Sweet cherry Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠒⠉⡙⠋⠉⡶⢦⣄⣠⡶⣿⠋⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠙⠲⣥⡄⠀⢡⡶⣾⢿⢹⠉⢰⡟⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣅⠀⠄⠀⢀⣂⣿⡿⠟⡜⠸⠘⢸⠆⣾⠁⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⠉⢉⣽⣿⠏⡜⠄⡼⠐⠀⢀⡼⢰⡇⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢀⣭⣿⡟⣿⡏⠄⠀⢀⠇⡄⣠⠟⠀⣾⠂⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⡰⠁⢄⣀⣿⡟⠻⠀⢸⠀⠀⢀⣾⡦⠛⠁⠀⢸⡟⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⣰⠅⣵⢿⠟⡸⠀⢁⣠⣯⠤⠚⠋⠁⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⢀⣃⢼⣁⠥⠶⠛⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣇⡀⠀⠀⠀⠀⣠⠤⣿⣷⡖⠒⠉⠙⠒⢦⡀
⠀⠀⠀⠀⢀⣾⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠿⠂⠀⠛⠚⠁⠈⠙⠲⣤⣾⣒⡀⠙⠋⠁⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢒⣂⡁⠄⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣝⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⠶⠒⠀⠉⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣲⠦⠤⠄⠀⠀⠀⠀⠀⠀⢀⡴⢯⣭⣍⣉⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⣤⣤⣀⣀⣠⠤⠖⠉⠀⠈⠳⠶⢶⣒⣀⣤⠤⠖⠊⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠶⠒⠚⠋⠛⠛⠒⠂⠤⣀⡠⠔⣠⡅⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⢾⣿⡟⡏⠀⡼⣸⢎⢧
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠉⠉⠉⠀⠀⠀⢈⣹⣿⡿⣫⠕⢹⠻⠁⡇⢠⢃⡇⠘⣎⣇
⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣯⡾⡟⠀⠀⠀⣸⠃⡘⢸⠀⠀⠘⡜⡄
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⡿⠛⠁⠀⡇⠀⠀⠀⡇⠀⡇⡮⠀⠀⠀⢳⢹
⠀⠀⠀⢀⣌⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠇⠁⠀⠀⠀⠀⠀⠀⢸⠁⢰⠀⡇⠀⠀⠀⠈⡎⣇
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⣾⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⢸⠃⠀⠀⠀⠀⢱⢸
⠀⠀⠀⡇⠀⠀⠀⢀⣀⣤⣤⣾⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⡾⠀⠀⡟⢸⠀⠀⠀⠀⠀⠸⡆⡇
⠀⠀⢸⠇⠀⠀⠀⢀⣶⣿⠟⠉⠀⠀⠀⠀⠂⠀⠀⠀⢀⡴⠋⠀⠀⠀⡇⡏⠀⠀⠀⠀⠀⠀⢧⢻
⠀⠀⢸⠀⠀⢀⣴⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⢸⡘⡄
⠀⠀⡟⠀⣰⠾⠟⠉⠀⠀⠄⠀⠀⠀⠀⣰⡤⠞⠉⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢣
⠀⢠⣧⣞⣁⣀⠀⠀⢀⣀⣠⡤⠴⠒⣩⠵⠚⠉⠁⠀⠀⠐⠦⣄⡰⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⡆⢀⣠⡤⠤⠤⢤⣀
⠀⠀⠉⠀⠀⠉⠉⠉⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢦⣜⡱⠧⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠷⡘⣍⠀⠀⠀⠀⠰⢤⡉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠑⡄⠀⠀⣠⠖⠉⠀⠀⠚⠉⠉⠀⠀⠀⠀⠀⠀⠙⠦⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⣰⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠃⠀⠀⡰⠃⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠶⠶⠶⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⠀⢀⣀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⡠⠤
⠀⠀⠀⠀⢀⠀⠀⠀⡀⢀⠦⡤⠠⢄⡀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠠⣄⠀⣠⣄⣀⡀
⠀⠀⠀⠀⢾⣧⠀⠀⡙⠀⠀⠀⠁⠉⠙⡄⠀⠀⠀⠀⠛⠛⣿⣿⣿⣿⡿⠿⠍⠀⠀⠀⠀⢤⠌⠑⠀⠄⡉⠹⣦
⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠹⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⣄⠇⠍⠀⠀⠀⠀⠀⡦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠃⠀⠂⣵⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢄⡠⣇
⠀⠀⠀⠀⠀⢄⠀⣦⡄⠁⠒⠒⢆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣉⠚⠒⠚⠓⠋⠘⢄⣀⠠⠄⢰⠞⠋⠀⠀⠀⡘⠁⠈⢦
⠀⠀⠀⠀⠀⠈⠶⠾⠿⣾⣧⣠⠜⠀⠀⠀⠄⢀⡀⠀⠀⠀⣀⣩⡽⠗⠒⠒⠈⠁⠀⡀⠀⠒⠁⠀⠀⠀⡠⠊⠀⠄⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡀⠀⠀⠀⠐⡈⠉⠉⠉⢉⢁⣠⠶⠛⠐⣒⠴⠎⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⠀⠀⠈⠓⠢⠴⠾⡟⠁⢠⡴⠋⠁⠀⣶⡀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⢰⠋⠀⠀⡀⣸⣾⠇⠀⠀⠀⣠⣇⡀⠀⠀⠀⠀⠀⠀⠱⠼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢰⠃⠀⣦⣰⡷⠿⠋⠀⠀⠀⠀⠈⠉⢁⡦⠀⢀⣇⢷⣄⡀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⣦⡤⡀⣰⠀⣸⣧⣝⡀⠄⠀⠀⠀⠀⠀⠘⣴⣴⡿⠛⠉⠀⠀⠀⠀⢠⣤⣀⣀⣶⡞⠀⠀⠈⠉⠀⢸⣿⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⣆⣀⣼⠏⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⢷⣄⣀⠀⢀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢳⡾⠋⠙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⠇⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠲⢦⡀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⠖⠛⠛⠆⠈⣇⣠⠏⠀⠀⣠⠶⢒⡶⠶⠶⢶⣷⣤⠶⠋⣡⣄⡀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡴⠀⠀⠀⠀⢠⡄⣠⠞⠋⠓⠲⢼⣇⡴⠋⠉⠛⠀⠀⢸⡇⢀⡀⠀⠀⠙⣧⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠃⡼⡵⢠⡗⡇⠀⠈⠻⠇⠀⠀⠀⢀⡀⠈⢳⡀⠀⠀⠀⠲⠾⠿⠋⣀⠀⠀⠀⠸⡇⠀⢷
⠀⠀⠀⠀⠀⠀⢀⡏⢰⡇⣇⠈⣇⠻⠄⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣇⠀⠐⠲⠶⠶⠖⢋⣡⠴⠀⠀⠀⣧⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠸⡇⠸⡇⠸⡆⠈⠀⠀⠀⣠⠆⠀⠀⠀⠀⢸⡇⠀⡏⠀⢈⠙⠛⠚⠛⣉⡤⠖⠀⠀⠀⡏⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠙⠀⠀⠀⠀⢀⣉⣡⠖⢁⡀⠀⢠⡞⠀⣸⠃⠀⢈⡉⠛⠛⣉⣡⠔⠀⠀⠀⣼⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠘⠶⠬⠥⠴⠞⠋⣠⠴⠋⢀⣴⡇⠀⠀⠈⢉⣉⣩⡭⠖⠊⠀⠀⡼⠃⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠐⠤⠤⠤⠴⠖⠋⠁⣠⡴⠋⠀⠹⣆⠀⠀⠠⣄⣀⣠⠤⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠶⠒⠋⠁⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⢀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢾⠟⢧⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠛⢉⣉⠍⢉⠉⢼⠁⠀⠀⣧⢠⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠤⠀⠀⢄⠀⢠⠆⣼⠀⠀⠀⣿⢸⢧⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠈⠀⠀⠀⠀⠂⠀⠀⠁⠀⡌⡴⠃⠀⠀⠀⡏⣼⠘⡞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠁⢀⠀⠂⠐⢀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⢠⢇⡏⠀⢷⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠄⠁⣰⠃⠀⢈⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡜⣸⠁⠀⢸⠸⡆
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⣊⣤⠔⠋⠁⠀⠀⠀⠀⠀⠀⣰⢡⡏⠀⠀⠈⡇⡇
⠀⠀⠀⠀⠀⠀⢠⡇⢀⣤⠤⠖⠓⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡟⠀⠀⠀⠀⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡾⠀⠀⠀⠀⠀⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠒⠒⠤⣄⡀⠀⣰⢋⡞⠁⠀⠀⢀⣀⣀⣽⢸⡤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠉⠺⣡⠏⠀⢀⡴⠚⠉⠀⠀⣿⢸⠂⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡎⠈⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠉⠓⠦⣤⣀⣀⣀⣀⣠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⠶⠒⠚⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠻⢿⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⠟⣿⡟⠀⠀⠀⣹⢿⡯⣉⣛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡟⢸⣿⡇⠀⠀⠀⢻⣸⣿⣾⡣⣄⣀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⠃⠘⣿⡇⠀⠀⠀⠈⣷⣿⣿⣿⣮⣦⡉⠛⢮⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣷⠀⠀⠀⠀⢹⡽⣿⣿⣿⣷⡱⣄⠀⠃⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣹⣿⡄⠀⠀⠀⠀⠙⢮⣛⢿⣿⣿⣿⡄⠢⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⢻⣏⠉⠁⠉⢻⣿⢷⣄⠀⠀⠀⠀⠉⠛⠛⠿⣿⣿⣆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡀⠀⠀⢠⣼⣿⡿⠀⠀⠀⢿⣧⡹⣦⣴⡾⠿⠿⠷⣶⣄⡈⠙⠛⠻⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⣾⣂⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⣿⣷⡿⠋⠀⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⢻⡿⢿⣶⡦⣤⣤⣤⣤⣾⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠁⠘⠉⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠠⢾⠿⢿⡿⣿⣿⣿⣿⣷⣗⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠛⢿⣿⠟⢛⠿⣿⣿⣿⣶⣤⣤⣤⣴⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣬⡁⠩⢩⢹⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠿⠾⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠉⠁⣀⣀⣤⣶⣿⡿⢿⡷⠚⠉⠁⠈⡓⣾
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⣀⣴⡿⠟⠋⠉⠁⢀⠞⠀⠀⠀⢀⡼⢿⢿⡀
⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⢴⣿⠟⠉⠀⠀⠀⠀⣴⠎⠀⠀⠀⡠⠋⠀⣿⠀⢳⡀
⠀⠀⠀⠀⠀⠃⠀⢀⣰⡷⠋⠀⠀⠀⢀⠀⣀⠜⠁⠀⠀⡠⠊⠀⠀⠀⣿⠀⠈⢧
⠀⠀⠀⠀⠜⠀⣠⣿⠏⠀⠀⠀⠀⣠⠾⠚⠁⠀⠀⢠⠞⠀⠀⠀⠀⠀⢻⠀⠀⠈⢣⡀
⠀⠀⠀⠀⡆⡼⠋⢙⣀⣠⠴⠗⠋⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⢳
⠀⠀⠀⠀⣯⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠈⢧
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⢾⡷⠶⣶⣶⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⣿⣷⡀⠀⢀⡏⠀⠀⠀⠀⣼⣷⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⢛⡽⢷⣦⣴⣏⣀⣀⡀⠀⠀⠀⠀⠈⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡿⠁⠀⠀⠀⠀⠉⠛⠛⠋⢻⣷⣦⡄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣤⣾⣿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠣⣄⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣦⣠⣶⡾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⢀⡴⠋⣀⡴⠂⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣤⣀⣰⣫⠴⠋⠁⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢒⣲⢤⣀⡇⠹⡌⠛⢷⡒⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠬⠽⢿⡇⠀⠹⡄⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠹⡄⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢳⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣀⡤⠤⠤⠶⣷⠤⠤⢤⣄⡀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⣀⠀⡏⣀⡀⠀⠀⣙⣦⣀⣧⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠉⠉⠉⣠⠞⠋⠉⠀⠀⢸⡄⠀⠀⠈⠉⠙⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⡀⠐⠦⣼⣧⠴⠂⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠖⠒⠒⢲⡿⠿⠦⢤⣀⠀⠀⠀⢠⡇⠀⣰⢫⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⡀⠀⢀⡞⡀⠀⠀⠀⠈⠳⡄⠀⠈⡇⠀⢿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡿
⠀⠀⠀⠀⠀⠀⣸⠁⠀⡤⣦⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⢹⡤⠤⢿⡀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⣿⠀⢸⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⢻⡀⠘⣆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⠀⠀⠀⠀⠈⠓⠦⣄⣀⡀⠀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠋⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠤⠤⠶⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⣀⣀⣀⣠⣶⠟⠉⠀⠀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⢀⣨⠽⢻⣿⡟⠁⠀⠀⠀⠀⠈⣿⣿⣇
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⣠⣴⠞⠋⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀
⠀⠀⠀⠀⠠⠊⠀⠀⠀⣠⡴⠟⠉⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⣸⣿⢿⣿⣇
⠀⠀⠀⠰⠁⠀⣀⡴⠟⠉⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⢠⣿⠏⠸⣿⣿
⠀⠀⢠⠂⣠⠞⠋⠀⠀⠀⠀⠀⢀⣀⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⢿⣿⡄
⠀⠔⠱⠋⠥⠠⠴⢶⣶⣶⣶⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢀⡠⠖⠒⠂⠐⠂⠦⣄⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⣑⣴⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⠀⣠⣿⠠⠄⠀⠠⠄⣀
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠀⠀⠀⠑⢄⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠿⠿⠇⠀⠀⠀⠀⠀⠑⡀
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘
⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠙⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠈⠑⠤⢀⣀⠀⢀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡡⡶⠤⠤⢀⠀⠀⠀⢀⣤⠤⠆⠒⠀⣤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢤⠃⠀⠀⠀⠉⢲⠮⣀⡄⠂⠀⠀⠀⠂⠀⠈⠀⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣵⣧⡱⢄⠀⠀⠀⠀⠆⠈⠑⠢⠖⠈⠀⠀⠀⠁⠀⠀⠒⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠉⣁⠈⠪⡳⡀⠀⠀⠘⢄⠀⠀⠀⠈⠀⣤⠀⠀⠀⠀⠀⠀⢀⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢢⠃⠀⠋⡄⠀⠈⢎⢢⡀⠀⠈⠢⡀⠀⠀⠀⠈⠃⠀⠀⣀⠀⠀⠀⠡⠎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠆⠀⠀⢠⢡⠀⠀⠀⠑⠕⢄⠀⠀⠘⢢⡀⠀⠀⠀⠀⠀⠉⠀⢄⠀⠀⠀⢚⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠎⠀⠀⠀⠀⡌⡆⠀⠀⠀⠈⠢⡢⡀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠐⣎⢣
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠜⡎⠀⠀⠀⠀⠀⢡⢣⠀⠀⢀⣠⠴⡛⢜⢏⠳⢲⢦⢤⣍⡒⢤⣀⠀⠀⠀⠀⠀⠀⠈⠁⢣
⠀⠀⠀⡠⠖⠁⠀⡀⠀⢀⠏⡘⠉⠳⣦⣄⡀⠀⠈⡎⣆⠶⠃⡠⠕⢈⠈⢂⠐⣄⠈⢮⠊⠙⠷⢄⡉⠀⠀⠀⠀⠐⠔⠢⠒
⠀⣠⣾⠃⠀⠀⠜⠀⢀⠎⢠⠁⠀⠀⠀⠐⠛⢦⠀⢡⢹⠈⠁⠀⠀⠈⠀⠈⠢⠚⠀⠀⠀⢉⠀⠀⠙⡄
⣰⡏⠃⠀⠀⠀⠀⠀⠈⠦⠜⠀⢠⠀⠀⠀⠀⠨⢷⠸⡈⡂⠀⠀⠀⠀⠀⠀⠀⠠⠔⣃⢌⠀⠀⠀⠠⢿
⣟⠄⢄⠀⠀⠀⠈⠀⠀⠤⠤⠔⠃⠀⠀⠀⠀⠠⣹⡇⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⢔⢟⡅
⣯⠪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠼⢳⡇⠀⡏⠉⠉⠉⠉⠉⢉⡷⣄⠀⠀⠀⠀⠀⢕⣿⠃
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⠉⠀⣠⠃⠀⠀⠀⠈⠜⡸⣷⡀⠀⠀⣒⢵⡟
⠀⠣⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠁⢀⠈⠉⡄⠀⠀⠀⠀⠀⢀⠔⠜⣷⠀⠀⢪⡟⠁
⠀⠀⠀⠠⣎⠔⡠⡲⣠⢉⣐⣂⣶⠃⠀⠀⠀⠀⢠⣺⢯⣆⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⢴⡤⠔⠉
⠀⠀⠀⠀⠈⠛⠾⣟⣵⣿⡷⠿⢾⠀⠀⠀⠀⠀⣴⣷⣳⣓⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣧⡀⠀⠀⠈⠫⠛⠚⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⡪⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⠀⠀⠀⠀⣀⡤⠖⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⠒⠠⠤⣀⡀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⣀⣀⡤⢶⠶⠖⠒⠺⢷⡾⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⣠⡔⠒⠙⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣠⠊⢀⠴⠎⠁⠘⠀⠀⠀⠀⠀⢀⣠⠖⣿⠃⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⡰⠁⠐⠁⠀⠀⣀⣀⣠⠤⠤⠒⠊⠉⠀⣸⡏⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠘⠓⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⢛⣿⣿⣿⣿⣷⣶⣶⣦⣠⡶⠛⠙⠻⣷⣿⣤⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠈⠻⠿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠈⢿⣧⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠘⣿⣇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣷⣶⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣭⡬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣁⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣷⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⢨⡝⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣥⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⠿⠿⠛⠋




⠀⠀⣀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡟⡉⣻⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣠⠴⣒⣶⣶⢀⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⢠⢋⣴⣿⣿⠟⡡⠂⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣒⣴⣶⠋
⠀⠀⣸⡿⠟⠋⠁⠐⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣴⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡏⣼⣿⣿⣿⠟⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⡿⠋⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠀⠀⢀⠁⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⡤⠤⠤⣴⣻⢿⣿⣯⣰⣗⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠰⣿⣶⡶⠈⠙⣦⡀
⠀⠀⠀⠀⢈⣾⣿⣿⣢⣿⣿⣷⣝⢿⡈⠻⡧⢣⠀⠀⠀⢀⠔⠀⣩⣭⣿⡒⢤⣼⣿⣿⣷⣦⣤⣤⣶⣿⣷
⠀⠀⣜⠀⠈⠛⠛⢉⣿⣿⣿⣿⣿⡎⢷⣄⠀⣸⠀⠀⢰⣿⠀⠀⠛⠿⢿⣯⣼⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⠏⠀⠀⣿⣿⣷⣦⣤⣶⣾⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⡿⡹
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⠟⠁⠀⠀⠀⢻⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢼⣿⣿⣿⠿⣋⠔⠁
⠀⠀⠀⠈⠻⣝⠛⠿⠿⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢂⠹⣿⣿⣿⣿⣿⣿⡿⠃⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠽⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⣤⣤⠆⠋⠀⠀⠀⠀⠀⢀⣤⣤⡄⠘⠁⠀⠀⠀⠀⣠⣴⣶⠴⡇⠀⠀⠀⠀⣤⣶⡦⢼
⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠿⠋⠁⠀⠀⠀⠀⠀⠸⠟⠋
⠀⠀⡼⠟⠁⠀⠀⠀⣀⣀⡀⠀⢰⠿⠋⠀⠀⠀⢀⣀⣀
⠀⠀⠀⣠⠶⡦⡄⠉⠑⠚⠋⠄⠀⡀⢠⣶⣤⣶⣿⣭⣼⣧⠀⢀⡴⠲⠂⢄⢘⠃⡀⠀⢀⣶⣶⣿⣿⣿⣆
⠀⠀⡂⠙⠓⠂⠀⡄⠀⠀⣠⠆⢸⣷⣤⣽⣿⣿⣿⣿⣿⠟⠀⠻⠷⠂⠀⠀⠀⠛⠃⢰⣈⣩⣿⣿⣿⣷⣴
⠀⠀⠐⢄⠀⠀⡠⠁⠒⠚⠁⠀⠈⠙⢿⣿⣿⠏⠙⠛⠁⠀⠀⠀⢀⣀⡀⠀⠂⠀⠀⠈⠿⠿⣿⣿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠛⠛⠛⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⢠⣤⣤⣤⣤⣤⠞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⢠⣾⣥⣤⣼⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠘⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢠⣤⣤⣼⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠘⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣤⣤⣼⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠟⢿⣿⣿⣿⣿⠀⢴⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣴⠆⠀⠸⣿⣿⣿⣿⠀⠀⠀⠐⣷⣄⣿⣧⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⡄⠀⣿⡆⢸⣿⣿⣿⠀⠀⠀⠀⠀⠛⢿⠟⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⣉⣉⣉⡉⠁⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⣿⣿⣿⣿⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣴⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠛⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⠿⠃⠀⠀⠀⠿⠷⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⢿⣿⢀⣀⣀⣀⣀⣀⣀⣀⣸⡿⠿⠿⠿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠛⠟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡿⠀⠰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣷⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡿⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡷⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣾⣧⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢴⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡴
⠀⠀⠀⠀⠀⡴⢋⣀⠄⢀⡞⣷⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⡼⠁
⠀⠀⠀⠀⠈⠀⠉⣀⡴⠟⠁⣿⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋
⠀⠀⠀⠀⠤⠒⠋⠉⠀⠀⠀⣿⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⢂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢳⣶⠟⠛⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠉⠙⠋⠉⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣸⠃⠀⠀⠀⡔⠘⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣷⡀
⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠉⠉⠙⢻⡄⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣸⠇⠘⠢⢤⣠⠤⠞⠁⠀⠀⠀⠀⠀⠀⣴⠟⠋⠉⡽⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠷⢂⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⣰⢟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡆⠀⢀⣴⠶⠾⠲⠶⣤⡀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⢀⣱⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠈⠻⠿⣶⣶⡶⠿⠋
⠀⠀⠀⠀⠀⠀⢠⠖⣦⡰⠀⢤⢀⣤⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠘⢆⠸⣷⢁⣾⣥⣾⣤⣀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⢴⡚⢲⡤⣄
⠀⠀⠀⠀⣠⠖⠒⠚⢂⣽⠾⠋⠁⠀⠉⠻⣧⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⢘⡥⢤⡿⠛⠦⣤⠷⢤
⠀⠀⠀⠀⠈⠓⣶⡾⠋⠁⡀⠀⠀⠆⠀⠀⢹⣇⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣧⣸⠀⢀⣧⡀⠀⠘⠣⠚⢷⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠁⠀⠀⡄⠀⠠⠈⣿⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⣰⢸⡏⠙⣇⠀⠈⡷⠒⢺⠙⢻⡅
⠀⠀⠀⠀⠀⠘⣧⠀⠂⠀⠰⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠀⠀⠀⠀⠹⣮⡳⠶⢾⡓⠛⢷⣤⡴⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠠⠀⠰⠀⣿⠀⠀⠀⠀⠀⠀⠈⠛⠷⣶⣤⣤⣤⣤⡶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢧⣰⣤⣬⣿⠶⠚⣹⠶⠋
⠀⠀⣀⡀⠀⠀⠀⠀⠉⠲⢤⡁⠀⠠⡀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⠶⠟⠶⠶⠋
⣴⠋⢹⣷⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠘⢆⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢻⣿⣿⠆⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠐⠶⣤⣄⡀
⠀⠈⠂⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠈⢀⡟⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⣀⠀⠉⠻⣦⡀
⠀⠀⠀⢀⠘⠛⠙⠛⠛⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣰⡟⠁⠀⢀⠀⠀⠀⠀⢀⡟⠲⣄⠈⢻⣆
⠀⠀⠀⣿⡇⠀⢄⡀⠀⠀⠀⠈⠙⠛⠷⠶⢶⣤⣤⣤⣤⣤⡤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⣿⠀⢀⠀⠀⠑⢄⠀⠀⠌⠀⠀⠘⣆⠀⢿
⠀⠀⠀⠸⣷⡀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⢀⣾⠏⠀⠀⠀⠀⢸⣿⠀⣼⠀⢀⣀⡤⢽⡿⠂⠐⠒⠒⢻⠀⢸
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠈⠙⠛⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⠶⠟⠋⠁⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠘⣿⡀⠸⡏⠉⠀⣠⠏⢠⠈⠢⣄⠀⣼⠀⢸
⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠹⣄⡰⠃⠀⠀⣇⠀⠈⣻⠃⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡈⠛⠶⠦⠤⠾⠶⠛⢁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣤⣤⣶⠾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠳⣤⣀⣀⣀⣤⣴⡖⠚⠉⠉⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣏⠀⠀⠉⠉⢢⡉⠉⠓⣶⢭⣀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⣹⡛⠋⠉⠩⠽⢿⣄⠀⠙⠀⠈⢻⣏⠁⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠉⠀⢲⣿⣷⡶⠉⠀⠀⠀⠘⢧⡀⠀⠀⠈⠀⠱⡦⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠐⠁⠂⠔⠋⠉⠉⠙⠀⠀⠈⠀⠀⠈⠻⣶⣄⠀⠀⠀⠙⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠰⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠲⣤⣄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⢸⠸⡇⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⡞⠫⣝⠛⡿⠧⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠃⡆⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣼⣂⡤⠞⠛⢏⡀⠘⢒⣲⡶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠎⡰⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠈⠑⣛⣽⢟⠀⢶⢹⢡⡑⠠⣹⣭⡓⢦⣄⡀⠀⠀⠀⠔⢁⠔⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢈⡶⣻⢇⡣⠛⡱⢸⡜⢎⢧⠳⢄⢢⣩⢟⡾⣿⠀⠀⠀⠔⣉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⣴⡛⡱⢺⠷⠇⠃⢘⣨⠒⠼⢛⣵⠟⢁⣿⣤⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠉⠛⠓⠛⠃⠛⠚⠚⣁⡤⠖⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠈⠉⠉⠁⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⣀⣄⡀
⠀⢠⣾⣿⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⢀⣀⣀⣴⣷⣦⣤⡀⠀⢠⣤⣆⣶⣿⡄⠀⠀⠀⣄⡀
⠀⣸⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⢃⣤⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⡧⠄
⠀⢻⣿⣿⠿⠋⠁⠀⠀⠀⠈⢿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠙⢿⣿⡿⠁⠀⠀⠀⢨⠁
⠀⠀⠈⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⢉
⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⢠⣾⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠸⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡶⠀⠀⠀⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠁⣀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⡀⢈⣀⣠⣤⣤⣀⠀⠀⢀⣠⣀⣾⣿⣿⣧⣠⣄⡀⠀⣾⣿⣿⣶⡀⠀⣴⠿⣿⣿⡃⠀⠰⣶⣾⣿⣿⠆
⠀⢸⣗⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠛⠛⠛⠛⠓⠀⢻⣶⣴⣿⠗⠀⠈⠉⠛
⠀⠈⠻⣿⣽⣿⣿⠿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⢠⣤⣤⡦⠀⠀⠈⠿⠿⠇
⠀⠀⢀⣠⣤⣆⣤⡀⠀⠀⠀⠀⢀⣀⢈⡙⠛⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣤⣤⣄⡀
⠀⠀⣽⣿⣿⣿⣿⣯⡀⠀⠀⣺⣿⣿⣿⣿⡀⠀⠀⣶⣦⣶⣶⣦⠀⢀⣾⡹⣼⣏⢿⣷⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠛⠉⠋⠋⠋⠛⠃⠀⠸⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⡇⠘⣿⣷⣽⠿⣸⣿
⠀⠀⢠⣤⣤⣤⣤⡤⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⠟⠁⠀⠈⠻⠿⣿⡿⠇
⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠙⠛⠋⠀⡀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⡤⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⣿⣿⣧⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⣁⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠒⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠑⠒⣤⡀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡰⣠⠄⠳⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣹⡿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⡠⣀⠀⢨⡿⠒⠛⠁
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⠙⠗⠃⠀⢱⠀⠀⠀⠀⠸⣅⠠⣙⠢⠄⠀⠠⠤⣒⠾⢁⡜⢉⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡩⠷⠤⡜⠓⢦⡗⠻⡅
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⢜⠷⢄⣉⡐⠒⢈⣉⡤⢖⠩⣢⢞⠏⢸⠀⠀⠀⠀⠀⠀⢀⢠⠎⢉⠖⠀⠲⣏⠟⠉⠉⡖⢧
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠫⣀⣒⡤⣭⣭⡥⢄⣒⠥⠚⡡⠋⢀⠆⠀⠀⠀⠀⡔⢊⣇⢈⠖⠳⣀⣀⣠⣏⣐⠤⠚⣷⠼⡀
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢿⠀⠭⠍⣉⣉⠡⠤⠖⠋⠀⢀⠎⠀⠀⠀⠀⠀⠓⠾⡀⢩⠣⢤⠼⠤⡆⠀⠈⡷⠚⣷⡴⠃
⠀⠀⠈⠲⢄⡀⠀⠀⠀⢂⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠓⠒⠋⠒⠊⠉⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠆⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡲⠖⢶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡈⣇⠙⠈⡞⡿⡆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠘⢦⡈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⡠⠊⢠⠌⢙⠳⣄⠋⠀⡗⢀⡢⠄⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⣠⢟⣀⡀⡀⠀⠀⠀⠀⠀⢠⠏⡄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠸⡄
⠀⢀⠜⠃⠠⠄⠀⢉⡁⠘⠳⡄⠉⣙⣆⠀⠀⠐⠥⡀⠀⠀⠀⠀⠀⠀⠀⠚⢡⣾⡷⡅⠀⠙⡮⠙⣦⡀⠀⠀⢸⡀⢇⣀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇
⢀⡾⠈⠃⢀⢄⠀⠑⠁⠦⠆⠹⡑⢿⡌⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⣀⡴⢻⠥⢷⡦⢵⡪⠔⢒⢼⠹⡄⠀⠀⠳⣄⠘⠦⠤⠀⠀⠀⣠⠏⠀⣀⡴⠃
⡸⠤⠰⠆⠀⠈⠀⠘⠀⠠⣢⢀⡇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⢹⡤⣚⢧⡦⣝⠲⠞⡼⠀⠙⡄⠀⠀⠀⠉⠓⠒⠒⠒⠉⠉⠉⠉⠁
⡷⠂⠰⠀⠀⠃⠀⠐⠓⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣸⢀⣀⢗⡔⢁⡴⠚⠁
⠙⢤⣷⣀⣛⣠⠴⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡆⣿⣶⣿⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⣠⠖⠒⣓⡲⢶⡶⠀⠀⠀⠀⠀⠀⠀⠛⠻⡗⠦⣿⢹⡟⡷⠟⢫⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡘⣾⠔⠂⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠳⡈⡧⠛⢈⣩⠽⠟⠒
⠀⠀⠀⠀⠀⢀⣤⢄⣀⢀⡦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⢷⡹⠲⠤⠤⠤⠾⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣯⠿⣰⣶⠗⠺⣿⢦⡌⠶⡄
⠀⠀⢀⡤⢚⡩⠝⠦⢠⣙⡦⠘⠖⠲⣌⠙⠢⡀⠀⠀⠀⠀⢰⢡⢊⠀⠀⠒⠾⠗⠂⠀⠀⠀⢀⢹⠀⠀⠀⠀⠀⢀⡤⢚⣩⣉⠉⣄⣚⡞⢿⠢⢸⠚⠇
⠀⢠⠏⠰⠟⠒⢸⡣⢶⢰⠦⢬⣯⠉⠉⠀⠀⢹⠀⠀⠀⠀⠘⣆⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⣰⠋⢉⠀⠀⢃⠀⢰⠀⠘⠉⡇⠸⠂
⠀⢼⢀⠀⠀⠀⠈⠀⠘⠇⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡟⠀⠀⠀⢰⢧⠀⠸⠒⠒⢺⠀⠘⠓⠒⣷⠇
⠀⠸⣜⢄⡠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠁⠀⠀⠀⣇⢠⣀⣀⣇⣀⣸⠀⢤⠆⢰⠏
⠀⠀⠈⠳⠤⣤⣅⣈⣉⣡⣠⣤⣤⡤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣠⠤⢄⣀⠀⢀⡴⠃⠀⠀⠀⠀⠸⡼⡄⣀⣇⠀⣘⣀⣸⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣇⣸⠥⠖⠉

⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣿⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⡆
⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⡇
⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠈⣉⣉⣉⣉⣉⡉⠀⠀⣿⣿⡇
⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⣿⣿⡇
⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⣷⣤⣤⣤⣤⣤⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠰⠿⠿⠿⠿⠿⠷⠀⠀⣿⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣯⣀⣀⣀⣀⣀⣨⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠀⢠⣶⣶⣶⣶⣶⣦⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⣿⣟⠉⠉⠉⠉⠉⢙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃


⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣷⣦⣀⡀
⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢹⣿⣿⠋⢻⣿⣿⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⢸⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⢸⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⢸⣿⡃⠀⠀⢻⣿⡇⠀⣿⣿⠁⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⠀⢸⣿⣿⠀⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣷⣦⣴⣿⡟⠀⠀⠸⣿⣷⣤⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⣸⣿⣿⣄⣼⣿⣿⣄⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢻⣿⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢈⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠀⠀⠀⠀⠀⠸⢿⢸⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⢻⢺⣿⡇⠀⠀⠀⠀⢀⠀⣒⢠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠶⢶⢦⠄⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢯⣿⡇⠀⢀⡀⠀⢰⡄⣿⡷⠖⣘
⠀⠀⢀⣤⠀⠀⠀⠀⠈⡢⣀⡀⢊⠄⠒⠰⠾⠿⢿⡿⠿⠶⠀⠐⠀⡀⠀⠀⢾⣿⡇⠀⢄⠠⡄⠄⣿⡥⠶⠄
⠀⣰⠏⠉⡇⠀⢴⡞⠟⠟⡇⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⠿⢧⠀⣀⠁⢸⡞⠁⡔⠁⢀
⠸⠯⠀⠤⡀⠀⠀⣑⣦⢜⠀⢰⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⣈⠐⠌⢳⣏⡡⣍⢉⡃⣴⠂⣠⠄
⠀⣠⠾⣆⠑⣀⡾⣋⡩⠈⢂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠸⢏⠑⢶⠄⣶⣠⡾⢿⣿⣀
⢸⠏⠁⢸⣤⡿⠳⣄⠐⢄⠘⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣉⠣⡄⠈⠛⠀⠊
⠀⠀⠀⠈⠛⠖⡚⠂⠉⢲⡷⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠐
⠀⠀⠀⠀⠀⡴⠿⢷⣤⣤⡶⠋⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡄⢠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⣵⠤⠠⠀⠚⠐⠃⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠉⠉⠁⠀⠀⠀⠈⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡴⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⣄⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠐⠒⠶⠀⠀⠉⠄⠛⠉⢉⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠤⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠
⠀⠀⠀⠀⡀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣀⠀⢀⡞⠀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⡀⠀⠘⠀⠙⠿⢷⣶⡶⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠂

⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢀⠀⢰⠂⣈⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡆⠈⠀⠈⢳⡞⢤⡴⠎⠀⠀⠹⣧⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣫⡷⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠠⠆⠀⠐⣮⠛⢉⣁⡛⠞⠓⠧⠾⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠈⠢⡀⠀⠀⠀⠀⢘⡀⡄⢀⣄⢐⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⣀⣠⣤⣼⠁⠀⡈⠛⢿⢠⡎⠀⠀⠀⠀⣧⡔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⣰⣠⡿⢳⡀⠀⡁⡁⠈
⠀⠀⠀⠀⠀⠒⠒⢀⡌⠁⠀⠉⠓⡄⡌⠋⠀⠁⠀⠲⠐⠒⠂⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⢀⣀⡥⠞⠋⠉⠓⠋⠀⠀⣀⠇⢠
⠀⠀⠀⠀⠀⠀⠀⠼⠃⢄⣀⠀⠐⠻⢀⡇⠀⡀⠀⠀⠀⣀⠀⠀⢠⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⡋⠀⠀⡀⠀⠀⡀⠤⡀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣠⣤⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠤⣀⡉⠒⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠌⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠠⠦⢞⠖⣲⣆⠁⡈⠴⠂⢒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢰⣃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠋⠙⠁⠀⠀⠀⠈⢿⣯⠦⣨⣿⡋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⢿⡂⠀⢠⠶⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⣈⠀⢘⣹⣷⢯⠁⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠀⠐⣄⣀⣐⡦⢄⠞⠉⠀⡛⢢⣠⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⣤⠀⠀⡙⠉⣲⣉⠹⠞
⠀⠀⠀⠀⠀⠈⠀⠀⠶⡏⠀⠀⠙⡋⠙⣤⡄⠏⠉⠉⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⡡⠃⢤⡄⠀⡴⠿⠑⠋⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠲⠀⠀⢠⢤⠄⠞⠁⠀⠈⠉⠈⠀⠎⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠱⣆⠂⣽⢧⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠛⠁⠘⠛⠃⢄⣀⠀⠀⠀⣁⠜⠂⠀⠀⠁⠀⠀⠁⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣟⣛⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⣰⠃⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣐⠤⣀⠀⠀⠀⠘⠁⡤⠞⠓⠄⢀⠠⠂⠀⠀⢀⣘⣷⣻⢆
⠀⠈⠒⠦⠘⠄⠀⢀⡰⠀⠀⠘⡆⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣄⠀⠀⠀⠀⠀⠘⠛⠮⠻⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠈⠐⠃⠀⠡⠖⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢠⠀⢄⡀⠀⠀⠙⠄⠀⠀⠀⠀⠒⡵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠈⠈⡀⢁⠀⠑⠀⠀⠸⣄⠴⠋⠱⡀⠀⠀⠂⠀⠀⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠑⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢁⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠤⠙⠂
⠀⠉⠃⠀⠈⠉⠒⠠⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢴⣀⣁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠴⠒⠂⠀⠀⠀⠠⠀⡠⠃⠂

⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀⣀⡀⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠉⠁⢉⠀⠈⢸⢳⠂⠀⢀⠴⠋⢠⠄⠀⠀⠈
⠀⠀⠀⠘⠀⠀⠈⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⢠⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⡄⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⣀⣴⣶⡿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⢀⢀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣧⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣀⣀⣀⣀⣀⣤⣾⠟⠁⠀⠸⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⡇⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⢠⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⡀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠇⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⢰⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡆⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠘⢿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⠃⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⢸⣿⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇⠀⢸⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⣤⣤⣤⣤⣤⣿⠃⠀⠀⣿
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⣿⠉⠉⠉⠁⠀⠀⢀⣼⡟
⣿⡇⠀⠀⣿⡇⠀⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀⠀⢸⣿⠀⠀⢸⣿⠀⣿⣦⣤⣤⣤⣴⣶⠿⠋
⣿⡇⠀⠀⣿⡇⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⡇⠀⢸⣿⠀⠀⢸⣿⠀⠉⠉⠉⠉⠉⠁
⣿⡇⠀⠀⣿⡇⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⢸⣿⠀⠀⢸⣿
⣿⡇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿
⣿⡇⠀⠀⠻⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠏⠀⠀⣸⡟
⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠈⠛⠻⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⠿⠋
⣿⣿⣿⠿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⠶⠶⠦⠤⣄⡀
⠀⠀⠀⠀⢸⢹⠁⠀⠀⢀⣀⡀⢀⠀⠀⠀⣤⠀⠀⠀⡏⢳⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡇⠀⠀⢀⣠⡀⠀⠀⣿⢹
⠀⠀⠀⠀⢸⢸⠀⠀⠠⣟⠀⠀⢿⠂⣶⠆⣿⠀⠀⠀⡇⢸⠀⠀⢀⣀⣇⣀⠀⠀⢸⠀⡇⠀⢰⣏⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠙⠓⠂⠙⠂⠛⠀⠛⠀⠀⠀⡇⢸⠀⠀⠈⠉⡏⠉⠀⠀⢸⠀⡇⠀⠀⠙⠓⠃⠀⠀⣿⢸
⠀⠀⠀⠀⢺⡰⡷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⢧⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⣳⠤⠤⠤⠤⠤⠤⠴⡿⣸
⠀⠀⠀⠀⠘⠷⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢧⣤⣤⣤⣤⣤⣤⣤⡵⠟

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡏⠀⠀⠀⠀⠀⠀⠈⣿⢦
⠀⠀⠀⠀⢼⢸⠀⠀⢀⡶⠛⠃⣶⡄⣤⡄⣿⠀⠀⠀⡇⢸⠀⠀⠀⠀⡆⠀⠀⠀⢸⠀⡇⠀⠀⣷⢠⡟⠀⠀⣿⢸
⠀⠀⠀⠀⢸⢸⠀⠀⠈⠷⣤⡄⢿⡄⢿⠀⣿⠀⠀⠀⡇⢸⠀⠀⠐⠛⡟⠓⠀⠀⢸⠀⡇⠀⠀⠸⣿⠁⠀⠀⣿⢸
⠀⠀⠀⠀⢸⢸⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣇⢸⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⢇⡀⠀⣀⣀⣀⣀⣀⣟⢸
⠀⠀⠀⠀⠹⣯⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡎⠀⠀⠀⠀⠀⠀⠈⣯⡿
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉





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

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠙⠛⠛⠁⠀⢀⠀⠀⠀⠀⠘⠑⠛⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠙⠛
⠀⡀⣀⢂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣠⠄⢙⡇⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢂⠀⠀⠈⠁⠀⠀⠀⠀⢠⣀⠄⢙⡇⠀⠀⠀⠐⣶
⠀⠱⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠈⠓⠇⠀⠀⠀⠻⠲⡰⠦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠓⠇⠀⠀⠀⠻⠲⡰⠶⠀⠀⠀⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠃⠢⠤⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠦⠤⠴
⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠂⠈⠁⠀⢀⡀⠠⠀⠀⠀⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠂⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠂⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢤⠤⠤⣄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⡁⠀⠀⠀⠀⠀⠀⢐⠀⠀⡀⠀⢀⢤⠤⠤⣄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠋⠁⠀⡋⢠⠂⠂⠀⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠁⠀⡋⢠⠒⠂⠀⠆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡠⠃
⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢠⢚⠶⢀⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢰⠾⠶
⠀⠀⠀⠸⣦⣀⢀⣡⠟⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠠⠀⠐⠀⠈⠁⠀⢸⠁⠀⠀⠸⣦⣀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠠⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠘⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠀⣿⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠉⠁⠀⠐⠀⠀⠸⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠘⢿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣤⢤⣼⠁
⠀⠀⠀⡀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠡⠆⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⣀
⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⠰⠇⠀⠀⠀⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣡⡰⠆⠀⠀⠀⠀⠟
⠀⠀⠀⠑⠀⠀⠀⠠⣄⡄⠀⠀⠀⡯⣑⠀⣘⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⢀⣄⡄⠀⠀⠀⣯⣁⠀⣘⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠐⢦⣀⡀⠁⠀⠀⠀⠈⠈⠘⠁⠀⠀⠤⡄⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⠁⠀⠀⠀⠈⠈⠊⠉⠀⠀⠤⡄⠀⠃⢀
⠶⠀⠄⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⢀⠄⠀⠀⠃⡀⠠⠍⠉⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠉⠓⠃⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠠⠉⠉⠁
⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈
⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠤⠆⠀⡴⠉⣉⡉⠃⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣀⠤⠇⠀⡴⠉⢉⡉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⡅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠄⠀⡅
⡆⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⢶⡽⠒⠀⠀⠀⠀⠘⠀⠤⠰⠊⠀⣠⣀⠀⠂⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⠶⠽⠖⠀⠀⠀⠀⠈⠀⠤⠰⠊⠀⣠⣀
⠃⠀⠀⢸⡀⠃⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⣀⠀⠸⡄⠉⢰⠇⠀⠀⢸⡀⠃⠀⢃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⡀⠀⠸⡔⠉
⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⢰⣿⡇⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠨⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢿⠟
⠀⠀⠀⠤⠄⠀⢀⣀⠀⢸⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⢰⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠦⠠⢤⡀⠀⠀⠀⠀⡜⠀⠀⢠⠔⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠓⠄⠀⢠⠄⠀⢀⠄⠀⠀⠐⠁⠀⠀⢀⡠⠤⠒⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠒⠀⡀⠈⢢⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄⣀⠀⠀⠉⢤⠀⠁⣠⠐⠉⢈⣁⠲⡄⠀⠌⠀⠀⠀⠠⠂⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠐⠦⡀⠀⢀⡀⠀⠄⠀⠀⠁⠀⠀⠈⠉⠀⠰⠀⠀⠤⡐⠒⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⡀⠈⠲⠁⠴⠗⠀⠀⠙⡆⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠑⢠⡇⠀⠀⠀⠀⠀⠀⡇⣰⣢⡤⠴⡇⠀⠀⢀⣤⢀⠄⠀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠓⢄⠀⠀⠀⡠⠞⠓⠣⣉⠉⠀⠈⠂⠤⢬⡍⠉⠒⠢⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡄⣠⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠑⠠⠀⣀⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠝⠉⢙⣇⠀⠀⢀⣀⠀⡐⠀⠀⢦⣆⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⢀⡇⠈⠟⠢⣀⠛⠋⠀⠉⢢⠀⠀⠈⢃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡔⠁⠀⠀⢸⠀⠀⠰⠀⠈⠂⠀⠀⠀⠀⠁⢄⡀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡽⣛⣻⣮⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣽⡷⣿⣿⣿⣧⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠻⠿⠿⠿⡄⢠⠊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡎⠙⠶⠾⠿⠟⢣⣤⠄⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣦⣄⣀⣰⣾⡯⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡧⡄⣤⣶⣾⣧⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⡉⣠⡆⠀⠛⢻⣾⣾⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻⣿⣿⣿⣿⣿⣿⣿⡝⠇⠃⠁⠀⠀⠀⠀⠈⠏⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⢴⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣮⣠⢀⣠⣀⣠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣛⣛⣛⣛⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠋⠙⠛⠙⠛⠋



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡒⣹⠷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠄⠴⠿⢷⣶⣄⡀⠀⢀⡄⡞⢮⠷⡗⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠛⠛⠒⠓⠚⢈⡰⡖⡩⡃⠍⣊⡻⣷⠌
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠭⢶⣿⣾⣿⠀⠀⢀⡴⢛⡙⣀⣷⠃⠌⢼⠞
⠀⠀⠀⠃⡏⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⢀⣴⣜⡷⢯⠱⢣⡞⣥⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣿⣿⠉⢠⣤⢛⠱⡈⢸⢯⡙⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇⠀⠿⣳⠎⠤⢚⢫⣇⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣣⣦⠭⣠⠛⠶⢹⠉⠛⠦⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠵⣤⡾⢋⣣⠋⠘⡏⠀⢀⣈⣴⣦⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠁⠠⣠⣤⣶⣳⡝⠁⢹⣲⣄⣰⣿⣿⣿⡿⠊⣴⠿⠁⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢂⣽⡿⣿⣿⠀⢠⣾⣿⣌⠙⢿⠿⣇⣠⣾⣿⠟⠁⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⣸⡿⣷⣿⡇⠀⣠⣈⢡⣼⡆⢸⣿⡎⠻⠗⠤⡠⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠒⢩⠟⠜⡿⠁⠀⠻⣿⣾⡿⡇⢸⡯⠁⠀⠀⠀⠙⢧⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣬⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⣴⡟⠻⣧⠀⢰⡟⠛⣷⠀⢠⡿⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⠷⠾⠋⠀⠘⠷⠶⠟⠀⠈⠻⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣠⡶⢶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⡶⢶⣄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡟⠀⠀⣿⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⣿⠀⠀⢻⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠆⡄⢠⢠⢠⢰⠀⡄⡄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠈⠈⠈⠂⠑⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⣠⣾⢿⣟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⠀⣼⣿⣥⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣿⠉⠉⠉⢉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⣿⠀⠀⢰⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⣿⠀⠀⠘⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⠀⣴⡇⢀⣠⣀⣄⣄⠀⣿⠀⠀⣀⣀⣄⣠⣠⣤⣤⣤⣤⣤⣄⣠⣀⣄⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠀⣿⣇⠈⠉⠉⠉⠁⠀⣿⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠗⠀⣿⣿⡄⠛⠿⠟⠗⠀⣿⠀⠀⠚⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣤⠀⢿⡞⢿⣄⠠⣤⣤⠀⣿⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⣀⠈⢿⣌⠻⣦⣄⠀⠀⣿⠀⠀⠀⢀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠛⠛⠃⠈⠻⣦⡈⠙⠿⣶⣤⣄⣀⣀⣿⢷⣤⡉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣤⣤⣤⣤⣤⣤⡈⠻⢷⣤⣀⡈⠉⠉⠉⣿⠀⠉⣻⣶⠀⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⣿⣴⡾⠋⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠛⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠃





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠁⠀⠀⠀⠁⠀⠈⠈⠁⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠘⢄⡙⣦⠀⠀⠀⠀⠀⠀⠀⠓⣤⣇⠀⠀⠀⠀⠀⠀⠫⣉⣲⡴⢊⠇⠀⠀⠀⠀⠀⠀⠀⠀⡏⠲⣄
⠀⠀⠀⠀⠀⢠⢖⠉⠛⠓⠂⠒⢄⠀⠀⠀⢀⡎⠀⠈⢇⠀⠀⠀⠀⢠⢋⠀⠌⡉⣉⡆⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢘⡄
⠀⠀⠀⠀⠀⢧⡇⠀⠀⠀⠀⠀⢸⠀⠀⢀⠞⠀⠀⠀⠘⢆⠀⠀⠀⠸⡠⠀⠄⠄⢠⠃⠀⠀⠀⠀⢀⡠⠞⠁⣠⠀⢨⠃
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡜⠀⠀⡎⢰⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢄⠂⣂⠎⠀⠀⡴⠖⠍⠡⠤⠴⠚⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠘⢆⣀⡤⡠⠞⠀⠀⠀⠘⢼⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠓⠒⠐⠒⡒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹
⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢹⡀⠀⠀⠀⠀⠀⡠⣒⠒⠚⢖⠳⢄
⠀⠀⠀⠀⠀⠀⣴⠿⠂⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⣠⠒⢾⡽⠓⠻⣼⠒⠒⢤⠀⠀⢸⢱⠁⠀⠀⠈⡇⠀⢳
⠀⠀⠀⠀⠀⢼⠉⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡞⡳⣤⠼⣇⠀⣠⡿⠷⢖⠉⠀⠀⠸⡘⠀⠀⠀⠐⠁⠀⡜
⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⣸⣛⠼⠣⡄⠀⡏⠉⣣⣀⠜⠀⠀⠀⠀⠑⠤⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⡠⠔⠃⠀⠀⠀⠐⢇⡸⠦⠤⠚⠒⠋⠚⠁⠀⠀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢇⠒⠀⠂⠀⡀⠁⠀⠁⠀⠢⠀⠂⡇⡬
⠀⠀⠀⠀⠀⠀⠀⣦⡀⡼⢳⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢦⡈⢠⠄⡀⠘⠀⠈⠠⡀⢉⡜⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡴⣌⢣⠔⢉⢼⡀⠀⠀⠀⠀⡠⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⡲⠤⣁⣈⣀⣉⡠⠴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢱⡤⣿⡴⠥⣜⠀⠀⠀⠀⠮⣤⡤⢾⠟⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⢀⡜⢇⢀⡼⠳⣄⡏⢦⠀⠀⠀⠀⠀⢠⢣⠂⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⢸⣤⡴⠻⢄⣠⠊⠉⡿⠀⠀⠀⠀⠀⢸⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡔⠉⠒⠊⠁⠒⠂⠉⢉⠆
⠀⠀⠀⠀⠀⢻⡀⢑⣤⣞⠉⢲⠾⣸⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⣀⣀⠴⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⢟⠻⢤⣈⡽⠛⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⡀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠫⠥⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⡏⣼⣷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⣿⡿⠿⠋⢩⣩⠆⢀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣿⡏⣋⠄⢠⣿⣿⣷⣦⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡰⣿⠺⠟⢃⣀⣿⣌⣡⣿⣻⣿⣿⣿⣿⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠇⡀⠃⠀⢰⣾⣿⠟⡻⣿⣿⠿⠟⠻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣎⠀⠟⡋⣻⣿⡁⣼⣷⣝⣿⣶⣿⠆⠀⠒⣶⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⠒⠲⣄⡀⠀⠀⠀⠈⢙⠿⠉⢠⣄⣻⣾⠛⠾⠿⣟⣿⣿⣿⡧⠒⠀⠀⠀⠀⠉⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⢹⣿⣪⣟⣵⡾⠗⠀⠒⣼⣿⣿⣿⠶⣶⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢠⣾⣿⡏⠉⠀⠀⠀⠀⠰⣿⣿⣿⣿⣾⣿⣿⣶⣶⡀⣀⡀
⠀⠀⠀⠀⡠⠀⠀⠿⣿⣿⣶⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠈⠛⠛⠻⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀⠀⠀⡔⠋⠱⠤⢶⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢠⠒⣄⠀⠀⢀⠚⠠⠂⢀⠤⣄⠓⠛⢢⡑⢄⣆⠀⡀⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⣄⠀⡴⢶⠲⡒⠒⡖⡚⢲⠲⣆⣠⠙⠚⡗
⠀⠱⡤⡑⠼⠟⢍⡑⣄⡀⠘⠂⠊⠀⢤⡠⣵⠋⠁⢌⣀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢠⣍⣘⢃⠀⢣⢸⠀⢰⢀⠀⡇⣿⣁⠀⠘⢆
⢀⠞⠀⠀⠀⠀⣠⠞⠳⠥⠀⠀⠀⢇⣠⠇⢸⡧⣵⠀⢠⠒⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⢀⡀⢹⣤⠂⢸⢀⠀⢸⡄⢠⢇⡿⢹⣱⠒⠋
⢇⠀⢀⡴⢾⡉⠙⠢⣄⣔⡇⠈⡂⢀⠤⣤⠋⠧⣈⣁⡜⠀⠀⠀⠀⢀⡀⠤⡤⠤⠤⢤⣤⣤⣀⡀⠀⠈⠓⢻⠃⣧⠜⠋⠈⠒⠞⠚⠒⠛⠛⠉⠉⠀⠀⠉
⠀⠉⠉⠀⠀⠑⠤⠴⠛⠾⣌⣉⣠⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡎⠑⠠⠀⣌⡶⡷⠷⢶⡀⠤⣍⣣⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⡒⠲⠤⠤⡶⠤⠤⠼⠖⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⡇⠀⠀⢀⡄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⡩⠤⢕⢤
⠀⠀⠀⠀⠀⡰⠲⡋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠠⠤⠤⠧⠤⠤⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢡⠀⡠⢀⠑⠤⠚⠀⣣
⠀⠀⠀⠀⠀⣧⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠒⠁⠀⠢⠴⠃⢀⣀⠸⣄⡆
⠀⠀⠀⠀⠀⢏⠳⣄⠈⠓⠤⣀⡀⠀⠀⢀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⡄⠀⠐⢄⠸⣄⡨⠃⡠⠁
⠀⠀⠀⠀⠀⠘⢦⠀⠑⠢⠤⣀⣉⡉⢉⢉⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⣀⡴⠂⠈⠉⠑⠢⠤⣀⠀⠀⠈⠣⣆⠀⠁⡁⠄⣀⣰⠻⠥⣀
⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⡀⠀⠈⣉⡡⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠂⠁⠀⠒⠀⠤⣠⠀⠈⠁⠀⠀⠀⠀⣀⠄⠊⠉⡄⠀⠀⠀⠀⠈⠈⡑⢟⡉⢠⠻⡖⠊
⠀⠀⠀⠀⠀⠀⠀⡼⠀⡰⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣎⣁⡘⠊⢇⡀⠀⠀⠀⠂⠀⠀⠀⠉⠓⢂⠔⠊⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⡀⠸⡄
⠀⠀⠀⠀⠀⠀⣰⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠈⠉⢀⠿⣓⣦⣀⠀⠀⢀⣤⣀⠂⠀⢸⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠱⡀
⠀⠀⠀⠀⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⣞⡋⠤⡀⠀⠀⠀⠀⠀⠔⠅⠈⠀⠀⠀⢉⡹⠓⡄⠉⡆⠀⣸⠗⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⣄⢑
⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⢬⠑⠒⠒⢮⠒⠉⠓⢦⠒⠒⠲⣤⠐⠀⢠⠀⡾⠊⠀⠀⠀⠀⠀⣠⠔⠛⠉⡡⢈⠩⠛⢦⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣆⠠⣀⣔⠠⠤⢄⣍⣀⠀⣀⣸⠀⡠⠞⠉⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⢏⠠⡀⢀⡴⢋⢀⢔⢹⡏⠩⢑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠚⡟⠀⠰⡉⢁⣼⢅⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠤⣼⠗⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠈⢷⡤⢀⣷⣀⠴⡻⠉⠈⠎⣆⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠚⠉⠙⠢⡈⢆⠀⠈⣷⡖⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣄⣙⣺⣤⡤⠴⡟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠐⠚⠉⠁⢄⠙⢆⠀⠀⠀⢹⠈⣄⡴⠙⠛⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢆
⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠔⠉⢍⡉⠲⣌⠢⠀⠀⠀⠑⠘⣀⣠⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠳⡄
⠀⠀⠀⠐⡀⠀⠸⡈⠑⠚⠒⢀⡀⠱⠀⠈⢆⣷⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⢆
⠀⠀⠀⠀⡝⠉⠀⡨⠛⢳⠔⠣⠤⠤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘
⠀⠀⠀⠀⢇⠀⣸⠽⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠙⠀⠀⡀⠀⢉⣵⣆⠀⠀⡀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠄⠀⠀⠀⠠⠀⠘⠋⠀⠐⢁⡴⠞⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣤⡔⠁⠀⠀⠀⢀⣴⠞⠉⢀⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠛⠶⣄⠀⠈⠛⠷⣦⣴⡶⠓⠈⠁⣨⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢈⠂⠰⠦⢤⡙⣿⡄⠀⠀⠞⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣀⣷⡄⠀⠀⠀⠙⠧⠀⠔⠂⢋⡤⠦⠈⡣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⠉⠛⠻⡦⠐⠿⠿⠶⠁⠀⠀⠞⠁⠚⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⣶⣤⠾⠶⣶⠮⠐⢶⡾⠂⢠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⢰⠆⣀⣁⣤⡶⠦⢶⣦⣾⡷⡄⠀⣄⡈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣇⣨⢉⢹⣿⣯⣀⣾⠋⠸⣿⡿⢶⣼⣿⡤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⢻⣿⠃⣿⡟⢠⠀⠈⣿⡡⠄⠸⢧⠀⠙⡎⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⠸⣷⢴⣿⡇⠉⠀⠀⣹⠀⠀⣄⠀⢃⡿⠀⠉⢠⡔⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⣤⡘⢷⠃⠙⣇⣠⠴⠚⠹⣆⠀⠉⠀⢈⢷⡶⢄⣤⠀⣄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⢿⣷⠋⠀⠀⠈⠁⠐⠶⡄⠈⣷⣀⠔⠁⠀⠛⣄⢀⡄⠁⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠁⣄⡈⠻⡴⠚⡉⠙⢇⠀⠋⠀⢀⣼⠿⡠⠴⠶⠄⠘⡟⠀⠸⡇⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢠⠀⣀⣾⡅⢻⣓⡀⢘⣧⣠⠔⠉⠀⠀⠻⣆⢀⠤⠂⢻⡂⠀⠁⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⢾⡟⣉⠉⢏⠉⠀⢉⣠⠴⢏⡒⠶⠿⠦⠄⡟⠧⢤⣄⡀⣷⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⡇⠧⡄⠈⢣⡴⠋⢀⡀⠀⠹⣀⣀⠤⠐⢿⣄⠘⠩⠉⠈⠉⠒⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣤⣧⡀⣤⠖⠘⢧⠲⠟⠧⢄⠠⣿⠀⢠⣆⠀⢘⣇⠀⠀⣠⡸⡇⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢙⢻⡇⣴⠃⠀⢀⡘⢀⣤⠄⢾⣀⠤⠟⠉⣉⠸⢷⡴⠋⠁⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡈⠻⣦⠁⠀⠈⣿⠉⠀⣀⠀⠙⣆⢠⠞⠁⠀⠀⠻⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠈⢡⣼⣿⣶⠶⠾⠟⣢⡴⠿⡄⠀⠙⣟⠀⠠⠞⠣⠀⠧⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣇⣶⣄⠀⢱⡄⢠⡶⠒⠉⠉⠳⣀⡄⠀⠘⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣆⠛⠽⢡⡼⢉⡛⠀⠠⣄⡀⠠⠥⢄⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣄
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣴⣴⣶⣴⣾⣿⣿⣷⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠈⠻⠿⠿⠿⠿⠿⠿⠿⠋⠀⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⢀⣤⣤⣤⣤⣤⣤⣄⠀⠀⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣉⣉⣉⣉⣉⣉⠁⠀⠀⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠠⣶⣶⣶⣶⣶⣶⡦⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠊⠁⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⡀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣠⠤⠤⠤⠤⣄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡖⠒⠛⠦⠤⣀⠀⠀⠀⢸⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣷⠀⠀⢄⡀⠈⠳⢄⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⢳⡀⠀⠀⠙⢆⠀⠘⢦⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠐⠒⠢⠤⢭⠦⣌⣧⠀⠀⠀⠈⡆⠀⢸⠄⠀⣠⣴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⣿⣀⠼⠶⢟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⡬⣶⠖⠉⠙⠢⣄⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠁⠀⢀⠂⠀⡞⣧⡀⠀⠀⠘⣆⠀⠘⡆⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⡂⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⣄⠀⠀⠘⠆⠀⠉⠑⠒⠒⠀⠀⠉
⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⢸⣈⠒⠤⡀⠀⡸
⠀⠀⠀⠁⠁⠒⠢⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠤⠊⠑⡼⠇⠇⠀⠀⠈⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⠂⠐⠉⠉⠀⠀⠀⠀⠀⠀⠘⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣸⠠⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⢱⢸⢸⠁⠳⡄⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠳⣾⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⢤⣤⣤⣴⣶⡶⠾⠶⣶⣤⣀⠸⠃⠈⣷⡀⣀⣤⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠛⠃⠀⠀⣀⣀⣀⣀⣀⣀⠈⠙⢷⡄⢠⣿⠟⠋⠀⠀⠀⠀⠈⢉⣷⣦⣀⣠
⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠚⠉⠉⠉⠀⠀⠀⠀⠉⠙⢦⣼⠿⣿⠁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠨⠽⠧⠤⣴⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⢠⣤⡤⠖⣂⣤⠴⠖⣲⡿⣿⠇⣺⣿⠟⠉⠉⠉⠉⠉⠛⠳⠶⠤⠤⠴⠶⢺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣶⣛⣭⣶⣶⠟⢁⣴⠏⣼⣿⣿⢠⣤⣂⣤⡀⠀⠀⣤⣤⣤⡤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢉⡽⠋⢁⣴⠿⡟⢸⡏⠘⠻⣷⣭⣭⣭⣤⣤⣶⠶⠶⠾⠿⠆
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⠟⠁⠀⢠⡟⢁⣴⠟⠁⢸⡇⢸⠁⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⣠⣶⠿⠛⡉⢉⡿⠿⠿⠷⣶⠏⢠⡞⠁⠀⠀⠸⡇⢸
⠀⢠⣾⠏⠀⠀⠀⠳⢮⡶⠂⠀⢀⡏⢠⣿⡄⠀⠀⢀⣠⣧⢸⣤⣤⣤⣤⣀
⠀⣾⡇⢠⡆⠀⠀⠀⠀⠀⠀⠀⣸⢠⡏⢸⣿⣀⣶⡿⠟⠻⡄⢫⣉⠉⠛⠛⠿⣦⡀
⠀⣿⡇⠸⣇⠀⠀⠀⣀⣠⣤⣤⡇⣼⣀⣼⣿⣿⠏⠀⠀⠀⠚⠾⠋⠀⠀⠀⠀⠈⠻⣦
⠀⠘⣿⣆⠉⢀⣴⡿⠟⠉⢁⠘⡇⡏⠉⠉⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠈⠻⣷⡿⠁⠀⠀⠀⠈⠻⣷⡷⠏⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⡇
⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣿⠇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⡴⠾⠋⣠⣾⠟
⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⢰⣿⣤⣄⣀⣀⣀⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠙⣷⣄⠀⠀⣀⣀⣀⣀⣤⡾⠏⢀⣴⣿⠋⠈⠉⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠈⠙⢿⣶⣦⣭⣭⣭⣭⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠐⢤⡀⠀⠀⠀⣠⠕⠖⠀⠐⠦⣄⠀⠀⠀⠀⠹⣿⣷⣆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⡿⡄⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⢹⣿⣿⣷⠀⠀⠈⢆⠀⠀⠀⢀⣤⡎⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⢦⡀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⢁⣿⢿⣿⡀⠀⠀⡠⠀⠀⠲⠥⣤⣬⡓⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠑⠀⠀⢈⠀⠀⠀⠀⠀⠈⠑⠒⠢⢤⣀⠀⠀⣀⡠⠔⠊⠉⠀⠀⠀⡠⠤⣺⠇⠀⠙⠇⢀⡤⠖⠉⠀⠀⠀⠀⠉⠙⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠉⢲⡀⠀⢣⡀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⢀⡴⠥⠚⠁⣀⡤⢤
⠀⠀⠀⠀⢰⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠁⠈⠓⢢⣤⡄⠀⠀⠚⠁⠂⣤⡤⠴⠚⠉⠀⣠⠔⠋⠁⠀⢠⣇⡀
⠀⠀⠀⠀⠀⢳⡀⠀⢀⡀⠀⠈⡀⠀⠀⠀⠀⣷⣀⠀⠀⠀⠈⠁⠀⠀⠠⣀⣴⡆⢻⡇⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠙⠦⢬⡀⠀⠀⢳⠀⠀⠀⠀⣿⣿⡷⢦⣤⣀⣀⡠⠤⠤⠤⣽⣇⠀⠀⢠⡞⡁⠀⠀⠀⣀⠀⠀⠀⠸⣿⣿⠀⠀⠨⠉⠉⡍
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠂⠀⠓⠄⠀⠀⠻⢿⣿⠀⠀⠙⠁⠀⠀⠀⠀⠀⠙⣆⢰⡟⢸⣿⣷⣄⣀⣈⠑⢂⡴⠄⠘⠿⣦⠀⠀⠀⢀⠘⢠⠄
⠀⠀⠀⠀⡀⠊⠁⣠⠔⠋⠁⠀⠀⠀⠀⠀⠘⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠘⠿⣿⠿⠟⠛⠛⠋⠀⠀⠀⠀⠀⠉⠀⠀⠘⠃
⠀⠀⠀⠀⠳⡀⠸⣅⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡠⠤⠤⠦⠤⣀
⠀⠀⠀⠀⠀⠈⠑⠊⠑⠒⠀⠀⢀⣨⠵⠚⠉⠉⠉⠂⢧⠀⠀⠀⠀⠀⠀⠀⡀⠠⠊⠁⠀⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⡸⠋⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⠀⠀⢁⣴⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠉⢲⣿⣿⣿⣿⣾⠗⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣿⣿⣿⣿⣿⡟⠉⠉⡀⠁⠀⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⡀⠀⠀⠀⣶⠞⠃⡐⠚⠻⠿⣿⡟⠛⢀⡀⠀⠈⠘⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡜⠁⣠⠘⠋⣰⠀⡄⢘⠛⡀⢠⡁⠀⠀⠀⣤⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢰⠇⠀⠀⠀⠀⠁⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠛⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠀⠀⠉⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠁

⠀⠀⠀⠀⠀⠀⢀⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⣰⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡅⠀⠀⠀⠀⠀⠀⠀⡴⠂⠒⢦
⠀⠀⠀⠀⠀⠀⢮⣀⣄⣄⡼⠀⠀⠀⠀⠀⠀⡰⠣⠭⢽⡀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠦⡀⠀⠀⠀⠀⢀⠷⠔⠒⢺⡄
⠀⠀⠀⠀⠀⠀⠈⢟⠢⡱⠁⠀⠀⠀⠀⠀⠀⣗⢒⠒⢒⡇⠀⠀⠀⠀⠪⣀⢤⣀⡠⣀⡼⠀⠀⠀⠀⠸⡀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢸⠁⠀⠀⠀⠀⠀⠸⣴⣤⣦⠇⠀⠀⠀⠀⠀⠀⠈⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣱⠦⡀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⡀⠀⠀⠀⠀⢀⡠⠚⣧⣼⣦⠀⠀⠀⠀⠀⡰⠁⠉⠉⡖⠁⠀⠀⠀⠀⠀⡴⠷⠞⢄
⠀⠀⠀⠀⢰⣫⢤⣀⠤⣄⡠⢌⣲⠀⠀⠀⣏⣩⣭⣤⣤⣤⡇⠀⠀⠀⠀⠳⡒⠒⢲⠞⠀⠀⠀⠀⢀⣠⣏⣙⣉⣹⣄⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠯⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⢹⢻⠏⠀⠀⠀⠀⠀⠈⠑⠒⣢⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠽⠦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠤⠶⠭⡉⠑⣄⠀⠀⠀⠀⢰⠣⢢⢔⢮⢣⠀⠀⠀⠀⠀⡔⠉⠀⠈⠱⡄⠀⠀⠀⠀⢸⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⡏⡞⡉⠳⡈⡆⢸⠀⠀⠀⠀⠸⡰⣐⣾⣮⡾⠀⠀⠀⠀⢰⠳⡖⢶⢲⡖⣷⠀⠀⠀⠀⢸⣿⣿⡛⢻⡇
⠀⠀⠀⠀⠀⠱⣱⢌⣒⣁⠷⠊⠀⠀⠀⠀⠀⠉⢲⣿⠃⠀⠀⠀⠀⠀⠈⣇⣧⢸⢸⢧⡏⠀⠀⠀⠀⢸⠋⠛⠻⠿⣯
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡔⠋⠀⢙⠲⡀⠀⠀⠀⠀⠀⠀⢀⣠⡓⢤⠀⠀⠀⠀⠀⠀⡞⡁⡙⡆⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀
⠀⠀⠀⠀⠀⡜⠡⠆⠀⠈⠀⢳⠀⠀⠀⠀⠀⡴⡏⢣⠈⡞⠁⠀⠀⠀⠀⡖⠚⠈⠘⠒⡆⠀⠀⠀⣰⡎⢱⡀⢀⠎⢑⡆
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠙⢀⠎⠀⠀⠀⠐⣮⠣⣸⡤⠋⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢏⠀⠀⠀⠀⠙⢌⡏⠙⠋⢹⣡⠃
⠀⠀⠀⠀⠀⠀⠈⠙⣾⠉⠁⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠋⠳⠬⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⡙⠉⢀⠀⢠⠞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⠀⠀⢀⡤⠚⠁⡀⢻
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠠⠀⢀⠤⠂⠉⠉⠉⠉⠀⡞
⠀⠀⠀⠀⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢣⡀⠕⠉⠁⠒⠦⠤⠖⢂⡜⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⠊⠀⠀⠀⠐⠀⢠⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⣠⣶⣶⣄
⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠉⠒⠒⠒⠒⢂⣹⣯⣽⣿⣿⡿⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣦⠀⠸⣿⣿⣿⣿⠂⢠⣶⣶⣶⣄
⠀⠀⠀⢸⣿⡏⠙⠳⢦⣤⣄⣀⣀⣀⣀⠀⢀⢀⣴⣿⣶⣦⣄⠀⢀⡤⠞⠉⣀⣹⢿⣿⣋⣠⣾⣃⣴⣀⣀⡴⠾⢿⣿⣿⣿⣿⣾⣷⣮⣿⣻⡥⠴⣏⣹⣿⣿⣿
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠉⠉⠉⢫⠉⠉⠉⣿⠯⣽⣿⣿⣿⣟⣻⣷⣿⣍⡉⠑⣾⣿⣿⣿⣿⡏⠙⡏⠉⠹⠳⢶⠭⢭⣹⡿⣿⣿⣿⣟⣶⣶⣦⡌⠛⠿⠟⠋
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⡸⢷⠰⠤⣜⣿⣿⣿⣿⠟⣼⡿⢿⣿⣿⣿⡆⢿⣿⣿⣿⡿⠃⢠⣿⣿⣷⣶⡌⣷⣿⣿⣿⣿⡟⠋⣿⣇⣿⣿⡿
⠀⠀⠀⣸⣿⠅⠀⠀⠀⠀⠀⠀⡞⠐⠙⡦⠤⠀⠀⠀⠈⠀⠀⠹⣿⣿⣿⣿⣿⠃⠀⠉⠉⠉⠀⠀⢿⣿⣷⣾⣿⣿⠻⣿⣿⣿⣿⠃⠀⠈⠛⠛⠛⠁
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⡸⡄⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠋⠀⠈⠉⠉
⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠹⠒⠒⠄
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠃⡀⠀⠀⠘
⠀⠀⠀⠈⠇⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⢯⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠈⢳⠄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢤⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣴⢾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⠷⡄
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⣠⣤⣤⠀⣀⠀⠀⠀⠀⣴⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⣠⣤⣤⠀⠀⠀⢸⠁⣿
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢸⡏⠀⠀⠘⣿⠃⢰⡶⠂⣿⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⣀⣸⣇⣀⡀⠀⠀⠀⡇⢸⡇⠀⠀⢸⡏⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠘⠿⣦⣤⠀⢿⡤⢸⠇⠀⢿⠀⠀⠀⠀⣿⠸⡇⠀⠀⠀⠉⢹⡟⠉⠁⠀⠀⠀⡇⢸⡇⠀⠀⠘⠿⠶⠶⠀⠀⠀⢸⠂⣿
⠀⠀⠀⠀⠀⢸⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠰⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⣿
⠀⠀⠀⠀⠀⢸⣧⢏⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⡝⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⡽⠛⠛⠛⠛⠛⠛⠛⠛⠛⣏⢣⣿
⠀⠀⠀⠀⠀⠀⠻⢾⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡶⠃


⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠶⠶⠶⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⢀⡞⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡙⣦
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢀⣴⠞⠓⢀⣤⡀⢀⢀⡀⣿⠀⠀⠀⠀⣿⢘⡇⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⢰⣆⠀⣶⠆⠀⠀⢸⡄⣿
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢸⣇⠀⠀⠈⣿⠁⢸⡟⠁⣿⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⣤⣼⣧⣤⡄⠀⠀⠀⡇⢸⡇⠀⠀⠀⢿⣰⡟⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠙⠛⠛⠀⠛⠓⠘⠃⠀⠛⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠘⠛⠁⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⢸⡇⣸⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣯⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⡀⣿
⠀⠀⠀⠀⠀⠘⣷⢱⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢣⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣹⡿
⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠁







⣿⣷⣶⣾⣶⡷⣾⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣿⣷⡿⣶⢶⠷⠶⠶⢶⣶⠷⡾⠷⠶⠾⠶⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠄⣃⡀⠀⢀⠖⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢀⠀⠀⠀⡀⠠⠀⠀⣸⡀⠀⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢄⡈⠐⣄⠀⠈⢿⠠⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠌⣄⠀⣻⣆⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⢄⣽⠙⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠁⠀⣀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠻⠋⢀⠀⠀⠙⠧⠀⠐⠀⢰⣔⠀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣂⠀⠀⠀⣰⠛⠀⠐⠚⠀⠃⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢙⡇⠋⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⡥⠦⠩⡟⠃⠳⠄
⠀⠀⠀⠀⠀⠀⠈⠹⢷⡤⠴⠁⠀⠀⠀⠀⠀⡀⠠⣤⣄⠀⣰⠇⠀⠀⢸⡇⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣤⣤⣀⠀⡠⠃⠀⠋⣈⠉⠀⠀⠀⠀⢨⣇⠀⠀⢀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠸⠀⣶⣿⣦⣀⠔⠀⠙⠀⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢠⠊⢀⡌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠉⠋⠉⠙⠓⠉⠃⠉⢙⡟
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀
⠀⠀⠀⠀⠠⠄⡴⠶⠀⠀⠀⠀⠀⡘⠄⠀⠀⠋⠛⢶⣗⠿⠇⠀⢠⣄
⠀⠀⠀⠀⢘⠂⢀⠠⣾⣷⠀⠀⠀⠦⠘⠢⡀⠀⠼⠚⢻⡶⠦⣄⠈⠛⠂⠀⠀⠀⠀⠀⠀⣀⢠⠐
⠀⠀⠀⠀⠘⠋⠉⠅⠀⢀⣶⣦⠤⠤⢤⣀⣈⣢⣀⠀⠀⠉⠀⣰⣀⠛⢁⣄⠀⠰⡀⠀⠰⠟⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⣒⡶⠐⠒⠒⢢⠴⠚⠛⠉⠉⠙⠉⠉⠙⠉⠛⠉⠉⣉⢙⢻⣿⡛⠶⠦⣴⡛⠃
⠀⠀⠤⠤⠄⠒⠊⠁⠀⠀⠀⠀⠀⠃⠀⠀⢰⡤⠀⢀⣀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠈⠓⠢⣀⣀⣹⣄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠈⢿⠷⠆⠀⠀⠈⢁⣀⡀⠞⣀⣀⡀⢸⣶⡌⠥⠄⣠⠴⠒⠋⢉⢉⣩⠴⠤⣄⡙⠢⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⢨⡄⠀⠀⠀⠛⠀⠀⣤⡄⠀⠾⠁⠜⢂⠀⠔⣊⢁⡀⠄⠒⠿⠁⠀⠀⠀⠀⢈⣷⣦⣀⠪⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢙⣉⠀⠰⠮⠀⠀⠀⠀⣠⡶⠋⠁⠀⠈⠙⠢⣀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢺⢟⠂⣤⡀⠀⠀⠀⣄⠘⠻⠀⠀⠀⠀⢀⣴⣧⠀⢰⣾⠂⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰⣀⠓⡀⢠⠿⠂⠔⠀⡛⠛⠀⠀⠀⠌⠀⠀⢠⣤⢔⡶⠛⣱⡌⠦⢈⡁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠨⠡⠄⠀⠀⠀⠀⠠⠤⠒⢙⠿⠋⠀⠀⠀⠀⠋⠚⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⡀⠀⠀⠀⠀⠀⠀⡈⠉⠀⠀⠈⠀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠰⠷⠀⠁⠀⠀⢀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⡧⠀⠀⠀⠀⠈⠁



⠀⠁



⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠄⠀⡀⠀⠌⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠡⡰⠀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⢀⣀⠀⠀⠠⠀⣒⠂⠒⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠉⠁⣵⠂⠻⡐⠂⠠⣀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠊⠉⠀⠆⠀⠀⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⡀⢸⠃⠀⠀⠈⢲⡄⠀⠀⠀⠀⠀⣠⣾⣿⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠭⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠘⠢⣤⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⡀⠀⠀⠀⠀⠀⠉⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠂⠀⠀⠠⠞⠉⠀⠤⡀⠀⠀⢀⠤⠤⠤⠦⠸⢿⣿⣿⣿⡿⢀⠀⠀⠀⠀⢀⣤⣶⣦
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠓⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠯⠉⢉⠔⠉⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠤⠊⠀⠐⠆⠀⠀⠀⠀⠀⠈⠉⠀⠁⠑⠀⠀⠀⠀⠀⠴⠈⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠄⣠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣿⣏⡀⠀⠘⣧⣤⢼⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢰⣿⣿⣿⡏⠀⠀⠀⢙⠟⠞⠁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢛⣿⣴⣿⡿⣿⢚⠁⠀⠀⠀⣡⣀⣀⣠⣿⣷⣤⡤⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⡟⣋⠈⠛⠤⣼⣿⠿⣤⣶⣟⣉⣿⣿⡄⠛⠤⢿⡏⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣴⢂⡀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠰⣶⠉⣿⡇⠛⠀⠀⣠⣀⠉⠀⠈⣹⠟⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣤⣤⠛⢿⣦⣴⣾⡷⠛⡟⢻⣇⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠿⠷⣿⠇⠠⣾⣗⣻⣏⣀⣀⣀⣸⣧⣀⢾⡄⠀⠀⠀⠀⣸⢾⣇⠤⢾⣿⣦⣾⣷⡺⣟⠛⠟⠻⠽⠟⠈⠋⠀⡀
⠀⠀⣴⣶⣶⠀⠀⠀⠀⠀⡿⢀⣶⣿⣿⠛⠋⠉⢛⣻⣇⣼⡏⠉⠀⢠⣄⠀⢸⡿⣶⠇⠀⠀⠉⠁⠠⢿⡦⠿⠿
⢀⣴⡿⢿⣿⣀⡾⣷⣄⢸⣷⣿⡟⠛⢿⣿⠀⠀⠀⠉⠉⠻⣷⣤⣤⠻⢿⣶⡄⠀⠏⠀⠀⠀⣴⣦⠀⠈⠀⠀⠀⣀⣀⣒⡠⠄
⠈⠻⣧⣼⣿⣿⣦⣾⣿⣾⣿⣿⣧⣀⣾⣿⡤⠂⠀⠀⠀⠀⠀⢙⣿⣤⣴⣿⣥⣤⣤⣤⣤⣤⣿⣙⣶⣦⠀⢠⡜⠉⠀⠉⠑⠂
⠀⠀⠈⠻⣿⢛⠉⢉⡿⠋⠘⠿⠟⠳⠟⠿⠁⠀⠀⠀⠀⠀⠀⠘⠿⠋⠉⠻⢁⣤⠀⠀⠀⠀⠀⠀⣭⠁⠀⢈⣶⣄⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠈⠀⣜⠀⢀⠴⠦⣀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢶⡎⢙⣷⠂⠀⡒⢶⡾⢛⣷⠤⣰⢏⣹⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠛⠿⠛⠋⠁⠀⠂⠀⠆⠀⠀⠀⠀⠸⠿⠛⣿⣴⠋⢻⣾⣿⠚⠿⡀⠈⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣿⠋⠿⠿⠟⠀⠀⠱⡸⠆⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠟⠀⠀⠀⠀⠀⠀⠀⢹⣦⠞⣷⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣷⠶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠂⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠌⢁⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⣿⠱⠒⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⠂⠨⡉⠓⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢢⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢧⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠷⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾⢀⠚⠃⠄⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠆⠀⠀⠀⠀⠀⠀⠢⠀⠇⠀⠀⠀⠀⠀⣸⠀⢠⠐⠿⠤⠛⢢⡔⠤⣔⣓⠴⣷⡼⠲⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢺⡄⠀⠀⠀⠀⠀⢀⡇⠸⣄⠀⠀⢠⡀⠛⠀⣨⠐⢁⠈⢄⢙⣋⣉⣉⠙⡘⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠧⠀⠀⠀⠀⠀⠈⠉⠁⠙⠓⢶⡞⠀⣕⡤⢤⢆⣁⣒⣁⡶⠴⣷⢚⣖⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠧⣄⣠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣰⡾⠓⠒⣏⣀⣼⡟⠶⠾⠶⠮⠭⠽⠿⠿⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠲⠲⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣀⣀⣸⣿⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣶⣶⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣾⠟





⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢄⠔⠀⠁
⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⢀⠈⠄⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠁⠉
⠀⠀⠀⢀⠐⡀⠄⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠁
⠀⠀⠀⠈⠓⠔⢦⡀⠀⡃⠀⠀⠀⠀⠘⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠄⠊
⠀⢄⡀⠀⠀⠀⠀⠈⠂⠃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠈⠀⢂⠐⠀⠀⠀⠀⢸⠀⠀⣜⡲⡄⠀⠃⠀⠀⠀⠠⠁⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⢩⣼⡎⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠁⠉⠂⠀⠀⠙⠀⠀⢳⡇⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠼⣞⠗⣄⠧
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠈⠀⠀⠀⠀⠰⢞⢘⣿⠭⠂
⠀⠀⠀⡀⠄⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢋⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⢠⡤⢈⠮⢷⡵⡀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⡂⠘⠇⠊⣀⣀
⠀⠐⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠙⡄⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⣀⡀⢀⠄⣠⠨⠛⢠⡜⠇⠚⠟
⠀⠀⡆⠂⠒⠀⠉⠢⠒⠠⠀⠀⠀⠀⠀⠠⠀⠀⢁⠀⠀⠘⠂⠂⠀⠀⠀⠀⠠⠀⠈⠀⠀⣀⠔⡽⡂⣐⣁⣀⡀
⠀⠀⠀⠠⠆⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠈⢢⠨⠔⠀⠀⠀⠀⠠⠄⠈⠁⠀⠀⠀⠀⠀⠘⠆⠀⣍⡤⠑⠙⠒
⠀⠀⢀⠀⠉⠐⠤⠎⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⡠⠐⠉⠁⠀⡀⢀⠀⠀⠀⠀⠼⠿⢅⡌⡉⠙⠅⠖
⠀⠀⠀⡄⠀⠀⠀⢣⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⠡⠀⠈⠀⠀⠀⠀⠀⣴⢄⠌⠙⠛⠁
⠀⠀⠀⠀⠀⠠⠄⠂⠀⠂⡀⠀⠀⠀⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⣠⠎⠀⠁
⠀⠀⠀⠀⠂⠐⠢⠀⠀⠀⠅⠀⢀⠜⠉⠀⠀⠀⣠⢱⠀⠀⠀⠀⠀⠀⡇⠀⡤⠚⠅
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⠀⠈⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⡃⠈⠀⠀⠈⠆
⠀⠀⠀⠀⠀⢠⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠹⠆⠄⠀⠀⡀⠀⡀⠄⠀⠀⠀⠀⠀⢸⠀⢀⡴⠋⠀⠈⢢⡄⠀⠀⠀⠀⠀⠀⠸⠀⣀
⠀⠀⠀⠀⡐⠃⠀⠀⢰⠆⠙⠃⠀⠀⠡⠀⠀⠀⠀⠸⡴⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠣⠈⡰⠀⠀⠁⠠⠀⢀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠆⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⠂⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⡏⠀⠀⠀⠀⠀⠻⣦⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣻⡇⢸⡇⠀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠇⠈⠀⣸⠃⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠚⠉⢀⣠⠴⠖⠚⢻⡆⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠠⠴⠚⠋⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⢀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⢷⠄⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⢀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠠⠞⠋⠁⠀⠀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣦⣤⣤⣤⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⡟⠀⡰⠀⠀⢻⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⣦⡀⠀⠀⠁⢠⡇⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠀⢰⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠻⣤⠏⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠃


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

⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣤⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢿⣾⣿⣿⣿⣿⣿⠏⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⢿⣿⣿⣿⣿⣯⢰⣿⡿⢡⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⡻⣟⡛⠛⣷⣝⣿⡟⠅⠀⢿⢹⢰⡟⠁⢀⣼⢳⡾⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠻⠟⠻⣿⣜⣷⣎⠀⠈⠈⡿⠁⠀⣾⠟⠋⣴⣿⣿⣿⣿⣿⣿⣿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣧⣌⠻⣟⢿⡀⢄⠀⠁⠀⠀⠋⠀⢠⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠿⣿⣿⡻⡛⣦⠘⢾⣃⠀⡴⠉⠀⠀⠀⢀⣿⣿⣿⡿⢛⡿⢻⣿⣿⣭⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢉⣹⡿⢷⣾⣩⠻⠶⣍⣧⡀⠹⡄⠀⠐⠀⠀⠀⠀⠈⠛⣣⣴⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣯⣿⣶⣍⡙⢿⣾⣆⠘⢷⠀⠘⠀⠀⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣬⡿⢷⣮⣙⢿⡆⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⣠⣿⡿⠿⠟⠋⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣋⣉⠺⡉⠃⠹⣆⠀⠀⢀⠀⣀⠀⠉⠀⣉⣤⣆⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣾⣿⣿⡛⠻⣿⢐⣦⣙⡇⠀⠀⠀⢈⣤⠂⡼⠉⠛⢛⣁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡅⠐⠿⠿⣖⣊⣻⠷⠌⢭⡛⢷⣶⠷⠞⠁⠀⠠⣠⡶⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠒⢾⡷⢏⣙⠲⣇⠀⢙⡾⠧⠤⢀⣾⡷⠃⢴⣉⣁⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡉⠀⣈⣿⡷⠠⣭⡿⠶⠶⢀⡼⠟⢠⣼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢏⣉⠩⣝⣦⣤⡯⠓⣣⠾⠦⢴⡟⣲⢏⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠊⠇⠐⢠⠶⡦⣾⣋⣉⣁⣄⣈⣃⣹⣦⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢿⠿⠋⠁⠐⠃⠀⠰⣿⠓⣼⣿⣿⣿⣏⡘⢿⣧⠀⠙⣦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇⠀⢀⠄⠐⠆⣀⠠⠛⡿⠁⠈⠹⣦⠉⠉⠛⣇⠀⠀⢃⠀⠻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⢻⡏⠀⠀⠀⠀⠁⠀⡃⠐⠢⣧⣤⡔⠂⠀⠠⣤⣰⠁⠀⠰⡾⠁⣰⣽⣷⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣲⣄⡜⠓⢶⡃⠀⠀⣏⣀⢀⡸⠃⠈⢣⣤⣤⡤⠀⡈⢿⣽⣻⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡁⠢⣴⠇⢬⣽⡋⠈⠉⣿⣂⣀⣼⠋⠀⢱⠖⠁⠀⠛⢼⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣭⠓⠐⣧⠀⣀⣹⣋⢀⣚⡟⠉⠉⢻⣄⣀⣼⠖⡇⠀⢖⠤⡀⠀⠀⠀⠀⠀⠈⠉⠚⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡀⢲⣿⣤⣵⣎⣁⠉⢹⣗⠚⣀⣿⢁⡍⣿⠊⢳⠶⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢛⣿⣿⣿⣿⣿⣿⣏⡉⠙⣿⣉⣤⣿⣂⣿⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣽⣿⣿⣿⣿⣿⣿⣹⣿⣿⣄⣨⣿⡧⢀⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡏⣉⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣠⣴⣾⢟⣻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⣰⣾⣤⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⣼⣿⡟⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁
⠀⠀⠀⣿⣿⣿⣿⣿⠿⠿⠋⢙⣿⣿⣿⣿⡿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣾⠋
⠀⠀⠀⢿⣿⣿⣿⣿⣯⠀⠀⠈⠙⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⢁⡼⠃
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣤⣀⣠⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣾⣉⣁⣀⡀⢺⣇
⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⡿⠿⠷⢄⠀⠀⠀⠀⠀⢀⣶⣾⣿⣉⣙⠲⣇⣀⠉⠉⠛⣿⣳⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⢀⣾⣟⣉⡡⣤⢬⣹⠟⠛⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡛⣿⣿⣟⣻⠏⠀⠀⠠⠀⣱⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⣿⣧⣼⢿⣶⠖⢛⣾⣾⢁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣿⣿⣿⣿⡿⣿⣋⣿⡿⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀
⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢄⣶⣄⣀⠀⠀⠀⠀⠀⠀⠘⠙⣀⡛⣹⡂⠀⠀⢀
⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡟⢻⠐⠦⠀⠀⠀⠀⠀⠀⠀⠙⠃⠨⡹⠆⠒⠁
⠠
⢤
⠈⠧⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⡄⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠄⠀⠀⠀⠤⠄
⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣭⠗
⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠞⠀⢀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⣸⣿⣗⣤⣀⣀⣀⣌⣀⣀⣀⣀⣸⣟⣁⣀⣀⣀⣶⣷⣂⣀⣽⣿⣀⣀⣀⣀⣠⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⡀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠂⠁⠀⠀⠀⠀⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⢰⠶⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠉⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠠⠄⡐⠂⠠⠈⠀⠈⡉⠞⠁⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣾⠒⠀⠀⠀⠀⢀⠀⣠⣤⡤⠴⠊⠉⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡔⠀⢸⡀⠰⠂⠺⣟⠁⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠁⠈⠀⣨⠀⠀⠤⡀⢤⠀⢤⣇⣤⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠀⠀⠀⠀⠀⠰⠁⠁
⠀⠀⠀⠀⠀⢰⠀⠃⠀⢹⠀⠀⠁⠀⠙⠀⠀⠘⠁⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠂⠁⠠⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⣠⢈⠀⠰⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⢐⣦⣀⠀⠐⠂⠀⠤⠀⠠
⠀⠀⠀⠸⡕⠪⢄⡀⡆⠀⠠⠀⠀⠐⢄⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠠⠃⠀⠀⠀⠄⢃⡀⠸⡆⠈⢠⡈⢂⠐
⠀⠀⠀⠀⢀⠀⠀⠘⠐⠢⠀⡁⠀⠀⠀⠑⠂⠀⠀⣀⠠⠀⠀⠠⠄⡤⠀⢀⢠⢀⠂⠀⠑⢰⡇⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠘⣦⠄⢀⠀⠀⠐⠉⠉⠐⠀⠀⠁⠀⠀⠰⠀⠀⢐⡂⠀⠀⢰⠓⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣆⠨⡇⠀⠀⠠⣤⠀⠀⠀⠄⢦⠀⠀⠀⠲⡇⠀⠈⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠐⠄⠀⠀⠙⡅⠀⠀⠀⠐⡀⠀⠀⠀⢿⠀⠀⠀⠸⡄⠀⠀⢨⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡉⡀⠀⠀⢣⠀⠀⠀⠐⢁⠀⠀⠀⢸⡄⠀⠀⠀⡃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠀⠀⠀⠇⡀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠚⣆⠀⠀⠀⠃⡀⠀⠀⢯⠀⠀⠀⠈⠀⠀⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣯⣦⣧⣾⣴⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⣿⣿⡿⣻⣿⣿⠀⣶⣶⣶⣶⣶⣶⢸⣿⣿⢛⢻⣿⡇⢰⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⢿⣿⣜⣟⣿⣿⡆⣿⣿⢵⡮⢻⣿⢸⣿⣿⣴⣿⣿⡇⢸⣿⣧⢩⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⠿⠿⠃⣿⣿⣷⣶⣿⣿⠈⠛⠛⠛⠛⠛⠋⣾⣿⣿⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣉⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣈⣉⣉⠉⠉⠉
⠀⠀⠀⣶⣶⣶⣶⣶⣷⠀⣿⣿⡿⣿⣿⣿⢠⣿⣶⣶⣶⣶⣄⣿⣿⡿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣶
⠀⠀⠀⣿⣿⡇⣪⣿⣿⠀⣿⣿⣥⣜⣿⣿⢸⣿⣿⡑⣿⣿⡇⢻⣿⠿⠸⣿⣿⡆⢿⣿⣧⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠿⠿⠿⠿⠿⠟⣾⣿⣿⣶⣿⣿⠃⢸⣶⣾⠷⠿⠿⠦⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⢸⣿⣿⠁⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⣟⠁⢻⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠷⠶⠶⢾⠀⠀⠶⠶⠶⠶⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠁⣭⣿⣉⣉⣉⣩⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⢩⡄⢸⡆⠀⠀⠀⠀⠀⠀⠀⣤⠤⠒⠄⠏⠀⠀⠀⠀⠀⠛⠶⠁⠀⠀⡎⠀⠀⠀⠀⠀⡀⠀⠀⠉
⠀⠀⠘⠃⠀⠀⣠⡔⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢽⡁⠀⠀⠀⠀⣴⡉⢤⠤⣄⡀
⠀⠀⠀⠰⣐⠞⠁⠀⠀⠀⠀⠀⠀⢠⡏⢨⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⡶⠆⠀⠀⢀⠀⢀⡀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠶⠀⠀⠀⠉⠛⠉⠁⢻⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠃⠏
⡄⠀⠀⠀⠀⡀⠀⠀⠈⣡⡛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢠⡄⠀⠀⠀⢀⣤⠘⠃⠀⠀⠀⠀⠀⢀⡦⢠⡀
⡈⠷⠀⠀⣰⠇⠀⠀⠀⢛⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⣼⠁⠺⠀⠀⠀⠀⠠⡅⢨⡇⠀⠀⠀⠀⠠⠏⠀⠶
⠘⠃⠀⡠⠾⠀⠀⠀⠀⠀⠱⠈⠁⠀⡀⡠⠀⠀⠀⠀⠤⠘⠋⠀⠀⠀⠀⠐⠃⠛⠀⠀⠀⠀⠀⠲⣘⠛⠁
⠀⠀⠀⠁⠦⠄⠀⠀⠀⠀⠀⢤⠠⡜⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢲⠄⣀⡤⠴⠒⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠦⢄⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢴⠊⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢩⣌⠋⠳⡤⠀⠐⡼
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣬⠑⠆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠒⠆⠀⣀⠈
⠀⠀⠀⠀⠶⠆⠶⠀⠀⠙⠙⠢⣤⠀⣠⠀⠀⠀⠀⠀⠀⠀⠈⠳⠌⣋⢠⠀⠀⠀⠑⠛⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⠋⣠⡞⠂⠀⠀⢀⡀⠀⠀⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⠁⠀⢐⠂⠦⣀
⢠⠀⠀⠈⠁⠀⠀⠠⠞⠋⣑⠆⠀⠀⠀⠀⠀⠀⠀⠘⢠⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠿⠀⠀⠙⠶⣤⠙⠃
⠃⠐⠶⢤⣄⠀⠐⣃⠲⠖⠁⠀⠀⠀⠀⠀⠀⠀⢘⠛⢠⡄⠀⣀⣀⠶⠸⠧⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠁⡟⠀⠈⠉⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⠶⠆⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠤⡄⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⠄⠀⠀⠀⠀⣠⠀⠘⢣⣤⠴⠃
⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢠⡃⠲⠒⠛⠁⠀⠀⠘⠇⢴⠇⠀⠀⠺⠋⢩⣄
⠀⠈⠇⢀⡀⠀⠀⢀⡴⠛⡰⠆⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠳
⠀⠀⠋⠉⠁⠀⠀⣈⢡⣤⠉
⠀⣠⡄⣤⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⣤⠀⠀⣀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢀⡀⢀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⣠⠞⢉⣠⣴⣶⣦⣶⣶⢶⣶⣨⣭⣝⡒⠤⣄⡀
⠀⠀⠀⠀⠀⣴⠃⣴⣷⢿⣿⣯⣿⣿⣾⣻⣿⣿⣿⣟⣷⣞⢦⣭⡒⢤⡀
⠀⠀⠀⠀⢰⣿⡀⢿⣿⣿⣿⣿⣯⣿⣾⣿⡃⠉⢘⣻⡟⣻⣿⣿⣷⡶⡌⢢⡀
⠀⠀⠀⠀⣿⣿⣷⡄⠰⣾⣿⣷⣿⢿⣿⣿⣿⣶⣻⣿⣿⠾⢷⢾⣽⣟⣳⠆⢱
⠀⠀⠀⠀⣿⣿⣿⣿⣶⣌⠻⠿⠿⣫⣿⣿⣿⣟⡛⢃⢶⣷⡄⠂⠀⠝⠻⣗⢸
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣿⣿⣷⣆⣰⣾⣿⣿⠁⠀⠀⠀⠈⢻⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⠀⠀⠀⠁⣠⣶⣾⣿⣿⣛⣉⡍⠛⢷⣦⣤
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣣⡄⠰⠀⢀⣾⣿⣿⣿⣿⣿⣿⣮⠀⢸⣶⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⢟⣔⣽⣤⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣝⠿⣿⣿⣿⣿⡟⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠦⠀⢴⣶⠆⠆⠹⣿⠃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡗⠀⠀⠀⠀⠆⡀⠸⠅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⣿⣶⣄⣤⡤⣾⢆⡄⠀⢀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⡟⠙⠂⠈⠙⠻⣿⣿⣿⠇⡠⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⢻⣷⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣟⠁⢁⠐⠠⠀⠀⡉⠉⠻⣿⣿⣤⣠⣄⣤⡈⢻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠄⠄⠀⢀⣴⣦⠙⢿⣿⣿⣟⣤⣉⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣴⣶⣿⣿⣧⣸⣗⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀⣀⣀⣠⢾⡉⠈⠁
⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⢀⢠⣠⠞⠋
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢰⠆⠀⠀⠀⡰⠚⠃⠀⠀⠠⡏⠀⠀⠀⢠⡠⠁⠄
⠀⠀⠀⠀⠀⠀⣇⡀⠀⢀⡴⠓⠀⠀⣸⠁⠀⠀⠀⠄⠉⣇⠀⢀⡰⠾⠏⠀⠐
⠀⠀⠀⠀⠀⣠⡿⠁⢀⡾⠀⠀⠀⠀⣁⠀⠀⠀⠀⠼⡶⢿⡴⠛⠁⠂⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂
⠀⠀⠀⠀⠠⢿⡇⠀⣸⠇⠀⠀⠀⠀⡆⠤⠀⠀⠀⠠⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⡀
⠀⠀⠀⠀⠀⠀⢷⣰⠋⠀⠠⠈⢱⡄⣻⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯
⠀⠀⠀⠀⠀⠀⡈⣿⠀⠀⠀⠀⠁⠁⠙⠃⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⠄⡀⢄⠀⢠⣴⠏⠰
⠀⠀⠀⠀⠀⠀⣧⣸⡆⠀⠀⠀⠀⠀⠀⢰⣤⡄⠀⢸⡇⠀⠀⣾⢄⠁⠀⢶⡴⢚⠉
⠀⠀⠀⠀⠂⠀⠉⠀⢻⡄⠀⠠⣄⠠⠄⢸⠁⠀⠀⣼⠟⠛⠛⠉⢾⣶⠀⠠⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡴⠈⠛⠀⠀⢸⡀⢼⣹⡿⠀⠀⠘⠀⠈⠟⠣⣄⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠌⢷⡄⠤⠈⠀⠀⢃⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣠⠔⠀⠀⠘⢧⣾⡁
⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⢿⡃⠀⠀⠀⠀⠈⣿⡁⠠
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠀⢸⣧⠀⠀⢀⠀⠐⡟⠑⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⢤⠈⣿⡄⠀⠀⡐⠛⠻⠀⠀⠆⠀⠀⠀⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣦⣼⣧⠀⠀⠁⢠⡆⠀⠀⠀⠀⠀⢂⡀⠀⣆⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⢀⣾⠃⠀⠀⠀⠀⠀⠛⠁⠀⡏⠀⠐⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⣿⣄⣼⡟⠀⠘⠂⡀⠀⠀⠀⠀⠁⢹⠀⠀⠂⢀⠀⠀⣄⡀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠀⠀⠀⠛⢿⣿⡄⠀⠀⠀⠙⢄⡀⢠⠀⠐⠺⠇⢀⠀⠈⡁⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢣⡄⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠸⣯⡁⠀⣢⠀⠀⠀⠀⠀⣜⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢀⠀⡆⠀⠹⣿⣦⡀⠀⠀⠈⢧⣴⠃⠀⣐⠀⠀⠰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠀⠘⠁⠀⠀⠈⠻⣿⣦⡀⠀⠈⢿⠀⢰⡏⠀⢮⡼⠃
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣴⠂⠉⠀⠀⠀⠉⢻⣿⣦⡀⢸⡄⠀⠳⣤⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠠⠀⠛⠓⠞⠛⠛⠻⣿⣿⣷⡀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠉⠉⠄⠉⠑⢄
⠀⠀⠀⠀⢠⠖⠉⠀⣀⠠⠂⠁⠀⠄⠐⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂
⠀⠀⠀⠀⠇⠀⠈⠀⠈⠀⠀⠂⠀⡀⠀⠰⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣬⡀
⠀⠀⠀⠀⢇⠈⢁⠀⠉⠀⠋⡀⠀⠀⠀⠀⠀⡠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡎⠐⠾⠓⢹
⠀⠀⠀⠀⠈⡆⠀⠀⠀⣀⠀⠁⢠⠋⠉⢆⠀⠰⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠠⠀⠀⡧⣀⣀⣀⠜⢦⡀
⠀⠀⠀⠀⠀⠸⡌⠀⣾⠉⠙⠒⠋⠀⠀⠈⠂⠐⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠐⠀⡁⠐⠀⠬⠀⠈⠀⠠⠙⡄
⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⡠⡶⡻⠃⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⣩⠊⡴⠁⠀⣇⠑⠤⣆⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⡰⠁⢰⠁⠀⠀⠈⢦⡀⠀⠉⠳⣽⢦⡔⢢⢀⣤⡀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣀⣠⡎⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⣦⣹⠃⢸⠤⠻⢖⠚⠉⡦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠔⠒⡏⠀⢸⣇⠀⠀⡇⠀⠈⢆⠀⠀⠀⠀⠀⡇⠀⠀⣠⠣⣈⠒⢛⣦⣀⠠⢵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⣱⢄⣾⠀⠑⠒⠚⠢⠄⣈⠷⠤⠠⡤⠚⠉⠉⠉⠀⠏⠉⠣⡀⠀⠑⢦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠓⠂⠉⢸⡁⠒⠪⠕⣤⠊⠉⠢⠔⠉⠑⠤⠊⠉⠲⠊⠙⢦⠖⠻⢶⣀⣉⠯⠽⠥⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠏⠀⡏⠒⢶⠐⠸⡆⠀⠐⡄⠀⠀⡆⠀⠀⡛⠀⠀⣇⡤⠚⡉⠀⠠⠀⠀⠂⠀⠠⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠰⠀⠘⡄⠀⢣⠀⠀⠇⠀⠀⡇⠀⠀⡇⠀⡼⠃⠀⠂⠀⠀⣠⢄⠴⠛⢤⣀⠀⢁⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣⠀⢱⣀⡈⡆⠀⢸⠀⠀⠁⠀⢰⠁⡜⠀⠈⡁⠉⢔⡲⠗⠂⠉⠉⠐⢦⠇⠄⠐⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⣧⠄⠠⢔⠂⠘⠿⠁⠀⠈⢷⡀⠀⡆⠀⠀⠀⡸⢠⠅⠈⠀⠀⠂⡈⠣⢄⣀⣀⡀⠤⠊⡀⠀⢠⠲⢄⡨
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠘⡂⠀⠀⠀⠀⠀⢸⠥⠄⠁⠀⠀⠤⠅⠤⠵⡞⠦⠚⢢⠀⠀⠀⠁⠄⠐⢀⠁⢀⠤⠃⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡸⣁⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠓⠒⠉⠑⠤⠔⠉⠁⠉⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠖⠊⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣀⣀⣀⣀⡀⠤⠔⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⣤⡐⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⡦⢄⡀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠳⡀⠉⠓⢤⣄⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠀⢃⠀⠀⠀⠈⠢⣄⠀⠀⠉⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠀⠘⣦⡄⠀⠀⠀⠘⡓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠿⠋⠀⢠⣼⡇⠀⠀⠀⠀⠀⣸⣦⣟⡀⠐⠒⠤⡀⠂⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⣉⡞⠿⠂⠀⠀⢰⣿⣿⣿⣿⣦⡀⠀⠈⠑⢄⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣽⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠱⡆⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⡙⡃⠀⠀⠹⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠘⢏⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡛⠃⠀⠀⠀⢿⣿⣿⣼⣷⣿⣿⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡓⠶⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆

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

⠀⠀⠀⠀⡀⣀⡀⠤⠒⠈⢈⠇⠀⣀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡤⠀⠐⠀⠐⡄
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠷⡤⠸⢗⡈⠁⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⡇⠝⠣⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠐⠈⠁⠀⠀⠈⠀⢀⠄⠀⠀⡇
⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡆⠀⠀⡴
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣼⠗⡯⣄
⠀⠀⠀⢀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⣆⡀⠀⠀⠀⠁⠀⠀⠀⣤⣷⣖⠅⣅⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢨⣿⣿⣇⠀⠀⠀⠈⠀⠀⠀⠿⡿⡔⠈⠀⠀⠀⠀⠀⠀⠠⠄⡄
⠀⠀⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣰⢧⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠁⠇⠀⠀⠀⠀⠀⢸⣟⣿⣷⡃⠀⠀⠀⠀⠐⠈⠉⠊⠀⠀⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⡅⠀⢘⡀⠀⠀⢰⡌⣽⣾⣿⣿⢫⢡⠀⠀⠀⠆⠀⠀⠀⠀⠐⠈⢠⡔⠠⢄
⠀⠀⠀⠀⠀⠀⣀⠀⠃⠀⠀⠀⠄⢸⣻⣿⢿⠏⠀⠀⠀⠰⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠸⣯⡿⡟⢠⠀⠀⠀⠀⠀⠀⠐⠀⢰⠀⢀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⡀⠹⡷⠃⢸⠀⠀⠀⠈⠀⢠⠁⠀⠀⠁⠼⣄⠀⣀⡀⣀⠖
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠁⠀⠀⠅⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠟⠁⠀⠀⠀⠏⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⢸⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⢸⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠴⠧⠤⠤⣄⠀⠀⠀⠀⠀⣼⣿⡿⢛⣛⣛⣛⣛⣛⣛⣛⣀⣀⣀
⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⣿⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿
⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠤⠤⠤⠤⠤⠤⠤⠄⠀⣿⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣛⣛⣛⣛⣛⣛⣛⣻⣿
⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⣿⠀⠀⠀⠀⠀⣿⣿⠗⠸⢿⢶⣶⣶⣶⣶⣶⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠸⠦⠤⢼⡇⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠛⠃⢘⣻⣛⣛⣛⣛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⣼⠄⠀⠀⠀⠀⠀⠀⠘⠻⣷⡀⠘⠀⠀⠘⠈⡽⠃⠀⠉⠁⠂⠀⠀⠀⠀⠜⠀⠠⠀⠀⠀⣄⠀⠄⠀⠀⠀⠀⠈⠆
⡀⠁⠉⠐⠰⠦⡀⠀⠀⠀⠀⢠⣎⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⡤⠀⠘
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⢀⣼⣮⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠛⠛⠒⠀⠠⠀⠀⠉⠁⠀⠀⠂⠐⠂⠀⠀⠀⠀⠤⠀⢷⡀⠄
⠠⠀⠀⢀⣠⠟⠑⠑⠞⠚⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠒⠃⡸⣇
⣴⣶⠶⠋⠁⠀⠀⠀⠀⠀⠀⣀⣄⣠⠀⣀⡀⠀⠀⠀⠀⠀⠜⣦⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⢀⣌⡀⡖⣢⠄⠀⠀⠀⠈⠳
⡀⠀⡀⠀⠀⠄⠀⠀⠀⠠⠜⠁⠀⠀⠀⠉⣿⣄⣀⡀⠀⠀⠀⠜⠳⣥⡄⠀⢀⡰⢃⡄⠀⠀⠀⠀⠛⠐⠬⡗⠻⣖⣺⣇
⡴⣒⠟⠳⠶⣄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡌⠁⠀⠀⠀⠀⠐⠶⠝⠳⠏⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠈⣿⡧
⡾⡃⠀⠀⠀⠈⠳⠤⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧⠙⠉⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠃
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⣤⠀⠀⢀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⣦⣠⣤⠶⠂⠁⠀⠠⣰⣤⣟⠒⡀⠒⠋⠀⠀⠀⠀⠡⢠⡟⠈⠁⠀⠀⢠⡀⠑⢤⠀⠀⠀⠀⠀⢃⣠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⡶⠟⠁⠠⠃⠀⢈⡅⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⢀⡄⠀⠀⠀⠀⠀⢻⡆⠀⡤
⢀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠃⠀⠸⠂⠀⠀⠀⠀⠀⠈⠲⢦⣤⠤⠶⠖⠛⠡⣈⠀⠀⠀⣱⣶⠊⠧⠄⠀⢸⠀⢀⣀⠁⠐⠂
⠈⠀⠀⠀⠀⠀⠛⠥⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⢾⡿⠉⠃⠀⠀⠀⢸⡆⠀⠈⠉⠀⠐
⣀⣤⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠈⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠀⠀⠀⠐
⠟⢠⡈⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⢷⣦⣀⠀⠀⠠⠠⠒⠦⣄⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣔⣀⣀⡤
⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⢸⡆⠀⢠⠀⢰⣡⢌⣠⣿⣷⡖⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⣤⡀
⠀⠀⠄⠠⣤⠇⢤⡰⠂⠀⠀⠈⢿⣂⠀⢡⡴⡷⣶⠋⠀⠚⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⡖⠊⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠽⡃⢀⡀⠀⠀⠀⠀⠹⠿⣿⡶⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠿⠃⠀⠀⠀⠀⣀⣾⡇
⠀⠀⠀⠀⠀⣿⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⡦⠴⠋⠋⠀⠀⠀⠀⠀⠉⠁⣼⢆⡀
⣀⢀⡀⡤⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠃⠺⠙⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡝⠀⠀⠀⠀⠀⠀⠡⣄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠠
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⢀⠈⠁⠲⠉⠀⠀⠀⠀⠘⠃⣰⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⢀⣠⠴⠂
⣀⣀⣐⣀⣀⣀⣀⣀⣀⣠⣄⣠⣀⣒⣀⣉⣛⣷⣠⣬⣃⣀⣁⣀⣀⣀⣀⣀⣀⣸⣋⣀⣃⣀⣂⣐⣃⣀⣀⣀⣀⣂⣸⣋⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⢛⣛⡛⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠈⠿⣿⡶⠶⣤⣤⣤⣤⣤⣤⣤⡴⠶⠛⠋⠁⠐⢒⣤⣤⣾⠿⠛⠛⠛⠲⠿⣶⣄⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⣀⠀⠀⠀⠠⣀⢀⣈⣭⠿⢺⠏⠁⣰⠋⠀⢀⣠⡴⠚⠛⠚⠿⢷⣆⣰⠟⠂⠀⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣌⡉⠙⠛⠛⢋⠝⠋⠀⠰⠋⠀⠐⢁⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣀⣤⣤⣴⣾⣛⣥⣤⣤⣶⣶⣶⣶⣶⣤⣤⡿⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⣭⣶⣿⣿⠿⠿⠛⠛⠛⠋⠙⠛⠛⠛⣿⠃⢠⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠾⠿⠶⣿⣄⠉⠛⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⣤⣄⣀⣀⡀⠀⠀⠀⣀⣀⣀⣤⣴⣶⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⢠⡞⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⣦
⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣠⡶⠶⠆⣠⣄⠀⡀⣀⢸⡆⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢸⠄⣿⠀⠀⠀⣴⠶⠲⠂⠀⠀⠘⡇⢸
⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣿⡀⠀⠀⢹⡏⢸⣿⠉⢸⡇⠀⠀⠀⣿⠀⡇⠀⠀⢀⣤⣼⣧⣤⡀⠀⠀⢸⠀⣿⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠈⠛⠛⠃⠘⠛⠈⠛⠀⠘⠃⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠈⠛⠛⠃⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⢸⠇⡽⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⡽⣄⣀⣀⣀⣀⣀⣀⣀⣀⡼⣇⢸
⠀⠀⠀⠀⠀⠸⣟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⡿
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡴⢾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣷⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⠋⠉⠉⠉⠉⠉⠉⠉⠉⢻⡶⣄
⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⢀⣠⣤⡄⢀⡀⠀⠀⠀⢠⡄⠀⠀⠀⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⠀⠀⠀⣤⠀⢀⣤⠀⠀⢰⡇⢹
⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣾⠃⠀⠀⢿⡗⢰⣶⠖⢸⡇⠀⠀⠀⣿⠀⡇⠀⠀⠀⣀⣸⣇⢀⠀⠀⠀⢸⠀⣿⠀⠀⠀⢻⡆⣼⠇⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠙⠷⣤⠄⠸⣧⠘⡿⠀⢸⠇⠀⠀⠀⣿⠀⡇⠀⠀⠈⠉⢹⡟⠉⠁⠀⠀⢸⠀⣿⠀⠀⠀⠈⢿⠏⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⢸⡇⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸
⠀⠀⠀⠀⠀⢸⡷⢫⠏⠙⠉⠉⠛⠙⠛⠙⠉⠛⠉⠋⠙⠋⠋⠋⠙⣏⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⢫⠏⠋⠙⠋⠛⠙⠛⠛⠋⢫⡹⣼
⠀⠀⠀⠀⠀⠈⠻⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠐⠄
⠀⣠⣍⡀⠔⠰⡶⢦⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⢀⠀⠁⠀⠂⢤
⠀⠀⠠⠖⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢀⠀⠸⠇⠀⠴⠂⠀⠀⠀⠀⡤⠀⠙
⠐⠒⠲⠒⠲⠶⠶⠶⠠⠤⠀⠴⠖⠀⠚⠯⠄⠀⠨⠍⠀⠈⢥
⠀⠀⠀⡪⠓⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠈⠀⠀⠠⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⠒⠂⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⡐⠶⠖⠢⠀⢠⠒⠛⠓⡀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠚⠁⠈⣧⠀⣰⠈⠋⠀⠀⡀⠠⣧⣄⠌⠀⠀⠀⠀⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠐⠰⠇⠉⠀⣄⠀⠒⢀⠀⠈⠉⠀⢀⢤⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠤
⠀⠀⠚⠃⠀⠀⠀⠠⡀⠈⠢⠀⠠⠞⠀⠀⠀⠀⠑⠄⠐⣖⣹⢀⠀⠀⠀⠀⠀⠙⡐⠀⡀⠀⠀⠀⠀⠀⠠⠤⠶⣦⠄⢁⡀⠘⢢⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⢠⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣆⠐⠍⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣄⡀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡤⣤⡄⠀⢀⠀⠀⣀⠄⠀⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⠀⠀⠀⠀⣒⠰⡏⢁⢀⡀⠀⣽⠙⠲⠆⠀⠀⠀⠀⠀⠀⠈⣶
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢈⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⢈⠃⠀⣨⢇⡾⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⡀⢀
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⢂⠀⡀⠀⠀⠀⠀⠒⠀⢐⡂⣀⠐⠳⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢀⠀⠪⠼⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠓⡄⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠣⠿⠀⠐⠀⣀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠥⠶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠆
⠀⠃⢀⠈⠠⠇⡈⠉⠀⠀⠀⠀⠀⠈⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠆⠀⠈⠄⠃⠀⠀⢀⠔⠂⠀⠀⠂⠐⡄
⠀⠀⢨⠑⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠰⠀⠀⠀⠀⠀⠰⡜⠃⠈⢀⣀⠖⡆
⠀⠀⠈⠙⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠚⠒⠀⠀⠘⠀⠀⠐⠖⠃⠚
⣶⣦⣴⣴⣶⣴⣤⣶⣤⣶⣦⣴⣦⣤⣶⣤⣶⣦⣤⣴⣤⣦⣶⣶⣤⣤⣴⣤⣤⣤⣤⣤⣤⣴⣴⣤⣶⣶⣤⣤⣤⣦⣤⣶⣦⣤⣴⣴⣦

⢠⡄⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⡀⠄⠠⠄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡀⠔⡆⠀⢀⣤⡀⠀⠀⠀⢀⡤⠒⠒⢦⠀⠈⠁⠀⠀⠀⠀⠀⡼⢤
⠀⠀⠀⠀⠶⠀⠀⢀⡠⠔⡶⠔⠉⡆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣗⢚⣄⣠⡾⠉⠁⠀⠀⠀⠰⢁⡀⢀⠀⠇⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁⠒⡔⠃
⠀⠀⠀⢀⣤⣐⣈⣁⣀⣀⡁⠈⠭⠤⠄⠐⠒⢈⡆⢀⠀⠀⠀⠀⠀⢀⠤⠾⢽⣯⠗⢳⢄⠀⠀⢀⠀⠀⡶⠆⡆⡏⠦⣼⠀⠀⠀⠀⠀⠾⠠⠤⣠⠦⠜⠣
⠀⠀⠀⢸⣄⡂⠄⠀⠒⣒⣒⣖⣒⠂⠤⠘⠛⢀⠀⠀⢱⠀⠀⠀⢀⡟⣶⠚⠓⣿⣙⡏⠭⡄⠀⠈⠁⠀⡇⠀⣇⠃⠀⣿⠀⠀⠀⠃⠀⢂⠱⠀⠇⠀⡇
⠀⠀⡤⠚⠦⠄⣀⣀⡁⠀⠠⠤⠤⠤⠀⠒⠒⠉⢀⡠⠊⠀⠀⠀⠈⡄⡓⠄⢰⠢⠀⠔⢳⠃⠀⠀⠀⠀⢇⠀⠙⠀⠀⣹⠀⠀⠀⠀⢀⠔⢆⠁⠐⠀⢀⠁⢈
⠀⢨⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠒⠉⠀⠀⠀⠛⠀⠀⠘⠪⠬⢈⠀⠈⠔⠋⠀⠀⠀⠀⠀⠈⠈⠩⠈⠃⠀⠀⠀⠀⠀⠘⠤⢀⣁⡐⠠⠥⠒⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠀⠀⢠⡀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢠⣄⠤⠐⠒⠀⣐⠢⡀⠀⠀⠀⠀⢛⡢⠌⢰⡈⠁⠀⠀⠈⠉⠀⠀⢨⠑⠞⠄⢀⠌⠀⠀⠀⠀⠀⠈⠃
⠀⠰⠆⠀⢀⠎⢰⠊⠓⡊⢯⠱⣈⢢⠀⠀⠀⠀⡤⠊⣁⡠⠊⠒⠈⢀⠂⢰⠀⠀⠛⢄⡁⠈⠀⠀⠥⡀⠀⠀⠀⠀⢠⠒⣏⠢⢄⠀⠓⢤⡀⠀⠀⠈⠃
⠀⠀⠀⠀⡆⡾⠅⠠⠋⠉⠘⣷⠌⡙⠇⠀⢠⠊⢀⡌⠀⠀⠀⠀⠀⠸⡀⡞⠀⠀⠀⠀⠈⠁⡏⠀⠀⠈⡆⠀⠀⠀⠈⠢⢌⠙⠲⠏⠉⢈⣀⠀⠀⣀
⠀⠀⠀⠀⡗⠢⡸⠣⡀⠀⣀⠟⣗⡇⡄⠀⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⡐⢄⠀⠀⣀⠀⠀⠱⠄⢠⠖⠀⡉⢑⣲⠄⠀⠀⠉⠊⢠⠆⡵⠲⡤⠒⠒⡍⠢⡀
⠀⠀⠀⠀⠘⢄⠣⠥⢎⡉⡉⡮⢚⠜⠀⠀⠘⣦⣈⠑⢄⠀⠀⠀⠀⠀⠀⠘⡌⠢⡀⠉⠀⠀⠀⠀⠈⢦⢠⠌⣉⣢⠀⠀⠀⠀⢀⢡⠒⠁⡠⠄⠦⣄⠉⠒⣷
⠀⠀⣀⠀⠀⠀⠑⠢⠤⠥⠯⠒⠩⠄⠀⠀⠀⠀⠉⠳⣄⢣⠀⠀⠀⠀⡠⠔⢁⡴⠃⠀⠀⠀⠀⠀⠀⠨⡼⠀⠉⠁⠀⠀⠀⠀⢸⢎⡀⠰⡀⠀⠀⢨⠀⢰⢸
⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡉⠐⠒⢉⣠⡾⠋⠀⠀⣀⠤⡐⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠈⠒⠂⠁⣀⢜⠌
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⠒⢲⡆⠒⢄⠀⠀⠓⠀⠀⠈⠻⣶⡢⠛⠉⠀⣤⢀⡊⠀⠑⡻⠖⠚⠀⠀⠀⢀⡀⠀⠀⠀⠋⠀⠀⠀⠑⠭⣈⡓⣤⡊⠔⠋
⠀⠀⠀⠀⠀⡠⢖⡛⠄⠈⢲⠀⠀⠃⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠘⠋⠑⣶⠠⣤⠀⢤⣬⠥⠤⣤⡤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣠⢎⣣⠀⠐⡆⠀⠈⠀⢀⠄⡠⠂⠀⠀⠀⠀⠀⡠⣔⠚⠑⠒⠦⡀⠀⠀⠈⠑⠠⠄⠿⠤⠽⠤⠤⠽⠤⠀⠤⠥⠨⠧⠤⠃⠀⠀⠀⠀⣠⠄⠀⠀⠉
⠀⠀⠐⠀⠀⠘⠇⠀⠀⢀⡠⢔⡡⠚⠁⢀⡀⠀⠀⠀⢌⡴⠋⢠⡇⠘⢷⡌⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠻⡀
⠀⠀⠠⣀⠀⠀⢀⢒⡪⠅⠊⠁⠀⠀⠀⠈⠁⠀⡠⢄⠀⠀⠀⠀⠁⠀⠀⠀⡈⢢⠶⠀⠀⠀⢀⠔⠁⢀⣀⡀⣀⡈⠳⡄⠀⠀⠀⠁⠀⠀⡔⠁⠀⠘⡀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠑⡆⠉⠓⠒⠊⠒⠒⠉⡹⠁⠀⠀⠀⠀⡎⠀⡔⠁⢀⠤⢄⡀⠀⠘⡄⠰⠆⠀⠀⡰⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⡊⠁⠀⠑⢎⠁⠈⡆⠀⠀⠈⠉⠀⠉⠁⠘⠈⠉⠀⠀⠀⠀⠀⠀⡇⠈⡀⠀⢇⠄⠀⡱⠀⠀⡇⠀⠀⠀⠸⡀⠀⠉⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⡀⠀⠀⠘⡤⠚⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠱⡀⠑⢄⣀⣀⠴⠁⠀⡜⠀⣀⠀⠀⠀⢩⠶⣔⢶⣲⠞⠁
⠀⠶⠀⠀⢈⠦⢀⠀⠀⠀⠀⠰⣀⡠⠞⠀⠀⢀⠔⡩⠰⠒⡐⡶⣕⢆⠀⠀⠀⠀⢀⡀⠀⠀⢠⢞⠦⠤⠀⠀⠤⠔⠊⠀⠀⠉⠀⠀⠀⢸⢲⡋⣹⢥⠆
⠀⠀⠀⠀⡆⠀⠀⠑⠢⢄⣀⠔⠁⠀⠀⠀⡐⡅⢺⠣⡀⢣⠱⡐⡘⡆⠆⠀⡤⠀⠈⠀⢀⠔⡱⠃⠀⢀⡀⠀⠀⢠⠔⣠⡄⠀⠀⠀⠀⠈⠉⣯⡝⢰⠀⢀⡀
⠀⠀⠀⠀⡱⢄⠀⠀⡠⠂⠀⠠⡄⠀⠀⢀⠀⠦⡀⢣⠱⡀⢣⠱⣁⡀⠐⠀⠀⠀⢀⡔⡡⠊⠀⠀⠰⡁⠈⡃⠀⢏⣩⠕⢂⠀⠀⠀⠀⠀⡧⢦⢼⡎⠀⠈⠁
⠀⠀⠀⠀⢇⣀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢆⡘⢄⢣⠑⡌⠆⣸⢃⠃⠀⠀⠠⢊⠜⠀⠀⠀⠀⠀⠉⠉⠉⠒⢄⡀⠀⠉⠀⠀⠀⠀⠀⢰⡵⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⠢⢌⠒⠷⠧⠜⢋⡥⠋⠀⠀⠀⠓⠁⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠁⠰⠆
⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠀⠀⠀⠈⠁