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ඞ𐐘
⠰⣶⣶⣢⣖⣶⣖⣶⣏⣄⣶⡆⠀
⢀⣴⣿⠋⢫⣭⡍⢳⢠⠚⢷⣄⠀
⣾⢣⣟⣦⡜⠛⠣⠋⠈⠿⣇⡧⡆
⣿⢾⡟⣾⣷⣤⣖⣲⡄⣄⣰⣿⡇
⢏⠀⠘⢮⣣⢌⣸⠉⡋⡹⢏⣼⠃
⠈⠢⡀⠀⠉⠳⣶⣷⣶⣿⡿⠋⠀
⠰⠶⠟⠿⠟⡟⠿⠏⠿⠼⠶⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠀⠀⢹⠀⢀⣴⠗⠛⢳⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠛⣀⠀⡸⠁⡸⠇⠀⠀⣸⠁⠀⠀⠀
⠀⠀⣠⢤⡔⠒⡚⠓⠊⠉⢉⣀⠉⠉⠀⠀⠉⠋⠐⠲⠦⢤⡠⠏⠀⠀⠀⠀
⢀⣾⠗⠁⠀⠀⢹⡀⠀⢿⣷⡎⢙⡦⣤⢶⣶⡒⢦⡀⠀⠀⠉⠑⢦⡀⠀⠀
⢸⡇⢰⡆⠸⡷⢸⡇⠀⠀⠈⠉⠁⠀⠈⠛⠝⠰⠚⠁⠀⠀⠀⠀⠀⠙⣦⠀
⢸⣇⠀⠀⠀⢄⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠀⠀⠘⡄
⠀⠉⠷⣒⣒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠁⠚⠓⠶⢤⡒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠲⠶⠶⠶⠶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⡀⠠⠤⠀⢀⡀⠀⠀⠐⣧⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡰⣻⠀
⠐⠤⠀⠀⣀⠠⢜⠀⠀⢠⣼⣷⡢⢄⡀⠀⠀⠀⠀⠀⢀⣀⡤⣔⣭⣾⢿⣷
⠁⠀⠀⠀⠀⢀⣠⠀⢀⣽⣿⡷⠿⣷⡶⡯⣭⠭⠭⠭⢶⡾⠿⢍⣋⣘⠉⣿
⠀⠀⠀⠀⠀⠀⠙⢀⣀⣥⣤⢴⢶⣿⣿⣷⣿⡄⡰⠾⠿⠷⢦⣾⣿⣿⡄⣿
⢰⠀⠀⠀⠀⠀⠰⢠⣿⣿⠧⠾⠻⣿⣿⣿⣿⣧⣶⣶⣾⣷⣿⣿⣿⣿⡇⣿
ඞ - ¬ඞ
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠚⠉⠀⣀⣀⡀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢀⡠⢤⣄⡀⣴⡿⡷⢤⣿⢦⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢰⣿⠋⠉⠙⠻⠋⠀⠧⠼⠋⣾⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⢧⠀⠀⠀⠀⠀⠀⠀⠀⡼⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠣⣓⢤⣀⡀⠀⠀⢀⣞⡽⠁⠀⠀⠀⣀⣀⡀⠀⠀⣀⣀⣀⣀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠈⠙⠒⠯⠭⣓⣫⠞⠀⠀⠀⡴⣫⠔⠒⠺⢷⣮⣷⠶⣝⢦⣳⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡩⠷⠦⠀⠀⢀⣠⣤⣤⣀⠀⢰⠁⡇⠀⠀⠀⠀⢙⣥⣶⠾⠶⣾⣄⠀⠙⠂⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⣀⣀⣤⣤⣴⣿⣭⣅⣉⠙⢷⡌⢧⢳⡀⠀⠀⢠⣿⠋⠀⢀⣀⣈⣿⣦⣤⣤⣤⣤⣤⣄⣀⠀⠉⠓⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⣀⣴⠶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠛⠿⣾⣿⡈⠳⣝⣦⣀⣿⡇⣠⣼⡿⠛⠋⠉⠀⠀⠀⠀⠀⠈⠉⠙⠻⢶⣤⡀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡰⠋⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠉⠛⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠙⢄⠀⠀⠀⠀⠀⠀
⠠⠔⠊⠉⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣤⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠈⢧⠀⠀⠀⠀⠀
⠀⢀⣴⡶⠷⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠄⡤⠊⠻⣧⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠉⠈⠉⠢⣄
⢠⣿⠃⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⠋⠀⢸⠀⠀⠀⢻⡇⠀⢹⡆⠀⣶⣶⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠛⢷⣦⠀⠈
⢸⡏⠀⢰⣏⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣀⣴⣆⠀⠘⢆⡀⠀⢸⡇⠀⠈⣿⠀⠛⡿⠋⠱⣦⣄⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣄⠀⢹⣧⠀
⢸⣷⡀⠀⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠛⠛⠀⣴⣴⠾⠉⠁⢹⡆⠀⠀⠉⠁⣾⠇⠀⢀⡟⠀⡼⠁⠀⣴⠏⠈⠀⡇⣶⣶⡄⠀⠀⠀⡴⣄⠀⠀⢸⣇⣿⠀⢨⣿⠀
⠀⠙⢿⣦⣤⣤⣤⡴⠀⠀⠀⠀⠀⠀⢈⠵⠒⠢⢄⠀⠸⣧⠀⠀⠀⢸⡇⠀⠀⠀⣼⡟⠀⠀⠸⠃⠀⡇⠺⠛⣧⠀⢀⡼⠀⠙⠉⠀⠀⠀⢸⡁⣼⠀⠀⣸⡏⢁⣠⣾⠏⠀
⠠⣀⠀⠘⣿⡅⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢳⠀⠘⠷⣧⣤⡾⠁⠀⢀⣾⣿⡀⠀⠀⠀⠀⠀⠙⠦⣤⡭⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣿⠟⠛⠛⠁⠀⡀
⠀⠈⢆⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢀⣠⣿⣯⣿⣷⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⣠⠤⠒⠋⠀
⠀⠀⠈⢆⠀⠘⢿⣦⣄⠀⠀⠀⠀⠀⠀⠉⠒⠊⠉⠀⠀⠀⠀⢠⠶⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠨⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⡰⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠳⣄⠀⠉⠛⠿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⠟⠁⢀⡜⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⡀⠈⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡿⠃⠀⠈⠙⢻⣿⣿⠿⠿⠿⠛⠛⠋⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⢿⠿⠟⠛⠛⠉⠁⣰⠀⠀⠀⠀⠀⠘⣷⠀⠀⡀⠀⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢠⣾⠟⠉⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠁⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⢻⣇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⢻⣷⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⡀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣾⠋⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⣰⡿⠛⠙⣿⠻⠄⠀⢠⣦⠀⠀⠈⢟⣿⣦⣶⠀⢶⣠⣿⠃⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣾⠃⠀⠀⠀⠐⣸⠏⠀⠀⠀⠀⠀⢠⣿⠁⠀⠈⣿⠀⠀⠀⠈⢿⡆⠀⠀⠀⠙⠻⠛⠿⣿⡟⠁⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢿⣦⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣼⣼⡏⠀⠀⠠⣿⣤⣷⣤⣤⣼⣧⣦⣤⣶⣤⣤⣤⣤⣿⠃⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣠⢤⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡄⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⠀⠀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠀⠀
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⣠⣴⣶⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣦⣤⣀⠀⠀⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠰⠛⠋⠉⠁⠀⢀⣉⡉⠙⠛⠦⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠛⠉⠉⠉⠉⠙⠛⠻⠦⠀⢿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⠖⠋⠉⠁⠈⠉⢉⣷⣦⡄⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠉⠛⣶⣤⠀⠀⠀⢸⣿⣿⣿
⢸⡿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠹⣄⣀⠀⠀⠀⠀⠘⣿⡿⠋⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠘⣿⣿⣿
⣼⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠺⠭⠭⠭⠭⠯⠷⠒⠀⠀⠀⠀⠀⠀⠀⠙⠺⠭⢷⣒⣒⣶⠯⠝⠂⠀⠀⠀⠀⣿⣿⣿
⢣⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠸⡄⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢱
⠀⢳⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢸
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⣶⣤⣄⠀⠀⠀⢀⣠⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠻⠿⠷⡀⠀⠚⠟⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠙⣷⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠀⠀⠀⠀⠀⠀⢀⠇⠀⡇⠀⠀⠀⠀⠀⠀⠋⠉⠉⠳⡄⠀⠀⠀⠀⣠⣴⠋⠀
⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣄⡀⠀⠀⠀⠀⠸⡄⠀⢧⡀⠀⠀⠀⠀⠀⣀⡴⡄⠀⠙⠀⠀⠀⠀⣿⡏⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡀⠉⠒⠤⣄⣀⡀⠁⠀⠀⢁⣀⣀⠤⠖⠋⠁⣀⡇⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠉⠓⠤⢄⣀⣀⣀⣠⠤⠒⠉⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣄⣀⡀⠀⣀⣀⣠⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀