⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⢫⡿⠯⡍⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡍⠉⠉⠉⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣤⡏⣴⡆⡯⣴⡖⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢖⠺⣶⣯⡔⢞⣱⠎⠰⣙⡷⢠⡝⡾⠓⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣘⢚⣠⣤⠖⠲⠖⠶⣤⣈⠚⡁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⠤⠤⣀⠀⠸⣌⡥⣖⣒⣶⣒⣒⣢⢍⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠢⣀⠙⠦⠊⠁⠀⠀⢠⡤⠤⢄⣉⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠑⡲⠦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠎⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡳⢤⣩⠴⠀⠀⠀⠀⠀⠉⠒⠒⠊⠀⠈⠉⠉⠀⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⠁⠀⣣⣂⡹⠥⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⣳⠆⠀⡇⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⣠⢋⠔⡺⠃⠀⠀⠀⠀⣠⡴⢀⡤⢄⡀⠀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠉⠁⠀⠀⡰⠹⠆⠀⠀⠀⠀ ⠀⢀⠞⡜⢹⡄⢰⠀⣠⠖⢉⠎⠀⠀⠀⠀⠀⡰⢡⠋⣰⡡⡲⠀⠀⠀⢰⢱⠀⢸⠀⣀⣈⠉⠒⢦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡠⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⢰⠁⢸⠁⢸⢰⠃⠀⢸⠀⠀⢨⠑⠒⢩⣚⣁⠀⢀⠔⠁⠀⠀⢀⠌⣸⠀⡌⠎⠠⠤⣑⣂⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⣿⠀⠀⠀⠃⠐⠠⣄⣤⠀⠀⠀⠀⠀⠀ ⠀⢸⡜⡆⠘⡆⠈⡇⠀⠀⠸⠀⠀⠀⠁⠒⡖⡰⠁⣰⠃⢀⡀⠀⠀⢸⢠⠃⠀⠧⣀⣀⡀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡱⢡⠃⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠣⡘⢦⡘⡄⠀⠀⠀⠀⡆⠀⠀⠀⡞⢀⠇⠀⠓⠚⡹⠁⠀⠀⠈⠙⠃⢀⡠⠤⠠⠤⠄⠃⠀⠀⣠⡆⠀⠀⠀⠀⠀⢀⡔⣡⠎⣰⠃⠀⢠⠊⠉⠑⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡖⠈⢁⣀⣱⡜⢄⠀⠀⠀⢹⠀⠀⢀⠇⡸⢀⡤⠀⡰⠁⠀⠀⢠⡄⠀⠀⣚⠂⠉⠉⠁⠒⠒⠒⢉⡴⠁⠀⠀⠀⠀⠠⡊⢰⠁⡰⠁⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠀⣜⡥⠒⠒⠢⣌⢇⠀⠀⠸⡴⢖⣋⣀⡋⠹⠁⢠⠁⢀⣠⠔⠁⠇⢀⡴⣁⢣⠀⠀⠶⣒⣒⣋⠥⠄⠒⠋⠉⢑⣢⡄⠘⣄⠑⠃⠀⣦⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⡀⣩⠒⠉⠉⠑⢎⠛⠀⠀⢰⠃⠀⠀⡴⢁⡇⠀⠸⠔⠉⣀⠴⣇⠘⢪⠞⣈⢾⠀⢠⠒⠒⠤⠤⠤⠤⠒⠂⢉⣁⡀⠭⣄⡈⠉⠢⣀⠏⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠃⠀⠀⠀⠀⠈⡇⠀⠀⢸⠀⠀⠀⡇⠈⡇⠀⠀⣠⠞⢁⠀⠈⠲⠃⢠⠹⠀⠀⠘⡄⠀⢶⠀⠀⠀⠀⠀⠠⠭⣙⡒⠤⡈⠑⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡞⠀⠀⠀⣸⠀⢡⠀⡰⠁⡜⡝⠀⢰⠇⠀⠀⢦⠑⠤⡀⠘⡄⠈⢣⡀⠀⠀⠰⡢⢄⡀⠉⠢⡉⢆⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⢀⠃⠀⣤⠴⠃⢀⡀⠳⠁⢸⠀⢇⠀⢸⡘⢦⡀⠀⢇⠀⣌⠙⠻⡀⢄⠱⡄⠀⠀⠈⢆⠙⡄⠀⠹⠈⢣⡀⠑⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡜⠀⠀⠈⠁⠈⢉⡇⠀⠀⠈⢆⠘⢆⠀⠇⠀⡉⠲⠼⠀⢸⠉⠲⢄⡜⠣⡈⠓⢤⡀⠈⡄⢡⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠋⠙⢢⠀⢠⠄⠊⠀⠀⠀⠀⠈⢣⠀⢣⡄⠀⡏⠒⢄⠀⡼⠀⠀⠈⠁⠀⠈⠒⢄⡈⠓⢽⡀⠱⢄⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠃⠀⣠⠤⠒⠤⠇⠀⠑⠲⠒⠊⠱⠀⠀⠀⡇⠀⠁⡸⠀⠀⠈⠒⠁⢶⠢⣄⠀⠀⠀⠀⠀⠈⠓⠄⡁⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠔⠋⠑⠢⡞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠁⢀⡜⣱⠄⠀⠀⢶⢄⡀⢣⢀⡑⠤⡀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⡠⠊⠁⠀⢠⠖⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⢀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠒⠉⣠⠖⡩⢎⠏⠀⠀⠀⠈⡆⠹⢀⣿⣙⢆⠈⠑⠦⡀⠀⠀⠀⠀⠀⠑⠦⠤⠤⠚⠁⠀⣠⣴⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⠋⠀⠙⣄⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢊⠕⠋⣠⠊⠀⠀⠀⠀⠀⡇⢰⡬⠟⠹⠘⢀⡶⡄⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⠴⠒⠚⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⠔⠁⣠⠞⠁⠀⠀⠀⠀⠀⠘⠤⠤⠒⡹⢰⡠⠿⢲⢸⡠⠉⢀⣀⢚⡛⠒⠀⠀⠀⠀⠀⠠⢖⡒⠦⠤⠤⣿⠀⠀⠀⠀⠀⠀ ⠀⠠⠗⠒⠒⢄⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⠃⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡮⠤⠐⠊⠁⠀⠀⠈⠢⣄⡀⣀⣠⢄⠀⠀⠈⢆⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡆⠀⠈⠢⣀⡀⠀⠀⠀⠀⢸⡁⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⣀⡠⠔⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠒⠤⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⡜⢗⠤⣀⠈⠉⠉⠉⢱⠀⡇⢸⠀⠈⡇⠀⠀⠀⠀⠀⣰⠋⢀⡤⠒⠉⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⢕⣢⠬⠉⠉⠨⢌⡄⡇⠀⠀⢠⠇⠀⠀⠀⠀⠀⠱⡀⠘⠆⠀⠀⠀⠀⠀⢀⣀⡀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⡤⣤⣤⣤⠤⠤⠤⠤⠬⠭⠭⠭⠭⠭⠤⠷⣚⣀⠘⢤⣀⠀⠀⠀⢠⠀⠙⡄⠘⠄⣒⡮⠭⠉⠀⠀⠈⠭⠭⣒⠪⠇⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⣑⢄⢀⡞⡧⢚⠵⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀⠀⠀ ⠀⠀⠀⠈⠢⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⡀⠀⠀⠀⠈⢢⡛⢀⠔⠁⠀⠀⠀⣀⠤⠄⠒⠒⠒⠒⠂⠠⢄⡀⡇⡇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠈⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⡴⡱⠃⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣰⢡⠃⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⡇⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⡼⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢀⡤⠚⠀⠀ ⠀⠀⠀⠀⢰⠒⠒⠒⢲⠀⠀⠳⡒⠒⠒⠒⠒⠒⠋⠁⠀⠀⠘⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠉⠑⠦⡀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⣀⣠⠤⠚⠀⡄⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡄⠀⠀⠙⡆ ⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠱⣄⠀⠀⠀⢳⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠈⠣⡀⠀⠀⢣⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⣄⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠈⢦⡀⠀⠱⣀⠀⠀⠀⠙⠢⠄⢀⣀⣀⣀⣀⣀⠠⠴⠊⠁⠙⢎⠣⡘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠚⠁⠀⠀⢀⡌ ⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠑⢄⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣣⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀ ⠀⠀⠀⠀⠸⠤⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⠤⠵⠀⠀⠀⠈⠑⠒⠤⠤⠄⠀⠀⠀⠤⠤⠔⠚⠉⢶⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠒⠊⠁⠀⠀⠀