⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠚⠈⠉⠁⡀⡿⡿⡿⡿⡿⡿⡶⡤⡄⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⡠⡴⡞⡿⠿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡤⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⡿⡿⡿⡿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡴⠒⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡿⡿⡦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠨⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠙⠿⡿⡄⠠⠀⠐⠀⠀⠀⠀⠀⠀⠈⠠⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⠎⠘⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⡀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠃⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠢⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⡯⠳⠀⠀⠀⠈⠀⠀⠠⠀⡀⡤⠲⠉⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠢⠐⠀⠀⠀⠀⠋⠉⠠⡠⠀⠀⡀⡀⡀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠀⠀⠀⠀⠀⠠⠈⠦⠄⠀⠀⠀
⠀⠀⠀⡧⠀⠀⠈⠸⡀⡤⠀⠀⠁⠤⠀⠀⠀⠀⡀⡾⠿⠿⡿⠉⠹⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠸⠉⠦⠀⠀
⠀⠀⠀⠈⠀⠀⠀⠁⠀⡀⠀⠀⠈⠀⠀⠐⠄⠀⠈⠘⠐⠀⠉⠁⠩⠀⠠⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠠⠀⠠⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀
⠀⠀⠀⠀⡷⠀⠀⠀⡤⡾⡿⡍⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠮⠈⠠⠀⠉⠫⠛⠈⠀⠀⠀⠘⡄⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀
⠀⠀⠀⠀⠹⠳⠀⠀⠨⠛⠒⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠨⠀⠀⠀⠹⠄⠱⠀⠈⡌⠄⠐⠀⠀⠐⠀⡯⡄⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠠⠑⠄⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠢⠹⡴⠸⡀⠙⠀⠀⠐⠰⠈⡿⠀⠀⠀⠐⠀⠀⠀⠪⠀⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡸⡠⡿⡦⠀⠀⠀⠀⠀⠚⡆⠀⠀⠀⠀⠀⡤⠍⡾⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠫⡿⡟⠠⡸⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⡯⠞⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⠐⠀⠀⠀⠈⡦⠀⠀⠀⠠⡤⡔⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠐⠁⡿⠁⠨⡿⠈⡞⠀⡠⡼⠀⠈⡠⠉⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⡐⠀⠀⡄⠹⡿⡦⠀⠀⠀⠠⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⡴⠛⠀⠀⠀⠘⡀⠒⠀⡯⠊⡊⠀⡼⠀⠨⠉⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡔⡀⠢⠩⡿⡿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⡾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡮⠤⡔⠐⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡖⡉⠬⠻⡻⡿⡄⠀⠀⡀⡤⡶⡿⡿⡿⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠋⠻⡿⠿⡿⡶⠙⠻⡈⡯⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⡿⡿⡿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡤⡾⡿⡿⡿⡿⡿⡿⡿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⡀⡤⡤⡶⡾⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠬⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠻⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠒⠀⠤⡀⠀⠀⠀⠀⠀⠀⡴⠚⡆⠀⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⡤⡮⡀⠀⠀⠀⠀⠀⡤⠴⠒⡿⡿⡿⡿⡦⠰⠉⠉⡛⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡿⡤⠀⠀⠀⠀⠀⠀