Smurfette Text Art

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡠⠤⠔⠚⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⣉⣉⣉⣭⠿⠁⣀⡤⠔⠒⠈⠉⠉⠉⠉⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠚⢋⣉⡉⠤⣤⡶⢖⠻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⢉⡤⠔⢋⡥⠊⠁⢀⣀⠀⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠉⠒⠈⠀⢿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣤⡾⠋⠁⣀⠴⠚⢁⡤⠞⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⢶⡛⠻⣍⠉⠉⢻⠂⠀⡼⢀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣾⠏⢁⣠⠾⢅⣀⠀⠀⢀⣀⣀⠤⠴⠒⣉⣁⣀⠀⠀⡀⠀⠀⡀⠈⠑⢦⣀⡠⠊⢀⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠁⣠⡟⠁⠈⢦⠈⠉⠉⠉⠁⣿⠀⠐⠁⠀⠀⠀⠉⠪⡀⢀⡀⠈⠡⡀⠀⠙⣦⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⢀⡾⠋⠀⠑⡄⠀⠑⢄⠀⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠈⢿⡿⢀⡠⠓⠒⠲⢬⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢠⡿⠁⠀⠀⠀⢸⠀⠀⠈⠳⡄⠀⠀⠀⠀⠙⠻⠃⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⢸⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⣰⣿⠁⠀⠀⠀⠀⡸⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠖⢩⡟⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢸⡇⠀⢀⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⠒⠤⠄⠤⠄⠂⠀⠀⣀⡠⠖⠉⢠⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀ ⠀⠀⠀⢀⣤⠔⠚⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣤⣤⣄⣀⣀⣀⣀⣀⣤⠤⢤⢶⡚⢯⣅⠀⠀⢀⡎⠀⠀⠀⠀⠀⡘⢸⡇⠀⠀⠀ ⠀⢀⡴⠋⢀⠔⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⣠⣾⠟⢁⣠⠞⠁⠀⠀⠈⠣⡈⢢⡀⠀⠀⠱⡙⢦⡈⠙⠲⢤⣀⠀⠀⠀⠀⡰⠃⣼⠃⠀⠀⠀ ⢀⡿⠁⠀⡎⠀⠀⠀⠀⠀⠄⡹⠁⠀⠀⠀⠀⠀⢠⣿⣿⡴⠋⠁⠀⠀⠀⠀⠀⠀⠘⡄⠙⠦⣄⣠⠃⠀⠙⢆⠀⠀⠉⠛⢦⣀⠜⢁⡴⠃⠀⠀⠀⠀ ⢸⠇⠀⠸⡇⠀⠀⠀⢠⠂⢠⠁⠀⠀⠀⠀⠀⠀⣸⠟⠉⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⣹⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠙⢷⡎⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⢧⠀⠀⠀⡆⠀⡌⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⢀⡤⠚⣯⣤⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠹⣄⡀⠈⢧⡀⠀⠇⠀⢇⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠋⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠒⠬⣙⢦⣘⢄⠘⡄⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⣀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠿⢦⣤⣀⣀⣀⣀⣀⣀⣀⣩⣭⠽⠿⢟⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⢤⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠚⣩⠄⢲⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⠂⢄⠀⠀⠀⠀⣈⡑⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠁⠀⠀⠅⠠⠌⢀⣀⣀⣀⠀⠀⠀⡔⠀⢃⠀⠀⠀⠀⠀⠘⢄⠀⠂⠀⣰⠋⠉⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣠⡼⣏⠀⠀⠈⠳⣄⠀⠑⠀⠂⢀⡴⠛⠶⣤⡀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠈⠙⢦⡀⠀⠈⠳⠦⠤⠴⠾⣇⠀⠀⠀⠉⠓⠒⢺⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡟⠁⠀⠀⠀⠤⠬⠗⠚⠻⠄⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⣿⠦⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⡀⠀⠀⣀⣾⠟⠱⡈⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠫⣒⠤⣀⠈⠙⠛⠉⠁⠀⠀⢻⠀⢹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠑⢦⡀⠀⠀⠀⠀⣸⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⡀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢿⣆⠀⢀⣰⠏⠀⠀⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠙⠲⣄⡀⠀⠀⠀⠉⠑⠒⠤⠤⣄⣀⣀⣀⣀⣀⠤⠊⠀⠀⢸⣿⠉⠉⠀⠀⠀⣰⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠋⠙⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣃⣀⣀⣀⣤⣾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠶⠤⠤⠤⠤⠶⠶⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠁⠀⠀⢀⣀⠠⠬⢉⣸⡯⠁⠀⠀⠈⠁⠀⠢⡄⠀⠀⠀ ⠀⠀⠀⠀⡘⠀⠀⢀⡠⠔⡊⢅⡪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⢀⠃⠀⠀⢈⡴⢊⠔⠁⠀⠀⣀⠠⠀⠀⠒⠫⠉⠃⠐⡘⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⢉⠔⠁⠀⠀⠀⠇⠀⡀⠀⠀⣤⠀⡀⢳⡊⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡀⢠⠋⠀⠀⠀⠑⡀⠀⠈⠋⠀⠀⠀⠀⠀⡨⡇⢀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⠿⠀⠀⠀⠀⠀⡁⠀⠴⠀⠀⠀⠀⠈⡉⠜⠀⠀⢱⠀⠀ ⠀⢀⠔⠂⠉⠀⠀⠀⠀⠀⣠⠾⡥⠄⠤⠤⠤⠴⠢⢅⡀⠃⠀⠀⢼⠆⠀ ⣰⠁⠀⠀⠀⠀⠁⠀⠀⢸⠧⠊⠀⠀⠀⠀⠂⠤⠈⠢⡈⠒⢤⣈⠌⠀⠀ ⢃⠀⠄⠀⠂⡄⠀⠀⢰⠁⠀⠀⡠⢲⠥⠄⠀⠀⠀⠀⠐⢄⠀⡵⠀⠀⠀ ⠀⠑⠈⠦⣁⣃⠀⠀⠘⠦⠀⣀⣀⡘⠀⠀⠀⠀⠀⠀⠀⠈⢏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⢂⠩⠙⠁⠀⠀⠀⠀⡀⠀⠀⠀⠠⠉⢀⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠠⠆⠀⢄⠘⠀⡠⠢⢄⠀⣠⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠖⠀⠰⠦⠳⠀⠉⠉⠙⡄⠀⠀⢱⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⠀⠀⠀⠀⠀⠒⠒⠎⠄⠒⠒⠋⢠⠱⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠈⣆⢀⡘⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠬⠆⠤⣀⠈⠀⠀⠀⠀⠈⣀⣟⢀⣀⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀

⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜🏽⬜⬜⬜⬜🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏽⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽🏽⬜⬜⬜⬜ ⬜⬜⬜⬜⬜🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽⬜⬜⬜ ⬜⬜⬜⬜⬜🏽⬛🏽🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽⬜⬜ ⬜⬜⬜⬜⬜⬜🏽⬛⬛🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛🏽🏽🏽🏽⬜⬜⬜⬜⬜⬜⬜🏽⬜⬜ ⬜⬜🟨🟨🟨🟨🟨⬛🏽⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽🏽⬜ 🟨🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽⬜ 🟨🟧🟨🟨🟨🟨🟨🟨🟨🟧⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜🏽⬜ 🟨🟨🟧🟧🟨🟨🟨🟨🟨🟨🟧⬜🏽🏽⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜ 🟧🟨🟨🟨🟧🟧🟧🟦🟦🟧🟧🟧🟧⬛🏽⬜⬜⬜⬜⬜⬜⬛⬜⬜ ⬜🟧🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟧⬛🏽⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟧🟧⬛🏽⬜⬜⬜🏽⬛⬜⬜ ⬜⬜⬛🟦🟦🟦🟦🟦⬛🟦⬛🟦🟦🟧🟧🟧⬛🏽⬜⬜🏽⬛⬜⬜ ⬜⬛⬛🟦🟦🟦🟦🟦⬛⬛🟦🟦🟧🟨🟨🟨⬛🏽⬜🏽⬛⬜⬜⬜ ⬜⬜⬛⬛🟦🟦⬛⬛⬜🟦🟦🟦🟧🟨🟨🟨🟧⬛🏽⬛⬛⬜⬜⬜ ⬜🟦⬜⬛🟦🟦⬛⬛🟦🟦🟦🟦🟧🟨🟨🟨🟨🏽⬛⬛⬜⬜⬜⬜ ⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟧🟨🟨🟨🟨🟧⬛🟧⬜⬜⬜⬜ ⬜🟦⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟧🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟧 ⬜⬛🟦⬛⬛🟦🟦🟦🟦🟦🟦🟦🟧🟨🟨🟨🟧🟨🟨🟨🟨🟨🟨🟨 ⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟧🟨🟨🟨🟨🟧🟨🟨🟨🟨🟨🟨 ⬜⬜⬛🟦🟦🟦🟦🟦🟦🟦🟦🟦🟧🟨🟨🟨🟨🟨🟧🟨🟨🟧🟨🟨 ⬜⬜⬜⬛⬛🟦🟦🟦🟦🟦🟦🟦🟦🟧🟨🟨🟨🟨🟧🟨🟨🟧🟧🟨 ⬜⬜⬜🟨🟧⬛⬛⬛⬛⬛⬛🟦⬜🏽🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨 ⬜⬜⬜🟧🟨🟨🟨🟧🟦🟦🟦⬜⬜⬜🟧🟨🟨🟨🟨🟨🟨🟨🟨🟧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⠉⠉⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣤⣠⡄⣤⣄⡶⣤⣤⣤⡠⣄⣠⣀⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢀⣀⣤⣤⣴⣦⣿⣾⣿⣾⣯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣶⢶⣦⣤⣤⣀⡀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡴⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⣶⣄⠱⡀⠀ ⠀⠀⠀⠀⠀⢀⡎⢀⡤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡷⢹⠀ ⠀⠀⠀⠀⠀⢺⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢁⡇ ⠀⠀⠀⠀⠀⠸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⣁⠞⠀ ⠀⠀⠀⠀⠀⠀⢣⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⢋⡩⠤⠖⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠢⢍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣿⣿⣿⡇⡴⠒⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣻⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠈⢿⣿⣿⡿⢏⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⣏⠒⢦⣀⣀⡀⠀⠳⡙⢷⣟⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠙⢿⣿⣿⢿⡄⠀⠀⠀⠈⠿⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢘⣿⠛⣾⣷⣬⢣⠀⠉⠢⣙⠻⣾⣽⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⣝⣤⣀⡘⣿⣾⣿⣿⣿⣶⣶⣦⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣁⢻⣿⣿⣿⢸⡆⠀⠀⠀⠉⠒⠀⠒⠤⠴⢍⢻⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣶⣿⡼⣖⣻⣿⣿⣿⣿⣿⡳⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⢠⣿⣿⣿⣎⡛⣆⢤⣤⠠⡆⠀⠀⠀⠀⠀⠑⢬⡛⢿⡾⣽⣻⣽⣷⣻⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣹⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡧⢹⣿⣿⣿⢱⣝⢿⣎⢻⡆⢷⠀⠀⠀⠀⠀⠀⠀⠈⣳⣿⣿⣽⣿⣾⣿⣟⡾⣽⢿⣟⣯⣿⢿⣟⣯⠿⣛⣁⡧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠾⠯⣷⣘⣿⣿⣿⡇⠯⠓⣝⣯⣽⣏⠢⢀⣀⣀⣠⢤⣿⣭⣽⣿⣻⣿⣿⣿⣿⣿⣟⡿⠤⠬⢍⣋⣙⣉⠤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠋⢀⢲⡼⣿⣾⣿⣿⡇⢸⠀⠀⠙⣿⣿⣿⣷⣶⣿⣿⣿⡟⣿⣿⣿⣷⣿⣿⣿⣿⣿⣍⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⢧⢶⣬⣿⣿⣿⣿⣿⣿⠆⣿⠀⠀⣰⣿⣿⣿⣿⣿⢿⣛⡧⣟⣿⣿⣿⣿⣿⣿⣿⣻⣿⡝⠄⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢶⣯⣿⣿⣿⣿⣿⣿⣿⣧⡘⢄⠀⣻⣿⣿⣿⣿⣏⣶⣹⣾⣿⣞⡷⣯⡿⣟⢿⣯⣧⠙⠘⠀⠀⠀⠚⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣊⣦⣽⣿⡿⢏⡳⣮⣷⣿⣿⣿⣯⣿⣽⣟⣮⠷⣌⠛⣿⣆⡄⠀⠀⠰⡄⡱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⡿⢋⣽⣚⣷⣿⢟⢻⣽⣿⣿⣿⣿⣿⣿⣾⡽⣦⣛⡤⢚⣿⣦⠀⠀⣹⣷⣌⡓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢛⣿⡿⠿⣿⡿⣿⢷⡾⣡⢯⣿⣿⡿⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣯⢞⡵⢊⢻⣧⡀⢿⢭⡻⣷⣦⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⢀⡼⣡⣿⣿⡿⠏⠀⠀⠀⣸⣻⣿⣿⣿⣿⣿⣿⣿⡿⣝⣧⢏⡰⠀⠂⢹⣧⠘⡇⠙⣎⢿⣽⣦⠈⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠤⢐⣈⣩⢷⣳⡟⣽⠁⠀⠀⣰⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣮⡳⣌⠳⣈⠤⢹⣇⢷⠀⠈⢹⠟⣯⠑⢢⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠤⢒⣵⣶⢿⣽⣾⣿⣿⡱⡇⠀⠀⠀⣇⢠⡙⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⢷⡻⣜⣣⢓⠎⢦⢻⡞⠀⠀⡞⢸⡇⣀⣠⣀⠀⢤⡀⠈⠐⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣶⣿⣿⣯⣿⣾⣿⣿⣿⣳⠀⢠⠖⠚⡩⠟⠰⢦⠙⡛⣿⡽⣻⣷⢿⡿⣽⣏⠿⣜⠢⣍⠚⡤⠂⡇⠀⠀⡇⣿⡹⣿⠫⠿⣿⣶⣳⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⢋⣹⣟⣿⣿⣿⣿⣿⠯⠋⠀⠀⢷⣾⡿⠁⠀⠀⠘⠳⠧⣄⠲⠉⠉⠯⣹⠷⣞⡿⣬⢳⡌⠓⢌⠡⡟⠀⠀⠹⣽⣷⣻⡄⠀⢹⡿⣿⣄⢻⣘⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⢿⠟⣿⣿⡿⡯⠛⠁⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠈⠀⠰⢦⡐⠈⠇⠘⠅⢋⠣⠘⠀⠀⢀⣽⠀⠀⠀⠉⠛⠋⠀⠀⠀⡇⣿⣿⣿⠾⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⣧⡾⣻⠕⠋⠀⠀⠀⠀⠀⡠⠐⠒⠒⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡼⣀⢠⡅⠀⠈⢓⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠉⠉⠉⠁⠐⣂⠠⠤⣄⡀⠀⠀⠀⠀⠈⠳⣌⡈⠑⠠⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣀⠀⣠⢦⣄⣆⢳⠲⣈⠷⣆⠌⠙⠂⣄⠀⠀⠀⠀⠁⡔⢌⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣘⠶⣙⠾⣽⣯⡋⣷⣩⢶⣍⡛⢦⡐⠘⠳⡀⠀⠂⠀⢹⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⡳⢄⠺⡍⣞⠲⡼⠀⠻⣏⠓⠯⣛⡄⠒⠨⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠑⣌⡱⢊⠌⡓⠀⠀⠀⠈⢦⠀⠈⠙⢶⣀⣀⣀⣀⣀⣤⣿⡄⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⢦⣟⡾⡙⢦⢊⠥⣉⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⣀⣤⠟⠟⢁⡉⠁⢈⣉⣀⡤⠤⠄⣈⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣽⣷⣮⣮⣵⢧⠶⠀⠀⣸⠃⠀⠀⠀⢶⣊⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠙⠢⢀⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣷⣿⣾⡽⢦⠶⠃⠀⠀⠀⠀⢸⡉⢀⠀⡀⢀⡁⢀⠀⠀⢂⠀⣤⡄⢂⠀⣀⡀⠠⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢢⠐⠰⢡⣈⠦⡜⢶⡉⣶⣖⣺⣽⣻⣿⣾⣵⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣰⢎⡗⣫⡜⣷⢻⣷⣽⣶⣿⣿⣿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⢷⡾⠽⠿⠽⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠰⡯⠃⢄⠀⠀⣐⣒⠉⠛⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⠀⠀⠀⠑⠞⠁⠀⠙⡶⠋⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠀⠑⠄⠀⠀⠸⡀⣠⡀⠀⠀⣠⠀⡠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⢢⠀⠀⠙⠿⣁⣀⣀⠼⠒⠁⠀⠀⠀⠀⠀⠀⣼⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠉⣉⡩⠇⠀⠀⠀⢀⡤⠓⠒⠒⠒⠤⠤⢄⣀⣀⠀⠀⠀⠀⣀⡤⠚⠈⠂⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⣠⠞⠉⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⢶⣶⠤⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠁⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠙⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠐⠒⠶⠾⢿⣥⣀⣀⠀⣰⠛⠉⠛⠒⠛⠀⠀⠀⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠋⠁⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⢀⣶⠶⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢇⠀⠀⠀ ⢀⡴⠶⠦⣄⣀⣴⠞⠛⠛⠿⠋⠁⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡶⠶⠤⣤⣀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠡⡀⠀ ⣾⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢱⠀ ⢿⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠀⠀⠀⢸⡄⠀⠀⠀⠀⢤⡖⠁⠈⢦⠀⡸⠀ ⠀⠙⠛⠛⣿⣆⠀⠀⢠⠀⠀⠀⠀⠀⢺⡀⠀⢀⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠹⡄⠀⢘⡟⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⠳⡀⠀⠀⠀⠈⣇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣧⡀⠀⠀⠀⠀⣿⡤⠞⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠐⢤⣀⡀⢀⠀⠀⠀⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⠛⠶⠤⠴⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⡼⠋⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢆⢸⡀⠀⡇⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠉⠉⠙⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠳⣄⣈⡷⠚⠉⠉⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠿⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⣠⣴⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠀⠀⢀⣶⣦⡴⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣦⣴⣦⡀⠀⠀⠘⠻⢦⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⣠⡾⠛⠉⠀⢀⣠⡴⣿⠟⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⣶⠠⣶⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠻⣿⣦⡀⠀⠀⠀⠙⢿⣄⠀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⠉⠛⠻⢿⣄⣀⣠⣶⣿⠁⠀⠀⣸⡇⠉⠻⢿⣿⣦⡀⠀⠀⠀⣿⢀⣿⠀⠀⠀⣀⣶⣿⡿⠛⠁⢹⡆⠀⢹⠻⣷⣄⠀⣠⡶⠟⠋⠉⠉⠛⢷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡏⠀⠀⠀⣿⠀⠀⠀⠀⢹⣿⣿⣷⣤⡀⣿⢈⣿⢀⣤⣾⣿⣿⡇⠀⠀⠀⢸⣿⠀⢸⡄⠘⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡰⠶⣶⣤⣤⣀⠀⠀⢀⣿⣹⠀⠀⠀⠀⢿⡄⠀⠀⠀⠸⣿⣽⠟⠻⣿⣿⢰⣿⣿⠟⠻⣯⡿⠇⠀⠀⠀⢸⡿⠀⢸⠃⠀⣿⠀⠀⠀⣀⣤⣤⣶⡶⠀⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡎⢧⡀⠀⠈⠙⢿⣿⣦⣼⣇⣏⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⣠⡾⣟⣉⣻⣷⣄⡀⠀⠀⠀⠀⣀⣴⠟⠀⠀⣸⡀⣀⣼⣤⣴⣾⡿⠋⠁⠀⠀⣼⢿ ⠀⠀⢀⣠⣤⣤⡀⠀⠈⢿⡌⠳⣄⠀⠀⣾⠛⢻⣿⣿⠛⠻⣶⣦⣤⣤⣄⣈⡛⠳⢶⢴⣶⣿⡿⠛⠛⠛⠛⢷⣾⣟⠶⣶⣶⣾⣿⣥⣤⣴⣾⣿⣿⣿⣿⣿⠟⠛⣷⠀⠀⢠⡼⣡⡟ ⠀⠀⣿⡏⢹⡟⣧⠀⠀⠈⠻⣷⣈⠳⣄⠿⠄⢸⣿⣿⣷⣹⣟⣿⣿⢉⣿⣿⣯⣿⣿⣿⣿⣿⣷⢾⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢻⣿⣿⣵⣿⣿⡿⠀⢰⠟⣀⡶⢋⣴⠟⠁ ⠀⠀⢻⣇⣀⣿⣾⣆⣀⠀⠀⠈⠻⢷⣬⣻⣦⣼⣿⣿⠻⣿⢿⣿⣿⣿⣿⣿⣿⣷⣀⣿⣿⣿⣛⣦⣿⣿⣴⣛⣿⣿⣿⣤⣾⣿⣿⣷⣿⣿⣿⡿⣽⣿⣿⡇⣀⣤⣾⣥⡾⠛⠁⠀⠀ ⠀⣠⡿⢛⣩⣭⣭⡙⢿⣷⣖⣻⣷⡶⣯⣝⠙⠻⣿⣿⢦⣿⣸⣿⣿⣿⣿⣤⣾⡿⢿⣿⣿⣯⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣿⣿⣤⣼⣿⣿⣠⣇⡘⣿⡿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀ ⢸⠟⣴⣿⣿⣿⣿⣿⣧⣻⡿⣿⣿⣿⣿⡻⣿⣦⠈⢻⣾⣿⣿⣟⢛⡻⣿⣿⣿⣷⣾⣿⣿⣿⣶⣋⣿⣻⣝⣷⣿⣿⣿⣤⣽⣿⣿⠟⠻⣿⣿⡿⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⣷⣿⠙⣏⢿⠀⢹⡿⣧⠀⠈⠻⣿⣿⡾⣿⣿⣿⠋⣹⣿⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡿⠻⣿⣷⣾⣿⣿⢡⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣦⠻⣿⣿⣿⣿⣿⠟⣼⢯⡿⠀⣿⢸⣷⡈⣿⣿⠀⠀⠀⠈⠙⠿⣾⣿⡿⠿⣿⣿⣿⣿⣿⡏⣙⣿⣟⠛⣿⣿⣷⣾⣿⣿⣶⣿⡟⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⢷⣮⣉⣉⣉⣴⠾⣫⡾⣃⣼⢏⣾⣼⢻⡇⣿⠀⠀⠀⠀⠀⠀⠈⢻⣷⣮⣿⣿⣨⣿⣿⣿⣿⠿⣿⣿⣿⣿⣅⣻⣿⣧⡈⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⡆⢿⡻⣿⣷⠶⠛⠉⣠⣿⣳⣿⡏⣵⣿⣽⠟⠀⠀⠀⠀⠀⢀⣴⠟⢹⡟⣿⣿⣿⣿⠟⢿⣿⣤⣿⣿⠛⢿⣿⣿⣿⣿⣿⠏⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⢯⣻⣾⠟⢿⣿⣿⣽⣧⣽⣿⣿⣷⡟⠁⠀⠀⠀⠀⠀⢀⣾⠋⢀⡟⢀⡏⠈⠻⢿⣌⣿⡭⠿⣿⣿⣟⢻⣿⣿⠿⡏⠘⣧⡀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠛⢻⡟⠁⢸⡇⠀⣻⣿⡿⢷⣦⡀⠀⠀⠀⢠⡾⠃⠀⣾⣇⣾⠀⠀⠀⠀⠙⢿⣟⠒⢿⣿⣿⠞⠋⠀⠀⢰⠀⢻⣟⠳⢤⣄⠀⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠸⣿⢪⣿⣿⠀⠀⢹⣧⠀⠀⢠⡿⠁⠀⣰⣿⢸⠇⠀⠀⠀⠀⠀⠈⢿⣿⠿⠋⠁⠀⠀⠀⠀⢸⡆⠈⣿⠳⣶⣌⡛⣦⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣮⣷⣤⡿⠟⠛⣿⣄⠤⣾⡿⠶⠶⠟⠀⢀⡴⢻⠇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⢹⡇⢸⡀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⣀⣴⣿⣿⣿⣿⣧⠀⠀⠀⣠⠟⢡⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⣿⠀⠈⣷⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣋⣁⣼⣿⣿⣿⡓⠶⠾⣁⣴⠟⣿⣼⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣠⣾⣿⠀⠀⣿⠀⣿⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠋⠙⠛⠓⠚⠛⠁⠀⣿⠀⠈⠙⠛⠛⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠟⠛⠋⠁⢠⣿⠀⢠⣿⣄⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣼⣟⣿⠋⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡿⠸⡇⠀⠀⠀⠀⡀⠘⢿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣼⣧⠀⢿⠀⠀⠀⣴⡇⠀⠀⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠉⢿⣽⠋⢻⡿⣿⠀⠀⠀⣿⠁⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠈⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⡶⠟⠋⠁⠀⠀⢸⣷⣴⢏⡼⠁⠀⢀⣼⣧⡄⠀⢠⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢨⡿⠉⠉⠉⠉⠉⠉⠉⢹⣧⠀⠀⠀⠀⠀⠀⢻⣧⠟⠁⠀⢀⣼⠋⠈⠀⣰⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⢸⣿⣷⣶⠶⠟⠁⣀⣠⡾⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠈⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⢰⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠟⠋⠉⠉⠉⠉⠙⠛⠓⢾⣿⣤⡀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⣠⣾⡷⠖⠛⠛⠉⠉⠉⠉⠉⠛⠻⣦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣦⡀⠀⠀⢻⣆⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣠⣶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢻⣧⠀⠀⠀⢠⡿⠁⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠹⣧⠀⢠⡿⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⠀⢸⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⡾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣧⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡾⠁⠹⣧⡀⠀⠈⠙⠲⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⠶⠦⣤⣤⣄⣀⣀⣀⣀⣠⣤⣤⣤⠤⠶⠶⠟⠛⠉⠀⠀⠀⠈⠙⠛⠷⠶⠤⣤⣤⣬⣥⣤⣤⣄⣤⣤⣤⡤⠤⠤⠶⠶⠞⠛⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠴⠖⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠶⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢑⣶⣒⣖⣶⣭⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡴⠶⠖⠛⣍⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀ ⠀⠀⠀⠀⡼⠋⠀⠀⠀⢀⣴⢻⣁⠀⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀ ⠀⠀⠀⢰⣃⡀⣀⣤⠖⠋⣿⣾⣏⣩⣿⣵⠾⡿⣷⣶⠴⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀ ⠀⠀⣰⠟⠉⠉⠉⠻⣴⣴⣿⣿⣿⣏⣿⣧⠶⢛⣉⠉⡆⠀⢹⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠈⠿⣾⣿⡏⣿⠉⠀⠀⣾⣿⣆⡇⠀⠈⠀⠀⠙⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀ ⢸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠸⣄⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀ ⠸⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡶⠶⠶⠶⠶⠤⣀⣸⠃⠀⠀ ⠀⠀⢸⡷⢦⣄⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠈⠝⢦⡀⠀ ⠀⠀⢸⡄⠀⠻⣍⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢄⣀⡀⠀⠀⠀⠘⣷⡀ ⠀⠀⠀⠻⣄⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⡶⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⢿⣿⡖⠙⡆⠀⠀⢠⡟⠁ ⠀⠀⠀⠀⠈⠙⠲⠤⠬⣳⢦⣄⠀⠀⠉⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠿⠃⢀⣶⠞⠁⠁⠰⠇⠀⢠⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠳⠶⢤⣀⣀⡈⠿⠀⣀⣠⣶⠶⠶⣤⡀⠀⠈⠁⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣈⡶⠚⠉⠓⠦⣀⣹⠏⠉⠛⠿⣀⠉⢷⠀⠀⠹⣤⣀⣀⣀⣠⠶⠖⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡇⠀⣴⣏⠀⠀⠀⠀⠀⠈⠙⢧⠀⠀⠀⠉⣆⠈⣧⣀⡾⠙⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⣄⠈⠉⠛⠦⣀⠀⠀⠀⠀⠈⠷⣄⣀⣠⢿⣤⠇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⢤⡏⠶⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠉⠶⣄⡀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠉⠒⠲⠶⠚⠉⠀⠀⠀⠀⠈⣧⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠙⣆⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠷⠤⣄⣀⣀⣀⣀⣀⡤⠤⠴⠖⠊⠉⠀⠀⠀⢹⣄⣸⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢦⠀⠀⠀⠀⣀⡤⠾⠋⠀⠀⠀⠀⠀⠀⢠⡟⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠁⠀⠈⠓⠦⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣷⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠋⠉⠀⠀⠈⠙⣶⣼⡿⠶⠤⣀⡀⠳⣀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠈⠉⠲⠿⣦⠀⠀⠀⠀⠿⣤⡴⠖⠒⠶⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢺⠃⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣧⡄⠀⠀⠀⠈⠳⣦⠀⠀⠀⠈⠹⣦⠀⠀⠀⠀⠀⠀ ⠀⣼⡆⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠳⣄⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠶⣄⡀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠶⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠣⠤⠋⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⠈⠑⢄⠀⠀⢰⢑⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⡇⡰⠀⠈⠣⠄⢀⣤⡂⠠⠄⠀⠀⠱⡄⠀⠉⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠒⢽⠒⠉⠑⠠⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⢐⠐⠌⠀⡧⠤⢉⢤⡀⢧⡀⠈⠂⠉⠁⠄⠘⢂⣁⢺⠀⠀⠀⠀⠀⠀ ⠰⣀⡢⡊⢹⣀⣴⢻⡧⡅⠀⢧⣉⠄⠀⠴⠃⢀⡴⠧⠊⠀⠀⠀⠀⠀⠀ ⠀⠃⠰⠋⠧⣀⢦⠻⠿⡆⢙⠄⠐⠊⠉⡍⠉⡈⠣⢄⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠒⠁⠀⠈⢗⣊⠒⣎⡰⠒⠈⠉⡇⠀⠱⠀⢃⡍⠣⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡆⠀⢀⣀⣸⡤⠄⡇⠈⠘⠐⣆⡀⢀⠠⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠿⣶⠼⠀⣄⣙⡍⡀⠀⠆⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⠸⡀⠓⡾⠋⠉⠁⢀⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⠰⠀⠙⠒⠒⠂⠉⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

███████████████████████████ ███████▀▀▀░░░░░░░▀▀▀███████ ████▀░░░░░░░░░░░░░░░░░▀████ ███│░░░░░░░░░░░░░░░░░░░│███ ██▌│░░░░░░░░░░░░░░░░░░░│▐██ ██░└┐░░░░░░░░░░░░░░░░░┌┘░██ ██░░└┐░░░░░░░░░░░░░░░┌┘░░██ ██░░┌┘▄▄▄▄▄░░░░░▄▄▄▄▄└┐░░██ ██▌░│██████▌░░░▐██████│░▐██ ███░│▐███▀▀░░▄░░▀▀███▌│░███ ██▀─┘░░░░░░░▐█▌░░░░░░░└─▀██ ██▄░░░▄▄▄▓░░▀█▀░░▓▄▄▄░░░▄██ ████▄─┘██▌░░░░░░░▐██└─▄████ █████░░▐█─┬┬┬┬┬┬┬─█▌░░█████ ████▌░░░▀┬┼┼┼┼┼┼┼┬▀░░░▐████ █████▄░░░└┴┴┴┴┴┴┴┘░░░▄█████ ███████▄░░░░░░░░░░░▄███████ ██████████▄▄▄▄▄▄▄██████████ ███████████████████████████

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡟⠋⠁⠃⠀⠄⠡⡽⠛⠓⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡏⠀⢀⠀⠴⡀⠰⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⡟⡩⠙⠀⠀⠔⠁⠀⠀⠒⠤⠀⠄⠊⠀⢡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡠⠈⠀⠀⢀⠀⠠⡀ ⠀⠀⠀⠀⠀⠀⠈⢐⡶⠄⠀⠤⠤⠔⠒⢂⠀⠙⠒⠤⠎⠉⠈⢀⡠⠃ ⠀⡠⣀⢀⠤⠤⠖⠉⠀⠀⡠⠀⠀⠀⠀⠈⠤⢀⡀⠀⠀⠀⠀⠚⠀⠀ ⢸⠀⠀⠁⠀⠀⠀⠀⡠⢊⡀⠀⠀⠀⠀⠀⣸⠀⠸⠀⠀⢀⡔⢂⠸⠀ ⠀⠉⢹⠂⠀⢄⠀⠘⡄⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⢃⠀⠀⢱⡠⠃⠀ ⠀⠀⢸⠀⠐⡦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⠀⠁⠀⠀⠀ ⠀⠀⠈⠒⢄⢠⠤⢺⣿⣿⣿⠋⠉⠉⢈⣻⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣦⣄⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠈⠙⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀ ⠀⠈⠻⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠉⠀⠀⠀⠉⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡟⠾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⢻⣿⠉⢉⣉⣉⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⠀⠈⢻⡙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣖⡚⢛⣩⣍⡉⠉⣹⣯⡉⠉⠛⠲⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣧⠀⠀⠹⣄⢻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣫⣽⣿⢿⣁⣸⠿⠟⠉⠙⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡛⠧⣄⡈⢿⡟⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠼⣯⣁⠽⢺⣿⣣⠖⠋⠙⢳⠈⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣷⢦⣬⡉⠛⠿⡄⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⢻⣄⣾⡟⠁⠀⢀⣀⣸⠀⣼⡿⣦⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠛⠳⣦⠀⠀ ⠀⠀⠀⣿⠉⠿⣮⡳⣄⡻⣄⠀⢸⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⣿⠿⠃⣰⣿⣷⣜⣧⠀⢀⠀⠀⠀⢀⣿⠀⠀⣠⠟⠁⠀⢀⣾⠀⠀ ⠀⠀⠀⠸⡆⠀⠀⠙⠲⣍⣻⣆⣸⠁⢻⠀⣄⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢻⣽⣖⣊⣵⣴⡾⠛⠁⠈⠽⠟⠋⠉⠉⠲⣄⣼⠇⠀⡼⢡⡄⣀⣤⡚⠁⠀⠀ ⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠉⢿⣇⠀⢸⣇⣿⠆⠀⠀⠀⠀⠀⠀⢻⡷⣦⣀⣀⣀⣀⠀⠈⠉⠉⠉⠁⣤⣄⠀⠀⠀⠀⠀⠀⡀⠀⣹⡏⠀⣼⠁⢀⣻⣯⠥⣈⣷⣀⡀ ⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⢿⣆⣸⣿⣯⣤⣤⡀⠀⠀⠀⠀⠈⢷⡀⠐⢦⣀⠀⠀⠀⠀⣀⣠⠜⠉⠀⠀⠀⠘⠙⣿⡿⠉⢿⡿⠁⠀⡇⠀⠘⠋⠀⠀⠈⢻⡈⢷ ⠀⠀⠀⠀⠀⠀⠰⣍⣙⣒⣶⣶⣾⣿⣿⡏⠀⠀⢸⠁⠀⠀⠀⠀⠀⠈⠻⣦⡀⠉⠙⠿⣿⡿⠛⢦⡀⠀⠀⠀⠲⠦⠶⠋⢀⣤⠟⠁⠀⠀⣷⠀⠀⢠⢶⠀⢀⣠⣧⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢁⡴⠋⠛⣿⣆⠀⠀⣘⠛⠛⠛⣧⠀⠀⠀⠀⠀⠙⠓⠦⣤⣄⣈⣛⣋⣀⣀⣼⣦⣤⣤⣶⣛⣋⣀⣀⣀⣀⣀⣿⡄⠀⠀⠘⢻⣿⠥⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣠⣿⣿⣏⡝⠁⠀⠀⢠⣇⣠⣤⠤⠤⠒⠒⠒⠉⠉⠁⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡸⠃⢀⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣓⣶⢿⡿⣝⢧⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣀⣠⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠋⠁⠀⢸⣇⢹⣞⣯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠃⠀⠀⠀⠀⠀⠀⢲⣦⣤⣤⣤⣤⣤⠤⠶⠖⠒⠛⠛⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⠞⢁⡽⠿⣧⢳⡟⣦⣴⠶⠶⠶⠖⠒⠛⠉⠉⠉⠉⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣴⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠃⣠⠋⠀⢠⡏⠳⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠘⢧⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣤⣤⠿⠀⠀⠈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⠯⣭⣽⡲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡀⠀⠀⠀⠀⢸⡶⠂⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣏⠏⢁⡼⠶⣦⡈⢻⡞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠻⠿⣿⣶⣤⣄⡴⠋⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⣧⣘⣧⣠⣟⣁⣼⢯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⢿⣄⠀⠀⠀⠠⠯⡾⠁⠀⠀⠀⠀⢰⣿⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⣿⢿⣄⣽⠿⠯⣤⣄⠀⠀⠀⠀⠀⢀⡤⠞⠉⠁⠀⠀⠀⠉⠛⠶⢶⠀⣀⣿⣄⠀⠀⠀⠀⠈⠉⠓⢦⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⣯⣈⣛⠛⠛⢛⣿⣿⣅⠼⠁⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠁⠀⠉⠛⠶⣤⠤⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⣿⣿⣿⣿⣿⠿⠿⠝⢦⣀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⡟⢻⣷⣾⣷⣄⡀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣄⣶⣿⣿⡜⢻⣿⣿⣿⣿⣶⣦⣶⣤⣴⣦⠏⠘⠛⠿⠛⠿⠿⠟⠳⠶⠶⢟⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠾⠟⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠛⠛⠷⠯⢭⣩⣉⣩⣭⠽⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠒⠒⠒⠒⠒⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠛⠛⠛⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠈⠳⣤⣀⠀⠀⠀⣀⣠⠴⠛⣁⣠⠴⠖⠋⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠉⠙⠛⠛⠛⠓⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠀⠀⣤⣤⡤⠖⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠶⣤⣤⣄⠀⠀⠳⢦⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣠⠞⠋⠁⣀⡴⠺⢟⡿⣷⣦⣀⠀⠀⠀⢰⡆⢶⠀⠀⠀⠀⣠⣶⡿⣿⠻⢷⣄⠀⠀⠙⢳⣄⣤⣄⣀⠀ ⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠉⠙⠲⣤⣾⡿⠀⠀⢸⠃⠈⠙⢿⣶⣤⡀⢸⡇⣾⠀⣀⣴⣿⡟⠉⠀⢻⡄⢸⠙⣷⣤⠶⠋⠁⠀⠀⠉⢧ ⠀⠀⠀⠀⠀⠀⣿⢇⢤⣤⣀⣀⠀⠀⢨⣷⠁⠀⠀⢸⡀⠀⠀⠸⣟⡿⢿⣾⡇⣽⣾⠿⣟⣿⠃⠀⠀⣸⠇⢈⠃⢸⡇⠀⠀⣀⣀⣤⡄⣸ ⠀⠀⠀⠀⠀⠀⢿⡞⣄⠀⠉⠛⣷⣦⣿⣽⡀⠀⠀⠈⠳⣄⡀⠀⠀⢀⣤⣾⣃⣛⡧⣄⡀⠀⠀⣀⡴⠛⠀⣸⣀⣠⣧⣴⣾⠋⠉⠀⣠⢻ ⠀⢠⣴⢶⣦⠀⠀⢻⣌⠢⡀⢸⡉⢹⣿⣏⣩⣿⣶⡶⣦⣬⣭⣿⣿⣯⣟⣩⣭⣭⣿⣿⣽⣿⣿⣿⣶⣶⣿⣯⢿⣿⣿⠋⢹⡇⢀⡔⣣⠏ ⠀⠸⣧⢸⣏⣇⠀⠀⠙⠶⣌⡺⣍⣸⣿⡿⣿⣿⣿⣶⣿⣿⣿⣛⣿⣿⡿⣽⣽⣫⢿⣿⣿⣙⣿⣿⣥⣤⣿⣿⣻⣿⡏⠀⣨⣖⣫⠞⠋⠀ ⢀⣴⢟⣫⣭⣟⢿⣶⣖⣶⣾⢽⡛⠻⣿⣧⣿⣸⣿⣿⣯⣭⡿⢿⣿⣯⠽⣿⣿⣿⢭⣿⣿⢿⣿⣯⣽⣿⣏⣿⣹⣿⠗⠛⠛⠉⠁⠀⠀⠀ ⣼⢱⣿⣿⣿⣿⣷⢽⢻⣻⣯⡯⢿⣦⠈⠷⣿⣿⣍⣝⣿⣿⢿⣾⠿⣿⣾⣽⣿⣯⣿⣿⣿⣶⣿⣿⡏⣻⣿⡟⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡸⣿⣿⣿⣿⡿⣸⣿⠏⣷⣧⡈⣯⣇⠀⠈⠻⢿⣽⣿⣯⣾⣿⣶⣿⡟⢻⣿⢿⣿⣿⣽⣿⣯⣽⡿⣽⣿⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡷⣬⣛⣛⣫⡴⣫⢟⣰⢛⣯⢇⣇⣿⠀⠀⠀⠀⠙⢻⣧⣿⣟⣹⣿⣷⣿⣿⣶⣿⣟⣹⣿⢏⣿⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⡸⣟⣿⣖⣛⣡⣾⢷⣿⣩⣾⡽⠃⠀⠀⠀⠀⣴⠋⡾⢻⢿⣿⡟⣻⣿⣼⣿⣛⣿⣿⣿⡿⣟⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⠭⣽⡿⠟⣿⠚⣿⣿⣯⡀⠀⠀⠀⢀⡾⠃⣸⢇⠇⠀⠙⠳⣿⣞⣻⣿⣟⡿⠟⠉⡇⢻⡦⣀⡈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⠀⣿⢔⣿⡏⠉⢻⡄⠀⢀⡞⠁⢠⡟⡸⠀⠀⠀⠀⠙⣷⣾⠟⠋⠀⠀⠀⢣⠀⣷⢬⣝⡲⣄⠈⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢯⣦⡼⠛⠛⣧⣤⣾⠳⠶⠋⠀⣰⢻⢃⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠈⣧⢸⠀⠘⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⡾⠟⣿⣿⣦⣀⣀⠜⣡⣿⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸⡇⠀⣿⠘⡄⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣶⣾⡿⠟⠷⠬⠵⠾⠃⢸⠛⠓⠶⠤⣤⣀⣀⣀⣀⣀⣀⣀⣤⡴⠷⠚⢋⡇⠀⣿⡀⡇⠀⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⠇⢠⡿⡽⠁⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣼⠀⡇⠀⠀⢠⡄⠹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣷⣲⠿⣤⣵⠀⠀⣾⠃⠀⢹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⠳⢦⣄⣀⣀⣀⣀⣀⣀⣤⠶⠛⠉⠀⢸⣧⡴⡽⠃⠀⣰⣯⡀⢀⣼⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠉⢿⡄⠀⠀⠀⠀⣿⣜⠁⢀⣴⠏⠈⣠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⡟⠿⢯⣥⡤⠾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣀⡀⣿⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⠇⢀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠈⠉⠙⠻⠷⣤⡀⠀⠀⢻⣆⠀⠀⠀⠀⠀⣾⠃⠀⠀⣀⡴⠟⠛⠉⠉⠀⠀⠀⠈⠉⠳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠹⣆⠀⠀⢀⡾⠁⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄ ⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣆⢀⡾⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠸⣆⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⢤⣤⣄⣀⣀⣀⣀⣠⣤⡤⠤⠴⠖⠋⠀⠀⠈⠓⠶⠤⢤⣭⣭⣦⣤⣀⣠⣤⣤⡤⠤⠤⠴⠒⠚⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⣐⣶⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠒⠉⠉⠉⡁⠀⠀⣈⠉⠉⠙⢲⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠉⠉⢳⡄ ⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⠓⠊⠁⠙⠉⢲⠞⠁⠀⠉⢷⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⡧ ⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠁⠀⠠⠶⠦⠐⠻⠏⠀⠀⠀⠀⡼⠀⠀⠀⠀⣼⠁⢀⡠⢴⠀⠀⠀⠀⢠⡇ ⢻⡀⠀⢀⡀⠤⢀⣀⡞⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣀⢠⡾⠁⠀⠀⠀⡼⠉⠉⠁⠠⣏⠠⠐⢳⢀⡟⠀ ⠈⢷⡴⠁⠀⠀⠀⠈⠙⠉⠁⣾⠚⠉⣷⠀⠀⠀⢀⡴⠃⡼⠁⠀⠀⠀⢼⣅⡀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀ ⠀⠐⣇⠘⠉⢿⡏⠑⠂⠀⠀⠈⠓⠒⠓⠀⠐⠊⣁⠤⠊⠀⠀⠀⠀⠀⠀⠀⢉⡷⠶⣤⣄⡀⣠⠏⠀⠀⠀ ⠀⠀⠙⠦⢄⣀⣉⡡⠴⠒⠤⡤⠤⠄⠀⠒⠲⠯⣀⠀⠀⠀⠀⠀⢀⡴⠒⠲⣎⣀⣠⠯⠤⣈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠠⡀⠉⠒⠦⠤⣀⡟⠈⣇⠀⠀⣹⠤⠤⢄⣸⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⡇⠀⠀⠀⠘⣄⠀⠀⠀⠈⠁⢀⡟⡷⠚⠳⢤⠀⢀⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣸⠀⠀⠀⠀⠀⠘⣏⠓⠢⢾⣄⡜⠀⢻⠄⢀⡼⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⢤⣄⢠⣟⣻⠀⠀⢀⣏⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠸⣇⣰⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢧⣀⠈⠓⠋⠁⠀⠀⠘⢯⣙⠒⠤⠤⠤⠐⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⠋⠉⠙⠂⠀⠀⠀⢀⠀⣼⣛⢧⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠒⢲⠶⠒⠀⠀⡰⢿⣄⣀⡨⠟⣷⣶⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣄⣀⠴⠮⡤⠚⠙⠁⠀⠀⣸⠟⠯⢁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⠤⠔⠚⠳⠤⣖⠋⠉⠉⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠋⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠈⠉⠁⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⢤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⢤⣤⣤⠀⠀⠀⢀⣀⡶⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣤⣽⣿⣙⣙⣿⡉⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣬⣭⣭⣉⣛⡛⢻⣷⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⢀⣤⠾⣿⢙⣿⢦⣝⣟⣿⣍⣿⠷⡦⣬⣙⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⣾⡧⣤⣍⣻⣿⣽⣿⣶⣝⣾⣇⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣠⣄⣀⣀⡏⠀⠀⠀⠀⠹⣿⡋⠀⢈⣹⣿⡷⠚⠉⠉⠀⠉⠻⣆ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⢁⠀⠀⠀⠈⡹⠗⠀⠀⠀⠀⠀⠙⠛⠛⠁⠉⠀⠀⠀⠀⠀⠀⠀⣽ ⠀⠀⠀⠀⠀⠀⠀⠻⡇⠾⠿⣿⡿⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⣀⡼⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡈⠻⣷⢾⣳⠀⠀⠀⢠⣶⣲⣶⣶⡆⠀⠈⢉⣹⠿⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣽⢯⡝⠛⠒⠒⠶⠞⠛⠒⢦⡤⠖⠒⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⡞⠁⠀⠀⠀⠀⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⡴⠋⠀⠀⠀⠀⠀⣠⣷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠏⢠⠞⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠶⠒⠒⢺⣥⣴⠿⠴⠦⠤⢤⣤⣀⠀⠀⠀⢸⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣇⠀⠀⢰⡞⠉⠉⠉⠳⣄⠀⠀⠀⠈⠉⠑⠲⢬⣇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⡇⣹⡶⠲⣾⣷⣄⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⣰⡶⠛⠁⠀⠀⠈⠋⠓⠲⢦⡀⠀⠀⠀⠀ ⠀⢷⣹⠀⠀⣻⠎⢯⡙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀ ⠀⠈⠙⠒⢺⣍⣀⣼⣻⡶⣤⣀⡀⠀⠀⠀⠀⠀⠀⣈⣿⠂⠀⣤⡄⠀⠰⣶⠃⢸⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢸⣾⡯⢭⣶⣶⣤⣄⠈⢿⣌⠁⣀⣾⠁⠀⢰⣧⠼⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠾⠃⠉⠉⢩⣿⣀⣈⣷⡄⠀⠉⠁⢹⣗⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⣠⠴⠞⠛⠶⠶⠟⠁⠀⢀⣄⡴⠟⠉⠉⠉⠉⠛⠶⣄⠀⠀⠀ ⠀⠀⣴⡇⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀ ⠀⠀⠈⠳⣄⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠒⠒⠛⠓⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠤⠞⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠒⠶⠤⢄⣀⣀⣠⠤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀ ⠀⠀⠀⠀⢀⣠⠤⠴⣒⠞⠓⠚⠛⠓⠒⠒⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀ ⠀⠀⠀⡞⠁⠀⢀⣠⢺⣁⣀⡄⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⣸⡤⢤⣶⠉⣸⣾⣧⣾⡿⢻⣿⡿⡖⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢀⡾⠃⠀⠀⠈⠳⡗⣿⡿⡾⠛⢉⣞⣂⡇⠀⠇⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⣾⢰⠀⠀⠀⠀⠀⠘⠛⠃⢧⠀⠸⣿⡿⠃⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⡞⠀ ⠻⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠁⠀⠀⠀⠀⠀⠀⣀⡼⠖⠒⠒⠒⠤⣸⠁⠀ ⠀⠐⡏⠳⡦⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠊⢳⡀ ⠀⠀⢧⡀⠘⢦⡀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣿⡷⢦⡀⠀⢠⠟ ⠀⠀⠀⠙⠢⠤⢝⡦⣄⠀⠈⠁⠀⠈⢳⡄⠀⠀⠀⠀⠰⠏⢀⡵⠋⠁⠰⠁⢀⡞⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠒⣉⣓⠒⠤⣤⣙⣃⡤⠴⣖⠒⢦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⢠⡞⠁⣰⠋⠀⠀⠉⠒⢯⠀⠀⠑⢆⠘⡄⢀⡿⡶⠒⠒⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢣⡀⠛⠲⣄⠀⠀⠀⠀⠳⡀⠀⣸⣀⡏⠉⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠒⠤⢼⠑⢄⠀⠀⠀⠈⠉⠀⠀⢀⡰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠑⠦⣀⡀⢀⣀⠴⠋⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡠⢿⠋⠳⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠤⢄⣀⣀⣀⣀⡠⠤⠴⠒⠉⠀⠀⣧⣨⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠚⠱⣄⠀⢀⠴⠊⠉⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠖⠋⠉⠉⠙⢢⣹⠦⠤⣀⠘⢆⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡼⠁⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠉⠛⢷⡀⠀⠀⠓⢶⠒⠉⠒⠢⣄⠀⠀⠀⠀⠀ ⢸⡅⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠛⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⠈⠳⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀ ⠀⠀⠈⠓⠦⣀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠪⠧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠐⠒⠒⠒⠛⠛⠓⠒⠦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠁⢈⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠖⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⢀⣀⣀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣴⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢼⣁⡴⠖⢋⣉⡿⢿⣶⣿⠟⠉⠉⣉⣿⠿⠛⠛⠛⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣤⣶⣋⠀⠀⠈⠉⠹⣧⣠⡾⠋⠀⠀⠀⠀⠀⠘⢧⡙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡄ ⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠈⠛⣦⡀⢀⣀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇ ⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⡿⠟⠛⠛⠛⠿⣶⣦⣤⣀⡀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⡟⢦⣀⡀⠐⢿⣿⣷⠊⠁⠀⣠⡿⠿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣸⠃ ⠀⠀⠀⠀⠀⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠉⠙⠛⠛⠋⠁⠀⢀⣴⠟⠀⠀⠀⠽⠛⠛⠛⠛⠒⠦⣄⠀⣸⠇⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⣤⣤⡤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡋⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠉⠉⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠶⣄⠀⠀⠀⠀⠀⣀⡤⣴⠶⠒⠚⠉⠉⠿⠀⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠲⢤⣤⣀⣠⣤⡤⠖⠋⠁⠀⠈⠁⠀⠀⣀⠈⠁⠀⣸⡆⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⢭⣿⡓⠦⢤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠉⠛⠛⠉⠀⢀⣀⡤⠞⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⠁⡀⠀⠀⠀⠈⠉⠳⣦⡶⢟⠉⠉⠉⠉⡭⠭⠭⢍⡉⠉⣿⠉⠉⠓⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⢿⣀⠴⠚⠉⠓⠶⣄⠀⠹⡆⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⡾⠧⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣤⣀⡀⠀⠀⠘⢇⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣄⡼⠛⠁⠀⠈⠙⢦⠀⠀⢸⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠿⣜⣠⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⢈⡷⠖⠋⠀⣠⠞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⠃⠀⠳⣄⠀⠀⠰⡄⠀⠀⠀⠀⠀⠈⠙⠶⣤⡴⠟⠃⠀⢀⡜⠁⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡀⠀⠀⠈⠓⠦⠔⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣤⣀⠀⢀⣶⣦⡖⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⣞⣃⣤⡴⠚⠋⠀⠈⣿⠉⠙⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⡏⠉⠙⠒⠻⠷⢦⣀⣀⣀⣴⠾⠉⠉⠉⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡄⠀⠀⠀⠀⠀⢠⡾⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠙⠶⣄⣀⡀⠀⢸⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠲⣄⡀⠀⠉⠉⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣾⡇⠀⠀⠀⠀⠉⠓⠒⣺⠃⠀⠀⠀⠀⠀⠀⠀⣠⣼⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠖⠋⠁⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠙⢷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣦⠤⠤⠾⠷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠈⠉⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠊⠉⠀⠀⠀⠀⠀⠀⠉⠙⠲⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀ ⠸⣧⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀ ⠀⠘⠷⣄⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠲⠶⠤⣀⣘⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠒⠚⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠐⠂⢄⠀ ⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠀⠀⠀⠀⢱ ⠀⠀⠀⡐⠁⠀⠀⢰⡶⣼⠿⣿⣀⠈⠁ ⠀⠀⠀⡇⠀⠀⡠⠚⣩⣻⣿⣿⣳⡕⠄ ⠀⠀⠀⡗⠒⠒⠅⠀⠘⠣⠜⠛⠁⠀⢙ ⠀⠀⠀⠫⢉⣯⣧⠀⢠⡤⠤⢐⡲⠖⠊ ⠀⠀⠀⠀⠔⠝⠁⠀⡁⠈⠇⠀⠀⠀⠀ ⢀⡀⢠⣪⣊⣀⠀⠀⢡⠀⢸⠀⠀⠀⠀ ⣮⢀⣎⠉⢰⠀⠈⠁⡺⠄⠈⠤⢀⠀⠀ ⠻⠤⣋⣯⣁⡀⠀⠀⣣⡄⡀⠀⡄⡧⠀ ⠀⢀⠀⠤⠜⠛⡻⣰⠍⠒⣣⣜⡉⠀⠀ ⠠⡁⠀⢀⠊⠁⠀⠁⠀⠉⠀⠀⠀⢱⠀ ⠀⠈⠐⠚⠒⠠⠤⠤⠤⠤⠤⠄⠐⠁⠀

⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂ ⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀ ⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀ ⠀⠸⣿⣿⣷⣦⣀⡴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣴⣾⣿⣿⠇⠀ ⠀⠀⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⣠⣻⡿⠿⢿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣻⣥⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⡜⠋⡾⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣿⣻⣾⣭⣝⣛⣛⣛⣛⣃⣿⣾⣇⣛⣛⣛⣛⣯⣭⣷⣿⣿⡇⠀ ⠀⠰⢿⣿⣎⠙⠛⢻⣿⡿⠿⠟⣿⣿⡟⠿⠿⣿⡛⠛⠋⢹⣿⡿⢳⠀ ⠀⠘⣦⡙⢿⣦⣀⠀⠀⠀⢀⣼⣿⣿⣳⣄⠀⠀⠀⢀⣠⡿⢛⣡⡏⠀ ⠀⠀⠹⣟⢿⣾⣿⣿⣿⣿⣿⣧⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀ ⠀⠀⢰⣿⣣⣿⣭⢿⣿⣱⣶⣿⣿⣿⣿⣷⣶⢹⣿⣭⣻⣶⣿⣿⠀⠀ ⠀⠀⠈⣿⢿⣿⣿⠏⣿⣾⣛⠿⣿⣿⣿⠟⣻⣾⡏⢿⣿⣯⡿⡏⠀⠀ ⠀⠀⠤⠾⣟⣿⡁⠘⢨⣟⢻⡿⠾⠿⠾⢿⡛⣯⠘⠀⣸⣽⡛⠲⠄⠀ ⠀⠀⠀⠀⠘⣿⣧⠀⠸⠃⠈⠙⠛⠛⠉⠈⠁⠹⠀⠀⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣶⣀⣠⠀⠀⠀⠀⠀⠀⢠⡄⡄⣦⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣷⣻⣿⢷⢶⢶⢶⢆⣗⡿⣇⣷⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣛⣭⣭⣭⣭⣭⣻⣿⡿⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠛⠛⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀ ⢸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⣀⣀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀ ⠈⡍⠳⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣘⡲⣀⣦⡒⠂⠀⠀⠐⡀⠀⠀⠀⠀ ⠀⢹⡢⢝⡏⠢⡀⠀⠀⠀⠀⢠⠿⠯⠝⡿⠓⢲⢹⡄⠀⠀⠀⡇⠀⢀⣀⠀ ⠀⠘⡝⠳⡸⡄⡗⡀⠀⠀⠀⡇⠀⠀⠹⣅⢰⣋⠾⢾⠤⢀⣀⠇⡀⠁⡨⠀ ⠀⠀⠡⡀⠀⠙⡅⣷⣂⠀⠀⠘⡒⠤⠄⠉⢉⠱⠀⠀⢤⢤⡝⠰⠨⠟⠹⣠ ⠀⠀⠀⠘⠷⠒⢿⡏⠀⠥⢤⠀⠘⠢⢉⣛⣵⣀⣄⣒⣥⣚⣀⣰⠀⠲⣤⡿ ⠀⠀⠀⠀⠀⠣⣶⣿⣏⢀⠘⠒⠀⠀⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣡⠃ ⠀⠀⠀⠀⢰⠁⡀⡣⣟⣦⡤⠤⠤⠀⠒⡂⠀⠀⠀⠓⢒⡤⡈⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠸⠠⠃⠙⠄⠀⠀⠀⠀⣇⣀⣀⡀⠄⠂⠈⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠶⢶⣤⠀⠀⠀⠀⠀⠀⢀⣥⣀⠀⢰⠄⠀⣠⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣶⣭⢧⡿⠀⠀⠀⠀⡀⠤⠲⣀⡉⢿⠁⠀⠰⡥⠄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣯⣿⣻⣾⡑⠀⢠⠋⠀⠀⢀⠔⠃⠉⠑⠂⠀⠀⠀⠘⠀⠀⠀⠀ ⠀⠀⣠⣜⣿⣿⣅⣀⣈⡇⢾⢧⡄⣀⣰⡀⠀⠀⠀⠀⢀⣀⠤⠞⠀⠀⠀⠀ ⠀⠀⠉⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏⠀⠀⣿⠀⢀⡾⠛⠋⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡏⠀⠀⠀⣿⢀⣾⠁⠀⣰⠆⢹⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣧⠀⠀⢠⡟⢸⡇⠀⣰⠟⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣆⢀⣸⣇⣸⠃⢠⡏⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⠾⠟⠛⠉⠉⠉⠈⠉⠉⠛⠁⢾⠁⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⠾⠟⠛⠛⣻⣿⣙⡁⠀⠀⢾⣶⣾⣷⣿⣶⣄⠀⠀⠀⠀⠰⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⣶⣶⠾⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⣿⣻⣟⣻⣿⡦⠀⠘⣿⣿⣛⡿⢶⡇⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⣿⣿⡗⠀⠀⠿⠉⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣿⡿⠁⠀⠀⠘⢦⣿⣿⠇⠟⠁⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠛⠆⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⢶⣶⣦⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣤⣴⣾⣿⣿⣿⣓⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣟⣯⣽⠟⠋⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⠀⠉⠛⠷⣮⣍⣩⡍⢻⡟⠉⣉⢹⡏⠉⣿⣹⣷⣦⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⠇⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢠⣠⡶⠀⠀⠀⠀⠘⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣥⢠⣤⠼⠇⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡄⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠾⠷⠄⠀⠀⠀⢀⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠋⠀⠀⠀⠀⠀⠀⢰⣾⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣠⣿⣿⣶⣶⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠉⠛⢿⣿⣯⣿⡟⢿⠻⣿⢻⣿⢿⣿⣿⣿⣿⣿⠿⠟⠹⣟⢷⣄⠀⠀⠀⢀⣼⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠘⢷⣌⡻⠿⣿⣛⣿⣟⣛⣛⣋⣉⣉⣉⣀⡀⠀⠀⠈⠻⢿⣷⣶⣶⢛⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠹⢯⣟⣛⢿⣿⣽⣅⣀⡀⠀⣀⡀⠀⠀⠀⠠⢦⣀⠰⡦⠀⢸⠀⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⠀⣸⠀⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⢦⡀⡀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⠳⣝⠦⢄⠀⠀⠀⣟⣷⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣷⡀⠀⠀⠈⠙⠂⠀⠀⠀⢸⣿⡄⠀⠀⠘⢦⡙⢦⡀⠀⠀⠀⠀⢰⣷⣷⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢧⣤⣀⡀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⢿⡍⠛⠳⠶⣶⣤⣤⣤⣤⣤⣤⠼⠟⡟⢿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣷⣶⣶⣶⣶⣶⣶⣦⣀⣀⣀⣻⡀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠁⠀⠀⠈⠻⣿⡆⢹⣯⣽⣿⣿⠟⠋⠙⣿⣶⣿⣿⣿⣿⣾⣿⣿⣿⣟⠋⠉⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡀⠀⠀⠀⠈⢻⣆⣿⠀⠀⠀⢁⣶⣿⠿⠟⠛⠷⣶⣽⣿⣿⣻⣏⠙⠃⣴⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⠀⠀⠉⠀⠀⠀⠀⠀⢹⣿⠀⣀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠉⠻⣿⣧⣿⢀⣰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣤⣤⣤⣤⣤⣤⣾⣿⣟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣅⣾⢿⣵⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⢹⣜⠷⠦⠤⠤⠤⠤⠤⠴⠶⠛⣉⣱⠿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⣦⣤⣤⣄⣠⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⣶⣿⣿⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⢀⣤⣤⣶⠶⢶⣦⢤⣤⣴⣶⣶⣶⣦⣄⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⠟⠛⠻⡿⠋⠛⠁⠀⠀⠈⠑⠉⢿⠛⢿⣿⣿⣿⡇⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢠⣿⠀⠀⠀⣀⣀⣀⣀⠀⣠⠤⢤⣄⡀⠀⠀⢈⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⣿⠀⢰⡞⠉⠉⠉⠉⠻⣧⡀⠀⠀⠙⢶⣄⣾⡟⠁⠀⠀⠉⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠉⠉⠀⢿⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣽⡟⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠲⣄⡀⠀⠀⠘⣧⣤⣤⡀⠀⠀⠀⠀⢹⣶⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠈⠻⣦⡀⠀⠘⣿⣿⣇⣀⠀⠀⢀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠈⢿⣆⣀⣈⣉⣉⣉⣙⣋⣉⣁⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠋⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⡄⠀⣀⣤⣶⣿⡿⠿⠿⠿⢶⣿⣿⣄⠀⠀⠀⣠⣤⠾⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⢰⣿⣿⣿⡿⠟⠛⠁⠀⠀⣠⣖⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣶⣿⠟⠉⠁⣀⣠⣤⣤⣴⣶⠿⠿⠄⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡟⠀⠀⠀⢀⣀⣀⣴⠿⠇⠀⠀⢀⣼⡿⠟⠁⢹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣏⢀⣴⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⢶⣄⡀⠀⠀⠀⠀⠀⠀⣴⡿⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠻⠷⣦⣽⣿⣶⠄⠀⠀⠀⠀⢿⣦⣀⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⣤⣤⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣿⣿⡿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣯⣝⣛⣛⣒⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀⣤⣭⣿⣿⣿⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢿⣯⣥⣤⣀⣀⣀⣠⣤⣤⣴⣾⣛⣠⣴⣶⣿⣿⣾⣿⡾⠁⠀⠈⠉⠙⠃⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣉⣲⣾⡿⠟⠛⠉⠉⠁⠟⠉⢠⠿⠋⠀⠀⠀⠻⢦⡀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠛⠋⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣿⣷⣄⠀⠀⠀⠀⠙⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠙⢻⣿⣷⣶⣶⣶⣿⠟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢠⣿⠋⠁⣠⡿⠋⠀⠀⠀⠀⠉⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣏⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣦⣤⣤⣤⣤⣤⣤⣴⣶⠶⠟⠛⠉⠁⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠋⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣴⣶⣿⣿⡿⠛⠉⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠛⠛⠻⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠺⠟⢿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣤⣤⣴⣿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠈⠁⠀⠀⣀⣠⣴⣿⣿⡟⠁⠉⠛⠿⣷⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠁⠀⠀⠀⠾⠿⠟⠋⠁⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠐⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣾⣿⣿⣿⠿⠛⠛⠛⠿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⠿⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡟⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡾⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⢸⡇⠀⢀⡶⠛⢶⣶⢶⣶⣶⡿⠶⣤⣤⣼⡇⠉⣛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠘⣧⣀⢸⡇⠀⣼⠁⠀⠀⡟⠀⠀⣤⡀⢉⡹⣟⠉⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠀⠐⠟⠛⠛⢿⡇⠀⣿⠀⠀⢸⡇⠀⠀⢘⣷⡿⠁⢻⡀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢷⣤⡀⠀⠀⠘⣇⠀⣿⠀⠀⢸⡇⠀⠀⠘⢿⣿⣄⢸⡇⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⢦⣄⠀⢿⡀⢹⡄⠀⢸⡇⠀⠀⠀⠀⠙⠿⠿⠷⠶⠶⠦⣤⣀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢷⣼⡇⠸⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⡹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠷⠶⠶⢤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠚⡄⢫⠉⢩⠃⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⡞⠳⡜⠦⠚⠘⠒⠋⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⡀⣠⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⠉⠉⢰⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠛⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⡇⠀⡰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⢰⡆⢻⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⠀⠀⠀⠀⢰⠁⡰⠁⠀⠀ ⠀⠀⠀⠀⣶⣦⣤⠘⣿⣿⣆⠀⠀⢿⠇⣼⣿⣿⣿⣿⠛⢸⡇⠀⠀⠙⣿⣿⣿⣇⠀⠀⠀⠈⠒⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣁⠀⠻⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣇⡀⣾⠃⠀⠀⢠⣿⣿⣿⡇⠀⡔⠒⠲⡄⠀⠀⠀⠀ ⠀⠀⠀⠘⠛⠋⠉⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⠟⠀⠀⠱⠤⣀⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⡀⠀⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀ ⠀⡗⡤⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣫⢸⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⡙⠛⣉⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣾⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⠻⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣶⣤⣼⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣶⣦⡌⠻⡿⢁⣾⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣦⡀⢸⣿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⢿⣿⣿⣆⠙⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠻⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣴⣤⡘⢿⣿⣿⣧⡈⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣁⠘⢿⣿⣿⣆⠙⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⢠⣶⣤⡈⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⠋⣰⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⡿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠛⠛⠛⢛⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠂⠁⠀⠀⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡌⠀⠀⠀⠀⠤⠬⠍⠸⠭⢄⡀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢄⠀ ⢸⠀⠀⠀⠀⠀⢀⡞⠒⠊⢂⣢⠋⠉⢢⠀⠀⢀⠔⠁⠀⠀⠀⡇ ⢸⠀⠀⣀⣀⡔⠁⣀⠈⠉⠀⠁⠀⣠⠎⠀⢀⠞⠐⢨⡀⠤⢠⠃ ⠀⢳⠁⢤⡀⡉⠁⠣⣉⣂⡀⠄⡢⠊⠀⠀⠚⠤⣀⡀⠀⢠⠃⠀ ⠀⠈⠢⠄⠡⠔⠢⡤⠀⠐⠲⢌⡀⠀⠀⡠⠒⠎⡠⠯⢅⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠀⢠⠀⠀⠢⡀⠁⠒⠀⢧⠤⢇⠀⡪⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⡇⠀⡌⠀⠀⠀⢹⠁⠚⡜⢨⠆⠜⠁⠀⠀⠀⠀ ⠀⠀⠘⣅⡑⠋⠁⠀⢧⡒⠀⠀⢺⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠺⠤⡤⠀⢀⣄⠙⡺⣤⡴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠒⠓⠈⢁⣠⣞⡙⠜⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢣⠀⠀⠀⠀⠁⠀⠀⠙⡄⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠐⠂⠀⠤⠀⠐⠚⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀

⣰⡿⠿⠿⣷⣦⣠⣤⣾⠟⠛⠳⣦ ⡏⢀⢀⣠⣶⠟⣹⣿⠷⣦⡀⢀⢘⡇ ⢣⣤⣴⠿⠃⢀⡿⢿⡆⠈⠻⠿⠟⠁ ⠀⠀ ⠀⠀ ⣠⠃⠈⠳⡄ ⠀⠀ ⣰⡟⠁ ⠀⠀ ⣸ ⠀⠀⢰⡏ ⠀⠀⠀ ⢠⡟ ⠀⠀⠘⣇ ⠀⠀⠀ ⢸⡇ ⠀⠀ ⢿ ⠀⠀⠀⠀⠈⢷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠾⠛⠛⠋⠉⠉⠉⠉⠛⠛⠻⠷⠶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣤⣴⣶⣶⣶⣶⠿⠟⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠛⠛⠛⠛⠒⠶⠶⢦⣤⣽⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣦⣄⡀⠈⠉⠛⠓⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⠛⠿⠿⣦⣾⡿⣷⣿⣿⠿⠷⣶⣤⣀⠀⢹⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⣠⣴⠶⠶⠒⢿⣦⣴⣿⣩⣝⡓⠶⣤⣉⢻⣷⠟⠉⠉⠙⠳⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣼⡟⠁⠀⠀⣴⠏⠉⠉⠙⠻⣍⠉⠳⢦⡙⣿⠇⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣿⠁⠀⠀⠀⣿⠀⠀⢀⠀⠀⠘⢧⣶⣤⣽⠇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢿⡇⠀⠀⠀⠈⢧⡸⣿⣿⡄⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿⡄⠀⠀⠀⠀⠉⠻⠿⠿⣤⣶⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠉⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣴⣿⠟⢿⣦⣀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⣀⣠⣤⣴⣿⣿⠛⣿⡆⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⠀⠀⠀⣠⣤⡶⠞⠛⠛⠛⠛⠿⣿⠁⠀⠀⠉⠻⢿⣶⣤⣤⣶⡿⠛⠁⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⣿⣠⡿⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣦⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⡄⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⡇⠀⣠⡤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠿⣿⣿⡿⠃⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣾⣶⣿⣶⡖⠚⠓⠶⣦⡄⠀⠀ ⠀⠀⠀⠀⠻⡇⠀⠻⠀⠘⣿⣿⣏⠀⠉⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢀⣠⣼⠛⠁⠀⣠⣾⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣩⣼⠛⠉⠙⠛⠶⣤⣸⣿⡆⠀ ⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠈⠙⠻⣤⣴⡿⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⣀⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠻⡟⢿⣦ ⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣀⡀⠀⠀⠀⢀⣠⣼⣿⣿⣀⣀⣀⣠⣤⣤⣶⣶⡾⠿⠿⠿⢯⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣿⠖⠀⠀⠀⠀⠀⣠⣴⡆⠀⢀⣠⠇⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠛⠛⠉⠉⠉⢹⡏⠉⠉⠉⠉⠁⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣋⣠⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣠⠾⠉⠛⣿⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣤⡶⠶⣤⣀⣹⡿⠿⠯⣛⣶⣾⠃⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⠛⠛⠿⠷⠶⠶⠶⠶⠶⠾⠶⠶⠿⠿⠷⠶⠶⠾⠿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠋⠉⠙⠒⠿⢯⣕⣶⣦⣤⣽⠇⠀⠀⠀⠀⠀⣸⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⠞⠋⠙⢻⡏⠀⠀⠀⠀⠀⣰⣿⣿⣟⠻⠭⣿⣿⠦⣤⣤⣀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣌⣀⡤⠖⠛⠁⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⣿⡿⣿⠿⢿⣒⠦⣤⣙⠛⠲⢬⣹⣿⡆⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡟⠉⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣼⣿⠇⠸⣆⠀⠉⠙⠶⣾⣿⣄⣼⡏⢹⡟⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⢠⣿⡿⠀⠀⠘⣆⠀⠀⢠⠇⡏⠉⣇⡇⣾⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⣤⠟⠋⠙⠁⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠘⣧⠀⣼⠀⡇⢰⣿⣧⡿⠤⢤⣤⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣧⠀⠀⠀⠈⣷⡿⢸⠀⢸⣿⢿⠃⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢾⡏⠙⠲⠶⢶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⣿⠀⢸⣼⣸⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⡇⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⢶⣼⠃⡏⠀⡾⡇⣧⣀⣴⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣦⣄⡀⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡟⢠⠃⠀⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢷⠀⢀⣶⠀⠀⢹⣦⡀⠀⠀⠀⣠⣿⣿⣄⣀⣠⣾⡇⣾⠀⠀⣿⢿⣿⡿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣬⣯⠀⠀⢸⡟⠛⠂⠀⣰⣿⡁⠀⠉⠛⠋⢠⠀⢿⣴⣾⡏⢸⠗⠒⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣆⠀⣸⠇⠀⠀⠀⠛⢿⡿⠷⢦⣄⡀⠘⡆⠘⢿⣿⢇⡞⢀⣴⡿⠟⠓⠚⠓⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠉⠙⢿⠿⣳⣄⠀⢀⣠⣾⠃⠀⠀⢈⣿⣿⣿⣷⣶⣾⣿⣄⡘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠉⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠁⠟⠿⣿⣿⣿⣿⣿⠿⠻⠈⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠇⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⠸⠀⠀⠁⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠈ ⣿⣿⣿⣿⢠⠀⠀⠀⡄⣿⣿⣿⣿⠀⠀⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣾ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣼⣧⣿⣿⣧⣿⣿⣧⣿⣿⡄⣠⢀ ⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⡀⣤⢀⡄⣶⢠⡇⣿⣿⡄⣦⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣴⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣴⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⣰⣿⣿⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⢠⣿⣿⠃⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⣼⣉⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⠀⠀⠀⢹⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠉⠁ ⠀⠀⠀⠸⣿⣿⣄⠀⠀⠘⢿⣿⡵⠋⠙⢿⣦⡀⠀⠀⣤⣠⠀⣠⣿⡅⠀⣿⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣄⣀⠀⠀⠀⠈⠻⣷⣄⣠⣿⣿⡼⠋⠛⣡⡼⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠷⠶⠶⠾⣿⡿⠋⠻⣟⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠑⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣄⠀⠀⠀⠀⣠⠜⣁⡠⠀⠀⠀⠹⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠉⠒⠒⠛⠒⠉⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⢀⣀⠤⠴⠒⠒⠒⠒⠒⠤⢄⣀⠀⠠⢜⡆⠀⠀⠀ ⠀⠀⠀⠀⣠⠖⠲⢴⣉⣠⠖⢫⠟⢶⣄⠀⢰⢰⠀⢀⣴⠞⢯⢳⢦⣀⡹⠖⠢⢄ ⠀⠀⠀⢰⣧⠤⣄⡀⢨⡟⠀⠸⡀⠀⠿⠿⢾⢸⡾⠿⠇⠀⣸⢈⠈⡏⢀⣀⠤⢸ ⠀⣠⣄⠈⢿⡢⡀⡟⣿⡓⣤⣤⣝⣂⣤⣶⣛⣒⣷⣢⣤⣶⣥⣾⣶⣿⢻⠄⡠⡻ ⠀⣧⠿⣦⣀⣙⡾⣧⣿⣻⣿⣷⡿⣯⣽⣿⣿⣿⣿⣿⣽⡿⣶⢿⢿⣇⡬⠮⠊⠀ ⣮⣾⣿⣷⣽⣿⣿⢳⡌⠻⣿⣿⣿⢷⡿⣿⣿⣿⣿⣿⣿⣿⣻⡿⡿⠁⠀⠀⠀⠀ ⢳⣻⣿⣟⣼⣇⢿⣎⣿⠀⠈⠻⣿⣿⣿⣿⣽⣯⣿⢺⣟⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠘⢾⣽⣮⣵⣿⣿⡾⠃⠀⠀⡴⢹⡛⠻⣿⡷⣿⣽⣿⠟⣏⠑⠦⣀⠀⠀⠀⠀⠀ ⠀⠀⠈⢽⡀⣧⣿⠙⣆⢀⠜⢀⣧⠁⠀⠈⠯⠟⠋⠀⢸⠸⠯⡂⡌⢳⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣁⡼⣿⣏⠉⡰⣹⡾⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⢁⠸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠒⠛⠛⠒⠚⢸⠉⠒⠒⠠⠤⠤⠤⠒⠚⠉⡇⣸⡼⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⡏⡁⠀⡄⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⠦⣀⡀⠀⢀⣀⡠⠞⠙⣏⢝⠃⢠⡃⢠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠉⠉⠁⠈⡆⠀⠀⢹⣥⡴⢋⡰⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠎⠀⠀⠀⠀⣁⠀⠀⢸⠀⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠢⢧⣀⠀⠸⡀⠀⠀⢀⠇⠀⣀⡼⠐⠒⠒⠒⠢⣄⠀ ⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠈⠑⠄⠱⡀⢠⠏⠠⠊⠁⠀⠀⠀⠀⠀⠀⠈⢣ ⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡞⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠈⠓⠤⠤⣀⣀⣀⣀⣀⣀⣀⡠⠴⠊⠑⠤⢉⣐⣠⣀⣀⣀⣀⡀⠠⠴⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣛⣋⠉⠉⠉⠉⠉⠒⠲⠤⣤⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⡴⡱⣿⠦⡀⠀⢀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⡉⠒⣺⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡑⠀⡿⠀⠈⠞⠁⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡰⠁⠸⡇⠀⠀⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣀⣠⠄⠒⠈⠀⠀⠀⠀⠀⠀⢠⠏⠀⠁⠉⠀⠈⠛⢥⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡠⠖⠋⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⢔⡏⠀⠀⠀⠀⠸⣷⠠⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠔⠋⠉⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⢠⢣⠊⠀⠀⢀⠆⠀⠀⠀⢀⠊⠀⢠⢁⡎⡸⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣅⠀⠀⠀⡼⠀⠀⢀⡔⠁⠀⣠⡇⡞⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣒⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⡇⠀⢠⡞⠀⢀⠔⢹⡎⠀⡞⠀⠀⠀⠀⠀⠀⢠⡒⠒⠷⠿⠷⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠇⢀⢻⢃⣴⠁⠀⢨⠇⣸⠁⠀⠀⠀⠀⠀⠀⢸⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⡈⠸⠃⡇⢰⠀⡜⢀⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠑⢄⠀⠀⢳⠀⠀⣸⢁⢆⡼⡡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢣⠀⣼⠰⢠⣇⠮⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡞⠁⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠲⢤⡀⣃⣷⣡⢷⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢷⢄⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀ ⠰⡇⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡴⠋⠁⠀⢠⠎⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠁⠢⡀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⡠⡶⢀⡜⡰⣡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠈⠲⣄⡀⠀⠈⠳⢄⠀⠀⠀⠀ ⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠳⡄⠀⠀⠘⠁⠗⠃⢿⡟⠙⣿⡈⡄⠀⠀⠀⠀⡄⡀⣰⡟⠀⠀⠀⠀⠀⠀⠈⢯⡑⠢⠄⣀⠑⠢⢀⣀ ⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠦⣀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⡇⠀⠐⢣⢹⡀⠀⡆⣼⣴⠗⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠻⣄⠀⠀⠀⠀⠀⠀⠀⠸⡴⠚⡟⠢⢄⣀⠀⠳⣄⠀⡟⢲⠒⡇⠀⠀⠀⢑⡇⡼⠛⠉⠁⡼⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢳⡀⢷⠀⠀⠈⠙⠒⠬⣿⣇⣸⡀⡇⠀⠀⢀⠏⢹⠀⠀⠀⣰⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠳⣸⠀⠀⠀⠀⠀⣠⠃⠀⢨⣧⡇⠀⠀⡼⠀⡟⠀⠀⢠⠇⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀ ⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⢳⢦⡀⠀⠀⠀⠙⢆⠀⠀⣀⠔⠁⢀⡠⢛⣿⠀⠀⢰⠃⢀⡇⠀⠀⡞⠀⠀⠀⠀⠹⡢⢀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⢧⠉⣳⣤⣀⠀⠈⠳⣮⡥⠴⠚⠉⠀⢸⡏⠀⢀⡟⡀⢸⠁⠀⢸⠁⠀⠀⠀⠀⠀⠱⡀⠑⢤⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠈⢿⡁⢀⡏⠑⢢⢤⣈⠳⢄⡀⠀⠀⢸⠇⠀⡼⠀⠑⢿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⠓⠦⣄⡀⠀⠑⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣀⣀⠙⢼⡀⠀⣿⠀⠈⠉⠓⠻⠶⣄⣸⠀⢠⣧⡀⠀⠈⡇⠀⢸⠈⢲⢄⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠈⠉⠐⠒⠓⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡿⢷⡤⣿⢤⠀⠀⠀⠀⢀⡤⣧⣄⣼⣽⣽⠀⠀⢳⠀⠀⢳⡢⠧⠌⠒⠤⢄⣀⡀⠀⠈⠑⠤⢀⣀⣀⠠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡼⠧⠼⠼⠀⠀⠀⠀⢿⣰⡇⢸⡆⣹⠀⠀⠀⠸⡄⠀⢄⢹⠓⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀ ⢸⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⢀⣿⡟⠀⢀⣴⣄⠀⠀⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⢸⣿⠇⠀⠀⠙⢿⣷⣄⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠘⢿⣿⣄⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠙⢿⣷⠄⠀⢸⣿⠇⠀⠀⠠⣾⡿⠋⠀⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠿⠟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⣧⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠙⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠹⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣠⣤⣴⣶⣶⣾⣟⠟⠀⠀⠠⠃⢠⠎⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠑⣟⢿⣷⣶⣶⣶⣤⣤⣀⠀ ⠀⠸⣿⣿⣿⣿⣿⡿⢻⠋⠀⠀⠀⠁⡰⠃⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠈⢺⠛⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⢿⣿⣿⣿⡿⢳⠃⢀⡀⠀⠀⡼⠁⠠⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠑⠄⠀⠳⡛⢿⣿⣿⣿⡟⠀ ⠀⠀⢸⣿⣿⣿⣤⡇⠃⠀⠀⠀⢰⠃⠀⢡⡎⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⢱⢸⣿⣿⣿⠃⠀ ⠀⠀⠀⣿⣿⢫⡟⠸⠀⠀⠀⠀⡏⠀⠀⡎⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⣄⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⢦⠀⠀⢫⡹⣿⡟⠀⠀ ⠀⠀⠀⢸⣿⣿⠁⣏⠀⠀⠀⢸⠁⠀⡸⠀⠀⣼⠟⡇⠀⠀⠀⠀⠀⠀⠘⣼⡆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⡆⠀⠀⢧⠀⠀⢻⣿⠃⠀⠀ ⠀⠀⠀⠀⣿⠇⠀⠮⠀⠀⠀⡏⠀⠀⡇⠀⡰⠧⠤⠼⡀⢰⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠘⣧⡀⠀⠀⠀⠀⠹⡀⠀⠸⡄⠀⠈⢿⣄⠀⠀ ⠀⠀⠀⢠⡟⡄⠀⡳⠀⠀⢰⠇⠀⣼⠁⡰⢁⣀⣀⠀⠹⡄⢣⠀⠀⠀⠀⠀⠙⣌⠛⠦⡀⠱⡙⢦⡀⠀⢣⠀⢣⠀⠀⢇⠀⠈⢏⣏⠛⢖ ⠀⠀⢠⢳⠃⡇⠀⢑⠀⠀⢸⠀⡜⢉⣦⣯⡵⠶⢦⣌⠐⠜⢄⠳⣄⡀⠀⠀⠀⠈⢲⣈⣭⣵⣿⣑⠳⣄⠈⡇⠘⡆⠀⢸⠀⠀⢸⠘⡆⠀ ⠀⣠⠃⡞⠀⢱⠀⢸⠀⠀⢸⡜⢠⣿⠟⢁⠐⢿⣷⣌⢳⡀⠀⠑⠸⠯⠉⠑⠒⢢⡟⠁⠘⣿⣶⡍⠻⣬⡷⣧⠀⢳⠀⠨⡄⠀⢈⠆⢹⡀ ⡜⠁⣼⠇⠀⠈⡆⠈⡆⠀⢸⠐⣾⠃⠀⣿⡖⣶⡽⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⣾⠀⣷⣶⣷⣹⣿⠀⢹⡾⢾⢀⣾⡀⠀⡇⠀⢸⠀⠀⢣ ⣠⡾⢼⡁⠀⠀⠹⡄⢱⠀⢸⠐⣻⠀⠀⣿⣏⣿⣧⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⢿⣿⢿⣻⠀⠀⡷⠞⠉⣯⡇⢀⡇⠀⣸⠀⠀⠘ ⣿⡝⣾⠀⠀⠀⠀⢳⠈⢇⠸⡀⠹⡄⠀⠘⢇⣐⡨⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣔⣂⡸⠃⠀⢸⠓⠂⢰⢿⡇⢰⠀⢀⡇⠀⠀⠀ ⣷⣛⣼⠀⠀⠀⠀⠀⠣⡈⢆⢇⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠋⠁⢀⡷⢫⣗⡸⠀⡼⠀⠀⠀⠀ ⢷⣝⣾⡄⠀⠀⠀⠀⠀⠑⣌⢾⡀⠀⠀⠀⠀⠀⠀⣠⡖⠒⠒⠒⠒⠒⠒⠒⠒⠦⠤⣄⠀⠀⠁⠁⠀⠀⠀⡜⠛⣫⣷⠃⡼⠁⠀⠀⠀⠀ ⠸⣿⣸⣇⠀⠀⠀⠀⠀⠀⠀⢣⣇⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⡇⠀⠀⠀⠀⠀⢸⣧⢿⢿⡟⡸⠃⠀⠀⠀⠀⢀ ⣧⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⢠⡿⣼⡹⣾⡟⠁⠀⠀⠀⠀⠀⢸ ⠈⠁⠈⠻⡽⡄⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠓⢦⡀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⢀⣴⣟⡳⢧⣻⡽⠀⠀⠀⠀⠀⠀⢀⡯ ⣿⣶⣤⣄⣹⡽⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠚⠉⠀⠀⠀⢀⣠⣴⢯⡳⣞⣿⣷⣹⡇⠀⠀⠀⠀⠀⢀⣾⢳ ⣿⣿⣿⣿⣿⣿⣯⠷⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣒⣦⢤⣤⣠⣀⣄⣠⣤⣤⣴⣶⢻⡽⣻⣮⣗⣻⢼⣻⡟⢾⡇⠀⠀⠀⠀⢀⡾⣭⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣽⣳⢦⣀⠀⠀⠀⠀⠀⠹⡏⠁⠉⠓⠦⣉⡉⠛⣙⣩⠵⢚⠩⠳⣽⣽⣼⣿⣾⣷⣷⣿⣿⠆⠀⠀⠀⣠⣾⣻⣾⣿

⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠛⠛⠛⠛⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠛⢻⣿⣿⠀⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠁⠀⠈⠉⠉⠛⠛⠿⠿⢿⣿⣷⣶⣶⣶⣤⣤⣤⡴⠶⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⢈⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠘⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⣸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠠⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⢳⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠓⠦⠤⣑⡛⢷⣄⡀⠀⠀⢀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠻⢯⡑⠒⠚⠁ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠤⠤⢤⣀⣠⠤⠴⢶⢒⠖⠒⢲⢲⣦⣤⣈⠳⡄⠀ ⠀⠀⠀⠀⠀⡀⢀⢸⢡⣤⣀⠀⠙⠆⠀⠀⢰⣿⠄⠀⣾⣀⡹⠽⣏⣱⠟⠀ ⠀⠀⢀⣴⣿⣛⣿⠛⢦⡀⠿⣉⣶⠀⠀⠀⠀⠙⠀⠀⠉⠁⠀⠀⠈⡷⠀⠀ ⠀⠸⣿⣸⣿⣿⡿⠀⠀⠉⣶⣦⡤⡀⠀⠤⣄⡀⣀⣀⢴⣦⡤⠴⡾⠁⠀⠀ ⠀⠀⠉⠛⣿⠿⣶⠊⠹⡅⠀⢠⡇⡏⠑⠒⢤⣤⣧⠈⢆⠹⡙⣞⠁⠀⠀⠀ ⠀⠀⡴⠚⠧⣀⠘⣆⠀⠉⠉⠀⢈⠹⡄⢠⣇⢿⡟⠃⠀⠀⢁⡼⠀⠀⠀⠀ ⠀⢰⣿⡦⣀⣀⢝⣿⠤⡤⠀⡇⣸⠀⡷⡸⣇⠈⣳⠆⢰⡖⠉⠀⠀⠀⠀⠀ ⠀⠈⠹⣝⡲⠄⣼⠀⠳⢷⡒⠛⠑⠚⢁⡇⠈⠳⠄⠀⠜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠛⣿⠀⠀⢀⡈⠉⠉⠉⣩⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠊⠉⠩⣷⡽⠄⠀⢸⠶⠤⠶⣾⡟⠋⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡇⠀⠀⠀⢀⣀⣀⣀⡼⠃⠀⢀⡠⢿⠀⠀⢀⡿⠒⠢⠤⢄⣀⠀⠀⠀⠀ ⠀⢻⡄⠀⠀⠀⠁⠈⠁⠑⢤⢠⡏⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀ ⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢈⡏⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀ ⠀⠀⠀⠀⠙⠒⠠⠤⠤⠔⠋⠁⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠚⠋⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡞⡏⡏⡏⠻⣦⠴⠶⠶⠶⢦⣤⣤⣤⣤⣤⣀⡀⣠⠶⢛⢟⠷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⡀⡇⣇⠟⠹⢹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⣀⠂⢌⢤⠊⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠐⠉⠽⠺⡁⢸⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠗⠉⠉⠁⠀⠀⠀⢠⠀⠀⡤⡠⣀⢤⡤⡀⠀⠀⠀⠀⠀⠀⠃⠱⠚⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⠀⠄⢠⠀⠰⡉⠉⠉⠉⢉⠇⠀⠀⠄⠀⠀⠀⠀⠀⡇⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⣄⡎⠀⠄⠘⢄⡈⢢⠗⠒⠣⡀⠀⠀⠑⡶⠶⠬⡼⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣧⠀⢈⣒⠖⠊⠁⠀⠀⠀⠁⠀⠀⠈⠀⠀⠘⠠⡄⠤⠃⡀⠀⡆⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠏⢑⠂⣡⠐⠒⢲⣶⡖⠢⠀⠀⠀⠀⣤⣤⣀⣀⡈⠱⣈⣠⢠⣿⡀⠀⠀⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠈⡄⢸⠀⠀⣀⣙⡓⠊⠀⠀⠀⠀⠘⠿⠤⠜⠀⠁⡦⠌⣿⠸⣇⠀⠀⠸⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⠀⣸⢿⡀⠀⠉⠉⠉⠀⣀⣠⣤⠀⠀⠛⠛⠓⠀⢰⠁⣰⠇⠀⢿⠀⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡏⠀⠀⢀⡟⠈⢷⡄⠀⠀⠀⠀⡟⠋⢹⠀⠀⠀⠀⠀⢀⡟⠛⠉⠀⠀⠸⡇⠀⠀⠸⡇⠀⠀⠀⠀ ⠀⠀⠀⣼⠁⠀⠀⣸⠃⠀⠀⠙⠷⣄⡀⠀⠡⣀⠆⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢿⠀⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⠙⠳⠶⠦⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⡆⠀⠀⠀ ⠀⠀⣸⠃⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⠀⠀⠀ ⠀⠀⡿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⡄⠀⠀ ⠀⢸⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⣇⠀⠀ ⠀⢸⡇⠀⢀⢴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢄⠀⠀⣿⠀⠀ ⠀⢸⠃⡠⠊⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠑⢄⢹⡄⠀ ⢠⡾⠋⢀⠞⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠢⡀⠙⢷⡀ ⢸⡧⠒⣡⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⢌⠒⢼⣇ ⢿⡠⠞⣡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠑⢤⡟ ⢸⣥⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣤⡇ ⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀

⠀⠀⢀⡠⠄⠐⠒⠒⠒⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠀⠀ ⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀ ⠀⠀⠀⠈⠀⣒⣠⣤⣖⣊⡀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⡐⠈⢁⣴⣀⣀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆ ⠀⡠⠓⠚⢦⣿⣿⠯⢻⢻⠉⠂⠄⠀⠀⠀⠀⠀⡅ ⢐⡇⠀⠀⠀⠉⠘⠄⢻⠏⠀⠀⠈⠱⣀⣀⡀⢀⠃ ⠀⢸⠢⡤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠙⢆ ⠀⠈⠢⢈⣢⡀⠀⠐⠒⡄⠀⠀⠀⡔⣛⠟⠱⠀⡜ ⠀⠀⠀⠀⠠⢒⠥⢒⣢⠭⢔⢲⠒⣄⣀⣀⠠⠊⠀ ⠀⠀⠀⠸⡐⠣⣀⠀⠈⢆⣀⣆⠗⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⣎⠑⢄⠀⠀⢀⠔⢃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠁⠀⣀⠼⢇⢲⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠩⡁⠀⠀⠈⡉⠀⠀⠸⡎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡎⠙⢠⠔⠉⠀⠀⢀⠜⠁⠀⠀⠀ ⠀⢀⠔⠈⠉⢲⠗⠠⢜⣄⠀⠀⡎⢀⡀⠀⠀⠀⠀ ⠀⡆⠀⠀⠰⠁⠀⠀⠀⠈⣦⠀⠈⠂⠀⠉⢆⠀⠀ ⠀⠑⢄⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀ ⠀⠀⠀⠈⠑⠳⠄⣀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠘⣿⣿⠟⠋⠉⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠹⣿⡿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠿⠿⠿⠿⠏⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠠⠾⣿⠀⢿⠿⠛⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠒⠛⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡇⢸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠷⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡆⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⢻⣦⣄⠀⣀⣀⣀⡀⢀⣤⣤⣤⣶⣶⣾⡇⠀⣿⣿⣿⣿⡇⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿ ⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡀⠀⢀⠀⠀⠀⣿⣿⣿ ⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣄⣾⣆⣾⣤⣿⣿⣿ ⣿⣿⣿⣧⣶⡀⣸⣦⣸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠚⠛⠛⠛⠛⠲⠶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⠿⠃⠀⠀⠀⠀⠀ ⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⣀⣈⣙⣛⣛⣋⣿⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢀⣀⣀⠈⣉⣉⡛⢲⣄⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠋⠛⠙⠀⢈⡉⠋⠻⣿⣴⣟⠀⠀⠀⠀⠀⠀⠀ ⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠼⢠⠊⠉⠑⢇⠈⠑⣴⠋⠉⠉⢻⣆⠀⠀⠀⠀⠀ ⢿⡇⠀⠀⠀⠀⠀⠀⣰⠟⠢⣀⠈⢦⣄⠀⠀⢳⣶⠃⠀⠀⠀⢀⡿⣄⠀⠀⠀⠀ ⢸⣧⠀⠀⣀⣀⣀⣰⡏⠀⠀⢈⣧⡬⠭⠷⠮⢭⣅⢀⣀⣤⡴⠛⢀⣸⠁⠀⠀⠀ ⠀⠻⣷⡟⣉⡡⠤⠿⠛⠀⡞⠁⠀⠀⠀⠀⠶⣆⣀⣨⡭⠓⠀⠰⠟⢹⡇⠀⠀⠀ ⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⢧⣀⣤⣀⠀⠀⢰⠟⣿⡿⠁⠀⠀⢀⡤⡎⠀⠀⠀⠀ ⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠛⠾⠭⠉⠀⠀⠈⠉⠉⠀⠀⣀⣠⣴⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⠿⢶⢆⡀⠀⠀⠀⠀⣀⠀⣀⣀⣀⠼⠿⣯⣉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢑⣉⡿⠟⠓⠋⠛⠝⠋⠀⠢⡀⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⣀⣤⡤⢦⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣽⣧⣀⠀⠐⣫⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣀⡟⣫⠟⠉⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⣀⣤⢼⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⣷⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠁⢀⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣴⠟⠙⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠈⠑⢶⠾⠿⣏⠁⠀⠀⢸⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣽⢷⣆⠀⠀⠀⠈⢳⡈⠙⠃⢀⣠⣼⠟⠳⢦⣀⠀ ⠀⠀⠀⠀⢠⡾⠉⠀⠀⠈⠉⠀⠀⠁⠀⠀⣀⣠⣼⠃⠀⠀⠛⠋⠁⠀⠀⠀⠙⣧ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠺⠿⠟⠋⠉⠉⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣀⣀⣠⣤⡾⠋ ⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⣤⣤⣤⣤⣴⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠂⠉⠁⠀⠀⠀⠀⠉⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠢⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢻⠇⠉⣉⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠛⠉⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀ ⠀⠀⠀⠀⠀⠀⣠⠊⣁⡤⢤⣤⣀⣤⡤⠤⢤⣦⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀ ⠀⠀⠀⠀⠀⠀⣷⣏⣡⠖⠊⠹⠛⢷⣀⡴⠚⠉⠀⠀⢸⣏⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇ ⠀⠀⠀⠀⣠⠎⠉⠀⠈⠙⢦⡀⢀⣠⣿⠀⠀⠀⠀⠀⠀⠈⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣛⡉⠉⠙⣷⣶⡤⠄⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠈⠛⣏⠛⠤⠤⢽⠿⠃⠀⢠⡞⠙⠛⢶⡦⠤⢤⣀⠀⠀⣴⠃ ⠀⠀⠀⠀⠘⡧⣄⡀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⣀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠋⠀ ⠀⠀⠀⠀⠀⢧⠀⠉⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⠼⠓⠄⠀⠀⠀⠤⠒⢖⠊⠉⠉⠙⢃⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣈⣑⡶⢤⣈⣉⠑⠒⠉⠉⠀⠀⠀⠀⠀⠀⠲⠤⠤⠞⠀⠀⢀⡴⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠉⠀⠀⠈⠙⠲⣬⡽⡛⠙⠒⢒⠶⠶⣒⠒⣟⠒⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠉⠁⠀⠀⠀⠀⠀⠙⣅⠔⠋⠙⠲⣄⠈⢧⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠟⠉⠉⠂⠀⠀⠀⠀⢠⠀⣠⡷⠶⠶⣄⠀⠈⣦⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⣠⠀⠀⠀⠀⠀⠀⠈⠻⣅⠀⠀⠀⠈⣧⠴⠃⢀⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢈⡟⠀⠳⣄⠀⠠⡀⠀⠀⠀⠀⠑⠦⠤⠾⠃⠀⡠⠋⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣧⠀⠀⠈⠑⠚⠙⣆⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣰⠾⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠲⠤⠺⡟⠧⠬⢷⣄⡀⠀⠀⣀⡴⠟⠒⠊⠉⠀⠀⢹⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⢸⣆⣰⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣨⢧⡀⠀⠀⠀⢀⡞⢀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⠉⠒⠤⢤⣼⠖⠁⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣼⠀⠀⠈⠒⠤⠤⡼⠁⠀⠀⠀⠀⠀⣀⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⠋⠁⠘⢦⡀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠘⠃⠙⢦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡞⠁⠀⠀⠀⠀⠀⠉⣙⠶⠖⠒⠚⠢⢄⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠲⢄⡀⠀⠀⠀⠀ ⡾⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠈⠳⢄⡀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀ ⠀⠀⠀⠉⠓⠒⠤⠽⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠶⠤⠤⢤⡤⠤⠤⠤⠶⠖⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬜🏽⬛🏽🏽⬛🏽⬜⬜⬜ ⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜ ⬜⬜🏽🏽⬛🏽🏽⬛🏽🟥⬜⬜ ⬜⬛⬛🏽🏽🏽🏽🏽🏽⬛⬛⬜ ⬜⬜🟥🏽⬛🏽🏽⬛🏽🏽⬜⬜ ⬜⬜🏽🏽🏽🏽🏽🏽🏽🏽⬜⬜ ⬜⬛⬛🏽⬛🏽🏽⬛🏽⬛⬛⬜ ⬜⬜🏽🏽🏽🏽🏽🏽🏽🟥⬜⬜ ⬜⬜⬜⬜⬜🟦🟦⬜⬜⬜⬜⬜ ⬛⬜⬜🟦🏽⬛⬛🏽🟦⬜⬜⬛ ⬜⬛⬛🟦⬛⬛⬛⬛🟦⬛⬛⬜ ⬛⬛⬛🟦⬛⬛⬛⬛🟦⬛⬛⬛ ⬜🟥🏽🟦⬛⬛⬛⬛🟦🏽🏽⬜ ⬜🏽🏽⬛⬛⬛⬛⬛⬛🏽🏽⬜ ⬜🏽🏽⬛⬛⬛⬛⬛⬛🟥🏽⬜ ⬛⬛⬛🏽⬛⬛⬛⬛🏽⬛⬛⬛ ⬜🏽🟥🟦🟦⬛⬛🟦🟦🏽🏽⬜ ⬜🟦🟦🟦🟦⬛⬛🟦🟦🟦🟦⬜ ⬜🏽🏽🟦🟦⬛⬛🟦🟦🏽🏽⬜ ⬛⬛⬛🟦🟦⬛⬛🟦🟦⬛⬛⬛ ⬜🏽🏽🟥🟥🏽🏽🟥🟥🏽🟥⬜ ⬜⬛⬛🟥🟥🏽🏽🟥🟥⬛⬛⬜ ⬜🏽🏽🟥🟥⬜⬜🟥🟥🏽🏽⬜ ⬜🏽🏽🟥🟥⬜⬜🟥🟥🏽🏽⬜ ⬜🏽⬜⬛⬛⬜⬜⬛⬛⬜🏽⬜ ⬜⬜⬜🏽🏽⬜⬜🏽🏽⬜⬜⬜ ⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜ ⬜⬜⬜🏽🟥⬜⬜🏽🏽⬜⬜⬜ ⬜⬜⬜🏽🏽⬜⬜🏽🏽⬜⬜⬜ ⬜⬜⬜🏽🏽⬜⬜🏽🏽⬜⬜⬜ ⬜⬜⬜🏽🏽⬜⬜🟥🏽⬜⬜⬜ ⬜⬜⬛⬛⬛⬜⬜⬛⬛⬛⬜⬜ ⬜⬜⬜🟥🏽⬜⬜🏽🏽⬜⬜⬜ ⬛⬜⬜🏽🏽⬜⬜🏽🏽⬜⬜⬛ ⬜⬛🏽🏽🏽⬜⬜🏽🏽🏽⬛⬜ ⬜🏽⬛🏽🏽⬜⬜🏽🏽⬛🏽⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡈⠻⢿⣿⠿⣿⣿⣿⠇⣴⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠉⠀⢿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢛⣉⣍⡛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣄⣉⠛⣛⡉⠁⠀⠀⣀⣤⣶⣦⣤⣀⣶⠄⣿⣿⣿⣿⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠇⠀⠀⣸⠛⠉⠉⠙⣿⣿⣿⡆⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣮⡻⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢋⣩⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣶⡾⣿⣟⠛⣋⠁⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⣩⣤⣶⣤⣄⡀⠀⢀⣼⣿⠟⠁⣩⣿⣿⢿⣿⡿⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢧⣾⣿⣿⣿⣿⣿⣿⡄⠻⠿⠁⢠⣾⣿⠟⣡⣾⣿⠛⢮⡛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢳⣾⣶⡄⠀⠈⢿⢸⣿⣿⣿⡟⣩⣶⣿⣿⣿⣷⣄⢿⡿⢫⣾⣿⣿⠏⣠⣼⡿⠾⣻⣽⣤⣶⡶⣦⣄⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⡿⠃⠈⠛⢿⣦⣀⣈⠈⢿⣿⡏⣼⣿⣿⣿⣿⣿⠿⣛⣂⣀⡛⢿⠟⣡⣾⣿⡿⢁⣾⣿⣿⣿⣿⡷⢹⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣼⡿⠋⠉⠀⠀⠀⠀⠀⠹⢿⣼⢧⡈⠻⠀⣿⣿⣿⣿⢋⣴⣿⣿⣿⣿⣿⣷⣄⢿⡟⠋⠀⣾⣿⣿⡿⠉⠩⠷⠿⣿⣿⣿⣿⡿⣫⣶⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠋⠀⢠⣶⣶⣶⣾⣿⣿⣿⣿⣷⡄⣶⣶⣆⣿⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠁⣀⣤⣶⣜⢿⠁⢸⣷⡄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⢰⣯⣿⠉⠉⢩⣍⣉⣉⣭⣭⣥⣭⣍⣻⣥⣭⣭⣜⠿⣿⣿⣿⣿⣿⣿⣿⠿⢓⠸⢿⣿⣿⡟⠀⠀⠀⢻⣧⣀⡀⠀⠈⠐⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⢀⣼⠿⠁⠀⢸⣿⡇⠀⢸⣿⠿⠟⠿⠿⠿⠿⢿⣿⣟⠛⠛⣻⣥⣴⣶⣄⠉⠛⠿⠟⢱⣿⣿⣿⡄⣀⠈⠀⠀⠀⠀⠈⠉⠛⠁⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡇ ⣠⡴⠟⠛⠁⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⢠⣼⣻⣿⣿⣿⣿⣿⣿⠾⣿⠿⠛⠁⣀⣴⣿⣷⠈⣛⠻⠟⠁⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢿⣿⡇⢀⣾⣿⡃⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⣟⡛⠻⣿⡁⠀⣿⣇⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠿⠁⠀⢤⣤⣶⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⡇⠸⣿⣿⡇⠀⠀⠀⣤⠾⠻⣿⣿⣶⣿⣿⣿⣦⠻⠃⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⢠⣼⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢸⣶⠁⢐⡿⠏⠀⠀⠀⢠⣶⣿⣷⠘⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠀⠀⠀⠀⣀⣼⣿⡿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠀⢻⣧⠘⣿⣦⠀⠀⢠⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣿⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠘⣿⣧⠀⣾⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠀⠀⠀⣼⣿⠆⣿⣿⣿⣿⣿⢿⣿⣥⣴⣶⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⢹⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣤⣤⣤⣤⣶⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⡉⠉⠛⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⠟⠉⢼⣿⣿⣦⣆⢀⣠⣴⣦⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠉⠉⠉⠉⠉⠑⠲⠤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀ ⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢈⡇ ⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣤⣤⣄⣸⣿⣟⢻⣗⠒⠒⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣹⣿⣬⣽⣭⣛⣛⣿⠦⢄⡀⠀⠀ ⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⢠⠞⠛⢡⣟⠻⢿⣿⣿⣟⢳⣲⠟⡆⠀ ⠀⠀⠀⠀⠀⠸⣇⢀⣀⣀⢰⠃⠀⠀⠛⣿⠏⠙⢻⣿⡿⠟⠛⠛⠳⡄ ⠀⠀⠀⠀⠀⢰⠟⣁⣀⣈⡉⠓⠀⠀⠀⠈⠑⠚⠉⠉⠀⠀⠀⠀⠀⣽ ⠀⠀⠀⠀⠀⠘⢆⠛⠻⣿⣛⣇⠀⠀⠀⢀⣀⣀⡀⠒⠤⢤⣤⡤⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⣾⣿⠿⠤⠤⡴⠿⢯⣉⡡⠤⠔⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠜⣡⠏⠀⠀⠀⢀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⢃⠜⠁⠀⠀⠀⠀⢿⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⠤⢤⣏⣠⣏⣀⣀⣀⠀⠀⠀⠘⡆⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⢠⣏⠀⠀⡾⠋⠉⠓⢄⠀⠀⠉⠑⠂⠤⣇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀ ⢸⢼⠟⢳⣿⣦⣀⣀⠼⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠉⠉⠒⢄⠀⠀⠀ ⠈⠻⠤⣴⠃⢹⣦⣀⡀⠀⠀⠀⠀⠀⠑⣦⠀⢀⡀⠀⢠⡄⢸⡆⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠈⣿⣵⣶⣶⣤⡀⠺⣍⣀⣸⡃⠀⣼⠤⠚⠁⠀⠀ ⠀⠀⢀⡠⠤⠐⠒⠒⠃⠀⣨⣿⢤⣼⠆⠀⠀⢨⡿⠯⢁⣀⡀⠀⠀⠀ ⠀⢀⡞⠀⠀⠀⠀⣠⠖⠉⠀⠈⠉⠀⠀⠐⠚⠉⠀⠀⠀⠀⠉⣆⠀⠀ ⠀⠈⠧⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠉⠒⠢⠤⣄⣀⣀⣀⣀⡤⠤⠤⠤⠖⠚⠁⠀⠀⠀

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⠻⠿⣿⠿⣿⣿⣿⠏⣰⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⡆⠀⠀⠀⠀⠉⠀⠻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⠛⣉⣭⣙⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣉⠛⣛⣉⠁⠀⠀⢀⣤⣴⣦⣤⣀⣶⡆⣾⣿⣿⣿⣯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡏⠀⠀⣰⠟⠉⠉⠙⢿⣿⣿⣇⢻⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⣿⣿⣦⡙⠿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢋⣩⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣴⡾⣿⣿⡛⢋⠉⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣉⣤⣶⣤⣤⡀⠀⠀⣴⣿⠟⠁⣩⣿⣿⣿⣿⣿⣻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢇⣾⣿⣿⣿⣿⣿⣿⡆⠺⠿⠋⢀⣾⣿⡿⢫⣾⣿⠟⢮⣝⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣳⣾⣷⡄⠀⠈⢿⢸⣿⣿⣿⡿⣫⣶⣿⣿⣿⣷⣄⢻⡿⢋⣴⣿⣿⠟⣠⣴⡿⠷⣟⣯⣤⣶⡶⣶⣄⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠃⠈⠛⢿⣦⣀⣈⡈⢿⣿⡟⣼⣿⣿⣿⣿⣿⠿⣛⣃⣀⣘⠿⠟⢣⣾⣿⡿⠃⣴⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣼⡿⠋⠉⠀⠀⠀⠀⠀⠘⠿⣸⠧⡄⠻⠁⣿⣿⣿⣿⢏⣴⣿⣿⣿⣿⣿⣷⣄⢻⡟⠋⠀⣼⣿⣿⣿⠋⠉⠵⠿⣿⣿⣿⣿⣿⢋⣷⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠋⠀⢠⣶⣶⣶⣾⣿⣿⣿⣿⣷⡄⣶⣶⣆⣻⣿⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠁⣀⣠⣴⣮⢻⠇⠀⣷⡄⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣷⣤⡀⠀ ⠀⠀⠀⠀⣿⡇⠀⢰⣯⣽⠉⠉⢩⣍⣉⣉⣩⣭⣥⣭⣍⣻⣥⣭⣭⣜⠿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡸⢿⣿⣿⡿⠀⠀⠀⢹⣷⣀⣀⠀⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⢀⣼⠿⠃⠀⢸⣿⡇⠀⢸⣿⠻⠟⠿⠿⠿⠿⢿⣿⣿⠋⠛⣻⣭⣴⣶⣄⠉⠛⠿⠟⢫⣾⣿⣿⣆⣀⡈⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿ ⣠⡴⠟⠛⠁⠀⠀⢸⣿⡧⠀⣾⣿⡀⠀⢠⣼⡻⣿⣿⣿⣿⣿⣿⠎⣿⠿⠟⠃⣀⣴⣿⣿⠈⣙⡻⠿⠃⢾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⢿⣿⡇⠀⣼⣿⡇⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⣾⡛⠻⣿⡇⠀⣿⣧⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠃⠀⢠⣤⣴⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⣠⠾⠛⢿⣿⣷⣿⣿⣿⣧⠹⠃⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⣼⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⢸⣶⡅⢐⡿⠏⠀⠀⠀⢀⣴⣿⣷⡌⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⢀⣤⣿⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⢻⣧⠘⣿⣦⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠘⢿⣧⠀⢸⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠀⠀⠀⢰⣿⠆⢸⣿⣿⣿⣿⢿⣿⣧⣤⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⢸⣿⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⣤⣤⣤⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣉⠉⠻⠋⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠋⢰⣿⣿⣧⣦⡀⣀⣴⣶⣤⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⢿⣿⡟⠛⠛⢻⡀⢸⣿⡆⣠⠟⠉⠛⣹⣿⡿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠙⠦⠤⠻⠿⠶⠴⣆⠉⣈⣉⣀⣀⠁⠒⠚⢛⣃⣀⣤⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⡀⠉⣿⣴⠖⢈⣤⡴⠒⢰⡦⠠⡀⠈⡏⢠⣿⠟⠉⢁⣦⡀⢣⣤⣌⠉⠰⡁⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⡀⠄⠋⢀⣉⠉⠉⠻⣗⣠⠞⠁⣼⣿⡄⠀⠛⠃⠀⣴⡏⢈⡇⠀⠈⠉⢑⡀⢋⠙⠛⢀⣀⣩⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣁⣈⡻⠋⣠⠖⢸⠁⣸⣿⢷⡀⠀⠀⠀⢠⣣⠤⠀⣀⡀⠀⢸⣿⡗⠈⠀⡠⠒⠻⣿⠃⠸⣿⣷⠀⠙⢻⣤⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣴⢀⣴⣷⣠⣿⠀⢿⣿⡀⠈⡣⠀⠀⢸⣿⢀⡴⠛⢡⠀⠀⠉⠀⠀⠰⠶⠶⠚⠁⢀⣀⡉⠛⠇⣴⡄⠢⣀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⠛⠓⢿⠛⠋⣁⣀⣀⣀⡀⠀⠈⠛⠿⠿⠿⠀⠀⢸⣿⢾⢀⣴⡿⠀⠀⠀⠀⣀⣤⣤⣤⣴⣾⣿⣿⢿⡿⠀⣧⡉⠒⢆⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣧⠖⠒⢚⠋⢠⣾⣆⠘⠻⢿⣿⣿⣶⢄⡀⠀⠀⠀⠀⠈⢇⢈⣿⣿⠃⠀⠀⢀⣾⣿⣿⠉⢡⠋⢈⣿⡁⡸⠁⢠⠋⢻⠂⡀⠹⠶⠶⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣯⡖⠀⣱⢀⡿⠟⠛⠓⠀⠀⠹⡄⠉⣆⠀⢹⣿⣷⡄⠀⠀⠘⠿⠏⠀⠀⠀⠘⠛⠛⠁⠈⠑⠲⠾⠿⠃⠀⠰⠿⠐⠃⢰⣿⡆⠐⢦⣤⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⣀⣴⠟⢀⢤⣶⣾⣿⠗⠀⠀⠈⠁⠘⠓⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⠀⠀⣀⠤⣄⠀⠀⠙⠿⠀⠰⣄⣀⣈⢻⣿⣿⣿ ⣿⣿⣿⣿⡿⠋⢩⠇⣰⣧⡀⠉⠉⠁⣀⡤⠒⣢⢠⣤⢄⣀⣀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⢹⣿⣷⣾⣿⠟⠹⡄⠈⡇⠀⢰⣦⡀⠀⣇⣀⣉⢿⣿⣿⣿ ⣿⣿⣿⣿⣇⣴⡿⠀⣿⠏⣀⣀⠀⣸⣿⣠⡎⠀⣸⡇⠀⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⣿⣿⣿⣿⡄⢠⣿⣧⡇⢠⡈⠻⣷⡀⣦⠉⢻⣿⣿⣿⣿ ⣿⣿⣿⡟⠉⡹⣴⠀⣠⣾⡿⠃⢠⣿⣿⣿⣷⣼⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⡈⠻⣦⡈⠃⢹⣦⢸⣿⣿⣿⣿ ⣿⣿⣿⣧⡞⠁⡇⢰⡿⢁⣴⠃⢣⣀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠐⣌⠻⡆⢰⠙⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣀⣿⠈⠁⣾⣿⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢀⣿⡆⠀⢸⣄⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠀⡆⠻⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠀⣸⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣼⡇⢀⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣴⣿⣧⠀⡈⠙⠛⠛⠛⠿⠿⠿⠟⠋⠀⠀⠉⠁⠀⣀⣀⡀⠀⢀⣴⣿⡆⠀⢀⣤⡀⠀⠀⠈⠛⠿⠿⠿⠿⠿⣿⣿⠟⠁⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⠷⣶⣶⣤⡀⠀⢠⣶⠆⢀⣤⠀⢰⣿⣿⠟⠁⠀⢸⣿⠋⠁⠀⢸⣿⣿⣷⡆⠀⢀⡄⠀⠀⠀⣀⠀⠀⣰⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢤⣌⡙⢿⣆⠈⣿⠀⢸⣿⣦⡈⠻⠃⡀⢠⣄⡈⠃⣴⣿⠀⡀⡿⠛⣁⣤⣶⠟⡀⠀⢠⡞⢁⣴⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢻⣿⡄⢻⣆⠸⣷⣄⡙⠿⠋⣠⠘⡧⠘⢋⣼⣦⣈⠋⢸⡏⣠⡘⠿⠋⣠⣾⡇⢠⣿⢁⣾⠟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡉⠓⠈⢿⡄⢻⡇⢠⣶⣦⣤⡄⢱⣆⠩⣠⣤⡉⢴⣶⢠⣤⣴⣶⡆⢨⡿⢀⣿⠇⠘⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣉⣀⠩⡄⢲⣦⣤⠑⢼⠁⠶⠌⡡⠾⠀⣿⠨⣤⣶⡶⢀⡌⢁⣨⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣀⡉⠡⣼⣌⠳⠖⢚⡓⠒⠾⢁⣧⠤⠉⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣭⣉⣉⣥⣶⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⣶⣿⣿⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⢀⣤⣤⣶⠶⣶⣦⢤⣤⣶⣶⣶⣶⣦⣄⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⠟⠛⠻⡿⠋⠋⠁⠀⠀⠈⠑⠈⢿⠛⢿⣿⣿⣿⠇⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢠⣿⠀⠀⠀⣀⣀⣀⡀⠀⣠⠤⢤⣄⡀⠀⠀⢈⣿⣿⣿⣿⣿⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⣿⠀⢠⡞⠉⠉⠉⠉⠻⣇⡀⠀⠀⠙⢷⣄⣾⡟⠁⠀⠀⠉⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠉⠉⠀⢿⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⣽⡟⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠲⣄⠀⠀⠀⠘⣧⣤⣤⡀⠀⠀⠀⠀⢹⣶⣶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠈⠻⣦⡀⠀⠸⣿⣿⣇⣀⠀⠀⢀⣸⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠘⢿⣆⣀⣨⣩⣬⣩⣽⣯⣉⣁⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠋⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣿⣿⡄⠀⣀⣴⣶⣿⡿⠿⠿⠿⢶⣿⣿⣀⠀⠀⠀⣀⣴⠶⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⢰⣾⣿⣿⣿⠟⠋⠉⠀⠀⣠⣶⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣶⣿⠟⠋⠀⣀⣠⣤⣤⣤⠶⠿⠿⠄⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡟⠀⠀⠀⠀⣀⣠⣤⠿⠇⠀⠀⢀⣼⠿⠟⠁⢹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣏⢀⣴⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⢶⣄⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠻⠷⣮⣽⣿⣶⠆⠀⠀⠀⠀⢿⣦⣀⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠚⢋⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣶⣤⣤⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣲⣶⣿⣿⡿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯⣟⣛⣛⣒⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢀⣤⣽⣿⣿⣿⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢿⣿⣥⣀⣀⣀⣀⣀⣤⣤⣴⣾⣛⣠⣴⣶⣿⣿⣾⣿⡾⠁⠀⠈⠉⠉⠃⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣒⣾⡿⠟⠛⠋⠉⠀⠟⠋⢠⠿⠋⠀⠀⠀⠻⢦⡀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠛⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣿⣷⣄⠀⠀⠀⠀⠛⢋⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠋⠉⢻⣿⣷⣶⣶⣶⣿⠟⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣠⣿⠋⠀⣠⡾⠋⠀⠀⠀⠀⠉⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣏⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣦⣤⣤⣤⣤⣤⣤⣴⣶⠶⠿⠛⠉⠁⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡿⠋⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣴⣶⣿⣿⠿⠟⠉⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠛⠛⠻⠿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠺⠟⢿⣧⠀⠀⠀⠀⠀⢀⣼⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣦⣤⣤⣴⣿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠈⠁⠀⠀⣀⣠⣴⣿⣿⡟⠁⠉⠛⠿⣷⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠁⠀⠀⠀⠾⠿⠟⠋⠁⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠐⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣾⣿⣿⡿⠿⠛⠙⠛⠿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⡿⠛⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⡄⠀⠀⡀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⠁⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣾⣿⣿⣿⣿⡿⠋⠹⣿⣿⣿⣿⣿⡇⠀⠀⠙⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀ ⢀⣿⣿⣿⡿⠃⠀⠀⢰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⢸⣿⣿⡏⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠘⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠙⠙⠉⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣶⣦⣿⣿⣿⣧⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠉⢠⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢉⡙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡛⠛⠛⣋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠉⠻⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⠛⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠶⠶⠶⠤⢤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠶⠶⠦⠤⣄⡈⠙⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠉⠑⠦⡀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠹⡄ ⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣠⡀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢳⣀⡇ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠀⠀⠀⠀⠀⣷⠖⠋⠉⠑⠒⠦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⢧⡀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⠀⠀⣀⡤⠤⢤⣘⢦⡙⠢⠤⢤⡤⠴⠋⡇⠀⠀⠀⠐⠶⠀⠀⠀⢸⠀⠀ ⠀⡼⢁⣴⣶⣶⣌⠑⠉⠑⢠⠞⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀ ⢸⠁⣿⣿⣿⣿⣷⠷⣄⠀⣏⣀⡴⠊⠀⠀⠙⠦⢄⣀⣀⣀⡤⠚⠁⠀⠀ ⠸⡄⣿⣿⣿⣿⣿⣿⡏⢳⣄⣀⠀⠀⠀⠀⠑⢦⣀⣀⣀⡄⠀⠀⠀⠀⠀ ⠀⢳⡸⡿⣿⣿⣿⣿⣿⣿⣤⣿⣩⣿⣩⣷⣶⣤⡀⠀⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠱⣝⢿⢻⣿⣿⣿⣿⣿⣿⠻⠿⢿⣿⣿⣿⣿⣦⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠓⠙⢦⣿⠛⣿⣿⣿⣷⣦⠀⠙⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠑⠯⣼⡿⠛⡿⣇⠀⢹⣿⣿⡿⣰⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢛⣒⢛⣋⡩⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢸⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⠟⢻⣿⠀⠀⠀⠀⣸⡿⠻⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⡿⠋⠀⠀⢸⣿⣀⣀⣀⣀⣿⡇⠀⠀⠙⢿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣸⣿⣿⡟⠁⠀⠀⣠⣾⡿⠟⠛⠛⠻⢿⣷⣄⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀ ⣿⣿⠿⠿⠿⠿⠿⠶⣶⣾⣿⠋⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⠶⠾⠿⠿⠿⠿⢿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣶⣿⣿⣿⣿⠿⠿⠿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⠿⠿⠿⣿⣿⣿⣿⣶⣾⣿ ⠀⠀⠀⠘⣿⣿⣿⡄⠀⠀⠈⢻⣿⣷⣶⣶⣾⣿⣿⠋⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣿⣿⣦⣀⠀⣿⡇⠈⠉⠉⠁⢸⣿⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡇⠀⠀⠀⠀⢸⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠄ ⠀⠙⢿⣿⣿⡿⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠙⠋⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣶⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠉⢻⣿⣿⣿⡿⡙⢿⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣴⣀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡿⠛⠻⠿⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⢠⢒⠉⠓⢦⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠇⠀⠔⠒⡤⡦⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⢿⣿⣿⡄⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⣀⡀⠀⢤⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠐⠇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡜⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠿⠍⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠠⠁⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠣⣿⣿⣿⠱⣴⣶⣶⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣁⠀⠀⠇⢈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠗⣿⣿⠀⢀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠧⠂⠐⠀⠀⢹⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⡔⠀⠀⠀⠀⢿⣿⣿⣛⣛⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠇⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠟⠁⠀⠀⠀⢌⠈⠙⠿⣥⣒⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢠⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⢀⠀⡢⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢢⠀⠀⠒⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠴⡀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠡⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠐⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠘⠘⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣤⣠⠑⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⡐⠀⠀⢀⠛⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⢣⡀⠀⣤⡀⠀⠀⢀⠀⢉⠢⠄⠀⠤⡔⠏⠉⠙⢃⠈⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠤⢠⡄⠀⠈⢿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⢣⠸⠵⡶⢄⠇⠀⠀⠈⠄⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢺⠃⠀⢀⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⣕⠦⣶⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⢂⠀⠀⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⣸⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣮⡟⡄⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠈⠀⠛⠒⠒⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠐⡀⠀⣰⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠈⠂⠬⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⣰⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠢⡀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠈⠉⢁⠌⠀⠀⠀⠀⠆⢠⠀⢠⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠘⢠⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⡀⠀⠄⣤⡀⠁⠠⡀⠀⠀⢹⣆⠀⢀⠀⣳⣰⣟⠤⠊⠁⠀⠀⠀⠀⠀⠠⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠄⠀⠀⠛⠋⢰⡶⡸⠀⠤⠼⢿⡐⠲⠽⠛⠉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠀⡐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠗⡿⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⡞⢩⣯⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⡹⠁⢰⠃⣩⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⠿⣉⣩⠛⠲⢶⡠⢄⠐⣣⠃⣰⠗⠋⢀⣯⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⣠⠬⠦⢤⣀⠈⠓⢽⣾⢔⣡⡴⠞⠻⠙⢳⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⣳⠖⠉⠉⢉⣩⣵⣿⣿⣒⢤⣴⠤⠽⣬⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣟⠟⠋⢡⡎⢿⢿⠳⡕⢤⡉⡷⡽⠁ ⣧⢮⢭⠛⢲⣦⣀⠀⠀⠀⠠⡀⠀⠀⠀⡾⣥⣏⣖⡟⠸⢺⠀⠀⠈⠙⠋⠁⠀⠀ ⠈⠻⣶⡛⠲⣄⠀⠙⠢⣀⠀⢇⠀⠀⠀⠘⠿⣯⣮⢦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣥⡬⠽⠶⠤⣌⣣⣼⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣧⣤⡴⢤⡴⣶⣿⣟⢯⡙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣗⣞⣢⡟⢋⢜⣿⠛⡿⡄⢻⡮⣄⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⠮⠴⠵⢋⣇⡇⣷⢳⡀⢱⡈⢋⠛⣄⣹⣲⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣱⡇⣦⢾⣾⠿⠟⠿⠷⠷⣻⠧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠽⠞⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⣿⢩⠖⠈⠐⠒⠒⠒⠴⠫⢍⢢⠀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⢀⣂⠀⠀⠀⠈⠐⠼⡜⠀⠀⠀⠀ ⠀⠀⣇⠀⡀⡘⠣⠀⠀⠀⣀⣠⠀⠀⢠⠱⡀⠀⠀⠀ ⠀⠀⢈⠦⢦⠮⣀⠀⠀⠀⣀⣁⠢⡕⣸⠀⢱⠀⠀⠀ ⠀⠀⡜⠀⣠⠀⠾⠅⣀⡀⠩⠬⠀⢃⠇⡆⠀⡆⠀⠀ ⠀⢠⠁⢠⠇⠣⢄⠀⢋⠅⠀⣀⠜⠉⠀⢱⠀⢰⠀⠀ ⠀⡜⠀⢸⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠸⡀⠈⡆⠀ ⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢡⠀ ⢠⢀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀ ⢸⢁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⡆ ⢗⡕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⡺ ⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⠁⣀⣤⣤⣤⣤⣀⠈⠙⠻⢿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⡿⠋⠀⠀⢀⣾⣿⡿⠿⠿⢿⣿⣷⡀⠀⠀⠙⢿⣿⣷⡄⠀⠀ ⠀⢠⣿⣿⠏⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠹⣿⣿⡄⠀ ⢠⣿⣿⠏⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠹⣿⣿⡄ ⢸⣿⣿⠀⠀⠀⢠⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⢸⡇⠀⣿⣿⣿⠋⠀⠀⠙⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡇ ⢸⣿⣿⠀⠀⠀⢸⡇⠀⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡇ ⠘⣿⣿⣆⠀⠀⢸⡇⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⣰⣿⣿⠃ ⠀⠘⣿⣿⣆⠀⢸⣧⣠⣿⣿⣿⣿⣄⣠⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⣿⠃⠀ ⠀⠀⠘⢿⣿⣷⣄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣠⣾⣿⡿⠃⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣧⣀⣀⣿⣧⣀⣼⡟⠀⠀⠀⠀⠹⣧⣀⣀⣿⣇⠀⣰⡷⠀⠀⠀ ⠀⠀⣰⠟⠉⠀⠀⠀⠀⠈⠙⢷⡄⢀⡴⠚⠉⠀⠀⠀⠀⠉⠻⣇⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⡴⢋⣭⣽⣷⠀⢷⠀⣰⢚⣭⣽⢣⡀⠀⠀⠀⠘⡇⠀ ⢸⡀⠀⠀⠀⠀⠈⣇⢿⣿⣿⣿⠀⡾⠀⢧⢿⣿⣿⢇⡇⠀⠀⠀⢀⡇⠀ ⢸⣧⣤⣤⣤⣀⠀⠈⠓⠾⠒⠁⣰⣇⠀⠈⠓⠾⠶⠛⠀⠀⣀⡤⠼⢄⠀ ⢸⠁⠈⠠⠄⠛⠳⣄⠀⣀⡤⠞⠁⠈⠳⣄⡀⣀⣠⠴⠖⠋⠁⠀⠀⣰⡇ ⠀⠀⠐⢲⡶⠄⠠⠟⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⣀⣠⡴⠾⠋⠀ ⠀⠀⠀⢸⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣋⡉⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⡶⠶⠶⢶⣶⣶⠶⠒⠒⣶⠛⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣀⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢷⣄⣀⡀⠉⠀⠀⠉⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣤⣈⣉⣙⡛⠛⠛⠛⠛⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠂⠴⠊⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠉⠓⣤⡀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⠜⠕⠒⠀⠀⠀⠀⢀⡬⢦⡀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⠎⢀⡔⠉⠉⠲⡀⢸⢁⣀⣀⣱⠾⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠾⡤⠒⠒⢚⡇⠘⡧⣀⡠⠾⡄⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠀⠀⠀⠀⠠⣌⡆⠀⠈⠒⠒⠊⠀⢀⡸⠀⠀⠀⠘⡜⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⢀⣠⣶⣶⡄⠀⠀⡇⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡄⠀⠀⠸⣿⣿⣛⣛⣻⠋⠀⠀⡜⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⠻⠿⠿⠟⠁⡠⠎⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡤⡀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⡠⠤⠤⣀⠁⣸⠀⠀⠀⠀⢨⢀⣀⣀⠀⠀⠀⠀⠀⠗⠒⣇⡀ ⠀⠀⠀⡸⠀⠀⡜⠀⠀⠀⠈⠋⠀⠑⢄⣠⠤⡜⠋⠀⠀⠙⡄⠀⠀⠀⠀⠈⠁⡜ ⢔⠒⠊⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡜⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⡴⠁ ⢈⣲⣤⡀⠀⣀⢗⣖⣵⣯⣽⣑⠦⡀⠀⠀⠀⣀⠀⠀⠀⠘⢎⡀⠀⢀⡠⠊⠀⠀ ⠘⢄⠀⠀⠀⢳⣿⣿⠿⠿⠿⣿⣿⣯⣢⢄⣀⣹⣄⣀⣀⡤⣞⣽⠚⠁⠀⠀⠀⠀ ⠀⠀⠑⢤⣀⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣷⣿⣮⣥⣿⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀ ⢀⣀⣤⣾⣿⣿⣿⣷⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠟⠛⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄⠀⠀ ⠀⠀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠻⣿⣟⠛⢻⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀ ⠀⠀⠙⢿⣆⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⣤⣶⣤⣤⣿⣿⣿⣿⣿⠟⠉⢹⣿⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀ ⠈⣿⣿⣟⠿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⡿ ⠀⠈⢿⣿⠀⠀⠀⣠⣴⡿⠛⢻⡟⠉⠀⠀ ⠀⠀⠈⣿⡄⠀⠘⠛⠻⣿⣶⣾⡇⠀⠀⠀ ⣠⣴⣾⣿⠧⠀⠀⠀⠀⠀⢸⢿⣷⣤⡀⠀ ⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠹⠝⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠢⠖⢲⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣸⠟⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠉⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⢤⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⢰⠒⠤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠸⣀⣠⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠗⢀⣱⠀⠀⠀⠻⠦⣄⣀⣀⣀⣤⢖⣀⣀⠠⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠁⠀⠀⠀⠀⠀⢀⡠⠜⣛⣉⠽⠦⣄⡀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠉⢾⠁⠁⢀⡀⠈⠉⠲⣄⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡖⠲⢄⡎⠀⠀⠁⠀⠀⠈⠉⢀⡀⠀⢻⡀⠀⠀⠀⠳⡄⠊⠉⠂⢀⣀⢈⣷⠖⠒⠒⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢳⡀⠈⣧⣀⣠⡗⠉⠉⣇⣴⣹⠛⡄⠀⢳⡦⢄⣀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠠⢶⡶⢆⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡏⠉⢛⣶⠁⠀⢹⣀⣀⣴⠋⡟⡻⠴⡇⠀⠀⢷⣄⡀⢄⣀⣀⣀⡴⠋⠀⠀⢠⣴⣯⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠏⠁⢈⠗⢶⠋⠈⢻⡛⢳⣿⣿⣾⠛⠲⣤⠈⠉⠉⣒⣦⠤⠤⠤⠤⠔⠒⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠊⡋⠀⢘⡧⢄⡴⢣⡋⠸⠛⢿⠇⠀⡜⠓⠉⠁⠀⠀⠀⢸⠂⠀⠀⣀⠀⠈⡶⢄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠦⠜⠀⠀⠀⠈⢻⡤⠴⠻⢦⣴⡗⢚⣤⠤⠖⠒⠉⠻⡀⠀⠀⠙⡆⠀⠸⡀⢹⠺⢧⣀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣶⣩⣼⣷⠚⠁⠀⠀⠀⠀⠀⣧⠀⠀⠀⢱⠀⠀⢳⠎⡀⠀⠹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⢀⠀⢹⣦⠤⠤⠼⡆⠀⠈⠙⠧⠒⠲⡇⢀⣀⡀⠀⢄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⡴⠚⠉⠉⠛⣿⣧⣄⡀⢳⡀⠀⠀⠠⣶⣾⠿⠋⠀⠈⢦⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠸⡙⢿⡿⠛⡇⠀⢶⣤⣀⣱⢀⣠⠀⠀⠸⡆⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠹⣬⡇⠀⠸⣤⣼⡿⠛⠓⠛⠉⠀⠀⢸⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢸⡀⠀⠀⠀⠀⢀⣠⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⢀⡼⠀⠀⠈⠙⠒⠒⠚⠛⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠶⣟⡉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠒⠲⢤⣀⠀⠀⠀⠀ ⠀⢸⠀⠀⠉⠑⢶⠒⠒⠒⠒⠒⠒⠒⠒⠀⠤⠬⠽⢶⡀⠀ ⠀⡼⠠⢀⢈⠀⡞⠰⠈⠉⠉⠉⠉⠉⠀⠀⠒⠒⢠⠀⡇⠀ ⠀⡇⠀⠀⠌⢀⡇⡆⠀⠀⠲⠂⠀⠀⠀⢴⠄⠀⠀⠀⡇⠀ ⢠⡇⡤⣄⠀⢸⠁⠇⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⢸⢸⠃⠀ ⢸⡇⣘⠻⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀ ⢸⠁⣩⡿⠀⡆⢀⡢⠤⠄⠀⠀⠀⣀⣀⣀⣀⡀⠃⡏⠀⠀ ⣼⠀⣉⡛⠀⣷⠁⠵⠦⠤⠤⣤⣤⠀⠀⠀⡄⠀⠀⡇⠀⠀ ⣿⢸⡛⣿⣠⢃⠜⢠⢄⠀⠀⠀⠀⣀⠀⠀⠀⠀⢸⡙⠢⣄ ⡿⠀⠑⠦⢤⠊⠀⠡⠀⠃⠀⠀⠀⢃⡁⠎⠁⠀⣾⡿⢀⡜ ⠙⢦⣀⠀⢸⠀⠀⣀⠀⢀⣀⠀⠀⣏⢀⠆⠀⢀⡿⣥⡏⠀ ⠀⠀⠈⠙⠚⠶⢤⡤⣤⣤⣄⣀⣀⣀⣀⣀⣀⡸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠜⢈⡇⠀⢀⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣆⡞⠁⠀⠀⡜⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⣇⣛⡲⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣶⣦⣀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣏⠀⣠⣴⣾⡿⠟⠛⠋⠉⠁⠀⠀⠀⠀ ⠀⢀⣠⣤⣤⣤⣤⣤⣤⣀⣈⠙⠻⣷⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠀⠀⠀⠘⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠟⠋⣁⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀ ⠈⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣶⣄⣿⣿⣿⣿⣿⡇⠀⠀⠀⣾⡆⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣧⠀⠀⠀⣸⣿⣿⣿⣿⣿⣤⣶⡿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁ ⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢿⠃⠀⢀⣼⣿⣿⣿⣿⣧⡀⠀⠸⡏⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣄⠀⠀⠀ ⠀⠀⠊⠉⠁⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣿⣿⣿⠿⠿⣿⣿⣿⣶⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠈⠉⠑⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⢿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⠿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠒⠒⠠⡀⠀ ⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⢠⠀⠀⠈⢢ ⠀⠀⠀⠀⢀⠂⠀⠀⠀⠉⠐⠊⠕⡢⠄⠸ ⠀⠀⠀⠀⡾⠄⠤⡤⠄⢲⡒⢲⠶⣤⣕⡄ ⠀⢠⣴⠶⢞⢱⣢⡌⠀⠘⠧⠘⠒⠁⢲⠁ ⠸⣿⣿⣟⣀⠱⠶⢠⣀⠠⢠⠤⠶⣒⠎⠀ ⢀⠄⠏⡹⡈⠒⠚⡲⡀⣌⡿⠊⠐⡱⠀⠀ ⠸⡳⣂⢘⢷⣆⣧⡣⠃⠳⡸⢀⠏⠀⠀⠀ ⠀⢈⡑⢺⠀⡉⠐⢒⣼⣄⠀⠁⠀⠀⠀⠀ ⡌⠀⠐⠛⠀⡉⠉⠙⡏⠀⢱⠀⣀⠀⠀⠀ ⠰⡀⠀⠉⠉⠡⣰⠁⠁⠀⠉⠀⠀⠈⢢⠀ ⠀⠈⠢⠄⠀⠴⠃⠉⠒⠒⠀⠤⠤⠤⠊⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟨⬛⬜⬜⬜⬜⬛⬜⬜⬜⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟨⬛⬜⬜⬜⬛🟨⬛⬜⬜⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟨⬛⬜⬜⬜⬛🟨⬛⬛⬛⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨⬛⬜⬜⬛⬛🟨⬛⬜⬜⬛🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨⬛⬜⬜⬛⬜⬛🟨⬛⬜⬜⬜⬛🟨⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨⬛⬜⬛⬜⬜⬜🟨⬛⬜⬜⬜⬛🟨⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨⬛⬛⬜⬜⬜🟨🟨🟥⬛⬜⬜⬛🟨⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨⬛⬛⬜⬜⬜🟨🟥🟥⬛⬜⬜⬛🟨⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟨🟨⬛⬛⬜⬜🟨🟥🟥⬛⬜⬛🟨🟨⬛⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨⬛⬜⬜🟥🟥⬛⬜⬛🟨🟨⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨⬛⬜⬜🟥🟥⬛⬜🟨🟨⬛⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨⬛⬜🟥🟥⬛⬜⬛⬛⬛🟦⬛⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜🟥⬜⬛⬛⬛🟦🟦⬛⬜⬜⬛⬛🟦⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬛⬜⬜⬛⬜🟦⬛⬜⬛🟦🟦🟦🟦⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟦⬛⬛🟦⬜⬜⬛🟦⬛⬜⬜⬛🟦🟦🟦🟦🟦⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛🏻🏻🏻🏻🟦🟦⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜ ⬜⬜⬛⬜⬜⬜⬜⬜⬜⬛🏻🏻🏻🏻⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬜⬜⬜⬜⬛⬜⬛⬛⬛⬛⬜⬜⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬜⬛🟨⬜⬜⬜⬜⬜🟨🟨⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛🟨⬜⬜⬜🟨⬛⬛🟦⬛⬜⬜⬛🏻⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🏻⬛🟦⬛🟨⬛🟨⬛🟦🟦🟦⬛⬛⬛🏻🏻⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟦🟦⬛⬛⬛🟦🟦🟦🟦⬛🏻🏻🏻🏻🏻⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🏻⬛🟦🟦⬛🟦🟦🟦🟦⬛⬛⬛🏻🏻⬛🏻⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🏻⬛🟦🟦🟦🟦🟦🟦⬛⬛⬛⬛🏻⬛🟥⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🏻⬛⬛⬛⬛⬛⬛⬛⬛🟨⬛⬛⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟥⬛🟥⬛🟥⬛🟥🟥⬛🟨⬛⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟥🟥⬛🟥⬛🟥🟥🟥⬛🟨⬛⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟥🟥🟥⬛🟥🟥🟥🟥⬛⬛⬛⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛🟥🟥⬛🟥⬛🟥🟥🟥⬛⬛🏻🏻⬛🟥⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛🏻⬛⬛🟥⬛🟥🟥🟥⬛🟥⬛🟦⬛🏻⬛🏻⬛🏻⬛⬜⬜⬜⬜⬜ ⬜⬛🟨🟨⬛🏻⬛🟦⬛⬛🟥🟥🟥🟥⬛🟦🟦🟦⬛🏻🏻🏻⬛⬛⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟨⬛⬛⬛🟦⬛🟥🟥🟥⬛🟦🟦🟦⬛🟦⬛⬛⬛⬛⬜⬜⬛⬛⬜⬜ ⬜⬛🟨🟨🟨🟨⬛🟦⬛🟦⬛⬛⬛🟦🟦🟦⬛🟦⬛🟥⬛🟨🟨⬛⬛🟨🟨⬛⬜ ⬜⬜⬛🟨🟨⬛⬛🟦⬛🟦🟦🟦⬛🟦🟦🟦⬛🟦⬛🟥⬛⬛🟨🟨🟨🟨🟨🟨⬛ ⬜⬜⬜⬛⬛⬜⬛⬛🟥🟦🟦⬛🟨⬛🟦🟦🟦⬛🟥🟥🟥⬛⬛🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥⬛⬛🟨🟨⬛🟦🟦🟥⬛⬛⬛⬛⬜⬛🟨🟨⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛🟥⬛🟨🟨🟨⬛🟦⬛🟥🟥🟥⬛⬜⬜⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥⬛🟨🟨🟨⬛⬛🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛🟥⬛⬜⬛⬛⬛⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟥🟥🟥⬛⬛⬜⬜⬜⬜⬜⬛🟥🟥⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜⬛⬛🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛🟥🟥🟥🟥⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜

👽🟦👤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠚⠛⠛⠛⠛⠛⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣀⣀⠀⠀⣀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀ ⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠀⠀⠀⠀⠀⠀⡀⠀⠉⠙⠳⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠈⠙⢷⡄ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⡟⠲⢤⡴⠋⠛⡖⠲⢤⣤⡼⠋⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿ ⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡿⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠜⠉⠛⠊⠉⠸⠏⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣾⡁⠀⣀⠴⢚⡇⠀⠀⠀⠀⠀⣸⠏ ⠈⣿⡀⠀⠀⠀⣀⣀⣀⣀⠀⡾⠁⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⢀⣼⠋⠉⠉⠀⢀⣾⣁⡠⠖⠛⡇⢠⡟⠀ ⠀⠘⣷⣀⡴⠋⠁⠀⠀⠈⠙⠳⠦⠒⠋⣼⡧⠶⠲⣦⠀⠀⠀⠀⠀⠀⣻⠍⢀⡟⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢳⡿⠀⠀ ⠀⠀⠈⣿⠁⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠙⣧⡀⢀⡿⠀⠀⢀⣠⡴⠚⠁⣠⠋⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀ ⠀⠀⠀⢿⡆⠀⠀⠙⢿⡀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠛⢳⡶⣤⣄⣰⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⠦⣄⣀⣀⣉⣉⡴⠾⠷⠶⡤⠤⠶⠶⠶⠖⠒⠿⢭⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠒⠶⣾⡁⢀⣠⡯⢤⣄⡈⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠳⠤⣄⣀⠀⠀⣾⠁⢺⠀⠀⠀⠙⣿⠀⠀⠀⠀⣻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣄⠀⠀⠀⠈⢳⡄⠀⠀⠀⠉⠙⢻⠇⠀⢸⣧⣄⣀⣴⡋⠉⠉⠙⠻⣯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠙⣦⣀⠀⠀⠀⠀⠀⠀⣼⢡⣟⠁⠉⠙⢷⣀⣀⡴⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠹⡏⠙⠒⠶⢿⡄⣸⠃⠈⢻⡦⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣶⠻⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢹⣇⠀⣰⡟⠑⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡋⠋⠛⢷⣞⣿⠾⠃⠀⠀⠀⣿⡷⢤⣀⡀⠀⠀⠀⢀⣀⣼⡗⡀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣻⣦⣄⡀⠉⠀⠀⠀⠀⠀⠀⠙⢳⣤⡌⠉⠉⠉⠉⠉⢁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣾⠉⠉⠉⠉⠑⠀⠀⠀⠀⠀⠀⢠⣾⡉⡻⡄⠀⠀⠀⢀⣾⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⠤⠤⢤⣴⠖⠂⠀⠀⣠⣾⡇⠀⠀⢉⣽⢻⣤⣴⣾⡿⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡋⠀⠀⠀⣠⠞⠁⣈⡿⡖⠒⠋⠁⠀⣿⣿⣗⠾⠂⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣈⡷⠤⠔⠚⠛⠻⠞⠁⠀⠀⠀⠀⢀⣤⠟⠉⠒⢁⣴⣋⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠚⠋⠛⠒⠦⣎⡉⠉⠉⠉⠉⠉⠉⠉⠓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠤⣄⣀⣀⣀⠀⠀⣀⣀⣀⣀⠤⠾⣏⣀⣀⣀⣀⣀⣠⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢈⠉⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

(͡°͜ʖ͡°)💋

⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟥🟥🟥⬛⬛⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥🟥🟥⬛⬛⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜ ⬛🟥🟥🟥🏻🏻🟥🏻🟥🟥🟥⬛⬜ ⬛🟥🟥🏻🏻🏻🏻🏻🟥🟥🟥🟥⬛ ⬛🟥🟥🏻⬛🏻🏻⬛🏻🟥🟥🟥⬛ ⬛🟥🏻🏻⬛🏻🏻⬛🏻🏻🟥🟥⬛ ⬛🟥🏻🏻🏻🏻🏻🏻🏻🏻🟥⬛⬜ ⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜ ⬜⬜⬛🏻🏻🏻🏻🏻🏻🟫🟫⬛⬜ ⬜⬜⬛🏿⬜⬜⬜⬜🟫🟫🟫🟫⬛ ⬜⬛🏿🏿🏿⬜⬜🏿🟫🟫⬛🟫⬛ ⬛🏿🏿🏿🏿⬜⬜🏿🟨🏿🏿⬛⬜ ⬛🏿⬛🏿🏿⬜⬜🏿🏿⬛🏿⬛⬜ ⬛🏿⬛🏿🏿⬜⬜🏿🏿⬛🏿⬛⬜ ⬛🏻⬛🟫🏾🟫🟫🏾🟫⬛🏻⬛⬜ ⬜⬛🟫🏾🟫🟫🏾🟫🟫🏾⬛⬜⬜ ⬜⬛🏾🟫🟫🏾🟫🟫🏾🟫⬛⬜⬜ ⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬜⬛🏻🏻⬛⬛🏻🏻⬛⬜⬜⬜ ⬜⬜⬛🏿🏿⬛⬛🏿🏿⬛⬜⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜

⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛ ⬛🏻🏻⬛⬜⬜⬜⬜⬜⬛🏻🏻⬛ ⬛🏻🟩🏻⬛⬛⬛⬛⬛🏻🟩🏻⬛ ⬜⬛🏻🏻🏻🏻🟩🏻🏻🏻🏻⬛⬜ ⬜⬜⬛🏻🏻🟩🏻🟩🏻🏻⬛⬜⬜ ⬜⬜⬛🏻⬜🏻🟩🏻⬜🏻⬛⬜⬜ ⬜⬜⬛🏻🟥🏻🏻🏻🟥🏻⬛⬜⬜ ⬜⬜⬜⬛🏻🏻⬛🏻🏻⬛⬜⬜⬜ ⬜⬜⬛🏻⬛⬛⬛⬛⬛🏻⬛⬜⬜ ⬜⬜⬛🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜ ⬜⬜⬛🟩🟩🏻🏻🏻🟩🟩⬛⬜⬜ ⬜⬜⬛🏻🏻⬛⬛⬛🏻🏻⬛⬜⬜ ⬜⬜⬜⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠚⠛⠛⠛⠛⠲⠶⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⣀⣀⣀⣀⣤⡴⠟⠃⠀⠀⠀⠀⠀ ⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣛⣋⣉⣿⣉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⣀⣀⣀⣀⣉⣉⡛⢲⣄⠀⠀⠀⠀⠀⠀⠀ ⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠋⠛⠉⠁⢈⡉⠋⠻⣿⣴⣟⠀⠀⠀⠀⠀⠀⠀ ⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠼⢠⠊⠉⠑⢇⠀⠑⣴⠋⠀⠉⢻⣆⠀⠀⠀⠀⠀ ⢿⡇⠀⠀⠀⠀⠀⠀⣰⠟⠢⡀⠈⢦⣄⠀⠀⢳⣶⠃⠀⠀⠀⢀⡿⣄⠀⠀⠀⠀ ⢸⣧⠀⠀⣀⣀⣀⣠⡏⠀⠀⢈⣧⠬⠭⠵⠮⠭⣀⢀⣀⣠⠴⠛⢀⣸⠀⠀⠀⠀ ⠀⠹⣷⡟⢉⡥⠤⠜⠛⠀⡞⠁⠀⠀⠀⠀⠶⣆⣀⣨⡭⠓⠀⠰⠛⢹⡇⠀⠀⠀ ⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠧⣀⣦⣀⠀⠀⢠⠛⣿⡿⠁⠀⠀⢀⠤⡎⠀⠀⠀⠀ ⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠙⠦⠭⠉⠀⠀⠈⠉⠉⠀⠀⣀⣠⣔⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⠷⠖⢂⡤⠀⠀⠀⠀⣀⠀⣀⣀⣀⠼⠿⣿⣍⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣉⡽⠟⠓⠋⠛⠙⠋⠀⠢⡀⠀⢻⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⣀⣤⡤⢦⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣽⣧⣀⠀⠐⣫⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣀⡟⣩⠟⠁⠉⠒⢄⣀⠀⠀⠀⠀⠀⠀⣀⣠⢼⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠹⣷⡇⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠁⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣴⠟⠙⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠑⢶⠿⠿⣏⠁⠀⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣽⢷⣄⠀⠀⠀⠀⢳⡈⠙⠃⢀⣠⣼⠟⠓⢦⡀⠀ ⠀⠀⠀⠀⢠⡾⠉⠀⠀⠈⠉⠀⠀⠁⠀⠀⣀⣠⣼⠃⠀⠀⠛⠉⠁⠀⠀⠀⠙⣦ ⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠛⠉⠉⠙⠲⣤⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣀⣀⣀⣤⠾⠃ ⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⣤⣤⣤⣤⣤⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⢀⣾⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠻⢿⣿⣿⣿⣿⣇⠀ ⢀⣿⣿⣿⣿⣿⠏⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣙⣿⣿⣿⣿⣆ ⣼⣿⣿⣿⣿⡟⣰⡿⠛⠉⠛⢷⡄⢀⣾⠛⠋⠙⢻⣿⣿⣿⡿ ⠸⣿⣿⣿⣿⡇⣿⡀⠰⠆⠀⢸⡿⢸⣿⠀⠶⠄⠈⣿⣿⠟⠁ ⠀⢻⣿⣿⣿⡇⠙⢷⣦⣤⣴⡿⢃⣤⠻⣶⣤⣤⡾⣿⣿⠀⠀ ⠀⣴⣿⣿⣿⠇⠀⠀⠀⠉⠀⠀⠀⢻⣆⠀⠈⠁⠀⣿⣿⣦⡀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⠀⠀⠀⠀⣿⣿⢸⣿ ⠘⢿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠃ ⠀⠀⠉⠙⣿⣧⠀⠀⠀⣠⣀⣀⣀⣀⣠⣾⠃⠀⢸⣿⠇⠀⠀ ⠀⠀⠀⠀⠸⣿⣦⡀⠀⠈⠙⠛⠛⠛⠋⠀⠀⢠⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠻⣿⣶⣤⣄⣀⣀⣀⣠⣤⣶⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀

⠀⠀⣼⣀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣀⣧⠀⠀ ⠀⠀⠸⠻⣿⣶⣦⣤⣈⢻⣶⣮⢿⣿⣿⡿⣵⢶⡟⣁⣤⣴⣶⣿⠟⠇⠀⠀ ⠀⠀⠀⢪⢦⣙⠻⣿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⠟⣋⡴⡕⠀⠀⠀ ⠀⠠⠤⣤⡩⡿⡇⣠⡙⢻⣯⣟⣿⣿⣿⣿⣻⣽⡟⢋⣄⢸⢿⢍⡤⠤⠄⠀ ⠀⠀⢀⣀⣤⣶⣽⡿⣿⡮⢭⣬⣽⣯⣽⣯⣥⡭⢵⣿⢿⣯⣶⣤⣀⡀⠀⠀ ⠒⠚⠛⠛⠛⠛⠛⠛⠓⠋⠛⢟⢿⣿⣿⡿⣻⠟⠙⠚⠛⠛⠛⠛⠛⠛⠓⠒ ⠀⠀⠀⠀⣀⣤⣴⣾⣿⠿⠃⠸⠷⠤⠤⠾⠇⠘⠿⣿⣷⣦⣤⣀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⠿⠋⠁⠀⠀⢸⠧⠠⠄⠼⡇⠀⠀⠈⠙⠿⣿⣿⣧⡀⠀⠀ ⠀⣠⣾⠿⠋⠁⠀⣀⣴⡾⠁⢠⠀⠀⠀⠀⡄⠈⢷⣦⣀⠀⠈⠙⠿⣷⣄⠀ ⠴⠋⠁⠀⠀⠀⢀⣿⡟⠀⠀⢸⡇⣷⣾⢹⡇⠀⠀⢻⣿⡀⠀⠀⠀⠈⠙⠦ ⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠁⠛⠛⠈⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢰⣀⣀⡆⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣿⣿⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣄⠀⠀⢸⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⢿⣿⣧⡀⠈⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣄⡀⠀⠻⣿⣿⣦⠸⠟⠛ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣷⣤⣈⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣶⣶⣦⣤⣀⣙⡻⢿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⢠⣤⡄⠀⣿⣿⣿⣿⣿⣷⣶⣶⣿⠀⣤⣤⡄⠀⠀⠀ ⢸⣿⡇⠀⣉⣉⣉⣉⣉⣛⣛⣛⣟⠀⣿⣿⡇⠀⠀⠀ ⢸⣿⡇⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⣿⣿⡇⠀⠀⠀ ⢸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⡇⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀

⢠⣶⣿⣿⣿⣶⡄⠀⣶⣶⣶⡆⢰⣶⣶⣶⡆⠀⣶⣶⣶⣶⠀⢰⣶⣶⣶⣶⣶⡄ ⣿⣿⣿⠉⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⣿⣧⢸⣿⣿⣿⣿⠀⢸⣿⣿⡏⢻⣿⣿ ⢿⣿⣿⣦⣉⠉⠁⠀⣿⣿⣿⡇⢸⣿⣿⢻⣿⢸⣿⢻⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿ ⠈⠻⢿⣿⣿⣷⣄⠀⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⣿⢸⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟ ⣤⣤⣤⠙⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⢸⣿⣿⣿⢸⣿⣿⠀⢸⣿⣿⡏⠉⠁⠀ ⢿⣿⣿⣀⣿⣿⣿⠀⣿⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀ ⠘⠿⢿⣿⣿⠿⠋⠀⠿⠿⠿⠇⠸⠿⠿⠀⠹⠿⠇⠸⠿⠿⠀⠸⠿⠿⠇⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⡁⠶⢶⡖⠒⠒⠒⠒⠒⠒⠒⠖⣲⠶⠆⣿⣿⡇⠶⢶⣖⠒⠒⠒⢒⡶⠶⠀⣿ ⠛⠛⠻⢦⡙⣦⡀⠀⠀⠀⠀⠀⢰⠡⣾⣿⣿⣿⣿⣿⣶⠘⡆⠀⡴⢫⡶⠛⠛⠛ ⠀⠀⠀⠀⢹⡼⢷⡄⠀⠀⠀⠀⠘⣆⢻⣿⣿⣿⣿⣿⡟⣰⡇⡞⣱⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡌⢿⡄⠀⠀⠀⠀⠘⣆⢻⣿⣿⣿⡿⣱⣿⡞⣰⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣌⢻⡄⠀⠀⠀⠀⠘⣆⢻⣿⡿⢡⣿⡟⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣄⠀⠀⠀⠀⠘⢆⠻⢣⣿⡿⢡⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣆⠀⠀⠀⠀⠈⢦⣾⡿⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣆⠀⠀⠀⠀⠀⢻⢡⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⢻⣆⠀⠀⠀⢰⢃⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢻⣆⠀⢠⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠹⠦⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⢀⣀⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣀⠀⠀⠀⠀⠀⠐⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⣀⣴⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⡿⠁⢀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠘⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⡿⠁⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠀⠀⠸⣿⣿⡄⠀⠀⠀ ⠀⠀⣸⣿⣿⠃⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢹⣿⣿⡄⠀⠀ ⠀⢰⣿⣿⡏⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀ ⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀ ⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⢠⣾⣿⣿⠃⠀⠀⠹⣿⣿⣷⠀⢀⣴⣿⣿⣿⣶⣶⣶⣦⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀ ⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇ ⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣄⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣤⣤⣤⣄⣀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⢿⣿⣿⣷⣄⡀⠀⠀⠀⣀⣠⣤⣤⣼⣿⣿⣿⡏ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠉⠉⠙⠛⠻⠿⢿⣿⣿⡿⠟⢁⣠⣾⣿⣿⣿⠿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣦⣄⠙⠻⣿⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣴⣿⣿⣿⠿⢋⣵⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣭⡛⢿⣿⣿⣷⣄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠟⢁⣶⣿⣿⡿⠋⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠻⣿⣿⣿⣦⠉⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⢸⣿⣿⣿⠁⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣿⡄⠀⠈⠛⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⣀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀ ⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀ ⠀⠀⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀ ⠀⠀⠸⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠀⠀ ⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡄⠀⠀⠀⠀⠀⠀⣰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠉⠉⠛⠿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⣀⣴⣾⣿⠿⠛⠉⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⢿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠈⠻⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠐⠲⢼⡏⠀⠈⠟⠻⢷⣄⣀⣀⣸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣸⠟⠛⠛⠛⠛⠛⣿⡧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠻⣧⣴⣶⡛⠉⠙⠲⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⢿⣦⡀⠀⠀⢀⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⡿⠋⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣳⡄⠀⠀⠀⠀ ⠀⠀⢀⣼⣟⡼⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠉⠻⣿⡄⠀⠀⠀ ⠀⠀⣾⡿⠋⢠⠛⣿⣧⠀⠀⠀⠀⠀⣾⠟⠛⠛⠉⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠉⠉⠛⢿⡿⣿⣦⠀⠀⠀⢀⣼⣿⢿⡀⢢⡈⢳⡄⠀⠀ ⠀⣼⠟⢀⣠⢇⡼⠛⢿⣷⣄⣀⡀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠈⣿⠀⣤⣤⣾⣿⣏⠀⣻⣆⠻⡷⣿⡆⠀ ⠘⣿⢻⠋⢁⡾⢷⣤⡾⢻⣿⣿⣥⣀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢠⠖⠛⠛⢶⡀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠸⣿⣤⣿⣿⣿⡁⠉⢻⣿⡙⢷⣄⣼⡇⠀ ⢸⡿⢶⡶⠋⢠⡟⠀⣠⡿⢻⣿⠿⣿⡟⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠘⠲⠦⠶⠛⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢹⡟⢿⣦⣀⣿⢷⣄⢸⡍⣷⠀ ⢸⡇⢸⣷⣴⡿⣦⣼⠋⣀⣼⣧⣴⡿⠀⠀⠀⠀⠀⠀⢠⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣷⣼⣧⣄⣽⣿⡇⠸⣹⡟⡇⢸⡆ ⣾⠀⣾⢸⡄⢀⣾⢻⠟⢻⡘⠁⣾⡇⠀⠀⠀⠀⠀⢀⣾⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⡇⡿⢸⡏⠉⢻⣀⣻⠇⢱⢸⣇ ⣿⠀⡇⠀⢻⡟⠹⡀⡇⢘⡇⠀⣿⣧⠀⠀⠀⠀⣠⣿⣿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣾⣿⣷⡀⠀⠀⠀⠀⢸⣿⣇⠁⣾⡇⠀⣾⢹⣿⡀⢸⠀⣿ ⣿⠀⡇⠀⣼⠁⠀⣇⣀⣸⠟⠟⣟⣿⢿⣶⣶⡿⠟⠉⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠙⠿⣷⣤⣤⣴⣿⣿⣌⢻⡟⣧⣠⡏⡼⣸⡇⠘⠀⣿ ⢸⣇⠀⣰⣿⡇⣠⣏⠉⢿⠀⢸⡿⠁⠀⢸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠉⠁⢹⡏⢸⡇⠀⣽⢃⡇⡟⢿⡀⢸⡇ ⠸⡟⠿⡟⠈⡏⠉⢻⠀⠸⡆⣾⠁⠀⠀⠘⢿⣿⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣾⣿⣿⡃⠀⠀⠘⣿⢸⠀⢠⡟⠸⢰⠇⣸⣿⣿⠁ ⠀⣿⠀⡇⠀⣇⠀⠘⣇⠀⢿⡿⠀⠀⠀⢀⣾⡟⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁⠈⣿⣷⡀⠀⠀⢿⣾⠀⣼⠃⠃⡾⠀⡿⢸⡇⠀ ⠀⢻⡄⢸⠀⢸⡀⠀⢹⡄⢸⡇⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⢸⣿⢠⡏⠀⢰⡇⢰⠇⣸⠇⠀ ⠀⠸⣧⠀⡆⠈⣧⠀⠀⢷⣼⠇⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⢻⣿⠁⠀⣾⠀⡸⢀⣿⠀⠀ ⠀⠀⢿⡄⠘⡀⠘⡆⠀⠘⣿⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⢸⡏⠀⢸⡇⠀⠃⣸⡇⠀⠀ ⠀⠀⠈⣷⡀⠁⠀⠹⡄⠀⣿⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⢸⣧⣀⣿⠀⠀⢠⣿⠀⠀⠀ ⠀⠀⠀⠘⣷⠀⠀⠀⢻⡾⠋⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠙⣿⡇⠀⠀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⡀⠀⠈⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⡇⢀⣼⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣦⣴⠏⠀⠀⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⠀⠀⠀⠹⠿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠛⠿⢿⣿⣷⣶⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡟⠹⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠏⢻⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡟⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⢻⣿⡄⠀⠀⠀ ⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀ ⠀⢀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀ ⠀⣾⣿⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣷⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⢸⣿⣿⡟⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⢻⣿⣿⡇ ⢸⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⡟⢻⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⢸⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⡟⠀⠀⢻⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⡇ ⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀

⠀⠀⠀⠀⡀⠀⠀⠢⠨⣔⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠤⢖⣚⠳⢒⠀⠀⠘⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡈⢭⠟⠁⣀⣭⢀⠀⠈⠁⢆⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣆⠀⠀⠀ ⠄⢐⡋⡤⠀⠈⢎⠃⠑⠜⠀⢰⣷⣦⠶⠞⠛⠛⠛⠲⠤⠤⣊⣾⣿⢠⣯⣕⢄⠀ ⠐⡯⣴⣤⠀⡐⣼⠕⡀⠘⠀⣿⣿⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣫⠿⢛⠆ ⠘⢴⣻⢷⠠⡷⡟⡈⢣⠀⢀⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠛⢛⠛⠦⠃ ⠈⠈⠻⡌⢑⡝⣴⣿⠌⠃⢸⡇⠠⣿⣿⠿⠿⢟⠻⡛⢿⣿⣿⣷⣴⣿⣷⣿⡆⣹ ⠀⠀⠀⠀⢈⠻⡮⣮⠀⢠⠸⣷⢸⣿⣿⣿⣿⣷⣦⠘⢄⣛⣛⡻⠟⠋⠈⠫⠿⠁ ⠀⠀⠀⠀⠀⢕⢽⣮⢦⣋⢆⣿⡀⣿⣿⣿⣿⣿⣿⡇⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢇⣿⣿⣿⣮⣻⡗⣿⣿⣿⣿⣿⣿⣿⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢐⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⢋⡷⠾⣧⣤⣤⣤⣒⣉⡡⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢉⣉⣉⣉⣋⠑⡆⢙⣢⣤⣤⡬⠤⠍⠉⠉⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠍⠛⠛⠉⠀⠀⠻⢿⠿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛🟥🟥🟥🟥🟥🟥🟥⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜ ⬜⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥🟥⬛⬜⬜ ⬜⬛🟥🟥🟥🟥🟥🟥🏻🟥🟥🟥🟥🟥🟥⬛⬜⬜ ⬜⬛🟥🟥🟥🟥🏻🟥🏻🟥🏻🟥🟥🟥🟥⬛⬜⬜ ⬜⬜⬛🟥🟥🏻🏻🏻🏻🏻🏻🏻🟥🟥⬛⬛⬜⬜ ⬜⬜⬜⬛🏻🏻🟥🏻🏻🏻🟥🏻🏻⬛🟥⬛⬜⬜ ⬜⬜⬜⬛🏻🏻⬛🏻🏻🏻⬛🏻🏻⬛🟥⬛⬜⬜ ⬜⬜⬜⬛⬛🏻🏻🏻🏻🏻🏻🏻⬛🟥🟥🟥⬛⬜ ⬜⬜⬛🟥🟥⬛⬛⬛⬛⬛⬛⬛🟥🟥🟥🟥⬛⬜ ⬜⬛🟥🟥🟥🟥⬛🟥🏻🟥⬛🟥🟥🟥🟥🟥🟥⬛ ⬛🟥🟥🟥🟥⬛🏻🟥🟥🟥🏻⬛🟥🟥🟥🟥🟥⬛ ⬛🟥🟥🟥⬛⬜⬜🟥🟥🟥⬜⬜⬛🟥🟥🟥🟥⬛ ⬛🟥🟥⬛🏻⬜⬛🟥⬛🟥⬛⬜🏻⬛🟥🟥⬛⬜ ⬜⬛🟥🟥⬛⬛🟥🟪🟪🟪🟥⬛⬛🟥🟥🟥⬛⬜ ⬜⬜⬛⬛🟥🟥⬛⬛⬛⬛⬛🟥🟥🟥⬛⬛⬜⬜ ⬜⬜⬜⬜⬛⬛⬛🟥⬛🟥⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜

⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛ ⬛🟥🟥🟥⬜⬜⬜🟥🟥🟥⬜⬜⬜🟥🟥🟥⬛ ⬛🟥⬛🟥⬜⬛⬜🟥⬛🟥⬛⬜⬛🟥⬛⬛⬛ ⬛🟥🟥🟥⬜⬜⬜🟥⬛🟥⬛⬜⬛🟥⬛⬛⬛ ⬛🟥⬛⬛⬜⬛⬜🟥⬛🟥⬛⬜⬛🟥⬛⬛⬛ ⬛🟥⬛⬛⬜⬛⬜🟥⬛🟥⬜⬜⬜🟥🟥🟥⬛ ⬛⬜⬜⬜🟥🟥🟥⬜⬜⬜🟥⬛🟥⬜⬜⬜⬛ ⬛⬜⬛⬜⬛🟥⬛⬛⬜⬛🟥⬛🟥⬜⬛⬛⬛ ⬛⬜⬜⬜⬛🟥⬛⬛⬜⬛🟥🟥🟥⬜⬜⬛⬛ ⬛⬜⬛⬜⬛🟥⬛⬛⬜⬛🟥⬛🟥⬜⬛⬛⬛ ⬛⬜⬛⬜⬛🟥⬛⬛⬜⬛🟥⬛🟥⬜⬜⬜⬛ ⬛⬛⬛🟥⬜⬜⬜🟥🟥🟥⬜⬜⬜🟥🟥🟥⬛ ⬛⬛⬛🟥⬛⬜⬛🟥⬛⬛⬜⬛⬛🟥⬛🟥⬛ ⬛🟥🟥🟥⬛⬜⬛🟥🟥🟥⬜⬛⬛🟥⬛🟥⬛ ⬛🟥⬛🟥⬛⬜⬛⬛⬛🟥⬜⬛⬛🟥⬛🟥⬛ ⬛🟥🟥🟥⬜⬜⬜🟥🟥🟥⬜⬜⬜🟥🟥🟥⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⣿⣿⣿⣧ ⠀⠀⠀⣿⣿⣿⡿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿ ⠀⠀⠀⣿⣿⠁⠀⠀⣠⣶⣄⠀⠀⠀⠀⣠⣶⣄⠀⠀⠘⣿⣿ ⠀⠀⠀⣿⣿⠀⠀⠀⢻⣤⡟⠀⠀⠀⠀⢻⣤⡟⠀⠀⠀⣿⣿ ⠀⠀⠀⠹⣿⣷⣆⠀⠀⠛⠀⠀⠀⠀⠀⠀⠛⠀⠀⣰⣾⣿⠏ ⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣤⣤⣤⣶⣿⠟⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀

👸🍄👱‍♀️

👱‍♀️💙🍄

👱‍♀️👠🍄

💙♀️👱‍♀️

👱‍♀️🤍👠💙

💙👱‍♀️🍄

👱‍♀️🟦🍄

👱‍♀️💙👗

👱‍♀️🔵🧢

🪄➡️👱‍♀️💙

💙👱‍♀️🌸

🫐👱‍♀️🤍

💙👱‍♀️👗👒

👩🔵