⣟⡽⣯⣟⡽⣯⢻⡽⣹⢯⡽⣫⣞⡽⣳⢏⡖⡡⠂⠀⠀⠀⠀⠀⠄⠠⠀⡀⠀⠀⠀⠀⠀⢼⢣⣏⡞⡵⣋⡼⢣⡝⡲⣍⠶⢣⠞⡴⢣⢎⠲⣡
⡿⣽⢯⣟⡽⣯⢻⡽⣹⢯⡽⣫⢷⣫⢟⡼⣣⠆⡂⠄⠀⠀⠀⢀⢆⡄⢂⠄⡀⢠⡤⣀⡀⠈⠞⣱⢫⠞⠱⠋⠚⠱⣣⠝⡲⣍⠶⢣⢎⡖⢥⢎
⡝⣯⣟⡽⣯⢻⡽⣫⡽⢯⡽⣫⣞⡽⣹⢞⡥⢂⠄⠀⠀⢠⢆⡖⣡⠆⡠⡘⣱⢋⡬⣑⢣⠆⡄⢂⠄⡀⠀⠀⠀⠀⠀⠸⣜⡱⢎⡖⣣⢎⠖⡥
⡜⣯⣟⡽⣯⢻⡽⣫⡽⣏⡽⣞⡽⣹⢎⠵⣊⠶⡱⣊⠔⠢⢂⠖⡡⣒⠆⣆⡔⡤⢒⠤⢃⠰⣂⠔⢢⠄⡀⠀⠀⠀⠀⠀⡳⢣⢞⡥⣚⠴⢣⢎
⢺⡽⣯⣻⢽⣫⣟⡽⣫⢷⢯⣛⡵⣏⡞⣱⢏⣞⡵⣎⠔⡠⠀⠀⠄⣊⠖⣱⢆⡒⠤⢂⠄⡠⠀⠀⠖⡨⠄⠀⠀⠀⠀⠀⢘⡼⣘⠖⣣⢎⠖⡥
⡽⣫⣟⡽⣹⢯⡽⣫⡽⣞⡽⣹⡽⢪⣗⢿⣹⢯⠛⠜⡢⠄⡀⠀⠀⠀⢘⡖⣣⠞⡰⢣⢞⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⠲⣣⠞⡴⢣⢎
⣻⡽⣯⣻⡽⣫⣟⡽⣹⢯⣳⢏⡷⣹⠖⣯⣿⢯⡐⣬⠒⡤⠀⠀⠀⠀⠀⢺⣳⢭⡖⣣⠎⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣊⠵⣊⠖⡥⢎
⣻⢽⣫⣟⡽⣫⡽⣫⡽⣞⡽⣚⡽⣺⢅⢺⣿⣿⣏⡞⡔⢂⠄⠀⠀⠀⠀⢸⢯⣳⢣⠆⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣚⠴⣣⢎⠖⣡
⢯⡽⣫⢽⡞⡽⣳⢏⡷⣫⢞⣳⠽⣳⡃⠜⣿⣿⢯⠞⡤⠂⠀⠀⠀⠀⡀⢀⠽⣎⠒⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡚⡴⢣⢎⠖⣡
⡳⣝⠾⣹⣳⢯⣛⡽⣹⣳⢯⡽⣺⡝⢦⠀⠸⣏⡗⠆⡄⠀⢀⢠⠔⡠⢂⡖⠤⢂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡖⡱⢎⡖⡥⢎
⢳⢭⡞⣳⢏⡽⣺⣝⡽⣺⣝⣳⢯⣞⠥⢂⠄⣿⣻⡽⣳⡭⡞⡔⡂⠄⠰⣋⡔⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣎⠖⣱⢎⠖
⡜⣱⢫⢞⡵⣫⢞⡽⣚⡽⣳⢯⡞⣽⠲⡄⠠⢹⣯⣟⡿⣽⢎⠖⡠⠄⠰⣣⠆⠄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡞⣜⠲⡱⢎⡖
⡜⣎⠼⣱⠭⣚⡵⢫⡞⣵⢫⢷⣫⢟⡜⡤⠀⢸⣟⡽⣻⡽⣎⠖⡤⠂⠰⡡⢂⠀⠀⠀⠀⠀⠀⠀⢰⢫⠀⠀⠀⠀⠀⠀⠀⠀⣳⣍⢞⡱⢎⡖
⡜⡲⣍⠶⢣⠞⡥⣚⠵⣫⢞⡽⣚⡽⢎⡖⠀⢸⣯⢽⣻⡳⣭⢒⡅⢂⡐⢂⠄⠀⠀⠀⠀⠀⠀⠀⣞⡵⣃⠀⠀⠀⠀⠀⠀⣏⡞⡵⣋⡼⢎⡵
⡜⡲⡱⢎⡖⡱⢎⡖⡭⣚⠵⣫⢞⡥⢚⡥⠂⣼⣻⡽⢯⡳⣍⠆⠄⢂⠄⡂⠀⠀⠀⠀⠀⠀⠀⢸⣳⡝⣧⢧⠀⠀⠀⢠⡞⣱⢏⡞⡵⢫⡞⣱
⡒⡵⣊⠖⡥⣚⠴⢣⠞⣱⢭⡞⡥⢂⠄⢠⡾⣻⣽⣻⡽⢎⠆⡄⠀⠠⡞⡤⠀⠀⠀⠀⠀⠀⠀⢸⣯⣛⡵⣫⣗⡽⣎⠷⣭⢞⡵⣫⢞⡵⣫⢞
⡒⡥⢎⡖⢥⢎⠖⡥⣚⡜⣽⡒⡅⠠⢲⣿⣻⣟⣿⡽⣳⢣⠆⠀⠀⠂⣏⠆⡄⠀⠀⠀⠀⠀⠀⠀⢻⡽⣺⡽⣞⡽⣳⠽⣳⢭⣞⣳⢽⣚⡵⣫
⢢⢇⢎⠲⣡⢎⠖⣡⠞⣱⢏⠄⠠⣼⣿⣿⣻⢿⣻⡽⣣⢎⡄⠀⢠⢪⠇⡆⡀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣻⢽⢯⣻⢳⣯⢻⡼⣏⡽⢯⣞⡽⣚
⢢⢣⠎⣒⠥⣊⠖⣡⢞⡧⠂⠄⣼⣿⢿⣧⣿⣻⡽⣳⢍⡖⡄⢂⠔⡌⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡽⣯⣟⡽⣳⢯⣟⡽⣞⡽⣫⢷
⢢⢃⡜⡰⢡⢎⠴⣃⡾⡀⠄⢸⣿⣻⠽⢳⢱⣫⢗⡭⢒⠆⡄⠂⠄⡂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣽⣻⡽⢯⣻⡽⣯⣟⡽⢯⡷
⠰⣡⠒⡥⢒⠥⣊⡼⡁⠀⢀⣿⣻⡽⣫⡽⡃⣷⡷⣌⠆⡄⠀⡀⠄⡀⠄⠀⠀⠀⢀⡀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣻⣟⣽⣻⡽⣻⣽⣻⡽⣯⣟
⠰⢢⡑⢆⡜⡰⢺⡇⠀⠀⣼⢿⡝⣮⠳⣝⢮⢽⣻⠼⣘⡖⣡⢎⡑⣉⠌⡄⢠⠂⠄⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⢿⣽⣻⢿⣻⣽⣻⡽⣻
⠰⣂⠜⡰⢂⡕⣿⡄⠀⡀⣿⢯⡚⡜⢦⠓⡬⢂⣿⢧⣹⠖⡱⣎⠱⣌⠆⣘⠄⠠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⣻⣿⣻⢿⣻⣟⣽
⡐⢆⡒⡔⡡⢒⣿⡽⡀⠀⣿⡳⣌⠒⡤⠂⠄⠂⠈⣟⡷⢣⢎⡖⣡⠆⡡⠂⡀⠤⡐⢆⡰⣀⠆⠀⡀⠀⠀⠀⠈⣿⣿⣿⢿⣿⢿⣿⢿⣻⣿⣻
⡐⢆⡒⡔⢢⢺⣏⢿⡀⠀⣿⣳⢌⠆⡀⠀⠀⠀⠀⠘⣿⡱⢎⡌⡄⠂⠄⡀⠆⣰⢯⡗⣣⢎⡒⠤⢂⠄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣻
⡐⢆⡒⡔⢢⢺⡇⠀⡇⠀⣿⣝⡖⠢⡀⠀⠀⠀⠀⠀⠈⢳⣇⠆⡄⠀⢤⠂⣼⣟⡽⣚⡵⢣⢎⡔⢂⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿