⠀⠀⠀⠀⠀⠀⠀⢀⡾⣖⢯⡲⣖⣲⢲⡤⣀⠀⠀⠠⡄⠀⠀⠀⠈⠐⢥⡦⠀⠀⣀⣠⣤⡀⣀⣀⠀⠀⠀⢀⢇⠢⡑⣸⠁⠀⣴⡟⢻⡆⠀⠈⠀⠀⢀⣤⠜⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣟⡞⢯⣮⡵⢣⢧⣛⡼⢦⡀⠈⢡⠃⠀⠀⠀⠀⠀⠀⠈⣠⣾⣩⢿⡽⣤⣤⣈⣁⠀⠀⠈⡎⡔⠱⣈⡄⠀⠸⠻⠛⠁⠀⠠⢃⠀⠀⠉⠑⠶⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡛⢀⡿⣞⠛⢿⣞⣽⢲⣣⢝⣮⣷⡔⠁⠀⠀⠀⠀⠀⠀⡠⣸⢯⣻⡝⣯⡽⣳⡝⣷⢫⡷⡄⢄⠈⠉⠉⠀⠀⠀⣀⠀⢀⢠⣴⣿⣓⣆⡄⡀⠀⡀⢄⡢⡀⠀ ⠀⠀⠀⠀⢈⠤⠭⡁⠀⢉⡀⢽⣿⣷⡝⣮⣗⢯⡆⠹⠃⠀⠀⠀⢀⠴⢶⣟⣿⢧⣻⣧⣿⣱⣿⣼⣯⣷⡗⠜⠀⠀⠀⠀⢀⠔⠁⠀⡎⡇⠀⠘⠉⠙⡶⡛⢀⡐⢀⢻⢕⡄ ⠀⠀⠀⢀⠊⡠⠠⡈⠒⠨⡀⠀⠀⠘⡛⢶⣹⢾⡕⡜⠁⠀⠀⡰⠁⠀⢀⠀⠉⠙⠯⡈⠉⠹⠿⢹⡾⣏⢣⠀⠀⠀⢠⠊⠓⠠⠤⡔⠊⣸⣄⠻⠀⠳⡟⣿⠂⡐⢠⣸⣃⡅ ⠀⢀⠔⠀⢀⡄⠈⠄⠢⠀⠀⠀⠉⠐⢗⡩⣠⠟⣰⠃⠀⠠⠊⠀⠀⡐⠎⠄⠂⢄⠀⠈⠂⠤⢴⣜⡗⢃⡜⠀⢠⠐⠁⠀⠀⢀⢤⢌⠑⠣⡉⠂⢄⡀⠑⢫⢧⡆⢡⠂⡲⠁ ⠠⠊⠀⠀⢀⠅⠊⠉⠐⠠⡂⣀⣂⠠⡀⢫⢈⡸⠂⠀⡐⠁⠀⠄⡌⢠⣄⠀⠀⠀⠔⠨⠀⠀⠈⡇⠀⡖⠁⡰⠁⠀⠀⠀⢠⠘⡁⡀⡉⠪⠎⢆⡀⠑⢩⣜⣁⣠⠥⠛⠁⠀ ⡄⠀⠀⠀⢠⠐⢄⠀⠀⠀⠘⠀⠀⡐⠁⢀⡗⠁⠀⢠⠃⠀⠀⠀⢇⠀⠉⣆⣶⡄⠀⠊⠀⠀⢀⢼⠈⠀⢠⠁⠀⠀⠀⡔⠁⢶⣶⣀⣭⠂⡇⠀⠉⠲⠥⠃⡨⠃⠀⠛⠁⠀ ⠱⡄⠀⠀⠀⢆⠐⠃⠒⢀⠜⠀⠀⠀⣈⠇⠀⠀⠀⠈⢦⡀⠀⠀⠀⠂⠀⢀⠀⢄⠊⠀⠀⢀⡰⠁⠀⠀⠈⡆⠀⠀⠀⠱⡀⠀⠐⠋⠉⠀⢸⠀⠀⠛⠀⡎⠀⠀⠀⠀⠀⠀ ⠀⠈⠓⠴⣀⢀⠀⠁⠁⠀⠀⠀⠠⡬⠂⠀⠀⠀⠀⠀⠀⠉⠂⢆⡄⡀⠀⠀⠀⠀⠀⠀⣐⠕⠁⠀⠀⠀⠀⠰⠤⠤⠤⢤⡤⣈⣒⡂⡀⠂⠁⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠢⢆⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⢀⠀⠀⠠⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⢈⠉⠙⠢⡄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡔⡆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣴⣖⣇⣦⣫⣬⣅⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠊⠀⠄⠀⠀⠀⠀⡴⠓⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣾⣟⣶⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠔⣁⣴⣿⣿⡯⣟⣳⣟⣷⢫⡗⢀⢈⡀⢢⠀⠀⠠⢏⡇⠀⡄⡀⣀⡐⡀⣀⠈⠈⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⡷⣟⣽⣾⢷⡋⠀⠈⠱⠄⠀⠀ ⠀⠀⠀⠀⠀⡠⢊⡮⠥⡃⠨⠦⠻⣿⣳⣞⣭⢿⣄⣮⠖⠕⠁⠀⠀⣠⠃⣱⢺⠳⠳⢦⡎⠂⢀⣙⣀⠄⠀⡀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠉⠛⠿⣻⡾⣟⣿⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⢀⠎⠀⠀⢈⢁⠳⡀⠃⠐⡍⢿⣞⡞⣏⡿⣾⠀⠀⠀⢀⠊⠀⠈⠉⠒⠦⡀⠁⢍⡀⠀⢿⣬⣁⠴⠥⠴⠆⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⣦⣴⣿⠇⡠⠀ ⠀⠀⡔⠁⠀⠀⢠⢋⡆⡆⢈⢂⢄⡀⣛⢻⡿⡽⣞⠇⠀⢀⠔⠁⠀⠀⣀⣀⢀⡀⠈⠐⠨⢄⣀⡠⣣⠏⣸⠂⠃⠀⢀⠔⠁⢀⠊⠀⠀⠉⠤⡀⠀⠀⠀⠈⠫⢿⠃⡃⡓⠀ ⢀⠊⠀⠀⡴⠒⠉⡑⠣⣎⡳⡰⠀⠙⠒⢿⠝⣻⠃⠀⠠⠂⠀⢀⠔⠁⠀⠀⠀⠀⢢⠀⠀⠀⢇⡕⠁⠬⠃⠀⠀⡠⠃⠀⠀⢈⠂⠀⢥⠀⠀⠀⠀⠡⠀⠀⠀⢀⢱⠁⠀⠀ ⡈⠀⠀⢸⠡⣴⣤⢆⡌⠀⢏⠀⠀⠀⠀⣈⡞⠁⠀⢀⠆⠀⠀⠨⡀⢺⡷⢈⣐⠀⠊⡄⠀⠀⠀⢠⡐⠁⠀⠀⠰⠁⠀⠀⠀⢢⠈⢛⣧⣬⢌⠸⠀⡠⠀⠀⠐⡡⠁⠀⠀⠀ ⠳⣄⠀⠈⢦⠁⢖⠻⠟⢀⠇⠀⠀⠀⣜⠏⠀⠀⠀⠘⡄⠀⠀⠀⠙⢄⠓⠊⠓⢁⠔⠀⠀⠀⢠⠊⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠓⠄⡁⠈⠁⡐⠀⠀⢀⡪⠔⠁⠀⠀⠀⠀ ⠀⠈⠓⢦⡄⡉⠐⠒⠊⠁⠀⠀⢀⡮⠋⠀⠀⠀⠀⠀⠈⠲⢄⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⡢⠃⠀⠀⠀⠀⠀⠈⠳⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠱⣤⠀⣀⡀⢔⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠔⡀⢀⠀⠀⢀⢐⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠴⡀⡀⠀⠀⠀⢀⢔⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠠⠂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠲⢸⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠚⠚⠒⠶⠶⠒⠶⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣐⠆⣀⠀⢀⠀⠀⢃⠄⢠⡌⢀⣀⡐⡁⢰⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠋⠼⢀⠣⡠⢊⠬⠜⠤⠄⢰⢐⠠⡢⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⡢⢈⣇⣶⣴⡂⢲⠀⠈⠉⠘⢂⠱⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡒⡂⠄⣀⠈⠐⡹⠂⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⢿⡿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢊⢀⠊⠏⠛⠟⠀⡮⢖⡳⡄⠀⠂⠀⡇⠀⠀⠀⠀⠀⢀⠔⢠⠂⠁⠀⠁⠐⠅⡢⢁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⣟⣿⡽⣿⣻⣧⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⡔⠀⠀⢈⣁⠓⢄⠛⢖⠈⠙⠘⣛⠄⢀⡜⠸⠂⠀⠀⢀⠔⠓⠠⠅⡀⠀⠀⠀⠀⠀⠈⠲⡕⠄⠀⠀⠀⣸⡟⣼⣿⣿⣻⣽⣿⣿⣿⣿⣷⣿⣿⣿⡿⡄⡄⠀⠀ ⠀⠀⡠⠊⠀⠀⠀⠡⠂⠀⠠⣵⠙⡰⢒⠈⢱⡞⢁⡄⠀⠀⠀⢀⠊⠀⠀⠀⢀⣀⡈⠐⠠⡀⠀⠀⠀⠘⡊⣆⠀⢀⣿⢞⣿⣿⣻⣿⣻⣷⣿⣻⣿⣿⣿⣿⣻⡿⣧⠁⠀⠀ ⠀⠌⠀⠀⠀⠄⠒⠐⠂⠣⣴⣃⡠⣆⣸⢔⠓⣀⠏⠀⠀⢀⠔⠀⠀⠀⡠⢊⣖⣧⡷⢱⠀⠀⠑⢄⡠⠞⣑⠇⠀⠸⣟⡾⣿⣿⢿⣽⣿⢯⣿⣿⣿⡿⢝⠉⠙⣯⣿⠚⡄⠀ ⠈⠀⠀⠀⢰⠀⣄⠀⠀⡔⡬⣠⠀⠀⠀⠠⡠⠂⠀⠀⢀⠎⠀⠀⢀⠎⠄⢌⠄⠉⢳⢸⠀⠀⠀⠀⢃⡨⠃⠀⠀⠀⢻⣻⡽⣿⣿⣟⣯⣿⣿⣿⣯⠀⣸⣤⣡⣷⠇⠁⠀⠀ ⢱⡀⠀⠀⠈⢄⠉⠖⢺⠀⠓⡀⠀⠀⠠⡝⠀⠀⠀⠀⢨⠀⠀⠀⢨⠀⡑⣼⣒⠂⠀⡎⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠈⢳⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠾⠄⠀⠀ ⠀⠈⠣⢆⠀⡀⠀⠁⠈⡄⠀⠈⠆⢰⠎⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠂⢄⠁⠀⢠⠝⠀⠀⠀⣐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣟⣾⢷⣻⣿⣿⣿⡿⢟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠑⠔⣀⠀⡸⣀⡠⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠴⡄⡀⠈⠉⠀⠀⠀⡠⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠁⠀⠀⠑⠒⠒⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⡀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀