⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠠⠠⠄⡤⡀⣀⡀⠊⠈⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⡀⠃⠀⠀⠀⠁⠑⠄⡀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⢆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠁⠀⠐⠁⠁⠉⠑⠄⠘⠉⠉⠓⠅⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⣀⠅⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⡏⠢⣌⣀⠀⠀⢀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⡇⠀⠀⠀⠉⠉⠉⠸⠤⢄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠆⠄⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢂⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡁⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣩⢭⡿⠛⠛⠛⠛⠛⠛⠛⢯⢭⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠍⠉⢉⡉⢉⡉⠈⠉⡍⠩⣍⠹⠁ ⠰⠂⠁⢀⠈⢉⡙⢦⡁⠈⠄⠡⠈⠄⠡⠈⠄⠡⠈⠄⠡⣨⡴⠿⠉⠀⠀⠀⠀⢁⡠⠤⠤⠥⠤⠄⠀⠈⠙⢷⣄⠈⡐⠠⠁⡈⠐⠈⡐⠈⠠⠐⢀⠡⠀⠠⠁⢈⠁⠂⠄⡡⢄⡰⡀ ⢘⠀⠌⢀⠐⡀⠹⡎⣧⠈⢀⠂⢁⠐⠠⠁⡐⠠⠁⣰⠾⠥⠀⠀⠀⠀⠠⠴⠊⣡⠔⠊⠉⡉⠒⠢⠤⢤⠀⠀⠹⡇⠀⡐⠠⢀⠁⠂⠄⡈⠰⠄⠆⠆⠉⡐⠁⠂⠌⠐⡀⠱⠂⠔⠁ ⢸⠀⡐⠀⢂⠠⢰⣇⡿⠀⢂⠈⠠⠐⡀⠁⠄⣐⣼⠃⠀⠀⠀⠀⠀⢀⡤⠔⠊⣀⢴⠊⠉⢭⡉⠑⠀⠀⠀⠀⠀⢿⡄⠐⡀⠂⢈⠐⠠⣐⠃⠈⠄⠂⢁⠠⠈⡐⢠⠃⠈⠁⢆⠈⡀ ⢸⠀⠠⠁⢂⣴⣫⠞⠁⠂⠤⠈⠄⣡⣀⡁⠂⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡵⠚⠑⢄⡴⠉⠒⠒⢦⠀⠀⢀⣿⠇⢀⠐⠈⠠⢀⠱⡌⢄⠁⠂⠌⢀⠐⠠⠀⠦⢀⠡⠘⡄⠂⡀ ⢸⠀⠀⠁⡿⣸⠁⠰⠈⠰⢀⠁⠆⠀⠈⠹⣆⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⡇⠀⠀⠀⠀⡇⢀⣾⠏⠀⡀⠈⡀⠁⢀⠀⠸⢀⠎⠰⠀⠆⠈⡀⠉⠆⡀⠰⠈⡆⠰⠀ ⢸⠀⠁⠢⣅⠡⠤⠂⢁⠐⠠⠀⠌⠠⠁⣹⢸⠎⢧⡀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣶⡆⢡⠀⣿⡆⠀⣹⡿⠉⢀⠐⡀⠁⠄⡈⠄⠈⠄⠂⡈⠄⠉⡐⠠⠈⡐⠠⢀⠁⡘⠤⡁⠄ ⢘⡀⠈⠀⡟⣒⡲⢦⣤⣈⡠⠈⣐⣠⡵⣫⠞⠀⠄⠓⢦⣀⡀⠀⠀⠀⠀⢸⡀⢀⣀⠾⣿⣿⠟⠿⢗⡲⣿⠃⢀⡂⠄⠠⠁⡐⠀⠄⡁⠂⡐⠀⠄⡁⠠⢀⠁⠄⡐⠠⠐⠀⠄⠑⠂ ⢸⠀⠐⡁⠳⣅⠉⢓⡲⠬⣭⣭⣭⠥⠞⠁⠠⠈⠄⢂⠀⠌⠉⠛⠛⠲⣿⠙⠻⣍⠀⣀⡬⠿⡀⠀⠀⠙⢷⠞⣩⣉⡙⢦⡐⠀⠌⡀⠐⠠⠐⠈⡀⠄⢁⠠⠈⡀⠄⡐⠠⠁⡈⠐⡀ ⢸⠀⠀⠠⠐⠈⠙⠲⠌⠳⣄⠀⢀⠀⠂⢁⠂⢁⠐⡀⠈⠄⡈⠄⠂⣴⠟⢃⡤⠤⠭⢥⢤⠤⡇⠀⠀⠀⠈⣷⣺⣿⣿⡌⣷⠈⢀⡤⠗⠲⢎⡀⠐⡀⠂⠠⠁⠠⠐⢀⠐⠠⢀⠁⡀ ⢰⠀⠁⢰⠈⠠⠁⠄⠂⢱⡘⡆⠠⠈⡐⠠⠐⠀⢂⠀⠡⠐⢀⢰⡼⠃⣴⣿⣟⡨⠿⢛⣛⣿⡇⠀⠀⠀⠀⢹⣦⡝⢿⠇⡧⠴⣜⡙⣄⠠⡀⡇⢐⠠⠡⣂⠁⡐⠈⠠⢀⠡⠀⢂⠀ ⢰⠀⠸⡌⢧⡐⠈⠠⢈⠼⣡⠇⠠⠁⠠⠐⡀⢁⠂⠈⠄⢂⠀⣿⠁⣼⣿⣿⠏⣴⢾⠉⢠⡟⡇⠀⠀⠀⠀⣸⡇⢻⡖⡞⠁⢐⣢⡙⢈⣷⠁⣃⠠⢀⠐⡈⢷⠀⠌⠐⡀⠄⡈⠠⠀ ⢰⠀⠁⡙⠦⣭⣙⣭⡥⠞⠁⡈⠐⠈⠄⠂⡀⠂⠠⠁⢂⠠⢘⣿⠘⣿⣿⠃⣼⠃⣸⠅⣸⠀⠳⣄⣀⣀⣴⠟⠀⡀⠑⠦⣉⠥⠀⢸⢅⠠⠋⠈⠍⣓⣊⡵⠋⠠⠈⠄⠠⠐⠀⡁⠄ ⢨⠀⠂⠄⠠⠀⡀⢀⠠⠐⠠⢀⠡⠈⡀⠂⠄⠁⠂⡁⠄⡀⠂⠙⢦⣈⣧⠞⠃⠐⣼⡃⡏⠠⠐⢀⠈⠠⢀⠐⠠⢀⠁⢾⠱⣊⣁⢠⠏⡇⣆⡈⢁⡀⡷⠀⠠⠁⢂⠈⡐⠠⠁⠠⠀ ⢨⠐⠈⡀⠂⠁⠄⠂⡀⠂⢁⠠⢀⠂⠄⢁⠠⠁⠂⠄⡐⠀⠌⢀⠂⠠⢀⠀⠂⢡⣿⠆⣷⡀⠌⠀⠂⡁⢀⠂⢁⠀⢂⠈⠓⠚⠓⠋⠀⠙⠲⠹⠛⠋⢁⠠⠁⠂⠄⠂⠠⠐⢈⠀⡁ ⢰⠀⠂⠄⠁⠌⢀⠂⠄⠁⢂⠀⢂⠠⠈⡀⠄⡈⠐⠠⠀⠌⢀⠂⠠⠁⠠⠈⠐⣾⣏⣷⣿⣿⡀⠁⢂⠐⠠⠐⡀⠌⢀⠐⢈⠠⠁⠌⠠⠁⠄⠂⡐⠈⡀⠄⠂⡁⠐⡈⠐⡀⠂⡐⠀ ⢸⡀⠁⠆⠁⠆⡀⠆⠈⠰⢀⠈⠀⠰⢀⠰⢀⠀⠁⠆⠁⠰⠀⠆⠁⡈⠀⠁⣾⡇⢹⡏⠿⣹⣷⠀⠆⠰⠀⠆⡀⢰⠀⡈⢀⠀⠆⡈⠀⡆⠈⣀⠰⢀⠰⢀⠁⡀⠆⡀⢁⠀⠆⡀⠆ ⢸⠤⣉⢆⡑⢢⠔⡌⠲⣁⠦⡘⢤⠃⢆⡒⡄⣊⠥⡘⣄⠣⢌⡰⢡⡐⡩⢰⣿⢍⢺⡇⡱⢿⢻⡔⠬⢡⣉⠒⣌⠢⣑⠰⢊⠜⠢⢅⡋⠴⣑⢢⠱⣈⠦⣡⠚⡤⢓⡌⢦⡉⢦⡑⢢ ⢸⡃⡜⢢⡙⢆⠭⣘⠱⣂⠦⡑⠦⡙⣂⠦⢱⡐⠎⡔⠢⢍⢆⠲⣁⠦⡁⣿⡟⣌⢺⡇⠥⣿⡚⣿⢀⠣⢄⠣⢄⠣⢄⠣⠌⡌⡑⢊⠜⡱⢌⡒⢣⠱⣊⠴⣉⠖⡩⠜⢢⠙⢢⠙⡄ ⢸⡡⢎⠱⡌⢎⡒⡡⢍⠦⡡⢍⡒⡱⡈⢆⢣⠘⡌⣰⣭⣦⣬⣦⣁⣆⣱⣘⣿⠾⣿⣿⣆⣿⠛⣿⣌⡒⣬⣴⣈⣴⣨⣴⣮⣄⢡⠉⡆⡑⠢⢌⢡⠒⡌⠒⣄⢊⠔⣉⠢⡉⢆⠱⡀ ⣽⢢⡍⠶⣉⢦⡱⡱⣊⢖⡱⢎⡴⢣⡙⡬⢦⡙⡴⣿⣹⡧⣧⣯⣿⣯⡏⣿⣿⣦⣿⣯⡯⣿⣟⣿⣟⣿⣧⣭⣿⣿⣿⢾⣿⣇⢎⡱⢬⣑⠫⡜⢢⢓⣌⠳⡌⢎⡜⢤⢣⠱⣌⠲⣡ ⣿⣣⢞⡳⣭⢶⣱⢳⡭⣎⠷⣭⢖⡧⡽⣜⣣⢽⣲⢻⣿⣟⡿⣟⢯⣻⢿⣿⡟⠛⣟⢛⣿⣿⡏⣿⢟⣻⢻⡟⣿⣛⡿⣿⣿⡭⢮⡵⣣⢎⡷⣩⢧⣋⢶⡹⣜⣣⢞⡱⣎⡳⣌⡳⢥