Bookish Emojis & Symbols

⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⣤⡤⠴⢦⣤⡤⠶⣀⣤⢶
⠀⠀⠀⢰⠾⢭⣤⣤⠖⣉⣁⣤⢖⣉⣠⣶⡿⠁⡠⢾
⠀⠀⠀⢸⠀⢰⣯⣿⠀⠂⠀⣇⠀⠀⢸⣿⢣⠄⢠⣿
⠀⠀⠀⡞⠀⠀⡆⢸⠐⠒⠂⡗⠀⠺⢹⡏⠂⠀⠀⢽⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⣸⠀⣀⠀⣻⠀⠀⠀⡇⠀⡀⢸⡇⠀⠀⢂⣾⠀⢀⡠⠤⠒⠊⠁⠀⠀⠀⠀⠀⢉⡩⠝⢛⣢
⠀⠀⠀⡇⠀⠈⠀⣽⠀⠛⠀⡇⠈⠛⢸⡏⠘⡣⢻⣗⣈⣁⣀⣀⣀⣀⣀⣀⣀⣠⠔⢊⠁⡤⣾⡿⣋⣀⡀
⣰⢀⠀⡇⠀⠀⠀⣿⠀⠀⠀⡇⠀⠈⢸⡇⠀⣩⣅⣿⣀⣀⣁⣉⣉⣉⠉⠉⠉⣻⣿⣿⣟⣛⠉⣠⣴⣿⠃
⠀⠁⢀⣇⠁⠐⡟⡟⠀⠐⠂⡇⠒⠚⢺⡇⠀⣇⠀⠈⢉⡉⠉⠉⠉⢉⡍⠉⠉⠉⠁⠘⠀⠀⣽⢛⣿⣿⡶
⠀⠀⠒⡇⠈⠈⠟⡏⠀⠀⠆⡇⠀⢐⢸⠁⠀⡞⠙⠓⠛⠛⠓⠒⠒⠒⠒⠒⠒⠚⠗⠾⠷⠶⢿⣿⡿⡏⠀⠀⣀
⠀⠀⠀⣇⠀⠘⣇⡿⠀⠙⡅⡇⠀⠩⢸⣇⣴⣇⣄⣀⣤⣄⣀⣀⣀⣈⣁⣀⣀⣨⣀⣄⣀⣀⣸⣇⣴⣿⡷⠞⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⢁⣀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠭⢵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠲⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠚⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠞⠋⠉⠀⠀⠀⠀⠀⠀⣀⣤⡷⠆⠀⠀⡀
⠀⠀⠀⠈⡟⠀⠤⣀⡀⠉⠉⠙⠒⠲⠦⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠚⠳⣦⣀⣠⣴⠶⠿⠯⠑⠒⠂⠀⠀⠀⢡
⠀⠀⠀⠀⡇⠀⠀⠀⠉⠙⠲⠦⣄⣀⠀⠀⠀⠀⠉⠉⣓⣒⣶⠤⢤⣄⣹⣄⣤⠶⢿⡏⠁
⠀⠀⠀⣀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⡞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⣠⣤⣟⡛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠄⠐⢀⣠⣯⣿⠗
⢰⡿⠁⠉⠙⠛⠶⠬⣝⣳⣦⣤⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠔⠒⣒⣈⣩⠥⠤⠔⠒⠒⠉⠉⠉⠀⠀⡟
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣶⣬⣤⣶⠶⣞⣛⣛⣭⣭⡵⠶⠖⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠙⠷⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠛⠋
⠀⠀⠀⠀⠀⠉⠛⠳⠶⣦⣠⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡤⠶⠖⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠦⣤⣄⣴⠄⣀⣀⣀⣤⠤⠶⠗⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⠿⠟⠛⢉⣡⣤⣿⡿⢷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⡿⠿⠛⠛⠉⢁⣠⣤⣶⡿⠿⠛⠉⣁⣤⣾⣿⣿⣿⣷⣶⣦⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⡿⠿⠛⠋⠉⢀⣀⣤⣴⣶⡿⠟⠋⠉⣀⣠⣴⣶⣿⣿⠿⠛⠛⠉⣉⣡⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠟⠛⠋⠉⠀⢀⣠⣤⣴⣾⠿⠟⠋⠉⣀⣠⣴⣶⡿⠿⠛⠋⠉⢀⣀⣤⣴⣶⣿⣿⣿⣿⠿⠿⠛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⠿⠟⠛⠉⠁⠀⠀⣀⣠⣴⣶⣿⠿⠛⠋⠁⣀⣠⣴⣾⠿⠟⠛⠉⠀⣀⣠⣤⣶⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣠⣴⣶⡿⠟⠛⠉⠁⠀⠀⢀⣀⣤⣶⣾⣿⠿⠛⠋⢁⣀⣤⣴⡾⠿⠛⠉⠁⣀⣠⣤⣶⣾⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢰⣿⣿⠉⠁⠀⠀⣀⣠⣤⣶⣿⡿⠿⠛⠋⣁⣀⣤⣶⠾⠟⠛⢉⣁⣠⣤⣶⣾⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢸⣿⣿⣶⣶⣾⣿⣿⠿⠛⢋⣡⣤⣶⣾⣿⣟⣋⣩⣤⣶⣶⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣾⣿⠋⠉⠛⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⣠⣤⣤⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⡇⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇
⢀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟

⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⣿⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃
⣿⣿⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡿⠏
⣿⣿⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡿⠟⠛⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⡿⠟⠋⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⠿⠛⠋⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⠿⠟⠋⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⡿⠛⠋⠁
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⣠⣴⣶⣿⣿⣿⠿⠟⠋⠉
⠙⢿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠙⢿⣿⣷⣶⣦⣴⣶⣶⣶⣿⣿⣿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡤⢄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡤⠤⣤⣄⣀⣠⣤⣤⣭⣭⣭⣤⣤⣿⣟⣛⡶⠂⣀⣿⣿⣿⣿⣿⡿⢻⣷⡾
⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢯⣭⣭⣛⣻⣿⣿⣿⢇⣯⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⡀⠠⠤⢤⣴⣶⣶⠶⠒⠒⠒⠒⢛⣓⣫⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠗⠃
⠀⠀⠀⠀⠀⠀⣴⣮⣴⠒⣒⣴⣶⣿⣿⣿⣿⣿⣶⣶⢶⠀⠀⠀⣉⣽⣿⣿⣿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡶⢾⡉⣹⣿⢿⣿⣿⣿⣟⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠛⢛⣻⣿⣯⣽⣯⣽⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢘⡿⢫⣿⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠻⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠋
⠀⠀⠀⠀⠀⠀⠸⡀⡀⡘⢆⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣤⠀⢤⡸⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠙⠺⠿⢿⡿⠿⢿⣿⣷⣶⣶⣶⣶⣶⢶⣶⡶⠿⠤⢤⣭⣭⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣷⣷⣶⢷⣶⣿⣿⣶⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⠒
⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠄⠉⠉⠋⠹⠿⠂⠙⢹⡿⠛⠉⠉⠻⠟⠛⠛⠛⠛⠛⠛⣻⣛⣿⣿⣿⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⣊⣉⣉⣉⣉⣉⣉⣍⢩⡭⣿⣿⣿⣿⡘⣧
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀⣤⣛⣂⣠⣿⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠙⠛⣛⣛⣛⣫⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣽⣯⣭⣭⣿⠿⠿⡟⢻⡿⠟⠋⢉⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠛⠿⢿⣿⡉⠉⢈⣙⣿⣍⣉⣉⠁⠈⠁⠀⠀⠀⡀⣀⣸⣧⠀⠀⠸⣿⣿⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⢰⣂⣤⣤⣤⣭⣭⣭⣅⣛⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣦⣀⣐⣿⣿⣷⣄⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⡼⠛⣠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠄⠒⠒⠂⠉⠉⠩⠐⠒⠒⠢⠤⠤⣤⣀⣀⣀
⠀⠀⠀⠀⢀⣀⣤⠤⠐⠒⠒⠈⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠉⠉⠛⠒⠒⠶⠦⠤⣤⣀⣀⣀
⠀⠀⠀⠀⡎⡀⠀⠉⠉⠒⠒⠲⠤⢤⣄⣀⣀⠀⠀⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠬⢿⡟⠁
⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠶⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠛⠉⠁⠀⠀⣼
⠀⠀⠀⠀⠱⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠲⠶⢤⡴⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⣠⣄
⠀⠀⠀⠴⣴⣖⡛⠛⠉⠓⠒⠶⠤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣀⣀⣀⠀⠀⠀⠀⢀⣤⣶⠾⠟⣋⣁⡠⠭⠽⠗⠲⡀
⠀⠀⠀⠀⢹⠉⠉⠛⠲⠦⣄⣀⠀⠀⠀⠈⠉⠙⠛⠲⠶⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠈⢻⣷⣤⡶⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠉⠙⠒⠦⣤⣀⡀⠀⠀⠀⠀⣀⣀⣉⣩⡿⠷⠶⠶⣦⣤⣿⣤⡶⠿⠛⡿⠇
⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡞⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⣀⣠⣽⠿⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠶⠖⣲⣿⣓⡶
⣰⡿⠛⠻⠾⢷⣤⣍⣻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⣿⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠶⠒⠒⣋⣉⣭⣥⡴⠶⠶⠛⠛⠛⢹⡏
⣿⠃⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣶⣤⣀⡀⢠⠏⣌⠀⠀⢀⣀⣀⣤⣴⠶⠶⠒⢛⣋⣉⣭⣥⡴⠶⠖⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢷⣶⣾⣟⣋⣩⣭⣤⣶⡶⠾⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀
⠀⠛⠿⢶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠶⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠉⠙⠛⠿⢶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡶⠶⠞⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣶⣤⣄⣀⠀⣀⣆⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠶⠾⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣯⣵⡶⠶⠿⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠴⠶⠖⠒⠒⠂⠀⠀⠀⠀⠀⠐⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢈⠐⠦⣍⣛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣉⡓⠦⣌⣙⠒⠌⠉⠛⠷⣦⣄⠀⠀⠀⣀⣠⡤⠴⠖⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⠬⣅⡒⠬⣕⡂⠌⠙⠒⠄⠀⠀⠀⠙⢷⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠙⠲⢭⣑⠲⠬⣑⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠒⠒⠛⠛⠶⣤⣌⣀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢀⣀⣤⣤⠶⠾⠛⠛⠛⠓⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⠾⠿⠷⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣄⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢩⡿⣍⠿⣯⣉⣉⣉⣉⣉⣁⣤⣤⣤⣤⣴⠶⠶⠟⠛⠛⠋⠉⠁⠀⠀⠀⢀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠘⠀⠹⣆⢸⡏⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠁⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠇⠀⠀⣀⣀⣘⣿⣧⣶⣶⣶⡶⠶⠶⠶⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⢀⣠⣴⠶⠞⠛⠉⢉⣿⣴⠟⠛⠉⠉⠉⠉⢙⣛⣛⣛⠛⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣦
⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠭⠭⠭⠍⠉⢓⣒⣒⣒⣒⣒⣒⣒⡂⠀⠀⠀⠀⠀⢉⡿⣥⣀
⣸⠏⠀⠀⠀⠒⠤⣀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠤⠤⠤⣀⣀⣀⣀⣀⡒⠒⠒⠒⠶⠶⠶⠍⠁⠀⠀⠀⢸⠁⠀⠉⠓⠦⣄⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⢀⠀⣀⣈⡉⠉⠙⠛⠛⠛⠒⠒⠒⠒⠒⠒⠢⠤⠭⠭⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢈⣙⣷⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣭⣭⣭⣍⣛⣛⣛⣛⣷⣶⣶⣶⣶⣤⣤⣤⡤⠤⠀⡀⠀⠀⠀⠐⠒⠀⠀⠀⠈⠳⡶⠶⠛⠛⢹⡏⠉
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣍⡉⠉⠉⠉⠉⠉⠉⠉⠛⠛⣛⣛⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠀⠀⠀⣸
⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣤⠶⠛⠉⠉⢁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠤⠤⠀⠂⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣄⡀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠶⠶⠶⢒⣛⣋⣩⣭⣤⠴⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣙⣮⣍⣁⣀⠀⠀⢈⣉⣉⣭⣤⠤⠶⠶⠞⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢶⣖⣒⣒⣚⣻⣯⣭⣭⡍⣩⣤⣤⣭⣵⣶⣒⣒⣲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣾⣿⣿⣿⠿⡿⢿⡿⣿⡿⣿⢷⡏⠀⠤⠤⠤⠤⠭⢩⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⡏⣜⠸⢿⢸⠇⠾⡀⡿⢱⣿⢸⠁⠠⠄⠀⠈⣀⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣷⣾⣤⣾⣤⣦⣴⣧⣴⣮⣿⢸⡄⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⡤⠤⠼⣿⣯⣿⣿⣿⣟⣛⣛⣻⣿⣿⣿⣾⣧⣀⣭⣭⣭⣭⣭⣭⡭⠿⣂⡀
⠀⠀⠀⠀⠀⢠⣟⡭⣭⣥⣀⣒⣒⣀⣀⠤⠤⠤⠈⠉⠉⣙⡋⠉⠙⢛⣉⡉⠭⠭⢭⣀⣀⣒⣦⡤⠽⠿⢷⠟⠃
⠀⠀⠀⠀⠀⢸⢸⣇⡂⠀⠐⠀⠈⠩⠍⠉⠙⠛⠛⣒⡒⠒⢂⡤⠤⠖⠒⠺⠿⠯⠉⠉⠀⠀⠀⠀⠀⡀⢸⡀
⠀⠀⠀⠀⠀⠸⣏⣓⣒⡒⠂⠀⠭⠥⣄⣀⣠⣤⠤⠤⣤⣄⢼⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⣂⣀⣠⣥⣥⣼⣷⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣸⠿⣿⣿⣿⣷⣶⣶⡾⢁⠐⣶⢶⣒⡩⠙⣲⢤⣈⣩⣤⣴⣶⣶⣿⣿⣿⣯⣽⠿⠶⠞⠛⠋⢉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡿⠹⠏⣿⣿⢡⠁⠀⠀⠀⠀⠩⢓⡦⣍⡺⢽⣻⣿⣿⡟⠉⠉⠁⠀⠀⠀⠅⢀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣼⣿⣼⣧⣾⣿⠃⠂⣠⣴⣦⢠⣠⣀⡀⠈⠑⠫⢗⡾⣝⢮⡟⣦⠀⠀⠒⠀⢀⣀⡠⠤⣖⣚⣿⠆
⠀⠀⠀⠀⣀⣠⣤⣶⠛⠻⠿⠿⣿⠏⠌⠀⠉⠈⠈⠈⠘⠹⠔⡀⠀⠀⠐⢰⠃⡠⢱⣯⡴⣾⣾⣿⣽⠶⠞⢛⣋⣽⣷⣤⣄
⢀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣦⣴⡏⡈⠀⠀⠀⠛⠷⣦⡆⡀⠘⢿⠁⠀⢠⠇⢸⢣⡿⠿⠟⠛⣉⣥⣴⢶⣾⣿⣿⠿⣟⣻⡽
⣾⣿⣷⣶⣦⣬⣍⣙⣛⡻⢿⡟⡐⣥⡁⠀⠈⠈⠓⠂⣉⠛⠀⠀⠀⢀⡏⢠⢇⣾⣥⣶⣾⣿⣿⣿⠾⣟⣫⡽⠶⠛⠩⣸⣧
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⠁⠘⠿⣦⣷⣄⡀⣀⠀⢠⡀⠀⠀⡞⠀⡞⣾⢿⣿⣿⣛⣩⡵⠞⠛⠉⢁⡠⠴⣒⣯⠽⠚
⠀⠀⠉⠉⠙⢛⣿⡿⠿⣿⢃⠃⠀⠀⢠⣄⣹⡟⠿⣿⣤⣄⡀⠀⡜⠀⡜⣼⣿⣭⣽⣿⠍⣀⡠⠴⣒⣩⣵⣾⡛⠉
⠀⠀⠐⢾⣿⣿⣿⣯⣽⠇⠂⠀⠀⠦⠀⠉⠛⠷⠤⡀⠉⠁⠀⣼⠁⣸⣰⣿⣿⣿⣿⣿⣭⣵⡶⠟⣋⠉⢺⣿⣿⣿⣶⣶⣤
⠀⠀⠀⠀⠈⠙⠻⠿⣿⡈⠀⠀⠀⠙⡲⢍⠐⠤⣀⠀⠀⢀⢰⠇⢀⢧⣿⠦⠤⡭⠿⠛⠉⠀⢀⡡⢐⣀⠼⢿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠉⠃⠀⠁⠀⠀⠀⢢⡟⠀⣞⣾⣏⡀⠀⢫⠀⠀⣀⠬⠖⣊⣭⣶⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣻⣦⡴⠶⠶⢦⣀⠀⣾⣀⣘⣼⣿⣦⣬⣉⡉⢛⣩⣴⡾⠿⠛⠉⠁
⠀⠀⠀⢀⣀⣤⡤⠴⠖⠚⠛⠉⢉⡀⡀⡀⣀⣠⣀⡌⠛⠿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⢠⡞⠉⣁⠀⠀⢀⠀⣀⣦⡰⠼⠋⠉⠉⠙⠁⡀⢄⣠⣀⠀⠙⠻⢿⣏⡁
⠀⣿⢀⠑⠢⡁⠀⡈⠃⠉⠁⠀⠀⣄⢦⣰⠬⠷⠽⠚⠋⠉⠀⠀⠀⠀⠈⠛⠷⣤⣀
⠀⣿⠸⢞⣠⢈⠐⢄⡀⠀⠀⠸⠒⠋⠁⠀⠀⠀⠤⢄⡲⠤⠴⠖⠒⠋⠀⠀⠀⠀⣙⠳⣄
⠀⠈⠷⣌⡙⢻⣶⠀⠈⠢⢈⠂⠀⠀⠀⠀⠐⠂⠉⠠⠖⠒⢉⠀⡤⠤⢐⣒⣨⡥⢴⡶⠃
⠀⠀⠀⠈⠻⢦⡀⠸⢴⣤⣀⠑⠠⡑⠀⠀⠀⠠⠄⣒⣈⣥⡤⠶⠚⠛⠩⠉⡀⠂⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠙⠷⣄⠈⠳⡏⠀⠈⢠⠃⣴⠚⠋⡉⠡⠄⢀⠀⠀⠀⠀⢈⡡⠤⠞⣹⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣈⠘⠃⡞⣸⡯⠉⠀⠀⣀⠠⠤⠐⣒⣢⣭⡴⠶⠞⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣇⠹⠗⣒⣨⣥⡴⠶⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠄⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂⢀⣠⠀⢀⡀⠶⠘⠉⠐⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢀⢴⡁⢷⠀⣀⠀⢾⡿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣥⠁⠁⠀⠀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⡆⣧⡆⠄⠸⡄⠘⠙⠃⠀⢀⠀⠀⠀⠀⢸⣿⠛⢥⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⣿⡖⡀⢙⡄⠠⠀⠀⠄⠀⠀⠀⠀⠀⣿⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⢻⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢿⡌⣇⠈⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠇⢀⣀⣤⣤⣄⣀⣀⢸⡧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⢷⠛⡆⠈⠃⠀⠀⢀⠀⠀⣀⣠⣤⣬⣿⣿⣶⣿⣿⣿⣿⡶⠶⣬⣽⣿⣲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡇⠁⠀⠀⠀⢐⣯⣷⣾⣷⣿⣿⣹⣿⣿⣿⡿⠿⠿⣿⣿⠿⣶⣽⣾⣯⡍⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢿⣄⣀⣲⣿⣿⣿⣿⠿⠛⠉⠈⠳⠭⠽⠿⠃⠀⠀⠀⠈⠉⠛⠒⠯⢽⣟⣻⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⣈⣛⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠁⠀⠀⠀⠉⠐⠂⠤⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠤⠤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠐⠠⠄⠀⠒⠠⢀⡀⠀⠈⠑⣤⠔⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⡂⠀⠠⠀⠠⠄⡀⠀⠀⠈⠀⠀⡐⠁⠀⡠⠄⡀⠀⠀⠀⠀⢀⣀⡀⠒⠀⠄⠀⠀⠀⢠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠄⠀⢀⡈⠐⠂⠩⠒⠥⡂⠅⠢⠀⠀⠌⠀⠀⠐⣀⣀⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠠⠀⠀⠀⡀⠀⢀⠀⠀⡂⠄⡀⠀⠀⠀⢀⠎⠀⢀⠐⠂⠀⠀⠀⠀⠒⠂⠀⣈⠀⠉⠀⠀⠀⠀⢠⢃⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠄⠤⠀⠐⠀⠤⢁⠐⠉⠐⠠⡁⠢⠁⠀⢀⠂⠀⠠⠐⠂⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⡾⣿⡏
⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠨⢐⠂⠤⡈⠐⠠⡑⠠⡀⠈⠀⠀⠠⠁⠀⠐⠠⠁⠀⠀⢀⣀⡀⠀⠈⠉⠁⠂⠀⠀⠀⠀⡰⡳⡿⣽⣿⣀
⠀⠀⠀⠀⠘⡠⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠈⠀⠀⡐⠁⠀⠀⠠⠄⠀⠒⠂⠀⠀⠀⣐⡂⠀⠅⠀⠀⠀⢀⡔⡜⡽⣼⣿⢏⣾
⠀⠀⠀⠀⢘⠖⠶⠤⠤⢉⣑⠒⠤⣈⠂⠀⠀⠀⠀⠙⠀⠀⠀⠀⠌⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠎⣜⣞⣼⣯⢫⣻⠃
⠀⠀⠀⠀⣿⠖⠒⠒⠲⠒⢶⢬⢵⣺⢥⣢⣄⡀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⣮⢎⡾⡼⢣⡿⠁
⠀⠀⠀⠀⠘⡐⠡⡠⢤⠄⠀⣀⣈⣉⣋⣻⣿⣿⣦⣔⠀⡑⢉⣀⣤⣤⠴⠶⠲⠶⠰⠒⠆⢒⠒⠢⠤⣤⣀⠀⠠⢀⢪⣮⢋⣾⡵⣡⣟⠁
⠀⠀⠀⠀⠀⡴⢼⠲⠟⠭⠉⠈⡩⢍⣙⣷⣮⣮⣷⣿⣿⣿⣭⣯⣽⣶⣿⣿⣻⡿⠿⠟⡑⠒⠍⠃⣅⠂⠌⣙⠓⢪⡻⣣⢿⠟⣱⡟⠁
⠀⠀⠀⠀⠀⡳⡶⣶⡞⢽⡿⠻⠟⠛⠻⢿⣟⡓⣒⣒⠾⠬⠽⢝⣿⣯⣦⣿⣍⣽⠽⠖⣒⠪⠤⣆⣀⠉⠈⠑⡙⠱⣷⢿⠋⣴⡟⠀⠄⠀⠠⢀
⠀⠀⠀⠀⠀⠁⠅⢙⣷⣿⣂⣐⣒⡲⠦⠤⠤⣤⣥⣅⣭⠭⠯⠋⣍⣉⣉⡋⣩⣾⣿⣷⢖⡬⣕⡂⠬⢙⠲⢦⣽⢪⣿⢋⣾⠏⠐⠌⣀⠠⠁⢒⠠
⠀⠀⠀⠀⠀⡇⠘⡤⣻⢸⡃⠖⠂⠙⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢨⠣⣫⣿⡿⡳⡋⠀⢀⠈⠙⡒⢌⡒⢍⡷⣣⡿⠋⡐⠀⠀⢀⠈⠼⠀⠐
⠀⠀⠀⠀⠀⢽⠈⡆⠙⣿⣕⣿⣭⣤⣒⣒⣒⢄⣀⠀⡀⠀⠀⢀⣀⣬⢸⣾⡿⣫⣾⣳⡄⠀⢀⡤⠃⢒⠃⠨⡒⠺⠿⡀⠀⠔⡂⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠘⣧⠀⢀⣀⣀⣀⣭⣭⣭⣿⡿⠶⠾⠭⣶⢮⣘⣫⠾⠭⢡⠏⠁⠨⠀⡀⠌⠀⣂⠥⡄⠠⠁⠐⠈⣁⣄⠑⠐
⠀⠀⠀⠀⠀⠀⢻⢆⣠⢴⡝⠋⠉⠀⢀⣀⣉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠲⠉⠀⠀⢸⣄⠀⠀⠐⢀⠐⢉⡠⢒⠥⠒⠋⠰⠋⠊⠁
⠀⠀⠀⠀⠀⠀⠐⢧⠃⣟⡿⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢎⣻⣷⢀⠐⠄⠐⠈⠀⡐⣠⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⢇⣊⣉⡥⠤⠤⠠⡂⠰⠶⢒⢒⣂⣠⠔⠴⢀⠴⠽⡂⠔⢒⠩⠀⠀⠀⠡⢒⠉⠉⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠂⠒⠒⠂⠛⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠈⠀⠈⠀⠂⠁⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠂⠈⠉⠀⠂⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢘⠧⠀⠰
⠀⠀⠀⠀⠀⡄⠀⠀⢀⣁⡐⡇⠀⠀⢸⣆⠈⠃⠈⠀⠀⠀⠀⢀⡀⠀⣼⠇⠀⠀⠀⠀⠂⠀⢎⠁⢰⡀
⠀⠀⠀⠀⠀⠉⠽⠼⠀⠙⢤⢻⠍⠂⠀⠋⣴⣿⣿⣷⠀⠠⣾⣿⣿⣷⠙⠀⠀⠪⠅⢠⠀⣀⠐⡄⠓⠉
⠀⠀⡀⣀⡴⢶⡖⣚⡳⣄⠘⡇⢀⡀⠸⠀⠿⠿⠿⠋⣰⣦⠙⠿⠿⠿⢀⠀⠂⣴⠒⢛⠉⣓⠲⣄⣎⣀⡘⠻⠲
⠀⠀⠀⠋⣇⠀⠘⣫⠁⣼⡰⠓⠻⢆⡀⠑⠲⣖⠄⠀⠉⠙⠀⠠⣶⠒⠁⠀⠀⣋⡀⠸⠿⣭⠗⢠⣏⣅⡐⠀⠁
⠀⠀⠠⣀⡙⠾⡿⠧⢾⠿⠀⠈⠀⠀⠁⠀⠀⡿⠶⣤⣤⣤⣴⠴⡿⠀⠀⡠⡀⣽⠯⢧⡴⢊⠠⠼⠃⠀⢤
⠀⠀⠀⢈⣣⡶⠃⢀⡏⢀⣯⣶⠁⠀⠀⠀⠀⠈⠢⣀⠀⠀⢀⡰⠃⠀⠘⠗⠀⢀⡔⡶⠞⢋⠰⢦⠀⢆⢠⣄
⠀⠀⠀⣤⡴⠽⣄⣬⡃⢀⣺⢷⡧⡠⠶⣠⡦⠶⡶⣾⠏⢽⣦⠶⢖⣠⡴⢦⠀⣈⣷⣤⡄⢼⠁⠠⢀⠯⡋⠁
⠀⠀⠀⣰⠂⠢⠚⣿⡀⢸⡿⠛⠰⠣⠴⣽⣻⣯⢥⣴⠂⢰⣦⢶⣿⡿⠗⠊⠁⢉⠠⢿⣧⣾⡆⢴⡅⠄⢲⡄
⠀⠀⠀⠉⠁⠀⠀⢼⣿⣿⣶⣧⣤⣤⣀⡀⢁⡉⠛⢿⠅⢸⠟⠋⡁⢀⣄⣢⣬⣶⣿⣿⣿⣿⢗⢚⠀⠀⠈⠉
⠀⠀⠀⢀⡀⠀⠀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⠶⠶⠾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⢸⠀⠀⠀⣀
⠀⠀⠀⠐⠛⢲⢀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡟⡀⣧⡰
⠀⠀⠀⠀⢀⣏⡔⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⠀⠀⢡⠀⣠⠤
⠀⠀⠀⠀⠾⡯⡏⠟⢺⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣬⡋⢠⣝⣦⡗⣉⣀
⠀⠀⢈⠶⠀⣇⢶⣛⠤⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣟⡳⢮⣅⡰⢮⣰⣢⠶
⠀⠀⠀⣲⣷⠿⣏⣶⡚⣯⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⣭⡶⠃⢁⣤⡄
⠀⠀⠀⣁⠤⡐⣌⡯⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⠀⠰⣉⢉⡴⢖⡀
⠀⠀⠈⠉⠚⠛⣋⣁⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣿⠿⠟⢠⠜⠀⠁⢈⠀⠙⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠜⢭⣹⠖⢦⠠⠌⢙⠙⠛⠻⢿⣿⣿⣿⠛⠋⠉⠀⠠⠓⢩⡁⢆⠒⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠉⠛⠛⠒⠒⠲⠶⠶⠦⠤⠤⣤⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠒⠒⠲⠶⠶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢹
⠀⠀⠀⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⡠⠒⠙⣆
⠀⠀⢠⡞⠉⠛⠛⠛⠛⠷⠶⠶⠶⢶⣤⣤⣤⣤⣄⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢁⠔⠊⠀⢀⡴⢻⡄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠶⠶⠶⠶⢦⣤⣤⣤⣤⠖⠋⡠⠐⠁⠀⢀⡴⠋⡴⠋⣇
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠄⠊⠀⠀⢀⡴⠋⢠⠞⠀⣠⠋
⠀⠀⠀⡿⠒⠒⠲⠶⠤⠤⢤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋⠀⡴⠃⠀⣴⠁
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠓⠒⠒⠶⠤⠤⢤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠸⡄⢀⡴⠋⠀⢠⠞⠀⢀⠞⠀⠉⠒⣤
⠀⠀⠀⠈⣏⠙⠒⠒⠢⠤⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠒⠷⠿⠶⣤⡴⠁⠀⣠⠋⠀⣀⠴⠋⡇
⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠈⠙⠻⢮⣭⡉⠑⠒⠒⠶⠤⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡴⢁⡤⠚⠁⡠⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠈⠙⠳⢦⣤⡀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠲⠤⠤⠤⣀⣀⡀⠀⢸⣇⣮⠔⠉⠀⠔⠈⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡽⠋⢀⠠⠊⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⡀⠔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⣀⠔⠋⢀⠄⠊⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠈⢙⠏⠁⡠⠀⠁⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠘⡇⠈⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⣇⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡘⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢂⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠣⡀⠀⠀⠄⣀⠤⠐⠂⠁⠀⠀⠀⠀⠀⠁⠠⡈
⠀⠀⠀⠀⠈⠀⠀⢀⠊⢠⠤⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⣁⣀⠠⠤⠤⠀⠐⠂⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠚⠀⢀⣀⡀⠀⠀⠀⢠⠀⠂⠈⠁⢀⡀⣀⡠⠤⠤⠴⠲⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⡀⠸⡀⠂⠘⠉⠓⠋⠀⠀⠀⡀⣀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠂⠈⢂⡒⠒⢚⡛⠉⢉⡉⠭⢁⠒⠄⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣠⠀⠠⠁⢥⣒⣪⣁⣒⣈⣉⣤⢤⣬⣬⡶⣶⠖⠁⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠉⠡⢾⠛⠯⠉⠓⠚⠛⠂⠍⠁⢀⠄⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠸⠀⠀⡃⠀⠇⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡼⠄⠠⢤⠤⠤⢄⣀⡀⢀⣀⡀⠀⠅⡔⠁⠑⣌⡀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣠⡀⠀⠒⠀⠀⠈⠉⠉⠁⠉⠁⠋⠀⠁⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠈⠂⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⡤⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠐⠀⠀⠓⠂⠓⠉⠉⡀⠀⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠐⠂⠀⠀⠀⠀⠀⠒⠀⢸⠀⢠⠦⠔⠒⠒⠒⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡉⠙⢶⡶⢢⠶⢦⣤⣄⣠⣾⡴⣓⠂⠬⠤⢀⣁⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠻⡎⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠑⠖⠒⠒⠒⠒⠒⠊⠉⠉⠉⠉⠉⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⣀⡀⠀⠀⠀⠄⠀⠀⠀⠠⠤⠔⠒⠒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠴⠶⠶⠒⠒⠂⠀⠀⠀⠀⠀⠐⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢈⠑⠦⣍⣛⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣉⡓⠦⣬⣉⠒⠌⠉⠛⠷⣦⣄⠀⠀⠀⣀⣠⡤⠴⠶⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣂⠬⣍⡒⠬⣕⡢⠌⠙⠒⠄⠀⠀⠀⠙⢷⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠈⠙⠲⢭⣑⠲⠬⣁⠂⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠒⠒⠟⠻⠶⣤⣍⡀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢀⣀⣤⣤⠶⠞⠛⠛⠛⠓⠒⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⠾⠿⠷⠶⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣀⣄⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢉⡿⣍⠿⣯⣉⣉⣉⣉⣉⣀⣤⣤⣤⣤⣴⠶⠶⠿⠛⠛⠋⠉⠁⠀⠀⠀⢀⣀⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠸⠀⠹⣆⢸⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠁⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠇⠀⠀⣀⣀⣘⣿⣧⣶⣶⣶⡶⠶⠶⠶⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⣀⣠⣴⠶⠞⠛⠉⢉⣿⣴⠟⠛⠉⠉⠉⠉⢙⣛⣛⣛⡛⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣦
⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠭⠭⠭⠍⣉⢛⣓⣒⣒⣒⣒⣒⣒⡒⠀⠀⠀⠀⠈⢉⡿⣭⡀
⣸⠏⠀⠀⠀⠒⠤⣀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠥⠤⠤⠤⣀⣀⣀⣀⣐⠒⠒⠒⠒⠶⠶⠦⠀⠀⠀⠀⠀⢸⠁⠀⠉⠓⠦⣄⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⢀⣀⣀⣈⠉⠉⠙⠛⠛⠒⠒⠒⠲⢶⣶⣶⠶⠬⠭⢭⣍⣉⡙⠛⠛⠒⣒⣀⠀⠀⢸⠀⠀⠀⠀⢀⣈⣙⣷⡦
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣭⣭⣭⣍⣛⣛⣛⣟⠠⠒⠠⠢⠑⠩⠀⢩⣤⣤⣄⣀⡀⠙⠛⣛⣒⣒⣒⡀⠘⢷⡶⠾⠟⠛⢻⡟⠉⠁
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠬⣉⡉⠉⠉⠛⠛⠙⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠿⠿⣶⣶⠶⠿⠀⠀⠀⣾⠁
⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⢀⣴⡶⠚⠃⢀⣀⣠⡤⠤⠤⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠀⠀⠀⣿
⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⠤⠤⠐⠂⠀⠀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣄⡀⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⠶⠶⠶⢚⣛⣋⣩⣭⣤⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣙⣮⣍⣁⣀⡀⠀⢈⣉⣉⣭⣤⡤⠶⠶⠖⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢤⡠⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢠⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⣀⠴⠚⢁⡀
⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢠⣼⣿⠿⢶⣄⡀⠀⠀⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⢸⣧
⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠙⠛⠶⣬⣿⣦⣀⣠⡶⣁⣀⣀⣀⣠⣀⣠⠞⠁⠀⠀⠀⠀⣠⠟⠉
⠀⠀⠀⢀⣿⣧⣤⣤⣄⣀⡀⠀⠀⠀⠀⠃⠀⠀⣀⣠⣤⣔⠒⠒⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⢈⡽⠿⠿⢿⣛⠛⠲⠤⣄⡀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⢸⣿⣶⣶⣖⣒⣪⣭⣭⣶⣦⣀⣠⣴⣿⣿⣿⣿⣶⣾⣿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠈⠙⠲⢤⣀⣙⣧⠀⢀⡴⠋
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⡟⠋⠉⠉⠉⠉⠉⠛⠛⠛⠛⠃⠀⠀⠀⠀⠠⠐⠈⠀⠀⢔⠤⣀⠀⠀⠀⠀⠈⠙⠻⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣌⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠿⣦⣈⠙⢦⣄⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠁
⠀⠀⠀⠀⢰⣷⣄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⢞⡀⠀⠈⠙⢷⣤⣈⠓⢦⣔⡢⠔⠊⢉⡠⠔⠊⢁⡴⠚⠒⠒⠲⠤⠤⢄⣀
⠀⠀⠀⠀⠺⡉⡊⠳⡄⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⢀⣔⣥⢟⡩⠔⡀⠀⠀⠀⠈⠛⢷⣾⣋⣦⠶⠋⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⣠⣄⠙⢦⠀⠈⠳⡄⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⢠⣿⣿⢞⣛⣺⣿⣷⡀⠀⠀⠀⠀⠀⠉⠁⠀⠳⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⠇
⠀⠀⠀⠈⠳⡄⠀⠑⢄⠀⠀⢀⠴⠤⠤⠄⠀⠈⠛⣦⣠⣿⣿⣿⡿⠷⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣡⠞⠁
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠱⠄⣔⣐⣤⣿⡶⢾⣿⣿⡿⢿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⡉⠒⠲⠦⠤⢄⣀⣀⢀⡔⢁⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢈⡥⣄⣬⡵⠖⠛⠉⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠉⠓⠒⠦⢤⣀⣀⠉⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣬⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⢷⣶⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠙⣍⢻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⢸⡏⣿⣿⣿⣧⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣴⡿⢿⡄⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣦⡾⠋⠉⠉⠻⣿
⠀⠀⠀⠀⠀⣾⠏⠀⠈⢿⣄⡀⠀⠀⢠⠖⠒⠦⣌⠹⣿⣿⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⠻⣦⣄⠸⣄⠀⢀⡞⢀⣿⣿⣇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠈⠙⢷⣮⡳⠟⣀⣾⣿⣿⣿⡄⠀⠀⣸⣧⡀
⠀⠀⠀⠀⠀⠀⠙⣷⣤⡀⠀⠀⠀⣇⠂⠈⠉⠋⠉⠙⠻⣿⣿⣿⡀⠀⢸⡏⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠉⢻⣦⣄⡈⣧⠀⠀⢠⡞⠉⠙⢓⡎⢿⣿⣧⢠⡾⢣⡟⠈⠙⠻⢷⣦⡀
⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠙⡙⠻⣿⣷⣤⣀⠳⣄⠀⣾⠁⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠇⠀⢇⢛⢻⣿⣿⣶⣭⣧⣾⣿⣿⣿⣿⡶⣤⣄⡀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣤⣀⠀⠚⠸⡞⠀⠈⠉⠉⠉⠁⢿⣿⣿⣿⣷⠦⣭⢻⡄⠀⢠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠈⠙⠻⠶⣤⣤⣄⣀⣀⣀⣀⠀⠘⣿⣿⣿⣿⡆⣸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⠀⢉⡏⠙⠻⠿⢿⣿⣷⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣄⣀⣀⠀⠀⢘⠃⠆⠀⠀⠀⠀⠉⠉⢿⠿⣿⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡟⠛⠛⢻⠟⠛⣻⠿⠟⠛⠛⠛⢋⣷⡉⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣐⣋⣴⣎⣁⣄⣀⣀⣀⣴⡟⠁⢳⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠛⠛⠛⠋⠉⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣠⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡟⢉⠙⠛⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠛⣁⠀⣠⢠⣿⣿⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣏⠀⣄⣀⠀⠉⢸⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠘⡂⠈⠁⢀⠔⠉⣿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠃⠀⢤⣿⠋⢀⣇⠀⢀⢰⠖⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⣰⣧⣬⣄⡉⠁⢘⣷⣄⢸⢀⣆⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⣸⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⠉⠁⢠⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢀⠆⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠎⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢠⠃
⠀⠀⠀⠀⣠⠤⠤⠤⠼⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⣦⣤⣎⡤⠦⣀
⠀⠀⣠⠌⢱⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⢻⠋⠉⠉⠀⠈⢿⣿⣿⣿⡟⠁⠀⠀⠈⠳⣎⠽⡀
⠀⠀⢹⡆⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⣀⠜⠻⠿⠋⠀⠀⠀⠀⠀⠀⠈⠳⣇
⠀⠀⠈⣧⠀⢰⠀⠀⠀⠀⢀⣠⡔⠀⣀⠀⡀⠁⠀⢱⠀⠤⡚⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢳⡄
⠀⠀⠀⢹⡈⡀⡆⠀⣀⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⠢⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢹⡀
⠀⠀⠀⠘⣇⠀⢸⠀⠁⠀⠀⠐⠀⣀⣀⣀⣀⣀⠀⠀⢱⠀⠀⠀⠈⢢⡀⠀⠐⠀⠀⢀⡠⠖⠉⢈⣉⡠⠇
⠀⠀⠀⠀⢻⡰⢀⣦⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣷⣿⣿⣿⣿⣿⣦⣀⣠⣶⣿⣦⣴⣾⣏
⠀⠀⠀⠀⠘⣷⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋⠉⠀⠀⠀⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄⡀
⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⡀
⠀⠀⠀⠀⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠋⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⢸⣿⡀
⠀⠀⠀⠀⢹⣿⣯⣿⣿⣷⣽⡻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠁⣠⣴⣾⣿⣿⠟
⠀⠀⠀⠀⣿⣿⣿⣿⣷⣿⡻⣿⣾⣝⡿⣦⣄⠀⢀⣤⣶⠿⠛⠁⢀⣤⣶⣿⣿⣿⣿⣯⡀
⠀⠀⠀⠀⣿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣽⡾⣝⣿⠟⠉⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢿⣿⣿⣿⣮⢿⣿⣿⣿⣿⣿⣟⣿⣿⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⢀⣤⣶⠾⢿⣿⣯⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠋⠉⠉⠁⣸⣿⣄⡀
⠀⣿⠿⣦⡀⠀⠻⣿⣿⣿⣿⣿⡿⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣙⣿⡦
⠀⣿⡆⠙⢿⣦⡀⠙⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⢿⣯⡀
⠀⠈⣿⣶⡀⠙⢿⣦⡈⢻⣿⣿⡇⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⡿⠿⠿⢋⣿⣿⠆
⠀⠀⣿⣿⣿⣦⡀⠙⢿⣦⡹⣿⣿⣾⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⠟⠋⠁⠀⠀⣀⣴⣾⣿⡋⠁
⠀⠀⣿⣜⢿⣿⣿⣦⡀⠙⢿⣮⡛⠛⠉⠉⠁⣀⣤⣶⠿⠛⠉⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢻⣿⣎⢿⣿⣿⣿⣦⡀⠙⢷⣄⣠⣶⠿⠛⠉⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠈⢻⣟⢯⢻⣿⣿⣿⣿⣦⡀⣿⠋⠁⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⣤⣶⣿⣿⣮⢧⡻⣿⣿⣿⣿⣿⣿⣆⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⢉⣿⣷⣦⡀
⣼⣿⠿⣿⣿⣿⣧⢳⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣦
⣿⣿⢷⡈⠻⣿⣿⣷⡹⣼⡟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿
⣿⣿⢦⡙⢦⡘⢿⣿⣷⣽⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣿⠇
⢻⣿⣦⡙⢦⡙⢦⡙⢿⣿⣧⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⢰⣿
⠘⣿⣯⡳⣌⠻⣄⠻⣆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠸⣿
⠀⠹⣿⣷⣌⠳⣌⠳⣌⠳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷
⠀⠀⠈⠻⣿⣷⣌⠳⣈⠳⡌⠳⣌⠻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠟
⠀⠀⠀⠀⠘⢿⣿⣧⡙⢧⡘⢧⡘⢧⡘⢿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡙⢦⡙⢦⡙⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡙⢦⡙⢾⠁⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣌⠳⣼⡂⠀⠀⠀⢀⣠⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣼⡇⢀⣤⣶⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⢉⣉⣀⣀⣀⣉⡉⠙⠛⣿⠛⠋⠉⠉⣉⣉⣉⣉⣉⣉⡙⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠡⠖⠊⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⡟⠀⠀⠊⠉⠁⠀⠀⠀⠀⠀⠈⠉⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⢀⠤⠄⠒⠒⠉⠉⠉⠉⠉⠒⠀⢰⡇⠀⠤⠔⠒⠊⠉⠉⠉⠉⠉⠉⠂⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⣀⠀⠀⢸⠁⠀⠀⠀⣀⣀⠠⠤⠤⠤⠤⣀⡀⠀⢹⣿⣇
⠀⠀⠀⠀⠀⣸⣿⣿⠀⠐⠊⠁⠀⠀⠀⣀⣀⡀⠀⠀⠁⠀⡟⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⢀⣿⢧⡇⢀⡤⠔⠒⠉⠉⠉⠀⠀⠈⠉⠓⠀⢠⡇⠀⢀⠤⠔⠒⠊⠉⠉⠉⠉⠒⠒⠦⠄⠘⣿⣿
⠀⠀⠀⠀⣸⡿⣾⠀⠀⢀⣀⡠⠤⠔⠒⠒⠒⠒⠤⠄⠀⢸⠃⠀⠀⠀⣀⣀⠤⠤⠤⠤⠤⠄⣀⡀⠀⠀⣿⣿⡇
⠀⠀⠀⢠⣿⢷⡇⠀⠚⠉⠀⠀⠀⣀⣀⣀⣀⡀⠀⠄⠀⣼⠀⠀⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣿⣇
⠀⠀⠀⣸⡿⣼⠀⣀⠤⠒⠊⠉⠉⠀⠀⠀⠀⠈⠉⠁⠀⡏⠀⠤⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠐⠒⠢⠀⢸⣿⣿
⠀⠀⠀⣿⣿⡇⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⡦⢤⣄⡀⢠⡇⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⣐⠂⠈⣿⢹⡇
⠀⠀⢰⣿⣿⢁⣤⣾⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣾⣧⣾⣿⣿⠿⠿⠿⠷⠶⠶⠾⠿⠿⠿⣿⣿⣿⣶⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⣭⣥⡶⠶⠶⠶⠶⠶⠶⠿⠿⠿⠿⣿⣿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⠇
⠀⠀⠘⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⣀⣘⡿⠟⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡛⠁⠀⠀⢰⡟⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⡀⠀⠀⡞⠀⡠⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠚⡢⠊⢀⣴⣿⣷⣦⡀⢀
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡿⠋⠁⠀⠈⠻⣾⣧
⠀⠀⠀⠠⣾⣿⣿⣿⣦⣷⣿⣿⣿⣄⠀⠀⠀⣀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣪⠄⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢠⣦⢸⣿⣿⡆
⠀⠀⠀⢸⣘⣛⣛⣛⣹⣿⣿⣿⣿⣿⣿⣿⣗⢡⢀⣆⠀⠈⢀⡾⡞⠓⣂⣀⣀⠘⣿⠀⠀⠀⠀⠀⣸⡗⣞⣿⣿⡇
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⡃⠉⡏⠀⠈⠀⠠⣀⡉⢫⠀⡍⠀⠀⠀⠀⣰⠋⡼⣹⣿⣿⡇
⠀⠀⠤⠤⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠓⡄⠀⣀⠀⠀⠀⠀⠈⠙⢺⠣⡀⠀⠀⣰⣷⣞⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢹⠉⠁⠀⠈⠉⠢⣄⠀⠀⠀⠶⠱⠈⠀⣴⣿⣿⣿⣿⣿⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⣀⣀⠜⣿⣿⣿⡟⠛⠟⠈⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠃⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣀⠤⠄⠒⣈⡡⢤⡐⠧⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⣚⠔⠁⠈⠑⠢⢀
⡔⠻⡤⣐⠾⠟⠊⣉⡠⠴⡖⠀⠀⠀⠀⠀⡠⡔⠒⠊⠉⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠉⠒⢄⡀
⡇⠀⡟⠉⢱⠂⠉⠀⢀⠴⢂⣁⣠⠀⠀⠀⣄⠑⣄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠈⠒⣤
⡇⢀⡇⠀⢸⠀⠀⢰⡵⢉⣙⣯⡓⠀⠀⠀⠌⢢⡈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⢀⡠⠖⡻⣅
⡧⣼⢱⠀⡏⠀⣎⡉⠋⠀⠀⠉⠉⠓⢤⡀⢧⢀⡱⣄⠑⣄⠀⠀⠀⠀⠀⠀⠀⣀⣙⡎⢁⢔⡮⠊⠉⠲⢄
⠀⠘⠻⢤⡷⡚⢿⡨⡑⠦⣀⠀⠀⠀⡠⠜⠾⠣⣀⠈⢦⡈⢣⠤⠴⠒⠒⢉⡩⢅⡿⢮⡒⠁⠀⢀⣠⠔⡏
⠀⠀⠀⠀⠻⡫⡑⠪⣮⣄⠀⠙⣲⢉⡠⣶⠟⠢⣈⠑⢤⡑⢿⣂⣀⠤⠝⠒⠉⢁⣠⢴⣋⠴⠚⢉⠤⣪⠝
⠀⠀⠀⠀⠀⠈⠑⢕⡄⠉⢻⡖⢚⡭⠚⢇⠙⠢⣀⠑⢤⡈⠲⢄⡀⠀⣀⡤⠒⢉⢔⡮⢻⡤⣒⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠓⠁⠀⠀⠀⠑⢤⡈⠓⢤⡈⠲⣄⢉⡎⠁⠀⣪⣶⠵⢊⡿⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠈⠳⢄⡉⢓⡶⠟⠉⡠⢔⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⢸⠑⠀⢔⡭⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣶⣤⣤⣄⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠴⣟⣿⠸⠿⣿⣻⠉⢡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣼⣿⡿⢾⣿⣶⣤⡉⠉⣠⣾⣿⣿⣦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡀⠛⢿⣿⣿⣿⣿⣿⣿⣏⡉⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣆⠀⠙⠻⠿⡿⢿⡿⣷⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡏⠀⡀⠿⢿⣿⣷⣿⣦⣶⣿⣇⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⠿⣿⣟⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠁⢸⠟⢛⣿⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠾⣿⣄⣐⣶⡆⠋⠁⠀⠀⠀⠰⣦⣤
⠀⠀⠀⠀⠀⢀⠆⢀⠀⠀⠀⠀⠀⠀⠄⢰⣿⣿⣝⣛⣷⣬⣶⣦⣄⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣾⠇⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠸⠿⣿⣿⠿⠿⠓⠁⠀⠋⠂⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⣶⠜⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢀⣿⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣿⣶⠄⠀⣐⠂⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⢸⣿⣿⡒⠛⠁⠙⢳⡤⠂⠈⣻⣾⣿⣧⠀⡀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⠀⠀⠻⠿⠿⠿⠿⠶⠤⠈⠁⢽⢤⣿⣿⣿⣿⣷⡰⣄⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⠛⠷⠦⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣤⣀⢀⣾⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠂⢀⣉⡀⡄⠤⠀⠒⠀⠉
⠀⠀⠐⠐⣁⠀⠠⠔⠐⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣤⣤⣄⡀
⠀⠀⠈⠉⠀⠀⢀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣷⡤⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠁⠘⢿⡽⢿⣿⠿⣿⡇
⠀⢲⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⡟⣿⣿⡇⣅⠐⠟⣉⠀⠁⠀⠃
⠀⠾⢿⣿⣿⣿⠯⠅⡄⢀⠈⢹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠀⠀⠀⠀⠀⣠⠚⠁
⠀⠀⠘⠷⠈⠋⠐⠚⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⢀⣀⡤⠚⠁⡖⣢⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠳⠄⠀⡘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢡⢀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠐
⠀⠀⠀⠔⠈⠃⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠀⠀⠘⠢⢀⡀
⠀⠀⠀⠈⠈⠈⠄⠐⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡚⠂⢀⠀⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠄⠰⠄⠈⠀⠀⠀⠈⠩⣳⠃
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⡃⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢄⠐⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣰⣦⡿⣹⡟⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣂⣦⠔⠛⠿⠿⠾⠋⠀⠀⠀⠀⠺⢧⣀⡀⢀⡾⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⣠⣾⡷⢷⣄⠀⠀⠀⠀⢀⣤⣠⡤⠞⠉⢀⠁⠱⠀⠒⠂⣴⡄⠀⠀⠀⠀⠀⢈⠿⠋⠀⠰⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⢀⡼⠋⠁⠀⠀⠙⢻⣦⠀⠦⣉⢱⡏⣀⠄⠀⠋⠐⣠⡄⠀⢀⣿⣷⠀⠀⠀⢀⣴⣯⠖⠀⠀⠀⢀⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⣀⡀⠂⢀⡀⠀⣻⣿⠀⣼⣿⣿⡀⡤⠚⠥⠋⠀⠘⢀⣼⠠⣻⣿⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠋⣠⠆⠠⠀⠀⠀⠀⠀⠀⢦⣼⣿⠞⠁⠀⠔⠉⠀⠠⣾⣿⣷⣿⣿⣿⣇⠀⠀⠀⠀⡠⠌⢉⣠⡾⠿⠋⠁
⠀⠀⠀⠀⠠⣿⣧⣤⣀⡐⢡⡔⡁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠃⠀⠀⠀⡀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⡟⠀⡀⢀⠴⠶⠟⢁⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣮⣼⣿⣦⣤⣀⠀⠀⠀⠀⣤⣿⡷⠀⠀⣀⠀⠂⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡷⢾⣷⢀⣴⣦⣀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢢⣌⠙⠛⠁⠀⠀⠹⣷⣄⣤⣿⡿⠋⠀⠀⢰⣿⣆⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣿⣿⠿⠛⠋⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠢⣤⡀⠀⠀⠈⠉⠻⠿⠦⢶⣤⣶⣾⣿⣿⣗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠐⠠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⣀⣠⣄⠖⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠈⠻⠟⠑⣷⣄⣀⠀⠀⠈⠓⢶⣤⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⠀⠐⠋⠟⠋⠀⠀⠀⠀⠀⣀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠛⢦⣦⢀⣄⠙⠷⣦⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⠻⣿⡷⢿⣿⣿⣿⣿⣿⣿⠛⠋⠋⠁⠙⠁⠀⠀⠀⢀⣴⣧⣠⡴⠂⠀⠀⣠⠞⠋⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢁⣾⣿⣿⠿⠛⠛⠛⠀⠀⠀⠀⠀⠔⠀⢀⠾⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠛⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⡀⡀⠀⢀⣾⠛⠛⢤⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠙⠃⠀⠈⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠿⣇⠂⠀⠀⠀⢀⡀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠈⡅⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢱⡀⠀⠀⢀⡐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢀⠀⠀⢐⡏⠉⠲⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠙⢦⠸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⠀⠀⠀⠘⣃⣀⡀⠀⠀⠀⠀⠀⢀⣤⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠛⠋⢹⣿⣿⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣶⡿⣆⣀⣀⣀⣀⣀⣠⣤⣤⣤⠶⠶⠶⠄⠀⠀⠠⡔⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠂⢀⣭⣭⣭⣵⣾⣿⡿⣛⡛⢛⣉⡭⠿⣛⣫⡄⠀⠀⠀⠀⠀⠀⣗⡀
⠀⠀⠀⠀⠀⠀⡀⢀⣠⣀⠀⠀⠀⢱⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢀⣴⠉⠁
⠀⠀⠀⠀⠔⠫⠒⠕⣫⡵⢛⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠏⣠⣤⣶⡿⡿⠟⠒⠂⠤⢤⣤⡤⢤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠈⠉⠉⠙⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠿⠿⣅⣀⠸⣤⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠡⠤⠖⠂⠀⢀⠀⠀⠀⢀⢀⡀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⡀⢁⣀⣤⣴⣶⣶⣶⣿⣾⣾⡖⠉⠀⠀⠃
⠀⠀⠀⠰⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡟⠉⠉⠀⠀⠀⠈⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⣀⣔⣿⣿⣿⣿⣿⣯⣶⣶⣶⣶⣶⣶⣶⣤⣀⡀⠙⢿⣷⣄
⠀⠀⠀⠀⢲⣿⣿⣿⣿⢿⣿⣿⡿⠛⠉⢀⣾⣿⣿⣿⣿⣿⣿⣿⢶⣄⠙⢿⣷⣤⠀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠉⠩⠉⢠⣤⣥⣿⣷⡀⠀⢸⣿⣿⣿⣿⣿⣧⣶⣿⠀⠉⠳⢦⣙⠻⠿⠿⠟⠓
⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⣉⣻⣿⣧⡀⠈⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣯⣍⡓⠒⠩⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⠂⠂⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠰⡰⠁⠀⠀⠀⠀⠀⡀⠀⠁⠀⡀⠀⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⢀⢧⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⡘⠀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢣⣄⢀⡀⠲⠉⠁⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⡂⡀⣀⡙⣿⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡄⢠⠈⠀⠀⠀⠀⠀⠀⠈⢱⢀⠤⢀⣀⣀⣀⡀⠤⠴⠚⠁⠀⠀⢩⠁⠉⠈⠻⡃⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢀⠀⠠⠈⠀⠔⢃⠀⢠⠀⠀⠀⠀⢬⡜⠀⠀⠀⠀⠀⢀⣤⢴⣦⡀⠀⠀⣀⣁⡄⢰⠞⠀⡀⠁
⠀⠀⠀⠠⠠⢠⠀⠀⠀⠀⢠⠃⢀⠀⠀⡁⢤⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⣼⡟⠀⠀⠈⣿⠀⡴⠁⠐⠀⠀⠀⢰
⠀⠀⠀⢀⠀⠨⢠⠀⠀⢀⠸⡄⠈⠂⠀⢱⠊⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢻⡗⠀⠀⡶⠟⠀⢀⠀⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢡⠈⠃⠀⢀⢐⠛⠀⠀⠀⠀⢀⡤⠋⠁⠀⠁⠀⠁⢄⠀⠀⠀⡸⠀⠐⠒⠡⢀⡓⠀⠁⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⠘⠀⠀⢀⡆⡆⠂⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠡⠀⠀⡄⠀⡜⢣⠄⡀⠐⣤⡖⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠶⣸⣶⠀⠀⢀⡆⠀⠀⠀⡜⠑⠂⢠⠊⠀⠀⠀⠀⠈⠈⠁⠈⠀⠀⠑⠀⠈⠀⠳⠐⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡗⠠⠄⠲⠋⠁⠀⠀⠱⠼⠘⣶⢀⡀⠈⠀⠀⠕⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠈⠉⠀⢠⠔⠃⡀⠈⠀⠀⠀⠀⠀⠀⠀⢰⡁⡀⢠⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠁⠀⠒⠒⠀⠈⣀⠶⠁⣠⠄⠀⠀⠀⠸⠀⡥⠄
⠀⠀⠀⠀⠀⠰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣅⡀⠀⠀⠀⠀⠀⠠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠔⠂⠀⢦⠀⢀⣠⠐⠁

⠀⠀⠀⡀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠀⡀
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠂⠀⠀⠨⠇⠀⠀⠀⠀⠀⡰⠀⠀⠀⢀⡀⠈⡁⠀⠀⠀⠀⠉⠒⠀⠁
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⢀⣴⣷⠆⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⠀⠀⠀⠃
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠂
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠒⠒⠒
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⡀⠌⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠌⠀⠤⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠘⠃
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠄⠀⠑⠀⠀⠈⠃
⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠂⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢌⠀⠀⠀⠀⠒⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠆⠀⣀⣀⠀⠀⡠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠰⠇⠀⠐⠒⠋⠀⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠰⡀⠀⠀⢀⢓⠀⠀⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣮⢔⢆⠀⠘⢆⠢⣀⣀⠈⠁⢐⠀⢠⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠠⠀⠐⠂⠀⠀⠻⣾⣧⡢⡀⠠⠑⢄⠈⠉⠃⡴⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡔⢄⠀⠀⡁⢰⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢠⠤⠚⢿⣿⣦⠀⠀⠉⠠⠀⠀⠐⠀⠀⠄⠀⡀⠀⠀⠀⠈⠐⠠⡀
⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠻⣏⠻⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡤⠤⠄⢂⣔⣀⠨⡐⠠⡀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠑⢄⡀⠀⠙⢿⣽⣷⡜⠀⠀⠀⠀⠔⠀⠠⠅⠐⣠⣀⡁⠀⠀⠁⠪⠀⠡
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠂⢉⡢⠒⠃⠀⠀⢀⠀⠀⠀⡀⢤⢊⡄⡀⠀⠀⠀⠈⣆⢀⣀⡀⣀⠆
⠀⠀⠄⠀⠀⠀⠀⠀⠄⡁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢉⡢⠵⢆⠈⠀⠚⠊⠳⠶⠦⠛⠂⠘⠋⠉⠀⠀⠀⠀⠀⡂
⠀⠀⢆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⡘⠒⠊⠉⠉⠁⠀⠀⠊⠳⠀⢀⣀⠤⠤⠂⠀⠀⢂⠠
⠀⠀⠀⠵⠄⠀⠠⠤⠀⠀⣰⣦⡀⠈⠁⠀⠀⠀⠀⠀⢀⡠⠤⠒⠈⠁⠀⣀⠠⠤⠒⠂⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⢿⣆⡀⠀⠀⢀⠀⠀⢀⠀⢀⠂⠄⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡔⠛⠋⠛⠒⠒⠒⠳⠄⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠶⠶⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠍⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣴⣶⣶⠶⠶⢲⡶⠒⠀⠀⠀⢤⡤⢤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣀⢀⡈⣀⣀⣀⣀⣀⣘⣤⡀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⠟⠋⠻⠟⠿⠋⠑⠿⠃⣿⠉⠉⠁⠀⠀⠀⠉⠋⠙⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⣿⣶⣶⣾⣶⣶⣟⣤⣿⣦⣰⣾⡐⣯⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠛⠻⠿⠿⢿⣿⣿⣿⠿⣿⣿⣿⡀⠀⠀⠀⠀⣀⣀⣀⡉⠀⣀⠀⠀⢀⣀⣤⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢶⣾⠟⠛⠉⠉⠉⠉⢉⡴⠖⠒⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠐⠂⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠒⠒⠶⠦⣤⣤⣤⡴⠋⣩⠤⠂⠀⠀⠀⠀⠀⢀⣸⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠇⠀⠀⠀⠀⢀⣠⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠒⠒⠶⠤⠤⠤⢤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⣠⠴⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠲⠤⢤⣀⠖⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢰⣾⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠛⡛⠂⠈⠙⣷⡀⠰⣦⡴⢄⢀⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣀⣀⣠⣶⣶⣿⣿⣿⣿⣏⠂⢄⠀⠈⠁⠀⠈⢿⣼⠋⠙⠙⢢⣀⣀⣼⣿⢷⣤⣀⠀⢀⡾⠿⢧⡄
⠀⠀⠈⠻⠻⠌⠻⠿⢉⣽⣿⣿⡄⠀⠀⠀⢀⣀⣤⣤⢀⡀⠁⠀⠀⢀⣁⣈⠉⠀⢀⣥⣾⣟⠣⠀⠀⠀⠐⠳⡤⠴⠤⢦⣀
⠀⠀⠀⠀⠠⡶⠾⣆⠈⠻⢿⠁⠀⠀⢀⣴⣾⣿⣿⣿⣇⠙⠳⠀⠀⠀⠉⠉⠁⠀⠁⠀⢀⣿⠀⠀⠂⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠿⣿⣿⣿⢿⡟⡩⠛⣿⣾⣷⣦⡀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⣼⣿⡁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠀⠀⠀⠀⠙⠯⠀⠰⠁⠀⣫⠿⠛⠙⠁⠀⠀⠀⠀⠲⣿⣿⡌⠀⠀⠀⢠⣿⣿⣇⣀⡄⠸⠁
⠀⠀⢸⣿⣷⣤⢤⣀⡀⠀⠀⠁⠀⢀⡀⠀⠀⠁⠤⠐⠁⢀⣶⣶⣼⣦⡀⠀⠀⠀⠀⠱⠿⢾⠂⠀⢸⣿⣿⣿⣋
⠀⠀⠀⠛⠉⠉⣻⣿⣿⣾⣷⣀⣄⢸⣿⡄⣠⡀⠀⠀⠉⠚⠿⣿⡝⠋⠙⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⡀
⠀⠀⢀⡀⣠⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣀⠀⢠⣶⣀⡄⠉⠙⠦⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣦⣦⣀⣤⡀
⠀⠀⠀⠉⠙⠛⠛⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣠⡄⠀⣠⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣟⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠓⠉⠙⠋⠋⠉⠛⠛⠛⠿⠶⠿⠇⠀⠀⢠⣦⣼⡿⠟⠛⠛⠻⢿⡿⠟⠉

⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣭⠛⡭⢿⣭⣭⣭⣭⣭⣭⣭⣭⢭⣭⣭⢭⣩⣉⣩⣭⣉⣉⣭⣉⣉⣩⢭⣩⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠫⢴⣖⢴⡄⠃⠜⣤⣐⡼⢶⣷⠼⣦⠤⠼⣤⣷⡼⣦⣷⡤⠤⠰⣧⣤⣄⢠⣧⠤⠀⠼⡌⠂⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢊⣿⣿⢶⣷⢤⣀⣿⢸⣤⡟⣻⠿⣯⢹⣍⣭⣽⣯⣿⣿⠎⠖⣒⣲⣶⣴⡾⠛⢷⣄⠀⡏⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢧⡿⠟⣟⡰⠿⢿⠍⢻⢽⡅⡜⠁⢐⠆⣧⢩⠋⠱⠜⠂⣸⠶⣾⠘⡛⠛⢷⣷⡤⠶⠋⠑⡇⢸
⠀⠀⢀⣾⣿⠀⠀⠀⠀⢸⣧⣠⠷⠇⠠⢋⣜⡾⠀⢿⡇⠀⢸⣏⠂⣹⠀⠀⡆⠀⠍⠋⠉⢻⡃⠀⣠⣤⣀⠀⡤⣀⡇⢸
⠠⣦⣭⣿⡳⠀⠀⠀⠀⢸⣽⠉⠐⠂⠀⠠⠈⣯⣴⡋⡇⢰⣋⡝⠰⡏⠀⢠⠁⠀⠀⠀⠀⠸⠭⡏⣅⣉⣀⣀⣸⡯⠇⢸
⠀⠀⢹⠫⢋⡱⠀⠀⠀⢘⡾⢄⠀⠦⠆⠀⢀⣼⣽⠀⡇⠀⡟⠒⢯⡇⠦⢼⣠⢠⣤⠃⠀⡬⠭⣿⣉⡉⠀⠈⣸⣗⡀⠠
⠀⠀⠀⠣⡤⢾⠀⠀⠀⣀⡤⡄⠿⠷⣎⠉⠻⢻⢛⠠⡇⢠⡝⠀⠀⠃⠀⠀⠇⠸⣿⠓⣲⡯⢭⣿⣓⡚⠛⢛⣻⠶⠀⢠
⠀⠀⠀⢸⡷⡿⠀⡠⠊⠑⠀⠃⠒⠐⠉⢱⠀⢸⠀⢹⠚⠸⠏⠀⣨⣀⢠⠄⠐⠀⣯⠉⢹⣏⣿⣿⣔⣦⣤⣴⣿⣯⠀⢸
⠀⠀⠀⢠⠀⠷⠊⣠⢴⡇⢀⡔⡀⠀⡄⠘⠀⢸⢱⠦⠭⢄⠀⠀⠉⢉⡽⠀⢀⡔⣿⠀⢨⢱⣻⡇⠸⠇⠀⠀⠀⠘
⠀⠀⠀⠈⠂⠐⠋⠀⢸⣁⣀⣉⢀⣠⣇⠀⡤⠞⢉⣜⠀⠀⣱⢄⠀⠙⡶⠧⠤⠶⡏⠀⠸⣥⢽⡇⠘⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⠷⠿⠿⡇⢸⢀⣠⣾⡛⠛⠓⠒⠻⠿⡴⣴⣆⣀⣀⣰⠁⠀⢸⠆⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠁⠀⠀⢸⣉⣀⣀⣠⢤⣀⣀⣀⣺⠀⠀⠀⢸⣦⣤⣤⡆⣶⣇⣀⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⢀⠀⡆⠀⠀⠀⠃⠀⠀⠘⠛⢴⡄⣤⣽⣤⣀⣀⡀⠉⠉⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⢩⠉⢹⡇⠀⠀⠸⣾⢇⣆⣀⣀⣋⣉⣁⡮⠈⠁⡟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⢸⠀⢸⠀⠀⠀⠀⠁⠀⠃⠀⠀⡀⠀⢸⡇⠀⠀⡇⢺⠀⠀⠀⠠⠼⢀⣞⠋⠍⢩⠂⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣸⠀⢸⠀⠀⠀⠀⠀⢠⢀⡴⠋⢹⠞⠋⡅⣀⢀⣇⣼⠿⡿⠻⠟⢲⣼⢌⣱⠀⡆⠀⢰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⠈⡴⠚⣄⠀⠀⠀⣣⢶⣯⠶⡞⠁⣠⠞⠑⠜⠺⣿⣁⠀⠁⣀⢘⣸⡟⢺⣿⠀⢡⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠊⠀⠀⠘⣢⠀⠀⣿⠠⣍⣉⢡⣎⣠⠂⠁⣄⣠⠀⠀⠀⢴⡋⢉⡉⠐⠿⢃⣠⣀⡧⠴⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠘⢒⡀⠌⢌⠑⠮⣀⠀⠈⠉⠁⠀⠈⠁⠁⠀⠀⠉⠉⠉⠈⠘⠻⠭⠔⠴⠋⠉⠁⠀⣀⠀⠆⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢹⠦⡀⠈⠐⠀⣇⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢀⣈⠤⡄⢰⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢽⣔⣛⠀⠀⢠⣙⣓⣒⣒⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠐⠒⠃⠐⠳⠦

⠀⠀⠀⠀⣼⣿⢸⣿⢀⣿⣿⣿⣿⣶⣿⠿⢿⣄⠀⢸⠈⣀⠜⢳⣆⠹⣧⢰⣿⣿⢸⣿⢿⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⡇⣿⣿⣼⣿⣿⣿⣿⣿⣟⠀⢀⣿⣿⠈⢸⣿⣶⢿⣿⠀⣿⣾⡇⠀⢴⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⡿⣻⣿⣿⣋⠀⠚⠿⣿⣿⣿⣇
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣾⣿⣿⠀⣾⣿⣯⣾⡿⠀⣿⣿⡇⠀⣼⣿⣿⣿⠛⣫⣽⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⡀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣽⣿⣿⡀⣿⣿⡟⠀⢠⠈⣿⣿⡇⠀⣿⣿⣿⣻⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣹⣿⣿⣿⠃
⠀⠀⠀⢰⣿⣿⣿⣿⣿⡟⠉⣿⣿⡏⠀⢸⣿⣿⣿⢰⣿⣿⣇⠀⣿⣠⣿⣿⡇⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣗⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⣸⣿⣿⣿
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣏⠀⣿⣿⡿⠀⣸⣿⣿⣿⣾⣿⣿⣧⠀⣿⣿⣿⣿⡇⠘⣿⣹⣿⣿⣿⡇⣿⣿⣿⠟⣀⣿⣿⡇⢺⣿⣿⣿⣿⡇⣭⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡗⢰⣿⣿⡇⠀⣿⣿⣿⣿⡿⣿⣿⠏⢠⣷⠌⣿⣿⡇⢰⣿⣿⣿⣿⣿⡇⣿⣿⣿⠀⠐⣿⣿⡇⢰⣿⣿⣿⣿⣆⣽⣿⣿⡏
⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⢸⣿⣿⡗⠀⣿⣿⣿⣿⠂⣿⣿⠀⢸⣯⣖⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⢻⣿⣿⠂⢨⣿⣿⡇⠀⣿⣿⣿⣿⠃⣿⣿⣿⣇
⠀⠀⠀⠀⣽⣿⣿⣿⣿⠇⢸⣿⣿⡇⢸⣿⣿⣿⣿⠀⢻⣿⠀⣸⣿⠃⠛⣿⡇⢸⣿⣿⣿⣿⣿⡇⣿⣿⣿⡀⢸⣿⣿⡇⠀⣿⣿⣿⣿⠘⢿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⡇⢸⣿⣿⣿⣏⠀⢸⡟⠀⣿⣿⠀⠀⣿⡇⢸⣿⠼⢿⠿⠫⢟⢫⢝⣻⡇⢸⣿⣿⡇⠀⣽⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⢸⣿⣿⡇⢸⣿⣿⣿⡏⠀⣿⡇⠀⣿⣿⡗⠀⢿⡇⢸⣿⣴⢀⣠⠈⠀⠀⠐⣼⡄⢸⣿⣿⡇⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⣾⣿⣿⡇⢼⣿⣿⣿⡇⠀⣿⡇⠀⣿⣿⡇⠀⢺⢣⢁⣿⠉⠀⠀⠄⣰⡇⠰⣛⡇⢸⣿⣿⡇⠀⣿⣿⣿⣿⠀⢺⣿⣿⣿⡅
⠀⠀⠀⠀⢾⣿⣿⣿⣏⠀⣼⣿⣿⣧⢸⡿⣿⣿⡇⠀⣿⡇⢨⣿⣿⡇⠀⢾⡧⠄⠸⢆⠀⠀⠈⠁⠀⠀⣨⡇⣸⣿⣿⡇⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣾⣿⣿⡗⠸⠗⣛⣸⡇⠀⣿⠇⢸⣿⣿⡄⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠿⣇⢺⣿⣿⡇⢠⣿⣿⣿⣿⠀⣼⣿⣿⣿⡎
⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⢻⣿⡇⠀⠀⠀⠀⡇⠀⠋⠀⠈⡇⣿⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⣿⣿⡇⢸⣿⣿⣿⡿⠀⢿⣿⣿⣿⡏
⠀⠀⠀⠀⢸⣿⣿⣽⣇⠀⢿⢸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡌⣿⡇⢸⣿⣿⣿⣧⠀⢺⣿⣿⣿⡗
⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⣾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣸⣿⡇⢸⣿⣿⣿⣿⠀⢺⣿⣿⣿⡇
⠀⠀⠀⠀⣸⣿⣿⣿⣏⠀⣾⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢸⣿⣿⣿⡿⠀⣻⣿⣿⣿⡧
⠀⠀⠀⠀⢸⣿⣿⣿⡷⠀⢿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⡃
⠀⠀⠀⠀⣾⡇⢿⣿⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣄⡤⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⢸⣿⣿⣿⠁⠀⢹⣿⣿⣿⡇
⠀⠀⠀⢸⣿⡇⢸⣿⡧⠀⢸⣿⠀⠄⠀⠀⠀⠀⠀⢠⣦⠀⠈⢣⢀⡀⠀⢀⣶⠁⢃⠀⠈⡀⠀⠀⠀⠀⠀⠀⣿⡟⠟⠀⢨⣿⣿⡇⠀⠀⣼⣿⣿⣿⡇
⠀⠀⠀⣺⣿⡧⠀⣿⡇⠀⠘⣿⢀⡆⠀⢠⠀⠀⠀⠀⠻⠿⢿⡟⠁⢻⣿⣆⠼⠆⠙⠁⡤⠧⠀⠀⠀⢀⡀⠀⡿⠁⢠⠀⠈⢻⣿⠁⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣯⡀⠹⡅⠀⢠⡏⢹⠀⠀⠈⣧⣀⡀⠀⠀⠀⢸⡇⠀⠄⢿⠟⣰⡄⠀⠀⡇⠀⣠⠆⠠⠘⠁⠀⠰⡀⠀⠱⣤⣾⠋⠀⠀⠀⣧⢸⣿⣿⣧
⠀⠀⢀⣿⣿⡏⣷⣾⣧⣴⠿⣃⡜⠀⠀⠀⢻⣿⣿⣶⣶⣶⣾⣿⣶⣴⣶⡾⢋⡛⢠⡄⠉⠀⠁⠒⠒⠃⠀⠀⠀⢱⡦⠐⠊⠁⡂⠶⠀⠀⢻⣿⣿⡟⢢
⠀⠀⢸⣿⣿⡇⢿⢿⡿⢡⣾⠟⠄⠀⠀⠘⢿⡛⠛⠋⠉⠉⠉⣿⣿⣿⣿⡇⠉⣿⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠓
⠀⠀⢐⣿⡿⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⣿⠈⢿⣧⣸⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⢉⡀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠈⢿⣿⣠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠰⠖⠂⠰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡜⢃⣀⡀⣀⣋⠐⣤⣤⡤⢤⡶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠉⠀⠀⠐⠁
⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠔⠀⠻⢷⣀⠀⠀⠈⠉⠛⢻⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢎⡁⠈⠱⠀⠀⡼⠇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠈⠹⠀⠀⠀⣠⠂⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡼⠁⠀⠀⠀⠘⢧⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⣧⠀⠀⠀⡙⠀⠀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢢⡀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠄⢀⣄⡀⠀⠀⠀⠀⠀⡅⠀⠀⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠠⣤⢊⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⢰⠁⠀⠀⠀⠶⠂⠀⠀⡀⠀⠞⠀⠁⠀⠀⠀⠀⠘⡀⠀⠀⠀⠈⡦⠀⠈⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢟⠁⠀⠄⡈⠁⣼⠆⢀⠰⠾⠀⠂⠀⠀⠀⠀⡀⠃⠀⠀⠀⣎⠀⠀⠀⠈⠁⠀⠀⠉⠁⢉
⠀⠀⠀⠀⠀⠀⠀⠉⠘⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢴⠀⢈⡉⠁⡴⠄⢠⣤⠀⢀⣀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠓⠂⠀⠈⠁⠈⠁⠐⠀⠁⡀⠀⠀⠀⠀⠈⠉⠋⠀⠀⠶⠀⠂⠄⣀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡐⠃⠀⠀⣈⠂⠘⠀⠀⠀⠻⠀⠈⠀⢈⠉⠀⠀⠘⡉⠉⠛⠀⡈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡆⠀⠀⣀⠆⠀⠀⡀⠀⠀⠀⡀⠀⢀⠀⠀⢠⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠆⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠉⠀⠀⠀⢠⠀⠈⠀⠠⠀⠈⠁⠐⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⢛⠀⠀⠾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠂⠆⠀⠀⠓⠀⠀⠀⠛⠀⠒⢶⠦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢋⣤⠶⠀⢀⣆⡀⠀⠀⠀⠀⡤⠀⡀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡗⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢡⡜⠋⠀⠀⠈⠹⠇⠀⡾⠃⠈⠇⡀⠛⠀⠀⠈⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⢀⣤⢀⣵⣄⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢿⠁⠀⠀⠀⠀⢸⠇⠀⢶⡄⢼⣠⠀⠀⠀⠀⠘⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⠉⠛⡋⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣀⠃⣄⢠⡔⠉⠀⣀⣴⠡⣾⣿⠗⢀⠀⣠⣞⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠘⠖⢡⠀⠀⣿⣦⠘⠂⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠉⢙⣄⣁⣈⣷⡄⠀⠈⢿⠀⠸⣏⠁⠀⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⣾⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢠⠀⠘⠉⠉⠉⠁⠀⠀⢶⠋⠀⠀⠙⠛⠛⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⡀⠀⠀⠀⣠⢀⠀⢸⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⢿⣿⡿⠀⠀⠀⠘⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠃⠀⠀⣫⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠙⠁⠀⣄⠐⠀⡙⠀⠀⠰⠊⠁⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡉⠀⠀⣿⠐⠓⠊⠁⠉⠉⠉⠁⠀⠐⠒⢠⡄⠀⠀⠀⠀⠀⠀⣀⣦⠈⢳⡆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢹⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⢳⣤⡤⢦⣤⣽⠁⣈⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠆⠀⣤⡶⠒⢶⡶⠀⠀⢀⣀⡀⢸⡗⢠⡆⢹⣷⠊⣿⣤⣿⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⠀⣴⠀⣤⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠻⢿⣧⣌⣷⣾⡿⣷⣯⡉⣷⣴⣴⣶⠤⠤⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠐⠛⡷⠀⠉⠀⠐⠣⠄⠀⠀⠀⠀⠀⠠⠤⠘⠁⠀⠀⠀⣿⠃⣿⡿⣄⣼⠁⠀⣿⣏⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⢀⣀⡄⠀⠀⡀⠈⠛⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠛⠻⡟⠋⢻⡟⠁⢺⡟⠛⣿⠁⠀⠀⠀⢀⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣴⣶⣤⣴⣮⠉⠃⠀⠀⠑⠒⠒⠂⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⢠⡆⠀⠸⡇⠀⢠⡄⠀⣧⠀⠀⠀⠰⣇⠀⢠⣤⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡄⠲⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣸⢤⡴⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣲⠘⠲⠉⠈⠁⠁⡔⢆⠐⠂⠀⠀⠰⢦⠐⠀⢉⠸⣥⢸⣟⡄⠃⠂⠉⠀⠙⢤⠒⡄⠐⠀⠀⢀⠴⠄⠰⠀⠘⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠃⠋⠀⠀⠀⠀⠓⠚⠶⠒⠻⡀⢀⡓⠈⡏⠀⠀⠀⠀⠀⠘⠑⠁⠀⠐⠀⠀⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⡄⠄⠀⠐⠲⣤⡼⠃⢺⡏⢐⡇⠀⠀⣀⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡀⣡⠀⣤⠈⠀⠀⣴⡀⢺⡹⠇⢠⠀⠀⠉⠙⠉⠛⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠘⠛⠀⢻⡇⠀⠀⠈⠁⠈⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠀⢦⠄⠈⢢⣴⡏⠀⠛⠃⡀⠀⢀⠀⠉⠀⠀⠀⠀⢀⠀⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠗⡒⠀⠐⠀⢼⠟⡯⢠⠀⢸⣅⣠⠏⠀⠀⠀⠿⣁⠀⠩⠀⠐⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡇⢠⣭⠉⢲⣆⠘⠃⡧⢸⠀⠀⠉⠁⠀⠀⠐⡇⠀⠈⡀⠀⠀⠁⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠸⠦⠀⠿⠄⠀⠃⠸⠄⠠⠀⠀⠀⠀⠸⠁⠀⠈⠁⠀⠀⠀⠞⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⣒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡪⠁⢸⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠰⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡪⢑⠡⢂⠁⡠⠗⠀⠀⠀⠀⡠⠘⡇
⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡄⠙⡡⢀⠁⢊⠤⠊⠀⠀⠀⢀⠔⢈⠄⡀⡇
⠀⠀⠀⠰⡁⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⢸⡇⠀⢐⡡⠖⠁⠀⠀⠀⡠⠒⡡⡒⢕⠩⠀⠉⡻⠋⠉⠉⣉⢿
⠀⠀⠀⢀⡵⠤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣒⣁⣀⣀⣀⣀⡤⠊⠔⠉⠈⠀⡡⢔⠕⠊⠀⢀⠠⡪⠀⢘
⠀⠀⠀⡎⠀⠀⣾⣿⠃⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠀⠀⡠⢐⡥⠞⠁⠀⡠⢐⠅⡪⣦⠔⠉
⠀⠀⢀⡇⠀⠀⣿⣿⡀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢀⠥⠚⠁⠀⢀⠔⡨⢐⢕⡬⠊
⢀⠴⠿⠿⠦⠤⠿⠿⠷⠼⠿⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠿⠏⢥⣠⣄⡤⠂⣠⡪⡪⠒⢹⠁
⡏⠀⠐⠆⢰⣶⣶⣶⣶⣶⣶⡶⣶⣿⣿⣿⢿⣿⠿⠿⠿⠿⠷⠾⠿⠿⠷⣶⣶⣶⠆⠀⠆⠀⢰⠁⢹⡿⢟⡫⢄⠘⣦
⠑⠒⠒⠒⠒⠒⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⡉⢕⠩⠂⠅⣂⡵⠊
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⢸⡇⠀⡀⠔⢈⠔⠊⠀⡇
⠀⠀⠀⠀⠀⡸⣇⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⢸⣧⣀⠤⡊⠁⠀⣀⠔⠋
⠀⠀⠀⣰⠟⠒⠚⢳⣶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣶⠖⠒⠒⠒⠒⠒⣶⠖⡻⠑⠀⢀⠴⠊⠁
⠀⠀⠀⡇⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢠⣿⠀⢀⡡⠊⠁
⠀⠀⠀⢣⣀⣀⣀⣹⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣆⣀⣀⣀⣀⣀⡿⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠦⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⢀⡐⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠄⡛⠉⠀⠐⢢⡤⠀⢀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢆⠀⠀⠀⠀⠠⠘⠃⠀⠀⠉⠛⠁⠀⠙⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡧⠑⡀⠀⡐⠀⢀⢟⠀⠀⠀⠀⠢⠄⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣎⣜⢤⠀⠀⠸⡌⠦⡀⠀⠈⠙⠁⢰⠀⠀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠄⠐⠈⢿⣬⣧⡣⡀⠀⠝⠦⡈⠉⠓⢒⠆⢈⠀⠀⠁⠁⠀⠂⠀⠑⢄
⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠠⠀⠀⠈⢻⣿⣷⡜⢆⠈⠄⠈⠢⠀⡀⠴⠁⠀⠀⠈⡀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣿⣿⣆⠢⠈⢄⠠⡀⠃⠀⠠⠀⠀⢀⠀⡀⠀⢠⠀⠀⠀⠐⢄⡀
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢸⢀⠰⠖⠋⠙⢿⣿⣷⡑⡀⠠⠀⠒⠀⠀⠀⠁⠂⠰⠄⠀⡄⡀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠈⢻⣧⠙⣽⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣤⠤⠔⠒⢢⣔⣀⠀⢌⠒⢤
⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠙⢿⣌⣿⣦⠓⠀⠀⠀⠀⢀⠄⠀⠠⠍⠑⢢⡠⡚⠁⠀⠂⠉⠒⢅⠀⢣
⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠣⠍⠒⢄⠤⠎⠀⠉⠉⠀⠀⠀⠠⠀⠀⡡⠊⡀⠀⠀⠈⠉⠉⠳⡄⠀⠄⠀⠆⠠⡀⠁⠈⠉
⠀⠀⢀⠁⠂⡠⠀⠀⡀⠀⠐⠂⠀⠒⠂⠀⢠⠊⠁⠐⠀⢀⠒⢤⡑⣄⡀⠠⠊⢡⣇⣸⣁⣂⡀⣠⠤⠀⠠⠷⠶⠒⠊⠉⠉⢁⣀⣀
⠀⠀⠘⠀⠀⠀⠄⠈⠀⠌⠐⠁⠀⠀⠀⠀⡆⣄⣀⣀⠴⠦⠬⠖⠋⢈⡳⣄⠀⠀⠠⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒
⠀⠀⠘⢄⡀⠀⠀⠀⡐⠠⠇⠒⠀⠒⠒⠀⣯⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⠤⠔⠒⠛⠉⠀⠀⠀⡕⢒⡂
⠀⠀⠠⠤⠛⠂⠒⠐⠒⠢⠍⠀⣜⣗⡄⠉⠀⠀⠀⠀⠀⠀⠀⢄⡠⠤⠒⠊⠉⠀⠀⢀⡀⠤⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⢿⣶⢄⠀⠂⠀⡀⠀⠀⠀⣀⠀⢀⡂⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣿⠟⠀⠀⠀⠀⠁⠢⠔⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢘
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠤⠤⠤⠄⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⡠⠃⠀⠁⠐⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡋⠀⡔⠁⠀⠀⢀⢤⠢⠓⠃
⠀⠀⠀⠀⠀⠐⢶⣤⣤⣠⣄⡀⣤⣄⣀⠀⠠⠤⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠎⠀⠀⢄⠎⠊⠁⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠂⠒⠦⣠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡡⡰⠕⠈⠀⠀⣀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠐⡷⢆⣀⡄⣀⠀⠀⠀⠀⠉⠐⠉⠲⢀⡠⢀⡀⠀⢀⢄⠢⠑⠁⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⣠⢊⣀⠀⠀⠀⠉⠒⠚⠴⢆⡠⢀⡀⠀⠀⠀⠈⠐⠺⠃⠁⠀⢀⡤⢖⠟⠁
⠀⠀⠀⠀⠈⡏⠈⠉⠉⠉⠉⠐⠒⠂⠙⠒⠚⠛⠛⠾⠥⠶⢄⣤⣀⣠⠴⠚⠉⡔⠁
⠀⠀⠀⠀⢠⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡠⠊
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠒⠒⠒⠒⠂⠠⠤⠤⠤⠤⠤⠤⠊





⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⢁⠖⠋⣓⣾⣆⢄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡄⢁⠄⢠⡉⢆
⠀⠀⠀⠀⣀⣤⠤⢄⡀⠀⠀⠀⠀⣀⣀⣔⣭⡿⣝⢗⢦⢊⡎⣿⢫⡽⠞⢋⡩⠭⢙⣷⣶⣚⣒⢶⣉⢿⡷⡓⢤⠙⢲⠛⠁
⠀⠀⢀⡾⠋⠀⢛⣲⣈⠲⡶⠴⠏⣉⠉⠚⢓⣏⠻⢮⣸⣼⡰⣸⣏⡔⠒⡧⠂⠀⠒⠏⢀⣤⣉⠫⡛⢯⣁⡆⢠⠀⢘⡀⠀⢀⣀⡀
⠀⢀⡏⠀⡀⠀⠉⣸⡹⡷⢟⡤⠊⠉⠈⠉⠁⠀⠀⠀⠀⠈⠻⡿⠻⠀⢸⠁⠀⠔⠉⠧⠊⡇⠈⢿⠉⢢⣫⣷⡴⡿⠛⠛⠛⢯⣁⠈⣙⠢⣄
⠀⢸⠃⣸⠀⠀⡰⠉⠉⡙⠸⠁⠀⠀⢀⠀⣦⠹⠈⡀⠆⡄⣶⠘⢰⠀⢸⣆⠀⡀⠀⠀⢠⠁⢀⡞⠀⡜⠈⡏⢠⠀⠀⡰⣊⡲⣷⣶⣶⠩⡊⡷⢤⣶⠿⢍⡙⢦
⠀⢸⠀⡆⠀⠀⡆⠀⠀⣇⠀⠀⢠⠢⡘⣆⡇⠣⠧⠷⠶⠶⡹⣰⣀⡷⠿⠏⠁⠛⠀⠐⠓⢚⣿⣵⡞⠁⢀⡷⠡⢃⢌⠜⠙⠚⠿⢏⠋⠃⠈⣧⣏⣤⠶⡦⡈⣾
⠀⢸⡄⠁⠀⢰⢡⠀⠀⠢⣑⢚⢦⠷⠋⢉⣈⠀⠀⠀⣠⢴⣏⡗⢮⠽⠖⠙⠷⠄⠀⠀⢠⡴⠒⠶⢵⠞⢯⡷⠷⠦⠂⠀⠀⣀⠊⡨⠜⡀⢠⡈⡟⠁⠀⠇⣧⣿
⠀⠸⡇⠂⠀⠀⠀⢡⡱⣺⠟⠣⣵⣄⠶⠋⠉⠁⠀⠀⠀⠀⠹⡏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠘⣼⡶⢶⠀⠀⠀⠀⠙⢳⠵⠇⡆⣸⠱⠃⢀⢀⠘⣿⡍
⠀⠀⡇⠀⠀⠀⠀⢸⡿⣤⣮⠀⠈⡅⠄⠀⠀⠀⠠⠄⢀⡄⢠⣌⡾⢄⠀⠀⢠⣄⣀⣠⡄⠀⠀⢰⣥⠔⠃⠀⡀⠀⠀⠘⠛⠻⡄⠀⠦⡅⡼⢄⢡⣨⠌⢳⠊
⠀⠀⡗⠀⠀⠀⢸⠈⣧⠙⣷⣲⣶⣽⠀⠀⠀⠀⠘⠈⠟⣰⠷⠧⡝⢂⡶⠀⠀⠋⠉⠋⠀⢀⠰⡏⠈⣝⣇⢸⣔⡀⠀⣄⠀⠀⠀⠀⠀⡠⢤⠎⠈⢮⣳⣋⣙⡇
⠀⠀⡇⠀⡄⢠⠀⠂⣿⡀⠈⠛⠛⣿⡟⢢⠴⠒⠂⠤⣾⣙⣀⠔⠋⠀⠉⢺⠑⠄⠀⠠⡴⠀⠒⠻⡍⢇⠚⢂⠋⠁⠈⠀⠀⠀⢀⡴⠒⠲⠁⠀⠀⣠⣄⣀⡝
⠀⠀⢣⢸⡇⢸⣷⠀⣿⠇⠀⠀⢀⡽⠛⠁⠀⠀⠀⠀⠀⠈⠉⠒⠠⠄⡀⡼⠀⠀⠀⠀⡤⠀⠀⢀⣈⣺⡧⠴⠦⠐⠂⠀⠀⠘⠻⣄⣀⣰⡃⢦⠀⠈⣯⠆
⠀⠀⠀⠻⠷⣸⣿⡼⡹⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠓⠒⠠⢤⣴⠁⠒⠀⡟⠈⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⠁⠘⠓⣎⠲⠓⠉
⠀⠀⠀⠀⠀⠉⠛⠀⢡⠤⣴⣁⠀⠀⠀⠲⠰⢄⣀⣀⡀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢛⡁⠀⠉⠑⠢⣴⣖⣖⠚⠉⠁⠈⠉⠉⠘⠉⠉⠐⣒⠦⠤⠤⠤⠤⢤⠤⠤⢤⣤⣤⣤⠤⠤⡄⠤⠠⠤⢀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣖⠀⠀⠀⠀⠀⣯⣹⣿⣤⡤⠰⠖⢰⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣖⠊⠹⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⣷⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⠐⠒⠀⠐⠀⠈⠉⠁⣼⣗⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⣆⠄⢇⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⠄⣠⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣄⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣠⣖⣉⣩⣷⣖⣢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠈⣩⡷⣾⠛⠛⠉⠉⠻⡿⢿⣿⣿⣿⣿⠿⡷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⠛⣿⡏⠀⠘⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⢽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⡿⣿⣶⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠻⣷⣘⠛⠁⣠⣾⣷⣤⡀⠀⠀⢠⢶⣻⣿⣶⢿⣿⣿⣛⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢨⡛⠛⠛⠋⠀⠀⠙⠿⣷⣄⣸⣾⣿⡶⣿⣿⣿⡾⣿⣿⣼⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⢶⣦⣴⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣿⣿⣿⣿⣿⣻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡅⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠋⣉⣉⠉⢻⡟⣿⣽⣿⣿⣿⡇
⠀⠀⠀⣀⣠⡤⠶⠛⢻⡄⠀⠀⠀⠀⣀⠤⢤⣤⣄⡀⠀⠀⠀⠠⣯⣀⣀⣀⣠⣤⠶⠛⠁⠀⠀⠀⠀⠀⠉⠀⢀⣼⣷⣿⣿⣹⣿⠋
⣴⡾⠛⢉⣁⣤⡴⠀⠀⠻⡄⠀⣠⢞⡵⠚⣉⣀⠀⠹⣆⢀⣀⢸⣏⠉⠉⢉⣥⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠞⠙⢿⣿⣻⡿⡿⠁
⠘⣽⣆⠙⢉⣡⣠⠶⠞⠀⠙⢶⣅⣯⣴⣯⣥⣾⣿⣿⣿⣯⣨⡇⠙⠛⠿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠿⠟⠁
⠀⠹⣿⣆⠙⢉⣀⣀⣴⣛⣿⣿⣽⣿⣍⠙⢿⣛⣻⠋⢹⡅⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⠀⠀⠀⣴⠋⠁
⠀⠀⠘⣯⣧⡈⠉⠀⠀⠈⠉⠉⠀⠀⠈⢷⡀⠈⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⣄⡀⢹⠷⠶⠶⠶⠶⢾⡇
⠀⣴⢾⡏⣷⣽⡞⢳⠀⠀⠀⠀⣀⣤⠞⠋⢹⣄⣀⣠⣬⡇⠀⠀⠀⠀⠀⣸⡿⢿⣿⣶⣤⡆⠀⣠⣾⡇
⣠⢇⢿⢰⡘⣌⣇⠸⣦⣠⠴⠛⠉⠀⠀⠀⣿⢉⣉⣀⣀⣿⠀⠀⠀⠀⠀⢈⡴⣿⠀⠟⠁⣠⠞⣽⠉⣇
⠹⣌⠻⡷⡝⠈⠙⠀⠙⠧⣄⣀⡀⠀⠀⠀⢿⠉⠉⠉⠀⢿⠀⠀⠀⠀⣰⠏⢰⠇⢀⣤⢞⣥⡼⠃⠀⣿
⠀⠙⠳⣾⣄⠀⠀⠀⠀⠀⠀⠉⢻⠛⣶⠶⠾⠦⣤⣤⣤⣼⣧⣤⣤⣴⣯⣤⣿⣴⣿⠤⠼⢧⣤⡀⠀⢹⡀
⠀⠀⠀⠀⠉⠛⠲⠶⠤⣤⣀⣀⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣧⣠⣇⣒⣰⠆⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢿⣛⠛⠛⠛⠛⠛⣺⠗⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣿⠋⢉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣸⠇⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠈⠉⠉⠉⠉⠉⠉⣹⠏⠉⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣯⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡟⢸⡦⠶⠶⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠒⠒⠒⠚⡇⠸⠷⣶⣶⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⠛⣛⣿⣿⣿⣥⣤⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⢿⣿⡿⠿⠛⠋⠘⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣷⢠⣤⠄⠀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠀⠀⠀⠀⠀⠈⠁⠚⠘⠁⠀⢀⣉⣶⣙⣃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠆⠀⣠⣶⣀⣤⣤⣾⣶⣠⡁⠀⣘⣙⢽⠟⣻⣿⣦⣤⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢠⣼⣀⠟⢛⠿⣟⠻⠿⢿⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣄⢰⣼⣿⣤⣤⣤⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣶⢶⡀⠀⠂⠀⣠⠟⢉⣾⣾⢡⣟⡙⠛⣻⣿⡟⣿⣿⣿⣿⣽⣿⣿⢿⡯⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢈⣯⣤⣤⠼⠆⠓⠃⣰⡶⠦⠠⢉⣻⣿⣿⣿⣄⠀⠀⠁⠰⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⣠⣴⣿⡾⠟⠋⠙⠛⠛⠺⣟⠃⠈⠈⠒⢊⣭⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⠐⡚⠀⠀⣤⣸⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢛⣻⡈⠛⡻⠄
⠀⠀⠈⢋⣍⣀⠀⠶⠷⠀⣥⡔⠀⠷⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⣿⡿⣽⠶⣷⣆⡈⣷⣆⢀⠀⠀⣰⣴⡟⠀⠀⠀⠀⢤⢤⠀⠀⢠⡄⢈⠄
⠀⠀⠀⠀⠛⠀⢸⠀⢈⣽⣿⢀⣏⢡⣤⣿⣿⣿⣿⠓⠀⢀⣀⣤⡾⠓⠛⠁⠈⠉⠀⣀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠈⠧⢰⣿⠇⢹⡿⠛⢹⠿⡷⠄⣈⣰⣀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⢀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡧⠀⠀⠀⣀⡀⠀⣠⡾⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⣿⠇⣀⣶⡶⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣼⡿⢺⣿⠋
⠀⠀⠀⠀⢀⠄⣫⡵⠟⠁
⠀⠀⠀⠀⠀⣘⡿⠁
⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣾⢸⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⡇⣷⣤⢀
⠀⠀⠀⠀⠀⢀⣴⠏⡇⡟⣸⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⣇⢻⢸⠹⣧⡀
⠀⠀⠀⢠⣤⣾⣿⠀⡇⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢸⠀⣿⣷⣤⡄
⠀⠀⠀⣸⣿⡟⢻⠀⡇⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⢸⠀⣿⢻⣿⡇
⠀⠀⠀⣿⡏⢷⢸⢸⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⡇⡼⢹⣿
⠀⠀⠀⣿⠇⢸⠈⢸⢱⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡌⡇⠃⠇⢸⣿
⠀⠀⢠⣿⠸⠀⡇⢸⢸⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡇⡇⢀⠀⠃⣿⡄
⠀⠀⢸⣿⠀⠀⡇⢸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⢸⠀⠀⣿⡇
⠀⠀⢸⡏⠀⠀⠃⡈⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⢁⠘⠀⠀⢹⡇
⠀⠀⣼⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣧
⠀⠀⣿⡇⠀⠀⠀⠁⠀⠄⣐⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣂⠥⠀⠘⠀⠀⠀⢸⣿
⠀⠀⣿⠃⠀⠀⠀⠂⠤⠤⣀⣉⠓⠪⢵⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣮⠗⠚⣉⣀⠠⠤⠀⠀⠀⠀⠸⣿
⠀⠀⣿⠀⠀⠄⠀⠀⠐⠐⠀⠤⠭⠕⣲⣭⣛⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣛⣭⣖⠫⠭⠤⠀⠒⠂⠀⠀⠠⡀⠀⣿
⠀⢸⣿⠀⠀⢀⡀⠤⠄⣀⣒⠢⠬⣍⡒⠮⢭⣛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣛⡭⠵⢒⣩⠥⠔⣒⣀⠠⠤⢀⡀⠀⠀⣿⡇
⠀⢸⣿⣌⣒⡲⠤⢭⣑⡒⠤⢍⣓⠲⠬⣙⡒⠬⣙⠢⢍⠻⣷⡄⠀⠀⢀⣾⠟⡩⠔⣋⠥⠒⣋⠥⠖⣚⡩⠴⢒⣊⡭⠤⢒⣂⣩⣿⡇
⠀⠈⠉⠛⠻⠿⢿⣶⣦⣬⣉⣒⠂⠍⠁⠂⠈⠁⠀⠁⠀⠁⠀⠙⢆⡰⠋⠀⠈⠀⠈⠀⠈⠉⠐⠊⠩⠐⣒⣉⣭⣴⣶⡿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢷⣶⣤⣄⣀⡀⠀⠀⠀⣀⣴⣾⣷⣦⣀⠀⠀⠀⢀⣀⣠⣤⣶⡾⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢶⣶⡿⠿⠿⠿⠿⢿⣶⠶⠿⠛⠛⠉⠁

⠀⣀⡄⡀⠀⠀⢀⠆⣂⠀⠀⢀⢀⠀⠀⠀⡤⠠⠀⠀⠀⠀⡀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⣀⡀
⠀⠆⣴⠇⠀⠀⠀⠒⠋⠀⠀⢚⡰⡖⠀⠀⠁⠛⠁⠀⠠⠇⣵⠆⠀⠈⠄⠟⠁⠀⢐⠚⣦⠀⠀⠀⡲⢐⡄⠀⠀⣊⣴⠆⠀⠀⠀⢸⣠⡦
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⢀⠤⡄
⠀⠀⠐⣨⡉⠄⠀⠀⠀⢰⠁⠀⠀⠀⡈⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣫⠽⠛⠿⢍⠳⡄⠀⠨⠶⠌⠀⢠⠤⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠘⡏⢠⣔⣵⠞⠠⣊⡀⢱⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⠤⡄⠀⠀⢸⡞⣵⡊⠉⢱⣼⠑⣯⠀⠀⠀⠀⠀⠑⠶⠄
⠀⠤⠂⠄⠀⠀⠀⠀⠀⣱⠬⠍⠀⠂⠀⢺⠓⠉⠀⠀⠀⠀⠀⢰⠀⠀⠀⡏⠀⠀⠀⠣⢄⡀⢴⢾⠏⠄⠀⠠⠸⢶⣱⠄⠀⡐⠒⡄
⠀⠁⠛⠁⠀⠀⠀⠀⠀⠙⢲⠷⣄⣳⣢⠚⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠉⡀⠀⠀⡞⠉⠀⡇⢺⣄⠐⠒⠂⣠⠟⠈⢆⠀⠘⠛⠀⠀⡀
⠀⠀⠀⡰⠦⠀⠀⠀⡴⠿⡍⣻⣛⠻⣿⠀⢥⢌⡯⠑⣦⡀⠀⢸⠀⠸⣿⣿⣿⡇⠀⡇⠀⠀⢱⣄⡬⣼⣶⣎⠤⣤⡤⠊⠀⠀⠀⠀⢡⡌⠅
⠀⠀⠀⠚⠗⠁⠀⠀⣷⡐⢚⠓⢄⢨⡽⠀⠿⠚⠀⣈⡷⠛⠀⢰⠀⠀⠈⠛⠉⠀⠀⡇⠀⢐⠛⠐⢦⣶⠉⡐⡾⢋⠀⡦⠀⠀⢀⠀⠀⠁
⠀⣀⠆⠄⠀⠀⠀⠀⢸⣅⣈⡕⣤⠠⢴⠂⠺⠆⢲⡸⠀⠀⠀⢈⡶⠄⣶⡶⢲⠦⣆⡇⠀⠈⣿⠀⠚⣧⠄⡄⢸⠁⣨⡴⠀⢬⣩⡐
⠀⠐⠸⠋⠀⠀⠀⠀⠘⢿⡴⠙⢧⠘⠘⠂⣀⣨⠓⠁⠀⠀⠀⢸⠁⠈⠀⠀⠉⠈⠁⡇⠀⢰⡣⠄⠞⠋⢂⡘⠉⢇⣤⡃⠀⠀⠉⠁
⠀⠀⠀⡀⠄⡀⠀⠀⠀⡟⢉⠁⢹⣍⠸⣿⣽⠦⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣉⣉⣉⢀⠀⠀⠙⣲⣴⢚⡎⣻⠑⡖⠀⠀⠀⠀⠀⢠⡒⠆
⠀⠀⠀⠂⠶⠂⠀⠀⢠⣏⡜⠓⠝⠻⡀⣾⣠⠇⠀⠀⠀⠀⠀⠀⠀⠐⡇⢠⣠⠀⢠⣄⠀⢰⠀⢸⡶⠴⡶⠠⢼⠃⠀⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⢀⠠⣀⠀⠀⠀⢹⠛⠓⠛⠃⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠉⢠⠀⠉⣲⠇⠀⠈⠀⢐⡏⠀⠀⠀⠀⠀⠀⣐⣉⡂
⠀⠀⠀⠀⠈⠶⠔⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⣀⣠⣴⡟⠀⠀⠀⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⠤
⠀⢀⠂⠂⡀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠑⠀⠀⠀⢂⠀⢀⡀⠀⠀⠀⠀⢰⢿⣿⡯⣻⡻⢷⠀⠀⠀⡇⢸⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠣⠶⠁
⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⢈⠀⠀⢸⠀⢠⠀⠀⠈⡔⣏⣀⠆⠀⠀⠀⠷⠀⠉⠿⠋⣀⢾⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⡄⡀
⠀⠀⠀⡄⣀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡎⢀⢀⡰⠁⠀⠀⣠⠤⠀⠀⢰⡀⠢⣀⠘⢁⢸⠀⣀⡀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠢⡶⠅
⠀⠀⠐⢶⠬⠁⠀⠀⠀⣀⢮⡀⠀⢸⢰⠓⠁⡨⢸⣀⠀⣮⡈⠀⡆⠄⢈⣣⠀⠁⠠⠋⡞⣩⠉⣵⢇⢸⡇⠀⡄⠐⠂⢠⠀⠀⠀⠀⠀⠴⢄
⠀⢀⠀⠀⠀⠀⠀⠀⠚⠐⠀⢣⡥⢸⡜⢺⠀⠀⠖⡹⠎⡁⠉⠀⣡⢾⡙⠃⠀⣠⠐⠰⠓⠤⠀⣉⢾⣸⡇⠀⣆⠉⢀⣽⠀⠀⠀⠀⠈⠞⠂
⢘⣭⣙⠀⠀⠀⠀⠀⢰⠃⠀⢫⠀⡛⣧⠎⠀⢀⠖⠁⠀⢹⢀⠀⠹⡝⡰⢄⠀⢼⡰⡀⠐⠁⣠⢑⠀⣡⡇⠀⡃⠀⢹⠁⠀⠀⠤⠆⠄
⠀⠈⠀⠀⠀⠀⠀⢀⠊⡀⢰⢸⠀⢸⣦⡀⠀⠈⣶⠤⣴⡳⢈⡀⡠⢀⡁⠈⠋⡄⠉⢤⠀⡄⢸⣤⡅⠈⢧⣀⣿⣿⠋⠀⠀⠈⠑⠟⠂
⠀⠰⣒⢆⠀⠀⠀⡼⠀⢀⣆⠈⣖⠯⠩⢲⣿⡰⡷⠒⠃⠀⠘⠇⠣⠭⠟⠲⡐⢅⣈⠏⡓⢻⣭⣼⠋⢀⠄⠈⣻⣿⣶⡀⠀⠀⠀⠀⢐⢚⡠
⠀⠈⠙⠁⠀⠀⠀⠃⠀⠉⠙⠛⠈⠑⠀⠉⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠈⠐⡋⠀⠉⠛⠉⠉⠛⠛⠀⠘⠛⠻⠶⠁⠀⠀⠀⠀⠀⠋⠁
⢠⠂⣃⠀⠀⡠⠄⠀⠠⠌⣬⠄⠀⠀⠄⣂⡀⠀⠈⠤⠾⠃⠀⢀⠔⣂⡀⠀⢚⣡⡵⠀⠀⢠⠔⣀⠀⠀⠀⠤⢂⡀⠀⠠⠇⣵⠆⠀⠀⡤⢄
⠀⠋⠋⠀⠘⠤⠟⠀⠀⠀⠈⠀⠀⠈⠒⠛⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠀⠀⠀⠀⠀⠀⠀⠉⠞⠋⠀⠀⠀⠱⠚⠁⠀⠀⠈⠈⠀⠀⠈⠤⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡔⠛⠋⠛⠒⠒⠒⠳⠤⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⠶⠶⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠉⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⣤⣤⣤⣴⣶⣶⠾⠖⢒⡶⠒⠀⠀⠀⣤⡤⢤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⡀⢀⠈⣀⣀⣀⣀⣀⡘⢀⡀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⠿⠋⠹⠛⠿⠛⠐⠿⠋⣿⠁⠉⠁⠀⠀⠀⠉⠋⠉⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣿⣶⣶⣾⣶⣶⣏⣤⣿⣤⣰⣾⡐⣯⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠙⠛⠛⠿⠿⢗⣿⣿⣿⠿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣠⣠⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠛⠻⠿⠛⠛⠛⠛⠉⢩⣿⡿⠟⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣠⠤⠒⠊⠉⠉⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠒⠒⠶⠦⣤⣤⣤⡴⠋⣉⠠⠂⠀⠀⠀⠀⠀⢀⣸⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠨⠂⠀⠀⠀⠀⠀⣠⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠒⠶⠤⠤⠤⣤⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠴⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠐⠲⠤⢤⣀⠖⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡤⠴⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠒⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠐⠢⢭⣙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣈⠒⠦⣌⡉⠒⠦⣍⡛⠿⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡐⠤⢍⣒⠦⢌⣙⠲⠤⣀⡀⠀⠈⠙⠻⣦⣄⠠⠐⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠒⢬⣝⡲⠬⣉⡒⠤⢌⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⣙⣳⣦⣍⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣛⢻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⠉⠉⠉⠉⠛⠷⢶⣤⣄⣀⠀⠀⢀⣀⣼⠇⢀⣀⣠⣤⣶⠶⠞⠛⠉⠉⠉⠉⠉⠉⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⡶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⢶⡶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡟⢧⡛⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠾⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢀⣀⣤⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠸⠀⠈⢷⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠇⠀⠀⢀⣀⡈⣻⣿⣤⣴⣶⣶⣶⠶⠶⠶⠾⠟⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⣀⣠⣴⠶⠞⠛⠋⢹⣿⣴⠾⠟⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣆
⠀⢀⣴⠿⠛⠉⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⣛⣒⣒⣒⣒⣒⡒⠲⠶⠶⠤⠤⠤⠭⠭⠭⠭⠉⠉⠉⠉⢉⣿⡉⠉
⢠⡿⠁⠀⠀⠤⣄⡀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣂⣀⣀⡀⠀⠀⠀⠀⠈⠭⠭⠭⣭⣭⣭⣭⣅⣒⠒⠀⠀⠀⠀⣾⠀⠉⠓⠦⣄⡀
⣿⠁⠀⠀⠀⠀⠀⠈⠉⠂⠀⠘⣷⡀⠀⠀⠀⠐⠒⠒⠂⠤⠤⠤⠤⠤⠤⠤⢭⣍⣉⣉⣉⣉⣒⡒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠙⠳⣦⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⣐⡒⠲⠶⠶⠶⠶⣤⣤⣤⣤⣄⣀⣀⣀⣒⡒⠂⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢷⣀⣀⣤⣤⡴⠶⣶⠟⠛
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠻⠷⠶⠶⠶⠾⠿⠿⠿⠿⣿⣿⣽⣿⣭⣭⣤⣀⣀⣀⣀⣀⣀⣐⣒⣀⣀⣀⣙⣏⠁⠀⠀⢰⠇
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠶⠶⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣼
⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠠⠤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠙⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠄⠐⠂⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⡀⠤⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⣀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡴⠶⠶⠶⠚⣛⣋⣉⣥⣤⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣌⣛⣬⣑⠒⠀⠀⠀⠀⠒⠚⢉⣉⣉⣩⣭⣤⡴⠶⠶⠚⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡀⠀⡀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⡺⠃⠀⠤⣄⠀⡠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠄⠀⠀⠀⠐⡃⠀⠈⠉⠁⠀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡌⢂⠀⠀⢠⠨⡀⠀⠀⢬⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢿⡗⣕⠀⠀⠳⡁⠂⠤⢄⠀⠃⠀⠂⠀⠀⠀⠢
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢻⣿⣎⢂⠀⠈⠓⠄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⡑⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠉⠀⠙⢿⡟⢶⡄⠀⠈⠀⠀⠀⠀⠈⠀⢐⠀⠀⢀⡀⢀⠀⠂⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣦⣻⣆⠠⠀⠀⠀⢀⡀⠀⡘⠫⠁⠠⠔⠁⠑⠈⠂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠓⢄⡠⠏⠉⠉⠀⠀⠀⠀⠀⡠⢂⠀⠀⠈⠉⠓⡄⠀⠀⠄⢠⡸
⠀⠀⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⡢⢔⢤⠀⠊⠡⠧⠧⣤⣄⠴⠄⠀⠗⠚⠉⠀⠉
⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠴⠶⠒⠚⠀⠉⠀⠂⠑⠄⠀⠀⣀⣀⠤⠀⠀⠀⢀⡀
⠀⠀⣈⠦⠀⠄⠄⢀⠀⢀⣤⡀⠂⠃⠀⠀⠀⠀⠀⢀⡀⠤⠐⠊⠉⠀⣀⠠⠄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡿⣧⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠄⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡠⢼⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢹⡤⡀
⠀⠀⠀⠀⠀⠀⠀⡆⡇⣾⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⢸⡇⡇⡆
⠀⠀⠀⠀⢀⣼⠉⡇⡇⡟⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠈⡇⡇⡏⢹⣄
⠀⠀⣠⣤⣿⣽⢸⢇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⢷⢸⣿⣧⣤⡀
⠀⠀⣿⣿⣿⡟⢸⢸⢡⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢹⢸⠸⣿⣿⣿⡇
⠀⠀⣿⡿⡏⡇⢸⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⢸⠀⡏⣿⣿⡇
⠀⢸⣿⠰⠁⡇⣸⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⠀⡇⠡⢹⣿
⠀⢸⣿⠀⠀⡇⡏⡘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡈⡇⡇⠀⢸⣿
⠀⣸⡇⠀⠀⠀⡇⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⡇⠀⠀⠀⣿⡀
⠀⣿⡇⠀⢀⠀⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⢈⠀⠀⣿⡇
⠀⣿⠇⠀⠈⠀⠃⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⠇⠈⠀⠀⢿⡇
⠀⣿⠀⠀⠀⠀⠀⠄⣐⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢐⡀⠄⠀⠀⠀⠀⢸⡇
⢸⣿⠀⠀⠀⠀⠀⠀⣀⡉⠑⠺⢽⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⢋⣁⣠⡤⠼⠘⡅⠀⢸⣿
⢸⣿⠀⢀⠄⠀⠀⠀⠠⠬⠭⣓⣲⠬⣝⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⣟⡭⢤⣚⡯⠭⠥⠶⠒⠒⠒⢧⠀⠸⣿
⣼⡇⢀⠂⠀⠀⢀⣐⡒⠤⠬⣑⡒⠯⢝⣛⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⢟⣛⠭⠗⣒⡩⠥⠔⣂⣀⠀⠀⠈⢂⠀⣿
⣾⣇⣒⠢⠭⢍⣒⠲⠬⢍⣓⠢⠬⣙⠒⠬⣙⠲⢍⡛⢿⣆⠀⠀⠀⢠⣾⠟⣋⠵⢚⡩⠔⢚⡩⠤⢒⣋⠭⠴⢒⣊⡭⠥⢒⣂⣿
⠙⠛⠿⠿⣷⣶⣤⣭⣙⡒⠢⠭⢑⠂⠌⠑⠂⠉⠂⠈⠂⠙⠳⡀⡰⠛⠁⠊⠀⠊⠁⠒⠉⠅⢒⡩⠥⠒⣚⣩⣥⣴⣶⡿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⢀⣤⣽⣥⣄⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡾⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠷⣶⣤⣴⣿⡿⠿⣿⣿⣷⣤⣴⡶⠿⠛⠛⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠀⠀⡀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣧⣬⣽⣿⣾⣿⣦⣀⣩⣿⣿⣶⣶⣿⣿⣿⡇⠀⠀⠛⠒⠋⠉⠀⠉⠻⡿⠒⠄⠉⠉⠉⠁⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠖⠶⠶⠤⠤⢤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⠍⠙⠛⣛⣛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠉⠁⠒⠒⠒⠒⢶⠄⠀⠀⠈⠉⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⣌⣁⣈⣁⠶⠂⠉⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠤⢀⣀⣀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⣴⡿
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣼⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⡟⣰
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢏⣾⠏⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣰⡟
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⢋⣾⠏⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⣰⡟
⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⢃⣾⠏⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⣰⡟
⠀⣾⣻⠿⣷⣾⣿⣯⣭⣭⣿⣛⣻⣿⠿⠿⠿⣿⡿⣱⣿⢃⣾⠏⠀⠀⠀⠀⠀⢸⢛⡶⢶⣶⡦⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣾⠃⣰⡟
⠀⣿⡿⠈⠀⠐⢚⡉⠉⠉⠙⠛⢛⡻⠿⠿⢿⢷⣶⣿⢃⣾⠏⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⡉⠉⠉⠉⠘⠛⡋⠿⠟⠿⠖⢲⣾⠃⣰⡟
⠀⢿⣷⣤⣤⣤⣤⣀⣀⣉⠠⠀⠀⠀⠀⣉⡀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢸⣜⣦⣤⣄⣠⣀⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⠿⠾⣶⣶⣶⣮⣥⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠓⠒⠿⠯⠴⣶⣔⣖⣂⣡⢼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠸⣖⡄⠀⠀⠀⠀⣠⠽⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢀
⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⣸⠁⠀⣰⡿⣾⣏⡉⠙⠓⠶⠴⢚⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢸⡟⠀⠀⠀⠀⠀⠀⣀⠤⠂⡴⠋⠑⢫⠋⠁⠀⠀⢠⡄⠀⢈⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡾⣤⣄⠀⠘⠀⠀⠀⠀⢠⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠃⡼⠁⠀⢸⡇⠀⠀⠀⠀⠀⣶⣄⠄⣿⣄⠀⢷⢘⡇⠀⠀⠀⠀⠀⣠⠾⡹⠛⡛⠫⣥⡀⠊⠳⡦⠛⢆⢤⣴⢏⠡⠻⣄
⣀⢤⠴⠰⢚⠟⠋⠉⠀⠀⠀⠈⡇⠀⣠⣆⠞⣾⣋⣸⡼⠣⣬⣳⣾⠋⠀⠀⠀⠀⢀⡎⢀⡴⠶⠿⢮⢂⢹⡙⣶⣄⣹⡄⠀⠀⠀⢈⠲⢀⡈⡟⠶
⠀⠀⠠⣐⠈⠌⠀⠀⠀⠀⠀⢾⡁⢨⡿⣷⣾⠟⢹⠇⠀⠀⠋⢹⣿⠀⠀⠀⠀⠀⣸⢇⢸⡄⠀⠀⠸⣻⣿⣀⡟⣸⣿⡇⠀⠀⠀⠀⠂⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣜⢷⡚⠿⡆⠀⠀⠀⠑⡀⣸⡤⠀⠀⠀⠀⠀⢿⢮⣳⡞⣂⠀⠀⢱⠆⠉⢷⡟⢿⣿⡯⣝⣦⡄⠀⠀⢼⢸⠆
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣞⣉⣵⣤⣀⠀⠁⠈⣴⣫⣙⢦⠀⠀⠀⠀⠈⠑⢾⢇⠉⠠⠀⠀⠀⠀⢈⢿⡿⠛⡄⠀⢹⡖⠀⠀⠈⡙
⠲⠤⠀⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠹⢻⣏⡻⡍⢙⣩⣾⠉⣹⠞⢓⡦⣄⠀⠀⠀⠠⣞⢣⢄⡀⠀⣠⠖⠁⢘⣧⣾⣾⣿⣿⢷⣤⠀⠀⠃
⠀⠀⠀⠘⠈⠘⠉⠀⠀⠀⠠⠤⢤⣾⡡⢃⡈⠘⢿⣮⣟⣿⡿⠟⢁⠞⢋⣩⣼⠄⠄⠀⠀⢧⡸⣄⣬⣿⠟⢶⡐⣟⣿⣿⠋⠉⢿⣷⡙⢷⡲⠸⠂
⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⣠⡟⠀⠀⠈⣇⠀⠈⠻⡿⢋⡴⣤⣆⠀⠘⠷⣾⠒⠒⠒⠒⠊⠹⠟⣿⢿⠀⠈⠛⠘⡷⡏⠀⠀⢸⡟⣧⠘⣷
⠰⠖⠒⠚⠓⠚⠉⠙⠉⠈⣹⠟⠀⠀⢠⡞⠹⡄⠀⠀⠀⠸⢆⡞⣻⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⡟⣿⣧⠀⠀⠀⢧⢳⡀⠀⢸⡇⢹⣇⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣀⡀⢀⡞⠀⠀⢻⡀⠀⠀⠀⠀⠉⢹⠀⠀⠀⢻⠀⠀⠀⠋⠀⠀⣼⡟⢿⣿⡧⢄⠀⠈⠳⡇⠀⢸⢸⠈⣿⡌⣿
⠀⠀⠀⠚⠓⠀⠀⠀⢰⣷⣿⣾⣿⡞⠀⠀⠀⠀⢷⠀⠀⠀⣀⣠⡼⠒⠶⠦⣸⠀⢀⣤⢤⣀⣀⡽⢤⣾⣿⣪⠌⢦⣤⠤⠷⡆⢸⢸⡄⢸⡇⢹⠇
⠀⠀⠀⠀⠀⠀⠀⣠⢞⡿⡇⠀⠘⣷⠦⣄⡀⠀⢨⣧⣼⣿⣯⣿⠗⠒⢤⣸⣼⢰⡏⠀⣰⠉⠉⠉⠓⠿⣿⣯⣅⣼⣼⡄⠀⠀⢸⠀⡇⣨⡧⠼⠁
⠉⠉⠉⠉⠉⡉⢻⠇⠀⠉⣹⡟⠉⠹⡇⠀⢉⡽⠋⠉⣿⣷⣧⡏⠀⠀⠸⣏⣹⠼⡇⠀⢿⠀⠀⠸⠉⡢⣀⠉⠙⠛⠿⣝⢶⡒⠃⢀⣟⠟⠺⣷⠄
⠀⠀⠀⠀⠀⠀⣼⠀⠀⡜⡝⡇⠀⠀⡷⠀⣼⠀⠀⠈⡏⠙⠻⡇⠀⠀⠀⢿⣿⡆⠹⡄⠸⡄⠀⠀⠁⢳⡀⠁⠢⢄⡀⢹⣊⠵⠀⢸⡽⢮⣵⣏⠉
⠀⠀⠈⠀⠀⢰⠇⠀⡰⠰⠀⡧⣶⢠⢧⣄⡇⡀⡀⢰⡏⠐⠲⡇⠀⠀⠀⢸⣾⣇⠀⣻⡀⢳⡀⠀⠈⡘⡏⠲⣄⡀⠀⢹⣗⣚⣷⡟⠉⢉⡉⠙⢷
⣀⣀⣀⣀⣀⡟⠀⢀⠃⠃⢸⠳⠖⠁⠁⠈⢧⣻⣿⣶⠳⠶⠤⡇⠀⠀⠀⡄⣟⣹⣾⢡⢷⠀⢣⠀⠀⠀⢹⠳⢦⣽⣶⣾⣵⣶⢿⡗⠂⠒⠲⢴⣾
⠀⠀⠀⠈⡽⠀⠀⠈⡘⠀⡟⠒⠓⠒⠒⠲⠦⠽⠿⠤⢤⣤⣤⣿⠀⠀⠀⠃⢿⠈⠛⠻⠿⣧⠈⣇⠀⠀⠊⣇⠀⠀⠀⠀⠀⠘⠮⡿⣗⣂⣶⡻⠿
⠤⠤⠤⣼⠃⠀⢀⢣⠁⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡉⠉⠉⠉⢻⠀⠘⡆⠀⠀⠸⡦⠤⠤⠤⢤⣤⣈⣀⣀⣉⣁⡀
⠀⠆⢰⠇⠀⠀⠈⠀⠀⣾⡉⠉⠉⠉⠛⠓⠒⠒⠒⢲⡶⠤⠤⡇⠀⠀⠀⠀⠈⣇⣀⣀⣀⡼⠠⢤⡇⡀⣀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⢀⣖⠋⠐⢤⡀⢁⠀⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡇⠀⠀⠀⠀⠀⣯⠈⣩⣯⣶⣿⣿⣴⣦⣤⡉⠒⠽⣶⢦⡤⡦⠤⠤⢤⣤⣀⣀⣀
⣿⣿⣿⣦⣄⠉⢿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠤⠀⠐⠠⡀⢸⣠⠟⢉⡿⠷⣿⡿⠋⢿⢿⡷⢤⡉⢯⠁⠀⠘⠁⠀⠀⠀⠀⡀
⣉⣡⣾⡿⠾⠻⣬⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⣷⣾⣿⣿⣷⢦⣸⣿⣧⣼⡤⠄⢸⣆⣤⡤⣷⣷⣾⠟⠉⠀⠀⠀⠀⠀⠈⠁⠛⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⢷⣦⠀⠀⣰⠟⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⣾⠋⠀⣼⠏⠀⠀⠀⠀⠀⣠⡦⠀⠀⢀⣤⠄⠐⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⠿⠶⢶⡿⢀⣴⠟⣳⠂⢠⣿⠖⣿⠆⣾⡷⢺⡇⢘⣿⠃⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣿⠃⢼⣃⢼⣏⣠⣿⣗⣾⠏⣸⣿⣲⡿⠁⣾⣃⢼⡟
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠘⠧⠀⠀⠻⠦⠈⠁⠀⠉⣼⠇⠈⠀⢠⡟⠈⠁⠀⣀⣈⣡⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠿⠀⠀⠀⠸⠃⠀⠀⠸⠯⠴⠟⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⠀⣠⡄⠀⠠⣄⠀⢀⣄⠀⠀⠀⠀⠀⠸⢿⠆
⠀⠀⠀⠀⢀⣴⠶⣾⠟⠓⢦⠀⠉⣉⡉⠙⠛⠓⠶⢶⣿⣥⣾⣏⣀⣀⣠⡿⠀⣼⠏⠀⠀⠐⠂
⠀⠀⠀⠀⠘⠇⣼⣯⣤⣤⠞⣀⣤⡍⠡⣞⡆⠀⢠⡿⢁⡾⢁⣭⡭⢉⣡⡤⣴⠏⠀⢀⣴⠶⡤⠀⣠⡖⢀⡶
⠀⠀⠀⠀⠀⣸⡏⠈⠀⢈⡇⣸⠏⢀⡴⣫⡟⢀⣾⠁⣸⡷⢫⡿⢡⡟⠁⣰⡏⠀⣠⡿⢁⣾⠃⣰⡟⢠⣿⠃
⠀⠀⠀⠀⠰⢿⣤⣤⠶⠋⠀⠛⠚⠉⠀⠻⠞⣻⡇⠀⠟⠀⠘⠓⠚⠛⢛⡉⠛⠛⠉⠓⠁⠛⠂⠙⠓⣽⠇
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠏⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠓⠲⠶⠶⠶⠦⢤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣾⣏⣀⣠⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢉⣩⣿⠟⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⠿⠛⠋⠁⡀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣯⣽⣿⣭⣯⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠒⢿⠀⠀⠀⢀⣤⡴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢼⠀⢀⣤⠞⠛⢁⣠⣿⡍⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⢀⣿⡟⠛⠻⠿⢶⣋⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⢸⠘⡿⠆⢀⠛⠀⢉⡛⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⠀⢸⣋⣠⠦⣈⠢⢾⣨⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣷⡈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣧⡻⣿⡿⠿⠿⢿⣿⣿⣿⣿⠀⢸⡿⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⡿⠻⡟⠶⠻⣇⡀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣧⠀⢹⠒⢤⣼⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢿⣿⣧⣸⠀⢸⡀⠉⠉⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠻⣿⡿⠒⠚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠘⢿⠉⢳⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢿⡟⠛⢻⣿⣿⠟⠋⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢸⣧⠀⢸⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⠘⣆⠘⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡼⠀⠘⣆⢧⠀⠀⠀⠀⠀⠀⢸⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⢸⡸⡀⠀⠀⠀⠀⠀⠈⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⣧⣷⡀⠀⠀⠀⠀⠀⢣⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣇⠀⠀⠀⠉⠙⠷⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠄⠐⠂⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠤⠐⠀⠉⠀⡠⠒⠀⠁⠀⠂⠄⡀⠉⠐⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢆⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⣀⠀⠠⠘⠂⠀⠀⠀⣀⠁⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠐⠀⠈⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠈⠑⠠⡀⠀⠀⢀⡀⠤⠄⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡠⠂⠁⢀⣈⡢⢄⠠⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠎⠁⠒⢠⡀
⠀⠀⠀⠐⠁⠀⡔⠁⠀⠈⠢⠑⠢⣀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠠⠄⠒⠂⠈⠁⠁⠀⣀⠠⠐⠊⠁⠄
⠀⠀⠀⠐⡀⠀⢄⠀⠀⠀⢀⠇⠀⠀⠑⠠⠰⠤⠤⠴⢒⡀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠊⠉⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⢄⡈⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠠⢤⠀⠤⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄
⠀⠀⠀⠀⠀⠀⣨⡕⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠖⠋
⠀⠀⠀⠀⠀⡘⠀⠀⠀⠉⠘⠙⠒⠦⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⢁⠔⠁⠀⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⠄⣀⠀⠀⠠⠀⠀⠀⠀⣀⠤⠐⠊⠁⠀⡠⠚⠁⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠒⠓⠐⠚⠌⠁⠈⠀⡐⠈⠁⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠒⠂⠀⠤⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢈⠀⠀⢀⠃⠀⠀⠀⠀⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠒⠠⠤⠈⠒⡠⠄⠊⠀⠀⠈⡀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠠⠥⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⢁⠈⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠋⠁⠐⠀⢈⠐⠠⢀⠉⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⠕⠊⠁⠐⠀⣠⠐⠀⠀⠀⠀⠉⠂⢄⡈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⣠⠶⢬⣐⠠⣀⠀⠄⠁⠀⠀⠁⠀⠈⠀⠀⡈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⣀⡐⠯⣁⠀⠀⠈⠑⠦⣕⠠⡐⠀⠀⠀⠀⠀⠀⠂⠀⠑⠢⢀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⣠⡾⠋⠀⢀⠀⠉⠂⠀⠃⠳⠈⠙⠢⣄⠢⢀⠒⠀⠁⠂⠠⠈⠀⡠⢂⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⠁⢀⡴⠋⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⢀⠀⠀⠀⠑⠢⣁⠢⢄⠀⠀⢀⠔⣠⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⠔⢁⡴⠋⠄⠀⡠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠱⣄⠈⠐⣡⣾⢋⢔⣷⡀
⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⡠⢟⡄⠻⠀⢴⡔⠺⣧⡮⠀⠗⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣠⣾⢏⢕⣵⡿⢿⡿⠂
⠀⠀⠀⠀⢠⡊⠵⠃⢠⣊⠀⠈⠉⠠⠦⠰⢁⡠⠂⠀⠀⠄⢀⠀⠚⣤⠀⡃⣠⢀⢄⣴⠞⣡⣾⢟⢕⣵⣿⣧⣽⣿⠁
⠀⠀⠀⠀⠸⣿⠷⣤⡀⠈⡳⣤⡘⠦⢹⢧⡼⣠⣆⠜⠃⡾⣧⠀⣄⠁⠀⠄⣽⣿⠟⣡⠞⢛⢕⣵⣿⠫⣛⣿⡟⠙⣧⡀
⠀⠀⠀⠀⠀⣿⢒⠢⡙⠳⣬⡐⢝⡦⠀⢤⡷⢌⣞⠀⣈⡓⢘⠠⠀⠘⠠⣪⠟⣡⣾⡏⢀⣵⣿⣓⢍⣻⣾⠏⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠻⣶⣍⡢⢕⠠⡙⠳⣬⡒⠤⡀⠞⣃⠚⠚⠉⡢⠀⠀⢠⠞⢁⣾⡿⢋⣴⣿⣟⣾⣵⣿⡿⡫⣪⡾⠋
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣶⣍⠪⢕⠄⡉⠑⠮⣑⠀⠲⢦⡀⠀⢀⡴⢁⡴⠿⢋⣴⠿⢫⢎⢝⣿⡿⠋⣨⣾⠏
⠀⠀⠀⠀⠀⣶⢦⣍⡻⣿⠿⣿⣆⡉⠀⢄⡈⠘⠵⣦⡑⠩⠓⢈⣴⣿⠗⣴⡿⢯⣔⢕⣠⣿⢟⢕⣾⠟⠁
⠀⠀⠀⠀⠀⢸⡗⠪⣙⠻⢿⣷⣽⡻⢶⣤⣌⡐⠥⡢⣙⠳⡶⢟⠝⣡⡾⢫⢘⢕⣹⣿⡿⡡⣴⡿⠃
⠀⠀⠀⠀⠀⠸⣷⣅⡂⢕⠢⢉⠳⢯⣷⣮⢿⣮⣕⡤⡑⢸⠕⣡⡾⢛⠢⠢⢕⣶⠋⠩⣪⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣬⡒⠅⡢⢉⠋⠒⢾⣽⡻⢶⣤⡾⠻⣶⣷⣍⣠⡿⠋⣤⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣌⠁⠁⢀⠈⠚⠿⣷⣦⣴⡻⡿⣿⣿⠟⣱⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⣍⡒⠄⡢⢙⠻⢦⣶⡟⣡⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢯⣖⠬⡑⠃⣾⠉⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣥⣉⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠲⣽⡭⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⢼⡯⢆⡊⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠄⡀⠀⠀⡤⣁⡀⣏⡀⡿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⠀⢠⠀⠠⣇⡒⣏⣰⠧⠀⢙⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠂⠀⢀⡀⠀⠀⠺⠀⠀⠸⠂⢈⣩⣾⣷⣯⠴⣤⣌⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡦⢜⡲⣿⣾⣿⣿⣿⡿⣤⣨⠷⠖⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠠⠠⡇⠀⠐⢸⡀⠴⣽⠟⢹⣿⣯⢿⣿⣯⣿⣆⡞⣂⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠴⡒⠆⠰⣏⣦⣿⣀⠀⢽⣽⣶⢿⣻⢿⡷⣾⡧⠌⠟⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡴⢀⡀⠀⠀⠀⣼⣦⠤⢛⣲⡍⡾⣿⡿⡀⠀⠘⢟⣿⣿⣿⣿⣯⣁⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡇⠀⠀⠀⠇⢠⣤⡤⣷⣺⣿⣿⣿⣿⠏⠀⠀⡀⠂⠈⢿⣿⣿⣿⣿⣛⢂⣌⠀⠕⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠢⡈⠀⠀⡈⢀⡴⡶⣆⠀⠘⠁⠈⠛⠿⠛⠋⠁⠀⠀⡐⠁⡀⢘⠈⣿⣿⣿⣿⡿⣟⠋⢴⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⡻⣾⡑⣷⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠄⠁⣿⣿⣿⣿⣿⢻⢃
⠀⠀⠀⠀⠀⠀⢀⣀⣐⠒⣾⣿⡿⣼⣛⢧⡏⠀⠀⠀⠄⢀⢄⡀⠀⠄⠰⠁⠂⠀⠀⢽⡟⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣽⣤⣷⣿⣷⣾⢽⣿⡿⠀⠀⠀⠀⢉⠀⠀⡀⠄⠀⠀⠈⠀⣀⠀⢺⡯⣾⢿⣿⠿⢿⣍⡷
⠀⠀⠀⠀⠀⢀⠀⣾⣿⣿⣿⣬⣿⣳⠟⠁⢀⡴⣦⡈⣤⢀⠀⠀⡀⠰⠀⡀⠄⢵⣀⡹⡷⣿⣾⡿⢶⣄⡽⣿
⠀⠀⠀⠀⠀⠈⣠⣽⣿⣿⣿⣿⠿⠁⠀⢰⣿⣿⣷⣧⠈⠁⢆⡀⠀⠀⠈⢀⠀⠙⣽⡟⢠⣿⣿⣷⣿⣯⣷⣿⠠
⠀⠀⠀⠀⢀⠰⠏⢿⣹⣿⣬⣧⣶⣶⣶⣾⣿⣿⣷⣿⢷⣶⡀⠘⠉⢀⠀⣆⣹⣿⣿⣷⣿⣿⣿⡟⢿⡏⣽⡽⠯⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠛⢛⢬⢛⣈⡿⣽⢿⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠟⠛⢯⣄⣷⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠼⠛⢻⡷⢍⢻⣿⡃⢀⡉⠉⠀⠀⠀⠀⠀⢀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⣏⡥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⢶⣖⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠶⠒⠓⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠈⠁⠈⠀⠀⠀⠈⠙⠢⣄
⠀⠀⠀⠀⠀⢀⡴⢋⢭⠋⠉⠉⢲⠊⠁⠀⠙⠖⠩⡳⣄⠀⠀⠀⠀⠀⠀⡼⠁⠁⠀⡁⠀⡄⠀⠀⠀⠀⠈⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⡞⢠⠁⠈⠀⠀⣏⡀⢚⣙⡆⠀⢸⠀⠰⣞⢦⠀⠀⠀⠀⡼⠁⠀⠄⡔⠁⠀⢓⢀⣄⢘⣦⡠⡐⢄⠠⠀⠈⢧
⠀⠀⠀⠀⡔⡛⠹⠀⠀⢂⠀⡇⠀⠀⠀⠇⢀⡘⠀⠀⠂⢣⢳⠀⠀⢸⠁⠀⠌⡎⢠⠔⠙⢌⢳⠿⢷⣧⣉⠳⢤⡑⠀⠀⠈
⠀⠀⠀⢸⠃⡇⠀⠡⡴⢺⠿⠃⠀⠀⠀⠛⢽⠁⢳⠊⠀⠸⣸⠀⠀⠸⣾⠀⣿⡳⠏⣤⠘⠓⠈⠁⠀⠈⢉⠱⣄⢹⢀⢦⠱
⠀⠀⠀⢸⡆⢱⡀⢠⡝⠃⠀⣄⠀⠀⠀⣴⠀⠀⣿⢃⡤⣧⣇⣠⠀⠀⣇⠀⢸⢿⠘⠁⠐⠟⠀⠀⠀⠀⠿⠀⠈⢸⣿⠂⢠
⢀⡠⠾⠭⣷⣔⡟⡾⠁⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⢰⢄⡟⡛⠊⠑⢦⢹⣄⠈⠲⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣸⢼⡴⠋
⡞⠐⡕⢀⡠⢤⣵⣼⡄⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡼⠯⡷⠌⢆⢐⢸⡆⡙⠷⣤⡑⢄⡀⠀⠠⠄⠠⠐⠀⢀⡴⠣⡏
⢧⡀⣇⡎⠀⠈⠳⠊⣝⣦⣄⠀⠈⠠⠉⠀⣀⣤⣮⢈⠋⠀⠄⠘⢄⣦⣭⠟⠀⠀⠵⣴⣉⣦⣄⠀⢀⡠⣴⣭⣴⠞⠁
⢾⣧⠏⠉⣀⢈⢡⣈⠞⠀⢸⣏⠐⠀⠒⣹⠟⠀⢯⠷⠬⠥⠵⠦⠴⠟⠋⠀⣠⡠⣴⣾⣯⣻⢳⠉⠁⡰⢩⡡⣿⣶⠢⢤⡀
⠘⢷⡏⠉⠉⢉⡭⠗⠒⠋⠉⡟⠛⠛⠛⠛⠉⠒⠒⠒⢤⡀⠀⠀⠀⠀⠀⡼⠛⠚⠋⠉⠙⠏⠀⢣⠜⡁⠉⠛⠁⠘⠉⠋⢻
⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠡⣀⠀⢀⠐⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⢠⡇⠀⢠⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⠀⠀⡄⠀⠈
⠀⠀⠀⠀⢸⠆⠀⠀⢰⠤⠄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠘⡆⢠⢠⢰⡀⢸⢽⢰⡗⣲⣲⣴⡀
⠀⠀⠀⠀⢸⡆⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⠇⠀⠀⠀⢸⠃⠀⠀⣿⠛⠛⠛⠛⠘⢸⢸⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠘⡇⠀⠀⠈⡗⠂⠀⠀⠀⠀⠐⠒⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⠓⠖⠒⡿⠀⠀⠀⠀⢸⣿⢸⠀⠀⠀⡸⡗⡒⡊
⠀⠀⠀⠀⠀⣧⣤⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣠⣼⠀⠀⠀⠀⢸⠤⠀⠀⣿⠀⠈⠉⠁⠀⠀⠀⠉⠁⠀⢸⡇⠄⣄
⠀⠀⠀⠀⠀⡏⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⣹⠀⠀⠀⠀⢸⠉⠛⠛⣻⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡋⠉⠉
⠀⠀⠀⠀⠀⢳⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⡸⠀⠂⠀⡏⠀⠀⠀⠀⢸⠀⠀⠀⣾⠀⠀⠀⠀⢸⣺⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠘⡆⠀⠀⠀⠀⠀⢹⠃⠀⠀⢰⠃⠀⠀⠀⠀⠸⡀⠀⠀⢹⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠹⣄⠀⠀⠀⣠⠏⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⠀⠀⣴⡶⠀⠀⠀⠀⠈⡇

⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠎⠀⠴⣾⣿⣿⣇⠀⠑⠈⠛⠒⠀⠀⠐⠀⠀⠀⠀⠞⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠤⠔⠚⣱⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⢧⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠞⣿⠏⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰
⠀⢀⡠⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠄⠀⠀⠉⠉⠈⠁⠀⠀⠤⢀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⠀⣾⡿
⣠⠋⠀⠀⠀⠀⠀⠓⢀⠀⠀⠀⠀⠛⠢⢀⠀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠁⠒⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣡⣾⣿⠗
⡄⣠⡤⠤⡀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠀⠉⠉⠉⠉⠀⠋⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠁⡄⢀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠠⠀⣀⣢⣤⣤⣶⣶⣦⣀⣶⣿⣿⣿⡥⠐
⠀⠀⠀⠀⢈⠀⠀⠀⢀⠀⢀⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠀⠓⢦⡄⠊⠋⠘⠁⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⢿⢿⣿⣿⣿⣯⣤⡤
⣄⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⣤⢦⡀⠀⠀⠀⠀⢀⡀⠀⢀⣩⣿⣿⣏⠻⢿⣿⣿
⠉⠁⢄⠀⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡄⠠⠒⠉⠀⠀⠀⠀⣾⡿⠉⠀⠸
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠃
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠑⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⣷⣆⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠠⠓⣄⠀⠀⠀⠀⠀⢱⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⢀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⢀
⠀⠀⠀⠀⠀⢿⠙⠒⠒⠒⠀⠀⠳⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡀⠀⣸⡇⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠁⠈⠙⠷⠀⠄⠀⠀⠀⠐⠲⠤⢬⣿⣿⣿⡇⢀⣿⣇⣠⣤⠤⡀⠊⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠖⠒⠂⠀⣠⣤⣿⣿⣿⣷⣸⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⣠⠃⠀⠀⠺⠆
⠀⠰⠀⢠⡀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⣶⡿⠿⣿⡆⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣰⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⡀
⠀⠐⠠⠼⢷⣠⠀⠀⢀⠠⠀⠘⠁⠀⠀⠀⡀⠀⠀⠀⠀⢉⡉⣤⠶⠟⣡⠂⠀⠈⠻⡄⠀⠀⠀⠀⠉⠉⠓⠀⠀⠊⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚
⠀⠀⠀⠀⠈⠋⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⠩⠄⡔⠁⠀⠘⠁⠀⠁⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⠀⠀⠀⢀⣠⣰⣶⣤⣄⣇⠀⠀⠀⠀⠀⠄
⢀⡴⠀⠀⠀⠀⠀⠀⠀⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠀⠀⠀⠀⠈⠻⠙⠻⠰⠦⢤⡄⠀⠀⠀⠀⠈
⠉⠀⠀⠀⠀⢀⠀⠀⢀⠄⠀⠈⠓⠊⠧⣀⠠⠤⠴⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣈⠀⠀⣤⠀⡀⠀⠀⣠⣮
⠀⠀⠀⠀⢶⠠⠤⡀⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⢿⣆⢀⣻⣦⣵⣶⣿⠟⠉
⣀⡀⠀⠀⠤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠀⠀⠀⠀⠹⣦⣷⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⠛⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⠀⡎⠀⠀⠀⢠⣴⣿⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢟⠿⣠⢀⠀⠁⠈⠁
⠀⠀⢀⣠⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠊⠀⠀⠐⠦⢄⡀⠀⠀⠀⢽⣿⣿⣦⣄⡇⠀⣰⣿⣿⡿⢁⠤⠀⠂⠀⠀⠀⠐⠂⠀⠞⠀⠈⠀⠘⠳⢌⣀⠒⠂
⠙⠀⢄⠀⠀⠀⡀⠀⠀⠐⠄⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⣀⠀⠙⠻⣿⡏⠁⠀⣿⣿⣫⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣿⣿⣿⣶⡄⢤⠚⠒⣨⣿⣯⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠘⠀⠀⠀⠀⠒⠛⠉⠉⠀⠐⠚⠛⠙⠉⣻⡿⢿⠇⣀⣶⠚⣵⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⣀⠀⢀⠀⠀⢀⡠⠒⠊⠉⠀⠀⠀⠀⠀⠉⠐⠢⣀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢰⡀⠀⠀⠀⠀⡇⠐⢘⡀⢂⠇⢠⠋⠀⡄⢠⢠⣤⠄⡀⠀⢀⠀⠀⠀⠀⠑⠄⠀⠢⠅
⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⡦⣸⣼⠛⢁⡄⠀⠀⠀⠅⠀⠀⠀⢩⠀⠸⡀⠘⠛⠏⠾⠭⢸⣥⣠⣏⡀⣴⠚⡇⡴⠀⢀
⠀⠀⠀⠀⠂⠀⢠⢰⣼⡞⠖⠃⠀⡔⠁⠀⠀⠀⠐⠦⠠⡢⠐⠁⠀⠘⢌⠢⢄⡀⠀⠀⠀⠀⠀⠁⠁⠉⠉⠑⠀⣀⠀⠑⡀
⠀⠀⠀⠁⠀⠀⠈⠛⠈⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠒⠬⠉⣐⠒⠀⠤⠤⠤⠄⠐⡂⠨⠠⡑⢄⠘⡀
⠀⠀⠀⠀⡀⢁⠀⠀⠀⡠⢊⠔⠁⠀⠀⠀⠂⠀⠒⠁⠀⠀⠁⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠢⢂
⠀⠀⠀⠀⠐⠀⡀⠀⡀⠐⠁⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠈⠂⢄⠀⠀⠐⠀⠀⠉⠀⡀⢀⢀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠆⠀⠀⠁⠀⠀⠀⠄⠃⠀⢠⡖⡆⠲⣌⣳⡐⡯⡅⢸⠀⠀⡐⠀⠀⠀⠀⠱⠘⡆⣯⠈⠋⠀⡀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠤⡀⠀⠘⠢⠇⠘⠘⠃⠁⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠁⠀⢀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠈⡆⠀⢀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠁⡀⠤⠀⠀⠀⠀⠀⠀⠀⡉⢀⡀⡀⠀⠀⠀⠐⠀⠆
⠀⠀⢈⠀⠢⡀⠀⠄⠀⠀⠀⠐⠀⠀⠈⠁⠉⠂⠂⠐⠀⠂⠀⠀⠁⠀⠀⠀⠘⠈⠀⠀⠐⠋⠀⠀⠐⠀⡨⢁⠇⠖⡇⠀⠈⠈
⠀⠀⠤⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠒⠒⠐⢄⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠜
⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠠⠀⢰⢤⡦⠶⡶⠲⠀⠴⠴⠦⡆⠠⠆⠖⠴⠀⠀⠀⢀⠀⠀⠐⠡⠢
⠀⠀⠀⠀⠀⠠⠀⠀⠁⠂⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡐⢄⠀⠀⣀
⠀⠀⠀⠠⢖⠔⠊⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡎⠀⢀⡖⡶⠛⢶⠂⠀⠠⡁⠀⠀⠀⢰⠰⢥⠪⠕⠯⢲⠕⠀⠂⠀⠀⠀⠀⠔⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠
⠀⠀⠀⢠⠁⠀⢀⣄⡀⡀⣁⣠⠀⠀⠈⡆⠀⠀⡄⠀⠀⡆⢶⢡⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠂⠀⣀⠀⠀⠁
⠀⠀⠀⢂⠀⠀⠛⠘⠙⠛⠙⠓⠀⠀⢀⠃⠀⠀⠁⠈⠉⠋⠈⠈⠉⢀⢈⠀⡀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢠
⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⢀⣀⠤⠒⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⢀⡠⠌⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠈
⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠤⠤⠤⠄

⠲⣌⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣃⠀⠀⠈⠉⠉⠉⣏⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⣀⣀⠀⠀⢠⡀⠀⠈⠁⢰⠀⠀⠀⠠⡈⠁
⠀⣿⡸⠀⢀⣠⣄⠀⠀⠀⠀⠀⠘⠻⠛⠛⠛⠛⠛⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⢥⣤⣤⣤⣤⣤⣤
⣐⣻⠠⠀⡈⠈⠀⢡⡀⣠⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⠈⠙⠁⠀⣀
⠈⠉⠀⠀⠀⠠⢀⣾⡆⠈⠙⣦⡀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠠⣾⡿⠟⠛⠿⣿⡆⠀⠀⠂⠀⠀⠀⠁⢀⣀⠤⠴⠚⠓⠀⠠⠈⡏⠈
⠐⠐⠆⠀⠠⠶⠿⠟⠀⠀⠈⠛⠿⢦⡀⠀⠀⠀⢀⠀⠤⠀⠠⠀⣺⠇⠀⠀⠀⣿⠃⣀⠀⠈⠈⠀⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠐⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠆⠀⠀⣤⣠⡀⠉⠉⠛⠶⣄⣠⣤⣤⣤⣤⣤⣀⠀⠉⠙⠒⠶⠤⠴⠚⠋⠉⠉⠁⠀⠀⠀⠀⢢⡁
⠛⠛⠛⢀⡀⠀⡀⢤⠀⠀⠀⠀⠠⢺⠟⠁⠙⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⣠⣆⣤⣤⣤⣠⣤⣴⠖⠀⠀⢰⣴⠶⠶
⣤⣤⠀⠀⠀⠏⠁⠀⠉⠀⠀⠀⡦⡍⠈⠀⠁⢸⢼⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠉⠟⠁⠀⠈⢻⠟⠃⠂⡄⠰⠈⠈⢠⣤
⠝⠉⠉⠋⠀⠀⠄⠠⠀⠚⠀⢀⡯⠦⡄⠀⠀⢾⡡⠕⠀⠀⠀⡴⠦⠀⠀⠠⠐⠂⠄⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠉⠁⠉
⠀⠀⠀⠐⣠⠂⠀⠀⠠⠀⣄⠋⠀⠀⠀⠀⠀⠀⠀⣠⢀⡴⠋⠀⠀⠑⢆⠁⠀⠀⠀⠀⠀⡈⠙⠛⠒⠤⡤⠤⠒⠒⠒⠀⢀⠀⠀⠈
⠈⠀⠀⢠⡾⠛⠿⠷⠶⣦⣷⡄⠀⠀⠁⠀⢀⠐⠋⠘⠋⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐
⠶⠶⠀⠉⢤⣤⣄⣀⣀⣀⠰⠿⣤⣀⠀⣀⣬⠤⠴⠒⠂⠀⠀⠂⠀⠂⣤⣤⠀⠒⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣄⣂⢀⣀⣤
⠀⠀⠀⠀⠉⠉⠉⠈⠋⣙⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡤⠠⠤⣰⣶⣶⣶⣦⡄⠀⠀⠉⠉⠁
⠀⠀⢀⠀⠐⢋⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠴⡤⠀⠐⠀⣀⣀⣀⣠⣤⣤⣴⣄⠀⠀⠀⠨⠇⠉⠀⠁⣹⠛⢿⡅⠓⡍⠀⣀⣀
⠀⠀⠉⠉⠛⠒⠶⠤⡴⠖⠛⠁⠀⠀⢐⡀⢀⠀⠀⠀⠚⡿⠉⠉⠉⠀⠀⢀⣙⠃⠀⠀⠘⠀⠂⠀⠂⠂⠀⠠⠀⡼⠏⠉⠄⠨⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠼⠖⠺⠿⠿⠛⠻⠟⠀⠒⠓⠶⠦⠤⣄⣀⣠⠤⠶⠶⠂⠠
⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⣴⣄⡠⠖⠒⠒⠀⢀⡀⠀⠈⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠠⠀⠀⢀⡴⡶
⠉⠀⣀⣠⠤⠶⠚⢠⠀⢀⠀⠄⢀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠈⠁⠂⠀⠂⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠬⢤⣀⡀⠀⠘⠑⠁
⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡞⠛⢿⣿⣷⡀⠀⠀⠀⢲⡄⠀⠘⠉⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠉⠉⠊⠀⠈
⣠⡤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡀⢀⣸⣿⡏⠀⠀⠄⢻⣿⡟⠀⠀⠤⠭⣴⣁⡐⠀⠐⣀⣠⠄⠀⡘⠀⠀⠂⠀⠀⠀⠀⠀⣀⢀⣀
⠁⣤⠀⠀⠀⡠⢀⢀⡀⡀⠀⠐⠛⠦⣄⣡⠹⢇⡀⡀⢀⡟⠛⠀⠀⡀⠀⠀⠀⠀⠉⠁⠋⠉⠀⠀⠠⡇⠤⠤⡀⠀⠀⣀⣀⠘⠛⠉⠉
⠾⠷⢀⠀⡁⢠⡼⠃⠛⠻⡾⠄⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠀⠈⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⣤⠡⠌⢅⠑⡤⠼⠷
⠀⠀⠀⠀⠀⠘⠅⠄⠠⠀⡞⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⢱⠀⠉⠀⠀⡦⠄⠀⠄⠰
⠉⠉⠉⠓⠢⢤⠤⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⣀⣠⠴⠖⠒⠀⠈⠀⠀⠀⠛⠛⠛⠛⠾⠶⡤⡤⠴⠒⠒⠒
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣄⣀⣀⡒⠳⠤⣤⣤⠬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠉⠉⠉⠉⠛⠒⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⣠⠤⠤⠶⠶⠦⠤⠤⢤⣀⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠋⠉⠉⠉⠉⠙⠲⣴⠋⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⣄⡈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⢀⡠⠶⠒⠒⠒⠆⠀⠹⣄⠀⠀⠀⢀⠔⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠤⠤⠤⢤⣀⡀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠙⠓⠀⠀⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⢤⣤⣀⣀⣈⠑⢦⡀
⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⡠⠖⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠈⠓⢤⡀
⠀⠀⠀⢺⠣⠤⣀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⣀⠀⠀⠀⠀⢀⡤⠴⠖⠒⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⢀⡠⠖⢋⠉⠄⠒⠂⠀⠀⠊⠉⠉⠓⠒⡿
⠀⣠⠴⢪⡇⠀⠂⠍⡒⢤⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡴⠚⠁⠀⠀⣀⡤⠤⠖⠒⠒⠒⠚⠷⢄⡀⢀⡴⣫⣶⠀⣠⠴⠚⢉⡉⠉⠉⠉⠙⠳⠶⠤⣗⢄
⡾⣄⠀⠀⠈⠓⠮⣑⠤⡑⠨⢓⢤⡀⠀⠀⠀⠀⢀⠔⠋⠀⠀⣀⠔⠋⠁⡠⠄⠂⢁⠐⠋⣉⢿⢲⣷⠿⡶⢾⡡⠪⠖⠊⠉⠉⠀⣀⣀⣀⣀⣀⣀⣀⣈⣱⡗
⠉⠺⢝⡦⣄⠀⠀⠈⠓⢬⡑⠤⡁⠪⢳⢄⡀⠀⠁⠀⠀⢠⠞⠁⢀⠔⢉⠤⠒⢉⣠⠤⢖⣚⣽⣿⣄⣀⣠⢼⡷⠿⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠋⠉⠉⠉
⠀⠀⠀⠉⠲⢽⡲⢄⡀⠀⠈⠳⢌⡑⠄⡁⠻⣦⣀⠀⣰⠃⡠⠊⡠⣊⡥⠖⠋⣁⠤⣺⠽⠊⠁⠈⠙⠓⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠓⠬⣓⢤⡀⠀⠙⠢⣌⠐⠠⡙⠛⡇⠈⣀⠴⠊⢁⡠⢔⡯⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⣕⠦⣀⠀⠙⠢⣄⣸⣡⢞⣡⢴⣺⠵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢽⡢⣄⣀⠽⣛⠭⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣙⣉⣻⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠛⠛⠋⠛⠛⠉

⠀⡠⠴⡤⡄⠀⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠀⠒⢀⠀⠀⠀⠀⠲⣄⠀⠀⣴⠖⠀⠀⠀⠀⠐⠂
⠀⣇⣐⠂⠬⠀⠸⣷⣿⡿⠇⠀⠀⠀⠀⠀⣠⣦⣤⣤⣼⣦⣤⣤⣶⣤⣾⣷⣶⣾⣶⣤⢵⡤⠀⠟⠀⠘⠁⢀⣴⠇⠀⠊⠀⠁⢈
⠀⠈⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣆⡀⠀⣠⣶⣄⣀⣀⣴⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣤⣼⠋⣁⡍⣁⢽⣁⣾⣡⠗⢿⠇⠷⢸⠗⣽⣾⣀⣽⠀⡇⢸⡟⢸⣧⣿⣩⢷⣿⡹
⠀⠀⠀⠉⠉⠀⠀⠀⠐⠂⠀⠀⠠⣤⣀⣴⠃⣉⠀⠈⠀⠡⠄⠹⣿⣄⠀⢉⣀⣉⣀⣁⣠⣄⣀⣌⣁⣤⣬⡁⡀⣀⡀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢂⠀⣼⠀⢉⡟⣈⠿⢆⣚⠃⣷⣼⣁⠏⣹⠏⣯⢽⠁⣬⣹⠌⠛⢸⣦⣟⡙⢯⡿⣍⠃
⠀⠀⠀⠀⠀⣠⠛⢁⣠⣼⣧⠐⢄⠀⠀⡇⠈⠀⣷⣥⣆⡈⣉⣀⣴⣄⠈⠛⠉⣛⣹⣶⣿⠉⠋⠛⢀⣤⠀⠄⠀⠀⠰⠉
⠀⠀⠀⠀⠀⠃⣽⣿⡏⣹⣶⣿⡀⠀⠀⢀⣿⣶⣿⡌⣯⣛⢫⡟⢘⣿⠻⡆⣬⡜⡛⢘⣟⢹⡟⢽⣧⣿⡄
⠀⠀⠀⠀⠀⡇⢿⣀⠀⠈⢉⣿⣴⠃⠀⠘⠫⣿⠋⣿⢳⡿⠗⠋⢈⣿⡳⡌⠷⢾⡟⠎⠉⠈⠑⠊⠑⠉
⠀⠀⢰⠶⣦⣧⡌⠉⠀⠈⢋⡿⠃⠀⠀⡼⢳⣿⠀⣿⠈⠃⠈⣧⠛⢾⣷⡀⣠⢾⡇⢀⣤⠖⢿⣿⠳⢆
⠀⠀⠈⡷⠠⣾⣟⣷⢤⡴⢞⡟⠀⢻⠀⣷⣾⣿⠀⠙⣧⣀⠰⡆⠀⠤⢹⠛⡿⠈⣿⠀⠀⠀⠀⠀⢀⠈⢠⡀
⠀⣠⣤⣀⣿⢿⣿⡅⢀⣿⣎⣄⠀⡌⢰⠇⣿⠏⠀⠀⠻⠛⢶⣍⠉⢀⡀⢰⣁⢤⡿⢾⠇⠀⠻⠟⣿⠒⢱⡆
⠀⠛⠈⣿⣏⣷⣿⣷⣾⢛⣼⠠⠛⡅⠸⢾⡿⠀⠐⡾⠃⠀⠀⣀⣀⣈⣁⠌⠉⠿⠱⣾⣄⡀⣀⣄⡻⠤⠂
⢀⣰⣦⣿⢻⣏⣹⡌⣭⣿⠃⠿⠢⠂⠷⢸⣷⠀⠀⡇⠀⠀⠠⠁⠀⠀⠀⠀⠀⡀⣰⣉⣿⣋⣤⡿⠗
⠿⣿⣿⠏⠀⠙⣿⣿⣽⡇⠰⠂⢾⠀⠀⢠⠈⢢⣤⢛⡀⠀⡄⠀⠚⠓⡀⠀⣹⣷⣿⣟⡝⠉⣼⠃
⢀⡟⠁⣸⣿⣿⣿⣭⣿⡇⠀⡄⠸⠀⠀⠘⢀⡾⠀⠌⠁⢐⠀⠀⠀⢸⡅⠀⠀⢹⣦⣄⢵⠼⡟⢀
⠸⣇⣴⣿⣿⣿⣿⣿⣿⠄⠀⣧⠀⠀⠀⠀⡞⠛⠁⢶⡶⣿⠀⠀⣴⣶⡤⠀⢓⢸⠿⡟⣳⡦⣤⣾⡆
⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀⠄⠈⡆⠀⠀⠀⠁⠐⠀⠀⢀⡏⠀⢰⣿⣹⡇⠀⠀⣀⠛⢣⡤⠤⠾⢶⡍⠀⠀⡇
⢀⣾⣿⡿⠁⣿⣿⣿⠇⠰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡾⠀⠀⠀⢿⠀⠛⢰⠀⢹⠋⠛⡿⠖⠳⡾⠁⠀⠀⠃
⣿⣿⡟⠀⠀⣿⣿⡏⠀⠀⠀⢣⠀⠀⣠⠜⠁⠘⠛⠸⢇⠀⠀⢀⠀⡄⠀⡀⠂⢸⠇⠀⠋⠀⢰⠃
⣿⣿⡀⠀⣸⣿⣿⠁⠀⠀⠀⠈⠀⠀⣿⣆⠘⣃⠤⠀⢻⡄⠀⠈⣤⠀⠀⡇⠀⣿⠀⠀⠀⠀⡞
⢻⡿⣷⠀⠿⣿⡟⠀⠀⠀⢠⠀⠀⢸⣫⡍⠻⠋⠰⢶⡿⠁⠀⠀⠈⠀⠀⠁⠀⣿⠀⠈⠀⢸⠁
⠀⢻⡄⢿⡇⣽⠀⠀⠀⠀⠀⠀⢠⠈⠉⣷⣤⣤⡤⠂⠀⠀⠀⠀⠀⠀⢠⠀⣴⡏⠀⠀⠀⡏⠀⠀⠀⡄
⠀⠀⠻⣏⣾⡏⠀⠀⠀⠀⡄⠀⠈⠛⣨⣿⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⢹⡇⠀⠀⠀⠁⠀⠀⠀⠇
⠀⠀⢀⣿⣿⢧⣀⠀⠀⠀⠁⠀⡄⠘⠧⠼⠏⣤⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡄⠃⢀⡄⢀⡇⣀⠰⠗
⠀⠀⣼⡟⣿⣦⣿⣷⡄⠀⢠⠖⠁⣄⣀⡄⠀⠀⠀⠀⠀⠀⣀⣼⣇⣀⠃⠘⣧⠀⣸⠀⣈⡿⢉⣾
⠒⠂⣿⣧⣿⠼⣷⣿⡄⠻⣷⣦⣸⣼⣿⢾⣿⠿⠿⢿⣆⣈⣁⣹⣂⡍⠀⣆⠻⠀⣿⠸⣿⣶⠿⠋
⠀⠀⠀⠙⠛⠀⠸⠟⣁⢀⡁⢚⣽⡿⣿⠋⠻⠷⠶⡻⣇⣨⣉⠉⠉⠁⣀⣹⡆⢀⠏⠀⡻⠁
⠀⠀⠀⠀⡀⠀⠀⢠⣿⣿⣟⣏⣿⢹⡇⠀⠆⠀⠀⠋⢸⣄⡀⣰⢿⣿⣏⣉⣉⡽⢿⠒⢷⣤⣠⣄
⠀⠀⣴⣆⣀⣀⡀⠀⠀⠉⠉⣿⡏⣼⠀⠰⢶⠀⠀⣿⡦⠌⡻⢦⣆⠁⠀⠀⠀⠀⢼⣦⣿
⠀⠈⣿⣾⣭⣭⣡⠀⠀⠀⢸⣯⡀⣿⠀⠀⣋⡀⢲⣿⠃⠀⣀⡀⠉⠁⠀⠀⠀⠀⠈⠧⠴
⠀⠀⠀⡉⠁⠉⣡⣴⣶⡀⢘⣛⢓⣈⣉⣒⣍⠉⠉⠛⠀⠀⣥⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦
⠀⠀⠀⠁⠀⠀⠻⣿⠿⢷⣿⣟⡛⣙⣹⣿⢣⡀⠀⢠⣎⡁⠤⠶⣉⠉⠱⡉⠀⠀⠠⢄⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠈⠉⠛⠉⠁⠀⠿⠿⠛⠿⠋⠀⠀⠀⡀⢷⠀⠡⣄⢰⣀⣾⣀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⣶⡄⠒⢺⡜⠋⠹⠟⠙⠋⠉⠉⠉⠛⠛⠛⠛⠛⠛⠀⠀⠀⠻⣿⡿
⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣾⡿⢿⣿⣿⣿⡿⠏⣠⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣾⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠒⠀⠉⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠁⠐⠂⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⢦⡀
⠀⠀⠀⠀⠀⢠⡑⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢧
⠀⠀⠀⠀⠀⡦⠡⠁⠀⠀⠀⠀⢀⡀⠤⠀⠒⠀⠀⠀⠀⠀⠀⠐⠂⠄⡀⠀⠀⢰⠀⠀⠀⢀⠤⠒⢀⠈⠭⠥⠤⠤⠭⠥⠄⢀⣀⠂⠠⠄⡀⠀⠈⠌⣧
⠀⠀⠀⠀⣜⢠⢃⠀⠄⣒⠈⠠⠄⠒⠀⠈⠉⠀⠀⠀⠀⠈⠉⠀⠒⠤⠀⡑⢄⢸⠀⡠⡊⠔⠊⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠤⠤⠀⠉⢐⣂⠑⠺⠞⡄
⠀⠀⠀⢸⡃⣉⣀⡀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⣀⣤⣄⠀⢺⠎⢀⣄⣀⣂⣈⡉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠒⠂⠀⠀⠨⠄⠀⣹⡄
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉






⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠀⠐⠂⠀⠀⠂⠂⠂⠀⠒⠂⠀⠂⠀⠐⠀⠂⠀⠀⠀⠂⠐⠈⠃⠀⠐⠀⠐⠂⠐⠐⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠤⠀⣠⢄⠠⠀⡄⢠⠀⠀⡄⡤⡀⣠⠀⢰⢠⡆⠐⡂⠐⠀⡖⠀⠄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠁⠈⠀⠁⠁⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠈⠁⠀⠀⠓⠀⠂⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡄⠀⢰⣄⢰⡄⠀⡄⠀⠰⠀⠀⠐⢐⡀⡄⠆⠀⠀⣦⡆⡔⢀⠰⢀⡆⠒⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢰⠀⢀⠔⠁
⠀⣧⠀⡔⠒⣂⠐⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢆⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⢄⢠⡔⡂
⠀⢻⠀⣇⣨⢃⡚⠤⡌⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⢶⡲⠖⢿⡆
⠀⢸⠀⣿⢿⠇⠀⠀⠈⠀⢀⡀⡄⠀⠀⠀⠀⠀⠀⠀⣨⣤⣤⡤⠶⢦⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡉⠓⠈⡵⠀⠈⡁
⠀⢸⠀⡇⠀⠀⠀⣠⠒⠘⢁⠴⠖⠉⠓⡂⠦⣀⣰⢋⠏⢁⠀⠀⠀⠀⠉⠂⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠈⡝⢢⣅⢁⡤⠚⢻⠁⠤⡇
⠀⢸⠀⡆⠀⠀⢰⡇⠀⡔⡇⢸⠀⠊⠀⠙⠄⠇⣇⢸⠀⣈⠀⠀⠀⠀⠠⢤⡤⠄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢣⠀⠘⠙⠀⠀⡟⠒⠈
⠀⢸⠀⡇⠀⢀⣘⣵⢤⡄⢹⣌⣿⠁⠀⠸⠛⡖⢹⣨⡆⢸⡄⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⣴⡟⢫⠋⠛⠚⡶⠴⡄⠢⠄⠓⠂⠐⡄
⠀⢸⡁⠇⢰⠏⠀⢻⣹⠘⠋⠀⠋⠁⠀⠻⢹⢧⠀⠸⡗⠁⣠⡄⢺⠿⢦⠐⡇⣼⡿⠤⣄⠀⠀⠀⠀⢠⠞⠓⢣⡌⠘⠛⠓⠲⠉⠹⠍⠶⠀⠐⠇
⠀⢞⣣⣶⣀⡀⣀⣢⡿⣷⡀⠀⠀⢀⠀⢀⣤⡀⠀⠀⢃⠀⡯⡐⠁⡠⠀⢃⡽⠋⠐⠀⠈⡄⠀⠀⠀⠈⡀⠀⣹⡇
⠀⢸⡿⢣⠈⠉⠙⠁⣀⠆⠈⠐⣤⠤⠒⠿⠋⠀⠀⠀⠈⣶⣇⣀⣀⡀⠄⠈⣿⣀⢀⠀⠀⢳⡄⠀⠀⠀⡄⢰⡷⡀⠀⠀⠀⠀⠀⣠⠄⠄⠠⠄
⠀⢸⠁⠋⢠⣔⠾⣶⣝⠒⠶⠾⠛⠂⣴⣶⣄⠀⠀⢀⣴⣤⣿⣟⠛⠛⠛⠛⣛⣬⣭⣍⠛⠉⠀⠀⠀⣼⣶⡏⠀⠀⠀⠀⠀⠀⠀⠘⠠
⠀⢸⡄⣠⣿⣝⠷⣦⣉⡛⠳⠶⠿⠛⣋⣵⢟⣷⡴⣷⣦⣍⣉⣛⣛⠛⠛⠛⣛⣛⣉⣭⣧⡀⠀⠀⠀⠻⠋⠸⠀⠀⠀⠀⡔⢢⠀⣀⠀⠄
⠀⢸⡇⠀⠙⢿⣷⣮⣭⣙⣛⣛⣛⣋⣭⡴⣿⣿⣷⣤⣍⡙⠛⠿⠿⠿⠿⠿⠿⠛⣛⣋⣭⣧⠀⠀⠀⢀⡄⢰⠀⠀⠀⠀⠀⠁⠠⠃⠴⠂
⠀⠈⡇⣿⠆⠊⠘⢦⣄⣉⣉⣉⣉⣥⣤⣶⢿⣷⣬⣹⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡟⢻⣭⣾⣧⡀⠀⢩⠇⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⡇⢸⣦⠀⠀⢸⡿⠿⠿⠿⠿⠿⣿⣥⣤⣽⣏⡉⣻⣷⣶⣶⣶⣶⣶⣶⣶⣾⠁⠀⠻⣷⣶⣷⡔⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡇⢸⠁⠈⠑⢼⣧⣀⣀⣀⣀⣀⣼⣿⣉⡥⠻⡟⢻⣉⣉⣉⣉⣉⣉⣉⣉⡇⠀⢠⠞⢧⣈⠝⠁⠀⠀⢀
⠀⠀⡇⠀⠈⢰⣤⣠⣿⠿⠿⠿⠿⠟⠛⠛⡙⢦⡀⠙⣼⡿⣿⣿⠟⠛⠿⠿⠿⣧⡴⠋⣀⠜⠁⠀⠀⠀⠀⢸⠀⠀⠀⢠⢂⡄
⠀⠀⡇⠸⢾⡟⣡⣼⣧⣤⣤⣤⣤⣤⣶⣶⡇⢸⣳⣾⠁⠰⢿⢡⡿⠿⠿⠿⠿⣿⡶⣾⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉
⠀⠀⡇⠘⠋⠋⣸⣍⣙⠛⠛⠛⠛⢛⣉⣉⣽⠖⠙⣿⣣⣦⣴⣶⣴⣤⣤⣤⣤⣤⣿⠿⠃⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣿⠀⠀⠀⣿⠻⠿⠿⠿⠿⠿⠿⠿⠿⡟⠀⠀⢸⢿⠟⠛⠋⠙⠋⡏⠙⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢩⡆
⠀⠀⢻⠀⠀⠀⣻⠀⠀⠀⠀⠰⠀⠀⠀⣈⡇⠀⠀⢸⢰⠐⠤⠤⠞⢀⠑⠶⠤⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢡
⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⡀⠀⠀⠀⢻⠁⠀⠀⠸⣸⠀⠀⠀⠀⡟⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡕⠀⠰⠁⠀⡠⠆
⠀⠀⢸⠀⠀⠀⢻⠀⠀⠀⠀⡇⠀⠀⠀⣼⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠌
⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⠀⢀⣏⣀⣀⡀⢠⡇⡆⠀⠀⢰⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠺⣄⠀⠜⠒⠒⠒⠒
⠀⠀⠸⠀⠂⠐⣚⣀⠀⠈⠉⠉⠁⠤⠤⠄⠀⠀⠐⠸⡇⡅⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⢤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠚⠛⣷
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢀⣀⣤⣄⢠⣿⠤⣤⠀⣠⡤⠤⠶⠶⣦⣠⠖⠒⠲⢶⣤⠶⠒⠒⢲⡆⢀⣀⣀⣀⢀⣠⠖⠚⢳⡄⠀⣠⠞⢛⣛
⠀⢀⡾⠁⠀⠘⠋⠀⠀⠸⣶⢻⠀⠀⠶⣶⢿⠻⣄⡀⠘⠯⣏⠓⢢⠀⠛⣷⡿⢁⣄⠹⣾⡇⢠⣺⡿⠷⢾⠋⠀⠈⢙
⠀⣾⡇⠀⠀⡀⠀⣀⠀⠀⠹⣸⠀⠀⠴⠿⡾⣷⠒⠋⠀⢠⣿⠉⠉⠀⢠⢿⠇⢀⡁⠀⣿⢇⡀⣩⡀⢠⣾⠀⠀⠈⠛
⣸⠻⠤⠤⠼⠙⠶⠉⠲⠒⠒⡿⠶⠶⠦⣴⡇⠙⠶⢖⡶⣿⠘⠒⠒⣺⣯⠘⢓⣯⣈⣒⣿⣄⣭⡁⣳⡟⢸⣐⣲⣒⣶
⠻⠤⢤⣤⡴⠳⠤⣾⠳⠶⠚⠛⠓⠛⠛⠋⠙⠛⠛⠋⠀⠙⠛⠛⠋⠉⠉⠉⠉⠀⠉⠁⠀⠀⠀⠉⣿⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠲⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⠂⠀⠀⣠⡾⠋⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠖⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⢀⣀⣀⣀⣠⡀⢀⣤⣤⣤⣄⣀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣤⣬⣧⡀⠀⢀⡤⠤⢤
⠀⠀⣼⠛⠉⠳⡞⠉⠉⢻⣠⢿⠉⠁⣠⣤⣷⣟⠀⠀⢤⣼⡿⠤⣄⠀⠾⣥⣴⠛⠛⢳⣴⡏⢀⣴⣼⣇⣰⠿⠀⠰⠿
⠀⣼⡇⠀⠀⠀⠀⠀⠀⠈⢿⢸⠀⠀⣨⣿⣹⣬⠭⠗⠀⢨⣷⠶⠞⠀⢀⣿⡇⠘⠃⠈⣿⡄⠘⠚⠁⢀⣹⠀⠀⠠⠾
⢰⣿⣀⣀⣰⢦⣠⠶⣄⣠⣬⣾⣄⣀⣈⣀⡇⢧⣀⣀⣤⡾⠻⣤⣤⢤⡎⠼⢤⡼⠳⠤⣿⠙⢒⠚⢦⡟⣿⠰⣄⣀⣀
⣿⣀⣁⡈⣡⣤⣁⣤⣤⣠⡴⠧⠤⠤⠤⠟⠷⠤⠤⠞⠋⠳⠤⠤⠶⠚⠳⠶⠞⠉⠛⠛⠉⠉⠙⠳⢺⡇⠈⠛⠒⠒⠋
⠀⠉⠉⠉⠁⠀⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⠶⠶⠶⠶⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠙⠷⣄⡀⠀⠀⢻⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣻⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤⣤⡒⠒⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡤⠚⠋⢦⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣰⠟⠻⠟⠉⢻⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢹⡅⠀⢀⢠⣠⣠⣷⣤⣴⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡠⠚⠀⠀⠆⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⢷⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⡀⠀⣠⠎⣱⣶⡶⠖⠒⠍⣁⠴⠀⠀⠀⠀⠳⠀⠀⠀⠈⠻⢶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡜⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⠜⣡⣾⠿⠃⠀⠀⠀⠀⠈⠄⠰⣄⡀⠀⠀⠠⠀⠀⠀⠀⠀⠙⠻⠦⠤⠄⠀⠀⠀⠁⠀⠀⠀⡇⠰⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⡰⢁⣾⡟⠁⠀⠠⠄⣄⣀⡀⡠⠂⠀⠈⠛⠀⢄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢀⣤⣴⠷⣔⠀⠺⣿⣿⢋⢩⠙⣿⠐⠄⢹⣿⣿⣿⡇
⠀⠀⢠⡴⠿⠋⠀⠀⠀⠀⠀⠀⠢⢄⣀⡀⣀⣀⠂⠀⢸⠆⣆⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠐⠁⠀⠒⠀⠈⠹⡿⣿⣿⣄⣁⣤⡿⠿⠦⠞⣛⠋⠙⠁
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⢀⡀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣘⣧⡤⠶⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡄⢸⡀⠀⠀⢸⠀⣿⠀⣼⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⠀⣿
⣼⣾⡇⠀⡀⠀⢸⠀⣤⡄⢸⠀⠀⣿⣿⡄⠀⡇⠀⠀⠀⡄⠀⢸⣇⠀⢸⡇⣼⡇⠀⠀⢸⢀⣿⠀⣿⠀⡇⠀⢠⠀⣴⡇⣶⠀⢸⠀⣿
⣿⣿⣧⠀⡇⡇⢸⠀⣿⡇⢸⣀⠀⣿⣿⣿⠀⣇⡄⢀⢰⣧⠀⣾⣿⠀⣾⡇⣿⣧⠀⣦⢸⣸⣿⠀⣿⡇⣧⠀⢸⢀⣿⣿⣿⠀⣼⢰⣿
⣿⣿⣿⠀⡇⡇⣾⠀⣿⣷⢸⣿⠀⣿⣿⣿⢀⣿⣷⢸⣼⣿⡀⣿⣿⠀⣿⣿⣿⣿⠀⣿⣸⣿⣿⠀⣿⡇⣿⡆⢸⣾⣿⣿⣿⡀⣿⣼⣿
⣿⣿⣿⡀⣷⡇⣿⡄⣿⣿⢸⣿⡆⣿⣿⣿⢸⣿⣿⣾⣿⣿⣦⣿⣿⢠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣤⣿⣷⣿⡇⢸⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣇⣿⡇⣿⣇⣿⣿⢸⣿⡇⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⡇⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠦⠤⢼⣀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣸⠤⠤⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠲⢄⠀⠑⣄⠀⠀⠀⢀⡜⠁⢀⠴⠊⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠉⠑⠒⠢⢄⡀⠙⢦⡈⢆⠀⢀⠎⣠⠞⠁⣀⠤⠒⠒⠉⠉⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣑⣜⡆⣞⣔⡡⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠛⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠤⠤⣄⡀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⠀⡇⠀⠀⡇⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠴⠴⠛⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⢉⡭⠿⠿⠿⢿⢿⡙⠿⠯⣉⣉⠍⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⣿⠦⡶⠒⠒⣿⣛⡟⠒⢶⣿⠟⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠾⠁⢻⠛⠓⠞⠋⠛⠛⡒⠚⠛⠻⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢀⡄⢼⠷⡶⠀⠀⠀⠀⡿⠲⠄⡁⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⡼⣷⠿⠛⠃⠀⠀⠀⠀⠙⠻⣾⣷⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡇⣿⠀⠀⣴⠀⠀⠀⢰⡆⠀⢸⡿⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣿⡄⣰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣶⢠⣷⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⣿⣿⣆⠀⠐⠀⠀⠀⠀⠀⠂⠀⡰⠛⣿⠏⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠙⠻⣿⠷⠤⣀⠀⠀⢀⣀⠴⠚⠟⢾⠁⠀⢸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣟⣀⣀⡿⠄⢀⣤⣿⣿⣿⣧⣤⡀⠳⠌⢓⣶⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣤⣴⣶⣿⣿⣬⣿⣿⣵⣿⣿⣶⣶⣭⣷⣤⢶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠛⠟⠛⠛⢧⠈⠉⠉⡴⣿⣽⣛⣻⣿⣏⣹⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣶⡶⠶⠾⠿⠶⠾⣿⢿⣿⠿⣿⢹⠋⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣠⡏⢠⠄⠠⠀⠀⠀⠄⢴⡿⢄⡿⢿⣦⣼⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⠀⠄⠀⠀⠀⠀⠘⢣⠰⣿⣾⣿⣟⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⠳⣤⠀⠆⠀⠀⠀⠀⠰⠂⠀⠙⠊⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⡇⠀⠀⠰⡆⠀⢀⣠⣾⣧⠀⠀⠀⠀⠀⣘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣄⢀⣀⣤⣶⣾⣿⣻⣟⡟⠱⣦⣄⣀⣀⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠟⠻⢿⣷⣾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣷⣄⣀⣀⣀⣀⣈⠉⣉⣉⠛⣿⣿⡟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣠⣏⡦⢄
⠀⠀⣠⣄⢀⠀⠀⠠⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣷⣽⣿⣴⣏⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠄
⠐⢻⡟⢠⣏⡄⣰⣦⢰⣦⡆⣼⡃⠂⠀⠀⠀⠀⣿⡿⠋⣿⢻⣿⣿⡿⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠰⣆⡸
⠀⢿⠀⣾⢸⡇⠇⣻⢘⡙⣇⠛⠹⠄⠀⠀⠀⠀⣿⡏⣼⢇⡆⢁⠸⢃⢹⠃⢿⣿⡇⠀⠀⠀⠀⣤⣾⢓⡖⠀⢐⠒⢈⠀⠀⡤
⠀⠀⠀⠀⣾⣰⢹⠋⢸⡇⡟⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡞⡷⡻⢛⡞⢺⢿⣾⣿⡇⠀⠀⠀⠀⢸⠃⢸⠙⡇⡏⡇⡾⢿⢸⣧⡁
⠀⠀⠀⠀⠀⣃⣬⣤⢤⡖⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⢣⣇⣿⣇⣮⣸⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⣶⢰⣠⠆⣴⢠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠩⠃⠙⠀⠙⠘


⣠⣤⡶⢀⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⣀⣴⠖⣠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⠆⣠⠀⠈⡈⠀⡁⠀⠀⣀
⢠⡟⠀⡾⢴⢠⡞⡆⣼⢶⡆⣾⣔⠁⠀⠀⠀⠀⢸⠏⢰⠇⡶⣼⢱⢠⡷⡆⢸⣃⠂⠀⠀⠀⠀⢻⡏⢰⡗⣷⣾⢹⢰⡿⡇⢸⣧
⠈⠃⠀⢣⡜⣨⢡⡅⢩⡌⣅⠉⠙⠂⠀⠀⠀⠀⠘⠀⠘⢠⣃⡍⣼⠘⣅⢣⠘⠘⠃⠀⠀⠀⠀⠸⠀⠘⢠⣏⣌⣼⠈⣥⢫⠌⠘
⠀⠀⠀⠘⢣⠇⠿⠀⠺⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣸⢹⡇⠸⠇⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣸⠙⠇⠀⠟⠻⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠉⠒⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠐⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠐⠦⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⣙⠯⠋⠀⠤⢤⣀⠀⠀⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⡀⠞⠕⠀⠀⠒⠚⠁⠀⡚⠂⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡕⢄⠀⠀⡐⠀⡈⡦⠀⠁⠀⠀⠦⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⢊⢢⡐⠀⠀⣧⠱⡀⠠⠀⠐⠶⠖⢠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⡀⠌⢿⣿⢳⡱⡀⠀⠨⠣⡈⠓⠒⠦⠤⡄⠘⡄⠀⠃⠂⠀⠤⠈⠑⢄
⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠠⡀⠀⠀⠻⣿⣿⣌⢢⠀⠡⠈⠲⢄⠀⠈⢀⠞⡇⠀⠈⡀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠠⠀⠀⢀⠻⣿⣿⣦⡱⡀⠡⡀⢨⠀⡇⠁⠀⠁⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡆⠀⣆⣤⠾⢿⣯⣷⣌⢄⠑⠌⠂⢅⠀⠈⠀⠦⢀⢀⣐⠀⠀⠁⠀⠀⠀⠀⠑⠢⣀
⠀⠀⠀⠀⠘⠐⠀⠀⠀⠀⠀⠀⣗⠊⠁⠀⠀⠀⠻⣯⠟⢦⢦⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⠐⠀⠁⣀⡀⢀⡀⢀⢑⠤⣀
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢀⠀⠈⠢⢀⠀⠀⠀⠹⢷⣤⠿⣷⡈⣤⠂⠀⠀⠀⠀⢀⠀⠀⠸⠮⣉⠁⢀⠤⠛⢚⠒⠌⡒⠄⠱⡀
⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢠⠑⣤⡀⠀⢈⡻⠳⠿⠿⡀⠀⠀⠀⢀⠐⠧⢀⠔⠉⠐⡀⠷⠵⢦⡀⠀⠀⠁⢈⠢⡀⢱⠀⡠⠤
⠀⠀⠀⠎⢀⠀⠀⠠⠀⠠⠀⣃⠀⢀⡀⢀⡉⢀⣨⠖⢉⠁⠄⡐⠠⢄⠀⠀⠀⣡⠤⣶⢁⡞⢠⠀⠀⠀⠀⠀⢹⣀⣀⣁⠬⠤⠼⠎⠀⠂
⠀⠀⢠⠄⠂⠔⢁⠂⡄⠀⠄⡡⠂⠀⠀⠀⠀⠎⠀⠀⠀⠀⠂⢨⣑⣬⠳⣆⠈⠀⠐⠛⠮⠷⠦⡶⠴⠛⠒⠀⠛⠉⠉⠀⠀⠀⠤⠀⠒⠒⠂
⠀⠀⢠⠀⠀⠀⠂⠀⠀⡈⠠⠁⠀⠀⠀⠀⢠⡴⡶⠶⠖⠛⠋⠊⠁⠐⠒⠬⠳⡄⠐⠂⠀⢀⣀⣠⠄⠀⠀⠠⡀⡀⠀⠀⠀⠀⠂⠉
⠀⠀⠨⡓⣄⠀⠀⡀⡐⢀⣉⠀⠀⣤⡤⢤⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠉⠉⠀⠀⢀⣀⡠⠴⠡⠤⠁
⠀⠀⠒⠊⠉⠉⠀⠀⠉⠙⠂⠈⢱⣿⡿⡀⠄⠀⠀⠀⠀⠀⠀⠁⠢⠔⠚⢉⡀⠀⢀⣀⠠⠔⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⣟⣻⣎⣄⠀⠀⠀⠄⡀⠀⠀⠤⣀⠨⠅⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢾⣆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠤⠤⣦
⠀⢻⣆⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡀
⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣠⠊⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣿⣿
⠀⠀⠀⠹⣧⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂⠈⠀⠀⠀⠀⢀⣿⣁⣤⠀⢀⣴⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡷⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠘⣷⡄⠀⠁⠀⢀⠠⠐⠉⠀⠀⠀⢀⣠⣤⣶⣾⡿⠟⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠘⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡇⠀⣠⣴⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣀⣤⡶⠿⠋⠹⢦⣈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⢡⣤⡤⠘⢿⣤⡚⠶⣤⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢸⣶⡆⠀⠈⣻⣶⣿⡌⣁⣶⣓⣿⣦⣀
⠀⠀⠀⠀⠀⠀⣀⣴⣾⠋⠀⠀⠀⠈⢈⠁⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡿⢿⢷⣄
⠀⠀⠀⠀⠀⠀⠙⠛⠋⠋⠛⠉⠻⠟⠛⢙⣋⠉⣉⣋⢻⠿⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⡆⠄⠀⠀⢸⣤⠀⣧⡀⠀⠀⠀⣶⣲⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠓⠀⠀⠀⢸⣿⠀⡟⣷⠀⠀⠀⣿⣾⢾⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠠⠀⣄⠀⠀⠀⣀⣀⣠⠀⢠⢀⣀⣀⣄⣀⣀⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠘⢻⣿⣿⡿⡾⠛⢻⣟⢻⣿⣷⠺⢷⢿⣾⠟⢶⣿⣿⣿⣿⣿⣷⠶⠶⠤⠿⠿⠷⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⣇⡀⠋⠉⠙⠉⢈⡀⣀⣸⠻⡀⠀⣯⣽⣤⠁⠈⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢄⣀⡀⢀⣿⠇⣀⣀⠀⠀⠙⠃⠛⢫⠀⠀⣀⡿⠿⠿⠀⢀⡀⢠⣤⡀⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠀⠘⠛⠐⠻⢷⠄⠰⠀⠀⠀⠰⠀⣤⣿⣿⠧⠠⠿⠿⢿⠇⠤⡀⠿⡏⠩⠭⡀
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠐⠛⠱⠰⠀⠀⠀⠀⣰⠶⠶⢾⡾⠐⡤⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡴⠓⠂⠀⠀⢇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄⠀⢀⢊⣴⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠁⠀⠀⠀⠈⠙⢤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠇⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠓⠒⠲⠶⠶⠶⠤⢤⣤⣤⣄⣀⣀⣀⣠⣴⣾⣿⣗⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⡿⣛⣩⡄⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠚⠒⠠⠄⠀⠄⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣿⣿⠽⣶⣿⣏⠽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠶⠤⢤⡀⣀⣀⠀⠀⠀⠀⠉⠉⠙⠛⣛⣿⠿⣟⡧⣾⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⣤⣤⣤⣄⣀⣈⣉⣛⣓⣒⣒⣲⣦⣤⣿⠷⣫⣵⡾⣿⡯⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿⠿⣫⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣻⣿⣿⣿⠿⠿⠛⠛⠉⠀⠈⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⢀⣀⣠⣤⣤⠶⠖⠛⠛⠉⠁⠀⠀⠀⠀⢰⣮⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠖⠒⠞⠿⠟⠛⠛⠓⠒⠚⠓⠒⠒⠒⠛⠛⠛⠛⠛⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠀⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⣿⢿⡿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣷⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⢉⢲⠇⢀⡠⠲⣌⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣾⠉⠿⢿⠛⠳⠤⣀⠀⡞⢀⠤⡈⣳⠏⡄⢢⡘⣏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡸⢯⣱⡀⣮⢂⡏⠈⠀⠀⠠⠑⣿⢰⡠⠾⠻⠻⠒⢧⣱⣿⣽⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣗⣺⣼⡁⠀⠤⣀⡀⠀⠁⠂⠀⢹⣫⡖⢏⣩⠍⠛⠺⣏⢸⣿⣻⡤⠶⠒⠶⠶⡖⠲⠦⢤⠴⠶⡔⠒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢦⡤⠾⢛⡿⣄⢀⠤⠄⠄⠀⠉⠐⠠⣄⣸⠏⢀⣶⣤⠖⣄⠀⢹⠙⣏⣿⡀⡤⢪⠥⠀⡈⢠⣤⢯⣴⢶⣷⣤⠈⠀⠈⣧
⠀⠀⠀⠀⠀⠀⢸⣟⣻⠓⢺⠷⣚⠥⣋⠵⠳⠒⠦⣤⣀⣄⠀⠹⣤⢼⠁⠀⠀⢸⣊⠟⢦⠃⢻⣚⣛⡇⠀⠌⠇⢠⡛⠀⠻⣇⣠⣿⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢯⣨⣵⠎⢹⠀⠏⠈⠁⡾⠀⠀⠀⢀⢻⢹⡶⢤⡿⠒⠇⠀⠀⠋⠉⠙⣇⠀⡟⢀⡏⠉⠳⢜⠀⢿⡆⡞⠀⢿⡁⠂⡨⠇⠀⢸
⠀⠀⠀⣀⣀⠨⣿⣿⣿⠤⡼⣷⠀⠀⠀⠀⠀⠄⠀⠞⢈⣆⣧⣰⡇⠀⣦⠀⠀⠐⠇⠀⠿⣾⠁⠛⠀⠀⠀⢚⠛⣇⡹⢁⡰⢻⡟⠃⡇⠀⠀⡾
⠀⠀⠼⠷⢉⢀⡙⠦⣤⣐⣉⣩⣄⠀⠀⠀⠀⡆⠀⠀⢠⣫⣿⣈⠁⠀⠀⢀⣀⡀⠀⠀⠀⣇⠀⣠⠀⠀⠀⠛⠁⢻⡗⠋⠀⣸⠃⠀⠁⢀⣴⠓⠒
⠀⠠⠖⡁⠀⠀⠁⠀⠂⠰⠟⢩⠘⠣⣀⡀⠀⣀⣤⣴⡟⢡⣨⡿⢄⠀⠀⠁⠀⠁⠀⢀⣼⡟⣆⠀⠀⠀⠀⡀⣀⢜⠝⢢⡼⢋⢧⣄⠂⣸⠣⠤⠀⡀
⢠⠔⠒⠒⠂⡀⣃⡈⠀⢂⠖⠘⣠⡇⠈⠈⢡⡤⢬⠯⣴⠷⠼⢦⣄⣹⣆⡤⡤⣠⡾⠓⠓⢮⡈⠲⣤⣤⣤⣽⣶⣆⣠⣾⠠⢽⡆⠙⢞⣁⡈⢅⢀
⠀⢈⡀⢉⠀⣀⠤⢠⣀⠩⠈⠉⡟⢧⡀⠀⢸⠃⠀⢀⢬⠣⡽⠊⢳⠘⠛⠃⠀⢿⡁⢀⡸⡄⣝⠝⢿⢉⣋⠟⠿⢳⣜⠋⡘⣐⡠⣳⡦⡜⠻⢣⠀⠑
⠀⠨⠄⠀⠋⠄⢒⡎⠸⢎⡁⠘⢷⡤⣷⣄⣾⢨⢹⡌⠀⡖⠀⠘⣿⠒⣯⡖⢺⣧⠜⣟⠂⡽⣃⣶⠈⠉⣟⡴⣥⣜⠈⢻⣁⡞⢡⠿⠟⠄⠀⠰⠁
⠀⠀⡞⠠⠕⢀⣽⠁⠂⢄⢳⡄⠈⡏⠉⠀⡧⠈⢆⢣⡇⡷⣴⡞⡡⢻⣟⣉⠻⡿⡛⣿⣳⡉⣪⡽⠉⠩⢿⣆⡃⡼⢀⣾⡟⠀⡸⠈⢡⡟⠓⢆⣠⠘
⠀⠀⠀⠀⠁⢸⠛⢲⡇⢠⠀⠹⣍⣃⡉⠀⣾⣳⡎⠈⢞⡀⣹⠐⣧⡉⠘⢠⠃⢳⡬⣟⠉⣯⣿⠛⠄⠀⡟⣯⠛⢳⣾⠾⠡⡰⠁⡀⠄⣿⢀⠬⡉⠄
⠀⠀⠀⠀⠀⠘⠀⡸⢸⠁⢠⢰⡟⠡⢥⡀⢡⣤⡹⡒⠊⣀⡅⠈⣹⠁⡧⣺⣤⢻⡇⣿⡷⠶⣻⣀⡀⠀⣧⡟⡲⠃⠈⢻⡀⢣⠐⠁⢠⠇⠀⠌
⠀⠀⠀⠀⠀⡇⠀⡇⢸⠅⠈⡝⠀⠀⠀⠠⢸⡛⡁⠹⡻⢿⡅⠃⡌⢥⡊⡨⠳⠈⡅⡆⢰⡧⠴⡏⡄⠀⢈⣿⠁⠀⠀⠈⢇⠈⣦⡵⠋
⠀⠀⠀⠀⠀⡇⢸⡀⢶⠀⠰⠁⠀⢀⢆⠇⠸⣿⢷⢊⠍⠾⡍⢣⠀⢇⠈⠀⠀⢹⡰⠀⣮⡇⠀⡿⡇⠉⢹⡏⢆⣅⠀⠀⣸⡀⢰
⠀⠀⠀⠀⠀⢇⠀⠙⠻⢙⣁⣀⡠⠂⠀⠀⣀⣼⢾⡇⠀⠊⢳⡿⣴⣀⣾⡄⠀⣸⣧⡔⢹⣅⣀⡉⠃⠀⠸⣈⣀⣬⣿⡞⢥⣷⣹
⠀⠀⠀⠀⠀⠀⠑⠲⣞⡾⠟⠉⠀⠁⠈⠁⠠⣴⠲⠧⠤⠶⡿⢅⣀⣈⡇⠈⠏⣿⣻⡇⠀⡷⠒⠂⠈⠀⠉⢉⣉⣹⠸⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⡀⢀⣀⣀⠀⠬⢽⠀⠀⠀⠀⡇⠀⠀⠈⢹⠉⠉⠀⠁⣇⠀⣯⠀⠈⠍⠉⠁⠀⠈⢏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠂⠀⠀⠀⠆⠀⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⠀⠆⠀⠀⠀⠀⢸⠀⡟⠀⠀⠀⢄⠀⠀⠀⠢⡜⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠠⣻⡇⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠾⠀⠀⢣⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⢹⠁⠀⢀⡙⠀⠀⠀⠚⠋⠉⡉⠀⠀⠀⠀⠠⠰⣄⠰⣄⡻⣎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⣼⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠡⡈⢳⣜⢿⣦⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠙⡿⠛⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢓⣆⣰⣇⣀⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠓⠁⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢴⣶⣿⣿⣿⢿⣿⣿⣿⣯⣟⠛⣶⣶⣤⣄⡀⠀⠀⠀⠀⢀⠞⠓⠒⠤⣀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⢻⣿⣻⢿⡞⠟⠛⢻⣏⣷⡿⣾⠀⠀⠙⠻⠿⣿⣶⣤⣴⣿⡾⠋⠀⣠⡈⠌⠳⠲⣤
⠀⠀⠀⠀⠀⠀⠁⢽⠻⡿⠊⠈⠁⠀⠀⠀⠀⠀⢏⢸⣵⠃⢟⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠀⢠⠎⠁⠁⣀⠒⢄⠀⠙
⠀⠀⢀⠀⠀⠀⠀⠩⠀⡃⠀⠀⠀⠀⠀⠀⠀⢠⠏⣺⣼⠂⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⠔⠀⠐⠆⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠄⠀⠀⠀⢠⡑⠀⠀⠀⠀⠀⠀⠀⠀⢘⠗⣿⡖⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡒⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠒⠀⠀⠀⠀⣍⠃⠀⠀⠀⠀⠀⠀⠀⣾⡇⣷⡏⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆
⠀⠀⠀⠈⠁⠀⠀⣀⣽⢳⠀⠀⠀⠀⠀⠀⢸⠙⢶⣶⠅⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢁⠢⣀⠀⠀⠐⠀⣆⣜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠾⠿⠶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣻⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⠿⢛⣫⣿⣇
⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⠟⣛⣭⣶⣿⢿⠛⡇⢹
⠀⠀⠀⠀⠲⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⠿⢛⣫⣵⣶⢿⢿⠏⡇⢹⠸⠁⠃⢸
⠀⠀⠀⠀⠀⢸⣏⠉⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡿⠟⣛⣭⣶⣿⢿⡟⡏⠏⢸⠘⠀⣃⣸⣤⠶⠛⠉
⠀⠀⠀⠀⠀⣸⡗⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⠀⠀⣀⣤⣴⣾⣿⣿⣿⠿⢛⣫⣵⣶⣿⡟⣿⢹⢸⠈⠁⡇⣀⣬⠴⠛⠙⠻⣶⣄
⠀⠀⠀⠀⠻⠿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⠿⣛⣭⣴⣾⡿⣿⢻⠙⠇⠃⠀⢀⣠⡴⠖⠛⠉⠀⠀⠀⠀⢀⣀⣉⣿⣦⣤
⠀⠀⠀⠀⠀⠀⢀⣉⣿⠿⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠈⢹⡿⣿⠻⢹⠁⠇⠟⠀⣀⣤⡶⣛⣉⣥⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠘⢿⣯⠀⠀⠹⣏⠛⠻⢶⣤⣄⡀⠀⠀⠀⣇⠘⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⡿⣿⠿⡟⣿⢻⡏⣿⢹⠉⡇⢸⠁⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠈⢳⣶⣶⣿⣿⣿⣿⣦⣼⣷⡾⣿⢿⠛⡏⣿⢹⡇⣿⢸⡇⡿⢸⠀⡇⢹⠈⠇⠏⠸⠀⢃⣚⣀⣇⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⢸⡇⡟⢸⡏⡇⡇⣿⣼⣧⣇⣼⣸⠀⡇⠘⠘⠃⣟⣸⣁⣥⣯⣴⣦⠶⠶⠶⠟⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⣸⠇⡁⢸⣃⣷⠿⠋⠀⢉⣉⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣥⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⡿⠛⠁⠀⢄⣐⣂⠠⠬⠭⠭⣍⣁⣒⣒⠶⠤⢤⣀⠉⠛⢿⣦⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠉⢀⠠⠈⠁⢒⡒⠤⠭⢭⣉⣒⣒⠲⠤⢬⣍⡑⠒⠀⠀⣠⡼⠛⢉⣉⣉⠙⠛⠛⠷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠁⡀⠂⠤⠄⣁⣐⡒⠠⠬⢉⣀⣒⠂⠤⢬⣉⠒⠂⠁⢀⣤⠞⠉⣀⡒⠠⠬⠭⢉⣉⡒⠢⠤⣈⡙⠛⠷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⢀⡐⠂⠠⠄⠈⡀⠂⠀⠭⠉⣛⠒⠢⠬⣉⠓⠒⠈⠀⣀⡴⠛⢁⣀⠀⠭⠭⠉⣛⠒⠲⠤⢍⣙⠲⠤⣍⡓⠦⣄⡉⠛⠻⢶⣤⡀
⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⣀⠒⠨⠭⢍⣓⣒⠢⠬⣀⣀⠒⠠⢉⡑⠀⠀⢀⣴⠞⠉⠀⢀⡐⠈⠈⠍⢉⡐⠒⠠⢍⣙⡒⠮⢍⣑⠢⢭⡑⠂⠁⢀⣤⠞⠉⢷⡀
⠀⠀⢰⡿⣏⣁⡐⠂⠤⠄⣀⣀⠀⠡⠉⢃⠒⠨⠭⣙⡒⠠⠍⠓⠀⠀⣠⠶⠋⠀⠀⠈⠀⠀⡐⠈⠩⠉⡐⠂⠬⢅⣐⠢⠍⣙⠒⢬⠙⠂⠀⣠⠴⠋⠀⠀⠀⣨⣿
⣀⣴⡿⠀⠀⠍⠉⠙⠛⠲⠶⠤⣭⣉⡓⠒⠤⢍⡐⠢⠌⠁⠀⢀⡴⠛⠁⢀⠒⠂⠠⠄⣀⡐⠒⠠⢅⣒⠢⠬⣁⠒⠬⣉⠒⠤⠉⠀⢀⡴⠞⠁⠀⠀⢀⣠⣾⠿⠋
⠙⠛⠶⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢦⣌⠁⢀⣤⠞⠉⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠩⢁⡒⠦⢭⣐⠂⠍⡐⠂⠁⠀⣠⠖⠋⠀⠀⠀⣠⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⢶⣤⣌⣀⠀⠀⠀⡠⠬⢿⣏⣀⡀⠂⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠄⡒⠠⠅⡂⠠⠉⠂⠀⣀⡴⠋⠁⠀⠀⢀⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⣆⠰⣿⣶⡍⠀⠀⠉⠁⠀⠀⠄⠤⣀⠀⠀⠨⣁⠂⠀⠉⠒⠄⠁⢀⣠⠞⠉⠀⠀⠀⣠⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⡴⠷⢦⣤⣀⡀⠀⠀⠀⠀⠉⠓⠶⣤⣉⡂⠀⢀⣠⠶⡫⠐⠁⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢶⣤⣄⡀⠀⠀⠀⠉⠛⢷⣟⡵⡊⠀⠀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⡀⠀⢳⡊⢀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠛⠚⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠠⠀⠀⡿⠀⠀⠀⠀⠀⠀⣴⠶⣟⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⢠⣠⠾⠁⠀⠀⠀⠀⠀⠀⢹⠄⣿⠛⢿⡵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡶⣞⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿
⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⡚⢻⣍⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⠟⠀⠉⣩⣿⣿⡷⠶⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⢛⠙⠛⢧⡉⠠⣄⡴⣿⠋⣠⣵⣦⣄⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣴⣿⣿⣿⣧⡀⣿⠀⢹⠁⣿⣴⣿⣿⣏⣺⣿⡆⢸⡇⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣿⣿⣿⣴⣿⡇⣿⠀⢸⠀⢿⣿⣿⣿⣿⣿⣿⠃⠈⡇⠀⠀⠀⢠⠋⢉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⢋⣽⣿⣿⣿⣷⣿⣧⢰⠀⢸⣿⣧⣿⡿⠟⠃⣀⡾⠁⠀⠀⠀⠘⢤⣄⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣍⣟⣛⣭⣿⠟⢁⡀⠀⠀⠀⣅⠙⢿⣛⣛⠻⢽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠈⡿⠜⢳⡾⠁⣀⣫⣤⡤⠶⠦⢬⣤⣄⣳⣌⠀⢸⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⡀⠈⣦⠀⠀⢹⣤⣾⡷⠛⠉⠁⠀⠀⢀⡀⠀⠄⠀⠉⠛⢶⡸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢹⠀⢹⣷⡀⣸⠟⠁⢀⣠⡴⠶⢾⣿⡿⠛⠛⠳⣶⣤⡀⠈⣷⣼⠀⢰⣿⡀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⣀⣄⠴⠃⠀⢸⣧⣿⠃⢀⣶⣿⠃⠀⠀⠈⣿⣷⠀⠀⠀⠸⣿⣿⡅⠸⣿⣇⣸⢻⡇⠀⠀⠀⠘⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢀⣿⣿⣿⣦⣖⣲⣤⣿⣿⡆⠀⠀⠀⣿⣿⣿⡄⣿⣿⣿⠸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣤⣤⣤⡤⠾⣿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⡧⠆⠈⠙⣛⣿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⡀⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠛⠿⠿⣿⣿⡿⠁⠀⣶⠛⠉
⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠙⢳⣞⣿⡟⠋⠁⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠸⣿⠃⣀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣠⡽⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⢿⡛⠛⠻⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠉⠀⠀⢸⡟⢻⣆⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠘⣷⣤⡀⠀⠈⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢘⡿⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢙⡇⠀⠀⠀⢸⡇⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠊⠁⠀⠀⠀⠀⢻⣆⠀⠙⠿⣦⣤⣀⡀⠀⢀⣀⣤⣶⠟⠁⠀⡀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠙⠉⠛⠛⠛⠛⠉⠠⠐⢂⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠲⠷⠶⠶⠞⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠒⠉⠉⠉⠉⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⢀⠄⠐⠒⢠⣤⠀⢆⣠⢀⣼⣀⣀⣀⣀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠔⠁⠀⠀⠀⠀⠉⢇⣀⠀⠀⠀⣠⣀⣀⠠⡍⠉⢡⢄⣙⡻⢯⠈⠉⠉⢳⠉⣼⡊⠉⠉⠒⢤⡀
⠀⠘⠀⠀⠀⠀⠀⢠⠀⡇⠈⠀⠀⠘⠀⣿⣯⡆⠀⠀⠈⢸⣿⣼⠀⠆⠀⠀⢸⢹⠀⢹⠀⠀⠀⠀⠙⢆
⠀⡇⠀⠀⠀⠀⢠⠇⠀⠈⠘⠁⠀⠀⠳⠬⠩⠔⠱⠲⠌⠂⠭⠥⠚⠀⠀⠀⡶⠊⠀⠀⡇⠀⠀⠀⠀⠘⣆
⢐⠀⠀⣀⠠⠒⠁⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠹⣄
⠸⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⢑⡂⠚⠁⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⢀⣨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⡬⢥⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡇⢠⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⢉⣥⠀⠋⠉⣲⡴⢎⡁⠙⠫⢄⠁⠙⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠋⠀⠀⠀⢰⠁⠀⠀⠰⡄⠀⠀⠇⠀⠀⠀⠀⡏⠢
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⠛⠀⠀⢀⠁⠘⢀⡇⠦⡄⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠈⠁⠠⡀⠀⠀⠀⠀⠈⠀⠀⡔⠀⠀⠰⠀⠀⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠾⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⡸⠀⠀⠀⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⢑⠶⡂⠀⠀⠀⠀⠀⠀⠀⠀⣢⠛⢏⠀⡆⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠒⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠐⠃⠀⠀⠇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡠⠊⠓⠒⠂⠠⠤⠔⠖⠚⠙⡀⠀⠀⠀⠀⢰⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡶⠶⠮⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠋⠑⠲⡶⠦⠤⢤⠴⠦⢲⠖⠒⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⣸⠃⠀⠀⡸⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⢁⡰⠃⠀⠀⠀⠇⠈⠓⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢠⠞⠁⠀⠀⠀⢸⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠔⠁⠀⠀⠀⠀⠀⠸⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡏
⠀⠀⠀⢀⡤⠚⠁⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰
⢀⡴⠚⠁⠀⣀⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠈⠢⡀
⡎⠀⠂⢀⠖⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠉⠢⣄
⠱⢤⡤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⠀⠚⠁⠁

⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⢸⡏⠀⠀⠀⠀⠀⠉⠉⠙⠛⠲⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠛⠉⠉⠁⠀⠀⠀⠀⠈⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠈⠓⡶⠛⠛⠓⠒⠒⠶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠒⠒⠛⠛⠓⡖⠋
⠀⠀⠀⠷⠤⡶⠶⠶⠶⠤⠤⢤⣤⣉⣛⠲⢤⣀⠀⠀⢸⠀⠀⢀⣠⠴⢚⣋⣡⣤⠤⠤⠴⠶⠶⠶⡶⠴⠇
⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠛⠓⠒⠚⠛⠿⠷⢿⣷⣦⣼⣤⣶⣿⠶⠿⠿⠛⠒⠚⠛⠛⠛⠛⠛⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠈⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣹⡁⠀⠀⢰⣾⢢⡑⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⢀⣽⡄⠀⠑⠮⡣⡀⠉⠣⠞⠀⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢁⠈⠀⠀⠈⡏⠀⠀⠀⠀⠀⠈⠘⠂⠀⠀⠈⠁⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡅⠀⠀⠀⢀⡄⡀⢀⠀⠀⠀⠘⠃⠀⠰⢦⠀⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠞⠀⠉⠙⠉⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⣀⣤⣄⡀⠀⣴⠀⠐⠀⠀⠀⠀⠀⠀⠀⣰⠀⢘⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢺⣿⣿⣿⣷⠀⣿⡀⠀⣀⣠⣄⡁⠠⣯⠀⣿⣆⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠐⣾⡖⣀⣸⣿⣿⣿⡟⣀⣿⠂⠀⣿⣿⣿⣷⢰⣿⣼⣿⡍⠿⠿⢿⡿⣿⣶⣶⠇
⠀⠀⠀⠀⢀⣤⣮⣿⣿⣿⣿⣇⣏⡁⣄⣿⣿⣷⡀⠽⣿⣿⠿⣾⣿⣷⣿⡧⢴⡒⠾⠟⠻⢩⡿
⠀⠀⠀⠀⣺⣓⣀⣀⣒⣚⣚⣓⣻⣭⣽⣿⡿⣿⡂⢠⠀⣳⣶⣻⣿⢿⣉⣀⣐⡂⠀⠀⠀⣐⣾⡂
⠀⠀⠀⠀⡯⠉⠉⠀⣀⣀⣉⣉⣉⣉⣙⡛⠻⠿⣿⣿⣿⡿⠟⠛⣛⣉⣉⣉⣉⣁⣀⠀⠉⠉⠩⡅
⠀⠀⠀⠀⠷⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠭⠵⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠶⠴⠇