⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣴⣿⠁⠀⣀⡀⠤⠤⡀⠄⠤⠤⠀⡀⠂⠤⢀⣀⠀⠀⣿⢷⡹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⣾⣿⣿⠲⣉⠖⠨⣉⠔⢀⠀⠂⠀⠄⢀⠐⠀⠀⠀⠉⠢⣼⣿⡿⣜⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡉⢹⣷⡟⢺⡿⢄⡃⠄⢠⠣⣜⠔⠁⠂⡈⠀⠄⠂⢀⠀⠁⠀⠀⠀⠀⠙⠧⢹⡞⣿⣐⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣓⠭⣿⣿⣷⣿⣣⢷⡘⢆⠡⢚⢤⠢⣍⡐⠀⠠⠈⠸⠀⠀⠐⠈⠀⠀⠄⠀⡀⠠⣿⣿⢹⢷⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⢌⡳⣿⣿⣿⣿⣯⢷⡙⡎⠴⢩⡸⣳⡖⡡⠀⠐⢀⣻⣇⠌⠀⠠⠐⠀⠀⡀⠀⠄⢸⣿⣮⠳⣜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠐⡀⣟⣻⢿⣿⣿⣟⣮⣝⢮⣓⢧⣳⢿⢧⡁⠄⠂⠀⡟⢿⣆⡐⠀⠠⠀⠂⠀⡀⠄⠺⣽⣿⡑⠌⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⢸⢧⢻⣼⣿⣿⣿⢾⣽⣳⣝⡞⠁⢸⡷⣈⠆⠀⠂⡇⠈⠻⣷⣭⢖⠢⠀⠁⢀⠀⡱⣻⣿⡇⠈⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⡀⣿⢎⠲⣿⣿⣿⣿⡿⣷⣛⡞⠉⠒⢌⡷⣥⢊⠄⠐⡇⠠⠔⠛⣿⣿⡱⢈⠀⠄⠠⡱⣿⣽⣿⠀⠠⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⢸⣧⢏⡳⣿⣿⣿⣿⣿⣳⡟⠀⠀⠀⠀⢹⡧⣏⡒⢀⡇⠀⠀⠀⠈⢿⣿⣆⠂⡌⣐⢳⣿⣟⣿⡆⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡑⠠⠁⣿⢧⣏⣼⣿⣿⣿⣿⣳⡿⣰⠟⠛⢲⡄⠀⢻⣧⣛⠤⡇⢠⠶⠓⠲⡄⠹⣿⣇⢲⣡⢻⣯⣿⢿⣷⠀⠀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠓⡈⠄⣼⣟⡳⢮⠼⢿⣿⣿⣿⣳⣧⠹⣄⣀⣰⠇⠀⠀⠙⠿⣧⣃⠹⣄⡀⣠⠇⠀⢻⣿⣳⡜⡿⣿⣽⣿⣿⡆⠀⢀⠀⢃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⡑⢈⢰⣿⢞⡽⢣⠇⠸⣿⣿⣷⣿⣿⣆⣉⡉⠁⠀⠀⠀⠀⠀⠉⠻⠀⠈⠉⡁⠀⠀⣼⢚⣷⣿⠃⢹⡷⣿⣿⣿⡄⠀⠠⠈⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠂⠄⢢⣿⣛⣮⡝⣽⠀⠀⢹⣿⣿⣿⣿⠀⣒⢋⡆⠀⢰⣤⢤⢤⣠⠀⠀⢰⢒⢢⠡⣨⢧⣫⣿⠃⠀⠘⣿⢿⣿⣿⣷⠀⠀⠄⠐⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡿⣈⠁⣀⣾⣯⢟⡶⣙⡆⠀⠀⠀⠙⣿⣧⡙⢷⣤⣶⣗⡦⣿⣞⣯⢾⡽⡀⠀⠀⣓⣤⡾⣏⡞⠉⠁⠀⠀⠀⣿⡿⣿⣿⣿⣧⠀⢀⠂⠱⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣾⡓⠄⠀⣼⣟⡾⣝⠾⣱⠃⠀⠀⠀⠀⠈⠻⣹⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⡷⢿⠹⣿⣱⡙⡊⠀⠀⠀⠀⠀⠀⢹⣟⣿⣿⣿⣿⡆⠀⠠⠀⢃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⡿⠠⠈⢠⣿⡻⣾⣋⠿⣃⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⠿⢿⣷⠄⢈⣡⢠⠀⢀⢌⠈⠀⠈⠉⠸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠠⠀⠈⡀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⡅⠃⠀⣼⢷⡻⣵⢫⡳⢭⠀⠀⠀⠀⠀⠀⠀⠀⡠⠗⠀⣼⢃⠻⣦⠊⠑⢣⠀⠘⢆⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣾⣿⣿⣿⣿⡆⠁⡀⠁⢱⠀⠀⠀
⠀⠀⠀⢀⣿⣿⡆⠀⢡⡟⢧⣛⡼⢣⣝⢣⡆⠀⠀⠀⠀⠀⣀⣼⠁⣀⣴⣏⠢⠐⣿⠄⠠⣏⠐⢂⠘⡄⠈⠓⡀⠀⠀⠀⠀⠀⠀⣯⢷⡿⣿⣿⣿⣿⣿⠀⠀⠌⢀⢃⠀⠀
⠀⠀⠀⣾⣿⣿⠁⠀⢸⢏⡳⡜⣜⢣⢎⠧⡇⠀⠀⢀⣤⣾⣿⣿⣷⠞⢸⣿⢠⢃⡇⠀⡀⢡⠉⠉⠀⣷⣀⣴⣷⡀⠀⠀⠀⠀⠀⣯⢟⡽⣯⣿⣿⣿⣿⡄⢃⠀⢂⠘⡄⠀
⠀⠀⢸⣿⣿⣿⠀⠀⡺⢌⠳⡩⢌⠣⢎⣜⣇⢴⣾⣟⣿⣿⣿⡿⠁⠀⣿⣿⣎⢿⠁⠄⠀⡘⡁⠀⠀⡇⢿⣿⣿⣷⣄⠀⠀⠀⠀⣧⠻⣜⢷⣻⢾⡿⣿⡗⣌⢒⠠⠌⣰
⠀⠀⣿⣿⣿⣿⡀⠀⠳⢌⢣⡑⢎⡱⢊⡝⣾⣿⣾⣿⣿⡿⠋⠀⠀⢠⣿⡗⢮⡟⠻⠀⠂⠀⠇⠀⠀⢰⠘⣿⣿⣟⣽⣷⣄⠀⢰⢂⠯⡜⣡⠏⣭⢹⣹⣟⡼⡆⡘⠰⡆
⠀⠀⣿⣿⣿⣿⡇⠀⢩⣘⣢⠜⠬⠖⠛⣋⢨⢿⣿⡿⠋⠀⠀⠀⢀⣾⡿⣙⢲⡃⠠⠐⠀⠁⢸⠄⠀⠀⢣⠘⣿⣿⣿⣷⣽⣷⣼⠘⢪⡕⣣⠞⡴⢣⣿⣟⡾⡅⢎⠥⡇
⠀⠀⢻⣿⠷⡈⡿⠈⠉⠀⢀⣀⣤⡴⢾⡷⡎⠉⠋⠀⠀⠀⠀⠀⣾⣿⡰⠁⠂⠉⡲⢄⡬⡂⠁⠀⠀⢀⣤⡆⠸⣿⣿⣿⡏⢁⢝⡬⢡⠘⣥⠻⣍⢷⣻⣾⡿⡜⣬⢳⠇
⢀⣄⠂⠁⡀⠙⣀⣤⠴⡚⠭⠓⡜⡸⢱⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣄⢼⣽⣿⣿⣯⠦⢀⣴⣵⣮⡻⣄⠙⠿⠉⠉⠉⠁⠀⣇⠚⡤⢛⣬⢳⣟⣿⣿⣿⣼⣻⠀
⠈⢿⠧⠷⠾⣿⣿⢌⡣⢘⠠⠁⠌⢡⡛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢬⣉⣉⡙⠛⠛⠻⠛⠛⠛⠚⢋⣉⡠⠘⠙⠂⠀⠀⠀⠀⠀⠀⢡⡹⣰⢋⡾⣽⣾⣿⣿⣿⡾⠃⠀⠀
⠀⠀⠀⠀⠀⠈⠻⢷⣌⠣⢌⠡⠌⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⣈⡏⠉⠉⣿⣉⣀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣱⢯⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠦⣁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣷⣶⣶⠃⠀⠀⣿⣿⣶⣶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣼⣿⠀⠀⠀⢻⣿⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⡿⠀⠀⠀⢸⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⡇⠀⠀⠀⠈⣿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⡇⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⢉⣩⠽⠟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠄⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⣀⣤⠴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡄⢀⡴⠚⠉⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠹⡏⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢬⣳⣄⣠⠤⠤⠶⠶⠒⠋⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢃⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠮⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡤⡴⠃⠈⠦⣀⠀⠀⠀⠀⠀⠀⢀⣷⢸⠀⠀⠀⠀⢀⣀⠘⡄⠤⠤⢤⠔⠒⠂⠉⠁⠀⠀⠀⠑⢄⡀⠀⠀⠙⢦⡀⠀⠀⠀
⠀⠀⠀⠀⣼⠃⠀⠀⢠⣞⠟⠀⠀⠀⡄⠀⠉⠒⠢⣤⣤⠄⣼⢻⠸⠀⠀⠀⠀⠉⢤⠀⢿⡖⠒⠊⢦⠤⠤⣀⣀⡀⠀⠀⠀⠈⠻⡝⠲⢤⣀⠙⢦⠀⠀
⠀⠀⠀⢰⠃⠀⠀⣴⣿⠎⠀⠀⢀⣜⠤⠄⢲⠎⠉⠀⠀⡼⠸⠘⡄⡇⠀⠀⠀⠀⢸⠀⢸⠘⢆⠀⠘⡄⠀⠀⠀⢢⠉⠉⠀⠒⠒⠽⡄⠀⠈⠙⠮⣷⡀
⠀⠀⠀⡟⠀⠀⣼⢻⠧⠐⠂⠉⡜⠀⠀⡰⡟⠀⠀⠀⡰⠁⡇⠀⡇⡇⠀⠀⠀⠀⢺⠇⠀⣆⡨⢆⠀⢽⠀⠀⠀⠈⡷⡄⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠁
⠀⠀⢸⠃⠀⠀⢃⠎⠀⠀⠀⣴⠃⠀⡜⠹⠁⠀⠀⡰⠁⢠⠁⠀⢸⢸⠀⠀⠀⢠⡸⢣⠔⡏⠀⠈⢆⠀⣇⠀⠀⠀⢸⠘⢆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⡜⠀⠀⢀⡜⡞⠀⡜⠈⠏⠀⠈⡹⠑⠒⠼⡀⠀⠀⢿⠀⠀⠀⢀⡇⠀⢇⢁⠀⠀⠈⢆⢰⠀⠀⠀⠈⡄⠈⢢⠀⠀⠀⠈⣇⠀⠀⠀⠀
⠀⠀⢸⡀⠀⢰⠁⠀⢀⢮⠀⠇⡜⠀⠘⠀⠀⢰⠃⠀⠀⡇⠈⠁⠀⢘⡄⠀⠀⢸⠀⠀⣘⣼⠤⠤⠤⣈⡞⡀⠀⠀⠀⡇⠰⡄⢣⡀⠀⠀⢻⠀⠀⠀⠀
⠀⠀⠈⡇⠀⡜⠀⢀⠎⢸⢸⢰⠁⠀⠄⠀⢠⠃⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⣶⣿⡿⠿⡛⢻⡟⡇⠀⠀⠀⡇⠀⣿⣆⢡⠀⠀⢸⡇⠀⠀⠀
⠀⠀⢠⡏⠀⠉⢢⡎⠀⡇⣿⠊⠀⠀⠀⢠⡏⠀⠀⠀⠎⠀⠀⠀⠀⠀⡇⠀⡸⠀⠀⠀⡇⠀⢰⡆⡇⢸⢠⢹⠀⠀⠀⡇⠀⢹⠈⢧⣣⠀⠘⡇⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⡇⠀⡇⢹⠀⠀⠀⢀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠠⠟⡯⣻⣇⢃⠇⢠⠏⡇⠀⢸⡆⠀⢸⠀⠈⢳⡀⠀⡇⠀⠀⠀
⠀⠀⠀⣇⠀⡔⠋⡇⠀⢱⢼⠀⠀⡂⣼⡇⢹⣶⣶⣶⣤⣤⣀⠀⠀⠀⣇⠇⠀⠀⠀⠀⣶⡭⢃⣏⡘⠀⡎⠀⠇⠀⡾⣷⠀⣼⠀⠀⠀⢻⡄⡇⠀⠀⠀
⠀⠀⠀⣹⠜⠋⠉⠓⢄⡏⢸⠀⠀⢳⡏⢸⠹⢀⣉⢭⣻⡽⠿⠛⠓⠀⠋⠀⠀⠀⠀⠀⠘⠛⠛⠓⠀⡄⡇⠀⢸⢰⡇⢸⡄⡟⠀⠀⠀⠀⢳⡇⠀⠀⠀
⠀⣠⠞⠁⠀⠀⠀⠀⠀⢙⠌⡇⠀⣿⠁⠀⡇⡗⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⠁⠀⢸⣼⠀⠈⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⠀⠀⢀⡠⠔⠚⠉⠉⢱⣇⢸⢧⠀⠀⠸⣱⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠦⡔⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⡏⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠋⠀⠀⠀⢀⡠⠤⣿⣾⣇⣧⠀⠀⢫⡆⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣠⠇⠀⠀⢀⡠⣶⠋⠀⠀⡸⣾⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⡄⠀⠀⠀⠀⠠⠊⠁⠀⠀⢸⢃⠘⡜⡵⡀⠈⢿⡱⢲⡤⠤⢀⣀⣀⡀⠉⠉⣀⡠⡴⠚⠉⣸⢸⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢧⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠚⣤⣵⡰⡑⡄⠀⢣⡈⠳⡀⠀⠀⠀⢨⡋⠙⣆⢸⠀⠀⣰⢻⡎⠀⠀⡎⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡸⢌⣳⣵⡈⢦⡀⠳⡀⠈⢦⡀⠀⠘⠏⠲⣌⠙⢒⠴⡧⣸⡇⠀⡸⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣿⠢⡀⠀⠀⠀⠠⠄⡖⠋⠀⠀⠙⢿⣳⡀⠑⢄⠹⣄⡀⠙⢄⡠⠤⠒⠚⡖⡇⠀⠘⣽⡇⢠⠃⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⡼⣄⠀⠀⠀⠀⠀⠑⣽⣆⠀⠑⢝⡍⠒⠬⢧⣀⡠⠊⠀⠸⡀⠀⢹⡇⡎⠀⡿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⠻⣺⣧⠀⠀⠀⠰⢢⠈⢪⡷⡀⠀⠙⡄⠀⠀⠱⡄⠀⠀⠀⢧⠀⢸⡻⠀⢠⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⣿⠀⠀⠀⠀⢣⢇⠀⠑⣄⠀⠀⠸⡄⠀⠀⠘⡄⠀⠀⠸⡀⢸⠁⠀⡾⢰⡏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀