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