⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣦⡀
⠀⠀⠀⣴⡿⠟⠷⠆⣠⠋⠀⠀⠀⢸⣿
⠀⠀⠀⣿⡄⠀⠀⠀⠈⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢠⠏⡆⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⡟⢦⡀⠇⠀⠀⣀⠞⠀⠀⠘⡀⢀⡠⠚⣉⠤⠂⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⡇⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠘⢧⠔⣉⠤⠒⠒⠉⠉⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣤⠶⠶⢶⡄⠀⠀⠀⠀⢹⡆
⠀⣀⠤⠒⠒⢺⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⢸⠀⡿⠀⡀⠀⣀⡟⠀⠀⠀⠀⢸⡇
⠈⠀⠀⣠⠴⠚⢯⡀⠐⠒⠚⠉⠀⢶⠂⠀⣀⠜⠀⢿⡀⠉⠚⠉⠀⠀⠀⠀⣠⠟
⠀⠠⠊⠀⠀⠀⠀⠙⠂⣴⠒⠒⣲⢔⠉⠉⣹⣞⣉⣈⠿⢦⣀⣀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣄⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡩⠭⣿⣿⣿⣒⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢣⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣇⣼⡄
⠀⠀⠀⠀⢿⠓⢶⣤⣴⣶⣿⣿⡿⠋⠉⣝⢷⡀
⠀⠀⠀⠀⠈⢿⣿⡟⠁⠀⠮⢿⡇⠀⠀⠀⣸⣧⣒⣒⡒⠤
⠀⠀⠀⠀⢀⣈⣿⣧⡀⠀⠀⣸⣿⣶⣶⣾⣿⣿⠷⠦⣘⠁
⠀⠀⠀⢊⠥⢒⡺⣿⣿⣶⣾⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⢀⠈⠁⠀⠈⢻⣿⣿⣿⣿⡿⠿⠋⠀
⠀⠀⠀⣿⡇⠀⢠⣶⣿⣿⣷⡄
⠀⠀⠀⣿⣧⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠈⠛⠿⣿⣿⡿⣿⡿⠿⠀

⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⢰⡿⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⢹⡇
⠀⠀⢸⡇💗⠀⠙⠿⣦⣀⣀⣤⣤⣤⣄⣀⣠⡾⠛⠁💗⢸⡇
⠀⠀⢸⣷⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⣤⣾⣇⡀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡗⢀⣠⣿⣤
⠀⢀⣿⣈⡁⠈⢷⣤⣼⣿⠠⣄⠀⢀⠀⢀⡄⠘⢷⣤⣼⡇⠀⣩⣿⣂
⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⠟⢷⡾⠁⠀⠀⠀⠀⠀⠀⢠⡿⠉
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⣶⣤⣤⣤⣶⡶⠶⠟⠛⠉

⠀⠀⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣼⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣼⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣿⣿⡗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⡇⠜⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀
⣿⣿⣿⣶⣿⣿⣿⣿⣿⠋⡹⠙⣿⣿⣿⡇⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⠛⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀
⣿⣿⡿⠻⠿⠿⠿⠿⠛⠹⠑⠀⠀
⠟

⠀⠀   ⠀⣀⣀⡀⠀     ⣀⣀
⠀⡴⠚⠛⠲⣤⠞⠁⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⡇⠀⡷⠛⢳⠀
⢸⡇      ⣹⠀    ⣇⣀⣀⣀⠜⠀
⠈⢇     ⢀⡟⠋⠉⠙⠳⣄⠴⠛⠋⠋⠛⣷⡄
⠀⠈⢦⡀   ⢀⡞⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠙⠦⣀⣀⣠⠏⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
  ⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣆
⠀⣴⠏⠀⠀⠀⠀⠠⣶⠦⠀⠀⠀⠀⠾⠷⠀⠀⠀⠀⠀⠀⠘⣧⡀
⢠⣿⠀⠀⠀⣀⣀⣀⡀⠀⠤⠞⠢⠄⠀⠀⣀⣀⣀⣀⡀⠀⠀⢹⡆
⢸⣇⡠⠚⠋⠉⠉⠉⠉⠳⣄⠀⠀⢠⠞⠉⠀⠀⠀⠈⠉⠳⣄⢸⡇
⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣸⣾⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⡆
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣴⡟⠀⠀⢿⣶⣤⣤⣴⠾⣿
⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢠⡿⠁⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠈⠛⠛⠀⠀⢶⡤⣿⣀⣀
⠀⢀⣿⠁⢠⡾⠛⠉⠀⠀⠉⠻⣦⣀⡴⠞⠛⠛⠛⠷⣦⣀⡾⡒⠤
⠀⢸⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⢻⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉