⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠿⣿⣶⡦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠀⠀⠉⠹⣵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠀⠀⠀⢀⣠⣤⡀⠣⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠶⢿⡿⣤⡀⠰⢿⡷⠋⣙⡿⣽⡯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⢻⣼⢞⣍⢿⣅⡴⣏⣥⡴⡤⡝⢞⡜⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠳⣍⠉⢙⣿⡾⣻⣰⠼⠋⢀⡼⠁⠀⣙⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠠⢄⢘⢷⠎⠁⣴⡟⢉⣍⠾⠋⠀⠀⠀⠘⣻⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⠆⣾⠦⣙⠨⣷⠬⠋⠉⠀⠀⠀⠀⠀⠀⡰⢺⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠈⠃⠅⣖⣓⣷⠇⠀⠀⠀⠀⠀⠀⠀⠐⡸⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⢀⠀⠀⠀⠀⠀⡀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡠⠤⢔⢒⠒⢒⣲⣒⣦⠽⡭⠍⢚⣩⣷⣖⣖⣶⣤⣄⣤⣤⣤⢠⣤⡤⡤⡰⠲⢢⣤⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⣾⣣⣳⣿⣼⣯⡶⣻⡦⣿⣥⣿⡦⢠⡀⡼⣿⡷⣅⣄⠀⡝⣝⢿⡿⣽⣿⣱⣿⡰⣤⡑⠰⣿⣷⣷⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣾⣯⣶⣵⣦⣷⣿⣿⣿⠮⠘⠉⣤⣗⣕⣝⣷⣔⠹⣫⢔⣬⡂⢻⣏⣿⣿⣿⣿⣯⣾⠳⣦⡀⠀⠀⠀⠀ ⣷⢿⣿⣿⣿⣿⠿⣿⣿⣿⣻⡶⣿⣿⣿⣿⣿⢿⣿⠏⢥⣜⠷⠁⣀⣻⣽⢿⣿⣮⡆⠙⠊⠟⢷⣦⣿⣿⣿⣿⣿⣿⡞⣧⣿⣿⣆⠀⠀⠀ ⢾⣿⣿⣿⠟⣠⣞⠏⠁⣭⣾⡞⣿⡿⣿⢿⠻⣗⣃⡜⢻⠬⢔⢛⣪⣸⢧⣟⡧⢗⣞⡄⠂⠀⢕⠝⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⣿⣿⣿⢿⣍⣯⣼⣶⣿⣿⣿⣅⡿⡯⢘⣑⡽⣋⣽⢏⢖⡜⢤⣼⢔⠠⣸⡦⣇⣿⢾⣴⡘⢂⠠⠁⠀⠉⠻⢿⣿⣿⣿⡿⠹⣿⣿⣿⣗⠦ ⣿⠁⠐⠞⠫⣹⣿⣿⢟⠃⡯⠶⢨⠐⣇⣾⣽⡿⣶⣏⣻⠼⣕⢍⡶⢯⢾⢷⡻⣷⠿⣡⡎⢄⠀⠀⠀⠀⠀⠀⠊⠨⠈⣀⣀⣻⣿⣿⣿⣯ ⠿⠁⠀⠀⠀⣿⡿⣏⣸⢃⠿⠨⡳⣌⡟⡔⢅⠨⣥⣷⡏⠈⠻⡂⣤⣥⣥⣿⣿⠌⣲⣍⠏⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿