⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢐⠒⠒⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠘⢲⣄⢿⡵⢯⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⡤⡙⣦⢿⣛⣾⣿⣽⣎⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠠⢄⣳⢟⡕⡾⣼⣳⣟⣿⣾⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⢀⣡⠞⠁⡎⣽⣻⣽⣷⣻⣿⣾⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⢆⠀⠀⠀⢀⠞⠑⠀⡼⡸⣜⣿⢾⣽⢿⣻⣾⡅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠔⠒⣒⠒⠒⢃⠀⠀⠉⠓⠒⠯⣀⣑⠾⣕⡳⣽⣿⢻⣾⢯⣟⣿⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⠁⠀⠀⠀⠀⢠⠃⠀⠀⠈⠧⣄⠀⠀⠠⠐⠒⡨⣍⢛⠿⠿⢯⣿⣞⣿⣾⣽⡓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠴⠁⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⠈⡉⠓⢦⣁⠣⢔⡩⣜⡺⡽⣾⣷⣿⡶⣷⣞⡛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⠄⠂⠀⠐⠀⠉⠙⠓⠚⠵⠷⢽⣷⣻⣾⣽⣳⣭⠧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠂⠀⠀⠀⠀⠀⣳⣮⡄⠀⠀⠀⠀⠈⢉⠉⡉⢁⠒⠤⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢀⠂⡔⢠⡁⢦⠘⡔⢣⡙⠦⡑⠤⡘⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢁⠊⠴⡘⣄⠚⡤⢋⠜⣡⢊⠱⡈⡕⡨⡑⠆⡕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣡⠖⠁⠀⠀⠀⠀⠀⠀⠐⢬⡢⠀⠀⠀⠰⡨⢌⠳⡴⣨⡑⢢⠁⢎⠰⣈⠱⡐⢆⠱⡘⢌⡘⠜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠮⠃⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠌⠳⠦⠬⢃⠥⢉⠒⡑⠦⢭⠳⢬⡂⢁⠢⡑⠬⣘⠢⣉⠒⡌⠦⣩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡌⠀⠀⠀⡀⠀⠀⠀⠈⠪⢄⣀⡀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡄⠃⠌⡱⢈⠅⡈⠄⢢⠑⡌⡱⢊⠵⢣⡙⢦⡐⠨⡑⠤⠓⣌⠱⣌⢓⡰⢪⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⡐⢉⠰⢠⠁⠎⡐⢌⠢⡱⢌⡱⢍⠮⣅⢏⠧⢯⣱⡌⢧⡹⠤⣓⡴⣫⠞⡱⢆⠷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⡠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡁⠤⠁⢎⡐⠌⢢⠑⡌⢆⡱⢊⠴⣉⠶⣘⢎⡙⢮⡱⢎⡳⣜⢣⠳⡜⣥⢫⡕⣫⠞⡜⡄⠀⠀⠀⠀⠀ ⠀⠀⢀⠎⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⢂⠉⠤⡘⢄⠣⣜⣴⣧⣆⠙⢦⡑⢎⠴⣊⠝⣢⠝⣮⢱⢎⢧⢫⠵⣎⣳⢚⡵⢪⡕⡹⠀⠀⠀⠀⠀ ⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠂⡘⠄⡘⢌⢲⣿⣿⣿⣿⣯⠠⡱⢎⣧⣭⣼⣡⣛⠖⣯⢺⢬⢣⣛⠴⣣⢏⡞⣱⢎⡝⢇⠀⠀⠀⠀ ⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⡴⣶⣶⢦⡐⡌⠰⡈⢆⠻⣿⣿⡿⢏⡠⢳⣾⣿⣿⣿⡿⣷⡝⢦⣋⠞⡵⣎⢯⠵⣮⢝⡎⡞⡜⠾⡀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣄⠀⠸⢿⣿⣿⠏⠀⠀⠀⠀⣴⡝⠋⠙⠛⠛⠋⠉⠁⠈⢛⣿⡄⢁⠢⠌⡒⢡⢊⡜⠤⡓⢿⣿⣿⣿⣳⣿⢿⣿⡆⣹⠺⡵⣎⡻⣞⡵⢮⣝⣣⢏⡳⢃⠀⠀⠀ ⡌⠀⠀⠀⠀⠀⠀⠀⣐⠋⠀⠂⠏⣣⠀⠀⠈⠀⠀⠀⠀⠀⠀⢻⢧⡀⠀⠀⠀⠀⠐⡀⣡⣾⡿⢁⢠⢂⠱⣈⠥⢒⡘⢦⡙⢺⣿⣿⣾⣿⣾⣿⡿⢡⡳⢏⡷⣭⢳⡝⣞⣳⢎⣧⢻⡜⣋⡄⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⣶⣲⣖⣲⣷⠿⠟⠋⢠⠐⡂⢆⠱⡄⣋⠦⣑⠦⡙⢆⠶⡹⢿⠿⠟⣋⢴⡳⣝⢯⡞⣵⢯⣽⢫⣞⢯⡞⣧⢏⣧⢳⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠻⡦⣰⡶⡫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⢂⠡⠌⠰⡈⢆⡱⠐⡜⣌⠲⣉⢎⡣⢝⠪⣜⢢⡙⢦⡝⣮⢗⣯⢷⣫⣞⡟⣞⣯⣞⢧⣟⣲⣋⡄⠀ ⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠆⠂⡌⠢⠉⢆⡑⠦⣈⠳⡘⢤⠓⣬⠢⡝⣬⢓⡜⢦⡛⣦⢻⣜⣯⡞⣷⣻⣼⣻⡽⣶⣫⢿⡜⣧⢽⡇⠀ ⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠠⡈⠰⠀⡅⢋⠴⣈⠲⣡⠣⡝⢢⠝⣢⢝⡲⢥⢫⡜⣣⡝⣮⢗⡾⣞⣽⣳⡽⣶⢯⡷⣯⣟⣷⡻⣝⡾⠇⠀ ⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠡⢀⠂⣁⠒⡈⢆⠸⣌⠱⣂⠧⢭⡙⣎⠵⣪⢕⡫⢶⣩⢧⡻⣜⣯⢟⡽⣞⣷⣻⡽⣯⣟⣷⣻⢾⣽⣛⣦⠁⠀ ⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠁⠂⠡⠐⡀⠢⠀⠆⡁⢎⡒⣌⢣⠱⣊⠳⡜⣬⢳⡱⢎⢷⢣⢧⣏⢷⣛⣮⢿⣽⣻⢞⣷⣻⢷⣻⡾⣽⣻⢾⡽⡜⠀⠀ ⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡠⢈⠂⠡⠐⡀⠡⠘⠰⢁⠎⡴⣘⠬⢳⣉⢳⡙⢶⢣⣝⣫⢞⡭⣞⡼⣏⡿⣞⣟⡾⣽⣻⢾⡽⣯⣷⢿⣯⣟⣯⠷⠁⠀⠀ ⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠐⠄⠃⡁⢃⠐⢂⡁⠣⢜⡰⢆⡓⣎⢇⡎⢧⡹⢎⡷⣎⢷⣫⢾⡵⣫⣟⡵⣟⡾⣽⣳⢯⡿⣽⣳⣯⢿⡾⣽⣞⣃⠀⠀⠀ ⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⡠⢁⠂⠌⢠⠐⡡⢆⠰⢣⠹⡜⢮⡜⣣⡝⣮⢳⡝⣞⣧⢿⣹⢷⣫⢿⣝⣯⢷⢯⣟⣽⣳⢯⣟⣯⣟⣷⣻⣎⡄⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠠⠐⠈⠄⢃⠘⠤⢈⠎⢥⢋⡜⣣⢞⡵⢻⣜⡷⣻⡽⣞⣯⣟⣯⣟⣯⣞⡾⣯⢿⡾⣷⢯⡿⢾⡟⣞⡻⣝⣯⢾⢆⠀ ⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢠⡩⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠂⠈⠄⠌⠢⡘⢦⡙⣦⣋⡞⣷⢫⣾⢷⣻⢯⡷⣯⣷⣿⣾⣧⠃⠀⠁⠜⢠⠃⣎⠱⣚⢶⡹⣝⡾⣯⣛⡄ ⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡰⢧⣟⣿⡹⠒⠤⢰⣒⠂⡄⢀⠀⡀⢀⠀⠀⠀⠀⠈⢀⠐⡈⠔⡱⢪⣕⣣⢞⣽⣚⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠣⢄⠳⣘⢮⡽⣾⣽⣳⣯⢡ ⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⣌⠷⣟⡺⠊⠀⠀⠀⠀⠀⠈⠉⠒⠂⠥⠌⣠⣁⠄⠒⡀⠢⡐⢤⠒⣵⢳⣮⣿⢿⣾⢿⣿⡿⣿⣿⠟⠿⠟⠙⠊⠉⠀⠀⠑⢄⠀⠀⠁⢂⠢⣑⢮⢷⣻⣾⣽⣻⡘ ⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠛⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠓⠚⠤⠙⠴⠋⠥⠉⠛⠚⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠑⠦⣐⡍⣞⢯⣷⡿⢽⠕⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡒⠪⠽⠿⠻⠭⠓⠁⠀⠀