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