Chip Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢷⣤⣄⣀⣀⣀⣤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣶⣶⣷⣆⣀⣨⡉⠉⠉⠉⠁⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢛⣛⡛⠿⠿⢿⣿⣿⣿⣿⣷⣿⣷⣤⣤⣿⡉⠀⠀⠀⠙⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢰⡿⠉⢻⡇⠀⠀⠀⠈⡉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣦⣤⣤⡽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣾⡷⠾⢟⣥⣤⣄⠰⣾⣿⡄⢀⠀⣀⢀⣈⣽⠛⠻⠿⣿⣿⣿⣿⣿⣿⣆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⣿⠀⠀⠸⣯⣤⡿⠀⣼⡇⣾⡛⢻⡿⠈⢻⡿⢃⣤⣤⣄⠈⠙⠛⠿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⣠⣴⣶⣤⣀⠀⠀⠀⠀⠁⠀⣀⣬⣄⠙⣛⠻⠗⠀⠺⠃⠻⣧⣬⡿⠀⠀⠀⠀⠀⠉⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢸⡏⠀⠀⠈⠻⣷⡀⠀⠀⢠⡿⠋⠉⠁⢰⣿⣀⡀⠀⠿⠂⣴⣦⣄⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⣀⣀⣀⣸⣧⠀⠀⠀⠀⠘⣿⣀⣀⣘⢿⣶⡶⠦⠸⠏⠹⡷⢠⣿⠀⣿⣼⡿⢸⣿⠛⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠛⠛⠛⠉⠉⠙⢷⣦⣤⣤⣾⠟⣙⣛⣿⣟⣛⡻⠿⠷⢶⣶⣦⣬⣅⣐⡛⠀⠀⢶⣿⠇⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⣠⡶⠿⠿⠿⢶⣌⠁⢠⣾⠛⠉⠉⠉⠉⠛⢿⣦⡀⠀⠀⠈⠉⠙⠛⠻⠷⣶⣤⣄⣀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢻⣧⣾⠿⠶⠶⢶⣤⡀⠀⠀⣹⡇⢀⣤⣤⣄⡀⠀⠀⠀⠀⠈⠉⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠙⣷⣶⡾⠟⢱⡿⠉⠉⠙⠻⣷⡄⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣦⣄⡀⠀⠈⢿⣦⡀⠀⠀⠀⢈⣿⠀⠀⠀⢠⡾⠟⠛⠛⠿⠿⠿⠷⣶⣄⠀⠈⢻⣆⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠹⣿⣿⣿⣿⣿⣷⣦⣤⣙⠻⠷⠶⠶⠿⠿⢶⡶⠾⢿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢈⣿⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⢿⡿⠿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⢻⣦⣀⠀⠀⢀⣀⣤⣴⠿⣦⣤⡾⠏⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⢿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠈⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠻⣿⣿⠿⣿⣿⣿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠿⠟⠛⠻⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢋⠉⡍⠉⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⢀⠀⠀⢀⡙⢛⠛⠉⠉⡽⢛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠉⢁⠔⠅⣇⣼⠷⠖⠛⠛⠛⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡨⠄⣀⣀⠀⢀⣠⢴⣫⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢚⠉⡁⡀⠀⠀⠈⠀⠉⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⣥⣊⠥⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠚⠥⠚⠂⠐⠓⠌⠄⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣭⡥⢵⣦⣰⢤⣂⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢯⡣⠱⠤⠀⠀⠐⢄⠂⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣞⠲⢆⢀⡀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠈⠐⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠖⠚⠉
⠀⠀⠀⠀⣤⠴⠶⡶⠤⢤⡤⣤⣤⠴⣞⠉⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠘⣯⡹⣗⢦⣌⠁⠀⠀⠁⠁⠀⠹⠀⠊⠀⠀⠀⠀⠀⠀⣀⣀⡞⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠉⠉⠉⠓⢄
⠀⠀⠀⠀⠈⠙⠺⠯⣬⣷⣄⢤⣀⠀⠀⠀⠀⠀⠀⠠⠀⠁⡄⠀⢀⡼⠁⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠐⢂⡄⠢⢀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢮⣛⠦⡄⠀⢄⠀⣐⢄⢢⣠⠖⠋⠀⠀⠀⠀⣠⢞⣁⡐⠀⢀⠀⠀⡀⠆⡈⢕⠈⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠛⠛⠋⠁⠀⠀⠀⢀⡤⢞⣁⣊⣙⣀⡀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠿⠷⠶⣮⣿⡳⠦⣹⢏⣑⠀⠀⠐⠂⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠮⣷⣄⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣀⣐⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⡴⣶⡍⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣬⠁⠀⠀⣀⣠⡈⠁⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠰⠋⠁⡀⠈⠁⠀⠀⠀⠉⠀⠀⣤⣠⠆⠀⠀⡀⠋⢀⡀⠀⠀⠀⠀⠀⢴⣄
⠀⠀⢠⠁⠀⠀⣴⡦⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠈⠁⠀⣤⠄⠀⠀⠐⠀⢈⡽⠁⠀⠀⣎⡄⠐⠟⠁⠀⠀⠀⠰⣦
⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⠌⠁⠀⡀⣀⠠⠂⠀⢰⣿⠶⠒⠁⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢸⠀⠀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠞⠓⠒⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⡴⢦⠀⠀⠀⣠⡄⠀⠐
⠀⠀⠸⣦⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉
⠀⠀⠀⠀⠂⠀⠚⠳⠀⠀⠀⠀⣴⠀⢰⡿⠁⠀⠀⢀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣴⠋⡧⠀⠀⠀⠀⣀⠀⠀⠀⠈⠠⣠⣤⠀⠀⠉⠓⠀⠀⡴⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣾⠋⣹⡷⠀⣾⠟⠛⠻⠿⠶⣾⡿⠞⠁⡶⢀⣀⣸⣍⠇⠀⠀⠀⠀⠈⠉⠂⠠⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⣾⡿⠁⣠⡶⡄⢰⡞⢲⢠⣿⢖⣽⢸⡏⣾⠵⢃⠟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠛⠗⣰⣿⡀⣿⣾⠧⣼⢿⡿⣿⡅⠸⢗⣙⡒⠱⣏⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣴⠻⣯⡽⠃⠙⠒⢁⣈⣥⣼⠿⣿⣉⣉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠛⠁⠀⠀⠀⠻⠿⠿⠟⠛⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠛⢁⣀⣉⠉⠀⢤
⠀⠀⠀⠀⠶⣀⠀⠠⠆⠀⠀⠀⠉⠁⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⣉⠉⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⢠⣯⡴⠟⠋⠁⠀⡀⠉⠀⠐⠀⠐⠋
⠀⠀⠀⣦⠀⠙⠃⠀⠀⠀⠀⠰⠟⠃⠀⠀⠀⠁⠀⠀⠀⠀⣠⠊⣉⠁⠀⠈⠋⢡⡄⠀⠰⠦⠀⢤⡄⠀⠀⠀⠈⠻⠀⠴⢦⣠⣤⣥⣤⣄⣲⠀⠀⠰⡄
⠀⠀⢀⣿⣦⣀⠀⠶⠀⠚⠿⠂⠀⠰⠟⠳⠀⢈⡞⠀⠀⠸⠇⠀⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣷⠞⠁⠀⢠⡄⠀⠀⠈⠑⠠⡦
⠀⠀⢸⣿⣿⠿⠿⠿⠿⣤⣮⣷⣦⣤⡤⢶⡖⠿⣀⠀⠀⢼⡁⠀⠀⠀⢀⠀⠀⠀⠄⣻⠆⠀⢀⡀⠁⠀⠀⠀⠐⡿⠉⢀⣦⠄⠀⠀⠀⠀⢶⠄⠀⠀⡀
⠀⠀⠀⢑⣷⣶⡴⠖⢀⢉⠁⡀⢀⣄⣰⣿⣿⣾⡧⠀⠀⠈⠁⠀⠈⠁⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢻⠛⠻⠛⠋⠛⠛⠛⠛⣻⡋⠉⠉⠀⡀⣠⡄⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠐⠖⠀⠈⠁⠀⠔⠲⠄⠀⠸⣷⠋⠀⡀⠀⠀⠈⠛⠂⠀⠀⢰⡀
⠀⠀⠀⠟⣿⠟⢲⡶⠶⠶⢶⡾⢧⡴⠶⠶⠟⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠻⠂⢀⣀⠀⠀⠀⠃
⠀⠀⢠⡿⡶⣤⣬⣝⣀⣀⣈⣁⣈⣁⣤⡦⠶⠒⢋⢣⠀⠀⠀⠀⠉⠑⠀⠈⠀⠀⣤⣀⡀⠀⠀⠠⠗⠀⣀⠀⠀⠀⠱⣄⡀⠀⠀⠀⢠⣠⠀⣀⡀⠄
⠀⠀⠈⣻⣥⣿⣇⠙⠩⣿⠉⠉⠉⠀⠀⠀⠾⣆⡤⠊⠀⠀⠀⠀⠄⠈⠃⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠉⠙⠲⠦⠤⠥⠚⠁
⠀⠀⠀⠀⠁⠉⠉⠉⠓⠀⠲⠶⠒⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⠛⠃⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠄⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣵⠟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠃⣈⠒⡙⢶⢦⣠⡤⠴⢳⠶⢲⣟⡋⢨⣦⣻⢏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⢘⣤⡶⡾⢿⣷⣶⣭⣿⣌⣦⣧⣴⣶⣦⣶⡾⣿⠟⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⠀⠀⠀⠘⢛⣟⢿⣯⠀⢔⣿⣿⢿⣿⣿⣟⡿⠡⡄⠀⣶⡟⢅⠃
⠀⠀⠀⠀⠀⠀⣴⣿⣤⣔⠀⣀⠀⡀⠀⠀⢀⣀⣀⣂⣐⣶⣟⣟⠀⠀⠀⠘⢷⣾⣦⣬⠹⢦⡀⢀⣬⠞⣉⢫⣟⣷⣶⣣⣷⣾⡟
⠀⠀⠀⠀⠀⠀⠘⣥⣮⠿⣿⣭⣽⣛⣛⣫⣿⠿⠟⣑⣿⣿⡿⠃⠀⠀⠀⠀⠀⠙⠛⠷⢯⣿⣿⣿⣷⣾⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡇⡉⠐⠒⠒⠛⠒⠒⠒⠚⠋⠉⢉⡥⡮⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣦⣤⣀⣀⣀⣀⣀⣀⣤⠼⠝⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠔⠀⠴⣄⢠⡇⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡴⠖⢴⠖⠀⡤⢧⡀⠹⠤⠒⢸⣏⡀⠒⠤⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣰⠖⠁⠐⠃⠐⠩⠛⢠⡀⢺⠟⣒⣉⣠⣤⡀⠙⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⡠⠠⠉⡁⠖⠶⠋⢀⣠⢶⣄⠀⡀⢀⣉⢈⣉⡧⠠⠴⠮⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢁⣤⣶⠿⠊⠀⠀⠀⢫⣤⠤⣤⠤⢤⣤⣍⡉⠛⠶⢶⣶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⠁⠹⠦⡤⠶⠞⠛⡟⢁⡴⠛⠶⢤⣙⠛⠛⠒⠂⠂⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣟⣟⣿⣯⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⠀⠸⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⣄⣀⠀⢀⣠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢸⡻⢿⣿⡤⠍⠉⢻⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢜⣼⠀⠀⢰⣝⠻⠶⠦⠒⠀⡽⢋⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣤⣤⡀⠀⣀⢨⣿⡀⠀⠠⣜⠻⢿⣧⠀⠁⣐⣿⡧⠀⠀⠀⣴⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⣭⣽⣏⣩⠴⣾⠏⣷⠀⢀⣿⣿⣒⣖⠀⠀⠱⢊⣼⠀⠀⠘⣮⣂⡀⠀⠀⠀⠠⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⣒⣒⣀⡈⠀⠚⣿⣿⣿⣯⡓⠦⠅⠀⠀⣀⡿⢣⠂⠀⡘⣌⡛⠯⠤⠀⠀⢐⡿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢢⠀⢨⡻⠿⣿⣿⡧⠠⣲⣿⢻⠿⣿⣿⣽⣃⠀⠀⠀⠐⠃⠀⠀⢹⣮⣍⣓⠀⠀⠠⢛⣵
⠀⠀⠀⣜⠀⠀⠀⠀⠀⢀⣡⠷⣶⣿⡿⠶⣶⠶⠟⠛⣡⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣧⣙⠷⠶⠆⠀⠀⣹⢏
⠀⠀⠀⢻⣝⣒⣂⣀⠄⠿⠋⣰⣿⣿⣿⣿⠿⠶⠌⢛⡩⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠁⢐⡵
⢀⣤⣤⣾⢷⣤⣤⠀⠀⠀⢺⣽⢋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠮⣭⣙⠁⠀⠀⠚
⢿⣿⣿⣿⣷⣬⠍⠀⠈⠠⠚⣡⠞⠀⠀⡀⢰⠀⢀⢀⡀⢀⣤⣤⢜⣼⣥⣤⣀⣀⣐⡥⠂⠀⠐⠀⣀
⠀⠈⠉⠉⠉⠙⠓⠂⠀⠀⠈⠁⡌⠐⢀⣤⢼⠟⢿⣿⠇⣾⣏⠏⠈⠙⠘⠿⠋⠀⠉⠁⠀⠀⠀⠀⠀⠁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⡇⠿⠊⠿⠀⢈⣠⣴⣿⣿⠋⠀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⢙⠀⠀⣷⣿⠀⢸⣿⣿⡿⢃⠀⠈⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⣿⣿⠀⠈⣿⡿⠁⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠀⠀⠀⠀⠀⠀⢀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⣿⣿⠀⠀⡟⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⣿⣹⠀⠀⠦⢤⣈⡓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠀⠐⠀⠀⠀⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠐⠃⠘⠄⠀⠀⠤⠄⠈⠙⠚⠳⠦⣀⠀⠀⢀⡜⠟⠀⠀⠀⠳⢤⣀⡀⠈⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠦⠄⠐⠒⣒⡒⠦⠒⠚⠋⠉⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⡸⠀⠃⠛⠘⠀⢇⣀⠀⠀⠀⠀⠀⠀⡇⠸⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⡃⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢲⠀⡖⣲⢰⡂
⠤⠀⠏⡭⠭⢭⢹⠠⠤⠀⠀⠀⠤⠄⠀⠁⠐⠀⠂⠀⠴⠀⠀⠀⠰⠠⠆⠧⠂⠖⢀⠄⠴⠀⠀⠀⠒⠲⠙⠊⠁⠩⡚⠱⠒
⣀⠀⡆⡀⠀⢀⢘⠀⣛⠀⠀⠀⣘⢐⡃⡂⠀⠀⠀⠀⣚⠀⠀⠀⢘⠀⡀⣃⠘⡀⠁⡃⢐⠀⠀⠀⠘⠚⠀⢀⠀⢀⠄⠀⠚
⠭⢄⠓⠂⠂⠐⠚⡠⠭⠀⠀⠀⠈⠀⠁⡆⢈⠰⠆⠀⠈⠀⠀⠀⠈⠀⠁⠏⢡⠉⡄⠁⠈⠀⠀⠀⠙⠉⢺⠑⡆⢶⢸⠎⠉
⠀⠘⠐⠃⠛⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠃⠚⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠉⠈⠁

⠀⢀⢠⠰⣀⠆⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⢢⡀⠀⠀⠀⠀⠀⠀⢀⢠⠐⢲⠒⠢⠄
⠠⠌⠤⢓⡉⠚⠤⠡⠄⠀⠀⠀⠀⢳⠴⠛⠭⢜⢰⡞⠃⠀⠀⠀⠀⡠⠊⡼⢘⠸⡌⠢⡀⠀⠀⠀⠀⡪⢸⠀⠈⠁⣰⡄⠡
⢐⡂⣃⢠⠅⠚⢘⢐⡃⠀⠀⠀⠀⠠⣃⢅⠀⠀⢐⠇⠀⠀⠀⠀⠀⡀⠋⣀⠞⢄⡘⠃⡈⠀⠀⠀⠀⠀⢀⠀⠘⠃⢀⡀⢃
⠀⠰⢡⠛⠶⠐⡄⠆⠀⠀⠀⠀⠀⠛⠈⠓⠰⠔⠉⠙⠃⠀⠀⠀⠀⠈⠢⡉⢦⠎⡡⠊⠀⠀⠀⠀⠀⠠⣰⠀⠲⠀⢈⡫⠂
⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠉

⠀⢀⠔⣆⠀⢰⠢⡀⠀⠀⠀⠀⠀⠀⡆⠤⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠄⠄⢰⠰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⠂⢀⠆
⠴⠁⡠⢁⠛⡈⢄⠈⠦⠀⠀⠀⢨⠈⢠⢠⠀⠀⠄⠁⢭⠀⠀⠀⠠⠥⡆⠃⢠⡜⠂⠠⠅⠀⠀⠀⠈⠑⢐⠙⠸⣇⠡⡦⠊
⣀⠓⠇⠃⠻⠘⠸⠚⣀⠀⠀⠀⢐⠒⢒⢀⠄⣓⢒⠒⣒⠀⠀⠀⠐⣚⠅⣀⢤⢱⠀⢘⡒⠀⠀⠀⠐⠂⢸⠐⢌⠡⡒⡇⠐
⠈⠀⠈⠆⠛⢰⠁⡠⠁⠀⠀⠀⠰⠀⡄⢰⠀⠁⠀⠄⠲⠀⠀⠀⠀⠐⠁⡃⢀⢘⢐⠐⠀⠀⠀⠀⠀⠖⠘⡭⠨⠅⢤⠃⠲
⠀⠀⠀⠐⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠑⠉⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⠃

⠀⠖⠰⠂⠒⠀⠆⠲⠀⠀⠀⠀⠀⠀⠀⡀⢠⢰⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠰⡀⠠⡀⠀⠀⠀⠀⠀⢀⠤⠖⢰⠀⠲⢄
⠀⠠⡀⢄⠶⡠⢀⠄⠀⠀⠀⠀⠀⢨⠀⢤⠀⠸⠀⢀⠀⠀⠀⠀⠀⠈⠡⢆⠔⢌⠆⠁⠀⠀⠀⠀⢀⠇⠰⠷⠘⠀⠶⠀⠳
⠀⠰⠈⠀⠉⠀⠁⠆⠀⠀⠀⠀⣐⣚⣂⣒⣀⢔⣀⣐⣐⠀⠀⠀⢰⠂⠀⢁⠀⢀⣃⠔⠊⠀⠀⠀⢸⠒⠐⡂⢸⠀⠓⠐
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠨⠀⡀⢀⢀⠀⠄⠀⠀⠀⠀⠘⠀⢌⠑⠌⠀⠁⠖⠀⠀⠀⠀⠀⠣⣈⠁⣈⡁⠁⢀⠎
⣀⣸⣠⣇⣶⣸⣀⣇⣀⣀⣀⣀⣀⣀⣀⣤⣠⣸⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣘⣀⣉⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠛⠋⠉⠉⠉⠉⠉⠉⠛⠒⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠶⠶⠄⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠘⡆
⠀⠀⠀⡴⠃⠀⠀⠀⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠸⡄
⠀⢀⠞⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠤⠤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⢠⠏⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠦⠤⢤⡀⠀⠀⠀⠀⢳
⡞⠀⠀⠀⠀⠀⠀⠉⠻⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡄⠀⠀⠀⠉⠓⠀⠀⠀⠀⢀⣀⡀
⣷⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡆
⠘⣇⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠃⠀⠀⠀⠀⢰
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠸⡇⠀⠀⠀⠀⠀⣠⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⣷⠀⠀⠀⠀⠠⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠘⣷⡀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠆⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠙⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣤⣤⣤⣤⣴⣶⣶⣾⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣤⣤⡄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣬⠝⠉⠀⠀⠀⠀⠀⠀⠉⠙⣭⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣴⣶⡶⠀⠀⣤⣤⡄⠀⠰⣾⣶⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⣛⣛⡀⠀⠸⠿⠿⠇⢀⣠⣟⠛⠻⠀⠠⢶⡶⠄⠀⠛⠛⠋⠀⠠⢶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠁⠀⣾⣿⣷⠀⠀⢹⣿⢧⣤⣽⠛⣃⣀⠀⠀⠀⠀⠀⠀⢀⣀⣘⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⣶⣷⠖⠋⣩⣭⣤⠀⠐⢶⣶⡄⠈⢼⣿⡏⠀⠀⣿⣿⣷⠀⠈⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢛⣈⡛⠃⠀⠀⠿⠿⠿⣀⣀⠘⠻⣧⣴⣶⠄⠀⣠⣤⣉⠙⠻⢶⣦⡄⢘⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠁⠀⢼⣿⣿⠀⠀⢹⣿⡿⠰⠶⢾⣇⣀⣀⡿⣿⣿⣀⡀⠸⢟⣧⣍⡉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⡶⠋⠙⣿⣷⣶⠀⠉⢻⣿⣆⣠⡾⢿⣇⠀⠀⣿⣿⣿⠀⠀⢹⡿⠷⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⣭⣷⡦⠤⢻⣿⣿⣀⣠⣼⠋⠉⠿⠟⣋⣽⡏⠀⢸⣿⣷⡄⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠀⠀⣸⣟⠉⠈⠉⠁⠀⠀⠀⣠⣭⣤⠈⠀⠼⡿⠟⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⠁⠀⠀⠀⣀⣠⣄⠀⠉⠻⠟⠀⠀⣀⣀⠛⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⢡⣾⡟⠀⠀⢿⣿⠿⠀⢸⣿⣿⡄⠀⠙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁





⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡖⢀⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⠄⡀⠆⠀⠀⠦⢙⢁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡊⠀⠘⡀⢆⡛⡠⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠳⠵⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠷⠴⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢉⣩⣋⣀⣤⠐⠁⠀⠀⣴⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡮⠖⠀⠉⠁⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠁⠀⠀⠀⠀⣴⠉⠘⠻⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠐⠤⢒⣭⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⡏⡑⣄⣀⣠⣴⣿⣿⡶⢟⡛⠿⠟⣢⣀⠄⠸⡦⣔⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢐⣢⣿⣿⣿⣿⣿⡟⠀⢉⣙⣉⠭⠐⠠⠙⣦⡍⢡⡁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣟⣠⣦⣤⣤⣴⣭⣴⠶⠔⡿⣎⡀⠑⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⠀⠀⢒⠰⠀⣃⣾⣿⠶⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠛⠛⠻⠿⠿⣿⡿⡟⣣⣙⡷⠶⠶⠶⠿⠟⠛⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠤⠴⠀⠤⠤⢀⣀⡴⠛⠤⡀⠀⠀⠀⠀⠀⣀⠖⡡⠂⠀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢤⠀⡁⢀⣈⠱⠖⠒⠒⠙⠓⠩⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⡀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠁⠀⠀⠈



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⡀⠀⠀⢸⣿⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣿⣧⣤⣤⣿⣧⣤⣤⣼⣿⣤⣤⣼⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⡇⠀⠀⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡆⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣿⡇⠀⠀⠀⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠇⠀⠀⠀⠀⢸⣿⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⣿⡟⠛⠛⣿⡟⠛⠛⢻⣿⠛⠛⢻⣿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⣿⡇⠀⠀⠈⠋⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢰⢀⣀⠀⢀⠀⣀⣀⡀⡀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠒⠒⠒⠒⡄⢹⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⠘⠒⠐⠒⠒⠒⠒⠂⠒⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⠀⠀⠀⢸⢠⣀⣀⣀⣀⣀⣀⣀⣀⣈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠇⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠈⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢸⢸⣀⣀⣀⣀⣀⣀⣀⢀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡸⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠠⠠⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⣀⣀⣒⣒⣒⡒⣂⣀⣀⢀⠀⠀⠀⠀⠀⠒⠒⢒⡲⢁⡇⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢨⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠇⠀⠀⠸⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠦⣤⣤⣤⣤⣤⣤⣤⣴⠴⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠁⠉⠉⠀⠀⠀⠈⠀⠉⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⡉⠉⡉⠉⠉⠉⠁
⠀⠀⠀⡔⢀⠀⠠⢀⠀⢀⡀⠀⣀⠀⢀⡀⠀⡀⠂⢀⠀⣀⡀⠀⣀⣀⢀⡀⡀⡀⠀⢀⠀⢀⡀⠀⢀⠀⠀⡀⠠⠀⠀⣠⠈⢠⡤⣄⠀⠑⣄
⠀⠀⡼⠀⠦⠤⠤⠬⠤⠦⠡⠴⠌⠠⠄⠥⠴⠭⠥⠤⠥⠤⠬⠤⠬⠥⠬⠭⠴⠤⠤⠤⠅⠰⠨⠄⠀⠠⠀⠸⠄⠣⠀⠈⠓⠓⠲⠬⠦⠤⠊
⠀⠀⠳⠖⠲⠒⠒⠒⠶⠲⠖⠒⠒⠖⠒⠒⠒⠒⠒⠒⠒⠒⠖⠒⠒⠒⠒⠖⠲⠒⠒⠒⠲⠒⠒⠶⠒⠒⠒⠖⠶⠚

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠘⠷⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡠⠀⠀⠈⢻⣷⣦⣀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠉⠐⠲⠶⠶⢶⣶⡶⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠶⠄⠴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠟⠀⣳
⠀⠀⢠⣤⣀⠀⠀⡀⣤⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⠀⣴⣿⡿⠀⠀⠀⠀⠀⠼⠆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠈⠛⠟⠀⠀⠻⢛⠏⠀⠀⠀⠀⢠⠶⠉⠀⠀⢐⡄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠡⠂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠒⠤⢄⣀⣀⣀⣀⠤⠴⠚⠉
⠀⠀⠀⠈⠀⠀⠀⠐⠁⠀⠀⠀⠀⠠⠀⠀⠀⣀⡀⠀⣛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠔⠁⠀⠀⠠⠃⠀⠀⠀⡗⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣈⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡶⠤⠄⠀⣤⡤⢤⠰⡄
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢄⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⣀⣀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡇⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⠹⣷⣄⣘⠃
⠀⠀⣤⠤⣶⣾⣥⣤⣤⣤⣤⣽⣷⣶⣤⡄⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⠌⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠶⠾⠶⠆⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠘⠻⠟⠛⠛⠿⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠆⠁⠀⠀⠀⠀⠇⠀⠐⠂⢠⡀⠀⠀⠀⣤⣤⣤⡄⢀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠃⠀⠀⠀⠀⠳⢦⣤⣀⣀⣀⣀⣉⣩⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⢘⣉⣉⣋⣠⣀⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣤⣄⢠⣼⠀⠀⠀⠀⢡⣶⣄⠀⢀⣴⣶⠅⠀⠀⠈⢻⡿⠟⠋⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠠⠠⠀⣤⢀
⠀⠀⠀⠀⠈⢁⣈⠀⠀⠀⠀⠀⠘⢍⠉⠀⠈⢩⠝⠀⠀⠀⢠⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠂⠀⠀⠀⠺⠧⣄⣀⣀⣠⣠⣿⠹
⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢤⡄⠀⠀⢴⣦⣤⣤⣤⣤⣤⣤⣤⣭⣿⣶⣶⠄⠀⠀⠈⠚⠀⠀⢀⣀⣀
⠀⠀⠀⢠⡀⠀⠀⠀⡀⠀⠀⠀⢠⠀⢸⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠁⡀⠀⠀⠀⠉⠋⠛⠿⠿⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⢀⠰⢋⣉⠠⠀⠉⠑⢆
⠀⠀⠀⠈⠁⠀⠀⠸⠃⠀⠀⠀⢸⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢀⠉⠠⠀⠂⠀⢄⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⠀⠈⡇⠀⠀⠀⢀⠀⠀⠐⠂⢀⣴⡮⠁⠀⢀⣀⣤⣤⣤⣄⣀⣠⣄⣀⣤⣤⣤⣄⣀⠀⢘⠠⡄⠀⡀⠀⢙⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢸⠀⢰⡇⠀⠀⠀⠀⠙⠒⠶⠟⠛⠉⠀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⢈⣶⣿⣿⠟
⠀⠀⠦⠀⠀⠀⠀⠀⠀⠴⠀⠀⢸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⡀⢸⣺⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⢄⠀⠀⠀⠀⡀⠀⠄⠤⠆⠀⠀⠄⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⣿⡇⢸⡏⠀⢸⠀⠀⠀⢾⣿⡷⠀⠰⣾⣿⡿⠀⠀⠀⠀⠀⠑⡾⠓⠋⠾⠿⠻⠟⠛⢀⣱⣿⣟⠋⠑⣾⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠃⠀⠉⢃⢀⡟⠀⠀⠀⠈⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⠀⠀⠀⠢⢤⣤⣤⣤⣤⣤⡶⠿⠛⠛⠻⠦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠀⠀⠐
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠛⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠐⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⢀⡀⡀⡀⠀⠛⠀⠀⠀⠀⠀⠂⠈⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠂⠸⠉
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⡀⠂⠂⠀⠀⠀⡀⠀⠀⠈⠑⠀⠊⠂⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠐⠅⠂⠀⠀⠀⠀⠀⠀⠺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠤⠈⠀⠀⠤⠀⠀⠀⡀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠠⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡈⢀⡀⡀⠈⡰⠀⠁⠀⠰⠄⠀⠀⠀⠰⠄
⠀⠠⠀⠠⠀⠀⠀⠀⠀⠠⢐⠄⠀⠀⠀⠀⠠⠄⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠄⠀⠉⠀⠠
⠀⠀⠀⠀⠀⢠⠄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⡀⠈⠀⠁⢈

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠠⠄⡀
⠀⠀⠀⠄⣠⡖⠋⠉⠁⠀⠀⠀⠀⠀⠐⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠁⠢
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠐⣾⣿⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠘⣧⣄⣀⣀⣠⣾⣿⡟⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠
⠀⠀⠀⠀⠘⠉⠳⠖⠂⠀⠀⠀⠈⠛⠿⠿⠿⠟⠉⠀⠀⠀⠀⢫⡶⣦⣄⠀⢀⡤⣶⣮⠃⠀⠀⠀⠟⣀⣀⡀⠀⠀⠀⣀⣀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⢷⣦⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠱⡛⢿⣿⠀⢸⣿⠟⡳⠁⠀⠀⠀⢌⢷⣾⣿⡄⢀⣾⣽⣿⢇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⢀⠜⠀⠤⠀⡔⡄⠈⢣⠉⠛⢁⢈⠛⠋⡵⠁
⠀⠀⢠⡖⠉⣡⡀⡀⠀⠀⢠⣿⡾⠀⠀⢀⣴⡾⠵⣿⣥⣶⣄⠀⠀⠈⠣⣀⡠⠉⠀⠀⢡⢂⡇⠁⠀⠀⠱⡄⠀⠀⢠⠖⠁
⠀⠀⠀⠀⠀⠀⠉⠤⣴⣾⠿⠛⠁⣠⡶⠯⠿⠁⠀⠈⠛⠿⣭⡷⣤⠀⠀⠀⠀⠀⠀⠀⡴⠮⠱⠄⠀⠀⠀⠘⡦⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣖⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣮⣿⢿⣶⣦⣄⡀⠀⠈⢜⠁⡄⠀⠀⠠⠚⠀⠀⠑⠠⠠⡀
⠀⠀⠀⠀⠀⣠⣴⣾⣵⣿⣿⣷⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣿⣿⣿⣿⣶⣤⠀⠆⠡⢸⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠛⠿⠿⣿⣿⣿⣿⣿⣽⣿⣧⠀⠀⠀⠀⠀⣶⣿⣳⡿⣿⣿⣿⣿⣿⡿⠿⠟⠁⢀⠀⠃⣸⢣⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣯⣿⡷⠶⠶⠶⠶⢿⣯⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠇⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠁⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠉⠐⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡈⡍⣜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀⠂⠞⡜⢈⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⣂⠒⠀⠐⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡀⠲⠖⠒⠀⠀⠀⣰⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠁⠀⠀⠀⢠⠒⠀⢾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠙⠤⡁⠁⠉⢉⡭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠉⠠⣄⣀⣤⣾⣿⣶⢟⣛⣻⡓⢀⡠⡀⣆⢴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣠⣿⣿⣿⣿⡿⠁⠀⠕⣈⡍⠒⠈⢳⡬⠊⠅⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣥⣤⣥⠦⠶⠶⠶⠖⠙⢧⣄⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠁⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⣄⡀⠀⠄⢀⣠⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉⠙⠛⠯⢥⡤⠼⠛⠛⠋⠙⠋⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠆
⠀⠀⠀⠄⡀⣀⣀⠀⠀⣠⢆⠉⠀⠀⠀⠀⠀⢀⡑⠠⠠
⠁⠀⠀⠀⠀⠀⠀⢈⡉⠐⠀⠈⢒⠤⠤⠤⠶⠅⠚⠁⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠱⠚⠆⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⢟⠁⣡⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠐⣷⢃⣼⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡇⢠⣶⠃⣾⡿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢠⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⣿⢿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠿⣿⣿⣿⣿⣿⣿⣿⣞⣧⡀⠹⣿⣿⣿⣿⣿⣿⣿⣸⡀⠀⠐⢿⣮⣷⡏⠁⣸⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⢿⡿⣿⣏⠻⢯⣏⢲⠀⠀⠸⢿⣥⡀⢀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⢉⡁⠀⢺⢋⠋⠀⠀⠀⠀⠀⣰⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇
⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⠀⠀⡼⣠⡀⠀⠠⠀⢨⣿⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣏⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⢿⣧⠀⠀⢻⣿⠇⠀⠀⢸⣿⣿⣅⣾⣿⣿⡿⣿⣟⣿⣟⣿⣿⣷⣿⣿⡇
⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡇⠊⡀⠀⠁⠀⠀⠀⡿⡿⣿⣿⣿⡿⣿⡿⣿⢿⣿⣿⣿⣿⢛⣿⣿⡇
⠀⠀⠈⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣰⣄⣴⣶⣾⡶⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⢿⣷⣤⣻⣿⣿⣿⡇
⢰⣾⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣫⣿⡽⢿⡍⢻⢏⢸⠿⣿⠿⣝⣻⡟⣿⣿⡿⢇⣼⣿⣼⣿⣃⣽⣿⡇
⢾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣟⢷⡎⠂⠘⠈⣾⣲⢾⡾⡿⣿⣠⠯⠰⢆⠀⢁⠻⣿⡏⡴⣿⣿⡇
⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡟⣄⣹⣿⣿⣿⣍⣀⣤⣰⡏⡄⠛⣶⣿⣯⣽⡾⠓⢞⡣⠬⡙⣯⣸⣀⣿⣿⡇
⠿⢿⣟⣯⣿⣿⣿⣿⣿⣿⡿⢿⣻⡟⣕⣼⠳⣿⢿⣿⣿⡿⢁⠘⣿⢶⠑⣾⠟⣽⠀⢿⢹⣯⣴⣖⣠⣯⣿⠓⣸⣿⡇
⢁⢷⡿⠽⣟⢿⢿⣿⣳⣿⣽⠟⣡⣙⣿⠇⠀⢹⠀⣿⣿⡇⢸⡆⠈⠳⣄⣚⠵⠛⠀⠚⠀⠸⠃⠤⢹⣿⣿⡷⣿⣿⡇
⠀⠋⠀⠲⠻⠏⢄⣿⡽⣋⣵⣾⣿⣿⣿⠃⢰⣿⠀⢿⣿⡇⢸⣷⡈⠲⠤⠍⠓⠒⢦⡐⠁⠈⠱⠀⠉⠉⠉⠃⢿⣿⡇
⢀⣡⣿⠃⢀⠔⠉⠠⠀⣉⠉⠛⠛⠛⠃⠀⠈⠁⠀⠈⢿⡇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠳⣄⠐⢕⠀⣁⠄⠄⢸⣿⡇
⡾⠛⠁⡐⠁⠄⠐⠀⠶⠰⣿⣷⠾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠠⠄⢀⠀⠇⣺⣿⡇
⠀⢁⡘⠀⠀⠐⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠇⠀⠈⢞⠀⢸⣿⡇
⢀⢶⠃⠀⠆⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⣼⠀⠀⠀⠀⢿⣿⡇
⡀⢸⣀⣶⡦⠄⠀⠀⣿⢐⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⡀⢸⠀⠀⠀⠀⢸⣿⡇
⢩⣼⣾⣿⠣⢆⣾⣶⣿⣿⣿⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠈⢀⠀⠀⠀⢸⣿⡇
⠀⠘⣿⣿⣿⣸⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠷⠘⠀⠀⠀⠀⢸⣿⡇
⠠⣴⣿⣿⠛⣻⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣇⠀⢂⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠻⠿⠿⠿⠀⠘⠀⠀⠀⠀⠸⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⡟⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡙⢻⡆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣾⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣷⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠶⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣿⣿⣿⡿⠛⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣀⣀⣹⣿⣄⣀⣼⣏⣀⣈⣿⣿⣇⠀⣀⣿⣿⣿⣿⣿⣇⠀⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣤⣀⣀⣤⣴⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⡖⠳⣶⡝⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠈⠻⣿⣿⣇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣏⠀⠀⢈⣿⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⠧⣴⠿⣣⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⢠⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡴⠒⢀⣈⡀⠀⠀⡤⠒⠁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠁⠀⡠⠏⠽⠓⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⢀⡩⣉⢄⠠⣀⣀⣀⣀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠉⠁⠈⠉⠐⠂⠀⠤⠤⠤⠄⠐⠊⠁⢸⠀⠀⠀⣀⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢤⡀⢴⡀⠲⡀⠀⠀⠀⢠⠀⠀⣜⡵⠖⠒⡊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠓⠁⠀⠀⡱⠀⡇⠀⠀⠀⢸⠀⠀⠉⢠⠔⠊⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠄⠮⠤⠘⠀⠀⠀⠀⢸⠀⠀⡀⠄⣑⣀⣐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡤⡆⡆⡿⠚⣅⠀⠀⠀⢘⠀⠀⡁⢀⡰⠋⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠤⠄⠨⠥⠅⣁⣁⡁⠈⢁⣀⠠⠔⢩⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠭⠥⢌⠩⡉⢍⠉⡩⢁⠀⡈⠉⢍⡉⣙⠄

⣾⢾⣶⡾⢶⣦⣦⣤⣤⡤⠠⠤⢄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠠⡔⠃⠀⡀⢤⡄⢶⢧⢼⡄⡛⠅⠁
⠀⠀⠘⠑⠀⢀⣠⣠⣤⣶⣧⣶⣶⣟⣥⣴⣤⣽⣛⣛⣓⣶⢶⡶⡤⢀⡀⠀⠀⠀⠀⠙⠇⢀⠀⡄⠂⢀⡈⢄⡀⢤⡀⠀⢀⣤
⣦⣾⣟⡐⠀⠈⠿⠿⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣄⣑⡦⣄⠀⠀⠀⠀⡒⠆⠛⢰⡶⠒⠂⠀⠀⣨⣡⠤⠤⠤⠒⠐⠒⠒⠒⠀⠤⠄
⠙⠋⠹⠿⢶⢾⣦⣤⡐⢠⡤⣻⣟⡋⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣕⢠⡀⠀⠀⠀⠃⠈⠀⢘⡦⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠛⠒⠻⠉⠙⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢀⠠⠒⠁
⣤⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠈⠳⠦⢭⣙⣻⡿⣿⣿⣿⣿⣿⡿⢻⠄⠀⠤⠠⡠⠊
⣿⣿⣿⣿⢸⢙⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷⣶⣦⣤⣄⣀⡈⠀⠙⠐⠒⢨⠘⠣⠰⠀⣄⠀⢀⠞⠁⠀⣀⣤⣤⣤⣀⡀
⣿⣿⣿⡟⠀⢸⣿⡿⠿⠛⠉⠉⠉⠉⠉⠙⠛⠿⡿⠛⣿⣿⣿⣷⣦⣀⠀⠂⠀⠀⠔⣠⡤⡤⠊⠀⢠⢾⣵⣾⣿⣿⣿⣿⣷⣄
⠛⠛⠻⠛⠙⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⠇⣿⣿⣧⣤⣄⣤⣼⡧⣴⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⡧⢟⣧⣽⢿⣿⢻⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠁⠀⠀⠀⠀⠀⠀⠀⣪⡤
⠀⠀⣲⡄⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢿⠿⠃⠀⠈⠉⠁⢉⠘⢆⠀⢿⣿⣿⣿⣿⣽⣿⡋⢀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⡶⣠⡀
⠀⠀⡿⣾⢆⠀⠀⠀⢀⡾⣽⣿⣾⣿⢻⣿⣿⡿⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⢿⣿⣯⣤⡞⠉⠁⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣬⣋
⠀⢠⢠⡶⠟⢧⠀⠀⢸⡇⠙⠻⠛⠟⠛⣽⠟⠀⠀⠀⣰⣿⣤⠀⢸⣠⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⣿⠏⠀⠀⠀⠀⠀⠀⣠⣼⣿⠏⠹⣿⣿⣿⣿⣿⣿
⠀⢈⠸⣧⣀⣸⠀⠀⠸⣷⡀⣀⣤⣴⣿⠋⠀⠀⣠⣶⣿⣿⣿⢀⡇⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠄⠀⠀⣀⣤⣴⣿⣿⣿⠃⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠘⡀⠈⢹⠟⠀⠀⠀⠈⠛⠿⣿⡟⠁⠀⣀⣴⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠋⠉⠀⠀⠀⠘⣿⣟⠏⠉⠉
⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣴⣿⣿⣿⡏⠸⡿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡀⠀⠀⠀⢸⣿⠿⠛⠛⠛⠳⠀⠀⠀⠀⣸⣿⡏
⠀⠀⠀⠈⢦⠀⠀⣀⣴⠄⠀⠀⣾⢿⠛⠛⢿⡃⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣜⠋⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⠁
⠀⠀⠀⠀⣈⡇⠀⠹⠃⠀⠄⠀⠃⡙⠀⠀⡿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋
⠀⠀⠀⠀⠀⢹⠀⣠⣤⣀⣀⠀⠀⢄⠀⣀⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃
⠀⠀⠀⠀⠄⠘⡏⠁⠀⠈⠉⠙⠀⠈⣠⣇⡠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣽⡶⠦⠄⠀⠀⠀⠀⠀⣸⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⢹⠀⠀⠠⠄⠀⠀⣰⣿⣿⣿⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠛⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠐⠂⣤⡀⢧⣀⣀⣀⡤⢾⣿⣿⣿⣿⡇⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠆⠀⠀⠀⠀⠀⢠⣾⠿⠛⠛⠋⣽⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡭⢋⠀⠈⢋⣿⣿⡿⢀⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢀⣀⣴⡿⠁⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣠⠔⠋⡠⠊⠀⠁⠀⠺⣿⠃⠈⠇⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠿⠟⠉⠀⠀⠀⠀⠀⠀⡏⣿⣿⡇
⠀⡶⠐⠒⠊⠉⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠢⣄⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠉⢸⠇⢸
⠉⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠈⡁
⣠⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠿⠿⢿⣶⣶⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⠤⠤⣤⣀⣀⡉⠉⠙⠛⠿⠿⣷⣶⣶⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠀⡟⠀⠀⠀⠀⠉⠉⠙⠓⠒⠶⠤⣤⣀⣉⠉⠛⠚⠿⠿⢷⣶⣦⣤⣄⣀
⠀⠀⠀⣀⣠⠤⠖⠛⠉⠀⢠⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠤⣤⣀⣈⡉⠉⠛⢿⢷
⣴⣾⣋⣉⠀⠀⢀⣠⠴⠒⢻⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡇⠀⡟⣸
⡇⠀⣀⡉⠉⢻⠉⠀⠀⠀⡿⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⢃⡇
⣇⠀⡏⢹⠀⢸⠀⠀⠀⢠⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡾⢸⠁
⣿⠀⣿⢸⠀⢸⠀⠀⠀⢸⠃⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡇⡟
⢿⠀⣿⢸⠀⢸⡆⠀⠀⣾⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⢸⠇
⢸⠀⢸⢸⡄⢸⡇⠀⢀⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡇⡾
⢸⡄⠘⠾⠇⠸⡇⠀⢸⠃⠈⠙⠓⠲⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣼⣸⠇
⠘⡇⠰⣿⡇⠀⡇⠀⠈⠙⣒⡶⢤⣀⡀⠀⠈⠉⠙⠒⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢰⣏⡿
⠀⠙⠲⠦⢤⣤⣧⠴⠞⠋⠁⠀⠀⠀⢉⣽⠶⠦⣤⣀⡀⠀⠈⠉⠛⠲⠦⣤⣀⣀⠀⠀⢀⡏⠀⣼⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠯⣭⣙⡓⣶⣤⣄⣀⡀⠀⠉⠉⠛⠚⠁⢠⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⢹⡟⠓⠶⠤⣤⣀⣼⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣍⠳⠦⣄⣀⡀⠀⠀⠀⠀⢀⣠⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠬⣭⣭⣛⣛⣛⣭⠴⠋

⠀⠀⢀⣴⣶⡄⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⢭⡯⠁⠀⠀⠀⠀⠀⡼⢿⣿⣿⠿⡄⠀⢠⣿⣿⣿⣿⣧⠀⠀⢳⣨⡇⡜⠀⠀⠀⠀⠀⠩⣯⠁⠀⢀⡆
⠀⠀⡰⣶⣷⢦⠀⠀⠀⠀⠀⢷⣀⣹⣁⣠⠇⠀⠈⡟⠛⣟⠛⡏⠀⠀⠀⣿⣿⡇⣀⠀⠀⠀⢠⢶⣷⣶⡀⠙⠃
⠀⠠⠇⢿⡿⠘⡆⠀⠀⠀⠀⠈⠻⣿⣿⠋⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠀⢻⣿⠋⠀⠀⠀⠀⡏⢸⣿⠇⢧⡇
⠀⠸⠀⢸⡷⠀⢧⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⠂⢸⣿
⢀⣄⠀⣾⣷⠀⣨⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢰⣿⡆⠀⣬⡀⣸⣿⡆
⠘⠍⠀⡿⢻⠀⠩⠃⠀⠀⠀⠀⢂⣡⣼⣾⡿⠟⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠯⠁⢿⠹⠇
⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⣠⣶⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⢸⢸⡆
⠀⠀⠀⠇⠸⠀⠀⠀⠠⠾⠟⠋⠙⠉⠀⠀⠀⠀⠀⠀⠠⣾⡆⠀⠈⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠸⠘⠇
⠀⠀⠀⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠁
⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠠⢴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡦⠄⠀⠀⠀⣠⣶⣿⣿⣿⡿⠋⠁⠀⠀⠀⢀⣤⣶⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⠉⠁
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣦⣄⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠈⢿⡿⠿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣿⣿⣦⣤⡀⠀⢀⣤⢼⡿⣿⢿⣿⢿⡧⣤⡀
⠀⠠⢄⣀⣀⣀⣀⣘⣃⣀⣀⣙⣀⣀⣀⣀⠤⠀⠀⠀⠀⠨⠏⠛⡟⠛⡯⠀⠀⠀⠀⢈⡽⠉⠉⣿⠉⠉⢯⡁

⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⢀⣀⣈⠀⠀⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣷⣾⣶⡄⠀⢸⣿⣿⣿⡿⠟⠋⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⠉⠀⠀⠀⠀⣠⣤⡀⠬⠲⠎⢻⣿⣿⣿⣿⣿⣴⣿⣿
⢸⣇⣀⠄⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠙⣿⣿⣿⣿⣿⣿⢹⡇⠀⠀⠀⣀⣀⠻⣿⠇⣀⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⢸⡇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣿⣼⣧⢸⡇⠘⠂⠘⢿⣿⠇⡀⠺⣿⣿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿
⢸⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣶⢶⣿⣿⣿⠉⠉⣿⣿⣾⡇⠀⢀⣀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⢸⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠀⠀⠙⠛⢿⣯⣾⣿⣿⣿⡄⠈⠉⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⢸⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡤⠀⠀⣤⣴⢸⡏⠻⣿⣿⡿⠃⠀⠈⠀⠂⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡴⢿⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⢸⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢹⣧⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣿⣿⣿
⢸⡇⠀⠀⢤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⣿⣿
⢸⡇⠀⢴⣶⠄⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣋⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⢸⡧⠘⠀⠈⠀⢰⣿⣿⣿⣿⣿⠟⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⢸⡇⠀⠀⠀⠀⠀⠙⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿
⠸⣇⢀⣀⣀⣀⣀⡀⠀⠀⠀⠠⠤⠀⠤⠠⠤⠤⠤⠤⠤⠄⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠉⠁⠉⠉⠉⠁⠀⠈⠉⠉⠁⠈⠛⠛⠒⠠⠖⢖⡐⡀⠒⠒⠒⠢⠶⠦⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⢖⠲⡲⡆⢤⢤⣤⣄⣀⣀⣀⣀⠀⠀⠁⢰⠊⠌⢥⠔⠕⣑⣕⣑⣡⣢⣺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢀⢁⠈⠈⠀⠑⠐⠈⠈⠊⠫⠩⠙⡐⢟⢞⢿⡙⡩⢋⢟⠝⡩⡩⢊⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⣿⡍⣹⠛⠿⠛⠲⢷⠶⠦⠦⠤⢤⣬⣈⠘⣎⠔⠑⡠⢊⢎⠔⣡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⣷⣧⢈⠔⡀⠀⠀⠀⠊⠀⠀⣸⣭⡆⠘⡄⢷⡪⢊⠔⡱⢀⠜⡱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢹⣺⢀⡨⠄⣨⠹⣣⠀⠀⠀⠙⠀⠃⠀⡇⢸⡕⡡⢊⠔⡡⢊⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣿⢀⣒⣆⠉⠀⠊⠀⢠⣦⣶⠀⠀⠀⡇⢸⠞⡐⢣⠊⡠⢋⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⡏⡁⡉⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⡇⢸⣋⠔⡡⢊⠔⡡⢚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⡇⠻⣂⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡇⢸⡣⢊⠔⡡⢊⠔⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⢄⢿⣑⡂⠄⣀⠻⠾⠀⠀⠀⠀⠀⠀⠀⠇⢸⡕⡡⢊⠔⡡⢊⢜⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢝⡓⠂⠤⣉⡉⠒⠢⠬⣉⣐⠂⠠⠤⢄⣴⠀⢸⢎⠔⡡⢊⢔⡡⣪⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣴⣣⣼⣷⠀⣠⠜⠓⢶⠦⠤⢄⣈⡉⠉⠍⠡⠄⣾⠅⡨⢆⠵⡫⢊⠴⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡔⢊⣴⢂⣢⡍⠙⠋⠁⠀⠣⣔⣢⠞⠀⠀⠀⠀⠀⠉⠉⠀⢲⡯⠊⡴⡣⢊⠔⡡⢪⡇
⠀⠀⠀⠀⠀⢀⠔⡡⠀⠸⢍⣻⠷⠊⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡠⡫⢊⢔⠡⣊⢴⠟⡇
⠀⠀⠀⠀⠀⡷⣈⠺⢂⠀⠀⠀⠀⠀⠀⠀⠀⣴⣞⠻⣾⣹⠉⢲⡀⠀⠀⠀⣴⡥⡪⢊⢖⠕⡫⢊⠔⠡⢊⡇
⠀⠀⠀⠀⠀⡆⠈⠓⢄⣁⠢⡀⠀⠀⠀⠀⢸⡣⡈⡑⠬⣴⣧⡿⠁⠀⢂⠾⡫⣪⢞⠵⡡⢊⠴⢁⠜⡱⡪⡇
⠀⠀⠀⠀⠀⡃⠦⣄⠈⢉⡱⠶⠤⣀⡀⠀⠀⠉⠋⠛⠛⠛⠉⡀⢈⡴⡣⣪⢔⠵⡫⢊⠔⢃⠔⡡⡪⣪⢾⡇
⠀⠀⠀⠀⠀⠃⠰⢦⡍⠈⣑⣒⣤⠀⢈⡉⠒⠢⠤⣄⣀⠐⢂⣤⡞⡩⢊⡕⡡⠊⡠⢊⠔⡡⡪⢊⢔⠕⡱⡷⠂
⠀⠀⠀⠀⠀⠁⠘⠒⠀⠁⡙⢏⠀⠀⡜⢉⡛⠥⢖⣤⣌⡉⡿⡡⢊⡔⣣⠞⡠⢊⠔⡡⠪⢊⠔⡕⢡⢎⣔⣇⠀⠠⠬⠀⠀⠀⢂⣀⣀
⠀⠀⠀⠀⠀⢰⡜⠇⠴⡀⠹⠙⠓⠀⡇⢸⣿⠀⣤⣄⣹⡇⣟⡠⢫⠜⡡⢊⠔⡡⢊⢜⡔⡡⢊⠔⡡⣢⣾⣇⠂⠄⠀⠉⠀⠀⣤⠀⠀⠐
⠀⠀⠀⠀⠀⠈⡆⠸⠂⠈⠲⠇⠀⠀⡇⠈⠛⠘⣭⣿⢿⡇⣏⠔⡡⢊⠔⣡⢎⠔⡡⡪⠊⡰⢃⢎⠔⣣⣾⠃⠉⠭⠄⠀⠀⠐⢒⡒⠒
⠀⠀⠀⠀⠀⠀⠃⡆⠀⠀⠀⠀⠀⠀⢃⣶⣤⣀⠀⣄⢸⡇⣏⠘⡡⢃⠖⡡⡣⢊⠔⡡⢊⡴⠏⣅⣾⠋⠉⠤⠀⢀⣉⡐⠁⠂
⠀⠀⠀⠀⠀⠀⢸⢍⡁⠀⠀⠀⠀⠀⠹⣽⣌⡽⠶⠇⢸⡇⡥⢊⠔⡡⢊⢎⠔⣁⣪⢔⢃⣤⡿⢃⡒⠀⡬⠉⠡⠤⠄
⠀⠀⠀⠀⠀⠀⠈⢷⣉⡢⢄⡀⠀⠀⠀⠀⠁⠋⠻⠒⠿⢀⡶⡡⢊⠔⣡⡣⢞⢩⣠⡿⠏⠁⠀⠐⠒⢒⣒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣠⠈⢐⠐⠢⠄⣀⠀⠀⠀⠀⢸⢋⣴⡥⢛⢁⣠⡦⠿⠉⠁⠉⠀⠐⠛⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⣄⠀⡀⠈⠉⠁⡒⡚⡛⣈⣷⡷⠞⠋⠉⣍⣉⡉⠭⠭⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠒⠛⠛⠛⠓⠚⠒⠒⠒⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠚⠋⠉⠉⠁⠀⠉⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⣀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠒⠁⠀⠈⠀⠐⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢀⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠒⠁⠀⠀⠑⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢧⡇⠀⠀⠀⠀⠀⠀⠀⠒⠲⠤⣤⣉⣉⣤⠤⠖⠒⠀⠀⠀⠀⠀⠀⠀⢸⡼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⡿⠒⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠒⢿⣷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣐⣒⣛⣛⣓⣒⠤⣀⠈⠢⠀⠀⠀⠀⠔⠁⢀⠤⣒⣚⣛⣛⣒⣒⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠾⣿⣿⠉⠉⠙⣿⢿⣶⣄⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⢿⣭⣿⣿⣿⠳⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢿⣿⣿⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣧⣤⣴⣿⣿⣿⣿⡿⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡈⠻⣝⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⣫⠟⢡⣲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⠛⠾⢿⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿⣿⣿⠷⠛⠁⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠺⠃⠘⠗⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⠐⠒⠒⠂⠀⠀⢰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⢀⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠒⠒⠒⠒⠒⠀⢄
⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⠄⠠⠀⠀⠀⠀⢡
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠂⠖⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠑⠢⠀⢀⣀⡀⠀⠠⠂⠄⠀⠀⠀⠀⠈⠉⠉⠉⠉⠏⠉⠉⠉⠩⠽⠿⠿⠿⠿⣷⠀⠀⠂⠀⡠⠀⠀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠦⠂⠀⠀⢀⢂⠄⢎⣡⠀⠀⠀⠀⠀⢰⡠⠤⠔⠀⠀⠀⣿⠀⠤⠄⠊
⠀⠀⠀⠀⠀⡠⠔⠂⠉⠉⠉⠑⠢⡀⠀⠄⠀⠀⠰⠾⡀⢸⠣⠃⠀⠀⠀⠀⠨⡁⠀⠀⠀⠀⠀⣿⠀⠀⡠⠀⠂⠈⠀⠀⠈⠐⠢⡀
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠉⠀⠀⠀⠈⠄⠀⠀⠀⠀⠢⣙⡓⠂⠄⠀⠀⠀⠀⠠⡳⣴⠣⠄⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠂⠀⠀⡁⠀⠀⠉⠉⡡⠀⢄⠀⠀⠁⠈⠉⠉⠁⠉⠉⠍⡉⠉⠁⢸⠀⠂
⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⢀⡀⢎⠀⠀⠀⠀⢐⠒⠐⠄⠀⠀⠀⠀⠀⠀⢈⠊⠀⠓⣤⠀⠀⢸⠀⠈⠂⠀⠀⢀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠆⠈⠀⠀⠀⣠⣄⣤⡀⠀⠀⢰⠀⠀⠈⡳⢄⠴⡓⠀⠀⢸⠀⣠⠊⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣂⣀⣀⣀⣒⣠⣬⣦⣤⣴⣤⣤⣤⣬⣦⣶⣤⣥⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠤⠠⠄⠀⠄⢠⠈⡗⡺⣾⣽⣧⣗⣛⣗⠒⠚⠛⠛⢭⡷⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⡤⠬⠤⡅⢭⠸⡅⢯⠿⣿⢹⡿⣤⠀⡤⠕⣀⠱⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠤⠤⠤⠤⠤⠍⠉⠁⠨⢭⣁⣉⣉⣩⠭⠽⠬⢤⢬⠭⣬⣥⣭⣿⣆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠈⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣤⣄⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣁⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣁⣠⣠⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣠⡋⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⣀⠰⠁⢃⡄⠀⢀⠀⠀⠀⠀⠀⠀⠠⢀⠸⠁⠘⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠠⣀⡈⠉⠑⠦⠄⢂⢧⣤⠤⠠⠄⠲⢀⡼⠀⣀⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠔⢋⠰⠶⡒⣮⡙⣦⠀⢀⣀⣀⠁⣀⣠⡤⠖⠃⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠘⣿⡄⡉⣰⡿⠿⣓⡋⠴⠒⠀⠟⠛⠋⠁⠀⠀⠀⡀⣤⣤⣾⡏⠈⢦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣿⣷⠿⠳⠛⠻⠏⠀⡄⢀⣤⣤⡶⢲⣆⣘⣠⣰⣶⡶⣾⣟⣅⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠰⠤⣤⣿⣴⡿⠁⢀⠄⢴⡦⠴⢶⠿⠋⢉⣽⠋⠗⠀⢿⣿⣿⠿⢻⣷⡟⣫⣭⡿⣷⡄
⠀⠀⠀⠀⠀⣠⣳⣤⣐⠇⣘⣦⣴⡞⠙⡿⠷⠦⢀⡌⣠⠞⠀⢀⣴⠂⠠⢻⣷⣿⣯⣷⣿⣿⣷⣽⡿⠃
⠀⠀⠀⠀⠰⣫⣭⣋⣽⡃⠉⡔⢙⠛⠁⡁⣀⣤⠊⠁⢀⠐⢠⣬⠉⠑⢲⡦⠄⢉⡛⠛⠋⠛⠛⠉
⠀⠀⠀⠀⠀⠂⠈⠉⠉⠛⠀⠈⠂⠉⠉⠉⡾⠋⣱⠛⠒⠠⠀⠜⠐⠺⠥⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠋⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⡀⡄⣀⣀⠐⠀⠀⠀⠀⠀⠰⢖⣖⣂⣒⣀⡤⡄
⠀⠀⠀⠀⠁⠈⠉⣀⢠⠀⠀⠀⠀⡒⢐⡀⠀⠀⠰⠒⣍⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢺⠀⠀⠀⠀⠙⠐⠁⠀⠀⠀⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠈⢠⡄⢠⡄⠠⡤⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡔⠈⠂⡀⠎⠀⢀⣀⢀⠀⡀⡀⠀⠀⡇⠀⠀⢀⠔⢀⠒⢄
⠀⠀⠀⠀⡀⠀⠀⠀⡉⠤⡔⠀⠀⠀⠀⠈⠉⠉⠉⡹⢋⣹⣏⢹⡶⠠⠒⠦⢤⡀⠀⣡
⠀⠀⠀⠀⢠⠘⠒⠒⠛⠒⠒⠒⠒⡀⠀⠀⠀⠀⠀⣇⡂⠀⢹⡴⠗⠂⠂⠀⠘⠶⠧⠟
⠀⠀⠀⠀⣄⠁⠀⠀⠀⠸⠟⠿⠿⣿⡛⠛⣟⠉⠋⡟⠑⢄⠈⠓⠒⠶⠂⠉⡀
⠀⠀⠀⠀⠄⡀⠈⠑⠁⣍⡈⠋⠀⠈⣽⣛⣙⠛⡙⠛⠟⠀⠉⠒⠤⠤⣤⡤⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠸⢯⠥⡄⠀⠀⠀⠀⡠⠚⠁⠈⠀⠀⢼⠀⠀⠀⠘⡇⠠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠖⠖⠛⠀⡀⠀⠠⠀⣐⡚⣇⠀⠀⠀⠣⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠋⠀⠙⣄⠀⠀⠠⠝⢲⡟⠋⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠈⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠉⠳⣄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⡇⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⢤⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⡠⠚⠛⠛⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⠉⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠀⢀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠘⢿⡿⠃⠀⠀⢀⣀⣼⣄⣀⣀⣧⣀⣀⣸⣇⣀⣀⣼⣀⡀⠀⠀⠀⠈⠻⡿⠃⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⢸⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⡇⠀⠐⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⡇⠁⠉⠉⠁⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣅⣀⣀⣀⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡧⠤⠤⠤⠤⠤⢴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣉⣉⣉⣉⣉⣉⣡⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⡀⠀⠀⠀⠀⠙⠿⢿⠿⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⠿⠟⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⣤⣶⣄⠀⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⣠⠞⠀⠀⣤⣷⣄⠀⢸⡇⠀⠀⠈⠉⠉⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠒⠚⠁⠀⠀⠀⠿⣿⠟⠀⠘⢧⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢖⣚⣭⣭⣭⣶⣶⣶⣶⣶⣮⣭⣭⣓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣫⡵⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣭⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣼⢳⡏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢳⡀
⠀⠀⠀⠀⠀⠀⢠⢏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣇⠷⣄
⠀⠀⠀⠀⠀⠀⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⣶⣤⡀⠙⢷⡜⣧
⠀⠀⠀⠀⠀⠀⡏⣾⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⣿⣿⣿⡇⠈⠉⠐⠒⠒⠉⠉⠀⣿⣿⣿⣿⣿⣿⣷⠀⣼⢇⡟
⠀⠀⠀⠀⠀⠀⡇⣿⡇⠀⠀⠀⠀⠀⠀⠘⠁⠻⣿⣿⣷⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠏⠰⡇⣾⠁
⠀⠀⠀⠀⠀⠀⣧⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠋⠁⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡿⣸⠇
⠀⠀⠀⠀⠀⠀⠈⣧⢻⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣆⢿⣄⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠋⠀⠀⠀⠀⠀⠀⢀⡼⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⠄⠀⠀⠀⢸⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣭⣛⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣝⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢻⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⣿⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢟⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⣣⡟⠀⠀⠀⠈⣸⡟⠶⠶⠶⣞⣛⣫⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢒⣚⣭⣭⡵⠶⠟⠉⠀⠀⠀⠀⠈⢸⡗⣏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⠖⠻⠋⠉⠑⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠻⣮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⣾⠃⠀⢸⣄⣠⠎⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣝⡳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣸⢻⡏⠀⠀⡼⠀⠀⠀⠤⠌⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣝⢧⡀
⠀⠀⠀⠀⠀⠀⡼⣡⡟⠀⠀⢸⡇⠀⠀⡀⠀⠀⣠⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⡇
⠀⠀⠀⠀⠀⢸⢣⡿⠀⠀⠀⠀⣄⠀⠀⠀⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢰⡇
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠈⠁⣲⣮⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢣⠏
⠀⠀⠀⠀⠀⢹⡜⣧⠀⠀⠀⠀⢀⣼⢟⣤⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⡏
⠀⠀⠀⠀⠀⠀⠳⣝⠶⢦⣴⠾⣋⡵⠋⠀⠙⣮⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡺⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋⠉⠀⠀⠀⠀⠈⢧⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠳⣮⣛⢦⣀⠀⠀⠀⠀⣀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⠳⣮⣛⠶⣞⣫⣭⣵⣾⡦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠶⢦⣄⡀⠀⠀⠈⠉⠉⢀⣴⡞⢫⣵⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣕⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣱⠗⢮⣝⠲⣄⠀⠀⠀⠈⣉⣛⡷⠶⢮⡝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠈⠻⣌⡳⢦⡄⢦⣌⠻⣿⡟⢛⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡎⢿⣼⠟⡳⠦⠿⣪⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠵⠛⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡋⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣠⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⡿⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⠀⠀⢰⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣷⡀⠀⠀⠀⢠⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠻⣿⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⣿⠟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠈⠙⠛⠛⠃⠀⠀⠀⠈⠋⠉⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠛⠛⢿⡿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⣿⣀⡠⠤⣔⣫⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠲⠶⠴⠂⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣶⣬⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣠⣹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⠹⣦⣠⣴⠶⠟⠛⠛⠛⠻⠶⢶⣤⣀⣴⠟⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣽⠟⢋⡁⠀⠀⠀⣠⠤⣤⠀⠀⠀⠈⠙⠻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⢠⡾⠃⠀⠿⡽⠀⠀⠀⠻⣤⠼⠃⠀⠀⢴⣛⡆⠈⠻⣦⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣠⣤⣤⣤⣴⠶⠶⠶⠶⠶⠶⠶⠶⢶⣦⣥⣤⣀⣀⠹⣧
⠀⠀⠀⠀⠀⣀⣤⡴⠾⢛⣛⣉⣩⣭⠤⣴⣶⣶⡖⠒⠒⠒⠒⠛⠒⠒⢒⣶⡶⠬⢭⣭⣛⡻⢷⣤⣀
⠀⠀⠀⣴⠞⣫⠵⠖⠛⠉⠉⠀⠀⠀⠸⠿⢿⣿⣃⣀⣀⣤⣄⣀⣀⢾⣽⣿⣽⠇⠀⠀⠈⠉⠓⠮⣝⣷⣤⡀
⠀⠀⢸⣇⡞⠁⠀⢀⣀⣀⣀⠀⠀⠀⣠⣶⣿⢿⡿⠿⠿⠿⠿⠿⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣷⡄
⠀⠀⠸⣿⡀⠀⠀⢯⣿⣭⣿⣿⠀⠀⣿⣺⣄⣾⠃⠀⠀⠀⠀⠀⠀⢹⣏⢛⣿⣧⠀⠀⣞⣩⣙⡍⣳⠀⠈⢻⡷⠸⠇
⠀⠘⢦⠙⠷⣤⡀⠀⠀⠉⠉⠀⠀⠀⠈⠛⣿⠃⠀⠀⠃⠀⠀⠀⡄⠀⢿⣯⡿⠃⠀⠀⠈⠙⠛⠉⠁⢀⣠⡿⠁
⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣄⣀⣀⣀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⣧⠀⠀⠀⠀⢀⣀⣠⣴⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣹⡟⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⢿⡟⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⡆⠀⠀⠀⠀⡆⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⣇
⠀⡀⠀⠀⠀⠀⠀⠀⢀⡿⢁⣀⡤⠴⠖⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠲⠶⢤⣄⣀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠋⠁⠆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉⠁
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢰⡆⠀⠀⢸⣿⢸⣿⠀⠀⠀⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣿⣴⡆⣿⣿⢸⣿⣿⣶⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⣄⣴⣿⣿⣸⣿⣿⡷⠶⠾⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢿⣏⣽⣿⣯⠿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣰⣿⣼⡟⣿⣩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠿⠿⣺⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣯⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⣷⡖⣻⣿⡇⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡇⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⡇⣿⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡖⣶⣼⡏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠹⣿⣶⣯⣿⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⢸⣏⣻⣿⣟⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡶⠛⠸⣿⣿⢹⣿⣿⡷⠶⢶⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠻⠇⣿⣿⢸⣿⣿⡿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠸⠃⠀⠀⢸⣿⢸⣿⠀⠀⠈⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠚⠛⠛⠛⠛⠓⠶⠶⣤⣄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣞⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣫⡿⠖⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒⠶⠶⠦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠓⣾⠋⢰⡾⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⠾⢻⡇
⠀⠀⠀⠀⠀⠀⣿⠀⡏⠉⠉⠉⠉⠉⠉⠛⠓⠒⡆⠀⣿⠀⢸⠀⠀⢀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠉⣙⣛⣛⡓⠒⠒⠒⠒⠒⠃⢀⡏⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢻⠀⠀⠀⣿⠀⠀⣾⣿⣦
⠀⠀⠀⠀⠀⠀⣿⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⢸⡇⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⡇⠀⠀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⠃⠀⣿⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠇⠀⢰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⢀⡏
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡟⠀⠀⣾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠓⠒⠒⠚⠛⠛⠀⠀⢀⡟⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⢀⡟⠀⣾
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢿⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠁⠀⢸⣇⡴⠇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡖⢲⠀⠀⠀⠀⣸⠃⠀⢀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠩⠉⠉⢩⠉⠉⠉⠛⠛⠛⠛⠛⠀⠀⡿⠀⣠⡿⠉
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣿⣀⡴⠋⠈⠉⠉⠉⠛⡟⢛⡿⠛⠓⣷⡒⠶⠶⠶⠶⢶⣦⢤⣤⣤⣤⣤⣴⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⣠⠖⠚⠁⢾⣇⡀⠀⠈⠙⠛⠓⠒⠒⠛⠁⠀⣠⡿⠀⠈⠣⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣧⣀⣀⣀⠈⠻⠯⣿⣶⣶⣶⣶⣶⣒⣒⣾⡽⠟⠁⠀⠀⠀⠀⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⡤⠤⡤⢤⡤⠤⣤⢤⣤⣄⣈⣉⣉⣉⡉⠙⠛⠛⠛⠷⠾⠯⢭⣭⣥⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠋⡿⠓⡾⠓⣲⠓⡶⠧⢤⠧⢤⡯⣤⣽⣉⡟⢀⡖⢲⠖⢦⠤⢤⡀⠀⢩⠟⣇⠀⠀⠀⠀⣠⡴⢶⢞⡿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢸⣉⡽⠉⣹⠛⢲⠟⢲⠓⢲⠿⢤⡾⠤⣼⢥⣼⠁⡜⢉⡟⢒⠟⠒⡾⠁⡰⠋⣴⠏⠀⠀⣠⣞⣁⣠⣧⠋⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠤⠤⠬⣉⣉⣉⣙⣛⣒⠛⠒⠛⠲⠾⠤⠴⠧⠴⠃⢸⣉⣽⣉⡟⠓⡾⢀⡜⣡⠞⠁⠀⠀⣰⠋⠀⠀⠀⠈⠉⠲⢄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠓⠒⠶⠶⠶⠯⠭⣭⣭⣉⣓⣒⣒⣒⠒⠒⠦⠤⠤⢭⣭⣉⣠⢋⡼⠃⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠓⠲⠶⠶⠶⠿⠟⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣴⣲⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⣿⣿⣿⣿⣿⠟⠋⠉⢩⡿⠿⠛⣿⣿⣏⣹⣿⠋⠀⠀⠀⠁⠉⠉⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⠟⠉⢿⡿⠁⠀⠀⠀⠀⠀⠀⢰⠟⠻⣿⠟⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⣰⣿⣷⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⣿⣿⣿⠿⠿⠿⠿⠿⠿⣟⣿⣿⣿
⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⢹⡇⣧⢀⠻⢿⠟⢀⣤⣤⡀⠸⣿⣿⠏⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡿⠿
⣦⢠⠏⣵⣾⣙⡢⠤⢔⣉⣷⣮⢱⢸⣿⣿⠣⣄⠰⠆⢸⣿⣿⡿⠀⣬⠁⢀⣴⣾⡿⠀⠀⢀⡀⠤⠔⠊⢿⢁
⡿⠘⡆⣀⣀⣨⣽⣤⣯⣅⣀⡀⡸⠈⣿⣿⣷⡈⠛⠤⠤⢍⣉⣠⣤⠤⠞⣃⣾⣿⡗⠈⠉⣠⣤⠀⠀⠀⠀⠁
⠷⡀⢹⣿⣿⣿⣿⣿⣿⣿⣾⣻⡇⢠⣿⣷⡆⢿⣄⡀⠀⢈⡀⠀⢀⢀⡶⠛⣿⡿⠁⠀⠴⠛⠁⡄⠠⡄
⢠⣿⠿⢿⣿⡟⣻⣳⡟⢿⣿⡿⠃⠠⢸⡿⠈⢆⠘⠛⠛⠻⠻⠟⠛⢉⣀⣾⡏⠀⠀⠀⠀⣾⣍⡆⠀⠀⠀⢀⣀⠔⠛
⣤⠿⣦⣿⣿⣁⡈⠋⣁⣸⣿⠁⠀⠀⠈⠇⠀⠀⠙⠲⠦⣶⣤⣤⠶⠛⢸⣿⠁⢱⡄⠀⠀⢈⠉⠀⠀⠀⠚⠉
⣄⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⣾⢛⣻⣆⢨⣀

⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣅
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⣰⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠦⢄⠀⠀⢀⠊⠀⠁⠀⠀⠠⠀⠀⠀⢠⠀⠀⠀⠀⣠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣀⡀⢰⡶⠶⠁⢀⠤⡮⠛⠛⢦⠀⢀⡤⠾⡄⠀⠀⢀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⣠⠞⠁⢀⣠⢟⡒⠦⡀⠟⠈⠑⢿⡦⡀⠹⣿⣻⣷⠈⡶⠒⠺⣧⣀⡈⠑⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠑⠉⠑⠋⠐⢇⣛⡽⣻⣶⢸⡤⠀⠀⠀⣿⣧⡀⣿⣿⡷⠛⠺⢷⡄⠈⢿⠁⠑⢠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⠇⠀⢳⡀⠀⠀⠙⣾⣽⣿⡈⠀⠀⠀⢰⠟⠉⠀⠀⠙⣿⣦⠀⠀⢻⡆⢸⠀⠀⠀⠹⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡼⠡⠠⠂⠉⠉⠉⠒⣄⠀⢁⣀⣼⡂⠀⠐⠳⣆⠀⣀⡤⣄⣝⣿⡄⠀⠘⡇⠌⠂⠀⠀⠀⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⢋⡇⣤⣀⡀⠀⠀⠀⠙⠉⠀⢹⣗⡒⠀⠀⢀⡇⠚⠁⠀⠑⢺⢿⣥⡂⠀⠀⠀⠀⠀⢀⣔⣄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡻⢷⣽⣿⣙⣄⠀⠀⠀⠀⠠⣫⡳⠂⠀⢀⣼⣧⣷⣦⣄⣤⢨⠉⠿⣵⣤⣀⣀⣤⣶⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡳⠮⣭⠝⢋⡓⠶⠦⠶⠾⠯⠥⠤⠾⠼⠿⠿⠥⠴⠴⠒⠊⣁⣈⣭⣤⡿⣿⣿⠏⣴⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣽⣁⡀⡀⠀⡀⠉⠀⠉⠐⠒⠒⠒⠀⠐⠒⠒⠒⠒⠈⠉⠉⠉⠉⢉⡐⠚⠉⣀⣰⢟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣳⣥⡑⠀⠣⡀⢄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡾⠀⠈⣴⣽⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣕⠻⣶⡆⠑⠀⠂⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠌⣀⠡⢮⣞⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣉⠙⠻⢧⣤⣦⣤⣤⣀⣠⣀⣠⣀⣤⣤⣤⣴⣴⡾⠿⠞⣛⡭⠞⠁⣀⡀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢄⠀⠀⠉⠙⠓⠲⠶⠤⣬⣭⣭⣭⣭⣭⣭⣥⣤⣤⠴⠶⠖⠚⠋⠉⠀⠀⠁⠀⠉⠢⣄⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⣀⠀⡤⠊⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠊⠉⠉⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠷⣃⠈⠁
⠀⠀⠀⠀⠈⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠛⢢⡄⢀⣠⠄⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⢀⡇⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠚⠻⠷⣦⡴⠦⠴⠂⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⣠⢊⣀⣠⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠶⠶⠟⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣦⣴⣦⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢯⣟⣿⣷⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⢿⣿⣷⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠈⠉⠙⠻⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣝⢿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣴⣶⣿⣿⠷⡶⣶⣾⣶⣷⣦⣌⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡉⣷⣌
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣤⣾⣿⣯⡉⠋⠘⠖⠉⠈⠡⠉⠉⠙⠻⢶⣤⡉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣟
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣴⣄⣤⣤⣧⣤⣽⣛⣶⣷⣷⣶⣶⣶⣤⣴⣤⣶⣝⢻⣶⣄⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠏⠼⠽⢫⠀⠞⣿⣿⣿⣦⣻⡟⢛⠻⣤⣀⠌⠛⠙⠻⠿⣿⣶⣄⠉⠳⣤⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣤⠴⠴⠆⢷⣿⣿⣿⣿⣿⣷⣿⢶⣉⢉⠘⠿⣶⣄⠀⠈⠙⠻⢿⣦⣄⠙⢦⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⢳⡞⢿⣶⣿⣿⢻⣿⡟⣻⣵⣶⣿⣯⣩⣷⣶⣬⡟⡛⢷⣦⣤⡌⠻⣷⣄⠙⢦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣇⡼⢇⢲⢾⡟⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⡛⠿⣮⣟⠻⣷⣦⣈⠻⣷⣌⢷⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣏⣉⣨⣯⣈⣥⣿⣿⣿⣿⣯⡭⣼⣏⣿⠳⣿⣿⣿⣯⣻⣿⣿⣿⣷⣝⣿⣿⣗⠈⢿⣷⡙⣦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⠤⠭⠿⢿⣿⣿⣿⣿⢿⢻⣿⣻⡷⣣⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⡿⠷⣦⣽⣷⣌⠷⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⣰⣮⣶⣿⣿⣽⣯⣥⣿⡾⣿⣙⣿⡷⢞⣿⣿⣿⣿⣿⣿⣿⣷⡟⠙⢛⣻⣍⣻⣯⣿⣦⠙⣦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⡋⠸⢻⣿⣿⣿⣿⣿⣿⣹⡧⢹⣯⣿⣳⡿⢻⡆⠿⢹⣿⠟⣍⠀⠀⣴⣿⣿⣟⣿⣿⡟⣿⣧⠘⣆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠰⠎⢿⣿⣻⣿⣿⣿⠁⣿⣿⣟⣿⣰⢤⣤⣴⢿⡻⠖⠦⣠⣼⣿⣿⣿⣿⣿⣻⣿⡏⢿⣧⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⢀⡶⣿⣿⡇⢸⡏⣿⣿⣿⣿⣿⢿⣴⣶⣾⢿⣷⣶⣾⣿⣷⢯⣵⣞⣛⣿⣿⣿⣿⣯⣟⣿⣾⣿⣇⣸⣿⡎⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢠⡿⣴⣿⣿⣷⣦⡴⢿⡿⠛⠛⢻⣶⣷⠆⠻⠛⠿⣿⣧⠿⠓⢮⣿⣾⣿⠟⣛⣥⣾⠻⣏⢿⣮⣿⣿⣿⣿⢿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡇⢸⣧⣾⣿⡟⣿⣿⣶⣶⠶⠞⠃⡸⢛⣛⡃⠛⠛⠛⠶⡟⠳⠞⣋⣿⣿⣏⣴⣟⠃⢨⠄⣿⣄⢻⣿⣦⣿⡿⣼⠃
⣿⠀⠀⠀⠀⠀⠀⣾⠉⢦⣠⡴⡟⣿⡇⢸⡇⠹⣿⣿⡛⣯⣷⠞⠶⠶⠾⢿⣍⣉⣉⣉⠛⠛⠻⢶⣿⣶⣿⣿⣿⠿⣿⢻⣞⣯⠀⣾⢿⣷⣼⣿⡟⣹⠏
⣿⠀⠀⠀⠀⠀⡾⢡⡀⢢⠹⣾⣥⣿⡇⠘⣇⢼⣟⣯⣥⣭⣌⡥⢚⣚⣟⠻⡼⠏⠙⢿⡿⢿⣷⣤⣿⣤⣼⣾⣿⡆⠻⣦⠻⣷⡮⠛⣀⣙⣿⣿⣿⠍
⣿⠀⠀⠀⠀⠀⣽⢋⡑⣀⣐⣻⣿⡽⠁⣴⢿⡀⣼⣿⣿⣟⣠⡶⢟⣻⣿⣷⣶⣶⣶⣌⡙⢷⣮⣍⢹⣿⡿⣿⣿⣷⣼⣿⣷⣽⣿⠛⣉⣉⣿⣿⣿
⣿⠀⠀⠀⢰⡟⠰⣾⣿⣿⣿⣿⣿⠁⣸⠋⣾⠁⣾⣿⣿⣿⣿⣶⣾⣿⣿⡿⣿⣿⢹⣿⡿⣶⣍⡛⢿⣿⣶⣿⣿⣿⣿⡿⣾⡟⠻⣆⢹⣿⣿⡟⡏
⣿⠀⠀⠀⢸⡣⣶⡈⢿⣿⣿⡟⣿⢀⡏⣰⣟⣶⣽⣿⣿⣿⣿⣿⣿⡸⣿⣗⢿⣏⢸⣿⢁⣿⢻⣿⠿⣷⣯⣿⣿⣿⣿⣿⣿⠗⠀⣿⢀⣿⡟⣼⠳⣄
⣿⠀⠀⠀⠀⣿⡇⣄⣘⣿⣿⣷⣿⢏⡾⢋⣿⠿⣿⣿⣿⣿⡿⣷⣼⣿⣿⣄⣿⣩⢿⣿⣾⣿⣾⣿⢾⣛⣛⣛⡿⠟⠻⣿⣿⣶⣤⡟⢸⣿⣿⣿⣶⣌⣳⡀
⣿⠀⠀⠀⢰⣿⣧⣿⣿⣦⡿⢠⡿⠿⣴⣿⣿⣻⢯⣿⣟⡿⠛⢾⣿⣿⣿⣿⡿⣿⣿⣭⣷⣶⣾⣿⣶⡟⠉⣩⣥⣚⣿⣦⣼⠛⣿⡻⢿⣿⣿⣿⣿⣾⣴⠻⢦
⣿⠀⠀⠀⣿⢻⣏⣿⣿⣿⣷⡞⣀⣴⣿⣻⣿⣯⣿⣿⡟⠁⠀⠈⣷⢿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⠏⠁⣮⣷⣾⣿⣵⠾⣿⣷⣎⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶
⣿⠀⠀⢸⡟⢫⣿⣿⣿⣿⣿⣦⣿⣿⡛⠛⣤⣿⣿⡿⠁⠀⠀⠀⢿⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⠧⢄⣴⣷⠠⠄⣿⣾⣿⣿⡟⣿⣽⣿⣻⣿⣿⣆⠉⠉⠙⠛
⣿⠀⠀⣿⢠⡋⠹⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣸⣿⠣⢠⠿⡹⣯⠙⡀⠛⠹⣿⣿⣧⣿⣿⡿⣹⣿⢿⣿⣄⡀
⣿⠀⠀⣿⣴⣥⠀⣻⢿⣿⣿⣿⣿⣿⣿⣟⡽⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⣘⣿⡿⢏⣴⡿⢃⣴⣣⣾⠃⣄⠸⡏⢳⣄⣹⣿⣿⣩⣿⡾⣿⣷⡙⠲⠶
⣿⠀⠀⣯⢿⠈⢿⣏⢚⣿⣿⣽⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⢹⣿⣠⣿⣟⣵⣿⣿⣿⢃⣼⣿⢖⣿⡟⢿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿
⣿⠀⠀⠱⣎⢳⣬⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣿⣿⢻⣿⣿⣿⣿⣹⢿⣵⣿⣿⣿⢟⣡⠟⣽⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣯⠙⠛⠋⠉
⣿⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣾⣼⣿⣘⣿⣿⣿⣿⣷⣾⣿⣿⡟⣫⣾⣵⣷⣿⣿⣿⠟⣿⣿⣛⣿⣿⣛⣿⣿⣏⠓⣤⡀
⣿⠀⠀⠀⢤⣾⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⡽⢻⣿⣏⢩⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣻⡿⢿⣿⣿⣿⣷⡄⠳⣄
⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣧⡼⣷⡾⣾⣿⣇⢸⣿⣿⣿⡯⣿⣿⡿⡛⠉⣷⣿⢿⣿⣏⠿⣿⣿⣿⣷⠀⠈⠻⣿⣿⣿⣷⣬
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠛⡾⣷⣸⣷⡟⣿⣿⠠⣿⢠⣿⣷⣿⣿⣷⣧⣠⡿⠃⣄⣻⡾⠘⣿⣿⣿⡟⡆⠀⠀⠀⠙⠿⢿⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠁⠾⠃⢿⣄⣿⣿⢿⣿⣇⣿⠀⢹⣿⣿⣿⣤⡝⣷⠀⠹⡾⢳⣿⢿⣸⣿⣿⣧⣇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡆⠰⠿⠀⣠⡅⢹⣿⡌⢿⣿⣿⠀⣿⣿⣿⠁⠸⣿⠘⣷⠀⠁⣞⢻⡦⡅⢻⣿⣿⡼⣆
⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣿⣡⣾⣿⣀⣿⣠⣾⣿⣇⣸⣿⣿⣙⣿⣿⣿⣇⣀⣘⣷⣈⣧⣀⣿⣸⣄⣻⣮⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀

⠀⢀⣀⣀⣀⣠⣤⣤⠤⠤⠤⠶⠶⠖⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠒⠒⠒⠲⡆
⡏⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⢳⡀⢀⣀⣀⣀⡀⠤⠤⠤⠄⠒⠒⠒⠒⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⢀⠠⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢸⠁⠀⠀⠀⠱⡀⠀⠀⠀⠇⠀⣀⠀⠠⠐⠒⠈⠀⢀⡋⣂⠀⠀⠀⠇⠀⡎⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⢸⡇⠀⠀⠀⠀⠱⠀⢀⠌⡐⠁⠀⠑⠄⠀⠈⠀⠀⠈⠀⠈⢂⠀⠀⠀⠀⢇⡀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠈⣧⠀⠀⠀⠀⠀⠱⡉⠀⢇⠀⠀⠀⡀⠀⠀⠂⠀⠁⢀⡀⠀⠤⠤⠤⠤⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠹⡄⠀⠀⠀⠀⠀⠱⡀⠈⠑⠒⢈⡡⠄⠂⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠐⠠⣀⠀⠀⠀⠀⡏
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡇
⠀⢠⡇⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣷
⠀⢸⠃⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢻
⠀⡿⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡄
⢸⡇⠀⢠⠁⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⡇
⢸⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡇
⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠀⠀⣿
⢸⡄⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡟
⠘⣇⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠀⢠⡇
⠀⢻⡀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠊⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠈⢧⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠤⠀⠀⠀⠀⠀⠀⠠⠄⠐⢂⣈⠁⠠⠔⠒⠠⡌⠢⠀⠠⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⢠⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠰⠀⢀⣀⡄⠀⠈⡀⠀⠰⠂⠁⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠸⡄
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⠀⠀⢠⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⣀⣸
⠀⠀⢸⠗⠒⠒⠒⠊⠙⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠷⠒⠒⠚⠒⠛⠋⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢟⡛⠉⠍⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠞⠑⠁⣠⣤⡀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠟⠛⠓⠦⠤⠤⢴⣒⣺⣭⣿⣶⣆⠀⠀⠀⠙⠾⠃⡴⢲⡄⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠋⠂⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠀⠀⢼⣿⡇⢀⣉⠋⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⣶⡀⠀⠀⠀⠈⠛⠛⠙⠉⠉⠀⠀⠀⠀⠉⠀⢯⣨⠇⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣀⣤⡛⠣⣾⡿⠆⠀⢀⣀⠀⠀⠀⢰⠋⣳⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠛⠛⠁⣿⣆⠀⠀⠀⣏⣀⠇⠀⠀⠀⢈⣁⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣇⠀⡀⠀⠀⠉⠁⠀⠀⠀⢀⣠⣤⠴⠖⠛⠉⠉⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠥⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣿⠃⡊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠛⠁




⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢿⡿⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢻⠳⢤⣖⠉⠀⠠⡇⠀⠉⣲⠤⠚⡟⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⢸⠀⠀⠈⢱⠀⠈⡇⠀⡏⠀⠀⠀⡇⠀⣤⣀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⡇⠀⣿⣿⣿⣦⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⣇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠛⠢⣄⡀⢸⠀⢀⡇⠀⡇⠀⣀⠼⠿⠧⡈⠙⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠔⠊⠀⠀⠀⠀⠀⢉⠿⠀⣨⣏⠰⣷⣉⠀⠀⠀⠀⠀⠑⠠⢄⠁⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢁⠀⠀⠀⠀⢀⡠⠔⠊⠀⣠⠔⠻⠟⠢⣄⠈⠑⠢⣄⡀⠀⠀⠀⠀⡨⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠤⠒⠁⢀⡠⠖⠉⠀⣀⢴⣦⣀⠀⠉⠲⢤⣀⠉⠲⠤⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠄⠊⠁⢀⡠⠔⠈⠀⠐⡇⠈⠙⠢⢄⡀⠈⠑⠦⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⡉⠀⠀⢠⠂⠁⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠉⠲⡄⠀⠀⢙⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢼⠀⠀⠀⡠⠔⠊⠉⠉⠙⠢⢄⡀⠀⠀⡧⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⢀⠠⠐⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡠⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠥⠤⢄⣀⣀⡔⠀⠀⠀⡅⠀⠀⠒⢄
⠀⠀⠀⠀⣾⠂⠀⠀⠀⠀⢳⢀⠀⠀⠀⢀⠀⠀⠈⠒⢁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀⠀⠀⡀
⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⣀⣀⣀⣀⠀⠀⣠⡤⢤⣀⠀⠀⡆⠀⠀⢴⠃⠀⠀⠁⠄⠂⠉⢉⢢
⠀⠀⠀⠒⠀⠀⠁⠀⢈⠀⠀⠁⠀⠀⠀⠀⢀⣘⣀⣀⡀⠉⢵⢖⠋⠀⠀⠈⠣⠀⠱⢄⠠⠃⠀⠀⠀⠀⠀⠀⠀⡡⢹⠁
⠀⠀⢀⠍⠀⠀⠀⠄⠈⠀⠠⠞⠛⠛⠒⢀⠏⠁⠀⠈⠉⠒⡎⠆⠀⠀⢀⠴⠒⠒⠠⡀⠀⠠⠄⠐⠀⠀⠀⠠⠊⣠⠋
⠀⠀⠁⠀⠀⠀⠀⡸⠀⠠⠀⢠⠤⠤⣀⠀⠀⠀⡐⠉⠉⠑⣿⠄⠀⣰⠁⣠⠄⠒⠒⠀⠉⠳⣄⠈⠒⠲⠐⠒⠊⠁
⠀⠀⠀⠀⣠⠤⠊⠁⠀⡠⠆⠘⣦⠀⠀⠉⠙⡸⠃⠀⠄⠜⡟⠀⢀⢯⡶⠁⠀⠀⠀⠀⠀⠁⠈⠳⣔⢄⠀⠰
⠀⠀⠀⠈⠁⠀⠘⠂⡎⠀⠀⠀⢯⢧⣀⡀⠀⠀⠀⠀⠈⢀⠉⠀⠰⠿⠶⠿⠛⠛⠓⠲⠶⠂⠀⢀⣸⠺⠂
⠀⠀⢀⠠⡀⡀⠀⢠⣑⠰⣦⣀⡤⠙⠊⠁⠤⠤⡦⢴⡿⠵⠧⠢⠤⢤⡠⢄⣀⣀⢤⡞⠶⡶⣟⢫⣡⡗⢀⠤⠠⠤
⠀⢠⡁⠀⠀⠈⠢⢀⡇⣭⠙⠓⠒⠤⠤⠦⠤⢾⣧⣰⣤⣐⣤⣄⣀⣀⣭⣩⡿⠿⠭⠴⢞⣛⣻⡍⣿⠀⡇
⠀⠀⢦⠀⠀⠀⠀⡀⢷⢹⡀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠶⠶⠶⢶⣶⢶⣶⣾⣿⣿⣿⣿⣿⢠⡟⠀⠈⠢⢀⡀⠢⠄⢀
⠀⠀⠀⠑⠂⠀⠈⠀⠘⣎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠈⠈⠁⢸⣿⠇⡼⠁⠠⠄
⠀⠀⠀⠀⠀⣀⠀⠤⠂⠘⣎⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⡼⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠣⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⣦⣕⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⣡⣾⣥⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠚⠋⠉⠉⠒⠬⢄⣀⣀⡀⠀⣀⣀⣀⣠⣴⣶⣿⣿⠿⠗⠒⠈⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢷⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⠖⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠲⡄⠀⢸⠀⠀⠈⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠾⠃⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣒⣀⣒⣀⣀⣀⣠⣏⣀⣤⣤⡤⠴⠶⠖⢺
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⣒⣖⣒⣶⣒⣒⣖⡒⣲⠖⠒⡶⠖⢤⠤⠭⢭⠭⢭⣍⠉⠉⣩⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡾⢁⠾⢤⠾⢤⡾⠥⣤⠯⢬⡽⠭⢭⠿⠭⣽⢯⣉⣽⣋⡲⣾⠋⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢠⠟⡠⠛⢲⠛⢲⠞⠒⡴⠃⢢⠞⠤⡴⠧⢤⠾⠥⣤⠮⣤⢞⡗⠁⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⢠⠟⠐⠿⠿⠿⠿⠿⠿⠿⠷⠾⠟⠖⠾⢷⣶⣿⣶⣺⣗⣲⡽⠋⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⡿⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣀⣤⠴⠞⠋⠉
⠀⠀⠀⠀⠙⠛⠛⠛⠒⠒⠲⠶⠶⠶⠶⠶⠦⠤⢤⣤⣤⣤⣄⣀⣀⣀⣀⣿⣤⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⢠⣤⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⢀⢤⡤⢄
⠀⠀⠀⠀⣘⣟⡸⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠉⠃⠀⠀⠀⣼⢿⣿⣿⢿⡆⠀⠀⣤⢾⣼⣿⣼⢦⡄⠀⠀⠀⠈⠚⡟⠊
⠀⠀⠰⠊⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢶⣿⠞⠀⠀⠀⠀⠡⣤⣽⣥⡤⠀⠀⠀⢈⡛⠛⠚⠛⢋⠁⠀⠀⠀⢀⠘⡏⢀
⠀⠀⠀⢀⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣆⣤⣷⣄⡼⠇⠀⠀⠀⠙⢿⠿⠃⠀⠀⠀⠈⠀⠀⠃⠀⠈⠀⠀⠀⠀⠈⠠⠧⠈
⠀⠀⠀⢈⣀⡈⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦
⠀⠀⠐⠁⠀⠀⠑⠀⠀⢰⡿⣿⣿⡿⡇⠀⠀⠲⣄⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣾⣿⡶⡆⠰⡶⣾⣿⠶⣦⠀⠀⠰⣿⠖
⠀⠀⢘⠷⠄⡾⠷⠀⠀⠈⢧⣬⣧⣴⠃⠀⠠⣤⣈⣶⣾⣷⡖⠋⠀⠀⠙⠀⠂⠂⠘⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⢰⣿⣷
⠀⠀⠀⠐⠀⠄⠁⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠙⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⡿⡄⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⣤⣤⡀⠀⠀⠀⠱⣾⠞⠁⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠺⠿⣿⠿⠇⠀⠀⠀⢠⡟⢿⣿⣿⠄⠀⢠⣶⣾⣿⣿⣿⣿⣶⣦⠀⠀⣴⣿⣿⡿⠿⠿⠿⠿⠁⠀⢀⣴⣶⠿⢶⣶⡄⠀⠀⠀⣀
⠀⠀⠘⣶⣿⣶⠃⠀⠀⠀⣾⢿⣿⣿⠆⠀⠀⠀⠈⠉⠙⢉⡉⠉⠉⠀⠀⠀⠉⠛⠁⠺⠛⠛⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠀⠂⠉⠀⠛
⠀⠀⠀⠨⠿⠼⠀⠀⠀⠀⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⣠⣤⣶⣿⣷⣤⣤⡀
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⢿⠀⠀⠀⠉⢹⣿⣿⢿⢿⠉⠁⠀⠀⣀⣀⡀
⠀⠀⠨⣻⣛⢡⡆⠀⠀⣠⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⢤⣾⣦⠜⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⣶⠘⢻⣟⠃⣰
⠀⠀⢀⣽⡧⠊⠀⠀⠐⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠉⠁⠀⠀⣴⣿⣿⣿⣶⡄⠀⠀⠀⠀⠈⠦⣼⣿⠤⠋
⠀⠀⠈⢿⡏⠀⠀⠀⠀⢧⣬⣯⣤⠇⠀⠀⠀⣤⡀⢠⡤⠀⠀⠘⣦⣸⣏⣠⠇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠤⠞⠷⠄⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠼⠻

⣶⣶⣶⣶⣶⢶⣶⣶⡶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣵⣶⣶⣷⣶⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⡀⠀⠀⠀⠰⡆⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢏⠀⡗⠀⠀⡇⠀⢸⠂⢸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠳⡈⢢⠀⡇⡴⠋⡔⠋⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⡔⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣟⡍⣭⢹⣭⡍⣭⣩⣩⡝⣿⣿⣀⣀⣀⣀⣀⡤⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⣀⣀⣀⣀⣿⣿⣯⣥⣭⣬⣭⣥⣭⣭⣬⡅⣿⣿⣀⣀⣀⣀⣀⠔⠉⠉
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠉⠉⠉⠉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠉⠉⠉⠉⠉⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠔⢁⠜⠀⡇⠳⣄⠣⡀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣇⠀⡧⠀⠀⡇⠀⢸⠄⢹⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠁⠀⠀⠀⠰⠇⠀⠀⠀⠈⠀⠸

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠸⠀⠐⠶⠾⠿⠾⠿⠿⠶⠖⠀⠀⣀⠀⠀⢠⡇⠀⢴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣅⢀⡀
⠀⠠⣤⠀⢀⣼⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠷⠶⠟⠁⢀⠀⣀⠀⠉⠙⠛⠛⠉⠈⠿⠍⠀⣀
⠀⠀⠃⠀⠀⠃⠀⢠⠔⠒⠉⠁⠀⠉⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠦⠴⠶⠤⠶⠖⠋⠀⠀⢠⢤⠀⠀⠀⠀⠀⠀⠐⠒⠠⠤⣤⣤⡼⠟⠓⠒⠂
⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⡄
⠀⢀⣄⣀⣤⡿⠀⠀⠀⠀⣤⡀⠀⣠⣰⠀⠀⠀⢠⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⡿
⠀⠀⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠘⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠐⠚⠋⠁
⠀⢀⡤⠀⠀⠁⠤⠭⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠴
⠀⠀⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠁⠀⠘⠓⠶⢶⣶⣶⣶⣶⡶⠾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠁⠀⠀⠎⠀⠀⠀⠀⢠⣀⡀
⠀⠰⠚⠷⢤⣤⣽⣀⣉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠙⠻⠗
⠀⠀⠀⠀⣼⡟⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏

⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡏⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠁⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣹⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⣏⡀
⠀⠀⠀⠀⠀⢀⡼⢋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡙⢦⡀
⠀⠀⠀⢀⡴⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢦⡀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠛⣿⢸⣿⣿⣿⣿⣿⣿⠈⠋⠉⠉⠉⠉⢹⠉⣍⠉⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣾⠟⠉⢠⣤⣤⠈⠙⢿⣶⣿⢸⣿⣿⣿⣿⣿⣿⠀⡆⠀⠀⠀⠀⢸⠀⠟⢀⣴⡶⠒⢲⣦⡀⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⣠⣤⣘⢿⢟⣠⣄⠈⣿⣿⢸⣿⣿⣿⣿⣿⣿⠰⠇⠀⠀⠀⠀⢸⠀⢰⡿⠿⣷⣤⣼⡿⠿⡄⢿⣷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠻⠿⢟⣤⡝⠿⠿⠃⣿⣿⣌⣛⣛⣛⣛⡛⠛⢸⣥⣤⣤⣤⣤⠾⠀⢸⣄⣀⣿⣿⣿⣀⣀⡇⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣄⠀⠸⣿⡿⠀⢀⣴⠿⠛⠛⠻⣿⣿⣿⣿⣿⠀⠁⠀⠀⢀⣠⣤⣤⣈⠻⣿⡏⠀⢸⣿⠟⠁⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⢃⡾⣻⣽⡳⡌⢻⣿⡿⠟⢠⡇⠀⢀⡟⠡⠒⠢⡙⣆⠈⠉⠛⠉⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢯⣻⣿⣱⠇⣼⣿⣧⣀⠸⠏⠀⠈⣧⠐⠤⠴⣡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣭⣭⣥⣾⢿⠿⠿⠿⢀⣤⣀⣄⡈⠙⠓⠛⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠉⠉⠅⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠠⠀⠀⠀⠐⠊⢁⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠐⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⣄⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿
⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⠶⠟⣋⣡⡴⠟⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠒⠛⢛⣃⣈⣤⡴⠶⠛⢋⡁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⠖⠚⠛⠛⠋⠉⢉⣤⠄⠐⠂⠉⣛⠛⢶⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⡴⠋⠁⠀⠀⣀⣸⣯⢶⡆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣰⠟⠀⠀⠀⣀⢾⣏⣿⠀⠛⠁⣸⠇⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢰⡏⠀⠀⣀⠺⣮⡳⡝⠃⠀⠀⢠⡟⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⣠⠶⠙⢿⡍⠛⠀⠀⢀⣴⠟⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡙⢷⡼⠃⠀⢀⣠⡴⠟⠁⠀⠀⠀⣠⣤⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠙⠛⠲⠞⠛⠋⠁⠀⠤⠶⠶⠃⢸⡇⠀⠙⠳⠶⢶⣶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠠⠖⢋⣤⠶⠛⢷⡄⢈⠙⠛⢷⡄⠀⠀⣀⡾⠃⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢿⡛⠛⠛⠋⠁⠀⠀⢸⡇⠘⠻⠶⠤⠶⣶⣦⡈⠤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠻⢦⣄⡀⠀⠀⣠⡾⠁⠀⠀⢀⣠⡴⠋⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⣭⣽⠿⠛⠉⠀⠙⠿⢿⣯⣭⣤⠶⠋




⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⠖⣡⠔⠈⠓⠐⠂⢦
⠀⠀⠀⡀⣀⣀⠀⡎⠈⢤⡊⠓⠓⠖⢤⡚⠉⢸⢋⠴⢊⠀⢀⠔⠁⢀⡔⠁
⠀⠀⣀⠷⡀⠀⠈⢡⠀⠀⠙⢦⡀⠀⠀⠙⣤⠞⠡⠒⠁⠀⠁⡠⠚⢣⠈⠒⠦⣤⣀⣀
⠀⠐⢥⣀⡘⢆⠀⠀⢧⠀⠀⣀⣙⢢⠤⠼⢅⣀⡀⠀⢀⠔⠋⠀⠀⠈⢿⡉⠉⠉⠉⠉⠛⠛⠫⠤⢇⣀⡀
⡦⢠⡀⠀⢹⡀⢱⡀⢠⠷⠋⠀⣀⠀⠀⠀⠀⠀⠀⠈⠣⣄⡀⠀⠀⠀⠘⢦⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠈⠉⣖
⢣⠀⠉⠉⠁⢈⡩⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢂⢀⣀⡖⠊⠀⠀⠀⠁⠁⠂⠀⠀⠀⠀⠀⠀⠂⠤⠀⠀⠘⡄⠊⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⣸
⠀⠀⢻⣤⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⠇
⠀⢠⠊⠁⠀⠀⠉⠉⠐⠂⠤⠀⡈⠁⠒⠒⠤⢄⣀⡀⠀⠀⢠⢿⣌⠉⠓⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠐⠦⠠⠔⡤⣄⣠⠤⡤⠖⠔⠒⠃⠠⣀⠀⠀⠄⣈⠁⠀⢸⠀⠙⢗⠐⠖⠦⠄⣈⡏⠙⠒⠒⠒⠂⠀⠈
⠀⠀⠀⠀⠀⢀⡴⢿⠀⠀⠄⠀⠀⠀⡰⠉⠑⠦⠤⠄⣁⡠⠊⠀⠀⠈⡆⠀⠀⠀⠈
⠀⠀⠀⠈⠑⠒⠒⠒⠛⠦⢄⡴⠀⣠⢃⡤⠒⠛⠋⠉⠑⠦⠤⠤⠖⠊

⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠤⠤⠤⠤⠶⠶⠒⠒⠒⠒⠒⠒⠲⠶⠦⣤⣀⡀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣶⡶⠦⠤⠤⠶⣖⣒⣒⣒⣒⣒⣒⣒⣶⠦⢤⣈⣉⣉⣉⣀⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⠯⠭⠽⠖⠚⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣤⠴⠖⠒⣛⣛⣋⣛⣛⣛⣒⣶⠤⣤⣀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠓⠺⢽⣳⢦⣀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⡳⢤⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠹⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠙⢦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⠞⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡀⠉⠙⠛⣧⣤⣀⣤⠴⠋⢈⡧⠴⠚⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣉⡷⠒⢾⠁⠘⠷⠦⣤⠴⢛⣇⣀⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣰⠞⠛⠛⣿⣅⣀⡴⠋⢻⣟⠛⠷⢼⣿⣿⠛⠁⠈⡇⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⡇⢀⣀⡴⠳⣏⣿⣄⣀⣼⣉⣉⢛⡿⣟⣁⣀⣀⡴⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠿⣍⡁⠀⠀⠀⠀⠈⠉⠀⠈⠉⠉⠀⠀⠈⠉⠁⠀⢀⡤⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣃⣀⣀⣀⠉⠛⠲⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⠤⠶⠚⠉⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠷⠶⠯⢭⣟⣒⣲⡶⠤⠤⣭⡭⠭⢿⣷⣶⠶⠤⠤⢶⣖⣯⠽⣇
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠉⠙⠛⠛⠶⠦⣭⣭⣍⣙⣛⣛⣩⣭⣭⣭⣭⣍⣉⣭⣥⡴⠶⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠛⠛⠉⠉⠉⠛⠓⠒⠒⠒⠛⠛⠓⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣄⣀⣀⠀⢀⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢈⡿⣯⡶⠿⢾⣝⢿⠠⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀
⠀⠀⠀⠀⠀⠀⢰⣾⣿⡇⠰⣷⠀⣿⢾⣷⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢈⣧⡿⢦⣤⡼⣿⣾⠁⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠻⣿⠛⠉⣋⡼⣿⡽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⡃⢶⠄⣄⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣷⣶⣾⡿⠂⢄⠀⠀⠙⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠀⠁⠄⠀⠘⢦⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⡇⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⠄⠐⢃⣀⠭⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠔⠚⡈⠁⠀⠐⠢⣶⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠀⠀⠀⠄⠁⠘⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠒⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣃⡀⢀⣤⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⡏⠉⣉⣙⣒⣖⣒⣲⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡟⣛⡧⢨⡷⢶⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢣⠀⢱⠀⣇⠀⣀⡀⠀⠀⠀⠈⠉⢱⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⡧⠀⠯⠇⠹⠞⠙⣾
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢸⠀⢸⡄⢹⠈⢛⣋⠘⡛⠀⣛⣀⢸⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡤⠶⢶⠿⣄⠩⠖⠲⠄⢀⡶⢾⠟
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠸⡆⠀⡇⢸⠀⣭⡍⢈⣛⠁⣌⣉⠈⣿⡆⠀⠀⠀⠀⠀⠀⣴⣹⢏⡏⣡⠴⠒⣇⠀⠈⠣⣤⣤⠴⠋⡏⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⡇⠀⣇⢸⠀⠀⠀⠀⠉⠀⠈⠁⠀⡟⡇⠀⠀⠀⠀⠀⢰⡃⣿⣿⡿⣅⠀⠀⠈⠙⢦⠀⠙⠦⠤⠞⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣧⠀⣿⢸⡇⠀⠀⢠⣦⡄⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⢸⡻⡉⠀⢣⡌⠳⢤⡀⠀⣸⠀⠀⠀⣠⠆⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠚⢧⠀⠀⠀⣿⠀⣿⢸⠇⠀⣀⡬⠭⠔⣒⡾⢭⠗⠃⠀⠀⠀⡠⣾⣿⣿⡝⠦⣀⠸⠿⣓⠣⣄⡇⠀⠀⢰⠃⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠙⠲⢦⣿⡀⣟⢈⣛⣩⠴⣖⣫⠭⠤⠖⠋⠀⠀⠀⠀⣼⢱⠃⠀⠀⠈⠲⢬⣽⠶⠟⠀⣀⣉⡛⠒⠺⠦⣀⡀⢸
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠟⡸⠀⠀⠀⠀⠀⠀⠉⢉⣉⠿⢯⣀⠉⠙⠛⠚⠁⠈⢯
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣦⡀⣀⠀⠀⡸⢱⠛⠓⠚⠁⠀⠀⠀⠀⠀⠀⡰⢯⡀⢀⣠⡌⠑⠲⠦⠤⠤⣴⠚
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⡯⣄⣨⣿⣭⠝⢲⣇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣿⢏⠀⠀⠀⠀⠀⣠⣴⣯⡙⣲
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⠤⠤⠤⣤⡤⣿⡶⢩⣻⠟⠒⠚⠋⠉⢙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠁⠀⠑⣤⡴⠚⠉⢁⣨⣄⣉⣓⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠤⠤⠴⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠴⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠶⠶⢿⣿⡿⠿⠶⠶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⢟⠫⠉⠀⠀⠀⠷⠀⣩⡀⠝⠀⠀⠀⠀⠩⢛⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠉⢫⣧⠙⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠘⢣⣮⠉⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠈⠄⢴⣶⠀⠀⢠⡀⡀⠀⠀⠀⣰⡿⠁⠻⣧⠀⠀⢀⠀⡠⠀⠀⠀⠀⢿⠗⢀⠘⠛⣦⡀
⠀⠀⠀⠀⠀⣠⡾⠏⡀⢀⢂⡚⠂⠀⠀⠀⠐⢌⠢⡀⠀⣰⡟⠁⣀⣀⠙⣷⡀⠩⣊⠄⠀⠀⠀⠀⠀⠚⣂⠂⠀⣘⠙⣦⡀
⠀⠀⠀⢀⣴⠏⠁⢼⠁⠀⠠⠀⠀⠀⠀⣀⠀⠀⠁⣀⣰⣿⡿⠟⠛⠛⠛⠻⣷⡀⠁⠀⠀⠀⣀⠀⠀⠀⠈⠀⠂⠸⡆⠉⢻⣄
⠀⠀⢀⣾⠣⣦⠀⠆⠀⠁⠀⠀⠀⠀⠈⢫⣿⣿⣿⣿⣟⣡⠶⢛⣉⣉⣓⣦⣘⣿⣿⣿⣿⠟⡼⠁⠀⠀⠀⠁⠀⠀⠃⠀⣶⠹⣆
⠀⢀⣾⡁⠀⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠛⣡⣾⣿⣿⣿⣿⢿⣮⠻⣿⣿⢋⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠈⡽⣇
⠀⣼⣿⢷⣆⠹⣆⠀⠀⠠⠀⠀⠀⠀⣂⠤⠀⢸⣿⡁⠺⣏⠻⣿⣻⡿⠃⣠⠟⣡⠞⢿⡃⡰⠅⣀⠀⠀⠀⢀⠁⠀⢀⡾⠁⣶⢾⣿⡆
⢠⣿⣿⣇⠻⣦⡈⠃⠀⠀⠁⠀⡀⠀⠀⠉⢠⣿⠁⠉⠓⠶⠭⠤⣥⣬⣿⢗⡿⠁⠀⠘⣷⡌⠁⠀⠀⡀⠀⠀⠀⠀⠊⢀⣾⢋⣾⣿⣷
⢸⢹⣿⣿⣦⣈⠻⠦⣄⡀⠀⠀⠐⠀⠀⢠⣿⣧⣤⣀⣀⣀⢀⠀⡀⣈⠀⡈⣀⣀⣀⣠⣽⣿⡄⠀⠐⠠⠀⠀⢀⣤⠶⢛⣡⣾⣿⣿⢹
⣿⢸⡿⠇⠙⠻⠿⣷⣶⣿⣶⣶⣦⣦⣀⠙⠛⠛⠛⠛⠛⠻⡿⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠋⣠⣴⣶⣶⣶⣷⣶⣿⠿⠟⠋⠹⢻⠸
⣿⢸⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠛⠻⣦⣄⠀⠐⠄⠀⠈⢾⢿⣿⠟⠀⠀⠔⠀⢀⣤⡶⠛⠛⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⠀⢸⣇
⢹⢸⠚⣫⡽⠿⠛⠋⠉⠉⠉⠓⠒⠦⢄⡀⠈⠹⣷⣄⠀⠀⠀⠀⠳⠋⠀⠀⠀⠀⣴⡿⠋⠀⣀⡤⠔⠒⠛⠉⠉⠉⠛⠻⠿⣯⣙⢺⢸
⢸⣿⡏⢁⣤⡶⠚⠈⠉⠉⠁⠑⠒⠲⠦⣌⡓⢦⡈⢻⣦⠀⠀⠀⢐⡂⠀⠀⢀⣾⠏⢀⠴⣋⣥⠶⠒⠒⠁⠉⠉⠉⠈⠓⣶⣄⠉⣼⣼
⠈⣷⣧⣼⣮⣷⣾⣿⣟⣻⡟⠛⠶⣶⣤⣈⠙⢦⡙⢄⢻⡆⠀⠀⢙⡃⠀⠀⣾⢃⡔⣡⠞⠉⣠⣤⡶⠾⠛⢻⣟⣿⣿⣷⣿⣼⢦⣿⡟
⠀⢹⣏⠀⣿⣿⣿⠻⢟⣿⣏⣷⣶⣤⡉⠻⢷⣄⠙⣮⢯⣿⠀⡄⠈⠁⡄⢰⣿⢏⡾⠃⣰⡿⠋⣁⣴⣶⣞⣽⣿⡿⢻⣿⣿⡏⠈⣿⠃
⠀⠈⣿⠀⣿⣿⣿⡄⠈⣾⣿⣿⣿⣿⣿⣷⣄⠹⣧⡈⢧⣿⡇⢹⠀⠀⠃⣾⣯⡞⢠⡾⢋⣴⣿⣿⣿⣿⣿⣿⡟⠀⣸⣿⣿⡇⢰⡟
⠀⠀⠸⣧⢹⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣷⡈⢿⣧⠸⠀⠀⢀⣿⡟⣠⡿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢣⣿⠁
⠀⠀⠀⢻⣧⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⣿⠀⠀⠀⢸⡿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⠃
⠀⠀⠀⠀⢻⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⣿⠀⠀⠀⢸⡇⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣱⣿⠏
⠀⠀⠀⠀⠀⢻⡿⢦⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡾⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣡⡾⣿⠏
⠀⠀⠀⠀⠀⠀⠻⣆⢻⠓⠪⠿⠿⠶⠶⠶⠿⠛⠛⠿⠛⠉⠁⠀⠀⠀⠀⠉⠙⠛⠿⠛⠿⠷⠶⠶⠾⠿⠽⠖⢊⢃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⣧⡡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣜⢃⣄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣄⠛⣴⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡉⠆⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠦⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠄⠀⠀⠈⢙⣿⣟⠋⠀⠀⠀⡀⠀⠀⠀⢠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⠀⢀⣀⣤⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠖⠒⠒⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢀⡀⠀⡙⠖⠒⠛⡛⢒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢀⡔⣀⡴⠾⠛⠉⠉⠉⠙⠁⠀⠀⠀⠀⠀⣀⠤⠤⠴⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣡⣴⣂⢤⣲⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣋⡀⠀⢀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣻⣶⣸⣄⣠⣄⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣅⠐⠀⠀⠐⠄⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠄⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⣥⣐⣀⡠⠇
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢿⡲⣶⣌⠃⠀⠁⠀⠈⠃⠀⠁⠀⠀⠀⠀⣀⣸⠁⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠙⠛⠶⠷⢶⡤⣀⠀⠀⠀⠀⠀⠀⠆⢀⡰⠃⠀⠀⠀⡠⠊⠁⠀⠀⠀⠠⠒⠢⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠿⣤⣀⣄⣼⠽⠖⠋⠀⠀⢀⡠⠊⠶⠀⠀⠀⠀⠆⠁⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠿⣭⣝⣲⠤⡀⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠺⢷⣄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠴⠊

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠈⠉⠉⠀⠐⠠⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣴⣶⣶⢢⣄⠀⠀⠀⢀⣤⣶⣖⣲⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠸⣿⣿⣿⣷⣿⠄⠀⠀⢸⣿⣿⣿⣿⡿⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠙⠿⣿⡿⡟⠀⠀⠀⠘⠿⣿⡿⠟⢡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠉⠉⠀⠀⠀⠀⠀⠈⠉⢉⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠈⠑⠢⠀⠠⠒⠉⠀⠈⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡸⠀⠉⢆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠸⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢠⠃⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢣⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢸⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⢸⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡘⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠘⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⠀⠀⠀⠀⡇⠀⡚⠀⠘⡀⠀⡇⠀⠀⠀⠀⢱⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢀⠀⠀⠀⠀⠀⡇⢀⠇⠀⠀⢇⠀⡇⠀⠀⠀⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⠄⠣⠀⠀⠀⠀⡇⠈⠀⠀⠀⠘⠀⡇⠀⠀⠀⠠⠃⢤⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠌⠒⠁⠀⠀⠀⠇⢠⠀⠀⠀⢰⠀⠇⠀⠀⠀⠑⢊⠜⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣸⠤⠀⠀⠀⠀⠀⠰⢘⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠨⢼⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠤⡊⢀⢃⠀⢀⡇⠈⠢⢤⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⠑⣄⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠸⣍⢹⠋⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⣿⣿⣿⣿⡷⠀⠀⠀⠀⢠⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠸⠠⠇⠟⠶⠰⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢠⡐⣿⣿⣷
⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠠
⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠐⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠛⠻⠙⠛⠋⠀⠀⠀⠐
⠈⢠⢤⠤⠀⠀⢠⣀⠄⡀⢰⣶⣶⣶⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠐⠒⠊⠉⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⢛⠻⠿⠋⠛⠛⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠁
⠀⠀⣤⣤⣤⡄⠀⠀⠄⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⢠⢠⠆⠀⠀⠐⣢⡤⠀⠈⠅⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢹⣿⣿⡷⣀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠁⠐⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠀⠀⠉⠀⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡈⠅⠜⢦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠓⠖⠀⠀⢠⢿⡶⠾⠉
⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡞⢉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣤⣶⣤⣶⣧⣴⣦⣴⣦⣤⣶⣤⣶⣤⣵⣦⣴⣦⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⢻⣿⣾⣿⣾⣿⣶⣿⣷⡟⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠐⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠂



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣠⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣫⢴⣺⣿⠟⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣷⠟⣫⠤⠒⡾⢯⠑⢄
⠀⠀⠀⠀⠀⠀⢀⡤⡾⣫⡾⣫⠔⠉⠀⣠⣼⡁⣸⠃⠀⠑⢦⡀
⠀⠀⠀⠀⠀⣰⡿⣫⣾⢿⠟⠁⠀⣠⡏⢹⡏⡹⢁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠠⣎⡏⣼⠟⢡⠃⠀⣀⣯⢔⣻⠞⢶⠋⣡⠝⠊⠉⠉⠑⢢⡙⡄
⠀⠀⠀⠀⠈⠻⣏⢀⡇⢠⠎⠀⣿⢿⠖⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⡇⡼⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⠴⠛⣻⣰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡜⡴⠁⣠⡾⠓⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⡫⠊⣠⡾⢋⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⢦⣀⠀⠀⢀⣀⣤⡶⠟⠋⢀⣴⠟⣡⢊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡒⠛⠛⠛⠉⠁⢀⣠⣾⠟⣡⣞⡟⠉⢹⡗⠦⠤⠤⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⢠⡾⠟⣩⢴⣎⠁⠀⣸⠓⢤⡙⡦⠤⢤⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡟⣡⠊⠀⠀⠙⠖⢺⡀⠑⢦⣑⣯⣕⣶⠥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡎⠙⢗⡮⠿⢿⣧⣀⣀⣸⣀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⢙⡦⠤⡞⠑⠒⢼⡀⠀⠀⠻⣤⠀⠀⠈⢳⡜⣭⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡥⠤⠷⣤⡠⠖⠫⣟⡹⠋⠙⡷⡤⣖⠾⠋⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠽⣿⣤⣞⣉⣯⣀⣯⣉⣁⣀⣀⣜⣠⣴⣅⣀⣀⣠⣤⣾⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢲⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠛⠻⢿⣿⣽⣿⣿⠀⠀⠀⠆⢀⣀⣉⡉⠉⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⢄⡠⠤⢤⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⡠⢊⠤⠀⡔⠄⠀⠀⠆⠀⠀⠀⠀⠀⠀⣀⣴⠶⠒⠒⢀⠀⠀⠀⡀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡅⠘⠤⠂⠃⠂⠀⠀⠀⠀⠀⠀⡀⠤⠾⠋⠀⠀⠀⠀⢸⡇⠀⠐⠁⡔⠀⣆⠰⠶⢠⡄⠀⠀⠀⠀⠀⢀⣤⡀
⣬⠀⠂⠀⠈⠁⠀⠀⠈⠁⠀⠂⠀⠀⠀⢈⠀⢀⠃⠀⠀⠀⠀⢤⣼⠃⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠃⠙⠶⠃⠀⠃⠀⠒⢬
⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢀⡐⠃⠀⠀⠀⡰⣠⡿⠋⠀⠀⢀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠀⠀⠀⠀⠀⢸
⡇⠀⢠⣤⠀⠀⣀⣠⡀⠁⠤⢈⠳⡀⠀⠀⢀⡀⠀⠀⢢⣀⡉⡠⠁⠀⠀⠉⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢠⠀⠘⠿⠟⠃⠐⠃⠌⠀⢳⡀⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠿⠿⠗⠀⠀⠃⠀⠀⠠⠔⠀⠀⠀⠀⠈
⠀⠀⠐⠚⡎⠁⠀⢀⢀⠁⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶
⠀⠀⠀⠀⠀⢠⠎⠉⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⡆⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡘⡆⠀⢀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⡟⠀⠀⡰⠞⠂⠀⠀⠀⢀⠀⠂⠀⠈⠂⣈⠇⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠔⠒⠂⠄⠀⠀⠀⠘⢿⣶⠀⠀⠀⠀⠈⠋⠉⠙⠛⠃⢰⡇⠀⠀⠈⠆⠘⡀⠀⠀⢡⣈⠥⡀⠄⢯
⠒⢢⡀⢄⠀⠀⡁⠀⠀⠀⢸⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⠄⠀⠄⠘⠃⠀⢸⡇⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠐⠒⠊⠀⠀⢀⣠⠤⠒
⠈⢉⣃⠌⠀⠀⠈⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣆⠀⣉⠀⢀⠀⠀⠀⠀⠀⠀⢀⡯⡥⠤⠔
⠀⡸⠃⠀⠀⠀⢠⣶⣿⣿⣶⣦⣤⣆⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣀⣀⣀⣼⠁⠀⠀⠀⠀⠀⠀⣉⠔⠋⠀⠀⠀⠀⠀⠑⠤⣁⡀
⠖⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠲⠠
⠐⣠⠄⠀⠀⠀⠘⠛⠛⠋⠛⠿⣿⣿⠿⣟⣿⣷⠀⠀⠀⠀⣀⣤⣤⣶⣶⣤⣤⡀⠀⣀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠻⣿⡇⠀⠀⠀⠀⡀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⠃⠀⠀⠀⣼⣿⣿⣿⣿⣟⣿⡿⣿⣾⠃⠀⠀⠀⠀⠀⢸⠳⢍⠄⢸⣿⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣿⢿⣧⣿⣶⣿⡇⠂⠀⠀⠀⢀⠀⠈⠓⠊⠀⣼⡿⠀⠀⢀⠀⠠⠄
⠀⠀⢀⠀⠀⠀⠀⢄⠀⡏⠀⠀⠀⠀⣪⠃⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠘⠀⢦⣅⠆⢠⣿⡇⠀⠀⠠⠀⢠
⠀⠃⠙⠀⠀⠈⠈⠁⢀⠇⠀⠀⠀⠀⢲⠒⠒⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠑⠙⠁⣸⡿⠀⠀⠀⠀⡀⠈⠄
⡴⠒⠛⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠳⠖⠂
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣤⣤⣤⣠⣀⣀⣿⡀⣾⣿⠃⠀⠀⠀⠀⠀⠂⠀⣰⠀⠀⠀⠀⠀⠀⠐
⠀⠒⠀⠀⠀⠂⠃⢠⣶⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢻⡏⠉⢯⣽⡼⠛⢛⡿⠀⠿⠃⠀⠐⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠌
⣁⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣀⣜⣻⣦⣼⣿⣤⣴⣟⣁⣀⣈⣀⣀⣰⣃⣀⣀⣀⣀⣀⣃⣀⣁⣀⣀⣀⣀⣀
⣿⣿⢛⣻⡟⡛⢻⡻⣻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⣀⣀⡀⣀⠀⣀⣀⠀⣀⡀⠀⣀⣀⣀⣀⢀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⢧⡿⠉⡏⢡⡿⣧⢩⡏⠹⣭⠇⠸⣧⡅⡿⣿⢸⣼⡟⢩⣿⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠂⠀⠀⢀⣀⣄⠐⢒⣋⠛⠋⠉⠉⠹⠋⠈⡷⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠠⠤⠤⢀⡀⠀⣠⣾⠿⡿⣋⣀⣀⣈⠉⢙⡉⠒⠀⠀⠀⡧⣀⣼⣿⣷⣦⡀
⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⡷⠟⠉⠀⠨⠀⠹⠦⠀⠀⠀⠀⠀⠴⣁⠤⠒⠒⠛⠻⣿⣷⣄
⠀⠀⠀⠀⢅⠀⠀⠀⠉⠉⠒⠂⠀⠀⢾⠿⡌⠀⠀⠀⠀⠀⠀⠀⡨⠀⠉⡙⠲⠖⠚⠁⠀⠀⠀⠀⠀⠘⠹⣿
⠀⠀⠀⠀⠈⠢⡢⣀⣀⣀⠀⠀⠀⠀⢾⡀⡿⠂⠀⠀⠈⠲⡄⠈⠠⢒⡆⠤⠁⠀⢑⠤⠀⠀⠀⠀⠀⠄⠚⢹
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠯⣅⣀⠀⢰⠋⠀⠀⠀⠀⠀⢀⠇⠀⠔⠁⢀⡠⠄⠤⢄⡀⠠⡄⠄⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢄⠀⠀⢀⡀⢴⠋⠂⠆⣠⣞⠡⠒⠐⠂⠀⠛⠛⠻⣤⣤⣴⣚⣁⣀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠀⠉⢉⡤⠒⠁⠦⠀⠈⠁⠈⠳⠶⡤⠃⠀⢩⠁⢀⣠⠩⠝⣿⠿⠿⠉⠙⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠃⠀⠀⠒⠀⠙⠢⢤⣀⡠⠔⠀⠀⠀⠈⠒⣋⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣀⡀⠂⢄⠀⠀⠁⠙⢍⠙⠠⠤⣀⣀⡤⠶⠁⠀⠀⠀⠀⠈⠢⣄⣀⣀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠅⢀⣀⠀⢀⠀⡀⠀⠠⠀⠀⠈⣉⣁⢀⡨⢠⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠐⠢⠔⠒⠊⠀⠀⠀⢈⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠋⠉⠛⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠤⠤⠶⠒⣒⠶⠚⠁⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡽⠋⠉⠉⠉⠀⠒⢦⠀⠀⠀⠀⠀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⣀⣤⣤⡶⣶⣶⣶⣶⣶⣾⡿⠿⠿⢻⡻⠷⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣿⣿⣿⣻⣿⡏⣽⠟⠿⢳⣿⣿⣿⣿⣿⠟⣠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⣿⣟⣧⣛⣹⣿⣷⣿⣶⣶⢸⣿⡏⠛⣋⣵⡾⠛⠁⠀⠀⠀⢆⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠙⠿⠿⠿⠛⠋⠉⠉⠀⠉⢉⡥⠔⠒⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⣧⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣀⣰⣶⣤⣤⣤⣶⣶⣶⣶⣾⣦⣄⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢸⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⠿⣿⣿⣷⣤⣀⡀⠀⠈⠙⠲⢄⡀⠀⢸⢠⠇
⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⣴⣿⣿⣿⣿⠉⠉⠉⠉⠉⠀⠀⠀⡿⠀⠀⢈⣿⣿⣿⣿⣿⣷⣦⣄⣀⠙⠀⣸⠋
⠀⠀⠀⠀⢀⡼⠁⣀⣴⣾⡿⠿⢿⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⡾⣭⠟⢻⡿⠿⣿⡿⢿⣿⣿⡾⠁
⠀⠀⠀⢠⠎⣰⣾⣿⣿⣿⣆⠀⠀⠈⠹⣧⣽⣦⣄⣀⣀⣤⢾⣅⠀⠀⢀⡽⢷⡄⣸⠀⠀⠀⠹⣶⣿⡿⠁
⠀⠀⢀⣯⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢹⣿⣿⣿⣯⡙⣀⣴⣿⠷⣶⣿⡷⢿⣷⣿⠀⠀⠀⠀⠙⣿⠃
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣵⣿⠀⠀⣠⣿⣿⣿⣿⣿⡿⠋⠀⢠⠞⠁⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⣟
⠀⠐⠻⠿⣿⣿⣿⣿⣿⣿⣿⣯⡴⠞⠋⠉⢸⣇⣉⣻⠁⠀⠀⠀⠀⣠⣧⣀⠀⠙⣿⣧⠶⠚⠒⢾⡋⠙⠲⣄
⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣦⣤⣤⣴⣿⣿⡿⢽⣷⣤⣤⣤⠾⠋⢀⣽⠖⠛⠉⠁⠀⠀⠀⠀⠹⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⣸⢦⣤⣤⣭⣿⣲⣦⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣧⡀⢀⣴⣶⣾⠉⠳⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⠙⠛⠁⢀⡿⣆⢰⡏⠙⠷⣤⣤⣀⣀⡀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⣀⡴⢋⣤⢼⣏⣀⠀⠀⠀⠀⠘⡏⠉⠙⠓⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠺⣤⣀⣀⣉⡳⢦⣄⣤⡾⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣓⣚⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⣠⣤⣤⣄⠀⢀⡀⣀⣠⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⣿⣟⣿⣷⣿⡇⠘⠓⠛⠛⠚⠐⢠⣺⣷⡄⡀⠀⠀⠀⠰⢆⣂⣂⠈⠀⢀⣀⣠⡶⠋⠀⠀⠠⣀⠀⠀⠀⠀⠳⢎⡸⠀⠀⠀⠀⠄
⠀⠀⠈⠛⠿⠟⢿⠋⠀⠀⠀⣠⠶⢄⠀⠀⠉⠉⠀⠀⠀⠲⢣⣞⠁⠈⢻⣛⣆⠛⠋⠁⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠸⠟⠻⠇⠀⣠⡄
⠀⠀⠀⣠⣴⣤⣌⡀⠀⣀⡤⣷⣤⡾⠃⠀⡀⠀⢠⠀⠀⠀⢾⣿⡄⠀⠈⣿⡏⡇⣰⠆⣠⡦⠀⡴⡄⠀⠀⢠⡶⣦⢠⣶⣦⡸⣧⣸⣿⡀
⠀⠀⢰⠻⣿⣿⡿⠟⠋⠑⠀⡼⠁⡀⠐⡤⡾⣿⡯⠑⢏⠀⠘⢏⡁⣠⣤⣍⡠⠃⠋⠊⠁⠀⠐⣃⡀⢠⣦⠘⢷⡿⢻⣧⣴⣷⠘⠋⠹⣧
⠀⠀⡏⠀⠘⣯⣠⣄⣀⣀⣾⣇⠀⣧⠈⠳⢤⣮⣦⠴⠋⠀⠀⠀⠉⠙⠛⡉⣠⡄⢠⣠⣦⢠⣿⠛⣿⡌⣿⣤⣴⡆⠀⠻⢿⠿⠀⣀⡀⢀⡄
⠀⠀⢿⠀⢤⠁⠉⠻⢮⣿⣿⣿⡇⠈⠷⣶⣆⠀⠀⠀⢤⣰⠚⢣⣤⣄⣺⣧⣸⣷⢻⣿⣿⣎⣿⣦⣿⠇⠻⠿⠛⠋⠀⠀⢰⣾⣿⢿⡇⠈⠇
⠀⠀⠈⢷⣤⡀⠀⠀⠀⣈⡽⠟⠁⠀⠀⠉⠀⣀⣤⣴⡄⠈⣀⣿⡏⠙⠛⣿⡏⢿⡞⡿⠙⠟⠈⡉⠁⠀⠀⠀⣧⠀⠀⠀⣸⣷⣤⣄⣧⣀⡀
⠀⣤⣶⣾⣍⣛⣻⣿⡛⠉⢀⢤⡒⠄⣇⡀⠹⠛⣿⡏⢺⣿⣽⡜⢿⣶⣿⠻⠗⠈⠀⠀⠀⡀⠛⠁⠲⠄⠀⠤⠞⠀⠀⠘⣿⣷⣾⣿⣿⣿⠃
⠀⣿⣟⠛⠛⠛⠛⠛⢻⠃⡜⠀⠀⠀⠀⠂⢀⠀⢹⣿⡘⣿⣷⠶⠀⠉⢁⠀⠀⠀⢹⡀⠀⠸⡄⢠⠤⠒⠀⣀⣠⣤⣤⣀⠀⠙⢿⣿⣿⠃
⠀⣿⠿⡀⠀⠀⠀⢀⡏⠀⢷⠀⠀⠀⠀⢈⡆⠀⠀⠉⠀⣀⡀⠀⠀⢰⣬⣟⣲⠤⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣟⣿⣿⡟⠀⢠⡀⠙⠁
⠀⠻⣧⣇⣀⣀⣀⡼⠁⡀⠀⠑⠂⠔⠐⠀⢀⣠⠤⠒⠉⠙⣁⣀⣤⣼⣿⣿⡿⢿⣿⣶⡆⠀⡁⠀⠀⠈⠙⢿⣿⣿⣿⠀⠰⡏⠘⠳⠆⣀⡀
⠀⠀⠀⠉⠉⠉⠁⠀⢄⠀⠠⣀⡀⠰⠞⠛⢉⣀⣤⣶⣺⣿⣿⣿⣻⣿⣿⣾⣿⣿⡿⠃⠈⡥⠁⠀⠀⠀⢀⡀⠈⣵⡆⠀⣼⣿⣦⣦⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣆⡔⠀⠸⣃⣤⣶⣾⣿⣽⣿⠿⠿⠟⠛⠛⠛⠉⠹⣿⡿⠋⠀⠂⡠⠔⠉⡁⠀⢤⣿⣷⡄⢸⡆⠀⠻⠿⠛⠁⠐⣿⠂
⠀⠀⠀⠃⠁⡔⠀⠀⠉⠉⠀⠈⠛⣛⠋⠉⠉⠀⠀⠀⠀⠀⢈⣶⠃⠀⠀⠉⠈⠆⡆⠀⠀⣀⣀⢿⡿⠄⢉⣩⠥⠔⠧⢄⡀⠀⠀⠀⠬⡁
⠀⠀⠀⠂⠀⠀⠀⠀⠂⣤⡞⢉⣻⣅⣈⠑⣤⠢⠐⠀⠻⢷⣾⠋⠀⠀⠑⠈⠢⣠⠖⣆⠀⡇⠈⡎⠁⣰⠋⣠⣶⣶⣶⣦⣙⡄⠀⠠⣤⣄
⠀⠀⠀⠀⡀⠰⡆⠀⣾⣤⣾⣿⣽⠶⠶⠟⠾⠷⣉⡴⠠⠐⠀⠀⠀⣤⣦⣤⣤⡘⣦⣈⠛⣷⣤⠇⢰⡇⣬⣿⣿⣿⣿⣿⣿⣇⠀⢨⣷⣾
⠀⠀⣠⣾⣷⡀⠉⠘⡿⢋⠉⠀⢻⡀⠀⠀⢤⣤⢸⣷⡀⠐⡅⢰⣟⣛⣿⠻⡟⣿⣎⠙⢻⣿⣿⣆⠈⣧⠸⣿⣿⣿⣿⣿⠏⢹⡀⠘⠿⠟⠂
⠀⠀⠛⣿⡟⠓⠀⢸⣿⡾⠆⢠⣾⣿⣷⣦⣄⣀⠞⠙⣿⡀⢇⢸⣿⣛⣿⣠⣇⣿⣿⠀⠘⣏⡕⡻⣷⣿⡦⠄⣉⣉⣉⡤⠒⠉⢿⡵⣦⡀
⠀⠀⠀⣿⡇⠀⢠⣿⠉⠓⢦⣾⣿⣿⢿⣿⠟⢅⠀⠀⢸⣧⢪⢸⣿⢙⠏⡿⡏⣿⣿⠀⠀⠙⣾⣱⣹⣿⢴⢒⣍⣩⣭⡍⡭⣽⠸⣿⣒⣳
⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠘⢯⣛⣛⠛⣋⡠⠆⠀⠀⣴⣛⢦⡀⣿⡞⡿⣷⣗⢿⣿⡆⢰⠄⠈⠛⠿⣿⡸⣙⠞⠙⢿⠇⢉⡼⠀⣿⣿⣾⡆
⠀⠀⢀⣿⡇⣴⠋⢿⣳⡄⠀⠀⢨⠏⠛⠂⢲⠀⠀⢸⣿⡦⡌⢷⢹⣷⣤⢿⡼⠼⣿⣧⠘⡄⠀⠀⠀⢸⣦⣄⣉⣘⣛⣋⣥⣴⣾⣿⡿⠙
⠀⠀⢸⣿⡇⢹⡀⡏⢿⡷⠀⠀⣸⣀⠀⠀⡇⠀⠀⠈⠛⠓⠘⠉⣿⣿⡆⣾⡿⠾⣿⣿⡙⡄⠀⠀⠀⠈⣿⠿⠿⢿⣿⣿⡿⢟⣹⡞⢷⣰
⠀⠀⣾⣹⣷⠀⠉⢡⣴⣶⠆⠀⠀⢸⠁⠀⢉⠇⢀⣀⣾⣀⡀⠀⣾⡿⣻⢻⡟⢿⢻⣿⡧⡇⠀⠀⠀⢀⣿⣭⣭⣭⣧⢸⣿⣿⣶⡷⣶⣄
⠀⢰⣿⣹⣿⣧⡀⢀⡏⠀⣾⠆⠠⠚⠚⣧⠎⠀⠀⢹⢿⡏⠁⠀⢻⣷⠹⢿⡇⣆⢘⣿⠇⡸⠀⠀⢰⣯⣛⣿⣿⣿⣿⠸⣿⣿⡿⠿⠿⢿⡆
⠀⠈⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⠁⠀⠀⠈⠛⠿⠿⠿⠿⠿⠋⠀⠁⠀⠀⠘⠋⠋⠛⠛⠛⠉⠀⠉⠉⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣒⠒⡖⣢⠨⣡⣶⡔⠦⠃⢀⠀⠂⠀⡤⠀⠒⠒⣂⣀⡐⠒⠒⠂
⠀⠀⠀⠀⣀⠤⣺⠁⢠⣤⣤⣤⣶⣶⣶⣾⠀⠀⣾⣦⣴⣿⣿⡧⠀⠨⢎⠌⠜⡼⠠⣖⡻⠷⣔⠃⡎⠀⠀⡀⢰⣷⠀⠁⢻⣿⡇⠀⠿⠿⠿⠿⠗⠐
⠀⠀⠀⠸⢐⠥⠚⡁⢸⣿⣿⣛⣟⣻⣿⣿⠀⠀⠙⢿⣿⣿⡟⠁⠀⣐⣠⣂⣊⣾⡀⠢⠄⠉⣹⡶⣄⠀⢀⠁⠸⠿⠀⢠⠘⠛⣁⣤⣤⣦⣤⣄⠀⠀⡀
⠀⠀⠀⡋⠤⢂⠥⡇⠈⠛⠛⠛⠛⠛⠛⠻⠀⠀⠀⠄⠙⠉⠀⠀⣸⡿⠿⠿⠿⢿⣧⣀⠀⢀⡟⠃⠙⠆⠘⠀⢠⣶⣦⠸⠀⣼⣿⢟⣩⣍⡝⠻⣿⣄⠁
⠀⠀⠀⡇⠊⡡⠔⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢀⣼⡟⠁⠀⢀⡀⠀⡉⢻⣧⠈⠁⠆⠀⠀⠀⠀⠈⠻⠋⠀⢸⣿⡇⣾⣿⣿⣿⣇⢹⣿
⠀⠀⠀⡇⣈⠔⣊⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠹⣿⣇⠀⠀⢘⡁⠉⠁⣸⡟⠀⠀⡃⠀⠀⠀⠀⠀⠀⢠⠀⠘⣿⣧⡹⠿⣿⠿⣣⣿⡟⡀
⠀⠀⠀⣋⡠⢊⠅⠘⠼⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣼⠀⠀⠙⢿⣷⣤⣨⣁⣠⣴⠟⠁⠀⠀⠃⠀⠀⢠⠀⠀⠀⠈⠀⠀⠈⠻⢿⣷⣶⣿⠿⠋⠀⠂
⠀⠀⠀⠧⢈⣤⢊⣠⡀⠀⠀⠀⠀⠀⢀⢼⠀⠀⡒⠄⡁⠠⠐⠀⠀⠈⢻⡻⠻⠟⣿⠀⠀⠀⠀⡆⠀⠀⠀⢄⣀⣀⣀⣠⡄⣠⡠⠠⠤⠤⠤⠤⢠⠲
⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠐⠊⠀⠀⠈⠢⣿⠤⠚⠀⠀⠀⠘⠒⠀⠒⠞⢀⡴⣤⠀⠘⠀⠠⡶⣦⠈⠓⠓⠚⠓⠒⠒⠂⠋⠂⠈⠈⠁
⠀⠀⠀⠋⠀⠀⠀⣀⠄⣆⣂⣖⡠⡀⠀⠀⠀⡌⠁⡀⡀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠚⠿⠂
⠀⠀⠀⠀⠀⠠⡎⢰⠊⠉⠙⢿⣿⣮⣢⠀⠈⠀⠁⠠⣿⡴⠂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣥⣥⣤⣤⡀⢱⡀⠀⡊⠁⠰⠈⠀⣧⢀
⠀⠀⠀⠀⣐⢃⡡⠁⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⣠⣤⣿⢀⡀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⠛⠉⠉⣉⣉⡉⠉⠙⠛⢻⣿⡇⢸⡇⠀⠀⡀⠀⠀⣰⠏
⠀⠀⠀⠀⡉⢀⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⢸⣿⣿⣿⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⢷⣆⠀⢸⣿⡇⢸⡇⠀⢀⠀⢠⡴⠃
⠀⠀⠀⢠⡁⣈⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⠀⠈⠛⠛⠁⠀⠀⢀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⠀⠸⣿⡇⢸⡇⢀⠀⠀⣸⣿⠀⠻⠃
⠀⠀⠀⠀⡁⢌⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⠀⢠⣄⣰⡆⢀⠀⣿⣿⠀⠀⠀⠀⠐⠘⢿⣷⣿⣽⣿⡛⠋⠀⠀⣿⡇⢨⡇⢸⠀⠀⣿⣿⡆
⠀⠀⠀⠀⢅⠈⣭⣉⠛⢶⣄⠠⠐⠂⢩⣙⢻⣿⡄⠀⠈⢿⡿⠃⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣿⡇⢠⡇⠸⠂⠀⣿⣼⠇
⠀⠀⠀⠘⠂⠁⠈⢿⣷⣄⠻⣧⠔⢠⣿⣿⡆⣿⣷⠀⠀⠀⠀⠀⠀⢄⠻⠿⠿⠿⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣾⠿⠿⠿⢃⣸⠇⠀⠀⠄⠀⡀
⠀⠀⠀⠀⢰⣾⣿⣆⠻⣿⡄⢻⣇⣿⣿⣿⡇⣿⣿⠀⠁⠀⠀⠀⠄⠂⠀⠀⠈⠉⠁⠁⠈⠻⢿⣿⣿⣷⣾⣟⣃⣉⣀⣀⣉⣑⣒⡄⠀⠀⠸⠀⠰⠁
⠀⠀⠀⠀⣿⣿⣿⣿⡆⢹⣷⢸⣿⣿⡿⠏⣰⣿⡟⠀⠀⠠⠀⠀⢷⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠠⠀⠐⠀⠈
⠀⠀⠀⠀⠻⣿⣿⣿⡏⢨⣟⣿⣧⣤⣴⣾⣿⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⣲⠄⣀⡲⠄⢠⠰⠤⠀⣀⣀⡀⠀⠀⠀⢀⠠⠐⣒⣒⣒⡀⠄⠁
⠀⠀⠀⠀⠄⠈⠛⠛⠴⠛⠋⠀⢀⠉⠁⠀⠈⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠘⠛⠀⠀⢹⣿⣷⠀⠁⠀⠓⣿⣿⠿⣿⣿⠿⢷⣾⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⢠⠂⠚⠀⠠⡎⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⡆⠀⠀⠀⣿⡇⠀⣿⡏⠀⣾⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠨⠀⠀⠀⠀⠒⠂⢀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠡⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠘⣿⠀⢹⣷⠀⢸⣇⣼⠏
⠀⠀⠀⠀⠀⠀⠒⣴⣶⣶⢽⣿⢿⡍⠃⣉⣶⣶⣿⡙⠻⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⠀⢀⣿⠀⣸⣿⠀⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣼⣿⣽⡧⠧⣿⣿⣿⣿⡷⠀⠀⢐⢂⠀⠀⠀⠀⠀⠉⠉⠈⣈⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣴⣾⣧⣀⣿⣧⣸⣿⣷⣦⡀
⠀⠀⠀⠀⢀⠀⠀⠙⠛⠛⡉⢩⣉⣠⡂⠙⠻⠿⠛⠁⢠⠀⠈⠀⠀⠀⡦⠠⠤⠀⠤⠤⠤⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠒⠐⠂⠂⠒⠒⠒⠓⠚⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠂⠀⠀⠐⠶⠶⠊⠉⠉⢉⣭⡉⠉⠁⠀⠒⠂⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢀⡠⠄⠐⣀⣀⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⣀⣀⣀⣀⣀
⠀⠀⢀⠴⢋⡴⠞⠋⠉⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠋⠉⠉⣉⣉⣉⡍⣉⣉⡓⢦⣄
⠀⣰⠎⡰⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⢀⡀⠤⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⢹
⢠⠉⠸⠁⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠁⣀⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡄⠀⠃⠀⠀⠀⠀⠀⠀⠲⣾⣟⠛⠶⣦⣤⣄⣀⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⠖⠋⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣴⣮⣀⣈⣉⣉⣉⣉⣹⣃⡼⠋⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣀⡀⣀⠤⠄⠒⠉
⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⠝⠉⠀⡠⠚⠁⠀⠀⠀⠀⢀⡀⠤⠐⠒⠉⠉⠁⠀⠀⠀⠀⠀⠈⢦
⠰⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠀⠀⠀⣀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⣀⣤⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠁⣠⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠄⠀⠐⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⣽⠶⢦⣬⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⣀⣠⣴⣿⠉⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⣼⣏⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⢈⣷⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠈⡇⢹⣇⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠙⠻⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡠⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⢠⣇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⠀⠀⠀⠀⠀⠄⠀⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣶⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿