⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣾⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⡀⣠⠏⠀⣠⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤⣤⣶⣼⣿⣴⢃⣾⢣⡾⣽⠿⢢⡴⣷⢠⣤⢸⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⢿⣿⣯⡏⣿⣿⢇⣧⡿⢇⡼⣱⡇⣶⠟⡽⣃⡿⣿⣸⠻⢿⣼⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⢄⡰⣄⠀⠀⢠⣤⣾⣿⣿⠛⠻⣯⢿⠿⡟⣼⣧⠹⢡⢏⢁⡠⠏⢰⡿⣆⠃⠀⠁⠁⠘⠂⠉⡃⠈⠻⠛⢻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⣿⠀⢰⣀⢀⡈⣿⡿⡟⣿⣮⣻⣷⡿⡝⠯⢭⡭⠍⠁⠀⠛⠛⢀⠀⢸⣾⡁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠰⣬⡻⣾⣿⣮⡻⣟⢮⣛⢷⣽⣻⣻⠄⠄⠀⠀⢀⡠⣄⣤⣋⡜⠈⣁⣠⣄⣤⣴⡳⢶⣴⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢢⠙⠷⣄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠰⣤⣬⣶⣾⣿⣿⣿⣻⣿⣷⣄⠈⣙⣚⣛⠪⢽⣶⣴⣯⣬⣿⣿⡿⣿⣿⣿⣉⠉⠛⢾⣿⣿⣿⣿⣿⣿⠿⣷⣦⣄⡀⡀⠀⠀⠀⠀⠘⠂⠀⠀⠈⢽⢦⡄⠀⠀
⠀⠀⠀⠀⣨⣿⣟⢿⣿⡿⣿⣿⣯⡟⠟⠛⣲⣬⢭⢍⡽⣷⣿⣿⣿⣿⠿⠿⠿⠿⠟⣿⡛⠷⣿⣏⣩⣿⣿⡿⠋⠙⠿⣿⣿⣿⣿⣷⣄⣀⣀⠀⠀⠀⠀⠀⠈⠳⡝⢦⡀
⠀⠀⣦⣾⣿⣿⣿⣧⣹⣿⠷⣶⣷⠠⡶⠾⣫⢾⣵⡿⠛⢻⣿⠛⢹⡀⢀⣴⣒⣛⣉⣭⣿⣿⠞⡿⢿⣿⣿⣿⢽⡶⠀⠀⠈⠹⡌⢛⣷⣦⡐⠀⢀⡀⠀⠀⠀⠀⠈⠀⠉
⠀⢀⣾⣿⣿⣿⣿⣿⣽⡿⠇⠀⢀⡞⣡⣭⡵⠛⠉⠀⠀⠀⣿⣧⠘⣧⠀⢙⣿⣿⣿⣬⣻⠙⠞⠀⠈⢳⣿⣿⡾⣀⠀⠀⢦⣀⣿⣤⡏⠈⠻⣆⠀⠀⠦⡀⢀⠀⠀⠀⠀⠀
⠲⣿⡿⣿⣿⠿⠶⣖⡋⠀⢀⣔⣯⡾⠟⠉⠀⠀⠀⠀⠀⠀⠹⣿⣦⡜⡇⢬⣾⡛⠁⠀⠁⠀⢀⣼⣧⡄⠙⣿⣿⡿⣧⣜⠂⢆⣹⡟⠁⠀⠀⠸⣗⢦⣌⡓⣖⣆⠀⠀⠀⠀
⣸⣿⣿⣿⣿⣿⡿⠉⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⣿⠇⠀⠀⠀⠀⠰⡿⠟⣿⡁⠀⢿⣿⢡⡻⠉⣙⠛⠛⠀⠀⠀⠀⠀⠘⢮⢹⢛⠿⣯⣳⣆⢀⠀⠀
⣭⣿⠿⠏⣷⡀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣯⣾⡿⣀⣶⣒⠀⠀⣿⡇⠰⣦⣽⣾⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⡿⣿⣄⠀⠀⠀
⣶⣶⣶⡾⠁⢀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠺⠷⠶⠿⡿⡼⠷⠳⠻⠾⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣸⡟⠁⠈⣝⣷⡠⠀
⣿⣏⡥⢃⣴⣟⣿⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢐⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⣄⣠⣴⣥⢿⡧⠤⠶⠾⣾⣷⡀
⣠⣵⣶⣿⣿⣿⢿⠄⠀⠹⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴⠋⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠃
⣽⣿⣿⣿⢶⠶⣂⣀⣀⡀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⡼⠈⢣⡀⠀⢀⠀⠀⠀⠀⠀⢀⣠⣀⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣿⣿⣿⡿⢋⡭⠑⣂⡀⢠⣤⣬⠙⠛⠲⠶⣤⣤⣤⣀⣀⣀⣀⣳⣇⣀⣠⣭⣭⣭⡶⠖⠒⠛⠉⠉⠁⠒⠀⠀⠀⠤⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣛⣿⠝⣂⣴⣢⣭⣀⡐⠲⠄⠀⣈⣈⠉⠉⣉⣉⠀⠀⠀⠀⣀⡤⣖⣊⢀⣠⠞⡁⡀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣾⣽⠟⢽⣿⢿⡾⣿⡿⣫⠟⣫⠞⣩⡵⣾⢿⢖⣶⢿⡿⠛⠁⠀⠉⣠⠌⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣴⣿⣿⣿⢸⠟⡼⣧⣾⢡⣾⣩⠾⢃⡏⢈⣴⢏⣴⢠⣰⡇⢠⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣸⣼⣿⣿⢧⣾⢷⡿⣱⡟⣷⢸⡿⣼⢁⢸⣿⣁⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡦⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡏⣿⣿⠋⡟⡏⢻⣷⡟⢻⡽⡾⣇⡏⠼⠸⡉⢵⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋⠀⠀⠀
⣿⣿⣿⣿⣷⡟⠿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣹⡇⣽⡏⠀⣗⣿⢺⣿⠃⠀⢳⣻⣻⠁⠀⠠⡖⠋⠙⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⠟⠁⠀⠀⠀⠀⠀
⠏⣿⣌⠙⢧⡍⣀⠈⠻⣿⠟⢷⣸⣿⠿⢿⣿⣿⢡⣿⢡⣤⠃⠿⠘⠙⠀⠀⠀⣧⣳⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠍⠁⠀⠀⠀⠉⠀⠀⠀⠀⣰⣿⠉⠀⠀⠉⠹⠚⡿⠀⠀⠀⠀⠀⠀⠀⢠⢷⠃⡇⣷⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣴⣶⣶⣤⣤⣤⣤⣠⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⠤⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀