Damp Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠈⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠢⣤⠁⠀⠈⢂⣀⠀⠀⠀⠀⡀⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠒⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⢁⠔⡡⢂⠄⡐⢁⠌⡠⠀⠔⡡⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⡀⠀⡠⢀⠔⠡⠢⠀⠄⠀⠠⢀⠀⡢⢀⠔⡠⢊⠔⡡⢊⠔⡡⢊⠔⡡⢊⠔⡡⠊⡠⢊⠔⡡⠀⠓⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⠂⠂⠑⠀⠊⠐⠑⠁⠀⠐⠁⠊⠀⠁⠊⠐⠁⠈⠀⠁⠈⠀⠁⠈⠐⠁⠊⠀⠊⠔⠡⠊⠞⠔⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠉⠉⠉⢉⠉⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⢐⠖⠒⢒⣲⠤⢂⠖⠀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠁⣰⠂⢠⠂⠀⠚⠀⠀⠘⠁⠀⠘⠀⢠⠟⠀⠀⢠⠊⠀⢀⠚⡠⠐⠁⠀⠀⠰⠁⠀⠀⠀⢀⠆⠰⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠐⠃⠠⠆⠀⠞⠀⠀⠉⡴⠁⡴⠁⠀⠀⠀⠞⠐⠒⠀⠲⠤⠬⠈⠝⠁⠀⢈⡄⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⢠⠃⠀⢀⡄⢀⡄⠀⠀⡰⠂⠀⠀⠾⠐⠒⠒⠒⡲⠂⠀⠀⢀⠄⡠⠊⠀⡴⠃⠀⠀⣠⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⡀⠀⠛⠀⠘⢀⡄⠀⠀⠀⠀⠀⠀⠴⠀⢀⠔⠁⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡬⠀⠀⢠⠆⠀⠈⠀⠀⠜⠀⢀⠆⠀⠀⡰⠁⠀⠀⢀⠔⠉⣀⠀⠀⠀⢰⠃⠀⠀⠘⠁⢰⠂
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⠚⠀⠀⢠⠏⠀⡆⠀⢀⡀⠈⠀⡠⠊⠀⠀⢀⠔⠁⠀⠐⠃⠠⠃⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⢀⠎⠀⠀⡠⠔⠁⠀⢠⠄⠀⠀⠀⠀⡴⠀⠀⣀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠰⠇⠀⠀⡘⢃⠔⠁⠀⡠⠊⠀⠀⠀⠀⠉⠀⣠⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣎⣀⣠⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⢀⠃⢀⠀⣊⠥⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠉⠀⣠⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⡠⠔⠀⠐⠠⠐⠀⠁⠒⠄⠒⠀⠁⠐⡀⠁⠀⠂⠠⠐⠠⡤⠦⠤⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠂⠁⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣻⣛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢞⣫⣷⣿⣿⣿⣿⣾⣝⡳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣛⣽⣾⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣷⣭⣓⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⣿⡿⢿⣣⣈⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣼⣿⡇⣾⣿⡆⡟⣫⣵⠾⣿⣿⣿⣿⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣛⣛⣃⣛⣛⣃⡇⣿⡇⠿⣸⡿⢿⣿⡿⣫⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⢫⣾⡮⢫⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢶⣶⣶⢰⣶⣶⣶⣶⣶⣾⡇⣿⣿⡧⡿⣫⣾⣷⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⡆⣿⣶⡷⣿⡿⣿⣿⡿⣧⡻⡿⣣⣜⣻⣟⣣⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣙⣛⣛⣛⣛⣛⣛⣛⣃⣛⣛⣋⣛⣓⣈⣻⢿⣿⣿⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠙⠛⠛⣩⣿⠿⠿⠯⠙⠷
⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣠⣼⠥⣴⡀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⢠⣄⣤⣀⠀⠀⠀⠀⢀⡀⣤⣀⢀⣠⣠⣄
⠀⠀⠀⠀⠀⠠⣙⠷⠖⠲⠷⠶⡮⠅⣭⣿⣷⣖⣻⣾⣿⣶⣿⣿⣿⣷⣶⣶⣶⣞⣿⣿⠿⣿⣿⣿⣏⣽
⠀⠀⠀⢀⣀⣀⣈⣓⣲⣿⣖⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣭⣤
⠀⠀⠀⢰⣷⣶⣶⣶⣤⣤⣭⣭⣍⣉⣉⣙⣛⠛⠛⠛⠛⠛⠿⠻⠿⠛⠿⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⢤⣝⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣶⣴⣶⣤⣄⣉⣀⣉⣀⢀⣉
⠀⠀⠀⠘⣿⣿⣶⣬⣉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣦⣄⡉⠛⠿⢿⣿⣿⣿⣿⣿⣿⢡⣶⠎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠉⠙⢿⠟⢏⣸⡈⢑⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀⠈⠙⠃⢺⡿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣀⠀⠀⠀⠈⠉⠋⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⣶⠶⠶⠶⠶⠾⣿⣠⣿⡶⠶⠶⠶⠶⠶⠶⢶⡶⠾⣿⣨⣿⢀⣿⠶⣶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠉⢹⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠙⠛⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠿⠶⠶⠶⣶⡶⠶⠶⠾⠷⠶⠶⢶⡶⠶⠶⠾⠷⠶⠶⢶⣶⠶⠶⠶⠿⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣦⣿⣦⣶⣶⣶⣶⣶⣶⣾⣷⣴⣶⣶⣶⣶⣶⣴⣿⣦⣶⣶⣶⣶⣶⣾⡇

⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠰⠆⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⠀⢀⡀⠀⠰⠦⠀⠀⠀⠰⠆⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⡄⠀⠀⠀⠀⠶⠆⠀⠀⢠⡄⠀⠀⠀⠈⠁⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠘⠓⠀⠀⠀⠀⠀⣤⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠈⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠉⡇⠀⠀⠀⠀⠀⡞⠉⠉⡟⠉⠉⡇⠀⠀⠀⠀⠀⢈⡋⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⠤⠤⣧⠤⠤⡇⠀⢀⡠⠔⠊⠁⠈⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣗⠀⠀⡇⠀⠀⡇⡞⠁⢠⠒⡄⠀⠀⠀⠀⠀⡨⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⡇⠀⠘⠶⠋⡴⢦⡀⣠⠞⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠞⠀⣠⠿⡅⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⡏⠉⠉⢻⠉⠉⠉⠉⠉⠉⠁⡇⠀⠀⢸⡠⠞⠁⠀⡗⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠓⢰⠒⠛⠒⡆⠀⠀⣀⣀⣀⠘⢆⡠⠞⠑⠶⠶⠊⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⠒⠒⠃⠀⣸⠉⠉⢉⣇⠀⠙⠢⢄⣀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⢠⠀⠠⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣿⣿⠛⠿⢻⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠴⠃⠀⣀⠀⠀⠀⣀⣀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡄⠀⡠⠒⠢⡈⠛⠀⢀⡼⠴⠃⡀⢰⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠉⠂⠀⠀⠀⠀⠀⠘⠒⠋⢀⠴⢊⢥⠀⡠⠠⡌⢹⣳⠈⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⠤⣾⠁⠀⣀⢜⡉⢱⣠⠴⠊⡑⠉⢉⡟⠰⣭⡾⠏⠀⢀⠎⠀⠳⡀⠸⣥⠗⢰⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⢘⢁⡴⡝⢉⡇⠀⠀⠘⠲⠟⠀⠿⠂⠀⣠⠔⠊⢠⠒⢢⠱⡔⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢫⢚⣤⣜⠛⠁⡔⠉⣴⣶⠀⠀⢰⡦⢀⠃⢠⠒⠉⠐⡟⠀⠘⢦⣥⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠙⡦⠒⠉⠀⡀⡈⠋⡄⡎⠀⠔⠋⠉⣿⠀⡤⡄⠈⠁⠈⡄⠰⣀⢰⡠⠁⠀⠀⠈⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣰⡁⣙⡄⡐⢰⠠⠡⣘⢰⠀⠀⠢⠤⣮⠃⢀⢿⠃⠀⠀⢀⠘⠄⠀⠀⠀⠀⡀⠀⢶⠀⢻⡆⠀⢀⡔⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⢨⢉⢀⢡⢃⢁⠣⣏⣽⠀⠀⠀⠀⠀⠰⣭⡟⠀⠀⠀⠓⢃⠄⡴⡂⠀⠸⣭⠃⢠⠁⠸⠀⡰⠚⠓⣄⡪⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠂⠀⠀⠀⠈⠆⣄⠆⡌⡌⡘⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠉⣹⠀⠈⠉⠀⢀⢠⠀⠈⠇⡀⡆⠑⠴⠡⡊⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢠⠀⠪⢀⠰⡘⡰⢠⢠⢁⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⡨⠳⢫⣤⠀⠀⠀⣦⡴⠐⢀⡀⠱⡇⠀⠀⠀⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠘⣄⣂⢀⠸⣄⠀⠡⡀⠁⠁⠆⡆⠘⡜⠀⠀⠀⠀⡠⠔⢢⠀⡜⠳⠤⠵⠁⠀⠉⠀⡀⠄⠉⠀⠀⡌⡇⡹⠡⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣦⡄⠀⠱⡀⠴⡂⠸⢠⢁⠣⠀⠀⡠⠤⡀⢉⠲⠋⢀⠃⠀⠀⠀⢀⡆⠇⠀⠀⡴⢤⠀⢰⠆⠈⠁⠐⠰⠏
⠀⠀⠀⠀⠀⠀⢰⠁⢸⠂⠘⣷⠀⠀⢱⡀⠑⢄⠈⠌⡘⡀⠸⠰⠆⠓⠁⠣⠔⠃⠀⠀⡀⠆⣠⠔⠊⠱⠐⡂⠀⠓⠘
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⢀⡀⡀⠙⡄⠀⢀⣀⠁⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⣡⠔⠊⠀⠀⠀⡇⠠⢡
⠀⠀⠀⠀⠀⢔⣲⠀⠀⠛⠂⠀⠮⠶⡑⠀⠘⠒⠋⠀⠣⣀⡼⠀⠀⡀⠀⢀⡠⡀⢠⠁⠀⠀⠀⠀⠀⣄⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⠢⠀⠀⠙⣌⠄⡀⠀⠀⠀⠀⢀⠀⢘⡡⠖⠉⠀⠳⠜⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠲⠃⠀⠀⠀⠈⠳⢤⡀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡉
⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠊⠀⠀⠀⠀⠀⠀⠀⡠⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠎⢀⣈⡵⠺⠂⠪⣍⠁⠒⠀⠀⢐⣲⡒⢤⣀⡤⠴⠒⠒⠒⠦⣄⣀⣈⣃⣘⡉⠁⠤⠴⠊⢩⢢⡄⠀⣀⣀⡀⢀⠀⠪⠤⠾⠆⠀⠀⡀⠠⡄⠠⣄
⠀⠀⠀⠀⡖⠈⠉⣉⣉⠤⢤⠈⠵⠿⣬⣭⣍⣠⣉⠈⠉⠅⠀⢀⡩⠧⣐⣂⣂⣀⣒⣒⣒⠒⠐⠋⠙⣂⣒⣒⣤⣲⣮⠁⠀⠭⣍⡅⠒⡄⢓⡒⠛⠚⠋
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠳⠤⠤⠤⠠⠆⢂⡦⢤⣉⢉⡟⠿⣀⣀⣈⡷⢓⣀⠞⠛⣤⠴⠞⠛⠳⣀⠒⠀⡆⠑⠪⣽⠻⢰⠁⠈⠉⠁⠑⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⢩⣔⣾⡱⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠈⠓⠶⠃⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣪⣭⣔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡻⠿⣿⣷⣝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡆⠀⠀⠈⠉⠛⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠃⠀⠀⠀⠀⡠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣠⠀⠀⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣒⣶⣤⢄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠨⠵⠀⠸⣀⠛⠛⢿⣿⣿⠄⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣛⣀⡀⠀⠀⠀⠠⠝⠳⡀⠠⢠⠟⠀⠛⠀⠀⠄⠈
⠀⠀⠀⠀⣀⠀⠤⣤⠶⠶⠒⠛⠂⠀⣉⣡⣭⠤⠤⠆⠒⣒⡒⠒⠒⠒⢂⡇⠘⣟⠀⠒⠚⠭⠽⠥⢬⣥⣀⣂⠐⠛⠒⠒⠦⠒⣂⠤⠄⣀⣀
⢀⠤⠒⠉⡠⠒⠉⠀⠀⠀⡀⢖⡵⠛⠉⣀⣤⠶⠒⠊⠉⡥⠐⠒⣂⡀⠜⠁⠘⢩⣍⠉⠛⠛⠒⠶⣤⡠⠦⠙⢷⣥⡀⢀⠀⠀⠀⠈⠐⣤⡀⠈⠓⠢⢄⡀
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠌⡂⢼⠂⠀⠀⡻⣇⠀⢀⠀⠀⠣⢀⡀⠀⠀⠀⠀⠲⠶⣌⣋⢒⠂⢈⡆⠘⡿⢷⠀⠀⠉⠿⢷⠅⠀⠀⠀⢀⠠⡪⣦⠀⠀⠀⠉⠲
⠀⠀⠀⠹⣔⡠⢂⠀⠀⠑⠂⠽⣇⡀⡀⠈⠙⠶⢤⣂⠄⠀⡄⡈⠙⠶⠦⠒⣒⣒⣒⡂⠁⢀⢁⢠⠾⢩⡰⠀⠀⢀⡸⢐⠆⠀⠀⠀⠂⡑⢌⡺
⠀⠀⠀⠀⠈⠒⠥⣦⢪⢂⢄⠄⠈⠲⢜⡔⣄⣀⢄⠀⠉⣚⠚⠹⠿⠿⡿⢧⠻⠾⠿⠷⠿⠯⠳⠒⢋⣁⡄⠔⢝⣅⡼⠊⢀⢀⢈⢂⣱⠼⠊
⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠘⠪⠼⢠⣠⣨⣀⢈⠈⠈⠘⠪⠼⠯⣇⣾⣷⣴⣵⣿⣤⣤⣄⡭⣤⠭⠏⠮⠒⠂⠉⢠⣄⣄⡆⠶⠚⠋⠀⠀⣀⡀⠄
⠀⠀⠀⠀⠀⠉⠒⠒⠤⠤⢄⣀⣀⠀⠀⠀⠉⠉⠛⠓⠓⠒⠢⠦⠶⠶⡶⠶⠲⠶⢲⣰⣶⠬⠤⠴⠴⠒⠂⠛⠉⠉⢁⣀⡀⠤⠄⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠀⠐⠒⠒⠒⠐⠀⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠉⢉⣉⣉⠉⠤⠤⠄⠐⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠢⠤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡄⠀⠀⢀⡖⢚⠀⣀⣀
⠚⠲⢤⣀⣀⣀⣄⣸⠇⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⡆⢒⠀⠀⢀⡀⠀⠀⢸⡈⣁⠀⠀⢀⡘⡦⢶⢤⢾⡇⠿⠯⠋⠁⠁
⠀⠀⠀⠈⠀⠚⠠⠍⣅⡐⠒⠀⠀⠀⠀⢀⡶⢺⡗⣤⣀⣀⣀⣴⠀⠚⠗⢺⡩⠉⠩⢹⡅⠀⢘⠯⣬⢸⠛⠻⣇⠁⢠⠰⢸⣷⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡿⠀⠀⠀⣿⡇⢤⠚⠏⠀⠀⢠⣉⡣⠀⠀⠉⠛⢿⡀⢰⠿⡄⠈⢀⡽⡏⠀⣠⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢈⣇⠄⠀⠀⢀⡀⠀⠀⣠⠂⠀⠀⠈⠀⠀⠀⠉⠉⡄⠘⡀⣸⠀⢧⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠓⣾⣿⠛⠀⠀⠀⠐⠀⠀⠀⡀⠃⠀⢹⠇⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡁⢀⠖⠸⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢂⡉⠭⣀⠀⠄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠄⡅
⠀⠀⠀⠀⠀⠀⠀⢐⠁⣰⠒⡄⢱⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠠⠜⠉⠁⠀⠉⠙⢇⡇⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃
⠘⢌⡑⠒⠲⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⣀⠤⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣤⡦⠴
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠒⠂⡈⠀⠀⠃⠒⠂⠀⠚⠘⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣀⣀⣂⣀⡀⠄⠀⠀⠀⠄⠀⠴⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠐⠀⠀⠀⢀⠠⠀⠀⠀⠀⠃⠉
⡄⠄⠀⠀⠀⠀⢁⢂⡀⠀⠀⠀⠈⠈⡦⠀⠀⠀⠀⠀⠡⡄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡀⠀⠀⠀⠁
⠈⠸⢌⠢⠀⠀⠀⠁⢭⣠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡑⠀⠀⠄⠃⠀⠈
⠀⠀⠈⢠⢥⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡄⡇⠀⠀⠀⠀⠀⠠⢀⣆⠐⠀⠔⠬⠤⠄⠢⠬⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⢴⠃⠀⠀⠀⠀⡆⠆⠀⠀⠀⠐⠡⠀⠀⠠⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠁⠀⠀⠀⠄
⠀⠀⠀⠀⢲⣤⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠠⡠⠊⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠌⠃⠀⢷⠀⡈⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠆⠱⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⢀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢔⡁⢊⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⢀⠸⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠁⠀⣄⠀⠀⡘⡠⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⣬⡄⠀⠀⡠⠁⠄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢦⠀⠀⠀⠠⠀⠀⠀⠀⠩⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠨⡄⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠄⠐⠀⠈⠀⠀⠀⠀⢀⠝
⠀⠀⠀⠀⠀⠄⠃⡀⠀⠀⠀⠀⡇⠂⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠈⠀⠀⠀⠀⠀⢀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠺⣵⡀⠀⠀⠀⠃⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⡀⢀⠟⠐
⠀⠀⢢⡀⠀⠀⠀⢫⣇⠀⠀⠸⠄⠁⠀⠤⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠉⠄
⠀⠀⠘⢝⣢⣀⠀⠀⢳⣆⠀⡴⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠁⠐⠿⣦⣀⡟⠀⢥⠇⠀⠀⠀⠀⠀⠀⢃⠄⠀⠀⠀⠀⠠⣀⠀⠤⠄⠀⠀⠀⠀⣈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⡙⢥⠰⣈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢨⡔⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠸⣦⣻⢄⣀⣄⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⢠⡽⠅⢠⣀⠠⠄⢀⣀⣴⣾⣶⣤⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢈⢤⣶⢶⣴⡤⠦⠷⠚⠛⠉⠉⠉⠉⠙⠀⠉⠉⠉⠋⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡿⠋⠁
⠀⠀⠀⠀⣾⡿⠾⠛⠋⠁
⣶⣶⡶⠶⢿⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠄⢠⣼⣶⠸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠸⢃⣿⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⢠⣌⣿⠀⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣛⡇⣰⣶⡹⣷⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⣿⣿⠇⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⣾⣿⣤⣿⡿⢱⣿⣿⡇
⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡏⠸⠿⣿⡇⢺⣿⣿
⢤⡀⠀⣀⡐⢁⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣧⢰⡇⣿⣟⣿⣿⡟
⠀⡉⠻⣿⣿⣿⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣇⠈⣿⣿⣯⣿⣿⡇
⠀⠈⠠⡈⠻⣿⣿⣷⡄⢀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶
⠀⠀⠀⠈⠢⡈⠛⢿⣿⣿⡄⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⡄⣿⣿⣉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡰⢶⣽⠟⣣⣽
⠀⠀⠀⠀⠀⠈⢢⠈⠻⣿⣿⣆⡙⣷⣄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠻⢶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡟⢋⠑⢎⣷⣾⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠑⣄⠈⠻⣿⣷⣴⢻⣄⠀⠀⠀⠀⠀⢻⠀⠀⠀⢨⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⢁⢧⡔⣢⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠙⢿⣷⡎⢻⣆⠀⠀⠀⠀⣿⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢈⠑⢠⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠈⠻⣿⣧⡿⣃⠀⠀⠀⠹⠀⠀⢸⢻⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠌⠀⠄⣠⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠙⣿⣿⣿⡄⠀⠀⠀⠀⠀⢸⡿⠇⣽⣿⡿⠀⠀⠀⠀⠀⠀⣤⡉⠀⢠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⢸⢄⣼⣿⣿⡇⠀⠀⠀⠀⢀⡞⢃⠤⣸⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠈⢻⣿⣿⡄⠀⡄⠀⠰⡟⢻⣿⣿⣇⠀⠀⠀⠀⣮⠀⣇⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄⠀⢻⣿⣧⠀⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⢀⡿⢠⣶⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⢿⣿⣆⠀⠀⠈⠹⣿⣿⣿⠁⠀⠀⣼⠁⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠘⣿⣿⡆⠀⢰⢠⣿⣿⣿⠀⠀⢸⣏⢦⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠸⣿⣿⠀⢺⠏⣿⣿⣿⠀⢠⣄⢻⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢻⣿⠀⠸⣶⣯⣻⣿⠀⣀⡹⢁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⠀⠀⣿⣿⣿⣿⠀⠯⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠻⡇⠀⣿⣿⣿⡿⠀⠐⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠘⠇⠀⢿⡾⣿⣦⠈⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡆⢿⣿⣿⡿⠂⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠱⣿⣿⣿⡟⢀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢰⣿⣿⣿⠀⠋⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⣿⣿⡇⠈⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢹⣿⡏⠸⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⣿⠁⠀⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠋⠀⢲⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠃⣠⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣿⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣷⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⠀⢀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠆⠀⠘⠀⢸⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⡇⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡾⠁⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠘⠋⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠐⢦⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢺⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⣀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠰⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣷⣼⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⡟⠁⢙⠛⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣄⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⠏⠁⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢈⣽⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡙⠻⠟⢋⣤⣤⣌⠙⠿⠟⣉⣤⣤⣉⠻⠿⠋⣡⣤⣤⡙⠻⠟⢋⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣉⣿⣿⣏⣉⣩⣿⣿⣏⣉⣩⣿⣿⣏⣉⣹⣿⣿⣀⠀⠰⣶⠾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⣿⣿⣿⡿⢿⣿⣿⣿⠿⠿⣿⣿⣿⡿⡿⣿⣿⣿⢿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣾⣿⣷⣶⣶⣾⣿⣷⣶⣶⣾⣿⣷⣶⣶⣿⣿⣷⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃

⣿⣿⢻⣿⢿⣿⣿⣷⣿⣿⣿⣿⠉⠀⣧⣸⠻⣿⡇⣿⡼⣿⣿⣿⣿⢻⣿⣿⡏⢰⠙⣤⡤⠤⢠⢠⣾⡠⠀⠒⠁⢀⣿⣿⡇
⢿⡟⢸⡏⠘⣇⣼⠿⠿⣿⣿⣟⣛⠀⡟⠁⠀⢨⣧⢻⣥⡿⠟⣿⣿⡞⣿⡏⠀⣀⠁⢈⠀⠀⠀⠨⡏⠀⠒⢠⡰⠙⠉⠿⢡
⣾⠃⢸⠧⣴⣿⣟⠀⠀⣿⣿⣿⡿⠰⡇⠀⠀⠘⡟⠈⢏⣧⢠⣾⣿⣵⣻⣏⠀⠇⣿⡾⠶⠖⣸⣠⣦⣾⣿⣶⣶⢠⡤⠄⠈
⡿⠀⠐⠀⢹⣿⣿⠂⠀⣼⣿⣿⡇⠀⡇⠀⠀⠀⠁⠀⠘⣿⠀⠹⡟⣿⣿⣿⢠⠆⣿⣇⠀⣀⡟⣿⢉⣿⣿⠹⡟⠉⠰⠉⣄
⡇⠀⠀⠀⢸⣿⣟⣿⡼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠛⡿⣿⠀⠀⣿⣿⣿⣯⣿⣿⠋⠹⡏⠀⢠⣶⡆⠀⣿
⠃⠀⠀⣰⣿⣿⣿⡟⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⣠⣤⣶⣧⠰⣿⣿⡿⡟⠉⠀⠀⠀⠀⢀⣼⣿⠁⠰⡿
⠀⢀⣯⣿⣿⣿⣿⣷⡟⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⡟⠛⣿⣿⣿⢿⢿⣿⠛⠀⣿⣿⡇⠁⠀⠀⡀⣸⣿⡿⠏⠀⠁
⢠⣾⡿⡿⢼⠟⣿⣿⡁⢻⣿⣿⣿⢿⡄⠀⡀⠀⠀⠞⠀⠀⠈⠇⠀⠀⠈⠃⠀⠀⣿⣿⣧⡀⠀⣤⣠⣿⣿⣇⡐⠃⠐
⡆⣿⡇⠀⠀⠀⠛⠟⡃⣸⣿⣧⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡮⣿⠟⠉⠉⠉⠀⠋
⣷⠻⡇⣤⣀⡀⠀⠰⣤⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣿⣿⣿⠁
⣿⣷⣼⣯⣢⠶⠀⣼⣿⣿⣿⣿⣿⡠⣿⣿⣿⣿⣿⡟⢻⠿⠀⠀⠀⠀⠀⠀⣴⡟⠘⡇⣹⡿⡇⠆
⣛⣉⢡⠿⢏⡤⣾⣿⣿⣿⣿⣿⣿⣥⣿⣿⣿⣿⣤⡄⣼⠤⠀⠀⠀⠀⠀⣰⣿⣿⣷⣤⣿⣧⣻⣘⡄
⣼⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⢨⠀⠀⠠⠄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣯⣄
⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣻⣠⠀⡀⠀⣀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡷⠛⠉⢻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠃⠈⠁⠀⠈⣿⣿⣿⣿⣿⣿⢻⡤
⣿⣯⣴⠀⢠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢀⡄⢀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣾⣧⣀⠀⣰⢀⡄⣤⠘⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡤⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⣤⣄⠀⠈⢀⣯⠋⠋⣀⣄⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⡋⠃⠀⠸⡿⠟⢉⣋⣭⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⣀⣼⣿⡆
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠐⡟⠋⢉⣯⣿⠅⢀⡠⣄⣀⠐⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣷⢈⣹⠟⢀⡀
⣄⠀⠀⠀⠃⠀⠀⣠⣤⠖⠂⠁⠀⠴⠞⠋⠀⢀⠋⠀⢿⣿⣷⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠒⠛⠻⠻⢴⡾⠇
⠉⣦⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠚⢻⠟⠀⣀⠀⠃⠀⠀⠀⠀⠀⠀⠐⠂⠀⣡⣾⣾⠟⠙⠋⠀⠀⠀⠀⠺⠿⣿⣦⣀⣀⡀⠀⠈⠀⠐⠆
⠀⠈⠳⡀⠀⢀⣈⣠⣶⡛⢤⡂⠀⠀⠀⠀⠀⠀⠀⡄⠈⠈⠃⡉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⠴⡾⠟⠀⣀⣠⣀⠀⠀⠀⠈⠉⣥⢿⣧⡟⣡⣿⡀⠀⢀⣷⣃
⠀⠀⣤⣤⡴⣯⣿⡻⠞⡀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠛⣻⠁⣀⠳⠒⠀⢦⣌⠉⣹⠟⣾⠃⠠⢀⡈⠃⡄
⣴⢿⢟⢯⠑⣯⠉⢧⣀⢘⣀⡙⢒⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⣠⡠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣝⠛⡃⠐⣠⡇⠃⡻⢋⡟⠿⠛⠹⣧⠈⣸⣿⠀⣠⠟⡀
⣟⣣⣤⣌⣁⣘⣀⣾⣿⣿⣿⣥⣭⣼⡷⢄⣀⠠⣤⣠⡀⠀⣶⣿⠀⠀⠀⠀⠀⡐⠂⠴⡷⠾⠇⠘⢿⣷⣿⣤⣿⡏⢈⡼⠋⠉⡀⠀⠀⣿⣿⣿⣧⠞⠁⠀⢀⣄⣶
⣾⣿⣿⣿⡿⣿⡟⣿⣿⣿⣿⣯⣹⣿⣷⣾⣿⣦⣤⣿⣿⡆⣿⣿⣤⠶⠂⠀⠘⠋⢄⢂⠀⠐⢠⣶⣬⡟⣿⣼⣿⣿⣿⣅⣶⣤⠜⠋⢢⣿⣿⣿⣷⠶⢶⣿⣿⣿⣿
⣾⢿⠯⠛⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣹⣟⡁⢀⢀⣀⠀⡀⠠⢀⣠⠞⢃⣾⣿⢷⣾⣿⣟⣿⣿⣿⠙⠛⡫⣥⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿
⣥⣿⣿⣼⠏⣿⣟⣿⣟⣿⣿⣟⣿⣿⣿⣿⣿⠟⢻⣽⣿⣿⢯⣿⣷⣿⣻⣿⡽⠷⢤⡾⠿⣶⢿⡏⠘⣾⣿⣿⣿⣿⣿⣿⡟⠟⣿⣿⣿⣿⣗⣾⣿⣿⣾⣿⣿⣿⣿
⣿⣿⣿⢯⣽⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⢯⡟⠓⢴⣮⣿⣿⢿⣿⣾⠿⣿⡁⣠⣤⣼⣿⠦⡉⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣿⣿⡿⣿⣿⣿⡛⠻⢿⣿⣿
⣿⣿⣿⣶⣿⣷⣶⡿⣿⡟⡿⠿⣿⣿⣿⡿⠑⠿⢶⣿⣿⣭⣾⡇⣭⠳⣍⣿⠋⣡⣿⣿⠿⠿⠛⠛⠛⠿⣿⡿⣿⣿⣿⣿⣿⣿⣥⣿⠷⣻⣵⣿⣧⠏⣉⠚⣷⣽⣿
⠉⠀⠀⠀⠀⠉⠻⠿⠟⠛⠛⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠙⠃⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠘⠛⠙⠺⠟⠋⠈⠛⠛⠛⠉⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡟⢿⣿⡿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣠⡅⢰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠛⣿⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠋⠐⢉⠉⠉⠀⠀⠈⠻⣿⠉⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⠀⠀⠀⠀⠦⠀⠀⠀⠀⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡇⠹⣄⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⡹⢻⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠉⠀⠀⠈⠓⣤⣀⣀⠀⠀⣀⣀⣴⡚⠁⠸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⣠⠴⠒⠉⠁⣸⣭⠽⠛⠉⠁⠀⠈⢦⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣾⡉⠀⣀⣀⡤⢯⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡱⣴⣏⢷⡫⠵⠚⠛⠉⢁⣀⣀⣸⣆⣀⣠⠤⠶⠒⠚⠹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⡽⣭⡽⣀⣴⣶⣒⣿⡉⠉⡽⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⣿⡿⠧⠋⠉⠁⢀⡿⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠉⠉⠙⠓⣲⠶⠋⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣳⡤⠴⠒⠋⠁⠀⠀⠀⠀⠹⣖⠒⠒⠒⢒⣖⡒⠒⢖⣒⠖⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠳⣄⠀⠀⠀⠀⠈⣣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠘⠴⠃⠀⠀⣀⣄⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⢶⣄⣠⣴⣿⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⡔⢦⠀⠀⠀⠳⠜⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⣇⣸⠟⠛⠒⠲⠤⢭⣍⣙⡛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡙⠉⠀⠀⣏⣳⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣟⠀⠀⠀⠀⠀⣀⡴⠯⢤⡯⠼⠦⢤⠤⠬⢤⠴⠿⠦⠿
⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠴⠖⠋⠁⡇⠀⢸⠃⠀⠀⢸⡆⠀⢸
⠀⠀⠀⠀⠀⠐⠁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⣾⠀⠀⠀⠸⡇⠀⢸
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⡴⠒⢶⣋⣉⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⠁⠀⡇⢀⣀⣀⣀⡏⠉⢹
⠀⠀⠀⠀⣨⠤⢤⡖⠒⣲⣵⠒⠙⣒⠋⢰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢀⣀⣠⠤⠴⢺⡟⠉⠉⢀⣀⣀⡤⠼⠃
⠀⠀⠀⠀⢱⠦⠘⠭⠜⠩⡭⠟⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠈⠓⠚⠉⠉⠁
⠀⠀⠀⠀⠈⠒⠒⠉⠓⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠻⣿⣿⣿⡿⠿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣱⡟⢎⢻⣿⣿⣿⣦⡙⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢰⣿⣿⣬⡇⣿⡿⠻⣿⣿⡎⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣝⣛⣩⣾⠟⣴⠿⣌⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢻⣿⣿⣿⣿⣿⣿⠏⣾⣿⣷⡙⣧⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣎⢿⣿⣿⣿⣿⣿⡌⢿⣿⣿⣿⡟⣸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⣀⡙⣦⡻⢿⣿⣿⣿⣿⣦⣍⣉⣭⣾⠟⣣⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠟⣩⣶⣿⣿⢿⣿⣿⡶⣭⣛⡛⠿⠿⠟⣛⣫⣥⡘⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏⣼⣿⣿⡿⠃⣾⣿⣿⣷⠘⢿⣿⣿⣧⢻⣿⣿⣿⣿⣦⠙⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡐⢛⣛⣭⣾⡇⣿⣿⣿⡿⢸⣷⣭⣛⡛⢈⣿⣿⣿⣿⣿⡇⠀⠙⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣣⠞⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣠⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢼⣿⡏⣵⣶⡆⣠⣾⣿⣿⣿⣷⣦⢰⣶⣮⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣇⢻⣿⣷⣜⣛⢻⣿⡟⣛⣫⣾⣿⡟⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣍⡛⠿⣿⣿⣿⣿⣿⣿⣌⢿⣦⡙⢿⣿⣿⣷⣶⣾⣿⣿⡿⢏⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣶⣤⣭⣿⣿⣿⣷⣝⠿⣶⣭⣛⣛⡛⣛⣛⣭⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠉⠙⠛⠛⠛⠋⠉

⣿⣿⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣴⢴⠢⣤⢀⡀
⣿⠟⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠈⠻
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⢠⣴⣶⣶⣄⣤⣄⠀⠈⠁⠀⠀⠀⠀⡀
⢆⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⣤⣁⠀⠀⠀⠩⠅⠀⠀⠀⠰⠆⠠⠄⣵⠶
⣮⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣶⣦⣶⡆⠀⠀⠀⠈⠻⠟⠀⠀⣠⣤⠀⢀⣠⡄⠀⠀⠀⠙⠲
⡏⠙⠻⢶⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⣄⡁⣨⣧⣩⡄⠈⠉⠉⢣⡼⠿⠀⠁⠀⣤⣴⣿⣿⣿⣿⣿⣿⣷⣆⢐⣄
⠇⠀⠀⠸⡿⣿⣦⠘⠶⡄⠀⠀⠀⢀⡀⠿⣹⡶⠀⠀⢠⣉⣙⡤⠿⢿⡏⠃⠂⠀⡈⠀⠀⠀⠀⠚⠃⠀⠙⠘⠋⡿⢿⣿⣿⣿⠋⡏
⠀⠀⠀⣀⠃⣹⡆⠀⠀⠀⠀⠐⠿⡞⢿⣆⣏⠴⠒⠀⠘⣟⡉⢀⠀⠀⠁⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠙⣿⡷⠀⠁
⠀⠘⠁⣿⡆⣿⡇⠀⠀⠀⣀⡀⠀⠁⠸⡞⠀⠀⠀⠀⣄⠃⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡂⠈⢱⡶⢆⡠
⠀⠀⠀⢿⠇⢹⡇⢀⣀⡄⠙⠁⠳⠀⠀⢳⠀⠀⠁⠀⠉⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠦⢼⠑⢺⠃
⠀⠀⠀⠀⠀⠸⠇⠈⠛⠷⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠒⠒⡀⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢽⣿⣿⠟⠀⠓
⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢸⣿⡇
⣄⡀⠀⠀⠀⠀⠀⢻⣾⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣼⣿⣁⣠⡀
⡏⣴⣦⣤⣶⣤⡀⠘⢻⣿⣿⣿⣶⡄⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢻⣟⣹⣿⣧⡀
⡇⢸⣿⠙⠋⠉⡇⢳⠈⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣷⡈⢻⡿⣿⣿⠖⢶
⡇⢸⣷⣤⣄⣴⣯⣭⡀⣿⣿⢻⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢨⣿⣏⣻⣿⣽⡇⠀⠀⣿⠏⠀⢸
⠁⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠘⡿⠁⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡟⠻⣿⡋⠀⠀⠙⠛⠉⣿⣿⡇⢀⡀⣿⣤⢄⠘
⢸⣿⣿⣿⣿⣿⡿⣿⠉⣻⠀⠀⠀⠀⣠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠈⠟⣿⡧⢸⡿⣿⣿⠸⠃
⣾⣿⡿⣿⣿⣿⡇⠀⠀⠉⠀⠀⠀⠀⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⣠⠀⠀⢀⠀⠀⠀⠀⣿⡇⠘⡇⣿⣿⣿⡄
⣿⡟⠃⠙⠋⠀⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇⠁⠀⠀⠀⠀⠀⣀⢰⣿⡇⠀⢀⣸⡟⠋
⡿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢰⡏⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠁⠀⠉⢨⣿⣷⡆⠸⢽⣷⣶⣄
⡇⠀⠀⠀⠀⢾⣿⣶⡄⠀⠀⠀⠀⢸⠇⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠃⢠⡌⣿⣿⣿⣾⡂⠿⠙⢻
⣿⣄⡀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢰⠀⠀⠠⣾⣿⣴⣿⣿⣿⡿⣷⡆
⣿⣿⡇⢰⡇⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣏⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣿⣷⣤
⣿⣿⣿⡿⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣻⡟⡆⠀⠀⢠⣄⠈⠻⣿⣽⣿⣿⣿⣿⢻⣷
⣿⣿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠁⣄⠀⣼⢻⡇⠀⣿⣿⣿⣿⣿⣿⣾⣿
⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠉⠀⠁⢿⣿⠀⣼⣿⣇⡟⠈⠻⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⢸⠇⠀⠘⣿⣧⣿⣟⣿⡿⢀⣀⡛
⣿⣿⣿⣿⢻⣿⣿⣿⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⡇⠀⠋⢀⣿⣿⢿⣿⢻⡅⠘⠋
⣿⣿⣿⣿⣿⣿⢿⣿⢶⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠟⠁⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⡇⠀⠀⠸⢿⠋⣿⣿⣾⣿⡆⠀⠀⣧
⣿⣿⣿⢿⣿⣿⣤⣍⠹⠞⢿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠸⠃⠀⠀⢠⣿⣀⣿⣿⣿⣿⣿⣄⠀⠈
⠁⠁⠈⠘⣿⡇⠙⠁⠀⠀⠀⠀⠁⠀⠙⠃⠀⠀⠀⠀⢀⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⣰⡀⠀⠀⠈⣏⠉⣽⣿⣿⡿⠛⠁
⠀⠀⠒⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢽⡇⠀⠀⢰⣿⣿⣿⣿⣿⡇
⠆⠀⡶⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡅⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠘⡇⠀⠀⠘⠻⠿⠿⠿⠿⠃
⣶⣴⣷⣴⣿⡇⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⣿⣷⣤⣀⣀⣀⠀⢀⣀
⣿⣿⣿⣿⣿⣦⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⡀⣸⣿⠋⣿⣿⣿⣿⠀⢸⣿
⣿⣿⣿⣿⣿⡟⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠰⣷⣿⣯⣀⣿⣿⣿⣿⣼⣿⣿⠇
⣿⣿⣿⣿⣿⣀⣸⣾⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣇⣀⣀⣀⣟⣻⣿⣿⣿⣿⣿⣿⣉⣀⣀⣀

⣿⣿⣿⣿⣮⡑⠀⠀⠀⠀⠀⣜⠁⠀⠀⠀⣀⡀⣠⣷⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠴⠂⠀⡀⢸⣿⡇⠈⢽⣿⣿⣿⣿⣿⣿⡟⠈
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢠⠇⠀⠀⠀⠀⢾⢖⣼⣿⣷⠏⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢺⡟⠂⡀⢬⣿⣿⠁⠀⠸⣿⣿⣿⣿⣿⣿⡃⣠⢠
⣿⣿⣿⣿⣿⣿⢀⠀⣠⠖⠛⠁⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⢀⣤⡀⠀⠀⣴⣟⢴⣾⠃⠠⣈⢶⣿⠇⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⢺
⣿⣿⣿⠈⠟⣯⡾⠿⣯⣶⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⢰⠻⠷⡷⣿⣏⣤⣾⣧⡀⡀⢮⠻⠜⠀⠀⠀⣆⢸⡿⣧⣿⣿⣿⡏⣿⣾
⣏⠛⠛⠻⣷⣶⣤⣠⣬⡉⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣄⣀⣴⣿⣟⣭⣿⣿⡟⠿⡆⠃⢀⡇⠀⠀⢸⡜⠇⢹⢸⣿⣿⡇⡿⣁
⣤⡄⠀⠀⢈⠙⠟⢿⡯⠁⠀⠠⠀⠁⠀⠀⢤⡀⠀⠀⠀⠀⠂⢀⠸⡟⢉⣿⣿⣿⣿⣿⣿⣿⣦⢹⡆⢺⡇⠀⡉⠙⣧⢰⠘⠈⣿⣿⣇⣿⢋
⣿⣤⠀⠀⢸⣧⡠⡐⢩⠀⠀⣦⡄⡀⠀⠀⠀⣃⠀⠀⠀⠀⡀⣀⠀⢧⣸⣿⣿⣿⠟⣹⣿⣿⣿⠆⢃⢸⣇⠀⢇⠻⣿⣿⡄⠁⡇⣿⣿⣿⣿
⣽⣿⢄⣠⣘⣷⢷⠷⠀⠀⠀⠙⢡⡇⣾⠆⠀⠘⢳⣄⣀⢐⣿⡋⣀⣜⣿⣿⣿⣿⢸⣿⢿⡏⠉⠀⢨⣘⠥⠀⢀⣀⣿⡿⣷⠀⠀⣿⣿⣿⣻
⡏⣵⣿⣿⣿⣿⣄⡆⠀⠀⠀⠀⠀⠁⠇⠀⠀⠀⠈⠹⣟⡋⣤⡿⠟⡅⢿⣿⣿⣿⣾⣿⣾⣧⣄⡀⡼⠘⣇⠀⠠⢉⣸⣷⣻⡄⢠⣿⣿⠋⡟
⢡⣿⣿⣿⣿⣿⣿⠀⠀⠘⣧⡀⠄⠸⠀⠀⠀⠀⠀⠀⡈⠇⢸⡦⠶⡆⠈⢻⣿⣿⣿⡿⢿⣿⣻⣧⣾⠀⣿⠀⠀⢸⡟⣿⣿⣷⢾⣿⡏
⡏⣿⣿⣻⣿⣿⠏⢀⢲⣆⠹⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⢼⠀⠷⠀⢿⣾⣿⣿⣿⣿⣷⣼⣿⣿⣻⣿⡄⢸⡄⢠⠘⣟⣿⡟⢻⣼⣻⡇⠀⠈
⣘⢽⣱⣿⣿⡿⠀⠘⣆⢿⡀⢹⣿⣿⣦⣴⠆⠀⠀⠀⠀⢀⣄⢸⣾⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣇⠸⡇⠈⠀⣿⣿⣧⢸⢿⣿⣇
⣠⢿⣽⣿⡿⠁⠀⢰⣿⣼⣷⣧⣿⣿⣟⢻⣶⣂⠑⢀⣠⣈⣻⡆⠻⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀⣇⠀⡆⣿⣿⣿⣿⣼⣿⡟
⣯⣾⢟⡿⠃⠀⣠⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣯⡼⢫⣍⣿⣿⣧⣄⣀⣸⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⠀⡇⢿⢻⢿⡈⢿⣿⠁⠀⢸
⣿⣿⣿⠁⠀⢀⡟⢿⣿⣤⣹⣿⣿⣿⣿⠿⠋⣨⣿⣿⣿⣿⣿⣿⡿⣟⠉⢹⡟⣿⡏⠙⠀⢻⣿⣿⣿⣿⡇⢸⠀⢰⣼⣾⣼⡇⢸⣿⠰⠀⠈
⣿⠟⠀⠁⣠⡞⣰⣿⣿⠿⣿⣿⣿⣿⡉⠠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⢻⣇⠩⣦⠀⢲⣿⣿⣿⣿⣿⡷⢸⡀⢸⣾⣿⣿⣧⡿⣿⣷
⡏⠀⠰⣴⡿⢠⣯⣿⣿⣦⡈⢹⡟⠻⣧⣄⠀⠉⠉⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣯⣤⠈⡇⠈⣷⣷⣷⣶⢇⣿⣟⣤⣤
⠀⣨⣾⣿⠁⡾⣠⠌⣉⣭⣿⣾⣷⣾⡟⢯⣷⡋⣾⣬⣭⡀⣾⣦⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⢿⣿⡆⠀⠃⠀⣿⣿⣥⣿⡾⢾⠚⠈⠁
⣼⡿⣿⢇⣸⢟⡛⣷⡈⠈⠉⠙⢿⣿⣿⣶⠈⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⡴⠒⠻⣿⠀⢀⠀⠸⢟⣿⣾⣧⣿⢀⡠⡘
⣧⣽⡟⢠⣷⣾⣧⣼⣷⣾⣀⣹⣼⣿⡶⠘⠛⠿⣷⣿⣿⣿⣿⣿⠛⠛⠛⢛⣫⣭⣭⣙⣛⣻⣿⣦⣾⣿⣿⠀⢸⠀⢸⣿⣿⣿⡼⠁⣞⠀⣠
⠉⠛⠀⡾⠛⠟⠛⢯⣼⣿⣿⡿⣿⣟⢱⣷⣀⠀⢈⠁⠀⠀⠀⠉⠉⠉⢉⡉⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⢺⡀⠘⣿⣿⣿⣿⣤⡇⢰⣿
⢁⠒⠲⣧⣠⣆⣸⠦⢼⣿⡿⣷⡾⠋⣿⣿⢿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢻⣿⣿⡿⠛⠟⠿⣿⣿⡿⢸⡇⣾⣿⣧⣿⣿⣯⡅⢸⣿
⣤⣀⣾⣿⣄⠁⣀⣼⡶⡿⢷⣿⡿⢛⠃⠀⠈⠙⡿⠗⠳⠂⠀⠀⠀⠀⠀⠘⠙⠞⠀⠁⠀⣀⠀⡀⠀⠻⣷⣾⣾⣷⣿⣿⡿⣿⣯⣾⢻⡈⢿
⠑⠀⠀⠀⠀⣿⣿⣿⡅⠀⡵⠿⠱⠾⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣢⡉⣠⡆⣀⢀⣤⣞⣻⣿⣿⣿⣿⣇⢸⣿⡿⣡⣶⣿
⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠊⠀⠁⣰⡿⢋⣡⣤⣿⣿⡻⡾⣸⣗⢿⠟⡋⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡩⣐⣻⡿⣛⣛⣻⠿⠿⣿⣿⣯⠿⠛⠛⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⡄⠀⠀⣀⠨⠛⣿⣷⣤⣤⡤⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠷⡿⣽⠿⠯⡾⢿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢰⣶⣿⡁
⣿⣿⣾⣿⣿⣿⣿⣷⣶⣶⡶⣷⣾⣿⣷⣿⣶⢶⣿⣿⣶⣶⣿⣿⣷⣶⣾⣿⣷⣶⣿⣷⣶⣶⣶⣾⣷⣶⣾⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣭⣽⣿⣿⣿⣭⣯⣽⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⠛⠛⠉⠉⠉⠉⠉⠉⣉⣉⠉⠁⢀⣀⣠⣤⣄⣀⣀⣀⣀⣄⣄⣀⣀
⢿⣿⣿⠿⠿⠿⠻⠛⢻⣿⣹⣽⣿⣽⡿⠻⠿⢿⡿⠟⠛⠉⢹⣿⣿⠛⣽⣿⡅⠀⠀⠀⠀⠀⠀⠀⠒⠻⠿⠿⠿⠿⠟⠀⠹⣯⣽⣿⡿⠿⠿⠯⠽⠿⠿⠿⣛
⣿⣥⣾⡿⢿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣴⡀⠀⠀⡀⠀⠀⠸⠿⠟⠀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠠⣴⣶⣾⣿⣷⡶⣾⣶⣿
⣿⣿⣿⣿⣮⣿⣭⣽⣍⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣶⣀⣀⡀⠀⠈⣿⣿⣿⣿⣧⣿⣟⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣃⣤⣄⣠⣤⢄⣠⣤⣤⣶⣦⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠲⠶⠆⠠⠤⠀⠀⠀⢶⡀⢹⣿⣿⣿⣿⣿⢿⣷⣶⣦⣌⡋⢛⣿⠏⠙⣻⡿
⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⡟⣿⣽⣟⠉⠀⠀⣰⡐⠶⠶⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣤⣤⣬⣏⣉⣿⣿⣾⣿⣾⣿⡿⡷
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣤⣴⣶⣷⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⣤⠀⠀⠀⡄⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠻⠿⠏⠈⠻⡿⠋⠘⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⠁⠀⠀⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⣠⣦⡀⢀⣴⣦⡀⠀⢀⣴⣶⣦⡄⠀⠠⠀⠀⠀⢠⣶⣶⣤⠀⠀⠄⠠⠀⠀⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠈⠉⡏⠉⠈⢹⡏⠁⠀⠸⣿⣿⣿⡟⠀⠀⠀⠁⠀⢿⣿⣿⣿⠃⠀⠀⠈⠀⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠇⠀⠀⠸⠇⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣾⣿⣷⡄⠀⡀⠀⡀⠀⣴⣾⣿⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⣿⣿⣿⠇⠀⠀⠈⠀⠀⢻⣿⣿⡿⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠈⠻⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡿⣛⣿⠏⠀⠀⠂⠀⠀⠈⠉⢸⣿⠁
⠀⠀⠀⠀⠀⠀⢧⠉⠈⠀⠀⠐⠇⠀⠀⣀⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠜⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⢀⣀⡴⠖⠁
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠘⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢰⣿⣿⣿⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣶⣶⣤⡂
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⢸⣿⣿⣿⣿⡯⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠈⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣿⠃⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣾⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⢰⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋
⠀⣾⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠟⣿⠻⡿⠿⠿⠟⠁
⢠⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏
⣼⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣷⣦⡀⠘⠛⠛⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠂⠀⠌⠙⠻⠿⠿⠿⠆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁

⣿⣿⣿⣿⡿⠛⠻⡿⢟⣥⠔⠉⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢛⡿⠷⣾⣥⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⢀⣴⣯⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠉⠠⠜⠿⠹⣧⣀⡀⠀⣿⣿⣿
⣿⣿⣿⣿⣇⣴⡿⠋⠀⠀⠀⠉⠹⡖⠲⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠃⠀⢀⠔⠉⠀⠀⠀⠀⠀⢤⣿⣏⠀⢸⢻⣿
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠃⠙⢳⣼⣸⣿
⣿⣿⣿⣿⣿⠁⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠔⠒⠋⣠⣴⣶⣿⣿⣾⣿
⣿⣿⣿⣿⣿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡏⠀⠀⠀⣶⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠐⠒⠎⠀⠠⠴⠿⡿⠋⠛⢻⣿⣿
⣿⣿⣿⣿⣿⣶⣶⠄⠀⡄⠀⣰⣶⠄⣄⣠⣴⣦⡄⢴⣠⣤⡀⠿⣤⣄⣸⡀⣷⣼⡄⢠⣤⡄⢠⡶⢀⣴⣶⣖⣶⣤⣾⣧⠈⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⢀⡇⣰⣿⣿⣷⣏⡿⠿⢿⣕⣿⣺⣿⢷⣾⡿⢿⣿⣿⣿⣿⣿⡼⢿⣶⣿⣾⣋⣿⣧⣿⣫⣾⣿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣄⠀⠉⣽⣿⣧⣴⠀⣹⣿⡿⠧⢸⣿⠧⠴⣿⣿⠚⠉⣁⡀⣀⣬⣹⣀⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⡿⠤⠤⢿⡟⠛⡿⠃⠸⡿⠀⠀⠀⣿⣠⣤⣽⣿⢀⣸⣿⣿⣿⣿⣿⣿⡿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⣿⣿⣏⠻⠋⠉⠀⢹⠇⠀⠀⠀⠀⠃⠀⠀⠀⡏⠀⠀⢸⣿⡾⣟⣛⣛⣻⣛⣿⣿⣿⢺⣟⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣼⣿⣿⣷⠀⢀⣀⣾⠀⠀⠀⠀⢠⡇⠀⠀⠘⠛⠛⢿⣿⣭⣭⣭⣿⣿⣿⣿⣿⣿⣟⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⠀⠀⠀⠀⠸⠃⠀⠐⠛⠒⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣾⣿⣀⣶⣦⣤⡀⠀⠀⠀⠒⠛⠛⢛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣄⣀⣀⠀⠈⣉⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡘⠦⠈⡀⠶⠀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠹⣇⠈⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠂⣾⠀⠐⢶⠀⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡕⢀⠠⠁⡄⢀⠀⠀⠀⣟⠡⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⣷⠺⣤⣼⡴⠀⠀⡟⢀⡐⡤⣤⢴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣷⠆⠀⠀⠀⠁⠚⠂⠀⠀⠀⠀⠀⠀⠀⣤⣤⣡⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠁⠋⠀⣿⢦⠐⢀⣿⢿⣿⡆⠀⡨⠱⣏⠃
⠀⠀⠐⠄⠠⡠⠤⠀⢰⣿⡏⡀⢀⡦⠐⢀⣴⠆⠀⢀⠀⠀⠀⠀⠀⠿⢹⡟⠂⠂⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢻⠀⠣⠁⠒⠸⠈⢳⠀⠁⣸⠈⠁
⠀⠀⠀⠀⠤⠀⠀⠄⢸⢿⣇⢠⣿⣴⡞⠛⢁⠀⠀⠈⠀⠂⠀⠀⠀⠀⡎⠈⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢤⣼⡇⢸⠀⠀⠀⠀⠓⠀⢸⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⡧⢾⠏⠉⠠⠈⠀⠀⢈⠀⠀⠀⠀⠀⠺⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⡆⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⢠⡿⡷⠃⠀⠀⠀⠀⠀⠀⠸⡀⠀⠄⠀⠀⢸⣀⠀⢺⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⣀⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⣉⠄⠀⠀⠘⠈⠁⠋⠉⠁⠈⠁⠀⠀⠀⠈⠉⠉⠈⠁⠁⠉⠁⠰⠄⠀⠀⠀⠸⡆⠀⠐⠀⠀⠀⢈⠧⠀⠀⠀⠄
⠀⠀⠀⠐⠋⣼⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⣀⣠⣤⣤⡴⠶⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣳⠔⡂⡀⣀
⡄⠄⠀⠀⠰⣿⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠛⠛⠿⠏⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠰⠒⣫⡉⠘⠈
⠀⢆⠈⠀⢾⣿⣿⣷⣦⠴⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠃⠉⠉⠤⠿⠤⢥⣤⣶⣶⣶⣤⣤⣄⠴⠤⠠⢾⣿⠔⠂⠀⠚
⠀⠈⣀⠀⠈⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⣿⣿⣿⣿⣦⣠⣤⣾⣵⣆⣀⣤⣤
⠀⠀⠀⠀⢀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣾⣿⣿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠛⠛⣿⣿⣿⡋⠛⣿⣿⣿
⠀⢀⣤⡄⣀⠀⠀⡀⠀⠀⣤⡀⣀⣀⣠⣤⣾⣿⣿⣿⣿⣟⡙⠁⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿
⣴⣿⣿⣽⣋⣂⣔⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠉⠉⠁⠀⠀⠀⠀⠠⣤⣤⣶⣴⣾⡿⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢶⣶⣤⣤⡄⠀⠀⠈⠛
⣿⣿⣿⣿⣿⣿⣿⡙⠻⣿⣿⣿⣿⣿⡭⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣿⣿⣿⡷⠀⠀⠀⠀⠀⢠⣴⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢶⣶⣶
⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣻⠇⠀⠀⠀⠀⠀⠀⠉⠒⠶⠶⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠰⣺⢂⡀⢀⠀⠀⠀⢀⡀⢀⠀⢀⡀⠀⠀⠀⠀⠍⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠿⠿⣽⠋⠁⠋⣶⣦⣀⣸⣿⣿⢿⣿⣿⣧⣤⠀⣀⣧⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⡀⢹⣿⣶⣾⣿⣿⠹⣭⢻⠃⣹⣿⣿⣿⣿⣧⣿⣿⣦⡆
⠀⣄⣠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣾⣶⣿⣿⣿⣟⢿⠻⣿⡤⡀⠈⡆⠏⡽⣷⣶⣿⣿⣿⡿⡿⡄
⠀⣿⣿⣿⣿⣏⣰⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣮⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣿⣦⣷⣴⣦⣸⣷⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣽⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇
⠀⣿⣿⣿⣟⣿⣿⣧⣢⢀⣤⣤⣤⣀⣤⡄⠀⣠⣤⡀⠀⣀⠀⡟⢰⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⠛⡉⣉⣉⣋⣛⣋⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⢿⡿⠛⠟⠛⠋⠁⠀⠉⠙⠛⠃⢸⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⠅⠀⠄⠊⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡟⠉⠁⠤⠠⠀⠀⠀⢠⢾⣿⢿⣷⠿⠀⠀⠀⣠⡆⢰⢰⣤⠀⡀⠀⣿⣟⢛⣿⣿⣿⣿⣷⣿⣿⠈⡁⢈⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠉⢀⡄⠀⠋⣿⣿⢿⡿⢿⣿⣿⣿⢿⠀⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⡆⣷⣶⣦⢀⡃⠃⣠⣀⣾⣿⣿⣷⣾⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠦⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠿⠿⠿⠿⠿⠿⠾⠧⠾⠿⠇⠭⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⣄⠀⣿⢹⡿⠀⠙⠻⠛⠁⠀⠙⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠉⠉⠐⣩⠿⣇⢠⡟⠂⠤⠐⢷⣶⡿⠉⠙⢷⠀⠴⡰⠄⠀⠠⣄
⠀⠀⠁⠀⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠘⣧⠠⠐⡳⣋⠠⠛⢻⠇⠀⠀⠀⠘⢿⡀⠀⠈⠁⡙⠤⠹⠇⣿⣃⣹⣆⠐⢀
⠀⠀⠀⠐⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣌⠃⡀⠛⠁⠀⠚⠀⠀⠀⠀⣀⣤⡲⠉⠀⠀⠀⣯⠀⠀⠀⠈⠁⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢙⠷⣥⣤⠄⢀⢴⠂⣴⣶⠐⠈⠁⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⣾⣯⢐
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⢬⣄⢿⡤⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀⠀⢀⠙⠟⣾
⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⠀⠀⠈⠐⠂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠨⣾⣷⣖⣿
⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢂⠀⠀⣦⡀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠛⡇⡹⣿
⠀⠀⠀⠇⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⣦⡀⢀⡈⠑⠟⡿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠐⠀⠀⠰⣽⣿
⠂⠀⠀⠀⠀⠀⣿⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⢀⣶⠀⢋⢁⣈⣉⡡⠄⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⢹⢿
⡃⠀⠀⠀⠀⠀⣿⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠰⣤⡀⠀⣿⣿⡇⠺⠋⠉⣀⠖⢀⠆⠀⠀⢠⣌⣛⠉⠀⠀⢀⣀⣰⡁⠀⠀⠀⠀⣠⠀⣶⣿⢴
⠇⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣠⠂⠀⠀⠀⠙⠶⣿⣿⡦⣀⡄⠈⢁⢰⡟⠀⠀⠀⠀⢸⣯⡀⠀⠒⠉⠉⠉⠉⠂⠀⠀⣴⣿⠀⡿⣿⠛
⣧⡀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢸⠃⠀⠀⣠⣾⣿⡿⢻⣿⣿⣿⣷⠀⠻⡌⣃⣶⠀⠀⠀⠻⡗⠉⠀⠀⠀⠀⠀⠀⠀⠰⣌⠋⢻⠀⣴⣿⠟
⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⡞⠀⠀⢰⣿⠿⠋⢠⣿⣿⣿⣿⣿⣷⣄⡦⣿⡇⠀⠀⠀⡀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⠉⠁
⣿⡇⣀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠁⠀⠀⠚⠁⠀⠀⣿⣿⢹⣿⢻⣿⣿⡈⠁⣿⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢸⠼⢷⣶⡟
⣿⣿⡇⠀⠀⢀⡆⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⢿⠀⠙⣿⡆⠀⠀⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣻⠀⢸⣧⡜
⣿⡿⠃⢸⡇⢸⣷⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠨⠀⠀⠇⠻⠀⠀⣂⠀⠆⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⢡⡀⣀⣼⡀⢸⢉⣿
⣻⠠⢞⣿⡇⣾⣿⡄⣿⣿⣿⣧⠀⠀⢀⣀⣠⣶⣄⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢠⣧⢶⡄⠀⢈⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⣿⣿⣾⢋⣁⣛⠃⠈⢿⡿
⣷⣄⣿⣿⣻⣿⣿⡇⢿⣿⣿⣟⡀⠈⠉⠉⠉⢳⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⡀⡰⠂⡅⠀⢸⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢹⡏⠰⠁⡙⢿⡁⠀⣤⡄
⣿⢟⣿⢣⣿⣿⣿⡇⢸⣿⣿⣿⣿⣦⡀⢠⣤⠀⠃⠀⡀⠀⡆⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠀⠀⠐⢿⣿⡀⠀⠀⠀⢠⠂⢴⡇⢠⠇⠼⠛⠁⣠⡌⠁
⡿⠟⣡⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⢋⣥⣔⢆⣤⡐⠀⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⢃⠋⡆⠀⣼⡇⠀⠀⠀⣿⠏⠠⠀⡀⣈⣴⡳⠦⠛⡖⠳⠿⠈⠉⡟
⣴⣾⣿⠟⣿⣿⣿⣿⢸⣧⠙⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⡀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣰⡀⠀⣗⢃⢤⠄⢾⢧⡄⠈⠀⠡⡘⠈⠁⠢⠜⢝⡉⠀⠌⠦⡹
⡿⣿⠏⠀⣷⣿⣿⣿⠀⣿⡍⢻⣯⠛⢛⣛⡁⠀⠀⠀⠀⢃⠀⣼⠆⢠⡶⠀⠀⡇⢠⣄⠀⠀⢹⠃⠀⢿⢻⠸⡒⠲⢦⠘⣖⠁⠐⠣⠌⣋⡔⠦⠈⢀⠉⠈⠳⠦⠤
⣷⠎⠉⠂⣬⣿⣿⣟⠀⣿⣗⠀⢰⡾⣿⣿⣿⡀⠀⠀⠀⠘⣦⣾⠀⠀⢴⣶⣤⣀⠈⠚⢶⣄⠈⠁⣰⣶⣼⣇⢑⠟⣿⣿⠯⣧⠀⠛⠛⠉⠉⡅⠰⣤⠉⠀⢄
⣠⠀⠠⣠⣿⣿⣯⢹⡇⠹⣿⡄⠀⢻⣻⣿⡿⣧⠀⢠⣜⠦⣹⣿⢻⡏⠀⠉⠉⠻⡿⣗⣎⣻⣷⠄⠈⢳⣟⢶⢾⡇⣿⣿⣆⡀⠃⠀⠀⠀⠀⠀⠀⣳⠃⠀⠈⠱⡄
⠀⠰⢰⣿⣿⣿⢣⣿⣿⠀⢻⣟⠀⠀⠃⠟⢿⡘⠃⠀⢨⣿⣌⣿⣾⠽⠆⠀⠀⣤⣰⡏⣛⠏⣿⢀⣧⣄⢹⣿⣿⣿⣭⣭⣽⠃⣴⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⣼⣿⠿⢫⣿⣿⣿⠀⠈⠿⠛⠀⠀⠀⠈⠀⠀⠀⠀⠈⢻⣏⠴⠲⡶⣠⡀⠀⠉⠀⢴⣶⠇⢈⣁⡩⢅⢉⣬⠻⣿⣧⡜⢿⡒⢛⣠⣤⣴⡶
⠀⠀⢿⣿⠀⣾⣿⣿⣇⠀⠀⠀⠀⣽⣾⣷⡀⠀⠀⠀⠀⠀⠘⣣⡛⣀⠀⠻⣿⣆⠂⣀⠀⠻⠀⣦⣭⣿⣾⣟⣷⠶⠂⣶⠛⢫⣾⣿⣿⣿⠛⠓⠂⠀⠀⠀⠀⠀⠑
⣆⠀⣾⠻⣇⣿⣯⣼⣿⠳⣆⠀⣿⣼⢿⣼⠗⠀⠀⠀⠀⠀⠀⣹⣯⣉⠑⢆⠸⣿⣴⣿⠿⠂⢀⠻⢿⣾⣿⣿⠋⠀⠀⠀⠀⠺⣿⡿⠋⠅⠐⡿⠀⠀⠀⠀⠀⢄
⣿⡀⣿⣀⠈⠻⠉⣿⠿⣟⣻⣦⣿⣋⠈⠉⠂⠀⠁⠀⠀⣤⡼⠿⠟⢷⣽⣎⣶⣛⣿⡏⠋⠀⠀⠻⡶⢿⢿⡏⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠁
⣽⣧⣿⣿⢶⡀⣮⣏⣠⣽⣿⣏⣽⣻⣶⣄⡀⠀⠀⢴⡶⡾⢃⣤⣤⣜⡿⣿⢿⣿⣿⣧⣤⣠⠀⢐⡿⣤⠀⢤⠀⢀⡄⠀⢀⣄⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣯⣍⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠸⢄⢢⡅⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠙⠿⣿⣇⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⢞⢚⠿⡻⢆⠂⡀⠀⠀⠀⠀⠀⢀⠀⢀⢶⣀⠀⠐⠠⡀⠀⠀⠀⠀⠘⠂⠘⠀⢈⣻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠏⢘⢣⣧⡡⢾⡈⠓⠌⠤⡚⠀⠀⠎⡊⣀⣀⢤⡈⡉⡁⠠⡀⠁⠂⣄⠀⠰⢤⡀⠀⢺⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⣟⠽⣀⠿⡗⡇⠀⡰⢆⠀⠀⡠⠚⠉⠀⠀⠀⢱⡛⠋⠂⠌⡐⠄⣼⠀⠀⠿⠀⠀⣩⡄⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⢸⠅⠀⠪⠿⢦⡀⠉⠉⠢⢉⠁⠀⠀⠀⠀⠀⠀⡗⠂⠄⡀⠀⠀⠐⠀⠯⡧⠙⠉⠀⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢦⠀⣀⠀⠔⠊⠀⠀⠀⠀⠈⠐⠠⢀⠀⡆⠀⠀⠀⣀⠄⠀⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⢀⡀⢙⠁⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠈⠁⢀⠀⠙⠀⢰⡞⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠘⠃⡠⠈⠀⢘⠃⠸⡗⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠰⠂⠀⡌⠀⢿⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠉⠀⠀⠆⠀⠀⠀⠸⣆
⠀⠀⠐⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠀⢀⡄⠀⢺⠀⠀⠒⠉
⠀⠀⠀⣉⣻⣿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣦⡤⣴⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢠⠗⠀⠘⠀⠀⠀⠀⡆⠀⠀⠐
⠀⠀⢀⡀⢛⢽⡆⠈⣸⡆⠀⢰⡦⣠⠊⠀⠀⠀⠀⠀⢀⠀⠀⠈⠄⢉⣱⡵⡆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠦⠀⠖⠀⢘⠂
⠀⢀⡈⠱⠸⢟⡿⣏⢺⡔⢀⣏⡼⢋⠈⣰⣴⡖⠘⠂⠈⠷⠈⢀⢤⢄⢼⡿⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠂
⠀⢀⡹⣦⣀⣿⣿⣃⠰⢶⣼⣾⡟⢃⣴⠟⠡⣐⠖⠀⠆⢈⠴⠄⡀⠋⣻⠹⠿⠁⠡⠀⠈⠁⠀⠀⠀⠀⠀⠣⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠴⠋⠈⢪⢿⣿⣿⣿⣶⣿⣿⣿⡾⣯⣶⣔⢾⣄⠠⣀⡷⠀⠰⠈⠉⠀⢹⠰⠆⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣀⣹⡉⠉⠉⠉⣯⣴⣾⣷⡄
⠀⠀⠠⢡⠋⠛⣻⣷⣷⡻⠛⠻⡗⡞⡿⣯⣟⠃⣀⡨⣮⢊⠐⠷⢀⣧⣞⣤⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⡴⠀⠀⠀⢻⠏⠈⠺⠿⠷⠳⠘⣰⠌⠀⠀⠈⠀⣻⡌⠃⠀⠀⢡⣤⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣽⣿⣿⡿
⠀⠀⠃⠀⠘⡄⠋⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠃⡠⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢶⡶⠶⣶⣶⣦⡤⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣷⡄⠀⢀⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡟⢠⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠾⠟⠉⠀⠀⠙⠿⠶⠾⠟⠉⠀⠈⠙⠿⠶⠾⠟⠁⠀⠈⠙⠿⠶⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠆⠀⠀⠸⠿⠿⠆⠀⠀⠺⠿⠿⠆⠀⠀⠾⠿⠿⠂⠀⠀⠾⠿⠿⠀⠀⠀⠾⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠺⠿⠿⠃⠀⠀⠺⠿⠿⠂⠀⠀⠻⠿⠿⠂⠀⠀⠻⠿⠟



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠂⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣅⠀⠀⠀⠀⠀⠑⠿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠂⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠘⠀⠀⠊⠀⠄
⠘⠛⡗⠞⠠⠀⠰⠰⠀⢀⣀⠀⢀⣀⣆⡀⠀⠀⡀⣠⣀⠀⠠⠄⢀⣀⠐⠓⠊⠀⡀⠀⠀⠀⠈⠈
⠁⠀⠀⠌⠠⠆⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⡀⡠⠀⠁⠂⠀⠀⠀⢈⠁⢀⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠤⢤⣶⣾⣤⣤⣀⣶⣿⣧⣦⠆⣀⣀⣀⣀⣀⠀⠀⣀⠀⠀⢀⣠⣤⣤⣄⣀⡀⠀⢀⣦⣤⣤⣾⣶⣶
⠀⢀⡀⢀⡀⠀⠀⠀⠉⠙⢿⣙⡿⠿⡿⠿⡯⠭⠽⠟⠋⠉⠉⠉⠙⠛⠻⢋⣉⣀⠀⠈⠉⠙⣿⣛⣿⣿⣿⣿⣿⣿⣿
⣶⣿⣿⣾⠀⠀⠀⢀⣀⣠⣼⣿⠞⠋⠁⠀⣀⣤⠤⠀⠀⠀⠀⠀⠛⠃⠀⠀⠉⠙⠛⠒⠀⣀⠀⠉⠴⠵⣶⣦⣞⢛⠛
⣿⣟⣛⣳⡿⠿⢿⣭⣭⣤⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣤⣤⣠⣤⣤⣴⠶⠾⠛⠁⠀⢀⣀⣀⡉⠉⠛⠳
⠛⠿⠿⢿⣷⣶⡾⠟⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣷⡀⠀⠫⠙⠁⠰⠏⣿⣿⡗⠀⣄⡿⠦⢀⣤⠠⣽⣶⡖⣿⡟⠙⠘⢷⡦⠀⢠⢇⣦⡄⠀⠀⢴⣄
⠻⣷⡀⢠⠀⣠⣐⣹⠇⠈⣿⣸⣯⠇⠀⠀⢀⠀⠨⣽⣱⠋⠀⠀⠀⡮⠑⣄⠈⠸⢧⡅⢴⣦⠤⢿⡄⠀⢀⡀
⡀⠹⣷⠐⠂⣉⣬⣱⠄⠒⢈⡡⣞⠀⠀⠀⠀⠀⠀⠈⠻⣤⠀⠁⠀⠀⠐⡌⠳⠂⠈⠇⢼⣧⡳⣄⣿⣦⠀⠙⢦
⢿⣦⡘⠆⠁⠀⠛⠁⠀⠆⠘⠁⠀⠀⠀⠀⠀⣠⢠⡤⣱⠍⠀⠀⠀⠀⠈⣽⠀⠁⠀⠀⠀⠀⠀⠀⢸⣟⣗⠀⠄
⠀⠉⢻⣦⣂⠀⠒⠀⠀⡀⣠⣤⠀⣨⣅⡰⠤⠉⠓⠋⠁⠀⠀⠄⠀⢀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⡝⠇⠦
⠀⠀⡶⠈⠻⠝⣯⡈⢁⡇⠓⠀⢠⠿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⡆⢦
⠀⠀⢀⣀⠠⠔⠶⣶⢈⣫⠷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠧⠀⠀⠀⠀⠀⠀⣀⣁⠹⠿⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠘⠓⢸⠂⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢫⠀⠀⠀⠀⠀⠀⢚⣲⣿⣶⡆⣿⣿
⠀⠈⠃⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢡⡐⠀⠀⠀⠀⠈⣿⣿⠟⢴⣿⡟
⠀⠈⠀⠀⠱⠄⣀⡀⢹⣶⣀⢀⠀⠀⠀⠀⠀⣀⡴⠂⠀⠀⠀⠀⢀⡀⠀⠐⠀⠉⢀⠀⠀⠀⠀⠈⠙⠁⣼⣿⣷
⠀⢘⢆⠀⢀⡀⠀⠙⠪⡗⣿⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠲⠀⠀⠀⢶⣼⣿⣿
⠀⢸⠜⠓⠀⠛⠚⠶⠀⠀⠁⠀⠀⠀⣀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢻⣿⣽
⠀⠀⣦⣤⣶⡶⠖⠛⣉⠍⡺⠲⠆⠀⠀⠀⢠⣤⡄⣤⠀⠀⠀⠀⠀⠀⢴⠃⠀⠀⠀⠚⠁⠀⢱⠀⠀⢀⣼⡏⢿
⡇⠀⠛⠉⠀⠀⣠⠞⠁⣸⠁⠀⠀⠀⣀⣶⣤⣝⠃⠀⠀⠀⠀⣀⣀⣠⣇⠀⠀⠀⠄⠀⠀⠀⣼⠀⢶⣿⣿⠱⣿
⣥⡄⠂⡀⠀⠚⠁⢠⣦⡏⠀⠀⠀⠀⠀⠐⢧⣍⡀⠀⠀⠴⠚⡉⠉⠋⠉⠛⠢⠀⠀⠀⣠⣴⣿⠀⢸⣿⣏⡾⡛
⣷⣾⣷⣏⠀⠀⣾⢸⢷⠀⣀⠀⠀⠀⠀⢐⣿⣟⡻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡿⠻⣿⠀⠘⣡⣾⣦⣆
⣿⣿⣿⣿⣃⠀⠻⢺⢸⣰⣿⠀⠀⠀⠀⠉⠹⡇⠡⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠩⠢⠀⠀⣹⠀⠠⡟⣿⠙⠉
⣿⣿⣿⡿⣿⣧⡀⣾⢸⣿⡯⡄⠀⠀⠀⠀⡀⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠉⠉
⣿⡻⣿⣿⣾⡏⠓⠜⢸⣽⠂⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣦⣠⣾⣂⣀⣦⣧
⣿⡇⠹⣿⣿⣷⠀⠀⢈⠟⡀⢠⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣼⡇⠉⣿⠿⠳⣤
⢹⠁⠀⠈⢻⢿⡄⠀⠀⢹⢱⠸⡄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣹⡅⠀⣿⣷⣤⢛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠶⡭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⣁⣤⡁⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠁⠈⢿⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⡒⠀⠋⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠀⠀⠁⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡄⠀⡠⠎⠹⣷⣦⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠒⠓⡒⣾⡅⠤⠄⠒⣨⢋⠳⢤⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢚⠋⠀⠀⠀⠀⠶⣀⡎⠸⠀⠀⠀⢀⡜⠃⠀⠀⠀⢷⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠞⠐⠒⠒⠒⠊⠉⢙⢁⡀⠆⠀⣠⠏⠸⠂⠀⠀⠀⢸⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⠤⠚⠁⢠⠃⠀⠀⠀⢠⡟⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⢀⡌⠀⠀⠀⠀⣼⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⡖⠉⢛⣦⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠤⠁⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿⢣⡤⠈⠀⠘⠀⠒⠲⠖⠒⠛⠛⠛⠛⠃⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢸⠤⠴⢶⡉⠉⠙⠒⠶⢤⣄⣀⡀⠀⠀⠀⢀⠀⠀⢸⡄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠁⠿⠀⠀⢸⠆⠀⠀⠀⠀⢰⠆⠉⠉⠛⠛⠛⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈⠂⠚⠁⠖⢀⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⢸⡀⡠⠞⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢸⠙⠳⠶⠶⠶⠞⠛⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⢷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡠⠤⠀⠀⠀⠀⠀⣿
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⢩⡅⠀⠀⠀⠀⠀⠀⣸
⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⡇⠀⠀⠀⠀⢀⡟⠀⠀⠒
⠈⠓⠀⢀⡀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⠀⠀⠀⡼⠁
⢀⠈⠀⠸⠈⢆⠀⢸⠃⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠓⠚⢅⠸⠂⠀⣇⢀⠠⠐⠀⠂⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡀⠀⠀⡇⠀⣀⠤⢤⡀⠀⠀⣠⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠾⠀⠀⠀⠀⢧
⠀⠀⠐⠉⠈⠉⠉⠰⠋⠀⠀⠀⣹⠪⡁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⡀⠀⠀⠀⢸
⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⢸⠆
⠀⠈⠀⠀⢃⠀⢀⠃⠀⡜⠃⠀⠀⠀⠀⠀⣠⡴⠛⠙⢳⠄⢠⠀⠀⠀⢠⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠂⠈⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠒⣤⡄⠀⠉⠉⠉⠉⠈⠁⣼⠃⠀⢀⡰⠏⠀⠘⠀⠀⠀⡎⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣀⠀⠠⡎
⣀⠀⠀⢀⡀⠘⠀⠈⣂⠀⠀⠠⠀⠀⢰⠇⣠⠖⠋⠀⠠⠀⠛⠛⠓⣤⠁⠋⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠰⠁⠀⠈⠁⠀⠛⠊⠀⠀⠐⠃⠜⠁⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⣀⠠⡤⠴⠊⠁⠀⢀⣠⡤⠞⠁⠀⠀⠀⡇⠀⠀⡝
⠀⠀⢤⡠⠔⠂⢀⠔⠓⡀⠤⠀⠀⠁⠀⠀⢀⠤⠒⠛⠓⠈⠁⠀⡄⢀⠔⠋⠉⡢⢀⣠⠖⠈⣷⣉⣁⣀⣀⠠⣴⡶⣾⠁⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⡁⠀⡠⠖⠒⠲⠦⢠⡀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠉⠀⢾⠁⢀⡴⠛⢦⣤⠀⠌⠉⠀⣰⠏⠀⠀⠈⣿⠀⠀⠀⠀⠀⢀⠴⢄
⠤⠤⢄⣀⠀⠀⡄⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠔⠁⠀⢱⠀⠀⡰⠋⠀⠀⢀⡾⠟⣀⠤⣄⠀⢰⡏⠀⢸
⠀⠀⠀⠉⠙⠂⠶⡀⠀⠀⠈⠳⠤⢄⡀⠤⠶⠚⠀⡔⠀⠀⠠⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠜⠀⢀⡴⠃⠀⢸⢆⡠⠦⣰⠞⡡⠊⠁⢀⣼⠃⠀⠀⢀⡞
⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣭⣴⣤⣤⣤⣭⣭⣭⣤⣮⣤⣴⣶⣿⣮⣥⣤⣴⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠙⠃⠁⠈⠈⠁
⠀⠀⠀⣰⠦⡜⢁⠀⡜⢠⣨⡀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠
⠀⢀⡌⠋⠀⢀⠁⠀⠀⠑⣟⡉⠁⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⡄
⠀⣨⣃⡴⠂⢼⣯⣄⣠⣜⡉⣀⣀⣀⣤⣤⣠⣄⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠘⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡀⢀⡷⠋⠹⡄
⠘⣾⠃⠀⠂⠀⠿⠄⣠⣼⠿⠋⠁⠁⠀⣀⠀⢀⢀⣁⢁⢠⡇⠀⠀⠀⠀⠀⠀⣣⠄⠀⠀⠀⢤⠀⠀⠀⠀⠀⠄⠳⣄⣤⡀⠀⠻⣿⡇
⠀⣿⣃⣀⣀⣠⣤⣤⣿⠂⡀⢠⡔⠉⠀⠀⠀⠀⠈⠀⠀⣿⠇⠐⠂⠀⠀⠀⠀⡅⠀⠀⠀⢀⠀⢀⡶⠀⠀⠀⠀⠀⠸⠉⠳⢤⡀⠘⢇⣀⠀⠀⠆
⠀⠙⣿⣿⣿⢿⠸⠛⠿⠿⠟⠧⢶⣶⣦⣼⢦⣄⣀⣀⣐⣏⠀⡀⠘⠋⠀⢀⣠⠁⢆⡀⠀⣀⡀⠉⢁⠀⠀⠀⠀⠀⠐⠀⢀⠀⠃⠀⡾⠉⠛⠓⠂
⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⣄⠀⠀⠃⡇⠈⠀⠛⠙⠻⠿⠛⠛⠅⠀⢄⠀⠀⣉⣀⣀⣉⣉⡉⠉⠭⠉⠩⠅⠀⠀⠄⠀⣠⣠⣄⢀⢾⡷
⠀⢀⣨⠀⣔⢦⠀⣀⢀⠀⡀⠇⢀⠀⡆⣠⣤⢴⣖⡀⣀⣀⣀⣀⣀⠀⣙⣉⠈⠉⠙⠉⠀⠀⠀⠀⠀⠀⢀⣘⣓⡃⡘⠛⠿⠿⠟⠈⠿⠶⠤⠄⠴
⢀⣿⣿⡶⠸⣏⣓⣛⣻⡀⣑⣈⣠⣁⣤⠤⠄⠀⠸⣿⣿⡿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠈⠓⢼⣬⣙⣻⣿⣿⣲⠶⡦⢠⠤⠆⠴
⠀⣻⣿⣿⠿⠿⠿⠿⠞⠻⠿⠛⠃⠒⠒⠒⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠿⢯⣽⣩⡛⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡶⠀⠀⠀⠘⡆⠿⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⡆⠀⠀⢰⠇⢀⡀⠀⠄⢅⡔⠀⠠⠀⠀⠀⡧⠡⠀⣸⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⢛⠀⠀⣾⠀⠢⠷⡀⢠⡀⢀⣀⣄⡌⠀⢳⡰⠋⢀⡏⠀⢰⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣈⡔⠲⠤⡇⢰⡄⠀⠂⢚⢧⡆⣽⣯⡶⢰⡗⠀⣘⡵⠂⠈⢀⠀⢳⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠢⡀⠀⠀⠡⡸⡀⢀⢈⣐⢢⠀⡈⢫⠟⢧⣿⠔⡛⢀⠀⠿⣁⠄⠘⢉⣷⠛⣡⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠂⠀⠈⠺⡆⢸⠟⠈⠄⠃⣀⢩⣔⣦⣿⣧⣟⠤⡘⣦⠎⠰⡆⡾⣡⣾⠯⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣤⣶⣎⣖⣊⣀⢠⡄⣶⡎⢛⣲⣶⣦⣼⣶⣶⣿⣤⣍⣗⣿⣶⣤⣿⣶⣓⣿⣭⣳⣼⣯⣶⣯⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠉⠛⠛⠋⠋⠛⠛⠉⠿⠙⠛⠊⠿⠟⠋⠛⠋⠛⠋⠙⠋⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠁
⣿⢿⢿⡿⡿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣟⣿⣟⣿⣿⣻⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣠⠦⣤⣤⣦⠰⡆⡄⢠⢰⣦⢴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠉⠙⠛⣈⠁⣙⠋⡘⠙⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⡟⡾⢧⢹⠹⣿⢸⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⠙⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣋⠀⣀⠜⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡡⠚⠉⠲⡄⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⠴⠖⠻⡇⠀⠀⢀⡿⢁⣨⣿⡶⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⣘⡦⠤⣞⣰⠋⡰⢦⠈⡀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⢠⠀⠈⠁⠀⠀⠀⠙⢦⣙⣚⡰⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠄⣈⠁⠀⣤⣄⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢦⡼⠁⠳⡀⠀⠀⠀⠀⠀⡐⣒⠂⣠⠿⠼⣔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡰⢒⢢⡹⡀⠀⠀⠀⠀⠀⠀⡤⠟⢲⡖⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⣇⠹⠤⠞⢠⣇⣀⣀⡀⠀⠀⠀⡗⣒⣚⣓⣒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣈⡓⠒⢚⣉⡀⠀⢀⡀⠀⠀⡀⡇⡇⢴⡦⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣋⡀⠈⣓⡋⠀⣉⠓⠉⠀⣀⡼⠃⡇⣇⣒⣒⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠳⠶⠶⠶⠶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢘⣷⣴⠶⠶⠶⠶⠶⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠛⠛⠛⢻⠀⠀⢰⡟⢛⡄⢠⡉⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⢀⠶⠞⠃⠀⠘⠛⠛⠀⠈⠙⣣⠀⠀⢀⣴⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢄⣸⣄⣀⣠⣄⣀⣀⣀⣤⣤⠴⠿⠗⠛⠋⠁⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠚⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⢀⣰⠟⠁⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⣠⡾⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⠤⠤⠤⠶⠶⠶⠶⠄⠀⠂⠀⠀⠉⠉⠉⠉⠒⠶⠶⣄⠀⠀⠈⢷⡀
⢠⡟⠀⠀⠀⢀⡠⢤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⢷⡀
⣸⠇⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠛⠀⠀⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⣇
⣿⠀⠀⠀⠀⡇⠀⣠⡄⠀⠀⠀⠀⠊⠀⠀⡀⠠⡄⠀⠀⠉⠀⣀⠰⢆⠀⠀⠳⡄⠙⠀⠀⠠⣄⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⡇⠀⠀⠋⠀⠀⢀⡀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠄⠀⠀⢀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠠⣄⢤⡀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⢠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠇
⢹⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠢⠌⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⡄
⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠁⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀
⢸⡇⠀⠀⠀⢸⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠃⠀⠀⠀⠀⢸
⠀⣇⠀⠀⠀⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠀⠀⠀⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢿⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⣿⠀⠀⠰⠀⠱⠄⠀⠀⠀⠈⢦⠀⠙⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠸⣧
⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠓⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⢸⡆⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⣇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠲⠄⠙⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠘⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢹
⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⢸⡀⠀⠀⠀⢸
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠋⢀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠸
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠐⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠
⠀⠀⠸⡇⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠞⠁⠀⠀⠀⣸
⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠙⠶⠶⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠠


⠀⠀⠀⠀⠀⠀⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⢀⠀⠆⠀⢀
⠀⠀⠀⠀⠀⠀⣴⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀
⠀⠀⠀⢀⡀⠜⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠈⠰⢁
⠀⠀⢠⡞⢀⣴⢃⠀⠒⠰⠄⠂⠀⠂⠲⠤⠄⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢀
⠃⠐⠛⠉⠛⢫⢾⠳⡄⠠⣦⣴⣦⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠞⠛⠃⠀⠀⠀⠊⠂⠁⠈⠁
⠀⠀⠁⠀⠐⠀⠀⠀⠹⠻⠟⠛⠟⠛⠛⠫⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠹⠏⢿⣾⣷⣷⣾⣶⣶⣷⣶⣼⣶
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⡀⠀⠐⡀⠀⠀⠐⠀⢀⡈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠶⠈⣉⠛⠻⠯⢿⣿⣿⣿⣦⣤⣀⣀⣄⣀⣀⣀⣠⣀⣤⣀⣤⣶
⠐⡄⡀⣀⡆⣼⣶⣼⣠⡶⢀⣀⣠⣄⣄⡀⣄⣀⠀⠀⠀⠀⠉⢁⣀⣄⣤⣤⣄⣠⣀⠀⠀⠀⠀⡀⠈⠉⠈⠀⠉⠙⠛⠋⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣿⡿⣿⣿⣿⣿⣿⣿⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⣀⡄⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠛⢻⣤⣦⣶⣦⣬⡁⠠⣀⠰⠦⣤⣀⣀
⠉⠙⠋⠉⠉⠁⠈⠁⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠟⠿⠿⠿⠿⠿⢿⢾⣿⣿⣶⣾⣦⣿⣷⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⠾⣦⣴⠾⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠛⠛⠛⠋⠛⠋⠀⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⢛⣛⣛⣛⣛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣥⠶⠛⠉⠉⠉⠉⠉⠛⠶⣮⣙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⣇⢀⠀⠀⠀⠘⢷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⢋⡿⢿⣤⠀⠀⠀⠈⢻⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡶⢋⡴⢋⡴⠋⠙⢶⣄⠀⠀⠈⢷⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⣠⠞⢡⡼⢋⡴⢋⡴⠛⠀⠀⠀⠀⠙⢧⣀⠀⠸⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣠⠞⣁⡶⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢹⡄⣠⠞⢁⡼⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣬⠟⢁⡴⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⡼⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⣯⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣻⣗⠲⠶⠶⢦⣤⣤⣤⣀⣀⣈⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⠞⠉⠉⠛⠳⠶⢤⣄⣀⡀⠈⠉⠉⠉⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣤⣀⡀⠀⠙⣦⡀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⣿⣦⡀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⢰⣿⣯⡉⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣯⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⢿⡉⠙⢿⡀⣿⠀⠀⢀⣤⠶⢛⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⣡⡾⠋
⠀⠀⠀⠀⠻⢦⣤⠿⢧⣾⢠⡟⣿⣴⠿⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣷⣟⣁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠈⠉
⣴⠞⠓⠚⠛⠛⠛⠓⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⢶⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠙⠶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠟⠁
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⡀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡇⠀⠀⠀⠀⡆⠀⢸⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠟⠻⠛⠀⠀⠀⠙⠃⠀⠀⠀⠛⠛⠿⠿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠐⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠒⠒⠒⠒⠒⠲⠒⠒⠂⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⡀
⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠆⠀⠀⠀⠙⠷⣶⣤⣤⣤⣴⠾⠋⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀
⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⣀⣤⣾⠶⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣠⣴⡿⠟⠋⠀⠀⣀⠀⠀⠀⠀⠀⠈⢻⣿⣆
⢰⣿⡿⠀⠀⠀⠀⢀⣤⣶⠿⠛⠁⣀⣴⡾⠟⠋⠀⠀⢀⣠⣶⡶⠆⠀⠀⠀⢀⣤⣶⠿⠛⠁⠀⢀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⢻⣿
⣿⣿⠁⠀⠀⠀⠰⠿⠋⢁⣠⣶⡿⠛⠉⠀⠀⢀⣤⣶⠿⠛⠁⠀⠀⣀⣴⡾⠟⠋⠁⠀⢀⣤⣾⠿⠋⠁⠀⠀⣀⣴⡆⠀⠀⠀⠀⠈⣿
⣿⣿⠀⠀⠀⠀⢀⣴⣾⠿⠋⠁⠀⠀⣀⣴⣾⠟⠋⠁⠀⢀⣠⣶⡿⠟⠉⠀⠀⣠⣴⡿⠟⠋⠀⠀⢀⣠⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠛⠋⠀⠀⢀⣠⣴⡿⠛⠉⠀⠀⣀⣤⣾⠿⠛⠁⠀⢀⣠⣶⠿⠛⠁⠀⠀⢀⣤⣶⠿⠛⠁⠀⠀⣀⣤⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠁⠀⠀⣀⣴⡾⠟⠋⠁⠀⣀⣤⣾⠿⠋⠁⠀⠀⣀⣴⣾⠟⠋⠁⠀⠀⣠⣴⡾⠟⠋⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠾⠟⠋⠁⠀⢀⣠⣴⠿⠛⠉⠀⢀⣠⣴⡿⠟⠋⠀⠀⢀⣠⣶⡿⠟⠉⠀⠀⢀⣤⣶⠿⠛⠁⠀⣀⣤⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠁⠀⢀⣤⣶⠿⠛⠁⠀⠀⣀⣤⣾⠿⠛⠁⠀⠀⣀⣤⣾⠟⠋⠁⢀⣠⣴⡾⠟⠃⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⢰⡾⠟⠋⠁⠀⣀⣤⣾⠟⠋⠁⠀⠀⣠⣴⡾⠟⠋⠁⠀⢀⣠⣴⡾⠟⠋⠀⢀⣤⣶⠿⠛⠉⠀⣀⣤⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠛⠉⠀⠀⢀⣠⣶⡿⠛⠉⠀⠀⢀⣤⣶⡿⠛⠉⠀⣀⣴⣾⠟⠋⠁⢀⣠⣴⡾⠟⠉⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⢠⣶⠿⠛⠁⠀⠀⣀⣤⣾⠿⠋⠁⠀⠀⣀⣤⣾⠟⠋⠁⢀⣠⣴⡾⠟⠉⠀⢀⣤⣶⡿⠛⠉⠀⣠⣤⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠈⠁⠀⠀⣠⣴⡾⠟⠉⠁⠀⢀⣠⣴⡾⠟⠉⠀⢀⣤⣶⠿⠛⠁⠀⣀⣴⣾⠟⠋⠁⢀⣠⣶⡿⠟⠁⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⢀⣠⣶⡿⠛⠉⠀⠀⢀⣤⣶⠿⠛⠁⠀⣀⣴⣾⠟⠋⠁⠀⣠⣴⡾⠟⠉⠀⢀⣤⣶⠿⠋⠁⠀⣠⣤⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠘⠋⠁⠀⠀⣀⣴⣾⠟⠋⠁⠀⣠⣴⡿⠟⠉⠀⢀⣠⣶⠿⠛⠁⠀⣠⣴⡾⠟⠋⠀⢀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠉⠀⣀⣤⣶⠿⠛⠁⠀⣀⣴⡾⠟⠋⠁⢀⣠⣶⡿⠟⠉⠀⣀⣤⣾⠿⠋⠁⢀⣠⣴⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⣴⠿⠛⠁⠀⣀⣴⣾⠟⠋⠀⢀⣠⣴⡿⠟⠉⠀⢀⣤⣾⠿⠋⠁⠀⣠⣴⡾⠟⠋⠀⢀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠉⠀⢀⣠⣶⠿⠛⠁⠀⣠⣴⡾⠟⠋⠀⢀⣤⣶⠿⠛⠁⠀⣀⣴⡾⠟⠋⠀⢀⣠⣶⠀⠀⠀⠀⠀⣿
⢹⣿⠀⠀⠀⠀⢴⠿⠛⠁⠀⣀⣴⡾⠟⠋⠀⢀⣠⣶⡿⠛⠉⠀⣀⣴⣾⠟⠋⠁⢀⣠⣶⡿⠟⠉⠀⣀⣤⣾⠿⠋⠁⠀⠀⠀⠀⠀⣿
⢸⣿⡆⠀⠀⠀⠀⢀⣠⣴⡿⠛⠉⠀⣀⣤⣾⠿⠋⠁⢀⣠⣴⡿⠟⠋⠀⢀⣤⣾⠿⠛⠁⠀⣠⣴⡿⠟⠋⠀⢀⣤⣶⠀⠀⠀⠀⢀⣿
⢸⣿⡇⠀⠀⠀⣼⠿⠛⠁⠀⣠⣴⡾⠟⠋⠀⢀⣤⣾⠿⠛⠁⠀⣀⣴⡾⠟⠋⠀⢀⣠⣶⠿⠛⠉⠀⣀⣴⡾⠟⠋⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⢀⣠⣴⠿⠛⠉⠀⣀⣤⣾⠟⠋⠁⢀⣠⣴⡿⠛⠉⠀⣀⣤⣾⠟⠋⠁⢀⣠⣴⡿⠟⠉⠀⣀⣴⡶⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⢾⠿⠋⠁⢀⣠⣴⡿⠟⠉⠀⢀⣤⣾⠿⠛⠁⢀⣠⣴⡿⠟⠋⠀⢀⣤⣶⠿⠛⠁⢀⣠⣴⡿⠛⠉⠀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⢀⣤⣶⠿⠛⠁⢀⣠⣴⡾⠟⠋⠀⢀⣤⣾⠿⠛⠁⠀⣀⣴⣾⠟⠋⠁⣀⣤⣶⠿⠛⠁⣀⣤⣶⡿⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⢾⠟⠋⠁⢀⣠⣶⡿⠛⠉⠀⣀⣤⣾⠟⠋⠁⢀⣠⣴⡿⠛⠉⠀⣠⣴⡾⠟⠋⠁⣀⣤⣾⠟⠋⠁⣀⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠀⣀⣤⣶⠟⠋⠁⢀⣠⣴⡾⠟⠉⠀⢀⣤⣶⠿⠋⠁⢀⣠⣴⡿⠛⠉⢀⣠⣴⡿⠟⠉⢀⣠⣶⡿⠛⠀⠀⠀⠀⢸⣿
⢸⣿⡇⠀⠀⠀⠼⠟⠉⠀⢀⣤⣶⡿⠛⠁⠀⣠⣴⣾⠟⠉⠀⢀⣤⣶⠿⠋⠁⢀⣤⣶⠿⠛⠁⣀⣤⣶⠿⠋⠁⣀⣤⠀⠀⠀⠀⢸⣿
⢸⣿⣧⠀⠀⠀⠀⢠⣴⣾⠟⠋⠁⢀⣠⣴⡿⠛⠉⠀⣠⣴⣾⠟⠋⠀⣠⣴⣾⠟⠋⠁⣠⣴⣾⠟⠉⠁⣠⣴⡾⠟⠃⠀⠀⠀⠀⣼⣿
⠈⣿⣿⡀⠀⠀⠀⠈⠉⠀⣀⣤⣾⠿⠋⠁⢀⣤⣶⡿⠛⠉⢀⣠⣴⡿⠛⠉⢀⣠⣶⡿⠛⠉⢀⣤⣶⡿⠋⠁⣀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⢻⣿⣧⠀⠀⠀⠀⠀⠘⠟⠉⠀⣀⣤⣾⠿⠋⠁⢀⣤⣶⠿⠋⠁⣀⣤⣾⠿⠋⠁⣠⣴⣾⠿⠋⢁⣠⡶⠟⠁⠀⠀⠀⠀⠀⣼⣿⡟
⠀⠀⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⢠⣴⡾⠟⠋⠀⣠⣴⡾⠟⠋⢀⣠⣴⡿⠟⠉⠀⠠⠶⠛⠉⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟
⠀⠀⠀⠀⠈⠻⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣶⣶⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣶⣿⣿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⣀⠀⡀⣀⡀⣀⣀⢀⠀⡀⣀⡀⢀⣀⠀⠀⣀⠀⡀⡀⢀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠫⣨⠇⡇⢝⡦⠈⠇⠸⣠⠇⠗⢯⢸⣒⠀⠨⣓⠆⠟⢧⢸⠸⠳⡇



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⡴⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣱⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⢸⠁⠀⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢹⣿⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣐⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠯⠾⠃
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠐⠦⡠⠔⠲⢤⠤⠒⠦⡤⠔⠲⢤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣛⣛⣭⣍⣛⣫⣭⣝⣛⣭⣭⣛⣋⡅
⠀⠄⠀⠀⠀⠀⠠⠄⠀⠤⠀⠠⠤⠀⠤⠄⠀⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣛⣿⣟⣻⣿⣟⣿⣿⣛⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂⠀⠒⠀⠐⠂⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣽⣿⣯⣽⣿⣭⣿⣯⣽⣿⣯⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠀⢠⢆⠰⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣊⡥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣤⠃⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⡦⠤⡼⣶⡄⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠤⢤⣠⣼⣤⣷⣴⣴⣀
⣀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣦⣴⣤⣀⣀⣤⣤⣤⣤⣴⣴⣤⣶⣦⣴⣾⣿⣿⣷⣯⣠⣤⣬⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠂⠐⠀⠀⠒⠐⠒⠂⠘⠀⠀⠀⠀⠀⠀⠀⢰⠇⠁⠸⢹⠻⣿⠰⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡟⣸⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣆⠀⠀⠀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣾⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠿⠿⠿⠀⢹⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠻⣷⣌⡙⠻⠿⢿⣿⣿⠟⢀⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠛⠋⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⢀⣾⡏⠙⣿⡆⠀⠀⠀⣰⡟⠀⠀⠀⢀⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢸⣿⠆⠀⣿⣷⠀⠀⣼⠏⠀⠀⠀⠀⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⣿⡆⢀⣿⠇⢀⣾⠋⣀⣤⣤⡀⠀⢸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⠉⠛⠁⣠⡿⠁⣸⣿⠀⢸⣿⡄⠸⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⣴⠟⠀⠀⣿⣿⠀⢸⣿⡇⠀⠻⣿⣦⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⢀⣼⠋⠀⠀⠀⠘⢿⣄⣼⠟⠀⠀⠀⠙⢿⣷⣤⣀⠀⠉⠛⠛⠿⠿⢛⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠙⠻⢿⣿⣷⣶⣶⣶⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⡿⠏⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣶⣶⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠄⡈⠓⢄⠀⠀⡀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣇⠀⠈⠢⣠⠇⠀⠀⠟⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⡤⣑⢦⣸⣷⣦⣀⣀⣦⠎⢻⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠚⠇⠘⠛⢬⣯⠈⢿⣿⠇⠘⢿⡟⠁⠀⢠⢀⣤⠌⠀⠀⠀⠀⠀⠀⢠⣀⠀⠴⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠘⠀⠀⣹⠀⠀⠘⠀⠀⢠⣾⠟⠃⠀⠀⠀⠀⠀⢀⡖⢸⢃⠀⠀⠴⠛
⠀⠀⠀⣀⣀⣀⢡⡀⠈⠀⠁⠀⠠⣧⣃⡟⠀⢀⣄⣠⡶⠏⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠏⠰⠀⠐⣯
⠀⠠⠟⡉⠉⠉⠉⠉⠓⠐⠢⠤⣤⣤⣼⠷⠶⣿⠷⠤⠤⡀⠀⠠⠴⠂⠀⠀⠀⠀⣻⣴⢣⡆⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠂⠄⢂⡤⢦⡴⠎⠁⠀⠀⠐⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢾⣷⣶⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣀⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⢨⠋⠀⠀⠀⡀⠂⠀⠀⠀⠀⠄⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣴⠃⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠚⠀⠖⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣴⠀⠀⠀⠃⠀⠀⠀⢀⠀⢢⠀⡀⠂⢀⡤⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠇⠀⠀⠀⠀⠀⠀⠀⠐⠩⡶⢿⣷⣱⣶⣴⠦⠀⠀⠚⠂⠀⠀⠀⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⡄⠂⠀⠀⠀⠘⠁⠶⠺⢧⠩⡭⣝⠀⠠⠀⠐⠖⠶⠤⢄⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠃⠃⠀⠐⢤⠀⠀⢀⣒⠐⠂⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢸⠀⠀⠀⠻⣟⠣⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠄⠀⠀⠀⠈⠙⠲⢴⣶⣆⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢁⠀⠀⠰⢂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⠉⠉⠋⠚⠛⠲⠤⠬⠦⠤⠵⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠠⡇⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡘⠃⠀⠀⠀⣰⡏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣁⣀⣀⣀⣀⣠⣆⣀⣀⣀⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠉⠀⢈⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢿⣿⣿⠋
⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠐⢾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠉⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠈⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣶⡾⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⣴⠏⢻⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣿⣶⠄
⠀⠀⠀⢸⣿⢠⣿⣿⢟⣼⠟⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡉⠉⠁
⠀⠀⠀⠘⣿⡈⢿⣏⢸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠶⣾⣷⡶⠄
⠀⠀⠀⠀⠘⠻⢶⣤⡤⠿⠿⠿⠶⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⣴⣾⣯⣽⣤⣤⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⡴⢿⣿⠟⣿⠿⠻⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⣿⣿⣿⣿⠟⠿⢿⣷⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⢰⡇⢸⡇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠙⠉
⠀⠀⠀⠘⣧⡘⣧⡻⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀
⠀⠀⠀⠀⠈⠛⠦⢭⡬⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡠⠤⠠⠤⠤⣂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠶⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⣠⡾⠿⠠⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⢄⠈⢀⠀⠂⠀⠀⠡⠄⠤⠌⢤⣈⣀⠄⡀⠀⠀⠀⢇⠀⣀⣰⣽⡿⠞⠡⠰⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⢀⡂⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣢⠽⢟⠋⠄⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡴⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡜⠀⠀⠁⠒⣅⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠐⠄⠀⠄⡀⠀⠀⠀⠀⠔⠀⠌⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⣂⣀⡠⠤⠖⢒⡋⠉⠉⠈⠂⢄⠀⠀⣂⡠⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠀⢁⣀⣁⡀⠔⠁⠀⠀⠁⠀⠀⠀⠴⡈⢋⠢⣤⣺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠄⡄⠀⠠⠀⠁⠀⠀⠀⠀⠀⠆⣠⠑⢢⢁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠄⠃⡄⡈⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠐⠒
⠀⠀⠀⠀⠠⠒⠠⣀⢁⡒⡐⠒⣂⡂⡄⣀⢢⠀⠀⠀⠀⡄⢁⣤⣷⠚⢠⢠⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠂⢾⠃⠋⣄⣶⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⢁⡼⣗⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠿⢼⠷⠋⢠⠁⡀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⠠⡂⢧⠰⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⣀⡃⣸⢀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠠⠤⠠⠄⠰⠆⠴⠀⠀⠙⠋⠠⠇⡈⢼⠏⠁⠀⣠⡀⣠⠀⠀⡀⠀⠀⢂⡠⠀⠤⡈⠉⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠉⡱⠀⢡⣤⠀⠀⠶⠀⠁⢠⡅⠀⢄⣄⠁⠘⡋⠌⣛⣁⠀⠂⠁⠀⠁⠀⠀⢀⠀⠀⢀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡄⠀⣸⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣠⡄⠠
⠀⠀⠀⠀⢀⡄⣀⠈⠹⢿⣧⣾⣿⡿⡎⠀⠀⡠⣠⣦⢠⣤⣤⣤⡀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠐⠀⠂⠑⠀⡀⠂⠀⣄
⠀⠀⠀⠰⠿⣿⣷⡄⠄⠀⠈⣿⣯⡕⠆⠀⠀⠙⣿⣦⣺⣿⣿⣿⣤⣔⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣀⠸⢀⠀⢀⠘⡆
⠀⠀⠀⠀⠀⠈⠐⠻⣾⣥⣢⡽⣋⠛⢷⣦⡆⠀⢿⣷⠻⣿⣿⣗⠉⣉⣿⡍⠀⠀⠀⠀⣶⣶⠄⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⢀⠀⡈⠋⡆⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠐⠢⠄⠙⢿⣯⣴⡀⠈⠙⠛⣿⣿⡁⠀⠹⢿⣿⣧⢰⣿⣷⡄⠀⣀⣀⣻⣿⣦⠀⠀⠀⠀⠰⣁⡀⠀⠀⠼⡆⠠⠀⠀⢠⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠂⠀⠀⠀⠹⣿⠇⠀⠀⠀⢞⠛⣿⣿⠀⣿⡾⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣳⣤⠀⠀⠀⢸⣧⠁⠀⠀⠀⣾⠆⠸⣿⡇⣿⡖⣎⠸⣿⡯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠊
⠀⠀⠀⠀⠀⠀⢈⣿⠗⣤⣤⡀⡡⣯⠤⠀⠈⣸⣿⠂⠃⠀⢠⠉⠀⠈⠹⣿⠙⠛⠐⢼⣿⠡⠁
⡀⣤⡀⣀⡀⣶⡿⠏⠀⠉⠉⢻⣿⢻⣷⢶⡴⢿⣿⣦⣄⣨⡉⠁⠀⠀⠀⢹⣷⡇⠀⢸⣿⠙⡀
⠉⠻⢷⣿⣿⡿⠗⣶⣧⣦⣤⣠⠀⠁⠈⠉⠀⠒⠂⠍⢻⠿⡿⣿⣴⣄⡀⢪⣿⣷⣈⢻⣿⡆⠋
⢰⣼⣏⠉⠩⣻⡳⠂⠀⠋⠗⠐⢿⣂⣄⡀⠀⠀⠀⠀⠀⠀⢐⣻⢺⢿⣿⣿⣾⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠐⢤
⠙⠻⣿⣂⠀⣸⡯⣦⣄⣀⣀⣀⡼⠋⠉⠛⠷⠶⣤⣦⣰⣾⣵⣿⣶⣾⣶⣷⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⠀⠀⠀⠀⢦⢠⡀⠄⢄
⠀⠸⢿⣿⣿⠟⠁⠈⠈⠉⠘⠛⣃⣂⡀⠀⠀⠀⡺⢿⠟⠅⠠⠍⠙⡍⠑⠱⠸⢩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡀⣾⣿⣷⠀⠂⠐⢀⡈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⠋⠚⠗⠇⠘⡈⡳⠀⠀⠀⠀⠁⣠⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢑⢈⡋⠁⠈⢀⣠⡘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠓⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡸⠿⠄⠀⠀⠵⠎⠀⠛⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠂⠠⠀⠃⠀⢀⣈⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⠀⡔⠀⢁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⣇⢠⠃⠈⣆⠀⡀⣆⢲⡀⢀⠀⢀⠀⡀⢰⠀⣿⠀⣆⠀⢧⡀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⢆⠰⣸⡏⠀⢀⣽⠀⡇⠹⢌⢇⢸⠀⣿⠀⣇⢸⡄⡟⡀⢹⠀⣼⠃⡸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡱⠀⠈⠄⡻⣧⡦⢸⡟⢽⡇⠀⢈⡜⣦⠀⠿⠠⢟⡆⢣⡿⠁⡼⣿⠃⡇⠃⡘⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠙⠲⣄⢡⠃⢰⣿⡛⣿⡇⠡⡇⠀⣷⢀⣾⣿⣸⡀⢸⡦⡏⣧⡟⡇⣼⢣⣿⢠⣿⢠⠇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠠⠲⡟⡸⣿⢇⣿⢱⡄⣇⢀⢹⣾⣨⠁⣿⣥⡼⣁⣧⢿⢠⡏⡏⣸⣿⡆⣿⢋⡆⡜⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢤⠀⢀⣧⠃⡏⢸⣿⣾⢹⡹⣾⡟⣿⣿⡇⣻⣟⡇⣿⡏⢈⡾⣿⡾⡇⢻⡄⣿⢸⢳⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⠳⡈⡄⢳⢸⣿⠀⡇⢸⣿⡟⢸⡇⣿⡇⣿⢸⡇⣿⡃⠇⢸⠇⣾⠃⣿⢱⣷⣾⢠⣿⣾⣼⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⣁⢠⠘⣼⡞⠄⠙⠀⡇⠻⣿⡄⢸⡗⢿⠀⠿⢸⡏⢷⡇⢸⡾⢂⢻⠃⠿⡘⣿⡟⠈⠈⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠛⠳⠐⠒⠀⠃⠀⠉⠁⠈⠃⠈⠈⠁⠀⠐⠺⠇⠈⠁⠀⠀⠀⠘⠋⠇⠈⠠⠄⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠐⠈⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠟⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢠⠀⠀⠀⠀⡐⠃⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁
⠃⠀⠀⠀⠀⠀⡄⠀⠀⣿⡿⠀⠀⠀⠀⠎⢀⣀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣗⠀⠀⠀⢠⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠰⠒⠠⡀⠀⠀⣹⣏⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠂⠀⠀⠀⠁⠐⠀⠀⠀⠀⢀⣴⡆⠈⠘⢀⠞
⠀⠀⠀⠀⠀⠀⠑⣄⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⢆⠀⡆⠀⠀⢰⢀⣾⠟⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠐⠀⠙⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢌⡃⠉⠀⠀⣣⣾⣻⠂
⢀⢀⠀⠄⠀⠀⠀⠀⠹⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠉⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣧⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣄
⠀⣀⠀⢀⡄⠀⠀⠀⢨⡿⠈⠀⠀⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢿⣷⡄⠀⠀⠀⠀⢰⠀⠂
⠀⠈⠒⢻⣧⡄⠀⠀⢸⣟⠴⡀⠀⣿⣿⣴⡶⠥⠤⠠⠶⠀⠀⣠⡄⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⠀⢀⠀⢀⠀⠀⠀⠂⢸⣿⣿⣅⡀⠸⡆⣸⣴⡞
⠘⠓⠀⠀⠀⠠⠄⠀⠀⠉⠘⠁⠃⠛⠙⠉⠁⠀⠀⠉⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⣿⠀⠀⠀⠀⠀⠀⠀⠂⠚⠛⠉⠉⠉⠁⠉
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠀⠀⢠⠿⡆⠀⠀⠀⡐⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠘⠀⠀⢀⠃⠀⠀⡴⠋⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠇⢰⠇⢠⢦⠀⠀⡌⠀⢀⡞⠀⠀⠀⣠⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣦⠀⠀⠀⠀⣾⠹⣆⠀⢠⠀⠀⡏⢰⠀⠰⠰⢻⡜⠀⠀⠀⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⡇⠀⠘⣆⠸⠀⠈⠁⢸⡇⡌⠀⣸⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⢀⡀⢹⡄⡄⠀⠀⠘⢣⠀⡔⢰⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠑⢄⠀⠎⠀⠀⠃⡇⠀⢠⠂⠆⠀⣀⠈⢠⠃⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠈⠳⡌⢢⠀⠀⢆⠀⠁⢀⡏⠠⠀⡰⠁⡰⢁⡴⠞⠉⠁⠙⣆
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠤⠤⢄⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠐⠒⠲⠦⣤⡀⢣⠀⠘⡆⢸⢸⠁⠸⢰⠃⠠⣡⠏⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠙⡄⠇⠀⠁⠀⠈⠀⡆⠋⢠⠁⠁⣠⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⢤⡀⠀⠀⠀⠀⢀⠁⠀⠎⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⠤⠤⠀⠸⠀⠀⢀⣀⣠⠔⠒⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠤⠶⠶⠶⠤⠄⠤⢶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠉⠉⠀⣀⣀⡀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠖⠒⠒⠒⠚⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⡀⣀⣀⣀⣀⡀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢚⣉⣉⣩⣉⣹⣖⣒⠦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣡⠶⠓⠉⠉⠀⠀⠀⠀⠈⠉⠙⠓⠶⣝⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣤⠋⠁⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⡼⠁⠀⠀⠀⡴⣫⣴⣦⡹⡉⠒⠦⢄⣀⠀⠀⠀⠀⠸⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣺⠁⠀⠀⢀⣞⡾⣿⣿⣻⣧⠃⠀⠀⠁⠘⠹⢳⡶⢤⣀⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣿⠀⠀⠀⡞⣾⡽⣟⡿⡝⡜⠀⠀⠀⠀⠀⠀⠀⠈⠓⠺⠷⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠸⡄⠀⢸⠁⠈⠙⠻⠿⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡘⢦⡏⠀⠀⠀⠀⡼⢁⠎⠔⡄⡄⡄⡀⡀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡉⣦⠆⣢⢞⡵⡣⣪⢮⢊⠜⡔⡱⢁⠃⠄⡴⠠⢀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠴⢮⣕⣍⡊⢔⣕⠵⡣⢊⠜⡵⢣⢎⠜⡰⢁⢮⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡟⠙⠓⠺⢾⣵⣪⣖⡵⣫⢎⣔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡽⠀⣀⠴⢚⣡⠵⠋⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣼⡧⠊⣁⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣱⢣⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣶⠖⠒⢒⢒⠒⢏⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠈⣷⠈⢣⠹⣯⢆⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡎⠠⠀⠐⠀⠚⣧⠡⢳⢸⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠩⠀⠆⠀⠉⠰⠋⠆⡀⢳⠦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⡱⠰⠀⠐⠁⠰⠂⡰⠀⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⢠⠠⠀⠀⠂⠀⡄⠀⡄⡃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡄⡠⠀⠰⠀⢀⠀⠀⠄⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⠁⡁⠀⠆⡀⢈⠀⠀⢀⢁⠀⣄
⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠘⠀⠁⠀⠀⡀⠈⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⣤
⠀⠀⢀⡀⢰⢧⢀⠐⠀⠀⠘⠈⠁⠀⠀⡁⠈⠁⣶⣄⡜⠀⠈⡀⠀⠀⡶⣿⣤
⠀⠀⠈⠻⣾⠶⢀⠔⠒⠤⠴⠘⡥⣤⠤⡔⠒⡐⢻⣧⡛⠦⠤⢠⠤⣀⣷⡯⠜
⣠⢔⡉⠙⢡⣴⡦⣤⡤⠶⠦⣂⡴⠦⢳⢇⢦⠥⢶⢶⡅⡀⣤⣀⣦⣀⣀⢉⣑⡎⣍⡒⠦⠠⠄⡠⣠⢔⡤⣢⢔⠥⣊⢔⡠⢒⠠⡢⢀⢄⡀

⠄⠀⠀⠀⠀⠀⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⡀⢀⢰⡀⠓⠃⡈⣛⣃⡀⣈⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⠀⠀⢠⠀⢀⠀⠄⢹⣿
⡇⠀⠀⠀⠀⠀⣿⣆⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠠⣤⡈⠁⣾⣿⡇⠸⠛⠋⢉⡴⢂⡎⠉⠀⢀⣈⣻⠃⠁⠀⠀⠀⣠⠁⠀⠀⠊⠀⢀⠀⣤⣿⣨
⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⠄⠀⠀⠈⠻⢦⣽⣿⡥⡀⣀⠐⠋⢠⡾⠁⠀⠀⠀⠸⣯⡀⠀⠔⠛⠉⠋⠛⠂⠀⠀⣤⣿⠀⣿⢯⠾
⣧⡀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢰⡏⠀⠀⢀⣴⣾⣿⢿⣿⣿⣿⣷⠀⢺⣼⠃⣴⠀⠀⠀⠿⡗⠙⠀⠀⠀⠀⠀⠀⠀⢠⡄⠋⢻⠀⣰⣿⠿
⣿⡇⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡼⠀⠀⢠⣿⣿⠟⢁⣿⣿⣿⣿⣿⣷⣄⣼⣾⣟⠀⠀⠀⠀⠃⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠋⠂
⣿⡇⢀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠞⠋⠀⠠⠁⠀⠀⠸⠋⠀⠀⣾⣿⠻⣿⢻⣿⣿⡉⠊⢹⠃⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡴⢯⣤⡾
⢾⣿⣏⠀⠀⠀⡆⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⠀⠙⣿⡇⠀⠰⡦⢡⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡃⢸⣯⣹
⣽⣿⠋⢰⡇⢠⣿⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠨⠀⠀⠗⠹⠀⠀⢳⠀⢆⠀⢼⠀⠀⠀⠀⠀⠀⠀⢀⣮⣣⡀⢀⣸⡅⢸⠟⣿
⢟⠁⡴⣿⡇⣸⣿⡇⣿⣿⣿⣯⠀⠀⠀⣀⣀⣶⣄⠀⠈⡽⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⣶⣴⡄⠀⢈⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⣾⣻⣼⠇⣉⢻⡇⠀⣿⡿
⣿⡤⣿⣿⢷⣿⣿⡇⢹⣿⣿⣿⡀⠐⠋⠋⠋⢳⡘⣿⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⡇⠀⠈⢠⠆⡃⠀⠸⡀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢻⡿⠰⠃⡹⢿⡇⠀⣆⡀
⣿⣿⣿⢯⣾⣿⣿⣿⢸⣿⣿⣿⣿⣦⠀⠠⣤⠈⠃⠁⠀⠀⠤⠀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠧⠀⠀⠁⠀⠀⢿⣿⡀⠀⠀⠀⢠⠎⣼⡵⢀⡇⢱⠿⠇⣀⡌⠁
⣿⠾⣣⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⢟⣥⣤⠭⣄⡐⠂⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠈⠵⣇⠛⡇⠀⣸⡇⠀⠀⠀⣿⣇⠠⠀⡀⢈⣠⣦⡧⠞⡦⠶⢿⠀⠋⡿⠂
⣡⣶⣿⡟⣿⣿⣿⣿⢸⣷⡙⣿⣿⣿⣿⣿⣎⠉⠀⠀⠈⡀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢸⡀⠀⣿⢳⢠⡄⢴⡗⡄⠂⡀⠱⡘⠈⠁⠆⠙⡻⢎⠀⢌⢆⢹
⣿⣿⠟⠀⣷⣿⣿⣿⠀⣿⡏⢹⣿⠿⠟⠛⠃⠀⠀⠀⠀⢇⠀⢸⡇⢀⣶⠄⠀⣇⢀⣄⠀⠀⠹⠇⠀⢿⢾⡬⡷⠶⠮⣘⣲⢈⠠⠣⠄⣟⢐⢦⠨⠁⠃⠎⠳⢦⣄
⣿⡎⠛⠲⣬⣿⣿⣿⠀⣿⣷⠀⢱⣶⣿⣿⣿⡀⠀⠀⠀⠈⣆⣼⠇⠈⢰⣶⣤⡀⠈⠛⢠⣄⠈⠃⢰⣶⣼⣇⢑⡖⣾⣷⡯⣣⠀⠑⠓⠛⠊⡁⠰⣌⠈⠀⢄
⢤⠀⣠⢠⣿⣿⣿⢋⣇⠸⣿⡄⠀⢻⡿⣿⡿⣷⠀⠀⣜⢦⣹⣿⢷⣞⠀⠉⠙⠹⣿⣷⣄⡻⣷⡄⠈⢧⣿⢶⣾⣷⣿⣻⣧⠉⠋⠀⠀⠀⠀⠁⠀⢷⠖⠀⠀⠱⡀
⠁⠀⢤⣿⣿⣿⢏⣾⣿⠀⢻⣿⠂⠀⠋⢿⢿⡙⠒⠀⠉⣷⣝⣿⣼⠽⠦⠀⠀⣄⣐⡾⢿⠏⣻⠀⣦⣄⢹⣿⣿⣿⣭⣭⣽⠇⣠⣶⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⢸⣿⡿⢟⣾⣿⣿⠀⠈⠿⠟⠃⠀⠀⠈⠉⠀⠀⠀⠉⢻⠟⠡⠶⣦⢀⡀⠈⠉⠊⣸⣦⡏⢈⣋⠸⢕⠙⣩⢻⣿⣧⣽⠿⡺⠟⢁⣤⣤⡤
⠀⠀⢸⣿⠇⣼⣿⣿⣿⠀⠀⠈⠀⣽⣶⣷⡄⠀⠀⠀⠀⠀⠘⢏⡶⢂⠀⠻⣿⣆⠰⢀⠀⠻⠆⣴⣩⣿⣾⣿⣿⠶⠒⣶⡚⢪⣴⣿⣿⣿⣛⠻⠦⠌⠁⠀⠀⠀⠑
⣆⠀⣬⢻⣇⣿⣿⣹⣿⠳⣦⠀⣿⣽⢿⣽⠟⠄⠀⠀⠀⠀⠀⢺⣿⣛⠓⢆⠹⡿⣤⣿⡷⠆⠀⠹⢿⣿⣿⣿⠟⠁⠀⠈⠀⠰⣿⣿⠟⠭⠀⡾⠀⠀⠀⠀⠐⢄
⣿⡀⢿⣇⠈⠻⠉⣿⢿⣟⣻⣧⣿⣛⡀⠉⠂⠀⠁⠀⠀⣠⣴⠿⠟⠟⣽⡎⣶⣛⣿⡯⠓⠁⠀⠻⡶⢿⣿⣿⠀⠀⠀⠀⠀⠀⢽⠄⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠁
⣽⣷⣼⣿⡶⡀⣦⣟⣀⣽⣿⣏⣽⣻⣧⣄⡀⠉⠀⢠⣦⣽⢗⣤⣤⣘⣻⣿⠿⣿⣿⣷⣄⣀⣀⣰⣿⣄⠀⢡⠀⢀⡀⠀⢀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⠶⠶⠶⠶⠶⣤⡾⠛⠓⠶⠶⠶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⣴⠀⠀⢀⡤⠔⠢⠤⠤⠴⠶⠶⢦⠀⠀⢠⡀⠀⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠈⠉⠉⠉⠉⠙⠣⣄⣤⠞⠉⠉⠙⠛⠛⠋⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠊⠀⠀⠱⢤⡄⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠙⢦
⠀⢠⡟⠀⠀⠀⢀⣤⢤⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠀⠀⠀⠀⠈⣆
⠀⣾⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠸⡀
⢰⡇⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⣷
⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⢸⠀⠀⠀⠀⠀⢹⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⡇
⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣷
⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢼
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣀⠀⠀⠀⣿⡆⠀⠀⠀⣺
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠠⣶⠄⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸
⠀⢸⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣸
⠀⠈⣷⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⣿
⠀⠀⠘⢧⣄⠀⠀⠀⠀⠙⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠓⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠚⠛⠋⠉⠁⠀⠀⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠻⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿

⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⣍⢢⡀⢀⡤⢒⡦⣄
⠀⠀⠀⣠⢴⣶⢤⠸⡄⠸⠤⠴⠃⢸⠀⠻⣍⡼⣀⠤⣄
⠀⠀⢰⡃⠸⠬⠼⠀⡨⠗⠒⠋⠉⠙⠓⠢⢄⣸⠁⡴⢦⢳
⠀⠀⠀⠳⠤⡤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠘⠂⠋
⢀⡔⡺⢲⠀⢰⠁⠀⠀⠀⠠⡄⠀⠀⠈⠀⠀⠀⠈⢄⠔⢒⡲⡄
⠸⡀⠑⠋⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⡇⠟⣹
⠀⠉⠓⠊⠁⠘⡀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡤⠞⢀⡞⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠉⠉⠉⠉⠉⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡶⠶⠶⠖⠒⠚⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⡠⡖⠉⣀⣉⣩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡘⣽⠀⠀⠀⠀⠀⠀⠀⠀⢷⠙⠒⠤⠄⠊⠁⠈⠖⠛⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡠⠊⠑⠒⠂⠄⣸⠀⠀⢀⣄⡄⠠⠆⠀⠦⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈⢢⠤⠜⠹⠄⠀⠐⠀⠠⠀⠀⢀
⠀⠀⠀⢀⡴⠒⠻⡄⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠤⠚⠤⠆⠀⠠⠀⠀⠀⠂⠀⡀
⠀⠀⠀⢯⡠⠾⠴⢣⣧⡄⠀⣤⣄⠀⣠⠀⠰⠆⠀⠉⠘⡆⠀⠙⠲⠤⠤⣀⣀⣀⣠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠉
⠀⠀⠀⠀⠀⠀⠰⣇⠤⠤⠄⠐⡶⠒⠊⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠉⢳⠀⠀⢠⠖⢢⡤⠠⣡⡖⠲⡶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⡜⢲⡏⠉⡞⠙⢣⠚⢄⢤⣧⠗⡔⢢⠴⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⡍⠈⣻⠑⡖⠈⣠⣁⡴⠻⣄⡽⠋⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡄⠀⠀⢀⡼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡟⠋⠁⠀⠙⠚⣷⠀⠀⠀⠀⠙⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⢆⠀⠘⢆⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡼⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠰⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠆⠀⡀
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡄⡀
⠀⠀⠀⡄⠈⡰⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠠
⠄⢀⡾⢴⣾⢁⣆⠈⠈⡀⣀⣀⣈⣉⣁⣠⣄⣠⣤⣤⣤⣦⣤⣤⣤⣤⣄⣀⣀⣠⣤⡄⠀⠠⠀⢆⠄⠐⠆
⠀⠐⠈⠀⠄⠉⠀⠳⢮⣿⣿⠿⣿⣿⡛⠛⠉⠉⠉⠛⠛⠋⠉⠛⠿⠿⢻⢻⣿⣧⣤⣤⣤⣤⣤⣠⣦⡄
⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⢩⠙⠛⠻⠿⣿⣿⣿⣷⣤⣀⡀⢀⡀⡀⠀⢀⡀⣀⣀⣠⣤
⣲⣤⣄⣶⣴⣶⣴⣦⡤⢀⣀⣀⣀⡀⣁⠀⠀⠀⠠⠉⠂⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡀⠀⠁⠂⠘⠛⠿⠿⠿⠛⠛⠛⠛⠛⠉⠋⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⢿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣈⣥⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⣳⣿⣤⣶⣤⣍⠠⢄⠲⠦⣤⣀⣀
⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠶⠶⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠃⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⡜⢠⠁⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠘⠀⢸⡇⢠⠇⡆⠀⣷⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠂⠀⡰⠁⠀⠀⢳⠀⠀⢰⠀⢸⠁⣼⢸⠀⠀⠸⡆⠀⠀⠀⡏⠀⠀⠀⠃⡸⠀⠀⠀⠀⠂⠀⢠⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢊⣴⠁⠀⠀⠀⠀⢠⠀⣸⠀⣾⠀⣿⠇⠀⠘⠀⢹⡀⠀⠀⠁⠀⠀⠀⣦⠃⠀⠀⠀⢆⠁⠀⢨⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢀⢯⡀⠀⠀⠀⠀⢸⡀⣿⠀⣿⢸⡟⠀⠀⠂⢀⠀⢷⠀⠀⡄⠀⠀⠀⡏⢠⠀⠀⠀⢸⠀⠀⢸⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⣧⡀⠀⠀⠀⠘⣧⣿⠀⣟⡾⠃⠀⠀⢀⠆⠀⠈⣇⠀⡅⠀⠀⢰⡇⡈⠀⠀⢀⡏⡄⠀⠈⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⣟⣆⠀⠀⠀⣿⣿⢰⣿⣧⠀⠠⠀⡞⠀⠀⠀⢹⡄⡇⠉⠐⣼⣼⡇⠀⠀⢸⠀⡇⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⣿⡆⠀⠀⣿⢿⣿⡏⡿⠀⠀⣸⠃⠀⠀⠀⢸⣷⡇⠀⣼⠇⣿⡇⡇⠃⢸⡄⣿⠠⠀⢸⡇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠻⣏⠀⣀⣷⣸⣿⢰⡇⠀⠒⣿⢀⢤⣤⡆⢸⡟⣷⣆⣿⣰⢻⢣⣿⣦⣾⡇⣿⠀⡆⢾⢻⠀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠠⠿⠶⣀⠸⡇⣀⠸⠇⠉⠩⠾⣤⣻⠛⡍⠘⠁⠈⠥⣥⣁⠉⠋⠉⢘⡂⠒⠋⠀⠀⠚⠂⠔⠻⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⣾⡿⠿⢧⣄⣀⡄⠀⠀⠀⢉⡹⢿⣅⣀⣀⣀⣀⣤⠧⠤⢠⣤⡶⠶⠿⠷⣶⣀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠐⠒⠒⠚⠁⠀⠀⠈⠛⠃⠀⠀⠀⢸⢟⣒⡀⠉⠉⠉⠉⠉⠉⠙⣆⣉⣟⠯⣝⠒⠙⢿⣄⠀⠀⠀⠉⠙⢏⠉⠁
⠀⠀⠀⠀⠀⣀⣤⡽⠯⣆⢛⡶⡖⢀⠀⠠⠤⣀⣀⣠⣤⣄⡠⣤⣾⣣⣙⢯⣷⣄⣠⣤⣤⡶⢾⣷⣿⢗⣼⣿⣞⣳⣴⣷⣤⣤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠤⠤⢾⠯⣤⣤⠶⣧⣀⢃⣔⣀⠄⠀⠀⠀⠤⣩⣭⠉⢩⣿⣿⣟⣿⣟⣻⣿⣷⣟⣻⣿⣷⣬⣉⣙⠛⠃⢫⢤⠉⠉⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠉⠙⠙⠚⠟⢳⠿⠟⠒⠁⠉⠉⠀⠀⠀⠉⠉⠁⠐⠋⠋⠁⠻⠝⢛⠙⢉⢩⡭⠿⠽⣿⠟⣓⣡⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⢒⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠉⠉⠉⠉⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠄⠂⠂⢈⡀⠀⡉⠀⠀⠀⠢⢌⠔⠆⠩⠴⠇⠈⠢⠈⢀⠀⠐⠐⠠⢀⡠⠬⠤⠄⠀⠀⠀⢀⣄⣐
⠀⠀⠀⠀⠀⠉⢤⣤⣤⣥⡄⣤⣤⣤⣂⡠⣄⣅⣀⣀⣄⣠⡄⡐⠒⠂⠁⠄⠩⢄⠂⠀⡄⠀⢠⠐⠒⠀⠒⠀⠄⢀⠀⡀⠀⠑⠂⠐⠀⡀⠁⠀⠀⠠⣀⡤⠀⡀⢀
⠀⠂⠀⢀⣀⢀⠀⡉⡹⢛⢿⣚⡛⠳⡩⠷⡏⠉⡟⠻⢙⣿⡚⢷⣴⠶⣄⠲⣄⢺⣶⡆⡔⣠⣬⠼⣠⣰⣶⢴⡖⠰⣶⡶⢆⣶⣜⣶⣷⣿⣿⣲⣋⡛⣉⢀⡀⠴⠔
⠀⠀⠀⠈⠙⠺⣭⣏⡯⠟⠛⠉⠀⢠⠄⠀⠘⠒⠀⠀⠀⢸⢰⠈⠀⠀⠀⢹⠉⢷⠠⠈⠉⡉⠘⢫⠉⠉⠓⠸⣏⠎⠙⠓⡬⠋⠿⠙⠀⢟⠙⣯⣳⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠊⠙⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⢸⠀⠀⠀⠂⢰⡇⠀⠈⡄⠀⠀⢠⠋⠒⢛⣘⠀⠀⠀⠀⠀⠈⠂⠁⡷
⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠈⠻⠀⠀⠀⠀⠘⠄⣀⡠⠟⠈⣁⠀⠀⠀⠀⡀⠈⠀⡀⠘⣽⡀⡀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠠⡅⠀⠀⠀⠀⢀⠁⠤⠐⠚⠀⠀⠀⠀⠉⠉⠂⠀⠐⠀⠀⠀⠐⠒⠄⢠⡿⢄⠁⠀⠀⠀⠌⠀⣤⣰⡚⣂⣀⣐⠀⢀⠐⠀⣄⣤⣄⣠
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⣎⣷⣤⣤⣀⣤⣄⣀⣶⣶⡆⠀⠐⠀⠀⠀⠀⠠⢴⣷⠊⣿⡦⣤⣴⣦⣴⣧⣤⣤⡜⠁⡿⣉⣋⣉⣿⡽⠻⠋⢻⠃
⠀⠀⠀⠀⠀⠀⠠⡂⠀⠀⠀⠀⠈⢻⠿⠾⠳⣬⣟⡿⢿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠀⠁⣈⠟⠁⠙⠤⠈⠳⢦⡤⠄⠂⡉⠋⠣⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠐⠦⠀⡀⢀⣀⡦⢠⠆⠀⠀⢐⣏⠀⠘⢠⠂⡔⠀⠂⠐⠀⠀⠠⢀⡐⢠⡇⠀⠨⡀⠀⠀⠀⠀⠀⣀⡀⡧⠐⠀⢡⠄⣀⠀⠀⠐⠅
⠀⠀⠀⠀⠀⠀⢀⡀⡤⡌⣨⢄⣤⣠⠄⠀⢠⡜⠈⠀⠁⠘⠆⢄⢠⣡⡄⡀⢠⡀⣠⡄⣀⡄⠀⠈⡁⠤⠀⠄⣀⠀⠉⠀⡷⢶⠶⠸⠒⠛⠀⠀⢘⠂
⠀⠀⠀⠀⠀⠀⠀⡉⠙⠁⠂⠁⡁⢸⠀⠀⠀⣢⢀⢲⡄⠘⡇⠀⠉⠉⠛⢣⠚⠉⠀⡀⢰⡄⠈⢴⣶⢠⠶⠒⠂⠈⠀⠰⡅⢸⠀⠀⠀⠀⠀⠀⢘⡄
⠀⠀⠀⠀⢀⠀⣰⣾⢳⢠⠀⣾⡗⢸⡄⠀⠔⡇⠐⡋⠡⢶⠳⡀⠀⠀⠢⣆⠀⠀⡼⡟⠈⣤⡄⠨⠀⠅⠀⠀⠀⠀⠀⢀⢀⢸⢀⠀⠀⢠⡀⠁⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠘⢀⣤⠯⠺⣁⠸⡟⠤⡀⡏⢁⣾⠋⠙⣴⠋⠁⢓⠀⠈⡅⡀⠅⠀⢀⣹⣶⠐⡆⢤⠀⢀⡊⢵⠀⠝⢻⠁⠀⠸⣆⠀⠀⠀⠀⠀⠵⡆
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢀⡷⠒⠠⡸⠉⠑⠀⠹⡖⠀⠉⠀⠀⠀⠀⠁⡥⢈⠴⠆⣸⠈⠐⠰⣧⡘⢰⣭⢷⣀⢡⡄⠘⡀⢨⢀⣫⠀⠩⣆⠀⠀⠌⣳
⠀⠀⠀⠀⠕⠈⠸⠆⠔⠠⣺⠟⠁⠀⠀⠣⠀⠁⠐⠇⢠⠁⠁⠷⠐⠋⠹⠰⠆⠈⠁⣠⣻⠄⠀⠁⣏⠁⠨⡙⠀⠙⠀⠀⢈⢒⡏⠇⠁⠳⡤⣸⠥⠘⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠃⠀⠲⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠿⠧⠀⠀⡰⠄⠀⠙⠀⠣⠼⡆⠀⠀⣵⡃⠠⢄⣀⠋⢧⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⠦⡄⠀⠀⢰⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠛⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⢿⠀⠀⣼⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣤⣀⡼⠃⢀⡼⠖⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠰⢯⠀⠀⠀⠀⠀⡞⠛⠛⠛⠒⠒⠲⠶⠤⢤⣄⣀⠀⠀⠀⠻⣄⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⠀⠹⠤⠴⠦⠴⠾⣃⣠⣤⠤⢴⣇⠏⠉⠉⠙⠒⠒⠒⠤⠤⠤⡌⢹⠆⣀⣴⣋⣀⣀⣰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⣈⣳⠀⠀⠀⣠⠖⠋⢁⣀⡤⠤⡾⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⣄⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢉⣡⣤⣤⡾⠁⣠⠖⣋⡁⠀⣰⣣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣯⠘⣖⣒⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⠉⢩⡇⡼⠁⠀⠙⠃⢀⡏⡼⠑⠒⠒⠲⢤⣀⣀⣀⡤⠴⡿⢼⠏⣧⢹⠉⠉⣇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣀⣈⣷⢧⣀⠀⠀⠀⣸⢱⢣⡖⣆⠀⠀⠀⠤⠥⠤⠄⢠⡇⣾⣠⣿⣿⣀⣠⠇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠷⣼⠃⠈⠉⠓⠲⠷⠿⠤⣭⣥⣄⣀⣠⣤⣤⠤⠶⠚⠛⠉⠁⠸⡦⠤⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠈⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡇⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⢰⠛⣯⡟⣷⣦⣤⣀⣠⡄⠀⠀⠀⣶⣀⢀⣀⣤⣶⣞⣿⢸⠻⡄⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢠⠏⠀⢻⣷⣿⣍⠙⡏⣧⠙⠿⢯⠿⠟⠹⢿⣿⡞⣁⣡⠟⡿⠀⢻⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠉⠛⠿⢿⣃⣻⣷⣶⣶⣶⡶⠿⢛⣘⣫⡭⠗⠋⠁⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⢠⣞⣁⣀⣀⣀⣀⣀⣀⣀⣸⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣽⣿⣯⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣿⣀⣀⣀⣀⣀⣀⣀⣀⣳⡄
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⠈⠁⠉⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠄⠤⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⢠⠀⠋⢐⡀⠁⠀⠀⠀⠘⡄⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⡀⠀⠙⣄⠲⡆⠀⠁⠀⠀⠀⠆⠀⠀⠇⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⠀⠀⠁⠀⠀⠈⠳⢄⣀⣀⣀⠠⠊⠀⣀⠄⠸⡀⠀⢛
⠀⠀⠀⠀⠀⢔⠢⠀⢒⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⢬⡉⠁⠀⠈⠉⠈⡄⠀⢧⠀⢸⡄
⠀⠀⠀⠀⢀⠈⠠⠐⠀⠀⠀⢠⣐⠀⠀⠒⠀⠀⠀⠀⠀⡀⠠⡈⠁⠑⠀⡀⠀⠸⢻⡀⠸⡄⠈⡇
⠀⠀⠀⠀⠀⠘⠀⠀⢡⡠⠂⠰⠇⠔⠁⠀⠤⠀⢀⠞⠀⠁⠀⠹⡟⠀⠀⠁⢠⡏⠀⢧⠀⢳⡀⢹⡀
⠀⠀⠀⠐⠀⠑⠀⠀⣄⡃⡆⢠⡤⠃⠴⠂⠀⠀⣊⠉⠀⠀⠀⠀⠑⠌⠄⠀⠊⠐⠀⠈⢂⠀⢷⡀⢇
⠀⠀⠀⠀⠐⠁⠀⢦⠈⠁⠛⠀⠀⠀⢠⠠⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠘⠄⠀⢀⠀⢠⠘⡤⢄⠳⣌⢆
⠀⠀⠀⠀⢀⠔⠀⠈⠥⠴⠤⠠⠤⠤⡄⠀⠢⡃⠀⠀⠈⠢⡀⡠⠀⠀⠀⠘⠉⠸⠀⠈⠉⢡⠀⠉⠀⠈
⠀⠀⠀⠀⠘⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁
⠀⠀⠀⣠⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠠⠤⠀⠀⠀⠒⢒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢱⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣬⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⣦⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠀⠘⠋⠉⠉⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢿⡟⠀⢠⣄⠀⠀⠀⢀⠠⠀⠀⠀⠀⣄⣏⠤⠀⠀⠀⣴⠁⠀⡜⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡎⠀⠀⠘⠁⠀⠈⣿⠀⢸⠀⣼⡆⠀⠀⢠⣡⡞⡁⠠⠀⣼⠁⣏⡎⠀⡉⣸⠀⠀⠰⠇⠀⠀⠀⠀⠀⡔⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠁⠀⠀⡆⠀⠀⠈⠋⠈⢲⠀⠻⡡⠂⠀⠸⡟⢀⣷⠁⠀⢉⡠⡞⡠⠀⣠⡇⠀⠠⣀⡜⣤⠔⠁⠀⡀⠿⠁⠀⣼⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠐⠒⠈⠙⠰⣤⠀⠀⠀⠀⠀⣄⡆⢸⢠⠘⢡⢀⠀⢀⠀⠋⢠⠀⢠⡏⡰⣷⠃⢀⡴⠂⠀⠀⡉⢀⡔⠀⠀⠀⢿⡴⠁⠐⢃⠀⡠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⢮⠎⠀⠀⡹⠇⠀⠀⠁⠃⠈⠞⠀⣧⣶⢿⠀⠈⠋⠀⣟⣰⠏⣰⠆⠀⠸⣵⠋⠰⢠⠀⠀⡼⠀⢸⣠⠎⠀⣷⢋
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⠈⠁⣏⢾⡎⠀⠀⢸⠞⢀⡇⣰⠃⠘⠂⠀⠈⡧⣼⠀⡄⠀⢷⢸⣡⠞⣱⠀⠀⣠⠖⢠⣿⠇⠀⣾⠁⢀⡠⡇⠀⠰⣧⠎
⠀⠀⠀⠀⠐⠒⡿⠉⠀⢸⡇⣀⡉⢯⠄⡴⠃⠸⣆⡾⠸⠃⣶⠃⠀⠀⡀⡌⢸⠄⣷⠦⠚⠻⣡⠞⣵⡖⡟⠁⠀⠈⣧⠀⡀⣽⠞⠋⠀⣤⠀⠀⠉
⠀⠀⠀⠒⠀⠈⠛⠀⠀⢠⣧⠦⠴⡌⠞⡁⢈⣅⣬⠀⡴⠐⣿⣠⡂⠀⣧⣧⣸⡾⠹⣧⡆⢾⠏⣉⣿⡼⣰⣤⣦⡦⢾⢸⡏⠋⡀⠀⢻⢡⠀⡆
⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣽⠤⠄⣷⣷⣋⣉⣹⣦⡴⠷⢷⣿⣁⣤⣆⣿⣿⡿⡏⣡⣼⣤⣼⣿⣋⡿⢹⠙⣿⡇⢇⢘⡼⣿⣷⠃⢀⠀⢸⠀⠀⣠⠏
⠀⠀⠀⠐⠂⢀⣁⣠⡥⢴⡷⠒⠒⠛⣿⣁⣀⣬⣿⡦⠽⠿⠿⠛⢻⣍⣨⣇⣷⣧⢤⣿⡼⠛⠏⠸⣧⠇⠀⢹⣃⡸⣿⡇⣿⡟⠀⢸⣄⠘⣦⣾⠃
⠐⠒⠚⣛⣭⣭⣥⣶⣶⣿⣿⣿⣯⣭⣿⠿⠿⠛⣻⣉⣤⣼⣿⣿⣿⣿⣿⣿⣿⠿⢿⠅⢀⣀⣃⣤⣯⣤⣽⣿⣶⠿⠿⠁⡟⠀⠀⠀⠿⠀⡟
⠀⠴⠶⠖⠚⡪⠀⠉⠉⠙⠃⢀⣀⣤⣵⣴⣶⣤⣽⣭⣟⣛⣿⠟⢿⠏⢭⣠⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠆⣀⣠⣀⣀⠀⣒⡢⠨⠈⡯⡍⠁⢀⡀
⠀⠐⠀⠀⢀⣀⣤⣤⡶⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣓⣋⣡⣤⣴⣿⣿⣿⣿⣿⣿⣾⣩⡙⠻⠛⠊⠉⠀⠈⠺⠟⠛⢿⠹⠏⠁⣀⣈⣤⣐⣀⡀
⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⢛⣒⣀⣬⣭⣤⣶⡶⣶⣿⣟⣛⣛⣒⡉⠉⠛⡿⢿⡟⠛⠓⠉⠀⠁⠀⠀⠒⠢⠤⣄⣀⠨⢠⣗⠒⠒⠲⡿⠲⡗
⠀⠀⠀⠀⠙⠻⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢛⣛⣋⣭⡭⠿⠿⠓⠳⠮⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠀⠀⠉⠘⠓⠀⠀⣀⡣⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⣄⣀⣀⣀⣀⣀⣄⣂⣀⣀⣀⡠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠⠄⢠⡄⢀⡤⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡏⠀⣿⠀⢼⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠻⡄⠙⣦⠘⢧⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡟⠀⡿⠀⣸⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠋⠀⠘⠁⠘⠃⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣝⠻⠿⠟⣩⣭⣭⣙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⢛⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣼⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣘⠿⠿⢋⣼⡏⣴⣮⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣛⠻⣷⣬⣥⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡘⠿⢃⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⣀⠀⡀⣀⡀⣀⣀⢀⠀⡀⣀⡀⢀⣀⠀⠀⣀⠀⡀⡀⢀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⢫⣨⠇⡇⢝⡦⠨⠇⠸⣠⠇⡗⠯⢸⣒⠀⠨⣓⠆⡟⠇⢸⠸⠳⡇



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠈⡰⠋⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⣴⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢸⠁⠀⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⣼⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣐⣫⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠤⣄⣀⡤⢤⣀⣠⠤⣄⣀⡤⠤⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⠤⢤⣀⣠⠤⣄⣀⡤⢤⣀⣠⠤
⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⢀⣀⠀⢀⡀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⠀⢀⡀⠀⣀⡀⠀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠄⠀⠤⠀⠠⠤⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠄⠀⠤⠀⠠⠄⠀⠤⠄

⠸⡀⠀⠀⢸⠈⣇⠀⠀⠈⣾⠀⢲⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠙⣀⠀⠀⠀⣸⠀⠀⣿⠙⣿⣷
⠀⠁⠀⠀⣤⠀⣤⠀⠀⠀⠻⠄⠸⠘⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⡜⣿⡅⠖⢺⣿⡇⠀⢹⣤⣿⣿
⣼⠁⠀⢠⠿⠖⠻⡇⠀⠀⡤⡄⢀⠀⠠⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⡿⢿⠀⡦⣀⣭⡅⠀⠘⡻⠛⠃
⠷⠀⠀⣀⢠⠞⡇⣇⠀⠀⠄⡃⢸⠀⠀⠆⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⡸⡟⠀⠞⠀⣡⠻⣻⠁⠀⢰⣀⣠
⠀⠀⢀⠅⠘⠀⡁⣏⠀⠀⠀⡉⠸⠀⠀⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⡌⠁⣍⢫⠀⢈⡆⠑⣴⢿⠃⠀⢠⠉⠛
⠀⠀⢤⢀⡄⢀⣦⠊⠀⠀⣤⣤⢈⠀⢀⠏⢻⣿⣧⣀⡀⠀⠠⠀⢱⠃⢹⠸⡎⢠⣿⠁⣈⣡⣼⠀⣴⣿⣧⡀
⠀⡄⠈⠎⡏⡜⣘⡖⠀⠀⣼⢿⠘⠀⠨⠀⢸⣿⠿⠄⠔⠐⡤⡀⣦⣮⡼⠶⡃⠮⠩⡗⠋⡟⢗⠀⠈⠰⣟⠁
⠀⠀⠀⠀⡇⡇⣿⠀⠀⠀⣿⢸⡄⣀⣀⠰⢾⡷⣒⠀⠒⠀⡈⣆⠕⠈⠉⡅⣖⢉⢗⡯⣉⠫⢂⡌⢢⡀⢽⡀
⠀⠀⠀⠀⠀⠳⣿⡗⠀⢀⣿⢸⡇⢙⣤⣈⣁⡚⠁⡆⡄⠃⠄⣠⠇⠁⢴⣖⢀⣅⠚⠱⠬⢥⢢⢨⢦⣋⡎⠁⢀
⢹⡸⣦⠀⠀⠀⢨⡇⠀⠈⠛⠃⣷⠸⡍⠉⠹⢩⣃⢷⣳⡀⠁⢨⣝⢇⢪⡗⣻⢈⠂⠈⢆⡀⣀⠓⠀⠙⠽⠒⠏
⠈⠉⠏⢶⣆⡀⠀⠉⢀⣟⢿⣤⣿⣇⠑⡻⠕⣿⣿⣿⢦⣳⠀⢠⠋⠛⠋⠉⠃⢩⠀⠹⡦⡌⠁⠀⢦⡀
⡗⣶⢤⡈⢿⣿⣦⠀⠈⠫⣍⡼⣩⣨⡐⣷⡄⣿⣿⣿⡀⠉⠱⢛⠂⠀⠀⠀⠀⠈⠀⠀⡻⣴⠴⠀⠀⠙⢄
⢛⣘⣲⣾⣷⣽⣟⠃⢀⠀⠘⡷⢦⣻⣝⣿⣧⣿⢴⣿⣷⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠈⢳⡄
⣠⡟⠳⢉⠙⢀⣯⠀⣿⡿⣆⡘⢿⣏⣿⣿⣷⣶⣴⣵⡟⠃⣰⣼⣿⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠙⠀⠁⣹⣦⣼⠅⠀⡙⠁⢬⡙⠊⠛⣁⠹⡿⣿⠷⣨⡽⣿⠶⢭⡿⠁⣀⣤⣤⣤⡤
⠄⠀⠀⠉⢿⣟⠀⠀⢿⢛⣦⣈⣧⣶⣿⣀⣉⣉⢋⣍⣷⡠⢛⣴⣾⣴⣿⣿⣿⣿⣤⠀⠀⠤⠀⠀⠀⠀⠁⠢⣀
⠁⢢⣦⡀⠀⠑⠀⣿⣤⣿⢿⣿⣿⣧⣿⡍⠉⠀⢸⠦⠀⢱⢿⣿⣿⣿⣿⡯⠤⢈⡉⠉⠑⠀⠀⢀⡀⠀⠀⠀⠈
⣤⣿⣿⠿⡖⠀⠀⠙⢿⣿⣶⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⢾⣿⣿⠟⠉⡆⠈⢿⡇⠀⠀⠀⠀⠀⠈⠢⣄
⣿⣿⠹⡆⠃⠀⠈⣷⣦⣭⣻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⣿⣿⡁⠀⠀⠀⡄⠀⢻⡍⠙⠙⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠊⠁
⣿⣿⣧⣤⣤⢤⢤⢨⣟⢻⣦⡀⠀⣧⠀⠀⣠⠄⠤⠀⣠⣤⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄

⠀⠀⣴⣿⣿⣿⣿⣿⣿⣧⣿⢴⣳⣢⣾⡿⠛⠫⠡⢶⣵⣶⣿⣦⣤⣶⣀⣤⠀⢆⢒⣷⣶⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⡆
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠈⠋⠁⠐⢻⡿⠽⠿⠿⢆⣉⣻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡦
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡴⣾⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢛⣿⣿⣿⣿⣿⣿⣿⣁⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣾⣤⢀⡄⣀⠀⠀⠀⢠⡄⢺⣿⣿⣿⡛⣻⣿⣯⣿⡿⠺⠯⠉⢙⣿⡿⢿⣻⣿⣿⢺⣿⣿
⠀⢸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡷⢿⣿⣯⣿⡿⣿⣿⣵⣶⣭⣥⠿⢷⢶⠀⠀⢠⢹⡵⣿⣿⣽⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢫⡋⣠⠀⠀⠀⠉⠘⠁⢘⣿⡟⣷⠬⠛⠐⢦⠿⢤⣠⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿
⠀⢘⣿⣿⣻⣿⣯⣿⣿⣟⣯⣿⣿⣿⣿⣿⣧⡼⢫⠟⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠃⠛⠲⠶⣿⣿⣟⣻⡿⣿⣿⡿⣿⣿⡟
⠀⢸⣿⣿⣿⣛⣿⣻⣉⣿⡻⣿⢿⣿⣟⣿⣿⡯⡥⠜⠛⠁⠁⠀⠀⠃⡀⢀⠀⢀⣀⡀⠀⣀⣀⣀⣀⠀⠀⠀⠛⠟⠯⠻⠝⠋⠙⡇
⠀⠸⣿⣿⣿⣿⣿⣍⣾⡗⢿⣽⣾⣿⣿⣿⣶⢤⣄⡀⢆⣰⣀⣀⡀⠀⠀⣀⠶⣲⣤⣀⣀⣠⣤⣿⣯⢼⣿⣿⣿⣿⣷⡦⣀⣀⣾⣿
⠀⢐⣿⣿⣿⣿⣿⣿⣿⣾⡿⢛⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣭⣿⣿⣟⣛⣋⣹⣿⠿⣿⣿⣯⣤⣶⣾⣿⡿⠿⠱⢿⣿⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣀⣤⣭⣽⣿⣿⣷⣶⣶⣼⣦⣿⣿⣿⣿⣿⣯
⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠩⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⢠⣴⣶⣶⣶⣤⣶⡶⢇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠆⢰⣿⣿⣿⣿⣶⣿⣿⣿⣿⢻⣿⣿⣶⣿⣿⣿⣴⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣟⣏⣽⣿⣿⣷⣿⣿⣻⣿⣾⠛⠿⠟⠹⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⠟⢻⣿⣿⣯⣿⣦⣍⣿⣿⣋⣿⣿⡿⠿⠟⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠌⠻⡿⠃⠙⠋⠙⣿⣿⣿⡟⠁⠀⠀⣠⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠰⢢⣤⣹⡆⠀⡽⣣⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⡌⠸⠟⠋⠉⠉
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠄⢀
⠀⠀⠀⠀⠀⠾⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣅⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠈⣛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⢀⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠉⠀⢀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠀⢹⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⢠⠉⠙⠀⠀⠀⠀⠀⣸⣯⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡀⣿⠧⠀⠀⠀⠀⢀⣾⡿⣯⣿⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣤⡀⠀⠀⠀⠀⠈⢸⡇⣿⠉⠐⠛⠁
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠑⠀⣤⣄⡀⠀⠚⠀⣿⠀⡀
⠀⠀⠀⠀⠀⡤⠀⠀⣠⠀⠃⠀⡀⠀⠀⠀⠸⡟⠀⠈⣧⣀⠀⣿⣿⣧⠀⠀⠀⠀⣠⡁⠲⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⣿⠛⠐⢃⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⢃⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⠀⣥⢰⣆⠀⣦⠀⢀⣤⡤⣞⠁
⠀⠀⠀⠀⠀⣷⡄⢰⡏⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⢄⡘⢦⠠⣼⠙⢷⠇⠀⠙⡏⠁⠉⡠⠶⢠⣀⡄
⠀⠀⠀⠀⠀⢹⣇⢠⣷⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⡉⠀⠀⣀⡀⠴⠋⠀⠀⡇⠀⠀⠀⢿⡆
⠀⠀⠐⠀⠀⠸⠟⠀⠻⡄⠀⢀⡀⠀⠀⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠵⣾⣤⠉⠀⠀⠀⠀⠀⠘⠀⠀⢀⡛⣷
⠀⢂⣀⡄⠀⠐⠋⠀⠀⣾⣦⢾⠁⠀⠀⠆⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠿⣾
⠠⠀⣿⠀⠀⠀⠀⣠⡄⢿⣏⣿⠀⠀⠰⠆⣨⡃⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠠⠄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿
⠀⠀⣏⣀⠀⡈⠀⠘⣷⣜⠿⢯⠀⠀⠀⣴⠈⣿⠀⠀⠀⢸⣤⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⣄⣰⣿⠐⠋⠉⡀⠁⠀⣤⠇⠀⣀⣤⠀⠀⠀⡀⣴⣿
⠊⠀⠙⠏⠀⠀⠀⠀⢸⣿⣿⣶⠀⠀⢸⣿⣿⣿⡀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠠⡎⠀⣠⣴⣾⣿⣶⡄⢴⢡⡄⠀⠸⠇⠀⠀⠀⠀⢀⠻⡃⢹⡯
⠀⠀⠀⠀⠀⠀⠂⠀⢾⣿⣿⣿⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠠⠟⠀⠁⠐⠟⠋⣾⣿⣿⣿⠄⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣌⣠
⠀⢀⡀⠀⠀⠀⢀⢾⣶⣮⣁⡉⠀⠀⠈⣿⣿⣿⣿⠆⠀⣀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⡏⢻⡄⢠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡏⢸⣍
⡴⠉⠁⠀⠀⠀⠀⠂⠙⠛⠿⠇⠀⠀⠀⣿⣿⣿⠋⣰⣇⣿⢹⣿⣧⠀⢀⣀⣄⠀⢢⠀⠀⠀⠀⠀⠀⢠⣄⠈⠀⠀⠀⠀⠀⠀⠀⣼⣷⢂⡇⠰⡾
⢥⡀⠁⣀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢻⣷⣿⣶⣿⣿⣿⣿⣿⣿⣄⠈⠁⠛⠛⠀⠀⠀⠀⠀⠈⠀⠀⠸⠀⠀⠀⣼⡆⠀⠀⠀⢿⠀⠨⡇⠀⠆
⠂⠀⠀⣨⢠⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢻⡿⢟⣿⣿⣿⣿⡿⣿⣿⣦⡅⠄⠀⠀⠀⠀⠀⠀⠀⠀⢤⠃⠀⡗⠀⢸⡷⠀⢀⡀⠞⣸⠸⠂⠙⡆
⣶⣷⠀⣇⣰⠛⣷⣦⣤⠀⠀⠀⣄⠀⠀⠀⢀⣶⣿⠏⣽⣿⡏⣿⢻⡿⢿⡗⠀⠀⠠⢰⠀⡤⠀⠀⡀⠈⠲⠀⢧⡴⠿⣁⣐⠠⢀⣂⡀⠀⠀⠸⠁
⠙⠧⣤⡴⢧⣤⠛⣉⣤⣶⣄⣠⣄⣀⣀⠐⢻⡿⠃⠀⣼⣿⢧⢿⡆⢺⣿⣿⡄⢀⡀⣿⣤⠸⠶⢦⣌⢶⣄⠰⣿⢧⣏⣿⡛⠄⠉⠉⠀⢠⡀
⢿⡀⢿⣤⡞⠳⡶⠿⢿⡿⣾⢟⣛⣉⣉⣉⠈⠁⠀⣾⣿⣯⣿⠈⢿⡀⠘⠻⠋⠈⢿⣿⠞⠂⠀⠤⠞⡛⡏⢦⢸⠿⣿⣾⣧⣴⡆⠀⠀⠀⠀⠀⠘
⡟⠁⠀⠀⠈⢠⠀⠀⠀⢰⣐⣎⣻⣿⣿⣌⠀⠆⠀⣿⡇⣿⣿⡁⠀⢠⣴⡄⠀⠀⠀⢹⣆⡙⢶⡄⣀⠹⢡⣾⣦⣶⡾⢫⠟⣶⣾⡿⠧
⠃⠀⣴⣾⣷⣿⡇⠀⠀⠐⠉⠻⣿⣿⣿⣿⣷⣾⡀⣼⠻⠿⣿⣿⣦⣿⠻⠋⠀⠀⢀⣸⣿⣄⣀⣷⡿⠇⢠⣿⣿⡏⠀⠀⠀⢿⠋⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⢠⣦⣠⠴⢦⢠⣄⣴⠦⠰⣶⠆⣤⠀⣦⢴⠶⣄⣴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠟⠿⠹⠦⠼⠹⠇⠭⠿⠀⠿⠀⠿⠤⠏⠼⠻⠇⠿⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡄⣠⢀⣤⠀⣤⣤⢠⣤⡄⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡾⢳⡏⣼⠿⣧⢸⡇⢸⣟⡃⡿⢾⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⡤⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢋⠁⠀⠀⣰⠟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣴⠋⣡⡴⢿⣅⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡞⠁⠀⠀⠈⢳⣠⡇⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣤⠶⠶⠘⣾⡇⠀⠀⠀⠀⣸⡿⠁⣀⣈⣛⡶⢶⣴⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠖⠋⠉⠀⠀⠀⠀⠀⠀⠻⣄⡀⢀⣰⠏⢠⠞⠉⣠⡈⠙⠦⠀⠈⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠏⠉⠉⠻⢦⣿⠀⢸⡋⣻⠄⠐⠂⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣈⡙⣉⣠⠞⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣀⡀⠀⠀⠀⢠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⡀⠀⢀⡼⠻⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⣁⣘⣛⡀⠀⢸⣏⢹⡆⣀⣴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢃⡾⠁⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⡈⢩⣭⠁⢠⡾⠷⠾⢷⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢡⡶⠶⢦⡘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⢦⡴⠼⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢿⡄⠂⢨⠇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣀⣀⣸⣇⣀⣀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠠⠼⣧⡀⠙⠛⠋⣀⡾⠤⠤⠤⠤⠤⠀⠀⠀⠀⢸⡇⣤⠴⠦⠤⠦⣤⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡙⠓⠒⠛⣉⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⡇⣿⠀⣞⣳⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠦⠴⠋⠁⠙⠷⠤⠞⠉⠈⠻⠦⠴⠋⠁⠀⠀⣠⣾⢸⡇⣿⠠⣬⣥⠄⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⠐⠒⠂⠀⠐⠛⠂⠀⠀⠀⠰⠞⠋⠀⢸⡇⠻⠶⠶⠶⠶⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⡈⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡥⠻⠗⠁
⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⢀⠀⡑⢈⡐⠉⢂
⠀⠀⠀⠀⠀⠀⡄⢶⠎⡄⢉⠁⠀⣈⡤⠅⠀⠈⠰⠄⡄
⠀⠀⠀⠀⠀⠀⠈⡡⠀⠇⡐⠓⠞⢉⠄⠀⢦⢄⠄⠄⠠⠄
⠀⠀⠀⢠⠒⢢⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠙⠉⠓⢆⡀⡄⠀⠀⠀⠀⢀⡀⠀⠤⠤⠠⠤⠤⠤⣀
⠀⠀⠐⠁⢠⡮⠠⠚⡠⡂⠀⠀⢧⠀⠀⠀⠀⠀⠀⡂⠠⣇⠜⠀⠀⢀⢼⣡⡦⣤⠴⠤⡦⢤⣠⢤⣼⣦⡀
⠀⠀⠈⠫⠜⢀⠒⢀⠐⠄⠀⣤⠿⠀⠀⠀⠀⠀⢈⢮⠀⡸⠀⠀⢀⠂⠏⠀⠀⠀⢀⠀⡀⠀⠀⠐⠀⢁⢳
⠀⠀⠀⠀⠀⠜⠀⢀⢏⠀⠼⠃⠀⠀⠀⠀⠀⠠⡀⠩⡥⠁⠀⠀⢠⢸⠀⠀⠀⠀⢣⣲⠞⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠣⢀⠉⢘⡁⠀⠀⠀⠀⠄⠠⢀⠀⠈⠢⡐⠄⠀⠀⠀⢄⢇⣠⠐⠊⠉⠚⠛⠒⡤⠄⣀⡱⠁
⠀⠀⠀⠀⠀⠡⠠⠑⠄⠝⡆⠠⠒⡀⠉⠉⣰⡷⢢⣢⠮⢊⣷⡀⢀⢴⠏⠀⠀⠀⠈⠉⠉⠀⠀⠀⠢⠝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠙⠒⠉⠀⠈⠈⠁⠈⠀⠉⠁⠈⠛⠿⣧⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠂⣴⣶⣼⣶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠨⢛⠺⠁⠀⠀⠀⢀⣀⢀⠀⣀⣛⢀⣉⣛⣛⣋⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠈⠁⠈⠈⠉⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠂⡀⠀⠄⠐⠐⡈⠀⠀⠀⠀⠀⠀⠀⠘⡘⠄⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⠢⢄⣀⢂⠀⠌⠊⠌⢄⢀⢄⠀⢂⡢⠡⡀⡸⣡⣷⠚⠁⠀⠀⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣂⣠⣀⠨⠉⠀⠂⠒⠲⠲⠖⠖⠒⢲⢒⣫⣽⠋⠀⠐⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠒⠛⠚⠛⡉⠉⠁⠀⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⣠⠀⡀⢨⣎⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣀⣀⡀⣀⣤⣀⣀⢠⡀⣀⠀⠀⠀⡀⢀⣤⡀⢠⣀⣀⣀⣤⣠⢐⣾⣸⣿⣿⣰⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠈⠉⠈⠀⠈⠉⠘⠛⠻⠛⠛⠛⠛⠛⠛⠻⠟⠛⠟⠛⠛⠛⠙⢻⠿⠿⣿⠿⢿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⠋⠉⠁⠘⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣤⣶⣖⣂⣠⡀⢴⡄⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣷⣜⣄⠙⣿⣠⣆⢿⢱⣾⠠⢼⣵⢀⣇⠀⠀⠀⠀⠀⠀⠀⢠⣠⠀⠀⢀⠀⠀⠀⠀⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢿⣿⣿⣿⢿⣿⡛⠛⢻⣺⣾⣿⠄⠀⡀⣆⡆⡀⡀⣿⣿⡇⠰⣸⡇⠀⠀⠠⢱⡀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⢿⡟⠛⡛⠻⠿⠦⠀⡅⡹⢻⣷⣇⣿⣿⣧⢀⣉⣿⠀⠀⠰⣼⣼⡄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠭⠄⠁⠈⠀⢰⣉⣉⡩⣛⣿⣿⣭⣄⣠⡖⠂⠲⠷⢿⡃⠉⣁⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠃⠀⠀⠀⠻⠷⠶⠖⠶⣿⣏⡛⠭⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡘⣌⣲⢤⣀⡀⠀⠀⠀⠀⠀⣀⣠⣴⣦⡀⠀⠀⠤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄⣘⠻⠙⠉⣌⣾⣿⣾⣟⣻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠂⢈⠿⢿⡿⢿⠿⠟⡛⡙⡷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⢐⠣⠴⢦⡝⢃⡓⢠⢓⡻⣤⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠹⠇⠉⠖⢸⠟⠛⠀⠁