⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠀⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⡀⠀⣆⣀⠀⠐⢦⠂⣀⡀⢠⢰⣰⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⡇⠀⠀⣀⢄⣰⠖⣦⢼⠁⡀⠸⣏⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⠽⠉⠉⠙⠀⠘⠊⠉⠁⠈⠃⠉⠊⠑⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡴⠀⠀⠀⠹⣄⣴⠏⠀⠀⠀⢀⡜⠁⢠⠁⠀⠀⡟⢲⠿⠭⠋⠀⠉⠁⠀⠀⢄⢀⡀⠀⠀⠀⠀⢰⢦⠀⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢸⣀⣀⡀⢀⣠⣔⡀⢀⣀⠀⣆⢒⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⢹⠏⠀⠀⠀⢀⡞⣠⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⡞⢸⠀⡅⢸⡇⠀⠀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠈⠉⠘⠽⠊⠉⠁⠈⠉⠈⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⠁⠀⣜⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⣸⡄⣿⢻⡇⠀⠀⢻⡿⠀⠀⠀⢠⡀⢀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⢁⣀⡤⢦⣴⠀⢠⣴⠈⣠⢰⠀⢠⣤⣠⢤⡆⠀⣄⠀⢠⣤⢃⣼⠀⢸⠀⠀⠀⠀⠀⠀⢀⡠⢤⠶⡇⡘⢠⡮⠗⢚⣋⣭⡽⣶⣦⣄⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠃⠘⣇⢷⠸⠇⠀⠀⠛⠀⠀⠀⠀⠀⢿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠀⠈⠁⠈⠉⠁⠁⠀⠀⠉⠉⠉⠉⠀⠀⠋⠁⠈⠉⠈⠁⠃⠈⠀⠀⠀⣀⠴⢪⠱⡘⢆⡞⢓⠗⣉⠴⡚⢍⠲⡐⠦⣐⠢⡔⣩⠳⣤⠊⢡⠊⣀⢤⠞⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⣄⠀⠀⣠⠀⣶ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡠⠄⠀⡰⡀⣀⠀⠀⠀⢀⡀⡄⠀⠀⠀⡀⢠⠄⠀⠀⢀⠀⠀⠀⠀⠤⠜⠓⠋⠉⠉⠛⠍⡰⣡⠚⡥⢓⡘⠬⡑⣜⠰⡡⢃⠖⠤⠓⡬⢲⡃⠉⠚⠉⠉⠉⠉⠉⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡄⠀⠀⣸⣿⠀⢠⣿⡇⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠐⠛⠃⠋⠻⠀⠰⠶⠉⠟⠣⠀⠾⠞⠃⠐⠋⠛⠋⠹⠄⠀⠀⣠⢋⠳⢤⠤⣤⢤⠔⣩⠚⡤⢋⡔⣡⠞⡳⣵⡉⠖⡡⢍⡸⢌⠓⡌⠥⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⢄⣀⡀⠀⠀⣮⣀⣇⠀⢠⡧⢿⢀⡞⠈⡇⠀ ⠀⠰⣄⡦⣄⡆⠀⣤⢰⢠⣤⣀⣄⣀⣀⢠⣠⣤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⢎⠱⢊⠲⣰⠃⡴⢃⠭⣐⣣⡞⡡⢎⣿⠰⢌⢣⣑⠮⡐⢎⡱⡌⢣⢃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⡒⠚⠋⢠⠃⠀⢿⠀⡼⠀⢻⠌⠀⠀⡱⠁ ⠀⠀⠀⠀⠁⠈⠀⠀⡀⢁⠀⡈⠀⣈⡚⠐⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡌⠦⡙⡌⡱⣇⠞⣑⢊⠦⣽⢃⠖⣱⣯⢃⠞⣰⠞⡡⢎⡵⡪⢼⢡⢳⢂⢽⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⡘⠀⠀⠘⠀⠁⠀⠀⠀⣠⠞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠗⠾⠲⠗⠈⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⢻⢏⠀⠀⠀⡟⡘⣌⠒⢥⡘⢴⣎⠓⣌⢎⢾⡕⠛⣳⣿⢃⠎⡼⣁⣎⣵⠟⠊⢀⠀⡇⢺⡌⢾⠀⢀⡼⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀ ⠀⠀⣄⢰⣆⣄⣀⣤⠀⠀⠀⣀⠀⡄⣆⡂⠀⡆⢀⠀⠀⠀⠀⡀⢰⠀⢀⣀⡀⠀⠀⠀⠀⠀⢳⠻⠜⠀⠀⠀⢰⡙⢔⠢⢍⠢⡜⣸⠆⢭⢞⡎⡟⠀⢠⣿⠇⢎⣞⠕⠊⣥⣄⣑⣤⡉⠀⣏⢼⡌⣽⡴⠯⠤⣧⢡⠆⠀⠀⠀⠀⡆⢀⠀⠀⢀⣈⢦⡀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀ ⠀⠀⠙⠋⠉⠑⠁⠑⠀⡹⠉⠉⠀⠑⠉⠈⠙⠛⠈⠉⣘⡃⠀⠛⠚⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢌⠢⡍⢆⢓⡰⡇⢎⡏⣼⠒⢷⣠⢻⡋⡼⠊⠀⠀⠀⠹⠀⠀⣨⠛⠒⣇⢺⡇⣇⣁⣀⠀⠸⡎⣦⠀⠀⡀⢰⡟⠌⢄⡴⡋⢀⡦⢝⠦⠤⢤⡜⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠠⠀⠀⡀⠀⣀⡀⠀⡄⠄⠀⠀⣀⣀⠀⢤⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⢀⡾⡑⣊⠱⡘⡌⢆⣱⡭⡓⢬⢇⠚⣼⢋⡾⡱⠁⠀⠀⠀⠀⠀⠉⠐⠃⠀⢰⡧⡏⣿⠉⢠⢟⡟⠄⠙⣞⢤⣰⣡⣏⣱⡈⠑⣥⢌⢟⣀⡜⠒⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⠛⠂⠃⠈⠛⠙⠛⠛⠚⠂⠙⠘⠋⠲⠙⠛⠀⠸⠀⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⠀⣠⢋⠦⡑⠬⡑⡜⣠⢃⡷⣡⡳⢋⢆⣹⠇⢎⡳⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢿⡑⡇⠈⠁⢉⠱⠀⠀⢃⣟⠟⠻⣻⠍⣿⣇⠸⡈⢪⡀⣱⠞⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⢠⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⠤⣚⣤⠷⠒⠛⠒⠳⢮⣤⡋⢦⠵⣱⡭⠞⡝⡸⡼⠁⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣠⠋⠘⠶⠄⠸⠀⠀⠀⠈⠦⠀⠉⠒⢠⠇⠙⢒⠽⢿⣿⠋⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀ ⠀⠀⠀⠘⠊⠖⢆⢶⠻⠍⠻⠿⠆⠘⡖⠚⠃⠰⠦⠛⠛⠷⠶⠀⠶⠖⠻⠇⠀⣷⡇⠸⣡⢔⣧⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⡗⠋⠁⠀⡸⠰⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⣔⡠⡌⡘⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⡸⠀⠀⢸⣴⠟⠁⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⡰ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⠀⠀⠀⠈⠀⡀⡀⡀⢀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠐⠀⣡⠞⣡⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢰⢇⣹⠁⠀⢀⣀⣄⣀⠀⠀⠀⣀⠀⠀⣠⠣⡑⢇⠀⠀⢀⣀⣀⠣⠀⠀⠀⠄⠀⠀⣰⡃⢲⡶⠛⠁⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⠌⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣦⠚⠾⠽⠸⠅⢰⠐⠳⠳⠎⠯⠀⢰⠚⠀⠀⠀⠀⠀⢠⡞⠥⣺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠡⢠⡿⢢⠃⢀⡴⠿⣚⣭⡾⠟⠋⠉⠉⠉⠉⢹⡀⢏⠒⠛⠛⡩⠾⠭⠷⢤⣤⣤⣤⣤⣾⡥⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⠜⣲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⣌⣧⠏⠀⢸⠒⣻⡟⠉⠀⠀⠀⠀⠀⠀⠀⢈⠃⡜⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⣠⠞⠀⠀⠀⠀ ⠀⠰⢆⡿⣰⡶⠀⣤⣦⠁⢧⠮⠴⠠⡬⡤⣄⣆⠠⡤⠴⠆⠀⠀⠀⢀⡞⠬⣡⢎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣧⣹⡼⠀⠀⠀⣻⠏⠀⠀⡌⠀⠀⠀⠀⠀⠀⣼⠞⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡞⢌⣱⢃⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⡟⣸⡇⠀⠀⣰⠃⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀ ⠠⠤⢤⡤⡄⠡⠦⠴⣬⣜⡆⢠⣄⢡⣄⣖⣀⣀⡀⠈⢂⢡⡀⢀⡾⡘⣰⠣⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⠸⣧⡀⢠⡇⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⠤⠤⠾⠥⠤⢤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⡠⢖⣹⢣⢱⠇⣽⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡖⣿⣿⣾⠀⠀⠀⠀⠀⠀⡀⠀⠁⠢⢄⠀⠀⠀⠀⢹⣿⣿⣿⠏⠉⡍⠁⠉⠉⠉⠈⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠸⢿⣠⡼⠀⣤⣸⡇⢠⠌⡁⠀⠀⣀⠼⡈⣄⡏⡄⡿⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣿⣿⣧⢀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈⠠⣀⠀⢸⣿⣿⠁⠀⠀⡇⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣅⠲⣡⢺⢱⢨⣷⡟⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠑⠲⡠⡀⠀⠀⠐⢄⡈⠀⠀⠒⠀⠕⠺⠟⠁⠀⠀⠀⠂⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣠⠋⢤⠟⡄⡟⡤⣿⡞⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡀⠄⠈⠢⡁⠂⠠⠀⠑⢅⠒⠀⠀⠀⠀⠈⠁⠐⠠⢀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠐⠒⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡱⡘⠤⣹⢣⢞⣱⡏⣴⡿⠀⠀⠀⠀⠀⠀⠀⣰⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⣀⡁⠀⠤⠥⠀⠀⠠⠀⠉⠀⠒⡠⠀⠀⠄⠂⠄⠀⣑⠀⠀⠀⠀⢸⣴⡖⠒⠒⠂⠉⠉⠉⠁⠀⠀⠀⠀⠀⢰⣄⠀⡠⡄⢠⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣡⠱⢌⣱⡷⣫⣶⣿⣸⡟⠀⠀⠀⠀⠢⣄⠀⢠⠃⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢛⡫⠅⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠐⠂⠀⠐⣲⠜⠉⠈⠁⠒⠤⢸⠟⠀⠀⠀⡄⠀⢰⠀⠀⠀⠀⠀⠀⠀⡿⢻⠀⡇⣷⢨⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡴⢁⢎⠒⣼⣷⠟⠁⡈⣿⠁⠀⠀⠀⠀⠀⠈⠑⢏⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠀⢸⣤⠀⠀⠀⠀⠀⢠⣧⢼⣧⡏⢹⢸⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⡤⢋⠤⣻⠟⡓⠤⣀⣗⢫⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣤⠤⠴⠶⠒⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⠳⡄⠀⠀⠀⠀⠀⠀⠀⣺⠏⣿⠀⢸⢽⠀⠀⠀⠀⠀⢸⠃⢸⡿⡇⠸⢾⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠳⡼⠡⢎⠋⠈⠠⠀⠀⢻⠢⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⠤⠯⢍⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⣿⠀⢸⠸⠀⠀⠀⠀⠀⡞⠀⠙⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢃⡧⡙⡜⢂⠕⠈⠀⠀⢻⠢⡐⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡙⠒⠤⡲⡄⢀⡟⠀⠀⡄⠀⡄⡆⠀⠀⠁⠀⣿⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠼⡆⣗⠡⡇⠁⠀⠀⠀⠀⠈⣧⡾⠋⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠶⢄⠈⡱⠋⠀⠀⣞⣀⣤⡧⡗⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⣄⠀⣀⣀⠀⣀⠀⡆⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠂⠉⠙⢿⡔⡇⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣉⠠⠔⠋⠀⠀⠀⠀⠓⠴⠋⠃⠁⠀⠀⠀⠀⠸⣦⡞⠀⠀⠀⢾⣋⡾⢿⣻⣼⢸⠁⣀⡏⡏ ⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠼⡀⠀⣀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⢞⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⡀⠀⠀⠀⠂⠉⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢹⠤⢻⣸⡇⠀⠀⠀⢄⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⢠⠀⢠⢄⠠⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣀⣰⣁⣤⠒⠁⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡠⠚⢡⡇⠀⢸⢌⣹⡆⠱⡀⠀⠀⠸⠄⠗⣤⡀⢰⠶⠾⠛⠁⠰⠖⠛⠹⠿⠄⠐⠖⠃⠞⠧⠖⡴⢇⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⢀⠠⠂⠁⠀⠀⣀⡠⠔⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠑⡀⠀⠱⡄⠀⠠⠀⠀⠀⠀⠈⢀⠔⠋⠀⢀⡶⠁⠀⢸⢂⡿⠁⢀⠀⣀⠀⠀⠀⠀⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡧⠐⠁⠀⢀⡠⠔⠊⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⠀⡧⡄⢈⡆⠂⠃⠀⣀⠴⠊⠁⠀⠀⣀⣞⠁⠀⠀⣼⠋⠁⠀⠀⢹⠀⣤⣶⠖⠀⣧⢠⡖⡶⣇⠀⣤⡤⣰⡂⢸⡀⠈⠇⢠⣴⡆⠀⣄⡰⣖⠖⢖⡀⢠⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠃⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣎⠀⡇⠸⡁⢰⢰⣼⢞⠁⠀⠀⣼⣾⠀⡿⠂⠀⠀⠘⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣿⠀⡇⢀⡵⢼⢹⢸⠈⢆⠀⠀⠃⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣗⣠⡠⣰⣀⣀⠀⢀⠀⢀⢆⣀⡀⣤⢰⣀⡀⢠⢣⢀⣀⠰⣤⠄⠀⣃⣀⣀⣤⡀⣀⣀⣘⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢤⠋⠁⠀⠁⠘⢸⠀⠈⢆⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠙⠂⠉⠹⣉⠆⠘⠈⠉⠘⠈⠁⠸⠀⠈⠀⠉⠊⠂⠈⠁⠈⠉⠈⠉⠁⠙⠙⠀⠉⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡮⠄⠀⠀⠀⠀⠎⠀⠀⠀⢣⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⢰⠀⠀⣰⠀⠀⡀⠀⣀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠖⠁⠛⠎⠙⠛⠋⠇⠰⠛⠢⠙⠲⠀⠼⠄⠘⠳⠶⠙⠳⠀⢹⠛⠛⢳⠀⠰⠄⠘⠓⠶⠋⠻⠄⠀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠉⠑⡒⠪⠴⠄⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡄⣊⡬⠒⢹⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣵⢢⢌⡀⢀⡀⠀⠰⠉⠉⠐⠒⢒⡒⡂⠧⠔⠤⠬⡳⣄⣐⣶⠖⠋⢁⣠⡞⠁⠘⣅⠀⠀⠀⠀⠀⠀⠀⠀⠐⡦⠶⠿⠃⠀⠗⠾⠾⢸⡐⠶⢄⠴⡄⢸⠕⠾⠾⠇⡴⡄⢀⣇⠀⠶⣤⡰⠦⡄⠐⡶⠶⠾⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠈⠳⡲⠤⣀⡀⠀⣔⠄⠀⠉⠀⢀⠀⠀⠁⠳⠟⠻⢟⡀⢐⡞⠁⠈⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡳⡀⠀⠀⠀⠁⠊⠭⠉⠒⠒⠢⠤⠥⢂⣀⣀⠀⠀⢔⡀⠀⣽⠁⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣀⣴⢡⣼⠰⡦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠑⠋⠝⠦⣄⠀⢪⡧⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀