⣇⠡⣱⢿⡷⡈⣿⡇⢀⡖⢸⡄⠸⡀⠀⠸⣾⣿⡧⠃⣐⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢷⡰⠈⠀⡖⣠⣠⣽⡏⡆⡄⢇⠄⢠⠁⡙⣼⣼⣿⠏⠀
⠸⢢⡡⢿⡷⠀⣿⣧⠎⣴⣶⣷⡠⢡⣀⠨⢫⢻⡧⠋⠀⠀⠀⠀⢠⡖⠲⠀⠀⠀⠀⠠⣄⣴⣬⣶⡖⡜⣷⣯⣿⡛⣸⠷⢘⣠⠀⠜⣿⢸⣿⠏⢀⠀
⠀⠠⡇⢰⣷⡐⢽⢿⠠⡎⡜⠿⠫⣨⡣⣃⠔⠁⠀⠀⠀⢀⣀⣀⡸⣧⣖⣦⣽⣷⢼⣿⣿⣿⣿⣿⣿⣦⣟⣵⣽⣔⡥⢻⡬⣊⢝⣜⢱⣿⢿⣄⠆⡀
⠀⢠⠰⠀⢛⡮⠡⢬⡷⠥⠰⣸⣱⣁⠔⠁⠀⠀⠀⢀⡴⠛⠉⢀⠄⡑⣄⠞⡤⢄⠀⠈⠫⠻⣿⣿⣿⣿⣿⣿⣶⣮⣿⠩⡌⣌⡪⣶⢼⣞⣄⡭⣒⠀
⠀⠐⣰⢡⢰⠩⠡⣁⣷⣐⣜⣼⡗⢁⣀⣠⣐⣲⣿⠏⠀⠀⢎⡂⠉⠨⠂⠎⠀⢌⢡⡀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣦⣝⢭⢸⠏⣩⠿⠯⠏⠷⠎⣘⣀
⠀⡾⣍⠀⡏⠸⣄⢫⢻⣿⣶⣷⣿⣿⣿⣿⣿⣿⠁⠀⠀⡈⢋⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠈⢿⠿⢹⣿⣿⣿⣿⡯⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢸⠝⢿⡖⣝⡟⠘⢢⣿⣿⣿⣿⣿⡏⠿⠟⢠⡾⠀⢀⢡⣸⣀⣀⠀⠀⠀⢀⡤⠤⢤⡎⠠⠐⠌⢻⡬⠽⢿⣿⡟⠁⠀⡀⠀⠀⠀⣀⠀⢀⠀⠀⠀
⢠⡘⢿⡮⣺⡸⡫⡇⠜⣿⣿⣿⣿⣿⡙⠲⠖⡉⠁⠄⢓⢴⠋⣈⢁⠀⠀⠀⠐⣵⣦⣤⣈⢴⢄⠀⣀⣀⣴⣿⠏⠀⠀⠈⡄⣀⠔⠊⢄⠉⡲⢖⣦⠀
⡜⣿⣇⠉⠺⣟⡘⡧⡡⠿⢟⡻⢿⢿⣗⣄⣠⡿⣄⣁⠋⢷⠿⠿⠛⠀⠀⠀⠀⠉⠉⠙⠙⢹⢱⠍⠒⠹⣿⡏⠀⠀⠀⢀⠓⡇⠀⡠⣄⠔⠀⣸⡏⠧
⣿⣼⣿⡆⠀⢹⡚⠉⠑⠂⠤⣈⠢⠱⠻⣿⣿⣃⠈⢹⡠⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠵⢥⠊⢀⠲⢾⣿⠀⠀⠀⠀⠘⡄⠘⢐⠿⡁⢔⠂⢏⠆⠐
⢯⡿⠟⠋⠉⣁⣤⡤⠭⣕⡢⢌⠆⢳⠀⣿⣦⠁⠴⠏⡱⣴⠛⠀⠀⠀⠀⢀⣀⣀⣐⡀⠀⡈⣀⢈⠣⡛⣟⡆⠀⠀⣴⢏⠶⡀⢠⣚⢱⠁⠠⠀⠀⠀
⠊⠀⠀⠀⢎⠦⢅⡝⢴⣬⣏⡢⡙⡎⢸⣿⡷⠦⢌⣀⡿⡌⠀⠄⠲⣮⠅⠀⠀⣐⠾⠁⠀⢀⠟⠺⣄⠥⣙⣧⠀⠀⠀⡍⠘⢸⠎⣦⢹⠄⠠⠤⠀⠀
⠀⠀⡠⢄⡈⠉⠐⠒⠽⣻⠕⡅⢷⠈⣿⣿⡟⢂⣂⡌⡐⠈⠢⣄⠀⠀⠩⠉⠉⠄⠀⠀⣰⠇⠀⠀⠀⠻⣿⣿⣷⡄⡰⠁⠄⣸⠠⠈⠻⣚⡡⠆⠀⠀
⠀⠀⠓⠒⠁⠀⠀⠀⠀⠈⠣⣟⡼⠀⢸⣿⣿⠏⣀⡓⠀⠒⠀⠈⣷⣦⣀⠀⠀⢀⣠⠾⢻⡆⠀⠦⣠⣥⣽⣿⡿⠻⡀⢰⣰⠛⣆⠈⠐⢄⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⠼⠬⢿⣿⣯⣶⣦⣾⢀⡄⠇⣠⣌⡉⢉⡭⠤⣠⠬⠓⠚⠓⢺⣿⠟⠛⢂⣀⠭⠥⡌⢹⠈⢑⠺⢦⠉⠉⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⡴⡦⠼⠭⠘⠻⡩⡩⠍⠋⣁⠀⠐⢿⣔⠐⠾⡄⠤⠤⣂⠆⠀⠏⡑⣦⠀⠀⠀⡇⢸⡠⠊⠀⠈⠁⢀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⡇⣴⣃⡇⠇⠀⠀⠀⣈⡽⠋⠉⣹⠒⠬⠥⡔⠁⠀⠀⠈⢫⢉⠐⢠⠊⣠⠧⠼⢧⡤⢤⠇⠈⣦⠴⠒⠉⠉⠀⠀⠀
⢀⠀⠀⠀⠀⣀⡠⠔⢊⠩⢔⠞⠊⠀⠘⠳⠶⣭⡢⡈⠉⠀⠀⣜⣭⣅⢦⡀⢇⣩⣠⠤⠤⢤⡗⠀⠀⢘⡇⠀⠀⠀⠀⠁⠻⣦⠑⠶⢍⣀⠀⠀⠀⠀
⠈⢏⢲⠊⣉⠠⠐⠈⢀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠻⣌⠢⢒⣉⡼⠀⠈⠳⠤⠼⠀⠀⠀⠀⠀⠙⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠄⡈⠙⠲⠦⡀
⠀⠘⣿⠘⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⢙⠸⠵⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠑⠂⠀⠀
⠀⠀⢸⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀
⠀⠀⢸⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⠀⢘⢰⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀
⠀⢀⣼⢸⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀
⠀⠀⠸⠘⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⢄⣀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣿⣿⠋⠀⠀⠀⠀⠀⠀
⠀⠀⠇⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠂⡆⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠃⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣾⣥⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⠊⠕⠂⠀⠀⠒⠒⠀⢄⢹⠐⢲⠲⠄⣀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠄⠂⠀⠀⠁⠂⢤⣀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠹⣿⣿⣿⣿⣿⣿⣿⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀
⠀⠀⢰⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧