⡍⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠒⢲
⠘⢦⡀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⢀⡴⠋
⠀⢻⣍⠲⢄⡐⠤⣉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣁⠀⠀⣀⡴⠟⣪⠇
⠠⡤⠽⢦⣀⠈⠑⠢⢍⣒⠤⣉⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣉⠤⢒⣩⠴⠒⠉⢁⡠⣚⢥⠀
⠀⠙⢶⡀⠈⠙⠒⠤⣐⡪⠭⣒⡘⢍⡁⢍⣒⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⠪⠭⠈⣉⠽⣐⠮⢕⣊⡤⠤⠒⠋⢉⡤⠊⠀
⠀⠀⠰⡛⠓⠢⢤⣀⡀⠬⢝⣒⡪⢏⡈⠝⣒⡨⣿⢿⡑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⡰⢅⣖⡲⠾⠍⣩⢯⣒⣋⠥⢤⣒⠠⠤⠐⢛⡶⠂⠀
⠀⠀⠀⠈⣒⠤⢄⣀⡈⠍⣒⡒⠠⠵⣏⠙⠒⢺⣅⢿⡍⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣹⢥⡗⠶⠌⣉⠯⠔⣒⣊⠩⠁⠀⣀⣠⣖⣏⠀⠀⠀
⠀⠀⠀⠀⠑⢤⡀⠀⠈⠉⠒⠒⠫⠭⢼⣛⠒⠒⡧⣽⣏⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣈⣷⡲⡏⠉⣙⡯⠭⠥⠒⠒⠊⠉⠉⠀⢀⡴⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠠⡌⠙⠒⠊⠬⠭⠥⠤⠰⣞⡉⠉⣟⡵⣯⣠⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡁⢠⡾⣟⣍⡎⠭⢖⣏⣉⡥⠤⠤⠤⠤⠴⠭⡅⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠲⠤⢀⡀⠀⠀⠀⠴⠦⢍⡉⢿⡜⡽⢸⢾⣦⣤⠉⡕⢲⣒⡆⠀⠀⠀⠀⠀⠀⡖⣺⠻⣏⣰⣄⣿⣟⡼⡿⣾⣞⣉⠿⠭⢐⣀⣀⣀⣀⣤⡴⠚⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⢏⣉⠉⠀⣀⣠⢴⠖⠽⡴⣞⢿⣇⣎⠋⡇⢫⢻⡱⣞⣿⡤⡄⠀⠀⠀⠀⡼⣽⣟⡟⢿⢛⣎⡏⣾⢮⣟⣽⡷⡛⠧⢖⣒⣂⢀⣀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠖⠁⡴⢋⡤⡳⢻⢀⢿⢹⢹⢞⢳⢏⣯⣹⠳⡷⡀⠀⢀⣜⡗⣏⣹⡏⢻⣯⣻⢹⢱⣟⢼⢻⣳⡌⠑⠄⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠤⢒⣟⠜⢁⡎⡝⡸⡶⢻⢳⢯⣢⠻⡝⡌⢮⠿⠀⢸⣪⡎⡰⣫⢷⣻⢳⢻⠒⡿⡝⡍⣆⠱⠜⣶⠤⠄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣊⠴⠻⠜⢠⡇⠃⢸⡸⠀⣧⠃⢸⢆⡼⠀⠀⠀⠘⠦⢞⡇⢪⠇⠘⣸⠀⡗⣧⢳⢸⠙⠦⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣠⠋⡇⢠⠎⢧⢂⡜⠢⠎⠀⠀⠀⠀⠀⠀⠀⠈⠧⠾⡄⣠⠋⢧⣠⠎⠣⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠙⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀