Electrical engineer Emojis & Symbols

⠀⠀⢀⠉⠈⢁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⣠⣶⠆⠀⠀⠀⠀⠀⢀⢠⣶⠄⠀⠀⠀⠰⣷⠴⡏⣀
⠀⠀⠘⣛⣙⡛⠀⠀⠀⠀⢀⡖⠀⠄⠀⠀⠀⠀⢠⣾⣷⡏⠀⠀⠀⠀⠠⠤⣤⠴⠿⠦⠀⠀⠀⣾⣿⡇⡷
⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠋

⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⢰⡴⠀⠀⠀⠀⠀⠀⢠⡴⡓⠀⠀⠀⠀⠀⠀⠐⢀
⠀⠀⣴⣯⠁⠠⠀⠀⠀⠀⠀⡾⠟⢻⡀⠀⠀⠀⠀⣿⣾⡆⠐⠀⠀⠀⠀⠈⢳⡤⠚⠁⠀⠀⠀⠐⠻⣬⣻⡃
⠀⠀⠛⠛⠛⠂⠀⠀⠀⠀⠀⠥⠀⠈⠁⠀⠀⠀⠀⠻⠛⠃⠀⠀⠀⠀⠀⠀⠈⠀⠛⠀⠀⠀⠀⠀⠀⠘⠛⠛

⠀⠀⠀⣤⣦⡄⠀⠀⠀⠀⠀⠀⡶⠄⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⣦⡆
⠀⠀⠀⡁⠠⠁⠀⠀⠀⠀⢠⡀⣴⠄⡤⠀⠀⠀⠀⢈⣭⡅⣿⡆⠀⠀⠀⢈⣿⣥⡾⠁⠀⠀⠀⠀⢠⡾⣷
⠀⠀⠾⠿⠼⠻⠆⠀⠀⠀⠀⠻⠿⠟⠁⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⠀⠹⠻⠿⠀⠀⠀⠀⠀⠀⠈⣿⡽

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⣽⠋⠀⠀⠀⠀⠀⢘⣛⣛⠠⠄⠀⠀⠀⠀⢀⣸⣷⡀⠀⠀⠀⠠⣶⣿⣿⣿⣶⠀⠀⠀⠀⠲⢿⢢⡄
⠀⠀⠿⠿⠷⣤⠀⠀⠀⠀⠐⠶⠶⠀⠁⠀⠀⠀⠀⢠⣭⣿⡇⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⢸⠇

⠀⠀⠄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀
⠀⠀⠑⣴⠲⢶⠀⠀⠀⠀⠀⢲⠶⢠⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡃⠀⠀⠀⠀⠀⡹⢏⣹⣇
⠀⠀⠀⢹⣷⣌⠁⠀⠀⠀⢰⣿⡿⠿⠁⠀⠀⠀⠈⠻⢷⡦⠈⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠘⣷⣾⣿⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠿⠛⠛⠛⠛⠛⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⡟⠁⠈⠉⠛⠛⠻⠿⠿⠿⢷⣦⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣾⠇⠀⠀⠀⠀⠀⠀⣾⡷⠷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣠⣾⣦⣠⣴⣾⡿⠀⠀⠸⣿⣶⣤⣀⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⣀⣤⣾⠏⠀⢠⣾⡟⠁⠙⠋⠁⢠⣶⣶⣶⣶⣦⠀⠙⠛⠁⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠻⠿⠿⠿⠿⢛⣿⡁⠀⠀⠀⣹⣿⠀⠀⠀⢀⣾⡏⠀⢀⣿⠇⠀⠀⠀⠀⢸⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠟⠻⣷⣄⡀⣠⣶⠿⠛⢿⣄⣀⣠⣿⠃⠀⠀⠀⣼⡿⠀⠀⣼⣟⣀⣀⣀⡀⠀⠀⢻⣷⣀
⠀⠀⠀⢀⣤⣶⡾⠿⠟⠛⠛⢿⣦⣄⣀⣽⣿⣿⣅⣀⣴⡿⠛⠛⠛⠿⠷⣶⣤⣠⣿⠃⠀⠀⠉⠉⢉⣿⡟⠁⠀⠀⠈⠛⢻
⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⣿⣍⠀⢈⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⢿⣷⠀⣠⣿⠋⠀⠀⠀⠀⢀⣠⣼
⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣷⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣏⣼⠟⠁⠀⠀⠀⠀⠀⣼⡟⠉
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⢰⣿⡁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣄⡀⢀⣿⠟
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢰⣶⠿⠛⠛⢿⠟⠁
⣿⣇⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣿⣅⣄⣤⣤⣄⣿⣧⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣿⣷⣶⣾⡇
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⡰⣚⠉⠙⠲⡄⠀⠀⠀⠀⠀⢠⠴⢒⣹⢦⠀⠀⠀⠀⠀⢠⢖⠋⠉⠙⠢⡀⠀⠀⠀⠀⠀⣰⢋⢻⡆
⠀⠰⡷⡁⠀⠀⠀⣻⠀⠀⠀⠀⠀⢼⣋⡭⠴⢺⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⢳⡁⠀⠀⣰⠃⠀⠀⠀⠀⠀⠺⡥⢰⠛⠇⠀⠀⠀⠀⠀⢣⡃⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠿⠠⢸⡇
⠀⠀⠀⢧⣤⣤⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠙⣦⣤⡴⠋⠀⠀⠀⠀⠀⠀⠻⣿⣿⠇
⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠴⢲⡗⢻⡔⠦⠀⠀⠀⠀⠰⡍⢑⣂⠄⡀⠀⠀⠀⠀⠀⡟⣷⣿⠟⣿⣾⣿⠀⠀⠀⠀⠀⠸⣧⡾⠇
⠀⠾⠇⣾⠀⠘⡶⠸⠷⠀⠀⠀⠀⢰⣿⡍⢵⣵⣆⠀⠀⠀⠀⣇⣿⡏⠀⢛⣿⣿⠀⠀⠀⠀⠀⠡⡀⣠⠃
⠀⢻⠇⢿⣏⡼⠿⢼⡟⠀⠀⠀⠀⠘⣿⣿⣮⣙⢫⠀⠀⠀⠀⠹⣿⣿⣇⣾⣿⠃⠀⠀⠀⣠⡄⣾⣦⣾⡇⢠⡄
⠀⠀⠛⠜⠯⠿⠣⠋⠀⠀⠀⠀⠀⠼⠿⠿⠟⠙⠨⢦⡀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⢿⡇⠉⠉⠉⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣀⣀⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⢀⡤⠤⠤⢄⡀
⠀⣿⣿⣿⢀⠀⣀⣸⡇⠀⠀⠀⠀⢸⣥⣶⣬⡇⠀⢀⠀⠀⠀⠀⣿⠋⠉⢹⣿⠀⠀⠀⠀⡴⠁⠀⢄⡀⠀⠙⣆
⠏⣿⣿⣿⢸⡏⢩⢹⡇⠀⠀⠀⠀⣿⣽⣭⣯⡇⢸⣿⠀⠀⠀⠀⣿⡷⠶⢾⣿⠀⠀⠀⠀⡇⠀⢱⣾⣿⡂⠀⢸
⠀⣿⣿⣿⠸⠗⠺⢸⡇⠀⠀⠀⠀⠘⠻⢿⠟⠃⠀⢾⠀⠀⠀⠀⣿⣄⣀⣸⣿⠀⠀⠀⠀⠳⡀⠀⠉⠉⡣⣠⠏
⠀⠉⠁⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠻⠦⠤⠾⠊⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠈⠓⠒⠚⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣄
⠀⠀⢀⣀⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠘⣿⠇⠀⠀⠀⡇⠀⢰⠀⠀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⢸⣉⢀⡙⠛⠃⣀⠀⠀⠀⠀⠀⠀⢠⣟⡀⠀⣸⡷⣖⠀⠀⠀⣇⠀⠸⠀⠀⡇⠀⠀⢠⡖⠚⠇⠒⠒⠹⠐⢢
⢀⣀⣈⣙⣿⣷⣦⣯⣬⣧⣀⠀⠀⠀⡞⠉⢷⢰⡏⠀⢹⡇⠀⢀⣿⠀⣹⡇⢰⣿⠀⠀⢸⡿⣛⣿⣿⣿⡿⣛⢿
⠸⢿⡟⣿⠿⠿⠿⠿⢿⢛⡿⠇⠀⠀⡇⠀⢸⠈⡇⠀⢸⡇⠀⢸⣿⠀⣿⡇⢸⣿⠀⠀⢰⣶⣭⣾⣿⣿⣷⣭⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣴⣿⣿⣦⣤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣡⣦⡝⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠁⠀⠀⠉⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣰⣿⣿⣿⣌⢷⡀⠀⠀⠀⠀⠀⢠⣶⣿⠇⠀⠀⠀⠀⠀⠀⢻⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⣿⣿⣿⣿⣿⣎⢿⡄⠀⠀⠀⢀⣈⢰⢰⡆⡆⣀⡀⠀⠀⢀⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢏⣾⣿⡟⣩⣭⡍⣹⣿⣆⢻⣆⢀⣴⣿⣿⢸⣾⣷⡇⣿⣿⣦⡰⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢣⣾⣿⣿⢃⣿⡿⢱⣿⣿⣿⣧⠁⠾⠿⠿⠿⠸⠿⠿⠇⠿⠿⠿⠷⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣡⣿⣿⣿⡟⢸⣿⣷⣶⢂⣾⣿⣇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣰⣿⣿⣿⣿⣿⣶⡆⡾⢣⣿⣿⣿⣿⡔⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⣿⣿⣿⣿⣿⣿⣿⠙⣡⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣾⣿⣿⣿⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠙⠿⢿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⣿⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢠⣦⢰⡆⢿⣿⣿⣿⣿⠇⣶⢰⣦⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢸⣿⢸⣿⣮⣛⠛⢛⣫⣾⣿⢸⣿⢸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣌⣉⣉⣉⣉⣉⣉⣉⣉⣼⣿⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⣹⠋⠀⠀⠀⠙⣯⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣸⠃⠀⠀⠀⠀⠀⠘⣇⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡷⠶⠒⠛⠛⠛⠒⠶⢾⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠟⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠻⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠻⣇⠀⢀⣴⠞⠋⠉⠉⠉⠙⠳⢦⡀⠀⣨⠟⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠋⠛⠛⠉⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠘⠷⢤⣤⣤⠾⠃⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⣄⣀⠀⠀⠀⣀⣠⠾⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⢾⣇⠀⠀⠉⠉⠛⠋⠉⠀⠀⣨⡷⠦⣤⡴⠖⠒⢦⠀⠀⢀⡞⠉⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠋⢻⡁⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⢀⣤⠞⠁⠀⠀⢾⡀⠀⠀⠈⠷⠶⠞⠁⠀⠀⢠⡏
⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⠙⢦⣤⡴⠋⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠴⠚⠳⣆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡼⠋⠙⠓⠋⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣼⣇⠀⠀⠀⠀⠀⢀⡾⠉⠀⡾⠁⠀⠀⣠⣄⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⢠⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢲⡄⠀⠀⢸⡇⠀⠀⢷⣄⣀⣴⠃⢹⡄⠀⠀⢸⣆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠈⣷⠀⠀⠀⠈⠉⠀⠀⣸⠃⠀⠀⠀⠈⠙⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣻⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⣰⠞⠁⠀⠀⢀⣤⣤⡤⠞⠃⠀⠀⣀⡀⠀⢀⡿
⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣿⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣦⣀⣴⠟⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡴⠋⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡴⠋⠀⢀⣀⣀⣀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⢀⡴⣏⠀⠀⠀⣼⠉⠀⠹⣆⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⡴⠋⠀⠈⠙⠓⠛⠁⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢀⠢
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠁⢰⠀⠙⠀⠀⠀⠀⠀⠀⠀⠠⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣱⠀⠀⡆
⠀⠐⠀⠐⠀⠰⠀⠀⠀⠀⠀⡀⢫⡀⡅⢤⠼⣀⠀⠀⠀⠀⠀⠀⠀⠄⠺⡬⠒⠀⠀⠀⠀⠀⠀⠀⠀⠷⠺⠂⢀⣇
⠀⢀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠇⠤⠅⠤⠤⠤⣀⠰⠀⠀⠀⠀⠘⠀⠁⠀⡇⠀⠁⠐⠂⠀⠀⠀⠀⠸⡀⠀⠇⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠊

⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⡴⠉⠀⠈⠐⡀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠄⢡⠀⠀⠀⠀⠀⠀⠈⠀⠠⠢⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⠓⢃⠀⡇⢀
⠀⡄⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣅⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⡀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠣⠘
⠀⢘⠦⠤⠴⣺⠀⠀⠀⠀⠀⠀⠀⢊⠅⠍⠅⡁⡄⠀⠀⠀⠀⠀⠐⠄⠭⠬⠅⠄⠀⠀⠀⠀⠀⠀⠀⢖⡀⠃⠀⠀⠉
⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠥⠬⠤⠥⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⢀⠤⠄⠀⠀⠤⠄⠀⠀⠀⠀⠀⢰⢱⠠⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠐⡀⠀⠀⠀⠀⢀⠄⣴⠁⠀⠈
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⡀⠀⠈⠀⠀⠀⠀⠀⠠⠠⠑⠤⠶⠰⠀⠈⠀⠀⠀⠀⠀⣸⡀⣿⠔⠀⠀⠒
⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠐⠄⠂⠀⠀⠀⠀⠀⠔⠀⠅⠆⣜⣁⣘⣀⣀⡀⠀⠀⠈⠈⠀⢹
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠒⠒⠘⠀⠀⠀⠀⠀⠊⠰⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⡇⠂⠓

⠀⠀⣠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣾⣫⡿⠀⠀⠀⠀⠀⠀⠀⠄⠐⠐⠂⠃⠲⠀⡀⠀⠀⠀⠀⠤⢨⡥⠥⣩⡢⠄⠀⠀⠀⠀⠀⡠⠤⠀⠀⠶⠀⠆
⠀⠀⡷⠼⠵⡆⠀⠀⠀⠀⠀⠠⠀⠈⠘⣀⠓⠘⠀⠀⠀⠀⠀⠀⠚⠐⠎⣛⠶⠘⠂⠀⠀⠀⠀⠔⡑⠄⠀⠀⠀⠉
⠀⠀⠠⡀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠉⠹⠆⢀⠀⠀⠀⠀⢳⢶⠃
⣶⣶⠶⠿⠷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢡⠏⠀⠀⠀⠈⢧⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⡟⠀⠀⠀⠀⠀⠈⣇⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣇⣠⣤⠤⢤⣤⣀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡴⠋⠉⠀⠀⠀⠀⠀⠀⠉⠳⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣏⠀⢀⡤⠖⠛⠛⠛⠓⠦⣄⠀⠀⡿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠉⠛⠛⠛⠛⠃⠀⠀⠛⠛⠛⠛⠛⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠈⠓⠒⠒⠋⠁⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠙⠲⠦⠤⠤⠶⠚⠉⢳⣀⠀⢀⣀⣄⡀⠀⠀⢠⠴⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⡞⠋⠉⠙⠳⣄⠀⠀⠀⠀⠀⢀⡴⠋⠉⢹⡏⠁⠀⠻⣄⣤⡟⠀⠀⢀⡇
⠀⠀⠀⠀⠀⡴⠚⠉⠀⠀⠀⢷⠀⠀⠀⠀⠈⠙⢦⣀⣠⠞⠉⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡤⠶⣄
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡴⠛⠒⠾⠁⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⠁⠀⠀⠘⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⡤⣤⣤⠤⢤⠤⡼⡤⠤⣼⡇⠀⠀⠀⠀⢀⡞⠁⢠⠏⠀⠀⣠⣄⠀⠀⠀⡴⠚⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣆⠀⠀⢸⡇⠀⠘⢧⣤⡴⠃⢸⡄⠀⠀⢧⣀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠀⠀⢀⡿⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢠⠞⠉⠀⠀⣠⠖⠒⠚⠋⠀⠀⣠⠦⣤⣤⠟
⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢳⡾⠋⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣾⠁⠀⠀⡞⠛⠻⡄⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⣠⠞⠃⠘⠲⠶⠞⠁⠀⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⣢⣶⣜⣷⣦⡀⣀⣀⠀⠀⠀⢀⣤⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠿⠋⠉⠉⠛⠛⠃⡾⠭⢭⣽⣛⣋⢿⣿⣿⣿⣷⣿⣿⣿⠏⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢣⣿⣿⣿⣷⠀⠈⢉⣿⠛⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⣛⡛⠛⠁⠀⣀⣼⣿⠀⠀⠙⢿⣿⣷⣶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⡺⠿⠟⠋⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢸⣷⣿⣼⣻⣽⡇⠀⠀⠀⣰⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣾⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⣿⣿⣿⣿⣿⣿⠀⢀⣼⣿⡟⣾⢧⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢐⣳⡾⠯⣭⣭⡏⢀⣾⣿⡿⣼⣯⣬⣭⣭⣹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⣾⣶⢘⣿⠿⢟⡝⣶⡆⣾⣿⣿⣷⣶⣶⣆⣿⢣⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⣦⢭⣭⢸⡇⣿⣷⡻⣿⣿⣿⣿⢛⣼⡏⣛⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡝⢷⣾⣿⣿⣷⡽⣿⣿⣿⣧⣫⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣿⡿⠁⠀⠙⠿⠿⣿⣿⡙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠈⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⡿⠿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⣿⠋⠀⠀⠀⢻⣯⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⢸⡟⠀⠀⠀⠀⠈⣿⡆⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⣾⡿⠿⠿⠿⠿⠿⣿⣧⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠟⠁⣀⣤⣤⣦⣤⣄⡀⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⢿⣶⣾⣿⣿⡄⠀⣤⣿⣿⣷⣴⠟⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⢀⡀⠀⠀⠀⣀⠀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡘⠻⢷⣶⠾⠟⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡟⠿⢶⣦⣤⣶⡾⠟⣿⣆⣀⣀⣤⣤⡀⠀⢀⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⠟⠛⠻⢷⣤⡀⠀⠀⠀⣠⣴⠿⠛⢿⡟⠉⠙⣿⣤⣾⡏⠀⢈⣿⠂
⠀⠀⠀⠀⣴⡿⠛⠉⠀⠀⢿⡇⠀⠀⠀⠙⠻⣶⣤⡾⠟⠁⣀⡀⢘⣿⡄⠀⠈⠁⠀⠀⠀⠘⢿⣦⣶⠷⣦⡀
⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⢸⣿⠀⢀⣾⠟⠛⠿⠋⠀⣠⣴⣶⣶⠀⠀⠀⠀⠉⠀⠀⣹⡷
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣤⣀⠀⠀⣼⡟⠁⣿⡃⠀⣴⣷⡄⠀⢰⣿⠛⠁
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⡀⠀⢻⣧⠀⠙⠿⠿⠟⢹⣿⠀⠘⠿⢶⣦
⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⣠⡾⠟⠀⢀⣤⣤⣴⡿⠃⢀⣀⡀⢀⣿⠃
⠀⠀⠀⠸⣿⣶⣶⣶⣶⣿⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣤⡾⠛⠁⢀⣴⡿⠋⠉⠁⠀⢠⣾⠟⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⢀⣴⡿⠋⢠⣶⣶⣦⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⢀⣴⡿⢿⣦⣤⡿⠃⠀⠻⢷⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⠿⠋⠀⠀⠀⠉

⠀⢀⣴⣶⣿⣿⣿⣶⣦⡀
⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⣶⣷⣎⢻⣿⣷⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣦⣄
⠹⣷⣶⣶⣴⣿⣿⣿⣿⣿⠟⠛⠿⠿⢿⣿⣿⡿⢁⣛⡛⠻⠿⠸⣿⣿⣿⡌⣿⣿⣿⣷⣶⣶⣦⣤⣾⣿⣿⣿⣿⡿⠻⠿⠿⣷⡀
⠀⠈⠛⠿⢿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⣍⢛⣛⣛⠳⠶⠶⠮⢤⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣾⣿⣿⣿⣿⣿⡇⠀⠀⠉⠉⣉⣛⠛⠻⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢸⣿⡟⠀⠀⠘⢿⣿⣿⣿⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⡀⣰⣮⡭⠉⠀⠀⢀⣀⣤⣴⣾⣿⡇⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⣧⢹⣿⣿⣷⢠⢻⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡛⠻⠿⢇⣿⡸⣿⣿⡿⢸⡇⠉⠀⠀⠀⠀⠀⢠⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⣸⣿⣿⣿⣷⣦⣥⣶⣿⡇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⡟⣛⣛⠛⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣾⣿⣿⡿⢱⣿⡏⣼⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⣶⣮⣭⣭⣍⣛⣛⠛⠿⠇⠀⢀⣾⣿⣿⣿⢃⣿⣿⣐⣛⣛⣛⡛⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⠻⢰⣶⣶⣬⣭⣭⣙⣛⡛⠿⠀⢠⣿⣿⣿⣿⠏⠾⠿⠿⠿⠿⣿⣿⠇⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠶⣦⡄⣾⣿⣿⡌⠛⠿⠿⠿⡏⣤⠉⣿⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⡟⣼⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣁⢛⣛⣛⠷⢠⣿⢰⣿⣿⣌⢿⣿⣿⣿⣿⣿⣿⡿⠿⢃⣿⡿⠱⢿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⡙⢿⣿⠸⠿⢸⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⣷⡰⣾⣿⠗⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⠙⢿⣿⣿⣿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣷⣈⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣛⣻⣿⣿⠏⠀⠀⠙⢿⣿⣿⣿⣿⣿⣧⠹⠿⢿⠿⠿⠿⡿⢿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠉⣉⣉⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢰⣮⣝⡛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⣶⣶⣶⣿⡆
⣶⣶⣶⢶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣧⣤⣤⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢍⠙⡶⠊⣀⡤⠬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣶⣿⣷⡟⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⠉⠘⢶⣟⣺⣿⢦⣴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⢉⣿⠞⣹⠮⠿⠟⠂⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⣠⢽⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⣷⠞⢉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠖⠻⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠌⣿⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠺⠻⠿⣯⣟⢻⣿⣾⣿⣤⣊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠘⠛⠽⣿⢿⣽⣗⣖⣠⢄⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣄⣀⣀⣀⣀⣀⣰⣧⣤⣿⣥⣤⣭⣭⣋⣉⣀⣀⣰⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣝⣛⣩⣛⣻⣟⣽⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠠⢤⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⣰⢰⣶⠀⠀⠀⠀⠒⠂⠀⢤⠀⠀⠐⠂⠀⠀⠀⠐⠀⠈⠉⠡⠈⠉⢠⡴⠶⠿⡀
⠀⠀⠀⠀⠀⠀⣿⣉⠇⠠⠤⠀⠐⠀⠲⠀⠈⠉⠂⠀⡀⠀⠄⠀⠃⠀⠈⠀⠀⠀⢀⣈⣤⡴⠖⠃
⠀⠀⠀⠀⠀⠀⢎⣿⠗⠸⡆⢀⡆⠀⠰⠀⠄⠀⠀⠰⠶⠀⠄⢐⣀⣠⠔⠲⠚⠋⠉⠀⠘⠃⠀⡀
⠀⠀⠠⠀⠀⠀⠈⠙⣾⣷⡀⡈⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⢛⡉⠹⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⡄⣲⡀⠄⢐⣒⡉⠙⠛⣏⠸⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠀⣳⡋⠉
⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣿⣿⢿⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⣿⣿⠿⣿⣷⡿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣾⣿⣿⣿⣿⣟⡉⠙⢛⠭⣈⢻⣷⢈⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⣿⣿⣿⡿⠉⠀⠀⠉⢹⣿⢯⠟⡽⠛⠉⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⢺⣿⣀⠀⣤⣖⣂⠀⠀⣿⣼⣼⠁⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠘⠛⠋⠉⢠⣿⣿⣿⣷⣿⣷⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣠⠶⠀⠀⠀⠸⠿⢻⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢳⢆⠀⠀⠀⠀⢀⣼⢿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠀⣀⣤⣶⣿⠃⢘⡿⠟⠋⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⡿⠒⢉⡤⢖⣴⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡿⠛⠛⠁⢀⢰⣃⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣎⢿⠀⣠⠔⢁⣾⣽⣿⣿⣿⣏⣩⣷⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⡏⣿⠧⠤⣽⣿⣿⣿⡿⣿⠟⠛⠉⠻⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣻⣿⣿⣿⣴⣪⣾⣿⣿⣿⣿⢋⠀⠁⠀⠈⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢹⡿⠑⣿⣿⡿⢃⠞⣹⣿⠟⣿⠟⠁⠃⠀⠀⠀⣀⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⢀⡿⠋⠀⠔⣰⠟⠃⠀⠉⠀⠀⠀⠀⠀⠈⠉⠉⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢦⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠶⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢄⣀⡈⠙⠛⠛⠛⠋⠉⣁⣀⣀⡴⠶⠛⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠲⠗⠀⢸⠀⠀⠉⠁⠀⠛⠚⠛⠛⠫⣤⣍⢡⡀⠀⠀⢸⡇⠀⡀⢨⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢀⡀⠶⢾⡀⢶⣿⣟⡄⢱⠄⠀⡎⣿⣶⡞⢀⠙⠀⣰⠚⠓⠐⡇⢸⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣤⠛⢛⠀⢶⣽⣿⣧⠴⠂⠀⢷⣈⣿⣣⣼⠶⠀⠙⢳⡶⠺⣷⠸⠁⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⢸⠀⠀⠁⢀⡤⠀⠠⣄⠀⠉⠀⠉⠀⡀⠀⠀⢸⡇⠀⠘⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣤⠶⣍⠀⠀⢀⣼⠂⠀⠀⣠⡾⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⣄⠀⢀⣷⠴⠛⠁⣀⣠⠾⠋⠀⡃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠉⠛⠿⣥⠤⠚⠟⠋⠉⠀⠀⣿⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠿⢧⡀⠀⠀⠀⠈⠢⣄⠀⡀⠀⢂⣴⠏⠀⠀⣠⡾⠉⠉⠀⠀⠉⣩⡟⠛⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠋⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠙⠛⠚⠛⠁⣴⣿⠶⠛⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⡴⠷⢦⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢀⡴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⣴⠶⠒⠶⢾⣧
⠀⠀⠀⠀⢰⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡞⠁⠀⠀⠀⠀⠙⣧
⠀⠀⠀⢠⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠘⠷⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠂⠛⡈⢳⠀⠀⣿⠀⠀⣿⡀⠀⠀⠀⣀⣀⣤⣴⡶⠿
⠀⠀⠀⠀⠀⠀⡏⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠦⣤⠀⣄⠀⣀⠁⢸⠀⠀⣿⠀⠀⠉⠛⠛⣿⡟⠛⠉⢹⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠈⢻⠛⢿⡷⠶⠶⢦⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠉⠀⠀⣿⡀⠀⠀⠀⢀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠘⣷⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠳⠶⠶⠶⣶⣤⣤⣤⣀⣀⣽⣇⣠⡶⠞⠋⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠃⠀⠀⣿⠀⠀⠙⠛⠶⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⠉⠁⢀⣠⣾⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣠⣾⣦⣤⣤⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠿⠿⠶⢶⣶⣦⣤⣤⣤⣄⣀⣀⠀⠀⣘⣠⣴⠿⠋⠀⣿⠀⠀⠀⣾⡇
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠄⣀⣀⣀⣀⣀⣉⣉⡿⠟⠛⣿⡟⠛⠋⠀⠀⠀⢀⣿⣄⣀⣀⣽⣇
⠀⠀⠀⠘⣧⣀⣀⣀⠀⢀⣾⠀⢀⣀⣠⣤⡤⣾⡇⠀⠀⠀⠤⠀⢉⡉⠉⠉⣉⣉⣤⡴⠛⣿⣇⠀⠀⠀⠀⠀⡏⠁⠉⠉⠉⠉⠙⣷
⠀⠀⠀⠀⠈⣿⠋⠉⣿⠋⠁⠀⣾⢿⡄⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣤⡴⠚⣿⠋⠉⠛⣻⣶⣶⢃⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⡟⠀⠻⣦⠀⠀⠻⢶⣤⣀⣀⠉⠁⠀⠀⠙⠋⣉⣀⣴⠾⢋⣠⡶⠟⠁⠀⡟⠘⣷⠶⠶⠶⣶⠿⠃
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⣷⡀⠀⠘⢳⣄⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⣉⣡⡶⠛⠁⠀⠀⠀⣀⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡯⠀⠀⣟⠀⠀⠀⠙⣷⡄⠀⠀⠙⣷⠶⠶⠿⠟⠛⠛⠚⠛⠛⠛⢿⡏⠁⠀⠀⠀⢀⣠⣶⠟⠁⠀⣿⠀⠀⢨⣿
⠀⠀⠀⠀⣰⡷⠶⢶⣏⠀⠀⠀⠀⠈⠻⣦⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⢀⣠⣶⣿⡏⠀⠀⠀⠀⣿⠀⠀⢸⡟
⠀⠀⢀⡾⠁⠀⠀⠀⠙⡿⣆⡀⠀⠀⠀⣿⠻⣾⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣧⣾⠟⠋⠀⣿⡇⠀⠀⠀⠐⣿⣤⣤⡾⢷⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⣰⡟⠀⠀⠀⠀⠀⠀⣇⢸⣧⠀⠀⠀⣿⠀⠈⠉⢹⣟⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠀⠀⠀⠀⣿⠁⠀⠀⠀⢰⠋⠳⢦⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⣩⡿⣦
⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣻⡀⢀⣿⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⢦⣀⠀⠀⠙⠛⠶⣄⣀⡰⠶⠛⠋⠀⣠⣿⣀⣀
⡿⠒⠦⢤⣤⣤⣀⣸⡀⣿⠿⠾⣿⠇⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡽⠳⣤⣀⠀⠀⣼⠋⣀⣀⣤⠞⠻⣯⣤⣩⡽
⠘⢧⡄⠀⠀⠀⠀⠉⣻⣿⣤⠾⠁⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢰⣯⡀⢠⡞⠛⠳⢾⢿⡖⠉⠉⢳⣤⣤⢾⠇⣏
⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⣀⣼⣏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⢸⡇⢹⡇⠀⠀⠀⠀⠀⠙⣶⡶⢾⡏⠀⢸⠄⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠿⢷⣶⣿⣧⠀⠀⠀⠀⠀⠀⢰⡿⠿⣶⣶⣶⣶⡿⢿⣷⠀⠀⠀⠸⣧⣄⣳⠀⠀⠀⠀⠀⢰⠏⠀⢸⡧⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠿⣤⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⢷⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠿⠿⢿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠛⠿⠷⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣿⡁
⠀⠀⠀⠀⠀⣀⣠⠶⠞⠛⠁⠀⠀⠀⠀⢀⣴⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣏⠉⠉⠉⠛⠶⢦⣀⡀
⠀⢀⣤⣾⣛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣤⡀⠀⠀⠀⠉⠙⠛⢦⣄⣀
⠀⣼⠋⠉⠉⠙⠛⠶⠶⠶⣤⣤⡶⠋⠁⢀⣴⡟⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣄⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠈⠉⣷⣦⡀
⠀⢿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠇⢀⣴⠟⠉⣥⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⡷⣦⡀⠀⠉⢻⡶⠶⠚⠛⠛⠛⠁⢹⡃
⠀⠀⣹⠉⠹⠛⡿⢳⡶⣤⣤⣴⡿⢻⠅⠀⢀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣶⣾⠃⠈⠻⣦⣄⣸⡇⠀⣀⣀⣀⣀⣠⣼⠇
⠀⠀⠹⣄⣼⡄⠁⣼⡀⠠⡄⠀⢀⣼⠷⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠃⣴⠏⠛⠛⠿⠙⡟⢛⠙⡏⢹
⠀⠀⠀⠀⠀⠙⠶⠜⠛⠶⠼⠷⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠹⣆⠀⢀⣸⣠⣷⣀⣶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡾⡧⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡷⣥⡀
⠀⠙⠋⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣽⣯⡧⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠠⡷⠷⢚⠆⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣟⠐⠀⠀⠀⣀⠀⠀⠀⣴⣖⣉⡁
⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡷⡿⠉⠀⠠⠤⠴⠦⠄⠀⠗⡆⣖⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠤⠰⠀⠀⠀⢛⣻⣿⠒⠒⠒⠒⠶⠒⠂⠈⢷⡥⢶⠛
⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡤⠄⠀⠀⢀⠀⠀⠀⡼⠓⢘⡆⠀⠀⠀⣶⣾⠄⠼⢾⡗⢀⣸⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠨⠇⠀⠀⠈⢉⠀⠀⠰⠛⠃⡠⠷⠀⠀⠀⣟⠻⠀⡈⢿⡅⠸⠁⣇
⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠘⢶⡀⠀⠀⢀⡤⢾⠭⣧⢀⠀⣂⣀⡀⡰⠛⢠⣤⣼⣉⢛⣿⢻⠄⠀⢀⡇⠀⣧⠁⡞⣇⠐⡟⣿⠒
⠀⠀⠀⡇⠀⣼⣠⣸⣧⣷⣶⣶⣿⢶⠶⠿⠿⢷⣛⣛⣛⡙⠯⠭⢿⣷⢰⣾⠿⠻⣿⡿⣿⡟⣷⣾⣿⣴⣦⣻⣶⣯⣿⣅⣿⣿⣷⡆
⠀⠀⣠⣧⣸⡭⣟⣹⣿⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠛⠓⠦⠬⢭⣍⣀⣚⠛⠾⠿⢿⣷⣿⣿⣿⣿⠍⣿⣿⣿⣷⡽⠿⣷⠃
⠀⢠⠤⣗⣨⠶⣫⠽⠋⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⢠⡀⠀⠀⠀⠀⠉⠉⠙⠓⠒⢶⣤⣤⣥⣉⡛⠺⠿⠿⣿⣿⣷⣶⣾
⠀⠀⢘⣩⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢯⣷⣦⣤⣄⡉⠁
⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣴⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⠀⠈⠉⢉⠉⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣀⣈⠉⠉⠉⠉⠙⠛⠛⠛⡉⢉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠆⠛⠂⠄⠠⠄⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣤⡀⠀⠀⠠⡀⢰⣤⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠀⠀⢀⣶⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⣾⣿⡿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠏
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⠉⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠢⠀⠀⠁⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠶⠀⢀⠀⠶⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠐⠂⠀⠀⠠⠀⠉⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠃⠀⠀⠀⣀⢠⠀⠀⠶⢤⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠁⠀⠂⠀⠀⠒⠐⠈⠀⠀⣠⠔⠀⠀⠀⠀⠱⣀⡧⠴⣁⠴⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⣤⣄⣀⣠⣤⡤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⣖⣋⠨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠒⠈⡋⠈⠉⠁⠈⠓⠈⡶⠠⢄⠀⠀⠀⠀⠀⠀⢀⡕⢤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠋⢠⠃⠀⠀⠙⠲⠤⠤⠤⠴⠊⠁⠀⠀⢻⠐⢄⣀⡠⡔⢋⡠⠃
⠀⠀⠀⠀⠀⠀⡠⠚⣀⣤⠀⡎⠀⣴⣿⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣇⡀⠴⠊⠁
⠀⠀⠀⠀⠀⣘⢁⠖⠁⠈⢳⠁⠀⠙⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠁
⠀⠀⠀⢀⠴⠣⢿⠀⠀⠀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⡠⠤⡇⠀⠀⢀⡇⠀⠀⡇⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡆
⠫⡤⠊⡽⠲⠶⢮⠙⣆⠀⠈⢑⠒⠤⠤⢀⣀⣀⠂⠀⠀⣀⣀⡀⢬⠴⠚⠁
⠀⠉⠲⠆⢨⠇⠀⠉⠁⠀⠀⢀⢒⡁⠒⢄⠀⠀⠀⢀⠔⠋⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣱⣤⠂⡀⠀⣇⣔⠁⠈⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠒⠒⢎⠀⠀⠀⠀⠀⢨⠗⠒⠚⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣶⡶⡎⠀⠀⠀⠀⠀⢘⡶⣶⡶⡏
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠰⠴⠣⠄⠤⢱⡀⠀⠀⠀⠀⣸⡡⠤⠤⠣⠤⠤⢄
⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠐⠈⠠⠀⠀⠙⢆⠀⢀⠞⠁⠀⠀⠈⠄⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⣏⣩⣉⣹⣉⣹⣉⣩⣉⣹⣹⠀⢸⣸⣁⣋⣈⣛⣀⣙⣈⣋⣘⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣠⢞⡥⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⡖⢋⣩⡼⠷⡄⠀⠀⠀⠀⠀⠀⢠⢞⡭⠂⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⡞⢡⠘⣿⡆
⠀⠀⠀⠀⣏⢸⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣼⠛⣉⣥⠴⠾⡇⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⡇
⠀⠀⠀⠀⠹⣌⠆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢼⣋⠉⣤⠶⡟⠁⠀⠀⠀⠀⠀⠀⣧⢣⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡧⢸⠀⣿⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣤⣿⣤⣧⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⣯⣼⣤⣿⡇
⠀⠀⠀⠀⠀⠈⣳⣶⣶⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠐⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿

⠀⠀⠀⠀⠀⣀⢀⣤⢠⣄⢀⡀⠀⠀⠀⠀⠀⠀⢠⠖⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⣤⣶⣤⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⣰⣞⠛⣶⡀
⠀⠀⠀⢀⣘⠋⢾⡏⠉⡽⠎⢛⣀⠀⠀⠀⠀⠀⠙⠦⣀⣬⣬⡃⣤⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⡿⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡙⠿⠾⠏⡁
⠀⠀⠀⠾⠿⠸⡿⠀⠀⢛⡿⠸⠿⠆⠀⠀⠀⠀⠀⢠⣿⣿⡸⢞⣵⢟⣀⠀⠀⠀⠀⠀⣧⣿⣿⡇⠀⠘⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡸⠁
⠀⠀⠀⢶⣶⠰⣿⡶⢠⣾⡷⢰⣶⠆⠀⠀⠀⠀⠀⠘⣿⣿⣧⣌⠡⠿⡋⠀⠀⠀⠀⠀⠹⣿⣿⣷⡗⣰⣿⣿⠇⠀⠀⠀⠀⠀⣠⠀⣾⣮⣩⣶⡆⢠⡀
⠀⠀⠀⠈⢩⣄⢶⣷⢻⣶⢆⣬⠉⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢻⡂⢯⡀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⠀⠿⠿⠿⠿⠇⢸⣿
⠀⠀⠀⠀⠀⠈⠀⠛⠘⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠑⠻⢦⡀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⣀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡀
⠀⠀⠀⣿⣿⣷⣿⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⢸⠟⢉⣉⠛⣿⠀⢠⢀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠻⣿⣿⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠳⣄
⠀⢀⡄⣿⣿⣿⣿⢰⣀⣠⣶⢾⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⣴⣴⠀⠀⠀⠀⠀⣿⣿⡈⠀⢁⣿⣿⠀⠀⠀⠀⠀⡞⠀⢠⡀⢙⣶⣄⠀⠀⠸⡆
⠀⠘⠇⣿⣿⣿⣿⢸⣿⠶⠶⢸⣿⠀⠀⠀⠀⠀⠀⣿⣶⣷⣾⣷⣿⠀⢿⢿⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⣿⠀⠀⢀⡇
⠀⠀⠀⣿⣿⣿⣿⠸⣿⠛⢻⢸⣿⠀⠀⠀⠀⠀⠀⠙⠿⣿⢿⠿⠟⠀⢸⢸⠄⠀⠀⠀⠀⣿⣿⣈⣠⣀⣿⣿⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠉⡇⢀⡼⠁
⠀⠀⠀⠛⠋⠩⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣄⣀⣠⣎⡞⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣤⠼⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄⠀⠀⠀⠀⢼⠄
⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⢫⣻⠇⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⢀⠰⠚⠋⠁⠸⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠀⠀⠀⣾⣭⣶⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣤⡤⢸⠩⣭⣭⡭⢻⠠⣤⡀
⠀⠀⠀⠉⠛⠗⣶⣶⣤⣀⡀⡶⠒⢦⠀⠀⠀⠀⠀⠀⢨⡿⢿⡅⠀⣴⡟⠉⢻⣆⠀⠀⠀⣶⡆⠀⢬⡥⠀⢠⣥⠀⠀⠀⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡆
⠀⠀⢠⣶⣶⣴⣬⣿⣿⣿⣿⣿⣾⣿⣷⣦⣄⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⣾⣧⠀⢸⣷⠀⠀⠀⠿⠟⣵⡎⠿⠿⠿⠿⠏⣶⠹⠿⠃
⠀⠀⠘⠿⣟⢙⡿⠿⠿⠿⠿⠿⢿⡟⢙⡿⠿⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⡟⠀⠀⠀⣿⡇⠀⣿⣿⠀⢸⣿⠀⠀⠀⢸⣿⣮⣴⣿⣿⣿⣿⣷⣭⣾⣿
⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠉⠀⠀⠉⠀⠉⠀⠀⠀⠃⠀⠀⠀⠙⠁⠀⠙⠋⠀⠈⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⣉⣀⠀⠀⣈⣉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡟⡄⢎⢸⣉⠆⢸⠰⣉⡇⡜⡕⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠵⢧⡬⠭⠭⠤⠤⠭⠭⣤⠵⠵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠋⠙⠛⠛⠛⠛⠛⠛⠉⠋⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡇⠀⡖⢲⠓⡖⢲⠒⡖⢲⡖⢲⠀⣿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡙⣌⢲⡇⠀⠓⠛⠒⠓⣚⡒⠛⠚⠓⠋⠀⣷⢊⡼⣱⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣉⣉⡉⠙⣦⣑⡬⠛⡇⠀⠀⠀⠀⠘⠧⠟⠀⠀⠀⠀⠀⡟⠫⣔⣡⡞⠋⣉⣉⣱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡆⢸⠋⠀⠀⡇⢠⡴⠧⣄⣠⠜⢤⡀⡤⠷⣤⠀⡇⠀⠈⢻⠀⡎⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡜⠀⠀⠀⡇⠀⠷⠾⠅⠸⠶⠾⠀⠹⠶⠇⠀⡇⠀⠀⠘⢤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡏⠭⢭⡏⠉⠉⣯⠭⠭⣽⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣗⣒⣒⡇⠀⠀⣗⣒⣒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡧⠤⠴⡇⠀⠀⡷⠤⠤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡯⠭⢭⡇⠀⠀⣯⠭⠭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣓⣒⣒⣇⡀⣀⣗⣒⣒⣻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠃⠓⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⣦⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⣼⡗⡜⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢳⢷⠋⣤⡴⣦⣛⣒⣒⣛⣛⣟⣛⢛⡷
⠀⠀⠀⠀⣀⣠⣤⠶⠖⡛⡵⣡⣦⡸⣯⣽⣿⣭⣴⠋⣥⣻⣾⣿⠟⠁
⠀⠀⠰⣟⡉⡵⣢⣉⣹⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢟⣹⣿⣿⠋
⠀⠀⠀⠈⠙⠶⣕⡿⣯⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢸⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠾⣵⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡒⠒⠒⠲⠶⣶⠤⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢻⣻⣿⣿⣿⠿⣟⠟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⣩⣝⡛⠷⣦⣄⠀⠙⠪⡑⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⡵⠿⠿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⣿⣿⣿⣷⣿⣿⣿⣷⣄⠀⠘⢌⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢞⣿⠟⠉⠀⠀⠀⠀⠈⠉⠛⠛⠟⠀⣠⠴⡟⢦⠀⠀⠀⠀⠀⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⡁⠀⢸⣦⣀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠷⡒⣻⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⣸⡽⠈⠙⠢⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡞⠈⣾⣿⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⢫⡀⠀⠀⡐⠈⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣥⣿⠏⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⠀⠀⠈⢿⣾⣭⣟⣛⣛⣛⣛⣩⣭⡶⢿⣘⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⡞⠀⠉⠛⠛⠛⠛⠛⡏⠁⠀⠀⠈⢢⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⠒⠒⠲⢦⡀⠀⠀⠳⣄⠀⠀⠐⠀⠀⠉⠓⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⢸⣀⣏⣈⣿⣉⣉⣉⣉⣉⣳⣦⣥⣀⠀⢠⡏⠉⠉⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠴⠤⣦⣤⡿⠉⠉⠉⠉⠁⠀⣼⡇⠈⡟⠛⠛⠒⢦⣨⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣇⡼⠁⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⣠⡀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣤⣶⡾⢿⠙⣤⣄⣀⡤⢼⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⣀⡀⣀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠐⢹⠀⠈⢯⡉⣉⡥⠞⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⠀⠀⠀⢣⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣠⠎⠀⠀⠀⠘⡄⠀⠀⠀⠀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠖⠚⠁⠀⠀⠀⠀⠀⠙⠦⣤⡤⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⠇⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢠⣀⢖⡁⠀⠀⠀⠀⠐⠖⡄⠀⣀⠀⠀⠀⡀⠐⠀⢀⠉⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣽⣿⣇⠀⠀⢀⠄⣄⡀⠀⡟⠅⠋⡙⢻⣃⡴⠖⠻⠓⠛⠓⠛⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠃⠘⡇⠀⢀⡘⢀⣋⢁⠀⡄⣲⣾⣇⣀⣹⡇⢹⠀⠠⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⣰⣤⣶⣛⣡⡶⢰⠇⣰⡇⢈⣽⠊⠙⣿⡇⠘⣧⠀⡆⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣴⡿⠤⣄⠙⢻⣶⣿⡶⠃⠙⠁⠸⣷⣾⣿⠃⠀⠙⢶⣿⣆⢻⣆⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⡇⢻⠒⢄⡙⣾⡿⠛⠀⠀⠀⠀⠱⠙⠛⠏⠀⠀⠀⠈⣿⣇⠈⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠁⣇⢸⡐⠲⣬⣿⣷⠀⠀⣠⡄⠀⠀⠀⡎⠀⠀⠀⠀⣰⡟⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣠⣇⠀⠁⢻⡿⣿⣿⣆⠀⣸⣧⣤⣤⣤⣅⣀⡀⠀⣠⣯⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠐⡉⠉⣿⣿⠍⢹⠂⠙⠀⠈⢩⣟⠛⠫⠍⠉⣉⢉⣽⣿⣿⣿⣿⠿⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣋⡎⠹⡏⠀⠀⠀⠀⣴⠟⠝⠋⡒⠁⠀⠂⠄⠒⠻⠿⠿⣿⡍⠳⢌⡁⢄
⠀⠀⠀⠀⠀⠀⠀⠐⣋⡼⠀⠑⠈⠀⠀⠀⡏⠙⠓⠶⠀⢠⠀⠀⠀⢰⠀⠸⠗⢺⣟⡠⠀⠙⢺⣤⢶⠄
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⡄⠂⠀⠀⢠⡇⠀⠀⠀⡄⢼⣄⠀⠀⣸⣷⡙⠀⠀⣿⡅⠀⠀⣸⢷⡿⣶
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡇⠀⠀⣀⣀⡇⠀⠀⠀⢺⣿⣿⠀⣰⣿⣿⠁⠀⠀⢸⣷⣄⣠⣿⢿⡴⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⡴⢃⣤⣾⣿⣿⠃⠀⠀⠀⢸⣿⠁⠀⠹⣿⣿⠉⠀⠀⠀⢻⣷⣿⡟⢈⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢺⢀⡾⣡⣿⣿⣿⡟⢻⠄⠈⠃⠀⣻⡇⠀⠀⠀⠘⠿⢷⡀⠄⠀⠀⢻⠛⠙⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠉⣿⠉⠀⢸⣇⡀⠀⠀⣿⣧⠀⠀⠀⣠⣾⣼⣧⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣠⣼⠀⠀⠈⣏⣙⢻⣿⢻⣿⠀⠀⢴⢻⠟⢉⠹⣇⠉⠁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⣿⢉⣿⣿⢼⡏⠀⣶⣻⣎⣴⠃⢰⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣠⣴⣾⡈⠋⣹⣾⣿⣶⣯⣬⣭⣇⣠⣾⣞⠛⠓⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣤⣶⣿⣿⣿⣿⣇⣰⣯⡽⣿⣿⣿⡇⠀⠈⠉⠘⢿⣿⣿⣿⣧⣤⣄
⠀⠀⠀⠀⠀⢀⣤⡖⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⠋⠀⠀⢹⡟⣿⣧⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣶⣄⣀⠀⢸⣿⣿⣿⣿⣿⣯⣁
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣴⣾⣿⣿⣿⣟⠋⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠂⠀⠀⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣁⣤⠔⣾⡷⠒⠒⣒⣲⡶⠶⢾⣶⣶⡒⢒⣲⡶⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢉⣙⣷⡶⠾⣟⣁⣠⠴⠚⢁⠨⢛⣉⠫⡀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢒⣿⠟⠋⣁⣤⣶⣛⣉⣐⣀⣿⣥⣬⣭⣤⣴⣮⣦⣄⡀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⣋⣶⣿⡾⠿⠛⣛⣩⣿⣿⣿⡿⠷⠟⠋⠙⡩⣭⣟⠉⣠⠞⠁⠠⠂
⠀⠀⠀⠀⠀⠈⠲⠀⠀⣀⣤⣾⣿⠿⠟⠛⢹⣧⡴⠶⢿⣿⡿⠞⣋⠄⠈⠋⠀⠀⠠⢀⠙⠯⠿⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠐⣴⡿⠟⠋⣁⠤⣴⠞⠋⠉⠀⠀⠀⠈⠱⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⢈⡷⠖⠻⠯⠛⠛⠿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠗⣠⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⠀⠀⠀⠀⠀⠀⠀⣠⡄⢠⡄⢠⣀⣀⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⢀⣸⡆⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⢧⠟⠸⠇⠈⣯⣉⣉⣉⣉⣩⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⠛⠉⠉⠁⠀⢀⡀⠀⠉⠉⠙⢻
⠀⠀⠀⣶⣸⣿⣿⢸⣿⣿⢠⣾⠂⠀⠀⠀⠀⡤⣄⡤⣄⠀⠘⢿⣭⡉⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⠏⠿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⢸
⠀⠀⣰⣟⣿⣿⡏⢼⣿⣿⢸⣿⠀⠀⠀⠀⠀⠷⠟⠣⠟⠀⠀⣠⡍⠻⢶⣄⠀⠀⠀⠀⠀⣴⡿⠿⠿⠿⠿⠿⠿⢷⡆⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢸
⠀⢀⣽⣿⣽⣿⣷⣾⣿⣿⣼⣿⣨⠀⠀⠀⠀⢰⡄⡴⣦⠀⡾⠛⠒⠒⠚⠻⣆⠀⠀⠀⠀⠈⢁⠀⠈⠸⠀⠀⠐⡈⠀⠀⠀⠀⠿⠛⠋⠉⠉⢩⣿⣯⠉⠉⠙⠛⠻
⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠘⠃⠳⠋⠘⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠣⠤⣀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠉⠛⠳⠆
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⣠⠄⢿⣿⠇⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢋⣍⠉⠳⢦
⠀⠀⠀⣞⡟⠉⣠⣿⣀⠉⢟⡦⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣌⢹⣄⠀⠈⢳⡀
⠀⠀⢴⠻⠀⣾⣟⢙⣿⡆⠠⠟⠄⠀⠀⠀⡴⠿⢷⣤⣀⣀⣀⣉⣧⣀⣀⡀⠀⠀⠀⠀⣀⣴⣤⣤⣤⣀⣤⣤⣾⠟⣛⣛⡢⠀⠀⠀⠘⣿⣿⣿⣿⣶⣝⣲⢶⢂⡇
⠀⠀⣴⣶⡾⠛⠻⠿⠛⠻⣶⣶⡆⠀⠀⢠⡾⣛⢷⡌⣿⣿⣿⣿⣿⣿⢛⣭⣓⠀⠀⠜⣩⠶⢮⡙⣛⣫⡙⠿⢡⣿⣫⣝⢿⡄⠀⠀⣀⢈⡻⢿⡿⢟⣫⣭⣭⣭⠅
⠀⠀⠘⠛⠡⡵⣴⢶⡴⡥⠙⠛⠁⠀⠀⠸⣷⣟⣽⠏⠿⠿⠿⠿⠿⠇⢿⣒⣽⠂⠀⠀⢷⣛⣽⠇⠛⠛⠛⠛⠘⢿⣼⣯⡿⠃⠀⠀⢇⡈⢛⠁⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠆⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣮⠛⣤⠀⠀⠀⣠⣶⣶⣦
⢀⡄⠀⠀⣤⣶⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡤⣠⣾⡋⣹⠏⠀⠀⠀⠀⠀⠀⠀⣿⠓⢺⣿⣿⠀⠀⠀⠀⠀⠀⠉⢣⡝⢪⡲⢄⣤⡹⣿⣿⡿⠁
⠈⠁⠀⣼⣿⣿⣿⣿⣿⣿⡿⠇⣉⣽⠇⠀⠀⠀⠀⠀⠈⠛⣫⣾⣯⣨⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⢺⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣵⣿⣿⣿⠆⠁
⢠⡖⠀⠻⠿⣟⣛⣻⣭⣵⠶⠟⠋⠁⠀⠀⠀⠀⠀⠴⣾⣿⣿⣿⡿⣫⣾⠀⠀⠀⠀⠀⠀⠀⠀⡴⢛⠛⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢟⣵⡿⣦⡀
⠈⠙⠛⠛⢛⣻⣭⣭⣷⣶⡿⠃⢀⣴⣄⠀⠀⠀⢰⠁⠘⠿⣿⣿⠀⠻⡿⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⠂⠀⠂⠂⠀⠀⠀⠀⠀⠀⠾⢿⣿⣿⠟⠁⠙⢫⣿⢏⣳⡆
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠙⠁⠀⠀⠀⠘⠂⠤⠆⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠶⠿⠁⠛⠤⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠙⠟⠉

⠀⠀⠀⠀⠀⢠⡞⠛⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢴
⠀⠀⠀⠀⢀⣬⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣥⣄⡀⠀⢀⣹⣁⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣾⡶⣄
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠙⢻⠛⢹⡇⢰⡟⢟⠟⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⣛⣛⣛⣛⡃
⠀⠀⠀⠀⡯⢸⣿⣿⣿⠀⡟⠀⠀⠀⠀⠀⠀⡟⢰⡾⣷⠘⡇⢸⣅⡾⣦⣸⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⣿⣿⣿⣿⣿⣿⢰⡆
⠀⠀⠀⠀⠻⢰⣿⣻⣿⠐⠇⠀⠀⠀⠀⠀⠀⠉⢹⡇⣿⠋⠁⠈⢹⡇⣿⠉⠀⠀⠀⠀⠀⠀⣀⣀⣐⠶⢖⣂⣀⡀⠀⠀⠀⠀⠀⠀⢿⠸⣿⣿⣿⣿⣿⡟⣸⠇
⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡆⣴⠀⠀⠀⠀⡅⣥⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⡇⠉
⠀⠀⠀⠀⠀⢸⣿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣻⠀⠀⠀⠀⠇⠏⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠉⣽⡉⣹⡍⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡠⠶⠒⠛⠉⠉⠉⠉⠛⠒⠶⢤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠋
⠀⠀⠀⠀⣰⠋⡠⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠟⠀⢴⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠆
⠀⠀⠀⣰⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡄⠀⠔⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣠⠉⢠⡀⠀⠀⠠⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⢂⡀⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⢠⡀⡀⠀⠀⡰⡛⠁⠀⠀⠀⠀⠀⠀⢘⡄⣀⣡
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢆⠀⢁⠜⡝⠁⠀⠀⠀⠀⠀⢀⠤⠚⠛⠛⠋⠀⠀⠀⠀⡀⠀⠀⠱
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣿⢠⠃⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠑⠚⠋⠀⠀⠀⠐⠀⠀⠂⠁⠀⠀⠀⡀⠠⠀⠀⠒⠂⠀⠀⠀⡔
⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⡇⡞⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢀⣤⣴⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⣜⠣⢄⡀⣼⣸⠁⠀⠁⣀⡖⠋⠁⠀⠀⠀⡴⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠤⠂⠈⠁⠀⠁
⠀⠀⠀⠀⠀⣍⠳⠄⢀⠀⠈⠉⠉⠉⢑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⡡⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸
⠀⠀⠀⠀⠈⠆⠉⠒⠢⠄⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⠀⡄⢪⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠑⠢⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢢⣄⣀⣀⣀⠀⢀⠔⠒⠀⠀⠀⠀⠀⢐⣉⣶⠆⠀⣀⢬⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⣠⠴⠛⠉⢀⡤⣚⡭⠟⠀⠀⠀⣰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⡠⢚⡥⠋⠁⠀⠀⠀⠀⠐⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢢⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠛⣓⡶⠀⠀⠈⠑⣣⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠐⢁⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣸⠞⠁⠀⠀⢀⠔⠋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡰⠂⠀⠰⠤⠀⠀⠠⠂⠀⠀⠀⣠⠛⡀
⠀⠀⠀⠀⠚⠢⠀⠈⠁⠀⢀⡴⠊⠁⠀⠀⡠⠚⢁⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⣤⡄⠀⠀⢯⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⠲⠶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡴⠋⠀⠀⠀⣀⠬⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⡠⠔⠊⠁⢰⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⣀⠀⠀⡀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⢀⠞⠁⡠⠔⠉⠀⢀⡴⠒⠁⠀⠀⠀⠀⠀⠀⢰⠀⠈⠂⠐⠋⢹⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⣰⣫⠖⠉⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⣀⣀⠀⢨⠀⠀⠠⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢀⡾⠋⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠉⡄⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢲⡀⠀⠂⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠤⠤⠴⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡒⢒⣶⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢉⣀⣤⣤⣤⣤⣀⡉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠙⠂⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣡⠞⠋⣽⣿⣿⣿⣿⣿⣿⣷⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⢡⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠋⡽⠳⠯⠭⣉⣋⠭⠽⠞⢏⠙⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡸⠁⠀⢀⣀⣀⣀⣀⡀⠀⠘⡆⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡜⠣⠤⢤⠁⠀⠀⢠⠀⢹⠤⠤⠞⢢⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣥⣄⠀⢹⡗⠒⠺⣆⢀⡘⢺⠂⣺⠒⠒⢻⡉⠀⣠⣬⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠴⡪⠁⠀⣹⠗⣿⢳⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⡏⣿⠺⣏⠀⠈⠕⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠻⢾⡶⠋⠉⠁⠀⢻⣼⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣇⡟⠀⠈⠉⠙⢶⡷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣠⡏⢧⣄⣀⣀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠉⠈⢹⠁⠘⡍⠙⠋⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⠒⠂⡏⠀⠀⢿⠐⠒⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⠁⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣠⠞⠀⠀⠀⠀⠣⣀⣀⣀⠜

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠉⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⢀⣀⣤⣤⣬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠀⠀⣼⠃⣠⣾⣿⣿⣿⣿⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⠀⠀⠀⠀⢸⣧⣾⣿⡟⢀⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢱⣟⣿⡆⠀⠂⢸⣿⣟⡁⠖⠻⢿⠛⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠛⠛⠁⢠⠆⢸⣿⣿⣿⣦⣠⡀⠸⢷⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣷⣶⣾⣿⣦⠾⣿⣿⣿⣿⣿⡿⢔⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢹⣿⣿⣿⣿⣷⣀⠈⠛⠿⣿⣿⣿⣦⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⣴⣿⣿⣻⣿⣿⣿⣿⣿⣖⠠⠀⠀⣉⠉⢙⣉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣯⣭⣛⣿⡻⣟⢯⣻⣿⣿⣿⣶⣶⣶⣶⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠉⠙⠓⠮⠛⢯⣿⢿⣗⡿⣿⣿⣿⢿⣶⣾⣿⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢫⣤⡀⠀⠀⠀⠀⢦⣻⣦⢿⣿⣿⣾⡿⣿⣿⣿⠗⢻⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠿⠿⠇⠀⠀⠀⠀⡈⢳⣻⣿⣥⠙⠛⠿⠆⠀⠀⠀⠘⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⡀⠀⠀⠀⠀⠀⠀⠘⢼⣧⢻⣿⢧⣄⠠⠀⠀⠘⡇⠨⣼⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠐⡈⣿⠀⢻⣷⣷⠀⣀⣀⠀⠻⠒⠉⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠛⠀⠘⣿⢿⠉⠙⠀⠀⠀⠀⠀⠁

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣷⣶⣶⣶⣶⣶⣦⡀
⠀⠀⣠⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢃⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⣥⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢏⠁⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠋⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠁⠀⠘⠋⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⢘⠓⠄⠀⣠⣿⣿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢠⣄⡐⠁⠙⡀⠈⠉⠉⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠁⡠⠐⢲⣿⡟⠀⠀⠀⠐⢤⣀⣠⠟⣱⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣉⣽⡶⣶⣤⢴⣤⣎⠀⢠⡿⠃⠃⠀⠀⠀⣠⣾⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡝⠀⠀⣰⠇⠀⢰⠞⣉⠆⠀⠈⠻⣿⣽⠈⠠⠑⢢⣴⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡟⢷⡀⠀⢿⠀⠀⠀⠀⠉⢀⠵⠀⠀⢹⣿⣧⣠⣴⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⡀⢨⣿⣦⣼⣷⣆⠀⠀⠀⠀⠰⣄⠀⣤⣙⣿⣿⣿⣿⣿⠋⠛⠓⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⡩⣩⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢀⣿⣾⠛⠙⠉⠻⣿⣿⣿⣧⣄⡤⡁⢼⣿⠿⠿⠿⠛⠛⠛⢛⠉
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣤⣼⣧⡍⢸⠇⢾⣿⣿⣿⣇⠀⠀⢀⣾⡛⠁⠀⢀⣤⣴⣿⣿⡿⠛⠿⣷⣶⣯⣿⠄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣛⣻⠿⠳⣆⢸⣿⡇⢀⣼⠋⠉⠉⠉⢿⡇⠀⠀⡀⠙⠿⣿⣾⠂
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠳⣮⣻⣿⣿⣾⡏⠀⠀⠀⠀⢸⣇⢀⣀⣀⣰⡄⠙⣿⡔⠀⣄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣄⣀⣨⣿⣿⣿⣿⣿⣦⣄⣠⣤⣿⣿⣿⡿⢿⣿⣿⣿⣿⣟⣀⣿⣷⣶⡂
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⣈⣛⣛⣛⠻⢿⡿⠉⣀⢛⣿⣿⣿⣿⣿⣿⣾⣿⠟⠻⣿⣿⣿⣿⣟⠿⣧⠄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⣀⠴⠾⣿⠿⠛⣭⡗⠈⢹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣾⣿⣿⣿⣟⠛⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣠⡴⠛⠁⠀⢢⣝⣻⣿⠿⢻⣿⣿⡿⠟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠢⠴⠛⠁⠀⠀⠀⢾⣆⣈⣭⣴⠾⠛⣉⣤⣶⣿⣿⡿⠟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠂
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⠡⠏⠔⠇⠀⠀⠀⠀⠹⠿⣿⣿⣛⣩⣴⣾⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣿⣿⣿⣿⣯
⠀⠀⢸⣿⣿⣻⣿⣟⣿⣾⣅⣀⢀⠀⣂⣀⣀⣠⣼⣾⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠉⠈⠙⠻⣿⡟⢿⢿
⠀⠀⠘⣿⣿⡿⢿⡿⢿⢯⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠋⠁⠀⠀⢀⠀⠈⠀⠈⠏⠑
⠀⠀⠀⠈⠙⠁⠈⢙⣛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠌⡽⠛⣿⡳⠾⠿⠛⠻⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠁

⠀⠀⠀⠀⠬⠀⠀⠀⣀⡀
⠀⠀⢠⣄⣾⣦⡀⣠⠤⡹⠻⣆
⠀⢀⣠⣼⣿⢿⠄⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠖⠓⠘⠛⣿⢰⡄⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣧⣿⣞⣋⠉⠈⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⠾⢻⡙⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⣿⡃⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸
⠁⠀⠸⢳⣿⢳⡦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⢙⢹⣧⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⠒⢰⣾⣖
⠀⣀⣴⣶⣿⠻⠇⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⠯⠅⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢈⣽⡟⠙⠢
⠛⠁⢘⠹⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠰⢸⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠘⠀⠉⠨⣿⣿⣤⡀
⠀⠀⡝⢂⣿⠄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⢴⣾⣟⠇⠀⠙⠆⠀⠀⡠⠖⡀⣠⣤⠀⠀⠀⠀⢀⣤⢤⣾⡶⠀⠈
⠀⠀⡄⠘⣿⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⢹⡏⠃⠀⠀⠀⠀⠀⠀⣀⡀⣹⡿⠲⢄⡀⠀⠁⠀⢘⣽⡿⠖⡤
⠀⠰⠈⢤⣿⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡇⠃⠀⠀⠀⠀⠀⠘⠉⠉⢿⣿⣤⡀⠀⠀⠀⠀⢀⢸⡇⠂
⠀⠐⠀⢸⣿⡂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⡇⠤⠀⠀⠀⠀⠀⠀⡠⠀⢺⡏⠀⠈⠀⠀⠀⠀⡀⢼⡇
⠀⠁⠈⣺⢿⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⡇⢈⡀⠀⠀⠀⠀⠀⠀⠀⢾⡟⡉⠂⠀⠀⠀⠀⠁⣸⡇⠰
⢸⣳⣄⢼⣾⡧⣀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⣭⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⢊⡇⠀⠀⠀⠀⠀⠠⠁⣼⡇⢀⡄
⣻⣀⣈⣻⣻⣃⣉⣹⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣏⣈⣿⣗⣉⣵⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣸⣉⣻⣟⣉⣇
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⠉⠉⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡠⠀⠬⠀⠀⠱⠁⠀⠃⠀⠀⡠⣤⢼⠁⠀⠀⠀⠀⣴⠟⢉⣽⣿⣿⣿⣿⣷⣦⡀⢸
⠀⠀⠀⠀⠀⢂⡀⠀⠁⠀⠈⠀⠈⠂⠀⢘⡜⠉⢻⠀⠀⠀⠀⣼⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠶⠤⢾⡇⠀⢸⡀⠀⠀⢰⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠒⠈⠡⡀⣀⠠⠀⠀⠀⡰⠓⢴⠉⢣⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣜⡗⠉⢣⠀⣠⠞⠁⠀⠀⠳⡀⠑⢄⠘⠿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠕⠁⠀⢀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢋⡽⣦⡀⠀⠀⠀⠈⠢⣄⠙⠲⠬⣙⣛⣿⣿⣯⠭⢞⣁⠀⢀⠤⠏⠀⣸⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢵⡢⠖⠋⠈⠃⠉⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⣠⠟⠚⡆⠀⠉⠻⠀⠀⠀⢱⣀⣀⣠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⢈
⠀⣀⣀⣀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⡴⠞⢀⣀⠤⢆⠀⠀⣀⠀⠉⣹⠁
⢀⣿⠏⠀⠙⠒⠒⠋⠿⣷⣄⠀⢀⠠⣤⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠙⠉⠁⠀⠀⠀⠉⠉⠀⠉⠉⠁
⢸⣿⠀⠀⠀⠀⠀⢰⠀⠀⠀⣊⠄⠈⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⣠⠎
⣼⣿⠀⠀⠀⠠⡠⠈⡀⠀⠈⢇⠀⠀⣀⣔⠁⠀⠀⠀⠀⣀⡤⠚⢇
⣼⡏⠀⠀⡪⣳⠓⠧⣽⠖⠲⠒⠓⠋⠁⠈⣉⡿⠟⠛⠛⢿⡄⠀⢸
⣿⡇⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠙⣄⠀⠀⠀⠈⢳⠆⠊
⣿⡇⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠈⠓⠄⣀⣠⠊
⠙⠛⠒⠉⠀⠀⠀⠀⠀⠀⠀⢾⣷⡀⠀⠀⠀⠀⡴⢅⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠪⡽⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠉⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣠⠂⠀⠀⢀⣠⠿⠛⠛⠙⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣾⣁⠀⠒⢻⠋⠁⠀⠀⠀⠀⠀⠀⢄⠸⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢶⡜⢿⡟⢿⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠈⣗⠊⣿⢸⡇⣫⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣰⣿⣧⣟⣼⠁⠴⣇⣁⠀⠀⢀⣈⣉⣓⣦⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⢄⠀⣯⡿⠀⠀⠘⠻⠯⠿⠇⠃⢠⣾⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣛⣳⣺⣾⣿⠗⠌⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡏⠹⡦⠀⠀⠀⠀⠀⠀⠀⠠⠤⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠂⠀⠀⠀⣀⣤⣌⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⡋⢹⡿⣿⣷⣄⡴⠀⠀⠀⠀⠉⣭⣭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣾⡇⢈⣿⣿⣿⣶⣦⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣝⢿⣿⣿⡿⠋⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠉⠻⣿⠿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠿⠿⣷⣦⣀⣤⢙⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠦⣄⡀⠈⠻⠁⠙⢭⡙⢿⣷⣽⣿⣿⣿⣿⣿⣏⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣠⡔⠈⠄⠀⠙⠆⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⡦⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠠⣄⠈⢿⣿⣿⣿⣿⣿⡿⠿⠾⢿⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠈⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣤⠔⠉⠉⠉⠑⢤⡄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⡣⣴⣶⣶⣶⣶⣤⡻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡗⡍⠁⠀⠀⠂⠀⠉⡛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣮⡑⠒⠀⠐⠒⣩⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠯⡉⠉⠙⠝⠫⠭⠉⠩⠭⠛⠙⠉⠉⣩⣝⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠆⢹⡄⠁⡠⠤⠤⠤⠤⠤⠤⡄⣦⣸⠨⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⠠⣼⣧⠀⡂⠀⠀⠀⠀⠀⠀⡁⣾⣟⠀⢙⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠈⣻⣿⠃⠀⠈⠖⠀⠤⠄⠐⠎⠀⢿⣿⠀⠩⣿⣮⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣰⣾⣿⣿⢀⣾⡷⠠⣀⠀⢀⡠⢰⣿⣿⣿⣧⡀⠘⠽⣿⣟⡄
⠀⠀⠀⠀⠀⠀⣀⢌⡀⣀⣤⣿⡿⠙⣿⣿⠋⣄⣠⠉⠋⠋⢡⣀⡌⢻⣿⡟⠱⣀⠈⠸⢻⣯⠄
⠀⠀⠀⢀⡤⠐⠋⠑⣮⣿⣵⠗⠚⢉⣩⣿⣶⣦⣤⣤⣤⣤⣤⡴⢒⡋⠉⠉⠙⠲⠷⣄⢠⠖⠉⠓⠤⣄
⠀⠀⠀⣎⣴⠖⠂⢠⣿⠟⣁⣶⡻⢷⠿⠗⠤⠠⡴⠲⠖⠋⠑⠬⣻⢿⣿⣿⣷⣶⣤⣬⢿⡆⠀⠒⢶⣌⡆
⠀⠀⣔⣇⡱⣡⠆⡼⣁⠤⢐⣂⡹⡎⣆⠀⡄⡀⡀⢠⣀⣄⣄⡀⠈⠑⢯⡢⡀⢀⠀⠈⠳⡽⡄⢦⡱⣁⣗⡄
⠀⠀⠀⠘⠒⠻⣎⣞⣵⣫⡌⣶⣶⣷⣼⣿⠿⢿⢿⣛⠿⠭⠛⢧⠀⢠⣿⣿⣿⣾⣶⣴⣶⣧⣼⣾⡟⠚
⠀⠀⠀⠀⠀⠀⠹⣿⢿⣛⣃⡯⣽⣣⠵⠒⠚⠉⠉⠀⠀⠀⠀⠀⠑⠾⠿⠿⠛⠻⠭⢽⣛⣩⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠶⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢸⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⡗⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢇⡽⢻⠿⠿⣿⠿⠻⣫⡿⠁⣿⣠⠀⠤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⢀⣞⠘⣿⡇⠙⠶⠖⢠⠀⢶⠟⠁⢸⣽⣿⣿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣠⡞⡯⠀⣄⣀⣀⠀⠀⡘⣶⡘⠀⠀⡀⣼⣿⣿⢠⡄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⣰⣅⣽⠀⠀⠀⠀⠀⣤⠘⡇⢻⠃⠀⠀⠀⢀⢀⣿⣿⠁⢀⣼⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⢫⣹⣿⡯⣍⣉⡁⢰⠇⠀⢹⣿⠃⠈⠉⠉⠉⢉⣿⣿⡶⠋⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢲⣻⣶⣿⠏⠀⢸⡍⠹⠃⠀⠀⠈⠁⢠⣦⣿⣿⣿⣿⣿⣿⠀⣀⣠⣤⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠉⣿⡟⠀⣧⡘⣧⠀⠀⠀⢀⣶⠀⠈⠡⢿⣿⣿⣿⣿⡇⣺⣭⣤⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡐⣿⠁⠀⠀⠹⢄⠀⠀⠀⢸⡷⠤⠐⢰⣿⣿⡿⠿⣿⠇⠘⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠉⠁⠀⠀⠃⠀⣮⣿⡆⠀⠀⠒⠚⢻⣿⠿⠋⠀⣰⡟⠀⠈⠁⠐⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣉⢹⡈⠀⠀⢀⠀⣤⣿⣷⡁⢦⡀⠐⣴⠞⠁⣠⣴⣾⣿⣿⠀⣰⡷⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠃⠀⠀⠄⠤⠽⠻⠿⢷⣀⣏⢹⣧⣴⠞⠁⠀⠀⣠⢶⠀⠛⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⣹⡟⠁⣈⡉⣉⡉⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡍⠀⢠⣿⡧⣿⠁⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢘⣿⠀⠏⠀⠀⠙⠛⠛⠃⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠺⠏⠀⢠⠀⣀⣀⠀⣀⣀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⣿⠀⠀⢈⡛⠻⠿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣄⣐⣿⣿⢿⣆⠀⠀⠉⠉⠛⠛⢋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡙⠻⣷⣶⣾⣿⠀⡄⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⠇⠀⠀⠀⠀⣶⣦⣤⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠛⠀⠀⠀⠀⠀⢸⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠟⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⣋⣷⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠶⠟⠻⠬⣝⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠄⠀⠀⠀⠀⠀⠙⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣏⣀⠀⠀⠀⠀⠀⠀⣴⠚⣒⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠶⢒⠒⡛⢛⣉⡙⠷⣌⣾⣿⢛⡛⠿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠘⣿⣿⡇⢠⣿⡋⢻⠀⣿⣽⣿⣼⢰⣋⢺⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠐⣿⣿⡅⡟⢿⣿⡿⠀⠟⣿⣿⡿⣟⢟⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣒⣒⣿⣦⣠⣴⡿⠚⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠛⣷⡈⣿⡏⠈⣽⠛⣙⢳⣠⣤⣤⣴⣾⡾⣿⣽⠿⠿⠿⣻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣏⣽⣧⣿⣿⢸⣿⣿⣯⣾⣿⡿⣿⣷⠿⢋⣤⡶⠖⠒⠦⠿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⣿⣿⣿⣾⡿⣡⡶⠋⣠⣶⣾⣿⣿⣦⣬⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⣻⣿⢯⣾⠿⢿⡆⣷⣾⣿⣿⢟⣾⠋⣠⣾⣿⣿⡟⠁⠀⠉⠉⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢱⡿⢡⣿⠃⢠⣿⠓⠛⠻⡿⣣⡿⠃⣼⣿⠿⣿⣿⡇⠀⡶⣡⡠⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⣶⣿⣿⣂⣾⣃⣀⣀⣼⢳⡟⢁⣾⡿⠛⠠⣌⣿⣧⠘⣧⣫⣃⣸⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠹⣿⣿⣿⣿⣟⣛⣿⣧⣿⢀⣾⣿⣁⠀⠀⢢⣿⣿⣄⠈⠙⠚⠋⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⠈⣿⣿⣿⣿⣶⣴⣿⣿⣷⣾⣿⡿⠉⠨⣷⣦⣿⣿⣿⣷⣶⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢸⣿⣾⣍⣩⣿⣿⣿⣿⣿⣿⡏⠠⣄⠙⢻⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠛⠿⡿⠟⠋⠙⠛⠉⠱⠄⠈⡗⠼⡛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠂⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣼⣿⣿⣾⣿⣟⣠⡤⠶⡏⠕⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠿⠏⠁⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠟⠁⠀⠀⠀⢠⡠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⣿⠟⠁⠀⠀⠀⠀⣴⠞⢁⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣛⣷⣾⠫⠀⠀⣀⣠⣴⡿⠗⠚⢣⣠⣶⣿⡿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣶⣾⡏⠉⠉⠀⠀⣠⣿⣿⣿⣿⡿⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⢳⡄⠀⣠⣾⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⠿⠿⣷⢷⡾⠿⠿⠛⡽⠋

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡇⠀⠈⠀⣀⣴⠮⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡚⢢⡀⠀⣜⠡⠂
⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢰⢃⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠁⠀⠁⠀⠀⣀⡴⠆
⠀⠀⠀⠰⠀⠀⢰⠁⣠⢴⠶⢛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⠞⠁
⠀⠀⠀⢀⡀⡰⢃⣴⡷⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡴⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠟
⠀⠀⠀⠀⠛⠻⠞⠛⠋⢃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⠏⠀⠀⠐⠈⠀⠀⠠⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣎⠀⠀⠀⢀⡠⠔⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢘⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠁⠀⠈⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠐⢀⠄⠂⠈⠁⠈⠉⠀⠢⢄⠀⠈⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢠⠀⣆⣔⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠎⠁⠀⢈⠆⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠄⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠴⠠⠀⠀⠀⠊⠄⠀⠀⠀⠐⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠂⠀⢸⠀⠠⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣽⠟⢻⣏⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢁⢠⢴⠊⠐⢀⣨⠉⠕⡢⢦⢬⡉⠁⠀⢁⠅⢤⣀⠀⢂⢤⣄
⠀⠀⠀⠀⠀⢀⠌⢠⠔⠚⣉⡀⠀⢠⡖⠗⢒⣦⣐⣂⣁⢄⣩⡆⣤⢷⠖⠢⡆⣐⣀⢌⠑⢿⣆
⠀⠀⠀⠀⠀⡈⠀⣎⠀⠞⣁⡅⢀⠏⠘⢠⠋⠀⠀⠀⠀⠀⠀⠀⡉⠉⢹⡇⢡⠀⢈⠽⠂⢈⠈
⠀⠀⠀⠀⠀⠠⡀⠈⠓⠤⠤⣉⣀⢤⣀⡆⡄⠉⠙⠀⠀⠀⠐⢡⡴⠾⢼⡧⣤⣭⢥⣤⣴⣶⣷
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠠⠀⠼⠯⣈⡻⠓⠲⣒⠲⠶⠴⠲⢾⠷⠶⠊⡀⠤⠄⠰⠼⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠐⠉⠠⠾⠅⠠⠀⠀⠢⠸⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠄⠂⠐⢀⠀⢠⠀⠀⡐⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⠈⠀⠌⡂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠀⢁⣀⡔⢐⠨⡀⠐⠒⠑⠀⢸⠀⣀⡄⠄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠉⠚⠛⠉⠄⠂⠔⠨⢘⠳⡦⠄⡠⠐⠜⠡⢐⠠⠀⠁⠈⠪⠐⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠕⠀⠀⡠⠤⠤⠄⠒⠐⠠⢤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢲⣶⣤⠒⣶⣢⡄⡆⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⡏⠁⠀⠈⠓⠀⠀⠀⠃⢆⡞⠚⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⠀⡇⢰⠐⠒⠒⠒⠂⢤⢀⢸⡇⠀⠀⣿
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠈⠢⢄⣀⣀⡠⠏⢸⠀⠳⠤⡞⠁
⠀⡴⢢⢫⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠟⠛⠒⠒⠲⠶⣶⠾⠤⢶⠒⠃
⡴⢜⢦⣱⡵⠛⢣⠤⣤⡠⡤⠤⠤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢀⢳⣀⣀⡀
⠈⢪⡗⠁⠀⠀⢸⠊⠁⡇⣇⠀⢠⡇⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⡇⣏⠀⠀⠀⢸⠛
⠀⠀⠓⢄⡀⠀⣸⠀⠀⠇⡏⠉⢹⠀⠀⠀⠠⠀⠀⠁⢸⢘⠀⠀⢿⠈⠉⢹⠉⢹⢸
⠀⠀⠀⠀⠈⠉⠡⡳⡀⠀⠇⠀⡿⠀⠀⠀⠀⠀⠀⠓⠃⠊⠀⠀⣼⠀⠀⢸⠀⡼⢸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢾⢳⡀⠀⡇⠀⠀⠀⢀⠀⠤⠀⠨⣈⡄⠀⡇⠀⠀⢸⠀⡇⢸⠀⠀⠀⠀⢩⢱⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⡗⣾⠤⠤⠤⡔⠊⠁⠀⣿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⠀⠉⠉⠉⠉⠉⠙⠢⣄⣀⣿⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣱⡖⠒⠤⠤⠤⣤⣄⣀⣀⣀⣸⣃⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠏⡝⠉⠓⠚⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⠦⣀⠀⠀⠀⠀⠀⡜⠀⢦⡤⠤⠤⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠛⡆⠀⠀⠀⠈⠉⠒⠒⠒⠛⠂⠉⠁⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠓⣧
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠺⣀⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡏
⠀⠀⠀⠀⠀⠀⢸⠉⠁⠒⠤⡤⠒⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⣇⡀
⠀⠀⠀⠀⠀⢴⡋⠑⠠⢄⡀⡇⡠⠔⠊⢉⠦⠀⠀⠀⠀⠀⢰⠚⠭⢄⣀⠲⠃⣈⠥⠶
⠀⠀⠀⠀⠀⠀⠉⠓⠢⢤⣈⣻⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠈⢙⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠧⣄⡉⠒⠢⢼⡤⠒⠊⣁⡼⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣓⣲⣤⣧⣖⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠿⠿⠿⠿⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⣤⣤⡄⠀⣿⣿⠀⣤⣤⡄⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠀⠿⠟⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⠾⠿⠟⠋⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠊⠔⢈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⡁⠢⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡡⡄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⢱⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠆⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡡⡀⠀⠀⠀⠀⠀⠀⣜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡵⡀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠉⠉⠀⠐⠒⠚⠛⠀⠒⠒⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⣄⡄⠀⠠⠐⠒⠒⠤⡀⠀⠀⠀⠄⠀⢉⡐⢄⠀⠁⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡿⠇⠀⢂⠀⠿⠆⠀⡁⠀⠀⢘⠒⢢⣴⡖⠊⠇⠀⠠⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠑⠂⠐⠊⠀⠀⠀⠈⠢⢄⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠒⡄
⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣧⣐⣠⠂
⠀⠀⠀⡄⠨⢊⣦⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠑⠠⢀⡀⠀⠀⠀⡀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣪⠞⠁⣜⡇
⠀⠀⠀⠀⠹⣟⢅⠉⠑⠒⠭⢖⡠⢄⡀⠀⠀⠀⠀⠀⠑⠢⠤⠄⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⠜⠀⠀⠀⠀⢀⠔⣠⠞⠁⠀⡔⡻⠁
⠀⠀⠀⠀⠀⠈⢧⡱⡀⠀⠀⠀⠈⠛⠮⢵⣦⣄⣠⠄⠀⠠⠀⠠⠤⡠⡿⢿⠟⠿⣯⠤⠤⠤⣤⡄⢀⡀⠀⡠⣎⠴⠊⠀⠀⠀⠐⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢌⠢⡀⠀⠀⠀⠀⠀⠈⡿⠁⡖⣤⠀⢰⠒⠒⠀⠀⠀⠀⠄⠠⡀⠀⠀⠀⠀⠀⠹⢙⡟⠁⠀⠀⠀⢀⠈⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⢠⡀⠀⠀⠀⠀⡇⠀⣨⡁⠀⢸⠈⠉⠀⠀⠀⠀⠀⠀⠂⠀⠲⠞⣛⠚⠃⠀⠙⠀⠀⠀⡠⢁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢆⠀⠀⠀⡅⠀⠓⠋⠀⢸⠀⠀⠀⠀⣠⠀⠪⡄⠃⠀⣙⠓⠒⢚⡁⠀⢠⣤⡴⢮⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⣤⢄⡀⠀⢨⠬⠀⢸⠀⠀⢒⠒⠓⡲⠕⠂⡆⠀⢉⡩⠤⢍⡁⠀⣸⠀⢱⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡥⢎⡗⠀⠴⢢⠀⠀⠉⢉⣉⣉⣉⠀⠀⠈⠁⠀⢨⣑⡚⣉⡀⠀⣿⠀⣠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⢧⠀⠈⠉⠀⠀⠘⠻⠹⣿⠉⡟⠁⠀⠀⠀⢠⡤⠒⢪⡄⠀⠉⠴⣫⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣥⢹⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠛⠢⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⢾⣘⡂⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣶⠿⠚⠵⣩⣩⣉⣉⣌⣽⠛⣭⡟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠉⠀⢀⠉⠳⡀⠀⠀⠀⠀⠀⡠⠂⠉⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢀⠀⢤⢠⡎⠀⠀⠤⠱⠸⠀⣃⡗⠀⠐⡀⠀⣰⡀⠲⠢⠠⠀⡀⡀⠉⢶⡠⠀⡀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠉⠐⠈⠐⠂⠙⠒⠺⠓⠷⠛⠍⠃⠅⠂⠥⠂⠅⢂⠍⠋⠖⢲⠤⣥⢤⠴⠪⠐⠍⢂⠔⡩⠢⠓⠡⠢
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠃⠀⠀⠀⠻⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⣦⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣠⣾⣿⣿⣷⣄⠀⠀⢀⣼⣿⠟⠁⠀⠻⠟⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠙⢿⣿⣆⠀⠀⣠⣾⣿⣿⣷⣾⣿⣿⣷⣾⣿⣿⣷⣾⣿⣿⣷⣄
⣿⣿⡁⢈⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠁⠈⢿⡿⠁⠈⢿⡿⠀⠈⢿⡿⠁⠈⣿⣿
⠘⠿⢿⡿⠿⠃⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠻⠿⠿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠿⠿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣧⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⢰⣿⣾⣿⠟⠁⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠉⠉⢩⣿⡍⠉⠉⣉⠉⠉⢉⣿⡏⠉⠉⣽⣿⠇⠀⠀⣿⣿⠀⠀⠀⠀⣤⣴⣿⣿⣤⣤⠀⠀⣤⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠈⠉⠁⠀⢸⣿⡇⠀⠀⠉⠁⠀⢠⣿⡿⠀⠀⢀⣿⣿⡀⠀⠀⠀⣿⣿⠛⠛⣿⣿⠀⠀⣿⣿⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⣼⣿⠃⠀⢿⣿⣿⣿⣿⡿⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⣰⣿⡟⠀⠀⣤⣦⣤⣤⣤⣤⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠻⠿⣿⡿⠟⠀⠀⣰⣿⡿⠁⠀⠀⠉⠛⣿⣿⠛⠋⠀⠀⣿⣿⣦⣶⣿⣿⠀⠀⣿⣿⣶⣶⣿
⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⡀⠀⠀⠀⢀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠉⠛⣿⣿⠛⠉⠀⠀⠙⠛⣿⣿⠛
⣾⣿⠛⠛⣿⣷⣤⣤⣤⣤⣤⣤⣦⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣤⣤⣤⣤⣤⣴⣿⣿⣦⣦⣤⣴⣤⣶⣿⣿⣶⣤⣴⣶⣦⣶⣿⣿
⠻⣿⣶⣶⣿⡟⠛⠛⠛⠛⠛⠛⠛⢛⣻⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⡟⠛⠛⠉
⠀⠈⠉⠉⠁⠀⣀⣀⣤⣤⣶⣾⣿⣿⡿⢿⣿⣷⣦⣤⣤⣶⣿⡿⠿⣿⣿⣷⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢀⣴⣾⣿⡿⠿⠟⠛⠋⠉⠙⣿⣷⣄⠀⣹⣿⣿⣿⣏⠁⢀⣾⣿⠟⠉⠉⠛⠻⠿⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢟⣥⡹⣿⣷⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣦⣤⣶⣿⣿⣿⣾⣿⡟⠁
⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⢸⣿⡇⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠋⢁⣼⣿⠿⣿⣷⡀
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⢸⣿⡇
⢸⣿⡇⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠘⣿⣿⣄⡘⢿⣿⣦⣿⡿⠁
⣾⣿⡁⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⢿⣿⣧
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⠃
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡟⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣶⣿⣿⣿⣿⣿⡿⠻⠿⢿⣮⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠿⠿⣿⡙⠛⠟⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣦⡈⢻⣦⠀⠀⠀⡀⠀⠀⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣸⡇⠀⣿⡆⠀⣤⡬⠙⠂⢠⣖⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣾⡏⣧⠀⠀⠀⠀⠀⠉⠘⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⢿⣿⣿⣿⡿⠃⢻⠀⠀⠀⠀⠠⠄⠰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⢻⣿⣷⣄⢸⡀⠀⠀⠀⡠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣿⡏⠻⢿⣷⣤⣀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣄⡀⢸⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⣘⣿⣿⣿⣿⣇⣩⣙⢾⣿⣟⡻⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠛⠭⣙⠻⣿⣿⣿⡏⢸⣿⣿⣧⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣼⣿⣷⣿⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⣭⣿⣿⠿⢿⣿⣿⡐⠳⢸⣿⣿⣯⡿⣿⣏⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠐⠋⠉⢿⡍⢺⣿⣷⡹⣿⣽⣽⣿⡜⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⠛⠙⠋⠁⠉⠁⠙⠋

⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⢉⠙⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠒⠂⠀⠀⠘⠒⠀⠤⡀
⠀⠀⠀⢀⣠⡤⠟⠓⠛⠉⠁⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⢀⡠⠒⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⡞⠀⠀⠀⣀⠤⠴⣶⣻⡯⠥⠼⠥⠀⠀⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⢧⠀⣀⡤⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢠⠟⠁⠀⠀⠀⢀⣀⣤⡤⠤⠐⠒⠐⣒⡛⠩⠤⣄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣿⠀⠀⠀⢰⣼⡿⠷⠖⠒⠚⠉⠉⠉⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⠂⠄⡄⠀⠀⠲⠀⠀⠻
⠘⡷⠖⠋⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡴⠋⠀⠀⠀⠀⠀⠀⢸
⣾⠁⠀⠀⣀⣠⠤⠶⣖⣛⣫⣭⠥⠦⠔⠂⠀⠈⠑⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠺⡈⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⢻⡀⠀⠊⢉⡴⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣹⢗⣽⠋⠀⠀⢀⣀⣤⠤⠶⠶⣲⠾⠿⠯⢥⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠃⢸⠇⠀⠀⢰⢟⠉⠈⠙⠻⣼⠃⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠀⠈⠢⠤⠴⠋⢸⡀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣼⠄⠒⠚⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠁
⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⢀⠇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡸
⠀⠙⢆⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠂⠒⠀⠚⠀⠀⠀⠀⠤⠧⠠⠴⠒⡶⠁
⠀⠀⠀⢻⠛⠉⠉⠛⠉⠉⠙⠯⠉⠙⠯⠉⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣙⣓⠀⡇
⠀⠀⠀⢸⡆⠀⠀⠤⠤⠤⠤⠤⠤⠀⠄⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠀⠠⠤⠤⠤⠤⢤⣤⠶⡶⠶⠀⡇
⠀⠀⠀⠺⡉⠀⠰⠶⠶⠶⠒⣒⣒⣛⡫⠁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠁⠀⠀⠀⠀⠠⠤⠤⠴⣶⣾⣿⠀⡆
⠀⠀⠀⢺⡅⠐⠶⠶⠶⠚⠛⣛⣚⣓⡭⠁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⠀⠀⣀⣀⣀⣀⣠⣵⣶⣶⢶⠀⡇
⠀⠀⠀⢾⡅⠀⠶⠶⠶⠒⠚⢛⣒⣛⠻⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⣤⣤⡶⣶⡃⣠⠇
⠀⠀⠀⠈⠳⣄⡀⠒⠒⠒⢚⣓⣛⣾⣥⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠈⠉⠭⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠻⡍⠉⠉⠉⡭⢉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣛⣛⣿⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣧⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢
⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⠀⠀⣟⡧⣄⣾⠃⠀⠀⠀⡀⠀⠀⠀⢸⣠⠆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣰⠄⣄⡀⢠⡀⣆⣾⣇⢠⢾⠀⣰⣟⣟⣴⣿⢇⢤⠀⠈⡿⠀⠀⠰⢸⠯⠶⣼⣷⡀⢸⣿
⠀⠀⠀⠀⠀⣖⠀⢸⣿⣿⡆⢰⣦⣀⣿⣷⣾⣧⣼⣸⡿⣿⣧⣿⣼⢠⢿⣧⢳⣿⣿⡞⣿⣦⠀⣿⣠⣤⣾⣿⣠⠼⢿⣿⢧⣼⣿⠀⣤⣼⡄
⠀⠀⠀⠀⠀⣿⣤⢼⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡿⢿⣾⠀⣼⣧⢸⣿⣿⣿⣿⣿⡌⣿⣿⣿⡟⢛⣹⣾⣽⣿⣿⣿⣿⣇⡝⣿
⠀⠀⠀⣄⣐⣿⣿⢸⣿⡿⣿⢿⣿⣿⣾⣿⣿⣿⣿⣸⡇⢠⣿⠻⢿⠖⣿⠓⢸⣿⣿⣿⣿⣿⣧⣟⡿⠎⢯⣿⣿⣿⣷⣿⣏⣿⣿⡿⠀⢸⣿⣦
⠀⠀⠾⣿⣿⣿⣿⢸⣿⣽⡿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣟⠋⠓⠚⣡⡄⠻⡆⠀⠋⣿⣿⣿⡿⠛⠉⠙⠇⠶⣛⣮⣿⣽⡍⠁⠻⣿⢷⣶⡾⠿⠿⡀
⢠⣶⣎⣿⣿⣿⣿⣿⣿⣭⣭⣯⣿⣭⣽⣿⣿⣿⣿⣤⣬⣤⣤⣤⣤⣥⣼⣍⢠⡈⠉⠉⠁⠁⢠⡴⠾⠴⢯⢿⠿⠉⢡⣤⢧⣆⣸⠭⣉⣽⡛⡉⠁
⠀⠁⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡶⠶⠿⠿⠿⠶⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣴⡾⠟⠉⢁⠤⢖⣒⣒⠒⠦⣄⣀⡀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⠟⠛⠛⠻⣿⣾⣿⣅⣀⠀⡰⠁⠀⠀⢀⣽⠿⠿⠿⣿⣿⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣄⣀⢀⣼⠟⠁⠈⠉⠙⠽⡇⠀⢀⣴⡏⠀⠠⡶⢦⠺⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠈⢉⠛⢦⠀⠀⠀⠀⠀⢻⢇⡞⡻⠇⠀⠀⠀⠀⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣿⠷⣦⣄⠀⠀⠀⠺⣷⣤⣄⠀⠀⠀⠀⠉⢿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢱⠀⠈⠻⣏⡽⢷⣦⣼⣀⠈⠑⠶⣶⢶⠖⠋⠀⠈⠻⣕⢄⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⡜⠀⠀⠀⣻⣿⠿⣿⣿⣿⣶⣮⣐⠾⣿⡗⠢⠄⣀⠻⠟⠒⠛⠐⠆⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠃⠀⢠⠎⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣦⣝⡻⢶⣾⣷⣾⠀⠀⠀⠸⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠠⠀⡞⠀⢻⣿⣦⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣶⣿⢻⣿⣯⣤⢄⠀⢣⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢿⣿⡿⣿⢿⣿⣷⣄⠀⢸⣿⣿⢿⣿⣿⣿⣿⠉⠻⢿⣿⣿⠘⣷⠈⣆⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡉⠻⣮⢣⢻⣿⣿⣦⣸⣿⣿⡀⠉⠻⣿⣿⣷⣄⠀⠉⠻⢧⣿⡀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠃⠀⢻⣇⣸⢏⣿⣿⣿⡉⠻⣿⣦⡀⠈⠙⢿⣿⣷⣦⡰⠎⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⡀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠟⣻⣿⣷⣄⣿⣧⣙⢦⡰⠆⢹⣿⣿⣿⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢇⠀⠀⠀⠀⣠⣿⣿⠿⡇⠀⠈⢽⣿⣿⣿⣿⣿⣷⣝⠶⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠴⠚⠛⢷⣦⣄⣧⣀⡈⠒⠺⠿⣿⣿⣿⣿⣿⣷⣌⣀⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠁⠉⠁




⣶⡶⢶⢶⠶⠶⢶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠐⠶⠛⠤⠐⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⢀⠀⠀⢙⠀⠀⡀⠀⠀⢢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⢂⠀⠀⠛⠁⠀⡬⠀⠙⠁⠀⠀⠆⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠑⠄⠀⠄⠊⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠑⣍⡓⠒⠂⡆⠀⠀⡤⠀⠀⢰⠒⠈⡏⠠⠂⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣇⣀⡀⣇⣀⣀⡸⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠥⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⡋⠘⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⡄⠀⠀⠀⠀⠀⡇⢘⠒⠂⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠘⡤⠄⠳⣀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⡇⡰⠢⢤⡜⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠠⠉⠑⡔⠋⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠀⡇⠀⠀⠀⠀⣸⠉⠀⠀⠀⠈⠲⡔⠉⠡
⠀⠀⠀⠀⠀⠰⠧⣀⡞⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠈⠐⠐⠂⠐⠂⠐⠀⠐⠒⠀⠀⠀⠀⠂⠂⠀⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠘⣄⡠⠧
⠀⠀⠀⣀⣠⣅⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣀⣧⣀
⠀⠀⢰⣁⡄⠠⠌⣱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡉⡠⠀⣈⣱
⠀⠐⠉⠀⡀⢀⡀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣆⣀⣰⠀⠀⠀⠀⠀⠀⢰⣀⣀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⣀⠀⡀⠈⠠
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂
⡇⢀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠉⢹⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⢀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⢺⠀⠀⠀⠀⠀⠀⢸⠒⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣒⡒⢺⠀⠀⠀⠀⠀⠀⣚⠒⣒⣺⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠁⠀⠀⠀⠉⠑⡄⠀⠀⠀⡔⠉⠁⠀⠀⠀⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⣶⡶⣤⣴⣶⣤⢀⡀⠀⠀⠀⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⠟⠉⠉⠛⠛⢱⡿⣯⢽⣿⣛⢿⣿⣿⣷⣾⣿⡿⠋⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣾⣿⣿⡿⠀⠈⣹⡍⠛⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣨⣭⡉⣀⣤⣴⣿⠃⠀⠈⠛⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⣿⣿⣿⢷⡎⠉⠁⠀⣠⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⠀⢀⣼⣿⣫⣏⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢓⣿⡿⢭⣿⡏⢀⣾⣿⢯⣿⣽⣿⡟⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢼⣷⢜⣟⣿⣩⣿⡆⣾⣿⣿⣶⣶⣖⣿⣻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡻⣇⣿⣿⣿⣟⣿⣿⣿⣏⣾⢷⣽⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⠻⣿⣿⣿⣞⢿⣿⣿⣶⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠃⠀⠀⠈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⠀⠘⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠹⡿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠶⢦⣤⣄⣀⡀⠀⠘⡇⠈⡏⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣀⠉⠙⠛⠲⠮⢽⣿⣛⣺⡷⠶⣧⣤⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡷⢲⣦⣤⣄⣀⡈⠩⢿⡟⠲⠶⢭⣭⣛⡓⠶⠦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠿⠞⠃⣼⣿⣭⡽⢻⡶⢲⡦⣤⣄⣀⡈⠉⠙⠓⠲⢬⡟⣿⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⢀⡾⠁⠈⠉⠀⢸⡇⢸⡇⣸⣿⣏⢉⣿⣷⡶⢶⣼⣷⠟⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣤⣀⣀⣠⣤⠴⠞⠋⠁⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⢸⡇⣨⡟⢹⡏⠛⠋⣠⠿⣿⣶⠟⠉⠓⠶⠦⢤⣤⣤⣤⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢛⣁⣀⡀⠀⠀⠀⠀⠀⣸⡟⢹⡇⢸⡇⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉⠁⣿⠫⢭⣉⡉⠛⠲⣦⣴⣏⣹⡇⢸⡇⢸⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣄⣠⡽⠟⠿⢧⣤⣈⡉⠙⣻⡷⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠙⣷⣈⣽⠟⣷⣦⣤⣄⣉⣽⣟⠿⢶⣤⣌⣉⠛⠻⠶⣤⣄⣀
⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⢀⡿⢷⣤⠿⠛⣷⡾⣤⣄⣀⠈⠉⠙⠓⠶⢤⣌⣉⡽⣷⠀⠀⠀⢀⡀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣿⠀⢸⡏⢹⣿⡶⢦⣤⣤⣀⡀⣹⣀⣿⠖⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧⢾⡟⠛⠋⠻⣿⣏⣽⠿⢯⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶⠶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡶⢻⡇⢸⡇⠀⢀⡾⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⣿⠀⢸⡇⢸⣧⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠶⠶⠖⠒⠋⠉⠀⠀⠀⠀⣿⠀⣸⡧⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⣿⠋⢹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢻⠄⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣼⠶⠛

⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣒⠿⠗⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠒⠒⠋⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠃⣠⣴⣤⡄⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⢈⣿⣿⠀⣿⡋⢙⣿⣾⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⣿⣿⣿⣿⣿⣿⡀⠙⠛⠿⠋⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣾⣹⡍⠚⠋⣈⣉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣍⣿⣿⣿⣇⡉⢿⣷⣾⣩⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡆⠀⠀⣿⣿⣿⢾⣿⣿⣿⣿⣿⣿⡷⣿⡿⢋⠄⢘⠀⠀⢸⡟⢿⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⣿⣿⣷⣶⣦⣿⣿⣿⠿⢿⠿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠘⣶⣶⣾⣿⡈⡄⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡇⢇⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣫⣭⣭⣭⣭⣭⣭⢙⠀⠀⠀⠀⢹⣿⣿⣿⡇⣿⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣸⣿⣿⣿⠿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡿⢸⠸⠯⠆⢀⢸⠿⣿⣿⣀⣿⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⣿⣿⡿⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡆⠀⠀⠀⠈⣾⠆⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⢿⣿⡿⢀⣾⣿⣿⣿⣿⣿⣏⣛⣋⣉⣉⣛⣒⡀⠀⠀⢀⣾⣿⣷⡀⢿⣿⡟⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠠⢿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠻⠄⢀⣾⣿⣿⡯⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣆⣲⠴⠒⠒⠒⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⣴⠞⠁⠀⠀⠀⠀⠀⠀⠙⢖⠒⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡆⡽⣹⣶⣶⣿⣷⣶⣦⣤⡀⠀⠘⡗⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠘⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣏⡀⠠⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⡶⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⣬⣥⠗⡄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢴⠞⠙⠀⠈⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢰⣟⡏⠀⡿⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠋⠛⠿⣿⣿⣿⣿⣿⡿⠛⠀⠈⢩⠁⠐⠇⠀⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢄⣤⣀⣤⣤⡀⢠⡦⠠⠀⠀⠀⠀⠈⠉⠉⠠⠊⠀⠀⠆⠨⠀⠀⠀⠈⢑⠿⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠁⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠁⠒⢄⠀⠀⠀⠀⠀⠘⡤⣾⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠂⠖⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢙⠈⠓⢦⣀⣸⣶⡝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⡀⢈⡿⠷⣶⣽⠀⠀⠀⠈⠉⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢦⣀⡀⠀⠀⠀⠀⠀⡇⠐⠰⠃⢡⣆⠀⣠⣿⢏⡀⠀⣠⡄⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠙⠛⠁⠀⣄⣀⣼⠀⠀⣬⡄⢸⣏⠜⢉⡟⠀⠈⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣛⠿⠿⠂⢴⣃⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⠀⠀⠀⠀⢀⠢⣄⣀⡀⣀⠄⠔⠂⠀⠀⢸⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣿⠏⢹⠄⠀⠀⠀⠠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣠⣣⠇⠀⠈⢦⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣾⡋⠀⠀⠀⠈⢧⠀⠀⡚⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠒⠚⣿⠧⠙⠢⢤⡀⠀⠈⠳⡈⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠁⠀⢶⣄⢠⠇⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣠⣄⠐⠒⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢧⣠⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣴⣶⠶⠶⠶⠶⣶⡦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢄⡴⠋⢀⣀⣀⣀⣀⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣼⢫⣾⣿⣿⣿⣿⣭⡙⢷⡐⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣾⣿⣿⣿⣿⣿⣿⣿⡆⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠂⢤⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠧⠊⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠐⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⡄⣉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⡇⢰⡀⠀⠀⠀⠂⠀⡀⢀⡄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡀⢸⣿⣼⣷⣦⡄⠄⠂⢿⡀⠸⣧⣃⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠀⠀⠀⣴⣠⢛⡄⠀⠀⠀⠀⢀⡀⠈⣧⡀⠀⠈⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⢀⡸⣿⡿⣟⢿⠀⠀⠀⠀⠦⠱⠄⢻⣷⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⡵⢸⣯⢿⡃⢿⡿⠁⠀⠀⠀⠂⠀⢁⠨⠙⣇⠀⣀⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠑⠎⢲⡎⠙⠯⢦⡐⠒⠒⠒⡶⠱⠞⠁⠚⢹⣟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠸⠀⣼⠀⠀⠄⠰⡟⠉⠈⢡⠀⠠⠄⠀⣀⠀⣿⠞⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢠⠀⢀⡇⠀⠀⠀⠀⠛⠄⢠⡂⠸⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠁⢸⡂⠀⠀⠀⠀⡀⠀⠀⢳⣌⢀⣀⣀⠀⠆⠈⠑⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠒⠀⠀⢀⡄⠀⠀⠀⠀⢹⡄⠤⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⢤⡤⠄⠀⠀⠀⠀⠀⠸⡇⢤⡄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣛⣓⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡞⠛⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⣶⣶⡶⠶⠶⠶⠷⠾⠷⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣿⢹⡇⠀⢸⡟⣿⡆⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣿⢸⡇⠀⢸⡇⣿⡇⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣼⡇⠀⠸⠷⠿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⣀⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⣿⢻⡿⠀⠀⠀⠀⠙⣿⠟⠁⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⠀⠀⣠⡿⣱⡟⠁⢀⣼⢿⣶⣾⠛⣿⡄⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⣯⣙⠻⣶⣟⣼⠟⠻⣶⡾⣣⣿⣷⣿⣿⣿⣷⣶⣶⣶⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠉⠛⢿⣿⣿⠻⢶⣴⡟⣵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⣿⣾⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣹⣿⣿⣿⡛⠛⣛⣛⡛⠛⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⣿⡇⠀⣿⣿⡇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣿⡇⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠿⠷⡿⠃⠀⠛⠛⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠙⠻⣦⣄⣀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⣦⣀⠀⠀⢀⣽⠟⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠈⣻⣟⠁⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢀⣼⢿⡿⢶⡿⠃⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⢸⣏⣹⣧⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⡾⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠶⠶⠶⠿⠿⠿⠿⠶⠶⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⣠⡾⠋⠀⠀⠘⢷⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⢀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⢀⣤⡾⠛⠁
⣠⣤⣤⣶⠶⠟⠛⠉⢀⣠⣴⠾⠛⠁
⠉⠁⣀⣀⣠⣤⡶⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠀⠀⠀⠙⣿⣷⣦⣄⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⢀⣼⡿⠋⢹⣿⠀⠀⠀⠀⠀⢿⣿⠙⢿⣷⣄⠀⠀⢀⣤⣤⣄⣤⣤⣤⣤⣤⣤⣠⣤⣤⡀
⠀⠀⠀⠀⣾⣿⠉⣻⣿⣶⣶⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣿⣶⣶⣿⠏⠙⣿⡟⠉⢿⡿⠉⢻⣿⠋⢹⣿⡄
⠀⠀⠀⠀⠘⠿⠿⠿⠋⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠀⢘⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣠⡍⠙⠛⠛⠛⠻⠿⠿⠛⠛⠛⠋⢩⣄⣴⣿⠟⣿⡟⠛⠛⠛⠛⣿⣿⠛⠛⠛⠛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⠁⠠⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠉⠩⣿⡍⠉⣉⡉⠉⢹⣯⠉⠉⣿⡟⠀⠀⣿⡇⠀⠀⢠⣤⣿⣿⣤⡄⠀⣤⣼⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠉⠀⠀⣿⣇⠀⠀⠁⠀⢸⣿⠃⣀⣤⣿⣧⣄⠀⢸⣿⠉⠙⣿⡇⠀⣿⡏⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⣿⡟⠀⢙⣛⣛⣛⡋⠀⢸⣿⠀⠀⣿⡇⠀⣿⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⢾⣶⣾⡷⠀⢀⣾⡿⠀⠀⠛⠿⣿⡿⠟⠀⢸⣿⣄⣠⣿⡇⠀⣿⣧⣄⣿⣿
⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⣀⣤⣾⡟⠁⠀⠀⠀⠀⣿⡇⠀⠀⠈⠛⣿⣿⠛⠁⠀⠙⢻⣿⡟⠋
⠀⠀⠀⠀⣾⣿⠉⣻⣿⣶⣶⣶⣶⣶⣶⣶⣿⡿⠿⠿⠿⠿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣾⣿⠇
⠀⠀⠀⠀⠘⠿⠿⠿⠋⠀⠀⢀⣀⣠⣤⣼⣿⣧⣀⠀⢀⣠⣽⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⠿⠟⠛⢿⣿⡉⠙⣻⣿⣿⡟⠋⣩⣿⡟⠛⠿⠿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⠀⠀⠀⠻⣿⣾⡿⣫⡽⣿⣾⡿⠋⠀⠀⠀⠀⠀⠀⠉⢻⣷⣤⣴⣶⣷⣶⣾⡿⠁
⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣿⡇⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⣠⣾⡿⢻⣿⡄
⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢸⣿⡟⠻⣿⣇⣸⣿⠇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠘⣿⣿⣶⣿⣿⣿⣏
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠉⠀⠹⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⣰⠀⠀⠀⠀⡎⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣢⡞⠀⠀⠀⠀⠀⠘⣦⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣥⣼⣤⣤⣤⣤⣤⣼⠥⠭⠤⠤⠤⠤⢤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⣀⡤⠖⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠤⠤⠤⢤⡶⠛⠉⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⠒⣿⢀⣴⣶⣿⡤⣄⠀⠀⢀⣤⣤⣶⣦⡀⢸⡇⠀⠀⣰⠋⢉⡟⢹⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢪⠀⣿⠀⢸⢿⣿⣷⣏⠀⠀⢸⢸⣿⣧⣼⠛⢸⡇⠀⠀⣿⠀⢸⡁⢇⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢤⣿⠀⠀⣉⣉⠁⠁⠀⠀⠘⠈⠉⠉⠛⠀⠘⡇⠀⠀⠘⢦⣬⠷⣼⠒⠁
⠀⣤⠴⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣧⣄⣀⣀⣀⡀⢈⣙⣟⠁⠀⠀⡇⠀⠀⠀⠀⣠⡴⠛
⢀⡈⠙⢳⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⣦⢤⣤⣭⣭⣉⣉⣉⣉⡉⠀⠀⠀⣷⢀⣤⠶⠋⠳⢤⡀
⢾⠙⠲⢛⣷⠓⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⡀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠋⢳⡀⠀⠀⠀⠻⣄
⠈⠙⠒⠋⠙⠲⡏⣰⠳⣤⣀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⣤⣽⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠻⠿⣄⠈⠙⠛⠒⠒⠖⠛⢋⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢠⡏⠀⠀⠀⠀⠈⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⢤⣤⠶⠶⣾⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠷⠾⠿⠿⣶⣶⠁⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠂⠀⢀⡈⡇⠀⠀⠀⠐⠂⠀⠐⢲⠈⡇⠀⠀⠀⣀⡤⣷⠈⣷⡀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠀⠒⠒⠒⠒⠶⠶⠤⠤⢤⣭⣭⣄⣉⣈⣀⣚⣚⣀⣧⡠⠔⢊⡡⠖⣿⠀⣸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠀⠒⠒⠒⠒⠢⠤⠤⠤⠤⠤⣤⣤⣄⣀⣀⣈⣉⣉⣯⠤⠚⠉⠀⠀⢸⢻⣉⠉⢉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⠀⠀⠀⠀⠀⢸⣰⡋⣻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⣤⢏⡽⠛⢯⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⢦⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠾⠋⢹⠸⡇⠀⣸⠃⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠠⣿⠉⠉⠉⠉⠉⠛⠛⣿⠛⠛⢻⡿⠾⠟⠋⠁⠀⠀⠈⠛⠁⠀⢻⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠐⣿⡄⠀⠀⠀⠀⠀⠀⣧⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠈⠙⢛⡽⢻⡀⠀⠀⠀⠀⣠⠿⣤⣒⣺⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣶⣛⣁⣀⣀⣀⡴⠋⠀⢘⡇⠀⣠⠴⠋⠁⠀⠀⠉⡽⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⣬⣭⣭⣽⡤⠖⠛⠉⢰⠻⠷⠦⣤⣤⣀⣀⡾⠁⣠⠟
⡀⠀⢀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⡒⠲⠶⣤⣭⣷⢞⡁⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⢀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠶⣦⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠦⣄⡀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠘⣧
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠉⠉⠉⠉⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠘⠇⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⡟⠁⠙⠞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠙⣧⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠾⠃⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⣠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣿⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⣷⢄⣼⠟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣤⣤⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠘⢷⣌⠳⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠁⠀⠀⠈⠉⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣤⡀⣰⣄⣠⣄⢀⡦⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢻⠛⠃⠙⠋⠙⢻⡇⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢸⡆⠀⠀⠀⠀⢸⠇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠈⣧⠀⠀⠀⠀⣾⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢿⠀⠀⠀⠀⡟⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡆⠀⠀⢠⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣇⠀⠀⢸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣛⣛⣛⣛⣛⣛⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣭⣭⣭⣭⣭⣭⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⠶⠶⠶⠶⠶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣛⣛⣻⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⣸⣿⠯⠤⠄⣼⣆⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣥⢠⠀⠀⡠⡖⠲⣤⣤⢲⠲⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠞⠉⠑⡀⠀⢧⣳⣴⢻⢿⣘⣶⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣡⢀⣤⠃⠀⠈⠉⠁⠈⠀⡉⡁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣻⠀⠀⢸⢿⠽⠾⢾⠶⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠅⢧⣤⣤⣈⣩⣭⣭⣭⠭⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡲⠶⣶⠀⠠⡘⡿⠿⠿⠿⠿⠶⠎⠈⠒⠒⢒⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠤⡀⠀⠈⢃⠀⡇⠀⢐⡐⠄⠀⠀⠀⠀⠀⠀⠧⠃⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠘⠤⠆⢀⣀⡜⠀⡇⠀⢀⣤⣤⣴⣶⣶⡶⠶⠿⢯⠆⠀⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⢷⣤⣴⣿⣿⢇⡏⡇⠀⣿⠀⡴⠚⢏⠉⠉⠉⠳⢸⠀⠀⡆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⠀⢀⣿⣿⣿⣿⣸⡇⡇⠀⣿⠀⠑⠔⠈⠁⠈⠀⡁⣸⠆⠀⡄⠈⣄
⠀⠀⠀⠀⠀⠀⠀⡰⢋⣈⠳⣀⣾⢿⣿⣿⣏⣿⠇⠁⠀⣿⢸⠠⡁⡀⠤⠤⠀⢓⢻⡃⠀⣿⡤⠈⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⡸⠀⡟⠛⣿⣿⣿⢿⡿⠀⡇⠀⣿⠀⠆⠒⠐⢀⣁⣁⣬⡼⠂⠀⣿⣧⣤⣄⡀⣀⠬⢿⠒⠒⢐⠢
⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⣾⠁⠈⣾⣿⣿⣿⡇⣾⠃⠀⠙⠒⠚⡿⠛⠛⠛⠹⠀⠀⠀⠀⡟⠫⠍⣁⡀⡏⢀⠄⣷⣶⠤⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠀⠀⠀⢻⣿⣿⣿⢱⡇⡆⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠙⢶⠚⠛⠉⢙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣦⠀⠀⢸⣿⣿⣯⣾⠃⣇⠀⠀⠀⠀⠆⣤⠀⣠⣞⣠⠠⠤⠚⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡜⠲⣤⡤⢍⡉⢹⣿⣶⣯⣦⣤⣶⣶⣾⣿⡿⠟⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠆⣌⠑⠀⢱⠈⣿⣿⡏⠉⠀⠀⠀⣿⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠏⢹⠀⣇⡼⠀⡟⣿⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠚⠋⠉⠁⠀⢁⣿⣀⠀⠀⠀⠀⢿⠲⡦⠖⠒⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⣈⠹⡆⠒⠒⠙⠂⣷⣶⠾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢂⢈⠆⣳⣶⠾⢿⡶⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⣁⣠⡏⠀⠀⢘⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⢰⡏⡏⠀⠀⠀⢸⡇⠀⠀⠈
⢀⣠⣤⣶⣶⣶⣦⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣿⣼⢸⠃⠀⠀⠀⢸⣇⣀⣤⡾⠒⠠⠄⣀
⠈⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠌⠀⠀⠀⠀⢘⣿⣯⣤⡀⣀⣤⠴⢾⡇
⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣐⣛⠷⠶⠚⠋⠉⠉⠙⠻⠯⣒⡈⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢿⣿⣿⣿⣻⡿⣿⣿⣿⣷⣦⣤⠶⠒⡋⠽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢾⣯⣟⣻⣇⠨⠅⠒⠈

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠹⣿⣿⣿⢉⣭⣿⣿⣿⣿⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣽⣏⢻⣷⢦⠈⠉⠻⣿⠛⠭⠅⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣁⠺⢃⣼⣷⣿⣄⡀⠀⠈⠿⣄⠀⠀⢀⣶⣴⡏⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⢀⣠⣾⣿⣿⣿⣿⠀⣀⠀⠀⠈⣁⠀⢼⣿⣿⠋⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣣⣽⢻⠀⣠⣼⣿⢿⣿⣟⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢢⣴⣾⣿⣿⣄⣀⣿⣿⣿⡏⡹⣿⠟⠀⢬⣭⣁⠀⢙⣿⡅⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠉⢻⣾⣿⣿⣿⣿⣿⣿⣿⣛⠟⠒⠶⠛⠟⠋⢠⣾⣿⠀⣈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠙⠿⢿⠿⣿⣿⣟⣿⠋⠀⠀⠰⠀⠀⠀⢰⣿⣿⠀⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢦⡔⢀⣴⡀⠘⠿⣟⣷⠀⣀⣀⡠⢀⣀⠀⢾⣇⣰⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⣀⣤⣰⡿⠿⠖⠐⠿⢀⣸⡿⣴⣾⣿⣿⡃⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣤⣤⣀⡀⠈⢉⣀⣠⣿⣿⣿⣿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠛⢿⣿⣿⣿⣿⣿⣿⠶⣾⣿⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⢻⣷⣶⡾⠟⠁⠀⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⣾⣿⠉⣷⠀⠀⠀⣘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠀⠀⠀⢈⣿⡄⢟⡀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⣀⣿⣿⡇⢸⡅⠀⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠈⢉⣻⣿⡇⢸⣿⣇⣀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⢽⣿⣇⠸⡏⠀⠉⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠈⣽⣿⢸⡇⠀⠀⠲⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⣿⣿⢨⡅⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣨⣿⢢⡄⠀⠀⣈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀⣼⣿⣶⣄⡀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡋⠰⣿⣿⠿⣿⡏⠉⠹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣥⡾⠟⠁⠀⠙⢿⣄⣀⣉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣀⣀⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⠀⠈⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢠⡶⠲⠶⣤⣤⣤⣤⡀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⢹⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⠀⠀⠀⠀⠀⠀⠀⢠⣤⡟⠀⠀⠀⠀⣴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢀⣼⠃⢀⣴⢷⣴⠾⠛⠀⠘⠻⢶⣴⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡷⠶⣤⡴⢶⣿⠁⠀⢹⡧⠀⠀⢰⡟⠛⣻⠇⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡟⠙⢶⣄⡴⠟⢙⣦⣤⣾⣁⠀⢀⡿⠀⢰⣯⣤⣤⠀⠀⢻⣦⣄
⠀⠀⠀⠀⠀⣠⡴⠟⠋⠉⠀⠀⠙⢷⣞⠋⢻⣶⠟⠁⠀⠉⠉⠛⢾⣧⣤⡄⢀⡾⠋⠀⠀⢀⣈⣿
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⢠⡟⠷⢿⡇⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠟⠀⠀⠀⠀⣼⠋⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⡀⠘⣷⠄
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡶⠛⠻⠞⠁
⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠿⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠉⠙⠛⠓⠒⠶⠶⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⠋⠉⠉⠛⠒⠒⠦⠤⢀⣀⣀⡈⠉⠙⠳⢤⡀
⣠⢤⠞⢻⢹⣧⠶⣆⠀⠀⠀⠀⠀⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⡄⠈⠟⠳⣄
⠙⢦⠱⡴⢾⢃⡼⠃⠀⠀⠀⠀⢸⠃⢰⠁⠀⠀⠀⣴⡆⠀⠀⢀⡄⠀⠀⠀⠀⠀⡇⢰⠀⠀⠈⠳⡄
⠀⠈⣗⣋⡉⢽⡄⠀⠀⠀⠀⠀⡟⠀⡎⠀⠀⠀⠰⠤⠤⣄⣀⣈⡁⠀⠀⠀⠀⢠⠁⠃⠀⠀⠀⢠⡇
⠀⠀⡏⠀⠀⢸⡁⠀⠀⠀⠀⢰⠃⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡎⢸⠀⠀⠀⠀⣸
⠀⠀⣧⠤⠀⠀⢧⠀⠀⠀⠀⣾⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡎⠀⠀⠀⠀⡏
⠀⠀⣇⠀⢀⡀⠘⡆⠀⠀⠀⣏⠀⠳⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠁⠀⠀⠀⢸⠃
⠀⠀⠸⡏⠉⠀⠀⠹⣄⠀⠀⠙⠲⢤⣀⣀⡈⠉⠉⠓⠒⠲⠤⢤⣀⣀⣀⡰⠃⡼⠀⠀⠀⣠⠏
⠀⠀⠀⢳⡠⠖⠁⠀⠈⠲⣄⡀⣠⡞⠁⠀⠉⠙⠓⠒⠶⠤⢤⣀⣀⡀⠀⢀⣠⠥⣶⠚⠉⠁
⠀⠀⠀⠀⠱⣄⢀⡔⠀⠀⡀⠉⣳⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡀⠀⢸⣆⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠻⢤⣀⡴⠀⢀⠏⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠟⢺⠉⠉⢹⠁⠈⢩⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⢀⣀⣈⡀⠀⠋⠀⠀⣠⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠿⠋⠉⡏⠉⠙⠓⠦⣄⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠴⠶⠶⠶⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣦⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠶⠀⠀⠀⠀⠀⠀⠈⢉⠓⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡇⠀⠀⡠⠀⠀⢠⡇⠀⠀⠀⠀⣀⣟⣒⡒⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠰⣞⣋⣭⡾⣥⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣼⠀⠀⠀⠉⠁⡼⢁⢀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡗
⢶⠶⢄⣀⣠⣠⠞⠻⡁⠀⢣⠈⠙⠓⠒⣶⠦⠤⠤⠤⠤⠤⢤⡤⠾⠶⠖⠒⢶⠚⠁
⠈⢧⠀⠙⢆⠘⣄⠀⠑⠀⠀⢀⠀⣠⠴⠏⠀⠀⠀⠀⠀⠀⣼⠀⠀⣀⠀⠀⡈⠋⠛⠛⣆⡀
⠀⠈⢧⠀⢈⡆⠈⢀⡴⠶⠶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠀⠀⡰⠁⢀⠆⡰⠋⣷
⠀⠀⠈⠷⠞⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⣰⡀⣀⣌⣰⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁⣿⣠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⡶⠁⢠⠃⠀⡜⠉⠢⡀⠀⢀⣠⣴⠏⢀⣠⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡏⠀⢰⠁⢠⢃⣀⣰⣁⣀⣀⣼⣾⣿⣿⣿⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣧⡀⠈⡄⠘⣶⢄⣀⠀⠀⠀⠙⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⢛⣿⡿⠟⠋⡝⠂⠉⠢⠚⠒⠋⠀⠀⠀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠉⠁⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⡜⠉
⠀⠀⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠠⠤⠤⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣥⡴⠶⠶⠶⠛⠛⠛⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣛⣩⣴⠶⠞⠛⠛⠛⠛⠛⠻⠶⢶⣭⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠐⠿⠿⣷⣦⣌⠙⢷⡝⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡈⢷⡸⣧⠀⠀⢀⣀⣤⣄⠀⢹⣿⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠸⣇⢹⡆⢰⣟⣩⠥⢿⡇⢸⣿⠀⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⣿⠈⣷⠘⣷⣔⣚⣻⡿⢸⣿⣰⣿⠉⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠈⠉⠉⠁⠀⣿⡟⠛⣿⡗⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣿⠀⠀⠀⠀⠀⣼⡿⠁⠀⣿⡷⠦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢰⡟⠀⠀⠀⠀⣼⡿⠁⠀⠀⣿⣇⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣾⠁⠀⠀⣠⣾⣟⠀⠀⠀⢠⣿⠇⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣧⣼⣧⣤⣶⢿⣿⣟⣻⣷⣦⣴⡿⠋⠲⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⠿⣿⣍⣉⣉⡉⡉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣩⣴⣟⣡⡿⠁⠀⠈⠻⣿⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣦⠚⢿⣿⣍⠉⠉⠉⠛⠛⠛⠛⠋⠉⢉⡽⢿⣡⡾⠋⠀⣠⡴⠶⠛⣋⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣫⡿⠈⠻⣷⣶⣛⣿⣷⣶⠾⠿⠿⠿⠿⠿⠿⢿⣿⣿⠋⠀⠀⠀⠹⣶⣋⣉⠤⠴⢛⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠋⠀⠀⠀⠀⢹⣿⠿⠿⠶⠶⠛⣛⠛⠛⢛⡛⣿⠉⣿⡆⠀⣿⡄⠀⠘⢯⣤⠶⠞⠋⠉⣿⡆⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⢀⣿⡏⠀⠀⠀⠀⣀⠀⠸⣿⢰⣟⣿⠆⢺⣿⡇⠸⣿⡿⢻⡆⢿⡇⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⡟⠛⢶⣄⡀⣸⣿⠀⠀⣿⡇⢉⣥⣤⣤⣤⣤⣤⣤⡀⠘⣧⢸⣿⠀⠀⠹⣷⣄⠀⠀⠀⠀⣀⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢉⣿⣿⡏⠀⠀⢹⣷⠘⣧⣀⣀⣀⣤⣤⣼⡇⠀⣿⢸⣿⡀⠀⠀⠘⢿⣦⣤⠶⠟⠋⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣶⣶⣾⣿⣿⢀⣠⣴⣾⠿⣷⣾⣯⣭⣭⣭⣥⣤⣤⣴⣾⣿⣿⣻⡿⢷⣶⣶⣿⣷⣦⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢠⣿⣿⠟⢿⣉⣵⣾⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠛⠿⣷⣾⣥⣤⣟⣻⣿⣶⣶⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣛⠶⢦⣤⣤⣀⣀⣴⡿⠟⠛⠛⠛⠛⠛⣿⣧⣤⣤⣄⣠⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⡏⠉⠛⠳⠶⠾⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⣿⠟⠶⢦⣬⣭⣤⣴⣿⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⣾⡿⠃⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠈⣿⣆⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⣦⣴⣶⣶⣶⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣤⣤⣤⣤⣤⣬⣿⠇
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⢰
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣄⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⢠⣾⣇⣸⣿⣿⣿⣿⣀⣷⣄⠀⠀⠀⠀⢀⠀⠀⡀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠘⠛⠀⠛⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣤⣤⣿⣧⣼⣿⣤⣿⣷⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠿⣿⣿⣿⣿⣿⠿⠿⠿⣿⡄⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⣶⣤⣤⣤⣤⣤⣤⣤⣶⡞⠟⠁⣠⠀⣤⣤⣤⣤⠀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⢉⣉⣉⣉⣉⠉⣉⣁⠀⣸⣿⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣬⣿⡏⢹⣿⣤⣿⡟⢀⣿⣿⠀⣿⣿⣟⠀⣀⡀⢸⣿⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⣼⣿⣿⣿⠁⣸⣯⣤⣤⣤⣽⣗⠀⣿⡇⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣏⣉⣉⣹⣿⠃⢠⣿⣧⣤⠀⣤⣼⣟⠀⠛⠃⢸⣿⠀⠛⠃
⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⣀⣀⣀⠈⠛⠿⠿⠛⠁⣴⣿⣿⣿⡿⠀⢿⣿⣿⡶⠀⢶⣿⣿⣶
⠀⠀⠀⠀⠘⠛⠀⠛⠛⠛⠛⠛⠛⠀⣶⣶⣶⣦⠀⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠰⣤⡀⠉⠉⣠⣴⠀⢀⣀⣉⠙⠛⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣆⠈⢁⡔⢆⠈⢁⣴⣿⣿⣿⣿⣷⣦⡀⠛⠋⣉⠉⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠚⠋⢠⣦
⠀⠀⠀⠀⠀⣿⣿⣿⡟⢈⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠹⣿⣿⣿⣿⠀⠘⠦⠈⠃
⠀⠀⠀⠀⠈⠛⠛⠛⠁⠈⠛⠛⠛⠛⠛⠁⠈⠛⠛⠛⠛⠋⠀⠙⠛⠛⠛⠀⠀⠀⠀⠸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣶⢄⡀⣠⠔⣀⣵⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣎⠹⡿⠉⣿⣷⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⣧⢠⣌⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢻⣿⣿⣿⡿⢠⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣬⣿⣿⣯⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡃⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣛⠻⣿⣿⣿⣧⣦⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣏⡛⠻⢿⣿⣷⣬⣻⣿⣿⣧⣭⣙⡛⠻⠯⠽⠿⠿⢛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢟⠿⠟⠋⠀⠀⠀⢽⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡶⢂⠀⠀⠐⠘⢿⣿⡇⢉⠛⠛⠿⠿⣟⣛⡻⠿⠋⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⠻⠛⠟⢡⠃⣰⠀⠀⠁⠸⣿⣿⣽⡆⣠⡄⢄⣤⣆⢰⣶⢶⡈⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⣉⠉⠙⠓⠃⢰⠃⢰⢀⠀⠀⢿⣿⣿⡇⣿⣿⡝⠛⠋⠙⣿⡏⢛⠸⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉⠛⠀⡼⠏⠀⣿⣾⣿⠟⣾⣿⣿⡇⠀⣀⡀⢿⣇⣹⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠿⡿⠋⠀⡿⠽⠋⠋⠉⠉⠁⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⢄⣀⣀⣀⡠⠉⠀⣠⠁⠀⠀⠀⠀⠀⢀⠤⠀⠀⣉⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⠀⡀⠀⠈⠀⠀⣠⡌⠀⠀⠚⠉⣩⣴⢤⣤⣄⡴⠇⠂⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⣶⠛⠛⠉⠉⢙⣿⡿⠿⠿⠛⠛⠛⢛⣿⠗⠚⠛⣻⠋⠁⢀⣀⠿⠿⡖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠚⠉⠁⠀⣀⣠⠤⠤⠒⠛⠉⠁⠀⠀⠀⠀⠀⢀⣼⠋⠀⠠⠾⠗⠚⠉⠁⠀⠀⠀⠐⠊⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡿⠟⠳⠶⠒⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠃⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⣾⡛⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣶⣾⣿⣿⣥⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠚⠛⠛⠿⠿⠯⡉⠉⠉⠁⠙⡋⠛⠉⠉⠓⠂⠐⠒⠋⠻⠯⠍⢐⡰⢤⠤⢀⡀⠀⠀⠀⠀⢀⣀⠴⠞⠋⠉⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠿⢶⣀⣋⡁⠀⠀⠀⠀⠀⠀⣠⠖⣲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡤⠒⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⢴⡮⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣧⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣫⣝⢷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠋⠉⠙⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣴⣿⣿⣆⢻⡄⠀⠀⠀⠀⠀⣤⣾⡏⠀⠀⠀⠀⠀⠘⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣼⣿⣿⣿⣿⣧⢻⣄⠀⠀⠀⣀⡁⡆⡆⡆⣀⠀⠀⠀⣰⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣾⣿⡏⣭⣭⢉⣿⣧⡹⣆⢠⣾⣿⡇⣷⣷⡇⣿⣿⣦⠺⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣾⣿⣿⢸⣿⠃⠾⢿⣿⡷⣁⣛⣛⣛⣃⣛⣛⣃⣛⣛⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣡⣿⣿⣿⣇⣛⠛⣿⢃⣾⣿⣧⢛⡛⣛⣛⣛⣛⣛⣛⣛⣛⠛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣱⣿⣿⣿⣿⣿⣿⠱⢣⣿⣿⣿⣿⣎⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣼⣿⣿⣿⣿⣿⣿⡏⣠⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣜⠿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢰⣮⣭⣭⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⣤⠸⣿⣿⣿⣿⠇⣤⢠⡄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢸⡇⣿⣷⣝⣛⣛⣫⣾⣿⢸⡇⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣸⣷⣬⣭⣭⣭⣭⣭⣭⣥⣾⣇⢿⣿⣿⣿





⡶⣶⢶⠶⠶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⠶⣶⠶⢶⣶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣀⡤⠚⠃⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠚⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠑⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠲⠆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⢀⡀⠄⣀⡀⠀⠀⠀⢀⡠⠄⣀⡀⠀⠀⠀⠀⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠀⢀⠋⢠⣤⠉⢿⡆⠀⠰⠋⣠⣄⠙⣿⡄⠀⢠⡶⠙⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠰⠄⠈⢦⡈⠋⣠⣾⠇⠀⠸⣆⡙⠋⣠⡿⠁⠀⠉⡇⠀⠀⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣤⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠙⣧⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⣀⡀⢀⡀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣯⢸⣿⡅⣿⣧⣸⡇⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠈⠉⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠟⠛⠻⣿⠛⠛⠛⠛⠻⣿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⢢⣤⡐⠒⢺⣇⠀⣘⣿⠗⢺⣆⠀⣘⣿⠒⠒⠒⠒⠲⡶⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢠⣶⡟⠉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉⠙⡿⠀⣰⣶⡄⠙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣀⠘⠿⡇⢸⠇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢹⠂⣷⡀⠛⠟⠃⣠⡿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡌⢶⠉⢶⠶⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⠁⢶⢶⡖⠉⣤⢡⡄
⠀⠀⠀⠀⠀⠀⠀⢇⡸⠀⢠⡎⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣯⠀⠸⠀⢱⡄⠀⠆⠱
⠀⠀⠀⠀⠀⢀⠻⡜⠃⢀⠏⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣏⠀⢰⠀⠀⠱⠀⠘⢃⠾⡀
⠀⠀⠀⠀⢠⡌⣶⠁⢠⠟⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⡆⣿⠀⢸⠀⠀⠀⠻⡀⠈⣤⢃⡄
⠀⠀⠀⠠⣆⡸⠀⢠⡎⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⣿⠀⢸⠀⠀⠀⠀⢡⡄⠈⢎⣱⡀
⠀⢀⡰⠛⠉⠓⢲⡆⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⢱⡖⠊⠉⠛⢦⡀
⠀⠘⠁⣴⣿⣦⠀⠃⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠈⠀⣶⣿⡆⠈⠃
⠀⠘⣆⡈⠛⠋⡠⠇⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠰⣄⠙⠛⢁⣴⠃
⠀⠀⢹⠉⠀⢻⠁⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠀⠙⠏⠀⠉⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣧⠘⠓⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠀⣏⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⡿⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣸⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣇
⠀⢘⣋⣉⣉⣉⣉⣱⠀⠀⠀⠀⠀⠀⢀⡴⢛⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠁⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⣎⣉⣉⣉⣉⣹⠇
⢀⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢸⠁⢠⣿⣆⡀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣿⣷⠀⢈⡆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧
⣾⣿⠿⠋⠉⠉⠙⠻⣿⣧⠀⠀⠀⣰⠿⣆⡈⠛⠛⠉⠶⠆⠀⠀⠰⠾⢿⡀⠙⠛⠋⢀⣼⢷⡄⠀⠀⠀⣾⣿⠟⠋⠉⠉⠙⠻⣿
⣿⣿⡄⠀⠀⠀⠀⠀⢻⡿⠀⠀⣠⡿⠟⠛⣻⣶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⠃⢶⣶⣟⠛⠻⣿⡀⠀⠀⢿⡏⠀⠀⠀⠀⠀⢠⣿
⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣡⡶⢋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠻⣦⣈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⢉⡴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣌⡙⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⠾⢋⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠻⢦⣜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠛⠳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⠛⠛⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⣴⣶⡄⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⣤⣶⣆⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠘⠿⠿⠃⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⠻⠿⠟⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⣤⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢯⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣭⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣤⣴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠉⣡⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡍⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠋⣸⡇
⠀⠀⠀⠀⠀⠀⣴⠚⠛⠛⠛⠚⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠚⠛⠛⠛⠻⠂
⠀⠀⠀⠀⠀⣴⣿⣶⣶⣶⣶⣶⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣶⣾⣶⣶⣿⣷⡆
⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⢹⣿⠃⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡟⠉⢉⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣧⣤⣼⣿⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣧⠀⣼⣿⣄⠀⠀⣿⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⢹⣿⠀⠀⠀⠀⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⠋⠺⣿⣿⡿⣷⣼⣿⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠸⣿⣄⣀⣀⣼⡿⠁⠀⠈⠑⠠⣀⠀⢀⡴⠛⠁⢸⣿⠀⠀⠘⣿⣿⣾⣿⣿⣦⣀⣀⣠⣿⠃⠄
⠀⣶⣤⣀⠀⠀⠛⠃⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⡵⠋⠀⠀⠀⠘⠋⠀⠀⢸⣿⣿⡟⠛⠉⠙⠛⡛⠋⢋⣠⠆
⠀⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⣄⠀⠀⠀⠀⣠⠔⢻⣿⣿⣿⠀⣀⣴⡾⢋⡴⠋⢁⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠹⡄⢀⡠⠊⠁⠀⣾⣿⣿⣿⢸⠟⣩⠞⢉⣠⡾⠟⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⣿⣿⣿⣿⡇⢊⣠⠶⢛⣩⣴⣾⡇
⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⢀⣠⣞⣁⣤⣤⣴⣶⣶⣿⠿⠟⠋⠘⣿⣋⣥⡶⠟⠛⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⣀⣤⠖⢿⣉⣠⣤⣴⣶⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⠿⠿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠸⣏⣭⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠒⢶⣶⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⣀⣤⣴⣶⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣴⠾⣖⠒⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⠷⠄⠀⢀⣀⣤⣴⣾⣿⡿⠿⠛⠉⠁⠈⠻⣿⣿⣿⣿⣆⠀⠘⠛⠛⠿⣶⣤⣼⣦⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣠⠎⢉⣠⣴⣾⣿⣿⡿⠿⠛⠉⠁⠀⢀⣀⣤⠤⠶⠒⠛⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠉⠙⢿⠟⠻⣦⣼⡇
⠀⠀⠀⢀⣴⣿⣷⣾⣿⠿⠟⠛⠉⢀⣀⣤⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠈⡠⣄⠈⠙⡇
⠀⣤⣶⣿⠿⠛⠋⣉⡠⠄⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⢧⣈⠳⣄
⠀⣫⣥⣴⣶⠟⠘⠿⢿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⢸⣿⣷⣼⠇
⠀⣿⠿⠋⠁⠀⠀⠀⠀⠈⠉⠛⠻⢮⠍⠙⠀⠄⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠙⢿⣿⡄⢠⣀⣤⣾⣿⡏⠛
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⣀⣤⠴⠖⠚⠉⠀⠀⠀⠀⡀⣀⣽⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠉⠀⢀⠤⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠿⣿⣍⡀⠹⣿⣿⣿⣿⠆⢀⠁
⠀⣤⣤⣤⣤⡄⠀⠀⣠⣀⣀⢀⠀⡰⠟⠁⠀⡠⠐⠁⠀⠀⠀⠀⣸⣿⣿⣿⠿⠛⠉⠀⠀⠈⠛⢿⣶⣌⣿⣿⣿⠀⠰
⠀⣿⠿⠋⠁⣠⣴⣿⠿⢋⣵⣿⣷⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡿⢻⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⡿
⠀⢱⣿⣿⠿⣿⣍⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣸⡷⠀⠀⣴⣿⣿⢿⣦⠙⢷⣄⠀⢠⣷⠀⠀⠀⢩⣿⣿⡆
⠀⢾⣿⠁⢀⣼⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⣿⣇⡿⠀⠀⠀⢠⡿⢦⣾⣿⡆⠀⠀⢠⣿⣿⡇
⠀⣼⣿⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠈⢻⣷⣦⡀⣴⢏⣤⣾⣿⢾⣿⠀⢀⣾⠋⣿⣷⡄⠀⠀⡄
⠀⣿⡏⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⠀⢸⡇⣿⡿⠛⠛⢩⣿⠃⠀⢻⣧⣿⢇⠀⢻⣧⠘⢄⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣴⣤⢦⣶⣶⣶⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⢀⣤⣄⣀⣀⣄⣀⣀⣀⣤⣀⠀⣿⣤⣼⣤⣧⣼⣦⣽⡇⠀⠀⠀⣨⣿⣿⣆
⠀⠀⠀⠀⠀⠺⠟⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠻⠁⠈⠇⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⢸⣯⣥⡷⣼⣧⡞⣛⣸⣾⣧⣼⢸⣯⢽⣿⡅⣿⣷⢸⣼⢦⣾⣼⢛⣇⠀⠀⠐⢣⡝⠀⠄⠀⠀⡄⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠊⠃⠙⠃⠛⠛⠙⠙⠁⠙⡘⠛⣊⠛⠃⠃⠙⠈⠙⠀⠙⠈⠛⠋⠈⠀⠀⠘⠁⠀⠀⠀⢀⣀⣀⣼
⠀⠀⠀⠀⠀⣤⣤⡜⠛⠁⠀⠀⢈⠁⠀⢀⣐⠂⠒⡤⠨⠿⠟⠿⠿⠿⠀⠀⠀⠀⢀⡴⣤⠀⠰⠂⠀⢠⣴⢄⠀⠀⠀⣬⡉⠉⢢
⠀⠀⠀⠀⠀⠿⠾⢃⡀⢠⣭⣤⣥⣥⠀⣿⣹⡇⠀⠀⢀⣀⠶⠶⠖⢠⢂⠀⠀⠀⠈⠓⠛⠀⠀⠀⣸⣨⣍⣤⡄⠀⠘⠛⢃⡀⢸
⠀⠀⠀⠀⠀⠀⡶⢺⠳⠶⡲⠖⠶⠒⡖⠲⠓⣶⠀⢸⣿⡏⣁⠀⠀⠆⠀⢀⠀⠀⢀⡉⠀⠀⠈⠀⠉⣂⢁⡘⠁⢙⡖⠟⣼⠁⢸
⠀⠀⠀⠀⠀⠀⠛⠚⠒⠒⠒⠒⠒⠒⠓⠒⠒⠟⠀⠀⡙⠃⠻⠇⠀⡀⠀⣿⠂⠂⠈⢁⣯⠈⠠⠴⢏⡽⠿⢿⣷⣮⣙⣿⣟⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠿⠀⠀⠀⠀⠿⠀⢰⡟⡻⢻⠟⠿⢟⠶⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⠾⠷⠶⠶⠶⠶⠿

⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⠤⠤⠤⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠃⠈⣻⣿⣿⣿⣿⣿⣿⡿⢃⠋⣀⣀⣀⣀⣬⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡏⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣿⣿⣿⣿⡇⣹⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⠃⠉⠠⣝⣿⣿⣿⣿⣿⣿⣿⡏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⣿⣿⣭⠉⠹⢿⣿⡟⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢩⣿⣿⣿⡿⣦⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣷⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⢷⣾⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⡇⢩⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡟⢼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⣷⡈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡀⠀⠀⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠇⠈⠞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠁⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⡆⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⡇⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢸⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⣿⣟⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⣿⠟⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡯⠈⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣐⣿⣿⣇⣀⣦⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣶⣷⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣹⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣾⣿⣿⣿⣿⣿⡿⢿⠯⠭⠭⠭⠭⠭⠥⠄