⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠰⣹⠛⣻⡧⡪⢑⡍⢳⠀⠉⠻⡿⠃⠀
⠀⠀⠀⠀⠀⣠⠔⡖⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠦⣴⠟⢛⡳⠵⢤⠘⠋⣀⣼⣥⡞⠀⣀⡴⠇⠀⠀
⠀⠀⠀⠀⠈⡀⢠⠃⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⣧⠀⣀⣀⣀⣀⣠⣤⣤⣤⡼⠇⠀⠀⠀⠀⠀⠀⠑⣎⠉⠃⠀⠛⢧⢸⣥⠀⢀⡀⠀⣄⡉⠙⡎⢿⣁⡴⠛⠛⠉
⠀⠀⠀⠠⢚⠆⢸⠀⠀⠀⠀⠈⣿⣀⡤⢖⣉⡤⠶⠒⠉⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠀⢀⠀⠸⣄⣨⣽⢿⣀⠰⣼⣿⠾⣳⣟⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢘⠀⡆⠀⠀⠀⠀⣠⣼⠿⠚⠉⠀⠀⠀⣀⣀⣤⠤⠶⠶⠒⠒⠒⠋⠉⠉⠉⠙⠛⠛⠛⠒⠲⠶⠶⠦⣤⣵⣶⣋⠳⠤⠏⢇⠸⡄⢹⣴⡉⠻⡎⠀⣿⡦⠤⣀
⠀⠀⠀⠀⠊⢀⠃⠀⢀⣤⡾⠛⠁⢀⣠⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⣬⣧⡉⢹⢿⠛⠓⢀⠈⣉⡛⡷⣤⠤⢠
⠀⠀⠀⠀⢀⡜⠀⣴⠿⠋⣀⡴⠞⣫⡟⠁⢀⡄⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠈⠙⠻⣬⣳⣶⡏⣀⢹⣯⠵⠛⠀⠀
⠀⠀⠀⠀⠊⣠⡾⢁⡴⠞⠉⠀⣰⠟⠀⢀⡞⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⢷⠀⣀⣀⡀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣰⢟⡽⢛⣦⣉⣾⣓⡶⣄⡑
⠀⠀⠀⠀⣼⢏⡴⠋⠀⠀⠀⣰⡏⣀⠀⣾⠃⠉⠉⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⡀⠈⠉⠹⡀⠢⠤⣀⡀⠀⠀⠀⠈⢷⠀⠀⠀⢸⠃⣾⠀⢸⡟⣸⡜⡿⣝⣮⢳
⠀⠀⠀⣼⢣⡟⠀⠀⠀⠀⢠⡟⡋⢠⣿⡟⠀⠀⡜⢸⡇⠆⠀⢀⣀⠀⠀⠀⠀⠀⢠⢸⣿⣧⠀⠉⢢⠀⢷⡀⠀⠀⠈⠉⠒⠤⣀⠸⡆⠀⠀⠸⣇⠘⠲⠞⣱⢿⢧⠳⣌⣻
⠀⠀⠀⠹⣾⣆⠀⠀⠀⠀⣾⢱⠁⣼⡏⢠⠔⠋⠁⣾⣧⠀⠀⠁⠀⠀⠀⠀⠀⠈⠋⠘⡇⢻⡇⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠈⢦⣿⠢⢄⡀⠈⠛⠒⢻⣇⠼⡌⠳⠤⣥⠼
⠀⠀⠀⠀⠙⢿⣷⠀⠀⠀⡏⡇⠀⣿⠀⠁⠀⠀⢰⠏⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⣄⠀⠀⠀⢹⡿⣅⠐⠤⣀⠀⠀⠈⣿⠀⠀⠈⠲⣄⠀⣼⠋⠀⢹⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠳⢤⣸⠓⠀⠀⣿⠀⠀⠀⣠⣿⠛⠩⢷⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢹⡄⠈⠛⢷⣄⠀⠀⢳⡙⢦⡀⠀⠁⠀⠀⢹⡆⠀⠀⠀⠀⢳⡏⠀⠀⠀⢷⠀⠇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⡏⠀⠀⢾⣿⠋⠀⠀⠻⣧⡀⠀⠀⠀⢸⣦⡀⠀⠀⠈⣧⠀⠀⠀⠉⠳⣄⡈⢳⡀⠙⠳⣄⠀⠀⢸⡇⠀⠀⠀⠀⠸⡇⠀⠀⢰⡘⣾⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣇⠀⢠⡟⠁⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⢻⣻⣤⡀⠀⠘⣧⠀⠀⢀⣀⣀⣙⠓⠛⠂⠀⠀⠙⠒⢼⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢧⢹⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠻⣧⡙⠶⢤⣈⡳⣀⡥⠴⠒⠒⠒⠶⠶⣖⣢⢄⣀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⢿⣿⠀⠀⢀⣀⣨⠭⠭⠭⣐⡀⠈⠛⢦⡀⠀⠈⠳⣄⠀⢠⣞⡡⠤⠖⠒⠒⠲⠤⣄⣀⢉⡽⢁⡟⠀⠀⠀⠀⡼⠀⢻⡀⠀⠀⠀⠀⢈⡗
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡇⠀⠀⠸⣟⡇⣴⡟⢋⣠⠴⠒⠒⠒⠛⠦⠀⠀⠙⠳⢤⣀⡈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⣼⠁⠀⠀⠀⡼⠁⠀⠘⣷⣥⣤⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠏⡸⣷⢡⡀⠀⢻⣷⠘⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⡞⠁⠀⠀⢀⣴⣿⡧⠋⠀⠀⠀
⣆⣴⠋⠻⣦⣀⡴⢋⠞⠀⠸⣇⠳⣄⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠒⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢀⣠⠾⠋⠀⠀⢀⡤⢪⣾⠋⠁⠀⠀⠀⠀
⠉⠉⣷⠙⠮⡙⢾⣻⡷⢶⣄⣻⣆⠸⡳⣶⠼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢀⠤⠒⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠶⣶⠟⠁⠀⣀⡠⠖⣉⡴⣫⡿⣧⡀⠀⠀⠀⠀
⡞⠉⠉⣧⠤⠊⠪⢿⡇⠀⠉⠛⢿⣧⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠔⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠒⠚⠉⣀⣤⢾⡯⠞⠁⠀⠈⠻⢶⣄⠀⠀
⣤⠔⠚⢻⡄⠀⠀⠈⡇⠀⠀⠀⠀⠈⠛⣶⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⢶⡶⠖⠛⠋⠉⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠛⠶
⠀⢀⡤⠾⣇⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠘⣯⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡶⣿⠁⠀⠀⠀⢀⠔⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⠀⣰⠟⢆⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠛⠉⣴⠇⣀⡠⠖⣦⠏⣸⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠈⠹⡄⠘⢦⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠈⠻⡝⠻⣷⣶⣦⣤⣤⣤⣤⣤⣤⢤⡶⠶⠚⠛⠉⣀⣴⠿⢶⡾⠛⠉⠁⠀⣸⠃⣰⠏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢹⠛⠒⠚⢷⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⡄⢧⠀⠀⢹⡄⠈⢹⣿⠈⠙⠛⣿⢀⣹⣎⡄⢀⣠⡴⠛⠉⠀⣠⡿⠁⠀⠀⠀⠐⡡⣰⠏⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀
⣼⠀⠀⠀⢨⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⠃⣸⠀⠀⠀⢷⠀⠀⣿⠀⠀⠀⠈⢿⣟⣻⠟⠋⠁⠀⠀⠀⣴⠏⠀⠀⠀⠀⢀⡞⢡⡿⢦⣄⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀
⡟⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⡾⠀⣏⠀⠀⠀⢸⡇⠀⣿⠀⠀⣠⣴⣿⢉⣿⣦⡀⠀⠀⢠⡾⠃⠀⠀⠀⠀⣴⡟⢠⡿⠠⣄⡉⠻⢶⣌⣷⡀⠀⠀⠀⠀⠀⠀
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠈⠛⠾⣬⡀⠀⠀⢈⡇⠀⢹⣠⣞⣛⣲⢄⡀⣒⣛⣛⣦⣤⡟⠀⠀⠀⠀⢀⣾⣿⣣⣼⠁⠀⠀⠈⠑⠢⣍⡛⢷⣤⣀⣠⣀⡀⠀
⢻⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀⢸⡇⠀⡾⠁⠀⠀⢘⢸⢇⡇⠀⠀⢠⡟⠀⠀⠀⢀⣀⣾⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡙⢻⡈⠙⠳
⠀⠀⠉⠉⠉⠉⢛⡿⠛⠛⠛⠉⠛⠓⠶⠶⠶⣤⣤⣀⣀⣀⣹⡾⠀⣼⠁⠀⣠⠤⣌⣦⣎⡠⢤⣀⣿⣤⠶⠞⠛⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀