⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⠢⠐⡄⢣⠘⡌⢦⠑⡼⠰⣡⢊⢼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠂⠠⢁⠢⠐⠣⡘⢄⢃⠞⡤⢋⡔⢳⡐⢎⣺ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠐⠠⡈⠐⡈⢔⡈⢆⡱⢊⡜⣜⠢⣍⠲⡱⡜⢢⣽ ⠀⠀⠀⡀⢲⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⢐⠰⠉⡜⣀⠲⢌⡐⢣⠸⡔⡳⣈⢧⢱⠎⡕⣺ ⡀⠀⠠⠀⠀⠠⠀⠒⠻⠟⡻⠶⡲⠤⣄⣀⡀⣀⡤⣖⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠒⠠⠤⠤⠄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⠐⠂⠤⠑⠌⡔⢊⣔⣜⣡⣓⣬⣱⣍⡞⣬⣛⠴⣻ ⠀⢀⠀⠀⠀⠐⠤⢤⣀⢀⡀⠀⢀⠉⠉⠉⠹⠽⢤⣐⣷⣾⣽⣶⣤⣀⣀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠈⠁⠛⠘⠚⠓⠒⠓⠛⠚⠉⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢀⠀⠄⢂⠀⠄⢀⠀⠀⠀⢀⠂⠀⠠⢀⣘⠄⠀⠉⠀⢫⣽⣥⠌⠉⡝⠚⠛⣷⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢀⠿⢻⣇⣠⣠⣠⣄⠃⢃⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢘⠛⠸⠿⠛⡠⠀⠀⢄⠛⠤⢼⣟⣿⣿⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠩⠾⠛⠿⠶⠿⠦⠾⠯⡭⣽⣻⣲⣬⣼⣰⣦⣋⣄⣎⠴⡀⠀⢡⣂⡸⣐⠤⣀⣈⠀⠠⠀⠈⠃⢉⠲⡿⠷⣪⠿⣟⠲⡦⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠛⠚⠓⠒⠯⠥⠼⢽⣛⣓⣲⣮⣒⡲⠮⠥⠤⠧⣼⣶⣭⣼⠤⣆⣢⣭⣽⣿⣶⣶⠤⢤⣀⣀⠀⠀⠀⣀⣀⢀⣤⡴⠶⣾⣿⣯⡄⠈⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠞⠛⠩⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠉⠙⠛⠛⠛⠶⠶⠶⠶⠦⠤⠤⠤⣍⣛⣪⣵⣿⣒⠮⣟⣻⣉⠭⣛⣿⣭⠭⣓⣢⠭⠙⠾⠿⢿⣏⣉⡀⠠⠤⠀⠀⠀⠀⠀⠀⠉⣁⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠛⠉⠀⠀⠀⠀⠀⠀⠙⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣟⡻⡭⠽⢋⡞⠒⢲⠽⠥⠾⠯⣿⠿⢶⣵⣶⣾⣟⡷⠒⠫⢭⡕⣒⡡⠤⣤⡤⠤⢀⡀⢀⣀⣤⠴⣒⣋⣭⠵⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣄⠀⢀⣠⣴⣄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠲⠿⠭⠛⠉⠀⠤⠤⠀⠀⠀⠀⠀⠐⠒⠛⠻⠯⢿⣿⣿⣿⠧⢥⡲⠤⣗⣲⣫⣽⣶⣾⣷⣾⣿⣿⣷⣿⣍⣉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣿⣿⡞⠛⠙⠛⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡤⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣇⣄⣤⣤⣼⣿⠿⠿⠛⠛⠉⠁⠀⠀⠛⠉⠉⠙⠻⠿⣿⣿⣿⣶⣦⣤⣤⣄⣀⣀⣀⣀⠀⣴⣿⣿⣿⣫⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣦⣶⢶⠿⣿⡛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⠀⠀⠀⠐⡚⠿⠛⠛⠉⠒⣻⣿⣯⣿⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢤⣒⡲⢯⣍⡑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠤⢤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣾⡿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⢀⣀⣸⣾⣿⣿⠗⠢⣤⣤⣤⣤⣤⣀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣀⡤⠶⣬⠭⣩⣿⣿⣿⣿⢻⡕⣿⣷⣼⣯⣿⣿⣧⣤⣤⣀⣀⣠⣤⣤⣤⣤⣄⣼ ⣩⡿⠿⢿⣯⣛⢷⡾⠟⠳⠦⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠒⡛⣿⢿⣿⡅⠂⠈⠉⠉⠫⣹⣿⣿⣿⣇⣀⣄⣀⣀⣏⣠⣤⣤⣤⣤⣷⣤⣤⢴⣤⡶⣾⣗⠲⣛⣿⣿⣿⣿⣿⣿⣷⣾⣆⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣛⣓⣿⣛⣿⠯⡷⠥⢤⡀⠀⠤⠐⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⢶⣫⠉⢹⠈⠆⠈⠻⣼⣿⣇⠀⠀⠀⠀⣠⠚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣿⢻⣿⡏⣽⣻⣷⣿⣽⣿⣿⣿⣿⣿⡿⡟⠻⠾⣿⣿⣿⣟⣻⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠹⠇⣶⣟⡾⠒⣣⣮⣉⣻⣶⣤⡀⠀⠀⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿⡶⢊⣀⣼⡤⠬⠿⢿⣿⣛⣿⠿⣿⣷⣿⣫⣥⣋⣻⣟⣿⡛⠿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠙⢼⣽⡉⠹⠤⢿⣿⣿⢿⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢤⡐⡷⢾⡝⢓⣠⠌⢛⠿⣒⣽⣿⣆⡐⠀⢉⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢻⠟⣻⣷⠭⢧⠀⠀⠄⢳⣀⡀⢀⣉⢉⣷⣊⣿⣿⣿⣿⢯⣿⡟⣻⣷⣿⣶⣯⣿⣟⣿⣿⡿⢿⠛⠉⠁⠈⠉⠀⡀⣠⢴⣶⣶⣽⣷⡄⠀⠠⠀⠉⠉⠉⠉⠉⠋⠛⢟⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠉⠩⠿⢔⣂⠒⠬⢋⠉⠫⢛⠲⣭⣗⠢⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣟⠻⡵⢟⠉⠑⡄⠈⢇⠀⠀⠈⡞⠓⠘⠟⠨⢷⣿⣿⣿⣿⣿⣾⣿⣧⣿⣿⣿⡷⢾⠴⢿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣤⣝⠆⠛⠁⠀⠀⠀⠀⢀⠂⠰⠀⠀⠀⢈⣹⣿⣿⣿⣿⣿⣿ ⠀⢀⢰⣉⡀⠶⡸⠶⣀⢀⠁⠈⣆⢹⣿⠱⡎⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⢿⣾⢿⡿⢏⠹⠹⡀⢷⢰⠁⣶⢸⠀⠀⠀⡇⠀⠈⢀⡏⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⢀⣸⡿⣾⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣆⡀⠀⠀⠀⠉⡿⢷⡏⠉⡇⢸ ⠁⠀⠳⢬⣙⣠⡔⠀⣀⠀⠀⠂⠠⠨⠿⠚⠹⣟⠵⣦⡀⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣟⣿⣇⡆⠀⡋⣭⢤⢌⡫⢤⠗⠘⠚⢒⠚⢓⠖⠊⠉⣉⣽⣿⣿⣿⣿⣿⠽⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣀⣻⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠴⠀⠀⢸ ⣂⣀⣐⣂⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠲⣄⠉⠹⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠰⠦⣼⣷⠬⣄⠠⠆⠄⠥⣀⣤⣷⣴⣥⣶⡤⠤⠷⠾⠷⠒⠖⠛⠛⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣶⢶⣿⣶⣶⣦⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⡈⢽⠶⢤⣤⡀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠂⠄⠀⠉⠁⠀⠂⠘⣗⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣽⣾⣶⢖⠒⠁⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠈⠕⠶⢆⣀⣉⠀⠈⠀⠐⠀⡀⠀⠀⢀⣄⣶⣷⣧⣤⣤⣤⣀⣳⣦⡕⢸⢕⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠠⠄⠀⠀⠀⠁⠀⠐⠀⠀⠈⠘⠓⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠟⠊⠊⠦⡉⢢⡹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠀⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠈⠁⠀⠀⠀⠀⠀⠈⠩⠲⠀⠠⠤⣀⣤⡤⠀⠀⠀⠀⣠⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠂⠤⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠒⢭⣉⡁⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠗⠀⠦⢄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠨⠭⡂⢭⣥⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠀⠀⣀⠄⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⢌⡛⠭⣅⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠿⣿⣿⣿⣿⣿⣿⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢫⠂⠎⠂⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠈⠈⠁⠀⠀⠀⠠⠀⠤⠀⠀⠀⠈⠁⠀⢠⣾⣿⣿⣿⣽⣰⠡⠸⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⣀⡀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠄⠀⣹⣿⣿⣿⣿⣿⣷⣆⠟⡥⡉⢶⠀⢠⡀⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡶⠮⣅⠶⠤⠄⢤⣈⣠⡀⠀⠀⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⣿⣿⣿⣿⣿⣴⣯⡖⡜⣮⠀⡇⢫⡖⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢠⠀⠀⢹⢨⢲⣤⡄⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⢴⡇⣀⢲⢨⣿⣿⡿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠉⠁⢒⣯⠝⠢⠰⠕⠲⡛⢖⢠⣀⠀⠂⠄⠀⣄⣀⠀⠀⠀⠀⠐⠚⠿⣷⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠒⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡠⢨⠡⣿⣿⣥⠓⠂⠺⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⣀⠈⡘⢉⣈⣉⣭⠽⣗⠢⢍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢸ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⡾⢻⣿⣿⣿⣿⣯⢰⠃⡵⢻⣿⣿⠁⠀⠀⠘⡜⢾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢶⠤⠤⡐⢚⠢⣍⡠⠀⢴⣋⣉⡛⢛⠒⢏⡴⣆⠉⢁⠲⣤⣀⡀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠐⠀⠀⠀⠀⢀⣀⡀⠈⠁⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣗⣽⣿⣿⣿⣿⢚⢦⠊⢀⠊⡩⠁⠀⠀⠀⠀⠐⠻⣿⣷⣆⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠉⠒⠒⠤⠈⢒⡠⣀⠀⠙⠿⣙⣓⢾⣻⣟⠋⠉⠥⣐⠾⠏⢱⡾⢖⣓⣤⣭⣀⣀⠁⠠⠄⠀⠀⢀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⠢⢼⣿⣿⣿⣿⢾⣿⣝⣬⠴⠁⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣄⣈⡑⠲⠟⠌⢙⠲⣂⣈⠟⠕⠫⢧⡀⢲⠏⠹⠤⣤⣬⠽⢳⡏⣛⠦⠤⢤⣀⣘⠋⡙⠻⠒⣮⢷⣄⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡁⣊⣿⣿⣿⣿⣽⡿⣟⡷⡩⢄⣠⣠⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠘⠧⠛⠳⠉⣀⡈⠚⠦⢌⣛⣆⣀⣀⠀⠀⠙⠋⢐⣟⣣⣥⣤⡤⣊⡁⣑⠶⠀⠀⠀⠀⠈⢠⡤⢼ ⠉⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣯⠃⠀⢿⡿⡿⠟⠲⠑⠾⠶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠙⠟⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠉⠢⠄⠫⠍⢛⡷⠒⠒⠀⠀⠀⢩⣿⣗⣛⠛⠶⠦⠥⠀⠂⠲⡦⠄⣀⣠⣾⣋⣀