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