⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⢀⡄⢤⡀⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢆⠎⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁⡔⠉⠏⠀⠈⠁⠀⠀⠀⢀⠐⠀⠀⠀⢰⠀⠂⣾⡁⠀⠁⡀⢁⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⡠⠗⠪⠉⠄⠀⠉⠀⠂⠀⠀⠀⠞⠒⠁⣀⠔⠟⣀⢈⢇⡱⠀⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠀⠀⠀⠀⢀⠎⡀⢀⠔⠀⢠⠀⢸⠀⠀⢢⠊⢀⢀⠀⠠⡢⠈⢀⠣⠸⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣩⠋⠆⡒⡏⠂⡀⡆⠀⣸⠀⡄⠀⢂⠰⠡⠔⠀⠈⠄⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠤⠤⡟⠐⠹⡉⡮⣴⠵⢀⣴⣥⣀⠉⠨⠂⠀⢰⡁⠀⠀⠂⠀⠀⠀⠀⢠⢄⢂⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⢄⣊⣀⢀⣀⡀⣠⠇⡷⢰⡌⠅⠩⠀⠀⠀⠘⢻⢷⢄⠡⠐⢱⠰⠈⢀⠊⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠁⠀⠀⠀⠀⢀⣴⢰⢠⢰⣸⢙⠄⠠⠀⠀⠀⠀⠠⠂⠸⡮⠉⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⢤⠀⠀⣒⣴⣶⡎⠉⠓⠋⠈⢃⠀⢦⠀⠀⠀⢀⠄⠁⡠⠔⠀⢎⠔⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠄⠐⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⣀⣵⡶⣶⢿⣟⣿⣳⠟⠛⣩⢃⡠⠃⠀⢀⣆⢱⣶⢶⣾⣶⠊⠀⠀⠀⠈⡾⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⡀ ⢀⠀⠂⠁⠀⠀⣠⣾⢿⣽⣻⣽⣻⠞⢃⡶⣊⢎⡞⠛⠁⠁⠄⠸⠾⣟⣟⠞⡩⠁⡀⠀⠀⠀⡀⠁⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⠀⠀⠀⠀⠐⢿⠿⠋⠉⠋⠁⢀⠀⠼⡵⠫⠮⠄⢐⠊⠈⢀⠀⢂⠅⠠⠊⠀⠀⠀⠀⢀⢽⠀⢅⠀⡄⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⡀⠈⡠⠀⠁⠀⡠⠂⠁⠀⠠⠊⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠃⠀⢄⠈⠨⠄⡀⡌⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠬⠤⠂⠀⠠⠀⠀⠠⠀⠍⠀⢰⠉⠉⢀⡏⠉⠚⢡⠀⠀⠔⠁⠠⠁⠀⠀⠀⠀⠀⠠⠀⠀⠄⠈⠂⠄⠐⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⢀⡅⠀⢀⠂⠀⠜⠠⠐⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠆⠀⠀⠀⠀⠀⠀⠀⠌⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠰⡀⠀⡜⠙⣄⡈⠀⡔⠁⠄⣁⡠⠂⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣲⣣⣩⣷⣼⣿⣇⡱⡦⡰⢛⣿⢒⡖⣲⠎⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣀⣷⣹⠶⡹⣿⣸⡸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⠾⢹⣏⢏⡬⡉⢏⢻⣟⣿⡂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡊⢴⣏⡰⣹⠈⠿⡦⠛⢾⣚⣿⣹⣯⢆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⣀⡀⠙⠿⡷⣐⢤⡀⢄⠱⡘⣥⠳⡿⢯⢧⡠⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠂⠄⠀⡬⢀⠀⣀⠀⢴⠃⠳⡍⢶⡈⢪⣠⢁⠘⡆⠈⢎⠁⢓⡀⠐⠂⡀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠀⢁⠀⠀⠇⢰⢹⠀⠐⡹⢦⡙⢦⠘⠆⢂⠘⣄⠀⠑⢄⠁⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠁⠀⠀⠀⠀⢀⠀⠀⡌⠀⡜⡜⡄⠀⠀⠊⠑⠦⡑⢌⡐⠂⠌⠓⠄⠀⠀⣁⠀⠀⠐⠃⠀⠀⠁⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣧⡀⢸⠃⢹⢦⡀⠀⠀⠀⡨⣓⣠⢡⠘⡀⠂⠌⠑⠪⠶⣞⠷⣤⡀⠀⠀⠀⠠⠐⠄⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀ ⠀⢀⠀⠀⠀⠀⢀⣴⠾⠋⠉⠈⠢⠦⠀⢳⡙⢶⠖⡫⠊⠁⠀⠀⠀⠙⠢⢌⡤⢁⠦⡀⠉⡑⠫⢦⣄⡀⠁⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⡌⠀⠀⠀⠙⣤⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡖⠭⡒⣔⡀⢂⠉⠻⣗⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢀⡴⣫⠏⠀⠃⠀⠀⢀⠀⡆⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⠀⠀⠑⠻⣆⠈⠄⡈⠻⣽⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⢟⡽⠃⠀⠀⠀⠁⠀⠂⠀⢇⡠⢄⡀⢸⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠁⠀⠀⠀⠀⠘⡎⠐⡀⢂⠈⢳⢏⡷⣄⠀⠀⠀⠀⠀⠀⠀ ⡾⢫⡞⠁⠀⠀⡠⢂⢂⢐⠠⠘⢰⠈⠈⠁⡙⠈⠁⠉⠂⠢⠔⡠⠀⠀⠀⢀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠐⡀⠂⠌⡀⢣⡙⢗⣳⢄⠀⠀⠀⠀⠀ ⣱⡿⠁⠀⢀⢀⠂⠄⠊⠀⠀⠀⠀⡄⠀⣀⠃⠀⠀⠀⠀⠀⠀⠈⠂⢵⣀⠊⡄⠀⠀⠀⠀⠀⠀⠀⡀⠌⠠⢁⠂⡐⠠⣿⣌⠹⡮⣅⡀⠀⠀⠀ ⣿⠃⠀⠠⠐⠀⠁⠀⠀⠀⠀⠀⠀⢹⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢠⠀⠀⠀⠀⠀⠀⠀⣠⢥⢌⡰⡀⢂⢁⠎⠈⢺⣳⡌⢖⢭⢢⠀⠀ ⠃⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠄⠀⠀⠀⠀⠀⠀⠔⡱⠀⡌⠀⠈⢢⠂⠀⠀⠀⢳⡹⣀⠫⣎⢗⡄ ⠀⠀⠰⣡⠈⠀⠠⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⢰⡰⢁⠄⠀⡠⠊⠀⠀⠀⠀⠀⠀⡷⡱⢦⠙⡮⣜ ⠀⠀⠐⠉⢗⡂⠄⠢⠀⠒⠀⠁⠀⠀⠸⡀⠀⠀⠀⠀⠀⠘⠁⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢸⠑⢁⠔⠄⠈⠀⠀⠀⠀⠀⠀⠀⣳⣙⢎⢧⠱⡭