Transmit Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠚⢺⣿⡛⠛⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢤⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠴⡲⠏⢼⣿⡿⠶⢶⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠀⢸⣿⣇⠀⠸⠄⠳⠐⠒
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⢤⣾⣿⣿⢤⣤⣀⣀⣀
⠀⠀⠒⠀⠀⠻⠉⠹⠁⠇⠀⢸⣿⣿⣈⢀⣿⠩⣏⣣⣀⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠑⠒⠁⠐⠉⣻⣿⣿⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢸⣿⠟⢋⣅⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡡⠶⠊⢹⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣍⡤⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠁
⠀⠉⠁⠈⠓⠀⠒⠂⠄⠲⠶⡆⢀⣈⢀⣦⣀⣀⢀⣀⣀⣀⣀⠠⢄⣀⣀⣀⡀⣠⣀⡠⠠⠒⠒⠤⠄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠠⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⣿⡾⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣬⢮⣄⣀
⠀⠉⠉⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢉⣿⣭⡃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⡠⠰⠾⢳⣛⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⣯⣘⠀⠀⠀⡤⠀⠀⢰⡲⢬⢬⡀
⠀⠀⠠⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣿⠈⠀⠰⠒⠒⠓⠂⢈⠹⠴⢎⡄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⢩⡽⢿⠉⠉⠉⠉⠛⡉⠀⢈⢻⠒⠯⡁
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠂⠀⢀⣠⠄⠀⠀⣚⡉⠨⡇⠀⠀⠀⣷⣿⠀⣞⣻⡁⣥⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⣀⠀⠀⠀⠀⠀⠀⣀⣶⠄⠀⠋⠀⠀⢸⢸⠀⠀⢠⣉⣁⣄⣻⠀⠀⠀⣇⢹⢀⠌⣿⡀⢸⣸⡆
⠀⠀⠀⡀⠀⠠⡀⢠⠀⡀⠈⠷⣄⢀⣀⣴⣛⣓⣚⣶⣄⣡⣤⣤⣼⠘⢰⣶⣺⣤⣭⣿⣼⣃⢀⣼⠇⠂⣧⢈⣯⡧⢸⣬⣇⣀
⠀⠀⠀⠇⢀⡿⣷⣾⣶⣿⣿⠿⠟⠟⠋⠉⠙⠛⠥⢴⣤⣩⣟⡻⠿⣼⠟⠟⣩⣿⣟⣿⣯⣝⣿⣿⣿⣷⣿⣿⣿⣿⠶⣿⣿⣿
⠀⠀⠶⣗⡚⣒⣧⢼⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠦⢤⣬⣉⡛⠛⠛⠛⠿⢿⣟⣨⣿⣿⣿⣿⣛⣛⡇
⠀⠐⢫⡷⢚⡭⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠂⠀⢀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⣷⣶⣬⣍⣉⠛⠻⠿⢿⠿⠏
⠀⣠⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛

⠀⠀⠀⠀⠇⠀⠀⢀⣀
⠀⠀⠰⢶⣿⣤⠠⠴⠪⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡠⢶⣾⡟⠗⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠉⠁⢨⢸⡇⣷⣐⡲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⣠⣴⣿⣿⡵⠂⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣦⠀⠬⠗⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠛⠉⢸⣼⣯⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣖⡀⣠⣅⡀
⠀⠀⣈⣸⡷⣿⠉⠙⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢐⣼⣿⠚⠋⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣷⠦⣄
⠶⠊⠻⢿⡿⣬⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⢡⣸⣌⣀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠜⠛⠃⣻⣷⣀
⠀⠁⡣⢸⣏⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⠏⠉⠣⠀⠀⢀⣤⡀⢀⣅⠀⠀⠀⠀⢀⣀⣼⡯⠉⠑
⠀⢀⠀⢹⡧⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⢹⡟⠀⠀⠀⠀⠀⠀⠀⡀⢹⡷⠦⢀⠀⠀⠁⠀⣻⣷⡦⣄
⠀⠰⠁⢼⡟⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⡅⠃⠀⠀⠀⠀⠀⠉⠉⢿⣿⣤⡀⠀⠀⠀⠀⡹⡇⠂
⠀⡀⠀⢹⣷⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⡇⢄⠀⠀⠀⠀⠀⠠⠀⢪⣏⡀⠁⠀⠀⠀⢀⠠⣇
⢀⠁⠈⣿⣇⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⡇⠠⠀⠀⠀⠀⠀⠀⠀⢚⡏⠉⠁⠀⠀⠀⠀⠰⣏⠐
⣸⠗⢆⣺⣿⢢⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠤⣴⡷⣤⡄⠀⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⣀⣴⣯⣠⡆
⣿⣤⣤⣿⣿⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣤⣿⣷⣤⣧⣤⣤⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣧⣼⣿⣤⣮
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠧⠶⠶⢚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣤⡯⠉⠒⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣦⡷⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠛⠉⢩⣿⢽⣷⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡄⢉⣿⠚⣷⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⢾⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢈⣷⠚⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣖⢂⣿⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⠙⠛⠺⠭⣿⢿⣿⣾⣵⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠈⣿⠛⢻⠾⢷⠶⠶⠄
⣿⣿⠿⢿⠿⠿⢿⠿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠋⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣌⣤⠐⠺⠷⣀⣢⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⣀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣾⠋⠉⠁⠀⠀⠀⠀⠀⣀⠀⠀⣀⡤⠄⠀⣀⣀⠀⠀⠀⠐⠋⠉⠉⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢯⠀⠀⠀⠀⣻⡄⠀⠀⠀⠠⠄⠀⠀⠁⠀⠉⢁⡀⠈⠉⠉⠀⠀⣠⠤⠴⠄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡴⠋⢹⡇⠀⠀⠠⠖⠋⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⢠⠎⣀⣴⠞⢁⡈⠁⠀⠠⠶⠖⠂⠀⠀⠘⠃⠀⠀⠉⠉⠉⠉⠁⠠⠤⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠉⠐⠒⠀⠀⠛⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠙⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣙⢷⣄⠙⠀⠉⠀⠀⢤⣄⠀⠀⠤⠀⠀⠘⠛⠛⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢹⡆⠙⠀⢀⡀⠀⠶⣤⡀⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⡾⠃⠀⠠⣄⡉⠃⠀⣀⠀⠀⠀⢤⣀⠀⠀⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠙⠂⠀⠈⠓⠆⠀⠀⠈⠀⠀⠀⠀⢀⡀⠀⠀⠐⠦⣤⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠰⠀⠢⣄⠀⠀⠀⣄⡀⠀⠦⣄⣀⠀⠀⠀⠀⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠈⠙⠲⢦⣀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⣄⣀⣐⣀⣒⣽⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⢀⡀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠈⠛⠀⠀⠙⠶⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣧⣂⣯⣭⣭⣭⣭⣭⣥⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠴⠦⠾⣿⣿⠿⠶⠶⠶⠤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⠀⠤⢀⡲⣿⣿⢶⣒⠂⠤⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛⠛⡿⢿⠛⠛⠘⠓⠀⠸⠤⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣟⣺⡄⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢇⠀⠀⠀⠀⠀⢠⡯⢽⡇⠀⠀⠀⠀⠀⡤⠊⡇
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣀⢀⣸⡗⢺⣇⡀⠀⠀⠀⠉⠀⠀⡇
⠠⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⢀⣔⣤⡀⠰⠖⢿⣏⡡⠰⣮⣸⣟⣻⣯⣿⢿⠅⣒⣆⣰⢤⣥⣀⣀
⠀⠑⢦⡀⠀⠀⠀⠀⠀⠈⠐⠤⠀⣀⡀⠐⠁⣋⠀⠀⠀⢹⡏⠹⡁⢉⠩⣽⢏⡙⡏⠉⠉⠁⠉⠉⡟⠉⢩⠁⠈⠉⢳
⠀⠀⠀⠈⠁⠒⠀⠤⠄⠀⠀⠒⠋⠉⠀⠀⠀⣿⠤⠄⠀⢸⠇⠂⠙⡀⠀⣿⣤⡜⡇⠀⠀⠀⠀⢀⣇⠀⠸⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠘⡄⠀⡠⠋⠀⠀⠀⠈⠤⡿⣀⠤⣿⠀⠀⠀⠴⠉⡿⠀⢰⠄⠀⡜⣧
⠀⠈⢶⠤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⡀⠰⠊⠀⠀⠀⠄⠀⠀⢈⡿⣄⣁⣿⡤⠒⠀⠀⠀⡏⠀⠀⢱⠊⠀⢻
⠀⠀⠈⠙⠛⠿⠓⠒⠒⠀⠀⠉⠀⠀⠒⠚⠉⠀⠀⠀⠀⠄⠀⠀⠐⠀⢸⣷⣛⣿⣿⠀⠀⠀⠀⠀⢛⣠⠔⠈⢣⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢤⡴⢿⣿⠛⠳⣽⢦⣄⡠⠴⠖⡻⣧⠀⠀⠘⣷⢼⡇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠀⠀⠲⠂⠀⠀⠀⠀⠀⣼⣸⡗⣦⣈⠀⠀⠀⣠⡀⠙⣾⣆⡀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠈⣟⠛⣌⣨⣿⡷⣤⡀⠀⠙⠦⣌⣻⣎⠘⢶⣻⣿⣟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣟⡉⠉⢻⡟⠲⢌⡡⢄⡀⠀⠙⠛⠷⣏⢹⣏⢿⠻⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠟⠛⢯⣿⠀⠀⠀⠀⠉⠢⣤⣀⡴⠞⣿⣿⣺⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲⣤⣤⡖⢿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣿⣿⠈⣢⣥⡀
⠀⠀⠀⠀⣀⣠⣤⣶⣦⣄⣠⣴⣆⣀⣀⣄⠀⢀⣤⡀⠀⠀⠀⠀⠀⢼⠟⠋⠉⠉⠙⢻⡆⢀⣀⡀⠀⠀⠀⠀⠀⢠⣟⠿
⠀⠀⠀⠀⠙⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠻⠛⠿⠶⠾⠷⠶⣶⣶⣶⣾⣿⣿⣿⣾⣷⣾⣿⣿⣦⡶⢶⣤⣤⣼⣥⣬⣧⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣀⡤⠤⢠⠾⠒⣲⠞⠛⠛⠒⠚⠓⠒⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠈⠉⠉⠋⠀⠒⠂⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠳⡀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠤⠾⣗⢚⣻⣿⡈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢶⣾⣴⠶⠒⠛⠛⢫⠉⠉⠘⣷⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⠅⣾⠛⡄⠐⠦⢀⠀⢼⣔⢄⠐⠈⠁⠐⢄
⠀⠀⠀⠀⠀⠀⡰⠋⡴⠋⠀⣿⠀⠘⢦⠙⣤⡉⠓⣿⡠⠈⠰⠆⢴⡄⢷⡤
⠀⠀⠀⠀⣠⠞⣡⠞⠀⠀⠀⠛⠀⠀⠀⠳⣐⠙⢦⢸⠀⢱⡶⣿⡁⠙⠢⢷⡄⠁⠀⢀
⠀⠀⠀⠘⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠈⢷⡃⠒⣺⡿⢷⡄⢤⣷⣤⡴⠞⠁
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡴⠾⢻⣖⣯⣿⣿⡌⣻⣆⣹⣿⡟⡉
⠀⠀⠈⠀⠀⠀⠀⢀⡀⢶⡾⠷⠿⠶⠟⠛⠛⠋⠉⠙⣷⣀⢲⡌⣻⣿⡅⠚⢞⠿⢄
⠀⠀⠀⠀⠀⢀⡞⢁⡅⣿⠟⣄⠀⠰⠄⠀⠀⠐⠂⠐⠛⢿⠫⣅⣼⡃⠹⢶⠙⢾⠀⢢⡀
⠀⠀⠀⠀⡴⠋⣰⠏⠀⣿⠀⠈⢦⠀⢢⠀⠀⠐⠤⢽⡗⢀⢳⡜⣻⣿⣧⣈⣿⡷⡇⠀⠻⡀
⠀⠀⣠⠞⣡⠞⠁⠀⠀⣿⠀⠀⠀⠳⡈⡆⠀⠀⠀⠈⠙⡟⠛⢯⣽⡓⠘⠟⠳⣷⣾⠓⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠
⢀⡾⢁⡴⠋⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⣄⠀⠀⠀⢧⠀⠘⣢⡶⢿⣿⣆⠀⢳⡆⠹⡓⠦⣄⣌⢧⡀⠀⠀⢀⣀⡤⢴⣻⠭⠖
⠁⠨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠐⢛⣷⡾⠛⢖⣻⣧⠼⢷⣶⡷⢶⡈⠀⠀⠉⠳⢷⠔⠺⠟⠛⠉⠁
⠀⠠⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⡴⠷⣾⣻⣟⣧⣭⣴⣿⢷⣖⠀⢿⣽⣾⣇⠀⠀⡠⢀
⠀⠀⠀⠀⠀⢴⣶⣾⣭⣭⣭⣭⣥⣶⡶⠶⠖⠲⠿⢿⡯⣽⢿⡆⢿⣞⣘⣆⣀⣽⢆⣽⢣⡼⡵⠋
⠀⠀⣠⠎⢻⢸⡿⢧⠈⠁⠂⣤⢀⠀⠀⠈⠓⢀⠀⠀⢷⡞⠒⣥⣾⣯⣀⣿⢳⣅⢊⣿⣣⢿⡡
⢀⡾⢃⣴⠋⢸⡇⠈⢳⡀⠀⢰⠀⠀⠁⠐⠆⣈⣿⠛⢉⣻⣖⠋⣿⣻⣿⣦⣠⣿⣿⢿⡇⠀⠑⣀
⠏⣠⡞⠁⠀⣿⡇⠀⠀⠹⣄⠀⣇⠀⠀⠀⠂⠛⠉⣿⡿⠏⠻⣏⣻⡷⠴⠻⣿⢷⣿⣶⡇⠀⠆⠘⢇
⡼⠋⠀⠀⠀⢿⠃⠀⠀⠀⠘⢧⡸⠀⠀⠀⢀⣴⠍⠌⢹⣄⢀⣉⣿⣷⣤⠂⠈⣧⣀⡝⢿⡲⠦⣄⠈⢧⠀⠀⠀⣀⣠⣤⣶⡾⠟
⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠈⠻⣄⡄⠀⢉⡱⣆⣀⣀⡱⣞⣡⣿⣿⠙⢶⣄⣈⢻⡄⠸⡃⠀⠀⠉⠛⠷⠐⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣗⠀⡈⢉⡹⢟⠉⢀⡼⣯⣿⣿⣏⠛⢿⠛⢾⡛⢶⡇⠀⢀⠔⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣁⣀⣈⣷⣾⡭⢹⣿⣿⣉⣇⠀⣱⣀⣛⢻⣿⡰⢯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣹⣷⣤⣿⡟⢣⣤⣊⣿⣿⡇⣠⣤⠤⡿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠁⣳⣟⡹⢧⣤⣻⣶⣿⣿⡿⣿⣶⠾⢋⣽⣿⠟⢷⡼⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠉⠀⠾⢲⡽⠋⢇⣠⡤⠛⢛⣿⣿⠸⣗⡛⣯⣶⣍⣾⣩⢳⣼⣧⡝⣶
⠀⠀⠀⠀⠀⠀⢀⡠⡞⠛⠛⠒⠒⡶⢺⡟⣶⠶⢾⣧⡤⣶⣯⢭⣿⣾⡿⢿⣾⣷⣿⠟⢿⡅⠹⣿⣇⠀⢣
⠀⠀⠀⢀⡤⠚⠁⠀⠉⢠⠀⠀⢴⣵⣷⣯⠴⠒⠁⢙⡖⢂⡠⠦⣿⢿⡟⣦⣄⣽⠻⡶⢾⣭⣷⣌⢻⣄⠀⢷⡀
⢀⡠⠚⠁⠀⠀⠀⠀⡼⣬⠠⣴⡿⢏⡉⠀⠀⠀⣠⡄⢛⠀⠀⢸⣿⣸⡇⠀⣼⠳⢦⡙⢆⡈⡙⠻⢿⣿⣤⣄⣳⡀⠀⣀⣠⣤⣴
⠛⢦⣀⠀⠀⠀⠀⠀⠸⡄⢀⡏⢹⡔⢀⣉⢵⠞⠁⠀⠀⢢⡴⠛⣿⠁⣿⣸⣏⣆⣀⣉⣻⣷⣤⠀⠦⡹⣷⣀⣉⠛⠈⠉⠉⠁
⠀⠀⠈⠑⠢⣄⠀⠀⢸⡇⠸⠀⡀⢷⡊⣰⠋⠀⠀⠀⠀⠉⡟⠂⣿⣤⣿⡧⠴⠛⠋⠉⠁⠞⠹⣦⣄⠁⣼⣿⡏
⠀⠀⠀⠀⠀⠈⠙⠲⢤⣧⠛⠉⠀⢠⣿⠁⠀⠀⠈⠂⠀⠀⠈⢠⣿⡍⣿⢷⡄⠀⠀⠀⢀⠀⢠⣝⣯⣿⣿⣿⡜⠄

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢄⣸⣶⣷⣾⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠛⠀⠠⣦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⠇⢀⣤⠀⢶⡆
⠀⠠⢼⣻⣿⣿⣿⡷⠄⠀⢀⣤⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠙⠃⠀⠀⠀⠉
⠀⠀⠊⣻⠿⡷⢟⠑⠂⠀⠀⠉⠀⣠⣦⣦⣼⣿⣦⣀⣄⣀⣴⣶⣶⣤⣄⠀⠀⠀⠀⠀⢸⣿⣦⣤⣤⣤⣤⣤⣤⣴⣤⣴⣶⣤
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣀⢀⠀⠿⠂⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⢸⠭⣿⣰⡆⠀⠀⢀⡶⠀⠀⠀⣆⠀⠀⢀⡀⠀⣀⠀⠰⡀⢸⣿⡇⠀⠀⢀⣦⠇⢠⡄⠀⠀⠀⠀⠀⡴⠀⠀⠀⢀⠄⠊
⠀⠀⢸⣴⣿⠈⡟⠀⠀⠸⡏⠁⠀⠙⣿⠀⠀⣾⣴⣶⣼⡆⠒⡇⢸⣿⡇⠀⠀⢸⣿⠀⣾⣿⠀⠀⡠⠤⠬⡷⠤⠐⠊⣁⣤⣾⡆
⠀⠀⠘⠛⠛⠀⠃⠀⠀⠀⠃⠀⠀⠀⠛⠀⠀⠛⠉⠉⠙⠃⠀⠃⠘⠛⠓⠀⠀⠀⠛⠀⠛⠛⠃⠀⠐⠒⠒⠓⠒⠒⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠩⠅⠻⠋⠉⡇
⠀⠀⠀⣀⠀⠀⢀⡀⢠⡀⠀⠀⠀⣤⢸⣿⣿⠀⠀⠀⢠⠍⢤⠀⠀⠀⢀⣀⠀⠀⠀⠀⠤⢠⡄⠀⠀⠀⡇⠀⠀⢀⣶⡀⣶⡇
⠀⠀⣿⡗⠀⠀⠈⠀⣿⡏⠀⠀⠸⣿⢺⣿⣿⠀⠀⠀⣟⠢⢺⠇⠀⠀⢈⣻⠓⠀⠀⢀⡀⣼⡇⠀⠀⠀⡇⠀⠀⢸⣧⠀⠙⡇
⠀⠀⠞⠛⠀⠀⠀⠀⠹⠁⠀⠀⠰⠋⠛⠛⠛⠀⠀⠀⠚⠀⠸⠀⠀⠀⠐⠉⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠧⠤⠤⠾⠼⠤⠤⠇

⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠶⠿⠛⠛⠛⠛⠻⠿⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⣠⣴⠿⠋⠁⡠⠒⠫⠭⣭⣙⣳⣦⣤⣄⠀⠉⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠉⠉⠉⣻⡿⠿⣷⣤⣄⡜⠁⠀⠀⣠⠾⠛⠛⠛⣿⠟⠀⠀⠀⠀⠈⠛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡖⠦⢤⣼⡟⠀⠀⠀⠈⠙⣷⡄⢠⣾⡇⠀⠘⠛⠓⣙⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⢩⣆⡀⠀⠀⠀⠘⣻⣇⠊⠁⠀⠀⠀⠀⠽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢹⠚⠻⢷⣤⣤⣄⡘⢻⠓⢦⢄⣀⣀⣀⣈⡟⠛⢿⣦⡀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢈⠄⠀⠀⢿⣾⣽⣿⣿⣶⣄⡠⣙⢿⣽⣁⠀⠀⢠⣽⣮⣢⡄⡀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⠀⠀⢠⢾⣿⡏⠻⣿⣿⣿⣿⣶⣭⡛⢧⣬⣕⣢⣌⡅⠀⠀⠈⡄⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⡀⢠⠇⢸⣿⡇⠀⠈⠻⣿⣿⣿⣿⣿⣷⣎⣙⠿⣿⣿⠀⠀⠀⢱⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⢡⣾⣦⣼⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠻⣼⣿⣿⡏⢷⡈⢇⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠘⡟⠿⣝⢿⢿⣿⣿⣄⢸⣿⣿⠉⠻⣿⣿⣿⣄⠈⠙⠿⣿⣸⡇⢘⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠱⠀⢹⣏⣿⡟⣿⣿⣿⠿⢿⣷⣄⠈⠙⢿⣿⣷⣦⡀⣬⢻⣷⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣵⡿⢿⣿⣧⡘⣿⣟⠣⡀⢠⡙⣿⣿⣿⣦⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⠀⠀⠀⠀⢀⣼⣿⡿⡟⠀⠉⣛⣿⣿⣿⣿⣷⣌⡢⣤⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡁⢀⣠⠶⠻⢿⣥⣀⣷⡀⠐⠾⠿⢿⣿⣿⣿⣿⣿⣮⣏⢈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣤⣷⣆⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢲⡷⠖⠛⠉⠋⠉⠸⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣⠊⢸⠈⢆⠇⡒⢹⡅⠠⠄⣨⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⠔⠁⠀⠈⠀⠀⠣⡍⠂⣂⡰⢺⣭⡓⣷⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣀⣠⣼⣦⣼⣶⡞⣽⢻⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⣿⠛⠛⠛⠉⢉⠉⣻⣆⡎⢻⢯⣙⣟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡱⠃⡇⠱⡀⠁⠀⠠⠤⡦⠉⡽⢿⣶⡹⣾⡆⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠎⠀⠀⠇⠀⠘⢎⠀⠀⠀⠉⢏⠛⣿⡈⢻⡻⣾⡂⠈⢆⠀⠀⠀⠀⠀⣀⣤⡴⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠁⠀⠀⠀⠀⠀⠀⠀⢣⡄⠨⣧⡴⢯⣽⡙⣦⣽⣼⠈⠛⠪⢧⡠⡴⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣤⣤⣤⠤⠴⢶⣳⣾⣿⢥⡥⢿⣶⠊⢿⡿⣄⢀⢄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢹⣟⠚⠛⡛⠛⠉⠩⠉⠋⣿⠯⣉⣽⡇⣳⣞⠷⣧⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠞⣸⠀⠣⡀⢈⠀⠀⠀⢼⣟⣃⣳⡚⣿⡿⣧⣼⣿⢿⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⢞⡴⠃⠀⣿⠀⠀⠱⣄⠆⠀⠀⢈⠜⢿⠉⠳⣾⣇⡙⢿⡛⢿⣄⡁⠱⡄⠀⠀⠀⣀⣠⣴⠶⠋⠃
⠀⠀⠀⠀⠀⠼⣡⠞⠀⠀⠀⠛⠀⠀⠀⠈⢦⡀⠀⣹⣄⣈⠵⣋⣿⡟⢦⣈⡿⡌⡇⠈⠑⠻⠄⠚⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⡟⠻⣆
⠀⠀⠀⠀⠀⣿⠛⢷⠀⠀⠸⣇⠀⢻⡄
⠀⠀⠀⠀⠀⣿⠀⠘⣇⠀⠀⢿⡀⠈⣷
⠀⠀⠀⠀⠀⢸⡇⠀⢹⡆⠀⢘⣧⠀⠸⣷⢶⣦
⠀⠀⠀⠀⠀⠀⢿⡄⠈⣿⡖⠋⠹⣧⣴⣿⡾⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡜⢷⣤⡿⠃⠀⢀⣠⡾⠋⠁⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⠙⠷⣦⡀
⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⣀⣀⡀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠙⢯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡟⠉⠉⠙⢷⡄⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⢻⡀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠤⢤⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠹⣆⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⡾⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⠻⢦⣀⣾⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⣹⠏⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠈⠙⠳⠦⣤⣄⣀⣀⣀⣀⣠⣽⠟⠁⠀⠀⢀⡿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢀⣴⠿⣅⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠞⠛⠁⠀⠙⢧⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⣌⠳⣄⡀⠀⠀⠀⠀⠀⣀⣴⠞⠁⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣈⡙⣺⡏⠛⠛⠖⠛⠛⠉⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⣀⣀⣤⣤⣤⠾⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢿⡄⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣿⣦⠶⠶⠛⠛⢋⠉⢁⣀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠛⠉⠁⣀⣠⣤⣴⣶⠟⣿⣿⡻⣆⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⢤⡶⠞⣛⣭⠿⠟⠉⠀⣠⠞⠻⣷⡙⣧⡀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣆⠀⠈⢿⡌⢻⣔⣄⣠⣴⡿⠷⠞⣛⣛⣥⡾⠗⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣆⠀⠈⢻⣄⠛⣋⣩⣤⠶⠞⠛⠉⠉⠀⠀⠀⠀⣀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⠀⢻⣆⠀⠀⠛⠛⠉⠁⠀⠀⠀⣀⣠⣤⡴⠶⠟⠛⠻⣆⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠹⣄⠀⢻⣆⠀⠀⠀⣠⣤⠶⠞⠛⢉⠁⠀⠀⠀⠀⠀⡀⠹⣧⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠘⣆⠀⠹⣆⠀⠀⠻⣆⠀⠰⣾⡿⠿⠀⠀⠀⠀⢸⣿⡄⠘⣷⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠘⢦⠀⠹⣧⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⢧⡀⠙⣧⡀⠀⠘⣷⡀⠀⢶⣿⡿⠆⠀⠀⢀⣀⣤⡴⠾⠃⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⢳⡀⠘⣷⡀⠀⠈⢷⡀⠀⣀⣤⡴⠶⠟⠋⠉⢀⣀⣠⣤⢶⣄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠳⡄⠈⢷⡄⠀⠈⠛⠛⠉⣀⣠⣤⠶⠾⠛⠋⠉⠁⠀⠀⢻⣆⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠙⣄⠈⢻⡄⠀⠀⢸⡟⠋⢉⣠⣤⣦⡀⠀⠀⠀⢠⣶⡀⠹⣦⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠈⢦⠀⢻⣆⠀⠀⠻⣆⠀⠙⠋⠉⠀⠀⠀⠀⠈⠛⠛⠀⠙⣧⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠈⢣⡀⠹⣦⠀⠀⠹⣧⠀⠀⢀⣤⣶⡄⠀⠀⠀⠀⠀⢀⣸⣷⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠳⡀⠙⣧⠀⠀⠙⣧⠀⠘⠛⠋⢁⣀⣤⣴⠶⠛⠛⠉⠀⠀⠀⠀⣹⣧
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠹⡄⠈⢷⡀⠀⠘⣷⣴⠶⠟⠛⠉⠁⠀⣀⣀⣤⣤⡶⠶⠟⠛⠉⣿
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠙⣆⠈⢻⣆⠀⠀⣀⣀⣤⣴⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠘⣆⠀⢹⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠚⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⢦⣸⡇⠀⠀⣀⣠⡤⠴⠚⠛⠉⠉⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢻⡖⠛⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠋⠉
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣸⡇⠀⠀⢀⣀⣤⣤⠶⠞⠛⠉⠉
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡶⠶⠛⠋⠉
⠀⠘

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⡾⠿⢿⠄⠀⠀⠀⠀⠀⢰⣿⣋⠀⠀⠀⠀⠀⣯⣭⣿⢀⡀⡄⠀⠀⠀⠀⢠⠏⢣⡀⠀⠀⠀⠀⠀⣠⣾⣷⣶
⠀⠀⢀⣧⣀⣰⡀⠀⠀⠀⠀⠀⠉⣿⠋⠀⠀⠀⠀⠀⣧⣠⣿⠸⣃⡇⠀⠀⠀⢠⠏⢺⠀⢳⡀⠀⠀⠀⢺⣿⡇⣸⣿⡗
⠀⠀⠸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠟⠀⠀⠀⠀⠧⠤⠥⠤⠤⠗⠀⠀⠀⠸⠻⠷⠿⠟⠃

⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⣀⡀⣤⡤
⠀⠰⢖⠿⠶⠿⡲⠆⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢀⣰⣷⠊⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⣴⡿⠛⢿⡄
⠀⠀⣷⣿⣿⣿⣾⠇⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠒⠋⠀⡇⠀⠀⠀⠀⠀⢀⣾⠞⠀⠀⠀⠀⠀⠀⢿⣦⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⢀⣦⣴⡀⠀⠀⠀⣾⡿⠿⠿⣿⠀⠀⠀⠀⣾⡿⠿⠿⣿⡆⠀⠀⠀⠀⡎⣉⡉⡦⠀⠀⠀⠀⠀⠀⠀⣼⣴⡦
⠀⠀⣷⠀⠀⢻⡟⠀⠀⠀⠀⣿⡐⠀⠂⣿⠀⠀⠀⠀⣿⠁⠈⠀⢹⡇⠀⠀⠀⠀⠇⠛⡧⣿⠀⠀⠀⠀⣤⠀⠀⢻⡿⠃
⠀⠀⠘⠲⠶⠋⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠀⠀⠀⠀⠻⠿⠿⠿⠿⠃⠀⠀⠀⠀⠣⠈⠁⠛⠀⠀⠀⠀⠙⠶⠶⠾⠁

⠀⠀⠀⡠⠤⢄⠀⠀⠀⠀⠀⢀⡠⣀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⣠⣶⣦⡄
⠀⠀⠸⡅⠀⢀⠇⠀⠀⠀⢀⢳⣿⡿⣻⣞⠆⠀⠀⢰⡟⠛⠛⠛⡛⣧⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠹⣽⣯⠇
⠀⠀⠀⠸⣤⠏⠀⠀⠀⠀⠈⢾⡟⠒⠚⣷⠇⠀⠀⠸⣇⣁⣀⣀⣁⡿⠀⠀⠀⠀⠰⢇⠹⠀⠀⠀⠀⠀⠘⢳⣯⣽⡛⠂
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠑⠃⠀⠀⠀⠀⠘⠋⠁⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⢀⠀⢨⠔⠄⠄⠄
⠀⠀⠀⠀⠈⠉⠁⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡀⠁⢈⠆⠤⠤⠄⠀⠀⠀⠀⢀⠠⠤⡀⠏⠓⠒⠒
⠀⠀⠀⠐⠈⠀⠈⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣄⣀⠀⠀⠀⠀⠀⠠⠀⠐⠁⡚⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠅⠹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡘⠂⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠄⢠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣃⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣠⢞⡥⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⡖⢋⣩⡼⠷⡄⠀⠀⠀⠀⠀⠀⢠⢞⡭⠂⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⡞⢡⠘⣿⡆
⠀⠀⠀⠀⣏⢸⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣼⠛⣉⣥⠴⠾⡇⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⡇
⠀⠀⠀⠀⠹⣌⠆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢼⣋⠉⣤⠶⡟⠁⠀⠀⠀⠀⠀⠀⣧⢣⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡧⢸⠀⣿⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣤⣿⣤⣧⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⣯⣼⣤⣿⡇
⠀⠀⠀⠀⠀⠈⣳⣶⣶⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠐⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿

⠀⠀⠀⠀⠀⣀⢀⣤⢠⣄⢀⡀⠀⠀⠀⠀⠀⠀⢠⠖⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⣤⣶⣤⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⣰⣞⠛⣶⡀
⠀⠀⠀⢀⣘⠋⢾⡏⠉⡽⠎⢛⣀⠀⠀⠀⠀⠀⠙⠦⣀⣬⣬⡃⣤⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⡿⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡙⠿⠾⠏⡁
⠀⠀⠀⠾⠿⠸⡿⠀⠀⢛⡿⠸⠿⠆⠀⠀⠀⠀⠀⢠⣿⣿⡸⢞⣵⢟⣀⠀⠀⠀⠀⠀⣧⣿⣿⡇⠀⠘⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡸⠁
⠀⠀⠀⢶⣶⠰⣿⡶⢠⣾⡷⢰⣶⠆⠀⠀⠀⠀⠀⠘⣿⣿⣧⣌⠡⠿⡋⠀⠀⠀⠀⠀⠹⣿⣿⣷⡗⣰⣿⣿⠇⠀⠀⠀⠀⠀⣠⠀⣾⣮⣩⣶⡆⢠⡀
⠀⠀⠀⠈⢩⣄⢶⣷⢻⣶⢆⣬⠉⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢻⡂⢯⡀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⠀⠿⠿⠿⠿⠇⢸⣿
⠀⠀⠀⠀⠀⠈⠀⠛⠘⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠑⠻⢦⡀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⣀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡀
⠀⠀⠀⣿⣿⣷⣿⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⢸⠟⢉⣉⠛⣿⠀⢠⢀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠻⣿⣿⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠳⣄
⠀⢀⡄⣿⣿⣿⣿⢰⣀⣠⣶⢾⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⣴⣴⠀⠀⠀⠀⠀⣿⣿⡈⠀⢁⣿⣿⠀⠀⠀⠀⠀⡞⠀⢠⡀⢙⣶⣄⠀⠀⠸⡆
⠀⠘⠇⣿⣿⣿⣿⢸⣿⠶⠶⢸⣿⠀⠀⠀⠀⠀⠀⣿⣶⣷⣾⣷⣿⠀⢿⢿⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⣿⠀⠀⢀⡇
⠀⠀⠀⣿⣿⣿⣿⠸⣿⠛⢻⢸⣿⠀⠀⠀⠀⠀⠀⠙⠿⣿⢿⠿⠟⠀⢸⢸⠄⠀⠀⠀⠀⣿⣿⣈⣠⣀⣿⣿⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠉⡇⢀⡼⠁
⠀⠀⠀⠛⠋⠩⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣄⣀⣠⣎⡞⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣤⠼⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄⠀⠀⠀⠀⢼⠄
⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⢫⣻⠇⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⢀⠰⠚⠋⠁⠸⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠀⠀⠀⣾⣭⣶⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣤⡤⢸⠩⣭⣭⡭⢻⠠⣤⡀
⠀⠀⠀⠉⠛⠗⣶⣶⣤⣀⡀⡶⠒⢦⠀⠀⠀⠀⠀⠀⢨⡿⢿⡅⠀⣴⡟⠉⢻⣆⠀⠀⠀⣶⡆⠀⢬⡥⠀⢠⣥⠀⠀⠀⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡆
⠀⠀⢠⣶⣶⣴⣬⣿⣿⣿⣿⣿⣾⣿⣷⣦⣄⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⣾⣧⠀⢸⣷⠀⠀⠀⠿⠟⣵⡎⠿⠿⠿⠿⠏⣶⠹⠿⠃
⠀⠀⠘⠿⣟⢙⡿⠿⠿⠿⠿⠿⢿⡟⢙⡿⠿⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⡟⠀⠀⠀⣿⡇⠀⣿⣿⠀⢸⣿⠀⠀⠀⢸⣿⣮⣴⣿⣿⣿⣿⣷⣭⣾⣿
⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠉⠀⠀⠉⠀⠉⠀⠀⠀⠃⠀⠀⠀⠙⠁⠀⠙⠋⠀⠈⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠒⠛⠛⠛⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠏
⠀⠀⠀⠀⠀⡴⠋⣠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣴⠃⢀⣤⡀⠀⠀⠀⡀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⡼⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠈⠀⠊⠉⢀⠀⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉
⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠠⠾⠂⠈⠅⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠐⢇⠀⠳⠀⠀⠀⠈⠃⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠈⡆⠂⠠⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢲⠀⠠⠄⠀⣴⡱⠁⠀⠀⠀⠀⠀⠀⠀⢀⣷⣰⣤⠇⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢰⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⣚⠜⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠉⠉⠉⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣾⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡠⠄⠒⠀⠀⠀⠉⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⢀⡇⡾⠀⠀⢀⠀⠀⢀⣠⠴⠋⠀⠀⢀⣤⣴⣦⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⢠⡛⠤⣄⡀⣼⢸⡃⠀⠀⠀⣰⠞⠋⠁⠀⠀⠀⣠⠟⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣠⠔⠂⠉⠁
⠀⠀⠀⠀⠀⢨⠙⢦⡀⠀⠉⠉⠉⠉⠉⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠰⡁
⠀⠀⠀⠀⠀⢻⠙⠒⠤⣄⡀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂⢁⡠⢖⡩⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠑⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⢀⣬⠄⠀⠀⠀⠀⠀⠀⡾⢧⣄⠀⠀⠈⣓⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⣶⣦⡴⠃⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⣀⠴⢫⡼⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠤⠤⠴⠤⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⣀⡤⣾⡵⠛⠉⠀⠀⠀⢀⣾⣷⡦
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡚⠁⠀⠀⢠⣞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡀
⠀⠀⡨⠂⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠄⣨⡽⠃⠀⠀⠀⣈⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠈⠠⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡠⠚⠁⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠘⠒⠀⠠⠔⠃⠀⠀⠀⢀⡜⠉⡄
⠀⠀⠀⠂⠊⠉⠂⠀⠈⠁⠀⢀⡴⠋⠁⠀⠀⣀⠴⠋⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⣤⡄⠀⠀⠸⣅⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠓⠲⠶⠶⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣴⠋⠁⠀⠀⠀⣀⣹⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⣠⠴⠊⠁⢠⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢀⡠⠔⠋⠀⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⡀⠈⠣⣀⠤⠖⢻⠀⠀⠉⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⣠⢞⣠⠖⠋⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⢀⣴⠷⠋⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠔⠒⢢⡀⠘⠀⠀⠀⠁⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠠⡞⠁⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢣⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡞⠁
⠀⠀⠀⠀⢰⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠹⠄⠀⠈⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠒⠛⠋⠁

⠀⠀⢠⡶⠞⠛⠻⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⢸⡇⠀⠀⠀⠀⢿⡟⢧⡀⣀⣀⣀⠀⢀⡼⢿⡟⠉⠀⠈⢻⣆
⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⣬⣿⠿⠉⠉⠛⢿⣷⡞⠁⠀⠀⠀⠀⢻⡆
⠀⠀⠀⢻⡄⠀⠀⠀⢰⣿⣿⣿⡶⠄⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡄⠀⢰⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⢻⡄⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⣀⣀⣀⣀⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣀⣀⣀⣀
⠀⣿⣿⣿⣿⣇⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⣿⣿⡿⣿
⠀⣿⣿⣧⣸⣿⣾⣿⣿⣿⣿⣟⣛⣛⣛⣛⠛⠛⣻⡿⢿⣿⣿⣿⡇⣿
⠀⣿⣿⣿⡛⣿⣿⣿⣿⣛⣛⣛⣛⣻⣿⣟⣛⣿⣿⣛⣻⣿⣿⣿⠃⣿
⠀⣿⡇⣿⡇⣿⡏⠙⠛⠛⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⡆⣿⡆
⠀⣿⣇⣿⢧⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⢻⡇
⠀⢻⣿⠹⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡇⢱⢸⡇
⠀⢸⣿⡇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⣿⣿⣟⣿⣿⣿⢸⡇
⠀⢸⣿⠇⡇⣿⡿⠟⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠷⠻⣿⣿⣿⢸⡇
⠀⢸⣿⡀⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⢸⡇
⠀⢸⣿⡇⡏⣿⣷⣶⣶⣶⣶⣶⡶⠶⣶⣶⣿⣿⣿⣷⠶⣶⣿⣧⢻⣸⣇⠀⡀
⠀⢸⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⢸⣿⣿⣷⣿⣿⡟⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⢿⣿⣿⣿⣸⣿⣿⡟⠿⡟⣿
⢰⣾⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣽⣿⣦⣤⣀
⢸⣿⣿⠛⣴⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⡟⢿⣿⣿⣿⢿⣿⣿⢿⣿⣷⡀
⠘⢿⣄⠻⣿⣷⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠙⡇⠀⠙⢿⣿⣿⣯⣿⡛⠿⣿⢷⡀
⠀⠀⢹⣦⡘⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣶⡿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠹⣿⣿⣷⡝⠳⢿⣧⣇
⠀⠀⢸⣿⣿⣿⣿⣿⡿⡝⢟⣿⣿⡇⠈⢿⣿⣮⡳⣿⡗⠹⣿⣿⡽⣿⣿⣷⣄⠀⠀⠙⢿⣿⣽⣷⣾⡿⠿⠁
⠀⠀⢘⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡇⢪⡻⣿⣿⣾⣿⣦⡙⠻⣿⣮⠻⣿⡻⣷⣄⠀⠈⢻⣿⡅⣿⡇
⠀⠀⠀⣿⡿⠙⣿⣿⣿⣿⣿⣿⡿⠼⢿⣆⠑⡌⠈⢿⣿⣯⠿⣆⠈⠻⣷⡌⠙⢿⡿⣧⡀⢸⣿⡇⣿⡇
⠀⠀⠘⣿⢇⢸⣿⡎⢻⣿⣿⡿⣷⣀⣈⣻⣷⣌⣢⣀⣻⣿⣧⣌⣧⣄⡙⣿⣦⣠⡝⣎⣻⣦⣿⣇⣿⡇
⠀⠀⠀⣿⡞⡀⣿⣷⣼⣿⢿⡏⣿⣿⣿⣿⠿⠛⠛⡛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠃
⠀⠀⢸⣿⡇⣽⣿⠀⢻⣿⢺⣇⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡄
⣶⣶⣾⣿⡇⢸⣿⣤⣼⣿⢸⣿⣹⣿⣤⣤⣀⣀⣀⣀⣀⣸⣿⣿⢠⣿⣄⣀⣀⣀⠀⠀⠀⣹⡿⣿⣿⡇
⠸⣿⣿⣿⡇⢸⣿⣿⣿⣿⠈⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⣿⣿⠿⡛⠛⢿⣿⣿⡇⢿⣿⣿⡶⣶⣦
⠀⢿⡿⢿⣿⣿⣿⣿⣿⣿⠀⢷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣷⣦⡀⠀⠀⢸⡇⢸⡿⣿⡇⠉⠹⣧
⠀⠸⣧⠈⠻⣿⣿⣿⣿⣿⣾⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣿⡇⢸⡟⣿⡇⠀⠀⠹⣇
⠀⠀⣿⡀⠀⠀⠙⢿⣿⣿⠗⣿⣏⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣸⢨⣿⣿⡀⠀⠀⠀⢻⣆
⠀⠀⠸⣧⠀⡀⠀⠀⠙⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠆⠈⠦⠀⠀⠰⢄⠈⠙⠻⢿⢿⢿⡿⠿⣿⠇⠀⠀⡀⠀⢻⡆
⠀⠀⠀⢿⣇⠙⡄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠤⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢈⣿
⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⢿⠿⢿⡿⠛⡿⠿⣿⣿⠿⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣶⣼⣷⣴⣧⣤⣿⣴⣼⣿⣴⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣆⠀⠀⠶⢿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠉⠁⠀⠀⠀⠀⠈⠙⠃⠀⠀⠈⠉⠙⠻⠿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇
⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⢠⣤⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷
⠀⠀⠀⠹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢛⣿⣿⣿⣿⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⡀
⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⣀⣰⣦⣄⡀⠀⠀⠀⣠⣴⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢿⣿⣿⠿⠛⠀⠀⠘⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉

⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⣀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢒⠂⠀⠀⠐⡄
⠀⢠⠁⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⠚⠀⡄⠀⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢨⠀⠀⢣⠃
⠀⠈⠀⠀⠙⠀⠀⡇⠀⠀⠀⠀⠀⢀⠸⡿⠀⠆⠀⠀⡇⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⣨⠒⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢋⢺⠀⠀⢸
⠀⢨⠁⠀⣉⠉⠉⡇⠀⠀⠀⠀⠀⢰⠤⠷⠄⠗⠒⠗⠃⠲⠅⡇⠀⠀⠀⠀⠀⡠⢂⡡⠘⣿⠃⠌⡐⢄⠀⠀⠀⠀⠀⠀⠀⢪⠉⠙⡄⢠⣚⡢
⠀⠰⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢨⢁⠂⠊⠒⠂⠒⠀⣤⠸⠃⠀⠀⠀⠀⠈⠂⠁⠀⠀⣿⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⢡⠀⠀⠆⠀⠁⡇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠗⠖⠀⠀⠀⠃


⠀⠀⡠⣄⠀⣀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡤⠤⢄
⠀⢨⠊⣀⣀⣀⡑⡱⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠔⠐⢀⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡄⠈⠉⠁⡀⡌⠀⣄
⠀⢰⡘⠒⠒⠒⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠓⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠐⠁⡕⠄⠋
⠀⠰⢮⣒⣀⣐⡴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠔⡋⢉⢹⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠆⣈⣉⣉⣉⢁⡠⠀⠀⠀⠀⠀⠀⠀⡆⢤⠔⠠⡂⠀⠁⠐⠛
⠀⠘⠷⠤⠄⠤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⢡⠂⠒⢂⠁⡇⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⢇⡈⣋⣈⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⣠⣤⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢰⢱⡤⡄⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠙⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⢀⡔⠁⠀⠈⠁
⠈⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⠈⠁⠃⠀⡎⠘⢑⠀⠀⠀⠀⠀⠀⠀⠀⢆⣃⣠⡄⡆⠀⠒⠁⠀⠀⠀⠀⠀⠀⠁⠀⡧⡤⠀⠀⢠⢤
⠀⠀⠘⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠓⠚⡀⠀⡀⢄⠀⠀⠀⠀⠀⠀⡩⠩⠀⡅⠣⣭⠁⢄⠡⠈⠂⠀⠀⠀⠠⡲⠓⠂⣇⠁⠀⠀⡠⠊
⡄⠀⠄⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⠘⠐⢸⡀⠀⠀⠀⠀⠉⠑⣈⠀⡁⢾⡤⠤⠤⠤⠤⠴⠀⠀⠀⠀⠈⠆⠀⢸⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠾⠖⠒⠚⠁

⠀⠀⠀⡀⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀
⠀⠀⢨⣾⡿⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣈⢨⡉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢆⠰⠸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣐⡀⣂⠈
⠀⠀⢘⠷⣿⠝⡁⠀⠀⠀⠀⠀⠀⠀⠘⠀⢩⢀⡅⢀⡀⢈⠀⠱⠀⠀⠀⠀⠀⠘⣋⠞⠖⣛⡱⠷⣙⡃⠀⠀⠀⠀⠀⠀⣐⠉⠉⡆⢀⠉⣁⠉⢀
⠀⠀⠸⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣃⣀⠁⠠⠀⠀⡆⠀⠀⠀⠀⠈⠉⢘⠃⣭⡘⡃⠈⠁⠀⠀⠀⠀⠀⡎⠤⢑⠀⡇⠀⠀⠘
⠀⠀⠀⢄⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⢈⣀⣠⣀⣈⣀⣀⣀⣀⣈⠀⠀⠀⠀⠀⠠⠠⠾⠈⠭⠉⠷⠄⢄⠀⠀⠀⠀⠀⢻⡶⡞⠀⠁⠀⠀⠈
⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠠⠀⠄⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡈⢌⡀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢠⠴⠊⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⢀⣠⣤⡤⠤⠀⠤⠄⠀⠀⠁⠀⠀⠀⡏⠀⠀⠀⠀⢀⣠⣤⣶⣞⣿⣿⠿⠗⠛⠋⠁
⠀⠀⢠⡶⣏⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⢾⣟⣿⣿⡿⠟⠛⠉
⠀⢀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣳⡾⠟⠛⠉
⠀⢸⠁⠀⠀⠀⢠⣤⡄⠈⠀⠁⠀⠀⠀⠀⠀⠈⡘⠁
⠀⠈⠀⠀⠀⠀⠈⣿⣿⡆
⠀⠀⠆⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠘
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠢

⣿⡟⣛⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⣼⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⢠⣿⡿⠿⠛⠛⠿⢃⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠈⣿⠿⠟⢋⣉⣤⣤⣶⣾⣿⣷⡀⢺⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⣿⣿⣿⠇⠹⣿⣿⣿⣿⣿⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣈⣉⣙⢋⣠⣄⡙⠛⠻⠿⠟⠀⠹⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣦⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣧⠀⣉⣉⣉⣙⣛⠁⣼⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⠿⠿⠿⠻⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡛⣛⣛⡛⢛⣻⣿⣿⠿⠿⢿⡿⠿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⡿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣼⣿⣿⣧⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⢀⡴⣚⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢚⣷⡀⠀⠀⠀⠀⠀⠀⢀⠴⡛⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⢠⠞⠛⣷⡄
⠀⠀⡞⣸⠁⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣸⠶⢛⣉⡥⣟⠀⠀⠀⠀⠀⢠⢏⡎⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⢸⠈⡇⣿⡇
⠀⠀⢻⡘⡄⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣽⠚⢉⡥⣶⠋⠀⠀⠀⠀⠀⠸⡜⡆⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠀⡇⣿⡇
⠀⠀⠀⢻⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢉⣯⣼⣧⣭⡄⠀⠀⠀⠀⠀⠀⠹⢄⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⣈⣃⣛⡇
⠀⠀⠀⠈⣳⣶⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃
⠀⠀⠀⠀⠘⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢀⡤⣠⣦⣴⡄⢤⡀⠀⠀⠀⠀⠀⣴⠋⠲⠄⣀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣶⣾⣷⣶⣶⣶⠀⠀⠀⠀⠀⠀⢰⣿⣉⣿⡄
⠀⢠⣮⢁⣽⠁⢰⣯⡨⣵⡄⠀⠀⠀⠀⠈⢡⣶⡿⢮⡰⣀⡀⠀⠀⠀⠀⢸⡇⣿⣿⠁⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⠈⠛⢁⡆
⠀⢘⣛⢈⣯⣄⢀⣼⡁⣻⡃⠀⠀⠀⠀⠀⢸⣿⣷⠉⠾⣫⡶⠀⠀⠀⠀⠈⣧⣿⣿⣤⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⢀⡣⠤⣊⡀
⠀⠸⠟⠘⣻⣧⣞⣛⢑⠻⠃⠀⠀⠀⠀⠀⢨⣿⣿⣿⣦⡍⢰⠀⠀⠀⠀⠀⠘⢿⣿⣿⣼⣿⡿⠁⠀⠀⠀⠀⣴⡇⢸⣿⣾⣿⡇⢸⣦
⠀⠀⠈⠳⠙⠇⠾⠋⠚⠁⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠁⠑⠨⠦⣀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⣿⣷⣾⣿⠛⠛⠛⠛⣿⡇⠀⠀⠀⠀⠀⣿⠛⣉⡙⢿⠀⢠⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⣿⣿⠀⠀⠀⠀⠀⢠⠖⠋⠁⠀⠈⠙⠲⡀
⡀⣿⣿⣿⣿⢰⣒⣰⡶⣿⡇⠀⠀⠀⠀⠀⣿⣾⣿⣷⣿⡄⢸⣴⠀⠀⠀⠀⢀⣿⣇⣡⣀⣸⣿⠀⠀⠀⠀⢠⡇⠀⣄⢈⣦⣄⠀⠀⢹
⠧⣿⣿⣿⣿⢸⡷⠶⢆⣿⡇⠀⠀⠀⠀⠀⣿⣾⣷⣷⣾⡇⢸⢿⠀⠀⠀⠀⢸⣿⠏⠙⠛⢻⡛⠀⠀⠀⠀⢸⡇⠀⠘⢿⣿⣿⡅⠀⢸
⠀⣿⣿⣿⡿⠸⠯⠉⠅⣿⡇⠀⠀⠀⠀⠀⠙⠛⡟⡟⠛⠀⢸⢸⠀⠀⠀⠀⢸⣿⣇⣁⣀⣽⣟⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠈⡷⣠⡟
⠀⠉⠉⠐⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠳⠧⣄⠤⠮⠞⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⡟⠀⠀⣄
⠀⢀⣠⠴⠆⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⣰⡷⣁⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⡆⠀⠀⠀⠀⠀⠀⡶⠶⠶⠶⢶
⠈⠰⢦⣄⣤⣄⡉⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⢰⣯⡦⠀⢀⣽⠟⣿⡄⠀⠀⢀⣧⠀⢀⣃⠀⠀⠇⠀⠀⠀⣴⣋⣁⣃⣉⣉⣉⣘⣈⣙
⠀⣀⣀⣀⣙⣿⣿⣷⣼⣦⣼⣧⣄⡀⠀⠀⢠⡟⠁⢻⡆⢸⠇⠀⠈⣿⠀⠀⢠⣿⠀⢸⣿⠀⢸⣿⠀⠀⠀⣿⡟⣟⢿⣿⣿⣿⡟⣻⢻
⠀⠿⡿⠻⡿⡿⠿⠿⠿⠿⣿⠛⣿⠿⠀⠀⠸⡇⠀⢸⡇⢸⡄⠀⠀⡏⠀⠀⢸⣿⠀⢸⣿⠀⢸⣿⠀⠀⠀⣶⣦⣯⣶⣶⣶⣶⣦⣿⣴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⡀⠀⠀⠀⡏⢹⠏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡉⠓⠚⠯⠭⣿⣗⣶⡷⢼⣇⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢲⡶⣤⣤⣈⣉⢿⠟⠲⠾⢭⣽⣓⡲⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠋⢁⡿⠿⡾⢛⡟⢻⡖⢶⣤⣤⣈⣉⠙⠒⡞⣻⣄⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⢀⡴⠋⠀⠀⠀⢸⡇⢸⣧⣾⢿⣤⠟⣿⣟⣻⡿⣏⣀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄
⠀⠀⠀⠀⠀⠛⠒⠒⠛⠋⠉⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⢸⣧⢾⡇⣿⠀⢀⡼⠉⠛⠋⠀⠀⠉⠉⠙⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠒⢫⡷⣛⠛⠒⠦⢤⣄⣴⢻⡇⢸⡇⣿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⣉⡵⠶⠾⣥⣉⡙⠛⢺⡷⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠻⣮⣽⠟⣶⡦⣤⣨⣽⢿⠻⠦⣤⣉⣙⠛⠶⢤⣄⣀
⠀⠀⠀⣄⣀⣀⣀⣠⠤⠖⠋⠀⠀⠀⠀⠀⠀⣠⠟⠳⠞⠋⢹⡗⢶⣤⣄⣀⠉⠙⠓⠶⢤⡽⢿⡄⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⢸⡇⢸⡄⣿⣿⣹⣷⣶⡦⣤⣧⠞⠉⠉⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⡏⣿⠀⠀⣨⠟⠒⠋⠙⠒⠦⠤⠤⠤⠤⠤⠴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢺⡇⢸⡇⣿⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠶⠚⠋⠉⠀⠀⢸⠆⢸⡤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠤⢾⠋⢹⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣸⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣸⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⠻⣿⣿⡟⠛⢛⣛⡛⠛⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⢸⣿⢹⡇⠀⣿⢻⡇⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⢸⡇⠀⣿⢸⡇⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠿⠿⠃⠀⠛⠛⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣠⣦⣀⠀⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⢟⣼⠏⠀⣠⣄⠀⣹⣿⡁⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣄⣀⣼⢯⣾⣇⠀⣴⢟⣿⢿⣯⣬⣿⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠛⢷⣦⣉⣿⣧⣿⡁⢙⣿⢫⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠈⠙⠿⣯⣍⢻⣿⣳⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣟⠛⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⠻⣷⠀⢰⣶⣶⠀⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢸⣿⠀⢸⣿⣿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⣿⣸⣿⠀⢸⣿⣿⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠙⠻⣦⣄⡀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠉⠉⣡⣶⣤⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠉⣻⡷⠶⡶⢶⡟⠁⠀⠀⠀⠀⠀⠻⣿⠿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢹⣿⣶⣤⣴⠟⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣾⠛⣷⡀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢀⣴⠟⢹⡇⠈⠁⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣤⣤⣿⣿⣿⣧⣤⣤⣤⣴⠿⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢁⣴⡿⠁⠀⠘⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⢀⣴⡾⠋⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⢀⣤⡾⠋⠁
⣀⣠⣤⣴⠶⠞⠛⠉⢀⣠⣴⠾⠋⠁
⠉⠉⣀⣀⣠⣤⡶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣽⣯⣿⢷⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄⢀⣀⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⣿⣿⡏⢘⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣿⣿⣧⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⡿⢿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣾⣿⣿⣿⡆⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠾⡿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠙⠿⡿⠟⠁⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠒⡗⠂⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣋⠵⢊⠓⣧⠀⠰⠄⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⣩⠔⢊⡤⠚⠉⡆⢿⠀⠀⠀⠀⢀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⣀⡴⠚⡡⠔⠋⢠⠊⣁⠀⢺⡇⡇⢸⠀⣸⣿⣿⣿⢸⡏⡍⠭⢝⢦⣤⣀⠀⠀⠀⠀⣀⣠⠄
⠀⠀⢀⡴⢞⡡⠖⢉⡤⡆⠀⠘⡀⣿⠀⠈⠀⡇⢸⠀⠛⠿⠿⢿⢸⡇⠀⢀⡨⣸⣿⠿⢿⣟⣶⣯⠿⠚⠃
⠀⢸⢯⣖⢉⡤⠒⢁⣤⢰⠀⠀⡇⠀⣠⣄⠀⡇⢸⠀⠀⠛⠛⢻⣼⠷⠿⠿⠞⠃⠀⣠⢟⡽⠛⢮⢷⡀
⠀⢸⢸⠀⡇⢴⡆⠀⠿⢸⠀⠀⡇⠀⢛⡡⠖⣩⡾⠀⢀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢠⣯⡏⠀⠀⠈⣿⡇
⠀⢸⢸⠀⢣⠘⠃⠀⠀⢸⠀⠀⠧⠚⢁⡴⠞⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⣇⠀⠀⣠⣿⡇
⠀⢸⡌⡄⢸⠀⢰⡶⢂⡸⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢬⣿⣿⠽⠛
⠀⢸⡇⡇⢸⢀⡠⠖⠉⣠⠴⠋
⠀⠈⡇⡇⡈⠁⣠⠴⠋⠁
⠀⠀⢷⣤⠷⠋⠁

⠀⠀⠀⣤⣶⣶⣦⡀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⣤⡶⢶⣦⠀⠀⠀⠀⠀⣴⣶⣶⣦⡀⠀⠀⠀⢀⣀⣦⢴⣆⡀
⠀⠀⢸⣿⣏⣹⣿⡇⠀⠀⠀⠰⣿⣏⣹⣿⡇⠀⠀⠀⢸⣏⠀⠀⣹⡇⠀⠀⠀⢸⣿⣏⣹⣿⡇⠀⠀⠀⢈⣿⠀⠀⣿⡁
⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠛⠿⠿⠛⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠈⠟⠻⠇
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢠⡿⢋⣙⢿⡄⠀⠀⠀⢠⡾⡯⢽⢿⡄⠀⠀⠀⢀⣾⡿⢿⣷⡄⠀⠀⠀⢀⡞⠉⠉⢳⡄⠀⠀⠀⢠⣞⣫⣽⣻⡄
⠀⠀⠘⣷⣌⣫⣼⠃⠀⠀⠀⠘⢷⣗⣺⣾⠃⠀⠀⠀⠘⢿⣿⣾⡿⠃⠀⠀⠀⠈⢧⣀⣀⡼⠃⠀⠀⠀⠘⢯⣝⣻⣽⠃
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⣤⣰⣦⣠⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠰⣟⣱⣞⣹⠦⠀⠀⠀⠠⣿⡫⠝⣿⡆⠀⠀⠀⢰⣿⡟⢹⣿⡇⠀⠀⠀⢰⣿⣟⢻⣿⣇⠀⠀⠀⢰⣿⡋⢙⣿⡆
⠀⠀⠀⠛⢳⡞⠛⠀⠀⠀⠀⠀⠻⠿⠾⠟⠁⠀⠀⠀⠈⠻⣿⣿⠟⠁⠀⠀⠀⠈⠥⡤⠿⠿⠃⠀⠀⠀⠈⠻⣿⣿⠿⠁

⠀⠀⢀⣾⡿⢿⣷⡄⠀⠀⠀⢀⣶⢿⡻⣶⡀⠀⠀⠀⢀⣶⡿⢿⣶⡀⠀⠀⠀⢀⡶⣿⣿⢷⡄⠀⠀⠀⠀⡴⠓⠓⢦⡀
⠀⠀⠸⣿⣦⣠⣿⡇⠀⠀⠀⠸⣷⣻⢟⣾⠇⠀⠀⠀⠰⣿⣄⣠⣿⠇⠀⠀⠀⠸⣿⣿⣿⣽⠇⠀⠀⠀⠸⣇⠘⠃⣸⡇
⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⣀⠴⢄⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠒⠒⠁⠀⢀⣀⣀⣀⡀⠀⠁⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠔⠀⢁⠤⠒⠉⠉⠁⠀⠈⠉⠉⠒⠦⡀⠀⠀⠈⠓⠢⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡁⠀⢀⠔⡁⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡎⠀⠀⠀⠀⠀⢶⠀⣳⠤⣧⠃⠀⠀⠀⠈⡆⠀⢀⡀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡉⠀⠀⠀⠸⠀⠀⠀⠀⠀⢶⠋⠁⠀⠀⢈⡵⠀⠀⠀⠄⠃⠀⠈⠁⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠐⡄⠀⠀⠀⠀⠈⡆⠀⠀⠀⡞⠀⠀⡀⡄⠂⡇⠀⠤⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠙⣄⠐⣀⠀⠀⢠⠀⠀⢰⠀⠠⠐⠆⢀⡜⠀⠀⠀⡔⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠯⠤⣁⠀⠀⠀⠑⠢⢄⠒⠈⢀⡄⡆⠔⠃⣀⠔⠋⠀⣄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠔⠀⠉⠀⢠⣀⣄⣁⣁⣸⠉⠀⠂⠀⡠⠒⠒⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⣄⣠⣄⣀⣸⡀⠁⠉⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠊⡵⣻⠟⣚⡿⣆⠑⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⣀⢤⡮⣊⠔⠪⠔⡙⢮⡃⠶⣠⡄⢉⡉⡉⠉⠉⠉⠉⠉⢉⡁⠐⠒⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⣀⢤⡂⠍⠊⠕⡨⠔⣩⢔⡩⢒⡡⢈⡩⢀⠰⢋⡱⢖⠲⢀⠀⡰⢎⠉⢉⠝⣋⠔⡊⠙⠴⣪⢕⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠠⣺⠟⢁⢠⣀⡀⢀⡡⢒⡿⠡⠋⢉⣙⣮⣕⣈⣥⣊⡕⣪⣕⣞⠐⣳⢞⡝⠋⠙⢺⡔⣨⣖⡩⣒⠴⠉⠻⡝⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣾⠁⠠⣼⠚⠁⡇⢀⡪⡞⢁⠇⢀⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡉⢻⣷⠀⢇⠀⠀⠈⣙⠗⠁⠀⠓⠘
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠹⢷⢄⡀⠉⠐⠗⣄⠡⠁⠀⠀⣜⠀⢥⠶⠶⡄⠀⠀⠀⠀⠀⡤⠌⠥⡀⡇⢸⣹⠀⠈⠲⠤⠎⠀⠀⢀⠔⡴⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠔⡠⡉⢛⠳⡒⣦⣤⣎⠝⡇⣼⡇⡸⠀⠀⠉⠁⠀⠀⢀⠀⠈⠁⣆⡖⠻⠀⠼⣿⠴⠷⢟⠶⣶⣶⣬⣵⡾⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠥⠌⢤⠁⢀⠬⣭⣀⠈⢻⠳⢒⡶⠖⡳⢯⡾⢬⡬⠶⠶⡥⠧⠶⣦⠚⠀⣀⣠⣄⣮⣽⣭⡥⠵⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠕⢊⠤⠊⡉⠿⢊⠡⣐⠟⣂⠅⢂⠡⢐⡡⠄⢡⠀⠸⠅⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣊⠥⢒⠩⢐⡪⠔⢸⠋⢣⠀⢊⠥⢂⠥⢒⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠔⣊⠅⢊⠥⠒⠃⡌⠀⠘⡄⠑⣊⠅⢊⠥⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⡩⠔⣊⠡⠔⣊⠁⠇⠀⠀⠇⠨⠔⣊⠥⢐⡉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠐⡩⠔⣂⠭⡀⢰⢀⠀⢀⢠⠐⡩⠔⣊⠥⢔⠂⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡀⠄⣴⠁⠀⠀⠀⠀⠀⠀⢀⣠⣬⠕⢊⡡⢞⠀⠀⠉⠒⠩⠥⠀⣸⠥⠂⣠⢔⡠⠂⢀⡤⠀⣀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠉⠤⠛⠱⠖⣒⠶⣚⠝⠋⣉⠤⠊⣡⠔⢊⡱⠦⣄⣀⣀⡠⢖⡡⢒⠽⢊⡡⠔⢊⡡⢒⡩⢖⡩⢒⡡⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠊⠁⠐⠉⠐⠋⠠⠚⠁⠊⠁⠐⠁⠠⠚⠁⠒⠁⠐⠉⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠰⡂
⠀⠀⠀⠉⠉⠈⠉⠁⠀⠈⠋⠃⠀⠀⠀⠀⠀⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠅⠈⢢⠤⠄⠀⠨⠄⠁⣄
⠀⠀⠀⠀⠀⢰⡖⠈⠒⠠⡌⠒⠂⢰⡤⠒⠀⢰⠆⠘⠋⢰⣦
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢙⠄⠀⠈⠋⠀⡠⡎⠀⠀⠀⢈⠏
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠖⠦⠀⠀⣴⠑⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠳⠀⣡⣤⠀⠷⠁⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣊⠀⠈⢁⠂⠀⠀⠀⠀⠀⠀⢀⡜⠧⣀⠀⡜⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡁⠐⡸⡄⠀⠀⠀⠀⠰⠏⠉⢲⡉⠸⠛⣸⠋⠉⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⡴⠁⢱⡀⠀⠀⠀⠀⠀⠀⠈⡳⠀⠰⡃⠀⠀⠀⠀⡀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡼⠹⣄⣀⣇⠀⠀⠀⠀⠀⠀⠀⢡⠛⢣⠁⠀⠀⠘⠁⠠⠘⠃⡌⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡼⠁⠀⠘⣄⣸⡀⠀⠀⠀⠀⠀⠀⡈⢠⠌⡄⠀⠀⠀⠀⠀⠰⢎⠀⠀⢀⠀⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡼⠁⠀⠀⠀⠈⣦⣥⠀⠀⠀⠀⠀⢠⣧⠎⢣⣳⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⣸⠏⠀⠀⠻⡇⠀⠀⠀⢰⠇⠈⢧⠀⠀⠀⡄⢀
⣀⣀⣀⣀⣀⣀⣤⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣯⣤⣤⣤⣤⣿⣤⣤⣤⣮⣤⣤⣬⣦⣤⣴⣤⣬⣦⣤⣤⣧⣤⣤⣄⣀⣀
⣿⣇⣸⣯⣙⣿⣯⣙⣽⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⠶⢶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⢀⣴⠟⠁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠻⣷⡀
⠀⠀⠀⢠⣾⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠚⠠⠻⢾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢫⠈⠀⠰⠄⢀⠀⡀⠀⣄⣀⡀⢠⠚⠆⠀⠀⠀⠀⡘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠋⠂⠱⠎⢿⡟⠉⠃⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢸⡇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠸⡇⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⣀⣴⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠀⠹⡅⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⢀⣼⠃⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⢀⣼⠃⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣉⣉⣉⣉⣉⣉⣉⣉⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⢿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⠀⠀⠀⠀⠀⣴⠞⠛⠉⠉⠉⠛⠓⠦⠀⠀⠀⠀⢀⣀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠉⠑⠲⠶⠦⢤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠒⠋⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣀⠀⠲⠶⠤⠄⠀⠀⣀⡀⠀⠀⠀⠄⠰⠖⠀⢀⣀⣤⠶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠙⠛⠓⠶⠶⠶⠶⠤⠤⠴⠶⠶⠖⠛⠛⠛⠉⠁⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⣙⡓⠒⠂⠠⠤⠤⠤⠤⠤⠤⠀⣀⣀⣀⣀⣤⡤⠴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠈⣉⡉⠛⠛⠓⠒⠒⠒⠒⠒⠒⠋⠉⠉⠉⠉⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠶⢤⣬⣉⣉⣐⡒⠒⠒⠒⠒⠒⠒⢂⣀⣀⣀⣠⣤⡤⠶⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠈⡉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠲⠶⠤⣬⣉⣉⣉⣉⣀⠀⠀⠈⢉⣈⣉⣉⣠⡴⠶⠞⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣦⣤⣤⣤⣄⣀⣀⣤⣤⣤⣤⣤⣶⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠈⠉⠉⠉⠉⠉⠉⠉⢉⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣤⣤⣤⣤⣤⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⡆⠱⡀
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡆⢀⣱⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣏⡇
⢀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⡇
⢸⣿⣿⡿⠟⠉⠻⠿⠿⠛⠉⠠⡠⠀⢈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡟⡹⣶⠇
⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡗⠀⠈⣿⣿⡿⠋⠉⠁⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠘⠳⢦⣀⠀⠐⠄⠀⠀⠀⠀⠀⣲⣶⠠⣤⣤⠀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠺⣿⣦⣼⣟⢿⠋⢁⡄⢀⣀⣀⠀⠀⢀⣉⣀
⢠⣤⣤⣈⠓⢦⣄⠀⠀⢀⣀⣤⡁⠈⣧⠈⠻⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠤⠠⠤⡄⠷⣟⠒⡀⣿⣿⢿⣿⣿⣤⣤⣧⣝⡟⣷⢶⣿⣿⡿⠋⡄
⠠⣍⠻⣍⣀⡀⠙⠙⢦⣰⣿⣽⡆⠀⠘⣿⣄⠀⠄⡦⠀⠤⠄⠀⣠⠄⠠⠂⠂⠀⠀⠠⠈⠀⠀⠀⠈⣨⣯⣭⣿⡇⠀⠘⣿⣿⣷⣿⣷⡹⣇⠀⠀⡟⠁
⠀⠘⢷⣭⣭⣿⣿⣴⣍⠙⠻⢿⣷⣤⡀⠘⣿⣇⢰⣧⡔⠁⠀⣴⢃⣀⣶⡀⠀⢀⡀⠂⠀⠀⠀⠀⠀⠐⡟⠻⠛⢳⣄⠐⣿⣿⡿⣿⣿⡷⢨⣶⠤⠂
⠀⠙⠋⠙⠿⠾⢿⣿⣿⡁⠑⠶⣮⣝⠻⣧⠸⣿⣿⣿⣶⣶⣾⣷⣮⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⣀⠤⠁⠀⠀⠀⠸⠜⢻⣧⣈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣶⣄⠘⠿⠀⣌⡁⢹⣿⣿⠿⣿⡿⠿⠿⠟⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠊⡑⠀⠈⠀⠀⠘⠀⠀⠠⡀⣀
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣙⣷⣴⣾⣿⣿⣶⣬⣓⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢞⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡯⡼⣋⡵⣻⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠿⢋⣿⣾⣿⣿⢷⣯⣾⣟⣿⣻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠊⠀⠉⠉⠰⠏⡁⠚⣿⣗⢝⣻⣯⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⡛⡻⢟⣩⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣽⣶⣤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⣿⣴⠏⠀⠀⠀⠀⠀⠀⣠⡾⣿⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣯⣿⣿⣿⣿⣿⣷⡏⠀⠀⠀⠀⠄⠀⠩⡾⣫⣔⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢋⣵⣿⣴⣯⡤⢄⠀⠀⠀⠀⣴⣿⣶⣶⣲⡾⠃
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⢨⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠉⠉⠉⣹⠏⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣤⣶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⡚⠁⣠⡏⠐⠂⢀⣇⡀⠑⡂⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣐⠐⣌⣯⠛⡀⠛⠄⢻⠟⢠⠤⠙⠛⠀⠾⠃⡜⢋⡩⡗⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁⠙⠀⠛⠀⢻⠿⡦⠶⠛⢿⠀⠘⠋⠚⠊⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⣿⡆⠈⠉⠠⣾⠦⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠰⠲⠊⠉⠉⠀⠀⠀⣿⣀⣐⣒⣁⣸⣂⠀⠀⠁⠈⠉⠲⠲⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠼⡴⠦⠶⠾⠂⠈⠙⠓⣀⠘⣟⠋⠅⣡⠉⠙⡟⢁⡚⠛⠓⠐⢾⠖⢠⠆⢨⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠒⠐⠴⠦⠤⢴⣿⣤⣤⢤⡀⠰⣷⠈⠀⠒⠊⠀⠛⠀⠀⠁⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠄⠀⠀⠀⢰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⣇⡀⠌⠋⠄⠈⣿⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢘⠃⠀⢸⡏⢉⠶⠶⢊⠁⣿⠀⠀⠛⠒⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⢂⣏⡁⠤⡄⠰⣖⠐⢿⠿⠷⣒⣓⡲⠿⣿⡗⠀⡦⠦⣤⣄⣩⣒⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠟⠲⠌⢠⣮⣡⣾⣤⡤⢉⡍⠱⣦⣼⡧⠉⠦⠜⠵⠞⠟⠃⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢑⣦⠴⠞⣉⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠚⠉⠁⠀⠉⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡙⠀⠤⢀⣀⠤⠄⠘⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⡇⠤⠀⠁⠀⠀⠀⠄⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡷⠀⠀⠀⠐⠐⠀⠀⡀⢸⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣿⠀⠉⠐⢀⣀⠐⠈⠁⣸⣇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠉⠠⠤⡀⠁⡠⠄⡉⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠉⠁⠀⠐⠒⠄⠀⠉⠑⢻⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⢠⡄⠀⠀⠀⠀⠀⠀⠀⣄⠰⡏⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠋⠀⠀⠀⠀⣠⢤⡔⠂⠁⡀⠴⢧⣼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠀⢠⠐⠚⠓⢀⣀⠐⠉⠂⠀⠀⢰⠇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⢀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⣇⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣾⠀⠀⠁⠆⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠛⢼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣧⣤⣤⣤⣤⣬⣤⣤⣤⣾⣍⣤⣤⣤⣤⣼⣤⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⠅⠀⠀⠀⢀⣤⠿⠙⠋⠉⡩⢀⠀⠈⠉⠉⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠁⠉⢂⢄⠀⢻⡞⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⣯⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢺⣇⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠾⠉⠤⠠⠤⠤⠤⠤⠤⠴⠧⠤⠤⠤⠤⠤⠤⠤⠉⠽⠷⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣤⣴⣶⡟⠉⠹⣿⠀⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢊⣉⣩⡍⠙⠛⠻⣆⠸⣿⣧⣼⣿⣗⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢁⡒⠛⠛⠿⢿⣧⢠⣆⣿⡛⣯⡭⠏⠛⠉⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡈⣽⣵⣁⡃⢀⣸⣿⣦⡿⣿⣿⣷⣶⣶⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⢿⢺⡇⣿⣯⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⣸⣘⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠈⢁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡟⡕⡻⢻⣿⣿⣿⣿⠙⢿⣍⠢⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣹⢏⠌⠀⠉⣟⢅⠙⣆⠻⣢⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡎⣀⡀⢀⣬⣺⣶⣌⣷⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣷⣶⣾⣿⣿⣿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⡿⣿⢸⣿⡟⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣷⣿⣽⡿⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠹⡇⣿⣿⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢿⣿⠀⢘⡇⠻⠋⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣾⡇⠄⢸⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⠇⠀⢸⡄⡄⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⢸⠀⠀⠈⡇⡇⠀⣿⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣷⡇⠀⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⢸⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠘⣿⠀⠘⣷⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⢹⠀⠀⢸⡼⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣃⣀⣀⣀⣀⣀⣈⣀⣀⣀⣓⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠁⠀⠈⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠐⢀⠄⠂⠈⠁⠈⠉⠀⠢⢄⠀⠈⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢠⠀⣆⣔⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠎⠁⠀⢈⠆⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠄⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠴⠠⠀⠀⠀⠊⠄⠀⠀⠀⠐⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠂⠀⢸⠀⠠⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣽⠟⢻⣏⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢁⢠⢴⠊⠐⢀⣨⠉⠕⡢⢦⢬⡉⠁⠀⢁⠅⢤⣀⠀⢂⢤⣄
⠀⠀⠀⠀⠀⢀⠌⢠⠔⠚⣉⡀⠀⢠⡖⠗⢒⣦⣐⣂⣁⢄⣩⡆⣤⢷⠖⠢⡆⣐⣀⢌⠑⢿⣆
⠀⠀⠀⠀⠀⡈⠀⣎⠀⠞⣁⡅⢀⠏⠘⢠⠋⠀⠀⠀⠀⠀⠀⠀⡉⠉⢹⡇⢡⠀⢈⠽⠂⢈⠈
⠀⠀⠀⠀⠀⠠⡀⠈⠓⠤⠤⣉⣀⢤⣀⡆⡄⠉⠙⠀⠀⠀⠐⢡⡴⠾⢼⡧⣤⣭⢥⣤⣴⣶⣷
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠠⠀⠼⠯⣈⡻⠓⠲⣒⠲⠶⠴⠲⢾⠷⠶⠊⡀⠤⠄⠰⠼⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠐⠉⠠⠾⠅⠠⠀⠀⠢⠸⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠄⠂⠐⢀⠀⢠⠀⠀⡐⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⠈⠀⠌⡂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠀⢁⣀⡔⢐⠨⡀⠐⠒⠑⠀⢸⠀⣀⡄⠄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠉⠚⠛⠉⠄⠂⠔⠨⢘⠳⡦⠄⡠⠐⠜⠡⢐⠠⠀⠁⠈⠪⠐⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⢠⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡾⠛⠻⣦⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡥⣤⠈⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⢿⣄⠈⠢⣄⠈⠻⣿⣟⣿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣆⠀⡀⠀⠀⠀⠀⠀⢠⣯⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⣛⣽⡻⡙⣍⢯⢳⣦⡈⠳⣄⠈⢻⣯⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠹⠞⢻⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⣿⣛⢧⣙⣼⣏⣛⣚⣚⣓⣓⣃⣹⣤⢾⡷⠶⣿⣧⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣠⢤⣘⡇⠀⠀⠀⡤⣤⣤⣤⠶⣚⣻⡭⠽⠷⠒⢛⣛⣉⣽⣿⣏⣏⠏⠀⠉⠀⠀⠀⠀⡜⠁⡞⠀⣼⠟⠹⡿⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠉⠋⢀⣤⣦⣿⣷⡦⢖⣫⡥⠶⠚⠛⠉⠉⠉⠉⠈⠉⠙⠛⠛⠛⠿⢷⣶⣦⣤⣴⣁⡜⢀⣼⡿⠶⠶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣸⡿⣛⡵⠞⠉⣤⣀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣫⠵⣛⡵⡋⠁⠀⠀⠀⠘⣯⠛⣁⡘⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢞⣫⠴⢛⡥⠞⠁⢰⣿⠀⠀⠀⠀⠀⠘⠛⠉⠻⣼⠇
⠀⠀⢀⣠⡤⠶⢚⣉⡤⠞⣋⣥⠞⠋⠀⠀⢀⣟⣈⠙⢳⡆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢩⠴⠖⢛⣉⡥⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠻⡿⠛⠿⢿⠿⢻⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⡀⠀⠁⠀⠀⠌⠀⠀⠠
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠁⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠠⠀⢀⡀⠀⠀⠀⠋⢁⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢶⣖⣯⠍
⠀⠀⠀⠀⡄⠀⠀⡀⠀⠚⠀⡀⠈⠀⢰⣛⠀⠀⠀⠐⠀⠀⢩⠠⢤⡤⠈⠀⠐⠀⠀⠀⠀⠀⣰⠀⠒⠋
⠀⠀⠁⠀⠀⠀⠀⠉⠀⠁⠀⠁⠄⠀⠀⠈⠀⠀⠠⡤⠲⠈⠀⠀⠄⢤⠐⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠒⢂⠀⠀⢠⠀⠠⠄⠀⠈⣃⠀⠁⠠⠀⡄⠀⠀⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⡀⢉⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠐⠀⠈
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⣀⢈
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣤⣄⣀⣀⣠⣤⣶⡶⠶⠦
⠀⠀⠘⣠⣾⣿⣿⠏⠀⠈⠉⠛⠛⠛⠛⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⣼⣿⣿⣿⣿⢶⡆⢐⣒⠀⣲⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣶⣿⣿⣿⣷⣶⣤⡀
⠀⠀⢸⣿⣿⣿⣿⡜⠁⠈⠉⠤⠉⠉⡽⠛⠋⠛⠛⠙⠙⠉⠋⠋⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⠿⠟⠛⠛⠋⠁
⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⣀⣀⣀⡀⠙⢤⣀⡀
⠀⠀⠀⠘⠻⠿⣥⠤⠖⠊⠁⠀⠀⠈⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⡀⠀⡀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠆⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠘⠁⢀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠈⠁⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠤⠀⠈⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠃⠀⢀
⠀⠀⠀⡠⠄⠁⠀⠀⠈⠀⠀⠀⢀⠀⠠⣀⠀⠈⠉⠀⡀⠂⠀⠠⠄⠀⠀⢀⠰⠀⡁⠐⠊⠀⠀⠀⠀⠐⠂⠀⢀⠈
⠀⠀⠀⠁⠀⠀⠖⠆⠀⠠⠀⠀⠈⠀⠀⠀⠀⠈⢀⠀⠀⡀⠀⠀⠀⠃⠐⠂⠀⠈⠁⠒⠀⠀⣀⠀⠀⠀⠀⠠⠀⢠⠀⠁
⠀⢀⠀⠀⠆⠀⠀⡉⠀⡀⠀⠀⠀⠈⢠⠀⣀⠓⠈⠁⣀⠁⠈⠀⠄⠈⠀⠀⠀⠀⠘⠀⢀⡀⠈⠁⠀⠈⠁⠀⠀⡀⣀
⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢘⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠰⠀⠀⠀⡈⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠆
⠀⠨⠀⠀⠆⠀⠰⠀⠉⠁⣌⠀⠈⠀⠀⣀⠀⠀⢀⣀⠀⠈⠀⠰⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢠⡄⢠⡄⠀⠀⠉
⠀⠐⠀⢀⠀⢀⠰⠀⠀⠀⠀⢠⠀⠠⢤⠀⠐⡀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠠⢀⠀⠀⠁⠀⠀⡐⠂⠀⠀⠀⠉⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢠⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⠠⠄⠒⠀⠰⠈⠀⠰⠀⠉⠀⠀⠀⢠⠀⣘⠀⠁⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⡘⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⠄⠄⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⡀⠀⠠⠄⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⢀⡀⠀⠐⢠⠠⠄⠀⠀⠀⠀⠀⠀⠀⡁⠔⠂⠀⣄⠀⠁⠐⠂⠀⠀⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡄⠀⠐⠂⠤⠀⠄⠀⠨⠀⠀⠀⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠒⠀⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃
⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤
⣿⣿⣤⣴⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠿⠿⠿⠿⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⣤⣤⡄⠀⣿⣿⠀⣤⣤⡄⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠀⠿⠟⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⠾⠿⠟⠋⠉




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

⠀⠀⠀⠀⠀⠀⢰⡾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⢸⣷⡏⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⣍⢳⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡟⡇⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡗⡇⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⠀⣸⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢠⣿⠀⠀⠀⠀⣀⣤⣤⣶⣦⣤⣄⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢸⣿⠀⠀⣠⡾⢋⡥⠶⠒⠒⠦⣍⠻⣦⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⣿⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⢸⣿⠀⣰⡏⡴⠋⠀⠀⠀⠀⠀⠈⣧⢹⡇⠀⣿⡇⠀⢸⡇⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡏⠀⣿⢸⠁⠀⣰⣿⣿⣿⡆⠀⢸⠈⣿⠀⣿⡇⠀⢸⡇⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⣿⠀⠀⣯⢸⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⢸⡇⠀⢿⣾⡀⠀⢹⣿⠀⣿⠁⠀⡼⢸⡏⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⢸⡇⠀⠘⢷⡻⢤⣸⡏⠀⣿⣤⢞⣵⠟⠁⠀⣿⡄⠀⢸⡇⠀⠀⠀⠀⠀⢠⣴⣶⣦⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⡇⠀⠀⠈⠛⠶⣼⣿⠀⣿⡾⠛⠁⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⣿⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣿⠀⢻⣄⣀⣀⣀⣀⣀⣿⡇⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⡀⠀⠉⠉⠉⠉⠉⠉⠉⢻⡆⢸⡟⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠸⣄⣋⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⠈⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣺⣀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⢼⠏

⠀⠀⣤⠺⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢢⡄
⠀⠀⢻⣇⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⢀⣿⠃
⠀⠀⠈⢿⣆⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣀⣾⠏
⠀⠀⠀⠘⣿⣿⡿⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⣿⣿⡟
⠀⠀⠀⠀⠸⣿⡁⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⣹⡿
⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠈⢻⣷⠆⠀⠀⣠⣤⠶⠖⠚⠓⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠋⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠁⢀⣴⠟⢋⡤⠒⠀⠀⠀⠉⠉⠀⠀⠀⠠⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣟⠀⠀⠀⠀⢠⡾⠃⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⢣⡀⠀⠀⠀⠀⠀⠀⢘⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣾⠁⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢷⡀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⢠⡏⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣇⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⣿⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢹⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣸⡇⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣷⡈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣰⡟⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠦⡁⠠⢄⠀⠀⢀⣀⣠⣴⠾⠋⡠⠞⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣬⣥⠄

⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⢉⠙⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠒⠂⠀⠀⠘⠒⠀⠤⡀
⠀⠀⠀⢀⣠⡤⠟⠓⠛⠉⠁⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⢀⡠⠒⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⡞⠀⠀⠀⣀⠤⠴⣶⣻⡯⠥⠼⠥⠀⠀⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⢧⠀⣀⡤⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢠⠟⠁⠀⠀⠀⢀⣀⣤⡤⠤⠐⠒⠐⣒⡛⠩⠤⣄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣿⠀⠀⠀⢰⣼⡿⠷⠖⠒⠚⠉⠉⠉⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⠂⠄⡄⠀⠀⠲⠀⠀⠻
⠘⡷⠖⠋⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡴⠋⠀⠀⠀⠀⠀⠀⢸
⣾⠁⠀⠀⣀⣠⠤⠶⣖⣛⣫⣭⠥⠦⠔⠂⠀⠈⠑⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠺⡈⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⢻⡀⠀⠊⢉⡴⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣹⢗⣽⠋⠀⠀⢀⣀⣤⠤⠶⠶⣲⠾⠿⠯⢥⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠃⢸⠇⠀⠀⢰⢟⠉⠈⠙⠻⣼⠃⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠀⠈⠢⠤⠴⠋⢸⡀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣼⠄⠒⠚⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠁
⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⢀⠇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡸
⠀⠙⢆⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠂⠒⠀⠚⠀⠀⠀⠀⠤⠧⠠⠴⠒⡶⠁
⠀⠀⠀⢻⠛⠉⠉⠛⠉⠉⠙⠯⠉⠙⠯⠉⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣙⣓⠀⡇
⠀⠀⠀⢸⡆⠀⠀⠤⠤⠤⠤⠤⠤⠀⠄⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠀⠠⠤⠤⠤⠤⢤⣤⠶⡶⠶⠀⡇
⠀⠀⠀⠺⡉⠀⠰⠶⠶⠶⠒⣒⣒⣛⡫⠁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠁⠀⠀⠀⠀⠠⠤⠤⠴⣶⣾⣿⠀⡆
⠀⠀⠀⢺⡅⠐⠶⠶⠶⠚⠛⣛⣚⣓⡭⠁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⠀⠀⣀⣀⣀⣀⣠⣵⣶⣶⢶⠀⡇
⠀⠀⠀⢾⡅⠀⠶⠶⠶⠒⠚⢛⣒⣛⠻⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⣤⣤⡶⣶⡃⣠⠇
⠀⠀⠀⠈⠳⣄⡀⠒⠒⠒⢚⣓⣛⣾⣥⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠈⠉⠭⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠻⡍⠉⠉⠉⡭⢉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣛⣛⣿⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣧⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⣤⣤⣤⣤⠀⠤⠤⠤⠤⠤⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⠀⣭⣭⣭⣭⣍⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣛⣛⣛⣛⣀⣒⣒⣒⣒⣒⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⣛⣿⣿⣛⡛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣆⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⠀⠀⣀⣀⣀⣈⣃⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⡏⣭⣭⡍⠩⠭⠭⠭⠭⠭⠭⢹⠀⠀⡏⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⠩⡇
⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⡇⢘⣛⣛⣛⣛⣛⣃⢸⠀⠀⡇⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⢠⡇
⠀⠀⠀⠀⠀⠀⢸⡃⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢸⠀⠀⡇⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢘⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⣛⣿⣿⣛⠛⠛⠛⠛⠀⠀⠛⠛⠛⠛⣛⣿⣿⣛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡶⠶⠿⠿⠿⠶⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣴⡾⠟⠉⢁⠤⢖⣒⣒⠒⠦⣄⣀⡀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⠟⠛⠛⠻⣿⣾⣿⣅⣀⠀⡰⠁⠀⠀⢀⣽⠿⠿⠿⣿⣿⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣄⣀⢀⣼⠟⠁⠈⠉⠙⠽⡇⠀⢀⣴⡏⠀⠠⡶⢦⠺⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠈⢉⠛⢦⠀⠀⠀⠀⠀⢻⢇⡞⡻⠇⠀⠀⠀⠀⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣿⠷⣦⣄⠀⠀⠀⠺⣷⣤⣄⠀⠀⠀⠀⠉⢿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢱⠀⠈⠻⣏⡽⢷⣦⣼⣀⠈⠑⠶⣶⢶⠖⠋⠀⠈⠻⣕⢄⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⡜⠀⠀⠀⣻⣿⠿⣿⣿⣿⣶⣮⣐⠾⣿⡗⠢⠄⣀⠻⠟⠒⠛⠐⠆⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠃⠀⢠⠎⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣦⣝⡻⢶⣾⣷⣾⠀⠀⠀⠸⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠠⠀⡞⠀⢻⣿⣦⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣶⣿⢻⣿⣯⣤⢄⠀⢣⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢿⣿⡿⣿⢿⣿⣷⣄⠀⢸⣿⣿⢿⣿⣿⣿⣿⠉⠻⢿⣿⣿⠘⣷⠈⣆⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡉⠻⣮⢣⢻⣿⣿⣦⣸⣿⣿⡀⠉⠻⣿⣿⣷⣄⠀⠉⠻⢧⣿⡀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠃⠀⢻⣇⣸⢏⣿⣿⣿⡉⠻⣿⣦⡀⠈⠙⢿⣿⣷⣦⡰⠎⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⡀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠟⣻⣿⣷⣄⣿⣧⣙⢦⡰⠆⢹⣿⣿⣿⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢇⠀⠀⠀⠀⣠⣿⣿⠿⡇⠀⠈⢽⣿⣿⣿⣿⣿⣷⣝⠶⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠴⠚⠛⢷⣦⣄⣧⣀⡈⠒⠺⠿⣿⣿⣿⣿⣿⣷⣌⣀⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠁⠉⠁




⣶⡶⢶⢶⠶⠶⢶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠉⠁⠉⠉⠉⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠸⡷⣴⠟⣷⠟⢧⣾⡇⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⢹⡀⠀⠀⠀⠀⣼⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣷⠀⠀⠀⢰⡇⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢹⠀⠀⠀⢸⠃⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣸⣇⣀⣀⣾⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣭⣭⣭⣭⣭⣭⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠶⠶⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠒⠒⠒⠒⠒⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⣉⣩⡿⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠶⣦⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠦⣄⡀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠘⣧
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠉⠉⠉⠉⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠘⠇⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⡟⠁⠙⠞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠙⣧⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠾⠃⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⣠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣿⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⣷⢄⣼⠟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣤⣤⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠘⢷⣌⠳⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢩⣿⠷⢦⡄
⠀⠀⠀⠀⠀⣴⢚⣿⣦⠀⠸⡌⠹⡆⠀⢻⡄
⠀⠀⠀⠀⠀⢻⡘⠋⢻⣳⡀⠹⡄⠹⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢳⡀⠀⢳⣷⡀⢙⣆⢻⡀⠀⠹⣷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠹⣷⡿⠋⠙⠳⡄⠀⣻⠙⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣄⠀⢘⣷⠀⠀⠀⠙⠛⣁⣤⣾⠟⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢼⢛⠉⠉⠉⢁⣠⣤⡶⠾⠛⠋⠉⠀⢀⣴⢷
⠀⠀⠀⠀⠀⠀⠀⠈⢷⠻⠿⠛⠛⠉⠁⢀⣀⣤⣤⠶⠞⠋⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣠⡴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⠀⠀⠀⠀⣀⣠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⣟⣋⣡⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢰⠏⠉⠀⠀⠀⠈⠉⠉⠓⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⣾⡤⠖⠒⠒⠓⠒⠶⢤⣀⠀⠀⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢸⠃⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣼⡀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡼⠙⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡼⠁⠀⢻⡀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢀⡜⠁⠀⠀⠀⠳⡄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⠏
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣠⠞⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠙⠲⠦⠤⠤⠶⠋⠁⠀⢠⠟
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⡀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠔⠓⠀⠀⠒⠑⠤⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠈⠉⠀⡀⣄⠠⠤⠤⠄⣀⣀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⢤⠤⠄⠒⠁⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠁⠀⢒⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠔⠁⠀⠀⠀⢀⠀⢠⠄⠠⢤⠀⠀⠀⠈⡆⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢘⠧⠤⠓⠻⢅⡀⠀⠀⠀⢠⠀⠀⠄⠀⢈⠆
⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⡔⠁⠀⠀⢀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⠰⠈⡌⠀⠘⠀⡀⠧
⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠘⠦⡐⠠⢀⠀⠀⠀⠀⠀⢀⠀⠈⢀⠜⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠢⡀⠀⠀⠨⠑⠂⠀⠀⠐⠀⠈⡠⠴⠊⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠓⠒⠀⠾⠴⡇⠠⠤⣀⡐⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣳⣶⠖⣶⣖⢣⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠂⢀⢌⠵⢃⠅⡻⡝⢦⠁⡐⠠⠀⠠⠤⠤⠀⠀⠄⠀⠀⠄⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⢀⡀⠄⠊⢑⠁⣊⠅⡉⠤⡈⠒⠍⣑⡚⣀⠠⢄⡀⡀⠀⠀⣀⠀⠤⢤⡤⠤⠠⢍⡒⠠⢄⡀
⠀⠀⠀⠀⢠⠞⠁⣠⡠⠔⠈⠁⠁⠀⢐⣨⡴⢪⠶⠡⣆⠭⡒⠅⢊⠥⣂⠕⣈⣔⣠⢂⢥⣤⢴⣂⠔⡠⢔⠠⢀⠉⠲⣭⢢⡀
⠀⠀⠀⢠⠃⢀⣀⠋⠠⢀⡼⠲⠀⢀⢁⡾⢡⠃⢠⠖⠚⠛⠒⠚⠐⠚⠐⠛⠚⠦⠼⠧⠾⢄⣤⠈⠟⠚⠃⠺⢴⣞⡄⠈⠇⢱
⠀⠀⠀⠘⠀⠘⣵⡀⠈⠫⠄⣸⡀⠰⢸⠀⠈⠀⡌⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠈⠿⠀⠘⣄⠀⡠⠖⠉⠀⢀⠄⢄
⠀⠀⠀⠸⡀⠀⡈⠚⠤⣤⡀⢈⡘⢀⢁⣤⠀⣸⠀⡘⠈⠁⠙⠀⠀⠀⠀⠀⠦⡁⢈⠰⡁⢀⣴⡄⣠⠨⠉⠁⠀⠀⢐⣡⠞⡌
⠀⠀⠀⠀⠙⠢⢄⣁⡀⠀⠈⠉⠓⣛⣲⠒⠙⢿⣴⣁⣀⣀⣀⣀⣀⠀⠀⢀⢀⡝⠂⣤⠀⢼⠟⠁⠺⠕⠩⠙⠝⠉⢋⣉⠜
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠃⠄⣊⠅⢓⠦⢤⢃⠥⠊⡩⢜⠥⢊⠥⢚⠡⠈⢙⠁⢉⡜⠀⡠⠒⠈⠁⠂⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⢂⠡⢒⡈⠔⡂⡵⠮⠐⢈⠄⡊⠅⢂⠅⢸⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠐⣊⠄⢊⠥⢂⡡⠀⠄⠀⠇⠐⡊⠔⢊⠤⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠐⡈⠔⠊⡀⠄⢠⠀⠀⢰⠀⠒⡨⠐⢈⠡⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢐⡡⠄⡂⠥⠐⠂⠈⠀⠀⢸⠀⠡⢐⡈⠄⢒⡀⠸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠁⠀⠁⠐⠉⠐⠀⠔⣂⠴⢺⠄⠀⠥⢒⠪⠔⠂⠀⠖⣂⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠠⠀⡡⠘⢳⠤⢤⡤⢤⣤⠤⡶⠞⠛⡁⠔⢂⡩⠲⣄⡀⠀⠀⠁⢀⠜⢋⠴⡢⠑⢈⠤⠒⣉⠔⣊⠔⡢⠔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠐⠉⠐⠁⠀⠐⠉⠀⠒⠁⠔⠊⠡⢚⠱⠒⣉⠔⠊⠔⠉⠔⠊⡡⠔⠊⠔⠊⠔⠊⠔⠊⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈