Asian food Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⠿⡿⣿⣿⣳⠄⠀⢰⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠠⠀⠀⠀⢸⡿⠏⠩⠭⠉⠙⠚⠇⠀⠸⡏⠀⠁⠀⠀⠁⡿⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠠⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⣃⡙⠻⠙⠀⠀⠀⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⣲⡉⠀⣺⠀⠀⠀⠀⠠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠠⠀⠀⠀⠠⠀⠀⠀⠰⠀⠄⠀⢀⢢⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠠⠈⠍⡤⠥⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⡓⠃⠁⠘⣈⡇⠀⠀⠀⡄⠀⠀⠀⡀⠐⡄⠀⢀⠀⢂⠀⢀⠀⢢⠀⠀⠀⣶⡄⣈⠛⠒⠀⠠⡄
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂⠀⠀⠙⠳⢿⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠉⠑⠀⠀⠂⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠒⢂⢲⠄
⠀⠀⠀⠀⠀⠂⠀⠚⠁⠀⢀⡇⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⣉⣉⠀⠀⠀⠀⠀⠈⠈⠀⠀⠆
⠀⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠃⠀⠀⠈⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⣤⡄⠀⠀⠀⠀⠀⠠⡠⢤⠠⢄
⠀⠀⠀⠀⠈⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠠⡤⡅⣢⣌⣅⣆⣂
⠀⠀⠀⠀⠀⡀⢷⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣷⣦⡀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠋⢁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠻⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠃⡑⣄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⡿⠷⡔⣝⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠋⢳⡀⠉⠚⠁⠀⠀⠀⠀⠀⠀⢸⣳⣄⣠⣴⣾⣟⣿⣿⣿⣿⣿⡿⢋⠁⠀⠀⢘⣎⢳⣬⡻⣿⣷⡄
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⣼⣷⣾⠟⠙⣆⠀⠀⢀⣀⣤⡼⣿⣿⣿⣿⣿⠻⣿⣾⢻⣿⣿⡟⣾⣿⠆⣠⣼⣿⣷⡹⣿⣮⡙⢿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣘⣶⣾⣿⣿⣿⡇⠙⠶⠽⢿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⣶⡅
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣦⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡟⣽⣾⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣧⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣛⠿⠿⣿⡿⠿⣛⣵⣿⠟⣋⣭⣥⣭⣭⣍⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣇⢾⣿⣿⣿⣿⣿⣿⠗⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣷⣮⣭⣭⣭⣭⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠒⠛⠛⠓⠲⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⣤⣶⢾⢾⡿⠿⠛⢻⣶⣶⣮⣍⠛⠷⣤⡀
⠀⠀⠀⠀⠀⢀⣴⠋⣠⣾⡿⠉⠀⢠⠞⠀⢀⣴⠋⠁⠀⠿⠛⣷⢬⠙⢿⣆
⠀⠀⠀⠀⣠⡟⢡⣾⣿⠃⠀⠰⠖⠉⠀⢄⠊⠀⠑⠖⠀⠀⠀⠃⡀⠱⢌⢪⢷⣄
⠀⠀⠀⢠⠏⢰⣿⡅⠈⠶⢀⠀⠀⠀⢄⠀⡰⠄⡀⢀⠜⠢⡀⠀⠀⠀⡌⢂⢻⣿
⠀⠀⠀⣾⠀⣾⠉⠿⠁⠀⠀⠑⠀⠀⠀⠋⠀⠀⠘⠉⠀⣠⠌⠀⢀⠴⠀⠀⠀⢿⡄
⠀⠀⠀⣷⠀⣿⠃⠀⢀⠴⢀⠀⢀⢖⣄⡀⡴⠒⣶⣦⡐⠀⡀⢴⡃⠀⠀⢺⡇⢸⡇
⠀⠀⠀⣧⠀⣟⠀⠰⠆⠀⠀⢰⣇⠈⠛⠛⠻⣟⣉⣙⢷⣄⠈⠀⢈⡤⣀⠀⣧⢸⡇
⠀⠀⠀⣿⡀⢿⣆⠀⠀⠰⢀⡀⠉⠟⠢⣄⡀⠈⠙⢿⡾⠁⠙⢶⠄⠠⡸⠻⡏⣼⠁
⠀⠀⠀⠸⣧⡈⢧⡳⠂⠀⢀⠝⠁⠀⠀⠈⠁⠀⡠⠋⠀⠀⡀⠀⠀⢀⣄⡞⣰⡏
⠀⠀⠀⠀⠘⢷⡈⠁⢤⡜⠁⠀⠀⠰⠋⢀⣠⠞⠁⠀⣀⠞⠃⡀⣤⡨⠋⣴⠏
⠀⠀⠀⠀⠀⠈⠻⣦⣈⠃⠀⠀⠐⢄⠀⠀⠁⢄⠀⠀⠈⠑⢦⡴⠟⢠⡾⠧⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠐⠛⠦⠤⠤⠟⠐⠒⣀⣡⠴⠚⣉⣀⣀⣀⣀⠀⠉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⠶⣶⡶⠶⠟⢛⣭⢖⡾⠛⠉⠉⠉⠛⠿⣝⣒⢦⣄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢙⡧⠀⠀⡴⠋⣤⣤⣞⣻⣶⡏⠀⢀⠀⠀⠈⠀⠀⠹⡟⠟⢴⣷⣄⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⣸⠇⠀⡼⠁⠀⣾⣿⣿⢹⢸⡇⠀⠀⠀⢈⢠⡀⠀⠀⣿⡆⠀⠘⡟⣷⡀⠀⢻⡄
⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⡟⠀⢸⠁⠀⣼⣿⣟⣿⢢⡘⣧⡀⠀⠀⠀⠀⠀⣀⡼⠃⢣⠀⢠⢁⡛⣷⠀⠀⣷
⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⡇⠀⣿⠀⢠⣿⡿⠹⢻⣋⣽⣤⣝⠓⢦⣤⠤⣾⢟⣤⣶⢼⣶⣶⡊⣇⠸⡇⠀⢸⡆
⠀⢠⡞⢁⡴⠖⠋⠓⠢⡀⠀⣷⠀⣿⠀⠀⣿⠁⡴⠋⠁⠀⠀⠈⡉⠻⡄⠀⣿⠋⠁⢀⠀⠀⠈⠙⢯⠀⡇⠀⢸⡇
⠀⡿⠀⡾⠀⠀⠀⠀⠀⢡⠀⢹⠀⢹⡄⠀⢿⣾⠁⠀⠐⠠⠄⠀⠀⠀⣻⣼⠁⠀⠀⠀⠀⠠⡄⠀⢸⡧⠀⠀⣼⡇
⠀⣇⠀⢣⠀⠀⠀⠀⠀⠀⠀⣾⠀⠈⣷⠀⠈⣿⠀⠀⠀⠐⠁⠀⠀⠀⢸⢿⡄⠀⠀⠀⠘⠉⠈⠀⣾⠃⠀⣰⣿
⠀⠙⣦⡀⠑⠀⠀⠀⠀⢀⡼⠁⠀⠀⠘⣧⡀⠘⢦⡀⠀⠀⠀⠀⠀⣠⠏⢸⠻⣄⡀⠀⠀⠀⢀⣼⠋⠀⣴⣿⠃
⠀⠀⠈⠙⠲⠦⠦⠴⠞⠋⠀⠀⠀⠀⠀⠈⢷⣄⠀⠙⠷⣶⠤⠴⣾⠁⠀⢸⡆⠈⢙⠛⡒⠛⠋⠀⣠⣾⣿⠃
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠈⠁⠀⠻⠄⠀⠤⠦⠀⠘⠋⠀⢀⡠⢞⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣤⣀⣀⣀⣀⢀⣀⣠⣴⣾⡽⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⡠⠐⠊⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠤⡀
⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡀⠂
⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⢠⠔⡡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡠⠂⠂⠾⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠒⠒⠈⢉⠁⡄⠠⠂⠀⠀⠀⠀⢀⢁⠈⠀⠀⠠⠖⠈⢡⠞⣓⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⢂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⡞⠀⠀⠀⠀⠀⢀⡈⠅⠂⠀⠀⡆⠀⢀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠐⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣴⠟⠣⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠐⠀⠀⠀⢀⡠
⠀⠀⢀⣴⠚⢣⣅⠀⠘⠋⠀⠀⠀⠙⠉⠠⠈⢀⠀⠀⠀⢀⣄⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠸⠀⣀⣧
⠀⠀⠟⠁⠀⣴⣿⡠⠀⠀⠔⠂⠀⠓⠚⠑⠈⠉⢴⣄⡄⠈⠁⠀⠀⠀⠐⠒⠂⠉⢀⣀⡀⢀⡠⠊⠁⠀⠀⠈⡉⠀⠀⣀⠵⠤⠊⠁
⠀⠀⠀⠀⠀⠉⠙⠛⢆⣀⠈⠀⡀⠒⢀⣔⢁⣠⢾⠎⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠈⢡⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠒⠒⠲⡾⠋⠀⣴⡷⠁⠀⠀⠀⠀⠀⠀⠂⠛⠋⠀⠀⠀⠰⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⢐⡀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⣠⠤⠖⠊⠉⠉⠁⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠦⠐⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⡒⠒⠠⠭⠖⠁
⠀⠀⠀⡴⠋⠁⠀⡀⢤⣶⣤⣖⡒⠠⠶⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠀⣀
⠀⠀⡞⠀⢀⡴⢕⣚⣩⡝⠳⠦⣠⣴⠾⣛⢽⣿⣥⡤⠤⡀⠀⢀⠀⠀⢀⢧⡇⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣀⢀
⠀⠀⠃⠀⣊⣠⠚⢃⡯⣵⢤⡀⠽⠛⡛⠓⠏⣉⠭⠅⠀⢀⠀⡜⠀⠀⣸⢸⠃⠀⠀⠀⡼⠃⠀⡐⡀⠁⠀⠀⢁⡊⠈⠁
⠀⠀⠘⠸⡁⠀⢀⣾⡇⠃⠇⡱⠃⠈⠀⣀⠀⠀⠀⠀⠀⣳⡾⠁⠀⠀⡇⢸⠀⠀⠀⢸⠇⠖⢁⡤⠄⠀⠀⢀⠞⠀⠀⠀⢠⠀⠀⢰
⠀⠀⠀⠹⡦⣐⠺⢟⡀⠀⠒⠀⠀⠀⠘⠁⠀⣀⡠⠴⣺⣵⠃⠀⠀⢰⠁⡎⠀⠀⠀⢨⢲⣀⠍⠀⠀⠀⠀⠄⠀⠀⠀⣄⠮⡀⢄⣼⡆
⠀⠀⠀⠀⠙⠀⢑⡒⠠⠭⢉⣁⣒⣛⣈⣩⠭⠴⣒⡫⡶⠃⠀⠀⠀⡌⠀⡀⠀⠀⠀⠈⡎⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠠⠂⣀⣞⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠲⠤⠶⠦⠒⠒⠉⣩⠔⠁⠀⠀⠀⢠⠁⠄⠇⠀⠀⠀⠀⠃⠀⠀⠐⠩⠠⢠⣄⣀⣠⣤⠤⣾⠟⣡⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⢤⣀⡴⠋⠀⠀⠀⠀⠀⠀⡌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⠛⠛⠛⠛⠛⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⠁⢀⣀⣤⣤⣤⣤⣤⡤⢤⣀⠀⠀⠉⠛⢦⣀
⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⣤⠞⣡⠞⠋⠀⠀⠀⠈⢹⣤⣬⣝⣲⢤⡀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⡴⣤
⠀⠀⠀⠀⣴⠋⠰⣴⣶⣯⣿⠾⣿⠀⠀⠀⠀⠀⠀⠈⢹⠉⢙⠏⠷⣿⣦⡀⠀⠹⣦⠀⠀⠀⠀⠀⢀⡇⢸⡇⠀⠀⠀⡼⢀⡟
⠀⠀⠀⣼⠃⠀⣰⣿⣾⡇⡏⠀⢻⣤⠀⠀⠀⠀⠀⠀⣞⠀⣴⠋⠙⠋⠙⢿⡄⠀⠘⣇⠀⠀⠀⠀⣸⢀⡿⠀⠀⠀⢰⢁⡼⠁
⠀⠀⢸⠇⠀⢰⣿⣿⡿⢷⡤⣠⣞⡿⣶⡶⠒⠚⠋⣷⠻⡞⠉⠀⠀⠀⠀⠀⢿⡀⠀⢹⡄⠀⠀⢀⣏⣸⠃⠀⠀⢀⣿⡿⠁
⠀⠀⣿⠀⠀⣿⡏⠀⠀⠀⠀⠈⣹⣷⠃⠀⠀⠀⠀⠙⣦⣿⣄⠀⠀⠀⠀⠀⢸⡇⠀⠸⣧⠀⠀⣸⢧⡟⠀⠀⠀⣾⣿⠃
⠀⠀⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⣧⣾⠀⠀⠀⠀⠀⠀⠘⣧⡙⣧⠀⠀⠀⢰⡞⠧⠀⠀⣿⠀⢠⡏⣼⠁⠀⠀⣼⢻⠇
⠀⠀⢻⡄⠀⢸⡆⠀⠀⠀⠀⠀⠘⡏⢷⠀⠀⠀⠀⣀⡴⢻⡁⠳⠶⡦⠞⠋⢁⠁⠀⢸⣿⠀⣼⢳⡏⠀⠀⣰⣯⡟
⠀⠀⠘⣧⠀⠈⢿⣶⣀⣀⣀⣴⡞⣠⣼⣿⣓⣲⣟⣯⠴⢺⣵⣤⢄⣕⢰⡟⡘⠀⢀⣾⡏⢠⣏⡾⠀⠀⢠⣏⡾
⠀⠀⠀⠹⣇⠀⠘⢿⢭⠛⢭⢫⡖⢤⣿⠈⠉⠁⠀⠀⠀⠀⢸⡟⠛⡇⢚⡴⠁⢀⣞⡿⠁⣼⣿⠃⠀⢀⡞⣾⠁
⠀⠀⠀⠀⠹⣧⡀⠀⠻⡀⠀⡏⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⠧⠛⠀⣠⣾⡿⠁⢠⣯⡟⠀⠀⣜⣼⠃
⠀⠀⠀⠀⠀⠈⠳⣤⡀⠈⠛⢧⡄⠀⢘⠳⢤⣤⣀⣀⣀⣴⠻⠒⠀⠀⣠⣖⣿⡟⠁⠀⡞⣾⠁⠀⡸⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⡀⠀⠀⠉⠉⠀⠈⠉⠉⠁⠀⢀⣠⣴⣞⣵⠟⠋⠀⠀⢰⢳⡏⠀⣰⢃⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣶⣤⣤⣤⣤⣤⣶⣾⣽⠿⠛⠉⠁⠀⠀⠀⢀⡏⡾⠀⢰⢇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣩⣭⣤⡴⠤⠤⣤⣤⣀⡀⠀⣸⣹⠃⢠⡏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⢉⣩⣤⣴⣤⣤⣤⣤⣈⡙⠛⢳⣯⣏⠀⡞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢁⣠⣶⣿⠿⠛⢻⠀⠘⣿⡄⠰⠛⠛⠳⣾⣼⠛⡿⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢁⣶⠟⠉⠀⠀⡄⠀⠀⡃⠀⠀⠀⠀⢀⣀⣰⣿⠟⣿⣻⠟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⣿⡯⠥⠴⢖⠙⠑⠀⠀⠠⠀⠀⠒⠋⠀⠀⣿⣽⢠⢿⡿⢦⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡿⠁⠀⠀⠀⠨⡀⠀⢈⠀⠀⠀⢀⢀⣠⡀⣰⣿⣏⣿⡟⠀⣠⣆⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣾⣷⡶⠖⢏⠁⠀⢀⡤⠘⠂⠀⠈⣹⣆⠀⣻⣿⣿⣽⣿⠋⠉⠀⠙⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡷⢦⣿⣁⠀⠀⠼⢄⠀⠈⡅⠀⢀⣠⡴⣼⡟⠀⢸⣿⣽⡿⠁⠀⠀⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣿⠟⠃⠀⠀⠠⠀⠒⠋⠉⢠⣣⡾⢻⣇⠀⠻⠇⠛⠓⠚⠁⠀⢱⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣧⡄⢹⠊⠛⠠⠀⠀⡀⢀⠤⠠⠘⢿⡄⣰⣿⠀⠀⠀⣀⣤⠴⠆⠀⠀⣿⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡄⢷⠀⢃⠀⠀⠀⠀⢀⡀⡀⠈⡿⠼⠟⠓⠉⠉⠁⠀⠀⠰⡀⢠⠇⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⡄⠣⠈⠤⠰⡖⠉⠙⢃⠀⠀⢷⠀⠀⢀⣀⡤⢸⡄⠀⠀⡏⠉⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡑⠀⣀⣀⠀⠀⠠⡞⠂⠚⠁⠀⠀⠹⠁⠀⣇⢀⠐⢡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣆⠀⠙⠷⣤⣀⣷⡐⠒⠀⣤⢄⣾⡴⠶⢛⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣍⣉⡁⠈⣉⣉⣉⣤⣴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣀⠤⢖⣚⣿⠭⣝⣛⡒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣄
⠀⠀⠀⠀⢀⡴⣫⣵⡎⠡⣄⢂⡅⠘⠉⠈⠙⠂⢝⠦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣙⠦⣑⢄⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⢠⢎⡜⠀⣰⣽⠶⢦⠰⡌⠀⠀⠀⣀⡀⠀⣷⡝⣆⠀⠀⠀⠀⠀⠀⠒⠒⠒⠺⠷⣮⣿⣿⠟⠁⠀⠀⠈⢻⡿⡿⢡⠆⠙⠉⠑
⠀⠀⢀⡏⣾⡗⠀⠃⠀⠀⣼⡏⢿⣦⣄⣀⣀⡠⢺⡿⢻⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣰⣿⣿⡏⠀⠀⠀⢀⡀⠀⣿⠦⠼⡀⠠⠀⣔⢰⣄
⠀⠀⢸⠃⡏⠁⠀⠀⣴⣋⣋⡏⢻⡤⣮⣿⡏⠀⠀⠀⠀⠇⣧⠀⠀⠀⠀⠀⠀⠀⠀⣧⡻⣿⣿⣿⣾⣧⣾⣿⣶⠟⠀⠀⠀⢹⣤⣼⡶⢏⡜
⠀⠀⠸⡄⣿⣿⣀⣴⡿⣿⡯⢜⡾⣇⣾⣿⠃⠀⠀⠀⠀⡆⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣮⣭⣿⣛⣛⣛⣛⣓⣂⣀⣀⣮⣭⣵⣾⣿⠁
⠀⠀⠀⢧⠹⣿⣿⣿⣯⣟⡶⣶⣿⣿⣿⣇⢀⠀⠀⢀⡸⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠳⡝⢿⣿⣧⣿⣶⣿⣿⣿⣿⣿⣼⣀⣤⢟⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠲⣍⡳⠽⣿⣿⣿⣿⣿⡿⢟⣫⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣭⣿⣿⣿⣿⣭⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠲⠶⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣲⣦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⢶⠓⠐⠀⠉⡡⢛⠀⠢⣄
⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠥⡀⣰⣄⣀⢄⡀⠀⠀⠀⠀⡠⣐⡈⠠⠖⠛⠉⠀⠙⣶⣶⡞⠃⠀⠀⢀⣤⣀
⠀⠀⢀⢰⣿⡿⣿⠿⢿⣿⣻⣿⡿⢿⣿⡿⣿⠿⢧⡀⠊⠉⠉⣿⣿⣦⠂⠀⠀⠐⠋⠉⠇⠀⠠⠤⣤⣴⠞⠉⠀⢀⠀⣀⣠⣼⡿⢻⠄
⠀⠀⠀⠑⢽⣻⠏⢀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣆⠀⢀⡠⢿⣻⠕⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠣⠤⠄⠀⠶⢭⣭⣽⣯⠭⠞⠃⠀⡠⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠯⠭⢭⣿⣶⣶⣶⣮⡤⠥⠭⠗⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠤⠀⠠⠤⠤⠤⠈⠁⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠛⠛⠻⠛⠸⠚⠀⠸⠜⠗⠪⠟⠛⠟⠃
⠀⠀⠀⠀⠀⠀⢀⣀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠐⠂⠑⠜⠣⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣿⣿⡷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⡀
⠀⠀⠀⠀⠀⣤⣮⡿⡿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⢼⡎⠳⢴⣤⡄⢳⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⣋⣻⣾⠏⠕⢀
⠀⠀⠀⠀⠈⠚⠓⠟⠛⠋⠿⠛⠡⠒⠂⠀⠀⠒⠛⠻⠳⠿⠿⠷⠲⠟⠛⠓⠂⠀⠀⠀⠀⠈⠙⠊⠀⠛⠛⠓⠐⠛⠋

⠀⠀⠀⠀⠀⢠⣶⣖⢶⡗⡖⡶⣄⠀⠀⠀⠀⠀⠀⣄⣤⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠯⣤
⠀⠀⠀⠈⠁⠞⠸⣼⡜⠟⠧⠃⠛⠟⠁⠀⠀⠀⠀⠄⠌⠀⠨⠃⠀⠉⠉⠀⠀⠤⠀⠀⠄⠘⢄⣤⣤⣤⣄⣁⣀⣌⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠛⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⡆⠀⣰⠒⣦⣟⡛⠓⠛⣷⣴⠁⠀⣤⣄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡗⢦⠄⠘⠿⠞⠁⠀⠘⠶⢿⣿⣷⣤⣶⡿⠋⠀⠀⠹⣿⠞⠀⣰⡀⠒⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢠⡄⠀⢤⡀⢤⣤⠶⣦⢤⡴⢤⡤⣤⢤⡖⣶⣠⢤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡎⡌⡆
⠀⠀⠀⠀⣦⡭⠼⠀⠚⠀⠒⠠⠼⠷⠞⠧⠽⠧⠽⠁⠸⠄⠃⢀⡤⠒⢒⣶⣦⣄⠀⠀⠀⡀⠀⠀⠀⠛⠁⠀⠀⣤⢄⢀⡀⣀⡀⠀⠀⠰⡷⠁
⠀⠀⠀⠀⡛⡷⠀⠀⠀⠀⠀⢀⣠⢔⣶⣲⠠⢤⡀⠀⠀⣀⢀⢋⣤⠀⣾⣿⣿⣿⣷⡀⠘⠿⠿⠯⠭⠭⠭⠭⠭⣽⡟⣿⣿⣿⣷⣐⡐⣦⢸⣠⠊⡆
⠀⠀⠀⠀⡇⣵⠀⣏⡭⠥⠭⣝⣚⡅⠀⣀⢨⠟⠁⠀⠀⠋⠸⡀⠁⠀⠘⠿⣧⣤⣿⡇⠀⢶⣶⣗⣀⣈⣀⠀⠠⣿⣧⣿⣿⡿⡷⠶⠶⠆⠀⢻⡧⠃
⠀⠀⠀⠀⡿⣏⠀⠈⢆⣀⡀⠀⡱⠗⠘⠋⠁⠐⠂⠀⠀⠀⠀⠑⢤⡀⠀⢀⣽⣿⠟⠁⠀⠀⢀⠀⠀⠀⠀⢀⠀⢸⣸⢸⣿⡙⡖⠀⠀⢠⠒⢬⡄
⠀⠀⠀⠀⣧⡾⠀⠀⠀⠑⠒⠊⢁⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡈⠉⠉⠉⠀⠀⠀⠀⠤⣼⠆⣔⠰⠦⡾⠀⣣⡁⢸⡄⣿⠃⠀⠀⠈⠂⠽⢧⡖⢲
⠀⠀⠀⠀⡏⣻⠀⠀⠈⠁⠀⡜⠁⠀⠈⠑⠀⡴⡟⠀⠀⢈⡀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⡠⠤⡀⠀⠈⣿⠀⣿⣾⠀⠀⠀⠀⠀⠀⣿⠧⠊
⠀⠀⠀⠀⡇⠷⡆⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⣱⠟⣇⣠⢿⠶⠖⢧⣀⣾⢁⡴⣇⣀⠾⣅⣠⠖⠀⠀⢇⠀⠹⡄⠀⠃⠀⠁⢙⣆⠀⠀⠀⡵⠀⠣
⠀⠀⠀⠀⡇⣪⡀⠤⢤⣶⠄⠳⠤⠴⠚⠁⠀⠁⠀⢈⡁⠀⠀⠀⠀⠁⠀⠁⠀⠉⠁⢀⠀⠀⠀⠀⠀⠀⠑⢄⢣⡀⠀⠀⠀⢸⡇⠀⢀⣰⣦⣄
⠀⠀⠀⠀⢣⣶⡁⠱⣤⠟⠀⠀⠄⠀⠀⣀⡄⠀⠀⠘⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⡰⡏⡛⡖⢤⣠⣀⣀⡀⠀⠱⡑⣄⠀⠀⠘⢣⢊⣿⢁⣿⢸⣿⠢⡀
⠀⠀⠀⠀⠨⡚⠁⠀⠀⢀⡀⠀⠀⢀⣼⠋⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⡴⢾⣥⣤⣀⠈⡴⣿⣟⠻⡟⠳⣦⡈⢮⣷⡄⠀⢈⢸⣿⢸⣿⢸⣿⠀⡔
⠀⠀⠀⠀⠘⠚⠀⠀⠀⡄⣿⡀⠀⣾⠗⠊⣀⣀⡩⠉⠙⠛⠓⠀⠀⢠⢾⠊⢰⢱⠻⢸⠑⡙⡇⠂⠀⠁⢸⠀⠀⣽⠀⠑⠚⠀⠈⠙⠻⣼⣧⠾⢛⡋
⠀⠀⠀⠐⠀⠰⣶⡀⣸⠇⣸⣧⠞⢶⣌⡉⠀⠉⠻⢶⣤⣄⠀⠀⠀⠸⣮⡀⠸⣄⠀⠘⠀⣡⠗⠤⠤⠔⢃⣀⣸⠏⠀⡀⠠⢀⠀⠀⠀⢸⠁⠀⠈⠂
⠀⠀⠀⠀⡀⠀⠈⢿⣞⠋⠈⣿⠀⠀⠉⠻⢦⣀⠀⠀⠀⠉⠁⠀⣠⣄⠙⠷⢶⣄⣩⠭⣉⠠⣄⣀⣴⣤⠟⡻⠁⠀⠀⢰⢸⠈⠆⠀⠀⠰⠃
⠀⠀⠀⠘⣧⡀⠀⠀⠙⣧⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠞⢏⣿⠂⠀⠀⠉⠙⠙⠛⠛⠛⠛⠉⠉⠁⡤⣄⢀⠴⣄⣀⢄⡀⠀⠀⠀⠀⢮⣷
⠀⠀⠀⠀⠙⣷⡄⠀⠀⠈⢦⡀⣅⠀⠀⠀⣠⣴⡶⡶⢻⣧⠀⠈⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠛⠀⢀⣤⣧⣾⢡⡞⢡⠙⣦⢹⣊⣦⡀⠀⣾⡽
⠀⠀⠀⠀⣠⡞⠛⠒⣄⡀⠈⢷⣿⠀⠐⠋⠁⢀⠜⠀⠸⣿⠀⠀⠀⢠⣿⠀⠀⠀⣼⠆⢰⡆⠀⠀⢰⢻⢧⣟⡿⢿⢇⣊⡴⢫⣾⣙⠁⠙⡄⣎⠘
⠀⠀⠀⢠⡿⠁⠀⣴⡟⠉⠒⢌⣿⡇⠀⠀⢠⢾⡆⠀⠀⠻⠀⠀⠀⠘⠷⠀⠀⠀⠻⠀⠸⡇⠀⠀⠘⢎⡈⠻⣿⣿⠾⡏⢙⢻⠧⠴⢃⡴⢁⡜⢑
⠀⠀⠀⠸⠁⠀⢰⢏⡀⠀⠀⠀⠹⣧⠀⣠⠃⢾⣧⠀⠀⠀⠀⣠⣴⣶⣞⡟⡟⣹⢿⡻⡻⡲⢶⣄⡀⠀⠻⣷⣾⣯⠤⠬⢲⣷⣶⡾⠏⠀⠈⣩⢂⡀
⠀⠀⠀⠀⠀⠀⠙⠘⡄⠀⠀⠀⠀⠻⣶⡇⠀⢸⣿⠀⠀⣀⠀⣷⣷⡿⡻⢾⣰⡛⣧⠹⣵⣵⠙⣼⣷⠀⠀⠀⠀⠉⢉⡉⣭⣥⠤⢄⣀⠀⠀⢷⣾⡇
⠀⠀⠀⠀⠀⣀⣤⢾⡷⣤⣀⠀⠀⣀⢹⣷⠀⢸⡏⠀⠈⠃⠀⣿⣻⣿⣟⣛⣳⣶⣾⣷⡿⠷⢿⣯⡿⠀⠶⠀⢀⡔⢁⣈⣁⡀⠀⢀⡝⠀⠀⢟⡩⡇
⠀⠀⠀⢀⠞⣽⡇⢸⡇⢹⣏⢣⠀⢸⡆⢿⡇⠈⣇⠀⠀⠀⠀⢹⣷⣤⣓⠚⠛⣄⣠⠞⠲⢤⣧⣼⠃⠀⠀⣀⠔⠉⠁⠀⠀⠀⠀⢙⣦⠀⠀⣴⡿⡃
⠀⠀⠀⠘⢆⣿⣧⢸⣿⢸⣟⡸⠀⢸⣷⠘⣧⡀⠈⠀⠀⠀⢠⢆⠹⣌⡙⣛⣛⣛⣒⡛⠛⣋⡽⠃⢀⠀⠀⠛⠢⠬⠥⠤⠭⠤⠔⠊⠀⢠⡀⢱⡄
⠀⠀⠀⠀⢀⡍⠉⠾⡿⠏⠁⠀⠀⠀⣿⡄⢸⣇⠀⠀⠀⠀⠀⠑⠀⠀⠙⠻⠿⣿⣿⡿⠏⠁⠀⠀⠈⠀⢀⡀⢀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣱⣗⠁
⠀⠀⠀⠀⠀⠁⠀⠀⡼⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡡⢤⠟⣜⣧⣸⣯⢹⣇⢹⠐⣂⣖⠠⢍⠰⠂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖⠖⠊⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠐⠂⣠⣄⠀⠀⠀⢀⡀⠀⠀⠀⣠⠤⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⢫⡀⠀⠀⡘⠀⠀⠀⢸⣦⣄⠠⠂⠄⢶⣆⠛⢶⢒⡀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⡴⠃⠀⠀⠀⢃⠸⣹⠗⠚⠿⡭⢿⡟⡳⠵⠏⠅⠃
⠀⠀⠀⠀⠀⠀⠀⣤⡾⣦⣼⠿⠶⠂⠀⠀⠀⠀⠀⠀⠀⣨⠉⠀⠙⣧⡀⠀⠐⢄⣀⠀⠀⠀⠀⠀⢠⣾⠍⠁⠀⠀⠀⠀⠀⠑⢄⠈⠉⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠘⠃⠀⢸⠛⣤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠼⠁⠁⠀⠘⠋⠹⠀⠀⢀⠙⠿⠒⢺⡿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠠⠄⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠴⠶⠲⠖⠒⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢀⠀⢠⣁⡤⢤⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠈⣉⣲⡎⢡⡈⣦⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠂⠐⠚⠻⡷⠂
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠰⡀⠀⠈⠣⡀⠀⠀⠁⠈⠓⠂⠐⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠰⠶⠎⠀⢠⠄⠼⠦
⠀⠀⠀⠀⠀⠃⢚⣦⠀⠀⠀⡀⠀⠀⠑⣄⠀⡀⣠⡞⢂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⡙⢋⡿⢥⣾⣶⢶⠀⣄⡀⠘⠃⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⡈⢷⣄⣴⣼⣦⣶⠶⠛⠛⠋⢉⠁⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠫⠃⣤⢶⣾⣿⠤⠀⣨⠂⠀⠀⠀⠀⢁⠅
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘⠉⠉⠤⠤⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣴⡆⠀⠀⠀⠀⠀⡀⠴⢦⡞⠀⣀⣠⣿⣇⡏⠃⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⡷⡀⠀⠀⠀⢈⡀⠀⠀⠀⠈⠑⠚⠟⠏⠁⠀⠆⠀⠀⠔
⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⡘⠁⠀⠀⠀⠀⠈⠑⠦⣄⡀⠌⡠⠀⠀⠀⠘⡠⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠉⠒⠟⠁⠀⠀⠀⠀⠂⠀⠀⠠⢠⠆⠀⠈⣡⡶⠦⠴⠀⠀⡈⠀⡀⢉⣉⣀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⡀⠐⢈
⠀⠀⠀⠀⠀⠒⠶⠀⠴⠒⠃⠀⠀⠤⠀⠀⠙⠛⠍⠀⠀⠀⠀⠀⠀⠳⣀⠂⠐⠄⠀⣰⣬⠉⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡠⠀⠀⠀⡄
⠀⠀⠀⠀⢀⡤⠖⠊⠉⠈⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⡀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠐⠒⠂⢈⣁⠤⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠲⠇⠀⠀⣠⡇
⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢀⡀⡀⢀⢀⣀⣀⣀⢀⡀⠙⢷⡄⠀⠀⠀⢨⣤⠤⠶⠖⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣿⡦⠤⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⢘⢡⠁⠀⣀⣠⣔⢾⣟⡉⠛⣼⡶⡬⢉⡀⢈⣁⣤⠿⡿⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠈
⠀⠀⠘⣧⡀⠸⣟⡶⣴⡦⣮⣙⡋⣿⠟⢋⣈⣉⠉⣭⣷⣴⠃⠀⠀⠀⠀⠀⠉⠉⢀⡄⠀⠀⠀⣦⡀⢀⡠⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⢉⠓⠿⣬⣅⠶⡄⡻⠟⢛⣚⠉⣩⣽⠶⠟⡡⠀⠀⠀⢠⠀⠁⠀⢀⣠⠀⠀⠀⠈⠀⣹⠀⠀⠀⠀⣀⣀⠀⠒⠀⠀⠀⠀⠀⡀⠀⠀⠈⠱⣤⡄⠠
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠉⠙⠛⠉⠉⠉⠀⢀⡀⠐⠁⠀⢀⡀⠈⠓⠄⠀⠀⠉⠒⠀⢀⣤⠴⠛⠀⠀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠢⠀⠄⠀⠀⠤⠤⠶⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠉⠉⠐⠋⠉⠙⠲⡀
⠀⠀⠀⠀⢀⠔⢚⠛⠉⡉⠩⠙⠢⡀⠀⠀⠋⠀⠀⠒⠀⡀⠀⢀⠟⠀⠡⠀⢀⣸⡚⠠⠄
⠀⠀⠀⠀⠋⢀⣼⠏⢠⠁⣠⣤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⡄⡀⡠⠈⢻⣷⣵⣔⡀⠒⠀⠀⠙
⠀⠀⠀⠀⠀⠘⠻⣄⠀⢠⠏⠁⠀⠀⡼⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣠⠇⠀⠀⠙⣿⣧⣁⢀⠀⠤⠀⠒
⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠙⢷⣄⡀⠀⠀⠀⠀⠀⡀⠖⠋⠀⠀⠀⠀⠈⠙⠛⠈
⠀⠀⠀⠈⠳⠦⠀⠀⠀⠀⢀⡤⠋⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⡠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⣄⠐⠲
⠀⠀⠀⠀⠀⠀⠐⠒⠀⠛⠺⡆⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢴⡀⠒⢯⠤⠄⠂⠀⠈
⠀⠀⠀⠀⠀⢀⠀⠲⠄⠐⠋⠀⠀⢀⣀⣀⡈⢡⠴⠂⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠀⣀⠔⠚⠙⠀⠀⠐⠀⠄
⠀⠀⠂⠐⠒⠋⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠉⠙⠒⡤⠒⠉⠈⠉⢀⣤⡀⠀⠀⠀⢴⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠠⠤⠤⠖⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠛⠉⢀⣴⣦⢄⣠⣄⣀⣐⡒⠒⠒⠿⠗⠉⠔⠈⢠⠀⢄
⠀⠀⢀⢔⣪⡶⠶⣶⠶⣶⣤⣄⠀⠀⠀⠀⣠⣤⠿⢯⣽⣿⡻⣿⡟⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⢡⣾⠛⢷⣤⣼⣦⣼⠉⠹⣿⡄⠀⠈⠇⠀⠀⠀⠀⠹⡿⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣾⣿⡦⠐⠻⣷⣶⡀⠤⢆⣀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠒⡀⠀⣠⣩⣤⣄⠀⠄
⠀⠀⢻⣿⣷⣠⣆⣿⠋⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⣰⡾⠁⠀⠁⣤⠭⡤⢉⡐⠓⠂
⠀⠀⠀⠙⠿⣿⣏⠉⠓⣤⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠙⠅⠀⠴⠟⣿⣖⠹⢃⢶⡶⠂
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠋⠁⠀⠉

⠀⠀⢀⠠⠄⠒⠒⠒⠂⠉⠉⠉⠉⠉⠉⠛⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠄⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠠⠤⢤⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⠈⠀⠀⠶⠤⠀⠑⠀⠀⠀⠀⠀⠀⠒⢄⡀⣄⠀⠀⠀⠈
⠀⠸⠦⣗⣤⣀⡀⠁⠀⠀⠀⠈⠁⠔⠌⠀⠁⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠔⠀⣈⡀⠒⠄
⠀⠀⠳⣤⡁⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢀⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠅⠐⠀⠄⠀⠤⣭⡀
⠀⠀⠀⠙⠬⡉⠓⠒⠂⠀⠀⠤⠤⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠅⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠤⠄⠓⠦⠤⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠤⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣂⠠⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠻⠟⠓⠚⠛⣁⣽⡚⠓⠂⠔⠞⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢄⠀⠂⠀⠀⠀⠀⠀⠀⢸⣷⠇⠐⢀⡀⡐⡈⠁⠐⠮⠀⠉⠉⠉⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈
⠀⠀⣶⠬⢵⠒⠀⣧⡀⠀⠒⠲⡉⠙⣒⠆⡀⠀⠀⠀⠐⡀⢉⠀⠈⠉⠉⠩⠙⠉⠁⠀⡀⠀⠰⠄⠀⠀⠀⠀⠀⠰⠂⠄
⠀⢰⡛⡷⡜⡓⠤⡈⠙⣀⣉⣀⠑⢤⡘⣅⡥⢀⡀⠀⠀⠱⡄⠤⠄⠀⠀⠀⠀⢀⠀⠀⠡⠂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌
⠀⠈⠹⢷⣯⣻⢟⣙⢣⡩⡄⣘⣅⢐⡉⠉⠙⢂⢤⠀⠀⠀⠈⠒⠀⢀⡀⠁⠀⠈⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠘⣿⣨⣙⣃⠻⡞⠀⠈⠁⠐⠒⠉⠅⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠹⢿⣏⠊⢡⡄⠃⠚⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡅⣢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡉⠀⠀⠀⠀⠀⠈⠉⠙⠒⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣙⣦⣀⣀⣀⣀⣀⣀⡀⢀⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠠⣀⠐⢦⠠⢠⡀⠀⠀⠀⠀⠀⣄⢹⠛⢻⠛⠛⠒⠖⠋⢉⠵
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠤⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⢀⡄⠒⠒⠀⠉⠀⣀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠜⠦⠤⠲⠦⠒⠁
⠀⠀⠀⠀⢀⠀⢀⣠⡤⠄⢈⠉⢉⠙⢻⡿⠟⠳⠀⠉⡄⠀⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠘⡒⠶⠶⠄⠋⠉⠉⠩⠠⠼⠼⠶⠆⢀⠀⠆⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣠⢤⡴⠿⣿⠾⢧⠭⣬⣁⣐⡂⢄
⠀⠀⠀⠀⠀⢀⠙⠒⠂⠤⠤⠤⠤⠤⠀⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢮⡉⠋⠙⡇⢐⣀⣀⣀⢢⣀⢚⠉⠏⢸
⠀⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡨⢤⣁⣈⡀⠉⣧⣘⣁⡀⠹⢅⡀⡐
⠀⠀⠀⠀⠀⣀⠀⠀⠈⠐⠆⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣌⠐⠀⢀⡀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠨⠤⠴⢦⢤⣤⣤⣈⣁⣀⣀⣀⣀⣀⣀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠛⢯⣅⣂⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁
⠆⠀⠀⠐⠀⠠⠤⠤⠀⠀⠀⠀⠉⠉⠉⠀⠈⠉⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠄⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠠⣿⠿⠷⣛⣣⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠈⠀⠐⠐
⠀⠀⠉⠂⣄⣀⢀⣀⣀⣄⠀⠀⠉⠓⠚⠋⠉⠁⠀⠀⠀⢀⣾⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠉⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠉⠀⠀⣀⡰⠤⠐⠀⠀⢀⢀⣤⣦⠄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄⣀⠀⠀⠄⠀⠀⡠
⠀⠀⠀⠤⢀⠀⠀⢀⡤⠀⣆⣀⣠⡤⣀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠡⠀⠀⠀⠀⠀⠀⠿⠞⠀⠀⠀⠀⠀⠀⠀⠙⢼⣬⠞⣧⣧⠀⢀⠀⠊
⠀⠀⠠⠄⠀⠀⠐⠿⠴⣶⣤⣤⣽⠷⠦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠘⠂⠼⠆⢰⡤⢀⠄⠠⠀⠀⠘⠿⠟⠀⠀⠀⠀⠴
⠀⢠⠘⠉⠀⠀⠉⠓⢄⠀⢀⡀⠀⠠⡀⠀⠰⣷⡛⠛⡻⣿⠁⠀⠄⠀⠀⠀⠀⠳⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂
⠀⠲⠢⠤⣄⡤⠴⠆⠖⠀⠨⡀⠀⢀⡈⠀⠀⠙⠿⣽⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣴⣶⣤⣴⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡆⠠⠈⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣤⣠⣤⣄⣄⣀⠀⠁⠀⠀⣀⣠⣤⣤⣤⣀⢀⠀⠀⠀⢀⠴⠀⠂⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠺⠿⠿⠟⠯⠿⠟⠟⠀⠀⠀⣈⠉⠉⠛⠛⠋⠛⡋⠀⠀⠀⠀⠀⠀⡀⣀⣤⡤⠀⠀⠀⠇⠁⠤⣀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⡀⠀⠀⠀⠺⠉⠀⠀⠀⠀⠀⠋⠉⠉⢰⠋⡓⠀⠀⠀⠑⠂

⠀⠀⢠⡊⢀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠨⠁⢺⡍⠃⣑⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠂
⡀⢀⠲⠁⠠⠀⠀⠀⠀⠚⠉⠀⠀⠀⠌⠀⠀⠑⠛⠋⠀⠙⠁⡀⠆⢀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠺⠉⠑⠂⢄
⠁⠂⠐⠊⠀⡀⠀⠂⠭⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠂⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠈⠙⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠆⠛⠛⣰⡄
⠀⠀⠀⠀⠀⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠉
⠰⠦⢒⢄⠄⠀⠒⠤⢄⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠒⠊⠺⠥⠼⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⣤⠐⡀⠀⠀⠈⠀⢁⠀⠀⠀⠀⠰⠌⠂⠀⠀⢀⢡⡀⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢠⠠⠂⠀⠀⣀⠂⠀⢰⡀⠐⠄⠀⡸⠀⢀⡇⢀⡜⠀⠈⣆⠀⢸⠆⠃⡀⠀⠀⠀⠀⢀⠁⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠀⠄⡁
⠀⠀⠀⠀⠀⠐⠶⠄⠀⠀⠀⠀⡄⠀⠀⠀⡀⣠⠀⠓⡄⠀⠀⡠⠈⠲⠀⠀⢀⣉⠑⣆⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠛⠀⠀⠇⠀⠀⡇⠀⠀⠆⠀⠈⠂⠀⠸⡀⠀⠀⠐⢊⡉⠠⠄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢆⠀⠀⠃⠀⠀⢇⠀⠠⡀⠀⠀⠢⠀⠀⡂⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶
⠀⠀⠀⣠⢀⠀⠈⠑⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡴⠿⠟⠛⠉
⣀⣈⣴⡟⠀⠀⢀⠀⠄
⠛⠋⠁⠀⠀⠈⢀⠀⠠⠄⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠤⢤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⡤⠠⠤⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠠⣀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜
⠀⡀⠀⠀⠀⡾⠀⠀⠀⠀⠈⠁⠀⠀⠰⠀⠐⠀⠀⣼⠀⠀⠀⠀⠀⠙⠀⠀⡠⠜⠂⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⢀
⠐⢢⣤⣁⢀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⣠⡤⠐⠁⠀⠀⠀⠀⠀⠘⠻⠟⠋⢀⣀⣠⣶⣾⣯
⠀⠈⠛⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⣀⠄⠉⢠⡒⢦⠟⠻⣉⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣋⣧⠿
⣀⣀⣈⣀⣀⣁⣀⣀⣀⣒⣀⣛⣀⣀⣨⣀⣀⣀⣀⣀⣀⣈⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣻⣿⣿⣍⣐⣋
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢠⡦⡠⢀⠀⠀⠀⢀⡠⠄⣒⣶⣶⠒⠠⢀⠀⠀⠀⢠⠤⠴⠴⠖⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢄⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠈⠡⠇⠰⠈⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠀⠄⠁⠀⠀⠸⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣯⣉⣩⣩⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻
⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⣄⠠⠤⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⣬⠇
⠀⠀⣠⡼⠁⠀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣶⡶⠃⠀⠀⣺⠃⠀⠀⠀⠀⣠⡾⠃⠀⠀⠄⢤
⠀⣴⠏⠀⠀⡀⡞⢡⠈⣲⡄⠀⠀⠀⠀⢤⣀⣀⣉⣴⣇⠀⠀⠀⠀⠀⠛⠿⣿⣿⠟⠀⠀⠀⠉⠀⠀⠀⠀⣰⡏⠀⠀⡈⣞⠡⠬⣓⡄⠀⠀⠀⠀⢠⣀
⠈⠃⠀⠀⠀⣿⣷⣗⠛⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣷⠛⣻⡇⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠻⠿⠿⠶⠟⠁⠘⣷⠀⠀⠀⠉⠉⠉⠁⠀⢀⠠⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠶⠟⠁⠐⢳⡀⠀⠀⠉
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⣶⣌⣐⣐⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢿⣉⣿⢏⠉⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡦⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⡐⠐⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠘⡧
⢀⣙⣁⡴⠀⠀⠀⠈⢻⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠣⢾⡀⠀⢸⡇⢩⣿⡿⢛⡄⠔⠀⠀⠀⠀⠀⠰⣄⣀⣘⣃⣤⠀⠀⠀⠀⠻⡄
⢸⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠳⠈⠀⠀⠙⠾⠿⣇⡂⢠⠍⡕⡀⠀⠀⠀⢠⣾⣿⣿⣿⣷
⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣳⣾⣿⡇⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠿⢿⡿⠿⠃
⠀⣀⠀⣀⠐⠛⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠁⠱⣆⠢⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠛⢀⠄
⢀⣉⡔⠛⣋⡙⢣⣀⡙⣃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢇⠀⣉⠉⢘⣂⠀⠀⠀⠀⠀⠀⠀⣀⡐⢠⣀⣉⡡⠛⢋⡙⠻⣀⣈⣋⣰
⠈⣭⡁⢠⣬⣤⣾⣿⣭⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠙⠀⠀⠀⠀⠀⣷⡤⣬⣤⠐⠋⢩⡁⠠⣤⣤⣾⣿⣭⣿⡿
⢠⣧⣴⣿⣿⣿⠟⠈⠉⠁⠀⠀⠀⠀⠀⠀⣄⡐⠊⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣾⡟⣶⣤⣤⣴⣞⣿⣿⡿⠈⠉⠁⠀⠀⠀⠀⠀⠀⣤
⢸⣿⡿⠏⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠉⠉⠙⢿⣿⣿⡿⠟⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢼
⠀⠁⠀⠀⠀⠀⠀⣐⠷⢕⢄⡀⠀⠀⢀⠤⢘⣛⣻⣛⣛⡀⢄⡀⠀⠀⠰⠖⠶⠶⠒⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢷⠖⠤⡀⠀⠀⢀⠤⢈
⠀⠀⠀⠀⠀⠀⠈⠰⠃⠘⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠆⠁⠀⠀⠸⣿⣿
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣦⣉⣱⣤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳
⠀⠀⠀⢠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⠀⣄⠀⠄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢠⣼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⣀⣀⣀⣀⣀⠈⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⡤⠊⠀⣠⡴⣊⣩⣭⣤⣶⣦⢬⣭⣳⣤⡀⠈⠳⣄
⠀⠀⠀⠀⢠⡞⠰⣶⣾⢽⠟⣿⠅⠀⡇⠆⢘⠀⠈⢹⠘⢿⣦⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⢀⡟⠀⣸⣿⢿⣜⢀⣻⡀⠀⡇⠀⢸⡀⠀⣌⠀⢈⠁⣷⡀⠘⣇⠀⠀⠀⠀⠀⠀⣠⠏⠀⣸
⠀⠀⠀⢸⠇⢠⣿⡿⡿⡿⠣⣓⠵⠜⢰⣔⣿⠦⣠⣬⣧⣬⢘⠈⣧⠀⢹⠀⠀⠀⠀⢀⡴⠃⠀⢠⡏
⠀⠀⠀⢸⠀⠘⣿⠁⡜⠀⠀⡇⠀⢸⠉⠀⡟⠋⠉⡛⠉⣿⠘⠃⠰⠀⢸⡆⠀⣠⠔⠋⠀⠀⠀⢸⡃
⠀⠀⠀⠸⡆⠀⣿⠀⣇⠀⢸⠁⠀⢯⠀⠀⡷⠀⢰⡄⠀⡌⢀⡀⠆⠀⣸⢃⡞⢁⡤⠒⠒⠢⡀⢸⡇
⠀⠀⠀⠀⢻⡀⠈⣷⣰⣴⣾⣂⢺⣿⣦⣾⠿⠶⣾⣼⣷⣗⣽⡰⠀⣰⡿⣼⠀⡎⠀⠀⠀⠀⠠⠀⡇
⠀⠀⠀⠀⠈⢳⡄⠈⢏⠈⣿⠷⢛⣫⣤⡶⢶⣶⢶⣶⣦⣅⡛⢷⢶⡿⠁⢻⡀⠣⡀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠙⢦⣠⠟⣡⡾⠛⢻⠃⠀⣜⠃⠠⠉⠠⠇⠘⠒⢝⢻⣷⡀⠻⢤⣈⣀⢀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⣸⠋⣼⡿⠀⣠⠓⠄⡈⠀⠉⠃⠠⢄⠀⠀⠀⠂⠐⡙⣷⡀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢰⠋⣾⢿⡀⠀⠁⠠⢀⣀⠖⠒⠤⠂⢀⡌⠀⡐⠁⠀⢷⠀⣧
⠀⠀⠀⠀⠀⠀⡟⢸⣷⣄⠈⠐⠠⠀⠀⠈⠀⢠⣥⣤⡐⠀⠬⠓⠄⣀⡀⣷⢹
⠀⠀⠀⠀⠀⠀⡇⢸⣇⠍⠀⢠⠀⠀⡰⢴⣶⣷⣞⣋⣻⣷⠦⢤⡬⠀⠝⢻⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠈⣿⠀⢠⡁⠀⠸⢷⣤⢄⡀⡈⠉⢻⠏⠀⠀⠁⠀⣤⡏⣼
⠀⠀⠀⠀⠀⠀⠘⣧⠸⣦⡀⠈⠐⠠⢤⠄⠀⠈⠁⢀⡌⠀⢀⠞⠀⣰⡞⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡙⢧⡲⠀⢠⠊⠀⠠⠃⠠⠞⠀⠀⠉⠑⢲⠞⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣉⠐⠧⠀⠀⠒⠤⣀⠀⣈⡶⠒⢂⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣄⣈⣉⣉⣥⡴⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⠒⠒⢒⠒⠒⠒⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠉⢀⣴⠾⠛⠋⢉⣉⣉⡙⢉⠙⠲⢦⣄⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⡵⠃⠀⣶⡟⠀⢠⡾⠛⠛⣉⣉⣙⡛⠻⣶⣀⠈⢷⣄⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢸⡇⠀⢰⣿⡁⠀⣿⣁⡀⠈⠛⠿⣿⣷⡄⠈⣿⡀⠸⣿⣿⡆⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⣇⠀⢸⣿⡅⠀⠘⠿⢿⣿⣶⣶⣾⠟⠐⢀⣾⡇⠀⠈⣿⣿⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⣿⡤⠀⢻⣿⡄⡂⠀⠀⠀⠉⠉⠀⠀⢰⣿⣿⠃⢀⠈⢧⣿⠀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠈⢿⣾⡁⠀⠻⢿⣷⣷⣶⣤⣤⣤⣶⣶⣾⡿⠃⢠⠞⣼⣿⡟⠀⡂⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠡⡈⢿⣷⣬⡂⢄⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠰⣯⣾⣿⢟⠂⡰⢃⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠈⠀⠙⠿⣿⣶⣦⣌⣢⣤⣀⣰⣤⣤⣦⣴⣿⣿⠟⠋⣠⣾⢇⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠈⠛⠿⠻⠿⠿⠿⠿⠿⠛⠛⠛⣉⠤⠒⠛⠱⣭⢿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠁⠀⠀⣀⢤⡴⣞⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣠⣀⡤⠤⠤⠤⡄⢠⣄⣀⡄⣠⣥⣾⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠤⠔⡈⠉⢭⠅⠀⠀⠉⠉⠙⠒⠒⠂⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠊⠁⠀⢀⠀⠠⠀⣈⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠉⢀⠀⠤⠀⠀⠀⠉⠙⠓⠒⠒⠚⠒⠒⠒⠒⠈⠉⠀⠀⣀⡠⠔⠁⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⢀⠀⠈⠓⠲⠤⢤⣤⣀⣒⣒⠤⠤⠤⠀⠀⠖⠒⠒⠂⠀⠈⠁⠀⠀⠀⣀⡤⠂⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢉⠑⠒⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠤⠐⠚⠉⠀⠀⠀⠀⠀⠀⣀⢬
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠲⣀⠀⠀⠉⠓⠒⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⢷⡀⠠⠃⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠗⠶⠶⣶⣤⡼⠁⠀⠀⠈⢷⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠘⡆⢀⣄⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⢀⡴⠚⠋⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⠃⠘⢻⠁⠀⡞⠉⠉⠀⠁⠙⠓⠤⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⢠⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠸⡆⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠦⠀⠀⢀⣤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠑⠂⠚⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠰⣯⣰⣶⣶⠀⠉⢻⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠻⢿⣧⣀⡀⠀⣀⢀⣀⣤⡾⠃⠀⢸⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣼⣿⠀⢻⣷⢀⠀⠈⠉⠉⠉⠉⠉⠁⠀⡀⢀⣼⡾⠛⠃⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣿⣟⠀⠀⠘⠳⠶⠴⢤⠤⠤⠴⠶⠶⠚⠛⠛⠉⠀⠀⠀⢸⣿⡇⢆
⠀⠀⠀⠀⠀⠀⠈⣇⠈⠀⢿⣿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣿⡿⠃⣾
⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠙⠿⣶⣤⣠⠀⠀⠀⠀⠀⢀⢀⣀⣠⣤⣤⣴⢶⠶⠟⠋⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠉⢻⡆⢀⣀⠀⠈⠙⠛⠳⠲⠚⠛⠛⠛⠋⠉⠉⠁⠈⠀⠀⠀⠀⣶⠟⠔⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡟⠛⢷⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣷⣦⠀⡏⠈⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⢸⠀⠀⢸⡀⣿⠋⣇⠀⣸⣿⡆⠀⣼⡿⠛⠒⠋⠀⠸⡆⢷⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣾⠀⠀⢸⡇⡟⠀⢸⢠⡟⠉⢻⣠⡏⠀⠀⠘⠀⠀⣤⣷⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣮⣽⣠⣧⣠⣼⣿⠡⣤⣼⣯⣅⠂⠠⣴⣾⣽⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠛⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠓⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠁⡤⣄⡀⢀⣠⠤⠔⠒⠐⠀⠀⠐⠀⠂⠤⢄⡀⠐⠠⠍⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⢀⣠⠶⠚⠁⠀⠄⠀⠀⠉⢲⣄⣤⡤⠤⠶⠒⠲⠠⢤⣈⡉⠓⠦⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢊⡠⠞⢹⠃⠀⠂⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⢀⠀⡀⠄⠀⠀⠈⢻⣅⡂⠌⡛⢆⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⣠⠊⣀⡴⢿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠈⠋⡲⠄⠀⠀⡇⠉⠓⢮⣄⠑⢦⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣞⡴⠒⡈⢉⠈⠉⠓⢮⣷⣄⠒⢀⣠⠤⠤⠤⠾⢧⡀⠀⠀⠀⠂⠁⠀⠃⠀⠀⠀⡇⠀⠀⠀⠉⠳⣄⠙⣌⣇
⠀⠀⠀⠀⠀⠀⠀⡼⠋⠰⢀⠍⠙⣅⠀⠀⠀⢹⡾⠋⠁⣀⣰⠰⡄⠀⠀⠈⠲⣄⠀⠀⡀⠀⠀⠠⢀⣼⡥⠤⠤⢤⣀⠀⠈⢢⡈⣿
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠀⠀⠈⠁⠀⢀⡎⠀⠀⢡⠊⡠⢠⠀⠀⠆⠀⠀⠘⡟⠶⠶⠆⡴⠚⠉⠀⠀⠀⣀⡀⠀⠉⠢⡀⠑⣽
⠀⠀⠀⠀⠀⠀⢸⢿⡄⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⣯⡀⢠⡿⠁⠀⠠⠐⠂⠀⠛⢇⠂⠀⠀⢰⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣼⠉⠲⢤⣄⠀⠤⠴⠋⢁⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠒⣾⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⢸⡏
⠀⠀⠀⠀⠀⠀⢈⡻⡆⠀⠀⠀⣀⡤⠶⠟⠛⠛⠛⠶⢤⣀⣀⠀⢀⣠⣴⠶⠟⠐⠂⠙⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⠏⡆
⠀⠀⠀⠀⠀⠀⠈⡅⠹⣄⢠⠊⠁⣤⣖⠀⠀⠀⠀⠀⠀⠹⡽⣻⡿⠋⠀⣀⣀⡤⣤⠧⠀⠀⠈⠳⣦⣄⣀⣂⡀⢀⡠⠔⢁⡎⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣄⠘⢇⡰⠁⠉⠁⠈⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⣠⠶⠾⠶⢍⠒⠀⠀⣿⠉⢉⠭⠉⠁⠀⣠⠎⣰⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠸⡘⢆⠈⢣⡀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠏⠆⠀⠀⠀⠈⠀⠀⠀⡰⠀⠇⠀⢀⡟⠀⠀⠀⠀⢀⠔⢁⡴⠋⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠳⡀⠙⠦⣄⡀⠀⠀⠀⣀⡴⠋⠀⢿⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⣠⠞⠀⠀⢀⡠⠞⢁⣰⠟⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠈⠂⢄⠈⠛⠿⣟⠋⠁⠀⠀⠀⠈⠳⣔⡀⠀⠀⠀⠀⣀⣴⠞⠃⣀⠤⠖⠋⢀⣴⠟⠁⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⢑⠢⣀⠀⠉⠓⠲⠤⠤⣀⣀⣀⣉⣙⣛⡿⠿⠿⠓⠊⠉⠀⣀⣠⠶⠋⠅⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠉⠛⠶⠤⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣤⠴⠶⠛⠋⠁⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣀⡀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣠⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⡟⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⡁⠀⠀⡇⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢚⡭⢀⣼⣿⡏⠀⢀⣇⠀⠀⠀⠾⣥⣌⣙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠐⢋⣀⣤⠭⠷⠒⠋⣽⠻⡏⠛⠒⠶⢤⣌⣉⡀⠀⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣚⣉⣤⠤⠖⠚⠋⠉⠁⠀⠀⠀⠀⡼⠁⠀⠹⣆⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⣤⣙⡳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠙⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⢠⣤⡼⠟⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣇⠀⠀⠀⣼⠋⢹⡆⣴⠃⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠛⠀⢀⣀⣠⡀⠀⠀⠀⡾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⢹⡀⠀⠀⠈⠀⠸⡿⠁⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠘⣯⣤⠀⠀⠀⢰⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣿⡇⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⡤⣤⡀⠀⠀⣠⣤⣄⠀⠈⢷⡀⠀⠀⠈⠙⠇⠀⠀⠀⡟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣹⠀⢸⡄⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠋⢀⣼⠇⠀⣸⠃⠀⠹⡇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⣿⣿⣙⡆⢷⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣴⠛⠁⠀⠀⢻⡄⠀⢠⡇⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⡏⠀⠀⢸
⢴⣶⣾⡖⢲⣤⣀⡴⠋⠙⢶⣿⠟⠉⠛⣾⣆⣤⣤⣤⣴⣧⣤⣄⣀⣀⠈⠛⠛⠛⠃⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠹⡄⠀⠀⠀⣼⠁⣴⢶⢸
⠈⢳⣿⣿⣶⣿⣿⡄⠀⢀⠈⣿⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢰⠇⠀⠛⣿⢸⠀⠀⠀⢀⡄
⠀⠀⠈⠛⢦⠖⠛⠻⠷⣬⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣾⠀⠀⠀⠉⢸⣀⣠⣴⡿⠁
⠀⠀⠀⠀⢸⠀⠀⠀⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢚⠚⠓⠓⠒⠖⠖⣲⣿⣷⣤⡴⠶⠶⠛⠋⠁⣼⠃
⠀⠀⠀⠀⠈⠓⠶⣲⠟⢷⣄⠀⠀⠀⠀⠀⢀⣀⣤⡤⣤⡤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢠⣀⠀⢀⡘⠋⣛⠀⠀⠀⠀⠀⠀⠀⠠⡟
⠀⠀⠀⠀⠀⠀⠰⡇⣀⣤⠼⡆⠀⢀⣴⡞⠉⣟⡛⣦⠈⠳⣄⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⣅⡘⣿⠛⠶⠶⢤⡀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⣀⣠⠖⠋⠉⠀⠀⢷⣠⠏⠀⠹⣷⢮⣉⢉⣄⣤⡌⠳⣄⠀⠀⠀⠀⢹⡷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠶⡏⠀⠀⠀⠀⣉⡿⢶
⠀⠀⠀⠀⠉⠉⠛⢦⡀⠀⠀⠀⠙⠲⠶⠶⢼⡆⠈⠙⠻⣤⡁⠀⠈⠳⣄⠀⠀⠈⠛⠚⠛⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣶⢾⣛⣁⣠⠼
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠉⠓⢦⣄⠈⠳⣄⠀⠀⠀⠀⠀⣠⠟⢳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡾⠭⠉⠉⢲
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⣠⠤⠶⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣧⡀⠀⣠⣾⡵⠞⠉⠀⠉⠛⠶⢤⣀⣀⠀⠀⠀⠀⣀⣴⠛⠃⢻⣦⡀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⣸⡥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⣇⠀⠀⢨⠇⠉⠉
⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢀⡠⠶⠒⠋⠉⣉⣉⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢖⣒⣒⡒⠲⢤⣀
⠀⠀⠀⠀⢀⡴⠋⣠⣴⣊⡭⢽⡶⢦⢭⣵⣦⣄⠙⢦⡀⠀⠀⠀⠀⡴⢊⣥⠶⠟⠻⡉⠿⠍⠛⠲⢬⡛⢦⡀
⠀⠀⠀⢠⠏⢸⣿⣟⠟⣿⠀⢸⠀⢸⠀⢈⠈⢻⢦⡀⠳⡄⠀⢀⡞⣵⣟⣡⡠⠆⠀⠃⠀⠠⠀⠂⠀⢛⣦⠳⡄
⠀⠀⠀⡟⢀⣿⣿⣗⣄⢷⣄⠌⣠⣼⡀⣈⣆⢀⢸⢷⠀⢳⠀⡞⣸⣋⣀⠀⠠⠀⡄⠀⢠⠠⣦⠀⡅⢀⠤⠆⢻
⠀⠀⠀⡇⠘⡟⢈⠃⠀⡏⠀⠚⠉⡻⠊⠻⠟⣏⠘⠊⠀⢸⢸⡇⣿⡉⠨⠆⠀⡃⠀⣠⣼⠇⢙⠀⠉⠀⢀⠀⢸⡄
⠀⠀⠀⢧⠀⣇⢠⠄⢰⠀⢠⡆⢀⡇⠀⣧⡀⡟⣠⠐⠀⣼⠸⡇⢿⠡⠀⠐⠈⠁⠰⣿⢻⡆⠘⠀⣈⡁⠈⡤⢸⠃
⠀⠀⠀⠘⣆⠈⢿⠓⣿⠖⢽⡝⢪⡬⠚⠯⠓⡗⡳⠃⣰⡟⠀⢻⡘⠄⠀⠀⢀⣁⠀⢹⠟⠓⠂⠉⠁⢠⣀⢇⡼
⠀⠀⠀⠀⠘⢧⡈⠢⢬⡀⢸⠀⠸⠆⢀⡢⠀⠋⣀⣾⠟⠀⠀⠈⢷⣌⠀⠈⡀⠀⡤⠸⠆⠀⠒⠘⡀⠈⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⡈⠁⠈⠉⢀⣀⣴⡾⠟⠁⠀⠀⠀⠀⠀⠉⠳⢌⣙⠦⣿⣀⣠⠤⠾⣒⡩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⠤⠤⣤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⠒⠒⠉⠉⢉⡡⡠⡄⡄⢀⠀⠠⠄⠘⡈⢆⢠⠀⡈⠉⡒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡠⠋⡔⡠⠀⠀⠀⠃⠂⠀⠈⠈⠀⠀⠀⠀⠁⠘⠀⢇⠰⡀⢱⡀⡌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢰⠁⠈⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⠀⠁⠀⠁⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣀⣥⡴⠶⠞⣛⡻⠋⠉⠋⠉⢛⡁⠈⠁⠀⠉⠁⠈⠋⠁⠙⠛⠉⠓⠒⢤⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡞⠉⠀⠁⠀⠐⠋⠉⠀⠀⢠⠊⠉⠉⠀⠀⡀⠀⠀⢰⠋⡧⠀⠀⠀⢀⣀⠀⠉⢳⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡴⠄⠀⣠⠄⠀⠀⢠⢦⠀⠀⢀⣀⠀⠀⡔⠋⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠸⣄⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠠⡇⣼⠃⠀⣴⠃⠀⠀⠀⠀⠀⢀⠀⠈⡈⠁⠀⠀⠀⠸⣄⣤⣀⠀⠀⠈⠨⠇⠀⠀⠉⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠈⠀⠀⢀⡖⠃⠀⢠⠶⠒⠋⠉⡿⠙⢢⣤⣤⣤⣀⡀⠀⠁⠀⠳⠖⠀⡀⠀⠀⠀⠐⠳⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢈⡷⠀⢀⡀⢿⠀⠀⣹⠉⠀⠀⢀⡼⢡⠞⠋⠁⠀⠀⡿⠉⢲⣤⣴⣆⠀⠀⠑⢦⡄⠀⠀⠀⠀⠀⣴⡃
⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠙⠂⠀⠀⠈⢧⢀⣠⡴⠋⡰⠋⠀⠀⠀⠀⡼⠁⣰⠋⣰⠏⣠⡿⢇⠀⠀⠀⠀⠀⠀⠶⡄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⠀⠀⠀⠀⢠⡟⠋⠁⣠⠞⠁⠀⠀⠀⣠⠞⢀⠜⢁⡴⠁⡴⠋⠀⢼⠁⠀⠚⣦⠀⠀⠠⠟⠀⢾⠁
⠀⠀⠀⠀⠀⠀⠀⡱⠂⠀⠀⠀⣞⠂⠀⣹⡴⠊⠁⠀⠀⣀⠴⢊⡡⠞⣁⠴⠋⣠⠞⠁⠀⠀⢈⠇⠀⠀⠘⠀⠀⠀⠀⠀⣜
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣏⠀⠘⢯⣤⠶⣒⣮⠭⠒⠋⣉⠴⠚⢁⡤⠞⠁⠀⠀⠀⠀⠘⣆⠀⠴⠄⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⣨⡷⠟⠉⠀⢀⡤⠚⢡⡴⠚⢁⣀⣀⣀⣀⡀⠀⠀⠰⡃⠀⠀⢀⠀⠀⠈⣳⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡟⠁⡠⢤⠀⢠⣄⠀⠻⡄⠀⢠⠖⠉⠀⠀⠘⠛⠉⢉⣀⣀⣀⣀⣉⠙⠲⣄⡹⠂⠀⡇⢀⠀⠀⡀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠾⡆⠀⠀⠀⡰⠁⠀⠙⠦⠤⠤⠤⠒⠒⠋⠉⠁⠈⠉⠉⢉⣙⣲⣬⣇⠀⠀⠉⠁⠀⠘⠙⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠘⡦⠀⠀⠈⣁⡀⠀⠀⠙⣶⠶⠶⠦⣤⣀⣀⣀⣀⣤⠤⠶⠒⠛⣋⣉⡉⠛⢿⠋⠀⠘⠙⠃⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠧⠄⠀⠀⠸⠧⣤⣴⣶⣒⣒⣒⠲⠶⠶⠶⠒⠚⠉⠉⢹⣿⠖⠛⠀⠀⠀⠀⠀⣴⠂⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠈⠙⠉⠑⠒⠉⠙⠒⠊⠙⠃⠀⠀⠀⠀⢠⠤⠄⠈⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠸⣤⡄⠀⠀⠔⠒⣄⠀⠀⠀⠀⠈⠹⠆⠀⠀⠀⠀⢀⠴⢦⡀⠀⠀⠋⡁⠀⠀⣴⠛⠀⠀⢠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣄⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⢠⣆⡀⠀⠀⠃⠀⠀⠙⠀⠀⠐⠧⢦⡤⠁⠀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠴⢦⣀⣤⣄⣀⣄⠀⢀⣍⠀⣠⡀⣠⣄⣠⠦⣤⣠⣴⣄⣠⡤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠙⠛⠋⠉⠉⠁⠈⠁⠀⠁

⠀⠀⠀⠄⠒⠒⠀⠈⠉⠉⠉⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⢀
⠀⢐⢀⠀⠀⠤⡤⠀⠀⠀⣀⠀⠐⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠈⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⢨⡑⠳⠶⠄⠠⠤⠤⠤⠤⠍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠁⠀⠀⠭
⠀⠀⠙⢗⠤⠤⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠔⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠠⣄⣀⠈⠙⠂
⠀⠀⠀⠀⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⡀⡀⠀⣠⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡈⠛⠋⠉⢉⡅⠻⠉⠉⢐⢊⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⡀⠄⣀⠀⡄⠀⢀⣉⠠⢄⣀⠀⠀⠀⠀⠘⠻⠄⠁⠤⠤⣤⣤⠬⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⢸⢯⡉⢦⣀⠛⠦⠰⠀⠡⡀⢰⠀⠀⠀⠀⠀⢂⠒⢀⠀⠀⠈⠐⠀⠀⠐⡠⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠘⢾⣴⢲⡾⠳⣜⣃⠉⡗⠘⠓⠟⠧⢁⡀⠀⠀⠑⠅⠀⠀⠀⠀⠐⢤
⠀⠀⠀⠈⢿⣉⣙⡊⢶⠉⠈⠙⠑⠒⠒⠠
⠀⠀⠀⠀⠀⠙⠿⡝⠈⠦⠃⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⠀⠀⠀⠀⠀⠀⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⡀⠛⠢⠵⢠⣄⠄⢀⡀⠂⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⠦⠈⠂⠈⠁⠈⠁⠀⠀⠀⠀⠙⠤⡀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣈⣀⠀⠒⠒⠲⢶⡶⡶⡄⠐⡄⠀⠐⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⣓⠬⠤⠔⠁⠉⠛⠁⠸⠴⠤⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⠶⡶⠿⡴⢄⣀⣀⠀⡀
⠀⠀⠀⠀⠠⠉⠒⠂⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢮⠙⡈⢏⣰⣄⣠⢐⣄⠚⠉⠋⠁
⠀⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⢐⠢⠤⠤⠈⡧⠬⠤⠀⠫⠄
⠀⠀⠀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡤⠀⠀⠀⠈⠁⠀⠀⢀
⡄⠈⠈⡍⣉⣙⣛⡓⠒⢓⠒⠶⠶⠂⠴⠾⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠌⠉⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⡅⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣆⢀⣤⠀⢰⣦⡀⢸⣿⣿⣿⡏⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⣠⣠⣄⣼⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣟⠃⡿⣿⣿⡇
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢧⡿⢿⣿⣿⣿⣿⣿⢻⠇⢿⡟⡇⡀⠀⠀⠀⡠⠠⢀⡀
⠀⠀⠀⢠⣿⣿⣻⣿⣿⣟⣿⣿⣿⣁⣠⣤⣦⡄⠈⠉⠉⣿⣏⠀⠀⠀⠀⡟⠻⠗⠐⠒⢰⡖⠒⠒⠒⠒⠒⢲⢶⠒⠒
⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣾⣿⣾⣿⣷⡶⠀⠀⢷⣾⣿⣾⣷⣿⣶⣷⣼⣎
⠀⠀⠀⠀⠈⠿⢻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣭⣻⣿⣿⣿⣿⣿⣿⣿⠻⠛⠻⢿⣶⢷⣴⣿⣿⣿⣿⡿⢋
⠀⠀⠀⠀⠀⠀⠀⠁⣀⣈⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣾⣶⣾⣷⣮⢿⠟⠿⢿⣿⡥⠌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⣗⢳⡤⣼⠿⠿⠃⠻⠿⢿⡿⠳⠄⣿⣿⠟⠛⠉⢨⠉⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⢨⡀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢉⡏⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⢭⡯⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠀⣀⣠⡤⠤⠒⡺⢷⡒⠦⠤⣤⣀⢀⡋⢓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣿⠥⠶⠒⠛⠉⠁⠀⢘⣋⡽⠁⠈⢫⣙⣃⠀⠾⠉⠙⠚⠷⠮⣽⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠉⠀⠀⠀⠀⠀⠐⠂⠀⣈⣉⡼⠁⠀⠀⠀⢣⣀⣄⠠⠄⠀⠀⠀⠀⠀⠀⠉⠙⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡝⠀⠀⠀⠀⠀⠀⢳⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡄⠀⠀⠀⠀⠀⠀⣀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⣀⠀⠀⠀⠀⠀⠀⢀⣧⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⢧⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣅⠄⠀⠀⠀⠀⠀⡸⠆⢺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢯⣿⠐⠘⡆⠀⡈⠁⢄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⢋⠀⠀⠰⢠⡟⠐⢾⡽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣿⠀⠀⢻⠀⠡⡄⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡞⢠⠀⡾⠁⠀⢿⣠⣿
⠀⠀⣀⣤⣤⣄⣀⠀⠀⠀⣀⣷⣈⣿⠀⠀⠈⡇⢦⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡜⢰⠓⠀⠀⢼⢁⣿⣀⠀⠀⠀⣀⣠⣤⣤⣀
⠀⠀⢻⣙⣾⣇⣹⡟⢶⠋⠁⠀⣯⣿⢧⠀⠐⢻⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡞⠂⠀⠀⢸⠏⠀⠈⠙⡶⢺⣏⣸⣷⣫⡟
⠀⠀⠀⠙⢦⣤⠟⢳⣼⣆⡀⢸⠿⣧⣼⣤⡶⠚⠹⣏⠫⡉⠋⠉⢯⠉⠋⠉⡏⠙⠋⠹⢉⡝⢉⡽⢉⡽⣫⠟⢹⠧⣴⡀⢸⢀⡄⢀⣰⣷⡞⠻⣤⡴⠋
⠀⠀⠀⠀⢀⣬⣿⠯⣭⣙⡻⠞⠣⣽⡿⠓⢬⣁⣀⣀⣷⣝⣂⣁⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⣩⠾⠁⠀⠀⠀⢉⣩⣿⡻⣴⢛⠋⠉⠉⢻⠁
⠀⠀⠀⠀⠀⠳⣿⣷⡾⣿⣄⠀⣀⢻⡤⡖⠏⠛⠊⠋⠁⠚⠀⠚⠉⠻⢷⣦⣤⣀⠀⠀⠀⠀⣠⡞⠁⠀⠀⣀⠴⣚⣹⣞⣻⣣⣿⣉⣡⡄⠀⣸
⠀⠀⠀⠀⠀⠀⠈⠛⡖⠊⠛⣳⡾⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⢕⠦⣀⠾⠁⢀⣤⣖⡟⠛⡿⠋⠰⠏⣽⣙⣧⢽⡿⡍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣽⣏⢈⠗⠀⠀⡀⠀⠠⠤⠤⢤⠀⢀⠀⠀⠀⠀⠀⠀⠉⠈⡳⢾⣿⡎⡯⠴⢾⡵⠒⢒⡺⠍⢉⠀⡼⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⢀⣹⣧⢂⠔⣩⠴⠞⠻⢋⡿⣿⡟⠛⠦⣕⡢⢄⠀⠀⠀⠀⠀⠀⢽⣿⣝⡖⠀⣿⣵⣢⡀⠡⠀⠀⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠙⢫⣳⣂⡮⠙⣆⣀⡴⡿⠀⠛⣆⡀⠀⠲⣽⢷⣬⡢⣄⠀⠀⠀⠀⠈⠙⠉⠓⡳⠴⠶⢼⡧⠐⢀⠈⢓⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⡀⠻⢢⠽⡻⠖⢾⡇⠀⣇⠀⢀⡤⠟⠛⣛⣿⡻⢿⣽⣾⣷⣦⡀⠀⠀⠀⠀⠐⠐⠈⠉⠹⣯⣥⣶⣟⣉⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠒⠀⣒⣏⣨⠏⠀⠈⠙⢻⡀⠀⠀⢉⣼⢻⡏⢷⡉⠀⠉⠺⣵⡢⠄⠀⠀⠀⠠⠬⠀⣺⣯⢿⠣⠉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠹⠦⠴⢻⡇⠀⠀⠸⡟⠦⠤⠞⠁⠈⠛⠲⠦⢤⣭⡭⠵⡏⠁⠘⡗⠤⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⣤⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠔⠁



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

⠀⠀⠀⢀⠰⠰⠶⠒⠒⠒⠒⠋⠁⠈⠐⠢⠀⠀⠀⠀⠠⠦⠤⠤⠤⣤⣤⡤⠤⠤⠠⠤⣤⡤⠤⠤⠤⢤⡀
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰
⠀⠀⠀⠇⠀⢀⡄⠈⠀⡔⠁⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⡀⠀⠈⠃⠀⢰⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠡⠀⠀⠀⠀⠸⡆⠀⠀⠀⠰⢄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠂⠀⢰⠀⠀⠀⢳⠀⠀⠀⢈⣰⣿⣿⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⢸⠀⢠
⠀⠀⠀⠀⠀⠤⠇⠀⠀⢘⣷⡀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⠄⠀⠀⠀⠀⠀⢸⠀⠘
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢿⣷⣄⢸⣿⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢸⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⣿⣿⣿⠋⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⡀⠀⠀⣾⢀⡄⡁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣿⣿⡟⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠲⣿⡆⠀⠀⠀⠀⠀⣧⢸⣧⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢐⣾⣷⠀⠀⠃⠀⠀⣿⣾⣏
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⣼⣿⡟⠀⠀⠀⠀⢸⡟⢻⠋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠘⣿⡟⠀⠀⠀⠀⠀⠈⡇⠹⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣼⡿⠁⠀⠀⠀⠀⠀⠀⣿⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠘⠀⠀⠀⠀⠀⠀⡿⣶⠀⡰
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⢠⡏⠀⠀⠀⠀⠀⠀⣿⣿⠀⠇
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⣸⠏⠃⠘
⠀⠀⠀⠂⠀⠀⡜⠀⠀⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠇⠀⠀⠀⠀⠀⠀⠅⠀⠻⡀⢠⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠀⠀⠰⠉⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠘⡄⠀⠈⠈⢀⡠⣀⡰⠃⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⠀⠀⠀⡄⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⢠⠊⠀⠀⠀⠀⠀⢸⠀⠀⡆
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢀⠴⢀⠘⠄⠀⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⣠⠞⠋⠠⠆⠀⢹
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣇⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣠⢤⡀⠀⠠⢀⡃⠀⢠
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡀⠀⢴⣮⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣠⠖⠋⠁⠘⠉⠓⠦⡀⢛⠀⣏
⠀⠀⠀⠀⠀⠹⣦⣒⠒⣂⣒⠂⠀⠒⣒⡒⠛⣋⡉⢉⣉⢉⡩⣭⣿⣞⡍⠩⠅⠵⢯⣓⠦⣄⣒⡂⣀⣒⣂⣩⣶⣷⡾
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⡿⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣾⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠹⣆⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣿⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣼⠁⠀⠀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⢉⡽⠟⠉⠙⠓⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⣠⡶⠋⠀⠀⠀⠀⢀⣠⠞⠉⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⣶⡦⠾⣧⣄⣀⠀⠀⢼⡁⢀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⣠⡴⠚⠉⠁⢀⣤⠞⠉⠀⠀⠀⠀⢉⡿⠶⣬⡉⠉⠁⠀⠀⠀⠀⢀⣠⡴⠶⠚⢛⣻⠟⠛⠛⠓⠶⢤⣀
⠀⠀⣠⠞⠁⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⣠⡶⠋⠀⠀⠈⠙⣦⡀⠀⢀⣠⠞⠋⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⣠⡾⠋⠛⢦⣄
⠀⣴⠋⠀⠀⠀⠀⡾⠁⠀⠀⢀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠈⢳⣤⠞⠁⠀⠀⠀⣴⠏⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠙⢧⡀
⢰⠃⠀⠀⠀⠀⠈⠷⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⢸⡃⠀⣀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠙⠳⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠞⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣯⣭⣥⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣀
⠀⠀⢰⡚⠛⠉⠁⡀⠈⠉⠉⠉⣩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢚⡦
⠀⠀⠀⠉⠣⣄⠀⠀⠀⠁⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠖⠋⠉
⠀⠀⠀⠀⠀⣈⣙⣓⣚⡋⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢴⣺⠿⠗⠋⠉
⠀⠀⢰⡞⠛⠉⠀⠀⠈⠉⠉⠉⣩⠇⠀⠀⠀⠀⣀⡠⢴⣲⡯⠗⠛⠉
⠀⠀⠀⠉⢧⠀⠁⠀⠀⢀⣠⡤⠏⢀⡠⢤⣒⡭⠗⠚⠉
⠀⠀⠀⠀⠈⠓⠒⠒⢚⣉⣤⣶⠿⠗⠋⠉
⠀⠀⠀⠀⣀⣤⣴⡾⠿⠟⠻⠶⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠒⣒⣋⣽
⠀⠀⢀⣼⡿⠋⠀⠀⠄⠀⠊⣰⠋⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⣶⣶⣯⠭⠿⠶⠒⠛⠛⠉⠉⠁
⠀⠀⠸⢤⡀⠀⠀⠀⣀⣠⣶⣥⣤⣶⣶⠶⠿⠭⠽⠒⠚⠋⠉⠉⠉
⠀⠀⠀⠀⠾⠿⠿⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⠶⠶⠶⠶⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⢀⣀⣄⡀⢀⠀⠀⠉⠙⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⠔⠒⠟⠉⢛⣉⣉⣉⠙⠉⠓⠢⣤⣀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⢀⡼⠋⢀⠀⣠⢶⡟⣡⣤⢴⡿⠟⢿⡟⠟⠛⢿⠘⠿⣷⣶⡭⣳⣤⡀⠀⠈⠻⣆
⠀⠀⠀⠀⣠⡟⠀⠼⣧⢿⣥⣾⡿⠛⣿⡀⠀⠀⣸⠠⠇⠀⡈⠀⠀⢀⣸⡀⠛⢷⣿⣆⠀⠀⠙⣧
⠀⠀⠀⢰⡟⠀⠀⣰⣿⣿⡏⠈⣷⡀⣹⠆⢰⡟⠻⢶⣄⡀⡧⠀⠀⣿⡉⠛⠶⢶⣏⢹⣷⡀⠀⠘⣧
⠀⠀⢀⣿⠀⠀⢰⣿⣿⡿⠱⣄⡀⠙⣿⣦⠸⣧⢈⠐⠈⠙⢷⡄⠀⢸⡇⠠⠐⠀⢹⣿⢻⣧⠀⠀⢹⡆
⠀⠀⢸⡇⠀⠀⣿⣿⣿⠇⠀⠄⣡⠀⠘⣷⠒⣿⠄⠀⢆⠀⠀⢻⡄⢼⡇⠀⠀⡀⠀⠻⣆⢻⡆⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⢸⡇⠀⠀⣿⡿⣿⠀⡀⣤⠋⠀⠀⣿⢀⡿⠀⠀⠈⠀⠀⠘⣟⣻⡇⠀⠀⢀⡃⠀⢹⣆⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢀⡿
⠀⠀⢸⡇⠀⠀⣿⡇⣿⠀⠀⡆⠀⠀⠀⣿⢸⣇⠀⠠⡼⠀⠀⢀⣿⣿⡀⠀⠀⢡⠁⠀⠀⣿⠇⠀⢀⣿⡇⠀⠀⠀⠀⠀⢠⠿⠁⠀⠀⣼⠇
⠀⠀⠈⣷⠀⠀⠿⡇⢹⡆⠀⢉⠄⠀⢠⡇⠀⣿⡀⠀⠀⡛⠀⣼⠃⣽⣇⠀⠀⡘⠂⠂⣠⡟⠀⠀⢸⣿⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⢰⡟
⠀⠀⠀⢹⣇⠀⠀⢳⣦⣿⠦⠈⠂⣠⡾⢧⢶⡟⣷⠀⠰⣠⣾⣇⠺⡞⢻⡆⠀⢁⣴⡾⢛⠃⠀⢠⣿⡏⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⣆⠀⠀⢻⣯⣈⣴⣿⣳⡟⠢⣜⢿⣿⣄⣠⡿⣥⠞⠑⣿⢾⢷⣤⡾⢋⡴⠏⠀⢠⣯⡿⢁⡴⠋⠁⢀⣀⣀⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠙⣏⠀⢦⡏⠀⠀⢸⡟⠀⠉⢉⡇⠀⠀⢀⠁⠀⠀⢉⡧⠚⠁⠀⣰⣿⡿⢡⡿⠁⢠⡶⠋⠉⠀⠈⠙⢦⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠈⠛⠾⣇⡀⠀⢸⠃⠀⠀⢀⠃⠀⠀⢸⡇⡧⠴⠁⠀⢀⣠⣞⣿⡟⠁⣾⡄⢠⡟⠀⠀⠀⠀⠀⠀⠘⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⡀⠈⠉⠀⠘⠒⠂⠀⠲⠺⠒⠀⠈⠁⠀⠀⢀⣴⢞⣽⡿⠋⠀⠀⣷⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣧⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣮⣿⡷⠟⠉⠀⠀⠀⠀⠹⣆⠀⠙⢄⡀⠀⠀⠀⠠⠄⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⢭⣽⣽⡿⠿⠷⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⡈⠀⠀⠀⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠿⠛⠛⠛⠛⠛⠻⠶⢶⣤⣀⡀⠀⠀⠈⠛⠳⠾⠿⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⢀⣤⣤⣶⣶⣾⡿⣿⠶⢶⣶⣴⣤⣙⠛⠛⡷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⣤⣾⠟⠛⠉⢛⡽⠋⠀⠁⢠⡿⠟⠋⢻⣿⣿⣦⡈⠲⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢀⣴⣿⠟⢇⠀⠀⡠⢾⠁⠀⢀⠖⠷⣀⠀⡠⠈⠑⢀⣼⠉⢳⡈⠫⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣴⡿⢿⡇⠀⠀⠘⠞⠁⠀⠉⠶⠁⠀⠀⠈⠛⣀⠀⠀⠀⠁⢂⡀⠙⢆⠰⢎⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⣿⡄⠀⠹⢦⣀⠀⠀⠔⠠⣀⠀⣰⡦⣄⠀⠀⡀⠓⢤⡀⠀⠂⠀⠂⡄⠣⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡿⠙⢿⠆⠀⠀⠈⠢⠂⠀⠀⠈⠛⠀⠀⠈⡱⠟⠀⠀⢀⡜⠁⠀⢀⡔⠁⠀⠃⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣾⣷⠖⠃⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⣠⣌⣀⡀⠀⡐⠋⠀⢀⡴⠋⠙⠂⣠⣾⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣿⡇⠀⠀⢀⠞⠉⠠⠀⣠⠛⢴⣶⣆⣾⣩⣼⣿⣿⣎⠀⠀⠦⡙⠣⡀⠀⠀⠈⣿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⣿⡃⠀⠘⢧⡀⠀⠀⢌⣿⣄⡈⠉⠛⠛⢻⣭⣀⣈⣙⢷⣤⡀⠀⠐⢬⠶⣄⣀⢾⡇⣸⡇
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⡄⠀⠀⢘⠦⣀⠀⠙⠿⠛⠲⣄⠀⡀⠉⠻⢿⣿⠞⠁⠙⢶⣦⠀⠄⣸⠻⣿⠃⣿
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠻⣏⢢⡔⠁⠀⠈⣳⠖⠀⠀⠀⠈⠋⠀⠀⢀⡞⠁⠀⠀⠀⠐⠁⠀⠀⠁⣰⠃⢬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠹⡏⠀⠀⣴⠞⠁⠀⠀⢀⡔⠁⠀⢀⡴⠎⠀⠀⢀⣦⡎⠀⠀⢀⠾⡿⠃⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠳⣿⠁⠀⠀⢀⠀⠉⠀⠠⢶⠟⠀⠀⠀⠢⣮⡀⠁⠠⣚⣷⠚⢁⣾⠋
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡈⠁⠀⠀⠈⠱⢤⠀⠀⠀⠑⢆⡀⠀⠀⠀⠙⢢⣴⠟⠁⣺⠟⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣤⡈⠁⠂⠲⠿⣧⣤⣤⣼⠟⠰⠖⠐⢊⣉⣤⡾⠋⠁
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢶⣤⣤⣀⣀⣠⣤⣤⣤⡶⠾⠛⠉
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠲⣤⡭⠿⠛⢻⡾⠛⠋⢭⣤⠶⠂⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢋⡥⠒⣈⣥⠤⠒⠒⠀⢸⡏⠐⠒⠒⠢⠬⣁⠒⠬⣙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣡⠞⣡⠔⢋⣁⠤⠖⠐⢛⣋⣹⣏⣙⡛⠓⠲⠦⣈⡙⠲⣌⠳⢌⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡧⠚⡡⠊⡡⠖⣩⡤⠒⠉⠉⠀⠀⢸⡇⠀⠀⠉⠉⠒⠦⣌⠓⢤⡙⢦⡑⢾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⣀⡴⠋⡴⠊⡴⠚⢁⡠⠔⠒⣉⡡⠤⢼⡇⠤⢌⣉⠒⠢⢄⡀⠙⢦⡙⢦⡙⠦⣀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠗⠋⢉⡤⠊⣠⠞⢁⡴⠋⢀⡤⠚⢉⡴⠒⢛⡟⠓⢦⡈⠓⢦⡀⠙⠲⡄⠹⣄⠙⢦⡈⠙⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡴⠊⠉⣠⠞⠁⣰⠿⠶⠊⠁⣀⠴⠋⢀⡴⠊⠙⢦⡀⠈⠲⣄⡈⠉⠲⠻⢦⠈⠳⣄⠈⠙⠢⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢀⡴⠚⣁⣤⣞⣁⠤⠤⠒⢋⣁⠤⠒⠉⠀⠀⠀⠀⠈⢓⣤⣌⡙⠒⠠⠤⠀⣑⣤⣈⠙⠦⣄⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⢁⡴⠎⣈⣁⣀⣀⠤⠶⠚⠋⠀⠀⢠⣾⠂⠀⢀⣠⣶⡿⠛⠉⠘⠓⠶⠤⣀⣠⣍⣉⠸⠶⡌⢳⡌
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⣯⣼⡑⠒⠊⣡⠼⡇⢀⢠⣤⣤⣆⣠⣻⣏⣠⣴⣿⠟⠉⠀⠀⠶⢤⣤⣄⡀⠸⢷⣌⠑⠒⠊⣹⣮⠓⢤⡀
⠀⠀⠀⠀⠀⠀⢠⠎⢠⠞⠁⡤⣛⠶⠛⢁⣾⣠⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢳⡈⠙⠷⣟⢤⡈⠙⣄⠹⡄
⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⡞⠱⠉⠀⣠⢾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⢄⠀⠈⢦⠙⡀⢸⠀⢱
⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⠀⢸⡇⢸⠆⠘⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣤⡀⡀⢀⠀⣀⣠⡞⠑⠀⠁⢸⠗⡀⢸⠀⡇⢸⠀⡸
⠀⠀⠀⠀⠀⠀⠈⢧⣘⣴⡄⢣⣀⠿⢡⣾⠀⣼⠗⠋⢹⢻⡟⠛⠉⠀⠀⠀⠀⠀⠉⠀⠋⠹⠇⠙⠀⠈⠀⠀⢸⡄⠻⣄⡸⢀⣧⣎⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⠛⡾⢁⡴⡡⢶⡀⠀⠀⠀⢇⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢌⠳⡌⢳⠞⡆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⢸⣿⠇⡘⣧⠀⠀⣼⠎⠀⠀⠀⠀⠉⢂⡒⠒⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⡸⢋⡰⣿⡷⢸⠀⡄⢸⡟
⠀⠀⠀⠀⠀⠀⠀⢻⡘⢄⠳⡑⢄⣙⣛⢣⣿⠀⠀⠉⠀⠀⠀⠀⣴⡾⠉⢉⣉⠉⢳⣶⡀⠀⠀⠀⠀⠀⠀⣵⣎⣛⣋⡡⢎⡴⣁⢎⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠙⢌⠳⣦⡬⣟⠹⣧⠀⠀⠀⠀⠀⠰⢦⣷⠚⠛⠛⠛⢾⣵⠧⠀⠀⠀⠀⠀⣰⠟⢹⠧⣴⡞⢩⠎⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢘⠀⣨⣷⠘⡇⢋⠳⣄⠀⠀⠀⠀⠈⣫⠳⠶⠦⠖⢹⠇⠀⠀⠀⠀⢀⡞⢹⠰⠇⣼⣥⠆⡇⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⡾⠞⠋⣸⢀⡄⡸⠀⠝⠢⣀⠀⠀⠀⠈⣦⣤⣤⣤⡃⠀⠀⠀⣀⡴⢻⡀⢰⠰⡆⢣⠘⠳⠷⠤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣬⠴⢃⣼⣣⣶⢟⣷⣄⡀⠀⠁⠀⠀⠈⠀⢀⣠⣞⣻⣷⣬⣵⡈⢧⣵⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣼⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣼⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢃⣨⣿⣿⣏⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣾⡆⠛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢛⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣴⡆⣻⣿⢋⣴⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢻⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣴⣿⣿⠸⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⢼⣏⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣦⣾⣿⣷⣬⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢻⡧⢺⡇
⢴⣶⣲⡶⢶⣄⡀⣀⡴⠞⢧⣼⣿⡏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢸⣧⠼⠓⢦⣀⢀⣠⡶⢶⣖⣶
⠈⢷⡟⠳⣦⣯⣹⡇⠀⠀⠀⢹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢹⣏⣼⣴⠞⢻⡾
⠀⠀⠙⠶⣎⣩⠿⣿⣦⡀⢶⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡶⢀⣴⡿⠿⣍⣱⠶⠋⠁
⠀⠀⠀⠀⣾⠁⠀⠀⣨⣽⡟⣽⣿⣿⣿⣿⡋⣯⢻⣿⣿⣿⣿⣿⣿⣿⣟⣋⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣾⣿⣿⣿⣯⢿⣏⣅⠀⠀⠈⣷
⠀⠀⠀⠀⠻⣤⣀⣠⣤⠾⣷⣯⣵⣿⣦⣽⠿⠶⠛⠛⠉⠉⠉⠉⠉⠉⠀⠈⠁⠀⠀⠉⠉⠉⠉⠉⠛⠓⠺⠿⢯⣵⣿⣯⣭⣿⠷⣤⣄⣀⣤⠟
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠐⠋⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⡘⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣄⠠⠤⢀⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢧⠀⠀⣀⣤⠴⢶⠋⣽⠛⣿⠋⠀⠀⠙⢷⢀⡆⣸⠟⠁⠀⠈⢿⠛⣯⠉⣳⠶⢤⣄⡀⠀⣰⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⣁⣀⠤⠤⢿⡏⠀⠙⢦⣀⣀⣒⣾⣟⣟⢷⡔⠂⡀⣠⠞⠀⢹⣿⠥⢤⠀⣈⣱⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠉⠀⠀⠀⢀⣿⡀⣠⠖⠛⠋⣩⢷⣿⣟⣽⣏⡙⠛⠳⣄⠀⣸⡇⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢃⣠⣤⠀⠀⢠⠞⠁⠉⢻⡄⠀⠀⢠⡾⠹⡏⢻⣄⠀⠀⢀⣼⠉⠁⠙⣆⠀⠀⣠⣄⣈⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⡇⠰⠏⠀⠀⠀⠀⠛⠲⠒⢋⠃⠀⠀⠈⡟⠓⠦⠞⠁⠀⠀⠀⠈⡧⢀⠇⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏

⠶⢤⠴⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠤⠀⣀⡀
⠄⡘⢀⡇⠼⠒⠉⡆⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣠⣤⣤⣤⡤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣈⠉⠙⠎⠙⡓⠲
⣒⣛⣚⣓⣗⣓⣚⡳⢤⡀⠀⠀⠀⠀⠀⣠⣾⢿⣲⡶⠤⠾⠥⢤⣄⣸⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠛⠢⢐⣤⠴⢯
⢀⠴⠒⠞⠛⠳⣦⠉⠓⣽⡄⠀⠀⠀⠀⢿⡞⣩⢂⡰⠶⢠⡢⢦⡰⠈⢗⣼⠇⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⣴⠊⠀⠀⣈⡆
⣇⢀⡁⠊⠀⢔⣽⡧⠔⡿⠀⠀⠀⠀⠀⠘⢿⣾⣧⣼⣿⣷⣶⣷⣿⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⡙⠻⠶⠶⠶⠿⠷
⡈⠉⠉⠉⠉⠉⢁⡤⠊⠀⠀⠀⡄⠀⠀⠀⠀⠙⣶⠬⠭⣭⡭⠯⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠦⠤⠤⠴
⠛⠷⣶⣶⣶⡾⠟⠀⣀⠀⡴⠒⠋⠀⠀⠀⠀⠈⢻⣦⣀⣀⣀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⡎⢙⡏⠳⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣞⠛⠛⢶
⣠⠶⠦⣄⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣥⠞⣫⣾⠋⣿⡁
⠃⢄⠀⠸⡆⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡄⠐⠁⣪⢿⠾⠦⣄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣼⣹⣋⣡⠉⡀⠜⢙⠉⠃
⠀⠀⣱⢞⣁⣀⠀⠀⠀⠘⡄⠈⠁⠀⠀⠀⢀⠀⢠⠖⠛⠙⣤⣀⣽⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠞⠁⢏⠩⢚⠰
⠛⠚⡱⠋⠀⠈⠙⢦⠉⠉⠁⠀⠀⠀⠀⠠⢂⠀⢾⠐⠀⠀⡼⡇⠀⠹⡄⠐⠄⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⣤⣦⣤⣤⡴⠾
⠀⢸⠃⠈⢲⠀⠀⣺⠄⠀⠀⠀⠀⠀⠀⠀⠈⢀⠎⢠⡤⠊⠁⠛⡂⢰⡑⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣄⣒⣂⣰⣤
⠀⠘⢆⡀⣸⣂⠴⠋⠀⠀⠀⠀⠀⠀⠀⢸⠟⢺⢂⠘⠀⠀⠀⠀⠹⠇⠷⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢈⠝⠂⠀⠀⠀⢚⠁⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⣤⣤⣀⣀⡀
⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⣱⢳⢳⢃⡟⣹⢋⠟⡿
⠉⠁⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢶⠟⠀⠀⠀⠀⠀⠀⢰⣧⢏⢯⠇⡞⣴⢣⢏⠞⣰
⠖⣱⢶⡶⣤⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⣴⣟⡤⠤⢶⡷⠦⠀⠀⣿⡟⡘⡜⡘⣼⢡⢣⠊⣼⡿
⣾⠿⢷⣸⡉⣿⣿⣆⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⡤⠚⠉⠹⣿⣶⣾⠟⠁⠀⢠⡞⠀⠀⠀⢰⡏⠁⠙⠁⢰⢣⠣⠃⣼⡿⣱
⣌⣱⡴⣷⣦⣙⣧⠏⠀⠀⠀⣠⣿⠃⠀⠀⣠⠋⠀⠀⣠⣾⠿⠙⢿⣦⣀⣴⠏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠃⠌⠀⣼⠟⣱⠏
⠈⢹⣷⠥⢿⡶⠀⠀⣀⣤⣾⠟⠁⠀⠠⡾⠿⠤⠶⠞⡿⠃⠀⠀⣸⠟⠉⠀⠀⠀⠀⠀⠀⢿⣅⣀⠀⠀⠀⠀⢸⡏⣰⠏
⣶⣶⣶⣶⣶⣶⡾⠿⠛⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⣁⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣶⣶⣿⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁

⠀⠀⠀⠀⠠⢴⣇⠀⠀⠘⠠⡄⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂
⠀⠀⠀⢄⡀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠁⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠉⠛⣿⡆⠀⠀⠀⠁⠀⠂⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠛⠃⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠈⠀⣀⣀⠀⠀⠈⢧⡀⠀⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣶⢲⢶⣢⠀⠀⠀⠀⢀⡴⣄⡔⠆⠀⠀⠀⠐⠛⠛⠁⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢊⠀⠋⠉⠀⠀⠀⠀⠀⢀⣄⠀⠀⡟⠜⠓⢻⠀⠀⠀⠀⣾⠧⡤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⣤⡶
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠒⣄⠘⠂⠀⠀⠀⠀⠀⠀⢤⣴⣶⣾⣿⡆⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠛⢛⢻⣧⣀⣀⠄⠀⠀⠀⠀⠀⠈⠻⢿⡿⠿⠁
⠀⠀⠀⠀⠀⠉⠛⠖⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠠⢤⣤⡄⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⢠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠄⠀⠀⠀⠄⠈⠛⠀⠴⠂⠛⠐⠠
⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⣶⡦⠄⠒⠀⠓⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠄⢐⡀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠢⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠋⡁⠀⠐⠀⠉⠉⡉⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠈⢄⠀⠀⠀⠀⡆⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠁⠂⢀⠀⠐⠀⢀⠃⢀⠃⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠤⠤⠄⠈⠂⠈⠀⠀⠀⠋⠀⠀⠘⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⢠⠂⡡⠐⠈⠉⠉⠉⠐⠂⠄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⠟⠁⡠⠋⠉⠉⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠃⠀⠀⠀⢠⣴⠾⡏⠀⠀⠀⠠⠀⠀⡀⠄⣀⣀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⣴⣁⣤⣤⣶⠾⣛⡉⠀⠀⠀⠀⠀⠀⢿⣅⠂⠀⠀⠀⠀⠀⠇⠐⠂⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣴⠾⢋⣉⣭⣥⡶⠾⠛⠻⠾⠛⠻⣦⣀⠀⠀⠙⢷⡄⠀⠀⠀⠀⡀⠠⠶⠦⠤⣀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠁⠠⠀⠀⠀⠀⠀⢀⠀⠉⠙⢷⡄⠀⠘⣷⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠉⠠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠟⠛⠿⣷⣦⣀⣠⣀⠀⠀⠀⠈⣿⡄⠀⠀⠐⢄⠀⠀⠀⠀⡠⠂⠈⢳⡄⠀⣿⠂⠀⡠⠋⠀⠀⠁⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠓⠤⠔⠀⠈⠛⠋⠉⠻⣧⠀⠀⠀⣿⡇⠀⠀⠀⠈⠀⠀⠐⠊⠀⠀⠀⢸⡇⢸⡟⠂⣀⠀⠀⠀⠀⠀⠈⠑⠤⢤⣼⠟
⠀⠀⠀⠀⠀⠀⠀⣾⣁⡠⠀⠀⠐⠂⡎⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠔⠒⠒⠂⠈⢻⡇⠈⠻⣦⡀⠀⡀⠀⠀⠂⠤⣀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠠⠀⠀⠇⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⠀⠀⠀⠀⠸⠀⠀⠀⠒⠂⠀⠄⠈⣷⠀⠀⠉⠛⠛⠻⣦⣤⡶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢿⡦⠔⠊⠀⣄⢸⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⢸⡇⠀⣀⠔⠁⠀⠤⠤⡀⠀⢀⣤⠾⠋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠆⢸⡀⠀⠀⠀⡀⢸⣇⠀⠀⠀⠹⠷⠿⣦⣀⣀⣠⣤⣬⣼⣴⠟⠀⠀⣾⠋⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠸⣧⣠⠞⠁⠀⢀⡑⢦⡀⠀⠈⠒⠻⢷⡄⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⣠⣶⠶⠿⠇⠀⢡⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⡔⡡⠀⠀⢈⡙⠒⢒⣶⡿⠃⠀⠀⠀⠀⣼⠟⠻⠶⠶⠿⠛⠉⠀⠀⠈⠀⢀⠃⠶⢺⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣄⣀⣤⣮⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⣿⡌⠀⠀⠀⠂⠄⢀⣀⡀⠠⠐⣁⣀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢠⠃⠀⢤⠀⠀⠀⠀⠤⠤⠀⠀⠈⠢⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡎⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢢⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⡆⠀⠀⢠⠀⠀⠀⢠⣤⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣄⣀⡁⠀⠀⠀⠢⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⠶⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠁⠀⡴⣿⣩⣤⣤⣤⣄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡈⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠉⠒⠀⢸⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⣀⢀⣀⠠⠊⠉⣠⣔⠈
⠀⠀⠀⠀⠀⠀⠇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠠⠀⠀⣾⠈⠃⠈⢧⠀⡁⠐⣿⡄
⠀⠀⠀⠀⠀⠀⠁⠈⣠⣾⣶⡦⠧⢴⣶⣇⠀⠀⢸⠀⠀⠀⠠⣄⠀⠀⠀⠀⠐⡀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠄⡘⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠙⠋⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠈⠢⠀⠀⠀⠮⣀⠀⠀⠀⠂⠁⠠⠀⠀⡰
⠀⠀⠀⠀⠀⠀⢀⠐⢰⣄⡀⠀⠀⠀⢀⡀⠐⠁⡆⠀⠀⠀⠀⠀⠀⣠⠈⠀⠒⠠⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⢸⠀⠘⠛⢻⠉⠉⠙⠛⠧⢀⠀⠃⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⡇⠘⠀⠂⠀⠀⠀⡀⡠⠴⣇⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠈⠉⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⡀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠉
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠉⠉⠉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂⢄⣀⠡
⠀⠀⠀⠀⠀⠀⣠⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠂⢋⡀⠀⠀⠀⠐⠶⠦⠤⠤⣄⠀⠈⠐
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠰⡆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠴⠶⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡘⢄
⠀⠀⠀⠀⣰⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⢠⠀⠸⠸⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢠⣿⠏⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠠⠤⣖⠁
⠀⠀⠀⢸⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠘⣿⠀⠈⠀⠀⠐⠀⠀⢀⠀⠀⠂⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠂⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠠⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣏⢹⣟⠿⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡻⢿⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢶⣶⣒⡏⣹⣦⣀⢆⡀
⠟⠛⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⢿⣿⠏⢛⣋⣉⠀⠄⠁⠰⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠖⠿⢿⣿⣯⣿⠴⣗⡏⠳⢿⡟⠷⢚⣡⢦⡤⣄⡐⠒
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣲⣶⣶⣶⢤⣤⣤⣄⣀⡀⣀⠀⠀⣤⡾⣿⣛⢷⣀⡻⣯⣟⡡⠽⠤⣦⠋⢡⡬⠴⢒⣋⣑⣛⠶⠾⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠬⢥⠭⠟⢟⡷⢌⠙⡝⢫⠡⣤⣄⢉⠉⠳⢷⣾⣯⣴⣼⢁⡗⣂⡾⡐⣀⣤⣜⣹⡫⠙⣫⡵⠚⣛⡋⠀⠐⠇⠤⢠
⠀⠀⠀⠀⠀⠀⠀⢠⣀⢄⠀⣚⣒⡐⠾⡯⠻⢋⠈⠡⠬⠼⢝⣷⣄⠀⠘⣿⣿⣿⣿⣯⣭⣿⣽⢿⣟⣷⡋⢳⡦⣔⠚⣃⣬⡴⣛⠱⠆⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⡕⠾⠷⠾⢾⣧⣟⣣⣿⣯⣾⡷⠟⠛⠋⢉⣨⣿⣿⣿⣿⡾⠿⣻⣽⢿⣿⣺⡟⣏⣻⠿⠎⡬⣤⠞⢩⣀⣠⢄⣢⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢀⣈⣻⡉⣟⣈⣭⣵⠿⠛⣁⠀⠀⠀⠠⠊⠓⠸⠿⣿⣽⣷⣦⣽⣦⣿⣙⡖⣻⢟⣿⣷⡖⢶⣒⣶⠦⡌⢕⢫⡴⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠶⠩⣤⠄⣤⠭⣜⣷⡌⠉⠉⠀⠂⠀⠀⠤⠭⠐⠂⠚⠉⢻⣿⣿⣿⣿⣯⡻⠿⢝⣝⣻⣉⣝⣽⣯⠆⠒⣨⡤⠴⠒⣄⠀⢀
⠀⠀⠀⠀⠀⠀⢠⣄⡴⢶⡐⢳⠴⠖⣆⣰⠋⣑⠻⠶⠶⣤⡀⠀⠀⢀⡀⠀⠀⠐⠀⠉⠁⠞⣹⣿⣿⣷⣟⣳⣯⣉⣼⣷⣯⢟⣠⣈⠋⡐⠒⢃⡍⠀⠨⠃⠙
⠀⠀⠀⠀⠀⡀⣈⠀⠠⠀⣁⠐⢖⠓⠰⠠⠶⠼⠟⢫⣱⡟⣿⣷⡄⠈⠉⠀⠀⠀⠀⠀⠀⡸⠛⠻⣿⣿⣿⣿⣿⣷⣿⠟⠻⣿⡀⠀⠀⢀⡀⢨⡄⠀⡈⡅⡀
⠀⠈⠁⠀⣠⣍⣩⣑⣄⣰⣦⣬⣍⣛⣡⡿⡓⠀⠈⢉⣽⣿⣿⢻⣿⣦⡈⠉⠀⠀⠀⠤⣤⢰⢤⢀⣿⣿⣿⣟⣛⣿⣴⣦⣙⠴⡇⡏⠞⠛⣧⠌⡄⠟⠉⠙⠋
⠀⠀⠀⠀⢠⣬⣭⣻⣷⣤⣛⡉⣵⣄⣁⠌⣼⠀⡐⢫⡙⣾⡋⢻⣿⣿⣿⡀⢠⢀⣀⣀⠀⠀⠘⣫⣾⣿⡿⣿⠿⠧⢼⡗⠚⢏⠄⣏⣨⣶⣟⢾⡟⠒
⠀⠀⣰⣦⣍⢻⡿⣟⡳⣶⣶⡆⣬⡙⣛⣠⢩⠦⠑⠻⢼⣟⣿⣿⣿⣿⣿⣿⣴⡶⡦⠖⢐⠀⡋⢘⡿⢿⡿⣷⣤⡙⣬⡿⣿⣋⠛⣿⣤⣾⣿⣼⣏⣥⣀
⢠⣠⡬⢶⡔⢠⣭⣛⣟⡃⠀⠁⠲⢧⣼⣯⣀⣶⣾⣿⣿⣿⣿⣿⣿⣯⡭⠟⠛⣊⣤⡾⢻⡄⠲⠾⢏⠨⡝⢰⢏⣿⣛⣬⣏⣉⡶⡞⢘⣁⣼⠽⢿⡁⠼⡗
⠀⠉⠀⣈⣫⣽⣿⣵⢡⠙⠛⠖⠋⡓⣠⣾⣿⣿⣿⢿⡿⠟⠛⠉⠙⠀⠀⠀⠺⢛⡫⣠⢾⣿⣿⡴⠶⠿⢉⣙⣿⣿⣿⡿⣟⣿⣲⣯⣼⡝⣷⣿⣶⡛⣫⡿⡔
⠀⣤⣻⡻⣻⣯⣶⣴⣦⣼⣶⣢⣀⣜⣿⣿⡏⠁⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠈⠸⠇⠙⢋⡛⠀⠦⣄⢚⡛⢿⣿⣟⣷⣟⣳⣿⣩⣻⣼⣿⣿⣟⡛⠉⣾⠓
⠺⢿⣿⢿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⡿⢋⠀⠀⠀⠀⢤⢤⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⢦⣀⣀⠀⢀⣘⡭⠳⠼⣏⣟⣿⣻⣿⣾⢀⠀⠚
⢘⠻⣯⠓⠻⣻⣿⣾⣿⣾⣾⡯⣿⣿⠴⢾⠃⠀⠀⠀⠀⠀⠀⠂⠉⣁⠀⠀⠂⠀⣀⠀⠀⠀⠈⠀⠐⠋⠀⠄⠈⠩⠽⣦⡜⠿⣿⣟⢿⣟⣻⡿⣿⣿
⠛⢠⣝⣶⣆⠻⣼⣿⣸⣿⣿⣇⣬⣯⣎⣵⡌⠓⢁⠀⢠⠤⠀⠂⠐⠛⣉⠉⢁⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⢀⣠⡴⣾⣿⢧⣀⣘⡻⠛⠛⢛⣓⣿⢯
⣨⣮⣿⣹⣿⣿⡿⠣⣝⢫⣽⣿⣿⣿⡟⠻⣷⣶⣶⣄⠀⠀⠀⠀⠀⠐⢰⣾⡿⡦⠤⠀⠀⠀⠘⡙⠧⣦⠶⠄⠠⠀⠀⠠⢠⣿⠏⠀⠈⠙⠯⠧⠲
⠉⠻⣿⡿⣿⣿⣿⣶⠿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠈⢀⣀⣤⣽⣿⣿⣿⣷⣿⣾⡟⣒⡂⠠⠄⢀⡀⣠⡚⠛⠁
⠐⠛⢿⠻⣿⣿⣷⣿⠻⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⢶⣤⣠⠴⠿⣿⣿⢿⣿⣿⣯⣿⣿⢦⣄⣀⡀
⠀⠘⢛⣟⣿⡴⣿⣿⣟⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠩⠀⠀⠐⠂⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠈⠙⢹⠇⠉⠻⣿⣯⢾⣿⣿⣿⣿⡟⠻⠁⠙⠽⠯⢡⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡩⠎⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣐⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠹⣗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⣙⣦⣸⠃⣐⢡⣇⡇⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡤⣼⣤⣠⠞⠛⠁⠘⠛⠓⣾⣾⠟⠀⠀⠀⠀⠈⠳⣦⢄⡀
⠀⠀⠀⠀⣠⢶⠋⠉⠁⢀⠀⣸⠀⣀⣈⣁⠐⣾⠯⣀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡹⣟⠓⠶⣤⣀
⠀⠀⢀⣴⡇⠀⠹⣆⣀⠈⠀⣺⢟⠉⠀⠀⣿⢁⡤⢼⠷⣄⡀⠀⠀⠀⠀⠀⢸⠇⠈⠳⡀⠀⠉⠻⡲⣄
⢀⡜⡹⠉⢳⡀⠀⠀⠸⠒⠋⢻⣀⠀⠂⠀⣬⣿⡊⣋⠀⢺⠟⠢⣄⣀⣀⣠⠎⠀⠀⠀⠘⢦⠀⠀⠙⡌⢣
⡞⠀⡇⠀⠀⠱⣄⠀⠀⠀⠀⠈⠉⢷⣶⡦⢾⣤⣉⣤⡴⠋⠀⠀⢀⣙⣍⠀⠀⢀⡤⢴⣒⠾⣧⠀⠀⡷⠀⡇
⣇⠀⢧⠀⠀⠀⠈⢦⠀⢀⣴⣺⣯⠯⢛⣇⣠⣞⣿⡫⢳⡄⢠⢾⠟⠷⡚⢦⣰⠛⣏⣍⠄⢀⡾⠀⢠⠇⢀⡇
⠘⢦⠀⠳⢤⡀⠀⠀⠳⣼⠈⠳⠒⠀⣸⢿⡇⠳⠦⠊⢀⡿⢿⣈⣉⢉⣀⡼⠛⠷⢦⣤⠴⠛⣡⡔⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠑⠦⣄⡈⠑⠂⠤⠬⣙⣛⣛⣋⠁⠀⠙⠛⠒⠛⠉⠀⠀⠉⠉⢉⣁⣀⣀⠠⠤⠔⠒⠉⣀⡤⠚⠁⠀⠀⠀⢀⣀⠤⠒⠋⣁⠴⠃
⠀⠀⠀⠀⠀⠉⠻⢖⣒⠢⠤⠤⣬⣍⣉⣉⣉⣉⣍⣉⣉⣉⣉⣉⣉⣉⣠⠤⠤⠄⣐⣲⠞⠋⠁⠀⠀⣀⡠⠔⠚⢉⣠⠴⠚⠛⠋⣉⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠂⠠⠤⠤⠤⠤⠤⠤⠤⠤⠴⠦⠴⠒⠒⠊⠉⠁⣀⣀⣤⠤⠖⠋⢁⣠⣔⣚⡭⠤⠖⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠴⠒⢒⣩⠭⠛⢉⣀⠤⠒⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠤⢒⡲⠞⢋⣁⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⠥⠖⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⣀⠀⠀⠀⠀⠤⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠉⢀⠀⠀⢀⣐⡚⠒⠂⠀⠀⠀⠀⠀⠀⠀⡁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⢠⡀⠀⠀⠀⠉⠉⠓⠒⠚⠒⠒⠒⠈⠁⠀⣀⠤⠊⠀⠀⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⢄⡈⠑⠒⠒⠒⠬⠅⠂⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⠤⠒⠁⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⢀⠠⢄⠀⠀⠢⠤⠉⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠁⠀⠀⠀⠤⣄⠀⠰⠘⡄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⠤⣦⣄⡔⠁⠀⠘⣆
⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⣤⡀⠀⣀⣀⡴⠦⣄⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠹⡄⠘⠁⠀⠀⠀⠈⠑⠒⠉⠀⠀⠀⠀⠀⠀⢰⠡
⠀⠀⠀⠀⠀⠀⠀⠳⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⠀⣀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠆⠙⠉⠝⡒⢄⣀⠀⡠⠤⢤⡤⠤⢤⠀⣀⡠⢒⠪⠉⠋⠰⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠙⠀⠀⢀⠀⠀⠀⠀⡼⢐⠠⠀⢸⡇⠀⠅⡀⠿⠀⠀⠀⠀⠀⠀⠀⠏⣆
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⣀⣀⠀⡀⡪⢂⠁⠀⢰⡇⢀⠨⡐⠡⡈⠢⣀⣀⠀⠀⠀⠐⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⡋⠄⡨⢂⠌⠐⡨⢀⠉⠋⡐⢅⠂⠱⡄⢅⠀⢉⡌⠆
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠃⠠⣔⡤⣒⣓⠂⠅⠂⠁⠀⠀⠈⠐⠨⠀⣊⣒⢬⣢⡅⠈⠐⠀⠠
⡀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⡪⢛⡤⠅⠃⠐⠀⠀⠀⠀⠀⠀⠀⠐⠠⠘⠢⢤⡛⢁⠀⣔⡆
⠹⣤⠂⠀⠀⠀⠀⢒⡥⠹⠀⠀⠉⢠⠚⠠⣀⠀⠀⣀⠀⠀⡀⠀⠀⣀⠄⠓⡄⠩⠄⢀⢏⢮⡒⠀⠀⠀⠀⢐⣤
⠀⠀⠛⢦⡀⠀⠀⠁⡠⠁⢀⡞⠴⢊⢼⠀⠈⠉⠉⠁⠀⠀⠁⠉⠉⠀⠀⡷⣕⢦⠷⡀⠘⢄⠈⠀⠀⣀⡴⠛
⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⢘⠄⣇⡻⢮⣄⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⢀⡷⢟⡴⢀⠇⠀⠀⠀⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡁⢻⡝⠉⢃⠀⠀⠲⣀⡀⠖⠀⠀⡰⠙⢉⡟⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠉⢀⠄⡬⠱⢄⡀⠁⠉⢀⣠⠮⢥⡠⡀⠉⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠊⠂⠀⠈⢈⠋⠙⡀⠁⠀⠐⠁⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠛⡔⣄⠀⢀⠂⠀⠀⠐⠀⠐⢋⡀⠚⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠈⠀⠀⠁⠠⠂⠠⡄⢀⠤⠈⠄⠈⠃⠀⠂⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⡴⢂⠀⠠⠁⠀⠾⠅⠸⠤⠁⠈⢄⠀⡐⣀⣯⡆
⠀⠀⠀⠀⠀⠀⠀⢿⠧⣲⠔⢊⣾⠐⠁⣄⢁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠀⠉⡗⠑⠦⣖⠿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⣙⡟⠛⣾⣷⣖⠈⣈⠢⡀⠀⠀⡀⣀⠀⠀⢀⠔⠡⠅⣢⣷⣴⠛⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⢯⣀⡿⠐⠉⠉⠁⠉⠀⠂⠿⣟⠀⠀⢁⣯⢶⠞⠿⡿⠓⣦⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⢎⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠉⠺⣿⡿⠛⠤⠐⠓⢈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⢃⡐⢟⠐⢏⠈⡦⢵⣦⣀⠀⠀⠈⠛⠶⠇⢢⡄⠈⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡸⠀⠀⠙⢄⣠⠏⠙⡗⣤⡀⠀⠀⠀⠀⢲⡾⠵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠁⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠁⠒⠒⠒⢉⠙⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⠉⠉⠉⣉⣩⣤⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠆⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⢿⣿⡿⢏⣿⣟⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢁⣥⣠⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠉⠑⠀⠀⠛⢧⡍⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣤⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣧⣄⠸⠀⠀⢠⠀⠀⢼⠀⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠷⣶⣦⣤⣄⡐⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡀⣨⣀⠀⠀⠀⠀⣠⣬⣿⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣧⣬⣿⣦⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣻⣿⡿⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣾⣿⣿⣟⣻⣾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣧⣉⠻⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣛⣷⣽⣟⣛⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣧⣄⠀⠀⠉⠀⠛⢻⡿⠿⠙⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣶⣦⣤⣴⣆⣀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡞⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣥⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⢎⣠⣾⣿⣿⣿⣏⠁⠉⠀⠙⣿⣸⡿⣾⢿⣿⣦⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠎⠘⠛⠛⠛⢿⣿⣄⣀⢂⣉⡩⠿⣇⢸⣿⣿⣻⣿⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣰⠏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣀⣤⣯⡘⡛⣿⣿⣻⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠀⠸⡏⢃⠸⡛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⡼⠁⠀⠀⠀⠀⠀⢀⣠⣴⣶⠋⠉⠀⠀⠀⠀⠀⢿⠸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⡼⠁⠀⠀⠀⢀⣠⡼⠖⠉⠀⠙⢷⣄⠀⠀⠀⠀⠀⠸⡆⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⡛⢧⡞⠁⣀⣄⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⢯⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⠳⣨⣷⡶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠸⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣺⣾⣿⣿⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢷⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣥⣿⣿⡿⠁⠈⠙⠉⠳⠶⢢⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠘⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠡⠶⢶⣤⣤⠀⢀⠙⣽⣯⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠻⢿⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣾⣿⡿⠿⣶⣿⣿⣿⣿⣾⣶⣶⣷⣾⣶⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣶⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿
⣿⣿⣜⠓⣯⣥⣭⣭⣭⣭⣤⣩⣬⣭⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⣼⠃⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⡁⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸
⠀⠀⠀⢠⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢤⣠⡴⠤⠴⠖⠒⠓⠀⠀⠠⠤⠤⠄⠀⢀⣀
⠀⠀⠀⢸⡀⠀⡸⠁⠀⠀⠀⡠⢔⣪⣭⣼⣷⢖⣻⡖⢠⠶⢚⠏⠉⠙⠛⠋⠉⠛⠑⠂⠒⠒⠂⠠⠤⠴⣒⠄
⠀⠀⠀⠘⢣⠀⡇⠀⠀⠀⣺⣴⣟⣽⣿⣿⢻⣮⣿⣝⣽⣬⡅⠖⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠘⣶⠀⠀⠀⠀⣈⣿⠻⣿⢿⣿⣟⡿⢟⡹⠧⢐⠋⠈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠛⠏
⠀⠀⠀⠀⠀⣽⡆⠀⠀⠀⢣⡝⠳⢏⡷⡴⠈⠉⠉⠚⠛⠛⠒⠪⠿⠶⠂⠀⠒⠒⠚⠃⠉⠉⠁⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠈⢲⠶⠷⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢻⡄⢀⢀⣠⡤⡔⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠈⢹⣿⣷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠈⠉⠀⠀⠸⣗⣢⠤⠤⠀⢀⣤⣀⣀⢠⣤⠤⠰⢶⣋⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠋⠉⠲⠲⠃⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣀⡀⣤⠤⣤⠴⠶⠒⠂⠀⠇⠠⠤⠄⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠁⠀⠀⠀⠉⠈⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠹⡂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠉⠐⠢⢀⣀⠀⠀⠀⠀⠀⠀⠰⠀⡆⢀⣀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠄⠀⠀⠀⠀⠀⠈⠉⢱⠒⠀⠀⠈⠃⢈⠀⠀⠀⠀⠀⠆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠘⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣠⠀⣀⠀⠈⠀⡆⠀⠀⠀⠀⠀⢁⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣽⡺⠀⠁⠈⠘⡆⢰⠄⡀⢀⠀⠀⡐⡆⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠸⠠⠆⢠⡄⢀⡀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠄⣃⠸⠀⠀⠄⠀⠁⡟⠹⡠⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠉⠀⠋⠀⠖⢠⠄⢀⠈⠠⠖⠛⠋⢜⠣⡄⠊⣀⠔⠫⡈⠓⠋⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠶⠀⡀⠠⡀⠀⠻⠉⠀⠀⠀⠈⠓⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠁⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⠾⠋

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

⠀⠀⠀⠀⠀⠀⢀⡤⢖⡚⠩⠭⠭⣍⡛⣒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⢄⡀⢀
⠀⠀⠀⠀⣠⢞⢩⢾⡃⠠⠔⠥⠀⠀⠀⠉⠁⠨⡑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣙⠢⣑⢄⠀⢀⠀⠀⠀⣀⣀⣀⣀⠀⢀⣀⡀
⠀⠀⠀⣰⢣⡏⠀⠦⠾⠚⣆⢣⡀⠀⠀⠠⠀⠀⣸⣮⢳⡀⠀⠀⠀⠀⠀⠉⠑⠒⠚⢛⣾⣿⡿⠁⠀⠀⠀⠈⢿⠻⠣⠎⠈⠁⠈
⠀⠀⢠⠇⣿⠁⠀⠀⠀⣠⣿⡘⣿⠶⣤⣤⡤⠚⠿⠙⣇⣇⠀⠀⠀⠀⠀⠀⠀⢀⡞⣼⣿⣿⡁⣀⠀⣀⡄⢀⡸⠟⠒⢄⠀⠀⡠⢰⢦
⠀⠀⢸⢰⡇⣀⠀⢰⣯⣨⡼⡈⣷⠠⣿⣿⠀⠀⠀⠀⠨⣹⠀⠀⠀⠀⠀⠀⠀⠀⢧⣛⠿⢿⣿⣿⣾⣿⣿⣟⠁⠀⠀⢸⣷⡾⢷⣫⡞
⠀⠀⠸⡄⣿⣿⣤⣾⣻⣟⠒⠽⣯⣼⣿⠇⠀⠀⠀⠀⡖⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣿⣭⣭⣭⣭⣭⣤⣤⣶⣶⣾⣿⡿⠁
⠀⠀⠀⢳⡸⣿⣿⣿⢷⣽⣻⣟⣿⣿⣿⡤⡄⠀⢠⡔⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠙⢌⡻⣯⡺⣿⣿⣿⣿⣿⣿⣿⣧⠴⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠢⢭⣛⣛⠛⠛⣛⣛⣫⠵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠶⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⡀⡀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣷⣿⣯⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢒⣠⡾⠏⠣⢄⣀⣀⡔⠁⠀⠈⢙
⠀⠀⠀⢀⣴⣶⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣿⣯⠉⠀⠞⠻⣶⣧⣄⠀⠀⠀⢠⡑⠒⠂⠈⣀⠀⠀⣀⡜⠏⠋⠀⠀⠀⢀⣾⡳⡄
⠀⠀⠐⢜⡿⣾⡏⠈⢽⣷⣿⣿⠉⠉⠋⠙⠉⠉⠆⠀⠀⠀⣼⡿⣫⠆⠀⠀⠀⠀⠀⠀⠀⠈⠹⣋⡁⠀⢀⡠⠦⠴⡿⠟⣋⠴⠁
⠀⠀⠀⠀⠉⠒⠯⠤⣜⣛⣿⡿⠤⠤⠤⠤⠤⣄⣘⣢⡤⠭⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⣀⠀⠉⠉⠀⠈⠛⠛⠉⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟⣫⣝⡿⢻⡟⣟⢻⡏⣯⢹⠿⡉⣿⢹⠉⡏⢹⠹⠍⡯⢹⠍⣿⣿⢀⡃⢿⠛⡟⣿⢉⡏⢹⠿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣬⣭⣿⡼⠷⠿⠾⠷⠿⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠾⠷⠾⠷⠶⠿⢼⣧⣾⣆⣽⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⣈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢬⠍⢩⡄⠀⢀
⠀⠀⠀⣠⠄⢠⢄⣴⠂⣭⣻⠟⣮⢪⡻⡦⡀⠀⠀⠀⠀⠀⠀⣶⠀⠰⡄⠀⠘⠉⡹⠀⡀⠀⡤⠀⠀⠀⠀⠀⠀⣠⡶⡷⠊⣴⢎⠾⠟⣐⣰⣏⡓
⠀⠀⠄⡾⠀⣿⣌⠛⠷⠶⠶⠾⠟⣰⣗⣿⠊⣷⠀⠀⠀⣤⠀⢻⣦⡀⠙⠂⠀⠀⠀⠊⠀⢠⠇⢠⠀⠀⠀⠀⣰⡿⠵⣵⢂⠁⠀⣰⢀⣤⠉⢻⢀⣦⡴⡄
⠀⢸⠂⣿⡄⠈⠙⠓⠲⠶⠶⠿⠿⠛⠋⠁⠀⣿⠘⠀⠀⢛⠧⠀⠙⠻⠦⣀⣀⠀⠀⠤⠖⢀⠀⠉⠀⠀⠀⢠⣿⣥⣦⢠⠏⣀⠘⢣⠾⢃⣷⠀⠸⡙⡧⣷
⠀⢸⠀⢈⠻⢶⣤⣤⣀⡀⠀⢀⣀⣠⣴⣶⠾⢋⠀⠀⠀⣿⣷⠘⠗⠀⠤⠄⠀⠀⠠⠤⠚⠁⣴⠿⣇⠀⠀⢸⢿⣿⠣⢆⠸⢷⡇⢰⣾⠸⠋⢀⡞⣄⠀⢾⡀
⠀⢸⡇⠰⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠙⣀⠀⠀⣿⢿⡇⢀⣶⣷⡄⢠⡶⠟⠲⠶⣾⠋⠀⣇⠀⠀⢸⡄⣿⡀⣾⣷⣶⢣⣬⡍⣴⣾⢼⣿⡄⢠⣼⡇
⠀⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠙⣧⣙⠋⠛⠟⠳⠞⠁⠀⠀⣰⣿⣦⣤⡿⠀⠀⠈⢿⣾⡀⡏⠀⢻⡾⠋⢳⡝⠘⠚⣹⡇⣸⣽⠇
⠀⠀⠀⠀⠉⠑⠲⠤⢤⣤⣤⣄⡤⠤⠄⠒⠉⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣤⣤⣾⣿⠿⠟⠉⠀⠀⠀⠀⠀⠙⠻⢿⣦⣾⣴⣤⣿⣿⣦⣤⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠭⠍⠥⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠭⣭⣭⠉⠁
⠀⠀⠀⠀⣠⠞⠉⠀⣀⢀⣀⠀⢀⡈⣽⡶⡄⠀⠀⠀⠀⢀⣴⠿⠁⠀⠀⢀⣀⣀⣀⣀⠐⠬⠑⢦⡀⠀⠀⠀⠀⣠⡶⠀⠀⣈⣉⣉⣁⡀
⠀⠀⢠⠞⠁⣠⢶⡿⡤⠒⠒⠐⠶⢉⣿⣿⡀⣶⣄⠀⠀⡼⠁⠂⢀⣴⠟⣋⣩⣭⣭⣉⠻⣷⡄⠀⢻⡀⠀⠀⣼⡏⠀⠀⠉⠁⠀⠀⠀⠉⠂⠀⠀⠀⠀⡀
⠀⢠⠃⠀⠸⠁⣼⡎⢀⡤⣄⠀⠈⡎⣻⢸⡆⢉⠉⡇⠀⠃⠀⢠⡟⣡⣞⣭⠿⠿⢿⡝⢿⡌⢿⡀⠘⡇⠀⢸⢋⡴⠀⠀⠀⢀⡤⠴⠤⣄⠀⠈⢦⠀⠀⢀
⠀⢸⣤⠀⡿⣿⢹⡇⠜⣫⠽⠁⢀⡗⢻⠘⢁⡈⠀⡇⠸⠀⠀⢾⠁⣿⣿⠣⣞⠹⠆⣿⢸⣿⢸⡇⠀⡇⠀⡞⣾⠁⠐⠀⣰⠋⠀⣤⣤⠈⡇⠀⠈⡀⢠⣿
⠀⠈⣿⡆⢳⠀⣍⠃⢢⠳⡄⢀⡟⡡⠋⣀⠘⠃⢠⠃⠈⠀⠀⢾⡄⣿⡹⣧⣙⡷⣚⣫⣿⠃⣸⠃⠀⡇⠀⠠⣿⠃⡀⠀⣿⠀⠀⠑⠄⠔⠁⠀⣸⠁⢸⣼
⠀⠀⠸⣿⡄⠰⡍⢢⡀⠙⠓⠈⡁⣰⣮⠡⠀⢠⠇⠀⠀⢧⢀⠘⣷⡘⢷⣬⣛⣛⣛⣉⣡⣾⠏⠀⢠⠃⠀⠀⢠⠀⠹⡄⠘⠆⠀⠀⠀⠀⢀⡴⠃⢀⣼⠏
⠀⠀⠀⠙⠿⣦⣄⡙⠛⠉⠭⠩⠛⠋⠀⣠⡴⠃⠀⠀⠀⠘⢦⡁⠈⠳⣄⡈⠙⠛⠛⠛⠉⠀⠐⣠⠎⠀⠀⠀⠀⠐⠆⠉⠂⠀⠀⠀⢒⡛⠉⣴⢋⡹⠋
⠀⠀⠀⠀⠀⠈⠙⠺⠭⠽⡦⠤⠤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠭⠿⠒⠶⠆⠐⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠦⢤⣴⣛⡿⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡖⠊⠉⠁⠀⠀⠈⢧⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⢻⢀⢀⣀⣀⣤⣤⣜⣧⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠛⠉⠉⠉⠀⠀⠀⠀⢀⡽⡏⠛⠢
⠀⠀⠀⠀⠀⠂⠀⠀⠒⠆⠤⢀⡀⠀⠀⠀⠀⠀⢀⡞⠥⠴⠲⣤⠀⠀⠀⠀⠀⢀⡠⠖⢯⠀⠘⡄⣠⡇
⠀⠀⠀⠀⠒⠂⠓⠒⠒⠤⢄⣀⠀⠁⠒⠠⢄⢀⣀⣇⣀⣀⣀⣤⣆⠤⠤⠒⡏⠁⠀⠀⠘⣆⣤⠾⠋
⠀⠀⠀⠀⡑⡄⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⣄⣀⠀⡇⢸⠉⠀⠀⡇⠀⠀⢀⣱⣠⡤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠙⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢉⣏⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⣩⡯⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡛⠁⢀⣀⣠⣤⠤⠶⣺⢷⠲⠦⣤⣠⡀⠀⠈⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣩⡴⠦⠖⠛⠋⠩⠀⠐⠒⣻⠃⠈⢿⡓⠒⠀⠩⠍⠛⠳⠿⢶⣌⣳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠋⠉⠀⠀⠀⠀⠖⠀⠀⠛⠛⡿⠁⠀⠀⠀⢻⡉⠁⡀⢀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡾⠁⠀⠀⠀⠀⠀⢻⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡞⠁⠀⠀⠀⠀⠀⠀⠀⠹⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣛⡄⠀⠀⠀⠀⠀⠀⠘⢲⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡴⠂⠀⠀⠀⠀⠀⠀⢀⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣿⠿⣷⠀⠀⠠⠄⠀⠀⢤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⢁⡄⢀⠀⠀⠀⣸⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⣴⡿⣇⠀⠄⠀⠐⣦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡤⢠⠀⠘⢠⣧⡀⢸⡇
⠀⠀⠀⣠⣤⣤⢤⣀⠀⣠⠼⠦⣽⣿⠗⠿⣄⠀⣦⣠⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠏⢰⠃⣾⠀⠁⢸⣷⡄
⠀⠀⠀⠹⣽⣿⣤⣿⣿⡁⠀⠀⢹⣇⡤⣖⠯⠭⠝⠓⠂⠺⠉⠩⠉⠻⢷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡎⢸⡋⠀⠀⢸⣇⣵⠀⠀⠀⣠
⠀⠀⠀⣤⡬⡿⢯⡥⠟⠿⢦⣹⠞⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⢝⡲⣄⡀⣀⣀⣀⣀⡀⣈⣧⡟⣃⠀⠀⢸⣧⠾⣄⣠⢾⡧⢤⣤⣤
⠀⠀⠀⠘⢾⡛⣾⡀⠀⠀⢲⡷⠡⢚⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠙⠯⣭⠟⢩⠟⣩⠯⢹⣷⠤⠦⠼⡛⠚⠉⢀⣿⣷⠛⡳⠃
⠀⠀⠀⠀⠀⠉⢳⠛⠒⡾⠛⠷⣖⡡⠈⡠⢒⣂⡤⠽⢶⡶⠾⠧⢴⣆⡠⢄⡀⠀⠀⠀⠀⠀⠉⠈⢳⢧⣞⠁⠀⢸⣗⣢⠬⠑⠂⡀⠁⢸⠓⢶⠋
⠀⠀⠀⠀⠀⠀⢫⡀⢘⣇⡤⣶⢿⡁⢊⠴⣯⡁⠀⣀⡐⡟⠦⣄⠀⠀⣉⠷⢮⣑⢤⡀⠀⠀⠀⠀⠈⠑⠯⣓⠦⣬⣏⣩⣛⡓⣶⢀⡀⠈⠧⣼⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣏⡁⠉⣸⠟⣧⣿⣒⠸⢿⣟⣹⣅⣳⠀⣄⣹⠞⠁⠀⠀⠈⠓⢮⣳⢄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠭⠭⠭⡿⠄⣀⣢⡴⠞⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢽⡆⠈⠁⠚⠭⢛⡍⣻⣿⡿⠿⠛⠳⣈⠏⡄⢀⣀⠀⠀⠀⢀⣈⠓⣯⡲⢄⡀⠀⠀⠀⠀⠨⠭⠤⠥⢻⣿⣿⣿⠶⠶⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢁⣈⣽⣤⣾⠛⠦⣄⣙⣛⣻⡆⢰⣿⣿⣿⠀⢼⣿⣿⣷⠀⣘⣓⣮⣕⡂⠀⠄⠀⡐⡒⡤⢽⡿⡟⣯⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⡴⠚⠉⠁⠈⠀⢣⣀⣀⡸⠁⣹⢫⢷⣈⠛⠛⠋⠾⠏⠛⠛⠋⣠⢏⢻⣧⣀⣉⡿⠒⠲⠶⠖⠚⡏⠀⠀⢹⠙⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⣧⠴⠚⠉⠻⣷⣶⢦⢶⣶⡾⠋⠙⠲⢬⡇⠈⠁⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁



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

⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⢀⣴⡿⠿⢿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⢿⣿⣦⡀
⠀⢰⠋⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠛⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠛⠉⡀
⠀⠀⠀⢠⣦⣴⣾⣮⣶⣾⣧⣷⣿⣗⣢⠀⠉⠙⠃⠀⠀⠀⠀⠀⠀⠘⠉⠁⠀⣔⣺⣿⣿⣶⣷⣾⣴⣷⣦⣮⠄
⠀⠀⠀⠈⠛⣿⡛⠋⠉⠙⠋⠀⠀⠉⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠉⠛⠋⠀⠈⠉⠙⢛⡿⠛⠁
⠀⠀⠀⠀⠀⠩⠻⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⢴⠟⠅
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠈

⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⡀⠀⠀⠀⡀⠀⣐⣲⣶⡒⠠⢀⠀⠀⠀⢤⠤⠦⠴⠲⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⢄
⠀⠀⠀⠀⠀⠀⠈⠴⠀⠂⠈⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠡⠆⠐⠈⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣶⣍⣩⣥⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖
⠀⠀⠀⣠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠰⠂⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⣴⠋
⠀⠀⡴⠟⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣽⣿⣷⣶⡋⠀⠀⢠⡏⠀⠀⠀⠀⣠⠾⠁⠀⢀⣀⢀⠄
⢀⡾⠃⠀⢀⣔⡑⢂⣠⣴⠀⠀⠀⠀⠐⢤⣤⣤⣾⣧⠀⠀⠀⠀⠀⠙⠻⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⣀⡌⠐⣀⣴⡆⠀⠀⠀⠀⠦⣤
⠀⠁⠀⠀⠀⣿⣿⡏⢩⣿⠀⣀⠀⠀⠀⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⠉⣽⠇⢀⡀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠈⣷
⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠶⢬⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠸⢦⣿⠀⠀⠂⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⠀⠀⠀⠀⠈⢷
⠀⢤⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠛⠀⠀⠀⠀⡀⣠⠀⠀⢸⡗⢦⣬⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠘⠃
⢠⣶⡶⣃⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢉⠠⠀⠘⢧⣸⣿⣋⡔⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⣶⣞⡀⠀⠀⠀⠘⠃
⠸⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠉⠉⣷⢤⣇⣴⣴⠀⠀⠀⠀⠻⢿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣻⣿⣿
⠀⠀⡀⠀⠠⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⢄⡃⣀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴
⠀⠒⢠⠶⠦⠶⡎⠀⠴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠂⠂⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠂⠴⠦⠰⢶⠁⠠⠄⢠
⠐⠻⠇⢀⣛⣁⣼⣞⣲⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠌⠖⠀⠀⠀⠀⢰⣄⡈⣋⡀⠿⠚⠿⠀⣈⣁⣤⣷⣓⣾⡿
⢀⣉⣤⢾⣿⣷⡟⠛⠛⠉⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣨⣿⢦⣀⣈⣡⡴⣿⣿⣾⠛⠛⠋⠁⠀⠀⠀⠀⠀⡀
⢸⣿⣿⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣶⣶⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢼⣿⣿⣿⡷⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠈⠉⠀⠀⠀⠀⠀⢰⣤⠄⡀⠀⠀⠀⡀⠈⠻⢿⠿⠟⠥⣀⠀⠀⠀⢤⠤⠤⠴⠠⣤⡄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⢀⠠⠙
⠀⠀⠀⠀⠀⠀⠈⠰⠁⠂⠈⠀⠀⠐⣷⣿⣿⣿⣿⣿⣿⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠁⠆⠰⠈⠀⠀⠀⢾⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⣭⣉⣩⣭⠗⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡧
⠀⠀⠀⢠⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⡄⠰⠆⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣤⠏
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣴⣶⣴⣶⣴⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠋⠀⢀⡴⠒⠉⠉⠉⢉⡳⠞⠛⠛⠛⠋⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠴⠚⠁⠀⣀⡠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠈⠻⣗⠤⣀⠀⠀⠀⣀⠴⠋⠁
⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠤⠤⠤⠤⠊⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢾⣭⣤⡴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉




⠒⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠈⡈⠠⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠤⠤⠤⠒⠊⢡⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠲⠤⣄⡀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⡏⠒
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⢀⣀⠤⠴⠤⠤⢍⣲⣶⣴⣤⡷⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣦⣄⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⢀⡠⠖⠉⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠓⠭⣶⣤⣤⠤⠚⢉⣠⠴⠚⠁⢀⣠⠤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠒⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠳⠤⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙




⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⢄⡀
⠀⠀⠀⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢀⠐⠐⢀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⣀⣀⣀⠈⠙⠓⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⡗⠦⢄⣀⣀⡡⠤⠔⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉
⢀⣤⠒⢋⡉⠀⢈⠉⢙⢦⣄⣀⢉⠑⣆⠀⠀⠀⠀⢀⡇⣀⠀⠀⠀⢀⡀⣀⢸⠀⠀⠀⠀⠀⢀⣠⢶⠊⠁⡀⠀⡀⠀⠀⡀
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡤⠶⠖⠚⠛⠛⠿⠿⠽⠿⠯⠽⣛⠓⠶⢤⣀
⠀⠀⣠⡤⠴⠶⢚⣋⠡⠞⠋⣁⡤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠙⠛⠛⠛⠓⠒⠲⠶⠦⣤⡀
⢠⡞⠁⠀⢠⠞⠁⠀⠀⠒⣉⣠⣤⡤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⣤⣤⣄⣉⡙⠛⠒⢄⠀⡀⠉⠳⣄
⣼⠁⠘⠄⢸⠀⠀⢠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢭⠓⢦⠈⠃⠙⣆⠀⢹
⢷⡘⢄⡀⠀⠑⠄⠈⠳⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣩⠴⠊⠀⠀⢀⠏⠀⠼
⠈⠙⠦⣭⣅⣀⡀⠀⣀⣀⠀⠉⠉⠙⠛⠛⠓⠒⠒⠒⠒⠒⠒⢒⣚⣛⣛⣉⣩⡥⠀⠀⠀⡠⠖⣁⡤⠚⣠
⠀⠀⠀⠀⠀⠙⣏⠉⡻⢯⣍⣀⣩⣭⣙⡒⠦⠄⠀⠀⠐⠊⠉⢁⣀⣤⣤⣤⣀⣀⣤⠤⢈⣠⣬⡥⠴⠞⠁
⠀⠀⠀⠀⠀⠀⢹⡄⠈⠁⢸⡆⠐⠒⠊⠙⡟⠓⡲⠶⠶⠚⢻⠛⠧⢤⣬⣤⣬⣥⠶⣚⠉⢀⡟
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣷⠀⠀⠀⠀⣷⠀⠈⠉⠉⠀⣿⠀⠉⠒⠒⠒⢰⠇⠈⢡⢂⡾
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢸⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡟⠀⢀⠎⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠧⠀⠀⠀⢸⡆⠀⠀⠀⠀⡟⠀⠀⠀⠀⣸⠁⠀⠌⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⣀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⣀⣠⡴⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⢠⢆⠀⡴⢦⠀⡴⡄⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠃⠈⠛⠀⠈⠛⠁⠙⠋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣺⠉⣰⣿⡇⠀⢸⡇⠀⠀⢰⣏⣍⡓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠚⣁⣠⡭⠷⠒⢊⡿⢻⡑⠒⠦⠤⣌⣉⡀⠀⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣚⣥⠤⠶⠒⠛⠉⠁⠀⠀⠀⢀⡞⠀⠀⢳⡀⠀⠀⠀⠈⠉⠛⠒⠶⠤⣬⣛⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠈⠉⠉⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢀⡴⣄⠀⢀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠰⣶⠞⠋⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢻⠀⠀⠀⠿⠀⣿⣴⠋⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠉⠀⣤⠴⠖⠀⠀⠀⡞⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⡇⠀⠀⠀⠀⠘⠃⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠼⢷⠃⠀⠀⢸⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⡿⣿⡀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⡾⠋⢻⠀⠀⣴⠛⠳⣆⠀⠘⣆⠀⠀⠀⠈⠀⠀⢀⡏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣥⣾⣇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⡶⠋⠀⠀⡇⠀⠀⣿⠀⠀⠘⢧⠀⠀⠀⠀⠀⣸⠀⠀⢸
⠀⠀⠀⣀⣤⣤⣤⣀⠀⢀⡤⠷⣸⣿⡿⠾⣄⠀⠀⢀⣼⠁⠀⠀⠀⠀⠿⠶⠶⠂⠀⠙⠶⠶⠃⠀⠀⠀⠈⢧⠀⠀⠀⢠⠇⢠⣤⢸⢦⡀
⠀⠀⠀⠹⣽⣿⣤⣽⣿⡏⠀⠀⠸⣟⣀⡤⠞⠛⠋⠉⠉⠉⠉⠉⠛⠛⠒⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡾⠀⠸⢾⢸⠋⡇⠀⠀⠀⣀
⠀⠀⠀⣀⣈⣛⣿⣩⠽⠿⣦⣘⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⢳⣰⠇⠀⠀⠈⢸⠋⣇⣀⣠⣾⢃⣀⣀⣀
⠀⠀⠀⢿⡷⢧⣹⡇⠀⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡓⠒⠒⠒⠒⣺⠛⢦⣄⣠⣤⠼⠿⠛⠋⢱⢟⣋⡼⢞⡿
⠀⠀⠀⠀⠑⠶⣋⡱⢦⣶⠞⠳⣄⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⣠⠞⠁⢀⣞⠁⠀⠀⠀⠀⠀⠀⣾⢏⣙⠶⠊
⠀⠀⠀⠀⠀⠀⡏⠀⠀⣏⣀⡤⠾⡆⠀⣠⣴⢯⣭⡇⠈⣳⣄⠀⠀⠀⠉⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣉⣻⠓⠲⠶⢤⡀⠀⠀⠹⣄⣹
⠀⠀⠀⠀⠀⠀⢙⣶⣖⠋⠁⠀⠀⢳⣴⠃⠈⢳⣦⣴⡶⢿⡈⠙⠲⣄⠀⠀⣼⢯⠿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⢺⡇⠀⠀⣀⣨⠽⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠙⣆⠀⠀⠀⠉⠛⠛⠒⢿⣿⣟⣶⣧⡈⠳⡈⣳⠶⢇⠀⢠⠀⣸⠿⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⣿⡯⣤⣤⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢻⠀⠀⠀⠀⢀⣀⣠⣾⡟⠋⢩⣭⣱⣤⣼⠋⠀⣌⡗⠛⠳⣇⠀⠘⣿⣹⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡙⠀⠀⢙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠴⠒⠛⠯⠤⢻⠃⠈⠓⣶⠤⣤⠤⣾⣤⣤⠞⣧⣀⣴⠳⢦⡤⣿⠤⣤⣤⠼⠛⠲⡦⠤⣤⣤⠤⢶⠋⠈⠀⣟⠢⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠘⠦⠤⠴⠃⢠⠏⠞⣁⡴⣇⠈⠁⣾⡈⠁⣠⠧⣌⡓⠘⣟⠦⠤⠼⠁⠀⠀⠀⠀⠈⠳⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠒⠉⠁⠀⠈⠑⠚⠁⠑⠚⠁⠀⠈⠉⠓⠿


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⢨⡿⠀⣰⡿⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣾⠃⢠⡟⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢇⣼⠇⢠⡿⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣼⡏⢠⡿⠃⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢰⡟⠀⣾⠗⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⢀⠠⠄⠒⠂⣈⣉⠉⠥⠀⢀⡿⢠⡿⠀⣼⠏⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠰⠁⠀⠀⠞⠁⠀⠀⠀⠀⠀⣾⠃⣾⠁⣰⡟⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢢⡀⠀⠀⠀⠈⠲⠄⣀⠙⠲⢄⠀⠀⠀⣸⠏⣼⠇⢠⡟⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⣿⡙⠫⣝⢷⣦⣀⣀⣩⣭⣭⣴⣦⣤⣤⣦⣤⣶⣤⣤⣰⡟⣰⡏⢀⡿⢁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⢡⣤⡙⢿⣍⣉⣳⣈⠻⠿⣍⡠⠤⣄⠠⡤⣘⠀⠡⣄⠀⢈⣿⢡⡿⠻⣿⢁⣾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣀⡘⠓⢽⡿⢧⣌⠁⢞⠈⢷⠀⠈⠀⠀⠈⢄⡀⠀⠀⣸⠃⡼⠁⡼⢁⣾⠋⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⣹⡿⠿⠷⣶⣯⣉⡑⣭⡀⢸⡶⢄⠀⠨⠀⢀⠁⢰⣶⣧⣼⡧⣾⠷⢾⣷⣶⣤⣄⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣠⣾⠋⠁⠀⢒⡂⠀⠍⠉⠻⠿⠛⣷⣶⡏⡐⠀⠈⣀⠜⡋⠀⠌⠀⡤⠀⣤⣞⣉⣍⢙⠻⣷⣌⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣠⣾⡯⠄⠀⢾⡶⣤⣥⣤⣤⣄⣘⠆⠈⠠⣼⣦⣑⣤⠞⡡⠀⡠⢀⠔⡠⠄⠀⢿⣻⡿⢻⣿⡷⠾⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⡟⢻⠿⣯⣽⡇⢀⠀⠈⠉⠙⣯⡀⢢⡒⢡⣾⡿⡡⢊⡤⢊⣤⡪⢶⣤⣠⣴⣼⣿⠟⠻⣿⠀⣄⣞⡷⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠠⢧⣎⢘⣷⠐⠚⢇⡀⠀⠈⢻⡅⣰⡿⢋⠜⡰⣡⢜⡠⢋⠔⢉⡿⡁⠠⠁⣬⠆⢘⣿⣷⣎⣁⣠⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠉⠛⠷⢶⣾⣦⣿⣄⣐⣂⢻⣀⡐⣾⡷⣛⢖⡡⣚⢚⡵⣿⣷⣥⣶⣽⣇⣵⣾⣯⣷⣶⠿⠿⠟⠛⠋⠉⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠳⢶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠾⠋⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⡀⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠶⠶⢶⣶⣶⣶⣶⣦⣤⣶⣶⣶⣶⠶⠶⠿⠛⠋⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣛⡛⠛⠒⠲⠶⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡈⡟⠀⠀⠀⠀⢀⣠⣶⣷⣶⣦⡀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⢀⠴⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣇⡠⠞⠛⠛⠛⢿⠟⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⡀
⠀⣀⣾⣷⣶⣦⣤⣤⣄⣀⣀⡉⠉⠛⠛⠿⣿⡿⠃⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢟⣯⣾⣷⣶⣶⡶⠂⠀⠀⠀⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⡝⠁⠀⠀⢸⡏⣶⣶⣿⡧⢟⣯⣾⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠿⢿⠿⠋⠀⠀⠀⠀⠈⠳⠿⣿⣿⣾⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣷⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣷⣯⣴⣺⠝⣛⢿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣇⣀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣹⣿⣷⠀⠀⠀⠀⢀⣴⣿⣿⣟⣿⢿⣿⣿⣿⣿⣷⣷⣶⣥⢪⠝⣿⣿⠿⠋⠀⠀⢀⣴⣿⣿⣷⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⣿⣿⢧⠀⠀⠀⠘⣿⣫⣿⣛⡿⢿⣿⣿⣿⣻⢿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠸⣯⣻⣿⣿⣟⣻⡿⢿⣿⣿⣿⣽⣿⣿⣿⠟⠁
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢹⠏⠀⡇⠀⠀⠀⠘⠻⢿⣽⣟⡻⠶⣭⣝⣛⣻⡮⣿⠿⠋⠀⠀⠀⠀⠀⠀⣀⣶⣿⢿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠟⠁
⠀⠀⠀⡜⠹⣿⣿⢹⣿⣿⣿⡞⣆⡾⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⠯⣭⡽⠞⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠸⣧⠀⠈⡟⣿⣿⣿⣿⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢿⣿⣟⣷⡶⣭⣭⣟⡿⠋
⠀⠀⠀⠘⢷⣤⡇⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠙⢸⡇⠙⠛⠁⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⢶⣶
⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⢿⣟⡁⠀⠀⠀⠀⠀⢰⣶⢶⣶⡟⠻⡿⠁⣛⡃⢈⣽
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣻⣿⣿⣿⣿⡿⢿⣛⣯⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢸⣅⡀⣶⣤⢰⣿⡆⠿⡿⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠃⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠈⠻⣋⡀⣩⣥⡀⣾⣷⡘⢿⣆
⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⠿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢹⣷⠸⢿⡷⠘⠻⠇⠈⢫⣥⡀⣹⣧
⠀⠀⢸⣿⠿⠿⣿⣿⣿⣿⣻⣿⣿⠷⠶⣯⣽⣿⣻⣶⡦⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢷⣤⢰⣶⣶⠸⣿⡿⠘⠛⡛⠈⠉⣷⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⠿⠿⠶⠿⣿⣿⣯⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠸⣏⣀⢩⣭⣄⠠⣶⣶⡀⢿⣿⡄⠻⢷
⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠀⠀⢀⣠⣤⣤⣽⣿⣿⣿⠿⣿⣝⢻⣿⣿⣻⣧⣤⣤⡀⠀⠀⢹⡿⠀⠛⣛⡀⠉⣩⣅⢀⣶⣦⡄⣾⣧
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡻⣯⣿⣿⣿⣿⣿⡆⠀⠘⣷⡆⢺⣿⡷⠘⠿⠟⠈⢛⣛⠁⢈⣿
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⡿⠀⠀⢛⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⠃⠀⠀⣿⡄⣠⣶⣆⣠⣿⣿⣤⠿⠿⠧⠛⠋
⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠯⠛⠿⠿⠿⠋⠉⠛⠊⠙⠋⠉⠁⠀⠀⠀⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⢀⣀⣠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⢺⣍⣉⡀⠙⢯⡁⢦⠉⠻⣟⡦⡀⠀⠀⠀⠀⠠⣴⡞⠉⣉⡭⠴⠦⣤⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡼⠁⡅⠀⠀⠑⢄
⠀⠀⠀⠀⠀⣠⠔⠊⢹⡄⢄⠀⠸⣷⠂⠈⠂⠈⢷⡄⢣⠀⠸⡇⠹⡄⠀⠀⢰⠀⣏⡠⠊⢠⣴⣶⡿⠿⠝⡆⠀⠀⢰⠃⠀⡠⠒⠉⠉⠀⠀⠈⠓⢦⡀⠀⢣
⠀⠀⢀⡔⠋⣰⡒⢆⠘⣧⠀⢳⡀⠹⣧⠀⠀⠀⠘⣷⠈⡆⠀⢹⣰⡇⠀⠀⣇⠀⠉⠀⡜⠁⠀⠀⠀⣀⣀⣠⡄⠀⣾⡄⠈⠉⠀⠀⢸⡆⡸⠀⠀⠀⠻⠄⢸
⠀⠀⡎⠀⠀⢻⡀⠈⠆⠈⢷⠀⢳⡀⠹⣷⠀⠀⠀⢹⡄⣧⣴⣾⠟⠀⠀⠀⠹⣦⡀⠀⠦⠔⠒⠋⠉⠁⠈⣽⠇⠀⣿⣿⣄⠀⠀⠀⠀⣧⠃⠀⠀⠀⣀⣠⡿
⠀⢸⡀⠀⠀⠈⠻⣄⡈⢄⠈⢳⣄⣇⠀⠙⣦⣴⣤⣴⣷⠿⠋⠁⠀⠀⠀⠀⠀⠈⠻⢤⣀⡀⠀⠀⠀⣠⡼⠋⠀⠀⠘⢿⣿⣷⣦⣤⣄⣠⣄⣴⣶⣿⣿⡿⠃
⠀⠀⠳⢤⣤⣀⣀⣀⣀⣺⣶⣶⣽⣿⣾⡿⠿⠟⠛⠉⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠈⠉⣉⣉⣉⣉⣉⠉⠁⠀⠀⠀⠀⢀⡔⠊⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⣀⠠⣤⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠊⠉⠉⠓⣶⢤⢄⣀⣀
⠀⠀⠀⣠⢚⠻⢤⡀⠀⠀⠈⢻⣷⢦⡀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢀⡔⠁⠀⠀⠀⢧⡇⠀⠙⡄⠀⠀⠀⠀⣠⣮⡑⡀⠀⠀⠀⠀⠀⠧⠀⢈⠄⣈⠗
⠀⣠⣾⣄⡀⠈⢢⡙⠀⠀⠀⢸⡗⠀⡱⣆⠀⡷⠚⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢸⣦⣤⣀⠀⢀⡟⠀⠀⠀⢱⡄⠀⢠⡞⠉⠀⠹⣌⢢⠀⠀⠀⠀⣇⠀⠞⠋
⠀⡖⠒⠒⠦⣍⣢⣿⣷⣀⣼⣿⣁⣰⡇⢘⠀⢱⡀⠀⠀⠀⠀⠁⠀⢀⡾⠁⢠⡞⠉⢉⠉⢻⡾⢀⠀⠀⣀⣾⡇⢠⠋⠙⣦⣀⠀⢘⣧⣣⣀⣤⡜⠋
⠀⡇⠀⠀⢀⣾⣿⠿⠿⠟⠉⠉⠉⠉⠓⠛⠀⠀⠙⠲⢦⣤⣤⡤⠖⠋⠀⠀⠀⡇⠀⠀⠀⠀⢣⠀⠀⠋⠋⡽⠁⠘⠐⠛⠛⠛⠗⢛⣛⡭⠭⠥⢤⣀⡀
⠀⠳⠚⠛⠉⣁⣀⡠⠤⠤⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣇⠀⠀⠚⣦⡄⠀⠊⠀⠀⠀⠀⢀⠤⠶⠛⠟⠷⢦⣄⡀⠀⠀⠉⠑⢦⡀
⠀⠀⠀⡔⣋⠁⠀⠀⠀⠀⠀⡀⠀⠺⣹⣳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣈⣓⠒⠛⠋⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠂⠀⠀⠈⠙⠳⣄⠀⠀⠀⢹⡄
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠈⠘⠛⠿⣿⣏⠉⠒⢄⠀⠀⠀⠀⠀⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢹⡆⠀⢀⣼⠃
⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⢀⠁⠁⢸⡆⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⡀⠱⡄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣿⠿⠛⠛⡿
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠇⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢡⣀⡇⠀⠀⠀⠘⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⣯⠀⠀⠀⡇
⠀⠀⠀⠀⡂⠂⠀⠀⠀⠀⠄⠀⠀⠀⢸⣷⠀⠀⠙⠶⢤⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠈⣿⣷⡿⠁⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠳⣄⣀⣀⣀⣀⣀⣀⣤⣬⠾⠟⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠢⠤⠤⢄⣀⣀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠻⣤⣄⣀⠀⢀⠀⠀⠀⠀⣀⢀⣿⣤⠖⠋
⣀⣀⣀⣀⣀⣀⣉⣁⣀⢀⣀⣀⢀⡀⢀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⠓⡒⠊⠂⢘⣉⣀⣀⣀⣀⣀
⣿⠉⠉⣿⠛⡟⡟⡛⡛⡿⡛⡟⡛⡟⡿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣛⣻⣿⣿⣛⣟⣟⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣰⠦⣀⠜⢦⣀⠶⣀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠁⠀⠉⠀⠈⠉⠀⠙⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠾⠂⠀⣤⠀⠀⠀⢠⡄⠀⠸⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠡⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠙⠄⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠚⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠶⢖⣀⣀⡀⠀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⠀⠾⣧
⠀⠀⠀⠀⠀⠀⠠⡏⠙⠛⠃⠸⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠉⡗
⠀⠀⠀⠀⠀⠀⣠⠗⣶⢤⡤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⢤⠴⡖⢻⡀
⠀⠀⠀⠀⠀⣠⣆⣰⢷⡞⠀⡌⢸⡅⠀⢀⣠⣤⠀⡄⢸⡇⠀⠀⠀⠀⢹⠀⣤⣀⣤⡀⠀⠀⣽⠀⡇⠀⠷⠿⣄⣷⡀
⠀⠀⠀⢠⢫⢏⡟⢁⢾⡃⣰⠁⡜⠑⠋⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠓⠘⡄⢱⡀⣻⢦⠙⣟⢯⢣
⠀⠀⢀⡇⡎⢸⠁⡎⡌⣹⠇⣰⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢻⡉⡌⡆⢹⠈⡆⡇
⠀⠀⠀⡇⡇⣿⠈⣧⠜⢁⡖⢹⠀⠚⢦⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣠⠞⠂⢸⠙⣦⠙⢥⡇⢸⡇⡇⡇
⠀⠀⠀⢣⠱⣧⡄⠈⡶⡛⢀⡜⠀⠀⠁⠈⠋⢙⡋⠻⢸⡇⢀⣄⣀⠀⢸⠸⠋⣛⠈⠋⠈⠁⠀⢸⣄⢸⡷⣎⠀⣤⡶⢁⠇
⠀⠀⠀⠈⡷⢩⡷⡞⣼⠷⢉⣼⠀⠀⠀⠀⠀⠈⠁⠀⢸⡇⠘⢤⠼⠀⢸⠀⠀⠉⠀⠀⠀⠀⠀⢸⣌⠓⣾⡜⡶⣯⠱⡏
⠀⠀⠀⢰⠁⢻⡆⡇⠻⣄⡿⢟⢣⡀⠀⠀⢠⡄⠀⠀⢈⡉⠛⠚⠛⠉⣉⠀⠀⠀⠀⠀⠀⠀⣠⢻⠾⣇⡼⠃⡇⣿⢁⢱
⠀⠀⠀⠘⡄⢦⠳⡜⠦⣌⣩⠜⢨⣇⠀⣤⣼⠃⠀⠀⣠⡈⣉⡙⣉⡉⣠⡄⠀⠀⠀⠀⠀⢀⣾⠘⢬⣉⡤⢞⡴⣣⠏⡜
⠀⠀⠀⠀⠙⢦⡱⣌⢳⣶⡴⣖⢫⡉⠷⣏⣹⠀⠀⠰⣯⣿⣍⠭⢍⣽⣯⡷⠀⠀⠀⠀⣠⠟⣩⢛⡶⣴⣶⢋⡔⣡⠞
⠀⠀⠀⠀⠀⠀⣷⠘⡄⣻⠿⡘⡄⢳⠀⣿⡁⠀⠀⠀⠹⢦⣄⣤⣤⣤⠞⠁⠀⠀⠀⣠⡇⢸⠃⡜⡰⢿⡃⡜⢰⡇
⠀⠀⠀⠀⠀⠸⠧⠴⠟⠁⣠⢡⠃⣼⠀⡇⣙⠦⣀⠀⠀⠀⠉⠀⠈⠁⠀⠀⢀⡠⢞⡁⡇⢸⡄⢣⢱⠀⠙⠷⠤⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⢎⡴⢃⡼⠛⣀⣀⣬⡽⢦⣄⣀⠀⢀⣀⣤⠶⣯⢀⣀⡈⣻⣄⠳⣌⢆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣫⠶⠟⠛⠂⠉⠁⠐⣀⣀⣩⠟⠑⠉⢯⣩⡀⠐⠋⠉⠁⠛⠻⠷⢮⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⣿⢹⠀⠀⠀⠀⠘⠁⢠⣭⣵⡏⠀⠐⠀⠘⣷⣴⠆⠲⠂⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢿⣸⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠈⢷⡞⠂⠀⠀⠀⠀⠀⣼⣽⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠁⠀⠀⠀⠀⠀⢀⡈⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⡁⠀⠀⠀⠀⠀⠉⠁⣾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⢀⠀⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⢂⠀⠀⠀⠀⢸⡟⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠈⡆⢠⠀⠀⢦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⡄⠀⠀⠃⣾⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⢸⠀⠰⣆⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⠃⡶⢰⠃⠀⠐⣷⡄
⠀⠀⠀⠀⠀⠀⠠⣍⡿⠀⠀⠀⡆⢦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⠃⣏⠁⠀⠐⣏⡥
⣴⣶⡦⢤⣀⡠⠔⢦⡟⠀⠀⠈⢹⣎⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣾⣩⠀⠀⠀⣧⠖⠤⣀⣠⠄⣴⣦
⠈⢿⣉⡾⣼⣅⠀⡀⣿⣏⠴⣯⠁⠙⢯⡳⣌⠁⠈⠣⠈⠁⠘⠀⠉⠀⠋⠰⠋⡼⠋⡴⣫⠟⠁⠟⠳⣦⣐⡇⡀⢀⣽⡼⢎⣹⠟
⠀⠀⠈⡏⠉⠉⣳⣿⣿⣿⣆⡀⠀⠀⠀⠙⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣠⣜⠃⠀⠀⠀⣀⣤⣿⣿⣷⡋⠉⠉⡏
⠀⠀⠀⠣⠀⣴⠿⡿⡿⡟⢦⣌⠳⢦⣀⠀⢫⠉⠲⣄⠀⠀⢀⣤⢤⣄⠀⠀⣠⡾⠋⢹⣃⣠⠶⢋⣤⠞⡿⡿⡟⢶⡄⠰⠃
⠀⠀⠀⠀⢸⡀⠀⢠⢗⠀⠀⣱⠬⣿⣿⣿⣾⣆⠰⣄⢱⠴⣇⠀⡄⢀⡷⢶⢋⡴⢀⣾⣿⣿⡯⢴⡁⠀⢀⢧⠀⠀⣸
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠙⡏⠀⠘⣽⢏⠉⠠⠌⠷⣼⡏⠀⣬⠛⠛⢻⡀⠀⣿⡴⠎⠥⠈⢙⡿⠀⠈⡛⠁⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠚⡃⠀⠉⡗⢲⡖⣺⠗⡶⢋⠷⡴⢏⠳⡖⠿⡒⢶⡖⠈⠉⡙⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣮⣠⠵⠚⠳⣄⡠⢷⣄⡴⠛⠲⢅⣨⡏⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠠⠴⠎⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠰⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⢠⠁⠀⡴⠉⠑⠢⣄⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠑⠤⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠋⠀⠀⠈⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⢀⠄⠀⠀⢀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠓⠤⡤⣈⠐⠀⠀⠀⠀⠈⠁⠀⠀⢀⡈⣀⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣤⠤⣄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠤⠰⠖⠂⠉⠉⡠⠄⠠⠗⢂⣀⢠⠀⠀⠀⠀⠀⠀⢠⠂⢀⠔⠀⠀⠀⠀⠑⡄⢇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠐⠈⠀⢀⣀⠀⠙⢄⠀⠀⠀⠀⠀⡀⠀⠎⠀⠀⠀⠀⠀⠀⠘⢸⠄⡄
⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠑⢌⠆⠀⢣⠀⠀⠀⠐⠀⠸⠀⠀⠀⠀⠀⠀⠀⢠⢾⠀⡇
⠀⠀⠻⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠊⠀⠀⠀⠀⠀⠀⢙⡄⠀⣷⡐⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⢠⠎⡼⠀⠇
⠀⠀⠀⠀⠙⢅⠀⡀⠀⠀⠀⠀⠀⠀⡌⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣾⣿⢣⠀⠰⠀⢢⣤⣤⣤⡤⠖⠋⠉⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠑⠢⣠⢀⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠀⠉⠳⢆⠀⠈⠁⠀⠀⠐⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢄⡀⢀⠂⠀⢐⣄⡀⠀⡀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⢀⡀⠤⠤⠤⠒⠊⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠟⠀⠀⢀⠁⠀⠀⠀⠙⡇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⡖⠀⠀⠀⠀⠁⠀⠈⠃⠐⡏⠀⢘⠆⠀⠁⢲⠀⠀⣀⠇⠀⢠⠞⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢶⠃⠀⡆⠰⢀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠇⠀⠀⠘⢧⡀
⠀⣀⠀⠀⠠⠯⢸⠢⢠⢠⡈⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠀⠐⠓⡀⠀⠈⠁
⠀⡁⣀⡀⠀⠀⠙⠱⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⢀
⠐⢻⠵⠂⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁
⠄⠁⠀⠐⠀⠁⠀⠀⠀⠰⣁⠈⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⣀⣀
⠀⡠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠦⣵⢿⡷⣯⣤
⠀⣏⠀⢳⣔⡀⠀⠀⠀⡀⠀⢠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠅⣂⡿⢿⣟⡶⡿⣗⠈
⠀⡏⠻⠾⠏⡦⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡽⠷⣴⠷⡍⡛⠒⠀⠆
⠀⡇⡂⠘⠐⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⣄⢠⣾⠧⢓⡀⠀⠀⡤
⠀⠁⠑⢀⠉⢀⠂⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣜⠹⣀
⠠⡆⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣄⠀⠀⠔⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠁⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⣶⣶⣦⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⢿⣽⠙⡏⣏⣻⣹⣘⣟⣸⣇⣇⣧⣭⣸⣼⣸⣄⣿⣇⣇⣺⣹⣙⡇⡏⢹⠻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⢀⠀⠀⠠⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠻⠧
⠀⠀⠀⣀⢄⣀⡴⣻⢻⡶⡦⡶⣄⠀⠀⠀⠀⠀⢀⣤⠀⡇⠈⠴⠓⡆⠀⠀⡀⠀⠀⠀⠀⠀⣠⣶⠜⣥⢯⣾⢁⣠⣲⠄
⠀⢀⢺⠇⢾⣜⠻⠦⠤⠾⢇⣿⣿⠗⡦⠀⠀⣠⠈⢿⣄⠘⠂⠀⠈⠐⠁⢠⠃⡄⠀⠀⠀⣾⠿⣷⢢⠁⢐⠂⣬⠛⠯⣴⡴⡀
⠀⢸⠸⣦⡀⠉⠛⠛⠛⠛⠛⠋⠁⢀⡿⠀⠀⣛⡃⣀⠙⠳⠤⠄⠀⠴⠒⡠⢀⣀⠀⠀⢸⣿⣶⠠⢋⣄⠉⠾⢣⡇⠀⣇⠷⢷
⠀⢰⠀⡌⠛⠶⠶⢤⣤⣤⡴⠶⠟⢋⣵⠀⠀⣿⣿⠈⠁⣀⠐⠂⣀⣒⠉⣠⡟⢻⠀⠀⣼⢻⡇⢣⣍⣻⠠⠿⢈⣁⣼⡿⠀⢻
⠀⠸⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⢹⣟⠦⠾⣿⢧⡼⠏⠁⢉⣿⣂⣸⡆⠀⠹⣼⡇⣾⠛⣯⡿⢿⡹⢿⣽⣿⠸⣿⠆
⠀⠀⠈⠙⠢⠤⣄⣀⣀⣀⣀⡀⠤⠚⠁⠀⠀⠀⠙⠳⣶⣾⣦⣤⣠⣴⣿⣿⠟⠋⠀⠀⠀⠙⠷⣿⣤⣾⣄⣼⣷⣄⣼⡿⠿⠋
⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠨⠭⠭⠩⠭⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⢭⣭⠉⠉⠁
⠀⠀⠀⡴⠛⢁⣠⠤⠤⢀⠠⣸⣿⠆⠀⠀⠀⢀⡾⠋⠀⣀⣠⣤⣤⣤⣄⡒⠙⢦⠀⠀⠀⣠⡶⠀⣀⡬⠭⠥⣄
⠀⢀⠎⠀⡔⣻⡛⠉⠉⠉⢃⢾⣿⡇⡿⢦⠀⡞⠈⢀⡾⣫⡵⣶⣶⣶⣭⢻⡆⠈⡇⠀⢠⠟⡀⠀⠀⠀⠀⠀⠀⠁⢄
⠀⢘⡀⢸⣤⢿⢁⡾⣿⠆⢸⣴⡏⠇⠀⢸⠀⡇⠀⣾⢰⣿⣟⡽⣯⢻⣽⣧⣿⠀⢹⠀⣿⡼⠀⠀⢠⠞⠉⣉⠱⡄⠈⡇⢀⣴
⠀⠸⣧⢠⡉⡛⠠⡼⣄⣀⣿⡰⢃⠸⠃⡸⠀⡇⠀⣿⢸⣿⣯⣳⠶⣾⣿⠇⣿⠀⠘⠀⢳⡷⠀⠀⣿⠀⠘⠍⠠⠁⠀⡇⢸⣽
⠀⠀⢿⣆⠰⠍⣦⡙⠓⢈⣁⣶⠥⠂⡠⠁⠀⢳⢀⠹⣆⠻⣮⣟⣛⣋⣥⡾⠃⢀⡆⠀⠀⢄⠘⣆⠙⠄⠀⠀⠀⣠⠞⣀⣴⠏
⠀⠀⠀⠙⠷⣤⣝⣁⡘⠐⠉⢀⣴⠞⠁⠀⠀⠈⠣⣀⠈⠳⢄⣉⡉⠉⠁⣀⡠⠞⠀⠀⠀⠀⠁⢈⣁⠀⠀⣩⣍⠡⣿⠽⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠚⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠓⠛⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⡤⠮⠽⢦⠄⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠁⠀⠀⢨⠀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅
⠀⠀⠀⢀⢆⠀⠀⢠⠞⠫⠭⠤⠆⠰⠄⠀⠀⠀⠤⠀⠀⢤⠀⠀⠀⠀⠆⠰⠤⠤⠕⠛⠄⠀⠀⢰⡄
⠀⠀⠀⠀⢢⡱⢄⡸⢲⢤⠤⣀⣀⡀⡀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⠀⢀⢀⣀⡠⠤⢖⢣⡠⠔⡱⠁
⠀⠀⠀⠀⠀⢉⣦⣑⢿⡇⢠⠀⠇⠴⠒⠈⠉⢸⡇⠀⠀⠀⠀⠉⠉⠒⠦⠐⡀⠇⢘⡽⢊⣴⡎
⠀⠀⠀⠀⢀⢣⢋⡉⢂⢳⠃⡘⢀⡦⢒⠾⢖⢾⡃⠀⠀⠀⡴⡲⠷⡒⢤⣀⢡⡘⡾⠱⠋⡟⡌⡆
⠀⠀⠀⠀⠸⠸⡸⣇⠘⣨⠎⡃⢨⡀⢧⣿⣿⢹⡇⠀⠀⠀⠸⢼⣿⡿⢀⡥⢰⠙⣇⠳⢀⡇⡇⡇
⠀⠀⠀⠀⠀⢢⡷⣎⠞⣍⠴⡅⠀⠉⠓⠱⠳⢺⡆⡔⢲⠀⠻⠒⠎⠒⠉⠀⢀⠶⢼⡱⣁⡾⡴⠁
⠀⠀⠀⠀⠀⠘⢸⠉⠸⣇⡾⡷⡀⠀⢀⡄⠀⠈⡓⠒⠓⢒⡃⠀⠀⠀⠀⠀⠼⢷⣨⠇⡈⢳⢑
⠀⠀⠀⠀⠀⠠⡰⡀⣑⠈⠑⣁⢧⣰⡼⠇⠀⠀⣉⢌⡫⢉⠀⠀⠀⠀⠀⡸⣆⠂⠡⣊⢔⢌⡌
⠀⠀⠀⠀⠀⠀⠙⡌⠌⢻⣟⠍⢂⢹⡖⠀⠀⠙⢇⠂⡁⣺⠏⠀⠀⢀⡜⠰⠡⢻⡟⢡⢢⠊
⠀⠀⠀⠀⠀⠀⠐⠇⠶⠊⠐⡐⡀⢸⠙⢢⣀⠀⠀⠉⠉⠁⠀⢀⣤⠊⢇⢀⢠⢠⠘⠲⠨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⢔⣡⠖⠊⠁⣈⠱⠦⣄⣠⠴⠎⣁⡀⠑⠺⢮⡢⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⡿⡯⠐⠂⠉⠁⠀⠀⡰⠁⠈⢦⠀⠀⠈⠉⠐⠂⠸⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⡅⠀⠀⠀⠀⠀⡰⠁⠀⠀⠈⢣⠀⠀⠀⠀⠀⢸⡼⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠰⢹
⠀⠀⠀⠀⠀⠀⠀⣠⣷⡈⡄⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⠇⠸⣄
⠀⠀⠀⠀⠀⠀⢠⣿⣏⡅⢱⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡌⠀⢸⢹⡄
⣀⣴⣶⡖⢤⣤⠜⠣⣿⠟⢰⣆⢠⣎⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢠⠁⠀⢸⣹⣇⡀⠀⣀⣠⣄
⠹⡟⠻⣿⡛⠿⣄⣠⠿⠊⠉⠀⠀⠀⠀⠀⠉⠉⠓⠢⢤⣀⠀⠀⠀⠀⠀⣹⣆⠀⠀⢸⠁⠀⢙⣋⣯⠾⢻
⠀⠈⠛⡴⣇⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⢀⡴⠋⠀⠉⠂⣼⣾⣴⠾⡟⢤⠛⠁
⠀⠀⠀⣇⣀⣙⣁⢱⡄⠀⣠⣴⣔⠒⠒⠶⠠⢤⡀⠀⠀⠀⠀⠀⠑⢮⡀⣀⣠⡊⠉⠉⠀⠀⢸⣀⡸
⠀⠀⠀⠠⢾⣉⠀⠀⢣⡎⠙⣷⡉⢷⣦⣄⡙⢦⣨⠗⢤⡀⠀⠀⠀⠀⠈⠛⠻⠏⣉⣲⡄⠀⠘⢍⣀
⠀⠀⠀⠀⠈⠺⡇⠀⠀⠀⠉⣹⠉⠽⣿⣿⠛⠓⢿⠀⡀⣸⠶⢄⡀⠀⠀⠀⠀⠀⠀⠈⣦⣴⣖⣈⡹
⠀⠀⠀⠀⠀⢠⣣⠔⠂⠈⠻⣅⡠⡾⠀⠳⣄⣀⣪⣷⣷⣧⢂⣀⡽⠲⣤⣀⠀⠀⠀⢀⡼⢿⡁⠈⣰
⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠳⢄⡴⠉⠉⢜⣿⣿⡿⠍⠉⢢⡤⠎⠀⠉⠉⠉⠙⣀⡠⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡤⡞⠀⠁⣻⢤⢤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠲⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⣠⣶⡶⣿⣿⠿⠿⠛⣿⣶⣶⣯⣉⠻⡷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢀⣴⣿⠋⠁⢈⡴⠃⠀⣀⡜⠛⠁⠸⢟⠿⡷⢌⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢠⡾⢁⣾⣿⠋⠀⠐⡴⠊⠑⢤⠐⠁⠉⠲⡎⠀⠀⠘⠃⠈⠳⡌⢮⢧⣄
⠀⠀⠀⠀⠀⢠⡟⢠⣿⡇⠈⠳⣄⠀⠠⡠⢀⠀⢁⢤⡀⠀⢈⠶⢄⠀⠀⠉⠦⡨⠆⢻⣿
⠀⠀⠀⠀⠀⣿⠀⣾⠋⢿⠂⠀⠈⠑⠀⠀⠀⠙⠁⠀⢈⠟⠁⠀⣀⠉⠀⢀⣔⠀⢈⠈⢿⡆
⠀⠀⠀⠀⢠⣯⢀⣿⠟⠁⠀⢠⡔⠀⠀⣠⢀⠀⢀⡴⢦⣤⣀⠜⠁⠀⣴⠃⠈⠁⢾⡆⢰⡇
⠀⠀⠀⠀⠸⣏⠈⡷⠀⢠⡜⠁⠈⡠⣾⠀⠻⠷⠿⣶⠾⠛⢿⣄⡀⠑⠈⡣⣀⠀⠈⣧⢸⡇
⠀⠀⠀⠀⠀⣿⠀⣿⡄⠀⠈⢢⡀⠈⠻⣷⠦⣀⠀⠈⠻⢿⣷⡾⠋⠢⣄⡜⠉⢻⢶⡯⣸⠇
⠀⠀⠀⠀⠀⢹⣇⠘⣟⢤⡄⠁⠈⢳⠖⠁⠀⠈⠛⠀⠀⣠⠋⠀⠀⠀⠈⠀⠀⠃⡼⠡⡿
⠀⠀⠀⠀⠀⠀⠻⣧⠘⢏⡀⣠⠞⠁⠀⠀⣠⠃⠀⣠⠔⠁⠀⢀⣴⡂⠀⣀⢸⡟⢡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⠧⠀⠀⠠⡄⠀⠀⠛⢃⠀⠀⠈⠻⢄⡀⣺⡿⢋⣴⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⠀⠤⠈⣳⣄⠀⠈⢳⡤⣀⠀⠠⠟⣉⣤⠟⠋⠉⠉⠉⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⣤⣀⣈⣉⣉⣉⣠⣤⡶⢞⡛⣭⣴⠶⠶⠶⣶⣖⠤⣄⡀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣄⠀⠉⠉⣹⠟⠋⠉⣥⣶⣋⡼⠋⠀⠀⠀⠢⠀⡉⢳⣶⣿⢷⣦⡀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⣿⠀⢀⡾⠁⠘⣶⣿⡷⡿⢿⠁⠀⠀⠀⠀⡀⠀⠁⠈⣷⡝⠘⠻⣿⣆⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣸⠇⠀⣼⠁⠀⣼⣿⣿⣇⠇⣸⠀⠀⠀⠀⠀⠘⠢⠀⢀⡟⡇⠀⠀⡇⢸⣧⠀⠀⢷
⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⣿⠀⢰⡇⠀⢸⣿⡿⣼⣏⡷⣌⠷⣤⡀⠀⠀⠀⢀⣴⠊⢁⢉⡃⡐⡃⢾⠹⣇⠀⠘⡇
⠀⠀⠀⠀⣠⠞⠉⢀⣀⣀⠀⠀⠀⣿⠀⢸⠁⠀⣾⣿⠃⢃⣮⠶⠾⠾⢥⣍⡿⠟⠛⣿⣩⠶⠟⠛⠳⠾⣥⡶⡄⢻⠀⠀⣿
⠀⠀⠀⣼⠃⣠⠞⠉⠁⠈⠉⢆⠀⢻⡀⢸⡅⠀⢸⡇⣰⠏⠀⡀⠀⠀⠀⠀⠙⣆⢠⡟⠁⠀⠀⠀⠁⠀⠀⠹⡄⠘⠀⠀⣿
⠀⠀⢰⡗⠀⡏⠀⠀⠀⠀⠀⠈⡄⢸⡇⠈⣇⠀⠘⣷⡏⠀⠀⠈⠐⡀⠀⠀⠀⣽⣾⠀⠀⠀⠀⠀⣀⠤⠀⠀⣿⠃⠀⢸⣿
⠀⠀⠈⣇⠀⠳⠀⠀⠀⠀⠀⡠⠀⣼⠃⠀⢹⣆⠀⠸⡇⠀⠈⠁⠉⠀⠀⠀⠀⣸⢻⣆⠀⠤⠤⠚⠁⠀⠁⣼⡏⠀⢠⣿⠇
⠀⠀⠀⠙⢦⡀⠈⠒⠀⠀⠈⣠⡾⠃⠀⠀⠀⢻⣆⠀⠙⢤⡀⠀⠀⠀⠀⢀⡴⠃⢸⡟⢦⣀⠀⠀⠀⣀⣼⠋⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠉⠛⠷⠶⠶⠛⠉⠀⠀⠀⠀⠀⠀⠙⢧⣀⠈⠻⢿⣶⡖⠒⡟⠁⠀⢸⠅⠀⢉⡛⣏⠝⠉⠀⣀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠈⠁⠀⠓⠂⠀⠜⠒⠂⠈⠁⠀⢀⣠⢾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣤⣄⣀⣀⣀⣀⣀⣤⣴⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠉⠁

⠰⠂⠀⢀⡔⢮⣻⠭⠶⠛⣠⡼⡢⠀⠐⣶⠀⣰⠀⡤⠐⠀⡀⣶⠀⠀⠐⠀⠖⠤⠀⠤⠔⠀⠀⢰⠰⣾⣻
⣀⠀⠀⠠⠳⠦⠤⠤⠔⠚⠉⠀⢠⠇⠀⠁⠠⠘⠀⠀⣀⣔⣀⡟⠀⠀⢀⠔⠒⠐⠀⢠⡀⠀⠀⠨⠳⠤⠤
⢻⠰⠄⠀⠠⣀⡀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠴⠄⡴⠦⠛⠊⠀⠀⠐⠡⢲⠃⠀⠒⣽⣧⠲⡄⠀⢦⣀
⠈⡄⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢠⣠⣀⠀⠀⠀⠀⡄⠶⠿⠘⠛⢀⠞⠉⡄⠀⠀⠀⠀⠉
⠀⠀⠂⠀⠀⡄⠨⡀⠒⠆⠀⠀⠀⠀⠀⣼⣋⣻⠈⡨⣁⢶⠕⠀⠀⢻⡅⢖⣘⠓⢛⣤⠀⡀⠀⠀⢠⡄⢈
⠐⠁⠀⠀⣧⠙⠦⣀⠀⢀⠀⠁⠂⠀⢸⣻⢡⡰⡆⣬⡽⢀⠿⡇⠀⠀⠙⠲⢥⠄⠈⠤⠚⠁⠀⢰⡆⠻⢆
⠀⠀⠀⢸⣿⠉⣠⡀⣀⣄⣊⡞⡇⠀⠘⣧⡏⣻⠷⡷⣶⣿⣀⡇⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢸⣷⢁⣄
⣤⠑⡄⠀⠻⣍⣻⣓⠃⢀⣽⣤⠗⠀⠀⠀⠙⠻⠾⠧⠴⠷⠞⠁⠀⠰⠁⣠⣖⣲⣖⡲⣄⠑⡀⠈⠯⣍⣻
⣾⡇⠃⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⢸⣱⣿⡿⣿⣿⣾⠀⡇⠀⠀⠈⠉
⣸⠁⠀⠀⠀⠀⣤⣤⣶⣶⣤⣄⠀⠀⠀⣴⠃⠐⠒⠐⠂⠀⠀⠀⠀⡆⢸⡸⣿⠿⠿⢟⡼⠀⠀⠀⠀⢀⣤
⢠⠆⠀⠀⡠⣾⠿⣗⣫⠾⠋⣸⢆⠀⠰⡷⠀⢠⠒⣁⠢⠈⠂⣠⠀⠘⠠⢑⣬⣙⠛⢉⡠⠂⠀⢠⢰⡿⢾
⠀⠀⠀⠈⢧⣉⣉⣁⣠⠴⠚⠁⠉⡆⠀⠛⢀⠹⠀⠁⠀⣠⠁⡿⠀⠀⠀⣀⠄⠀⠄⣀⠀⠀⠀⠸⣦⣉⣉
⣿⢠⡀⠀⢀⠈⠉⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⣀⡀⣀⡎⢷⠝⠁⠀⠠⠊⣡⡆⠒⠤⢺⣇⣤⡀⠀⣀⠉⠁
⢸⡀⠁⠀⠈⠙⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⣀⢈⠁⠁⠀⠀⠀⠀⠀⣤⣾⢰⠶⠀⣭⠛⠀⠁⠀⠈⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢒⠈⡉⡁⠀⠀⠀⠀⠀⠀⣉⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⣀⠀⢠⠴⡶⡏⠈⠀⢄⣀⠐⡣⠈⡙⠙⠀⠑⣄⠀⠈⠐⠤⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⢰⣣⠀⠁⡔⠀⠈⠀⠀⠰⣿⠞⠡⢊⣀⠀⢰⡀⣸⠤⠀⠀⡀⠀⠑
⠀⠀⠀⠀⠀⠀⠰⡅⠀⡠⠖⠉⣿⡁⠀⢰⣣⠠⡀⣀⠺⡴⠻⣄⢀⣿⠟⢈⠴⡷⠶⠄⠁⠄⠈⠑⢄⣸⡄
⠀⠀⠀⠀⠀⠀⠇⠀⢾⠀⠀⠀⠘⢷⡾⠁⠂⡸⠿⠺⠃⠀⠀⠀⢈⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠦⣄⠀⢸⠊⣠⠂⠀⠀⠀⠀⠀⠀⠂⢸⡀⠀⢀⠁⠀⠀⠀⠀⠀⡠⠖⣡⠞⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠑⠺⠶⣆⠀⠰⠀⠀⠀⠀⡠⠀⠀⠁⠀⢈⣆⢀⡀⠤⠒⢋⠠⠊⠁⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢉⡉⠁⠀⠒⠛⠒⠒⠒⠀⠀⠩⠁⠀⡀⠄⠘⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠐⠶⠅⣠⠀⠀⠀⢀⣀⠤⠞⠉⢸⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠤⣄⣀⣀⡀⠀⠀⣀⣀⠀⠠⠤⠄⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠘⠃⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠂⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠤⠀⢀⠀⢀⠀⠀⠠⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡿⠛⠑⠊⠐⠀⠀⠐⠀⠀⠀⠉⠀⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠢⠄⠀⠀⠀⠀⠘⠲⠶⣴⣤⣤⡀⠐⠈⢑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠈⠈⣹⣭⣭⣭⢸⡁⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠆⠀⠀⠀⢀⠑⠀⠀⠀⠀⠀⣠⠞⠁⢠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠈⠒⢄⡓⣄⢀
⠀⢀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢣
⠀⣉⠲⠿⠧⣀⣀⣀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣀⣀⡀⣤⣀⣤⡞⠀⢸⣿⡿⠁⠀⠰⠀⠄⠀⠀⠀⠀⠀⠀⣵⡀⠀⠀⡄⠀⢿⣧
⠀⠀⠀⠀⠀⠒⠀⠠⠤⠤⠵⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⣼⣿⠁⠆⢸⣿⠁⠀⠀⠰⠶⠀⠀⠐⠀⡀⠀⠠⠀⠀⠠⠈⡇⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠇⠀⠀⢸⣿⠀⢠⠀⠀⠀⠀⠀⣠⠀⠣⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠠⠤⠄⠐⠀⠉⠀⠀⠀⠂⠘⣿⠀⠀⠀⠀⠃⠀⠁⠀⠈⠒⠈⠀⠠⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠈⠀⠀⠀⠀⡀⠀⠐⠐⠂⠀⠠⡀⠀⢀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠂⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢇⠀⠀⠀⠀⠀⠀⠄⢀⡀⠠⠀⠂⠀⠀⠀⠀⠠⠀⡂⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⢨⠋⡩⠒⠠⡀⠀⢀⣀⣤⣤⢤⡤⣤⣤⣀⡀⠀⢠⠐⠒⢍⠙⡍⠲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠇⠀⠄⠀⠀⢀⠈⠁⡀⣹⡃⠄⠒⠀⢸⡇⠀⢒⠠⢐⣏⣀⠈⠁⠀⠀⠀⠠⠀⠘⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠌⢇⠈⠀⠀⠀⠀⠀⠀⢀⠔⡥⡂⠥⠒⣀⢸⡇⣀⠂⠬⢐⢬⠢⡀⠀⠀⠈⠀⠀⠀⠁⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⡠⢰⠴⢒⡱⡢⢊⠔⢊⠅⣂⠼⠧⣒⠬⡑⠢⡑⢜⢮⡒⠶⡆⢄⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡜⠀⡧⠂⡡⠊⡰⠓⣈⠡⢊⡡⠊⠑⢌⡑⠌⣁⠚⢆⠑⢌⠐⢼⠀⢃⠠⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⢡⠁⠀⡕⡩⠖⣉⣉⠅⠄⠊⠁⠀⠀⠀⠀⠈⠑⠀⠈⣁⣉⠲⢌⢪⠀⠘⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡸⡌⠠⢂⠟⣣⡭⠔⠧⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠸⠢⢭⣜⠻⡑⠄⢃⢇⠀⡇
⠹⣐⠠⠄⡀⢀⠀⣀⡸⠔⡁⠃⠂⠁⡈⠊⣠⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠱⣄⠑⢡⠈⢰⠜⢌⠢⢅⡀⣀⠀⣀⠠⠄⣂
⠀⠙⠕⣄⠀⠒⠀⠀⠲⠉⢀⠀⠣⣢⡍⣀⠟⡄⠀⠓⠆⠄⠖⠂⠀⠀⠑⠢⠤⠒⠋⠀⢠⠻⣀⢹⣔⠌⠸⡁⠁⠖⠀⠀⠒⠀⣠⠞⠋
⠀⠀⠀⠈⠛⠦⣄⣠⠀⠔⠁⠀⢰⠇⣿⢡⣎⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣱⡌⣟⠸⡆⠀⠈⠢⢀⣄⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⢨⢢⢙⣳⢦⡀⠀⠀⠀⢉⠐⣊⠁⠀⠀⠀⢀⡴⣎⡋⡴⠅⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⠊⣻⠡⢁⢳⡀⠀⠉⠇⣊⣐⠟⠁⠀⢀⡎⠌⠌⣟⠑⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⢡⢐⡜⣸⠱⡦⣀⠀⠁⠈⠀⣀⡴⠯⣇⠢⡂⡌⠙⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠊⠥⠐⠂⠉⢙⠖⠲⡉⠉⠀⠂⠬⠑⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠙⣄⣠⡀⠀⠀⢀⠎⠀⠀⠱⡀⠀⣤⠶⠀⣤⠋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡄⠀⠃⠷⠁⢠⠂⠀⠀⠀⠀⠐⡄⠀⢰⡖⠀⢠⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠰⠀⠀⠀⠠⠃⠀⢋⠇⢰⠛⡆⠘⡄⠀⠀⠀⠆⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡷⢓⠁⠀⡠⠁⠀⠐⠓⠂⠘⠒⠃⠀⠘⢄⠀⠘⢠⣨⢼
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⣗⡶⡴⠊⣷⡇⠊⠐⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⠃⠈⢱⠊⠑⠦⢶⡹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢺⠽⠿⢼⢿⣽⠔⠈⡙⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⡁⠢⣼⣖⡴⠿⢭⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣵⣖⠉⢹⣋⠵⠦⠛⠃⠑⠄⠤⢀⣧⣿⠀⠀⡠⢪⠔⣤⣤⢾⣿⡿⢥⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠙⢳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣊⣤⣶⣯⣴⠁⠈⣼⣈⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠛⣄⠀⢀⡠⠤⣤⢤⡤⢀⡀⠀⠀⠀⠈⠻⢿⣕⠀⡋⠈⠉⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣊⠁⠘⣴⡉⣏⠈⢇⣀⡸⠖⣺⣶⣄⠀⠀⠀⠀⠉⠛⠣⠍⡆⠀⠈⡢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⢀⡹⠀⠀⠈⢧⣀⠴⠉⠙⡯⣲⣄⡀⠀⠀⠀⠀⠘⣾⡿⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⠃⠀⠀⠉⠑⠂⠤⠄⠞⠁⡓⠠⠂

⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⠀⠀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⡉⠉⠉⠐⡀⠀⠀⠀⠀⠀⢀⡠⣎⣩⣷⠿⠛⠆⠀⢠⣼⣤⠶⠒⢓⠲⣆⠀⠀⠀⠀⣴⠽⣿⣙⢿⡄
⠀⠀⠸⣷⣾⢿⠀⣾⣾⡇⠀⠀⣠⡾⣱⣾⡿⠁⠐⠁⠀⠀⠈⠉⠉⠐⣿⡿⠇⠉⠀⠀⢠⡾⠁⢠⡼⣿⣆⠻⣆
⠀⠀⢄⠛⠛⠿⢁⡿⠟⠁⠀⠰⢻⣿⣿⠿⠑⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⢀⠄⠀⠐⠿⣅⠉⠈⠋⢙⣿⠟⠃

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡴⠰
⠀⠀⢠⠄⠐⠋⠡⢀⣀⢀⠀⠀⢀⣿⡐⠶⠷⠀⡀⡀⠀⠀⠀⠠⠜⠛⠛⠲⠟⣀⠀⠀⠀⡆⠊⠀⠀⠈⣿⣼⠂
⠀⠀⣈⠠⠤⠀⠘⠀⠋⠽⠀⠀⠈⠁⠷⣤⣤⣤⡤⣥⠀⠀⠀⠀⣴⡳⣄⠀⠾⣹⠀⠀⠀⠁⠀⠀⠀⠀⢻⣽⡆
⠀⠀⢐⡀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⢶⣬⣁⣁⡠⠟⠀⠀⠀⠀⠻⣿⣿⠇⢸⠏⠀⠀⠀⠠⠀⠀⠀⠀⠾⠛
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢀⠤⠴⢶⡶⠶⢄⣄⣴⠄⠀⠀⠀⠀⠀⣠⡀⠁⠀⠀⠀⠀⠀⢠⡄⠁⢴⡄⠀⠀⠀⠀⡀⢀⠧⡸⢛⣰⡆
⠀⠰⣤⣀⠀⣬⣿⣶⠟⠁⠀⠀⠀⠀⠐⢦⣻⡿⠇⠀⠀⠀⠠⠀⡀⠀⢉⡟⣿⠠⠀⠀⠀⢰⡗⣧⣶⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠗⠀⠀⠀⠀⠸⣇⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠚⠀⡀⢀⠀⡄⡀⠀⠀⠀⣄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣨⡥⡄
⠀⠀⠀⢰⡀⣀⣀⡄⣿⣄⠀⠀⠀⡗⠀⠀⠀⣿⣿⣿⠀⠀⠀⡐⢁⠠⠴⠋⠉⠁⠀⠀⠀⣷⠀⠀⠀⡋⢀⠀⡄
⠀⠀⠀⠠⠀⢹⣿⠇⣹⠋⠀⠀⠀⢧⡀⠀⠀⣿⣿⣿⠀⠀⣠⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡤⠀⠀⣤⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠄⠒⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⣁⠄⠂⠀⠤⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣋⠥⠂⢀⠔⠋⠀⠀⠀⠀⠀⠀⠉⣲⠶⠚⠁⠀⠉⠒⠶⣶⣶⣶⣤⡟⢩⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⡡⣾⠇⣠⠔⠘⣄⡤⠂⠘⠤⣀⡀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢈⣿⠟⠋⣰⡟⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁⣱⠋⢁⡴⠋⠁⠀⠀⠀⠀⠀⠙⣾⣧⣀⠀⠀⠀⣀⣠⡴⠞⠋⠁⣠⡾⠋⣀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢏⠿⣦⣄⣁⣴⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⡷⠾⠛⠋⠁⢀⣠⡶⠟⠉⠠⠚⠙⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣶⠶⣦⣬⣙⡛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⣉⡀⠀⣀⡤⠴⠞⠋⠁⠀⠀⠀⠀⠀⢀⣠⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⡈⠉⠛⠛⠻⠶⠶⠶⠶⠶⠶⠖⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠈⠁⠀⢪⡀⠀⠀⠀⠀⠀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠉⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠶⠒⠀⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠂⠠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢛⣛⣶⣶⡶⡶⢶⠶⠶⡶⠶⢶⣖⣚⠋⠏⠥⠀⠀⠐⡄⠀⢤⣷⡤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡀⠈⣙⠛⠿⠶⢿⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⠿⠛⠋⠁⣠⡞
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣷⣤⣈⡛⠛⠶⢶⣶⣶⣤⣤⣤⣴⣶⣶⡶⠶⠛⠋⢀⣠⡏
⠀⠀⢀⣤⠖⠛⠉⣡⣤⡄⢤⣀⡠⣤⠤⢤⡀⠉⠉⠁⠀⠀⠀⠤⣶⣶⣾⣿⣿⣿⣿⣿⣿⡆⠈⠉⠛⠛⠲⠶⠶⠶⠦⠤⠴⠶⠶⠶⠖⠚⠋⠉⡿
⠀⣴⠏⠀⢀⡔⠉⠄⠀⢢⠞⠩⠄⠀⠂⣴⡿⠀⡠⠔⠒⢒⠀⢲⡀⠉⠙⠻⢿⣿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⣼⠃⠀⠀⢎⠀⡀⠀⢠⣏⠀⡀⢀⣤⠞⠿⢳⠞⠀⠐⠀⢠⣴⡿⠧⠔⠲⣄⠀⠈⠳⣄⠀⢻⣦⣀⣠⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢀⡀
⢿⣆⠀⠀⢸⠀⠀⣰⣿⢿⠀⣠⠏⠀⠂⠀⣽⡆⠐⠀⣰⡟⠁⠆⠀⠁⣰⣿⠀⠀⠀⠈⣧⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⠉⠀⢠⠉⠛
⠘⢿⣦⡀⠀⠉⠊⠉⠁⠀⠉⢳⠀⠄⠀⣰⣿⠇⠀⠰⢯⡀⠄⠀⢀⣼⡿⠃⠀⠀⠀⢠⣿⡇⣀⠀⠉⠉⠛⠛⠛⠛⠿⠿⠟⠛⠛⠋⠉⠀⣀⣐⣭⡴⠞
⠀⠈⠛⢿⣷⣦⣄⡀⠀⠀⠀⠨⢀⣀⣼⠿⠋⠀⠀⠀⠨⡀⠀⣰⡿⠋⠀⠀⠀⢀⣤⣿⠟⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠉⠛⠿⣿⡷⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣤⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠿⠭⠿⣿⣛⣛⣻⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡇⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⡷⢆⡴⣛⣯⡛⣿⢣⣿⢿⣿⣛⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣯⣴⣏⢼⣿⡿⣣⣿⢸⣿⣌⢿⣿⢸⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣿⣭⣭⣽⣛⣛⣻⠿⠿⢶⣶⣾⣿⡏⣿⣿⣿⣦⣻⣬⣛⣛⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣿⣿⣿⢟⣛⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⡿⣁⣭⣝⣛⣛⡿⠿⠿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡜⣿⣇⠿⠿⠇⠿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⡹⣿⣿⣿⣿⣿⣿⣷⣶⣶⣯⣭⣽⣛⣛⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣹⣿⣷⣶⢰⣿⣦⢻⣿⣿⣿⢟⣵⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡿⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⢿⣿⣿⣦⣭⣵⣿⣿⡿⣣⠾⡻⣿⡿⠿⢿⣏⢿⣿⣿⣿⣿⣿⡿⢈⣿⣿⣿⣿⢟⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣭⣻⡟⣿⡞⣿⣿⣿⣿⣿⡿⢫⣾⣿⣿⡇⡿⣱⣿⡆⣿⡞⣿⣷⡰⣶⣶⣶⣿⣿⣿⡟⣵⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣜⡛⢡⢣⣿⣿⡹⣿⣿⣿⢟⣵⣿⣿⣿⢟⣼⡇⣿⣿⡇⣿⣿⡹⣿⣷⣽⣿⣿⣿⣿⣫⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣵⡟⣾⣿⣿⣷⢻⡟⣱⣿⣿⣿⣯⣑⣛⣻⣿⠻⡿⣣⣿⣿⣷⢻⣿⣿⣿⣿⢟⡽⠻⣏⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣭⡿⢿⣛⣅⣼⣛⣛⣿⠿⠿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣇⢿⣿⡿⣡⣿⢸⡇⢿⣦⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢟⣛⣭⣵⣾⣿⣿⣿⡜⣿⣿⣿⣿⣿⣷⣶⣶⣭⣭⣭⣛⣛⣛⠿⠿⠜⢫⣾⣿⣿⣶⣜⢇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⢫⣾⣿⣿⣷⣹⣿⣿⣿⠏⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢟⣴⣮⡻⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠘⣭⣮⡹⣿⣧⢿⣿⣷⢠⡮⣹⡿⣸⣿⣿⣿⣿⡿⣱⣿⣿⣿⣿⣮⣝⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣭⣉⣴⣿⣿⡎⣿⣿⠘⣵⣿⡇⡿⣿⣿⡿⣫⣾⣿⡏⣙⠿⣿⣿⣿⣷⣝⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡜⣿⣾⣿⣿⣤⣾⣿⢟⣵⣿⣿⣿⡇⡿⠟⢂⣹⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⢹⣿⣿⣿⣿⡿⣡⣿⣿⣿⣯⣶⣶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣇⢿⣿⡿⣫⣾⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠟⠐⠛⠉



⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⠿⠻⡿⠛⠿⢿⠿⢻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⣴⠶⢤⣄⡀
⠀⠀⢀⣀⣠⣼⡒⠀⠀⠀⠀⠀⠀⢘⠟⠀⠀⣀⣉⡿⠶⢤⣀⡀
⣞⠋⠉⠁⠀⠀⠈⠐⠀⠀⣀⡤⠤⠔⠒⠛⠍⠁⠀⠀⠀⣄⢘⣏⣷⠦⣤⣀
⠈⠓⢦⡀⠀⠀⠀⠀⢠⡏⠀⠉⣦⠀⢀⣀⡤⠤⠴⠒⠊⠉⠁⠀⠈⡆⠈⢹⡙⠲⢦⣄⡀
⠀⠀⠀⠙⠲⣄⠀⠀⠘⣗⡀⠀⡰⠋⠙⢷⣄⠀⠀⡈⠢⠀⠀⣀⣠⣥⠤⠞⠛⠋⢉⠉⠙⢿⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠈⠓⢦⡀⠈⠉⠉⢧⠀⠀⠈⣿⣀⣤⢴⣞⠋⠉⠁⠀⠘⠀⠀⠀⠀⠀⠑⡀⢈⡇⠀⠈⠉⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠈⠳⠤⠴⢿⣿⠀⠀⠈⢧⠀⠀⠀⢀⠀⠀⠀⣀⣠⠤⠗⠚⠀⠀⠀⠀⠀⢀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⢯⢆⠀⠀⢸⢃⣀⡤⠤⠒⠚⠉⠀⠀⠀⠀⠀⣀⣠⠴⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠈⠛⠓⠒⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠉⠉⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢣⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⣧⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⢌⢣⠔⣨⠙⠛⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡼⢉⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠑⠤⠀⠀⠠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⣀⠠⢤⣄⣠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣤⡤⠄⣀⣀
⠀⢀⡠⠖⠘⠉⠀⠀⠉⠀⣤⡿⠤⠀⠀⠀⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⢠⠿⣤⠀⠈⠀⠀⠙⠓⠲⢄⡀
⣎⠡⠄⣀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈
⠈⠑⠂⠭⠴⣍⠣⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⠌⡿⠲⠤⠐⠊
⠀⠀⠀⠀⠀⠈⠳⣌⠻⣤⣾⡅⣬⣹⠗⠀⠒⠶⠶⠒⠀⠀⠀⠀⠀⠐⠒⠶⠶⠂⠐⠺⣏⣥⣨⣧⡼⠋⡡⠎
⠀⠀⠀⠀⠀⠀⡠⣾⢷⣌⠻⣀⠄⠘⠀⠤⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠤⠀⡆⢃⡈⢋⡴⣿⢧⡄
⠀⠀⠀⠀⠀⢰⠱⠘⣷⠀⢃⠛⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣸⠃⡎⠀⢻⠌⡞⡀
⠀⠀⠀⠀⠀⢸⠀⡆⠰⡄⢋⡴⠻⠀⠶⣄⡀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣤⠆⢠⠛⣌⠃⣸⠀⠀⡇⡁
⠀⠀⠀⠀⠀⠨⡘⣧⡀⢹⠺⣁⣼⠀⠀⠁⠉⠸⠇⠋⠉⠀⠀⠀⠈⠉⠏⠚⠈⠃⠀⠀⠈⣦⣘⡿⡃⢠⣧⢡
⠀⠀⠀⠀⠀⠀⡝⣹⠟⢣⡟⢁⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡉⣷⢰⢻⡌⠇
⠀⠀⠀⠀⠀⠀⡇⡸⢀⢆⠛⠮⢹⢱⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠴⠂⠀⠀⠀⠀⠀⢀⠏⡩⠷⢋⡘⣄⢻⠰
⠀⠀⠀⠀⠀⠀⠰⡑⢎⠢⣍⣊⣡⡞⠳⡀⠀⠀⠀⢀⣠⠒⠠⠄⢠⣄⡀⠀⠀⠀⣠⠞⡧⣈⣈⣥⢜⠌⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⢩⣷⡜⡈⠆⢸⣄⠀⠀⠀⠙⣍⣠⣀⡽⠃⠀⠀⠀⣠⠁⠴⢰⠱⣾⠁⠆⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠧⠞⠋⣈⢣⠃⡆⢰⣈⠶⣄⠀⠀⠈⠁⠈⠀⠀⢀⡠⠞⣉⡀⢠⠸⠰⠀⠙⠦⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣤⢞⣠⡛⣠⡤⠶⠛⢶⣤⣄⣠⡴⡞⠳⢀⣤⡁⣻⣌⡢⣣⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⣷⠋⠉⠁⠀⠀⠀⠄⢲⠆⠀⠀⢶⡒⠀⠁⠀⠀⠉⠉⠛⣾⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡿⢸⠀⠀⠀⠀⠀⠐⢛⠋⠀⠀⠀⠀⠻⣀⠀⠀⠀⠀⠀⢀⢩⠇⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠉⠀⠀⠀⠀⠀⣨⠃⠀⠀⠀⠀⠀⠀⠱⣆⡠⠀⠀⠀⠈⠉⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠩⡤⢀⠀⠀⠀⢠⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠐⢇⠀⠀⠐⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⠀⠀⣼⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⡅⠸⣀⠁⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⡠⢠⡅⠀⢸⣷
⠀⠀⢠⣤⡄⣀⠀⣀⠾⣙⣿⠇⣠⢇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡼⠀⠀⢸⢾⣁⠀⠀⢀⣀⡀
⠀⠀⠈⢾⣷⡾⣿⡀⠀⣸⣧⡠⠶⠍⠙⠛⠛⠋⠹⠛⢿⣹⡏⠙⠙⠏⡝⢋⠟⡩⣻⠟⠳⢦⣄⣸⠃⠀⢙⣹⡔⠿⠃
⠀⠀⠀⠀⠉⡒⠈⠙⣶⡋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⣠⣄⠀⠀⢀⣟⠁⠀⠀⢀⣠⣿⣾⣖⠛⢁⡿⠁
⠀⠀⠀⠀⠀⠳⢠⡴⢿⣀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠳⢶⡋⢹⣤⡴⠞⣴⣼⡿⠿⠷⠛⡻⠃
⠀⠀⠀⠀⠀⠀⣸⣤⣤⣿⡁⢨⣔⠺⣿⣿⠿⠿⡙⢷⡮⢔⡠⠀⠀⠀⠀⠀⠹⣿⣿⣿⣺⣦⣀⡘⠃⠀⠀⡇
⠀⠀⠀⠀⠐⠿⢦⡀⠠⡛⢾⣇⣸⣶⠛⠢⢄⣂⣛⣻⣀⡸⣟⣴⣄⢀⠀⠀⠀⠀⠉⠙⠻⠮⣭⣽⡗⠀⠀⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡌⠀⢍⠈⣻⠆⠀⠂⣈⠃⣡⠼⡀⣁⣇⡉⡹⠷⣄⠀⠀⠀⠀⠀⠴⠁⠺⣯⣴⣶⢎⣁⠙
⠀⠀⠀⠀⠀⠀⢀⣇⡠⠴⠒⠚⠉⠁⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠉⠀⠀⠉⠛⠴⣂⠀⠀⠀⡀⠐⣾⡿⣟⠉⠉⠣
⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠈⠛⠁⠀⠹⠁⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡔⢀⠐⡀⠀⠀⢀⠀⡀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⣤⠡⠄⢘⣣⡜⡃⠰⠄⣡⣠⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠤⠓⠀⣠⡒⢂⣀⠴⡧⢁⡠⢒⣨⡠⠒⠤⠎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣚⠥⢒⡀⣿⠠⣀⡍⠀⢜⡧⠀⢈⣁⠀⢹⢈⡒⠩⢒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡉⠘⣋⣁⠉⠲⡑⢌⠄⢔⡧⠤⡉⢈⡖⠉⣌⣝⠃⢉⣓⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢖⡁⡆⢔⠂⠰⠇⠂⡙⠠⢘⡃⠄⠋⠀⠜⠇⡐⣂⢰⢀⣲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢈⢸⣿⣿⣿⣷⣾⣷⣷⣷⣿⣿⣾⣾⣶⣿⣿⣿⣿⣿⡧⡁⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣱⣿⢞⡇⡈⢹⠩⠀⣸⠀⠀⠀⠀⠀⠀⠀⠠⠍⣏⢠⢀⡓⣼⢆⠔⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⡌⠀⡌⡗⢀⠃⠀⢠⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⡄⢺⠡⠀⢡⣈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢃⡄⢫⡔⢡⠈⠑⢶⠦⠤⠀⠀⠀⠀⠠⠤⠤⠊⠁⢌⠢⡝⢀⡐⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢏⡟⢮⡆⣼⣠⡆⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢱⡴⢻⡙⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠠⠙⠝⣸⡀⠊⠀⠀⠀⡐⢂⠀⠀⠀⠀⠀⣤⠫⠋⢄⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⠊⢳⡌⠁⠁⡀⠀⠀⠻⣐⣀⠚⡀⢰⣀⠈⠌⢕⣞⠁⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠣⠀⢀⣉⡦⢄⠀⠁⠈⠀⣽⡼⢉⡀⠄⢄⠈⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠩⠀⠀⠈⠉⠖⠒⡉⠁⠀⠀⠉⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⣙⢀⡀⠀⠀⠀⠈⠀⠀⠱⡀⠀⣀⠦⠀⣉⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠉⠰⠀⢀⠌⠀⠀⠀⠀⠑⡀⠀⢰⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠘⡀⠀⠀⢀⠊⠀⢊⠆⢠⠒⡆⠐⡄⠀⠁⠀⠂⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢼⠚⢣⠀⠀⠀⠀⠀⠓⠂⠘⠒⠃⠀⠈⠄⠀⡘⢠⡥⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠯⣰⠤⠂⠉⣶⡜⠀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠁⠈⠷⠉⠐⠤⣆⠽⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡭⠛⠦⣼⢿⣵⠈⣉⠡⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠔⢉⡀⠂⣤⣆⠴⠛⠭⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⣞⠉⢺⡉⠰⠓⠓⠘⠂⠀⠀⣷⣾⠀⠀⠀⠡⠖⣤⣴⢿⣿⡿⣥⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⡵⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢮⣴⣾⡯⢼⡀⢀⣷⡀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡉⣄⠀⣀⠀⣰⠖⡆⠀⢄⠀⠀⠀⠀⠙⠻⣅⠰⣉⡁⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢍⠀⠀⠦⢈⡏⠱⣄⡤⠛⠺⣿⣦⢄⠀⠀⠀⠀⠉⠑⠐⠃⢀⡈⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⠠⠀⠊⠀⠀⠱⠤⢼⠁⠉⠧⠬⠦⢄⡀⠀⠀⠀⢸⢿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⠀⠀⠀⠉⠀⠈⠁⡀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣾⣿⣿
⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿
⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⡟⠀⢸⣿⣿
⠀⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⣿⣿⣿⠁⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⠃⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠿⠿⠿⠻⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣤⣤⣤⣀⠀⠀⠀⢸⡧⢼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⡧⢻
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⣶⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣦⣶⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣇⢸⣗⢹
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⡿⢸⡏⢽
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣶⣿⣿⣿⣿⠃⢼⠷⢾
⠀⠀⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁⠀⢪⣀⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⠿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣀⣀⣀⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⠟⢡⠴⠒⠲⣄⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢠⡾⢛⣭⣭⡻⣷⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⠀⡏⢰⠋⠃⢸⡆⣿⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣿⢡⡟⣴⣮⣷⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⡄⢳⡘⠲⠴⠋⣠⠏⠈⠉⠉⠉⠉⠉⠹⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⢻⡆⠿⢬⣛⣥⡿⣡⣿⣶⣶⣶⣶⣶⣦⡹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢦⣉⠛⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣑⠶⢦⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠶⠚⠛⠛⠛⠛⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠀⢀⣀⣤⣤⣤⣶⣶⣤⢄⣀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⣠⠾⠁⠀⣀⣴⠞⣡⠞⠋⠀⠀⠀⠈⢳⣤⣤⣝⣳⢤⡀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⣠⢤⡄⠀⠀⠀⠀⡴⣤
⠀⠀⠀⢀⡼⠁⢴⣴⣾⣭⣿⠿⣿⠀⠀⠀⠀⠀⠀⠈⢹⠈⢙⠋⠷⣿⣦⡀⠀⠹⣆⠀⠀⠀⠀⠀⢠⡇⣸⡇⠀⠀⠀⡼⢀⡟
⠀⠀⠀⡾⠃⠀⣴⣿⣾⡇⡇⠈⣷⡤⠀⠀⠀⠀⠀⠀⣟⢀⣼⠋⠙⠋⠹⢿⡄⠀⠘⣆⠀⠀⠀⠀⣼⢠⡿⠀⠀⠀⢰⢁⡞
⠀⠀⣸⠃⠀⢰⣿⣿⠿⢷⠤⣦⣞⣿⣲⡶⠒⠚⠉⣷⢻⡞⠉⠀⠀⠀⠀⠸⢿⡀⠀⢹⡄⠀⠀⢠⣇⣼⠃⠀⠀⢠⣿⡿⠁
⠀⠀⣿⠀⠀⣿⡏⠀⠀⠀⠀⠀⣹⣷⠃⠀⠀⠀⠀⠙⣦⣿⣄⠀⠀⠀⠁⠀⢸⡇⠀⠸⣧⠀⠀⣼⢣⡏⠀⠀⠀⣾⣿⠃
⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀⠀⠘⣇⠙⡧⠀⠀⠀⢰⡞⡣⠀⠀⣿⠀⢠⡏⣾⠁⠀⠀⣼⢻⠇
⠀⠀⢻⡀⠀⢹⡆⠀⠀⠀⠀⠀⢙⡏⢷⠀⠀⠀⠀⣀⡼⢻⡁⠓⠶⡶⠞⠋⢠⠁⠀⢸⣿⠀⣼⢱⠏⠀⠀⣰⣿⡟
⠀⠀⠘⣧⠀⠈⢿⣦⣀⣄⣀⣴⠞⣀⣼⣿⣛⣺⣟⣭⠖⢻⣡⣤⢀⣅⢔⡏⡘⠀⢀⣾⡇⢠⣏⡿⠀⠀⢠⣯⡿
⠀⠀⠀⠹⣇⠀⠘⣿⣭⠛⢭⣫⠖⢤⡟⠈⠉⠁⠀⠀⠀⠀⢹⡎⠛⡇⣚⡴⠁⢀⣾⡿⠁⣼⣿⠃⠀⢀⡟⡾⠁
⠀⠀⠀⠀⠹⣧⡀⠀⠻⡀⠰⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⠧⠃⠀⣠⣿⡿⠁⢠⣷⡏⠀⠀⣞⣼⠃
⠀⠀⠀⠀⠀⠈⢳⣤⡀⠈⠙⠧⡄⠀⣺⠳⣤⣤⣀⣀⣠⣼⠻⠐⠀⠀⣠⣮⣿⠟⠁⠀⡞⣾⠁⠀⡼⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣤⡀⠀⠀⠉⠉⠀⠈⠉⠉⠁⠀⢀⣠⣴⣞⣽⠟⠉⠀⠀⣸⢱⡇⠀⣰⢣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣶⣦⣤⣤⣄⣴⣶⣾⡿⠿⠛⠉⠀⠀⠀⠀⢀⡏⡾⠀⢰⢇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣭⣭⣤⡶⠶⠦⣤⣤⣀⡀⠀⣼⣸⠃⢠⣏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⣉⣥⣤⣴⣶⣶⣤⣤⣄⡉⠛⢳⣷⣏⠀⡞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣁⣤⣾⣿⠿⠛⢻⠀⠘⣿⠄⠴⠛⠛⠳⣾⣾⠙⡿⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣾⠟⠉⠀⠀⡄⠀⠈⡃⠀⠀⠀⠀⢀⣀⣰⣿⠟⣿⣿⠟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣰⣿⡯⠥⠴⠖⠙⠑⡀⠀⠹⠀⠀⠐⠋⠀⠀⣿⣿⢠⣿⡿⣦⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢰⡿⠁⠀⠀⡀⢨⡀⠀⢤⠀⠀⠀⢀⢀⣤⡀⣸⣻⣏⣿⡟⢀⣰⣆⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⣷⡶⠚⢏⠁⠀⢀⠤⠘⠀⠀⠈⣭⣆⠀⣻⣿⣿⣿⡿⠋⠉⠁⠙⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡧⢼⣿⡁⢀⠀⠽⠀⠀⠘⡁⠀⣀⣠⠴⣽⠏⠀⢸⣿⣹⡿⠁⠀⠀⡀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⣿⠛⠂⠀⠀⢤⠀⠚⠋⠁⣤⣣⡾⢻⣆⠀⠻⠇⠛⠓⠚⠁⠀⢱⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣯⡄⢻⠈⠻⠠⠀⠐⡀⣀⠄⢠⠘⢿⡄⣼⣿⠀⠀⠀⣀⡤⠶⡄⠀⠀⣿⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⡌⢧⠀⢃⠁⠀⠀⠀⢀⡀⡄⠘⡷⠿⠟⠓⠉⠉⠁⠀⠀⢰⡀⣠⠏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣔⡌⢢⠐⠄⠰⡖⠈⠙⢇⠀⠀⢷⠀⠀⢀⣠⡤⢰⡄⠀⠀⡏⠉⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡙⠀⣀⣀⠀⠀⢰⡞⠀⠛⠁⠀⠀⢩⠁⠈⣆⠀⠄⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡆⠈⠙⠷⣤⣠⣷⠒⠂⢀⣤⢄⣾⡼⠶⢛⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣬⣍⣉⣉⣉⣉⣉⣁⣤⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⢀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷
⣸⣿⡅⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢸⣿
⣿⣿⡇⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣼⡆⠀⠀⠀⠀⢰⣧⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿
⣿⣿⡇⠀⢸⣿⣧⠀⠀⣀⠀⠀⠀⠀⡀⠰⣆⢠⡆⢸⣿⣄⣤⣴⣿⣧⣠⣤⣤⣄⣼⣿⣤⣤⣠⣿⡇⢰⡄⣰⠆⢀⠀⠀⠀⠀⣀⠀⠀⣿⣿⡇⠀⣸⣿
⢻⣿⣿⣦⣼⣿⣿⡀⣼⣿⠀⠀⠀⠈⣿⣶⠋⠻⣿⠋⠙⣯⣠⣿⣿⣿⡿⠉⠉⢻⣿⣿⣿⣤⣽⠋⠙⣿⠟⠙⣶⣿⠁⠀⠀⠀⣿⣇⢀⣿⣿⣧⣴⣿⣿
⠈⠻⣿⣿⣿⣿⣿⣷⣿⣿⣶⣆⠺⠃⠈⢿⡀⠀⣿⠤⡶⢿⡍⡿⠁⠈⠻⣀⣀⡾⠉⠈⢿⢹⡟⢶⣤⣟⠀⢠⡿⠁⠘⠗⣰⣷⣿⣿⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⡳⡿⠃⢲⣄⣠⡾⠛⣦⣤⣽⣿⣿⣾⣤⣴⠛⢷⡄⣠⡶⠚⠷⢺⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿⣿⠟⢿⡁⢹⣷⣤⣼⣿⣿⣷⡎⠀⠀⣩⠿⠿⣅⠀⠀⢱⣴⣿⣿⣦⣤⣾⡏⠈⡿⠿⣿⣿⡿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠧⣤⣸⣤⢼⣿⣿⣇⠀⣨⠟⠻⣇⠈⣳⠊⣍⠀⠀⣯⠒⣶⠁⣸⠟⢻⣅⠀⣸⣿⣿⣧⣤⣜⣤⠼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣩⡄⣼⠛⢻⣄⣹⠫⣄⣠⡬⣿⣵⠋⠉⣰⣆⠈⠳⣼⡯⢥⣄⢴⠋⣯⢠⡟⠛⣧⢀⣍⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢉⡤⠿⢛⡄⠀⣯⢼⡾⠋⣩⡴⠋⣁⠴⠊⢹⡍⠓⢤⣈⠓⢤⣉⠚⢷⡥⣬⠃⢴⡻⠿⣄⡙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⣀⠴⠋⣀⡜⢁⣠⠴⠋⣡⡔⠊⠁⣀⡴⠋⠙⢦⣀⠉⠛⠦⣉⠓⢦⣀⡉⢦⡀⠙⢦⡀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⢁⣤⠚⠉⠁⣉⠡⠔⠋⣁⠠⠤⠚⠉⠀⠀⠀⠀⠉⠓⠤⠄⣈⡑⠦⢌⣁⠈⠙⠓⣄⠉⢂⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⢀⡾⣷⠓⡿⠋⡟⠓⠂⢈⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⠁⠒⠚⢿⠙⠗⠚⣿⢧⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⢀⢔⠯⡻⠃⡴⡇⢠⠋⢸⠀⠞⠋⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⠈⡄⠻⡀⣿⢆⠹⡟⡽⢢
⠀⠀⠀⠀⠀⠀⠀⠺⠘⠀⠃⣴⠹⢻⠎⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢳⠛⡎⣁⢸⠀⠇⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠇⣰⠀⣯⡸⠏⡰⠛⣄⡴⢦⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠⠶⣆⢨⠛⣄⠻⣇⡿⠀⢀⡂⡇
⠀⠀⠀⠀⠀⠀⠀⢲⠰⣇⡄⠈⡧⣞⠃⣰⠃⠀⠊⢩⡟⢳⡖⢻⠛⠏⠀⠀⠀⠀⠙⢻⠗⢲⠛⠟⠉⠃⠀⠸⣄⠸⢧⡜⠁⢰⡜⠇⡗
⠀⠀⠀⠀⠀⠀⠀⠈⡳⢟⣷⣦⢱⣾⠊⣩⡀⠀⠀⢸⡇⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢰⣍⠳⣯⡜⣴⢎⠳⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⡇⣀⢹⣇⣸⣾⢧⠀⠀⢸⡇⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢾⡷⣆⣸⠇⣿⠸⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠱⡉⢦⣈⢋⡤⢁⣤⠀⢸⡇⢰⡇⠀⠀⠉⠛⠓⠚⠙⠁⠀⠀⢸⠀⡇⠀⠀⣿⠐⣄⣋⣁⠴⡩⢆⠷⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠳⣌⢶⣤⡄⣴⢾⡙⢧⠘⡇⢨⡇⠀⢀⣼⣉⣉⣉⣙⣤⠀⠀⢈⠀⠇⢀⠞⢉⠷⣤⢠⣴⠞⣡⢊⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠈⡆⢹⡷⠀⡆⢓⡀⢾⡇⠰⡇⠀⠈⠣⣄⣀⣀⣤⠏⠁⠀⢠⠀⣢⡟⢠⠋⡘⣠⢷⡉⠸⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣮⣤⠷⠋⢠⠀⡇⢈⠃⣟⠑⢶⡇⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣠⡶⠋⣥⠸⠀⢃⠙⡀⠹⠶⣄⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠖⣠⠏⣰⢁⣴⠎⠙⠶⣤⣀⠀⠀⠀⢀⣀⡴⠞⠉⢳⢦⣈⣄⠳⡌⣤⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢮⡵⠞⠋⢠⡜⣷⠰⠒⠊⠉⢙⠗⠻⡉⠉⠐⠒⢶⡛⣧⠈⠙⠷⣬⣳⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⠖⠈⠉⠁⠉⠁⠀⠀⠀⢠⠏⠀⠀⠱⡄⠀⠀⠀⠉⠁⠈⠉⠁⢺⠛⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢱⣀⡆⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢸⣀⠇⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣧⠀⠉⠁⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠁⠀⣼⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡄⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡇⠀⢣⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⡜⠀⢸⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠻⡇⠀⠘⡀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⣠⠃⠀⢸⠟⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢶⡇⠀⠀⢛⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠟⠀⠀⢸⡖⢻
⠀⣶⣖⣶⠖⣤⣄⡀⣠⠜⠻⣤⡇⠀⠀⠈⡇⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠸⠀⠀⠀⢸⣤⠟⠣⣤⣀⣠⣤⠒⣶⣲⣶
⠀⠙⣾⠛⠳⣬⣍⣿⠁⠀⠀⢸⡇⠀⠀⠀⣸⣏⠀⣀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⠀⢀⡀⠀⢀⠀⣾⣇⠀⠀⠀⢸⡇⠀⠀⠀⣿⣩⣤⠞⠛⣷⠋
⠀⠀⠈⠛⠷⣍⡽⠿⣷⣴⢿⣦⣇⠠⠔⠊⠉⠙⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⠉⠓⠢⠄⣸⣴⡶⢷⣾⠿⢯⣩⠾⠛⠁
⠀⠀⠀⠀⢰⡏⠀⠀⣠⣧⣀⠭⢙⣧⡔⠻⠂⠀⣀⣉⣦⣀⡀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣀⣴⣋⣀⠀⠀⡾⠢⣼⡛⠩⢀⣨⣧⠀⠀⢹⡆
⠀⠀⠀⠀⠈⠳⣄⣠⣿⣟⠁⠀⣈⡽⠿⠛⠛⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠾⢿⣁⠀⠀⣹⣿⣇⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠉⢨⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢾⣯⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠻⣄⣈⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠴⠶⣤⡤⠤⠤⢤⣤⡴⠦⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣄⠀⣀⠴⠖⠻⣏⠉⣽⠟⣿⠃⠀⠀⠈⠷⣠⣆⣸⠏⠀⠀⠈⣿⠻⣯⠉⣹⠛⠲⢦⣀⠀⣠⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣅⣀⠤⠤⠼⣿⡟⠀⠈⠳⣤⣄⣙⣿⣻⣿⣳⣞⣀⣀⡴⠏⠀⢹⣿⠧⠤⠤⢀⣩⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣸⠷⣀⣠⠞⠉⠉⡭⢿⣿⣿⡾⢧⠉⠉⠳⣄⣀⠾⣇⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⣀⣠⡀⠀⠀⡴⠃⠀⠀⠹⣆⠀⠀⣠⡟⠹⠇⢻⣆⠀⠀⢠⡟⠀⠀⠘⣦⠀⠀⢠⣄⣀⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⢹⠀⡜⠁⠀⠀⠀⠀⠈⠛⠛⢹⡇⠀⠀⢸⡇⠙⠙⠋⠀⠀⠀⠀⠈⢣⠀⡏⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⡤⠐⠀⠀⠀⠀⠀⣟⠟⠀⣿⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠐⠀⠀⠈⠁⠀⠀⣄⣀⠀⠂⠈⠉⠀⠈⠁⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⢰⣆⣠⣀⢈⣉⣁⣤⣄⣈⢀⣺⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣛⣽⣿⡄⠀⠀⠀⠀⠘⠛⠻⢃⣬⠉⢙⡛⠛⠉⠜⠉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠉⠋⠉⠛⠁⠀⠀⠀⠀⡆⠀⠀⣤⡾⠛⡾⣿⢿⣿⠿⣷⠀⠀⠈
⠀⠀⠀⠀⣄⣰⠐⡠⠅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣴⢦⣆⣾⣶⣾⣴⣦⣴⡄⠀⠠
⠀⠀⠀⠀⠈⠉⠉⠳⠮⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢈⡉⠉⠉⠛⠭⠯⣉⡙⠁⠌⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣟⣿⣷⡼⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⠀⠠⠀⠮⠽⠿⠄⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠱⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠲⣦⣖⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⢉⡞⣳⣛⣻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠫⢠⣥⣼⣷⢚⣦⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⡁⠀⠀⠀⠀⠀⣰⣾⡯⣽⣿⣧⣴⡀
⠀⠀⠀⢀⣴⡀⠂⢀⠀⢦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣠⣴⡶⣶⣤⣤⢀⣄⡀
⠀⠀⠀⠀⠙⠛⠃⠭⠀⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠩⠿⠿⠏⠏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠁⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣖⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠠⠀⠀⢀⣀⣠⣤⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⢿⣿⢵⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠿⠷⠶⠒⠛⠁⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣠⢄⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠦
⠀⢀⠀⠀⠠⣰⡏⠡⢄⡅⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡶⠶⠶⠆
⠀⠀⠁⠀⠀⠀⠁⠙⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⣄⠤⣄⢠⡀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⢐⡦⠛⢉⣠⡴⠋⣀⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠱⠟⠐⠟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⣹⠀⠴⠻⠯⠃⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠤