⣻⣞⣿⢿⣻⡟⣿⢻⡿⣽⣏⢿⡜⣥⣋⠶⡩⢖⡡⢒⠰⡐⠄⡀⠂⠀⠂⡀⢀⠀⠄⢠⠀⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠄⡀ ⣻⣾⣻⢯⠷⠹⢏⢿⡽⣳⣞⣳⡽⢶⣍⣳⣙⢦⡙⠂⡁⢄⠰⢠⡁⢎⠐⡄⢢⠘⡌⢄⢊⠐⡀⠂⠌⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡁⠀⠁⠈⠠⠁⢂⠀ ⣿⣞⡿⡭⠀⠀⠀⠈⠱⣚⢾⠳⣯⣳⠾⣱⠎⠁⢄⢢⡉⢆⡱⢡⠜⡂⢧⡘⣅⢚⡰⡈⢆⡘⠠⢁⠆⠐⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠌⢀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠐⠀⠀ ⡿⣞⢧⠁⠀⠀⢀⠄⡀⢀⠑⣵⢳⡭⠊⢄⡰⣉⢆⡣⢜⠢⣕⠣⢎⡵⢂⠳⣌⢆⠲⣑⠢⢌⡑⠂⡌⠠⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡐⢈⠠⠀⠌⡐⢀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀ ⡿⣙⠦⠀⠀⠀⠂⠁⠐⠀⠀⠈⢋⢀⡘⢦⡑⢮⡜⢴⢋⡵⢪⡝⡲⣌⠏⡵⣊⡜⢣⣌⠣⢆⠌⡱⠠⢁⠂⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢂⠅⡒⢄⠊⡄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀ ⢷⠩⠄⠀⠀⠀⠀⠀⠀⠀⠀⢔⡉⢦⡘⢦⡙⢦⡚⡜⢮⡜⣣⢞⡱⢎⡝⣲⠱⣎⠳⣌⠳⡌⢎⡰⢁⠎⠠⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢘⡘⣨⠣⢌⠡⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⠖⡀⠀⠀⠀⢀⠠⢀⠢⡸⢔⡹⢦⡙⣦⠝⣦⢹⣜⣣⢗⡶⣫⡜⣧⠽⣬⢳⡜⡝⣬⠳⡜⢢⡑⢌⠢⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠑⠄⠈⡂⠃⡉⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡻⡐⠀⠀⠀⠂⠁⠀⢠⢲⢱⣋⢖⡣⣝⡖⣻⣜⡳⣎⢷⣫⢾⡵⣛⡾⣝⣮⡳⣝⢞⡴⢫⡜⢣⠜⢢⢁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠂⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⡄⠐⠀⠀⠀⠀⢀⢇⣪⣓⡞⣮⢵⣫⢞⡵⣞⣵⣫⣏⡷⣯⣞⡷⣻⡽⢶⡻⣝⡮⣝⢧⢞⡱⣊⠥⢂⠌⡀⠂⠀⠀⠀⠀⡀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆⠁⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡛⠴⠀⠀⠀⠀⠀⡞⣎⢶⣹⣜⣧⡻⣼⣻⣼⣻⣖⢿⡾⣽⢾⣭⣟⣷⣻⢯⣟⣳⡽⣎⣟⢮⠱⣌⠲⢁⠂⠄⠀⠀⠀⠀⠠⡐⡡⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡉⠅⠀⠀⠀⠀⢠⡻⣜⡯⢾⣹⢾⣽⣳⣟⣾⣳⢯⡿⣽⣞⣯⣿⣯⢿⣭⢿⡼⣳⣝⠾⣜⢮⡱⠌⢆⠡⢈⠀⠀⠀⠀⠀⠀⡕⢀⠣⠄⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡿⣾⣹⢿⣏⣿⡾⣿⡾⣷⣿⢿⡿⣿⢷⣏⣷⣏⡿⣿⡾⣏⣷⣉⢿⡸⣆⢇⠹⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠆⠆⠉⢶⠀⠈⢀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡵⢻⣜⣯⣟⣾⣳⣿⣽⣻⣷⡿⣯⣟⣿⣻⣾⡽⣾⡽⣳⡻⣞⢶⡹⢎⡖⢥⠊⢆⠡⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠠⡀⠄⢢⠘⡀⢈⠀⡐⢀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢝⣻⢾⣽⣻⣾⣟⣷⣿⣻⣽⡿⣿⣽⡷⣟⣾⡽⣖⣻⡳⣝⢮⣣⢛⡼⣘⠢⡉⠄⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠐⡀⠌⠃⡜⠤⠣⢜⠰⡀⠆⢄⠂⡄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⢨⡷⣿⢾⣿⢯⣿⣯⢷⣿⣻⣽⣿⣳⣿⣻⣽⣻⣭⢳⡽⣙⡎⠶⣩⢒⠡⢒⠡⢈⠀⠀⠀⠀⠀⢀⠂⠄⠀⠀⠀⠀⠂⠀⠀⠀⠐⠨⢱⠩⢌⠢⡑⡈⠆⢩⠐⣁⠂⡌⢠⠐⡠⢂⠀⠐⢀⠀⠠⠈⠀⠀⢀⠀⠀ ⠀⠀⠀⠀⠀⢸⢣⡿⣽⣟⣿⣻⢷⣻⣟⣾⣽⣳⢯⣟⣾⣻⣞⡷⣭⢻⠼⡱⢎⠳⡡⠎⡀⠡⠐⡀⠀⠀⠀⠀⠀⠌⡐⠀⠀⠀⠀⠁⠀⠀⠀⣠⢙⡕⡠⢄⡈⠁⠐⠁⠘⠠⢁⠆⡱⢈⢆⡱⠤⢁⠌⠐⡀⠂⠁⠄⠀⠌⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⣹⢷⡿⣞⣿⣻⢷⣻⣞⡷⣯⣟⢾⣳⢯⣞⡽⣜⢫⠞⡱⣍⠲⡁⠆⡁⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⢀⠲⣡⠓⡼⣘⢆⢇⠣⠄⡄⠁⠂⢈⠐⡁⠣⠌⡰⢈⠆⡘⠠⢀⠁⠠⢀⠁⠂⠌⢀⠂ ⠀⠀⠀⠀⠀⠀⠗⣯⢿⣻⣟⣾⡽⣯⣳⡽⣞⡵⣯⢯⣳⣏⠾⣜⢣⠏⡜⣑⠢⡑⠌⡐⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⢅⡣⢇⢸⡰⢃⢎⡌⢃⡒⡈⢁⠊⠀⠄⠐⠠⠐⠀⠂⠐⠁⠂⠄⠂⠡⢀⠌⡐⠈⠄⠀ ⠀⠀⠀⠀⠀⠀⠨⣟⣯⣟⡾⣽⣳⢷⡻⣼⢳⡻⣼⢫⡗⣮⢛⡬⢣⡙⠴⢁⠆⣁⠒⠠⢁⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣈⢆⠇⣏⠲⣡⠋⡔⡈⢆⡐⢁⠂⡀⠁⠄⠀⠀⠀⠀⠀⢂⠈⠐⠠⠂⡁⢂⠆⡈⠔⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡼⢯⣟⣳⢯⡷⣻⢽⡳⣟⡵⣫⠞⣥⠫⡔⢣⠜⠢⢁⠢⠀⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⢎⡹⢤⠓⡆⢣⠰⡁⢆⠐⡈⡐⠀⡀⠂⠀⠀⠀⠈⡐⠀⠀⢈⠀⠀⡐⢂⠐⠠⠐⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⣙⢾⣛⢾⣹⢮⡷⣽⢺⡵⣫⢞⣱⢋⠶⡱⢌⠣⡘⢠⠁⢂⠁⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡊⠴⢣⠍⣆⡑⢢⠑⡌⠄⠡⢀⠁⡀⠄⠀⠀⠀⠀⠐⢀⠂⠀⢀⠂⡐⠠⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⢮⡝⣯⢳⣏⡷⣭⣳⡹⢵⣪⠕⣋⠖⡱⠈⠆⡁⠂⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠹⢌⢣⠚⡤⡘⢄⠣⡐⣈⠁⢂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⢦⠻⣜⣏⠾⣱⢧⢳⡹⢣⢎⡝⣢⠙⠤⢉⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡜⡌⢳⠰⡉⢆⠱⡐⠄⡈⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀