⠀⠀⢀⢄⡘⠁⠀⠀⡄⠀⠀⠢⠀⠀⠀⠀⣠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⠀⠀⢁⠀⠀⠅⠀⠈⡀⠀⠀⠈⠀⢘⠀⠉⠈⠢⠀⠀⡄⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠂⠀⠈⡆⠀⠋⠀⠀⠇⠀⡠⠔⠒⠓⠢⡄⠠⠤⠤⠼⠀⠀⠐⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⢸⠉⠑⢆⠀⡸⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠂⠀⠀⢑⠀⠀⠄⠉⠀⢸⠀⠀⡀⠂⠁⠁⢨⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠑⠇⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⡂⠀⠀⠀⡀⡃⠀⠀⠀⢠⠃⠊⠀⠀⠀⠠⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢢⡜⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⠐⠐⠀⠂⠉⢹⠁⠀⠣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣀⠤⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡉⡆⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢸⡀⣀⠼⡂⠀⠀⢀⡠⠄⠤⣀⠈⠉⢀⡔⠒⠤⡀⠀⠀⠀⠀⢀⢎⣁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠎⠁⠀⠀⠀⠀⠱⡀⡊⠀⠀⠀⠀⠐⠀⢄⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⠀⠀⡀⡀⠀⠀⠳⠀⠀⠀⠀⡠⠆⠑⢄⢨⠃⣀⡄⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠂⠂⢄⡅⠀⠀⠠⠁⠬⠀⠀⠀⠀⠀⠀⠀⢨⢢⢀⡠⠒⠘⡏⢀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠩⡁⠀⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠈⠀⠀⡀⠂⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠂⠄⠂⠄⠄⠄⠠⠀⠄⠐⠀⠁⠁⠀⠀⠀⠀⠀⡔⡒⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠐⠀⠄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡈⠐⠂⠁⠉⠀⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡨⠀⠀⠀⠀⡀⠀⠀⠈⢄⠀⠀⠌⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⠃⠂⠈⠀⠙⣂⡄⠀⠀⠙⡄⠑⢀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠅⠠⠀⠄⠠⠠⢄⠆⠈⠫⡑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⢀⠠⠐⣅⢀⢁⢀⣊⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠂⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⡈⠄⠃⠣⠈⠀⠂⡀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠄⠂⠁⠁⠑⠒⠀⠄⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡅⠀⠈⠀⡀⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⡀⠁⠀⠀⠀⡀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠄⠀⠠⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡄⠀⠀⠀⢠⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠛⠒⠒⣦⠒⢒⠛⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⡏⠉⠁⠉⢻⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠁⠀⠀⠀⠈⠛⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⢀⠀⠀⡀⠄⠠⠀⠄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡀⢀⡀⡀⠀⢀⣀⣀⣀⡀⣀⣀⢀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⢀⠀⠄⡐⠠⠐⠠⠁⡌⢠⠡⡘⢄⠣⣉⠢⡑⢌⠣⣍⠢⡓⡜⢢⡕⢢⢉⠆⢦⡓⢦⡝⢦⣣⢏⡖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⠀⡀⢀⣁⠈⡁⣈⠠⢁⢂⡑⡈⠔⡠⢃⡘⣈⡑⢂⢣⠑⢎⠓⡜⡡⢎⡘⢲⡙⢣⠞⣣⢓⢮⡹ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⠘⠂⠐⠠⢀⡀⠀⠀⠀⠀⢀⢐⠏⠁⣀⡀⠀⠀⠀⠀⠄⠡⠘⠠⢁⠠⢀⠌⡡⠊⡍⢌⡩⣜⡱⢊⡜⡡⡙⣍⠚⡥⣋⠖⣙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠠⠂⠈⠑⡄⢀⡔⢁⡩⢐⢭⠀⠈⠐⡄⠀⠌⠠⠁⡌⡁⠆⢢⠁⢆⢡⠃⡜⢠⠒⣼⡱⣋⠴⣡⠓⣌⠳⣔⢣⢞⡰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡆⠀⠀⠐⠁⠀⠀⠀⢨⠊⡰⡫⢆⠡⢂⡷⠀⢃⢈⠒⢌⠠⢃⡐⢌⡘⠤⡉⢆⢢⠱⡨⢅⣋⢶⣣⢝⡺⢄⡻⣰⢫⡜⣣⢮⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠁⠀⠀⠀⠀⢡⡇⠰⡇⠒⠀⠀⠈⠐⠈⡠⠏⡔⣈⡶⣋⠜⢇⠘⡀⠈⠀⠉⠒⠎⣔⡈⢆⠱⣊⠔⣣⢑⢎⡼⣎⡷⣪⠵⣋⠶⡥⢧⢏⡗⣮⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⢀⠠⢐⠢⠀⠀⠀⢀⡏⡅⢰⣱⠀⠀⠀⠀⠀⣘⠣⣑⠢⢍⡴⢁⠎⣼⢸⠣⡀⠀⠀⠈⢦⠀⠈⠚⢵⣌⡚⣤⢋⢮⣙⢿⡜⣧⢻⡜⣳⣝⣫⢞⡽⣎⢷ ⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⠀⡎⠀⠀⠀⠀⠀⡾⢸⡷⢇⡸⣷⣆⣈⠿⣷⣾⢱⣾⣷⡾⣶⣉⡾⢁⡏⢰⠈⣇⡀⠀⠈⣇⢱⠈⠀⢶⡹⣰⠏⣶⢹⣾⣹⡎⣷⢹⢷⡎⣷⢏⣾⢹⡾ ⠀⠀⡀⠀⠀⠀⢀⡬⠁⠁⣔⡄⠀⣀⣤⡖⣏⠲⣍⡶⣛⠏⢱⡟⢺⣱⣎⣶⣭⡶⣦⣓⣦⣍⣳⡆⠜⣄⢋⢤⡙⢦⣀⢯⣼⡱⣄⠈⠳⣥⢻⡜⣧⣟⣧⣻⢵⣫⢾⣹⢮⣟⡾⣫⣽ ⠀⢀⠀⢀⣢⣒⠉⠤⠐⠸⠉⠃⡁⠻⣕⢫⡔⢣⢻⣜⡯⠖⠋⠙⠈⠉⠉⢉⠉⢡⠁⠉⠀⠉⠉⣣⢍⡔⣊⢦⡙⢦⡹⢆⣻⢱⢎⡷⣣⢎⣷⣽⢲⣟⡾⣧⠿⣼⢯⣽⣛⣮⣟⡷⣯ ⠠⠀⡌⠠⢁⠀⠄⢠⠁⢂⠌⡐⢘⠳⣽⣶⢩⡾⠛⠉⠨⠁⠀⠀⠀⠀⣶⡜⣀⠈⣶⣆⣀⣀⡀⠏⠞⠶⠭⠒⠙⠓⠛⠛⠒⠋⠊⠑⠛⠋⠾⠼⣻⡾⣿⣝⡿⣹⣾⣳⢯⡷⣯⣟⣷ ⠄⢡⢀⠃⠤⠈⠒⡠⢘⠠⠒⡈⢆⠣⢌⠛⢎⠇⠀⠀⠀⠈⠈⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⢯⣟⡷⣯⣟⣯⢿⣳⣟⣾ ⠌⢂⠆⡘⢄⠣⢘⠠⡁⢎⡑⢌⢢⡙⢢⣩⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡾⣽⣷⣻⣾⣟⣯⣿⢾ ⢌⠢⡘⠰⣈⠰⡁⢆⡑⢢⠘⢤⢢⡝⣡⣟⢧⡻⣽⢲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣿⡿⣽⣳⣿⣽⡷⣿⣯⢿⣿ ⢢⠑⡌⠱⣀⠣⡘⢤⢊⡑⢎⢆⡳⣜⢫⠿⣺⡝⣿⣛⢷⣫⢗⣳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣏⢷⣿⣿⣟⣯⣿⣾⢿⣽⣿⣽⣿⣻ ⡆⢣⠘⣥⢢⡅⢳⡌⢲⢩⠚⣬⠓⣮⡇⢻⡔⣯⣽⣽⡞⣧⣯⢹⠛⣾⣯⣿⣶⣦⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢰⠐⠒⠉⠉⠉⠉⠙⡌⠉⠉⠙⠚⢻⣾⣿⣿⢻⣽⣿⣽⣿ ⡜⣌⠳⡌⢦⡙⢦⡙⢮⣙⢮⣱⢻⡼⣹⣣⣿⡟⣯⣽⡽⣾⣽⡟⣟⡶⣹⢮⣟⣽⣶⢯⣟⣿⣻⣟⣶⢲⣖⣲⡶⠊⠀⠀⠀⠀⠀⠀⢀⣠⣴⣗⣄⠀⠀⠀⠀⠉⠻⣿⣿⣻⣿⣟⣿ ⡳⣌⠳⡜⣣⠞⣥⢛⡮⣝⢮⡳⣏⣾⣿⣿⣿⡿⣷⣯⣷⣳⢯⣟⡿⣿⣿⣿⣿⣿⣞⣯⢿⣞⣿⣯⣟⣿⣻⠋⠀⠀⠀⠀⣠⢴⣶⣿⣿⡿⣿⣻⣷⣿⣦⢄⠀⠀⠀⠈⢻⣿⣿⣻⣿ ⡵⢪⡽⠼⣥⢻⡜⣯⣷⣯⣾⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⢿⣽⣾⣟⣾⡷⠃⠀⠀⠀⠀⢀⠉⠙⠛⠿⢳⣿⣿⢿⡿⠿⠛⠚⠀⠀⠀⠀⠘⣿⣿⣿⣿ ⣽⣷⣿⣿⣾⣷⣿⡿⣝⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢿⣳⣿⣯⣷⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠄⣀⣨⣿⠿⠁⠀⢀⣀⠄⠀⠀⠀⠀⠈⠻⣿⣿