⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⣀⣤⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⣜⣣⠞⣿⣿⣿⡿⣟⡟⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣙⢦⣇⠻⡴⣛⣿⡵⢎⡼⣱⡚⣼⢻⣿⣿⡟⡽⣛⠿⣿⣿⣿⣷⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡳⣜⢺⡬⢏⡵⢣⡝⣹⢎⡵⢣⡝⢦⡛⡼⣻⣿⡵⣩⢞⡹⢿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⢎⡳⢼⡹⣜⢣⣝⡲⢭⣚⠵⣚⢧⡹⣱⢣⠞⣯⠵⣪⠝⣮⠹⣝⢫⢟⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡜⣣⢳⢎⡳⣬⢓⡳⢎⡻⣜⡲⡹⡥⢏⡞⣥⠻⣔⡛⢦⡻⣌⢏⡞⡼⣿⣿⣿⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣥⣋⢮⠵⣊⢧⡛⡼⡱⢎⡵⢳⢭⡓⡞⣥⢻⡜⣹⢣⠗⣮⢹⡜⣱⢿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣎⢧⢫⡝⢶⣹⡱⢏⡽⢪⣝⡲⢽⡱⣋⢶⡩⢇⣏⠾⣡⣛⢼⣣⢞⡻⢿⡻⣟⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣮⡓⢮⣓⢦⠽⣩⢞⣣⠮⡕⣧⢳⣭⣶⣿⣿⣾⣧⣷⣬⠳⡭⢎⡵⣋⠶⣍⠮⣽⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣯⣷⣾⣮⣳⣧⣞⣦⣿⣽⣾⠿⠛⠋⠉⠀⠀⠉⠙⣿⣟⡼⣩⠞⣭⢓⡮⣽⣾⣿⣿⣿⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠃⠀⠀⠀⠀⣀⣀⣤⣤⡀⠈⣿⣧⢇⢾⡠⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⣽⡿⢿⣾⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟⠁⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠿⠋⠀⢀⣿⠃⠀⠀⠀⠁⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⣀⣴⣾⠿⠋⣡⣾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⣿⣏⣀⣴⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣏⢧⢫⢟⡻⢏⡽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⡗⣺⢬⡓⣮⠳⣭⢲⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⡮⡼⡱⣎⠵⣎⢽⠲⣍⢯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣜⡳⢵⢪⠽⣘⠮⣝⡜⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢵⣊⣿⢥⡫⡝⣥⣛⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⢦⣋⡟⡶⣱⢋⡶⣹⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣭⡚⡵⢣⢏⡖⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣿⡼⣭⣾⣾⡿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠉⠁⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⣿⣿⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣰⣿⣿⣿⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣿⣿⣿⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠈⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⠀⠀⣠⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣦⠀⠈⣿⣿⣿⣠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⡇⠀⢿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣷⠀⠀⠉⠙⠋⠉⠀⠀⠈⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠟⠛⠛⠉⣰⣇⠀⠀⠀⣾⣿⡀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢰⣶⡄⠀⣿⣿⣆⠀⠀⢽⣿⡇⠀⣿⣿⣿⡀⠀⣸⣿⡄⠀⢀⣴⣶⣶⣶⣶⣷⣄⣠⣾⣷⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⣿⠀⠀⣼⣄⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⣿⣿⣿⣆⠀⢸⣿⡇⠀⣿⣿⣿⣧⠀⢹⣿⡇⠀⠘⣿⣿⠋⠛⠛⠛⠉⢸⣿⡟⠛⠛⠻⣿⣿⣦⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⡆⢸⣿⣿⡄⠀⢾⣿⡇⠀⢸⣿⡇⠀⣿⣿⣿⣿⡆⠘⣿⣿⠀⣿⣿⣿⣿⣇⠘⣿⣷⠀⠀⣿⣿⣀⢀⣀⠀⠐⢺⣿⡇⠀⠀⠀⣹⣿⣿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣧⣿⣿⣿⣿⡀⣿⣿⠀⠀⢸⣿⡇⠀⣿⣿⠈⢿⣿⣄⣿⣿⡀⢿⣿⡇⢿⣿⣾⣿⣿⠀⠀⣿⣿⣿⣿⣿⡿⠆⢸⣿⣿⣀⣤⣾⣿⡿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢹⣿⣷⣿⣿⠀⠀⢸⣿⡇⠀⣿⣿⠀⠈⣿⣿⣿⣿⡇⢻⣿⡇⠈⣿⣿⣿⣿⠀⠀⢻⣿⡄⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⢿⣿⣿⣿⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⠹⣿⣿⣿⣇⣿⣿⡇⠀⠸⣿⣿⣿⡀⠀⣻⣿⡇⠀⠀⠀⠀⠠⣿⣟⠉⠉⠉⢿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠘⣿⣿⡏⠀⠀⢸⣿⡧⠆⣿⣿⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⠀⠹⣿⣿⣧⠀⢽⣿⣷⣶⣶⣶⣦⣴⣿⣿⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢿⣿⣟ ⠀ :praisesun