⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠞⠋⠉⠉⠉⠉⠛⠛⢿⡲⣤⣄⠀⣸⣯⠋⠿⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⣿⣷⣤⣀⡴⠫⡝⠁⠀⠀⠀⢠⡤⢤⡀⠀⢠⠜⣦⡈⠳⣿⡇⠈⠀⠹⣯⢉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠂⣿⣷⣮⣿⡏⠀⢠⡗⠀⣤⣶⣶⣾⠀⠀⣿⠛⣷⠀⣾⠙⡆⢸⣷⠈⠀⠀⢻⣿⡇⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⡄⠀⣿⣷⣎⣿⡇⠀⠘⠳⡎⠁⠀⠀⢸⣿⣱⣿⢶⣿⣤⡿⠀⠹⣞⣿⡆⠀⠀⢸⣿⣿⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢸⡇⡀⡀⣿⢿⣯⣞⡷⠂⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⢸⡟⠻⣦⣤⣴⠛⢻⣿⡆⠄⠈⣿⣿⡆⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣼⡇⠄⠁⣿⡀⠻⡿⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣒⣿⣄⣼⣂⢻⣿⣷⡀⠄⢸⣿⣷⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⡇⠂⠀⣿⣿⣿⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣆⡀⠉⠹⣧⣼⣇⠀⠈⣿⣿⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢳⡀⡀⠻⣿⣿⠀⠀⢰⡄⣸⣷⡤⠀⢀⠀⠀⠀⠀⠀⠀⠒⢶⣿⠉⢷⣤⣷⡟⢻⡄⠃⣼⡏⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⢳⡀⡀⢻⣿⡀⠀⢸⣇⡟⠉⢧⣀⣼⣤⡀⣴⣄⣹⣿⣾⣿⣿⠀⠺⣤⡼⠁⢸⣧⠄⡉⢷⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⢻⡀⣰⣿⡇⠀⠘⣟⣷⣤⣀⣹⣛⡟⠛⠉⠉⠡⣶⣶⣷⣿⡿⠛⠉⣟⣿⣿⣿⣷⡥⢻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡏⣿⣿⡄⠀⢹⣿⣿⣷⣾⠿⠃⠀⠀⠀⠈⠙⠛⠛⠋⣿⠀⠀⣿⣿⣿⡟⢀⣿⡧⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣾⡍⣧⠀⠀⣿⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢨⡏⠀⠀⣿⣿⡏⠀⣼⠃⠙⢯⡽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢏⡖⣿⣧⡸⣇⠀⢹⣷⡀⠀⠀⠀⡀⠀⠀⣀⠀⠀⣠⣾⠗⢠⣺⣿⡿⠁⠀⣿⠀⠀⠀⠙⢧⣟⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠬⣼⡏⠈⣷⣻⣮⢨⣿⣟⣶⣦⣄⡉⠉⠈⠁⢀⣴⡻⢿⡛⣶⣿⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠙⢾⣝⢿⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢁⣶⠋⠀⠀⠘⣧⣻⣤⢸⡟⠁⢀⣾⣿⣷⠶⠟⠛⠻⣷⣿⣁⡿⠃⠙⠳⣄⢰⡇⠀⠀⠀⠀⠀⠀⠀⠙⢾⣳⢞⣿⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢡⣾⠉⠀⣀⡶⠟⠉⠀⠘⣮⠿⣄⣿⠁⠀⠀⠀⠀⠀⢀⣼⣿⡽⠁⠀⠀⠀⠈⢹⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⢾⡎⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢡⡾⠁⠀⡾⠋⠀⠀⠀⠀⠀⠈⠛⠻⢿⠀⠠⠄⠀⠠⠬⠛⢻⡇⠀⠰⢄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⢸⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣏⠁⠁⣼⠇⠀⢘⡷⢦⡀⠀⠀⢀⡀⠀⠀⠀⠘⡧⢤⣀⢀⣀⣠⠴⣿⠀⠀⠠⡤⣑⠀⠀⢠⠞⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⠁⣼⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣴⢧⡏⠀⢸⡟⠀⠀⠐⡇⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢷⡀⠈⠉⠉⠁⢰⠇⠀⢀⣾⣗⣎⣣⠖⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⣴⠟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠃⣿⠃⠁⢸⡇⠀⠀⠈⡇⠀⠀⠀⠙⢦⡀⠀⠢⡀⠀⠈⢧⠀⠀⠀⢀⡞⢀⣠⢾⣌⣻⠟⠁⠀⠀⠀⣸⣷⡄⠀⠀⢀⣰⠞⡁⠄⢠⣴⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⡟⣼⣿⠤⣤⣸⣷⡀⠀⠀⡇⠀⠀⠈⠣⠀⠙⢦⣄⠻⣦⡀⠈⢷⡀⢀⡞⢀⣸⣿⣻⣿⡃⠀⠀⠀⠀⠀⣾⠀⠻⣦⣤⡟⢧⡒⣵⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⢃⣿⣿⡇⠄⠁⢿⣧⡀⢀⡇⠀⠀⠀⠀⣾⠛⠛⠛⠲⢬⣟⡚⢈⢷⣿⣁⣾⡿⠛⠛⠉⠉⠙⢳⠀⠀⠀⣿⡄⠀⣸⢧⡹⢧⣽⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠸⣿⣧⠠⠀⠀⠸⣿⣜⣇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠛⢿⠟⠻⣟⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣿⠻⣿⡿⣄⣻⠟⠀⠛⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⣄⡙⠿⣷⣤⡀⡠⢑⠻⣿⡄⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢠⢾⣦⣰⡏⢽⡦⠀⠀⠀⠀⢰⠇⠀⠀⢀⣿⣶⣿⣻⣽⣧⣀⠤⣤⣀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠾⢷⣮⡧⠿⣴⣧⣀⡔⠀⠸⣇⠀⠀⠀⠀⠀⡰⢻⡏⢹⡟⢦⡀⠀⠀⠀⢠⡏⠀⠀⠀⢹⣿⣿⣯⣷⡟⠀⠈⠙⢦⣝⢷⣦⣀⠀⠛⢦⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠿⠛⠉⣠⣿⣿⣧⡀⠀⠀⠀⠹⣆⠀⠀⣤⠞⠁⣺⠡⢸⣧⠀⠉⠳⣄⣀⣾⡀⠀⠀⠀⢸⣿⣿⣳⣿⠀⠀⠀⠀⠀⠘⠳⣝⢿⣦⡄⠀⢻⡄⠀⠀
⠀⠀⠀⠀⢀⡴⠚⠉⠀⣠⣤⠾⠟⠛⢗⣾⣿⡀⠀⠀⠀⣴⡋⠛⠉⢁⣤⣠⣿⡄⠁⠸⣆⠀⠀⠀⠉⣀⡿⠂⠀⠀⢸⣿⣯⢿⡟⠀⠀⠀⠀⠀⠀⠀⠉⠷⣝⢿⣶⣨⣻⡄
⠀⠀⢀⡴⣋⠀⢀⣴⠟⠉⠀⠀⠀⢀⣼⣟⣻⡅⠀⠀⠀⠀⠙⡳⢦⣼⣻⣛⡿⠋⠀⠀⢹⡶⢒⣾⠋⠁⠀⠀⠀⠀⢘⣿⣯⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⢿⣷⡟⣿⠀
⠀⢠⣟⠖⢀⣴⠟⠁⠀⠀⠀⠀⣤⣾⣳⣾⣿⠀⠀⠀⠀⠀⠔⠀⢀⣾⡇⠋⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣯⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣻⡇⢻⡇
⢠⡏⢸⣴⠟⠁⠀⠀⠀⢀⣠⡾⣻⣽⣿⡽⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⡁⠀⠀⠀⠀⠀⠀⢿⣿⣷⣟⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⠀⣼⠇