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