⢀⠈⢺⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢽⣶⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢢
⣱⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡄⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⣟⢟⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠒⢿⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢀⣼⠿
⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣳⣷⣀⡀⠀⣠⣤⣤⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠳⣿⣿⡦⡀⠀⠀⠀⠀⠀⠉⠐⢻⢻⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡻⡿⠊
⠙⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⣿⣻⣿⣿⣿⣷⣿⣿⣖⣲⣿⣾⣧⣤⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣷⣷⣯⣦⡀⠀⠀⠀⠀⠀⢸⣿⡿⡇⠀⠀⠀⠀⠠⠈⢢⣤⣤⣪⣪⡺⠉
⡤⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠊⠚⠛⠛⠛⠒⠒⠃⠛⠛⠛⠛⠚⠛⠛⠓⠒⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣝⢽⢿⣦⣀⡀⠤⠴⣿⡿⣿⣇⠀⠀⠀⠀⠀⣺⢿⣿⠿⡾⠋
⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⡴⡿⡕⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣫⡱⠢⢀⣽⣿⡿⠗⠃⠀⠲⣤⣤⣞⡵⡧⡫⠋
⠿⠛⠿⠅⠀⡦⣴⣶⣿⠏⠀⣰⢻⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[L]UCY⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣟⡿⠁⠀⠀⠀⠀⠀⠀⠐⢶⣯⣿⣻⣿⣿⠋
⠀⠀⠀⠀⢱⣾⣿⣷⡿⠧⠀⠂⠹⣿⣞⢝⢦⣠⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣤⣤⣤⣤⡤⡀⠠⢄⣤⣄⢀⠀⣤⣄⣤⣄⣀⣄⠄⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠽⢻
⠀⠀⠀⠀⢸⣿⠚⡿⠀⠀⠀⠀⠀⠀⠱⣕⣵⣿⣭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠟⠛⠿⣿⣿⢛⣛⣻⡿⣷⡮⢭⣭⣮⣿⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡅⣨⡄⠀⠀⠀⠸⠃
⠀⠀⠀⠀⢸⢸⢀⣇⡀⠀⠀⠀⠀⠀⠀⠈⠱⣿⡿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠃⡈⠀⠀⠀⠻⠛⠻⠉⠉⠉⢻⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢾⣭⡷⡦⠤⠤⣿⣶⣷⣀⣀⣀
⠀⠀⠀⠀⢀⣭⣻⣟⣁⠀⠆⠀⠀⠀⠀⠀⠀⠈⠫⡪⣺⣷⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣳⣿⣿⣍⣉⣙⣛⣿⣷⣶⠶
⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡧⡀⡀⠀⠀⠀⠀⠀IN⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣯⣴⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠌⢈⠈
⠀⠀⠀⠀⠸⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⢾⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡿⣿⣿⣿⡿⡻⢓⠀⠀⣀⣀⡀⠀⢠⣿⣯⣿⠏
⠀⠀⠀⠀⢰⣿⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀THE⠀⠀⠀⠀⡠⢮⣪⢪⠞⠉⠉⠙⠀⣰⣿⢿⣿⡿⠀⢁⣣⣿⣾⣿⣦⠀⠀⠀⢀
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣻⣿⣿⠗⠀⠀⠀⠀⠀⢸⣿⣿⣿⠛⠉⠀⠀⠘⠻⡯⡫⣗⣞⣂⡀
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⡺⡲⠋⠉⠑⠠⠈⠀⠀⠀⠀⢸⠋⡇⡇⠀⠀⠀⠀⠀⠀⠙⠮⣿⣻⣿⡁
⠀⠀⠀⠀⢸⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣽⢿⡟⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣷⡷⠂⢤⠀⠀⠀⠀⠀⠀⠘⢿⣟⢵⢄⡄⠂⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣯⡃⠀[S]⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣿⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⢿⣷⡆
⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡇⠀K⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[D]⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣕⢤⡐
⠀⠐⣾⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢉⣿⡍⡇ Y⠀⠀⠀⠀⠀⠀⠀⠀⠀WITH⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ I ⢸⣿⣾⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣻⣿⡀
⠀⠀⠹⠿⡟⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀A⠀⢼⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠌
⠀⠀⠀⠀⢸⣿⣯⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣴⣾⡅⠋⠀⠀⠀⠀⠀⠀⠀⠀M ⢺⣈⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠈⠹⢫⡻⣷⣤⠀⠀⠀⠀⠀⠀⢀⡀⢰⣯⣿⡯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣤⣴⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀O⠀⠀⢸⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⣷⢄⠀⠀⠀⠀⠀⠀⠈⣽⠁⣷⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⡨⡻⢿⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀N⠀⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⢻
⠀⠀⠀⠀⠀⠀⠀⠘⢙⣻⡻⣷⣳⣄⠀⠀⠀⠀⢀⣿⣗⣿⡆⠀⠀⠀⠀⠁⣀⣽⣶⣿⣯⡾⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠ D⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠁⠙⢮⡾⣿⡵⣔⠐⠚⠻⣿⣻⢷⡧⢀⠀⠀⠀⣠⢝⣿⠗⡻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻S⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢷⣷⠟⠂⠼⠿⠛⠋⠉⠀⣀⣽⣶⣾⢿⣯⡮⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠹⢝⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⢽⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿
⣒⣶⣶⣶⣲⣒⣒⣶⣶⣶⡓⠗⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⢃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⢕⣕⣷⣄⠀⠀⠀⠀⠀⠀⠂⠠⣜⣿⢮⢇
⠛⠛⠿⣷⣿⡯⠭⢬⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡴⣸⡄⠀⠀⠀⣄⠈⡀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣏⡦⣄⠀⠀⠀⠀⠀⠀⠀⡇⢸⣸⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠃⠈⠁⠀⠀⠀⢻⠙⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣻⡿⣿⣷⣾⣿⡽⣷⣦⡤⣄⣶⣴⣀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⢿⢟⡪⡪⣦⡄⠀⠀⠀⠀⣸⣷⣺⣿⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣄⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠣⠿⠿⠿⠯⠭⠽⠹⠿⠿⠿⠯⠿⠿⠿⠭⠽⠿⠷⠶⠄⠀⠀⠀⠀⠀⠀⠑⠈⠈⠀⠹⣿⣿⣿⢶⡂⠉⢿⣟⣿⡟⣟⠀⣀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣖⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣄⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣾⡟⠉⠩⠿⠛⠋⠉⢑⣀⣨⢿⣾⣿⣮
⠀⠀⠀⠀⠀⠀⠀⡰⡪⡻⣿⡿⢿⣜⠉⢡⣀⣠⡴⣶⠂⠀⡜⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣻⡿⣿⠟
⠀⠀⠀⠀⠀⣠⣮⣿⣾⡜⠁⠀⠀⠀⠑⣺⣾⣽⣿⣷⡄⠨⠙⣿⣿⣿⢷⡀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣒⣻⣶⣾⢿⣿⣗⣴⣤⣶⣶⣶⢖⡶⠶⠶⣶⣶⣟⣺⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠁⡄
⠀⠀⠀⡠⡺⣿⡿⢿⡟⠋⠄⠀⠀⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠈⠙⣗⢕⣼⣿⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠍⠀⠈⠿⠻⠖⠛⠛⢿⢿⣿⠭⠭⢽⣿⣷⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢶⣧
⠀⣠⣾⣾⣮⠋⠀⠀⠈⠀⠁⠀⠀⠀⠀⣸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠈⠑⣼⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⢀⡈⠀⠀⠀⠘⡟⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣿
⠚⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠋⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠛