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