⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠉⠉⠁⠀⠀⠀⢀⣀⠤⠟⠛⠉⠉⠐⠒⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠙⠦⠤⠀⣀⡀⠀⠀⠀⢀⡞⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⡇⠀⠀⡄⠀⠀⠀⢀⣀⣀⣉⣉⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡠⠚⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣀⣠⡧⢶⠆⡇⠀⠀⠉⠀⣿⣤⠀⠀⢹⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀
⠀⡠⠊⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⣀⠤⣴⠞⠉⠁⢠⠏⡇⢸⠀⢰⠀⠀⠀⠀⣿⣿⡄⠀⠀⢧⠘⡆⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⢣⠀⠀⠀⠀⢣⠀⠀⠀⠀
⠘⠁⠀⠀⠀⢀⣤⠋⠀⠀⠀⣀⡤⠔⠊⠉⠀⡴⡿⠀⠀⢠⢯⠆⡇⢸⠀⢸⠀⠀⠀⠀⠙⢸⠹⡄⠀⠸⣆⠸⡄⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⢧⠀⠀⠀⠈⣆⠀⠀⠀
⠀⠀⢀⡤⠚⢩⠃⣀⠞⠚⠉⢠⠃⠀⠀⠀⡼⢡⠃⠀⢀⠏⠀⠀⠃⢸⣇⠈⡇⠀⠀⠀⠀⢸⠀⢳⡀⠀⢏⢧⠹⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⢇⠀⠀⠀⠸⡀⠀⠀
⠀⠚⠁⠀⢀⡟⢉⠏⠀⠀⢀⡏⠀⠀⠀⣸⠁⡼⠀⢀⡞⠀⠀⠀⢸⢸⠘⡆⢧⠀⠀⠀⠀⢸⠀⠀⢣⣀⣸⡀⢳⡱⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠘⡆⠀⠀⠀⣇⠀⠀
⠀⠀⠀⠀⡼⠀⡞⠀⠀⢠⡾⠀⠀⠀⢠⠃⢀⣧⠤⡾⠓⠛⠛⠀⠸⣾⠀⠘⣾⠀⠀⠀⠀⣾⠀⠀⠈⢯⠉⡏⠉⢻⡦⢤⡀⠀⠀⠀⠀⢸⣧⠀⠀⢹⠀⠀⠀⢹⠀⠀
⠀⠀⠀⢠⠃⡼⠀⠀⢀⡎⡇⠀⠀⠀⡎⠒⢻⠁⢠⠁⠀⠀⠀⠀⠀⣿⠀⠀⠹⣇⠀⠀⠀⢻⠀⠀⠀⠈⢣⣱⠀⠀⢳⣄⠈⠑⠂⠀⠀⠀⢏⢣⠀⠀⡇⠀⠀⢸⠀⠀
⠀⠀⠀⣸⢠⠃⠀⠀⡼⢰⡇⠀⠀⢸⠃⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⡄⠀⠀⢸⠀⠀⠀⠀⠈⢻⡆⠀⠀⠻⡄⠀⠀⠀⠀⠀⢸⡈⢇⠀⢸⠀⠀⢸⠀⠀
⠀⠀⠀⡇⡾⠀⠀⢠⠇⢸⡇⠀⠀⡞⠀⠀⡟⣴⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢳⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠹⡀⠀⠀⠀⠀⠈⣷⡜⡄⠘⡀⠀⢸⠀⠀
⠀⠀⠀⣧⠇⠀⠀⣼⠀⢸⡇⠀⢠⡇⠀⢸⠁⡟⠀⠀⠀⠤⠤⠤⠄⠀⢃⠀⠀⠀⠈⣆⠀⢸⠀⠀⠊⠉⠉⠉⠉⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⡇⢱⡰⠀⡇⠀⣸⠀⠀
⠀⠀⠀⢹⠀⠀⠀⡇⢀⡏⡇⠀⢸⠃⠀⣿⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣼⠀⠀⠀⠀⠘⡄⢸⠀⠐⠿⣷⣶⣶⣶⣶⣶⣦⣤⣴⢧⠀⠀⠀⠀⣇⣀⣳⠀⣷⠀⡟⠀⠀
⠀⠀⠀⢸⠀⠀⢰⠁⣸⠀⢣⠀⢸⠀⠀⡏⣇⠻⢿⣻⣿⠿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠹⣼⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠊⢹⠈⢧⠀⠀⠀⡇⠀⢹⣇⢹⠀⡇⠀⠀
⠀⠀⠀⢸⠀⠀⢸⢀⠇⠀⠸⡄⢸⠀⢸⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣼⠀⣼⣆⠀⢀⡏⠁⢸⠙⣾⢰⠀⠀⠀
⠀⠀⠀⠀⡆⠀⡿⣼⠀⠀⠀⢇⢸⠀⢸⢸⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⡇⠸⡄⢸⠃⠀⢸⢀⢹⣾⠀⠀⠀
⠀⠀⠀⠀⢷⠀⣇⡇⠀⠀⠀⠸⡾⡆⡾⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⠀⠀⣵⣸⣀⠴⠃⢸⠀⡏⠀⠀⠀
⠀⠀⠀⠀⠸⡀⢿⠀⠀⠀⠀⠀⢱⡁⣿⢸⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡇⠀⠀⡟⠻⠁⠀⠀⠈⠀⣇⠀⠀⡀
⠀⠀⠀⠀⠀⢧⢸⠀⠀⠀⠀⠀⠀⣣⣏⣿⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣀⣀⣈⠉⢲⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⡼⠀⠀⢠⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠙⣾⠉⠉⠉⠁⠀⠀⠈⠧⢸⡀⠀⠀⠀⡏⠙⡖⠦⢤⣀⡀⠀⠀⠀⠀⠀⠈⠶⠋⠀⠀⠀⣀⣠⠤⡞⠉⠀⣾⠃⠀⢠⢿⠇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⡇⢠⡇⠀⠀⠀⠙⡟⠒⠢⢤⡤⠤⠤⠔⠒⠊⢹⠁⠀⠀⡇⠀⠀⡟⠀⣠⠃⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡄⠀⠀⡇⢸⠀⠀⠀⠀⠀⣧⣠⡤⣼⡀⠀⠀⠀⠀⠀⣼⠒⠦⢤⡇⠀⣼⠁⡴⠁⠀⣼⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢧⠀⠀⡇⢸⠀⠀⠀⢀⡼⠋⢰⣦⠟⠃⠀⠀⠀⠀⠀⠙⢦⠆⠀⠙⣶⣧⠎⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡆⠀⡇⣞⢀⣠⠔⢫⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣴⠏⠀⠀⠀⠀⢰⠃⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡤⠒⣆⠀⠀⠀⠀⠀⡇⠀⠀⠹⣰⠃⣿⣹⡄⠀⠈⢣⡀⣿⡤⠔⠒⠚⠓⠒⠢⣴⢏⣠⠔⠋⡟⠀⠀⠀⠀⠀⣼⣿⣾⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢦⢾⡀⠀⠀⠀⢀⡇⠀⠀⠀⢻⣅⡿⣷⢳⡀⠀⠀⠙⡏⠀⠀⠀⠀⠀⠀⣰⠛⠉⠀⠀⡼⠀⠀⠀⠀⠀⢀⡿⠛⣉⣽⡆⠀⠀⠀⠀⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢣⠀⠀⠀⢸⡇⠀⠀⠀⢸⢹⣧⣻⣧⢣⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠃⠀⢀⣤⣾⠃⠀⠀⠀⠀⠀⡼⠚⠉⠀⠀⠘⢆⠀⠀⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⣇⠀⠀⡘⢳⠀⠀⠀⠈⣾⢻⣿⣻⣏⢧⠀⠀⢹⠀⠀⠀⠀⣰⢃⣤⣺⠟⣻⠇⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠳⣤⡗⢻⠀⠀⠀⠀⡏⠀⢻⣷⣿⣯⢧⠀⢸⠀⠀⠀⣴⣛⠵⣫⢔⣫⡟⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡜⢀⣀⡀⢀⡠⢹⡉⢻⠀⠀⠀⠀⡇⠀⠀⠹⣿⣿⣯⣷⣸⠀⠀⣼⣛⣵⣫⣶⠿⢻⠃⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡀⠀⠀
⠀⠀⠀⠀⠀⠀⡎⠀⠉⠀⠉⠙⢦⣰⠃⢸⡇⠀⠀⠀⢻⠀⡸⠀⠹⣿⣟⢿⣿⡄⣼⣻⣿⠟⠋⠀⠀⡸⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢹⣇⢸⣧⡶⡀⠀⠘⣤⠇⠀⣀⠨⢿⣮⢻⣿⡿⠟⠒⠒⠒⠤⣀⡇⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀
⣇⣿⠘⣿⣿⣿⡿⡿⣟⣟⢟⢟⢝⠵⡝⣿⡿⢂⣼⣿⣷⣌⠩⡫⡻⣝⠹⢿⣿⣷
⡆⣿⣆⠱⣝⡵⣝⢅⠙⣿⢕⢕⢕⢕⢝⣥⢒⠅⣿⣿⣿⡿⣳⣌⠪⡪⣡⢑⢝⣇
⡆⣿⣿⣦⠹⣳⣳⣕⢅⠈⢗⢕⢕⢕⢕⢕⢈⢆⠟⠋⠉⠁⠉⠉⠁⠈⠼⢐⢕⢽ reserved spot for ads Contact through
⡗⢰⣶⣶⣦⣝⢝⢕⢕⠅⡆⢕⢕⢕⢕⢕⣴⠏⣠⡶⠛⡉⡉⡛⢶⣦⡀⠐⣕⢕
⡝⡄⢻⢟⣿⣿⣷⣕⣕⣅⣿⣔⣕⣵⣵⣿⣿⢠⣿⢠⣮⡈⣌⠨⠅⠹⣷⡀⢱⢕ Comments
⡝⡵⠟⠈⢀⣀⣀⡀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣼⣿⢈⡋⠴⢿⡟⣡⡇⣿⡇⡀⢕
⡝⠁⣠⣾⠟⡉⡉⡉⠻⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣿⣦⣥⣿⡇⡿⣰⢗⢄
⠁⢰⣿⡏⣴⣌⠈⣌⠡⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣉⣉⣁⣄⢖⢕⢕⢕
⡀⢻⣿⡇⢙⠁⠴⢿⡟⣡⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣵⣵⣿
⡻⣄⣻⣿⣌⠘⢿⣷⣥⣿⠇⣿⣿⣿⣿⣿⣿⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣷⢄⠻⣿⣟⠿⠦⠍⠉⣡⣾⣿⣿⣿⣿⣿⣿⢸⣿⣦⠙⣿⣿⣿⣿⣿⣿⣿⣿⠟
⡕⡑⣑⣈⣻⢗⢟⢞⢝⣻⣿⣿⣿⣿⣿⣿⣿⠸⣿⠿⠃⣿⣿⣿⣿⣿⣿⡿⠁⣠
⡝⡵⡈⢟⢕⢕⢕⢕⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⠿⠋⣀⣈⠙
⡝⡵⡕⡀⠑⠳⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢉⡠⡲⡫⡪⡪⡣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⢉⣩⠽⠟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠄⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⣀⣤⠴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡄⢀⡴⠚⠉⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠹⡏⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢬⣳⣄⣠⠤⠤⠶⠶⠒⠋⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢃⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠮⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡤⡴⠃⠈⠦⣀⠀⠀⠀⠀⠀⠀⢀⣷⢸⠀⠀⠀⠀⢀⣀⠘⡄⠤⠤⢤⠔⠒⠂⠉⠁⠀⠀⠀⠑⢄⡀⠀⠀⠙⢦⡀⠀⠀⠀
⠀⠀⠀⠀⣼⠃⠀⠀⢠⣞⠟⠀⠀⠀⡄⠀⠉⠒⠢⣤⣤⠄⣼⢻⠸⠀⠀⠀⠀⠉⢤⠀⢿⡖⠒⠊⢦⠤⠤⣀⣀⡀⠀⠀⠀⠈⠻⡝⠲⢤⣀⠙⢦⠀⠀
⠀⠀⠀⢰⠃⠀⠀⣴⣿⠎⠀⠀⢀⣜⠤⠄⢲⠎⠉⠀⠀⡼⠸⠘⡄⡇⠀⠀⠀⠀⢸⠀⢸⠘⢆⠀⠘⡄⠀⠀⠀⢢⠉⠉⠀⠒⠒⠽⡄⠀⠈⠙⠮⣷⡀
⠀⠀⠀⡟⠀⠀⣼⢻⠧⠐⠂⠉⡜⠀⠀⡰⡟⠀⠀⠀⡰⠁⡇⠀⡇⡇⠀⠀⠀⠀⢺⠇⠀⣆⡨⢆⠀⢽⠀⠀⠀⠈⡷⡄⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠁
⠀⠀⢸⠃⠀⠀⢃⠎⠀⠀⠀⣴⠃⠀⡜⠹⠁⠀⠀⡰⠁⢠⠁⠀⢸⢸⠀⠀⠀⢠⡸⢣⠔⡏⠀⠈⢆⠀⣇⠀⠀⠀⢸⠘⢆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⡜⠀⠀⢀⡜⡞⠀⡜⠈⠏⠀⠈⡹⠑⠒⠼⡀⠀⠀⢿⠀⠀⠀⢀⡇⠀⢇⢁⠀⠀⠈⢆⢰⠀⠀⠀⠈⡄⠈⢢⠀⠀⠀⠈⣇⠀⠀⠀⠀
⠀⠀⢸⡀⠀⢰⠁⠀⢀⢮⠀⠇⡜⠀⠘⠀⠀⢰⠃⠀⠀⡇⠈⠁⠀⢘⡄⠀⠀⢸⠀⠀⣘⣼⠤⠤⠤⣈⡞⡀⠀⠀⠀⡇⠰⡄⢣⡀⠀⠀⢻⠀⠀⠀⠀
⠀⠀⠈⡇⠀⡜⠀⢀⠎⢸⢸⢰⠁⠀⠄⠀⢠⠃⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⣶⣿⡿⠿⡛⢻⡟⡇⠀⠀⠀⡇⠀⣿⣆⢡⠀⠀⢸⡇⠀⠀⠀
⠀⠀⢠⡏⠀⠉⢢⡎⠀⡇⣿⠊⠀⠀⠀⢠⡏⠀⠀⠀⠎⠀⠀⠀⠀⠀⡇⠀⡸⠀⠀⠀⡇⠀⢰⡆⡇⢸⢠⢹⠀⠀⠀⡇⠀⢹⠈⢧⣣⠀⠘⡇⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⡇⠀⡇⢹⠀⠀⠀⢀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠠⠟⡯⣻⣇⢃⠇⢠⠏⡇⠀⢸⡆⠀⢸⠀⠈⢳⡀⠀⡇⠀⠀⠀
⠀⠀⠀⣇⠀⡔⠋⡇⠀⢱⢼⠀⠀⡂⣼⡇⢹⣶⣶⣶⣤⣤⣀⠀⠀⠀⣇⠇⠀⠀⠀⠀⣶⡭⢃⣏⡘⠀⡎⠀⠇⠀⡾⣷⠀⣼⠀⠀⠀⢻⡄⡇⠀⠀⠀
⠀⠀⠀⣹⠜⠋⠉⠓⢄⡏⢸⠀⠀⢳⡏⢸⠹⢀⣉⢭⣻⡽⠿⠛⠓⠀⠋⠀⠀⠀⠀⠀⠘⠛⠛⠓⠀⡄⡇⠀⢸⢰⡇⢸⡄⡟⠀⠀⠀⠀⢳⡇⠀⠀⠀
⠀⣠⠞⠁⠀⠀⠀⠀⠀⢙⠌⡇⠀⣿⠁⠀⡇⡗⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⠁⠀⢸⣼⠀⠈⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⠀⠀⢀⡠⠔⠚⠉⠉⢱⣇⢸⢧⠀⠀⠸⣱⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠦⡔⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⡏⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠋⠀⠀⠀⢀⡠⠤⣿⣾⣇⣧⠀⠀⢫⡆⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣠⠇⠀⠀⢀⡠⣶⠋⠀⠀⡸⣾⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⠀⠠⠊⠁⠀⠀⢸⢃⠘⡜⡵⡀⠈⢿⡱⢲⡤⠤⢀⣀⣀⡀⠉⠉⣀⡠⡴⠚⠉⣸⢸⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢧⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠚⣤⣵⡰⡑⡄⠀⢣⡈⠳⡀⠀⠀⠀⢨⡋⠙⣆⢸⠀⠀⣰⢻⡎⠀⠀⡎⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡸⢌⣳⣵⡈⢦⡀⠳⡀⠈⢦⡀⠀⠘⠏⠲⣌⠙⢒⠴⡧⣸⡇⠀⡸⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⠢⡀⠀⠀⠀⠠⠄⡖⠋⠀⠀⠙⢿⣳⡀⠑⢄⠹⣄⡀⠙⢄⡠⠤⠒⠚⡖⡇⠀⠘⣽⡇⢠⠃⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⡼⣄⠀⠀⠀⠀⠀⠑⣽⣆⠀⠑⢝⡍⠒⠬⢧⣀⡠⠊⠀⠸⡀⠀⢹⡇⡎⠀⡿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⠻⣺⣧⠀⠀⠀⠰⢢⠈⢪⡷⡀⠀⠙⡄⠀⠀⠱⡄⠀⠀⠀⢧⠀⢸⡻⠀⢠⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⣿⠀⠀⠀⠀⢣⢇⠀⠑⣄⠀⠀⠸⡄⠀⠀⠘⡄⠀⠀⠸⡀⢸⠁⠀⡾⢰⡏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢧⠀⠀⠀⠀⣀⡠⠴⠚⠉⠁⡸⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⣇⠀⡠⠚⠁⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣧⡀⠀⠀⠀⢸⣾⠃⠀⠀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠈⣳⠤⣀⠀⠙⠀⣀⡠⠖⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣰⡯⠔⠒⠒⢒⣖⠲⢤⣙⢦⠀⠀⠀⠹⠢⡀⠀⠀⠀⠀⠀⠀
⠀⠀⡰⢡⠄⠀⠀⠀⠀⢀⡇⢠⠀⠀⠀⣺⡟⣆⠀⢫⠙⢧⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀
⠀⢰⠇⡛⠂⠀⠀⠀⠀⡼⣱⠃⠀⣠⢇⡇⢱⠘⡖⢺⡀⠀⠀⠀⠀⠀⢰⣖⠙⢦⡀⠀⠀
⠀⡟⠐⠁⢀⠤⢶⠀⢹⣿⠇⠀⡰⠃⣼⠀⠸⡀⢻⢼⢻⡆⠀⠀⠀⢠⡀⢹⠙⠾⣷⡄⠀
⢸⡇⠀⣮⠀⠀⢸⡆⢸⡟⢠⡼⠁⢠⠇⠀⠀⡇⠀⢻⡆⢣⠀⠀⠀⢸⣧⠘⣇⠀⠈⠻⣄
⢸⠀⠀⡇⢸⠀⠈⡇⢸⢡⣟⡁⠀⠸⠀⠀⠀⠁⠀⠘⣇⠈⣇⣀⠀⢸⣿⡇⢿⠀⠀⠀⠀
⢸⠀⠀⣷⠸⠀⠀⢻⣦⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠸⣾⡆⢸⣿⣷⣸⠀⠀⠀⠀
⢸⡇⢸⢹⢸⠀⠀⠸⡏⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣿⣷⢸⣿⣿⣿⡇⠀⠀⠀
⢸⡆⠘⢼⣼⣇⠀⠀⠇⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢸⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀
⢸⣧⠾⣆⣿⣿⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠸⣿⡇⠀⠀⠀
⠈⠃⠀⠘⣿⣿⣇⠀⠘⣦⣄⣀⠀⠀⠀⠀⠂⠀⢀⣠⣴⠏⢻⣿⣿⣿⡇⠀⠹⠇⠀⠀⠀
⠀⠀⠀⠀⠘⣿⠘⢧⡀⢻⣿⣿⣿⣿⠉⠉⠻⣿⣿⣿⡏⠀⢸⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠁⠀⠙⢾⣿⣿⣿⣿⣀⣀⣀⣸⣿⣿⡀⠀⠀⡇⠹⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣿⣿⣟⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡞⠉⠻⣿⣿⣿⣿⣿⣆⣸⣿⣿⣿⣿⠟⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣯⠿⢿⣿⣿⣿⣿⣿⡿⠟⣹⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀�