Node Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣽⣿⠀⠀⢸⣿⣤⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠁⠀⠀⠀⠉⠉⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠹⣿⣷⣄⣀⡀⢀⣀⣠⣴⡿⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢻⡇⠀⠀⠈⠙⠻⠿⠿⠿⠟⠛⠉⠀⣰⣿⡇⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⢀⡼⠁⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣴⣿⣿⠶⠆⣸⣿⡏⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⣠⠞⠁⠀⠀⠀⠰⠿⠿⡛⠋⠉⠉⠀⠀⣾⣿⡇⠀⢠⣿⣿⠁⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣄⡀⠀⠀⣠⣿⣟⣧⣠⣾⣿⠀⣼⣷⠀⠀⣿⣿⠁⢠⣿⣿⣯⡾⢋⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣦⣠⣿⡟⠁⣿⢸⣿⡇⢰⣿⡟⠀⡼⢿⣿⣰⠏⣿⣿⡿⢁⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢾⣿⡿⢸⣿⣇⣴⠇⢸⣿⡴⠛⣿⣧⠞⠀⠈⠛⢁⣤⡹⠿⠁⣼⣿⡏⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⣾⣿⢁⡌⠻⠿⠃⠀⠀⠉⠀⠀⠈⠁⠀⠀⢀⠀⠘⢿⣧⣀⠀⣿⣿⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⠿⠁⣼⠃⠀⡀⠀⣠⠀⣰⣆⡴⣿⠆⢠⡞⣻⣿⢀⣼⢋⡿⠁⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣰⠏⠀⣼⠃⣼⣿⣰⣿⡿⢡⡟⢠⣿⡴⠋⣙⡛⠁⣟⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢛⣿⠿⢦⣄⣻⠞⠉⣛⡋⠈⠀⠸⣷⠟⠀⠀⢰⣿⡏⠀⠛⢉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⡁⠀⠀⢈⣉⠙⠛⢉⣥⣀⠀⠀⠀⠀⠀⢠⣿⣿⠁⢀⣴⣿⡿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⣰⣿⣿⠀⠀⣿⡟⠹⣷⠀⣴⣿⠿⣿⣿⡇⠀⣾⣿⠏⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡷⢻⣿⡇⢠⣾⡿⢿⣾⡿⣿⣿⠃⢠⣿⣿⠀⣸⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⣿⡿⠀⣾⣿⠃⣠⣿⠃⢹⣿⣴⠏⠻⣿⠟⠙⣿⣿⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣿⣇⡴⠛⣿⣿⡿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁

⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠈⣷⢠⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉
⠸⢦⠀⠀⠀⠀⠀⠰⠄⠀⠀⠈⠳⣄⠀⠀⠀⠁⣦⡷⢦⣄⣀⣤⠴⢾⣰⡇⠀⠀⠀⣀⠤⠒⠉⠁⢀⣠⠘
⠀⠀⠱⣄⠀⠀⠀⠠⣄⣠⡀⠀⠀⠈⠱⣄⠀⣷⡿⠁⠀⠀⠀⠀⠀⠞⠸⣇⣀⡴⠊⠁⠀⣀⣴⢚⠏⠉⠀⠀⠀⠀⠀⣠⡶
⠀⠀⠀⠈⠳⣄⠀⠐⠮⠿⠹⡆⣤⠀⠀⠈⣳⣛⣐⣂⠀⠀⠀⠀⠀⢠⠀⣈⠁⣤⠰⡒⠖⢎⡩⢞⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠙⡛⢠⠼⠒⡽⠾⡝⠋⠉⠙⣆⠀⠀⠀⠀⠇⠀⠀⠀⠉⠀⠀⢀⣝⡙⠀⣠⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⠋⣋⡜⠀⠀⠀⠀⠀⢀⣠⢿⡄⠀⣰⡈⠀⠀⠀⠀⠀⠀⠀⢸⢉⢣⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢰⡏⠁⠀⠀⠀⠀⠀⠈⣉⣰⡇⠀⠦⡄⠀⠀⠀⠀⠀⠀⡄⣠⠾⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⢻⡄⠀⠀⠀⠀⠀⠀⣠⣤⡯⠀⡛⠁⠀⠀⠀⠀⠀⠀⠀⠹⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⣫⠀⠀⠀⠀⠀⠀⠀⠴⠒⢣⢠⣉⡁⠀⠀⠀⠀⠀⠂⠀⡾⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⠁⠀⠀⠀⠀⠀⠀⣒⡛⢸⠀⠦⠀⠀⠀⠀⠀⡘⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢁⠀⠀⠀⠀⠀⠀⢈⡭⢸⡄⣦⠀⠀⠀⠀⠀⠀⣨⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀⠀⠀⠀⠀⠀⠠⠾⢸⢇⡤⠀⠀⠀⠀⠀⠀⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠁⢦⠀⠀⠀⠀⠀⠀⠀⢾⢨⣀⣀⠀⠀⠀⠀⡀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣤⡉⠂⠀⠀⠀⠀⡃⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⣾⡅⠁⠁⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⠇⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⣥⠞⠤⣎⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠀⠀⠀⠀⠀⠀⠀⣤⢣⡗⡆⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠸⠦⡆⠀⠀⠀⠀⠀⢀⡆⠘⠈⠃⠀⠀⠀⠰⡆⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢢⠀⠀⠀⠀⠀⡆⠀⠰⠀⠀⢄⠀⠰⠇⡡⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⡀⠀⠀⠴⠏⠀⠀⠀⠀⠀⠈⠛⣀⠸⠷⢀⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢛⡐⢪⠜⡀⠀⠀⠀⠀⠀⠀⢀⠖⠏⠀⠀⠳⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠓⠉⣞⠙⡈⢀⡀⠀⠀⠀⠀⢆⠙⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠰⠚⡀⠛⠀⠀⣼⡇⠀⠀⠀⠈⡛⡁⢶⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠿⠚⠃⠀⠀⢰⠃⡇⠀⠀⠀⠘⠃⠁⠀⠀⠀⠀⠀⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⢀⠂⠀⠀⢀⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠻⡿⠀⠀⢀⠂⠀⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠸⡟⠁⠀⠀⠀⠀⠀⠀⠑⢄⣠⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⣸⣄⠐⠁
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⢀⣤⡔⠂⠉⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⢠⢀⠂⠀⠀⠀⠀⠁⠀⠀⠠⣿⡿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⡀⠑⠠⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢼⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠈⠐⢄⠀⠀⠀⢠⠀⠀⠀⠌⠀⠀⢈⣄⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⢻⠃⠀⠀⠀⢀⣶⡔
⠀⠀⡄⢠⠁⠀⠀⠀⠀⠀⠀⠈⠂⣀⡀⠀⠀⠈⠢⡀⠈⠀⠀⠈⠀⠀⠀⣿⡿⠀⠀⠀⠔⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠿⡟
⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠄⡆⠠⠀⠀⠀⠀⠈⡁⠀⠠⠊⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢃
⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠤⠀⢀⣀⣿⣇⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⣨⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠠⠀⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢏⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠃⠀⠀⠀⣾⣿
⠁⠀⠀⠀⠈⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠀⠀⠀⠀⠔⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠉⢀⠀⠀⠀⠀⠀⠀⡠⠛⢋
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠡⡀
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠄⠀⠃⠀⠀⠀⠀⢀⣶⡔
⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠄⠀⠀⠀⠉⠀⠘⠛⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠜⠃⠀⣾⣦⠀⠀⠀⠀⠀⠿⡟
⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⢀⠠⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠑⡀⠀⡠⠀⠁⠀⠀⠀⢻⣟⡀⠀⠀⠀⠀⠀⠐⡀
⠂⠀⠀⠀⠀⠀⠀⢡⣀⠀⠀⠀⠁⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⡀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⢰⣶⡄⠀⠀⠐⡀
⠀⠁⡄⠀⠀⢀⠄⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠢⡀⠀⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠈⠻⢟⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⢨⣦⡔⠁⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⡀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠸⡿⠃⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠄⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠠⠁
⠀⠀⠀⠃⠀⠀⠐⠀⠀⢡⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢱⣷⡆
⠀⠀⠀⡄⠀⠠⠁⠀⠀⠀⠆⠀⠠⠊⠀⠀⠀⠀⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣿⠆⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢐⣀⠀⠀⠀⠀⠸⡿⡃
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠐⠀⠐⡀
⠀⠀⠀⡇⡀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⡄⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢠⣶⡀⠀⠐⡀
⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠁⠀⠀⠀⠁⠀⠀⠈⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⠃⠀⠀⠈
⠀⠀⠸⡿⠃⠀⠀⡀⠀⠘⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠢⡀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢠
⠀⠀⢠⠀⠀⠀⠀⠈⢰⣿⡇⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠈⣼⡀⠀⠀⠀⠀⢠⠀⠊⠀⠀⠀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠑⠀⡀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠈⡀
⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣇⣀⣀⣌⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣃⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠚⠻⠋⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⡀⠠⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢿⣿⡿
⢸⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠙⠿⠿⠃⠀⠀⠨⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣿⣿⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟
⣆⠀⠀⠀⣠⣄⡀⢀⠠⠐⠈⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⢠⣴⣄
⠃⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⢀⡀⠀⠸⢿⠿⠓⠀⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣤⣤⡄⠀⠀⠈⠉⠁⠈⠐⠠⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣀⢀⣀⡀
⠘⠿⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠆
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠸⣿⡿⠇




⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣛⣿⣟⣟⣿⣟⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠁⠀⠉⢻⡟⠉⠀⠈⠙⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⢀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⡀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠋⠙⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠙⠻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠉⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⡀⠀⢀⣠⣼⣧⣄⡀⠀⢀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣿⣿⣿⣿⣿⣿⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⣿⣿⣿⣿⣿⣿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠁⠀⠈⠙⢻⡟⠋⠁⠀⠈⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣀⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣄⣠⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄⣠⣴⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠈⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠁⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣄⡀⠀⣀⣼⣧⣀⠀⢀⣠⣴⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄⡀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡿⠟⠛⠋⠙⠛⠻⢿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆
⠀⠀⠀⢀⣤⣶⣶⣦⣄⠀⠀⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠈⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣦⣤⣄⣠⣤⣴⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠈⠙⠻⠿⣿⣿⣿⣿⠿⠟⠋⠁⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⣀⣀⣀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⣀⣀
⠀⢀⣴⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣦⡀
⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠈⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠋
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣾⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠋⠁
⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠐⢀⠐⡆⣠⠆⠀⢲⡀⡶⠀⠀⠐⣶⠀⢀⠀⠀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠁⠀⢶⠀⠹⣇⠀⠀⣀⡼⣇⠸⣤⠞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣄⡀⢻⠉⣉⠙⢿⡀⢹⠴⠚⠣⣄⠘⣄⣣⠀⠀⢹⣀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢺⡞⠉⠀⠀⠙⣾⠀⡀⠀⣄⠀⢸⣃⣤⠖⠋⠉⠈⠀⠀⢀⡴⠛⢫⣋⠍⠏⣏⡛⠗⣤⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢐⡧⠚⠁⠀⠘⣦⡏⠁⠈⡆⠀⠀⠀⠀⡴⣋⣤⣤⠀⠙⣷⠶⠶⠶⠾⠾⢷⠆⡇
⠀⠀⠀⠀⠀⠀⢰⠤⠴⠖⠷⠶⠿⠷⠾⠧⢤⠤⣿⣤⣾⣀⣴⣈⣓⣾⠓⣶⠾⣇⢹⠠⢸⠀⠀⣿⣿⢻⢹⡆⠀⢸⡶⡇
⠀⠀⠀⠀⠀⠀⠘⠚⠓⠛⠛⠛⠛⠓⠒⠒⠦⠤⣤⡀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠻⠚⠶⠼⢦⣄⣾⣈⢙⠉⠁⠀⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣄⣀⣄⣀⣀⣄⣀⣀⣀⡀⡀⠀⠀⠀⠈⠉⠋⠓⠒⢼⣍⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠠⠄⠀⠀⠀⠈⠉⠉⠉⠉⠙⠒⠒⠲⠦⠤⣀⣀⣈⡇
⠀⠀⠀⠀⠀⠀⢸⢀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠤⠤⠤⢤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⡃
⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡠⢠⠴⣿⢻⡆⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⡀⢀⣀⢀⠉⠉⠉⠙⠒⠒⠶⠤⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡋⢳⣯⠭⡇⠀⠀⠀⠀⠀⠀⠀⠹⣟⠿⠿⠉⠩⠉⠍⠉⠙⢛⣺⡶⠦⣤⡀⠀⡅
⠀⠀⠀⠀⠀⠀⠐⠀⢀⣤⠶⣄⠀⢹⡉⡾⠴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡒⠂⠀⠂⠀⠂⠾⣍⣽⠁⠂⡌⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⡞⢩⠷⣤⣳⢷⡊⠀⢀⣤⠞⢻⢉⣯⣿⠃⠀⠠⠀⠀⣽⢷⣮⡀⡂⠐⠀⢾⡆⢄⣅⣠⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠲⢷⠋⣰⢻⠻⣾⢇⡴⡇⢸⣤⠞⠛⡶⠃⠀⠀⠀⠀⠀⣳⠾⠃⢹⣭⣅⣁⣹⡗⠻⣤⡿⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠲⠼⡞⠁⡞⠀⣏⣾⣠⠷⢯⣬⠽⠋⠀⠀⠀⢀⠀⠀⠀⣇⣤⡀⠀⣿⡏⠁⢽⡏⣁⣽⡉⡒⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠦⣧⢞⡁⠘⢿⠛⠛⠉⠉⠀⠀⠀⠀⡀⣹⡛⠻⡆⢸⠿⣼⠇⠀⣿⡧⠰⢾⡇⠦⢿⠀⣤⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠶⢾⡿⠛⢷⣮⣧⣶⣤⡦⠀⠀⠸⠀⠙⡹⢿⡴⠃⢸⠀⢿⠀⠀⡟⡇⠘⣸⡗⢐⢸⠒⠂⡇
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠧⠤⠤⠤⠵⠿⠩⠤⠦⠤⠾⠤⠴⠥⠤⠧⠠⠼⠦⠼⠤⠤⠧⠯⠩⠽⠍⠍⠽⠭⠭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⢠⠙⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣷⣼⡄⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠐⣶⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣺⣿⣿⣿⣿⣽⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠐⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢃⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣍⣉⠉⠉⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣟⡂⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣦⠄⠀⠀⠈⠩⠽⠿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣛⣛⣀⠀⠈⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢇⣀⠀⠀⠀⢤⢀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢀⣔⣉⣉⣀⣀⣀⠤⠚⠉⠒⠠⣄⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠃⠀⢀⣤⡴⠚⠉⠁⠀⠈⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣦⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠲⢤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢨⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣾⠁⠀⠀⠀⠀⠈⢳⣰⠟⣿⠲⡀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠳⡴⠶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⢀⣼⣿⠉⠳⡄⠀⠀⠀⢀⡴⠋⣸⡏⢳⡀⠀⠀⣠⠖⠶⠞⠃⠀⢿⡑⠉⠢⣄⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠙⣦⣠⣴⠟⠀⣾⢧⣙⡢⠙⠲⢮⣁⣀⣀⠀⠀⠀⠈⢿⠂⣀⣈⡷⢾⣧⡾⠁⠀⠀⠀⠀⢺⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⢀⡴⣾⠉⠀⠀⠀⠀⠻⣄⠀⠉⠂⠀⠀⠀⠉⠉⠑⠄⠀⠀⠈⠋⠉⠁⠀⢾⡈⠛⠶⢤⣤⣤⠞⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠁⠀⣿⡄⠀⠀⠀⠀⢠⡘⣯⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⢸⡀⠀⠀⣸⠃⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⢸⣿⡇⠀⠀⠀⠀⠈⢿⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⡀⢻⡄⣿⡇⠀⢠⢿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣾⣿⣿⡀⠀⠀⠀⡄⠘⣧⠈⠓⠦⢄⠀⣀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣿⠀⢹⣿⣿⣠⣯⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣷⠀⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⣿⣿⣧⠀⠀⢸⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣏⢢⡄⣸⣿⡄⠙⢆⠀⠀⠀⢸⣿⡇⠀⠀⢀⣿⣿⣿⠀⠀⣾⣿⣧⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠁⠀⠀⣾⣿⣿⠀⠀⢾⣿⣿⣿⣦⣠⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⡉⢻⠋⢲⠾⣿⣿⣿⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⡤⠤⡤⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣦⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⣸⠀⠀⣳⠀⠀⠀⠀⣰⢋⣴⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⢨⡷⡇⡤⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀⡾⠁
⠀⠀⠀⢹⠁⢐⡷⠀⠀⠀⠀⠘⢿⡟⣾⢂⣶⢐⣶⢰⣆⠀⠀⠀⠀⠈⠀⠈⡯⡇⠀⠁⠀⠀⠀⠀⠀⠨⠉⠉⠁⡾⣆
⠀⠀⠀⢩⡣⠊⠀⠀⠀⠀⠀⠀⠀⢬⡯⢨⣯⠨⣿⠬⣿⡄⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠙⠄
⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢙⣿⠉⠋⠉⠁⠀⠀⢀⣀⣀⣤⣋⣼⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠐⠠
⢤⡀⢀⣴⣦⣾⣷⣤⣄⠀⠀⠀⠀⠀⢀⡀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢳⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⢸⡇⣸⡇⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠿⠉⠀⠹⠇⠀⠀⠀⠈⡿⠿⣿⢸⣿⣿⡏
⠀⠘⣿⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢼⣹⣏⣿⣻⣻⡇⠀⠀⠀⠀⣁⠀⢰⣶⠆⠀⠀⠀⠀⠀⠀⢰⡉⡎⣹⢸⣿⣿⣷
⠀⠀⠉⠾⠎⠛⠱⠿⠊⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠠⠿⠀⠾⠀⠧⠀⠠⠄⠀⠀⠀⠾⠿⠿⠿⠯⠿⠿⠿⠆
⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠞⠳⢴⠀⠀⠀⠀⠀⠀⢰⣷⠖⣲⠒⡶⢲⢲⡇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⣇⠘⠇⣸⠒⠀⠀⠀⠀⠀⣼⠏⠀⠁⠈⠀⡿⣼⡇⠀⠀⠀⢀⣀⣰⣺⣲⣀⣀
⠀⠀⠀⢀⣻⣟⡅⠀⠀⠀⠀⠀⠀⢀⡀⣋⢙⡋⣙⣀⡀⠀⠀⠀⢀⣿⢀⡀⠠⠀⢸⣇⣿⡇⠀⠀⠀⢈⣿⣉⢹⠉⣹⣏
⠀⠀⠀⠚⠓⠓⠓⠂⠀⠀⠀⠀⠀⠐⠂⠒⠐⠂⠒⠐⠂⠀⠀⠀⠈⠀⠀⠁⠀⠀⠉⠙⠛⠃⠀⠀⠀⠐⠂⠒⠐⠒⠂⠒
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⡎⣭⣭⡝⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠⡀⡴⠋
⠀⠀⢰⣿⠀⠀⢰⡇⠀⠀⠀⠀⣀⣤⣄⢴⠟⠻⣇⠀⠀⠀⠀⠀⠀⠀⡇⠶⠶⢮⠀⣼⣿⡀⠀⠀⠀⢀⣴⣿⣿⣦⡀⢀⡴
⠀⠀⠘⣿⠀⢠⣿⡇⠀⠀⠀⠀⢿⣿⣿⣦⣄⢀⣭⣦⣄⠀⠀⠀⠀⠀⣏⣛⣛⣉⠀⠛⣿⠃⠀⠀⠀⢀⣿⣿⣿⣿⣿⣮
⠀⠀⠀⠻⡄⣾⡿⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⢺⣿⣿⣿⡇⠀⠀⠀⠀⡧⠷⠿⢼⠀⠀⠁⠀⠀⠀⢀⣼⣿⠿⠻⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⡄⠀⠃⠀⠀⡀⠀⠀⠀⠐⠐⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠙⢆⠀⠀⠀⠀⠀⡴⠋⡂⠔⠸⠀⠀⠤⠼⢦⠀⠿⠃⠀⠀⠀⠀⠈⣀⡶⠒⢡⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣤⠀⠀⠀⠀⠀⠀⠤⠀⠒⠀⠀⠰⠀⠀⠈⠃⠀⢐⠀⡸⠏⠀⠀⠀⠀⠀⠀⢠⡤⠀⣶⣶⠐⠿⠂⠀⠀⢯⡈⢇⠀⣠⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⡀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⢰⡇⠀⠀⠀⠀⠀⠀⠀⠰⠂⣤⠈⠀⣦⠀⠀⠀⠀⠙⠵⡎⡘⡳⠈
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡄⠀⢨⠀⠀⢀⡀⠀⠀⢃⠀⠁⠀⠓⠀⡠⠀⠀⠀⠁⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠖⠈⠀⠀⠀⠀⢠⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠃⢀⠀⠀⠇⠸⠃⠀⠀⠀⠑⠤⢀⢀⣀⣀⠤⠂⠀⠀⠀⠀⠀⡈⡠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠰⠄⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣰⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠆⠀⠘⢰
⠀⠀⠀⠀⠠⠀⠀⠠⠐⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⡀⠀⠀⠀⢀⠃⠁⣟⡀⠈⠀⠀⠀⠀⢀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠
⠀⠀⠀⠀⠄⠠⠀⠀⡀⡄⠀⠀⠀⠀⢆⠄⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠉⠄⠀⠀⠈⠁⢸⣏⡀⠀⠀⠀⣀⠀⡀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠤⠀⢐⢤⠼⠔⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⢀⠀⠀⢀⡀⢰⠀⠀⠀⠀⣶⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⠄⠠⢄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠐⠈⠈⠀⠀⠈⢁⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⠀⠀⠀⢇⢒⠆⠀⢱⠀⠀⡈
⠀⠀⠀⠁⠀⠀⠀⠀⡄⢠⡀⠃⠀⠀⠀⠀⠀⣇⠀⠀⠄⠀⠳⠀⠄⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢳⡄⠀⡠⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡀⠀⠈⠫⡀⢀⣠⡰⡶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠄⠁⠀⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠰⢁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⠄⠘⢋⣉⠘⠑⠢⡀⠀⠀⠀⠀⠀⠤⠈⠀⡀⠄⠋⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠘⠛⡠⠀⢀⠜⠀⠀⠀⠀⣀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠔⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠦⠴⠖⠚⠁⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠰⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠐
⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠞⠁⣈⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠚⠀⠄⠰⠀⠀⠄⡡⠆⠀⠀⠀⠀⠀⠀⣤⠀⠈⠒⠀⠀⠑⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠚⠐⠂⢀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠉⠑⠲⢼⡀⠀⠀⣆⠲⠀⡠⠠⢄⠀⠀⠀⠰⠞⠀⠀⢰⣤⣼⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠘⠄⡃⠀⠚⠃⣀⠨⠵⠤⣀⠉⠀⡟⠀⢶⡸⠀⠀⠀⠀⠀⠀⠘⣿⣭⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠀⠀⠑⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣀⠀⢇⠀⠲⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⢀⠀⠱⣄⠊⠀⠘⢀⡤⠀⠀⠀⠀⠀⠀⡸⢁⣀⠀⠀⠱⢸⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠢⣌⣁⣄⢸⣇⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠰⢈⡁⠀⠀⠀⣿⡰⠊⢁⠑⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠈⠙⠷⢶⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠐⢣⠃⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⡀⠀⣿⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠈⠉⣤⣶⣦⡉⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣷⣿⣷⡆
⠀⢰⣶⣶⣶⣷⣿⣿⣿⣿⡇⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠹⣿⡿⠁
⠀⠀⢻⣿⣿⣻⣿⣻⣿⡁⢤⠈⠁⠀⠀⠀⠀⠀⠀⠐⢤⠤⣿⡧⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠿⠿⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠇⠻⠿⠇

⠀⣀⣠⣴⣦⣤⣤⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⡀⠠
⠀⠛⢛⣉⣉⣉⢩⣭⠡⣤⡄⣶⡄⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢸⣿⢸⣿⠀⣿⡇⣿⡇⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠢⠄
⠀⠀⢸⣿⢸⣿⠀⣿⡇⣿⣇⣿⣇⡀⠀⠀⠀⠀⢸⡇⠀⠀⡀⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢰⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇⠠⣾⣿⣿⡆⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⠿⣿⣿⡿⠿⢿⣿⣿⡿⠿⠟⠁⠀⠀⣿⣻⣿⣿⣛⣿⣻⡿⢿⣛⢿⣿⡟⠿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠶⠿⠿⠿⠷⠾⠿⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣄
⠀⠀⠀⢀⡒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠛⠓⠂
⠀⠀⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣤⣤⣀⣀⡀
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠙
⠀⠀⢰⣿⢻⡖⣶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⢀⣀⣀⠘⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⢀⣸⣿⣼⣧⣿⣼⣇⣴⣿⣦⣤⣀⠀⠀⠀⣀⣿⣿⣿⣿⣴⣿⣿⣿⣿⣙⣀⡀⠀⠀⠀⠒⣁⡐⠀⠀⠀⠀⠀⠀⠼⠾⠆
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠰⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠋⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠀⣾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠀⠀⠈⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿
⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣤⡀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡿⠀⠀⢸⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⣠⣾⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠰⠄⠀⠀⠀⠁⠀⣤⠀⠀⠀⠁
⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⡌⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⢰⠀⠃⡆⠀⢠⣤⣤⡀⠆⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠑⠂⠀⠴⣤⣄⠀⠀⢀⣴⣶⣶⣦⠀⠀⣤⡀⠒⠀⠀⠀⠀⠐⠓⠂⠀⠐⠀⠛⠛⠀⢰⡆⣿⡉⢸⣿⣿⣡⡆⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⠙⢯⣽⣽⣿⣛⣁⣀⣉⠋⠐⢲⣶⣶⡀⢀⣀⣀⣀⠀⠀⠀⠈⠉⠙⠉⣩⠄⣾⣿⣿⡦⠀⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠊⠀⠀⠀⠒⠀⠀⠺⠿⠿⠿⠿⠿⠶⠶⠶⠛⠛⠙⠉⠉⠉⠁⠀⠀⠀⠀⠁⠒⠲⠬⢴⣿⣏⣹⣷⣠⣶⣿
⠀⠀⠀⢠⠀⢠⠀⠀⠇⠀⠉⣀⣌⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⣏⣩⣉⢀⡒⠂⣰⠄⠐⠢⠀⠠⠤⠄⢀⢩⣙⡛⠿⣿⣿
⠀⠀⠀⠈⠠⣤⡰⣶⡎⠿⣷⢹⣿⡜⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢐⠒⠂⡮⠤⢴⣀⣠⡂⡀⣼⠃⠉⡸⠁⠑⡒⠚⠀⡤⠆⠀⣀⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠙⡇⠀⢱⠀⠸⣆⠈⢷⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡠⠀⢀⠌⠀⢠⠃⠀⣰⠏⠈⠉⠋⠑⠓⡖⠐⠥⡤⢰⣀⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢿⠀⠘⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠤⢤⣆⣀⣠⠁⠀⣰⡟⠀⠀⡌⠀⠀⡌⠀⠀⢰⠁⠀⠀⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠁⠀⠀⠀⠀⠈⠻⠿⣶⣶⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⢿⣶⠛⠠⠤⠼⣀⣀⠰⠁⠀⢀⡇⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⡖⣾⠖⠤⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀
⣿⣿⡟⠛⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⠀⠀⢀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢼⢸⡆⠀⠀⣷⠀⠀⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢀⡇⠀⠀⠀⡄⢴⣯⣿⡄⠀⠀⠀⠀⠀⠀⢀⡀⢰⡇⠀⠀⠀⠀⠀⢸⣇⣿⣀⣾⣮⣇⣄⠖⣿⠀⣴⣠⣗⣷⢴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⣸⣷⠸⡀⢀⣇⣿⣿⣿⣷⠂⠀⠀⠠⣄⣀⣸⡧⢸⣧⣰⣆⠀⢀⣈⣿⣿⣿⠟⠻⣿⣿⣿⠤⠿⣞⣻⣷⣹⣿⢉⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢰⣿⣿⣿⣿⡈⡒⠘⣿⣿⣟⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⢻⠃⠀⠀⠹⢿⢛⣘⣧⣾⠛⣽⣟⠡⣛⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣆⣷⣿⣿⣿⣿⡿⢳⡏⠀⢻⣿⣿⠁⢅⢠⡀⠀⠀⡙⠈⢿⣿⣿⡿⠋⠃⠰⠴⠦⣴⡏⠀⠀⠀⠀⠼⣟⣡⡿⣟⠛⣿⠋⣸⣿⣗⣠⣿
⠀⠀⠀⠀⣠⣴⣿⣿⣻⣿⣿⣿⣻⣿⢋⣽⠀⠀⠘⣿⠟⣀⠈⣟⣰⣤⣴⡁⠈⠙⣿⣿⠀⠀⠀⠀⠗⠀⢈⡧⠀⠘⠐⠦⠀⣸⣿⠀⢸⣷⣾⠿⣗⡼⠳⣄⡀
⠀⠀⠀⣸⣿⣿⣿⣷⣿⣿⣿⣿⠽⢿⣼⠋⠀⠀⠀⣿⠍⠀⠀⢿⣌⣿⠇⠀⠀⢀⠻⣿⣿⣤⣤⣶⣄⡾⠁⠀⠀⠀⢀⠀⠀⢈⡿⣦⣿⢽⣿⠂⣹⣿⣤⡧⠁
⠀⠀⢠⣿⣿⠿⠟⠛⠋⠁⠀⠀⢀⠀⠀⠀⠀⠀⠐⠏⠀⠑⠒⢘⠛⠟⠀⠈⢁⡠⠄⠈⠀⠀⠀⠙⠘⠳⠀⠀⠰⠛⠻⠟⠟⢿⣤⣾⠸⠯⠐⠂⠉⢧⠀⠈⠆
⠀⠀⠈⠉⠀⠀⢺⠇⠀⠀⠐⠚⢻⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠁⠋⠛⠿⠶⠆⠊⢉⣉⡲⠏⣹⣦⡨⠷⢶⣄⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡀⠤⠤⣄⠀⠐⠶⣦⡀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠛⠓⠒⠚⠛⠛⠻⠓⠒⠺⠿⠀⠀⣀⣄⣀⣀⣀⠛⣫⣉⣱⡖⠂⠉⣳⣀⣀⣸⡧⠄
⠀⢠⠀⠰⠖⠀⢀⣠⣤⣄⠄⠀⠀⢠⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠙⠛⠛⠿⣷⣶⣾⣤⣼⣿⣠⡀⠰⣿⣆⢀⡄⣤⢷⣀⡄⡀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣄⣩⣿⣾⣧⣽⣧⣿⣷⣞⣻⢻⡄⣿⡆⠀⠄⠀⡀⠀⠀⠀⢰⣧⣦⡀⢂⢰⣄⠀⠀⠀⠘⣆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⢿⡿⢿⣿⣟⣉⣉⣹⣿⣿⣿⡇⠀⢠⡄⣧⣶⣄⣦⢸⡿⣿⡇⠘⡞⣿⠀⠀⠀⡄⢻⢄⠀⢠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠏⠛⠛⠛⠾⣓⠀⠠⠅⡽⢳⣿⣿⣼⣿⣿⣷⢀⣦⣿⠄⠀⠀⢸⢸⣿⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣉⣉⣁⣈⡁⠀⠀⢰⣉⣉⣩⡍⣻⣿⣿⣭⣄⣀⣦⠚⠀⢺⣿⢿⡟⠋⠁⢓⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠑⠈⠙⠋⠉⠍⠭⢙⣿⣦⡤⢤⣶⣾⣟⡿⣯⣭⡭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⢶⠲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⡇⢿⢹⣿⠾⡵⠆⢀⣴⣶⣀⣶⣿⣿⣿⣿⣦⠀⠀⠉⠙⠋⠉⠛⠛⠛⠛⠓⠒⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠖⠮⠅⢀⠸⢾⣿⣿⣿⣷⣶⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠌⠛⢻⠛⠛⠟⠋⢩⢥⠌⠟⠗⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⠚⠻⣶⣌⣁⡋⢠⠭⠬⣿⣶⡆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠹⠇⡉⠲⠒⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠼⠷⣶⣦⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢉⣙⣻⣶⡀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇⠁⠁⠀⠈⣿⣿⣧⢸⠋⠉⢻⣷⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣶⠏⠊⠣⢀⡀⠂⡀⠀⠀⢸⣿⡿⡟⠀⠀⢀⣿⡿⢇⡬⠿⢿⣷⣦⣤⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣰⡃⠀⠀⠀⠀⢻⡄⠀⢀⠐⣺⣿⡇⣷⠀⠀⣸⣿⢻⡟⠀⠀⠀⣿⣿⣿⡝⠛⠛⠳⠶⣶⣤⡄
⠀⠀⠀⠀⠀⠈⣽⣿⣤⣠⣀⣤⣼⣿⣦⣤⠑⣧⣙⡃⢋⣶⣶⢿⣷⢾⠃⠀⣠⣼⣿⡿⣶⣅⣀⡀
⠀⠀⠀⠀⠂⠀⠀⣙⢻⣿⠿⠟⢿⠟⠋⠹⣦⡈⢻⠃⣿⠻⠃⢈⣭⣶⠶⢠⣿⢋⠵⠊⠁⠀⠉⢳⡄
⠀⠀⠀⠀⠀⢄⠘⠠⡟⠘⠛⠛⠓⢦⣴⡦⠈⠳⣾⠀⣤⢠⡀⠺⠃⠑⢀⣤⠍⠈⠀⠀⢀⣀⣤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠗⢶⣤⣤⣤⣿⠏⡠⠒⢆⢹⣼⡿⢘⠃⢰⣾⣶⠈⠓⠒⠂⣶⠿⠿⠻⠻⠋⠀⠠⠀⣄⢠⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠛⢉⡕⡎⠀⠀⣼⡏⣿⠁⢁⣀⣸⠋⠠⠤⢀⠸⠖⢿⡆⠂⠀⠤⠊⠁⠀⢀⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠨⠿⣶⣶⡿⠃⣿⠀⢨⢏⡔⠀⠀⠋⠳⡀⢠⡤⢤⠀⢲⠟⠛⠟⠻⠿⠿⠿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠀⠀⠀⢹⣤⠏⡎⠀⠀⠀⣠⡦⠀⠀⠁⢠⣾⡓⣾⠉⠠⠖⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠚⢷⣶⣾⣿⠇⣼⠀⠀⠈⢛⣋⣋⡁⠈⠈⣹⣿⣿⣿⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠏⠀⡀⠀⢈⠙⠛⠁⠘⢽⣧⣬⣭⣭⣽⠛⠿⣿⣿⣿⠿⠿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⢉⡠⠊⠀⠀⠀⠈⠓⠂⠄⢈⣙⠛⠛⠛⠀⠀⠀⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠋⣱⣾⣿⣷⣿⡟⠛⠈⡻⠋⠁⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡄⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠛⠋⠀⣿⡀⠀⢀⠀⠀⠠⣿⣇⠀⠀⣾⣇⠀⠀⠀⠀⠃⠀⠀⠀⠀⣧
⣶⣶⣿⡿⠀⠀⠀⠀⢀⡄⠁⠀⣰⣿⠆⠀⠀⣼⣿⡇⠀⣼⡇⠀⣨⣿⣧⡀⢠⣿⣧⡀⠀⢸⡄⠀⠀⠀⠀⣰⣿
⣿⣿⡿⠁⣀⠀⠀⠀⠈⠁⠀⠀⣿⣿⠇⠀⢘⣻⣿⠷⠄⣿⡷⠀⣸⣿⣷⠀⡠⣿⣿⢀⣴⣿⣷⠀⠀⠀⣴⣿⣿
⣿⣿⡇⣼⣿⠀⠀⠀⠀⠀⠀⠠⢿⡿⣦⠀⣈⣿⣿⣁⠰⣿⡟⠒⢻⣿⡏⣾⣿⣿⡷⣶⣿⣿⠷⠀⠀⠀⠻⢿⣿
⣿⣿⣧⣿⡏⠀⠀⠀⠀⠀⢰⣗⢿⣷⣤⠀⢻⣿⣿⣟⣰⣿⣿⢐⣯⣿⣧⣾⣿⣿⡟⠂⢾⣿⣷⠀⠀⠀⠀⠀⣿
⠻⢿⣿⣿⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣤⠀⢾⣿⣿⢛⣇⣿⣏⣸⣿⣿⡯⣏⠹⣿⢷⣆⣹⣿⣟⠀⠀⠀⠀⠀⡟
⠀⣼⣿⡏⠀⠠⠀⠀⠀⢼⣿⣿⣿⣿⣼⡹⡒⣿⣿⠘⣿⣿⣿⡟⣿⣻⡆⣰⣶⣿⣰⣏⣽⣿⣏⠁⠀⠀⠀⠀⡇
⢰⣿⣿⠁⢀⠆⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⡆⢿⣿⣿⡿⣿⣠⡮⠸⣾⣿⣽⣿⡏⣍⣽⣿⣟⠃⠀⠀⠀⠀⠃
⣾⣿⡟⠀⡼⠀⠀⠀⠀⢸⣿⡏⣼⣿⣿⣿⣿⣤⡟⣿⣾⣿⣿⣿⣷⣶⡏⡗⢸⣿⣨⣽⣿⣿⡌⠁
⣿⣿⡇⢰⠇⠀⠀⠀⠐⠻⣿⡿⡿⠛⠟⣿⢷⢿⠉⢿⣿⣿⡏⢹⣿⣿⣷⠇⢨⣿⣿⣿⣿⡇
⣿⣿⣷⡟⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⢸⣿⠈⠀⢿⣾⠿⡏⣵⡜⣿⣿⣿⣶⡇⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢸⣿⡄⠀⠘⣿⣾⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣼
⣿⣿⡏⠀⠀⠀⠀⠀⢰⢠⠏⠀⠀⠀⣿⣿⡇⠀⠀⠸⣿⣀⣼⣿⣿⣿⣿⣿⡿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣠⣿
⣿⣿⡇⠀⠀⠀⠀⠀⢛⠿⠻⠿⠶⠶⠿⠿⠳⣤⠀⣀⣿⣿⣿⣿⣛⣋⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⣰⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠐⠿⣿⣷⣲⣶⣶⣶⣷⣶⣠⣶⣶⢶⣶⣼⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠟⠛⡛⠿⠯⠾⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⢀⣿
⣿⣿⣷⣤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⠤⠤⠀⣾⣧⣤⣤⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⣀⠘⠒⡀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠹⣄⠀⠈⠂⠀⠀⠀⠀⢠⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⠀⠀⠨⣆⠴⠁⠀⠀⠀⠀⠸⡇
⠀⣠⡠⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠀⠈⠻⣆⠀⠀⠀⠀⠀⢄⣡⠄
⠀⠀⠀⠮⠿⢦⣀⠀⠀⣀⠠⠝⠓⠦⣀⠀⠀⠀⠀⣀⣹⣆⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠘⣡⢘⡅⠀⠀⠀⠀⠀⠨⠟⠚⠛⠋⠉⠉⣩⠽⠒⠢⠄⣩⡆⠈⠳⣄
⠀⠀⠀⠀⠶⢦⡁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠖⠛⠛⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⣨⠐⠻⠶⣦⣄⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡄⠀⠀⢀⠀⠈⠉⠛⠶⠷⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⣶⣾⣿⣇⠀⠀⠀⠀⠀⠀⢬⠁⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠉⠉⠀⠀⠀⠀⠀⠀⠲⢀⠎⠀⠂⣀⠐⠂
⠀⡀⠀⢸⡄⠀⠀⠀⠀⠐⣄⠀⠀⠀⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠐⠲⠉
⠀⠘⢶⣄⢻⡄⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡷⢸⡿⠿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠻⣿⣷⣾⣿⣶⣶⡆⠀⠀⠀⠀⠀⣾⣿⣿⣵⠀⣇⣴⣿⣿⣧⠀⠀⠀⠀⠀⠸⣯⠸⠇⣀⣴⣿⠁
⠀⠀⠀⠀⢀⣀⣠⣴⣿⡿⠛⠛⢋⠝⠀⠀⠀⠀⠀⠘⠛⠁⢷⡼⢁⠜⢻⡿⠋⠀⠀⠀⠀⠀⠀⠘⢆⢸⣿⡟⢃⡀
⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣤⣶⣿⢪⣷⠟⢁⡀⠀⠀⠀⠀⠀⠉⠛⠉⠙⠛⠛⠛⠛⠛⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⣿⣿⡿⣾⠁⠾⣿⡿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⡜⢿⣿⣿⠙⣷⡴⠻⣍⡙⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣯⢟⠻⠛⠀⠀⠀⢠⣿⠀⢀⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠙⢦⣰⣆⠀⢸⣇⠠⣶⣿⣿⣿⡗⠉
⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣼⡟⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡟⠟⠀⠒⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠉⠊⠓
⠀⠀⠀⠀⠀⠸⣶⣄⠸⢆⠀⠀⠀⠈⠉⠋⠀⠀⠀⢹⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⢙⣻⣧⣼⣤⣶⣶⣦⣤⣄⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⠿⠿⠖⠚⠛⠂
⠀⠀⠀⣴⣾⣿⣿⡟⠉⠙⠻⠀⠈⠉⠉⠀⠀⠀⠀⢀⣀⣻⣿⣀⣀⣀⣀⣠⢔⣒⠼⠟⠋⠁
⠀⠀⠰⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠴⠖⠚⠛⢉⣉⣉⣉⣹⣿⣿⣯⣉⣉⣉⠉⠙⠛⠛⢷⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠙⠿⢿⠷⣶⣤⣙⡛⠿⣶⣶⢶⣦⣤⣤⣄⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣷⣶⣷⣶⣾⣿⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣶⣦⡀⢸⡟⣁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⡀
⠀⠀⠀⠈⠙⠻⠌⠜⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⢠⡀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠿⠛⠙⢏⡇
⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⡆⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠞⢛⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⣿⣷⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠸⡆
⠀⠀⠀⠀⠀⣿⡥⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢾⡧⣿⠴⡧⢼⡧⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸⠓⠒⢻⡀⠀⠀⠀⠤
⠀⠀⠀⠀⣸⡏⢉⡺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢺⡗⣿⠒⡗⢺⡗⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣷⡖⠒⠒⢧⠀⠀⠀⠶
⠀⠀⠀⠠⣿⣿⣧⣤⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡇
⠀⣀⣀⣀⣀⣤⣤⣴⣶⡞⢠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⢹⠋⠉
⠀⠻⣿⣿⣿⣿⣿⣿⡟⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⢠⣤⣄⣼⣿⡁⢹⣿⠏⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⣽⣄⣀⢀⣀⡀
⠀⠀⠈⢻⣿⠿⠟⠋⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⢨⣭⣯⣿⣭⡅⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⢡⣏⣺⣯⠽⠛⠉⠁
⠀⢰⡟⢳⡴⠖⠻⣭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣬⣿⣼⣿⣯⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢳⣿
⠀⠈⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠓⢾⡇


⠀⠀⠀⢀⣀⣤⣄⣀
⠀⣠⡾⠋⣤⣶⣶⠍⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠺⠓⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣯⣭⣤⣦⡔⣠⡀
⢠⡟⠀⠀⠘⢿⠏⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣀⣆⣀⣀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣵⣿⣷⡀
⢸⡇⣶⣶⣶⠎⢶⣶⣶⡆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣽⢹⣿⣿⡗⡀
⠀⢻⣜⠿⠋⠀⠈⠻⢟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣉⣿⠻⠟⠃⢻⣧⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣇⣺⣿⣿⡇⡇
⠀⠀⠉⠳⠶⠴⠴⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⠷⠝⠿⣿⡯⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠃⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢶⣦⠀⠀⠀⠀⣤⡶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢹⡇⠀⠀⢸⡟⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⢹⡿⠻⣦⡀⠀⠀⠀⠻⣧⣤⡿⠃⠀⠀⠈⢿⣤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⣽⡇⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠹⣷⡀⠀⠀⠀⠀⠀⠻⣧⣴⣦⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣨⣿⣤⣀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⣿⡁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡁⠉⢻⡆⠀⠀⠀⢀⣴⣿⣧⡀⠀⠀⠀⠀⠙⢷⣾⠟⠀⠀⢀⣤⣤⣤⣄⠀⢀⣾⠋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠿⠻⠷⠶⣶⣾⣇⠀⠈⢿⡆⠀⠀⠀⠀⠀⠙⠿⣦⣴⣿⠉⠀⠈⢹⣷⠾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣾⣇⠀⠀⠀⠀⣀⣀⣴⡾⠋⠛⠷⠶⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣾⠛⠉⣿⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣾⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢀⣿⠃⠀⠀⢠⣾⠟⠛⠛⢷⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⠟⠛⠻⠿⠷⢿⣧⣀⢀⣀⣼⠟⠻⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣷⣄⡀⠀⣀⣤⣄⣀⣀⣀⣀⣀⣤⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠋⠉⢙⣿⠉⠉⠉⣿⠏⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠛⠁⠀⠀⠀⠻⣶⡾⠟⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢷⣴⡶⠿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠆





⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⠶⠶⠶⠶⣶⡶⠶⠶⣶⠶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣶⣿⡯⠍⠀⡭⣙⠙⠀⠀⠢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡽⠾⢿⣿⠛⠁⠀⠀⠴⠀⠈⠁⠲⣄⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⠅⢀⣴⣿⣃⣠⣄⣀⡀⠀⠔⠀⠀⠀⠈⠛⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠁⡤⢫⣿⣿⠏⠀⠀⣉⠙⠳⢦⡀⠀⠈⠀⠀⠀⠳⣤⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠫⠐⡴⠃⢠⣿⡏⠀⠀⠘⠛⣆⠀⠈⠻⢶⡀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠠⣀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢟⠀⠀⣸⡟⠁⠀⣿⣿⣄⢘⠂⠀⢠⠃⠀⠀⠃⠌⡿⣶⡇⠂⠐⠲⠀⢷⡀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⣆⠀⡼⢻⣿⣿⠁⠀⡴⢦⡞⢉⣾⠄⠀⠒⠈⠻⣶⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣗⠀⣿⠀⢸⣿⠀⣦⠀⣾⣥⣾⣿⢿⣶⣴⢀⣴⣻⠿⣾⣶⡆⠀⣻⣦⠀⢀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⢏⡀⣿⠀⠸⣿⣿⣇⠀⣇⠈⢉⡡⠾⣿⣿⣧⣸⠁⠸⠟⣿⠃⠠⠃⡆⠀⡏⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠐⣿⣄⡀⠈⠛⢿⣷⣿⣧⣾⣷⣤⣿⣿⣿⣿⣤⣤⣴⣟⣤⣖⣨⠃⣘⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠀⠀⠀⠀⢻⣟⣫⣿⣦⡈⣠⣭⣿⣽⣿⣿⣉⢻⢿⣿⣿⣿⣿⣿⣿⡏⣈⢧⡀⠟⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠻⠋⠉⠉⠛⢻⣾⡿⣛⢻⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣧⣥⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠈⠛⠿⠿⠟⠷⠷⣾⣿⣿⣿⣿⣿⣿⣿⢿⣻⠅⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠄⠀⠀⢘⠟⠋⣿⣧⣿⣿⡿⢽⡿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡄⠈⠀⠘⣭⡾⢶⣿⡻⠟⠋⣰⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣉⣁⣄⣠⣬⠋⠀⠀⣽⣿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣟⠋⠁⠀⠀⢀⣀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉




⣿⠿⠿⠿⠿⡿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣠⡀⠀⠀⠠⠀⠒⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣀⢀⣀⣀⠀⣀⠀⠀⠀⢈⠉⡿⠁⠀⠀⡀⠒⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣘⣛⣛⣛⣛⠛⠛⠀⠀⠀⠈⢠⣇⠀⠁⣶⠁⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⡛⣻⣟⠋⠀⠀⠀⠀⠀⠀⠀⠿⣷⠈⠉⢹⣿⠋
⠀⠀⠀⠀⠀⠀⣶⣤⣤⣤⣤⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠉⢀⣽⠆
⠀⠀⠀⠀⠀⠰⣦⣬⡿⣦⣼⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⣼⡿⠀⠀⢹⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣿⣠⣤⡿⠁⠀⠉⠉⠉⠀⢀⡄⠀⠀⠀⢀⣀⣠⣤⣼⣏⡀⢠⣘⣾⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⣉⢁⢀⡀⠀⣀⡀
⠀⠀⠀⠀⢀⡀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡤⠈⠋⠁⠀⠉⢈⡟⢀⣉⣀⠀⠀⠙⠻⠑⣄⠀⠀⠀⠀⠀⠀⠈⣛⠛⠙⣻⠛⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠈⠛⠛⠛⠛⡿⠦⠿⠄⠀⣀⡄⠀⠀⢀⡼⠁⣤⡦⠀⠀⢠⣿⣇⣸⠏⣿⠀⠀⠀⠀⠀⣉⡀⠀⠀⠀⠀⡄⠈⠛⠛⠛⠉
⠀⠀⠀⠀⠻⠟⠻⠿⠿⠃⠀⠻⠶⠶⠿⡷⠆⢀⣀⠁⣠⠈⠀⠂⠀⢠⡿⢋⣷⣺⣻⡆⠀⠀⠉⠀⠋⠁⠀⠀⢄
⠀⠀⠀⠀⠀⠀⣴⣤⣴⣶⣠⣤⣤⡄⢀⡄⣴⢎⣭⣽⣿⡟⠀⠀⠀⠈⠳⢿⣿⣿⣿⡇⠀⠀⠀⢠⣉⣿⢿⣀⠀⠲⠆⠀⣀⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠠⣤⣬⣍⣍⣩⡅⠀⠀⠀⠄⠀⠀⣠⠻⠛⠛⠰⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⢠⠟⢋⠘⠋⠀⢸⠃⠀⠉⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⣬⣡⣤⣿⣉⡁⠀⠀⠀⣤⠀⠀⢸⣆⠀⠸⠇⠀⠀⣀⡈⠀⢀⡄⠄⢠⡄⠀⣀⢼⣄⣾⡀⡀⠀⣠⡇⠀⠤⢤⣄⢠⡀⣠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⠀⠀⠟⠀⠀⢸⡿⠀⠀⠀⡀⠀⠀⢤⡤⠄⢠⡈⣧⣀⣶⠇⠀⢈⡿⠈⠃⠀⠈⠇⠀⢠⣄⣉⠺⠀⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⠁⠺⠃⢤⣤⣄⣤⡶⢄⠇⢀⡤⠀⢾⡟⢀⠀⠈⠇⢠⠀⠀⠀⡀⠀⠈⠉⠉⠈
⠀⠀⢠⣤⣤⣠⣀⣄⣠⣤⣀⣀⣄⠀⠀⠀⠀⢼⡿⠀⠰⠄⠀⠃⠀⠠⢄⡠⠀⠸⡟⠀⠻⠧⠈⠠⠤⡆⢸⡤⠄⠀⠠⠄⠀⣦⣤⣶⣤⣤⣤⠄
⠀⠀⢠⣤⣤⣤⣭⣥⡈⢉⣉⣀⣩⣄⣀⡀⢀⠘⣷⢀⠀⠀⢃⡀⠀⣀⢄⠰⣾⠀⢴⡄⠀⠀⠀⠀⠀⠀⠐⣾⠂
⠀⠀⠈⠉⠁⠈⠉⠉⠀⠈⠉⠉⠉⠉⠉⠁⠋⣹⡉⠈⠀⢀⣤⠉⣲⠉⠈⣰⣿⣶⠊⠓⠶⢦⡖⠀⠲⠂⢾⡇⠐⠂⠀⠘⠀⢀⣠⠷⠿⣶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⡉⠁⠀⠋⢹⡎⢉⠀⠀⠀⠂⠈⠀⠀⠀⢻⣏⠉⠀⠀⠀⠀⠀⠹⠷⠾⠗
⠀⠀⢰⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠁⠀⠀⠀⠀⠈⠁⢀⡀⢀⣈⠿⠷⣤⡤⠀⢠⠀⠀⠐⡆⠸⣷⠶⠂⠆⠀⠆⠀⠀⠀⠀⣠⣄⣠⣤⣤⣤⡀
⠀⠀⣤⣠⣤⣉⣠⣤⡀⠀⠀⣀⠀⠀⢀⣴⡇⠀⣀⠀⠀⣠⣈⣡⣾⢿⡿⠋⠀⠀⣨⣿⠾⣁⠀⠀⠀⠀⠀⠙⡖⠀⠀⠀⠀⠀⠀⠀⣉⣉⣁⣈⣩⡍⠉
⠀⠀⣨⣅⣀⣼⣍⡀⠀⢀⠀⠀⠀⠀⢈⠋⠀⠀⠀⠀⠀⠀⠀⣤⠙⢀⣡⠀⠀⢀⠀⠈⢻⡧⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣉⣁⣀⣿⣉⡀
⠀⠀⠀⠁⠉⠈⠉⠑⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⣮⣠⡦⠘⠁⠀⠘⢢⣴⢿⡄⠠⠄⠀⠀⠁⠀⠀⢃⠀⠀⠀⠀⠀⠄⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣷⠀⠀⠀⠀⢾⡧⠆⠀⠂⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢠⠀⢤⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣿⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⡇⠘
⠀⠀⢀⣀⣀⣀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠋⢠⡟⣦⡌⣦⡘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣈⣉⣹⣏⣙⣛⠙⠛⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠀⠘⠀⡝⠀⠘⠃
⠀⠀⠘⠋⠉⠙⠃⠉⠀⠘⠋⠛⠙⠛⠛⠀⠀⠀⠀⢰⡄⠀⠀⠀⢀⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣤⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⢠⡖⠀⠀⠀⡴⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡚⢧⣀⠄⠀⠀⠀⡀⠂⠀⠀⢀⠀⠀⠀⠀⣠⡄⣀⣀⣠⣄⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠿⠀⠀⠐⡞⠻⠾⠀⠀⠈⠀⠀⠀⠀⣬⣁⣩⢏⣉⣭⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠘⠁⢶⠀⠀⠀⠀⠀⠀⠀⠀⢈⣋⣁⣸⣇⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠆⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⣠⣶⠚⢷⡄⠀⠀⠀⠀⠀⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⢤⣿⣿⣿⣏⠠⠁⠀⠀⠀⡀⠀⣘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠈⡆⠐⠛⠻⣿⠿⠷⡀⠀⠀⢠⣯⢥⣴⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠇⠀⣾⣿⣿⣷⣤⣶⣶⣄⣴⣧⣤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡻⠿⠿⠟⣱⣿⣯⡈⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣴⡄⢸⣿⣿⡛⢁⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⣦⣼⣿⣦⡻⡷⠦⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡋⠀⠀⠀⣸⣿⣿⣿⣿⢷⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠖⠙⠟⠉⠀⠀⠹⠋⠁⠀⠉⠉⠃⠛⢣⠆⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢰⠀⢀⣴⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⡀⠀⠀⠀⠀⠀⠀⢸⣷⣴⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣧⣼⣿⠿⠿⠟⠿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢠⣟⣿⣿⣿⣶⣄⡀⠀⠀⠀⠘⠿⠿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⠛⡟⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⠞⠛⠛⡟⠛⢿⣿⣿⣿⣷⣶⣿⣥
⠀⠀⠀⠀⠀⠀⣿⡇⣸⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣛⣿⡝⠛⠛⠒⠒⡿⡶⠲⠦⠝⡛⢩⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠟⢠⡏⠀⢀⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⣤⣄⡀⠀⢉⣿⡀⠀⠀⢣⡿⠛⣿⣿⣷⣄⠀⣄
⠀⠀⠀⠀⠀⢠⣀⣾⠃⠀⠈⢿⡿⠉⠙⠿⠙⣿⣿⣿⣿⣷⣿⣏⠙⠛⠛⠿⣿⡿⠛⠛⠻⡆⠁⠀⠹⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⡈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⢻⣿⣷⣄⡀⠀⣹⣷⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢬⣿⣦⣀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⠉⠁⣾⣿⡛⠛⠋⠀⢻⣿⣷⡤⡄⠷⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⡍⠙⠀⠀⠃⠀⠀⠀⠀⣿⣿⣏⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡙⢆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⠀⠀⠀⠈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠿⣧⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⡐⠦⠀⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⠷⠤⣤⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⣾⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣜⣶⣾⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠋⠀⢻⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣤⡈⢸⡿⢿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢗⣻⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢵⢟⣩⢿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⠏⣿⣳⣿⣿⣯⣞⣯⣿⢿⡿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠜⠁⠙⠙⠉⣾⠋⡩⣻⣟⢕⠿⣻⢻⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠺⠿⣷⠿⣻⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢊⣠⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣻⣿⣿⣠⡔⠁⠀⠀⠀⠀⠀⠀⣠⣾⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣿⣻⣿⣾⣿⣟⠕⠀⠀⠀⠀⢀⠀⡺⣫⣽⢟⢽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⢛⣿⠟⠁⠀⠀⠀⠀⠁⠀⠈⢫⣴⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢇⣬⢠⡔⠀⠀⠀⠀⠀⠀⢀⣤⠚⠁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣧⣾⣿⣿⣻⣷⠛⠔⠀⠀⠀⠠⢛⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⠿⢿⣿⡿⠃⠀⠀⠀⠀⠺⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣴⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⠀⠀⠀⠏
⠀⡀⣀⣰⠀⢀⡀⡀⣄⠀⢀⣰⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⢠⣷⣿⣿⣾⣾⣿⣷⣿⣷⣿⣿⣿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡆⠀⠠⠄⠀⠀⠀⠀⠀⢬⡧
⠸⠟⠟⠿⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢺⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠩⢍⡧⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠀⠳⠪⣽⣷⣂
⢀⣰⣷⣠⣼⣥⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⢠⣿⣀⠛⢭⣽⣯⠶
⠀⣿⣿⣿⣿⣿⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡧⠀⠰⢬⣿⠔⠂⠰⣬⣷⠞
⠀⣿⣿⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⣷⣄⠨⠽⣿⠭⠄⡼⣿⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡤⢶⡶⡶⢶⠶⡶⠒⠒⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣌⠹⠀⡜⢁⠀⠀⣇⠠⠂⢀⡃⠀⠀⠀⢀⡄⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⠀⠀⠀⠻⡐⠀⡾⠀⠀⣄⠠⠤⠊⠀⢀⠄⠂⠁⠀⠈⠉⠁⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠃⡤⠀⠁⢼⡀⡘⢃⠀⠰⡀⠾⢹⠄⠀⢀⠔⠋⠀⢐⣲⠶⣶⣦⣤⣴⣇⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣽⡎⠀⠀⠀⠀⢸⠀⠀⠙⢆⢻⠀⢸⡀⠠⠁⠀⣠⠖⠉⠉⠉⠉⣑⠪⠅⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⠀⢡⠂⠀⠀⡅⢺⠈⠢⣄⠀⢷⣇⠈⠃⠈⠀⢴⠁⠀⠀⠉⠉⠲⠢⣷⢦⣔⢸⣯⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠁⣾⠀⠡⠀⢸⠂⣧⣧⠀⣠⢋⣁⣨⣿⣧⡴⢫⠀⡟⠀⡀⠀⠀⢤⣀⣀⣽⠀⡀⣛⣻⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠸⠈⡇⠀⡀⢰⠂⡘⠀⡟⠀⡟⠸⣾⠟⢻⣧⡇⢽⢀⠃⠀⠳⡀⠀⠀⠉⡉⢉⣨⡤⣿⡯⣷⠼⣣⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⡖⠄⢀⢑⠜⡆⢡⠀⣇⢰⡑⣈⣻⣿⢻⣼⣼⡀⣰⣖⢻⡦⢤⣴⣎⣉⢩⡄⣻⣿⠛⠁⢙⠻⢦
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠣⣹⡄⠹⢺⣄⡓⣦⡷⠘⣆⠻⠉⣼⢿⣥⡇⠠⠉⠉⠻⢦⣼⢿⣥⡐⢮⣍⣵⣿⡿⣤⡚⢉⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⢧⡹⣄⠹⣆⠙⣎⣿⢷⣟⢄⣅⠙⠘⡟⠁⡄⠀⠀⣴⣾⣿⣽⣶⣙⠋⣹⣫⣽⣶⡋⢄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⢮⣿⣯⡑⢦⡙⠛⠻⣾⢿⠿⣿⣦⣤⣿⠐⡇⠀⢶⡿⢻⠿⣯⠉⣿⣻⠻⣿⣿⣿⣿⣿⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣔⢽⣷⣇⡀⢻⣦⡀⢻⣿⣰⡟⡿⡿⣿⡿⠋⡄⢿⢧⠘⣿⠁⠀⣿⣿⣼⣿⣿⣭⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣿⣫⡌⣲⣝⣮⣺⣿⢻⣛⣧⡈⢋⣿⣧⣇⣸⢇⣲⡏⠀⡴⢛⢛⢋⡗⠏⠀⡻⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣝⢿⣿⣿⡼⡏⠀⠁⢀⣻⣟⠻⣿⣶⣥⣾⣯⣤⣴⣾⣾⣶⡶⢾⡶⣾⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠿⣿⣳⡇⠀⠀⠀⠉⢿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣾⣷⣿⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡿⣿⣿⡀⠀⠀⠀⠀⠙⢿⣿⣿⡿⣿⣿⣿⢿⣯⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢱⣹⡼⣿⡄⠀⢱⣖⢲⠀⢻⣿⡟⣹⡟⣟⣿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡘⣿⡇⢹⣿⡄⠠⠉⣦⣶⡇⠻⢷⡿⠉⢿⡇⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡇⢸⣿⠀⣧⠹⣆⢀⣜⣟⣿⠂⡜⢳⣆⣼⣧⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣇⠀⣿⡘⣿⢰⣾⣏⣹⣟⡡⠛⢧⡀⠙⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣸⠟⢦⣹⣼⡿⡽⣿⡿⣷⡏⠀⠀⠈⢿⣦⣼⣿⣦⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠷⠋⠀⠈⣽⢿⣿⣦⣿⣷⣿⣇⠀⠀⠀⠈⢻⣿⣟⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠒⢰⣏⡁⠀⠀⠀⡄⣿⢸⡏⢹⣿⣶⣿⣿⡀⠀⢀⠤⠒⠛⢾⣧⣘⢿⢿⡆
⠀⠀⠀⢀⣠⣤⠶⠞⠉⠁⠀⠀⠀⠀⠀⠀⠉⠲⠤⢤⣀⠋⣟⠇⠛⠸⣧⠛⠙⣇⡾⠁⠀⠀⠀⡼⠛⢿⠈⠢⣈⠒⠒⠂
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠆⠀⣀⢸⠁⡠⠊⠁⢀⣀⠤⠊⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠞⠋⠁⠀⣸⠗⠋⠁⢀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡥⠒⠒⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣀⣀⠀⣠⠤⠶⠤⣄
⠀⠀⠀⠀⣠⠚⠉⠉⠉⠙⠢⠤⢤⡞⠑⠞⠁⠀⢸⠁⠀⠉⡡⠤⢤⡀⠈⢳⠲⠤⣄
⠀⠀⠀⢰⠁⢀⡤⠒⠦⣀⣄⡀⠀⠓⢤⡀⣠⠒⢉⣰⠉⠉⠀⠀⣀⣱⠀⠸⣄⠀⠈⠣⢤⡀
⠀⠀⠀⢸⡀⢺⠀⠀⠀⠉⠀⠃⠀⠀⠀⢱⣇⠀⠏⠀⠀⠀⠀⠘⠁⠀⣳⠀⠈⠳⠤⡀⠀⠙⠦⠲⢄
⠀⠀⠀⠀⢳⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⣌⡶⠒⠲⠤⠒⠢⢤⡀⠀⠁⠀⠀⠀⠀⢸⡤⠔⠒⠤⡼
⠀⠀⠀⠀⡾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡔⠙⠚⠉⢦⡀⠙⣄⡀⠀⠀⠀⡴⠲⠔⠉⠉⠳⡘⡆
⠀⠀⠀⠈⣇⠈⠉⠉⠱⣄⠀⠀⣀⢔⣒⣦⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣹⣄⣀⠀⠀⠀⠀⠀⠀⠰⢣⡃
⠀⠀⠀⠀⠈⠑⠒⢤⣀⠴⣍⠉⢁⡜⢲⠚⡖⢻⠒⠒⠒⣿⠒⠒⢺⠓⡞⢲⣾⣦⣀⣤⣄⣀⣀⣀⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠘⡏⣏⢹⠉⠉⠉⣿⠉⠉⢹⠉⡏⣟⣏⣻⣛⣛⣻⣛⣛⣿⣹⣛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣲⣀⣀⣖⣆⣯⢿⢹⠉⠉⠉⣿⠉⠉⢹⢹⢋⣧⣯⢼⠤⠤⣼⠤⠤⣯⣼⡼
⠀⠀⠀⠀⠀⢀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣹⢸⢸⡇⠀⢠⡛⡄⠀⢸⢸⢸⢹⣷⢸⠀⠀⢸⠀⠀⡇⣸⡇
⠀⠀⠀⠀⠀⠘⢦⢤⣤⣤⣤⣤⣤⣤⣤⣼⣼⣸⣇⣠⡻⠋⢞⣆⣼⣸⣼⢸⣿⣸⠀⠀⣸⠀⠀⣇⣻⡇
⠀⣀⣀⣀⣀⣀⣸⢸⣽⢼⢽⣭⡯⡯⣯⡽⡿⢸⡵⣿⣧⠀⣼⣯⢿⠘⡿⣼⡏⢹⠉⠉⢹⠉⠉⡏⢹⣇⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣸⣸⣺⢺⢺⣒⡗⡗⣗⡇⡇⣼⡝⠉⢉⣿⡉⠁⢻⣣⡇⡟⡇⢸⠀⠀⢸⠀⠀⣇⢸⢻
⠀⠀⠀⡏⢉⣉⠉⣉⠉⣉⠉⣉⠉⣉⣹⢡⠿⣼⠷⠶⠾⣿⠷⠶⢾⡧⢧⢹⠃⡎⠀⠀⢸⠀⠀⢸⠘⡜⡄
⠀⠀⠀⡇⢸⣿⠀⣿⠀⣿⠀⣿⠀⣿⡏⡸⠀⡇⠀⠀⠀⣿⠀⠀⠈⡇⠸⡈⣦⣇⣀⣀⣸⣀⣀⣸⣄⣧⣷
⠀⠀⠀⡇⢸⣿⠀⣿⠀⣿⠀⣿⠀⡿⢳⠗⢒⠗⠒⠒⠒⣿⠒⠒⠒⢷⠒⢷⠻⣄⣀⣀⣸⣀⣀⣀⣇⣘⣆⣧
⠀⠀⠀⢧⣸⣿⣤⣿⣤⣿⣤⣿⣴⠧⡼⠤⣼⠤⠤⠤⠤⣿⠤⠤⠤⠼⡤⠼⡦⢵⡤⠤⢼⠤⠤⠤⢼⡤⠽⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⡾⠒⢲⠗⠒⠒⠒⠒⣿⠒⠒⠒⠒⢷⠒⠺⡖⢻⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⡉⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠶⠒⠂⠀⠀⠙⠒⠀⠄⡀
⠀⠀⠀⢀⡠⠴⠛⠛⠉⠉⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀
⢀⡴⠊⠁⠀⠀⠀⠀⢀⣀⣀⣠⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⡏⠀⠀⠀⣀⠔⢲⣿⠭⠥⠔⠓⠒⠀⠀⠀⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⢳⣀⡤⠖⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠃⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⣰⠋⠀⠀⠀⣀⣠⡤⠶⠖⣒⣈⣉⣩⠭⠉⠒⠲⣄⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢿⡀⠀⣀⡻⠮⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠏⠀⠁⠂⠆⠀⠀⠋⠈⠀⠇
⢈⠟⠋⠁⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠰⠶⠶⢋⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⣿⠀⠀⣀⠤⠶⣚⣛⣯⠥⠶⠒⠚⠃⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢱⠀⡄⠁
⠙⢦⣀⣀⡴⠋⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠴⠋⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⢀⡞⢡⡞⠀⠀⢀⡤⠶⢶⣽⡋⣩⠟⠉⠋⠛⠢⡄⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠀⠸⡀⠀⢀⡿⢱⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠁
⢸⠀⣀⣈⣩⣭⠤⠼⠤⠤⠤⠤⠧⠤⢤⣤⣀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⠠⠁
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡀
⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⢰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣼
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠼⠀⠀⠀⠀⣸⣄⣀⣀⣀⣴⠁
⠀⠀⠘⢦⠤⠄⠲⠶⠒⠒⣶⣒⣒⣲⡒⠲⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠴⠤⢀⠃
⠀⠀⠀⢸⠀⠀⠀⣀⣀⣀⣀⣀⡀⢀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⠀⢀⣀⣀⣀⣀⣂⣉⣭⣽⡇⢈⠆
⠀⠀⠀⢼⠃⠀⢤⣤⣤⡤⠤⠤⠴⠶⡒⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⣀⣀⣈⣭⣤⣵⡶⢈⠆
⠀⠀⠀⣼⡃⠤⠤⠤⠤⠴⠶⠿⠿⠝⡓⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣐⣢⣭⣭⣥⢈⠆
⠀⠀⠀⢼⡃⠤⠤⠤⠤⠴⠶⠿⠿⠿⡖⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠉⠉⠉⢉⣩⣭⣥⣶⡎⣈⠂
⠀⠀⠀⠘⢧⣀⠀⠐⠒⠒⠒⠺⣋⣗⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠉⡭⢛⠜⠁
⠀⠀⠀⠀⠀⠉⢻⠛⠛⠛⠛⡿⢹⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡛⣛⣷⠞
⣤⣤⣤⣤⣤⣤⣤⣽⣷⣶⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⠿⠟⠻⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⣴⠗⠺⣦⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣶⡏⠀⠂⢸⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡿⠤⠴⠿⠿


⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠲⠀⠐⢀⡑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠀⠀⢲⡶⣤⡀
⠀⠀⠀⠀⢀⠔⠀⠂⢀⠀⢀⣀⠤⠌⢀⠈⠀⠐⠄⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠄⣀⣠⣤⣄⡀⠉⠳⣄
⠀⠀⠀⠀⠂⠂⠠⠂⠀⠀⠃⠁⠂⢄⠀⠀⠀⠀⠂⠂⠀⠀⠀⣴⠋⢀⠔⠁⠀⠙⠉⠛⠿⣿⣿⣦⡀⠘⣧
⠀⠀⠀⠀⠁⠠⠁⢀⠐⠀⠐⠒⠒⠀⠑⠀⠠⡀⠀⠀⠀⠀⢰⠇⠀⠂⠀⣰⣶⣷⣶⣶⣄⠈⠛⠛⢷⡀⠸⡇
⠀⠀⠀⢘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⠀⠀⠀⠀⣾⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣷⡆⠀⠈⡇⠀⡇
⠀⠀⢠⠈⡆⠈⠀⠌⠐⠀⠰⡀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⣼⡤⠈⣷⣄⠙⠋⠉⢿⣿⣿⣿⠀⣀⢀⠀⢰⡇
⠀⠀⠀⠈⠀⠀⠁⣀⠀⠀⠀⢀⠀⡠⠁⠐⠀⠁⠀⠁⠀⠀⠈⠁⠀⠘⢿⠀⠀⠀⠸⣿⣿⠏⠘⠫⠂⠀⠈
⠀⠀⠀⠀⠀⠋⡢⡀⠐⠠⠀⠀⠉⠀⠐⠁⡰⠂⡂⠀⠀⠀⠀⠀⠘⢦⡀⠁⠂⠀⠀⠈⠠⠀⠊⢀⣲⡶
⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠠⠀⠀⠀⠄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⣤⣤⠤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣴⢟⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡞⠁⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⣸⢾⣿⣯
⠀⠀⠀⠀⠀⠀⣰⢿⣿⣿⣆⣸⣿⣿⣿⣷⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢠⡏⣺⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⣾⡀
⠀⠀⠀⠀⠀⣾⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣸⣿⡧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴
⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣷
⠀⠀⠀⠀⠀⣿⡻⢿⣿⣿⣿⡿⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢻⡿⠿⢟⣿⣿⣷⣤⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⠿⣿⣦⣴⣦⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣷⣶⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠿⠯⠀⠀⠈⠉⠁⠉⠁⠀⠀⠁⠀⠉⠉⠉⠻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠋⡁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠠⢾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣟⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢻⠇⠀⠀⢀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⣇⣸⣤⣶⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⣤⣆
⠀⠀⠀⠀⠀⢀⣤⣤⣄⢠⣤⠀⢠⣾⠟⠀⠀⠀⠀⠘⣿⣀⣴⣾⣷⣄⣿⡟⠀⠀⣠⣴⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢸⣿⣛⡻⣿⣿⣀⣿⡟⠀⣀⡀⠀⠀⠀⣿⣿⡏⠀⠘⣿⣿⡇⢸⣿⣿⣋⣀⢀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⢙⣛⠿⣿⣿⣿⣿⡇⢠⣿⡇⠀⠀⠀⣿⣿⠀⠀⢰⣿⣿⡇⠰⣿⡟⠻⠿⠿⠟⠻⢀⡀
⠀⠀⠀⠀⠀⠀⢿⣯⣄⡀⠈⣻⣿⣷⣾⣿⣷⡀⢀⣼⣿⣿⣆⣠⣿⣿⣿⣤⣤⣿⣿⣤⣀⣀⣀⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠟⠁⠈⠁⠀⠙⠿⡿⠟⠁⠈⠛⠟⠋⠙⠛⠋⠙⠉⠉⠛⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣠⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠏⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⢳⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻
⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⣻⣿⣿⠟⠿⣿⣾⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢠⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣶⣦⣾⣿⣿⣿⣿⣿⣿⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⠃⣹⠇⠀⠀⠀⣤⣴⣶⣶⣾⣿⠋⢻⣿⣿⡛⠁⠀⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠃⠰⣿⣷⠀⠀⠀⠀⠈⠉⠙⠋⠹⣷⣴⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠛⠙⠏⣻⣤⣄⣀⣀⡀
⠀⢈⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠙⢿⣿⣿⣧⣄⣬⣤⣆⣤⣤⣴⣿⣿⡿⠟⠋⠉⠁
⢀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡟⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣻⡿⣧⣤⠀⠀⠀⠀⠀⠀⠀⡿⢹⣿⡿⠛⣿⣿⠿⠿⣿⣿⣿⣧⠀⢀⣴⣶⣄⣢⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣽⣿⣿⠀⠀⠀⠀⠀⢀⣰⡄
⡟⠁⠉⠛⠀⠀⠀⠀⠀⠀⠐⣿⢿⣿⣲⣀⡀⡻⡆⣀⡼⣿⡿⢿⣿⣏⣨⣿⣩⣿⢋⣿⣿⡿⣻⣉⠀⣌⣩⠿⣜⣿⢟⠀⠀⠀⠀⠀⢨⣿⡀
⡁⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⢉⣻⣿⣿⢿⢫⣿⢷⣾⣵⢿⣩⠁⠙⠿⣿⣖⣾⣿⣿⡿⡛⢿⣷⣿⠿⣿⣧⣽⡆⠀⠀⠀⠀⠀⠈⢻⣿⡄
⡶⠂⠠⣷⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣟⣽⡿⣍⡋⠀⠈⢹⣯⣟⣷⣦⣽⣾⣿⣟⡋⣤⣴⣿⡗⣋⣁⣼⣏⣍⣽⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠓⠀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⠭⢩⢩⡗⣈⣻⣿⣷⣶⡿⣿⣿⣿⠿⠯⣽⣿⣾⣿⣻⣍⣥⣹⣿⠭⣿⡵⠤⣷⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⣠⣬⣨⣶⣠⣿⠾⢿⡿⠟⢛⣋⣉⠱⣿⣿⣿⣿⣿⡶⠁⠈⠛⠿⠿⣶⣾⣷⣦⣷⣾⣁⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠹
⢀⣿⣿⡗⣠⣾⡀⠀⠀⠀⠉⣿⣿⣯⣉⣁⣽⣿⠁⠀⢻⡿⠀⣀⣈⣭⣿⣿⣿⣿⣿⣶⡀⣤⣀⣹⣻⡷⣿⠿⣿⣿⣿⣿⠃
⣸⣿⣿⢱⣿⣿⠇⠀⠀⠀⠀⠈⠙⠻⣯⡻⣾⣶⣿⢶⡆⢘⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠁⠨⠭⢁⣈⣠⣨⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢠⡀
⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⡄⠀⠀⠉⢻⣿⣿⣽⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⢠⣶⣶⣶⣶⡿⣿⣽⡋⠋⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣧
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢿⠟⢀⡀⠀⢸⡟⢻⡆⣿⣿⣿⣿⡿⢿⣿⣾⡶⢾⡿⢓⢻⣿⢡⣿⣿⠟⠀⣀⡙⠛⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡆
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠀⢸⣿⠐⠙⣿⣯⣼⣿⡀⡌⢿⢻⠀⣿⣷⣿⣿⣥⣻⢿⣿⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⠸⣿⢠⣶⣿⣿⣿⣿⣿⣧⣸⠀⢂⣿⣿⣿⣿⡟⠁⢸⣿⣀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⣍⠛⠟⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⡿⢿⠋⠀⢸⣿⠛⣿⠿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠃⢀⣀⡀⠀⠀⠀⠀⠀⠇⠀⠸⣿⣿⠂⠀⣿⣿⣿⡇⠹⣿⣿⣄⣿⣿⠋⠀⠀⠀⠀⢸⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡿
⣿⣿⣿⣿⣠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢁⡄⠀⢸⣿⣿⡇⠀⢻⣿⣿⡟⣧⣤⣤⡴⠂⠀⢸⠟⢀⣤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⡇⠀⣿⡏⠋⠀⣿⠿⣿⡅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⠈⠙⠛⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠀⣤⡀⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠉⠁⣼⣿
⠀⠀⠀⠀⠀⠀⠀⣤⢿⣿⡇⠀⠘⣿⣿⣟
⠀⠀⠀⠀⠀⢠⣿⣄⢰⣿⡇⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡇⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⠀⠀⢀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣎⡁⣤⠉⢳⡄⠀⠀⠀⠀⠀⠀⢀⣴⡾⢿⣮⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢻⡄⠀⠀⠀⠀⢀⣼⡿⠀⠀⠙⠉⠹⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⢻⡀⠀⠀⠀⢸⡏⠀⣲⡤⠀⣀⡀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡇⠀⠀⠀⠈⠟⠳⣦⡀⠘⠇⠀⠀⠀⠈⠉⠙⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣵⣄⣤⣗⠀⠀⠀⠈⢷⡀⡀⠺⢿⠿⣷⡄⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡹⣿⣿⠀⠀⠀⠀⠈⢿⣷⡄⠈⠀⣀⣴⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⠃⠀⠀⠀⠀⠈⠻⣿⣷⣾⣿⣿⠟⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡿⠻⠿⠿⠿⠂⠙⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⣿⣿⡆⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⣿⣿⣅⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⢿⡿⠿⣷⣄⣀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣈⣁⣀⠀⠀⠀⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⠀⢀⣿⣿⠀⠸⣿⣶⣄⣀⣀⣀⣀⣭⣿⣿⣆⠀⠆⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢄⠀⠀⠀⠉⠉⠀⡀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠙⢷⣄⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢀⡤⢶⠾⢻⡶⣄⡀⠈⠉⠹⢾⣿⣿⣿⠃⠀⠀⠙⢿⣶⣤⣀⢄⡀⠙⠓⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⠀⠀⠀⢈⠀⠀⠈⠛⢻⣿⣿⣿⣿⢿⣾⠃⠀⠀⠀⠀⠀⠈⠛⢿⣷⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣿⣿⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣀⠀⠀⠀⣨⣭⡉⣵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⣀⣠⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢀⣀⣀⡉⣀⣀⠀⢉⣈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⠀⠉⢀⠀⢦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣆⢰⣄⣀⠀⣀⡀⣀⣠⢤⣶⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⢙⣿⣿⣿⣿⣿⡿⠂⢻⣟⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⠈⢻⣿⣿⣿⣿⡶⣻⡆⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⡀⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⠟⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠙⠋⠻⠿⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠧⠷⠾⠼⠶⠧⠿⠼⠼⠧⠧⠾⠼⠶⠧⠷⠾⠼⠶⠧⠷⠼⠼⠧⠷⠾⠼⠼⠧⠷⠾⠼⠶⠧⠷⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⢻⡹⡏⠉⠉⠋⠙⢟⢻⠉⠉⠉⠉⠛⡟⡟⠉⠉⠉⠉⢻⠻⡏⠉⠉⠉⠉⠛⡟⡟⠉⠛⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣸⢸⠀⠀⠀⠀⢀⡇⡇⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣠⡇⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢠⠞⣽⢸⠀⠀⠀⡠⢋⡇⡇⠀⠀⢀⡔⣹⡇⡇⠀⠀⢠⢞⡵⡇⣿⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⣰⠣⠎⣸⢸⠀⠀⡼⠱⠃⡇⡇⠀⢠⠎⠜⣹⡇⡇⠀⣰⠣⢎⠐⡇⣿⠀⢠⠎⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢰⠃⢂⠎⢾⢸⠀⡼⠐⣰⠃⡇⡇⢀⠏⠐⡼⢹⡇⡇⣰⠃⢃⠎⠞⡇⣿⢀⠎⠐⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⠇⢀⡄⠈⣼⢸⣼⠁⢠⠀⢁⡇⣧⡞⠀⡤⠀⣹⡇⣧⠇⢀⡄⠈⡜⡇⣿⡞⠀⡤⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠏⠀⠀⠀⠘⢹⣸⠃⠀⠀⠀⠊⣇⡟⠀⠀⠀⠀⢻⣇⠏⠀⠀⠀⠘⠁⡇⡿⠀⠀⠀⢸
⠀⠀⠀⡠⢤⣤⢞⡩⣍⠲⡤⣬⢏⡔⣒⢢⣀⡁⡸⠃⢂⣀⡄⠈⢀⡟⠐⠂⢀⠀⠉⢰⠏⠐⠀⡀⠀⠁⣀⡟⠐⠂⢀⠀⢹
⠀⣠⠞⠀⠀⢯⣏⢀⡀⠀⠀⠈⠛⠙⠀⠁⠉⠉⣧⡯⡾⠶⣄⣢⠎⡰⣣⠃⠋⢐⡷⢃⡜⡼⡐⡁⠘⣠⠟⡰⣣⠃⠋⠀⢻
⠀⢧⠀⠀⡔⠋⠁⢏⠙⠋⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢳⣴⣵⣳⣳⡷⠋⣠⢞⣜⣝⣝⣽⠟⢁⣞⣵⡵⣱⣳⢣⣾
⠀⠀⠭⠭⠭⠭⠉⠉⠉⣭⣭⡍⠉⢉⣉⠉⢉⡉⠉⣉⠩⠭⡉⠉⠹⠿⠏⠉⠉⠉⠩⠭⠭⠭⠉⠭⠉⠩⠭⠭⠭⠉⡩⠭⠉
⠀⠀⠠⠬⠭⠉⠉⠥⠤⠀⠰⠆⠀⠐⠒⠒⠒⠀⠀⠐⠲⠈⠉⠉⠀⠉⠉⠩⠍⠉⠉⠡⠄⠀⠀⠒⠒⠂⠘⠛⠦⠌⠵⠶
⠀⠀⠀⠀⠚⠛⠓⠀⠀⠀⠉⠁⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠀⠀⠀⠉⠉⠉

⠀⡀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠠⠆⡤⣦⣶⠶⠶⠴⠶⠨⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠛⠛⠐⠑⠀⠀⠒⡄⣤⣤⣴⣾⣶⣦⣦⣀⠀⠂⠰⠀⠉⠀⠀⠀⠐⠀⠀⠀⠋
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣀⡀⠀⠄⣠⠀⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠠
⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⡤⢀⠈⠀⢠⣿⢿⣟⡿⢻⡿⣾⣿⣧⣌⣻⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⣾⣿⢟⣴⠀⢸⣍⠛⣿⣿⣿⣿⢿⣋⡿⣿⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠐⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⣿⠿⢻⣿⣿⣍⣦⣿⠛⣧⢀⡗⢠⣾⡏⢙⣿⣏⣽⠿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⡏⠳⣼⡿⢿⢻⣶⣿⡋⢤⡇⠹⣳⣶⣾⣿⣷⣽⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠄
⢈⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⣿⡗⢒⡸⣯⠆⢀⣀⣿⣿⣷⠾⡇⠀⠈⠛⢿⣭⣻⣿⣿⠟⣠⣴⣟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠈⠀⣄⢠⠀⠀⡀⣠⡆⣀⠀⡀⠐⠘⣟⠿⣶⣾⣿⢛⣯⣼⣆⣿⣷⣿⣶⣆⠀⠀⠈⣿⠋⠰⠛⡟⢻⡟⣰⣿⣇⠀⠀⠀⠀⠀⠀⢂⣀⣠⣄
⠀⠀⣸⠞⡷⣏⡅⣼⠅⡿⣿⣶⣆⣄⠈⠳⣏⠈⣿⣿⣿⣿⣿⣿⢿⣟⣿⣿⣿⡈⠀⣼⠄⣨⣾⢷⣻⣖⢾⡷⢻⡄⠀⠀⢠⣄⣎⣞⣉⣫⣿⣷
⠀⠕⢸⠀⣼⡋⢰⣴⣿⣷⣾⣿⣿⣿⡄⠀⠙⠫⣷⠙⡟⠩⠤⠙⠇⡺⣿⣻⠏⡷⠀⠸⠃⢸⣿⢾⡿⣟⡿⠐⢸⣇⠀⢰⣾⣿⣿⣿⣿⣿⡟⠟
⠀⢃⣮⣄⣽⠧⡘⢿⣿⣿⣿⣿⣿⡛⠉⠀⠀⠀⣧⠐⢷⣄⠁⠀⣸⣿⠝⢻⣹⣠⣧⣤⠀⣸⠛⣯⡽⣬⢈⠀⣯⡛⣇⢸⡿⠛⣿⣻⡿⣿⣷⣾
⠀⠸⢻⡅⡆⢿⣿⢿⣽⣿⣿⣿⣿⣧⠈⠀⠀⠀⠈⢾⣿⣿⣿⢿⣟⣙⣈⣾⠿⣼⡿⣿⢮⣶⣾⣷⣾⣿⣿⢆⣽⣿⣿⢸⣥⣷⣽⣿⢿⣿⡿⠛
⠠⠀⠀⠀⠂⢈⠁⠈⣿⠁⠻⡏⠘⣧⡀⡄⣠⡇⣠⣀⠟⢛⠿⢛⣻⣍⣙⣿⣄⢻⠼⣋⡆⠙⡻⢗⡛⢻⣟⣻⣿⣛⡷⠾⠯⠋⡉⠛⣻⣻⡇⠄
⠀⠀⠁⠀⠀⢸⠀⠀⠉⢣⡀⠀⢄⠈⣫⣗⣿⡷⣿⣿⣾⣇⠉⢹⡟⣧⢹⢿⣿⣦⠼⣿⣿⣧⠶⠷⠁⡾⢉⡼⠋⢀⠀⠀⠀⡀⠹⠢⠻⣿⡷
⠐⠀⠀⠀⠀⠈⠀⣀⠀⢠⢹⣠⣈⡿⢿⣿⣋⣼⣿⣯⡷⣿⡀⢈⣇⣿⡉⣽⣷⣿⣾⣿⣿⣿⠥⠀⠀⣤⣾⣗⠆⡈⢀⣈⣀⣥⢀⠀⠐⠋⠐
⠀⠀⠈⢅⠠⣠⠔⣫⣼⡇⣿⠋⠈⠀⠒⢰⢌⣛⣻⣿⣿⣟⠿⠿⣗⢸⣅⠘⣫⣋⣹⣯⣽⣿⣶⣆⠀⣦⣩⣭⢭⢥⣿⣽⡌⠙⢶⣂⠈⠑
⠀⠀⠀⠈⠻⣟⣿⣧⠻⣄⢔⣆⢁⡐⠉⠉⠰⣎⡛⢻⡟⣻⣿⣿⣯⣿⢿⠿⢇⣟⢻⣿⣻⣿⣀⠏⢱⣿⠾⣷⢎⣼⣿⣿⣿⣭⣟⡄⠀⠀⠀⣈
⠀⠆⠀⣁⡀⠈⣳⠞⢛⣽⠋⣿⠀⠀⠀⡾⡳⡉⠑⠻⣿⢽⣿⣿⣿⣯⣿⡏⡿⣧⣿⣟⠨⠇⠙⣑⣨⢟⢩⣧⣄⣹⣇⡾⣻⣿⢏⡄⠀⠀⠄⠄
⠀⡀⠀⠉⠀⠀⠀⠀⠐⠃⠀⠋⠜⣲⣁⣙⣉⡗⣀⠀⣔⠈⣉⣾⣭⣿⣿⣿⣿⡋⢀⣿⡆⣰⠜⠉⠫⣾⡄⠁⠆⠸⡿⠃⠘⢉⠁⠁⠀⠀⠂
⠈⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⡻⠌⠁⢻⠀⢛⣻⡏⢡⣀⢤⣿⣧⣦⣼⣿⣧⡖⢶⣆⠐⡇⠠⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠉⡤⣦⣿⣿⣧⣵⣤⣿⣻⣯⣼⣿⣶⡬⣿⣯⣶⠅⣁⢿⡟⢦⣾⢹⡾⠃⠀⠀⠀⠀⠈⠂
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⢀⣿⠂⠿⠋⣨⣦⡇⣿⣿⡻⣾⣿⣿⡳⢿⡾⣻⣴⡟⠬⢧⡼⢿⣧⣄⠀⠄⣄
⠀⠠⠀⠀⠀⠀⢠⠛⡀⣌⢣⡄⠈⢿⠀⠀⠠⣧⢽⡼⠻⣿⢷⣾⣅⣀⣆⣶⣿⣿⣿⠇⠴⣿⣷⢦⣠⣿⣿⣾⣿⢸⡇⣦⣰⡆
⠀⠀⠀⠐⠂⠀⠀⢧⣿⣇⣿⡏⠢⣠⠀⢀⡴⠻⡷⣤⡞⠻⠟⣍⢘⡿⣿⣷⣿⣿⣾⡰⣿⣻⣧⣿⡿⢿⣉⣷⣿⢿⠿⠟⣩⠇⠀⠀⠀⠈⠁⠁
⠀⠀⠀⢀⠀⠀⠀⠘⠳⡍⣟⣷⠈⠉⠄⠀⠀⠀⡸⣐⡶⢀⣴⠋⡿⢻⡟⢳⣻⢭⣲⣿⢻⡻⣿⡟⠵⢪⣳⣟⣏⡛⠈⠳⣦⣤⡄⠀⠀⠀⠉⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠌⡉⣌⡦⣬⣬⠷⠀⢰⣧⠀⠀⡹⣇⣷⣿⡎⢷⡼⣿⣻⣉⠨⠳⣿⣷⢈⣿⣷⠟⢉⡼⠁⠊⠉⠈⢁⠈⠠
⠀⠂⠀⠣⠖⠀⠀⠀⠆⠀⠈⠈⠙⢀⠔⠀⠀⠈⡧⣠⠤⣤⠀⠐⣳⣿⣆⣹⣿⣿⣿⡳⢲⣿⢷⣍⣿⠿⢛⡵⠟⠁⠀⠈⠀⢐⠀⢀⠈
⢹⣭⢍⡙⡉⠉⢤⠜⠖⠲⠖⡖⣒⢚⣢⡄⠀⠀⠻⣄⡀⣄⡐⢰⣿⣿⣧⡉⢈⣹⣿⣿⠏⠸⡦⣸⢽⡴⠀⠀⠁⠀⣤⠴⠂⠀⢒⠀⠀⠀⢆
⢸⣝⢋⣽⠗⢽⠈⠤⢀⠓⠁⠀⣦⠉⢀⠽⡀⠠⠀⢻⡀⠐⠈⠆⡰⣷⣄⠁⠉⠙⠛⠛⠒⠃⠉⣰⠇⠂⢴⡇⠀⠉⠉⠉⢉⣉⣉⣉⣙⣷⣏⠾
⠘⣧⠁⠴⣖⠠⢄⠐⢺⡈⡻⢒⣴⡎⡸⡊⠁⠠⠚⠂⠳⡜⠃⡀⠒⠉⢸⠊⠈⠠⠀⠢⠠⠂⢠⠞⠐⠃⠐⠘⠒⡀⠂⠈⢨⡗⠀⠲⣯⣿⣣⣛
⢨⣧⠆⢰⡿⠿⠿⣦⡿⣿⣴⢊⣡⠛⡃⢙⠃⠀⠀⡀⠀⣹⠀⠸⠅⠀⠀⠁⠀⠀⠰⡷⠄⣰⢏⢶⡀⣬⠱⠮⣻⡇⣾⣿⢠⣾⣿⣤⠿⠉⡝⢮
⢸⣿⠾⠋⠚⠃⢸⣦⡐⡿⠳⠊⢉⠀⢻⠉⠀⠀⠀⠘⡆⠠⠷⢆⣀⢂⠡⠶⠀⠌⠒⢀⣼⢡⠎⠀⢺⢢⠵⡎⠛⠻⣟⡟⠃⣿⣉⣽⣿⡀⠀⣡
⢼⡍⢛⡔⠃⠀⣠⡀⠈⠇⣴⣖⠉⡴⣇⠬⣯⡶⣥⣴⣮⠔⡴⠲⠈⢉⣱⡛⠒⠒⣛⠉⢠⠤⠈⡀⠀⠀⢂⠒⠀⠞⣷⣾⣥⣻⣶⣿⠉⠀⡴⢛
⣸⡷⠟⠗⢡⠄⠉⠛⣿⠟⠙⠿⠻⠶⠦⠄⠺⠾⠿⠷⠰⠿⡷⠾⠷⠤⠝⠿⠷⠦⠨⠔⠂⠴⠢⠹⠇⠿⠾⠷⠼⠻⠿⠿⠿⠿⠯⠟⠫⠾⠲⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⣄⠀⠀⢸⠀⠀⠀⢰⠁⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡄⠀⡅⠀⣠⠸⠆⠀⠀⡀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠲⠟⠲⡏⠀⠀⠰⠾⠁⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⢀⡴⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠘⠷⠀⠀⠀⠀⠀⠀⠀⡦⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠲⠀⠀⠀⠀⠀⣄⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣃⠀⠀⠀⠀⠀⣿⠐⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡀⠀⠀⠀⣠⣿⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⢠⣿⣸⡇⠀⠀⣮⣿⣿⣿⣯⣬⣔⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠛⠻⠿⢿⣿⣷⣤⣾⡿⠟⠉⠁⠈⠇⠉⠀⠈⠳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠠⠆⢰⡆⠀⠀⠹⣿⣿⢷⠀⠀⢀⠀⢴⡄⠀⠀⠀⠹⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠠⢶⠐⠆⠀⠀⠀⢠⠞⠊⣶⠀⠀⣠⠀⣿⣿⣾⠀⠀⣀⠀⣴⠃⣤⡄⠀⠀⢷⡈⡀⠷
⠀⠀⠀⠀⠀⢀⠄⠀⠂⡴⠀⠀⠀⠀⠈⠀⠀⠶⠀⠞⠉⠀⠈⠀⢸⡀⠀⠻⣤⠈⠃⠀⠘⢂⠀⠀⠀⠚⠄
⠀⠀⠀⠀⠀⠀⣴⢆⣈⠀⠀⠀⠠⠁⠀⠀⠀⠼⠀⠀⢸⠀⠠⠀⢸⠀⠀⠻⣄⠱⡶⠀⠀⠀⢂⠀⢣⣰⡟⢇⠀⡀
⠀⠀⠀⠈⠀⠠⠁⡉⣽⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⣮⠀⠀⠀⠁⠀⠙⡄⠀⠀⠀⠆⣸⣷⡉⠄⠀⠙⡀⠀⠄
⠀⢀⠊⠀⠀⢤⡺⠷⠷⣛⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠼⢤⣧⠀⠀⡀⠀⠀⣠⡄⠀⢀⡤⠴⢻⢟⠘⠗⠀⠀⠰
⠀⠀⠀⠀⠠⠎⠀⠀⠘⠈⢦⡄⠛⢆⠀⠈⠁⠢⢄⠀⠀⠀⠐⢸⡇⠀⠀⢀⠄⠉⠀⢀⡼⠃⠤⣶⠟⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠁⠀⠀⠀⠀⠐⠄⠀⠀⣿⡇⠀⠔⠁⠀⠀⠀⠈⠀⠀⠠⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄⠀⠀⠀⣄⠀⠀⠀⠘⢀⡼⢻⢧⠈⠀⠀⠀⠀⠋⠀⠀⠀⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⠸⡎⢳⡄⠤⢤⠘⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠰⠚⠁⡝⣠⠎⠀⠘⣦⡱⣄⣸⠄⠀⠀⠀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠠⠀⢀⣢⡼⢙⢫⠰⠀⣠⣻⣽⣝⣯⠕⠂⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⡰⠂⠈⣩⠏⣻⡟⠞⠀⠣⡤⠙⠊⢛⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠀⠀⠀⡈⠀⡈⠀⢈⠀⠀⠐⡀⠀⢨⠀⠠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⢰⡅⢀⠁⢀⠠⢄⠀⠀⢁⠀⠘⡇⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢀⡀⢀⡼⠋⢧⡌⠀⡎⠀⠈⡀⠀⠘⠀⣰⠛⣇⣻⠰⠖⠹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⡘⡳⠋⠀⣰⠜⡇⠀⠃⠀⠀⡇⠀⠀⣴⠛⠰⢆⣿⡶⠄⠲⡦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢙⠙⣇⠞⡂⢤⠐⢏⡄⠀⠀⠀⡇⢀⣴⣯⢠⡄⢻⡍⡃⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠈⠀⣹⠎⠁⢸⣀⣾⣽⠆⠠⠀⡷⡨⣮⠛⢠⠃⡜⢁⠑⠀⠀⠀⡆⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡏⠀⠀⠈⢡⡽⡏⠠⣴⠄⠊⣴⡇⠀⠈⠀⠀⠈⠈⠀⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸⠁⠀⠀⠁⠿⠁⠈⠀⠸⠀⠈⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⠇
⣷⣿⣷⡿⣿⣷⣾⣷⣿⣷⣿⣿⣷⣿⣿⣶⣿⣷⣿⣷⣿⣿⣿⣷⣿⣾⣿⣾⣾⣷⣾⣾⣿⣾⣷⣾⣶⣿⣿⣾⣿⣶⣿⣷⣿
⣿⣿⣿⣀⣀⣠⣄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣮⣵⣌⡥⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⡿⠀⣾⣿⣿⣍⣧⡄⠀⢠⣄⠧⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠶⠦⢀⣠⡶⢿⣜⣴⢗⠛⠋⠙⠋⠉⠟⠒⣦⡽⣶⣾⣤⣼⡝⢲⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡶⣳⢎⣰⣟⣩⣿⠛⣴⣿⣏⣉⣹⡿⠚⣩⡑⠖⠶⠍⠛⢿⡽⠿⢣⡀⢘⣠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣿⣷⣿⣿⣿⣿⡾⣿⣿⣿⢛⡟⣿⣛⠻⣿⡀⣴⡤⡎⢱⡄⠑⠉⢠⣆⡇⣨⠷
⠀⠀⠀⠀⠀⠀⣀⡖⣄⡊⢠⣥⣴⣿⢿⣿⣿⡾⣿⡟⠓⢿⠶⠿⠶⠿⡷⠿⢷⢹⣷⡞⠀⠀⠈⠉⣷⡁⠒⢒⡆
⠀⠀⠀⠀⠀⠘⠷⣾⣿⣧⣼⣿⣿⣄⣿⡟⡃⢴⣾⠖⢻⣿⠿⠷⠆⠀⣰⠆⠀⠀⢭⣳⣀⡠⣶⣴⡶⠟⢣⡟
⠀⠀⠀⠀⠀⠀⠀⣹⣹⣿⣿⡿⢷⣤⣽⣷⣿⡿⣿⣿⣷⣷⣆⣸⣆⣾⣿⣦⣴⣏⣤⡾⣻⣿⣯⣭⢈⣿⣦⠸⠆
⠀⠀⠀⠀⢀⣠⣾⣿⣏⣿⣿⣶⣆⣹⡟⣿⣯⣗⣋⣿⣟⣝⠿⢿⣿⡿⣿⠆⡼⣿⢿⣿⣻⣿⣿⠋⠀⢳⡄
⠀⠀⠀⠀⠉⠉⠽⢿⣿⣼⣿⣿⣿⣽⣿⣿⣿⣻⣷⣺⣿⣏⣳⢾⣿⢋⣿⡤⠫⣷⣤⠤⠀⠀⠉⢦⣤⣅⡁⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣋⠀⢀⣝⢿⣿⠿⠫⠋⠉⠻⣿⣿⣄⠛⡾⠻⣿⢶⣶⣈⢘⡛⠁⠀⠠⡤⢀⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠛⡿⠿⠟⠾⠃⠀⠀⢸⣿⡘⡖⢳⠀⢀⠙⠑⠿⠿⠇⠀⣠⣀⣠⣤⡂⣀⡄
⠀⠀⠐⠖⢀⣶⣞⢢⢄⡠⢀⣴⠶⣄⠙⡃⢀⡀⠐⠂⠀⣼⣿⠃⢠⢸⡄⠛⠃⠠⠂⠚⠛⠨⠉⠩⠉⠉⠉⠉⠁⠂
⠀⠀⠙⢃⢸⣿⡷⢿⢦⡇⢺⡿⣿⣼⢫⢱⣿⣬⣱⠺⣲⡿⣿⠀⣾⠴⣇⠰⡄⣰⣖⣓⠢⠀⣤⠦⡀⢀
⠀⠀⠀⠐⠡⠀⠒⠊⠃⠈⠠⠒⠃⠨⠏⠀⣨⣽⣷⣶⣿⣴⠋⣴⣿⣤⡹⠶⣴⢬⣍⣋⡛⡺⣛⡗⢺⢴⣯⣆⢠⣀⣀
⠀⠀⠀⠀⠀⠐⠒⣒⠛⣛⠻⠖⢺⠿⢻⡟⢛⡉⠀⠋⠉⠀⠀⡀⠀⠀⠉⠛⠲⠶⠚⠲⠯⠙⠋⠉⠑⠒⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⠂⠲⠴⠀⠠⡬⠛⠛⠂⠂⠂⠤⠤⠌⠒⠐⠂⠀⠀⠈⠐⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⡀⠀⠀⠀⠴⠆⠀⠀⠀⠐⠀⠀⣼
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚
⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⣄⡀⠀⣀⠦⠀⠤⡄⠀⡆
⣷⢹⣷⡀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠱⠂⠀⠀⠉⠁⠀⠀⠀⠑
⣿⣷⣿⡯⢹⣏⣉⣉⣭⣭⡥⠤⠤⡼⠃⠀⠀⣀⠀⡠⢄⠀⠀⠀⠈⠁⢀⡀⠀⡀⠀⠀⠃⠀⠀⠀⢠
⣿⣿⣿⡯⠘⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡏⠀⠀⠠⠘
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⣠⠛⠂⠤⠤⠤⠄⠀⠠⠀⡄
⠿⠛⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠄⠾⠯⡀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡀
⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⢨⠀⠀⠈⡲⠋⠀⠀⠀⠀⠀⠈
⠀⠸⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀
⠀⠘⠀⡷⠒⠒⠀⠉⠉⠉⠀⠀⠀⠀⠀⣱⠀⠀⠀⠒⠀⠤⠄⢀⠀⠀⠀⢹⡄⠀⠀⣀⡠⠀⠠⠄⠀⠀⠳⠄⡀
⠀⠀⠀⡏⠑⢶⣤⣀⣀⣀⠠⠤⠒⠀⠀⣿⣀⠄⠀⠀⠀⠐⠀⠠⡀⠀⠀⡘⡏⠀⠊⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡇⠀⠀⠀⠉⡉⠀⠀⠄⠀⠀⡀⣿⠁⠄⠀⠀⠀⠀⠀⠐⣛⣞⠀⣓⠂⠀⠁⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠘
⠀⢠⠀⡇⠀⠀⠀⠀⠂⠀⠀⠀⠀⡟⠳⢾⡀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠄⠸⠃⠐⠀⣀⣀⣤⠖⠛⠂⠀⠀⠀⢀⠂
⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠳⡆⠀⠀⢀⠀⠀⡴⠛⠒⠛⠛⠛⠉⠉⠉⢉⠃⠀⠀⠀⠠⠀⢠⠏
⠀⢸⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⢸⠑⠄⠀⠈⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠋
⠀⢸⠀⡇⠀⠀⠀⢸⠀⢀⢰⠀⢸⠀⠀⠀⢸⠀⠘⠀⢠⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠃
⠦⣼⢀⡇⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀
⠒⠲⠬⠕⡲⠤⢄⡀⠀⠀⠀⠀⢰⣯⣍⣩⠆⠀⠱⡀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠠⢄⡄⠀⠀⠰
⠀⠀⠤⠀⠀⢉⠀⠋⠀⠀⠀⠀⢨⠀⠀⢈⠇⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⡸⢦⢀
⠀⠀⣀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡸⠀⠀⢸⠒⢧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘
⠀⠀⠈⠠⠈⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣡⠞⠋⠛⢦⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡟⣰⠋⠀⠀⠀⠈⢷⣘⣧⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⡤⠶⠶⠶⣾⢠⣏⣙⣳⡶⠶⢛⣉⣭⣤⡶⠶⠶⠦⣍⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⢰⡇⣼⠿⢋⣡⠶⢾⣉⠻⢿⣄⣧⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠹⣆⠀⣠⣾⠇⣿⠞⠋⠀⠀⠀⠈⠛⢦⣌⠻⢦⡀⢀⡾⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⢿⣡⣾⠀⡏⠀⢀⡴⠖⢦⡀⠀⠘⡏⢻⣦⣹⠟⣱⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣦⡙⢿⠀⣇⠀⠘⢧⣀⣼⠃⠀⢠⣇⣼⠟⣡⣾⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⠏⠀⠙⢿⡆⣿⢦⣀⠀⠀⠀⢀⣤⠾⢋⣥⠞⠁⠈⢷⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠸⡇⢻⣦⣍⡛⠶⣾⣋⣥⣾⠋⡟⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠳⠶⠶⠶⢿⠘⣟⣩⡽⠷⠦⣬⣙⡛⠺⠷⠶⠶⠶⢋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠛⠛⣇⢹⡅⠀⠀⠀⠀⡽⢩⡟⠛⠓⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡙⢦⣀⣠⠞⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⣬⡤⠞⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⣿⣼⢒⡯⠁⣯⡷⢼⢫⡌⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠀⠉⠁⠁⠉⠈⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡉⢉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⡰⢻⠛⣎⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣶⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡴⠲⣞⣡⠤⣴⠧⢼⠶⠼⣦⠤⣌⣳⠒⢦⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⣿⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡤⢟⠒⢶⠧⣀⠼⠦⣀⠼⡶⠒⡻⢤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡞⠉⢳⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠑⣾⠀⢘⡦⢴⡃⠀⣷⠊⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⣄⠴⠚⠉⠒⠉⠑⠦⣄⠷⢄⠀⠀⠀⠀⠀⠀⠀⠈⢇⢀⠇⡹⠯⣄⣠⠽⣏⢸⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⡤⠧⣤⠞⠢⠤⠤⠤⠤⠤⠴⠻⣤⡼⢤⠀⠀⠀⠀⠀⠀⠀⢨⠚⢺⡥⠒⠉⠉⠒⢬⠟⠳⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠞⠉⠙⠛⠛⠋⠉⠳⠴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡤⠖⣩⠗⣶⠺⣍⠒⢤⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠙⡄
⠀⠀⠀⠀⠀⠈⠙⡎⠉⡿⢒⡞⠋⠉⣿⠉⠉⠳⡒⢾⠋⢱⡎⠁⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⢳⠞⢏⠓⢤
⠀⠀⠀⠀⠀⠀⠀⢹⢺⢉⠟⢤⣀⠀⣿⠀⣀⡤⠻⡍⡷⡏⠀⠀⠀⠀⠀⠀⢀⣠⠎⠀⠀⠀⢸⡅⠈⣇⠀⠱⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠈⣏⠀⠀⠈⣏⠀⣹⡁⠀⠀⢹⡁⣹⠀⠀⠀⠀⠠⠤⣏⠈⣳⠤⠤⢴⡁⢈⡦⢾⠤⣎⠀⣹⠤⠄
⠀⠀⠀⠀⠀⠀⠀⣸⣼⣘⣦⠖⠋⠈⣿⠁⠉⠲⣤⣃⣧⣇⠀⠀⠀⠀⠀⠀⠈⠙⣏⠓⠤⣄⣹⣏⣠⡿⠚⡹⠋⠁
⠀⠀⠀⠀⠀⠀⣠⣇⣀⡿⢬⣧⣀⣀⣿⣀⣀⣴⡥⢾⣀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣸⣥⣞⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠓⢤⣙⣦⠿⣤⣋⡤⠖⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠉⢉⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢠⡤⠌⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⢻⡀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣁⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣹⠛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠛⠛⢸⣧⠎⣻⣯⣝⢛⣶⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠁⢬⡿⣠⠊⢹⠀⣤⣾⡍⠙⣟⠁⡈⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡆⢀⡇⠀⢸⠅⣿⡿⣤⡂⢸⡇⢘⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⢸⡇⢈⠁⢀⠸⣆⢹⣷⣿⣱⣌⡁⢾⠠⠐⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⡷⠀⠀⢀⣀⣨⣯⣭⣭⣅⣰⠇⢸⠀⠀⠰⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⣿⠱⢶⣾⣿⣿⣿⠛⠉⠛⠟⢹⡇⠃⠘⡀⢀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡅⡎⣿⠀⠘⠟⢁⣡⣤⣶⣆⣉⣤⣿⢣⠁⠀⢣⠀⢀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⣿⡞⢰⡇⠀⣾⣿⣿⣼⣟⠁⢹⣿⠃⠀⠀⢸⠖⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⣀⡿⠀⠾⡇⠀⠛⡋⣿⠮⣻⣤⣿⡏⣾⠀⠀⢸⠆⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⠟⠁⠀⡆⠀⢦⣸⣽⣟⣶⣹⣿⢟⠀⣿⠀⠀⢸⡦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂⡾⠃⠀⠀⠰⢁⣤⠺⣵⣿⡿⢿⠿⢟⠛⠑⢿⡇⠀⢸⡇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠀⠀⠀⠀⢸⡏⠀⠐⠈⢻⢻⡇⠀⣸⡚⠀⢸⡃⠀⢸⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⠁⠀⠀⠀⠀⠀⣿⠄⠀⠀⢸⡾⣿⠀⣿⣇⠀⠀⣿⠀⠘⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⠷⣿⣄⣯⢄⠀⠀⣹⡆⠀⡷⠢⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⠘⣟⢻⣿⣾⠀⠀⢸⣇⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠸⣹⣿⠀⢿⣷⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠙⣿⠀⠈⢿⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢳⢿⠀⠀⠸⣿⣄⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠃⠠⡧⠀⠀⠀⢳⢿⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣼⡧⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⣿⣷⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⣾⠀⠀⠸⣟⠦⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⢿⡆⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢹⠀⠀⠀⠘⣇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⣿⢰⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⠶⠀⠷⠦⠀⣉⡲⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣹⣿⡁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⣛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠾⠋⠀⢠⣄⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣇⠀⠀⠀⠀⢠⣤⣬
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠄⠀⣾⣿⣶⣧⣤⠀⠀⢰⣆⠀⠀⠀⠀⢌⣧⣄⣤⠤⢶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣶⣆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⡄⠀⠀⠀⠀⢀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⢃⠀⣇⠀⠠⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢿⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠁⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⢀⡀⢠⠀⠰⠆⠀⠀⠊⠀⢀⣼⠀⠄⠘⣄⢘⡇⠀⠰⠤⠆⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⡽⠶⠦⡀⠐⣆⣘⣆⣈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠀⠀⠁⠈⢢⡈⠶⣠⠀⠺⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⣿⢿⣿⣿⠟⢫⡍⢡⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠰⡇⣿⢀⠐⠀⠀⠂⠁⠂⠀⢀⠸⣧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠋⠀⡿⠋⢱⡎⠠⡄⠀⡆⠀⠈⠃⢀⠴⢠⡄⢀⣼⠃⣸⠈⠁⠀⠆⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡗⠀⠁⡀⠀⠉⠁⢠⠀⠁⢺⠋⠀⡏⠀⠀⠀⡇⠀⡠⠀⠀⠀⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠆⠀⢠⡌⠀⣋⣧⡀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠈⠒⢤⣀⢇⣰⡟⠂⠠⢀⢨⠏⠉⠁⠀⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢃⡒⣲⢒⠂⢠⡤⠤⠀⢀⢀⡀⣀⡀⣀⠀⣀⢀⣠⣤⠄⣀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄⠤⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠠⣄⣨⠟⠉⠄⠀⠀⢐⠃⠂⠀⠸⣷⣶⣿⢽⣿⠀⢸⡤⣠⠂⠀⢿⡏⠍⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠋⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠺⠀⠀⠀⣼⠀⠀⠀⢘⣿⣿⡇⠀⠉⠃⠘⡇⠉⠁⠀⠻⠱⠆⠀⢨⠙⢋⠀⠀⠀⠀⠰⠀⠈⠀⠀⠈⠂⠀⠐⠀⠀⠐⡑⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠁⠀⠒⠉⠐⠀⠀⢊⠙⢿⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠠⡄⠨⠀⠀⡀⠀⡙⠛⠎⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⠰⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⡀⠀⠉⠃
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⠀⡐⠀⠸⡆⠀⠶⠒⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠘⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠⠄⠠⠄⠀⠀⠀⠸⣿⣿⠿⣤⣿⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣁⣤⣘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡈⠿⠉⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢉⡟⢂⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠞⣷⠀⣇⠙⢥⠠⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠓⠂⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⡏⢲⣧⠀⣿⠀⣾⠇⠹⣆⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣳⡤⣹⡇⠸⠃⠖⣿⡔⠿⠀⠰⠉⠂⣌⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢏⣷⣉⣀⠃⠤⣾⣍⣛⡤⠀⣀⡈⣠⠿⡻⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠇⢻⠴⣯⣽⡿⣃⢸⣝⣿⣯⣿⣿⣯⠐⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢘⠄⣿⠀⠀⠛⠺⣿⢈⣿⠇⠈⠃⢘⣿⠀⡁⠀⣇⠀⠀⠀⠀⠀⠀⠐⠒⠓⠐⠒⠒⠀⠂⠒⠂⠀⡄
⠀⠀⠀⠉⠉⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣸⣁⣻⠀⣿⠀⠀⠀⠀⠸⣸⡇⠀⠘⠃⢀⣿⡄⣣⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⢻⡔⠙⡇⠀⠀⠒⢲⣿⡖⠓⠀⠀⠸⠋⠱⣿⢛⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⡁⠀⡃⠀⡐⠾⠀⣜⠀⠷⢀⠀⠀⠀⢀⣿⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠇⠀⠿⣇⢡⡆⣰⣿⡄⢀⡤⣼⠿⠁⠈⢿⣧⠀⢃⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⣶⣿⢰⡇⠈⣷⡖⢉⣇⣜⣷⡆⠀⠺⣿⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠀⠀⢀⡀⣿⣿⡏⠰⣛⠆⠘⣿⣿⠁⡄⠀⠀⢹⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⡇⠀⠀⢸⡷⣿⠻⢿⣄⠀⢀⡸⠛⣿⣿⡇⠀⠀⠘⣿⠸⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣧⠀⠠⠼⠗⠚⠛⣿⡍⠀⢨⡽⡇⢫⡘⠻⠀⠀⢠⠋
⠀⠀⠈⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠈⢹⡷⠼⡆⠀⠆⠛⢠⠠⣨⣇⠀⢸⣇⠇⣄⢹⠰⠀⠀⠿⠶⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠳⡄⠃⢠⢠⡇⢸⠓⠸⣏⣦⣿⡟⡗⢇⢸⡀⡀⠘⢂⡴⡺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⣿⡇⠘⠀⣾⢫⣿⡟⢷⡀⡎⢰⡇⠆⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡇⠀⠘⣆⣿⣿⡿⢈⠇⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⡰⡇⢻⣿⢷⠸⣇⡀⢸⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠸⢁⠸⣦⠉⢸⡇⡇⢳⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠈⠀⣿⠀⣿⠁⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢀⣧⠀⢠⡇⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⢿⡿⠀⣿⣷⠀⠘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣾⠁⠀⠈⣿⢀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⣿⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢷⠀⢺⣄⠀⣴⢹⠀⡾⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⢸⣿⠀⣿⡜⠀⡷⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡄⠘⣟⠀⢹⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠳⠠⡇⠀⢸⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⢀⡇⠀⢸⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡼⣇⠀⣸⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡧⡛⠀⢹⡜⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣏⣷⠀⣾⣻⣷⣶⣤⡀
⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣴⣾⣿⣿⣿⡿⠟⠻⠛⠛⠛⠛⢿⡿⡿⣿⣿⣿⣿⣿⣶⣴⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢾⣛⣋⠉⠉⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠨⠙⠙⢻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢹⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡄⣠⣐⣚⣷⣷⡦⢀⣀⡀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⣤⣴⣦⣦⣽⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣶⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠛⠉⠉⢹⣏⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡄⠀⠀⣀⣴⣿⣿⣀⠀⠀⢠⣤⣄⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣷⣾⣴⣦⣤⣤⣤⣤⣤⣶⣾⣿⡛⠭⠥⢤⠤⣴⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣽⣽⡏⣿⡿⢿⣿⣽⣿⣿⡷⠁⠀⠀⠀⠄⠘⠟⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⣧⠌⣷⢻⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣦⣧⠀⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣾⡷⣧⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣯⣀⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡷⢜⠂⠀⠀⠀⣀⣴⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠈⣿⣀⣀⣤⣶⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣻⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣴⣶⡄⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣼⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⣉⣤⣤⣤⠈⣡⡌⠻⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⡦⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢠⣄⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠁⠀⣿⣿⣿⡏⢠⡄⢻⣿⡇⠸⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⢸⡇⢸⣿⢠⣦⢸⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣈⣁⣾⣿⠸⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠦⠤⠾⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠉⠁⠈⠁⠀⠀⠈⠁⠁⠉⠉⠈⠁⠉⠈⠉⠉⠉⠁⠈⠀⠉⠈⠉⠉⠉⠈⠀⠁⠁⠉⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠆⠀⡄⠀⠀⡀⡦⠀⠐⠆⠀⠐⠂⠰⠀⠀⡀⠰⠐⡂⠔⠐⠀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⢀⡿⠀⠐⢾⣿⣿⣦⡀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⡀⠰⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⢲⣼⣿⠿⠀⠀⠀⢀⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⢠⣇⠀⢀
⢀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣸⡼⠛⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⠀⠀⠀⢸⣿⣦⡙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⣸⣷⠀⣼
⣿⡀⠀⣼⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⠀⠀⣴⣿⠿⣿⣿⣷⣦⡀⠀⠀⠀⠈⠻⠿⠛⣿⣿⠟⠟⢛⣿⣿⣁⣼
⣿⡆⢐⣿⡆⢸⡆⠀⠀⣘⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣴⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⢀⣿⣿⡂⠀⠰⣿⣿⠷⣿
⣿⣗⣸⣿⣇⣼⡧⠀⠀⢽⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⣨⣿⣿⣧⠀⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠐⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣷⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠔⠀⠆⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⠀⢀⣀⣀⣀⠀⣠⠀⠄⠀⠶⠋
⠀⠀⠀⡄⠀⢀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⠸⣪⡽⡡⣲⢼⣦⣄⣠⡌
⠀⠐⠀⣄⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣁⡁⠑⡀⢁⠄⠁⢸⣿⣿⡇⠁
⠀⠀⠀⡄⢐⠀⠀⠐⢀⠀⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⣛⠈⣘⠁⡑⣀⠰⠄⡪⠟⣿⡗⢳
⠀⠐⠀⠀⠠⠀⢤⠀⠀⠀⠀⠂⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠉⠀⠀⠀⠰⠈⠄⢂⠐⠌⠾⢟⡟
⠀⡄⢣⠀⠠⠀⠀⠰⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠰⠄⠑⠠⠄⠀⡀⠀⠄⡠⣾⠃
⢀⢀⠃⡂⠐⠢⠀⠂⠀⢃⠸⢃⣀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠾⠀⢥⠎⠈⡤⠀⠌⠁⣸⣏
⡌⠈⠀⡁⠀⠠⠀⢀⠀⠀⠀⠀⢈⠁⢡⠀⠀⠀⠀⠀⠀⠀⠀⢷⡅⡀⠃⠐⠠⢁⣀⠤⠅⢤⢻⣾
⢧⠘⠀⠃⠨⡁⣤⠈⠀⠀⠀⢀⢰⠡⡘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣀⡨⡦⢀⠠⣉⢬⣌⣼⣿⡏
⠸⢀⠴⠐⢤⢃⠛⡠⠀⡀⡠⠸⣴⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠷⣈⣴⣔⠧⣰⣿⣾⡟
⠀⡇⠚⠀⠰⣄⠤⢃⠀⡘⠁⠀⡌⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⡿⣷⢾⡟⡿⠋
⠀⡑⠀⠀⠘⠁⠀⡰⠦⠀⢀⢊⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⣹
⠀⡇⠀⠂⠁⠀⠈⠁⠠⠐⠀⣼⣴⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢰⠄⡞⠁
⠀⠳⢑⢠⠂⠀⠀⠲⠈⡧⠆⣥⢷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰
⠀⠀⠘⣦⣀⣀⣰⡖⣠⣶⣻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠣⡀
⠀⠀⠀⠈⠉⠛⠉⢺⠁⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠈⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠀⠱⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣱⣶⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣤⣤⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⣶⣶⣶⣶⣶⣶⣶⡶⠆⠘⢛⠿⢿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⠀⠈⢻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠉⣀⣸⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠽⣿⠿⠛⠃⢹⣟⠿⣷⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠠⠄⠒⠒⠀⢘⠛⠛⠛⢿⣿⡯⠛⠹⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣀⣀⣀⣀⡀⢀⣀⣀⣿⣦⣀⣠⣤⣀⣤⡀⢀⣀⣀⣀⢀⣿⣇⣠⣄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠛⡛⠋⠉⠉⠉⠉⠉⠁⠈⠉⠉⢿⣿⡟⠉⠉⠉⠉⠁⠈⠉⣩⣯⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣾⣿⠶⠤⠤⠤⠀⠀⠀⠀⠀⢀⣸⣋⣤⣤⣴⣦⣶⡄⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣯⠥⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣯⣭⣭⣭⣿⡿⠇⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣮⣭⠀⠀⠀⠀⠀⠀⠐⣿⠟⠀⣛⠀⠀⠀⠀⢀⢈⣛⣡⣿⣿⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠿⠀⣬⡭⠅⠀⢠⡀⠙⠉⠉⠉⠉⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⣰⣿⣿⠀⣾⣿⣷⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣰⣿⣿⡏⢸⣿⣿⣿⡆⢹⣿⣿⡀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠐⠿⠿⠿⠀⠿⠿⠿⠿⠷⠈⠿⠿⠷⠀⠀⠀⠀⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣴⠟⣿⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠶⠟⠁⠀⣿⡇⠀⠙⢷⠄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⡀⠰⢶⣾⣿⣿⣷⣶⣶⣤⣀⡀⠀⠀⠀⠈⠇⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣠⣶⣿⣿⣿⣷⣦⣌⡙⠻⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⣰⣿⡿⢋⣡⣌⠹⣿⣿⣿⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣷⠄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⣾⣿⣿⡄⠻⠿⢿⣿⣿⡆⢹⣿⣿⣿⣿⣿⣿⠋⣰⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⠸⣿⣿⣿⣿⣷⡄⢹⣿⣿⣤⡙⠛⠿⠿⠟⢃⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣌⡙⠛⠛⠛⣠⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣤⡀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢐⡂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡔⠀⠀⠀⠂⠰⠆⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠀⠀⠀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠠⠎⠀⠈⢀⡀
⠀⠀⠀⠀⢰⣿⣿⣦⣄⡈⠁⣤⣤⠀⠀⠀⡈⠀⠀⣤⠀⠀⠂⠻⠿⠣⢀⣴⣿⠋⢀⡀⡀⠀⠀⠀⠀⠀⠄⠂⡀⠘⠀⠀⠀⢀⠀⠸⠀⠄⠀⠀⠉⠸⡍
⠀⠀⠀⠀⠀⠙⠻⢁⠈⠡⠄⡛⠛⠂⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠧⣀⡙⠛⠿⠃⠀⠀⠀⠸⠂⠚⣬⠁⠀⣁⡀⠀⠀⠰⠁⠀⠠⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⢉⡀⠚⠡⠄⠀⠄⠁⠒⢠⠄⠀⣀⠀⠀⠀⠀⠉⠀⢰⣶⠀⣠⢀⣠⣅⠈⠉⠀⠀⡄⣻⣿⣶⣿⣿⣷⣦⣄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠀⢀⣴⣿⣿⣿⢷⣧⠄⢰⡄⢡⠧⠀⢠⠀⠰⠎⠟⠀⠀⠚⠀⢠⠐⡘⠟⠸⠿⢺⣿⣿⢧⣶⣧⠰⣾⣿⣿⢿⣿⣿⣿⠛⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣶⣿⡆⠈⠛⠚⠆⠀⠉⠀⣀⠐⠀⠀⠃⠀⠭⠀⠀⠀⠙⠀⠀⠤⢹⠇⡈⠛⠋⣸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⠀⠀⠀⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠓⠘⢩⣁⢲⣦⠁⣳⣶⣾⣷⣂⡀⠀⠶⠰⠂⠀⠓⡀⠘⣓⣨⣷⣿⣿⡿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⢋⠡⠄⠘⠊⠉⠉⢁⡄⠙⠛⢋⡁⠛⡇⠀⠀⠀⠀⠀⠀⠑⠆⢿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣀⡀⠤⢤⡄⠀⢠⣶⣿⡟⣀⠀⠀⡀⠀⠀⠀⠀⢀⣠⠈⢿⣿⣿⣿⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⠏⢹⠿⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠶⠈⠁⣰⠚⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠻⠿⠻⣿⣦⠀⠈⠙⠋⣥⠈⡀⠀⠈⠀⢾⡦⠀⠀⠀⢀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠠⠀⠐⠀⢀⠀⠒⠀⠛⠀⠀⡀⠀⠁⠀⠀⠲⠠⣶⠀⠰⣆⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⠀⠀⠠⠌⠀⠀⠀⠉⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠘⠃
⠀⠠⠀⠀⠀⠀⠈⠀⠐⠀⠀⠆⡸⣉⠁⢀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠲⠰⠂⠀⠀⠀⠀⠐⠀⠀⠃⡀⠀⢀⡀⠀⠈⠀⠐⠂⠀⠘
⠀⠀⠉⠀⠀⠀⠀⠀⠀⣶⢦⠞⢹⡏⣶⡆⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠐⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢓⡀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠁⢠⠄⠑⠆⢀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢨⣤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠂⣴⣿⡆⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠁⠈⠀⠒⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠋⠙⠉⠋⠙⠛⠛⠛⠿⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠄⡀⠀⠤⠀⠀⠦⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠶⠂⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢶⠀⡊⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣤⣶⠶⠿⣿⣿⡷⢨⡦⣶⣶⣶⣶⡄⠝⠛⢷⡜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠁⠁⣼⣿⣀⣤⣶⡄⠉⣻⡿⢳⣿⣿⠛⢛⣛⠶⣮⣄⠀⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣴⡀⠉⣏⣹⡟⣂⠉⠻⢯⠀⠈⠉⣿⠿⠻⢟⣦⡈⣿⡄⠠⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠚⣿⣷⡿⠍⢠⠝⠛⠂⢠⠒⢶⡧⢧⣤⣁⣜⠋⠻⠟⠁⠀⣙⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡅⢠⡀⠀⠀⠛⠛⢛⢷⣽⣶⣎⣁⣤⣤⣹⡿⠿⣿⣷⣿⣗⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⡜⢹⣞⠣⠾⣿⣶⡟⠛⠲⢿⣟⣻⣋⣁⡈⠉⠀⢀⠉⠹⠋⢽⣿⡀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠠⣎⠡⠀⣄⠸⡾⡃⣾⡧⠀⠀⠉⠳⣮⢕⠒⠶⣍⣉⣤⣤⣍⡿⠶⣿⠷⠀⣠⣿⡁⠀⣄⠾⣿⢀⡀
⠀⠀⠀⠀⢀⠤⠒⢲⡆⠀⠋⣤⣡⠛⣺⡿⣅⣀⡀⠀⠙⢮⡛⠢⠀⠀⠄⠀⢀⡴⠊⠀⢠⠄⣿⠘⢣⠤⢨⠆⠌⠾⠃⢳⡄
⠀⠀⠀⡔⠀⠀⠘⠁⠈⠀⠘⠀⢈⣷⠟⢧⡉⠿⣎⢳⡿⠀⣙⠳⣶⣶⠶⠋⢁⢀⣠⡾⢃⠀⢿⡄⠺⡖⡙⢄⠀⣴⢦⡌⠂⡓⠠⡀
⠀⢀⡎⠀⠠⠀⠈⢠⠀⠀⠀⠀⠀⡘⣦⡈⠙⠶⢤⣽⣳⣷⣄⣀⢀⠀⣠⣽⡿⠎⠤⠃⣄⣀⡼⠗⣠⣿⣿⣮⠤⡆⠐⢶⣶⠟⠀⠀⠢⡀
⠀⢸⡇⠀⠀⠀⠀⠀⠂⠠⠀⢦⣄⣡⣿⣝⣦⣔⡀⠈⠛⢿⠿⢿⢯⣽⣯⣍⣤⠤⠶⠟⢛⣩⣴⣿⡿⠋⢹⢷⠀⠧⠀⢾⠃⡲⠀⠀⠀⠘⢦
⠀⠀⣧⢠⣦⠀⠀⠀⢷⠟⡃⠼⠟⠉⢄⢌⠙⠯⣿⣧⣤⣉⣟⣿⣶⣶⣄⣺⣅⣤⣾⣿⣿⡽⠟⠋⢀⣀⠘⣌⡠⢀⡀⠀⢘⢡⠆⠀⠀⠀⢘
⠀⠀⠈⢾⡇⠀⠀⠀⠈⣇⡀⠀⠀⠀⠀⠎⡄⠀⠀⠉⠛⠳⠿⢻⡿⢿⣯⠿⠴⠛⠛⠉⠁⠀⢀⠜⡹⢉⠂⡏⠀⣸⣣⣄⣤⠋⠀⠀⠀⠀⢈
⠀⠀⠀⢨⠁⠀⡀⠀⠀⠘⣷⣦⣀⣄⠲⣼⡛⢱⡆⠀⠀⠈⠑⠾⡧⣤⠋⠀⠀⠀⠀⠀⢀⣠⢵⣈⣀⣀⠀⠑⠮⠂⣽⠋⠀⠀⢰⡄⢰⠀⣾
⠀⠀⠀⠀⣄⠀⠘⣄⠀⠀⠈⢾⣽⠉⠀⣉⡀⠈⠸⢤⡤⢄⠀⢀⣀⣼⠃⠀⠀⣠⠄⣴⠛⠉⠐⢟⠁⣹⣷⢔⣶⡟⠋⠀⠀⠀⢘⣷⣾⣴⠃
⠀⠀⠀⠀⠹⡄⠀⠙⠣⢄⠀⡨⣻⣧⣀⣿⣿⣾⣿⣷⣷⡊⢱⢮⣥⣮⢠⣿⣶⣧⣗⡜⣳⣋⣷⠀⠉⣠⡿⠇⡁⠀⠀⠀⠀⠀⢘⠏⣿⠁
⠀⠀⠀⠀⠀⠙⡄⠀⠀⢻⡙⣽⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⣾⣿⣿⣷⣺⣿⣿⣿⣿⣷⣿⣿⣿⣷⣬⣵⣿⡟⡇⠀⠀⠀⠀⠀⢸⠗⡿
⠀⠀⠀⠀⠀⠀⠀⠒⢀⡘⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣺⣟⣼⡿⣿⣿⣯⣻⣿⣮⢿⣿⢋⣿⣿⣻⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣏⢲⣿⣿⣿⠈⣹⣿⣿⣿⡿⣿⣻⣶⣿⣮⡏⡛⣿⣿⣿⣿⣾⣿⣯⣿⣿⡳⣭⣘⢣⣰⣤⣦⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠙⠻⣿⣿⣾⣿⣿⣿⣇⣿⣡⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⠿⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡐⠹⠿⠿⢟⣷⢿⣛⣿⣛⢃⡽⠽⣏⠹⢿⣟⣛⣫⣿⣿⣿⣿⣿⣿⡿⢸⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠒⠉⠀⠀⠀⠀⠈⠛⠁⠀⠘⠷⠦⠶⠶⠒⠒⢶⣥⣤⡤⠴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⠀⢠⡆⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⠀⣸⣿⣿⠇⣼⢀⡟⠀⢀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣿⠀⣇⣿⣿⣾⣿⣸⣧⠔⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣤⣾⣷⣞⡿⣿⣟⣧⣟⣿⣏⡀⢀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠋⣿⣯⣾⡿⠀⠉⣽⣿⢿⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⣿⣿⣿⣷⠦⣤⣾⣿⠸⡄⠀⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⡿⡿⣷⣿⣿⣾⠁⢀⣿⣿⠏⣶⠁⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢿⣿⣿⢃⣇⣿⣿⣼⡇⠀⣸⣿⡿⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠀⠘⣿⣿⣸⣿⣷⣿⡿⠁⢰⣿⣿⡇⠀⣿⢀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠎⠀⠀⢠⠾⣿⡏⣿⢿⣿⣿⠅⣨⡎⠛⣿⣿⠀⣿⡎⠀⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⢠⠞⣰⢏⣿⢧⡾⢿⡉⣾⣿⣷⠈⢿⣿⠀⡿⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣖⠀⠀⠀⠀⣄⠎⣰⣛⣿⣿⡿⠛⣬⣿⣿⣿⣿⠷⣾⣇⢀⣇⠀⠀⣿⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⣿⠀⠀⠀⣻⠏⡼⣩⣿⣿⢸⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣿⣿⡇⠀⢀⠟⢀⣻⣿⠟⣀⣺⠛⣿⣿⣿⡇⢸⡇⠀⠀⠘⢲⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⣿⣿⣷⣠⡎⢀⣾⡿⣉⣶⣿⣿⣶⣿⣾⣿⠁⢘⣷⠀⠀⠀⡏⠀⠀⠀⣿⠁⠀⠀⠀⠀⠠
⠀⠐⠄⠀⠆⠀⠀⠀⠙⠄⣿⢿⣿⣏⣴⣾⣿⣿⣿⣃⣿⣿⣻⡿⣿⡅⢀⡼⠓⠀⠒⠰⢧⣀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠠⠀⣮⠀⣿⠿⣿⣛⡿⢏⣿⣿⣿⣿⣿⣿⣿⣿⢯⡟⠉⠀⠀⠀⠢⠁⠀⠈⠳⣴⣿⠇
⠀⠀⠀⠀⠀⠐⠀⢸⡿⣸⣿⣤⣾⣿⢡⣾⠿⣷⣾⣿⣿⣿⡿⢏⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⣠⡿⡧⠈⢿⣿⣿⣇⣼⣿⠇⠸⣯⠙⠻⢿⡵⠀⣤⠀⠀⠀⠀⠄⠀⠀⣿⣤⣀⣲⣿
⠀⠀⠀⠀⠀⣠⡿⠁⠧⠀⣿⣿⣻⣿⣿⣳⣲⠀⢹⣇⠀⠈⠂⠀⢸⣧⡀⠀⠀⠀⠀⢠⡟⠛⠛⠋⠁
⠀⠀⣠⠄⣰⠟⠀⠀⣿⠀⠉⣿⣿⣿⣿⠛⣫⠀⠸⣿⡄⢠⣷⣄⡀⣿⣿⣶⣦⣤⣤⡞
⠀⠀⠁⡴⠋⠀⠀⠀⣿⢰⡮⢿⣿⣿⡿⣰⣿⠂⢰⣿⣿⠈⣿⢉⣁⡘⢿⠛⠛⠋⠁
⠀⠠⠊⠀⠀⠀⠀⢀⣿⠚⠁⢸⣿⡿⡴⢋⠟⢀⣾⣿⡯⠀⡿⢸⠀⠑⢌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢼⣿⣿⣿⠎⢀⣼⣯⣿⡇⢠⡇⢸⠀⠀⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⣯⣿⠃⢀⡈⠩⠱⣿⣿⠀⡷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⢸⡿⠁⡰⣿⣇⣀⠀⢸⡿⠀⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⡇⡔⠁⢸⣿⣿⡷⠛⠀⠀⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⠋⠀⠀⠀⠀⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⡿⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⢶⣒⠻⣯⡙⠻⣯⡉⠙⢯⡙⢿⠲⡖⢦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣚⠛⠻⠶⣬⣙⠳⠮⣝⡲⢍⡓⠤⣙⠲⣄⠑⢌⠣⡙⠸⠸⠸⢩⢟⡷⢦⣄⡀
⠀⠀⠀⠀⠀⣠⡶⠛⠲⢟⠉⠉⢓⡛⠒⠬⢝⡓⠦⢍⣓⠮⣕⡊⠑⠢⠑⠀⠀⣀⠤⠤⢄⡁⠊⠐⠩⠔⢛⣲⣄
⠀⠀⠀⡴⣛⣟⠋⢀⡤⠮⡃⠀⠺⠀⠐⠃⠀⢹⣷⢶⣮⣍⡒⠨⠁⠀⢀⣠⣴⠁⠀⠀⠀⠙⡄⠀⡴⢯⡭⠵⠒⣛⣦
⠀⢠⣾⣯⣥⣶⣿⣿⣤⡀⡬⠒⣤⡤⠶⣤⠔⠋⠀⢻⣿⠃⠙⠢⢤⣖⡛⠀⣿⣠⠴⠦⣄⣠⣿⡟⠁⣼⡿⢶⣛⣯⠽⠳⡄
⢠⣿⣿⣿⣿⣇⣨⡍⣙⠳⢾⡉⣀⣤⡚⠁⠀⠀⠀⣣⣿⡇⠀⡾⠛⠦⡉⠛⠤⣤⣶⢶⡿⢿⠍⠁⠀⢹⣇⠀⠙⣾⣵⣴⣿
⣾⣿⣿⣿⣿⣞⢿⣿⢿⡿⣶⣌⠛⠿⣿⣷⣤⠀⣼⠟⠁⣠⣾⣵⣤⣰⢃⣀⣠⣬⣽⣯⣄⠁⠀⣀⣤⣿⣷⣴⣿⣿⣻⣿⣿
⣿⣿⣹⣿⢻⣻⣞⣿⣿⣿⣿⣿⣿⠦⢤⣙⠻⢾⣷⣶⣾⣿⣯⣭⡿⣿⣿⣿⣿⣿⣿⠿⠟⣛⣲⣿⣿⢻⣯⢿⣿⣿⣿⣷⣿
⢿⣟⣿⣿⡻⣭⡟⣿⢾⣿⢿⣿⣿⣷⣆⡉⠳⣦⣮⣉⡟⢿⡿⢿⠟⠋⣩⣭⣴⣒⡺⣿⢟⣿⣿⣛⣯⣿⣿⣽⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣼⣿⣿⣿⣿⣦⡌⠙⠫⣽⣿⡀⠙⠶⢦⣤⣉⡭⣩⣭⣽⣯⣷⣿⣛⣯⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⣟⡿⣿⣿⣿⣿⣿⣿⣷⣿⣽⢿⣿⣾⣿⣿⣵⣮⣿⣯⣳⣦⠀⠀⠉⠻⣿⣿⣿⣾⣿⣿⣿⡭⣽⣛⡳⢿⣿⣿⡿⠃
⠀⠀⠀⠻⣿⣷⣿⣻⣿⣿⣿⣿⣿⣻⢿⣶⠭⣒⢭⣻⣿⠿⠛⠉⠀⠀⠀⠀⠐⢸⣿⢿⣿⣿⣷⠾⣿⣛⣻⣯⣭⣭⠟
⠀⠀⠀⠀⠀⠙⠿⣿⣫⢯⣯⣽⣿⡿⣯⣺⣽⠾⠛⠉⠀⠀⠠⠀⠀⠀⠀⠀⢀⣼⣿⣻⠿⢟⣻⡭⢭⣖⣲⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣽⣷⣿⣻⣿⡀⠀⣀⠀⠀⠰⡀⠀⠀⠂⣠⢞⡯⣟⣭⢖⣻⣽⣒⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢭⣤⣾⣏⣈⣀⣀⣼⣿⡿⠾⠿⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣖⡒⠛⠉⠉⠉⠉⠉⠉⠒⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠫⠥⠤⢄⣀⠀⠀⠀⠀⠀⠀⠠⢔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠲⡖⠒⣲⠋⠤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⣑⣂⡀⣸⠃⢰⠃⢀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠲⠦⣄⡀⠀⠀⣀⡤⠖⠋⠉⠁⠀⢙⡇⠀⡿⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⠤⠤⢤⣤⣽⣶⠞⠁⠀⠀⠀⠀⠀⢀⡾⠁⡼⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠒⠶⠶⠦⠤⣤⣄⣀⣀⡈⢳⣄⣀⣀⣛⣺⡧⡦⠀⠀⠀⠀⢀⣴⠟⠀⣸⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⣍⠀⢷⣤⣤⣤⠴⠞⠋⠀⠀⢠⣯⠟⠚⠋⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⣀⠀⡀⢀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠙⠲⠄⠀⠀⠀⠀⠀⠘⣠⠴⠶⠒⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⣉⣈⣡⣤⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢦⠆⠀⠈⠛⠀⢠⣆⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⢻⠀⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢋⡭⣉⠗
⠀⠀⠀⠀⠀⢸⠃⠀⠀⣀⡞⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣲⠤⣀⠀⠀⣀⡤⠞⢉⣠⠽⠂
⠀⡠⠒⠲⢤⣸⢀⡴⣛⠉⠀⠀⠀⠠⣾⣭⣇⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⠤⠼⠾⠟⠛⢉⣡⠴⠚⠙⡇
⣠⢧⣀⠉⣷⠟⠸⢯⣼⠛⣦⣀⡤⠖⢋⡞⢹⣭⠽⡛⠉⠀⠈⠳⣦⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⡇
⠣⣄⣈⣽⠁⢀⣀⣰⠋⠀⡏⠀⠀⣠⠋⠠⠽⢳⡼⠁⠀⠀⠀⠀⠈⠳⠖⠋⠁⠀⠀⢠⠀⠀⠀⣴⠀⣇
⠀⠳⠤⠼⠥⠛⡏⣫⠄⣸⠷⢤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⠀⠀⠀⣇⣀⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠘⢶⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⢤⠾⠤⠀⠴⠗⣠⠏⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢸⠉⡟⠙⠒⠒⠶⣶⠋⡽⠉⡽⠤⠤⠤⢮⡀⠀⠀⠀⣈⡬⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠘⡇⢰⠀⠀⠀⠀⡏⠸⠁⡼⠁⠀⠀⣠⣄⡽⠿⠿⠟⠳⡶⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠷⣾⣦⡄⡀⢰⡷⢦⡀⢳⡀⣀⡠⠷⢶⡄⠀⠀⠀⠀⡿⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡟⠈⠙⠒⠸⣧⢸⣧⠘⡏⣀⣠⠴⣾⠃⢠⣄⡤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣉⣹⣹⣓⣶⡇⠀⠀⠀⠀⢿⣯⣈⢤⣿⡁⠀⠀⠈⠳⡎
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣯⣻⣓⣦⣤⣀⡞⠷⠶⠒⠋⣧⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠈⠙⠋⢽⣺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠋⠁⠀⠀⠑⠂⠄⠀⠐⠖⠠⠀⠀⠀⠀⣠⡤⠀⠀⣠⣶⣶⡤⠖⠋⠀⠀⠠
⣆⣠⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠁⠀⠀⠘⣛⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⠤
⣿⣿⣿⣷⣶⣷⣶⢀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⣠⡶⠚⠃⠀⠀⠀⠀⠀⢀⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣾⣴⣾⣦⡆⣶⢀⠀⣿⡀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣧⣾⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⠟⢿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⢸⡇⣦⣿⣿⣷
⠟⠛⠛⠋⠋⠋⠉⠈⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⠀⠀⣾⡀⠀⢀⡄⢀⢠⣀⡀⣶⢀⣆⣿⣿⣤⣦⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⢰⣿⣧⣆⣼⣧⣿⣾⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⠟⠻⣿⡿⠿⢿⡿⣿⢿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠙⠉⠀⠁⠙⠙⠋⠛⠻⠻⠛
⣿⡿⣿⣿⣿⣿⣧⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⣯⠀⢻⣿⣿⣿⣿⡆⣼⣿⠀⠀⣀⠀⠀⠀⣼⡂⠀⠀⠀⠀⠀⣾⣧
⠃⠀⢺⣿⣿⣿⣿⣿⣿⣿⣗⢠⣿⡀⠀⢠⣿⣧⠀⢠⡄⠀⢰⣿⣿⠆⠀⠀⣄⠀⠀⠀⢠⡄
⠆⠀⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣾⣿⣯⣄⣼⣧⠀⣺⣿⣿⣶⡄⢸⣿⠀⠀⠀⣾⣷
⠀⠀⠈⢻⣿⣿⣿⣿⡟⣿⣿⣿⣿⣷⣼⣿⣿⡿⢻⣿⣿⣬⣿⣿⣿⣿⣥⣿⠿⠇⠀⢸⣿⣿⠂
⠀⠀⠀⢀⣿⣿⣿⡿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⢰⣦⣿⣿⣿⣶⠄⠀⢠⣇
⠀⠀⠐⠶⠿⣿⣿⡃⠀⢐⣿⣿⣿⡏⢹⣿⣟⠀⠐⣺⣿⣿⣿⣿⣿⣿⣿⡃⠀⢒⣿⣿⣿⣿⣿⣆⠀⣾⣿⠄⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠉⣛⡻⠯⠀⠀⠀⢸⣿⣿⠀⠨⣿⠥⠀⠀⠈⣿⣿⡿⢻⣿⣿⡯⠀⠀⠀⢹⣿⣿⣿⣿⣿⣼⣿⣿⣦⠀⣦⠀⢀⣿⡇
⠀⠀⠀⠀⣀⡤⠂⠀⠀⠈⠭⢿⠇⠀⠀⠘⠀⠀⠀⠉⠽⣿⠁⠸⣿⡿⠃⠀⠀⠈⠭⢿⣿⡿⠉⣿⣿⡿⢿⣿⣲⣿⡂⣸⣿⣷⠄⡄⠀⢀
⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠿⠛⠀⠀⠀⠀⠀⠤⣿⠃⠀⢹⣿⠇⠘⣿⢻⣿⣿⡿⢹⣿⣿⣿⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢉⠉⠀⠀⠈⠋⠀⠀⠃⢘⣿⣿⠃⠈⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡄⠀⠀⠶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠟⠋⠁⠀⠀⠀⠀⠉⠛⠏⠈⠉⠉⠙⠛⠿⢿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠙⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡄
⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⠿
⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣦⣤⣤⣄⣼⣷⣦⣄⡀⠀⠀⢠⣶⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⢿⣿⡿⠟⠋⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⠆⣨⢟⡒⠦⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠠⠄⠀⠀⠀⠀⣀⠀⢾⣉⡟⡽⢣⠀⣂⡥⠜⠦⣄⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⢤⡙⡍⠲⠄⡨⡑⢖⠘⠚⠴⢰⣄⡗⡘⢆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠲⢝⠪⢑⡻⢼⣡⢘⢓⠧⡃⡀⣓⠽⣂⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⡤⣐⠅⠁⠩⣜⣹⡀⢕⡢⠤⠄⡤⣆⢠⢁⠚⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⠒⠀⠀⣒⠄⢢⢇⡿⢧⡀⠉⠲⢖⠒⠺⠥⣤⣨⠜⠓⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠄⠀⠀⡻⢔⣫⠞⠀⠀⠩⢦⠡⠈⣑⠩⣃⠞⠁⢢⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠒⢴⡙⣸⠏⠁⡝⠀⠐⢀⠀⡆⣂⡥⠚⠁⠀⠀⠁⠀⠀⠀⠀⠀⠙⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡰⠉⠚⠛⠒⠤⠤⠒⠚⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠤⡀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈
⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠄⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⡐⠠
⠀⠀⠀⠀⠀⠐⣀⠀⢀⠀⠀⢸⣔⠴⠁⠀⠊⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⢀⠀⠀⣼⡄⠴⠁⢀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠑⣘⡄⠀⠸⠰⠂⠃⢸⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣸⠀⠀⠘⠸⠀⠃⢺⡀⢀
⠀⠀⠀⠀⠀⠀⢀⠠⠏⠂⠀⢀⡄⠀⠀⠁⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠉⠀⢀⣠⠀⣂⡀⠁⠡⠆
⠀⠀⠀⠀⠀⢸⣂⢰⣿⣏⠠⢺⣷⠂⡙⠏⠃⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⠶⢻⠀⢸⣿⡗⢩⣿⡟⠁⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⢀⣿⣿⣃⣼⠋⠀⠱⡆⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡹⠀⣸⣿⡁⢊⣿⡇⠀⠀⠀⠀⠀⡀
⠀⠀⣄⠀⠀⠀⠀⢸⣿⣿⠏⣽⡪⠀⠀⡄⢨⠱⡤⠤⠖⠇⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢀⡶⢻⠀⠁⣟⣠⣼⣿⡇⡈⢦⢤⠤⠚⠁
⠀⠀⠈⠷⡤⣤⠞⣻⣿⣟⠢⣸⢙⠀⠀⢧⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠲⡞⢩⠞⠁⠀⠀⠁⠀⠸⣿⡇⠀⠈⠀⠂
⠀⠀⠀⠀⠁⠀⠀⡿⣿⣿⣷⣾⣲⠀⠃⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠐⠓⠀⠀⠀⠀⢹⣝⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⠿⢛⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢠⠊⢀⣀⠈⢿⡋⢳
⠀⠀⠀⠀⠀⠀⠸⣾⣿⠟⠁⣠⠥⢤⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠂⢁⣠⠱⢤⠀⠈⠁⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠊⠀⠀⠀⠈⠂⠀⡘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠉⠀⠀⠀⠀⠓⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢂
⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠂⠀⠀⠀⡀⠤⠐⠂⠁⡠⠌⡃⠛⠢⢀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠈⢢⠂⣔⣈⣀⡉⠀⠢
⠀⠀⠐⠄⡁⠐⢂⡄⠣⠊⠀⠀⠀⠒⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁⠢⢀⠐⠄⠀⠀⠀⠀⠠⠊⠛
⠀⠀⠀⠀⠀⠀⠀⠘⡏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠔⢀⠼⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠊⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠤⠆⠀⠀⠒⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠙⡖⠀⠈⠀⠀⠀⠀⢸⠀⠘⠀⠀⠀⠀⠀⠑⠒⡦⠀⠔⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠐⠀⠈⠉⠉⠉⠉⠉⠁⠀⢸⠀⠰⠄⢀⠀⠀⣀⠀⠠⠇⠀⠐⠂⠀⠐⠠⠄
⠀⠀⠀⠀⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢰⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠀⠁⠐⠂⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠦⠄⠀⠐⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠤⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠄⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡀⢀⡀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠊⠀⠐⠒⠒⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠒⠁