⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⢶⡶⣶⢿⡿⣟⣿⣶⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⡾⣯⢿⡽⣯⢿⣽⢾⡽⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠚⡁⢿⣯⡿⣽⢯⡿⣽⣻⢾⣯⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠄⢂⠳⡈⠓⡿⣾⢿⣽⣯⣟⣿⠞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠁⠌⡐⢠⠊⢁⠣⢁⠒⡚⢄⢧⡼⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡁⠌⡐⠂⠌⠁⡐⢂⠡⢊⠰⣡⢾⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠉⡐⢀⠢⡰⢁⠀⢆⠡⢊⠰⣡⢾⡗⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡠⡤⠖⠋⡁⠐⡠⢐⠨⠂⡐⠤⢉⠄⣊⡴⣫⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⠶⠶⠾⠏⠉⡀⠰⠀⠆⢁⠀⠇⠀⢁⠸⣀⠁⡆⣱⢾⣱⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡀⢂⠐⠠⠁⠄⠡⢈⠐⡠⠌⢄⠩⢐⢂⣤⣳⡭⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⠠⠈⠄⠡⢈⡐⠄⢡⠐⡨⢐⡬⣖⡿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⠌⢠⠁⣂⠰⢈⠂⢆⣱⢫⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡆⠂⡔⠠⢂⠅⡊⠔⣰⢣⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠁⢆⠱⡈⢆⠱⡈⠴⣩⢎⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣏⠐⢢⠑⡌⢢⠑⣎⠱⢎⡚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡍⢢⠱⢌⢣⡙⢤⠛⣌⢳⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠛⠦⠧⣮⣆⣍⣦⣿⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠼⣿⣦⣍⣆⣮⠧⠦⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢳⣌⠛⢤⡙⢣⢌⠱⢢⡍⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡚⢎⠱⣎⠑⢢⡌⠑⢢⠐⣏⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⢎⣩⠴⡈⠱⢆⡈⠱⢆⠁⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⢣⣰⠔⡊⠅⢂⠠⡔⠂⡆⠹⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⢫⣱⢆⠂⢈⠰⣂⠁⢠⠌⣇⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⡿⣖⡬⢐⡨⠐⢡⠄⡐⢈⠡⠄⠈⠠⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠗⡭⣳⣤⢂⢐⠩⢄⠌⡠⠐⢈⠡⠄⠁⠠⠐⢂⡀⢹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⣱⢾⣱⡆⠁⣀⠸⢁⠀⠇⠀⢁⠆⠀⠰⡀⠉⠏⠾⠶⠶⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⠽⣫⡴⣊⠄⢉⠤⡐⠂⠨⢐⡠⠐⡁⠋⠖⡤⡠⣀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠃⡗⢾⣡⠰⢊⠡⢆⠀⢁⡰⠢⢀⡐⠉⠴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠞⢾⣡⠰⢊⠡⢂⡐⠁⠌⠂⡐⠌⡁⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⡼⢧⢄⡚⠒⢁⠣⢁⠊⢠⡐⠌⠁⠎⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠞⣿⣟⣯⣽⢿⣾⡿⠓⡈⠳⢂⠄⠋⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⣿⣯⢾⣻⣽⡿⢯⣽⡿⣯⢿⡁⠚⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡽⢾⣽⢿⣯⡽⢿⣯⡾⣟⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⣶⣿⣟⡿⢿⣶⡶⢶⣶⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀