Black and white bird Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠛⠛⠉⠉⠉⢀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣋⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠕⠉⡠⠀⢡⡶⢀⠀⠀⠨⣽⣷⣾⣿⣿⡿⠿⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡀⠐⢃⠴⢉⠀⠀⠁⣴⡴⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣴⢆⡀⠀⠀⠂⡠⠀⢁⠖⢁⡶⣡⠄⡰⠃⠀⠔⠀⠐⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣨⣵⡤⠔⠂⠛⠓⡤⣂⡠⢞⡡⠌⡽⣷⠟⠀⠀⠀⠀⠀⢠⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣻⠭⣖⠏⠀⠀⢀⣤⣾⣉⡾⠽⢚⡵⠚⠃⠀⠠⠀⠀⠠⡀⢠⣥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠿⢛⣄⢀⣤⣤⢴⠿⣿⣿⣿⣿⡿⠭⠛⠁⠀⠀⠀⠀⠀⢀⡄⣸⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣅⡚⠛⠒⠐⠶⠽⠭⠭⠿⠿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠂⠀⠠⠸⠶⠋⠀⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣷⣶⣶⠿⢷⠺⢛⠛⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⡿⠉⠀⠀⢠⢂⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⢁⡠⠖⠫⠹⠧⢼⣓⣼⣄⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠛⠛⠻⣤⣴⠖⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⠏⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⣬⡅⠂⠀⠀⠀⠀⠀⠀⠀⣸⣟⣡⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⠝⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣠⢜⣻⠟⠻⠿⠁
⠀⠀⠀⠀⠀⢀⡠⢒⠭⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣦⡀⢐⣨⠶⠛⠁
⠀⠀⢀⡤⣚⡭⣞⣡⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣾⣿⠁
⢠⣾⣿⢟⡭⣊⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣠⣾⠿⠻⠼⠟⠋⠁
⠀⠘⢿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡭⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣤⣴⣤⣀⣴⣾⠿⣿⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣿⣿⣟⣿⡟⠀⠀⢰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⢾⣿⡿⣯⣯⣁⣄⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⠈⣟⠁⣿⡿⠛⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠁⠀⠀⢀⣴⡇⣠⣿⡀⢈⠀⠀⢀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣤⠶⣾⡿⠈⣿⠿⣿⠟⢻⣿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⠉⠀⠟⠀⠘⠁⠀⠀⣶⠀⢠⣾⠇⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡈⠻⣿⣷⣶⣦⣀⡀⠀⠀⣿⠃⠘⣿⡀⢈⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡆⢻⡇⠀⠀⠈⠀⠀⠚⠛⠀⠰⡏⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⣿⣿⠋⣹⣿⣿⣧⡀⠀⣀⡀⠀⠀⠀⠀⡀⠀⠀⢈⣤⠜⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠀⠸⠋⣡⣜⣻⣿⢿⣿⡇⠀⢿⡇⠀⠀⠀⣼⣇⠀⠀⣘⠁⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⡏⢻⣦⠀⣶⡦⢸⣿⠟⢳⣾⣻⡿⠀⠀⠀⠀⠀⠀⣿⡿⢠⣾⠏⠀⠸⣿⣇⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢰⠀⠉⠀⠛⣡⣠⣼⠄⢿⡿⢏⠁⠀⠀⠀⠀⠀⠀⠟⠁⠄⢠⣶⠀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠟⠉⢋⣠⣤⣾⠿⠁⠀⢀⡀⠀⠀⠀⠀⠀⣰⡿⣿⡀⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⣤⠀⠀⣠⣴⠿⣇⡼⠧⠀⠀⠀⢙⠃⠀⠀⠀⠀⢀⡬⢣⣾⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠏⣀⠀⢰⡿⠃⢀⣾⡿⣡⣾⣿⣷⠀⢠⠿⠛⠟⠁⣀⡀⠀⠀⠙⠁⣿⡏⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣼⡟⣠⡈⢁⡀⠚⠋⣰⣟⣻⣿⣿⠀⣸⣧⣤⠄⠀⠛⠃⠀⠀⠀⣾⡟⠁⣾⣿⣿⣿⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣈⣠⡿⠃⡿⠃⢠⣾⣿⣿⣿⣿⡟⠀⠙⠋⠁⠀⠀⢰⠶⠆⠀⠀⠀⠀⠀⠘⠿⣿⣿⡅⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠿⠃⣴⡿⣤⣿⣿⣿⣿⣿⡟⠇⠸⡷⠤⠀⠀⠀⠀⠈⠀⠀⣶⠀⣄⠀⠀⢶⣾⠏⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣤⠀⠉⣹⣿⣿⣿⣿⣿⣿⠧⢸⣿⣶⣶⠀⠀⡀⠀⠰⢲⡄⠀⠈⠋⢠⡀⠰⢣⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢰⡆⢸⡟⠀⣿⣿⡟⣹⣿⣿⣿⡿⣀⣿⣷⣶⡤⠠⠾⡃⠀⠀⠀⠿⠀⠁⠀⠘⢣⡿⠈⠁⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠀⠀⣙⠻⣿⣿⣿⣿⣿⣿⣿⣏⣝⠁⠀⠀⠄⠀⠀⠀⠀⣰⣶⠄⠀⣀⣿⠁⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢠⡄⠀⠀⠋⣤⡾⢿⣿⣿⣿⣿⣿⠿⠿⠓⠀⠀⠀⠀⠀⠀⡘⠋⠉⠀⢀⡟⢁⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⣇⣤⡀⢠⣿⣧⡾⢋⣼⣿⣿⣇⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⠊⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡄⢹⡇⣿⡇⣿⣿⣿⣷⣿⣿⣿⣿⣛⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣸⣿⠛⠁⠹⢻⣿⣿⣿⣿⣿⣿⣿⡿⠻⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠳⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⢋⣃⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠰⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⡅⣾⡆⣿⣿⣿⣿⣿⣿⣿⡟⣷⡔⠀⠂⢰⡆⠀⠀⠀⠀⡶⠁⠀⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢣⠈⢻⣷⠻⠇⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢈⠁⠐⠀⢠⠞⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣀⡘⠟⠀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⠀⠀⠀⡠⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⢸⣶⠘⠀⠀⢻⣿⠀⣼⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⣀⣀⣴⠏⠀⠀⠀⠀⠀⡼⠋
⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⠀⣿⢃⣼⣿⣿⣿⣿⣿⣿⢿⡷⠀⠀⠀⢀⣐⣾⣿⡧⠀⠀⢠⡀⣴⠆
⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⠁⣤⣄⢀⣼⢿⣿⣏⡁⢀⣰⣿⡇
⠀⠀⠀⠀⠸⠿⠋⠀⠉⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⡿⠟⣻⣿⡏⢠⣿⣿⣴⣿⠿⢻⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢃⣿⣿⣿⣿⣿⣿⣿⣣⡿⠉⠀⢀⣿⣿⡅⠀⠈⠻⢿⣅⣠⣾⣇⠀⠈⠁⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⡾⠀⣤⡤⣼⠟⠉⣠⣴⣶⣤⣤⣤⣿⢿⣿⠟⠳⣶⡶⢤⣤⣤⣤⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠐⣤⠳⡜⠁⣾⠶⣾⣿⡇⠀⠀⢠⠀⢠⡀⢸⠀⣀⢸⠇⣠⡄⠰⠆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⢠⠟⢀⠁⠀⠉⠐⣿⣿⡄⠀⠀⢸⠀⢸⣷⢸⠀⠀⠈⠀⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢿⣶⣏⣰⣿⡀⠀⠀⠀⢿⣿⡇⠰⡀⢸⠀⠸⣿⡆⠀⠀⠀⠀⢻⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⠁⠀⢀⠀⠘⣿⡇⠀⣧⣼⡄⠀⣿⡇⠀⠃⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⢠⣿⣿⣿⣿⡿⠀⠀⠈⠀⠀⣿⡇⠀⠹⣿⠀⠀⣿⡇⢰⠀⠀⠀⠸⡆⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⢰⣿⣿⢿⣿⣿⠇⠀⠀⠘⠀⠀⢻⣇⠀⢀⡿⠀⠀⣿⣿⡇⠀⠀⠀⠀⡇⠀⣾⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢀⣿⣿⠋⡈⢻⣿⠀⠀⠀⣴⡄⠀⢸⣿⠀⢸⡃⠀⢀⡏⣿⡇⠀⠀⠀⠀⠃⠀⠿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⢀⣾⣿⠇⠀⣿⢻⠁⠀⠀⣰⡟⠁⠀⣼⣿⠀⠀⠀⠀⢸⡇⢻⠆⠀⠀⠀⠀⠀⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣼⣿⡿⠀⣾⡏⠀⠀⠀⢰⣿⡇⠀⣴⠿⣿⠀⠀⠀⠀⠈⠇⢸⠀⠇⠀⠀⠀⠀⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⡿⠀⣼⠋⠃⠀⠀⠀⠻⣿⣿⣤⣿⣄⣿⠀⠀⡆⠀⠘⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⣿⠇⢸⠏⠻⠀⠀⠀⠀⠀⢻⣿⠏⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡏⠀⠇⠀⠀⠀⠀⢠⠀⠀⡘⣿⠀⠁⠹⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠑⠿⣤⣷⡀⠀⠀⠀⠀⠈⠀⠀⢙⡿⠀⠀⠀⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠙⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢰⠀⠀⠨⠠⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢣⠀⠀⡄⠀⠀⡄⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠑⣄⠠⡀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⢠⠀⠳
⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠈⢂⠈⠠⢁⠀⠀⣅⠀⠀⠀⠀⠀⠀⠀⡄⠑⠀⠀⠀⠃⠀⠀⠀⠀⢀⣰⢰
⠀⠀⠀⠀⠀⠀⢄⠀⡀⠀⠈⠀⠀⠑⠆⠈⠁⠀⠈⠀⠀⢀⠀⡀⠀⠀⠙⢰⡀⠐⠀⠡⣀⠁⡀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⢀⠀⠢⠈⠒⠄⠂⠀⠀⠀⠀⠤⣀⠀⠀⠀⠈⠢⡙⠀⠀⠀⡀⢦⠀⠱⠀⡏⠂⠐⠀⠿⢹⠱
⠀⠀⠀⠀⠀⠈⠯⡐⠘⠦⠤⢀⣈⠒⠀⠀⠀⠀⠈⠐⠀⢹⠂⠙⠀⠀⠀⠸⠄⠱⡀⠀⠣⠀⠀⠀⠠⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠊⢉⠑⢀⣀⠂⠠⠀⢣⡀⠑⡗⠀⠀⠀⠀⠀⠀⢀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠠⢄⣀⡀⠀⠀⡀⠀⠄⠀⠀⠒⠉⢀⠴⠀⢠⠃⠀⠀⢌⠛⡄⢀⣴⠃⠀⠀⠀⠀⢼⡧⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢀⡀⠀⠄⠀⠀⠀⡠⠀⠁⢿⠆⠀⠄⡀⠀⠀⠀⠙⠊⠁⠀⠀⠀⠀⠀⠀⢰⣏⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⣀⣀⠤⠀⠀⠀⠀⠄⠀⠐⡌⠀⠀⣀⠁⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠁⠑⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣀⠀⠊⡠⠀⠀⠘⢠⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠂⠀⠤⠀⢰⠣⠦⡞⠐⠈⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠔⠀⢐⡆⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣤⡀⡤⠀⠀⠀⢀⣀⠼⡇⠦⣀⠁⠀⣀⠀⠘⡄⢈⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠⠔⣀⡤⠖⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠀⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠒⢒⣩⠥⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⡔⡻
⠀⠀⠀⠜⠁⠀⠐⢊⡠⠔⢈⡡⠂⢀⠔⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠄⠀⠀⠁⠀⠀⠂⠈⣀⣀⠤⠞⡀⠔⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁
⠀⠀⠀⠈⠙⠛⠻⣿⣿⡟⠻⠓⣈⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠛⠛⠛⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⠀⠀⠀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠙⠳⠀⠀⡀⠀⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣷⣦⣄⣀⣉⣠⡀⡀⢄⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣶⣤⣬⣟⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠡⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣝⣟⣿⣿⣿⣿⣿⠿⠦⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣽⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠸⠟⠋⠉⠀⠀⣨⡟⠻⢿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠴⠒⠋⠉⠀⠀⢀⣀⣤⡴⠒⠋⠁⠀⠀⠀⠉⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠞⠀⢀⠄⠀⠀⠀⢀⡵⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣄
⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⣀⣀⣀⢀⣠⣴⣶⡶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠈⠙⠿⣿⣿⣾⣿⢷⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠙⠋⠀⣸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⢀⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠠⢤⣶⣶⣦⣄⠀⠉⠉⠙⠛⠻⠿⠿⢿⠿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣉⠛⠿⢿⡅
⠀⠀⠀⠀⠀⠀⠑⢠⣀⠀⠉⠛⠢⡤⠄⠂⠠⢀⣠⡴⠛⠙⠛⠛⢿⣿⣯⠉⠉⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠐⣀⣠⡶⠋⠁⡀⠀⠀⠀⠀⠀⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣾⣿⡿⠿⣧⣄⡀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡿⠀⠀⠘⣌⠁⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠙⠂⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⣴⣶⣾⣿⠿⢾⡉⠁⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⠋⠀⠠⠺⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠂⢀⡬⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⣿⠇⠀⣀⠠⣌⠿⣿⣦⡀⠰⣾⣧⣶⢆⡀⠀⣞⠃⠀⠀⠀⠉⠀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⣦⣀⠀⠀⣀⠙⠀⠀⠈⠀⢄⡀⢿⣿⣷⡀⠡⡽⠛⠟⠻⢞⡿⠦⠴⢀⠠⠀⠐⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠻⣿⣿⣀⣼⣟⣫⣽⣿⣦⣄⠹⡁⠌⠻⣿⣷⠀⠀⠀⠀⠈⠀⠀⠠⢄⠸⠇⠰⠶⠦⠤⡤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢉⣾⣿⣿⣿⣿⣿⣿⡿⠆⠇⠈⡀⠙⢿⣷⡀⠀⠀⢠⣤⣤⡤⣄⡴⢾⣟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⢿⣧⠀⠸⠛⠉⠀⠺⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢎⡀⠀⠰⣾⡆⢸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⣶⣶⣦⢘⣷⡀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠁⠙⡍⠘⣿⠉⠀⠀⠀⠀⢠⣄⣠⠴⠂⣨⠂⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⡠⠂⠀⠀⠘⣧⠀⠀⠠⠄⠀⠛⠁⠀⢸⡇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣷⠆⠀⠈⠀⠀⠀⠀⣰⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⡴⠟⠃⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠳⠀⠀⠀⠀⠀⠀⠸⠁⢄⠐⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠠⢀⣰⣷⣼⣄⣀⣤⣾⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠉⠹⠋⠹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠳⠆⠀⠀⠀⠀⠀⠀⠀⠰⣴⠟⠃⠛⡀⠀⠀⠀⠀⠀⠀⠠⠐⠆⢀⡤⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⣴⠶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⡔⠄⠀⠀⠀⠜⠁⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠈⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠛⠛⠂⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣀⣠⣴⣦⠐⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠉⠉⠑⣤⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠂⠙⢉⠿⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠻⠛⠀⠀⠙⠇⠀⠀⠀⠀⠀⢠⡚⠀⠀⠀⠀⠀⠈⠀⠉⡧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠅⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠙⠆
⠀⠀⠀⠀⠀⠀⠠⠎⠀⠺⠇⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠐⣿⠀⠁⠤⠸⣷⠀⠀⠠⠾⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠠⠀⠀⠤⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⢠⠀⠂⠠⡄⢠⠀⠀⠄⠠⡄⠻⠃⠀⠐⠂⠀⠆⠀⢠⠆⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⢠⣤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣶⣴⠶⡾⠒⠂⠐⠒⠓⠀⢀⣠⠄⠂⠀⠀⠀⠀⠀⠀⠀⣶⠀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⠙⠿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠘⣿⠃⠀⠃⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠰⠃⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⡀⠠⠄⠀⠀⠀⢙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⣠⣾⣿⠗⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠶⠛⠛⠛⠙⠛⢉⣡⠤⠀⠀⠀⠀⠀⠀⠀⠷⡄
⠀⠀⠀⠀⠀⠠⠾⣷⠆⠾⠿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⢠⠋⠰⠤⠶⠿⠓⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠹⡄⢢⠀⠀⠀⠀⠀⠐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢰⣤⠄⡄
⠀⠀⠀⠀⠀⣽⠂⠀⠀⠀⠀⠀⠀⠀⠛⣄⠇⠀⠀⠀⠀⠀⢻⡇⣐⠠⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠁
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠮⠻⡶⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⣧⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⢀⠀⠀⠀⠑⢤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠃⠀⢿⠛⠢⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢟⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡯⢫⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⣷⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣺⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢾⠃⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣿⡷⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣽⣿⢾⡀⣀⢀⠤⣴⣤⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢫⣎⡾⣡⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⡳⢏⣾⡿⣠⡔⠼⠋
⠀⠀⠀⠀⠀⠀⡸⢷⣷⡝⣿⣵⣳⢫⢿⣴⡦⢤⡀⠀⠀⣠⣾⣿⣿⠏⢉⣅⠟⣰⡿⡃
⠀⠀⠀⠀⠀⠀⡟⡘⣿⣻⡿⡿⡱⡿⣠⢎⡴⠫⣺⣷⣾⣿⣯⠶⠀⠀⢀⣾⡿⢻⣨⠌
⠀⠀⠀⠀⠀⢠⡏⣜⢿⣟⣏⣿⣽⣵⣷⣿⢶⣏⡿⢿⢿⡯⠆⢕⢀⡒⠮⢁⣤⡞
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⣿⣿⡿⣟⣩⣛⠷⠞⠗⠋⠐⠀⠀⢨⣸⣏⣤⢏⣹⠒⣰⡤⢀
⠀⠀⠀⠀⠀⠀⠙⠿⠛⣽⠟⣣⡾⠌⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣵⣿⣽⣿⣿⣾⣷⣮⣊⠐⢠⡞⡀
⠀⠀⠀⠀⠀⢀⣠⣤⣾⣷⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠽⣽⣿⡛⣿⣿⣿⣿⢷⠫⠟
⠀⠀⠀⢀⣴⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡿⣻⣿⣾⣽⣿⢷⡙⢟⣡⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⡼⠿⣧⣤⡤⠤⠒⠀⠀⠀⠀⠀⢀⣤⣾⣿⣷⣿⣯⢿⣿⣠⣷⣷⣷⡫⢦⠠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡄
⠀⢀⣼⣷⣦⡄⢉⠀⠀⣀⣠⣤⣄⣀⣠⣽⡿⣿⣬⣿⠷⣾⣟⣿⣿⣧⣿⡕⠚⡵⣚⢝⣻⠟⡸⢂⡶⠂⣐⡶⢖⣾⢷⣽⣟⡽⠟⠉
⠀⠈⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⣿⣉⣟⣭⣶⢻⣽⣾⠿⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡿⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣐⠺⠂⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣿⣿⣿⣯⣭⣝⣒⠊⣃⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠏⠗⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⣀⠱⣄⠀⢳⡀⠀⢠⡄⠀⢠⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠢⣀⠀⠐⡔⠁⠐⠈⠢⣀⢳⡀⠀⡱⠤⡬⠒⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢞⠀⠀⠀⢀⡀⠈⠺⢣⠊⠀⠘⠇⠀⠀⠀⠀⢰⠀⠀⠀⢀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠚⢥⢀⠎⠘⢧⡀⠀⡄⠀⠀⠀⢀⣧⠤⠒⠈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⡄⠀⠈⢳⡘⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⣿⣿⣿⣿⣶⣶⣶⣦⣧⣤⣀⡀⠀⢰⠀⠀⠀⢿⡤⠴⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡋⠙⠚⠛⠛⠛⠛⠺⠦⣤⣈⠈⣿
⠀⣀⣤⣴⣾⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣷⣶⣶⡶⠒⠒⠈⠻⣿⣿⣿⣿⣷⣦⣀⠀⠀⠠⠀⠈⠀⠚⠉⠛⠻⢀⣀⣤⠶⡿⠿⢿⡿⣶⣤
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠈⠻⠿⠿⣿⣇⢿⣿⡦⣀⠤⠤⠀⠀⠨⠀⠔⠛⠑⠋⢀⣴⣶⣿⣿⣿⣔⣽⣷⢶⡶
⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠄⣀⠀⠀⠀⠘⠻⢿⣯⣻⣷⡌⠻⣦⠀⠀⢀⣀⠀⣄⠀⠀⠋⠉⠉⠉⠉⠐⣹⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠀⠉⠛⠿⠿⠿⣮⡥⢤⢼⠯⠬⡝⠋⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⣤⠤⢀⣤⣤⡄⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡉⣸⣿⡃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⠁⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⣻⠟⠀⠀⢸⡀⠀⠀⠀⠀⠀⣀⠠⠐⠋⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠊⡼⠃⠀⠀⠀⠸⡇⢀⡠⣤⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣀⠚⣤⡀⠀⠰⣠⠄⣏⠁⠀⠈⠓⠦⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡑⢦⣰⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⡈⠃⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣽⠓⢤⡀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠬⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣻⣝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡻⣟⠣⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⣿⣗⢝⢎⠢⣀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣰⣻⣿⣿⣿⣿⣾⣿⣿⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣵⣿⣿⢿⣿⣶⣶⣿⣿⡿⠿⢻⣿⣿⣿⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣟⣻⣥⣔⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⢦⣤⣤⣦⣤⣛⡻⣿⠻⣍⣽⣯⠻⢿⣿⣿⣿⣿⣿⣿⣯⢀⣙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⡏⢹⣯⣿⣅⣨⠈⣿⣿⡿⠟⠛⢀⠀⢉⢩⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⢻⣇⢾⣡⠀⢨⣆⣐⣾⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣼⢿⡄⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢿⠈⢷⡀⠀⡏⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿
⠀⠀⠀⠀⢀⠸⡆⠈⢳⡄⢧⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⡿
⠀⠀⠀⠀⣿⠳⣽⣄⠀⠙⢾⣆⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⡞⠁⣸⡷⣿
⠀⠀⠀⠀⠹⣆⠈⠻⢦⡀⠀⠙⢦⡀⢸⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡼⠋⢀⣴⠏⢀⡟
⠀⠀⠀⠀⢀⣙⢦⡀⠀⠉⠲⢄⡀⠉⣾⠧⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢋⠔⣻⢂⡤⠋⠁⣠⡞⠁
⠀⠀⠀⠀⠸⣏⠙⠛⠶⣤⣀⠀⠈⠓⢺⣦⠈⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠁⠔⡿⠁⢀⡤⠾⠛⣿
⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠉⠑⠒⠻⣄⠑⠦⣀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣤⣄⣀⣠⠞⠓⠉⠁⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠶⠶⠶⠤⠤⠈⠷⢦⣄⣀⠀⠀⠈⣧⠀⠀⠀⠀⢀⡴⠋⠁⢀⣀⣀⡈⠙⢶⡖⠒⠻⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⡤⠤⠤⠤⠄⡴⠷⠤⠀⠀⢹⡄⠀⠀⢠⡟⠀⠀⠀⠀⣀⣀⠈⠳⡀⢳⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡟⠓⠒⠒⠒⠒⠈⠳⢦⡤⠄⠀⠀⠻⣦⣤⠾⠀⠀⠀⠈⠉⠻⠟⠀⢀⣿⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢲⡶⠶⠒⠊⠉⠹⣄⠀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⣤⠤⠒⠈⠉⠳⠲⡦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣤⠒⢁⡠⠊⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⢤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣇⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠉⠘⢧⠄⠀⠀⣀⡄⣀⣀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⣾⣋⠅⠀⢀⠄⠀⠀⠀⡾⣶⢿⢻⡏⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣀⣀⣤⣼⠟⠋⠀⢀⠔⠁⡠⠀⡔⢰⡇⢻⢸⡄⡇
⠀⠀⠀⠀⠀⠈⢙⡻⠛⠁⠀⢀⡴⠃⢠⠞⢀⡜⢠⠏⣿⢸⡜⢧⣿
⠀⠀⠀⠀⠀⠐⠿⠶⠤⠶⣺⠋⢀⡴⠃⢠⠎⢠⡟⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⢻⣧⡴⠿⡤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⣦⡀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⢻⣾⣿⡆⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢦⡘⣇⠈⠻⣦⡀⠀⠀⠀⣾⣿⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠙⠿⣆⠀⠈⠻⣦⡀⠀⣿⠙⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢦⡀⠈⠳⣄⠀⠈⠻⣦⣸⡆⠘⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠉⠳⢤⡈⠙⢦⡄⠀⠙⢿⣄⠘⢾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⢶⣄⡀⠉⠓⠾⣦⠀⠀⠀⠙⢷⣄⢹⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣶⠬⠍⠓⠲⠤⣷⣤⠀⠀⠀⠀⢻⣎⠣⣌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⣤⣤⣀⣀⣀⣣⣄⡀⠀⠀⠸⣏⠳⣂⡀⠈⢳⡄⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⣀⣀⣀⣈⣧⡄⠀⠀⠹⣷⣖⠆⠀⠀⢻⣤⣤⣤⡴⠞⠁⠀⠀⣾⣽⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣭⣉⣀⣀⣀⡠⠴⠧⡄⠀⠀⠈⠻⣶⡀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣭⣁⣀⡠⠤⠚⢓⡦⠆⢀⠀⠈⠙⠳⠶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠁⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣥⣤⡤⠒⠉⣀⠴⢻⡴⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⡴⠚⠁⣰⣋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣈⣷⠶⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡿⣷⠶⠶⣠⣦⣄⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⣡⡾⠃⢀⣴⣃⣼⣁⣾⣿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠋⠉⣀⣴⡻⠋⠀⡴⠃⢸⠏⣹⠋⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⢟⡵⠋⠀⣠⠞⠀⡰⠁⣰⠃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣾⡿⢋⡵⠋⠀⢀⡜⠁⢀⡞⠁⣴⠃⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⣠⡏⠀⢀⣴⡏⠀⣠⠏⠀⣼⣣⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠛⠙⠷⠞⠋⠈⢛⡾⠁⢠⡾⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢴⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠠⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡛⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠛⠶⣯⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠙⠲⡄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠒⡀⠲⠶⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢁⠎⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢦
⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⡀⡏⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢺⠀⠀⠈⢋⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠟⠀⣀⢴
⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠡⡑⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⡛⠃⠁
⣄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠑⠢⣈⠑⠢⣀⠀⠀⠀⠀⠀⡠⢘⡵⠋
⠛⣷⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠉⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢈⡲⣀⣀⣀⠞⡑⠉
⠀⠀⠉⠋⠶⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠠⡿⠿⣿⣷⣾⣦⣤⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⠣⢉⡉
⠀⠀⠀⠀⠀⠈⠁⣸⣟⠤⠾⠛⠛⠛⠛⠛⠋⠛⠏⠀⠀⣤⣹⣿⣿⠗⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣿
⠀⣀⣀⣀⣀⡐⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠈⠹⣿⣶⣄⡀⠀⣀⣀⣀⢀⠀⠐
⢀⡜⠋⠉⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠠⠆⠙⣄⠈⠉⠛⠛⠛⠭⠛⢀⡟
⡝⠀⠀⠀⠰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠚⠐⠛⠈⠀⠀⡀⠀⠀⠘⠦⠀⠀⠀⠀⡰⢀⡎
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠛⠋⠛⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢰⠀⠀⠀⡰⡵⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠀⢶⡀⢀⣵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⠆⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣄⢰⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡋⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠄⠀⠀⠀⠀⠀⢰⠀⢀⡰⠈⣁⣿⠁⠀⠀⠀⠀⢀⡀⠠⠤⠐⠂⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢤⣀⠀⠈⠛⢈⣠⣾⣅⠀⣹⠉⠖⠀⠉⠘⠿⢉⡅⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣇⡲⠴⣿⡿⣹⣷⣿⡏⠀⠀⢀⠀⠀⠀⡀⠀⣷⠐⢠⡸⠾⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢻⣿⡟⣏⠑⠦⠟⣇⠛⢘⣿⠀⠀⢠⣿⠀⣀⣤⣧⡶⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⣾⡏⣿⠽⠄⠀⠈⠇⢙⣄⢠⡔⠦⢸⠷⡿⣄⣀⣸⠽⠶⠟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠤⠄⠋⣉⣠⡀⠉⠡⠀⢀⣤⣆⣰⢦⡼⢿⠀⡾⢤⠆⠀⠱⠉⠈
⢠⣾⣿⣶⡖⠐⠚⠛⣡⣤⡆⠀⣀⣤⣼⣇⢀⡿⠿⢶⣤⠀⡰⠚⠛⠀⠈⠢⠽⣧⡼⢷⣿⣀⠀⠀⣧
⠠⠤⠒⠠⠄⡐⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⢿⡁⠀⠀⠆⠔⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⢸⡇⠀⠀⢹⠟⠳⢶⣤⣄⣀⡀⢀⣀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠷⢀⡸⡘⠀⠀⠀⠀⠀⠀⢀⣼⠋⢱⠀⠈⣿⠁⠀⠈⡁⠀⠀⠀⠀⠉⠉⠉⠠⣙⠻⣥⡀⠤⠈
⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⢨⣿⠁⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⣧⠀⠘⡷⠀⠰⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣷⣄
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠃⠀⠀⠰⠎⠇⠀⠀⠀⠀⢀⠔⡟⠁⠀⠀⠀⠈⠢⡀⢻⡆⠀⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠦
⠀⠀⠀⣀⡆⠀⢀⡀⢀⠄⢀⣼⠧⡼⠀⠀⠀⢰⡿⠀⠀⠀⠀⣰⣎⠜⠀⠀⠀⠀⠀⠀⠀⠱⡈⡿⠀⢰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠘⢿⡇⠀⠈⠁⢀⡠⠊⡍⠀⢰⠀⠀⠀⣼⠁⢀⠠⠔⣡⠟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠃
⣀⣀⣄⣘⣃⣀⣀⣀⣆⣀⣸⣀⣀⣘⣀⣀⣰⣧⣊⣁⣀⣬⣃⣐⣃⣙⣲⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡳⣦⡻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣽⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣷⣍⣿⣎⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⣿⣯⣿⣿⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⣶⣿⣿⣶⣹⣿⣿⣷⢹⣧⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣿⣝⠻⣯⡉⢷⡄
⠀⠀⠀⠀⠀⠀⣠⣾⣯⣻⣷⣽⢿⣿⣿⣯⣾⢿⣽⣿⡿⡜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡛⢷⣎⠛⣦⠀⡕⠨⣷
⠀⠀⠀⠀⢀⣾⣿⣿⣼⣿⣯⣝⡿⣍⣿⣦⣻⣿⢿⣽⣇⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣯⣝⠶⡍⢷⡈⠁⣔⠈⣯⣧
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣽⡻⢾⣽⡷⣿⣛⣾⣿⣿⣿⡾⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣶⣝⠷⣼⣤⣽⣶⣾⣷⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⡿⣟⣻⣷⣤⡀⠀⠀⠀⠀⢠⣼⣬⣿⣿⣯⣿⣿⣿⣿⣿⣿⣯⡿⢼⣷⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⢾⣿⣿⣿⣿⢍⣼⣻⣻⣭⣹⣿⣿⣷⣶⣤⣾⣿⣿⣿⣿⣿⡟⠿⢿⣿⣽⣿⣻⡇⠀⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣾⣿⣾⡙⣿⣍⣺⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⣀⣀⣻⣿⣻⠟⠿⠛⠁⠘⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⢺⠟⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣉⣩⣤⣼⣍⣈⠃
⠀⠀⠀⠀⠀⠐⠒⠶⢴⣤⣤⣤⣄⣀⡀⠀⢀⣀⡀⣀⢸⢿⣗⣯⣯⣿⠿⠍⠻⠿⠏⠿⢿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠛⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣟⣿⣿⣦⣶⡤⣻⣿⣦⣹⣦⣻⣿⣾⣦⠓⢌⡻⣿⣿⣿⣿⡿⣿⡿⣿⣿⡿⠱⢄⣤⣦⣄⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣯⣙⢶⣯⡿⠉⠹⣿⣦⣙⣏⠉⠀⡙⠈⢽⣿⣿⣿⣿⣍⠻⠛⠁⠀⠂⠀⠙⠉⣡⣟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣼⣄⢴⣿⣷⡿⠛⣻⡶⠂⠀⠈⢻⡏⠙⣍⡐⣤⣴⠶⠒⠒⢃⠉⠀⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠠⢌⣯⡙⣘⢯⣀⠦⠀⢀⣸⣇⢄⣈⢽⡻⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠚⠚⠁⠠⠞⠙⠛⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⡆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣴⣿⣿⣿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⡋⠚⢘⣫⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⠋⠁⢉⡟⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢠⠞⢀⣭⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⣉⡥⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⣶⣿⡑⢎⡳⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⡐⠁⢀⣿⡡⣙⣦⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⣴⠢⣤⣞⠁⣠⣾⣿⣷⣾⠟⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠑⠒⠒⢶⣦⠿⠢⢶⢿⣼⣿⣿⣟⡽⠃⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⣱⣿⣈⣀⠀⠀⠙⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠋⢉⠁⠉⠛⠋⡙⠥⣤⠀⢀⡀⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠃⠀⠄⢂⡀⣀⣠⣖⢿⣿⣿⠷⠂⠲⣬⣠⡔⠲⡆⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⣠⣄⢼⣇⠀⢀⣄⣤⣾⣿⣷⣌⣿⡿⠋⠀⠀⠀⠀⢙⡟⠷⢿⡡⠊⠁
⠀⠀⠀⠀⠀⠀⣺⣿⣷⣀⠾⢏⡻⢿⣿⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠉
⠀⠀⠀⠀⠀⢨⣿⣿⣿⣼⣾⡾⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡶⠟⠀⠀⠀⠞⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⣻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣣⣾⣿⢿⣿⠿⣹⣯⣉⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⢯⠝⠻⠿⣿⢷⣾⣩⣾⣿⡟⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⡶⠶⢟⡖⢻⣴⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠄⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⠀⠀⠀⣋⡤⠾⣿⣿⡿⣿⣿⡿⢿⣷⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠁⡼⠋⠀⠬⢴⣮⠗⠉⢺⣿⣻⣿⢳⡎⠁⠀⠆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⠀⡷⠴⠆⠐⠋⠀⠀⠐⢻⣿⣿⣿⣏⠁⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⢲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⠉⣤⠀⠀⠀⠀⠀⣀⡴⣿⣿⣿⣿⣿⣦⠀⢦⡄⢠⣤⠰⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋⠀⣀⢀⣴⣿⣍⠷⣿⣿⣿⣿⣿⡟⢿⣦⣾⣿⣿⣦⣶⣄⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢀⠰⠏⣜⠲⣹⠃⣦⣿⣿⣿⣿⣿⣷⡀⠛⢿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣸⣶⣟⣰⡞⢷⣿⣿⣿⢿⣿⣿⣿⣷⠀⠀⢹⣿⣟⠾⣧⠛⢆⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣼⣷⣿⣿⣿⣾⣿⣿⣷⣿⣿⣿⣿⣿⣤⣳⣄⠘⡟⠐⠏⠀⠈⢨⣿⣧⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣷⣽⣾⣿⣴⡆⠀⠀⡼⣿⢿⣤⢂⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡀⠀⢀⠚⠠⣿⣾⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠹⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⡜⣫⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠙⣿⣿⣿⣿⣿⣿⣶⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡣⣫⠍⢁⣸⡟⠙⢧⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⠁⠴⠺⠟⡇⡈⠀⠈⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⡻⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡟⢹⣷⠀⢀⡜⠻⠇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣟⣷⡹⢿⣿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⢿⢇⢹⣿⣶⢿⣿⣤⣷⠄⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⡷⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢻⡇⠀⠘⢿⣿⡅⠀⠙⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡌⠻⡀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⠘⣽⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠿⠷⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠛⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡶⡐⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠆⠭⣤⡝⢻⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⢋⣠⣤⠀⣀⡍⠀⠀⠀⠠⠄⠀⠀⠀⡸⢀⠀⢀
⠀⠉⠻⠒⠲⣶⠲⣤⣀⢀⣠⣤⣶⣿⡿⠁⡀⠈⠉⢿⡦⡀⠀⠀⠀⠀⢻⡅⠀⣠⣿⣷⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣴⠚⠛⢿⣿⠈⠉⠀⣸⣷⡄⠀⢸⣇⢀⣦⠒⣦⣒⣾⣷⡾⣿⣿⣿⣿⣏⠍⠉⠃
⣀⣀⣠⣤⣶⠟⠉⠉⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⡤⣿⣿⣿⣿⣾⣷⣸⣿⣿⣾⣿⣿⣿⣿⣿⡀
⠉⠻⢯⠀⠀⠀⠀⣠⠆⠠⠄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠁⠀⠀⢠⣿⣠⣤⣤⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤
⠽⠿⢿⡿⠿⣿⣿⣿⣶⣾⣯⣾⣿⣿⣿⣻⣿⢛⣟⠿⣿⣿⣿⣿⣿⡿⣿⡛⣂⣈⣷⣿⣿⣭⣃⡀
⠀⠀⠀⠀⠀⠠⣾⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣻⣿⣿⣿⣿⣟⣛⣿⣆⣐
⠀⠀⠀⠀⣀⡐⢿⡇⣙⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣈
⡐⣒⣶⣶⣿⣷⣿⣧⣬⣼⣿⣿⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠙⣗⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⡄⠀⠛⠿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋
⠀⠀⠈⠀⢠⠀⠈⠙⢿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠉
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠹⢽⣍⣍⣍⣽⣿⣿⣿⣿⣋⣍⠳⠴⡆⠄⢀⠀⢀⡀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠮⡻⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⡺⣝⠲⠾⣥⡿⣿⠙⠻⠷⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⠿⣙⣻⠧⠈⠷⠲⠿⣿⣛⠶⠶⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⣀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢻⡿⣋⣠⠨⠇⣠⠿⠁⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣏⣫⡿⡀⡨⠃⠀⡰⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠋⠠⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣉⠉⢹⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢷⣼⠠⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠹⣌⢦⡏⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠘⢎⣿⡄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠢⢈⢻⣧⠀⡇⠀⡀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠈⠻⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠓⢄⠀⣤⢽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠻⡿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢛⣃⣩⣭⡗⠊
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡼⢀⠐⠶⣶⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢠⠂⣄⠀⠀⢤⣤⠊⠖⠙⠋⠀⠀⠀⠁⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⣤⠀⣤⢀⠐⢰⣾⡧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢿⣏⣿⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠻⠥⠟⢻⣷⣧⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣻⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣀⡿⡿⠀⠀⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣚⣿⠇⠀⠀⣠⠆
⠀⠀⠀⣠⣀⠀⠴⣐⢻⡆⢡⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⢠⣽⠟⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠁⠀⠙⠛⠪⠛⡛⢧⣦⡞⢻⡦⠀⠀⣨⣤⠞⠁⠀⠀⣠⡶⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⠛⠀⠀⠈⣿⣵⣷⡦⡍⠳⡀⠀⠀⢀⡽⠁⣾⣑⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿⡁⢫⣜⣧⣼⣿⣁⣀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠿⣿⣿⢻⡷⢎⣼⣧⣽⣿⣬⣿⣿⣻⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⣧⣼⣿⣧⣾⣿⣋⣿⡝⣿⡋⣿⣿⣿⣷⠀⠀⠀⢀⣠⣶⠾⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣵⣿⣿⣿⣿⣿⣏⣠⣴⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⣿⣿⣿⣧⣽⣿⠿⣭⣽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡿⡟⣿⣿⣿⣿⣧⣼⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡞⣿⣿⣿⣿⣿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⠿⠟⢻⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⣁⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⡞⠙⠗⡀⠰⣿⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣷⣾⣭⣯⣧⢨⠝⣶⡌⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⡿⠀⠙⠛⠁⠙⡸⠿⠃⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄

⠀⠀⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡆
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠄⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⣶⣶⣶⣤⣦⣄⠀⠠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⣶⣿⣤⣾⣶⣼⣶⣾⣏⡵⠾⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⢿⣿⣿⣿⣿⣿⣷⣤⣈⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⣴⡟⣻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⢠⣾⣾⣿⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣧⣻⣶⡄⡀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣧⣽⣷⠘⠶⠂⠀⣸⡇
⠀⠀⡇⠀⠀⡀⢠⣿⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⣿⡆⠀⣇⠘⢿⡇
⠀⠀⡇⠀⢠⣿⣯⣾⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡇⣶⢻⠀⢸⡇
⠀⠀⡇⠀⠈⣿⣿⣿⣿⣿⣿⣿⡟⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣿⣧⡟⡟⠀⢸⡇
⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⢸⡇
⠀⠀⡇⠀⢴⣿⣿⣿⣿⣿⣿⣿⢿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠻⠋⠀⢸⡇
⠀⠀⡇⠀⡘⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⢿⡟⢳⡞⠀⢸⡇
⠀⠀⡇⠀⢳⡈⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⡞⠁⠀⢸⡇
⠀⠀⡇⠀⣦⣴⢽⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣱⣿⣿⣿⣾⣷⡿⣦⠀⠀⢸⡇
⠀⠀⡇⠀⠈⢿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠂⢠⣤⣤⡀⠀⣀⢀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⡙⣿⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣻⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣀⠁⠞⠶⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠈⢤⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡽⠾⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠳⡌⠻⢿⣿⣿⣿⡏⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢏⣰⣿⣿⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠙⠿⢿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠊⠽⢿⣿⣿⡿⣿⣿⣿⣛⣛⣛⠛⠁⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣌⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠁⠁⠁⠉⠈⠁⠁⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠐⠛⠛⢶⣿⣿⡺⠿⠆⣹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠛⠿⠫⠉⠛⣦⡀⠀⠀⠀⠀⠐⢀⠀⠢⠘⠆
⠀⠀⠀⠀⠀⠀⠠⠀⠀⢄⠀⠀⣀⡀⠀⠀⠁⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⢄⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠛⢆⠠⡀⠀⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣤⣤⣬⣥⣄⣀⠄⠀⣙⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⣶⣮⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⢛⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠋⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣉⠓⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣿⣿⣿⠿⠋⠛⢿⣿⣿⣿⣿⣿⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠙⠁⠀⢀⣠⡴⠟⠉⠙⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡌⠀⠈⠁⠀⠀⠀⢄⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢅⠠⠊⠄⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠂⠁⠠⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃

⠀⠀⠀⠀⢀⣤⣤⣀⡀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣷⣦⣽⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣷⣥⡙⠟⢿⣿⣿⡿⠛⠉⠙⠿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠉⠠⣶⣆⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣿⠀⢀⣠⣤⣤⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡴⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠟⠉⠀⠀⢀⣠⠤⠂
⠀⠀⠀⠀⠑⢄⣀⠀⠀⢠⢷⣄⣀⡀⠀⠀⠀⠈⠳⣌⠉⠛⣻⣿⣿⣿⣿⡿⠿⠛⣋⣁⣀⠀⢠⡖⠛⠉
⠀⠀⠀⠀⠀⠈⠳⣕⢤⡟⠀⠻⣿⣿⣷⣄⠀⣠⣤⣬⣷⣿⡿⣿⣿⣿⣿⣿⡿⠟⠛⠋⢻⣷⣠⣙⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠙⣦⢤⠀⢀⣤⡽⠿⠿⠿⠟⠙⢻⣿⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⠀⠀⠉⠉⠛⠿⣾⣍⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡟⠛⠋⠁⠀⡀⣠⣶⣾⠿⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠠⢾⣿⠿⣤⣴⣶⠿⠟⠛⠛⠻⢷⡤⢤⣤⣤⣤⡶⢶⡒⠂⢶⠧⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢴⣱⣟⠀⢱⣆⡟⣄⠠⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠟⠛⠃

⠀⠀⠀⠀⠀⢰⣾⡿⣿⣿⣷⣿⣿⣿⣷⣾⣤⠰⣿⣸⣼⣧⣾⣼⣧⣿⣈⡉⡿⢀⡠⡇⣤⢸⡆⣛⠉⠐⡇⠛⢸⣟⣿⣻⣀⡇⢈
⠀⠀⠀⠀⠀⢸⣿⣷⣿⢾⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣻⠙⡇⠺⢸⡇⢿⢸⡇⡇⢿⣿⣇⣿⣾⣿⣧⣬
⠀⠀⠀⠀⠀⢸⣮⣿⢿⣷⣆⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡃⠸⢈⡃⠾⢈⠁⣶⣿⣾⣟⣿⣿⣿⣿⡿⣶⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢼⢠⡇⡙⢸⡇⣿⣿⡿⢷⣿⣿⣿⣿⣿⠀⠃
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢻⣿⡟⢉⢹⡟⣋⣿⣿⣿⣿⣿⣿⣿⢲⣤⣤⠿⢠⣦⣾⢹⢿⣿⢿⢩⣟⣿⢽⡀
⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⠩⠀⠈⢻⠻⠇⠂⢰⣄⣧⣿⣿⣿⣿⣿⣿⣯⣸⠿⣟⣿⣾⣿⣿⢿⣧⣤⣿⡹⠿⣿⣾⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣏⡋⠻⠉⡝⠿⢠⡄⠀⢘⠀⣇⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⣼⣟⡯⣽⣺⣿⣿⣿⣿⣿⣿⣷⣦⣿⣯⡅
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁⠃⢰⠀⠇⢰⠀⡄⠀⠸⠀⣸⣏⠐⠚⢛⣹⣿⣿⣿⣿⣛⣿⠺⡟⣛⣽⣽⣿⣿⣻⡿⣿⣿⣿⣯⣿⣻⡇⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⡀⢐⠀⡇⢸⠀⡅⣷⣼⣍⣉⣼⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠅
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣃⠸⠀⡇⢸⠀⡇⢸⢙⡿⣿⢿⡿⡟⠻⢹⡧⠭⠻⠄⠆⠽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⡀⠀⢱⣄⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⣀⡀⡀⢀⡀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⡇⠀⠰⡆⢐⢸⡀⡇⢹⠀⣁⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⠠⡇⣿⣬⡁⠇⢸⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡋⣭⢹⡿⡟⠙⠻
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣹⡇⡿⢸⠃⠅⢸⠀⠄
⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⠸⠄⠆⠰⠀⠆
⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⣿⣿⣿⣿⣶⣄⣖⠐⠀⣧
⠀⠀⠀⠀⠀⠉⠀⠀⣁⢼⠋⠁⣠⣼⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⠿⣿⣛⣿⣟⡟⠘⠂⠃
⠀⠀⠀⠀⠀⣿⡿⠋⠁⢀⣠⣿⣿⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⡖⣿⣴⣿⣿⣧⣦⣼⣿⣿⣿⣿⣿⢀⡀
⠀⠀⠀⠀⠀⠈⠁⣒⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⢿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡟⡿⢿⣿⡿⣿⣻⡗⣶⣿⣿⣿⣻⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⣿⠿⣿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⡿⠿⢿⢴⡿⣿⢷⢏⣁⠻⢜⡻⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡛⢴⡄⡁⣿⢘⡃⣤⢸⡄⣇⢛⠸⠇⣉⢸⠦⡄⢠⠀⠃⠈⢠⠀⡂⠐⠀⠃⠈⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣇⣼⣥⣧⣤⣸⣧⣿⣼⣧⣤⣿⣈⣃⣳⣠⣄⣀⣘⣀⣄⣠⠀⠀⡃⢀⠀⡁⢸⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠛⠛⠋⠉⠉⢉⣿⠿⠛⣻⣿⣿⣿⡿⢾⣿⠛⠛⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠿⠟⠋⠁⠀⠀⡇⠀⠀⠀⠘⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠁⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⡟⠁⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⢄⣀⡾⠋⠀⣰⠟⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢁⡆⠀⢿⠀⢀⣴⠗⠒
⠀⠀⠀⠀⠀⠀⠈⠿⠑⠶⡚⠢⣤⡶⠆⠤⠤⠠⠤⠀⠀⠀⠀⠈⣧⠙⠁⠀⠘⣱⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣡⣤⣀⣀⣿⡆⠀⡀⠀⠤⠄⠀⠀⢀⣿⡦⠀⢀⣼⠿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⣿⣿⣿⢟⣿⣇⠀⡄⠀⠀⠠⠶⠶⣿⠿⠦⠶⠛⠁⠀⠀⠋⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⣠⡟⡽⢻⡿⠃⣼⣿⣿⠀⢹⣄⣀⠂⠆⠂⠀⠰⠀⢀⣀⠀⠀⠀⣤⡀⠈⠉⢀
⠀⠀⠀⠀⠀⠀⠘⠋⠰⠇⠘⠁⢸⣿⢹⣿⣿⣧⠉⣙⣿⡷⢷⣶⣶⣾⣿⣿⠇⠖⠀⢸⣏⣠⣴⢛⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⢷⣿⣿⠇⠀⠙⠉⣠⣾⣧⠀⠀⠀⠘⠿⠙⢃⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⡀⠀⢄⣤⢹⣿⠃⠀⠀⠀⠁⣀⡴⠛⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠟⠃⠀⠀⠀⠰⣠⣿⡿⠁⠀⣿⣷⠖⣿⣿⠡⢆⢠⣾⠔⠚⠂⠀⠀⠀⠀⠀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣼⣿⡿⠋⠀⢀⠀⠀⠂⠀⠀⠀⡜⠁⠀⠠⠙⠁⠀⢿⣿⡀⠘⠿⠁⠂⠀⡀⠀⢀⣤⣴⡾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠻⠋⡀⠀⠐⣍⣼⠇⠀⠀⠀⢊⣤⡀⠀⢀⣤⣤⡀⠘⠟⠋⠀⠀⠀⠀⣀⣶⣾⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣠⣄⡀⢸⣿⡟⠀⠈⠀⠀⠂⠀⠀⣳⣯⠀⡖⣿⣟⡿⠃⠀⠀⠀⠀⢀⣴⡿⠻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⡽⠁⠈⠋⢀⡤⣀⠀⠀⠀⠀⠀⠨⡿⣤⣿⣿⡭⠁⠀⠀⠀⢀⣴⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⡀⠀⠀⠀⠈⣧⡌⠀⠀⠀⠀⠀⠀⠙⢼⣿⠿⠇⠀⠀⠶⠞⢳⣾⡿⠇⢀⣴⣦⡀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢥⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⠀⠀⠀⣀⠀⠈⠁⣾⣿⣿⣿⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⠀⠀⠀⠐⠁⢠⠀⢹⣿⡿⠇⣀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠋⣾⠇⠀⢀⣀⠰⢀⡷⢴⣦⣨⣾⣿⣾⣿⣭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠄⠠⠄⠂⠀⠲⣦⠀⢀⣾⠛⠁⢀⠞⠁⠠⠐⠀⣈⣈⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⣦⡈⠁⢀⡔⠋⠀⠀⠀⠀⠀⠠⢩⣭⣽⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡿⢆⠘
⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡏⠰⡀⠘⣧⠀⠀⠀⣀⣀⣤⣤⣼⣿⣿⣿⠿⢿⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⠾⠟⠛⠓⠀⠀⢄⠻⣟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠴⠆⠴⢟⢻⠟⠛⠛⠋⠋⠋⠍⠙⠉⠹⠛⠟⠛⠛⠛⠉⠙⠃⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⣠⣶⣤⣀⡀
⠀⠀⠀⠘⠿⣿⣿⣿⣿⣷⣦⣄⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣷⣾⣿⣿⣶⣦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⣿⣿⣷⣶⣾⣿⡿⠿⣿⣿⣿⣿⣶⣤⣀⠀⣀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣶⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀
⠀⠀⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣌⡋⡻⢿⡿⠋⠁⠀⠘⠻⠿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠘⠿⣦⡀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣾⣷⣶⠿⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⡃⠀⠀⠀⠀⠈⠻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⣀⣠⠶⠚⠁
⠀⠀⠀⠀⠈⠳⡦⠀⢀⡎⢻⣶⣦⣄⠀⠀⠀⠈⠳⣄⣠⣽⣿⣿⣿⣿⣯⣉⣤⣴⣶⣦⡀⢻⡁
⠀⠀⠀⠀⠀⠀⠙⣮⠛⠀⠀⠙⠻⣿⣷⣤⣴⡿⣿⣿⣿⣯⣿⣿⣿⣿⡟⠉⠁⠀⠀⠻⠷⢷⣯⣖⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡤⡾⠿⠉⠉⠁⣁⣠⣼⣿⣿⣿⠟⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠆
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⢀⣀⣤⣤⣶⡼⣿⣟⣉⣉⡉⠁⠀⣀⣀⣀⣀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠙⠋⣽⣿⠟⠉⠁⠀⠀⠀⠉⠉⣩⢟⡿⠙⢧⡉⣦⠀⠙⠍⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠸⣿⡷⢷⠆

⠀⠀⢀⣀⢤⣶⣾⣿⣿⣷⣶⣶⣶⣤⣤⣀⣀⡀
⠀⠈⠉⠛⣛⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⠆
⠀⠀⠀⠀⠀⢀⣠⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠉⣩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣀⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⡿⠛⠛⣿⣿⣿⠿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠋⠀⠀⠀⠈⠁⠀⠀⠀⠘⠛⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠶⠶⠶⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠋⢉⣠⣤⣤⣶⣶⣤⣤⣬⣙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢁⣴⣾⡿⠟⣛⣉⣩⣭⣍⣉⣛⠻⢿⣦⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣰⣿⠟⣩⣶⡿⠿⠛⣛⣛⣛⠛⠻⢿⣶⣌⠻⣦⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣸⣿⢣⣾⠟⣥⣶⠾⠛⠛⠛⠛⠿⣿⣦⡙⣿⣆⠸⣇⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠇⣾⢏⡾⢫⠴⠞⠛⠿⢿⣶⣄⠈⢿⣧⢸⣿⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⢠⡟⠸⢁⣴⣾⣿⣿⣷⣦⡙⣿⡄⢸⣿⢈⣿⠀⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⠘⡇⢰⣿⡿⠉⠀⠀⠈⢹⣧⢸⡇⢸⡏⢸⡿⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣛⠛⠲⠄⡠⠋⢉⣉⠙⢆⡰⠚⠛⠻⣆⠀⠀⠀⠀⠸⡄⠸⡇⠇⣿⣿⠀⠀⠀⠀⠀⢸⡟⣸⢃⡿⠀⣼⠃⢰⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣾⠉⠀⡀⠈⠁⢰⠏⠉⡧⢀⠠⢾⡉⠢⠙⠀⠀⠀⠀⠀⠱⡄⢻⡄⢻⣿⠀⠀⠀⠀⠀⡼⢡⠏⡼⠁⣸⠋⠀⠾⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⣷⢯⣭⡀⠉⠙⣷⣬⡴⠋⣀⣘⣧⣴⣶⣦⣤⣤⣤⣀⣀⠙⢦⠻⣌⢻⡄⠀⠀⠀⠈⠀⠋⠈⠀⠘⠁⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⣧⣀⣨⣿⠀⠀⠀⣠⠶⠟⢋⠉⡉⠁⠀⠈⠉⠉⠉⠛⠻⠿⢾⣷⣽⣦⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣬⡽⠿⠷⠶⠶⡾⠅⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣽⠛⠉⣀⡤⣤⣤⡀⢀⡗⠀⠀⠀⠠⠄⠀⣠⣴⡿⠟⠛⠲⠶⣤⣀⡀⠀⠀⠀⠀⠙⠿⣷⡀
⠀⠀⠀⠀⠀⢀⠔⠁⢨⡇⠰⠙⠿⠿⠆⢁⣾⠁⢈⡉⠐⠲⠄⢰⣿⠏⠀⠔⠚⢶⣄⢠⡉⣉⠛⣛⠲⠶⢤⣀⡉⢿⡄
⠀⠀⠀⠀⠐⠿⠈⠀⠀⣵⣀⣀⣀⣠⣴⡿⠋⠲⢤⣈⠛⠦⠀⣿⣿⠀⠀⠀⢀⠀⣿⡄⢁⠑⣾⡥⢃⡶⣀⣌⡙⠾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠍⠉⠉⠙⠋⠡⠀⠄⠱⣦⠉⠓⠂⠀⢹⣿⡀⠀⠀⠣⡴⠏⢰⠀⠀⡼⢷⢾⣏⠡⣜⠐⡂⠘⠄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢠⠀⢷⠈⢦⠀⠀⢀⠀⠀⠈⠿⣷⣄⠀⠀⣀⣴⠇⡐⠁⠀⢼⡟⠻⣤⣀⠔⣡⠎⡌
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡻⡻⡟⠋⢁⠄⡰⠒⣂⠸⣤⠂⠀⠙⢧⢐⠚⠷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡞⢩⢝⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡑⢮⡑⠾⣭⣹⣐⢁⠀⠛⠀⠀⠀⠈⣸⠈⡆⢐
⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠐⢣⣌⠘⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢷⡽⣦⡉⠳⢦⣭⣙⠛⠿⠶⣶⣦⣬⣭⣉⣚⣁
⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠤⠖⢃⠈⢣⡘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡛⢷⣤⣈⡙⠛⠿⢶⣶⣤⣬⣭⣉⣛⣛⣋⡁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⢸⠇⠈⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣬⣙⠻⠿⣶⣶⣤⣬⣍⣉⣛⣛⣛⣋⡁⣇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠋⠀⠀⠀⠀⠙⠻⠷⣶⣦⣤⣤⣤⣤⣤⣴⣾⡿⠿⠿⣶⣶⣤⣭⣍⣛⣛⣛⣛⣛⣉⣁⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠉⠩⣉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠉⠒⢤⠄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠶⠚⠛⠉⣠⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⢀⡈⢩⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠞⡆⠁⠀⠁⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠻⠐⠇⠀⣀⠇⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⡛⠁⠀⡤⠶⣌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢡⠞⣱⠃⠎⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣲⡾⠟⢿⣿⡿⢂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡾⢷⡾⠆⣼⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣸⣧⣸⠇⠘⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡐⣷⣾⣿⣷⣿⣿⡃⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣮⣕⣻⣟⡿⠟⠿⠁⠀⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⣭⣪⣞⣽⣿⡿⠃⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⡿⠟⠛⠋⠙⠉⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⣤⡶⠟⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⡀⡰⠃
⠀⠀⠀⠀⠀⠀⠁⣀⡞⠁⠀⠀⠀⠀⢀⡐⡀⠀⠚⠁
⠀⠀⠀⠀⣠⣶⣿⠟⠃⠀⠀⠀⠀⠀⠀⠳⡈⠂
⠀⠀⣠⣾⠟⠋⠀⠀⠀⢀⣀⣀⣀⣀⣠⢤⣤⣤⣕⣀⣠⣖⣠⡄⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠂
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠈⢻⣼⣷⣼⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣠⣤⣶⣎⣿⣾⣩⣷⣦⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⢼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠸⢷⣦⣽⡿⢰⣿⢇⣿⡇⠀⣿⡏⣿⣷⣻⣟⣁⣤⡾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣷⣦⣿⣯⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⢸⣿⣿⣿⡿⢿⣿⣿⣿⣧⢿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣽⣿⢸⣿⣿⣿⣇⢸⣿⣍⣿⣿⣿⣿⣯⣅⡀
⢤⡀⣠⣄⣀⣀⣀⣀⠀⣀⣀⣤⡶⠞⠋⣡⣯⣄⠻⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⠛⣌⣿⡉⠙⠷⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠉⠉⠉⠉⠙⠉⠀⠀⢀⡴⢁⡼⠛⣄⣙⣿⣿⠿⢿⣿⠿⣿⡿⠃⢠⡿⣇⠁⠀⠀⠀⠀⠙⠓⠒⠚⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣠⡟⢃⡴⠀⠀⢈⠻⣄⡈⢁⣴⢿⠀⢙⠹⣌⠻⣦⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣡⢀⢀⣀⡲⣄⣼⢀⣿⣿⣿⣧⡀⠆⢈⢸⣈⠀⠈⡱⠄⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠊⠐⠁⠈⠋⠘⣷⣿⡏⠹⣿⣿⣿⡿⠁⣾⣦⣘⡉⠊⢡⠙⡚⠢⣉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡠⠊⡠⠁⠁⣰⠞⢰⣿⣿⣿⠆⣵⣿⣿⡇⣾⣿⣿⣿⡇⢰⡀⢁⠙⠄⠢⡙⠣⡀
⠀⠀⠀⠀⠀⠀⢠⢊⠔⠈⢀⠜⢀⡄⠘⠏⠀⠸⢿⣿⣿⢀⣿⣿⣿⣧⢈⡿⢿⣿⠁⠈⡗⣈⣄⠜⢆⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡰⠁⠁⠀⡀⠃⢰⡎⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣧⣐⣿⡗⠀⠀⠃⠀⠙⡠⠀⠁⠀⠱⡘⡄
⠀⠀⠀⠀⣠⠃⠀⢀⠊⠀⠀⣘⢣⡤⢼⠀⠀⠀⠈⣵⢿⣿⣿⣿⣿⣾⣿⣿⣟⠁⠀⠀⢸⣀⣰⠇⠀⠀⠑⡀⠐⠌⡄
⠀⠀⠀⢀⠁⠀⠠⠁⠀⠀⡰⠀⠀⢳⡄⠀⣀⠔⠈⠹⢿⣿⣿⣿⣿⣿⣿⡟⠉⠑⢄⠀⠸⣰⠋⠘⡄⠀⠀⠈⡄⠀⢱
⠀⠀⠀⠘⠀⠀⠀⣀⡀⠄⠁⠀⠀⡀⢿⡍⠀⠀⠀⠀⠉⠛⢿⣿⡿⠛⠈⠀⠀⠀⠀⠑⣲⡃⠀⠀⠘⢄⠀⠀⠈⠄
⠀⠀⠀⠈⡄⠀⠀⠀⠀⢀⠠⠒⠀⠀⢨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠓⢄⠀⠈⠁⠂⠂⠀⢀
⠀⠀⠀⠀⠈⠂⠀⠂⠈⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠁⠂⠠⠄⣀⣠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⣀⣀⣠⣄⣀⣀⣀⣀⣀⣀⣉⣁⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣬⣿⣀⣀⣀⣀⣠⣄⣄⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⠀⠀⡀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⣀⣤⡸⣿⣿⡏⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣹⣿⠉⠛⠻⠿⢈⡿⣿⣇⠶⡞⢻⠿⣶⣦⣤⣤⣼⣿⠖⠓⠛⠃
⠀⠀⣴⣤⣄⣰⣿⡦⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⣰⣼⣿⣿⣋⡁⣘⣷⣿⣇⢼⣼⡿⢿⣿⣿⠏
⠀⠀⠉⠻⣿⣿⣿⣿⡟⠁⢼⢿⣇⣀⠀⠀⠀⠀⠀⠀⢠⣶⣤⡿⢿⣿⣿⡟⠹⠿⠛⣻⣏⣽⣏⠀⠹⣶⣿⣿⣿⣶⣶⣄⡀
⠀⢀⣀⢰⣿⣿⣿⣿⣯⣶⣟⣀⣿⣿⠃⠀⠀⠀⠀⢰⠄⢢⠖⠀⣶⢍⣉⡉⠻⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⠿⠿⠷⠖⡂
⢠⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡃⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠙⢻⣿⣿⣏⣹⣿⣿⡿⣿⣤⡉⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⡯
⠀⠠⣾⠛⣿⡟⠛⢼⣿⠇⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡿⣿⣫⡝⣿⣿⣿⣟⠀⠀⠠⠛⠋
⠀⠰⢿⡿⠏⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⣩⣿⣿⣿⣿⣯⣳⣿⡀⣀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣆⠀⣉⣿⣿⠿⠿⠙⣙⠛⣃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣾⣿⣧⣿⣿⣿⣿⣿⣿⣦⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣤⣿⣿⣿⣯⣙⡿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣟⠟⠓
⠀⠀⠀⠀⠀⢀⣀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⣹⣿⣿⣿⣿⣿⢋⣿⣿⣛⣿⣿⢛⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⣤⣾⣦
⠀⠀⠀⠀⠀⢘⣿⣿⣿⡤⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⣶⣿⣿⣿⣿⣧⣴⣶⣼⣷⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⢠⣼⣿⣿
⠀⠀⠀⠀⢴⣿⣿⣿⣿⡀⠀⣘⡇⢰⣾⣷⣄⣀⣠⡾⣿⣶⣶⣴⣷⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡋⠀⢰⣿⣿⣿⠄
⠀⠀⠀⠀⠈⠋⠠⣿⣿⣿⣶⣩⣥⣾⡟⡶⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⠻⢿⣿⣧⡏⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠻⣦⣭⡅⡛⢻⣿⣻⣏⡘⠏⠰⠾⠻⣾⣿⠐⠈⢿⣁⣬⣯⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠂⠀⢀⣴⣿⣿⣿⣿⣶⣠⠒⠀⠒⠀⠀⠂⡘⢿⣿⣿⣿⣿⠛⢻⣯⣴⣿⣿⣇⣠⣥⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠸⣽⣿⣿⣿⣿⣿⣿⠋⣻⣷⠟⠃⠀⠰⣾⣿⣿⣿⣷⡤⣼⣿⣿⣿⣿⣿⠛⡿⣿⡛⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⣍⠁⠀⠈⠀⢀⣤⣿⣟⠋⠎⠀⠈⣿⣿⣿⣿⡟⢀⢀⢻⣿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣯⡉⠙⣿⢿⢿⡿⣷⡶⠶⠿⠛⠻⢿⣿⡷⠤⣤⣶⣿⣿⣿⡇⣀⡀⠀⠉⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠾⢟⣿⣿⣶⣤⣦⡤⠴⠍⠶⠀⠀⠀⠱⠾⠓⣦⠀⠐⢸⣿⣿⣿⡿⠿⠛⣡⣥⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠠⢸⠡⣿⠿⡿⠓⠀⠂⠂⠀⢀⣴⣷⣄⠀⠠⠁⠀⢀⣼⣿⣿⣝⣀⠀⠀⡿⠿⠋⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠈⠀⠡⣵⣮⣠⣌⣀⣠⢰⡾⣿⣿⣿⣿⣿⣿⡷⠶⣾⠟⣻⢛⣿⣟⣿⠛⠑⠄⣄⣀⣠⣾⡆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⣾⢯⣿⣻⣿⣿⠀⠈⠃⠘⠿⠙⣿⢿⡫⡵⡼⣿⣇⢋⠺⣛⠿⠂⠀⠀⢰⣿⡿⠟⠋⠻⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠐⠀⠉⢎⠠⣙⢏⠱⠈⠂⣄⣀⢀⡀⠀⠋⠀⠁⠀⠉⠀⠀⠀⣠⣾⣿⣶⣦⣈⠁⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⣀⣈⡄⠀⢀⣀⠀⠀⢀⣾⡿⣿⣿⣿⣶⣦⢴⣶⠆⠀⠀⢠⠟⣿⠙⠟⣽⣿⣿⡏⣁⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⣰⣿⣿⣿⡿⠻⠋⡄⠀⣘⢻⠱⣟⠿⣛⠻⠛⡆⠀⠀⠀⠈⠁⠀⡀⡜⢼⠿⡿⣿⠛⠛⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⠸⢏⠲⠽⡢⠄⠀⠀⠀⠀⠀⠙⠒⡓⢒⣾⠤⠃⠀⠀⠀⠀⠀⠀⠀⠈⠂⠭⠉⠑⠂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣥⣶⡄⠂⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣜⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣿⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⢫⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣤⣷⣴⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣶⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣶⣶⣄⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢠⣴⣿⣿⣷⣤⠎⠁⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠃⣴⣿⣿⢟⠻⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠺⣿⣿⣿⣿⣿⠁⠀⠀⢽⣿⢠⣬⣻⣷⣽⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢿⣿⣿⣿⣧⠀⠀⢀⣼⣿⣼⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠀⠀⠀⠙⠿⠿⠿⣧⢠⢾⣿⠿⠇⠹⠍⠻⢿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠐⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠠⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣧⣾⠁⠈⢧⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢿⣿⣿⣶⣦⣄⣠⣤⣤⣴⣿⣿⣿⡿⠀⠀⠈⢻⣿⣶⣤⣀⣀⡄⢀⣀⣤⣷⣤⣶⣶⠃
⠀⠀⠀⢀⡀⣀⣀⣤⣀⣤⣤⣀⣀⣀⡀⠛⠛⡛⠋⢙⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠻⠻⢿⡿⠛⠛⠟⠻⣟⠋⠉⠉⠉⠀⠀⢀⣀⡀
⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠃
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇
⣯⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠟⠁
⣿⣿⣦⡀⢑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠟⠋⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣴⣶⣆⠀⠀⠀⢀⢀⣸⣿⠁⡄⠀⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⢀⠙⠛⢿⣿⣶⣿⣿⣿⣿⣿⣧⣄⣼⣯⣿⣦⣤⣤⡀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣻⣿⡇⠀⠒⠻⣿⣿⣿⣿⣿⣿⣿⡏⠛⢻⠟⠛⠿⠿⢿⣿⣄⣾⣿⣿⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣤⡀⠀⠸⠟⠁⣿⣿⣿⣿⣿⣿⠀⠀⣾⣷⢄⣴⣄⣹⢻⣿⣿⣿⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣄⣸⠟⠋⠉⣉⣹⣆⣠⣤⣤⣄⠻⠛⠛⠿⠿⡇⠸⣦⡶⢦⣙⣩⣴⣬⣿⣁⣿⣶⡶⠂
⠀⠀⠀⠀⠀⠀⢺⣿⠟⠛⢛⣿⡷⠾⠗⣀⠛⠋⣻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢻⣿⡟⠻⢿⣿⡟⢋⣀⣀
⠀⠀⠀⠀⠀⠀⠘⣧⣴⣾⡿⠿⡏⢤⣼⣯⣷⡞⠁⠀⠉⠁⠀⣀⠀⠀⡀⠀⢀⣦⣄⣀⣠⣬⡋⠱⠀⠠⣨⣿⡿⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠹⣍⢿⡷⣡⣷⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣀⠀⠀⡈⠇
⠀⠀⠀⠀⠀⠀⠀⡀⣤⣿⣽⣿⠿⠋⠙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⢻⣿⣀⣤⣤⣄⣸⣿⡀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣷⡆⠀⠀⠀⣿⣿⠀⠀⠀⢀⣀⣀⡀⠀⠈⢤⠀⠐⠂⢸⢿⠟⠿⣿⡿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠉⠀⢀⡙⣿⡿⠁⢀⣤⣴⣿⣿⡦⠀⢰⣿⠿⠛⠻⣤⣄⠀⣀⣀⣀⡀⢸⠠⠀⠠⡄⡿⠻⣦⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠰⠂⠈⠀⠈⠃⠀⣿⣿⣿⡟⠁⢀⣛⣺⢃⠀⠀⡀⢸⣿⡿⠿⣿⣿⣿⣿⣦⣖⣦⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠙⢿⣿⣿⡅⠉⢀⣬⣭⣌⣠⣤⣁⣠⣿⡆⠀⢸⢿⣿⣿⡟⠛⠛⣇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠶⠤⠤⠼⢿⣿⠿⣻⣿⣷⣄⡀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣶⠖⠒⠒⠀⣤⠄⠛⠛⢛⣿⣇⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⣿⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠿⠇⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣉⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⣤⠤⠉⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠸⣯⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣿⡆⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⣄⣀⡀⠀⢘⣿⡄⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡦⣶⡀⠀⠀⢀⠞⠒⠂⠀⠶⠒⠒⠛⠙⢶⣍⠙⠛⠿⠿⢿⣇⠀⠀⠀⠀⠀⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠷⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠉⠙⠳⠶⢤⣤⣤⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡲⠀⠤⠖⠂⠀⡄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠹⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠩⠈⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠉⠆⠀⠀⠊⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⣀⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉

⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠉⠀⣠⣼⣤⡌⢿⣿⣴⠃⠀⠘⡿⢿⡆⠀⠀⠀⠠⠀⢴⠖⠡⠤⠆⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠬⢉⢿⣟
⠀⠀⠀⠘⢛⣿⣿⡿⠀⣉⣁⠀⢀⣟⣿⡋⠁⠀⢠⣾⢿⢷⣄⠴⠆⢠⣤⡀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠘⠯⠙⠉
⠀⠀⠀⠀⠑⠄⠉⠀⠸⠿⡀⡿⢻⣿⣟⠀⠁⠀⣿⡿⢾⡿⣿⡠⠄⠘⠿⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠴
⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠐⠨⠋⠄⣈⠀⣸⣿⡇⣻⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢒⠠⠀⠛⡦
⠀⠀⠛⠛⠛⠀⠀⠀⠤⣤⣤⣦⣤⣤⣤⣴⣾⣻⣿⣧⣥⣼⣿⣿⡗⢶⣤⣤⣤⣤⣤⣥⣤⠄⠀⠀⠁⠀⠀⢰⡍
⣤⣄⡀⠉⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢿⣿⣿⣷⡄⠀⠈⠀⢀⡀⣻⣿
⣿⣻⠇⠀⠀⠀⣀⠀⠻⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠘⠃⠂⡰⠄⠉⣀⣿⣿
⠀⠀⠀⠀⠁⠈⠋⠀⠀⠀⠀⡀⠀⣾⣿⣿⣿⣿⣏⣿⣷⣯⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁⢘⡭⡄⢀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡟⠰⠀⠀⠀⠀⠀⢸⣷⣷⡿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⡌⡸⠀⣀⣴⣿⢻⡇⣸⣾⣿⣿
⠀⠀⠈⠀⠀⠈⠃⠀⠀⠀⠀⠸⡀⠀⠙⠛⠉⣿⣿⣽⣿⣿⣾⣿⠀⠈⠉⢀⣾⢃⣴⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣾⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⣿⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠈⠛⠛⠿⠿⠿⣿⡄⠀⠀⣰⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⡴⠘⠁⢢⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢲⣶⣿⣿⣿⣷⣶⡟⢹⣿⣿⣷⢰⠀⠀⣀⣰⣞⣿⣿⣿
⠄⠀⠀⠀⢸⡇⣾⠆⠾⠏⢻⣿⣿⣿⣿⣿⣿⣇⢀⡀⢸⣿⡿⣻⣿⣿⣿⡿⣿⣿⣿⢿⣿⢂⠘⠿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣧⡗⢾⠒⡄⠈⣿⣿⣿⣿⣿⣯⡿⠎⢋⣾⣿⣷⠹⣿⡿⣿⣃⣻⣻⣿⠾⡏⠀⠀⠀⢠⡇⣿⣿⣿
⠐⠀⢀⣼⣿⢻⣿⣿⣿⣿⣶⠛⠙⠛⠛⣟⣿⠃⢈⣾⣿⣿⠟⠀⡝⢻⣿⣻⣿⣿⡏⠀⣏⠙⠀⠀⣸⣳⣿⣿⣿
⠀⠈⣿⡿⣿⡎⠏⠰⠿⠿⠿⠃⢀⠀⠀⠀⠟⢀⠠⠙⠿⠃⠀⠀⠘⠀⠀⣐⣸⣿⣀⣀⣿⡗⠺⠛⢿⣿⣿⣿⣿
⣷⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠰⠶⠶⢿⣿⠇⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿
⣶⣶⢆⠃⣶⣶⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠛⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢷⣬⣻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣷⣽⣿⣽⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⢿⣯⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣶⣟⢿⣿⣿⣷⡿⣷⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⡿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡙⣿⣿⣿⣿⣷⣿⣿⣿⣇⣿⣧⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣝⠻⢿⣌⠻⠷⡜⢿⡆
⠀⠀⠀⠀⠀⠀⣰⣿⣻⣷⣿⣿⣿⣿⢿⣿⠿⣿⣯⣿⡿⣯⢹⡞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠼⣮⡙⢿⣎⠹⣆⠐⡄⢸⣿⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣾⣟⢷⣿⡿⢯⣿⣟⣿⣿⣾⣿⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣻⢿⣦⡙⢧⡙⢧⡀⠰⢦⣨⣷⣧
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣟⢿⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣮⣛⣲⣷⣶⣿⣿⣿⣿⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣿⣿⡿⣯⣻⣿⣦⣀⡀⠀⠀⠀⠀⣴⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⡿⣵⣿⣛⣻⣭⣽⣿⣿⢿⣶⣦⣾⣿⣿⣿⣿⣿⢿⡿⠿⢿⣿⣿⣿⣿⣿⡀⠈⣁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣿⣯⣝⣿⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣄⣀⣀⣛⣿⣟⡿⢿⠟⠟⠀⠚⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠿⣟⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡛⡛⣛⣃⣠⣞⣉⣸⠆
⠀⠀⠀⠀⠀⠀⠤⠤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣽⣿⣿⣿⣿⣷⣛⡻⢿⣿⢻⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⢟⡛⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣷⣾⣿⣻⣿⣷⣧⣬⡉⢿⣿⢍⡱⣦⡻⣶⣮⣦⡐⢯⡻⣿⣿⣿⣿⣿⡶⣿⣿⣿⣿⣿⣿⣦⣁⣠⣄⡉⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣷⣿⡟⢷⣭⣻⣿⠟⢻⣿⣏⡻⣿⠿⢄⠙⢦⡙⣿⣿⣿⣿⣿⡟⣾⣿⡿⠗⠠⠌⢙⠿⠟⢛⣽⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣷⣿⣿⣿⡄⣀⣿⣿⣿⣾⢷⣦⣸⡫⠀⠹⢿⡿⠿⠿⠋⡇⠀⣡⣀⣤⠠⠤⠴⠂⠿⠿⠷⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢟⠈⠛⢿⢿⡄⣴⡟⢁⡐⠄⠀⢸⡇⠀⠙⢷⣾⣿⣃⡀⠠⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢸⣎⣟⣾⡍⠀⣰⢾⣷⣽⣷⣾⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉

⠀⠀⣠⣤⣤⣤⣀
⠀⠀⣿⣿⣿⢿⣿⣷⣄
⠀⠀⠻⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠟⣛⣙⡛⠖⣒⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⣠⣄⡀⡀⣀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⡗⠾⣿⣿⡿⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⣿⣿⣿⣿⡻⣿⢷⣿⠿⣿⣿⣿⣷⣶⣦⣤⣄⣀⠀⠀⠀⣀⣼⣿⠇⣿⡭⠇⣠⣿⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠻⣿⣿⣿⣿⣷⠜⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⠛⠁⠀⠴⠾⠟⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠻⣿⣿⣿⣷⡽⣿⣿⣿⣿⣿⣟⢳⡍⣷⡹⣿⣽⣿⠂⠀⠠⣂⡀⡣⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⡿⢿⣿⣿⣎⣿⣿⣿⣿⣿⡟⢿⣛⢷⣂⠟⠡⠠⠈⠴⠰⠂⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⢀⠉⠻⢫⣿⣿⣿⣿⣿⣿⡷⣬⣻⠏⡐⢁⡈⣀⠫⠌⢆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠅⢌⠙⡛⢓⠿⠛⢟⡋⠡⠂⠔⠀⢣⠆⢒⡐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⣁⠠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠓⠤⢄⣀⢠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡐⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⢨⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣀⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⡿⣍⠉⠑⢦⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⣟⠻⣿⣿⣷⣄⢸⡇⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠹⣄⠈⠙⢿⣿⣿⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠈⠙⠒⠚⣩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣝⠢⣄⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠕⣫⢇⡽⡸⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡵⢃⡴⡵⣫⠞⠁⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢮⡳⣟⣡⣪⠞⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠙⠺⠟⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⡰⣋⣤⣤⣄⡀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⣠⢞⣿⢿⣷⣄⠀⠙⡆⠀⠀⣠⠞⠁
⠀⠀⠀⠀⡞⠁⢸⡈⠻⢿⣿⣷⣄⡿⢀⡔⠁
⠀⠀⠀⠀⠑⢤⡀⠳⣄⣀⣙⣾⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠉⢉⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣝⠦⣑⢄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣷⣮⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⣿⣧⢻⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⣽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢻⠿⣿⠿⠛⠛⠉⠉⠀⠀⠸⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠄⠘⠀⡠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣄⠀⠁⣄⠀⢰⡊⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢻⣆⠀⠻⣆⠈⡆⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠙⢦⠀⠙⢦⡀⠙⣆⠰⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠼⣄⠀⠳⣄⠀⠘⢦⠈⢷⡑⡍
⠀⠀⠀⠀⠀⠀⠀⢆⠈⠑⢦⡀⠑⢤⡀⠽⢆⠳⡘⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠦⣄⡈⠒⠄⡈⣲⡈⢳⡙⢜⢆
⠀⠀⠀⠀⠀⠀⠀⡀⢶⣤⣄⣉⣑⠒⠈⣁⣈⠢⣝⠦⣕⢧
⠀⠀⠀⠀⠀⠀⠀⠣⣤⣀⡀⠀⠀⢠⣬⠧⢌⣓⣬⣙⣺⠿⠆
⠀⠀⠀⠀⠀⠀⠀⢼⣩⠤⠄⠀⠀⠰⠞⡓⠒⠨⠭⠀⠀⠀⣀⠦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⡤⠀⠀⠀⠈⠛⢊⣉⣉⣉⡁⠀⠀⠀⠛⠁⠈⠉⢿⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠚⠋⣉⣋⣱⠦⠤⠤⠤⠀⠀⠀⠀⠀⠲⡆⠀⠀⠀⢀⠀⠿⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⠉⣀⡤⠴⢞⣉⠩⠭⠥⠀⠀⠀⠙⠆⠀⠀⠀⣀⠘⢿⣋⠻⠘
⠀⠀⢀⠀⢀⣦⣄⠀⠀⠑⠲⠊⢁⣠⠖⠰⠀⣀⠂⠂⠀⠀⠀⠀⠆⢠⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠉⢠⣿⡟⠀⠀⠁⠀⠀⠆⢉⡗⠂⢠⡆⠉⢀⡀⠂⠀⠀⢀⠀⠴⠂⣀⣀⡀⢀⠀⡀
⠀⠋⠀⢸⣿⠇⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠶⡴⠄⢫⠄⠀⠐⡲⢠⠄⠀⠉⠁⠀⠀⠀⠉
⢘⡆⠀⢹⣯⡀⠀⠀⠀⠀⠀⢨⠓⠀⠁⠀⠘⠀⠀⢀⠀⣠⠋⡴⢋⠆⡠⢠⠀⡀⠀⠀⢠⢠⠀⠀⡶⡀
⠎⠀⠀⠈⣿⣷⡄⠀⠀⠀⠀⠈⠀⠀⠠⠐⠈⠃⠉⠨⠸⢁⡜⢀⢋⠔⢃⡎⢸⠀⡇⡅⢸⠈⡆⢃⢳⠱⡄
⠀⠙⠀⠀⠘⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠉⠰⢃⡜⠠⠁⠠⢋⡐⢁⢃⠸⡆⠷⠀⣆⢣⡈⠢⢈⠄⠀⠀⠀⡀⡄
⠀⠀⠶⠀⠀⠈⢻⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠨⠡⡆⠀⠀⣈⠀⠀⢰⠀⠁⠀⠈⢣⠘⠃⠐⠄⠀⢀⡲⠤⠖⠁
⠀⠀⠀⠀⠶⠀⠀⠙⢿⣧⣤⠀⣀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⠲⣇⣴⠀⢸⠀⢀⠀⠀⠀⢆⠀⠀⡈⠢⣀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠖⠀⢀⠈⠻⢷⣿⣷⣤⣀⣠⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠛⠀⣿⠀⢰⡀⠘⣆⠀⠱⣄⠈⠁⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠉⡀⣠⠀⠈⠉⠛⠻⠿⠿⢿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠙⠀⠈⠓⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠶⠀⠀⠶⢄
⣶⣶⢶⢶⠶⢶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⢶⣶⠶⡶⠶⢶⣶⠶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠀⣀⠀⣰⠚⠀⠀⠁⢤⡀⠀⠀⠀⣀⠀⠀⢀⣄⡤⢀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢶⡿⠷⣶⣶⣶⣿⠿⡿⢟⡇⠀⠈⠀⠀⢠⣷⡤⣐⣺⣿⣿⣿⣟⣛⠛⡋⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢰⡇⠚⠛⠛⠙⠓⠃⠀⠀⠀⠀⠀⡠⠈⠈⠀⠿⣿⢿⣿⣿⣿⣿⣿⢸⠻⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢾⡇⠀⠂⡀⢰⠀⠀⠀⠀⠀⢀⣰⠷⡀⠀⠀⠀⠈⠈⣟⣻⣿⣿⣿⢸⡇⣇⠀⠀⠀⢸⣿⡇
⠀⠀⢰⣼⠃⠀⣾⠉⣧⢦⣠⣒⣀⠶⣾⡿⠰⠁⠀⠀⠄⠀⠀⢈⡹⣿⣿⣿⢸⠀⣿⠀⠀⠀⢸⣿⡇
⠀⠀⠸⢡⡆⠀⢿⠶⢿⡁⠠⣬⠿⠸⡇⢋⠑⠊⣯⠘⠤⠀⠀⢒⠛⣛⣿⣿⢸⡄⢸⡆⠀⠀⢸⢻⡇
⠀⠀⢳⣾⡇⠀⠈⠀⠸⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠃⠀⠾⠿⢸⣿⣿⣿⠰⡃⠸⠃⠀⠀⢸⣸⡇
⠀⠀⠀⢿⠇⣀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣶⣤⣿⣿⣶⣶⣤⣴⣿⣿⣿⣿⠀⣡⣶⠀⠀⠀⢸⣿⡇
⠀⠀⢀⣴⡄⣿⣷⢠⣶⣿⣿⡟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡿⡿⠀⠀⠀⢸⣿⡇
⠀⠀⠈⣿⠆⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠸⠇⣽⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⡟⢠⢼⣿⣿⣿⣿⣿⠀⠟⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣆⠙⠻⠛⠁⠸⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢘⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⡿⠿⣿⣿⠀⣧⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠈⡃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣿⣷⡆⢰⣿⣿⣣⣾⣿⣿⠀⡗⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠈⣇⠿⣿⣿⡿⢻⢿⣿⣿⣿⣿⣾⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠀⣏⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠠⠀⢠⠃⣀⣌⡀⢉⢿⣿⣿⣿⣿⣿⣿⣽⣀⠿⣿⣿⣿⡿⠋⣉⠀⠁⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣄⣨⣿⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣷⣿⣿⠀⣧⡀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢦⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠀⣷⠙⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢨⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡻⡆⠀⠀⠀⢸⣻⡇
⠀⠀⠀⣾⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣷⢠⠄⠀⠀⢸⣿⡇
⠀⠀⠀⢹⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⠀⣿⠈⠀⠀⠀⢸⣷⡇
⠀⠀⠀⠀⣿⠙⢯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⢽⣯⣭⣭⣭⣽⣯⡿⠛⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣹⣦⣾⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣄⣈⡡⠂⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠸⠙⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣏⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠉⠁⠀⠄⣀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠈⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⣠⠔⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠
⠀⠀⠀⠀⢀⡤⠀⠀⠶⠀⠀⠀⠀⠀⠀⡀⣀⠀⠊⠁⠆⠀⠁⢀⡀⠐⠀⢀⡀⠀⠠⢈⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⡘⠉⠀⠀⠀⠀⢀⡀⢠⡀⢀⠀⠈⠛⠁⠤⠀⠀⠓⠀⠈⡯⢀⠀⠩⠅⣀⠀⡷⠀⠀⠂⠀⠀⠀⠀⠀⠰
⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⢰⡆⣀⢃⠀⢰⡂⠀⡘⡇⢰⡀⠀⠀⣇⠘⠀⢰⠀⢻⢐⢵⠀⠀⢄⠁⡶⠖⢀⢀⡄⠀⠀⠀⢀⠀⠄⢀
⠀⠐⡁⠀⠀⠀⠀⠀⠠⡢⡄⠀⢦⡤⠑⢄⡑⢀⢳⣹⣜⣇⠰⡄⠹⠀⡇⠸⢀⣏⣎⣸⢀⡦⣨⣿⠅⡠⠂⠀⠁⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠒⠤⡀
⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠳⢑⠦⣽⣵⣲⣭⣿⣷⣿⡝⣷⣧⣹⠒⣦⣍⣕⣿⣬⡓⢧⠆⢴⣿⡿⣪⢤⡴⠊⢁⣀⣔⠃⠀⠰⠚⠃⠉⠙⠻⡰⣤⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠐⠶⣦⣄⠀⢀⠈⡙⠛⣻⣿⡿⣿⣿⣿⣯⣵⢼⡿⢧⡏⢁⣿⡟⣯⣿⠏⡟⢻⣿⣾⣷⣯⣞⣿⣭⠄⡈⠁⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠲⠶⠤⠤⢤⣤⣀⡈⠛⠳⢶⣬⣉⣛⣛⣛⣿⡿⣿⣿⣿⣿⡿⣿⣿⢴⡖⣼⣷⣾⠏⠜⡹⠵⣿⣻⣿⣿⢿⣯⣷⠶⠚⠈⠀⡂⠀⠂⠀⠀⠀⠀⠀⣶⡬⠀⢠
⠀⠀⠀⠀⠀⠈⠉⠩⠽⠛⠓⠛⠿⠾⠛⠀⠈⠀⠀⠀⠀⠘⣆⢈⣏⣎⡇⠁⠈⠋⠀⣸⣤⣞⣻⠗⠒⠋⠻⠿⢿⡿⢴⣴⣤⣤⣀⣉⣁⣀⣀⣀⣰⠿⠖⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣻⢸⣠⡔⣰⡴⢀⠃⣠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣧⡏⣏⡏⣽⡀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡞⢩⠑⢻⡇⢹⢿⢸⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣼⡧⣾⠄⢺⠃⡞⢸⢈⡇⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢸⠙⠈⣼⢐⡇⣈⢸⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠐⠤⠛⠈⠇⠛⠈⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⠀⠀⠀⠀⢀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⡼
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣰⣿⠀⠀⣨⠔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⡧⣶⠛⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⣿⠀⢀⣴⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣷⠠⠗⠀⠀⠀⡀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⡄⣋⡀⠰⠊⠁⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠜⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠛⠛⠛⣉⠉⠀⠀⠀⠀⢀⣀⣤⣴⣾⣾⡏⣄⠀⠀⠀⢰⡄⣠⠐⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣄⠀⠀⠀⠀⢀⡀⠀⣂⣀⣠⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⠟⢠⣿⡈⠒⠂⣾⡇⠀⡼⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⠀⢀⢤⣠⣷⠀⠀⠁⠀⣦⡀⣠⠤⠰⢦⣈⡙⣿⣿⣿⡿⣟⠿⡿⠿⣿⡟⠛⠀⠀⢼⣿⡆⠁⠋⣿⣷⠠⣤⠇⢀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣧⣿⠶⠃⠀⣩⠗⠮⣂⠄⠘⡥⠈⠁⡄⢰⠈⣉⠭⠛⠩⠑⢊⠀⠊⢠⠈⠂⠒⠥⣢⡠⣀⠀⡌⠛⠜⠛⠿⡂⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠧⠊⠁⠠⠀⡠⢞⡄⢠⠀⠀⠁⡀⠀⠉⠀⠟⠃⠋⠀⠀⣀⡠⠂⠨⠂⠀⣾⡆⠐⢄⡀⠈⠉⠈⢸⠷⣦⠀⢂⠂⢘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢃⠤⢊⠁⠀⢀⠰⠀⡀⢸⡀⣆⠀⠙⠒⠁⠀⠀⠀⢠⠀⠂⠀⠀⠄⠀⣿⢠⣿⣇⠀⠂⠀⡀⠀⣁⠤⠊⠀⣦⢸⠀⢸
⠀⠀⢰⠐⡀⠄⠀⠀⡀⠀⠀⠀⠀⠁⠈⣁⣀⣀⡛⠗⠉⠀⣠⡠⠄⠀⡀⠀⣾⡆⠤⣌⣀⣀⠼⠿⠾⠟⠛⠋⠉⡉⠔⠈⠀⠀⠐⠀⡏⢸⠀⠘
⠀⠀⠸⠀⠤⡌⠒⠠⠄⠀⠉⠑⠂⠀⠿⢿⣿⡭⠿⠇⠀⠀⠂⠀⠀⠈⠝⠐⠿⠧⡈⢁⡠⠂⠅⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠈⠤⢆⡀⠰⢠⣦⣤⣄⡀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⠿⠃⠒⠀⠀⣤⣀⢀⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠭⢃⣆⠶⠀⠀⠀⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠏⠈⢷⡀
⠀⠀⠀⢀⣯⣈⡉⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⢦⣠⡏⠀⠈⠄⠀⢳⡄⠀⠀⣀⣀⣤⣤⠴⠶⠶⠶⠶⠦⣤⡀
⠀⠀⠀⢿⡁⠈⠉⠉⠓⠲⢬⣝⡳⠦⣤⣀⣀⠀⡾⠋⢀⠀⠙⢦⣄⣀⣤⡤⠤⠟⠛⠋⠉⠁⠀⠀⠀⠀⢀⠀⠀⢀⠂⠹⣦
⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠉⠙⠒⠢⡟⠉⡧⠀⠀⠑⢄⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⣤⠀⢸⣒⣶⠶
⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠋⠉⠉⠉⠉⢹⠇⠸⡇⠀⠀⠀⠀⠀⠀⠀⣀⠝⠲⢄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⢸⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠦⠴⠶⠶⠖⢻⠀⠀⠳⡄⠀⠀⠀⢀⠀⢀⠂⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠙⠦⣀⠀⠀⠈⢘⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠈⠙⠲⠤⣄⣆⣀⣀⣠⠞⠁⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⠔⠁⠀⠀⠂⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡄⢀⠀⢀⣤⠖⠋⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠙⠶⢤⣘⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠯⢿⣷⣦⣤⣽⣏⠙⣿⡒⠒⠚⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣟⣿⣯⡽⣇⠀⠀⠀⠀⠀⢀⣠⠶⠚⠛⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⢶⣄⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⢿⣲⡞⠉⠳⣤⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠈⣧⠙⣦⣀⡴⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠸⡏⠉⢻⣀⣠⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣷⠶⠞⣯⠉⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢠⡏⠀⠀⠘⣆⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠋⠀⠀⠀⠀⠈⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⢰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣤⣤⣠⣤⣄⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠤⠦⠄⠀⠀⠀⠀⠀⠀⣠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⣀⣼⣿⣿⣿⣿⣤⣀⣀⣀⢰⣄⡠⣀⣀⣀⣠⣤⣤⣾⣿⣿⣿⣷⣄⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠛⠿⠿⣿⡿⠋⠉⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⡄⢀⣴⣿⣿⣷⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠉⠉⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠿⢿⣿⣿⡿⠟⠋⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⠉⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢖⡼⠁⠰⠆⠀⠹⠆⠀⠀⠀⡀⠀⢀⣦⡀⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢍⠀⠤⡀⠄⡀⢣⠀⠀⠒⠀⠀⣴⣯⣤⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⣤⣤⣴⣼⠀⠀⠈⠈⠠⢿⡆⠀⠀⢰⡶⣿⣿⣿⣷⣤⣀⡀⣶⣦⡊⠁
⠀⠀⠀⠀⠀⠀⣤⣶⣦⣿⣿⣿⣷⣿⡇⢀⠀⠀⠀⠈⠻⠀⠘⢵⣾⣿⣿⣿⣿⣾⣿⣿⡿⠁⠀⠂
⠀⠀⠀⠀⠀⣴⣷⣿⣿⣿⣿⣿⣿⣿⠀⠘⠄⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠛⡿⢻⠗
⠀⠀⠀⠀⢰⣿⣟⣿⣿⣟⣮⣿⣾⣿⡀⠀⠳⡁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠫⠀⢁⣀
⠀⠀⠀⠀⣽⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡶⠦
⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣧⡀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣗
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣦⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⢂
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣾⣿⠟⣿⡟⢧⢠⣤⡁⡌⠑⠀⢀⡀⠀⠀⠒⢤⣀⠀⠀⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣐⣿⣄⡧⠐⣄⡀⠉⢨⠦⡀⡀⢉⡛⢦⣀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣴⡿⢃⡴⠁⠀⡷⠃⠀⠈⠳⢮⡓⣄⡈⢇⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡾⠁⠀⠀⠀⠀⠀⠀⣄⠹⣿⡝⣦⡀
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠈⢻⡆⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣯⢻⣏⠉⢫⡙⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⢶⣌⢛⠌⠛
⠀⠀⠀⠀⠀⠀⠉⠚⠛⠿⠿⠿⠯⠿⠷⠷⠀⠈⠓⠀⠛⠋⠛⠯⡙⠿⢿⣿⣿⢿⢷⢶⡄⣀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠍⠴

⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⣿⣹⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢀⣿⣿⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠹⣧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡅⢰⡆⠀⢹⣿⠀⠀⠘
⠀⠀⠀⠀⠲⡤⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠉⠀⠈⡅⠀⢸⣿⠀⠀⠀⠀⠠⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠀⠀⠄⢀⡘⢏⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢡⣾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠙⠁⠀⠛⣿⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣿⠧⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣦⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣎⡵⠀⠀⠀⡜⠁⠀⣀⠴⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⢰⡁⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢡⠿⠁⠀⢠⡞⣠⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⢸⠆⠀⠀⣿⣿⠏⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⣄⡰⠀⣴⣾⢽⠏
⠀⠀⠙⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⠀⠹⠀⠷⡈⠀⠰⠀⠀⠀⠀⠀⡀⠀⡼⢀⣀⠄
⠀⠀⠒⠺⡄⡶⠀⠆⠀⠀⠀⠀⠀⠴⡀⠈⠀⡀⠀⠀⡀⢾⠄⢀⡀⠢⡈⢀⡀⠀⠀⠧⣄⣸⡏
⠀⠀⠀⠀⡿⠉⢲⠀⡤⠀⡂⢀⠀⠀⠁⣀⢾⡆⠀⠀⠈⠃⠀⠀⣠⠀⢱⡆⠓⠀⠀⠀⣼⠟
⠀⠀⢀⠠⡇⠀⠸⡿⠀⢫⣀⣘⣦⣤⣄⡈⠑⠃⠀⠀⠤⠾⡀⠀⠀⣻⠬⣿⢞⡀⠀⠀⣿⣄⡁⠀⠀⢀
⠀⠀⠈⠲⣿⠀⠐⣧⠀⠀⠈⠋⠀⠈⢹⡇⡀⢐⠎⠐⠣⣄⠁⠀⠁⠁⠈⣿⡀⢀⡀⢦⠀⠈⠫⠷⠄
⠀⠀⠀⠀⠹⣷⣤⣹⣦⡁⠀⠀⠀⢀⣿⡟⠁⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠀⠀⠀⠔⠓⠦⠄⠀⡀⠀⢠
⠀⠀⠘⢣⡄⠀⠉⠛⠿⣿⣶⡆⠰⣿⣏⡀⠀⠀⠀⢨⣯⠁⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠈⠥⠐⠀⣼
⠀⠀⠀⠠⣷⣠⣤⣤⣄⣾⣿⡇⠀⠈⢻⣿⣇⣀⣿⣿⢇⡀⢀⡀⠀⠀⢠⢀⠀⠀⠀⠀⠐⠀⠀⡄⠀⣼
⠀⠀⠀⢤⠈⠉⠁⠈⠉⠉⣿⣿⣦⣠⣼⡿⠋⢉⠁⠁⠀⡿⠛⢽⣤⠤⠪⠴⠀⠀⠀⠀⠀⠲⣷⡂⠀⠘
⠀⠀⠀⠈⠶⠲⣶⣀⠀⠀⠙⠿⣿⣿⡿⠁⠈⢹⡀⠰⣶⡆⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣒⣠⣟⡁⠐⣢
⠀⠀⠀⠀⠐⠀⢸⡇⠀⢣⡀⣤⣾⣿⠷⠀⠀⣈⣤⣾⣿⡇⠀⠀⠀⠀⣠⠀⡄⠀⠀⠀⢿⣿⣿⠃⠀⣿
⠀⠀⠀⣀⠀⠒⢾⣧⣤⣿⣿⠟⠉⠡⠄⠠⣾⣿⣿⣿⣿⠛⠡⠄⡤⣼⣇⣼⡿⠀⠀⢀⣬⣿⣇⠰⣎⢿
⠀⠀⠠⣤⣯⣤⣠⣬⣿⣿⣇⢠⡄⢾⣿⣷⣯⣿⣿⣿⣿⢡⣶⡖⠈⢿⣿⣾⣡⡄⣴⣿⣷⣿⣿⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡢⠀⠀⠀⠀⠀⢀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠙⠶⡟⠠⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⡄
⠀⠀⠀⠀⠸⣷⡀⢀⢲⢴⡷⣧⣵⣄⣷⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⡐⡆⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣰⣿⣷⠈⠉⢙⣟⠁⢤⣠⠶⠚⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣙⡂⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⡀
⠀⠀⠀⠀⣿⣿⣿⣇⢷⢞⣩⠈⣻⡛⠒⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢈⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠍
⠀⠀⠀⠀⣿⢿⢸⣷⢿⣽⣿⣄⠻⢷⡿⢿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⡀⠀⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠙⣧⠈⠛⠛⣻⣋⢻⢶⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣌⠁⠄⠀⠀⠀⠈⢰⠘⡦⣄⠀⣁⡭
⠀⠀⠀⠀⠀⣽⣧⣀⠀⠻⡙⠁⠈⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣁⠀⠁⢀⠀⠀⣨⣴⠀⣻⡆⢀⠆⣼
⠀⠀⠀⣠⣾⣿⢾⣟⠳⡶⣷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⢠⣤⣾⣿⣿⡗⠹⢁⣾⠗⢋⡠
⠀⠀⢸⣿⣿⣿⣆⠈⢹⣶⣿⡄⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡄⡀⢀⣀⡀⠀⠙⠿⠟⠛⠐⠏⡁⠈⠉
⠀⠀⢸⣿⣿⣿⣿⣷⡘⢻⣿⡀⢿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠋⠉⣀⣤⣄⣤⣠⣴⠶⢚⡀⠀⡐
⠀⠀⢸⣿⣿⣿⣿⣿⣷⣼⣿⣷⣼⣿⣿⣿⣿⣿⣿⡵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠙⢳⣿⣿⣦⣄⢉⠛⠿⠃⠒⢈⢀⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⠃⠀⠂⠙⠛⠿⠟⠛⠓⠒⠂⠐⠂⠀⠛
⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠂

⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣖⠒⠀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣔⠁⠹⣿⣿⣦⣀⣠⣶⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⠷⢏⣶⣿⣿⢿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣝⣫⣦⡿⠾⠛⠛⠋⢸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣝⣷⠶⠛⠛⠁⠀⠀⠀⠀⠘⠿⢿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣾⢿⠘⡁⠀⠀⠀⠀⠀⠀⠁⠂⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣿⣿⢟⠉⠋⠁⠀⠀⠀⠀⢠⣴⢴⣀⡴⣟⣾⠃
⠀⠐⠒⠒⠒⠒⠒⠒⠶⠶⠿⣿⣿⣏⠉⠉⠈⠙⣻⢿⣿⣷⣾⣾⣿⢽⣿⣥⣶⣿⣭⣶⣾⣿⣧⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠒⠉⣰⣿⡿⠟⠋⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣤⠾⠋⠁⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠛⠉

⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⢿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⣤⡶⠀⠂⠀⣄⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣶⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣨⡷⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣤⡀⠀⠀⢹⢡⠙⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣄⠄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⡙⢂⡆⠀⠄⠀⠀⠂⠈⠠⠀⠀⠀⠀⠀⠀⡤⠞⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣷⣾⠃⠄⠀⠀⠀⠂⠁⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣳⣀⣹⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣵⢧⠋⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣛⠛⠛⡂⠀⣀⣀⣤⣾⣿⣿⣶⣶⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⢀⣀⠛⠛⠉⠀⠀⠿⡿⣿⡏⢍⡊⠼⢽⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢝⠧⠻⣷⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣄⠰⡱⡑⣕⢮⡝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣶⠔⠔⣱⢲⢿⢸⢹⠈⢢⣤⢀⡆⠈⠁⠓⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠴⢪⢦⢃⣇⣎⣄⢤⠖⠉⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡈⠀⢄⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠑⠋⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⢊⠁⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢞⠁⣀⠸⡀⠔⡂⣈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠉⠉⠀⠉⠉⠒⢄⠀⠀⠀⠀⢈⠶⢠⣔⠡⠴⣄⣒⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠃⠈⠷⢤⣀⡤⠚⠉⠁⠈⠑⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣀⠀⠀⠀⣠⠌⣉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡔⠋⢩⠿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⢧⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⢀⠶⡤⠤⢯⣍⣸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣀⡴⠊⡐⠀⠀⡀⠀⠀⠀⠀⢆
⠀⠀⠀⣀⠤⠖⠋⠁⣀⢄⡠⣪⢞⢅⠞⠀⠀⢛⡦⠜⢳⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⣩⠉⠢⠴⢅⡀⠀⡇⠀⠀⠀⠈⡌⢳⣄
⠀⣠⠿⠋⢀⣠⠔⣪⠔⣩⣾⢗⡵⠋⠀⠀⠀⢈⠒⢛⡩⠽⣟⡂⠙⠦⣤⣀⣠⣸⢜⡸⣆⠀⠀⠀⠉⠀⠁⠀⠄⠢⣀⠘⣄⠩⡳⣄
⠾⢥⡖⢚⣡⠴⣊⣵⡿⢋⡵⠋⠀⠀⠀⠀⠀⢨⠋⣁⡤⠊⡹⢭⣁⣠⠄⠈⠀⠒⢋⡴⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠺⠦⢕⣂⣤⣀⣠⣤
⠀⠈⠉⠉⠛⠻⣯⡥⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⡏⢀⠴⠋⣠⠄⠹⣥⡆⡀⠀⡀⠀⠒⠊⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⣠⠞⠁⡠⠂⡠⠛⢇⣰⢣⠀⠀⠀⡀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠁⢀⠜⢁⠜⠀⠄⢀⠓⠫⣀⡇⢂⢸⡄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡴⠃⢀⠎⢀⠎⠀⠆⠀⡐⠉⠛⠛⠛⠁⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠃⢀⠎⠀⠈⠀⢰⠃⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⢠⡏⠀⢠⠁⠀⡞⠀⠀⠀⢰⡄⢰⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠋⡄⠀⡆⠀⠀⠇⠀⢸⠀⠀⡇⠀⣇⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⡇⠀⢸⠀⠀⡄⠀⠀⡇⠀⢸⠂⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣾⠀⠀⣧⠀⠀⢣⠀⠀⢇⠐⢄⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢇⠀⡏⢄⠀⢸⢧⡀⠸⡄⠀⠑⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣬⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠘⣿⠯⣾⠇⠀⠀⡀⠀⣠⠀⠀⣦⡙⠑⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⡄⠠⠺⠛⠋⠁⠐⢦⡄⠈⠚⠛⠂⠐⠀⠐⣦⣀⡀⢀⣴⣿⢿⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣃⠜⠛⠳⠃⠈⣀⣀⡤⠀⠘⠁⠬⣦⣤⠲⣾⡖⠀⠀⠀⠈⢿⣿⡭⠾⣋⣾⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⢀⠀⣿⣧⣀⣀⣸⠏⠀⣴⠶⠀⢐⠸⣯⠙⣿⣷⣄⣼⣆⡀⡀⢀⠰⢾⣿⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⢀⣀⠈⢿⡿⣿⣷⣄⢀⠠⠆⠀⠀⠙⢞⣿⣿⣧⡿⣀⣰⣯⣽⣬⣶⣬⣿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⡀⢺⣿⡆⢸⠟⣰⣿⣿⡏⠀⠀⠀⣤⡀⢘⣿⡟⣿⡏⠀⠉⠉⠁⠋⣸⡏⢙⣷⡮⠉⠖⠉⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢶⣨⣧⣄⣩⠥⡤⡶⠹⢿⣿⣅⡀⠤⠼⢿⣧⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢱⣾⣿⡀⢠⣰⠒⣩⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠁⠻⣁⠓⢓⣶⣤⣀⠒⣜⡯⠀⠀⠀⠀⠀⠀⠀⡁⠀⣠⣶⣷⡆⠀⠀⠀⠺⣿⠏⠛⠉⠉⢈⣭⣤⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⢠⣾⣿⠿⠝⠋⠋⠛⠀⠀⢀⣶⡤⠁⠀⡔⣿⣷⣿⢿⣿⣿⠿⠶⢦⢀⠿⠂⠰⠤⣦⠈⠙⢿⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⢀⠁⠒⠀⠀⠉⠉⠀⠂⠈⠀⠀⣸⠀⠉⠈⢃⡉⠁⠈⠈⡳⣄⠀⡈⠂⣀⠀⠀⠁⠁⠄⠸⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⣠⣶⠟⠓⠻⠶⣶⣦⣤⢲⣄⣀⣀⡀⠉⠉⠀⠀⠠⠀⢻⠄⠁⠸⠻⠛⠃⠠⢿⣿⣿⠦⠤⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⠉⢀⠂⠀⠀⠀⠉⠛⣿⠏⣠⣿⠿⠻⣿⣷⣄⣇⠀⠀⠉⣁⠀⠀⢀⣠⣤⡲⣾⣿⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠉⣀⣀⠤⠀⠀⠠⢈⠜⠋⠉⢛⣿⣦⢻⠿⡅⠈⠉⠉⣤⡀⠀⢠⣴⡌⠀⠹⣧⣦⣤⡔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣤⡬⢹⡇⢸⠃⠀⠘⠀⠐⡿⢿⡽⠯⠄⠒⠆⢤⣴⣿⣤⡠⠀⠀⠉⣠⠄⠀⠈⢩⣭⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣻⣥⣴⣟⡁⣰⠍⠁⣠⠞⠉⠀⢸⣿⠶⢬⠛⠛⣀⣾⣶⡞⠻⠟⠀⠈⣴⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣻⣿⣿⣟⡻⠾⣿⣿⡚⡅⠀⠈⡁⢀⡞⣀⠘⠻⢾⣿⣄⠀⣤⢀⠸⠏⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣾⣯⡉⢁⡀⣿⣿⡭⠁⢈⡄⠈⡾⠀⢿⣿⢦⠀⠘⠛⠃⣸⢁⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣅⣚⠀⠀⠎⣿⡌⠛⠀⠀⠀⠀⠀⠁⠀⣢⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⣿⣿⡟⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⡶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡁⠾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⣹⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⢿⣿⣿⣿⣶⣤⣤⣬⣭⣭⣭⣤⣤⣴⣾⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢿⣽⣟⣟⣿⣛⣛⣟⣻⣻⣟⣿⣹⣏⡿⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉

⠀⡀⢤⠀⣴⣶⣦⠀⠀⢀⡀
⠀⠙⠈⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⢀⡀
⠀⠀⠀⠉⠉⠉⠀⠀⠆⠀⠂⠂⠦⠄⠤⠀⣀⠀⠀⠉⠉⠁⠀⠐⠒⠀⠀⠴⠄⠤⢀
⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢠⣠⢀⠀⠀⠀⠉⠛⠀⠒⠓⠒⠂⠐⠢⠤⠄⠀⢉⠀⣀⡆
⠀⠀⠀⠀⠑⠛⠲⠶⠤⠤⢀⣄⡀⠀⠀⢀⠘⠉⠈⠙⠈⠛⠀⠀⠐⠂⠘⠐⠐⠒⠀⠀⠀⠉⠋⠛⠒⠶⠤⠤⠄⢠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣁⡹⡀⣯⣶⠐⠶⢶⠦⠶⠦⣤⠀⢀⠀⢤⡀⣶⡦⢲⡖⣢⡖⠐⠙⡀⠀⠀⠘⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡚⠿⣿⣴⠸⡥⢗⡸⠿⣿⠳⣛⡢⢘⣱⡒⠒⢉⣔⣼⣶⣿⠧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢜⡱⡶⠀⠶⠁⠐⡟⠻⣋⣍⣰⠾⢾⡔⡭⠾⠃⢈⡗⢳⣟⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠏⠀⠀⠈⢷⣩⣟⢶⢳⣬⣻⠀⠀⠠⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⠒⠒⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠂⠀⠀⠈⠉⠀⢀⠠⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⢄⡀⠀⡤⢷⡪⣽⣶⠀⠀⠂⠀⠀⠀⠀⠃⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠌⡃
⠀⣀⠠⡀⠙⡊⢡⠶⢺⡭⢿⡽⠖⠀⠀⢴⢠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠀⠀⡳⢬⣀⡢⣠
⠀⡀⣠⡸⠊⠹⣤⠾⢶⣿⠿⢿⠙⠀⠠⣌⣘⡹⠚⡏⣣⣶⠶⢂⠀⢡⡀⠀⠀⠀⠀⠀⠂⢀⢃⠈⢹⠺⢦⢩⡞⢷⠆⡀
⠀⠀⠌⠐⠂⢃⠉⠦⣮⡟⣡⠯⠁⠘⣧⢋⣈⠳⣅⣟⠛⠊⣩⠉⢰⡀⠃⠆⠀⢈⡖⠄⡀⠀⠙⠆⢄⠣⢸⠳⠉⢒⣓⠍⠁
⠀⠠⠰⠆⠂⠪⠴⠚⠏⠓⠻⠀⠀⠬⠠⠐⠚⠠⠠⠀⠶⠌⠿⠼⠅⠐⠄⣦⠉⠀⠈⠲⠄⡄⠀⢀⠂⠈⠐⢨⠅⠲⠥⠙⠱

⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣷⠸⣧⠀⠀⣾⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢻⡆
⠀⠀⠀⠀⠀⠀⢿⠀⠙⣦⠀⣿⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢸⡇
⠀⠀⠀⠀⢰⣦⡘⣧⠀⠈⢷⣼⡆⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣰⠏⢀⡿⣠⡄
⠀⠀⠀⠀⠸⣇⠙⢿⣧⡀⠀⠙⢿⣄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⡼⠋⠀⣼⠟⢹⡇
⠀⠀⠀⠀⠀⠻⣆⠀⠉⠻⣦⡀⠀⠙⢦⣀⣾⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢋⣴⠋⠀⣠⡾⠋⢀⡾⠁
⠀⠀⠀⠀⠀⣤⣝⣷⣄⠀⠀⠙⠲⢤⡀⠈⣿⠣⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢉⠔⢋⡿⡠⠞⠁⠀⣠⣞⡁
⠀⠀⠀⠀⠀⢻⣍⠉⠛⠷⢦⣄⣀⠀⠈⠑⣿⣦⡈⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠔⢻⡏⠀⣀⡤⠞⠛⣹⠇
⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠉⠉⠓⠒⢿⣄⠙⠦⣄⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣁⣤⣄⣈⣀⡴⠟⠂⠉⠀⢀⣠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⠿⠶⠦⠤⠤⠤⠤⠽⠷⣤⣀⡀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⣠⡶⠋⠉⠀⣀⡀⠉⠙⢷⣤⠴⠶⠾⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣉⣿⣅⡀⠀⠀⣿⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⠁⠈⠉⠲⡄⠹⣦⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣭⣁⣀⠠⠤⠤⢿⣄⣀⣀⡀⠀⠘⣧⣀⣀⣰⡏⠀⠀⠀⠐⠶⣾⣿⠄⠀⢹⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⡠⠤⢼⡏⠁⠀⠀⠀⠈⠛⢿⣍⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣺⠟⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠋⠉⠀⠀⠀⣀⠿⢦⣀⡀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⣶⠛⠉⠀⣀⠄⠉⣉⠋⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢶⣋⣁⡠⠞⠁⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠷⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠛⠉⢿⣄⠀⠀⠀⠀⣠⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠞⡋⠄⠀⡀⠀⠀⠀⢠⣯⣤⣶⢶⡟⠓⠚⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣻⡿⠗⡉⠀⣠⠞⢀⠄⢀⠀⣼⠹⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠶⣶⣾⣿⠟⠋⠐⠈⣠⠞⠁⣠⠊⢀⠎⣰⢿⡄⣷⢹⠀⣇
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠈⢀⣠⠞⠁⢀⡜⠁⣠⠏⢰⠏⠘⣧⣿⠈⠳⠟
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⣹⠇⢀⣴⠋⠀⣴⠃⢠⡟⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⠛⢿⡶⠞⠻⠶⠋

⠀⠀⠀⢰⡷⣦⣄⣀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠈⣿⣮⣻⣿⣷⣄⣼⣿⢟⣵⣿⡟⠁
⠀⠀⠀⠀⠘⣿⣿⣾⢻⣿⢽⣯⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠙⠿⠏⢫⣼⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⣠⣴⣦⢶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⣴⣾⣿⣿⠀⠀⠀⣠⣶⣿⣿⣿⣿⣮⡻⣿⠿⢿⣷⡀
⠀⠀⠀⠀⢀⣀⣀⣿⠀⠀⠀⠀⣿⣿⣿⡿⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣩⣟⡛⠛⣠⡀
⠀⠀⠀⠀⠀⠉⠛⢿⡆⢀⡤⠀⠈⠉⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⢩⣼⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢠⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣺⣿⣿⣿⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣧⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⣦⣤⡀⢀⣤
⠀⠀⠀⠀⠀⠀⣠⣴⡿⢿⣿⡿⠛⠉⠉⠙⣿⣿⣿⠀⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⢻⡆⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢟⣟⢿⣽⣟⣷⣿⣿
⠀⠀⠀⠀⢀⣾⡟⠉⠀⣾⠋⠀⠀⠀⠀⠀⢻⣿⡿⠀⣿⡄⠙⣿⣿⣿⣿⣿⣿⣿⠀⢸⣷⡈⠛⠛⢀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣯⡿⣿⡿⣾⣿⣿⣿
⠀⠀⠀⢠⣿⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣠⣼⣿⣧⠠⣌⠻⣿⣿⣿⣿⣿⢸⠀⣿⣿⣷⣶⣿⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣷⣿⣾⣧⠙⠿⠟⠃
⠀⠀⠀⣼⣿⣷⠀⠀⠀⢻⠀⠀⢀⣀⣀⡀⠀⠈⢻⣿⣿⣿⠀⣿⣦⠈⠻⣿⣿⣿⠘⣇⠘⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡿⠟⠀⣦
⠀⠀⠀⣿⡏⢿⣇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⡄⠀⠹⣿⠿⠀⣼⣿⣧⠀⡘⢿⣿⠀⢻⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⠄
⠀⠀⠀⢹⣷⠀⠙⢧⡀⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⠀⠀⢀⣴⣿⣿⣿⡇⢹⣆⠹⠀⠈⠻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⢠⢿⣆⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠙⠿⣿⡿⠁⣼⣿⡆⢠⠸⣦⣈⢉⣀⣶⣄⠀⠀⠀⣀⣀⣤⠖⠀⠀⠀⠀⠀⣠⡾⠃
⠀⢀⡴⠋⠀⠻⣦⠀⠀⠀⠀⢰⣿⣿⣿⣷⣶⣄⣀⡀⠀⠀⠀⠀⠀⠠⢾⣿⣿⡗⢸⣧⡙⠿⠿⠉⠻⢿⣿⣾⣽⣟⣋⣁⣀⣀⣀⣤⣴⡾⠟⠁
⠀⠉⠀⠀⠀⠀⠘⠳⣄⡀⠀⣿⣿⣿⡿⣿⣯⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢫⣥⣾⣿⣿⣶⣶⡄⠀⠀⠈⠉⠛⠛⠻⠿⠿⢿⣛⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢘⡛⢿⣶⣿⣿⣮⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡽⣿⣻⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢿⡏⣿⣯⡻⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠾⠿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⢹⣿⣷⡘⢯⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿⠈⣿⣿⣿⡌⢳⡝⣷⣄⠀⠀⠀⠀⠀⠀⣼⣿⣿⡌⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢹⡆⠸⣿⣿⣷⡀⢻⣎⢿⣷⣄⠀⠀⠀⠀⢿⣯⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡘⣷⡀⠹⣿⣿⣧⠀⢿⣆⠻⣿⢷⣄⠀⠀⠀⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⡇⢻⣧⡀⠙⢿⣿⠀⠘⣿⡆⠹⣧⡙⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢻⡄⠹⣷⣄⠀⠁⠀⠀⣿⣿⠀⢹⣷⠈⢿⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠻⠀⠙⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠘⠃⠀⠃

⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠔⣠⠴⠚⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⡆⢠⠀⢀⣀⠀⣠⠀⠀⠀⠈⠃⠀⠘⠛⠀⠀⢹⠠⡄⠀⠀⢀⣠⡖⠋⠁⠀⠀⠀⠀⢀⠀⠆⢰⡀⠰⡆⢰⡀⠀⠇⢰⠀⠔⠂⠐⠋⢀⡉
⠀⠀⠀⠃⠀⠀⠀⠉⠀⣠⣄⢠⡶⢶⣶⡶⠆⣀⠠⠤⠸⠀⡇⠠⠂⠈⠉⠻⣦⡀⠁⠀⢀⠀⠙⢷⡀⣸⡇⠀⡇⠈⡇⢀⡠⢸⡀⠈⣁⠘⠀⠸⠇
⠀⠀⠀⢸⡀⣐⡇⢀⣠⣛⣻⠀⡴⠋⢀⠄⠸⡿⡇⢀⣤⠁⠃⢼⣿⡐⠗⠗⠈⠻⡷⣄⡛⢁⠀⢀⣵⠃⣆⢀⣧⡀⠃⠀⠁⠘⡇⠀⠉⣴⠿⣄⡃
⠀⠀⠀⠈⠛⣟⣿⢉⣀⡉⠁⢸⠀⣁⠀⢀⣀⡴⠁⣨⠁⠀⠀⣀⡴⠀⠀⡰⠷⠶⠃⠈⢛⡋⠐⠉⠡⠂⠘⠋⠉⠉⢰⣀⣀⣠⠁⠀⣠⠆⠀⠙⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠴⠂⠘⢧⣄⣀⡉⢉⣶⡞⠁⠀⠈⠉⠉⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁






⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣭⣦⣭⣤⣬⣼⣮⣴⣾⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⣸⣤⡄⣀⣀⠀⠀⠀⠀⠀⠉⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⣭⣾⣿⡿⣟⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠋⢡⠇⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡄⠀⠀⠀⠇⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣼⠅⢁⣰⣇⡃⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣠⣴⣦⣄⠀⢀⠈⢻⣷⣦⣤⣤⣤⣀⠀⠀⣯⣦⠍⢧⡘⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⣿⣿⣿⣷⠊⠁⠰⢿⣿⣿⣿⣿⣿⣧⡀⢿⣿⣿⣿⡿⣿⣽⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⣿⣿⣿⣥⡀⠀⠠⣮⣿⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⠇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡛⣹⣿⣿⡄⠀⠈⠛⠻⠿⠿⠛⠀⠚⠃⠈⠉⠁⢠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⣀⣠⣾⣽⣿⣿⡇⠀⠀⠀⠐⢦⣄⠁⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠚⠀⠀⠌⠀⠀⠉⠁⠀⣴⣾⣷⣦⣽⣦⣄⣠⡴⢾⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠰⠄⢠⢠⠠⡙⠿⠛⢿⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠤⠠⠤⠄⠊



⣿⣿⠛⢛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣧⣿⣿⠓⠬⣉⠛⢿⡇⠀⠀⣴⡶⠶⠶⠶⣧⡀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣮⠀⠀⠻⠓⠂⢄⢀⠀⠀⡄⢰⡞⠈⠳⡇⣼⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣆⠀⢠⠆⢀⡾⠀⠀⠀⢰⡀⠀⠀⠀⠀⢻⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣹⡿⠁⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⠁⠀⢀⠐⣃⣀⣀⣀⡀⢄⠀⠀⠀⠀⢸⠁
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠂⠀⡌⠈⠁⠙⠿⡁⠀⠈⠀⠀⠀⡀⠇
⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠃⣠⢊⣔⣃⣬⡀⠀⢁⡀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⢹⠃⠉⠻⠿⠿⠟⠋⠁⠻⡇⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠊⠀⠀⠀⢠⣀⠀⠀⠀⠀⠃⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠃⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣤⣤⡆⠀⠀⠀⣦⣾⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⡿⣿⣿⣧⡀⠀⡰⠋⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⡿⠋⠉⠀⠈⠀⠀⢿⡌⠄⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣤⣴⣟⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣸⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣠⡄⠐⠀⠀⠀⠈⣿⣿⣿⠹⣿⣿⣿⣿⣦⣀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⠀⣠⣀⡀
⠀⠀⣠⢴⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⢠⣤⣤⣼⣿⣿⣧⣀⣤⣤⣤⣶⣿⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⠿⣿⣿⣿⡽⠿⠿⠛⠛⠛⠛⠛⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⢀⣀⣿⣦⣀
⠀⠀⠀⠀⠀⠀⢤⣤⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⠟⢧⣤⡄⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠙⠛⠻⠿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠂⠀⠀⠀⠀⠀⠀⠠⣤⣶⠟⠙⠿⠏
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣿⣧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠙⢦⣽⣷⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠹⠟⠃⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⢤⣤⣽⣿⣾⣿⡿⠃⠀⠀⠀⠀⠀⢠⣤⣤⣾⡿⠻⠏⠀⠀⠀⠀⢾⣇⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣤⡶⠖⠀⠀⠀⠀⠀⠀⠈⠉⠻⠷⠒⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣭⣙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣀⣤⡴⠀⠀⠀⠀⢤⣾⣿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡋⠉⠀⠀⠀⠀⠀⢨⣿⡀⠀⠀⠀⠀⠀⠠⣄⣤⣶⣶⠦⠀⠀⢼⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠀⠀⠀⠀⣴⡿⠛⠻⡦
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣋⣀⣀⣀⣀
⣿⣿⡏⠉⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠁⠘⠻⣿⣿⣿⣿⣿⣿⣿⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠇⠀⠀⠀⠀⠀⠙⠿⣿⣿⠁⢸⡇⠈⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⠀⠀⠀⠀⠀⠀⢀⡴⢫⣿⣶⣼⣷⡀⢧⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⡆⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⣿⣀⢺⣹⣇⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡰⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢸⣿⡟⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡉⠉⠓⢄⠀⠀⢀⣾⣿⣿⣿⡿⣻⡿⣿⣿⣿⣿⣿⣼⣟⣿⡟⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⡼⠓⢤⣿⡟⠻⣿⣿⣿⡀⠛⠺⣝⠻⣿⣿⢿⣿⣯⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⠞⠀⠀⠀⠙⢷⣌⣿⣟⣿⣿⣼⣃⡀⣴⡟⢿⡝⣿⣾⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡰⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣧⡛⣼⢯⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⣹⣿⠏⣽⣷⣿⣿⣿⢛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣷⣄⣟⣾⣿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣾⣿⣿⣿⢹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⣀⣤⣴⣿⣿⣿⣿⡍⣣⣿⣿⣦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⣛⣿⣿⣿⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢧⣉⣽⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⡔⣿⣿⢦⣉⣹⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢹⡀⠀⢹⡟⣿⣿⣿⣿⣿⣧⣿⣿⣿⠟⣫⡿⣿⢿⡿⢛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣇⠀⠈⣧⠀⢸⣷⣾⣿⣿⣿⡏⣿⡿⠁⣼⣿⣿⡔⠻⢸⣿⠀⠀⡜⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠒⣰⠟⠁⠘⠋⢆⠀⢸⡀⣸⣯⣿⡿⣽⡏⣿⠟⣠⡾⣯⣚⣿⢿⣦⡸⣿⠀⡴⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⠞⠁⠀⠀⢸⠀⠀⢂⠀⣇⣿⣿⣟⡞⡡⢘⣿⣾⢿⣿⣿⣧⢿⣞⣿⡁⣿⣾⣱⣿⣜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡜⠁⠀⠀⠀⠀⡀⠀⠀⠀⢣⣸⣿⣯⡟⢁⣠⣿⣿⣿⣀⠈⡹⣿⣼⣿⡝⣧⣿⣿⣿⣿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢀⡅⠀⠀⠀⠀⢹⣿⢏⣴⡟⢿⠟⠹⣷⣻⢦⡔⣮⢻⡿⣷⣽⣿⣿⣿⣽⣷⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠑⡀⠀⠀⢨⡇⠀⠀⠀⠀⢸⣿⣿⣏⠣⠈⢱⣄⠈⠙⢣⣾⣿⣶⣻⣌⠻⣿⣯⣹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣼⠙⣄⠀⠀⠀⣿⡁⣹⡞⡇⠀⢈⢿⠀⠈⢾⣯⣿⣿⣿⡿⠿⠟⡋⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⣀⣀⠈⢢⡿⠀⠈⢆⠀⢠⡿⠿⣿⣿⣗⠄⣀⣌⣷⠤⠞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠂⠬⢧⣸⣯⣹⣷⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⠈⡇⠀⠘⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢂⠀⢻⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⢣⡀⠈⠀⠠⡀⡄
⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠘⠦⠀⠁⠀⠀⢠⡆⣿
⠀⣤⡀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⢀⢀⣾⣷⣿
⠘⢿⡛⠒⠀⠈⠙⠲⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠀⠀⠀⠁⢀⢠⣾⣿⣿⣿⡇
⠀⣀⡀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇
⠀⠙⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠤⡿⢿⣦⣶⣄⡀⠀⠀⠀⣅⡀⠀⠀⠀⢈⣿⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠙⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠇⠄⠛⠿⣅⡈⠳⢦⣤⡄⠀⠀⠀⣀⣻⣿⣿⣿⠟⠋⠉⠉⠀⠀⠀⣄
⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠖⠒⣂⣀⢀⣿⡟⢄⡻⣍⣁⣶⢤⣴⣶⣿⡿⠋⠄⢀⣤⣀⣠⣶⣦⣄⣹⣷⡄
⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠠⠀⠀⢀⡜⠋⢞⣽⢿⣷⡚⣷⢻⢡⣀⡄⠹⣿⣯⡀⢠⣴⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠸⠟⠒⠂⠀⠀⣠⠄⠊⠁⣠⠴⠛⢡⣿⡝⣷⡥⠀⠘⣿⣶⣤⣤⠀⠛⡄⠛⠆⢿⣷⡤⠉⠉⣿⠟⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠊⠁⠀⣀⡴⠊⠀⠀⠀⠀⣿⢰⣿⡅⠀⠻⣿⡏⠈⠀⠀⠀⠠⠗⠀⢀⡈⠄⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠈⠀⠿⣷⣆⡘⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⠛⠁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⡤⠂⠀⠀⠀⠀⡄⠀⠐⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢤⡴⠁⠀⡴⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⠇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣿⠀⢀⣴⣦⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣸⣿⢷⡄⠀⠀⢀⣘⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣉⡟⠁⢻⣇⡀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣴⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢋⣾⣿⣿⣾⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢀⡾⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡟⠁⢸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⡀⠀⠀⠐⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠩⠔⡾⠀⢠⠆⠀⡀⣸⣴⢰⠾⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉

⠀⠀⠀⠀⢀⢀⡤⣰⠲⣀⢤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⡀⠀⡀
⠀⠀⠠⡖⠾⡈⢣⡘⢄⢻⢠⠋⡧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⣰⣙⠲⢬⡳⣝⢮⢞⢸⣸⢡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⢘⡠⠬⣍⣒⣬⣳⣷⣿⣾⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄
⠀⢸⡒⠒⠒⠒⠲⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠐⠁⡔
⠀⠀⣝⣉⡭⢝⡲⢿⣿⣿⣿⣽⣦⣤⡠⠴⠶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⡀⢋⡄⠈⠢⠄⠄⠀⠂⠒⠒⠢⡀
⠀⠀⠀⢧⠖⣩⢞⡟⣿⣿⡿⢯⠡⠙⠐⠈⠀⠠⢄⣤⣻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠌⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀
⠀⠀⠀⠈⠹⠥⣞⢰⣿⣿⢐⠈⠀⠀⣀⣐⣿⣴⡷⠟⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠂⢠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⠘⡠⠤⣶⣿⢿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠪⡀
⠀⠀⠀⠀⠀⣀⣴⣿⣯⣿⡓⣶⣖⣫⣿⣿⣮⣝⣟⣶⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣄⡀⠀⣀⡀
⠀⠀⢀⣴⡿⢫⣵⣯⣼⣽⣶⣚⠽⠚⡡⢚⡕⡻⢿⢟⠛⣿⡿⣿⣿⡳⣾⣿⣶⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⢠⠞⣫⢂⡾⣏⡜⣸⢿⢨⢧⢤⠊⣠⠏⡰⠁⡌⢸⡈⣎⢫⡪⣑⠯⣝⣛⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠰⠯⡴⢅⡔⠱⣽⠡⢻⢸⠈⣷⠈⠛⢧⡰⣇⢠⢷⡘⣇⡈⢆⡙⣬⣻⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠐⢄⠠⠀⢀⢆⠀⡀⠀⢀⠀⢀⠐⠐⠁
⠀⣸⢁⡎⢢⢇⠇⢰⢸⠀⣆⠸⡄⠀⠀⠀⠈⠁⠀⠉⠁⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠈⠀⠀⠁⠁⠁⠈⠈⠁
⠀⠋⡛⢘⠨⡜⡀⣼⢸⡀⢸⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⢱⡧⡆⡇⡇⢸⠈⢳⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢃⢡⢇⠈⢦⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⠈⠋⠀⢻⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣌⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠐⠊⠁
⠀⠀⠀⠀⠠⢄⣦⣀⣀⠀⠀⠀⠀⣰⡉⢉⣉⡻⠋⠀⠀⠀⠀⠀⢀⣤⣶⣶⡏⠀⠀⠀⠀⠠⢤⣤⡀
⠀⠀⠀⠈⠐⠋⠁⠁⠀⠈⢉⣤⣾⠿⠻⡯⡭⠀⠀⠀⠀⢠⣶⣶⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠄
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡠⠒⠉⠀⠀⠈⠡⠄⠄⠀⠀⠀⠀⠀⠁⠀⠠⢶⣄
⠀⠀⠶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠀⠠⡀⣀⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢈⠋⠀⠁⠀⠀⠀⣀⣤⣦⣴⡶⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣤⡀⠀⠴⠒⠂⠟⠛⠛⠛⠛⠛⠀⠀⠀⠤⠀⠀⠉⠉⠉⠡⢤⠐⠠⢦⠄
⠀⠀⠀⠀⠀⢢⣀⠉⠋⠀⠈⠉⠐⠀⠀⠀⠀⠀⢰⠆⢀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠐⢲⠎
⠀⢀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⡀⡀⠀⠀⢀
⠀⠘⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠳⠖⢤⣶⣄
⠀⠀⠀⠀⠀⠈⠛⠻⡿⠷⠤⡀⠀⢀⡀⠀⠤⠩⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⣿⣿⣦
⠀⠀⠀⠀⠒⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠈⠙⢷⡄
⠀⠀⠀⠐⠓⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠈⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠞⠉⠻⣿⣿⠛⢄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠂⢠⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⠀⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠃
⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⢹⣿⣯⡄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⢿⣿⣧⣤⣴⣦⠀⣤⠄⠐⠊⠀⠀⢠⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣀⣠⣀⣀⣯⣿⣿⣿⣿⡟⠀⠈⣷⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢉⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣼⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣿⡛⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⡛⢁⣿⡇⠀⠀⣽⣿⣷⣄⣀⣀⣀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⣤⣶⣶⣾⣾⣿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⡇⠀⠖⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⣠⣴⣾⡏⣾⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡟⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣻⣿⣿⣿⣤⣤⣠⣤⣤⣄⣠⣤⣤⡀
⠀⠀⠀⢀⣀⣿⣿⣿⡃⠉⢻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⣴⣿⠏⠀⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢀⣠⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⣀⣶⠁⠈⠑⠀⢹⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⡇⠀⣼⠉⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠋⠁⠀⠀⠀⠀⠀⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⡼⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⡀⠀⠀⠀⠀⠀⠀⢿⣷⣆⢸⣿⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣾⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⣿⣦⠀⠀⠀⠀⠠⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣰⣿⣿⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⡑⣤⢀⣷⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠘⣿⣧⠀⠙⢿⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠘⣿⣧⡀⠀⠻⣿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠘⢿⣿⡄⠀⠈⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠑⠀⠀⢹⣿⣿⠻⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠙⣿⣇⠈⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡟⠠⠀⠀⠀⠀⠈⣿⣿⡄⠀⠙⣿⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣄⠀⢻⡇⡈⣋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣷⡀⠐⢦⣄⢿⣿⣿⣿⣿⣷⣧⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣦⡀
⣿⣤⡀⠹⣿⣿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⣄⠹⣿⣿⣿⣿⣿⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠰⢀
⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣧⠘⢻⣿⣿⣿⣟⡀⠹⣿⣿⣿⣿⣿⣆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢾⣷⣄
⣿⢿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣷⣤⣸⣿⣿⣿⠏⡛⢻⣿⣿⣿⣿⣿⣦⠀⠉⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⢙⠻⣻⣦
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⠈⢻⣿⣮⡻⣿⣿⣿⣥⢿⣿⣿⣿⣿⣿⣿⣧⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠻⢿⣦⡍⣠⡀
⣿⣿⣿⣿⡛⢿⣷⡻⣿⢻⣧⡄⠹⠿⣿⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⠀⠈⠉⠛⣅
⣿⡿⢿⣿⣄⡀⠙⢷⡙⢿⣋⡿⣦⡴⢆⣹⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⣠⣿⡷⠶⠆⢸⣿⡆
⣿⣧⣮⣿⣿⣿⣷⣄⠘⣄⠻⣄⠦⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠁⠀⠐⣿⠟

⠀⠀⣀⣀⣀⢀⣠⣴⣶⡶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠈⠙⠿⣿⣿⣿⣿⢷⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠘⠙⠋⠁⣸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠉⠈⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⣀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠠⣤⣶⣶⣦⣀⠀⠉⠉⠛⠛⠻⠿⠿⢿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠄⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣙⠛⠿⣷⡅
⠀⠀⠀⠀⠀⠀⠑⣠⣄⠀⠙⠛⠲⡤⠄⠒⠠⢀⣠⡴⠋⠙⠛⠛⢿⣿⣯⠉⠉⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠐⣀⣠⡶⠛⠁⡄⠀⠀⠀⠀⠀⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣾⣿⡿⠿⣦⣄⡀⠀⠀⠀⠀⠀⣰⡏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢿⡿⠀⠀⠘⣌⠁⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⠀⠙⠓⠄⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣴⣶⣿⣿⠿⣾⡉⠁⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⠋⠀⠤⠺⣿⣦⡀⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⡀⠀⠐⠂⢀⡼⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠹⣿⠇⠄⣄⠠⣬⠻⣿⣦⡀⠰⣾⣷⣶⢆⡀⠀⣟⠃⠀⠀⠀⠉⠀⡄⢄⣀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⣦⣄⠀⢀⣀⠙⠀⠀⠉⠀⢆⡈⢿⣿⣷⡀⠡⣽⠟⠟⠫⢚⡿⠦⠤⠀⠀⠂⠐⠛⠋⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠻⣿⣿⣀⣼⣟⣯⣿⣿⣷⣄⠻⡁⢎⠻⣿⣧⠀⠀⠀⠁⠈⠁⠀⠠⢄⠸⠇⠐⠶⠦⢤⡤⠄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢉⣾⣿⣿⣿⣿⣿⣿⡿⠆⠇⠀⡀⠙⣿⣷⡀⠀⠀⢠⣤⣤⠤⣂⣴⣾⡟⠛⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⢿⣧⠀⠘⠋⠁⠐⠾⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡿⢻⡿⠉⠉⠉⠉⣹⠟⠛⢻⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣿⡅⠈⣧⢴⣿⠟⣤⣿⣿⣦⣾⣤⣨⡿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣍⣹⡷⣾⣀⣽⣿⣾⣿⣤⣿⣿⣿⣿⣿⣽⣿⡄⠀⢹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣏⣙⣟⣿⣟⣿⣿⣹⡿⣿⣏⡿⡿⠋⠙⠉⠀⢹⣶⡟⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣻⣏⣩⣿⣿⣿⣷⣿⠋⠠⠈⠙⠃⠀⠀⠀⢀⣾⣷⣜⣷⢀⣨⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣾⣏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠐⢠⠠⠀⠀⠀⢀⣜⣻⡟⠀⣙⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢅⠀⢴⠆⢺⡟⠛⣿⣿⣿⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⢰⡜⢀⣤⣶⣾⣇⣾⣋⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢠⣶⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣼⠇⠀⠀⠀⠰⢀⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠾⠟⠁⠀⠰⠀⠀⠜⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣠⠀⠀⠀⠉⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠉⢹⡿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⢦⠉⠹⠋⢩⣿⠻⣿⣿⣿⣡⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠇⢻⠟⠿⠁⠌⠀⠂⠀⠘⠁⢡⠟⢻⣿⣧⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣶⣄⠐⠄⠀⠀⠀⠀⠀⠀⢀⡃⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣦⠀⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⢹⣿⠟⠉⠀⠀⠀⢀⣤⣼⣿⠃⢋⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡀⠀⠀⡀⠀⠀⠁⠀⠀⠈⣷⠀⠀⠀⠀⢀⣠⠊⠙⠿⢿⡿⡿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⣀⡀⢂⡀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠈⡀⢀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⢿⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠻⣿⣾⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠤⠀⠁⠉⣿⡿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠙⠁⠀⠀⣀⣴⣿⠷⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⢀⡿⠟⠀⠀⠀⢺⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣿⠂
⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇