Cold blooded Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣆⡔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢂⣠⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣤⣶⣾⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡟⠛⠻⢷⣄⣠⠤⠶⠂⠀⠀⠀⠀⠉⠻⠿⠿⢟⢿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⣀⣤⣀⠀⢰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣾⣄⣿⠉⠻⢿⣿⣿⣿⣦⣀⣤⣤⣀
⠀⠀⠰⠞⠁⠀⠙⠻⣿⣿⠿⠿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠃⣿⠗⠂
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣴⣶⣶⣿⣿⡷⠂⠀⢠⣿⠿⢿⣿⠀⠀⠁
⠀⠀⠀⠤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠠⢤⣤⣴⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠛⢷⣤⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣥⢄⠀⠀⠀⠀⠀⠀⠈⠉⠁⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠿⠿⠿⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠁⠀⠀⠀⠀⠀⠙⠙⠣⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⢀⣠⣤⣶⣿⣿⣿⣷⣶⣦⣤⣭⣉⣙⣛⣛⣛⣛⣛⣛⣛⡛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠈⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⢿⠋⠁⠀⣀⣻⣿⠉⠉⢉⣉⣽⡿⠋⠁⠀⠙⢻⣷⣦⠀⠀⠀⠉⠉⠉⠉⠉⣉⣉⣉⣉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠁⠉⠋⠉⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⡂⣠⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣦⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠛⠛⠛⢽⣷⡶⠛⠀⢿⣿⣿⣿⡿
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣴⣿⡿⠿⣷⣄⡀
⠀⢸⠀⠀⠀⠀⢠⣠⢀⣾⣿⣿⣿⣿⣿⠿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠈⠙⠻⠷⣦⣄
⠀⠸⣆⠀⠀⠀⢼⣿⣿⣿⣿⣿⡿⠋⠁⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠙⢦⣄⣀⣴⣿⣿⠿⠿⢿⣦⣆⠄
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠋⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣀⡀⠀⠀⢀⣠⣤⣶⣶⢻⡿⣲⡶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⣿⡷⣶⣿⢹⣇⣿⣿⢸⡇⣿⡣⣿⣟⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⠟⠋⠉⠛⢿⣿⣼⣿⣸⣧⢻⣧⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠶⠶⠶⣶⣶⠶⠶⠤⣤⣀⡀⠀⠀⢀⡠⣚⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣻⣿⣯⣶⢞⣛⣛⣛⣛⣛⣛⣛⣛⣳⣶⠾⣿⣶⣿⠾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⠿⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠶⠚⠉⠁⠀⠈⠙⠮⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡦⣀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⡕⢦⣤⣴⡶⣻⣯⣾⢟⣿⣺⡇⣿⣿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⡫⠖⠋⠉⠻⢷⣿⡫⣿⣼⡟⣽⡇⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣾⡷⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠄⠀⠀⠀⠀⠀⠀⠀⠈⠤⢀⣙⠃⠀⢘⣣⣄⠄⠀⠀⠀⠀⠀⠀⠐⠦⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠾⣿⣩⡷⠃⢀⡄⠀⠄⠠⠀⣀⠀⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⠆⠲⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠃⠞⠛⠲⠤⠚⠛⢃⣶⠛⠋⠚⠛⠶⠦⣄⣀
⠀⠀⠀⠀⠀⠰⠎⡀⠀⡾⣿⢤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡠⠈⠀⠀⠀⠀⠀⠘⠦⠤⢤⣄⠀⠀⠀⠀⠀⠈⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠸⡷⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⠈⢀⠀⡀⠞⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣛⣷⠀⢴⠎⠣
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠚⠒⠀⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⢤⡄⠀⠀⠀⠀⠀⠀⠀⣈⠢⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣠⣶⣡⡤⣴⠂⠀⠉⢀⣀⣰⣻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣶⠏⠙⢶⡿⠿⣿⣻⡚⠉⠉⠀⠀⠀⠙⠛⢋⣫⡛⢲⣤⣄⣀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡀⠀⠀⢸⡵⠛⠁⠀⠀⠀⠁⣀⠀⠀⠉⠁⠀⠀⠀⢀⢀⠔⠁⠈⠑⠈⠀⠀⠉⠑⠂⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡮
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⣡⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠰⣏⡡⠞⠀⠀⠀⠁⠀⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐
⠀⠀⠀⠀⠀⠈⠳⠉⠤⠒⣰⣠⣤⣐⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠃⣰⠦⢿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⢀⣁⣀⠨⠁⠁
⠀⠀⠀⠀⠀⡖⠀⣛⢳⣿⡽⣦⠞⣾⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠇⢠⠀⠥⣤⠤⠖
⠀⠀⠀⠀⠀⡅⠀⠔⢦⠿⢶⡟⠤⢌⡁⠀⠀⠀⠀⠀⠀⣄⡄⢀⠀⠀⢸⡧⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢺⠗⠉⠀⠠⢧⠀⢀
⠀⠀⠀⠀⠀⢷⠀⠀⢚⡯⠀⠝⡄⡀⠀⠀⠀⠀⠀⡄⠀⣡⡽⠁⠀⠀⣼⠣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠅⠨⠹
⠀⠀⠀⠀⠀⠀⢢⠀⠈⠀⠙⠂⡀⡀⡉⠓⡤⢤⣴⣮⡹⣅⠀⣀⣠⢾⡿⢃⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠂⠀⢤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⣄⡀⠀⠒⠐⣯⡏⠹⠃⢠⣿⡟⠳⠿⠯⠉⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣟⣐⢾⢧⡀⢀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡄⠈⠁⡂⡀⠀⢉⣀⣤⣤⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠹⣯⠾⡀⠈⠦⠑⣡⠄⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠷⠷⠚⢛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠂⠀⠀⠘⣆⠡⠀⠀⠀⠁⠀⠀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠛⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⢦⡳⡀⠀⠀⢀⣔⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡅⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⠀⠨⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠉⠙⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⡿⠿⠿⠿⠟⠛⠋⢻⣿⣿⣿⣿⣿⣿⠁
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⡆⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠉⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣄
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⣀⣀⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠤⣔⣢⣦⣠⣾⣿⣦⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⠋⠁
⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠙⠛⠛⠛⠛⠉⠙⠻⠿⠿⢅
⠀⠀⠀⣠⣾⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠙⢿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣈⡤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢥⣤⣀⣄⡀⠀⠀⢀⠀⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠙⠉⠉⠉⠉⢡⣝⠿⠿⠁⠀⠠⣦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⡸⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡜⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣯⡀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣄⣀⣤⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢡⣿⣿⣿⡏⠙⠉⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠁⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠂⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠈⣿⡏⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢰⣿⠃⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣶⣁⡀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⢿⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⠛⠋⠀⠀⠀⠀⠈⠛⠿⠷⠀⠀⠀⠈⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣟⣝⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⠀⠄⢀⠀⠀⠠⠀⠀⠀⣀⢠⡀
⠀⠀⠀⠰⡟⠛⣟⡹⠿⠿⣷⣒⣶⣶⣶⣦⣤⣤⣅⣂⠑⠂⢠⢿⠼⠊⡟⡠⠂⠸⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠙⠒⠆⣁⠈⠰⠘⢇⣿⡶⣷⣮⣿⣷⣿⣿⡿⣷⣬⣴⡢⢾⣴⣆⠘⠲⢤⡀⠐⡂⡈⡄⡤⠀⠈
⠀⠀⠀⠀⣠⣤⣤⣤⣘⣶⡄⢾⡟⢳⣾⢓⡛⠿⣷⣿⣷⠿⣿⣿⣿⣾⣥⣺⣷⣦⣤⣈⠣⣄⢳⣃⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡉⠋⠟⠛⢃⢘⣇⣀⣈⠉⠙⢻⢫⣿⢦⡽⡿⢿⣿⣿⣿⣷⣿⣿⣷⣮⠊⢙⠃⣀⡎
⠀⠀⠀⠐⢤⡀⠀⠊⠉⠹⠊⠙⠻⠛⡿⠿⣿⣿⣶⣤⣀⠉⠛⢻⣷⡶⠿⡿⠼⣿⣿⣿⣿⣿⣷⣿⠐⡿
⠀⠀⢉⣍⣸⣇⡀⠠⠄⠒⠒⠶⠤⠤⣤⠊⠛⢎⠻⠿⣿⣷⣶⣤⣿⣸⣾⡏⠀⢇⢻⣿⣦⣿⣽⣿⣶⡇⠤
⠀⠀⠈⠨⠧⠿⢷⣶⡒⣤⣀⣴⣅⠘⣤⠱⢴⣬⠀⡀⠮⣍⡖⠩⣍⣩⣤⣷⣤⣀⠀⠸⣛⣿⠉⡙⠻⠤
⠀⠀⠀⠀⠐⠂⠀⠃⢋⡙⡟⣰⣾⣳⡒⢔⡀⠫⡑⡘⣦⠘⠎⠳⢋⢫⠉⢛⣿⡿⣿⣆⠈⠿⣷⠉
⠀⠀⠀⠀⠀⠀⠒⠒⠀⠌⠛⢥⣙⡺⣄⣰⡽⣆⠹⡳⣘⠡⡀⢀⢌⠈⠐⠄⠀⢻⠌⢻⣷⠘⡿⣧⡀⡦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡌⠂⠃⠹⠫⠍⣇⠑⠚⢉⠉⠹⣻⠛⣂⣤⠀⠃⠠⠀⠈⠈⡇⢸⣿⡟⠈⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠂⠐⠁⣀⣀⠁⢊⣉⢨⢆⠨⠌⣀⣀⢀⣀⣐⡡⢾⣻⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠂⠀⠀⠈⣉⣎⠁⣾⠟⠛⠚⠛⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⣿⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠶⣶⣶⣿⣿⠿⢷⣶⣶⣶⣤⣤⣉⡁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⡄⠙⣿⣿⣿⣤⡀⠹⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⢸⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢛⢻⣿⣿⣿⠀⢹⣿⣿⠛⠁⣰⣿⣿⣍⡉⠻⣿⣿⣿⣿⣿⣷⡀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⣾⣿⣿⣿⠀⣸⣿⣿⣷⣿⣿⣿⣿⡿⠟⠀⣿⣿⣿⣿⣿⡿⢁⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡿⠃⣠⣿⠙⢿⣿⣿⣿⣿⣿⣦⣴⣾⣿⡿⠟⠋⠁⠀⢸⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠾⠿⠿⠦⠈⠻⣿⣿⣿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⡟⢁⣠⣿⣿⣿⠏⢀⣼⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠁⣴⣿⣿⣿⣿⣿⡿⠛⢻⣿⣿⡆⠘⠿⣿⣿⡟⠀⣾⣿⣿⡿⠿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⠘⣿⣿⣿⣿⣿⣿⠀⢾⣿⣿⣿⣿⣶⣶⣿⣿⡇⠀⣿⣿⣿⣧⣡⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡇⠈⠙⠻⢿⣿⣿⣦⣄⣨⣿⣿⣿⣿⣿⣿⠛⣿⡀⠹⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⡿⠃⣠⣿⣿⣦⠾⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⡤⡄⠀⠀⣀⣀⢀⣀⣀⣀⣀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠸⠟⠻⡿⠛⢿⡛⠛⠙⣿⠿⠿⠃⠘⠒⠀⠐⠙⠆⠋⢻⢽⣯⠟⠙⠛⠨⢿⣿⣛
⠀⠀⠀⠀⠀⠀⢸⡃⠀⠘⡅⠒⠁⠀⠀⠘⡧⡀⡆⠑⠀⣔⡄⠐⢠⢾⣴⠟⠁⠀⣀⠀⠀⠐⢻⣟
⠀⠀⠀⠀⠀⠀⠸⡇⡀⠀⠈⠀⠀⠀⠀⠀⢘⣤⣷⣶⣶⣶⣶⢶⣯⡜⠁⠀⢀⠀⠁⠀⠠⠋⢉⣯
⠀⠀⠀⠀⠀⠀⠈⢁⠤⠘⢇⠀⠡⠀⢠⣶⣿⣿⡛⣿⣿⣿⣯⣿⣿⣿⣷⣄⣀⠠⢐⡟⡠⠾⡥⠌⠄⠖⣲⠶⠀⡀
⠀⠀⠀⠀⠄⠿⠖⠂⠴⡀⠈⠉⠀⢰⣿⣷⣿⣿⣿⡿⠛⠛⠻⣿⡟⢿⣿⡟⣧⢀⣾⢄⠃⠑⠰⠐⠚⢉⠁⣀⡴⢇
⠀⠀⢀⠀⠐⠂⠀⠀⠀⠁⢀⢄⡀⠈⣿⣿⠿⠻⣿⠁⠀⠀⠀⢹⣷⣿⣿⡿⢋⡲⠁⣢⠐⢀⡞⠗⠹⠆⠁
⠀⠙⠂⠀⠈⠈⠂⠘⠤⠀⠀⠈⠥⠀⠈⢿⣶⣾⠇⡦⢰⣄⣴⣿⣿⣽⠟⢡⠡⠀⣚⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠘⣎⡄⡌⣯⣼⠀⠀⠛⢟⡻⢯⣽⡟⣠⠏⢀⡼⠂⢘⠃⠀⠀⠂⢀⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠈⠳⡄⠹⠴⢷⡨⠿⠁⠀⠀⠈⠁⠀⠟⢺⡞⠁⣸⣇⠀⣼⢁⣠⣶⣛⠃
⠀⠀⠀⠀⠀⠀⠀⣫⠗⠉⢠⠘⢩⠁⣊⣴⡁⠠⠀⠀⠀⠀⠀⠀⢸⠀⠃⢠⠗⢘⡆⢽⡆⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣹⣄⠄⠞⢧⢘⡋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡊⢀⣮⡑⢿⣿⣦⠀⣯
⠀⠀⠀⠀⠀⠀⠀⣸⣯⠹⡾⠋⠁⢗⠈⠣⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⣇⣀⡁⠀⠣⣼⢻⣿⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠄⢀⠸⠋⢁⣼⠛⠀⠀⠀⠀⠀⠀⠀⠠⣼⡇⠞⠋⡟⠛⣄⠀⠘⢾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠦⠄⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⡤⠂⡠⠂⠀⠀⣯⡅
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠠⠀⠀⠀⠈⠄⠈⠀⠀⣤⣴⣶⡾⡀⠀⡁⢠⠊⠈⡡⠂⠀⢨⣷⡀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢊⠁⡀⠸⣮⣺⣭⣵⣦⣭⣿⣥⣤⣷⢶⣿⢳⣤⠚⣿⣼⣟⣿⠻⣿⣿⡅
⠀⠀⠀⠀⠀⢰⣿⣿⢿⣧⣷⣾⣿⣿⣿⡿⠿⣿⣿⣿⡿⠟⠛⠷⣿⣿⣟⣛⣿⣿⣿⣿⣿⣉⣬⢞⣅
⠀⠀⠀⠀⢠⣶⣬⣷⣺⣿⣿⣿⣿⣿⣯⡀⠀⠀⢙⡏⠀⠀⠀⢀⠜⠉⠉⣹⣿⣿⣿⣿⣿⣿⣷⣿⠺⠟
⠀⠀⠀⠀⢈⣿⣿⣿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣾⣿⣿⣿⠟⠻⠿⠿⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠙⠛⠛⠛⠛⡛⣛⠛⡛⢛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠄⠀⠠⠄⠀⠠⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣛⣖⢭⣍⢓⠀⠐⣲⣼⡖⢂⡀⠀⢀⡀⢉⣁⡀⠆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡵⣽⣿⣿⣛⡷⣦⣄⠒⢭⣽⣯⡿⣟⣻⡖⢂⢀⣾⣿⣿⣦⠲⠉⠁⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠞⡾⣻⢿⣿⣯⣿⣵⣿⣿⢶⣿⣿⣿⣿⣿⡿⣦⣾⣿⣦⣿⣿⠀⠁⠀⠀⡀⠳⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠛⣏⡙⣩⣯⣟⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⣿⢿⣽⣽⣿⣿⣿⣿⣿⣠⣀⣤⡾⢿⢶⡏⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⣼⣷⣿⣿⣿⣾⣿⣿⣻⣿⣿⣿⣿⣿⣟⣿⣉⢠⣟⠻⣿⣷⣿⣫⡭⣽⣿⣿⣶⡶⣽⡷⢸⠊⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⡄⠈⠿⠅⣾⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⡿⠋⠉⠁⠀⠈⠉⠉⠛⠳⢽⣿⠻⣿⣿⣷⣿⣿⣿⡿⠇⠰⠸⠎⡳
⠀⠀⠀⠀⣀⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡛⣿⠿⢻⣿⣿⣦⣷⣶⣶⣃⡟
⠀⠀⢰⣿⠿⣿⣟⣿⣿⣛⣿⡿⠿⠟⣿⣿⣟⣵⡛⠿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣁⣿⣿⣿⣿⣿⣷⣝⣿⢀⠇
⠀⠀⠀⢿⡻⢿⣍⢉⠛⡛⣟⡻⢍⡿⠟⢁⣈⣍⣁⣌⣉⡉⠷⠾⣟⢿⣿⣿⣿⣿⣿⡏⢽⡟⣟⢫⡲⠒⠶⢤⣄⡀⠀⠈⢫⣿⣿⣿⣿⣿⣿⡿⠇⠀⠸
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠁⠀⠀⠀⠈⠛⠭⠙⠋⢽⣿⣷⣦⡀⢴⣮⣝⣿⣿⣿⣿⣆⢩⢄⣦⣶⢿⣻⣿⠅⠻⢷⣤⡈⢗⡠⠠⡝⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢄⢺⣿⣿⡿⣿⣆⠉⠸⣿⣿⣿⣿⣿⣄⣿⣿⣿⣯⢳⣿⠳⠀⠚⢻⣿⡆⣤⣶⣿⣿⣏⢋⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⠟⠳⡿⠟⣿⡀⢷⢹⣯⣿⣿⣿⣿⣟⣷⣿⢿⣿⠏⣥⣦⣼⣿⣿⡇⠹⣿⣿⣿⡿⣠⣄⡶⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⢁⠐⣘⣇⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃⢂⣿⢿⣿⣿⣿⡇⠄⠈⡉⣻⠛⡉⠉
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣻⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠘⠿⠠⣿⠙⣟⣹⣿⣷⣿⣯⠙⠮⠧⣿⣿⡽⣻⣿⡿⢰⣿⠿⣿⣿⣦⣄⡀⠀⠰
⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⢛⣫⣽⣿⣟⣿⣿⣟⣿⣷⢠⡀⠀⠀⠀⠀⠈⢰⣿⣿⣿⣿⣿⣿⣦⡁⠄⠽⢿⣾⣿⡿⢁⡜⢻⣴⣿⡇⠀⢉⣷
⠀⠀⢀⣼⣿⠧⠼⠿⣿⣏⣽⡿⠬⣝⠎⣻⣟⢿⣿⣿⣿⣻⣿⠛⣦⡀⠀⠀⠀⣘⠻⠿⠿⠟⣻⣿⣿⣿⣆⠐⠰⡽⠟⢡⣤⣤⣄⡾⠋⠻⠷⠋⠁⠀⠂
⠀⢀⡿⣿⣗⣚⢞⢞⡻⠛⠿⣙⡳⢌⣻⡛⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣦⡀⠀⢩⡄⣧⢠⣾⣫⣿⣿⣿⡟⣲⣾⣷⣦⣻⣯⣿⡟⢧⣄⠀⠀⠀⢠⠂
⢀⡾⠓⢉⣿⣇⠠⡤⡜⠉⡒⢾⠛⠀⠂⡉⣍⢏⣛⣻⣿⣽⣿⣿⣿⣿⣿⣿⣆⡀⠁⣧⡈⣻⣵⣿⡿⠋⢳⣿⣿⣿⣿⠗⢻⣯⠀⠠⢹⡃⠀⣀⠊
⢸⠗⠟⣛⢩⡜⠾⡶⠀⠀⠀⠀⠀⠀⠀⠉⠏⠀⠀⠚⠿⢭⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣅⣊⡅⠀⠀⢹⣯⣙⣧⣿⡇⠀⠙⠿⠛⢉⡐⠀⠀⠈
⠾⠀⠘⠄⠀⠂⠀⠀⠀⠀⠀⢀⠔⠑⠘⠲⣆⡰⠀⠀⠀⠋⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣝⡻⢲⣥⣮⣉⡛⠛⠛⠀⡀⣀⡄⠔⠋⠡⢷⡆
⡗⠺⠄⠀⠀⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠙⢶⡼⠿⡆⠀⢨⣩⡭⢷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⠙⠙⣗⡋⠉⢳⣍⢀⠀⠘⠛⠛⠁
⠳⠪⢤⠀⠛⠀⠀⠀⠀⠀⠉⠧⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⢀⢈⠋⠁⠈⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡾⣿⣗⣁⢻⣧⠂
⢠⠝⠀⡀⠀⡀⠀⠀⠀⠀⠀⠂⣷⣄⡀⠀⠀⠀⠀⠀⠀⠙⢷⣎⢢⣄⣀⠙⢂⣭⢿⢿⢯⣛⣿⣿⣿⣻⣿⡡⠈⡉⢻⣧⣼⡟⠂
⠀⢠⠂⠁⠄⠀⠀⠀⠀⠰⠒⠁⠤⠉⠟⠷⠶⣤⣤⣤⣠⣤⣤⣼⣿⣿⣿⣤⡀⠄⠂⠛⠛⠹⠭⠿⠿⠿⠋⠐⠊⠄⠁⠈⠀⠀⠀⠠⠀⠈⠀⢠
⠀⠀⠶⠃⠀⠖⠀⠀⢀⡆⣠⣤⣴⣶⣤⠖⢶⡦⢴⣾⠤⢤⣄⣈⡁⠈⠙⠻⣿⣶⣷⣤⣤⡠⣀⠀⠀⢀⣀⠀⠀⠀⠀⢤⡄⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠐⠀⠀⠀⢸⢀⣧⣿⣾⣷⣿⣿⣤⣿⣧⣸⡇⢰⡆⢀⡈⠙⠛⠢⣄⣀⣈⢙⡛⡿⠿⡿⣷⣾⠿⠶⠶⠒⠚⠯⢤⣀⠠⠂⠐⠀⠀⠀⠀⠂
⠀⠀⠀⠲⠀⣠⢼⡞⢏⣹⣉⡧⠷⠿⠛⠛⠛⠿⠿⢿⣾⣧⣴⣯⣀⣄⠀⠀⠉⠙⠻⢏⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣿⠞
⠀⢤⠀⣄⠾⠉⢣⠰⠚⠙⠢⠄⠀⣀⣀⢀⠄⠠⣀⣠⣀⣉⡻⠿⢿⣧⣼⡃⣤⠀⠀⠀⠈⠛⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁
⢀⢠⠒⢈⣵⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠉⠛⢿⣤⣟⠀⡄⠀⠀⠀⠈⠙⠷⠶⠦⠦⠶⠚⠋⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠤⠦⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠟⠟⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⠿⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠈⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣦⡀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⠤⠤⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠐
⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠢⠘⠖⠧⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠌⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⠀⣀
⠀⠀⠀⠀⠠⠀⠀⠈⠪⢔⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⠘⠦⠔
⠀⠀⠋⠀⠀⠀⠀⠀⠀⣀⣝⣛⣒⡲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠈
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠒⠉⠉⠉⠙⠀⠀⠀⠀⠂⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠤⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠩⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⡠⠔⠂⠈
⠀⠀⠀⠀⠀⠀⠀⡘⠹⠀⠀⠀⠘⠇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠁⠀⠀⡰⠁⠀⠀⣀⠀⠀⢀⡄⠒⢒⠲⢄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⠀⢀⡜⠀⠀⠀⠀⣷⠀⠘⠀⢧⣨⣸⣠⠌⠂
⠀⠀⠀⣄⠀⠀⠘⠠⢠⠃⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠹⣗⠒⠒⠄⠐⠂⡸⠁⠀⠀⠀⢄⠀⢸⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⡏⠀⠀⠃⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⢀⠌⠀⠀⠀⠀⠀⠈⠢⡽
⠀⠀⠰⠁⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠁⠀⠀⠀⠀⠄⠐⠄⠀⠀⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢘⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⠌⠀⠀⠰⠀⠀⢆⠀⠀⢀⣀⠠⠑⠀⠀⠀⠒⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠂⠀⠀⠀⠀⡀⢀⠀⢠⠋⠀⠀⢠⠃⠀⠀⠀⠃⠀⠪⣀⠀⠀⠀⠀⠀⠀⠁⠰⠆⠀⡀⠀⠀⠀⠀⠀⠚⢙⣿⠈⣿⠓⢦⠤
⠀⠀⠀⠀⡀⠀⠀⠈⢪⠄⡈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠢⠤⠤⠷⠐⠒⠁⠀⠀⠀⠀⣤⠄⠀⠐⢺⡅⢾⡁⠸⣀⡀
⠀⠀⠀⠀⠀⠂⠄⢀⠄⡈⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣽⢄⡿⠀⡼⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⠂⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠴⠟⠬⠛⢁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⢻⡋⡹⠉⠉⠛⠟⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠝⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠑⠚⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠈⣧⠀⠀⠒⠂⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⡠⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧
⠀⠀⠀⠀⠀⢻⣤⠤⢄⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⡄
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⡀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠹⣆⠀⢀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣧⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣀⠀⢠⠤⢄⠀⠈⠙⢶⣄⠀⠀⠀⢻⡄⠈⠂⠀⢳⠀⠀⠀⠀⠀⠀⠀⠹⣆⣀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠉⠛⠺⢦⣔⠀⠀⠐⠤⠘⢷⡄⠀⠘⣧⡠⢄⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠹⣆⡠⠙⢦⡀
⠀⠀⠀⠀⣠⡴⠛⠉⠉⡉⠙⠳⢦⡀⠀⠈⠳⣄⠀⠀⠀⠈⣿⡄⠀⢹⡆⠀⠃⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢻⣄
⠀⠀⠀⣰⠋⠢⠀⠀⠈⠁⠀⠀⠀⠙⠷⣤⣠⡿⠀⠀⢀⠀⣹⡇⠀⠀⢿⡀⠨⡈⡂⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠘⣧
⠀⠀⢠⡏⠁⠈⠀⠀⡤⠶⢤⣀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢢⣿⠇⠀⠀⠘⣧⠀⠈⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣷⠔⠦⡘⣇
⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠁⣿
⠀⠀⠀⢻⠈⠠⠂⠈⠧⢤⡀⠀⠀⠈⠛⠷⣦⣴⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⢄⠀⠙⣦⡀⠀⠀⠀⢀⣠⠏⠀⠀⢠⡇
⠀⠀⠀⢸⠀⠠⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⡹⠛⠒⠚⠋⠁⠀⢊⣨⠟
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠒⠂⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠹⣄⣶⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠶⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁
⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⣰⣿
⠀⠀⠀⢹⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠴⠶⠶⡖⣞⣿⣶⣶⣦⣄
⠀⠀⠀⠀⠻⣿⣿⣟⢿⢟⡻⢛⣛⣛⣿⣽⣥⣷⣶⣿⠿⠿⠿⠿⠿⠿⢿⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠛⣛⣛⣋⣭⣭⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠛⢉⣉⣁⣍⣉⡉⡙⡛⠛⠻⠿⠿⠛⠛⢉⣼⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣴⣾⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⢷⠿⢧⣼⠿⠿⠛⠁
⠀⠀⠀⠀⠀⢠⣿⢣⣶⡿⠋
⠀⠀⠀⠀⠀⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⢿⣿⡜⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣟⣋⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⡽⣷⡀
⠀⠀⠀⠀⠀⠘⢿⣷⡌⠻⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⠿⠛⣋⣴⡼⣛⡿⠟⠛⠉⠉⠉⠁⠈⠉⠻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡾⡄⠉⠛⠿⠿⣶⣶⣶⣶⠿⠿⠟⢋⣩⣤⣜⣿⡭⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⣯⣄⢂⠀⠀⠀⠀⡀⣀⣀⣠⡴⠿⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⢉⣦⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣒⣒⣬⣭⣴⣶⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⡝⡿⢿⣿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢿⡯⣵⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠖⠒⠒⠒⠒⠒⠲⠤⣄⡀⠀⠀⠀⠀⠀⢜⠉⣳⠀⠀⣀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⣈⣳⣄⣀⠀⠀⠈⠉⠁⠀⠐⣅⢀⡕⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡤⠤⠒⠒⠋⠉⠉⠉⠉⠉⠈⠉⣉⣉⠉⠓⠲⢦⣄⡀⠀⠀⠰⡁⢈
⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⡁⠬⠥⣀⠀⠀⠈⠙⢦⡀⠀⠈⠉
⡇⠀⠈⠉⠒⢤⡀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣀⠀⠀⠙⡄⠀⠀⠀⢻⣆
⡏⠉⠉⠀⠀⠀⢙⡶⠋⠀⠀⠀⢀⡤⠶⠲⠦⢄⠀⠀⠀⢀⣀⡀⠀⠀⡇⠀⢸⣻⡗⠀⠀⢸⠀⠀⠀⠀⢻⡄
⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢡⣴⠥⠀⠀⠘⣄⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⢸⡇
⡗⠒⠒⠀⠀⠀⠀⣤⡀⠀⠀⠈⠳⠤⣤⣠⡤⠤⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⢸⡇
⡗⠒⠂⠀⠀⢀⠴⠋⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⣇⣀⡤⠴⠚⠁⠀⠀⠀⠀⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡙⡿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣤⣀⡀⠀⠀⠀⠀⠉⠘⠛⠛⠓⠒⠒⣢⡤⠶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠛⠛⠛⠒⠲⠦⣤⡤⠤⠤⠔⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣁⣀⣀⣀⣀⣤⠤⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠍⠀⠀⠀⠀⢤⠂⢀⠤⠤⠤⠄⠔
⠀⠀⠀⢤⢒⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠠⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠄⠀⠀⠀⠐⢀⣀⠀⠀⠁⠀⠀⠀⠤⠤⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠉⠀⠀⠀⠀⠰⠀⠀⠈
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⠄⠒
⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠉⠀⠣⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠉⠐⠂⠀⡀
⡀⠐⡂⡐⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠈⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢤⠂⠀⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠀⠀⠀⠀⠉⠀⠂⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⠀⠀⠀⠀⢈⣠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠒⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠈⠀⢀⣀⡄⠐⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠠⠀⢀⡠⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠠⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⢠⠈⠀⠁⠃⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢴⠠⣄⡉⠁⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡠⠀⠀⠑⠠⠂⠐⠀⠀⠀⠀⢀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⢰⣿⣿⣿⣷⣝⢿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣥⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠸⣿⣿⣿⣿⡿⣱⣮⣝⣛⣛⡛⣫⣭⣶⣿⡿⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⣩⣭⢩⣵⣾⣿⣿⣿⣿⣿⣿⣶⣭⢉⣭⡁⠀⠨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢸⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣾⡀⠀⠘⣿⣇⠾⠇⠿⠇⠿⢆⣿⡟⠀⠀⠀⠀⢠⡀⢰⡆⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠂⠈⣿⡀⠀⠘⠿⣿⣿⣿⣿⣿⡿⠟⠀⠀⣀⠀⣷⠈⠻⣾⡷⠋⢀⡿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡦⠈⠛⠇⠀⠀⢠⣭⣭⣭⣥⠀⠀⠀⠀⣉⣻⣿⣇⡀⢸⡇⢀⣼⣷⣟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀⢴⣾⣿⣿⣿⣿⣷⡄⣠⢈⣉⠉⠀⠈⣹⣿⣿⣋⠁⠈⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣦⣙⠿⣿⣿⠟⣡⣾⣿⡦⢉⣻⣿⡟⠉⢸⡇⠙⢻⣿⣏⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣧⣫⡅⡿⠀⣠⣾⣷⣄⠈⣷⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠦⠘⠁⢸⡇⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡛⣟⣚⠻⠿⣶⢦⣄⣶⣤⣤⣀⠠⣤⣄⣠⣤⣶⣦⡽⠿⠹⠿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡾⣿⣿⣿⣿⡷⣬⣫⡝⣽⣯⣵⣹⡓⠈⣉⡼⢯⡙⢷⢤⡀⠀⠀⠀⠈⠉⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠾⠿⣹⢳⣯⣿⣿⣿⣿⣿⣿⣿⣝⣹⠿⣟⣭⣍⣿⣧⣵⡈⢩⡯⡿⢮⣯⠽⢖⣒⡒⠠⣄
⠀⠀⢀⣠⣤⣔⡲⠞⡿⣿⣻⡧⠾⠿⠿⠾⠵⠿⠛⠛⠉⡁⠙⠻⣦⣬⡴⢏⣽⣿⣦⣙⣾⣦⣙⣂⣹⢶⡯⢽⣽⡆⢧⣿⡄
⠀⣔⣏⣭⡿⠟⣛⣾⣗⢻⣧⣀⠀⠀⠀⠀⠀⠠⣸⣿⣯⣽⡏⠓⣢⣌⠉⠁⠉⠉⣉⣥⣤⢬⣿⣯⣍⣀⣿⣦⣈⣿⣲⡴⣺
⠘⡘⠪⠾⠧⠛⠛⠚⠻⣷⢠⣌⢳⡄⠀⠀⡀⠀⠀⣹⢭⣽⣿⡿⢾⣫⣷⣤⣶⢟⡽⣟⣒⣶⣩⡿⣷⣿⣌⡻⢿⣾⣟⣘⡟
⠀⠈⠁⠒⠀⠁⠀⠀⠈⠒⣾⣙⣧⣻⢆⠀⠈⠚⢩⣴⣩⢟⠱⢦⡥⠉⢋⣿⣿⡿⠚⠉⠨⣿⣼⡁⡏⡋⠉⠙⠓⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢅⣷⠉⣜⡷⠦⠄⣈⣉⣉⣤⣶⣿⠀⠀⢸⣠⣏⡀⣀⡀⢴⣋⡺⠏⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣿⡉⣷⢻⣸⡿⠿⢿⣿⣿⠀⠀⠈⣌⣹⣧⠜⣃⣒⢫⣗⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠋⠛⠿⠓⠚⠙⠉⠲⠄⣀⡈⠁⠻⠟⣋⣼⡯⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣀⢀⣠⡾⢿⣷⣄⠀⠀⢀⣠⣄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣤⣤⣾⠏⣿⠙⢿⣿⠏⠀⢸⢸⢿⣷⣿⢿⡏⢹⡆
⠀⠀⣰⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣿⢳⠈⠻⣿⣿⠀⠊⠀⢸⡿⠀⠀⠇⢸⢸⣿⡏⡸⠀⣾⠁
⠀⢰⡏⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⡿⠉⠉⢻⣿⠀⢀⣀⣻⣿⣀⣀⣀⣸⣇⣀⠀⠀⠀⢸⣿⠀⠁⢰⡟
⠀⢸⣷⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⣿⣄⣤⣴⣶⠿⠿⠟⠛⡟⠛⠛⠛⠛⠛⣟⠛⢿⠿⠷⣾⣧⣄⣀⣿⠁
⠀⣿⠻⢧⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣧⣴⡾⠟⠛⣉⠁⢸⡂⠀⠀⡈⠱⠀⡀⠀⣀⠸⠄⠋⠀⠀⡰⠋⠉⠉⠛⠿⣷⣤⣀
⠀⢻⣟⠦⣁⠀⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⠟⠋⢁⡦⠀⠀⠁⣯⠈⠀⠊⣸⠅⡄⠈⢰⡅⠧⠀⡄⣰⠀⢡⠃⠀⢒⣛⣛⣓⠢⠉⠛⢷⣦⡀
⠀⢸⡿⠿⣦⣅⡀⠀⠙⠳⣄⡀⠀⣠⣴⡿⢿⠩⠂⠛⢰⠂⡇⠴⠰⡏⠷⢸⡁⠖⢸⡁⡀⢾⠩⠆⢠⡀⡀⢼⠀⡾⣠⠞⢉⣥⣤⣭⠙⢦⡀⠀⠉⢿⡄
⠀⢻⣶⠦⢤⣄⣉⡁⠀⠀⠈⢹⡿⢛⢁⡄⠀⢀⡄⠖⠈⢉⡇⣠⠨⠆⣤⠸⠂⡤⠹⠂⠁⠽⠀⡤⢈⠀⠉⢠⠎⢰⠇⢰⣿⣿⣿⣧⣀⡀⢳⠀⠀⠘⣇
⠀⠀⢹⣿⣶⣶⣤⡤⠤⠀⠀⢸⣿⣾⡩⡂⢪⠨⡂⠀⢼⠂⡏⢝⠀⠀⣼⢢⡄⠗⠀⡄⢀⢰⡁⡀⢺⡁⢳⠃⠀⢹⡄⠸⣿⣿⣿⣿⣿⠇⣸⠀⠀⠀⣿
⠀⢠⣾⡛⠉⠉⣀⣠⠔⢀⡴⠋⠈⠻⢿⣷⣵⣘⠅⡖⢸⠍⠇⣪⢠⠆⡯⠸⠂⣠⣨⡇⡪⣨⠆⠉⡸⢢⡾⠀⠀⢈⢷⣄⠉⠛⠛⠛⢁⣴⠏⠀⠀⠀⣿
⠀⢸⣷⣶⡾⠟⢋⣠⠖⠋⠀⠀⠀⠀⠀⠙⠻⣿⣶⣯⢼⡂⡤⢜⠀⣡⣷⠶⠚⠉⠀⠙⢆⢺⠠⡃⣮⠀⡇⠀⠀⠘⢦⡙⠻⠶⠶⠾⢛⡵⠀⠀⢠⣤⠿
⣠⣾⣛⣭⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣶⡿⠟⠋⡀⠀⠀⠀⠀⠀⢸⢄⢸⠇⠗⣸⣿⠀⠀⠀⠀⠙⠶⠶⠶⠖⠋⠀⢲⡞⠋⠁⣠
⠻⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣡⣴⠔⠉⡀⠀⠀⠀⠀⢀⡞⠈⠐⣣⢀⡏⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢋⡕⣡⠎⣠⠊⡀⠀⢀⣾⣇⢼⠀⡏⢸⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣿⣾⢁⠜⢁⡞⠀⠀⣼⠿⠿⣿⣿⣿⣿⣶⣾⣷⡀⠀⠀⣀⣀⣤⣶⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣴⡟⢀⠂⣼⡟⠀⠀⠀⠀⠈⠉⠉⠉⠙⢿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢀⠆⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃

⠀⠀⢀⡽⢛⣽⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣠⢀⣟⣴⣷⠆⠂
⠀⠀⠈⣵⣟⡇⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠃⠀⠀⠀⠀⠀⣀⣴⣾⠖⠀⠀⠋⠀⠀⠀⠜⢡⡢⢟⣿⠒⠋⠀⠀⠀⠠⠄
⠀⠀⠀⠐⣷⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⣀⣄⣠⣂⡘⢁⣠⠞⠁⢠⡄
⠀⣄⠀⠐⢉⡿⣿⣷⣄⣤⣄⣠⢄⠞⠋⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠠⢾⠟⠁⠀⢠⣇⠀⠀⠛⣿⢫⣉⠴⢶⠞⠁⠀⠀⠀⠁⠠⣦
⠀⠈⠀⠀⠀⠰⣻⣿⣫⠟⣿⣧⣼⣤⣀⡄⠀⢠⢀⡀⡤⡒⢂⠒⠀⠀⠁⠈⡠⢀⣦⣄⣑⡀⣀⣰⣵⣊⡛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠂
⠀⠀⠀⠀⠈⠀⠀⠌⠴⠚⣉⣔⣿⡿⣠⡐⠛⣌⢿⣿⣇⡇⡘⠦⢠⣶⣶⡈⢫⡾⣟⣭⢿⣿⡿⠛⣹⣶⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣠⠀⠀⠀⠀⢀⡀⠀⠀⠈⠙⠛⠉⢡⠈⠳⠛⢠⡿⡿⠇⠝⠩⢏⣄⠦⠾⣯⣡⣟⡫⠷⠚⠋⢀⣦⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡌⣠⠔⠊⢀⠐⠁⢤⡃⡴⣼⠋⠀⠀⠀⠚⠉⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣼⠂⡝⡡⠋⠻⠽⠹⡒⢄⠈⢤⣿⠀⠀⠀⠂⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠐⠋⢀⡄⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢠⡄⠸⠇⠠⠃⠃⢨⠀⢸⡍⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠘⢀⠀⡑⢮⠀⡀⠑⡞⠁⣻⠔⠁
⠀⠀⠀⠀⠛⢄⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⣄⢧⠰⠶⠖⠶⢀⡎⠀⠼⡅⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣈⡧⠷⣃⡄⡗⠁⣀⠌⣄⠈⢮⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠚⠣⡜⣶⣂⠀⠀⠜⢢⠀⡶⠉⠀⠘⠛⠀⠀⠀⠀⠀⠀⡠⠾⠋⠉⠂⠙⠀⡇⢰⠋⡠⠅⣶⠋
⠈⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠃⡄⠁⠈⣻⡀⠓⣶⣼⣹⠀⠄⠀⠠⠠⡇⠀⠀⠀⠀⠄⠀⠀⠄⠀⡀⠀⠀⠀⣀⣀⢤⡤⢅⡦⣴⠀⠀⠰⠬⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⣶⣿⣷⠀⢈⠋⢻⠛⠲⠃⠀⣑⢠⡶⢤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢣⣭⢀⠃⠀⠀⠀⢀
⠀⠀⠀⠉⠀⠀⠀⠀⣀⣤⡤⠀⠀⠀⠀⠀⠑⢪⠀⣀⡀⢀⠦⠊⠉⠉⠋⠉⠀⠀⠀⠀⢤⣄⣀⣀⣀⠀⠀⠀⠀⣤⣀⣘⣿⢀⠀⠀⠤⠀⠈⠁
⠀⠀⢀⣀⠀⠀⠀⠘⠋⠉⠉⠀⢰⣂⡀⠉⠀⠀⠄⠽⠥⠬⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⣺⣿⡿⠇⠀⠀⠠⠄⠀⠙⠛⠓⣺⣿⣿⠹⠤⠛⠒
⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠄⠈⠁⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠈⠛⠀⠈⠉⠁⠐⠉
⠀⠀⠀⠀⠀⠐⣀⠐⠂⠀⠀⠀⢀⡢⠀⠀⠀⠀⠀⠀⠑⠂⠀⠁⠀⠈⠉⠉⠁⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣄⣀⡀⠀⠀⠀⠢
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠚⢯⠧⠤⠄
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣦⣵⣶⣤⣾⣵⣿⣽⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠠
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣄⡀⠀⠀⠀⠀⠈⠃⠘⠂⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠛⠁⠀⠉⢡⡀⢧⠀⢲⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠄⠀⠀⠀⠀⠀⠳⣌⠳⠜⢰⠁⠤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⡌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠃
⠀⠀⠀⠀⠀⠐⠁⠴⠆⠠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⠀⣄⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡄⠀⠰⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠐⠀⠀⠰⠧
⠀⠀⢠⠞⣀⠐⡀⠀⠀⠀⠀⡀⠁⡈⢢⠀⠀⠀⠁⠈⠀⠀⠀⠄⣀⣀⣀⡠⠀⠀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠉⠉⠉⠩⠉⠀⠉⠉⠉⠉⠉⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⡇⠀⠐⠒⠀⠀⠠⠀⡁⠀⠀⠀⠀⠀⡀⢀⣀⣀⠀⠀⢀⣈⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⡇⠀⢀⢀⠀⣀⣀⠀⡅⠀⠀⠀⠠⠎⢁⠀⠠⠀⠀⠀⠐⠐⠨⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠈⠇⢀⡀⢐⡀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⡇⠀⠀⠀⠀⠘⠂⠀⡆⠀⠀⠀⠀⢃⠈⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠤⠄⡇⠀⠠⠤⠀⣠⡄⠀⡁⠀⠀⠀⠐⠀⠓⢄⡀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢀⠉⠉⠀⠀⠀⢀⣀⡀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⠀⡅⠀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠛⠒⠋⣀⠈⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠐⠀⠀⠇⠀⠐⠀⠀⠤⠆⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡰⠊⠁⠅⡃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⡀⠀⢀⣀⠀⢀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢻⠀⡆⠀⠣⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡃⠀⠀⠀⠀⠉⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢡⡁⠠⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠃⠀⠀⠀⠅⠀⠀⠀⠀⠒⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠠⠤⠄⠇⠀⠠⠤⠀⣠⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠈⠉⠁⡁⠀⠈⠉⠀⠛⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⣃⡀⢀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣽⡇⠀⠀⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠘⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣿⡇⠀⠐⠀⠀⠒⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⣷⣤⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⠿⠻⡿⠛⠿⠿⠿⢻⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸
⠀⠀⠀⠀⡆⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡠⠀⡠⠄⠀⢀⣠⠀⠀⡀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸
⠀⠀⠀⠀⠈⠂⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣋⣤⣤⣤⣦⣤⣤⣦⣡⣤⡈⠩⠙⠓⠀⠂⠀⠀⠀⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢸⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠦⢀⣛⡠⠀⠀⠀⠀⠹⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠔⠉⠉⢢⡀⠀⠀⠀⠀⢀⡠⠊⠁⠈⠀⠀⠀⠀⠀⠐⠇⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠂⠠⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠐⡀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⠀⠐⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠈⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣀⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⢀⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠤⡁⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠇⠀⠀⠛⠀⠀⠀⠀⠁⠀⠘⠁⠀⣀⡤⠞⠁⠀⠉⠃⠀⠀⠀⠀⠈⠐⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠄⠒⠉⠋⠠⠘⠀⠀⠈⠉⠛⠛⠶⣦⣄⠀⠀⠀⠉⠒⠒⠒⠊⠁⠰⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢄⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⡸⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⣀⣤⣀⣀⣀⣀⣀⣀⠀⣀⡀⠀⠀⠀⠈⠉⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⢦⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⣀⠀⠀⢣⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⢸⣿⢛
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠀⣀⢀⡀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡄⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠓⠦⢀⡀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⠃⠀⠀⠘⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣦⠤⣀⠀⠠⡥⠾⢟⣉⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠈⠩⠤⠴⡩⠽⠛⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢸⡿⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠂⠀⠁⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠴⠶⢒⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⢗⡴⠏⠠⠀⠡⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢋⡴⠋⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣿⣿⠟⣩⡥⢚⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣼⣿⢃⣾⠟⣠⠋⠀⠀⠀⠀⣀⣀⢠⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⣿⣿⣧⣿⠏⢲⠇⠀⠠⣄⣴⣿⣿⣿⡿⡋⠁⠑⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠷⠈⣹⣿⣿⡏⢀⣹⠀⠀⠀⠐⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⠁⢲⣿⣦⡀⠀⠠⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⣿⣿⠟⠟⠃⠁⠀⠹⣿⣿⡗⠀⠀⠈⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⡀⢠⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠿⣭⣶⢆⣤⠓⠀⠀⠈⠂⢽⣻⠃⠀⠀⡘⣿⣿⣿⣿⣆⣦⣄⠠⢸⠀⣰⢞⣿⣃⠈⠐⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣶⣾⣿⣾⣿⠁⠀⠀⠀⠀⠀⢹⡇⣠⠎⢠⣿⣿⣿⣿⣿⣿⣿⡦⠊⡇⢠⠬⣿⢹⠦⡀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠝⣩⣼⡆⠀⠀⠀⠀⠀⠀⣿⠁⢠⣿⣿⣿⣿⠃⣿⣿⣿⣷⡛⢢⠠⠄⢼⢹⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣧⠀⠀⠀⠀⠀⣴⡿⠀⢸⣿⣿⣿⡇⠈⠀⣿⣿⣿⣟⡸⠀⠀⣸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣷⣤⠀⠀⠀⣸⡃⠀⠀⠻⣿⡿⣷⣄⠀⣹⣿⣿⡏⠀⠀⠀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠙⠛⠛⠻⠿⢧⠤⠴⠋⠐⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣧⡈⡱⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠛⣩⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣏⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣱⣿⣟⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠋⢸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋⠀⠀⣴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠃⠀⠀⣼⡟⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠀⠀⠠⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠀⢠⢀⡔⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡶⠷⣤⣴⡦⢉⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠓⣬⣛⣭⡿⢿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣏⣷⣤⣠⡙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⡏⡯⠘⣿⣿⠂⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣻⡙⡄⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣝⣦⡄⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⡳⣆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡜⢦⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠘⡅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡭⠼⠀⣀⣤⣂⢀⡀
⠀⠀⠀⠀⠤⠔⣒⣶⠖⣒⣤⢤⣀⡀⠀⠀⠀⢀⡴⣡⠁⣼⣗⣿⡯⣯⡷⣦⣀
⠀⠀⠐⢀⠠⢡⠬⠐⢥⡺⣏⢛⢇⣏⣋⠻⠿⣻⠿⢥⣾⠿⣟⢻⣯⣒⡾⢂⡹⠀⠀⠀⣀⣰⠛⠉⠉
⠀⠀⠀⠈⡰⠎⠼⡶⣶⣿⣬⣏⣳⣦⣵⣜⢇⡪⠠⢁⡐⡻⢝⣯⣿⡻⠫⠷⣿⣶⣶⠷⠛⠁
⠀⠀⠀⠀⠐⠄⢙⢛⣻⣿⣿⣿⠿⠿⠛⠛⠛⠛⠯⠼⠧⠭⠎⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠂⠀⠀⣠⣤⣶⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⣿⢇⡴⣊⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⣀⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⣞⡵⣚⡥⢒⡠⠀⠀⠀⠀⠀⠀⣰⣿⢏⣼⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣵⣦⡅⠀⠀⠀⠀⣰⣿⣿⣿⠟⣋⣴⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⢿⠿⠿⡿⡿⣿⣿⣿⣿⣿⠿⠿⠷⠒⠀⣠⣾⣿⣟⣭⣶⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠯⡁⠈⠀⠠⠰⣄⢄⢆⣯⣻⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡯⠭⠤⣖
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣕⣍⣤⣤⣴⣾⣾⣶⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡤⠶⠦⠤⣤⣀
⠀⠀⠀⠀⣠⣿⡟⢉⣙⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣷⡶⠤⠤⣀⡀
⠀⠀⠀⢰⣿⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣾⣇⠀⠀⢻⣿⣿⣿⠏⠐⠀⠈⢿⣿⣿⣿⣿⣿⠷⣶⣤⣤⣤⣀⣀⣠⣤⣤⣴⣶⠖⠃
⠀⠀⠰⣿⣿⣿⢿⣿⡷⠿⢫⣿⠟⣿⣿⣿⢧⡀⠀⠈⣿⠟⠁⠀⠀⠀⠀⠈⣿⢿⣷⣝⠻⣗⣦⣉⢙⣻⡿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠙⠩⣀⠀⠀⠀⠀⠡⢚⣽⣟⠻⠿⠦⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠘⣎⠻⣿⣷⣤⡙⠺⣗⢮⡛⠿⣶⣶⣶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣏⡛⠋⠙⣶⣶⣶⣶⣖⣛⠉⠀⠀⠀⠀⠀⠀⠈⢷⣈⠻⣿⣛⢦⣀⠙⠪⡓⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⢦⠀⠘⣿⣿⣿⣿⣗⡂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣬⡙⠳⢭⡳⢦⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠈⠻⢟⡻⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠍

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⢿⣷⣿⣾⣷⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢤⡟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⡿⠋⠉⠉⠉⠛⢿⣿⡿⣦⠀⠀⠀⠀⠀⠀⢀⣾⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣻⣮⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⢐⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡉⣹⢦⣀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠈⠛⢿⣿⣍⡳⣦⣀⠀⠀⠀⠻⣿⡿⣿⣶⣿⣿⠟
⠀⠀⠀⠀⠀⣴⣻⠟⠛⠛⠿⣿⣷⣄⠀⠀⠀⠈⠛⠷⣧⣿⡓⣦⡀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⢨⢿⡏⠀⠀⠀⠀⠘⢿⢻⣆⠀⠀⠀⠀⠀⠈⠙⢷⣿⣟⣦
⠀⠀⠀⠀⠀⢾⣳⣀⠀⠀⠀⠀⠘⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⢻⡿⢽⣇
⠀⠀⠀⠀⠀⠈⠙⢽⣶⣤⡀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣷⡞⠛
⠀⠀⠀⠀⢤⣄⠀⠀⠉⠻⢿⣶⡄⠀⠹⡿⣷⡄⠀⠀⠀⠀⣠⣾⣿⣯⠅
⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠹⣿⡄⠀⠹⣟⣛⢶⢶⣶⢾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⢀⣿⠁⠀⠀⠀⠙⠚⠮⠼⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⢀⡰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣢⠄⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⡠⠊⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡔⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣣⣀⢁⡀⡰⢀⣮⠀⢀⣈⠀⠀⠀⠀⠙⢂⣀⠀⠀⠀⠀⠀⠀⢀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠾⠛⠻⢿⣿⠟⠛⡳⣿⣿⣶⣾⣅⣀⠄⢂⡀⠀⠀⠀⠁⠄⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢺⡻⣥⣎⠀⠀⠈⠠⠘⣀⠴⠚⠞⢝⠱⠄⡩⠍⠻⡟⣀⣀⣀⣠⠄⠀⠀⠀⢀⡾⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⢀⣀⡀⠀⠀⢰⣿⣅⠾⠿⣫⡖⠀⢀⠄⢉⠀⠐⠂⠈⠒⠱⣔⠒⠀⢈⢋⠈⢝⡯⠉⠀⠀⠀⣠⣟⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖
⠀⠀⠀⠀⠩⠁⠀⣠⣴⣿⣟⣮⣧⡼⠃⠀⣾⣾⡢⠀⠳⠁⠁⠀⠀⠘⢈⡀⢀⠀⢠⠑⢀⠄⠀⠙⣶⣾⣿⣾⣟⡡⠂⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⢰⣶⠆⠀⣠⠾⠿⣾⠿⣍⠉⠛⠻⠗⠶⠋⠍⡓⠀⠀⢀⡦⡀⡱⠄⡈⢖⠡⡾⡁⠀⠄⠀⠀⠘⠛⡀⢿⣿⣿⣁⠀⠀⠀⠀⠀⡤⠚⠁
⢀⡜⠁⠠⢊⡔⢊⠛⢢⡙⡗⠀⠁⣳⠆⠀⢘⠈⠈⠀⢤⠜⠉⠼⠈⡇⢑⢪⠽⠇⣀⠀⠠⠀⠰⠀⢆⢢⣿⣿⣋⠁⠀⠀⠀⠀⢸⡁
⡞⢶⡀⠀⢸⠰⣿⡅⢀⡇⠀⠂⠉⠁⠀⠀⢀⡠⠀⠀⠀⠀⢘⢣⠃⡐⡂⢠⠃⠀⡀⢠⣥⠶⠴⣤⣤⣿⣿⣛⠁⠀⠀⠀⠀⠀⠈⢣⡀
⢣⠈⢷⡁⠈⠳⠦⠴⠛⠀⠀⠀⠀⠀⠀⠀⠸⠁⡄⢠⠀⠐⠈⢱⡄⠪⢶⡗⠨⢛⣼⠻⡄⠂⢀⠙⣿⣿⣿⠹⢧⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠑⢀⡀⠀⠑⠒⠒⠉⠀⠀⠀⠀⠀⣠⠆⣠⡦⠇⠀⠀⡖⠋⢘⠰⣻⣷⣾⣾⣿⠇⠀⠑⢀⠀⠀⣿⣿⡏⠑⠀⠁⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠙⠤⣠⠰⠂⠠⠀⠀⠒⠐⠁⠀⢰⣿⡇⠧⡀⠒⠢⠙⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠁⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠈⠙⠣⢀⣀⣠⣴⣬⣥⣐⢿⣿⣷⣀⣁⣀⣀⣰⡟⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣰⢿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡟⢷⢿⣿⣿⣿⣿⣗⢿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠒⠀⢀⡟⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠈⢲⣿⠿⠿⠿⠿⠿⣿⠻⢧⣀⠀⠀⠀⠀⠊⠀⠀⢸⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠉⠛⢶⣄⡀⠀⠀⠈⠁⠈⠀⠉⠁⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠌⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠡⠀⠀⠀⡀⢽⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⡐⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠣⡀⠀⠀⢐⠀⠈⠙⠒⠤⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢛⣿⠿⠛⠛⠛⠛⠿⢿⣛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣠⣤⠀⠀⢀⣤⡄⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠉⢀⣶⣌⡙⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡀⠈⠛⠛⠿⠷⠄⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠉⠐⠃⠘⠀⠁⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣬⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⠿⠂⠀⠀⠀⠀⠀⠀⠐⠻⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⣤⡴⠆
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠛⠳⠶⣤⣀⡀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⣀⣠⣤⡴⠶⠚⠛⠻⢧⣤⣀⡀
⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠷⢤⣄⣀⠀⠀⣠⣶⣶⡄⠀⠀⢠⠶⢿⡛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠉⠀⠀⠻⣿⣿⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡶⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠿⣿⡿⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣤⣤⣤⣤⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣽⣯⣍⣍⣍⣛⠛⠟⢻⠟⣛⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣟⣻⣿⣿⣿⣽⣿⣿⢿⣿⣿⣷⣶⣬⣉⠺⢿⣿⣿⠟
⠀⠀⠀⠀⢤⡀⠀⠀⢘⣿⣿⣿⣿⣯⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⠿⣄
⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣾⣿⣿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣿⣿⡷⠉⠉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⡙⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠂⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⣆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠁⠀⠈⣀⠀⠀⠀⡜⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣆⠀⢰⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠁⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡶⠮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡿⠀⠀⠀⡁⠀⣴⠁
⠀⠠⠄⠒⠒⠲⢶⣦⣤⣤⣀⣀⡀⠀⢀⣀⣠⣤⠶⠟⠛⠃⠀⠈⠀⠀⠀⠙⠿⠛⢻⣿⣿⣿⣿⣿⣷⣄⡀⠀⠁⣠⠊⠀⠀⠀⠀⠀⠂
⠀⠄⠀⠒⠒⠶⢬⣭⣉⣉⣩⣿⣿⣿⣿⣿⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⣿⢿⣿⠿⠃⡩⣟⣶⣾⣅⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠀⠀⠀⠀⠀⢀⣼⠁⠀⢸⣀⣠⢰⣴⣿⣿⣿⣿⣿⣿⠷⢶⣴⠋
⠀⠀⠀⢦⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣾⣿⣿⣿⡛⠉⠀⠀⠀⢬⣅⡀⠀⠀⠠⣤⠤⠤⠀⠀⠀⠤
⠀⠀⠒⣛⡛⠿⠘⠛⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣿⣿⣿⣿⣿⣭⣭⣿⣷⡊⠀⢀⣰⡿⠿⠆⠀⠀⠀⠀⠤⠶⠤
⠀⠀⢀⠈⠿⠓⠀⠀⠀⠀⠰⣾⣷⣄⠐⠚⠄⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠒⠒⠀⠀⢰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠒⠀⠒⠒⣒⡛⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠋⠉⠀⠀⠀⢀⡵⠢⠤⠴⠀⠈⢭⡐⠒⠀⠉⠀⠀⠸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠁⠀⠀⠑⠲⠶⠴⠷
⠀⠀⠀⣴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠾⢧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀
⠀⠀⠀⠘⠆⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣏⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠢⡀⠈⠙⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣁⣒⣒⣒⡂⠤⠤⠤⠤⠤⠴⠾⠃⠀⠐⠲⠶⠖⠒⠚⠁⠀⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⣧⡀⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⢀⣼⠸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣏⠙⣄⠀⠀⠀⠀⠀⢟⣆⠀⠀⠹⣾⣷⠏⠀⠀⣰⡿⠀⠀⠀⠀⠀⣠⠋⣹⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣦⠤⡀⠀⠀⠘⡜⣆⠀⠀⢸⡇⠀⠀⣰⢣⠃⠀⠀⢀⠤⣴⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡻⡮⣝⢒⡳⢷⡘⣕⢦⣸⣇⡤⣪⢇⡾⢖⡒⣪⢵⢟⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢳⢙⠮⣣⣀⠤⢧⢹⠓⢼⡧⠚⡏⡼⠤⣀⣜⠵⡋⡎⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢷⣒⠦⢼⣎⠀⡜⠛⢄⠀⢣⣧⣸⣇⣼⡼⠀⡠⠛⢣⠀⣱⡧⠤⣒⡾⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⢬⣍⣓⠤⣄⠻⡦⣿⡜⢣⣿⢴⠟⣠⠤⣚⣩⡵⡲⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣳⣦⣀⣀⣈⣳⣙⣄⣉⣻⣛⠿⢮⡷⢾⡵⠿⣛⣟⣉⣠⣋⣞⣁⣀⣀⣴⣞⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡽⠟⠉⠉⢉⡽⣩⠋⣉⣽⣭⣷⢞⡷⢾⡳⣾⣭⣯⣉⠙⢍⢯⡉⠉⠉⠻⢯⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠮⢞⣋⡭⠒⠋⣴⠗⣿⢣⡞⣿⠺⣦⠙⠒⢭⣙⡳⠵⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⡾⠭⠒⣺⢏⠀⢣⣤⠊⠀⡜⡟⢹⡏⢻⢳⠀⠑⣤⡜⠀⡹⣗⠒⠭⢷⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡼⢨⢖⡝⠉⠒⡞⣸⡤⢺⡗⢤⣃⢳⠒⠉⢫⡲⣅⢧⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣵⢗⣫⠬⡵⡾⢡⡩⠞⢹⡏⠓⢝⡌⢷⠮⠥⣝⡺⣮⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠟⠒⠁⠀⠀⢰⢣⠏⠀⠀⢸⡇⠀⠀⠹⡜⡄⠀⠀⠈⠒⠻⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣏⣠⠋⠀⠀⠀⠀⠀⣾⠏⠀⠀⣰⢿⡿⣆⠀⠀⠹⣷⠀⠀⠀⠀⠀⠙⣄⣹⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⡿⠁⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⢿⠆⠀⠀⠀⠀⠀⠈⢿⢰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⣀⣀⠤⠦⠄⢀⠀⡀
⠀⠀⢠⠙⠀⠄⡐⢏⡡⠀⠀⠀⠈⠀⠁⠐⠀⡀
⠀⠀⠀⠉⠐⠂⠠⠀⠄⠚⠙⠚⠶⢆⡀⠀⠀⠀⠃⡀⠀⠀⠀⡀⠄⠂⠀⠒⠀⠰⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡄⠀⠄⠘⠀⡠⠊⠀⠀⠐⠀⠀⠠⠀⠀⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠀⠀⠁⡖⠀⠀⢀⡴⠊⠉⠈⠙⢣⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈⠄⣸⡅⠀⠀⠌⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⢀⠀⠌⢸⠤⠀⠀⠃⠀⠀⠀⠀⠀⡼⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⠀⡀⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠬⠁⠀⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠂⠁⢀⠀⠀⠀⠀⠈⡠⠀⠀⠈⠀⣠⠋⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠈⠀⠀⠀⠀⠀⠀⡵⠀⠐⠀⡴⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠄⠀⠀⠑⠤⠀⡤⠚⠅⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠲⠴⠐⠒⠉⠀⠀⠀⠣⣀⠀⠀⠁⠂⠠⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⠒⠦⠤⠤⣄⣀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⣀⣠⠔⠁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠉⠃⠀⠀⠁

⣿⡏⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠈⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⡄⠀⠀⠈⠀⠀⢁⣀⠀⠄⠀⠈⣱⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⣶⡇⠀⠀⠀⠀⢫⡁⢀⣴⣾⣿⣿⣿⣶⣦⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠻⣿⣿⠀⠀⠀⠀⠀⠑⢾⣿⣿⣿⣿⣿⣿⣿⠛⠆⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏⠀⣿⡟⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣧⣀⡄⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⡟⠁⠀⠀⠀⠀⠀⠀⢸⡇⢘⣿⣿⣷⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠠⠘⣿⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⢹⣿⡏⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣸⣿⣇⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⡄⠂⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⢿⣿⣿⡅⢸⡇⠀⠀⠀⠀⠀⠀⢀⣼⠉⢻⢿
⠀⠀⠀⠀⠀⠀⠀⠘⡗⠘⠉⢻⣿⣿⣯⣿⣿⣿⣾⡇⠀⠀⠀⠀⠀⠀⣼⣿⠀⣸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠠⣤⣿⣿⣿⣿⣿⣿⣿⡷⢄⠀⠀⠀⠀⠀⣿⣿⣦⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⡿⠟⠁⢈⣣⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢏⡀⠀⠐⠀⠉⢁⠀⠀⡀⠀⠀⠘⢻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠝⡀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠈⣁⢠⢤⣄⠉⠉⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⠁⠨⡰⠤⠄⡄⠿⠔⠊⠁⢀⣠⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⠀⡢⠋⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠑⠀⠂⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡒⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠠⠑⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠐⡠⠅
⠀⠀⠀⠀⢀⣠⠤⡖⢒⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡠⠀⢩
⠀⠀⠀⣴⡋⠐⡨⠋⠉⠈⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣆⠊⠁⠀⡇
⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠷⡄⠀⠀⠀⠀⠀⠀⡇⠀⡒⢌⠁
⠀⠀⡗⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠃⠀⠀⠀⠀⠀⢘⠁⠁⠄⠲
⠀⠀⢯⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠣⡑⠈⢠⠃
⠀⠀⠐⡎⠡⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠡⡑⠀⡤⠁
⠀⠀⠀⠈⢠⠂⠄⠊⠟⠒⠦⠠⠤⠤⠔⢒⠲⠉⠀⡀⠄⠂⢠⠝
⠀⠀⠀⠀⠀⠙⠠⣀⡀⠄⠄⠀⠀⠈⠠⠐⢀⠀⠁⣄⡥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠚⠐⠠⠆⠦⠐⠒⠒⠉

⣿⡯⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣭⣿⡀
⠀⠀⠀⡘⠛⠻⠿⣿⣿⣤⣾⣽⣿⢏⣤⠖⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠂⠀⠀⠀⠨⣿⣿⣿⣆
⠀⠀⠀⠙⠻⠷⣦⣶⢟⣿⠿⠛⠋⠉⠀⠀⠀⠀⠠⢉⣍⣁⡒⠛⣀⣘⣂⡀⠀⠀⠀⠀⠀⠘⢼⡿⣿⣧⡀
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⠀⠀⠒⠄⠀⠐⠶⠤⠀⠀⣀⠒⠚⠂⠀⠬⠉⢛⣀⠀⠀⠀⢈⡖⣫⣎
⠀⠀⠀⢠⡞⠉⠀⠀⢽⣿⣿⣿⣷⡄⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢇
⠀⠀⠀⠘⡂⠀⠀⡀⠛⠋⠙⠋⣉⣇⠀⠀⠀⠀⠀⠀⢄⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢴⣾⢿⣆
⠀⠀⠀⠸⣿⣧⣴⣶⣷⣶⣿⣿⡿⠷⠀⢀⣀⣀⡀⢬⠐⢌⠀⢅⠠⣍⠑⢌⠁⣤⠳⠀⠀⣀⣀⠀⠀⠀⢹⠛
⠀⠀⠀⠀⠙⠯⣶⣦⣾⣿⣽⠿⠋⠀⠀⠀⠀⠀⠐⠂⠐⠄⠀⠀⠀⢀⡀⠀⠀⠈⠀⠬⠀⠋⠁⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⢠⣆⠻⢷⣆⡈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠐⠒⠒⠦⠀⠀⠀⠀⠠⡴⠖⢒⡂⠤
⠀⠀⠀⠘⣿⣦⡈⠻⢿⣦⣄⡄⠉⠲⢤⡀⠀⠀⢀⣾⠟⠁⠠⣄⡠⠾⢷⣷⡄⠀⠀⠀⢸⡇⠀⠈⢻⣿⣶⠄
⠀⠀⠀⠀⠘⢿⣿⣦⣄⠉⠛⠿⣿⣷⣈⣻⠀⠀⠼⣿⣄⣀⡄⢈⣦⠀⠀⣽⡆⠀⠀⠀⠀⢻⡄⠀⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣶⣶⣬⣿⠛⠀⠀⠘⢮⣏⣩⠄⠸⢋⣠⡼⠋⠀⠀⠀⠀⠀⠐⠧⢈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⠶⢞⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⢿⣶⣤⠀⠀⠀⠀⠀⠀⣴⣾⡿⢛⣺⣟⡿⢏⢻⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠈⠄⠙⢷⣄⡀⠀⣠⣼⢏⠥⠲⣙⡜⢣⡼⠋⣥⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠌⠀⠾⣥⠐⢄⡀⠀⠹⠛⢛⢋⣱⣧⣷⣷⣿⣏⣯⢀⣠⢶⠚⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣀⠈⡉⠂⣵⣦⣦⣤⡤⢇⣑⠷⣥⣞⡻⣿⠻⣿⣇⡜⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣦⡄⠐⣻⡉⢟⠓⠛⠊⠉⠉⠙⠲⣭⣲⣿⣿⠇⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡖⣽⠒⠁⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠘⠆
⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣠⣴⣿⣰⣋⡤⠦⡥⡀
⠀⣰⡾⠟⠋⡉⠉⢉⣍⣉⠉⠍⠝⢛⠿⢋⠀⠀⠀⠀⢠⠈⠑⢄
⣼⣟⠀⠁⠀⠈⠨⠚⠎⡛⠻⢭⠜⠃⠀⠀⢃⠀⠀⠀⢸⠀⢀⠀⡷
⣿⡇⠀⢠⠀⠲⠠⠋⠁⢠⠘⠉⡄⠀⠀⠀⠀⣀⢤⠂⠲⠴⣆⡀⢀⠅
⣿⣇⠂⠈⠣⣐⡀⠉⠍⠀⠂⠀⡇⢀⣴⣶⣾⡶⠷⣦⡐⠀⠀⣗⡁⠄
⠸⣷⣄⠄⠀⠀⠀⠉⠐⠒⢒⣪⣽⠿⠛⠉⠀⠀⠀⢸⡷⠠⠀⢸⠄⠆
⠀⠈⠻⢿⣶⣶⣶⡶⠾⠞⣛⣉⣀⠀⢀⣀⣀⣠⣴⠿⠁⠌⠄⣚⡹
⠀⠀⠀⠀⠀⢀⣴⡶⢟⠛⠻⠛⠻⠛⠻⠩⠩⠑⠀⠈⠀⠈⣸⠟⠁
⠀⠀⠀⠀⢠⡿⠋⠀⢀⣠⣤⣤⣤⣤⣀⣀⣀⣀⣀⢀⡠⠔⠁
⠀⠀⠀⠀⠸⣯⠀⢠⠁⠈⠳⠛⠚⢙⠉⡉⠙⠿⢿⢧⡀
⠀⠀⠀⠀⠀⠹⢷⣄⣢⣴⣁⣤⠴⠖⢶⣄⢊⣀⢨⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣠⠴⣞⢫⡁⣲⣦⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠂⠌⡑⠹⠿⣿⣿⡿⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⣉⠥⠉⢖⡏⠽⠛⠛⡇⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣛⢷⣦⣴⣶⡶⢖⣁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡟⠉⠉⠉⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣶⡶⠟⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠤⠤⠤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠐⢂⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢓⡆
⠀⠀⠀⠀⠀⢶⣶⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⢤⣤⣄⣀⠀⠀⠀⠀⢀⣨⡥⠞⠁
⠀⠀⠀⠀⠀⠸⣷⠞⠉⠛⠭⢭⣩⡭⠟⠛⠉⠀⠀⠀⠀⠀⠇⠒⠂⠈⠙⠻⡿⠾⣋⠁
⠀⠀⠀⠀⠀⠀⠉⣶⡦⢤⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠶⡏
⠀⠀⠀⠀⠀⠀⠀⠈⣷⢀⣀⡀⡀⢀⣀⣀⣄⣀⣀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠶⢏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠯⠤⣬⡾⣿⣷⣿⠿⠟⠋⠉⠑⠄⠀⠀⠀⠂⠀⠀⠀⠀⠉⠿⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⣠⡾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠠⣄⢲⣤⣴⠛⢁⢀⣀⣲⣿⣿⠿⣿⢿⠟⠿⡿⠶⡶⠶⣤⣤⣄⡠⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠙⣿⠋⢻⡿⠛⠋⠁⠈⠀⠀⠘⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠈⠙⢲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠶⠛⠃⠲⢶⣶⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⣋⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢿⠛⠻⢶⠶⠤⠤⣄⣀⣀⣠⠀⠠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⢤⡀⠀⠀⠠⡀⠀⠀⢂⠀⠀⠀⢡⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⣱⡤⠶⠚⠛⠋⠉⠉⠉⠉⢛⡚⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠉⠁⠀⠈⠙⢦⡀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⡔⠉⠀⠈⠀⠀⠀⠀⠘⢦
⢤⣂⠈⠀⠀⠀⠉⠒⢤⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢐⣾⡟⠉⠀⠀⠀⡅⢠⢶⡄⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠑⠢⣄⠀⠀⠀⠀⠙⣄⠀⠊⠀⢀⠀⠀⠤⣀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠑⢌⣛⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠘⠆⠀⡔⠁⠀⠀⠀⠀⠱⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⡀⠀⠀⠻⡿⠿⢿⣿⣿⣿⠋⠙⠓⠒⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠓⠧⠤⠀⠄⠘⠀⠀⠀⠀⠑⠤⡀⠈⠋⠙⠀⡀⣀⣀
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⠔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣹⠂
⢀⡀⠐⠁⠀⠀⠀⠀⡀⠔⠁⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁
⠀⠀⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢴⣶⢖⣲⠞⠒⣿⣷⣶⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠋⡶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠘⡐⣹⣥⣾⣿⣿⠿⠿⠿⠿⠟⠻⠿⢿⣿⡟⣿⢿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⡅⣼⣾⣿⠿⠋⠁⠀⢰⣶⣶⣤⣤⡀⠀⠀⠀⠈⠙⠻⠎⣛⣻⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⡛⣳⣿⣿⠃⠀⠀⠀⠀⠐⢯⣻⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⠈⠙⢏⡿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠇⠎⣿⣿⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠀⠐⢤⠄⠂⠈⠈⢿⣉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠆⠄⢼⣟⣷⣄⡀⠀⢴⣶⣖⣳⣾⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡀⣀⠿⠛⢛⣿⡶⡶⠺⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣠⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⣥⣴⣷⣿⣿⣿⣿⣿⣶⣶⣌⣝⣷⣦⣭⣉⠉⠻⣷⡿⡿⣿⣿⣿⣿⣿⣿⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢚⣷⢟⣿⡿⠛⠿⡿⢙⣯⣿⣝⢭⣙⣻⡄⠹⣿⣿⣿⣶⣬⣹⢷⢩⣭⡿⢻⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣤⡄⢰⡡⣟⣱⣿⠋⠀⣀⣀⣀⣈⡛⠻⠿⣸⣿⣶⡙⡆⢹⣿⣿⠿⡟⣿⣿⣦⡈⠁
⠀⠀⠀⠀⢀⣴⣾⣟⣹⠏⣭⣿⣿⣿⣿⣝⣛⣿⣧⣵⠿⠬⣶⡆⢭⡁⢠⣾⣿⣿⣿⠟⠃⠀⠀⠀⠈⠉⠛⠁⠠⣿⣯⣣⡀⠂⠻⢿⣿⣦⡀
⠀⠀⢀⣶⠿⣡⣻⣿⣿⣿⡿⣿⣿⡿⠿⠿⢿⣿⣾⣥⡵⢤⣽⣀⣀⣿⣿⣝⣿⣉⣀⣀⡄⠀⡐⠀⠀⠀⠀⠀⣸⣿⠛⠻⣷⣶⡎⠄⠻⣿⣿⣄
⠀⣰⣿⣟⣿⢯⠟⣹⣿⣿⣿⡿⠋⠀⠀⠀⠀⠈⠙⠿⣿⣿⣽⣿⣿⣼⣾⡿⣉⡉⠉⠁⠀⠀⠘⠁⠀⠀⢰⣠⣿⠇⠀⠀⠈⠻⠛⠐⠨⠹⣿⣿⡆
⢰⣿⣿⣷⣿⠃⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣟⢹⣿⢰⣯⢵⠀⠀⠀⠀⣀⣠⣴⣾⣿⡿⠃⠀⠀⠀⠀⠀⢴⣾⡕⢸⣿⣿⣿
⢸⣿⣾⣿⣿⠀⠈⣿⣿⣯⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣼⣿⣾⠾⢠⣤⣶⣶⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣟⢈⣾⣿⣿⣿
⢸⣿⠿⢇⣽⡆⠀⠘⢿⣿⣷⣯⣿⣷⣶⣦⣤⣤⡀⣀⣀⢣⣿⣿⣿⣿⣱⣿⣞⠝⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠋⣴⣿⣿⣿⣿
⠈⣿⡞⣻⣿⡿⣦⣄⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣽⣶⣟⢉⠿⣿⣵⣟⣯⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣻⣿⣿⣿⣿⠃
⠀⠈⢿⣟⡻⣤⠿⡿⢿⣷⣶⣦⣤⣤⣤⣴⣶⣶⣾⡿⣿⣟⢻⣶⣾⣿⣯⣿⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿⣿⣵⣾⣿⣿⣿⠃
⠀⠀⠀⠙⠿⣷⣿⣿⣶⣻⣻⣿⣟⢫⣽⣽⣯⣙⡵⣿⡾⡾⡨⡭⢿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠙⠛⠾⠿⣬⣿⣿⣾⣿⣿⣯⣿⠿⠷⠛⠞⠁⠀⣾⣯⡾⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣦⣶⣤⣤⣤⣀⣀⣀⠀⢀⣀⣤⣾⣿⡿⠁⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣠⣴⠶⢂⣉⣽⣿⣋⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⡿⢟⣛⣿⡿⠄⠁⠛⢭⡄⠀⢀⣄⠠⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⣿⡁⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⢀⢀⣤⣾⣿⣿⣟⣛⣿⣿⡿⢧⣶⣄⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣕⣀
⠀⠀⠀⠀⠀⣰⣿⣤⠈⢡⣶⡮⠻⣿⣭⣹⣥⣸⣿⠻⣿⣦⡀⠀⠀⠀⠀⠹⣿⣿⢻⣟⣇
⠀⠀⠀⠀⢠⣿⣿⣿⣰⣧⡿⠜⠃⠙⠛⠻⢻⣿⣟⢷⣿⣿⣿⣶⣄⡀⠀⢀⣽⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⢻⣿⢿⣯⠁⠀⠀⠀⠀⠀⠀⠉⠓⠀⣬⣙⣿⣿⢙⣿⣿⣿⣿⣿⢿⣵⡏
⠀⠀⠀⠀⢾⣿⣿⣷⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⣿⣿⣿⡛⣿⡏⠉⠛⠋
⠀⠀⠀⠀⢸⣷⣹⡟⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠘⣿⣿⣿⣯⠿⣿⣄
⠀⠀⠀⠀⠀⠹⣿⣿⡻⣷⣦⡙⠳⣦⡄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣴⣺⡅⢛⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⣿⣿⣯⣥⣽⣿⡶⢶⣟⣻⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣷⣬⣅⣽⣿⣿⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢉⣶⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣧⣿⣻⣿⣿⣿⣿⡿⢟⣹⣿⡘⡿⣿⣷⣮⣻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠟⣿⡾⠿⠿⠶⠒⠒⠀⠛⠋⠛⢿⡎⣿⣿⣿⣿⡟⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣿⣿⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢸⣿⣿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⣀⣤⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣮⣿⣖⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣞⡿⢏⣬⣽⣶⣬⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢿⣯⣶⠸⣿⣿⢰
⠀⠀⠀⠀⢀⣶⣿⡏⠉⢤⠞⢿⣿⢿⣿⢿⣿⡿⢿⣿⣿⣿⣷⣍⣽⡻⣛⡮⠟⠛⣳⣖⣒⣖⣐⣿⢛⣴⣿⡿⠃⠀⠈⢿⡿
⠀⠀⢠⡄⣾⣵⡿⠛⣛⣶⡶⢹⠿⣿⣿⣿⣿⣿⣦⣯⣽⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣯⣿⣿⣾⣿⣷⡄
⠀⠀⣾⣏⡙⣿⡷⠛⢉⡁⠾⠛⠋⠉⠉⠁⠉⠁⠉⠉⠙⠿⢿⣷⣾⣿⣯⣛⣻⣿⣿⣿⡟⠟⢿⣿⣿⠿⣿⣿⣿⡿⠆
⠀⠸⢻⣿⣯⣀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⡝⠿⢿⣃⣀⣸⣿⣶⡶⠿⠛⠉
⠀⢸⣿⣿⣿⣻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁
⠀⠘⣿⣿⣿⣿⣿⠙⡆
⠀⠀⣿⡻⣿⣟⢉⣦⢹⣶⣄⣀
⠀⠀⠘⣿⣾⣿⣯⣵⡿⣿⣍⣟⣹⣿⡖⠲⢶⣶⣶⣶⣦⠒⣔⠒⢀⣶⣶⣶⠴⠤⢀⣤⣀
⠀⠀⠀⠘⢿⣟⢿⣿⣿⣶⣭⡿⣿⣽⣛⣛⡿⣿⡍⣽⣾⣾⣿⡿⢶⣿⠿⠟⢣⣶⣾⣿⡿⠛⣴⣦⡄⡀
⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣯⣚⡙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣾⣋⣭⣿⣾⣻⣿⣿⣿⠇⣨⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠙⠛⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣟⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣇⡀⢫⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣏⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠋⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⣿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠸⢧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣘⠇⡾⠁
⠀⠀⠀⠀⢠⣤⠴⠖⠊⠉⠉⠉⠉⠉⠛⠛⠿⢶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠹⠾⣩⠟⠁
⠀⢠⠔⠻⠟⠹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⡶⣶⣦⣤⣤⣤⣤⣤⣤⣴⠶⠾⠛⢋⣠⡤⠞⠁

⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⡖⠀⠀⠀⠀⡄
⠀⠈⣏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⡞⠀⠀⠀⢀⡜
⠀⠀⢸⡀⠨⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠺⣅⠀⠀⠀⠀⠁⡇⠀⢀⣴⢼⠁
⠀⠀⠈⡇⠀⠀⠸⣇⠉⠙⠒⠒⠒⠶⠤⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣁⠀⢸⡄⠀⠀⠀⠀⠧⢊⣭⠒⡏
⠀⠀⠀⡇⠀⠀⣀⣹⡄⠀⠀⠀⢳⡦⣄⡀⢀⠂⣱⡏⠀⠀⣤⡤⡈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠋⠀⢸⡇⠀⠐⠀⠀⢔⠒⠂⠄⠇
⠀⠀⢠⣧⠔⠋⠀⠀⠘⢆⠀⠀⢈⡇⢘⡿⠶⢈⢶⡇⠀⠘⠽⡿⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡾⠁⠀⠄⠀⠀⠈⢆
⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣷⣄⠀⠉⠁⠀⠠⠈⣾⡇⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣀⣀⡀⠀⠢⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣈⣻⣦⣀⠀⠐⡂⡟⣇⠀⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠓⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣬⠀⠀⠙⠐⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢭⣤⢰⡖⠀⠀⠄⡀⠀⠀⠀⠈⢄⠉⠀⠀⠀⣀⠴⠈⠠⡌⠁⡒⠀⠄⠠⢄⡴⠁⠁⠄⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠑⠢⠀⢀⣠⡖⠋⡅⣴⡋⣾⣹⠀⣾⠆⠀⡈⠀⠀⠀⠀⠢⡀⠀⠆⢹⠁⡔⠐⠁⠀⠀⢀⡠⠴⡏⠆⢠⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡐⢿⡋⢨⡗⠀⣇⢸⣇⢸⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢥⣱⣁⣀⠤⠔⠋⠉⠀⠀⢣⡐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢺⠛⠦⣏⣃⠘⡀⢽⣃⢿⡬⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⠉⠉⠨⠙⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠖⠛⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⢄
⠀⠀⠀⠀⠀⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠤⡴⠊⠁⠃⡆⠀⠀⠀⠀⠀⡜⢁⡄⣀⠀⠈⢣
⠀⠀⢀⡆⢠⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⠈⡀⠀⠀⠘⡆
⠀⠀⢼⠇⠈⠄⠀⢣⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢿
⠀⠈⠘⡀⠀⢨⠀⢸⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⢀⣴⡞⢻⢹⠁⣀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁⠄⢈⣀⣁⣀⣸
⠀⠀⠀⠀⠀⡌⠀⡎⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⠂⠂⣾⡋⠸⣏⣮⡈⠀⠙⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠀⠩⠈⡀
⠀⠀⠀⠰⢰⠀⠰⠀⠀⠀⠂⠆⠀⠀⠀⠀⠀⠀⠀⠎⠀⣠⡟⠓⠦⣯⢥⣼⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠐⡄⠀⢃⢠
⠀⠀⠀⠂⠘⡀⠄⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⡀⢧⠀⠀⠀⢀⣀
⠀⠀⢀⠣⠀⠈⢂⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠱⡀⣇⠈⢧⡀⠀⠀⢠
⠀⠀⠀⠑⠄⣀⠀⣆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡬⠤⠶⠖⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡱⠸⠀⠀⡉⠒⠚⠁
⠀⠀⠀⠀⠀⢸⣴⡃⢐⠁⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢁⣀⠀⠀⠀⠃⢨⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠈⠁⠀⠣⣀⠄
⠀⠀⠀⠀⠈⠀⠀⠙⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠇⠈⠉⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠀⢠⡦⣴⠠⠆⡜⢷⣌⡓⠀⠀⠀⠞⠀⠐⡦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⡔⠰⠇⠈⠉⠢⠶⠈⢉⣡⠀⠀⢠⣀⣀⡀⠂⠼⢳⡤⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠄⠀⠀⠀⠀⣠⣠⣄⠦⠐⠀⠀⠐⠛⠋⠰⢆⣡⣘⣛⣟⠿⠓⠀⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣤⣀⡀⣠⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢂⠀⠀⣀⣄⠀⠀⠘⣿⣿⣶⡄⢠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠀⠀⠢⠀⣿⣿⣷⠀⠀⠘⣿⣿⣿⢺⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⣡⣿⣿⣦⠀⠀⠀⠘⠛⠀⠀⠀⠀⢸⣿⡇⣸⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⢀⣿⣿⣿⡀⠀⠀⡦⠀⠒⢁⠐⠀⠀⣿⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢀⣀⠀⡄⢤⣤⡆⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⡷⢮⣽⡿⠞⠃⠀⠀⣺⣦⣴⣿⡏⠀⢘⣿⣿⠟⠙⢿⠿⠿⣿⣿⣍⣹⣏⣴⣶⣾⣿⣿⣿⣾⠿⢛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣈⣛⠻⢿⣦⣦⣿⣢⣾⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⡍⢱⣶⣤⣼⣇⡀⠻⣿⣿⣿⣿⠿⠟⠁⢹⣿⡉⠁⣄⠁⠽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠛⢿⣍⢱⣤⢀⣿⣿⣧⣙⠿⣿⡿⢿⣻⣿⣿⠟⠋⠙⢻⠟⣭⣛⠻⣯⡀⢀⣹⡿⢿⣥⣤⣤⣴⠾⢿⣇⢠⠀⠀⠴⣿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣞⠃⠙⣷⣿⠀⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⠏⣤⣤⣤⡎⣸⣿⠿⢷⣾⣿⣿⣿⣤⣤⡿⢿⡉⠉⠀⠐⣥⣏⢐⣠⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠹⣿⣿⡛⢿⣿⣮⣭⣉⣀⣀⡀⠘⣿⡇⠈⠉⠀⢸⣿⣿⣍⠙⡛⠻⠿⣿⡇⠀⠀⠀⢹⢁⠘⣉⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡇⠀⠀⡿⠿⣿⣶⣯⡍⠉⠉⠉⠙⠷⠂⠀⠀⠀⠀⠀⠀⣽⣿⡥⠂⠐⠀⠀⢼⠁⠀⠀⠀⠈⢸⡧⠃⠐
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠛⠛⢿⣿⣷⡦⠶⠟⠒⠚⠛⠋⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠃⠐⠳⣑⣦⡩⢾⠀⠀⠀⢠⣄⡘⠃⢀⣄⣴⠃
⠀⠀⠀⠀⠀⠀⠟⢿⡏⠉⢠⡄⣨⢤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠲⣀⠖⣿⣿⣄⠀⠀⠀⠀⠸⢿⣿⡿⢉⣼⣿
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠉⠉⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⡀⠐⢉⠳⠣⠀⢶⠃⠀⠀⠀⣴⣶⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢺⡄⠐⣶⢄⣤⠓⠠⣉⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣀⠀⠐⠒⠒⠠⠀⠀⠀⠀⣿⣿⡻⠼⢟⣿⡟
⠀⠀⠀⠀⠀⢸⣿⠞⢫⣿⡿⢿⣶⠟⣷⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⡻⣿⣿⣿⣶⣶⣎⢳⡄⢻⣿⣿⣤⣄⣐⠿⠇⠀⠀⠀⣰⠟⣻⣿⣶⢿⣿⠇
⠀⠀⠀⠀⠀⠈⣿⡄⠨⢃⣄⢨⡿⠂⢸⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡆⣿⠈⣿⣿⠿⣿⣿⠇⠀⠀⠀⣴⢿⡄⢸⣿⣧⣴⠞
⠀⠀⠀⠀⠀⠀⠸⣷⡀⠈⠁⠉⢹⣦⠜⠛⢁⠴⣿⣿⣿⣛⣛⣻⣿⣿⣿⠓⠚⠛⢿⣿⣧⣿⢱⣿⠁⠀⣽⣿⣿⣧⡟⣀⢿⣿⡴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⣠⣀⠋⠀⠆⠀⠀⣿⣿⣿⣿⡿⠿⣿⣿⡙⠋⠰⣿⣿⣿⣿⣿⣿⡛⢀⣴⣿⣿⣿⡏⣰⣿⡜⣿⣷⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡀⣀⠀⠐⣿⣿⣿⣿⡟⠀⠀⠸⠉⣷⣟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣋⣻⣿⠋⢰⣿⡿⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡁⣾⠃⠠⣾⣿⣿⣿⠁⠀⢰⣷⢰⣿⣿⣿⣿⠿⠟⠛⠁⠀⠀⠀⠉⠈⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⠀⠀⣼⣿⡿⠿⠶⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄⠘⢿⣿⣶⣶⣶⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠌⠙⠛⠟⠛⠛⠻⠻⣿⣿⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠖⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠤⠶⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠛⠀⠉⠉⠁⡇⠸⠈⠉⠁⠀⠁⠛⠀⡇⠀⠀⠀⠀⠀⣠⠈⡤⠤⠠⠄⠀⠀⠤⠤⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠀⠀⠀⠀⡇⠐⠀⠀⠄⠠⣤⣤⠀⡇⠀⠀⠀⠀⠘⠀⡀⠀⠄⠀⠒⠒⠒⠒⠒⠒⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠁⢠⡀⢰⣔⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠛⠚⠂⡇⠈⠘⠒⠃⠈⠛⠃⠀⡇⠀⠀⠀⢀⠀⡆⠈⠋⠈⠉⠀⠀⠀⠀⠀⠀⡘⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⡇⢀⠀⡀⡀⢀⣀⠀⠀⡇⠀⠀⠀⠀⠇⠈⠦⣀⠒⠘⠋⠁⠀⠀⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀⠀⠀⠀⡇⠈⠀⠀⠀⠈⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠀⠈⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠒⠒⠂⡇⠐⠐⠒⠂⠀⠺⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠤⢀⣠⣤⣶⢤⡗⠊⠛⠁⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⡵⡖⡄⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠈⠀⡇⠈⠀⠀⠀⠘⠋⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠌⢳⡏⠸⠈⠂⠇⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡴⠀⠤⠤⠀⡇⠀⠠⠤⠄⠠⣤⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢷⠘⡀⠀⠘⢶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢸⠀⢳⡇⠰⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠀⠙⠛⠁⡇⠸⠘⠋⠃⠐⠓⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢸⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⣠⣠⠀⢀⠀⠀⡇⢠⠀⠀⠀⢠⣄⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠶⠆⠀⠒⠒⠂⡇⠐⠐⠒⠒⠰⠶⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢀⢀⠀⡇⢈⠀⣀⡀⠀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠶⠀⠠⠤⠀⣷⡆⠠⠤⠆⠀⠖⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠉⠀⠀⠉⠀⣿⡇⠀⠀⠁⠀⠈⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⢠⡶⣿⣿⣶⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⢿⠿⠿⠿⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡠⠀⠀⠤⠀⠀⠀⠀⢠⠀⡄⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠠⡄⠤⠀⠂⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⡤⢤⡀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠉⠉⠀⠀⠀⠀⣀⣹⡄⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢹⡇⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⢴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠁⠀⠀⠀⠀⢀⣀⠀⠀⣀⡴⠛⠉⠁⠀⣠⣷⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⢰⢶⠀⠀⢸⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣄⣀⣀⠀⣀⣀⡴⠋⠉⠙⠋⠉⠀⢀⣠⣴⣾⣿⠿⠓⠚⢉⣩⠭⠟⠁⠀⠀⠀⠀⣿⠀⠀⢸⢸⠀⠁⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣷⠈⠉⠉⠉⠁⠀⠀⠀⢀⣀⣤⣶⣿⡿⠛⠉⠀⣠⠴⣚⠉⠀⠀⠀⠀⣰⡄⠀⠀⣿⠀⠀⢸⢸⠀⠂⠠⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣆⣀⣀⣤⣤⣶⣶⣿⣿⣿⡿⠛⠁⢀⣤⠖⠋⠁⠸⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⢸⠀⠄⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⡿⠿⢛⡹⠛⠁⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⢸⢀⡀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠛⠁⢁⡤⢒⣉⡤⠖⠋⠁⠀⠀⠀⣶⠀⠀⠀⠀⠀⢠⡀⠈⣧⠀⠀⠀⠀⠀⣿⠀⠀⢸⢸⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣀⣀⣀⣀⣴⠾⠟⠚⠉⠀⠀⠀⣠⠶⠶⣄⠀⢿⠇⠀⠀⠀⠀⠈⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⢸⠸⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⣤⡿⠉⢉⡇⠀⠀⠀⣿⠀⠀⢸⢸⠀⠄⠀⡇⡇
⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⢧⠀⣀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠒⣟⠁⣀⣀⠀⠀⢹⠀⠀⢸⢸⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⡈⣳⡘⠊⠃⠀⠀⠀⠀⠛⢦⣄⣴⠇⠀⠀⠀⠀⣦⣠⠤⡴⠋⠀⠀⠸⡄⠀⢸⠀⠀⢸⢠⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⣾⠉⣉⣙⣓⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⡞⡀⠀⠀⠀⠀⢬⠀⢸⠀⠀⢸⣤⠀⠁⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⣿⣿⣿⣿⣿⣷⣾⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠱⡄⠀⠀⢀⠜⠀⢸⠀⠀⢸⣿⠀⠂⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⡻⡄⠀⠀⠀⠰⣶⠞⣡⠟⠀⠀⠀⠙⢠⡘⡯⠀⠀⢸⠀⠀⣾⣿⣷⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡓⠀⠀⣀⡴⠛⠋⠁⠀⠀⠀⠀⠀⢸⠇⠁⠀⠀⢸⠀⠀⠙⠛⠁⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⢾⠁⢤⡀⠀⠀⠀⠘⣆⠀⠀⠸⠄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⢳⣠⠛⣆⠀⠀⠀⠙⣀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠠⣶⣄⣿
⠀⠀⠀⠀⣴⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡠⢻⡆⠀⠀⠀⠘⣦⠀⠀⠠⠶⠀⠀⠿⠾⣧⣦⣴⣿⠁⠉
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠻⣿⣿⣿⣿⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢿⠃⣾⠆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠈⠻⣿⣿⠀⠓⢦⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⡀⠀⠀⠈⠙⢦⠀⠀⢿⢳⣄⠀⠀⠀⠛⠋⠀⠀⠀⠀⢀⣿⠀⠀⣿⠇
⠀⠀⠀⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⠇⠀⢸⡆⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠉⠀⠀⠙⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠘⢳⡄⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⠆⡔⡠⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠾⢾⡴⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠙⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢠⣤⣤⣄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠛⠛⢛⣻⣛⡱⠶⠈⡉⣭⢥⡀⠹⣿⣿⠂⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⢿⠟⣛⡙⠃⠀⢰⣿⣭⣛⡻⣀⡸⣟⣻⠞⢿⡌⢁⣴⣰⣞⣯⡁⣶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢛⣭⡀⣀⡷⣽⣟⢣⡾⢎⣡⡯⠻⠷⠬⠵⣿⠇⣾⣧⣛⣾⣧⢿⣛⡟⠀⠛⠚⢋⠁⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⣋⣭⣁⣼⢿⣾⡹⠿⠓⠀⠁⠀⠀⠀⠀⠀⣀⣄⡀⠈⠉⠉⠋⠸⣿⣿⡟⣂⣴⣟⣁⣿⠁⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⢸⠟⣉⣾⣟⣠⡼⠋⠁⠀⠀⢀⣠⣶⣶⠾⠻⣿⣟⠉⢿⣿⣯⣽⡦⢠⡀⠉⢡⡝⠻⣯⣯⡷⢠⡍⣥⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠷⣼⣆⠙⢿⣿⠏⠀⠀⠀⣠⣴⣿⢫⠾⣁⡐⣳⣏⣙⠛⡾⢿⣽⢿⡷⠶⠏⠀⠀⠘⠂⠈⢻⣤⣄⡴⣀⣴
⠀⠀⠀⠀⠀⠀⠀⢿⡴⠿⢶⡟⠋⣸⡇⠀⠀⢠⣾⢏⡼⢛⣷⢶⡿⢻⣿⣿⡿⣻⠛⣫⣉⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠹⠞⣷⠏⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢿⣦⡄⢸⡏⣈⢿⡇⠀⠀⢻⣿⣻⣧⣌⣉⣉⠑⠾⣿⣿⣿⣷⣞⠋⣿⡀⠀⠀⠀⠀⢠⠇⠀⣉⡀⠀⣻⡷⢾⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠋⢿⣆⣿⣇⠘⣿⣧⣀⣀⣿⡿⠟⠉⢀⠉⠀⣁⣶⡄⢻⣦⡉⠘⢧⡀⠙⠛⢷⣦⡼⠋⠀⠰⠆⠀⠀⢸⣧⣤⡹⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣮⠈⠙⣿⣦⣀⣼⣿⢏⡼⣷⠀⠀⣀⣛⡛⠁⠈⠙⠢⣌⣻⣧⣤⣿⢷⡄⠀⠀⠀⠀⠀⡂⠀⠀⠀⣰⣿⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣘⡛⣌⣉⣁⣴⣾⣇⠀⠀⠤⣌⣏⠁⠀⠀⠀⠀⠀⠉⠈⠛⠟⠛⠁⠀⠀⠀⢀⠄⠀⠀⠀⢠⢿⡟⢚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠛⠘⠛⠛⠑⠎⠀⠀⠀⣤⣭⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⣠⡿⠾⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢤⠀⢠⡀⠀⣴⣦⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⢀⣴⠛⠛⢷⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡐⠂⡀⠀⠀⠀⠀⢀⣠⣿⡧⢾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⠊⣬⣛⡳⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⣰⡶⠛⢿⣿⣼⣣⠿⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣤⣠⣤⣴⣶⣾⠛⢻⡿⣿⠆⣴⣾⣾⣿⣿⣶⣶⣶⣶⣶⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⡀⢀⠄⣴⣦⣾⣿⡿⣷⣟⡛⢉⡹⣿⢟⣷⣿⣴⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣷⣏⠉⣷⡶⡆
⠀⠀⠀⢠⠀⠀⠀⠀⣠⣀⣷⠛⡿⢛⣶⣟⠛⢡⣤⣛⡉⠿⢧⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢤⣼⣿⣟⣷⡟⠙⠛⠛⣃⠠⣼⣿⣦⡀
⠀⠀⠀⠀⠀⣠⣼⣛⠭⢿⠟⠻⣽⣿⡧⠛⠛⠉⠈⠉⢀⣴⠟⣿⡟⣿⣿⣿⡿⠻⠉⠉⠁⠀⠀⠀⠤⠠⠄⠤⠤⠀⠄⠉⠙⠿⣤⣾⣿⣿⣿⣭⣛⣉⣉⣤⡀
⠀⠀⢲⣤⣿⣯⣭⡙⣶⣾⣿⡟⠋⠁⠀⠀⠀⠀⠀⢰⣟⢳⣴⡛⠿⣿⠏⠁⠀⢠⠐⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⡘⠻⣿⡏⠸⡿⠛⢩⣻⣷
⠀⠀⣦⣀⣹⣧⠸⡷⢨⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣯⣾⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⠂⠹⣧⣤⠶⣶⣤⣻⣿⣧
⠀⢸⣏⣙⣁⢛⠉⣰⣾⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠸⢷⢿⠛⢿⣤⠀⠀⣀⣤⣤⣶⣾⣿⡿⢀⣩⣷⡾⢫⣾⣟⠻⡀⢦⣄⠀⠀⠀⣟⠻⣿⠟⢧⣹⣦⢰⡄
⠀⢸⡟⠛⣿⠛⣿⡛⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⡷⠰⢶⡆⣾⣹⡿⠟⢋⡨⠟⠛⢛⣿⡄⢋⣭⡴⢶⣌⠀⣿⣆⠀⣾⣿⣠⡄⠀⣼⣶⣧⣄⠀⠿⣿⠙⡆
⠀⠘⡷⠿⢿⣾⣿⠇⡰⣤⢷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⣶⠶⢤⣿⡷⣾⠃⣤⠴⣦⣌⣉⠀⢀⣾⣯⠿⣿⣩⣿⣽⠁⠘⠀⢉⣘⣁⣿⣟⡛⣿⢉⣇⣘⠈⣠⠁
⠀⠀⢻⣿⣶⠟⢃⣼⣷⡙⢊⡡⡐⢦⣀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡀⠿⠂⣸⠟⣾⣿⣽⠿⠛⠋⠁⠀⠀⠀⠀⠉⠙⢷⣤⡘⢻⡿⣿⣿⡏⢻⠿⠿⣿⠛⢀⠏
⠀⠀⠈⠻⣿⣿⣎⢹⣯⢰⣟⡷⠁⢾⠿⠖⠢⣄⣀⡀⠀⠀⠀⠉⠉⠛⠒⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣮⡑⠏⠙⢳⡿⢿⣴⣿⣿⠏⢠⠜
⠀⠀⠀⠀⠙⢿⡟⢉⣯⣌⡛⣤⡠⣬⣶⠶⠺⣦⠙⠙⢶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣷⡾⢧⣉⡷⠖⠁⢩⣇⠸⣿⠉⠁⢠⠏
⠀⠀⠀⠀⠀⠈⠛⠻⣯⣽⣇⣈⣡⣮⣹⠿⡑⠿⠃⠘⠷⢀⣰⣿⢻⣿⡋⣖⣰⡷⣰⣟⣉⣻⡿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣉⣽⠆⢠⢾⣿⣦⡇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠁⡌⠛⠻⠿⣿⣅⣼⣿⣿⡄⠻⠃⣼⠟⣡⣾⠿⣷⠈⡁⣨⣿⠿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⣯⣿⠿⡀⠻⣮⣳⡿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢀⡈⢉⠙⠛⠻⠶⢾⣷⣿⡉⣥⣶⣶⣄⣸⣿⣿⣶⣿⣿⣧⢴⡟⣿⣿⡿⠿⠟⠋⠁⢁⡼⠋⠀⢽⡋⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⣀⡀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠛⠛⠛⠋⠛⠘⠁⠉⠀⠀⢀⡀⠦⠈⢹⡷⢀⣰⢿⡀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠠⠄⠤⠀⠀⠀⠀⠀⠄⠤⠤⠄⠘⠛⠉⠀⠀⠀⢠⡟⠁⢿⡧⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡤⠀⠀⡐⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣀⡉⢁⣸⡷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⣉⠀⠀⣠⠦⣤⣔⣤⣴⢶⣤⣄⠠⡄⠀⠀⠀⠀⢀⣠⡴⢅⣸⣏⣽⢿⢋⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠆⣴⠛⣷⣄⣿⠷⠿⠿⠋⠱⣶⣿⣾⣷⣤⠀⠀⣠⡴⢋⣵⣶⣾⣿⣭⣵⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣿⣿⣾⣏⠀⠀⠀⠀⣀⣀⣈⣧⣰⣿⣸⣷⠘⣦⣱⣿⣙⣇⣾⣁⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠸⣿⣤⣍⠙⠿⢟⣉⡙⢿⣿⣿⣿⡀⣹⣿⡄⣿⠟⠙⠛⣟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⠰⣿⣷⡾⢿⣷⡼⢯⣽⠷⣿⣻⣿⢸⣇⣸⣿⣩⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⠤⢠⣶⣤⣟⣋⣉⣀⠾⢿⡟⢸⡟⠛⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⣩⠏⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⢻⣾⠋⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡿⠛⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⠆⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⣥⠄⢀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⢤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡿⣿⣓⣫⣷⣄⣛⣿⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢆⣫⣿⣿⠇⢛⡓⢾⡻⡕⣄⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⢋⡴⡣⠞⢁⣄⠀⢋⣿⠛⣾⢭⢦⣹⡎⣯⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠀⣠⣾⣹⠂⠀⢻⣤⣽⢬⣤⣷⡿⢻⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⢶⣶⣶⣶⣿⣽⣿⡆⠀⠀⢟⡶⠶⢷⡶⠂⣼⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣊⠳⠾⠟⠽⠄⣯⠝⠙⢿⣮⡽⠢⢀⡈⠑⠚⠻⣾⡍⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣶⣟⢾⡷⠖⣶⠦⣄⡙⢠⡶⢟⣿⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡶⢬⣭⡿⠜⠛⠘⠋⠛⠒⠋⠉⠉⢻⣾⣡⣟⠘⣟⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣤⣿⢉⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠚⠋⣳⡿⡖⢿⡹⡦
⠀⠀⠀⠀⠀⢀⡾⠿⡿⠃⠀⢀⡤⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢧⣼⢰⣶
⠀⠀⠀⠀⠀⡜⢻⡸⠁⠀⣴⠟⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⣏⣹⢰⣹
⠀⠀⠀⢀⣴⣣⡟⠇⠀⢠⣯⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣥⣉⡟⣼⣿
⠀⠀⣠⣭⣿⡫⠆⠶⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⣤⣿⢁⣽⠇
⠀⠐⢛⡟⠹⣿⠺⣷⢧⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠋⣤⠃⣼⡟
⠀⢺⡉⠁⠀⠹⡆⣿⠤⢓⣄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠛⣶⣰⢏⣾⡿
⠀⢸⣴⢇⠀⠀⢄⠺⣆⣼⣿⠃⢦⢌⣀⠄⠄⢀⣀⣠⣾⠽⡶⢚⡿⢡⣿⠟
⠀⠀⠈⡟⣣⡀⠀⢶⡉⠩⡸⣇⠶⣀⡷⠻⣎⠻⢛⡶⣀⣴⣼⣿⣴⡿⣏⣀⡀
⠀⠀⠀⢯⣋⣴⠗⠠⣝⠷⣶⣽⣶⡿⣥⣴⣿⣿⠟⢷⣽⢣⡿⣳⣼⣋⡿⢦⡽⣦
⠀⠀⠀⠀⠙⠷⠺⣥⡺⣇⡛⠀⣿⣒⢤⢘⡿⣿⣖⣾⣿⣿⠿⠿⠿⣿⢴⡶⣻⣿
⠀⠀⠀⠀⠀⠀⠈⠘⠓⠉⠙⢿⣥⣽⠿⠿⠟⠓⣛⠋⢥⣄⡶⣖⣻⣆⣬⢖⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢷⣿⣷⣯⣿⣿⣷⡿⠷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣻⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣿⣿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢽⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⢻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⠤⣄⢀⡴⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠄⠀⠀⣿⠈⢧⡴⣃⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠖⠀⠀⠀⣿⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⣿⠀⠀⠘⢧⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡟⢻⡆⠈⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⡇⢸⡇⢾⠀⠀⠀⢠⣠⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⡞⠀⠀⢳⡌⢳⡄⠲⣄⢹⡇⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡏⠀⠀⠀⠀⢹⠀⣷⠤⢬⣿⣿⠥⢴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢳⣄⠀⠀⣀⡞⢠⡏⣠⠞⢹⡏⠳⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣌⣉⣉⣡⡴⠋⠀⠁⠠⠿⠳⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠



⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢰⠀⠘⣄⠴⠀⠀⠀⠐⢦⣀⠠⠀⠀⠀⠀⠀⠀⣸⣷⡄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⣴⡶⠀⠀⠀⠘⠐⠀⠋⠀⠀⠀⠀⠠⠞⠛⠐⠀⠀⠀⠀⠀⠀⢻⡶⠟
⠀⠀⠀⠁⢰⣿⣿⣿⣿⣿⣿⡛⠻⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠾⠿⠿⠿⠷⢶⣶⣤⣄⣀⣀⠀⠐⠋
⠀⠀⢀⣀⡀⠀⠀⢀⠠⠛⠛⠓⠖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂
⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠸⠿⠋⠀⠀⠀⠀⠀⢀⣀⣀⡈⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⠇⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠐⠛⠷⠄
⠀⠀⠀⠀⢤⣶⣿⣿⣶⣤⣀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⠁
⠀⠀⠀⢠⠈⣿⣿⣿⣿⣿⣿⠷⠈
⠀⠀⠀⠀⠰⢿⣿⣿⠿⠛⠁⠀⠀⠉⠀⠀⡤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡀⠨⠨⠈⠐⣠⣤⣞⠁⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢁⠮⢌⡄⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⢙⠻⢿⣿⣿⣷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⠾⠛⠛⠻⠿⠟⠛⠛⠛⠛⠿⢶⣶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⢉⠝⠉⠀⠀⠀⠀⡠⠂⠁⣀⣠⣴⠶⠾⠛⠛⠛⠛⠛⠉⠉⠙⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⢀⠜⠁⠀⠀⠀⠀⡠⠊⢀⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁⠀⠀⠀⡐⠁⠀⠀⠀⠀⢀⠎⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢀⠂⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡉⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⢠⡿⠁⣠⣤⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠘⢷⡄⠀⠀⠀⠀⣀⣤⣤⠶⠶⠾⠛⠛⠻⠷⢶
⠀⠀⠀⠀⢀⣴⠟⠁⡾⣿⣿⣁⡀⢣⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠃⠀⠀⢻⣦⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾
⢀⣀⣤⡶⠟⠁⠀⠀⢆⠙⠿⠛⢀⡞⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁
⣿⠉⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠋⠀⠀⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⣇⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢀⣧⡤⠶⠒⠛⢉⡭⠿⠋⠁⠀⠀⠀⠀⠇⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡴⢚⠉⠀⠀⠀⣠⠞⠁⢠⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠹⣶⡀⠐⠂⠉⠀⠀⠀⠀⠀⡌⢀⡴⠛⠁⣀⠀⠄⠀⢀⡞⠁⠀⠀⠌⠀⠀⠀⠀⠀⠀⠆⠀⢠⡾⠃⠙⢷⡀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠈⠛⢷⣆⠀⠀⠀⠀⠀⠰⠀⠺⢤⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⣠⡿⠁⠀⠀⠈⠻⣦⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⡆⠀⠀⠀⠉⠓⢦⣄⣀⣀⣼⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠇⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠰⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠃⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠘⡀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠡⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠢⡀⠀⠀⠀⠀⠣⡀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣴⣄⠀⠀⠀⠀⠐⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⡀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣈⡻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣷⣶⣦⡄
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⡤⠴⠖⠉⠍⠉⢓⡆⢄
⠀⠀⠀⠀⠀⢀⡴⡏⠉⠉⠀⠀⠀⠀⠈⠀⠐⠁⠔⠨⠃⠥⢣⡀
⠀⠀⠀⠀⡰⠉⠋⠀⠁⠁⠀⠀⠀⠀⠀⠀⢀⠁⢒⡑⠂⠂⠄⣱
⠀⠀⠀⠰⠁⠀⠀⠀⢀⠀⠀⢁⠔⣮⡇⢀⠔⣡⣶⠲⡎⡀⢀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⣄
⠀⠀⠀⡇⠛⠀⠀⣀⠀⠀⠀⠀⢙⡩⢔⠵⠚⣯⢕⡀⠣⠐⣂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢣⢅⡶⠗⠁
⠀⠀⢀⢟⡦⣄⣈⣉⣠⢬⣴⡾⠕⠋⠀⠀⠀⣟⠅⠊⠀⡬⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠠⣘⢊⠎
⠀⡔⠁⡶⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡼⠁⠀⠠⣈⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣐⣂⡊
⠚⢩⠜⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⢀⠐⢊⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠬⠥⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡳⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡄⢂⢐⡞⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⢩⡴⠂⠀⠂⠀⢘⢳⣀⣀⣀⠀⠀⠀⠀⠀⠀⡆⡀⢪⠄⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢸⠄⠠⠐⡈⢺⣄⣀⢀⣀⣀⡠⠤⣊⣡⠶⠚⢁⡀⢂⡠⡀⡀⣀⡤⠽⠞⠋⠙⣦⠀⠀⠀⠀⢳⠀⠀⠥⣘⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠠⠘⣆⡡⢞⠠⠉⠀⠉⠛⠟⠛⢛⢉⠁⡀⢂⠀⠆⣘⣤⠤⠓⠉⡀⠠⡠⢃⠁⡁⡎⡇⠀⠀⠀⠀⢣⠐⠘⠐⡹⡄
⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠈⠳⢶⣜⣳⣬⣊⠐⡀⠀⢠⠀⡅⠴⢐⣠⣠⡤⠖⠋⡉⠠⢐⡀⢅⠒⢒⢤⠈⠁⠃⠆⡷⢦⡀⠀⠀⠈⣆⠁⡀⢠⠹⡄
⠀⠀⠀⠀⡠⠀⢋⣀⠔⡀⡀⠀⠀⠀⠉⠛⠓⠚⠒⠓⠓⠚⠒⠋⠉⠀⡀⡠⠐⠄⢀⠈⠐⠃⠙⠌⣤⣤⣰⣴⡴⠾⠯⢢⡜⣆⠀⠀⢸⡄⠰⣬⣥⣷
⠀⠀⠀⡄⠀⠀⢾⣷⡉⠤⠀⠅⠂⠄⡄⢀⠀⠀⠀⠠⠀⠀⠄⡠⠀⡈⠕⡐⡀⠈⠉⢀⣠⠴⠚⠋⠋⠀⡀⡄⠴⢠⢤⢤⢤⣿⠿⣖⣼⡇⠼⢿⡻⣿
⠀⠀⢸⠤⢐⢀⠀⠈⠛⠲⣄⡈⠐⡡⠊⠐⠠⢂⠈⠄⠥⠀⣀⠐⠅⠘⠐⢀⣠⠤⠖⠋⠀⠠⢀⠃⢖⡄⢤⢶⠍⠶⡄⠄⠤⣶⠦⡴⠀⠴⠿⡟⢯⣿⠂
⠀⠀⢸⡄⠀⣐⠂⡀⠀⠀⠀⠉⠓⠲⠮⣅⣄⣤⣠⣠⣠⡆⠼⠴⠒⠓⠉⠁⢀⠀⠔⠠⡁⠂⠥⠔⠄⠒⢈⠈⠀⠀⠀⣀⣞⣢⠖⠁⡃⠢⡑⣌⡾⡀
⠀⠀⠀⢷⡀⠀⠚⢠⠂⠬⠡⠄⠄⡀⢀⠀⡀⠀⠀⠀⠀⢀⠀⡀⠠⠀⠂⠈⠀⠀⠂⠦⠸⠀⠀⢀⢁⣆⣌⣬⣴⠴⠺⠛⠟⢀⠠⢁⠠⢡⣰⠞
⠀⠀⠀⠂⠙⠶⣄⡀⢰⠐⠈⣀⠀⠐⡐⠠⠄⡊⠤⢀⠡⠂⡂⢈⡀⠡⠡⠴⠂⠁⠄⠄⣀⣤⠞⠊⠉⠉⠂⢀⠂⠂⠀⢀⠀⢹⠀⢀⣠⠮⠁⠀⠀⠀⠒⠉⠉⠂
⠀⠀⠀⠀⠀⠈⠈⠙⢒⢲⣠⣀⡀⡀⡀⡃⠂⠐⠁⠀⡄⡁⠐⠠⠀⠀⡀⡀⣈⣬⡴⣾⣉⣀⡀⡀⡀⠂⡂⠀⠀⠠⠀⠘⣀⣨⡼⣋⣁⡀⢐⠒⠂⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠱⠷⠖⢒⢦⣼⣴⣴⠤⡦⠶⠾⠞⣳⣏⡉⠩⠽⠿⠞⣛⣟⣛⠓⢣⠷⠶⠶⠖⠟⠻⠷⢒⣖⣐⡛⠒⠒