Fruit Emojis & Symbols

⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠋⣭⣉⠛⣓⠲⢤⡀
⠀⠀⠀⠀⠈⠻⣿⡳⠶⠶⣤⡤⠤⠴⠶⠖⠛⢉⣁⠀⣉⣵⠶⢾⠛⠋⠉⠙⠛⡻⣶⣄⠀⠀⢀⡴⠤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⡶⢤⣄⣀⣀⣐⣤⣤⡴⠞⢋⠟⠀⡰⠃⠀⣠⡴⠚⠉⠉⠉⠛⢷⣴⡏⠁⠀⢬⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⡀⠀⠔⠈⠀⠐⠁⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⢶⣻⣿⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⢀⣀⣼⣇⣠⡟⠻⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠉⠛⠆⠀⠉⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀
⠀⠀⠀⠐⢠⡟⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⡢⢄⣀⠀⠀⠀⠘⢑⣠⠔⠓⢀⠀⣀⠴⠀⠀⠀⠁⡺⡞⣳⠄
⠀⠈⠢⠴⠈⠇⠀⠀⢀⡄⠀⠀⢰⠀⠀⠀⠢⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠓⠻⣙⣻⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠐⢀⠇⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠠⠭⣦⡄
⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠡⡀⠀⠄⠘⠠⠒⠂⢄⠀⠀⢰⡀⠣⡬⢺⡀⠀⠀⢈⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠐⡔⠀⠀⠀⠀⠙⠋⠁⠀⠑⠀⠀⠀⠀⠀⠐⢤⡤⢇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠷⠂

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠠⣤⡁⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠦⠐⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠊⠁⠒⠦⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠄⠀⠀⠀⠀⠀⠐⠳⠤⢴⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠚⠈⠁

⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⣀⣤⡀⠀⡀⢀⡆⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⢸⡹⠁⠀⠀⠔⠋⠠⠄⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠈⢈⢃⠀⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠁⠂
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⢀⡴⠋⢡⣴⣶⣷⣾⠿⡿⣿⣄⣬⣭⣓⠲⢤⣀
⠀⠀⠀⠀⢀⡾⢰⣿⣿⣷⣿⣽⣿⣿⣟⣿⣿⣿⣿⣵⣿⣷⣮⡕⠢⣀
⠀⠀⠀⠀⣼⣿⡈⠿⠿⣿⣿⣿⣾⣿⣿⣏⠀⢀⣽⣟⣽⣿⢿⣿⣷⡈⠳⡀
⠀⠀⠀⢠⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠿⡛⠻⠻⢾⣯⣿⡃⢳
⠀⠀⠀⢸⣿⣿⣿⣿⣷⣬⡙⠛⠹⣿⣿⣿⣿⠍⢁⣺⣿⣆⡅⠀⠈⠙⢧⡼
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣬⣿⣿⠟⠀⠀⡀⠀⢀⣱⣤⣴⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠳⠀⠀⠀⣠⣶⣿⣿⣿⣿⣴⠖⠀⣉⣻⣶⣃
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣞⣂⣭⠀⣴⣿⣿⣿⣿⣿⣿⣿⣇⠠⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠙⢊⣙⡛⢿⣿⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠁⠈⠛⣋⠈⠀⡿⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⠀⡀⣠⣏⠐⠀⠁⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⢿⣿⣿⣿⣿⣿⡿⠯⠉⠻⢿⣿⣿⣿⣧⠚⡀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠈⠻⣿⣽⣾⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠋⠉⢉⠉⠙⠛⠙⢿⣿⣗⡀⢀⠀⠀⠻⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣆⠈⠀⡀⡀⠀⠁⣠⣌⢻⣿⣿⣿⢏⡙⢂⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣤⣴⣾⣿⣅⢶⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠟⠋

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

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


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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠁⠀⠀⠑⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡆⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣄⠀⠀⠀⠀⠐⣶⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠐⠒⠤⠄⠀⠒⢢⠽⠛⠉⠙⠁⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠁⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠈⠉
⠀⠀⠀⠀⠃⠀⠀⠀⠑⢦⡀⠀⠀⠀⠎⠑⢶⣿⣤⣤⣤⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⠚⠀⢶⣬⣇⠘⣡⠚⠛⠚⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡶⢾⡀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⠀⠀⣠⢻⡮⠿⢩⣄⡤⣤⣈⡿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⢄⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⢀⢀⡼⠃⡀⢶⣶⡌⢀⠌⠉⠀⠈⠁⡀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⡀⢲⣶⡀⠊⠱⠐⠄⠑
⠀⠀⠀⠀⠀⣀⣀⡀⠲⠶⠛⠻⢥⡀⠒⢤⠌⠣⠛⢀⣀⣀⣀⠈⠻⠇⠠⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠠⢀⣴⠷⢿⣡⠾⠀⠐⠰⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⣼⡼⢠⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢢⣤⣤⣤⣶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠎⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠒⠂⠀⠈⠁⠾⠀⠐⠀⠀⢀⣰⡆⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢷⡀⠀⠐⠠⢄⣠⡀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠶⠞⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠄⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢀⠐⡖⢀⠀⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠶⠀⠒⠢⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡐⠛⠚⠏⠩⣿⣆⡤⠘⣋⣈⣭⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠁⠈⠁⠀⠀⢀⡀⢘⣷⣞⢣⣾⡯⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠙⣯⡀⢀⣼⠓⠀⣐⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⢀⣠⡀⢀⣥⡿⡟⠧⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢡⡤⢤⣗⢆⣜⠁⠀⢈⡉⣦⣄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⡀⢀⠀⠀⡤⠄⢂⣈⢁⣨⡧⠄⠟⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠺⠿⠀⠀⠀⣏⠀⠱⣶⡘⠈⠀⢸⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡉⠲⡶⣀⡴⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠑⢂⠀⢀⠦⠤⠐⠁⠀⠀⠈⠁⠀⢐⠈⠙⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠐⢶⠃⣾⡿⣄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⡀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠁⠀⠋⠙⠢⢀⡀⠀⠀⠀⠤⠛⠂⠀⠄⠀⠀⠀⠐
⠀⠀⣀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣟⣉⡻⠿⠿⠿⠿⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

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


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

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

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣻⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣛⣛⣽⣷⠿⣙⡿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣬⣴⣶⣿⠟⣻⣻⡻⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣾⡿⢿⣿⣿⣾⣿⡇⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢿⣿⣿⣿⣿⣿⣷⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣤⢤⡀⠙⢧⣼⣧⣴⣒⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣁⠀⠉⠛⠛⠛⠋⠉⢀⣿⣷⠓⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣰⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⡀⠀⣀⣄⣠⣾⡃⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⡟⠛⠿⠙⠇⣿⣿⡿⠻⡟⣷⠄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠉⢸⠀⡇⣴⣾⠀⠀⠸⢣⢷⣿⣿⡛⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠲⢾⠰⠇⠋⠈⠀⠀⠀⠀⠈⠘⢻⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣽⣿⣿⣿⣿⣿⣿⡽⣷⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣽⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡟⣿⣿⣿⣿⣿⣿⣧⣛⢀⠀⠁⠀⠐⢄⠀⣠⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣮⣻⣿⣿⣿⣿⣿⣿⣾⣆⣤⣾⣷⣮⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣷⣿⣿⣟⢉⣉⣉⣉⣉⣭⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠟⠿⠛⠿⠟⠛⠿⠿⠓⠂





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⢀⣠⡀
⠀⠀⣴⣿⣿⣿⣷⣄⠀⠀⢀⣶⣷⣶⣿⣿⣆⠀⠀⠀⣀⠀⣠⣶⣦⣠⡄⠀⠀⣠⣠⣄⣴⣽⣦⠀⠀⠀⠀⣀⡀
⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣷⣆⣀
⠀⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠙⣿⣿⣿⡿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⢻⣿⣿⣿⡏⠀⠀⠀⠀⠙⠋⠉
⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠉⠛⠛⠛⠛⠙⠉⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢀⣴⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣄⠀⠀⠀⠀⣠⣤⣷⣴⣰
⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⣿⣿⣿⠤⠀⠀⠀⠂⠀⠀⠄
⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠈⠻⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠀⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⢠⠄
⠀⠀⢀⠈⣡⣀⣤⣤⣤⣀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣇⣠⣄⡀⠀⣰⣿⣿⣿⣷⡀⠀⣼⠻⢿⣿⣟⡀⠀⠒⣿⣾⣿⣿⡓
⠀⢰⣏⢾⣯⣿⣿⣿⣿⣿⡂⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠛⠛⠛⠛⠛⠃⠀⢻⣷⣤⣿⡿⠀⠀⠈⠉⠻
⠀⠈⢿⣷⣿⣿⣿⣿⡿⠟⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣤⣤⣤⡄⠀⠀⠈⢿⣿⡯⠁
⠀⠀⠀⠈⡉⣩⠉⣁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠋⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⣀⣀⡀
⠀⠀⢐⣾⣿⣿⣯⣿⣒⠀⠀⠀⢠⣴⣶⣷⣾⡤⠀⠀⠀⣀⣀⣈⣤⣤⡀⠀⢀⣾⢿⣹⣟⢿⣷⡀⠀⠀⠀⠀⠠⠀⢀
⠀⠀⠾⠿⠿⠿⠿⠿⠿⠆⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⣰⣿⣿⣿⣿⣿⣧⡀⢸⣿⣎⢷⣿⢨⣿⡇⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⡿⠁⠈⠻⣿⣷⣍⣾⣿⠁
⠀⠀⠈⢻⣿⣿⣿⣿⠋⠀⠀⠀⠈⢻⣿⣿⡿⠃⠀⠀⠀⠙⢿⣿⣿⠟⠁⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠙⠛⠛⠁⠀⡀⠀⠀⠀⠀⠈⠉⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⡤⠈⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⢀⠀⠀⠀⠀⣰⢒⡀⣀⡠⣄
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡆⠀⠀⠐⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⣿⣿⢛⢿⢛⠟⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⢺⠒⢄⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⣑⣤⣵⢂⡀⠀⠀⠀⠀⠀⡹⠺⣄⠀⠀⠀⠀⠀⡱⠤⠵⣋⡜⠀⠀⠀⠀⠀⠀⠀⢸⠆⠑⡄
⠀⠀⠀⠀⠀⢎⠆⠀⠉⠁⠈⢣⠀⠀⠀⡸⠀⠀⠘⡄⠀⠀⠀⢸⠰⠀⠂⠂⢸⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⡜⡁⠀⠀⠀⠙⡄⠀⠀⠈⢎⢘⢀⢁⠆⠀⠀⣀⠠⠴⠚⢁⡠⠊⢀⠎
⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⣠⠃⠀⠀⢇⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⠒⠊⠀⠀⠘⢥⣉⣉⣉⣁⠤⠔⠋
⠀⠀⠀⠀⠀⠀⠈⠓⠉⠉⠁⠀⠀⠀⠀⠑⠒⠒⠲⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢢
⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢢⠀⠀⠀⠀⠀⢀⡤⠤⠼⡤⢮⡀
⠀⠀⠀⠀⠀⢀⣴⠍⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⢀⡤⢴⡺⠯⢷⡼⠤⠤⡀⠀⠀⡏⡎⠀⠀⠘⡄⠈⡆
⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢰⠚⢄⡠⢇⠀⣰⡿⠶⡖⠁⠀⠀⡗⠂⠀⠀⠐⠁⢀⡇
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢀⣟⡩⠻⢄⠀⡏⠉⣧⠠⠏⠀⠀⠀⠘⠦⣀⣀⣀⠴⠊
⠀⠀⠀⠀⠀⠈⠳⠤⣀⣀⠤⠖⠁⠀⠀⠀⠸⠤⠷⠤⠚⠐⠉⠉⠁⠀⢠⢤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠠⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⡌⠁⡈⠀⠄⢀⠀⢁⠀⠂⡈⡸⢰
⠀⠀⠀⠀⠀⠀⢸⠦⡸⠙⣤⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣦⡀⠂⠠⢈⠀⡄⠐⠀⡰⣡⠃
⠀⠀⠀⠀⠀⠀⢸⠳⢽⢊⡤⢻⠀⠀⠀⠀⡴⠊⠁⣶⣀⠤⢄⣀⠀⠀⠀⠀⠀⠙⠪⢕⡲⠤⠤⠤⣒⡭⠚⠁
⠀⠀⠀⠀⠀⠀⣠⠓⠻⣟⠙⣧⡀⠀⠀⠈⠓⠒⢩⣋⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⣎⠈⣦⡊⠈⡱⠧⣵⠀⠀⠀⠀⠀⡇⡃⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢀⠴⢒⠩⠭⣑⠒⠤⢄
⠀⠀⠀⠀⠀⡟⠻⣄⣩⠾⢄⣰⢹⠀⠀⠀⠀⠀⠳⣁⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⢳⠶⣊⠑⢢⠼⣉⠏⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠉⠁⠀⠀⠀⠀⠀⠇⣀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠑⠶⣋⡱⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠙⠛⠻⢶⣄⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣇⣀⡀⠀⠀⠙⣿⠁⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣙⡛⠛⠿⠿⠛⠛⠛⠛⠛⠛⠻⠷⣦⣄⠁⠀⠀⣿⣧⣴⡶⠟⠛⠛⠛⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠛⠉⠉⠉⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠈⠻⣷⡀⣰⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠠⣽⣷⣂⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠈⠈⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠙⢷⣤⣿⢿⣿⠃⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠤⣾⣥⣤⣴⣶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⢀⣀⣀⣠⡤⠄⢀⣀⣤⡤⢶⣶⣾⣿⠡⢖⣿⡷⠛⠋⠉⠉⠉⠛⠻⠷⣦⣤⣀⣀⣀⣤⣤⠶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣭⣭⣭⣤⠶⢛⣋⣡⣤⡶⠛⢉⡾⢁⣴⣿⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⣿⣿⣷⡾⢿⣿⠟⠋⢀⣴⣿⠃⣼⠿⣿⣿⣜⠿⣵⣶⡭⠖⠀⠀⠚⠛⠛⠿⢿⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠉⠀⣴⠟⠁⢀⣴⠿⢻⡏⢠⡿⠀⠈⠙⠿⣷⣶⣶⣶⣶⣾⠿⠟⠛⠋⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡿⠋⠀⠀⢀⣾⠋⢀⣴⠟⠁⠀⢸⡇⢸⡇
⠀⠀⠀⠀⣠⣴⡾⠿⢛⠋⠙⣿⡿⠿⠿⣶⣦⡾⠁⣠⡟⠁⠀⠀⠀⢸⡇⢸⡇
⠀⠀⢠⣾⡿⠋⠀⠀⠸⣦⣘⣫⡤⠀⠀⠀⡿⠁⣰⣏⠀⠀⠀⠀⠀⢘⡇⢸⣇⣀⣀⣀
⠀⢠⣿⠏⠀⡀⠀⠀⠀⠈⠙⠉⠀⠀⠀⢸⠃⣰⠟⣿⣧⠀⢀⣤⣾⣿⣿⡀⢿⠿⠿⢿⣿⣷⣦⣄⡀
⠀⢸⣿⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⡟⠀⢸⣿⣴⣿⡿⠋⠁⠈⢧⡈⣦⡴⠀⠀⠈⠉⠛⢿⣦⡀
⠀⢸⣿⡀⠻⣇⠀⠀⠀⢀⣀⣤⣤⣶⣶⡇⣾⣤⣤⣿⣿⣿⠏⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠈⢿⣷⡄⠉⠀⣠⣾⡿⠟⠋⢁⡀⢸⡇⡏⠀⠈⠙⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠻⣿⣶⣾⠟⠉⠀⠀⠀⠀⠻⣾⣧⣧⡶⠃⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿
⠀⠀⠀⠀⢨⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⣸⣿
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⢠⣿⠏
⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠰⠾⠛⠉⢀⣴⣿⠏
⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀⢀⣿⣿⣤⣄⣀⣀⣀⣀⣀⣤⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⠀⣠⣾⡿⠁⠉⠛⠛⠻⠿⠿⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⣉⡛⠛⠿⠿⠛⠋⣀⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⢠⠐⠂⠁⠁⠀⢀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢰⠋⠀⠑⣄⠁⠲⠄⠀⠀⠀⢀⣠⣤⡁⠄⠀⠀⠀⠐⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠋⠀⠀⠀⠈⢣⡀⠀⠀⠀⢠⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠈⠻⠿⠛⠁⠀⠴⠶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠀⢇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡦
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠈⢄⣀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠙⠋⠅⠁
⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠐⠀⠀⠠⠚⠁⠠⣀⠀⠀⠀⡀⠄⢤⣤⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣠⣤⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠓⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠺⠏⠉⡡⠌⠁⠀⠀⢠⣾⣿⣿⡿
⠀⠀⠀⠠⠖⠁⠀⠂⠀⠀⠀⠀⠀⠈⠉⠀⠁⠁⠀⠀⠀⠀⡴⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢷⠀⢸⠃⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡀⢘⡦⠶⠒⠺⢄⠊⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⡄⠀⠀⠀⣀⣠⠄⠾⠀⠀⠀⠀⠈⠇⢡⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠁⢀⣀⡿⠀⠀⠀⣀⠀⢀⢀⣶⠀⣀⠀⢀⢀⣤
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠁⠀⠀⣷⢰⣿⠀⣾⡾⢸⠌⣿⢠⣿⡟⣾⢔⡿⢀⣶⠷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⠛⠶⣌⠙⠃⠘⠛⠉⢁⠀⠀⠙⠋⠈⠀⠀⠘⠷⠻⣇⣠⡾⠋⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⡿⠀⠀⣆⢰⡇⣴⠀⣿⣽⠀⣾⡒⢠⡞⠦⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢻⣼⠀⣿⠀⣿⢸⢷⡇⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠙⠂⠛⠋⠈⠓⠂⠘⠾⠃


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢸⠀⢰⠇⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⢀⡵⠒⠋⠓⠢⡉⡠⠤⠖
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢶⡄⠀⠀⠠⠴⠖⠘⠁⠀⠀⠀⠀⠛⠐⠶⠆
⠀⠀⠀⠀⠀⠀⢰⠋⠀⠠⠼⠃⢀⡀⣠⡀⢠⣆⣾⣇⣤⠀⢠⣤⢾⢂⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⡀⠼⣧⠿⣇⡼⣿⠘⠋⢾⣰⠿⠏⠻⢫⡏⣰⠟⠋⣠⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠬⠉⢻⡆⠀⠀⠈⣀⠀⠆⣠⢤⡀⣀⣀⠀⣈⡉⠙⠲⠺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣤⠴⠁⠀⢸⣤⡇⢸⡇⣿⠛⡄⡿⠀⠸⣇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⡇⢿⡴⠃⣷⣀⢠⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠉


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⡏⠐⢁⢀⣰⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⣠⠀⢀⣰⣇⣴⣽⣦⣌⡖
⠀⠀⠀⠀⠀⠀⠀⣀⠙⢠⠻⠿⠋⣿⠀⢰⡇⠀⠀⠀⠀⣀⣰⣇⠱⡀⢀⡖⣯⣸⣷⣄⡠⢻⡄⠀⠀⠀⠀⠹⢄⡹⣧⣾⠏⢿⢋⢹⡁⡙⠁
⠀⠀⠀⠀⠀⠀⠀⣏⢀⠀⢠⠤⣖⢤⣠⢾⠁⠀⠀⠀⠘⠉⠀⠙⢆⠓⡏⠃⣹⠁⢹⡉⠃⡸⢁⠒⠖⠁⠀⠀⠀⠓⠀⣥⠘⣏⢾⢀⡜⣧
⠀⠀⠀⠀⠀⠀⠀⣿⢯⢸⡌⢳⡘⡏⠈⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠆⠈⣦⠙⠛⠾⠀⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠘⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡂⢀⠀⢰⡄⡆⣆⠰⢠⡆⠀⠀⠀⠀⠀⠀⠀⢁⠶⠙⢒⠸⠚⠆⠁⡀⠀⠀⠀⠀⢠⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⢠⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⢐⢸⠀⠀⢱⡇⡈⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⡌⡈⠀⠀⢀⠰⡄⡈⠀⠀⠀⠀⠀⠀⢣⢨⢸⢸⢰⠀⢡⠐⢰⠀⠈⣦⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠄⣤⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠏⠒⠀⡀⠮⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⢀⠁⢀⡀⢀⡁⣀⡀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡿⡀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠁⠠⠀⢀⠅⣠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⠂⠘⡅⡷⠁⡗
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠚⠃⠁⠙⠂⠈⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠃⣘⠀⢰⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠋⠁⠓⠁⠃⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣿⠄⢈⡀⠀⠀⠀⠀⠀⢀⡴⢢⡄⠀⠀⣈⣉⣉⣉⣉⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣦⣤⢦⠂⡀⢀⠀⠀⠀⠀⠸⣧⡜⠁⣀⢀⣤⣤⣠⣤⣤⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠯⢅⣿⣴⣟⠛⣇
⠀⠀⠀⠀⠀⠀⠀⡠⡀⡀⠀⠁⣡⣌⠀⠁⣸⠀⠀⠀⠀⠀⠀⠙⣷⠯⠻⠿⠘⠙⠋⠘⠹⠛⠄⢿⡹⠃⠀⠀⠀⠀⠛⠋⠈⠃⠈⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠃⣿⠁⡜⠧⠻⡌⠟⠿⢯⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣒⣒⣒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⢻⠀⣯⠁⣯⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠓⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠓⠀⠛⠙⠂

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠉⢷
⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣱⣄⣤⣤⣤
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢀⣤⠀⠀⣀⠀⢀⡄⠀⢀⢴⡄⠀⢀⣴⠶⣆⠀⠀⡇⠀⣰⡟
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⢀⣤⡄⠀⠀⣤⠀⠀⣼⡇⡴⢹⣇⠔⢡⡟⠀⢰⡏⡰⣹⢇⡜⢡⡿⠀⢰⡟⢁⠠⠃⠀⡴⠁⣼⠏
⠀⠀⠀⠀⠀⠙⣷⡄⢀⠔⢉⣿⠁⣠⢺⡏⠀⠀⣾⡟⠀⣿⠏⢠⡿⠀⠀⣼⡟⠀⠿⠋⢀⣾⠁⠀⣿⡇⠀⠀⣠⠎⠀⣸⡏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⢸⣿⣴⢃⣿⠀⠌⠀⠛⠁⠀⠋⢀⣾⠁⡔⠀⠿⠁⠀⠀⠀⣸⠇⢀⠂⠹⣧⡴⠚⠁⠀⠀⠹⢧⠤⠚⠁
⠀⠀⠀⠀⠀⢀⠎⠘⣿⠀⠈⠛⠁⢸⡇⡸⠀⠀⠀⠀⠀⠀⣸⢇⡜⠀⠀⠀⠀⢀⣀⠀⣟⡠⠃
⠀⠀⠀⠀⢠⠃⠀⠀⣿⠇⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⢀⣼⠋⢹⠀⠉⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⡇⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠴⠀⢀⣾⠃⢠⠋⠀⢀⣠⡤⣄⢀⣾⠋⣀⠟
⠀⠀⠀⠀⢧⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢏⣸⠁⢰⡖⠀⣼⣇⠔⠁⠀⢠⡿⠁⢀⠜⢸⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠇⢀⣿⠁⢰⡿⢁⠖⢄⢀⣿⠃⠉⠁⣠⠃⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⡞⠀⣸⡇⠀⣼⡇⠀⠓⣺⠁⢿⣄⣀⡴⢁⣀⡘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⡟⠀⠀⢹⣇⡴⢻⡇⠀⣠⠃⠀⠀⠉⠁⠀⡎⠀⢁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠀⠀⠀⠀⠳⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣤⣄⠀⠀⢠⣶⠂⠀⢲⣦⠀⠀⢀⣤⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⣖⠀⠉⣧⠀⠈⡟⢧⣀⡿⢹⠀⠀⢸⠻⣇⣠⠟⡿⠀⠀⣿⠛⢻⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣙⣃⡀⢻⡄⠀⢸⠆⢀⣿⡄⠻⠁⠼⠷⠠⠾⠄⠹⠋⣰⣇⠀⣰⠏⠻⠁⠀⢠⡟⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠉⢈⡷⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⢀⡔⣹⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠃⣠⡿⢦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠋⠁⠀⠀⠀⠀⠀⠀⣀⡤⣴⣯⡿⠱⢿⣷⠶⢢⡄⣂⣁⠀⠠⣤⣄⡀⠈⠁⠸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⢶⠋⣽⢣⡇⣼⢡⡾⢰⠇⣸⠿⢤⠍⠱⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⢠⣾⣿⡇⠀⠀⢰⢀⡡⠻⢈⢡⣬⣴⣿⠦⠔⢚⣒⣮⣅⣤⣄⣀⣹⣿⣿⣆⠀⣀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡀⢀⣾⣿⣿⣠⣤⣤⣤⣤⣤⡀⠀⠀⠈⠉⠀⠀⠘⠋⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣰⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⠋⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠠⠃⡨⠋⠉⠱⠦⢀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⠄⠀⡀⠇⠈⠀⢀⠀⡆⠀⠀⠀⢈⣡⣿⣿⡿⠛⣿⡿⠙⢻⡿⣿⣿⣷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢊⣿⣿⠟⠹⠃⠘⢿⠋⠙⠛⠿⡷⣄⠀⠙⠊⠐⠊⠁⠀⠐⠐⠃⠀⠛⠉⠁⠀⠀⠀⠛⠀⠀⢡⠀⠈⠋⠻⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠐⠂⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡟⠛⠻⠿⠿⢿⣿⣿⣿⣿⡿⠿⢶⣶⠶⠂⠀⠉⠁⠀⠀⠀⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠂⡆⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠠⠒⠒⠣⠤⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠧⠤⠚⠒⠒⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡂⠄⠄⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠑⠀⠀⠀⠀⠀⠀⠈⠰⣱⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠈⠯⠍⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠐⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⡀⠠⠤⠔⠂⠌⢉⣀⡹⠟⠁⠐⠂⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣟⠃⠈⢈⣀⣠⣤⣤⡴⠖⠊⠉⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠈⡀⢀⡎⠠⠽⠀⠋⠙⡿⠀⠀⠀⠀⠀⠠⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⢀⠀⡇⠀⣼⠀⠡⠀⢾⠀⠀⣷⠒⠂⠚⠛⠺⠋⠀⠀⠀⠀⠀⠀⠀⢀⣆⡠⠀⠀⠀⢀⠀⢑
⠀⠀⠀⠠⡚⡇⢢⠀⠘⠄⠀⠀⠀⠑⠀⠈⢀⡀⠀⠀⠀⠈⠒⠤⠀⠀⠀⠀⠀⢸⡁⠀⡀⡀⠀⡠⢀⡏
⠀⠀⠀⣿⠥⣇⠀⠉⠀⡈⠀⠠⡀⠀⠀⠀⠈⠂⠀⡀⠀⠀⡘⠄⠀⠀⡀⠦⢀⣾⡉⢃⡰⠄⠠⠐⠈⠁
⠀⠀⠀⠈⡀⠈⢑⠤⢀⣈⠠⠀⠈⠐⠄⠀⠀⢀⠀⢀⡠⢤⡄⠀⣀⣴⠖⠙⠓⣼⣁⡌⠁⠨
⠀⠀⠀⠀⠈⢶⡄⢀⡡⠀⠋⠻⢴⠒⠉⠀⠀⠀⣎⠀⢰⡂⠂⠀⡿⠄⠀⣿⠀⠀⠀⠄⠀⠸⠀⠀⠆
⠀⠀⠀⠀⠀⠈⢷⡸⡅⠈⠀⢤⡅⠁⠀⠐⡮⠀⠀⠰⣇⠀⠉⠀⡇⠀⠀⢹⠀⠀⠀⠄⠀⠠⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠣⡹⡀⠀⠈⢷⠀⠀⠀⢰⠀⠀⠀⢻⠀⠀⠀⣳⠀⠀⢸⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠄⠀⠸⡅⠀⠀⠈⡆⠀⠀⠸⡇⠀⠀⠻⠄⠀⢸⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡄⠠⢽⣤⠀⠀⠳⡀⠀⠀⣷⠀⠀⠘⠄⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡞⢹⠧⣄⠀⠀⠀⢀⡤⠼⡎⢳⣤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠗⠀⠀⠀⠺⣍⠀⣠⣄⠈⡽⠗⠀⠀⠀⠲⢏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢺⢃⡞⢳⡹⡟⣸⠁⠘⡞⣻⢋⡞⢳⡘⡗⢮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⣇⠸⡇⢰⠀⣿⠃⡼⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⣤⡴⣄⣤⣄⣠⡶⢻⣄⣧⣸⣠⠟⢶⣧⣄⣠⡴⠦⣴⢖⢶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡁⢺⣧⣾⠀⣿⣧⢸⠙⢠⠀⠋⠀⡟⠛⣄⠘⠃⢸⡇⢐⣓⣸⣮⢁⡍⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢲⡌⢻⡀⣿⡇⣼⠀⣾⡆⣸⠀⣷⠀⣿⢀⣿⢸⡇⠸⡿⢻⣿⣼⡇⢸⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠛⢳⡬⢶⣻⡇⣿⣿⠟⠀⠿⣴⡿⠛⠿⣼⠟⣓⢶⡏⠀⠈⠳⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⣿⢹⡇⣾⡂⣿⠇⣿⠀⣻⣥⣇⠘⢯⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢁⣿⡇⡿⠁⣤⡘⣿⡀⠿⢏⣿⡟⠶⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠓⠚⠷⠶⠞⠋⠙⠛⠋⠀⠙⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⡿⡻⡛⡟⠟⢟⢿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠫⡡⡑⡑⡔⠜⢌⢌⢎⢊⢢⠢⡫⡻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⠻⡡⡱⡑⡔⡔⣜⣌⣮⣮⣦⣦⣧⣥⣵⣕⣐⡜⠟⢦⣀⠀⠀⠀⣴⣶⣶⡄
⠀⠀⠀⠀⢀⣴⠿⡱⡑⣑⣴⠾⠾⠛⠙⠉⠉⢀⣀⣀⣄⣤⣤⣤⣤⣮⣴⣼⣯⣿⣦⣼⠓⢚⣿⠃
⠀⠀⠀⢠⡾⡓⠐⠌⠊⠉⠀⢀⣠⣴⣴⣾⠿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⡿⠤⠠⣿⣛⠦⣄⡀
⠀⠀⣰⡟⠑⠀⢀⣠⣤⡴⠿⢛⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣃⠀⣉⣹⣿⠷⠾⠧⢶⣤⡀
⠀⣼⣯⣦⠶⠛⠛⠉⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡀⢰⣿⣇⢐⣾⡟⠉⠀⠀⠀⠀⠀⠀⠙⢦⡄
⡼⠛⠁⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠁⠀⠀⠀⠀⢈⡻⠿⣿⢿⠣⣤⣤⣀⡀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠘⣦⠀⠀⠀⠉⠻⢦⡀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⢸⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢨⣤⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⣀⠂⠀⠀⠀⠀⠄⠠⠂⠈⠀⠀⠠⡀⣀⣠⣵⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣶⣶⣶⣶⣤⣶⣶⣶⣾⣿⣿⣿⡿⠟⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢹⡇⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠘⡷⠀⠀⠀⢰⠇⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠸⣷⢀⣠⠤⠒⠂⠈⠉⠁⠒⠲⢤⡀⠰⠋⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣰⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⢲⠄⠀⠀⠀⠘⠀⠀⠀⠀⢀⣤⡀⣠⣄⠀⢀⠀⢀⡀⢀⣤⡀⠀⠀⢀⡀⠻⢼⢤⣄
⠀⠀⠀⠀⠀⡀⠀⢀⠽⣿⣇⣠⠞⣿⠀⢠⣶⠀⠀⣷⠎⢸⣷⢣⡿⠀⣿⡠⠋⣷⠎⣸⡇⠀⣼⣯⠇⢠⠏⣼⡟
⠀⠀⠀⣰⠁⠀⠀⠀⠀⣸⣿⡇⠀⣿⣀⠎⣿⠀⡘⣿⠀⢸⡇⣸⡇⡼⣿⠃⠀⠟⠀⣿⠃⣰⣿⠁⣠⠋⢸⣿⠀⣰⠂
⠀⠀⠀⠑⠀⠀⠀⢀⡾⢁⣿⡇⠀⠈⠋⠀⣿⡸⠀⠀⠀⠀⠀⣿⡿⠁⠈⠀⠀⠀⠀⢿⡴⠋⠙⠋⠁⠀⠘⠿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢧⠾⠟⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠃⠀⣾⠀⡟⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢰⠗⢺⡇⢀⣧⣾⢤⣄⣴⣾⠹⠆⣰⣿⠘⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡼⠀⢸⡇⣸⡿⢁⣴⡏⢺⡇⠀⣠⠇⡼⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠈⠛⠋⠀⣎⠼⠁⠈⠛⠚⠁⠈⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢻⣟⣿⣷⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻⢷⣽⣷⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢷⣶⣦⣤⣄⡀⠀⠀⠆⠀⠀⠀⠈⢻⠀⠀⠸⢧⠀⠀⠀⢀⣴⣾⢿⠿⠟⠉⠉⠋⠛⠛⢻⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠒⠶⣤⣀⣈⠀⠀⠀⣈⡀⠀⠔⠙⠉⢀⣤⣄⣦⣴⣶⣶⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢻⣿⣿⣿⣄⠀⠀⠀⣻⡿⣿⣦⣾⣿⣿⣷⢰⣶⣿⠾⠟⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠙⠀⣸⣼⣿⣿⣿⣿⣿⣁⣀⠄
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠛⢿⠂⠀⠀⣰⣈⢠⣿⠿⠟⠛⠋⠁⠈⠁
⠀⣠⣴⣿⣿⣿⣿⣶⣦⠌⠿⢿⡆⠀⠀⠀⠀⣄⡴⠖⠓⠲⠋⠀⠀⠀⢄⣀⠀⠀⠢
⠠⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⠉⠑⢢⣄⠀⠀⢳⠠⣠⣤⣤⣤⣶⣶⣦⣤⣄⣤⣤⣤⡤
⠀⠀⠀⠀⠀⣀⣀⣄⣠⣤⣴⣂⡀⠀⣰⠏⠋⠡⣀⣠⣽⣷⣶⣾⠟⠋⠉⠉⠛⠿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠖⠛⠋⠉⠁⠀⠀⠀⠀⠨⣡⠞⠁⠀⢀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⡹⣏⠉⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣁⡀⠤⠚⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠐⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⠀⡀⠀⠀⠀⠀⠀⣳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣿⣴⣤⣀⣠⣬⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠤⢤⠂⠀⠁⠀⠀⠀⠀⠀⣠⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢉⣾⠃⠀⠀⠀⠀⣒⠲⢄⡁⠂⠀⠀⠀⠈⠸⣯⣶⣆⣴⢄⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⢠⣀⢀⡇⣿⡟⠀⠀⠀⠀⢈⡇⠀⠀⠙⠁⣤⡤⠀⠀⠀⠈⠻⠿⢿⣿⣿⣶⣰⠄⣀
⠀⠀⢀⡀⣤⡆⢾⣟⣛⣖⡻⣦⡵⣎⢷⣤⣤⣤⣤⠾⠷⣦⣤⣿⠈⠁⠀⠀⢀⣄⣆⣴⣾⣿⡿⣿⣾⣥⡞⣊
⠀⣠⣼⣹⢮⡟⣿⣟⣿⣟⢷⣏⣿⢹⡰⡭⠏⠁⣀⡀⠀⠈⢾⠿⣿⣤⡄⠀⠀⠈⠛⣿⣿⣿⡷⡿⣼⢿⣇⣷⣴⠀⠀⠀⣠
⢰⡟⢇⣿⢹⣧⣿⣦⣿⣿⣷⣯⡛⣾⢥⡅⣰⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣅⠀⣀⣾⣿⣿⣻⠿⠿⠛⠈⠉⣉⠡⠄⠀⢸⡟
⢰⣿⡾⣿⣯⡱⢯⣿⣼⣿⣻⣯⢵⣍⡶⣸⣿⣿⣿⡄⠀⠀⣀⣀⣼⣿⣿⠿⠛⠛⠋⠉⠀⠀⠀⠤⢖⡋⡡⠠⢀⣀⣴⠛
⢻⣾⡟⠷⣟⢿⣼⠹⢿⣿⣿⡿⠞⠉⣷⣿⣿⣿⣿⣶⣿⣷⣿⣯⣍⠁⠀⣀⣀⣠⣦⣄⣒⠲⠒⣒⣥⣴⣶⣾⣿⣿⢿⣷
⠀⣻⣽⣿⠋⠹⣿⣿⣦⣉⠀⢰⣿⣿⣿⣿⣿⣽⣭⣿⣿⣯⣿⣿⣛⣿⣿⣿⣟⣟⣻⣿⣿⡿⢿⣿⣿⣿⣛⣿⣿⣿⡟⠃
⠀⠀⠀⠉⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠿⠿⣿⢿⣦⢥⠲⠞⠯⢉⣿⣿⣿⣿⣯⣭⣽⣍⣟⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣛⣥⣼⣿⣯⣿⣖⣓⣐⣿⣿⣿⣿⣿⢧⣬⣚⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠙⠋⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⣿⡟⠻⠟⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠀⠀⠀⠀⠀⢠⣶⠖⢲⡦⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠘⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⣿⡇⠀⠀⠀⠀⢳⠛⠀⢀⠀⠪⣤⡀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣀⣀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠛⠠⣿⠃⠀⠀⠀⠀⠈⢣⣤⠞⠀⠀⠺⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⡀
⠀⠀⢠⣶⣿⣿⣿⣿⣶⣶⣤⠀⠀⠀⠀⢸⣿⣍⠁⠀⢈⡟⠀⠀⠀⠀⠀⠀⠀⡰⠆⠁⣠⠀⢫⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠈⣆
⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢸⣿⡏⠀⠐⢼⠇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠂⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠈⠛⠆⠉⣿⠿⣿⣿⣿⣿⠀⠀⠈⢿⣿⣆⣰⠋⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⣿⣿⣿⡟⠀⠀⠒⠀⡀⢰
⠀⠀⠀⠀⢀⣤⠶⣿⡿⠿⣿⣿⣿⡇⠀⠀⠈⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⣳⠂⠀⠀⠀⠀⠀⠀⠀⡀⠖⠀⠀⣘⣿⣿⣏⠁⡌⠀⠀⠀⠐⢸⠃
⠀⠀⠀⡴⠛⣁⣀⣄⣈⣉⠿⠋⠁⠰⠶⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠚⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣠⣤⣿⣿⣿⣿⣿⡷⠿⠄⠀⠀⠀⢸
⠀⠀⠈⠙⠳⠯⠽⠟⠉⠁⠐⠒⠀⠀⠀⠀⠁⠚⢦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⣻⣿⣿⡿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠄⡽⢹⠟⠲⠙⢷⠑⠀⠀⠀⠀⡀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠠⣄⠀⣤⠀⠀⠀⠁⠀⠀⢐⠀⠀⠐⠁⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⡲⠤⠀⠀⠀⠠⠄⠀⠐⠒⠁⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣤⣤⣀⣉⡉⠤⠶⠚⠉⠁
⠀⠀⠠⣤⣤⣚⡛⠋⠉⠛⠛⠻⠿⣦⣀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠙⠻⣷⣤⡀⠈⢉⣙⠛⠿⣟⠪⣿⣦⣴⢘⣉⡋⠀⠐⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⣿⣿⣿⡷⡻⢯⣿⣿⣦⣤⣄⡀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠋⠉⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙⠻⢿⣿⠟⠂⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⠀⠀⠀⠀⠀⢠⡏⠀⢀⡀⠀⠀⠀⠀⣶⣤⣼⣿⣿⡅⡂⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢶⣿⣿⡿⠏⠋⢻⣿⣿⣧⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⢿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣹⣿⣧⣄⣀⣼⣿⣿⡗⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⠇⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠈⠁⠻⢛⣿⡿⢿⣿⠟⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠂⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣤⡀⣀⠀⠀⠀⠀⢀⣀⣀⢰⣶⣩⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢦⣄⣀⠀⠀⠀⣀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁

⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠻⠔⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡻⠒⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠖⠛⠄⠳⡀⠀⠁⠀⢀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⣀⡤⠖⣃⠨⡍⠑⡺⢀⠣⡀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠛⠒⠃⠉⠐⠤⣀⡀⠁⠀⠀⠸⡄⠀⠀⢀⠦⡀⢀
⠀⠀⡴⠙⡂⠱⣄⠀⠈⠀⣀⣤⢁⠀⠳⡜⢦⡜⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡠⢤⡀⠀⣞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⡶⠒⠒⠃⠀⢠⢼⠀⠈⠩⠶
⠀⢸⠓⠚⡇⠀⠈⠉⠉⠉⠁⢸⢘⠀⠀⢡⢸⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣰⠗⠊⠉⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠒⢚⠂⠀⠀⠀⠰⢦
⠀⡿⠀⠀⠙⣄⠀⠀⠀⣠⠖⠛⠜⠓⢶⠛⠊⠉⠉⢳⡀⠀⣠⡤⠤⠤⠤⣼⠀⣯⣤⡴⠿⢤⣄⠀⠀⠀⠀⠀⠀⡤⠖⠛⠓⠦⣤⠟⠉⠙⠲⡜⢏⡀⠀⠺⠀⢀⠆
⠀⡇⠀⠀⠀⠈⠑⢦⣰⡁⠀⠀⠀⠀⢨⠀⠀⠀⠀⢠⠇⡜⠁⠀⠀⠀⠀⠈⠳⠟⠁⠀⠀⠀⠈⢳⡄⠀⢀⣠⠼⣅⣀⠔⠋⠐⡇⠀⢀⡀⠄⣿⠀⣩⠖⠒⠒⠓⢢
⠀⣧⠀⠀⢀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣞⣤⣀⣀⣤⠾⠾⠀⠴⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢠⠋⠀⠀⠀⡇⠀⠀⠀⠑⡖⠁⠀⠀⠀⢻⠖⠂⠈⠉⢙⡁
⠀⠹⣄⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠼⡄⢠⠖⠋⠳⢄⣠⠖⠚⣇⠀⠀⣀⠤⣼⠀⠀⠀⠐⠽⡇
⠀⠀⠹⣆⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢻⠀⠀⠀⠀⡇⠀⠀⠈⠓⠎⠀⠀⠀⢣
⠀⠀⣠⣬⡷⠤⠤⠤⠤⣤⠴⠦⠤⠤⠤⠤⠤⠴⠶⠤⠤⠾⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠷⠴⠤⠶⠾⠶⠶⠶⠶⠷⠶⠦⠤⠴⠧⠤⠤⠤⠾⣄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠙⣟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠹⣖⠒⠛⠛⠛⠛⠛⠛⠛⠃⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡿⠁
⠀⠀⠀⠀⠀⠈⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁





⣿⣿⡿⠿⣿⡿⢿⠿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡠⠤⡀⠀⡤⠤⣀
⠀⠀⠀⠀⠀⠀⡼⠀⡈⢢⢀⠎⠀⠀⠀⠈⢢⠀⣀⡀⠀⠀⠀⡤⠒⠦⡀⢰⠁⠀⠹⡄⠀⠑⠉⠁⠀⢨⡀⢠⠤⠤⠄⢀⡀
⠀⠀⠀⠀⡜⠉⠁⠀⠇⠀⠿⡀⠀⠀⠀⢀⠍⡜⠁⠈⠉⠐⢺⣀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠶⢅
⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠈⠒⢤⣰⠋⢚⠀⠀⠀⣴⠤⠏⠉⠉⠓⡦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣁⣀
⠀⠀⠀⠈⡙⠀⠀⠃⠀⠀⠀⠑⠀⠀⣹⣀⡂⠁⡐⠠⡇⠀⠀⠐⠀⠠⣇⢀⡴⠚⠙⠒⢅⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⢀⠇
⠀⠀⠀⠀⢣⡀⠀⠀⢀⢄⡀⠀⠀⠀⢹⠁⠐⠀⠉⢰⠁⢀⠀⠀⠀⡤⢨⣟⠂⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⢻⣇⠀⠒⠀⠀⠀⠘⡆
⠀⠀⠀⠀⡎⠁⠀⢈⠥⣤⡁⠀⠈⢻⠶⠗⠒⡲⠂⢸⢰⡯⢦⡀⠀⠩⢿⡃⠀⠀⠀⠀⢠⢷⣀⠆⠀⠀⠀⠢⠀⢣⠀⠀⠀⢰⠴⠃
⠀⠀⠀⠀⣇⠀⠀⡆⠀⠀⠉⠢⣄⡼⠀⣠⣞⠃⠀⢸⡾⠁⠀⠀⡰⠃⡿⡟⠒⠢⠤⣴⠣⣻⡎⠀⠀⠀⠀⢀⢀⡽⠀⠀⠀⠈⠑⡄
⠀⠀⣄⣀⡈⣒⠖⡹⢆⠀⠀⠀⠨⠷⢆⠁⠘⡧⠄⠘⠃⢄⢀⡜⠁⠀⢈⠞⣆⠀⠀⢀⣠⡟⠓⠜⠀⢀⠀⠘⠁⢀⠀⠀⠀⠀⠀⠽
⠀⠀⡼⠃⠀⠀⠉⠚⠈⠳⡄⠀⠀⠀⢀⠆⠀⢃⠀⠀⠀⡄⠊⠀⠀⠀⠊⡜⢨⡖⠈⣌⠀⣼⡀⠤⢱⠉⠐⠄⣀⢅⠀⠀⠀⠀⡤⠃
⠀⠀⠱⣄⠀⠀⠀⣐⠦⠀⠈⠢⣀⠤⡙⢄⠀⢸⠀⠀⢠⡁⠀⠙⠄⠰⢱⠀⡈⠁⡞⠔⢀⣽⠛⠢⣄⠓⠛⠒⢅⠀⠀⠀⠀⢴⠁
⠀⠀⡖⠒⠛⠀⠀⠈⠀⠀⠠⠀⠀⠀⠈⠊⠀⠘⠢⠤⠞⠀⠈⠀⢠⠘⣾⠮⠉⣴⡽⠀⠈⠀⠀⠀⠀⣣⢀⠈⠀⢳⠀⠀⠀⠀⢱
⠀⠀⠈⣢⡴⠆⠀⠀⠀⣀⠀⠀⠀⡰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠀⢠⣟⠀⠊⠀⡠⠀⠀⠴⠁⠀⠀⠈⡀⠇⠐⠠⣔⠁
⠀⠀⠀⡏⠈⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡠⠒⠉⠁⠐⢦⣰⠉⠉⠁⠛⠀⢰⢄⠀⠀⣠⠊⠀⡀⠀⠀⠀⢀⡏⠀⠀⠀⠱
⠀⠀⠀⠳⡀⠈⡀⠀⠄⠀⠀⢬⡀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣸⠔⡡⠊⠉⠉⠄⠑⠦⣀⣀⣀⡠⠎⢡⢀⠀⠀⠈⠆
⠀⠀⠀⠀⢨⡖⠛⠁⠀⠀⠀⡀⢇⣀⢀⠠⢤⠞⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡧⠔⠁⠀⠀⠀⠀⠀⠘⠠⠀⠀⠐⠄⢩⠀⡀⠀⡠⠃
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⢘⡤⡄⠀⢀⣀⣀⢴⠋⠀⠀⣸⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⡈⠀⠘⢣⡀
⠀⠀⠀⢼⡄⠀⠄⠀⠀⢀⡘⠙⠦⣀⡠⢶⣯⣞⠏⠂⠁⠀⠀⠸⢤⣀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠑⠀⠈⠠⣀⠀⠑⡀
⠀⠀⠈⠓⣅⣐⡀⣀⣀⠜⠀⠀⠀⠀⢠⠟⢉⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠴⢄⡀⠀⠀⠐⣲⣄⡴⣤⠐⠺⡀⠁⠀⣀⣅⠢⠕
⠀⠀⠀⠀⠀⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠑⠒⠊⠀⠁⠀⠁⠀⠀⠉⠑⠀⠉⠘⠀⠙⠚⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⡿⣿⣀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⡠⢂⣀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠄⢀⣠⣚⠃⠀⠰⠂⠀⠀⠀⠀⠀⠈⣿⣤⣾⡅⠀⣴⡀
⠀⠀⠀⠀⠹⣶⣴⡄⣠⣶⣾⣿⣿⣿⣿⣿⡿⠁⢀⠠⠀⠇⠀⠐⠂⠀⠉⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡅⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠂⠐⠀⠀⠀⠿⣚⢾⡄⠀⠀⢰⠆⠁⠀⠀⠀⠀⠀⡙⠛⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠈⠛⠢⣼⣦⡈⠛⠩⠷⠘⢃⠔⠀⠀⠀⠀⠀⠀⠈⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⠚⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣀⢔⡂⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣠⣐⣤⠄⡠⢤⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣀⣙⡂⠙⠚⠴⢂⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⢶⡽⠿⠙⠛⣛⣁⡆⠀⡄⠀⠀⠀⠈⣷⣦⣤⣀⣀⡀⣐⠬⠶⣄⢀⠀⢠⢶⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⢙⣿⡅⠀⠀⣠⢆⣧⠖⠀⠠⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠠⣦⢹⠻⠿⠖⠙⠁
⠀⠀⠀⠈⢶⣤⣴⣶⣿⣿⡄⠀⠙⠛⡸⢀⣡⣜⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠿⣧⢠⣄⠰⠅⣼⣾⣿⣶⠴⠊
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀⠁⠀⠀⢀⣊⣴⠏⠀⠀⠀⠀⠀⠀⣀⣤⣈⡉⣀⣉⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⣀⠚⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠉⠀⢀⡀⠐⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡵⠊⠀⠀⠀⠙⠀⠑⠄
⠀⠀⠀⠀⣀⠔⠊⢉⡉⠁⠲⣄⠀⡌⠀⢀⡎⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂⡏⢀⣀⠀⠄⠠⡀⢀⣀⠈
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢈⠗⠋⠁⠀⢸⠏⠒⠄⡀⠀⠀⠀⠀⠔⠁⠉⠈⠁⠇⠀⢁⣦⠀⠝⠀⢀⢀⡃
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠉⠀⠀⠀⠘⠄⢀⠠⠂⠀⠀⠀⠀⢃⠜⠙⣇⣀⠨⡧⢔⠉⠀⢀⠅
⠀⢠⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠘⠂⠎⠀⡠⢾⠀⢈⠈⢻⡠
⠀⠐⠤⢅⣀⢐⠒⠂⠀⠲⠤⠦⠀⠀⠀⣀⠀⠀⢀⣀⣼⡀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠉⠋⠀⢠⠃⢫⠐⢷⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃⠀⠒⠂⠀⠤⠤⠀⠀⠀⠤⡤⡤⠄⠀⠀⠀⠤⠄⠐⢇⣠⠞⠂⡶⢇⠀⡠⢄⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⢂⠀⣠⠀⠀⡉⠈⢲
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠊⠀⢹⠢⠔⠑⢤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡔⡇⢀⡆⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡘⠋⠘⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠺⠿⠶⠶⠶⠷⠶⠶⣶⣾⣿⣶⣶⣶⠾⠿⠶⠶⠶⠿⠷⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠉⢉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣄⣀⡈⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⠀⠈⢳⣤⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⡟⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣄⠀⠀⣿⣿⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣿⡆⠀⢸⣺⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠃⢿⡀⢠⠏⢀⣾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⠻⢦⠈⠇⢠⠟⠉⠉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠄⡀⠙⠀⠀⠋⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⠁⠀⠀⠀⠁⠐⠂⠺⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠁⢀⣤⠄⠀⠀⠀⠀⢈⠉⠉⠛⣿⣿⣿⣿⣿⣿⣿⡋⠀⢀⡄⢀⡠⠀⡀⠀⠲⣦⢀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠸⠁⠀⠰⣦⠈⢷⣌⢳⣶⣶⣾⣿⣿⣿⠛⢿⣿⣿⣿⡏⣰⡟⠁⣼⣧⡄⠀⢉⢸⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⣆⠀⢰⡇⣿⡄⠘⣿⣬⣿⣿⣿⣿⣿⣏⠀⢸⣿⣿⣿⣷⣿⠃⣰⣿⡟⣧⡀⢸⡸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣿⣴⣿⡇⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣴⣿⣿⡇⣿⣿⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⢨⡟⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿⣿⣿⠿⠛⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠄⠂⠁⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠐⢠⡀⠈⠑⡤⠀⠂⠀⠀⢀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢢⣲⡀⠀⢳⠀⠰⠁⡈⡀⠀⢾⡨⠄⠀⠂⠔⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣷⣄⠜⠃⠂⠀⠀⠛⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⢀⡝⠯⢀⣀⠃⠘⠃⠀⠀⠉⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⢳⡆⠀⠀⠨⠁⠀⡃⠀⠀⠀⠼⠉⢉⠙⣦⠀⠀⠀⠀⡀⠀⠐⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢢⡈⠂⠤⣿⡼⠀⡁⠀⠀⠀⠀⠀⠀⢱⣼⡇⣀⠀⡰⠀⠀⣸⡿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠓⢤⠈⠒⠦⣀⡉⠐⠂⠀⠀⠀⢀⡆⢀⡜⠁⠀⣀⣳⣀⠈⠟⢉⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⢀⠀⠀⠠⢿⠨⡆⠀⠀⠀⠈⠉⠒⠒⠂⠤⠤⢤⢤⡤⠤⢤⡤⠤⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠬⣶⡳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⡛⠿⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠌⣽⣟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈⢉⣿⣿⡟
⠀⠀⠀⠀⠀⠡⠔⠚⢆⢀⡀⠓⣤⣀⠘⢗⢌⣋⢿⣿⡷⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡞⠁⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢾⣁⠀⠈⠁⠉⠉⠀⠀⠀⠀⠈⣷⣂⠀⠀⢀⠀⣀⣀⣼⣽⣇⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⢀⣀⣼⠿⠛⠋⠉⠉⠁⠉⠁⠀⠀⠀⠙⠒⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢷⠀⠀⢿⠀⠀⡿⠀⢀⡎⠀⢠⠆⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠐⣄⠀⠈⢧⠀⠘⣇⠀⠸⠄⠠⠧⠀⣼⡀⣠⠏⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣾⡟⣿⡆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠈⢣⡠⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢎⠀⠀⠀⠀⠀⣀⣤⣤⡄⠙⣿⡿⢛⣿⠟
⠀⠀⠀⠀⣴⡟⠁⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣤⣤⣀⣴⣶⣦⠀⣴⣟⣽⠟⢀⣼⠟⢀⣾⠏
⠀⠀⠀⢸⣿⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⠀⢀⣤⣤⡀⣴⠾⣿⡆⢀⣿⣿⡟⠀⣿⣿⠃⣿⡇⢰⣿⡿⠋⢠⣾⠋⠀⣾⡏⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠘⢿⣆⡀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⢰⣶⠆⠀⣼⣿⣷⡟⠁⣿⣿⠏⢸⣿⠀⣼⣿⡟⠀⢰⣿⠇⢰⣿⣁⣾⣿⣤⡴⠟⠁⠀⠀⣿⣇⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⢀⣴⣿⣿⠀⢠⣿⣿⠀⣼⣿⣿⡟⠀⢸⣿⡏⠀⣿⣏⣼⣿⣿⠀⠀⠺⠛⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣶⠛⠁⣿⡇⢀⣾⣿⣟⣰⡟⢹⣿⠀⠀⠸⠟⠀⠀⠈⠉⠁⣠⡤⣤⡄⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⣿⣇⠀⠻⠷⠾⠋⠈⠛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢡⣿⠇⠀⠀⠀⠀⣾⡟⣽⡟
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣼⣟⣰⡿⠋⠀⠀⠀⠀⠀⢘⣿⣿⣅⡀
⠀⠀⠀⢰⣿⠁⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣾⡟⣿⡆⠈⠛⠀⢠⣿⣿⣋⠀⠀⣴⡟⣿⡇⢠⣾⠏⠀⠙⣷⡄
⠀⠀⠀⠈⢿⣦⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠻⣶⣿⠷⣿⡟⠀⣾⣿⢿⣽⣷⣼⣿⠟⠋⣰⣿⣷⡶⠷⢄⣿⠇
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⢀⣿⡏⠀⣿⡇⣸⣿⡇⢀⣿⡏⠸⣿⣤⣾⠟⠘⠿⣤⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣾⡟⠀⠀⣿⣷⡟⠙⠻⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠾⠋








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣾⣿⣾⣏⣿⣿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⢠⣟⣿⡿⣾⣿⣿⣿⣿⣷⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢆⠀⠀⠀⠀⠀⠀⣠⣼⡿⠁
⠀⠀⠀⠀⣰⣿⣷⣽⣿⣃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠈⡄⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠈⠀⢧⣿⣿⣿⣭⣿⣿⠉⠉⣿⣿⣿⣿⣿⣿⣶⠆⠀⠀⠀⠀⠀⣠⢯⣀⠀⠀⠀⠀⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠠⡀
⠀⠀⠀⠀⢿⢿⣿⡿⣛⡿⣻⣦⣶⣿⣷⣿⣯⣽⣟⣛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⢀⠃⠀⠆⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡄⢀
⠀⠀⠀⠀⠘⢏⢻⣿⣾⣻⣿⡏⣿⣿⣯⣿⣿⣷⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠣⡼⣯⣿⣿⣷⣿⣿⣿⣿⣷⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠁⠀⠀⠀⢀⣠⣤⣶⡶⣀⣀⣸⣿⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⣤⣿⡿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⠀⠀⣀⣤⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡃⠀⠀⠙⠿⠟⠸⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁⠘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠈⠀⠛⠶⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠡⠉⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠁⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡠⠤⠒⣀⣠⣤⣤⣄⣤⣤⣈⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢵⠋⡝⣷⠊⠀⠀⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢶⣿⣿⣟⣵⣾⣿⣿⣿⣿⣿⡄⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠖⠋⠁⢀⠀⠀⢒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢛⣯⣿⣿⣿⣿⣼⣿⣿⣿⡿⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠐⢚⡖⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣼⠟⠛⡛⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠔⢀⣿⣯⣿⡋⣲⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣿⣥⣴⣾⣿⣿⣿⢿⣿⠟⢋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣟⣮⣼⡟⣻⣫⣛⠀⠀⠂⠀⠀⠀⠀⠀⢻⡍⠀⣀⣠⣾⣿⣿⣿⣿⠇⢹⣿⣿⠞⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠾⢾⠓⣟⣿⠏⡵⠏⠀⡀⠀⠀⠀⠀⠀⠈⢄⠙⠛⠻⢯⣭⣤⣤⡶⠿⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠏⠘⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⣠⣄⣀⣀⣀⣠⠐⡂⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⢿⡿⡦⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠮⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡿⣿⣇⣤⣄⠀⠀⢠⣦⣰⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢠⣤⡀⠀⣿⣿⡇⣿⣿⣿⣿⣧⠀⣿⣿⡇⣾⣿⣷⣷⡄⠀⠀⣀⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢻⣿⣆⠸⣿⣷⡀⢻⣿⣧⢹⣿⡇⣿⣿⢸⣿⣿⢰⣿⡟⣼⣿⡇⢠⣾⣿⠟⢡⣿⡇
⠀⠀⠀⠀⠀⢠⣾⡟⠻⣷⣄⠈⢿⣿⣄⢿⣿⣿⡎⠿⠿⠈⠛⠃⠙⢋⠈⠛⠃⠘⠿⠁⣿⡿⢠⣿⣿⣏⣴⣿⠟⠀⢀⣤⣦
⠀⠀⠀⠀⠀⠈⢿⣷⣤⣈⣛⠀⠀⠙⢿⣿⠃⠉⠁⠀⣠⡀⠀⠠⣴⣿⣦⡄⠀⢀⣀⠀⠀⠀⠘⣿⣇⣉⠛⠉⣠⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠾⠛⠇⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠁⢠⣾⣿⠟⠉⠀⢾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠛⠀⠀⣠⢖⣿⣿⣿⣿⣿⣶⣦⣤⠀⣤⣴⣶⣿⣿⣿⣿⣿⡲⣄⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣼⣿⣿⣿⣿⣿⣿⣿⠏⣀⡹⣿⣿⣿⣿⣿⣿⣿⣧⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⢡⡾⠉⡇⠈⠻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠿⠶⠆⠀⠀⠉⠛⠋⠉⠀⠀⣾⠃⢰⠁⠀⠀⠀⠉⠙⠛⠉⠁⠀⠰⠾⠿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠀⠀⠀⠀⢀⡀⠀⠤⢸⣿⢠⢃⣀⡀⠀⠀⣀⠀⣠⣄⠀⠀⠀⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠋⠉⢀⠀⠀⣼⠀⢿⣆⣴⠆⢸⣿⣡⠋⢸⡇⣠⡾⠍⠀⣿⡘⢀⠀⠀⣀⠈⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⢻⡀⡜⠀⣿⠀⡜⣿⠷⢒⣿⠋⢸⡇⣠⠆⣨⢿⡁⠀⠀⠈⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠻⡴⢡⡏⣀⣾⠏⠀⠀⠉⠁⠀⠣⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⣠⢺⣏⠉⠙⣿⠋⠻⣷⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢫⢻⣶⣄⡀⠀⠀⢠⣿⣼⣿⠿⣾⣿⣷⣷⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣶⣿⢋⣭⠈⠉⢡⡌⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠈⠉⣻⠾⠛⢻⣿⣧⡆⠀⣠⣄⢤⡑⠲⡄⢻⣿⣿⣿⣿⣿⣿⣤⣼⣷⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢰⠿⠹⠗⢰⣼⣿⣿⣿⣿⣿⣿⣿⣷⣖⣿⣾⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡆⠀⡄⢠⠠⣯⣿⣿⣿⣿⣿⡟⣿⡿⣿⠟⠿⢻⣿⣿⣿⡿⠋⡳⢦⣤⣤⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣷⣿⣾⣞⣿⣿⣯⣿⣿⣠⣿⣷⣷⢦⣼⣿⣧⢚⣿⣿⣥⣺⡶⣛⠿⣿⠿⡯⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠈⣿⣿⣿⡿⠉⠉⣿⠙⣿⠛⠉⠙⠙⡏⢻⡿⠟⠙⠛⠉⡇⠉⡟⠁⠁⠀⠘⠀⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠳⢹⣮⣿⣷⣦⡶⠿⣼⡿⠤⠀⠀⠸⠇⣸⠿⠄⠀⠀⠀⣃⡀⢃⣄⠀⣠⣴⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣶⠛⠃⢻⣿⣥⡀⣿⠃⠁⣀⡀⡘⡛⠋⠐⢀⡀⢠⣮⠛⠉⠲⡆⣰⠀⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡉⠹⢵⣖⣍⡹⠟⠛⢻⡄⠀⣹⠿⠗⢧⡀⠀⣈⠿⠿⢐⢀⣠⢀⠟⠛⢉⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣦⣽⠿⠻⡀⣀⡀⢈⣿⠶⠛⣀⠀⠺⠿⠦⢧⠀⢀⡐⠾⠿⢻⡆⣀⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⣿⣶⡀⠽⣿⡿⢏⢀⠀⠘⠿⠿⠼⣄⠀⣠⣿⡾⠧⠄⣀⢸⠿⠏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢿⣿⣿⣿⠿⣄⣬⡿⣷⣿⡻⠀⡐⣿⣴⡸⠁⠀⠰⣶⠟⠻⠀⠚⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣬⣿⣿⣷⣾⣿⣈⣿⣦⣷⣿⠁⠀⢼⣾⣧⡁⣀⡷⠞⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⢿⣭⢤⡭⠆⠤⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⡀⠈⠀⣀⣠⣶⡄⠀⠀⢀⡴⠊⠀⠀⠂⡀⢀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠛⣾⢿⣤⡄⠙⠐⠤⣿⣿⣿⣷⣄⡀⢠⠀⠀⠀⠀⠀⢹⡦⢑⢦⣶⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠢⠀⠀⠀⠈⣷⣾⣿⡇⠀⠀⠀⡄⠀⢹⠏⠈⠀⢸⢀⠀⠀⠀⠀⠀⠙⠚⠀⠙⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⡈⠹⡅⠀⣠⠤⡿⠀⠀⠀⣠⡟⣸⣿⠽⠟⠛⢷⣦⣄⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢉⡷⢞⡻⠁⠀⠀⠀⢀⣼⡟⠁⠘⠋⠀⠀⠀⠀⠙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⣀⣔⣁⠀⠈⢹⣷⣶⣤⣀⣾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣿⡄
⠀⠀⠀⢀⡔⢎⠩⡯⠥⣴⣀⠀⠀⠀⠀⠒⠛⠛⠛⠉⠉⠁⡈⢻⡙⢾⣿⠑⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣯⠿⡇
⠀⠀⣄⡠⠶⠶⠛⠛⠛⠋⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⢁⣸⡿⢦⠈⢳⣿⣾⡿⠷⠄⠀⠀⠀⠀⢀⣿⣿⣶⠇
⠠⠞⠁⠀⠀⠀⠀⠀⠠⡿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠁⢰⢏⣠⠏⢸⣾⣧⠈⠻⣿⠀⠀⠀⠀⠀⣀⢾⣾⣿⣽⠋
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣰⡄⠀⠀⠀⠀⠀⠀⢠⢰⣫⡞⠁⠀⠀⢹⣼⠀⠀⠉⠠⢤⣈⣁⣉⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⢀⡫⠿⣾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣞⠨⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣤⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⣤⣶⣶⣿⣿⡿⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣩⣛⣭⣛⣿⣩⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⣤⠀⠀⠀⠀⠀⣀⣄⠀⢀⣀⠀⢀⡀⠀⣀
⠀⠀⠀⠠⣦⠀⠀⣀⣄⡀⠀⠀⠀⣿⠀⣃⢤⡟⢀⣴⠂⢀⣾⡣⣻⡟⢡⡟⢠⣿⡐⣿⠖⢹⡇⣰⡿⠃⠀⣸⡧⠊⠙⠀⠀⣤⢤⣄⠀⠀⡤⢄⡀
⠀⠀⠀⠀⢻⣧⣼⣯⣹⡏⠀⠀⠀⣿⠊⠁⠸⡷⠋⣿⡴⠁⠿⠁⠛⠀⣼⢣⢿⠟⠰⠏⠀⣿⣠⠿⡤⠴⠊⡿⠁⠀⠀⠀⠘⡿⠛⠛⢠⡾⢁⠀⠁
⠀⠀⠀⢰⠛⠛⢛⡻⠻⡁⠀⠀⣮⡾⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣄⠘⠁⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⣠⠛⠒⠘
⠀⠀⠀⠈⠃⠈⠹⣧⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⢠⡄⢸⣿⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣠⣤⣄⡀⠀⠀⠀⠀⢀⠀⠐⠃⠀⠁
⠀⠀⠀⠀⠄⠀⠀⠹⣇⠀⢃⠀⠀⠀⠀⠀⣿⡆⠀⢠⣿⠃⣴⠄⢸⣿⣴⣶⣦⡄⢠⡿⠋⢹⣿⢸⣿⣉⡙⠃⠀⠀⠀⠀⠀⠢⢀⠀⠀⡠⠂
⠀⠀⠀⠀⠐⡀⠀⠀⠹⠆⠈⠀⠀⠀⠀⠀⢸⣧⠀⣾⠇⠀⣿⠀⢸⣿⠁⢀⣼⡏⢸⣟⠛⠛⠁⠀⠉⠛⠻⣷⡀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠐⠄⠀⠠⠐⠊⠀⠀⠀⠀⠀⠀⠻⡿⠋⠀⠀⣿⠀⢸⣿⠟⠛⠉⠀⠈⠻⣶⣶⠗⠈⠻⣶⣶⠟⠀⠀⠀⠀⠀⠔⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠻⡜⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⡽
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⡤⠚⡡⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆
⠀⠀⠀⠀⠀⠀⠠⡟⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⡜⣳⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣠⠎⢀⠞⠁⠀⠀⡇⠀⣠⠄⣀⡔⠊⠑⡄⣰⣟
⠀⠀⠀⠀⠀⠀⠀⣷⣿⣴⡒⠒⠒⠢⢼⡁⠀⡼⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠁⣠⠋⠀⠀⠀⣸⢁⣞⠀⠀⢸⢧⣀⣠⡿⢻⡅⠉⠳⡄
⠀⠀⠀⠀⡠⠞⢉⡝⢻⠋⠉⠳⣄⠀⣀⣹⣦⡇⣏⣠⡤⢀⡀⠀⠀⠀⠀⢀⠞⢀⡜⠁⠀⠀⠀⢠⡟⠁⢉⡶⠒⠳⡏⠀⠀⣷⠀⠓⠤⣀⣹
⠀⠀⢀⡞⠁⠀⡼⠀⠘⡇⠀⠀⡼⠋⠀⠠⠴⣿⡷⠂⠀⠀⠈⢢⡀⠀⣰⠋⢠⠎⠀⠀⠀⠀⢠⠏⢳⠖⠘⢄⠀⢀⣿⠖⠚⢧
⠀⠀⣸⠀⠀⢰⠃⠀⠀⢷⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⠁⡰⠃⠀⠀⠀⠀⢠⣿⠴⣿⡀⠀⣼⠛⠛⢿⡀⢀⡼
⠀⠀⡿⠀⠀⢸⠀⠀⠀⠘⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡜⠁⠀⠀⠀⠀⢠⣿⠁⠀⠈⣿⠁⠹⣀⢀⣾⡉⠁
⠀⡴⠿⣄⣀⣘⡆⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠎⠀⠀⠀⠀⠀⡰⠃⠘⢦⣤⣞⡹⠶⠒⠋⠉⣈⡟
⠀⠙⣤⣀⠀⠉⠉⠉⠛⠓⠒⠓⠒⠒⠒⠒⠒⠒⠀⠠⠤⠤⠴⠾⠷⠶⠖⠒⠒⠒⠚⠉⠉⠉⠉⠀⣀⣀⡤⠴⠒⠋⡏
⠀⠀⠘⡇⠉⠛⠒⠒⠶⠤⠤⠤⠤⠤⢀⣀⣀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⢻⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣴⡀⠀⠀⢀⡔⠀⠀⢀⡟
⠀⠀⠀⠈⢧⠀⠀⠀⢳⡀⠀⢀⣸⣶⠋⠀⠀⠘⡄⢀⠴⠋⠙⣆⢀⡴⠋⠈⢧⡀⣠⠞⠀⠹⣄⣠⠋⠀⠀⠀⡾
⠀⠀⠀⠀⠘⢧⠀⠀⠀⢷⡞⠉⠀⠘⣆⠀⢀⡤⠻⡅⠀⠀⢀⡼⢯⠀⠀⠀⣠⠿⡅⠀⠀⣠⠞⢧⡀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠳⡀⠀⣀⡼⢶⠉⠀⠀⠘⣦⠞⠁⠀⠀⠳⣤⠞⠁⠀⠙⣦⡞⠁⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠿⣏⠁⠀⠈⠳⣀⡴⠊⠉⢣⡀⢀⡠⠞⠙⢦⡀⣠⠞⠉⠳⠄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠈⠀⠀⠀⠈⠙⠦⠀⠀⠀⠽⢯⠀⠀⠀⠀⠛⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣄⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣠⣤⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⣠⢸⣆⠀⢀⣴⣑⡄⠠⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠔⠀⢠⣄⢀⡐⢌⠐⣟⢹⣿⣿⡶⡻⢿⠉⣀⠐⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⡙⠉⠴⠿⠋⠤⠃⢀⣤⣍⣴⡿⢿⣷⣤⣠⣄
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣧⣿⣯⣀⣀⣀⡀⠂⠀⠀⠐⣢⡤⠶⡟⠇⠸⠟⠉⡧⠈⠁
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡿⠟⣛⣡⢄⡀⣀⢀⡀⠄⢨⠍⣉⠁⣈⣙⠃⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠛⠛⣯⣵⣾⣿⣿⢏⡾⣿⡝⠂⠉⠛⣹⣿⣷⣶⣾⡯⣹⠟⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢠⡄⢤⡴⣻⣿⣿⣿⣿⢿⣿⡖⣿⣦⡀⠀⠐⠈⠲⣿⢿⢛⡼⠃⠀⢀⢆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠳⡀⠈⢕⢋⡡⠞⠛⣻⣵⣣⣿⠿⣿⣻⠏⣷⡿⠋⣶⠴⠀⠐⠉⠀⠀⠀⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠄⠈⠻⠱⣟⠊⠹⢻⣧⣷⣼⣿⣷⠀⠀⠚⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣴⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠙⠛⠛⠛⠟⠛⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⡄⠀⢀⣀⠀⠀⣀⡀⠀⢀⡀⢪⣃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⢠⢶⣶⣇⢀⣿⣿⣤⢠⡏⠿⣶⡼⠗⠁⢸⡧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠁⠘⠋⠈⠉⠛⠀⠙⠁⠃⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⡿⡰⠃⣀⢀⡤⠀⠀⣀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⣀⠀⡀⡁⢠⡗⠁⣸⢋⢼⣤⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢸⠀⠀⠀⣿⡘⠹⡷⢺⡇⢻⠉⢁⠜⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠹⡇⠀⠀⢸⣇⠇⠀⠎⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⢸⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠠⠀⠀⠀⠀⠠⠄⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⢀⣀⡀⠠⠤⠤⠤⠄⣀⡀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⣀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠎⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⡄
⠀⠀⠀⠀⠀⠀⡘⠀⡜⠀⠀⠀⠀⢸⠉⠒⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢡
⠀⠀⠀⠀⠀⢠⠃⢰⠁⠀⠀⠀⠀⠈⢆⠀⢄⡇⠀⠀⠀⠀⡆⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠀⠀⠀⠀⢃⠈⡄
⠀⠀⠀⠀⠀⠸⠀⡆⠀⠀⠀⠀⠀⠠⡆⠘⠻⣇⠀⣠⠖⠉⠋⠢⡀⢸⠀⠘⢄⠀⣀⢀⠛⡄⠠⡃⢀⠆⠀⠀⠀⠀⢸⠀⢃
⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⢀⡤⡌⠁⠊⠁⢢⠃⠀⠀⡀⠀⢘⡀⠳⣀⢈⡞⡥⠊⠦⣸⣤⠽⠡⢄⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⢀⠀⡇⢀⡄⢤⠀⡎⠀⢸⢀⡠⠔⠊⠀⠀⠀⠀⠀⣨⠆⠒⠒⠻⠞⢤⡀⠀⢀⣈⣐⠒⢉⠜⡝⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠇⠀⠉⠢⣹⡇⢀⣦⠊⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠠⠈⢫⠁⠀⠀⠉⠪⣞⣒⣉⠽⢁⠀⡌
⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⡠⠜⠟⠃⢸⠀⠀⠀⠀⣀⠤⠄⠾⠠⠤⡀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠈⠑⡄⡌⢠⠃
⠀⠀⠀⠀⠀⠀⠘⡀⢣⠊⠀⠀⠀⠀⠈⡄⠀⡴⠋⠀⠀⠀⠀⠄⠀⠈⠳⡀⠀⠀⠀⠀⢠⠆⠀⠐⠀⡀⠂⠀⠀⠘⠁⡎
⠀⠀⠀⠀⠀⢠⠄⠳⠾⡐⠀⠂⠀⠢⢤⠘⠾⠂⠰⢤⠒⠢⠐⠚⠢⣔⠀⠳⠒⠂⠲⢤⠞⠰⠰⠦⣄⠀⠀⠤⡄⠐⠾⢄
⠀⠀⠀⠀⠀⠑⢤⠤⠄⠈⠑⢤⠀⠀⠀⠙⢤⠀⠀⠀⠙⢦⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠱⡤⠀⠀⠈⠣⠄⠀⠈⠦⢤⠜
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠒⠚⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰⢄⡠⠀⠀⠀⠀⠠⡀⢀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠒⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠠⣀⡠⠀⠀⠀⠀⠀⣄⣀⡄⠀⠀⠀⣄⠀⡀⠀⠀⠀⠀⠀⠑⠤⠖⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠈⠢⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠂⠀⠀⠀⠀⠖⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠠⠠⠶⢾⣿⡿⠿⣻⣿⢿⣿⣿⣿⣶⣤⡀
⠀⠐⠻⢿⣷⣯⣲⡒⠠⠤⠤⣤⣀⣀⣀⣈⣙⠛⠻⢿⣦⡤⢄⠀⠀⠀⡀⢢⣶⣤⣤⣤⣄⢀⡀
⠀⠀⠀⠀⠉⠻⣿⣷⣦⣴⡄⠀⠐⠄⠉⢉⠛⠻⣿⠷⠮⣝⣮⣹⢿⣶⡀⣧⠉⠛⠋⠛⠋⣀⠉⠱⢦⣀
⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣶⣥⡸⢶⣟⣮⣥⣾⣻⣶⣬⣩⣶⣼⣿⢿⣴⠾⠛⠛⠉⠁⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⠟⣩⠬⢳⠿⣌⠯⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠈⠀⠀⠂⠚⠋⠁⠈⠀⠀⠀⠀⠉⠱⢶⣿⣟⣿⣿⣿⣷⠲⠀⠀⠀⠀⢄⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢯⡙⠀⠀⠀⠀⠀⠀⠠⢳⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⢦⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⡟⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⣿⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⣻⣟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢢⣄⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡱⢼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣯⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢁⣼⣫⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣅⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣮⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣟⣦⡀⡀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣟⣷⡌⢈⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣵⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡖⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢰⢆⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣦⣀⣴⣄⠀⣀⡀⡀⠀⡀⢠⣶⠖⣤⣀⣠⣱⣿⢶⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣾⣿⣿⣿⣿⣿⣷⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⢰⣦⠀⠀⢀⡀⠀⠀⢠⣤⡀⠀⠀⣀⠀⠀⣶⠶⠆⠀⢰⣶⣶⣦⡀
⠀⠀⠀⢾⣇⠀⠹⠃⠀⠀⠀⠀⣾⡿⣧⣰⣿⣿⠀⠀⢸⡿⣷⣀⣾⣿⡄⠀⣿⡦⠀⠀⢸⣿⣿⡿⠁
⠀⠀⠀⠈⣉⠻⣧⠀⢠⣶⣶⠀⣿⠃⠹⠏⠀⣿⡇⠀⢸⡇⠘⠟⠁⢹⣇⠀⣿⡀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠛⠛⠃⠀⠈⠻⠃⠀⠉⠀⠀⠀⠀⠈⠁⠀⠘⠃⠀⠀⠀⠈⠛⠀⠉⠉⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣄⠀⢀⣤⣀⠀⢀⣀⣠⡀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⢸⡏⠀⣿⠀⢸⣿⡟⠀⢸⣏⡉⠀⣿⣁⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣼⠃⠀⣿⠀⢸⣿⣿⡄⢸⡏⠁⠀⢈⡙⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠐⠿⠀⠸⠿⠟⠁⠸⠷⠶⠀⠈⠛⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣂⣭⣴⡾⠿⠿⠿⠿⠷⢷⣿⢕⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣵⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣩⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡬⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⡇⠀⠀⠀⠀⢈⡏⣥⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣷⠀⠀⢾⡧⠟⠛⠋⢉⡷⠖⠈⢴⠀⠻⣿⣿⠿⣶⣢⡎⠀⠀⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣷⣷⣷⠖⠀⠀⢲⣼⠇⣀⣈⣀⠀⢠⡈⣾⣷⠾⠿⠿⣜⢂⡋⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⣷⣿⠉⠛⡇⠀⠿⠂⢄⣵⠟⠋⠙⢻⣿⠾⠷⠛⠾⠷⢾⡀⠈⠉⠁⠈⣿⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⣿⠿⢇⣤⣷⣄⢀⡀⣸⣏⡣⣀⣀⣸⣷⣨⣄⣐⠀⢾⣇⣿⡶⢤⣶⠶⢟⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠌⣙⡓⠛⠶⠊⠶⠯⠽⠥⣯⣵⣯⣿⣭⣹⣿⣿⣫⣽⣦⣻⣿⣶⠶⣟⣚⠉⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠁⠐⠒⠀⠀⠀⠒⠂⠐⠀⠤⠬⣭⠛⠻⣽⣿⣻⢇⠈⣹⡧⢄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠲⠴⣥⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠹⢿⣦⣤⣿⣷⡶⢦⣝⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠆⢶⣂⣀⣬⣭⣁⣀⣀⣀⣀⠒⣀⣘⣃⣀⣀⣀⣨⣤⠒⢛⡍⢾⣻⣿⣏⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡿⠮⠿⣏⡃⣛⣻⣦⣤⣭⣼⡿⠯⠽⠿⣭⣍⣩⣥⣟⠛⠙⣻⣿⡘⣿⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⡾⠇⢾⣟⣃⣚⣻⣦⣤⣴⣿⣿⠿⠽⢿⣿⣭⣤⣴⣟⠋⣙⣻⡶⠳⣿⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⡿⠽⢿⣉⣈⣩⣷⡤⢤⣾⡟⠿⠛⣻⣧⣤⣤⣾⣛⣃⣋⣿⠏⢾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢯⡍⣭⣷⡶⠲⢾⣿⣛⣛⣻⣶⡤⣴⣾⣽⣩⣽⠿⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠿⠿⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠦⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⢠⢠⠏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⢷⢄⢁⡿⢿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣎⠛⣾⣮⣧⠿⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢤⡂⠘⣿⡵⢋⡖⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⢿⢲⣿⠟⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠁⠊⡙⣦⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢠⠎⠉⡆⠀⠀⠀⠀⠀⢀⣤⣾⣧⡿⡾⣻⣕⣇⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣀⠔⠁⡠⠃⠀⠀⠓⠀⠀⠐⠀⠀⣰⣄⣷⣦⠿⠿⢭⡵⢾⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠁⠀⠐⠁⠠⡀⠀⢄⡔⠀⠀⠀⣀⢿⡾⠿⠁⠀⠀⠀⣱⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⣀⡀⠀⠀⠈⣆⠀⠀⠀⢐⣤⠁⠀⢀⠤⢄⠀⢠⠊⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⢚⠈⣧⠄⡄⣆⠩⡵⠒⠐⠳⣌⣤⠆⠁⠠⠁⢀⣼⠇⠀⠀⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠹⢊⣸⡆⣏⠡⢸⡇⠀⡖⠀⢹⠃⢀⣠⠇⣰⡿⠁⠀⢀⠄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣎⠤⠆⢸⡡⠠⡇⠀⢀⡤⠚⠛⠙⠈⣛⢿⢀⣀⠔⡏⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣟⠰⠛⣇⠀⠀⡇⠀⠀⡇⠀⠀⠙⠋⠀⢸⠋⠀⢀⠇⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢸⠀⠀⢫⠀⠀⠀⠀⢰⡇⠀⠀⡇⠀⠀⣸⠀⠀⢸⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⣆⡀⢰⠀⠀⡄⠀⢸⡇⠀⠀⡇⠀⠀⡇⣀⣀⠦⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠚⠓⠒⠚⠋⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣴⠞⠛⢳⠀⠀⠀⠀⠀⣀⠀⣤⡄⢀⣄⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⣿⠃⠀⡠⠋⣠⡄⢰⣿⠀⣿⡾⢸⣿⢫⣿⠀⣾⣇⠎⣿⣧⢶⣦⠀⣀⡀⠐⣧⡇
⠀⠀⠀⠀⠀⢿⣦⣉⣀⠀⢿⣇⣸⣿⢀⢿⡇⠘⠃⣾⡏⢠⠿⠏⠸⠿⢡⣿⠃⣼⡿⠝⠀⡸⣳⣶
⠀⠀⠀⠀⠀⠀⠉⠙⠛⢷⣆⠉⠀⠙⠋⠀⢀⣀⡀⠙⠛⣡⣴⠶⡄⠀⣿⣃⡸⣿⣄⡠⠈⣾⠟⢡⡀
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡿⠀⠀⠀⠀⣰⠃⠠⣸⠆⢰⡿⠁⡰⠃⠀⠈⠁⠀⠀⠉⠀⢸⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠑⠶⠒⠋⣰⠋⠻⣷⡀⡇⠒⢚⡋⠀⣿⡗⣪⢤⣄⠀⠀⣤⣦⠀⣴⠟⢦⠙⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⢹⣷⣧⠀⣿⡇⠀⣿⡷⠥⣼⣿⠤⣾⡟⠊⢀⢿⣆⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢿⣿⠀⢿⣧⠜⠘⢥⡴⠟⠁⠀⠻⠧⢖⡁⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⡴⠶⠶⠒⠒⠒⠒⠒⠒⠒⠚⠹⣆⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡝⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣰⣟⣁⣀⡀⠀⠀⠀⠀⢀⠴⢋⠞⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡀⣀⡀⠀⠀⡜⠁⠀⠀⠈⠙⠟⠂⠀⠀⠈⠱⡄⠀⣰⢣⢲⠁⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⣣⠀⠧⡄⠀⢸⠆⢚⣢⡜⠂⢶⣒⠢⣄⣀⠠⠤⠤⣄⡀⠀⡇⡰⢃⢀⠇⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⢰⠊⠉⠚⠉⣣⠔⠂⣈⣈⣈⣱⡞⣝⡡⠤⣽⣠⠋⠀⢀⡀⣴⠂⠀⠉⠙⢿⡡⢃⠎⠀⠀⠀⡀⠀⣸
⠀⠀⠀⢀⠤⡼⠊⠉⢱⠖⠣⢰⠋⠀⠀⠀⠠⠶⠗⠀⠀⠀⠈⢣⠀⠒⠉⠉⠁⠀⠀⠀⢘⡷⠋⠀⠀⠀⡰⠁⠀⡇
⠀⠀⠀⢏⡀⠓⢀⠄⠉⠉⢢⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣀⠤⣓⠭⠊⠀⠀⠀⡴⠁⠀⣸⣇⣀
⠀⠀⠀⠀⣇⠀⠀⢳⡄⡠⠜⠛⣦⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣇⣀⣠⣚⣉⣴⣨⡤⠤⠤⣤⠴⠚⢒⠞⠉⠉⡆⣈⡷
⠀⠀⠀⠀⠈⠑⠒⡟⠒⢶⠴⠮⠤⣤⣤⣴⣊⣀⣀⣀⡴⠋⠁⢀⣀⣴⣉⣠⡤⢮⡤⠤⠤⠼⢤⠶⠒⠚⠒⠲⡋⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠣⣀⠞⠁⢄⡰⠊⢣⡠⠋⠑⢄⣀⠎⠘⠀⠀⠀⠀⠂⠑⢄⠀⡐⠁⠀⢄⠀⡐⠁⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠔⢇⡀⠐⢏⠀⡠⢮⠀⠀⠀⡠⠋⠀⠀⠀⠑⡔⠁⠀⠀⠀⡘⠁⠀⠀⠀⠜⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠜⠁⠀⣠⠟⠀⠀⢐⠴⠊⠙⢄⠀⠀⠀⠚⠠⡀⠀⡀⠈⠀⢀⣀⡠⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⠉⠢⣤⠴⢅⠀⠀⠀⢀⡕⠂⠀⠀⠀⣀⠾⢀⠀⠀⡠⠊⠑⢂⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣈⠣⣀⠀⣁⢶⡂⠀⠈⠢⣤⠤⢎⠀⠀⢀⡽⠫⣀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡉⠛⠛⠲⠶⠬⠶⠶⠮⠷⠶⠤⠴⠿⠛⠛⢋⡿
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠢⠤⠤⠤⠤⠤⠤⠶⠒⠒⠋⠁
⠐⠲⠫⠖⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⡔⠀⢡⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⣠⠞⠁⠀⢰⠛⢉⠍⠉⠀⠀⠠⠀⠀⠀⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⡜⢁⡀⠄⢀⠎⣠⠦⠤⠶⠲⠶⠷⠾⠉⠉⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⠊⠁⢀⣰⠕⠛⠓⠒⠲⠤⣄⡀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢠⠀⡀⣻⠏⠄⢀⠀⢀⠀⢀⣀⣀⣉⡥⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡞⢦⣽⠷⡶⠶⠦⠌⣉⣉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠱⡒⡀⢹⠠⡀⠀⠀⠀⠀⠈⠉⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠤⠤⡠⠄⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣀⣀⣀⣀⣀⣠⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⣄⠀⡀⠀⣦⠀⣿⢹⡿⢹⡇⣼⠏⣽⠎⣿⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠻⠀⣿⡀⢿⡄⣿⢸⡇⠸⡧⠟⢰⠏⢸⣇⣾⢏⣠⡾⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣦⣽⠧⠜⠛⠁⠀⠀⠀⠀⠀⠀⠀⣈⣁⠙⠦⢤⡶⠟⠉⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⢀⣄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⣄⠄⠀⠀⠀⢀⠀⠀⣠⣴⣶⣶⣤⣘⣿⣷⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⡀⠀⢸⢀⡾⢿⠛⠋⢉⣩⣿⣿⣿⣥⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢄⠀⢱⡀⢸⡋⢠⠇⢀⣶⣿⡟⠁⢸⠹⣧⡙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠈⠣⠀⢃⣈⣁⠚⠠⠞⣿⣯⠆⠀⣿⠀⣿⡇⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣈⠓⣠⠞⠋⠉⠉⠙⠲⡄⢋⣻⠤⣼⡟⢸⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⢰⠃⠀⠀⠀⠀⠀⠀⠈⠀⢤⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠘⠀⠀⠀⢀⣀⣀⣀⣀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠥⣤⡀⢀⢾⡟⠛⢛⡉⠉⠙⠛⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢠⡿⠀⢀⡾⠁⠆⣼⠇⠀⠀⠀⣀⡀⠈⣿⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⣿⠁⢠⡾⢁⡿⢠⣿⠋⢹⣦⡿⢁⡿⢠⡝⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⣴⠏⠀⢸⣇⠼⣇⢀⡿⠙⢯⣉⡤⠛⠧⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣠⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⣷⡀⠰⠟⠛⠉⢹⣿⡆⠀⣿⡇⢀⡀⢀⣀⠀⣠⣤⣄⠀⢀⣀⡀⢠⡶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠿⠁⣾⠀⣰⡆⢸⡿⣿⣸⣿⣇⢸⣧⡿⢻⣿⠋⢰⡟⣰⣟⣽⠗⢸⣇⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⣿⣀⣿⠁⢸⡧⠸⡿⠸⣿⠸⣿⠇⣿⠏⢀⣿⠁⣿⣉⣡⡶⢸⣿⠙⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠻⣦⠈⠛⢁⣀⣼⠇⠀⠀⠀⠿⠀⠀⣴⣦⡀⢸⡏⠀⠈⠛⠉⠀⠈⠉⠀⢿⣄⠙⣿
⠀⠀⠀⠀⠀⠀⢠⣿⠙⢻⡆⢹⣇⠀⣈⡉⠁⢠⣤⠀⠀⠰⠄⢸⡏⣼⠇⠘⠛⠀⢀⣶⠿⣶⠀⣿⣦⡀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⣸⡏⢀⣿⣧⠀⢸⡿⣧⣤⣶⠀⢸⣿⢏⣤⣦⣤⣤⣾⣧⡶⠟⢠⣿⠈⣻⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⣠⡾⠃⢻⡆⣿⠇⠀⠀⣿⠀⣾⣿⡿⢡⡾⢻⡇⠹⣧⡀⢀⣾⠃⣼⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠈⣿⣿⠀⠀⠀⠙⠿⠃⠙⠃⠸⣧⡿⠁⠀⠉⠛⠛⠁⠀⠘⠷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢚⣽⡶⠴⠷⠶⠧⠮⠶⢵⣝⣔⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣭⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢵⡙⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣱⠝⠉⠀⠀⠀⢠⡾⣷⠒⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣬⠳⡄
⠀⠀⠀⠀⠀⠀⠀⡰⣣⡿⠁⠰⣶⠯⢶⢖⣚⡷⠟⠉⠉⠛⠙⠛⠓⠶⢤⣀⡀⠀⠀⠈⢆⡊⢆
⠀⠀⠀⠀⠀⠀⡼⢙⠝⠀⠀⠀⠹⠻⣦⣨⠏⠀⠀⣠⠄⢄⣀⠀⠀⠈⠐⠐⡝⢢⡀⡀⠀⠣⡆⢧
⠀⠀⠀⠀⠀⣸⣴⡟⠀⠀⢀⠤⠄⠐⠾⢧⡀⠀⠀⣘⣣⠔⠈⠉⢓⢒⠶⡤⢫⠬⣀⣈⠒⡀⢳⡆⢇
⠀⠀⠀⠀⢀⠗⡽⠀⢀⠔⠹⠃⠀⠀⠀⠀⠙⢆⣠⠿⠃⠀⢆⡼⠋⠉⠉⠉⠹⣔⣻⣜⡉⢉⡀⢇⡺⡀
⠀⠀⠀⠀⣈⡼⡇⠀⠘⠀⠀⣀⡠⠤⣤⣠⡶⣿⢿⠿⠛⠢⣾⠀⠀⠀⠀⠠⠚⠛⡧⠛⠿⠿⠢⣸⡇⡇
⠀⠀⠀⠀⣷⣽⠀⣀⢴⠶⠿⠣⡄⣠⢫⡿⠷⡿⠁⠀⣀⡠⡾⠶⡚⠛⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼
⠀⠀⢀⠔⠓⠾⠶⠿⢇⡀⢀⣰⣴⣁⣿⣿⣿⠀⢠⣿⣿⡟⠀⠀⣳⠀⠀⣡⣀⣀⣀⣀⢀⡀⠠⠿⠷⠚⠢⡀
⠀⠀⠀⠓⡤⠤⣤⢄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡠⣤⠤⢤⠚
⠀⠀⠀⠀⣧⣤⣤⢸⣀⣀⡀⠉⠉⡉⢸⠉⠉⠉⠉⠉⡏⠙⠉⠉⠉⠉⠉⡇⢉⠉⢁⣀⣀⣀⡀⣧⣤⢼
⠀⠀⠀⠀⡗⠂⠚⠛⠥⠭⠍⠉⡉⣳⢼⡟⣛⣛⣛⣛⣇⣚⣛⣛⣛⣛⣙⡏⡏⣉⠉⠭⠥⠼⠃⠓⠒⢺
⠀⠀⠀⠀⣻⠰⢶⣢⡤⡀⣄⡠⠤⣤⢀⠀⣀⣀⠀⢀⣀⣀⣀⣀⢀⡀⢀⣠⣤⣄⣠⣤⠤⢤⠶⠖⠒⣛
⠀⠀⠀⠀⢇⠈⢙⠀⠃⠐⠀⠒⠒⢻⢸⠏⠉⠭⠤⠤⡏⠹⠬⠭⠍⠭⠸⡇⡗⠒⠒⠒⠀⢸⠀⡋⣁⡸
⠀⠀⠀⠀⠘⡍⢹⣒⡟⠓⠒⠒⠶⢾⢸⡦⠶⠶⠶⠦⡧⢴⠶⠶⠶⠦⠴⡇⡷⠒⠒⠒⢛⣻⢲⡍⢩⠃
⠀⠀⠀⠀⠀⠱⠄⢀⣀⣀⣉⣉⠁⠉⠈⠁⠀⠀⠒⠀⠃⠘⠒⠂⠀⠀⠈⠁⠉⢉⣉⣀⣀⣀⡀⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢦⣌⣿⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⢿⣯⡌⠈⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠋⠉⢠⣾⠟⢸⣿⠀⠈⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⠉⡉⠙⠢⡐⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⢘⣿⣀⣀⠀⢀⣤⣤⠀⣀⣤⣀⠀⢀⣤⣄⢰⣿⢀⡀⠘⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢸⣿⠟⢻⡇⣾⣯⡿⠃⣋⣭⣿⣆⣿⠋⠿⢸⣿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠘⣿⣷⣿⠃⠻⣷⣾⠟⣿⣷⣿⡏⢿⣤⡶⢸⡿⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⣠⣤⣶⠄
⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⢸⣷⠀⣴⡷⣚⠀⣿⡆⣀⠀⠀⣠⣄⠀⢀⣤⡔⠫⠿⠂
⠀⠀⠀⠀⠀⠀⠀⣼⢻⡄⠀⠘⣿⣷⣿⠃⣿⡇⣿⡿⢿⣧⣾⣯⣿⠇⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠙⣦⡑⡀⠀⢻⣿⡏⠀⣿⠇⣿⣷⣾⡏⢻⣿⣵⣶⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣄⠀⠉⡀⠀⠉⠀⠉⠈⠉⠀⠀⠈⠁⠀⠉⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣧⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣴⣶⢠⡄⣦⣦⡖⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠁⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⣠⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⡆
⠀⠀⠀⠀⠰⠋⠠⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠩⡿⠁⠀⠀⠀⠀⠦
⠀⠠⣀⡐⠋⠀⠀⠀⢹⣥⡴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠀⠀⠀⠂⢴⡍⠂⠀⢄⢀⣒⠄⣀⣀⠠
⠀⠚⠀⠠⠖⠀⠀⠀⠀⠠⠎⢉⠃⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠱⡄
⠀⠂⠀⠀⠀⠀⠀⠀⢀⠔⠘⠋⠀⠐⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣵⠀⠂⠀⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠳⠶⠎⠀⢀⡁⠈⠑⠀⠠
⠀⡷⣯⢏⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⢤⠄⣂⣭⡄⡔⠂⠀⠐⡷⠀⠁
⢘⡃⠹⠇⡀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢉⡀⡘⠀⠀⠀⠀⠀⠐⠤⠀⠘⠂
⠀⠃⠀⠈⠃⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠒⠁⠀⠙⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⡇⠀⠘⠃⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣷⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⣀⠀⢇⢸
⠀⠀⠀⠀⠀⠀⠀⢠⣁⠀⠀⠈⢿⣆⠀⣀⠴⣿⠀⠀⣴⡀⠀⣴⣤⠏⢸⣧⠔⢻⡄⢀⣷⣰⠃⣿⣠⠞⣿⡆⠀⣼⠃⡼⠀⠀⡽⠃⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡠⠻⣿⡄⠀⣿⡆⣰⣿⡇⠀⣸⡏⠀⢸⡟⠀⣾⡇⢸⣿⠃⠀⣿⠏⠀⣿⡇⢰⣿⠁⠀⢀⡼⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢹⣿⠀⠙⠛⠁⠹⣧⡴⠛⠃⠀⠘⠃⠀⠹⣧⠜⠋⠀⠀⠀⠀⠀⠻⣧⠞⠿⣦⡴⠞⠀⠀⠘⢿⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⢠⡏⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⢀⣀⠀⠀⣼⡇⠜⠁⠀⠀⢠⡾⢹⠆⠀⢿⣧⡟⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢹⣷⠀⣸⠋⢩⣿⠀⠀⣿⡧⣆⠐⣆⡀⣿⡟⠁⠀⠀⢈⠟⢿⣦⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡿⠀⢸⣿⠀⢀⣿⡇⠀⢸⡏⠀⢿⡇⠀⢀⡴⠋⣠⠊⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃⠀⠀⠛⠒⠋⠘⠿⠶⠋⠀⠀⠈⠙⠚⠉⠀⠘⢧⣤⣾⠟





⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⠳⡴⠖⠒⠒⠒⠤⣀⠀⠀⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣩⢃⡤⠐⠮⣁⠀⢩⢍⡂⠈⢳⠢⣱⣨⣑⡆⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢡⠊⠀⢰⠀⡀⣤⢀⡵⠚⠒⠬⣕⠰⣾⢋⡀⠂⡑⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⡖⢢⣀⠀⢸⠀⠁⠘⡄⠈⠓⢦⡐⠁⡹⣷⠀⢳⡁⢀⠒⠈⠢⣈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⢩⠾⢖⡀⠀⢱⠀⠀⠀⠙⢶⢁⢾⡠⠀⠹⣄⠠⠈⠠⠈⢳⡕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣸⢵⡪⠦⠀⠈⢑⠒⠧⢤⣀⢀⠈⢫⠴⢣⢀⡐⠈⠑⢎⠀⠀⠂⠹⣎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⣨⠗⢢⠛⢐⠤⣄⠀⠀⡎⠖⣣⢼⠉⢙⣳⡛⢿⢱⢺⣢⣀⠐⢤⡄⢠⠈⢎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣢⡇⢹⠤⡴⠉⡙⡌⠾⡚⠉⠵⢤⣏⣜⣝⢀⣶⣍⠬⠜⢚⠠⠀⠙⡄⠹⣄⠐⡈⢾
⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⠃⠌⠯⠄⣸⣤⣕⣧⡦⠂⠄⠄⠀⠀⠙⠄⡏⠘⠀⠀⠀⠀⠀⠄⣀⣹⣠⡸⠦⠴⠞
⠀⠀⠀⢠⠊⠉⡝⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣁⠉⠓⠀⠐⠒⠓⠀⠐⠋⠉⠉⠉⠁⠀⠀⡀⠀⠀⠂
⠀⠀⣠⠦⢀⣮⡀⠀⠀⠀⢳⠠⠦⢄⣀⣀⣠⠔⠛⢍⡜⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⣀⣁⣀⣤⠦⢴
⠀⠜⠁⠀⢸⠈⡜⢄⡀⠀⠸⠀⣰⡠⠔⠊⠀⡠⠂⢰⠉⡉⠋⠉⠉⠉⢉⠟⠋⠉⠉⠉⡉⠉⢄⠀⢀⠄⠀⠀⣸
⡄⠀⠀⠀⢸⡀⠈⠢⣈⡉⠉⠉⠁⠀⣀⠄⣊⡠⠔⠓⠺⣩⠃⠑⣀⠔⠁⠀⠀⠀⢀⠀⠀⠀⠀⢱⠆⠀⠀⠠⡇
⡇⠀⡀⠀⠘⣕⠄⡀⠀⠈⠉⠙⠛⠉⠉⠉⠀⣀⠠⠀⢠⠏⠀⡠⠊⢄⠀⠀⠀⡠⠊⠂⠀⠀⡠⠁⠀⠢⡐⢰⠁
⢣⠀⠐⢄⠀⠈⠑⠤⠬⠥⣀⣒⣀⣒⡂⠈⠁⢀⡤⠚⠑⢄⠌⠀⠀⠀⠢⠀⠔⠁⠀⠀⠑⡔⠁⠀⠀⣀⣁⠎
⠀⠳⣄⠀⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢩⣛⡳⠤⠤⠤⠌⠤⣀⣀⣀⣠⣿⡄⠠⠤⠤⠴⠴⠒⠒⠊⠉
⠀⠀⠈⠑⠤⣄⣀⠀⠀⠈⠉⠁⠀⢀⣀⠤⠚⠁
⣶⣶⠶⠶⢶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

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

⠀⠀⠀⠀⠀⢀⣀⡀⠀⢄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠳⠄⣃⠄⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡠⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢠⡖⠺⣩⢨⠈⠀⠀⠀⠀⢀⡴⠋⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢸⡁⢁⣠⠒⠊⠀⠀⢀⣿⣉⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⡈⠰⢂⡙⢦⡘⢯⡇⠀⠀⣰⣺⡯⠟⠁⠀⠀⢸⡄⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠙⣈⠯⠷⠦⣝⣆⢱⠀⡰⠋⠀⠀⠀⠀⣀⡤⢾⡗⠀⠀⣰⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣄⠈⠀⠀⠀⠀⠙⢿⣶⠁⠀⠀⠀⢀⡾⡳⢤⣾⠃⠀⡜⢀⣿⢿⡄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠛⡭⠙⠀⠀⠉⠳⣄⠀⠀⠀⢘⣧⡀⠀⠀⢠⣿⡿⡗⢻⡿⠀⠀⣇⢀⣅⣾⠇
⠀⠀⠀⠀⣰⣟⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣲⡟⠋⢻⣇⠀⠀⣼⣿⣿⣴⣿⠃⠀⠀⢻⣷⣾⡋⠤
⠀⠀⠀⠀⣿⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠙⣽⡄⣰⣻⠿⠟⠋⠀⠀⢀⣠⣴⣋⡉
⠀⠀⠀⠀⣟⡗⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣼⣿⡇⠀⠀⢹⣷⠟⠁⢀⠤⠀⠐⠂⠉⢿⣿⣿⡍⠳⡄
⠀⠀⠀⠀⠘⣿⣦⢀⣀⠀⠀⠀⠀⢄⣴⡾⣿⣿⣿⠇⠀⠀⣸⢟⡤⢊⣥⢖⣤⢤⣤⡀⠈⠳⢷⡻⢾⡗⡀
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣀⣢⣿⣿⣿⣿⣿⣿⠋⠀⠀⣰⣿⢯⣴⣿⣿⠿⣩⡿⠿⢿⣄⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢠⣼⡿⠟⠚⠉⠉⠉⠋⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠁⠀⠀⠀⣠⣿⠏⢤⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠉⠚⠛⠂

⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢰⠛⣏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢈⠄⠘⢦⡓⢤⠀⠀⠀⠀⠀⣀⣀⣉⣷⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⡸⠀⠀⠀⠱⠠⢳⡀⠀⡔⠉⠀⠀⠐⠺⠟⠉⠀⠀⠀⠱⡄⠀⠀⣀⢀⡠⠄⣀⢀⡀
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢇⠀⠳⡀⡇⠀⣀⡤⠤⠄⣀⢀⡔⠒⣲⠔⠓⣤⣃⠠⠏⠀⢀⠼⠀⡜⠓⠢⡀
⠀⠀⠀⠀⠸⡇⠀⡀⠀⠀⠈⢆⠣⣹⠟⠉⠁⠀⢢⣀⣀⠀⠉⢃⣽⣡⣄⣉⢩⣔⣈⣁⣀⠐⠢⣜⠉⠓⠉⠑⡄
⠀⠀⠀⠀⠀⡇⠀⠠⡀⠀⠀⠈⠳⣏⠀⠀⠀⠈⠉⠈⠑⠀⣰⠋⠀⠀⠀⠚⠦⠄⠀⠀⠈⠙⣆⠼⠲⡎⠉⠑⣇⢀⡀
⠀⠀⠀⠀⣀⣸⡀⠀⠱⡀⠀⠀⠁⠨⣓⠧⣀⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠊⠉⢠⡀⠞⠀⡱
⠀⠀⠀⣎⠉⡌⠑⠒⠶⠺⠦⢤⡤⣤⣀⣉⣢⣉⣒⣤⡀⢘⡇⠀⠀⠀⢀⣀⣀⣀⣀⣠⢤⡤⠿⠧⣀⣀⡔⠀⠀⣸
⠀⠀⠀⠈⠙⡗⢲⠶⠾⠦⠤⢤⣵⣤⣀⣈⣙⣄⣈⣉⣫⣉⣉⠉⠙⢍⡉⣁⣈⣑⣄⣀⣀⣈⣵⢤⡤⠤⢷⠖⠒⠁
⠀⠀⠀⠀⠀⢹⠀⠡⡀⠀⠀⠀⠡⠀⢀⠔⠉⠀⠀⠀⠀⠈⠉⡄⢀⠔⠙⢌⡨⠙⢄⣀⠈⠢⣀⡔⠁⢤⡟
⠀⠀⠀⠀⠀⠈⣆⠀⠘⠄⠀⠀⠀⠳⠁⠀⠀⠀⠢⡀⠀⠀⠀⠘⢅⠀⠀⠀⠱⢄⠀⢱⠄⠀⢈⢆⢀⡞
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠔⠄⠀⠀⠀⠜⠑⢄⡄⠀⠈⠶⡁⠀⠘⢇⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠄⠛⢄⠀⠀⠀⠰⡈⠁⠀⠀⠀⠴⡈⠀⠀⠀⠙⣦⣀⡠⠚⠂⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⢑⢶⠈⠀⠈⠂⣄⣀⠠⠄⠁⠀⢤⡐⠊⠀⡩⠂⢄⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠶⠿⣶⣦⣈⣠⣭⣒⣤⣤⣔⣥⣬⠶⠾⠖⢊⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠖⠚⠉