⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢟⣷⢾⣻⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣯⣍⣚⢫⣵⢾⣿⣿⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⣛⠿⣘⠎⣞⠫⢾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣏⠖⣱⠚⣜⣧⡧⣫⣿⣿⣖⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡹⢿⣿⣿⡿⡎⣝⢣⡯⢳⣞⣼⣿⣿⣿⣿⣷⣦⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡤⡞⢫⢳⡛⡽⣧⣾⡱⡩⡌⢧⣹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢧⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⢮⠱⣉⣶⣷⣼⣎⣏⣲⡹⢷⡋⠾⣞⣋⠿⢿⣿⣿⣟⠛⢿⣿⣿⣷⣜⠀⠀⠀⠀⠫⠹⡠⠥⡢⡄⠀⠀⠀
⠀⠀⠀⠀⢀⣸⠫⠵⢦⣿⠿⠳⣜⣿⢣⡿⢯⡔⡳⣶⡌⢊⡔⢢⢲⣬⡆⢠⢻⣿⡇⠇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀
⠀⣠⠴⢫⡑⣦⣙⡼⢞⣟⠼⡝⠴⡹⢶⢇⠣⡔⡹⣍⠧⣃⡜⡰⢙⢿⠀⠈⠛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣎⣹⣿⣿⠷⣒⢣⣹⣾⣿⢗⡻⣷⡟⣌⡬⠱⣌⣙⣩⣪⣻⡔⡡⢣⣘⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡿⣿⡛⢦⢣⣵⡿⡯⠃⠹⣦⢟⣡⡗⣧⡲⢱⣿⡿⡿⢃⣿⢿⣔⣝⡌⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⣀⡀⠀⠀
⠳⡝⣾⣷⣿⡿⠋⠀⣠⠞⢳⣿⣿⣿⣏⣻⣿⣾⣿⣿⣿⡣⣾⣿⣽⣿⣻⣇⠀⠀⠀⠀⠀⠀⠀⠈⠢⣂⢋⠔⠉⠸⠁⠀⠀
⠳⠷⠁⠋⠁⢀⡤⠈⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⢣⡙⢗⠢⡀⠀⠀⠀⠀⠀⠀⡚⠁⠀⠀⡜⠀⠀⠀
⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⢈⠿⣿⡿⣯⣿⢿⣟⣿⡯⢏⡿⠟⠁⠙⡰⠘⡍⢣⡻⠤⢄⠀⠀⠀⠀⠱⡠⡀⠀⠀⠀⠀⠀
⠀⠂⠀⢛⡀⠀⠀⠀⠀⣠⡖⣯⣾⣷⢹⣿⠌⣂⣻⡟⣩⠞⠁⠀⠀⠀⠈⢳⢨⣶⣿⡮⣙⢦⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠆⡀⣠⣞⣿⣿⣿⣿⡻⡐⢼⡿⣴⡟⣢⣧⡀⠀⠀⠀⠀⠀⠀⠀⠻⠻⠿⣜⡌⢖⠲⣄⠀⠀⠀⠀⠑⠢⡀⠀
⠀⠀⠀⠀⠀⡠⢏⢿⣿⡿⣷⣼⣿⣿⡛⣜⣷⡿⣕⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡘⠹⢺⣮⣦⢇⢦⣀⡄⠀⠀⠲⠀
⠀⠀⠀⠀⡴⣹⡘⢼⠹⣷⣿⣿⣟⣻⣿⣿⢿⣾⣷⣿⡷⡟⠀⠀⠀⠀⠀⡀⠤⠒⠁⠉⡸⠀⠀⠨⣋⢆⡘⡹⢴⠀⠀⢸⠀
⠀⠀⠀⣼⢓⠦⡙⢆⡛⡴⢹⢟⣿⣿⣿⢿⣿⣿⣾⣿⢞⠃⠀⠀⠀⠠⠘⠁⠀⠀⠀⠰⠁⠀⢀⢠⠸⠒⠣⠹⠁⠀⠀⢰⠀
⠀⠀⠠⣗⠏⡖⣹⢪⠱⣉⠧⡚⢟⣿⣷⣾⢿⡝⢯⡘⢎⠵⣄⠀⢸⡇⠀⠀⠀⠀⠬⠵⠒⠃⠁⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀
⠀⠀⠂⣯⡝⡼⡑⣎⢳⡘⠶⡩⢎⢯⠽⣞⢤⢛⢤⡙⠮⣜⢸⢣⡄⣦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⡀⠠⢀⢡⡟⠀
⠀⠀⠀⣟⢮⡱⣙⢦⢣⢝⣱⡙⢲⢺⡝⡼⣊⠞⡰⣙⠞⣌⢣⢣⢞⡴⡖⡀⠡⠐⠠⡀⠐⢀⢂⠈⠄⠠⢁⠄⣡⠖⡉⠄⠂
⠀⠀⠀⢹⣣⠳⣍⢧⣋⡞⣰⣙⢣⡝⡼⡵⡸⢌⡱⢌⠞⡌⣎⢎⢬⢳⡘⢦⢀⢁⠂⠄⡉⡀⢂⢌⡰⡥⠞⠫⡐⢡⠐⡈⠁
⠀⠀⠈⠌⣷⣛⡞⣮⢳⡜⣳⢬⠷⣘⡇⠘⣧⠧⣙⠎⡞⡜⣌⠎⡶⢩⢧⠈⠳⢴⡨⣴⡤⠷⢚⠋⡍⠤⠉⡔⠠⠁⠂⠄⠀
⠀⠀⠈⠠⠹⣖⡻⣜⣧⢻⡵⣫⢞⡵⢣⡁⠌⢿⣊⢷⡸⡱⢎⢮⣑⢫⡞⡤⢁⠒⡀⠆⢆⠱⠌⡡⢒⡈⠅⠤⢁⠈⡐⢈⠀
⠀⠀⠀⠀⠠⠉⢓⠛⡜⠳⢙⠚⣋⠚⣋⠢⡘⢠⠉⠴⢉⠓⣉⠒⠊⠓⠚⢃⠂⡘⢠⠉⡂⠅⢊⠐⠠⠐⠈⠀⠄⠐⢀⠂⡁