⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠖⡀⡄⠀⠰⠶⠤⢤⡤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⢠⢂⡴⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠆⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⠹⠁⠀⠆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢡⠀⢇⠀⢸⢄⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠀⠎⠀⠈⠢⣈⣣⡕⠊⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠚⠩⠲⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⡾⠃⠀⠀⡜⠂⠀⠀⠈⠁⠀⠀⠀⠀⠯⣠⣀⡤⠤⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⡇⢸⠀⠀⢗⣺⠦⠤⣤⠀⠀⠀⠀⠀⠈⠂⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣇⠸⠀⠀⢆⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠠⢄⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠄⠈⢧⣄⢀⣔⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⣵⡇⠀⠈⠢⠄⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠋⠀⠀⠀⠈⢿⡻⠁⠰⣡⠀ ⠀⠀⠀⢀⣀⢀⣐⡷⠿⡀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⣧⡄⠀⠀⠀⠀⠀⠓⡀⠀⢹⡄ ⠀⠀⠀⠚⡏⠛⠊⠀⠀⠡⡀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠈⠹⢦⡀⢄⠀⠀⠀⡎⠂⢸⠧ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡵⡄⠀⠀⠀⠀⠀⠀⠴⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠈⢿⡲⣥⣤⣤⢾⡄⠀⡄ ⠀⠀⠀⢸⡇⠀⢸⣃⣶⣾⣷⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠻⣟⠺⠟⠀⢗⠀⡇ ⠀⠀⠀⠈⣧⠀⢹⡿⠋⢷⢿⠗⠁⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠰⠀⠈⢢⢳ ⠀⠀⠀⠀⢸⡆⠘⡇⢠⡗⠁⠀⠀⠀⠀⢸⠀⠀⠉⠐⠒⠀⠀⠀⠀⠐⠒⠉⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢻⡆⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⡷⣴⠃⠟⠃⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⢸⣿⣆⡀⠀⠀ ⠀⠀⠀⠀⠀⢱⢿⠂⢹⣷⠄⠀⠀⠀⢠⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢆⠀⠀⠀⠀⠀⠀⠀⢠⢁⣡⢼⢽⡿⣣⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⢸⡇⠀⠀⠀⠀⠈⢈⣿⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⠒⠁⠀⠀⠈⠐⠒⠀⠀⠀⠀⣠⣻⡅⠀⡘⠀⠈⣀⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⠠⠀⠀⢀⣀⡰⠶⣁⠠⣀⡀⠠⡏⢻⣥⢁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢉⣸⣟⣿⡇⠀⢠⡻⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣷⡞⡝⠀⠀⠀⠀⠈⠉⠉⡕⠀⠀⠑⠺⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⠞⠁⢉⡞⠑⠢⠦⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢣⠄⣀⠀⠀⠀⠀⠀⢥⡀⠀⠀⠀⠀⢄⣀⠀⠀⢀⣀⠄⠊⠁⠀⠀⠘⠛⠊⡝⠀⢀⠾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⠀⠀⠀⠀⠑⠠⣀⡀⠀⠀⠉⠒⠒⠈⠁⠀⢀⠬⡿⠟⠉⠉⠐⠒⠒⠒⠂⢒⠖⣀⡴⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⣟⣦⠴⠀⠀⢀⡤⠤⢔⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⢐⡥⠞⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠁⠀⠀⠀⠀⠀⠀⡰⣿⣿⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠫⢆⣀⡖⢦⣀⠀⠀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠎⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⢰⡓⠍⠀⠀⠉⠢⢾⡁⠀⠀⠀⠀⠀⠀⠀⣀⡀⢄⠶⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠀⢎⠋⠁⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠐⣨⡝⠎⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡗⢁⢠⠉⠉⢲⢀⣀⣀⣀⣀⣀⡠⣔⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠦⣹⣄⣗⢷⣼⠿⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢤⣤⣠⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⢀⡼⠋⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡏⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠏⢸⡄⠀⢾⣄⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠛⢦⣜⣿⣿⠺⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡞⠛⠛⠳⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⣿⠀⢀⡖⠋⠁⠀⠉⠓⠀⠀⠀⠀⣿⣀⣀⣤⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠃⣿⠀⠀⡗⢹⣏⣑⣢⡀⠀⠀⠀⠀⠉⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣧⣿⠀⠀⢾⠉⠁⠀⢨⠁⡆⠀⠀⠀⠀⠰⢄⣀⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠙⣦⠀⠀⣀⡀⠀⠀ ⠀⠀⠈⢹⡇⠀⠈⠲⠤⠤⠊⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠘⢷⣼⠁⢻⡄⠀ ⠀⠀⠀⣰⢷⡀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣷⣤⡀⠀⠀⠀⠈⠋⠀⠈⣷⠀ ⡞⠛⠞⠋⠈⢷⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠈⠫⣻⣦⡀⠀⠀⠰⣦⠀⢹⡄ ⡇⠀⢀⠀⠀⣨⡿⣦⠀⠀⠀⠀⠀⠠⠾⠭⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⢦⡹⢦⣄⣠⣿⣧⠸⡇ ⣧⠀⢸⡟⠛⠋⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⡄⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⣿ ⢹⡄⢸⡇⠀⠀⣠⡞⠛⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⣿ ⠀⢷⢸⡇⠀⣼⠋⠀⠀⠀⠀⢸⡍⠙⠛⠒⠒⠲⠲⠖⠒⠚⠛⠛⠉⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⣇⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⢰⡇⠀⠀⠀⠀⠀⣼⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢸⠀⠀⠀⠀⠀ ⠀⠈⠏⠀⠈⣷⡄⠀⠀⠀⢰⢟⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢷⡀⠀⠀⠀⠀⠀⠀⣠⣃⣤⣼⣦⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⡀⡀⢀⣴⠟⠁⠀⠀⠀⠙⠃⠀⠀⠀⢀⣾⡛⠉⣠⠀⠀⠈⣧⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣀⡰⢾⣅⣀⠀⠀⢰⣏⢹⡉⢩⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⢈⡿⣿⣽⡆⠀⣰⠇⠀⠀ ⠀⠀⠀⠀⠀⠘⠷⢶⡟⣿⠀⠀⠀⠈⠙⠛⠶⣿⠀⠀⠙⠾⠇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣠⠟⠀⣿⡾⠛⠶⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠶⣄⡀⠀⠀⠀⠀⣇⣀⡀⠀⠀⢀⣄⡀⠀⠀⣀⡠⠚⠁⠀⠀⠐⠿⠶⢛⡏⢀⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⠙⠓⢦⡀⠀⠀⠈⠙⠓⠋⠁⠀⣩⡽⠟⠛⠛⠒⠒⠶⠶⠤⣤⣠⣿⡵⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⠀⠀⢀⡀⠤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⠀⠀⠀⡏⣭⡟⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⡆⣠⡞⢦⣄⣀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⢱⡳⠽⠀⠀⠙⠳⣿⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⢮⡉⠁⠀⠀⠀⠀⠈⠙⠶⢤⠀⠀⢘⣫⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡽⣡⢠⡉⠂⢲⠤⢤⣀⣀⣀⣀⣠⣴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠷⠋⠦⠓⠚⠺⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀