Resale Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠔⠒⠂⠉⠉⠁⠂⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃⠂⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢘⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠪⢕⡢⠄⠀⣀⠀⠀⠀⠀⠀⣀⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠀⠀⠀⢠⡀⠀⠈⠁⠒⠢⠤⠤⠤⠤⠤⠐⠂⠈⠉⠢⠄⣀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠁⠀⠤⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠀⠀⠀⠀⢀⣀⣀⡀⠀⠈⢁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠀⢀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⡃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠶⢦⣿⡟⢰⠘⣿⡇⣿⣿⣿⡀⣶⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡋⠷⠆⡹⢡⣴⣦⢹⡇⠻⠿⢿⡄⠶⠾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣷⣿⣿⣿⣷⣶⣾⣿⣿⣿⡏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠶⠖⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠹⣧
⠀⠀⠀⠀⠀⣠⣴⣴⣶⣶⣦⣶⣶⣶⣴⣦⣶⣦⣶⣦⣶⣾⠃⢸⡇⠘⣷⣶⣶⣶⣶⣦⣶⣦⣶⣴⣶⣶⣦⣶⣦⣦⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢸⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⠉⠉⠉⢩⡿⠁⠀⠀⠰⠆⠀⠀⠈⢿⡍⠉⠉⠉⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠷⠆⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⡏⠻⡟⣭⣥⣼⣧⣤⣤⢴⣶⣶⣶⣶⡆⠀⠀⣤⣤⣤⣤⣤⣿⣦⣬⣭⣭⣭⡙⣿⠟⢹⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢠⣤⣼⣿⣤⣤⠰⠆⠀⠀⠀⠀⠀⠀⢉⣭⣭⣭⣭⣿⣭⣭⣭⣭⡉⠐⠁⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣷⣾⣷⣾⣿⠶⢶⣶⠶⠶⠶⠀⠀⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⠀⠀⢲⣾⣿⣿⣿⣷⠗
⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣷⣾⣷⣾⡿⠀⣾⡏⢨⡅⢤⠀⠀⠿⢃⡄⣴⡆⡀⣾⡆⠀⠀⠿⠀⠀⠀⠙⢿⣿⡿⠋
⠀⠀⠀⣀⣬⠿⠛⠻⢧⣀⠀⠶⠶⢾⡷⠶⠶⢰⡿⠐⠈⣿⡌⢷⣾⡿⠟⣡⡿⢡⠇⣿⡇⠀⠀⣶⡄⠀⠀⠀⠈⢋⣠⣤⣀
⠀⠀⠀⣿⠛⠲⣤⠶⠚⢻⠀⠀⠀⠸⠇⠀⠸⠿⠟⠛⢛⠻⠷⢸⡅⠶⠟⣋⠔⠁⠀⠛⠿⠷⠿⠟⢡⣶⣤⠶⠿⣿⡿⠿⢿⣤
⠀⠀⠀⣿⠀⠀⣿⠀⠀⣸⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠻⠿⢿⣿⣿⣾⣿⣿⣄⠀⢀⡀⠀⠀⠀⠀⠀⢿⡇⠀⢸⡏⣹⠆⠀⣿
⠀⠀⠀⠈⠛⠶⠿⠶⠚⠉⠀⠰⠶⣾⣿⡶⠂⠶⣾⣿⣷⠶⠆⣿⣿⣿⠿⠿⢿⡇⢸⡇⠀⠀⠀⠀⠀⠈⠿⢶⣶⣿⣿⡶⠶⠟
⠀⠀⠀⠀⠀⣠⣾⣆⠀⠀⠀⣤⡾⢻⣿⠛⣤⡾⢛⣿⠛⢷⣬⠁⠈⠛⢸⣿⢸⡇⢸⣷⣤⣤⣤⣤⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⢀⣾⣿⣿⣿⣷⣄⠀⠀⠶⠾⠷⠶⠶⠶⠶⠿⠶⠶⠀⠀⠀⠀⢸⣿⢸⡇⢸⡏⢰⣶⣄⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠉⠹⣿⣿⣿⡏⠉⠀⠶⠶⠶⡶⠶⣶⣶⠶⢶⠶⠶⠶⠀⠀⠀⢸⣿⠈⠃⢸⡇⢸⣿⣿⣷⣄⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣇⣠⡞⣡⣴⡾⠛⣀⣸⡇⠀⠛⢷⣦⣄⠀⢀⣀⣼⣿⣀⣀⣼⣧⣈⣉⣉⣉⡙⣷⣄⢸⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣬⣥⣾⠌⠛⠛⠁⠀⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣭⣭⣥⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⡿⣻⠛⣿⢻⡟⣿⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣉⠉⢿⠉⣿⣿⣿⡏⠉⢹⣿⠋⣉⠙⣿⠹⣿⠏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡃⣼⠀⣿⣿⣿⠃⣦⠸⣿⠀⣿⣧⣿⠘⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⣷⣽⠀⣿⣿⣿⠀⠿⠀⣿⠀⣿⡟⣿⠀⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣬⣿⢿⣆⠙⠛⡇⢰⣶⡄⢻⡀⠛⢁⣿⠀⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⢰⣶⢾⣿⣿⡀⣿⠀⣤⡈⢻⡿⠀⠸⣇⢹⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣟⢈⣿⢿⣷⣿⠀⣿⡇⢸⡇⢸⠀⣿⡀⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠃⢸⡿⠻⣷⢸⣿⣿⡄⣿⡇⢸⠁⠿⠂⢹⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⣿⢸⣿⢹⣿⣏⣁⣼⣀⣶⣆⣸⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢑⣒⠢⠤⠤⣀⣀⣀⣀⣀⣀⣀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡄⠀⠀⣉⠉⠁⠒⠒⠒⠒⠂⠐⠒⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣵⠀⠀⠹⡭⢿⣶⣶⣛⣿⡦⠀⢀⢾⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⢛⣊⣁⣀⣀⠀⠀⠀⠀⠀⠀⠛⠉⠀⣜⡞⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣒⠫⠉⠉⠉⠉⡉⢉⡙⠛⠓⠒⠲⠯⠭⢍⡛⠲⠦⡀⠀⠀⢠⣺⢞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠔⠉⠀⠀⠁⠀⠀⠀⠈⠑⠹⠳⠶⢤⣤⣄⣀⣀⣠⠤⠔⠃⢤⣒⡭⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡴⠁⠀⢀⣴⠾⣁⣀⢀⣀⣀⠀⠀⠀⠀⢀⡠⠖⢒⣩⠴⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠸⠁⠀⠀⠀⠻⠭⠶⠾⠯⣝⣻⡧⠀⣠⠞⢁⣤⠞⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⣌⣑⣒⠲⠤⢤⣀⡀⠀⠐⠋⠉⡰⠁⣠⠟⣱⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠢⠭⣓⡢⠀⠠⠁⣰⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠇⡸⠁


⣿⣯⢹⣟⠿⣿⣛⢟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢷⡄
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠏⣤⡌⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣿⠃⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠃⠀⠀⠸⠀⠀⠀⢻⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⣀⣀⣀⣙⣀⣀⣀⣀⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⡭⠅⠨⣭⣥⣤⣤⣤⣿⣯⣭⣭⣭⠀⣭⣭⣭⣽⣯⡍⠀⠩⣯⠁⠈⢩⣽⣿⣿⢿⣿⡇⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⡇⡒⢐⠀⣋⡉⢉⣉⣻⡿⠒⠒⠶⠒⠖⠒⠲⢿⣯⠴⠀⠷⠵⠾⠸⠦⣼⣿⣿⢸⣿⡇⢨⣭⣭⣽⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⡧⠅⠨⠤⣿⢁⣟⠹⣿⣧⣼⡏⢸⣿⢸⣿⡧⣾⣟⣛⡛⣛⠛⣛⢛⣛⣻⣿⣿⢸⣿⡇⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣶⣆⢰⣶⣃⣘⣉⣀⣻⡟⣋⣤⣿⣿⣈⣛⣃⣼⣏⣩⣴⠛⢀⣿⣦⣍⣹⣟⣋⣈⣛⣃⣘⣛⣛⣛⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠟⢛⣻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⠛⠿⢿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⡿⠿⠛⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢀⣠⡴⠟⠛⠿⣿⣷⣶⣤⣄⣀⣀⣀⣀⣀⣠⣄⢀⣠⣤⣶⣾⠿⣿⣿⣽⣶⣀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⠛⠲⢦⣤⠶⠛⣿⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣷⡶⠾⢿⣿⠿⠿⢷⣦⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⣿⣀⣠⣴⣶⣾⣿⣟⣻⣿⣿⣶⣦⠻⣿⠀⠀⣿⢈⣿⠀⠀⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⠳⢦⣬⣧⣤⣶⣿⠿⠛⠉⠻⠟⠛⠛⠛⠛⠛⠉⠙⠃⠻⢷⣶⣾⣿⣷⠶⠾⠟⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣤⣴⣾⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣷⣦⣤⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄
⠀⠀⠀⠀⣀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⡀
⣴⣶⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣷⣶
⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠉⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡅⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣤⣶⣿⡿⠃⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⣴⣿⡿⠟⠻⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⣀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿
⠻⠿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡿⠿
⠀⠀⠀⠀⠉⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡾⣡⣶⡄⢀⣤⣐⣂⣠⣀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁⣠⣀⣀⣠⢀⣤⢶⣄⣠⣤⣦⣿⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⠿⢿⣷⣶⠿⠿⢿⣿⣿⠿⠶⠾⠿⠿⣿⣿⣿⠋⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⣿⣧⡀⠛⠛⢺⣿⡇⣀⠀⢿⣿⡇⠰⣿⣿⢿⣿⠀⢘⣿⡦⣿⣿⣿⣷⠦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣭⣭⣥⣼⣯⣤⣭⣤⣬⣭⣥⣤⣭⣥⣤⣭⣠⣬⣭⣀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠐⠾⣟⡋⣹⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⡿⣿⣟⠛⠋⡾⠿⣿⣿⣿⠛⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⠙⢿⡿⠟⠁⠉⢀⠀⠀⠉⠙⠉⠈⡿⠁⠀⠀⠀⠀⠀⠉⠁⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⣀⣠⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠂⢩⣭⣭⡟⣛⣓⠲⠶⠶⢤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡀⢂⣿⣿⣍⣿⡿⣿⣧⣾⡿⣷⡄⠐⠀⠉⠉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⡿⡉⢹⣿⣵⣿⣿⣿⣿⠿⡣⠃⠂⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⣼⠀⠀⢀⣴⣿⣷⡆⣠⣶⣬⣩⣅⠛⠋⡻⠇⠐⠁⠂⠨⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⢿⣿⣦⡀⠀⠀⠀⡿⠈⠄⣮⣻⣿⣿⣷⣿⣿⣿⣿⠏⢰⣿⡿⢿⣾⡷⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣀⣠⣶⣿⣿⣿⡿⠁⠀⠙⢿⣿⣦⡀⢸⣧⣄⣀⣈⡛⠛⠻⠟⠉⣿⣿⣿⣤⣿⣟⡛⣼⡿⠡⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢀⣀⡀⠙⢿⣿⣦⡙⠛⠛⠻⠿⠿⠿⣷⣶⣶⣶⣤⣥⣉⣉⣉⠛⠃⢂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢋⣴⣾⠷⠀⠘⠛⠿⢷⣄⠙⢿⣿⣦⡀⠀⠀⠀⢀⣀⣸⠿⣿⡉⠛⠛⠛⠿⠿⢿⣶⣶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁⠋⡥⠒⠢⡀⢀⡔⠉⠳⡌⠀⠈⠻⣿⣿⣦⠀⠀⡇⢸⠤⠤⠄⢹⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⡇⠀⠀⢸⣠⣦⠀⡇⠸⢰⣶⠀⡷⠀⠀⠀⢸⠿⠿⠃⣀⡟⡿⠒⠢⠄⣸
⠀⠀⢰⠋⢱⠀⠺⠿⡟⠋⠉⠀⠀⣇⠀⠀⠈⠿⠿⠤⠇⠀⠿⠟⠒⠓⠀⠀⠀⣸⠒⠋⠉⣁⡵⢿⣾⡷⠚⠁
⠀⡠⠾⠶⡼⡀⠀⠀⢱⠀⠀⠀⠀⢸⠀⠀⣴⠀⠀⠀⠀⠀⠀⢀⣤⠓⠀⠀⠀⡿⠖⠚⠉⠀⠀⣸⣿⡇
⠘⡧⠤⠴⢳⡼⣷⠒⠚⠁⢀⠀⠀⢸⠀⠀⢰⣌⣉⣒⣒⣀⣩⡤⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⡿⣿⠅
⠀⠹⣖⣒⣋⠗⠛⠒⠚⢻⠁⠀⠀⠘⡇⠀⠀⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⡇⠀⠀⠀⠙⠻⠯⠽⠷⠞⠁⠀⠀⠀⢸⣤⡀
⠀⠀⠀⠀⠀⢀⣀⣾⣷⣾⣷⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣷⣖
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⣀⣈⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠉⠉⠀⠀⢸⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠤⠤⠶⠖⠒⠚⠛⠛⢉⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⣿⣇⣀⣀⣤⠤⠤⠴⠶⠒⠒⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠶⢾⠀⠀⠀⠀⢸⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣿⣿⡾⠃
⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⣿⣀⣀⣀⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⡿⠿⠿⠿⠛⠛⢛⣛⣹⡯⠩⠭⠄⢤⡀
⠀⠀⠀⠀⠀⠀⠘⣇⣤⣤⣤⣤⣶⣾⡇⠀⠀⠀⠀⣿⡿⣿⠛⣛⣛⣉⣉⡿⠉⠥⠤⠄⠐⠒⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠈⡇⠀⠀⠀⠀⣿⣷⣿⠀⡅⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⣿⣿⠀⡇⠀⠀⠀⠀⠀⣿⣿⠋⠉⣴⣿⠋⣿⡆⣼⣿⠋⣻⣷⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣿⢋⣿⠀⡇⠀⠀⠀⠀⠀⣿⡿⠟⠀⣿⡇⢀⣿⠃⣿⣷⣾⠛⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢿⣿⣿⠀⡇⠀⠀⠀⠀⠘⠿⠀⠀⠀⠻⠷⠾⠋⠀⠿⠈⠛⠷⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⣿⣿⠀⡇⠀⠀⢀⣤⣶⣄⠀⠀⣤⣤⣄⢀⣤⡀⠀⢀⣤⣤⣤⠀⣴⣤⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⣿⣿⠀⡇⠀⠀⣿⡟⢹⣿⠃⣼⡟⢻⡏⢸⣿⠁⠀⣸⣿⢁⠀⢠⣿⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢸⣿⣿⡇⠁⠀⢀⡙⠻⣦⣄⣼⣿⣶⣿⡇⣾⡏⠀⠀⣿⡟⠛⠁⠸⡟⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⡇⠠⠀⠈⠙⠓⠛⠉⠛⠀⠀⠘⠃⠙⠛⠛⠀⠛⠛⠛⠀⠛⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠘⣿⣿⡇⢸⣄⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⢀⢸⡆⣤⠀⣿⡿⣿⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣿⣿⣿⡇⣿⣀⣹⣿⣿⣾⣿⣦⣾⣥⡂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣀
⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣥⡄⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢨⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡏⠉⠉⣿⠀⠀⠀⠀⣿⠉⠉⠉⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣇⣀⣀⣿⠀⠀⠀⠀⣿⣀⣀⣀⣿⠀⢸⡇⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠟⢻⡇⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⢸⡇⠀⠻⣿⣟⠷⢶⣄
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⢸⡇⠀⢀⡴⢦⡀⢀⣤⠀⢠⡄⠀⢠⡤⠤⠀⠀⢸⡇⠀⠀⠀⠉⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⠀⢸⡇⠀⢠⡙⢳⡄⡾⠼⣧⢸⡇⡀⢸⡛⢛⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⠀⠀⢸⡇⠀⠀⠉⠉⠀⠁⠀⠈⠈⠉⠉⠈⠉⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠾⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠷⠶⠶⠶⠶⠞⠛⠁






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠉⠛⢉⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄⣈⣀⡇
⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⠀⢀⡀⡈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡂⠠⠘⠁⡁
⠀⠀⠀⠀⠀⠀⠘⠃⠃⠃⡐⠘⠂⠃⠋⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢀⠘⠊⠉⢠⡔⢉⡶
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠉⣁⢀⠀⠀⠀⠀⠀⠠⠚⠁⡀⠂⠀⠈⠐⠢⠄⠀⠀⠣⡄⠈⢂⠀⢠⠏⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠄⠀⠂⢸⠆⠀⠀⠀⠀⠀⠀⠠⠠⢀⣌⡀⠀⠀⠘⠈⠀⠸⠀⣈⡩⣁⠘⠀⠀⢀⠸⡄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣀⣠⠖⠠⠐⠀⠀⠈⠉⠓⠒⠉⠁⠀⠀⠉⡀⠄⠀⠉⢀⡎⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠚⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⡴⡄⠀⢀⣈⠔⣀⡅⠘
⠀⠀⠠⠎⡈⠖⠀⠙⢧⡄⣨⡀⢀⡀⠒⠀⣀⠀⠀⠨⢀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⢀⠈⠒⢻⣗⢾⣋⣇⠀⢡
⠸⠒⠂⠀⠀⠂⠀⠀⠀⡋⠛⠠⠈⠹⠧⡠⠄⣀⣁⠀⠤⠀⠃⠀⢀⠀⡙⣅⣐⠍⠄⢧⣠⣼⡀⣀⣸⣿⣿⡿⡿⢯⠈
⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠁⢁⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠖
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⣠⣄⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⡿⢶⣿⡟⢿⣧⢀⡠⣶⣄⣀⣀⣀⣶⡤⠤⠄
⠀⢠⣤⣄⣼⣦⣴⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⣁⣴⣷⣞⣁⣹⣷⣇⢬⡾⢿⣿⡟⠁
⠀⠀⠙⣿⣿⣿⡏⣰⠛⣦⣄⠀⠀⠀⠀⢸⢦⠛⡻⣿⢏⣿⣩⣽⣽⣧⠈⣳⣿⣿⣿⣷⣤⡀
⢀⣶⣼⣿⣿⣿⣿⣿⣶⣿⢧⠄⠀⠀⠈⠀⠉⢈⠉⠐⠢⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁
⠈⢻⣾⣿⣩⣿⣿⢿⣍⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⠆
⠀⣺⣯⡿⠉⢹⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⡿⣿⣧⣿⣿⣿⠄⠀⠈⠁
⠀⠉⠋⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡁⠘⣿⣿⣿⠟⠿⠗⠀⠀⠁
⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣷⣼⣾⣿⣿⣷⣤⣤
⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣏⣿⠉⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⣶⣿⣏⡀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣼⣯⣿⣿⣿⣬⣭⣿⣿⣷⣿⣿⣿⣄⠀⠀⠀⣈⣿⣿
⠀⠀⠀⢾⡿⣿⣿⡀⣼⠂⣿⢷⣤⣠⣾⣷⣶⣴⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠰⠿⠿
⠀⠀⠀⠀⠀⠻⣿⣿⣶⡺⠏⠿⣿⣿⡿⢿⢟⣹⣟⣭⠛⢿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠉⢀⣼⣿⣿⣦⣀⠁⠈⠉⠀⢈⢿⣿⣿⣿⠿⣿⣩⣿⣏⢉⣠⣄
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠸⢿⣿⣿⣿⣿⠉⣿⠟⠂⠀⠾⣿⣿⣷⠆⣿⣿⣿⣿⠛⢻⣟⢓⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠿⢿⣿⣿⣦⣀⣠⣤⢶⣿⣯⣀⣀⣼⣿⣿⠋⠀⠀⢟⠉
⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠠⠼⣿⣷⣬⣩⡌⡜⠯⠀⠀⠰⡾⢫⠈⠍⣿⣿⣿⠶⠒⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢀⠂⠁⢿⠻⠛⠀⠀⣀⣠⣾⣦⣀⡈⢀⣰⣿⣿⣯⣀⡈⠟⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢀⣾⣷⣾⣶⠂⠛⠻⡿⢿⣿⢿⣋⣿⡥⢧⣿⣿⠃⠀⣰⣶⡾⢿⠴
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠠⠘⠉⠉⡻⠹⠐⢀⣀⢀⡈⠛⠈⠉⠙⠁⠀⣠⣶⣦⣄⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣯⡀⠀⣤⣤⣀⣠⡄⠀⢠⣿⣻⣿⣿⣦⠲⠒⠀⠀⠜⠛⡙⣹⣿⣿⣥⡀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢸⡿⣻⡟⠉⠐⠀⠀⠰⠥⡍⣤⡁⠅⠀⠀⠀⠀⠀⠁⠋⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣽⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣤⣦⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠿⠿⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠛⢦⣴⢎⣁⢑⣊⣨⣭⠛⠳⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡠⡔⣞⣩⡿⠁⣠⣄⡀⠙⠫⣕⢼⠟⠋⠃⢀⣾⣿⣿⡟⢯⡛⢲⠤⣀
⠀⠀⠀⠀⡠⢞⢭⡈⢪⣾⠋⠀⣿⠿⠿⠇⠀⠀⠈⣓⣵⣶⣾⣿⣿⣿⣿⣷⣯⣽⡁⣠⡪⢕⣦⡀
⠀⠀⣠⣟⡮⣗⡷⣮⣞⠁⠀⠀⠀⣀⠀⠀⠀⢀⡀⠉⢹⣿⣿⣿⣿⠋⠉⠉⢁⣀⣀⣀⣟⣩⣴⣞⣢⡀
⠀⡼⠓⠻⡍⠁⣈⠈⠋⠀⣿⠇⢸⣿⠀⠀⠀⠙⠃⠀⣸⣷⣿⣿⠁⣴⣿⣿⣿⣿⣿⣿⣹⡄⠁⠠⠉⠹⡄
⡼⠀⠀⠀⠘⢭⠖⢸⣀⣀⣭⣤⣤⣴⣶⣶⣧⣭⣭⣭⣴⣮⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣹⡇⠀⠀⣀⠴⢿
⡏⠀⠄⠀⠀⠀⠉⢹⢻⢻⣿⠿⣿⣿⠛⢻⣿⡟⢋⣉⣹⣿⣶⣿⣿⣿⣿⡟⠋⠉⢹⣿⣿⠿⠚⠛⠑⠤⢈
⣿⠿⠧⠄⠀⠀⠀⢸⢸⢸⡏⠀⣿⣿⠄⣸⣿⣿⠏⢩⡍⡭⣤⣴⡆⠀⢹⡇⠀⠀⢸⡏⣏⠀⢀⣀⣀⣀⣠
⠸⣶⣶⣄⣀⣀⣀⣼⡿⠈⠁⠀⠉⠁⠋⢸⣿⣿⠀⣼⢁⣍⢡⠁⣭⠄⢸⡇⠂⠀⢸⣷⣿⣅⣤⣤⣄⣔⡞
⠀⠙⢷⣀⣉⠉⠛⢻⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣇⣉⣉⣉⣉⣃⣉⣁⣸⠇⠀⠀⢸⣿⣿⣤⣴⣶⣾⠟
⠀⠀⠈⠻⢶⣭⣽⣛⡻⠿⢿⣿⢿⡿⣿⣿⡿⠿⠛⠛⢨⣿⠛⣷⣶⣶⣖⣀⣀⣀⣘⡛⢛⠛⢷⠾⠃
⠀⠀⠀⠀⠀⠙⠻⣏⣛⣶⣶⢰⣖⣋⣉⣁⣀⣒⠒⠓⢺⣿⣤⣟⡛⠳⠎⠉⠉⠛⠛⣉⡭⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⢯⣤⣬⣁⣜⣬⠹⠋⣱⣍⣚⣽⣨⣽⣷⠤⠴⠒⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⠀⡀⠀⢀⣀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⣀⣠⣠⣤⣌⣤⣤⣤⣦⣠⢔⡄⣠⣔⣤⣠⣤⡄⡤⢠⠔⠴⠠⠢⠔⠤⠶⠢⠴⠤⠦⢆⢔⣐⣪⣠⣴⣤⢒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⡏⠀⠀⠀⠀⠀⠀⠀⡤⠤⠀⢀⡤⠀⠀⡀⠀⢄⠀⠀⠠⠀⠀⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠜⠀⡜⢀⠀⡀⠉⠆⠈⠀⡏⡂⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡭⢐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢠⠀⠀⠆⠀⠈⠀⠀⠀⠀⣀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠈⢰⠀⢀⠀⠀⠀⠀⠀⠀⡏⢆⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠀⠀⠀⠀⢂⡀⠉⠀⡠⠀⠀⠀⠀⠈⢣⠄⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢘⠀⠀⠀⡠⠒⠒⠒⠠⡀⠀⢠⠄⠀⢄⠀⠀⠉⡠⠤⠄⠈⠉⠁⠀⡀⠉⠩⠥⠤⠀⠀⢠⠤⠤⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠀⢠⠀⠀⡔⠠⣐⠤⠀⡈⠀⣀⠈⡄⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⡇⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠣⣀⠑⠀⠤⡀⠀⠇⠀⠭⠄⠐⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠂⠂⢲⠀⠀⢸⠀⢰⠀⠀⢸⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣇⠀⢀⠀⢀⠁⠂⠀⠘⠘⠀⠀⡀⡀⠀⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠒⠒⠊⠀⠀⢸⢀⣸⠀⠀⢸⡄⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⠀⠘⡀⠀⠉⢁⠀⠀⠀⢀⠠⠀⠱⠀⠈⠀⠀⠀⠀⠀⢀⡙⠀⠇⠀⠒⠂⠀⠀⠀⢀⠄⠠⡀⠀⣾⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠁⠀⠀⠁⠀⠈⠉⠁⠀⠀⠑⠙⠁⠐⠀⠀⠀⠈⠊⠀⠒⠂⠀⠀⠀⠀⠀⠘⠤⠤⠃⠀⡿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠦⢀⠄⡠⢠⠄⠤⠠⠤⠤⡤⢠⠤⠤⠤⢤⠄⣤⡤⠠⢤⣤⡤⠤⡤⠤⢄⢄⡄⣠⣠⣤⣠⣠⣠⢟⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠚⠰⠥⠂⠒⠐⠊⠂⠐⠴⠦⠶⠴⠥⠮⡴⠴⠴⠦⢶⠴⠬⠤⠤⠤⠴⠴⠴⠤⠦⠦⠶⠎⠤⠰⠤⠵⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠅⠐⠀⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡡⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠁⡄⣠⣺⡩⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠅⠺⠿⠉⣾⣿⡅⡀⠄⣀⠠⠠⠴⢄⠢⠀⠄⠢⠐⠢⠒⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⣴⣿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⢿⣆⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⣴⡿⠋⠀⠀⠈⢧⡻⡄⠀⠀⣤⡆⠀⠀⢀⣴⠟⠁⠀⠀⣠⣴⠿⡟⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡾⠋⠀⠀⠀⠀⠀⠈⢧⢱⡀⠀⠛⠃⠀⣠⡾⠋⠀⢀⣴⡾⠋⠁⠀⠁⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠞⣡⣤⣤⣤⣄⡀⠀⠀⠈⣧⢧⠀⢀⣠⣾⣿⣤⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢠⡾⠛⠋⠉⠉⠛⠻⣷⣄⠀⠈⢿⣷⢟⣛⣩⣭⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠇
⠀⠀⠀⢀⣀⣤⣤⣶⣶⠿⠟⣧⡈⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢸⠁⠿⠛⢛⣻⡷⠀⠀⣰⣶⣶⣤⣤⣴⣶⣶⣶⣶⣾⠿⣦⣄⣀
⠀⠀⠀⣿⠛⠻⠿⠿⠷⣶⣶⣾⣿⣷⣶⣶⣤⣤⣤⣤⣤⣴⣾⣿⣾⣿⣿⠟⣿⠛⠁⠀⠿⠿⠿⠛⠻⢿⣿⣍⣩⣭⣭⣥⣤⣶⣿⣿⣿⣿⣷
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⢉⣽⠿⠋⣡⡿⢫⡿⠋⠁⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⠛⠛⠛⠋⠉⠉⠉⠉⡏
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⣼⠋⢠⡟⠀⠀⠀⠀⠀⣶⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⡼⠃⢀⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣀⡇
⠀⠀⠀⠘⠻⠿⣿⠿⣿⣿⣿⣶⣶⣶⠟⠁⠀⠀⢸⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣾⣿⣿⣿⣿⠇
⠀⠀⠀⣶⠀⢰⡇⠀⠀⠀⠀⠈⣹⠏⢀⣠⡆⠀⠀⠀⣸⢷⣶⣶⣦⣤⣄⣀⡀⢸⡇⢀⣠⣤⣾⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠀⢸⡇⠀⠀⠀⠀⢠⣇⣴⠿⠋⠁⠀⠀⢀⡏⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⠿⠟⠛⠉⢹⠀⠀⢠⣿⣦⠀⠀⡸⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡟⠁⠀⠀⢸⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆⢀⡟⠀⠘⣇⣰⠇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢡⡾⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⢿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣶⣦⣤⣄⣀⣀⠀⠀⠀⣸⡇⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣶⣾⣧⣶⣶⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿
⠀⠀⠀⣤⣤⣤⣴⣶⣿⠛⣭⡉⠻⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⣿⠛⠛⠛⠛⠉⢁⣴⠲⣶⣤⠀⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⠀⢹⣿⣿⣿⣿⡇⠘⠷⣶⡄⢸⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⠀⢸⣧⣈⡉⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⢷⢻⣿⣿⣿⣿⣦⣈⣙⣤⡿⠿⠛⠛⠛⠛⠀⠀⠀⢸⣿⣿⣿⡘⡄⠀⠀⠀⠈⠻⠷⠶⠛⢀⣀⣤⣤⣤⣤⣿⣿⣿
⠀⠀⠀⠈⣧⠻⠿⠿⠿⠿⠛⣋⣡⣴⣶⣿⠿⠿⠿⠀⠀⠀⢸⣿⣿⣿⣷⡹⣄⣀⡀⣀⣠⣤⡶⠿⠛⠉⣁⣀⣀⣈⣿⣿⣿
⠀⠀⠀⠀⠘⣷⣶⣶⣶⣶⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠐⠀⠉⠉⣁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⢀⣐⡍⠑⣠⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⡠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢤⠛⠶⢤⠷⢸⡷⠞⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⣀⣾⢦⣷⠠⠂⢉⡳
⠀⠀⠀⠀⠀⠀⠓⡐⢲⡎⠋⣍⠉⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢸⡧⠓⢁⠋⢉⠉⠉⠉⠉
⠀⠀⠀⡀⠀⠀⠠⠀⢨⣇⢠⠈⡑⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⡂⡒⢄⢀⡠⠐⠂⣻⠕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⢰⣁⡀⢸⢀⡀⢡⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⡌⠈⠁⠀⠈⠃⠀⡁⠀⠀⠀⠀⠐⠀⠀⠊⢉⡹⢢⣍⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⠀⠀⠀⠈⠀⠈⣡⣬⠈⠁⠉⠈⢃⣀⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢁⡈⢈⠉⡇⠀⡦⠉⢀⡲⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⠀⠀⠀⠀⡇⠀⠃⠀⠀⠀⠐⠀⠈⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠈⠀⠀⢡⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⣀⠅⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠂⠚⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⡁⠀⠀⣀⡸⠀⢸⣀⣀⣀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⣄⠀⠦⡀⠀⢀⠀⠟⡀⠀⠀⠠⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⣀⠀⢀⣀⣀
⠀⠐⢄⠂⠈⠒⠁⠀⠀⣻⡆⠀⠞⠤⠊⠠⠖⠡⠂⠴⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠦⠶⣛⢉⡩⢒⡛⠛⠻⣟⡓⠁⡀⠀⠑
⠴⠂⠀⠒⠒⠰⠷⠾⠲⠿⠿⠿⠒⠒⠢⠔⢲⠄⠈⠰⠐⡆⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⡇⠀⠈⡀⠀⠀⠀⢆⠀⠀⡄⢠⠊⠉⠀⠁⠈⢛⠂⠀⠀⢀⡀
⠐⠀⠂⠉⠀⡀⠀⠀⠀⠰⠀⡎⠐⠂⠀⠀⠀⠂⠲⠘⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠜⠈⠉⣷⡋⠀⠻⠈⠁⠉⠈⠾⡅⠈⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⠀⣠⣄⡀⠀⠀⡀⠄⠀⠘⡆⠀⠀⠣⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡧⠸⣷⠟⠃⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠉⡻⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠩⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⣠⡆⠐⠃⠇⠤⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢸⡇⠀⢰⡶⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⢀⢤⠤⠤⢄
⠀⠀⠀⠀⠀⢰⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣑⣦⡋⣐⡠⠂
⠀⠀⠀⠀⡈⠉⠘⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⡀⢀⠀⡀⠐⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠉⠛⡿⠞⡋⠀⠀⠀⢀
⠀⠀⠀⠠⠇⠀⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠒⠒⠲⠶⠶⢧⡀⣅⡞⢁⠴⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠠⠖⠠⠄⣀⠀⢰⠂⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠴⠂⢤⠀⠀⠉⠁⠀⠀⢠⠄⠙⣀⠄⠀⠀⠈⠉⠈⠁⠓⠀⠤⠆⣀⠀⠇⠀⡨⠦⠛⠉⠁
⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⣀⠀⠈⠀⠐⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢰
⠀⠀⢠⠹⣧⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⢲⠖⠊⠀⡇⠀⣀⠂⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸
⠀⠀⠈⠐⠁⢲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠸⠀⠀⠀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⢠⢀⠀⠴
⠀⠈⠀⠂⠀⠄⢻⣷⡀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⣀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣈⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⣠⣤⣶⣾⠿⣿⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢀⣁⣤⣴⣶⠿⠟⠛⠉⠁⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⣁⣠⣤⣶⣿⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠛⠂⡉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⣀⣠⣤⣶⣾⡿⢛⠩⣀⠀⠀⠐⢨⠙⠿⠖⠐⠀⣀⣀⣠⣤⣴⣶⣶⠿⢿⣿
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⣀⣤⣶⣾⠿⠛⠛⢉⡼⠿⠴⠀⠀⠉⣀⣀⣤⣤⣴⣶⣶⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠉⠀⢴⣶⣿⠿⠟⠉⠁⠀⢀⣈⣀⣤⣤⣶⣶⣾⣿⠿⠛⠉⠉⠉⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣤⣶⣶⣾⡿⠟⠛⠛⠉⠉⢀⣰⡟⣁⠊⢀⣨⣧⣤⣄⠀⠈⢂⣻⣷⡀⠀⣀⢊⣠⣤⡈⣀⢸⣿⡆⢘⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠂⠈⡏⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡿⠟⠋⠩⢉⠭⠙⠛⢿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢋⠀⠁⢀⣤⣿⣤⡀⠀⠐⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣿⣿⠀⠀⢀⣀⠀⠄⠀⠀⣿⠇⠀⠀⠀⣾⡁⣿⠸⠿⠀⠀⠈⠈⣿⡄⠀⢀⠐⣀⡀⠢⠀⢸⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣿⣿⢰⠀⣿⣿⡧⢈⠀⢸⣿⠀⠀⠀⠀⠈⠻⣿⣶⣄⠀⠀⠀⠀⣿⡇⠀⠆⢸⣿⣿⠆⡁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⠀⠀⠈⠉⠠⠂⠀⠀⣿⡄⠀⠀⠀⣾⡆⣿⠈⣿⠀⠀⢀⢀⣿⠃⠀⠈⠀⠉⠁⠔⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⠀⡀⠈⠛⣿⠛⠁⠀⠠⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣹⣷⣦⣄⣒⣈⣐⣀⣤⣾⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⣀⣄⣐⣈⡦⠀⠀⠀⠀⠀⠀⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣶⣶⡆⠀⠂⠀⠀⠀⢀⠀⠀⢈⠉⣡⢾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠹⣷⣦⡀⡆⠂⠂⠂⠀⢠⠀⠀⠀⠹⢿⡇⡸⠊⡴⠃⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⢠⡏⠀⠀⠈⢝⣌⠓⡄⠀⢀⠐⠚⠂⠀⠀⠒⡰⠋⠀⣼⠃⠀⠀⠈⢷⡄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⢷⡟⠀⣿⣿⡃⠈⢊⢦⣿⠀⠛⠁⠀⠀⠋⠀⠀⠁⠀⣸⠃⢰⠿⡏⡅⠈⢿⡄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣐⠖⠀⣡⡾⠁⠀⠃⠂⠀⠀⠀⠩⣻⣤⣤⡀⠀⠀⠀⠀⠀⣠⢦⠏⠀⠘⠂⠢⠃⠀⠈⢾⣄⠃⠸⡂
⠀⠀⠀⠀⠀⠀⠠⠈⠄⠀⢾⡂⠀⠀⢣⠀⠾⣿⡇⠸⠿⠷⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⣿⠇⠀⡿⡟⡇⠈⡿⠀⠈⣃⠀⠘⠆
⠀⠀⠀⠀⢆⠀⠀⠀⠨⣌⢫⠁⠀⠀⢽⢰⠛⠛⠛⠒⠒⢲⣦⠀⠀⠾⡟⡆⠀⣶⣗⡇⠀⠀⠀⠉⢙⢻⠉⠉⠉⢹⡆⣅⠀⠀⠿⠠⠁⠘⡀⡠⡀
⠀⠀⠀⠐⠀⣀⠀⡴⢠⣄⠂⠀⠐⠰⢻⠈⠶⡶⠶⠶⠶⢾⡋⠀⠀⠑⠒⡆⠐⠒⠒⠓⠂⠀⠐⠚⠛⢺⣦⢴⣤⡾⠋⡇⠀⠀⠀⠁⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠈⠀⡂⡁⡨⠀⠹⢸⡾⠾⠀⠀⠀⠁⣁⠁⠁⠀⠀⠀⠀⠀⠃⠀⠘⠂⢌⡑⠾⠇⠀⠀⠈⠇⠂⠂⠊⠁⡇⠀⠀⠀⢢⠈⠁⠀⠂⢁
⠀⠀⠀⠀⠀⠀⠂⠄⠄⠂⠉⢀⣘⡃⢺⠀⠀⠰⠙⠯⠽⠀⣽⠄⠸⠿⠿⡇⠀⣄⠀⣄⠀⠀⢠⣤⠀⠀⣿⡇⢿⣿⢠⣅⢦⣌⢡⡀⢣⡄⢰⢀⠤⣀
⠀⠀⠀⠀⠀⢀⠐⠀⠠⠂⠲⠋⠀⠌⠈⡂⠀⠀⢀⣆⠀⡆⠀⠀⠀⣉⡉⠁⠀⠀⠁⠁⠀⠑⠀⠀⠀⠠⠇⢀⡀⡠⡼⠟⣗⠈⣟⢭⡢⣄⡘⠛⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠠⠐⠀⢹⣀⠀⠀⡅⣀⣆⣀⣀⠀⣀⠑⠬⣲⣀⣀⡐⢲⣖⣒⣒⣒⠞⠃⠀⠉⠁⠀⠈⠻⠀⠱⣍⡉⠙⠛⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠙⠰⠲⠳⠖⠲⠞⠁⠀⡀⠏⠀⠀⠰⠢⠎⠄⠴⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠐⠐⠂⠦⠷⠒⠐⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣬⠉⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⢠⠄⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⠈⠁⠀⠀⠀⢉⠴⡌⠁⢀⡀⠀⠀⢤⣀⠠⠚⠅⠁⠰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢂⣀⠒⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⣍⡐⢒⠀⡠⠀⠀⠀⠀⠀⢙⣶⠈⠀⠀⠐⢲⠆⢠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠠⠤⢤⡀⠐⠉⠲⠀⠀⠀⠈⠉⠍⠑⡀⠀⠀⠀⠀⠀⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠈⠑⠀⠀⠁⠆⡘⣀
⠀⠀⠀⠀⠀⠀⠠⠡⠂⠀⠀⠀⠀⠀⠈⠠⣤⠀⠀⠀⢀⠁⠀⠀⠐⠐⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠒⠢⡄⠈⠁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠂⠀⢀⡄⠀⠀⠀⠀⠀⠀⢠⡄⠀⠈⠄⠀⠀⠀⢸⠀⠀⢰⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠐⢀⠹⡄⠀⠀⠅⠐⠀⠀⠀⠀⠀⢀⣹⣄⠀⠈⢂⠀⠀⢸⠀⠀⠀⠀⠀⠴⢾⠊⠀⣀⠀⠀⠀⠀⠷⠤⠍⠄
⠀⢀⡤⢑⡒⠀⢿⠀⣀⠀⠀⠀⠁⠀⠒⠀⠄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠡⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⢀
⠀⠀⠠⠈⠐⠀⠀⠓⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⢀⣀⢠⡀⠀⡀⠑⣸⡇⠀⠀⠀⠀⠀⢰⣦⠤⠽⢦⠀⠀⢸⣯⡖⠀⠉⠃
⠀⠀⠀⠀⠀⢀⡠⠀⢠⠀⠤⢤⠀⠉⠐⠠⠀⠀⠀⢰⡀⠀⠀⠀⡀⠀⢤⡿⠄⠀⠠⠈⠑⡀⠀⠛⠋⠈⠉⠉⠀⡀⠸⠤⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⣉⠠⢀⠀⠀⠀⡂⠀⣀⡴⠃⠀⠀⣸⡇⠀⠀⠀⠈⠀⢸⡄⠀⠀⠀⠠⠀⣷⠒⠲⣦⣤⣤⣭⣼⣶⣾⣬⣤⣤⣤⣤⣤⣬⣅
⠀⠀⠀⠀⠀⠀⠙⠲⣆⠠⠀⠈⠙⠉⠉⠀⠀⢀⡔⠀⣧⣀⣤⡤⠤⠤⣼⡓⠒⠶⠚⠛⠭⠽⠤⠐⠀⠀⠀⠘⠋⠉⠉⠉⠉⠩⠤⠤⢶⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣤⣤⡤⢤⣴⠲⠛⠩⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⠖⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠄⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠀⠀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠅⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠄⡠⠀⠠⠂⠀⠀⠀⠒⠀⠀⠀⠒⠐⠊⠊⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠄⠄⠀⠠⠒⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠈⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠘⠻⣶⣦⣄⡀⠀⢻⣷⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣄⢻⣷⡶⠿⠿⠿⠿⠿⢿⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣤⣀⣀⣀⣀⣀⣀⣀⡙⣿⣧⣿⣷⣶⣶⣤⣤⡀⠀⢀⣨⣼⡿⠟⠻⠿⣶⣦⣤⣀⡀
⠀⠀⠀⣀⣀⣠⣤⣴⣶⣾⡿⠿⠟⠛⠛⠿⠿⣿⣿⣿⣿⠿⠿⣿⣿⣿⡿⠛⠉⠉⠙⠛⢿⣿⡟⠋⠁⠀⠀⠀⠀⠀⠈⠙⠛⣿⣷⣦⣤⣀
⣶⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⣿⣦⣬⣿⣿⡀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣶⣶⣶⣶⣶⣶⣶⣾⣿⣯⣁⡈⠉⠛⠿⣷⣦⣄⡀
⣿⣯⠙⠿⣷⣦⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡾⠿⠛⠛⠉⠉⠉⢛⣿⣷⣄⠀⠀⠀⠀⠀⢀⣿⣯⣀⣤⣤⣄⣀⠀⠀⠈⠉⠛⠿⣿⣦⡀⠀⠀⣉⣹⣿
⣿⣿⠀⠀⠈⠙⢿⣿⣶⣶⣶⠿⠻⣿⣉⡁⠀⠀⠀⠀⠀⠀⣀⣤⣾⠏⣹⣿⢿⣷⣶⣶⣾⣿⣿⡿⠛⠋⠉⠛⠻⣿⣦⡀⠀⠀⠀⠈⣿⣿⣾⠿⠛⠋⢹
⢿⣿⠀⠀⠀⠀⠀⢽⡿⣿⣶⣄⢸⣿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠛⢁⣴⠟⠁⠀⣠⣿⣏⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⣿⡷⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⢰⣿⠃⠈⠳⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠏⠀⠀⠀⣿⣿⣴⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⣦⣤⣶⣶⣿⠟⢋⣁⣼⣿⠀⠀⠀⢸⣿⡟⠛⠉⠀⢸⣿⠻⣿⣦⣄⡀⠀⠀⣀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸
⢸⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡿⠟⠛⠋⠙⢿⣿⡿⠿⣿⣿⠀⠀⠀⠘⣿⣇⠀⠀⠀⢸⣿⠀⠉⠻⠿⣿⣿⢿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⢿⣿⡀⠀⠀⠀⠹⣿⣆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⣧⡀⢀⣀⣀⣬⣿⣦⡄⠐⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠸⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⢿⣿⡿⠿⠛⠛⠉⠉⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣧⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢻⣿⡀⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⢿⣧⠀⠀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⢻⣷⡀⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿
⠀⠀⠀⠀⠻⣿⣄⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⢀⣠⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢀⣠⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⢸⡇⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣠⣴⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⢸⣿⡏⠀⠀⣀⣠⣴⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣼⣿⣷⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠟⠋⠁
⣿⣿⣿⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢟⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⡤⠴⠖⠌⠃⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢁⠀⠀⠠⠀⠀⢘⣥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢴⢆⠀⠀⠀⠠⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⠇⠀⠂⠀⣀⠄
⠀⠀⢠⠃⠀⠀⠀⢠⠋⠈⠉⠒⡷⢄⣤⡆⠀⢸⡇⠀⠀⠀⠈⠹⣧⠀⠀⠀⠀⠀⢘⣅⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⢀⢀⡠⠀⠘⠷⠙⠒⠛⡋
⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⡇⠄⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠋⠉⠈⠁⠀⠀⣠⠄⠀⠀⠀⠈⠂
⠀⠀⢪⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢠⡤⠤⠤⠔⠚⢱⡆⠀⠀⠁⠀⠀⠀⠀⣴⣧⣠⡄⠀⠀⠀⣠
⠀⠀⠀⠣⣑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣀⣀⣠⣠⡤⢤⠄⡟⣿⢧⣝⣒⣚⣽⠋
⠀⠀⠀⠀⠈⠁⠒⠋⠡⠒⠚⠛⠛⠦⣱⠄⠀⠀⠀⡆⠀⠀⠀⠿⠝⠒⠺⡠⠀⠀⠀⠀⠁⠠⠀⢐⣂⣈⣉⣉⣉⣤⣍⣉⣈⣀⣉⣉⣍⢉⠁⠈⠻⢯⣿⠿⠋
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢃⠡⣠⠤⣐⣒⣋⡩⠬⠭⠅⠙⠓⠛⠛⠋⠁
⠀⠀⠀⠀⠘⡕⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢀⢀⣠⠄⠀⠀⠀⠀⠈⠖⠊⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠪⡐⠄⠀⢀⣀⡀⠀⢀⢀⠾⣀⡩⠤⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⡄⠒⠒⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣿⠋⠀⠀⣷⠀⠀⠀⠀⠀⠱⡀⢀⠀⠀⠀⠀⢀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠀⠀⠀⠘⠀⠀⠀⢸⡄⠀⠂⠀⠀⠀⢻⠘⠳⣤⣶⠶⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⠀⠀⠀⣀⡈⢢⢴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣼⠇⠀⠲⠒⠠⣤⣀⢀⣀⡤⠴⠦⠴⠼⢏⡁⡀⠘⣿⣿⡄⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⡿⠄⢠⡤⠖⠋⠙⠉⠉⠁⠀⠀⠀⠐⠀⠀⠈⠱⢶⡙⣿⠃⠖⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⢿⡿⢾⣇⡰⠊⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠈⢻⣄⠠⡃⡀⠒⠐
⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⠴⠁⠀⠀⡾⢻⡏⠻⣦⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢻⣿⣯⡐⡀⠀⠄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡀⠸⣇⣸⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠿⢿⡁⠒⢀⠅
⠀⠀⢨⠀⠀⠀⠁⠉⠀⠀⣈⡩⠁⠀⠙⣿⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣾⠟⠂⠉
⠀⠀⠀⠀⡄⠀⠀⣀⠀⠀⠂⠀⠄⢀⡀⢹⡀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠠⠘⠋⣠⣷⣦⣄⡀
⠀⠀⠀⠀⠐⢀⣐⠀⠀⠀⠀⠀⠀⠀⡳⣤⣇⣠⠟⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⢀⡆⢀⣴⡏⡁⠒⠍⣿⣷⠆
⠀⠀⠀⠀⠰⠀⣒⡎⠄⣀⡀⠀⠀⠀⢳⡀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣠⣾⣿⣿⣿⣕⡬⣭⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠯⢀⠒⠒⠀⣨⣄⣈⣿⣦⡀⠀⠀⠀⠀⠀⠀⠢⣿⡿⠋⣨⡿⠿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠿⡇⠀⠀⠀⠀⠀⠞⢁⣾⡯⢇⡀⠀⠉⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⢰⣿⡏⢄⣛⣮⢶⣿⡟⠁⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣭⣵⣿⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⡄
⠀⠀⠀⠀⡒⠢⡤⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⠀⠀⢠⠤⢤⡿⠤⠤⡧⠤⠤⠀⠀⠀⢰⠚⠇⡆
⠀⢠⠤⠼⡖⠒⠛⠗⠂⠀⠀⠐⠒⠲⡶⠦⣧⣧⣤⠄⠀⠀⠁⠀⠀⠁⠀⠐⠚⠒⣾⠾⠠⣦⣇⣄⣀
⠀⢸⠀⠀⠀⠀⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡇
⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠀⡀⠀⢰⠀⠀⠀⠄⠀⠀⣀⡀⠀⠀⡀⠀⠉⠀⠐⠂⢀⡇
⢀⣅⠀⠀⠀⠀⣀⣀⡄⢀⠀⠠⢠⠀⠒⡀⠀⠀⡸⠂⠐⠀⠂⠀⠃⠉⠁⠀⡿⠿⠛⠛⠻⠟⠀⢸⣿⣏
⠀⠀⠉⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠐⠒⢀⣶⡳⠟⠋⠉⠈⠁⠀⠒⠀⠁⠒⠒⠒⠒⠶⠀⠙⣛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠤⠤⣄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠛⢄⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⡆⠈⢳⡀⠀⢹⡤⠴⠖⠒⠒⠒⠂⠂⢄⡜⠁⠀⠀⣀⣠⣦⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⡀⠱⡚⠉⠙⣄⠀⢇⠀⠀⠀⠀⠀⠀⣠⠋⠀⢀⣴⠋⠁⠀⠘⣆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠁⠀⠹⣦⡱⣄⠀⠘⣆⠘⡄⠀⠀⠀⠀⡴⠁⣠⠔⠃⣀⡽⢦⣀⠀⢸⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⡳⣄⠘⡆⢹⣦⡀⢀⠞⣡⣞⡥⠖⠋⠁⠀⢀⣩⣷⣄⡇⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢻⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣿⡞⠉⢩⡿⠛⠉⢁⣀⡤⠴⠚⣋⣉⣀⣀⣼⠇⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⣿⡀⠀⢸⠉⠒⠚⠛⠛⠛⠛⣉⣉⣩⡭⠥⠖⠋⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⠀⠉⠢⣄⣀⡤⠴⠖⠋⠉⠀⠀⢀⣨⠽⠻⡏⠁⠉⠉⠙⠯⣍⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⢨⡇⠀⠀⠀⣀⣠⠴⠚⠋⠁⠀⠀⠈⢢⡀⠀⠀⠀⠈⠳⢦⡀⠀⢀⣀⠤⠒⠋⠉⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠢⣀⠀⢸⡇⠀⠀⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣀⣀⡤⠖⢻⡟⠉⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠑⠼⣇⠀⠀⣿⠈⠑⢦⡀⠀⠀⠀⠀⠀⢀⠠⠄⠊⣯⠁⠀⠀⢸⡇⠀⠀⠀⠀⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠻⣤⡇⠀⠀⠀⠈⠢⢀⠠⠐⠈⠀⠀⠀⠀⢸⠄⠀⢀⣸⡧⠤⠶⠚⠉⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⢈⡗⢄⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⣀⡼⠓⠛⢹⡏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣸⠀⠀⣼⠁⠀⠈⠒⢦⡀⣿⠀⣀⣠⠴⠚⠉⠀⢻⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠀⡟⠀⢰⠇⠀⠀⠀⠀⠀⠉⡟⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣸⠇⠀⣾⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠸⣇⠀⢀⣀⣠⣤⠼⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⡀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣀⡤⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢸⠀⠀⠀⢀⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢸⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠚⠁
⣿⣏⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⢶⡄⠀⠀⠱⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⣀⣀⣀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡷⠤⣤⣙⣦⣄⠀⠙⣆⢣⠀⠀⠀⠀⠀⠀⡠⠃⢀⠔⠉⠀⠀⡘⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⡈⠙⠻⠷⣤⣈⢙⣠⣤⣤⡀⡠⠜⡡⠔⢁⣀⣀⣀⣔⣁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠠⠀⡀⠀⠉⠛⠒⠒⠒⠊⢹⣀⠀⢡⡏⣐⠛⣉⣉⣁⣀⣀⣀⠀⠉⠳⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⣄⣀⠠⢤⣤⡄⠁⠒⠒⠒⢒⠶⠾⣿⣆⣸⡇⠀⠙⣦⠨⢭⣉⣀⠉⠀⠁⣰⣧⠴⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠈⠁⠈⠒⢶⡎⣧⢀⣈⣉⣉⣁⠰⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠤⠤⢄⣀⣀⡤⠖⠇⢸⣦⡀⠀⠀⠉⢻⡇
⠀⠀⠀⠀⠀⢀⠁⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡀⡸⠀⠸⡇⠉⠛⠲⠒⠋
⠀⠀⠀⠀⠈⠓⠒⠛⡇⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠃⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⠀⠀⢸⡃⠀⢠⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡾⠉⠢⣸⠀⠀⢨⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠷⠒⠛⢆⢠⠇⠀⠀⢹⠀⠀⠸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡾⠀⠀⠀⢸⠀⠀⠀⠈⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⢆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠈⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡰⠀⡆⠀⠀⢸⠀⠀⠀⠘⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡜⠀⠀⡇⠀⠀⢸⠀⠀⢀⠠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣠⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠢⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⣄⡀⠀⡇⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁
⣿⣏⢹⣟⠻⣿⣟⠟⡻⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡭⠋⠉⠉⠉⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠴⠦⢤⣤⣀⠀⠀⠀⣿⢮⣅⣀⣀⣀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡫⡞⠉⠀⠀⠀⠀⢙⡇⠀⢠⡿⣦⣄⣉⣉⣉⣁⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡛⠶⢤⣤⣤⡤⢶⣿⡇⠀⢸⡟⠶⣬⣭⣭⣭⡭⣾⣿⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠟⠶⣤⣤⣤⣤⣾⡟⠁⠀⠀⠛⠦⣤⣤⣤⣤⡤⠿⠋⢀⣀⣤⠴⠞⠋⡡⠴⠞⠛⠦⣉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡙⠓⠶⠶⠶⠖⢻⣿⠇⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠶⠶⣛⣉⣤⣤⠶⠶⠚⠛⠋⠉⢀⡙⢿⣿⣿⣿⣷⣄⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠙⢿⣿⣿⣿⣷⣄⠈⢻⡀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣟⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠙⢿⣿⣿⣿⣷⣬⡃⠀⠀⠀⣀⡤⠞⣋⣥⠶⢿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡛⠷⣄⠀⠙⢷⣄⠠⢄⡀⠀⠀⠀⠈⠛⠿⠶⠤⠌⠻⣿⣿⣿⣿⣦⢖⣛⣭⢶⣛⣭⠶⢚⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣛⢦⣌⠳⣄⠀⠉⠳⣄⠙⢶⣤⡤⠤⠤⠀⢀⣀⣤⡴⣾⣿⣿⣿⣿⡿⠿⣛⣩⡥⠶⣛⣻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡙⢷⣝⢷⣌⠳⣦⡀⠈⠻⠦⠶⠶⢖⣛⣻⡭⢿⣞⣿⠿⣿⣿⣿⡷⠖⣛⣭⡵⠖⠛⢉⡴⢖⡛⠛⠛⠛⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢷⣝⠷⣌⠻⣦⠴⠶⠚⣛⣩⡭⠶⠚⣋⣥⠴⢾⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⣾⣄⠋⠀⠀⠀⠀⢀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢷⣌⠳⣤⡴⠖⢛⣉⣥⠶⢚⣋⣭⠶⠚⠋⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⢿⣍⠙⠛⠒⠒⠛⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢷⣤⠶⢛⣫⡥⠶⠛⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣿⣬⣉⡙⠛⠒⣚⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠶⣻⠝⠉⠉⠉⠛⢶⡄⠀⠻⣄⣉⠉⠉⠉⢉⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣁⣀⠀⠀⣀⣀⣴⡇⠀⠀⠈⠉⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣉⡉⠉⠉⢉⣩⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣧⣁⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣆⡦
⠀⠀⠀⠀⣠⠎⡵⠶⣦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⠠⠀⣸⠆⠀⠀⠀⠀⠀⡔⠃⠀⢄⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⢰⠉⢹⡆⠀⢀
⠀⠀⢀⠔⠁⠀⠡⠲⠏⠀⠀⠀⠀⠄⠀⠀⢀⡔⠀⠀⠀⠀⢀⣀⢈⠀⠀⠀⠄⠀⠠⡂⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⢄⡴⠊⠁⠀⠀⠀⠉⠉⠀⠀⠢
⠀⠐⠁⠀⠀⠀⣀⢂⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠃⠀⠀⠉⠉⠄⠀⠀⠀⠙⡀⠀⡠⠤⠄⠦⠀⠈⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠉⠄
⠈⠀⠀⠀⡴⠋⠉⠀⠀⠀⠉⢢⡀⠀⠀⠀⡇⠀⠀⠀⠀⡌⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠇⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢒⠍⠈⠁⠉⠉⠀⢹⡆⠀⠄
⠀⠀⠀⢸⠀⠀⠀⢰⢂⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢐⠃⠀⢸⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⢁⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣇⠀⠹⠁⠀⠀⢰⠒⠒⠚⠃⠀⠐
⠀⠀⠀⠘⡀⠀⠀⠸⣸⠀⠀⠀⣱⠀⠀⠀⠆⠀⠀⠀⡈⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⠀⢠⠀⠀⠀⢸
⠀⠀⠀⠀⢇⠀⠀⠀⠘⠣⡉⠁⠀⠀⠀⠀⢨⠀⠀⢰⠀⠀⢀⢻⠀⠀⠀⡂⠀⠀⠀⢜⠀⠀⠀⡀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠘⡄⠰⠀⠀⠀⠘⠒⠒⢲
⠀⡄⠀⠀⠀⠑⢀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠘⠀⠀⡎⠀⠀⠈⠉⠀⠀⠀⡂⠀⠀⠀⠥⠀⠀⠀⠇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⢀⣀⣀⣼
⠀⠁⠀⠀⠀⣀⠠⠍⢦⡀⠀⠀⠀⠇⠀⠀⠀⠆⢰⠀⠀⢀⠤⠄⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⢸
⠀⠠⠀⠀⠀⡄⠀⠀⠘⡝⠀⠀⠀⢐⠀⠀⠀⢀⡆⠀⠀⢰⠀⠐⠀⠀⠀⡃⠀⠀⢀⡇⠀⠀⠀⠀⡄⠀⠀⠰⣀⣀⣀⡀⡠⠀⢸⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠣⠃⠀⠀⢸⠀⠀⠀⢸⣀⣀⢀⠎⠀⢀⠀⠀⠀⣅⠀⠁⢸⠃⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⣿⠀⠀⠀⠸⠤⠤⢄
⠀⠀⡇⠀⠀⠈⢄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠈⠙⠁⠀⠀⠀⠑⠀⠀⠀⠀⠡⠤⠤⠤⠒⠒⢈⠁⠀⢰⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡆⠀⠀⠀⠀⠉⠀⠐⠀⠁⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠚⠈⠉⠀⠉⠉⠁⠉⠉⠀⠀⢀
⠀⠀⠘⠄⣀⣀⠀⠄⠤⠄⠄⠆⠂⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠠⢄⣀⠀⠀⢀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣓⠄⠰⡱⠙⠦⠠⢀⣩⠤⢀⠝⡦
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠈⠁⠀⠀⠉⠛⠒⠀⠒⠛⠋⠉⠁
⠀⠀⠀⣀⠤⣆⡒⠺⡺⢻⡅⡀⠲⣦⠴⠀⠀⠁⢐⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠰⢤⣀⡀⠀⢀
⠀⠠⠎⠘⠒⠛⠒⠬⠠⣈⠽⠛⠚⠁⠀⠀⠀⠀⠀⠈⢡⠄⠀⠀⠀⠀⢀⠖⠀⠀⠠⠂⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠠⠔⢠⠞⠂⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠿⣥⠭⡅⠂⠀⢀⢄⠞⠁⠀⠀⢀⠀⡂⠤⣀⠠⡀⢀⣼⠇⠒⠒⠀⣲⣤⣤⢀⣀⣠⡷⢶⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢘⠲⡀⠀⢀⠄⠠⠂⠁⠀⠀⠀⠐⠃⢈⡠⠤⢍⡿⢀⠾⢇⡀⠀⠀⠈⢚⣈⣡⠁⡠⢄⡀⠹⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠒⠒⣩⠔⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠉⠁⠀⠀⠀⠢⠀⠀⠀⠉⠀⠀⡀⠞⠩⠝⡟⡳⠁⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠰⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢆⢀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⠀⠸⠀⠀⠀⠀⠀⠊⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠢⢧⣀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠲⠥⠠⠄⠀⠀⠀⠐⠒⠦⠒⠂⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠕⣒⠀⠀⢰⠽⠒⠰⡦⠤⣔⢃⢷⣮⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠖⠒⠒⠒⢀⣢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢝⠚⠉⠁⠊⠀⠑⠫⣢⡰⠂
⠀⠀⠀⠀⠀⠀⣀⠀⡀⣀⣀⡠⣄⠀⠺⠄⢲⣆⣀⠨⣟⠐⠯⠕⠶⠤⠤⢤⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢥⣀⠐⣀⠀⠀⠈⠑
⠀⠀⠀⠠⡊⠁⠀⠏⠃⠁⢠⣄⡜⢢⠀⠈⠀⠀⠀⠈⠁⠛⠬⠤⠤⣥⡤⠤⠍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠉⠀⠉⠐
⠀⠀⠀⢠⡁⠂⢅⠱⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⡖⠚⠒⠲⠄⡀⠄
⠀⠀⠀⠈⢏⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠯⠷⡷⢄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠉⠊⠸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠆⢁⣠⠬⡈⠦
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣾⠁⢀⡴⠂⢰⠆⠀⣳⠦⡆⠀⣠⠖⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⢾⣿⠠⢼⣇⣀⢼⣀⠴⡇⢰⣇⡴⣧⣀⠸⣇⡠⠀⠀⠠⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⣻⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⡋⢹⠀⠀⠀⠀⠀⠀⠀⢠⠎⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠻⣧⠀⢀⡴⠂⢰⠂⢀⣿⠎⠀⣠⠒⡶⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢸⣄⣀⡽⠃⢸⣇⣀⣼⣀⠼⣧⣀⡠⣿⣁⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠢⠀⡈⠀⢈⠑⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠂⢜⠿⠀⠀⠀⢀⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠮⠀⠀⠄⡀⢀⣷⠀⠀⠀⠂⠀⠀⠄⢀⠀⠀⠀⠀⠀⣀⣀⣀⣭⣭⠀⢤⡀
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠰⡤⠎⠘⠂⠀⠀⠐⢀⣻⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⠚⠀⠀⠀⠀⠀⠀⠈⡇⠀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⣀⣬⣭⡸⢶⣶⣲⣦⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠀⣦⠐
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⠶⠏⠄⠀⠉⢹⠆⠐⠌⣀⠆⣀⠀⠀⠠⠤⠤⠀⠀⠀⠠⠇⠴⡤⣠⠈⠀⣙
⠀⠀⠀⠀⠈⠁⠦⠄⠀⣀⣤⠤⠆⠁⠐⠒⣒⣳⠂⠀⠀⠀⠀⢸⠀⠖⠦⢠⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠠⡀⠀⠀⠀⠐⠊⠙⠞⡛⡓⡀
⠀⠀⠀⠀⠀⠀⡆⠀⢀⡀⠠⢎⠋⠉⠉⠁⡘⠙⠲⢤⣀⣀⡀⢈⠁⡀⠬⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⣐⣸⠰⠀⠠⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠡⠄⠰⠤⣄⣀⡠⢒⣀⣀⣶⣱⣚⡓⣳⠆⣀⣀⣀⣀⠄⠀⠀⠈⡁⢁⣀⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢇⠀⠉⠉⢁⡘⠉⠉⠉⠉⠉⠁⠉⠉⠁⠀⠀⢸⠀⠀⠀⠀⠐⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠃⠄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠁⠉⣁⣁⡁⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠤⠤⠬⠭⠭⠭⠭⠭⠭⠭⠥⠤⠄⠀⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡠⠤⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠢⡀⠀⠈⠪⡉⠐⠂⠔⠁⠀⠀⡠⠊⡹
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⡲⠏⢉⡒⠈⢐⣄⣀⡈⣦⠎⣀⣀⡔⠪⠔⣊⠉⠲⢄⣀
⠀⠀⠀⡤⣒⠊⠉⠀⠀⠀⠀⠄⢀⣀⡀⠁⣂⣬⠭⡿⣤⠼⡯⣥⣄⠈⢁⣀⡀⠀⠜⠀⠉⠉⠒⡢⡄
⠀⠀⠀⡆⠀⠉⠑⠢⠤⣠⡄⣒⡩⠥⠒⠉⠁⠂⠉⡠⠋⠢⣀⠁⠀⠁⠐⠢⠍⡒⢤⡤⠔⠊⠁⠀⡆
⠀⠀⠀⡇⠀⠀⠀⠀⢀⠗⠋⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠈⠣⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠢⣄⣀⢀⡴⠁⠀⠀⠀⠀⢀⠔⠉⠉⠒⠢⢄⣀⣀⡤⠐⠊⠉⠢⡀⠀⠀⠀⠈⠂⠀⣀⡤⠂
⠀⠀⠀⠀⡇⠀⢋⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⡗⢄⠀⠀⢠⠛⠉⠀⡇
⠀⠀⠀⠀⡇⠀⠈⢆⠀⠀⢀⠜⠓⡧⢄⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡠⡷⠊⠢⡴⡇⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠈⠣⡤⠃⠀⠀⡇⠀⠈⠉⠒⠤⢄⣀⣃⡠⠔⠊⠁⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠧⢄⡀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⢀⡠⠇
⠀⠀⠀⠀⠀⠀⠈⠑⠢⠧⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠧⢄⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡠⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⣀⢸⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠓⢤⠀⠀⠀⠀⢀⠴⠒⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔⢲⣄⢳⠀⠀⣰⠃⢀⠴⠒⠦⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠙⢎⢧⣠⠇⢰⣋⠴⠊⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠛⠒⠚⠛⠒⢺⠆⠀⠀⢯⠤⠤⠶⠥⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠛⠛⢦⠀⠀⠉⠀⠀⡴⠉⠉⠳⣆⠀⢸⠁⠀⠀⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠤⣄⡀⠀⠀⠀⡼⢁⡔⡂⠀⡧⠀⠄⠀⠀⡇⠠⠙⣦⡘⣆⡼⠀⡴⠋⠀⣀⣀⠙⡆
⠀⠀⠀⠀⠀⡜⢁⣠⣄⡀⠉⢦⡀⠀⡇⣾⠃⠀⡰⠃⣀⣄⣀⣀⢱⢄⡀⠘⢧⢳⣇⡜⢀⡴⢋⡠⠊⢀⡇
⠀⠀⠀⠀⠀⢣⡈⠑⠤⣉⣳⡀⠱⠶⢣⣡⠴⠞⠓⠉⠁⠈⣇⠈⠉⠉⠙⠓⠲⠆⠍⠁⣜⣉⣁⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠙⠢⢤⣤⠤⢼⠂⠈⠈⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠉⠉⠙⠓⢢
⠀⠀⠀⠀⠀⢰⠒⠉⠁⠀⠀⠀⠆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⣇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢡⠀⠀⠀⠆⠂⠈⠀⠀⠀⢩⠀⠀⠀⠙⠀⠀⠀⠗⠀⠠⠄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠤⠀⠀⠈⠈⠄⠀⠀⠰⡀⠀⠀⠀⠈⠙⡆⠀⠀⡄⠀⠀⢀⣀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⠠⠀⠚⠀⠀⠀⢃⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⡈⠀⠀⠁⠀⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⣆⣀⣀⠴⠴⠒⠉⠉⠒⠒⠲⠤⠤⠴⣄⣀⣀⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡤⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠐⠇⠰⠄⢘⠈⠦⠠⠐⠐⠀⠤⠔⠦⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠈⠈⠀⠀⣀⢀⠀⡀⠀⠀⠀⠈⠀⠀⠁
⡷⢙⠆⠀⠀⠀⠀⠀⢂⠀⠈⡉⢉⠉⡉⣉⣈⢉⡸⡦⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢨
⡐⠀⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠂⡇⠀⠀⠀⠀⠀⠀⡁⠉⠉⠑⠎⠐⠀⠀⢀⠀⠀⠀⢃⠀⠀⡀⢀⠃
⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠶⠾⢻⡄⠀⠀⢣⠠⡄⢠⠇⠠⠀⠤⠈⠅⠤⡅⠀⠀⠂⠠⠤⠁⠈⠉⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢀⠀⠀⢠⠂⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠂
⠒⠀⠀⠈⠀⡀⠸⢀⠀⣀⠀⠞⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠠⠀⠘⠔⠀⠀⣀⠤⠦⣤⣤⡤⣄
⠀⢰⠀⠀⠀⠰⠊⢨⣿⡇⠁⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⡼⠃⠠⣚⠛⢻⠿⠨⠷⠀⠀⠀⣠⡌
⠁⠀⠀⠈⠁⠀⠈⠀⠠⠙⠷⠶⠤⠶⠾⠆⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣤⢥⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⢀⠁⠀⠀⠸⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠃⠀⣠⠀⠀⠀⠀⠐⠐⠐⠁⠃⠀⠀⠀⠀⠀⠀⠀⠄⠐⠄⠉⢤⠁⠀⢀⠀⠀⠘⠀⢀⣀⠀⠃
⠀⠁⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⡀⠀⠀⠒⠀⠀⠀⠘⠁⠀⠀⠀⠀⢃⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠦⡅⡸⠀⠀⠈⠆⣀⡠⠂⠀⠀⠈⠈⠁
⠀⠐⠒⠒⠒⠐⠀⠀⠂⠄⠤⢤⡴⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠈⠄⠉⢐⠀⠀⠀⢀⣶⠀⠤⠄⠘⠑⠲⠶⠖⠋⠓⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢀⡀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠦⠤⠴⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⣇⣀⠀⣀⣒⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⢀⠔⠀⠀⠈
⡾⠯⡧⣹⢚⡄⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠃⠀⡂⠀⠃⠀⠀⠀⣀⡄⠀⠼⠉
⠀⠀⠐⠾⢌⠅⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⠛⠀⠒⢷⠀⠀⠀⠀⠀⠀⡀
⢠⠀⠀⠀⡙⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠈⠀⠀⢠⠂⠀⠀⠀⢠⣏⠈⠀⠐⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡜⣄⠐⢀⣿⠀⠀⠀⢀⢀⠀⡀⠳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠘⠛⠀⠀⠀⢠⠀⠈⠈⠠⠇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠛⠛⠀⠀⠀⠀⡏⠀⠀⠀⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠈⠀⠠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠠⠀⠀⠀⠀⠁⠀⠠⡑⠀⠌⠀⠐⠀⠀⠁⠀⠑⠀⠁⠀⠀⠀⣔⡖⠁⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠺⠃⠀⠀⠀⠀⠀⢠⣀⣀⢠⠀⠀⠀⠸⡇⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠈
⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃⠀⣂⠀⠋⠀⠀⠀⠀⢀⠮⠸⠵⡆
⠠⢤⣦⣄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠐⠻⡦⠱⠯⢯⠈⠉⠉⠈⠁⠉⠈⠉⠅⠀⠂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣆⡀⠀⠀⠈⠀⠀⠀⠀⢠⣴⡦⡀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠈⠆⠠⢀⠂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡄⠀⠋⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡗⢃⡄⠀⡦⠠⠤⠤⠤⡍⠀⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠
⡂⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⡁⠀⠀⠎⠛⠀⠀⠀⠘⡇⠀⠀⠀⡏⠀⠀⠀⠀⠈⢀⡀⠙⠀⠀⠀⠤⢄⠀⠂⠀⢀⣠⢄
⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡢⠃⠀⠀⠖⠢⠀⠀⠀⠀⠀⠀⣧⡀⠀⣠⠃⠀⠀⠠⠈⠑⠈⢛⡆⠀⠀⠀⠀⠀⠀⠐⠐⠁⡠⠞⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠆⡀⠀⠀⠀⣠⠀⠀⣤⡔⠲⠂⠠⢀⠼⠀⠀⠹⢄⠀⠀⠘⠄⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠖⠀⠐⣤
⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⠀⠀⠸⠀⠀⠿⠄⠀⠀⠀⠀⢶⠄⠑⠐⠶⠴⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠐⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠅
⠀⠀⠀⠀⢠⡀⠀⠀⠈⠃⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⢿⡄⠀⡀⢠⡟⠢⣀⢔⡠⠃⠀⠠⠀⠴⠀⠀⠲⠠⠤⠀⠀⠀⠀⠀⠀⠀⠔⠤⠠⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋⠀⠀⠀⠀⠙⠻⣿⣦⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⢀⣀⠀⠈⢻⣿⣾⡿⠿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⣴⠟⠳⠶⠶⠛⢉⣷⣾⡿⠟⠉⠀⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⣠⠞⠁⠀⠀⢀⣠⣶⣿⠟⠉⠀⡀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⢠⡾⠋⠀⠀⣠⣶⣿⠟⠋⠀⣠⡴⠟⠙⠶⣤⣤⠶⣦⠀⠈⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠴⠏⠀⣠⣴⣿⠿⠋⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⣀⣴⣾⠿⠋⠁⠀⠰⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⢰⣶⣾⡿⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⢀⣴⣾⡿⠟⠁⢀⣀⠀⠈⢿⣦⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢋⣠⣾⡿⠟⠉⢀⣠⡶⠋⠁⠀⠀⣾⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⣀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣶⣿⠟⠉⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⢻⣷⣤⣴⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⢀⣴⣾⡿⠋⠁
⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠰⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⣿⣧⠀⠀⠀⠀⣠⡴⠟⠁⢀⣤⣾⡿⠛⠁
⠀⠀⠀⢀⣾⡿⠋⣿⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀⣤⣿⠇⠀⠀⠰⠞⠉⢀⣠⣾⡿⠟⠉
⠀⠀⠀⢸⣿⡁⠀⠙⣿⣦⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⢿⡆⠀⠀⢀⣠⣶⣿⠟⠉
⠀⠀⠀⠈⢿⣷⣦⡀⠈⢿⣷⡄⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠻⣿⣆⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⣠⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣜⣿⣷⡀⠈⢻⣤⣤⣤⣤⣀⢀⣠⡶⠋⠁⣀⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣄⠀⠁⠀⠀⠀⠙⠛⠁⢀⣴⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠀⠀⢀⣤⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣤⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⢂⠔⣈⡔⠊⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡠⣪⢚⠥⠚⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡤⠔⣚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠰⠑⠁⢼⠀⠀⠀⠀⠀⠀⠂⢀⣶⠶⠞⠺⢿⡖⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠤⠄⢀⠃⠀⠀⢸⠀⠀⣤⡤⠴⢖⠛⠙⡇⠁⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠁⠀⠀⠈⠰⠠⠆⠼⠶⢯⡇⠀⠀⢸⢸⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⠤⠖⢈⣀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠉⠀⠀⡘⠀⠀⠐⠗⠀⠀⢸⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠘⢀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠸⠀⢸⡇⠀⠀⢸⠀⢠⣷⠦⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠘⠠⠀⠠⠀⠀⠀⢠⠰⠀⠀⠃⠀⠀⠀⠀⠐⠀⣹⡇⠀⠀⣸⣿⣻⡿⢶⣾⣯⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠈⠂⠐⠨⠀⠀⠠⢰⡈⠋⠉⠙⢹⠀⢹⡗⠀⢨⣿⣿⠿⣧⣾⣯⣽⣿⡇
⠀⠀⠀⠀⠀⠸⡇⠄⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⣖⣊⡇⣁⣾⣷⣸⢶⣷⡿⢛⠚⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⡇⠀⠈⠉⠛⡟⡟⠛⠊⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠉⠐⠀⠄⡀⡗⠃⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠛⣻⣿⢿⡿⠷⠖⠒⠐⠶⠤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣿⣎⠻⡀⠀⢀⣴⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠻⣿⣿⡄⣷⠀⣼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣍⣭⣿⣿⣿⠿⠿⠆⡉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢡⣾⣿⣿⣿⢿⠋⢿⣧⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣿⣿⡿⠃⠞⣀⢈⡉⠃⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠁⢀⣤⣿⣾⣧⣄⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣽⡇⠀⣾⣿⣻⢸⡟⠛⠃⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠙⣿⣿⣾⣇⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⠿⠿⠄⠀⢀⢸⡟⣿⣿⣆⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠐⣷⣶⣶⣦⡤⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣇⣧⣿⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⠉⠛⠿⣿⣷⣴⣭⣿⣿⣿⣿⣷⣆⣠⠤⢲⣿⡏⢻⡿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⣸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡽⢛⣫⢤⣤⣼⣿⣷⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆
⠀⠀⠀⠀⢈⣿⣷⣶⣶⡦⣤⣤⣉⡙⠃⠀⠀⣀⠤⠊⣹⣿⣦⠀⣸⣦⣤⡄⠀⢀⣀⣤⠖⠋
⠀⠀⠀⢠⣤⣀⣉⢉⠉⠛⠛⠻⠿⢿⣿⣟⣉⡤⠔⣲⣿⣿⣿⣿⣶⣺⣾⡆⣲⠿⠉
⠀⠀⠀⠘⠿⠿⢯⣿⣿⣶⣶⣤⣤⣀⡤⠟⠓⢊⡉⠭⠃⠀⠈⡉⠉⠉⢹⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⠒⠉⠁⠀⠀⠀⠀⠀⣓⡿⠀⣚⣅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣯⡀⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⣀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⡴⠦⠌⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣤⣀⠐⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⢀⣠⣀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣣⣤⣾⣿⡿⣠⣤⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⣼⣷⣶⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢀⣴⣾⣧⢿⣿⢫⣴⣬⢻⣿⢧⣿⣶⣄⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⢻⣿⣿⠀⢰⣿⣿⣿⡀
⠀⠀⠀⠀⠘⠻⠿⣽⣿⣷⠹⢿⠿⢰⣿⣷⡽⠿⠟⠀⠀⠀⠀⠀⣀⣴⣿⣿⣤⣾⣿⣿⣦⣄⣹⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠛⠻⢱⣿⣿⣿⣷⠙⠛⠃⠀⠀⠀⠀⠀⠀⠐⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁




⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⢗⣤⣔⢿⣿⣿⠂⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣴⣶⣿⣶⣶⣶⣶⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣯⣅⣿⣿⣿⣇⣽⣥⣄⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣬⣭⣭⣼⣻⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⡿⣿⣿⣿⣿⡛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢀⠎⠀⠀⡃⠀⠀⠀⡆⠀⠀⢨⠀⠀⠀⢐⠀⠀⠱⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⣠⣮⣤⣤⣤⣮⣤⣤⣤⣧⣤⣤⣤⣥⣤⣤⣬⣤⣤⣤⣼⣤⣤⣤⣵⣤⣤⣤⣵⣄
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡸⢇⠀⠀⡨⢇⠀⠀⢨⢇⠀⠀⡸⢅⠀⠀⡸⢇⠀⠀⠨⢇⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠀⣠⣱⣪⣥⣤⣵⣪⣥⣤⣭⣨⣤⣬⣅⣬⣤⣤⣵⣊⣅⠀⠑⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡏⠀⠀⠀⢸⡇⠀⠀⠀⢹⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⡟⠛⠛⠛⢻⡟⠛⠛⠛⢻⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣧⣠⣤⣤⣼⣧⣤⣤⣄⣼⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⡿⠿⠿⠿⢿⡿⠿⠿⠿⢿⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⢀⡀⣰⣀⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣆⢀⡀
⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣆⠀⠀⠀⡀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣄⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⣶⣾⣦⢀⣄⢀⣠⣤⣤⣄⠀⢸⢻⣻⣻⣻⣳⠀⣀⠀⣭⣭⣽⠀⣤⢸⣿⣿⣿⡇⠂⢰⣿⣿⢿⣿⣿⡆⢠⡀⢸⣿⣿⣿⣽⡆
⠀⠀⠠⠴⠷⠾⠼⠀⠋⠨⠽⠉⠭⠭⠅⠸⠽⠽⠹⠽⠽⠀⠋⠀⠷⠀⠾⠄⠛⠰⠶⠄⠶⠇⠀⠀⠷⠾⠀⠷⠾⠄⠈⠁⠼⠤⠼⠤⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡄⠀⠀⢀⣄⣀⣠⣄⠀⠀⠀⠀⠀⢀⣄⣤⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣾⢿⢷⢠⣦⢠⣶⣴⣶⣤⡀⠃⠰⡷⠶⡇⣰⡀⠿⠾⢿⠿⢿⠀⠀⠀⠀⠀⢸⡿⠿⠿⡇⢠⣄⠀⣟⣟⣏⣟⣿⡇⢠⡄⠠⢾⢿⠧
⠀⠀⠀⠚⠛⠛⠞⠀⠁⠸⠾⠘⠶⠶⠂⠀⠻⠇⠲⠇⠈⠀⠶⠰⠞⠶⠾⠒⠂⠀⠀⠀⠸⠿⠀⠿⠇⠈⠁⠀⠷⠿⠃⠷⠿⠃⠈⠁⠐⠼⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣲⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠧
⠀⠀⠀⠀⢠⡄⠀⢠⣶⣶⣶⣶⡀⠀⡄⢸⣟⣻⠙⣟⣻⠁⠀⠄⠀⣴⣴⣦⣤⠀⠀⣤⠀⢸⠛⢛⢛⠀⣠⡀⠀⣠⣶⣶⣶⣶⡀⠀⢠⡆
⠀⠀⢠⣤⣬⣁⠀⢸⣛⢻⡟⠛⠃⠈⣋⣸⣿⣿⣶⣿⣿⣄⣀⠀⠀⣟⡛⢛⣻⠀⠀⣉⣠⣼⣿⣾⣿⣤⣌⡁⠀⢉⠉⣹⣉⣹⡇⠀⣈⣥⣤⡄
⠀⠀⠸⠿⠿⠿⠿⠾⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠷⠾⠿⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠉⠲⡄
⠀⠀⠀⠀⠐⠀⣁⠃⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢀⠉⠡⡀⡄⠠⠐⢀⠀⣀⠀⠀⠠⣄⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣿
⠀⠀⠨⠀⠁⠀⠀⠄⠈⠃⠋⠀⠀⠀⠀⠐⠀⠀⢒⠀⢢⣦⣄⠱⣤⣠⠊⢁⣨⠴⠠⠀⠂⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠙⠋⠁⠉⢉
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠜⠃⠀⠀⠀⠀⠀⠀⠀⠐⠓⠂⠀⠙⡿⠛⠓⢾⣃⣒⣚⣃⣀⣀⣀⠀⠀⠌⠀⡠⠀⠀⠀⠁⠀⠀⠀⠀⢸
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢉⠀⠈⠉⠉⠀⠀⠀⠀⠸⠁⠀⠀⠄⠀⠀⠿⠠⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠈⠀⠀⠐⠢⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠊⠐⡄⠀⠀⠀⠀⠀⠀⡀⠸
⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠠⠀⠰⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠠⠃⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢀⠀⠀⢹⠂⡀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠔⠀⠀⠀⠜⠐⡇⠂⠀⠀⢰⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠒⠓⠀⠘⠒⠂⠀⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠁⠀⠸⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⢀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠘⢾⢀⡠⠞⠀⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡶⠀⠀⠀⠀⠀⠀⠀⢀⡁⠂⠀⣳⡤⠨⡭⠖⠐⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠭⠅⠀⠄
⠀⠀⠀⢀⡠⠄⢲⠁⠀⣀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠤⠖⠁⣀⠀⢄⣀⠠⣀⠀⠀⢠⣠
⠀⠀⠀⠀⠤⠠⡰⡀⡠⢊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠲⡈⠳⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣿⡁⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢨⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠙⠀⠘
⠀⠀⠀⢀⣀⠀⢀⣿⢋⡀
⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⡀⠈⠠⡀⣜⠄⢸⣀⣄⢬⣄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢨⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠽⡶⢃⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸
⡄⠀⠤⠄⠀⠢⢼⠄⠸⠴⠤⠴⠶⠦⠤⠤⠄⠀⠀⠀⠀⡀⠐⠰⠁⠀⠀⣀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠠⠤⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠃
⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠁⠀⠀⠀⠀⠄⢠⣤⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣭⡉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⡏⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠿⠁⠀⠀⠀⠀⠀⠀⢶⣤⣄⣈⣘⣉⣤⣤⡆⠀⠀⠀⠀⢸⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⠏⠀⠿⠃
⠀⠀⠀⠀⠀⠀⣄⡀⠀⠼⠿⠁⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⢤⣤⣤⣀⣀⣤⣤⣤⡶⠀⠀⢶⣤⣬⣍⣉⣬⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠐⢶⣶⣶⣦⣴⣶⡶⠟⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠘⠶⣶⣭⣭⣽⣿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⡤⠉⢳⡤⠀⠀⠀⠀⢰⡏⢈⠁
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠐⣶⣾⣿⡿⠀⠀⠀⢾⣿⣾⣦⣀⠀⠀⠀⠠⣴⣷⣤⣀⢢⣶
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢀⣿⣿⠿⠁⠀⠀⠀⠘⠟⠉⠀⠉⠓⠶⠶⣄⡉⠀⠈⠻⣷⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠻⢷⠤⠀⠈⠛
⠀⠀⠀⠐⠖⢚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠴⠖⠀⠀⠀⠀⠽⠇⡀⠀⠀⠀⠀⠀⠀⠈⠀⢾⡗
⠀⠀⠀⠀⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠖⠲⣶⢾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠰⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠙⢻⣿
⠀⠀⠀⠀⠘⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⠿⠿⠗⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⣿⣟⣟
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢹⡏⠙⠳⣄⡀
⠀⠀⠀⠘⠔⠛⠲⠶⢿⣿⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠙⠂⠄⠀⠞⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠷⠶⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠶⠶⢏⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⠀⠀⠀⠀⠙⠠⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠸⣦⢀⠊⠀⠀⠃⠀⠀⠄⠠⣿⣆
⠀⠀⠀⠀⠀⠀⢠⠉⡀⠀⢠⠄⡤⠤⠄⠀⠀⠤⠠⠤⠤⠀⠧⠒⠢⡄⢀⣀⣂⠀⠀⡶⡞
⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠶⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠀⠀⠒⡄⢀⣀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣨⠀⠀⠡⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢈⢰⡆⠀⢘⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⠈⡅⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢨⠈⠁⠀⠈⠁⠀⣶⣦⡤⠀⠀⠠⠀⠀⠀⠰⠖⠐⠞⠀⠾⠀⠃⠃
⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠈⠉⠉⢄⣀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠊⠆⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠈⠀⠉⠀⠈⠀⠈⠁⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⢤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⠶⠿⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠶⠶⠿⣼⣧⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣽⣷⣤⣄⢀⢄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡉⠉⠉⠉⠉⠁⠀⠀⣷⠢⠎⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢷⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢬⡆⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢏⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠙⣾⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡹⡇⠀⢠⠂⠀⠀⠀⠀⠀⠀⡏⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢐⠄⡸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⠀⠀⠀⡔⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢜⠄⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠊⡀⠀⠀⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⢎⠎⣽
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠞⣸⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⡀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⡐⢈⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣧⠀⠀⠀⠀⠀⠀⢀⡾⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⠊⡇
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣬⠦⣄⣀⣀⣠⡴⡟⢰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⣷
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠴⢥⣾⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⢪⢺⡆
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⠆⢀⠔⠀⠀⢀⠔⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡱⢣⢾⡇
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠐⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠈⡰⢣⠞⡇
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⡡⠃⣧
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡱⠃⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠱⢁⢺⡇
⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠳⠦⢼⠇
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠻⠤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠒⢒⣉⠉⣶⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠔⠒⣂⡉⠤⠄⠒⠂⠉⠀⠈⢄⡚⢃⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠐⢂⣉⣡⠤⠒⠂⠉⠉⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢱⡀
⠀⠀⠀⠀⡀⠤⠐⠒⣈⡁⠤⠐⠒⠈⠁⢀⠔⠁⠀⣠⣿⣶⣦⡀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠈⡈⡇
⠀⠀⠀⠀⢡⠀⢣⠀⡃⠀⠀⠀⠀⠀⢀⠂⠀⠀⢸⣏⠸⣷⠈⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢣⢹
⠀⠀⠀⠀⠘⡄⡤⠒⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⠷⣿⣶⣤⣄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⡈⣆⡀
⠀⠀⠀⠀⠀⢡⢱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⣿⠈⢻⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⡔⢩⠁⢠⡄
⠀⠀⠀⠀⠀⠈⡄⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢰⣦⣤⣿⣷⡿⠃⠀⢠⠃⠀⠀⠀⠀⢀⣀⠇⠀⠇⢀⡇
⠀⠀⠀⠀⠀⠀⢣⠰⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠉⠉⠙⠛⠀⣀⣔⡁⠤⠄⠒⣊⡉⠥⠄⠒⠊⢹⠉⡇
⠀⠀⠀⠀⠀⠀⠸⡆⢇⠤⢀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠲⠶⠒⢒⣉⣥⠄⠒⢒⠏⠁⠀⠀⠀⠀⢠⠊⡤⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠲⡀⢡⠠⠤⠐⠂⣈⢩⡤⠀⠒⠚⠛⣿⠟⠁⠀⡠⠊⠀⠀⠀⣀⡀⠠⠼⠀⠘⠂⣸
⠀⠀⠀⠀⠀⠀⠀⣿⣄⣈⠡⡄⠒⠂⠉⠁⠀⠀⠈⠐⣀⣤⡤⠤⠤⠖⠛⢒⣈⣉⠡⠤⠀⠒⠒⠂⠉⠉⡇⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢘⡄⠸⠤⠤⠐⠒⢀⣈⢉⡤⠤⠀⠒⣶⠞⠋⠉⢀⠔⠁⠀⠀⠀⠀⠀⢀⠖⣀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⡏⠦⠤⠄⠶⠦⠭⠭⠭⠤⠤⠤⠬⠴⠦⠤⠤⠤⠴⠮⠥⠤⠤⠤⠤⠤⠤⠤⠼⠀⠵⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣀⣀
⠀⠀⠀⡐⠒⣲⡔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣧⣧⢜⡆
⠀⠀⠀⣘⣬⡼⢦⠾⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⣀⠎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠉⡝⢉⠟⡇⠀⠀⠀⣀⣴⢶⠚⢒⣊⣳
⠀⠀⢀⠀⠀⡄⢰⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠚⡀⡎⠀⡇⠀⠀⠈⡷⢧⡬⢶⣶⣮⣅⣄
⠀⠀⢸⡄⣠⠇⠸⠤⠤⠤⠤⠤⢼⠀⠀⠀⢸⠉⠉⠉⠋⠉⠉⣉⠉⠉⠍⡇⠀⠀⠀⡄⠀⣠⠃⡇⡴⡇⠀⠀⠀⣠⠊⢠⡎⢇⡱⣘⣾
⠀⠀⢸⠤⠤⡀⠀⡤⠤⠤⠤⠤⢼⠀⠀⠀⢸⠀⠁⠀⠈⢀⠀⠀⠀⠄⠀⢁⠀⠀⠀⡗⠊⠁⡠⢻⠀⡇⠀⠀⢸⣁⠜⠁⡳⠚⢀⡴⢻
⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸⠀⠐⠂⠀⡄⠀⠐⠀⠀⠆⣸⠀⠀⠀⡗⠒⠉⠀⡼⢀⡇⠀⠀⠀⡁⡠⠊⠀⡴⠋⡐⡻
⠀⠀⠈⠉⠀⠓⠚⠓⠒⠒⠒⠈⠋⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⢀⣀
⠀⠀⣀⣫⣄⣦⣠⣯⣖⡀⠀⠀⠀⠀⠠⡀⠐⡆⠀⣁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠤⢤⣤⣿⣧⣤⣤⠜⠀⠀⠀⠰⣒⢞⣛⣛⣯⡭⢀⣁⣱⠀⠀⠀⠀⠀⠀⠠⣈⣇⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠐⢄
⠀⠀⠀⠘⡀⢸⡇⢀⠇⠀⠀⠀⠀⢠⣡⠁⠀⠀⡀⠀⠗⠾⠂⠀⠀⠸⡁⠩⠍⠤⠤⠭⠯⠯⠭⠭⠭⠭⢽⠀⠀⠀⡏⠉⠉⠉⠉⠉⠷⡀⠀⠡⡀
⠀⠀⠀⠀⣇⢸⡇⣸⠀⠀⠀⢠⣔⠟⢹⢠⠀⠀⠇⠀⡄⠀⡅⠀⠀⠀⡄⢒⢐⡒⡂⢒⢖⠒⡒⣒⣒⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⣤⠊
⠀⠀⠀⠀⠘⠾⠷⠃⠀⠀⠀⠀⠈⠀⠸⠤⠤⠤⠤⠤⠤⠤⠇⠀⠀⠀⠃⠠⠥⠬⠬⠤⠥⠤⠤⠤⠥⠤⠞⠀⠀⠀⠣⠠⠤⠤⠤⠤⠤⠦⠼

⠀⠀⠀⠀⢀⢆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡠⠉⢢⡀
⠀⠀⠀⢠⢸⠴⣟⢰⣦⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠸⠂⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣋⣄⣊⣁⡀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣤⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠂⠄⠰⠛⠛⠂⠀⠤⠂⠀⠀⠀⡆⠀⠙⠛⠛⠛⠛⠋⠀⡂⠀⠀⠀⠀⠈⠀⠠⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠤⠤⠤⠤⠤⡇⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠄⠀⡃
⠀⠀⠀⠸⣀⢀⢘⠀⡸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣃⠀⠀⠀⣀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⡀⡀⣈⣈⣀⣀⡀⢀⡁
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⢀⡀⠐⠒⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠐⠂⠀⠲⠆⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡠⠀⠀⣄⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀⠀⢰⠁⠀⠙⢦⡀
⠀⠠⣄⡠⣦⣠⡞⠁⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⡀⢤⠼⡆⢳
⠀⠀⠘⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠛⣆⠀⠁⠈⣟⣷⡈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠣⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⠀⠀⠇⠀⠀⠇⠀⠀⠘⢆⠀⡠⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡴⡡⠀⠀⢸⠀⠀⠀⢰⠀⡇⠀⠀⠛⣧⠸⡏⠀⠱⣄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣇⠀⠈⠀⠀⠀⢸⠀⡇⠀⠀⠀⢉⠀⠙⢦⡀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠆⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠡⠹⡄⠇⠀⠀⠀⢸⠀⠁⠀⠀⠤⠴⠀⠀⠈⠉⠁
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠀⠀⣰⠀⠀⠀⠐⢄⠀⠀⣀⣀⠀⢀⡀⠴⠛⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢈⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢀
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠇⠀⣸⠇⠀⠀⠈
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⠀⠀⠑⢤⢌⠂⠀⢁⠀⠀⠀⠳⢿⠋⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣷⣔⣦⣦⣠⡀⢠⣴⣴⡷⢶⢤⡆⠀⠀⠀⠁⠠⣄⢤⠀⠉⠈⠀⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠙⠋⠉⠉⠉⠉⠛⠋⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡠⣀⠄⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠐⠒⠒⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣀⠄⠀⠀⢀⢴⠋⠀⠒⠄⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡈⡆⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣠⣔⣵⠏⠀⠀⠀⠰⠀⠀⠀⢠⠐⠂⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠉⠉⠁⠀⣀⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠅⠀⠀⠀⠀⣠⣶⠖⠂⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠄⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⣠⡇⠀⠀⣸⣶⡀
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠛⠳⠶⠚⠋⠀⠀⠀⠉⠙⠳⠀⡀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⢶⡄⠀⠰⣿⡀⢀⣽⠃⠀⢠⡶⠟⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣸⡇⠀⠀⠈⢻⡟⠁⠀⠀⠸⣇⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠉⠉⢻⡆⠀⢀⣀⣈⣁⣀⡀⠀⢰⡟⠉⠉⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⢾⡏⠀⢹⣷⠀⠀⠀⣠⣴⠟⠋⠉⠉⡉⠉⠛⠳⢦⣄⠀⠀⠀⣼⡏⠀⢙⡧
⠀⠀⠀⠀⠀⠀⠈⠻⠶⠞⠛⠶⢀⣾⠋⠀⠀⢀⣤⢼⣧⣤⡀⠀⠀⠙⢷⡀⠾⠛⠻⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⣿⠁⢸⡇⠈⠻⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⠷⢼⣇⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⡇⠈⢻⡄⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠘⢷⣄⣸⡇⣀⣾⠃⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⢠⡶⠛⢶⣴⠶⠈⠻⣦⡀⠀⠀⠉⢹⡏⠉⠀⠀⢀⣴⠟⠁⠻⣦⡶⠿⢶⡄
⠀⠀⠀⠀⠀⠀⢻⣇⣀⣸⡟⠀⠀⠀⠈⡻⠶⣤⣤⣄⣀⣤⣤⠶⠛⠁⠀⠀⠀⠻⣇⣀⣸⡗
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⣠⣤⣾⠃⠀⠀⠈⢩⡍⠁⠀⠀⠘⣧⣤⣄⡀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⢹⡇⠀⠀⣠⣼⣧⣄⠀⠀⢸⡏⠀⢘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠟⠁⠀⠰⣟⠀⠀⣿⠂⠀⠈⠻⠶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠟⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣴⣶⣿⣷⣶⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣭⣽⣷⣶⣿⣿⣿⣿⣿⣟⣻⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⢻⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣟⣛⠛⠋⠉⠀⠀⠀⠀⠸⣿⣿⣿⣿⣟⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣯⣿⣿⡆⠀⢠⣶⣿⡷⣮⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠋⠉⠙⠛⠇⠀⠸⠿⠿⠿⠿⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡇⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⢸⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⢀⡊⠽⣿⠉⠀⠀⠀⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠘⢿⣿⣿⡶⠬⠀⠀⣰⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⢹⣷⣄⠀⠀⠛⠉⠀⠀⣠⣾⠏⠃⠈⠑⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⡏⠛⠷⣤⣤⣠⣴⠿⠛⢿⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢣⡀⠀⠀⠉⠉⠁⠀⠀⡬⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠑⠄⠀⠀⠀⠀⢠⠞⡡⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣠⠞⠑⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣤⢀⡀⢠⠀⣠⣀⢀⣀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⠛⠛⣿⠈⠿⣤⢸⡷⣾⢸⡇⣿⢸⣿⠟⣿⠛⠛⠛⠛⠛⠛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⠛⠛⠛⠛⠛⣿⠀⠛⠛⠘⠃⠘⠈⠛⠋⠘⠃⠀⣿⠛⠛⠛⠛⠛⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡆⠀⢠⣤⣤⣤⣤⣤⣤⣤⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⣠⠟⢀⡼⠃⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⣴⠋⢠⡞⠁⠀⠀⢘⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠈⠁⠀⠉⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⣘⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡾⠋⠉⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣤⠀⠀⠀⠀⣤⡼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⡆⠀⠀⠀⣾⠛⠋⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡼⠁⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣼⣤⡄⠀⠀⠀⢠⣤⣷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠉⠀⠈⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠘⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣿⣿⣶⣤⣴⣿⣿⣿⣿⣿⣦⣤⣤⠤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⠛⠛⢻⣿⠛⢻⣿⠛⠛⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⢀⣀⣀⣠⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣼⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⢠⣤⣤⡄⠀⠀⣠⣤⣤⣄⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⢸⣇⣀⡀⢠⡾⠉⠀⠀⠙⣷⡀⢸⡇⠈⣻⠆⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⢸⡏⠉⠁⠸⣇⠀⠀⠀⠀⣼⠇⢸⡿⣿⡋⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠸⠇⠀⠀⠀⠙⠷⣦⣴⠾⠋⠀⠸⠇⠈⠻⡄⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⢀⣀⣀⣀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⣾⡉⠙⠃⠀⠀⢠⣿⡆⠀⠀⢸⡇⠀⠀⢸⡏⠉⠉⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠈⠛⠷⣦⠀⢠⣟⣀⣻⡄⠀⢸⡇⠀⠀⢸⡟⠛⠛⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⢷⣄⣤⠟⢠⡿⠉⠉⠉⢿⡄⢸⣧⣤⡀⢸⣧⣤⣤⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⢀⣤⣤⣼⣿⣤⣼⣿⣤⣤⡄⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠐⢠⠂⢀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠒⠬⢘⢭⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉
⠀⠄⠐⠂⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠰⠠⠀⠀⠄⠀⠀⠀⠀⠁⢀⠐⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘
⠠⠀⠌⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡤⠓⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠰⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠄⣖⡶⢔⡠⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠌⢘⣦⡀⠄⠀⠀⠀⠀⠠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠔⠚⠀⠀⠀⠀⠀⠀⠉⠀⠄⠀⠀⠀⠀⠈⠀⠈⠄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣤⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢿⣿⠿⢺⣿⣿⠆⠀⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣄⡀⠀⢶⣄⢈⣿⣦⢸⣿⠀⠈⣿⡏⢀⠐⣿⡦⠀⠀⠀⣠⣴⡄
⠀⠀⠀⠀⠀⠀⣤⣀⣀⢻⣿⣿⡦⠙⣿⣈⣹⣷⣾⣿⣷⣶⣿⣷⣼⣤⣨⠹⡆⢰⣾⡟⠋⣁⠀⣴
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠉⠛⢿⣶⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣶⡟⠉⠀⢀⣼⣿⠇
⠀⠀⠀⣤⣠⣤⡀⠙⠛⢿⣷⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡴⣿⠟⠉⠀⢀⡀⣀
⠀⠀⠀⠹⣿⣿⣿⣤⣀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡅⠀⣰⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣩⣨⣝⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠛⠛⠙⠁
⠀⠀⠀⠀⢀⠈⠙⠋⢻⡿⢀⣀⢀⣀⡀⣀⢀⡀⡀⢀⣀⡀⣀⣀⢀⣀⣀⣀⣀⣀⢀⡀⢿⣇⣰⡟
⠀⠠⣶⣿⣿⣿⣷⣶⣿⡇⣿⠈⣾⠈⣷⣿⣾⣿⣿⣾⣿⡇⣿⡿⣾⡇⡇⢈⡇⠘⡾⠁⢸⣿⠿⡅⢠⣀⣄
⠀⠀⠀⠉⣙⡉⠁⣀⣹⣧⠙⠚⠘⠛⠃⠃⠈⠋⠃⠘⠋⠛⠃⠃⠘⠛⠓⠈⠃⠀⠃⠀⣼⡿⠿⠿⢿⣿⣿⠛⠂
⠀⠀⣤⣿⣿⣿⠿⠿⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀
⠀⠀⠀⠈⠋⠉⡀⣀⣀⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠙⠿⣿⣶⡄
⠀⠀⠀⠀⢀⣼⣿⣿⡟⠁⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠇⠤⣰⠀⠰⠋⠙⠃
⠀⠀⠀⠀⠛⠛⠋⠉⢀⣶⣶⣦⠛⢿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡋⠡⣰⣞⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠋⡀⣴⣿⠛⢻⣿⣷⣶⣶⣶⣶⣾⠿⢿⣏⠉⢻⣷⣄⡀⢵⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡅⣰⣾⣇⠀⢸⣿⠀⣼⣿⠀⢸⣿⣷⡄⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠋⢸⣿⣿⠇⠀⣾⣿⣷⠸⠟⠀⠘⢿⣿⡇⠘⠛⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠁⠀⠀⠛⣿⠛⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠛⠛⠉⠙⠛⠓⠶⢤⡀
⠀⠀⠀⠀⢀⡴⠋⠁⣀⣤⠴⠖⠒⠒⠶⢤⣀⠀⠙⢦⡀
⠀⠀⠀⣠⠏⠀⣠⠞⠉⠀⠀⣠⡤⢴⣇⠀⠉⢳⡀⠀⢹⡄
⠀⠀⢠⡏⠀⢰⠏⠀⠀⠀⠀⢯⡀⠀⠙⠂⠀⠀⣷⠀⠀⣷
⠀⠀⢸⠀⠀⢾⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⡿⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⣋⣉⣉⣉⣉⣙⠛⠒⠶⢤⣀
⠀⠀⠸⡆⠀⠸⣆⠀⠀⠳⣤⣤⡴⠃⠀⠀⢀⡼⠃⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣤⠖⠛⣩⠉⠉⢉⡭⠿⠯⣍⣛⡲⣄⠈⢳
⠀⠀⠀⢻⣄⠀⠈⠳⣄⣐⠋⠀⠀⣀⣠⠴⠋⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠳⢬⣉⣛⡲⠚⠋⠀⠀⢀⣋⣠⡤⠞⠀⣰
⠀⠀⠀⠀⠻⣷⣤⣀⠀⠉⠉⠉⠉⠉⠀⣀⣤⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣷⣦⣤⣀⣉⡉⠉⠉⠉⠉⢉⣁⣀⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣶⣶⣶⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣽⣛⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣽⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣀⣀⡀⠀⢸⣷⣽⣻⠿⣿⣿⣶⣾⣿⣿⣷⣶⣿⣿⢿⣟⣯⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣉⣩⣤⠤⠤⠤⠤⠤⢤⣬⣉⡙⠻⢷⣽⣻⠿⣿⣷⣾⣿⣿⣿⣿⣷⣾⣿⠿⣟⣯⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠠⡞⢩⣤⣖⣀⣀⡴⠛⠉⢛⡶⠾⠙⣦⠀⢹⡿⣿⣿⣶⣾⣿⣿⣿⣿⣷⣶⣿⣿⢿⣻⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⠉⠓⠶⠭⣭⣭⣤⣤⣤⡤⠤⠖⠛⠁⣠⣾⡿⣷⣾⣿⣭⣭⣭⣭⣭⣭⣿⣷⣾⠿⣻⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⡿⣻⡿⣷⣾⣿⣭⣽⣿⣿⣯⣭⣿⣿⣾⠿⣛⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣷⣯⣿⣛⣿⣿⡿⠿⠿⣿⣿⣟⣻⣯⣷⡿⣻⣿⣷⠾⠛⠉⠉⠉⠙⠛⠿⣽⣿⣾⡿⣟⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡻⣷⣯⣿⣻⣿⡿⠿⢿⠿⠿⣿⣿⣻⣯⣷⣾⣿⠏⠀⢀⣠⠴⠶⠶⠦⢤⣀⠀⠙⢷⣿⢟⣿
⠀⢀⣠⠴⠖⠛⣋⣉⣉⣉⣉⣉⡙⠛⠲⠦⣿⣿⣶⣭⣟⣻⣿⠿⠿⠿⠿⠿⠿⣿⣛⣯⣽⣿⠃⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠹⣿⣿
⣴⠋⢠⠴⠛⣉⡍⠉⠀⣠⠶⠿⢭⣍⣟⢦⡀⠙⢯⣟⣻⡿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣻⣿⡟⠀⢠⡇⠀⢠⡄⠀⠀⠀⣀⣀⠀⠘⣦⠀⠹⡿
⣷⡀⠘⠲⢭⣙⣓⡒⠛⠁⠀⣀⣘⣁⡤⠞⠃⢀⣾⣟⣻⠿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⠀⢸⡇⠓⢿⡀⠀⢀⡞⠁⠈⣧⣀⢸⡄⠀⣷
⣿⣿⣷⣦⣤⣀⣉⡉⠉⠉⠉⢉⣉⣀⣠⣴⣾⣿⢿⣟⣿⠿⣿⣿⣷⣶⣶⣿⣿⡿⢿⣟⣿⣿⡄⠀⢷⡀⠀⠙⠶⠋⠀⠀⠰⠏⠈⢸⠃⠀⣿
⣿⣿⣽⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣯⣷⣿⠿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⡿⠿⣿⣷⡄⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⡇
⢿⣾⣽⣻⠿⣿⣿⣶⣶⣶⣶⣶⣿⣿⠿⣟⣫⣷⡿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠙⢿⣿⣦⡀⠈⠓⠶⢤⣤⣤⠴⠚⠁⠀⣠⠞
⠀⠙⠿⣿⣿⣿⣶⣾⣾⣿⣷⣷⣶⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣀⣀⠀⠀⣀⣀⣤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠘⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣿⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⡟⠀⠀⣿⡇⠀⠀⣾⣿⣿⣿⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡄⠀⢻⠇⠀⢀⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷
⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⡇⠈⠻⢿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⣦⣌⣉⡙⠛⠛⠛⠛⠛⠛⠛⠛⣉⣉⣤⣶⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣿⣶⣤⣉⣉⠛⠛⠛⠛⠛⠛⠛⠃⢠⣌⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢉⣤⠀⠛⠛⠛⠛⣿⣿⡛⢋⣉⣡⣴⣾
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣌⣉⡙⠛⠛⠛⠛⠛⠛⠛⠛⣉⣉⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠿⣟⢿⣿⡿⡷⣶⡤⠤⠄⠤⣤⣤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣿⣷⡽⢷⡄⠀⠀⠀⡠⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⣷⡀⠀⣼⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⢦⣼⣿⣿⣧⣿⣇⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣾⣿⣿⣿⣛⣛⣙⣠⢄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡉⢀⣴⣿⣿⣿⣿⢻⡏⠘⣿⣦⠐⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⠃⠾⢁⡀⣈⠊⠃⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⠁⠀⣠⣼⣷⣿⣤⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣟⣿⡁⠀⣼⣿⡿⡏⣿⠿⠿⠆⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⢀⠀⢻⣿⣿⣇⣿⡀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⠀⠀⠙⢻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠀⠠⣤⣷⢸⡟⣿⣷⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⠓⢶⣦⣤⣤⣀⣀⡀⠀⠀⠄⠀⠀⣀⣠⣿⣿⣾⣷⣿⡿⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣀⣙⣛⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣷⣤⠴⠚⢻⣿⣧⢙⣿⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢘⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣷⡾⢟⣫⣥⡤⣴⣾⣿⣿⡗⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⣹⣿⣶⣶⣤⣦⣤⣄⣀⡉⠙⠓⠁⠀⠀⣀⠤⠈⣹⣿⣷⡄⢢⣽⣤⣤⡄⠐⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⣀⣈⠉⠉⠛⠛⠻⠾⠾⣿⣿⣿⣷⣶⠖⢀⣀⡤⢴⣾⣿⣿⣿⣯⣬⣭⣽⡭⢠⣾⡟⠉
⠀⠀⠀⠀⣿⣿⣟⣓⣾⣶⣤⣄⣀⣀⠀⠈⠉⣻⡛⠭⠖⠒⢛⡏⠉⠙⠛⠛⠛⠛⢻⡆⣘⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⢿⣿⣿⣿⣏⣁⡤⠔⠚⠉⠁⠀⠀⠀⣳⣢⡄⠀⣸⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣑⢼⠇⠠⡾⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣭⣏⡬⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣶⣶⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⡀⠀⢠⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⢰⡆⡄⠀⠀⠹⣼⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⠁⢿⢰⣆⣿⠀⠠⢠⡅⠄⠀⢄⠶⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠤⠈⠭⠆⢽⣦⣴⠫⢱⣿⣦⣏⣴⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠂⠉⣿⡍⠀⢉⠡
⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢨⠂⠀⠀⠓⠁
⠀⠀⠀⠀⠀⠘⡦⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠄⠀⠀⡆⠀⣑⣻⣿⣘⠂⠟⣤⡦⠐⢀⣶⠄⡀⢀⠌⠀⠦⡭⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠊⣈⡴⢳⠀⡀⠛⢻⣇⠼⠂⠀⠀⢵⡆⠬⡵⠋⠀⢉⣀⠐⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠑⠦⠭⢤⣀⣀⣏⠀⠂⢬⡼⠡⠔⠀⣸⣶⡖⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡢⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠉⠁⢠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⠀⠀⠀⢃⠂⠀⠐⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠃⡈
⠀⠀⠀⠀⠀⠀⠀⠓⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⢠⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⣄⢁⢰⠂⠀⠀⠀⠀⠀⠀⠀⡆⠀⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠆⠀⠀⠀⠀⠀⠀⠠⣙⠆⢷⣄⠀⠀⠠⠻⣷⠀⣼⢠⠀⠈⢦⠀⠀⠀⣴⡋⠀⠒⡐⠀⠈
⠀⠀⠀⣽⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣿⣷⠗⠀⢨⣿⠞⡙⢀⡚⠉⣴⣶⣿⣻⢀⡠⣀⠀⣴⣦⠐⠊⠁
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⠁⠀⠀⠀⠉⠛⠂⠉⠈⠙⠛⠉⠛⠛⣭⢿⡋⠉⢉⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⢉⢃⢘⢒⡛⣛⠀⡈⢛⠛⡉⣉⣛⢋⢛⢻⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⢸⠸⢹⠸⠄⢠⠀⠇⠸⠀⠇⡼⡿⡿⢺⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⡄⠄⡄⠀⠀⠀⠀⠠⠀⢤⡄⡄⡄⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠞⠒⠃⠇⠿⠀⠀⠀⠀⠸⠐⠻⠓⠛⠳⠃

⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠏⠻⠵⠟⠙⡿⣭⣉⣹⠿⣿⡀⠈⠉⠉⣹⡿⠅⢄⠀⡃⠻⣷⣤⡴⣚⠋⠸⢷⡤⣞⠛⢿⣜⢷⣼⢇⡼⣆⢔⠒⣜⠻⣯⠀⠴⡿⠃⠤⣴⡇
⠀⠀⢦⣌⠀⠀⠀⠀⠉⠈⠁⠀⠈⠛⠶⠶⠿⠟⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠈⠡⠅⠊⠀⠙⠳⠶⠛⠁⠀⠁⠘⠈⠀⠈⠑⠋⠁⠀⠀⢯⡆
⠀⠀⠈⠛⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⡇
⠀⠀⣰⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠸⡇
⠀⠀⡛⡫⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡇
⠀⠀⡥⢂⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⡇
⠀⠀⣟⠿⣤⡀⠀⠀⠀⠀⠀⣶⣶⣿⣿⢻⢻⣿⣿⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⡿⣿⢻⣿⣿⣻⣿⣿⣿⡟⡆⠀⠀⠀⠀⢰⣟⠀⠀⡇
⠀⠀⡏⣻⠌⡷⠀⠀⠀⠀⠀⡇⣯⣿⣿⣸⣾⣿⣿⡿⣿⢿⣷⠇⠀⠀⠀⠀⠀⠀⠀⢿⣷⡇⣿⡾⣿⣽⣿⡿⣿⣿⣷⡇⠀⠀⠀⠀⠈⠿⣦⣤⡇
⠀⠀⣟⣯⠾⠃⠀⠀⠀⠀⠀⠘⣿⠛⠛⠻⠾⠿⠿⠓⠛⢻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠛⠛⠻⠿⠿⠿⠛⠛⠻⡏⠀⠀⠀⠀⠀⠀⠀⠈⠋⠇
⠀⠀⣿⡭⡀⢄⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣀⣀⣀⡀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⡇⣹⡭⠀⠀⠀⢀⣴⠟⠲⢖⠒⠚⠫⠉⠙⠈⠉⠉⠍⠉⢛⣳⣄⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⣴⣿
⠀⠀⣟⡛⠀⠀⠀⠀⡞⠉⠙⠛⠓⠖⠺⠶⠶⠲⠒⠲⠶⠚⠛⠋⠁⠽⡆⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣺⡋⢈
⠀⠀⡟⢏⢢⠀⠀⢰⡏⠀⢸⢻⠻⡟⡗⡖⡶⣶⢶⢶⣶⣶⣿⡆⠁⠁⣧⠀⡇⠀⢰⣿⢻⣿⢷⣶⢲⣶⣶⣶⣶⣶⣾⡇⠀⠀⢿⠀⠀⠀⠧⣣⣬
⠀⠀⡃⣸⡽⠀⠀⢸⡇⠀⢸⡾⠦⠧⣷⠷⣧⣿⣼⣼⣿⣿⣿⠇⠀⠂⣿⠀⣧⠴⠚⣿⣿⣿⣹⣻⣸⣿⣽⣿⣻⣿⣿⡏⠉⢛⣿⠀⠀⢀⢀⣬⣽
⠀⠀⡿⢟⠀⠀⠀⢸⡇⠈⠘⡇⠀⢏⠈⠁⠀⠀⠠⣿⣄⠀⢸⠀⠄⠀⡟⠀⣿⢋⣟⣯⠉⡛⠋⠉⠉⠉⠉⠉⠉⠉⢹⣷⣚⡙⣿⠀⠀⠀⢳⡏⢘
⠀⠀⠋⠐⡁⠀⠀⠈⡇⠀⠀⣇⡴⠚⢻⣰⢳⠀⡾⢩⠁⡄⢸⠀⠐⠀⡇⠀⣷⠾⣙⢿⡔⢚⠂⢀⣠⢲⣀⣒⡰⣂⢸⣷⡏⢛⡿⠀⠀⠁⠉⡹⣿
⠀⠀⢱⣠⠂⠀⠀⠀⣧⠀⠀⣿⣈⣐⣡⣬⣭⢯⣭⣮⣿⣥⣼⠈⠀⣸⡇⠀⣿⡘⠥⢾⣀⣀⣀⣀⣥⣿⣥⣬⣄⣈⣼⣟⢣⠿⡇⠀⠀⢠⡾⣻⣿
⠀⠀⠘⠻⢷⣆⠀⠀⣿⢀⠀⢸⣸⣸⡆⡇⢸⢸⠸⡎⡇⣿⣿⠀⠀⢹⠁⠀⢸⣙⡛⠾⣿⣯⣯⡇⣿⡟⣿⣺⣿⣿⣿⡧⣫⣻⡇⠀⠀⣯⢸⣏⡧
⠀⠀⠀⠀⠈⣿⠀⠀⢸⠀⠀⡀⠈⠉⠑⠛⠚⠚⠓⠓⠛⠋⠡⠀⠀⢹⠀⠀⢸⡷⣞⣷⢞⣩⢿⡟⡛⠻⠟⢿⣛⡋⡵⡐⢫⣹⠀⠀⠀⠘⠷⣬⡅
⠀⠀⢀⣀⣴⠟⠀⠀⠈⠳⣌⣀⠀⠀⠀⠂⠀⠀⠀⠄⠈⠀⢀⣠⡴⠋⠀⠀⠀⠻⢧⣗⢚⡽⢛⡄⣿⣲⡎⡒⢢⣷⢡⣿⡿⠛⠀⠀⠀⠰⠟⡨⡟
⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠒⠒⠒⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠚⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⡕⢤⡇
⠀⠀⢸⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡻⠇
⠀⠀⢸⡾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣴⣄⡅
⠀⠀⠺⡷⠀⠀⠀⣀⣀⠀⠀⢀⡀⣀⠀⢀⣤⠤⣤⡀⠀⡠⠀⠠⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⡇
⠀⠀⣾⠗⠀⣀⣾⠆⠘⣷⣬⠕⠥⠑⢣⡞⣱⠶⣮⣻⡆⣬⡷⠾⢴⡅⣰⡫⠝⠹⢷⣄⢊⠐⠢⢠⣼⡏⠀⠀⠀⠙⣧⣶⠛⣛⡳⣶⣀⣤⣤⣇⣇
⠀⠀⠙⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠈⠁⠉⠉⠉⠉⠉⠙⠓⠒⠚⠛⠛⠓⠒⠒⠚⠋⠉⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⢼⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈
⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢀⠄⡀
⠀⠤⠇⢀⠀⠵⠀⠤⠴⠇⠀⠄⠀⠀⠀⠄⠂⠀⠹⠀⠀⠀⠀⠀⠀⠀⣁⠀⢀⠀⠀⡀⠀⢀⢦⡄⠰⠇⡀⠈⡉⠀⠀⠈⡄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠠⠦⠈⠈⠂⠡⢄⣐⠿⠦⠦⠶⠶⠷⣄⠠⢀⢀⠂⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡔⠀⠀⠀⠂⢀⠏
⠒⠒⠂⠂⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⣤⢤⡴⠞⠀⠀⠀⢠⠐⠁⠰⡄⣤⢤⡤⡴⠂
⠀⠀⠀⠀⠀⣠⣀⠀⠀⣄⢠⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣡⠂⠀⠀⠀⠀⠀⠀⠐⡆⠀⠃⠀⠢⡝⢄
⠀⠀⠀⠀⠊⠉⠘⠀⠀⠈⠒⣃⠀⠀⠀⠀⠰⡧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣦⠀⠰⠀⠈
⠀⡀⠀⢀⡄⢠⡁⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠈⠀⡈⠉⠠⠊⡀⠀⠀⢸⠀⠀⡸⠀⠀⢰⠄⣀⡀
⢀⠐⠀⠀⠤⠀⠀⠄⠓⠀⡌⠀⢠⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠈⢦⢀⡀⠘⠁⠀⠀⠀⢀⠇⠀⡘⠀⠠⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠓⠚⠉⠀⢀⡎⠙⢀⡼⢀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⠺⠷⠤⣤⣤⣀⠀⠀⠀⠉⣨⣦⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⠀⠈⠀⠀⠀⠀⠈⠉⠓⠲⠤⣾⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡢⠌⠋⢸⠈⠙⠛⡲⠦⢤⣄⣀⠀⠀⡀⠀⣿⣿⣿⣿⢿⠉⣩⣳
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢒⠭⣦⠉⠀⠀⠀⠈⠳⢄⣠⣌⠦⠅⣺⣫⣽⠐⡕⡰⣿⡿⠿⢉⣼⣾⣿⡿⡄
⠀⠀⠀⠀⠀⢰⣎⡀⠰⠚⣡⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⣀⢔⣩⣾⣿⣿⠄⣼⣿⠿⠭⠴⣿⡷⣝⣟⡼⠃
⠀⠀⠀⠀⠀⢸⠚⢭⣙⡓⠮⣭⣒⠠⣠⠄⢒⣲⡖⣐⡬⣖⣿⣿⣿⣿⣟⡤⠿⠉⠀⠀⢠⢸⣯⣫⡞⠢⣄⣀
⠀⠀⠀⠀⠀⣸⠂⠀⠙⠪⢕⡒⣉⢿⣷⡲⢭⡴⣾⣶⢿⣿⣿⣿⣿⡛⠫⠥⣤⣀⣠⣼⢏⣸⣿⠟⠓⣤⠀⢘⠏⢒⡢⢄
⠀⠀⠀⠀⠀⠈⠑⠒⠠⢍⣒⠦⢭⣈⡈⠍⣛⣚⣯⣽⣿⣝⡋⠃⣀⠤⠤⢲⣫⣿⠗⡟⢊⡿⠟⠛⢉⠹⢖⠦⣐⣉⣵⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠲⠮⢍⡓⢃⣾⢿⡟⠩⠬⠀⠀⠀⢀⢔⣵⢿⣿⠙⢈⡞⠁⠀⡠⠂⠀⠀⠉⣋⠛⠿⣿⠿⣂
⠀⠀⠀⠀⠀⠀⢀⡔⠊⡡⠉⢠⡀⠐⠠⢍⣙⡉⠈⠀⢀⣀⣀⣀⢔⣩⣿⣷⣿⣿⣼⠯⠀⠐⠊⠀⠀⠀⠀⠤⠀⠀⠀⡃⠀⣆⡍⢁⣶
⠀⠀⠀⠀⠀⠀⣺⠦⠥⠌⠉⣀⢒⣂⠉⠱⠖⠦⠤⠂⣁⣰⣋⣴⡟⣫⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⢂⡱⣀⠤⢚⡭⢞⡇
⠀⠀⠀⠀⠀⠀⢸⣧⠍⠭⠄⠒⣒⣀⡀⠤⠍⠡⣤⠆⢤⣄⣐⣩⣮⣿⣿⣧⣀⣀⠠⣤⡀⣀⠀⠀⠀⢀⠀⠀⡐⡨⢔⣫⣴⣮⣵⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢋⣭⠩⣤⣔⣒⣒⣒⣒⣉⡩⣥⢭⣈⣭⡹⢫⣿⠟⠏⠉⠛⠷⡦⢌⡑⠎⣑⣲⣭⣐⠾⣽⣶⣿⣿⡿⠿⢛⡩⢔⡎
⠀⠀⠀⠀⠀⠀⠀⢸⡓⠑⠪⠢⢌⠐⠁⠩⠊⢔⡅⡩⢈⠑⡡⡩⠛⢶⣵⠀⠀⠀⠙⢳⠪⢹⣿⣧⣽⣷⡿⠿⢛⡋⠥⣒⣮⡾⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠼⡃⠀⠀⠀⠀⠉⠒⢷⡤⠄⠒⢒⣤⢄⣤⣶⣷⣿⣽⣷⣄⡀⠀⠈⠀⢽⢿⣟⠯⣭⣖⡾⡅⠯⠑⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠈⢮⢷⠬⣩⣴⣾⣻⣿⡿⣿⡻⠕⠁⠈⠐⠤⣀⠽⠟⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠈⢶⠀⣩⣷⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⢄⡼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡀⢀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠄⡠⢀⠄⡀⠐⡀⡠⠐⠠⢊⠄⡨⠀⠔⡡⢂⠄⠠⢂⠄⠀⡀⡀⢂⠔⠡⢂⠔⡡⢊⢄⠄⡠⢊⢔⠕⡵⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠊⠐⠁⠂⠁⠀⠂⠐⠨⢀⠄⠀⠔⠁⠪⢊⠀⠐⠡⠂⠔⠁⠊⠐⠁⠂⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡴⠶⢶⣶⣾⡧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣩⣿⣿⣥⣶⠶⠶⠾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⡶⢧⡀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣯⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⡾⣷⣦⣞⣱⠃⠈⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣶⣿⣟⡿⣿⣟⣿⣿⣶⣇⣀⡟
⠀⠀⠀⠀⠀⠀⢠⣿⡿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡟⢻⣿⣿⣿⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡛⣾⣿⣳⢿⣿⡄
⠀⠀⠀⠀⠀⢀⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⣸⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣯⣿⣿⣿⣿⣿⡪⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣾⣿⡟⢃⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣟⣛⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇
⠀⠀⠀⠀⢠⣿⣻⢡⣿⣗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣇
⠀⠀⠀⠀⠀⠉⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣛⣛⣉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢿⡿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠙⠻⣿⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠐⠟⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⠿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠁


⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠘⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⣇⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣾⣿⣿⣿⣿⣟⠆⠀⠀⠀⡿⠏⣾⣿⣿⣿⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⣿⣿⠟⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀⠀⠀⠀⡿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠄⠀⠀⠀⣱⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢠⡀⢠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠙⣿⣿⣷⣤⡀⠀⢸⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⢿⣿⣿⣿⣿⣆⠸⣧⡆⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠉⠉⠛⠛⠛⠀⣻⣟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡷⣦⡀⠀⠀⠀⠸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣾⡟⢦⡀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣿⣿⣌⢻⣄⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠉⠂⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⣠⣴⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡧⡆⠀⢠⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠻⣿⣿⣿⣿⣼⣿⢣⡇⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣦⣄⡀⠙⠻⣿⣿⣿⣿⡈⡇⠀⠀⢹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⠀⠈⠻⠏⣿⡇⠀⠀⠀⢸⣿⡿⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡀⠀⠀⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣄⠀⠀⣶⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⢿⡄⢠⣾⢿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⢸⣿⠈⣻⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠹⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣾⡟⠋⠉⢿⣴⠶⢤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢣⠀⠀⡼⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣳⡦⣤⡷⢶⣷⠲⢿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣊⡴⠚⢉⣴⠞⢹⡇⢸⠈⠳⣄⠈⠻⣆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣁⠀⣰⠟⠁⠀⢸⡇⢸⠀⠀⠘⢧⡀⣽⡇⠃
⠀⠀⠀⠀⠀⢀⣀⣐⠒⣠⠤⠤⠶⠶⣮⡭⠿⣞⣹⣄⠀⠀⢸⡇⢸⠀⠀⠀⠈⣿⠃
⠀⠀⠀⠀⣠⠟⠡⡍⢻⡇⠀⠀⠀⠀⡿⣸⠃⠈⠛⣷⡖⠒⢾⠀⢸⠲⠶⠶⢶⡟⠀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⠀⠐⣇⠀⠀⠙⣾⣇⠀⠀⠂⢸⣿⠏⠀⠀⣰⣿⠀⠀⢸⠀⢸⠀⢀⠀⢸⠇⠀⣤⠶⠶⠛⠛⠛⢷
⠀⠀⠀⠀⠈⢧⣤⠖⠚⠿⢤⣴⠤⠟⠛⢶⣡⣾⣋⣿⠀⠂⢸⡇⣿⠠⠀⠀⣿⣤⣼⡇⠀⠀⠀⠀⠀⢸⣷⠞⡛⠳⣦⡀
⠀⠀⣠⡤⠶⣾⠃⠀⠀⠀⣴⠛⣆⠀⠀⠈⢿⡉⠛⠛⢻⡆⢸⠃⢻⣠⡴⠾⠋⢰⡂⣇⠀⠀⠀⠛⠀⢸⡇⢠⠇⠀⠈⠙⣷
⠀⠀⡇⠀⢰⣏⣴⣦⠀⣼⠃⠀⢸⡆⠀⠂⠈⣧⠀⠀⢸⡗⢺⠀⢺⣹⡇⠀⠀⠀⢳⡸⡄⠀⠀⠀⠀⢸⣧⠏⠀⠀⠀⢀⡿⢰
⠀⡆⢿⣠⣼⣯⣤⣽⣴⡇⠀⠀⠀⢿⠀⠀⠀⢸⡶⢶⡾⠛⣽⠀⢸⠀⢳⡀⠀⠀⠀⠹⣷⠀⠀⠀⠀⣼⡋⠀⠀⠀⣠⡾⠁⠁
⠀⠘⡄⣿⠀⠀⠁⠀⠉⣧⠀⠀⠀⢸⡇⢰⠷⣬⡇⢸⣇⡀⢸⠀⣸⣀⣀⣿⣦⠔⠒⠒⠚⣳⡤⡖⠋⠉⠉⠳⣶⠾⠿⠶⠶⠶⠶⣦⡈
⠀⠀⠀⢿⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣷⡏⠀⠘⠁⢸⡇⠁⢸⣼⡏⠉⠁⢠⠏⠀⠀⠀⡼⠁⠀⠈⢦⡀⠀⠀⠘⢷⣀⣀⣀⣀⣀⣼⠃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⣿⠀⠀⠁⢸⡏⠀⠀⠀⠀⣸⠄⠀⢸⡝⣷⡤⢤⣿⡴⢶⡄⢸⠗⠖⠛⠛⠻⢷⡀⢠⣄⡈⢿⠉⠉⢉⡏⠁
⠀⠀⠀⢸⡇⠀⠈⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠠⠀⣾⠠⠀⢸⡇⣿⢹⡄⠁⠀⠀⠙⠟⠀⠀⠃⠀⠀⠈⣧⠟⠈⠙⠻⠆⠀⣾⠁
⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⡋⠀⢀⣀⣿⣤⣤⣼⣇⣿⣄⣱⣤⣤⣤⣤⣤⡤⣤⣤⣤⠤⠤⠤⠤⠴⠶⠶⠶⠶⠋
⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠶⠶⠶⠾⠋⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠄⠖⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠤⠀⠀⠀⢀⠠⡀⠀⢈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠⠄⠀⠀⡈⠢⡀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠊⠀⠀⡀⠀⢐⠀⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠉⠉⣁⠀⠀⠀⠀⠑⢤⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠁⠆⠀⠀⠙⢦⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢲⡄⡤⠀⡄⠀⡀⠀⠠⠀⠁⠀⡆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡇⠁⡀⠀⠀⠤⠥⠬⠀⠤⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⣀⣄⣂⠁⠀⠀⠀⠀⠀⠀⠀⣘⠀⢰⢀⡀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢠⡆⠐⡜⠙⡞⠙⠂
⠀⠀⠀⠀⠀⠃⠀⠃⠈⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠁⠀⠁⠀⠁
⠀⠀⠀⠀⠀⡄⠀⡄⢀⠀⠠⠀⠀⠀⠀⠀⠈⠂⡀⠀⢀⠀⡀⠀⠀⠀⠀⡅⠀⢀⡀⠀⡀⠀⡀
⠀⠀⠀⠐⠒⠓⠴⠷⠼⠷⠾⠤⠤⢤⠀⠀⠀⠀⠀⠀⠈⡧⠧⠤⠤⠤⠤⠦⣤⣼⣦⣬⣧⣨⣧⣠⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠶⢶⣄⣤⣤⣶⣾⠿⠿⣿⡦⠀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣯⣭⣭⣤⣤⣴⣦⣯⣭⡀⠀⠀⣴⠿⠿⠚⠋⠉⠁⠀⢀⣀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⣴⣿⠛⠉⣙⣧⣤⣴⡿⢿⣿⣷⣤⣶⣶⢾⣿⠟⠁
⠀⠀⠀⠀⠀⣀⣴⣶⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣄⠘⢿⣿⠿⠟⠛⠋⠁⢠⡟⠀⠀⠀⢀⣴⠟⠁⠀⠀⣀⣀⣀
⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀⠻⣷⡄⠀⠀⠀⠟⠀⠀⠀⣠⣞⣥⡶⠞⠛⣛⣉⣩⣿⡿
⠀⠀⢠⣟⣸⣿⠿⠋⠉⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⢀⣠⣴⡶⠶⣭⣭⣛⣻⣷⣶⣶⡶⠶⢶⣖⣻⣿⠻⠛⠛⠛⠛⠛⠛⠋⠁
⢠⣶⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠿⠿⢿⡄⢀⣤⣶⣿⠟⠁⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠋⠁⠈⠻⢶⣤⡀
⣿⠋⣤⡀⠀⠀⠀⣠⣶⠀⠀⠀⠠⡦⠦⣠⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄
⠹⣿⣿⣷⡄⠀⠸⠿⠁⣤⠀⠀⠀⣡⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠈⢿⣿⣛⠀⠀⠀⠀⡠⠊⢀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡶⢤
⠀⠠⡟⠴⠾⣅⠀⠀⠀⠀⣠⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣣⠾⡇
⠀⠀⠹⢦⣤⣀⣴⡂⢠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣥⠾⣷⡄
⠀⠀⠀⠀⠉⠁⠈⣻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⣀⣤⣿⣶⣾⣿⣷⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢞⣻⣷
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠛⠉⠉⢿⡀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⣧
⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⠹⣆⠀⠀⠈⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣾⠿⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣠⠞⣱⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠿⢿⡟⠛⠛⠛⣿⣿
⠀⠀⢰⡟⠀⢙⣛⣛⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢿⡀⠀⢠⣿⠏
⠀⠀⢸⡇⠀⠘⠛⠿⢬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣄⡀⠀⢿⡀⠀⣀⣸⣷⣾⠟⠁
⠀⠀⠀⠻⣤⡈⣛⣛⣒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠷⠿⣿⠿⠟⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠈⠻⣶⣶⣾⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣤⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣻⣿⣿⣿⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⣯⣽⡋⡻⢻⡿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⣟⣻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢧⣿⢿⣾⣯⣿⣻⢿⣾⣿⠉⠉⠉⠉⠙⢿⣿⣍⣻⢿⣹⢾⣻⣬⡿⣟⣧⡽⣧⠀⠀⣠⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣛⠾⣭⡾⣧⣮⣹⣋⣿⡿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⣾⣝⣾⡟⣮⡿⣟⡿⠟⢺⣧⡾⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣶⣟⡶⣏⣽⢻⡾⣯⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡟⣯⣷⣿⣷⣤⣿⣿⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢻⣷⣟⣷⣿⣽⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡟⠻⣿⣿⣿⡿⢋⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠻⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣿⣿⡿⠶⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠀⠀⠀⠀⠸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣄⠙⢿⣦⣴⠏

⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⢰⣿⠋⠉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣇⡀
⠀⠀⠀⠀⢸⣿⠀⢠⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷⡀
⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⢠⡟⠛⠛⠛⠛⠛⠛⠛⠁⠀⣶⡄⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⢿⡀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⣿⡇
⠀⠀⠀⠀⠈⢿⣷⣼⣿⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢹⣿⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣂⣀⣙⣁⣀⣀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣀⣀⣀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠤⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠈⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠀⡏⠉⠀⠈⢸⡏⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⡉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠘⠋⠒
⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠂
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠃⠀⠐⠂⠂
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠠⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠆
⠀⠀⠀⠂⠀⠀⠀⡄⠀⠀⢠⠀⠀⠀⠀⠁⠀⠀⠀⡁⢉⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠄⠠⠀⠀⠀⠀⠰⠄⢝⠀⠀⠀⠀⠈⣁⢀⠀⠡⠀⠀⠀⠀⣾⡿⢇⠦⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠍⡀⠈⠀⠀⡓⠀⠁⠘⢙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠏⠀⠀⣀⡀⠀⠀⠀⠢⠀⠀⠃⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⢀⠀⠆⠀⠀⠀⠂⠀⠀⠀⠀⡄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠂⠀⠘⠃⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠅⠃⠚⠐⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡀⠀⠀⠀⠉⠀⠀⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢢⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠀⠠⠀⠀⠀⣠⡄⠀⠁⠀⠀⢠⠀⠀⠈⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀⠀⠈
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠒⠁⠀⠈⠁⠀⠁
⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣷⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣾⡿⠿⠿⠿⠿⠿⠿⠿⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⢿⣿⣷⣶⣿⣿
⣿⣇⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢠⣿
⣿⡏⠘⠛⠃⠐⣶⣾⣶⣀⠀⢠⣾⣿⣿⠋⠀⣸⣿⢿⣷⠀⠀⠀⢸⣿⡿⢿⣶⣶⣄⠀⠸⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠻⠛⠀⠀⠠⢿
⣿⡇⠀⠀⠀⠀⠈⠙⢿⣿⣷⣿⣿⣿⠃⠀⢠⣿⣧⣼⣿⣇⠀⠀⣸⣿⣷⣤⣼⣿⠟⠀⠀⢹⣿⡟⠛⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣼
⣿⡟⠒⠀⠀⠀⠀⠀⠀⠙⣿⣿⡟⠁⠀⢀⣾⣿⠛⠛⢿⣿⡄⠀⣿⣿⣟⠙⢿⣿⡄⠀⣀⣸⣿⣧⣤⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢼
⣿⡟⠒⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠀⢠⣾⣿⡇⠀⠀⠸⡿⠿⠀⣿⣿⡿⠀⠘⡿⠿⠘⠿⠿⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⢼
⣿⣇⠐⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢹
⢻⡿⠛⠛⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄⠀⠀⢠⣿⣿⣧⠀⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⣼⡷⣶⠒⠒⠀⠀⠀⠀⠀⢿⣿⣿⣀⠙⡿⠛⠀⢠⣿⣿⠻⣿⡄⠀⢸⣿⡿⠀⠀⠀⢹⣿⣿⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿
⣿⣷⡦⠤⠀⠀⠀⠀⢀⣤⡈⠙⢻⣿⣷⡀⠀⠀⣾⣿⣷⣾⣿⣷⠀⣼⣿⡇⠀⠀⠀⢸⣿⣿⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿
⣿⡷⠤⠤⠄⠀⠀⠀⠻⢿⣿⣶⣾⣿⣿⠁⠀⣾⣿⣿⠉⠈⣿⣿⣧⣿⣿⣿⣾⣿⡿⠿⠿⠿⠿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣿
⣿⣷⠒⠒⠒⠒⠄⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠉⠉⠋⠙⠋⠙⠋⠉⠁⠀⠀⠀⠀⠀⢴⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠠⣼
⣿⣏⠁⠄⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣶⣶⣶⣦⣴⣦⣤⣤⣴⣶⣶⣶⣶⣦⣴⣶⣶⣶⣾⣿⣿⣿⣿⣷⣦⣤⠀⠀⠀⢀⣾
⣿⣟⠓⠒⠒⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣻⣿⣿⣿⠿⠟⠋⠁⠀⠀⠠⠤⣼
⣿⣿⠂⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠁⠀⠀⠀⢀⡀⠀⠀⠀⣾
⢿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⠿⢿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⠶⣶⣶⣶⣶⣶⠶⠾⠶⣶⣶⣶⣶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠂⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠋⠀⠀⠀⠀⠀⠀⠉⠉⠑⠐⠂⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⣖⠊⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠴⣏⣀⡀
⠀⠀⠀⠀⣄⣀⣀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠚⠻⢥⣀⠀⠀⠀⠀⠉⠒⠩⠽⣳⡆⠀⠀⠀⢀⣠⣴⢯⣥⣶⣶⣛⣫⡀
⠀⠀⠀⠀⢠⣌⣙⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠿⣾⣯⠓⠦⢄⡀⠂⢤⣀⡠⠬⠉⠑⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⣧⣈⠙⠒⠦⣍⡙⠲⢤⣤⡤⠤⠤⣶⣶⣶⣶⣶⣾⣿⣿⡇⠀⠀⠀⢀⠀⣷⣿⣿⣿⣿⣿⣟⣛⣛⣉⠁
⠀⠀⠀⠀⠀⢹⣌⠉⠂⠀⠀⠉⠙⠲⣶⡶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀⣤⠼⠶⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠈⣱⠦⢄⡀⠀⠀⠀⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⣝⠲⢬⣑⠒⠤⢀⣉⠻⣛⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠉⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⢍⣙⡒⠲⠤⠴⠚⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠐⠚⣏⡉⠀⠉⠐⠲⠶⡄⠀⠀⠀⢀⣀⣤⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠾⠁⠀⠀⠀⠀⠀⠀⢘⠣⠤⣀⠀⠀⠀⠀⠀⠙⠛⢋⣀⡄⣦⠄⠒⠀⢸⣿⣿⣿⡿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣤⣤⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⠂⠀⠉⠒⠴⢶⣾⣿⣿⣿⣿⡇⣯⣀⣀⣤⣾⣿⣯⣷⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢩⣑⣲⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠤⢀⡀⠈⣿⣿⣿⡿⠟⢛⣹⣾⡞⠉⢀⣼⣿⣿⠗
⠀⠀⠀⠀⠀⢭⣐⣒⣶⣾⣓⠲⠬⣿⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣔⠚⠣⢤⣀⠉⠈⠉⠀⣤⣾⣿⣿⣿⠓⠛⠛⠋⠉
⠀⠀⠀⠀⠀⢐⠂⠭⢽⣯⠤⢍⣛⣿⣿⣿⢄⣒⣶⣾⣿⠀⠀⠀⠀⠈⣇⠉⠉⠒⠢⠤⣀⡀⢐⣻⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠠⢌⣙⣻⣿⣑⡒⠶⣿⡿⣿⡀⠬⢿⣭⣽⡗⠀⠀⠀⠀⠉⠒⠠⠀⢀⡀⠀⠀⠽⣺⠟⠋
⠀⠀⠀⠀⠀⢘⠒⠲⣿⣿⠦⢈⣉⣛⣛⣿⠍⣙⣻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣓⣒⣺⣿⣿⣿⠃⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢧⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣄⣓⣤⣀⢳⣀⡤⠚⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⡤⠠⡄⠀⠀⣿⠀⠀⠈⠉⠙⡟⠺⡷⢮⣭⣉⣀
⠀⠀⠀⠀⠀⠀⠀⣼⡀⣈⠳⣄⣠⣼⣖⣙⣤⣯⣤⠀⠀⠀⢰⠀⠀⠇⠀⠀⠀⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣭⡿⡥⢞⠻⢍⡀⠀⠘⣧⣤⣄⡜⠀⢸⠀⠀⠀⠀⢀⡿⣀
⠀⠀⠀⠀⠀⠀⠀⣏⠉⠰⢯⡴⠇⠀⢳⡄⣾⠷⠶⣏⠀⠀⡇⠀⡼⢍⠙⢯⠁⣹⡇⠀⡱⠂
⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣸⡥⠾⡀⠀⢏⠃⠀⠀⠹⣆⠠⠇⣸⣀⣀⣙⠦⣧⣼⣴⣋⣠⣤⡀
⠀⠀⠀⠀⠀⣰⠋⠉⠉⠉⠙⠓⠦⣧⣀⠈⡆⠀⠀⠀⠹⣼⠀⢸⣁⣨⡭⠿⠿⣿⢿⠍⠀⠈⣷⡀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⣄⠀⢠⡶⠛⠛⠉⠁⠀⠀⣀⣀⣽⡎⣶⠚⠋⢻⡀
⠀⠀⠀⢰⣧⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⢧⣠⣤⠴⠖⢛⡏⠉⠀⠼⠛⢇⠐⣂⣈⣷⣠⣄
⠀⠀⠀⣰⠃⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⢹⡄
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⡾⠀⠀⠀⡐⡗⣀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢸⠃⠀⠀⠿⡪⡻⣗⠓⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠶⠚⠋⣧
⠀⣾⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠉⠛⠛⡛⠛⢻⠛⠛⠉⠉⠁⠀⢠⡄⠀⠀⢹
⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⠀⣀⠀⠀⠀⠤⣶⣶⠄⠀⠀⠀⢀⣇⠀⠈⠀⠀⠀⠀⠠⡮⣶⢕⠵⠆⢸
⠀⣇⠀⠀⠀⠀⠀⢀⢄⣹⣳⣿⣼⣏⡠⡀⠀⠀⠘⠀⠀⠀⠀⢰⠁⠀⣱⠔⠢⢄⠀⠀⠀⠈⠡⡇⠁⠀⢸
⠀⣿⠀⠀⠀⠀⠀⠈⠉⣽⠟⣿⡻⣯⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠴⡃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡟
⠀⣸⠤⠤⠤⢀⣀⠀⠀⠀⠀⢿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⠀⠀⠀⠑⠤⠤⠚⠁⠀⠀⢀⡀⠤⠒⠉⢧
⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈
⠉⠙⠛⠓⠒⠒⠶⠶⠦⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠴⠶⠒⠛⠋⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣄⠀⠀⡀
⠀⠀⡀⠄⠅⠀⠀⠀⠀⠀⠀⠀⠈⣋⡂⠸⠏⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⣟⠉⠀⠛⣿⣿⠇
⠀⠀⠓⠚⠧⠀⠤⠦⠀⠀⠂⠀⠛⠓⠦⠬⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣤⡠⢿⣿⣇
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⢿⣿⣿⡟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠈⠋⠉⠀⢀⣀⡀
⢶⣆⠀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣷⣤⣤⡄⠀⠰⠖⠒⠀⠉⠉⠉⠁⠀⠀⠀⠰⠷
⠀⠉⠂⣠⣄⡀⠀⡠⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠉⠙⠃⠛⣷⡦⠤⠴⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⠤⠖⠈⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄
⠀⠀⠀⠀⠀⢠⠔⠾⠋⠀⠀⠀⠀⠀⠀⠐⠁⣴⣿⣷⣄⣀⡀⠀⣀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣬⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣭⣭⣥⣤⣤⣤⣤⣤⣼⣵⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠂⠴⠶⢤⡾⠏⠁⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⢐⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⠀⣀⠀⠀⠀⡀⣀⡘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡾⢫⡖⢀⣴⣿⣤⣀⡀⠀⠀⠈⠙⠛⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠈⠉⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢉⣴⣿⣷⣿⡿⠛⠛⠻⠀⣂⡜⠓⠲⢦⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⢿⣷⣶⣄⠀⣠⣶⡇⠀⢸⣿⣿⣿⠿⣿⣦⣤⣤⣁⣶⣿⡌⠀⠀⠀⠈⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⣽⣭⣼⣿⣿⣿⣿⠟⠋⠀⠀⠀⣿⣿⣿⡆⠈⠉⠉⠉⠙⣿⠙⠁⠀⠀⠰⠂⠀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⢇⡘⢿⣟⣉⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⣷⢂⠈⠛⠋⣩⠋⢁⣷⠇⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠢⣤⡜
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠀⠀⠈⠁⠀⠀⠁⠀⢸⣿⠀⠀⠀⠀⢀⣾⢻⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⢀⣄⣠⠆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠻⠿⠋⠀⠀⠀⠀⠑⢤⣤⣦⣾⣿⠏⠀⠀⠀⣠⡞⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠁⠀⠀⢠⠾⢋⡂
⠀⠀⠘⣿⣦⢠⠀⠀⠀⣀⣤⣾⣿⠇⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢀⣁⠀⠀⠐⢁⠗⣴⣆⡀
⠀⠀⠀⣼⠛⠷⡄⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠖⠉⠀⠉⢁⠁⠀⠀⠂⠘⡿⠛⠉⠀⠐
⠀⠀⢰⣿⡀⢀⡇⠀⠀⠀⢣⠀⠀⡀⠓⠒⢄⢀⡼⠉⠉⢀⡄⢀⣴⠇⢀⠿⣀⣀⠄
⠀⠀⠘⢿⣷⢨⣷⣄⠀⠀⢈⡇⠉⠀⠀⢀⠜⠉⠱⠰⠖⡋⣠⣴⣿⣀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⢠⡟⢀⠙⣿⣷⣦⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⠀⠈⣶⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣠⠋⠀⠀⠀⠀⠀⣤⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣼⣿⣇⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠉⠀⢾⣷⠀⠀⢀⣀⠀⠀⠀⠈⣣⣤⣶⣿⣿⣿⣟⣷⡀⢹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⡀
⠀⠘⣧⣤⣤⣤⣤⡶⠞⢀⣤⡾⢻⣷⣶⣿⣿⠓⣺⠿⠛⠉⠉⠁⠈⠻⣿⣸⣿⣷⣬⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠄
⠀⠀⠘⢿⣿⣿⣵⣶⣿⡿⠏⢀⣾⠁⣠⣾⣏⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⠗⠈
⠀⠀⠀⠀⠉⠛⠛⣿⠋⠀⢠⡾⢿⣿⣿⣿⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠛⠋⠉⠛⢲⣶⣿⡟
⠀⠀⠀⠀⠀⣰⡿⠿⠷⣶⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⠆⣄⠀⠙⣯⣥⣤⣤⣀⢠⣶
⠀⠀⠀⠀⠀⣿⠞⠀⢀⡾⢿⡛⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣁⣀⣤⣿⠷⡾⠛⢁⡀⠀⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠑⠛⠈⢀⣀⡵⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⢞⠀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠊⠀⠐⠃⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⠀⠀⠀⠀⠈⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⣰⠆⠀⠀⠀⠀⠀⠀⠉⠂⣤⡀
⠀⠀⠀⠀⠀⠂⣀⣀⠰⠁⠾⠀⣀⠀⠀⠀⢀⢀⣀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠴⡀
⠀⠀⠀⠀⠀⠌⠻⠟⠁⢠⡄⠰⣿⠾⠧⢺⠗⡿⠟⠱⠧⠤⠀⠤⠀⠠⠀⠠⠄⠀⠀⢰⠏⠀⠀⠂⠀⠀⠐⢆⠈⠀⢀⢀⡀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠔⠀⠀⠆⢤⡔⠀⢱⡄⠺⡯⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⡀⠀⠰⡀⠡⢤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠴⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣛⣷⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠞⣫⣾⣿⣿⣿⡿⠋
⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⠀⠀⠀⠀⣠⡾⢿⣿⣿⡿⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣾⣿⣿⣦⡿⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣿⣠⣾⣿⣿⣿⡿⠋
⡇⠀⠀⠀⠀⢀⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠋
⡇⠀⠀⠀⢰⡏⠁⠈⠁⠀⠀⠀⠀⠀⠖⠒⠒⠒⠒⠒⠒⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖⠀⠀⠒⠖⢀⣴⣿⣿⣿⡟⠁
⡇⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⠄
⡇⠀⠀⠀⢀⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠶⣄⠀⠀⠀⠀⠀⢀⡞⣉⡿⠟⠁⣿⣿⣿⣿⣿⣿
⡇⠀⠀⠀⠀⠙⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠁⠀⢀⣀⣠⣟⣀⣀⠀⣀⣤⠿⠛⠉⠀⠀⠀⣿⠻⣿⣿⣿⡇
⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁⠀⠀⢀⡴⠚⢉⡽⠋⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣠⠴⠋⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⣿⠀⣾⣿⡏
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⢰⣿⣿⠁
⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣷⣶⣦⣤⣴⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⢿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠀⡈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠤⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠄⠠⠤⠤⠤⠀⣤⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠠⡄⡀
⠘⠀⠀⠂⠀⠀⠤⠀⠀⢠⢤⣰⣦⠀⣠⠤⢤⡀⠀⣶⣖⡠⡀⠀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⢀⡳⣦
⠂⠀⢀⠀⠀⠀⠀⠀⠀⢸⣸⣶⣦⢸⠱⡊⣹⣸⣦⣿⣶⡃⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⢹⠑
⠨⢀⠀⠀⠂⠀⠀⠀⠀⠸⠽⠇⠀⠈⠦⣌⡡⠞⠀⡯⡇⠹⡵⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠈
⠀⠉⠀⣠⣴⢖⡶⢶⣄⠀⠀⠀⠀⣴⣶⡶⣦⠀⠀⠀⠠⣶⠶⢦⠀⠀⠀⠀⠐⡾⢛⣯⣯⣽⣿
⠠⡀⢰⣿⡵⠋⠉⠧⠽⠀⠀⠀⣸⣟⣿⢿⡾⢧⠀⠠⠀⣧⠶⣻⠀⠀⠀⠀⠠⣏⡿⣧⣀⢀⣠⠀⠀⢈⣴
⠘⠀⠘⣇⢙⣤⣀⡀⠀⠀⠁⢰⣛⠵⡿⡼⠇⠨⡆⠀⠀⣿⣪⣯⠀⠉⠀⠀⠀⡇⡠⣞⣥⣵⣿⠀⠀⠀⢸
⠐⡀⠀⣈⣉⠛⠓⢿⠻⡄⠀⡾⣑⣸⠓⠒⢺⡤⡺⡄⠀⢻⣢⣾⡀⣀⣀⡄⠀⣇⣴⣇⠀⠀⠀⠀⢀⡀⠘
⠀⠆⠀⣧⡺⢲⣶⣚⡵⠃⢠⡿⠅⣻⠀⠀⠈⣶⢟⢱⡀⢸⠛⡡⠾⠁⣁⡇⠀⡿⣫⡻⣿⢿⣿⠀⠀⠀⢀
⠨⠀⠀⠈⠉⠉⠉⠁⠤⠀⠈⠉⠉⠁⠀⠀⠀⠉⠋⠉⠃⠈⠉⠉⠉⣉⠙⠃⠀⠋⠉⠛⠓⠛⠛⠀⠀⠀⣰
⠡⡀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠂⢀⢀⡀⡀⣀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠤⠁⠤⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠙⠕⡡⠡⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣴⠚⣲⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡕⢶⣈⢺⣿⣿⣹⢀⡅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⢿⣄⢻⢻⡟⣿⠋⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⣂⣆⣹⣦⣮⣧⣿⣠⣧⡞⡯⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠊⣉⡱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠸⠀⠈⢪⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠐⢄⠀⢣⠀⠀⢿⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡀⠀⠐⢤⡑⠄⠱⣄⠈⣧⡠⠤⡒⠁⠀⠀⣀⡀⠤⠊⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠖⣌⣉⣁⡀⣉⣉⣐⡊⣑⣦⣬⡗⢻⢡⠀⠘⣍⠉⠁⠀⠀⠀⠀⣀⣨
⠀⠀⠀⠀⠀⢸⠉⠉⠁⠐⠒⢲⠐⠂⢉⠭⠽⠟⠉⣉⢁⡉⣲⠰⠀⡴⠮⢍⠉⠉⠛⠛⠂⠈⠉⠉⠃
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠂⠀⢸⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⣤⠄⢀⡀⢀⣸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⢸⠀⠀⢇⡀⢀⡀⠠⡤⠆
⠀⠀⠀⠀⢀⠜⢸⠀⠀⠀⠀⢸⠀⠀⢸⠉⠉⠉⠁⠐⠚⠒⡇⠀⠀⢸⠉⢹⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠐⠓⠂⢹⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢣⠔⠂⠤⠄⠘⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠂⠐⠧⣀⡠⠄⢀⡀⢀⣀⣀⣀⣀⡀⢀⡀⠠⠴⠀⠠⠔⠐⠒⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢠⠠⠤⠤⠀⣠⡶⠖⠆⠂⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠖⣒⠲⠆⣭⠹⠋⡠⠀⢀⠀⠀⠆⠀⢓⠀⠄⡁⠀⠀⠀⠑⣀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⡏⠀⣠⡀⠀⡂⠘⠀⣀⡀⠈⢂⡀⠀⢸⠀⠈⠁⠀⢸⡆⠀⢱⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢆⠀⢀⠀⠀⢸⠀⠃⠀⣈⠁⠒⢄⡀⠀⣇⣱⠀⢸⡇⠀⠸⠆⠠⢾⠀⠸⠃⠀⣾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠩⡄⠀⢸⠀⢼⠉⠙⠃⠀⠠⠟⣀⠈⠁⠀⠈⢼⡀⢀⣀⣀⠿⢀⣤⡄⠚⡀⣀⣽⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠘⡇⠀⠈⡆⠀⠑⠂⢀⢰⢁⠠⠥⠞⠉⠓⠒⠀⠒⠘⠙⠂⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠜⠃⠀⠀⠃⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⣤⠠⠤⠶⠶⠖⠒⠚⠻⠟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣄⣀⣀⣤⣤⡄⠴⣶⠶⠄⠀⠉⠛⠉⠈⠉⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠠⠤⢄⢶⣶⠌⡉⢺
⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⢫⢸⡅⠀⣀⣀⣀⣤⢄⠄⠀⠀⠀⠒⠀⠂⣂⠂⠂⠉⡉⠄⠌⠠⢀⠀⢀⣴⠒⠅⠁⠈⠀⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡁⢸⠀⠈⠙⠁⠀⠀⢸⠉⠉⠁⢸⡔⠁⣀⠈⠱⡇⠀⠶⠀⠸⠂⣡⠆⠐⠀⠈⠀⠔⠃⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠘⠀⠀⠀⠀⠀⠀⢸⠀⠘⠋⠲⡇⠀⠾⠂⢀⠧⠀⣤⡄⠳⡈⠀⠘⠠⠰⠈⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢐⡅⠊⠉⡤⢀⡠⠞⢱⢠⡼⣜⠆⢋⠀⣀⠤⠀⠄⠒⢲⣄⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⢀⡠⠐⠀⠀⠸⡃⠀⠀⡝⠁⠉⠸⡀⠄⢿⠀⠈⡤⠀⠘⠇⠀⢀⡀⠀⣼⠛⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⠀⠀⠀⢠⡏⠀⠀⡤⣀⣀⠸⠁⢈⠇⠀⣆⠀⢳⠀⢹⠀⠀⡇⠀⠀⡦⠀⠈⠉⠉⠈⡔⢩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⢐⠀⠈⠑⠤⠄⢀⠉⠙⢀⠀⡹⠀⠀⣀⠀⠈⡶⢻⠀⠀⢧⣀⣄⡅⠀⠀⣶⣶⡞⡐⣡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠰⠐⠾⡇⠀⠈⠘⠁⠀⢀⢿⠇⠀⢰⠏⣆⠀⠘⣼⡀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠹⠉⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⢰⠀⠀⠘⠂⠠⡤⣤⣴⣄⣛⡂⣰⡠⠁⠀⢲⡶⠿⠩⠷⠔⠿⠿⠛⠁⠋⠋⠙⠋⠳⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⢸⠤⣾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡇⢸⠀⢸⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣀⠀⠀⣀⣀⠀⠤⠠⣤⠤⠀⣀⡄⡖⢰⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠘⠂⠂⠘⠛⠛⠓⠒⠛⠛⠛⠓⠛⠚⠛⠓⠛⠉⠁⠈⠁⠉⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠐⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⠒⠒⠒⠀⠛⠛⠂⠂⠀⠀⠐⠀⠚⠘⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒

⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣿⣿⣿⠟⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣄
⠀⠀⠀⠀⠀⣿⣿⡏⣼⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⣿⣿⡟⢰⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⡇⢸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⡆⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⢋⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣠⣄⡈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣍⡙⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿
⠀⠀⠀⠀⠀⢿⣿⡇⣿⣿⣿⣶⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡉⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠃⣿⣿⣿⣿⣿⣿⣘⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣇⣸⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣁⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣆⠹⣿⣿⣿⣿⣿⡟⢠⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠹⣿⣿⣿⡟⢠⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣛⣀⣙⣉⣙⣁⣈⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣴⣾⡿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⡁⠴⢦⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣧⡘⠿⠶⠆⣹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢋⣡⣤⣶⣶⣶⣦⣌⡙⠿⣿⣿⣿⣷⡈⢷⣾⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠋⣴⣿⣿⣿⣿⠛⢿⣿⣿⣿⣦⡘⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠇⣼⣿⣿⣿⠋⣴⣶⣦⣬⣿⣿⣿⣷⠘⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⣿⣿⣿⣧⣌⣉⡛⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⢻⣿⣿⣿⡿⠿⣿⡿⢀⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⣸⣿⣿⣿⣿⣿⣿⡌⠻⣿⣿⣿⣶⣄⣶⣿⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣉⣡⣤⣤⣤⣉⡙⠻⢦⣌⠛⠿⠿⡿⠿⠿⠛⣉⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢹⣿⣧⠸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⠛⢷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⣙⠛⠻⠿⠿⠿⠿⠿⢿⣿⣿⡿⠋⣠⣶⠿⠛⣉⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣌⠉⣀⣈⣉⣤⣶⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠙⠻⠿⢀⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠉⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉


⣀⡀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⢆⠂⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠢⣄⣀⠤⠄⠐⡦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⡀⠀⠀⠀⠈⠂⠀⠀⠀⠰⠉⠑⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠉⠀⠀⠀⠀⠁⠀⠒⠤⣀⠀⢰⠔⠒⠚⠓⠲⢄⠀⠈⢃⠀⠀⠀⡀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡤⠂⠀⠀⠀⠀⠀⠀⠈⠑⠦⡱⠀⠀⠀⠀⠀⠙⠦⡈⡄⠀⢰⠀⠀⠀⡿⠀⠁⠠⠤⠄
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠈⢷⠀⠀⠓⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠇⠠⠊⣤⠀⠀⠰⣶⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣛⡁⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⡀⡠⠀⣠⣏⣤⣤⣤⣉⣀⣀⣀⣀⠻⠇⠀⣀⣀⣀⣬⣿⡶⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠿⠀⢀⣈⣃
⢀⡀⠸⠇⠀⡷⠁⠀⣥⣹⡏⠀⢰⣿⣿⡉⠉⢹⣿⣿⠋⢉⠉⠉⣿⣿⠇⣿⣿⣿⡇⣀⠀⠀⢰⠄⠀⣾⣿⡆⣼⣿⣿
⢨⣇⢸⣿⠀⠁⠻⠀⢘⣹⡇⠀⢸⣿⣿⡇⠀⢸⣿⣿⢠⣽⣠⣤⣿⣿⢼⡿⢻⡿⣧⣟⠀⣰⣿⡆⠀⣿⣿⠹⢻⡿⣿
⢻⣿⠰⢹⠀⠀⠟⠀⢻⣿⠀⠀⠘⡏⠈⡇⠀⠈⡿⢿⠀⣿⣯⢸⣿⣿⣿⠁⢸⠃⣿⣏⡷⢸⢿⣁⡀⡏⣿⠀⣾⠀⣿
⠻⠿⠐⢸⡆⠀⠀⠀⢸⣿⠀⠀⠀⡇⠀⢷⠀⠀⡇⢸⡇⠇⠈⢸⠁⡇⢸⠀⢸⢰⠏⡟⠀⠀⠈⢹⡁⠁⠟⠀⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⣀⠀⠀⠀⠸⠀⠀⠃⠀⡇⠁⠀⠀⠀⠁⠈⠀⠈⠈⠀⠃⠰⡇⣰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⣠⡄⠀⠰⣶⠀⠀⠀⢠⣄⠀⠀⠀⣤⡄⠀⢀⣠⣴⡞⢹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡷⢦⣜⣁⣤⣶⣶⠶⠶⠤⣤⣥⡶⠂⠀⣼⣦⢸⡔⠉⢙⡇⣾⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⢸⣿⣿⠀⣿⣿⠀⠀⠀⣿⣿⡄⢀⣼⣿⣿⠀⠈⠒⠊⠀⠇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡇⠸⠏⢿⠀⣿⠘⡇⠀⠀⣿⢻⡇⢸⡏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠉⠀⠃⠀⠀⢿⠘⡇⠈⠁⠈⠹
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢋⣙⡛⣛⣩⣌⠛⣫⣴⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⣡⣿⣿⣿⠟⣋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⢣⣾⣿⠿⢋⣵⣾⣿⡿⢛⣥⣦⣍⣛⣋⣍⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣯⣴⡿⢋⣥⣾⣿⡿⢛⣡⣶⣿⣿⣿⣿⣿⣿⣿⣦⠹⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⢛⣡⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢟⣡⣶⣿⣿⣿⣟⠹⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⣩⣴⣿⣿⠟⣋⣴⣿⣿⠃⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⣠⣾⠟⣫⣴⣿⣿⠿⣋⣴⣾⣿⣿⣿⣿⡀⠙⠛⠋⠉⠙⢻⣿⣿⣿⣿⣿⣿⡿⢛⣥⣾⣿⡿⠛⠁
⠀⠀⠀⠀⢀⣾⡟⣴⣾⣿⣿⣿⡁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⡿⢛⣡⣶⣿⡿⠟⠁
⠀⠀⠀⣰⣿⣿⡇⢿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠛⠁⢠⣿⣿⣿⣶⣿⡿⠟⠉
⠀⠀⠀⢻⣿⣿⣿⣆⠻⣿⣿⣅⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠙⠿⣿⣿⣧⡙⣿⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣋⣴⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣌⢻⣿⣷⡘⠿⠟⠿⢿⣿⠿⣋⣵⣾⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠹⣿⣿⣾⣿⣿⣶⣤⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡜⢿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣰⠶⠶⠛⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⠟⠉⠉⠙⢶⡀
⠀⠀⠀⠀⠀⠀⢱⠀⠀⢀⠀⠈⠉⠉⠉⠉⣉⣁⡀⠀⣀⢀⣀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⢽⣿⡇⠀⠀⠀⠀⢰⣹⣿⣸⠀⠻⣿⠏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠁⣽⣿⡟
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡟
⠀⠀⠀⠀⠀⠀⠸⡄⡞⠉⣭⣭⣭⣄⢸⠀⡏⠀⠐⠀⠐⢸⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡇⡇⣸⣿⣿⣿⣿⠘⡀⡇⠢⠀⢴⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢸⠻⠿⢿⣿⠿⠆⡇⢇⠀⠀⠀⠀⠄⠿⡿⢻⡟⠛⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡇⢈⣒⣒⣲⠶⠎⢍⣁⣨⠭⠭⠽⠿⠟⠛⢇⠸⡇⠀⠀⠈⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⢠⣀⠤⡀⢸⡇⠀⠐⣄⠐⠆⠀⢸⠀⣷⠀⠀⠰⣶⣿⣿⣿⣿⣤⣤⠄⠀⠀⣼⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⡇⡇⢀⡠⠂⠈⠐⠀⢸⣷⠀⠀⠀⠗⠦⠄⠸⠄⠛⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⡇⢸⢻⡇⠀⠶⠇⠀⠈⣿⠸⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⣸⣿⣿⣿⡿⢃⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⣷⠘⠦⣤⣤⣤⣶⣖⣚⢉⣉⣉⣩⣭⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿⣿⣿⠟⣴⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⢸⢀⡤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⠐⠂⠀⠐⠂⢸⢸⠈⠁⢸⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠻⠃⠀⢸⠈⡠⠦⠆⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⣅⡘⣒⣒⣒⣒⣊⣉⣀⣓⣀⣭⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁⣀⣀⣀⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣮⡻⢿⠿⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣻⡟⠉⠛⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠿⠿⠿⠿⠿⠿⠿⠿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠒⠀⠀⠀⠐⠚⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⡿⠟

⠀⠀⢀⣄⣀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣶⣞⢈⣯⣞⣮⣦⣧⣷⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣾⣷⣶⣷⣶⣿⣶⣾⣶⣾⣶⣶⣶⣶⣶⣶
⠀⣿⣿⣿⣿⠛⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⠟⢫⣿⣿⣿⣿⣿⣿⣿⣿⣯⡝⢫⢹⣿⣿⣿
⢠⣛⣛⣛⣛⣐⣃⢛⣛⣛⣛⣛⣛⣛⣛⣛⡄⠀⠀⠀⠀⠀⠀⣔⣛⣛⣛⣓⢂⣚⣛⣛⣛⣛⣛⣛⣛⣛⡛⣃⣘⣚⣛⣛⣛

⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⡠⠒⣶⣶⠒⢶⣶⡖⢦
⠀⢹⣿⣿⡹⣯⣭⣽⣩⣉⡛⣿⣿⠁⠀⠀⢰⣛⣛⣛⣛⣛⢻⡿⠿⠿⠿⠿⠿⠷⡄⠀⠀⢀⠞⠀⣼⣿⡟⠀⢸⣿⣷⡀⠑
⠀⢸⣿⣷⣶⡶⠶⠶⠶⣶⣾⣿⣿⠀⠀⠀⠀⣿⠍⠛⠉⢹⣿⣶⣲⣶⣶⣶⣖⣶⠃⠀⠀⠫⣉⣽⣍⣩⣯⣉⣽⣍⣩⣯⣉
⠀⢸⣿⣿⣿⡇⡀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⠘⠛⠛⢸⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⠒⠒⠂⢺⡇⠀⠀⠀⠀⢹
⠀⣸⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⡀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠈⠉⠉⢸⡇⠀⠀⠀⠀⢸
⠀⠃⠂⠂⠒⠓⠒⠒⠒⠃⠂⠐⠂⠃⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠃⠀⠀⢀⣿⣀⣀⣀⣸⣭⣭⣭⣭⣭⣽
⠀⠀⠀⠀⡔⣶⢶⣶⣦⣲⣶⣲⢢⡀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⣿⡿⠿⢿⣿⠿⠿⠿⠿⠿⠿⢿⣿⠀⠀⠀⠀⠀⣤⣷⣤⣷⣿⣿⣷⣤⣶⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⣿⡇⠀⢸⣿⣀⣀⣀⣀⣀⣀⣸⣿⠀⠀⠀⠀⠀⣿⣿⠒⠒⠒⠒⠒⢲⣿⡇⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣽⣯⣿⣿⣀⣀
⢠⠿⠇⠤⠸⠷⠶⠶⠶⠶⠶⠶⠶⢿⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣸⣿⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢠⣿⣿⣶⣖⣶⣶⣶⣾⣿⣧⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⣯⣿⣿⡿⣟⣿⣻⡟⣿⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠾⠿⠿⠿⠿⠿⠿⠿⠿⣿
⠃⣭⣉⣛⣛⣹⣛⣻⣛⣛⣩⣩⠑⠀⠀⠀⢰⣒⣒⣲⣏⠯⠭⠯⠏⠏⢹⣔⣒⣒⡲⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠛⠛⠛⠛⠛⣯⠭⠭⠭⣽⠆⠀⠀⠀⠀⡟⠛⠛⠚⣟⣛⣛⣓⣻⠗⠛⠛⢻⡆⠀⠀⠀⡼⠦⠤⠤⠤⠤⠤⠤⠤⠤⠿
⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⢸⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⢹⠛⠛⢻⡟⠛⢻⡟⠛⠛⣿
⠀⣷⣀⣀⣀⣀⣠⣿⠁⠀⠀⣿⠀⠀⠀⠀⠀⣇⣀⣀⣀⣿⠀⢸⠀⢸⣀⣀⣀⣸⡇⠀⠀⠀⢸⠀⠀⢸⡇⠀⢸⡇⠀⠀⣿
⣰⣷⣶⣶⣶⣶⣶⣿⣶⣶⣶⣿⣦⠀⠀⠀⣰⣛⣛⣛⣛⣛⣒⣚⣒⣚⣛⣛⣛⣛⣳⠀⠀⢀⣾⣿⣿⣿⣇⣀⣸⣿⣿⣿⣿
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠄⠀⢠⣤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⠒⣆
⠀⠀⠀⢀⡟⢻⠈⠁⠙⠛⡃⠀⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⢈⣯⣉⣇⣸⡀⢀⣀⣀⡏⣭⡇⠀⠀⢸⣿⠛⣻⣗⠉⢑⣿⡛⢻⣿⠀⠀⠀⢘⡟⣿⠀⢸⠀⡇⠀⣿⢻⡇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠱⡄
⠀⠀⠀⣠⣤⣤⣿⣿⣤⣤⣤⠀⠀⠀⠀⠀⠴⠚⠉⠅⠀⠀⠉⠙⠲⠀⠀⠀⠠⣴⣤⣼⣷⣦⣼⠀⠈⣦⣤⣤⠄
⠀⢰⣤⡏⠉⠉⠉⠉⠉⠉⠉⣤⡄⠀⠀⠀⠀⠀⠁⠛⠙⠙⠣⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠐⡅⠀⢸
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄
⠀⠀⢠⠤⠖⢺⣿⣿⡿⠲⠤⢤⠀⠀⠀⡖⠒⠒⡆⠷⠤⠽⠇⡖⠒⠒⡆⠀⠀⠀⢰⣶⣯⠉⠉⠉⢽⣶⣦
⠀⠀⠀⠀⠀⢸⡟⢹⣿⠀⠀⠀⠀⠀⠀⣇⣀⣀⡇⠀⠀⠀⠀⣇⣀⣀⡇⠀⠀⠀⣸⣿⣷⠀⠀⠀⢺⣿⣗
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢶⡀⠀⠀⠀⠀⠀⠱⡆⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠃⠀⠙⢦⣀⡠⠊⠀⠀⠉⠀⠀⠀⠀⠘⠧⠤⠤⡒⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⠤⣄⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠒⣶⣄⠀⡖⠈⠀⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⡈⠀⣠⣤⣤⣤⣿⣿⠀⡆⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⣤⡀⡆⠀⣿⣿⠀⠀⠃⠀⣿⠿⠛⣿⣍⠁⠀⠀⠀⣾⣿⢃⣀⡀
⠀⠀⠀⠀⠀⠀⠐⡠⠂⣀⡐⣢⣀⠃⣤⠀⢹⣷⡅⠀⣿⣿⠀⠀⠀⠀⣠⣤⣤⣿⡿⠀⢀⠀⢰⣿⡟⣠⡾⠟⠁
⠀⠀⠀⠀⣀⡤⢈⠀⠘⠛⠛⢟⡛⠀⠿⠂⠀⢿⡇⠀⣿⡇⠀⢀⠀⠀⡿⠿⠛⠛⣷⣄⢀⠿⣿⡿⠇⠏
⠀⠀⠀⠉⠙⠲⡄⢙⠶⠶⡄⢀⠁⢠⣶⡆⠀⠸⠀⠀⠛⠉⠁⠀⠀⠀⠀⢀⣀⣀⣿⣿⠐⢤⣿⣷⢘
⠀⠀⠀⠀⠀⠀⡔⠉⠁⠈⢀⣈⣀⣾⣿⠱⣤⣴⣤⣴⣶⣶⣾⠿⠿⠿⠿⠿⠿⠛⠛⠛⠀⠀⠉⠁⠘⢆
⠀⠀⠀⠀⣠⣾⣬⣓⠶⠾⠿⠛⠛⠛⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣀⣤⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠤⣄⡀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⠟⠁⠀⠀⠀⠀⣠⣾⠟⠛⠓⠦⡀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠜⡟⠁⠀⠀⠀⠀⠈⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



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