Chocolat Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡓⢒⡀⠀⠉⣁⣉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠠⠐⠀⠀⠀⠀⠀⠀⠀⠘⣅⢸⣭⣛⠿⢶⣿⣿⣦⡄⠈⠁⠠⢀⣄⡀
⠀⠀⠀⢀⡀⠀⠀⠙⢦⣀⠀⠠⠂⠉⠙⠦⣄⠀⢀⣠⠄⠀⠀⠀⢿⣮⣷⣍⠶⢧⣤⠛⢻⣿⣿⣶⣤⣀⠀⠀⠀⢀
⠀⠀⢠⡾⣦⡀⠀⢀⠄⠛⠳⣤⡀⠀⠀⠀⣬⡿⠛⠁⠀⠀⠀⠀⠘⣿⣞⢿⣦⡊⢩⠛⢧⡄⢛⣿⣿⣤⡀⢁⣀⠀⢑⡀
⠀⠀⠀⠙⢾⣟⢶⣄⠀⠀⠀⠀⢙⣷⣾⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣝⠿⣷⣶⣀⡸⠣⣤⠛⣿⡿⠯⠅⠊⠁
⠀⠀⠀⠀⠀⠉⠙⠻⣷⣦⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣬⣍⣛⠿⠬⢟⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛



⠀⠀⠀⠀⠀⠀⢀⣤⡤⣠⢔⣶⣛⣿⡔⣠⣤⢠⡄
⠀⠀⠀⠀⠀⢠⠌⠚⠑⠺⠏⠟⠓⠿⠽⠷⠟⠚⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠈⠦⠤⠤⠴⣶⣤⣄⣀⠀⢀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣀⣠⡶⠋⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣛⣾⣿⣷⣿⣿⣦⡀⠀⠀⠀⣀⣉⠄
⠀⠀⠀⠀⠀⣀⠐⠀⣀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢆⠀⠀⠀⠀⠀⠈⢯⣿⣽⣿⣿⣿⣿⣿⣧⣴⢿⣾⠇
⠀⠀⠀⠀⠀⠓⠒⠒⠒⠢⠤⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢟⣿⡉⠇⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⡤⡄⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⢠⣾⣿⣷⣦⣀⠀⠀⠀⢀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⢀⣿⡇
⠀⢀⣤⡀⠀⠀⠙⠿⣿⣿⣿⣿⣶⡄⢪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⢸⣿⡁
⠀⠘⢻⣿⣦⣄⣀⣀⣤⣽⣿⠿⣬⣿⣿⣿⣦⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢻⡗⠛⠛⠛⠉⠈⡿⠋⠛⠋⠉⢹⣿⡇
⠀⠀⠀⠙⢉⣿⣋⣍⠁⠀⠀⠀⠈⠙⠻⠿⣟⣿⣿⣦⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⠀⠀⣀⣀⣤⣾⣿⡟⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢸⣿⣯⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷⠟⠛⠉⠀⠛⠫⠅⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠳⣤⡤⠤⠤⢾⣶⣶⡶⡶⠶⠶⣧⠶⠶⠶⠦⣼⡿⣏⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢉⡙⠛⢿⠖⠉⠀⠀⠀⠈⠉⠀⠨⣍⡁⠀⠀⠀⢉⢴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠚⠊⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⣽⣟⣿⣶⣦⣄⣀⠀⣠⠎⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⡿⣭⣿⣿⣿⣽⡾⢣⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢬⣍⡓⠦⣭⣛⣿⡿⠓⢉⣠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⡷⠦⢽⣿⣧⣶⣿⡏
⠀⠀⠀⠀⠀⣀⣤⣼⣐⣶⣤⠀⠀⠈⠉⠓⠒⠀⠀⠤⠀⠭⠉⢽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣰⠛⠟⣿⠉⠻⡏⢧⡀
⠀⠀⠀⠀⡇⠘⠀⠁⠀⠀⢁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠶⠒⠀⠀⠔⠠⠄⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢰⣯⡀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠸⡄⠀⠀⡇⠀⢰⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠆⠉⢻⠈⢣⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠙⣷⡀⣿⣄⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠐⢆⠠⡀⢠⠈⠂⡴⠀⠇⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⢠⡈⢳⠀⡀⠺⠀⠘⠀⢰⠀⣤⠈⠁⠀⠀⢰⣾⡏⠉⠀⠀⠀⠀⣀⡆⠀⠀⣀⠤⠐⠈⠀⠀⢱⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⣇⡟⢘⠀⣅⢀⡔⣠⠶⠘⠛⠀⠀⠀⠀⠀⠘⢿⣷⣤⣦⣶⣶⠾⠋⠀⠀⠘⢿⣷⣶⣶⣶⡾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠠⠄⠀⠀⠁⣈⢉⠉⡀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⡿⠻⡿⠛⠿⢿⡿⢿⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠘⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⣴⠛⠉⠉⢫⢰⠀⠘⡇
⠀⠀⠀⠠⣀⠀⠀⠀⠀⣘⠀⢀⣠⣤⣤⠴⠶⠺⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⣼⠀⢡⠀⢀⡄⣦⣤⣿⣤
⠀⠀⠀⠀⢁⠐⠔⠀⠰⠥⠈⠉⠀⠀⠀⠀⠀⣠⠾⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⢀⣰⣋⠂⠘⠛⠉⠡⠠⠁⣠⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⡄⣤⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠠⣿⠩⠀⠀⢀⠠⠀⢀⣇⡃⢻⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣀⡤⠶⣒⣿⣭⡍⠐⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣧⡤⠾⠖⢛⣙⠽⠁⠈⡆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠧⣨⣋⡹⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣀⡚⣹⠛⠉⠀⠀⠀⠀⢳⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠉⠙⡄⠀⠀⠀⠀⠀⠀⠈⡆⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⣳⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⣇⠀⠀⢀⡠⠔⠋⢁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢀⠸⠶⠚⠁⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣦⣠⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣦⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣤⠤⠤⣤⠖⠊⠉⠉⠍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠤⠤⠒⠒⢴⠒⠉⠛⠋⠙⡏⠀⠀⠀⠀⠺⡄⠀⠀⠀⠀⢸
⠀⡤⣶⠖⠒⠒⠉⠙⡏⠉⠀⠀⠀⠨⡄⠀⠀⠀⠀⢸⡐⠀⠀⠀⠃⢻⠠⣀⠀⠀⠄⣇⠐⠀⣀⣀⣸⠇
⠀⣿⢹⠀⡀⠀⠀⠀⢱⡀⠀⠀⠀⠀⣇⢠⡀⠀⠀⠈⣇⠁⣐⣀⣀⣸⣤⠤⠤⠖⠒⢻⠉⠟⠙⠓⠊
⠀⢹⠈⡇⠁⠐⠂⣀⣸⣗⣀⣤⠤⠤⢿⠞⠒⠒⠒⠉⣿⠉⠉⠁⠀⠈⣇⠀⠀⠀⠀⠸⡄⡀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠠⠄
⠀⠸⠞⣿⠋⠉⠉⠉⠈⡗⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⣇⠰⠀⠀⠀⠀⠀⠅⠁
⠀⠀⢧⢹⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣇⢠⠀⢀⠀⠘⡆⠆⠀⠀⠀⢸⣌⣂⣀⡤⠤⢿⡟⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡃
⠀⠀⠘⡼⡇⠀⠀⠀⠀⢸⣠⠃⣀⣀⣁⣹⣮⠤⠤⠦⠔⢿⠒⠒⠋⠉⠙⣿⢀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠘⠋⠲⠒⠒⠒⠃
⠀⠀⠀⢧⣷⠖⠒⠒⠊⡙⣿⢍⠀⠀⠠⠘⡇⠒⠂⠀⠀⠸⡆⠆⠀⠀⠀⢸⡆⢀⠀⠀⢀⢹⡄⠀⠀⠀⠀⠀⠀⠈⣉⠟
⠀⠀⠀⢸⡸⡆⠁⠀⠀⠀⢹⡄⠀⠀⠀⠀⢹⡐⡀⠀⠀⠀⢿⠸⠤⠀⠀⠐⣧⠀⣀⣀⣀⣬⣿⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠈⣧⢳⢀⣀⡀⠀⠄⣇⠐⠀⠀⠀⣸⣧⣁⡠⡤⠤⢼⡶⠶⠖⠒⣛⣻⠫⠭⠥⠤⠀⠞
⠀⠀⠀⠀⠸⡼⡧⠤⠴⠖⠒⠿⠊⣉⣉⣩⣬⠩⠤⠴⠆⠒⠚⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠙⠓⠈⠉⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆⠒⠒⠒⠤⠤⠄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣶⠒⠒⠒⠒⠶⠖⠠⠤⠤⡄⠀⠀⠛⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⠄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢺⠀⠀⠀⠀⣠⣤⠀⣤⢠⡤⠐⠁⠀⠀⠀⠀⢀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠀⠀⠀⠀⣔⡆⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠀⠀⢀⡟⠀⠀⣿⢸⠁⣷⠀⠀⠀⠀⠀⠉⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠠⠤⡀⠀⠀⠁⠆⠀⢆⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⢸⡇⠀⠀⡿⣿⠀⣿⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢺⠀⠀⠀⢸⡇⠀⢠⡇⣿⠀⡏⡳⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⣹⠀⠀⠀⠀⠙⠂⠘⠁⠟⠀⠿⡼⠦⠀⢴⣤⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠁⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠉⠑⠒⠒⠲⠦⠤⢤⣤⣄⣀⣀⣀⣀⣈⢢⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠰⠦⠴⠀⣄⣠⣀⡀⣀⣀⣁⢉⠹⣍⠛⠟⠙⠑⠒⠒⠒⠲⠒⠢⠤⠤⠤⠤⢤⢀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠃⠒⠒⠀⠤⠤⠤⠄⠀⠀⠀⢀⣀⣀⣀⠎

⣿⢿⠿⡿⠿⢿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣿⣿⣟⣻⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⡄⠉⠀⣿⣦⠀⢰⠀⠀⠀⠀⠀⠀⣯⣄⠀⢸⢰⣆⠀⣷⣠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣽⣤⣤⡤⣿⡤⣬⢼⠀⠀⠀⠀⠀⢸⣧⣬⣥⣼⣼⣥⣤⡩⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⡇⣦⠀⣿⠒⠀⢸⠀⠀⠀⠀⠀⢸⡇⠐⠀⢸⠀⠀⠀⣇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠷⢶⠶⢾⠶⠶⠶⣧⠶⠆⠈⠀⠂⠀⠀⠀⢸⡧⠦⠤⢨⢤⣤⠤⡡⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡂⠀⠀⠀⠀⢤⢸⡇⢠⠄⢸⠐⢀⠀⣿⠗⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡜⠁⠀⠀⠀⠀⠄⢸⣧⡦⠲⣼⠴⠮⠤⡥⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⡿⢿⠄⢿⡽⠗⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣷⣾⣿⣿⣿⡶⠟⠋⠉⠀⠀⠀⠀⠀⡷⠚⠒⣞⠒⠒⠒⡖⠒⠒⢺⠀⠀⠀⠀⠀⣀
⠀⠰⣆⠉⣀⣠⢴⣶⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⡀⠀⠀⠀⠀⢀⡟⠀⠀⠛⠠⠂⠀⡇⠀⠀⠨⠀⠀⢠⣶⡃⠀⣀⣠⣠⡄
⠀⠖⠉⠉⠁⠀⢸⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⡟⠛⠛⣿⠛⠛⠓⡞⠋⠛⠣⠀⠀⠀⠉⠙⠾⠿⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣌⣀⣀⣀⣀⣀⣀⣀⡠⠀⠀⠀⠀⠀⠘⣇⢀⣀⣉⠀⠀⢀⣇⣀⣀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣤⡤⠼⢷⡶⠖⠒⠓
⠀⠀⠀⢀⠀⢠⣮⣭⣿⣟⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢴⡀⠀⣙⡧⢤⣤⠐⠀⠀⠀⠀⠙⣧⣠⣄⣤⣤⡿⢩⢶⣶⡾⠧
⠀⠀⢾⣿⣷⣾⣿⣯⣈⣛⡿⠿⠛⠿⢾⡄⠴⣖⠀⠻⣯⣠⠤⠖⠙⠿⣁⢀⣀⠽⠢⣒⠆⠀⠀⠀⠻⠟⠛⠋⠁⠈⠉⠈⠁
⠀⠀⠀⠙⠻⣿⣿⡛⠛⣾⣿⣿⣦⣚⣭⠖⠛⢛⠯⠄⠈⢻⣷⣴⡲⡖⠁⠻⢯⣀⣤⣬⣳⣾⣿⡋
⠀⠀⠀⠀⠀⠀⠙⠻⠌⠁⠈⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣶⣿⣿⠿⠿⠟⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣦⢰⡇⢸⡆⣴⠛⣦⢰⡞⢷⡄⡾⢻⡆⣾⠀⠀⢠⣿⡆⠺⣿⠓⢸⡟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⢸⣧⣼⡇⣿⠀⣿⢸⡇⠈⠨⡇⢸⡇⣿⠀⠀⢸⠛⣇⠀⣿⠀⢸⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡿⢸⡇⢸⡇⢿⣀⣿⢸⣇⣼⠆⣧⣸⡇⣿⣄⣀⣿⠒⣿⠀⣿⠀⢸⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠈⠉⠀⠈⠉⠁⠁⠀⠈⠀⠁⠀⠈⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⡭⠙⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠠⠁⠠⡿⠙⠦⠒⠒⠒⠶⠤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡐⡼⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡴⠤⢀⣀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠄⡜⠀⠀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠊⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⡀⠀⠌⡜⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠨⠁⠒⠒⠒⠂⠀⠀⡀⠀⡀⣀⣀⠎⡜⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠀⠀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⠂⠀⠀⠀⠀⠈⠉⠉⠁⢰⠋⠉⢹⢃⡞⠀⢀⡾⣉⠀⠉⠐⠒⠒⠢⢤⡤⣀⣸⣀⣴⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠠⢁⡞⠀⠀⡼⠁⠀⠉⠉⠒⠂⠀⠚⠁⠀⢀⠝⢋⠤⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠁⠀⠀⠀⠀⠀⣀⠠⠀⠀⢴⣠⡀⠠⢁⡞⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠁⠈⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⠊⠀⠁⠀⠒⠀⢤⡇⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠘⠋⠀⠐⠂⠀⠀⠀⠀⠄⠤⠊⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠞⡄⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡶⠖⠶⠤⣤⣠⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⣼⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡇⢸⠃⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠠⠌⠁⠀⢀⣀⠀⠀⠀⠐⠀⠄⠀⠀⣼⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠘⠀⢠⡇⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⣾⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠤⠤⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠹⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠶⠶⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣠⠁⠀⠀⠰⠃⠀⠀⠘⢲⡄⠀⠃
⠀⠀⠠⡀⠀⠔⠂⠒⢂⠠⠚⠤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠙⣗⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠤⡐⠀⠀⠀⠈⠑⠃⠀⠀⣀⠀⠀⠀⢀⣀⣀⡠⠃⠀⠀⣐⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠇⠀⠉⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠘⠈⠓⠲⢞⠈⠀⠀⢄⠀⡀⡠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣰⠃⠀⠀⢀⠎⠀⢀⣀⣀⠀⠁⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠧⣄⣀⣠⡎⠀⠠⢟⠗⢟⣷⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠐⠦⠤⠄⠄⠠⠓⠀⠀⠘⠲⠤⠄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣤⣤⣷⠄⠀⠀⠀⠀⣀⠀⢠⣿⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠰⣠⠤⣴⣫⢿⣫⣵⠿⢶⡄⠀⠈⠻⡷⣄⠌⠓⠤⢙⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠙⠿⠟⠒⠛⠉⠛⠟⠛⠠⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠰⠀⠀⠰⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠀⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠒⠒⡀⠐⢤⡀⠈⠀⠀⠀⣀
⠀⠀⠀⢐⠄⠀⠀⠠⡀⠀⠀⠠⠆⠀⠀⠀⣴⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠘⢦⡀⢴⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠀⣦⠀⡀⠀⡹⠦⡀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠈⠁⠀⠠⠊⠀⠈⠢⣦⠖⠀⠀⠀⠠⠀⢀⠐⠠⠄⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣤⡴⠊⠁⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡔⠚⠉⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠉⠉⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⣠⣤⣶⡾⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢀⣀⣠⣴⣶⡿⠦⠘⠋⠭⠐⠂⠁⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢀⠀⠀⠀⢀⣘⣿⣄⣰⠿⠛⠋⠉⠐⠂⠱⣦⡀⠈⠄⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢈⣦⣶⣾⠿⠛⡩⢭⣄⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢆⠀⠀⠀⢀⣨⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠸⠋⠅⠒⠈⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠈⣶⡾⠿⢛⣫⠕⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⣀⣠⣴⣶⠿⠟⠛⢃⣥⣶⣿⣿⣽⡧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⣀⣤⣼⣷⡴⣛⣩⣵⣖⠩⠿⢍⣽⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢸⣿⠟⣛⣫⣴⠒⡿⣏⣻⣯⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡁⡼⢿⣿⣿⣿⠷⠞⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠉⠁




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠋⠁⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂⠙⢶⡉⢦⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠉⠀⠀⠀⠀⠈⢷⡀⣱⠄⣤⣤⣐⢚⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡛⢷⡀⠀⠀⢀⣠⡼⢿⠇⣰⡟⢠⠋⠉⠛⢷⣄
⠀⠀⠀⠀⢄⠜⢆⠀⠀⠀⠀⠀⠀⢣⠈⢻⣶⣾⢿⣧⠶⣿⢰⡿⠁⠏⠀⠀⠀⠀⠀⢹⡀⠤
⠀⠀⠀⠀⠀⠙⣄⢣⠀⠀⣀⣤⠖⣻⣧⣻⣿⣞⠉⠀⠀⡟⣽⣣⣾⣄⡀⠀⠀⠀⢠⡟⠀⠀⠀⠈⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠈⢇⣽⣯⣥⠾⠛⠉⠀⠹⣿⣋⣧⡀⠀⣡⠿⣿⣿⣿⣿⠗⣶⣤⡿⠀⠀⠀⠀⠀⠀⠀⣼⡅
⠀⠀⠀⠀⠀⠀⠀⠈⢫⡙⡄⠀⠀⠀⠀⠀⠘⣷⣭⢳⣴⡏⢠⠋⠛⢿⣿⣿⣿⣿⣧⣴⣄⣀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠘⣄⠀⢀⣀⣤⣴⣾⣿⡿⢹⢀⠏⠀⠀⠀⠈⠙⣿⣿⢿⣿⣾⣭⣛⠶⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢨⣿⣿⣿⣿⣿⣻⠿⡧⣇⡄⠀⠀⠀⠀⠀⣼⣿⠃⡼⠁⠉⠛⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣋⡥⠞⠈⠀⠀⡗⢿⣿⡶⢦⣄⡀⣰⣿⡟⣸⠁⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠛⠉⠛⠻⣷⣬⣝⢻⡟⣩⣇⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠤⠀⣄⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠛⠻⠋⠗⠦⢤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣦⢶⠖⢚⣉⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠋⠉⠉⠉⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣏⠀⠉⠒⠠⠀⠀⠀⢀⣠⡤⠖⠊⠁⠀⠀⢀⣀⠼⣃⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠨⣍⣒⠤⢀⠀⠀⢰⠁⠀⠀⣀⠀⠀⢀⣩⠤⡶⡺⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⢀⠢⠈⡏⠂⢀⣀⠚⠖⣋⣡⢤⢤⠞⠁⣈⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣦⣀⠀⠀⡇⢸⠋⠁⠀⣤⢋⣠⠴⠿⠞⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢹⡍⠻⡷⠦⣄⣸⣤⡤⠚⠉⠁⠀⠀⠀⣀⣁⣤⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠀⠹⣄⡿⠢⡈⠰⠧⠄⣀⢀⢀⣀⣠⣤⡤⠴⠒⢒⠖⢩⡽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢀⠀⠙⢇⠀⠙⢶⠒⠛⠉⠟⠋⠀⢸⡟⣀⡔⢀⠊⠐⣀⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠢⠴⠯⡿⠉⣹⠂⣌⠢⡘⢸⠀⠠⠀⠀⣠⢤⠮⠚⠛⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢱⣟⡆⠀⡐⠀⠀⠑⢆⡜⡇⠉⠈⠉⠉⠉⠀⠠⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠁⠈⠷⠁⠀⠀⠀⠐⠀⠒⠿⠟⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣲⠄⠀⠀⠴⠦⠶⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠉⠀⣰⠆⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠋⠉⠉⠒⠂⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠠⠤⠷⠧⠤⡤⠤⠀⠳⣀⠆⠀⠀⠰⣏⡂⣖⠀⠀⠀⣀⠈⡍⠁
⠀⠀⠀⢀⡀⠀⠠⠔⠂⠀⠀⢀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠒⠀⠦⠤⠄⠒⠂⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠈⠛⠋⠉
⠀⠀⠀⠨⡀⠲⢄⣀⢠⡴⠚⠋⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠒⠈⠿⣠⣒⣦⣅⡵⡀⠨⠐⠀⠀⠀⠀⠀⠒⠁⢀⡁⣄⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢔⠀⢀⠀⠀⠀⢠⡆⠄⣤⡀⠀⠀⠀⠀⠐⡦⠈⣶⡬⠔⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠰⣌⠀⠀⢐⣀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⢰⡅⠠⡔⡄⠤⠁⠔⠉⠔⡀⠀⠀⠀⠘⢆⢛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⢦⣱⡀⠀⠴⢂⡄
⠀⠀⠀⢀⣀⣀⣈⠀⢠⠥⠒⠂⠀⠀⢬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣡⣴⢺⠿
⠀⠀⢀⠂⡴⢀⠌⠾⠃⠀⠀⢬⣴⣤⣈⠼⡦⠃⠀⠀⠀⢀⡠⠤⠢⢂⠠⠴⢊⠍⠁⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠠⠠⡀⡀⠀⠀⠀⠙⠉
⠀⠀⠘⠶⠶⠾⣇⡀⣀⣵⠠⡶⣜⣩⠜⠀⠀⠀⠀⠀⠀⠀⡴⢘⣉⣠⠤⠚⣁⣀⣄⣀⠀⠀⠀⠀⠀⢸⡀⠉⠀⠒⠳⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠽⠛⠊⢁⢉⢀⠨⢄⢈⡇⠀⠀⠀⠀⠀⠷⢃⣀⣀⣀⣄⡀⢷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠤⠴⠾⠶⠒⠋⠉
⠀⠀⢠⠀⠒⡛⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠈⡀⠠⠄⠈⠾⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢯⠀⠀⠀⠀⢠⡋⠀⠄⠀⠀⠂⠈⠀⡀
⠀⠀⠀⢙⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠓⠂⠈⠀⣀⠒⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⣸⠏⠀⠀⠀⠀⠘⡴⠀⠂⠄⠲⡑⠚⣠⠖
⠀⠀⠀⠈⣆⡀⠀⣀⠴⠣⠀⠀⠀⠀⢠⢴⢤⣀⡠⠜⠃⣀⡈⠀⣠⡶⠀⠀⠀⠀⠀⠠⣉⣀⣤⠔⢢⠎
⠀⠀⠀⠀⢙⠋⠀⠀⠀⠀⠁⠀⠀⠀⠘⡀⡀⢠⢍⠠⠶⠒⢦⠚⠘⠓⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢧⡀⠐⠂⣀⠽⠀⠀⠀⠀⢇⠀⣠⣀⣀⡀⠤⠴⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠠⡀
⠀⠀⠀⠀⠀⠈⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⢤⡒⠚⠉⠁⠙⢧⠀⠀⣀⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢴⡒⢞⠉⠁⠙⣄⠀⠀⣀⣄⣱⣀⣤⠾⠷⠾⢿⡉⠉⡉⠈⠢⡀
⠀⠄⠀⠀⠒⠂⢀⠀⠀⠀⠀⠀⢀⡄⢀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠸⢷⡀⠀⠀⣈⠳⣤⣤⣤⠶⠾⢶⠛⠛⡉⠁⢻⡀⠀⠀⢀⣀⣻⣠⠤⠴⠷⠓
⣄⠤⢄⡠⠀⠠⠘⢆⠀⠀⠀⠀⠋⠀⠀⠀⠉⠑⠁⠁⠀⠀⠀⠀⠀⡈⣷⠚⠛⠋⠉⢩⠀⠠⠀⠀⠀⠄⠀⣁⣤⡶⠷⠔⠋⢉⠁⠀⢀⡄⠠⠤⠔
⠰⠀⠤⠤⠔⠇⠐⠀⠀⠀⠀⠀⠠⣦⡅⣡⣀⣮⡀⠤⠔⠁⠀⠀⠀⠘⡇⠣⢀⣀⣠⣤⠧⠔⠚⢛⠉⠉⠁⠀⢀⣠⠾⠤⠾⠃⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠑⠄⠂⠘⢛⠁⡄⠀⠀⠀⠀⠀⠀⠹⣾⠉⠁⣀⣀⡴⠶⠄⠒⠛⠓⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣄⡀⣉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠚⠛⠉⠉⠙⠓⠲⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣤⣀⣀⣠⡞⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠉⠉⠛⠛⢳⡾⢿⣿⣷⡶⢤⣄⣀⠀⠀⢀⣀⡤⠴⠒⠊⠉⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡜⡽⣷⡀⠀⠉⢻⡟⠉⠀⠀⢀⣀⠤⠐⣢⠼⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⣨⠞⠁⣮⢻⣶⠄⠘⠀⠤⣒⡩⠵⠒⢲⡞⠃⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⡀⣼⢻⠀⠀⢳⡾⠋⠙⠶⠞⠉⠉⠀⠀⠀⣸⣠⣴⣊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢀⠞⣠⠇⢸⠀⣠⣿⣧⣄⠀⠀⠀⠀⣀⣤⣴⣾⠟⠋⠀⠈⠶⣤
⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⣰⢋⡴⢷⡀⣸⡿⠉⠛⠛⠛⠻⠷⠾⣏⡉⠝⠋⠀⠀⣀⠔⢀⡞⢹
⠀⠀⠀⠀⠀⢀⣼⠋⠉⠛⠒⠶⠤⣄⣀⡀⠀⠀⠈⠀⢀⡼⣡⢿⡄⠀⣱⣿⣧⣤⣄⣀⣀⠀⠀⠀⠀⢹⠀⢀⠴⠊⣠⡞⣹⠀⢸⡄
⠀⠀⠀⠀⠀⢾⢯⣍⣒⠢⠤⢀⡀⠀⠈⠉⠻⣆⠀⣠⠟⣰⡏⠈⣧⣾⡟⠛⠛⠓⠲⠤⢬⣭⣍⣁⠀⠀⠀⣁⣴⠟⡟⢰⣁⡴⠋
⠀⠀⠀⠀⠀⠈⣆⠀⡉⠙⡛⠢⣄⣀⠀⠀⠀⠿⠾⢋⣴⢿⡇⢠⣿⣿⣥⣀⣀⠀⠀⠰⠋⠛⠋⠉⠉⠉⠛⢻⠁⢀⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠘⠲⠷⢤⣼⣦⣀⠈⠻⣶⡖⠦⢤⣾⠃⠀⢸⣿⠏⠉⠉⠉⠉⠙⠛⠒⠶⠦⢤⣤⣔⡂⠀⢸⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣕⣀⠈⢿⠳⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠀⣠⠞⠛⣶⣄
⠀⠀⠀⠀⠀⠀⡀⠒⠒⣒⡿⣧⡠⠚⣋⣉⡽⣧⡀⠀⠀⠀⣠⠞⠁⠀⢄⢈⣿⢷
⠀⠀⠀⠀⠀⠻⣤⣔⣊⣽⣟⠁⠐⠋⠁⡸⠳⡈⣨⡗⠀⢸⠓⠀⠀⠤⠟⠉⢸⣻⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠐⠒⠂⠲⠟⠛⠀⠀⠀⠉⠑⠒⠒⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⠋⠒⠲⠊⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠢⠀⠀⠀⠐⠠⣀⠀⠀⣠⣴⡩⠊⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡛⢡⡄⠐⠀⡀⠀⠀⠀⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣅⣼⡀⠬⠦⢀⣀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠢⡐⠇⠰⠆⠁⣀⣀⠔⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠃⠀⠀⠈⠲⢜⡠⢠⠉⣰⠦⡀⠂⠈⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⡰⠚⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⡄⠀⠀⠀⠀⠀⠀⠀⠑⢄⡰⢁⣒⢘⠒⢄⠀⠀⠀⠁⠀⠄⠊⠀⣀⡌⢑⢠⢀⣾
⠀⠀⠀⠀⠀⠀⢠⡊⠁⠀⠶⠈⠀⠀⠀⠀⠀⠀⠀⢀⠔⡠⠟⠷⣭⣎⠠⠆⡉⠢⢄⠀⠀⡀⡀⠾⢩⡍⢲⠼⠋
⠀⠀⠀⠀⠀⠀⣼⠃⠂⠤⠄⣀⡀⠀⠀⠀⠀⠀⡀⠔⠋⠀⣀⠼⡋⣤⠀⡀⠁⣾⢛⡡⠒⠏⠲⢆⡠⠞⠁
⠀⠀⠀⠀⠀⡼⠥⠀⠀⠀⠀⠀⠀⠉⠙⠁⡂⠁⠀⢀⠤⢚⡙⠘⣣⠴⠊⠉⠲⣍⡸⠂⣤⠁⡴⠊
⠀⠀⠀⠀⠀⡇⣠⣀⠛⣀⠀⢰⠀⡀⠤⢀⣼⠄⠾⢀⣠⢌⡵⠋⠁⠀⠀⠀⠀⠈⠻⢶⡴⠟⠁
⠀⠀⠀⠀⠀⠓⠒⠒⠤⣙⣁⣈⠴⠄⠘⣁⠀⠸⡃⣂⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠲⢤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠄⠤⠤⢠⠀⠤⣴⠂⠉⠉⠉⢀⢀⢀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣧⠀⠀⠂⠌⡠⠡⢂⠂⠂⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⣾⣧⠹⣧⠠⠈⠐⠱⠡⡠⠡⠠⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣐⠤⠉⡙⣧⢱⠁⠡⠀⠀⠀⠐⠀⢀⣀⡀⠹⣧⡀⠀⠄⣰⣒⣶⣶⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⡶⢤⣄⣈⠛⣧⠡⢠⣀⣤⣭⣿⣿⣿⣿⡿⠿⢿⣿⠟⠛⠛⠋⠋⠉⠉⠉⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠉⠓⠷⢄⣸⡩⢻⣆⢣⢟⠋⠉⠉⡀⡀⡠⠀⡠⠠⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠷⠢⣀⠀⠀⠉⠙⢻⣆⢫⣆⢂⠀⠀⠔⠀⠀⠐⡀⡀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠈⠮⡙⠓⢦⣭⣜⣿⡎⢯⡄⠂⠈⠀⠈⠀⠀⠐⠀⠀⢻⣇⠀⠀⢀⣀⣠⣤⣀⠄⠀⢧
⠀⠀⠀⠀⠀⢸⣿⣟⠷⣦⡀⠀⠀⠀⢀⡀⠤⣐⡺⠭⣿⠛⡌⣧⠀⠀⢠⣤⡶⠶⠶⠶⠶⣤⣋⣀⣤⡤⠥⠔⠒⠚⣓⣛⠟⢀⣀
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣮⣍⢀⠐⡈⠤⠚⠉⠁⠀⠀⠀⠉⢻⣼⣧⠤⠴⠶⠶⢒⣚⣉⣩⣭⡭⢤⡔⡒⠒⠛⠋⠉⠉⠁⠘⡁⢠⢼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣬⡳⣦⣄⡀⠀⠀⠀⠀⠀⢋⣉⠉⢻⡛⠉⠉⢉⣩⠐⣒⣉⠉⠄⠀⠈⠲⣄⠀⠀⢠⡖⠀⠀⠈⣾⣏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣍⠻⠦⠀⠀⠔⠊⠁⠠⠴⠊⣵⠀⠀⣿⣜⠳⣦⡐⠁⠀⠀⢀⠠⠈⣱⠀⠙⠀⠠⠤⠤⠼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⣄⢠⡄⠈⢢⡀⠱⠀⠉⠀⠀⠹⢿⣷⣌⠓⠄⢀⠀⠀⠴⠷⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡈⠅⠐⠉⠀⠀⠀⠀⢼⠄⠀⠈⠻⣿⣷⣴⠀⢠⣾⣧⢔⣽⡂⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⡀⠸⠋⠀⠘⠿⣯⣶⡎⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣄⢠⡀⣠⣄⢀⣤⡀⣠⣄⢠⡀⠀⣠⡀⣤⣤⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⣿⣼⣿⡇⣿⣻⠈⠓⡇⣿⢸⡇⠀⡿⣇⢸⡇⢸⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠇⡿⢸⠟⣧⡿⢺⣴⠗⣧⡿⢸⣥⣼⠗⢿⢸⡇⢸⣤⡄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠦⠤⠤⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⡽⢧⡠⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⡀⠀⠀⠀⠈⠉⠉⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠂⠀⠤⠀⠀⠀⠀⡀⠀⠀⡰⠁⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⣀⠀⠀⠀⠀⠀⠀⠐⠀⡰⠁⢠⡞⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠒⠒⢩⠗⠒⠞⡰⠁⢠⣟⠁⠀⠠⠤⠤⣄⢀⣨⣠⣴⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠗⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⡴⠁⢠⡏⠀⠈⠁⠒⠐⠊⠀⡠⢙⠥⠚⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠅⠀⠀⠀⢀⡖⠀⠀⠓⠂⠤⠼⢁⠀⡿⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽
⠀⠀⠀⠀⠀⠀⠀⡯⠂⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡰⡀⠀⠀⠀⠁⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡶⠒⠦⢤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣶⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⢠⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠊⡞⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠤⠤⠤⣄⣀⣀⣀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠛⢓⡒⠒⠲⠶⣶⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡟⠀⠀⠀⠀⠀⠀⣸⡏⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⣮⣅⣀⣀⣀⠀⠉⠉⠉⠉⠙⢛⡻⠋⢐⡂
⠀⠀⠀⠀⠀⠀⠀⢀⠨⡏⠀⠀⠐⠦⠄⠀⢰⡿⠀⡏⠙⠛⠶⣦⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠍⠉⠋⢉⠉⠙⠛⠓⠒⢦⠀⠐⠙
⠀⠀⠀⠀⠀⠀⠀⠞⠛⠛⠳⠶⠶⠾⠯⠽⣾⣥⣼⣇⡠⡤⣶⠷⠟⠋⣱⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⣾⣶⠶⢤⣤⣀⣄⣄⠀⠀⣘⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠷⡾⢶⣶⣶⡦⠴⠤⣤⣤⣠⣾⡿⠗⠋⣁⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⡞⠉⠋⠙⠋⠉⠉⠉⠉⠉⠍⠉⢉⠉⠉⠉⢁⡄
⠀⠀⠀⠀⠀⠀⣀⠺⡿⢷⣭⡛⠷⣤⣴⡿⠟⠋⢁⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⡿⠿⠿⠟⣛⣿⠿⠛⠛⠛⠋⠋⣉⠹⠏⠁
⠀⠀⠀⠀⠀⢾⣭⣛⡛⠿⢿⣽⣷⣼⣄⣠⡴⠚⡻⠋⣠⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢀⡔⠉⠀⠀⢀⡤⠤⠐⠂⠉⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢦⣍⡉⢻⠋⠠⢊⣀⣠⣉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠼⣀⠤⠐⠊⠁⠠⣆⡍⠄⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠘⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣀⠉⠁⠉⠉⠉⠉⠁⢬⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⡀⡐⠶⠒⠂⠈⠉⠳⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣄⠀⠀⠀⠀⠀⠀⠨⠗⠲⠦⢤⡄⡄
⠀⠀⠀⠀⠀⠀⣀⣠⡤⣤⣾⣿⣷⣾⣶⣆⡀⠐⠉⢥⠤⠤⠉⠙⠗⡂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠑⠻⢿⡇⠀⣀⣀⣀⣤⠤⠄⠄⠀⡾⠀⡄
⠀⠀⠀⠀⠀⠀⣿⣧⣭⣢⡈⠻⡿⢿⣿⣿⣿⣷⣤⠀⠀⠀⢀⣀⣠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣀⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠐⢶⡄⢀
⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣦⣤⣀⠑⢝⡻⠿⣿⠤⢖⠛⣉⣡⡙⠻⠂⢄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣏⡹⣟⢿⡓⠒⢶⣶⣤⣤⣤⣀⠤⠿⠃⠈⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠙⠻⢿⣿⣧⣕⣤⡙⠦⠐⠈⢒⣋⠭⠅⠐⠒⠈⢩⠀⠀⠀⠀⠀⠀⠦⠄⠙⣿⣿⣌⠳⣍⠩⠍⠀⠈⠁⠀⠀⠀⣀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⣉⢁⣀⠀⠙⠻⢿⣿⣿⣷⠊⠉⠁⢀⣀⡠⠤⠒⠊⠈⠀⠀⠀⠀⠀⠀⢠⡀⠀⠘⣹⡟⠉⠁⠀⢀⣀⠠⠄⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠒⠶⡶⠎⠙⠻⠆⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⠧⠀⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⢤⣄⣀⣒⣤⡤⠬⢥⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢤⣤⢤⣠⣤⣤⡤⢶⣖⣶⠛⠛⠒⠚⠋⢹⣿⡏⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠤⠄⠒⠒⠀⠉⠉⠂⠀⠀⠉⠁⠀⡄⡊⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⢶⠄⠉⠒⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⢹⣿⡂⠀⢀⣀⣀⣠⣿⣿⡤⠴⠶⠖⣒⡚⠻⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣧⠤⠶⣶⡒⠲⠟⣯⣋⣛⣩⣭⣥⠴⢶⣿⡾⠒⠚⠛⠋⠉⢻⡇
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣻⣽⠶⠒⠚⠛⠉⠙⣿⡿⠁⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣀⣀⣀⣠⣿
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⡆⠀⢀⣀⣀⣀⣿⡿⠦⠤⢴⡶⠒⠲⠛⣝⣛⣙⣩⣬⣭⠴⣶⡁
⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡰⢟⣿⡛⣉⣉⣭⣽⠶⢤⣿⡽⠓⠒⠚⠛⠋⢻⣿⡏⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠙⣿⣿⠉⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⣿⣿⠤⠀⠤⣀⠀⠀⣿⣿⠀⠀⢀⣀⣀⣠⣿⣿⣤⠴⢶⣒⠲⠾⠿
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⣠⠟⢆⠉⠀⠀⠀⠀⠀⢀⠁⠲⢟⠿⠛⠋⠉⠉⠑⠂⠀⠉
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠒⢋⡁⠀⠀⠀⠀⠀⠀⠙⠢⣀⠉⠢⠄⠐⠀⠁⠀⣀⣠⠼⠗⠂⢄
⠀⠀⠀⠀⠀⠀⠈⡐⠠⠤⠄⠒⠒⠂⠉⠫⡐⢅⢄⠀⠈⠢⡀⠤⠀⠀⠀⠀⠀⠈⢧⣬⡀⢀⠶⡚⠋⠁⠀⠀⠀⠀⠀⢈⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢅⠀⣀⠀⠀⣠⣤⠴⠖⠒⠋⠉⠁⠉⠫⢀⠈⠐⠄⡀⠀⠀⠐⠈⠀⢀⠬⠓⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⡬⡂⠞⠉⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⠕⢦⠀⡍⠀⣠⡴⠞⠊⠁⠀⠀⠀⠀⠀⡉⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡢⠀⠀⠑⢤⠀⠀⠀⠁⠀⡀⢄⡚⠹⠳⢽⡋⠀⠢⢀⠀⠀⢀⠤⠂⠈⢀⠄⠋⡰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⢄⢀⡀⣀⣠⡔⠎⠁⠈⠀⠀⠀⠀⠀⠉⠂⣀⠀⠑⠊⠀⠀⠀⠈⡠⠂⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣱⢏⠘⠁⠈⠢⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠷⣰⠔⢁⠢⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⡢⡀⠀⠑⠖⠀⠁⢀⠠⢀⠀⢀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠨⡀⣤⠀⠐⠈⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡂⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠙⠶⠤⠴⠞⠻⢦⣤⠟⠶⠚⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⠲⣄⡀⠀⠀⢄⣰⠞⠁⠀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠈⠹⣦⣤⠞⠁⠀⠀⠀⠀⠠⠀⠀⢀⣤⠟⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣱⠞⠙⢶⣤⡀⡀⠀⠀⠀⢈⣴⠏⠁⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣴⣯⣼⠷⠶⣤⠀⠀⠀⣰⠞⠁⠀⠀⠀⠈⠻⣷⣄⢘⣴⠟⠃⠀⠀⠀⠀⠀⢈⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠈⢉⣋⣀⠀⠤⣤⠀⢈⠛⢶⣾⠑⠀⠀⠀⠀⠀⠀⠀⢀⣽⠿⣷⡄⠀⠀⠀⠀⠀⣶⠿⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠟⠋⠋⠉⠉⢛⣦⠖⠦⠠⣃⡈⣿⠛⢷⡀⠀⠀⠀⠐⣴⠿⠃⠀⠈⠻⢮⣆⠀⣠⡿⣝⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡆⠀⠀⠀⠀⢀⡟⢦⡴⠛⠉⢟⣶⣄⡈⠿⢟⡳⠶⠾⣟⠀⠀⠐⠀⠀⠈⢛⣿⣿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⣠⠞⡁⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠉⠛⢦⣤⣤⠗⣀⠀⢈⠛⠛⣷⡀⠀⣴⡟⣮⠟⠁
⠀⠀⠀⠀⠀⣠⡾⠃⢀⡇⠀⠀⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠎⠀⠀⠀⠀⣽⠃⣀⠐⠉⠃⠀⠈⢳⣾⣿⣿⠃
⠀⠀⠀⢠⡼⠋⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠼⠉⣧⡰⠛⠃⠀⠀⠙⠛⠙⣧⡀
⠀⣠⣾⠟⠀⠀⠀⠀⢼⠀⠀⠀⢸⡀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⢿⣥⣤⣤⣶⣧⡄⠔⠳⠂⠘⣷⣄⣸⠇
⣸⡏⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠉⣿⡇⠈⢶⡖⠂⣿⡿⠁
⠙⣧⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⣠⠟⠁⢨⣼⠻⣧⣠⡾⠷⡾⠇
⠀⠈⠛⢦⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠈⠆⠀⠀⢀⣠⠟⠁⢀⣴⠟⠁⠀⠉⠛
⠀⠀⠀⠀⠙⢦⡀⠀⠀⢹⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠹⣦⡀⠈⣇⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣠⠞⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡘⠄⠀⠀⠀⠀⠀⠱⡀⢀⡼⠃⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⢀⡴⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⢀⣴⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣠⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⣡⠔⠳⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⢿⣄⠈⠀⠀⠀⠈⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠔⠋⠙⣆⠙⣦⠀⢀⠀⠀⠀⢀⣽⣧⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠻⣄⠀⠀⠀⠀⠘⠀⠘⣧⡈⢁⡤⠖⣩⣄⠻⣷⡀
⠀⠀⠀⠀⢠⡞⠁⠀⠊⠉⠣⠘⣦⠀⢀⠀⠀⠀⢀⡿⢿⣇⠀⠈⠀⠈⠁⠘⢷⡀
⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠈⢷⣌⣉⡴⢚⡥⠦⡄⠻⣦⠀⠀⠀⠀⠀⠀⠳⠂⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠹⣿⡄⠠⣄⡠⠀⣠⠼⣿⣇⠀⠀⠀⠀⠀⠀⠹⢧⠀⢀⠀⠀⠁⠀⠀⢀⡀⠈⠉⠉⣉⠖
⠀⠀⠀⠀⠀⠀⠘⣿⣦⡤⠖⠫⠖⠲⣄⠹⣧⠀⢀⡀⠀⠀⣀⠤⠎⠁⠀⠀⠓⢀⠀⣀⣻⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠙⢷⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠁⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠳⠀⠀⣀⢤⡞⠁⠴⣿⣶⡄⢀⣀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢸⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠔⢋⣡⡴⠿⠶⠾⠋⠋⠀⠀⠈⠒⢦⣤⠏⠀⠀⠀⠀⠀⠀⠁⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠄⠀⢀⡠⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣂⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠔⠁⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⠔⠋⡠⠊⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⠀⠀⠀⠀⡠⢊⡔⢈⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠜⠀⠊⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⣠⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⢀⣠⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠚⠉⣀⣄⣀⣀⠙⠒⠠⠄⠉⠉⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠾⢏⣉⣉⠤⢠⣤⣓⠶⣤⣉⠙⠛⠉⠓⠀⠀⢀⣠⠴⠚⠫⢑⣈⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢯⣝⣳⠦⣤⣉⠉⠛⠻⠾⣍⣁⠈⢉⣀⡠⠤⠖⠒⠋⣉⣤⡤⠖⣋⣩⡤⡖⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠠⠝⡹⡟⠓⢮⣙⣓⠲⠤⣌⣉⢉⡏⣀⣁⡤⠶⣚⡋⠭⠀⢶⢺⠁⠁⠀⣀⡤⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣢⣤⣃⡐⠂⠳⠉⣿⠓⠦⣬⣍⡉⣉⠭⡖⢉⠋⢠⠀⠀⢈⣨⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠁⠂⠬⢭⣛⡳⢦⣌⡀⠀⠘⠇⢻⠀⠒⠁⣀⣠⣤⠶⢏⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢥⣌⣓⠦⣄⣀⠀⠀⠉⠓⠲⢭⣓⡲⠦⠼⠴⠾⣟⣛⣭⠭⠶⡚⠋⢳⡤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣀⡘⠀⣌⠙⢦⣍⣙⠓⠶⣤⣀⠐⠤⠉⠳⡖⡊⠉⠉⢀⣀⣤⠤⣖⣿⢿⡶⠒⠋⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠞⠉⠻⣦⣄⡈⠀⠙⠉⠙⡓⢾⢿⣗⠢⠤⠥⠴⣒⣺⣋⣥⢶⠟⠋⡉⡜⠙⠋⣀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡼⡜⢆⠀⠠⡉⡛⠿⢶⣤⣒⡀⠈⠛⠉⠙⢲⡞⠛⠉⠁⠟⠀⣊⣀⣠⠤⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠈⠧⡳⡀⠘⣎⠂⠒⣀⣈⣉⣛⡦⣄⣀⣸⢀⣀⣤⠶⠞⢋⣉⣸⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠣⡤⢱⡝⢆⠊⠟⠛⠉⠉⢁⣀⣀⣠⠭⠿⠛⢛⣓⣻⣭⡭⢥⡶⠖⠚⢻⡀⠀⠀⠀⠀⠀⡠⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠉⠷⣀⠀⠀⢳⡈⠙⣎⢑⣒⣒⣚⣯⡭⠽⠖⠞⠻⠋⠹⠩⠃⠀⠀⠀⠊⢀⣠⣴⠾⠓⠀⠀⠀⠀⠎⠀⠀⣠⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠸⠦⣹⠂⠀⠀⠙⢆⢸⠙⠃⠘⢁⣊⣀⣭⣤⣤⣤⣶⠶⢾⣿⠿⠽⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠙⠟⢳⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠋⠀⠀⠀⠀⠈⠿⠾⠿⠟⠛⠉⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⣉⣳⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣖⣩⣏⣙⣦⠀⠀⠪⢨⣛⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⠀⠐⠐⠈⠉⠉⠉⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣇⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢸⣷⠘⠆⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣀⠀⠠⣧⠀⠀⠀⠀⠀⣠⣤⣤⣤⣹⠦⣀⣠⣥⠽⠶⠶⠿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠰⢩⡉⢲⠨⣧⠀⣻⠿⠛⠛⠋⠉⠉⠁⠱⣇⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠯⠆⠀⠀⠈⠀⠻⣆⠨⡀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣽⣆⢳⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠠⠤⠀⠀⢀⣀
⠀⠀⠀⠀⠸⡿⣯⡳⠤⠀⠀⠀⢀⡢⠄⠓⠚⠍⣎⢧⠀⠀⠒⠒⣂⣉⡹⠴⠥⠔⠒⣒⣈⣉⠭⠭⢋⠄⠀⡀
⠀⠀⠀⠀⠀⠉⠻⣿⣷⣄⠠⣀⠀⠀⠀⠀⠀⠀⠈⠛⢯⡭⠭⠥⠴⢒⠒⠒⠋⠛⠁⢄⠀⠀⠀⣀⠀⠀⢊⡿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣮⣙⠢⠀⠀⠀⠐⠀⢀⠄⢳⠀⠀⣞⡳⣄⠀⠀⠀⠀⠀⠑⡄⠐⠃⠀⠀⠀⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣷⣦⡀⡤⠀⢀⠀⠄⠈⠀⠀⠫⣷⣬⡓⠀⠀⠀⠰⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠸⠂⠀⠈⠻⣿⡆⠀⣾⠥⢨⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠁⠀⠈⠓⠚⠃⠒

⠀⠀⢀⠂⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⠀⠀⠀⡰⠁⠀⠀⠰⢤⡀⠀⠸
⠀⠀⢀⠐⠄⠀⠤⡰⣄⣀⣀⡸⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠀⠲⢦⠄⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠈⠉⠠⡈⠀⠐⠂⠒⢦⣔⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣼⠆⠀⢀⠄
⠀⠀⠀⢨⠓⠠⠄⠀⠀⠀⠀⠄⠀⠁⠘⠂⠀⠀⠀⠐⠒⢲⠊⣄⣀⣀⠌⠎⠀⠀⠑⠀⠐⡘⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠠⠀⠈⠀⠀⢀⡄⠀⠀⠈⢙⠆⠀⠀⠈⠓⠼⠄⠂⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠰⣤⣀⣠⡞⠀⠀⠀⢀⠎⠀⢠⣤⢤⣤⡀⠀⠀⠀⠀⢠⡄⡠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠙⠳⢦⣤⣠⡟⠀⠀⠞⡕⠙⢹⠿⡀⠀⠀⢰
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠤⠄⠄⠀⠐⠋⠀⠀⡀⠙⠒⠒
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢦⢀⣔⣤⢾⢆⠀⠀⠀⠀⢀⡀⠀⢠⣾⣡⣀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣠⡴⢻⡿⢊⣭⢾⣧⣄⠀⠀⠸⣿⣦⣀⠉⠲⣬⡙⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠘⢧⣾⡿⠴⠿⠛⠿⢷⢶⠏⡀⠀⠀⠈⠳⠍⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢎⠀⢀⡠⠂
⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠢⢀⡆⠀⠀⠀⠄⠀⠉⠃⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠊⠀⠀⠀⠘⣄⠀⠈⠀⠃⠀⠀⠀⠘⣧⠀⠀⠀⣀⣀⡲⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⠠⠀⠀⢜⠳⣄⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠃⠀⠀⠈⠀⠀⠐⠁⠀⠀⠳⢾⠞⠁⠀⠀⠀⠢⠀⠀⠘⠥⠒⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠙⠒⠲⠤⢤⣀⣀⠀⠀⠀⣠⠴⠋⢧⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠷⠒⠃⠀⠀⠀⠈⠱⠤⡀⠀⠀⣀⡀
⠀⠀⠀⠀⣤⣞⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠋⠁⠀⠀⠀⠀⠀⢠⣄⣤⠖⠚⢍⠁⠔⠁
⠀⠀⠀⣸⠁⠀⠉⠙⠒⠢⠤⣀⣀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⡀⣠⣢⠏⡉⠉⠀⠅⠀⢅⡀⠄⠈⡄⠀⠂⡠⡀
⠀⠀⠀⠛⠬⢄⣀⠀⠀⠀⠀⠀⠈⠙⠻⡍⠉⠉⠁⠀⠀⢀⣒⢵⡿⠯⠀⡁⠉⠐⠉⠄⠂⣀⠤⠁⡉⠀⠆⠁⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⣀⡀⠀⠓⠐⢲⡀⠀⠄⡸⠾⠋⡁⠀⠉⠀⠤⢐⢀⡰⠌⠀⠈⠑⠊⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⢤⠬⠃⠀⠳⣄⠀⠀⠉⠐⠀⠠⠈⡀⢀⠤⠂⠄⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠑⠘⠦⣄⣀⠀⠀⠀⠀⠀⣕⣀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠦⣀⣀⣀⡀⠀⠈⢏⠓⠒⠦⢬⣿⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⢳⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡁⠀⠈⠑⠂⠄⠀⠀⠀⠀⣀⡤⠤⠒⠉⠁⠀⠀⠀⢀⣀⠼⠇⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠢⢍⡓⠢⢄⡀⠀⠀⠀⢠⠉⠁⠀⠀⠀⠀⠀⠀⢂⣉⢥⡴⠾⠋⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡍⠙⠖⠦⡁⠀⠀⢼⣤⠴⠖⢈⣁⣀⡤⠊⠉⠃⠘⠀⠁⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠲⣤⣄⡀⠈⠀⠀⢸⡇⢠⡤⠖⠚⠋⠁⡼⠁⢀⣴⣊⣤⣴⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢿⠿⣶⣄⡀⠐⠀⢸⠀⠀⠀⣠⡿⠤⠚⠛⠉⠉⠀⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠸⣆⠈⢮⡙⠓⡤⣼⠶⠖⠋⠁⠀⠀⠀⢀⡀⠠⠤⠤⠶⢛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡄⠀⢹⡄⣿⠓⣄⠀⠸⠄⠀⣀⡀⣀⣀⣀⣤⡤⡴⠶⠒⠊⣹⠏⠀⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠙⣇⠀⠈⠷⢶⠒⠛⠉⠹⠉⠁⠀⢸⡞⢁⠤⠂⠰⠃⠐⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣞⣻⠖⠋⢳⢀⠈⢦⡀⠇⢸⠀⢀⠀⠀⠀⠀⣠⣏⡴⠿⠥⠴⠓⠒⠒⠋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣱⡦⡀⠀⢀⠛⠀⠰⢏⡀⢹⢦⠙⠦⠼⠴⠖⠒⠒⠘⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠃⠀⠞⠀⠀⠀⠈⠳⣇⡏⠀⠀⠀⠀⠀⠀⣀⣈⣭⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡐⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠘⠈⠂⠀⠀⠂⠚⠰⠰⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠳⠬⢒⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⠻⠶⣂⢀⠀⠀⠀⠀⠀⠀⣇⠈⢙⣿⠃⠉⣱⠀⠀⠀⠠⣦⠀⣔⡀⠒⣶⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣈⣉⣰⣤⢆⠀⠀⠀⢀⡟⠛⠻⣿⠛⠋⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠘⠻⠀⠀⠀⠸⣿⣷⣾⡟⠿⠻⠿⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⠀⠤⣤⣲⣤⣯⣽⣦⣠⣖⣀⡀⠀⠀⠀⠰⠟⠟⠋⠀⠀⠀⠢⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⢀⠁⠈⢋⣀
⠀⠀⠀⠀⠻⠟⡶⠶⠦⠤⣤⣤⡄⠬⢦⣵⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠁⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⢀⣄⠠⢀⠠⠐⠀⢀⣤⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠚⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⡀⠀⣠⡄
⠀⠀⠀⠀⠐⠛⠲⢿⣤⣴⣶⣶⣿⡿⠟⠋⠀⠀⠀⠀⠀⠂⠀⠀⠦⠄⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡄⠉⠉⠉⣔⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠬⠠⠔⢀⡂⢀⡀⠀⠀⢀⡀⠀⠈⣠⠍⠐⠢⣴⡺⠟⠁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣀⢠⡀⡂⡠⠀⠎⠁⢉⠀⡓⢂⣀⣐⠦⠶⠛⠀⠐⠻⠯⢔⣠⡄⣾⠔⠉⠀⠀⠀⠀⠀⠦⠤⡀
⠀⠘⢇⡀⠀⠑⢌⢡⠄⠢⣓⣠⡵⠶⠚⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢐⡠⠄⠀⠀⠈⢣⡼⣈⠑
⠀⠀⠈⠋⣨⣀⣠⣷⠶⠛⠋⠁⠀⠀⠀⠀⢰⣴⠁⡄⠁⠀⠀⠰⠒⠂⠬⠃⠀⠀⠀⠀⣤⣀⣀⡎⠀⢀⡒⣸⢸⠆⣬⢠⣸⠾⠇
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠈⠀⠀⠀⠁⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⢠⣄⣠⡤⠖⠒⣒⣟⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠉⠀⠀⠉⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⡆⢀⢻⠃⠀⠇⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡄⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠇⢸⢸⡄⡆⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡼⠃⡇⢹
⠀⠀⢠⣖⣋⠀⠀⠀⠀⡀⠀⠀⠙⠉⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⣿⢀⣸⡀⡀⠇⢿⣦⣤⣤⡤⣤⠤⠤⠄⠀⠀⠠⠤⠴⠄⠀⠤⠀⡱⡌⡄
⠀⡴⢸⣟⠷⣤⣤⠊⠁⠀⢀⣀⡀⠤⠴⠶⠶⠛⣉⣿⣦⠀⠀⠀⢹⡀⣀⡑⠀⠀⠻⠥⠶⠄⠀⠀⠀⠁⠀⠀⠀⠀⣂⡀⠀⠀⠠⠀⠁⡤⣤
⣼⠁⣼⡸⠀⠈⠙⣿⣶⣤⣌⣁⣠⣤⣴⡶⠞⠋⠉⠛⢠⠀⠀⠀⠘⣷⢰⡄⠀⡄⢹⣿⡿⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠙⢶⣧⢸
⡏⠈⠳⣄⡀⠀⠀⢻⡿⠘⠇⣀⠀⠀⢃⠀⢀⠀⠀⠴⠻⣄⠀⠀⠀⠹⣆⣧⠀⣇⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠈
⢳⡀⠀⠀⣝⠓⢦⣀⠀⠀⠀⢿⡀⠀⠘⡀⠘⣇⠀⣴⣤⡟⠀⠀⠀⠀⢻⣼⡄⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠘⢸
⠀⠙⠶⣤⣟⠀⠀⠈⠙⠂⣠⣼⣷⡌⢄⠛⠀⢻⡶⠚⠋⠀⠀⠀⠀⠀⠀⢿⣧⠸⠀⣀⣠⣤⣤⣤⣀⣀⠀⠀⠛⠓⠛⠛⠒⠒⠒⠒⠂⠈⢣
⠀⠀⠀⠀⠙⠻⢄⡀⠀⠀⠀⣩⣿⣿⠸⠷⢠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢀⣾⣋⣉⣀⣀⣄⡀⢀⣠⠤⠶⠶⠶⠦⠤⠤⠴⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⠀⠈⢩⣿⣤⡼⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠂⠢⠀⠿⢋⠔⠊⠉⠉⠉⠈⢥⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠽⠿⠶⠶⠶⠒⠒⠒⠒⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠃⠀⠈⠉⠉⠁⠀⠀⠀⢠⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡪⠟⠉⠀⣀⡠⠀⠀⠀⠀⠀⢀⣠⡶⢶⠛⠁⠀⢹⡌⢉⡙⠛⠳⠶⢶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠷⣦⣤⣤⣭⣤⣤⣶⣶⠾⠟⢛⣉⡀⢀⡼⠂⠀⢰⣿⡇⠀⠭⠝⠓⠲⣦⡀⠤⡎⠀⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢣⠇⠀⠀⠀⢰⡀⠈⠁⠠⠔⣒⣫⡭⠗⠚⠉⠀⠀⢀⡼⢸⡇⠀⠀⠀⠐⣋⡭⣖⠫⠄⡈⠁⢳
⠀⠀⠀⠀⠀⠀⢀⣠⠤⢶⠏⠎⠀⠀⠀⠀⠀⠙⠶⠖⠚⠉⠁⠀⣠⣐⣈⣿⣴⣾⠿⠾⠟⠁⠀⠔⠒⠤⠃⠈⠀⠒⣫⢕⣫⠞
⠀⠀⢀⡤⠖⠋⠩⠴⠆⠘⠲⠤⠭⠿⠿⠿⠿⠿⠶⠶⠿⣿⣿⡛⠿⢿⣧⣤⣄⣠⠴⣒⠤⠶⠔⠊⠁⠆⠀⠰⣛⡭⠖⠋
⠀⠀⡞⠐⠲⢤⣄⡀⠒⠤⣄⣒⠤⣄⣀⡀⠀⠀⠀⠀⢀⠉⠀⠉⢙⣒⣈⠙⣯⠐⠉⢀⠝⠃⠀⠀⣀⡤⠖⠋⠁
⠀⠀⣇⠀⠹⣳⣌⡉⠛⠲⢤⣉⡙⠲⠯⣭⣭⡥⠴⠚⣉⣤⣶⠟⠻⠟⠃⠓⠋⠀⣉⣤⣀⡤⠖⠛⢁⡀⢠⡦⢤⣀⡀
⠀⠀⠈⠲⢤⡠⣉⠛⠆⠀⣀⡈⠛⠳⢦⣤⣀⣠⢴⣿⠿⢛⣩⡄⠀⢀⣠⠴⢒⡩⠖⠋⠁⠀⣠⠮⠉⣠⡏⠀⠀⣨⡭⠟⠃
⠀⠀⠀⠀⠀⠉⠓⠯⣕⡢⣈⠋⢍⣙⣳⡌⣿⠵⠋⡔⡊⠅⠋⠀⣀⡥⠤⠖⠋⠀⠀⠀⠀⠀⠙⠶⣼⡿⠿⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⣶⣤⣀⠀⢸⠀⠀⠀⣀⡤⠖⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣲⣤⣴⣖⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠲⢏⡔⡠⢋⣝⠀⢄
⠀⠀⢰⣶⠤⢄⣀⠒⠀⠠⡀⠀⠀⠀⠻⢧⣴⣬⠉⠓⠎⠴⠠⠄⠀⠀⠀⠀⠄
⠀⠀⠈⢳⣝⢢⣄⡀⠓⠂⠀⠀⠀⠀⠀⠀⠉⠛⠳⠷⠾⠶⠴⠖⠒⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠙⠻⢮⣝⣒⣤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⢀⢀⡀⠱⣖⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠲⠌⠘⢃⠵⢹⣿⣭⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠄⠆⠀⠀⠀⠀⠈⠋⠳⠂⢤⠁⠬⠻⠧⢄
⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⠀⢀⠀⠘⢒⣿⢁⠰⣖⢛⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠈⠁⠤⠄⠤⠤⠶⠒⡛⠿⢿⠚⢒⣶⠾⠀⠀⠀⠀⠠⠤⡂⣄⢦⣂⠆⡀⠀⠀⠀⠀⠀⠈
⠀⠀⢄⣤⣌⣀⡠⠀⠠⠐⣊⠭⠳⡇⠋⣸⠆⠈⠀⠀⠀⠀⠔⢀⡐⣓⠭⠖⣋⠑⠤⠀⠀⠉⠠⠔⣲⣿⠆
⠀⠀⠀⠈⠙⠫⡂⢤⣲⡹⠬⢒⣩⣠⡾⠃⠀⠀⠀⠀⠠⠤⣬⣨⣅⣤⣦⣿⠁⢀⠄⠈⠁⣠⡴⣪⡵⠋
⠀⠀⠀⠀⠠⢤⣍⣨⣤⣴⣦⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣤⣤⣖⣾⣭⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⢀⣀⣀⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⢀⡖⣫⠄⣸⠂⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠟⠙⠲⣤⡀⠘⣧⣓⣚⣡⠖⣀⣴⠾⠛⢿⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠙⠳⢤⡀⠀⠀⠀⠙⠳⣤⡉⠉⣠⡾⠋⠁⢀⣴⠟⠋⣀⣙⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⢀⣠⢖⡛⢢⠉⠳⢦⣀⠀⠀⠀⣹⣿⡏⠀⢀⣴⠟⠁⢠⠞⡭⠆⡼⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⣅⡀⠀⢼⠱⣏⡴⢋⡀⠀⠀⣉⣷⣶⠾⠛⠀⠹⢤⣾⣅⡀⠀⠸⣦⣓⣚⡤⠆⢀⣠⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠺⢯⣉⠀⠀⠀⠙⠲⣌⡛⠲⠒⠋⢀⣴⠟⠉⠀⠈⣣⣤⣤⣤⣴⠟⠈⠙⠶⣤⣀⠉⠁⢀⡴⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠙⠲⣄⣰⠟⠁⠀⣠⡴⠛⠉⠀⢀⡉⠳⣤⡀⠀⠀⠀⠉⠳⣴⠋⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣠⠞⠁⢠⡴⣚⠙⡆⠀⠀⠀⠙⢳⣄⣀⠀⢀⡼⢇⠀⢀⡾⠋⠀⠀⣠⢞⡩⢉⡇⠀⠙⢦⡀⠀⠀⢰⡇⠀⠄⠀⠒⠀⢸
⠀⠀⠀⣠⣟⠁⠀⠀⣏⠸⣡⠞⣁⠀⠀⣠⠾⠋⢡⠈⠉⠉⠀⠈⠓⣾⡟⢦⣄⠀⢧⡸⠴⢊⡤⠀⢀⣤⡿⢦⣤⣼⠇⠀⠀⠀⢀⣴⠞
⠀⠀⠀⣿⠙⠳⢦⣄⡈⠓⠒⠛⢁⣴⠞⠁⠀⠀⠈⣦⡶⠚⠳⢶⣾⠋⠀⠀⠈⠳⣤⡉⠉⠉⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⠀⠀⠀⢸⠐⠂⠀⠉⡛⠶⣤⣠⠞⠁⠀⠀⢀⣴⠞⠁⣠⡤⠶⡄⠉⠳⣄⡀⠀⠀⠀⠙⢦⣴⠋⠖⠀⠀⠀⡀⠀⠀⣠⡶⠋⠀⠀⠀⠀⢠⣂⣶⡀
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⢷⠀⠀⢀⡴⠋⠁⠀⣾⢡⠚⣠⠃⠀⠀⠈⠛⢦⡀⠀⠀⢠⡇⠀⠀⠀⠀⢈⠆⣠⠞⠋⠀⠀⠀⠀⠀⠀⠈⠙⠚⠃
⠀⠀⠀⠀⢷⠐⠄⠀⠀⠀⠀⠘⣇⢀⡟⠻⢶⣄⡀⠙⠦⠭⠵⠚⠁⢀⣠⠶⠛⠛⠷⠤⠞⠁⠀⣰⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠂⠀⠉⠉⠀⠀⠀⠈⠛⠷⣤⡀⠀⢀⣴⠟⠁⢠⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⢠⣶⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⢀⠀⠀⠘⠀⢀⠈⠙⢷⢛⠁⠀⠀⠀⠀⠰⠃⠠⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢪⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⢸⡇⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣖⣉⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢼⣇⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠀⠂⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠺⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠲⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢤⠤⢊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠴⡀⠦⣤⣀⡴⠟⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠚⠀⠀⠐⣤⢀⣿⠁⠀⠨⣴⣴⣿⣻⣧⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠞⢶⡀⠀⠴⣠⣬⡵⣾⣿⡆⠀⠀⠛⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢤⠀⠀⠈⢿⣸⠂⠉⢉⢉⣉⡛⢿⣦⡆⢠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠱⣟⡷⠈⣵⠶⢦⣐⡺⢴⡼⠊⣿⣿⠿⣿⣿⣾⢿⣷⠦⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠲⣠⠞⣋⣷⣂⠀⣤⣶⡄⠈⢳⣖⣸⠿⢋⢴⣿⡀⠀⠰⢿⣏⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⠃⠀⢠⡟⠉⠉⠈⠿⠀⣼⣛⡓⣶⢨⡟⢡⣾⣧⡘⣿⣿⠷⢦⡐⢻⣅⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢡⡄⢰⣫⡶⣶⡀⠀⣻⠀⡆⢠⣤⣾⣿⣇⢒⡳⢨⣿⡜⡏⠀⣠⣾⠋⣰⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⡆⣡⣈⣧⣅⣉⠳⣤⣥⣾⡗⠩⢍⠿⣿⣿⣭⣶⢟⣼⢃⡏⠘⠿⢋⡴⢫⣾⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠹⣽⠣⢙⣭⣬⣻⠛⠟⢨⣿⡿⢿⣏⠀⠀⢀⣽⡿⠃⣿⡟⠉⣛⣽⣿⡿⣷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢦⣀⣼⣿⣡⣰⣴⣿⣧⢙⣋⣉⢀⣀⣭⠉⣀⢀⢏⣯⣾⡿⣻⣡⣶⡿⠟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⣬⡙⠛⠮⠼⠿⡿⣉⣉⣉⢉⡉⠙⣛⣛⣾⣿⣿⣿⠿⠿⠛⢋⣁⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⣇⠈⠉⣰⠲⠶⣦⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⢻⡀⠀⢡⠀⠀⠁⠀⠉⠟⡉⢿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⣧⢁⢸⣇⠀⠠⢠⣷⣤⢰⢾⣿⣿⣷⣿⣿⢟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠀⠘⣿⠆⣽⢸⣿⣶⠰⢾⣽⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠂⣿⢆⠚⣺⣿⣿⡉⣿⣿⣿⣸⣿⡟⡿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣷⢸⠻⡀⣿⣿⣿⣦⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡅⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⡗⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠉⠉⠉⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⡤⠾⠃⠻⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢉⡿⠷⠞⠁⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤⠽⡒⠊⢉⠽⠁
⠀⠀⠀⠀⣼⠋⠙⠓⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠖⠒⠫⠁⠂⡀⠌⢁⣀⠀⠒⢀⠠⢀⡀
⠀⠀⠀⢠⡇⠤⡀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣤⠤⠤⠤⠼⠀⠀⠀⠀⢀⠤⣪⣴⠾⠚⠥⢰⣀⡠⠦⢁⣀⠁⠃⢨⠀⠤⢃⠀⢠⠐⠙⡄
⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠈⢉⡇⠀⠀⠀⠀⠀⠀⣠⠵⣚⣿⠍⠂⣀⠤⠀⡀⣈⠙⠂⢠⠤⠔⣃⠠⢄⠀⠋⠀⠀⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⠀⠉⠊⠙⣄⡀⠀⠆⡽⠺⠋⢠⣀⠀⠀⠀⠑⠂⣁⠠⣚⠢⠤⣀⠤⠋⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⡤⠜⠀⠣⠳⣄⠀⠀⠀⠉⠉⠀⠠⠎⣀⠀⢀⠭⠒⠠⠀⠀⠀⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠓⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠔⠒⢦⡀⠀⠀⠀⠀⠈⠉⠛⡶⠦⢤⣀⡀⠰⡟⢋⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠙⠲⠤⠤⠤⠵⠀⠀⠀⠉⠙⠋⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣴⣿⣶⣄⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣧⠀⠀⠺⣿⣿⣿⡿⠃⠀⠀⠀⠉⠛⢿⡟⠀⢰⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠿⠂⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠄⠸⠇⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠶⣤⢀⣤⡴⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢉⠹⣇⠀⣠⡾⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⢀⡴⢿⡇⢸⡟⢁⣴⣦⢹⣇⣀⣀⣀⣠⡾⢶⣾⠃⢠⡟⣸⠿⣴⠟⠀⠘⠛⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡎⠀⣴⠁⡘⢀⠈⣤⠀⣠⣉⠉⠉⠉⠉⢀⣼⡏⠀⠊⣴⣿⣤⣄⠀⣠⣶⣿⣿⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣧⣈⣡⡾⠁⣼⣦⡤⠞⠛⣿⠟⠛⢻⠛⣉⠻⠀⢠⠞⢋⠙⢙⡇⢠⡟⢋⡭⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⠟⠁⠀⡁⠀⠁⠸⠇⠉⢠⣃⠄⢀⡛⣀⠀⠈⠀⠟⠀⠾⠁⢸⠀⠘⣡⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⠛⢁⣴⣃⣰⣇⣘⣄⣈⣴⣇⣘⣫⣦⣈⣵⣿⠀⠰⠴⠞⠀⠚⠓⠴⣶⣬⣥⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⢹⡏⠙⠛⠛⠛⠋⠉⠁⣀⡀⢴⣶⣶⣿⡷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣤⣤⠶⠾⠛⠉⠻⢶⣤⣭⣤⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠂⠀⠀⠀⣶⠲⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⡟⠀⢀⠀⠀⠀⢸⣀⠀⠀⣀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠉⠙⢉⡗⠛⠋⠉⠉⠉⣹⠋⠉⠉⠉⠉⢽⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢻⣿⣏⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠃⠧⣤⠤⠤⠤⢴⣧⣶⣶⣶⠶⠶⣿⡴⢶⠶⠶⠦⣾⡿⣏⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢙⡛⠻⣷⡔⠈⠁⠀⠀⠈⠛⠓⠨⢍⡘⠁⠀⠀⠀⢉⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠖⠚⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠐⠋⠀⠠⠄⠀⠂⠉⠉⠁⠀⠰⡴⠶⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣾⡿⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⣾⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⣠⡞⠁⣠⢾⣿⣿⠿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⢀⣴⠏⢠⡾⠁⢸⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⠘⢿⣦⡀
⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⡁⢠⡟⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠻⣷⡄
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠻⣷⡟⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⣿⣆
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢿⣦
⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠈⣿
⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⣀⣾
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣷⡄⠀⠀⠈⣉⣁⣠⣤⣶⣾⡿⠛
⠘⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⢿⣿⡿⠿⠿⠟⠛⠋⠉
⠀⠀⠈⠙⠿⢷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠆⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠟⠋⢁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣤⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⡿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⡟⢟⣙⠛⣻⢛⣻⢿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢉⣩⣭⣤⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣉⣉⣉⣉⣉⣿⡟⢉⣉⣉⣉⣉⣽⡇⠈⣿⠸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠃⢀⡸⡆⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣉⢻⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠁⣧⢸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠃⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠐⢸⣾⣿⠿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢸⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡏⣥⣭⣭⣭⣭⣿⡏⢨⣭⣭⣬⣥⣿⣿⢉⣭⣭⣭⣭⣽⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⡟⠀⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠁⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢀⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠙⠛⠷⣶⣶⣶⣶⣶⣿⡇⢰⣶⣶⣶⣶⣾⣿⢠⣶⣶⣶⣶⣾⠷⠖⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠠⢍⡙⠻⢿⣿⣷⣾⡿⠿⠿⠿⣿⡿⠾⠛⢋⣉⠥⠆⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣄⣀⠉⢛⠛⠾⠁⠀⠀⠤⣤⡤⣤⣀⣠⣭⠁⠀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠉⠉⠑⠉⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡗⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⠤⢤⠤⠤⠤⠤⠤⠤⠤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠼⠃



⣿⣿⣿⢿⣿⠿⢿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣶⣶⣷⣼⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠄⡠⣤⣤⠀⠀⠀⠀⠀⠀⠄⠶⠶⠛⠛⠉⠉⡉⢉⡽⢣⣤⠒⢆⠀⢀⡖⢢⣄
⠀⠀⠀⠀⠀⠰⡈⠐⢄⣀⠀⢁⡤⠒⠀⢉⡟⠁⡀⠀⢀⣀⠁⠤⠄⠠⢤⣄⣲⣦⡵⠞⠋⣠⠟⣈⠆⠐⡄⡔⠀⢎⡘⢷⡀
⠀⠀⠀⠀⠀⡆⠈⠑⠂⠂⠤⠉⠀⢀⡴⠋⠀⠀⢡⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢠⡟⠂⠀⢋⠖⠁⠑⢎⠊⠀⠚⣧
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⠚⠓⢮⠀⢈⠖⠛⠂⠀⢸
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠊⠉⠀⠀⠀⠈⠉⠂⠀⠘⡇
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡆⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡆⣇
⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠀⣉⢒⠂⠀⠀⠐⠒⠒⠛⠛⠉⠉⢿⡁⠀⠀⠀⢸⠀⢸⠀⠀⠀⠐⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣠⡤⣶⣯⣶⢿⡷⢿⣿⢿⣺⠟⢋⡩⠭⠝⢛⣓⣢⠉⠛⠒⠂⠘⠀⠘⠂⠒⠒⠋⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠞⣫⠾⣭⢴⡭⢖⢭⣺⣧⣴⠋⢉⣠⡏⢳⡀⠀⢠⠂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⡟⢸⠁⢰⠁⣰⢁⠎⠀⠀⠀⢉⠉⠀⢀⠔⠉⠉⢧⢳⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠃⡾⢀⡇⠀⢀⡏⢰⠀⠎⢰⡆⠠⣸⡿⢸⠀⠈⠑⠒⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⢷
⠀⡼⠁⠀⠀⠀⠠⠤⠄⠒⠁⣀⠔⠁⡿⣇⡀⠀⠀⠀⠀⣧⡼⠀⠀⢸⠀⡇⠀⠀⠘⡇⢀⡜⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⠀⠔⢈⣀⠀⠀⠀⠈⠉⠉⠀⣂⠜⠁⠈⠙⠓⠒⠒⠒⠒⠒⠒⠒⠶⠶⠤⠤⠴⠶⠗⠋⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘
⣼⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠴⠤⠴⢖⣒⠒⠒⠦⣄⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠
⣿⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⢰⠀⠀⠀⡐⣳⣤⠗⠚⠛⠓⠚⢭⣲⢞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠐
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠜⠀⠀⢰⡯⠗⠚⠉⠚⠿⠭⣙⠢⡀⠑⡙⡆
⠈⠓⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⠊⠀⢀⠤⠒⠒⠦⣌⠑⣜⣆⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠳⡜⡜⡖⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⢳⡦⠙⠁
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⡀⠀⣀⠀⠀⠀⣠⢄⡄⢠⣤⣄⠀⠀⢤⣤⠀⢀⡀⠀⠀⣤⡄⢠⠤⢤⣤⣄⠀⣀⣤⡤⡤⢤⣄⡀⠀⠀⠀⠠
⠟⠀⠀⣀⡤⠤⠤⣤⣄⣀⣀⠀⠉⠉⢩⣄⣙⡷⠋⡀⢠⡏⡞⣹⣟⠀⠈⢳⣦⣞⠉⡾⢸⠁⠘⠛⠉⣰⣋⣹⣿⢿⠉⣀⣿⣯⣿⠀⣿⣹⣿⣷⣤⣀
⣠⣾⣏⠀⠀⠀⠀⠀⠀⣙⣿⣟⠛⣇⣄⠉⠉⠀⠀⠅⣰⣹⡿⣇⠈⠲⣶⣾⠋⢉⡿⢡⠞⠀⠀⠀⣰⢥⣼⣿⠛⠀⣦⣿⣿⣾⣿⡹⣿⣿⣻⣿⠉⠻⣷
⣾⠿⠿⢿⣿⣿⣶⣿⣿⣿⣿⠿⣿⠿⣿⣀⣀⣠⠀⠀⣿⡽⢧⣤⡿⣿⠥⠾⣛⣭⣒⠁⢠⣠⡿⢠⠷⣾⢿⠉⢦⣼⣿⣿⡿⠦⣼⣱⣹⢿⣇⠈⠳⡀⠈
⣿⣤⣤⣴⣾⣿⡛⢻⣭⣤⠽⠷⣟⠓⠾⡻⢿⡿⣄⣀⠘⣿⣿⣯⠟⠲⠶⠛⠑⡋⣁⣀⡈⣉⡀⢸⣻⡟⣦⣷⣿⣿⡟⡼⠇⠤⣾⣉⡇⣼⣿⣦⡀⢹⡆
⢷⡿⠫⠤⣤⣈⣿⠿⠛⠓⠢⣄⣈⣻⣶⠿⢾⣻⢏⡏⠀⠈⠉⢁⣠⠶⠟⠛⣡⣴⠾⠋⢉⠅⣹⢨⠟⣷⠿⠛⣿⢻⣇⣷⣄⣠⣿⣈⢷⣧⣿⢿⣧⠀⢳
⡞⢛⢒⣶⣾⣿⠟⠒⠲⣤⡴⠾⢿⡁⠈⢷⣀⡟⣸⣷⠀⠀⡴⠋⣁⣤⠶⠛⢋⣡⣤⣾⣿⣾⠅⠘⠊⠁⠀⠀⣡⣸⣿⠧⠤⣼⣇⡼⣾⡾⣿⣄⢻⣄
⣀⣽⣿⣿⣿⣧⣤⣤⠞⠛⠳⡀⠀⢳⣄⣨⡟⢠⢏⡟⢀⡾⣁⡾⠋⠀⠀⢠⡾⠟⢛⣿⠏⡿⠀⢀⡀⢠⡀⠀⢸⣿⣿⠦⢤⡾⣼⡿⣿⠁⠈⠪⣵⣿⣶
⣿⠿⣯⣿⢣⣄⣴⣛⣳⣤⣤⣿⣤⡾⠟⢋⣴⣧⠞⠀⡿⣿⡿⠀⠀⣠⡴⠋⠀⣠⡿⣡⠔⠁⣤⣌⣽⠟⠋⠀⠘⣿⣿⡶⣾⢶⡟⣽⠏⢀⣤⠤⠀⠉⠓
⣏⣀⣿⣧⣬⢭⣭⣭⣭⣭⣭⣥⠤⢒⡾⣿⡟⠁⠀⣤⠞⢡⣴⡾⣛⢁⣀⡤⠞⢉⠞⠁⠀⠀⠀⠁⠀⠰⠽⠿⠂⠹⣿⣟⣵⡯⠞⠁⠀⠻⠇
⠉⠉⠉⠁⠀⠈⠙⠿⣭⣙⣛⣛⣯⠥⠞⠉⠀⠀⠀⠷⠶⣥⢶⠿⠿⠿⠭⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠟⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡆⢰⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠀⢰⠖⠒⠒⠒⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠖⢷
⠀⡇⠀⠀⠀⠀⠀⣤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸
⠀⡇⠀⢀⣀⣀⣀⣿⡦⠴⣦⣤⣀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⡤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢸
⠀⡇⠀⢠⣿⣿⣿⣧⡄⢾⣿⠟⠟⠁⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⢠⣤⣼⡏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢸
⠀⡇⠀⠀⠀⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⡇⠀⠀⠺⠟⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢀⡴⢻⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⢸
⠀⡇⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⣰⠋⢰⡟⢻⣿⢿⡀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⡇⢸⠂⠀⡴⠁⠀⠉⠀⠀⣿⠁⢧⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⢠⣄⣤⣼⣿⢋⡿⠁⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢀⡾⠁⠀⠀⠀⠀⠀⡙⠀⠘⡆⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⢩⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠐⠻⠿⠷⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠹⣀⠀⣇⠀⠀⠀⠀⠀⣸⡇⢸⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣿⠀⠀⠀⠀⠀⢿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠁⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣰⠀⠀⠀⠀⠀⠀⠈⠙⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠇⠀⠉⠀⠀⠀⠀⠀⠰⠁⠠⠛⠉⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠙⠶⣄⡁⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣰⠏⠀⠐⠀⠀⠀⠈⠙⠢⣄⠁⡴⠁⠀⠁⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⠋⢻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⢦⡀⠀⢀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠀⢠⡞⠩⠁⣌⠐⢤⡀⠀⠀⠀⢀⡴⢁⡘⠂⠉⠳⢄⡉⠠⠉⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠙⢦⠀⠈⠑⠦⡈⠀⠀⢠⠞⠀⠈⠀⠀⠀⠀⠀⠙⢲⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠷⠒⢦⠴⡄⠑⢄⡀⠀⠈⠱⣖⣃⠀⠀⠀⠶⠀⠀⠀⠠⣡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⡠⢀⠀⠀⢿⠴⡄⢙⣦⣀⠀⠌⠉⠑⢄⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠎⠐⠀⠲⣀⠀⠀⠵⠊⠁⣹⠓⢦⣀⠀⠀⠀⢠⣤⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠂⡅⣰⢋⡷⠄⠀⠘⠿⠋⣹⠀⠈⠙⠲⢤⣤⠟⣱⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠉⠑⠛⡐⣲⡶⠒⡀⣠⣯⢄⡴⢢⠴⢦⡄⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡼⠁⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣘⣤⢐⠘⠇⠈⠀⢀⡴⠋⠈⠉⠟
⠀⠀⠀⠀⠀⠀⠺⢤⡀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢔⡰⠁⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢛⣉⣛⣋⣠⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣋⣛⣋⣡⣤
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢏⣴⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣟⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠙⠻⢛⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⠻⠛⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠐⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⠀⠀⠉⢻⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⣾⣧⣄⠀⠀⠀⠀⢀⡴⡫⣪⠾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠉⠙⢿⣿⣶⡄⢀⡴⡫⣪⠞⠁⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⠀⠀⠙⢿⣿⡫⣪⠞⠁⠀⠀⠀⠀⠀⢉⡿⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⣾⣧⡀⠀⠀⠀⠀⢀⡴⡫⣪⢿⣿⣶⣀⠀⠀⠀⢀⡴⡫⣪⠞⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠉⠻⣿⣿⣦⡀⢀⡴⡫⣪⠞⠁⠀⠙⢿⣿⣦⣀⡴⡫⣪⠞⠁⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠞⠁⠀⠀⠀⠈⠻⣿⣿⡫⣪⠞⠁⠀⠀⠀⠀⠀⢙⡿⣯⣪⡞⠁⠀⠀⠀⠀⠀⢀⡼⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠳⢨⡀⠀⠀⠀⠀⢀⡴⡫⣪⣿⣿⣦⡀⠀⠀⠀⢀⡴⡫⣪⠾⢿⣿⣦⡀⠀⠀⢀⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠊⠀⠀⠑⡙⣦⠀⢀⡴⡫⣪⠞⠁⠈⠻⣿⣿⣦⣀⡴⡫⣪⠞⠁⠀⠀⠙⠿⢿⢦⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠊⠀⠀⠀⠀⠀⠐⣸⣿⡫⣪⠞⠁⠀⠀⠀⠀⠈⢻⡿⣯⢪⡞⠁⠀⠀⠀⠀⠀⢀⡴⡃⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⢿⣿⣄⠀⠀⠀⠀⢀⡴⡫⣪⠾⣿⣿⣦⡀⠀⠀⢀⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢻⠛⠳⣄⣀⡴⡫⣪⠞⠁⠀⠈⠻⣿⣿⣦⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠪⣣⡿⣯⣪⡞⠁⠀⠀⠀⠀⠀⢈⡿⡻⠊
⠀⠀⠀⠀⠀⠀⠀⡠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣪⡾⣿⣷⣄⠀⠀⠀⢀⡴⡫⠊
⠀⠀⠀⠀⠀⡠⡪⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡙⢄⠈⠻⣻⣷⣤⡴⡫⠊
⠀⠀⠀⡠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢈⡿⡫⠊
⠀⡠⡪⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣴⡫⠊
⠲⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⠊
⠀⠈⠮⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡨⠊
⠀⠀⠀⠉⢪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠊
⠀⠀⠀⠀⠀⠈⠪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡪⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⡢⡀⠀⠀⠀⠀⠠⡨⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⡢⡀⡠⡢⠌
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣪⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠒⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠳⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠀⠀⠀⠀⢸⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⡓⠤⣀⠀⠀⠉⠀⠀⢀⠴⠒⠋⠁⠀⠀⠀⠀⠤⠐⣒⣩⠔⢲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠢⢬⣐⠀⠀⠀⢸⢀⣀⡠⠄⠀⠀⣠⠖⠖⠩⠋⠉⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⣀⣈⠀⠐⠀⠁⢠⡄⢈⣉⡥⠴⠚⢋⡟⠁⢠⡤⣀⣀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⠀⠀⠁⢸⠁⠀⠀⣰⣎⡠⠖⠛⠛⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡀⢧⠈⠫⡛⠲⣄⣸⡤⠶⠊⠉⠀⠀⠀⠀⠀⠀⠤⠤⠿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⡀⠈⢧⢸⠗⢦⠀⠸⠥⠀⣀⣀⡀⣀⣀⣤⢤⠴⠒⠒⢩⠏⠁⡴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠈⠻⡀⠀⢱⢲⠒⠉⠁⠙⠉⠀⠀⣷⠋⣠⠊⠀⠃⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠎⣿⠊⠉⡗⢀⠑⢄⡈⢸⠀⠀⠀⠀⢀⣀⡴⠥⠾⠁⠐⠒⠒⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠗⡄⠀⠠⠁⠀⠘⣤⠀⢓⠌⠓⠚⠒⠒⠉⠉⢉⡀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠃⢀⡀⠀⠀⢳⡜⠀⠀⠀⠀⠀⠀⠤⣴⣶⢿⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⡟⢡⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣌⡙⢿⣿⣿⣿⢋⣴⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣦⣌⠛⢡⣾⣿⣿⣿⣿⣿⣿⠟⣡⣾⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⢋⣴⣤⡙⢿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠻⢿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣦⣌⠻⠟⣡⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣦⡙⠿⡿⢋⣼⣿⣿⣿⣿⣿⣿⡿⢃⣤⡙⠿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠗⣀⠛⢿⣿⣿⣿⣿⣿⠟⣠⣿⣿⣿⣶⣌⠙⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠿⣿⣿⣿⣿⣿⡿⢃⣼⣿⣿⣦⡙⠻⣿⡿⢃⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠉⠛⠻⠿⣤⣿⣿⣿⣿⣿⣿⣷⠌⠀⢿⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⢡⠞⠁
⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⣰⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠄⡠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠈⠑⢄
⠀⠀⠀⠀⠂⠀⢸⠁⠀⠀⠀⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢈⠇⠐
⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡉⠀⠘⠃⠈⠁⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢋⠙⠳⣄⠀⠀⠀⠀⠀⠀⣴⠟⢉⠙⠳⣄
⠀⠀⠜⣃⡀⢀⠤⣄⢑⣄⣀⣀⣀⣀⡊⢀⠤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠐⢺⠺⡁⠸⠀⠀⠀⠀⠀⠠⠇⠐⢪⠮⡁⠿
⠀⠀⠀⠉⠁⠹⢤⠜⠈⠉⠉⠉⠉⠉⠁⠸⠤⠜⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢠⠄⠀⠀⢀⠀⡄
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘
⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠈⡠⠤⠦⠤⢦⡬⠤⠤⠤⠄⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣠
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⠶⠶⢶⠶⠶⠦⠤⢤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣶⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠯⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⢻⠋⠙⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣰⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠿⣤⣄⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠰⠃⠞⡽⣹⢻⡾⣧⣤⣤⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠁⠛⠀⠏⡼⢉⡿⣷⢦⣼⣏⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⢶⠛⣦⠀⠀⠀⠀⠀⠀⠀⠘⠁⠋⠾⢸⢏⡟⢲⢦⣄⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣆⠀⠀⣠⠖⣶⠀⢀⣀⠀⠀⠀⠈⠁⠋⠸⠃⠿⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠶⠞⠁⠀⠈⠋⠉⠉⠙⠓⠲⢦⣄⣀⠀⡴⠶⢬⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡞⣴⢠⡆⡤⣰⢠⢆⡤⢠⡄⣤⢀⡄⣠⠀⣤⠀⡄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⠿⠾⠷⠿⠿⠾⠷⠿⠶⠷⠾⠶⠿⠞⠳⠚⠛⠛⠁

⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢂⣠⣴⣾⣷⣾⣷⣿⣿⣿⣿⣿⣿⠿⢷⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⣠⣶⣿⣟⣯⣿⣿⠟⣿⣿⣯⣀⠘⠻⠿⢦⣌⡙⠿⣦⡈⠻⣿⡟⠻⣶⣦⣄⡀
⠀⠀⠀⠀⠁⠀⠐⠁⢠⣾⡿⣫⣾⣿⢿⣿⣧⣤⣤⣭⣭⣭⣭⣝⣒⣒⠮⢭⣓⠦⣍⡲⢌⠻⢦⠙⢿⡏⢻
⠀⠀⠀⠀⠀⠈⠀⣰⠟⣩⣾⣿⣿⡃⢀⣉⣭⠤⠶⡒⠒⠒⠀⠀⢒⣈⡉⠑⠚⠭⣲⢝⡲⣕⢤⡑⢌⠻⡄
⠀⠀⠀⠀⠀⠀⠐⠁⣴⣿⣿⠻⠿⠟⣋⡥⣖⠯⣓⠠⠨⠅⣀⡭⠤⣤⣊⠉⠒⠤⡈⢑⢯⡪⣷⣝⢮⠳⡘
⠀⠀⠀⠀⠀⠀⠀⣸⢹⣿⣿⣤⡴⢞⡥⣾⢗⠍⠀⣐⠶⠋⠉⠉⠛⠛⠳⢖⡤⡀⠀⠀⠑⢌⢪⡪⡳⡱⡝
⠀⠀⠀⠀⡄⠀⢠⡇⡜⡏⠛⠋⣠⢞⢞⢝⢕⠕⡩⡢⢕⣠⠭⠭⠥⠴⢦⣔⣤⣄⠀⠀⠀⠀⠑⡑⡙⡝⡜
⠀⠀⠀⠀⡇⠀⢸⠀⠀⣷⣤⡾⢡⢎⣾⢣⢫⢊⢎⡔⢩⡶⠋⣩⡬⠭⢵⣾⣝⢿⣷⡄⠀⠀⠀⠘⡄⠘⡜
⠀⠀⠀⠀⡇⠀⢸⠀⠰⡘⠋⢀⡞⣸⣹⡎⡎⣾⢸⣇⠘⢷⡀⢻⡇⢠⣶⠮⣟⣷⣝⣿⡆⠀⠀⠀⠘⡀⠱
⠀⠠⠀⠀⢃⠀⠸⡇⢢⡻⣦⣾⠃⣿⢸⢷⢳⡹⣦⣉⡛⠦⡙⣄⢷⢸⡇⢀⣈⡻⣿⠻⡇⠀⠀⠀⠀⠁
⡇⠀⡀⠀⠘⡀⠀⣷⣾⣷⣌⡁⢠⣿⠘⣆⠳⡙⠦⣭⡉⢳⡽⡸⣾⢾⡇⣾⠟⠻⡜⠄⣷⠀⠀⠀⠀⠐
⡰⡀⠰⠀⠀⠐⠈⢿⣯⡻⣿⣟⡛⠛⠀⣿⡆⠹⣦⠈⣿⢸⢃⢧⢿⢸⢠⠇⣠⣤⡙⠀⢸⠀⠀⠀⢀
⢣⢣⠠⠣⠀⠀⠀⠀⠙⢿⣮⣝⡿⢟⣚⣋⣡⠴⢋⡴⡣⢫⢎⢎⠎⢃⠏⡼⠛⠙⡇⡀⣸⠀⠀⡀⠐
⢣⣳⡳⡱⡑⠀⠀⠀⢄⠀⢉⡛⠙⠻⠒⠒⠒⠩⠕⠪⣒⠕⠃⠀⡠⣫⠞⣠⣴⣆⣧⢆⡏⠀⠀⠁
⢳⡳⡝⣝⢎⢦⡢⠀⢐⠵⡢⢌⣑⠒⠤⠤⣤⣤⠶⣙⠢⣀⢤⣪⢞⡥⠞⠉⢹⣿⣿⡼⠁⠀⡌
⢧⡙⢌⢮⡳⣕⢯⡢⣄⠉⠚⠥⣊⡉⠛⠒⠒⠘⣐⠦⣽⡾⠿⣚⣩⣴⣶⣷⣾⣿⡿⢁⡔⡘
⡄⠳⣌⠳⣍⠢⣑⠮⣓⠭⣒⡤⢄⣂⣉⠀⠄⠤⠤⠴⠒⣚⣋⣉⣀⢀⣿⣿⣿⢏⣤⢞⠝
⢿⣤⣿⣧⡈⢳⣌⠓⢬⣙⠲⢭⣑⡒⠮⠭⢭⣍⣉⣉⣉⠉⢙⣿⣿⣿⡿⣻⣵⣿⡿⠃⠀⠀⢀⠄
⠀⠉⠛⠻⠷⣤⣿⣿⣆⠙⣿⣦⣌⠙⢻⣶⣦⠀⣩⣿⣿⣷⣿⣿⣿⣽⣿⣿⠟⣪⠂⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⠾⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠛⠩⠠⠕⠉⠀⠠⠞⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⠀⣀⡀
⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡌⠉⡀⠙⣶⣂⠀⠀⢠⣄⣀⣰⡿⠃⢦⣄⣀⣘⣿⠆
⠀⠀⠀⢻⡇⠘⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⢸⠀⣿⡏⡆⠀⠀⠉⠉⠁⠀⣤⣤⡈⠉⠉⠀⠐⢲⡄
⠀⠀⠀⠘⢷⣤⠐⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⢸⠇⠀⠀⢸⠀⣿⣿⠀⠀⠀⠰⢥⣄⣴⡾⠟⠁⠀⡀⢀⣴⡿⠁
⠀⠀⠀⠀⠈⢻⣧⣌⠐⢀⠀⢂⠄⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⢹⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⢻⣿⡦⡀⢪⠄⠐⡄⠀⠀⢀⠀⡄⠀⠀⠀⡇⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣜⠦⠀⠀⠀⠀⣆⣷⣆⠀⢸⣷⣿⡿⠀⠀⠀⠀⢀⡀⣹⠟⢻⣿⠷⠴⣾⡅⠄⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠦⠥⠀⠀⢻⣼⣿⡦⣸⣿⡿⠃⠀⠀⠲⣦⣀⠽⠃⢐⣿⡿⢶⣶⣿⣷⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⠄⢤⣤⣤⠄⢠⣤⢤⢍⠛⠿⠿⠛⠀⠀⠙⠲⢾⣿⣟⣶⣛⣻⣿⣷⣿⣿⡿⠟⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠁⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡰⠶⠂⣿⠠⠴⠆⢸⡅⠶⠦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡿⠀⠀⠀⢸⠇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⠛⠓⠉⣻⡙⠛⢂⣼⡇⠀⠀⠀⠀⠄⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⢠⡄⣀⡀⠿⣄⡄⣠⣿⣧⣤⣤⢽⢷⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣬⡇⠀⢹⡷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠛⠀⡤⠂⠀⠀⠀⠀⠠⠤⢦⣤⡔⠲⣶⠖⠚⠃⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣒⣶⣶⣶⣼⣥⣶⣿⠅⣀⡀⡛⠓⠶⣄⣲⣶⠶⠶⠤⣤⣄⣈⣡⣿⣿⣆⠀⣀⣤⡄
⠀⠀⣹⢦⡠⣄⣀⣾⣴⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢙⠞⢿⡒⢦⣄⣈⡁⠐⠂⠚⠋⠁⠀⢀⣠⣼⣿⣿⣿⠃
⠀⠄⣠⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠐⠀⠉⢺⣍⠉⠉⣛⣳⣶⣤⣀⠀⣽⣿⣿⣿⣿⣿⣿⠄
⠀⠘⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠌⣱⣿⣿⣿⡿⠿⠿⠷⠿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⢸⡄⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠠⠤⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠈⠁⠀⠈⠀⠀⠀⠀⠉⠁⠀⠐⠄⡀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⣠⣴⠀⠀⠀⠀⢀⠀⠀⠘⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠆
⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⠓⠚⠛⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠀⠠⠤⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠤⠀⢀
⠀⠀⠀⠀⠀⢄⣀⡀⠈⠁⠀⠀⠀⡀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣁⢀⡀⠀⠀⠁⠒⠁⣄⡤⠄⡀⠈
⠀⠀⠀⠀⠀⠀⢆⢀⠠⣄⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠈⠋⠉⡁⠀⠀⣀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠖⠃⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠠⠀⠂⠀⠤⠄⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠤⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⢀⣴⠊⠙⠁⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⡴⠆⠀⠐⠃⠀⠀⠐⠚⠂⡀⢀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⣀
⠀⠀⡘⠁⠀⣠⣄⠀⠈⠓⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⣀⠀⠀⠀⠀⠐⡻⠁⠀⢰⡀⠠⠟⠂⠀⠀⢠⣄⠉⠁
⠀⠀⠇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠋⠀⠀⣀⠠⠁⠀⢾⠦⠐⠉⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⡇⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠰⠦⠀⠀⢀⡤
⠀⠀⠻⠄⠀⢀⡀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠁⠘⠃⠀⢀⣤⢤⡄⠀⣤⣤⣤⣤⣀⣰⣏⡼⢀⠀⠀⣠⢤⠀⠀⠀⠘⠺⢇⡀⠀⣉⠠⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢡⣾⠇⢈⣋⠀⣨⢍⢩⣿⢭⡄⣾⣰⢒⠛⢮⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠸⠿⢠⣿⢸⣾⣧⣸⣾⣿⣞⠱⠧⠻⠄⢺⣆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⣠⠿⣏⠟⠙⠳⢋⣈⣥⡿⢷⣋⣉⣱⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠁⠀⠀⠘⠿⠿⠛⠋⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⠀⣀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢤⡀⠀⠀⠀⠀⠀⠀⣠⢇⣈⣉⠠⠄⣄⠀⠂⠀⣀
⠀⠀⠀⠚⢱⡄⠘⠁⠀⢀⣠⡀⠀⠘⠿⠀⠀⠀⠀⢀⠠⠞⠁⠠⡶⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⣿⠞⣉⠀⠀⠤⠀⠀⣀⠀⠁
⠀⠀⢸⣇⠀⠀⣀⠀⣤⡄⠁⢠⣤⣄⠠⢢⠆⠀⢠⡇⠐⠂⠀⠀⠀⠘⠀⠈⠉⠀⠙⠂⠀⠀⠀⣾⣶⡿⢷⠛⣛⠛⠛⠻⣄⣠⡗
⠀⠀⣾⣿⣿⣦⣦⣤⣠⣤⣄⣀⣀⣤⠴⠏⠀⠀⡰⠀⠈⠉⠀⠀⠀⠄⠰⣆⠀⠂⠀⠀⠀⠀⠀⣿⠋⢠⣄⠈⠋⠀⠠⣤⠀⠙⢆
⠀⠀⠙⣾⣶⣤⠆⠈⠉⢉⠀⣀⣰⣿⣧⡾⠀⠀⠈⠀⠀⠁⠈⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⡆⢀
⠀⠀⠈⣛⡛⠛⠉⠙⠛⠛⣻⡏⠉⠁⣀⣀⡤⠀⠀⠀⠀⠲⠀⠀⠀⠀⠘⠀⠈⠁⠠⠒⠂⠀⠀⣷⠉⢀⡀⠀⠀⠙⠀⢀⠀⡆
⠀⠀⢘⡹⠋⢹⣗⠛⠛⡿⢓⡖⠚⠛⠙⣋⡀⠀⠀⠀⠀⣀⠀⠠⠔⠒⠀⠂⠀⠀⢀⡀⠀⠀⠀⠘⡆⠈⠋⠀⠤⠀⠀⠀⠁
⠀⠀⢾⡿⣻⡗⢶⢤⡶⠶⠶⠶⠚⢋⣍⠡⢠⠀⠀⠀⠀⠀⣄⠀⠀⠀⣶⡆⠀⠀⠈⠁⣰⠂⠀⠀⠈⠲⠄⣀⡀⠐⠖⡠⠖
⠀⠀⠀⠛⠻⠷⠦⠍⢁⣀⣠⠤⠤⠤⠽⠚⠁⠀⠀⠀⠀⢤⠀⢤⠄⠀⠀⠀⠀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⣶⣶⣶⡾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢸⣿⣿⣯⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣿⣿⣿⣿⣿⣿⣿⣿⢽⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣽⣿⣿⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡘⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⡿⠁⠀⢹⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⢿⡆⢿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⠃⣀⠀⠀⣀⣬⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡄⠀⣿⢾⣧⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡏⠀⢈⣴⣾⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠘⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣴⠋⠝⣿⣿⠦⡜
⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⢹⣿⠉⢛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⡋⠀⠈⢹⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⣸⠟⠒⠀⠙⠀⢀⣈⣉⡻⣿⣿⣿⣿⣏⡴⠋⠐⠒⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠌⢹⠀⠀⣠⣾⣿⠛⠋⠛⠿⠹⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⣼⠀⣴⣿⣿⡉⠀⠀⠀⠀⢧⢹⣿⣯⠹⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡀⡏⣸⠏⠙⣿⡁⠀⠘⠀⠀⠈⠂⢻⡇⠀⠀⠀⠀⢀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡀⠈⢻⣤⠀⠂⠀⠈⢦⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠈⢁⡀⠀⠻⣧⠀⠀⠀⠈⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⡀⠀⠀⠀⠗⢀⠀⠈⢣⠀⠀⠐⡀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠁⡀⠀⠀⠄⠀⠁⠀⠰⡇⠀⠀⡐⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⡄⠀⠀⠀⠀⠀⠀⡀⢷⡠⠦⠀⠒⠶⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠉⣀⣀⣠⣄⣀⣀⣈⣠⣷⣶⡶⠶⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣽⣿⣭⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣶⣶⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⣩⣭⣉⣤⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣉⣉⣭⣍⣥⣴
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣈⣩⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣈⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁
⠀⠀⠀⢤⣌⣠⣤⣉⣳⢤⣀⡀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠁⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠁⠀⠁⣀⣀⣀
⠄⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣠⣤⣴⣿⠿⠟⠀⠀⠚⠻⢷⣦⣄⡀⣀⠀⠱⣦⣤⣄⣀⠀⣀⣠⣴⡿⢻⣿⠿⣿⢿⣿⣿⣿
⣤⣀⠀⠒⠂⠀⠀⠀⠐⠶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠁⠀⠐⢒⣢⣤⣦⣤⣤⣭⣽⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⣵⣿⠿⢻⣌⡱⣶
⣿⣿⣿⣷⣶⣶⣶⣤⣤⣴⣶⣿⣿⣿⣿⡿⠿⠛⠛⠁⠀⠀⠀⣀⣀⣹⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣥⡼⠻⣧⣉⢳⣤
⠈⠉⠉⠛⠛⠻⢿⣿⣷⣤⣤⣭⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠉⠁⠄⠛⠛⠉⠉⠻⠛⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣝⣷⣌⠻⣧⣄
⠀⠀⠀⠀⠀⠂⣀⣀⣈⡉⠛⠛⠿⠿⢿⣿⣷⣶⣶⣦⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⢉⣉⠁⠤⠤
⣦⡔⠛⠓⣦⣤⣯⣭⣭⣤⡤⢶⣶⣆⣀⣭⣭⣥⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⡀⠀⠠⢤⠄⠒⠒⠢⢤⣭⡉⠒⠲
⠛⠛⠒⠛⠿⠣⠤⠤⠬⣴⣶⣮⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠉⠉⠉⢁⣀⡀⠀⠐⠒⠒⠀⠉⢉⣁⣀⠐⠲⢤⣈⣉⠒⠶⢶⣬⣿⣷
⠛⠓⠲⠶⠶⠦⠤⢄⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⡀⠀⠠⠤⠶⠶⠶⠒⠀⠉⠉⠉⢁⣀⣀⠠⠤⠶⠂⣈⣉⡀⠒⠆⣈⣉⣱⣶⣶⡿⣿⣷⣾⣿⣿⣿
⠤⠶⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠤⠤⠀⠒⠛⠋⣉⣀⡀⠤⠤⠄⣘⡃⠤⢤⣄⣿⣷⣾⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⠤⠖⠒⢛⣉⣠⡤⠤⢒⡒⠢⣬⣽⣶⣿⣿⣿⣿⣭⣒⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⠉⠉⣉⣉⣡⣤⣤⠖⠒⠒⠋⣉⣡⣤⡔⣲⣮⣽⣿⣿⣿⣿⣿⣿⣟⣻⣯⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⠶⠶⠶⠶⠛⠉⠉⠉⠀⢀⣤⣤⠶⠖⢊⣩⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣴⠶⠶⠛⠛⣉⣠⢴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠛⠛⠉⠁⣀⣠⡤⠖⣛⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⠻⠿⣿⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣴⠶⠾⠟⠛⠋⠉⠁⢀⣀⣤⣤⠞⠛⢉⣡⣴⣾⣿⣿⣿⣟⠿⣭⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⣠⣤⡴⠶⠏⠉⠁⣠⣤⣶⣿⣿⣿⣿⣿⣿⣷⠻⢧⡝⢷⣹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⠶⠶⠾⠟⠛⠉⠀⠀⢀⣤⠶⣾⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣤⠶⢛⣫⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⡴⠾⠛⢛⣩⡴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢛⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣤⣴⠶⠛⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣶⡘⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣩⣤⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠛⠛⠛⠛⠛⣤⡿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⡿⠿⣿⣿⣿⡿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠿⠿⠿⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⡀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠷⠶⠿⠿⠿⣿⡿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡛⢻⣿⣷⣦⣀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠿⢿⣭⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣥⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠿⢿⠟⣉⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢡⡦⠀⢉⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠖⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠋⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠴⢆⠐⣦⣤⠴⠛⠁⠀⠀⣀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠊⠀⠀⠰⣠⠇⣼⠅⠀⠀⣶⣶⣿⣿⣿⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠙⣆⠀⢠⢢⣴⣷⣾⣿⣷⠀⠀⠉⢿⣿⣿⣿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⢦⢠⠀⠘⣤⡏⠠⠀⢀⡬⠍⠻⣷⣜⢠⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⠀⣻⣿⠃⠴⠞⠓⠼⠵⡲⠾⢃⣿⣿⠟⣿⠿⠾⠻⣿⠳⠄⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣶⠆⠈⢡⣞⣩⠼⣯⡄⠰⣶⣷⠀⠈⣿⡴⠟⣩⢞⣿⣄⡀⠀⠛⣧⡄⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣲⡏⠀⢀⡼⠁⠀⠀⢸⠂⡶⠯⢭⣹⣡⡿⠀⢾⠿⣄⢻⣿⠛⠳⢌⣸⠦⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⣈⢲⠀⢾⠾⠻⣷⡀⠼⠃⣑⢲⣶⣮⣿⣧⣬⠞⣡⢿⡆⣧⢈⣴⣿⠁⣼⢃⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⠀⣷⠘⢷⣦⣬⡛⣷⣾⣿⣀⠖⠞⠳⢶⣶⡿⢫⣾⢥⣇⣌⣋⣥⣞⣱⣿⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠹⣏⠂⢶⣿⣶⠏⡉⣁⣿⠿⣝⢿⠀⠀⣤⣾⠟⠁⣼⣯⢀⣴⣾⠟⢛⣹⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣉⠒⠴⣿⣇⠶⣿⣿⣿⠤⠦⡴⠤⢶⣾⣇⡳⣴⣧⣿⣿⣿⣽⣴⠿⠛⢩⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡓⣷⠀⠍⣑⣋⠛⢓⢐⠴⠄⠀⠀⠈⠊⠿⠟⠛⢛⣋⣉⣡⣤⣶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣻⡇⠀⢰⠉⠉⠙⢻⢻⣿⡶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢻⡰⠀⣇⠀⢀⠀⣠⠐⠰⢸⣿⣟⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⡇⠁⢿⣆⢠⠈⣿⣿⣊⣹⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢠⢸⡇⢈⡧⣿⣿⡅⢺⣿⣿⣳⣿⡿⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⡜⣿⡄⣷⣿⣿⣇⣸⣿⣿⣾⣿⡏⡟⣾⣿⣿⣿⡇⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣧⣇⣽⣿⣾⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣷⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠛⠂⠈⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⢠⠀⡄⣠⣄⢀⣤⡀⣤⣄⢠⠀⠀⣤⠠⣤⡄⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⢸⣤⡇⡇⢸⢸⠀⠁⡇⣿⢸⠀⢰⢿⡆⢸⠀⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠸⠐⠇⠷⠾⠸⠶⠇⠧⠟⠸⠦⠼⠛⠇⠸⠀⠿⠤



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠒⠒⠂⠀⠒⢒⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠳⠒⠒⠒⠦⠤⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠉⠀⠀⠀⠀⢂⠀⢀⠎⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠤⣀⣀⣠⢀⠎⠀⣼⠇⠀⠀⠀⠀⠀⠀⡇⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡃⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⠊⠀⡜⠓⠀⠄⡈⠁⠝⠃⠒⠷⢛⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⢀⠀⠀⢤⣀⢀⣠⠇⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⢐⠇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⠀⠀⠀⠀⠈⠀⠀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⢤⣀⣀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⡼⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡼⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠤⠤⠤⢄⣀⣀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡁⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⡆⢸⣏⡝⢄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⠘⡇⡀⠀⠀⠀⠀⣠⠟⠀⣼⠃⡈⣯⢂⠉⠉⠱⠒⢂⢄⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠖⠒⠊⠉⠁⠀⠸⠁⠀⡇⢹⡆⡑⠀⠀⠀⠈⠀⠉⠑⠂⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠚⣿⣛⡻⠟⠋⠀⠙⠀⣠⠀⠀⠀⡆⢸⠇⠳⣤⠤⢀⠈⠀⠈⠑⠀⠘⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣠⡴⠞⠁⠀⣀⠀⠁⠀⢠⡏⣶⠀⠀⡇⢸⠀⠠⡟⢀⠀⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠠⣾⠷⠋⠀⠀⣠⡜⠁⠀⠀⣿⣿⣷⠿⠀⠸⠀⣿⡄⠀⠁⠘⢦⡀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣿⡴⠃⠀⠀⢀⡴⠋⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠘⣿⣇⠀⠀⠀⠈⢳⠄⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣎⡁⢠⡟⠁⠀⠀⣠⠊⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⢄⣄⡀⠻⣿⡄⠀⠀⠄⡀⢢⡀⠀⠰
⠀⠀⠀⠀⠈⠛⠶⠾⣿⡾⠿⣷⡟⠀⠀⠀⠀⠁⠀⠀⠀⢀⣴⠟⢁⢈⡈⠁⠀⢐⣋⣡⠰⢿⣷⣄⢠⠀⡇⣾⢓⠦⢭⡆
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠉⠀⠀⠀⣶⠃⠀⠀⠀⢤⣼⠋⠠⠀⣨⠄⠀⡀⣺⠤⣼⠀⢿⣿⣿⣦⣇⣰⣄⣹⣿⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡰⠁⠀⠀⢀⢰⣾⠃⠀⠀⠀⠴⠀⠤⢤⡟⠲⠖⠀⢸⢹⣟⢻⣿⣿⣝⡛⠻⠛⠛⢓⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢀⣠⠁⠀⡄⠠⢄⣾⡏⠀⠀⠄⣴⠂⠀⠀⣼⠛⠓⡏⠀⠈⣼⣏⢀⠿⡄⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⡉⠐⠤⠀⣠⣾⣿⠃⠀⠂⠠⠈⠀⠐⢤⣌⠉⢻⠃⠀⠀⢿⣿⣇⢰⣷⣦⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡁⠄⣠⣾⣿⣿⣿⠀⠀⠐⠲⠉⠀⠒⢾⡅⠉⡋⠀⠀⠀⡞⠈⠙⢾⣿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣿⣿⣿⣿⣿⠀⢉⠐⢊⠈⠀⠲⠅⣀⡸⠁⠀⡴⡼⠁⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠋⠁⠀⡄⢨⢨⠄⠀⢀⡾⠦⢤⠃⠀⣰⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠰⣴⠂⠢⣼⣃⡒⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠃⠶⠗⠋⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠈⠁⢀⠀⠀⠀⠀⢀⢤⠀⡆⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣉⣉⡤⢬⣉⡉⠉⢉⣡⣈⡷⠁⠀⠀⠈⠒⠒⠦⠤⠦⠀⢶⡶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⡀⠀⢀⣠⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠙⣿⣁⢄⣒⢐⡄⠐⠊⠀⠀⠀⠀⠠⠄⠈⠑⣀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⠉⣭⢄⣀⡀⠀⠀⠀⠀⢠⡄⢠⣅⡬⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠓⠈⠁⠀⠀⠀⠀⢠⡉⢩⠀⠠⠀⠄⢉⡐⡀⠀⠀⠀⠙⡜⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠈⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠘⣬⣆⠀⠔⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡠⠂⠊⡀⠀⠰⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣴⡺⠟
⠀⠀⠀⠀⠀⠀⠀⡅⠒⢢⣀⠙⢁⠀⠐⠺⣶⢤⠚⠗⠁⠀⠀⠀⠤⠄⣪⠀⠐⢒⡩⠂⠀⠀⠀⠀⠀⠀⠠⡤⠄⢀⠐⡀⠠⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠷⠤⠴⠛⠚⠛⠒⠚⠀⠀⠀⠀⠀⠀⢰⠡⣤⣴⠒⣭⠄⠲⠖⢤⠀⠀⠀⠀⠀⠇⡀⠀⠈⠙⠖⠲⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢢⣖⣀⡠⠴⠃⠀⠀⠀⠀⠈⠒⠒⠒⠒⠢⠄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⣁⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠃⠀⠀⠀⢠⠂⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢃⠀⠀⠀⠀⠰⠈⡀⢄⡀⠤⠀⠀⠀⠀⠄⡤⠀⠀⠀⠀⠀⡐⠀⠀⠀⢠⡿⠁⠀⠀⠀⠸⡄⠀⣀⡠⠠⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⠰⠆⠀⠀⠀⢀⢠⣤⡀⠉⠰⠂⣀⠀⢂⣰⠄⠀⠀⠀⠀⢀⡓⢀⡠⠴⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠀⠀⠀⠀⡀⠀⠀⠈⢃⠀⢈⢉⠰⠶⠤⠄⠊⠛⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⣀⡌⠗⠀⠀⠀⠨⠀⢠⣤⠠⠀⠴⠆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠤⠔⠂⠲⡌⠉⠉⢀⠙⠆⣀⣀⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠺⡄⠉⠀⠀⠱⣄⣀⣤⣤⠴⣴⠖⠛⠛⠙⢧⡀⠠⠀⢐⡄
⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⢰⡀⠀⠀⠀⢠⡖⠠⠀⢤⢀⡀⠀⠀⠀⠀⠀⠙⡆⣀⣠⣤⠽⡶⠖⠛⠋⠛⠉⠀⠄⠀⢙⡄⢀⡠⠴⠌⠓⠒⠛⠉⢉⡄
⠀⠀⠀⠀⠐⡈⠑⠒⢀⡌⢀⡃⠀⠀⠀⠀⢀⢠⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⡜⡅⠀⠀⠀⠰⡀⢀⣠⠤⠴⠄⠐⠚⠋⣉⢀⣤⠆⠠⠴⠚⠐⠂⠈
⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡽⡙⠚⠲⢿⠆⠉⠀⠀⠀⠀⠀⠹⣠⠔⠒⠛⠉⣉⣀⢠⡦⠤⠠⠖⠂⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⡂⠁⠀⠀⠀⠀⠀⠀⠙⠤⠐⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠾⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠥⠶⠤⡀⡀⠀⠀⠀⠀⠀⢻⣤⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠠⢀⡽⠛⠦⡀⠀⠀⠈⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣾⣤⡈⠁⣠⣀⡀⠀⠀⠅⣈⠻⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠉⡻⢻⢻⣿⢟⣾⣿⣿⣿⠿⣧⣦⣄⠙⠓⠦⣉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠃⠈⡾⠇⢼⡏⣿⠋⠀⠀⠈⠙⢟⠀⠀⠀⠈⠑⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⡀⠀⠀⠄⠀⠻⠀⠘⠀⠀⠀⠀⠈⠀⢢⠀⠀⠀⠀⠀⠑⣔⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠓⠲⠶⢶⡶⣶⠇⠀⠀⠀⠀⠀⠐⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢊⠧⠠⡀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠇⠀⠀⠀⠀⠠⠀⠀⠠⠗⣦⠱⡄⠂⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⠀⠀⠀⠀⠀⠀⢀⠆⠀⣌⡃⠀⡹⣆⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣿⠀⠀⡞⠀⢠⣠⣞⠀⠀⣣⠁⠐⠈⡿⣷⣄⢄⢀⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⣰⢃⣴⡿⣏⢩⡀⠀⠦⠄⠰⠀⠇⢨⠙⠳⢷⣝⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⣿⡿⠛⣄⠹⣆⡦⠀⢺⡆⡀⠈⢀⠆⠀⠀⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠘⢆⠙⣿⣆⢸⠃⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⠻⣾⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣩⠞⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣭⡥⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⢰⣿⣿⣿⡆⠀⣁⣘⢶⠃⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⣿⡝⣿⡇⠀⠺⡩⠡⠂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⡖⡶⣄⡶⣖⠂⠀⣀⣀⣀⣀⠀⠀⠀⠈⠁⠁⠀⠀⠀⢠⣀⡄⠀⠀⣴⣾⠳⢻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠓⠃⠙⠀⠓⠂⠀⠨⠭⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠻⠿⠶⠾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⣾⡏⢀⡇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⢃⡞⠁⠀⠀⠈⠁
⠀⠀⠀⣤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠉⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⢤⡄⢀⣀⡀⠶⠆
⠀⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠠⣤⠀⢤⡄⠉⢠⡤
⠀⠀⠀⠀⠃⠀⠀⠐⠁⠀⠀⠀⠀⠰⠦⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⣷⣤⡀⠀⠀⠀⠀⠀⣠⣶⡟⠁⠀⠀⠀⠉⠉⠓⠀⠀⠀⠀⠀⢸⣿⣶⣿⡇
⠀⠀⠀⠀⠸⢿⡿⠏⠀⠀⠀⠙⠿⠇⠀⠙⠟⠀⠀⠿⠛⠀⠀⠀⠀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⢸⡟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠸⠇⠈⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⡀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠻⠋⠙⠟⠁⠀⠈⠛⠁⠘⠛⠀⠀⠀⠀⠀⠆⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁
⠀⠀⠀⠈⠁⠀⠀⣀⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠀⢠⣤⣤⣤⠀⠀⣴⣦⣤⣄
⠀⠀⢠⣀⣀⡀⠀⠙⠛⠛⠁⠀⢲⠶⣶⠆⠀⠀⠀⠈⠀⠀⠀⢸⡋⠈⢻⠀⠀⠉⣭⣍⠉
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⠶⠶⠀⠀⠀⢀⠀⠀⠀⠀⠈⣷⣶⡿⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⣠⠴⠒⠲⣄⠙⡄⠀⠀⣠⠖⠛⠋⢉⣉⣍⣈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⣠⠶⠶⢶⣇⡜⠀⢰⠇⠀⢀⣼⠫⠤⣤⡈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠈⠑⠒⠠⠔⠛⠁⠀⣾⠀⠰⣏⠙⠦⠄⠚⣁⣤⠴⠚⠊⠐⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢒⣦⡤⠀⠀⠀⠀⠀⣿⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⢹⡃⠀⠀⣠⠞⠋⠉⠉⠛⠷⣦⡀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠈⠙⠓⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠹⡀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣾⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⠶⠶⠤⢧⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡏⢸
⠀⠀⠀⠀⠀⠀⠀⣠⣸⠇⣿⣠⠶⠶⣾⡉⣧⠀⠀⣀⣤⣿⣄⣀⠀⠀⠀⢸⠇⢸⡇⢠⠔⣒⡶⠶⢶⣖⠒⠲⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⢰⠉⠟⠀⣿⠈⠓⠒⠋⠃⡿⠀⢰⡏⠀⠹⣷⣌⣷⣀⣰⠟⠀⢸⡇⢸⡼⡁⠀⢀⡤⠈⠑⢦⠀⠀⠀⢉⣷⡤⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆⠀⠀⠀⡰⠇⠀⣾⠀⠀⠀⠀⢹⡟⠋⠁⠀⠀⡼⠀⠈⢷⣿⡾⠟⠀⠀⠀⠈⡇⠀⡴⠋⣽⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢷⣿⠀⠀⣷⠀⠀⠀⢷⣄⣴⠏⠀⠀⠀⠀⢸⡇⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠘⢷⠾⠃⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠘⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⡀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢾⠋⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠘⣄⡀⢀⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣍⣉⠭⠟⠉⠉⠉⠓⢢⣄⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸⡿⠀⠀⢀⡴⠏⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⣤⣤⣀⡀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⣯⠴⠚⠁⠀⢠⡾⠋⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠈⠉⠓⣾⣏⠀⠀⠀⠀⠀⠀⠀⠘⢤⡤⠶⠚⠉⣿⠀⠀⠀⢠⠟⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣨⠷⣶⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⡞⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⡞⠁⣀⣈⡇⠈⡇⠀⠀⢀⡴⠶⣤⡀⠀⢸⡆⠀⠀⡇⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⢀⡾⠃⢸⠀⢸⡏⠙⢶⡄⢩⠀⢀⠟⣠⣤⣌⣷⠀⢸⡇⠀⠀⡇⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⢠⡾⠁⠀⢸⠀⢸⠛⠛⠛⠁⡆⠀⢸⠛⠧⠍⠿⠛⠻⢾⠷⠶⠾⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣠⠟⠀⠀⠀⢸⠀⢸⡆⠀⠀⢠⠃⠀⣿⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣧⠀⠀⠸⢦⣤⡇⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠈⣧⠀⠸⣆⣀⣀⣀⣀⣤⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠈⢻⡄⠀⠀⠸⡆⠀⠈⠉⠉⡩⠟⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠹⣆⡠⠖⠉⠀⠀⠀⣠⠟⠁⢀⣄⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠀⠀⠀⣀⣀⣽⢦⡖⠋⠉⠳⢦⣤⣤⣤⠞⠁⣠⠔⠋⠉⠛⢶⣄⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠁⠀⠀⠙⠲⣄⡀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠀⠀⠀⢠⡤⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠾⠤⠄⠤⡤⠤⠴⢒⣈⠁⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠄⣠⠄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠤⠤⠀⠊⠉⠠⣀⣐⠼⠀⠀⠀⠀⠀⠀⢈⠆⠈⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠛⠋⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠆⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠲⠀⠒⠂⠀⠀⠀⠀⠀⠀⢲⡟⡄⠀⠉⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⡇⠐⢊⡞⡰
⠀⠀⠀⠀⠀⣀⡠⠤⠴⢖⠋⠉⠉⠉⠙⠛⠒⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠇⡠⠒⠒⠒⠀⢀⣉⣉⡉⡉⠁⠀⠇⠰⢁⢌
⢀⡴⠀⠦⠤⣔⡠⠄⠠⠤⠀⠀⠀⠀⢀⣀⡠⠤⠀⠀⢰⡄⠀⠀⠀⠀⠀⢰⠀⢾⠉⣉⡉⢑⣈⣀⣀⣀⣤⡤⠤⢄⠀⠴⢋⠄⣠
⣇⠤⠙⠛⠦⢌⠉⠙⠒⢦⠀⠐⠛⠉⢋⣀⠤⠴⠒⠚⢃⣼⠇⠀⠀⠀⠀⠸⢷⠄⡀⠈⠉⠓⠒⠦⠤⣀⠀⠀⠐⢁⡤⢊⡴⠞⠁
⠈⠐⠲⠤⣄⡀⠀⠈⠀⠈⠐⠂⠉⠉⣀⡠⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⢠⠀⡀⠀⠂⡍⡒⠶⢦⣤⣄⡐⠀⢐⡲⣁⠞⠉
⠀⠀⠀⠀⠀⠁⠐⠲⠶⠶⠀⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⣃⠀⢠⠍⠂⠀⠊⢝⣛⠫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠠⣀⣘⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣢⠭⠵⠤⣤⠖⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠨⡍⠁⡄⠀⠀⠀⠉⠀⠈⢰⡀
⠀⠀⠀⠀⠀⣀⡴⠚⠓⠤⢈⢸⠀⢸⠀⠀⠀⠀⠀⠀⠈⡃
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢇⠞⢀⡀⠀⠀⠀⠀⠀⠀⠀⣟⡦⠀⠀⠀⠀⠀⠀⠸⢫⠙⣡⠤⡽⢏⣀⣙⣋⣀⣀⣠⠀⠶⠦⡄
⠀⠀⢤⡠⠘⠦⢄⡀⠀⢀⣨⠀⠀⠇⡤⠒⠒⠒⠒⠂⠀⠘⡇⠀⠀⠀⠀⠀⠀⡔⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡇
⠀⠈⠪⣍⡀⠢⣄⡈⠳⠉⢉⣠⠀⠀⣀⡠⢶⣶⣖⠂⠀⠀⢳⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢀⢡⠁
⠀⠀⠀⠀⢉⠦⡁⡈⠒⠒⠁⠉⠆⡆⠈⠛⠀⠀⠀⠀⠀⠀⢡⠆⠀⠀⠀⠀⠀⡀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠸⠸
⠀⠀⠀⡔⠀⠀⢘⠳⢤⣀⡠⠖⠑⡰⡄⠸⡄⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠌⡂⠤⢀⠈⠐⠨⠁⣒⠠⠕⢳⠀⠅⠀⠀⣀⣀⣀⡀⡿⡄⠀⠀⠀⢰⢄⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉
⠀⠀⠀⠀⠈⠑⠂⠄⡀⠀⠀⠀⠀⠘⣿⡧⠃⠀⠈⠉⠁⠀⠀⢠⠇⠀⠀⠀⠸⠋⠛⠋⢸⣉⣭⣵⣤⣄⡀⠀⠚⠳⣶⣦
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣐⣀⣁⣬⣿⣁⣤⣤⣐⣒⣒⣒⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣀⣈⣉⣉⣁⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡠⢄⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢀⡠⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠰⠅⠀⠀⠀⠀⠉⠉⢢⠀⠉⢰⠁⡠⠀⠈⢢⡀⠀⠀⡰⠁⡠⠆⠄⠀⡝⠌⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠐⠈⠆⠸⡠⠁⠀⣀⠤⠄⡤⢤
⠀⠀⠀⡀⠀⠀⠠⠄⠲⢥⡁⠀⠐⣄⠀⠁⠤⡀⠰⡀⠀⡅⢀⡀⢀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⡐⠀⠀⠀⠁⡜⠀⢠⣈⠁⠘⠗⠤⠤⠍⡏
⠀⠀⠀⢰⣐⠀⠀⠀⠀⢂⠽⠀⠀⠈⠢⢄⠀⠌⠢⠇⠀⠀⢎⣕⡲⠀⠀⠀⢀⠂⡀⡀⢸⠀⠀⡐⠀⠀⠀⣡⠊⡔⠀⠀⠈⠢⠀⡄⠀⠀⠀⡇
⠀⢠⠀⠀⠄⠀⠐⠈⠁⣠⠤⠤⡠⠠⠀⣄⠉⠐⠀⢠⣞⡃⢨⣊⠼⠀⠀⢄⡠⠃⠀⢱⠄⠈⢠⠠⠄⢀⠔⠁⠀⠸⠓⠤⠴⠄⠀⠁⠐⠒⠁⡀
⠀⠈⠃⠀⠨⠇⠀⠴⡃⠠⠀⠐⠡⢁⣂⡠⢕⡄⠀⠘⠋⠀⠀⢷⠇⠀⠀⠲⢇⠀⠀⢰⠦⣐⠈⠂⠐⠁⡐⡠⠀⠐⠦⠤⠀⠀⡀⠴⠈⡀⠀⠈
⠀⠀⡔⠲⡄⠀⡔⣀⡒⢒⣢⢁⣁⠼⠃⢊⡍⠀⣔⠒⠓⠼⢄⠘⠀⠀⠀⠀⢐⠀⡍⠀⠉⠀⠀⠀⠀⠀⠐⠁⢴⠄⠀⠤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣷⠀⠘⠄⠀⠢⠄⠄⠤⠤⠴⠒⠚⠉⠀⢄⡇⠀⠀⠀⡇⠀⠌⢀⠁⢀⠼⠰⠁⠀⠀⡠⣶⠿⣿⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢠⠚⠐⠆
⠀⠀⣇⠨⡁⢸⠀⠀⠀⢤⠤⢄⠀⠀⢀⣀⣤⠈⢧⠠⢄⡘⠁⠀⠈⠨⠆⠀⠀⠀⠂⠀⠈⠉⢻⡒⠛⠛⠛⠳⠀⠁⠀⠀⡍⠀⠈⠓⠒⠊
⠀⠀⠘⠦⠴⠊⢀⠄⠀⠈⠂⠤⠀⠤⠄⠔⠁⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠑⠒⠁⠐⠠⢖⠒⠒⠁⠀⢹⠉⠀⠀⢀⠤⠄⠠⠄⡀
⠀⡠⠀⢠⠀⡰⠁⠙⠀⠘⡀⠀⠀⢀⢀⣄⢠⢤⢰⡿⠞⢱⠀⡠⠩⠐⠒⠐⠒⠪⠔⠁⠀⠠⠄⠀⠈⠀⠠⠀⣀⠒⠀⠐⠀⠰⠃⠀⢈⠤⢤⢃
⠀⠙⠣⠁⠠⠁⠀⠀⠀⠐⢀⢤⠀⠠⠀⠐⠚⠈⢉⠠⠒⡱⠘⠏⠙⡠⣲⠖⠁⠀⠀⠀⠄⠀⠴⠀⠀⣀⠀⠀⣁⠀⠀⠀⢠⠃⠀⡔⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠈⠐⠂⠀⡈⠀⢀⣊⡭⡴⠦⠒⠋⣡⡀⠀⠀⠀⠀⡜⠀⠀⣠⠐⠇⠩⠠⠅⠩⠈⠣⡀⠑⣀⠽⠆⢀⡀
⠀⢀⠀⠂⠐⠙⢄⠀⠀⠀⠀⡲⠁⠤⠄⠀⠀⠊⠀⠈⠀⣠⡀⠀⠀⡺⠭⠃⣄⢀⠨⠊⣀⠀⠀⡀⠀⠄⠈⠉⠉⠀⠈⡀⠁⠀⠀⠀⡜⠀⠈
⠀⠘⠤⠀⠀⠈⢀⡄⠀⠀⠐⠚⡞⠠⠀⠀⣰⠶⠞⠛⠀⢛⡧⣤⡀⠉⢀⠔⠈⠀⠀⠀⠈⠀⠀⡆⠁⠀⠀⠀⠁⠈⠀⠈⡇⠀⠀⠠⢃⠐⢀⡁
⠀⢀⡀⠐⢊⠔⠃⠠⡀⠀⠂⠁⠉⠀⠀⠜⠁⠀⠀⠀⠐⠌⠈⢁⡀⠈⠀⢄⠆⠀⠀⠒⢀⠣⠈⠑⠀⠀⠐⠒⠒⠒⠊⡊⠝⢀⠀⠀⠀⠀⢀⠁
⠀⠰⠀⠉⠀⠘⠀⠠⢂⠄⣀⠐⠠⠀⠀⡀⠀⠀⠀⣀⣄⠀⠌⠀⠀⢂⠀⠀⠀⠀⠐⠀⢁⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡮⡆⠀⡒⠒⠊
⠀⠀⠣⠬⠄⠂⠁⠀⢇⢸⣁⡐⠀⠢⠀⣁⡀⠀⠉⠉⠀⢌⠀⠀⠀⢸⠀⠘⠀⠀⠁⠊⡀⠁⠀⠁⠠⠐⢒⠂⠠⡎⠈⠂⢀⠈⠁⠀⠧
⠀⠀⠄⡠⡀⡠⢆⡀⠀⡆⢀⠤⠄⠊⢀⠇⠈⢁⠁⠠⠁⠀⣄⠀⠀⡾⠀⠰⠀⠀⠀⠀⠀⠀⣀⠴⠋⠁⠂⠀⢉⢱⠤⣀⠤⠊⠀⣀⢀⠀⠆
⠀⠠⠂⠂⠃⠓⠀⠖⠀⢈⠥⠤⡀⠀⠢⠄⡶⡇⠀⢀⠀⠐⠈⠀⠀⡜⠀⠈⠀⢤⠀⠀⡰⠋⠁⠀⠀⠀⡔⠁⠀⠀⡴⢁⠀⠀⢀⠹⠗⠎⠈
⠀⠀⠀⠀⠰⠀⠄⠒⠀⠀⠐⠒⠊⠀⠀⠀⠀⠠⠀⠀⠑⠄⠠⠔⠚⠀⠀⠀⢄⡀⠠⡘⠄⠦⠄⠠⢭⠒⠤⣤⠤⢚⡀⠝⢀⠀⢈⠀⢀
⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠘⣠⠠⠁⠀⠁⠀⡠⠤⠴⢆⠀⠀⢄⠀⠠⠉⠈⠑⢊⠉⠐⠒⢒⡀⠉⢀⡀⠈⢁⡀⠀⠐⠀⠀⠁⠀⠀⠜⠔
⠀⢀⢀⠐⣀⢀⡀⠄⠀⢠⠁⡠⠤⠀⠁⠀⢎⣉⠆⠱⠀⠀⠚⠀⠀⠊⠀⢠⡀⠀⣀⠀⠀⠀⠐⣃⠟⢰⢁⠘⠐⢁⡑⠀⢀⣀⠄⠤⠤⢀⠄
⠀⠈⠚⢀⡀⠄⣀⠀⠀⠀⢨⠀⠀⡠⠤⢄⠈⠀⠀⠐⠒⠒⠂⠀⠐⠀⣤⠄⠀⠈⠉⠀⠠⡄⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠨⠉⡀⠀⠀⠀⠈⡹
⠀⠀⡔⢽⢃⢴⠋⠂⢠⠦⠈⡠⠂⠀⠀⢨⠅⠀⡠⠂⢁⣈⡰⡄⠀⠀⠀⠠⠰⡆⠀⠀⢀⠠⠐⠀⠐⡴⢶⠖⡂⠀⠀⠀⠈⢢⠄⠀⠀⢀⠔⠁
⠀⠀⢯⠴⠐⠁⠀⡄⠀⠀⠈⡀⠀⣀⡠⢊⡀⢰⢀⠜⠁⠀⢄⠈⠂⠤⠤⠔⠊⠀⠀⠂⢁⠀⡀⠀⠔⠁⠀⠐⢄⠀⠀⠀⠠⠄⠁⠀⠀⠀⡠⡲
⠀⠀⠀⠁⠒⠒⠒⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡿⢛⣋⣵⣾⣿⡇⠀⢸⣿⣿⣿⣿⡿⠛⠋⠁⠀⠁
⠀⠀⠀⠀⢀⣠⣤⣤⣴⣿⣿⣿⣿⣿⡇⠀⠀⠸⠿⣉⣩⣥⣴⣿⣿⣿⣿⣿⡇⠀⠸⠿⢋⠉⠉
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇




⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⠟⠻⠧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⢉⢀⠀⠐⠒⣘⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠞⡵⣇⣴⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠆⠀⠀⢀⣀⠀⢲⢋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣽⣇⡆⠀⠀⠀⢣⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣆⠀⢠⠀⠉⠉⡤⢾⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣭⣿⣿⡃⠀⠀⠀⠀⣽⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢫⣿⡅⠈⠀⠀⠀⡁⠦⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⠤⠠⠄⠀⠀⠀⡀⠀⠠⣼⡏⠸⠙⢫⠀⠀⠀⠀⠔⠁⢀⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠿⠀⠀⠀⠀⡤⠤⢒⡉⠀⠈⠉⠛⠘⣀⠠⢤⡀⠁⠂⠄⠈⠙⣇⢀⠈⠀⠀⠀⠰⢸⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⠀⠊⢀⠀⢊⠐⠶⢀⣾⠧⠚⠉⠀⠂⠙⢀⡁⠠⠀⠐⠀⠰⠀⠀⢀⠀⠂⠀⠈⡓⠴⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠢⢀⡸⠣⠀⣩⡗⣶⢴⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⣠⣴⣿⣶⣤⠈⣀⣫⣿⣶⠆⢈⣼⣿⣮⣽⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠐⢇⠀⠀⠀⢀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⣿⠿⡛⣋⣽⣿⣿⣐⡀⠻⣿⣿⣿⠛⣿⠿⣿⣷⣄⣆⠀⠀⠀⠀⠈⢳⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣶⡿⢋⣠⣿⡿⣿⣿⣿⣿⣿⣿⣶⣌⣹⣿⣿⣿⣷⡿⣸⣿⡏⠀⠀⠀⠀⠀⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣟⣼⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣾⠟⡋⠀⠀⠀⢀⠀⠰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣼⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣯⣴⠃⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡄⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⢰⠃⢈⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢃⣿⣿⣿⠵⡀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⡿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣻⡿⢷⣾⠃⠊⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡇⢶⠀⠘⢻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⣲⣾⣿⡿⢀⣿⠇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠁⠀⠀⠓⠀⣤⠀⠀⢽⣛⢿⣶⣿⣿⣟⠛⣋⠀⠈⠀⠈⠁⠉⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠢⠀⠀⠈⢀⣴⠋⠀⠀⠀⠙⢆⣙⣿⣿⣽⠶⠇⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠰⡆⠢⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣤⡵⠇⠀⠀⠀⠀⠘⣿⣿⠟⢁⣷⠜⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⢬⣿⡄⠐⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄⠆⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿⡃⠉⠀⠁⠀⠀⠀⠀⣠⠄⠆⠀⠠⠠⠌⢸⣿⠟⠈⠀⢨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⢨⣦⡄⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⣿⡧⠄⠀⣠⢦⣤⢶⠘⠈⢲⡄⠀⠀⠒⠃⠈⠛⠀⢀⢀⣬⡿⡆

⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⣠⣤⣶⣤⣄⠀⠀⠀⢀⣠⣤⣤⣤⣀⣠⣴⣶⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠀⠘⠿⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠋




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡀⠀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⢤⡀⣠⢆⢠⡤⣀⡤⢸⡇⣠⢄⢸⡏⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠛⠸⠕⠿⠞⠻⠄⠻⠵⠙⠗⠣⠺⠜⠅⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⠀⠴⠀⢂⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠊⠘⠀⠃⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣶⡀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣤⡻⣇⠀⢀⡤⠴⠦⣤⡀⠀⠀⠀⠀⢀⡠⠴⠶⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈⢰⢷⣙⣿⠁⣠⡶⠒⠶⠽⣲⣤⡀⣰⡉⠀⠀⠀⠀⠀⢀⠈⠙⢦⣀
⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠰⠃⠛⠉⢀⡼⠛⣳⣶⢀⡴⠋⢹⠷⠾⣷⣖⣶⡁⠀⣠⠏⠀⠀⢀⡈⠳⣄
⠀⠀⠀⠀⠀⡴⠃⠀⠤⠶⠓⢼⡀⣾⠏⢀⡄⠊⠁⡼⠧⣾⠁⣀⠖⢁⣸⠿⢿⣷⡉⠠⡈⠒⢯⢤⣀⣀⠙⠂⢤⣄⡠⢤⡀
⠀⠀⠀⠀⡼⠀⠀⠀⢀⡗⠀⠀⠛⠋⢹⡟⢀⡤⠊⢀⠴⠛⢹⣇⣤⠊⠀⡀⠾⣷⣹⡄⠰⡄⠘⠃⠀⠉⡟⠓⠚⣛⠟⠊
⠀⠀⠀⢸⠁⣀⠀⠚⢋⠁⠠⠄⡆⢶⠁⠸⠟⣧⣴⠋⠀⡴⠎⠀⣸⠶⣿⠀⢀⣼⣇⢳⡀⠃⠀⠀⡄⠀⢀⣤⠞⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠐⡆⠀⠀⢻⡜⣷⢀⡔⠉⢹⡶⡶⠁⣠⡼⠃⢀⣵⣾⢁⣈⣿⢨⠃⠻⣧⡘⠛⡛⣯
⠀⠀⠀⢰⠀⠀⠀⡤⠐⢧⠤⠄⠀⢳⣜⢿⣄⡤⠋⢀⠿⠛⣯⣤⠞⠈⢁⣨⣟⢉⡝⣸⠀⠸⠈⠹⣍⠁⢸
⠀⠀⠀⠈⣇⠠⠀⠀⠀⢸⡀⠀⠉⠁⢻⣧⠙⠷⣴⡁⢀⠞⢛⣧⣴⠟⠉⣉⣽⢛⣇⡟⠠⠀⠀⣤⢿⡀⠸⡄
⠀⠀⠀⠀⠘⣇⠀⠀⠀⢘⡇⠀⢀⡀⢨⠁⠈⠐⠠⢝⡛⠶⣾⣀⠿⣶⠋⢠⣤⣿⣽⠉⠙⠦⣄⠋⠀⠑⢦⡛⣄
⠀⠀⠀⠀⠀⠘⣆⠀⠴⠀⣦⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⠙⠢⠽⣶⢾⣇⣁⣠⣿⡏⠀⠀⠀⠈⠉⠀⠘⠂⠩⣌⡆
⠀⠀⠀⠀⠀⠀⠈⢧⠀⣰⡋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡙⠻⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢳⠁⣣⡞⠁⠀⠀⢀⠀⠀⠀⣀⣽⠃⠀⠀⠀⠀⠀⠙⢦⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢺⠀⠀⠀⠀⠀⠳⠶⠛⣩⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠦⣤⣄⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⢦⣄⡀⢀⣀⠀⠀⢀⠀⢀⡀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠒⠒⠀⠒⢤⣥⡀⣈⣙⠋⠉⠀⠻⠦⠆⠚⠏⢶⠀⠈⢉⣀⣀⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⣽⣾⡯⠶⠷⠚⠛⠙⡾⣟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⠒⡐⠚⣡⠀⣠⡦⣥⣼⣯⣁⣀⠀⠀⠀⠀⢰⡆⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⡴⠃⠀⠀⠛⣤⡇⠐⠀⠈⡇⢸⡄⢳⠀⠀⠀⡾⠀⢰⡄⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢎⡄⠀⠺⠀⠀⠀⠀⢠⣾⠁⡇⠀⢾⡃⢸⡀⣼⠀⠀⢸⠃⢀⠜⠁⢦⣄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⣾⣄⡀⠀⢀⡿⠃⠠⠇⠀⠸⡇⢸⡇⠸⡄⠀⠸⡇⠋⠀⠀⢸⣦⡀⠁⠷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⣠⠔⢻⠀⠉⢰⡿⠀⠀⡀⠀⠀⠀⠃⠀⠇⠀⠙⢄⠸⣇⠀⠀⣠⠊⠈⣧⣀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⣧⠀⣻⠀⠀⠘⠀⠀⠀⢠⠇⠀⠐⠀⠀⠈⢂⠙⡆⠰⠁⠀⠀⡈⠡⠉⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣽⠉⣛⠀⠀⠀⠀⠀⠀⢰⠀⠀⠐⠀⠀⠀⠘⢤⡆⠀⠀⠀⠀⠁⠀⠳⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡴⠹⠀⢹⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢠⡆⢱⡄⠀⠀⠀⠀⠀⣸⡇⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢠⣦⣀⣧⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⡸⠁⠈⠇⠀⠀⠀⠀⢀⠇⣵⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡾⠁⢸⡟⢢⡄⠀⠃⠀⠀⡌⠀⣸⠀⠀⢰⠇⠀⠀⠀⠹⣆⠀⣴⠃⣀⣼⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣖⠴⠋⠀⠀⠙⢦⡀⢦⠀⠀⠰⠁⠀⣰⠃⠀⠀⠀⠀⠀⠈⠓⠇⣀⠋⢹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠹⣞⡀⠀⢞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠐⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠭⠁⠠⠤⠄⠍⠦⠀⠁⠀⠀⠘⠉⢱⠒⠂⠀⠀⠐⠂⠀⠀⠀⠀⢀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⣀⣀⡄⠸⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡃⠀⠀⠙⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠒⢚⠀⠀⠀⠀⠠⢄
⠀⠀⢸⠉⠉⠉⢉⡉⣉⠉⠉⠉⠉⢉⢀⣀⠀⠀⡀⢀⡐⢲⠀⠀⠀⠀⠀⠀⠀⢠⠄⠰⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢸⠀⢠⠊⠁⠀⠀⠉⠢⡀⢰⠁⠀⠈⡆⢌⠀⠀⢘⢘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢱⠈⠓⠤⠐⠁⠘⢂⡐⠊⢸⠀⠀⠈⠀⠁⠀⠀⢸⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠙⠂
⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⠙⡆⠜⠁⠈⢱⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⢸⠀⠘⢆⡀⠀⠀⠀⡠⠃⠈⠢⠄⠴⠁⠐⠤⠤⠚⢸⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠘⠤⠤⠤⠬⠭⠬⠭⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢐⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡠⠄⠀⠒⠂⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⢻⠁
⠀⠀⠀⠀⡀⠀⠀⢃⠀⠀⠀⠀⡇⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠲⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢸
⠀⠀⠀⠀⠃⠀⠀⠘⠀⠀⠀⣼⢁⡜⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⡒⠒⠲⢌⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⢘
⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⠀⢀⠀⠀⠀⠀⠰⠁⡀⠈⠂⡀⠄⠀⢱⡀⠀⠀⣠⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡇⠈⠈
⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠑⠄⠀⠀⢘⡀⢃⠀⠀⠠⠀⠀⢠⡇⠀⡎⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⢀⠄⠀⠀⠀⠣⣀⠀⠀⡄⢊⠀⠔⠀⠀⢇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢀⠀⠁⠀⠀⡠⠒⠢⡈⠑⠉⠈⠂⠁⠀⠀⠀⠈⠓⠲⠔⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠒⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⡄⠀⠀⡁⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠀⠀⡆⠀⠀⢁⠀⠀⠀⢀⠄⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠐⠀⠀⠀⠤⠠⠠⠀⠀⠀⠈⠢⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⢰⣴⣀⣀⣀⣐⣀⢐⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢺⣟⣭⣿⣿⣿⣿⣿⣽⣿⣿⣗⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⢱⣼⣤⣶⣾⣿⣿⡿⢿⣿⣟⣛⣻⣿⣟⣛⣿⣿⢿⣿⣿⣿⣿⣶⡠
⠀⠀⠀⠀⠀⠀⠀⢀⠰⡜⢄⡳⣦⣷⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠈⠉⠻⡿⠿⣷⣿⣿⣿⣿⣿⣦⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣲⣤⣈⣻⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠠⡀⢠⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠊⢀⣴⣿⣷⣾⣿⣿⣿⣿⣧⠙⢦⡀
⠀⠀⠀⠀⠀⠛⢚⣶⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⡀⠓⠤⠤⠤⠤⠔⠒⠋⠁⣀⣠⠔⢹⣿⣿⣿⣿⠋⠁⠀⠀⢙⡷⠀⠙⣄
⠀⠀⠀⠀⠀⠉⠈⠟⠋⠀⢀⠀⠈⣿⣿⣿⣷⣿⣿⣦⡤⠤⠤⠤⠔⠒⠚⠉⠁⠀⢀⣼⣿⣿⣿⡇⠀⢀⣠⣴⠾⢃⠄⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⠿⠟⡛⠫⠁⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠟⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠳⣄⣀⠀⣀⣤⣾⣆⠀⢠⣦⣄⣤⡴⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣄⠀⠀⠉⠉⠉⠀⠠⣉⡿⠋⠀⠀⠀⠀⠈⠹⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠘⠳⢦⡀⠀⠀⣡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⠹⣶⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⣨⡷⠋⠙⠿⣦⣄⢀⠀⠀⠀⠀⠐⣴⡾⠁⠀⠀⠀⠀⢈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣴⣯⣬⣷⠤⣤⣄⠀⠀⠀⣀⣶⠋⠀⠀⠀⠀⠈⠻⣷⣆⡀⢘⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⣠⣼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠙⠚⠋⠀⠈⣉⣀⠀⠈⡛⠶⣦⣴⠟⠀⠀⠀⠀⠂⠀⠀⠀⠈⠝⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢢⣾⣏⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⠶⠶⠞⠛⠶⢦⡀⣉⣅⡀⣳⠄⠸⣿⣦⣤⡀⠀⠀⠀⠀⠀⡀⣰⣾⠍⠀⠙⢿⣄⢦⠀⠀⠀⣴⡿⣣⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢡⠀⠀⠀⠀⠀⠰⣿⡅⠈⣀⣵⢶⣆⣹⠁⠈⢷⣤⣤⡀⡀⣠⡼⡏⠁⠀⠀⠀⠀⠙⢿⣧⣠⣿⣟⣱⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡏⠀⠀⠀⠀⠀⠐⡇⠙⠛⠉⠠⠀⢪⡿⣷⡦⠈⠉⠩⣍⠙⠋⠻⣆⣀⣐⡈⠀⠀⠀⢀⣾⢿⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⢸⠀⠉⠹⠶⠶⣶⠋⡤⠄⢀⣀⠉⠙⢿⡀⢄⣰⣿⣝⡾⠋
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣼⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡿⠁⣀⡐⠋⠉⠀⠀⠈⢻⣾⣿⣿⣏
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⡾⠉⣷⡀⠔⠛⠆⠀⠀⠉⠻⠋⢻⣆
⠀⠀⣠⣾⠏⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣁⣀⣂⣬⣝⣀⡀⡰⢦⡄⠰⣶⣄⠀⣹⡇
⢠⣾⠛⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢋⣿⠟⢿⣿⠃⠠⣀⣤⡄⣹⣿⣾⠋
⢾⣟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⢁⠀⣼⣿⠠⠀⣹⣧⡀⣿⠛⠁
⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⣴⠛⠀⢀⣠⡾⠃⠹⣦⣼⠋⠙⠛⠋
⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡴⠛⠁⠀⢠⡾⠋⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠛⣦⣄⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠸⡄⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣠⠟⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢳⡀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣠⠾⠉⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣅⠀⠀⠀⠀⠀⠀⠀⢁⡴⠏⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⡴⠛⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣴⠟⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣴⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⠰⠅⡆⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣛⡛⠢⢍⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢘⠗⣸⢀⠀⠣⢠⢠⢸⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠻⠦⡉⠁⠀⠀⠈⠀⡊⡈⡇⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣮⠑⡄⢀⠀⠀⠀⠀⠀⠐⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢾⠀⠁⠒⡡⠂⠀⠀⠀⠀⠀⢀⠁⣁⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⣢⡀⠀⣿⣻⢰⠍⡦⠂⠀⠀⠀⣀⣴⣶⣾⠿⠛⠃⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⡄⣶⢾⣿⠹⡄⠘⣾⣆⠈⢁⣠⠴⠚⣽⡿⠋⠀⠀⠀⠀⢀⣞⡟⢉⡽⢧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠽⠓⣺⣦⣧⡿⣿⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⠾⣥⠤⢚⣷⡀
⠀⠀⠀⠀⠀⢀⣿⣷⠸⣿⠿⢷⠘⣄⣱⢳⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣿⢞⡽⡖⢉⢞⣷⡀
⠀⠀⠀⠀⠀⠸⣿⡟⢐⣾⣯⡘⠣⣻⣿⣏⡆⠘⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⣀⣯⢟⡿⣯⠔⢻⡄⢊⡿⣧
⠀⠀⠀⠀⠀⠀⠙⢧⣿⣿⠛⠀⠀⢹⣟⢻⣧⠀⠀⠀⠈⠀⠀⠀⢺⠀⠀⠘⢫⣹⡲⣧⡷⣂⡠⢷⣊⠀⣻⣀
⠀⠀⣠⣶⢿⣿⠛⣷⡺⣿⣦⣠⢄⡀⠈⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢋⣾⣟⣥⡤⠼⢃⠀⠁⠸⠧⡄
⠀⢸⣲⠏⣨⣍⢡⠟⠛⢙⡺⣽⣿⢽⣦⣻⣿⣴⡆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠏⠆⠈⠘⢻⣧⡴⠚⠑⢻⣅⡠⠴⠿⡀
⠀⠸⡟⣷⡰⢆⣜⣛⠷⣶⣖⣿⣿⠿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⣀⠀⠙⣯⡗⣦⠁⠀⢹⡆⠀⠐⠛⢀⣀⣀
⠀⠀⠙⠺⠷⠾⠿⠛⠋⠉⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⠶⠤⢿⣽⣧⠤⠤⣿⡁⢸⣻⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠉⠛⠲⢧⣸⠯⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣤⣄⣠⣤⡤⠴⠶⠶⢲⣿⡟⠋⠉⠉⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠄⠀⠒⠄⠀⠐⠒⠀⠉⠉⠁⠈⠉⠉⠁⠀⣿⣧⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣷
⠀⠀⠀⢰⠆⠀⠀⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢹⣿⡀⣀⣀⣀⣠⣯⣷⠤⠴⠶⢒⣚⣻
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⠶⠖⢒⣓⣫⣯⣩⣥⠤⠬⠴⢶⣷⡞⠛⠉⠉⠉⢹⠂
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣟⠉⠉⠉⠉⠈⣿⡇⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⠀⠀⠀⠀⠀⣿⣧⠀⣀⣀⣀⣠⣿⠧⠤⣤⠶⠖⢚⣣
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡼⣿⠦⠴⠒⠒⣚⣛⣟⣩⣭⠭⠶⠤⢾⣷⠒⠚⠛⠉⠉⣿
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠲⣷⡟⠉⠉⠉⠉⢹⣿⡇⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⣇⠀⠄⡀⠀⠈⣿⣇⠀⠀⣀⣀⣸⣿⣧⠤⠤⠴⠖⠚⠇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⣠⠜⠃⡀⠀⠀⠀⠀⢀⠀⠶⡿⠙⠋⠋⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⣀⣠⠀⠖⠉⢄⠀⠀⠀⠀⠀⠈⠐⢠⠈⠰⠀⠀⢀⣀⡤⠴⠚⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠁⠀⠀⠑⢄⠀⠀⠀⠀⠆⠀⠀⠀⢀⣀⣠⠽⠶⢤⠞⠫⠀⠀⠀⠀⠀⠀⠄⠈⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠂⢲⠄⡰⠖⠉⠉⠁⠀⠀⠀⠀⠀⢂⡀⠁⡖⠀⠀⣀⠄⠖⠂⠈⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡀⠀⠀⠀⠂⢀⠀⠠⠀⠂⠁⠀⠸⢦⣆⠲⠛⠀⠀⠀⠀⠀⠀⠄⠂⠀⠴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠐⠄⡈⠀⣀⡤⠒⠐⠈⠀⠀⠀⠉⠂⢀⠀⠀⠐⠀⠀⠀⢀⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠎⠨⠁⠁⠀⡀⠀⠀⠀⠀⠀⠂⠀⠱⢰⢄⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠂⠀⠈⠒⠈⢀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢰⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣼⠣⡘⠿⠀⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⡉⢔⡲⠈⢢⠘⠒⡩⠔⣉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢤⣀⠴⢚⢁⠈⢄⠑⣤⠴⢊⠡⡒⢌⠣⡘⢛⡠⢸⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢣⡁⠈⠂⠉⢄⠈⠉⣀⠔⣣⡄⢊⠀⠻⠇⢈⠆⠉⣵⠊⣵⡆⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⢡⠀⠀⠄⠀⠀⠳⡭⠒⡭⠄⠈⢢⠱⢄⡪⢂⣉⠳⡈⢦⡨⣔⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡂⡁⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠙⢦⣈⡡⠔⠪⠦⡧⡀⠀⢊⣠⡷⠦⡘⣄⢣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠋⢀⠃⣀⠀⠀⠀⠈⠢⡀⠁⠢⡀⠀⠀⠱⣎⠐⠯⠂⣸⠎⠊⡟⠡⢦⢀⠽⡸⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠀⠀⠀⠀⢸⠀⣬⠾⢒⣆⠘⠄⠀⠀⢱⠀⠀⢀⠀⠀⠀⠈⠢⣔⡮⢚⡉⢦⠈⢦⡪⠔⠟⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣆⠀⠀⠀⠀⣘⢀⣠⠖⣏⡜⢠⣠⢤⠀⠀⡆⠀⠀⠉⠐⡀⠀⠀⠈⢦⡉⢊⣴⠗⢎⠣⡜⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⢧⡀⠀⠀⠈⠁⠈⢣⡄⣤⢡⠇⡸⠀⠀⠘⠦⢄⠀⠀⢁⠀⠀⠀⠀⠹⡇⠐⠯⢀⠷⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢳⡀⠀⠀⠀⠀⠀⡄⠘⠋⣠⠗⡄⠀⠀⠀⠀⠙⣆⠘⠒⠒⠲⡀⢠⠘⡦⣂⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡸⣄⠀⠀⠀⠀⠓⢤⠐⢡⣊⡡⣀⠀⠀⠀⠀⢘⠀⠀⠀⠾⠁⢀⡰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡜⣦⠀⠀⠀⠀⠘⡄⠀⢡⢔⡡⡀⠀⠀⠀⠈⣉⣵⣀⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡳⡄⠀⠀⠀⠘⡀⠈⢉⠔⠃⢀⡠⢐⣫⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⢦⡀⠀⠀⠙⢊⣡⡴⣺⡥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⠙⣄⡤⢖⣫⠵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡾⠒⠉





⣿⠿⠿⡿⡿⠟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣛⣻⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠒⠊⠙⠿⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠯⡀⠀⠀⠀⠀⠀⠀⠙⠟⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠐⠊⠉⠀⠀⠁⠀⡈⠒⢄⠀⠠⠔⡈⠄⣂⠤⠌⡙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠈⠢⡀⠀⠀⠀⠀⢀⠠⢓⠀⠁⠒⢹⠀⠀⠀⠀⠀⠀⠀⠄⠙⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⡏⠀⠀⠀⠀⠀⠀⠂⢀⠑⠄⠐⣨⡔⠂⠅⠒⠀⠂⠀⠑⠤⡀⠀⠀⢀⠠⠀⣈⣀⡼⠿⠃
⠀⠀⠀⠀⢀⡤⠦⠖⠛⠈⠐⠀⠈⠢⢀⠀⠀⢀⠠⠒⠈⠀⢀⠈⠀⢇⠀⠀⠀⠀⠀⠀⠁⣢⠈⠀⢈⣵⠾⠟⠋⢁⣠⠴⠂
⠀⠀⡏⠁⠀⠠⡀⠀⠀⠀⠀⠀⠈⣰⠄⠁⠠⠔⡾⠁⠂⠁⠀⠀⠀⢀⠁⠢⡀⠀⠠⢒⡠⣤⡤⠖⠋⢀⣀⣴⠟⠋⠁
⠀⠀⠳⣄⠈⠠⢌⠐⢄⠀⠤⢐⡡⢄⡢⠤⠄⡀⠑⢄⠀⠀⠀⠀⠀⡀⠜⠂⠀⣑⣾⣿⠟⢉⣀⣶⠶⠛⠁
⠀⠀⠀⠈⠻⢦⡀⠑⠠⡀⠂⢹⠀⠀⠀⠀⠀⠀⠐⠀⡈⠂⢀⢒⡩⢔⣪⠶⠟⠋⣉⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠐⢄⠑⠤⡀⠀⠀⣀⠄⠂⡉⠀⣠⡵⠚⠋⣀⣤⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠉⠢⣌⠀⠨⠔⣊⡤⠒⠋⡀⣠⡶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠑⠔⠋⢁⣢⡾⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣼⠞⠋⠉





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

⠀⠀⠀⠀⠀⠀⣠⣄⣤⣀⣀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⢼⢑⡢⡰⡄⠀⠀⠀⠀⢰⠿⡎⠋⡾⣷⠀⠀⠀⠀⠀⢛⡟⢻⠛
⠀⠀⠀⠀⠀⠀⠸⠿⣛⠿⠇⠀⠀⠀⠀⠀⣮⣿⣿⣷⡆⠀⠀⠀⠀⠀⣿⠙⠸⢿⡏⠀⠀⠀⠀⠀⣻⣏⣹⣋⠄
⠀⠀⠀⠀⠀⠀⠰⡿⠂⡾⠇⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠃⠄⡄⡄⡿⠀⠀⠀⠀⠰⣾⢍⡸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⣥⣶⣤⠅⠀⠀⠀⠀⠀⠈⠥⠁⠝⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠈⠑⠛

⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⣀⢠⣄⠀⠀⠀⠀⢀⣤⠀⡀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣷⣾⣴⡀⠀⠀⢹⣿⣿⣦⣴⢴⣦⣾⣿⣿⡅⠀⠀⢸⢻⡿⢅⠀⠀⠀⠀⠀⠀⣞⡙⢋⣷
⠀⠀⠀⠀⠀⠀⣼⠿⠈⢿⣦⠀⠀⠀⠀⠙⣼⠿⠘⢿⡞⠀⠀⠀⠀⠀⡼⢾⣟⠻⡄⠀⠀⠀⠀⠀⡿⠥⡬⢿
⠀⠀⠀⠀⠀⠀⡥⢼⣤⡵⠾⠀⠀⠀⠀⠀⠸⣧⣬⣽⠁⠀⠀⠀⠀⠀⢰⣟⢛⡷⠀⠀⠀⠀⠀⠀⣿⡓⢓⣻
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠘⠛⠑⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠰⣦⣿⣠⡆⠀⠀⠀⠀⠀⢠⣴⣢⣤⠀⠀⠀⠀⠀⠀⠠⣄⣆⡤⠀⠀⠀⠀⠀⠀⣄⣠⣦⣠
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠛⠁⠀⠀⠀⠀⡿⣿⢹⡿⡆⠀⠀⠀⠀⠀⢨⣼⡤⣭⠀⠀⠀⠀⠀⠀⣉⡙⢟⣉
⠀⠀⠀⠀⠀⠀⠀⢉⣭⡍⠀⠀⠀⠀⠀⠀⣟⣛⢘⣛⣇⠀⠀⠀⠀⠀⢸⣶⠱⡘⠀⠀⠀⠀⠀⠀⢿⠃⠸⣿
⠀⠀⠀⠀⠀⠀⣴⠁⠉⠨⢽⠀⠀⠀⠀⠸⣆⡋⡇⣓⡼⠀⠀⠀⠀⠀⢸⡧⠤⣿⠀⠀⠀⠀⠀⠀⢣⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁

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