Santa Claus Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⣀
⠀⠀⠀⣰⣲⡄⢄⣛⣡⣴⣿⣶⣶⣾⣦⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣉⣁⣀⣀⡈⠉⠛⠷⣤⣀
⠀⠀⠀⠈⠉⡀⠈⡹⣿⣟⣛⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣛⣉⣹⣿⣿⣿⣿⣿⣶⣦⣄⠙⠻⣶⣄⡀
⠀⠀⠀⠀⢰⠁⢾⡿⠂⠹⠋⠉⠙⠁⣰⣄⣀⠀⠀⣀⣤⡤⠎⠐⠿⠛⠛⠟⠛⠛⠉⠉⠻⠿⢿⣿⣿⣿⣿⣦⣈⠻⣿⣷⣶⣤⣀
⠀⠀⠀⠀⣼⣦⣀⠀⡈⠂⠀⢨⠻⣿⣦⣹⣿⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠻⢿⣿⣿⣶⡈⢿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⣼⣷⣝⢿⣿⣿⣷⣶⢰⠐⠋⠉⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣄⣀⠀⠀⣿⣷⣶⡘⢿⣿⣿⡄⠹⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠹⣦⣽⣿⡿⣿⣷⠷⠖⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣯⣿⡄⣈⠹⣿⣿⣿⡃⢿⣿⣿⡄⠘⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠛⠉⠙⢿⠏⠀⠀⠰⣦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣟⠀⠻⣷⣶⣾⠟⠡⣾⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⢀⡠⠀⠴⠶⣶⣶⣶⣤⣤⣀⣀⣀⡀⠀⠀⠀⢘⣏⢠⣥⢶⣦⣌⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣦⠀⠀⠁⠀⠀⣤⣄⠀⠨⠟⠋⠛⠛⠛⠛⢿⣷⣦⣤⠈⠛⠘⠻⣿⣿⣿⢯⣭⡝⢰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠈⣠⣶⣦⡤⠤⢤⣝⡻⣶⡀⠀⠀⠀⠀⠀⢀⡈⣻⣿⣧⠀⠀⠀⠀⣰⣴⣿⡟⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣤⢤⣴⣿⣿⣶⡇⠲⣤⣤⠄⣀⣠⣤⣼⣍⢻⡇⠀⠀⢰⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣤⠀⠟⠃⠀⣬⣽⠟⣽⡷⢀⡔⠛⠋⠻⠿⣿⣷⣿⣃⢱⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣼⣿⠋⠀⠀⠀⢉⡉⠀⠰⠟⠁⠀⠉⠒⠠⢿⡾⢿⣟⣼⣯⠈⠀⠂⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⢀⡄⠀⣼⣿⡅⢤⣧⣶⣾⣿⡀⢼⣥⠔⠉⠉⣶⣄⠀⠀⠀⣿⣿⣝⢿⣷⡦⠀⢻⣿⠛⢿⡇⠀⢹⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢀⣀⡋⠀⢬⣴⠀⠀⣏⣽⣤⡀⠀⠈⠁⠘⠷⠾⠷⠞⠻⠟⠋⠘⠷⣶⣿⡿⠟⠙⢤⡞⠻⠷⠘⣿⡀⠀⠁⢀⣸⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠠⠚⠉⢀⣀⣤⡤⠤⠤⠒⠂⠹⠟⠙⠒⠧⣶⣶⣤⡀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⡤⠘⢶⣬⡻⣶⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⣠⡤⠖⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣟⠙⠦⣄⣀⡠⢦⣤⣶⠿⠿⠯⣥⣄⣺⣿⣿⢾⡟⠶⠊⠉⢉⠉⠻⣷⣤⡀
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠙⠋⠙⢿⣷⣦⡄⠀⠀⠀⠈⠁⠀⠀⢠⠈⣿⣿⠋⠁⠀⠁⠀⠀⠀⠀⠀⢲⣿⣿⣅
⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢏⢻⡿⠂⠀⢄⠀⠀⠀⠀⠀⢱⣼⡟⡀⠀⠀⠀⠀⠀⠀⣈⡶⣷⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠘⠁⡆⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡼⠀⡇⠀⠀⡀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⠻⣿⣿⣿⣿⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢀⡄⠀⢿⠀⠴⢠⡎⠁⠀⠀⠀⠀⠀⠀⠁⠀⢷⠀⢰⡇⠰⣿⢸⣷⡈⢢⣄⠐⢤⣀⣀⡒⣿⣿⡿⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⢈⠀⠛⡜⠋⣇⠀⢠⠀⠀⠀⡆⠀⣠⡀⠀⠀⢸⡄⠀⢡⣾⣿⣿⣿⣿⣿⣶⣿⣿⡿⡁⢿⣧⢻⣶⢷
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠘⠛⣼⠂⠀⣽⣠⠁⠀⠀⢸⠇⢰⣿⡄⣠⣇⠀⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⢸⣿⣷⡜⠻
⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠀⠸⠇⢠⣍⠁⠀⠀⠀⢀⣞⢠⣆⡘⣷⣿⣾⢀⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣾⣿⣿⣶⡦
⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⢀⣡⠈⠊⠁⡧⠘⢠⡴⠛⠻⢸⣿⣿⣜⣿⣿⣸⠇⠀⣿⣿⣿⣻⣿⣿⣿⣏⡑⠾⣏⢰⣿⠿⠋⣰⣦
⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠀⠀⠀⠀⣬⠃⠜⠀⠀⡠⠊⠋⠁⢀⢠⡿⣿⣿⣿⣿⣿⡅⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⣽⠟⠁⠻⣷⡏
⠀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠊⠇⢀⠄⠀⠈⠀⠀⠀⢠⣿⠟⢰⣿⣿⣿⣿⡿⢄⣿⣿⣿⣿⣻⣿⣿⠟⠋⠀⣔⠊⠁⠂⣸⣿⡿⣣⡀
⠀⢧⡰⠇⠀⠀⠀⠀⣀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⠄⣠⣿⠇⢠⣿⣿⣿⠓⢯⣶⣿⣿⡿⣿⣿⢺⣿⣯⣴⣯⣴⣤⣦⠀⢻⣿⢟⣼⡏
⠀⠀⠄⠀⠀⢀⠔⡝⠋⠉⠀⠀⠀⣀⣀⡀⠀⠀⣀⣤⣶⠾⢛⣥⣾⠟⣃⣴⣿⣿⡟⣧⡼⢿⣻⣿⠿⠛⡛⠩⠉⠓⠚⠛⠓⠒⠶⠧⠴⠿⠓⠚
⠀⠀⢧⡄⠀⠠⠊⢀⣴⠾⣿⣿⣿⣿⠏⠁⣤⣾⣿⠛⠁⣰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⠿⠕⠀⠈⠁⠀⠀⠒⠋⠉⠉⠙⠛⠓⠒⢤⣀
⠀⠀⠀⠁⡀⠀⠀⠉⠸⣷⣿⣿⣿⣅⠀⠀⢰⣿⡅⢂⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠄⠀⠿⠟⠃⢈⣩⣽⣿⣿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠄⠐⠒⠒⠒⠉⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠓⠈⠘⠊⠉⠀⠀⠙⠦⠔⢦⠤⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⡼⠃⠀⠀⠀⠀⣀⣀⠠⠕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣼⠁⠀⠀⢀⡄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣸⠇⠀⢀⡠⠌⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣿⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⢻⠿⠖⠛⠓⠉⠉⠁⠀⠰⠟⢢⢠⣄⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣧⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠠⡎⠛⠁⠀⠀⠀⢉⡆⠀⠀⠀⠀⢈⣀⡀⣀⠈⠙⣇⡀⠀⠘
⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢻⠆⠀⠀⠀⠀⠀⠀⠀⣤⣀⢀⡥⠖⠉⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⢁⣀⣀⠈⠒⣿⠈⣧⠻⠂
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣼⠃⢹⠋⠀⡠⢞⣉⠉⠲⣄⠀⠀⠀⠀⢠⡶⢣⣤⡀⠑⣆⢀⢰⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⢿⣀⠀⠀⠀⠀⠠⠁⢀⠎⠀⢸⠁⣹⣿⣷⠀⠈⣆⠀⠀⠀⣾⡓⠾⡿⠃⢀⣨⣰⡄⠳⢄
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⢽⡀⠀⢰⡿⢆⠀⠈⢧⡀⠥⢤⣙⣿⡥⢄⡠⠊⠀⠀⠀⠻⡉⠒⠒⠊⠁⠈⠉⠉⠐⠎
⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⡴⢇⡏⢹⡦⣉⣠⡾⠁⠄⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠙⣆⠀⠚⠀⠢⠀⠀⠀⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠐⠒⠚⠁⢎⡤⠊⠁⠷⠀⠀⠀⢈⠉⠀⠀⢀⠠⠧⠤⢤⣀⣀⠤⠛⠒⠤⠤⠖⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠐⢄⣀⡴⠋⠀⠀⠠⡆⠀⠀⠀⠀⠐⠄⠐⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⣤⣴⠲⠿⢿⣿⣿⣾⡿⠒⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠃⠁⠀⠉⠳⢤⣀⣈⣻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣠⢀⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⠀⠀⣠⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠓⠚⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⡀⠠⠎⠀⠑⠉⠀⠐⠈⢻⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡌
⢱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉
⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⠀⠈⢢⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠈⠲⠃⣄⢀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⠀⠀⠀⠀⠈⠺⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢧⡈
⠀⠀⠀⠀⠀⠘⠣⠐⠢⠄⠣⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡟⠦⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⣴⡄⠀⣯⠗⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⣘⡆⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠲⢄⣀⠐⠂⢤⣤⡤⠄⠚⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠰⢀⠂⠐⠂⣆⢂⡶⠖⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠁⠀⠀⠀⠀⠈⠉⠈⠛⠡⠌⠀⠀⣄⠀⠀⠀⠍⡲⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠁⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠴⠋⢀⡀⠀⠙⢤⠀⠠⠏⠀⠀⠁⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⢀⡔⢄⣀⣤⠵⠶⠚⠛⠛⠛⠻⠷⢶⣦⣥⣐⠀⡀⠀⠀⠀⣀⠀⠬⠦⡀
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⢀⠦⠠⢞⣭⡶⠛⠉⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠈⠙⢿⣶⣅⡠⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠠⠀⠒⢂⠒⠈⢁⢒⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣮⡢⣾⠆⠐⠤⢀⡵⡀
⠀⠀⠀⠀⠁⠀⠀⠀⢒⡄⣰⣿⣿⡟⣥⣶⡿⠁⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⢾⠆⠀⠘⠃⠑⡀
⠀⠀⢀⠂⠀⠀⠀⠀⠌⣼⣿⣿⣿⣷⣿⡅⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠸⡆⠀⢿⣿⣿⣿⣆⠀⣈⡀⠀⠀⠰
⠀⠀⡀⠀⠀⠀⠀⡀⣼⣿⣿⣿⣻⣿⣿⣷⣴⣦⢀⣬⡇⠀⢀⡠⠖⠚⠉⠉⠹⠛⠛⢶⣿⣄⣸⣿⣿⣿⣿⣇⢛⡣⠈⠐⠀⠃
⠀⠀⠀⠀⢀⠂⠀⢸⣿⣿⣿⣷⣚⢿⣿⣿⣿⣿⣿⣿⣷⣾⠿⠒⠀⢀⠀⢰⡔⠒⠒⠀⢿⣙⢿⣿⣿⣿⣿⣿⡈⣁⠀⣄⡀⠘
⠀⢸⠀⢀⠀⠀⡗⣼⣿⣿⣿⣿⣿⣈⡿⣿⣿⣿⣿⣯⠈⢹⣤⠶⠛⢻⣧⡀⠑⢐⡀⠀⡖⡂⠉⠙⠹⣿⣿⣿⡇⠀⠀⠄⠙⠶⡆
⠀⠈⠀⠈⠀⢀⠃⣿⣿⣿⣿⣿⡿⡏⢉⠛⣿⣿⡿⣿⣶⣤⣄⠀⠀⢀⡝⢁⣀⡸⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠂⠀⠘⠀⠀⡅
⠀⢐⢀⠀⠀⠎⠀⣿⣿⣿⣧⠈⠄⠁⢀⣴⣿⣿⡇⠀⠙⠛⠁⢀⡒⠋⠙⠁⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠈⣿⡇⠀⠀⠠⡄⠀⡇
⠀⠀⠘⡄⠀⠀⠀⢸⣿⣿⣧⠏⠀⢠⣿⣿⣿⣿⡷⠀⠀⠀⠀⠈⠀⠀⣀⣀⣠⢤⠔⠖⠛⠛⠋⠀⠀⠀⠀⢹⢃⡥⠀⠀⠛⣦
⠀⠀⠀⠰⣄⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⣀⣹⣿⣿⣆⠀⠀⢀⢰⢾⣾⡟⠛⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⢧⡌
⠀⠀⠘⠀⢈⣴⣿⣿⡿⠃⠀⠀⠉⠀⠀⠀⡈⣿⡠⠙⣿⠀⢄⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣆⡀⠺⠁
⠀⠀⢠⣿⡿⢛⠄⠀⡁⠀⠀⠀⠀⠀⠀⡀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⡀
⠀⣠⣿⡟⢱⠃⡄⠐⠁⠀⠀⠀⢠⠀⣠⣤⣾⣿⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣇
⢠⣿⡉⢀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠸⣿⣿⣿⣿⣿⣟⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏
⢸⡋⡇⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦
⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣟⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠋⠙⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠻⠟⠿⢿⣿⣷⡀⠰⡧⣠⠄⠀⠀⠠⠀⣶⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠆⠐⣿⠁⢶⣂⣴⣾⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⣿⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣻⠉⠉⠉⠉⠀⠉⠀⠀⠀⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⡄⢀⠀⠀⠀⠘⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⣯⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡤⠴⠖⠹⠒⠁⠙⠉⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢰⠃⠀⠀⣀⠀⠀⠀⠀⠀⡜⠷⠃⠀⠀⠀⠀⠀⠀⠐⠚⣣⠄⠀⠴⢋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣀⠀⠋⢠⠂⠀⠀⡶⠚⠀⡠⣀⡛⡐⠀⠀⠀⠀⠐⣉⢉⠉⢃⡐⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠨⡇⣀⠀⠘⠁⢠⡴⠃⢤⣜⠯⠥⠀⠀⠑⠐⠉⠲⢀⠀⠀⠀⡘⢁⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠻⢿⠀⠀⣄⣸⠀⠀⠀⠲⢀⡀⠀⠀⠀⠀⠀⠀⢀⢹⡀⠉⠀⢼⢌⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⡴⣆⣿⠃⠀⠂⠀⣀⡀⠉⢉⡔⠀⠐⠦⠴⠋⠁⠈⠙⠢⠼⠀⡇⠻⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡔⠉⢸⠀⠰⡇⡎⠸⣀⡬⠋⠀⠀⢀⣠⠎⣑⠦⠖⠤⠤⠴⠊⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠆⠀⢰⠁⠰⣇⠀⠀⠀⠙⠦⢤⣄⣤⠖⠉⠁⠀⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠐⠋⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠾⣧⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠠⣇⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⢧⠀⠀⠀⠀⠀⠀⢠⠞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠴⣷⣀⣈⠧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⢧⣀⢀⡄⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡈⠁⠀⠀⠀⠘⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣄⣷⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠳⠦⠷⢤⣤⣄⣀⡀⣄⠈⡀⠀⠀⠘⢦⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠙⣄⠀⢀⡞⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠐⠚⠛⠿⠿⣿⣿⣿⣻⢿⣿⣟⡲⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⡠⠆⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣯⡻⣿⣌⡻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡴⠋⠀⣠⡤⠀⢀⡀⠀⠀⠀⠀⠀⠠⠌⠑⠌⢻⣿⡹⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⣉⣤⣶⣿⣯⡽⠿⠒⠩⢭⣥⣖⣀⣠⠀⠈⢢⡀⠈⢻⡇⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡟⢀⣿⣿⠦⠄⠉⠁⠈⠩⠉⠛⠻⢿⣦⡀⠀⢻⡌⢊⠃⣾⡿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠈⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠱⠀⢺⢟⣠⠍⣛⣻⣿⣿⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⣴⣆⣠⣶⣷⣄⢀⠈⣿⡆⢠⡀⠀⢽⡆⠀⢀⡄⠈⠐⠋⠉⠉⣩⣿⠋⠉⠻⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠒⠫⠵⡻⠟⠋⠙⠆⣐⠐⠚⠉⠁⠀⠈⢧⡀⠂⠀⠀⠠⠀⠤⠾⠋⠁⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀⢿⢸⣆⣤⠴⠛⠁⠈⠀⠀⠁⠉⠉⠢⣤⣤⡄⡆⠀⢈⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠓⠌⣼⣿⠃⢠⠀⡁⣴⣿⣿⣦⡀⢄⡀⠈⠙⠓⠛⠂⠀⢃⡀⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠃⠀⢠⠀⠀⣤⠻⠀⠁⠙⢿⡿⠋⠈⠀⠙⠒⠒⠂⠀⠀⠀⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠑⠀⠀⢀⠀⠊⣄⠀⠀⠦⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠑⠦⠤⢤⣄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣨⣦⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢿⢰⣾⣶⣤⡆⣷⣼⡖⠄
⠀⠀⠀⠀⢀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣾⣿⣿⣿⣿⣿⢛⣤⣶
⠀⠀⠀⠀⠘⣿⣿⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣾⣟⠁
⠀⠀⠀⠀⠀⣽⣿⣿⠟⠂⢄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠢⠛⠛⣽⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠙⢫⠃⠀⢀⣾⠓⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠳⣌⣉⣋⣤⣿⣿⣿⣿⣫⡼⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⡋⢠⡄⢲⡖⢠⣾⣦⣹⣿⣿⣶⣶⣶⣾⣧⣴⣿⣿⣿⣿⣿⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠜⠠⢄⣠⠴⠿⠿⠈⠛⠻⠿⠿⠿⠿⠿⠟⠛⠉⠙⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠋⠉⠉⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠉⠉⠉⠉⠉⠉⢛⡳⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠀⣀⠤⠟⠓⠒⡶
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠚⠋⠀⠀⠉⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡃
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⢇
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢠⣄⣠⣀⣸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠋⢀⠄⠀⠐⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠉⠉⠰⠶⢄⣤⡙⣆
⠀⠀⠀⠀⢠⠞⢷⠀⣀⠴⠃⠈⣉⣉⣉⠶⠲⡶⢦⡤⠚⠃⠀⠀⠀⢀⡤⠶⢛⡉⠁⠀⠀⠀⠀⠀⢠⠤⠠⠦⡀⣿⠋
⠀⠀⠀⢀⡏⠀⠈⢷⠉⢢⣀⣀⡀⢀⡸⠊⠛⢢⣀⠇⠀⠀⣀⠤⣪⠕⠚⠉⠉⠁⠀⠑⢦⠀⠀⢠⠁⠀⠀⠀⠈⣿⡀
⠀⠀⠀⡜⠀⠀⠀⠈⠁⠈⠁⠀⠈⠋⠰⣄⣠⠜⠁⢀⠴⡎⠁⠀⠉⠉⠙⠃⠒⠦⠄⠴⠃⠀⠀⠘⣠⠒⠂⡀⠀⡇⠛⠋⠉⠛⠲⢤⡀⣀
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡠⠚⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠘⡄⢷⣼⣇⣧⣤⠷⠓⢤⡀⠀⠀⠀⠻⣼⡷⣀⡀
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠊⠀⠀⠀⢀⣇⣀⠀⠀⠖⠀⠀⠐⢒⣼⠗⠒⠲⣤⡽⠚⠛⠛⠻⣇⠀⠀⢀⡇⠀⠀⠀⠀⢹⠃⠹⡍⠙⠲⣄⡀
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢀⡴⠋⠉⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⡷⠾⠛⠲⠦⣄⣠⠴⠋⠀⠀⣷⠀⠀⠠⣵⣄
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠌⢷⣤⡴⢚⠁⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠈⠳⣄
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠈⠑⠁⠀⠲⠤⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡷⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡿⡀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠋
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⢣⡙⠢⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣤⣀⠀⢀⣀⠀⠤⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠃⠰⢇⡨⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠉⠲⠤⣀⣀⣀⣀⣀⠠⠔⠚⠒⠛⠒⢯⡑⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢀⣀⣹⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⠏
⠀⢀⡴⠉⠁⠀⠉⠛⠒⣦⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠈⠓⠠⣶⣤⣤⠔⠻⠞⠁⠀⠀⠀⠈⠛⠦⢤⣄⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⢀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠛⠉⠲⢄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠛⠳⢦⣄⣀⡀⠀⠀⠀⠀⠀⢰⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠀⠒⠀⠆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠴⠏⠒⠢⠤⢀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⢀⠤⢀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⡁⠱⡄⠀⠀⠀⠀⠀⠀⠀⡎⠲⢉⣉⠬⢋⠀⠉⠐⠲⡐⢄⠀⢰⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠈⢉⣉⢁⠀⣈⠦⠤⣀⠀⠀⠀⠴⠀⠀⠀⠑⠠⣝⠓⠢⢠⡄⠈⢺⠀⠈⠆⢀⡰⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⢀⠌⠁⠀⡀⢌⣱⢠⠊⠀⠑⠢⠄⠀⠀⣠⡅⠀⠒⠀⠄⠓⠒⠀⡶⠚⠈⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠀⡔⠁⠀⠈⢻⠀⠀⠀⠀⠀⠀⠠⠈⠙⠦⠤⠀⠀⠀⠤⠊⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠐⡀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠈⠒⠢⠄⠀⠀⠤⠤⠤⠒⢍⡁⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠊⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⢦⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠇⠀⠀⠀⠑⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠑⠢⡔⠁⠣⡀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢈⠶⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣖⢉⡁⠀⢆⠀⠀⠈⠢⠄⠠⠲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⠘⠉⠉⠁⢒⠈⡇⠀⠈⠉⠉⠉⠀⠀⠘⠀⠀⠄⡈⠃⣄⠀⠀⠀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⢔⣤⣀⣀⣠⢀⠃⠀⠀⠀⠀⠀⣀⣀⠠⠤⠖⠊⠉⠉⠀⡍⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠲⡄⠀⢨⠀⠀⠀⠉⢉⠁⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡃⢘⠃⠘⢰⠉⢄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣤⡙⠨⠀⡘⠀⠣⡀⠉⠂⠀⠚⣧⢀⣀⠀⠀⠀⠀⣀⣀⠠⠤⠔⠒⠈⠁⠀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡑⢷⣈⣷⠧⣤⠀⠈⢲⠄⠤⠤⡛⢄⠀⠈⠉⠉⠁⠀⠀⠀⣀⡀⠤⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠒⢁⠜⢚⣶⠦⡀⢲⠒⢲⠊⠁⠀⠀⠡⠀⠉⠉⠀⠀⠘⡉⠉⠁⠀⠀⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⡇⡄⠀⢸⠈⡀⢸⠀⠀⠀⠀⠀⡤⣀⠀⠀⠀⣀⠙⠠⠤⠤⠄⠄⠒⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠸⢀⣸⠀⡇⢁⠀⢀⣠⠷⠊⢀⡠⠤⡄⠰⢄⡀⠉⠉⠁⣈⢱⠄⠀⠀⠀⠀⠒⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡌⢖⠉⠀⠀⢠⠃⠀⠀⠈⠂⠀⠀⠉⠉⠁⠀⠀⡄⠀⠀⠀⠀⠀⠄⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣑⣄⠀⢘⠄⡀⠀⠀⢀⠀⠀⢀⣀⠀⠤⢰⢆⠀⠀⠀⠀⠀⠀⠀⡾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠀⠈⠢⠄⣉⣉⣉⣉⣁⠠⠤⠤⠒⠚⡈⠄⣀⣀⣀⡠⠔⠊⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⡠⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠉⠁⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠒⠒⠀⠀⠀⠀⠠⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣀⣠⠤⠖⠒⠋⠉⠉⠉⠉⠒⠂⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢠⠞⠁⠀⠀⢀⠀⠀⠀⣠⠒⠉⠁⠈⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠰⣁⠄⠀⠀⠀⠀⠀⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠁⠀⠉⠀⠀⣀⠀⠀⠀⠀⠀⣭⡬⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣀⣀⠀⠡⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⣠⠖⠋⠉⠉⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠆⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠉⠂⢾⠁⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠿⣌⠀⠑⠀⠀⠀⠀⠀⢀⡠⠔⠀⣤⢤⡤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣤⠈⠃⠀⠀⠀⠄⠀⠀⠀⠀⣠⠾⣁⠒⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⢀⣀⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⢸⠹⡇⠘⠂⠀⠀⠀⠀⠀⠤⠴⠒⠋⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠈⠧⣼⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢺⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡄⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠁⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢠⠇⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠠⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣠⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⢀⡀⠀⠀⠀⢈⣀⡤⣀⠀⠁⠐⠒⠀⠀⠴⠚⠁⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠁⠀⠈⠳⢤⣀⣀⠀⠀⠀⢀⣀⣤⠖⠋
⣀⣀⣀⢀⡀⡀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀⣤⣤⡴⣶⣶⣤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠉⠉⠉⠉⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⠶⠤⣤⠀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠲⠄⣶⡄⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣭⣯⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠁⠴⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢬⡧⡄⠀⠀⠀⠀⢹⣿⣿⣿⣿⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⠴⢀⣭⣩⠛⢶⣤⠀⠀⠠⣆⣀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠙⣼⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠁⠨⢺⠋⠀⠀⠀⠋⠙⣭⡯⣤⣀⠨⣝⠲⠄⠀⠀⠸⣿⠂⢤⠄⢸⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁⠀⠀⠀⠀⣿⢳⣤⠀⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡄⠀⠀⠀⠀⣠⣈⣴⣀⣀⣀⣤⣀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣧⡐⢻⣿⣿⣿⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢆⡀⠐⣀⣀⠤⠞⠋⠉⠉⠉⠉⠙⠛⠻⢦⠾⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢹⡿⠟⠁⠈⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠳⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⡄⠀⠈⡆⠁⠐⠀⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠶⣿⣿⣿⣞⡒⣚⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠲⢦⠞⠋⢀⡀⠀⣿⣶⠒⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠠⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠈⠙⠛⠙⠉⠛⠙⡷⣶⣦⣀⣀⣀⠀⢁⣴⡾⠁⠀⢹⠇⡆⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢰⡏⢠⠇⠀⡠⠾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⠀⣟⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠈⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀
⠀⠀⠀⠀⠀⠀⠀⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⢶⣤⣅⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠈⣦⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⣠⣧⠃⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡾⠋⠀⠀⠀⢀⡰⡇⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠁⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢃⠸⠁⠀⠀⠀⡀⢸⠃⢣⠀⠐⠶⠌⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢰⡤⠾⡁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣴⡞⠀⡞⢀⠀⠙⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣠⠄⣴⢀⠀⢀⣼⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣼⠃⠐⠀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣥⠞⣿⡄⠠⢾⡏⠀⠀⠀⠀⠀⠀⢿⡀⠀⢠⡄⠀⠀⠀⠀⣴⠿⣤⣤⢠⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢠⣽⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢸⠃⠀⠀⠀⡼⠃⠀⢠⡔⠁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣠⡞⠀⠀⢀⣶⠀⠀⠀⠀⢦⡀⠀⠸⠀⠀⣠⠞⠳⠶⠖⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡼⠋⠀⣹⣇⡴⠖⠁⢿⡄⠀⠀⠀⠀⣀⠀⠀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠚⠋⠀⣠⡼⢣⡜⠀⠀⢀⣾⡿⢲⣤⣴⡞⢁⣴⠛⠀⢾
⠀⠀⠀⠀⠀⠀⣀⡀⠤⠔⠋⠁⠀⣸⠀⠀⠀⢠⠛⣇⣼⠁⢸⣧⡘⢳⣄⠀⣾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠇⠀⠀⡠⠋⠀⢻⡏⠀⠈⣿⠀⠀⠉⠀⢸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠘⠉⠀⠀⠀⠈⠁⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠒⠉⠉⠉⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠈⠙⣆⣠⡤⠖⠚⠉⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠀⠀⠰⣯⣭⣤⣤⣤⣤⣀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣠⡼⠁⠀⠀⢀⡬⠗⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⢀⡴⠛⠒⠒⠒⠋⠉⠉⠉⠉⠙⠒⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⢿⠹⡏⡶⡆⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠸⣏⠃⠀⡔⢱⣇⠀⢀⡞⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⣤⣸⠞⣇⡴⣆
⠀⠀⠀⠀⠀⠀⢀⣼⣧⣤⡄⣺⣾⣦⠟⣠⠶⡟⠉⠁⣽⠷⢛⡛⣏⠉⠁⠙⠳⢦⣄⠀⠀⠀⠀⠀⠈⠳⣼⠀⠿⠸⠏⢠⢇
⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠉⠉⢰⣽⠞⢁⣾⣧⡀⠀⢀⣀⣸⣛⣋⣀⡀⠀⢀⡀⣌⢻⢲⣄⠀⠀⢀⣤⣽⠀⢰⡆⠀⢟⣩
⠀⠀⠀⠀⠀⠀⣨⠷⢤⠤⠴⢚⡟⠁⠀⢸⡙⠟⠛⠚⠋⠁⣼⠋⠁⠀⠉⠳⣜⡛⠃⠀⢿⠉⠳⣄⡎⢸⡑⠦⠈⠁⠐⠋⣹
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢀⠎⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⣰⠏⠙⢳⡄⠈⠀⠀⡿⡇⠀⠉⠳⠤⣀⡴⢻⠁
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠈⠲⣄⣀⣀⣀⣀⣬⣿⡖⠚⠁⠀⠀⠀⢿⣀⣀⡰⠁⡟⢦⣀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠦⡤⢬⣷⣀⠀⠀⠀⠀⠀⣼⡿⣵⠀⢹⠀⠈⠉⠓⠒⣞⠁
⠀⠀⠀⠀⢸⡇⠀⢀⡴⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡗⣾⠁⠈⠳⠦⣤⣄⣀⣤⠶⠋⠀⢸⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠈⣧⡴⠋⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠈⠳⣄⠀⡿
⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠁⠀⠀⠙⣾⠁
⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠸⡆
⠀⢰⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡄⣀⣠⡤⢶⠖⠦⠤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⢠⡞⢧⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡜⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡆
⡏⢡⠈⠳⣄⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡇
⢇⠈⢳⡀⠈⠳⣄⠈⠙⠲⠦⢤⣤⣀⠀⠀⠀⠀⢸⠇⠀⢸⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⣀⡴⢻⡄
⢸⢧⠀⠙⢦⡀⠈⠙⠒⠤⢄⣀⡀⠈⠉⠉⠉⠉⢻⠟⠓⠛⠓⠛⠳⡖⠒⠢⠴⠤⠤⠤⠒⠒⠋⠁⠀⣀⠤⠚⠁⠀⣸⢷
⠈⡎⠳⣄⠀⠙⠲⢤⣀⠀⠀⠀⠉⠉⠒⠢⠤⣤⠼⠧⣄⣀⣀⣀⣠⣃⣀⣀⣀⣀⣀⡠⠤⠴⠖⠒⠉⠁⠀⠀⠀⣠⠏⢸
⠀⠘⢦⡈⠳⣄⡀⠀⠈⠙⠲⠤⣄⣀⣀⣀⣀⡿⠀⠀⣽⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⡇
⠀⠀⠀⠙⠦⣄⡙⠳⠦⣄⣀⠀⠀⠈⠁⠈⠉⠀⠀⢀⣜⠀⠀⠓⠶⠤⠤⢤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠚⠋⠀⠀⣠⠞
⠀⠀⠀⠀⠀⢸⠙⠳⢤⣀⡉⠉⠙⠛⠃⠐⠶⠒⠛⠉⠉⠓⠲⢦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢖⡿⠃
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠉⠙⡳⠶⠤⢤⣤⣀⣀⣀⣀⣀⡀⢀⣀⣀⣉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣥⠤⠖⠋
⢀⡴⠒⠒⠒⠚⢧⡄⣀⡀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢿⠉⠉⠉⠉⠉⠁⢀⡇
⡞⠀⠀⠀⠀⠀⠀⠃⠀⠈⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣸⣀⣀
⠘⢦⣀⡀⠀⠀⣀⣀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠙⠒⣶⠊⠉⠀⠈⠉⠳⣄
⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⣤⠷⣄⣀⣀⣀⣠⠴⠋
⣿⣿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣠⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠒⠚⠛⠉⠉⠉⠉⠉⠛⠒⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡴⠋⠀⠀⠀⢀⡤⠤⡤⠤⠤⠤⡖⠲⢄⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢧⣀⣀⡤⠖⢫⣠⠜⠡⠀⠀⢰⡙⠲⡚⠂⢰⠇⢠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡎⠰⣋⣀⡀⢐⣇⣰⡿⠇⠀⠿⣷⡦⣇⣀⣈⣄⡨⠇⢸
⠀⠀⠀⢀⡴⠒⠒⠊⠉⠒⡇⠀⣇⠀⠀⠀⠉⠉⠀⢻⡀⠀⠀⣀⠄⠀⠀⠀⠈⠀⠀⢀⠞
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⡇⠀⡸⢧⡀⠀⠀⠀⢀⣠⡼⠋⠉⣓⣤⣄⣀⣀⣠⠤⠖⣹⠀⠀⢀⣐⠄⠠⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠤⠴⠃⠀⢳⠄⠉⠛⠛⠉⠉⠱⣝⢿⡿⢟⠝⠀⠀⠀⠀⠀⠀⡟⠒⠂⠉⣰⡱⠚
⠀⠀⢧⠀⠀⠀⠀⠀⠑⠤⣄⣀⣨⣦⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⣠⠞⠁
⠀⠀⠀⠑⢦⡀⠀⡀⠀⠀⣠⣫⠋⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠠⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⣰⠃⠀⠀⠘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠃⢀⡴⠀⠀⠀⠈⠳⠤⠤⣄⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣰⠂⢧⡑⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡏⠉⠋⠁⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⠓⠙⠟⠉⠈⢧⠀⠀⠀⠀⠀⠀⠠⣀⠠⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⠔⠒⣛⣒⡲⣄⠀⣀⣀⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣶⣤⣤⣤⡇⢧⣤⣶⣶⡧⢸⣿⡿⠿⠟⠋⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣉⣉⠉⠉⠉⠙⠮⢭⣤⡤⠖⠁⠀⢀⣀⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣉⡩⠗⠒⠒⠚⠁⠙⠒⠛⠫⢍⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏

⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠲⣆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠤⠐⣮⡀⠇⢀⣠⣤⡶⢄⡲⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⡀⡎⠐⢠⣼⠉⡛⠋⠀⠀⠀⠘⠉⠛⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠁⠁⠁⠀⡈⠛⠛⢁⠀⠉⠉⠛⢶⡄⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠰⣿⣤⡀⠀⣀⣾⣇⣀⣀⣸⠀⠁⠒⠤⠈⠙⣄⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠟⠃⡄⡄⠀⡦⠘⠹⢷⠊⠉⡇⠻⢿⣿⣧⣄⡀⠀⠀⠀⠀⣸⠂⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣷⡀⠀⢣⢼⡅⠀⡀⢰⡀⠀⢻⠀⠀⢸⣿⣿⢹⣿⣶⡞⠋⠁⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡇⠀⠀⢸⠜⣀⣼⢷⠀⠁⠀⢸⠀⠀⡾⢿⣿⣿⣶⣭⣀⣠⣶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠘⠧⠈⣢⡼⠁⠜⠉⠀⠀⢆⣀⢤⣤⣤⣴⣾⣿⡿⣯⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠻⡿⣿⢿⢿⠟⠛⠉⠀⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡄⠀⣄⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣀⠀⠀⢀⣀⠀⠀⠠⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠈⠙⢿⣿⢠⠀⠀⠠⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠞⠘⠈⠃⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀⣾⠁⠀⠀⠈⣄⣠⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⠄⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣹⣿⡏⠀⠀⠀⠀⠀⡿⣏⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠙⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⣀⠤⠒⠉⠉⠉⠙⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠚⠉⠁⠀⠀⠀⠠⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣀⣀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡴⠖⠉⠘⠃⠈⠁⠀⠐⢇
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡤⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⣔⢀⣤⠋⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡤⠂⠠⡄⠀⠀⠹⡄
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⣾⠑⠉⠀⠀⠀⠀⠀⡠⠀⠀⠀⣣⡤⠔⠒⠠⣄⣈⠳⡋⠚⠃
⠀⠀⠀⢠⠻⡄⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣠⡠⠔⡛⢈⡀⠀⠀⢀⠄⠀⠌⣿⠃
⠀⠀⢠⠃⠀⠹⡄⠀⠀⠀⠀⡆⠀⠀⠀⢀⡠⠔⠉⠀⢁⠎⠀⠀⠈⡀⠀⠅⢀⠀⠀⡻⣄⣀⣀⡀
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠔⠉⡆⠀⠀⠀⠈⠐⢉⢢⠀⡇⢀⢺⣠⣔⢀⣧⣄⡀⠀⠈⠳⣰⡄
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⠀⠀⢠⣇⠀⠀⠀⣬⣴⣾⣷⣲⠦⣼⠾⠛⠛⢿⡀⠀⡵⠀⠀⠀⢹⠊⢏⠓⠦⣄
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠔⠉⠀⠀⠀⠀⠀⠀⢺⡀⠀⣠⠇⠀⠀⠀⠀⡟⠛⠑⠒⠤⠔⠉⠀⢸⠀⠀⠨⣦
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⡞⠀⠀⠀⠀⢀⡤⠒⠀⠀⠙⠯⠄⠀⣀⠀⣀⠼⠁⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠈⢧
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠘
⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠢⡑⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢳⠤⠀⢠⠤⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⢀⣄⣠⣤⡴⡊⢁⠹⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢣⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⢀⠀⢨⣁⡄⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠃
⠀⣼⠁⠀⠀⠈⠉⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⡜⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⣇⠀⠀⠀⠀⠀⠀⠀⢸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠘⢦⠀⠀⠀⢀⣀⡠⠛⠀⠑⢄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠉⠉⠁⠈⠀⠀⠀⠀⠀⠈⠉⠚⢆⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠺⠛⠓⢄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⢄⣀⣀⣀⠀⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⠤⠤⠤⠤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠨⠭⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣠⡤⣤⣀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡟⠀⠀⠀⠀⠀⣀⡴⠚⠉⢹⡟⠉⠉⠉⠉⣹⣄⡀⢈⣧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⣷⣀⣄⣀⡴⠚⠉⠳⣤⠴⠋⡒⡄⠀⠀⢰⣏⠈⠛⣏⠁⠁⢀⡟⠀⢠⡖⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢠⠟⠡⡞⣋⡀⠀⠀⠀⡇⠀⣤⣿⣧⣤⣄⣸⣿⣷⣆⣸⠀⠀⠈⢣⡀⣈⡽⠃⢸⡆
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⢤⣀⣿⠀⢸⠀⠀⠉⠉⠉⠳⠶⠖⠛⠛⡟⠁⠀⠀⠀⠀⠈⡋⠉⠉⠛⠉⠑⠋⠉⠉⠀⠀⣸⠁
⠀⠀⠀⠀⢀⣴⠋⠁⠀⠉⠀⠀⠀⠈⣿⠀⠘⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠁
⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣴⢻⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠛⠒⠚⣳⣤⣄⣀⣀⣀⣀⣤⠴⠞⢉⡿⠀⠀⠀⠀⣞⠢⠒⠲⡄
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡇⠀⠀⣧⡀⠙⠳⠶⠶⠶⠖⠛⠉⢧⡻⣿⣿⣿⣿⠟⡼⠁⠉⠉⠉⠀⠀⠀⠀⢸⡧⠴⠶⠶⠋⢬⠱⣄⠴⠃
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢬⡉⠈⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠟⢭⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣠⠾⠖⠁
⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⣤⣤⣤⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⣱⠏⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡾⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠈⠓⠲⠖⠲⠤⠴⠶⠋⣴⠃⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠏⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣼⠁⠀⢀⡼⠁⠀⠀⠀⠀⠈⠓⠶⠤⠴⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢾⠀⢧⣀⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢶⡖⠛⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⣀⣨⣗⢦⣭⠼⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠉⠆⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠋⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠤⠋⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠓⠒⠦⣄⠀⠀⠀⠀⢀⣠⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣀⣀⡀⠀⠀⢀⡞⢱⡊⢉⣉⣉⣉⣷⠈⢳⣶⣾⣿⣿⣿⣿⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣇⠈⢿⡿⠿⠿⠿⠟⢀⡾⠿⠛⠛⠉⠁⠀⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣄⣀⡀⠀⠀⠈⠀⠉⠳⠤⣤⣤⣤⠴⠚⠉⠀⠀⠀⣀⣠⡤⠶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⠛⠓⣲⣶⠶⠤⠤⠴⠃⠈⠷⠴⠶⠶⣟⡋⠉⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣶⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠧

⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠠⢔⣂⣁⣀⣒⢢⣄
⠀⠀⣿⣿⣤⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣃⡍⠁⠈⠁⠰⢯⣦⡀
⠀⠘⠩⣽⣿⣥⠶⠛⣃⣤⠤⠀⠀⠀⠀⢀⡼⠣⣠⡞⠋⠉⠐⢾⣿⣿⡄⠀⠀⠀⣴⣦⡄⡄
⠀⠐⠶⢛⣫⡶⢲⣿⣋⣤⡄⠀⠀⠀⠀⣾⠇⣴⢯⣠⣤⠀⣤⣤⣿⣿⡟⠀⢐⡆⢿⣿⣷⠃
⠀⠀⠀⠙⠿⣿⣿⣿⣉⣧⣤⠿⠛⠋⢀⡿⢰⣧⡀⠉⠉⠀⣯⠉⢸⣿⠁⠀⠸⠇⠸⠋⠤⣤
⠀⠀⣀⣰⣷⣿⣟⣻⣿⣿⣤⣴⠖⠂⢹⣷⣾⣿⣻⠚⣉⣭⣉⠑⢿⡇⠀⠀⣿⠀⣆⠐⠀⣴⡆
⠀⠛⠿⠋⠉⢹⣿⣿⡿⣿⡋⣷⣤⣤⣀⠻⠿⢻⡏⠐⠋⠌⠈⠳⣤⣴⣶⣴⡏⢘⠿⠤⠠⢉⣠⡀
⠀⠀⠀⣀⣴⡟⢻⣿⣷⣾⣿⣿⣿⣿⢥⣴⣿⠆⠀⠁⠚⠀⠠⠀⣈⣿⠉⠀⢎⢙⡄⠀⠀⣏⠀⡴
⠀⠐⠺⠋⠀⢰⣿⣿⠋⠭⣿⣿⣿⠏⣾⣿⣷⡀⠀⠁⠐⠈⠀⠈⢀⣿⡷⠶⢷⠿⠟⡀⠀⢀⡰⣷
⠀⠀⠀⠶⠴⠟⠛⢿⣷⣶⣿⣿⣛⣾⡅⢈⣿⣏⡁⠀⣤⠂⡈⠀⠈⣿⡧⢀⡀⠄⢆⡀⠀⠀⠙⠀⢲⡄
⠀⠀⠀⣀⣶⣆⢛⣾⣧⣿⣿⣿⣿⡏⠈⠉⠙⢛⠓⠶⣜⣠⣤⡄⢠⣟⣰⣄⠀⠀⢼⣿⡇⢠⣄⠴⡿⣿⣦
⠀⠀⠀⠑⠛⢻⣿⣿⠋⡈⠡⡨⠙⣀⣄⣀⣲⡏⠈⠄⢸⡟⣡⣜⠉⠻⣿⣿⣿⠖⠿⡟⢀⣿⣿⡈⢷⣩⣷
⠀⠀⢀⡞⠁⣠⠟⠁⢹⠲⣄⡀⣰⠏⣿⣽⣿⣯⡇⠀⣻⣫⣿⡿⠎⢸⠏⣿⣁⢻⣿⣿⣿⣿⣿⡥⢸⣧⣿
⠀⠀⢸⡇⠀⣿⡟⡃⠀⠒⣈⠻⢿⣾⣯⠿⢌⠉⣼⣿⣿⣿⣿⣗⠲⠚⠛⠫⠍⢀⢉⣟⣿⣿⣿⣿⣸⣿⡟
⠀⠀⠈⣇⢰⣿⣿⣿⣿⣿⠆⠒⠶⠈⣿⣿⣾⠟⠿⠛⣩⠆⠛⠧⢲⠀⠈⠀⡆⠀⠀⠀⠛⢸⡏⢿⠽⠋
⠀⠀⠀⠘⣼⣿⣿⣽⣿⠃⢾⡎⠀⢐⡢⣴⡟⢿⣶⠻⠫⡷⠖⣶⠨⠆⠀⡀⠀⠀⠀⢠⠁⡀⠃⡶
⠀⠀⠀⠀⢸⠹⣿⣿⣯⣄⣿⣷⣤⣄⣼⢻⣿⣦⡙⣧⡀⢠⣴⣄⠨⣶⠀⢉⠀⢠⡯⢰⣒⣠⠈⠃
⠀⠀⠀⠀⠞⣡⣿⣿⢿⣿⣿⣿⡏⣸⣿⠈⢿⣿⣿⣌⠳⡌⢩⡽⠁⣿⠃⢾⠶⣠⡴⠘⠉⠀⣄⠀⢰⣾⣆
⠀⠀⠀⢠⠀⢻⡿⣿⡎⢯⡾⠉⠀⢹⣿⠀⢸⣿⣏⠹⣷⡉⢶⣭⣀⣇⣀⣈⣰⡋⣰⡇⢠⡀⠈⠄⣹⣟⣽
⠀⠀⠀⠀⣦⣾⣿⣤⣤⡶⠀⠀⠀⢸⣿⠀⠘⣿⣿⣷⡈⢷⠘⣷⣯⣭⣏⣽⣩⡍⠉⠛⣼⠁⠉⡚⣳⠞⠁
⠀⠀⠀⣠⡿⣳⡄⢸⡕⢏⣲⡀⢰⣿⣿⠇⠀⣿⣿⣿⣿⣦⠀⢿⡿⢟⣹⣿⣾⢁⣤⣦⣾⠂⣽⠈⡇
⠀⠀⠀⣿⣿⣿⣿⣾⠿⠿⣿⣿⢶⣟⣛⠧⠀⢸⣿⣿⡿⣿⣿⣦⣿⣿⠻⢛⣅⠿⢷⣿⡿⣢⣛⠄⣴
⠀⠀⠀⣿⣿⣱⣟⣶⣷⣼⢯⡿⣿⣿⣿⡏⠙⢺⣿⣿⢿⣾⢿⣽⣷⡀⣼⡿⣏⡿⢶⡌⢴⠃⠉⢢⣷
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠛⡽⢟⣿⣿⠇⣤⣾⣿⡈⠁⡻⣧⣿⣭⣼⣏⣻⣿⣼⣿⠟⢛⣿⣄
⠀⠀⠀⠈⢿⣿⣿⣿⢟⣇⣜⡷⣻⣷⣿⣧⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⡟⣿⣿⡂⣿⡽⠉⣿⡄
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣉⣤⣛⣽⣿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠹⣿⠏⣿⡟⣼⣿⣿⣿⣧⣠⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡙⢉⠿⡼⣁⣙⣿⣿⣧⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢱⡿⣿⣿⣿⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣤⣉⣛⡛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⢸⡟⢻⣿⡟⠀⡄⠻⣿⣿⢿⠟⢻⣿⣿⣿⣿⣿⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣾⣿⡇⢀⡴⣆⢿⣟⠀⣫⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠀⠀⣨⡿⣿⠀⠸⣿⣿⣿⣿⣟⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣿⣿⣿⣿⣿⣦⣭⣿⠋⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢢⣴⣾⣿⣿⡿⠟⢉⣿⢟⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢚⠃⠈⠻⣿⣧⣴⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠿⠿⠟⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠛⠛⠉⠉⠉⠉⠛⠛⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⢀⡴⠋⠁⣀⣀⣤⡤⠴⠶⠶⠶⠶⠤⣤⣭⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣴⣿⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠶⠶⠶⣶⣭⣭⣙⡲⠦⣄⣀⡇⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡆⠀⠀⢀⣠⠶⠛⢋⣡⣤⣠⣄⡀⠀⠀⠀⣠⣤⣠⣍⡙⠻⢦⣭⣁⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡇⣷⡶⡋⠁⠀⠀⠤⣤⣤⣌⣀⡿⠀⠀⠻⣁⣁⣄⣤⠤⠀⠀⠈⠻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣼⢁⠛⡼⠇⠀⣀⣤⡚⣿⣿⠀⠀⡆⠀⠀⢰⠀⠀⢿⣿⠛⣦⣀⠀⠀⠑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣰⢃⣾⠀⠀⠀⡀⠀⠀⠤⠤⠥⠉⠀⠁⠀⠀⠀⠀⠈⠤⠔⠤⠄⠀⢀⠀⠀⢼⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⣦⡀⠐⢁⡼⣫⡆⠀⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠘⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠘⢷⣄⡾⠀⡽⠃⠀⠻⡆⠀⠀⠀⠀⠀⣀⡦⠶⠄⠀⠴⢤⣀⡀⠀⠀⠀⠀⢰⠿⠁⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⠀⠀⠀⣸⣏⠀⡼⠁⠀⠀⠀⢻⣆⡀⠀⣰⠏⠁⠀⣀⣤⣦⣀⠀⠀⠙⢦⠀⢀⣰⡞⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣴⣄⣠⣤⣴⣿⠏⢸⣷⣂⡀⠀⠀⠈⠙⢃⣼⣟⣀⡤⠊⡙⠛⠛⠛⠙⢦⣀⣸⣧⡈⠋⠁⠀⠀⠀⣀⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠟⠛⠋⠀⠈⢻⣿⠀⠀⠀⠀⠀⠛⠋⠉⠉⠀⠀⠉⠛⠛⠋⠁⠀⠉⠉⠉⠛⠂⠀⠀⠀⠀⢻⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠞⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣇⢰⣷⣾⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡞⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠒⠚⠉⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠋⠉⠁⣀⣤⣶⠿⠛⠶⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⢠⠂⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠉⡢⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⠃⣴⣿⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢤⣿⣿⣿⣆⣁⣀⣀⡀⠀⠀⠀⢀⣀⡀⠁⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⣾⣿⣿⣿⡭⠉⠉⠛⠛⠛⠛⠋⠉⠛⠛⠒⠒⠲⢶⣘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⢀⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⠌⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅⢸⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣾⣃⣦⡴⠞⡋⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢦⡀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢈⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⠿⣿⣄⣼⣾⣿⡿⢿⢟⠻⠳⣦⣤⣴⣶⣶⣤⣶⣤⣄⠳⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢸⣿⣿⠿⡫⣛⣉⣉⣁⡘⠋⣷⢰⡆⠀⡾⢤⣍⣉⣛⠻⣟⠓⢀⣆⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢨⠁⣼⣿⠏⣜⡼⠛⠉⠉⠉⢿⣿⡅⠸⠿⠈⢶⣤⡤⠶⠿⣿⣾⣦⣸⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣿⣿⣾⣟⠄⠄⣠⠒⠒⠺⠻⡟⠀⠀⠀⣾⠀⠄⠀⢤⢬⣏⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⠋⣠⣤⣾⣿⣿⣶⡤⣿⣇⠀⠀⢸⡿⣷⢾⣻⡿⠾⣿⣟⠉⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢰⡟⣿⡿⠛⠛⠉⠁⠠⠛⢧⣀⢀⡟⢄⠀⠈⠳⣦⡜⠁⠀⠀⠀⢹⣷⣸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⡀⠆⢠⡿⢛⡏⣾⠀⠀⠀⠀⠀⠀⠀⡈⣻⡷⠉⠑⡀⠀⠘⢷⣦⡀⣀⣀⣼⣿⡍⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢂⠘⣠⣿⡶⢸⣷⣿⣷⣤⣴⣶⡶⣶⣿⣿⣏⣀⣀⡠⡆⠀⠀⠀⣿⣉⣭⡏⠉⣿⠇⢰⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⠰⠈⣰⠏⢸⡇⠚⢿⣿⣿⡋⠈⣿⡾⠟⠉⠉⠿⠿⣿⣿⣀⣶⣂⣴⣿⠟⠉⠿⡾⠁⠀⢰⢎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢄⠂⢀⣼⡏⣴⣽⣷⡀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⣦⠉⠋⣌⠁⠀⠀⠀⣠⣾⡷⠃⡀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣐⠄⢠⡾⣿⣴⡟⠁⡈⢻⣿⣷⣾⣦⡀⢀⠠⢤⣄⡛⠓⠤⣂⣠⣿⣶⠶⣿⣿⣷⣾⣿⡛⠿⣮⡻⡻⣿⡇
⠀⠀⠀⠀⢰⣖⠒⠶⢤⣀⡟⣀⣤⠤⣴⡏⠀⣿⡟⠀⠚⢰⡿⠛⣿⣿⡿⠿⣿⣾⣿⣿⣯⣿⣛⣛⣋⣁⣤⣤⣿⣿⠿⣻⣄⢩⠀⠘⣷⠈⠘⣷
⠀⠘⢻⠿⠏⠉⠀⠀⠀⠈⠉⠁⠀⠀⠙⢦⡀⣹⠃⠀⠀⣸⣷⠟⣱⠏⢠⠾⠋⣸⠟⣿⣏⠻⠿⣿⣿⣿⡿⢿⣿⡿⢧⡁⢻⡀⠃⠀⢸⠤⣢⢸⡇
⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡱⣿⠀⣆⣤⡟⠉⡴⠏⠀⢀⡶⠸⡁⢼⢿⣿⣷⣶⣤⣦⣤⣾⡿⠛⠀⠀⢱⢸⡇⢂⠘⣯⢇⠻⡆⢿⡀
⣸⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣪⠞⠝⠁⡄⠃⠇⠀⣼⠁⠀⡇⢸⠀⠀⠋⠙⠉⠉⠉⠀⠀⠀⠀⠐⡀⡆⣇⢾⠀⠱⡘⠃⠘⠈⢷⡀
⣿⡏⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣿⡟⠀⠀⠠⠁⡠⠀⠀⣿⡆⠀⠁⠘⣰⠀⠀⠀⠀⠀⠀⠀⠀⡄⢱⢀⣷⡇⣿⠈⠀⠀⠑⠄⠀⠀⠀⠑
⢸⡇⣶⣶⣦⡑⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠁⠀⣀⣴⠞⡐⠀⠀⣿⠇⠀⡀⣄⠻⡆⢄⠳⠀⠐⡀⡄⡜⢡⡻⣾⠷⠀⡼⡆⠀⠀⠀⠀⠀⠀⠀⢰
⠀⢧⡈⠹⣿⠻⣦⣍⡓⠀⠀⠀⠀⠀⢠⣎⡽⢇⣀⣸⣿⠏⢘⡀⠀⢠⠏⠀⠀⡳⣜⠓⢹⣦⡹⣦⣰⡜⣷⡰⠟⣱⠏⠀⠀⠘⣱⠄⠀⠀⠀⠀⠀⢀⡞
⠀⠈⠳⣄⠈⠁⠈⠉⢻⣳⣤⠤⢊⡴⠛⠋⠀⠀⠀⢠⣏⣠⠟⠀⠐⡫⢂⢀⡀⠘⣟⢦⡀⠙⠻⣎⢻⢿⡝⠸⢰⡏⢠⠂⠀⠀⠈⠳⠄⠀⠀⠙⢶⡞
⠀⠀⠀⠈⠓⠤⡷⢦⣤⣰⣖⠛⠉⠀⠀⠀⠀⠀⠀⠈⠸⡁⠀⠀⠀⠐⣡⠸⢁⠀⠌⢧⡙⢶⣆⠘⣿⠀⠀⠀⢿⠁⠆⠀⠀⠀⢢⠀⣀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢡⡾⠀⠈⡄⠙⢄⠻⣆⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠁⣨⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣠⡟⠀⠀⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠀⠁⠇⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠶⢤⣤⣤⣀⣦⣄⡀⠣⠀⠀⡄⣰⡤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢓⡛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠛⠛⢿⣦⡈⢻⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⠟⠚⠓⠐⠒⠲⠿⢷⡄⠙⠛⠙⢿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣿⠀⠀⠀⠀⠈⠹⣍⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠘⠏⢙⣷⣼⣇⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⢀⡀⠠⠀⠀⠰⠟⠅⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣶⣶⡤⠶⡶⣻⣷⣶⣶⣶⣄⣀⣸⣷⡀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣭⢯⣦⡀⠀⢹⡿⠶⣶⣭⡼⠉⢿⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠷⣿⠛⢿⠀⠀⣈⠉⠁⠀⠀⣀⣼⣽⡇⠀⠀⠀⠀⠀⣼⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡀⢠⣎⡀⠁⠨⠳⢶⣦⠰⠛⣷⣿⡇⠀⣀⣰⠁⣼⠏⢩⡄⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠿⠷⣿⠟⣩⣤⣄⣀⣀⣤⣤⡾⠋⣹⠀⢀⠾⣡⡼⠋⠀⠈⢃⢸⣿⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣷⣴⣷⣿⣯⣙⣉⣤⡿⠛⣋⠶⠒⠛⠦⢺⣾⠳⣤⠾⣏⠝⠉⠁⠲⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⢿⠋⣿⡏⢹⠻⢹⠛⠁⣴⠏⠀⠀⠀⠀⠈⢻⣷⡷⢋⡤⠄⠒⠒⠐⠀⠈⠙⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢇⠀⠞⠙⣧⢀⠄⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠸⢫⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠿⣿⠀⡀⠀⠉⢁⡞⠁⠀⠸⣿⣦⣤⣀⣀⣠⣴⣿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡖⢹⣧⡇⡀⠈⠉⠀⠀⠀⠀⠈⣻⣿⣿⣿⠏⢻⣿⠁⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡀⣨⢿⠇⣧⡀⠀⠀⠀⠀⠀⠈⠈⠁⠃⠁⠀⣿⡏⠀⣰⣿⠏⠀⠀⣠⠈⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣼⡿⣿⣦⣤⣼⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣸⣿⠋⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⢀⡔⠒⠀⠐⠛⠛⠒⠚⠻⠟⣧⣤⣹⡀⠀⠀⠀⠀⠀⢢⣀⣠⡄⢸⣿⡇⣿⢃⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠸⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⡄⣐⣃⡀⠀⠐⠉⠉⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣸
⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠛⠉⠉⠙⠉⠓⠓⠒⠾⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠀⠘⣹⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣤⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣉⣼⣟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⣀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⢷⣿⢃⡿⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⢿⣾⣇⠸⣇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠸⣿⡌⠂⣿⡄⣧⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⡜⢿⣄⡘⢷⣽⡿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣴⣤⡒⠀⠀⠀⠀⠘⣿⣿⣷⣄⡙⢿⣎⠻⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢷⣶⣶⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠀⠈⠉⠛⠛⠛⠿⢿⣿⣿⣶⣤⣤⣤⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣷⣶⣶⣦⣄⠀⣀⣀⣠⣤⣀⣤⠀⣤⣤⡀⠀⢰⣶⣶⠾⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣌⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⠟⠛⠿⠷⠲⠿⡿⢿⡀⢀⡀⠀⢸⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠁⢿⣿⣯
⠀⠀⠀⠀⠀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣿⣯⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢷⡤⣭⢽⠟⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣋⣉⡉
⠀⠀⠀⢀⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡐⠐⡆⢺⣯⣯⣿⡿⡿⡿⢿⣿⠟⠋⠸⠇⠸⡷
⠀⢠⡴⣋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠃⠀⠀⢿⣿⣿⠏⠁⠀⢡⣼⣿⡓⢂⣀
⠀⣀⠀⣉⣿⣟⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⡟⠛⣟⠻⢿⣦⣄⣴⠞⣿⡟⢶⡀⠀⠈⢼⠏⠉⠙⠳⢦⡈⠂
⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣧⡄⠙⠈⠋⠂⢁⣡⡟⣁⡀⠀⠀⠀⠀⠈⢿⣷⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣴⣿⣿⠉⠀⠉⠀⣦⣐⣶⣯⠷⠈⠁
⣿⣿⣿⣿⣿⣯⣩⣿⣿⣿⣿⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⢀⡶⣿⡽⠏⠙⢀⠐
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⠋⠀⢀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⣀⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⠿⣿⣿⣿⣿⣿⣷⣬⣿⣏⡁⠄⢀⣆⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⣻⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡟⢛⣟⣋⡟⠛⠋⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣶⣦⡉⠉⢀⣁⢀⡀⠀⠀⠐⠠⠀⠀⠚⢾⣿⡦
⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣽⣶⣿⣩⣷⠀⠰⠆⠀⠀⡄⢠⣿⡿⠋⠻⠟⠛⠿⣿⣿⣿⣷⣿⣿⣿⣿⡶⣶⣄⣀⢉⣀⣀⣾⣿⠙⠲⠆
⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣭⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣶⡾⠛⠁⠀⠀⢠⡈⣦⡈⢻⣟⠛⠛⠁⠀⠀⠀⠀⠀⠠⠿⠿⡟⠋
⠀⠀⠀⠀⠀⠀⠈⢉⡿⠙⣛⣿⣿⣿⣿⣿⣻⣿⣻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠐⢸⡁⠈⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉⢡⣿⣿⣿⣿⣿⣿⡍⠀⢨⣾⠉⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⣸⣿⣿⣿⣿⢿⣟⣻⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣿⣿⣿⣿⡟⢃⢹⡿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠛⠛⠛⠉⠀⣼⣿⡷⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠆⠀⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣡⣶⣤⡿⠱⠀⠀⠀⠀⠀⠀⠀⢀⠀⣹⠀⠀⢀⠀⢄⡀⠀⠀⠀⢀⣾⣁⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣶⣤⣀⣤⣐⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠚⢶⣿⣿⡿⠛⠓⠖⠀⢀⠼⣃⠉⠀⠰⠂⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡯⠉⣉⠿⠀⠀⠆⣠⠞⡆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠈⠛⢻⣿⣿⡿⡿⠇⠲⠀⠀⠀⠀⠀⠀⠀⠈⢩⡴⠂⠀⠙⠂⠒⠛⠁⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢺⢿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠰⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠄⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⣀⠤⠀⠐⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠲⣶⡆⠀⣠⢴⣶⣶⣄⣴⠖⠒⠢⣄⡠⠒⠉⠀⠀⣠⣴⠖⢢⣀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣾⢟⠔⠋⠀⣴⣿⡟⠙⠷⠦⠖⠚⠁⠑⢄⠀⢠⣾⡟⢁⡰⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢠⣿⡟⠁⠀⣠⣾⡿⢋⣴⡾⠛⠆⢀⣠⣬⡔⠂⢱⣿⠿⠒⠉⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠺⠆⠀⣾⠀⡶⢠⣿⠏⠀⢀⣼⠟⠉⣴⣿⠻⠋⣹⣰⣿⠋⣠⠆⢠⣿⡏⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⣾⠇⠀⢠⡾⠃⠀⢰⣿⠇⢀⡴⢱⣿⠓⢋⡁⠀⣸⣿⠀⢀⡤⣲⠆⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⢤⠀⢰⡏⠀⠀⡾⠁⠀⠀⠈⠻⠖⠉⠀⢸⣿⠀⠘⡘⠀⣿⡇⢀⠎⢠⠃⠀⣀⣀⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠠⠞⠁⢸⠁⠀⢸⡇⠀⣀⡤⠶⢶⣤⠀⠀⠈⠛⠒⠊⠀⠀⠘⠷⠊⢀⠼⡆⠉⠀⠀⢉⣷
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠞⠁⠀⠀⣸⠟⡠⠤⡀⠀⠠⠆⠀⠀⢀⡠⠊⠀⠀⠈⠐⠂⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠛⠀⠀⢀⡠⠞⠙⠒⠒⠒⠋⠁⢸⠀⠘⠁⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠚⠉⠀⠀⠀⠀⢀⣠⡀⠀⠀⠑⠢⠤⠖⠊⠁⠀⠀⢠⡄⠀⠀⠀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢫⢊⣕⠌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣑⣩⡦⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣾⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢿⣿⣿⡿⣿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⠁⠐⠒⠲⠀⠀⠀⠉⠈⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠿⠾⢁⣦⣤⣼⣤⠷⠤⣤⡀⠀⠀⠀⠀⢿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣴⡿⢻⣿⠴⠟⣧⡀⠀⢀⣉⢻⣦⣄⣲⣿⡏⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣶⣶⣤⣄⠈⠛⢹⣿⠇⢀⡾⠉⠛⠛⠻⠃⣰⣿⣍⣁⢸⣿⣿⣀⣁⣤⣶⣿⣿⣷⣆⣀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣸⠃⠀⠸⣇⣤⣠⡴⢦⣤⣨⠁⠉⠀⢨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢉⣿⠁⠙⠟⢻⣿⣿⣿⣿⣿⠁⢾⣶⠶⣾⣿⣷⣦⣾⣧⣥⣽⠲⠶⣿⠛⣿⣿⣿⠋⠀⡐⢻⣿⣿⣿⣿⣿⡁
⠀⠀⢀⣀⠀⠀⢿⣿⠆⠀⠐⠄⠈⣽⣿⣿⣿⣦⣬⣥⣴⣾⢭⡶⣷⣭⣭⡽⢿⠳⢈⡙⠺⣿⣿⣯⠶⠂⠈⠉⠻⣿⣿⣿⣿⡿⠀⠀⡀
⠀⠀⡿⣩⣷⣄⠀⠉⠀⠒⠀⠀⠀⣠⡼⠛⢉⣽⣿⢻⠻⣇⡘⠋⠁⠈⣷⠀⠸⢦⡿⢇⣴⣿⣿⣷⡀⠴⠵⠆⢀⣿⣿⣿⣿⣿⣶⠚⢟⠂
⠀⠀⡀⣘⣷⣿⠿⠖⠻⣤⣤⣤⣾⠋⠀⣴⠟⠉⣿⣟⠀⠞⠁⢶⠄⢀⡿⠇⠘⢈⠁⣄⣿⣿⡛⠻⠿⣦⣤⡶⠟⠉⠀⣀⣡⣼⣿⣣⠘⢻⡇
⠀⠀⠈⠉⠉⠙⢀⠀⠀⠀⠈⠙⠛⢳⡾⠋⠀⣸⣿⣯⠄⣤⣠⡜⢂⠘⠳⡄⠀⣼⣺⣿⣿⣿⣁⢢⣠⣿⣏⢀⣤⣤⠞⠛⣿⣇⣈⣉⣷⡎
⠀⠀⠀⠀⠀⠰⠞⣻⣇⠠⢤⢠⣀⣀⡀⣀⣼⣿⢻⣿⣦⠙⡋⣀⢸⡄⠛⣷⢄⣸⡛⠿⠿⠛⠋⠛⠉⠁⣤⢉⣉⡇⢸⣶⠀⣉⣿⡿⣿⣷
⠀⠀⠰⠀⠀⠀⠀⢉⣽⠿⠿⠷⠟⢻⣿⠿⣿⣿⠆⢿⣿⣿⣷⣟⣛⣿⣤⣧⡿⠋⣡⡶⠶⠶⣦⣠⡶⣿⡿⣦⡙⠃⢸⣿⢿⣿⣾⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠂⢀⡿⠀⠀⠀⠚⢛⠛⠁⠒⡉⠿⠓⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡀⠀⢉⠿⠉⠇⠈⣿⡌⡛⣶⣿⣿⣀⡿⣷⡿⢩⡷⡇
⠀⠀⠀⢀⠀⣄⠸⣧⠀⠀⠀⠀⢙⣛⣻⣿⣄⣀⣠⣸⣿⣿⣿⣤⠉⠿⠟⠻⢿⣿⠿⣷⠶⠈⢀⡶⢃⠀⣿⣿⣴⡘⣿⣻⣿⠷⠈⠛⢿⣁⠃
⠀⠀⡀⠀⡠⠾⡇⢹⡷⢶⣦⣤⣼⣿⠋⠀⠈⠛⠉⣹⣿⣿⣿⡄⣶⣾⣯⡿⠿⠧⠈⠀⠀⠀⠁⢀⡏⢠⡿⢿⣏⠣⠘⠛⢻⡏⣤⠀⢸⣿⢀
⠀⢠⣬⣯⣥⣤⣴⣾⠁⠀⠉⠉⣹⣿⠀⠀⠀⠀⣺⡿⠛⢛⣿⣿⣧⣾⣏⣷⣶⣤⣔⠺⡟⢲⡖⠉⣿⣧⣴⡶⠛⢛⣾⠟⠈⠿⣿⣿⣾⣿⣿
⠀⠈⢿⣿⣿⣿⣿⣷⣶⣦⣴⣹⣿⣿⠃⠀⠀⠰⣿⠃⣿⣿⢫⣿⠟⢁⣼⣿⣿⣿⣟⣿⣧⣉⣿⠛⠿⠟⠋⣠⣾⣋⣥⣶⡷⢦⣼⣿⣿⣿⣿
⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡯⢿⣿⣿⣷⣷⠲⣿⣿⣤⣿⣿⢸⣿⣄⡹⠟⢋⣿⣿⣿⣿⣿⣿⣿⣧⣤⣷⣾⠻⣿⣿⣿⣤⣴⢶⣿⡿⢿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⣽⡇⣿⠆⣼⣿⣿⣿⣿⠁⣼⣿⣿⣾⣷⣿⣿⣿⠷⣄⠈⠉⠛⠻⣿⣿⣿⠿⢿⣯⣽⣸⣿⡟⣿⣷⣮⡹⣷⣜⠇
⠀⠀⠀⠀⠀⢀⣀⣿⠀⡟⢰⣿⣿⣿⡿⢿⣧⢰⣿⣿⣿⣧⣌⡉⠶⠙⠿⣿⣾⣷⣶⣤⣌⠁⡐⠻⣿⣟⡴⠟⠀⣿⠿⣟⣛⣶⠟
⠀⠀⠀⠀⢸⣿⣿⣦⣀⠉⢾⣿⣿⣿⣧⡄⢹⡾⠻⢿⣿⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡶⣤⣀⠰⠆⠉⠛⠋
⠀⠀⠀⠀⠀⠉⠹⣿⣿⣿⣾⣿⣿⣿⣿⣶⣾⠃⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣭⣴⣶⣿⣿⣿⡧⠘⠀⢹⣧
⠀⠀⠀⠀⠀⣠⡶⠿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣏⣿⣟⣯⣿⣿⣿⣿⣿⠿⠂⢘⣠⣾⠿⢿⣧⣶
⠀⠀⠀⠀⡸⠃⠐⠀⠐⠈⠉⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣟⣿⣿⡿⠿⠛⠋⠉⠛⠀⠀⠀⠈⠙⣷⡄
⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡏⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣿⡇
⠀⠀⠀⠀⢸⡖⠁⠀⠀⠀⠀⡀⢷⠀⠀⠀⠀⢼⠃⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⣿⠟
⠀⠀⠀⠀⠈⢿⣤⢀⡀⠀⠀⠈⢀⠁⢀⡀⠀⢸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠓⠶⠲⣶⣦⣤⣤⣤⣀⠈⣷⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⢀⣀⣠⡔⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⠟⠳⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠙⠛⠿⠿⠿⠋⠉⣿⣿⡷⠀⠘⣿⣏⠙⠿⠿⠿⠿⠛⠁⠀⢈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⡀⠀⠀⢀⣤⠔⠀⣉⣿⠇⠀⠀⠻⣿⣴⣀⣀⡀⢀⣀⣠⣴⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣶⣶⣦⣶⣾⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠦⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⢀⣴⣿⣭⣹⣯⣿⣿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠒⠀⠀⠐⠂⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢠⠾⠐⠢⣀⣀⠀⠀⠀⠀⠀⠀⠱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣀⣀⠀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡆⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣤⠓⠒⢑⠞⠀⠘⠂⠤⡄⢄⡀⠀⠆⠀⢦⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣹⠸⠒⠒⠓⠀⠙⢦⢀⠀⠀⠀⠀⠀⣰⠀⠀⠈⠮⡀⣲⠦⢄⠀⣀⠈⠢⡜⠀⠡⡀⠀⢠⡀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢤⡉⠀⠀⠠⠚⠉⠀⠉⠢⡀⢠⠎⠈⢦⡀⠀⠀⠀⠙⠂⠄⠬⣛⠀⢠⣙⣀⣀⣅⢼⠡⡉⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠴⠁⠀⢀⡔⠉⠑⢣⡇⠀⠀⠀⠈⠉⠀⠀⠛⠳⡀⠀⠀⠈⠀⠀⢀⡴⠁⠘⡀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡞⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢥⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠘⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⣀⡀⠀⠀⠀⠀⠉⠐⠤⠀⠤⠤⠤⠤⠚⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠘⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⡆⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢹⠀⠀⠀⠈⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢍⡉⠑⢤⠚⠐⢇⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡳⠤⠤⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⣉⠀⠸⡀⠀⠀⠙⠢⢀⡠⠰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢇⠋⠉⠁⠐⠄⢹⠀⠀⠀⠉⠉⠉⠁⠀⠘⠥⠤⠤⡀⠘⢄⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢇⢄⣀⠀⠀⡠⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⠁⠈⠙⠓⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡀⠀⠨⠀⠀⠉⠘⠋⠏⠁⠛⠒⠒⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡄⠱⢀⠞⣄⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠙⢇⠀⠀⢠⠈⢆⠈⠓⠄⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠒⠊⠁⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⢝⡄⢨⣄⣎⠀⠀⠑⢄⣀⠀⠀⢘⡏⠒⠒⠂⠀⠀⠐⠒⠒⠈⠉⠀⠀⠀⣀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠓⢬⣻⢚⡛⠁⣛⣁⣈⣙⠯⠈⠉⠹⠈⠂⠤⠄⠀⠀⢠⡤⠤⠄⠒⠒⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⢁⡜⡋⠑⢢⠸⠀⠀⡄⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡠⠋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡅⢸⠀⡇⠀⠸⠀⡇⢀⠄⠀⠀⠀⠀⠰⠒⠤⢀⣠⠠⠴⡀⠁⠒⠒⠀⠉⠁⣀⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢆⣸⡇⠄⠀⣠⠶⠋⠁⢀⠔⠊⠻⠉⠑⠢⢄⣀⣀⡀⠤⠘⡋⠀⠀⠀⠉⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢫⠀⠀⠀⠀⡏⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠐⠠⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣬⢦⡀⠀⡗⠄⣀⣀⣀⣁⣀⣀⠀⠤⠠⠔⢚⢇⡌⠀⠀⠀⠀⠀⠀⣠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠑⠠⢀⣀⣀⣀⣀⡀⠤⠤⠒⠂⠙⢄⠣⣀⣀⣀⣀⠤⠚⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠀⣀⠀⠤⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠿⠟⠋⠛⣛⣛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠋⠀⢠⣄⣤⣴⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⢡⡾⣼⣷⣿⠟⣻⣿⣿⡋⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣴⣿⣿⣋⠛⢿⣧⠈⠁⣼⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢿⣿⣤⣿⡆⠀⠉⢀⣀⣈⠀⠹⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⣡⢞⣷⡄⣀⣀⣈⣇⣠⣭⣿⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣍⣀⡉⠛⢿⣿⠟⢁⣀⣉⠿⣿⡣⣄⣙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠉⠉⢻⣿⣿⣿⣤⠏⠀⠈⠀⠋⠉⠉⡀⠘⠈⣺⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⠀⠀⠠⠢⣽⣿⣿⣿⣶⣤⣴⣴⣦⣀⠀⣩⣯⣿⣿⣿⣿⣿⣶⣶⠖⠒⠒⣐⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡤⠤⢦⣼⣿⣿⣿⣷⣦⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣜⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣤⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠚⣿⣿⣿⣿⣿⣯⠀⠀⠀⢹⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⢠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡀⠀⢿⣿⢻⣿⣿⣿⣠⣀⡄⣘⢿⣷⣄⠀⠀⠀⠀⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠄⠀⠆⢛⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡁⠈⣹⣿⣷⠙⠛⠛⠻⣿⣷⣤⡾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢃⣘⣀⣫⡿⠟⠋⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠅⢠⣿⣿⡏⠀⠀⠀⠀⠀⠈⠉
⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⣤⣀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣟⣥⣿⠟⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣤⣀⡀⠒⠀⠤⠀⠠⠀⠩⠏⠉⢉⢠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠀⠠⣌⣵⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⣼⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠐⢴⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢈⣼⣿⣿⣿⣿⣿⣿⣿⣿⠛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⠈⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⢸⣏⠞⠻⣿⣿⣿⡿⠛⠀⠀⢈⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣼⣿⣯⠀⠀⠙⠋⠁⠀⣀⣀⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠷⢶⣤⣴⣤⣣⣀⣀⣀⣀⣀⣤⣴⠟⢀⠙⢾⣧⣀⣤⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠟⠋⠉⠉⠁⠀⠁⠀⢸⣷⣶⣭⣽⣭⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣦⣄⠀⣀⣠⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣯⣼⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⣀⣀⣠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢰⠊⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣰⣾⣦⠀⠀⠀⠀⠀⠀⠀⠑⡆⠀⠀⠘⠛⠀⠀⠀⠀⠀⠈⠀⠈⠙⠳⣼
⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⢀⠀⠘⠛⠋⠀⠀⣀⣰⣇⣀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⢀⣤⣶⣤⠀⠀⠚
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠜⣿⣿⠣⠀⠀⢀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⡀⠀⠐⠻⣿⠟⠂⠀⠀⣿⣿⡏
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠄⠠⠀⠄⠀⠈⠛⠋⠀⠀⠠⠁⠄⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⠞
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⣐⣐⣰⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⡤⣤⣤⣤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣼⣿⣿⣿⣿⡄
⠀⠀⠘⠃⠀⠀⠛⠛⠛⠛⠛⠃⠀⠛⠻⠟⠋⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⠛⠛⠛⠛⠁
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣭⣉⢃⡀⠀⠀⠀⠐⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠐⢻⣿⠏⠀⢀⣀⠀⠀⠀⢀⣠⣄⠀⠀⢀⣷⠈⠉⠉⣼⣷⠀⠀⠈⠀⠼⡀⠀⠀⠀⡀⠀⠐⢺⣷⡄
⠀⠀⣰⣿⣿⡄⠀⣸⣿⡀⠀⠀⢻⣿⣿⠂⠀⢸⡿⠷⣄⠾⠿⠿⠇⠀⠌⠀⠠⡄⠀⠀⢼⣿⠃⠀⢸⣿⣷⡀
⠀⢀⣿⣿⣿⠷⢠⣿⣿⣿⠃⢠⣾⣿⣿⣦⠀⠘⠿⢷⠉⣾⡿⠷⠀⠀⠀⠀⠐⠊⠠⣴⣿⣿⣇⢠⣿⣿⣿⣷
⠀⠸⢿⠟⣋⠀⠘⣿⣿⡟⠀⠘⣿⣿⣿⡇⠀⠀⢠⣶⣶⣶⣦⠀⠀⠀⠀⠄⠀⢰⡀⠘⣿⣿⡟⠀⠈⠻⢿⣿⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠈⠀⠀⠉⠉⠀⠀⠀⠁⠈
⠀⢀⣄⣤⣄⡀⠀⠰⠶⠄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⣠⣀⡀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠘⢿⣿⣿⡆⠀⠀⠀⠀⠀⣴⣿⣷⡄
⠀⢀⣶⣿⣿⣧⣤⣤⠀⠀⣀⣿⣿⣧⡄⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣸⣿⣷⣇⠀⠀⠀⠀⠀⣳⣿⣟⡁
⠀⠀⣽⣿⣿⣿⡏⠀⠀⠠⣶⣿⣿⣷⠶⠀⠈⢿⣾⣿⣿⣶⡄⠀⠀⠠⣾⣿⣿⣿⣿⣦⣄⠀⠀⣾⣿⣿⣿⣿⡆
⠀⢸⣿⣿⣿⣿⣿⠀⠀⠴⢾⣿⣿⣿⡶⠄⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⣼⣿⣿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿⣿⡅
⠀⠘⣿⣿⣿⣿⣿⡄⠀⠺⠻⠿⣿⠿⠛⠂⠀⣬⣿⠿⢿⣿⠇⠀⠀⠠⣽⣿⡿⠿⣿⣷⡄⠀⢠⣿⡿⢿⣿⣿⠃

⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠀⠉⠉⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢃
⠀⠀⠀⠀⠂⢀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸
⠀⠀⠀⠀⠀⡀⠤⢡⠂⠀⢰⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠒⠲⠤⢄⣀⠀⠀⠀⠀⠀⡼⠁⠀⢸
⠀⠀⠀⠀⠁⠀⠉⠉⠓⠘⠉⠁⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠑⢦⡀⢀⠎⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢠⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠙⡅⠀⠀⠀⠀⠁
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠂⠂⠀⡅⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⢀⠀⡠
⠀⠀⠀⠰⠀⠀⠀⠁⢰⠀⠀⠀⠀⢰⠋⢀⡌⠀⠀⠂⠐⠂⠐⠖⠀⠀⠀⠀⠠⢤⠊⠉⠀⠀⠀⠀⠔⠃⠊⠉⢣
⠀⠀⠂⠀⠠⠄⠀⠀⠘⠀⠀⠀⢀⡸⠀⠈⠀⠀⠀⠉⠀⠀⠀⢄⡀⠀⠀⠀⠀⠜⠁⠓⡄⠀⠀⠐⡄⠀⠀⠀⠀⠣
⠀⠀⠐⠀⠈⠀⠈⠁⠉⠒⠀⠀⠀⡐⠀⡀⠀⠀⠀⢀⡠⢴⠆⠐⠁⠈⠑⠢⠤⠀⢀⠄⣆⠀⠀⠀⠠⣀⢀⠠⠤⠃
⠀⠀⠀⠁⠀⠀⠐⢂⡤⠀⣀⠔⠈⢀⠀⠠⠘⠋⠉⢀⡔⠀⠀⠄⢀⣀⣀⡀⣤⠐⠀⡰⠉⠙⠦⣄
⠀⠀⠀⠀⠀⠀⢊⠁⠠⣀⣈⡃⠀⠀⠁⠐⠒⠂⠙⠀⠀⢘⠀⠀⠀⠀⠀⠀⠘⡤⠚⠁⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⣀⠗⠠⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠆⢀⠎⠀⠀⠀⠀⣀⣠⠔⠊⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⣄⠘⠒⠒⠒⠚⠁⠁⠀⣠⠔⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠄⠐⢢⠟⠁⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡆⢠⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠇⠘⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢰⠀⣰⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢸⠀⢿⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⢠⠄⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠢⢀⡀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠹⠄⢀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⢀⡴⠋⢳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠤⠋⠀⢢⠒⠒⠚⠓⠢⣄⠀⡠⠒⠁
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠉⠙⠓⠲⠦⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠀⠀⠀⠀⡠⠋⠀⠐⠠⣄⢀⠼⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠑⠐⠲⡉⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣤⠶⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠲⠶⠖⠲⡖⠒⠒⠶⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡴⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠰⢄⣀⠀⠀⠈⠉⠉⠉⣉⣡⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⠐⠓⠄⠉⠉⠉⠉⠉⠁⠋⠉⣩⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠃⠀⢃⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠉⠑⠒⠒⠠⠤⠤⠤⣀⣀⣀⣀⡠⠖⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣭⢁⣀⠈⠉⠉⠉⠉⠀⣀⣤⠴⠂⠷⠔⠀⠀⠀⠀⠀⠧⠠⠏⠓⠦⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠖⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣠⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣒⣋⣛⣲⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣤⣉⡛⠿⣿⣿⣷⣄⣉⠙⠓⠒⠶⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠴⠿⡿⠿⠛⠻⠿⢶⣾⣝⣿⣿⣷⡄⠰⣄⠀⠈⠹⣷⡈⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠓⢾⣵⣿⣶⡾⠿⢧⣴⣾⣿⣷⣦⣭⣝⡻⠿⢿⣿⣦⡙⣷⣶⣶⣸⣷⡀⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠙⠿⢿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣾⣿⣍⠈⣿⣷⡀⠰⡄⢉⡛⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠹⣄⢷⣄⠀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠇⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠙⠛⣿⣿⣿⣿⣿⣿⣷⠀⢹⣾⣿⣆⠀⣶⣤⡌⣷
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⡄⣿⣿⣷⠏
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢿⣿⣆⢿⣿⣿⣧⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⣀⣤⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣇⣿⠏
⠀⠀⠀⠀⠀⠀⢼⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠉⠻⣿⣦⡄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⢻⣿⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣾⡁⢀⡟⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⡴⠖⠂⣩⡿⠈⠙⢷⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⠸⡆⣰⡿⠷⣶⡚⠉⠋⠻⡟⠛⠀⡴⢀⣤⣶⣶⣆⠀⢹⣿⣿⣿⠹⣿⣿⣶⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⡤⠻⣾⠃⣲⠶⣶⣤⢱⣴⣶⣶⣤⣴⣿⠹⠿⠟⣻⣾⣿⣿⣛⠿⢀⣄⢿⣿⠛⢿⣿⣿⠏⢉⣹⣿⣿⣿⣿⠿⠋⠉⠉⠙⠳⢶⣀
⠀⠀⠀⠀⠀⠀⣴⠋⢠⣶⣩⡞⠿⣷⣛⣭⣿⣹⣿⣿⣿⣧⣈⠓⣀⣨⣥⣤⣌⣿⣿⡇⢸⣿⠀⠏⠀⠀⠋⡏⣰⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⢸⠃⠀⠸⣿⢻⣿⣶⣿⡿⠛⡏⣿⣿⣿⣉⣟⡛⠉⠉⠉⠁⠙⢿⣿⣿⣷⠀⠁⠀⠀⠀⠀⠀⢘⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⢀⡿⠀⠀⠀⢿⡆⣿⠋⠁⠀⣸⠃⠈⠙⠛⡁⠀⣿⣦⡀⠀⠀⠀⠀⢹⣿⣿⣷⡄⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠰⢶⣿⣤⡀⠀⠀⠘⣧⠛⠀⢀⣾⣿⣷⣦⣶⣿⣷⣾⣿⣿⡻⢷⣤⣀⣀⣨⠟⣹⢁⡇⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣠⠜⠝⠁⠀⠀⠀⠀⠀⢠⣾⡿⢿⠟⠋⢈⠛⠉⠋⠀⠙⠛⠂⠈⠀⠀⠀⠀⠁⣼⠃⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠀⢀⣴⣿⣷⣶⣶⣶⢶⣤⣀⠀⢤⣀⣀⣲⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⣿⠏
⠀⣽⣿⡴⠋⠀⠀⠻⡉⠒⠊⠉⠀⢀⣀⢶⣿⡟⠛⠛⠛⣉⡥⠞⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⠀⣀⣀⣀⣤⠞⠃
⠀⠈⣿⡀⠀⠀⠀⠀⠉⠓⠲⠤⠚⠛⠁⠀⠙⣿⣿⣷⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⣿⣿⣿⠉⠉
⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⡀⣄⠈⠻⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠇⠛⢼⣿
⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡈⠲⣦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢤⣤⣤⠞⠁
⠺⣿⣿⣟⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠈⠛⣿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿
⠀⠀⠀⢻⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣀⣄⣸⣿⣿⠃
⠀⠀⠀⠀⠻⣿⣷⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡞⣿⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠉⢻⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⣶⢀⢠⣀⢃⡏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣄⣏⣼⢠⣿⢟⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⣿⣿⣿⣧⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣴⣏⠔⣱⣿⣆⠀⠀⠀⠀⠀⠀⣦⣀⢀⢀⠀⡄⡄⢰⡄⠀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢿⣮⣦⣦⣦⣹⣦⣬⣙⣿⣾⣞⣢⢿⣼⣮⣷⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠴⠶⠶⠖⠒⠒⠒⠲⠶⠶⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠀⠀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⠀⠀⠈⠘⠻⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⠏⠀⠀⠀⠀⠀⡠⠖⠒⡶⠒⠚⠓⠚⣏⠉⠳⡄⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠸⣆⣀⣀⡤⠖⠛⢄⡤⠞⠳⡄⠀⠀⣼⡉⠻⡟⠉⠀⣸⠃⢀⡴⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣰⠋⢴⣋⣀⠀⠀⢸⡀⣴⣿⡧⠤⠄⣿⣷⣆⣼⢀⡀⠙⣄⣀⡽⠂⢹
⠀⠀⠀⠀⠀⣀⡤⠤⣴⠒⠲⢤⣿⠀⣹⠀⠀⠀⠈⠙⠒⠋⠉⣿⠁⠀⠀⠀⠀⡍⠀⠈⠉⠉⠉⠉⠁⠀⢀⡟
⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⣿⠀⠘⢲⡀⠀⠀⠀⠀⠀⠀⠈⢓⣤⢤⣶⣎⡁⠀⠀⠀⠀⠀⠀⣀⡴⣯⠀⠀⠀⢀⡀⢀⡀
⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢰⡋⠳⣤⣀⣀⣀⣤⠤⣖⢯⣭⣭⣥⣾⢟⠗⠲⠶⠖⠚⠋⠁⢰⣃⣀⣀⡤⢺⢌⠁⣸
⠀⠀⣾⠀⠀⠀⠀⠀⠀⢐⠒⠛⠁⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠈⢦⣙⢿⣛⡡⠊⠀⠀⠀⠀⠀⠀⠀⢾⠉⠁⠀⢀⣼⡧⠋⠁
⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠑⠦⣤⣀⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣰⠏
⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⢀⠜⡽⠁⢻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠲⠶⠚⢋⡞⠁⠀⠀⠸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡠⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⡞⠀⣀⡜⠁⠀⠀⠀⠀⠀⠉⠙⠋⠳⢤⣀⣀⡠⣄⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⢣⣌⣒⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠚⠉⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠠⢀⡠⠇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠓⡒⠦⣄⠀⠀⠀⢀⣀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣀⣀⣀⣀⡞⢱⣉⣉⣩⣥⣽⠈⣷⣾⣿⣿⣿⠿⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⠿⠿⠿⠿⠿⢷⡈⠿⠛⠛⠛⢛⡴⠛⠋⠉⠁⠀⢀⣠⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⡶⠤⣄⣀⣀⣀⡉⠛⣲⠚⣏⣉⣀⣀⣤⠤⠖⠚⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⡖⠋⠉⠉⠉⠁⠀⠈⠉⠉⠉⠓⢦⣤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣯

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢶⣿⣶⣶⣦⠀⠀⠀⠀⠀⢠⣶⣴⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣅⣾⣿⣿⣿⣿⡄⢤⡀⠀⢠⣿⡿⣿⣿⣿⣿⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣗⣛⢡⣭⡯⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠻⠿⠯⠈⣬⣿⣿⠃⠀⢿⡿⠛⠋⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠻⠀⠀⢀⡀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣤⣈⣀⡀⠀⠀⠀⠀⠀⠀⣀⡈⠙⠳⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠉⢿⣿⣦⢀⡀⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠙⠂⠀⠀⠀⠀⠀⠀⠀⢰⢿⡄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⢖⠒⠒⠂⢒⠐⢒⡶⠆⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⢀⠀⠀⠈⠉⠀⠒⠻⣑⠭⠀⢀⣀⠀⡀⠀⠉⡒⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⠀⠀⠀⠀⠀⠀⠂⠀⠀⣴⠂⠀⠀⣰⠆⠀⠀⠉⠲⣄⠀⠀⢸⡗⠁⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠆⢀⠁⠀⣛⣛⣬⣬⣭⣭⣭⣥⣼⣒⡀⠤⢈⡃⠀⠜⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠀⠀⢠⡴⢓⣨⣴⠾⠋⠉⠉⠀⠀⠀⠀⠀⠉⡉⠛⠛⠻⣶⣮⣔⡠⡀⠀⠀⠰⠀⠘⠉⠙⢦
⠀⠀⠀⠀⠀⠀⡠⡁⠀⠀⠀⣠⠞⢃⢜⣥⣾⡟⠉⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣦⣕⠄⡀⢀⡀⠄
⠀⠀⠀⠀⢀⠌⠀⠉⠩⡍⠀⢀⢜⣵⣿⣿⡟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣔⢾⠟⠀⠱⢆
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠘⡤⣢⣾⣿⣿⡿⣤⣾⡿⠃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠹⣿⣿⣿⣧⡹⠿⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⡰⣱⣿⣿⣿⣿⣵⣿⡍⠀⠀⠀⠻⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢳⡀⠀⢿⣿⣿⣿⣷⡐⡀⢡
⠀⠀⢐⠀⠀⠀⠀⠀⠠⢱⣿⣿⣿⡿⣿⣿⣿⣷⣦⣶⡀⢀⣹⡆⠀⠀⢀⣤⠶⠚⠛⠉⢹⠿⠷⢶⣮⣇⡀⢸⣿⣿⣿⣿⣿⡘⠻
⠀⠀⡎⠀⠀⠠⡆⠀⢣⣿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⣷⣿⣿⣧⣴⣾⡥⠄⠀⠀⠀⢠⣠⡤⠤⠈⢻⡟⢿⣿⣿⣿⣿⣿⣿⣧⢹
⠀⢠⠀⠀⠀⠉⠀⣤⢸⣿⣿⣿⣿⣷⣗⢹⣿⣿⣿⣿⣿⣿⡟⠛⢿⠃⢀⡤⢤⣷⡀⠙⠇⠀⠀⠀⢈⣉⡉⠻⠿⢿⣿⣿⣿⣿⡈
⠀⠸⠃⠀⣦⠀⢀⠇⣿⣿⣿⣿⣿⣿⣿⡿⣧⣿⣿⣿⣿⣿⣷⡀⠘⠛⠉⠀⠀⠙⣿⡄⠀⠀⡆⠀⠊⠐⠀⠄⠀⠈⠙⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡌⠁⣿⣿⣿⣿⠿⠿⠫⠟⠐⠈⢺⣿⣿⡏⠻⢿⣿⡇⠢⠄⣀⡴⣁⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠸⠀⡀⠀⠘⠁⢠⢻⣿⣿⣿⣢⡐⠀⠀⣠⣶⣿⣿⣿⠃⠀⠀⠈⠀⠀⡬⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⠀⠀⠀⠀⢘⣿⠃
⠀⠀⡆⢇⠀⠀⠀⠀⠸⣿⣿⡟⡼⠁⠀⠰⠿⡿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢤⣤⠖⠛⠛⠉⠙⠁⠀⠀⠀⠀⠀⣿⣰
⠀⠀⢐⠀⢷⡀⠀⢀⣠⣿⣿⠋⠄⠂⠀⠀⠀⣀⢸⣿⣿⣷⡄⠀⠀⢀⢰⣿⣿⣿⡋⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠈⠆⠀⢙⣴⣿⣿⣿⠟⠀⠀⠀⠉⠀⠀⠀⡀⢻⣇⢍⠟⣷⠀⡈⡀⠐⠤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣴⣾⡿⢟⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⣴⣿⡟⣡⠏⠐⠀⠳⠀⠀⠀⠀⢀⠀⢀⣋⣠⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⣾⡟⠟⠀⡉⠀⠁⠀⠀⠀⠀⠀⠰⠀⣠⣾⣿⣿⣿⣧⣴⣿⠃⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣦⠀⡆⠙⠀⠀⠀⠀⢠⡴⠂⠀⠀⠙⣿⣿⣽⣿⣿⣿⣶⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⢺⠀⠀⠀⠀⠀⠀⠀⠌⠐⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠉⢁⣀⣀⣀⡈⠉⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠿⠿⠿⠛⠛⠿⠿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⣴⣾⣉⡉⠉⠉⣉⡻⣦⡄⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠋⠉⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠙⠻⢿⣷⡀⠀⠀⠀⠀⠀⢠⠈⢱⣿⡇⠀⠠⠆⠀⠠⠆⠀⠀⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⢀⣠⡶⠟⠛⠛⠛⠛⠛⠛⠻⣶⣤⡀⠀⠙⣷⠀⠀⠀⠀⠀⢈⡀⣾⠁⢦⣤⠤⠆⠀⠀⠦⣤⣴⠂⠹⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⢠⣴⠟⠟⠡⠶⠶⠂⠀⠀⠐⠶⠶⠌⠻⠛⣦⢀⣸⡇⠀⠀⢀⣶⣿⡷⢦⣀⠀⠀⠀⣠⣤⣀⠀⠀⠀⣀⠤⠈⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢹⣿⣿⠘⠀⠀⠄⢾⡀⠀⠀⢀⡿⠀⠄⠀⠃⣿⡏⠁⠘⢆⠀⠀⠙⢿⠇⠀⠈⠉⠁⠁⠀⠭⠀⠈⠈⠁⠀⠀⠀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⣸⠟⠙⡆⠀⠀⠀⢀⠀⠀⠁⠀⡀⠀⠀⠀⣰⠋⠳⣤⠀⡿⠀⠀⠀⠀⣶⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣦⠈⠻⢄⡀⠙⠷⠶⠚⠉⠙⠓⠈⠉⠙⠳⢶⣿⣋⠀⠀⠋⣰⣷⣄⠀⠀⠀⠙⣦⠀⣧⡀⠀⠀⠀⠀⠀⠀⠤⠆⢰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢷⣄⡀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢸⣿⣷⣄⠀⠀⠙⣷⠘⠷⢶⣤⣀⣤⣸⠚⠀⣰⠋
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⠀⠈⠛⠻⠶⠦⠴⠓⠋⠑⠶⠞⠉⠛⠳⠴⠢⠚⠛⠁⠀⠀⢻⣿⣿⣿⣦⣀⠀⠈⠙⣆⢀⡀⠉⢀⠀⡔⠋⠁
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣄⠀⠀⠉⠓⠶⠋⠉
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠘⠳⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠾⠃⠀⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣷⡀
⢸⣿⣿⣿⠟⠉⠀⠀⠀⠈⠉⠛⢿⣿⣷⡆⠀⢿⡤⣶⡀⣀⠀⢀⡀⢀⡷⠶⠇⠀⢲⣾⣿⣿⡿⠋⠁⢀⠀⠀⠀⠀⠈⢻⣿⣿⡇
⣹⣿⣿⡏⠀⠀⢀⣤⣶⣶⣶⣦⠤⠿⠿⠳⣄⣤⠀⠙⠛⠛⠷⠾⠛⠛⠃⣠⣀⣤⣿⡟⠉⠛⠓⠒⠿⣿⣿⣷⣦⠀⠀⠀⣿⣿⣿
⢸⣿⣿⠀⠀⢠⣾⣿⡿⠛⠉⠀⠀⠀⠀⢀⣾⣿⡄⠀⣀⠀⠀⠀⣀⠀⢀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⠀⠀⢸⣿⡏
⠀⢿⣿⡀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⣾⠟
⠀⠀⠙⣧⡀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠉⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢀⡼⠋
⠀⠀⠀⠈⢷⣤⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠃⢀⡀⠈⢻⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠶⠋⠁
⠀⠀⠀⠀⠀⢈⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠋⣭⣭⣭⣭⠙⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⢀⣀⣴⠟
⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⡀⠿⢶⡿⠿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⡆
⠀⠀⠀⠀⠀⢸⡇⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠒⢲⣶⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⣿⠇
⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠟⠀⠀⢠⣿⠀⠀⠘⠿⠿⠿⠿⠿⠛⠋⠉⠀⠀⣀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠲⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠚⠓⠦⠤⣤⣈⡓⠦⣄⣀⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⣟⣀⣀⡈⣳⢤⣤⠤⠤⠤⡀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⢭⡭⢭⡷⣼⡲⢤⡀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢱⠃⠀⢸⢹⠶⢬⣷⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡃⡿⠀⢀⡞⡼⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠁⠀⢸⡤⢷⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠊⠉⠉⠓⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⠒⠶⠤⠤⠶⣶⠾⠛⣓⣲⣤⠀⠀⠀⠀⠀⠀⣤⣖⣛⠛⠶⣶⠦⠤⠤⠶⠒⣆⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢳⢀⡇⠀⠀⠀⠠⠾⠖⠋⢩⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡍⠙⠲⠷⠄⠀⠀⠀⢸⢀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⢱⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⡄⠀⠀⠀⠀⠀⠀⠀⠈⡿⠒⠤⣀⣀⣀⣀⣀⣀⠤⠒⢿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣿⡁⠀⠀⢈⣿⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠉⠒⠈⠀⠉⠉⠉⠉⠀⠉⠒⠉⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⢤⡀⠀⠀⠀⠀⠀⠀⠻⣤⣤⠟⠀⠀⠀⠀⠀⠀⣀⠴⠊⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠑⠲⠤⢄⣀⣀⣀⠀⠀⢀⣀⣀⡠⠤⠒⠋⠁⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⠉⠉⠉⡟⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠤⠔⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠒⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠁⠀⠀⠀⠀⠀⡔⠀⠙⢄⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠑⢄⠀⠀⠀⡀⡠⠊⠀⠀⠀⠈⢆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⢀⡸⠂⠠⠀⠈⠀⠒⠊⠁⠀⢊⠔⠂⠁⠐⢄⡃⠀⠀⠀⠆⡀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠄⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠇⠀⠈⠁⠀⢠⣄⣠⡿⠈⠁⠀⠀⠀⠑⠄⠀⠀⠠⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠉⠉⠁⠀⠀⠈⠉⠁⠂⠀⠀⠀⠀⠀⠈⠦⢀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠺⠃
⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠂⠸⠀⠀⠀⠀⠀⠀⢀⠀⠂⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠑⡀⠀⠀⠀⠈⠀⠀⠃
⠀⠀⠀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠈⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠉⣄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢆⠀⠀⠦⠂
⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⡀⠈⠁⠀⢉⠉⠁⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠀⠖⠂⠊⠀⠀⠁⠈⠀⢀⡀⠐⠚⢤⠀⣀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢱⠀⠀⣀
⠀⠀⢀⠀⠀⠀⠀⠀⠘⠒⠒⠀⠀⢀⣀⣈⡉⠀⠀⠀⠀⡀⠀⠠⣤⠤⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠂⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⠀⠀⠀⢘⠀⠀⠀⠀⠀⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢄
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠦⠀⠀⢬⠁⠀⠀⠀⠀⠀⠀⠘⠁⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⠀⠀⢠⠀⠨⠕
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠑⢄⠀⡀⠀⠀⠀⠀⠀⠠⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠎
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢦⠀⠀⠀⣁⣄⠀⠀⠀⠀⠀⠀⠀⢙⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠓⠀⠀⠀⡀
⠀⠀⠀⠐⠅⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠈⡄⢀⠝⠒⠀⠀⠀⠂⠈
⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣘⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠲⠄⠠⠠⢀⠀⠀⠀⠀⠀⠄⠠⠠⡤⠀⠤⠤
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⣀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⣿⠇⣠⠴⢶⣷⣦⡖⠋⠑⡢⢔⠊⠀⠀⣠⡶⠛⡣⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢠⣾⡯⠊⠀⣴⣿⠟⣀⣽⡋⠉⠀⠈⡓⢄⣾⣟⡡⠊
⠀⠀⠀⠀⠀⠀⣠⠀⢠⠃⣀⢠⣿⠏⠀⣠⡾⠋⣵⡿⡏⢄⣡⣶⠛⡁⢀⣾⡏⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠃⣾⠃⠀⣴⠏⠀⢸⡿⠁⣠⢳⡿⠓⠊⠀⣸⡿⠀⢀⢤⠄
⠀⠀⠀⠀⠀⠀⣀⠤⠠⡀⢸⡏⠀⣸⠃⠀⠀⠘⠗⠊⠁⢺⡇⠀⠫⠀⣿⡇⡰⠁⡎⠀⣀⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠰⠁⠀⠚⠁⠸⠀⠀⡟⠀⡠⠔⠒⢶⡄⠀⠈⠙⠈⠀⠀⠘⠓⢀⠔⠋⠁⠀⠀⣹
⠀⠀⠀⠀⠀⠃⠀⠀⢠⠀⠀⠀⢀⣷⡊⠀⣀⡤⠟⠕⢐⠄⠀⠒⠀⢀⡤⠊⠀⠀⠀⠀⠁⠉⠁
⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⡤⠔⠋⠀⠀⠀⡀⠀⠈⠦⣀⣀⣀⠤⠒⠁⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡢⡔⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⠴⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⡠⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⣠⠄⢀⣄⣠⣴⠿⠤⣶⡂⣄⣀⣐⣀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⠀⣠⡿⠛⠛⠛⠛⠛⠒⠢⠀⠀⠉⠛⢩⣽⠂⠤⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⡿⠶⠟⠂⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠈⠙⢫⡀
⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⢀⠀⠀⢸⠇⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢄⠀⠐
⠀⠀⠀⠀⠀⠁⠀⢀⠺⣀⠿⠁⠀⠀⠀⠒⢄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢰⠀⠀⠀⠀⠀⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠛⠀⠀⠀⠀⠀⠀⠈⡆⡈⠀⣷⠀⠁⠀⠀⠠⠂⡸⠀⠀⠀⠀⠀⠀⠀⠃⡸⠍⠇
⠀⠀⠀⠀⠀⠀⣀⡀⢻⡆⢀⠀⠀⠀⠀⠀⠀⡗⠀⢀⣧⠂⠀⠀⠠⢒⠆⣇⠌⢀⠔⠊⠀⠀⠀⢀⢷⣼
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣇⠽⠀⠀⠀⠀⠀⠀⡇⠀⡼⠈⡧⠤⡴⢾⣁⡠⢏⡰⠃⠀⠀⠀⠀⠀⠎⢀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣬⣹⣄⠀⡀⠀⠀⠀⠀⠁⠀⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⢷⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⡉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⠻⣦⢸⡀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠀⠘⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢪⣟⣧⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢶⡾⠋⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⢶⠦⠈⠷⣄⣀⠀⢤⣀⡀⠀⠓⢶⣶⣤⣤⠛⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠤⠤⠿⢷⣶⠿⣛⣷⠟⠉⢠⡔⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠈⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⠁⠀⠀⠀⠉⠂⠀⠤⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⢀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠀⠐⢤⣀⡀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡙⠲⣄⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠉⡱⠂⠀⢀⠀⠀⠀⠀⠀⠀⡍⠀⢀⡴⠛⣉⠉⠳⡄⠀⠀⠀⢰⠃⠀⠀⠀⠀⡨⠛⠲⡤⣀⠈⠣
⠀⠀⠀⠀⠐⢖⡁⣤⠀⠐⠌⠀⠀⠀⠀⢀⡼⠁⠀⠸⡄⠀⠀⠑⠢⠏⠈⠉⠉⢈⡅⠀⠀⠀⢀⡀⠄⠀⠀⠀⠈⠀⡞⠉⠉⠳
⠀⠀⠀⠀⠀⢀⠔⠁⢀⠈⠀⠀⢀⡄⠖⠋⠀⠀⠀⠀⠀⠀⣴⣶⢦⠁⠀⠀⠀⠸⠿⠀⠀⠀⠀⠐⠒⡀⠀⠀⠀⠀⠑⠄⠀⠈
⠀⠀⠀⠀⠲⢥⡶⠀⣀⠉⡁⠀⠈⢧⡀⢀⡄⠀⠀⠀⠀⠀⠐⠀⠉⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠒⠀⠀⠠⠃⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠠⠎⡴⠂⠀⠉⠀⠀⠀⠀⡉⠀⠱⡀⠀⠀⢀⠀⠀⠀⠀⢀⠔⠂⠀⠖⠒⠀⠀⠀⠀⡨⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠾⠤⡶⠀⠀⠀⠤⠴⠊⠀⠴⠁⢠⣀⠑⠈⢧⡤⠀⠊⠁⢀⠤⢲⠄⠀⠠⠆⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⠤⠤⠤⠂⠙⠤⣲⠵⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⡙⠆⠀⠀⠒
⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⣟⡆⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠸⣇⠀⣠⠀⠀⡟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡍⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⡼⠁⠀⠀⠀⠀⠆⠀⠀⠸⡀⣄⠀⠀⠣⠀⠀⠀⢀⢶⢀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢦⡀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰⡀⠀⠀⠰⡄⢆⠀⠳⠈⠁⠀⠀⠀⠀⠀⠁⢁⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠌⠣⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⣉⠑⠀⠓⠢⢄⡀⠀⠀⢰⠤⢄⣀⣀⣀⠀⢠⠀⠙⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠴⣶⣿⣿⣿⣿⣿⣿⢿⣿⣶⣶⡶⢤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣷⣮⣝⢿⣿⣦⡙⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⣀⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢷⣌⠻⣿⣦⡜⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣠⠞⠃⠀⣠⠤⠤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠃⠘⢿⣿⡌⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠋⢁⣤⡶⣛⣛⣭⣽⡷⠒⠚⠿⣭⠤⠤⠀⢀⡀⠀⠈⢣⡀⠀⠸⢿⡇⠰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢾⠋⢩⣯⣿⣄⣉⠐⠒⠆⠀⠒⢚⠛⢻⣿⣿⣧⡀⠀⠀⢻⣄⠰⡘⠇⢸⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢘⠀⠱⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣆⠀⠀⠻⡄⠐⢀⣾⡟⠘⠿⣿⣿⣿⣶⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠘⢷⡀⠀⠉⠀⠘⢋⡴⢞⣠⣤⣴⣿⣿⣿⣿⠿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⢺⣿⣤⣶⣾⣿⣧⠀⠀⠨⠿⠏⠀⣦⠄⠀⢨⣷⠀⠀⢀⠖⠀⠀⠉⠁⠀⠀⢀⣼⡿⠁⠀⠀⠙⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠄⠀⠐⠀⠿⠥⠞⠫⠙⠋⠙⠣⠄⠐⠠⠖⠋⠉⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠟⠋⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⣸⡀⣿⠀⢀⣠⡴⠟⠃⠒⠀⠀⠐⠀⠙⠒⢦⡀⠀⠀⠀⡆⠀⠉⠃⠀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⢄⠙⢃⣿⣼⡟⠁⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠙⠳⣭⣀⣙⡀⠄⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠤⠀⠀⠁⠘⠛⠋⠀⢰⠇⢰⠠⣿⣿⣿⣿⡷⢄⠳⢤⡀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⢲⡄⠂⠀⠴⠙⠃⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⡢⢀⠱⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢱⡤⠐⠂⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣀⣶⣦⣄⢠⠆⣶⣈⡖⢄
⠀⠀⠀⠀⣴⡾⠟⠓⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣶⣿⢿⡏⠀⡅
⠀⠀⢸⣆⣿⣧⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣧⣿⣾⣿⣿⣿⣿⣿⡿⢀⣾⣿⡏
⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣯⡀
⠀⠀⠀⣼⣿⣿⡿⠟⠓⢄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠛⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠙⠟⡻⠀⠀⠀⣼⡗⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠛⠒⠒⣠⣾⣿⣿⣿⡿⢟⣡⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⡟
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢸⠀⢀⠄⠀⢀⣀⣀⠀⢀⣀⠈⣿⣷⣄⣀⠀⠀⠀⢀⣠⡀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣾⡟⠀⠀⠀⠈⠀⡶⠀⣿⣯⠀⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠋⠀⠀⠊⠤⣀⣤⡠⠾⢿⠟⠀⠉⠉⠛⠿⠿⠿⠿⠿⠿⠟⠛⠉⠁⠈⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⢿⠛⡟⢻⡿⢻⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠖⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢲⠠⠀⠒⠂⣤⡀⣀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠉⠙⠛⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢠⡞⠀⠀⠀⠀⡀⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢀⡿⠀⠀⠀⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⣸⠃⠀⡀⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣦⠤⠴⠦⠖⠒⠂⠀⣴⠤⡄⢀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣿⠀⢚⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠶⠋⠁⠈⠈⠲⡀⠀⠀⠀⠀⡀⠈⠀⠁⠛⢷⡀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢹⡆⠁⠀⠀⠀⠀⠀⠀⢀⠀⠈⢀⡤⠖⠒⠒⠲⠒⠁⠀⠀⠀⠀⠉⠈⠉⠁⠲⢸⡏⢣⡀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣠⡏⢻⠞⠁⢀⠴⠒⠒⢦⡀⠀⠀⠀⠀⢠⡰⣫⣉⠙⢢⡈⡁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⢛⡀⠀⠀⠀⠀⠀⠟⠀⡼⠀⢰⠃⣻⣿⣦⠀⠹⡄⠀⠀⠀⣾⠣⣾⡿⠂⠀⣧⢡⠸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⢻⡁⠀⢠⣶⡄⠀⠀⣇⠀⣠⣀⣛⣿⣃⣀⡀⠇⠀⠀⠀⣿⠒⠀⠠⠒⢉⠛⠋⠒⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⣡⠶⡜⠻⣄⡑⢂⣾⠃⠀⠈⠉⠀⠀⠀⠀⠀⡠⠀⠀⠚⠓⢲⡀⠀⠖⠒⠄⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠤⠞⠃⠘⣠⠜⠉⢰⠀⠀⠀⠐⠙⠀⠀⠀⣀⠦⠀⣀⣀⣀⡴⠗⠤⢀⡠⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠘⢆⡀⣠⠞⠁⠀⠀⡄⠀⠀⠀⠈⠢⠤⠔⠁⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⡽⠃⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠿⣿⣿⣷⣾⡖⠂⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠒⠒⠂⠁⠀⠙⠲⣄⣀⡉⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠉⠀⡄⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡼⠇⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠐⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾
⠀⠀⠀⠀⠀⠀⠀⠴⠁⠈⠊⠀⠀⠉⠹⠞⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⡸⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡔⠁
⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁
⠀⠀⠀⠰⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠋⠀⠀⠀⠑⢄⢰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠁
⠀⠀⠀⠀⠈⠋⠐⠄⣀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠙⠀⠻⢦⡀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠉⠒⠈⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠏⠓⢤⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⢿⣄⡸⠗⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢬⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣄⣁⡶⠶⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⡾⣾⡿⠿⠿⠋⠰⠒⠢⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠉⠉⠉⢹⠗⠳⣾⢷⣶⠆⠀⠀⠀⠀⣠⠌⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⣴⣿⣟⣶⣦⣤⣤⣤⣤⣄⣀⣑⣠⢹⣇⣧⣤⣴⣶⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣍⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⢳⡀⠀⠀⠀⢀
⠀⠀⠀⢀⣾⠟⠁⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢿⣿⣿⣭⣏⣙⣿⣿⡇
⠀⠀⠀⢸⣏⢀⣀⣴⣿⣯⣀⡀⠈⢿⡿⣯⣽⡉⠛⠋⠀⣸⣿⣿⡇⠈⣿⡉⠉⠀⢀⣸⣟⡀⠀⠀⠀⠀⣄
⠀⠀⠀⢸⣿⣿⣿⣿⠟⢿⣿⣿⣖⣿⠀⠈⠙⢦⣀⣀⣤⣿⣛⡿⡇⠀⣸⠛⣿⠛⠛⠉⠘⠗⢀
⠀⠀⠀⠀⢻⣿⣿⡏⠁⠀⠉⢋⣿⣿⣆⠀⠀⠀⢀⣠⣾⡿⢿⣿⣷⣶⣧⡾⠛⠠⣤⡀⢠
⠀⠀⠀⠀⠈⠻⣏⣄⣠⣤⣶⣿⣿⣻⣿⣿⣷⣿⡿⠟⠛⠁⠀⠈⠉⣉⡉⠀⠀⠀⠈⠅⠛⠲⢶⣷⠀⠐
⠀⠀⠀⠀⠀⠀⠛⠛⠁⠿⠋⠀⡻⠻⠋⠉⢹⠏⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣶⣶⣤⣤⣤⡶⠚⢁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣤⡦⠄⠈⣀⣶⣶⣿⣿⣿⢿⠿⠋⠛⢿⠋⠁⢀⠀⠙⢦⠁⠀⢂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⡀⡰⠀⡀⠀⠀⠈⠙⠣⠚⠛⠛⠡⠎⠿⠀⠄⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠃⠜
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠱⠀⢸⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣝⢿⡏⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢹⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⢿⣧⣼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⣠⣴⣶⠶⠿⠿⠿⠿⠷⠶⣶⣤⣀⠀⠀⠀⠀⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣠⣾⠛⣉⡤⠀⠠⡀⠀⠀⠀⢀⣀⢠⠬⢿⡿⢦⣄⠀⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢻⡇⠸⠶⠶⢤⣤⣤⡀⠀⠀⣼⣦⡴⠖⠲⠽⢸⣿⢷⣸⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⣿⠀⢠⠞⢿⣿⣿⢇⠀⠘⣿⣿⡿⠷⡄⠀⢻⡏⠸⣿⣱⠏⠁⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣾⡏⣞⠉⠀⠈⣉⠴⠃⠀⠈⠦⣉⠁⠀⠀⢹⣎⣿⣦⣈⣿⣶⣀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⠏⢸⣉⣀⣴⠿⠿⠰⢤⣤⣴⠶⠿⠿⣦⣀⣸⣿⠎⢿⣛⡟⠻⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠀⣄⠉⠉⠀⠀⠀⠀⠀⣠⡀⠀⢀⠀⠀⠈⠉⢁⡾⠈⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡷⠂⠀⠘⢷⣶⣶⣊⣤⣶⠞⠛⢛⣶⣮⣳⣶⣶⣶⠿⠁⠐⢶⣟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠁⠀⠙⠉⠉⠁⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⠰⡀⣰⠊⠀⠀⠀⠀⡀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣄⠀⠀⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⣿⡇⠀⠀⠀⠙⠀⠀⠀⠀⠲⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⠊⠀⢸⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣼⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⡄⠀⢀⠀⠀⠀⠀⣷⣸⡿⢻⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢦⠀⠙⠛⠋⠀⠀⠀⠀⣿⣿⣷⣿⣧⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⣿⣇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⢀⡀⠀⣼⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣆⢿⡄⠀⠀⣤⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣼⢃⣼⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⡀⢸⣧⡀⠀⠀⠞⣡⡇⠀⣠⣾⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣦⣻⣿⡄⠀⣰⣿⣠⣾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣍⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢁⡠⠤⠠⠤⣄⣼⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⠋⠀⡀⢀⡦⢀⠿⣿⣿⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠽⠯⠈⣻⣬⣭⡤⣶⣼⣿⣿⠇⠀⠙⣶⣶⣤⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⠄⠒⢒⣢⣤⣤⣶⠛⠛⠋⠉⠉⠁⠀⠈⠈⢏⠁⠀⠀⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠛⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠹⣄⣀⣻⡿⠿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⡀⠀⠉⠛⢻⠁⣭⣉⢹⡿⠿⠛⠛⠉⠀⣠⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠸⣿⣿⣷⣶⣤⣼⠀⢏⣲⠙⣧⣤⣤⣴⣶⣿⣿⠇⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠛⠿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⠟⠋⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⡀⠀⠀⠀⠉⠉⣻⡟⠋⠉⠉⠉⠁⠀⠀⣀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣶⣶⣶⠾⠛⠛⠶⢤⣤⣤⣴⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⠛⠻⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⠛⠛⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣑⣋⣀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢹⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣷⣶⠦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣼⣿⣿⣦⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠼⣇⢠⣿⣿⣿⡿⣟⣿⣿⣯⢿⣿⣿⣠⣷⣬⣿⣿⣿⣿⣿⠿⢿⣿⣷⡶⣾⣻⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡴⠷⢶⣅⣾⣿⡟⠽⠟⠋⠉⠉⠽⣤⠹⡽⠉⠉⠉⠉⠉⠛⠛⠻⠿⠶⣌⠻⣿⣿⣏⡟⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣸⣷⣀⣼⣿⡋⠁⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠌⠳⣜⢿⣿⣯⣱⡿⠂⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡉⡿⠉⡿⣿⢿⡱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⣿⣷⡿⣿⣟⣿⡛⡩⢛⣶⣿
⠀⠀⠀⠀⠀⠠⣤⡴⠛⡻⢿⣶⠃⠉⢹⡇⡧⠀⠀⠀⣀⣀⣤⡴⠶⠶⠚⠛⠻⠷⠶⠶⣶⣤⣤⣀⢀⣀⣽⣿⣯⢰⣦⣄⢹⠈⠉⠳⡿⢯⡈⠳⢦⣤
⠀⠀⠀⠀⠀⠀⣿⠑⢄⡘⢦⣍⠟⣿⣾⣇⣹⣶⣶⡞⠉⣁⣀⣀⣀⣀⣀⡀⢰⠀⠀⠀⠀⠀⢀⠉⠛⠿⣿⡟⠿⣸⠃⢈⢻⡤⠤⢤⣹⡄⠉⢻⡥⣿⡀
⠀⠀⠀⠀⠀⢼⡃⢠⣀⠉⣘⣿⣷⢹⣿⡉⣽⡿⢿⡇⢈⣩⣾⣭⣦⣭⣿⡟⠊⣿⣿⢿⣛⣛⣿⣷⠶⣤⡌⣝⢿⣷⣴⡟⢦⣤⣤⠄⢈⡓⠛⠳⡶⠛⠛⠂
⠀⠀⠀⠀⡿⢦⣽⠦⣬⣿⡻⣧⣄⡤⣾⠃⠟⣠⣿⡗⠀⠉⠀⠙⠛⠿⠟⣦⠀⢸⡟⠛⠭⢾⣿⡯⢷⡟⢈⡛⢠⣟⣝⣠⣶⡀⣿⡤⣾⡇⠀⠀⠀⣠⣤⣄⡀
⠀⢀⣠⠼⢃⣤⣢⡣⣶⣻⣻⣆⠛⣿⣿⠀⠀⠉⠸⣧⠀⠀⠀⠀⠀⠀⣀⠹⠀⢸⣧⠈⠙⠋⠉⠀⠈⠁⢸⣿⢈⣿⠛⣿⡟⡟⢋⡶⢁⣙⣦⣄⣸⠏⠿⣽⣷
⠀⠀⣷⢰⠎⢉⣥⠞⠉⢉⡭⢭⣹⣿⣿⢀⠄⠀⠀⣸⡇⠀⠀⠀⢀⣴⡀⠀⠀⢸⢯⡀⠀⠀⠀⠀⠀⠀⢀⢻⡺⣿⣼⣿⣥⠖⡛⠉⢉⣾⢟⠉⢻⣦⣤⣾⠟
⠀⠐⢿⡈⡾⣿⢃⡖⢻⣿⣦⣄⣾⣇⢷⠃⢀⡤⢠⡟⠛⢁⡄⠐⠁⠈⠙⣷⣶⠟⠞⠻⠦⣤⡄⠀⢤⣀⣾⣿⠁⣿⣟⣛⡉⢉⡽⡿⢾⣿⣽⣲⣾⣷⣿⡟
⠀⠀⢈⣿⣥⠿⠾⡇⢰⣟⠛⢻⣿⣾⣧⡏⣼⣷⣄⣠⣾⣃⣀⣠⡤⣰⢀⣹⣿⣤⣄⠀⠀⠙⢟⠛⢛⡻⣟⣫⣾⣼⡃⠸⢳⣾⢔⠕⡟⣽⡟⡹⢻⣿⣭⡶⠖
⠀⠀⡼⠋⠀⢠⣞⡋⠙⢿⣷⠟⢻⣭⡿⠇⠀⢩⡿⠿⡟⠹⠿⣿⣻⢿⣟⣛⣛⣾⣯⠻⢦⢴⣿⡷⢬⠛⢛⣿⡟⣹⣵⠾⢿⡷⠿⠾⣾⡛⠋⠻⣝⢦⡾⠁
⠀⣀⣄⣀⠀⢘⣏⣷⣖⡾⢿⣴⣺⣿⣳⡀⠐⠋⠀⠀⣰⠀⣴⡻⢿⡿⠛⢻⣿⠀⢿⣷⡶⣄⢀⡀⣼⣧⣙⢿⣱⣿⣵⣶⣾⣍⢂⡬⠶⢾⣄⡶⠛⠛⠃
⣾⠛⠳⡟⣿⠅⠚⠉⠉⠀⢀⣿⡫⣧⣾⢁⡦⠀⣤⢸⠁⠘⣱⠁⠀⠀⠀⠀⠛⠂⠘⢟⣄⠈⠻⣵⣌⠸⣟⠃⢻⣴⠛⠛⣿⣯⣿⣤⣤⣶⣿⣦⡀
⠻⣤⣸⣷⠏⢀⡼⢛⠳⢶⣻⣗⣺⢻⣿⠟⢁⢞⡷⠉⠀⠀⠀⠀⠀⢀⠆⠀⠀⢠⣄⠈⢿⡀⠀⢹⡷⡇⠈⠀⡾⣿⠳⠶⢿⡯⠒⢹⡿⢏⠉⢈⡇
⠀⠀⠀⠘⣏⠩⢤⣕⡿⠛⣁⠜⠏⢀⣿⡆⢨⡟⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠘⣿⡀⠀⠁⠀⠀⣿⡆⠀⢀⣿⡯⢿⡿⢿⣷⣤⣖⡻⠿⠾⠛⠁
⠀⠀⠀⠀⡿⢀⣶⠶⠾⣿⠋⢸⣿⢏⣿⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀⢿⠄⠀⠀⠀⣾⡇⠀⠀⠀⢰⣿⠀⠀⣼⣿⢿⣟⢁⢏⣜⡭⠛⢷⣀⠀⣠
⠀⠀⠀⠸⠿⢭⣀⠀⢰⠃⠀⠸⣴⢯⠿⣷⣄⠉⣙⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⣰⠉⢹⡀⣉⡻⣾⢡⣄⣄⣄⣹⡻⣿⡄
⠀⠀⠀⠀⠀⠀⠉⢷⡈⣠⡞⠓⠛⡐⣶⣹⣿⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⠀⠀⢿⣸⡿⣽⣻⣿⣿⡄⠈⣇⠈⠻⡍⢻⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⣿⣠⡾⢣⢹⣌⠛⣿⣇⠀⠀⣠⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠃⢸⡀⢠⢠⣿⠛⣉⡄⠉⢿⢇⠀⠸⣀⡤⣼⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡟⠁⢸⣬⣾⠉⣛⡋⢳⣀⢘⡬⠁⠀⢠⡞⠀⠀⠀⠀⠀⠀⢠⣀⡞⠁⣸⣿⠃⣷⣈⣓⣠⡾⠛⠛⠳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢧⡀⠀⠇⢸⠦⣸⣿⣟⡿⠻⣿⣁⠀⠀⠚⣧⠀⠀⠀⠀⠀⠀⢺⣏⠤⣶⡽⠋⣠⡷⣾⠋⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠤⢤⣌⣠⠏⠹⣯⣶⣤⠏⠙⣧⠀⠀⠻⣷⡀⢀⡀⢠⣷⢸⡆⠀⣷⢹⠚⢿⣟⠻⣶⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠉⠀⠀⠀⠈⠳⣤⣀⠹⡇⠸⣿⣶⣿⠀⢀⡴⢷⣨⣤⣌⣁⡷⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀⠀⣿⠛⣽⠛⠋⠀⠈⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡞⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠀⠐⠖⠷⠀⠀⠀⠉⠉⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠿⣿⠶⠀⣄⣀⣸⣄⣷⣄⣀⡀⠀⠀⠀⠀⢿⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⡶⢿⣯⣭⡷⣏⠀⠀⠈⡑⢲⣦⡀⢠⣶⣿⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠹⠎⣹⣿⠋⢠⡾⠓⡶⠾⢿⠇⢠⣾⡟⠛⠹⣿⣿⠋⠉⢀⣠⣴⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⢿⠉⠀⢿⠃⣀⢀⣀⣄⣀⢙⠗⠛⠋⠀⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠘⣿⡟⠛⣿⠿⣿⣿⣿⣿⣿⡿⢃⣤⣄⣤⣿⣟⣻⣁⣸⣟⢛⣳⣤⣤⣼⡿⣿⣿⣿⣿⠛⠋⣹⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣅⠀⠀⠄⠙⠿⣿⣿⣿⣧⡈⠾⣏⣈⣹⢛⣭⣛⣛⠛⣻⣿⣦⡀⠿⢧⣿⣿⣿⣣⣄⠘⠶⠻⣿⣿⣿⣿⣿⣦
⠀⠀⣰⠿⣦⡀⠈⠛⠋⢀⡀⠀⠀⠘⢛⣿⠿⠿⣿⡿⣿⢿⡏⢹⠷⠛⠛⣟⠃⢹⡄⢰⡇⢀⣿⣿⣿⡉⠀⣴⣤⡀⠹⣿⣿⣿⣿⣧⣀⣴⣦
⠀⠀⠍⢸⣿⣿⣤⣄⣠⡆⠀⠀⣀⣷⠟⠁⣠⡾⢿⣧⡾⠈⡳⠂⣄⠀⠀⣿⡆⠸⠸⠏⠉⣿⣿⣿⣿⣷⣄⢉⣉⣤⡾⠟⠋⠛⠛⣻⣧⡄⢷⣶⡆
⠀⠀⠀⠶⠟⢿⠉⠁⠀⠙⠛⠻⣿⣧⣀⣼⠟⠀⢸⣿⠃⠈⠁⠀⢹⡁⢰⣏⠀⠀⢠⡄⣿⣿⣿⠖⢀⠉⢻⣿⠟⠉⠀⢀⣤⢶⣿⡛⠻⠶⣄⠾⠃
⠀⠀⠀⠀⠀⠀⢱⣤⡆⠀⠀⠀⠀⠀⠛⠃⠀⣤⣿⣿⣯⠀⢷⡿⠃⢴⠀⣭⣕⠀⠹⣾⣿⣿⣿⣷⢮⡶⠿⠛⠢⠾⢿⠏⡁⢸⠙⠷⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠉⠸⢿⣮⣵⣆⣲⣤⣶⣤⣾⣿⣯⠹⣿⣷⣴⣢⣧⣼⣥⡄⡟⣱⣾⠇⢉⣉⣀⠀⠀⠀⢠⣼⣅⠲⣾⠁⣸⣧⣤⣶⢿⣯⣿⣿⡄
⠀⠀⡈⠀⠀⢀⠀⣴⠾⠋⠉⢉⣩⣭⣿⠏⡙⢿⣿⡀⢻⣿⣿⣿⣶⣾⣷⣾⣷⣟⣡⣴⡟⠉⢩⣿⡶⣿⠛⣿⡿⢦⣌⣀⣿⡏⠻⣿⠛⣿⢿⣏⡇
⠀⠀⠀⠀⠀⠈⠀⣿⠀⠀⠀⠀⢀⣤⣄⣠⣥⠊⢉⠀⣸⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣇⡀⠠⠙⠃⣨⠀⢸⣿⡀⠙⣿⣿⣿⣼⡛⠛⣋⣸⠟⡇
⠀⠀⠀⠀⠀⢲⡌⢿⣄⡀⠀⠀⠠⣤⣼⡿⠷⢶⣤⣶⣼⣿⣿⣿⠒⠈⢉⣭⣝⣻⡷⢋⠟⠛⠁⢠⠞⢃⡄⢸⣿⣷⣧⠘⣿⣽⣿⡁⠀⠈⢻⡆
⠀⠀⢄⣀⡄⠚⠛⢀⡿⠉⠿⢿⡶⢿⡇⠀⠀⠀⠀⣠⣿⣿⣿⣿⣦⡿⢿⣿⠟⢛⠃⠀⢀⣀⡀⠀⢠⣮⣠⠞⠋⢿⣤⡄⢉⡉⢿⣅⣶⣀⣸⣿⣠
⠀⠰⣾⣷⣶⣶⣾⣿⠃⠀⠀⢀⣠⣿⣿⠀⠀⠀⢀⣿⠏⣉⣩⣿⣿⣷⡿⢧⣿⣿⡷⣶⣉⡿⢩⣿⡀⣼⣿⣾⡿⠋⣉⣽⠟⢃⡘⠛⢿⣿⣿⣿⣿
⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣶⣦⣿⣿⣿⠀⠀⠀⣸⣿⠀⣿⡏⢸⣿⠋⣠⣾⣿⣿⣿⣿⣿⣷⣦⣽⣏⠛⢋⠉⣠⣾⣫⣴⡾⠿⠟⢳⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠻⠿⣿⣿⡿⣿⡿⠹⣿⣿⣿⣿⣟⠛⣿⣿⣶⢿⣧⣼⣿⣦⡸⠟⢡⣿⣿⣿⢿⣿⣾⣿⣷⣴⣽⡿⡏⢻⣿⣿⠶⣶⡶⠾⢿⡟⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⡗⢰⣿⣿⣿⣿⣧⢀⢿⣿⣿⣿⣷⣿⣿⣿⠻⣆⡀⠀⡊⠉⠾⠿⣿⠿⢟⣿⣼⡧⢿⣿⢹⣿⣷⣎⣛⢷⣸⠃
⠀⠀⠀⠀⠀⢀⣀⣿⠃⠘⠁⣿⣿⣿⣿⠿⣿⣆⢼⣿⣿⣿⣶⣤⡙⠊⠉⠻⣿⣿⣿⣶⣦⣤⡈⣀⣙⣿⣿⡵⠞⠉⠸⡿⢿⣏⣽⣾⠃
⠀⠀⠀⠀⠸⣿⣿⣷⣤⡈⠹⣿⣿⣿⣿⣦⠀⣻⡟⠛⣿⣿⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⢿⣶⢦⣤⡄⠖⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣷⣿⣿⣿⣿⣿⣶⣿⠃⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣭⣴⣶⣿⣿⣿⣿⠔⠃⠈⣿⣆
⠀⠀⠀⠀⠀⢀⡴⠿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⣠⣾⣿⣿⣿⣿⣿⣿⣏⣿⣟⣿⣶⣾⣿⣿⣿⡿⠓⠀⣁⣴⡿⠿⣿⣶⡆
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠊⠉⠹⠿⠿⢿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣟⣻⣿⣿⠿⠿⠋⠋⠙⠋⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡏⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⣿⠇
⠀⠀⠀⠀⢸⣦⠂⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⣿⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠀⣸⣿⠟
⠀⠀⠀⠀⠀⢿⣤⠀⡠⠀⠀⠀⠁⠀⠀⣀⠀⠀⣿⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⣧⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠻⠷⢤⠤⣤⣤⣤⣀⣈⣀⠀⠹⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣷⣶⣶⣶⡿⢦⣤⣴⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠙⠿⣿⣿⣿⣿⠿⠿⣿⣿⣆⠀⢰⣿⡟⠿⣿⣿⣿⣿⣿⠟⠋⠙⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⡀⠀⠻⣿⡇⠀⠀⢿⣿⣀⡀⠀⠀⠁⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⣀⣘⣉⣤⣤⣾⣿⠀⠀⠀⠈⠙⠻⣷⣶⣶⣶⣶⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⢿⣿⣿⣷⠀⠀⠀⢀⠀⠀⠀⠀⠸⣿⣿⣟⣛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡈⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠛⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣶⣷⣿⣿⣿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠀⠉⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢉⣢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡞⠁⠀⠠⠒⠋⠁⠂⠀⢠⡒⠊⠾⠾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡞⣀⠜⢁⠀⠐⢤⢀⡤⠐⢂⣽⣴⠃⢄⣨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠏⠀⠆⠰⢃⣸⣿⡾⠷⠿⠿⢾⠓⠺⢿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣘⡀⠟⠉⣻⣿⣿⢇⡰⣶⡷⠛⠿⠄⣰⣤⣁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠘⣷⣶⣿⣿⡿⢹⡌⠀⠹⣿⠁⠀⠀⠸⡆⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⣸⣿⣿⡟⠧⠔⠉⠂⠀⠀⠀⢀⣤⣄⠀⢄⠐⢧⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢐⣿⡿⣻⠃⠈⢀⠆⢤⣀⠀⢀⠁⠀⡦⠙⣮⣽⠏⠉⠙⣿⣆⣀⣀⠀⠤⠔⠚⠉⠀⠈⠉⠒⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠒⠸⢿⠒⠐⠃⠀⠀⠘⠁⠓⢾⢟⠓⠉⠻⠟⠚⠏⠀⠀⠀⢩⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠊⠀⠀⣀⡀⠀⣯⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠦⠤⠊⠀⠀⠀⠀⢲⣿⣛⠀⠀⢀⢀⠀⠀⣠⠀⡀
⠀⠀⠀⠀⢀⡠⠴⠃⡖⠒⠒⢒⣶⡃⠋⠛⠾⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣽⠗⠒⠒⣆⡹⠅⠾⢃⠘⠇⠀⠀⠐⠀⢰
⠀⠀⠀⡔⠁⠀⠀⠀⡇⠀⢀⣿⣓⠃⠀⠀⣠⠺⡟⠻⡷⣶⣎⣀⢀⠀⢀⠀⠀⠀⠀⠀⢁⡠⣝⢷⡞⠃⠀⠀⠐⠐⠂⠒⠲⠐⢢⡀⠀⠀⠀⠐⡏
⠀⠀⢸⠀⠐⠀⠈⠀⡇⠀⠸⣿⣿⡗⣶⣬⣥⠼⠃⠀⠀⢉⡿⠵⢿⠶⢼⢼⣴⣶⣷⣌⢷⡻⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣁⣼⠖⠴⡔⠉
⠀⣰⠋⠀⠀⢀⣺⠀⡇⠀⠀⠉⠛⠿⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⠈⠥⠆⠘
⢠⡟⠠⠐⡣⠈⠀⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠻⠇
⣽⠀⢀⡴⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠁⠒⠂⠀⠀⠀⠀⡇
⠸⣇⠈⠚⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠈⠛⠃⣂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⢁⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡗⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⣤⣤⣤⣤⣤⣤⣤⣼⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣮⣦⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡴⠒⠢⣄⠀⠀⠀⢀⣠⣴⡤⠶⠷⠺⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄
⠀⠀⠀⠀⠀⡄⠄⡀⠀⠐⠺⢇⡀⠀⠓⠀⠀⠈⢦⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣯⡤⡤⣤⣤⡤
⠀⠀⠀⣠⢩⠒⠅⠆⠐⠨⠀⠠⠧⠀⠀⠄⠀⠀⠈⢣⡀⠀⠀⡆⢀⡉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡀⡀⠀⠤
⠀⠀⢀⡁⠈⠀⢀⠅⠈⢸⡢⢷⠦⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⢭⡐⠁⠀⢀⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠚
⠀⠀⠀⢱⠀⢪⡀⠁⠕⡂⢀⡈⢁⡀⢠⡀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠸⣿⣿⡿⠃⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠿⠆
⠀⠀⠀⠀⡇⣧⠋⢧⠰⡆⠙⣺⣻⣇⡏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⡗
⠀⠀⡠⠄⠆⡈⠀⠘⠂⠹⠄⠘⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣠⡆
⠀⢸⣦⢾⢟⢈⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠛⠌⠀⠞⢀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠒⡲
⠀⢀⣦⣆⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠰⣿⡇⠡⠄
⠀⠀⠈⠁⣠⡿⠃⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠰⠂⢃⡴
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣲
⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⠃⣠
⠀⠀⠀⠀⠀⠀⣀⠀⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡯⠃⠀⠀⠀⣀⡀
⠀⠀⠒⠐⠂⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡿⠛
⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡶⠛⠋
⠀⠀⠀⠀⠀⠈⠺⢿⣻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠉⠀⠀⢀
⠀⠀⢀⡞⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢤⠀⠀⠀⠈⠀⠀⠀⠠
⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣆⣤⠀⠀⠀⠀⠀⠐⣾⣷⠂⠀⢀⡰⠒⠒⡄⢀⠔⣚⠉⠉⣓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠘⣆⠀⢠⣞⠋⢻⣆⠀⠀⠘⢧⠋⠛⠒⢦⣄⡀⠀⠈⠁⠀⠀⠀⠀⣀⡼⠁⠐⢨⠞⣋⡻⣎⢳⢷⡀
⠀⠀⠀⠀⠀⠈⠀⢸⠻⠶⠞⡟⠀⠀⠀⠈⠓⠀⠀⠀⠀⠉⠀⠀⠀⣀⡤⠄⠚⠁⠀⠀⠃⢹⣌⠻⠴⠟⡸⣾⠃⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⢋⡵⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡤⠤⠄⠀⣀⣀⠀⢀⠀⣿
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣠⣦⣷⣶⣿⣯⣉⠁⠀⠀⠀⠀⠀⢀⣠⣴⡿⣶⣿⡇⡟
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⣀⡤⠖⠋⠉⠀⡿⠛⠉⠙⠉⠙⠿⠇⠀⠀⠀⠀⠀⠛⠉⠁⠀⠁⠈⡟⢠⠴⣢
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠊⠘⡁⣀⠴⠀⠀⠀⠀⠀⣀⠄⣠⢀⠄⠀⠀⠀⠀⠠⠂⠀⢔⣶⢄⠀⠀⣸⣀⣚⡭⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠻⡏⠈⠢⠄⢀⠀⠀⠨⠕⠃⠈⠐⠛⢉⣈⡁⠀⠀⠀⠊⠑⠀⡀⠉⠩⠭⣥⣭⣛⠢⠤⠞⠁
⠀⠀⠀⠀⣾⣿⣿⣿⣿⠑⠛⢄⡐⠶⠛⠀⢀⡄⠠⠒⠀⠀⠀⠀⠉⢿⣧⣀⠀⠆⠀⠀⠉⣦⠀⠀⠀⠀⠻⣿⣄⡔⠀⡄
⠀⠀⠀⠀⢻⣿⣿⣿⣿⢦⣤⡤⠋⠀⢠⠀⠈⠆⢁⠀⠀⠀⠀⠀⠠⣒⡿⠙⠤⠶⠒⠤⠶⠋⠠⣄⣀⣀⣸⡿⠋⠀⢀⡇⠀⣀⡀
⠀⠀⠀⠀⠀⢹⠋⡩⠁⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠉⠒⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡾⠀⠀⠀⠉⠓⣄
⠀⠀⢀⣴⣾⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣦⣄⡀⠀⠀⠀⠀⢀⣰⠋⠀⠀⠀⠀⠀⢀⠞
⠀⠀⣾⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢓⣶⣤⠤⢒⣀⣠⡤⠴⣾⣿⣿⡿⠟⠉⠛⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠙⢿⣿⣿⣿⣷⣿⠄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣦⣤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠉⠉⠁⣿⣿⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⡔⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡇⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⣕⣄⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣶⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣇⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⣰⡀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠗⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⢿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠀⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⢀⡀⣀⡀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⠄⠂⠉⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠈⠁⠀⠉⠀⠑⠀⠀⢀⡠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠴⠊⢀⣀⣠⡄⠀⠀⢠⣀⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠁⠀⠀⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠂⢰⠋⠁⠀⠀⠘⠉⡎⠀⠀⠀⠀⠉⠑⢄⠀⠀⠀⠀⠀⠀⠁⠰⡚⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄⠈⠁⠳⡀⠀⠀⠀⢀⠔⠁⠀⠀⢸⠦⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠊⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡰⣂⠀⠈⠉⠉⠉⠀⠀⠀⠀⡠⠊⠀⠁⠀⠀⠀⡧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡤⠄⠀⢄⠀⠀⠀⢨⠆⠀⠀⠈⠑⠢⠤⠄⠀⠤⠄⠐⠊⠀⠀⠀⠀⠀⠀⠀⠛⢄⠈⠁⠀⠀⠠⠎⠉⢢⡔⠈⠉⠀⠄
⠀⠠⠈⠉⠁⠰⠂⠈⡁⠀⡐⠁⠀⢠⠚⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉
⡔⠀⢐⠀⢠⠃⠀⠸⠀⠀⠂⠀⠀⡄⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⠀⠀⡈⠀⠀⠠⠀⠀⠀⡴⠀⠀⢸⠒⠒⠂
⠑⠀⢠⠤⢤⠀⠀⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡌⠀⠇⠀⠀⡄⠀⠀⠀⠀⠀⢀⠖⠠⠠⠠
⢐⠁⠈⣀⡤⠆⠀⠀⠀⢀⡄⠀⠀⠀⠤⠒⠀⠁⢠⠃⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠐⠀⠈⠀⠉⠀⠂⠄⠀⡀⠔⠃⡠⡄⠀⢀
⠀⠁⠠⠁⢀⠔⠁⠀⠀⠀⠘⠢⠤⠔⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣀
⠀⠀⠈⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠳⢌⡑⠂⠠⢀⡀⠀⠀⠀⠀⡠⠠⠀⠀⠠⣀⡀⠀⠠⠀⠒⢉⡀⠄⠊⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⡀⠈⣉⠉⠉⠃⠀⠀⠀⢀⡇⠤⠄⠒⠂⠉⠀⠀⠀⠀⠀⠀⢀⠋⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠈⠑⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠆⠤⠍⣉⡁⠒⠠⠤⠀⠀⢠⠼⣒⣒⣀⣀⡀⠉⠩⠤⠄⠒⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠀⠀⠀⢀⣀⣀⡉⠀⠄⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠤⠧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠠⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠠⠀⠀⣇⡀⠼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠤⠔⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣐⣲⣤⣤⣤⣤⣤⣤⣤⣔⣒⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣐⣒⣠⣤⣄⣒⣒⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠙⡍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣫⡤⠶⢴⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡖⡒⠐⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠄⠀⠁⣑⡀⣰⣆
⠀⠀⠀⠀⠀⣠⣤⠂⢿⡿⠆⠴⠌⠭⣖⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠀⠁⠀⠀⠹⠏
⠀⠀⠀⠀⠀⠻⢿⣶⣴⣄⡀⠀⠀⣀⣿⣿⣿⠀⣹⡿⠛⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠊⠁⠀⠀⠀⠀⡠⠔⠛⠛⠻⢛⣉⣤⣶⣿⣶⣦⡀
⠀⠀⠀⠀⠀⢀⢴⣍⠛⠻⠟⣛⡻⠿⠛⣩⣄⠀⠀⠀⠀⠀⠀⠯⢬⠆⢐⣴⣿⣿⣿⠿⠟⠛⢋⣉⡠
⠀⠀⠀⠀⠀⢸⠈⠿⣿⣷⣶⣭⣵⣾⣿⠟⢁⠀⠀⠀⠀⠀⠀⣠⠃⢸⠁⠍⡛⠉⠀⢴⣾⡿⠓⠊⠁
⠀⠀⠀⠀⠀⠀⢱⣤⣀⣉⡉⣿⣉⣀⣠⣴⠊⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠈⠛⢻⠁⠀⠀⠀⠙⠟⠛⢄⠀⠀⠀⠀⠀⠸⡄⢀⡀⠀⠀⢀⣠⣀⣼⣧⡄
⠀⠀⠀⠀⠀⠀⠐⠒⠚⠀⠀⠀⠀⠀⠈⠊⠉⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠒⠒⠤⢄⡈⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠤⠄⠠⠤⠄⣀⠀⠀⠀⠀⠡⡀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢊⠤⠒⠉⠁⠀⠀⠀⠀⠌⣂⠄⠑⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡂⠀⠀⠀⢌⠀⠀⠀⠀⠶⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠤⡀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠐⠁⠀⣠⡀
⠀⠀⠀⠀⠀⠀⣀⢀⠔⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠢⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠈⠳
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡊⠁⠑⠄⡀⠀⠀⠀⠈⢆⠀⠀⠀⠠
⠀⠀⠠⡔⠀⠀⠀⠀⠀⠀⠐⠤⡠⠁⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠦⣀
⠀⠀⠀⢠⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⢀⠀⠠⢀⠈⠣⡀
⠀⠀⢠⠸⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢢⠀⠀⠑⢄⠘⠄
⠀⠀⢸⠀⠳⣀⠤⠀⠀⠀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⠀⠀⠀⠈⢇
⠀⠀⠀⢣⡀⠈⠃⠩⡉⣁⠤⠒⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠰⠃⠀⠀⢰⠇⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠑⢄⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠑⠲⠤⠖⠁⠀⠀⣀⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠤⠤⠴⠒⠋⠁
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠉⠉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⠈⠇
⠀⣀⠀⢎⠳⡀⡔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⢠⣎⠀⠘
⠸⣅⠑⢌⢆⣹⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡠⣴⠦⣌⡀⠀⠙⢦⡀⠀⢀⡴⠃⠈⢳⡀⡁
⡄⠀⠵⡶⠋⣡⠼⣄⣀⠤⠤⡀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠺⠻⣄⠀⠀⢳⡴⠋⠀⠀⠀⢀⣧⣥⣀
⠈⠉⠙⡇⠘⠁⠀⠀⢡⠒⠒⠃⠀⠀⣠⠴⠲⡎⠀⠀⣹⠤⠤⠼⢤⣄⣠⠆⠀⠀⠀⢰⡋⠁⠀⠈⢳
⠀⠀⠀⢳⣄⣠⢖⣩⡭⢳⠀⠀⢠⠎⣠⠀⢸⡀⣠⡾⠁⠀⢤⣄⡀⠀⠉⠓⢦⡀⠀⠈⢷⣄⠀⠀⣸⠃
⠀⠀⠀⠀⡜⡵⠋⠀⢳⡁⠀⠀⡇⠀⠑⢦⣀⠉⠁⠀⢀⢀⢀⣸⠛⢦⠀⠀⠀⠙⡆⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠂⠳⡀⠀⠀⠙⢦⣠⠇⠀⠀⠀⠙⢿⣭⣥⡴⣒⠟⠁⠀⠈⠂⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠤⡀⠀⢀⠔⢊⡝
⠀⠀⠀⠀⠀⠀⠈⠢⣀⡠⠊⣸⠀⠀⠀⠀⠀⠀⣀⣉⣉⣠⠄⠀⠀⠀⠀⠀⠀⢀⡟⢦⡀⠀⠀⠀⠀⠀⠀⠈⢃⠀⣁⠄⢰⡖⠅⠒⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠻⡙⠒⠶⠤⢤⡑⡖⠁⠀⢳⠀⠘⡦⠒⠂⠉
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠙⣆⠀⠀⠀⢃⠇⠀⢀⡜⠀⠀⢯⢭⣍⣉
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⢯⠲⢤⣽⢠⣀⣉⣠⠤⢦⡈⢣
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠁⠂⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⡸⠧⠀⠀⢀⠀⣀⠠⠤⠀⠀⢀⠀⢀⠘⡞⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠤⠄⠤⠤⠤⠤⢀⣀⠠⣿
⠠⠮⢤⣤⣄⣀⣀⡀⠀⠀⠉⠉⠉⠉⠀⠒⠒⣲⢖⠒⠒⠒⠒⠒⠒⠒⠂⠉⠉⠉⠉⠉⠀⠉⠉⠁⠀⠁⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠉⣉⠹⢏⣛⣒⣒⠒⣶⠒⠃⠈⠒⠒⠒⠲⣖⣉⣉⣉⣉⡿⢝⡓⠒⠒⠒⠒⠚⠛⠉⠉
⠀⠀⣀⡠⠔⠂⠉⠁⠀⠀⠀⠀⠀⡀⠀⢹⡄⠀⠀⠀⠀⠀⢰⡇⠀⡄⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠈⠉⠓⠒⠲⠶⠦⠶⠶⠶⠋⠳⠶⠚⠃⠀⠀⠀⠀⠀⠈⠉⠛⠛⠦⣄⡀⠀⠀⠀⠀⠙⢆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣶⣶⣶⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣅⣅⣤⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿