Heart dot art with hole Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣶⠋⠉⠉⠙⠲⡄⠀⠀⣠⠞⠋⠉⠓⢦⣄⣰⣿⣯⡀⠆⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠻⣷⣀⣀⠀⠀⠘⠢⣴⡏⠀⠀⠀⠀⢀⣿⢿⡧⠸⡗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠠⣤⣙⣛⣀⠀⠀⠀⠀⠀⠀⣀⣀⡾⠏⠁⠨⣧⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠉⠉⠉⠙⠚⠋⠉⠉⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢬⣧⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⡀⠈⠻⣿⣿⡫⠛⠙⠛⠒⠓⠂⠻⠻⣯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢭⠅⠙⠶⣿⣏⠉⠛⢦⡀⠀⠀⠀⠀⣠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣰⠥⠂⠈⠀⠉⠁⠀⠀⠀⠙⠦⣄⣲⡾⠋⠀⠛⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠛⠉⠉⠉⠛⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠛⠛⠻⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡀⣤⣴⣻⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷
⠀⠀⠀⠀⠀⢨⡛⣿⣿⣷⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⣰⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⢙⣿⣻⣿⠋⣈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣙⣋⢻⡏⣾⣿⣴⣖⣶⠄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠐⣗⢦⠀⠙⠿⣿⣿⠿⠯⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠾⣿⡤⣶⢸⡟⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠺⢯⣿⣟⠋⠘⣇⠀⠀⠹⡆⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋
⢠⣶⠛⠛⠻⢦⣀⣿⣀⣣⣷⣿⠛⠉⠉⠉⠙⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁
⠈⢛⣥⡶⠞⠛⢛⣻⣿⣿⣿⣷⣿⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏
⠀⠸⠷⠦⣤⡀⠉⢿⣿⣿⣿⣿⣿⢦⣤⠞⣣⣤⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⠁
⠀⠀⠀⠀⠀⠉⣿⢣⢿⠿⢹⣿⣟⣤⠿⢶⣏⢀⡀⢸⡿⠛⠻⣦⡀⠀⠀⠀⣀⠀⣤⣠⣾⡿⣻⣟⣀
⠀⠀⠀⠀⠀⠀⣿⠈⠀⠀⣸⣏⣸⡇⠐⢤⣹⣦⣷⣾⡵⠆⢀⣸⡇⠀⠀⠀⣿⣾⣿⡿⠛⣶⠟⣛⠉⢀⣤
⠀⠀⠀⠀⠀⢠⣟⣀⣠⡼⠃⠈⢹⡿⠓⢒⣻⣿⣷⣻⣿⣯⠉⠉⢷⠀⣿⣰⣿⡿⠋⠹⣦⡿⢞⣫⡶⣿⣷⠄
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢿⡀⠈⣩⡾⣻⢿⠻⡟⠲⣤⣤⣿⣼⣿⣿⣋⣠⣤⣾⠿⠞⠛⠛⠳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣏⠀⠁⢸⣇⠉⢀⣼⠿⣿⡿⠿⠻⠿⣭⣵⡶⣆⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠟⠉⠛⠋⠹⣿⣿⠃⠀⠀⠀⣸⡏⠻⣟⠛⠳⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢁⠂⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠎⠀⠾⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠻⠦⣤⡈⠀⠀⠀⠀⠀⢰⡇⠀⠀⢠⠞⠁⠀⠚⠛⢿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣾⠁⠀⣴⠉⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣿⡿⠀⠀⣿⠀⠸⠷⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡏⠑⢸⡟⠇⢀⣰⡟⠃⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⣿⢻⣿⡏⠃⠀⠀⢀⣀⣤⣴⣖⣴⢿⣿⣧⣀⣀⣀⣤⠾⠿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣗⠀⣴⣿⣿⣿⠁⠀⠀⣠⣿⣯⣉⣉⠿⠻⠾⠛⠛⠉⠉⠀⠀⠀⢀⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣷⣿⡟⠆⠀⠀⠀⣬⣿⣷⡉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⢿⣿⠂⠀⠀⠐⣿⣿⣿⡗⠀⠀⠀⠀⢀⠴⠟⠛⠙⠉⢻⡏⣩⣌⣙⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣥⢻⣿⣷⡄⠀⠈⣿⣿⣿⠃⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⡸⠋⠻⢿⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡯⢟⣺⣿⣿⣵⣶⣾⡿⢉⡏⡀⢀⠀⢀⡿⠁⠀⣠⣶⣄⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣾⣿⣩⡿⠟⠿⢿⡿⣫⣠⣾⠏⠁⠀⠀⣼⣇⣴⡞⠟⠁⠈⠃⢤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁⠀⠀⠀⠙⠺⣿⡃⠀⠀⠀⠠⣿⣿⣿⠋⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣡⣽⡇⠀⠀⠀⠀⠀⢀⡏⠙⢶⠀⠄⠀⢿⣿⣇⠰⣆⠀⠀⣠⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣿⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠈⠛⠻⡿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⣰⡟⠛⢦⡀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠁⣠⠞⠋⢉⣿⡆⠀⠀⢧⡀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠌⠀⠀⠀⢸⡿⠀⠀⠀⢸⡇⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣥⠄⠀⠀⠀⠀⠀⠀⣠⠟⢻⠀⠀⠀⠀⠙⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣼⠏⠀⠘⠇⠀⠀⢀⢤⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠷⠂⣠⣾⠏⠀⠀⠀⠀⠀⠀⣾⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣯⣿⡿⠀⠀⠀⠀⠀⣀⣤⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⢄⣠⣀⣴⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠉⠀⠰⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣠⡌⠀⠛⠃⢴⡦⢠⣤⠀⠀⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣠⡄⢀⡈⠁⠰⠆⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣴⣦⣠⣽⢋⣿⡿⣶⣾⣦⣼⡟⢐⡿⠂⣴⠄⢀
⠀⠀⠀⠀⠀⠀⠘⠀⢴⡆⣠⣬⢁⣻⠟⢴⣿⣦⣤⡄⣀⡛⠀⠶⠀⢀⡀⠀⠈⠀⠰⠆⣠⣮⣁⣿⡟⣿⣿⣷⣿⣿⣽⣿⣿⣿⣷⣴⣦⢀⡈⠁
⠀⠀⠀⠀⠀⠘⠃⣴⣦⣤⣽⣏⣿⣿⣿⣿⣷⣼⣿⣹⣿⠇⣾⣶⢠⣄⠀⠘⠃⢰⣶⣠⣾⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣏⣘⠛⠀⠦
⠀⠀⠀⠁⠰⠷⢠⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣥⣽⡋⢸⠿⢠⣶⣦⣼⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠃⣴⠄
⠀⠀⠃⠠⣶⢄⣼⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣷⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣴⣦
⠀⠒⠀⣴⡆⣬⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣮⡁⠀⠁
⠀⠀⢠⣄⢀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⡏⠀⠛
⠀⠀⣄⠁⣹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⠃⠻⠂
⠀⠀⠁⠘⠿⢳⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⠛⠰⠖⠀⡀
⠀⠀⠀⠺⠃⣴⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⠿⠰⡶
⠀⠀⠀⠆⢀⣬⠁⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡿⠃⣴
⠀⠀⠀⠀⢀⠁⠘⠿⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⠇⢠⡄
⠀⠀⠀⠀⠀⠀⠺⠃⣴⣿⣩⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠟⣾⡷⢀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⣌⠁⣙⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⠿⢰⣦⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠂⣤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢰⡦⢠⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⠆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣘⠋⠹⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠇⣴⡆⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠾⠆⣼⣿⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⡿⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣉⠉⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡟⢿⡿⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠿⠠⣾⣏⣽⣿⣻⣿⣿⣿⣿⣿⣿⣟⣻⡿⠳⣶⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⡌⢀⣛⠛⢿⣿⣿⣿⣿⣿⡿⠻⣿⠇⣴⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠰⣿⢦⣿⡏⣹⡿⠛⣿⡗⢠⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴⠀⢀⡉⠁⠻⠋⢰⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠃⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣴⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠿⣿⣿⣿⣿⠿⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠻⡟⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠿⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⡿⣷⡿⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⣴⣦⣾⣿⣿⣿⣿⣿⣿⣏⣿⣿⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣼⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣥⡤⣲⣿⣚⠻⣧⠉⠉⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢺⣵⡿⢓⣵⣿⣿⣿⣯⣿⡾⣷⡄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣾⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣷⣽⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣌⣛⣻⣿⣿⣿⣿⣿⣿⡄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⣟⢿⣿⣿⣿⣿⠷⣿⣿⡿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⣷⡝⠳⣽⣿⣿⣿⣿⣛⣛⣻⣿⣟⣫⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣍⡢⣌⡙⣻⣿⣿⣿⣿⣿⣟⣛⣿⠷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⣿⠷⠀⠨⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣠⡤⣤⡀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠛⢶⠞⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⡶⠄⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠸⢧⡤⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠿⠟⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠋⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠁
⠀⠀⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢖⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠆⡀⠚⠀⠀⠀⠀⠤⠀⠀⠀⢀⢄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠣⠧⠀⠀⠀⠀⠀⡠⡾⡁⢷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠠⢊⠆
⠃⠌⠂⠀⠀⠀⠀⠠⠤⠂⠒⠀⠀⠀⠀⠀⠁⠈⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠉⠁⠀⠀⠀⠀⢴
⢄⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢢⣠⠘⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢨⠕⠁⠈⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀
⡠⣤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠴⢈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⢦
⢆⡄⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠺⣃⠄⠀⠀⠀⠀⠀⠀⡤⡠⠰⡀⠀⠀⠀⠀⠀⢐⡦⠴⠃
⠀⠓⠔⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠂⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄
⠀⠀⢠⠀⣄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⡀
⠀⠀⡛⠀⠵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠸⠂⠀⠀⠀⠀⠀⠀⣤⠀⠂⢲⠀⠀⠈⠀⠀⠀⠀⠉⠈
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢠⡄⠖⠊⠀⠀⠀⠀⠀⠀⠹⣤⢀⡋⠀⠀⠀⠀⠀⠀⠑⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠐⠆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⢰⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢲⠆⠛⠁⠀⠀⠀⠀⠀⢰⠨⠉⢸⠀⠀⠀⠀⠀⠀⠀⠀⡩⣦⣀⠀⠀⠀⠀⢠⢄
⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣧⡀⠀⠀⠀⠀⠀⠀⠈⠒⠂⢼⠀⠀⠀⠘⠃⠀⠀⣀⠘⣡⠍⠀⠀⠀⠀⠘⠲
⠁⠀⠀⠀⣤⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡄⠀⠀⠀⠠⣀⠌⠃⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⢸⣃⢀⣈⠄⠀⠀⠀⠀⠀⠀⡐⡹⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣔⢀⢀⣢⡀⠀⠀⠀⠀⠈⠊⠙⠁⠀⠀⠀⠀⠀⠀⠶⠪⠌⠀⠀⠀⠀⢐⣐⣢⢂⡇
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠶⠒⠘⠛⠁⠙⠛⠐⠦⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠶⠂⠘⠛⠙⠛⠐⠲⠆⣀⡀
⠀⠀⠀⠀⢀⡴⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⣀⠀⠀⠀⢀⡴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⣄
⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⢀⡶⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆
⠀⡬⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡄
⢈⠁⠀⢼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠛⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣶⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠨⡄⠀⠀⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡬
⠀⠉⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠃⡘⠁
⠀⠀⠙⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢁⠘⠁
⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠋
⠀⠀⠀⠀⠀⠈⠁⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠶⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢀⡀⠀⠀⠀⠀⠀⠀⢀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣀⠀⠀⠀⠀⡐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⠀⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⠰⠇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣍⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣄⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣠⣴⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠸⣿⣿⣿⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣄⠀⠈⠙⢿⣿⣿⣆⠈⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠈⣿⣿⡟⠀⠀⠀⢸⣿⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢀⠝⠛⠳⠦⣀⠀⠀⠀⠀⠀⠀⢀⣤⠿⠟⠋⠁⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡔⠁⠀⠀⡘⠀⠀⠀⡄⠀⢠⠀⠀⠀⠈⠀⠈⢢⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡠⠊⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢃⠀⠀⠑⡀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⡘⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠈⡄⠀⠀⠈⢆⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠐⢤⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡌⠀⠀⠀⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⢆⠀⡠⠒⠘⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠇⠀⣀⢀⣘⡀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠐⢠⡀⠀⠀⠀⠀⠀⠀⠰⡎⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⢀⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⢠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⣫⣭⣶⣶⣶⣦⣤⣀
⠀⠉⣵⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⢟⣵⣿⣿⡿⠿⠿⠿⢿⣿⣿⣷⣄
⠀⠀⠙⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⣶⣾⣿⣿⣿⠿⢋⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡆
⠀⠀⠀⠈⠙⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣭⠽⠟⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⠛⠛⠿⢶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣃⣀⠀⠀⠀⠀⠉⠙⠻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠞⠁⠈⠉⠉⠛⠲⠦⣤⡀⠀⠀⠙⢿
⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠈⠓⠤⣀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣧⠀⠀⣸
⠀⠀⠀⠀⠸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣾⣫⣥⠴⠞⠉
⠀⣠⣤⡀⠀⠘⢿⣿⣿⠆⢠⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠿⠻⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁
⠀⠹⣿⣿⣄⠀⣴⣿⣥⣄⠈⠻⣿⣄
⠀⠀⠈⠛⠋⠀⠈⣻⣿⠿⠛⠊⠉⠹⣆
⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⢀⣴⣿⠇⠘⢧⡀
⠀⠀⣴⠟⠁⠀⠀⠀⠀⠐⠿⠟⠋⣀⣄⠈⠻⣄
⢀⣾⠋⠀⠀⠀⠀⢀⣀⡀⠀⢠⣾⡿⠋⠀⠀⠈⠳⣄
⣼⡇⠀⠀⠀⠀⠀⠘⠿⢿⠿⠈⢹⣶⣦⣄⠀⠀⠀⠈⠳⣄
⣿⣇⠀⠀⠀⠀⠀⠰⣿⣦⣄⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠁
⢹⣿⣆⠀⠀⠀⠀⠀⠈⠻⠿⠇⣰⣿⣷⠄
⠀⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏
⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠈⠙⠿⣿⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣷⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠶⠶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠴⠖⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⣀⣀⡃⠀⣄⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⢒⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠰⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⡀⠀⡠⢴⡄⣶⢲⡄⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡆⠀⠀⡇⢀⠁⠈⡇⣿⢸⡇⣿⠉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢸⡇⠠⠤⡧⢼⠤⠤⡇⣿⢸⠇⢿⠄
⠀⠀⠀⠀⣀⡐⠠⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⢸⠀⠀⡇⣿⠉⠀⢸⠀⢀⡴⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠄
⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠠⢤⠄⠀⠀⠀⠇⠸⢤⣠⠀⣿⠀⠀⠸⠖⠁⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠉⠀⠀⠀⠂⠄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠀⠀⠀⠠⠄⠀⠠⠤
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠈⠠⠠⠊⠀⠀⠀⡀⢀⡄⠀⠀⠀⠀⢄⠠⠀⣂⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣀⣀⣈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠔⢈⠇⠀⠀⠀⢘⡆⠀⢸⣄⠀⠀⠀⠀⡁⠢⡀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣉⠳⣌⡠⠔⠁⠀⠀⠀⡔⠁⠙⠋⠉⠀⢱⠀⠀⠀⠀⠤⡀⣊⠴⠓⣄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⠀⠂⠀⠀⠠⣄⣀⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⢑⠎⠀⠀⠀⠀⠀⢘⠉⠉⠁⠉⠉⠉⠉⡂⠀⠀⠀⠀⠈⠡⢔⠩⠈⠀⠀⠠⠀⠀⠰⠂⠠⠀⠀⠂⠀⠀⠀⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢉⡉⠉⠉⠉⠉⡉⡅⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⠀⠤⠀⠂⠀⡆⠐⠀⠀⠀⠀⠀⠈⢠⡌⠀⠘⠁⠌⠃⠀⠀⠀⠀⠀⢀⠂⠀⠀⠖⠀⠀⠀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠈⢷⠀⠀⠀⠠⠤⠥⠤⠁⠤⠀⠼⠄⠂⠀⠀⠀⡇⠘⠀⢀⡇⠨⠅⢈
⠀⠀⠀⠀⠀⠀⠀⠤⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠣⠄⠄⠀⠒⠚⠒⠒⠒⠂⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠶⠀⠀⠌⠀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⠔⠉⡄⠀⠀⠀⠀⠠⠈⠂⠈⠀⠀⢰⠅⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⢰⠠⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠟⡠⠔⠊⣁⠴⠀⠀⠀⠐⠁⠈⠀⡤⣃⠀⡀⢀⡀⣀⢀⡀⢀⠀⡀⠀⡁⠀⠀⠀⠀⡀⠠⠄⠘⠀⠐⡀
⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠱⠖⠂⠉⠂⠀⠀⡐⠀⢀⠀⠠⠄⠁⠉⠀⠀⠀⠀⠁⠈⠈⠉⠈⠁⠈⠁⠉⠉⠁⠁⠀⠆⠰⡀⠀⠐⡀
⠀⠀⠀⠀⠀⢭⣩⣉⣉⡁⠀⠀⠁⠀⠀⠀⠀⡜⢠⠀⠞⠁⠀⢠⢄⡀⠀⠄⠤⠤⠤⠠⠄⠤⠠⠀⠤⠠⢄⠤⠠⢄⠀⠀⠀⠹⠄⠤⠐⡄
⠀⠀⠀⠀⠀⠲⠤⢤⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠄⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢠⠂⠀⠀⠤⠁⢀⡆⠀⠠⠆⠀⠀⠀⠀⠈⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠘⢤⠀⠡⠀⠀⠘⢂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠈⠀⠀⠀⢀⠔⠁⠂⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠈⠤⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⡠⠊⠀⠀⠀⠀⠀⣀⠀⠀⠸⠁⠀⠀⠀⢰⠀⠀⠀⢼⠀⠀⠀⡀⠀⠀⠈⠣⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡔⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⠀⣀⠀⠇⠀⠀⠀⠀⠐⡄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⡜⠀⠀⠀⠀⠀⠰⠒⠀⠒⠐⠀⠂⠀⠂⠐⠄⠢⠤⠄⢄⠠⢄⢤⣠⠀⠀⠀⠀⠀⠀⠘⡄⢀⠀⠀⡡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⡀⢀⡜⠀⠀⠀⠀⠀⠀⢠⠤⠠⠤⠤⠠⠠⠤⠄⠀⠀⠄⠤⠠⠄⢤⢠⡤⡘⠀⠀⠀⠀⠀⠀⠀⠐⡤⢀⠉⠐⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢁⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡎⠀⠅⡠⠂⠀⠐⠃⢀⠀⡆⠈⠠⠁⠘⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠚⠉⠉⠉⠉⠉⠓⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣫⢔⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣡⢞⠕⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡙⣆
⠀⠀⠀⠀⠀⠀⠀⣠⢋⡞⡵⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⢌⢳⡀
⠀⠀⠀⠀⠀⠀⣰⢣⢏⠞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⢆⢳⡀
⠀⠀⠀⠀⠀⢰⢃⠏⡎⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠆⢳
⠀⠀⠀⠀⠀⡏⡼⠸⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡈
⠀⠀⠀⠀⢸⠁⡇⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠇
⠀⠀⠀⠀⢸⢰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠘⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡄⡇⠇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠇
⠀⠀⠀⠀⠀⢧⢹⡸⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠰⢠
⠀⠀⠀⠀⠀⠘⣆⢧⢣⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢡⢃⡎
⠀⠀⠀⠀⠀⠀⠘⣎⢧⡳⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡱⣝⢎⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠣⡙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⣎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡘⡜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢣⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠷⠶⠶⠶⠿⠟⠛⠛⠛⠛⠋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠿⢿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠿⠛⠚⣛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⠷⠶⠶⠶⠶⠶⠷⠒⠛⣿⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⣾⣿⣿⠿⠶⠤⠤⠤⠴⠶⠶⠶⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⢶⣿⣿⣿⣶⣦⣤⣤⣤⣤⡤⠤⣶⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⣿⣿⣿⠳⠤⠤⠔⠒⠒⠒⢋⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⣶⣾⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠒⠀⠀⣠⣴⣾⠿⠿⠿⣶⡄⠀⠐⠀⠀⠀⣤⠀⠀⣠⡶⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠈⣿⠠⠶⠶⠶⢶⡿⠾⠛⢫⣶⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣿⣿⣿⣿⣿⣧⠀⠀⣿⡇⠀⠀⠀⢀⡀⢠⡏⢠⣾⠀⢀⣿⠃⠀⠀⣀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠻⣿⣄⠀⠀⠸⠷⠏⠀⣤⠁⠀⣼⡟⠀⠀⣼⡟⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢟⣡⢀⣠⣤⣀⠈⠻⣷⣄⠀⠀⠀⣸⡏⠀⢰⣿⠃⠀⣼⣿⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⢠⡟⣵⡟⠉⠀⣹⠀⣀⡈⢻⣧⠀⢰⡿⠁⡰⢹⡟⠀⣰⣿⡇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠰⡟⠀⠀⣠⠏⣾⠋⠀⠀⣿⠀⢸⣇⡴⠁⠸⣧⠞⠁⢿⣇⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠙⠷⣤⡤⠞⠁⠀⠙⢧⣤⠾⠃⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠆⠀⣀⣤⣤⣀⠀⠀⠀⢀⣤⡀⢀⠀⣦⣰⣦⣿⣠⡷⢀⡆⠀⠀⠉⢀⣾⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢶⡀⢠⣾⠟⠉⠉⠙⣷⡀⠀⢈⡛⠀⢸⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⣠⡴⠋⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⣇⠀⠀⠀⠀⢹⡇⢀⣾⡇⠀⠛⢻⣿⣿⣿⣿⠿⠏⠀⠙⠛⠁⠀⢠⣿⡇⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠻⣦⣀⠀⢀⣸⡗⣹⣿⠀⠀⢠⠀⣿⣿⣿⣿⠀⠀⣤⡬⠊⠻⠿⢿⣿⣷⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣿⡇⠀⠀⠉⠉⠁⣿⠀⣿⡇⠀⢠⠃⠀⣿⣿⣿⡟⠀⢰⣧⠀⠀⠀⠀⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣸⠇⠀⢿⣇⡴⠁⠀⠀⣿⣿⣿⡇⠀⠈⢿⣄⣀⣀⣴⡿⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢿⡇⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⣀⠀⠉⠉⠉⠀⠀⢠⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⢿⣦⡴⠋⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣦⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠄⠰⢂⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢳⣼⣿⣿⣧⣶⣀⣶⣢⣀⣀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠙⣳⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣦⣤⣶⣾⣿⣆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣴⣾⣆⠀⠀⠀⠀⠀⠀⠀⢀⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⠀⠀⣸⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠈⢀⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣿⡖⠐⠀⠀⠀⠀⣀⣴⣦⠝⠛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⢻⡿⠿⠿⣿⣿⣟⠛⡿⠋⠉⠀⠈⠳⠶⠍⠉⠁⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⢈⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢸⣷⣀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⣿⣿⡗⢶⣾⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢹⣿⣿⣯⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⣿⣧⠀⢈⠁⠀⠀⠀⠈⣾⣄⠰⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⠈⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣷⡿⠀⠀⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣧⣴⣶⣼⣿⣄⣶⣿⣿⣿⠸⣦⠀⠀⠀⠀⠀⣿⣿⠏⢀⡞⢠⢯⣿⣿⣿⣿⣿⣿⣿⢟⡡⠀⠀⠀⠠⠔⢤⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢿⣷⣤⣀⣠⣶⣿⣿⣷⣞⣷⣏⡾⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣠⣄⣲⣥⣙⣿⣿⣿⣿⣿⣿⣿⡾⡻⠂⠈⢻⣿⣿⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡋⠀⠀⠊⠁⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡿⠚⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡇⠐⣄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⠄⠀⠀⠊⠹⢿⣿⣿⣿⣿⣿⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣆⠉⠑⢀⡀⠀⠀⠀⠀⠀⠈⠛⢿⡃⠀⠀⣀⣀⣤⠾⢿⣶⣿⠿⠍⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡋⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠏⢀⠎⠀⢱⡌⡆⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠤⠤⣼⢆⠈⠛⣷⠀⠀⣣⢘⢐⡇⣧⠄⠤⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⣀⡾⠿⠖⠃⢘⣠⣄⡁⠺⠺⠿⢷⣐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣀⣐⣦⢼⣤⠘⣃⣘⠀⣦⡧⣄⣂⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡿⣿⣮⣳⣿⣄⣛⣓⣰⣿⣾⡗⣀⢿⡄⠁
⠀⠀⢐⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢴⣠⡽⠿⠛⠋⠛⠳⠜⠛⠙⠛⠿⢧⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠐⡄
⠀⠀⠀⠇⡀⠂⠀⠁⠀⠀⠀⠀⠄⢄⠀⠀⠐⠀⠦⢶⡿⠀⡠⠞⠉⠓⣆⣰⠞⠋⠓⣄⠀⢿⡷⣶⠒⠒⠂⠀⠠⠀⠀⠀⠀⠀⠈⠀⠐⢀⠸⢀
⠀⠀⠀⠀⠑⠄⠀⠂⠀⠑⠠⣀⠠⡀⠑⢄⣐⣠⣶⣿⡇⠀⡇⠀⠀⠀⠈⠁⠀⠀⠀⡈⠀⣾⡁⢈⠁⠉⠀⠈⠀⠀⢀⠄⠊⠀⠐⠀⠠⠋
⠀⠀⠀⠈⠄⠀⠂⠀⠈⠂⠀⠈⠐⠽⡆⠀⠙⢄⢻⠿⠿⡀⠑⡀⠀⠀⠀⠀⠀⠀⢀⠋⢀⡿⣉⡁⡠⠊⠀⢰⠧⠀⠀⠀⠐⠁⠀⠖⠀⡀
⠀⠀⠀⠰⠀⣤⠀⠀⠑⠄⠀⠀⠀⠀⠈⠀⠀⠀⢦⣠⠝⣻⣄⠁⢀⠀⠀⠀⢀⡄⠉⣠⣟⢀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⡤⠐
⠀⠀⠀⠀⠀⠀⠢⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠊⡙⢲⣀⠘⠂⠐⠃⣀⠖⠻⣆⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠔
⠀⠀⠀⠀⠀⠐⠄⡀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢃⠀⢠⠏⠉⠷⠆⠰⠚⠉⠀⠂⠈⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠃⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠐⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢀⢞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡳⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠔⠢⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠔⠢⠝⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠀⠁⠀⠀⠈⠀⠃⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣽⣷⣿⣾⣷⣿⣵⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡈⠂⠀⣠⡶⠟⠛⠛⠛⢶⣄⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢿⣮⣿⡿⢋⣡⣤⣤⣤⣍⠻⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡉⠀⣼⠋⠀⠀⠀⠀⠀⠀⠙⣧⠀⢉⡠⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢷⣿⡏⣰⣿⣿⣿⣿⣿⣿⣷⡌⢿⣷⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠤⠀⢰⡇⠀⠀⢤⡀⠀⡤⠀⠀⢸⡇⠀⠤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣻⣿⠀⣿⣿⣟⢿⣿⢟⣻⣿⡷⢸⣿⣛⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠂⠀⢿⡀⠀⠀⡀⠀⠀⠀⢀⡾⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣆⢻⣿⣿⣿⣿⣽⣿⣿⠃⣼⣿⣭⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠋⡀⠈⢻⡄⠀⡇⢸⠀⢠⡞⠁⢀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣵⡿⣿⣆⠹⣿⡿⣿⣿⣿⢃⣾⣿⢷⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠀⢿⠀⣵⣾⠀⣿⠀⠲⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⢾⢿⣿⡆⢻⡗⠉⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣿⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡿⠿⢿⡿⠷⠘⠃⠀⣛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠋⠉⠉⠁⠀⠁⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣷⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣾⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣻⣿⢷⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⣿⣷⣾⣎⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⣴⣿⣷⣿⡟⣻⢿⣿⣿⣿⢫⣹⡉⢿⣟⣻⣿⢿⡿⣿⣯⡗⣻⢻⣿⣿⡿⣾⣯⣶⡀⠀⠀⠀⠹⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠀⠀⠀⣴⣿⣿⢿⣿⣧⢿⣟⣺⣿⣿⣏⠽⡿⡷⣸⣿⣿⠾⣿⣯⣿⣿⣜⢿⣻⣿⣿⣿⣬⣷⣿⣿⡄⠀⠀⠀⠹⣿⣿⣿
⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⣿⡿⡻⢶⣿⣿⣿⡿⡿⢾⣿⣿⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠹⣿
⣿⣿⠏⠀⠀⠀⢰⣿⣿⣿⣿⣿⣟⣫⣻⣿⠀⣿⣿⢿⣿⣿⣿⣿⣿⢲⣿⡏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⡀⠀⠀⠀⠀⣼
⢻⠏⠀⠀⠀⢀⣾⣿⣯⣿⣿⣿⣏⣟⣻⡟⣸⣽⠇⣾⣿⣿⣿⣿⣻⡿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣹⣿⣧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢰⣿⣯⣿⣟⣻⢭⡭⣿⡿⢀⣯⡟⢠⣿⠋⣴⣿⢿⡿⠁⡽⣶⢻⣿⡿⣿⣍⣿⣿⣿⣋⣿⣿⣾⣹⣭⣿⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣷⣷⣿⣻⣹⣯⢷⣿⣇⣾⣿⡏⢸⣿⡄⢓⣻⣿⡟⠰⡿⢋⣿⣿⠁⣽⣿⡟⣿⣿⣟⣿⡿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⣿⣿⡿⢿⣿⣟⡾⣿⣿⣿⣿⢷⢾⣿⣿⠿⣽⣻⠇⣤⣾⣿⣿⣿⣦⣌⣥⣞⣫⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⣿⡶⣿⣏⣽⢿⣿⣽⣮⣾⡗⡾⣆⡟⣿⣷⣭⣾⢠⡿⣼⣿⢾⣿⣷⣿⣿⡿⣿⣿⣿⣿⡟⢙⡟⣿⣿⡇⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⣿⣟⣟⣟⡟⢳⢹⠟⣿⣿⣿⣿⣦⣾⣿⣿⣉⡿⢻⣯⣼⣶⠚⣿⣿⣿⣸⣯⡿⢿⡿⠂⠀⠀⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣏⣿⣼⢻⣿⣿⣘⣾⣿⢾⣹⣿⣟⣻⣿⣳⢿⣧⣾⣙⣿⢟⣶⣯⣽⠿⡿⣿⣿⣶⣿⣿⠃⠀⢀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡼⢷⢿⣽⣿⣿⣽⢋⡟⣶⣛⣿⣿⡯⣿⢿⣿⣿⣿⣿⣿⣞⣏⡿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢠⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⢻⣾⣹⣿⣿⣿⣟⣿⣿⢤⣿⡄⣹⣿⣿⣿⣿⢺⣿⣿⣻⣿⢹⣾⡼⠃⠀⢀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⣷⣶⣿⠿⣟⣿⣿⣷⠿⣼⠛⣧⣿⣿⣿⣿⣿⣿⣾⣶⣿⣿⠾⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠟⠋⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠟⠻⠿⠟⠛⠛⠛⠛⠋⠁⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⣤⡀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠀⠀⠀⢲⡄⢸⡄⠀⠀⡟⢸⡇⠀⢸⠃⡀⠀⠀⢳⠀⢸⠃⣿⠀⢀⡄⠀⣿⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⣷⠀⣾⠁⢠⡇⠘⣧⡀⠸⡇⢸⡇⠀⣼⠀⣷⠀⠀⣿⠀⢿⠀⣿⠀⠀⢧⠀⢹⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣿⠀⠰⠃⠀⠈⠀⠉⠀⠀⠹⡇⠀⠉⠀⠑⠀⠈⠁⠘⢦⠼⠁⠀⠈⠁⠈⠂⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡇⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠉⠑⠒⠠⠤⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠴⠒⠒⠋⠉⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠰⠄⣄⢛⠩⢀⡄⠍⡛⢠⡀⠦⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠡⣐⣬⣤⡁⢒⡀⣾⠟⠻⣷⢀⣐⢈⣤⣥⣇⠌⠳
⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⢃⠙⠄⠱⣿⡉⣹⣿⢙⣅⡻⣷⣾⢟⢨⡏⣾⣏⢉⣿⡎⠡⠋⡘⡓⠶⣄
⠀⠀⠀⠀⠀⠀⣰⢃⣐⣴⣶⣦⡜⢧⡙⡛⢛⡁⡁⢖⠰⠐⠆⠤⡰⢨⢈⡛⠛⢋⡼⢇⣴⣶⣦⡂⡘⣆
⠀⠀⠀⠀⠀⠀⣍⠐⠸⣿⣄⣼⡗⢊⡳⡐⣠⠅⠒⡨⠘⢉⡉⠁⢄⠒⠢⢅⢃⠞⡑⢸⣯⣀⣽⠇⠂⣩
⠀⠀⠀⠰⠞⡃⢆⡁⠶⢎⡹⢉⡐⣨⠔⠐⠀⣰⠶⣦⢰⣏⢹⡆⣴⠶⣆⠀⠂⠢⣅⠂⡉⢍⣩⠶⢊⡠⢈⠳⢆
⠀⠀⢠⡏⡐⣾⡟⠻⣷⠨⢙⠫⢀⠁⣰⠞⢶⡹⠶⢟⣉⡉⠉⣉⡛⠶⢏⡶⠳⣆⠈⡂⠅⣋⠅⣾⠟⠻⣷⢂⢹⡄
⠀⠀⠐⠇⠅⠻⣷⣾⠟⠰⠆⠞⢀⣠⣜⡳⢛⣠⡀⢿⣭⡷⣸⣏⣽⢂⣀⡛⢞⣣⣤⡀⠱⡀⠆⠻⣷⣾⠟⠠⠐⠂
⠀⠀⣤⢉⠘⠰⠷⠴⢥⢌⡘⡠⠸⣧⣼⠇⢺⣥⡿⢈⠄⡒⢒⠨⡁⢿⣉⡿⠘⣧⣬⠇⢀⠃⡉⡌⠶⠺⠇⠃⡉⣤
⠀⢐⠃⢂⣾⠟⢿⣮⢁⡃⡖⢀⡴⢶⡇⣠⠶⣮⢀⠡⠋⠀⠀⠈⠌⡆⣫⠶⣄⢨⡶⢦⡀⢲⠘⡂⣵⡿⠻⣷⡐⠐⡆
⠀⠨⡄⠍⢿⣦⣾⢟⡈⡅⠣⠊⠳⠶⠇⠙⠶⢻⠘⡄⠀⠀⠀⢀⢀⠇⡽⠶⠟⠘⠷⠞⠑⠸⢠⠅⡻⣷⣴⡿⠡⢠⠇
⠀⠀⠛⣈⢠⢰⡦⠲⡚⢊⢡⠁⢰⡟⢻⡆⣾⣋⣷⠈⠂⠬⠬⠐⠁⣾⢛⣷⢠⣟⢛⡆⠈⡄⣁⢃⠶⢴⡆⡄⣁⠛
⠀⠀⠠⡌⠂⣴⡾⢿⣦⠰⠎⢦⡈⠙⢫⡵⣬⠉⠁⣿⣙⡇⢾⣋⣷⠈⠉⣥⢮⡝⠋⠑⡠⠁⠆⣴⡿⢿⣦⠐⠠⠄
⠀⠀⠘⣇⠡⢿⣧⣴⡿⢀⣨⠔⠨⡀⠹⠦⠾⣱⠶⣬⡉⣁⣈⡉⣥⠶⣎⠷⠴⢏⢀⠅⠂⣍⡀⢿⣦⣴⡿⠬⣸⡃
⠀⠀⠀⠹⢦⡅⠎⡉⠶⢎⣑⣈⠡⠙⠢⠠⠀⠹⠦⠞⠸⣏⣹⠇⠻⠶⢟⠀⠄⠔⠊⠄⣁⣊⡉⠶⢌⠁⢈⡴⠎
⠀⠀⠀⠀⠀⠀⣋⠠⢰⣿⠉⢻⡧⢌⡵⢡⠑⠢⠤⠐⢠⣈⣁⡀⠂⠤⠔⠊⡌⠤⡡⢸⣟⠉⣿⡆⠄⣙
⠀⠀⠀⠀⠀⠀⢹⡌⠩⠻⠿⠟⢣⡜⣡⣥⣬⡁⡃⠬⠰⠠⠄⠒⢥⢘⢈⣥⣤⣍⢣⡌⠻⠿⠟⠅⢡⡍
⠀⠀⠀⠀⠀⠀⠀⠙⠱⢬⡌⣠⠊⡰⣿⡁⣹⣿⣨⡇⣵⡿⢿⣮⢘⣇⣿⣏⢈⣿⠆⡑⣄⢡⡥⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡐⢹⢛⡛⡁⠬⠁⢿⣦⣴⡿⠈⠭⢈⠛⡛⡏⢂⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠗⠶⠰⠂⠋⣬⣐⠈⠃⣂⣥⠘⠁⠖⠶⠚⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣟⣿⣟⣻⣟⣟⣻⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣤⣤⣤⣀⡲⠟⠀⣠⡶⣶⡄⠀⠀⣠⣶⡄⣾⣠⡾⠃
⠀⠀⠀⠀⣺⣼⠇⣶⣿⠟⠛⠉⣉⣀⣠⣬⣭⣉⣙⣛⡻⠿⣶⡿⠀⣿⠷⣶⣾⡟⣿⡇⠐⠫⠶⠿
⠀⠀⠀⠀⠉⠉⣴⣿⣥⣴⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠟⢳⡆⢸⣟⣆⣛⣭⣾⣟⢷⣤⣴⡶⢿⣧
⠀⠀⠀⠀⠀⢸⣿⡇⠈⠿⠛⢿⣿⣿⠿⡻⡟⠰⣣⣿⡿⠓⢻⠁⣾⡏⢈⣿⠉⣿⣽⢘⡛⠋⣀⣢⣿⣤⣄
⠀⠀⣶⣄⢿⡘⣿⠇⢠⣦⡀⠘⢟⡅⠠⠿⣁⠀⢿⣿⡟⠀⣼⢰⡿⠀⣼⡟⠀⣿⢯⡿⠀⣰⣿⣿⠟⣩⣿⡇
⠀⠀⢬⣽⠓⠀⣿⠀⢸⣿⡷⠀⣿⠁⣾⣿⣿⣦⠀⢿⠃⢰⡏⢸⠃⢠⣟⣄⠀⢏⣾⡇⢠⣿⢟⣥⣾⡿⠋
⠀⠀⠀⠀⢀⣾⡏⠀⢸⣿⡷⢀⣿⠀⣿⢧⣿⢿⠆⣸⣀⣻⣾⣤⣷⣤⣾⣿⣷⡟⢻⣷⣶⣿⠿⠛⣡⡄
⠀⠀⠀⠀⣸⣿⢷⠀⣾⠻⢃⣼⣿⣦⣽⣿⢿⣷⡟⢻⠛⣿⠁⣿⣿⠿⢿⣿⣿⠀⣼⣿⣯⡀⠀⠸⠷⠶⠶
⠀⠀⠀⠀⣿⣿⣾⠀⣿⣿⣿⣿⣿⢿⣍⠃⠀⠛⠀⠞⣒⠁⢠⣶⣾⠿⣿⡿⠋⢰⣿⠋⡉⣿⣤⣤⡙⠷
⠀⠀⠀⠀⣿⣿⣿⢠⣿⣿⡿⠋⡀⢸⣿⠁⣾⠃⣼⠏⣹⠀⡏⢠⡟⢰⠏⢠⠂⣸⠇⣰⣾⡿⣡⣿⣿⠂
⠀⠀⠀⠀⣿⣿⠟⢸⣿⡿⠀⣼⢇⣿⡏⢰⡏⢰⠏⢠⡏⢸⠁⢸⠇⡟⠀⢊⡆⢫⣄⣻⣯⣾⣿⠿⠃
⠀⠀⠀⠀⣿⣿⡄⢸⣿⡇⠸⢏⢸⡿⣶⣘⣦⣈⡆⠸⣤⣨⣷⣶⣿⣾⡷⣿⣿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠸⣿⣷⣿⠋⡙⡲⢿⣿⠞⠉⠻⠛⠻⢿⡿⠛⠛⠋⠀⠉⠉⠁⠴⠟⣱⣷⡆
⠀⠀⠀⠀⠀⠀⠉⢡⡆⣿⡝⠇⠀⠀⠀⠀⠀⠀⠴⠟⣱⣷⡆⠀⠀⠀⠀⠀⠐⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢳⡀⠀⠀⠀⠀⢠⠏⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠲⡄⠀⠀⠀⠀⠀⢸⡀⠀⣧⠀⠀⠀⠀⢸⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠹⡄⠀⠀⠀⠀⠈⣇⠀⡟⠀⠀⠀⠀⣿⢀⡞⠀⠀⠀⠀⠀⢀⡴⠚⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢤⡀⠀⠀⠀⠱⣄⠀⢳⡀⠀⠀⠀⠀⠸⣀⡇⠀⠀⠀⠀⢹⡞⠀⠀⠀⠀⢀⡴⠋⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⢆⠀⠀⠀⠈⢦⡀⢇⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⣴⣫⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⢧⡀⠀⠀⠀⠙⠾⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⣳⡀⠀⠀⠀⢀⡠⠖⠋⠉⠁⠀⠀⠀⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⣠⠖⠉⣀⣀⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠲⠤⢤⣀⡀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⣤⡖⠒⠒⠓⠒⠚⠓⠲⡄
⠀⠀⠀⠀⠀⠈⠓⠲⠶⠶⠒⠒⠒⠋⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠉⠙⠒⠲⠶⠤⠤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡄⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠠⣶⠶⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠀⣀⠴⠋⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠲⠶⠶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣰⠃⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡶⡀⠀⠀⠀⠀⠀⢧⠀⠈⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡴⠁⠀⠀⠀⢠⠏⢸⠀⠀⠀⠀⢸⠃⠙⡄⠀⠀⠀⠀⠈⢳⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣠⠞⠀⠀⠀⠀⢀⡎⠀⢸⠀⠀⠀⠀⢸⠀⠀⢹⡄⠀⠀⠀⠀⠀⠙⠦⣤⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⠀⠀⠀⣼⠀⠀⡞⠀⠀⠀⠀⢸⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡼⠁⠀⠀⠀⠀⠀⢧⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣼⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠴⠒⠙⠻⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⢟⡻⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢫⣓⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢶⠒⠉⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠷⠒

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄



⣤⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⢢⣶⣤⣶⣶⣤⣤⢠⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣴⣤⣤⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣦⣤
⠀⠉⠻⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠁⠀⠀⠀⠉⣿⣿⡏⠉⠉⠉⠉⠉⠙⣿⣿⠀⠀⠀⠀⣴⣿⡿⠉⠀⠀⠀⠉⠻⣿⣿
⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢿⣿⣿⡄⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⣿⣿⣶⣄⡀⠀⠀⠀⣠⣾⣿⠟
⣀⣀⣀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⣉⣛⣻⣿⣿⣿⣿⣿⣟⣛⣁⣀
⣿⣿⣋⣛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⢀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⢣⠋⠀⠑⡄⠀⣇⠊⠀⠀⠈⠆⠄⡠⠖⣉⢠⠭⠤⠌⡉⠂⢄⡘⠁⠤⠠⠄⠀⠭⢕⡲⠒⢒⣉⣉⣩⠉⠽⢧⡒⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠴⠀⠦⢸⢹⢀⠐⡹⢱⢠⠋⡰⠚⠓⠀⠈⠀⠀⠀⠁⠀⠁⠀⠄⢀⠂⠀⠀⠒⠉⠻⣅⠱⠖⠀⠄⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⣴⡸⢸⠀⠈⠀⠀⠸⡎⠀⠀⣀⠠⠥⠀⡀⠀⠀⠀⠑⢀⠈⡄⢀⣀⠐⠀⠈⠠⠙⢦⠜⣀⣀⣄⡬⠥⠂
⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⡃⠀⢸⠀⠀⠐⠀⠠⠁⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠄⠈⡏⠙⢦⠀⠀⠀⠘⡆⣀⡠⡤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠁⣈⠉⠀⠀⢀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠠⠈⡇⠀⡘⠂⠀⡃⢀⡗⠂⠀⠀⠂⠘⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠐⠞⢧⠇⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠⠀⠵⠀⠀⠓⠈⠀⠀⠂⠀⡘⠀⠀⠄⠈⠃⠠⠇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠁⠀⡀⡀⠀⡆⠐⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⠠⠎⠀⠀⡖⣠⠥⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠊⠐⠆⢰⣀⣀⡀⠄⢹⠃⠀⠁⠀⠐⠲⠄⠀⠶⠎⠐⠀⠀⠀⣸⠀⠀⣠⠃⣀⠜⠈⡇⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠁⠁⢸⡁⠀⠄⠀⠀⠀⠀⡏⣀⠀⠂⠀⢀⠀⠀⠀⠀⣀⠎⢸⠁⠸⠃⣊⡔⠉⠃⢡⠀⠈⠂⠸⠬⠭⠄⢒⡲
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠁⠀⡞⠁⠀⢀⠐⠀⢀⠀⣠⠭⣒⠄⠤⠤⠄⠤⢐⣊⠕⢻⢸⠀⢠⡁⢻⠁⠀⠀⠸⡀⠀⠷⠀⠀⠀⠠⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠃⠀⠀⠀⠘⠀⣀⠀⡏⠀⠀⠉⠁⠂⠈⠉⠁⠀⠀⠸⠠⠀⠀⠀⢸⡀⠀⢀⠀⣇⣼⠀⠀⠈⠀⣠⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉⠩⠥⠂⠀⠀⠀⠀⠐⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡇⠀⠀⢀⡇⠀⠈⠢⠬⠥⠤⠤⠔⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢉⡃⡀⠅⠃

⠀⠀⠀⠀⠀⠀⣞⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠄⣤
⠀⠀⠀⠀⠀⠀⢹⣿⣿⠏⡱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣸⠁⡜⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣼⣯⠴⠃⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⡠⢁⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠀⢸⡞⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡞⣰⣿⣯⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⢀⣠⡾⠋⣠⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣹⣾⣿⠟⠃⠀⠈⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢹⡛⠉⠉⣠⡾⠷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⣶⠛⢦⠀⠀⠐⠒⠒⠒⠦⢄⡀⠀⠀⣀⡤⠔⠒⠒⠒⠒⠀⣜⠁⠈⢀⡴⠚⠅⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠙⡶⠚⠁⠀⠀⠀⠀⠀⢀⠎⠀⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣧⡔⠁⢀⠀⠀⠀⢀⣨⡟⠀⠀⠘⠁⠀⠀⠀⠀⠀⢠⣠⠊⢀⡴⠋⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣶⣿⠀⠀⠈⠛⣶⢾⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⡿⠀⠀⠀⠈⣄⣤⠔⠂⠉⢀⡀⠠⠤⠀⠀⠘⠻⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢾⣿⣟⣀⠀⠀⠀⣽⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⡇⠀⠀⠀⠀⣿⡏⠀⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⣼⠿⠀⠀⠀⠉⠀⠉⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠀⠀⠀⠀⣿⣇⣀⡠⠤⠒⠈⠉⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣁⠀⠀⠀⢰⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⢤⡤⠄⠠⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠒⠤⢤⣀⡀⠀⠀⠀⢠⣿⠛⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠛⠛⣿⣷⣄⠀⠀⠀⣾⡶⠀⠀⠀⠀⢀⣴⡛⠿⠙⢻⡆⠉⣳⣦⣄⣼⠃⠀⠀⡝
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡤⠴⠂⠈⣿⣿⠖⣠⡞⣹⠀⢘⣿⠀⠀⠀⢹⣷⣄⠀⠀⠙⣶⣿⣿⡿⢿⡆⠀⠞
⠀⠀⠀⠄⣀⣀⠀⠀⠀⠀⠀⡀⠀⠠⠔⠂⢡⡴⠋⠉⠻⣻⢷⢾⡇⠀⠀⠀⢰⡟⢻⣧⡀⠀⠈⢻⠉⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡶⠋⠀⠀⠀⢀⣹⠛⠾⡇⠀⠀⠀⠘⣧⠞⠋⠙⢦⠀⠀⠑⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⠋⠀⠀⢀⢀⠀⡿⠁⠀⠀⠛⢦⡀⢀⡞⠁⠀⠀⠀⠀⠙⢌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠔⣩⠴⠃⠀⠀⠀⢀⡼⢆⠀⠀⠀⠀⠈⢷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠚⠋⠁⠀⠀⠀⠀⢠⢋⡴⠋⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠗⠋⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠐⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⡀⢀⢀⡀⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⠛⠉⠈⢣⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡀⠀⢣⠀⠀⡄⠀⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠑⠨⡀⠀⠀⢠⠀⣠⠔⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⠄⠠⠤⠐⠒⠢⢰⠠⣆⣺⡴⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀⣸⣥⡤⢶⣖⣯⣀⠄⠒⠀⠉⠁⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⡀⡀⢄⠠⣠⡿⠋⠁⠀⠀⠙⣿⣿⠆⠱⡀⠀⠀⢠⠚⠈⡝⢦⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠐⢄⣀⠀⢀⣠⢬⣺⠷⠔⠚⠋⠁⡄⢢⠀⠀⠀⠀⠈⣷⠃⢀⠇⢦⣀⢏⢀⣠⡴⠋⠈⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⣄⠈⠒⠄⠀⠻⠾⢛⡿⠞⠁⠀⢀⠢⠆⠀⠈⠀⢀⡀⠠⡔⢰⠿⢾⣇⣠⣤⠴⠶⠋⠁⠠⡱⢞⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠙⠦⡀⡀⣤⠜⠋⠀⠀⠀⠀⠀⠁⠀⠀⠄⠂⠀⠀⢂⢼⣡⡤⠞⠋⢉⠀⠀⠀⣀⣠⡵⠾⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠀⠉⢂⠠⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠠⠐⢀⣠⣴⣻⠿⠟⠚⠈⠑⠞⠅⣓⡿⡋⠄⠀⡜⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠌⢙⡟⠿⠚⠋⠀⠀⣀⠄⢂⠡⠀⠚⠓⠓⠒⢰⣵⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⢐⠉⠁⠆⠚⠉⠒⢦⠀⠂⣉⠤⠊⠁⠀⠀⠀⠀⠀⢄⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⡞⠀⢣⢰⣏⠀⠀⠁⠈⡦⠁⠀⠀⠀⠀⠩⣆⠀⣀⠜⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡏⠀⠐⠀⢣⡄⠉⠲⡤⡀⠀⠀⡀⠀⠀⠀⢀⠜⠋
⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠙⡄⠔⠀⢀⠈⠳⢤⡱⠱⠀⠀⢺⡄⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⢸⣧⠈⢦⠀⠀⢆⠄⠀⠁⢡⠁⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⢈⠹⡆⠈⡛⢊⠤⠀⢡⠀⢸⢂⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠠⠠⠀⡘⠀⠷⠀⠁⠈⢧⡡⠁⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠁⢀⠀⠀⣻⠒⠀⠀⠈⠗⠕⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠒⠒⠡⠄⠀⣟⡪⠀⡂⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠀⠈⠀⢫⡢⢊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠠⠀⡈⡿⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠉⠉⠁⠀⠀⠀⢀⠀⠀⠄⠀⠔⡀⠄⡠⠀⠠⢀⠀⢂⠄⠠⢐⠀⠀⠄⠀⢀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠈⠢⠀⠄⠀⠐⠀⠀⠀⠐⠈⠂⠀⠀⠁⠈⠐⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁

⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠂⠠⠀⠀⠀⠀⠀⢀⠀⢤⠄⠂⢀⢀⣄⡀⠀⠂⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡁⠀⢀⠠⣔⣈⠰⠶⠆⡙⠙⠉⠐⠊⠁⠁⠀⠀⠀⠀⢀⠈⠠⠆⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⡀⠀⠀⢉⠀⠐⠉⠀⠔⡫⠅⠈⢀⠠⠆⠀⠈⠉⠀⠀⠉⠀⠀⠓⠠⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⠀⠀⠉⠀⠀⠁⠐⠂⠈⠀⠄⡠⠔⠉⠉⠀⠀⠀⠀⠀⢀⡀⠀⢀⡐⠂⠁⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠
⠀⠀⠛⢀⠀⠈⠁⠀⠄⠀⡀⡠⠚⠁⠀⠀⠀⠀⠀⠐⣀⣠⣄⣠⠀⠀⠈⠑⢄⠂⠀⠀⠑⠀⠀⠀⠁⠃
⠀⠀⠀⠈⠀⠀⠀⠊⠀⡀⠊⠀⠀⠀⣠⠔⠀⠀⠐⠈⠀⣠⠉⠉⣛⡾⣄⠄⠀⠑⡀⠀⠀⠠⢀⠀⠀⠀⠀⠘
⠀⠀⠀⠰⡄⠀⡆⠀⡜⠁⠀⠀⠀⠊⠀⣀⠀⢚⠓⠁⠀⢃⢀⠀⣦⠑⢚⠃⡀⠀⠀⠀⠀⠘⠀⠀⠈⠈⠀⠀⠆
⠀⠀⠀⠀⡀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠠⡅⠀⠂⠀⡄⢀⢀⡀⠀⠈⢢⠀⠡⠀⠀⠀⢠⣳⠄⡃⠀⠀⠈⡀
⠀⠀⢱⠀⡁⠀⠱⢸⠀⠀⠀⠒⠀⠀⠀⠁⢸⠀⠠⠥⠀⣐⠘⠈⠀⠀⠞⠁⠁⠀⠀⠀⠙⠁⡇⠀⠀⠒⠀⠀⠜
⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⡀⠀⢀⠀⠐⠃⠜⢄⠀⠀⠁⠉⠀⠀⢀⠔⠤⠀⡤⠀⡀⠀⠀⠀⠩⢀⠂⠸
⠀⠀⠀⠀⠀⠀⠁⠀⠐⢄⠀⢀⢄⢀⠆⠀⠈⠓⠁⡂⡠⢀⠠⡈⠴⠀⠀⠠⠁⠀⠂⠬⠀⠀⠘
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⠈⢧⡅⣄⠠⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠑⡐⠈⡳⣶⣁⠆⠠⠄⠂⠀⠄⠀⠀⠀⠀⠀⠀⡠⠁⠀⠁⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⣤⠁⡀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠙⠗⠀⠌⠀⠀⠀⠀⠀⠀⠀⡄⠈⠑⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⢂⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠃⠠⠀⠀⢀⡁⡄⠀⠀⠀⡀⠠⠆⢂⡀⠁⠀⠀⠀⠀⠀⠀⢀⠐⠁⠒⠀⠄
⠀⠀⠁⠀⠀⠀⢀⡤⠑⠄⠀⠀⠀⠰⠀⠀⢀⠀⠠⢀⡀⣀⣤⡜⠶⠒⠉⣠⠀⡐⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠩⠉⠁⠀⢂⠀⡡⠔⠋⠀⠀⠀⠀⠀⠀⠐⠀⠃⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠘⠁⠀⠻⠄⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠁

⡟⠉⣿⣛⣻⣛⣻⣛⣟⣛⡟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣻⣟⣻⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⢿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧
⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣶⣤⣀⣀⣀⣀⣤⣶⣿⠿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣻⣿⣿⣿⣿⣿⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡶⣛⣹⣯⣹⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠻⣦⡶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⢹⣇⠀⠛⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⢾⡇⠈⣷⠀⠀⠀⠀⠙⣷⣶⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣄⣀⣴⡏⠀⠀⠀⠀⢀⡿⢸⠇⠀⠀⠀⢀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢧⠹⡄⠀⠀⠀⢸⡇⣿⠀⢀⣴⣾⣿⣏⣻⣝⣿⠿⣛⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢻⡄⠀⠀⣿⢱⡇⢰⣟⣿⣿⣿⢧⢻⣽⡾⣿⣚⣿⣯⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢻⡄⢠⣿⣼⢁⣿⣷⣿⣿⣿⡞⢯⢷⣛⢩⣭⣷⣾⡖⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣿⡾⠻⣿⢛⡿⣿⣮⣿⠛⣧⢘⣼⣿⣿⣿⠿⣿⣿⠿⣿⣄⡀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣞⣿⡿⢫⣿⣁⠢⠩⣟⢳⠞⣵⡿⣹⣿⣷⡿⢟⡿⣩⡞⣫⢶⡝⢯⠶⣩⠿⡛⣿⣭⣛⣵⣾⡍⢟⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡳⣟⣭⣿⢁⣿⢣⣥⢉⣿⢂⠇⣼⠏⣽⣫⣿⢋⡜⣧⠞⣥⢚⡴⢫⠝⣥⠿⣡⡜⢯⣩⣿⣟⣽⡴⡾⡟⣮⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡼⣱⣟⣾⡧⣜⡏⣗⡮⡙⡙⠾⠽⡟⣼⣳⣿⣋⣏⡸⡏⡶⣹⢎⡸⢇⢿⠙⡤⠹⣧⠚⣇⠴⢻⣿⣷⣻⣿⣱⢾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣯⣽⣿⣗⣿⣗⣶⣽⡃⢯⣿⣳⣲⢦⣆⣿⣿⣸⠇⣸⣀⢇⡘⢢⡜⢆⣗⠈⡆⠹⡖⢫⣨⣼⡿⣿⣭⣿⣬⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⡷⠟⠛⠛⠛⠛⠻⠷⣧⣽⡒⣬⡼⠟⠉⠉⠉⠻⢶⣦⡟⡴⠣⡜⠳⡜⢻⡆⢡⠜⣧⣾⣥⣾⡷⠿⠷⠷⣷⣯⣀
⠀⠀⠀⠀⢀⣀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⣯⣤⣑⣮⣉⣮⣽⡾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⢠⡾⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠷⣦⡀⠀⠀⠀⠀⣠⡾⠋⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠻⣆⣤⣤⣴⡏⠀⠀⢈⡷⠀⠀⠀⢀⣀⣤⣤⢶⡶⠶⠶⢶⣤⣤⣀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠙⣦⣀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠙⢷⣄⣀⣏⠀⢀⣿⣥⣤⡴⠞⢁⣤⡶⠟⠋⠉⠠⠀⠈⠀⠀⠀⠀⢀⠈⠙⣻⣶⣤⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠉⠻⡟⠛⠛⠉⢉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⣶⡾⠛⢹⣿⣿⡙⢷⣤⣶⠞⠋⡁⠀⠀⠃⠀⢀⠀⢠⠄⠀⠂⠀⠁⠀⢐⡟
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠂⠀⠀⠀⠀⢁⠀⠀⠈⠀⠀⣿⠋⠀⢀⣾⠋⠙⣷⠀⠻⣧⣀⠀⠄⠀⠐⠂⠀⠈⠀⠀⠀⢀⠄⠀⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠉⠈⣿⣤⣀⣼⠏⠁⠀⢻⣦⠶⠟⠃⠀⠀⠀⢀⡀⠀⠰⠀⠘⠁⠀⡀⢠⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠨⠙⠫⠀⠀⠀⠰⠀⠂⠂⠀⢈⠁⠀⠠⠤⠀⠄⠐⠐⠁⠀⠁⣀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢈⡀⠈⡀⠀⠰⠀⠀⠀⠀⠀⠆⠀⠂⠘⠁⠘⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠄⠀⠒⠀⠘⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣡⣀⠀⡀⠀⠁⠀⠈⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠓⠲⠷⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠖⠛⠛⠉⠁


⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠠⡀⠘⠀⠀⡇⠀⡇⠀⡄⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⡀⠀⠐⢆⠀⠈⢦⠀⢳⠀⡆⠀⡇⢸⠁⡸⠁⡠⠃⠀⣠⣦⡤⠤⠤⠴⠯⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣶⢶⡞⠒⠒⠒⠓⠒⠒⠓⠒⠓⠓⠒⠓⠚⠒⠓⠚⠓⠒⠚⠓⠒⠚⠛⢲⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣭⠀⠀⠀⠀⠀⢰⡀⡦⢰⡆⣴⠀⣤⢰⢢⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢣⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⣿⣶⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠛⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣉⣛⣿⣭⣛⠛⠛⠛⠻⠏⠛⠻⠋⠟⠻⠛⠻⠭⢍⣉⣉⣉⣉⣉⣉⢉⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⣓⣲⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣑⣲⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡶⠦⠤⢿⢬⡄⠀⠀⣀⢀⣀⠀⡀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣽⠉⠁⠐⠒⠢⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢸⣾⡍⠀⠀⠋⠘⠔⠀⠃⠀⠘⠀⠀⠋⠘⠘⠀⠉⠀⠀⠀⠀⠀⣿⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠘⠶⢶⡒⠲⠖⠒⢲⠖⢲⠒⡶⠲⡖⢲⠒⢶⠒⢖⠒⠲⡖⠒⠒⠺⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡽⠋⠀⡰⠃⢠⠃⢀⠃⡤⠁⠈⡇⠈⢆⠈⢣⠀⠈⠢⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⠇⠠⠂⠞⠈⠓⡆⢱⠀⠘⡆⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠎⠀⠐⠤⠂⠀⠐⠁⠈⡆⠀⠘⡄⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣸⠀⠀⠀⡇⠀⠀⢱⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡏⠀⠀⠀⠇⠀⠀⠘⡄⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠟⠛⠻⠷⣦⣄⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠻⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⣿⣿⣦⣀
⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣀⣀⣤⣤⣤⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠿⠛⣿⠋⠉⠉⠀⠀⣿⣿⡿⠟⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠘⠿⢶⣤⡀⠀⢙⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠚⠿⢶⣤⠙⣡⣾⡟⠁⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋
⠚⠳⢶⠄⣠⡾⣋⡀⢻⣦⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⠀⠠⡾⠋⣶⡌⢻⣆⢿⠆⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⣀⣴⡾⠛⠁
⣀⣀⣀⣀⣀⣈⣿⣈⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣿⣿⣿⢿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣟⣻⠾⣏⣉⣷⣿⣿⣿⡿⣿⣿⣿⣿⠿⠻⣿⣿⣿⣿⡿⣿⣿⣿⣾⣁⡽⠶⡯⢿⣿⣿
⠀⠀⠀⠀⣿⣿⡿⢷⣤⣼⣿⣿⣿⣿⣿⣧⠒⣽⣿⢿⣦⣰⣿⣽⣿⠉⠁⣿⣿⣿⣿⣿⣧⣤⠟⢿⣿⣿
⠀⠀⠀⠀⣿⡟⢳⣾⣿⣿⣿⢝⠛⣿⣿⣽⣯⣿⡟⢹⣷⣿⡟⢺⡿⣳⡿⢿⣿⡟⠻⣽⣿⣿⣶⣋⣻⣿
⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣴⡻⣿⣌⣿⡿⢿⣿⡟⢻⢿⡿⣿⣿⣉⣿⣟⣤⣤⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣻⠿⣿⣯⠛⢻⣿⠛⢯⠷⣾⣟⣿⣿⣻⣷⣿⡿⠿⣿⡟⢭⣿⣷⢟⠻⢿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡶⣾⣽⣷⡿⢯⣿⣿⣿⣷⣼⣿⣿⣷⣿⢿⣿⣿⡿⢿⣿⣯⣷⣤⣼⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣍⡋⣹⣳⡾⢿⣽⣿⣿⡿⣿⣻⣿⣿⣿⣫⡿⣷⣟⣿⣁⣹⣻⣽⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣟⡏⡎⣹⣽⣿⣿⣉⡿⣿⣿⣿⣿⣽⣿⣿⣹⣿⣿⣯⣽⣿⣭⣿⣿⣟⣏⢉⢙⣻⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣟⣽⣿⣇⣽⡷⢳⣿⣿⣿⣿⣽⣷⣾⣮⣿⣿⣿⣿⡟⢲⣿⣠⣹⣿⢳⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⣿⣩⣿⢿⣞⡧⣿⣽⣿⣿⣿⣿⣿⣿⢶⣷⠾⣝⣿⣿⣭⡿⠛⢻⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣷⣶⣴⢿⣟⣷⣼⢿⣷⣿⡾⢻⣟⣿⣿⣿⡿⢿⣿⣦⣻⣧⣴⣻⣿⣬⣴⣽⣿⣿⣿
⠀⠀⠀⠀⣿⣻⣿⣿⣿⣿⣾⠟⠛⣽⣿⢇⣽⣿⡾⢿⣧⣽⣾⣷⣾⣿⡀⣹⣿⠛⠻⣿⣾⣿⣿⣿⢟⣾
⠀⠀⠀⠀⣿⣧⡼⠻⣿⣿⣯⣤⣥⣿⣷⣿⣯⣿⡷⣶⣿⣻⣇⢸⣿⣽⣿⣾⣿⣬⣜⣿⣿⣿⡟⢳⣾⣿
⠀⠀⠀⠀⣿⣿⡷⡞⠉⢻⣿⣿⣿⣿⣿⠑⣄⣿⢿⣿⠫⡨⣻⣿⣿⠀⢈⣿⣾⣿⣿⣿⡟⠉⢻⢿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣻⢲⣿⣉⡿⣿⣿⣿⣾⣿⣿⣿⣿⣗⣾⣿⣿⣿⣿⣾⣿⣿⣿⠿⣅⣹⣖⣧⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣮⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠙⠄⠑⠉⡄⠀⡠⠒⢄⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⡄⠃⠀⡂⠟⡀⠀⠀⢠⢀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⣄⡀⠀⢀⡀⢠⠔⢄⣙⠃⠁⠀⠀⡀⠁⢋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⠴⠀⠂⠀⠀⠐⢻⠀⠀⠹⠖⠃⠀⢠⣘⢤⠁
⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠈⠙⠄⠘⡀⢀⡈⢑⣤⢠⠄⡄⠀⠀⠠⣀⡉⠁⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠼⠆⢡⠀⠉⠴⠂⠈⠀⢄⠀⡙⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣥⠤⢾⢀⠳⠾⣀⠰⠦⢶⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠐⠘⠃⠂⠒⠐⠒⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠠⢀⡀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⢀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡀⠀⠀⠰⠁⠀⠢⡠⠊⠉⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣍⠣⠡⣻⣦⠔⠀⠀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠢⡑⠁⠀⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠤⠒⠀⠀⠀⠀⠰⢂⠀⠀⠀⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠑⢄⠀⠀⠀⠀⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠿⡏⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣾⢻⣿⡗⢶⣆⠀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢮⣿⡟⣼⣿⡇⡎⣿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣡⣾⡟⣸⣿⣿⢡⣿⢜⠹⢿⣶⣶⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⣿⣿⣿⣿⡏⣰⣿⣿⢣⣾⡏⣿⡄⠀⢻⣿⡿⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢾⣿⣿⡏⠀⣿⠿⠟⠛⠛⢛⢸⡛⢣⡙⡿⢶⣿⡟⠁⣸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠿⠠⠎⠠⡶⠀⠀⠀⠘⣄⠇⠀⢧⡽⠀⠈⠳⠞⢿⢋⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⣸⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⠃⠀⠀⢀⣠⠴⠶⠶⠶⠦⣄⣀⠀⣀⡤⠶⠒⠒⠒⠲⢦⣈⠁⠀⢻⡀⠀⠀⠀⡀
⠀⠀⠀⠀⣤⠖⢒⣽⠛⠀⠀⠀⠀⡇⠀⣠⠞⠋⠖⠛⠛⠻⢿⣿⣶⣯⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡇⠀⠀⠀⠙⣯⡒⠲⣤
⠀⠀⠀⠀⠘⣆⢠⢬⣉⡓⠲⠤⣬⣧⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣧⠤⠖⢒⣉⡥⡆⣰⠃
⠀⠀⠀⠀⠀⠈⢿⠀⠀⠉⠉⠒⠲⢬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠒⠉⠁⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣈⣿⠤⠞⢛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡛⠳⠴⣯⣀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠰⢖⡛⠉⠀⠙⣲⠖⣚⣉⠥⠴⠚⠻⣯⣈⡿⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣡⡽⠛⠓⠢⠬⣉⡓⠲⣖⠋⠀⠉⢙⡲⠆
⠀⠀⠀⠀⠀⠀⠉⡶⠀⠀⢠⡏⠁⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀⠀⠈⢷⣾⣿⡿⣫⡴⠟⠉⠀⠀⠀⠀⠀⠀⠉⠹⡄⠀⠀⢾⠉
⠀⠀⠀⠀⠀⠀⢠⣃⣠⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠻⢫⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣄⣘⡄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡴⠶⠶⠶⠶⠶⠶⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣟⣋⠉⠀⠀⠀⣠⠶⠒⠲⢄⠀⠀⠀⣠⡴⠛⢿⡷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⡝⠉⠀⠉⠳⡀⠀⠀⡃⠀⠀⠀⠀⡇⠀⢸⠋⠀⠀⠀⢑⡌⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢸⠁⠀⠀⠀⢀⡇⠀⠀⠱⢤⣤⣤⠞⠁⠀⠀⠳⢦⣤⣤⠾⠁⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠛⠶⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⢀⡤⠶⠶⢦⡄⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣠⠴⠦⣤⡀⠀⠀⢀⡴⠋⠉⠳⣄⠀⠀⣠⠏⠁⠈⠙⣆⠠⡏⠀⠀⠀⠀⢸⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢾⠁⠀⠀⠀⠙⡄⠀⢸⠀⠀⠀⠀⢈⡄⠀⢇⡀⠀⠀⢀⣴⠀⢣⣀⠀⢀⣠⠎⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠶⢦⣾⡇⠀⠀⠸⡀⠀⠀⢀⡼⠁⠀⠈⠳⣤⣠⡴⠋⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠉⠉⠉⠁⠀⠀⢹⡇
⠀⠀⠀⠀⢀⣴⠟⠉⣀⣀⠀⠀⠀⠀⠹⣆⠀⠀⠙⠒⠚⠋⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣶⡶⠶⠶⠶⠶⠶⠿⢷⣤⣀
⠀⠀⠀⢀⡾⠁⣰⠊⠉⠉⠛⠓⢦⠀⠀⢹⡆⠀⠀⠀⠀⠀⢀⣴⡶⠶⠟⣛⡋⠉⠉⠉⠉⠉⠀⢀⣠⣤⣄⡀⠀⠀⠀⢀⡴⠶⠖⠦⣄⠀⠙⢷⡄
⠀⠀⠀⣼⠃⢠⠇⠀⠀⠀⠀⠀⠈⣧⠀⠸⣧⠀⠀⠀⠀⢠⡿⠁⢠⠞⠉⠉⠉⠉⢢⠀⠀⠀⣰⠋⠀⠀⠀⠈⢢⠀⠀⡟⠀⠀⠀⠀⠀⠱⡄⠀⢻⡄
⠀⠀⢀⡟⠀⠀⠣⣀⠀⠀⠀⢀⣰⠏⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠸⡀⠀⠀⠀⠀⢸⠀⠀⠀⢣⡀⠀⠀⠀⠀⣸⠁⠀⠳⣄⠀⠀⠀⣀⡴⠃⠀⠸⡇
⠀⠀⢸⡇⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠑⠢⠤⠤⠴⠋⠀⠀⠀⠀⠉⠲⣤⣤⣚⣁⣀⣠⣤⣬⠭⠿⠯⠥⠴⠶⠴⢶⡇
⠀⠀⣼⠃⠀⠀⣠⠞⠉⠉⠉⠓⢤⡀⠀⠀⣿⠀⠀⠀⠀⢸⡷⠒⠒⠒⠒⣚⡿⠿⢏⡉⠉⠉⠉⠉⢉⣩⠤⢤⣀⠀⠀⠀⠀⣠⡤⠤⢄⡀⠀⠀⢸⡇
⠀⠀⣿⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢷⠀⠀⣿⠀⠀⠀⠀⠘⣷⠀⠀⠀⣸⠋⠀⠀⠀⠘⡆⠀⠀⢠⡟⠁⠀⠀⠈⢳⡀⠀⣼⠃⠀⠀⠀⢹⠀⠀⣾⠁
⠀⠀⣿⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⡾⠀⠠⣿⠀⠀⠀⠀⠀⣿⡀⠀⠀⠣⡀⠀⠀⢀⡴⠃⠀⠀⠘⣅⠀⠀⠀⢀⡾⠁⠀⠙⢤⣀⣀⣴⠏⠀⣰⠏
⠀⠀⣿⠀⠀⠀⠈⠳⠦⠤⠴⠖⠋⠀⠀⢀⣿⠀⠀⠀⠀⠀⠸⢧⣄⣀⣀⣈⣙⣛⣋⣀⣀⣀⣀⣀⣈⣙⣒⣛⣉⣀⣀⣀⣀⣀⣉⣉⣠⣴⡾⠋
⠀⠀⣿⠀⠀⠀⠀⣀⡤⠶⠤⣄⠀⠀⠀⠀⣿⠀⠀⢀⣀⣀⡀⠀⠈⠉⠉⠉⣉⣉⣉⠉⠉⠉⢉⣉⣉⡉⠉⠉⠉⢉⣛⣛⠛⠛⢙⡿⠉
⠀⠀⢸⡇⠀⠀⡼⠋⠀⠀⠀⠀⠹⡄⠀⠀⣿⠀⣴⠋⠁⠈⠉⠳⡄⠀⢀⡞⠉⠀⠈⠱⡄⣰⠋⠉⠈⠙⣦⢀⡼⠋⠀⠉⢳⡀⢸⡇
⠀⠀⢸⡇⠀⠀⢇⠀⠀⠀⠀⠀⢠⡟⠀⠀⣿⠀⡏⠀⠀⠀⠀⠀⡇⠀⢸⡁⠀⠀⠀⣠⠇⢣⡀⠀⠀⢀⡿⠸⣅⠀⠀⠀⣸⠇⢸⡇
⠀⠀⠈⡇⠀⠀⠈⠓⠦⠤⠴⠖⠋⠀⠀⢀⣿⠀⠙⢄⣀⣀⣠⠞⠁⠀⠀⠙⠒⠲⠚⠁⠀⠀⠙⠒⠒⠋⠀⠀⠈⠓⠒⠛⠉⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⣠⠴⠶⠒⠤⡀⠀⠀⢸⡿⠀⠀⢀⣨⣁⣀⠀⠀⠀⠀⣠⠤⠦⠤⢄⠀⠀⠀⡤⠤⠤⣄⠀⠀⢀⣠⢤⣀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⣰⠇⠀⠀⠀⠀⠘⣆⠀⢸⣿⠀⢰⡏⠀⠀⠀⠙⣆⠀⢰⠇⠀⠀⠀⠀⡇⠀⡾⠁⠀⠀⠈⣷⢰⠏⠀⠀⠈⣷⢸⡇
⠀⠀⠀⢻⡄⠀⢯⡀⠀⠀⠀⠀⢀⡟⠀⠸⣿⠀⠸⣇⠀⠀⠀⣠⠏⠀⠈⢦⣀⡀⣀⡴⠃⠀⠧⣀⣀⣀⣠⠟⠸⣆⣀⣀⡼⠃⢸⡇
⠀⠀⠀⠈⢿⣄⡀⠉⠒⠲⠒⠚⠋⠀⠀⣰⡿⠀⠀⠈⠲⠶⠞⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠉⠙⠛⢻⣶⠒⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣠⡤⠤⢤⡀⠀⠀⠀⠀⠀⢠⡾⠋⠈⠙⢷⡀⠀⠀⠀⠀⣤⠶⠛⠲⢦⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠃⠀⠀⠀⢙⡀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢸⡇⠀⠀⠀⣸⠃⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⣀⠀⢀⣠⡞⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠹⣄⣀⣀⣠⡼⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣩⠿⠳⢦⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣠⠞⠉⠉⠛⢦⡀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⣼⠃⠀⠀⠀⢹⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣇⠀⠀⠀⠀⢰⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠹⣄⡀⠀⢀⣼⠃⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⠙⠦⠤⠤⠶⠋⠀⠀⠀⣀⣾⠃⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣉⣉⣉⣀⣠⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠶⠶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣤⡝⣆⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣀⣤⢤⡤⣤
⠀⠀⠀⠀⣀⣀⠤⠤⠔⢲⣀⣀⣀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣀⣀⣀⣠⣞⣁⣀⣠⣴⠁
⠀⠀⠀⠀⠈⠉⠉⠓⠒⠚⠉⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⡟⢹⠏⠉⠉⠉⠉⠉⠙⠫⡉⠉⠉⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣟⣹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁






⣏⣈⣯⣭⣿⣭⣿⣽⣽⣽⣋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢰⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⣶
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⢰⡄⢠⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠘⣧⢸⡇⣾⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣀⡘⠆⣨⠄⠠⣅⠋⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⢸⡇⠀⠀⢸⠆⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⣈⠛⠦⠔⠋⢤⡓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠞⢁⡞⢰⡇⢳⡈⠳⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠁⠀⡾⠁⢸⡇⠈⢷⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⡴⠋⠀⠀⠈⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⣸⠁⠀⣿⡀⠀⠀⢿⡇⠀⢀⠀⠀⠄⢀⡀⠀⢠⣾⠃⡼⠀⠀⣠⡤⠤⠤⢤⣿⠤⠴⠚⠁⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⡏⠀⠀⣿⡇⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠈⠁⣿⡟⠊⠀⠀⠈⠀⢀⡀⠀⣼⡟⠀⢀⡴⡄⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠁⠀⢀⣿⠀⠀⣰⠟⢀⣠⢄⣤⠀⠀⣠⡖⢺⣿⠁⢠⠀⠀⣴⢛⣿⠃⢰⣿⡇⠀⣾⠗⢃⡴⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⢀⡖⠒⢾⣿⣀⡴⠋⠀⣾⡇⣸⡇⠀⣰⣿⠀⣼⡟⢠⣿⠀⣸⣯⢾⡿⢠⠇⣿⠁⡼⠻⡤⠏⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠉⠒⢺⣿⢿⣄⠀⠀⠿⠖⢻⣇⡴⠹⣧⡼⠹⣧⠋⣿⣰⠋⠁⠸⣧⠞⠀⠻⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⢸⡟⠀⠙⠳⣤⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⢀⣴⠞⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⢠⡟⠁⣶⠀⠀⠈⣿⠀⠀⠀⠀⠀⠠⠴⠶⢤⣿⣅⣀⡤⠀⠀⠀⠀⠠⠖⠒⣾⡷⠤⠶⠛⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⣿⠁⢠⣿⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⡞⠀⠀⢠⣿⠀⠀⠀⠀⠀⣠⡄⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠿⠀⢸⣿⠀⠀⣼⠃⠀⠀⠀⡀⠀⢠⡆⠀⣾⡇⢀⠀⢠⣿⡄⣸⠁⡒⠀⣾⡟⠀⢠⡄⠀⣰⣿⠁⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣠⠞⣡⣤⡀⠀⣰⣿⣠⢿⡇⣸⣿⠀⣤⠀⡆⣿⣇⡏⣸⡇⣼⣿⠇⣠⣿⠃⣰⣿⡏⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⢸⡿⠀⢰⣿⢦⣧⠔⠁⣿⡇⠸⣧⠏⣿⢰⣿⢸⠀⢹⣿⠁⣿⣰⠃⣿⣰⠏⣿⣼⢻⡿⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⢀⠇⢀⡼⢹⡇⠀⠉⠀⢿⠏⠛⠋⠀⠀⠁⠀⠈⠁⠀⠙⠉⠀⠀⠀⣾⠇⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠘⠇⠀⠀⠉⠁⠀⣼⢁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠓⢶⡄⠀⠀⣸⡟⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⠖⠋⠉⠁⠉⠉⠙⢿⡧⢤⣄⣤⠾⠋⠀⣠⡿⠁⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣶⠇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣤⠤⠶⠶⠦⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠉⠛⠒⠲⠶⠶⠶⠒⠚⠛⠋⠉⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣀⣠⣀⡀⠀⠀⠀⢀⣀⠀⠀⢀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢻⠀⢨⠛⣦⣤⣴⠛⣍⠳⢴⡏⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⡾⠀⢸⡀⡇⠀⢸⠀⢸⠀⢸⡇⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠀⠀⢧⡇⠀⠀⡇⡇⠀⠈⡇⢸⠀⢸⡷⠋⠉⠙⣆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⠞⠁⠀⣿⠀⠀⢸⡇⠀⠀⣧⡇⠀⠀⣧⢸⠀⠠⣧⠀⠀⠀⠈⠉⠈⠉⢻⣄
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⢻⠀⠀⢿⣷⠀⠀⢸⢸⡄⠀⣶⠀⠀⠀⠀⠀⠀⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⠸⡀⠀⢸⣿⠀⠀⢸⡀⣇⣀⣽⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄
⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⣿⠟⡗⢲⠾⢶⠷⣶⠾⠿⡶⢲⡟⠛⣯⢉⣧⡼⠃⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠹⢦⡄⠀⠀⠀⠀⠀⠀⠈⠻⠷⢼⣤⣼⣤⣼⣤⣤⣷⠴⠷⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⡴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠛⠉⠉⠳⣄⠀⠀⢀⣠⠖⠚⠓⠶⣄⡀⠀⢀⡴⠋⠁⠀⠉⠙⠲⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⢿⣿⣷⣄⣤⣤⣶⣶⣶⣾⣿⣿⣶⣶⣶⣾⣿⠟⢉⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠠⡈⠻⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠁⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣤⣤⣤⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⣀⣤⣴⣶⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⣿⣿⠿⠛⠋⠉⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣼⣿⡟⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠁⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁⢹⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣦⣤⣤⣤⣶⣶⡶⠀⠀⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠻⢿⣿⣿⠟⠋⠁⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇⠀⠀⠀⢻⣿⣿⣦⣤⣤⣶⣶⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣶⣦⣶⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢠⡤⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣼⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣼⠿⠿⠿⠟⣚⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⣄⡀
⠀⠀⠀⣨⣿⢿⠿⡿⣿⡫⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡿⠭⣳⡄
⠀⠀⣼⠏⠁⠈⡀⣇⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⢺⣵⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢺⠭⢽⠗⠩⢄
⠀⢰⡏⠀⢀⢺⣿⡇⡇⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠎⠀⣠⡀⢘⣀⠀⠀⠱⡀⠈⠁
⠀⠀⣇⠀⠘⠊⠊⠑⠁⣠⠟⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢘⠀⠀⣹⢯⡿⢫⡆⠀⠀⡇⠀⠠⠄
⠀⠀⠙⠷⢤⣀⣀⣤⠞⠋⠠⡀⠀⠀⠀⠂⠀⣸⠃⢠⣷⡎⠁⠀⠙⣇⠀⠀⠀⠀⠁⠘⡄⠀⠘⠃⠁⠀⠀⠀⡰⠁
⠀⠤⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠆⠈⠢⢀⣀⣀⠀⠄⠊⠀⡀
⠀⠀⠀⠈⠀⠸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠠⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣿⣿⠀⠀⣄⠀⠀⢰⣿⣧⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠀⠀⠚⠛⠋⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣶⡄⠀⠀⠉⠀⠀⢀⣠⠴⠶⠚⠛⠛⠛⠉⠛⠛⠛⠲⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⣀⠀⠀⠀⡄⠀⠀⠀⢣⣤⣶⣄⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠘⣷⣄⢸⣿⡇⢀⡞⠀⠀⠀⠀⠈⣿⣻⣛⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⡠⠤⡿⢿⡀⠀⠀⠀⠈⣮⠺⠋⠙⣿⠀⠀⠀⠀⠀⠀⣹⠈⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠆⠀⠀⢳⠀⠀⠀⠀⢸⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⡇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢸⡁⠀⠀⠀⣇⠀⠀⠀⠀⣰⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡀⢁⠀⡇⠀⠀⢠⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠻⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡷⢷⡟⠁⠀⠀⠀⠙⢶⣤⣤⣖⣸⡇⠀⠀⠀⠀⢻⠟⠲⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣧⠀⠀⠀⠀⠀⢸⠟⠀⠹⣯⠀⠀⠀⠀⠀⠘⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣲
⠀⠠⠤⠠⣤⣤⣬⣤⣤⠤⠤⢤⣤⣬⡶⠶⣿⡦⠒⠀⠀⣤⣬⡤⠤⢨⣼⡤⠤⠤⠤⠤⣷⡦⣤⣤⣤⣄⣤⣀⣐⣀⣀⣀⣤⣿⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣴⣿⡏⠀⠀⠀⠙⣿⣿⣶⣿⣿⣤⡄⠀⠀⠘⣿⣦⣼⣿⣦⡍⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⠆⠀⠀⠂⠂⠀⠂⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠐⠀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠄⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⡰⠀⠀⠀⠀⠀⠀⠀⠘⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⢰⢀⠃⠀⠀⠀⠀⠀⠀⡐⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡇⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠂⡄
⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠐⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢠⡒⠁⠀⠀⠀⠀⠀⠀⡠⠊⢀⠔⠁
⢌⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠣⢐⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⠞⡠⠂⠁
⠀⠑⠠⡀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⣔⠁⠊
⠀⠀⠀⠈⠒⢄⠑⢄⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠐⠢⢤⡀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠢⠱⡀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⣀⣀⠀⠀⠀⠀⢀⣴⣶⣶⣄⡈⠑⢦⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⡰⠋⠀⠀⣠⣾⠿⠿⠿⠧⠀⠀⠀⠈⠉⠉⠛⠻⣷⡄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⣼⠋⠁⠀⣀⣀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠈⠃⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠁⠠⠊⠀⠀⠀⠉⠢⢀⠔⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⠁⠀⠀⢀⡀⠀⠀⢩⠀⠀⠀⣀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢀⠴⠶⠶⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢯⡿⠀⠀⢸⠀⠀⠸⣽⠇⠀⠀⡅⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢠⡇⠀⠀⠀⠘⡖⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⣠⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠠⠁⢀⣀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡄⠀⢄⠀⠀⡇⠀⠀⡃⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠋⢁⡀⠀⠈⠢⣀⡀⢀⡠⠈⠀⠑⠤⣀⣀⡀⠔⠁⠀⠀⠙⠛⠀⠀⠀⣸⠀⠀⠀⠀⢧⠀⠀⠙⠉⠑⠤⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡱⢀⠁⠀⠀⠀⢈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⠠⠄⠀⠀⠀⠄⠀⠀⠀⠃⠀⢀⣶⡾⠀⠀⠀⢰⠇⠀⠀⠀⢀⠜⢠⠋⠉⠒⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢿⣶⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⠃⠀⠀⢠⣯⠄⠤⠤⠚⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢹⣦⠀⠈⢿⣿⣿⣿⣷⣶⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⢿⣿⣄⣀⠤⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⣀⠼⠋⠳⣄⠈⠻⠟⠉⠀⠀⠀⠉⠁⠀⠀⠀⠉⠛⢿⣿⡿⠃⠀⣠⠞⠁
⠀⠀⢀⡀⠠⠤⢀⡴⠁⣠⠚⠁⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠟⠁⠀⡼⠁
⠀⡐⠁⣀⡀⠀⠀⠀⠼⠁⡀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⢀⠟⠉⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠌⠀⠀⠀⣠⣶⠀⢢⠀⠀⢆⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠘⠦⡤⠼⡏⠼⠀⠘⢆⡀⢀⡁⠀⠀⠀⠀⠀⡗⠈⠁⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣇⢀⠀⠤⠀⠀⠀⠀⠀⠀⠈⢀⣀⣀⠠⠤⢤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣍⠀⠤⠤⠄⠐⠒⠂⠈⠉⠉⣀⣀⡀⠠⠤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣥⠠⠤⠤⠐⠒⠒⠈⠉⠉⣀⣀⠀⠀⢤⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⣤⡀⠒⠒⠀⠉⠉⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢶⣶⣤⣤⣴⣶⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠛⠳⣤⡀⠀⠀⠀⠀⢀⣤⡴⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⢠⡞⠀⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠉⠛⠳⠶⣤⣤⣀⣀⣠⡞⠁⠀⣠⠏⢀⣰⣯⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⡉⠋⠙⣯⡉⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣃⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠈⠳⡄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠉⠁⢀⣤⣔⠀⠀⠀⠀⢿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣰⡊⠀⠠⣿⣿⣍⡀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣀⣈⢧⡟⢀⣤⣴⣾⣿⣿⣤⣄⣀⢐⣿⣿⣿⣬⣿⣿⡄⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⡋⣉⣀⣤⣈⢿⣿⣿⣿⡟⣹⣿⣿⣿⣿⣿⣿⡇⠀⠛⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⢋⣰⣾⣿⣿⣾⣿⣋⣻⠟⠛⣋⡉⠉⠛⠿⣿⠿⠟⢳⣤⡀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣨⣿⣿⣿⣿⣿⣿⡇⣰⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣗⠿⢿⣇⡄⠻
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡾⣿⣿⣿⣿⣿⡟⡡⣤⣴⣿⡦⢀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣭⣾⣝⡿⠽⠿⢫⣄⠙⠉⠂
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣻⣿⣿⠿⣿⣿⣿⣿⣷⣶⣆⠙⢿⣷⣿⣑
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣗⠀⢠⣿⣿⣿⣿⣿⡟⠀⢶⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣮⣿⣿⣿⣷⣿⣿⡤⢻⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣹⡏⠁⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣯⣥⣦⣤⠔⣀⢀⡀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠿⠿⠿⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢚⣩⣥⣶⣶⣭⣽⣳⢦⡀⠀⢀⣤⢞⣫⣭⣤⣤⣌⣉⠛⠦⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣨⣷⣴⠿⢿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⡞⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢰⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣇⢇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⡜⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⢮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⣠⣿⣄⢀⣤⡶⠟⢮⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⣠⣾⣿⣿⣿⣟⠁⠀⠀⠀⠈⠳⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⢀⣴⣿⣿⡿⠿⠿⠿⠂⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠖⠛⠛⠛⠛⠛⠛⠓⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⢲⡷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠠⠄⢀⢴⡦⠴⠈⠀⠀⠀⠄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡌
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡇⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠊⢿⠒⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⡞⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠤⠾⠤⠤⠤⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡏⠉⢹⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⠀⠀⢀⡴⠧⠤⠼⣄⡀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠓⠲⠦⠤⢬⣤⣤⣤⣤⡤⠤⠴⠶⠒⠋⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠓⠲⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠚⠋⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠦⠤⣄⣀⣀⣒⣒⣒⣀⡀⢤⠤⠤⠶⠲⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⣐⠂⠀⠠⠤⠤⠤⠄⠀⠀⠀⣀⣀⢤⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠈⠉⢉⣋⠉⠙⠊⠉⠛⢋⡉⠉⠀⢀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠐⠒⠒⠒⠠⠤⠤⠤⠐⠒⠒⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣤⣤⣀⣀⣀⣀⣠⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⢀⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢰⣿⣆⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⢀⡄⢀⣀⡀⢰⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⣡⣴⣶⣴⣿⡏⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⡝⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⡿⠋⣷⣿⣿⠇⠀⠀⠠⠄⠀⠤⠴⠂⠀⠀⢠⣼⢿⣿⣿⣿⣿⣷⡀⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⣿⣿⣿⣿⣿⠁⠀⣀⣴⣶⣾⣿⣿⣶⣷⣶⣶⣤⣉⠀⠙⣿⣿⠿⢿⡇⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠁⠸⣿⣿⡿⠃⣸⣾⡿⠿⠿⠯⠙⠁⠈⠉⠛⢿⣿⣿⣷⡄⠈⠛⠀⠀⠁⠀⠋⠙⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⠀⠀⠀⠁⠀⣼⠃⠀⢶⣶⣶⣤⣤⡀⢠⣶⣶⣾⣯⠛⣿⣿⡀⠀⠀⠀⠀⠀⢰⣦⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣾⡀⠀⠀⠀⠀⢷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡇⠠⠀⠀⠀⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⠀⠀⠠⠂⡨⣿⣿⣯⣻⣯⣵⣿⣿⣿⣿⣿⡟⢉⣿⢻⣿⡇⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢿⣾⠟⠀⠀⣤⡀⠀⠀⣿⡿⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⣠⡀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢢⡀⠀⠹⠃⠰⠀⣿⠛⠂⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠻⣷⡄⠘⣿⣧⣰⣿⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⠟⢛⠁⠀⢀⠀⠀⠀⢹⣦⣦⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣾⣿⡇⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣽⡟⠀⢀⣿⣷⠀⠀⢸⣿⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠘⢿⣷⣿⣿⣿⡟⠛⠉⠉⢉⣉⣿⣿⣿⣿⡇⠀⢠⣽⣿⡇⠀⠈⢿⣿⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⡟⠙⠻⠺⣦⣼⣿⣿⡛⠛⢿⣿⠂⣆⠉⠀⠈⠉⠬⠛⠛⠶⣿⣿⣿⠃⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡟⠀⣾⣧⡝⣿⡟⠋⡙⠛⠳⠤⠈⠀⠉⠰⠶⠂⢀⣠⣤⣄⠠⠼⠟⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠠⡟⠀⠀⠈⠑⢤⣬⠊⠀⠲⢶⣶⣶⣶⣶⣿⣿⣿⡿⠁⠀⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠉⠁⠀⠙⠉⠀⠈⠁⠀⠀⠀⠸⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⢦⡀⠙⢷⡈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡶⠶⠃⠀⠈⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢷⡀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣷⣄⢠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⣭⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠋⠉⠉⠁⠀⢀⣤⣤⣄⡈⠉⠉⠛⠛⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠾⠛⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠙⠒⠂⠀⣱⠀⠀⠀⠀⠀⠀⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠴⠖⠒⠒⠚⠋⣁⣀⣠⣤⣶⠶⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠛⠛⠛⠋⠉⠉⠀⠀⠀⢰⣏⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠉⣉⡙⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡾⠟⠛⠛⠷⣦⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢀⣿⠃⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⣿⠸⣧⣤⣤⣶⠟⠋⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⣿⣤⣬⣥⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⢿⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⡀⠀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⣠⣀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢷⡶⠋⠙⢧⣀⣴⠟⠙⢷⣄⣿⠙⢷⣄⣿⠉⠛⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠉⠁⠀⠀⠙⠋⠀⠀⠀⢘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠉⠛⠳⣦⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⡶⠶⠶⠶⣤⣤⣤⣤⣴⣶⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣴⣶⣿⡽⠿⠛⠛⠛⠋⢉⣉⣉⣛⣛⣛⣛⣛⣻⣿⣯⣭⡴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣛⠳⠶⠶⣤⣤⣤⣄⣤⣤⡶⠞⣋⣉⣤⣴⠶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠶⠶⠿⠿⠿⠟⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀
⠀⠀⠀⠀⢐⣷⣤⡀⠀⠀⠀⠀⣀⠼⢿⣴⠒⠦⣄⡀⠀⠀⠀⢀⡠⠤⠴⠦⠤⣄⣤⣾⡴⢾⠿
⠀⠀⠀⠀⠀⠀⠙⠛⠳⢄⣠⠎⠀⠀⠀⠹⡄⠀⠀⠙⢦⢀⠖⠁⠀⠀⠀⣀⡴⠾⠿⣍⠈
⠀⠀⠀⠀⠀⠀⠐⢶⣦⡀⡏⠑⠦⣀⠀⠀⠹⡄⠀⠀⠀⠋⠀⠀⣠⠴⠊⠁⠀⠀⠀⢸⡀⣀⠴⠞⠁
⠀⠀⠀⣀⣀⠀⣀⠀⣀⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣸⣋⣀⣀⣀⣤⣄⣀
⠀⠀⠒⣓⢛⢛⣿⣿⠻⠟⠻⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⡟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⣷⣽⡷⠦⠤⠶⠶⠒⠒⠂⠀⠀⠀⠀⠀⠛⠲⣤⣠⠚⠒⠒⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣋⣁⠽⠛⠁⠙⠢⣀⣠⠴⠚⠀⠀⠀⠀⢠⣄⡈⢑⠶⢮⣍⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠠⠞⠛⠁⠀⣤⣠⠔⠊⠁⠙⠢⣄⠀⠀⠹⡄⠀⡠⠛⠙⠦⣤⣬⣅⡈⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠾⡿⠟⠁⠀⠀⠀⠀⠀⠈⠑⢄⠀⡹⡋⠀⠀⠀⠀⠙⠹⡿⣶⣕⡂
⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢱⣀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣬⣿⣧⣴⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠈⠙⢿⣿⣿⣿⣶⣄
⠀⠀⠀⢠⣾⣿⣿⠿⠛⠉⠉⠉⠁⠀⠀⠀⠈⠙⠻⠛⠁⠀⠀⠀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣋⣠⣤⣶⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⣦⣄⡀⠀⠈⠁⠰⣿⡇⢿⣿⣿⡆
⠀⠀⢸⣿⣿⡿⠟⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⣾⣧⡀⠀⠀⠀⠀⠀⠁⢸⣿⡇⠈⠙⠻⢿⣶⣤⠀⠐⣿⡇⠸⣿⣿⣷
⠀⢠⣿⣿⣿⠃⠀⣿⡏⠀⠠⠀⠀⠀⠀⠀⢀⣿⣿⣷⡀⠀⠀⠀⠀⠀⢸⣿⠇⡀⠀⠀⠀⠙⢿⣷⣄⣿⡇⠀⢻⣿⣿⣇
⠀⣾⣿⣿⡏⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⢻⣷⣄⠀⠀⠀⠀⠘⣿⣇⠀⠀⠰⠀⠀⢀⠉⢿⣿⡇⠀⠈⣿⣿⣿⣆
⠀⣿⣿⣿⠃⠀⠀⢻⣿⡀⠀⠀⠀⠀⢀⣾⡿⠏⠀⠀⠻⣿⣦⡀⠀⠀⠈⢿⣿⠀⠐⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠘⣿⣿⣿
⠀⣿⣿⣿⡄⠀⠀⠀⣿⣷⠀⠀⣠⣴⣿⠟⠁⠐⠀⠀⠀⠈⠻⢿⣷⣶⣤⣼⣿⣧⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⢹⣿⣿⣷⠀⠀⠀⠈⢿⣧⣾⡿⠟⠁⠀⠀⢠⠄⠀⠀⠀⠔⠀⠉⠩⠙⠛⠉⠁⠀⢠⠀⠀⠀⠀⠀⢀⠁⠀⠀⢸⣿⣿⡿
⠀⠀⢻⣿⣿⣷⡀⠀⠀⢈⠛⠃⠠⠀⠀⠀⠀⢀⠀⠀⡠⠀⠐⠄⠠⠐⡀⢀⠐⠀⠀⠀⠀⠀⠁⠀⢠⠁⠀⠀⣴⣿⣿⣿⠃
⠀⠀⠀⠹⣿⣿⣿⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠁⠀⠐⠀⠄⠀⠀⠰⠀⢻⣿⣿⡇
⠀⠀⠀⢰⣿⣿⣿⠁⠀⢀⠄⠀⠠⠀⠀⠀⠀⠄⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠸⣿⣿⣿⡀⠁⠁⠄⠀⢀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠂⠀⠄⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣇⠀⠤⠂⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⣼⣿⣿⡏
⠀⠀⠀⠀⠘⣿⣿⣿⣦⣀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⣤⣀⣀⡃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣧⠈⠀⠁⠀⠀⠀⠀⠤⠀⠀⠊⠀⠀⢀⣀⠀⠀⠃⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⡆⠀⠔⠀⠐⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣶⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⣄⡀⠀⠁⠀⠀⠃⢀⣴⣿⣿⣿⡿⠿⠿⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠸⠞⠁⣠⡤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⡤⠶⠚⠋⢉⣉⣉⠙⠀⠚⠁⣀⡤⠶⣤⠉⠳⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣠⡴⠞⡋⠉⢩⡇⠀⠀⢸⡃⠂⣤⠟⠀⠁⡀⢠⠈⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⠞⠉⠀⣼⢁⣴⣏⠀⣴⠦⠈⠳⣤⣤⣤⡤⣴⢣⡏⣀⠀⣠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡼⠁⢠⠇⢰⡿⠋⢀⣸⡧⠿⣧⢀⡴⡆⣀⡀⢰⠇⣾⣴⢏⣼⣱⢃⡌⠙⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣧⡴⠋⢀⣿⠀⡴⢋⡼⢁⡾⠁⣾⠋⣼⣽⡷⣿⡼⡟⠹⠞⣏⣡⡞⠁⢠⡇⢀⡀
⠀⠀⠀⠀⠀⠀⢠⣌⠳⠶⠀⠀⠄⢸⠇⣀⡛⠋⠀⢸⣃⡞⠛⠋⠉⠀⠀⠉⠀⠂⠀⠀⡈⠁⠀⢴⡏⠐⣯⡅
⠀⠀⠀⠀⠀⠀⠴⠿⠃⠀⢰⡆⠀⣰⠟⠙⣧⠀⠄⠈⠉⠀⠀⢀⣤⠖⡀⠀⣤⢀⠀⣶⠗⡂⢀⡄⣿⠀⠘
⠀⠀⠀⠀⠀⠀⠰⠂⠀⢠⣿⠀⣼⠃⠀⢠⣿⠀⠀⢰⡿⠀⣈⢀⡟⣠⢠⡼⣼⣨⢠⡟⣰⢃⣾⠱⠏⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠀⣾⡏⢰⠇⠀⠀⣸⣯⣤⣿⠖⣧⣴⡏⣾⣱⣧⣾⣠⢻⣧⢿⠞⠙⣿⠇⣠⡼⠃
⠀⠀⠀⠀⠀⠀⢰⠇⢰⣿⢃⡏⠀⣠⠞⣿⠇⣿⡞⣠⣿⠸⠏⠙⢉⠁⡿⢃⠈⠁⠀⢀⣼⣿⠿⢋⡀
⠀⠀⠀⠀⠀⠀⣿⠀⣸⣿⢸⠁⣼⠃⢸⡟⢀⣩⠰⣧⠏⡴⠤⠖⠙⠷⠶⠋⢀⣤⢾⣿⣿⣠⡴⠋
⠀⠀⠀⠀⠀⢰⡇⠀⢿⣿⡾⢰⡇⢠⡿⠁⠀⠙⠦⠴⠊⠀⠰⠀⠰⢀⡄⣠⠟⢡⣾⢟⡟⠀⠀⡄
⠀⠀⠀⠀⠀⠸⣇⠀⢸⣿⡇⠀⣙⣋⣠⠆⢰⡄⣦⢰⠄⠀⠀⠁⠀⣿⠠⣏⣴⡿⣫⠟⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠛⠁⢠⠏⠉⠁⢠⡿⠀⠋⠀⠀⠀⠀⠀⠀⠙⢧⣭⡵⠞⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣤⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠛⠛⠛⠓⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢠⠏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢀⡏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⣼⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⣟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢡⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⢿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠢⡀⠀⠀⢸⠀⢀⠂⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠸⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⡀⢸⡀⢀⣸⠖⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢳⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢈⠁⠀⠀⢂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⠝⠢⡀⠀⠈⠄⠀⠀⠀⠀⡄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠑⠀⠐⠋⠀⠀⠈⠢⡀⠈⢆⠀⠀⠀⢰⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠣⡀⠀⠀⢃⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⢢⠀⠘⢄⠀⠀⠂⠳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⢂⠀⠀⠑⣄⡴⢚⠝⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠈⣆⡴⢚⡡⠊⡡⠊⠁⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠚⠡⠂⡡⠐⠁⠀⠀⡠⠊⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠒⠁⡀⠔⢈⡠⠊⡠⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠉⠀⠂⡡⠔⣉⡴⢺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⡥⠴⠾⠥⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠈⠙⣷⡄⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⢠⡾⠋⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠈⠻⣿⣿⣿⣿⣿⡿⠋⠀⢴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡶⠀⣠⡾⠋⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠈⠙⢷⣄⠐⢶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⣠⡾⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⢷⣄⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠋⠀⠘⠋⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠛⠁⠀⠙⠛⠛⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡔⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡉⣀⣤⣄⡙⡏⠀⠀⠀⠂⠀⠀⠀⠐⣠⣤⣤⣌⢂
⠀⠀⠀⠀⠀⠀⠀⡇⢿⣿⣿⠇⣀⠀⠀⠀⠀⠀⠀⠀⠄⠿⠿⠿⠇⡅⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠏⠠
⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠐⠁⢠⣤⠀⠀⣠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⣆⣾⣿⣷⣿⡀
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠌⠀⣀⣀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢩⣿⡷⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠁⠀⠀⠀⠈⣿⣿⣿⡟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠀⢃⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠸⠀⠀⠀⠀⠁⠀⠀⠐⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢆⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁

⠀⠀⠠⡄
⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁
⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⡙⠦⠀⠠⠀⠀⠀⡄⠀⠀⠠⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠆⠀⠀⠉⠃⠀⠀⠚⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡷⠢⠤⡇⠀⠀⠈⠀⠀⠀⠀⢡⠀⠐⣄⠀⠹⡄⠀⠀⠎⠀⡠⠉⠃⢀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄
⠀⢀⡄⠀⠀⠈⠳⣿⠀⠀⠀⠇⠀⠀⠃⠀⠀⠀⠀⠀⠈⠑⡄⠢⠀⠘⠀⠀⡇⠀⠀⢸⠀⠀⠀⠃⠐⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⢱⠆⠀⠀⠄⣼
⠀⢸⣆⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠘⢤⣆⠀⢀⠀⡇⠀⠀⠈⠀⠀⠀⢀⣠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⡄⠀⢄⠀⠀⠸
⠀⠀⠻⣷⣄⠀⠐⠀⡔⠀⠀⠰⠒⢒⡀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠉⠓⢼⠀⡇⠀⠀⠀⡖⠒⠉⠉⣤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢂⠀⠀⠁
⠀⠀⠀⠈⠻⢇⣠⣼⠂⠀⠀⢀⠀⠀⡇⠀⠀⣀⡇⠀⣣⠎⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⡇⠀⠀⠜⠉⠀⠀⠀⢘⡀⠀⡔⠀⠀⠀⡼⡄
⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢀⠈⠡⠍⡁⠀⠀⠀⠀⠀⢘⣄⠀⢀⠀⠀⡸⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⣶⠆⠀⠐⢿⡇⠀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⡎⡀⠀⠀⢀⠀⠀⠀⠀⠀⡈⠈⢲⠀⠀⠀⡄⠀⣸⠀⠀⠀⢸⣤⠀⠀⠐⣇⠀⠻⡄⠀⠀⠘⣿⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⠁⠈⠀⠀⢜⡀⠂⠀⠀⠀⣇⠀⡜⠀⠀⠀⠃⣠⠏⠉⢳⡀⠸⣿⡋⠀⠀⠹⠀⣿⠈⠀⠀⠀⠸⢆⠈⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣧⠁⠀⠀⠀⢠⢤⠟⠀⠀⠠⣼⣿⣿⠇⠀⠀⠀⣿⢻⠀⠀⡠⠧⠤⢽⠁⠀⠀⠀⡟⠉⡆⠀⠀⠀⠀⠘⣦⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠐⣳⡟⠀⠀⠀⡟⠂⠀⢠⠀⠀⠀⠓⠀⢡⠀⠀⠀⠀⠀⠸⣆⣀⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠂⡠⠄⠀⢠⡟⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⣰⣾⡿⠋⠀⠀⢀⣧⠀⠀⠘⣤⡀⠀⠀⠀⠈⡆⢀⡀⠀⠀⠀⠙⠛⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣦⣠⣤⠤⠸⣆⠀⢠⡄⠀⣸⣿⣦⠀⠀⣸⣿⣿⠁⠀⠐⣤⡟⢻⡷⠂⠀⠹⣧⣀⣀⠀⠀⠐⠄⠈⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⢶⣼⡷⠎⠀⠛⠷⠶⠞⠁⠈⢹⣀⣀⣻⡿⠁⠀⠻⠤⠀⠈⠙⠛⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉