⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠒⠦⣄⠀⠀⠀⢠⠀⠀⢀⣀⣴⠶⣯⣽⣳⣶⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⠀⠨⣳⡀⢀⣷⡾⠻⠝⢹⢱⢀⡄⡄⣸⢩⣭⡀⠈⠺⠺⠐⣼⡄⠀⠀⠀⠀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠐⠰⡝⣾⢻⣡⢀⣣⣿⣿⠞⠛⠋⠉⢉⠉⠉⢕⡳⢧⡆⢈⠻⣦⠀⠀⢰⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⡉⠒⠒⠀⢠⡤⠖⠒⠉⠛⠪⣷⢟⢟⡝⠍⡐⣞⠾⠁⣔⡎⡀⠀⢸⠑⡈⡹⣾⡟⢎⣷⠴⠋⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠷⠤⣤⡾⠁⠀⠀⢀⡠⠄⠀⡟⣮⠚⠰⡘⠀⢠⠀⠀⡎⡿⠀⢀⡇⠀⢡⢳⢺⢻⣟⣡⢴⠶⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡾⠃⣀⠴⠒⠈⠉⡿⣿⡟⢾⠃⢀⢣⠇⠳⣄⠀⠀⣇⣰⢃⠸⡄⠀⠈⢸⠀⡟⠺⣟⠺⢤⣈⡳⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡠⢔⣵⡡⠊⠀⠀⠀⠀⣸⣾⣿⠿⣸⢼⣏⣸⡼⡤⣧⡧⢸⣿⡇⢻⣯⢣⢠⣠⡌⠀⡇⡆⣿⡦⢄⣀⠉⠛⠒⣶⠦⠀⠀⠀⢀
⠃⠤⠭⠤⠐⡧⡿⠀⠀⠀⠀⠀⢠⡿⡝⡝⣆⢿⣿⣷⢿⣿⣧⢻⣿⣞⣟⣥⢸⣿⢻⣶⣵⣦⣶⢧⣷⢟⢜⣄⠉⠻⣍⠙⠂⣤⣤⡴⠜⠀
⠀⠀⠀⠀⢸⠁⣷⠀⠀⠀⠰⣖⡚⣿⣛⢿⣎⣸⠀⣹⣿⣿⣿⣿⣿⡕⣏⢿⣾⣧⣶⣿⣿⣿⣿⣾⢹⢸⡘⣸⠷⢄⠘⡍⢢⠍⣻⣄⡒⠀
⠀⠀⠀⠀⠈⢄⠘⠵⡄⠀⠀⢸⡿⡗⠮⣽⣏⣇⢷⣸⡟⠻⠮⠯⠇⠀⠙⠢⠘⣿⣿⣿⣿⣼⣿⠇⡬⣾⣣⢿⡄⠀⠀⠘⡄⡄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠑⠸⠶⠷⠚⢿⠀⡼⠤⢾⣇⠱⣪⢟⢯⡓⠀⠀⠀⠀⠀⠀⠀⠺⢿⠿⣿⡿⠁⣸⠑⢧⡏⢾⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡆⠀⡗⠀⣾⣿⡜⡌⣿⣾⠻⠤⠢⡀⠀⠀⠀⠀⠠⠤⣄⣾⡴⠞⣿⣙⠾⣿⣏⠻⣤⣤⢐⢝⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡇⢸⡇⣰⣿⣿⡇⠘⡿⣿⣷⣄⡀⠀⠈⠉⠉⠀⣠⣾⣿⣿⢃⢼⣿⡐⢲⡬⡧⡀⠘⡿⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢀⡇⡇⢿⣾⣿⣯⣿⡇⠋⣧⡿⢸⣿⣷⣶⣶⣺⣿⣯⡿⢿⣧⢙⣿⢟⣋⠆⢆⠐⣵⡉⠻⣮⣱⡦⢄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⣔⠎⡰⠏⠱⣧⠾⡏⠙⠙⠻⢿⡼⢻⠷⣾⣯⣿⣿⣟⠿⢻⣿⣷⣿⡾⣾⣿⣼⠩⡺⡘⡄⠸⣳⢄⠘⢧⡎⠂⠤⠀⠀
⠀⠀⠀⠀⡠⢔⢏⠊⣰⠏⢀⢼⡟⠄⠳⡀⠀⠀⠀⢟⣟⡗⠢⣴⣿⣿⣷⠿⣾⣾⣿⣿⡁⣷⣿⡄⠀⠘⡯⢷⣒⣣⢧⠳⣅⠳⣄⠀⠀⠀
⠒⠒⠀⢁⠔⡱⢃⢬⣿⢂⠂⡇⠐⣀⠀⠙⢤⣀⡠⠈⡜⢴⡄⣻⡟⢛⣿⠋⠉⠉⠋⠀⠈⠑⢮⣥⡇⠀⡃⢸⢸⡇⢮⡄⢡⢳⡪⢦⡀⠀
⣀⠠⢒⣥⠪⢐⣵⣿⢃⢃⢤⢇⠀⠀⠀⠀⠀⢸⠃⠀⠐⡈⢻⢼⡷⠬⣻⣀⣀⠠⠁⠀⣯⠀⠀⣇⡇⢰⠷⢸⣿⠁⠘⣿⠘⡎⡗⡌⢏⠑
⠈⣩⠞⢁⡠⣾⣿⡽⡞⢋⣡⠾⠀⠀⠀⠀⠀⠘⠀⣠⠞⢉⣶⠝⠿⣈⣍⡛⣷⡀⠀⢀⣣⡀⢀⣸⣷⡃⡤⠁⡿⡆⠀⣿⡁⢷⢱⠘⡌⠄
⠚⢁⣲⡭⢞⣿⢿⠼⠚⠉⣉⣶⣇⠀⠀⠀⠀⠀⠟⠁⣠⠟⠁⣰⣤⣤⡘⣕⡾⣇⢔⡿⠥⠬⣫⣀⠡⢿⣇⠀⠘⡇⠀⢰⡇⢘⡇⠆⠰⠀
⠚⠉⢠⣾⠟⠋⠁⠀⢀⣴⠿⠘⣾⠀⠀⠀⠀⣀⡶⠚⠁⣠⣾⣿⠋⠀⢿⡿⣷⠋⣻⠞⢉⡑⠲⡉⢧⠀⢻⢷⣤⠛⢰⠈⡅⢰⣧⣘⡀⠀
⠉⣔⡿⠁⠀⢀⡤⢔⠍⢔⡗⣼⣏⠀⠀⢀⡾⠋⠀⠀⠀⠞⠉⣇⠀⠀⠀⠀⠉⠈⠁⠉⠁⢸⡆⠀⠘⢆⠀⢇⠙⣷⣄⠀⠁⣼⢣⠹⡡⠀
⠔⢛⠖⠒⣪⠋⠀⣞⠠⡾⣱⠋⠸⡧⡰⠛⠁⠀⠀⣀⣀⣀⡐⠉⢳⡄⠀⣠⠀⠀⠀⠀⣠⠿⣿⡀⠀⠀⢣⡘⡀⠙⢎⢷⣔⠘⡈⡆⠳⡣
⠜⠁⠀⣴⠙⠀⡸⢿⢀⣾⠇⡇⢰⡿⠁⠀⠀⠀⢀⡜⠁⢀⣈⡓⠴⠻⠖⠀⠀⣴⣚⣉⣀⣀⠀⢡⠀⠀⠐⠷⣇⠀⠈⢷⣽⣷⣄⠰⢰⠈
⠀⢀⣾⠇⢠⢰⢳⣠⠞⡝⠄⢠⢨⠁⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⣁⠀⠸⠀⡿⢷⣄⢻⡏⢎⠙⢷⣿⡄