⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡤⠤⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠀⠀⠀⠀⠹⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣑⠶⠬⠭⠭⠥⠶⢆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠊⠉⢩⢼⡹⢉⠉⠑⠓⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣑⠊⠁⠠⡬⠔⢱⡢⠩⠓⣀⠠⠡⢊⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠉⢐⢄⢈⠬⣩⡘⠃⠈⢡⣎⠡⣀⠁⠖⠉⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠤⡐⡮⡐⢃⡇⠸⡑⠁⠈⢊⠇⢈⡼⠐⣺⢢⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠢⡈⣢⠔⡂⠬⠍⠛⢫⠅⠩⡭⠍⠭⠄⢒⠤⡒⣐⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢥⠎⢅⠥⠂⠈⠉⠉⠉⠐⠂⠉⠉⠉⠀⠒⢅⡊⣃⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠶⡀⠀⡄⠀⠀⠀⠀ ⠀⠀⢀⢠⡄⢀⣓⣲⡁⠀⠀⠀⢀⠔⠂⠈⠁⠐⠢⢴⡓⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⣱⡣⠔⠒⠒⠒⠤⡀⠀⢖⠴⠀⡞⠀⠘⡀⠱⠂⠇⠀⠀ ⠀⡜⠁⠐⢄⣰⠄⡺⡠⢄⠀⡔⢁⠄⠊⠉⠉⠁⠢⡌⢻⠇⠀⠊⠉⠐⣄⠀⠀⠦⠴⠀⠀⡴⠊⠐⠒⠌⣷⠏⠠⠂⠈⠁⠐⢤⠈⢆⠘⡀⢄⢧⠀⠀⢃⠇⡜⠀⠀⠀ ⠸⠀⠀⠀⣆⡸⢀⠉⡰⡸⠸⡐⠁⠀⠀⠀⠀⠀⠠⢔⡏⠀⠠⣮⣥⣂⠀⠀⠀⠀⠀⠀⠈⢀⣰⡤⠢⠀⢸⣎⠠⠤⠀⠀⠀⠀⠑⠌⡆⡨⠓⡹⠓⠚⡷⣉⠩⠓⠀⠀ ⠀⠣⣰⠁⠀⠇⡜⢏⡠⠁⠀⠀⡆⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠙⠉⠘⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠁⠀⢸⠀⠀⠄⠀⠀⠀⠀⢠⠊⠁⠃⠁⠀⠉⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡤⣼⠉⠁⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢠⢧⠋⢙⠀⠀⠀⠀ ⠀⡰⡉⢣⠈⠀⢣⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢰⡀⠀⢀⡀⡐⠀⠀⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⢠⠁⡞⡒⢁⠼⢄⠀⠀ ⠔⠢⡘⣄⠏⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢀⠠⢂⢗⣄⠘⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⢑⡄⡠⢎⢃⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⡇⠀⢸⣤⡂⡔⠊⠂⠀ ⠈⠁⠋⡏⠀⠀⢀⠀⠀⠀⠀⡀⡀⠀⠀⣸⠀⠤⠐⠺⠩⢜⣧⠽⠉⢰⠀⠀⠀⠀⠀⠀⠀⢷⠁⠹⡸⠭⠴⣅⡀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⡝⢅⢃⠇⠀ ⠸⡀⠀⠃⠀⠠⣎⠀⢀⣰⠉⠀⠋⢡⠊⠀⠀⠀⠀⢰⢨⢡⢂⢇⠈⢱⠀⠀⠀⠀⠀⠀⢰⠁⢑⢲⠎⡩⠁⡇⠀⠉⠁⠀⠙⢆⠀⠀⠀⠀⠀⣠⢷⠀⠀⠁⠈⣎⠄⠀ ⠀⡷⠆⠀⠤⡂⢊⡇⡎⢸⠀⠀⢈⢸⢀⣀⠀⡄⠀⠈⠆⣊⢏⠷⡢⢸⠀⠀⠀⠀⠀⠀⠘⣔⡡⢏⠁⡱⠱⠀⠀⠀⡀⠀⠀⠀⢣⠀⠀⠀⡠⠦⡢⠑⣢⠤⢞⡌⠋⡆ ⠀⢫⠤⠬⠕⠂⠁⠈⠁⢸⣀⡄⠸⠀⡏⢰⢱⠀⠀⠀⠈⢆⢞⡸⡬⣑⢆⠀⠀⠀⠀⠀⠀⠱⡜⡌⡖⡑⠁⠀⠀⠀⠇⠀⠀⠀⡸⢱⢀⠔⠁⠀⠈⠀⠒⠛⡒⠀⠀⠀ ⠀⠐⡄⠀⠀⠀⠀⢠⠀⠉⠀⠀⢀⠤⠁⠘⣼⠀⠀⠀⠀⠀⢊⢂⢳⠀⠈⠢⡀⠀⠀⠀⠀⠀⠘⡜⠌⠀⠀⠀⠀⠀⡆⠀⠀⡰⢡⠧⢣⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀ ⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⡇⠇⠀⠀⡀⠀⠀⡌⣁⡄⠀⠀⠸⠉⠠⡀⠀⠀⠀⠹⠀⠀⡀⠀⠀⢠⣁⠠⢈⠄⢹⡀⣄⡄⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀ ⠀⠀⠈⢄⠀⠀⠀⡰⣇⠀⠀⠸⠀⠀⢀⡜⠔⡌⠂⠄⠉⡀⠀⠠⡇⠇⠀⡌⠀⠰⠤⠞⠀⠀⢀⡇⣀⡒⣁⡀⠴⡚⢀⠜⡉⠬⠐⠪⠤⣇⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀ ⠀⠀⠀⠈⠦⡀⢠⠱⠣⡣⢒⣀⣀⠲⡙⡅⢸⠇⠀⠀⠀⠀⠀⠰⡇⢅⠀⠐⣀⠀⠀⠀⠀⣠⡎⡄⠀⠀⠀⠀⠀⢧⠢⠋⡀⠤⠤⢄⣰⠁⠈⡆⢀⠴⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢎⠀⠁⠪⠄⠀⠀⠬⠊⣰⠏⠀⠀⠀⠀⠀⠀⢰⢱⣘⡀⠀⠀⠉⠀⠈⢁⠥⢢⠀⠀⠀⠀⠀⠀⠈⢦⠊⠀⣀⠰⡁⠀⡱⢎⠀⢀⠦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠈⢆⢆⢑⢄⣀⣀⡀⢤⢫⢍⠎⠀⠀⠀⠀⠀⠀⠀⠸⣠⣴⠁⠀⢈⠊⠀⠀⢱⠁⠀⠈⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠢⢀⣀⡀⠤⠂⠁⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢅⡒⣤⢤⠧⣈⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠱⢞⠩⠥⠬⠥⣄⡠⡮⡴⡬⠍⠳⣅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⢔⣀⠺⢯⡵⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢔⠢⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠺⣧⢘⠲⠤⡔⠒⠁⢹⠀⡎⠀⠶⠥⠊⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠈⠑⠂⢌⠢⡙⢮⡂⠕⠢⢄⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⡠⠔⡪⢜⡟⠤⠙⠚⣤⣥⣜⣠⣃⣴⠤⠚⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠚⠪⢎⠂⠌⡂⠠⢍⡒⠀⠠⠤⠤⠄⡀⠠⠤⠤⠄⠀⣒⠩⠄⢒⡡⠈⡡⠐⢊⣁⣀⣀⡀⠀⠉⠂⠀⠈⠂⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠉⠒⠀⠠⠤⢽⣉⡏⡍⣣⣉⣉⠠⠤⠀⡲⢫⡬⠄⠚⠉⠉⠉⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠙⣦⠤⡤⠄⢒⡵⠗⠉⡑⢍⣉⣉⣥⠴⡚⠃⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠀ ⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢠⠢⢁⠀⠱⢩⢲⡮⢠⠒⠓⠫⣕⢠⠘⢕⢄⠑⢄⠀⠈⠁⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⠀⠢⡀⠀⠈⠒⠤⠤⠤⠤⠒⠈⠀⠀⡠⡂⠃⡈⠀⡘⡐⡘⢰⠀⠑⡀⠀⠈⡄⠱⡀⢂⠡⡀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⣑⢌⠐⠄⢀⡀⠀⠀⠀⣀⠠⢔⠨⠊⠀⠐⠁⠠⡁⢡⠁⠎⠀⠀⡇⠀⠰⡏⡄⠱⡀⠡⡈⠢⡀⠈⠁⠒⠠⠤⠤⠄⠒⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣲⣑⠤⣄⡀⠉⢉⡃⠀⠈⠀⢀⠠⠊⢀⢔⠅⢑⠡⠊⠀⠀⠀⢣⠀⠀⠰⠈⢄⠐⢄⠀⠢⡈⠁⠢⠤⠀⠀⠠⠄⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢎⠒⢨⠋⠀⠴⢀⢀⣧⡔⣂⣈⠁⠠⠒⡁⠕⠈⠹⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⠄⢑⣠⣁⠒⠤⢁⡐⠢⡤⠤⠤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠗⠀⠀⠀⢀⠄⠉⠀⠀⠈⠉⠀⠉⠓⠒⠐⠀⡝⠄⠆⠀⣃⠀⢪⠀⠢⢠⠙⠀⠀⠀⠀⠈⠉⠁⢀⠔⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡀⣜⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠶⠤⢅⠥⠊⠣⠭⠋⠀⠀⠀⠀⠀⠀⡠⠒⢆⠀⡤⣀⠗⠙⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡎⠀⠀⠀⠂⢄⠠⣈⠩⢕⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢎⠀⢀⣠⠃⠀⠈⢂⢄⢀⠗⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⢀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢲⠁⠀⢀⡕⠁⠈⠑⣄⠔⠁⠀⠙⡄⠀⠘⠀⠤⠀⠀⠀⠀⠀⠀ ⢀⢄⡲⠍⠤⣀⡀⠠⠾⢯⣝⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠬⢖⣂⡸⠤⠤⠤⠤⠼⠤⠤⠤⠤⠊⣐⡚⢥⠔⠀⠀⠀⠀⠀⠀ ⠆⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠤⠤⢄⣈⣈⣁⣁⣀⠤⠤⠄⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠚⠡⠖⠶⠒⠦⠴⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀