⢡⠇⡟⢸⣣⠷⠋
⠀⠀⢸⣷⣠⣴⣶⣿⢿⢏⡟⢡⢏⣾⡤⠟⠋⠉⠀⠀⠀⣼⠃⠀⠀⢀⣴⣿⢋⡇⡼⠰⣣⠞⠁
⠀⠀⠈⠻⣿⡼⢱⢣⣧⠼⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⡾⠋⡞⢸⠁⣧⠞⠁
⠀⠀⠀⠀⠉⠛⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣠⡾⣋⣰⢰⠃⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣫⠀⡟⢇⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⡇⢸⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠋

⠀⠀⠀⠄⢰⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⡀⠀⠀⠀⠀⠔⠈⠈⠐⡈⠉⠐⠆⠀⠀⠀⢀⠠⡀⠀⢀⠀⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠂⠀⠀⠐⠉⠐⠂⠈⠁⠀⠀⠀⠈⠀⠀⠐⠤⠁⠀⠀⠀⠀⠀⠐⠁⠀⠁⠀⠁⠀⠀⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡀⠀⠀⠀⠀⡀⠁⠠⠂⠀⢀⡀⠀⠀⠀⡀⠀⢀⡄⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠡⡀⠀⠀⢂⡀⠄⠀⠀⡀⠀⠀⠀⠠⠁⠀⡠⠊⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⢄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠶⠀⠀⠀⠀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠐⠀⠀⠐⠁⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠠⠊⠀⠀⠀⠀⠀⠁⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠈⠀⠀⠑⠄
⠀⠀⠀⢀⠀⠂⠐⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠠⡄⠀⠁⠂⠀⠤⠄⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠠⠀⠤⠐⠁⠀⠀⠀⠘

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

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⢋⣉⣥⣤⣤⣤⣤⣤⣤⠄⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⣡⣾⡿⠿⠛⠛⣻⣿⣿⠟⠁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⣸⣿⠏⠀⠀⣠⣾⣿⣟⣁⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢀⣿⡟⠀⠠⠾⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⣾⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣶⣶⣿⣿⠟⢁⣾⣿⠃
⠀⠀⠀⠀⣠⣾⣿⡿⠟⢛⣋⣉⣉⣉⣉⣛⣛⣛⣛⣛⣛⣉⣩⣤⣾⣿⠟⠁
⠀⠀⠀⣼⣿⠟⣡⣶⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉
⠀⠀⢸⣿⡏⣰⣿⠟⠁
⠀⠀⣿⣿⡇⣿⣿
⠀⠀⢹⣿⡇⢻⣿⡆
⠀⠀⠘⣿⣿⡈⣿⣷⡀
⠀⠀⠀⠹⣿⣧⠘⣿⣷⡀
⠀⠀⠀⠀⢻⣿⣧⠘⣿⣷⡀
⠀⠀⠀⠀⠀⢻⣿⣧⢙⣿⣧
⠀⠀⠀⠀⠀⠀⢻⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠳⡀
⠀⠀⠀⠀⠀⢀⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠘⢄
⠀⠀⢀⡤⠊⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⢳⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢲⠀⠀⠀⠀⠖⠘⠂
⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠁⠀⠀⠐⡖⠚⠀⠀⠀⠀⠓⡲⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠉⠢⢄⠀⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠘⠛⠚⠓⠛⠛⠚⠚⡆⣀⠔⠋⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣠⣶⣿⡀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣆
⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⠋⠉⠁
⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠿⣿⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢰⡦⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠉⡩⢦⡀⠀⠀⠀⠀⠁⠙⢆⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢜⠀⠀⠀⠀⠈⠋⠢⡀⠀⠀⠈⠈⠑⠤⣀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠑⢪⣼⠄⠀⠀⠀⠀⠎⡞⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢄⠃⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠐⠚⣡⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⢀⡴⠾⣿⠟⠋⠀⠀⠀⢀⣶⠟⠉⠉⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⠄⠀⠀⠀⠠⠊⠉⠀⠉⠉
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡆⠀⠀⠀⡆
⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⠀⠀⠀⣷⡄⠀⠀⠀⠀⢸⠇⠀⠀⠀⠹⣤⣀⣤⣀
⠀⠀⠀⠀⠀⠙⠶⣶⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠁⠀⠀⠀⠈⠛⠶⠤⠄⠔⠃⠀⠀⠀⠀⠀⠀⠉⠿⠛⠋

⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⢦⣄
⠀⠀⠀⠀⠈⠙⠻⠟⠻⢦⡀⠀⠀⠀⠀⢀⡴⠒⠒⢀⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣰⡏⠀⠀⠀⠀⠹⣆⠀⠀⣼⣷⡀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⢰⣿⠀⠀⠉⢿⡀⠀⠀⠀⢀⡟⠀⠀⠀⢀⣠⣴⣦⣴⠞⠁
⠀⠀⠀⠀⠘⠻⠿⠟⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠛⠦⠤⠀⠁⠀⠀⠀⠀⠈⠉⠙⠋

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

⠾⣿⣿⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠉⠛⠿⣿⣿⣍⡛⠛⠿⠿⢿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡀⠀⠀⠉⠙⠛⠿⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⡀⠀⠀⠀⠀⠈⠉⠻⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣍⠉⠉⠉⠉⠉⠉⠹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣄⠀⠀⣠⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣾⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀
⠀⢀⠀⢠⠤⢄⣀⣠⠞⠳⣄⠀⢀⣨⣷⣄⠀⠀⣤⣶⣤⣤⣴⠞⠋⠙⣦⣠⠞⠻⡄⠀⠀⠀⠲⢤⡀
⠀⢸⠀⠀⠀⠀⠈⠀⠀⢀⠈⠛⠋⠱⠟⠁⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠈⠉⠀⣀⠑⠀⠀⢀⣀⡀⣹
⠀⢸⡄⢀⣤⡀⠀⠀⣜⠁⠀⠀⠀⠀⠀⢠⣴⣾⣃⡀⠀⠀⠀⠀⢀⡴⠒⣶⡏⠉⢳⡄⠀⢿⣭⡽⢿⡄
⠀⠀⠙⣿⡴⠇⡀⠀⠘⢆⠀⠐⣆⠀⠀⠀⠙⠃⠈⠉⠳⢦⡀⠀⢸⡀⠀⠻⠃⠀⢸⠇⠀⣀⣤⣄⣠⡇
⠀⠀⠀⠘⠳⠤⢿⡿⠁⠈⣇⠀⠈⠳⢦⣀⠀⣄⠀⠀⠀⠀⠹⣦⠈⠳⣄⠀⠠⠿⣯⡀⠐⢿⣭⠿⠻⣆
⠀⠀⢀⡴⠂⠀⠘⠁⢀⡴⠃⠀⠀⠀⠀⠉⢛⣿⣷⣄⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⡿
⠀⠀⢾⣀⣀⠀⠀⠀⢺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣀⡀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⣼⣿⣿⡁
⠀⠀⣾⠳⠾⠀⠀⠀⠀⣻⣆⣴⠆⠀⠐⣄⠀⣠⣄⠀⢠⡞⠁⠙⠦⣄⣠⡴⠛⠇⠀⠀⠀⠀⠛⠉⠉
⠀⠀⠙⠦⣤⣀⣀⡀⠀⠹⡿⠃⠀⠀⠀⠈⠙⣗⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠛⠓⠶⣄
⠀⠀⠀⠀⠀⠀⠉⠙⢷⡀⠀⠀⠠⢴⣿⠀⠀⠈⠉⠉⠀⠀⠱⡄⠀⣄⠀⠀⠐⠁⠀⢀⠔⠀⠀⠘⣧⢀⡤
⠀⠀⠀⣀⣀⣀⣀⣠⡼⠃⠀⠀⢠⡾⠙⠇⠀⠀⠀⢀⡀⠀⠀⠘⡾⠹⡆⠀⠀⠀⢠⣿⠛⢳⡄⢰⣿⡟⠁
⠀⢠⡟⠉⠉⠉⠉⠁⠀⠀⢀⣴⠟⠀⣠⠄⠀⠘⣩⣿⡇⠀⣀⡀⠀⠀⢿⣀⡇⠀⣿⠈⠛⠋⠀⠀⠉
⠀⠘⣧⡀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⢧⣤⡀⢠⡟⠘⠃⣠⠟⠟⠀⠀⢺⣿⠃⠀⠙⢦⣄⣤⠶⠛⠳⣄
⠀⠀⠈⠉⠛⠛⠋⢉⣠⡤⠀⢀⡀⠀⠘⠋⠀⢸⡇⠀⠀⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢰⠞⢳⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠇⠀⠀⣧⣠⣤⡀⠀⠈⢷⡀⠀⠀⠀⡞⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣹
⠀⠀⠀⠀⣰⠛⢶⠟⠀⠀⠀⠀⠈⠁⠘⣧⣶⠀⠈⠻⢶⣤⣀⣳⣤⡼⠃⠀⠀⠀⠀⣠⣴⣂⣀⣀⡴⠋
⠀⠀⠀⠼⠁⠀⢀⣀⣀⣼⢿⡆⢠⣄⡀⠛⢿⠀⠀⠠⣀⠈⠉⠉⠉⠉⠛⠒⠒⠒⠀⠹⣯⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠀⠈⠛⠦⡄⠀⠀⠀⠀⠈⠛⠲⢶⣷⠆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣟⣛⣟⣛⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠈⣉⣀⡀⠀⠄⠀⠀⠒⢺⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠤⠆⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠛⢠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠤⠄⠠⠤⠄⢀⠀⢀⠞⠅⢈⣦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠹⡂⠀⠀⠴⢁⡔⠁⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠁⣁⠊⢡⠦⣌⡀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠠⠃⢐⣺⠋⠑⠢⢅⡂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠠⢅⠀⣿⠃⠀⠀⠀⠀⠉⠓⠮⣐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⠆⡀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢘⢦⣷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣅⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢬⣐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣍⡂⠄⣀⠀⠀⠠⢄⢸⡀
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠋⠳⣤⣘⠯⢽⣷⡦
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠌⣛⣾⣿⡿⠒⠛
⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢊⣄⡈⡯⠛⠁
⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⠴⠶⠒⠋⠉⠁⠈⠁
⠀⠀⠀⢀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⠖⠚⠉⠉
⠀⠀⠀⠈⡄⢳⠀⠀⠀⠀⠀⠀⠀⣀⣠⣠⠤⠶⠚⠛⠋⠉⠁
⠀⠀⠀⢀⠶⣺⣤⠤⠔⠒⠛⠋⠉⠁
⠀⠀⡀⢘⡹⠁
⠀⠂⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠒⠂⠀⠔⠀⠊⠂⠪⠀⠀⠄⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⣀⡤⠖⠒⠋⠉⠉⠉⠉⠓⠲⠤⣄⣀⠀⠲⢤⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⢦⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⢦⣀⡀⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠘⢦⡀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⣠⣖⣒⠒⠒⠤⣀
⠀⠀⠀⢠⣞⡿⡏⠉⣻⡄⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠽⡫⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⠀⠀⡠⠀⠀⡠⠒
⠀⠀⠀⢹⣏⠀⠹⡜⠉⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠲⠤⣀⠤⢄⣰⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣩⣻⣯⣤⢥⣄⡠⠔
⠀⠀⢀⡇⢣⠙⠲⡝⠟⡇⠀⡰⠃⠀⠀⠀⠀⢀⠔⠒⠊⠓⡷⡄⠀⢸⠉⢳⣰⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢩⣿⣷⡿⣿⣿⣤
⠀⠀⠘⡇⠀⠑⠒⠋⣀⣷⠋⢀⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠣⠝⠀⠘⢆⣸⠙⡄⠀⢱⡀⠀⠀⠀⠀⠀⠀⢀⠄⠊⢻⠻⣿⣏⣙⡫⢤⠃
⠀⠀⠀⠈⠓⠒⠒⠉⠁⠈⠲⠤⠍⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠜⠁⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠉⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉


⠀⠀⠀⠀⡠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠶⠤⣦⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⣐⣢⡀
⠀⠀⠀⠊⢰⢰⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢠⡄⡄⠈⠃⠀⠀⠀⠀⢀⡞⠀⠀⠈⠉⠛⡇⠀⠀⠀⠀⠀⠠⡼⢀⠀⠸⣀⣀⠜⡆
⠀⠀⠀⠀⠈⢆⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇⠀⢣⠀⠀⠀⡠⠁⢀⣨⡶
⠀⠀⠀⠀⠀⠀⠳⣝⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠃⡇⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠜⠀⠀⠰⠁⢀⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠬⠭⠍⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠢⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠭⠆⠀⠀⠀⠀⢀⣹⠆
⠀⠀⠐⠊⠉⠉⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⣄⠀⠀⢰⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠼⢦⣀⠀⠀⠀⠀⠀⠀⢰⣋⠉⠉⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⢀⡤⣀⢐⣇⣩⡾
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡇⠙⢦⡀⠀⠀⠀⠘⢮⣷⠃⠀⠀⠀⠑⣼⡞⠀⠀⠀⣧⣏⠤⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠲⠒⠋⠀⠀⠀⠙⢦⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁⠀⠈⠀⣀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⡒⠒⠒⠒⠊⠁
⠀⠀⢀⣀⣀⠤⢤⣀⠀⠀⢀⣀⣀⣢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠠⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⠤⢭⡷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⣀⣀⣀⡀
⠀⠀⣠⠖⠋⠉⢹⡉⣳⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠀⠀⠀⠉⡧
⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⣒⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠟⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠘⠥⠴⠃⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⢚⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦⢤⡀⠀⠀⠀⡸⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡬⠇⠀⠀⠀⠀⠈⡹⠹⠇⠀⠀⣴⣆⠀⠀⡰⡷⡄⠀⠀⠘⠳⣄⠀⠀⠀⠀⠙⠼⣟
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⣠⣄⣸⠁⠀⠀⠀⠘⠁⡏⠃⠀⠁⠳⣍⠀⠀⠀⠀⠈⠲⢤⣠⣖⠆⠀⠈⠑⠂
⠀⠀⢰⠋⠉⠉⠁⠀⠀⠀⠀⠀⢠⠋⠀⠀⡏⢳⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠺⡦⢄⠀⠈⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢗⠲⢄⠙⠢⠷⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⠑⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠀⠀⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⢄⡀
⠀⠀⠀⠀⠀⡠⠪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣝⢦
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠆⠀⠀⠀⠀⠀⠉⠐⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡱⡄
⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄⠀⠀⠀⠀⠀⠀⠀⠙⣞⢆
⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⢀⢔⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠈⡻⣆
⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⢇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠈⠘⡆
⠀⢢⠃⠀⠀⠀⠀⠀⠀⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘
⢀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠘⠁
⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢠⠁⠀⢀⠁⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠰⠃⠀⠀⠀⠉⠑⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⢀⢀⠤⠄⠐
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠒⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠖⠠⠄⣀⣀⡀⣀⣀⣀⡀⠀⠀⣀⠠⠔⠲⠚⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣥⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⡿⠟⣋⣉⣉⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣫⣭⣶⣾⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⢸⣇⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⣾⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⣿⣿⣿⣿⡄⢠⣿⣿⣿⣿⢿⡟⠁⠀⣠⣶⡟
⠀⠀⠀⢻⣿⣿⣿⣧⣿⣿⣿⣿⢷⠿⢀⣴⣿⣿⠟
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃⢀⣴⣿⣿⣿⠏
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠛⠁
⠀⡀⠀⠀⠀⠀⠘⣿⣿⠟⠉

⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣦⣄
⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠙⢿⣧
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢨⣥⠀⠀⠀⠀⢛⡃⠀⠀⠀⠀⠀⠀⣭⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢨⣥
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠈⠛⠿⢷⡾⠿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠻⠿⣶⡾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠙⠁⢶⣶⡾⠿⠋


⠀⠀⠀⠀⠀⢀⣴⡿⠗⠸⠿⣷⣦⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⠃⢿⣦⡀⠀⠀⠀⠀⠀⢀⣀⢺⠿⠿⠗⣰⣄
⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠈⢻⡷⠀⠀⠀⠀⣤⡌⠁⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⢈⣭⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣬⡆⠀⠀⠀⠘⣉⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠈⢻⣷⣄⡀⠀⢀⣤⣿⠏⠀⠀⠀⠀⠹⢟⣀⡀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠁⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠌⠉⠀⠀⠀⠀⠀⠀⠀⠙⠀⠿⠿⠿⠂

⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⢀⣤⣤⣼⣦⡀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⣀⣤⣤⣄⡀⠀⣀⣤⣤⣄⡀⠀⣀⣤⣴⣦⡀
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠻⠿⠛⠉⠉⠉⠙⠻⠿⠛⠉⠉⠙⠁⠀⠀⠀⠻⠿⠛⠉⠉⠙⠻⠿⠛⠉⠉⠙⠻⠿⠛⠉⠉⠙⠻⠿⠛⠉⠉⠋
⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⣀⣠⣤⣤⣤⣦⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠻⠿⠟⠛⠉⠉⠉⠉⠉⠛⠛⠿⠿⠛⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠛⠋⠉⠉⠉⠉⠙⠛⠿⠿⠟⠛⠋⠉⠉⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⢸⣿⣿⣿⣿⣿⠀⠀⢀⣤⣾⣿⣿⣷⣤⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣷⣤⡀
⢀⣸⣿⣿⣿⣿⣿⣄⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠂⠀⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓
⠀⠈⠛⢿⣿⠿⠋⠁⠀⠀⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠋⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠠⢾⣿⣿⡷⠄⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡆
⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠠⠾⠿⠿⠿⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣷⣀⠀⠀⠀⠐⢶⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋⠀⠀⠀⠀⠀⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⠾⠿⠿⠿⠿⠿⠿⠿⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣷⣤⡀
⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠛⠛⣿⡿⢷⣦⣤⡀
⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⠙⠻⢷⣤⡀
⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠙⢿⣦⡀
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⠀⠘⣿⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣼⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀⣸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁






⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠸⠈⠑⢄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠐⠒⠀⠀⠀⠙⠈⠀⠀⠀⠑⠀⠀⠀⣴⡟⠻⢧⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠳⣄⠁⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠷⣄⣨⠦⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡉⣠⡤⠚⠉⠀⠀⠀⠀⠀⠀⠈⠳⣕⢄
⠀⠀⠀⠀⠀⠀⢀⢊⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢠⠀⠀⠲⠀⠀⢀⢴⠆⠚⠀⠰⣁⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣢⡀
⠀⠀⠀⠀⠀⡠⣣⠋⠀⠀⠀⠀⠀⠀⠀⡠⣢⢞⡭⠀⠃⠈⢰⢸⡄⡰⠞⠀⠀⠀⠀⠀⠉⠓⢄⡀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠙⠱⡀
⠀⠀⠀⠀⢠⣲⠇⠀⠀⠀⠀⠀⠀⠀⣐⡴⠗⠉⠀⠀⠀⠀⢰⠼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢦⡄⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢀⢂⠋⠀⠀⠀⠀⠀⠀⠀⠰⠻⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡤⠀⠠⢆⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⢜⢡⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣣⠀⠊⢃⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣖⠈⡄⠀⠀⠀⠀⠀⠀⠀⠜⡀
⠀⠀⠀⣇⠆⠀⠀⢠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠣⠈⠀⠀⣤⠀⠈⠑⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣿⠄⠅⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⢀⠈⡀⠐⠀⢈⡳⢢⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡡⢠⠉⠲
⠀⠀⠀⠈⡄⠰⠆⢀⣼⠁⠀⠙⠓⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠹⡀
⠀⠀⠀⠀⠈⠀⠀⡾⠎⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠠⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀
⠀⠀⠀⠀⠀⠀⡤⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠨⡄⠀⠀⣠⡤⠔⠒⠞⠀⣈⡽⠁
⠀⠀⠀⠀⠀⢀⠔⣇⣠⡴⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢞⣼⣛⣉⡠⠤⠴⠔⠊⠈⠁⠈⠁
⠀⠀⠀⠀⠀⢡⣬⠯⠜⢀⠈⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠈⠉⠈⠁
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡀⠄⠈⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣀⡀⠁⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣀⡀⠈⠑⠲⠦⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⡂⠝⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⡤⣅⡄⠀⡀⠁⠈⠉⠉⠙⠐⠒⠛⠋⠙⢁⠁⢀⠈⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠛⠋⠚⠒⠒⠰⠓⠂⠐⠚⠁⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒
⠀⠀⠀⠀⠁⠀⠀⢀⠀⠤⠤⢤⠀⠀⠀⠀⠀⠀⡠⠂⠉⢁⠄⠂⠀⠀⠀⠀⠈⠁⡠⠊⠀⠀⠀⠀⢀⠓
⠀⠐⣀⠀⠠⠐⠈⠀⡀⢠⠀⠀⢀⠠⠆⠀⡠⠊⢀⠠⠔⢅⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⢡⠇⡀⠄
⠀⠀⠉⠀⢀⠄⠊⠁⠀⠈⠀⠐⠁⠀⠀⠐⠀⠠⠁⢰⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠄⠂⢁⠄⠐⠀⠀⠉
⠀⠠⠠⠐⠁⢀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠠⠁⠀⠈⠤⠔⡀⠄⠚⠀⢀⣀⡀⠀⠀⠊⠀⢀⠔⠃
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠈⠀⡠⠀⠀⠀⠙
⠀⠀⠀⠊⠀⠀⠀⡀⠀⠀⡴⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠋⡆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢈⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⢀⠛⢀⠄
⠀⠀⠀⡠⠐⠀⢁⠠⠀⠐⠂⠀⠀⠐⠲⠀⢀⠄⠂⠀⠈⠁⡠⠃⠀⠀⠢⡀⠀⠀⠀⠀⠀⡀⠐⠁⢀⠂
⠀⠀⠊⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢀⣀⡀⠀⠀⠄⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⢀⠀⠀⠉⠐⠄⠀⠀⠀⡥
⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⢀⠜⠂⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⡀⠔⠈⠀⡰⠆⠀⠰
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠐⠀⠄⠠⠄⠐⠈⣀⠀⠀⠀⠑⠄⠀⠠⠚
⠀⠀⠀⠀⠠⡇⠀⠀⢠⡅⠀⠀⢀⠠⠃⠀⠀⠄⠀⠀⣀⠁⠂⠄⠀⠀⠠⠀⠂⠉⠀⠀⠀⠠⠀⠀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠿⢦⣄
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣔⣠⡿⢿⣦⣀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡟⢻⡿⠿⠿⣿⠿⢿⡷⡶⢶⣿⠿⢡⡾⠗⣀⠹⢻⡷⣄⡀
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⢿⡿⢟⡫⠘⠁⠀⠁⠐⡀⠘⢀⠊⢁⡴⡢⣶⡋⢈⡄⠈⠥⠀⢀⣴⠟⠁
⠀⠀⠀⣠⣾⣿⣿⣫⣿⣿⣷⣿⣥⣤⣤⣶⣵⣶⣿⣾⠾⠿⠷⠷⠾⠾⣿⠿⢫⣶⢁⣠⡾⠛⠁
⠀⠀⠀⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⣀⡤⠖⠛⠋⠉⠉⠛⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⠃⠀⠀⠀⠀⣠⠞⠙⡄⠀⠀⡠⠚⠙⣦⠀⢠⢋⡇
⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡇⠀⢠⠃⠀⠀⡟⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢽⣦⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠁⠀⢸⠀⠀⢰⠇⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⠀⡸⠀⠀⠈⢧⣠⠜
⠀⠀⠀⠀⠀⢀⣤⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⡴⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡯⣄
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⢄⠀⠀⠀⠠⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠈⠢⣀⣠⠜⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠛⠻⡄⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⢄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢣⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾
⠀⠀⠀⠀⠀⠀⠋⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⢀⡏⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⡠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠂⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⣾⣿⠶⠤
⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⣤⠞⠉⠁⠀⠀⠀⠁
⠀⠀⠈⠓⠲⠦⠤⢤⡀⠀⠀⠀⠀⠀⠀⠐⢆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠋⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⣠⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡠⠦⡄
⠀⠀⠀⠳⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⣀⡠⢶⡶⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠹⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠉⡦⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡁
⠀⠀⠀⠀⠀⣀⡤⠖⠁⠀⠀⠀⠀⠚⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⢀⠰⠁
⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⢠⠴⠒⠲⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠉⠑⠓⠒⢢⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢳⡄⠀⠀⡏⠀⠀⠀⠈⢓⣉⣲⡤⠀⠀⠀⠀⠀⢸⣾⡠
⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⠦⠶⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠋

⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣷⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠀⢀⣤⡄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⠀⠀⢸
⠀⢰⠿⠁⠀⠈⠿⠧⠀⠀⠀⢀⡞⠛⠀⠀⠉⢳⡄⠀⠀⠀⢶⣷⠈⠀⠈⠙⢦⠀⠀⠀⢠⠞⠛⠀⠈⠙⢦⡀⢸
⠀⠿⠀⠀⠀⠀⠀⢰⡆⠀⠀⢸⡁⠀⠀⠀⠀⠰⣿⠂⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠰⣶⣆⠀⠀⣸⡾⠀⠀⠀⠈⢡⣤⣄⣀⣠⡶⠀⠀⠀⠀⠘⢦⣀⠀⢀⠸⡿⠆⠀⠀⠘⢦⣀⠀⢀⣠⠞⠁⢸
⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠛⠛⠉⠉⠉⠀⠀⠀⢀⣠⡾⠛⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⡻⣄⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣅⡳⣮⠾⠋
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⢠⡟⢱⡀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣉⣳⣄
⠀⠀⠀⢀⡞⠀⠀⢷⠟⠁⠀⠀⠀⠀⢀⣠⣤⡶⠚⣿⡻⡉⢫⠀⢂⢂⠘⠄⡀⠀⠐⠀⠀⠁⠀⠈⠈⠉⢩⠩⡓
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣀⣴⡞⠻⢍⡑⢑⣕⣬⠿⠾⠷⠓⠒⠚⠒⠒⠚⠓⠛⠓⠒⠛⠒⠲⠒⠶⠺⠴⠁
⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⣾⣯⣑⣚⣭⠖⠊⠉
⠀⣸⠃⠀⠀⠀⠀⠀⠀⠈⡖⠿⣛⠌⠁
⠀⠈⠳⣶⣤⣄⣀⡀⠀⠀⠹⣷⢦⡄
⠀⠀⠀⠈⠙⠺⠿⢿⣝⣻⣛⣛⡷⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

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

⠀⠀⣿⣶⣄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣐⣦⣤⡀⠀⠀⣀⡤⠶⠒⠛⠛⠶⢦⣄⣄
⠀⠀⠙⠙⢷⣤⣤⣤⡴⠚⠁⠀⠀⠀⠸⣄⠀⠀⠉⠙⠛⠋⠿⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⣠⡶⠶⠶⠦
⠀⠀⠀⠀⠀⣠⣴⠦⠀⠀⢉⡟⡇⠀⠀⠀⠙⢷⣄⠀⣀⠀⠀⠀⠀⢩⠟⠃⠀⠀⣼⠃
⠀⠀⠀⢠⣾⠛⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢻⣾⣷⣄⠀⠀⢸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢸⣿⡥⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠘⣧⠀⠀⠀⠻⣷⣤⣀⣀⣠⡿⢿⠁
⠀⠀⠀⠋⠀⣠⣄⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈⠉⠛⠛⠉
⠀⠀⠀⠀⢰⢿⣿⢆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠰⣶⣶⣖⣀⣀⣀⣀⣴⠆⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠘⠊⠙⠛⠛⠛⠉⠀⠀⢀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡿⠋⠀⢀⣤⣴⣆⣀⣤⡴⠞⠁⠀⠀⠀⣼⠇⠁
⠀⠀⠴⣶⣶⣂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⡖⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠈⠻⠉⠙⠛⠻⠷⢶⣶⣤⡄⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠸⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡷⠄
⠀⠀⠀⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠋⠙⠛⢷⣤⣧⠀⠀⠀⠻⣷⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠶⠚⠋⠀⠀⣸⠁⠀⠀⠀⠉⠛⠿⢿⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⠃
⠀⠀⠀⢀⣤⡶⠟⠛⠋⠉⠙⣻⣿⣧⠀⠈⠻⢶⣤⣤⣤⠴⠂⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⠿⠛⠹⠃
⠀⠀⠀⠀⠁