Bath Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠐⠀⠐⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡻⡀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡘⠀⠀⠀⠀⠀⠈⡀⡀⠄⠀⠀⠃⠠⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠀⢠⢇⡓⢤⡄⠐⠒⠐⡞⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣠⠁⠀⠀⡘⠈⠃⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠐⠁⠀⠊⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄⠀⠀⠀⠀⠀⠆⠀⠘⠀⠀⠀⠀⡐⠹⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠐⠦⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⢀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠙⠉⠉⢣⠰⢎⣠⠀⠀⠀⠀⠄⠀⠘⡀⠀⠀⠀⠈⠂
⠀⠀⢰⠁⢅⠀⠀⠀⠀⠉⠉⠉⠛⠓⠂⠠⠶⡈⠀⠀⠀⡀⠀⣷⠀⠈⠢⣀⣠⡤⣤⠤⠤⢷⡶⠒⠃⠇⠴⢠⡠⢀
⠀⠀⠠⠀⠀⠑⠢⢤⡤⠤⠤⠤⠔⠀⠄⠠⠤⡁⠀⡀⠚⡐⠚⠸⡍⠢⡀⢁⠘⠀⢤⢠⡄⠼⠀⢐⡀⠯⠷⠠⣄⠱⠍⡄
⠀⠀⠀⠗⠢⢄⡀⠀⠀⠉⠑⠂⠲⠤⠤⣀⡀⠱⡄⣈⣠⠔⠒⠀⠁⠀⣄⣈⣦⠂⣠⣊⠠⠌⠄⠂⠚⠉⠈⠁⠀⢀⣠⠃
⠀⠀⠀⠘⡀⠀⠀⠉⠐⠀⠤⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠉⠁⠉⠁⠀⠀⠀⠀⣀⣀⡀⠤⠄⠐⠂⠉⠀⠆
⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠒⠂⠀⠀⠀⠐⠒⠀⠒⠒⠂⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢰⠎
⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⡠⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠉⢳⠣⢀⠀⠑⣄⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠠⠄⠒⠨⠋⠉⡱⠈⠠⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⢁⠤⠊⠐⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣟⠉⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⡿⠿⠛⠋⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠐⠰⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡁⢘⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠄⠀⡃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠀⠀⠆⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠂⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠂
⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣶⣶⣶⣶⣶⣶⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⢿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⡻⠿⣟⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢰⡒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⢦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠞⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠶⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣠⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣠⠖⡄⢸
⠀⠀⠀⠀⠀⢀⠤⢤⡰⠊⠁⠀⠈⠙⠁⠀⠀⠀⠀⢡⡔⠊⠉⠉⠐⠖⠒⢢⣀⠤⠤⣄⢀⠠⢤⡀⠀⡠⣇⠸⠧⢤⣄
⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠙⢫⢣⠜⢰⢀⣦⢼
⣠⠊⢉⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⣈⣀⢏⠈
⡇⠀⠣⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠤⠒⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡤⠖⠁
⠀⢸⡉⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⢸⡑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠊⣆⡀
⠀⠀⢀⡽⠀⠈⢉⠗⠒⠲⠶⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠶⠒⠊⠉⣳⠀⠀⢀⣹
⠀⠀⠘⠤⣀⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠓⠚⠁

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢨⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠤⠤⠤⠤⠤⣤⠤⠤⠤⡤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⡤⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠄⠀⠠⠀⣠⠕⠒⠘⠒⠤⡁⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⢠⠒⠉⠉⠑⠚⠀⠀⠀⠀⠀⠀⠈⠦⠔⠒⠬⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠠⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⣬⠉⠲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠸⡀⢸⠛⠈⠺⡇⠀⠀⠀⠀⢠⠦⠄⠤⠔⠉⠓⠒⢲⢸⠗⠁⠋⣧⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⢀⠞⢁⠆⠀⡠⠊⠀⢰⠢⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠳⢄⠀⠹⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡸⡀⡜⠀⡰⣳⠤⠴⠃⠀⠀⠀⠀⡇⠀⠀⠀⠘⡇⠀⠀⢸⠀⠸⡆⠀⢡⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠠⠀⠁⢸⠀⠀⡿⣹⠀⠀⠀⠈⢦⣤⠴⠃⠀⠘⣲⠀⠙⠲⠒⠃⠀⢰⢱⠀⠈⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⢇⢈⢆⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⠀⠀⡀⠀⢀⢀⠎⡟⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠄⢀⠈⠘⡆⠀⠈⢢⡈⢆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰⢋⡔⠁⠀⢰⢁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡄⠀⠀⠈⠒⠱⠦⢄⣀⣀⡀⢀⣀⣀⣀⠤⠶⠏⠒⠁⠀⠀⣠⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠰⠀⠂⠘⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠐⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠘⠀⠈⠀⠐⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠁⠠⠀⠁⠀⠀⠃⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⢸⡇⠀⠀⢀⠘⠀⠀⠀⢈⠀⡀⢀⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠂⢀⠀⠀⠀⢀⡀⠈⠀⠈⠀⡀⠀⢀⢘⡇
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⢀⣤⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠘⢳⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡱⠀⠀⢀⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⣀⠤⠤⠤⣀⡀⠀⠀⣠⡔⣃⠙⠃⢀⢤⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⡇⢀⣤⣀⡀⠀⢱
⢀⠔⠋⠙⠲⢤⡀⢀⡐⠉⠙⠞⠀⠀⠈⠖⠉⠀⠀⠀⠀⠀⠙⢆⠀⠀⠿⠛⠁⠀⠈⢛⡀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠑⠊⠀⠀⢹⡀⢸
⡌⠀⠀⠀⠀⠀⠈⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⢿⠀⠀⠀⢸⡇⢸
⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠰⠆⠉⠉⠳⡁⠀⠀⠀⠀⠀⠀⠀⡷⠒⠒⢄⠀⠀⠀⡀⣔⢀⢸
⠈⠢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⢱⠯⣷⣊⣨⣧⣤⣀⡀
⠀⠀⠈⢇⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠒⠒⠒⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠙
⠀⠀⠀⢸⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⠄⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⡤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠘⠐⠈⠂⠒⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠽⠂⠩⢥⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⡀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠠⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠁⠀⢀⡸⠄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⡜⠀⠀⢀⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡜⠀⣄⣸⠆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢡⠀⢹⣤⠃
⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣴⣼⣿⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣿⣽⣾⣧⣶⣶⣶⣶⣴⣶⣶⣶⣶
⣿⣿⣥⣤⣴⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣠⣄⣀
⠀⠀⠀⣰⠋⠀⠀⠀⠈⠑⡄
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⡴⠒⠚⠒⠲⡄
⠀⠀⢸⡇⠀⠀⠀⠼⠥⠤⠤⠤⠤⠼⠄
⠀⠀⢸⡇
⠀⠀⢸⡇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠋⠀⠀⡀⠉⠉⠉⠒⠒⢦⠞⠉⠉⠙⢦⣀⣀⠀⣀⣀
⠀⠀⢸⡇⠀⠀⠀⣠⠖⠒⠲⠴⣒⠃⠀⢠⡦⢀⡈⠋⠀⠘⠃⠀⠀⠶⠆⠀⠰⠆⠀⡀⠈⠋⠁⠈⠙⢦
⠀⠀⢸⡇⢀⡤⠚⠁⠰⠇⠀⢀⣍⠀⠀⢀⡀⠈⢁⡀⠠⡦⠀⠀⢠⡄⠀⢀⣄⠀⠈⠛⣀⠀⢤⡄⠀⢉⡉⠓⣄
⠀⠀⢸⡇⡏⠀⠀⠀⠀⠠⡦⠀⠁⢤⠄⠘⠁⣤⠈⠉⠀⠀⠴⠆⠈⠀⠶⠀⠁⠠⡦⠀⠛⠀⠀⠰⠆⠈⠁⠀⠚⠒⠲⣄
⠀⣠⠚⠓⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⢢
⠀⠙⢤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⠜⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⡤⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋
⡖⠒⢲⠶⡶⠶⠶⢶⠶⡶⠶⢶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⢶⣶⣶⢶⠶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠖⠒⠚⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⠀⠲⢄⡀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠉⠓⣐⡃⠀⢸⢵⠀⠀⣿
⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠉⠉⠯⠠⠜⠁⠀⠁⠸⡤⢤⠏⠓⢤⡀
⠀⠀⠀⠀⡰⠋⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⣄⡀⠀⠉⠲⣄
⠀⠀⠀⠀⡇⠀⠀⠀⢁⠀⠀⠀⠀⡔⠂⠒⠐⠁⠈⡇⠀⡦⣈⠓⢄⡀⠀⠑⠦⣀
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠑⢴⠉⠉⠀⠀⠀⠀⠀⠐⠃⠀⠣⠌⢃⠀⠉⠢⣄⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⡀⠉⠢⣄⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠑⠢⡀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠙⢦⡀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢄⠈⠑⢄⡀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠙⠆⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣸⠆⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠁⠀⣰⣄⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠉⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠉⠁⠈⠓⢤⡀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠉⠒⠦⢄⣀⡀⠀⠀⠀⠀⠀⣀⠠⠔⠊⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⢀⣠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡄⡔⢂⣤⠀⠀⠀⢀⣀⣠⠴⢶⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠰⡋⠉⠉⠉⠁⠀⠀⠙⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠚⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣡⠤⠤⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⢹⡄⠀⠀⣠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢰⠃⠀⠀⠘⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠴⠊⠀⠀⢸⠁⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢸⠀⢸⠀⠀⠀⡰⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⠳⠤⠤⠊
⠀⠀⠀⠀⠀⠀⢰⠃⢹⢸⠀⢸⢠⠒⣦⠙⠋⡴⡀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠙⢦⠀⢀⡠⢄⡀⠀⠀⠀⠀⣠⠖⢦⡀
⠀⠀⠀⢠⠖⠋⠉⠉⠉⠙⠒⠚⠺⠤⢼⣀⣘⣷⡃⠀⠀⠀⠀⠀⠀⠀⣇⢀⣀⣀⣀⣸⣀⣼⡀⣀⡏⠉⠑⡶⠒⠳⣄⣴⡃
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⢦⣀⡴⠃⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠈⢳⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⢤⣤⣀⣀⣀⣀⣀⣠⡤⠤⢾⣉⠗⡞⠁
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡰⠋⠙⠒⠒⠲⠶⠦⠤⠴⠶⠖⠒⠚⠉⠁⢹⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⣄⠀⠀⠀⠀⣠⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⢰⠋⠉⠉⢧⠙⠚⠀⡴⢦⣸⡁⠀⠀⢸⠖⢲⡀⠀⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠻⣤⠼⠹⣄⠀⢀⡼⣠⠞⠛⠳⣞⠁⠑⠶⠶⠛⠦⢼⣁⠘⢧⣤⢏⡤⣄
⠀⠀⠀⠀⣞⠛⠿⢿⣿⣒⣒⡶⠶⢾⣿⣭⣭⣤⣿⡀⠀⢀⣿⣀⣀⣀⣀⣀⣤⣯⣈⡷⠤⠶⢾⣗⣻⣿⠿⠿⠛⣷
⠀⠀⠀⠀⠉⠙⠳⡄⠀⠈⠉⠉⠛⠛⠓⠶⠶⠦⠤⠽⠿⠯⠭⠤⠤⠤⠤⠤⠴⠶⠶⠒⠛⠛⠉⠉⠀⠀⣴⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣠⡤⠞⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⢤⣄⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣄⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣲⠊⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣭⡏⢸⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠒⢦⡀⣀⣀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣄⠀⠀⢀⡀⠀⠀⠀⠀⢸⠃⣤⣶⡄⢠⠟
⠀⠀⠀⠀⠀⠀⣠⠴⠒⠶⠏⠀⠀⠀⠀⠀⠀⠉⠉⠈⠙⠖⠒⠒⢶⡏⠀⠀⠀⠈⡷⠋⠉⠉⢷⣤⣀⠀⠘⠓⠋⡟⠀⣿
⠀⣠⠤⡴⠚⠛⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⢦⡀⣧⠀⢸⣄⣀
⢸⣁⠀⠙⢲⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠛⠒⠛⠀⠈⣹
⠀⢩⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠤⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁
⢀⡟⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢰⠃⠈⠛⠉⠣⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⣸⠁⠀⠀⢸⢀⣤⡀⠀⠀⢀⡏⠹⡀⣰⢦⡀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠈⠁⠀⢳⠀⠀⢸⠀⠀⠈⠁⠀⠓⠤⠏
⡇⠀⠀⠀⠀⠀⠀⠈⠧⣀⠟
⣧
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠙⠲⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠄⠀⢀⣠⠶⠋
⣀⣀⣀⣀⣘⣶⣤⣤⣤⣞⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣷⣤⣤⣤⣶⣞⣁⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠒⠒⠒⠒⠒⠲⠶⠦⠤⠤⠤⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣖⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⣶⣮⣭⣥⡬⣱⡦⣢⠄⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢻⣿⣿⢫⣼⣿⡿⠁⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠈⡿⣱⣿⣿⣿⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹⡆⢸⣿⣿⣿⣿⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⣇⣽⣿⣿⣿⡿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠛⠒⠂⠀⠐⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣓⠀⣿⣿⣿⡛⡃⠀⠋⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡥⢠⣤⣬⣦⣤⣄⠀⠀⣽⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠾⠿⠿⠟⠿⠑⠶⠾⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡵⠦⠶⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠇⡴⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠀⠀⠀⠀⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⣫⣾⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⣰⣿⣿⢐⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⢀⡄⠀⢀⣀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣾⡄⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣤⣷⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⣿⣿⣿⣏⠧⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠙⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⣿⣿⣿⣇⣷⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣶⡤⢶⣿⣶⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⡿⣿⣿⡆⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣿⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣴⣶⣶⣶⣶⣶⠀⠘⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⡃⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣿⠇⣷⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠁⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⢇⢀⡀⣛⠻⠤⠐⠒⠂⠈⠉⠏⠈⠁⣀⠀⠈⣙⠉⠍⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡭⢭⠭⠍⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠈⠫⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢀⠀⠁⢈⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣐⣀⣀⠲⡒⣶⣶⣢⣾⣿⣧⣿⣿⣿⠃
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠬⠭⠭⠭⠭⠽⠿⠿⠟⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⡿⣿⣿⣿⣿⣿⡿⠛⣹⡿⡿⣿⣧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⢿⣗⣾⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⣿⣿⣯⣿⠟⠛⠉⠉⠛⠛⠛⠻⠿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⣩⣄⣠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣥⣤⣴⣶⣶⣶⣾⣷⣶⣦⣤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⣝⣻⣿⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣿⡏⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⠋⠀⢹⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⣷⣸⣆⠈⢦⡀⠀⠀⠀⠀⠈⢩⠁⣀⡀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣆⠀⠳⠀⠀⠀⠀⢀⣀⣤⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⢻⣷⣄⡀⠀⠀⢰⡿⠛⠉⠁⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣷⣴⣶⣿⡁⠀⣲⣶⡖⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠈⠻⣿⡻⢷⣍⠓⠀⠉⠙⠛⢛⡍⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⢧⣿⣿⣿⣿⡎⢇⠀⠀⠀⠙⢦⡈⠁⠀⠀⢀⣴⣿⠃⠀⣿⣷⣄⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠉⢦⣀⣰⣿⣿⠏⢀⡀⢸⣿⣿⣧⡘⢿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣴⣄⠀⠘⣿⣿⣿⡟⢠⣾⣷⢸⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢰⠛⠻⣦⡀⠘⣿⡿⠀⢸⠟⢻⡆⣿⣿⣿⣿⣿⢟⣬⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡞⠀⠀⠈⠳⢠⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠲⠤⠶⣤⠴⠒⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢲⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⠴⠂⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣡⠖⠁⠀⠐⠒⢤⡁⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣁⠴⠖⠒⠚⠓⠶⣄⠀⠀⠀⠉⠒⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠞⠁⠀⠀⠀⠀⠀⠀⠘⡆⢀⠐⠒⠦⠄⠀⠀⠙⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⠀⠀⠀⠀⠀⠀⢠⣤⢠⠟⠉⠉⢢⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠘⣆⠀⠀⠀⠀⠀⠘⠋⣿⠀⠀⠠⣼⠀⠀⠀⠀⠀⠀⣨⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠬⣗⠦⣄⣀⣀⣀⠴⠛⢢⠤⠐⠃⠀⠀⠀⠀⠀⠀⡿⠴⠒⠒⠲⣤⠀⢀⣴⠛
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⢄⣀⡅⠀⠰⢀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠶⢍⡲⠦⢸⡷⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠘⠂⠐⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⡠⢄⣀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠠⠊⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢓⠦⠤⢀⣀⣀⣀⣀⣀⣀⣀⡤⠴⣺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢁⡠⠂⠀⠀⠀⠉⠉⡁⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡀⠘⠓⢭⡉⠐⠲⠤⠚⠳⢤⣀⡜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠉⠀⠉⠓⢤⡀⠀⢀⠀⠉⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⠤⠤⣄⣀⣀⣀⡈⢐⣉⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⢿⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠠⠧⣼⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢖⢳⢤⣀⣹⡀⠀⠀⠀⠀⠀⣀⡼⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣏⢙⣩⣅⠊⠿⡩⣉⣉⡙⠟⠿⢚⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠈⠑⠒⠲⠬⠭⠭⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣆⠀⠀⠀⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢒⣡⠼⠋
⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢘⠀⠀⠀⠀⠀⢀⠚⡆⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠢⢄⠀⠀⠀⠀⠀⡄⢠⡀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠈⠴⠃⠠⡓⠋⠀⠀⠀⠀⣀⠠⠔⡊⠠⠤⠴⠀⠤⠴⠀⠄
⠀⠀⠀⡠⡀⠀⠀⠈⢦⠐⢌⠓⠢⣀⡤⣀⡏⠀⣷⡀⠀⠃⠀⠀⠀⢰⠀⠀⡀⠤⠴⠣⣇⣀⣀⡤⠖⠋⢡⠤⠊⠀⠠⠃
⣀⠀⠀⠀⠜⠀⠀⠀⠀⢳⢠⠳⠤⢄⡀⢀⡀⠤⣀⡀⡑⢲⠀⠀⠀⢘⡉⠉⠀⠐⠀⠀⠈⠉⠠⡤⢤⠠⣇⡀
⠃⡁⠤⠤⠄⣀⣠⠖⠀⠁⢚⢄⡀⣀⡈⠉⡄⠐⠀⣤⢀⣾⡀⠀⠀⡘⠁⡀⢹⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠈⠑⢉⠉⠲⠶⠚⠉⢀⡤⣄⡒⢒⣲
⠀⠈⠐⣆⠠⣤⣤⠶⠒⠂⠛⠋⠉⠀⠍⣙⠶⠤⠤⠝⠋⠉⠉⠢⢴⡥⠞⣃⠈⢗⠤⠤⠤⠤⡒⠉⠙⠳⠤⠤⢂⡡⢐⣶⠾⠛⠋⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠘⠢⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⠤⠤⢶⣆⣀⣠⠞⡁⠀⠀⠑⠐⠦⠴⠚⡁⠂⠒⠒⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠤⣤⡄⠴⠊⠀⠀⠀⠀⠉⠉⡁⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠈⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠃⠀⠀⠙⠒⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣀⠤⠄⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠊

⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣾⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡶
⠀⠰⠿⣿⢿⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⡶⠲⠶⠶⠶⠶⠶⠶⠶⢾⢿⡿⠿⠂
⠀⠀⠀⠿⠆⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠠⣿⣿⡟⠛⠛⠛⠛⣻⣯⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠐⣿⠃⢿⠀⠀⣠⡿⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣀⣨⣀⣀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡍⠻⣿⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠉
⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⣀⢸⣿⣿⣿⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⡄
⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⢩⢨⡇⠹⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⣶⡘⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠀⠀⠀⠀⠈⣻⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠉⢈⡃⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣶⣆⣶⣤⣤⣦⣹⣿⣿⣷⡿⠁⠀⠀⠀⣾⣷⣾⣾⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⢘⢉⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⠟⣻⠛⠁
⠀⠁⠀⠀⠀⠘⣿⣿⣿⠃⠙⠀⡁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⢠⠛⡄⠄
⠀⠄⠀⠀⠀⠀⠛⠛⠛⠀⠸⠀⠇⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣶⣴⣾⣿⣙⡋⠀⠀⠉⠀⠀⢈⣋⣹⣷⣶⣾⣾⣍⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠘⠮⠄⣀⡙⢋⣽⣶⣦⣶⣿⣍⣛⢁⡠⠬⠥⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢠⡐⠂⢰⠐⠄⢠⠀⡆⠀⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣐⠀⡀⠀⢱⣎⣈⠐⠡⣀⡨⡅⠀⠉⠠⡀⢀⠴⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠃⠠⡆⠀⡂⠙⣏⡥⢀⠛⢿⢏⠀⠃⣤⡀⣿⡏⡄⠧⢀⢀⠁⠀⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢠⠀⣜⣠⢾⠛⡏⢫⠿⣦⣼⠒⡿⣠⡁⠀⠷⣷⠂⠜⡠⠁⠖⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣠⢉⣽⡈⢛⣶⣬⣏⠘⢁⣍⠿⢻⣿⡴⠛⢻⣿⡅⡲⢎⣽⣇⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢘⡟⢃⣞⣱⣧⣿⣵⣾⣷⣞⣿⣿⣽⡤⣿⣬⣤⣤⠜⢃⡈⡛⠂⠊⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠚⢆⠈⣋⣀⡍⢫⣯⣽⡍⠥⣿⣿⣿⣿⣿⣷⣿⣞⣷⣾⣿⢂⣻⣶⣎⡹⡇⢀⢦⡆⠁⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠹⠀⢠⣿⠈⡙⠘⣬⣿⣷⣶⣿⣿⡿⠿⣿⣿⢿⣿⣿⣿⣿⣿⢻⣏⣻⡓⢻⠮⣨⣁⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡾⢗⣁⣈⢓⣻⣿⣿⣿⣯⠿⣾⣷⣾⣯⣈⣿⣿⡶⣟⣻⡿⣿⠛⢫⣶⡄⢞⠣⢙⠁⠰⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡈⢠⡏⠉⣴⣡⣽⣯⣷⣮⣿⣴⣯⣿⣿⣿⣿⣿⣟⣛⣿⣿⠟⡿⣋⣿⣵⣦⢎⠟⣈⠠⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠈⡴⢣⡍⢟⣲⠼⣿⠿⣿⣯⣾⣿⣿⣿⣟⣺⣿⣿⣇⡟⠸⣧⡟⢬⠉⢁⡀⠤⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⢊⠋⠉⠷⣬⣿⢶⣸⣻⡿⣿⣿⠻⣿⣿⢛⣽⣿⣛⣿⡅⠿⣞⢃⠁⣸⣻⠃⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢂⢃⡀⢽⣯⣀⢾⣽⢮⣤⡤⣿⣿⡟⣿⢹⣿⡷⣼⣿⣟⠻⠟⢟⡰⠅⠱⠒⠊⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠌⡙⠳⠆⡸⠚⠫⠙⢻⣾⢗⣾⠟⣟⠱⢦⡽⢻⢷⣬⡸⢋⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡀⠠⠓⠃⠒⠉⣼⣠⣥⡴⢦⠐⣀⣼⢿⡐⢻⣯⡴⣤⠐⠴⠻⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢀⠠⠒⡀⠉⢻⠳⠛⠊⢁⡱⠥⠚⠙⠂⡁⠀⠀⢀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠋⠁⡀⠁⡀⠈⠴⢆⢉⡆⠹⠄⠋⠒⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠤⠄⠂⠐⠀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠿⠿⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⣠⣤⣤⣴⣶⡾⠟⠻⣷⡀⠀⠀⠹⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣿⣏⠉⠁⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠘⠻⢷⣶⣤⣄⣀⣀⣀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠉⠉⠛⠛⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡾⠿⠛⠉⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢷⣶⣶⣶⣶⣶⣶⣶⡾⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠸⠁⠠⢤⣤⡀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠻⠃⠀⣄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⠀⠈⠰⣦⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠇⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⢹⡄⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⠾⣧⠀⠀⠈⠀⢈⡁⠀⠀⢀⠄⠀⠀⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀⠀⣶⢄⣀⠀⠌⣡⣄⣰⣤⠶⡦⠤⣴⣟⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠊⠀⠀⠀⢠⣽
⣀⣠⣤⣤⣤⣴⣶⣶⣶⠿⢿⣿⡿⠿⣿⣾⣿⣿⣦⣜⣛⡛⠁⠀⠀⣠⣤⣿⣿⣿⣶⣶⣄⣠⣤⣤⣄⣤⡀⢀⣠⣤⣀⣀⣴⣦⣘⠀⠀⠀⠀⠀⣴⡿⠋
⣿⣿⣷⣾⣿⡿⣿⣿⣿⠿⠟⠉⠷⠂⠰⠾⡿⣿⣿⣿⡿⠿⢿⣶⡾⠿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⠿⣿⣿⢿⢿⡿⢿⣿⣿⣿⣿⣿⣦⣤⣴⣶⠟⠁
⠛⠿⠛⠋⠉⠀⠈⠁⠀⠀⠀⠒⢴⣶⣿⣿⣿⣦⡀⠈⠛⠦⠾⠦⠶⣦⣈⠉⠿⣿⣿⣿⣿⣿⣷⣶⣾⡿⢶⡶⣶⣖⣀⣤⣤⣀⣁⣀⣁⣬⣤⣽⣿⣶⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣄⢦⣴⣦⠤⣮⠙⢷⣄⠈⠹⣯⣍⣹⡏⡉⣠⣤⣤⣿⣿⣿⡋⡹⢟⣹⣍⣙⣿⣍⣹⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⣬⡉⢳⣬⣿⣶⣹⣦⣴⣦⣤⣿⣿⣍⣿⣿⣿⣿⣿⠉⠹⠗⢺⣟⢻⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⢦⣽⣿⣭⣝⣿⣿⣀⣿⣿⠷⣬⢻⣾⣽⣿⣶⣴⣶⣶⣴⣿⡿⠛⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠆⠻⣿⣿⣯⣽⣿⣿⣿⣿⣿⣾⠿⠋⠛⢉⡭⠉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠿⢿⠛⠛⠛⠉⠛⠛⠉⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⢀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠐⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣷⣠⣷⡄⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡅⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⡆⠀⢠⡆⠘⠆⠀⠀⢢⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⡬⣷⣴⣿⠃⠄⠀⠀⠀⠀⠀⠀⠘⢁⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠂⠀⠀⠀⠀⠀⠀⠭⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⠀⣀⠠⠀⢰⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠉⠀⠀⠰⣿⣙⣻⠄⠀⠈⠁⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣉⠀⠀⠀⢀⣤⣶⣄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠿⣧⣈⣷⡀⠀⠀⠀⠀⠀⠀⠰⣼⣄⣤⣾⣿⣿⣿⣿⣷⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠛⣿⣿⣿⣶⣌⣻⣿⣧⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣿⣿⡿⠿⠋⢷⣦⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣞⣳⣤⣭⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠛⣿⣿⣶⣿⠟⠋⠀⠀⠀⠀⠙⢷⡘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠛⠿⣿⣿⣿⣻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⠟⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁






⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⠛⠿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣼⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣾⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠛⠈⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣦⣦⠀⠀⣈⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣄⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣎⣋⣿⡿⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠠⠒⣄⢀⡤⠀⠀⠙⢿⣿⡏⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⠀⠀⠀⢠⣾⠋⣻⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣤⣼⣿⠀⠈⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠖⠐
⠀⠀⠀⠀⠀⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⠛⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢴⣿⡆⠀⣦⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⣍⡀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⠀⠀⣠⢶⡀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢭⣿⣟⡶⠶⠶⣶⣺⠷⡾⣹⡇⠀⠀⠸⢔⡟⠀⢠⣾⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠉⣻⣿⡟⠁⠀⣽⣼⣷⣀⠀⢰⣮⢤⠺⣽⣿⣷⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠘⠀⠀⠀⠐⠟⠿⣿⣿⣿⣿⡋⣌⣢⣍⣋⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢘⠀⠀⠀⠀⠀⠰⠿⢯⣹⣷⣷⣬⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣴⢺⣿⣿⣿⢿⡍⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡃⠀⠀⠀⣦⣇⠀⠀⣀⢹⣾⣁⣾⣣⣽⢷⣾⡗
⠀⠀⠀⠀⠀⠀⠰⠂⠀⢠⠀⠀⡈⠛⠁⠀⠐⠚⠛⢿⠃⣴⣝⣿⣷⣿⣿⣿⢯⣹⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠠⠄⠀⠀⠀⠀⢀⣿⣿⣿⡿⠛⠉⢻⣗⠝⢛⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⣿⣿⣿⣿⣶⡾⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣾⠟⣿⢟⣯⡿⠋⠠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⢟⣡⣾⣷⡿⠟⠁⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠷⣾⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⣩⣴⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠘⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠰⠋⠁

⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠄
⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⣿⠁⢳⠶⢥⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠂
⠀⠀⠀⠹⡧⠌⠀⠀⠹⡎⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠞⠀⠐⠢⡀⠀⢠⠈⠉⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⣀⠀⢰⣄⢻⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⡠⠚⠁⠀⠈⠀⢄⠀⠁⠀⠄⠀⢰⣋⣤⠝⠛⠃⠐⠾⠟⠓⢄⠻⠟⠛⢺
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢩⢄⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠘⡇⠀⠀⢀⠀⠀⠐⣿⣆⠈⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠏⢂⠀⠀⠀⠀⠀⠠⡀⠐⠂⠀⢰⡷⠻⡀⠈⠭⠁⠀⢈⡁⠔⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠢⠁⠀⠀⠀⢀⠋⠰⠃⠀⠀⠀⠀⠀⠀⠆⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢁⠀⠀⡼⡄⠀⠀⠐⠞⠀⠀⠸⡆
⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠒⠛⠀⠐⠀⠀⠀⢠⠀⠀⠀⣇
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠀⣀⠠⠄⠀⠀⠈⠢⡀⠀⢸⡤
⠀⠀⣵⠊⠉⠆⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠡⠌⠉⢆
⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⡀⠀⠀⠈⠂⠀⠀⠀⢀⣤⠖⠉⠃⠀⠀⡀⠀⠀⠤⠂⠀⡕⣊
⠀⠀⠓⠤⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠈⠩⠤⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠆
⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣰⠏⠀⠀⠀⢀⣀⡴⠖⠂⠀⢛⡛⠑⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⣠⠴⠛⠉⠀⠀⠀⠀⠐⠀⣈⡀⠤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠰⠒⠤⠤⠒⠀⠌⣉⡀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠬⠧⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠏⠁⠀⠀⠉⠦⠒⠒⠢⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣠⠂⠋⠀⠀⠀⠀⢀⠔⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣥⣤⣤⣤⣤⣮⣭⣭⣤⣤⣤⣀⡀⣤⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⣀⣀⣠⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣶⣿⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣷⣾⣶⣶⣶⣶⣶⣷⣾⣷⣶⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⣹⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠉⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠬⠇





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠁⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠐⠂⠐⠋⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠋⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠁⠀⠀⣆⣠⣶⠀⣄⡀⣿⣿⠏⢻⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢁⠀⠠⠄⢸⡿⠋⠅⠀⣿⡇⠀⠀⡦⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠀⠀⠀⣴⠀⠀⠀⠀⣿⡇⠀⢰⠃⣼⣿⣿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿⡀⢰⠀⠀⣿⡇⠀⡈⢸⣿⣿⡇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⣿⠁⠸⠀⠀⣿⣇⠀⠁⣿⣿⣿⢠⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⡀⠀⣿⣿⣿⢀⠞⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⢀⡴⣿⢿⣇⠀⢸⣿⣿⠆⣐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠋⠉⠩⠞⠉⣋⣹⡀⠚⢻⣿⠐⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⡛⠦⣀⠐⠛⠛⠛⠛⣧⠀⣾⠃⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⣧⣤⢀⡀⢠⣤⣤⡀⣼⣷⠀⡀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢸⠛⠛⠀⠀⠈⠋⠉⠁⠉⣹⣇⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠿⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⢠⠄⣀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⣿⣿⠟⠉⠀⠙⢻⡟⠀⠀⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⡿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠁⠀⠀⠀⠈⠉⠃


⠀⠀⠀⠀⠀⡀⢀⡀⢀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠿⣿⡿⠿⢿⣿⣿⠿⠿⠿⠿⢿⡿⠿⠿⠿⣿
⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠠⢤⡟⠄⢠⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠰⠄⠀⡈⣠⣤⠀⠀⠀⠀⠀⠞⠉⠉⠙⢦
⠀⠀⠀⢰⠙⠺⠐⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠦⡄⢧⠀⠀⠀⠰⠋⠐⣁⠉⠀⠀⠀⢶⢮⡑⡀⠈⠀⢸⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢨⠆⠀⠀⠀⠀⣰⣁⡀⢀⡰⠆⠀⠀⠀⠀⡴⠃⠀⠈⠊⠓⠀⠀⠀⠐⠁⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠛⠒⠒⠒⠒⠒⠉⡅
⠀⠀⣰⠃⠀⠀⠀⠀⠠⣤⣀⣈⣉⢴⠆⠁⠀⠀⠰⡷⠦⣤⠴⠆⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠎⠀⠈⣠⠔⠒⠒⠒⠒⠙⠀⢰⠃
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡺⢀⠆⠀⠀⠀⢷⢦⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢆⠀⠀⠁⠀⠀⠀⢀⡾⢗⡴⠃
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣀⣀⡸⣣⠎⠀⠀⠀⠀⠀⠁⠉⠭⢍⣁⣀⣀⣠⠤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣬⡭⠥⠖⠋
⠀⠀⠀⠉⠲⠤⣄⣀⣀⣠⣤⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠚⠋⠛⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⢀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠃⠘⣤⣠⡀⠀⢀⠀⠀⠋⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠡⠖⠒⠀⡀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠊⠀⠼⠀⠀⠘⢧⡙⠆⠐⠂⠀⠀⠀⢸⠤⢶⢴⡀⠀⣠⠖⢄⡀⠀⠈⠻⢵⣮⠕⢙⠁
⠀⠀⣾⠦⣄⣀⣀⡠⠴⠒⠀⠀⠀⠲⢤⠀⠀⠀⠀⠘⠦⠽⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡇⠀⣀⣬⡭⣀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⢠⡀⠀⠀⠀⣤⠤⠒⠉⠁⠀⠀⠀⠁⠀⠀⠀⡆⠀⠘⠒⠂⠐⠒⠀⠀⠀⢀⣀⡄⡴⠈⡇⠪⠥⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠱⣄⠀⠀⠻⣀⣀⣀⣀⡴⠁⢀⡀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠐⠋⠉⠉⠉⣠⡾⠃⠀⠈⢀⠁⣀⠀⢀⣠⠎⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠈⠑⠲⠤⠤⠬⠭⠤⠶⠒⠋⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣈⣒⠶⠾⠟⠋⠀⠀⠀⠀⠀⠑⠺⠭⣉⣀⣀⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠄⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢋⠜⢁⡤⢒⣢⡴⠼⢿⣳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⠃⡜⣰⢋⡴⢋⡡⣀⢀⠝⠳⠉⡲⣄
⠀⠀⠀⠀⠀⠀⠀⢀⢡⢇⡇⠀⣷⢇⡞⢋⣁⡀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠆⣼⠸⡇⢠⠏⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠠⢓⡫⠌⠀⠚⢠⣾⣿⠇⢠⠀⣠⣴⣤⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⢂⠘⣆⠀⠿⠀⠀⠀⠀⠉⡁⠀⠈⠓⠙⠛⠉
⠀⠀⠀⠀⠀⠀⡠⠴⢆⠁⣹⣼⢢⡀⠀⠀⠀⠛⠲⠟⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠸⣅⠀⡜⣾⣩⠈⠉⢀⣴⣀⣠⣤⣤⠠⡶⢨⣤
⠀⠀⠀⠀⠀⠀⠸⡀⣃⠏⠉⠀⠀⣈⡉⠉⣉⣉⣿⢠⡟⢸⡟⠀⠀⠈⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠈⡎⡎⠙⠈⠀⠀⠈⠙⠛⠋⢉⣅⣀⣾⠃⠺⠋⠀⠀⠀⠤⠀⠀⠈⠀⠯⠤
⠀⠀⠀⠀⢀⢴⣱⠧⠀⠀⠀⠀⠛⠛⠛⠛⠉⣙⡁⣀⣄⠀⠀⠰⠂⢵⡛⠄⢀⣀⡔⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡠⡾⣹⠞⠀⠈⠀⠀⠀⠰⠶⠾⠿⡟⠛⠙⠛⠉⠘⠉⠀⡀⠠⢘⣶⠃⠀⡀⢤⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⠄⣀⣀⣠⠀⠆⠁⠀⠀⠻⣿⠀⡄⠀⠀⢘⠀⠀⠈⡦⠀⠠⠤⠀⢀⣀⠈⠐⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⢹⣤⠂⠀⠑⢀⡀⡀⢈⡁⠀⢦⡔⠁⠀⠀⠁⠄⠀⠀⠀⠀⡌⢳⡃⢀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠃⠀⠀⠈⠉⠉⠙⢦⡀⠰⠤⢄⣀⣈⣀⠐⠈⠃⣰⠀⠀⠀⠀⡈⠁⣄⢀⡀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢢⣄⣀⠀⠀⠀⡀⠄⠙⢾⡄⠀⠨⠩⠁⠀⠃⠀⠈⠀⠉⠀⠀⠉⠀⠀⠀⠀⠐⠀⡀
⠀⠀⠀⠀⠀⡠⠔⠋⠰⠚⠁⠀⠀⠀⠀⠀⠀⠀⠁⠚⠤⠒⠈⠀⠹⠀⠀⠀⠀⢢⣤⣤⣠⣀⣠⣤⣤⣤⠤⠴⠶⠒⠛⠉⠁
⠀⠀⠀⠀⠊⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠀⠂⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡆⠉⠀⠲⢤⠄⢀⣀⠀⢀⣠⢤⢃⣈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⡀⢀⡴⠒⠂⠀⠀⠀⠀⠀⠔⠉⠀⢸⣇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⡿⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⣸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⡀⠈⠐⠄⢀⠀⠄⠈⠐⠀⡦⠁
⠀⠀⠀⢑⠀⠀⠀⠁⠛⠁⠀⠀⠐⠀⠈⣠⡸⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠒⠒⠒⠚⠉
⠀⠀⠀⠈⠙⠳⠐⠳⠦⠤⠤⠖⠛⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⠉⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣴⡶⠚⠓⣲⡆⠀⠀⠀⠚⠓⠂⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⣤⣤⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡎⠀⠀⠀⠀⠁⠈⠳⠾⣦⣴⣤⠴⠒⠲⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⠑⠁⠀⠀⠘⠀⠈⠓⠲⣤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠦
⠀⠀⠀⠀⠀⠐⠀⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣈⠐
⠀⠀⠀⠒⠀⠀⠂⣤⣤⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣁⠀⠀⠀⢀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠈⠀⡀⠀⠷⠀⢠⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠻⠟⢋⣿⠿⢷⡄
⠀⠀⠀⠀⠀⢀⠜⠀⠉⢉⠀⠈⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠀⠀⠀⠀⠀⠀⢈⠿⣆⠀⠡
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠈⠓⠶⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⣆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠀⠀⠀⠀⠈⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⢀⡀⠀⠀⣀⣴⡇⠀⠀⣾⣧⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠐⣏⠉⠛⠋⠉⠈⡀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠙⣆
⠀⠀⠀⠘⢷⣄⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠈⠛⠶⠶⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠈⠙⠳⠶⠤⣤⣤⣤⣤⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠉⠙⠛⠛⠛⠶⠶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣦⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠉⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣤⣶⣿⣿⣿⣦⣄⣀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣿⣿⣷⣾⣲⣛⣿⡳⠴⣝⣿⣷⣷⣴⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡚⠉⣿⣟⢿⢣⣿⠹⣿⣿⣿⣿⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣏⡴⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔
⠀⠀⠀⠀⠀⢠⣀⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣽⣿⣿⣿⣿⣿⡿⢧⢻⣿⢿⣟⣻⣿⣿⢻⣿⣿⣿⣟⡏⠁
⠀⠀⠀⠀⠀⠀⠩⠛⠿⢃⡇⠽⢻⣿⣷⠾⢿⣿⣿⡵⣖⢻⣿⣿⠿⢿⣿⣿⣿⣯⣟⢛⡟⢢⠛⠈⠾⠿⠛⣯⡿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⣀⠀⡤⠀⠀⠀⣿⣿⣟⠿⢜⣿⣿⠇⣘⠹⣧⣯⠀⠀⢛⢫⡈⣻⢀⠂⠣⠊⠀⠀⠄⠀⠀⠈⠀⠂⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠺⣿⡧⡀⠀⡀⢰⠁⠀⠄⢈⠻⠇⠀⠀⠐⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠃⠂⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢍⠁⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠴⠃⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⡶⠦⠾⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠙⣄⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⢠⡤⠠⣄⡜⠋⠹⡀⠀⠀⢠⡆⢀⠦⣄⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⡀⠀⠀⠀⣰⢿
⠀⠀⠀⠀⠀⠉⠀⠀⠀⢇⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⢸⠷⡄⠀⠀⢀⡇⠀⢳⡀⠀⣰⠃⢸⡀⠀⠀⠀⣀⠀⠀⠀⢀⡖⠲⡆
⢀⡠⠊⠁⠀⠀⠀⠀⠁⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠙⢦⡀⡼⠀⠀⠀⠻⡴⠃⠀⠈⡇⠀⣠⠞⡻⠰⡖⠂⠋⠀⠀⠻⢠⣤
⠉⠒⠠⣤⠀⠀⢀⢀⣀⡀⠠⠖⠋⠀⠀⠀⠀⠀⣟⠒⠦⣄⡀⢸⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⡇⠀⢈⠆⠀⠀⠀⠂⣾
⠀⠀⠀⢸⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢸⣄⣀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⣸⣤⣴⡷⠤⡤⠟
⠀⠀⠀⠀⣧⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠃⠀⢈⠻⡀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠈⣹⠛⢦⡀⠀⠀⠀⠘⠛⠉⠀⢠⠏
⠀⠀⠀⠀⠀⠀⡴⠤⣄⠀⠀⠀⢰⡖⠒⠛⠳⡆⢠⡤⠐⠋⠀⠀⡠⢶⣉⠁⠀⠀⠀⢀⠔⠁⠀⠀⠈⠲⢄⠀⠀⠀⠀⣴⣃
⠀⠀⠀⠀⠀⡜⠀⠀⠽⠦⢤⣤⡀⠙⠢⣄⠀⠛⠚⠁⠀⠀⠀⡜⠁⠀⠈⠉⠒⠤⣤⠋⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠉⠉⠒⠒⢤⣤
⠀⠀⢶⡐⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣈⣳⡄⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣦⡀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⡦⠀⠀⢀⡀⠀⠀⠸⣞⠉⠉⠉⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⡸⠁⠰⣎⠁⠀⠀⠀⠀⠀⠀⠀⢀⡽⠀⠓⣻
⠀⠀⠀⠀⣇⣀⡠⠞⠉⠉⠘⠚⠉⠑⢤⡀⠀⠀⠀⢀⠇⠒⠀⠀⠤⠤⠀⣀⠀⠀⠀⣃⠀⠠⠔⠊⠁⠀⠀⠀⠀⠰⠁⠀⠀⠈⠉⠲⢄⠀⠀⠀⠀⠛⠢⡄⢀⣀⣨
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣠⠶⠒⠒⠋⠁⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣀⣉⡶⠀⠀⠀⠀⣧⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠚⢛⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢠⡴⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠎⠋⠀⣠⠔⠉⢇⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠙⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢀⡰⢻⣄⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣀⡞⠉⠳⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠙⠉⠓⢄⠑⠄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠃⠀⠀⠀⡜⠀⠀⠀⠀⠀⡶⠦⠿⢦⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⣀⣀⠀⠉⠂⢵⣼⡆⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⣄⠀⢀⡞⠀⠀⠀⠀⠀⠀⠙⡄⠀⣸⣠⡟⠲⠛⠁⠀⠀⠀⠀⡴⠋⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠁⢈⠉⠉⠉⠁⠀⢠⣦⠀⠀⠀⠀⠀⠀⠑⡄⠀⣷⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⢍⡁⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠞⠉⣇⠀⠀⢀⡴⠋⠸⡆⠀⠀⢀⣶⡀⠀⠈⢦⣿⣮⣀⠀⠀⠀⢸⡟⠒⠦⢤⣀⠹⡄⢀⢀⠀⠀⠀⠀⠀⠀⢸⣀⡶⠦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣰⠏⠀⠀⠀⢳⡀⢀⡞⠀⢳⡀⠀⣼⠋⠀⠈⠛⠲⢤⣘⡆⠀⠀⠀⠈⠙⢋⠏⠈⢳⡀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠳⠟⠀⠀⠀⢳⡀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠠⠤⠄⠚⠀⠀⠀⠛⠒⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⡀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠙⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⢠⣀⠀⢁⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠊⠀⠀⠀⠀⠀⢉⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⣀⡔⠁⠉⠳⠾⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠀⠀⠀⠀⠀⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠟⠒⠤⠦⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣖⣠⠤⠖⠒⠛⣉⣩⠭⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠋⠁⠀⠀⠀⠀⠀⠈⠀⢉⣉⡰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠤⠴⣖⡒⠋⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡽⠀⠀⠀⣀⡀⠤⢰⠂⠉⢠⠖⠈⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡶⠀⠀⣴⠎⠉⠀⠔⢡⠔⠓⢦⡇⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⠀⠀⠘⢧⡀⠀⠀⢻⣀⣠⠤⠛⣶⡏⣁⣴⠡⠒⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠛⡄⠀⠀⠀⠙⢆⠀⠀⠙⠥⣀⠰⠃⠀⠀⣁⣀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡰⢄⠀⢀⣈⣣⠀⠀⣤⡤⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠋⠴⠶⠂⣠⠀⠐⡻⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠔⠋⠀⠑⡀⠱⣚⣦⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⢤⠛⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠁⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠈⠹⡧⣀⣀⣀⠀⠀⠀⠣⡸⠖⡂⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢱⠀⠈⢹⡧⠤⠄⢊⣠⠈⡆⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠀⢳⡄⣸⠓⠂⠉⠁⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣤⣴⡶⠧⡤⢤⠄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⢠⠃⠀⠇⢸⠀⠀⢣⡀⠀⠀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢠⢸⡤⠢⠁⠈⡦⡤⠒⠣⢀⣀⠀⢰⣿⠧⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠈⠀⢰⠁⢀⢀⣷⡘⣄⣀⠀⠀⠉⢻⣿⣈⡉⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡖⣊⡤⡤⣼⠋⠛⠛⢳⠋⠉⠉⠒⠢⣄⢸⣧⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⣠⣇⢘⠢⡀⠀⡌⠀⠀⠀⠀⠀⠀⠙⢿⡄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠝⢺⠆⠆⠄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⢚⢄⢀⡀⠀⠠⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠨⡓⠖⣀⡤⠬⣀⠀⢰⡲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⠎⢁⠀⠑⠢⡱⡄⢳⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡙⠤⢤⠀⣷⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⣀⢳⠀⠈⢹⡰⢡⠃⢨⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠠⠜⠈⢧⠀⠀⢡⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠤⡄⢸⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⠇⣸⠀⠀⠀⡇⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢠⣒⣢⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⢁⡰⠋⡰⠃⠠⢞⡵⡁⢍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢊⣁⠤⠔⣁⣠⡤⠤⠤⠤⠤⠤⠤⢤⣄⣀⣀⠀⠀⠠⠤⠔⠊⠥⠒⣋⠴⠊⣠⠴⢚⡥⣊⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣊⠴⢚⡩⠔⠚⠉⠁⠀⢀⣠⡤⠤⠤⢀⣀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠚⠋⠉⢀⠔⠋⠀⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢊⠴⠊⠁⠀⠀⡔⡰⣠⠞⠉⠀⠀⠙⠛⠭⢐⡪⢕⡢⢄⡀⠀⠠⢀⣠⢠⠠⡇⣇⠀⠀⠀⠀⣀⡀⣒⠎
⠀⠀⠀⠀⠀⠀⠀⠜⣡⠞⢁⡀⠀⠀⠀⠀⠀⠁⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠙⠀⢉⠓⠦⣔⡤⢀⡀⠙⠀⠉⠉⠉⢉⢍⡽
⠀⠀⠀⠀⠀⠀⣠⠞⢁⠄⠊⣉⣉⡛⠒⠦⣄⠀⠈⠑⠒⠤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠻⢦⣄⣉⠓⠺⠭⠭⣶⠿⠿⠛⣋⣠⠤⠤⡄
⠀⠀⠀⠀⢀⡼⠁⠰⠓⠊⠉⠓⠊⠭⢝⢢⡀⠉⠢⢔⡠⣄⡠⢀⡄⢐⢼⣆⠄⠒⠒⢆⠀⡀⠙⠲⢭⣁⡒⠒⠒⢂⣉⣉⡠⢄⣠⠜⠁
⠀⠀⠀⢠⢞⡤⠴⠒⠒⠒⠒⠒⠲⠤⠤⠤⠃⠀⠢⠀⠈⠓⠯⠥⠴⠭⠊⠈⠺⣆⡤⠂⠐⠘⠀⠒⠀⠀⠉⠉⠓⠒⠒⠒⠚⠉
⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠰
⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡴⠚⠓⣶⡼⢿⣾⣷⣾⡗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣶⠏⠀⠀⠀⡰⣿⠃⢋⣴⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⣠⠋⠀⠀⢺⡂⠁⠀⠐⠛⠛⠛⠿⠛⠶⠇⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⢽⠀⠀⡁⠀⠠⢔⣾⡅⠀⢀⣻⣛⣻⡟⡟⢛⡟⠉⠉⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢀⡾⠏⠀⡇⠀⢀⡼⣻⢸⣷⣦⣽⣏⢙⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⣇⠐⠡⣰⡇⠻⠛⣧⡈⣻⣿⣿⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⢀⠀⠀⠀⢀⣠⣤⣆⣀⣨⣿⣿⣧⠶⢻⣿⣿⠟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⠲⢶⡿⠟⠛⢉⣽⠟⠉⠁⢈⣿⡿⠛⣧⣠⣼⡿⠿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠏⠋⠌⣿⠂⢤⣾⡟⠊⠁⢉⣿⢻⡗⢂⡾⣻⡟⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⢀⣁⣈⣆⠔⠋⠀⠀⢠⣿⣿⣿⣴⠪⣭⣬⡙⢦⣀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢚⣿⣿⣏⣀⠀⣠⣟⣯⡿⠋⠁⢚⣃⣨⣤⣤⣤⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣥⣽⣿⣿⣿⡿⠿⠿⠿⠿⠿⠻⠛⠛⠋⠉⠉⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠋⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⡴⠚⠋⠉⠛⢦⡈⠙⢦⡖⠛⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣸⠥⢤⠤⠤⢤⠤⣷⠀⠀⠹⣦⠤⠤⠤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢻⠒⠚⠛⠛⠋⢛⡟⠀⠀⠀⢹⠛⠛⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣤⠴⠚⠀⢀⡤⠒⠚⠓⢦⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠙⠲⠦⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠴⢤⣀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⣠⣤⢭⣍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⠤⠤⢤⣄⣀⣀⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣀⡤⠖⠚⠉⠉⠀⠀⠀⠀⠀⡠⠤⢄⡀⠀⠀⠈⠉⠉⠛⠲⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⢦⡀
⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⡔⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠋⠁

⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇
⠀⠀⠈⠢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲
⡠⠒⠢⡄⠀⠀⠀⠀⠀⠀⠀⠐⢍⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⡜⠧⠴
⠳⣄⣀⠼⠀⠀⠣⠗⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠣⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢊⡦⠀⢮⡠⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⢇⣠⠇
⠀⠀⠀⢀⡞⠉⠓⢦⣀⡀⠀⠀⠀⠱⠘⣄⠀⠀⠀⢸⡑⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢐⡉⠀⠀⠀⠀⠀⣠⠤⣠⢔⡶⠓⢒⣲⠒⣫⣟⡭⣄⠀⡠⢄
⠀⠀⠀⠀⠓⠒⠒⠢⣄⠘⣆⣀⠀⢀⡧⠈⡉⢒⢤⣰⠾⠈⠋⠁⠀⠉⠒⠒⢤⡤⠒⠓⠔⠋⣠⣄⣠⢹⢻⡲⠒⠤⢒⣁⣄⡼⠉⠀⢠⡏⢂⣾⠔⠒⠒⠁⠀⠑⠚
⠀⠘⠁⠀⠀⠀⣠⠴⠊⠳⣜⠣⣽⣥⠶⣼⣸⠚⠁⣠⣄⠀⣀⣠⠀⠀⢴⢦⣠⠆⠀⠀⠈⠩⠉⠈⣰⢋⠞⠹⠲⢶⠋⢈⠏⠀⠀⠀⣨⠇⣼⠁
⠀⠀⠀⢀⠔⠚⢁⣀⣀⣉⠻⣵⡀⠉⠳⢼⠟⠿⣯⡁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠙⠦⣤⠤⢤⣮⠄⠀⠀⡞⠁⠀⣿
⢎⡨⠇⠈⠂⠐⠁⢈⡀⠈⠱⣈⢻⣦⡀⠀⠀⠀⠀⠙⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⣠⣄⣀⠀⠀⠀⠀⠈⠢⣀⣁⣀⣀⡀⠀⠀⠀⡠⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠨⢸⣇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠙⢯⣠⠀⠤⣤⡴⠶⠶⢚⡓⠒⠖⢚⠁⢀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⡟⢦⣄⣀⣀⣤⠶⣦⣀⣠⠤⠠⣀⡤⣍⡂⠄⠀⠀⠀⠀⠀⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡈⠀⠆⠉⠉⠀⠀⠰⡈⠁⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢫⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠰⡀⠀⠀⠀⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠁⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠐⠒⠒⠂⠉⠉⠁⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣮⣭⣐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟⠿⣿⣿⣷⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡅⠁⠀⠈⠋⠻⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠇⠀⠀⠀⠀⠠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠠⠀⠀⣄⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠋⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠀⢸⠁⠿⡿⣷⣾⣦⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⢠⡄⠀⠀⠀⠁⠀⠈⠷⣆⠀⢈⠝⡿⠁⠶⠀⠀⣀⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀⠠⠤⠤⠀⠂⢒⣒⣂⣀⣈⣩⣭⣩⣡⠈⡆⢰⣼⠁⣄⣀⣐⢶⢁⠠⠤⠤⠄⠀⢠⣤⣤⣄⢀⣀⡀
⠀⠀⣀⠤⠒⣀⠭⠙⠉⠈⠁⢀⡠⣠⡴⠞⠛⠉⣉⣡⠤⠔⢒⢂⣤⠐⠀⣰⠃⣡⠷⠤⠤⢤⣤⣍⣉⠉⠉⣓⠲⣤⡠⠀⠀⠈⠉⠐⠂⠍⣉⠐⠒⠤⣄⡀
⠐⠉⠀⢠⡎⠁⠀⠀⠀⠠⣒⢩⣞⠁⠀⢰⣾⠛⠁⠀⠀⠰⡁⠀⠐⠒⠊⠁⠀⣀⣐⠳⣤⣀⡀⠠⡌⠛⡷⣭⡀⠈⠻⢷⣤⡢⠀⠀⠀⠀⠀⢛⡦⡀⠀⠈⠐⠤⣀
⠀⠀⠀⢺⢁⡀⠀⠀⠀⠨⡒⠽⡧⠀⠀⠐⠽⣖⡠⢀⠀⠀⠉⠒⠠⢄⣀⡀⣀⣈⡛⠒⡒⠕⠁⠤⠊⢀⡿⠙⡇⠀⠀⠈⡍⣋⠀⠀⠀⠀⡠⢕⠌⡳⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠣⣆⡀⠀⢀⢀⠀⠉⠙⣔⡠⡀⡀⠈⠉⠃⠶⣴⣰⣡⢤⣤⣭⣁⣀⣶⣲⣦⣤⣤⣤⢔⢔⣊⠩⠒⠁⡠⡤⡢⣑⠌⠀⠀⢄⠢⡈⢆⡳⠃
⠀⠀⠀⡀⠀⠈⠙⠓⠃⠃⢊⣎⠄⡀⠙⠺⠔⠔⠖⠄⠀⡀⡦⠭⣉⣉⣙⣚⠛⠌⣋⠛⠛⠊⠭⠈⡁⣤⡔⠖⡑⣑⠴⠚⠁⢄⠄⢆⣆⡧⠚⠉
⠀⠀⠀⠉⠢⢄⣀⠀⠀⠀⠀⠉⠙⠒⠓⠶⠦⢦⣄⣀⣀⢈⠉⠉⠓⠒⠛⡿⠿⣽⣛⠾⠿⡴⠘⠖⠒⢊⣈⡉⣀⣀⣄⠶⠼⠘⠚⠉⠀⢀⣀⡠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠲⠠⠤⠤⠄⢀⣀⣀⡀⠀⠉⠉⠉⠚⠛⠛⠛⠋⠉⠉⠑⠒⠒⠓⠒⠚⠉⢉⣉⣀⣀⠠⠤⠄⠀⠒⠂⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⣈⠉⠀⠀⠀⢈⣀⡀⠀⢀⣀⠀⠠⠤⠤⠀⠐⠒⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⠤⠤⠄⠀⠀⢀⣀⡀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⠇⠀⢠⡿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠉⠙⠛⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠦⠤⠤⠤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⢠⡞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⡾⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⣸⠃⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣤⣤⣤⣤⡤⠴⠞⢉⣠⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⣷⡲⠦⢤⣤⣤⣤⣤⠤⠶⠚⠋⠁⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠘⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⡟⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠶⠶⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠲⠶⠶⠖⠒⠒⠛⠛⠋⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠚⠂⠈⠀⠘⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠤⣄⡀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠰⠂⠀⠀⠀⠤⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠑⡤⢎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠤⡀⠀⠑⠤⣠⢌⠆⠀⣉⢥⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢹⡐⠆⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⡁⢄⠀⠀⠀⠱⡤⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡄⠀⠀⢀⠀⠀⢀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠸⡆⠀⢸⠂⢀⠾⡄⠈⠁⠐⢄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⢡⠀⠈⡠⠃⠀⠈⠀⡀⠀⠀⠁⠀⠈⢦⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠇⠔⠀⠀⠀⠀⠀⡵⠄⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⠁⠀⠁⠘⠤⠀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⣧⡀⠈⢦⡀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⢠⠃⠀⠀⠀⠀⢸⠀⠙⠢⠄⢉⡲⠄⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠏⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⢸⢠⡀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡒⢦⠀⡴⠋⠁⠤⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⢀⡴⠀⠀⠀⣰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⠁⣾⠀⠀⠀⠀⣿⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠇⠀⠀⠀⠀⠘⢦⠀⠙⠦⠀⠀⢤⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣤⣄⠀⠀⠀⠐⠒⠲⠦⠀⠀⠀⠀⠸⡧⣄⡀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠀⣷⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠸⠿⠀⠀⢇⠀⣤⢀⡀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠙⣣⠏⠀⢀⡀⠤⣄
⠀⠀⠀⠀⠀⠀⢴⣿⢉⠽⠛⠀⠀⠀⠀⠸⣯⡼⢀⣴⡌⠱⡄⠀⠸⡄⠁⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣁⠀⠀⢿⣛⣀⣼⠃
⠀⠀⠀⠀⠀⠀⣀⡈⠈⠀⠤⢤⡀⠀⠀⠀⢀⡀⠘⢿⣁⣴⠇⠀⠀⠹⣄⡀⠀⠠⣀⣀⣤⡴⠊⢀⣠⠔⠀⠀⠈⣧⠀⠀⠉⠉⠀⠀⠀⠀⠀⢿⠼
⠀⠀⣰⢃⠔⢛⣭⠖⠀⠐⢦⠀⠙⣆⠀⠀⠛⠛⠀⠀⠀⠀⠀⢠⠖⠁⠀⠉⢻⣶⣶⣶⡶⠖⠻⢯⡀⣀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢿⠘⠂⢋⡇⠀⠀⠀⢸⠆⠀⢹⡀⠀⠀⣠⢶⡆⢀⣄⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣌⢲⠱⣄⣽⢀⡴⢻⠀⠀⠀⠀⠀⠸⠾⠁
⠀⠀⠈⠛⠚⠋⣀⡀⠀⠀⠘⠖⠚⡏⠀⠀⠘⠕⠋⠀⠛⠁⠀⠀⠙⠓⠲⡶⠆⢀⡦⣤⣄⠠⣹⠟⠀⢈⠴⠋⠀⢸⠀⠀⣀⣄⡀⠀⠀⠀⢠⣶⣲
⠀⠀⠀⠀⠀⠀⠉⠉⠀⣤⣀⡇⠀⡇⠠⠚⣧⡴⠞⠻⣇⡀⠀⠀⠀⠀⢸⡣⠄⠻⣥⠾⠈⢁⣠⡴⠂⠀⠀⠀⠀⢸⠀⢸⡯⣁⡗⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠠⠤⠤⠤⠼⠭⠬⠥⠴⠶⠶⠶⠿⠶⠖⠒⠒⠒⠒⣂⣤⠖⠋⠀⠀⠀⣀⠼⠾⠉⠄⠤⠤⢤⣤⣄⣀⣀⣀⣀⣉⣉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡀⡀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣷⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠙⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⢀⣠⠆⢀⠆⠀⠈⠉⠛⢳⠲⠶⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠤⠶⡶⠒⠛⠋⠉⠱⡀⠐⢄⣀
⠀⢀⡴⢋⣩⡤⠴⢋⣀⡤⠔⠃⢀⡎⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢹⡀⠈⠢⠤⣄⡙⠦⢤⣌⡙⢦
⠀⠘⠓⠛⠁⠀⢠⣏⣰⠖⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠲⣦⣹⡆⠀⠈⠙⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠒⠄⠞⠁⠀⠀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⡞⣸⠁⠀⠀⣇⠀⣆⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠁⠃⠀⠀⠀⣙⡂⠈⠂⠀⢲⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠈⠉⠀⠀⠀⢈⡁⢢⡘
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣠⡀⠀⠲⠆⠀⡀⣤⢀⠀⠀⠖⠀⠀⠀⠀⠈⢓⡞⠀⣀⠠⣄
⠀⠀⠀⠀⠐⠯⠙⠋⠁⠀⠀⠘⠓⠃⣶⠈⣧⠀⢳⡀⠉⠀⠀⠀⠀⣀⠀⠀⠀⠁⣄⠀⠯⡤⠞⠀⠀⢀⣄
⠀⢀⡄⠠⢖⡦⠀⢈⠑⢦⠀⠀⠶⠄⠙⠚⠁⢀⠄⠙⠦⣤⣴⣾⣯⢥⡖⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠸⡘⢐⡫⠀⠀⢀⡇⢈⡇⠀⢀⣴⠆⣠⠀⢯⡀⠀⠀⠀⠉⠁⠠⣄⣪⢌⡵⣠⢾⡀⠀⠀⠀⠺⠃
⠀⠀⠉⠉⠰⡦⠀⠈⡉⢩⠀⣀⡉⣁⣤⡅⠀⠀⠉⢹⡇⢠⡖⣶⠆⠺⢃⠠⠚⠁⢸⠃⣠⠶⡄⠀⠀⠰⡿
⠀⠀⠀⠀⣀⣀⣼⣛⣇⣼⣤⣴⠯⠥⠬⠥⠄⢀⣠⠔⠁⠀⠉⣥⡖⠋⣁⣀⣀⣀⣘⣀⡙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⢠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣰⡿⠇
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠑⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋
⠀⠀⣀⡠⠄⣠⠂⠈⡉⠉⠒⠒⠶⠤⠤⠤⣤⣤⣀⣀⣀⣀⣀⣠⣤⡤⠤⠤⠶⠖⢒⠚⠋⠉⠱⡀⠢⢄⣀
⠀⢼⡥⠖⠛⡥⢒⣬⣤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣬⣵⡒⣍⠛⠲⢬
⣤⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣤⣤⣤
⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠛⠻⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢾⠗⠀⢸⠷⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠉⠉⠉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⠀⠀⢀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠉⠉⠉⠁
⠀⠀⠀⠀⡼⠁⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢰⠇⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⣸⠀⠀⠀⠀⠀⣈⠙⠒⠶⠦⠤⠴⠖⠚⣉⡤⠖⠦⣄⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣭⡟⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢸⡀⠀⠀⠀⠀⢹⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠶⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣒⣒⣦⣤⣀⣠⡤⢄⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠑⠒⠮⠥⣌⢻⡗⢦⢡⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠀⠀⠀⠀⠀⠀⠀⢰⣖⡒⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠡⠇⡸⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⡢⢄⡀⠀⠀⡀⢴⡩⢉⢹⢎⠢⡀⠀⠀⠈⠢⣀⠀⠀⠀⢀⡰⠂⠈⣩⡶⠾⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡙⠒⠤⣄⡧⠞⠋⠀⠑⢌⡑⠸⠤⠤⠜⠁⢸⡉⢁⣀⣴⠞⡡⢊⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠂⠈⠑⠒⠤⣈⠑⠢⣠⠀⠀⠈⢑⡶⠀⠐⠀⢠⣌⣙⠛⣓⣫⠴⢃⡀
⠀⠀⠀⠀⠀⠐⠤⣀⣤⣤⢴⣴⡒⣢⣀⣠⣄⣎⣩⣉⣳⣄⣈⣒⣂⡰⢙⣱⣋⣣⣳⣿⣏⣀⣉⣄⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠈⠭⠵⣆⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠽⠈⠉⠀⠀⣠⠐⠀⠀⠀⢀⢴⣙⠆⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣠⡺⠋⠉⠉⠉⠁⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠙⢴⡀⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣴⣾⠋⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣿⣿⠇⠠⣒⡆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⠀⠈⠉⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⡗⣀⡇⠑⡄⡀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣶⣮⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⢧⡿⢿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡐⢶⣿⣦⣁⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⣡⠀⠹⣿⣿⣿⣿⣿⣿⡘⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⢁⣰⣤⣦⣿⡿⠀⢠⠀⠹⢿⣿⣿⡿⢧⡐
⠀⠀⠀⠀⠀⠀⠀⡠⢚⣁⣰⣿⣿⣿⡿⣿⣿⡇⠇⠀⠀⠀⠀⠙⣿⠁⢸
⠀⠀⠀⠀⠀⢀⢊⣴⣿⣿⣿⡿⠟⠁⢹⡼⣿⠁⠀⠀⠀⢀⠠⠀⠳⡄
⠀⠀⠀⠀⠀⢀⡿⢿⣌⠻⢤⡀⠀⠀⠈⣷⠏⠀⠀⡀⠀⠘⣧⡘⢤⡵⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠙⠂⠹⣷⣷⣾⣷⢤⣀⢸⣶⣀⡀⢣⢐⣦⣫⡑⠀⠖⠁⡠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⡟⠛⠋⠉⠉⠙⠋⠉⣉⣉⣉⣀⣀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢻⣿⣿⣿⣥⣜⢿⣻⣿⣿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⢻⠛⠫⣝⡯⢩⡓⠮⠍⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⡈⠑⠋⠑⠈⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠐⢁⠄⠀⠀⡀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⢠⠎⠀⠀⠀⡃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢻⡟⠀⠀⠀⠀⢸⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠿⠟⠛⠻⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⠻⡄⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡼⠀⠀⠀⠀⠀⠀⠀⢸⣇⣾⣏⣳⡇⠀⠀⣿⠇
⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠓⠒⠒⠒⠲⠦⢤⣀⠀⠙⠿⠿⠟⠁⠀⢠⡿
⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠈⠻⢷⣤⣄⣀⣀⡤⠤⠖⢀⣀⡴⠞⠁⠀⠀⠀⠀⢠⡿⠁⠀⣀⣀⣤⠶⠶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⡿⠁⣠⡾⠋⠉⠁⠀⠀⠸⠷⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣥⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠓⣦
⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠉⣆⠀⠀⠈⣷
⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠋⠀⠀⠀⢀⡞⠀⠀⠀⣿⡄⠀⠀⠸
⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡇
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⡿⠀⠀⢰
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢠⡿
⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠤⠤⠖⠋⠀⢀⣴⡟⠁
⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋
⠀⠀⠈⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣶⡶⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠁⡾⢂⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⡛⠃⠑⢦⣤⣤⡄⠀⠀⢈⣿⣷⣶⣧⣝⣯⡄⠀⢰⣦⣠⡤⠶⠊⠀⠒⢀⣤⣄
⠀⠀⠀⠀⠀⠀⣀⠈⢻⣿⣀⣀⡀⠀⢹⣿⣷⣦⣀⡬⢡⣿⣿⠈⢹⣤⣶⣶⡆⠙⠃⢀⡀⠤⠀⠁⠈⠛⠛
⠀⠀⠀⠀⠀⠀⣉⣤⠾⠟⣛⣛⠿⣷⡦⢨⣿⣮⣹⣿⣿⣿⣷⣶⣾⠿⠿⠉⠤⠀⢀⣀
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠁⠀⠸⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⣷⡆⠘⠛⠀⠀⣾⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣟⢄⣀⠀⡀⠈⣻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠰⠞⠉⠀⠀⠀⠀⣶⡀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢤⠀⠉⢻⣿⡆⠁⣀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⢀⣾⠷⠚⠋⠉⣙⣿⣿⣿⣋⠉⠀⠀⠉⠙⠉⠉⠙⠿⠇⠶⠀⠀⠀⠀⠀⠂⠈⠁⠉⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢀⣤⣠⣴⡿⠟⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠇⣤⡄⠀⠠

⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠒
⠀⠀⠀⣾⢁⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⣿⠘⡲⠲⢯⣢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⣰⠰⣿⠉⠆
⠀⠀⠀⠻⠶⠃⠀⠀⢻⡍⠁⢠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠛⢘⣿⢠⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡴⠋⠀⠀⠢⠀⠀⢲⠉⠉⠀⠀⢀⡠⠀⣠⣤⣤⣴⠶⠶⠤⡀⠀⢺⣴⣿⡌⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠠⠛⠁⠀⠀⠑⢄⠀⠁⠀⢤⠀⢰⣏⣥⠮⠛⠛⠀⠲⠿⠛⠓⡈⠿⠛⠛⣿⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⢣⢄⠐⠀⠀⠀⠀⢀⠑⢄⠀⢀⠇⠈⣟⠀⠀⠀⡀⠀⠀⠸⣷⠀⢠⠀⠀⠀⡟⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⠟⠄⠈⠄⠀⠐⠀⠠⡀⠨⠎⠀⠀⣷⠞⠄⠀⢩⠝⠀⠀⣉⢁⠸⠀⠀⢸⠡
⠀⠀⠀⢀⠔⠈⡃⠀⠀⠀⠀⠐⡐⠀⠀⠀⠀⠀⠢⠉⠀⠀⠈⠀⡏⠡⠖⠀⠈⠀⠀⠀⠀⠐⢤⠂⠀⣿
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠠⠑⡄⠐⠀⠀⣇⠜⣀⠀⢈⢦⠀⠀⠀⠶⡎⠀⠀⢹⣠
⠀⠀⠀⣀⠤⠀⠀⠠⠀⠀⠀⠀⠀⡆⠀⡀⠈⢆⠀⠑⡈⢂⠀⠀⠹⡄⠳⠶⠋⢀⠂⠀⠀⠀⡇⠀⠀⠸⣇⡄
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠹⡞⠃⠀⣈⣠⠄⠀⠀⡻⣄⠀⠀⣿⠇
⠀⠘⡤⠒⠒⠀⠀⠀⠀⣀⡄⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡏⠁⠀⠀⠀⠀⠇⠈⠁⢀⠼⣂⠒⠒⡄
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢀⣠⠖⠻⠀⠀⠀⠀⠀⢀⡀⠄⢘⡡⠔
⠀⠙⢄⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠐⢒⣋⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠆⢁⡄
⠀⠠⡎⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠙⠶⠂⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⣠⠤⠀⠰⠵⠶⣀⣤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⡉⠀⠠⢀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠐⠋⠉⠀⠀⢀⣤⣀⣀⣀⠠⢈⠳⠂⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⡿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⢀⣼⣷⡀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠘⠛⠻⣿⣿⠿⠛⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣤⣀⣀⠀⠀⠀⠀⠀⠀⠈⠟
⠀⠀⠀⠀⠠⠤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡤⠄⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠺⠿⣿⣿⡿⠿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡆⠉⠀⠲⢤⠄⢀⣀⠀⢀⣠⢤⢃⣈⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⡀⢀⠴⠒⠂⠀⠀⠀⠀⠀⠜⠉⠀⢸⣇⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⡿⠉⠉⠃⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⣸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⡀⠈⠐⠄⢀⠀⠀⠉⠀⡀⡦
⠀⠀⠀⢑⠀⠀⠀⠁⠛⠁⠀⠀⠐⠀⠈⣠⡸⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⠒⠒⠒⠊⠉
⠀⠀⠀⠈⠙⠓⠐⠳⠦⠤⠤⠖⠛⠓⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠈⠉⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣴⡶⠚⠓⣶⡆⠀⠈⠀⠚⠓⠂⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⣤⣤⣀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⡎⠀⠀⠀⠀⠁⠈⠳⠶⣦⣴⣤⠴⠒⠲⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢜⠑⠁⠀⠀⠘⠀⠈⠓⠰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠒⠂⠀⠂⣤⣤⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡅⠀⠀⠀⠀⠀⠐⣒⣒⣒⠲⣄⣀⡀
⠀⠀⠀⠈⠀⠀⠀⠷⠀⢠⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠛⡛⠙⠛⠛⠛⠓⡀⠀⠃
⠀⠀⠀⠀⠀⢀⠜⠀⠉⢁⠀⠈⠠⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠘⠃⠋⠀⠋⠀⠉⢻⠿⣇⠀⢳
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠈⠓⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠁⡾⠿⣆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣤⣤⣶⣦⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⠿⠿⠟⠛⢿⠋⢉⣉⣛⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⡿⢿⠏⢉⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⢿⠟⠉⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⠿⠛⠁⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡇
⠀⠀⠀⢀⣠⣿⣿⣿⠟⣁⣴⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⡀
⠀⠀⠀⣿⣿⣿⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⡄⠀⠀⠀⢻⣇
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⢿⣇
⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⣤⣤⣤⡀⠀⠀⣿⡇⠀⢀⡀
⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠛⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠈⣻⡆⠀⠈⣿⡿⠛⠛⣿⣆
⠀⠙⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠙⢿⡟⠛⠛⠃⠀⠀⠹⣷⡄⠈⠀⣿
⠀⠀⠀⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⣀⣀⡀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣀⣀⠾⠃⠀⠀⠀⣿⣇⣀⣴⡿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⢹⣇⣀⣀⡴⢶⣶⣶⡟⠋⠁⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠈⣿⡟⠛
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⡟⠉⠉⠀⠀⠈⠛⠁⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠹⠷⣤⣀⣀⢀⣀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⣰⡿⠋⣉⢉⣉⠙⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢠⣦⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢰⣿⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣤⣤⣆⣀⣤⣴⡾⠟⠀⠀⢠⡜⠋⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⢹⣷⡀⠛⠀⢀⣤⡾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠀⠀⠀⣰⡏⠁⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠛⠉⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⠛⢢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢢⣤⣤⣄⠀⠀⢀⣴⣦⡜⠛⠁⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠟⠉⠉⣿⣿⣿⣤⣤⣄⠀⠀⢀⣀⣀⣤⣴⠿⠋⠹⣧⡸⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣷⣦⣤⡾⣿⣿⠉⣿⠋⠻⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠸⣧⣼⢿⡿⢿⣷⣶⢆⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⢹⠏⣿⡟⠉⠀⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⢸⡇⠀⠉⠙⠿⣯⣁⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠸⠇⠀⢹⣷⠀⠀⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⣹⡆⠀⠀⠀⣿⡇⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⢸⡇⠀⠀⢸⣿⠀⠠⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⣴⡟⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⢀⡌⠁⠀⠀⠸⣿⣤⣶⣿⠟⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⠀⣠⡿⠃⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⣼⣿⣧⣴⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠛⠁⠀⣿⠃
⠀⠀⠀⢠⣶⠈⠙⠛⢤⣤⣀⣀⣸⠃⠀⢸⣇⣀⣀⡀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⢠⡿
⠀⠀⠀⣀⠁⠈⣻⣶⠞⠛⠛⠛⠋⠀⠀⠘⠛⠛⠛⠛⠻⣶⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢀⣀⣠⣿⣇⡀
⠀⠀⠀⡟⢠⣾⠛⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣠⣿⣿⢿⣿⠿⠶⠾⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⣷⡾⠷⣿⣿⠁⠙⠛⠻⣷⣟⣿⡀
⠀⠀⢠⡇⠸⣿⣀⡶⠃⠀⠀⠀⠀⣰⡟⠛⠟⢛⣷⣶⡶⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⠀⠀⠀⠀⢙⣿⠇
⠀⠀⣿⠀⠀⢹⡏⠀⠀⣰⠆⠀⣼⠏⠀⠀⠀⠈⠁⢤⡤⢄⣈⠉⢷⡶⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠙⠛⠓⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠀⢸⣧⢀⡼⠃⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⣷⡆⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⣷⠀⠀⠀⠀⢹⣿⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⣼⣿⣆⣿⡇⠀⠀⠀⢰⣶⠆⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⣿⡇⢸⣿⡆⠀⠀⠀⠀⣷⠀⠀⠀⠀⢸⣿
⣦⠀⠀⠀⠀⠀⠀⠹⠷⠐⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣿⡇⠀⣿⠁⠀⠀⠀⠀⣟⠀⠀⠀⠀⢘⣿
⠁⠐⠒⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⡟⠃⠈⠻⠿⢿⣿⠿⢿⣿⠿⢿⣿⡿⠿⠟⠃
⠀⠀⠀⠀⠀⠘⠛⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⣿⡇⠀⠀⠀⠀⢸⣿⠆⢸⣿⠀⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⣤⠀⠀⠀⠀⠀⠀⠀⣶⠀⣿⡟⠃⠀⠀⠀⠀⣼⡟⠀⠘⣿⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⣤⠄⠀⢀⣿⡶⣿⣷⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣶⣿⣶⣶⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣯⣀⣀⣀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣶⣶⣶⣿⣶⣿⣿⣿⠛⠛⠻⣿⠛⠛⠛⢿⣿⣷⣾⣿⣶⣶⣶⣶⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠛⢿⡏⠁⠀⠀⠀⠈⠿⠿⠿⠇⠀⠀⢸⣿⠀⠀⠀⠸⠿⠿⠿⠃⠀⠀⠀⠀⢙⡿⠛⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡛⠶⠋⢳⡶⣶⠙⢳⣶⠀⢰⡖⠐⢶⠀⠙⢿⡆⢸⣿⠳⣶⠀⠶⠶⠀⡴⠇⠀⠶⢆⠙⠃⠐⢂⡀⠾⣶⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠟⠷⠾⠛⠳⠛⠿⠶⠛⠻⠶⠛⠛⠞⠛⠶⠛⠿⠞⠛⠿⠿⠿⠓⠲⠿⠛⠻⠶⠛⠛⠟⠛⠛⠋
⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣾⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣾⣶⣶⣶⣶⣾⣿
⣿⣿⣿⣿⣿⠟⠛⠙⠿⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠤⡠⠖⢢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠈⠃⠀⠀⠀⠃⢀⣙⠉⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠉⠁⠀⡨⠇⡠⠠⠔⠐⠲⠤⣄⠘⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⣀⡀⠉⠋⠁⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠤⣤⣀⣀⡀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡠⠼⠋⠀⠀⠀⠈⠷⢀⡀⠀⠀⠀⠀⠀⠈⠉⠓⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢠⠞⡕⠒⠛⠒⠂⠀⠀⠀⠀⠀⠀⡆⠀⠉⠉⣱⠟⠂⠀⠀⠀⢇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⢢⠑⠀⠀⠀⠀⢰⠏⠀⠣⣀⠀⠀⠻⠲⣀⠀⠀⠀⠀⡆⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢠⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⠜⠀⡀⢀⠀⠀⡏⠀⢠⠄⠬⡙⠒⠒⠈⠋⠁⢀⣀⣜⠀⠀⠀⠀⣯⠀⣀⡀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣧⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⡩⠭⣉⠙⡦⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡠⠖⠢⣀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣄⣈⠉⢈⣉⡼⠁
⠀⢀⠠⠤⠀⠀⠠⠠⠀⠀⠀⡀⣠⣲⠉⠙⣏⠉⠑⠔⠒⠒⠉⠙⠒⠀⠤⠤⠀⠀⠠⠤⠤⠴⠒⢾⠭⡀⢏⣉⢉⠉⠁⢸⠂⠁⠈⠒⠀⠀⠀⠀⠀⠀⣀⡀
⠰⡁⢰⣖⠆⠐⠀⠀⠑⠢⠠⡙⢁⡠⢤⣠⠬⡄⠢⣠⠔⠲⠄⠀⡄⠀⠒⠀⠀⠰⠖⠆⠀⢂⠙⡋⠙⢆⣠⠷⠈⠙⠒⠙⠲⠀⠀⠀⠀⠀⠀⠠⠄⢤⣲⠝
⠀⠙⢦⣍⣙⡒⠀⠤⠀⣀⣀⠀⠀⠀⠀⠙⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⠉⣠
⠀⠀⠀⢻⡈⠉⠙⠒⠒⠀⠤⠄⢈⣉⡀⠐⠒⠂⠀⠤⠤⠤⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠠⠤⠄⠐⠒⠀⢁⣀⡤⠤⠖⠒⣽⠁
⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠀⠤⠤⢤⣬⣉⣉⣉⣉⣉⠛⣉⣉⣉⣉⣉⠀⠠⠄⠀⠀⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢻⣤⠘⠙⠁⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠃⠀⠋⠷⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠙⣇⡔⠂⢀⢀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠐⢦⣘⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡾⠈⠉⠛⠀⠲⠶⠀⠤⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠤⠤⠴⠶⠒⠚⡇⠀⣨
⠀⠀⠀⠀⠀⠀⢠⠖⠊⠁⠀⠛⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠔⠃⠀⠙⠒⢦⡀
⠀⠀⠀⠀⠴⢶⣿⣶⣧⣀⣀⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣧⣀⣠⣷⣶⣷⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠁⠂⠂⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠁⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⢀⠠⣾⣡⡀⠀⠀⣤⣤⡀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⢼⣛⢦⣽⠿⣷⡄⠻⠿⠃⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⢿⣟⠉⠉⠁⠀⢀⣠⣿⣿⣄⣀⣀⣤⣤⡤⠖⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠷⣶⣶⣶⡿⠿⠻⠿⠛⠛⠻⢶⣄⠀⠀⠀⢠⣿⡆
⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⢠⣶⣒⣀⣀⣠⣿⡿⣿⠢⣤⠾⣿⡇⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠐⢦⣉⠉⠉⠉⢉⣁⣴⡿⠁⠀⣰⣿⠃⠀⣠⣴⡾⠟⠛⠛⠛⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠛⠋⠁⠀⣠⣾⡿⠋⣠⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠈⠻⠷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⡿⠟⠋⠀⣰⣿⡟⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⢀⡘⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⣠⣞⣩⡿⠛⣩⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠛⠿⠛⠁⣴⠿⠟⢛⣩⡴⠾⠛⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠙⠛⠛⠛⠶⢶⣾⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠉⠛⠛⠛⠓⢲⣦⣤⣤⣶⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠟⠛⠛⠿⠿⠯⠻⢿⣿⣿⣿⣶⣶⣶⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⣀⣴⣾⣿⣵⠶⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠈⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠷⠟⢉⣿⠻⣿⣿⣷⣦⣤⣤⣤⣬⣭⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠹⣿⣧⡀⠀⠉⠉⠉⠉⠛⠛⠛⠉⠁⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⡀⠀⠀⠈⠛⢿⣿⣶⣶⣦⣤⣤⣤⣴⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⡿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠟⢉⠈⠁⠀⢀⣋⣀⢿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⣿⣷⣿⣶⣶⣿⣿⣿⡿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⠿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠈⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣀⣀⠀⠀⠀⠀⠀⣠⣴⠞⠉⠁⠷⢻⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢩⠽⢿⠟⠂⠀⢸⠟⠛⠋⠉⠀⠀⡌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣼⡏⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡀⠀⠀⠂⠀⠀⠀⣠⣾⠟⠀⠀⣠⠟⠋⠙⠛⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠗⠀⠀⢄⣠⡤⠞⠻⠋⠀⠀⣼⠋⠀⠀⠀⠸⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡴⠖⠛⢻⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⣀⡤⠊⠁⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⣰⠃
⠀⢀⣤⡖⠚⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡄⠀⠀⠠⠀⠀⢠⠇⠀⠀⠀⠀⠀⡀
⠀⣾⠉⠓⠐⠀⠀⠀⠀⠀⢠⣤⢤⣀⡀⠀⠐⢻⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣤⣾⠇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠸⡇⠘⡇⠀⠀⠀⠀⠀⠀⠞⠋⠁
⢀⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠰⢤⡀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠠⠁⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸
⠀⠀⠀⠀⠀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢀⣇⠀⢀⡏
⣿⣻⣛⣛⣛⣛⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣔
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠋⠀⠚⠒⢲⣆⣀⡀
⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⣀⣀⠈⠀⠠⣝⠃
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⡔⠉⠠⠂⠉⠐⢤⢘⡇
⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⠀⠀⠈⢙⠄⣀
⠀⠀⠀⠀⣽⠀⢠⠞⠉⠒⠃⠀⠀⠀⠀⠀⠀⠀⠼⠀⠈⡆
⠀⠀⠀⠀⠈⠢⣼⣆⡁⠀⠀⠀⠀⠈⠻⣑⢦⠒⠁⠀⢸⠁
⠀⠀⠀⠀⠀⢠⢏⠎⠱⣄⠀⠀⠀⠀⠀⠈⠙⡦⠀⠀⡎
⠀⠀⠀⠀⡴⠁⣾⠶⡤⠘⡆⠀⠀⢠⠤⢤⠼⠁⠀⡸⠁
⠀⠀⠀⡼⠁⣬⢁⠰⡞⠁⢸⠀⠀⠀⠳⣇⠀⠀⣰⠁
⠀⠀⣰⠃⣴⠓⠀⡸⢁⠔⠋⠀⠀⠀⠀⠈⢣⣰⢃⣀⣀⣀
⠀⠀⠓⠞⢧⡀⡰⡱⠃⠀⠀⡀⣀⣀⠀⠀⠀⠹⣅⣀⡀⠀⠹⠖⠒⠲⣦⣀⣀⡀
⠀⠀⠀⠀⠀⣙⣥⠧⣤⡠⠚⠉⠉⠉⠑⠟⠲⠏⠁⠀⠉⠱⠖⠋⠉⠙⠏⠁⠀⠈⣷⠋⠉⠙⣦
⠀⠀⢠⠞⠙⠁⠀⢀⣀⡀⣠⠤⣄⣠⣤⣄⣀⣀⢀⠄⠒⠒⠲⣤⠄⠠⢤⠔⠲⢤⡀⠀⠀⢀⣉⣹⣆⣀⡀
⠀⠀⢸⣀⣀⣔⣒⠋⠀⠈⠁⠀⠀⠁⢀⡞⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠛⠒⠉⠁⠀⠀⠀⠀⠉⠳⣄
⢀⡴⠋⠉⠀⠀⠉⠙⠓⠦⣤⣀⣠⣊⣉⣁⣀⣀⣀⣀⣠⡤⠤⠖⠒⠋⠉⠀⠀⠀⠀⢀⣀⠀⠀⡤⠊⠉⢲⡀⠈
⡞⠀⠀⠀⢠⠤⠤⢄⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠣⠀⠘⠊⠀⢠
⢧⠀⠀⠀⢇⣀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠖⠁
⠈⠣⣄⠀⠀⠁⠀⢀⡼⠉⠛⠓⠶⠶⠶⠶⠶⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠉⢲⡒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢲⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠠⡈⢶⠤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠠⡜⢡⠄⢙⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣉⣀⠎⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢧⡈⠙⢉⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⣠⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⢀⢀⠘⠀⡔⠋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⠀⡈⠐⠀⠁⠠⠄⠀⣄⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠆⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠄⠠⡀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⢀⣀⡾⢃⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠢⡄⠀⠠⠀⠈⠲⠄⡀⠁⢠⠄⠘⠀⠀⠀⠀⢀⡧⢤⣎⢹⡟⣻⠯⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⢀⠐⠶⠆⠀⠈⠀⠉⠈⢈⠀⠀⠀⣉⠀⠊⠋⠄⠐⠆⠐⠦⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⡀⠐⢒⣈⡁⣤⠄⠀⢠⠹⣑⠶⠟⣀⠐⡀⡄⢰⠒⠲⢇⢼⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠱⠀⠈⠂⠀⠉⠉⠉⠉⠈⠁⠀⢀⢀⣤⠄⠔⢂⠠⡒⢛⢋⣟⠛⠛⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠃
⠀⠀⠉⠀⠉⠈⠈⠁⠀⠀⠀⠀⠀⠀⢊⠒⠀⠤⢁⡀⠐⠛⠒⢚⠳⠒⠉⢉⠁⠀⠀⠀⠋⠁⠀⢈⠉⠉⠄⠠⠀⠀⠀⠀⠀⡋⢀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠐⠂⠀⠠⠀⠀⠀⠀⠈⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣏⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠉⠊⠁⠀⠑⠤⠒⠢⣄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠒⠋⠀⠀⣀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⠚⠒⠒⠒⠚⠒⠒⠒⠒⠒⠤⠴⢄⠀⢀⠤⠤⠴⢄⣀⡠⠤⠔⠒⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢀⠞⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠙⢆⠘⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣴⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣿⡿⣿⢋⣭⣾⡋⡉⣸⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠋⠀⠉⠉⠉⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣤⣤⣴⣾⣿⣶⣶⣶⡶⣶⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢍⠻⣿⠇⠀⠀⢾⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣷⢸⡇⠀⠀⠈⠛⠿⡿⠟⠋⢈⠀⠙⠛⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⢡⣇⠀⠀⠀⠀⠀⠀⢀⣡⣭⣷⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⣶⠿⠿⠿⠯⠟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣦⣄⣠⣾⣧⡀⢀⣿⣿⡇⣸⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣇⠀⠀⠙⣿⣿⣿⣿⣿⡏⠁⠀⢈⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠟⡄⠀⠀⢸⣿⠿⠿⠋⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⠀⢹⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣧⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠛⠻⠿⠛⠋⠉⠉⠉⠉⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠹⡆⠀⢠⣤⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⣾⢷⡀⠹⡀⢸⡘⡆⠀⠀⡟⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡄⠀⢹⡈⣧⠀⠀⠀⢷⡇⠀⠀⢀⣀⠀⠸⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣶⣤⠀⠱⡀⠈⢧⢸⡄⠀⠀⢸⡇⠀⢰⠃⣿⠀⠀⢰⢻⠀⠀⢀⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠙⣷⡄⠀⠀⠈⣆⣇⠀⠀⠘⠁⢀⡏⢠⡏⠀⠀⣞⡞⠀⣰⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠰⡓⢦⣄⠀⠀⢻⡀⠀⠀⠈⢿⣄⠀⠀⠘⣿⠀⠀⠀⠀⣸⠁⣾⠁⠀⢸⡟⠁⠀⠁⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢝⣷⣄⠀⠻⣄⠀⠀⠀⢻⣆⠀⠀⠘⣧⠀⠀⠀⣿⣼⠇⠀⢠⠟⠀⠀⣠⡾⢛⡇⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⢷⣄⠀⠀⠻⣦⠀⠀⠈⠀⠀⢀⣿⡏⠀⠠⠋⠀⣠⡾⠋⢀⡞⠁⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠉⠳⣦⡀⠹⣧⠀⠀⠀⠀⢸⡟⠀⠀⠀⣠⣾⠟⢁⡴⠋⠀⢠⠞⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⠭⠷⠶⠤⠀⠀⠀⠉⠳⢼⣷⡀⠀⠀⠟⠀⠀⣠⡾⢋⣡⡴⠋⠀⠀⠀⠀⢀⡤⢞⣿⠗
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠖⠂⠈⠑⠀⠀⠀⠴⠿⠟⠛⠉⠁⠀⠀⠀⣀⣴⣞⣭⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠉⠀⠀⣀⣀⣤⣤⡶⠚⠁⠀⠀⣰⠂⠀⢠⠀⠢⣀⠀⠀⠀⠐⠒⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⢛⣋⣩⠅⠂⠁⠀⠀⠀⣠⣾⠁⠀⠀⠀⣧⠀⠈⠳⣦⣄⡀⠀⠀⠀⠠⣤⣤⣤⣴⣚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢀⡀⠀⠀⣀⠜⡱⠃⠀⡄⠀⠀⠸⣷⡀⠀⠈⠻⢍⡓⠶⣤⣀⠀⠤⣄⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⣠⠞⢁⡼⠁⠀⢀⣧⠀⠀⠀⢳⠙⣄⠀⠀⠀⠉⠓⠦⢌⣹⣶⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⠀⣴⡟⢁⣴⠏⠀⠀⠀⢸⣿⠀⠀⠀⠀⠣⡈⢧⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⢠⡆⠀⠀⢼⢸⡇⠀⠐⣄⠀⠀⠾⠆⠀⠈⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠸⣿⠁⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠒⠒⠒⠒⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠫⠥⡀⠀⠀⠀⠀⣀⠤⠤⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠘⠂⠐⠒⠉⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣍⡩⠀⠀⠀⠀⠀⠀⢀⣶⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣀⣀⣀⣀⠀⢀⡀⠀⠀⠨⣈⣉⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠑⠂⠠⢄⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡺⢋⠜⠱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣁⣐⠒⠀⠤⠄⠤⢀⣀⡱⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⣀⠀⠤⠀⠐⠈⠀⠁⠊⠔⠁⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢞⢿⣿⣿⣷⣶⣶⣾⠟⣁⠠⠄⠂⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠢⠝⣛⡛⠫⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⣀⠠⠔⢚⡄⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢉⡠⠔⠊⣠⢆⠂
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠈⢀⡠⠔⢉⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠁⣀⠔⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠈⠁⠀⡠⠔⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠁⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⢀⡒⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠀⠀⠀⠀⠀⠐⠒⠈⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⣢⠀⠀⠨⠀⠀⠀⠀⠀⠀⠐⠆⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠁⠀⡀⠀⠀⠑⠀⢀⠀⢂⣠⠔⠃⠀⠉⠀⠁⠤⠀⠀⢈⠀⠈⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢁⠀⠀⠀⠀⠀⠐⡤⡀⠀⠀⠀⠀⠀⠀⠀⡵⡶⡄⠁⠀⠀⢢⠠⠀⠠⠁⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠚⠂⠈⠀⠀⠰⠀⠐⠀⢂⠏⠆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠌⠀⠀⡸⠝⠡⢀⡀⣠⡆⠄⠀⠀⣈⡁⠁⠀⠀⢰⠇⠤⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡲⡤⠮⠌⠀⢓⡒⠊⠀⢨⠀⠐⠤⠄⠊⠉⠁⡘⠉⢉⠍⠙⡗⡟⣹⣯⣃⠐⠈⠁
⠀⠀⠀⠴⠀⠀⠀⠀⠉⠓⢄⡀⢠⣎⢩⠺⣝⠉⠀⠠⠔⠓⠻⠤⠔⠳⠔⢙⠄⠀⠉⠄⠋⠀⠈⠁⠀⠀⠁
⠀⠀⠀⠂⠐⠐⠀⠂⠀⠀⠀⠑⠩⠀⣴⣞⣁⡀⢩⣠⠆⠁⢁⠖⠂⢉⡠⠈⠀⠀⠂⠀⠀⠈⠀⠉
⠀⠀⠀⠐⢁⢁⣀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡀⢠⢐⠞⠋⠒⠋⠀⡀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡄⣠⣈⡇⠀⢤⡠⠔⠇⠀⠀⢀⡸⢠⠶⠞⠡⠂⠐⠀⡀⠡⠠⠐⠁⠠
⠀⠀⠀⠀⠉⠙⡄⠀⠀⢀⣬⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡀⠀⠀⠀⢑⡤⠀⠀⠠⠈⠀⠀⠠⠀⠀⠐⠂
⠀⠀⠐⠀⢀⠴⠋⠊⠂⠀⠀⠂⠀⡠⠢⠀⠠⠈
⠀⠀⡀⠘⠻⠀⠐⠈⠀⠀⠀⠀⠀⠐⡀⠐⠁