⠀⠀⠀⠀⢀⣴⢟⣭⣾⠋⡴⠋⠀⢀⣼⠟⡄⠀⡄⠀⢀⡴⠁⢀⡔⠀⢠⡇⢀⣾⡿⠛⠷⣾⡗⢌⡑⢮⡳⡀⢠⡀⠀⠀⠈⢾⢞⣔⢤⢦⡀⠀⠀⠐⠤⠄⠤⠄⠀⠀⠀⠀
⠀⠀⣠⣴⣿⠗⢫⢮⠇⡼⠃⣀⣠⡞⢁⡜⠀⡞⠀⡠⠋⠀⣠⠊⠀⣴⣿⢁⣜⡜⠀⠀⠀⠈⠙⢷⡿⣢⠈⢻⣆⠱⡄⠀⠈⢫⢫⣮⠳⣕⠝⢟⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠨⣻⠟⠁⢀⣟⠞⡼⠁⡰⣝⡟⠀⡜⠀⣰⣡⠞⠁⠀⠀⣀⣴⢿⢣⣣⣮⠎⠀⠀⠀⠀⠀⠀⠀⠹⣮⡓⠦⣙⢷⡘⡄⠀⠀⠣⢿⡧⡈⠳⣤⡳⡄⠈⠉⠒⠀⠀⠀⠀⠀
⠀⠜⠁⠀⠀⣼⠎⡾⢡⣾⣽⡞⠀⠞⠀⣠⠟⠁⣠⡤⡶⣿⣷⣫⣧⣿⠿⠵⠶⠶⠶⣤⣀⡀⠀⠀⠀⠀⠙⢷⣮⡑⠿⣼⡆⠀⠀⠀⡽⣌⠲⣌⠛⣌⢦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⡻⡸⣱⢣⢿⢿⠁⢀⡴⣊⡤⢶⡊⡇⡸⢝⡩⠟⢡⡴⠁⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⠄⠀⠈⠙⢿⣿⢦⡹⣿⡄⠀⠀⢇⢫⢳⣌⠑⣮⡳⣕⢄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣧⣳⢃⡟⢊⣧⣾⣿⣿⡿⣔⠌⢇⠇⣠⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣉⠻⣿⣄⠀⠘⡄⢣⠈⠳⣝⠌⢈⠳⢅⠄⠀⠀⠀⠀
⠀⠀⠀⠀⢣⣿⠃⣾⢙⠵⣻⠛⣱⢟⢆⡎⡴⡉⢷⠁⠀⠀⠀⠀⠀⠀⣠⡴⣶⣾⣿⣿⣶⣆⣤⡀⠀⠀⠀⠀⠀⠘⣮⣯⠓⢿⡝⣦⣄⠸⡓⢷⡀⠈⠳⢄⠑⢶⡣⠀⠀⠀
⠀⠀⠀⠀⡾⡏⡸⡾⢠⣿⣷⢰⢯⡿⠉⡞⠀⠘⠚⠀⠀⠀⠀⠀⠀⠰⣫⣾⡟⠋⢁⡤⣭⣽⡻⣿⣗⠀⠀⠀⠀⠀⢸⣷⣽⡶⠌⠺⣷⣍⠛⠦⣝⣶⡠⠀⠙⠢⣍⠀⠀⠀
⠀⠀⠀⣸⣱⣇⢧⣧⣸⣇⣿⣞⡞⣄⣤⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⣽⠏⠀⢰⣇⣠⣿⡟⢻⡜⢿⣷⡄⠀⠀⠀⣼⣧⣿⣿⣦⣿⣮⣻⣷⣄⠀⠉⠛⠶⣦⠤⣀⡀⠀⠀
⠀⠀⡴⣁⡇⣿⣼⡏⣿⣿⠃⠏⣴⡿⠛⢛⣻⣮⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡟⢻⣿⣿⠀⣿⠈⣟⣗⡀⠀⢠⡏⣿⣿⣯⣿⡿⣿⣿⣛⢻⢷⣄⡀⢀⣀⠉⠑⠢⠤
⠀⡼⣱⣿⢷⣧⣿⣿⣿⣿⡇⢠⣿⠁⠀⣞⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣀⠉⠁⣠⡏⢠⠟⠃⠀⢀⡞⢁⣿⣿⢫⣵⣾⣿⣿⣿⣿⣷⣮⣿⣶⣭⣙⡒⠂⠀⠀
⠀⡴⢻⢏⣿⣿⣿⣿⣿⣝⣿⣸⣿⡀⠀⣿⡏⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⢰⡟⠀⡜⣸⢡⣿⣷⣭⢻⣿⣾⣿⠭⣛⡉⠿⠚⠻⠿⠷⢖⡀
⠀⢀⣟⣜⣷⡷⡿⣨⡏⡟⣏⣿⢿⣧⠀⠘⣷⣤⣁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠋⠜⠀⠏⣨⠇⢹⣿⣧⢉⣾⡯⣿⢤⣈⠙⠛⠦⣄⠀⠀⠀⠀
⠠⣟⢮⡸⣝⠔⡵⠃⣷⡇⣾⣟⣧⠙⠳⠄⣨⠝⣭⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⢸⡿⢵⡸⢞⣡⢞⠛⠫⢊⠓⠊⠑⠦⣄⠀⠀⠀⠀⠀
⠀⡰⢨⢇⡿⣼⠁⠀⢻⢡⠛⢻⣸⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣆⣏⣀⣤⣴⣟⣁⠀⠨⠓⠮⣳⡄⠀⠀⠠⠉⠀⠀⠀⠀
⠀⢡⡟⠇⣷⠃⠀⠀⢸⡾⠀⣿⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⣮⣿⡕⠻⠭⣝⡒⠒⠛⢷⠵⣖⠀⠀⠀⠀⠀
⠀⠀⡻⠊⡞⠀⠀⠀⠸⠃⠀⠘⣷⣧⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⣕⡭⠛⠯⢽⣚⠭⣷⠒⣚⡟⠚⠒⠒⠒⠒⠀⠀⠀⠀
⠀⡶⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⢫⡞⣿⣽⣳⢶⣤⣀⡀⠈⠄⠀⠚⠁⠀⠀⠀⠀⢀⣀⣠⣤⣤⡤
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢔⡝⠅⠹⠀⡇⢹⣧⢀⣉⣙⣺⣭⣔⠂⢒⠖⠊⠙⠛⠛⠻⠧⣤⡀⠀⠀⠈
⠀⠈⢳⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡴⠋⠀⠀⠀⠀⠁⠘⢻⣿⣓⡲⠏⢁⡩⠟⣓⠒⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡭⠙⢿⣶⣤⣀⠀⠀⠀⣀⣠⣴⣾⣿⢿⠋⠁⠀⠀⠀⠀⠀⣠⣴⣶⠿⠿⣿⣿⣯⣤⣋⠲⢭⡤⢴⣤⣀⣀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠙⢿⣿⣻⣿⣻⠿⡿⢻⣯⡃⡴⡀⡆⠳⡀⠀⣠⣾⣟⠿⠂⠀⠀⠀⢙⡿⣯⠛⠿⣶⢝⡻⡒⠦⠬⠉⠉⠀⠀⠀⠀
⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣖⡅⠝⣎⡙⠦⣌⣂⢄⡹⣷⡰⡱⡃⠀⢣⡾⠯⠚⠁⠀⠰⠂⣀⣀⣀⠒⠿⣷⡀⠀⠙⠿⣝⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣎⣿⣦⡀⠉⠉⠙⢻⣷⡹⣷⡶⣋⠀⠀⡀⢀⣤⣶⠿⠋⠭⢭⣉⣻⣿⣿⣦⣀⠀⠈⢪⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠢⠀⢀⣿⢯⢟⡕⢁⠴⣪⣾⠟⠉⣀⠤⠒⠚⠉⠁⠙⠛⢯⣿⣯⡀⠀⠀⠹⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡿⠋⢘⣵⣾⠟⡵⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⡀⢀⡠⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⣹⣿⣿⠇⢀⣴⣿⡟⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡞⠋⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⣰⣿⢿⣿⠂⡜⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⣷⢹⡵⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⣻⡏⣠⢞⡿⠁⡹⡸⢰⠁⠀⢠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣻⣧⢔⡋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣗⡿⣷⡿⣻⠏⠀⣴⠇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠀⠀⢸⢷⣯⢿⢃⡤⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⢟⣿⠏⠀⣾⠎⠀⡇⡇⡄⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⡰⠃⣠⣶⢟⣽⣿⡾⡟⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢷⣿⠋⠀⠜⠁⠀⠀⢻⡸⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⡅⠊⠚⠁⣱⠟⢹⡇⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢟⣵⠿⠋⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⡰⠃⢀⣠⠾⠋⠀⣠⠤⠊⠀⡎⢽⡧⢻⠀⠀⠀⠀⠀