Modest Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⢀⢀⣀⣍⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡛⢁⣀⠠⣾⠁⠀⠀⣀⠤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣾⡓⠪⣼⠛⣯⠇⠀⠎⠀⡀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⣿⣿⣷⣾⣿⣿⠁⠘⠓⠤⢀⣀⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢹⠁⢇⠻⢿⣿⣿⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠓⠒⠸⡀⠒⠂⡀⠉⣩⠧⠏⠑⢄⠀⠀⠀⠀⠀⠀⠀⢠⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠚⠉⠓⠔⠋⢹⡞⠉⠑⠛⠉⠓⠱⡄⠀⠀⠀⠀⠀⡸⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢋⠉⠉⠀⡠⠤⣠⠄⠀⠔⠦⠔⠈⠉⠉⠙⣆⠀⠀⢰⠋⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢀⢸⠉⠉⠉⠀⢸⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⡄⠉⡹⢋⣷⠀⢘⠄⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⣞⠳⠢⠤⣠⠟⠉⠛⣁⡀⢀⠋⠉⢉⡥⣈⢃⠞⡴⠃⠀⢵⠊⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠒⡦⢾⠀⡀⠈⠀⠈⠉⠀⣀⠀⠀⠀⡛⢴⠁⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢯⠉⠙⠁⠀⠀⠋⠉⠙⠁⠀⡇⠀⠈⠒⢤⣀⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠳⡀⠲⠖⠉⠃⠀⠉⠓⠚⡇⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢱⡤⡄⣰⣧⠠⠴⠄⠤⢇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣶⣄⣀⠤⠒⠀⠀⠈⠁⠀⠉⠀⠀⠐⠂⢤⣀⣴⣾⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣄⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢴⣶⣶⡾⠛⢻⣶⡶⠆⠀⠀⠀⠀⠀⢸⣿⠟⠻⣿⣿⣷⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢻⣿⣶⣾⣏⠀⠀⠐⠿⣯⠟⠀⢸⣿⣧⣴⣿⣿⣿⡇⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣾⠟⠉⠙⠿⡆⠠⣀⣠⢧⣀⡠⠀⢻⣿⣿⣿⣿⣿⠃⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠠⠙⠻⠟⠋⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⣖⠠⠤⢀⣀⣀⣀⣀⣀⠠⠤⠄⢀⣦⡁⠀⠐⡄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣶⣤⣀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⡖⠊⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⣿⣿⣿⣿⣿⣿⣷⡀⣴⣿⣿⣿⣿⣿⣿⠿⠇⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠈⡆⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⢰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢖⠀⠘⣦⡀⠀⠈⠻⢿⡿⠟⢿⣿⠟⠋⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⠉⠑⢻⣿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⣿⣿⣿⣿⣿⣏⠀⢸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠀⢾⣿⣿⠿⠁



⡿⠉⢻⡟⠿⠿⠿⠻⢿⠻⠿⠿⠿⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⡿⢿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠒⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⢀⡠⠔⠒⠈⠉⠉⠉⠉⠉⠓⠢⣄⡀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⡴⠁⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢸⠁⡞⡽⠁⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠈⡘⠰⡇⠀⠀⡇⠀⠘⢦⡀⠀⠈⠢⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠋⠀⢀⡗⠀⠤⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡇⠀⢸⠧⠀⠀⠀⠙⢦⣀⠀⠈⢳⣦⣄⣀⠀⠀⠀⣀⠤⠂⠘⠦⠀⢦⠀⠀⠀⠙⡆⠀⠀⠀⠀⢻⡀
⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠟⠀⢀⡀⠀⠀⠀⠉⠛⠶⣤⣽⣦⣌⣉⠉⠉⡀⠀⢠⡆⠀⢀⡸⠃⠀⠀⠀⡇⠀⠀⠀⠀⠘⣇
⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠁⠘⠋⠀⠀⠀⠀⠀⠈⢹⢟⠉⠻⡁⠀⠀⠀⠑⠠⠀⠠⡀⠀⢀⠜⠁⠀⠀⠀⠀⠀⢿
⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢨⠀⣯⣾⠁⠀⠀⠐⢆⣀⣀⠔⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠴⠁⠀⠜⠁⢠⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⡞⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠘⢷⣤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡟⠀⠀⠀⠀⠀⠸⡝⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠊⢤⣀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⣠⠞⢁⠃⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠻⠷⠶⠶⠚⢋⠢⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⢠⣠⠔⡃⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠀⠀⢷⣤⡤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠦⢤⣤⣤⣀⣀⣀⣀⣠⣤⡤⠴⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠠⡈⠁⣤⣀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣩⣯⣄⡀⠀⠀⢳⣶⢻⡷⠂⠀⠀⠀⢸⣿⢸⠏⠀⠀⠀⠀⡜⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠽⠋⠀⠀⠀⠘⠛⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⡘⢡⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⡤⢤⣤⢤⣶⠒⠲⣶⣖⡶⡟⠛⠻⢿⣽⡟⠏⢻⣷⣾⣿⠉⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⢉⣿⣏⡅⠀⣽⣿⢭⠀⠠⢿⣿⠼⠀⠀⢸⣿⡇⠇⠀⠀⢸⣿⡇⡇⢸⣿⣿⢽⣤⣧⣀⣀⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠳⠶⣼⠠⠟⠧⠂⠐⠞⠛⠚⠀⠐⢚⣛⣊⣀⠘⠋⠉⠉⠁⠀⠈⠉⠉⠉⠀⢸⢿⣛⣸⡧⠀⠇⠀⠾⠀⠤
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠼⢀⣀⣀⡀⠀⣠⣠⣄⢈⢉⣹⣏⡁⠏⢀⣢⣠⡄⠀⠀⠀⣴⣠⡄⡀⢸⢦⣽⣧⣀⡀⢀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⢈⣿⣏⡇⠀⣸⣿⣸⠀⠈⣿⣿⡄⠀⠀⢸⣿⣇⠀⠀⢀⣸⣿⡁⠃⢸⢸⣱⣿⣿⡃⢘⡟⠀⣿⠂
⠀⠀⠀⠀⠀⠀⠈⣙⡟⡃⢠⣿⣧⠇⠀⣸⣿⣴⠀⢘⡏⣉⡀⠀⠀⢸⣿⡅⠀⠀⠀⢹⣿⠁⠀⠹⢸⢻⣿⣿⠄⢸⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⢿⣾⣯⣓⠇⠤⠽⠴⠊⢓⣭⡷⠟⣾⣿⡭⣯⣢⣴⡟⠛⡍⠉⠀⢰⣄⣸⣿⠉⠁⠈⠉⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠉⠀⠙⠋⠀⠀⠀⠔⠙⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢲⠖⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣼⣾⣦⣠⡏⡅
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⢀⠀⠀⠀⢀⠉⠙⠻⢯⡾⠇
⠀⠀⠀⠀⠀⠀⢈⠠⡈⣶⠀⠧⠀⠟⠉⣡⠺⢀⡄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⣘⣫⢦⠔⡕⠤⣒⣄⢄⠀⠛⢑⣖⣀⢂
⠀⠀⠀⠀⠀⠀⢰⠏⠉⡀⣤⣤⣤⡅⢠⢃⠂⣬⢂⡱⣇⡸⠂
⠀⠀⠀⠀⠀⠀⠀⣤⡿⠋⠉⠁⣈⣁⠓⠪⣵⡄⠈⠞⣌
⠀⠀⠀⠀⠀⠀⢠⠏⣠⠖⢋⡼⢟⡍⠉⢴⣀⠹⣦⣄⠛
⠀⠀⠀⠀⠀⠀⠌⢰⣧⡞⠋⠀⠀⢱⣮⣒⠝⣆⠉⠈⣦
⠀⠀⠀⠀⠀⠀⠀⣾⡇⢭⠆⠀⠈⠀⢤⡍⠫⢿⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠉⠀⠀⠀⠉⠁⠀⠀⣿⠇⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⡤⢄⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⣄⣿⣇⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⡰⠄⠈⠀⠀⠀⠀⠀⠀⠁⠒⢦⣀⣴⠶⣖⠚⠉⣼⢧⡏⣾⠑⠄⠤⠐⢈⣉⠁
⠀⠀⠀⠀⠀⢅⠉⠙⢽⡀⠒⠓⠃⠀⠀⠀⠿⣽⠟⠁⠀⠀⠐⠀⠀⠀⠀⠀⡀⣤⠈⣵⠰⢗⡄⠋⢰⡏⡾⢰⣟⡈⠒⠂⠀⠤
⠀⠀⠀⠀⡠⠜⣈⠄⠸⠥⠛⠄⠸⠃⢀⣼⣤⡀⠤⢦⡤⢄⠀⠀⠀⠀⠀⠀⣀⡐⣫⢡⠟⡁⠘⠁⣾⢸⡇⡾⠤⡈⠀⡁⠄⠤
⠀⠀⠀⢨⠀⠀⠀⠰⡇⣸⢳⣄⣀⠤⢎⡳⢷⠀⠀⠀⠈⡸⠁⠀⠀⠀⠀⣀⢡⡄⠊⣶⠆⡉⡣⠐⠉⠉⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠃⠁⠈⠀⣵⢧⣿⣋⣩⢿⣿⠏⠙⠀⢀⢊⣜⣤⡀⠀⠈⠁⠸⠧⠀⠠⠛⠒⠉⠁
⠀⠀⠀⠀⡆⠈⢤⣞⣻⣾⡇⠥⡟⣾⣿⠀⠀⡠⠒⢈⠉⠀⠁
⠀⠀⠀⠀⠈⠁⠀⠉⠛⠿⢿⢟⣛⣋⡁⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⠤⣤⣴⣶⣶⠗⣸⣿⣥⣄⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⠟⠛⠛⠛⠛⠉⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡇⢀⡀⠀⠀⠀⠀⣀⠀⠹⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣿⣬⣙⣀⣄⠀⠘⠋⠀⠀⠀⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣶⣶⣤⣄⣀⣼⠏
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⣿⡘⣿⣿⣿⣿⢧⣿⣿⣿⣿⡿⣱⣿⣿⣧⣀⡀
⠀⠀⠀⢰⣿⣿⣿⣧⣙⠿⣿⣿⣿⣿⣷⡙⢿⣿⣿⣧⢿⣿⣿⡟⣼⣿⣿⣿⢟⣵⣿⡟⠁⠈⡉⢛⡷⣤⡀
⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣮⣛⣿⣿⣿⣿⣮⠻⣿⣿⣾⣿⣿⡇⣿⣿⣿⢻⣾⣿⣿⣤⠒⠀⠀⠨⣶⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣮⡙⢿⣿⣷⣽⣿⣿⣿⣿⢷⣿⣿⣣⣿⡟⠁⠘⠻⣷⣎⠀⢀⣤⠄⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣮⡻⢿⣿⣿⠿⠿⣿⣿⣽⣿⠏⠀⢠⠀⢠⣈⣿⣷⡾⠃⠀⣄⣠⠶⠾⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⣿⣿⣿⣿⡇⠉⠀⠀⠈⠛⠷⣀⠀⠀⠁⠈⠁⠀⣿⢿⣄⣴⣿⡇⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠿⠻⣿⣿⡉⠀⠀⠀⠀⠀⠙⠻⣿⣦⣤⣀⣀⣧⣀⣿⣿⣿⣀⢀⣠⣶⡆⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢀⣴⠟⠛⠻⣷⣶⣶⣒⣦⣤⣤⣽⣿⡉⠛⣿⡿⠟⣿⣿⣿⡟⠋⣁⡀⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣤⠾⠿⠖⠀⢀⣼⣿⣿⣿⣿⠿⠟⠿⠟⢷⡀⠉⠀⣴⠋⠀⠋⣤⠞⣭⠟⠉⠁⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠰⠋⢀⣴⠖⠀⠀⣾⣿⠿⠋⣡⣤⣶⣶⣾⣷⠈⢿⡄⣼⡇⠀⠀⣾⡷⠿⠇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠳⢶⡾⠋⠀⠀⠀⣼⣿⣷⣾⣿⣦⣶⣦⣤⣤⣀⣀⠈⢻⣿⣆⠀⢘⣧⣤⠀⠀⢀⣀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⢀⡾⠀⠀⢠⡄⢀⡿⢹⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣷⡀⢻⣏⣻⠟⠋⣡⡴⠛⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⡷⠾⠻⣞⢻⣿⠁⢸⣧⣤⣴⣶⣶⣶⣦⣤⡤⠉⠙⢣⡀⢻⡟⣷⡾⠉⣀⣤⠄⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣥⡶⠉⠻⣿⡟⠀⣸⣿⠿⠛⠛⠉⣉⣁⣠⣤⣤⣤⣼⣧⠈⢿⡿⠀⡾⠉⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⢰⣿⠁⠀⣿⠁⠀⠶⠿⠛⠛⠟⠟⠛⣫⡿⠟⢿⣧⠈⣿⡾⠳⡶⠀⢈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⣾⡇⠀⢰⣿⠀⢀⣠⠶⠛⠋⢀⣤⠘⢁⠠⠖⠛⣻⣧⠘⣷⡖⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠀⢸⣇⣴⠋⢀⠴⠶⢀⡼⢃⠔⠁⠀⡔⠋⠈⢻⣦⣿⣷⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣠⡬⢃⣤⠞⢳⣎⣀⣀⣤⣄⠀⠀⠀⠙⠿⢟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⠿⠖⠋⡁⠀⢀⣨⣭⠛⠉⠁⠀⠀⢀⡀⠀⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣠⠛⠉⣰⠟⠁⠀⠀⣠⣴⠶⠀⠈⠿⣿⠹⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣼⣷⡾⣿⡏⠀⢀⣴⣿⠿⠟⠁⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣀⣀⣉⣥⣾⣿⡇⢰⣿⡋⠁⠀⠀⠀⠐⢀⣾⠛⠂⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠛⠉⢉⣀⣿⣧⣤⣿⣷⣾⣿⡆⠀⠠⣿⡇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠠⣶⠿⣡⡼⠛⠀⠀⢉⣿⠏⠁⠰⣷⣤⣍⠉⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣇⡀⠀⠖⣀⣀⣀⡀⢀⣈⠉⣤⡄⢀⣤⡌⠁⠀⠀⣀⡀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⣴⢾⡿⠟⢿⡟⢻⣿⣷⣿⠿⠟⠋⠀⠀⠶⠛⠋⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣼⢏⡏⠀⣰⠋⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣀⡤⠚⠁⢀⡴⠃⣀⣠⡤⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣭⣉⣤⣤⠶⠋⠑⠟⠉⠁⢀⣀⠀⠀⠀⠾⠋⢀⣠⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠉⠀⠀⠀⠀⠀⢀⡴⠞⠛⠻⢷⣤⣤⠶⠞⠉⠁⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠉⢿⡇⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠘⠛⠛⠛⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣠⡴⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⡴⠟⢉⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠰⠶⠉⠀⠀⠀⠀⠀⣠⣤⣴⠀⠀⠀⢀⡾⠉⢠⠶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣤⣤⡤⠀⠀⠀⠀⢠⡾⠋⠉⠀⠀⠀⠀⠸⣷⣤⠴⠞⣉⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠉⣻⣿⡿⠿⠶⠿⠷⠿⢿⣷⣶⣶⣶⣶⣿⣿⡿⠻⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠁⠀⠀⠀⡀⠠⠤⠬⣍⣀⣤⡀⠱
⠀⠀⠀⠀⠀⠀⡠⠂⢠⠞⠁⠀⠀⠀⣠⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⢀⠈⠙⡦⣅
⠀⠀⠀⠀⢀⠜⠀⠀⠁⠀⠀⠀⡠⠒⠁⡀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠋⠀⢰⡇⠈⠂
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠐⠁⠀⠘⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠂⠀⡶⠀⠀⠀⠈⢆
⠀⠀⠀⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡜⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡄⠀⠠⠀⠀⠎⠀⠐⠃⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣠⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣄⠀⠀⢀⡴⢃⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣠⠆⠀⠀⠁⠀⠀⢠⡴⠋⠀⠉⠈⠩⠛⠃
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣦⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡄⢀
⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⠀⠀⠀⠀⢾⣭⣿⣿⠆⠀⠀⠠⠂⠀⠀⠀⠀⢸⠇⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⡸⠀⠠⠀⠤⠠⠄⠀⠀⠀⠀⠑⠤⢀⡀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⠤⠤⠤⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆



⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣠⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⡏
⠀⠀⠀⠰⠂⠀⠀⢀⠀⠛⠀⣠⣤⣾⡿⣷⣶⣶⠆⢀⣀⣀⣀⣀⣀⣀⣠⣄⠀⢀⡀
⠀⠀⠀⢀⣴⠶⠿⠛⠛⣆⠀⣹⣿⣿⡿⠛⣉⣴⣾⣿⣿⣿⣿⣿⢟⣿⣿⠿⠟
⠀⠀⠀⢸⡁⠀⢀⣈⣴⣾⣿⣿⣿⣿⣷⣿⣿⣿⣵⣾⣿⣿⣯⡿⠟⠁⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀⣄⣀⡀
⠀⠀⠀⠈⢯⢹⣿⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⠿⣟⣿⡿⣿⣯⣽⣿⣿⣿⣽⣿⣿⣶⣤⣤⣀⡀
⣤⣶⣴⣶⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣾⣿⣿⣦⣤⡀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣧⡀
⠀⢻⣿⣿⣻⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⣶⣿⣯⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡆
⠀⠀⠈⠙⠿⠻⢿⡏⠙⣧⡀⠀⠄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⣿⣷⣿⣟⣿⣾⣟⣛⣿⣿⣿⣿⣿⣟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⢀⡸⣯⡉⠉⠙⠻⠿⣿⣶⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠂⠉⠁⠠⠙⠶⣄⢠⣤⣀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣸⣷⣀⣠⣼⣿⡿⠛⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣏⣿⣿⣭⣿⣿⡿⣿⣿⣷⣿⣿⣿⣟⣿⣿⣿⣿⣶⣄⣠⣤⣤⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢸⡟⣾⢻⡟⣿⢿⡹⣆⡀⠀⢀⣠⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡏⠉⠻⣿⣿⣿⣿⣿⡿⠟⠛⠛⣿⣿⣿⣿⣭⣿⡯⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣴⢟⣸⠇⣿⢊⡟⠼⠓⠀⠛⢿⣇⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠼⠧⠟⠀⠀⣀⡀⠀⠘⠟⠉⠀⠀⠀⣼⣿⣿⣟⣻⣿⣿⣟⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠿⠆⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⠿⢿⣟⣽⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣯⣿⣿⡀⠀⠀⠀⠀⠀⠈⠉⠻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⡀⠀⠀⢀⡤⠄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠛⠃⠀⠀⠈⠛⠋⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣦⠀⣀⣀⡀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⡌⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡝⢿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣼⣿⣋⣥⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣾⠓⠀⠀⣼⢹⣿⣿⣿⣿⣿⡆⢿⣿⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠁⠀⢠⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⠲⠶⠟⠁⣸⣿⣿⣿⣿⡿⢃⣿⣿⣃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⡾⠟⠃⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣛⣵⢫⣾⢋⣴⡿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣄⡻⢿⡼⣿⣾⡟⠀⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠧⠀⢸⣿⣿⠿⠿⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣿⣾⣿⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣠⣾⡿⣥⣶⣶⣤⣴⣾⡿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⡤⠔⣫⢿⠟⢀⣀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠻⠤⠄⢰⡿⠓⠾⠻⣿⣟⢿⣿⠃⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⠂⠀⠙⣾⠰⣿⣍⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣾⣯⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣼⣥⣤⣬⣭⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣭⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⣾⣿⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⢀⡴⠋⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠉⠳⣄⡀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⣧⢀⡴⠋⠀⣯⠀⠀⠀⣠⠞⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⠙⢦⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⣿⣀⡴⠟⠁⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠙⠳⣄⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡞⠁⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⣤⡤⠴⠶⠶⠶⠶⠶⢤⣄⡀⠀⠀⠀⠙⠛⠛⠉⠉⠉⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡈⣧⠀⠀⠀⠀⠀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣍⠉⠉⠛⠃⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⣴⣋⣀
⣀⣤⣤⣤⠤⠤⠤⠤⠤⣤⣤⣤⣄⣹⡆⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⠉⠉⠉⠉⠉⠉⠛⠛⠒⠲⠶⠤⠤⢤⣄
⠉⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠐⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⣯⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡁⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣀⣤⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⢻⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣼⠋⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⠀⠀⠻⣆⠀⠀⠀⠙⠢⢄⣀⠀⡀⡀⣀⣀⡤⠞⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠸⡟⠲⠦⣤⣤⣉⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⢀⣠⣴⡄⠀⠀⠉⠛⠲⠦⣤⣤⣤⠴⠶⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⡴⠞⠋⠁⣾⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣤⠴⠚⠋⠁⠀⠀⠀⢰⣏⣠⠾⠋⢹⡀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⢠⡇⠀⠙⢦⣄⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⢸⡇⠀⠀⠀⢰⡏⠀⠙⣦⡀⠀⢸⡇⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣾⠀⠀⠀⠈⢳⡄⣾⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢸⠇⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣀⡅⢰⠐⡎⠠⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢫⠉⠀⠸⣿⡄⢻⡤⠆⣸⣿⠗⣠⠙⣁⠋⣸⡻⠀⠀⢠⢃⡧⠀⠀⠀⠀⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠇⠀⠐⠘⠘⢠⣉⠺⣿⠀⣧⢆⠔⢁⣔⡟⠁⢀⠀⠟⠜⠀⠀⠀⠀⢠⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠱⢀⡀⠀⠄⡇⢉⠁⣸⠀⣿⡢⢶⡿⢰⢀⣤⠀⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡃⢀⡀⠉⣸⠃⢿⠀⡿⣈⣁⡀⠁⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⣤⠤⠤⠀⠄⠄⡤⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠛⢸⣷⣶⣾⡤⠓⢀⡀⢀⠀⠀⠀⠀⢀⣰⢶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣿⠀⢈⠿⢫⠟⠁⢰⣟⢷⡇⠀⠀⠀⠈⣏⠁⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⣄⠀⣼⠀⠀⠀⠉⠁⣀⠀⠀⠀⣄⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠋⠀⠀⠀⢈⣿⠄⠀⠀⠀⠀⠀⢇⣼⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⡄⠀⠀⠄⠋⠀⠀⠄⠂⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⢁⣊⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠐⠛⣌⡵⠻⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠟⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠰⠃⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢍⢀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠈⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢦⡀⠀⠈⢿⣿⡿⣧⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⡉⠒⠤⠜⣿⣶⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⣤⡀⠀⠀⠰⠚⠉⠁⢀⣀⡀⠀⠀⠀⠈⠀⠀⠀⢹⣿⠟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣤⣽⡆⠀⠀⠐⠶⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡖⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⠟⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⢿⣿⠛⢳⣶⣾⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢡⠸⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣼⠠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠁⠹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀




⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠈⢣
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠆⠤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⠁⠀⠄⠀⠀⠄⠀⡀
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠠⢄⡀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⣶⡀⡀
⠀⠀⠀⠀⠀⠐⠀⡜⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠐⠂⠄⠋⠓⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠢⢄⡀⠈⠒⠀⡠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠒⠄⠀⠀⠀⠀⠰⠈⠉⢳⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠈⢆⠀⠀⠀⡰⠁⠀⢠⠀⠀⠠⠀⠀⠀⢀⡇⠀⠀⠀⢄⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡽⠁⠀⠀⠀⠈⠓⠀⢸⠃⠀⢀⢿⡧⠄⠂⠀⠀⢀⡞⠀⠀⠀⠀⡀⠑⢦⡙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠞⢀⠎⢀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢎⠂⠬⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠢⡀⠙⠢⣄⠙⠲⢤⣀⡀
⠀⠀⠀⠀⠀⢀⣠⠔⢋⠔⠁⡠⠋⢠⠎⢀⠆⢀⡀⠔⠉⢧⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡀⠘⢦⡀⠈⠲⢄⡀⠉⠒⠤⣄⣉⡉⠒⠒⡒⠒⠁
⠀⠀⠄⠔⠚⡉⠤⠒⢁⡠⠚⢀⡴⠃⠔⠃⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠙⠳⠦⣤⡤⠤⠈⠢⢄⡉⠢⣄⠀⠉⠓⠦⢤⣀⣀⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠐⠒⠉⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡀⠀⠀⢀⡀⡉⠓⢦⣀⠀⠀⠀⠀⠉⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠐⠈⠁⠀⠀⢀⣶⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⡆⢷⢿⣷⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠊⠁⠀⠀⢀⡇⣸⢸⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠐⠀⠀⠀⠀⠀⢀⡾⢡⡟⣼⢻⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣰⠟⣰⢏⡿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣼⠋⢰⡏⣼⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⠃⢠⡟⢰⡇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⡏⠀⣼⠁⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢻⡇⠀⣿⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⣇⠀⣿⡀⣿⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠹⡄⠸⣇⠸⣇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠹⣆⠙⣆⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⠳⣌⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣮⠤⠤⠖⠒⠒⠒⠂⠤⢤⣀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠱⡀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡋⣡⡽⣷⣄⠀⠀⠀⢀⣴⣶⣋⡉⠁⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡁⠈⠓⠛⠀⠑⠀⠀⠁⠈⠯⠼⠋⠀⠀⠂⣿⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⡟⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠈⣟⠀⠹⣶⣒⡒⣶⠖⠀⠀⡔⠁⠀⢸⠁⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠋⠁⢸⠀⢋⠢⡀⠙⠛⠓⠁⠀⣠⠌⠀⢠⠀⡌⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⡆⠘⣆⠈⠂⠤⢤⡴⠞⠁⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢻⡉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⢳⠀⠈⠐⠤⠬⠤⠔⠋⠀⢠⠏⠀⠀⠀⡌⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢡⠀⠈⠣⡀⠀⠀⠀⠀⠀⢀⠴⠃⠄⠀⠀⠀⠃⠀⠀⠀⠀⠀⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⡆⠀⠀⠈⠂⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⡄⠀⠀⠤⠤⡤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡈⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠀⠀⠰⢤⠤⠤⠤⠄⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⢴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡟⠙⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⠖⠑⠀⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠀⠉⠀⠟⠀⠃⠀⠀⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠿⠋⣤⠄⡆⠀⠀⢀⠀⠓⠠⠀⠛⢱⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣉⠀⣳⠂⠃⠀⣄⠐⠁⣀⠙⢦⢻⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡆⠻⠟⡀⠛⠀⠀⠀⠉⠀⠀⢉⡶⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠴⢾⡷⠃⠀⡀⡀⠀⠃⣴⠐⠀⠁⠀⠛⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡷⠁⠀⡤⠀⢠⡀⠁⠈⠀⠄⠁⠠⡦⣾⢧⡆⡘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡴⣧⣄⢠⣶⠄⠀⣿⢀⠀⠀⢀⠀⢤⡄⠀⠀⢾⠇⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⡈⠉⡌⠁⠀⠀⢀⠈⢞⠗⢁⣀⠀⡀⢀⡄⠀⠀⠀⠀⢆⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠛⠋⠁⠀⠀⠆⠠⠶⡜⢀⡀⢰⠎⠛⠂⠉⠀⡀⠀⢀⠈⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⢸⡆⠁⠀⠀⡠⠞⠒⠘⠳⠶⠾⣀⡀⠘⠈⠀⠠⡌⠓⠢⡀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⠀⠀⠂⢀⠊⣠⣾⠏⠶⢸⣦⠐⣮⣀⠈⣾⠆⡈⠠⠴⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠂⠠⠄⠲⣿⠰⠈⣥⣰⣀⡌⠁⠖⠉⠁⠀⠀⠻⠃⡐⢃⡄⡀⠂⡀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠡⣶⠂⢫⡶⠀⠙⣆⢀⠀⠟⡡⣴⡶⠁⣼⠇⣀⡻⠟⠱⠿⣯⣂⡐⠓⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⠆⠴⢫⡍⡑⠂⢈⡉⢈⡑⢤⣎⠴⠚⠓⣿⡐⠓⠻⠤⢴⠐⠃⢬⠍⠁⡳⠂⣠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣌⠁⠀⠀⠀⢰⣄⠀⠀⠘⣃⡘⠿⠇⠉⠀⠙⡃⣠⣦⠸⠇⠀⣦⡈⢳⠂⢐⠋⢢⣄⠈⣠⣭⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠀⠘⣷⠀⠈⡉⠁⢀⣘⣿⠇⠐⠚⡛⠃⠛⠂⠘⠤⠄⠀⠆⠛⣵⡎⢡⡾⢠⡍⣀⡀⠹⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡦⠀⠀⠀⣠⡌⠈⠡⠦⠀⣩⣄⠙⣠⣤⠀⠠⣦⣄⢢⣛⡤⠀⢀⣈⠀⠀⠀⢀⠈⠟⠣⠤⠄⠐⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠘⠇⣛⠋⠈⣿⠀⠀⠈⠉⠁⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢿⡛⠃⢐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠄⠈⣡⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⠞⠱⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠲⠀⠀⠀⠂⠂⠂⠂⠀⠀⠂⠀⠂⠐⠐⠐⠀⠀⠀⠀⠀⠀⠈⠀⠁⠃⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⣤⣥⣧⣐⠛⣻⢄⣈⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⡩⣋⠄⡉⢨⣥⣤⣥⣿⠋⢤⢲⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠚⡗⠋⣠⣾⣿⣿⣿⣿⣿⣶⡪⣑⢿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢸⡌⢡⣾⡿⠿⠛⠛⠛⠛⠻⢿⣷⣤⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣬⣽⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢱⡏⠀⠐⠒⠲⠤⠀⠀⠠⠴⠒⠒⠀⠘⣟⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣾⡇⠈⠉⠹⠑⠀⠀⠀⠀⠀⠹⠉⠋⠀⡆⣁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢂⢛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠧⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠠⠜⡡⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡁⢖⡑⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣶⠀⠸⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡅⠉⣘⣭⡟⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡕⣨⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣉⡴⠩⡟⣇⠀⢀⡐⢰⠄⠀⠀⠀⠀⢠⠀⣱⠋⢆⡙⠋⢤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⣧⣘⣷⡿⣣⠆⠉⣘⠧⠀⠓⠐⣣⡁⠀⠐⡔⢸⠏⠐⠈⠊⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⠳⣜⡧⣧⠖⢀⡄⠀⠙⢉⠉⠉⢁⠐⢁⢀⣶⣌⠳⠷⣤⠰
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⠐⢀⠀⠘⢷⡜⢾⠋⠁⠀⠠⡗⢐⡑⠈⠧⢹⢌⢈⡇⡈⠐⢠⠀⣉⠰⣄
⠀⠀⠀⠀⡀⠄⣘⠻⠞⠓⢶⡉⣈⠀⢸⠏⢘⣳⢶⠀⢀⡲⣿⡑⢿⡶⢊⡖⠛⠁⠀⠒⠜⣼⠉⣇⣼⡢⠦⢤⡀
⠀⢀⢎⡡⠴⠒⢎⣤⠡⣃⡠⠇⢘⡛⠃⠀⠀⠛⠆⢹⠸⢷⡞⠗⢿⢲⡿⡱⣃⡁⠀⢄⠀⠀⢀⣭⡷⢡⣶⣴⡩⠦
⠀⠈⢛⣥⣼⣶⣶⣶⣶⣀⠰⢶⢯⠹⠧⡆⠀⠠⠀⠀⠀⠄⢄⠖⠘⠀⠐⢦⠵⠁⠂⣁⠰⡄⠀⠉⠀⠀⠳⣀⠞⠀⣆
⠘⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⢈⠤⢘⡗⠙⠄⠠⠂⠀⠘⡄⠀⢈⢀⠀⠘⢃⣴⠦⡶⢶⣌⠄⠀⡇⠋⢠⣰⣾⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠲⡚⠁⠀⠂⠄⠀⠀⠐⣀⠀⠀⠁⠀⡀⢠⣭⠷⣅⢻⡏⡙⠗⠀⣰⣿⣿⣿⣿
⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠂⠃⠉⠱⠀⠈⠈⠈⠥⠌⠁⠈⠈⠀⠀⠒⠀⠙⠚⠛⠋⠐⠀⠀⠂⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⠀⣿⣿⣇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣴⠂⠀⠠⠈⠀⣼⣿⡟⢋⣁⡈⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠙⣏⠀⠀⠆⠀⠀⢈⣭⡖⠚⠿⠃⢨⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣄⠀⠀⢸⣿⠃⢸⡿⠀⠀⠃⠀⠀⠙⢿⡿⢣⣶⣾⡝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⠉⠙⣆⠀⠈⢿⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡂⠜⠀⠀⠀⠀⠘⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢺⣿⣿⣿⣠⣶⣦⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⢄⣁⠈⠹⢿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡧⠀⠾⣿⡗⠀⣻⣦⣄⠀⠀⠀⠀⡍⠀⠀⠀⠋⠙⢋⣈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⡔⢀⣀⣤⣿⣿⡟⠀⠀⠀⢠⠉⠀⠀⠚⠀⠲⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢿⣿⣿⡷⠀⠉⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡜⠀⢠⠆⠀⠀⣼⣷⣿⣷⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡠⠃⣴⣶⣤⣹⠿⠿⢻⡥⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠄⠀⢾⣿⣿⡿⠈⢣⣄⣌⠀⠙⣻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠐⠀⠀⢉⣩⡖⠒⠺⠿⣷⠀⢉⣽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠰⣿⣿⣿⣆⣴⢀⣀⣰⢼⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⡀⠂⠘⠿⠟⠉⢼⣿⣿⣿⡇⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠔⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣶⣄⠀⡘⡏⠀⠀⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣄⣀⣈⡀⠙⠛⢠⡿⠁⠀⠀⢀⠖⠉⠛⠛⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠿⠷⠒⠐⢮⠃⡄⠀⠀⠉⠀⠐⢶⣶⡄⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡥⠀⠀⠀⠀⠀⠀⠈⠻⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⠀⠙⠳⠤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⣷⣤⡀
⠀⠀⠀⠀⠈⣿⠙⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆
⠀⠀⠀⠀⠀⣷⣬⣓⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⣿
⠀⠀⠀⠀⠀⠘⢦⠀⠈⠁⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⢰⡟
⠀⠀⠀⠀⠰⣦⠔⠛⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠊⣤⠄⠈⠳⡄⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠂⠈⠉⠁⠀⠀⢀⠞⢁
⠀⠀⠀⠀⠀⠈⠓⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡿⠃⠀⠄⠀⠐⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⣺⠏
⠀⠀⠀⠀⠀⠀⢀⣴⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⡤⡏⠀⠀⢄⡀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠛⢹⠀⠀⣀⠀⡀⠄⠀⣠⠀⠀⣿⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠁⠘⠋⠀⠈⠋⠀⠛⠀⠜⢷⠞⠁⠀⢀⡄⢂⣀⠄⠀⠀⠀⠀⠀⡀⠀⢸⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠈⠁⠀⠙⠎⠠⡄⡸⠈⠓⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠀⠀⡆⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠫⢡⠀⠀⠀⠀⡇⠀⠆⠀⠀⠉⡒⢤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⢀⡀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠈⠓⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣠⢞⠍⠀⠀⠀⠀⣿⠀⣇⠀⠀⠀⠀⠰⡢⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠁⣼⠀⠀⡀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⢱⠘⢦⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣠⢞⠃⠀⠀⢹⡄⠈⣧⠀⠀⣦⡀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠒⠋⡴⢋⡠⠂⠀⠀⢷⡀⣿⠐⡀⠱⣍⠢⢬⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⢸⣧⡟⠀⠀⠳⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⡾⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁
⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠼⢿⣦
⠀⠀⠀⠉⠳⢤⣆⣰⠐⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⣠⡄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠃⠓⠀⣸⠏
⠀⠀⠀⠀⠀⢀⠽⠋⡱⠛⣻⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⠿⣿⠛⠈
⠀⠀⠀⠀⠀⠀⠤⠀⢰⣲⣶⡦⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⡭⣞⠿⠁⠀⣇
⠀⠀⠀⠀⠀⠀⡠⠻⢋⡵⣿⢦⡀⠀⠀⠀⠠⠈⠰⠀⡠⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⢠⣿⢋⡞⢡⢤⡀⠀⠀⠀⠀⢰⠚⠳⡄
⠀⠀⠀⠀⠀⢺⣏⠙⣁⠤⠋⣲⣇⠀⠀⠀⠀⠈⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡼⡆⠀⣀⡇⠀⠀⠀⠀⢈⡀⣠⠁
⠀⠀⠀⠐⡻⢓⢊⡏⡉⠎⠛⠏⠁⠀⠀⠀⠘⡜⠁⠀⢢⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠶⢯⢯⣰⡿⣦⣶⣲⡥⠚⡇
⠀⠀⢀⣰⠧⠱⠪⢆⡀⠄⣍⢶⡅⠀⠀⠀⠀⠇⠀⠒⠀⠀⠀⠐⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⢰⢮⣋⢦⡏⢐⢢⣧⡐⠁
⠀⠀⡊⠃⢚⡐⠳⠈⢱⠤⠣⢭⣁⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠈⠁⠈⠀⢄⠠⠀⠒⠀⠀⠈⠙⠤⠜⠛⡹⣝⡫⣿⢟⡷
⠀⠀⢫⠫⠇⡀⣋⠘⢈⠃⠇⡘⢁⠀⠀⠀⠀⠘⡀⠘⡖⠀⠄⡱⠀⠐⠋⠁⠀⢀⡄⠀⠀⠀⢀⣠⣄⡀⠘⠋⣿⣻⣛⣿⡆
⠀⠀⡞⠒⢂⠉⡅⢤⢈⠧⢸⠀⠃⠁⠀⠀⠀⠀⠑⢀⠓⢦⢐⡀⣢⠀⠀⠀⠉⠉⠀⠀⠁⠀⡟⠀⠀⣷⠖⠲⠟⣹⡳⠋⠁⡀
⠀⠐⠙⡧⠬⠂⡑⣄⡼⠐⠞⢀⠁⠀⠀⠀⠀⠀⠀⠠⠀⢈⠁⠉⢂⠀⠀⠀⠁⠁⢈⠂⠀⠀⢳⣀⠀⠘⠦⡤⢔⡵⣟⠁⡰
⠀⠀⠀⠇⢠⣠⣁⠎⡙⠃⡇⠃⠀⠀⠀⠀⠀⠀⠀⢁⠠⠈⠠⢄⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠚⠋⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠁⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⠀⡀⢀⠀⠀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀
⣿⣿⢛⠿⢛⠛⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⢀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠔⠁⠀⠐⠆⢀⠀⠀⠀⠀⠔⠁⠠⠂⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣀⣀⠠⡀⠈⠑⠒⢀⠀⠈⠉⠂⡀⠐⢦⠀⡀⠈⢀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⡠⠄⢀⠩⠈⠂⠀⠀⢀⡀⡈⠰⠀⠰⠀⢄⠀⠈⠢⠁⠠⠈⠀⠀⠀⢀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠁⠀⠀⠀⢀⠄⠒⠀⣠⠔⠈⠀⠐⠖⠃⠀⠀⠈⠀⠐⠂⠀⠀⠀⠀⢰⠀⠠⠁⡀⠀⠔⠐⢔
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠒⠂⠐⠒⠀⠈⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠶⠅⠔⠀⠲⢠⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⡀⠄⡰⠀⡠⠢⠴⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣬⣻⣦⠔⢂⣉⠤⠒⠀⠀⠁⠀⠀⠀⢀⡀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠋⠀⡰⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣾⡿⠿⠏⠀⢀⣾⣷⣶⣦⡀⢀⣠⡶⣖⡿⠫⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⡠⠐⠀⠄⡪⠁⠀⠀⠀⠀⣰⣏⣵⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⣠⣴⣿⣿⣿⠿⣿⣿⣯⠴⠊⠁⠐⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠋⠈⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⠽⢿⣻⣿⠿⠋⠀⠠⠟⠉⠀⠀⠀⠰⡄⢀⠆⠀⠀⡸⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠊⠂⡀⠀⢀⡤⠞⣻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠒⠒⠉⠉⠀⠀⠸⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢈⠄⢀⡁⠠
⠀⠀⠀⠀⠀⠀⠀⡠⠞⢀⠀⢠⠑⠃⠜⢁⣤⣾⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⡁⢀⠀⠀⢑
⠀⠀⠀⠀⠀⠔⠃⠀⠠⠀⠀⠘⣀⢴⡾⡻⢷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣄⡀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⢰⠁⠑⡤⢟⠀⠀⠀⢠
⠀⠀⠀⠀⠋⠀⠀⠀⣴⡚⢄⠀⢧⡼⢊⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠉⠉⠳⢤⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⡆⠀⠀⠊⠀⣀
⠀⠀⠀⠀⠀⠅⠀⠀⠀⢨⠀⠂⠜⢰⠟⣽⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠑⠀⠀⢠⡆⡀⠀⠀⢠⢄⠃⠀⠀⡰⠂⠠
⠀⠀⠀⠀⠀⠂⢀⠁⠰⡁⠀⢋⠀⣛⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠒⠶⠖⠀⠀⠀⠈⠠⡠⠂⠊⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠀⡠⠁⣼⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠘⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠐⠂⠄⠚⢢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠚⠈⡁⠂⠀⠙⠿⣿⣁⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠁⡖⠀⠀⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠖⠂⠊⠀⠌⠠⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠀⠐⠀⠃⠀⡄⢐⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠰⠄⠀⡤⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡁⠤⠔⠀⠈⠂⠀⠀⠀⠀⠁⠀⠀⠠⢄⠀⡀⠀⠀⢀⠤⡄⠀⡘⠶⠂⠀⠤⠐⠊⠀⠀⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠐⣀⠐⢀⠢⡀⠀⠐⠀⠄⠀⠦⡀⠀⠁⠀⠀⠠⡀⢂⠁⠐⠊⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠡⡀⠈⠀⠳⠄⠈⠠⣀⡀⠀⠁⠤⢀⡁⠘⠒⠉⠉⠀⠀⡁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠂⢀⠔⠀⠀⠀⠄⡁⠠⠄⠀⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉⠂⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠄⠀⠀⢠⣦⠀⠀⠀⠀⢸⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡀⠀⠀⠀⠠⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡂⢀⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⡠⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⡄⠐⠀⠂⠀⠀⠀⣀⠄⠀⠀⡤⠀⣀⡀⠀⠀⠀⠁⠠⠄⠀⡀⠲
⠀⠀⠀⠀⠀⠀⠀⠻⢄⠀⠀⠀⠊⠀⠀⣀⠀⠐⢅⠀⠀⠀⢐⠶⡐⠚⠡⡈⠑⠢⢄⠀⠈⠀⠉⠘⠉⠛⠂⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠑⠈⡣⢀⠀⠑⠀⢀⠀⠁⠊⢑⠤⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠒⠈⠢⢙⡡⡀⠀⠀⠀⠐⠒⠉⠊⢁⠤⣔⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠈⠀⠠⠄⢠⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠂⢑⠀⡀⠀⠀⢄⠀⠈⠑⠈⡀⢀⠀⠀⠈⠂⢀⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠐⠎⠠⣀⠄⠄⠀⠀⠈⠈⠓⠄⡠⠀⠀⠈⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡖⠂⠈⢉⡀⣾⣤⣶⣿⡶⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⣴⣿⠯⠍⠩⢤⢐⣮⡟⣉⣛⣿⣿⣿⣷⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⢀⡠⢿⣦⣌⠉⢻⡿⣦⠙⠣⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡀⡀⠀⢀⡠⠞⠉⣴⠏⠙⣿⣧⠈⠉⠉⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣼⡜⣁⠔⠋⣀⡴⠞⠁⠀⠀⢹⣿⡆⢧⠀⢠⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⠗⠚⠉⠁⠀⠀⠀⠀⠀⢈⣿⡇⡘⠀⠀⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠸⣟⠿⣦⠀⠀⢀⣤⣤⣄⣀⣸⠻⣧⣷⡄⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡏⠀⠉⠁⠀⣸⡟⠙⠿⢓⠄⢀⣿⣿⣿⡆⢿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢿⣿⣻⡟⡇⢸⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡙⣧⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⣸⣿⣽⣷⠣⢸⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⡘⢷⡈⢆⠒⠍⠍⢀⠀⠀⠀⠒⠉⠁⠘⣼⣿⠀⣸⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣆⠻⡎⠆⠀⠣⠔⠊⠉⠀⠀⠀⣠⡼⣿⢏⡇⣿⣿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣭⡻⠆⠘⠀⠀⠀⠀⠀⢀⣶⣿⣵⢞⣁⣾⣷⡏⣿⢼⡟⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⣭⡛⠃⠀⠀⠸⣿⠀⠀⠸⣿⣿⡿⢫⡾⣿⣿⢣⠿⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣦⡍⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⣷⣾⢟⣼⣿⠃⠈⠸⢸⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣠⡶⠞⠉⠀⠀⠀⠀⠀⠀⢸⣯⣥⡾⠛⠁⠀⠀⢀⢸⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢹⡄⠀⠀⡀⠀⠀⠀⠀⣸⣿⣏⠁⠀⠀⡰⡠⡘⣸⡎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣘⠿⣷⣶⣶⣶⣿⣿⣧⢀⣷⢇⣇⡇⣷⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠉⠙⠛⠛⢸⡿⠸⣿⡇⠹⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙

⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⡀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⡀
⠀⠀⠀⢧⡸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢏⣼⠁
⠀⠀⠀⢈⠻⣮⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⡾⡃
⠀⠀⠀⠀⠱⣮⡻⣾⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⢟⣭⠞⠁
⠀⠀⠀⢣⣄⠈⠻⢷⣯⣿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⣟⣿⡿⠟⠁⣀⡴⠁
⠀⠀⠀⠀⠙⠻⣶⣤⣌⣙⣻⣿⣮⡙⠛⠛⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⠛⠛⢛⣵⣾⣟⢛⣩⣤⣶⠾⠋
⠀⠀⠀⠀⠀⠓⢦⣭⣙⣛⣲⣶⣤⡤⠀⠠⠗⢴⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡦⢚⠅⠀⠤⣤⣴⣶⣛⣋⣭⡤⠖⠁
⠀⠀⠀⠀⠀⢄⣀⣈⣉⣩⣭⣿⣗⣂⠀⠈⠤⠀⢻⣆⠻⣷⡀⠀⠀⠀⠀⢀⣴⠟⣰⡟⠀⠠⠉⠀⣐⣺⣿⣯⣭⣉⣁⣀⡠
⠀⠀⠀⠀⠀⠀⣈⣉⣉⣩⣥⣶⢿⣔⣀⠀⠀⠁⡀⠉⢳⣜⣿⣆⠀⠀⣰⣿⣯⡾⠋⠀⠘⠀⠀⢀⣲⡿⣷⣮⣭⣉⣉⣉
⠀⠀⠀⠀⠀⠀⠀⠉⡉⣉⣩⣴⠿⣻⣷⣯⢀⠀⠀⠀⢌⣿⣿⢉⡂⢀⡁⣿⣿⡥⠀⠀⠀⡀⣽⣾⣟⠻⣶⣍⣉⠉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⣤⡾⢛⣽⢿⣿⣾⣄⣤⣼⣿⢣⡟⠀⠀⠹⡌⣿⣧⣴⣤⣵⣿⣿⣷⡙⢿⣦⣉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠑⣫⣾⣿⣅⡌⡘⣹⣿⡁⠀⠀⢀⣿⡏⠉⢩⣠⣿⣿⣝⠊⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⢞⣿⣿⣿⣾⢻⣿⠃⠀⠀⠈⣿⡟⢷⣿⣿⣿⡿⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡟⢸⣿⡏⢸⡟⠀⠀⠀⠀⢻⡧⢸⣿⡇⢻⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠁⢸⣿⠇⠸⠁⠀⠀⠀⠀⠀⠇⠘⣿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠈⠀⠙⠨⠀⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⣤⣄⡄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣰⢂⡇⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠛⢇⠈⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣈⣆⠀⢠⠀⠁⠀⠠⡆⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡑⢀⣫⡽⢿⠶⠂⠀⠀⢀⡇⠐⠂⠚⠃⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣛⡥⣀⡀⠈⠀⣤⠀⠀⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠀⢧⡀⠀⠙⠒⢶⠊⠐⠄⡀⠀⠂⠠⠤⣀⠀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢠⠀⠀⠙⢦⡄⠀⠀⠑⢦⠀⠁⠀⠀⠀⠀⠸⠇⠀⠀⠀⢠⠋⠀⠀⠴⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠆⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠉⡄⠀⢀⠂⣀⡀⠀⠁⠀⠀⢀⡣⡌⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠔⠁⠀⠀⠀⠐⢒⠐⠀⠈⣄⠀⠀⠀⠀⠈⠀⠃⣴⠀⡀⢀⠀⠓⠒⠀⠀⢀⠀⠁⠀⢲⣀
⠀⠀⠀⠀⠀⠀⠄⠀⣀⠄⠀⠐⠀⢀⠀⠄⠀⠀⠀⠀⢹⡂⠀⠁⠀⠀⠀⠇⠈⠛⡇⠈⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢴⣤⡀⠀⣚⣚⢉⣠⡜⠂⠀⠀⠀⠀⢁⠀⠀⠀⠄⠀⠁⠀⠀⠘⠑⢀⣘⡃⣄⣠⠀⠁⠈⠉⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠀⣉⡡⡬⠐⠙⡀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⢈⡿⢄
⠀⠀⠀⠀⠀⠀⠈⡄⠐⡗⠉⡉⠉⠀⣁⡤⠔⠒⠒⠒⠛⢣⡀⠀⠀⠀⠐⡖⣦⣆⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡤⠚⠉⠀⠀⠀⣤⠀⠀⠀⠉⠉⢀⠤⠀⠘⠃⠿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠁⠀⠀⠀⢀⠄⢰⠁⠋⢳⡀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠐⢶⠆⠛⣶⠑⠂⠀⠀⠀⢘⠁
⠀⠀⠀⠀⠀⠋⡀⠹⡟⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠇⠐⠑⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠰⠓⠾⡏⠐⠂⠀⠀⠠⠀⠀⠈
⠀⠀⠀⠀⠠⡀⠒⠹⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠢⡜⠁⠀⠀⠀⠀⠱⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠠⠀⢄⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠠⠠⠦⠤⠶⢄⣀⠀⠀⠀⠀⠀⡠⢰⠈⠓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠗⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠋⠙⠒⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⢀⣀⣠⣤⣤⣤⠶⠶⠶⠶⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣤⣖⣚⠋⠉⣉⣈⣀⣠⣤⣤⣤⣤⣤⠾⠧⠤⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠾⠿⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣬⣤⣷⣶⣶⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⡀⠤⢐⣀⣤⡴⠶⠛⢻⡿⣿⣿⣿⣿⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⣊⡭⠶⢟⣋⠁⠀⠀⠀⠀⠀⢡⡿⠟⠋⠁
⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣀⡤⣒⡭⠖⠋⠁⠲⠶⣶⠪⠉⠀⢀⣰⣄
⠀⠀⣠⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠷⣪⣵⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣀⡤⠔⣡⣾⣏⣴⣿⡋⢦⣉
⠀⠀⠀⠀⠉⠻⢿⣶⣦⣭⣭⣷⣾⣿⣿⢿⠟⢻⣿⢷⣤⣀⣼⠆⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠸⢦⠀⠹⣧⡀⣍⣁⣰⠀⠀⠀⠀⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣆⠈⠻⢶⣭⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣮⡉⢀⡀⠨⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⠋⠀⠀⠘⣿⣮⣧⣀⠀⠐⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡿⢹⡿⠈⣷⡄⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣸⢿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢚⣫⠸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡇



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣯⣿⣭⣭⣯⣬⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠐⠀⡀⢀⡀⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢻⠈⠁⢸⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠘⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠊⠣⡀⠀⠘⣿⢻⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⠑⠄⠘⡃⠀⠁⠀⣠⣇⠺⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢄⠀⠀⠀⠀⠀⢶⣸⣿⡿⢞⠒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠶⣄⠀⠁⠀⠈⠐⢬⢺⣯⣋⣳⣅⠺⣢⡀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠚⢉⡷⠟⠋⡙⠃⠀⠀⠀⠀⢀⠜⡹⢁⡀⠀⣀⠀⢰⣿⢡⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣭⣁⠀⠀⣲⣴⣏⠴⠂⠘⣄⡀⠉⠉⢀⣀⣉⠤⠞⣫⠔⣫⠄⢀⡽⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣤⠶⣿⡟⠀⣤⡞⠀⠈⢻⣟⣋⣉⡁⠀⠀⠚⠁⢨⣵⣦⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⢁⠀⢿⣇⠀⡘⠶⠍⠉⠙⢋⣁⣶⣦⣄⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⢩⣇⠀⣕⢶⡔⢦⡘⢉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⢨⡅⣿⠾⠻⣧⡀⠀⠙⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠂⠀⡜⣯⡑⢻⠀⢀⡙⣝⣀⠐⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠂⠀⠀⠀⠙⢌⠓⡄⣸⡆⣷⣈⠙⠛⢦⡈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⣠⣦⠈⠧⠘⣿⣧⠙⠻⣆⠡⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠛⠁⢀⠀⠀⠉⢿⣷⡌⢦⡀⠀⠐⣆⠀⠠⣬⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⢴⣶⡴⣡⡟⢀⠀⢀⠀⣿⣷⠀⢿⣎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠀⢿⣿⢰⡟⢡⠏⣧⡘⢧⡈⢿⣧⠈⠻⣦⣀⠀⢂⣠⣴⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡇⠀⠀⠸⣷⠈⢿⣆⠙⠷⣦⣈⠙⠛⠋⠉⠁⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⡀⠙⢷⡌⠙⠳⠦⣬⡛⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⡌⠛⠿⠶⠤⣦⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⢌⠳⢶⣄⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠑




⣿⣿⣿⡿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣥⣤⣧⣤⣦⣤⣷⣥⣾⣯⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣾⣿⣿⣿⣿⣿⣿⡟⠁⢀⠀⣴⣿⣾⣠⣿⣿⣼⣿⠆⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣆⠀⢸⣿⣿⣧⠈
⣿⣿⣿⣿⣿⣿⠋⠀⢠⣣⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣯⣿⣿⣿⣿⣿⡿⢻⣛⡿⢿⣷⣿⣿⣿⡀⢸⣿⣿⣿
⣿⡟⣱⣿⣿⠃⠀⢠⣿⣏⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⡄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣁⣶⡿⣫⡟⢻⣇⣸⣿⣿⣿⡀
⡛⣰⣿⣿⠃⠀⢠⡿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣷
⢡⣿⡿⠁⠀⢠⣿⣷⠏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣞⣿⠁⠀⠀⣾⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣥⣤⣭⣿⣿⣿⣿⣿⣿⣷⣿⣧⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⠿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠏⠀⠀⢰⣿⢻⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⠿⠁⠈⠉⠿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⢠⣿⢣⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣤⣄⠀⣄⣠⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣛⣿⣿⣿⣿⣿⣿⠃
⠀⢀⣿⠇⣾⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣉⣿⣿⣾⣿⣿⣿⣿⣿⣿⣶⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⣋⣉⠁⢀⠀⠚⣿⡿⣿⣿⣿⣿⡟
⢀⣾⡟⣸⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣷⣾⣧⣬⣥⣀⣀⠀⠀⠈⠙⢰⣿⣿⣿⣿⠃
⣼⡟⢰⣿⣿⣿⣟⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠈⠙⠻⢿⣷⣦⣈⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏
⠟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣿⣿⣿⣿
⢠⣿⡿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⣿⠏⠃⠀⠛⢿⣿⣿⣿⣿⣿⣿⠿⠛⠻⠿⢿⣿⣿⠷⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠋⣦
⣽⠇⠐⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠹⡆
⠁⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠃⠀⠀⠀⠹⡄
⣴⡿⣷⣤⣀⠀⠀⠀⠀⢾⣿⣶⣿⣶⣶⣤⣠⣤⣦⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣽⡿⠁⠀⠀⠀⠀⠀⠹⣄
⣿⣤⣿⣿⣿⣷⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⡛⢁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋
⣿⣿⣿⣿⠿⢿⡏⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠁
⠁⠉⠙⣿⣧⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠙⠛⠛⢿⣦⡀⠀⠀⠀⢀⣤⣶⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⢀⣠⣼⣿⣶⣶⣶⣿⠟⣯⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠋⠀⠀⢀⣀
⠀⠀⠀⣰⣿⣿⠛⠿⠋⢻⣿⣏⠀⠈⢧⠸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠋⠀⠀⣠⣴⡾⠋
⠀⣠⣾⣿⡿⠃⠀⠀⣤⣀⢻⣿⠧⠀⠸⣄⠉⠉⠉⠛⠃⠙⠟⠙⠓⢀⣠⣴⣾⠿⠛⠉⠀⣠⠤⣶⣿⡿⠋
⢀⣿⣏⡈⠁⠀⠀⠀⢲⡙⢷⣌⣁⣤⣤⣷⣤⣄⣀⣴⡆⠀⣀⣴⣾⠿⢛⣩⣤⣶⣾⣿⣧⣤⣶⣿⣿⣤⣤⣴⣶⣾⣿⡿⠿
⣾⣿⣿⣿⣷⠢⣤⡀⠰⣛⣿⣿⠛⢹⡿⠛⠛⠛⣛⣭⡷⠟⢛⣩⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣉⡉⠠
⠻⣿⣿⣿⣿⣷⣾⣷⣶⠟⠿⠏⠀⠀⣀⣤⡶⠟⣋⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⠇⠘⠁
⢛⣛⣿⣿⣿⣿⣿⣿⡟⠀⠀⣀⣴⡞⠋⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣴⣦⣶⣾⣿⣿⡿⢋⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣶⣤⣀
⣻⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⣿⣶⣤⣄
⠠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⡙⠻⢿⣶⣤⣀⡀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣬⡛⣿⣿⣷⣄
⣼⣿⣿⣿⣿⣿⣿⣿⣿⢁⣼⣿⣿⣿⣿⣿⣿⣫⣦⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠛⠳⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⢹⣿⣿⣿⣿⣿⣿⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⡿⠛⠓
⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃
⣿⣿⣿⣿⣿⣴⣬⣿⣿⣴⣿⣿⣿⣿⣿⣿⡿⠿⣿⣯⣤⣶⡿⠋⠉
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⢻⣷⣶⡿⠿⠛⠋
⣿⣴⣿⣿⣿⣿⣿⣧⣾⣿⣧⣶⣴⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡻⠉⠛⡿⠋⢛⠛⠛⡛⠏⣛⡿⢟⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⣿⣿⣾⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡔⣀⣀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠀⢀⡠⢊⣀⡠⠂⡀⠀⠀⣚⡫⣇⣤⣠⣄⠨⠄⠀⣃⡀⠀⢀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⢦⡐⠖⡉⠛⣷⠀⠀⠻⣅⠈⠩⢅⠈⠓⠲⠌⠉⠀⠈⠙⠀⣞⠁⠀⠂⠀⢍⠲⠭⠉⠉⠉⠩⢏⠂⠋⡇
⠀⠀⠀⠀⠀⢀⠉⠀⠉⠐⠒⠁⡀⠀⠘⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⠃⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠨⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠄⢁⠀⢘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠈⠀⠠⣀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠬⢥⠴⠤⠤⠤⠮⠤⠤⠴⡿⠄⠀⣶⣾⡆⠀⠀⠤⠤⢒⠒⡶⢐⠿⣄⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠀⡐⠀⠀⠀⠠⠔⠉⠐⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⡹⠁⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⠀⠈⡟⠁⡀⠐⡤⠀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣉⠀⡌⠁⠀⢳⡥⡞⠀⡥⢠⠆⠀⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠠⡱⣇⣅⣂⢴⠡⣀⢄⣠⠄⠐⢈⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠘⠀⠀⠀⠀⠅⣠⠖⠉⠀⠀⢹⠟⠉⠉⠙⡄⢈⠋⠠⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠁⡀⢀⣡⡄⠀⠀⡞⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠙⡅⠰⠂⠀⠠⠀⠀⢤⢀⠀⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠛⠁⠀⠀⣰⠷⠓⠂⢄⡀⠀⢸⠀⠀⡀⢠⣀⠴⠁⠀⠁⢂⠀⣰⠰⠟⠓⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠃⡠⠤⠀⡜⠁⠀⠀⠀⠀⣤⢖⠟⠙⠛⠫⡙⢥⣀⠀⠀⠀⠘⡌⠉⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⡄⠄⠀⠐⢉⠁⠀⡀⠀⠀⢸⣷⠁⡠⠀⡀⠀⠀⢂⢳⠠⣀⣠⠴⢧⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠘⠓⠚⠀⠀⠀⢼⣀⠀⠐⠂⠈⠐⢀⣼⣿⠚⠁⠀⠀⡼⠀⡐⠈⠐⠲⢤⣂⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⡲⢆⠀⠀⠀⠎⢿⣶⡤⣄⢠⣤⡾⠏⠀⠈⠐⠒⣹⠰⣂⡀⢀⠂⠀⢢⠀⠙⠉⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣤⣄⣆⢴⠁⠀⢀⡥⣖⠀⠀⠀⠀⠩⠋⠙⠈⠀⠀⠀⢹⠒⠊⠪⠼⣆⣲⠋⣘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠜⠃⠚⢆⠀⠈⠀⠈⢄⡀⢀⣠⠂⠀⠀⠀⢀⣀⣠⣼⠳⣷⣞⠁⠈⠇⠋⠱⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⡄⠀⠁⠀⠄⠐⢩⡆⠠⠀⠐⠂⠀⠈⠁⠁⢠⡖⠒⢲⠉⢽⠅⡛⠀⣿⢫⠩⠁⠶⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠀⡤⠈⠀⢀⠣⣌⡾⢀⠤⢀⡠⡀⠀⠑⣷⡖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠀⢀⡀⠀⠁⠀⠛⢻⠀⠀⠀⠀⠇⠒⠀⠀⣳⣀⠠⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈⠛⠂⠀⠀⠀⠐⠀⠀⠀⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢶⣄⢀⣤⢦⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠱⠆⡀⠈⣧⡀⠀⢀⣄⢀⠀⠄⠻⡿⣶⣇⠇⢭⠇⣳⡾⡽⠃⢠⠀⠀⣇⠀⠈⢠⡎⠀⣀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠄⣠⠘⠓⠨⡀⠀⠈⢃⠤⣍⠁⠀⣴⣷⡿⠀⣲⠠⣷⣶⡄⠀⢉⡅⠠⠈⠀⠀⣈⠓⠚⠀⣄⠄⠈⠉
⠀⠀⠀⠀⠀⡔⠓⠚⠂⠈⠉⠀⢹⣶⣾⣇⠀⠀⠘⠲⠀⢇⠀⣀⣋⠂⠶⡵⠆⢊⣓⣀⢀⡇⠰⠚⠁⠀⠀⣽⣶⣿⠁⡈⠉⠁⠘⠒⠓⣂
⠀⠀⠀⠠⠂⠀⢀⠀⠀⠀⢀⡄⠉⣀⣁⣉⣁⣙⣲⣦⣁⣈⣳⣉⣽⣷⣾⣹⣷⣼⣏⣹⣋⣀⣡⣴⣖⣁⣈⣁⣉⡈⡉⣀⡀⠀⠀⠀⠀⠀⠠
⡤⠠⠀⠀⠀⠠⠀⠄⠀⠀⠀⠤⠀⠠⠀⠀⠄⠠⠀⠀⠀⠄⠀⠠⠠⠠⠄⠀⠀⠀⠠⠠⠄⠄⠠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⠄⠤⠀⠀⠀⠄⠀⠄⠀⠠
⡇
⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⣈⡄⢢⢠⢢⢇⢀⢠⢎⢀⡀⢀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠈⠀⠀⠈⠀⠀⠏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⡟⣠⢀⡄⣠⢀⡄⣠⢀⠄⡄⣠
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⠐⠃⠘⣰⠃⠊⡼⠁⠊⠘⢱⠇
⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠰⠃⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡇⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⡇
⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠐⠀⠀⠀⠒⠖⠒⠒⠒⠲⠲⢒⣶⠶⠒⠒⣶⠒⣶⢶⣶⢲⡶⣶⠖⢲⡒⠒⠲⣶⡒⠶⠲⠒⠒⠒⠂⠖⠀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠑⡂⣀⣀⠀⠀⠀⠊⣹⣾⣷⠟⠈⠁⢀⢠⠁⡾⠙⢛⠻⠁⣝⢯⣄⠹⡛⠋⠹⡄⢁⢀⠈⠁⠙⣷⣿⣮⠑⠀⠄⠀⣀⣀⡀⡆
⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠘⠜⠦⢉⣁⡘⠃⠀⠀⠙⠠⠞⠁⠀⣬⣿⡦⢰⡢⢠⣾⣥⠆⠈⠑⠠⠜⠀⠀⠀⠻⢀⡉⠱⠏⠈⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⣀⠰⠊⠀⡿⠀⠀⠘⡆⠀⠹⠁⣠⢦⣾⠃⡼⠄⡈⣷⣧⣦⡀⠉⠂⠐⠟⠀⠀⠺⡆⠉⠂⣠⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠈⠁⠐⠀⠀⠁⠀⠀⠀⠛⠉⠸⣵⠗⠰⢷⡅⠈⠙⠃⠀⠀⠀⠀⠀⠐⠀⠉⠐⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣠⡾⠻⣦⣄
⠀⠀⠀⢀⡼⠋⠀⠀⠈⠻⢷⣤⡀⠀⣠⡾⠻⣦⡀
⠀⠀⣴⣿⣡⣤⣤⣤⣤⣤⣤⣽⣿⡾⠟⠀⠀⠘⠻⣆⠀⠀⣠⣶⣤⡀
⠀⢰⣿⢠⠤⢤⠀⠀⢠⠤⡤⡀⣿⠉⠉⠙⠛⠛⠒⢻⣷⣟⣩⣤⣬⣿⣦⣀⡴⢦⡀
⠀⢸⣿⢸⣒⣚⡇⠀⢸⣂⣐⠁⣿⢰⣙⡇⠀⡮⠆⢸⡇⣤⡄⠀⢀⣀⠟⠛⠒⠚⢳⣤⣖⣦⡀
⠀⠀⣿⠀⠁⠀⣀⣀⢀⡁⠀⠀⡿⠀⠀⠀⠀⠉⠀⢸⡇⠛⠁⠐⠒⢸⠸⠇⠘⠗⢸⢭⠉⣍⢹⠾⠳⣄⡀
⠀⠀⢿⡆⠀⠀⢻⠀⠀⡇⠀⢀⡇⠀⠀⠨⠉⠀⠀⣿⠁⠀⠐⢂⣀⣸⣀⣐⣂⣀⣨⣀⣤⣤⣼⣠⣄⣏⣹⣦⣤
⠀⠀⢸⣇⣀⣀⣸⣤⣤⣧⣶⣾⣷⣶⣶⣿⣾⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠀⠀⠀⠒⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠰⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡜⠀⢠⠋⠈⠀⠀⠀⠠⠤⢧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠃⠄⡀⠀⠀⠀⠀⠀⠈⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠈⠉⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠌⠀⠀⠀⠀⡄⠈⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠇⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢥⠀⠙⠀⠀⠀⠀⠈⠃⠀⡃⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠨⡄⠀⠀⠘⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢦⡀⠀⠀⠁⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠐⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⡄⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢸⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠘⠀⠂⠠⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⢨⠀⠀⠀⡄⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠃⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠁⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠊⠀⠀⠀⠀⠀⠢⠌
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠏
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⢡⠀⠀⠰⠄⡀⠀⠀⠈⠑⠤⠂
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠀⠀⠄
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⢬⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⣠⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠀⡅⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡆⠀⠀⠀⢰⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠾⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠒⠤⡇⠀⠀⠀⢠⠔⠉⠣
⠀⠀⠀⠀⠀⠀⠂⠈⠑⠤⠤⠊⠉⠐⠂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠤⠀⠁⠀⢀⠔⠃⢀⡀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⢸⣧⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣴⡏
⠀⠀⢠⠈⢿⣷⣌⣷⣄⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣠⣾⣡⣾⡿⠁⡄
⠀⠀⢀⠳⣄⡙⢿⡿⠆⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠱⢿⡿⢋⣠⠞
⠀⠀⠀⠢⣈⠻⣮⣝⣓⠲⢷⣝⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⣫⡾⠷⣚⣫⣴⠟⣁⡔⠁
⠀⠀⠀⢠⡈⠻⢿⣶⡒⠥⠭⣿⡏⢳⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⡞⢹⣿⠯⠼⢒⣶⣿⠟⢁⡄
⠀⠀⠀⠀⠙⠿⣶⣯⣭⡭⠤⠿⣷⡀⢾⣿⣷⣹⣆⠀⠀⠀⠀⣰⡏⣾⣿⡷⢀⣾⠷⠬⢭⣽⣿⣶⠿⠋
⠀⠀⠀⠀⠈⠓⠶⠿⣿⣶⣺⢭⡻⣷⣄⡉⣽⣷⣿⡆⠀⠀⢰⣿⣾⣯⢉⣠⣾⣟⡬⣗⣶⣿⠿⠶⠒⠁
⠀⠀⠀⠀⠀⠀⠒⠶⢛⣻⣟⡭⠂⣈⠝⠻⣶⣙⢏⣻⡄⢠⣟⡹⣋⣶⠿⠫⠃⠐⢭⣻⣟⡛⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠘⠛⢉⣼⠟⢹⢿⣶⣄⡞⡏⢻⡀⠀⠀⢀⡿⣻⣳⣠⣶⡿⡏⠻⣧⡉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠏⣼⠏⣿⣇⣿⡎⠁⠀⠀⠈⣱⣿⢻⣿⡹⣧⠹⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠋⣸⣿⣧⢿⣉⠀⠀⠀⠀⣉⡿⣽⡿⣇⠘⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⢁⡴⣿⢾⡟⠦⠁⠀⠀⠀⠀⠈⠴⢻⡿⣿⢦⡈⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⣋⡼⠃⠘⣇⣠⠀⠀⠀⠀⠀⠀⣄⣺⠃⠈⢧⣙⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠈⠈⠁⠐⣄⠀⢰⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠂⢀⠀⣀⣀⣴⣀⠀⠀⠀⠈⠁⠀⠉⢴⣿⣇⣸⡿⠲⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⣵⣿⣿⣿⣿⣷⡶⠒⠂⠉⢷⡀⠀⠉⠛⠉⠛⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠠⡄⢙⠤⠤⠀⢼⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢀⡅⠈⠂
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢀⡀⠀⢃⡄⢠⣿⡄⠀⠀⠈⣻⢿⣿⣿⡿⠟⠓⠦⣄⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⣤⣀⠔⠁⠀⠈⠈⢇⠀⠀⢀⢘⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡄⠀⠀⠀⡌⢦⣴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠉⠁



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣽⣯⣮⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⡅⣸⡿⠿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣷⣿⣧⣸⣿⣿⡟⣴⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡝⢦⡙⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣷⡈⢳⡄⠙⣿⣿⣿⡏⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⡈⢷⡌⠳⠀⢿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠑⠀⠙⣷⣀⢸⣿⣿⣿⡇⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣼⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⡏⡇⢠⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⡘⢹⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⢻⠀⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⡈⠳⡀
⣿⣿⣿⣿⣿⡿⠋⠁⠀⠐⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⣸⡆⠻⢁⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠁⠀⠃
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣷⣾⣿⣿⣷⣶⣯⣿⠿⠿⢯⠹⣿⣿⣿⣷⣤
⣿⣿⣿⣿⣶⣤⣀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⠏⠙⠁⠀⠀⣄⢠⣤⠃⠀⠻⣿⣿⣿⣎⣧⢀⠂
⣿⣿⡿⠿⣿⣿⣿⣿⣶⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠟⣻⣛⣶⣶⣶⣶⣶⣶⣴⣿⣾⡿⠀⠀⠘⣮⣿⣿⣿⡟⡿
⣿⣿⠁⣀⣨⣽⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠉⡏⢿⡿⠉⠻⣿⠿⡿⠁⠀⠀⠀⣿⣿⣿⢋⡼⢁⠁
⣿⣿⣶⣿⣿⡿⠛⠛⠛⠛⣿⣿⣶⡂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠈⠂⢀⣤⠾⠟⠀⠀⠀⠀⠀⠀⠊⣿⣧⠏⢀⣄
⣿⠛⠻⣿⣿⣆⠀⠀⠈⠆⠙⠛⠀⠙⠛⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⢞⣿⣆
⣿⠀⠀⠀⠈⠉⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣾⢺⣿⣿
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⢁⡟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢷⠊
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⡀
⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⠛⣷
⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣿⣿⠀⠻
⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣧⡀⠀⠀⠀⠠⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⣿⠏
⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢿
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢃
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠴⡦⣤⣤⣤⠐⡶⢶⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⣿⣿⡿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢶⣾⣿⣦⣼⣷⣿⠾⠿⠛⠓⣛⣿⡿⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⣿⣿⡇⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⢿⡟⢺⢹⢹⣿⡟⡟⠿⠉⠃⠷⠘⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢱⡀
⣿⣿⣿⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠻⣿⡈⠃⠉⠁⠀⠀⡀⠤⣴⠆⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠱⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠙⠓⠺⠿⠶⠖⠛⠛⠉⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡞⠀⠀⠠⠘⠛⠀⡀⠀⠙⢆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⢀⣤⠛⣿⠖⣷⢷⠀⠀⡹⢦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠍⠙⠁⠀⠚⡃⠝⠁⠀⠀⠙⢦⣀

⠀⠀⠀⠀⠀⠀⣳⠘⠁⠀⠀⠠⠂⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠑⠀⠀⠀⣷⣶⣾⡓⠀⠀⢡
⠀⠀⡀⠄⠀⠀⠛⢀⡌⠀⡴⢁⠔⠉⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢂⡀⠀⠴⠖⠈⠈⢹⡿⠏
⠀⠀⠀⠀⣘⣿⣀⠀⠀⠈⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣸⠃
⠀⠀⠀⠀⣿⠟⠻⡁⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠈⡇⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣐⣿⣧
⡀⠀⢀⣌⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙
⠿⣿⣿⣍⠀⠀⠘
⠀⢨⡿⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠤⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠲⣀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⡂⢇
⠀⣴⣄⢀⡠⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈
⠉⢹⣿⣿⠉⠀⢤⠀⠀⠀⣀⠔⢁⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⣶⣤⣴⠯
⣠⡾⠋⠁⠀⠀⠐⠁⢀⡔⠡⠠⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠙⣿⣿⠆
⠁⠀⠀⠀⠀⠂⣺⣶⣾⡋⠁⠉⢖⠒⠂⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠉⠁⠀⢹⡟⠁⠀⠀⡀⠀⢀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣶⣶⡆⢀⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢠⣄⣀⣀⠄
⠀⠀⠀⠀⠀⠀⢀⠰⠎⡠⣾⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡘⢃⠈⠀⠀⠀⢰⠉⠂⢉
⠀⠀⠀⠀⠀⡠⠜⠒⣲⠀⣀⣄⠀⣤⠐⠂⠀⠀⠀⠀⠀⠀⠀⣀⠴⠶⠤⣶⠀⠤⡀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⢤⠿⠷⣬⣹⣶⣧⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⡛⠁⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⢀⡐⠀⠀⠠⠀⣀⠁⠀⠀⠜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⠃⠀⠀⠀⠠⠀⢺⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⢠⣄⠊⠀⠀⠀⠀⠀⠉⠀⠀⠒⠖
⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⢰⠀⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠈
⠀⠀⠀⠀⠀⢦⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡘⠀⠀⠀⠀⠀⠀⠈⠋⠀⢘⠀⠀⠀⢠⠁⠀⠀⠄⢉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⠀⠀⡖⢀⣤⡾⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡀⠂⠀⢸⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠐⠒⠀⠌⠁⠉⠉⠲⡀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠐⢍⠲⣄⠐⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠢⡀⠀⠀⠀⢀⠋⠀⠀⠀⠊⠀⠈⠛⠲⡈⠿⣄
⠀⠀⠀⡠⠀⠀⢼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⣤⡿⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠁⠀⠠⠊⠀⠐⠀⠀⠄⠀⠀⢀⠀⠀⠃⡀⠠⠀⠁⣁⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⡋⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠒⠀⠉⢠⠀⠀⠀⠀⠂⠒⠒⠈⠀⠀⠸⡋
⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐
⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢢⡀⣷⠀⣰⠏⠀⠘⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢀
⠀⠀⠀⢀⠋⠀⠀⠀⠀⢀⣈⣡⠟⢃⡟⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⡀⠀⠀⠀⠈
⠀⠀⠀⢸⠀⠀⠀⢀⠀⠈⠀⠁⢀⢾⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠐⠰⣎⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢀⠄⠀⠀⠀⠈⠀⠀⠀⠠⠔
⠀⠀⠀⢸⡄⠀⠀⠁⠀⠀⠀⠀⠈⠘⠁⠀⠀⠀⠀⠀⠀⠄⠐⠆⠡⠀⠀⠀⡀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢸⠀⠀⡰⠃⠘⠃⠄⠁⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠛⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠐⠀⢹⠀⠀⠀⠀⠀⠘⠀⠀⠇⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠓
⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢓⠜⠠⠄⠈
⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠢⡀
⠀⠀⠀⠀⡄⠀⠀⠀⡄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠉⡠⠆⠀⠀⠈⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠋⠄⠂⠀⠀⠀⠀⢠⠀⠁⠀⢀⠁
⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠜⢀⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⡀
⠀⠀⠀⠀⠸⠃⢸⣶⢓⢒⠛⡄⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⡀⠀⠀⠉⠀⠀⠐⠀⠀⠛⠓⠙⠀⠁⠁
⠀⠀⠀⠀⠀⠂⢸⠃⣬⣄⢘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢿⠀⠠⠴⢂⠐⠀⠀⣉⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠁⠸⣿⣅⣀⣤⠒⡅⠀⠀⠀⠀⠀⠀⡀⠉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠟⠁⠀⠘⠆⠀⠀⠀⠀⠀⠁⠀⠀⠤⠀⣤
⠀⠀⠀⠀⠀⠘⢾⡧⠀⠙⢤⠀⡇⠀⠀⠀⠀⠀⠀⠘⠄⣀⠀⣀⠖⡁⠀⠀⠀⢀⠀⠀⢀⠠⠀⠀⣀⡀⠐⠄⠠⠀⠀⠀⠀⡠⠀⠀⢀⠀⠀⠂⡀⠀⠀⠀⠤
⠀⠀⠀⠀⢠⢠⡀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⢹⠞⠀⠀⠁⠀⠁⠈⠁⠠⠄⠀⠀⠠⠄⠁⠀⡄⠀⠈⠱⠀⠀⠀⠀⠄⣤⠀⠀⠘⢢⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⠟⠃⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⢸⠄⠀⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⢨⠞⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⢤⠀⠡⠀⠁⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠛⠅⠀⠟⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠦⣤⣶⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⡇⠀⠀⢘⣿⡧⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡟⠋⠀⠀⠀⢸⠿⣧⠀⠘⠏⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⢠⡏⢀⣿⣷⡀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣠⡀⠀⠀⠱⢦⡿⣤⣾⣿⣿⠃⡠⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣿⡀⠀⠀⣠⡏⠀⣿⣿⣿⠃⠀⠀⠆⢀⠘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⣾⡇⠀⣰⡟⠀⠰⢻⡿⠃⠀⠀⠀⠀⢘⠿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣆⣿⣵⣠⡿⢿⣦⡄⢾⡧⠀⠀⠀⢀⣤⣊⣴⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⣿⣧⣬⠽⠍⣴⠇⢠⡀⠈⠀⠹⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣠⣿⡿⢻⠷⠀⠉⢱⣄⠀⠚⢃⡴⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣾⡿⠋⠶⣾⣷⣻⣿⣿⣿⣦⠀⠘⣿⡎⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣤⣄⠀⠘⠋⠀⠻⢠⣿⣿⡹⠿⣿⣿⣿⣧⠀⣼⡇⢙⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠛⠛⠛⠀⠛⠁⠀⠀⠀⢠⣼⠛⣿⠿⣷⣬⣻⣿⡿⠀⣿⡇⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡿⠁⠀⢀⣹⣿⣿⠇⠀⣿⡆⢠⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⣸⣿⣿⠃⠀⠀⣿⡇⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⢠⣿⣿⡟⠀⠰⠀⢿⡇⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣾⣿⣿⠁⠀⠀⡄⢸⣇⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⣼⣿⣿⠃⠀⠀⠀⠠⠀⠿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣼⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⣡⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣏⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠿⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡦⢙⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠘⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠔⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣵⠃⠀⠀⠀⢀⣀⣠⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠉⠁⠈⠁⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠞⣀⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣧⢀⣀⢠⣤⣤⣴⣶⣶⣤⣄⠀⢨⡿⢯⡽⠉⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⣀⢰⣤⣄⣎⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣷⣿⣿⣿⡻⠆⠀⠀⠢
⠀⠀⠀⠀⠀⠀⢀⣯⣿⣿⣧⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣖⢳⣶⢢⡄
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡯⣯⠻⢿⣿⣿⡿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣆⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠠⣹⣿⣿⣿⣿⣿⣿⠿⣿⣇⠜⣐⣲⣦⠐⢿⣿⣿⣿⣿⣿⣶⢟⣻⣿⣿⣿⣿⣿⣿⣤⡙⢿⡧
⠀⠀⠀⠀⠀⠐⠹⣿⣿⣿⣿⣿⣧⣾⣭⣿⣟⠝⠇⢱⠇⣿⠿⣆⡿⢫⣶⠉⢛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠗
⠀⠀⠀⠀⠀⠘⣴⢿⣿⣿⣿⣿⣿⣟⣿⡋⣩⣶⣿⡄⡘⠻⡄⣹⣗⠉⠁⠀⠀⠉⠙⠛⣿⣿⣏⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠘⢿⡟⢿⣿⣿⣿⣶⣡⣾⣷⣦⡀⣽⡶⠂⠠⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⡏⠛⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⣉⢙⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⣈⣻⣿⣃
⠀⠀⠀⠀⠀⠀⠀⢐⠀⡀⠈⣿⣿⣿⣿⡿⣿⣏⣛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⣿⣿⣽⣿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢽⠉⠦⠙⠻⢿⡿⢉⣝⡟⢿⡿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⢫⡄⡹⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⠀⠉⠒⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠋⡑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣿⣿⣿⢻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡾⣿⣿⡿⣸⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣧⢻⣿⡇⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⢿⣾⣿⣷⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡘⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣻⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣺⣇⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣯⣿⣦⠀⠀⠀⠀⠀⠀⣰⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⢾⣻⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣟⡋⣭⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⣿⣭⣵⡾⣿⣿⣿⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠛⢻⣿⣿⣿⣿⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⢠⣿⣿⣿⢹⣿⣎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢀⣾⣿⣿⣿⡌⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣍⣉⣉⣉⣭⣭⣭⣵⣾⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢦⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣵⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡻⣿⣿⣿⣿⠿⣛⣭⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⡤⠶⠒⠶⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣋⣭⣮⣭⣛⢿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣠⣔⣚⣉⣀⣀⣀⣀⣈⣧⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣱⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣛⣿⣻⣟⣙⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⣿⠟⡟⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⢠⠊⠙⠀⠀⠀⠀⣀⣰⣦⣄⡳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠿⣌⢷⣀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠦⣑⠜⢦⢊⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⠪⠦⠈⢷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⢠⠀⡀⠀⠀⢈⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣤⠀⡇⠀⠀⣼⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⡇⠀⠀⢙⢷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣰⡅⠀⡇⠀⠀⠈⡌⡄⠹⣿⣿⣿⣿⣿⣿⣿⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢰⠛⡀⢽⠀⠀⠀⣧⠲⠀⢫⠀⢻⣿⣿⣿⣿⡆⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣼⠀⢳⠘⠇⠀⠀⣏⣶⠀⢠⣷⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡾⠀⠈⠦⠆⠀⠀⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢸⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⠞⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⢀⠔⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠰⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠎⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠁⠀⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠲⢤⣡⣀⣠⡔⡾⠻⢿⣿⣶⡜⠻⠿⠿⣿⣶⣦⡤

⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⢣⡀⣆⠀⣴⡿⠛⢣⠴⢶⡄⢀⣠⠂⡔⠻⠳⡀⢠⡀⠀⣠⡶⢠⠛⠻⣶⡄⠀⡆⢰
⢄⠀⠀⠀⠀⠈⠋⠙⠧⣽⣆⡘⠦⣴⣾⡄⠀⣿⢯⣥⡾⢅⡀⢈⣹⣦⡹⣷⡇⠀⣼⣦⣄⠌⡀⣈⣠⠿⠋⠙⠁⠀⠀⠀⢀
⠘⠧⠰⣄⠀⠀⠀⠀⠀⠈⢻⣥⣀⠙⠟⠁⢀⠀⠀⣰⠆⠈⢩⠉⠀⢴⠀⠀⠀⠀⠻⠟⢃⣀⣿⠋⠀⠀⠀⠀⠀⢀⣴⠂⠞
⠀⠀⠀⢘⣷⡄⠠⢴⣟⡀⠀⠈⠉⢉⣜⣛⣛⣿⠟⠁⠀⠀⠿⠇⠀⠈⠻⣿⣟⠛⢳⣌⠉⠉⠁⠀⢘⣵⠤⠀⣰⣿⡁
⠀⠀⠀⠈⠁⢀⣠⠜⠻⣟⠻⢦⡔⣱⠏⣹⣋⣄⣈⡙⠭⠃⠂⠐⠭⠝⣃⣀⣍⣿⡉⣯⠱⣠⡶⢛⣿⠛⠦⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⠁⠯⠴⠿⠭⠭⠭⠭⠤⠤⠯⠥⠤⠭⠭⠭⠭⠽⠷⠼⠇⠽⠶⠟⠁











⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣖⢲⡖⢶⣖⣒⣒⣒⣒⠒⢲⢲⠒⠒⣒⣒⣒⣒⣶⠖⣲⢒⡶⣤⡀
⠀⠀⠀⢀⡀⠀⠙⠲⣤⣿⣵⠾⠛⢄⣻⣈⣿⣙⠉⢩⡔⢒⠄⠡⢠⣢⣌⠉⠙⣩⣏⣰⢏⠜⠷⣮⣽⣦⡔⠋⠀⢀⡀
⠀⠀⠀⢨⣿⠏⠀⠒⢟⡅⠀⢀⣀⣀⡙⢥⣭⣽⣷⣦⠀⠀⢰⡶⠀⠀⢀⣴⣿⣭⣭⡝⢁⣀⡀⠀⠈⡻⠓⠂⠙⢿⡍
⢀⡴⠡⠟⠁⠀⠀⠀⠀⠀⣠⣟⠉⢡⣴⣆⠀⡀⠀⠀⠗⠀⣈⣃⣀⠰⠏⠀⠉⠁⢀⣴⣍⠉⢹⣆⡀⠀⠀⠀⠀⠀⠙⠆⢲
⠘⠁⠀⠀⠀⠀⣄⣠⣶⢻⡝⠈⡵⠛⠿⡟⠀⢸⢿⣜⠻⣏⠁⠈⢑⡾⢓⣲⣟⠀⠘⡿⠟⠲⡈⠙⡝⢲⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢐⠃⠸⠀⠘⢿⣦⣤⠃⠶⠋⠀⠈⠃⠈⢦⣆⠌⠠⠋⠁⠘⠶⠖⢣⣠⣾⠟⠀⠹⠈⢃⠈
⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠞
⣿⣿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⡸⣿⣧⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣼⣿⢇
⠀⠀⢠⡀⢀⠹⣽⣿⣷⡀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⣾⣿⣯⠟⡀⢀⡄
⠀⠀⠈⣷⡈⢧⡙⠿⣿⣿⣄⠀⢳⣄⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢠⡞⠁⣰⣿⣿⠿⢋⡼⢁⣾⠁
⠀⠀⠀⠘⣿⣦⡙⢦⡈⠙⢟⡷⢦⡙⠦⡙⢦⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡴⢋⡴⢋⡴⠾⡟⠋⢁⡴⢋⣴⣿⠃
⠀⠀⠀⠀⠈⠻⣿⣦⣙⠳⣤⣉⠲⠬⡑⠮⣶⠍⢺⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⠯⣶⠵⢊⠥⠖⣉⡤⠞⣫⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣀⠙⠛⣿⣶⣬⣍⣓⠲⢶⡾⠷⢾⣏⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⣹⡷⠾⢷⡶⠖⣚⣩⣥⣶⣿⠛⠉⣀⠄
⠀⠀⠀⠀⠀⠀⠈⠳⢶⣬⣭⣍⣛⣛⣿⣿⠷⠢⢿⣏⣽⣿⣯⣷⡀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⣯⣹⣿⠷⠾⣿⣿⣟⣛⣩⣭⣥⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠢⣬⣉⣉⣉⣉⣩⣭⡯⠥⢼⡃⢾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡷⢘⣿⠭⢭⣭⣍⣉⣉⣉⣉⣥⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⣭⣭⣭⡥⢶⡶⢮⣥⢟⠙⣿⣿⣿⣹⠦⠀⠀⠀⠀⢴⣏⣽⣿⣿⠏⡻⣭⣵⢶⡶⠬⣭⣭⣭⠥⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢒⡚⣭⣶⣿⢿⣯⡔⡻⢻⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡟⢿⠢⣽⣿⣿⣶⣭⣛⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠩⠭⣺⡟⣽⣿⡷⣧⣏⣹⢾⢇⠀⠀⢸⠷⣏⣙⣼⣾⣿⣿⢻⣷⠭⠍⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⢏⡾⢻⠛⡈⡹⢫⡏⠈⢸⠀⠀⡇⠀⢸⡟⢧⢁⠙⣟⢷⡹⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡴⠛⢁⠏⣼⣿⣷⣿⡱⠀⠌⠀⠀⠁⠀⢇⣿⣾⣿⣧⠸⡄⠙⢦⡉⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣼⣿⣿⢿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣿⣿⣧⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢰⣿⣿⡇⠘⣇⠑⠀⠀⠀⠀⠀⠀⠊⣸⠃⢹⣿⣿⡆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⠹⣿⣷⡀⠘⠂⠀⠀⠀⠀⠀⠀⠰⠃⠀⣾⣿⡏⣇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡄⢧⠻⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⡸⢀⡿⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⠂⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢫⣍⣽⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢛⣿⠿⠙⠛⣉⣹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣎⠹⣶⣶⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡛⡄⠈⠉⠙⠋⠉⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⠀⣌⣹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⣀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⢤⣾⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⣋⠁⠠⡀⠀⠀⠀⠀⠀⠋⠁⢀⠒⠚⠛⠁⡴⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⡗⣀⡈⠀⠀⠀⠀⠀⠀⠖⣡⠆⠀⠀⠐⢁⣾⣽⡿⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⠙⢯⣉⡓⠀⣰⣤⣄⠀⠄⠁⠀⣴⣾⣿⠟⠉⠋⢀⣴⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢀⠀⢰⣯⡾⠋⠀⠀⣀⣾⣿⣿⠇⠼⠀⠀⣾⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢠⡿⠋⠀⠀⠀⠀⠈⢉⣁⣀⡀⠀⠀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡄⠀⠀⣀⣼⠃⠀⠀⣴⣅⡀⢶⣿⣿⠿⠀⠀⠀⣿⣿⠏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣠⠶⣴⣋⡀⡐⠿⣿⣿⣻⡿⣡⣄⠀⠀⣰⣿⠏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣮⣉⣽⣿⣿⡔⣦⠈⠻⢶⣿⣾⣾⣿⠟⣱⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣎⢷⣿⣄⠺⠛⠙⣡⡾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢸⠉⢻⢿⣿⣿⣷⣿⣿⣛⣵⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⠀⠙⢿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣾⣿⣶⣿⠂⢀⣴⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⣿⣿⣿⣷⣶⣟⣿⣿⠟⠛⣇⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡘⢿⣿⣿⣿⣿⣿⣿⣷⣾⠿⣿⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠈⠙⢻⣿⣿⣿⣿⣯⣶⡾⢟⣈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷⣿⣿⡿⣿⡵⠟⠋⣡⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠸⡿⠋⠈⠁⠀⣠⣾⣿⣿⡿⢻⠇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠗⠀⠀⠀⢀⣼⣿⣿⡿⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣠⣾⣿⣿⠟⡰⢋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⣾⣿⣿⡿⣣⢄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠟⠛⠋⠗⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣠⣶⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣼⠿⡟⣿⠶⠂⣶⢦⣀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣴⡟⠋⢀⣽⣄⣤⢠⠀⣿⡏⠀⣀⡀⠀⠀⡅⢀⣿
⠀⠀⠀⣤⣼⣷⣤⣀⢀⣴⣶⣾⣧⣾⠀⠙⠉⠀⢸⣁⣄⡆⢀⡀⠀⠉⠿⠋⡉⠀⢠⠃⣼⣿⣀⣀⣀
⠀⠀⠐⣠⡟⢻⣿⣶⣿⣿⣿⣿⣿⣿⡆⠀⣀⣀⡀⠀⠀⠀⠉⡁⠀⠀⣄⣠⣴⣼⣷⣈⣿⣿⣯⣽⣿⣇
⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⣿⢽⣿⣷⣾⣿⣿⣿⣀⣀⣀⣤⣴⣶⣤⣘⣈⣿⣿⠟⠯⣽⣯⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⡏⠋⣿⣿⢿⣿⣿⣿⠉⠉⣿⣿⣿⣯⣿⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠿⢿⣿⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⣀⣀⣼⣿⣿⣿⣿⡷⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠋⠝⠛⠛⠛⠛⠛⠛⠻⠟⠛⠋⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⡔⠉⠙⡆
⠀⠀⠀⠀⠀⠠⠠⢄⠠⠀⠀⠀⡞⠀⠀⠈⠉⢑⠀⠀⠀⠒⠤⡤⠂⢱⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠢⡀⠀⠁⠀⢄⣼⡠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣨⠔⠁⠀⢰
⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⢐⣿⡭⠏⠉⠉⠁⡆⢈⠁⠢⡀⠀⠀⢠⠃⠀⠀⠀⠈⠢⢤
⠀⠀⠀⠀⠀⠙⠂⠐⠀⡠⠊⠀⢹⡄⠀⢠⠒⢁⠜⠀⠀⠈⠲⣤⣦⣀⣤⡤⠐⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⡛⣆⢀⡱⠘⠤⣤⢄⣤⠶⠊⢻⡁⠀⠈⠉⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠑⠚⠉⠳⣀⡰⠀⠈⢦⠀⠀⠀⡴⠋⠀⠀⠀⢸⢱⠀⠀⢀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠑⢄⠀⠑⠒⠢⡀⠀⡼⠀⢇⠀⡯⠑⡄⠈⢦⡀
⠀⠀⠀⠀⠀⡰⠋⠉⠆⠀⡠⠄⠠⡀⠀⠀⠈⢄⠙⢦⡀⠀⠙⠚⠁⠀⠀⡉⠁⠀⠘⢆⠀⢋⠢⡀
⠀⠀⠀⠁⠉⠃⠀⠀⠘⢸⠁⠀⠀⠑⠤⠄⡀⠄⠁⢀⠈⠓⢤⡀⠀⠀⠀⠑⢀⠀⠀⠈⢧⠈⢆⠘⢆
⠀⡀⢀⡱⡀⠀⠀⠀⢰⣼⠀⠀⠀⠀⠀⢀⡔⠀⠀⡀⠀⠂⠄⡉⠳⢤⡀⠀⢀⠀⠢⡀⠈⢧⠘⡀⠀⢣
⠘⡀⠀⠀⠙⠢⡀⠀⠈⡇⠀⢀⡠⠔⠊⠁⠀⠀⠀⠈⠢⡀⠀⠀⠑⠢⢝⠦⣀⢢⠀⠈⢄⠘⡆⢡⠀⠀⠃
⠀⢱⡄⠀⠀⠀⠈⠑⣶⢿⣖⠛⠀⠐⠒⠒⠤⡀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠈⠪⡳⢧⡀⠀⠡⣽⠸⠀⠀⠘
⠀⡎⠀⠀⠀⣀⡤⠖⠉⠉⠧⠀⠀⠀⠀⠀⣠⠞⠐⠢⠤⣀⡀⠀⠑⢄⡀⠀⠀⠈⠢⡑⡄⠀⢹⠀⠀⠀⡆
⠀⠉⠉⠉⡩⠊⠀⠀⠀⠀⠠⠀⠀⠀⠀⢻⠀⢄⡀⡀⠀⠀⠉⠉⠒⠲⠬⢦⣄⡀⠀⠘⢌⠂⠀⢆⠀⠰
⠀⠀⠀⠀⠀⠀⡠⠶⡄⠀⠀⠆⠀⠀⠠⠜⠀⠀⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠶⢤⡀⠑⡅⠸⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠐⠀⠀⠀⠠⠄⠈⣙⣾⣄⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠉⠉⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⣷⡶⠆⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⢀⣼⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠈⠁⠚⠛⠛⠓
⠀⠀⠀⠀⠀⠘⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀
⠀⠀⠀⠀⠀⠴⣆⠀⠀⠀⠁⣠⣶⡀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⢀⣶⣄⢀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣶⣤⣾⣿⠋⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣿⡟⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢐⡅⠀⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⣻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⢴⣾⣿⣿⡄⠈⠂⠙⠛⠀⠀⠐⠀⠀⠀⠀⠎⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠋⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣐⣀⣀⠀⠀⠀⠀⠀⠀⠋⡿⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣼
⠀⡠⠒⠃⠀⠒⢀⠀⠀⠀⠀⠀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⢀⣾⣟
⠞⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⠀⠉⠉⠤⠤⠤⠄⢀⡴⠒⠒⠒⠠⡀⠀⠀⠈⠃⡀⠀⠀⠀⠄⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⣀⣶⣿⡟⢉
⠂⠒⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⣄⡀⢈⢢⠤⢤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣷⣿⣿⣷⣾⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠐⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠩⢯⣿⣿⢿⣿⣿⣯
⠷⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⠀⡠⠒⠀⠀⠐⢉⣿⡿⠄⠉⠏⠛
⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢵⣤⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣆⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣶⠇
⠀⠀⠀⠀⠈⡟⠒⠠⠀⠀⠀⠣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠉⠉⠙⠧⠀⢀⠀⠀⠀⠒⠤⢤⣿⣿⣿⡇⠀⣿⣇⣠⣴⢅⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠠⣤⡼⣿⣿⣿⣸⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⢈⡄⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠠⠀⠀⠀⠑⠀⢀⡎⠀⠄⠺⠃
⠀⠚⠀⢤⡀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢔⣾⠿⠛⢿⡇⠐⠦⠀⠀⢀⣀⡀⠀⠀⠀⠃⠀⠀⠤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠈⠐⠛⢧⡀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠄⣀⣀⣀⡀⠤⢰⠞⠋⡠⠀⡀⠀⠙⣄⠀⠀⠀⠀⠀⠉⠁⠀⠊⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠁⠀⠀⠀⠀⠀⠀⠀⠸⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠖⠒⠻⣷⢶⣷⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠔⠋⠀⠀⠀⠀⠀⠀⠀⠂⠣⣄⣀⡄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠄⠀⠀⠀⠀⠀⠁⠉⠉⠉⠚⢆⠀⠀⠀⠀⢀⠀⠀⠀⣠
⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠁⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⢸⣇⣸⣀⣠⣾⠿
⠀⠀⠀⢀⡇⠉⠉⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢱⣄⣆⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⣽⣧⣾⣿⣿⡿⠿⠃
⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⢿⣿⣆⡀⠀⡜⠁⠀⠀⢀⣴⣞⡥⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡏⡁⠀⠀⠀⠐
⠀⠀⠀⡀⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⢤⣀⠀⠀⠀⠀⢻⣿⣷⣀⣠⡄⠀⣤⣿⣿⠟⢀⡀⠀⠀⠀⠀⠢⡄⢀⠍⠀⠂⠉⠷⣁⠂⠤
⠒⠀⡉⠁⠀⠈⠀⠀⠐⠄⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠈⠙⢿⣿⡛⠃⢰⣿⣿⣩⠆⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠓⠒
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⣿⣶⣶⣉⡄⠓⢦⣹⣿⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠁⠀⠀⠀⠒⠋⠉⠉⠈⠞⠛⠙⠋⢻⡿⢿⠅⣠⣆⠋⣼⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡴⣡⣾⠋⠀⠀⠀⠀⠀⠈⠳⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣴⡿⣱⡟⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣎⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⡞⡿⢱⡟⣸⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⢳⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡼⣧⡇⡾⠇⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⢷⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⢷⣿⣷⡧⣾⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣿⠈⠻⣽⡇⢿⣄⢹⡆⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣄⡿⣿⣿⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢻⡇⢢⠈⢁⡈⠛⣦⡻⡄⠀⠀⠀⣞⡵⢛⠿⣞⠻⢙⡻⢮⠿⢯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡌⢿⡀⠳⡄⢻⣶⣌⠿⠻⣦⠀⢸⡟⠀⡎⢀⣸⡶⣤⣧⢾⣠⣿⣿⣏⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⣿⣿⣌⢷⡀⡙⢦⣿⠻⡕⢤⡙⢷⣸⡁⠀⢷⣿⣿⣿⣿⠼⢶⣿⣿⡟⡼⢱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠸⣿⣟⢦⣳⡹⣷⡿⠷⢌⠀⠳⠀⢻⣧⡀⠈⠻⡻⣿⣷⣿⣿⣿⡟⡼⣡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠹⣆⠀⠈⠛⠊⠑⣄⠀⠀⠀⣠⢈⣿⡱⡄⡀⠙⢎⠻⢿⡿⢋⣨⣾⣿⠃
⠀⠀⠀⠀⠀⢀⡤⠀⠈⣿⡷⣄⡈⠢⣀⠙⠻⢏⡀⡀⠀⠀⠈⠉⠈⡇⢱⢰⠀⠈⣧⠘⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⣾⡅⠀⠀⠘⣧⡀⣉⡑⠛⠓⠂⠀⠴⢿⡦⡤⢠⠀⠀⣿⣸⣸⠀⠀⣸⢀⣻⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣄⡀⠀⠈⠳⣌⠻⢿⣛⠛⠋⢰⡏⠼⢖⣽⣠⡇⠟⠱⠃⢀⣆⡿⡼⠛⠁
⠀⠀⠀⠀⠀⡀⠘⢿⣿⣿⣿⡶⣾⡷⣦⣉⣿⣶⡈⠻⠿⠟⠋⡵⠃⠀⢀⡤⣊⠞⣵⠃
⠀⠀⠀⠀⠀⠹⣶⣶⣯⡙⠿⠿⣾⣿⠀⠀⡵⠈⣭⡿⠧⠂⠀⡤⢤⣴⣟⣯⡥⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣦⣤⣌⡲⠤⢤⣤⣶⠴⠶⠟⠛⠒⠂⠐⠶⣶⣶⠶⠿⠿⠶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⠶⠾⠟⠛⠻⠿⢶⣶⣶⡶⠶⢒⣒⣿⣿⣿⣶⣶⣖⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠚⠛⣛⣛⣿⣿⣿⣿⣿⣿⡿⠭⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠋⠉⠁⠠⠭⠿⠿⠿⠟⠛⠛⠛⠛⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠋⣉⣷⣖⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠘⠟⠀⢬⣾⡋⠁⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠔⣰⠇⣰⠒⠛⠀⠀⠽⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡖⠀⠀⠀⠈⠉⠠⡄⠀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠎⡻⠁⠀⠀⠀⠀⠀⠀⠸⠿⢿⣿⠻⣾⣳⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢰⣷⣖⠃⠀⠰⡿⣏⣊⠀⠀⠌⢻⡧⠨⢻⣷⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⣴⠎⢻⣧⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢽⣿⢰⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠶⠓⡦⠀⠀⠀⠀⠀⠀⠀⠉⣺⡙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢢⢰⡇⠀⠀⠉⠀⠀⠀⠀⢠⡖⣦⢔⣿⡟⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⣼⣇⣤⠀⠀⠀⡀⠀⠀⠀⡠⠎⡸⠀⠀⠈⢑⡄⠀⠄⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣽⣿⡆⠀⠰⠟⢛⠂⠉⢀⡔⠁⠀⠤⠚⠉⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⢛⣻⡟⠁⠀⠀⠠⠇⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠏⡻⠁⠀⠀⠀⠼⠀⠀⠀⠀⠀⢀⡆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣶⢏⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⡾⠟⠀⠀⠐⠛⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣿⣿⡘⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⣀⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⢸⠃⠀⠀⠠⡀⠰⡀⠀⠀⢓⣶⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⣄⠀⠀⠀⠁⠀⠀⠀⠂⢈⣙⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣠⡜⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠊⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢠⠟⢠⠀⠀⠀⠉⠙⢯⣀⢦⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠄⡀⢁⣄⠲⣽⣷⠦⣿⢳⣔⠏
⠀⠀⠀⠀⠉⠉⠙⠛⠋⠙⠋⠉⠉⠋⠐⠀⠀⣀⣇⠀⠀⠀⠀⠀⡙⣦⠙⢷⠀⠹⡷⢻⠆⠐⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡀⠀⠀⠀⠀⠁⣈⣠⣬⣇⣀⠀⠀⣧⢦⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣷⡿⣟⣿⣿⣄⠰⣻⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠹⣯⠙⢿⣿⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣴⠀⢰⠂⢰⠀⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⠇⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠀⠀⠀⠀⠀⠀⢰

⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄⠀⠸⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⢿⣿⣿⣾⣿⣷⣶⣶⣤⣀⡀
⠀⠀⣠⣶⣶⣶⣤⣤⣄⣀⣿⣿⣿⣿⣿⣷⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣴⣶⣶⣶⣶⣦⣤⡀
⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠹⣿⣿⣟⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣄⣻⣿⣿⣆⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣼⣃⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡿⠩⠂⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡗⠵⠀⠀⠀⠀⣄⡀⠀⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⡄⡠⠀⠀⠀⠀⡄⠈⠆⢸⠛⡡⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠥⡄⠀⠀⣷⣤⠐⢄⣰⢃⡼⠀⠔⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡨⡄⠀⠀⠻⣿⡇⠀⡹⢁⣤⣤⠀⠀⡀⠄⠚⠅⣀⠄⠒⡩⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⢄⡀⠛⡄⠀⠀⠀⢠⢿⡂⢅⠀⠀⠠⢌⠣⣀⢣⣿⣿⠏⠀⠌⢡⠀⢰⢊⡀⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠌⣦⡘⡄⢰⣶⠀⣐⣗⠧⠀⠀⠐⡄⢱⣸⠼⠛⠁⠀⡐⠀⢀⡴⠋⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠑⣆⠀⠁⠀⠃⣿⢎⠄⠀⢀⠜⠁⠀⠀⠉⠐⠒⠇⣀⣼⠤⠐⢒⠞⠀⢀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠤⠀⣈⣤⡀⠘⡟⠪⣷⣂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡔⠋⠀⢠⠁⢀⠌⢀⡠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢧⠀⡷⠊⠀⠇⠀⠀⠀⠀⠀⢀⠄⠒⠒⠄⡀⠀⠀⠈⠐⠤⣴⠖⠃⠒⠮⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠠⠄⡉⠒⠤⠄⡤⠋⠀⠀⠀⡀⠤⠤⠤⠄⣀⡎⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠈⢋⢣⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠥⣦⠊⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⣠⠊⠀⠈⠢⠀⠀⡤⢀⡀⠀⠀⠸⠄⣉⣁⡉
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⣀⢰⠖⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠉⠉⠑⠄⠀⠀⡄⢀⡅⠀⠈⠢⡀⣰⠢⡘⠦⠈⠆
⠀⠀⢀⡤⠒⠫⡀⠀⠀⠱⡄⠀⠈⠑⠺⡀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢣⠀⠀⠶⠂⠀⢠⠗⠈⢡⠀⠀⠀⠘⡅⠣⣈⠄
⠀⡴⢋⡠⠄⠒⠒⠓⣒⣦⠬⠶⣄⣀⡀⢡⡀⠀⠀⠈⠄⠀⠀⠀⠀⡠⠥⡀⠀⣀⠔⠁⠀⠀⡘⠀⠀⠀⠀⢰
⣰⣀⠁⠀⢀⡔⠊⠉⠀⠀⢀⠠⠂⠉⠉⠀⡱⣄⠀⠀⠈⡶⠠⠄⠚⢄⠀⠈⠈⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⠃⢀⣠⡟
⠁⠀⠀⠀⠀⠀⠁⠒⠂⠴⠥⠄⠤⠄⠒⡨⢤⣫⠶⢆⠈⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡤⠊⠁⠀⠀⠀⢀⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣬⢛⡡⠑⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⠀⠐⠒⠂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⢏⠢⠀⠀⢀⠔⠊⠱⢄⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⡟⠌⠊⠀⢀⠜⢁⣀⠤⣴⠋⠉⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡸⡗⡌⠀⠀⢀⠊⠉⠀⢀⠔⡇⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣾⠣⠈⠁⠀⠀⣈⠀⡀⢴⠏⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⣆⣽⢣⠉⠀⠀⠀⠀⡏⠁⠀⠎⠀⠀⡄⠔⠁
⠀⠀⠀⠀⠀⠀⠮⣽⣉⡍⠀⠀⠀⠀⠀⢀⠀⠐⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠰⡰⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⣿⡏⡗⡎⢽⡏⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⣁⡆⠀⠀⣠⡈⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠙⠃⠀⠀⠛⠃⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⣠⣄⣤⣄⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠈⠛⠛⢀⣴⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠔⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⡇⠀⠀⢠⣦⠀⢰⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠙⣷⣌
⣀⣀⣀⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢹⡅⠛⢻⡿⢿⣿⣿⡇⠀⠀⠀⠈⠋
⠻⠿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⢉⡿⠁⠀⠀⠀⠀⠀⠁⠀⢀⠈
⠀⠀⠀⠓⠒⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⣠⡴⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣦⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠠⠀⠀⠀⠬⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠆⣀⠠⠔⠂⠉⠉⠁⠀⠀⠀⠀⠀⠠⠄⠀⡇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠠⠚⠂⠔⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⢠⠀⠰⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢃⠀⠓⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠆⠀⠀⠀⡆⠀⠀⠘
⠀⠀⠀⠀⠀⠈⠳⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠰⢴⢶⠂⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⡀⠀⠁⠀⠀⠀⠰⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡶⠤⢄⣀⣀⣀⣡⠔⡞⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⢀⠀⠀⠀⠀⠀⢀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⢸⠀⠀⣄⠀⡠⣀⡀⠃⢠⠈⠂⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢈⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⡀⠳⡀⠀⠀⠘⠀⠀⠀⠉⠀⠂⠀⠀⠈⡀⠊⠑⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠠⠆
⠀⠀⠀⡀⠀⠀⠀⠀⡱⢤⠞⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠄⠀⠀⠀⠈⠀⠈⠀⠀⠂⠀⠀⠀⠐⠀⠀⢁⠀⠈
⠀⠀⢰⡁⢀⠀⠠⠋⠀⠸⠀⠀⠀⢠⠀⠀⠀⠀⢀⠁⠀⢸⠈⠻⢆⢎⡀⠀⡦⠀⠀⡆⠀⠨⠁⠀⠀⠀⠀⠀⠀⢈⡀⠀⠂
⠀⠀⠈⠀⠘⠂⠀⠀⠀⡇⠀⠀⠀⠀⠃⠤⠄⠀⠊⠀⠀⠈⠀⠀⠈⠉⠀⠸⡡⠀⢉⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠘⡇⡀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠄⠀⠀⠀⠀⠀⠄⠐⠀⢹⠀⠀⠀⠀⠀⠘⠚⠁⠘⠤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠈⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠓⠢⠀⠀⠄⣀⠆⢁⠀⠄⠒⡠⠚⠓⡄⠀⠀⠀⠀⠀⠀⡠⠘⠙⢍⣓⠀⠁⠐⡂⢀⠟⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠸⡒⠀⠀⠑⠀⠀⡨⠀⠸⣤⠤⠔⡂⠂⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠥⡄⠀⠄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢖⣶⣾⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⣴⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣠⡆⣸⣿⣿⣿⠿⠋⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠛⢡⣿⣿⣿⠃⠀⠀⠀⣠⡤⠀⠀⠘⢿⣿⣽⣿⣟⣿⢷⡀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣸⣦⠀⣸⣿⣿⣗⠒⠲⠀⠀⠁⢀⡤⠀⠀⠈⠉⣻⠿⣿⣿⣟⢦⣂⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣼⣿⣿⢠⣿⣿⣿⣿⡷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣧⢿⠄⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠛⣉⡵⣟⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⢺⣷⣿⣿⣿⣿⣿⣿⣿⣦⡠⢖⡳⠆⠀⠀⠀⢀⠀⠀⢻⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢀⣀⡤⠂⠁⠀⠀⠈⢿⣿⣿⣿⣦⣤⡴⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣦⣄⣠⡴⠁⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠲⣿⣿⡆⠹⡝⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠄⠀⠀⠀⣰⣿⣿⣿⡿⣿⣿⡿⠋⠀⠀⠀⠀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠈⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣠⣶⣻⣿⣿⠿⣫⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⢫⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠦⠤⢤⣄⣀⣀⣀⡤⠤⠴⠖⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡩⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⢀⡴⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠐⠿⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⡴⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠿⠿⢿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣷⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⠻⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⣴⡿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⢀⠀⠠⠀⢀⣃⠀⠀⠀⢀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠻⡿⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⡉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⡤⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠀⠀⢀⡤⠚⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠙⠄⠀⠀⠀⢀⢈⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⣄⠀⠀⠀⠀⢀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⠂⠀⡀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠴⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠔⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠄⢀⣄⣠⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠂⠀⡈⠀⠀⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⢠⣄⠀⠉⠉⠁⠁⠀⠀⠚⠃⠠⠀⡀⠀⠀⠂⠴⠒⢃⠀⠑⠢⣄⠐⠀⠀⠀⠈⠢⣀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣓⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣂⠐⢁⣰⠐⡐⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡮⠿⣧⠟⡈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠲⠊⠁⠘⠠⠢⠄⡖⠒⠆⢹⠊⠁⠈
⠀⠀⠰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⣄⠘⠓⢂⠀⠀⢀⡀⣾⣗⠦⢀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⢀⡴⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠐⠀⠀⠀⠀⠘⣏⠑⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣰⡦⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠉
⠀⠀⠀⠀⠀⣀⠩⠉⠀⣀⡿⡄⠀⠠⣤⡄⠀⠀⢀⣄⠀⠀⣀⠀⠀⠀⠀⢠⣄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠤⠛⣿⡆⠀⣤⣾⣷⠟⡴⢾⣿⢀⣠⠾⠋⣠⠁⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⢈⣀⠀⠀⢀⡀⠂⠺⢃⡈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠊⠁⠀⠘⡂⠈⠡⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣀⡤⠶⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣷⣾⣧⣤⣴⣾⣹⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣿⣿⡏⣻⣣⣿⣿⠁⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠾⠿⣿⣿⣷⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡫⡾⣿⣿⣿⣷⡿⠟⣋⣭⣶⠾⢿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⢋⣥⣶⣿⣿⣅⠀⡴⠺⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠿⣋⣤⣾⣿⢿⣿⣿⣿⡿⠀⢿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢟⣵⣾⢟⣿⠟⠁⠀⠙⠛⠋⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⣿⣿⠸⠃⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠋⠀⠀⣶⣿⡂⠀⠠⡀⠀⠀⠀⠀⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⣹⠀⠀⠀⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⢰⣷⠃⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⠈⢿⣷⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⣄⡙⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣶⣍⡻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣦⡙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣮⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇

⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣦⡀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢹⣿⣧⣧
⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⡍⠉⠀⠉⠹⣷⣯⣡⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠸⣿⡏⠀⠁⣤⠀⠀⠀⢠⡄⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⢂⠀⠀⠀⠀⢀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⡀⠹⣦⡴⠃⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⣏⣦⣽⣿⣟⣿⣿⣿⣿⣿⢟⣣⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⠀⡀
⠀⠀⠀⠀⠀⢸⣯⣍⣙⠛⠿⣿⣿⣿⣿⡿⠟⠛⢉⣡⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣉⠀⠀⢀⡀⠀⢀⡠⠄⠂⠀⣀⠠
⠀⠀⠀⠀⠀⠀⠈⣽⣿⣿⣶⣤⣌⣉⣡⣤⣶⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠐⠠⢄⣀⣁⠠⠔⠊⠭⠴⠂
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⠛⠛⠛⠛⠉⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⣀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⢿⣟⣯⣷⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣛⣛⠿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⠴⠚⠁⠀⠀⠙⢆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢠⡆⣤⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡛⢀⠔⠀⠀⠀⠀⢤⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢄⠀⠐⠁⠀⠀⠘⠁⡀⠀⠒⠲⢄⢀⠠⠀⠀⡥
⠀⠀⠀⠀⠀⠀⠣⣀⠂⠠⠆⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠡⠈⣿⣵⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠳⢄⠤⣤⣀⣁⠐⠤⠀⠐⢞⣻⠎⡁⠀⢭⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠠⠅⠀⣼⣿⡿⠀⠒⢄⠀⠀⠉⡆⠈⠀⠀⠉⠸
⠀⠀⠀⠀⢀⠄⠀⠀⠼⠀⠀⠀⠐⢇⠀⠋⠹⠁⠀⠀⠀⠑⠀⠁
⠀⠀⠀⠀⠂⠀⠀⢀⡜⠒⢀⣤⡂⠀⠀⠀⢰⡀
⠀⠀⠀⠁⠀⠀⠁⢁⣤⣴⠊⢨⠀⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠁⡾⠆⢀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠲⠀⠈⠀⠰⠀⠀⠀⠀⢰⠄⡃⠰
⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠈⠂⠤⣤⣷⣠⠀⠀⠀⢐⠂⡀⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⢠⠰⠆⠀⠀⢀⢿⣾⡯⠓⠒⢀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡐⠀⡀⢈⠠⠁⠀⡏⡐⠒⠠⢀⣰⠿⡐⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠈⠆⢘⠀⠳⡀⠀⣰⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢢⠀⠀⠀⠴⠐⠀⢠⠃⠀⡬⣿⣹⠶⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠈⠀⠁⠢⣤⡷⠛⣮⣀⠤⠚⡁⢀⡄⠀⠀⠻⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠰⠄⠱⠤⢴⣀⡀⠠⢽⣷⣤⡿⣇⠀⠀⠀⢨⠃⢶⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⡄⠒⠁⣘⢹⡀⢀⠀⠀⡘⠙⠀⠘⢆⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⣀⠠⢶⠻⠠⠂⣡⠀⡛⠰⠀⠈⢃⡀⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠀⠀⠸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⣷⠀⠀⢰⠋⠉⠙⡄⢠⠖⠒⠒⠒⠒⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⣿⣿⣿⡆⠀⠘⠛⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⢸⣿⠀⠀⠘⢄⣀⡠⠃⢸⣀⣀⣀⣀⣀⣀⡇⠀⡶⠶⠶⠶⠶⠶⢶⠄⠘⢷⣶⡿⠟⠛⠁⣴⣿⣿⣷⡀⠀⠈⠻⣦⡀⢀⡼⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣬⣽⡄⠀⢠⣾⣿⣷⡄⢸⣛⣿⣻⣟⣿⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⢸⣿⣿⣿⣿⣷⠀⣠⢤⣬⡿⣿⣁⡤⣄⠀⠀⠀⣿
⠀⠀⠀⠸⣿⣿⡇⠀⠹⣿⣿⡿⠃⠸⣭⣿⣽⣯⣿⣭⠇⠀⠶⠶⠶⠶⠶⠶⠶⠆⠀⠈⠿⠿⠃⠀⠘⠿⠿⠿⠿⠛⠀⠳⠶⠋⠀⠀⠙⠷⠞⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠸⣿⣿⣆⠀⢀⡏⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⣠⣾⣶⣾⣦⡄⠀⠀⢸⢿
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⡄⠹⣿⣿⣆⠈⣧⡀⢀⡼⠀⣶⣶⣶⣶⣶⣶⣆⡀⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⡇⣤⠀⣼⣿⣿⣿⣿⣿⣿⡄⠀⠀⣀⣀
⠀⠀⠀⣼⣧⣿⠀⠀⢰⡆⢽⡇⠀⠹⣯⠁⠀⠈⣿⣏⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⠃⡟⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⡟
⠀⠀⠀⠉⠈⠉⠀⠀⠸⠇⢿⠇⠀⠀⠹⣧⠀⠀⢿⡟⠀⠀⠛⠛⠛⠛⠛⠛⠛⠁⠈⠉⠉⠇⠀⠀⠀⠙⠛⠋⠀⢈⣃⡀⠹⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⢀⡀⠀⣠⣤⡀⠀⢀⣠⡆⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⡀
⠀⠀⠀⢀⣀⣿⣿⣧⣀⠀⠀⠀⢠⣀⣀⡅⠀⠀⠀⠀⢰⣤⠀⠸⣿⠃⠀⣸⣿⡇⠀⢠⣴⠋⠀⠀⠈⢳⣤⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⡞⠀⠀⠀⠀⠘⡆⠀⠀⢸⠛⠛⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⠞⠛⠣⠀⠸⣿⡄⠀⠀⠀⣸⡿⠀⠀⣿⡿⠿⠀⠀⡴⠶⠆⠀⠶⠦⡄⠸⣿⡿⠃
⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢰⣶⣶⣶⠀⠀⠙⢿⣷⣒⣾⠟⠁⠀⠀⣿⡇⠀⢠⠊⠉⠑⢄⢀⠔⠉⠉⠢
⠀⠀⠀⣇⣀⣀⣀⣀⣀⡇⠀⠀⢺⣀⣀⡇⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⣿⣿⣿⠀⠀⠀⢀⣀⣯⣀⡀⠀⠀⠀⣿⡇⠀⠸⡀⠀⠀⡝⠙⣇⠀⠀⣠⠃⡀
⠀⠀⠀⠈⣡⣤⡄⠀⠉⠀⣤⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠈⠛⠛⠛⠀⠀⠀⠈⠉⠉⠉⠁⣤⠀⠀⠈⠀⠀⠀⠈⠉⠁⠀⢀⣈⠉⠉⠀⢠⡟
⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢹⠀⠀⠀⠀⣠⣶⣷⣶⣄⠀⠀⠀⢰⣿⠛⣿⠛⢻⡇⠀⠀⠀⣀⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢸⣿⡂⠀⠀⠀⡝
⠀⠀⠀⣠⣿⣿⣿⣄⠀⠀⢸⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⡀⠸⣿⠛⣿⠛⢻⡇⠀⣴⠿⣹⢟⣳⣆⠀⣿⠀⠀⠀⢀⣴⣷⣾⣦⡀⠀⢸⣿⡇⠀⠀⢠⣶⡄
⠀⠀⠀⣿⣿⣿⣿⣿⠀⣶⣿⣷⠆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠛⣿⠛⢻⡇⠰⣿⢿⢿⣳⡿⣿⠀⣿⠀⣶⠀⣾⣿⣿⣿⣿⣿⠀⢸⣿⠇⠀⠀⢸⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⠀⢿⣿⣿⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠀⢰⣿⣿⣿⣿⣿⡇⠀⠙⢯⣶⣽⠾⠋⠀⣿⠀⣿⡀⢿⣿⣿⣿⣿⡿⠀⢸⣿⠁⠀⠀⠸⣿⠃
⠀⠀⠀⠉⢉⣋⢉⡁⠀⠈⠉⠉⠀⠀⠈⠉⠉⠉⠉⢉⣁⣀⣀⣀⣛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠉⠉⠉⠉⣤⣄⠀⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠄⠀⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠸⠿⢿⣿⣿⣿⠿⠇⠀⣰⣶⣄⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⢸⣿
⠀⠀⢀⣴⣶⣶⣶⣤⡀⠀⠈⢳⣄⢀⡴⠋⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⠤⠾⠿⠿⠿⠤⢤⡀⢻⣿⣿⣦⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⣸⣿
⠀⢠⣿⣿⣿⣿⣿⣿⣷⢀⡴⠲⣽⣿⡵⠲⣄⠀⢈⣉⣉⣉⢉⡉⢉⣉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠈⣟⠉⢻⣷⣄⡀⠈⡉⠉⠀⠀⠀⠀⠀⣿⣿
⠀⠘⣿⣿⣿⣿⣿⣿⣿⠈⢦⣤⠞⠘⢦⣤⠏⠀⠙⡟⠙⡏⢹⡏⠘⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠹⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⣿⣿⠄
⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡇⠀⡇⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠚⠛⠁⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉
⠀⠀⢰⠛⣿⠒⣶⠒⣾⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠛⠛⠛⠛⢻⣿⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠚⠿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠂⠐⠒⠒⠒⠒⠒⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠰⠦⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⣉⣄⣠⡀⠁⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣼⡏⠉⠉⠛⣷⡄⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⢻⣦⣤⠄⠀⠘⣧⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⢀⡿⢀⣴⠾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣟⠐⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣶⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢰⡿⠋⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢷⣄⠀⣿⠁⠀⠘⠦⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡁⢙⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢠⣶⠿⠿⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢻⣏⠀⠀⢀⠹⣷⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⣈⠙⠛⠁⡰⠂⣿⠀⠀⠀⣠⡤⠞⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠟⢰⡇⠓⠀⢀⡿⠀⣠⠟⣩⠖⠛⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠁⠂⠀⣾⠃⣼⣣⠞⡕⢺⠇⣧⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢀⠖⠁⠀⠈⠛⠀⠀⠈⣸⣾⣏
⠀⠀⠀⠀⣀⣀⣤⠤⠤⠶⠦⠶⣤⣄⡀⠀⠀⠀⠙⣶⣦⣴⡿⠀⠀⠀⠀⠘⢃⣼⠟⠉⠀⠈⠳⢄
⠀⠀⠀⠀⠙⢿⣄⠰⣖⢛⡿⣶⢶⣬⣇⠀⠀⢀⣀⣽⣿⣿⡷⢦⣤⠶⠖⠋⠛⢿⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠛⣷⡈⠫⡻⣄⡈⠉⢛⡷⠀⠉⠁⠉⢻⡏⠁⣾⠁⠀⠀⠐⠀⢼⣿⣆⣤⣤⣶⠷⠚⠓⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣌⠊⠗⣦⣌⠀⠀⠀⠀⠀⣈⡳⠂⠉⠀⠂⣤⣤⣴⣾⣿⣏⣹⣿⡿⠂⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠆⠉⠘⢦⡀⠀⡀⣤⡿⠁⠀⠀⠀⠀⠁⠈⠙⠛⣻⣿⣿⣿⣷⣄⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⢿⣿⣂⠠⠤⠤⢤⡁⢀⠊⠉⠁⠀⠙⢯⡀⠙⢣⣤⣜⣓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢚⣿⠶⣿⣏⡿⠀⠀⠀⠀⠙⢬⡄⠀⠀⠀⠀⠀⠉⠀⠀⠛⢉⠻⢿⠦⡙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢻⣌⡇⠀⠀⠀⠈⠀⣸⣷⠀⠀⠀⣀⡀⠂⠠⣶⣁⠦⠤⠴⠴⠙⣣⡘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⣿⠗⣀⡀⣤⣤⣤⣼⣿⡷⢿⣾⠉⠀⠀⠀⠀⢩⣤⣥⣉⣉⣉⣉⣥⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⢻⡄⠀⠀⠀⣠⣳⠞⠉⠁⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢡⠉⠈⠉⠁⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢁⡼⣻⠟⠁⡋⢃⡤⡆⠀⠀⠀⠀⠀⠀⢸⡿⠁⢻⠿⣦⡀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⡿⢱⣯⣴⠶⠟⡫⠜⣣⡀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠀⠈⠟⡹⢿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⠧⠖⠒⠒⣉⣡⣴⠞⠛⠁⠉⠒⠀⠂⠹⠀⠀⠀⠀⠀⠀⠈⡅⠉⢋⢷⡹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣠⣤⣴⡶⠾⠿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⠀⢀⣤⣾⡓⢦⣈⡌⣧⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠙⢷⣝⠦⣍⡃⣿⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣮⣙⠛⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⢀⡞⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠓⠢⡀⠀⢧⣯⠎⠀⠀⠀⢀⡴⠊⠁⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣉⠓⢾⣆⢸⡏⠀⠀⠀⣠⣫⠖⣉⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠉⠉⢺⡇⠀⠀⣠⠟⣛⡭⠤⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠉⠑⣄⠀⠘⡇⠀⣴⣡⣾⣓⡚⠉⢀⣠⠞
⠀⠀⠀⠀⠀⠀⣞⠉⠉⢉⡒⠦⢄⡘⢆⠠⡘⡄⠀⣧⣸⠋⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡈⠙⠲⢭⣪⡓⢽⣇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠺⠿⢦⡘⡄⠘⡇⠀⠀⠀⠀⠀⠀⢀⠔⠉⣀⠄⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣄⡀⠀⠀⠀⠈⠻⡀⡇⠀⠀⠀⠀⠀⡰⢋⡤⠚⣁⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠒⠦⢍⡳⣄⠀⠀⠀⢹⡇⠀⠀⠀⣠⠾⠟⠛⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠦⠤⠭⣾⡆⠀⠀⠀⡇⢀⣴⠮⠥⠤⣶⡾⠭⠍⠉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢰⣧⠋⠀⠀⠀⠀⠀⠉⠓⠲⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠩⢵⣦⡘⡆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠳⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⢀⣀⣀⣀⣀⣀⡄
⠀⢀⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣄⡀
⢰⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀
⢸⣿⣿⣿⣿⣶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠛⠛⠛⠟⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿
⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠸⠋⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠶⢤⣀⡀
⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣤⣬⠁⡀⣹⡦
⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣾⣿⣿⣤⡄⢈⠀⣀⡀
⠀⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡰
⠀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠛⠻⢿⣿⣿⢿⣿⣿⣄⡀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠄⠠⢍⠛⠿⢿⣿⣿⣿⣿⣟⠋
⢸⣿⣿⣿⣦⣶⣶⣾⣷⣦⣄⠀⠀⠀⠈⢀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣁
⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⢰⣿⡟⠛⢿⣿⡟⠉⠉⢻⣿⣿⣷⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠈⠉⠀⠀⣾⣿⠇⠀⠀⠈⠛⠋⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠘⠻⠿
⠀⠀⣠⢈⡙⠛⠁
⠀⢴⣿⣿⣷⣦⣦⣤⣼⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣀⣀⣀⣽⡻⣿⣿⣿⣿⣿⣷⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣀
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠉⠾⠿⠿⠿⠋⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁
⣿⣿⣿⢿⣿⠿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣦⣶⣷⣶⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣪⠵⢒⣋⣙⣻⣶⠂⠀⠀⢬⠍⠙⠛⠗⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⡎⠜⠁⠞⣁⠤⠔⠺⠃⠀⠀⠀⠀⠀⠀⠀⣀⣠⣁⠻⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡯⢄⠸⢋⠗⠀⠀⠈⠀⣒⣒⣾⡀⠀⠀⠢⣄⣀⡤⢞⠕⠈⠉⠱⠟⡌⢳⣄
⠀⠀⠀⠀⠀⠀⡀⣐⠹⣄⢃⠀⠀⠀⠀⡆⠀⠀⣾⠁⠰⠙⣇⠀⠀⠀⠀⠈⠦⡘⡇⡄⠃⢀⠻⠢⠓⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠉⢤⠳⠶⠚⢀⣠⢠⠇⠀⣼⢤⠀⢀⠞⢿⣆⠀⠀⠈⢦⡀⠈⠑⠳⣄⣴⣿⡀⢂⢙⠉⠁⡤
⠀⠀⠀⠀⢸⡄⠀⠀⣐⢲⢳⡶⢿⣤⡁⠰⡖⢲⠼⡄⠸⠃⠈⡟⣆⠀⠀⠀⠈⠀⠀⠀⠀⠑⢾⠊⣤⢘⠖⠢⡀⠃
⠀⠀⠀⢀⡿⣅⣐⣁⡉⠐⠈⢘⠂⣊⢎⠂⠀⠀⣶⠃⠀⢧⠀⠄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢠⠀⠀⣀⠳⡸⣄
⠀⠀⠀⣎⠔⠉⠀⠀⠙⢶⠀⠈⠀⠉⣼⠲⡶⠚⠁⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠃⠀⣤⠜⢣⠑⠈⠆
⠀⠀⢠⠁⠀⢠⢞⣩⡵⡌⢆⢀⣤⠞⠏⢁⣘⣧⣠⣤⣤⡤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠜⢄⠈⡆
⠀⠀⡆⠀⢠⠃⣾⠁⠀⠀⣨⣻⣅⡼⠋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⣣⠎⠀⡴⣁⡇
⠀⠀⡇⠀⢸⠀⢻⠰⠄⢄⠻⢳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡤⠖⠉⠁⠀⠀⢆⡨⢁
⠀⠀⢸⡄⠈⠄⠀⠳⡀⢘⢧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣷⠀⠀⠀⠀⠠⡉⠢⣿
⠀⠀⠈⣷⢄⡀⠀⠀⠸⡌⠋⢿⠀⡀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣠⣤⣤⣤⣀⣀⣠⡤⠖⢫⡁⢀⠅⢴⡶⠞⠀⠀⣙⣾⠇
⠀⠀⠀⢻⡀⠉⠢⡀⠀⢹⠀⠈⢧⡙⢄⡀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⢰⠀⠀⠉⠀⠀⠉⠁⡄⠠⠂⢁⣠⣤⠘⢲⠋
⠀⠀⠀⠈⣧⡀⠀⢑⡀⠈⠁⠀⠀⠙⠶⢤⣀⡀⠀⠀⠀⡞⠀⠀⢀⠤⠈⠁⠀⠀⢰⠘⠖⣺⡇⠀⠐⠀⠘⢀⢐⣡⠂
⠀⠀⠀⠀⠘⢿⣆⠘⠁⠸⡀⠀⠤⠀⠀⠀⡁⠈⡆⠀⡸⠁⠀⠀⢃⡔⠒⢢⡀⣠⡏⣰⠞⢁⠗⢊⣈⡉⠣⠈⠐⠁
⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⣟⠲⠒⠁⡔⠁⢠⠾⠄⠀⡇⠀⠀⠀⠸⡀⠀⠀⠻⣿⠰⠋⢀⡴⠚⠒⢦⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠸⡆⠀⠀⠘⢦⡘⠦⢀⡀⠳⡀⠀⠀⠀⢉⡁⠀⠀⢫⣷⣶⠯⠴⣦⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠯⣭⣉⡳⢦⣅⣌⠢⠉⣢⣙⠴⣄⢀⣈⡤⠔⠊⠁⠁⠁⠀⢦⠞⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢤⣈⠋⠿⣱⣆⡈⠛⣿⠶⠢⡀⢀⣠⠀⠂

⠀⠀⠀⠀⠁⠀⢤⣧⣤⣀⡀⠀⠤⡃⠀⠿⣿⡷
⠀⠀⠀⠀⠀⠉⠿⢿⡿⠏⠀⠀⠐⠚⠁⠀⢸⡇
⠀⠠⡄⠰⡂⣠⠀⠀⠀⠀⠀⠈⠙
⠀⠈⠹⠀⠀⠨⠀⢰⡀⠆⠀⠉
⠀⢀⣰⣀⡀⠀⠀⢀⡡
⠐⢲⣿⣿⣿⠉⠀⠀⠸
⠀⠀⠀⠉⠀⠀⠀⠒⠆⢀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣤⣾⣇
⠀⡇⠀⡄⢠⡀⠐⠒⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠛⡆⠀⠀⣀⠄⠉⢻⡏
⠀⠀⠀⠉⠈⠠⢦⣀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠎⠀⢀⡀⠸⠃
⠸⣿⣶⠯⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠈⠛
⢀⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⣠⣀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣾⡃⠀⠈⢐⣆⠘⡀⢴⡀⠠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢀⠄⠉⢻⡇⠀⠀⠀⠸⠀⠀⠈⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠀⠸⠃⠈⠀⠠⣼⣤⣀⠀⠀⠠⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢀⡀⢄⠀⠀⠀⠈⢹⡿⣿⠿⠉⠀⠀⠘⠂