Anesthesia Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⢀⡶⠒⢲⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠛⢿⣷⠀⠀⠀⠀⠀⠀⠀⢠⠞⢦
⠀⠀⠀⠀⠀⢺⡷⠆⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⣀⡀⠀⣻⠀⠀⠀⠀⠀⠀⢠⠏⡤⡈⣦⢀⡤⢤⡀
⠀⠀⠀⡀⠀⠸⣷⣶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⣿⣿⣰⠟⠀⠀⠀⠀⠀⠀⠸⠤⢽⡥⠼⡿⠀⠀⠁
⠀⠀⠀⢇⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁

⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣦
⠀⠀⠀⠀⠀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠾⣿⡿⢿⣿⠶⡆⠀⠀⠀⠀⠀⠀⠀⢨⢀⣀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⡇
⠀⠀⠀⠀⠀⢿⡿⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⡇⢸⡏⠀⢹⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣡⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⣿⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠃⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢠⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣗⠂⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠈⢷⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⢤⡄⠈⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⢠⣴⣾⣍⣩⣷⣶⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠁⠉⠻⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣧⣭⣭⣭⣤⡀⠀⠀⠀⠀⢀⣀⡼⠿⠋
⠀⠀⠀⢸⣿⣿⣿⣿⣏⣉⣿⠀⠀⠀⠀⠀⠀⠸⣄⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠓⠛⠛⠂⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠉⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣴⡄
⠀⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⣿⣿⣿⣿⠾⠛
⠀⠀⠀⢸⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠜⠙⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆⠀⣶⣆⢰⡆⢰⡶⠶⢠⣶⠶⠆⠲⣶⠶⠂⣦⠀⣶⠀⣶⠶⠆⢠⡶⠶⠄⢶⡶⠀⢰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⢿⡄⣿⠙⣿⡇⢸⣏⣉⢀⣙⣻⡧⠀⣿⠀⠀⣿⠉⣿⠀⣿⣉⡁⢈⣛⣻⠆⣸⣇⢠⡿⠼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠈⠀⠈⠉⠉⠀⠉⠉⠀⠀⠈⠀⠀⠁⠀⠈⠀⠈⠉⠁⠀⠉⠁⠀⠉⠉⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⠀⠀⠄⢄⠤⠠⠤⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⡀⣀⢀⠛⡀⠀⠀⠹⠛⠒⡉⠗⠛⠁⠀⠀⠀⠰⠂⣺⡇⠀⠀⠀⠀⠀⠅⢸⣅⡁⢁⡃⠘⠀⠀⠀⠛⡁⠒⠀⠈⡉
⠀⠀⠀⠀⠀⠛⠈⠀⣍⡍⢐⠋⠀⠀⠀⠁⠠⢠⡄⡦⠤⠈⠀⠀⠀⠐⣤⡔⢳⠀⠀⠀⠀⠀⠂⠸⠦⠄⠤⠃⠤⠀⠀⠈⠀⠀⢒⣁⠒
⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⡤⡄⠀⠀⠀⠁⠡⢰⡇⡦⡬⢈⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⠀⠀⣥⣤⡄⠃⠆⠇⢠⠀⠀⠀⠠⠆⠁⠀⠹⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡔⣤⠀⠀⠀⠀⠀⠀⠀⠔⡀⠀⡀⠀⠀⠀⠀⠀⢠⡄⢀⡄⠀⠀⠀⢀⣤⣤⣤⡄⢀
⠀⠀⠀⠀⠀⠀⢰⠀⣿⡏⠠⠀⠀⠀⠀⠀⢀⣀⠃⠁⠀⠀⠀⠀⠀⠀⢀⡄⠔⠈⠁⠀⠀⠀⠀⢠⢀⣀⢈⠀⠀⠀⠀⠈⠡⠭⢥⠁⣉⠴⡶
⠀⠀⠀⠀⠀⠀⠀⠞⠒⠂⠄⠀⠀⠀⠀⢯⠿⠥⠭⢬⠥⡽⠀⠀⠀⠀⠒⣷⠴⠦⠀⠀⠀⠀⣞⣂⣆⣀⣸⣀⣠⠀⠀⠀⢠⣀⡤⠀⢈⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠻⣒⡂⠁⠀⠀⠀⠀⡼⠋⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠶⣤⡤⠀⠀⠀⠀⢈⠍⠉⠉⠉⠩⡉⠀⠀⠀⠒⠒⠒⠂⠉

⠀⠀⠀⠀⠀⠰⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⢀⠴⢍⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖
⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⠑⣤⠀⠀⠀⠀⠸⠒⠲⡇⠆⠀⠀⠀⠀⢰⣖⡆⠀⠙⠀⠀⠀⠀⡄⠰⣴⣠⡈⣄⠀⠀⠀⠀⠀⣄⢉⣤⣅
⠀⠀⠀⠀⠀⠀⠀⣇⠑⣈⢁⡿⠀⠀⠀⠀⢰⠄⢀⡇⠀⠀⠀⠀⠀⠢⠄⠁⢠⣄⡄⠀⠀⠀⠀⠀⡄⠈⣤⠳⢦⡀⠀⠀⠀⢿⢀⡟⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠇⠋⠀⠀⠀⠀⠀⠘⠀⠸⠀⠀⠀⠀⠀⠀⠻⠁⠄⠀⠽⠀⠀⠀⠀⠀⠠⠴⠲⠀⠶⠶⠄⠀⠀⠀⠸⠿⠃⠟⠇

⠀⠀⠀⠀⠀⠀⣤⣷⠄⠼⠂⠄⠀⠀⠀⢶⢺⠡⢘⢲⡆⠀⠀⠀⠀⠀⡃⠀⠀⠠⡀⠀⠀⠀⠀⠭⢼⣇⣩⡏⠀⠀⠀⠀⠀⠀⠂⡈⠀⣠
⠀⠀⠀⠀⠀⠀⡃⠀⣄⠀⠀⠀⠀⠀⠀⣿⢰⣖⣖⢸⡇⡇⠀⠀⠀⢰⠇⣠⡆⠊⠀⠀⠀⠀⠀⠠⡀⠶⠶⢇⡀⠀⠀⠀⢘⠁⠐⠦
⠀⠀⠀⠀⠀⠀⡏⠉⠇⠁⠀⠀⠀⠀⠀⣿⢨⡤⠅⢸⡇⡇⠀⠀⠀⠸⡆⠁⠦⠤⠄⠀⠀⠀⠀⢈⢁⠁⠀⢨⡅⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠚⠃⠃⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠘⠂⠀⠛⠀⠀⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⡄⠀⠀⠈⠉⠉⠁⠀⠀⠉⠉⠙⠛⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡋⠉⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⠈⢿⣿⣦⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣿⣿⠿⠛⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣶⣤⣄⣀⣀⣀⣠⣤⣴⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠟⢻⣿⣧⠀⣀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣹⣿⣿⠿⠿⠿⠿⠿⢿⣿⣏⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⠇⠀⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⡿⣿⣿⣯⣀⠀⠀⠀⢀⣸⣿⣿⡿⣿⣿⣿⣿⣷⣶⣶⣦⣤⡀⠀⠘⠿⠛⠋⠁⠀⠀⢀⣼⣿⡟
⠀⠀⠀⢀⣠⣾⣿⡿⠟⠛⠉⠉⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠉⠉⠉⠛⠻⢿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣎⠉⢡⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠿⠿⠋
⢀⣾⣿⠟⠁⠀⠀⠀⣠⣶⣶⣶⣶⣄⣀⠀⠀⠀⠈⢿⣿⣦⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄
⣼⣿⡏⠀⠀⠀⠀⣸⣿⡟⠉⠉⠻⠿⣿⣿⣦⡄⠀⠈⢻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆
⣿⣿⠀⠀⠀⠀⢠⣿⣿⠃⠀⢀⣀⠀⠀⠙⢿⣿⣆⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧
⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⢻⣿⣧⣤⣤⣾⣿⣿⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀
⣿⣿⠀⠀⠀⠀⢸⣿⣇⠀⠀⣰⣿⣿⠿⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣷⣶⣦⣤⣄⣀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⣿⣿⠀⠀⠀⠀⠈⢿⣿⣷⣶⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣶⣦⣤⣄⣀⡀⠀⠀⠀⠙⣿⣿⡄
⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣿⣷⣤⣀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⠆⠀⠀⠘⣿⣿⡄
⣿⣿⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠉⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣶⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣿⣿⣿⣿⣶⣦⠀⠀⢀⡀⠀⠀⣴⣿⣿⠃
⣿⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠉⠉⠁⠀⠀⢿⠿⠀⠀⠛⠛⠁
⢿⣿⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣼⣉⡉⠉⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⣗⣂⡀⢀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⣗⠒⠊⠁⠀⠀⢹⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢫⡉⠁⠀⠀⢀⡜⠀⠀⠉⠑⠲⠤⣀⣀⠤⠒⠋⠉⠀⠀⠈⠉⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣉⣸⠁⠀⠀⠀⠀⠀⢀⠤⣀⣀⢤⡔⠉⠉⠉⠉⠳⡤⣄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡇⠀⠀⠀⠀⠀⠀⢸⣤⠟⠺⠼⣇⠀⠀⠀⠀⢀⡧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⣀⣴⣊⣉⣳⡀⠀⠈⠑⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣀⠴⠒⠓⠒⠒⠒⠒⡇⠀⢀⣀⠤⠤⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢰⠃⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠀⠀⠀⠀⠀⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠈⢦⡀⠀⠀⠀⢀⡠⠤⠒⠢⢄⡀⠀⠀⠤⠤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢀⠤⠿⠖⠒⠻⠷⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⣀⠤⠒⠉⠉⠉⠉⠑⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢠⠞⠁⠀⠀⢀⣀⣀⣀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡈⠲⡀
⢠⠃⠀⠀⡠⠊⠁⠀⠀⠀⠈⠲⡀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⠀⠀⠀⢀⡽⠀⠈⠢⡀
⡆⠀⠀⢰⠁⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠑⢄⡴⠋⠀⡠⠒⢦⡈
⡇⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⠀⢀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠑⢤⠊⠀⠀⠀⠉
⢱⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠳⡀⠀⠀⠈⠒⠀⠄⠐⠊⠁⠀⠀⡠⠂⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢄⠀⠀⠀⠀⣠⠦⡠⠃
⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⣀⠠⠊⠁⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠈⠢⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠐⢄⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⢢⣀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⠔⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⢀⠔⠁
⠀⢀⠔⠁

⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡖⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠰⣷⡄⠀⠀⠀⠀⠀⢠⣦⠐⢰⠀⠀⠀⠀⠀⣠⡤⠄⡀⡀⢄
⠀⠀⠀⠌⠠⠒⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡘⣿⠒⠀⠀⠀⠀⠈⠊⢀⠐⢣⡴⠊⠀⠀⠀⠀⠀⠄⠚⠀⠒⢈⠀⠀⠀⠀⡌⠠⠀⡡⡌⢠⠤⠁
⠀⠀⠀⠀⢀⠢⠚⠷⠵⠀⠀⠀⠀⠀⠘⠁⠔⠛⠢⠀⠀⠀⠀⠀⢀⡬⠑⠊⢀⡀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠡⡐⠜⣈⠀⡀
⠀⠀⠀⠁⠀⡉⡀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢙⠈⢻⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠊⠀⠀⠀⠀⠈⠐⢄⣀⡠⠞⠀⠀⠀⠀⠀⠑⠀⠁⠐⠁

⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⣠⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⡤⠔⠠⢄⠀⠀⠀⠀⠀⠀⢠⢴⢄
⠀⠀⠀⣠⠀⠰⡃⠈⠊⡀⠀⠀⠀⠈⠀⠀⠀⣴⠃⢀⠀⠀⠀⢰⠁⡠⠂⠰⣄⠐⡀⠀⠀⠀⠐⠸⠈⠈⡄⢰⠀⠀⠀⠀⢀⠀⠈⡀⡦⠤⠷⠦
⠀⠀⢰⡤⠦⠶⠷⠃⢀⣣⠀⠀⠀⠸⡉⠀⠀⢉⠃⠉⠀⠀⠀⢃⠀⣄⠀⢀⡠⠄⣇⠀⠀⠀⠀⢠⠀⠀⠣⡜⠀⠀⠀⠀⢀⡀⠚⠃⡀⠠⣀⠄
⠀⠀⠀⣉⡛⠘⠉⢛⣈⠁⠀⠀⠀⠀⠈⢲⡖⠁⡆⠄⠀⠀⠀⠘⢦⡀⠁⠈⣀⡴⠃⠀⠀⠀⠀⢠⠰⠴⠄⡤⠀⠀⠀⠀⠋⠉⠉⠉⠉⠂⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⠉⠉⡩⡉⡆⠀⠀⠀⠀⠀⠀⡇⢀⠐⠀⠀⠀⠀⠀⠀⠀⠌⢀⡀⠡⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⡀⠀⠀⠀⠀⡠⢤⡀⠀⠺⠃
⠀⠀⠀⠀⠈⠀⠑⠁⡇⠀⠀⠀⠀⠀⠀⡇⠀⣄⠀⠀⠀⠀⠀⠀⣈⣀⢡⡌⣄⡁⠀⠀⠀⠀⠂⠀⠀⠀⡌⠹⠄⠀⠀⠀⢤⡴⠦⢧⠤⢭⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠠⣠⠇⢀⠴⠦⠀⠀⠀⠀⠈⡈⡕⠂⠐⢺⠁⠁⠀⠀⠀⠀⠀⠀⣀⢸⡆⠍⠀⠀⠀⠀⡽⠃⠀⠘⢯
⠀⠀⠀⠈⠃⠐⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠓⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⢀⠀⣀⠐⢀⣀⣀⠀⠀⠀⠀⠀⡄⠀⠚⡆⠀⠀⠀⠀⠈⠀⠠⢀⠀⠅⡀⠀⠀⠀⢀⠄⠀⡰⢠⠠⠻⣅⠀⠀⠀⠀⢠⠎⠀⠈⢣
⠀⠀⠀⢀⡀⣛⢉⠙⠛⠘⠀⠀⠀⠀⠀⠠⢐⠸⡇⠀⠀⠀⠀⠀⠐⢀⡠⠀⠄⠃⠀⠀⠀⡀⠀⡠⠤⠥⠥⠡⢉⠀⠀⠀⠀⡆⠀⡇⡁⠀⡆
⠀⠀⠀⠁⠑⠀⠉⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠐⢄⡀⠔⡀⢈⡆⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠦⣸⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠬⠆⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠈⠀⠀⠀⠀⠀⠀⠞⠃

⠀⠀⠀⣠⠞⠁⠑⢦⠀⠀⠀⠀⠀⠀⡀⠀⠐⡠⢁⡄⠀⠀⠀⠀⢸⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠌⠣⠀⠀⠀⠀⠀⢘⠉⠉⢉⡙⠀⢀
⠀⠀⠀⠀⢠⠈⡂⠀⡇⠀⠀⠀⠀⠢⠩⡀⠄⢤⡈⠀⠀⠀⠀⠀⢘⠀⠜⢋⡄⠀⠀⠀⠀⠀⠀⠫⠂⡄⠀⠄⠀⠀⠀⠀⠨⠀⠀⢸⠀⠀⠉
⠀⠀⠀⠲⣄⢲⢀⠴⠁⠀⠀⠀⠀⠀⠑⠒⡆⡖⠊⠀⠀⠀⠀⠀⠈⠁⢰⠠⠌⠂⠀⠀⠀⠀⠀⢸⠉⡖⢄⡄⠀⠀⠀⠀⠀⢄⡀⡈⠀⠀⠈
⠀⠀⠀⠀⠀⠸⠀⠈⠚⠀⠀⠀⠀⠀⠀⢠⠶⢦⠈⠠⠀⠀⠀⠀⠀⠀⠸⠤⠛⠇⠀⠀⠀⠀⠀⢰⠉⡆⠀⠁⠀⠀⠀⠀⠀⠀⠱⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠠⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣶⣝⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠿⠿⠟
⣀⡠⠖⡤⡀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣿⣿⣿⣿⠀⠀⠀⢴⠖
⣷⣶⣶⣾⣩⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢯⣄⡀⢶⣶⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠙⠉⠻⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⡀⣀⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣧⢒⣣⣿⣷⡂⡀⡀
⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⣾⣿⣿⣿⣿⡆⢓⠺⠏⣿⠿⠓⠶⣄
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⡟⣐⡲⣾⣕⣒⣒⡢⢤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠚⣿⡍⣿⢿⣿⣿⣷
⣿⣿⣧⡀⢠⣌⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣾⡿⢿⣮⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⡋⠙⠶⢞⣻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⡟⠉⠀⠀⢀⡟⠀⠀⠀⠀⢀⣼⡿⡿⣿⠛⢿⣿
⣿⣿⣿⠿⢿⣿⣤⣿⣿⣿⣿⣿⣿⣿⠿⢿⡍⠙⡇⠀⠀⡄⠀⠀⠀⢹⣿⣤⣤⣤⣴⡿⠿⣦⡀⠈⠉
⡙⣯⣈⠀⠘⠛⢻⣿⣿⠝⠿⠻⠋⢁⠴⠖⠛⡆⡃⠀⠀⢸⣦⣠⣜⠈⣿⣿⣿⣯⠀⠀⠀⠀⠈
⣿⣿⣿⣷⡂⠀⠀⣤⣤⣤⣤⣤⣤⣾⣶⣶⣿⡇⣁⢤⣴⣿⣿⡿⢯⣄⣀⣨⣿⠇
⣿⣿⣿⣿⡃⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠞⠋⠹⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⢤⣀
⠟⡹⣿⣿⡅⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⡷⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠛⠷⣆⡀
⠀⠙⠺⢭⣇⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣟⢠⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛⠿⢵
⠀⠀⢀⣴⣤⣬⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣀⠀⠌⣳⣄
⠂⠀⠀⠨⠍⠑⣲⡖⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠉⠁⠈⠀⠉⠀⠉⠙⠛⠛⠛⠓⠦⣤⣤⣤⣀
⣿⣿⠿⠶⠶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⠛⠛⠛⠛⠛⠛⢳⡄⠀⠀⠀⠀⣴⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⢚⣓⣚⣛⣛⣛⣛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠚⢦⠀⣤⠤⠴⠛⠦⢼⡇⠀⠀⠀⣠⣿⢠⡤⠤⠤⠤⠤⠤⠤⢤⠀⡏⢩⣭⡉⢩⣭⡉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠈⢿⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⣿⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⣿⠚⡇⣿⠚⡃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⣀⣀⣀⣀⣀⣸⠃⠀⠀⠀⡇⣿⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⡧⠀⠀⡇⣿⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠼⠧⡤⣤⣤⣤⣤⢤⣤⡇⣿⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⡇⢺⠀⡇⣿⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢿⣈⣉⣉⣉⣉⣉⣉⣉⠉⠀⣧⣈⣛⣁⣈⣛⣁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⢦⠀⠈⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡁⡈⢁⠉⡈⡈⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⠁⠀⠀⠀⢸⡇⠀⠀⣀⣀⠀⠀⠀⠀⣻⣄⣄⣀⣠⣀⣀⣤⣤⣄⣀⣄⣀⣀⣀⣀⣀⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡆⠀⣠⠤⠼⠧⠤⠴⠧⠼⠦⣤⠤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠈⣣⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢠⡇⠀⠳⠤⣤⠤⠤⠤⠤⣤⣤⡼⠤⢵⡀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠞⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⡇⠀⠀⣹⠘⠃⠛⠛⠃⠀⠀⠈⠘⠛⠃⠛⠘⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢤⢤⣤⠤⣼⠀⡇⢰⠋⣻⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⣀⣀⣠⠞⠀⡇⢸⠀⢼⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠬⠥⠤⠤⠞⠁⢸⠀⢸⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣸⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠲⡏⣹⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣰⠋⠉⠉⠀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠄⢀⡉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⡏⠉⠳⣄⣩⣭⣭⣍⣭⣍⠉⢉⣍⣭⣭⣭⣡⡞⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⠀⣠⡀
⠀⠀⠀⢶⣶⣶⣶⣶⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣹⣿⣶⣶⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⢠⣿⠃⠉⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⢿⣦⠈⣿⡆
⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⠀⠀⠀⠀⠀⢠⣶⠿⠿⠿⠿⠿⠿⢷⣦⡀⠀⠀⠀⢠⣿⠃⠀⠈⣿⠀⢿⣇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢻⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣿⡇⠀⠀⣸⡿⠀⠘⢿⣄
⠀⠀⢀⡀⠀⠀⢸⣷⡶⠿⣿⠀⠀⠀⢀⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣿⠀⠀⠀⢻⣧⣀⠀⠈⠁⠀⠀⠈⣿
⠀⣾⠟⠻⣷⡀⠀⣿⡄⠀⣿⡇⠀⠀⢠⣿⠉⠉⢉⣉⣉⣉⠉⠉⢹⣿⠀⠀⠀⠀⣿⡟⢻⣿⣦⣀⣀⣴⠿
⢸⣿⣄⣰⣿⠀⠀⠘⠻⠟⠋⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⠀⠀⠀⠀⣿⣇⢸⣿⠉⠻⠛⠁
⣾⡏⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠈⢻⡿⠃
⠻⣧⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⢾⣿⠆
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣼⣿⡿⠿⠿⠿⣿⣿⣤⣤⣄⣀⣀⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠛⠋⠉⠉⠁⠙⢿⣦⣀⣴⠟⠁⠈⠉⠉⠙⠛⠛⠿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⣿⡇⠀⢸⣇
⠀⠀⠀⠀⠀⠀⣿⣦⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⢻⣿⠀⣿⣷⣤⣼⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⣸⣿⠀⣿⡇⠀⠸⣿
⠀⠀⡀⠀⠀⣸⣿⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⣿⣇⠀⢀⣿⡀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢻⡀⠀⣀⡄⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠷⢿⡉⠀⠀⠁⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⣏⠀⠀⠈⢷⠀⠀⢠⡾⠋⠉⠉⠉⠛⢦⣤⠞⠋⠁⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡶⠂⠀⠘⣧⠀⣾⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡤⠀⠸⡆⠸⣆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢀⡀⢻⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡋⠁⠀⣿⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣿⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣼⣦⠤⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⢻⡀⠀⣿⠀⠀⠀⢀⡶⠛⢳⡄⠀⠀⠀⢿⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠇⠀⣿⠀⠀⠀⣾⠀⠀⠀⢹⡄⠀⠀⢸⡇⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣰⠇⠀⠀⠀⠀⢻⡄⢀⣼⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠶⠶⠶⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠭⣆⢸⢙⠠⡏⠇⠸⡅⢻⠀⡏⢱⢸⠹⠂⢯⡀⡇⡭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠁⠈⠁⠈⠀⠁⠈⠀⠉⠀⠉⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢸⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣴⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠞⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡄⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠲⠿⢦⡄⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣙⣒⠚⠒⢛⠇⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠘⢻⣤⣀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠡⠀⠀⠀⢈⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠲⠚⠛⠋⠉⢵⣶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡛⠁⠀⠁⠀⠈⠀⠀⠖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢀⠢⠮⣙⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠄⣄⣐⣦⣤⣳⡾⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⠿⠟⠿⣛⣻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⣄⣙⣲⢮⣿⣿⠟⠋
⣤⣶⣶⣶⣿⣿⡿⢿⣭⡀⣀⢺⣶⣽⣥⣌⣭⣿⣷⣿⣦⣤⣤⣤⣤⣶⣶⣶⣾⠿⠛⠉⠀⠈⠉⠙⠋⠉⠁
⠙⠉⠉⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⣿⣯⣿⡿⠋⠉⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⡏⢹⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢤⡄⢠⡤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡖⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣤⣤⡀⠀⠀⠀⣠⣤⣤⡄⠀⠀⠀⢠⣤⣤⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⡇
⣰⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⠀⠀⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠀⠀⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣤⠤⠤⡄⠀⠀⠀⣤⠤⠤⣄⠀⠀⠀⢠⠤⠤⣤⠀⠀⡇
⡇⠀⠀⠀⣾⠛⠛⣷⠀⠀⠀⢸⠀⠀⣿⣀⣀⡇⠀⠀⠀⣿⣀⣀⡿⠀⠀⠀⢸⣀⣀⣿⠀⠀⡇⠀⠀⠀⣾⠛⠛⡇
⡇⠀⠀⠀⠻⠤⠤⠟⠀⠀⠀⢸⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⡇⠀⠀⠀⠿⠤⠤⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⠒⠒⡆⠀⠀⠀⣴⠒⠒⣦⠀⠀⠀⢰⠒⠒⣶⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⣤⣤⡇⠀⠀⠀⢿⣤⣤⡟⠀⠀⠀⢸⣤⣤⡿⠀⠀⡇
⡇⠀⠀⠀⣴⠶⠶⣦⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣴⠶⠶⡆
⡇⠀⠀⠀⢿⣀⣀⡿⠀⢀⡴⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⢦⡀⠀⢿⣀⣀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠴⣯⡤⣤⡤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡽⠦
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠉⢳⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣠⣤⣤⡄
⡇⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣥⣤⣤⣤⣤⣤⣤⣤⣧⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⡇
⡇⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠋⠛⠛⠛⠋⠙⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣒⠭⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣫⠕⡊⠁⠀⠀⠀⣀⣤⡼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⢀⡩⠖⠉⠀⢈⡠⣔⠿⠋⠁⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⡚⠉⢀⡤⠞⠉⠀⢀⣤⡾⠝⠊⠁⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⣀⠴⣊⠵⢊⠤⠚⡉⠔⣀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⢠⠖⠛⢲⡄⠘⢦
⠀⠀⢠⡊⠁⠈⠀⠀⠀⠀⢀⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡴⡿⠀⠈⠳⣄
⠀⠀⠀⠱⣄⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⢀⠤⠤⠤⣤⠤⠤⣤⠖⣾⠻⣗⡋⠁⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠈⠳⣖⠕⠉⠀⠀⠀⠀⠀⠀⡏⠐⠒⠲⢼⠆⠀⣯⠀⢿⢀⡿⢀⠵⡒⠒⣦⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢀⡴⡟⠶⣶⠚⡿⢻⢉⡹⡗⠛⡿⢥⣯⣀⣬⠖⣻⣀⣀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢾⢧⠈⢦⢸⡇⢷⠘⣯⣀⡿⠀⡼⣋⣉⣙⣶⠊⣹⠉⠉⠙⡆⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠘⢮⣛⣶⠟⣡⡎⠛⢞⢯⣠⠶⣷⣶⣖⣻⠟⠀⢿⣒⣖⣺⠇⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⢳⣙⠲⢤⣞⠻⡶⣄⠻⣍⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⡸⡋⠉⠀⣹⠈⠺⠶⠋⠀⢠⠤⠤⣄⠀⠀⠀⠀⢀⣄⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠱⣌⣓⣲⠟⠀⠀⠀⠀⢠⣇⣀⣀⣼⠀⠀⠀⣪⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⢀⡔⢻⠓⣆⠀⠛⠻⠛⠃⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢸⣄⣸⣠⣾⠀⠀⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠈⠛⠛⠛⠁⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣄⣀⣄⣀⣀⣀⣄⣀⣀⣀⣠⣀⣀⣄⣀⣀⣄⣀⣀⣀⣀⣀⣠⣄⣀⣄⣤⣀⣠⣠⣄⣠⣤⣀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⣀⠀⠀⢀⣀⠀⠀⢀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡇⠀⠀⠀⠘⠋⠃⠀⠘⠤⠇⠀⠀⠽⠂⠀⠸⠈⠀⠀⠛⠀⠀⠸⠀⠀⠘⠻⠀⠀⠻⠄⠀⠀⢰⡇
⠀⠿⠤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⢀⣀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠛⣿⡟⠛⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠄⠀⠠⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠄⠀⠠⠀⠀⠀⠸⠀⡄⠤⠤⠤⠄⠤⠤⠤⠤⢤⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⣦⣤⣀⠀⠀⠀⢀⣠⣤⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢶⣤⣄⡀⠈⠙⢷⣦⣴⠟⠉⠉⠹⣧⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⠀⣼⢏⣤⣄⡀⠀⠉⠛⢷⣄⠀⠈⢿⣄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⣤⡀⠉⣿⡆⠀⢿⡜⣿⡉⢿⡄⢾⡟⢷⣝⢷⣄⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠛⣿⠛⠀⢺⡇⠀⠘⣷⡈⠙⠛⠁⠈⠻⠶⡿⠀⢻⣆⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠶⠶⠶⠶⠶⢿⡇⠀⠀⠘⢷⣄⠀⠀⠀⣴⢶⣤⡀⠀⣿⡄⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠶⣶⣤⣶⠶⣾⡇⠀⠀⠀⠀⠙⢷⣄⡀⠻⣦⣽⣷⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣦⣀⣀⣀⣴⣟⡁⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣬⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠛⠛⠻⣿⡛⣿⠟⠛⠛⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⣀⣀⠀⠀⢀⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠉⠙⠛⠛⠿⣿⡶⠶⣶⣄⡀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣀⣀⣀⣀⣀⡀⠀⣿⠀⠀⢠⣭⡛⣷⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠷⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⣛⣉⣛⣻⣿⣦⣤⣤⣤⣤⣤⣤⣄⣀⠀⣾⠋⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⡶⠶⠶⠿⠟⠛⣿⠛⠉⠉⠉⠁⠀⢀⣀⣀⡀⠀⠀⠉⠙⢿⣿⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢁⣴⠶⠶⠶⠶⠶⠶⠶⠿⠷⠶⠶⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⣿⣧⣄⣀⣀⣤⣾⠿⠟⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡄⣀⣼⣿⡶⠿⠛⠋⠁⠀⠀⣀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠿⠿⠾⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠀⠀⣀⣤⣴⠶⣿⡃⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠾⠛⠋⠁⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣄⡤⠀⢠⠖⡄⠀⠠⣆⠀⠀⡶⠄⠀⢠⠀⠀⡶⠀⠀⣤⡀⠀⢠⠀⠀⠀⢸⡇
⠀⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡧⠤⠤⠤⠥⠤⠤⠤⠭⢤⠤⠬⠭⠤⠤⠥⠤⠤⠤⠤⠤⠤⡤⠤⠤⠥⠤⠬⠥⠤⠤⢼⠃
⠀⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠙⡇⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠇⠐⠀⠐⠀⠀⠂⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⠿⠂⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⠀⠂⠀⠂⠀⠐⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠀⠐⠀⠐⠀⣿
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠀⠀⠀⡇⢰⠒⠒⠒⠒⠒⠒⠒⠒⠂⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠁⠀⠀⢸⡇
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣀⠀⠀⢀⣀⠀⠀⢀⣃⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡘⠧⠔⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⣀⣀⠀⠀⠀⢈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢉⠒⠶⢤⣄⠀⢠⣀⣤⡼⠟⠿⣄⡉⠇⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠿⢷⣶⡾⠀⠀⠀⠀⠁⠈⠂⠀⠀⠘⡄⢯⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠒⣄⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⠀⣿⢱⡖⠁⠀⠀⠁⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢀⡏⠘⠆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⣠⠞⠑⠒⢻⡷⠆⠀⠀⠀⠀⡼⠀⠀⢀⣼⠇⠀⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠛⠋⠀⠃⠀⠁⡀⢀⠈⠀⢢⣤⡾⣧⠀⠈⠉⠁⠀⢀⠐⠀⠀⣾⠀⠁⠀⠀⢀⣤⠆⢤
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣤⠄⠀⠀⠈⠦⠀⠀⢀⠁⡀⠀⠀⠑⣔⡁⠀⣀⡔⣇⠀⠀⠀⠀⠈⠁⠀⡐
⠀⠀⠀⠐⠀⠤⠀⠀⣶⠀⠀⠀⠀⠀⣔⢀⠐⠛⢹⡗⢤⣤⣤⡅⣳⡆⠀⡀⠀⠀⠀⢸⡟⠛⠛⠉⠁⣤⠿⠦⡀⢇⣤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢽⠋⠀⠀⠀⢹⣀⣬⠋⠀⠀⠙⡄⢸⣿⣦⣀⢰⣅⣀⣀⣠⣴⡿⣌⠑⠂
⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⢀⡀⠀⠀⠘⢦⣄⣡⣤⡾⠟⠛⠀⠀⠀⠀⠨⣿⠋⠉⠉⢿⣿⣿⣯⣁⠀⠘⡌⠑⢀⡀
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡙⢲⡖⠚⠛⢿⣿⣿⡇⠄⠀⠑⠼⡁⠀⠀⠢
⠀⠈⠀⠀⢀⢠⠭⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⢴⠀⠀⠀⣀⣾⣷⢚⡿⢶⣄⠀⠀⠈⠓⡄⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⠁⠀⠘⢿⠀⠲⠆⢀⣀⣀⣠⠑⠦⠤⠜⢰⠛⢙⠛⢻⣹⢀⣠⣤⣤⠛⠠⠄⠙⠦⠤⠐⢁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣀⡀⠘⠀⠀⠀⠀⠀⠈⢡⠀⠀⢠⡄⠀⠀⢸⠀⠰⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠀⠤⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⡀⠂⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢠⠞⡇⠀⠀⠀⠐⠀⢰⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢑⡤⠋⠁⠀⠀⡀⠐
⠀⠀⠀⣀⠜⠂⠀⠀⠀⠈⠿⠷⡀⠀⠀⠀⠀⠀⠀⢀⠜⠰⠀⢈⠀⠀⠀⠀⠀⢠⣤⠎⠀⠀⡀⠐⠊⠉⠀⠀⠀⠀⠐⠉⠀⠀⢦⡀
⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠛⠡⠖⠁⠀⢀⡀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣦⣀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣏⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠙⣫⣥⣶⠟⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠶⠚⠉⠁⠀⠀⣿⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠒⠒⣒⣛⣒⠒⠒⠶⠦⢭⣍⣓⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢉⣤⣤⣄⡀⠀⢿⣁⣀⣈⡽⠀⢀⣠⣤⣤⡉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠯⣄⣀⣤⠟⠀⣀⡬⠭⠥⣄⠀⠻⣤⣀⣠⠼⢀⡸⠃
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠙⠲⠦⣤⣀⣀⣀⠻⣤⣤⣤⠞⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⢀⡴⠋⠉⠀⠈⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⡭⠟⠛⠉⠙⠓⢦⡀
⠀⠀⣼⣄⣀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡀⣠⣷
⠀⠀⢸⣠⠏⠉⠛⠿⣍⡽⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣠⡤⢤⡴⠚⠉⠣⣼
⠀⠀⠠⣏⠀⠀⠀⠲⢦⣩⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡷⠋⠀⠀⠀⠀⡼⠂
⠀⠀⣠⠞⠙⠲⣤⣀⢠⠞⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢈⢳⡀⠀⠀⣠⢞⡓⣄
⠀⢰⠃⡆⠀⡆⢸⠉⠉⠀⣠⢴⡶⠖⠒⠚⠉⠙⢦⠀⠀⠀⢀⣿⡀⠉⠲⣞⢱⡀⠙⣌⣇
⠀⡾⠰⡇⠀⡇⣼⠀⠀⢸⠁⠾⠤⢤⣄⠀⠀⠀⢈⣇⣠⠴⠻⢤⣭⣽⣟⡉⠉⠁⠀⢸⡿⠤⣤⣀
⠀⡇⠀⣇⠀⢹⡇⠀⠀⡿⣆⠀⠀⢀⣈⣷⣤⣠⡼⠋⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠓⢦⠀⠈⠙⢦
⠀⡇⠀⠘⢦⡀⠙⠶⣤⣷⣀⣀⣠⣬⣅⠀⠀⠈⢳⣴⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⡇⠀⠀⠀⢹⡶⢤⣤⣤⣼⠭⠵⠶⠾⠶⠶⠶⠶⠿⠷⠶⠶⠶⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠧⣄
⠀⢻⡛⠛⢛⣛⡇⢿⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣸⠂
⠀⠀⡷⡄⠈⠉⣇⠀⠉⠙⠛⠛⡟⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⢶⡆⠛⠛⠛⠛⡟⠉⠁
⠀⢸⠇⡇⠀⠀⢻⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇
⠀⣼⠀⣿⠀⠀⢸⡀⠀⠀⢀⣀⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⠀⣿⠀⠀⢀⣀⣇⣀
⠀⠙⡏⢻⣶⠛⣿⠷⠦⣼⡉⠉⠉⠉⢙⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⢿⠛⣷⡟⠙⡏⢀⣾⠉⠉⠉⠉⣹⣄
⠀⢾⣁⣸⣏⣀⣿⣀⣀⣀⣳⠀⠀⠀⣿⣹⡇⠀⠀⠀⠀⠀⠀⣼⣁⣀⣀⣸⣀⣸⣇⣀⣳⣿⣹⡇⠀⠀⠀⣏⣹

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣀⣄⡀
⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⡇⠀⠀⠀⠀⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶
⠀⠀⠀⠀⠛⠛⠛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⢛⡃⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠠⠤⠧⠼⠀⠀⠤⠤⠤⠄⠀⠠⠼⠧⠄⠀⠠⠤⠤⠤⠀⠀⠴⠤⠮⠄⠀⠠⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠰⠲⠒⠲⠀⠀⠖⠾⠖⠂⠀⠰⠖⠒⠆⠀⠐⠶⠒⠒⠀⠀⠖⠲⠷⠂⠀⠐⠲⠒⠆
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣄⣠⣠⣠⣤⣠⣠
⠀⠀⠀⠀⠀⠠⠤⠤⣬⠥⢤⠄⠀⠀⢰⡆⠁⠀⠁⠈⠀⠀⠀⢉⡉⠀⣶⠀⠀⠀⠤⢤⢧⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠜⠓⠐⠂⠀⠀⠐⠀⠀⠀⠐⠀⠛⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⣶⠀⠀⠿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣛⢉⣿⣿⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣿⣟⡽⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣨⣮⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡔⣯⣾⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣯⡺⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡙⢅⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢦⡴⠋⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⢋⣴⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢄
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⠁⠀⢀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠷⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰
⠀⠀⡈⢰⠁⠀⠀⠠⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠓⠄⠀⠀⠀⠀⠀⠀⠂⠦⢀⡀⠀⠀⢀⠀⠤⠄⠠⠀⠄⠀⠄
⠀⠀⣦⠀⠀⠀⠀⢀⠠⢂⠐⠀⠀⠈⠀⢀⠄⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐
⠀⠀⠁⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠠⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠑⠄⠀⠸⠀⠀⠀⠀⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢁⠐
⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄⠄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⢀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠄⠀⠀⠀⠀⢀⡄⡀⠁⢺⠀⠀⠀⠁⠀⠀⠀⠂⠀⠤⡀
⠀⠀⠀⠀⠀⢄⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⢀⠀⠂⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⢀
⠀⠘⠄⠀⠠⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠊⠰⠀⠀⠀⠀⠈⠉⠀⠀⢠⢄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰
⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠅⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠒
⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⡈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣤⡨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣌⡱⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡂
⣀⣀⣁⣀⣀⣁⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣈⣐⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣷⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⡇
⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣾⡆⠀⠀⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⢸⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿
⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿
⠀⢸⣿⣿⣿⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⣀⣀⣸⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⡏⠉⠉⠉⢹⣿⣿⣿
⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿
⠀⢸⣿⣿⣿⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣧⣤⣤⣤⣼⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿
⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣀⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠯⢭⣭⣭⣭⣍⣉⣉⣉⣉⣉⣭⣭⣿⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⠙⠳⠦⢤⣤⣄⣀⣀⣀⣀⣉⣁⣀⣠⣤⡤⠾⠛⢳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢻⡶⢶⣶⣦⣤⣤⣭⣭⣭⣥⣤⣤⣴⣶⡶⢿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣼⣧⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣸⣇⣼⣧⣾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢾⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⠆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠗⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠰⠷⢶⣶⣶⣶⡦⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⣿⡇⠀⠀⠀⠀⢀⣴⠟⡽⠊⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣶⣦⣤⣄⡀⠀⠀⢸⣿⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⣿⣇⠀⠀⠀⣰⡿⠛⠳⣄⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣸⠒⠲⠍⣿⠀⠀⢸⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠄⠀⣿⡀⠀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣿⣶⣦⣶⠟⠀⠀⠀⠙⠿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠟⠋⠀⠀⠈⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⢿⡟⠛⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠈⠉⢹⡇⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠔⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠒⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠂⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡇⠀⠀⠉⠙⠳⢶⣤⡀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⡄⠀⠀⠀⠀⠀⠉⠻⣇⡒⠉⡁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠐⡿
⣰⡂⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢨⡄⠿⣦⠀⠀⠀⠀⣀⠔⠀⠙⠦⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠠
⣏⠀⠀⠀⠈⢆⠀⠋⠉⠀⠁⠀⠰⠇⠀⠈⠳⡀⠀⠊⠀⠀⠀⠀⠀⠈⠣⡠⣀⠀⠀⡆⠀⣀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄
⠘⣆⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡡⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⡹⢾⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣀⣤⠖⠉⠁⠀⠀⠀⡀
⠀⠸⣧⣼⡖⢺⣿⣦⠀⠀⠀⠀⢰⣷⣿⢀⣰⢦⠟⢜⣳⣤⣤⣵⣦⣴⣦⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⢛⡁⠀⠀⠀⠀⣀⣴⠇
⠀⠀⠹⣿⣿⡄⢹⣿⣆⠀⢀⠠⠿⠁⠃⠀⠀⠀⠀⠀⠀⠈⡟⠛⠿⠿⠿⡟⣤⠀⠀⠀⠀⠀⠀⢰⠉⣋⣡⣴⣾⣿⣯⣀⡤⠶⠛⠉
⠀⠀⠀⠹⣷⣿⡄⢻⣿⡄⠀⠈⠐⢤⣀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⢡⡇⠀⠀⠀⠀⠀⠈⢷⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠹⣿⣿⡏⠘⠁⡤⠄⠀⠀⠉⠳⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⢀⠑⣼⣿⣷⣀⠀⠀⠒⠒⠂⠚⠉⠁⠀⠀⠠⢾⡿⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢦⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠠⣄⠙⠳⣶⣿⡆⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠛⠐⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠷⢤⣤⣤⠄⠠⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢢⠈⠛⢿⣿⣦⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠙⠻⠿⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡀
⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠘⣝⠶⣴⡧⠒⢲⢋⣽⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣿⣇⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⠛⣿⡟⠛⠃⠀⢸
⠀⡠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠉⠡⠤⠤⠤⠼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀
⠀⠢⠠⡤⠄⠠⠠⠠⠤⠄⠀⠠⠤⠄⠠⠀⠀⠠⠠⠀⠀⠀⠤⠠⠀⠠⠤⠄⠀⠀⠀⠠⠤⠤⠠⠀⠄⠤⡄⠠⠌
⠀⠀⠀⡆⠀⠀⢰⠒⠒⠒⢲⠀⠀⠀⢰⠒⠒⠒⢲⠀⠀⠀⢰⠒⠒⠒⢲⠀⠀⠀⢰⠒⠒⠒⠲⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠸⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠎⠀⠀⠀⠈⠇⠀⠀⠎⠀⠀⠀⠈⠇⠀⠀⠎⠀⠀⠀⠈⠇⠀⠀⠏⠀⠀⠀⠈⠇⠀⠀⡇
⠀⠀⠀⡇⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠸⠀⠀⠀⠸⠀⠀⠀⠘⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⣸⢀⢀⠀⢸⡄⠀⠀⣸⠀⠀⢀⢸⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⡇⠀⠀⢰⠒⠒⠒⢲⠀⠀⠀⢰⠒⠒⠒⢲⠀⠀⠀⢰⠒⠒⠒⢲⠀⠀⢀⡔⠒⢲⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢘⣠⡮⠤⠤⠤⢥⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠞⠀⠀⠀⠘⠆⠀⠀⠞⠀⠀⠀⠘⠆⠀⠀⠞⠀⠀⣀⡾⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⣶⣶⣾⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠟⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡠⠋⠛⠒⠐⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⣸⣀⣀⣀⣸⡀⠀⠀⠀⢸⠀⠀⠀⢰⣄⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠑⠀⠂⠀⠀⠃⠀⠀⠀⢸⠀⠀⠀⠀⣿⢈⣽⡀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⢸
⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠍⠁⠀⠀⠁⣿⠿⠋⢡⡾⢋⣴⣦⣌⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣡⣴⣤⡙⢷⡄⢸⡀
⡖⠒⠒⠓⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠒⠒⠚⢇⠸⣿⣿⡿⢸⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⡇⢿⣿⣿⠇⠘⠓⠒⠚⠒
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠬⠥⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠬⠅⠂
⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢠⡤⠀⠀⠀⠠⠄⠀⣔⡹⠃⠀⠀⠀⠀⠞⠆⠂⠀⠀⠀⠐⠂⢀⠔⡀
⠀⠀⠀⠀⠴⠶⠆⠀⠀⠀⠐⠃⡜⠃⠀⠀⠀⠀⢠⠅⠈⢀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⡄⠔⡈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠑⠠⠔⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣠⠀⢔⠈⢁⠀⠀⠀⠁⠀⢀⡏⢀⠀⠀⠔⢁⡄⢠⡀⠀⠀⠀⠀⠂⠈⡄⡄⠀⠀⠀⡀⢀⡠⠤⠦⠄
⠀⠀⠖⣻⣿⣋⢩⠂⠀⠀⠁⠀⡈⠁⠁⠀⠀⢅⠀⠄⠠⠀⡱⠀⠀⠀⠀⡀⠑⠃⠀⠀⢀⠄⠈⠡⡐⡤
⠀⠀⠐⠂⠀⠀⠂⠀⠀⠀⠀⠘⠁⠁⠁⠀⠀⠀⠑⠂⠐⠊⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠤⢡⠄⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠒⢀⡀⠩
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⢘⣄⠀⠀⠀⠀⢲⠄⠠⡖⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠈⢹⠏⠉⢿⠉
⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⡠⠀⣄
⠀⠀⠀⡰⠖⠲⠏⠂⠀⠀⠀⢁⠀⡆⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢈⡀⠘⠂⠀⠀⠠⠀⠀⠘⠄
⠀⠀⠈⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡀⢀⠄⠄⠀⠀⠂⠀⠀⠀⠀⡐⠀⠀⠈⠢⣯⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢠⠄⠐⢄⠀⠀⠀⠀⡀⠀⠄⠀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠀⠀⠀⠂⠀⢒
⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⢈⠄⠄⢌⠀⠀⠀⠀⣇⠘⡱⠀⠀⠀⠀⠀⢃⡠⠐⠄⠀⠀⠀⠁⠀⠁⠀⠉
⠀⠀⠈⠂⡇⠪⡄⠀⠀⠀⠀⢉⣘⠁⠀⠀⠀⠀⠀⢈⢀⣬⠀⠀⠀⠀⢐⡌⠐⠁⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢐⣈⣢⣄⣀⣔⣁⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡁⠀⠀⠀⠀⡁⢀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡀⠀⡀⠀⠀⢀⠀⡀⠰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⡄⢀⡀⡀⠀⣀⣀⠀⢀⢀⡀⢠⣨
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢂⠀⡀⠀⡀⢀⠀⢀⠀⡀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⡀⠅⠀⠀⡀⢸⢈⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⠠⠀⠀⠀⡄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢹⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡧⠯⠠⠤⠤⠤⠠⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠣⠀⠘⠓⠠
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠰⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡂⠀⠀⠠
⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⠈⡄⠀⠐⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⡌
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣬⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠈⠻⣿⣦⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠻⣿⣦⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⠙⢿⣿⡋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠘⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣿⣦⡀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠙⢿⣦⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢿⣦⡀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⢠⣾⠿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣷⣄⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⣠⣾⠟⠁⠙⢿⣷⣤⣾⠟⠁
⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⣠⣾⠟⠁⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⣠⣾⠟⠁⠀⠙⠿⠟⠁
⠀⣠⣾⠟⠁
⣾⡟⠁
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠒⠒⠒⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⢀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣳⠶⠋⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣦⡀
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣫⠞⠋⠹⣆
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⠀⠀⠸⣆
⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣫⠞⠁⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⣀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢋⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⢃⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠛⠛⠋⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠶⠲⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠴⠤⠴⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⠶⠶⠶⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡅⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣀⣀⣀⣀⣀⠀⣿⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⠀⣿⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⠀⣿⠐⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⣠⣾⣿⣿⡿⣿⣿⣿⣦⣌⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⣡⣴⣿⣿⣿⢿⣿⣿⣷⣤⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣴⣿⣿⣿⣿⣍⡁⢉⣽⣿⡿⣿⣷⡌⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢡⣾⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣦⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢸⠇⣼⣿⣏⠃⠸⣿⣿⡇⣿⣿⣿⠆⢋⣽⣿⡄⢻⡄⠀⠀⠀⠀⠀⠀⢀⡟⢠⣿⣯⡙⠻⣿⠟⠛⠛⠻⢿⡿⢛⣹⣿⣧⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣧⣶⣶⣬⡙⠃⠛⣉⣴⣶⣦⣽⣿⣷⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⣾⣿⣿⣿⣷⠃⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⡛⠻⠟⢋⣡⡄⣤⣍⠛⠿⠟⣻⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⢿⣿⣿⣿⡿⣆⠀⠀⠀⠀⢀⡿⣿⣿⣿⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠹⣿⣏⡄⢸⣿⣿⡇⣿⣿⣿⡆⣬⣽⣿⠃⣾⠁⠀⠀⠀⠀⠀⠀⠈⣷⠘⣿⣯⣥⣶⣿⣶⣤⢤⣴⣿⣷⣦⣹⣿⠏⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠙⢿⣿⣿⣿⣋⡄⣈⣹⣿⣿⣿⡿⢁⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡈⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠋⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡙⠻⠿⣿⣷⣿⡿⠿⠛⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣈⠛⠿⢿⣿⣾⡿⠿⠟⣋⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠶⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⠶⠶⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠛⠻⢷⣦⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⢠⣿⠋⠀⠀⡏⢻⠀⠀⠙⣿⡄⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠾
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡏⢰⡞⢚⠃⠘⡓⣲⠀⢹⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣿⡀⠉⠉⡇⢸⠉⠉⢀⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⢿⣦⣀⣉⣉⣀⣴⡿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣤⣤⣤⣤⣤⣤⡄⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇
⠀⠀⢸⡿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣾⡇
⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇
⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⡇
⠀⠀⢸⣿⣀⣀⣸⣇⣠⣤⣤⣄⣼⣇⣀⣀⣿⣄⣤⣤⣤⣄⣄⣼⣧⣠⣤⣄⣄⣼⣧⣤⣤⣤⣤⣤⣤⣿⣄⣤⣸⣧⣠⣤⣤⣄⣼⣧⣠⣄⣿⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⢀⣤⣴⣤⣄⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣾⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠞⠿⠿⠟⢿⡿⣦⣠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⡄
⠀⠀⠸⣋⠈⢉⠀⣿⣿⡏⢀⠀⠀⣻⢿⣿⣿⠀⠀⠀⠀⠀⠀⢖⠂⠐⠦⢸⣿⣿⣿⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⣶⣶⣬⡋⠁⠘⣿⢿⣿⡧
⠀⠀⠀⠎⠂⠘⠄⣠⠜⠁⠸⠃⠐⡁⢼⡿⠃⠀⠀⠀⠀⠀⠀⡏⠓⠈⠃⠘⣩⠏⠀⠠⡀⠙⣹⣿⣿⡇⠀⠀⠀⢰⡿⣿⢿⣿⣿⣿⡶⠠⠉⠸⡿⠃
⠀⠀⠀⠐⠀⡴⠛⢅⠀⠀⣀⣠⡰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠎⠁⠀⢈⡀⢀⣂⣽⠛⠋⠀⠀⠀⠀⠈⢃⡉⢀⡁⢻⢿⡄⢀⢬⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣑⠂⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢱⠒⠉⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⣱⠐⠈⢀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⢈⠃⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠻⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣳⣧⡚⠁⠀⠁
⠀⠀⢀⡤⠆⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡎⠀⠈⠀⡀
⠀⠀⠀⠜⠁⡴⡈⠧⠀⠀⠀⠀⢠⠢⡀⢀⡀⠁⠄⠀⠀⠀⢸⣿⣿⣿⡋⠣⠀⠀⠐⠈⡤⢤⠤⣀⠈⠠⠀⠀⠀⠀⠋⠇⣴⠚⠏⠀⠀⠀⢠⠢⡄⢀⡀⠁
⠀⣀⣔⣦⢠⠤⠄⠀⠀⠀⠀⣀⣸⠶⣆⣠⣀⠀⠀⠀⠀⣀⣼⣿⣿⠧⠤⠀⠀⠀⠀⢀⣌⠔⣄⣀⡀⠀⠀⠀⠀⠀⣼⡷⢧⠄⡀⠀⠀⢀⣈⠶⢆⣸⣀
⠀⠉⠙⠂⠉⠀⠀⠁⠀⠀⠂⠀⠉⠘⠃⠙⠋⠛⠀⠀⠀⠉⠙⠋⠉⠁⠀⠈⠀⠀⠀⠀⠉⠙⠉⠛⠁⠃⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠉⠈⠛⠘⠋⠙⠃
⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣶⣦⣄⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⣝⠛⠋⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣆
⠀⠀⣿⢠⠈⢹⡛⣿⣿⣿⠙⠋⠻⡿⣿⣿⣿⠀⠀⠀⠀⠘⠇⡀⠀⣉⢈⣿⣿⡿⣦⠄⡸⠋⣿⣿⠃⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⠻⠟⢿⡿⣿⣿⣿
⠀⠀⠙⡈⠁⠈⣴⣿⣿⠟⠅⠲⢀⢰⣿⣿⠟⠀⠀⠀⠀⠀⠐⠓⠀⠩⠈⠛⠋⠀⠉⠀⡰⠈⢟⠁⠀⠀⠀⠀⠀⢸⡏⠸⡏⠈⢻⣿⣆⠀⠄⠠⣾⠿⠟
⠀⠀⠀⠀⡰⠎⠙⣢⣀⢀⣶⣤⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣵⣤⣀⣠⣶⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠰⢆⠈⡹⠃⠀⠸⠄⠛⢀
⠀⠀⠀⠀⡇⠀⠀⣤⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣯⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣄⡄⠺⠿⠃⡀
⠀⠀⠀⢀⡁⠀⠀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⠛⠂
⠀⠀⠀⠁⠀⠀⠠⡁⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠩⠋⡉⢹⡃⠀⠀⠀⠂⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠴⣿⣿⣿⣧⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⢤⡠⢳⠀⠁⠀⠀⠀⠘⠉⡋⢹⠂⠀⠀⠀⠀⠀⠀⠀⣸⢸⢒⠀⠁⠀⠀⠀⠀⡍⢀⢰⠀⠀⠀⠀⠀⠀⠀⣰⡦⢹⠀⠁⠀⠀⠀⠘⠉⡋⢱⠂
⠀⠀⠰⡜⠾⠛⠀⠄⠀⠀⠀⠲⢌⡽⢶⡶⢤⠀⠀⠀⠀⠀⠾⡿⠽⠚⠀⠄⠀⢀⠐⠶⢯⡭⢾⡦⣤⠀⠀⠀⠀⠘⠻⠟⠙⠀⠄⠀⠀⠀⠲⣮⣽⢾⡶⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠔⠋⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡰⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⠁⠀⠀⠁⠢⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠶⠲⠤⣀⠸⣄⣀⣀⣀⣀⣀⡀⠤⡏⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠂⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⢄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠠⠀⣀⣑⣅⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠻⡀⠀⠀⠀⠀⠀⢠⠏⠀⢀⣠⠴⠒⠋⣉⠝⢓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⣠⠤⠖⠁⠀⢠⠏⠀⢀⠄⢊⠤⠊⠀⢠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠫⢍⡉⠈⠉⠒⢄⡀⠀⠀⠀⠀⢸⠤⠎⣀⣐⡁⠀⠄⢊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠁⠂⠌⡑⠢⢄⡀⠙⢆⠀⠀⠀⠀⠑⠒⠶⠶⠶⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠐⠠⠀⢀⡀⢁⣢⡬⠑⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠻⣦⡀
⠀⠈⠻⣦⡀
⠀⠀⠀⠈⠻⣦⣤⡀
⠀⠀⠀⠀⠀⠻⣄⠙⠷⣄⡀⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⣨⠟⢁⣽⠟⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣨⠟⠁⣴⠟⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣷⠟⠁⠀⠀⢀⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⢁⡴⠀⢀⡴⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡴⠋⣀⠀⠀⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⣠⠖⢀⣴⠗⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⠟⢁⡄⠀⢀⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡾⠃⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡴⠋⣠⠞⠁⠀⠀⠈⠻⣦⢀⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀⠀⠀⠀⢀⣼⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠈⠻⣦⡀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣞⣋⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠛⠛⠉⠁⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢮⣀⣀⡀⠀⠀⠐⠈⠉⣀⣀⠤⢀⣀
⠀⠀⠀⠀⠀⡴⡴⠚⠁⢀⣀⣁⠈⠉⠀⢀⡴⠊⢡⣶⣶⠏⠛⢿⣿⣄⡀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠺⢟⢵⣿⠃⠀⠀⠀⣰⠀⢠⠋⠀⣰⢋⡟⢁⣤⠀⣄⢙⠻⠛⠶⢤⣀⡈⢡⣖⠷⡀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⢠⣿⣳⠃⠀⢀⣴⠃⢠⡏⠀⢰⢃⡞⠁⠀⠁⠠⠧⢸⠀⠀⠀⠀⠀⠉⢛⠓⠳⢶⡤⢤⡶⠋⠀⠀⠛⠛⠛⠲⠤⡀
⠀⠀⠀⠀⠀⡞⣿⡇⠀⢠⡟⠁⢀⡾⠀⢠⠟⡞⢡⠰⠀⠀⠀⠀⠋⠀⠤⠀⠀⢠⢦⠂⠀⡴⢁⡠⠊
⠀⠀⠀⠀⠀⡇⣿⠀⢠⡟⠀⢀⡾⠁⡴⡟⣸⠁⠘⡆⡇⠀⠀⠀⠀⠀⠀⢰⣠⢷⠃⢀⢎⡴⠋
⠀⠀⠀⠀⢰⠗⣿⠀⣸⠀⢠⡞⠀⡼⢱⢣⣇⠀⢀⡟⠀⠂⠀⠀⠀⢀⣠⠴⠁⠃⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠸⡀⣯⠹⢯⣄⡟⠀⣸⠃⣸⡬⢿⣧⠞⠀⠀⠀⠀⠈⠉⠉⠀⠀⠘⡄⡼⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠁⠹⡀⠀⠈⠙⢦⣿⣄⡃⣴⠡⣄⠇⠀⠀⢠⠂⠀⠈⠀⠀⠀⠀⢳⠁⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣀⡦⠖⠒⡖⠂⠺⠗⣿⠀⡇⠀⠀⢠⡏⠀⠀⡆⠀⠀⠇⢀⡼⠀⠀⠀⠀⠀⢀⠘⡄⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡓⠒⠣⠶⡄⠀⢱⣶⠇⠀⢤⠾⠀⠀⣀⣣⠄⣠⡴⠛⠁⠀⠀⠀⠀⠀⣾⠀⢷⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠛⠿⠿⠼⠀⠀⠀⠀⠀⠉⢩⡇⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢸⡄⢼
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡇⠀⠀⣠⡿⠀⠀⠀⠀⠘⠃⠀⠈⡇⢸⣀
⠀⠀⠀⠀⠀⢰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢸⡇⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠏
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢸⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢰⠞⠋⠁
⠀⠀⠀⠀⢀⣠⢵⣒⠯⠍⠓⠂⠀⠀⠉⠈⣉⠤⠐⠀⠀⢾⠃⠀⢸⠇⠀⠀⡿⠀⠀⢀⣤⣤⣤⡶⠾⠃
⠀⢰⠰⢚⠭⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡀⠀⠀⠒⠂⠀⣸⠀⠀⠀⠁⠀⣴⡶⠧⠀⠀⠀⠀⠀⠠⢤⣀⣀⣀⣀⣀⡀
⠀⠙⠛⠒⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣀⣀⣈⣦⠒⡚⣥⠟⢿⠀⠀⠀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣉⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⣛⣓⡦⠀⠀⠄⠤⠼⠤⠬⠭⠭⠷⠶⠷⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⢋⡴⣫⡼⠛⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⢿⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⡥⠤⣤⠄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢰⡏⣠⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣭⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⣷⣝⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⠶⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣭⡅⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢸⡇⣒⡂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⣦⠀⠀⠀⠀⣸⠀⣧⠀⠀⠀⠀⢸⡇⠭⠥⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣼⠀⠀⠀⠀⡟⠀⢹⡀⠀⠀⠀⢸⡇⣛⡃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠳⡄⠀⠀⠐⣇⠀⢸⠇⠀⠀⠀⢸⡇⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠈⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⣤⡄⣿⠀⠀⣴⠋⠀⠈⢷⠀⠀⠀⢸⡇⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠳⠴⠃⡞⢹⠄⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣾⠛⢻⠀⠀⣠⡼⣧⣤⣤⣤⣼⣧⣤
⠀⠀⠀⠀⣰⠻⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣿⠀⢸⠀⠀⠙⠛⠻⡟⣿⢻⡟⠛⠋
⠀⠀⠀⠀⠳⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⢿⠀⢸⠀⠀⠀⠀⢰⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣤⣤⣤⣤⠇⣿⠀⠀⣿⠀⠘⠒⢾⠀⠀⠀⠀⣸⣇⣿⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠞⠃⠀⠀⠙⠶⠶⠶⠋⠀⠀⠀⠘⠷⠿⠿⠿⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠲⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠙⣷⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣽⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡀⣔⠀⠀⣎⡄⣐⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢻⡇⠀⠀⠈⣿⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡄⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣧⣤⣤⣴⣿⣦⡄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣀⡀⠀⣰⠋⠀⣧⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠂⠒⠉⠈⠙⢛⣛⣿⡶⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣮⡭⢱⡤⣇⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡋⠙⠛⠛⠛⠛⠛⣿⣷⣄⠀⠀⠀⡂⠀⡇⠀⠀⠀⠀⣿⣷⢸⡿⢿⣶⣶⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣯⣬⣁⣀⣉⣤⣬⣤⣴⣿⣿⣷⡄⠀⡃⠀⡇⠀⠀⠀⠀⠘⣿⣾⠃⠀⠙⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⡿⠉⠉⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠙⠃⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⢻⡆⠀⠀⠀⠈⠻⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⡄⠀⠀⠀⢀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡄⠄⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⡄⠀⠀⠀⠀⠚⠿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

⣿⣏⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠂⠈⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣀⡤⢄⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠈⢁⠄⣊⣭⡙⣯⡟⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠠⣀⡀⡀⢈⣩⣼⠻⣿⣿⣿⣷⣿⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠟⢿⠔⠁⠈⠟⠁⢹⣿⣿⣿⣿⣱⢦
⠀⠀⢀⣠⠴⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡚⠂⠙⠖⠛⢀⣴⣿⣿⣿⡿⢀⣾
⢠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⣿⡗⠂⠀⠀⠀⠈⠻⢿⣿⣇⡸⠃
⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⢎⣿⠗⠚⠀⠀⠀⠀⠘⢿⠟
⢨⡳⢤⣄⣀⣀⣀⣀⣀⡠⠄⢀⠀⠜⠀⠀⠀⢀⠀⠀⠈⠛⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠙⠷⢤⡄⠀⠀⠀⠀⠠⠀⠋⠀⠀⠀⠀⠀⠀⠁⣦⡀⠀⠀⠀⡅⠀⠀⠸⠂⠀⠀⠀⠀⠳⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⢤⡂⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠈⠒⠒⠀⠀⠀⠀⠀⠙⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀

⠀⠀⠀⣠⠞⣉⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⡙⢦⡀
⠀⠀⠀⣿⢸⠁⢹⠀⡇⡒⠒⠀⠀⠀⠀⠀⢸⠁⡏⠈⡇⢹⠠⠤⠄⠀⠀⠀⠀⠀⡇⢸⠁⣿⢸⡇⡒⠒
⠀⠀⠀⣿⢸⠀⢸⠀⡇⠂⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇⢸⢨⠀⠀⠀⠀⠀⠀⠀⡇⢸⣄⣿⢸⡇⠂
⠀⠀⠀⣿⢸⠀⢸⠀⡇⠥⠤⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇⢸⢐⣀⡀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢨⡇⠥⠤
⠀⠀⠀⡟⢸⠀⢸⠀⡇⡁⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇⢸⠐⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢰⡇⡁
⠀⠀⠀⣷⢸⠀⢸⠀⡇⣂⣀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡇⢸⠨⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢰⡇⣂⣀
⠀⠀⠀⣿⢸⠀⢸⠀⡇⠆⠀⠀⠀⠀⠀⠀⢸⠀⣷⣾⡇⢸⢈⠉⠁⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⡇⠆
⠀⠀⠀⣿⢸⠀⢸⠀⡇⠅⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⢐⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢨⡇⠅
⠀⠀⠀⣿⢸⠀⢸⠀⡇⡋⠉⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⠰⠒⠂⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⡇⡋⠉
⠀⠀⠀⣿⢸⠀⢸⠀⡇⡂⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⠨⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⡇⡂
⠀⠀⠀⣿⢸⣷⣿⠀⡇⠍⠉⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⢘⠒⠂⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⡇⠍⠉
⠀⠀⠀⣿⢸⣿⣿⠀⡇⠅⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⢐⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⢸⡇⠅
⠀⠀⠀⡏⢸⣿⣿⠀⡇⠒⠒⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⢸⠨⠤⠄⠀⠀⠀⠀⠀⡇⢸⣿⣿⠐⡇⠒⠒
⠀⠀⡴⢃⣼⣿⣿⣄⠳⡄⠀⠀⠀⠀⠀⢠⠞⣠⣿⣿⣧⡘⢦⠀⠀⠀⠀⠀⠀⡴⢃⣼⣿⣿⣄⠳⡄
⠀⢸⡇⣾⣿⣿⣿⣿⡆⢻⠀⠀⠀⠀⠀⡟⢰⣿⣿⣿⣿⣷⢘⡇⠀⠀⠀⠀⢸⠃⣿⣿⣿⣿⣿⡆⣿
⠀⠈⢧⠙⢿⣿⣿⠟⢡⠟⠀⠀⠀⠀⠀⠹⡌⠻⣿⣿⡿⠋⡼⠁⠀⠀⠀⠀⠈⢧⠙⢿⣿⣿⠟⢡⠏
⠀⠀⠀⠙⠶⠤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠈⠑⠶⠤⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠛⠛⠛⠛⠛⠻⢿⣷⣄⠀⠀⠸⠿⠛⠛⠛⠛⠿⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⡇⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡇⠀⠀⠀⢀⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠸⣿⣇⠀⢹⣿⣆⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⡆⠀⢻⣿⣄⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣤⣴⣿⣿⠷⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣀⣀⣀⣀⣠⣤⣾⣿⠇⠀⠀⠀⠀⠀⠀⢾⡿⠟⢿⣿⡀⣀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣩⣿⣿⠻⠿⠿⠿⠻⣿⣯⣅⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⠿⠃⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠿⠿⠟⠻⣿⣿⣤⣀⣀⣠⣴⣿⣿⠛⠿⠿⠿⣿⣿⣿⣶⣤⡀⠈⠋⠉⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠿⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⠀⠀⠀⣴⣿⠿⠃
⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⢀⣤⣤⣄⣀⠀⠀⠀⠘⣿⣷⣠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠈⠁
⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⢰⣿⠟⠛⠻⠿⣿⣶⣄⠀⠈⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⡿⠀⢀⣀⠀⠈⠙⣿⣧⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠘⣿⣷⣶⣶⣿⣿⣷⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠸⣿⣧⣀⣰⣿⠟⠉⠉⠀⠀⠈⠉⢉⣿⡿⠛⠿⠿⣿⣿⣶⣦⣾⣿⣄⡀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠘⠻⠿⠿⣿⣧⡀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⣿⣿⣶⣦⡄⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢠⣶⡄⠀⠀⠙⠻⢿⣷⣶⣶⣶⣾⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠹⣿⣯⠉⠁⠀⠈⠉⠛⠻⠿⢿⣿⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡿⢿⣿⡆⠀⢠⣄⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠘⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣶⣶⣤⣼⠏
⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⢰⣿⡆⠀⠳⡦⢷⣌⣿⣦⠀⠀⠀⠀⢠⣾⣦⠀⢀⣤⡀
⠀⠀⠀⢀⣙⣛⣃⠀⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⢈⡻⠋⠀⠀⠀⠀⢀⣸⣛⣇⡀⠀⠈⠢⠷⣬⡿⠁⠀⠀⠀⠘⠿⠟⢀⣹⣿⣟⣀
⠀⠀⢠⣿⣿⣿⣿⣷⠀⠀⠀⣠⣿⣿⣿⣦⡀⠀⠀⢰⣿⣏⣀⡀⣠⡄⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠙⣧
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢠⡏⣿⣿⣿⡏⣧⠀⠀⢸⣿⡏⠉⠉⣁⣁⣀⣈⣿⣻⣿⣁⡀⣠⣶⡄⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇⣿⣿⣿⠐⠛⣦
⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⢻⣇⣀⣸⣿⣛⣛⣛⣿⣿⣿⣿⣿⣹⣿⣃⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠉⣿⡄⠀⣿
⠀⠀⠀⠈⣿⣿⣏⠁⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⢸⡟⠉⠉⣉⣉⣉⣩⣿⣿⣿⣍⣉⣉⣉⡉⠉⠀⠀⠀⠀⠀⢸⣿⣿⢸⣿⠀⣿⡇⠀⣿
⠀⠀⠀⠀⠿⠻⠟⠀⠀⠀⠀⠀⠸⠟⠿⠀⠀⠀⠀⠀⠻⠇⠀⠈⠛⠿⠛⠛⠟⠛⠻⠟⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠸⠟⠟⠘⠿⠀⠿⠂⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⢼⣿⡧⣦⣣⣦⠀⠀⠀⠀⠀⣠⣶⡄⠀⣾⣿⡆
⠀⠀⠀⢠⣴⣿⢡⡀⠀⣶⣶⠀⠀⠀⠀⠀⣾⠛⠛⠛⢻⣄⣰⠂⡰⢽⠥⡂⢲⠀⠀⠀⣠⣾⣏⠀⠍⠏⠁⠀⠀⠀⠀⢀⣹⡛⠁⠠⣯⣿⣦⡀
⠀⠀⢠⣿⣿⣿⠶⠶⠶⠈⣷⠀⣀⠀⠀⠀⣿⠈⠈⠉⢸⡇⢘⡄⢘⣸⡸⠀⢸⠀⠀⠘⣿⣿⠉⠛⠶⡗⠀⠀⠀⠀⠀⣾⣿⢷⣶⣾⣻⣿⣿⣷
⠀⠀⣸⣿⣿⣿⠀⢀⣴⣾⡿⢠⡟⠀⠀⠀⢼⣿⣿⣿⣿⠁⠘⠓⣶⣾⣶⠖⠚⠀⠀⠀⢻⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣤⡀⠉⢸⣿⣿⣿
⠀⠀⠻⠿⣿⣿⠇⠸⠓⠛⣾⠛⠃⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡇⠀⠀⠀⠀⣶⠒⣧⠙⣿⠀⠸⣿⣿⠿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣸⡿⠀⠀⡀⡧⣀⠀⠀⠀⣿⠀⣿⠘⠟⠀⠀⢸⣿
⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠁⠈⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⠁

⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢰⣿⡿⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⡀
⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⠀⠀⢘⣿⠿⠐⠿⠷⠾⠿⠇⡀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠿⡏⠛
⠀⠀⢠⣾⣶⠾⣦⠀⠀⠀⠀⠀⢰⣿⣿⣦⣀⡀⠀⠀⠀⣿⣿⢀⡀⠀⠀⠀⠀⢠⣿⣿⣤⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠿⣧⡆⠀⠀⡇
⠀⠀⠘⣿⣅⣼⡏⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣶⣾⣿⣷⣠⣿⠏⠀⠀⠀⠀⠸⣿⡏⠛⠛⠃⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣾⠟⠀⠀⠀⡇
⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢹⣇⠀⢤⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⡇
⠀⠀⠈⢹⣿⣿⠉⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⠀⠀⢸⡧⠀⠚⠛⣛⣛⣛⣛⣿⣿⣿⣟⣛⣛⣛⡛⠛⠂⠀⡇
⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⠘⠿⠿⠻⠿⠛⠛⠛⠛⠛⠛⠻⠿⠟⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠛⢿⠟⠛⠛⠛⠛⠛⠛⠿⠟⠃⠀⠀⠆⠟⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣏⡉⣹⣄⠀⠀⠀⠀⠀⠀⠛⠋⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠋⠀⠙⡇⠀⠀⠀⠀⠀⢀⠎⠹⡄
⠀⠀⠀⠀⢸⣯⣥⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⣷⢠⣶⣦⢰⡇⠀⠀⠀⠀⠀⣎⢸⡆⣹⡜⠉⠑
⠀⠀⠀⡀⠀⠉⡻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⡆⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⠉⠛⠕⠃
⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆
⠀⠀⠀⠀⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⢨⣭⡍⣿⡇
⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⠋⢹⡏⢹⡏⠙⡀⠀⠀⠀⠀⠀⢠⣴⣶⢊⡄⡄⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠋⠙⠁⠀⠀⠀⠀⠀⠀⠐⠀⠘⠇⠺⠃⠀⠃⠀⠀⠀⠀⠀⠀⠉⠻⠉⢀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⣤⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣶⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠆
⠀⠀⠀⢀⣸⡿⢿⣯⣀⠀⠀⠀⠀⠀⠀⡏⠀⢻⠛⠻⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢀⣶⠟⠁
⠀⠀⠀⣿⣿⣿⣾⡛⣻⡇⠀⠀⠀⠀⠀⢇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤
⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣀⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣾⣷⣻⡄
⠀⠀⠀⣄⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠠⠬⠿⠿⠿⠿⠥⠄
⠀⠀⢀⠟⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠉⠻⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣀⣴⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⣶⣶⣶⣶⣶⣶⣿⡇⠀⣿⠀⢸⠁⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⣹⣉⣹⣋⣉⣿⣿⡟⠛⣿⠛⢻⠛⠛⣿⡇⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⣹⣉⣹⣏⣉⣿⣿⡷⠶⣿⠶⢾⠶⠶⣿⣧⣤⣤⣤⣤⣤⣤⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⣹⣉⣹⣉⣉⣿⣿⣇⣀⣿⣀⣸⣀⣀⣿⣿⡯⠤⢽⠥⢼⡧⠤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣉⣹⣉⣹⡏⣉⣿⡟⠛⠛⣛⠛⣛⠛⠛⠛⣿⡗⠒⣺⠒⢺⡗⠒⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠀⠉⠀⠀⠀⣿⣯⣭⣽⣍⣽⣯⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⣤⡄⣤⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠛⠛⠛⠛⠛⠛⠁⠀⠈⠉⠁⠉⠁⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠡⣄⣠⡄⠛⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠉⠀⢸⡇⡴⠀⡅⣰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀⢸⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢨⠄⠀⡀⠀⢿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠀⠀⠀⠀⠀⠀⠟⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⠀⠀⠀⠔⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠸⣶⡤⠴⠆⠠⠰⠶⠖⠠⠖⠶⠆⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠠⠶⠀⠀⠀⠀⠤⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠘⠛⠒⠊⠀⠀⠀⠀⠈⠰⠋⠉⠙⠃⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡷⠀⠀⠀⠙⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⣠⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⣿⠀⣿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣤
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣿⠀⣿⣶⣶⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠟⠀⠻⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠒⠒⠒⠒⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢀⣠⡏⢹⣄⡀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠼⠯⣿⠸⠦⡄⢠⠴⠇⣿⠽⠧⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠛⠛⣿⣀⣀⣛⣛⣀⣀⣿⠛⠛⠛⡟
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⢻⠀⢀⣀⣉⠉⠉⣉⣉⠉⠉⣉⣀⡀⠀⡟⠛⠛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡏⢹⠀⢸⠀⢸⡁⣿⠀⢸⡇⢸⡇⠀⣿⢈⡇⠀⡇⠀⡏⢹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⠧⠼⠀⢸⠀⢈⣉⣉⠀⠀⣉⣉⠀⠀⣉⣉⡁⠀⡇⠀⠧⠼⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡶⢶⠀⢸⠀⢸⠉⣿⠀⢸⡏⢹⡇⠀⣿⠉⡇⠀⡇⠀⡶⢶⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⠀⢸⠀⠈⠉⠉⠀⠈⠉⠉⠁⠀⠉⠉⠁⠀⡇⠀⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢈⣉⣉⠀⢸⠀⠸⡿⠿⠿⠿⢯⡽⠿⠿⠿⢽⠇⠀⡇⠀⣉⣉⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡏⢹⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⡇⠀⡏⢹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠷⠾⠀⢸⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⡇⠀⠷⠾⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠧⠤⠤⠤⠤⠾⠤⠤⠧⠤⠤⠤⠼⠧⠤⠤⠤⠼⠤⠤⠷⠤⠤⠤⠤⠼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⣀⣸⣿⣀⡀⠀⠀⣠⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠛⠿⣿⣦⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣿⠿⠛⠛⠻⢿⣷⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⣴⣾⣿⣦⠘⣿⣇⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⠀⣿⣿⠀⢠⣤⣤⣤⣤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⠀⣿⣿⠀⠈⠉⠉⠉⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⣠⣾⡿⠻⢿⣷⣶⣶⣶⣿⠿⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠸⠿⠋⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠈⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣿⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠀⣿⣿⣿⣿⠀⠻⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⢀⣿⣿⣿⣿⡀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣠⣿⣿⣿⣿⣿⣿⣆⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠈⠙⠛⠛⠛⠁⠀⢀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣤⣄⣀⣀⣀⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⣶⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣼⠀⠀⠀⠀⠀⠉⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠈⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡁⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⢻⣄⠀⠀⠢⣠⣀⣀⠘⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⣼⠘⡇⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠈⠻⢶⣆⡀⠀⢹⣿⢷⣦⣄⠙⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⢛⡄⠀⢀⠔⠁⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠉⠻⢾⣿⣿⣿⣿⣿⣿⣶⣄⣙⣿⣍⡑⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣾⣻⣶⣁⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣳⣿⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⢫⡟⢱⠒⣤⡽⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣾⣌⣹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠾⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⢠⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠒⠊⢡⠆⠀⠀⠀⢀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾
⢰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠊⠉⠀⠀⢀⣠⣶⠟⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠹⡇⠀⠄⣀⡀⢀⢇⣀⣠⣶⣿⡿
⣿⣿⡰⠦⠐⠂⠒⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠰⣤⣀⢀⣀⣀⣠⣶⢔⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⣉⢾⣿⣿⣿⠟⠁
⠙⢿⣷⣤⣀⣈⣡⣤⣤⡤⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣦⣭⠼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠘⠋⠉
⠀⠀⠈⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⡀⠂⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣡⡤⠶
⠀⠀⠀⢠⠞⠟⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⢿⠏
⠀⠀⠀⣇⠀⠰⠚⠋⠀⠡⠀⠀⠀⠀⠀⠀⠀⠘⣧⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⣿⣴⠇
⠀⠀⢸⣯⡖⢾⠉⠹⣧⡀⢡⠀⠀⠀⠀⠀⠀⠀⢿⡼⡀⠀⠀⢀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⢀⣀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⡀
⠀⠀⢸⡿⢶⡤⠦⠐⠛⠯⠸⠆⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠈⣿⠈⣷⠀⠀⠀⠀⠀⠀⢸⣷⣶⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠈⣿⣿⠁⣀⢀⡀⢱⣤⡁⠀⠀⠀⠀⠀⠀⠀⢻⠎⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆
⠀⠀⠀⠘⣿⡶⠿⠿⡛⢽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠽⢶⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠈⠷⡖⠋⠙⡩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⠧⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣀⣀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⠲⠞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣦⠀⣾⣦⣸⠄⣿⣛⡃⣶⣛⡓⠘⢿⡟⢰⣇⣀⣷⢰⣟⣛⠠⣾⣛⠂⢻⡟⠀⣴⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠓⠻⠆⠿⠈⠿⠀⠿⠤⠄⠤⡭⠿⠀⠾⠃⠸⠏⠈⠿⠸⠯⠤⠠⢬⡽⠇⠼⠧⠰⠟⠚⠧


⠀⠀⠀⠀⠀⠐⠒⠐⠒⠀⢤⠀⠀⠀⢄⣤⡠⢤⣤⡀⠀⠀⠀⢀⡈⣡⡏⠀⠀⠀⠀⠨⠈⡯⠩⠩⠡⠀⠀⠀⠀⣴⠄⡄⠀⠦⠄
⠀⠀⠀⠀⠀⡆⠃⠒⠒⠀⡦⠂⠀⠀⠀⠀⠀⠀⣀⡀⠂⠀⠀⠀⡂⢚⡇⠀⠀⠀⠀⠀⠀⡇⠊⠀⡆⢀⠀⠀⠐⠐⠂⡔⠂⠐
⠀⠀⠀⠀⠀⢀⡀⠈⠋⠀⡀⠀⠀⠐⠀⣀⢼⠨⡁⡁⠂⠀⠀⠀⢹⠁⡆⠀⠀⠀⠀⢐⣀⡀⠄⠄⡄⠈⠀⠀⠀⢠⡐⠐⠒⣆⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⠐⠂⠚⠂⠐⠂⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡄⢸⡿⠠⠀⠀⠀⠀⠀⠀⠘⠈⠁⠀⠀⠀⠀⠀⠀⡔⠁⠈⠀⠀⠀⠀⠀⡀⣀⠈⠇⠀⠀⠀⠘⢩⠭⡈⢀⡁⣴
⠀⠀⠀⠀⠀⠀⠰⠂⠂⠀⠀⠀⠀⠠⣧⢯⠭⠤⡤⢤⠆⠀⠀⠀⠐⣧⠤⢄⠀⠀⠀⢰⣒⣠⣉⣠⣀⣀⠀⠀⠀⣀⣀⡄⠀⡁⠆
⠀⠀⠀⠀⠀⠀⠘⢆⠂⠀⠀⠀⠀⠀⠼⠋⠀⠀⠈⠣⠀⠀⠀⠀⠀⠲⢤⠔⠀⠀⠀⠀⠩⠉⠉⠉⠩⠉⠀⠀⠐⠒⠒⠒⠈⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡠⠛⢌⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⠂⠀⡂⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⢼⢀⠀⡀⢲⠀⠀⠀⠀⠋⠉⢹⢐⠀⠀⠀⠀⠸⠯⠇⠀⠈⠀⠀⠀⠀⠀⠛⠀⠂⠰⠀⠀⠀⠀⠀⠄⢠⡄
⠀⠀⠀⠀⠀⠀⠸⣄⣰⢠⠎⠀⠀⠀⠀⣼⠂⣼⠐⠀⠀⠀⠀⢸⣐⠀⠰⠶⠀⠀⠀⠀⠀⠀⢀⠙⢁⠀⠀⠀⠀⠀⢡⢸⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⣠⣀⣀⣄⠀⠀⠀⠀⣀⣠⠀⢄⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⠀⣤⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠘⠉⠃⠈⠁⠀⠀⠀⠀⡇⣘⢈⡁⢹⢠⠀⠀⠀⠀⡅⠀⡀⠘⠀⠀⠀⠀⠈⠉⢻⣎⡛⠀⠀⠀⠀⠤⠄⢀⡀⠈⠁
⠀⠀⠀⠀⠀⠰⠒⢺⠣⠀⠀⠀⠀⠀⡇⢚⢘⠒⢸⢸⠀⠀⠀⠀⡇⠚⣁⣀⠀⠀⠀⠀⠀⠏⠁⠉⢹⡆⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠄⠀⠀⠀⠧⠬⠭⠤⠼⠸⠀⠀⠀⠀⠙⠆⠀⠈⠀⠀⠀⠀⠀⠃⠇⠀⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⢠⣦⡀⣴⠀⣶⠶⠆⢠⡴⠶⠄⠶⣶⠶⠄⣦⠀⣴⡄⣴⡶⠶⢀⡴⠶⠄⠰⣶⠆⠀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣇⢸⡏⢻⣿⠀⣿⣛⡃⢈⡛⢳⡆⠀⣿⠀⠀⣿⠛⣿⡇⣿⣛⡛⢈⡛⢻⣦⢀⣿⠀⣸⣯⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠈⠁⠀⠉⠀⠉⠉⠉⠈⠉⠉⠀⠀⠉⠀⠀⠉⠀⠈⠀⠈⠉⠉⠈⠉⠉⠁⠈⠉⠁⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢉⠁⠘⠉⠀⠺⠆⠀⠀⠀⣰⢦⠔⢲⡶⡆⠀⠀⠀⠀⠠⠄⢴⣗⠀⠀⠀⠀⠀⢐⠠⡓⠐⠐⠰⠀⠄⠀⠀⢐⠟⠠⠄⠀⠚⠂
⠀⠀⠀⠀⠀⢰⠘⠃⡓⢚⠂⡷⠊⠀⠀⠐⠀⢀⢈⠀⣀⣀⠒⠀⠀⠀⢈⡒⡻⢯⠀⠀⠀⠀⠀⠸⠀⡍⣉⢈⣻⢀⡀⠀⠀⠂⠘⠁⠔⠢⡌
⠀⠀⠀⠀⠀⠀⢀⠀⠉⠋⠀⢠⠀⠀⠀⠐⠐⣀⢽⠨⡁⡃⠒⠀⠀⠀⠀⢹⠁⢮⠀⠀⠀⠀⠀⠂⣀⡀⠄⠤⠤⠈⠂⠀⠀⠀⢠⠐⠈⠁⢢⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠀⠀⠀⠐⠐⠂⠛⠂⠓⠃⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠘⠙⠋⠀⠀⠀⠁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡀⣷⣽⠆⠀⠀⠀⠀⠀⠀⠀⠸⠉⠃⠀⠀⠀⠀⠀⠀⠀⡡⢃⠂⠂⠀⠀⠀⠀⠀⠀⠉⠀⠞⠀⠀⠀⠀⠾⠛⠛⠹⠂⠖⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢣⣚⣓⠀⠁⠀⠀⠀⢠⢤⡖⠂⠀⠀⠀⣄⠀⠀⠀⠀⢐⣏⢁⡀⠀⠀⠀⠀⢠⠄⡁⠒⠀⠃⠀⠀⠀⠀⠀⠉⠉⠃⠀⠷⢉⠃
⠀⠀⠀⠀⠀⠀⠀⢨⣀⡀⠀⠀⠀⠀⠀⠈⣯⠟⠉⠉⠹⣽⠉⠀⠀⠀⠀⠀⣛⠉⠉⠀⠀⠀⠀⠹⠶⠿⠶⠶⠷⠶⠇⠀⠀⢀⣓⣒⣃⠀⡖⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡀⡐⠁⠀⢈⠠⠀⠀⠀⠀⠀⡜⠙⢢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢐⣀⡁⠀⡄⠀⠀⠀⠀⠀⠀⣀⣂⠸⠅
⠀⠀⠀⠀⠀⠀⠀⡟⢀⡀⡀⢱⡆⠀⠀⠀⠀⡏⠉⢹⠈⠀⠀⠀⠀⠀⠚⠲⠇⠀⠀⠄⠀⠀⠀⠃⠈⠻⠳⠗⠺⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠫⡄⣴⢠⡞⠁⠀⠀⠀⠀⡟⠀⣸⠐⠀⠀⠀⠀⠀⣗⡂⠀⠰⢶⠆⠀⠀⠀⠀⠀⠖⠀⠐⠂⠉⠒⠀⠀⠀⠈⣧⣼⠃⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠑⠀⠊⠀⠀⠀⠀⠀⠀⠓⠐⠂⠀⠚⠀⠀⠀⠀⠀⠀⠒⠚⠁⠐⠚⠓⠀⠀⠀⠀⠛⠛⠘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠿⠗⠒⠃⠒⠀⠀⠀⠀⡏⠵⠒⠊⢹⢀⡀⠀⠀⠀⠀⡀⠀⠀⠐⠄⠀⠀⠀⠀⠳⠖⠿⠤⢾⠀⠀⠀⠀⠀⣀⡀⠀⠄⠠⠶
⠀⠀⠀⠀⠀⠀⢀⣀⣠⠄⠀⠀⠀⠀⠀⠀⡇⣿⢹⣥⢸⢸⠇⠀⠀⠀⢸⠁⢴⠇⠀⠀⠀⠀⠀⠀⠀⡆⡞⠷⠺⣄⠀⠀⠀⠀⡍⠀⠘⠂⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠙⠘⠀⠀⠀⠀⠀⠀⡇⠶⠴⠀⢸⢸⠀⠀⠀⠀⠘⢆⠀⠒⠶⠄⠀⠀⠀⠀⢀⡃⡅⠀⢸⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠂⠂⠀⠀⠀⠀⠓⠒⠒⠒⠙⠈⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠈⠃⠀⠀⠀⠀⠀⠀⠂⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡗⠒⠀⠀⠀⠀⢰⡋⠉⡆⠀⣠⠞⠋⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⠚⠁⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢸⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣤
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⢸⠀⠀⡏⠉⠉⠉
⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⢸⠀⢸⠀⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡇
⠀⢠⠇⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⣇⣀⣀⣀⣀
⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡇
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢈⠀⢸⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡇
⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡧⠤⠤⠤
⠀⠃⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⢸⠀⠀⠧⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⣴⣶⣿⣷⣶⣄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢰⣿⡟⠉⢻⣿⣿⣿⣷⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢺⣿⣿⣶⣿⣿⣿⣿⣿⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠘⢿⣿⣿⣿⣿⣿⣿⠟⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠙⠛⠿⠟⠛⠁⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣤⡤⠔⠚⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⢀⡴⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠈⠳⣄⢀⡴⠋⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠁⠈⠉⠙⠲⣄⠀⠈⠿⣄⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⣀⣤⠴⠞⣧⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⡤⠶⠚⠛⠉⢁⣀⣤⠴⢾⠄⠀⠀⠀⠙⢶⣤⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡤⠶⠖⠛⠉⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠒⠲⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⣀⣤⠤⠀⠀⠀⢀⡄⠀⢀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢠⠖⠃⠀⠀⢸⠀⠀⠀⠀⠀⢳⠴⠃⡔⠉⢢⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠤⣄⠸⡖⠁⡀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠸⣄⣠⢎⡞⠀⢀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢰⠁⢀⡤⡄⠳⠊⠀⣀⡤⠴⠒⠒⠒⠒⠦⢤⣀⠀⠀⠸⣤⠴⢋⡴⢦⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠸⣄⣀⡴⠃⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠰⢛⠗⠉⠀⠀⢳⡀
⠀⠀⠀⠀⠀⣼⠀⠀⢀⠄⠀⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠸⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢀⡇⠀⠀⡼⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡶⠋⢶⡄⠀⢱⡀⠀⠀⠘⡆⠀⠀⢸⡀
⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠴⢏⣀⠜⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠀⠀⠈⡇
⠀⠀⠀⠀⢸⡀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⠀⣴⠚⢁⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⡇
⠀⠀⠀⠀⠈⡇⠀⠀⠘⡆⠀⠀⠈⢇⠀⠐⣶⣾⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡞⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⠆⠀⠀⠘⢦⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⡄⠐⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢀⡐⠛⢦⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⢨⠷⠄⠀⠉⠑⠲⠤⠤⠤⠤⠖⠊⠉⠀⢀⢰⡃⠙⡆⠈⠃⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⡰⠓⠂⣠⠏⠀⢠⠀⠀⡀⠀⢀⡤⠆⠀⣆⡸⣆⠳⠤⠃⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠰⣅⡄⠀⡇⠀⡸⠁⠀⠘⠒⠒⣦⠘⠄⠈⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠓⠚⠁⠀⠀⠐⠒⠋⠁⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⠤⠤⠴⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⢀⠀⠂⠄⠀⠒⠒⠦⠐⠂
⠀⠀⠀⠀⠒⠤⣍⡁⡀⣐⠐⠀⠤⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠒⠚⠒⠲⠶⣦⣄
⡈⠀⠀⠀⠀⠀⠀⢣⠀⠢⠂⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢀⠀⠀⠈⠙⠦⠀⠀⢀⣦
⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠉⠒⠶⣤⣄⠐⢠⡄
⠄⠠⠀⠀⠀⠀⠀⠁⣮⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠸⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠐⡀⠀⠀⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠚⠋⠀⠀⠀⠀⠀⠉⠐⠲⠴⠶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢤⠜⠁
⠀⢡⠐⠄⠐⠢⠠⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⡏⢀⢵⣾
⠀⠀⠢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⠇
⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⢀⠈⢂⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⠀⠀⠀⡀⠈⡉⠲⣈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣞⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠉⠛⣎⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠝⠛⠛⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣠⣤⣤⠄⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠈⠉⠉⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠁⠀⣷⢆⡀
⠀⠀⢀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣋⣁⣀⣀⡀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⡟⠛⡏⡒⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣉⡁⠀⣁⣹⣾⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠓⢒⡒⠒⢒⠂⠂⡀⢒⡒⠳⢄⣳⡤⢏⣿⣟⠒⣐⠒⢒⡒⢒⡂⠒⢻⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠛⠀⠘⠃⠘⠃⠀⠂⠐⢛⡋⠂⠘⠂⠛⠀⠘⠃⠘⠂⠀⢸⣀⣘
⠀⠀⠀⠀⠀⠀⠛⢩⠍⠈⡭⠉⢩⡄⠩⠅⢩⠉⢩⠉⠩⠉⣭⠉⡭⠉⢩⡄⢩⡭⠉⢹⠉⢹
⠀⠀⠀⠀⠀⠀⣄⡈⡉⠀⠉⠀⠀⠁⠠⠀⠠⠠⠀⠀⠈⠀⠉⠀⠀⠀⠈⠀⠀⠠⠤⣼⣶⣾
⠀⠀⠀⠀⠀⠀⠂⠀⠯⠀⠺⠄⠨⠅⠐⠇⠸⠅⠰⠄⠨⠀⠿⠀⠯⠀⠸⠂⠐⠇⠀⣠⣀⣸
⠀⠀⠀⠀⠀⠀⠙⠉⣥⠉⠡⡌⢠⠍⢠⡌⢩⡍⢩⡉⣩⠈⡌⠉⣬⠉⢩⡍⢩⡍⠁⢯⠉⢹
⠀⠀⠀⠀⠀⠀⢀⣀⠉⢁⠈⠁⠈⠁⠈⠁⠀⠁⠈⠁⠭⠤⠭⠤⠤⠤⠤⠤⠤⠤⠤⣿⣶⣽
⠀⠀⠀⠀⠀⠀⠈⠀⠔⡂⢐⡂⢒⡂⠀⠰⣄⣐⢂⣀⣄⣀⡆⠀⣒⠀⣶⡂⢰⣒⠀⢹⠀⣸
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠼⡇⠂⠐⠀⠀⠀⢡⠀⠠⠄⠈⠁⠄⠁⠀⣼⢤⢼
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠁⠉⠉⠉⠉⠉⠉⠉⠙⠐⠒⠐⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⠖⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣀⠀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠴⠖⠋⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⠓⠀⠀⠀⠀⢰⡏⠉⠙⠓⠲⢤⣀⡀⠀⠀⠀⣀⡤⠶⠒⠛⠉⠉⠙⠓⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⠠⠤⢠⠴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁⣠⠤⠤⠤⠤⠤⢤⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⢤⠾⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦⠤⡖⢺⠁⠀⠀⠀⠀⠀⠀⢹⢳⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢴⡟⠛⠳⢾⡀⠀⠀⠀⠀⠀⠀⣸⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⢳⡀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⢀⣀⣤⣟⣉⣉⣉⣉⣉⣹⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣠⠴⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⣀⠀⠀⠀⠠⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⢀⣙⣦⣤⣤⣤⣖⣋⣁⣀⣀⣀⣀⣈⣓⣦⣄⣀⣀⣀⣈⣉⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠸⠰⠣⢐⠢⠀⠘⠀⠈⠀⠈⠘⠂⠂⠀⠐⠀⠃

⠀⠀⠀⠀⠰⠞⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣴⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠟⠛⠛⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⣋⣅⠀⠀⠀⠀⢸⠁⠀⠀⠀⠰⣷⣾⡆⣿
⠀⠀⠀⣀⣤⢀⢁⣄⣠⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⢰⡿⠿⠛⠀⠀⠀⠀⢸⠀⠀⢀⠆⠀⠈⠉⠀⣿
⠀⠀⢸⣿⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡴⣸⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣈⣁⣀⣀⣠⡿
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠃⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣀⣠⣴⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⡋⡀⠀⢀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣟⠀⠀⠀⠀⠀⠀⢸⡇⠙⡛⠛⠁⡇⠀⠀⠀⠀⠀⢸⣾⣿⡤⢠⣿⣷⡇
⠀⠀⠸⣿⣬⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⢀⡴⡻⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⡇⠉⠑⠉⠀⡇⠀⠀⠀⠀⠈⢿⣿⣿⠇⠈⣿⣿⣷⠃
⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⡹⢮⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠉⠉⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣻⣿⠃
⠀⠀⠀⠐⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠁⠀⠀⠀⠀⠀⠀⣿⢩⠉⣷⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⠰⣿⣷⡄
⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⣠⠔⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣶⣿⠀⠀⠀⠀⠀⠀⢸⣿⣷⢶⡀⡴⣾⣿⣷
⠀⠀⢸⡇⣿⣿⣿⣿⢸⡇⠀⠀⠀⠀⠀⠈⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⡌⠉⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⣿⢿⣿⡿⠇
⠀⠀⠘⠁⠛⠛⠛⠛⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⣰⣾⣿⣷⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⢐⣿⣿⢫⡝⣿⣿⠄⠀⠀⠀⠀⢀⡠⢤⣀⣿⠴⠖⠋⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⡖⠋⡟⣶⣧⣹⡏⢳⡄
⠀⠀⠈⢿⣿⣷⣾⣿⡿⠁⠀⠀⠀⠀⠻⠤⢾⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠉⠳⠿⣯⣭⡾⠗⠋
⠀⠀⠀⠀⠘⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠺⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣡⣬⡻⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠓⢠⡙⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡻⣮⡻⠟⠑⠽⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢤⡙⢦⣠⣾⣗⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⣪⢻⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⡝⣆⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢾⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠇⠀⠀⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⡾⣀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠉⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⣋⣭⣤⣶⣦⣤⣭⣭⣭⣭⣭⣥⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠻⠿⠿⠿⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⡀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣤⣀⡀⠀⣀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⠿⠷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⣀⣀⣀⣠⣴⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⠸⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣤⣄⣀⢀⡆⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡏⣾⡇⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣦⡀⠙⠻⣿⣿⣿⣿⣿⡇⣿⣧⢻⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⡀⠈⠻⣿⣿⣿⣷⢹⣿⣎⢿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⠻⣿⣿⣧⠻⣿⣧⡙⢿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠈⠻⢿⣷⠙⢿⣿⣦⣝⠻⢿⡇⠀⢸⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣮⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⣀⣵⣿⠇⠙⠻⢿⣿⣷⣦⣤⣬⣭⣭⡭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣭⣭⣭⣭⣭⣭⣵⣶⣿⣿⠟⠁⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⠿⠛⠉

⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣫⡭⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⣾⣶⣿⢿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣾⣿⠋⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠈⢿⣿⣿⡞⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⠶⣌⡄⠀⠀⠀⠀⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢿⣿⡗⣾⣽⠷⣾⣿⣟⡇⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠿⢿⣿⣿⣿⡟⡍⢷⣦⣁⢀⠃⠌⠀⠀⠀⢀⣺⣇⡄⢀⣀⢢⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⢠⣿⣟⣴⣿⣿⣿⣟⣈⣽⣿⡇
⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢰⣾⣿⣿⣟⠁⠤⠀⠉⢉⠫⠉⠀⠀⠀⠀⠸⣷⠀⠊⠀⠉⢽⣿⠀⠀⠀⠀⠀⠠⣄⠀⠉⠁⠙⠿⣿⣿⣿⣿⣷⠙⠻⢿⡇
⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠐⡀⢋⠻⣿⣿⣦⡰⠶⠤⠌⠀⠀⠀⠀⠀⠀⠀⠘⠃⠋⠀⢀⡾⠃⠀⠀⠀⠀⢀⣀⣈⠀⠀⠀⣠⡶⣿⣿⢿⣾⠃⢀⡀⠀⡇
⠀⠀⢸⣿⣿⠟⡇⢁⢢⡀⠀⠀⠀⢙⡈⢠⠈⡛⡻⠝⠁⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⠤⡿⢛⡉⠷⠤⠀⠀⠀⠀⠀⢹⠅⠀⠄⡈⠁⠀⠈⡋⣸⣳⠂⣿⡿⠗⡇
⠀⠀⢸⠛⠤⣸⣻⣾⡀⠳⣄⠀⠀⠘⢿⣶⣨⣴⣁⣠⡆⣼⣠⣀⣼⡎⠀⠀⠄⢤⣤⠖⠀⠀⠀⡠⠀⠀⠀⠀⢀⠀⠘⣦⠀⠀⠀⠀⢳⡄⠈⣿⠃⠀⠀⢀⣴⡇
⠀⠀⢸⡀⠀⢈⠉⠉⠉⠳⢮⠗⠀⠠⠟⠀⠀⠉⠯⡉⠙⠛⠋⠹⢁⡀⠀⠂⣬⣿⣁⠀⠀⢠⣄⠀⠀⣸⡆⠀⠘⡀⠀⣿⡗⠄⢀⠀⢸⣷⠀⡟⡇⠐⠘⠉⢀⡇
⠀⠀⢸⢧⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠙⠋⣉⣱⣁⠛⣶⣿⡏⠈⠀⣴⣿⡇⠀⠀⠁⠀⣼⣿⠀⢘⠀⠈⣿⠠⠠⠟⠀⠀⠀⠸⡇
⠀⠀⢸⠈⢳⡄⠳⡵⣄⠀⠀⢀⣄⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠒⠚⠛⠋⢱⡤⠉⢛⠁⢔⠀⠃⠀⢸⣿⠀⢘⠀⠀⣿⠂⠀⣰⣖⠛⠒⢸⡇
⠀⠀⢸⡀⠀⠀⠀⠉⠈⠙⠈⠛⠿⣷⣤⣄⣀⣀⡀⢻⣷⣄⠰⣤⡠⠀⠀⠀⠀⠺⣆⣠⣅⠀⠤⠀⠀⠀⠰⣿⣂⣓⣀⣘⣋⣀⣘⡀⠀⣟⣐⠋⢩⠟⠒⣻⣿⡇
⠀⠀⢸⣷⣄⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠛⠘⠛⠓⠈⠒⠀⠀⠘⢿⣿⣿⣯⣄⡄⠀⣰⡇⠁⠃⠀⢸⣿⠡⠴⠄⠤⢿⡌⠀⡋⠀⠚⣻⣿⡇
⠀⠀⢸⣿⣿⡔⣰⢼⣿⣶⣦⣰⣆⣦⡀⠀⡄⣄⣆⠀⠀⠠⡄⢠⡀⠀⢠⠀⣀⠀⣤⣄⡈⠉⠻⢿⣿⣟⠛⣧⡀⠄⠀⢹⡇⢸⣿⠏⢀⣀⣿⡶⠀⠀⠚⢙⠛⡇
⠀⠀⠈⠛⠋⠉⠙⠉⠋⠉⠋⠉⠉⠉⠉⠀⠉⠉⠉⠁⠈⠈⠉⠈⠉⠀⠈⠀⠉⠁⠉⠉⠉⠈⠉⠈⠉⠉⠀⠈⠁⠁⠀⠈⠁⠉⠀⠀⠉⠉⠉⠁⠀⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣪⠭⠭⠭⢑⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡸⢇⠸⢄⣀⣀⡠⠜⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠀⠒⠒⠈⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠒⠒⠒⠒⠊⠉⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠉⠒⢬⡑⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠴⢒⢤⠀⠱⡘
⠀⠀⠀⠀⠀⠀⡗⢦⡀⠀⠀⠀⠀⠀⢀⣀⠤⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣠⣾⡵⢻⠇⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠂⢬⡉⠉⠉⠉⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⣀⠀⡠⠚⣡⣴⡿⠟⣋⠴⣁⣀⣠⠗
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢉⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠉⠉⠲⡝⢦⣾⠟⢋⡤⠊⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣗⠠⣀⠇⠀⠀⠀⠀⠠⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠧⠚⠉⠉⠉⠑⢄⠘⡞⣧⠔⠁
⠀⠀⠀⠀⠀⠀⠙⠢⣀⡀⠀⠀⠀⠀⢀⣀⠴⣪⠃⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠈⡆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠢⢍⣉⣉⣉⣉⡡⠤⠊⠁⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠈⠉⠢⡀⠀⠀⢀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡠⠐⠒⢄⠀⠀⢱⠀⠀⣨⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡍⠢⣀⠜⠀⠀⣸⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣫⠖⠛⠊⠁⠀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⢀⡠⣞⠵⠊
⠀⠀⠀⠀⡠⢖⡽⠊
⠀⣀⢔⡫⠖⠁
⣾⠕⠋

⡏⠛⠛⠉⠉⠉⠉⠉⢉⡉⢉⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⡀⣀⠀⠀⠀⠀⢰⡆⢰⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢄
⡇⠈⠒⠃⠚⠀⠈⠉⠉⢸⡄⢸⠀⠉⠉⠁⠀⠐⠂⠛⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠀⠁⠀⠀⠉⠒⢦⡀
⡇⠐⠂⠃⠜⠀⠁⠈⠉⢰⠆⢸⠀⠉⠉⠀⠀⠐⠀⠟⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡐⣁⡀⣠⢤⠤⡄⡄⣤⢠⣄⢙⣆
⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡔⠋⠈⠉⠁⠀⢀⣀⣀⣀⡀⣀⣈⣀⡉⣣
⡇⠘⠓⠃⠛⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⠘⠃⠛⠀⡇⠀⠀⠀⠀⠀⠀⣥⠐⠐⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⡇⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⢠⣌⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐
⡇⠀⠈⠿⠃⠀⠀⠐⠀⢨⠀⢸⠀⠐⠒⠀⠀⠻⠌⠂⠀⡇⠀⠀⠀⠀⠀⡀⢰⠀⠈⠛⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢳⠀⠳⡄⠀⢀⣀⠠⠤⠐⠀⠀⠀⠀⢀
⡇⠀⠼⠣⠇⠀⠒⠒⠒⢈⠀⢸⠀⠒⠒⠂⠀⠿⠧⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠈⠓⢤⣀⣀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠢
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⠤⠄⣤
⡇⠀⠀⠛⠃⠀⠒⠒⠒⠀⠀⢸⠀⠒⠒⠂⠀⠙⠛⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠀⣀⣤⣲⣄⣭⡟⠁⠉⠻⠀⠀⠁⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠄⢸⢀⡤⢄⠀⡇⠀⠀⢸
⡇⠀⢴⠴⠇⠀⠒⠒⠒⢈⠀⢸⠐⠒⠒⠂⠀⣤⠼⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠌⠳⣄⡼⠉⠐⢦⠇⡇⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡘⠀⠘⡇⠀⣄⠀⠀⢣⠀⣀⣴⣷⡄⠂
⡇⠀⠸⠿⠇⠀⠒⠒⠒⢀⠀⢸⠐⠒⠒⠂⠀⠷⠽⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⠀⠈⠻⡀⠏⠀⠀⠈⠻⣿⣿⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢈⠀⢱⣎⠀⠰⠀⠀⠈
⡇⠀⢤⣴⠇⠀⠒⠒⠒⠀⣶⣾⠐⠒⠒⠂⠠⣤⡄⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢸⠀⠀⢻⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢸⠀⠀⠀⠁
⡇⠀⢰⢴⠆⠀⠒⠒⠒⠀⣿⣿⠀⠒⠒⠂⠀⡤⠤⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃
⡇⠀⣰⠄⠆⠀⠀⠀⠒⠀⣿⣿⠀⠂⠐⠀⢀⡆⡖⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠰⢄⠆⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠠⠀⡶⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⢀⠆⠀⠤⠤⠤⠀⣿⣿⠀⠤⠤⠀⠀⢰⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢸⡅⠐
⡇⠀⠀⢴⠆⠀⠤⠤⠤⠀⣿⣿⠀⠤⠤⠄⠀⠀⣤⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⡁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⡇⠀⠀⠀⠀⠀⠀⢀⣨⠟⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⡇⠀⠀⠀⠀⠀⠀⣤⣟⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⠀⠀⠀⠀⠙⠋⠿⠭⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⣇⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⡄⠴
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣭⣥⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣤⣾⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠯⡄⠀⠀⠀⠀⠀⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠏⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠤⠤⠀⠀⠘⣧⠀⠀⠈⠂⠄⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡶⠀⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠆⠐⠃⠣⡀⠀⠀⠀⠐⠀⠶⠀⠀⠀⠀⠀⠀⠀⡤⢰
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠄⠆⢀⠀⠀⠀⠃⠀⠀⠤⠓⠋⠙⠒⠲⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠀⡈⠆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠨⡀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡴⣶⣦⣤⣤⣖⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠡⠛⠋⣹⣿⣧⣯⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁
⠀⠀⠀⠀⢀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣓⠀⠁⠀⠀⠀⠉⠀⠀⠙⠓⠀⠀⠀⠆
⣿⣿⣿⣿⣷⢶⣾⣿⣿⣷⣶⣿⣿⣿⣶⣶⣾⣶⣶⣶⣾⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣷⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡉⠉⠉⠉⠉⣉⠉⢹⡄⠀⠀⠀⠀⡞⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣭⣭⣩⣭⣭⣍⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠹⣄⡶⠒⠚⠉⠓⢺⡇⠀⠀⠀⡖⡇⢰⠒⠒⠒⠒⠒⠒⠒⡆⢸⢠⡶⣆⢰⣶⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠃⠀⠀⠀⠀⢸⡇⠀⠀⠘⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⠉⣿⢸⠉⡅⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠤⡤⠤⠤⡤⠤⠤⠾⠁⠀⠀⠀⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⡇⢸⢀⠀⣿⢸⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠙⠒⠚⠓⠒⠒⠒⠒⠒⠒⠚⣇⡇⢸⣤⣤⣤⣤⣤⣤⣤⡇⢸⠸⣄⡟⠸⣠⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣍⠙⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠶⠶⠶⠶⠶⠶⠶⠆⠀⠘⠲⠶⠶⠶⠶⠖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⡇⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⠂⠐⠐⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⢀⢀⣇⠀⢀⣖⣲⡀⡀⡀⣠⠟⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠻⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣼⠀⢼⡉⠉⠉⠉⠉⠉⠉⠉⣻⠉⣇⠀⠀⠆⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⡿⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢠⠇⠀⠈⠉⢙⠉⠉⠉⠉⢹⠉⡏⠉⠙⡦⠤⠤⠤⠤⠄⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣾⣀⣀⣀⣀⣸⠀⡇⢠⠖⡇⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠉⠉⢉⡽⠀⡇⢸⠀⡷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣛⣉⣀⡴⠃⢸⠀⡇⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡇⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢴⡏⣷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⣴⠛⠛⠃⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⢻⡍⠙⢦⣈⣉⣉⣉⣉⣉⡉⠉⣉⣉⣉⣉⣁⡴⠋⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠾⠿⠿⠿⠷⠶⠶⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄
⠀⠀⠀⠀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⣉⣡⣤⣴⣶⣶⣿⣿⣿⣿⣶⣶⣶⣤⣍⣙⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦
⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣠⡾⠋⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧
⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣼⠏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣧⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧
⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣼⠇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢹⣇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇
⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢻⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⡿⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡈⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡿⢁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣿⡏⠀⠀⡶⠟⠛⠛⠻⢶⡄⠀⠀⣴⡾⠛⠛⠛⠛⠷⠆⠀⢸⣿⡀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿⡇⠀⠠⣦⣄⣀⣀⣠⣴⠄⠀⢸⡏⢶⣤⣀⣀⣠⣴⠦⠀⢸⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠸⠇⠀⠈⠉⠉⠉⠀⠀⠀⢸⣿⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠈⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠈⣿⣇⠀⠀⠀⠀⠀⣀⣼⠏⠀⠀⠙⢷⣀⠀⠀⠀⠀⠀⣰⣿⠃⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣆⠀⠀⣴⠟⠋⠁⠀⣴⣦⠀⠈⠙⠻⣶⠀⠀⣰⣿⠃⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏
⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡈⢿⣷⡄⢻⣦⡀⢀⣴⠟⠉⠀⠀⢀⣰⡿⢀⣼⡿⢃⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⡾⠛⠻⠿⠷⠄⠙⢿⣷⣬⣿⠿⠿⠶⠶⠶⠞⢛⣩⣶⡿⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠻⣿⣿⣷⡄⠀⠀⠀⠀⢿⡄⠛⠻⠶⠶⠶⠟⠛⢋⠛⠿⢿⣶⣶⣶⣶⡿⠿⠛⣉⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠈⠛⠻⠷⠶⠶⠶⠿⠛⠛⠻⠶⣶⣤⣤⣤⣤⣶⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⢳⣀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⣠⣎⠈⢂⠀⢀⣀⣠⠤⠔⠚⣁⣠⠄⣿⣌⣿⣄⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⠿⠛⠉⠀⢘⡏⠤⣴⠾⠟⠛⠉⠀⠙⠛⠛⣏⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠶⠛⢩⣿⡇⣠⣤⣶⢿⢉⠹⢛⠓⠶⠤⢤⣤⣀⣀⡀⠘⣿⣯⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⡁⠀⠀⠀⠀⠄⢹⠵⠛⠒⠚⠛⠻⠧⠾⣄⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠃⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣴⣿⡇⢀⣀⡤⠴⠚⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠋⠉⠀⠀⠀⠀⢿⣶⣶⣦⣤⣤⣤⣀⡀⠀⠠⠀⠀⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡋⠀⠀⠀⠀⠀⠉⠁⠒⢴⣾⣿⣿⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣀⡀⠀⠀⣀⠀⠀⠀⠈⠙⣿⡈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠀⠀⠀⠀⠀⠁⠢⢤⣴⣿⠟⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⣄⣀⣀⣀⣀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠨⠿⣿⡿⢻⣿⢿⣟⣥⡴⣣⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣭⣀⣘⡋⠛⠛⠿⣿⣷⣿⣿⣶⣶⣶⣶⣦⣶⡾⢟⣵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠶⠦⣤⣬⣭⣽⣿⣿⡛⠛⠟⠿⣛⡵⣣⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡈⠩⠾⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣽⣯⣿⣽⣬⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣿⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⢀⠊⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠑⢄⠀⠀⡠⠁⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠢⡀⠀⠑⠈⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠳⡄⠀⠀⠈⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢢⠑⡞⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠈⠢⣄⠠⡈⣂⢢⠇⠋⠐⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡈⠳⣄⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠉⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣣⠎⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠑⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠊⡤⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣨⡇⠀⠀⠀⠀⡸⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠈⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⠠⠔⠁⠀⢀⠀⣰⠗⡀⠀⠐⠄⡀⠃⢀⠀⠀⠀⠀⠠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠑⠀⣄⠀⠀⡀⠀⢀⡀⠀⠽⠀⠥⣜⣳⠆⠀⠁⠀⡄⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠈⠲⣄⣡⣄⡈⠁⠀⠰⡆⠒⢺⣄⣀⣀⣠⠞⣰⢇⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢉⠓⠀⠁⣄⠠⠉⠀⠀⢲⠄⠀⠛⠦⠼⠿⢖⡋⠀⢀⣌⣦⡄⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠒⢇⠀⠀⢉⠖⠐⡶⢀⣾⡀⠀⢠⢄⠀⢤⠀⠀⢀⡠⠄⣀⣷⣀⠀⠈⣦⡀
⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠒⠒⠺⠛⠄⠀⣄⣀⢀⡔⠁⣀⡴⣳⣞⠉⠉⠒⢄⣀⣱⡎⣀⠔⠋⠀⣀⣟⡩⠞⢁⡼⠁⣸⡆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣨⡯⠅⠠⠤⢖⣁⣀⣈⣤⠀⠉⠉⠓⠚⢻⣈⣉⣩⠴⠛⠶⣞⣛⣒⣩⡼⠁
⠀⠀⠀⠢⠴⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⡤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⢿⣿⣿⣛⣻⣿⣿⡿⠿⢿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣤⣤⣤⣿⣿⣿⣿⣤⣤⣤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠛⠛⠛⣿⣿⣿⣿⠛⠛⠛⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⡀⣠⠤⠤⢤⣤⣤⣀⣠⣤⠤⣴⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣰⣇⠀⠙⢥⣀⣀⣀⣿⣿⣿⡀⣀⣸⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠈⠳⢤⣴⣿⣯⠉⢻⣿⣿⣋⡉⢉⣽⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡶⣤⣀⣀⣾⣿⣿⠶⠛⠉⣽⣿⣿⠟⠻⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣬⣍⣛⣛⢋⣀⣤⡴⢞⣛⣉⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣿⡟⢻⣿⣀⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣿⡟⠛⠁⠈⠛⢻⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣼⣇⠀⠀⠀⠀⠀⠻⠿⣿⡆⢰⣿⠿⠟⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠐⣿⠛⣿⡆⢸⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣿⡇⠀⣿⠛⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠿⠿⠿⠃⢸⡇⠀⠀⣿⣁⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣿⡇⠀⣿⡇⠀⠿⠿⠿⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⠛⣿⡆⢸⡇⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣿⡇⠀⣿⠛⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠿⠿⠿⠃⢸⡇⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⠀⠿⠿⠿⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠛⢻⣿⠛⠛⢻⣿⠛⠛⢻⡿⠛⣿⡇⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠰⣿⠛⣿⡆⢸⡇⠀⠀⣿⠀⢸⣿⠀⠀⢸⣿⠀⠀⢸⡇⠀⣿⡇⠀⣿⡇⠀⣿⠛⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠿⠿⠿⠃⢸⡇⠀⠀⣿⠀⢸⣿⠀⠀⢸⣿⠀⠀⢸⡇⠀⣿⡇⠀⣿⡇⠀⠿⠿⠿⠃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⣀⣀⠀⢸⡇⠀⠀⣿⠀⢸⣿⠀⠐⢿⣿⠃⠀⢸⡇⠀⣿⡇⠀⣿⡇⠀⢀⣀⣀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠰⣿⠛⣿⡇⢸⡇⠀⠀⣿⠀⢸⣿⠀⠀⢸⣿⠀⠀⢸⡇⠀⣿⡇⠀⣿⡇⠀⣿⠋⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⣿⠀⣿⡇⢸⡇⠀⠀⣿⠀⢸⣿⠀⠀⢸⣿⠀⠀⢸⡇⠀⣿⡇⠀⣿⡇⠀⣿⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠾⠿⠿⠿⠷⠾⠿⠶⠾⠿⠷⠾⠿⠶⠶⠿⠿⠶⠷⠿⠿⠶⠿⠿⠶⠿⠷⠾⠿⠿⠿⠷⠾⠟






⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡤⠴⠖⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⣀⡠⠀⠀⠀⠰⠄⠈⠳⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠀⢠⠀⢈⠊⠀⡀⠀⠀⠀⠀⠀⠀⠰⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣳⣶⡊⠀⠈⠀⡀⢦⠀⠃⢠⣶⣿⡍⠧⠰
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⢀⠘⡅⢿⡿⣿⡗⡀⠀⡑⠀⠀⠀⠻⠜⠛⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⣱⡀⠀⠀⠀⠀⡇⠀⣦⠎⠈⡒⠈⠙⠋⣄⣀⣈⠀⠀⢀⡄⠀⠠⢤⠄⣀⡠⣧⣧
⠀⠀⠀⠀⠠⡋⠋⠹⡀⠀⠀⠛⠃⢿⡿⠁⠉⠉⠉⠉⠉⠉⠩⣛⠍⠁⠀⠀⠀⠀⠀⠀⠩⢍⠨⡙⠄
⠀⠀⠀⠀⠀⠡⠀⠀⢣⠀⠀⠀⢸⠘⣧⡀⠀⠀⠀⢀⣀⣀⡀⡅⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⡋⣧
⠀⠀⠀⠀⠀⠀⢣⠀⡀⢧⣀⠴⡐⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢗⡓⡎⢏⠆⠱⣸⢹⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠼⡶⠄⠘⢾⡀⠀⠀⠀⠀⠉⠙⠓⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⢺⣥⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⣜⡄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠊⠢⢄⡀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠿⣷⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⠙⢷⠄⠈⠻⣿⣍⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡁⠙⠗⠀⠀⠀⠀⣸⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣧⡈⠛⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣬⣁⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠛⠛⠻⣶⣴⣾⣿⣿⣿⣷⣤⣀⣴⠟⠻⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢻⣿⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⡿⠃⠀⠀⠀⠻⣿⣿⡿⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀⢀⣀⡀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⢸⡷⣼⢸⡷⠅⠻⢭⠈⣿⠁⡷⢼⡇⡿⠇⢘⢯⡀⡇⣸⣿⡄⠀⣿⢸⡉⡁⣾⠉⡷⢸⢧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠈⠈⠉⠁⠈⠉⠀⠉⠀⠁⠈⠁⠉⠉⠈⠉⠀⠁⠁⠀⠁⠀⠉⠀⠉⠁⠈⠉⠁⠈⠀⠉


⣿⠿⠿⠿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣛⣿⣿⣛⣟⣻⣛⣛⣛⣟⣿