Cheery Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠋⠉⠉⠀⠀⢀⣤⣿⣿⣷⣶⣦⣤⡤⠤⠤⠀⠤⠬⡄⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠗⠀⠀⠀⠤⣤⣤⣴⣾⣿⡿⠷⠛⠋⢹⠟⠁⠀⠀⠀⠀⢠⣆⡺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣠⣶⣫⡿⠋⠉⠀⠀⠁⠀⣠⠋⠀⠀⠀⠀⠀⣀⡵⢿⡿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⣴⣾⣿⠟⠋⠁⠀⠀⠀⠀⠀⣄⣰⠃⠀⠀⠀⠀⠀⣰⠟⠀⣸⡇⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⣀⣋⡟⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⡠⠞⠁⠀⠀⣿⡇⠀⠀⣧
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⢀⠀⣠⣠⠖⠋⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⡼⠄⠀⣨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣸⡤⠟⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢰⠀⠀⣴⡟⣿⡇⠀⠀⠀⢠⡄⣤⠴⠛⠉⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢰⢀⡾⠋⠀⣈⣃⡤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⢠⣞⣠⡶⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠁⣧
⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⣇⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠨⠛⠋⠙⠛⠛⠛⠋⠛⣿⣿⣿⣷⣀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠁⠐⠂⣷⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠍⢺⣿⣿⣿⣿⣄⠀⠀⢀⡀⡇⠀⠀⠀⠀⠠⣀⣞⣿⣶⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⣿⡿⠿⢛⣿⣀⣀⣨⣤⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⢻⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠟⠁⠐⠛⠋⠈⠙⣿⣿⣾⣷⣶⣾⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⠋⠀⠀⠀⠀⠀⠀⠄⠀⠉⠉⠉⠀⠈⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣧⠀⠀⠀⠀⢠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡄⠀⢀⣸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⣀⣀⣿⣿⣿⣿⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⡿⠿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⢇⢰⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⣧⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠷⣦⣶⣤⣠⣶⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠛⠛⠉⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⡀⠀⠄⠀⠀⢀⠀⠠⠈⠻⣦⠀⠀⠀⣰⠟⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠄⠰⠂⠘⠁⠀⠉⠀⡀⠁⢀⠀⠂⠘⡷⢶⡾⠃⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢾⣿⣏⠀⢀⡴⢻⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣀⣀⣀⣀⣀⣤⣤⠶⠟⢋⡴⣫⠟⢩⠗⣾⠻⣾⠉⠀⣀⠀⠈⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⢀⡴⣫⠞⠁⠀⡾⣸⠇⠀⣿⠀⠀⠀⠀⠈⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⡴⠁⠀⠀⢠⢇⡿⠀⠀⢸⡆⠀⠀⠀⠈⢀⠂⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡱⠋⠀⠀⠀⠀⣸⢸⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠢⠠⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⡞⠁⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢡⡀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢡⠏⠀⠀⠀⠀⠀⠀⢰⠃⣿⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⢠⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⠏⠀⠀⠀⠀⠀⠀⠀⢸⢰⡏⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠘⢁⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠘⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢾⡇⢸⠇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢧⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠋⠉⠀⣸⣀⡼⠀⠀⠀⡤⠄⠀⠀⠀⣳⣤⠤⠤⠤⢼⡄⢹⣦⡶⠛⠛⠛⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣐⣶⡤⠚⠁⠀⠀⠀⠀⠀⢷⠀⣧⣀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠁⢤⡀⠀⠀⠠⠀⠄⠁⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠐⠾⠇⠀⢀⠀⠀⠀⠀⡀⠀⢸⣽⠂⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⠶⠶⠶⠶⠛⠋⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⣀⠀⠀⠀⠀⢀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⠋⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢲⣄⢬⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⣰⠏⢊⢳⡙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠁⠀⠀⣀⠬⡽⠋⠀⠈⠘⡘⡌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⣀⡤⠖⠚⠉⢀⡴⠁⠀⠀⠀⠀⡇⠘⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⡤⠖⠋⠁⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⢀⠇⠀⢇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢠⠖⠉⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⡰⡸⠀⠀⢸⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡔⠁⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⡱⠃⠀⠀⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡜⠁⠀⠀⠀⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢀⡴⠊⠀⠀⠀⠀⣀⣀⣠⣄⣀⡀⠀⢠⣣⠏⣀⣀⣀⣀⣰⠳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠊⠀⠀⠀⣠⡶⠋⠉⠀⠀⠀⠀⠉⡻⣳⢷⡋⠁⠀⠀⠐⠷⠛⠛⠉⠉⠛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠃⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⡞⢡⠃⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣀⣠⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣄⣀⣀⣀⣀⣠⡴⠞⠋⠉⠙⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⣠⡄⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠻⢿⣿⣿⣿⣿⣿⠟⣁⣰⣿⡻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⣀⣤⠀⣈⣉⣛⠿⣫⠙⣥⣾⡿⠿⣌⠙⢿⣿⣿⣦⠀⠀⠀⠀⢀⣤⣞⣫⣭⣽⣿⣿⣿⣿⠘⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⣶⣞⣉⣀⣾⣿⣿⣿⣆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢻⣿⡿⢀⣿⣿⣿⢯⣞⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣿⣿⣝⠻⣿⣿⣌⡳⣿⣿⢇⣸⣿⢿⢯⣟⣛⡙⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⣭⣵⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢙⣉⣛⣛⣿⣿⣿⣻⠿⡰⠿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⡾⢿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢨⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣎⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣾⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣤⣀⠀⠀⢀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣶⣤⣤⣤⠶⠶⠤⣬⣿⣶⣿⡿⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣐⣲⡶⠚⠋⠉⢨⠃⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠐⣒⢶⠖⠋⠉⠀⠇⠀⠀⢠⠎⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⣰⠋⠀⠀⢠⣤⠖⠋⠁⡸⠀⠀⠀⡸⠀⠀⠀⠁⠀⠀⠀⣠⡴⢻⣿⠏⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⢀⡼⠁⢀⡠⠞⢉⠇⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⢠⠞⠀⠐⠋⠀⠀⠊⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠛⠉⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⣰⣏⣤⣤⣤⣤⣤⠤⠤⠶⠶⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⣿⣿⣿⣿⣷⣦⣿⣿⣠⣤⣤⣀⡀⠀⠀⢀⣤⣶⠶⠷⣶⣶⣤⣸⣿⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡿⠋⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡆⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠢⡀⠀⠉⠉⠉⠉⠉⠋⠉⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠢⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡰⠆⠚⠉⠀⠈⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠚⢁⠐⠠⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠋⠀⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⢀⣀⡠⠤⠔⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⠾⠿⠿⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠘⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⣼⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⢀⣉⣤⣤⣴⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⢻⣿⣿⣿⣶⣦⣄⠀⠀⣤⠀⠀⠀⢠⣆⠀⠀⠀⠀⠀⠉⠻⢿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⣀⠀⠘⣿⡟⠁⠀⠙⠻⣿⣤⡈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⣾⣿⠀⢀⣿⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⣠⣾⠋⢰⡿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⣶⣶⣶⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢀⣼⡿⠃⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢀⣾⡿⠁⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢀⣾⡿⠁⠀⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⣼⡿⠀⠀⠀⠀⠀⠸⣇⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⢻⣷⡄⠀⠀⢀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⢻⣿⣤⣤⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠻⣿⣦⣶⡿⠛⠉⠉⠉⠉⠛⠛⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⡇⠀⢸⣿⡄⠀⠀⠈⠉⠛⠿⣦⡀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠘⢿⣯⡀⣠⡶⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄
⠀⠀⠀⠀⣠⣶⡿⠛⠉⠁⠀⠀⠀⠀⣷⠀⠀⣿⣇⢀⣀⣤⡀⠀⠀⠈⠻⣦⠀⠀⢀⣴⠾⠻⣦⠀⠀⠀⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⣠⣾⠟⠁⠀⠀⠀⠶⢶⣦⣤⣤⣼⣆⠀⣹⣿⡟⠉⠀⠀⠀⠀⠀⠀⠹⣧⣴⠟⠁⠀⠀⠙⣷⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠙⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠙⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋
⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠃⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣶⣶⣶⣶⣶⣾⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⡿⠟⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣿⣿⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠤⢖⣚⣭⣄⣭⡶⢞⡉⠉⠉⠙⠳⣄⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠤⠀⠄⠂⠀⣈⡭⠵⠒⠈⠉⠀⠀⠀⠀⠀⠀⠑⢆⠀⠀⢸⣄⣠⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣨⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠔⣲⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢠⡼⣵⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢰⠇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⣤⠀⠀⠀⣠⠊⠀⠀⠀⠀⣰⠋⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠠⠀⠀⠀⠀⡴⠀⠀⠀⣸⠀⢀⡔⠁⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠌⠀⠀⠀⠐⢃⡴⠋⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠋⠀⠀⠀⢠⡶⠂⠀⠀⠀⠈⣹⣦⣾⡋⠀⢀⡀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢤⣎⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⢠⣮⠀⠀⠀⠀⠈⠷⣿⠿⠛⠉⢺⠟⢯⣽⣿⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠂⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠋⠁⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠨⡆⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⣰⠄⠚⠁⠐⣤⣤⣇⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠐⠀⠀⠀⠀⠀⣠⠇⠀⢀⡀⣴⠿⢆⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠙⠻⢯⣷⣄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠆⠀⠈⠁⠀⠀⠑⠦⢤⢄⡤⠶⠒⠁⠙⠓⢶⣄⣀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⢼⡀
⠀⢳⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣀⠀⠀⢠
⠀⡀⠀⠀⢀⣿⠡⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⢀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠗⠁
⠀⠀⠀⠀⡸⠀⢠⠀⣈⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠚⠻⠛
⠀⠀⠀⢠⡇⡦⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠤⠀⠤⠄⠀⠀⠒⠒⠉⠉⠀⠀⡰⠁
⠀⠀⠙⠜⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣀⣀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⣀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⣼⣿⠋⠁⠘⣷⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠹⠛⣀⠀⠀⢿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠉⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠳⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⢀⠀⣀
⣿⡟⣉⡻⠿⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠌⢦⠂⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠄⣧⠠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢸⠆⢸⠀⠀⣀⣀⣠⢤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣠⠼⢚⣩⣋⣤⣤⣄⣀⠠⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣄⠀⠁⠀⠀⠀⠈⠑⠄⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⡀⢸⠉⠓⠶⠤⣤⣤⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡼⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⡜⠀⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡼⠀⠀⣇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣸⠃⠀⠀⢹⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣰⠃⠀⠀⠀⠸⡆⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡏⠀⠀⠀⠀⠀⣧⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⣼⠀⢸⣁⣀⣀⠀⠀⠀⠸⡄⠸⣄⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠐⠻⣀⣸⠤⡀⠉⢳⣀⡠⠤⢧⠀⢻⣀⡤⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣯⠀⠤⠼⣆⡞⠁⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠛⠋⠁⠈⠛⠲⢤⣤⣀⣀⣀⣤⡤⠖⠋


⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣏⡉⠙⢯⡛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⣀⡀⢳⡕⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠄⣐⣒⣹⠏⠪⣕⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⢀⣠⠔⢳⡀⠐⠀⠀⠈⠑⢦⡍⠑⠒⠶⠤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣠⠖⠋⠀⠀⠀⢳⡀⣇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⢧⠸⡄⠀⠀⠸⣀⠀⠀⠱⣄⠒⠂⠒⠠⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢳⠀⠀⠀⢸⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⡄⠀⠀⢸⠀⠀⠀⠀⠐⠙⢦⣄⡀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠹⣌⠑⠲⢤⡀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢰⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⢧⡀⠀⠈⠓⠄⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⢸⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⢸⠀⢻⡖⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⢤⣤⠋⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠛⠉⠉⠉⠉⢇⠘⠛⠲⢦⣄⠀⠹⠀⠀⠀⠀⠀⠀⠀⢸⠹⡄⠀⠉⠲⡄
⠀⠀⠀⠀⣀⡤⠞⠉⠁⠀⠀⢀⡴⢁⠞⠉⠙⠳⢦⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡀⣸⢰⡄⠀⠀⠙⢷⡈⡇⠀⠀⠀⠀⠀⠀⠘⠀⠹⣤⡀⠀⠈
⠀⠀⣠⠞⠉⠀⠀⠀⢸⡤⠶⠋⢀⡏⠀⠀⠀⠀⠀⠹⣆⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠘⢯⣁⡈⣓⡧⠀⠀⠀⢻⡼⣠⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠢⡀
⠀⡴⠃⠀⠀⠀⠀⠀⠀⠙⢦⣄⣸⡀⣠⠀⠀⠀⠀⠀⠸⣇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢
⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣀⠤⠀⢄⢻⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠑
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⣿⢸⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢳⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⢀⡿⠀⢷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡇⣠⠏
⠸⣆⠔⠉⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⠟⠁
⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠉⠢⡴⠲⠏
⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣤⣤⣤⣤⡴⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⣿⣿⣿⣿⡍⠉
⠀⠀⠀⠀⠀⣴⠀⠀⠀⢦⠀⠚⠛⠉⢈⣳⣤⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠦⠀⠀⠀⠀⠜⠲⣖⡒⠒⠶⣦⣄
⠀⠀⠀⠀⠀⢿⣧⡀⣀⣬⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠉⠉⠻⠿⠿⠿⠛⠛⠛⠒⠀⠀⠀⠀⠀⣟⠀⠈⠀⠙⢦⡀⠙⣷
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⡀⠀⠀⢳⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢤⡸⢆⠍⠀⠀⠀⠀⠀⢰⡵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠐⠊⠉⠄⠰⠄⠠⠍⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠂⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠈⡛⣁⠆⢠⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣤⣤⣴⡤⠶⠘⡇⠀⠀⠀⣀⣀⣠⡴⠚⠋⠁⠀⡸⠇⠙⣆
⠀⠀⠀⠀⠀⠀⢣⣀⣹⣿⢀⣄⠀⠀⡡⠀⠀⠀⠀⢀⠀⠀⠂⠒⠓⠓⠶⠦⣤⣀⣀⣀⣠⠤⠁⠒⠒⠉⣀⠼⠃⠀⠀⠀⠀⡴⠃⣰⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠻⠿⠶⠖⠁⠀⠀⠀⠒⠀⡤⣤⣤⣤⡤⠤⠴⠛⢉⡁⢀⣀⠀⢀⡠⠄⠂⠉⠀⠀⠀⠀⢀⡴⠋⠀⢀⠂⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⢀⣀⡴⠞⠋⠁⣀⡤⠒⠫⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⠀⠀⠀⠀⠈⠓⠒⠴⠟⡟⠁⢀⣴⠞⠁⠀⠀⢰⣆⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢰⠁⠀⠀⢀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⢀⡞⠁⠀⢠⠀⣸⣾⡿⠀⠀⠀⠀⢠⡇⡀⠀⠀⠀⢠⠀⠀⠁⠘⢦⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⡞⠀⢀⣄⣠⣷⢿⠟⠁⠀⠀⠀⠀⠉⠋⠉⣰⡄⠀⢸⡀⣶⡀⡀⠀⠀⢀⣼⠆
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠁⠈⡄⠀⣴⠀⠶⠀⡄⠀⠀⠀⠀⠀⠀⢸⢠⣁⣴⣶⠿⠛⠃⠀⠀⠀⠀⡄⢀⠀⠀⢄⣴⠋⠀⠀⠙⠓⠈⠹⣿⣦⣦⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠻⣭⣱⠾⢡⠒⠛⢻⡿⣧⡅⠀⠀⠀⠀⠀⠀⠀⠛⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣿⣿⣿⡀⠀⠀⠀⠀⠀⣸⡟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣿⣁⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢿⣶⣦⣤⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⢀⣴⡾⠿⠶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣖⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⣀⡀
⠰⠿⠿⠿⠟⠋⣸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⡧⣌⡉⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢸⢻⡑⢦⠙⣆
⠀⠀⠀⠀⠀⠀⡇⠈⢧⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠳⣄⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡾⠀⠑⢄⡀⢸
⠀⠀⠀⠀⣀⣀⣇⣐⠿⣿⣿⣳⠀⠀⠀⢀⡤⢴⣧⣄⠀⢀⣼⣦⠴⣤⠀⠀⠀⠀⠀⠀⣤⣶⣷⡶⣄⠀⠈⠉⠁
⠀⠀⠀⢸⣿⣿⣿⣿⣷⢻⣿⡿⠀⠀⠀⣿⠀⠀⠀⢈⡇⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣿⣿⣿⣧⣼
⠀⠀⠀⠘⢿⣿⣿⣿⠇⠙⠋⠁⠀⠀⠀⠘⠦⣤⡤⠞⠁⠘⠦⣤⡤⠞⠁⠀⠀⠀⠀⠀⠻⢿⣿⡿⠏
⠀⠀⠀⠀⠀⠉⠉
⠀⠀⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠻⣍⡀⠒⢒⡻⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⢀⣒⣲⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡾⣆⢶⣭⡻⣿⡄
⠀⠀⠉⠉⢁⡞⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠘⡄⠙⠛⠿⠟⠂⠀⠀⠀⠀⠀⠀⢰⠃⠸⡆⠙⠿⣿⣷
⠀⠀⠀⠀⠼⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⣀⣀⡇⠀⠀⠈⢢⣀⣀⠀⠀⠀⠀⠀⣠⠖⠶⠯⠄⠀⡇
⠀⣰⠋⠙⠛⢳⡄⡞⠛⠋⠉⣧⠀⠀⠀⣾⣿⣿⣿⢻⡄⣾⣿⣿⡏⣳⠀⠀⠀⠀⣇⠀⠀⢠⡞⠛⠛⠙⢦
⠀⠹⣄⠀⢀⡼⠁⢷⣀⠀⣀⡟⠀⠀⠀⠹⣿⣿⣿⡾⠁⢻⣿⣿⣿⡟⠀⠀⠀⠀⠙⠶⠤⠘⣇⠀⠀⢀⡞
⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋

⠀⢀⣠⣤⡤⠄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⣶⣿⣷⣦⣀
⢠⣿⣿⣿⠿⢋⡏⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣥⣶⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢫⡛⠻⠿⠛⠋
⠀⠀⠀⠀⣠⠎⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠛⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢳⡀
⠀⣰⣶⣶⣶⣦⡀⣠⣶⣶⡷⢦⡀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⢳⡀⠀⠀⠀⢀⣴⣶⣾⣤⡀⢀⣤⣷⣴⣤⡀
⠀⣿⣿⣿⣿⣼⠇⣿⣿⣿⣿⣼⠇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⠇⠀⠀⠀⢸⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⡇
⠀⠈⠻⠿⠟⠋⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠤⠶⠋⠀⠀⠀⠀⠈⠻⠿⠿⠟⠁⠘⠻⢿⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⢀⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠻⠷⣄⠀⠀⠀⠀⠀⠀⣠⠾⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠁⠀⠈⠁⠢⡀
⠀⡠⠂⠁⠀⠀⠀⠑⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠈⡐⠠⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠐⡀⠀⠉⠐⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣴⣶⣶⣶⣶⣶⣶⣶⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠖⠒⠒⠐⢦⣤⣄⣀⡀⠀⢀⣀⣀⠀⢀⡠⢐⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠋⠁⠀⠀⡀⢀⣠⣴⣿⣛⣿⣿⢿⡿⠛⠉⠉⠀⠀⢉⠙⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠀⠀⣀⣭⣻⡿⠿⠛⠋⠉⠀⢀⡜⠁⠀⠀⠀⠀⠠⣺⣿⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣠⣼⣾⣿⠟⠋⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣰⡾⠁⣼⠁⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⡠⢞⣿⠟⠃⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠀⠁⢻⡄
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⣀⣼⡷⠛⠘⠀⠀⠀⠀⠀⢀⠀⣠⠞⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣿⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣸⡤⠀⢒⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⣿⡾⠟⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⡁⠀⣴⡿⣿⡇⠀⠀⠀⣤⢀⣤⠿⠛⠉⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠐⢿⡄
⠀⠀⠀⠀⠀⠀⠇⡼⠋⠀⣸⣀⣤⡴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣻⡄
⠀⠀⠀⠀⠀⢰⣞⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣰⣏⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠟⠛⠙⠛⠛⠛⢋⣻⣿⣿⣿⣦⡀⠀⠀⠀⠀⢹⡀⠄⠂⠀⠀⠀⠒⣿⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠆⠀⠀⠀⠀⠀⠈⠀⠘⢞⢻⣿⣿⣿⣿⡄⠀⠀⢠⢸⠁⠀⠀⠀⠠⢤⣶⣿⣿⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⠀⠤⢠⣴⣿⣿⠿⢛⣻⣿⣤⣄⣸⣼⠆⠀⡀⠀⠀⠀⠀⠉⠁⠀⠈⠻⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠟⠡⠘⠛⠃⠉⠹⢿⣿⣿⣿⣿⣷⣿⣄⣀⡀⠀⠀⠀⠀⠀⠎⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⠃⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠈⣿⣿⣿⡗⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣿⣧⣿⣆⠀⠀⠀⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⣄⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣶⣀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⢒⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣾⣿⣿⣿⣿⡇⢙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠙⠘⢧⣆⠀⠀⠀⠀⠀⠀⠀⠤⢒⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⣀⣀⠀⢀⣄⣠⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠿⠛⠉

⠀⠀⠀⠀⢀⠤⠒⠒⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠢⢄
⠀⠀⠀⡰⠁⠀⡀⠀⠀⢀⠀⠙⡆⠀⠀⠀⠀⠀⠀⣴⣥⣤⣤⣤⣤⣤⣤⡵⡄⠀⠀⠀⠀⠀⠀⡞⠁⢀⠀⠀⠀⡀⠀⠱⡀
⠀⠀⠀⡇⠀⠈⠁⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⢰⠁⠛⠿⠟⠁⠛⠿⠟⠃⣷⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠉⠀⠀⡇
⠀⠀⠀⢇⠀⠀⣄⣀⣀⡠⠀⠀⡜⠀⠀⠀⠀⠀⠈⣆⠀⠠⣀⣀⣀⡠⠀⢀⡏⠀⠀⠀⠀⠀⠘⡄⠀⠀⣤⣤⣤⠀⠀⢀⠇
⠀⠀⠀⠈⠣⣀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠈⠑⢦⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠑⢄
⠀⠀⠀⡎⠀⠀⠆⠀⠀⠰⠀⠀⢣⠀⠀⠀⠀⠀⢀⠇⠠⠖⠦⠀⠠⠖⠦⠀⢇⠀⠀⠀⠀⠀⢰⠃⠀⢠⠀⠀⠀⡤⠀⠈⡆
⠀⠀⠀⡇⠀⣀⣀⣀⣀⣀⣀⠀⢸⠀⠀⠀⠀⠀⠸⡀⢀⣀⣀⣀⣀⣀⡀⠀⡸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠱⡄⠑⢤⣀⣀⠴⠃⣠⠃⠀⠀⠀⠀⠀⠀⠳⡀⠳⢤⣀⣠⠴⠃⡰⠃⠀⠀⠀⠀⠀⠀⢣⡀⠐⠉⠉⠉⠃⠀⡴⠁
⠀⠀⠀⠀⠈⠓⠦⠤⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠤⠖⠋


⠀⠀⠀⠀⢀⠴⠒⠚⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠚⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⢄
⠀⠀⠀⡰⠁⡠⠀⠀⠀⠠⣄⠘⣆⠀⠀⠀⠀⠀⠀⡜⠁⣠⡀⠀⠀⣠⡀⠙⡄⠀⠀⠀⠀⠀⢀⡞⢀⡤⠀⠀⠀⠤⡀⠱⡀
⠀⠀⠀⡇⠀⠈⠃⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⢰⠁⠈⠁⠉⠀⠀⠁⠉⠀⢱⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⠀⠉⠀⠀⡇
⠀⠀⠀⢇⠀⠀⡤⠴⠦⢄⠀⠀⡜⠀⠀⠀⠀⠀⠈⣆⠀⠠⣄⣀⣀⡤⠀⢀⡎⠀⠀⠀⠀⠀⠘⡄⠀⠀⣤⠤⢤⠀⠀⢀⠇
⠀⠀⠀⠈⠳⣄⡀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⡀⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠓⠈⠁⢀⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⡐⠀⠀⡸⠀⢱⡀
⠀⠀⠀⠀⢀⠰⠀⠀⢀⡀⠤⠒⠉⠀⠀⣠⠃⠀⠀⢣
⠀⠀⠀⠀⠠⡣⠖⠋⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⡎⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠡⡀⠀⠀⠐⠊⠀⠀⠙⠢⠤⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠲⣄⡀⠀⢀⡠⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⠲⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠠⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠰⡙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠈⠢⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠂⠀⠰
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠐⠂⠀⠀⢀⡆
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠡⡄⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢤⣀⣀⣀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⣄⣀⢀⣀⡠⠖⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡿⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠉⠛⠉⠉⠋⠙⠛⠛⠉⠙⠛⠻⠟⠛⢛⠛⠛⠛⠛⠛⠿⠟⠻⢿⡿⠿⣿⣛⠙⠛⠿⠟⠋⠉⠙⠛⠿⠿⠿⠿⠛⢛⠛⣿⣻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠐⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⣿
⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣿
⣿⡄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠰⠆⠈⠀⠀⣾⣿
⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠎⠀⠐⠂⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⢁⠀⠐⠀⠀⠐⠈⠀⠀⣿⣿
⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠚⠀⠀⠀⠀⠁⠈
⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠄⠀⠤⠁⣈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠰
⣿⠇⠀⠀⠀⠀⠈⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠐⢂⠻⡀⠐⠒⠞⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡪
⣿⣁⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠁
⣿⡿
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⠀⠀⠀⠀⠀⠐⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠤⠀⠀⠀⠀⠀⢰
⣿⠄⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⣸
⣿⡆⠀⠀⠀⠀⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣆⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣤⣤⣶⣶⡄⣀⣴⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⢀⡴⠚⢉⣠⠆⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⣄⠀⢠⢏⣠⠖⠋⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡤⣤⣀⢰⡏⢿⡙⠿⣯⠤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣍⣛⣻⣿⠃⠀⢳⡀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢷⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣧⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣀⣀⣇⣀⣀⡀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡴⠞⠋⠉⠉⠉⡿⠉⠉⠉⠛⠲⣄⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠐⠲⠤⠷⠶⠂⣀⡤⠶⠞⠓⠺⡗⠒⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣿⣇⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡤⣤⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠉⠉⠉⡽⠉⠉⠙⠓⢦⡀⠀⠀⠐⡇⠀⣸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢠⣄⣀⣼⣡⠄⠀⠀⠀⠀⠙⣆⠀⠀⣧⠀⠸⣄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⡇
⠀⠀⠀⠀⠀⠀⢸⠃⠀⣴⢻⠆⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠖⠒⠻⣆⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠻⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡾⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⣀⣤⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠒⠋⠁

⣠⣄⡀⣀⣠⡄⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠛⠿⠋⠻⠟⠃⠀⠀⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠁⠰⠊⠂⡂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⢀⣀⡀⠀⠄⠀⠀⠀⠐⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢀⠀⠀⠀⠀⠀⠄

⢀⣀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠑⠂⠐⠊⠁⠀⠀⠀⠀⡂⠀⢐⠀⠀⠀⠀⢀⡠⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢀⣀⠲
⠀⠀⠈⠁⢀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠠⠀⠘⠊⠀⠈⠀⠀⠀⢀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠶⠂⢀⠀⠀⠀⢀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠
⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠤⠄⠁⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠆⠀⠀⢈⠊⠁⠀⠙
⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣄⣀⣔
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⡻⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠔⢻⢱⠏⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠞⠁⠀⣇⡟⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⣿⣿⡕⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⡇⠙⢿⣦⠲⣝⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠻⣷⡙⣿⣮⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠙⣿⡜⢿⣿⣦⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣿⡜⣿⣿⣿⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⣿⡜⣿⣿⣿⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠸⣿⠸⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⢹⣇⢿⣿⡇⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⣿⡸⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣀⡤⠔⠒⠢⢤⡀⠀⠀⠀⠀⠘⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⣽⡇⣿⢡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠂⢺⣤⡿⠁⠀⠀⢀⣴⣶⣿⣧⡀⠀⠀⠀⢡⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣷⠛⡌
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠈⠉⠀⠀⠀⣠⣿⣿⣿⣿⣿⠷⠒⠂⠐⠒⢆⢻⡤⠒⠈⠉⠉⠒⠤⡀⠀⠀⠀⠀⠀⠘⣿⠰
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢟⣵⣿⠇⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢃⢲⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢆⢻⣷⣦⣄⣤⣤⣾⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⣶⣀⣠⠀⢀⠀⣠⢠⣄⣿⣾⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠝⣛⠿⠿⠿⠿⠿⣛⡫⢷⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠑⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⢝⣛⠿⠿⠿⢛⣛⠩⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣿⠿⠿⡿⡿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣻⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠂⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠂⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠓⠂⠀⠀⠀⠀⠀⠀⠚⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠿⠷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠿⠟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠐⠠⡀⠀⠀⠀⠀⠀⠐
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢢⠠⠂⠀⠀⠐⠣
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠦⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣤⡀⠀⢹⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⠀⠀⠀⠀⠀⢁
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠆⠈⣆⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠠⠐⢀
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉⠀⠀⢀⠂
⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣂⣤⣤⣤⣤⣤⣤⣤⣄⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣧

⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡤⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣤⣨⣿⣯⣻⢞⡍⢻⣿⡄⠀⢠⣴⣾⣿⣷⣶⢰⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣟⣿⣿⣿⣏⣾⢿⣿⣛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⣿⣿⣯⡾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠟⠛⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣕⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⢀⣤⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⢼⠋⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠿⠿⠿⣷⣦⣄⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⢀⡀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡋⠀⠀⠀⣴⣿⠿⠿⣿⣦⣤⣤⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⢸⣿⡇⠀⠀⠈⠛⠛⠋⠉⠛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠟⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⢀⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⠿⣿⣦⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⣿⣿⠿⠿⠿⠛⠛⠉⠀⠀⠈⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣏⣉⣛⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⢠⡟⢻⣆⢹⣿⢿⣤⣀⣽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣾⠃⠀⢻⣾⡇⠀⢹⡿⣿⣀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢰⡟⠀⠀⠀⠹⣧⡀⣸⡇⠀⢻⣿⡟⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠈⠻⣿⣇⠀⣸⡏⠛⢷⣌⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣶⣶⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣀⣴⠶⠿⠛⠲⠶⣾⣿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⣴⠟⢁⣀⠀⠀⢤⣤⣿⣋⠈⠉⠛⠷⣦⠀⠀⠀⠀⠀⠀⢿⡄
⢸⡏⣰⡟⢻⡇⠀⠀⠈⠉⠉⠉⠁⠀⠀⠹⣧⠀⠀⠀⣀⣠⣼⣷⣤⣴⡶⠶⠶⢶⣤⡀
⣿⠀⣿⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣠⡾⠛⠋⠉⣙⣿⣀⣠⡄⠀⠀⠈⠻⣦
⣿⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⣀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⢹⣇
⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⣾⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣿⠈⣷⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⢻⡆⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠈⠙⠻⠶⣶⣤⣶⠶⠟⠋⠁⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢶⣤⣤⣤⡶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠞⠛⠛⠛⠛⠛⠛⠳⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⣼⠏⠀⠀⠀⠀⠀⣰⠿⠋⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠙⠿⣆⠀⠀⠀⠀⠀⠙⣧
⠀⣸⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠛⠛⠛⠷⢦⣄⠈⠀⠀⠀⠀⠀⠀⠹⣇
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣀⣀⡀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⢻
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⠈⣧⠀⠀⠀⠀⠀⠀⠸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⠛⠿⣷⣄⠀⠀⠀⠀⠀⣯⠀⠀⢿⣶⣾⣿⣿⣿⣿⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠈⠻⣿⣿⣿⠟⠃⠀⣰⠏
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⡀⠀⠀⠀⢀⣠⡾⠋
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⣿⣛⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣼⠋⠉⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉⠛⣿⡆⠀⠐⣿⠀⠀⠀⠀⠛⠛⢷⣄⠀⠀⠀⠀⠀⣰⠏
⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⢸⣧⣀⣄⣠⣤⣤⡴⠟⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⠇⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⣶⣶⣦⣤⣤⣴⣶⣶⠶⠛⠛⠉⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠚⠓⠲⠲⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⡀⠀⠀⠀⠈⠱⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⠀⠀⠀⠄⠀⢂⡀⠀⠀⠀⠀⠀⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⡠⠊⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢠⠊⠀⠀⠸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠤⣤⣤⠀⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⡀⠀⠀⢢⣀⣀⠞⠀⠲⠦⠶⠦⣄⠀⠀⠀⠀⠀⠐⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⡴⠦⣄
⠀⠀⠀⢳⠀⠀⠘⣿⣿⠀⢀⢀⠀⠀⠀⢘⡄⠀⠀⠀⠀⠀⠈⠓⠘⢃⠀⠀⠀⡆⢀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣧
⠀⠀⠀⠀⠻⣶⣶⣿⡿⢦⣿⣬⣆⠀⣀⡼⠁⠀⢘⠣⣤⡀⢀⠀⠀⣸⡆⠀⠀⣿⡛⠀⠘⠿⠂⠈⡀⠀⠐⣆⠠⡜⢦⡀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠛⠉⠀⠀⠀⠈⠳⣦⣀⡙⢒⣴⠟⢁⡤⠖⠛⠳⣸⡟⢶⡖⠐⠁⠀⠀⠈⠻⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⣿⡀⠀⠀⢠⣽⡿⠈⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⢹⣷⡶⢖⣻⣯⠃⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⡿⠷⠖⠉
⠀⠀⠀⠀⠀⠀⢀⡐⠂⠀⠀⠀⢀⡄⠀⣀⡭⢤⠔⠒⠠⠴⣄⡈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣤⣤⣤⣤⣤⡤⠴
⠀⠀⠀⠀⠀⠀⣼⣷⡀⠀⠀⠀⠈⠷⠈⠀⠀⠀⠉⠐⠠⠴⠞⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠿⣿⠿⠿⠿⠿⠧
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⠄⢤⠤⠄⡄⠀⠠⡤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡶⠀⠀⠀⠀⠂⠑⠀⠀⠀⠀⠀⣎⡀⣈⡇⠀⠀⠠⠤⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⣤⣦⠀⠀⣀⡀⠀⣀⡀
⠀⠀⣀⣘⣁⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻⡵⡾⠃⠀⠀⠀⠀⠈⠩⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⠟⠃⠀⠀⠙⠁⠀⠋⠁

⠀⠀⢦⡀⠀⠀⠀⠀⠀⣶⢤⣐⡆⠀⠀⠀⠀⠀⡀⡄⠀⠀⢠⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⣷⣤⣼⡇⠀⠀⠀⠀⢠⡷⢿⠀⠀⢸⢸⣿⡆⠀⠀⠀⠀⢄⡀⠸⠂⠀⠀⠀⣁⠀⡀⠀⠀⠀⠀⣆⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠐⠋⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠉⢁⡠⠀⠀⠀⡰⠂⠒⡄⠀⠀⠠⣶⣶⡤
⠀⠀⠠⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠘⢃⠒⢂⠙


⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠸⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡆⠀⠀⠀⠀⠀⠇⠀⠀⠐⢿⣿⣿⠇
⠀⠀⠉⠉