Dissociation Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣶⣶⣾⣿⣿⣶⣶⣦⣤⣀⠀⠀⢀⣤⣴⣿⣿⣶⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠛⣱⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⠟⠋⠁⠀⣠⡄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠉⠀⠉⢩⣿⣿⠟⠉⠀⠀⠀⠀⠀⢻⣿⡀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⢀⣴⣿⣿⡏⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠙⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣴⡇⠀⠀⢰⣿⣿⣿⣿⣁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⢿⡃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠋⠀⣴⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠁⠀⢀⣾⣿⣿⣿⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣰⣠⠀⡄⡄⠀⠀⠁⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣴⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⢇⡾⢁⡀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠠⣸⠮⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀⠀⠀⠀⢐⣿⣿⣿⣿⣿⠞⠁⠀⠈⠀⠀⠐
⠀⠀⠰⣿⣿⣿⣿⣿⡝⠛⣟⢟⡫⣻⢿⣿⣿⣿⡆⠀⠂⠀⢪⣯⠃⠀⠀⠀⠀⠀⠀⠀⠰⠶⣿⣗⡪⣴⢶⣶⣮⣏⣿⣿⣿⣿
⠀⠀⢸⣿⣉⣋⡱⣂⣤⣿⣫⢟⣉⣭⣹⣿⣿⣿⡇⢀⣐⢸⣌⡓⠂⠀⠀⠀⠀⠀⠀⠀⠤⠻⠿⢉⣋⣳⠾⠿⢿⣿⣿⣿⣿⣿⡀
⠀⠀⠸⣭⣿⠛⢻⣟⣿⠉⣿⣿⡏⢹⣿⡏⢸⣿⣧⠀⠀⠀⠁⠉⠙⢙⡻⠚⠉⠈⠁⠀⠀⠀⠀⡠⠀⠉⠁⠡⠄⠋⠃⠙⠫⣟⡿⠦⠐⢤
⠀⠀⠀⣿⣾⡆⢸⣿⣿⠀⣿⣿⡇⢸⣿⡇⢸⣿⡇⠀⢤⣤⡀⠀⠀⢸⡆⠀⠰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠬⠀⠀⠀⠀⠐⠈⠃
⠀⠀⠀⣿⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⣿⡇⣸⣷⣷⣾⣿⣿⡿⠾⢷⣶⣦⡀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠄⠀⠀⠇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢻⣿⡇⢸⣿⣿⠀⣿⣿⣇⣼⡿⠃⠸⣿⣿⣿⣿⡿⠃⢀⢸⣿⡿⢿⠠⠀⠀⠀⡁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⢹⣿⡇⣸⣿⣿⢀⡿⠿⢟⠁⠀⠀⠈⠻⣿⣿⡿⠀⠀⠀⣼⣿⣿⣿⣆⢸⣯⢁⠠⡄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢽⣍⠉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠟⢧⠀⢒⠂⢬⣿⣿⠿⡟⠈⠀⠀⠀⠀⠘⠒⠀⠂⠂⠀⠀⢢⣴⣜⣤⢁⡀
⠀⠀⠘⣿⣯⡷⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⠀⠈⠠⠎⠀⠈⠛⠻⡟⠉⠉⠀⠀⠀⣀⣀⣀⠂⠀⠀⠀⠀⠙⠿⣏⣿⠸
⠀⠀⠀⠀⢽⣷⣿⡄⠀⠀⠀⠀⠀⣀⡤⢠⡏⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠲⢟⣿⣿⢏⣿⡇⡈⣤⣀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠉⠹⢿⡄⠀⠤⠒⠿⠓⠠⢸⡄⠉⠻⢀⡀⠠⢤⠀⠰⡐⠂⠀⡀⠀⠀⠀⠋⠛⢇⠳⣷⣈⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣄⢀⡀⠓⠋⠉⠙⠈⠿⠷⠶⢀⢀⠀⠀⠀⠀⠀⠀⠘⠛⡟⠲⣦⣉⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠐⠲⠖⠊⠉⠙⠛⠑⠀⠋⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⠛⡓⢤⡈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠀⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠌⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢛⠳⠰⠆⠂⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⣴⡁⠚⡀⠨⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠰⠦⠀⠠⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠶⣴⡖⠀⠐⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣤⣶⣤⣀⠀⢈⣠⣤⢤⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⣍⣩⣯⣍⣉⣩⣅⠈⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣳⢠⠀⡤⢀⣰⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣹⡴⢿⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣹⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⠄⠐⠁⡠⠀⢀⠀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⠋⣸⣿⡏⠀⠄⠀⠀⠀⡠⠂⠁⠀⠀⠀⣁⢀⠚⠀⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠸⠃⠠⣄⡘⠲⢄⡀⠀⠀⠀⠄⠀⣿⡴⠛⢀⡿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣝⡶⡄⠻⣯⡀⠀⠀⣸⣿⣷⠁⣾⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣧⠀⠀⢽⣷⡟⢡⡞⡟⢰⢻⣿⣿⠏
⢷⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣍⣿⣛⢆⣶⣿⣼⣿⣿⢿⣶⣿⣿⠇
⠈⢻⣿⣶⡄⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣿⢻⣧⣽⣿⡟⣿⣿⡿⠋
⡔⠉⠿⢟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣿⣿⣮⣻⠟⣿⣿⣧⣿⣿⠀⡐
⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣿⣿⡻⣹⣾⣿⣿⣿⣿⣯⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠋⣩⡍⠻⣦⡄⠀⠀⠀⠀⠀⠘⣿⣿⣟⣿⣿⣿⣿⣟⠁
⢰⡄⢂⣀⠀⠀⠀⠀⠀⠀⠠⠶⣛⣯⣼⡃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡌⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣿⡿⣽⣿⣷⡎
⠀⢳⡈⣩⠉⠓⡿⠦⠀⠀⢀⡶⠋⢥⠀⠀⠀⠘⠂⠀⠀⠀⠀⣇⠀⠀⠠⠀⠀⠀⢠⣾⠿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡼⣟⣿⣿⣿
⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢫⠀⠀⠀⠀⠀⠀⠈⠈⠛⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣛
⠀⠀⠀⠀⠀⡄⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣸⠀⢠⠀⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⣿⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠋⠃⢀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⡟⠉
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⣠⡿⠃⢀⣾⣧⠜⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠤⠬⠤⠤⣦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡟
⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣧⠁
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢼⠷⣴⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⠦⠁⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠘⢧⡀⠑⠆⠀⢩⡖⠃⠄⠀⣀⣀⣤⣤⢀⣤
⠀⠀⠀⠀⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⡹⠀⠀⠀⠛⠉⠁⠘⠃⢩⠀⠓⠀⡀
⠀⠀⠀⠀⡠⠾⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠄⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢨⡌⠀⠀⠀⠀⠀⠙⡧⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠃⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⢀⣤⣶⡖⠛⢀⠀⠀⠀⠀⠀⠀⢀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣨⣷⠀⠐⣧⠀⠙⠛⠁⣸⣿⠁⠀⠈⠀⠀⠀⠀⣠⣾⢿⣿⠁
⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠈⡟⠀⠀⡏⠀⠀⠀⣠⣿⢿⡄⠀⡇⠀⠀⢀⠊⠈⠉⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣾⠁⢀⠐⠁⠀⠀⠰⣿⡋⢸⡇⠀⡇⠀⠀⠈⠓⠦⢄⠀⣿⡄⢀
⠀⠀⠀⠀⠀⠀⢀⣼⠁⠄⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣷⠀⢁⠀⠀⠀⠀⠀⠀⠑⢿⣷
⠀⠀⠀⠀⠀⠀⡈⠀⠀⣰⠿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢠⠞⠁⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠘⢢⡈⢻⣶⢸⠄⠀⠀⠀⠀⠀⠀⠈⣿⣆
⠀⢀⠀⠀⠀⠀⢧⠀⣰⡏⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣇⣰⠋⠀⠀⠀⠀⠐⠃⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⢬⠀⠀⠀⠀⠀⣰⠟⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⢠⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡜⣧⠀⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠘⢇⠀⠀⠀⣼⡇⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠇⠀⠀⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⡾⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠸⠀⠀⠀⢠⣿⣹⣿⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢈⣁⠀⠀⠀⠆⠀⣀⠈⠀⠘⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠲⡄⠄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠈⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠀⠀⠀⠀⠀⠃⣠⡤⠂⠀⠂⠈⠩⠏⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡶⠀⠀⠀⠉⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢠⡄⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠤⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡄⠀⡤⢜⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢠⣆⠚⢦⠏⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⡀⢤⣀⠀⠀⠀⠈⠁⠀⠛⠇⣠⡟⠀⣄⣈⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠰⡄⠀⠘⠄⠀⠀⠐⠀⠁⠘⢿⣆⠀⢠⣴⣄⠐⠀⢰⠊⢡⣤⠿⠋⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⣀⠖⠁⠈⡀⠙⠛⠈⠹⣿⣿⣦⡀⠀⣼⡏⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡘⠁⠀⠀⠀⠐⠀⠀⠀⠀⢻⣿⡇⠀⢀⣿⠀⠀⢲⣤⣨⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⢦⡀⠀⠘⣿⣧⣠⣿⠃⠀⣀⣰⣿⣿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⣾⠿⣿⣷⣰⡿⠋⠉⣥⢦⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄⠀⠀⢀⢀⠀⡀⢀⡀⢀⡀⢸⣧⠇⠻⣿⡟⠷⢶⣤⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠘⠀⠸⠀⠘⠐⠐⠘⠀⠘⠐⠁⠂⢸⠊⠙⠂⠛⠃⠀⠛⠛⠐⣬⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⡴⠀⠤⠤⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣶⣦⣤⣴⣾⠿⠛⠉⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠛⠿⣷⣶⣤⣀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡗⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢠⡀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠛⢃⣠⠄⠸
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⡒⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡀⣄⠰⣤⣀⠀⠀⠀⠀⣄⠀⢿
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣎⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⡈⢿⣷⡄⠀⠀⢸⣇⣿
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡝⢷⠀⠀⠀⠹⢿⣦⠙⢯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣻⣿⣦⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠈⠃⠀⠀⠀⠀⠈⠁⠀⠁⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣰⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣠⣤⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡷⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠜⠹⣿⣿⣿⡓⠄⠀⠀⠀⠀⠀⠀⠃⠿⣿⣿⠃⠈⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠿⠛⠃⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠉⢠⠀⠀⠀⠀⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⠇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠉⠙⠟⠉⣿⣿⡿⠁⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⣿⣿⡟⣿⣿⡟⢷⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡇⠘⣿⣿⠈⠃⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠸⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠹⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣤⣶⣤⣶⣿⣷⣿⣿⣷⣦⣬⣿⣦⣔⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⡏⡩⠿⠟⠛⠛⠛⠛⠿⠯⣍⡛⠿⣦⣚⣿⡛⠿⣿⣿⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡞⣩⣵⠧⠟⠂⠀⠀⠀⠐⠒⠒⠒⠓⠲⠶⣤⣄⠉⠛⠷⣮⣾⣿⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢫⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠠⢙⢿⣧⡻⣿⣿⣆
⠀⠀⠀⠀⠀⢪⣿⣿⣿⢳⡿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠹⣷⣽⣿⣿⣦
⠀⠀⠀⠀⢱⣿⣿⣿⢷⡿⣱⠁⠀⠀⠀⠀⠀⠀⢀⠴⠊⠉⠁⠈⠉⠐⠂⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⣿⣿⡀
⠀⠀⠀⠀⣾⣿⣿⡏⡸⠁⠀⠀⠀⠀⢀⠶⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⢟⠀⣿⣿⣿⣷⡀
⠀⠀⠀⢰⣿⣿⣿⣷⡇⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠉⠒⢤⠀⠀⠀⠘⠇⠀⠀⠀⠀⢸⠀⢨⣿⣿⣿⡃
⠀⠀⠀⢸⣿⣿⡟⣿⣥⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣩⡄⠀⠀⠀⠈⢧⠀⠀⠀⠃⠀⠀⠀⠀⢀⡇⢨⣿⣿⣿⣷
⠀⠀⠀⢸⣿⣿⡗⡧⣯⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⣿⣿⣿⣯
⠀⠀⠀⠸⣿⣿⣇⣿⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢲⠀⠀⠀⢸⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠀⠀⢹⠀⡞⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣬⢠⢉⣽⣿⣿⡏
⠀⠀⠀⠐⡜⣿⣿⣷⣿⡿⣄⠀⠐⠂⠀⠀⠀⠤⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢠⣾⢸⣿⣿⣿
⠀⠀⠀⠀⠐⣾⣿⣿⣿⣿⣌⢣⡄⢻⡄⠀⠀⠀⠙⠶⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠠⠄⠉⠀⠀⢀⣴⣿⠃⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⢈⡳⠝⢦⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣹⢋⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣤⣀⠉⠑⠢⣤⡀⠀⠀⠀⠀⠀⢀⣀⣤⠔⣊⠄⡴⣊⢝⣡⣾⣵⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠊⠻⣿⣿⣿⣿⣿⣻⣿⣿⣦⣤⣀⣙⠛⠛⠛⠛⠛⢉⣉⡤⢦⣤⣾⣽⣷⣿⣯⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠻⢿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⣿⠿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣷⣿⣿⡿⠋⠉⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⠛⠛⠿⠿⠿⢿⡻⠿⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⡀⠀⠠⡄⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡴⠖⠛⣋⣽⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠯⢭⡉⠙⠳⠤⠞⠁⠀⠒⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⢀⡞⣁⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⠧⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⠞⢀⠀⠀⠐⣦⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠉⢷⠀⠀⣷⠈⠛⠦⣽⣟⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⢀⣀⠌⠉⠛⠲⠦⣤⣀⡀⠹⣏⠙⠛⠲⣶⠤⣤⣈⣛⣦⣄⠉⠉⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠀⠀⠀⠀⣩⠖⠚⠓⠶⣤⡀⠀⠀⠈⠉⠉⠁⣀⠀⠹⡄⠀⠀⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣸⠇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠙⣦⠀⢀⣤⠖⠒⠛⢧⠀⠹⡄
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⡾⣠⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⣧⠞⠁⠀⠀⠀⠘⡇⠀⣹⠦⠤⡄
⠀⠀⠀⠀⢠⡟⢁⣀⣀⣀⠙⠻⣵⠋⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⢉⠟⠒⠳⡄
⠀⠀⠀⠀⠈⣇⠀⠀⠙⠮⠿⡄⠙⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢀⡀⢠⡇⢠⣤⣄⠀⠀⢸⡇⠀⠈⢷⣉⠛⣧
⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣯⣿⡿⠣⣷⣾⡿⢀⣠⠟⢀⣠⠤⣄⠸⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠰⣄⣈⢙⣓⣶⠞⠁⠀⠀⠉⠉⠉⠀⠠⠋⠀⠀⣸⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠞⠁⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡄⠀⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⢀⡄⢀⡴⠒⠛⣚⣧⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡼⠀⣼⠀⠀⠀⠀⢠⡏⠉⠙⢲⣒⣒⣾⣤⣬⠵⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⣇⣠⡇⠀⠀⠀⠀⢸⡗⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠚⢧⡞⠀⢸⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⡑⠀⠁⠀⡞⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠤⠤⠤⠞⠁⠀⠀⠀⠀⢀⣀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⣦⠤⠶⠶⠶⠒⣾⢻⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢀⣿⣸⡤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⠀⠉⣹⣉⣁⣼⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠢⠤⠤⢴⢶⢖⠟⣻⢀⣈⣷⡤⣾⠇⠀⠀⠀⠀⠀⠀⠲⠶⠶⠤⢤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢝⣒⣒⣒⣛⣛⣚⣉⡩⠥⠖⠋⠉⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⡶⠒⠒⠀⠠⠤⠬⠭⠉⠉⠻⠿⠿⠷⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠶⠯⠭⠥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠋⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣆⠀⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠛⠉⠁⢀⣤⣤⣤⣉⡻⢿⣿⣿⣷⣌⠻⣧⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⡄⠀⠁⠀⠀⠉⣙⣿⣾⣿⣿⣿⡏⠁⠘⡆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⣸⠀⠀⠀⢠⣾⡟⠛⣿⣿⣿⣇⣾⡇⢰⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⡀⠀⠸⣄⠛⠁⢸⣿⣿⡿⢙⣿⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠙⢦⣤⡙⠿⡲⣿⣿⣿⣷⠞⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣠⡄⣤⢒⢀⠀⠠⣄⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣉⡟⣷⣧⡞⣫⠤⣰⣼⡟⣾⣛⣿⣷⡢
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⠿⣾⣿⣿⠻⣴⡶⠀⡸⠟⣯⢽⢩⣟⢿⣿⣏⠈⣀⠢⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣽⠀⠀⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣼⠀⠀⡇⠀⢸⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣿⠀⠀⡇⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣸⠀⢀⣧⣤⣼⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣻⠀⠈⡏⠈⢻⠀⠀⡇⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡟⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣾⠀⢴⣇⣀⢸⠶⠶⡇⠀⣿⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⢴⣶⠄⠀⠀⢸⠀⠀⡇⠀⢸⣞⣭⡯⠭⣽⣏⣹⣷⢯⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⡇⢀⢿⢹⢖⣟⣛⣺⣒⣲⣧⡳⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⢠⡄⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⠀⠼⡿⠸⣿⠸⢿⣗⣒⣾⠯⠽⡷⠉⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⡌⠃⠀⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⢸⠀⠀⡇⠀⢾⠀⢉⡿⠦⢿⠍⢙⡏⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⣂⡀⠀⠨⣯⣉⣻⣏⣭⡧⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠀⣿⠀⣽⣟⣒⢺⠖⢚⣟⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢹⠀⠶⡯⠭⢸⣏⣩⣯⠄⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡄⠀⠀⠀⢸⠀⠀⡇⠀⢹⠀⣛⣟⠃⢸⠨⣭⡷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠇⠀⠀⠀⢸⠀⠀⡇⠀⢼⠰⠶⡷⠀⢸⠀⣒⣟⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢸⠀⠀⡇⠀⣼⢨⣿⡇⠀⢸⠀⢨⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⠘⠒⡇⠀⢸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⢸⠀⠀⡇⠀⣾⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠹⣄⠀⠀⠀⡤⠤⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢶⠒⠤⠤⣀⠀⠀⠈⣇⠀⠀⢰⠋⠀⠀⢀⡼⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠽⢳⡄
⢸⠀⠀⠀⠸⣀⠀⠀⢸⠀⠀⠈⡇⣠⠖⠉⠀⢀⡴⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣶⡚⠛⠛⠒⠒⠃
⠸⣆⢤⣀⠀⠀⠑⠢⣼⠀⠀⠀⠙⠁⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⠉⠒⠤⡀
⠀⠁⠀⠈⠑⠦⣄⠀⠀⡖⢦⡄⣖⢴⡆⣰⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠆⠀⢠⠎⠀⠈⠲⡀⠀⢑⠦
⠀⡠⠛⠦⠤⠤⠬⠿⠦⢦⣤⢰⣇⢲⠂⠑⠒⠒⠦⠤⠞⠳⣄⠀⢠⠖⠒⠲⠤⣄⡀⠀⠀⠀⠀⣠⠖⠒⠒⠲⣤⡠⠴⠒⠛⠓⣆⡴⠋⠀⢀⣀⠤⠼⠀⣌⢳⠆
⠾⣅⡀⢀⣀⣀⣄⠤⠤⢤⡄⠀⠀⡨⠤⠤⣄⣀⣀⡀⠀⠀⠈⢢⡘⢦⣂⡀⠀⠀⠈⠉⠓⠲⠤⣽⣄⡀⠈⡷⣯⠄⠀⠀⢀⡼⠃⠀⠀⣠⣿⡶⠚⠓⠦⠉⠃
⠀⠀⠉⠚⠀⠀⠀⣀⣀⡞⠀⠀⡰⠁⠀⠀⠀⠀⠀⢹⣀⠴⠚⠁⠀⠀⠈⠙⠓⠲⡦⠤⠤⠤⠤⠷⠂⠉⠉⢳⣄⣀⣠⠶⠋⠀⠀⣠⠾⠿⣏
⠀⠀⠀⠀⠀⠀⠀⢳⠉⠁⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠄⠀⠀⢀⡞⡵⠶⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣴⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠚⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡴⠒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡴⠚⣻⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣰⣯⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡴⠋⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠒⠒⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡰⠥⠾⣇⠀⠲⢄⡀⠀⠀⠀⣠⠴⠋⢀⡴⠋⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⢒⣼⣆⠀⠀⠀⢀⡤⠚⠁⢀⡴⠋⠀⠀⢀⠀⠀⠙⠖⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡱⢯⣮⣬⣧⣠⢖⡉⠀⠀⡰⠋⠀⠀⣄⠀⠀⠣⡀⠀⠀⠀⠈⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡼⡏⠉⠁⣎⣿⣧⠀⠙⠢⠞⠁⠀⠀⠀⠈⣆⠀⣠⠟⠀⢀⡤⠞⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢚⣿⣿⢀⣴⡏⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⡿⣧⠴⠋⢀⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠿⢫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⡜⢆⢠⢫⠷⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⠤⢤⣤⣤⣤⠤⠤⠶⠒⠋⠉⠀⠀⠀⠘⢦⡛⠉⣈⣉⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠳⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡘⣌⣢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠉⠙⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠋⠽⣛⣙⣿⣿⣛⣷⠶⠶⠖⠒⠒⠒⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣙⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠹⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠟⠛⠉⠁



⣿⣿⡿⠿⣿⡿⢿⠿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣾⣶⣶⣶⣿⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠓⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠒⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⠄⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠲⠤⢤⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡆⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢄⡀
⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠙⣦⣀⠀⠀⣷⡄⠀⣀⠤⠖⠚⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⠤⠄
⠀⠀⠀⠀⠀⠘⢾⣦⣀⠀⠸⡆⠀⠀⠀⢽⡧⠄⠒⢾⠧⡠⠄⢸⣿⢸⠁⠀⠀⠀⠀⡀⠀⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠁⢀⠀⠀⠈⠀⠀⠀⣘⡆⣤⠀⠀⢛⠚⠣⠄⠾⠞⠛⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠘⣷⣀⣈⠶⠴⠒⠉⠙⡙⠀⠠⠈⣄⡀⠀⠠⢰⣤⠶⠆⠐⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠙⠛⠻⣄⡀⠀⠴⠾⠧⠡⠀⠀⠛⠁⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡁⠀⠀⣠⣧⡀⠀⣰⠶⠦⠀⠐⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⢿⣿⣟⣛⣚⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⠛⣏⠉⠉⠁⠐⣠⣠⠘⠀⠀⠦⢤⣦⣥⣤⣀⣀⣀⣀⡤⠴⠛⠛⠉⠉⠀⠀⠀⠀⠉⠙⠒⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠈⢿⣮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡝⣩⣳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠶⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠁⠛⢸⣧⡀
⠀⠀⠀⠀⠀⠀⣀⠀⣼⠇⠀⠤⠲⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠳⠸⣿⣽⠅
⠀⠀⠀⠀⣀⣾⡿⠷⠀⠀⠀⠀⠼⠷⠙⠹⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣏⡰⠚⠀⢤⣿⣿⣷⣦⡀
⠀⠀⠀⢘⣸⡟⣤⠀⠀⠀⠀⠀⠀⠀⠀⡌⠿⣿⣿⣿⣿⣦⣀⣀⣀⢶⣷⣦⣄⡀⠀⠀⢀⣀⣤⣴⣾⣿⣿⡿⠀⣀⢀⡀⠀⠀⠀⠀⠈⣍⢻⡂
⠀⠀⠀⠀⢿⣁⡟⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⣉⣿⣿⣿⣿⣿⣿⣏⠛⢿⣿⠟⠛⠿⠿⠿⣿⣯⣉⠉⢻⡇⣀⣿⢸⡇⠀⠀⠀⠸⣿⣿⡄⣷
⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢹⡇⢠⣴⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⣿⡶⣦⣤⣄⣀⡀⠀⠀⠀⠸⣿⣿⣿⣼⠇⠀⠀⠀⠀⣸⣿⣧⣿
⠀⠀⠀⠀⢠⢿⣾⡧⠀⠀⠀⠀⠀⢠⣿⡇⠺⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣍⡛⠋⣿⣿⣧⡟⠀⠀⠀⠀⠀⠘⣿⣿⡿
⠀⠀⠀⠀⢸⣅⣿⡃⠀⠀⠀⠀⠀⠈⣻⣿⣄⠈⠹⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣾⣯⣍⠉⠙⠛⠿⢿⣦⣽⢿⣿⡃⠀⠀⠀⠀⠀⢐⡟⢿⣸
⠀⠀⠀⠀⠁⡿⠉⠀⠀⠀⠀⠀⠀⠀⠻⣿⡍⠛⠶⣶⣾⣿⣿⣿⣦⣀⠈⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⣨⣿⠂⣼⣇⠀⠀⠀⠀⠀⢸⣻⠃⠿
⠀⠀⠀⠀⣼⣇⡄⠀⠀⠀⠀⠀⠀⠀⢸⣾⡿⠋⠀⠀⠀⣀⣈⣹⣿⣿⣷⡄⠙⢿⣿⣿⣿⡶⠶⠶⣶⣿⣿⣿⢳⣹⣿⡄⠀⠀⠀⠀⢨⣿⠂⣴
⠀⠀⠀⠀⠿⠼⠇⠀⠀⢠⣶⡀⠀⠀⢸⡟⠤⠤⠬⠼⠿⠿⠟⠛⠛⠋⠉⠀⠀⠀⠛⠛⠛⠻⠟⠿⠤⠤⠌⠉⠻⠁⣟⡇⠀⢠⠀⠀⢠⣿⠅⠁
⠀⠀⠀⠀⠀⠀⣰⠀⠘⢼⣿⡇⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⣿⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠙⣧⠀⢸⣿⣇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⣾⡆⢰⣏⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⢸⣿⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠨⠿⣿⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢸⣿⠁⢀⣧
⠀⠐⣦⠐⢄⣀⣴⣿⡇⠀⣀⡟⠀⢸⣷⣀⠀⠀⣀⣀⣀⣤⣤⣴⣶⣶⣶⣞⡛⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠀⣿⣇⡾⡏⠀⣸⡏
⠀⠀⠀⠒⣹⣿⡅⢻⡇⠀⢻⡇⠀⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⠙⠛⠃⠀⠀⠀⠀⠀⠉⣉⣈⣀⣮⣿⣱⡇⢠⣿⠻⠀⠰⡶⠶
⠀⠀⢰⣾⣿⣿⣿⣾⣧⠀⢸⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣄⡉⣩⡉⠀⣿⣃⣾⣿⢾⣿⣦⣤⡄
⠀⠀⠸⣿⣿⣿⣿⢰⡿⠹⡄⢆⣀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⠀⢻⣯⣿⡟⢿⣿⣿⣿⡇
⠀⠀⠀⣿⡿⢛⡻⠘⣷⣄⣧⠈⠣⣼⣯⣿⣿⠿⠿⢿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣧⡀⠁⠀⠀⠙⣻⠋⢘⠟⠋⠙⠁
⠀⠀⠀⠙⠁⠛⠒⠒⢻⣿⣧⣀⣿⣿⣿⣿⣇⣀⣀⣀⣠⣶⣶⣤⣤⣤⣤⣤⣤⡶⠞⠛⠛⠛⠿⠿⠿⠿⠿⣋⣽⣿⡿⢿⡃⠀⣛⠀⠀⡄⢐⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠀⣀⣀⣀⠀⠒⠀⠀⠀⢀⠙⢻⡏⣉⢿⡆⠵⣿⣿⣿⣿⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠯⠃⠀⠋⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠑⠊⠁⠉⠘⠷⠚⠻⠟⠙⠛⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠿⠿⠿⠿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣻⣿⣟⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡿⢿⠟⠛⣟⣉⡋⠉⠙⠿⢛⣿⣿⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣽⠿⠟⠛⠛⠛⠉⠉⠉⠂⠠⣀⠀⠀⠙⠽⣿⢿⣿⣟⠳⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⡋⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠌⠻⣷⣝⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣎⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⡀⢨⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⠎⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠙⢾⣤⢿⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣽⣏⣿⡆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣿⣼⣿⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻⣿⢿⣴
⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠾⢸⣿⠟⣿
⠀⠀⠀⠀⠀⠠⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠘⣿⡆⣿⡀
⠀⠀⠀⠀⠀⠐⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⣿⡇⢹⡇
⠀⠀⠀⠀⠀⠀⢿⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢹⡃⢸⡇⡆
⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠈⡇⢿⠀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣾⡏⢸⣧⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢹⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣮⠋⢸⡏⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢹⢿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠂⣴⣥⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⠸⣯⢹⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⣾⢻⣿⡣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⣾⠐⠋⠈⢠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠘⣇⠛⣷⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠍⢰⠆⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠘⢷⡹⣿⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⣠⠎⠀⣿⠘⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠐⠃⠀⡜⠸⠃⡀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠷⡼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠣⠎⠀⣀⠀⠰⠀⡆⠀⠀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢷⡀⠙⢯⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠁⢀⠐⠁⣀⠁⠘⠁⡀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠙⠷⡀⠻⣍⠿⢗⡶⣤⠄⠀⠀⠀⣀⠀⣀⣤⠴⠋⠀⠀⠀⠰⠀⠀⠚⠁⢰⠃⠀⠁⣬⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠈⠳⠦⡑⠤⢆⣀⠀⠈⠉⠀⠀⢀⣀⡀⠤⠊⠀⠀⠀⠀⠀⣠⠃⠀⠀⣰⣌⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠂⡀⠀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢰⢃⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠂⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁⠀⢀⢴⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠁⠠⠀⠀⠲⣄⡀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⢀⠔⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⡀⠀⠀⠑⠦⣄⠉⠓⠀⡀⠀⠀⠀⠀⠀⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠉⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠶⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣄⣀⣀⡠⠤⠄⠀⢀⣀⡀⠀⠀⠀⠉⠁⠶⠆⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢾⠏⠉⠉⠉⠳⣄⠀⠀⠈⠉⠉⠶⢦⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠶⠶⠀⣀⣴
⢀⣠⣤⣀⣀⠀⡀⠐⠒⠾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡈⠿⣦⠀⠀⠀⠀⠘⠻⣶⠶⠶⠄⣀⡀⠀⠀⠀⠀⣀⠴⠋⠉⠰⠆⣀
⠈⠻⠃⠈⠁⣀⡀⠐⠲⠶⠖⠀⣼⣆⡀⠀⠀⠀⠈⠀⠀⠈⠶⡀⠀⠀⠀⠀⠘⠧⠀⠀⠈⢩⣶⣄⠰⠂⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠿⢧⣀⠀⠀⠀⠀⠀⢹⣤⣀⣠⣀⠀⠸⡿⠒⠂⠀⠈⢹⡆
⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠈⠀⠀⠉⢳⣤⡀⠚⠓⠀⠉⠻⣄⠀⠀⠀⢰⡆⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⣦⡀⠀⢀⡄⠀⢻⡇⠀⡄⣼⠗⠚⠀⠺⠋⠙⣿⠟⠢⣤⡀⠀⠈⢳⣄⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠂⢀⡌⠀⠀⢸⠀⠀⠀⠈⣶⡄⠘⠿⠃⠛⠋⠙⠻⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢈⣷⠀⠀⠀⠀⢸⡄⠀⠀⠘⠋⠀⠀⠀⠆⠀⠀⠀⠁⠀⠘⠛⣦⣤⠤⠄⠀⠀⡀⠀⠤⠤⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠈⠻⡆⠀⠀⠀⠀⠙⣷⣄⣀⠀⣴⡄⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⢤⣄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢋⡄⠀⠀⠰⠆⠀⠀⠀⠀⠀⠈⠉⠙⢿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠈⢶
⠀⣴⣇⡀⠉⠀⠀⠀⠈⢣⡀⠀⠀⠘⢇⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠉⠁⠁⠀⠀⠀⠀⠀⠘⢣⡀⠀⠀⠈⠁⠀⠀⠀⠶⠶⢾⣉⠉⢉⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣀⣀⣀⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⢀⠀⠀⠂⠈⠉⠁⠈⠉⠉⠁⠲⢦⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⢾⡷⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⢀⣀⡀⠀⠀⠀⣀⡀⠀⠶⠦⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡆⠀⠉⠉⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠒⢀⣀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢂⣀⠀⠀⠀⠀⠹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⣄⠀⠀⠘⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣄⠘⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣼⣷⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣭⣤⣤⣦⣤⣤⣄⣀⣀
⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⠀⠉⠁⠀⠀⠀⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣴⣦⡀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⠀⠀⠀⠀⠀⠀⢠⣾⢿⣷⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣴⣶⣾⣦⣄
⣿⠀⠀⠀⠀⠀⠀⠸⠇⣀⡸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⣶⡄
⣿⠀⠀⠀⠀⠀⣰⣶⣤⣈⣡⣾⣦⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣤⢀⠱⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣤⠄⠀⠚⠻⢿⣿⡛⡃
⣿⠀⠀⠀⠀⠀⣿⣿⣿⠋⠙⣿⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣼⡆⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣶⣦⣀⣻⣿⣿⣷⡉
⣿⠀⠀⠀⠀⠠⣟⢀⣻⣤⣤⠉⢻⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠁⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡏
⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣶⣾⣾⣆⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡟⣿⣿⣿⣿⡇⠉
⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⡠⠏⣀⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⡤⢄⣀⣀⣀⣀⣤⠤⠖⠒⠳⠬⠙⠃⠉⠀⠛⠒⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⠓⠺⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠿⢝⡂
⠀⠀⠀⠀⠀⠀⠻⣖⣒⣒⡛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡴⠃⣀⣤⠴⠶⠶⠦⣄⡀⠙⢆⡀
⠀⠀⠀⣀⡴⠚⠉⢉⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠤⣄⣹⣞⡴⠚⠉⠀⠀⠀⠀⠀⠈⠹⣄⠀⠙⢦⡀
⠀⠀⠀⠈⠉⢉⠟⠁⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠹⠏⠀⠠⠶⢤⣄⡀⠀⠀⠀⠀⢹⡄⠀⠀⣳
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢬⣙⠳⡄⠀⠀⠘⡇⠀⠀⣧
⠀⠀⠀⣼⠖⢹⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⡇⠀⠀⢻
⠀⠀⠀⠁⠀⣿⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣿⠶⠒⢸
⠀⠀⠀⠀⠀⢸⠠⠤⢼⡄⠀⣀⣀⣀⣀⣤⣤⣴⠾⠛⠋⣴⡄⠀⢠⣆⠀⠀⠀⠀⠀⢀⣿⠀⢠⡏⠑⠂⢸
⠀⠀⠀⠀⠀⢸⠀⠈⠉⡇⠀⠈⢻⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⣼⠁⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢧⠀⠀⢳⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⣀⣤⡿⠁⠀⢠⡇⠀⠀⣰⣧⣄⡀
⠀⠀⠀⣠⠶⠒⠚⠢⠤⠼⠂⠀⠀⠀⠈⠉⠛⠛⣟⡿⠋⠀⠀⠠⠖⣦⠀⠀⠉⠉⠉⠀⠀⠀⠳⠶⠊⣡⡴⠒⠙⣆
⠀⠀⠀⡏⢀⡴⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠫⣿⠀⠀⢹
⠀⠀⠀⢷⡀⠀⠼⠈⡧⢸⡀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⠒⠂⠁⠐⠒⠒⠤⣄⡀⠀⠀⠀⠀⢠⣆⠙⠀⠋⠀⢀⡿
⠀⠀⠀⠀⠛⢦⣄⣀⣠⠼⢧⠀⠀⠀⢠⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣠⣤⣾⣿⣿⡆⠀⠀⠀⣼⠉⠛⠶⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⢧⡀⠀⠘⢿⢿⣿⢿⣟⣋⣛⣛⣛⣿⣿⠿⠿⣿⣿⡇⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠉⠲⠤⢄⣀⣀⣉⣁⣀⣀⣠⠴⠞⠉⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠚⠛⠋⠉⠁
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣟⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣩⣄⡸⣰⡿⠭⢗⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢰⣇⣿⣵⠿⠁⠀⢀⢧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢤⣼⣡⠾⠿⠒⠛⠁⠀⠀⠀⢸⡞⠀⠀⠀⣠⣴⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣁⡈⢻⠏⠀⠀⠀⠀⢀⣀⣠⣤⠤⣤⣶⡶⠶⠾⢯⣾⣿⣿⣿⠿⣟⡳⠦⣍⡁
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠏⠀⢀⣤⠖⠛⠉⠁⠀⠀⠘⠁⣈⣻⡇⠀⠀⠴⠖⢺⣭⠙⠛⠿⣷⣦⣈⠁
⠀⠀⠀⣴⣿⣿⣿⣿⣿⠃⣠⡾⠋⠀⠀⠀⠀⠀⢾⣉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢩⠇⠀⠀⠀⠉⠻⢿⣦⡀
⠀⢠⣾⣿⣿⣿⣿⣿⠃⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠈⠛⠛⢿⣿⡿⠁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣤⡀
⠀⠀⠀⠀⠀⠛⠁⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠐⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⣿⣿⠏⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠆⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠂⠉⠉⠁⣀⢤⡠⠻⡷⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠑⠀⠀⢠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠔⠉⠣⡀⢆⠀⠀⠀⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡐⡄⡄⠐⠈⠀⠰⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠀⠀⠣⠄⡎⢩⢸⣕⠦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠤⢑⣠⠀⠁⡰⠊⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢨⢀⠊⠈⠀⠈⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡠⠀⠀⠀⠀⡇⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠁⠀⠀⠀⠀⡇⠀⢸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡒⠠⠀⡀⠀⠀⠀⡈⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠈⢄⠀⠀⠀⠀⡇⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡤⠄⡈⠉⠈⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⡄⠀⠈⢆⠀⠀⠀⡇⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠈⠐⠀⠐⠊⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⣄⠀⠀⢣⡀⠀⡇⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢢⣂⠅⠛⠄⠇⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡄⢀⣀⣑⣄⣀⣨⣃⣀⣸⡓⡃⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡇⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⠀⠀⡼⠁⠀⠠⠄⠙⡆⠀⠀⠅⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⣺⡇⠠⠀⢀⠀⢠⠇⠀⠐⠠⣀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡧⠤⠤⢈⣀⣼⠦⠀⠀⠀⡇⠀⢨⠉⠇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢀⠎⠀⡀⠀⠒⡈⢣⠀⠀⠀⠀⢃⠀⢨⠀⢸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠎⣀⡆⠬⠁⠀⣇⣈⡆⠀⠀⠀⠈⠀⠀⢂⠀⢃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⡳⠤⠄⠤⡮⠴⠁⠀⠀⠀⠀⡇⠀⠸⠀⠸⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡀⢰⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⢸⠀⠀⠀⠀⠀⠀⢀⠋⠀⡎⠀⢀⠃⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⣀⣂⣀⣺⠄⠀⠀⠼⠒⠛⠀⠀⠀⠀⠀⠀⠀⢀⣧⣴⣸⠀⠀⠀⠀⢀⠴⠃⠀⠀⠁⡠⠂⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠛⠀⠂⠀⠀⠀⠑⠀⠐⠂⠈⠀⠁⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⣻⡿⠃⠀⠀⠀⠀⠀⠀⢸⡟⠁⠉⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⣘⠋
⠀⠀⠀⠀⠀⣀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠻⣷⣦
⠀⠀⠀⠀⣼⡏⠉⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣼⣿⡇
⠀⠀⠀⠀⠹⠷⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⡗⠦⣀⠀⠀⠀⠙⣟⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠘⢋⣤⡄⠀⠀⠀⣀⡀⠀⢀⣹⠀⠀⠙⠲⠤⣤⠼⠀⠈⠳⣄⠀⡷⢦⡀⠀⠀⠸⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠈⠻⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠃⠀⠀⠀⠀⠀⠀⣈⡃⠀⠀⠀⠀⠄⠠⠀⠸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡴⠋⠉⠉⠓⣆⠀⠀⣠⣤⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠁⠀⠀⠀⠀⠘⡆⢸⠱⠀⠈⣧⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠦⣀⡞⠀⠀⠀⠸⡄⠀⠀⠀⠀⢿⡇⠘⣆⠀⢀⡟⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⠛⠓⣌⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⡼⠀⠀⠈⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠙⢆⠀⠀⠀⠀⠀⠈⠦⠒⠚⠁⠀⠀⣈⠀⣸⠂⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠓⠦⣄⡀⠀⠀⠀⠀⡄⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⢀⡔⠀⠀⠀⠉⡷⠒⠶⠴⠶⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠉⢲⠞⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣍⡛⠃⠀⡞⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣖⣂⣀⡴⠧⣄⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠉⠁⠀⠠⢤⠬⢍⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣁⠉⢻⣙⣒⣶⣶⢟⡒⣻⠋⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⠭⠭⠟⠚⠉⠈⠑⠛⠽⠿⠯⠝⠁

⠀⠀⠀⢀⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⢻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠉⣿⣿⣿⡿⠿⠛⠿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣿⣿⡋⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣤⣤⣤⣼⣿⢿⣿⣿⣫⡴⠿⡿⠟⣝⡻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡋⠽⣟⣿⣿⣷⣾⣿⣿⣻⣿⣿⡟⣭⣿⣿⡟⣾⣿⣿⣿⣷⠂⡁⠒⢉⠀⡙⢛⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣷⣶⣿⣿⣀⣽⣯⣿⣿⣧⣻⣿⣷⣽⣿⡿⢸⣿⣿⡧⢾⣿⣿⣿⣿⣿⡿⣿⣺⣣⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣏⠻⣾⣿⣿⣿⣿⣿⣿⣿⣽⣧⠟⢿⣿⣿⣻⣿⡿⣓⣻⣿⣷⣾⣿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣯⣥⣿⡿⢹⣿⣿⣿⣿⠿⠛⠛⢠⠔⣤⢯⣬⠩⣶⣬⣽⣿⠿⣿⣇⣹⣽⣿⣿⣿⣿⣟⡿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣇⣤⣺⢷⣻⢾⣷⡿⢏⣶⡉⣴⢧⣾⣿⣿⠓⢀⢿⣧⣼⣿⣒⣽⢛⣯⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣞⠻⠿⢿⠿⠁⢠⣾⣷⠶⠆⡿⠁⣿⡟⣬⢹⣖⣿⣾⣿⣿⣿⣿⣿⣟⣿⣿⡟⠧⣾⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠰⣶⡖⣾⣿⣏⣡⡃⣼⡶⢸⣵⣿⣁⣿⣿⣿⣻⣿⣿⣿⣿⣏⣿⣧⠶⠶⢿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢰⣾⣿⣾⣿⢿⣿⣟⠿⡅⢉⣤⣿⣿⢿⣷⣿⠛⣿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣙⢻⣿⣿⣾⡿⠋⣶⣮⡁⠐⣿⣬⣿⣿⣿⣾⠾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣆⢭⡹⠏⣽⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣷⣌⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠉⠈⠁⠀⠘⠳⣌⣠⡿⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠛⠛⠛⠉⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡽⠘⢛⢿⣿⢿⣿⣿⣗⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢤⣀⠀⠀⠴⠂⢒⢋⡠⣿⡿⢋⡁⣡⣴⣾⢹⡆⢿⣿⣍⣻⡟⢰⣼⣦⣄⣠⣆⡀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣲⠬⠁⠀⠔⢢⣿⠖⠉⠀⡀⠀⠀⠭⠾⠿⢻⠿⢙⣶⣟⢿⡏⢲⣩⣿⠿⣶⡿⠿⠤⣉⡛⣫⣓⠺⡿⢿⣏
⠀⠀⠀⠀⠈⠉⠀⠠⠀⠐⢗⠀⠈⠀⠰⠦⠎⢷⠾⢦⡀⠋⢹⣿⣿⠿⢇⣿⢿⢹⡿⡷⢶⣶⣤⡴⣊⢈⡝⠟⣿⢿⠂⠁
⠀⠀⠀⠀⢐⣴⠀⠴⠀⠀⣍⠁⠈⠀⠐⠃⣴⡤⠞⠛⠷⣪⣿⡿⣇⡀⣹⣯⣯⠉⢃⢩⡼⠎⣡⣶⣉⣾⣫⡒⠓⢮⡵
⠀⠀⠀⠀⠰⠋⢥⠴⢯⡓⠂⠀⠂⠀⢠⠐⠛⢩⣼⠛⣄⢉⡴⣧⢩⣿⣿⡇⢹⢻⣿⣦⣄⣹⡿⠟⠷⠘⠋⠫⠑⠤
⠀⠀⠀⠀⢀⣪⣨⡔⢨⡉⣠⠄⠦⣀⠂⣤⡴⠉⢅⠉⠀⠰⣞⣍⡈⡟⠟⣿⠓⣈⣯⣍⠹⠃⠀⢠⣄⠁⣰⣌⠑⡊⢴⡄
⠀⠀⠀⠀⠠⡕⡯⠀⢿⡂⠥⠀⢀⡉⣠⠀⠂⠰⢯⠑⠃⢀⣀⡉⢶⠇⢠⢁⣼⣟⠛⢋⡀⢢⠀⢯⠁⠀⡉⠿⠃⣡⣦⢀
⠀⠀⠀⠀⠀⠲⠆⠘⠂⠀⠂⠴⠼⠟⠃⠄⠄⠀⢌⠃⠠⠀⠉⠃⠀⠂⠉⠀⠊⠉⠀⠀⠀⠋⠐⠀⠀⠦⠀⠀⠈⠿⠦⠼

⠀⠀⠀⠀⠀⢀⣴⠶⠾⠟⠛⠛⠛⠛⠿⠶⢶⣤⡀
⠀⠀⠀⠀⠀⣿⠡⠤⣄⣀⣀⣀⣀⣀⣀⡤⠤⢈⣿
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⣿⠟⠒⠲⠶⠤⠤⠤⠤⠶⠖⠒⢻⣯⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⠿⠿⣟⣛⣛⣻⣿⠿⢏⢩⡿⣿⣷⣹⣿⣷⣦⣄
⠀⠀⠀⠀⣴⠿⣍⣒⡒⠶⠶⠶⠶⠶⠶⢒⣚⣩⢿⣆⠀⠀⠀⠀⠀⠠⣿⣟⡁⢖⣉⣉⣉⣉⣹⣹⣧⣽⠶⠮⠴⠚⠋⠉⠀⠀⢈⣹⣿
⠀⠀⢀⣾⠋⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠹⣧⠀⠀⠀⠀⢀⣿⠙⠻⠿⢷⣶⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣴⣶⡶⠿⠟⠋⢿
⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠏⠀⠈⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾
⠀⠘⠿⣯⣭⣓⣒⣒⠒⠲⠶⠶⠶⠶⠖⢒⣒⣒⣋⣭⣽⠟⠁⠀⠀⠀⠀⠙⢿⣭⣭⣓⣒⣒⠒⠶⠶⠶⠶⠶⠖⢒⣒⣒⣩⣭⡿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢷⠆⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣠⣤⠤⠤⢄⡀⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠚⢉⣉⣉⡙⠳⠄⠀⠀⢺⣯⣴⠶⢶⣤⡈⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡀⠀⢀⣼⠟⣟⠉⠙⢷⣿⡿⠢⣿⡏⢠⢎⠀⠀⠗⢸⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣄⣾⣿⣤⣭⠤⢔⣺⣿⠃⠀⢿⣄⠘⢧⠀⠀⠀⠈⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡟⠛⠛⠛⠛⠛⠋⢹⣿⠀⠀⢸⣟⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣸⣧⣄⠀⠀⠀⠀⣰⡇⢈⣀⠀⢀⡘⢷⡄⠄⠀⠀⢰⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣦⡀⠀⠀⣿⡷⠚⠉⣰⠉⠳⣴⡇⠀⢀⣴⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣌⢻⣿⣇⠀⢸⠏⣀⣤⣴⣿⣥⣄⢸⡁⠀⠺⣿⣿⣿⣿⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡉⠉⠀⠀⠚⠛⠿⣉⣛⠛⠻⣾⡇⠀⢰⣿⣿⣿⣿⣿⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣄⣤⡀⠀⠀⢀⣟⠳⠀⠻⢃⣤⣾⣿⣿⣿⣿⣿⡿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⡀⢀⣽⣿⣿⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣤⡀⠀⢘⣽⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⠟⢿⣿⢿⣿⡿⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢅⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠈⠉⠃⠘⠁⠀⢸⡿⣿⡿⠿⠇⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠺⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⢌⠀⠀⢠⣼⠂⠀⠤⢐⠺⣵⠤⣄⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⢀⣀⡴⠀⢸⣧⣶⡿⢩⠷⠆⠐⠒⢙⠛⣟⠩⣿⣿⣦⡀⠐⣪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠶⡯⠐⣚⠛⢻⡷⣔⠉⠐⠋⠛⠳⠄⢲⣍⠁⠾⡖⢋⡕⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠢⢼⡇⠁⠈⡌⠉⠁⠀⠀⢈⣀⣀⡀⠀⠈⠀⠉⠲⣷⣀⣓⣧⡴⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢾⠣⠐⠦⠘⠄⠀⠁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⠀⠀⠂⠾⠫⡥⠀⠀⠘⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⢀⣰⣇⢠⠎⠀⠀⠀⣾⣿⣿⣿⠋⠉⢻⣿⣿⡇⠀⢠⠀⠈⠠⣄⠐⠻⠖⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣉⡾⣝⡋⠛⠂⠀⠀⠀⠉⠉⠉⢁⠀⠀⣸⣿⣿⡏⠀⢈⡿⣅⡀⡽⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠈⠻⢬⠩⠤⠀⠀⢹⢀⡄⢔⣢⡤⠂⢀⣴⣿⣿⣿⠃⠀⠈⠁⠡⡆⣱⡶⡄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠐⣧⠄⡸⠃⣀⣚⠁⠂⢠⣿⣿⣿⡿⠁⠀⠀⡀⢀⡞⠀⠀⣄⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠁⠉⣀⣡⠠⣶⣹⡀⢿⡁⠀⠀⣿⣿⣿⡏⠀⠀⠄⠒⠋⢻⡟⠢⢁⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣽⣇⠂⠀⠻⣤⡏⣁⡀⠈⠛⠛⠉⡡⢀⣴⠒⠐⢂⡉⠸⣏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢛⢯⠠⠔⢃⣿⣿⡟⠃⠀⣿⣿⣿⡄⠀⢛⢡⣀⣼⠀⠀⠉⠋⠓⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⣇⢠⣿⢿⣹⣿⡄⠀⠿⠿⠿⠃⢀⣞⠚⡉⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢋⣼⣇⣹⣿⡥⠃⠀⠤⠠⠖⠞⠉⠛⠉⡙⠉⠙⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢈⣁⣀⣁⣤⣤⣄⣠⣄⠉⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠉⠉⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡠⠤⡄⠀⣠⠤⠄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⣷⠀⠀⠀⣾⡆⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠚⠻⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡠⠀⠐⠀⢀⠐⢀⠀⠒⠈⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⢇⠒⠠⠓⠀⠀⠐⠁⠉⠀⠀⠀⢂⡀⠈⠀⠐⠦⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡤⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⢶
⠀⠀⠀⠀⠀⡀⠀⢘⠀⠀⠀⠀⠀⠀⠊⠀⠁⠀⡀⠀⡌⢀⠀⠀⠀⠀⠂⢀⠠⠴⠀⠀⠀⠀⠀⠐⢠⠄⠀⠖⠀⠒⠀⠀⡀⠀⠱⣂
⠀⠀⠀⠀⠀⠀⠅⠈⢀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠁⠀⠀⠀⠄⠑⠁⠀⠀⠀⠀⠀⠀⢐⠀⠤⠀⡀⠠⠐⠉⠂⠈⠑⠀⠄⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠂⠸⠄⠐⠀⠀⠀⠀⠂⡀⠄⠐⡀⠀⠀⠚⢁⠄⡘⠀⠀⠀⠂⠀⠈⠁⣄⠈⠐⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⣀⠐⢀⠂⠌⠐⠀⠉⢡⠀⡄⠀⠠⠉⢩⠀⠉⠉⠁⠀⠉⠀⠈⠁⠀⠈⠀⠀⠀⠀⢀⠀⡄⠀⠀⢸⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⠠⠲⠐⠈⠁⠄⢀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠀⠈⠀⠀⠀⠠⠠⢠⡶⡦⣦⢴⣤⡔⠁⠐⠂⠁⠠⠀⠀⠀⠐⠀⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠤⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠷⠆⢳⣗⣮⠀⣙⣣⡀⠀⢈⠐⢀⡠⡡
⠀⠀⠀⠀⠐⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠉⠉⠁⠀⠐⠰⢦⢯⠈⢐⢚⠉⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢥⡄⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠊⣽⠂⠀⠀⠀⠀⠀⠀⠀⠘⢘⠀⠀⠀⠀⢀⡠⠐⠠
⠀⠀⠀⠀⠀⠀⠁⠂⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣄⠀⠀⢀⡄⠀⠀⠈⠉⠀⠁⠈⠉⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡆⠈⠁⠈⠁⠠⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣿⢧⡀⠀⠀⠀⢰⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣧⢿⣶⣤⣤⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣱⣿⣻⣿⣷⠩⣽⡟⢩⣿⡇⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡻⣿⣽⠯⠶⣟⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⣶⣿⣿⡧⠀⠀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠠⠀⠀⣰⣾⣿⣿⣷⣄⣴⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠆⣼⣿⣿⡟⠀⣠⣾⣿⣿⡿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⠻⣿⣿⣿⣿⡿⢻⠀⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⠁⣰⣿⣿⣿⡟⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⢻⣿⣿⣿⠃⢸⠀⣿⣿⣿⠀⠀⠀⢼⣿⣿⡟⢠⣿⣿⣿⣿⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⢠⣾⣿⣿⣿⣦⣸⣿⣿⡏⠀⠈⢀⣿⣿⣿⡆⠀⠀⣾⣿⣿⠇⢸⣿⣿⣿⣯⣠⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠛⠛⠀⢀⠀⣸⣿⣿⣿⣿⡄⠀⣿⣿⣿⠂⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⢻⣿⣿⠹⣿⣿⣿⣧⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠀⣸⣿⣿⣿⡄⠀⠀⢀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⢸⣿⣿⣆⠙⢿⣿⣿⣷⡀⣰⣿⣿⡿⠁⢿⣿⣿⣿⣿⣿⡿⠀⢸⣿⣿⣿⡇⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⣿⣿⣆⠈⢿⣿⣿⣿⣿⣿⡟⠁⠀⠈⢿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣧⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣀⣤⣴⣶⣿⣿⣿⣷⣦⡿⣿⣿⣿⣿⠀⠀⠀⠀⠈⠻⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⢿⠛⣿⠛⠻⠿⠇⠀⢹⡏⣿⠀⠀⠀⠀⠀⠀⢨⡋⠁⠀⠀⠀⠀⠈⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠘⠀⣿⠀⠀⠀⠀⠀⢸⡇⠛⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠈⠀⢻⠀⠀⠀⠀⠀⢸⡇⣀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠻⠏⠙⠃⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡀⠄⠂⠀⠈⠉⠉⠀⠒⠢⢄⠀⢀⡼⠇⠀⠀⠀⠀⠀⠤⢱⣄⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠦⣄⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠛⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢤⡄⠀⠀⠀⢳⠀⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠒⠚⢛⣉⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⠚⠉⢀⣀⡉⠓⣄⠀⠀⠀⠀⢀⠔⠋⠉⠉⠓⢦⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠋⣽⠀⠀⠀⠀⠀⢠⡇⠀⢠⣿⣿⣧⣤⢸⡄⠀⠀⠀⡏⣴⣿⣿⣀⡀⠀⣣⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠈⢧⣀⠈⠿⡿⠿⠋⣸⠃⠀⠀⠀⣇⠻⣿⣿⡿⠃⠀⡼⠀⠀⠀⠀⢸⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⡆⠀⠀⠀⠀⠀⠀⠈⠉⠑⠐⠀⠒⠁⠀⠀⠀⠀⠈⠂⠀⠐⠒⠂⠈⠁⠀⠀⠀⠀⣸⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⣴⠲⢦⡀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣠⠴⠲⡄
⠀⠀⠀⠀⠀⠙⢦⣄⠉⠳⢤⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⠦⣄⡀⠀⠀⠀⠀⠀⢀⣴⣫⠴⠛⢁⣤⠞⠁
⢀⣴⢒⡛⡏⠉⠉⠉⣤⣤⡀⠹⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠞⣽⠁⢀⢤⡌⠉⠉⠉⣿⣿⡲⣤
⣿⠥⠤⠒⠒⠀⠀⠀⠀⠀⢹⢸⡅⠀⠀⠀⠑⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠂⠀⠀⣽⢠⡁⠀⠀⠀⠀⠀⠒⠲⠦⢬
⢳⣀⣤⠤⠤⠤⠤⠴⢶⡖⠋⠀⢧⠀⠀⠀⠀⣠⠏⠉⣟⠲⠶⠦⣤⣤⡤⠶⠶⣾⠛⢯⡀⠀⠀⠀⢠⡏⠀⠓⣶⠶⠦⠤⠤⠤⠤⣄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⢧⣄⣤⠞⠁⠀⢠⡏⠢⠤⠚⢿⣿⠟⠢⠄⢹⡀⠀⠙⠦⣤⣠⠞⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⡴⠋⡇⠀⠀⠀⢰⣼⡄⠀⠀⠈⡷⣄⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠖⠒⠒⠚⠉⠀⠀⡇⠀⠀⠀⠈⢙⣧⠀⠀⠀⢣⠈⠉⠒⠒⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣿⣿⡄⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⢿⣿⡯⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣶⠒⠲⡆⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⢰⠀⢸⠇⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀⣠⠞⠀⠘⢧⡀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠠⣟⠁⠀⠀⠀⠀⢹⡄⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣬⣧⡀⠀⠀⣴⣏⣀⣀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠉⠛⣋⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⠂⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣀⠉⠻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠇⠀⠈⠻⣿⣿⣿⣿⣿⢿⣿⣿⠀⠀⠀⠈⠻⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠋⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⠙⠰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⣼⣿⣿⣷⣤⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣤⣼⢿⣿⣿⣿⣷⡀⠀⠀⠀⠸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈⣿⣶⣾⣽⣿⣿⣿⣯⣿⣿⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠹⠟⠻⠟⠛⠛⠛⠉⠋⠇



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢐⠀⢀⠠⢀⢤⡠⠀⢀⡄⠤⡠⠄⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠁⠈⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢉⣁⣈⣉⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡋⠉⠉⠉⠃⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠃⠀⠀⣠⠆⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠁⠈⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⡟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⡇⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⠀⠀⠀⠀⡀⠀⠳⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⠶⠄⠀⠀⠀⠀⠀⡞⠉⠙⠃⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣤⣤⡉⠒⠊⡇⠀⠀⠀⢀⠀⠀⣠⢒⡩⢙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠋⠀⠙⣦⠀⠀⠀⠀⢸⣄⣀⣀⡏⠀⣸⠃⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⣟⠓⠈⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢤⠀⡜⠉⠑⠂⠓⢶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢫⣻⠟⠀⠀⠀⠀⠀⠀⠈⣪⣉⢼⣄⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⡘⠒⠀⠀⠀⠀⠀⠀⠈⢁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠣⡀⠀⠀⠀⣀⠴⠊⠙⣿⠃⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡝⠀⠀⠀⠀⠀⣀⣤⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⣉⣈⡩⠤⠖⡋⢸⣻⡄⠀⠀⣤⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⣀⣤⣄⠐⢯⣀⣨⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡯⣒⡇⠀⠀⡏⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⠽⢷⢶⡏⣀⡸⠀⠀⠀⣾⡕⠉⢱⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠖⠁⠀⠀⡁⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⡼⠀⠀⠈⠙⠒⠶⢤⡟⠳⢤⡻⠔⠊⠈⢆⠀⠀⡔⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣀⣀⣀⣀⢀⡁⠀⡆
⠀⠀⠀⠀⠀⠀⣀⣀⠠⠼⠀⠒⠒⠀⠀⢻⠀⠀⢀⡠⠔⠉⠀⠀⠀⠀⠀⠓⢨⡥⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠓⠚⡄⡳⡇
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⣠⣼⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⣧⣷⠇
⠀⠀⠀⠀⢀⣀⡀⢡⠀⠀⠀⠀⠀⢸⠁⢀⣤⠀⠀⢣⡞⠉⢙⡂⢠⡴⢦⠀⠀⣈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⠀⠀⡏
⠀⠀⠀⢰⠁⠀⢉⣈⡀⠀⠀⣠⣤⢤⣍⠀⠈⡆⠀⠀⠰⡖⠋⠀⠹⣀⠠⠷⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⡀⠀⡇
⠀⠀⠀⠈⢦⣤⠼⠁⢩⠀⠀⢯⡀⠀⣹⣀⣤⡥⠀⠀⠀⢣⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠛⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⠷⣾⡤⣇⡀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠿⠿⠿⠿⠿⠿⠿⣱⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣖⣿⣷⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⡿⢿⣿⡿⠛⢿⣿⣿⣿⣿⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣶⣒⣶⣶⣾⣿⣿⣿⣿⣿⣷⣦⡝⠙⠀⠘⠛⠛⢻⣿⣿⣧⣤⣤⣤
⠀⠀⠀⠀⠀⢀⣾⣿⢟⠉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣇⠀⠛⠃⢀⣤⠺⠉⢿⣿⣿⣿⣿⣤⣀⠀⢀⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣾⠀⢹⣿⣿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣷⣾⡷⠃
⠀⠀⠀⠀⣾⣿⠟⢋⣹⢿⡏⣿⣿⠀⠀⠟⠉⢹⡿⠉⠉⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⠃
⠀⠀⠀⠀⣿⣿⣴⣯⣤⣼⣶⣷⣧⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣷⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣭⣭⣭⣽⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⢛⣛⣛⣛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢏⣴⠾⢛⣉⣉⠙⠻⢶⡝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⣾⢋⣾⣿⠟⣡⣾⣿⡎⢻⡆⢿⣿⣿⣿⡇⣿⠿⠿⢛⣛⢻⣿⣿⣿⡿⢛⡛⣋⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⢸⠟⣡⡾⢿⡿⢋⣴⠈⣿⢸⣿⣿⠟⡁⣴⠂⠆⣿⣿⣾⣿⣿⡟⠰⠟⠰⠿⠆⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡌⢿⡀⢾⣋⡴⢋⣴⣿⠟⣼⠇⣼⣿⣧⣘⣰⣿⣷⣾⣿⣿⣿⣿⣿⣷⣌⠻⠌⠿⠃⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣌⠻⣦⣍⣐⣛⣋⣥⡾⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣧⢹⡟⠩⣴⠶⠿⠛⠻⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣭⣉⣉⣩⣥⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣛⣓⡛⠻⠶⣶⡶⠚⣿⣿⣿⣷⣶⣌⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣡⡶⠟⣛⣋⣉⣛⠛⠷⣮⡙⢿⣿⣿⣿⣿⣿⣿⣷⡘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⡾⢩⣴⣛⣩⣽⠙⠛⣿⢷⣌⠻⣦⠹⣿⣿⣿⣿⣿⣿⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⡟⣰⣿⣿⣿⣿⣿⢸⣇⢹⣦⣹⣧⠹⣧⢹⣿⣿⣿⣿⣿⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠁⣿⣿⣿⣿⣿⣿⡄⢿⡌⢿⣿⣿⡇⣿⠀⣿⣿⣿⣿⡿⢃⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡄⣿⣿⣿⣿⣿⣿⣿⣌⠻⣦⡙⢿⠇⣿⢀⣿⣿⡿⠛⣡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣷⡘⢿⣿⣿⣿⣿⣿⣿⣷⣌⡛⠷⣦⣥⣬⣭⣤⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡌⠻⣦⡙⠻⢿⣿⣿⣿⠿⢛⣡⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⠶⠶⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠚⠉⠉⠉⠉⠙⠒⠒⠰⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡀⠀⠀⠀⢰⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⣀⠤⠤⠤⠤⠤⠀⣀⣀⡀⢀⢀⣀⡴⠊⠀⠰⡄⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢹⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢤⣤⣤⡄⠀⠀⠀⡤⣴⣦⣦⢀⠀⠀⢸⠓⠠⠀⣿⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠈⠉⠉⠁⠘⠄⠀⠉⠉⠉⠉⠉⠀⠀⠸⡡⠀⣠⣧⡀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠐⠂⠺⠶⠀⠀⠀⠀⠂⠲⡶⠤⠀⠀⠀⠙⣄⢋⠀⠇⠀⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⢀⡇⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡼⠁⠀⠻⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⣰⠯⠤⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠙⠂⢈⡉⠈⠀⠌⠈⠀⠀⠀⣠⠞
⠀⠀⢀⣀⣀⣸⣌⠢⡀⠀⠀⠀⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⢠⠞⡱
⠀⢰⠟⠒⠃⠀⠐⠦⢈⡄⠀⠀⠀⠀⠀⠈⠉⠙⣳⠞⡛⠛⢯⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⣁⠌⠁⠙⠟⠟⣆
⠀⠈⠓⠒⠒⠒⠠⡔⠋⢳⡀⠀⠀⠀⠀⣤⠒⠚⣧⣾⣆⣀⠜⠓⠦⣄⠀⠀⠀⠀⠀⡠⠓⠧⡀⠤⠤⠤⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠑⢶⠁⠙⢦⡀⢠⠞⢸⠀⠀⣴⣿⠠⠀⠀⠀⠸⠋⠳⡀⠀⠀⠴⠓⢤⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⡁⠀⣰⠆⠀⣿⡟⠀⠀⠀⣰⠢⡀⠀⠙⡖⠁⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣘⡤⠞⠁⡇⠀⠛⠀⠀⠀⢠⡇⠀⠈⠢⣄⠃⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠛⣄⣀⡠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⠇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⠀⢹⣀⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠖⠋⢉⠓⡾⠉⠙⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣤⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣷⣦⡄⠀⠀⠀⠀⠀⠘⢡⣿⠆⠀⢀⣀⣀⡤⠄⠀⠀⠀⠀⢀⣻⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⢀⣿⣿⣀⣠⠤⠆⠀⣀⡤⠶⠚⠋⠉⣀⣤⠤⠶⠒⠛⠉⠉⠉⠙⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠋⢁⣀⠤⠒⠉⣀⣀⣤⣶⣚⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣩⣭⡠⠖⢋⣠⣴⣾⣿⣿⣿⣿⣿⣿⡟⣰⣾⣶⣦⡀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠋⢀⡠⠟⠛⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠸⣿⣿⣿⣿⣿⣦⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡴⠋⢀⣤⣾⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⣀⣀⠀⠹⣏⡙⢿⣿⣿⡄⢋⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠉⢸⣿⡿⠟⣿⣿⡟⠁⠀⣀⣉⡙⠛⣩⡤⠂⠀⠉⠁⠀⣿⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡠⠚⣁⣀⠀⠘⣿⡅⢠⣿⠏⠀⠀⠉⢁⣈⠉⠛⠁⢀⣴⣶⡄⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠞⠀⠘⢛⣿⡷⠀⢻⡇⠘⠿⠀⠀⣴⣾⠿⠻⣿⠀⢰⠟⠋⠹⠇⠀⢸⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢧⣀⠀⠀⢨⣥⠀⠀⠘⣷⠀⠀⠀⠸⠋⠁⠀⠀⠁⢠⡀⠀⢀⡀⠀⠀⢸⣿⣭⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠀⠀⠀⣠⠶⠦⣿⡄⠀⠀⠀⠀⢠⣶⡆⠀⠀⢷⠀⠻⡿⠀⠀⣾⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡀⠀⢰⣿⠀⠛⢻⣷⠀⠀⠀⠀⠀⠙⢡⠆⠀⠸⣇⠐⢦⡀⠀⣿⣿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣿⣇⠀⠀⠀⠀⠴⠋⠀⣀⠀⢻⡀⠀⠁⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣀⣹⡟⠀⠀⠀⠀⠀⠀⠀⢻⡟⠋⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⣁⣤⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠺⢿⡟⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠠⠿⠶⣦⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣼⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣀⣀⣴⡧⠾⠋⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣦⣤⣍⣩⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠻⠿⠟⠛⠻⠿⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉