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