Futurist Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡯⠓⠈⠉⠉⠉⠉⠉⠉⢱⣶⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⢠⠴⡒⠒⠒⠒⠒⠒⠒⠛⢻⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⣿⠀⠁⠀⠀⠀⠀⠀⠀⠰⣾⣿⠈⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣾⣿⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⣶⣿⣿⣿⣿⡀⠻⢦⣤⣤⣤⣤⣤⣾⣿⣿⡽⠟⢠⣿⣿⣿⣿⣶⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⠀⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣰⣶⣿⣿⣿⣿⣿⣿⣉⣁⠈⠉⠙⠿⠿⠋⠉⠁⣈⣩⣿⣿⣿⣿⣿⣿⣶⣄⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⣿⣿⣷⣶⣤⣤⣶⣾⣿⣿⣿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣰⡿⠛⢿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠛⣿⣦⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣶⡿⣻⣿⣿⡇⢸⣿⣿⣟⢿⣶⣿⣿⣿⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⢿⣿⣇⣝⠿⣿⣿⣿⡿⢃⣿⡇⢸⣿⡘⢿⣿⣿⣿⠿⣫⣸⣿⡿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣄⢁⡄⢸⣿⡇⢸⣿⡇⠀⠀⣡⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣎⢿⣿⣿⠀⠁⣾⣿⠃⣸⣿⣷⠀⢀⣿⣿⡟⣱⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣃⣠⣿⡿⠿⠿⢿⣿⣄⣛⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠯⠶⠶⠶⠶⠶⠶⠶⠶⠽⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣯⡍⣭⣭⣭⣭⣭⣉⣭⣭⣭⣽⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⡴⠋⢡⣤⢤⡈⠙⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣏⠷⣾⡦⣿⣿⣷⣷⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠗⣿⣠⣾⣶⣨⡇⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⠉⠉⠙⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣫⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⠿⣿⠟⠻⣿⡞⢻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣿⡿⠒⠀⠐⢯⣷⣞⡿⣾⠟⠿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣿⣟⠉⢀⣠⠤⠀⠈⣿⣜⣼⠁⣴⣶⣿⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠈⠿⠟⠓⢀⣿⣿⣿⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢀⡰⠀⠀⠀⠸⠿⢿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡶⡀⠀⠀⠀⢀⡼⣿⣿⣿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣀⣠⣤⣾⣿⠃⣹⠟⠛⢱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⠟⠈⡠⠒⣡⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⠋⠉⠀⡀⣺⣤⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣼⣆⡔⠋⢰⣿⣾⣿⣿⣿⣦⠾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣻⣿⣷⣾⢋⡩⣻⣿⣿⣿⣿⠏⠠⠀⠈⣽⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡿⢱⣿⣿⡿⣻⢛⣿⡿⣿⠿⠣⠂⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠁⢸⡿⠋⣀⢡⡾⠏⠐⠏⠀⠀⠀⠀⠀⠶⠲⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡶⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠸⢶⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠑⠆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣕⡲
⠀⠀⠀⠈⠱⠄⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠬⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⣌⠀⠀⠀⠀⠀⠀⣱⣄⠀⠀⠀⣀⠀⠀⠀⢠⢾⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⣰⣆⠀⠀⢀⣦⠀⠀⢸⣿⡀⠀⢀⣠⣀⣴⠠⣄⠀⣀⡀⣴⣀⢿⣿⠄⢠⠀⡄⣠⣬⣿⣿⡇⠀⣴⣾⡇⠀⣰⣾⣿⣷⣦⣄⣀⢀⡠⢄⡴⣀⢀⡱⣤⣴
⠀⠀⠿⣿⡂⠀⣻⣿⠆⠀⠘⠛⢧⣄⡀⠀⠻⠿⠀⠃⠀⠈⠉⠉⠉⠀⢿⣦⡀⠁⠀⠨⠼⠿⢿⣧⣆⣐⢶⠶⠾⠿⠛⠿⠿⢿⣛⡛⣋⠁⠈⠁⠘⣴⣧⢿⣿
⠉⠘⣿⣿⠁⠈⠏⠁⠐⠖⠂⠠⣾⡿⠛⠛⣉⢁⣀⣄⠀⠀⠀⢤⣤⣤⣈⣿⡟⠀⠀⢴⢾⣿⣿⢩⣭⣉⣭⣅⣄⢁⠀⠒⠒⠐⢺⡖⣤⣶⣠⣠⣤⠥⡥⣼⣿
⣿⣿⣿⣿⣦⣤⣤⣤⣤⡄⠇⠇⣿⣧⠤⢖⣻⣿⣿⡟⡡⢤⡠⡄⢰⠐⠏⣿⣷⣦⠤⠼⠎⠁⠀⠀⢁⠉⢉⠉⠁⠀⠀⠀⠀⢠⣶⣶⢿⣷⣤⡻⣿⢸⡆⢸⣟
⣉⣸⣟⣿⣿⣿⣿⣿⣿⣏⢀⣀⢻⢛⢘⢋⢛⢉⠃⠃⠑⠣⠿⡇⠀⠀⠀⣿⣗⣤⣴⣶⣶⣶⣤⣠⣄⣄⣤⢡⣄⡄⣀⠠⡄⣀⣙⣀⣀⣓⣀⣐⣭⣈⣃⣿⣿
⠋⢻⠀⢙⣹⣹⣭⣿⣿⣏⣈⡉⠈⠉⠙⠙⠻⠻⠻⠻⠟⠿⠿⠺⡷⡷⡞⣿⣿⣿⣿⣿⣿⣿⣛⣉⠉⠃⠛⠻⠛⠇⠻⠻⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠘⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⣤⣥⣭⣬⣉⣙⣉⣻⣿
⠿⣀⠀⠰⠟⢻⠛⠻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢙⣀⣠⡤⣼⡖⢾⠟⢻⠛⠻⣿⣹⠈⡇⣈⣿⣿⡿⠿⡟⢻⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⢹⣉⣴⣿⡟⠁⣶⢢⣾⣿⣿⣿⣿⢶⡟⠋⠉⡀⠀⠀⡇⠀⠈⠀⠈⢹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⢻⣿⣿
⣿⣿⣿⣿⣿⣧⣶⠹⢸⣿⡟⣿⣿⣿⢹⡁⠀⠀⠀⠂⠀⡗⠸⠽⢱⢶⣶⣯⢽⣷⣆⣯⠀⠈⠙⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠒⠒⣶⣾⣿⣿
⠉⠉⣉⠙⢻⠿⣿⣿⣾⢻⠁⠻⣿⣽⢈⠁⠀⣿⠇⠀⠠⡇⡀⠀⠀⣴⣿⢱⣿⡋⣇⣿⠊⢹⡏⠽⡿⠚⢾⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣼⣿⣿⣿⣿
⣉⢠⡉⠙⠛⠙⢻⠧⣤⣷⣾⣿⣿⠋⠰⡄⠀⣿⠀⢠⠀⡏⠁⠠⣤⣽⣿⠈⠙⣷⣧⣿⣀⢸⣅⣈⣨⠀⠰⣿⡿⠏⣿⡷⣿⠋⢨⣿⢨⡔⡃⠘⡈⣿⣿⣿⣿
⣬⡈⣁⡀⣴⣦⣀⢀⣀⠀⠀⠀⠉⠉⠘⠓⠚⠧⢀⣀⢀⣇⢀⣀⠼⠿⢿⢸⣿⣟⢷⣿⠾⠋⠙⠿⣷⢶⢶⡏⠀⡞⡛⠀⣿⡐⣻⣿⣸⡇⠇⠈⡅⣿⣿⢻⡿
⠿⣿⡿⢿⣿⣿⣿⣿⡟⣷⣧⣶⣴⣤⣀⣀⠀⠀⠀⠐⢀⣭⣉⢙⠒⠀⠼⠿⠋⠛⡃⠔⠦⠤⠀⠀⠀⠉⠈⠓⠈⠁⠉⢹⠻⡟⠻⣿⣛⣿⣧⣀⣆⣿⠛⢸⢀
⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⣬⡁⠀⠀⠻⠷⣦⣴⠀⠀⣀⣠⣠⡀⣤⣠⣦⣴⣦⠀⢀⣀⡀⣀⣀⠀⠉⠁⠀⣥⣯⣩⠀⡄⢸⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣠⣷⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣈⣉⣉⣀⣠⣤⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣿⣿⣇⣀⣤⣤⡀⠀⠀⠀⣀⡤⠴⣒⠦⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⣿⣿⣿⣿⣿⣡⣤⠶⠛⢋⠄⠊⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠁⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⡄⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⢄⣪⣞⠁⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠟⠋⣽⡿⠋⠀⠀⠀⠀⠠⢀⣴⡟⠋⣠⠆⠀⠀⢀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣟⣛⣻⣿⠻⢁⠀⠤⠐⣀⣤⣾⣿⡿⠖⠛⢳⣄⣠⣾⣿⣿⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢿⣿⣿⣿⣷⣄⣤⣶⡿⠟⠛⠋⠁⠀⠀⢀⣽⣿⣿⣿⣿⣿⣧⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡌⣷⠄⢀⣴⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⠿⠿⣿⣿⣷⣿⠿⠻⠟⠋⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠈⠀⠀⢸⡄⠀⠀⡀⠀⠀⠀⠀⣠⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⢄⣠⠞⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣴⡾⠥⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢉⠙⢳⡄⠀⢀⣊⠥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡇⠀⠀⠀⠀⣸⠁⣀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠁⠀⠘⠁⠀⠀⠀⢀⣠⡮
⠀⠀⠀⠀⢀⡀⠀⠀⢀⡞⠀⠀⣀⣀⣴⢷⣞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣦⡴⠛⠁
⠀⡀⠀⠀⠈⠁⠀⠀⡜⠁⣰⠟⡹⠋⢡⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⢈⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⣸⢋⠄
⠀⡀⠀⠀⠠⣄⣀⡞⢀⣼⣿⠏⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠞⠁⠀⠀⢀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠹⠛⢓⠾⠿⠛⠛⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢨⡞⠁⠀⠀⠴⠂⠁⠀⠀⢀⡔⡁⠀⠀⠀⠀⢀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡄⠀⠀⠈⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡼⠂⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⣆⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠳⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠧⠄⡀⡀⠀⠴⠒⠉⠁⠀⠀⠀⣨⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣢⠖⠃
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⣠⣆⢸⣿⠀⡀⠀⠀⠀⠿⠋⠇⢸⣭⣭⣭⣽⠇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⠛⠉⠉⠉⣉⠉⠉⠙
⠀⠀⣧⣿⣿⣾⣿⢸⡇⠀⠀⠀⣶⢶⡦⠀⢙⡶⣜⠁⠀⠀⠀⢀⣤⣤⣭⣥⣤⣄⠀⠀⢸⠀⠀⠀⠀⠉⠃
⠀⣸⣿⣿⣷⣿⣿⣼⣇⡀⠀⠀⢤⢠⡄⢰⠟⠶⠚⢳⡄⠀⠀⠈⡁⠀⠐⠀⠀⠋⠀⠀⠸⠖⠚⠛⣹⣿⠙⠛⠒
⠘⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠈⠈⠁⠈⠉⠉⠉⠉⠁⠀⠀⠀⠑⠂⠄⠄⠊⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙
⠀⠀⠀⡀⢴⣶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡾⣛⠲⢤⡀
⠀⠀⡾⠋⣤⣧⡈⢻⡆⠀⠀⠀⣠⠴⠒⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⣀⡀⠀⠀⢾⣿⣷⡽⣆⣀⠱
⠀⢈⣬⡼⢿⣼⠧⣬⣅⠀⠀⣨⣭⣟⣶⣶⣶⣷⡶⣦⠀⠀⢴⣻⣛⠶⢶⢿⣟⣵⣶⣧⠀⠀⠈⢿⣿⣿⢷⣿⣷
⠀⠈⠛⠥⢦⡤⠦⠙⠋⠀⠀⢿⣿⠟⠿⠿⠿⠿⠺⣿⠇⠀⠸⣿⡿⠘⠛⠓⠚⢿⣿⠿⠀⠀⠄⠛⠀⠘⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⢰⡄⢸⡇⠀⠀⠀⠀⢀⡴⢄⠀⠀⢠⣶⣤
⠰⠀⢠⣾⣿⣿⣷⣦⠠⢤⡀⠀⠀⠀⠰⣶⢶⡴⣯⡽⠁⠀⠀⠀⠀⢸⣏⣿⣿⠀⠀⠀⠀⠈⠺⡱⢗⣴⣽⠿⠟
⣠⠄⠿⠿⣿⣟⣻⣭⠶⠋⠀⠀⠀⢠⣤⣾⣿⣷⣯⠀⠀⠀⠀⠀⢀⡼⠧⠿⡿⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣤⡀
⠈⠙⠛⢿⣭⣿⣷⠟⠀⣴⡄⠀⠀⡂⠘⢻⡿⠈⠻⠀⠀⠀⠀⠀⢸⢸⣇⡀⢁⡀⠀⠀⠀⠺⢿⡿⠏⠈⠻⣿⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈
⠀⠀⠀⠀⡖⢲⡄⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⢲⣄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣶⣿⣿⣷⡄⠀⠀⠀⠀⡴⣾⣷⣦⢀⣴⣷⡄⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦
⠀⠀⠐⡏⣿⣿⡏⡇⠀⠀⠀⠀⡇⣴⣦⠸⠸⣡⣦⡹⠀⠀⠀⠀⠀⠻⣟⡿⠁⠀⠀⠀⠀⢀⡄⣾⣿⣿⣿⡆⡄
⠀⠀⠀⠃⣿⢿⡇⠃⠀⠀⠀⠀⠁⡟⢻⠀⠀⠹⠿⠁⠀⠀⠀⣠⣤⣬⣗⣧⣤⣄⡀⠀⠀⠀⠷⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⣿⢾⡇⠀⠀⠀⠀⠀⠀⡇⠿⠀⠀⠸⡿⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠙⣿⢻⡟

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠛⠋⢹⣿⡇⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⣿⠉⠉⢹⡆⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣸⣿⠇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⢀⣿⣧⡀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠿⠿⣿⣿⠀⠀⠀⠐⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣃⣼⣿⣿⣿⣆⠀⢸⣿⡇⠀⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣾⣿⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⣿⠀⠈⠻⣿⣿⣿⢻⣷⣾⣿⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⢻⣿⣦⣀⣀⣀⣼⣿⠇⠀⠀⠀⠉⠓⠦⣄⠀⠀⢂⡴⠋⠀⠀⣿⡿⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣧⣀⡀⣀⣴⣿⡟⡠
⠀⣶⣤⣀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠉⠛⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⡠⣫⠞⠋⠀⠀⠀⠀⠛⠃⠀⠀⠀⣾⣿⣿⣿⠻⠟⠋⠛⠻⠿⠿⢛⠝⢊⣠⡄
⠀⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⠀⠀⠀⢀⣤⣶⠖⣁⡴⠟⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠊⠁⠀⠀⠀⠸⣧⠀⠀⠀⠀⣠⠞⠉⠀⣿⣿⣿⣿⡇⣠⣾⡿⠟⣡⠞⠋⢀⣠⣶⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⢀⡤⠊⠁⠀⠀⢸⣿⣿⣿⣿⣇⠹⢋⡴⠛⢁⣠⣶⠿⠛⢁⡀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠐⢋⣠⡶⠟⠋⣠⣴⣾⣿⡇
⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⡠⠞⢁⣀⣀⣠⣤⣤⣴⣶⣿⣿⠿⠛⠉⣿⡷⠛⣉⣤⣶⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⣀⣼⡷⠟⠛⠉⠀⣀⣠⣤⣴⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⢀⡤⠶⡛⠉⠈⣷⡴⠶⠿⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡿⠿⠿⢿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢹⣦⣤⣤⣴⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⣀⣠⣴⣶⣶⣶⣶⣷⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣦⢤⠄⠀⠈⠉⠉⣻⡇
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢤⣤⣶⣶⣟⣉⠁⢹⡆⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠿⠟⠛⢀⣀⣤⣴⣶⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣷⣦⣀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠏⢀⣤⣶⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⢀⣀⣠⠴⠶⠚⠛⠉⠉⠻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⡈⠻⢿⣦⣿⡇
⠀⠀⠀⠀⣀⢴⣾⣭⣶⣿⣿⣿⠿⠟⠛⠉⠁⠀⢀⣀⡠⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢧⡀⠀⠙⢻⡇
⠀⠀⣀⣤⣾⣿⣿⠿⠟⠋⠉⠀⢀⣀⠴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⢦⡀⠀⠁
⠀⣿⠿⠛⠋⣉⣠⡤⣠⣶⣿⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠙⢦⡀
⠀⣴⣶⣿⣿⡿⠛⠁⠈⠉⠛⠿⣿⣿⣶⣦⠤⣄⣀⣀⠠⠐⠂⠉⠀⠀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡎⠁
⠀⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠀⠉⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⢻⣿⣷⡀⢢⣀⣤⣾⣿⣿⡿⠘⠃
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⣀⣀⡤⠶⠒⠋⠉⠀⠀⠀⠀⠀⢀⠤⣙⣿⣷⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣬⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⠈⢿⣿⣿⣿⣿⣿⠀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠁⠀⠀⡠⠜⠁⠀⠀⠐⠀⠀⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠙⢿⣷⣦⣀⠹⣿⣿⣿⣿⠀⢨⡁
⠀⣿⣿⣿⣿⠿⠛⠁⢀⣤⣾⣿⣿⠶⣤⣆⠐⠋⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⣿⣿⡏⠀⠌
⠀⣿⠟⠋⠁⢀⣠⣶⣿⠿⠛⢉⣴⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣿⡏⠻⣷⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠺⣿⣿⣷⡹⠇
⠀⠀⣾⣿⣿⡿⣿⣿⣀⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣴⣿⡿⣿⢿⣷⠌⠻⣷⣄⠀⠀⣸⣧⠀⠀⠀⠀⣷⣎⣿⣿
⠀⣴⣿⡿⠁⠀⢈⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠐⣿⣿⢰⡏⠀⠁⠀⠀⢈⣿⣧⣠⣿⣿⡆⠀⠀⠀⢰⣾⣿⣿
⠀⢰⣿⣇⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠻⣿⣿⣇⡀⠀⠀⣠⡿⠋⣠⣿⣿⣻⣿⠀⠀⠀⣼⡿⢿⣿⣆
⠀⢸⣿⡿⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⣿⠿⣿⣦⣼⣫⣴⣿⣿⣿⠟⠛⣿⣇⢀⣾⡿⠁⢸⣿⡟⢦⠀⠀⠘⠃
⠀⣿⣿⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣤⡀⠀⣿⢀⣿⣿⠛⠉⠁⢠⣿⡏⠀⠀⢹⣿⣾⡟⢧⡀⢸⣿⡇⠈⢣⡀⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⣿⣿⣿⣿⣿⡿⠉⠙⠛⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⣿⣿⣿⣿⣶⠙⢛⠻⡿⠃⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣄⠈⠻⣿⣆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣭⡉⢻⣷⠀⠘⣿⣶⠀⠀⠀⠠⢤⣀⠀⠀⠀⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣤⣿⡇⠀⣿⣿⡄⠀⣤⢤⠤⡈⠉⠀⢠⣟⣡⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⡿⣷⣶⣿⢘⣇⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⣿⣿⣿⣿⣿⣿⣽⡿⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣿⣿⣿⣿⣿⣟⠁⠀⢧⠀⠀⠀⠀⠀⠀⠉⠓⠠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠹⣿⣿⣿⣄⡀⢸⡀⠀⠀⠀⠤⠠⠤⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⣀⣀⣀⣹⣿⡍⢿⣿⣾⣧⣀⠀⠀⠀⠘⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣇⠀⠀⠙⠿⣿⣿⣶⣤⣀⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣶⣦⣄⡀⠠⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣉⡛⢶⣯⣽⣛⠿⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⢿⣿⣿⣿⣿⣷⡿⣿⠆⣿⣿⣿⣿⡀⠀⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⣥⣤⣍⣙⣲⣤⣉⣿⣿⣿⣿⣧⠀⣿⣿⣿⢿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣇⣿⣿⣿⣷⣾⣡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢚⣻⣿⣿⣿⣿⣿⣿⣿⡏⠀⢶⣤⢹⣿⣿⣿⣿⠸⣿⣿⡏⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣽⡿⠛⠁⣈⡞⠿⣿⣟⢦⣀⣠⣾⣯⢻⣿⣿⢷⡼⣿⣿⡌⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠈⢻⣆⠈⢿⣿⣿⣧⡹⣿⣏⣷⢹⣿⣧⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠛⠛⠋⠙⠛⠈⠀⠉⠉⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣀⣤⠄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣀⣄⣤⣤⣔⢋⣽⣿⠿⠓⠶⢀⡼⠣⠀⢀⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⣀⣴⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠈⣟⢁⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⢻⣿⠟⠁⣉⣽⣿⡿⠋⠀⣀⣴⣶⣶⡄⠈⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣫⣾⠟⠁⢀⣴⣿⠟⠋⠀⠀⢰⣿⣿⣿⣭⡿⠀⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢟⡽⣿⣿⣿⣿⣿⣿⠿⢤⣤⣾⡿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠛⠀⠀⣩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣤⣠⣞⠟⢁⣴⣳⣾⣿⣿⣯⡽⠋⣁⣴⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠔⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿⣿⣛⣿⠿⠋⠉⠙⡾⠏⢡⠞⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣾⣦⡄⣹⠿⣅⠀⠀⢀⣾⣡⠖⢁⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⠘⣉⣆⣼⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠿⣿⢟⡼⠋⠀⠈⠇⠄⠘⠏⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠋⠉⠛⢻⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⡀⣴⠏⠀⠀⣠⠶⣄⠀⠐⢦⡐⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠖⠉⠀⠀⠀⢀⡶⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣻⡿⠃⠀⠄⠀⠀⠀⠈⠳⣄⠀⠱⣄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠴⢐⡀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡿⣡⠞⠁⠀⠀⠀⠀⠀⠀⠈⡷⢀⡉⠳⠀⢀⡀⠀⢀⡀⠘⣡⠔⣋⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⢀⠞⠀⠀⠀⢀⡼⡀⠞⠁⣠⠴⠚⠳⣄⠈⢁⢚⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⠀⠀⠁⠀⠀⠀⢀⡾⠁⠀⡴⠞⠁⠀⢀⡀⠈⠁⠀⡈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠘⢦⡀⣴⠀⠀⠀⠀⢠⡞⠁⣠⡞⠁⠀⠴⠾⠛⠁⠀⠀⠹⢄⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⢠⡟⢄⡾⠋⠀⠀⠀⠀⠠⠶⠟⠋⠀⠀⢸⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣾⣵⠟⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠈⠉⠉⢉⡩⢏⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⠂⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣾⣭⣛⡋⠂⠐⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠉⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⠿⣿⣿⠀⣴⡾⣶⣄⣸⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⣠⣿⣿⠈⣿⣤⣼⡿⣿⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⠆⠈⠉⠉⢠⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⣻⢿⠿⣀⡀⠠⠤⢾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣾⡧⠠⣤⣖⣲⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⢰⣾⣿⣷⣿⣿⣿⣷⣦⣿⣿⣿⣾⡟⠑⠆⠀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣤⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠊⠀⢰⣠⣤⣿⡎⠇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⠇⠉⠉⠙⠛⠏⠉⠀⠀⠀⠀⢠⣼⣿⣿⣿⣷⢸⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣧⡶⣖⣶⣶⣶⣲⣖⢦⠀⠀⠀⠙⣿⣿⣿⣿⢸⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⡿⡘⢰⣲⠀⠀⣿⣿⣿⡟⢸⡇⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠉⠀⢡⣿⢸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡿⣿⣿⠏⣰⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠐⠁⠀⠀⢂⣾⣿⣄⠹⣿⣿⢏⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠂⣹⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⢷⡀⢀⣾⣿⣿⣏⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠉⠉⠻⠟⠉⠀⠀⠀⠀⠀⠀⠈⠛⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⣶⣄⣰⡇⠀⠀⢀⠀⠀⠀⣆⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢠⡆⣤⠀⡄⣴⣼⣇⡴⡇⣰⣿⣧⣾⠇⣴⠀⢸⡆⠀⢀⣽⠓⣴⣷⡀⣿⡇
⠀⠀⠀⠀⣇⠀⣿⣿⣇⢸⣶⣼⣿⣿⣶⣶⣿⢿⣷⡷⡅⢻⡗⣿⣿⣯⣿⣇⢸⣷⣶⣿⡷⣖⢿⣿⣷⣿⡇⢲⣼
⠀⠀⠀⠀⣿⣟⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣯⣿⣇⣼⡗⢿⣿⣿⣿⣿⣺⣾⡻⣯⣵⣿⣿⣿⣿⣿⣷⠂⢿⣄
⠀⢀⣾⣷⣿⣟⢾⣻⢿⣿⣿⣿⠿⣿⣿⣿⣿⠞⠧⢘⣁⢸⡄⠸⢻⣿⣿⡿⠟⠛⠆⡽⢿⣿⣿⡛⠻⣿⣯⣤⣼⡿⡇
⢠⣶⣸⣿⣿⣿⣿⣯⣭⣯⣿⣽⣿⣿⣿⣯⣭⣤⣤⣤⣤⣴⣋⣀⠉⠉⠉⠁⡤⠶⠤⠿⡿⠏⢡⡴⢤⣈⡯⢉⣵⣊⠋
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⡇
⡇⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⢿⣿⣿⡇
⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⠀⣿⣿⡇⠀⠸⢻⣿⡇
⡇⣀⣤⣤⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢰⣿⣿⠇⠀⠀⢸⣿⡇
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠘⠋⠀⠀⣾⣿⣿⡿⠀⠀⠈⠛
⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⢸⢿⡟⠋⠉⠀⠀⣀⣠⠀⡆⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣴⣾⣿⣿⣥⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣿⣿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢹⠏⡿⠟⡇
⠀⠀⠀⡄⠀⣻⡟⠋⠀⠀⠀⣸⣿⠀⠀⠀⡀⠀⠀⠀⠀⡇⠈⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⢠⣤
⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣷⠀⡇⠀⣷⠀⠀⠀⣸⣿⣽
⢠⣧⣴⣷⣦⣤⠀⢠⣤⣀⣸⣿⣿⣧⣶⣾⣿⣿⣶⣤⠀⠀⠀⠀⠀⢀⣠⣤⣶⣸⣿⣿⣮⣷⣤⣿⣃⣄⡀⣿⣿⣿⣄
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠶⠂⣠⣶⣶⣶⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⠛⠛⠉⠀⠀⠀⣛⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠙⠛⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠒⢚⡟⠉⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣄⣤⣖⠊⣽⣿⠟⠉⠉⣉⣭⡽⠾⠛⠛⣟⣿⣟⣋⢉⣩⡿⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⢙⣿⣶⣴⠾⣟⣋⣀⣠⡴⠞⠋⡀⠭⠛⣉⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⣲⣿⠾⠛⠉⣀⣤⠿⠛⠉⠁⠰⣦⣋⡀⣒⣛⣉⣠⣾⣃⣄⠀⠀⢀⡀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣶⠞⣩⣴⣠⣶⣿⣿⣶⡿⣿⣿⣿⣿⡿⣏⣹⣿⠿⢿⡟⠻⠿⣿⠷⠊⢁⡴⠋⠀⡠
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⣤⣾⣿⡿⠟⠋⣉⣠⣴⣶⠟⣿⡿⠿⢛⣭⡍⠀⠀⠀⠬⢹⣿⢥⣠⣶⠋⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⢀⣠⣴⣾⣿⠿⠟⠛⠉⢁⣹⡷⠖⠛⡛⢻⣿⠾⠛⡉⠤⠀⠀⠁⠀⠀⠀⠀⠤⠀⠙⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣲⣶⡿⠟⠋⢉⡀⠤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠰⠶⠊⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠼⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣧⡤⠶⣟⣓⠶⠮⣟⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠉⠙⠛⠻⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢀⣠⣴⣶⣶⣶⣾⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠂⠀⠠⠀⠀⠀⣼⣏⣴⣿⣿⡿⠁⠀⠀⠀⠈⣿⣿⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⣤⣤⣄⠀⠀⢆⠀⣿⣿⣿⡿⠋⢓⣲⣾⣶⣶⣿⣿⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠸⣿⣽⣿⠆⠀⢈⠀⢿⣿⣿⣦⡈⠉⠀⢙⠟⢁⡀⠹⣿⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠛⠉⠁⠀⢀⡼⠂⢼⣿⣿⣿⣿⣦⣤⣤⠀⠛⠷⣾⣿⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣴⣶⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣗⠤⣒⣻⣿⣷⡄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⢻⣿⣿⣿⣿⣿⣿⡋⠀⠹⢿⣿⣿⣿⣿⣷⣬⠈⠉⣽⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⢀⣼⣿⣽⣿⣿⣿⣿⣷⣤⣄⡀⠈⠉⠛⠿⢿⣿⣿⣿⣿⠿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⣴⣿⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣯⣑⠒⠠⠄⢀⣀⣀⣀⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣯⣍⣙⠻⣿⠿⣝⠿⣏⡻⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠛⠾⢭⣉⠻⣾⡞⣻⣮⡷⢬⣻⣾⣿⣿⣿⣿⣯⣭⣽⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠈⠉⠌⠻⣿⡍⢻⣷⣬⣝⡻⠿⣿⣏⣻⣯⣷⢟⣻⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡏⣴⣶⡆⠀⠀⠀⠀⠀⠈⢷⡘⣷⣟⢻⣿⣿⣿⣿⣛⠿⣿⡿⢿⠏⠈⣿⠷⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠏⠠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣏⣤⡈⠙⠻⠿⠷⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣷⡘⣿⣽⣷⡀⠀⢀⠀⠀⠀⠰⡆⠀⡂⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⢀⠘⣿⣧⠘⣿⡇⣻⡇⠈⠈⠀⠀⠀⣷⣀⣸⠿⡃⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⣿⠀⢸⣿⣿⣧⣀⣠⣤⠴⠀⠈⠉⠁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠞⠁⠀⠀⢿⣿⣿⠀⠀⠃

⠀⠀⠀⠀⠀⠀⣠⡴⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣖⣒⣒⣒⣛⣒⣒⣒⣒⣒⣒⣒⣒⣒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⣼⠋⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⣿⣿
⠀⠀⠀⠀⠀⣿⠀⡶⠒⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⠀⣿⣿
⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡏⣿
⠀⠀⠀⠀⠀⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇⡿
⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⡇
⠀⠀⠀⠀⠀⢻⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⡇
⠀⠀⠀⠀⠀⢸⡇⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⠇⢸⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣊⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠀⢀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⢻⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣋⣙⣛⣛⣛⣃⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣠⠶⣖⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣴⣲⣒⣶⣒⣶⣒⣶⣒⣶⣒⣲⣒⣲⣒⣲⡀⢰⠛⣿⠛⣿⠿⡍⢷⠀⠀⠀⢸⣣⠖⠋⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠟⡼⠲⡿⠲⠗⠒⡷⠒⢿⠒⢾⠖⢺⠖⠺⡧⠸⡇⠈⣯⠽⣭⠽⣭⠽⡌⢷⡀⠀⠈⢷⡄⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢠⣏⣀⣉⣉⣉⣉⣉⣉⣙⣛⣉⣛⣛⣛⣛⣛⣛⣙⣛⣋⣀⣸⣶⣿⣶⣟⣶⣟⣈⣷⠀⠀⠀⠹⣦⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠸⠧⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠁⠀⠀⠀⠈⠛⠶⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢶⡦⠤⠤⠤⠴⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡿⠻⠿⠿⠿⠿⠿⠿⠻⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡷⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡷⠶⠶⠶⠶⠶⠶⠶⠶⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢚⠃⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣙⡁⣿⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣬⣥⣿⠀⠀⠀⢿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣧⣀⣀
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠁⢙⣿⣿⣿⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⠴⠶⠶⢦
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡿⠥⣽⠥⢼⠯⢬⡯⠬⡿⠭⣿⠥⢽⠥⢽⡯⠬⣯⠬⢿⠤⢽⡭⠽⣷⠀⠀⠀⢸⣀⣠⣄⣀⡇
⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⠿⢿⡿⢿⣿⣿⠀⠀⠀⣾⠓⠒⠛⠒⣿⠒⣺⡓⢺⡟⠒⣿⠒⢺⡗⠚⡗⠒⠛⠒⢻⡗⠚⣷⠒⢻⣇⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣤⣾⣦⣼⣧⣼⣿⣿⠀⠀⢰⣏⣉⣽⣉⣹⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣄⣈⣿⣉⣹⣏⣉⣿⡄⠀⠘⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠬⠭⠭⠭⠭⠭⢭⣭⣽⣿⣟⣛⣓⣒⡶⠶⢶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣉⠉⠉⠉⢻⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣼⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⢹⠂⠀⣿⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⠉⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡿⣿
⠀⠀⠀⠀⠀⢠⣶⣿⣭⣤⣤⣤⣄⣠⡴⠟⣿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⡇⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡤⢤⡀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⡇⡟
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⢸⠃⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⢻⡇
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡇⢸⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣾⢸⠇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⢸⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣸
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⣸⠀⡿⠀⠀⢿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢠⡇⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢉⠁⠀⡇⠀⠀⢸⡄⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢸⡇⠀⢸⡇⡏
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡠⣄⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢸⣹⡇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠙⠋⠀⡧⠀⣀⡼⠷⢲⡶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠦⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣬⣥⣤⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⣤⣤⣴⡷⠛⠉⠀⠀⣏⡀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠓⠒⠒⠒⠒⠒⡺⢻⡇⠀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣉⡓⢲⡀⠀⠘⣯⡭⠭⠭⠭⢭⣭⣭⣭⣭⡷⠋⠀⠀⠀⠈⠉⠓⠒⠒⠲⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⠿⣿⠯⢭⡭⢭⡭⠭⣍⣙⣛⣛⣛⣛⣒⠒⠶⠶⠶⠶⠦⠤⢤⣤⣤⣤⣄⣀⠀⠀⠀⠀⣈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⠼⢭⡽⢭⣭⣏⣩⣟⣛⣲⠓⢒⡞⠓⡾⠧⢬⡽⢭⣭⢇⣼⣹⣗⣲⣒⡶⠀⡼⢻⡀⢀⡴⠛⣿⣏⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣀⣉⣉⣚⣓⡒⠓⠴⠯⠤⠽⣭⣩⣏⣉⣟⣓⣲⠟⠒⣲⢣⠾⣴⢧⣴⣁⡜⢁⠞⣴⠏⠀⣼⠗⠉⠱⠒⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⠶⠦⠭⣭⣭⣍⣉⣙⣒⡒⠒⠶⠦⠤⠭⠭⣭⣍⣁⣛⣚⣓⣾⠶⢎⡴⢋⡼⠃⠀⠀⢿⣇⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠒⠶⠶⠶⠶⠤⠤⣤⣤⣬⣭⣹⣴⠛⠀⠀⠀⠀⠘⣯⣢⣤⣤⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠻⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⢦⣤⣀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠴⠶⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢄⣀⡈⠙⠛⠛⠛⠋⠉⣁⣀⣀⡴⠶⠛⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠲⠗⠀⢸⠀⠀⠉⠁⠀⠛⠚⠛⠛⠫⣤⣍⢡⡀⠀⠀⢸⡇⠀⡀⢨⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢀⡀⠶⢾⡀⢶⣿⣟⡄⢱⠄⠀⡎⣿⣶⡞⢀⠙⠀⣰⠚⠓⠐⡇⢸⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣤⠛⢛⠀⢶⣽⣿⣧⠴⠂⠀⢷⣈⣿⣣⣼⠶⠀⠙⢳⡶⠺⣷⠸⠁⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠀⢸⠀⠀⠁⢀⡤⠀⠠⣄⠀⠉⠀⠉⠀⡀⠀⠀⢸⡇⠀⠘⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⣤⠶⣍⠀⠀⢀⣼⠂⠀⠀⣠⡾⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢺⣄⠀⢀⣷⠴⠛⠁⣀⣠⠾⠋⠀⡃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠉⠛⠿⣥⠤⠚⠟⠋⠉⠀⠀⣿⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠿⢧⡀⠀⠀⠀⠈⠢⣄⠀⡀⠀⢂⣴⠏⠀⠀⣠⡾⠉⠉⠀⠀⠉⣩⡟⠛⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠋⠀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠙⠛⠚⠛⠁⣴⣿⠶⠛⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⡴⠷⢦⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢀⡴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢀⣴⠶⠒⠶⢾⣧
⠀⠀⠀⠀⢰⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡞⠁⠀⠀⠀⠀⠙⣧
⠀⠀⠀⢠⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠘⠷⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠂⠛⡈⢳⠀⠀⣿⠀⠀⣿⡀⠀⠀⠀⣀⣀⣤⣴⡶⠿
⠀⠀⠀⠀⠀⠀⡏⠀⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠦⣤⠀⣄⠀⣀⠁⢸⠀⠀⣿⠀⠀⠉⠛⠛⣿⡟⠛⠉⢹⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠈⢻⠛⢿⡷⠶⠶⢦⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠉⠀⠀⣿⡀⠀⠀⠀⢀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠘⣷⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠳⠶⠶⠶⣶⣤⣤⣤⣀⣀⣽⣇⣠⡶⠞⠋⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠃⠀⠀⣿⠀⠀⠙⠛⠶⢦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⠉⠁⢀⣠⣾⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣠⣾⣦⣤⣤⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠿⠿⠶⢶⣶⣦⣤⣤⣤⣄⣀⣀⠀⠀⣘⣠⣴⠿⠋⠀⣿⠀⠀⠀⣾⡇
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢹⠂⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠄⣀⣀⣀⣀⣀⣉⣉⡿⠟⠛⣿⡟⠛⠋⠀⠀⠀⢀⣿⣄⣀⣀⣽⣇
⠀⠀⠀⠘⣧⣀⣀⣀⠀⢀⣾⠀⢀⣀⣠⣤⡤⣾⡇⠀⠀⠀⠤⠀⢉⡉⠉⠉⣉⣉⣤⡴⠛⣿⣇⠀⠀⠀⠀⠀⡏⠁⠉⠉⠉⠉⠙⣷
⠀⠀⠀⠀⠈⣿⠋⠉⣿⠋⠁⠀⣾⢿⡄⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢁⣤⡴⠚⣿⠋⠉⠛⣻⣶⣶⢃⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⡟⠀⠻⣦⠀⠀⠻⢶⣤⣀⣀⠉⠁⠀⠀⠙⠋⣉⣀⣴⠾⢋⣠⡶⠟⠁⠀⡟⠘⣷⠶⠶⠶⣶⠿⠃
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⣷⡀⠀⠘⢳⣄⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⣉⣡⡶⠛⠁⠀⠀⠀⣀⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡯⠀⠀⣟⠀⠀⠀⠙⣷⡄⠀⠀⠙⣷⠶⠶⠿⠟⠛⠛⠚⠛⠛⠛⢿⡏⠁⠀⠀⠀⢀⣠⣶⠟⠁⠀⣿⠀⠀⢨⣿
⠀⠀⠀⠀⣰⡷⠶⢶⣏⠀⠀⠀⠀⠈⠻⣦⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⢀⣠⣶⣿⡏⠀⠀⠀⠀⣿⠀⠀⢸⡟
⠀⠀⢀⡾⠁⠀⠀⠀⠙⡿⣆⡀⠀⠀⠀⣿⠻⣾⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣧⣾⠟⠋⠀⣿⡇⠀⠀⠀⠐⣿⣤⣤⡾⢷⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⣰⡟⠀⠀⠀⠀⠀⠀⣇⢸⣧⠀⠀⠀⣿⠀⠈⠉⢹⣟⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠀⠀⠀⠀⣿⠁⠀⠀⠀⢰⠋⠳⢦⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⣩⡿⣦
⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣻⡀⢀⣿⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⢦⣀⠀⠀⠙⠛⠶⣄⣀⡰⠶⠛⠋⠀⣠⣿⣀⣀
⡿⠒⠦⢤⣤⣤⣀⣸⡀⣿⠿⠾⣿⠇⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⡽⠳⣤⣀⠀⠀⣼⠋⣀⣀⣤⠞⠻⣯⣤⣩⡽
⠘⢧⡄⠀⠀⠀⠀⠉⣻⣿⣤⠾⠁⠀⢸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢰⣯⡀⢠⡞⠛⠳⢾⢿⡖⠉⠉⢳⣤⣤⢾⠇⣏
⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⣀⣼⣏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⢸⡇⢹⡇⠀⠀⠀⠀⠀⠙⣶⡶⢾⡏⠀⢸⠄⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠿⢷⣶⣿⣧⠀⠀⠀⠀⠀⠀⢰⡿⠿⣶⣶⣶⣶⡿⢿⣷⠀⠀⠀⠸⣧⣄⣳⠀⠀⠀⠀⠀⢰⠏⠀⢸⡧⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠘⠿⣤⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⢷⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠿⠿⢿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠛⠿⠷⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣿⡁
⠀⠀⠀⠀⠀⣀⣠⠶⠞⠛⠁⠀⠀⠀⠀⢀⣴⠞⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣏⠉⠉⠉⠛⠶⢦⣀⡀
⠀⢀⣤⣾⣛⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣤⡀⠀⠀⠀⠉⠙⠛⢦⣄⣀
⠀⣼⠋⠉⠉⠙⠛⠶⠶⠶⣤⣤⡶⠋⠁⢀⣴⡟⠉⡃⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣄⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠈⠉⣷⣦⡀
⠀⢿⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠇⢀⣴⠟⠉⣥⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢻⡷⣦⡀⠀⠉⢻⡶⠶⠚⠛⠛⠛⠁⢹⡃
⠀⠀⣹⠉⠹⠛⡿⢳⡶⣤⣤⣴⡿⢻⠅⠀⢀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣶⣾⠃⠈⠻⣦⣄⣸⡇⠀⣀⣀⣀⣀⣠⣼⠇
⠀⠀⠹⣄⣼⡄⠁⣼⡀⠠⡄⠀⢀⣼⠷⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣀⠃⣴⠏⠛⠛⠿⠙⡟⢛⠙⡏⢹
⠀⠀⠀⠀⠀⠙⠶⠜⠛⠶⠼⠷⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠹⣆⠀⢀⣸⣠⣷⣀⣶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢻⠉⠙⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⡆⠀⢸⡄⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠍⠉⠤⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⣀⣀⣠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⡛⠛⠛⠓⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡾⠛⠛⠛⠛⠋⠉⠉⠉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⡴⠯⣴⠿⠶⡾⠷⠶⡴⠧⢤⣤⢏⣍⣽⣏⣉⣩⣏⣉⣉⣟⡓⣳⣶⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⡜⠓⡲⠛⢒⠞⠓⢒⠞⠓⢲⠞⠓⢲⡞⠳⢶⡾⠷⢤⡴⠯⢤⡝⡿⠁⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⡟⣠⠞⠓⡾⠛⢲⠟⠒⢲⠟⠒⣲⠟⠒⣶⠟⠶⣶⠿⠶⣤⠾⢤⡴⣫⠟⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⣠⠟⠀⠿⠶⠾⠷⠶⠿⠶⠾⣿⣶⣺⣗⣒⣺⣗⣒⣺⣗⣒⣾⣷⠶⣯⠟⠁⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢠⡿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠁⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢻⡇⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠸⣧⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣤⠶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠒⠶⠶⠶⠶⠶⠶⠶⠼⠷⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣼⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠲⡋⠖⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢀⡀⠀⢩⠀⢀⡀⠀⠀⠧⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⡀⠀⠉⠁⢀⠶⡀⠉⠀⠀⠠⠂⠀⠈⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠐⠀⠒⠁⠀⠀⠐⠐⠈⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⡒⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠲⢬⠀⠀⡋⠀⠀⡏⠀⠀⢹⠀⠀⡇⠊⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠤⠷⠤⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡭⠩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢏⠀⣠⡇⢸⠀⠀⠀⠀⠀⢸⠁⠀⠄⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⡆⠈⠀⠀⠀⠀⠀⢸⠀⣇⠀⢈⠗⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠺⣄⣠⠞⠉⠀⠙⠺⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⡼⠒⠁⠈⠛⢄⠀⡼⢆
⠀⠀⠀⠀⠀⢠⡁⠀⡜⠁⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠹⡄⠀⣠
⠀⠀⠀⠀⢀⠆⠈⡛⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠸⡋⠀⠆
⠀⠀⢠⠊⠉⢉⠒⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡶⠶⠶⠦⠤⠤⠤⠤⠴⠶⠶⠶⠤⠤⠤⠤⠤⠤⠴⠦⢴⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠂⠉⠙⢦
⠀⠠⠚⠈⠁⡈⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠉⠀⠉⠙
⠀⠀⠀⠀⠀⠉⠀⠄⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⠀⠀⠀⠀⠀⠀⢸⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠈⠁⠁
⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠒⢺⠀⠀⠀⠀⠀⠀⢸⠐⠐⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠤⠴⠀⠀⠀⠀⠀⠀⠸⠠⠤⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠤⠴⡇⠀⠀⠀⠀⠀⡶⠤⠄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠈⠀⠀⠉⠓⡄⠀⠀⠀⡴⠋⠁⠈⠁⠈⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠈⠀⠀⠩⠆⠀⠸⠁⠁⠈⠉⠉⠉⠁⠈⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⠉⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠢⠀⠀⠁⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠶⠀⢀⠀⠶⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠐⠂⠀⠀⠠⠀⠉⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠃⠀⠀⠀⣀⢠⠀⠀⠶⢤⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠁⠀⠂⠀⠀⠒⠐⠈⠀⠀⣠⠔⠀⠀⠀⠀⠱⣀⡧⠴⣁⠴⠉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⣤⣄⣀⣠⣤⡤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⣖⣋⠨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡤⠒⠈⡋⠈⠉⠁⠈⠓⠈⡶⠠⢄⠀⠀⠀⠀⠀⠀⢀⡕⢤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠋⢠⠃⠀⠀⠙⠲⠤⠤⠤⠴⠊⠁⠀⠀⢻⠐⢄⣀⡠⡔⢋⡠⠃
⠀⠀⠀⠀⠀⠀⡠⠚⣀⣤⠀⡎⠀⣴⣿⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣇⡀⠴⠊⠁
⠀⠀⠀⠀⠀⣘⢁⠖⠁⠈⢳⠁⠀⠙⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠁
⠀⠀⠀⢀⠴⠣⢿⠀⠀⠀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⡠⠤⡇⠀⠀⢀⡇⠀⠀⡇⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡆
⠫⡤⠊⡽⠲⠶⢮⠙⣆⠀⠈⢑⠒⠤⠤⢀⣀⣀⠂⠀⠀⣀⣀⡀⢬⠴⠚⠁
⠀⠉⠲⠆⢨⠇⠀⠉⠁⠀⠀⢀⢒⡁⠒⢄⠀⠀⠀⢀⠔⠋⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣱⣤⠂⡀⠀⣇⣔⠁⠈⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠒⠒⢎⠀⠀⠀⠀⠀⢨⠗⠒⠚⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣶⡶⡎⠀⠀⠀⠀⠀⢘⡶⣶⡶⡏
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠰⠴⠣⠄⠤⢱⡀⠀⠀⠀⠀⣸⡡⠤⠤⠣⠤⠤⢄
⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠐⠈⠠⠀⠀⠙⢆⠀⢀⠞⠁⠀⠀⠈⠄⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⣏⣩⣉⣹⣉⣹⣉⣩⣉⣹⣹⠀⢸⣸⣁⣋⣈⣛⣀⣙⣈⣋⣘⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠀⠀⡠⠤⠤⠐⠒⠒⠠⢤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⣰⣶⡤⠒⣿⣲⡀⠂⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡲⠁⡘⠀⠀⠀⠁⠀⠀⠀⠁⢢⠋⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⡇⢸⡉⠉⠉⠃⠒⡶⢰⢸⠀⠀⢠⡇
⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣑⡢⠤⠤⠔⠃⢸⠈⠓⢺⠋
⠀⢎⠳⡱⡘⣀⡀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠍⠉⠉⠙⠛⢿⡛⠚⢻⡉
⢎⠢⣳⡵⠋⠉⣗⣲⢦⢲⠒⠒⢲⠃⠀⠀⠅⠀⠀⠀⠀⠀⠱⡀⡤⠷⠤⠤⣄⡀
⠀⠱⡏⠀⠀⠀⡏⠀⢸⢸⠤⢤⡏⠀⠀⠀⠀⠀⠀⠤⢤⠀⠀⡇⠧⠤⣤⢤⡇
⠀⠀⠈⠒⠤⠤⠣⡀⠈⢸⠀⢰⡇⠀⠀⠀⠀⠀⢄⡘⣸⠀⠀⡇⠀⠀⣷⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠑⢕⣤⡈⠀⢸⠀⠀⠀⠀⠀⠠⠀⠠⠠⡀⠀⡇⠀⠀⢸⢀⡇⡇⠀⠀⠀⢠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠇⠀⢸⠀⠀⠀⠐⠀⠉⠁⠈⠒⠁⠀⡇⠀⠀⣿⢸⣇⡇⠀⠀⢀⡨⠖⠛⢻⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡏⠘⠶⠃⠀⠀⠻⣄⡀⠀⢸⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⢄⣀⣀⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⢇⠀⠀⠀⠈⠉⠉⠙⠛⠖⡚⠒⠞⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠉⠙⢦⡀⠀⠀⠀⠀⠀⡰⠐⣄⣀⣀⣰⠡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢧⠀⠀⠀⠉⠒⠲⠦⠤⠖⠓⠒⠉⠁⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⡄
⠀⠀⠀⠀⠀⠀⢀⡀⠤⢆⡰⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⠃
⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⢤⠔⠂⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢘⣀
⠀⠀⠀⠀⠀⣔⡉⠒⠤⣀⢰⣀⠤⠂⢉⡶⠀⠀⠀⠀⠀⢰⠚⠭⣄⣐⠖⢀⡩⠴⠆
⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣙⣅⡤⠖⠁⠀⠀⠀⠀⠀⠀⣸⣀⠀⠀⠈⠉⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⣉⠑⠂⢾⠐⠈⣁⡤⠗
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣳⣾⣖⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣿⣿⣷⡆⠀⠀⡤⢶⣿⠀⠀⠖⠿⠿
⣿⠛⢻⡿⠹⠿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢟⣫⣵⣾⣿⣿⣿⡇⠀⠀⢀⣴⣿⠀⢀⣠⣶⡇⠀⠀⢀
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⣋⣽⠞⣋⣝⡛⢹⣿⣿⣿⣇⡀⠀⠀⣿⣟⠀⠈⢻⣿⡇⢠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣛⣥⡶⢿⣽⣾⣟⣛⢛⣻⣤⣿⣿⣛⣉⣡⡶⠿⣿⣿⣷⡀⠿⠿⣧⣼⣿⠿⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣛⣭⣶⡿⠛⣡⣴⣶⠆⣿⣿⣿⡎⢿⡇⠈⣿⣿⣿⣿⣟⠁⢹⣿⣿⣥⡀⠀⢻⣋⣠⣤⠤⠶⢞⣛⣯⣿⢟⣿⣏
⠀⠀⠀⠀⠀⢀⣠⡤⠾⢛⣩⣴⣾⡿⣛⣭⣶⠟⢋⣩⣴⠂⠉⡹⣏⣿⡿⠿⠒⢰⣶⠿⠿⠛⠓⣾⠟⠛⠋⣉⣿⠛⢋⣁⣤⣶⣾⡿⠟⣫⣴⣿⣿⣿
⠀⠀⠀⠀⠈⢻⡟⠀⠘⠻⣿⣿⠷⠿⠛⣉⣴⡾⠟⠉⣀⣤⣾⠁⢻⣿⣿⡏⢹⡟⠿⣷⡶⠿⣿⣿⣆⠐⣿⣿⣿⡾⢿⡿⠿⠋⠀⣠⣾⢟⣿⢿⡟⡿
⠀⠀⠀⠀⠀⠀⠁⢤⣶⠖⠈⠁⣤⡶⠿⠿⢁⠖⡒⠠⣌⣻⡟⣰⡞⣿⣿⢃⣾⣷⡀⠙⣿⡄⠀⢻⣿⡆⠙⣿⣿⣷⠀⠀⠀⣠⣾⠟⣱⣿⣣⡿⢡⠇
⠀⠀⢀⣠⠀⠀⠀⢀⡁⣶⣿⣷⡌⠙⢦⣰⣤⣴⣜⣞⠛⠛⣆⠉⠻⠟⣡⣾⣿⣿⠿⠀⢽⣿⡄⢨⣿⣇⠀⢹⣿⣿⢀⣴⣿⡿⢋⣾⣿⣳⣿⠃⣾
⠀⠘⣿⣿⡀⠐⣾⣿⣿⡌⠻⣿⣿⠀⠀⠙⢦⡀⣼⠟⣆⣰⣽⣧⣶⣾⣿⡿⠋⠁⢀⣠⣴⣿⣧⢀⣙⣿⠀⢾⣿⣿⣿⣿⠋⣰⣿⡿⣳⣿⠇⢸⡏
⠀⠀⠈⠻⣿⡄⠈⠻⣿⣷⠀⠈⢻⡆⠀⢠⡀⠸⢋⡤⠘⢿⣿⣟⠛⢻⠃⣀⠴⠞⢻⣿⢿⠟⠛⠛⠫⣥⣤⣌⣿⠇⠹⣯⣾⣿⡿⣱⣿⡟⠀⡿
⠀⠀⠀⠀⠘⢿⡀⠀⠘⣿⠀⠀⣠⣴⣶⣿⣧⣄⣼⠃⣠⣿⣻⣿⣿⣮⠘⢿⣷⣤⣿⠸⡞⣷⣦⣀⠀⠉⠉⠉⠉⠀⠀⢻⣿⡟⣴⣿⡿⠁⣸⠇
⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⢾⣿⣿⣧⡻⡛⠻⣧⡀⠹⣿⣿⡆⢧⣻⣿⣿⣿⠶⠄⠀⠀⠀⠀⢸⡟⣼⣿⣿⠇⢀⣃⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣀⣤⠔⠂⠓⢠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⠿⢷⣽⣏⡉⠁⡀⠹⣿⣧⣬⡷⢶⣶⠐⠲⠶⣶⣶⣾⣿⠀⡰⠁⠁⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠐⣶⣿⠁⠀⠀⠀⢾⣿⣿⣿⡏⠙⢿⣿⣽⣿⣿⣽⣯⣶⣿⡷⠈⢫⡟⣼⣫⣦⣽⣿⢱⡹⣦⠻⢷⣦⣬⢿⣿⣿⠇⠀⠁⠀⠀⠀⠰⠿⠿⠿⠟⠛⠉⠉
⠀⠁⣿⠇⠀⠀⠀⠀⠸⣿⣿⣿⡇⢀⣼⢿⠿⠿⠟⠙⠛⠛⠋⣹⣶⣿⣶⠛⠛⢿⡉⢹⡇⢻⡌⢷⣄⣠⣯⣶⠾⠉⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤
⠀⠀⠘⢦⠀⠀⠀⠀⠀⢿⣿⣿⣇⠘⣆⠀⠀⠀⠀⠀⢀⡞⢠⣿⠛⠃⠈⠙⠟⠀⠉⠻⣿⣤⠟⠈⠉⠉⣁⣀⣀⠈⠡⠄⠀⠀⠀⠀⠒⡾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠈⠳⢦⣤⣤⠴⢟⣡⣿⣿⣦⡀⢀⣀⣀⣠⣤⣤⡜⠳⣶⣿⣿⣿⣿⣿⠟⢀⣀⣠⣤⣶⣶⠟⠋⠀⠀⠉⠛⠋⠉
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠓⠀⣄⠀⠀⠒⠻⡋⠉⠉⠁⠈⠻⣿⣿⣿⣿⠋⢀⣤⣾⡿⣿⠟⠛⣿⣾⣿⣿⠿⠟⠛⠋
⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠘⢆⠀⠀⠀⠀⠈⠻⡿⠁⠒⠋⠉⠀⠀⠀⠀⠘⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⢉⣉⣁⣀⣄⣒⣒⣒⣒⣂⣐⣂⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠰⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⢀⡀⠀⡠⠐⠀⢀⣉⠁⠐⢄⠀⠀⣠⢘⠃⠀⠀⠀⠈⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⡄⢘⢈⣅⠊⢀⠔⠉⡀⠀⣉⡆⠠⠆⠀⣭⢰⡆⠀⠀⠈⠀⡅⣺
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢼⠀⠀⡆⠼⠀⡀⠀⠼⣀⣀⣀⣀⣤⣰⣀⣼⡆⢠⠠⠆⠀⢀⠀⠀⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⡃⣒⢘⠀⠀⠐⠀⠀⢠⠠⡄⠀⠀⠀⠁⠃⠀⠀⠄⠀⠶⠀⠄⠖⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠁⣭⢘⠀⠀⠀⠀⠀⢸⣅⡎⠀⠀⠀⠀⠗⠀⠐⠇⣄⠺⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠄⡇⠀⠰⠄⡄⠀⠀⠀⣼⡥⣷⠀⠀⠀⠀⡄⠀⠀⠂⣉⠀⠈⠁⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠰⠀⠀⢇⡄⠀⠀⠃⠛⠙⠡⠖⠛⢅⠀⠀⢀⡇⠉⠀⠀⠁⠁⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣁⣉⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⠀⠀⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡨⠶⠤⠶⠶⠂⢀⡈⠛⣿⣛⣟⣯⡿⣿⣿⣿⡺⢻⣺⣖⣶⡷⡿⡿⢿⣭⡿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⡐⡠⠀⠀⠀⠀⠠⠴⠤⠴⠤⠴⠤⠾⠦⡮⢠⠰⢤⠠⢄⠠⢄⡀⣄⡰⡄⠀⣀⢸⣕⡀
⠀⠀⠀⠀⠀⠀⠐⡐⠀⢀⠀⣐⣀⣱⢀⡑⣈⣱⠀⣱⠈⡒⠉⣎⢓⣜⢲⡚⠒⠆⠲⢶⠒⢦⠐⠃⢘⣇⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠒⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣬⣶⣤⣤⣤⢤⣤⣤⢤⣄⣷⡇
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⢀⡄⠈⠒⢤⡑⢌⡓⢤⡀⠈⢗⠤⢺⠠
⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠈⠀⠈⢡⠀⠀⠀⠉⠲⢌⠒⢌⡓⠄⣌⡳⠅⠆
⠀⠀⠀⠀⠙⠛⠿⠭⠽⠯⠟⠝⠝⠴⠵⠴⠶⠔⠶⠲⡶⡶⡖⡖⡔⡖⡖⠶⡶⡶⢶⢾⢿⡾⡶⡳⡶⠿⠗⠃
⠀⠀⠀⠀⠀⠄⠀⠀⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣒⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢊⣉⣀⠀⠀⣈⣉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡟⡄⢎⢸⣉⠆⢸⠰⣉⡇⡜⡕⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠵⢧⡬⠭⠭⠤⠤⠭⠭⣤⠵⠵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠋⠙⠛⠛⠛⠛⠛⠛⠉⠋⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡇⠀⡖⢲⠓⡖⢲⠒⡖⢲⡖⢲⠀⣿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡙⣌⢲⡇⠀⠓⠛⠒⠓⣚⡒⠛⠚⠓⠋⠀⣷⢊⡼⣱⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣉⣉⡉⠙⣦⣑⡬⠛⡇⠀⠀⠀⠀⠘⠧⠟⠀⠀⠀⠀⠀⡟⠫⣔⣡⡞⠋⣉⣉⣱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⡆⢸⠋⠀⠀⡇⢠⡴⠧⣄⣠⠜⢤⡀⡤⠷⣤⠀⡇⠀⠈⢻⠀⡎⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡜⠀⠀⠀⡇⠀⠷⠾⠅⠸⠶⠾⠀⠹⠶⠇⠀⡇⠀⠀⠘⢤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⡏⠭⢭⡏⠉⠉⣯⠭⠭⣽⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣗⣒⣒⡇⠀⠀⣗⣒⣒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡧⠤⠴⡇⠀⠀⡷⠤⠤⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡯⠭⢭⡇⠀⠀⣯⠭⠭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣓⣒⣒⣇⡀⣀⣗⣒⣒⣻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠃⠓⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⡴⠀⠀⠀⣎⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⠀⠀⠀⠀⢸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⣻⣀⣀⣀⣀⣸⣛⣛⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠉⠉⠉⠉⠉⠏⠀⠀⢀⣠⠔⠋⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠓⠒⡒⠒⠒⠒⠒⠶⠶⠶⠶⢶⠚⠉⠀⣀⣀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠉⡇⠶⣿⣷⣲⠀⠀⢰⣶⣾⢷⡆⢸⠀⠀⡼⠀⡼⢙⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣈⡇⠀⠛⠛⠛⠀⠀⠸⠻⠿⠿⠀⢸⠀⠀⢹⡀⣳⣘⠤⠃
⠀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠈⣇⣀⣀⡀⠀⠐⣶⠂⠀⢸⡀⠀⠀⢀⣠⠞
⢠⡉⢙⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢒⡶⠶⠦⢭⣭⣭⣍⣉⣀⣀⣸⣇⡤⠞⠉⠳⣄
⠣⣈⣩⢿⣉⡷⣶⡀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠠⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘⡆⠀⠀⠈⢧
⠀⠀⠀⠀⠈⣦⣇⠙⠲⠤⢤⣤⠤⢴⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣠⠚⠉⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠈⠒⠤⢤⣤⣤⠤⡾⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠹⠶⠶⢶⣤⡄⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⣀⡂⢀⢐⠸⡇⠀⢀⡠⢼⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢈⣉⣉⡉⠉⠛⠒⠒⠒⠒⠲⠦⠬⠤⠴⡷⢊⡡⠖⠉⣧⡼⠧⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠒⠒⠒⠒⡏⠁⠀⠀⠀⣇⡷⢦⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣤⢫⠟⢿⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠶⠶⡶⠤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⢸⣇⣠⠖⠋⢷⣻⠀⣸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⠀⠁⡟⠉⢩⡟⠉⠉⠀⠀⠀⠈⠁⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠶⢾⣷⡀⠀⠀⠀⠀⣯⡀⢬⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣚⣉⣀⢀⡴⠋⢀⡇⢀⣠⠔⠋⠀⠉⢻⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠬⠭⠽⠶⠚⠉⢰⣛⡒⠦⠤⢤⣤⠏⣠⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣷⣾⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣠⣼⣄⢀⡀⡀⡀⢀⡀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢠⠒⠉⡉⠐⢄⠀⠀⠀⠀⡠⠂⢉⠉⠒⡄⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⡇⢰⠡⠌⠣⠀⡆⠀⠀⢰⠀⠜⢡⠌⡆⢸⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢹⠀⠀⠀⠀⠣⡈⠑⠒⢁⡴⠁⠀⠀⠈⢦⡈⠒⠊⢁⠌⠀⠀⠀⠀⡏⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⢀⡀⣀⡀⢀⣀⡀⠀⣀⡀⣀⣀⣀⡀⠠⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢤⠤⢠⡄⠤⠤⠤⠤⠤⠤⠀⠇⠀⠀⠸⠀⠤⠤⠤⠤⠤⠤⢤⡤⠤⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧⡀⡀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⡆⠀⠀⢸⠦⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠴⠇⠀⠄⢰⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠛⠐⠃⠘⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠃⠘⠀⠛⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⠒⠒⠒⠀⢴⡃⠀⠀⢘⡦⠀⠐⠒⠒⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢱⠀⠀⡎⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡍⠉⠉⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠂⠀⠴⠶⠤⣤⣤⠠⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⠀⡌⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡼⠀⣀⡤⠒⠋⠑⠒⠢⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⠀⠠⠩⠐⠀⠀⠈⠉⠀⠀⠀⠀⠀⠇⠀⠀⠂⠀⠀⠘⠀⠀⡇⢸⠁⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⣀⠀⠀⠑⠁⠀⠀⠀⢀⠶⠀⢤⣄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⢀⢀⡇⡈⠀⠀⣸⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⣠⡤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⢸⠃⡇⠀⠀⡟⠀⠀⠀⠀⠠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠴⠒⠄⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡞⢰⠁⠀⢸⠀⠀⠀⠀⠀⡀⠰⡏
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⠀⠀⠀⠀⠀⠁⠈⠀⢀⠰⠖⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣿⠀⠤⠍⠁⡠⠠⢠⠇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠔⠏⢤⣾⣀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠀⠀⡏⠁⠀⠀⠀⠀⢰⠁⡟⠀⠀⡇⠀⠒⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣤⡇⠀⢠⣇⠀⠈⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠄⣀⣀⣀⣀⣠⡴⣞⡁⠀⠀⠈⣠⣖⣀⣀⣀⣀⣀⢠⡤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⢥⡎⢨⡀⠀⢸⠇⠈⠀⠀⠰⠀⢰⠃
⠀⠀⢀⡤⠔⠒⠋⠉⠉⠉⠉⠉⠓⠢⠄⣉⠛⠀⡁⠀⣀⣀⠀⠀⠀⠀⠀⠆⠤⠐⠀⠀⠀⠙⠳⠤⠄⠲⠒⠲⢤⣧⠀⢸⠀⠀⠀⠀⠀⠀⣸
⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡙⢦⠉⠑⠉⠏⠉⠉⢉⠹⠃⠀⠀⠀⠀⠀⠠⠅⠀⠀⠐⡄⠀⠀⠀⡛⢆⢸⠀⠀⠀⠀⣩⠁⣯
⡎⠀⠀⠀⠀⠀⠠⠊⠀⠃⠀⠀⠀⠀⠀⠀⠈⠈⡇⠀⠠⠁⢘⠃⠀⠀⠠⠀⠀⠠⡄⠁⡰⠂⠂⠀⠀⣀⠤⠖⠊⠀⠘⣾⣀⣀⣀⣀⣀⣠⡏⢧
⢇⠠⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠠⢠⠇⢀⠂⠀⠖⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣸⣤⣠⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣧
⠘⢦⡁⠀⠀⠀⣸⠁⢀⢈⢻⡀⠀⠀⠀⢐⡵⠋⠛⠛⣛⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣸⡊⠅⠀⠀⠠⠶⠶⠄⠀⠀⠀⠀⠀⣿
⠀⠀⠙⠲⠤⣄⣼⠀⠀⠀⢸⡧⠄⠒⠊⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⢽⠉⠉⠁⠀⠉⠉⠻⠤⠬⠛⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠋
⠀⠀⡀⠂⠀⠀⠸⡇⠀⠀⠘⡧⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠙⡖⠒⠒⢒⣇⠀⠀⠀⣷⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣸
⠀⢰⠞⠉⠉⠉⠉⢹⢀⣀⠀⣿⠀⠀⠀⠠⠈⠉⠙⣦⠒⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠈⠣⣄⣀⣀⣀⠊⠁⢀⣤⣟⣀⣀⣀⣀⣀⣤⡴⠟⠀⠀⢀⠈⡇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠉⢱⡆⠉⠉⡏⠉⠉⢨⡟⠛⠁⠀⠀⠀⣠⣁⣠⡇⠀⠀⠀⠀⣧⠀⣀⢀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⡃⣉⠀⣇⠆⡀⢾⡁⠀⠀⠀⠀⠀⡹⠁⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠐⡇⠠⠀⡟⠢⠰⣏⡀⠃⠀⣄⠠⠔⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⢈⡇⠠⠀⡇⠰⠀⠩⡈⡁⠀⠺⢿⠛⠻⠶⠶⠶⠶⠶⠿⠿⠿⠿⠏⠛⠃
⠀⡀⣀⣀⠀⡀⡀⢈⡇⠒⠀⣏⣀⣡⣄⣤⣡⠶⠴⠶⡀
⢾⣁⣀⣭⣭⠭⠭⠥⣤⡄⢤⣤⠔⠐⠒⠢⣤⡤⢠⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⠇⠀⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⢠⣀⢖⡁⠀⠀⠀⠀⠐⠖⡄⠀⣀⠀⠀⠀⡀⠐⠀⢀⠉⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣽⣿⣇⠀⠀⢀⠄⣄⡀⠀⡟⠅⠋⡙⢻⣃⡴⠖⠻⠓⠛⠓⠛⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠃⠘⡇⠀⢀⡘⢀⣋⢁⠀⡄⣲⣾⣇⣀⣹⡇⢹⠀⠠⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⣰⣤⣶⣛⣡⡶⢰⠇⣰⡇⢈⣽⠊⠙⣿⡇⠘⣧⠀⡆⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣴⡿⠤⣄⠙⢻⣶⣿⡶⠃⠙⠁⠸⣷⣾⣿⠃⠀⠙⢶⣿⣆⢻⣆⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⡇⢻⠒⢄⡙⣾⡿⠛⠀⠀⠀⠀⠱⠙⠛⠏⠀⠀⠀⠈⣿⣇⠈⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠁⣇⢸⡐⠲⣬⣿⣷⠀⠀⣠⡄⠀⠀⠀⡎⠀⠀⠀⠀⣰⡟⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣠⣇⠀⠁⢻⡿⣿⣿⣆⠀⣸⣧⣤⣤⣤⣅⣀⡀⠀⣠⣯⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠐⡉⠉⣿⣿⠍⢹⠂⠙⠀⠈⢩⣟⠛⠫⠍⠉⣉⢉⣽⣿⣿⣿⣿⠿⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣋⡎⠹⡏⠀⠀⠀⠀⣴⠟⠝⠋⡒⠁⠀⠂⠄⠒⠻⠿⠿⣿⡍⠳⢌⡁⢄
⠀⠀⠀⠀⠀⠀⠀⠐⣋⡼⠀⠑⠈⠀⠀⠀⡏⠙⠓⠶⠀⢠⠀⠀⠀⢰⠀⠸⠗⢺⣟⡠⠀⠙⢺⣤⢶⠄
⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⡄⠂⠀⠀⢠⡇⠀⠀⠀⡄⢼⣄⠀⠀⣸⣷⡙⠀⠀⣿⡅⠀⠀⣸⢷⡿⣶
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡇⠀⠀⣀⣀⡇⠀⠀⠀⢺⣿⣿⠀⣰⣿⣿⠁⠀⠀⢸⣷⣄⣠⣿⢿⡴⡇
⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⡴⢃⣤⣾⣿⣿⠃⠀⠀⠀⢸⣿⠁⠀⠹⣿⣿⠉⠀⠀⠀⢻⣷⣿⡟⢈⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢺⢀⡾⣡⣿⣿⣿⡟⢻⠄⠈⠃⠀⣻⡇⠀⠀⠀⠘⠿⢷⡀⠄⠀⠀⢻⠛⠙⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⠉⣿⠉⠀⢸⣇⡀⠀⠀⣿⣧⠀⠀⠀⣠⣾⣼⣧⣀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣠⣼⠀⠀⠈⣏⣙⢻⣿⢻⣿⠀⠀⢴⢻⠟⢉⠹⣇⠉⠁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⣿⢉⣿⣿⢼⡏⠀⣶⣻⣎⣴⠃⢰⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣠⣴⣾⡈⠋⣹⣾⣿⣶⣯⣬⣭⣇⣠⣾⣞⠛⠓⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⣤⣶⣿⣿⣿⣿⣇⣰⣯⡽⣿⣿⣿⡇⠀⠈⠉⠘⢿⣿⣿⣿⣧⣤⣄
⠀⠀⠀⠀⠀⢀⣤⡖⣿⣿⣿⣿⣿⣿⣿⣿⠏⠘⠋⠀⠀⢹⡟⣿⣧⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣶⣄⣀⠀⢸⣿⣿⣿⣿⣿⣯⣁
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣀⣴⣾⣿⣿⣿⣟⠋⠉⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠟⠛⠋⠉⠁

⠀⠀⠀⣠⢤⠆⠀⠀⠀⠉⠉⠀⠉⠉⠉⠀⠀⠁⠀⠉⠉⣉⠉⠙⡆
⠀⠀⢀⡃⢸⠆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⡇⠀⡇
⠀⡴⢹⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⡟⢹⡇⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⡇⢸⡅⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣻
⠈⡇⢸⡯⢸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠐⢇⡐⡇⢼⡇⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠑⢯⣈⡅⠀⠁⠑⠠⠤⠀⠀⠀⠤⠀⠤⠄⠀⠀⠀⠀⠃⠀⢹
⠀⠀⠀⠀⠙⠣⣤⣤⣤⡤⡠⣤⡤⣤⣠⠄⡤⡤⡤⣡⣬⣬⠀⠅⠊
⣴⢦⡀⠀⠀⠀⢀⣦⣍⡁⠙⠛⠪⠁⠈⠈⠙⠉⠉⣉⡯⠑⠒⠤⣀
⣿⠀⠙⠢⣄⠀⠀⠈⠉⠙⠛⠛⠒⠂⠐⠒⠒⠛⠋⠀⠀⠀⠀⣀⡀⡉⡒⠦⣄⡀
⡗⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⢲⢠⡇
⠳⣄⠑⠕⢸⠁⠉⠀⠘⠛⠛⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⢸⢺⢸⡇
⠀⠈⠢⡀⢸⠉⠉⠉⠉⠀⠀⠉⠉⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢨⢨⡅
⠀⠀⠀⠈⠺⢄⣄⡀⣀⣀⣀⣀⣀⢀⣀⣈⣉⣁⡁⢁⢀⣀⣀⢀⣀⣀⠈⣼⡀⠇
⠀⢀⣤⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⢀⣀⣤⣤⣤⣤⣄⣠⣠⣄⣀⣀⣀
⠀⠀⠓⢝⡪⣒⢝⡐⠾⠓⣀⣷⠀⣀⣟⠀⠺⡓⢀⢹⡒⢒⢟⡒⠒⢟⣒⡺⠷⠤⠭⡮⠽⠷⣤⡀
⠀⠀⠀⠀⠑⢮⣓⣭⡲⠀⠀⢿⡐⣈⢻⡂⢁⠲⣌⣃⣀⣈⣃⣀⣈⣃⡀⠻⠅⠲⠙⠉⢺⣛⣻⣛⣷⢤⣀
⡀⢀⣀⣀⡀⣀⣈⢳⣿⣥⣄⣤⣤⣸⣫⣠⣭⣠⢎⡽⠣⠷⠃⠘⠽⢏⠬⢭⣍⣨⣁⠃⠎⠞⠻⠡⠥⠪⠝
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⣦⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⣦⢄⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⣿⠀⠋⢰⡟⠲⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠏⠈⣧⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⡟⠀⠀⢸⠁⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠘⠻⠦⠤⣿⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣠⠖⠛⠛⢶⣀⡇⠀⠀⣼⠀⠀⣀⣀⣀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢿⡀⠀⠀⣸⢿⡇⠀⠀⡿⢠⡟⠁⠀⠈⢷⠀⢿⠀⠀⠀⠀⠀⠀⠘⢳⠦⣤⣄⣀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⡈⠛⠲⠚⠉⢸⠀⠀⠀⡇⠈⢧⣄⣀⣠⠟⠀⢸⡇⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢩⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠷⠶⠦⢬⣭⣥⣤⣄⣸⡇⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠀⠶⠴⠤⠤⠄⠀⣀⣤⣀⣀⡀⠀⠀⣀⠀⠀⠀⠈⡅⠀⠀⠀⠀⢠⡏⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⡀⢀⣀⣀⣀⣧⣠⣤⣤⣤⣤⣄⣄⣠⣄⣠⣄⣉⣉⣉⣽⣇⣈⣁⣀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⢸⣧⡅⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⢸⠤⢴⠇⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⡏⠀⡆⢸⣿⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠓⠒⠶⣤⡀⠀⠀⠀⠀⠀⣸⡇⢸⠀⡾⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣸⠓⠒⠃⠈⣿⡄⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣿⠃⢸⣺⡃⠀⣀⡴⠋
⠀⠀⠀⠀⢰⡇⠀⠀⠀⢠⡏⠀⠀⠇⠀⢹⣷⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣼⡏⠀⢸⠈⠉⠉⠁
⠀⠀⠀⠀⣾⠀⠀⠀⠀⣾⠀⠀⠀⡀⠀⠀⠹⣷⡀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢀⣼⠟⠀⠀⢸
⠀⠀⠀⢰⡇⠀⠀⠀⢰⠇⠀⠀⠀⡇⠀⠀⠀⠙⢿⣦⡀⠈⠳⣄⣀⠀⠀⠀⣀⣤⠞⢁⣠⡿⠋⠀⠀⠀⢸
⠀⢀⣤⣾⣁⡀⠀⠀⡿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⣉⣛⣛⣋⣉⣤⡶⠟⠉⠀⠀⠀⠀⠀⢸
⡴⠋⠀⠀⠈⠉⠙⠛⢳⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⡇⠀⣿⠙⠒⣶⠄⢰⠏⠀⠀⠀⠓⠂⡄⠐⢶⡶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⢶⡶⠢⠞
⠀⢻⣀⣻⡄⣰⠋⢠⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⢦⡀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢀⡴⠋
⠀⠀⠉⠉⠉⠛⠲⠟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⣦⣀⣀⣿⢦⣄⣠⣤⣿⣀⣀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⠤⣤⡤⣬⡉⠙⡏⠀⠀⠀⠀⡏⠉⣽⠷⠶⠶⢦⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⠾⠃⠀⠀⠀⠈⠷⢶⡇⠀⠀⠀⢀⣷⠞⠃⠀⠀⠀⠈⠓⢶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠖⠛⠉⠉⠙⠛⠶⣄⣿⠀⠀⠀⢸⣠⠶⠛⠋⠉⠙⠛⠶⣤⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠀⠀⠚⠀⠀⣠⠞⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡰⠞⠛⠋⠛⠛⢶⣄⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣰⠎⠳⣆⠀⠀⠀⣠⠞⠙⣧⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡟⠀⠀⠈⠳⣤⠞⠁⠀⠀⢸⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢻⣤⣤⣤⣤⣤⣾⠁⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣗⠲⠶⠤⢬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡁⠸⣏⣉⣛⣛⣺⡇⠀⢛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⡜⠁⠀⠻⣍⣉⣉⡽⠁⠀⢯⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⠀⠀⢠⡄⠈⠉⠉⠀⠀⠀⠈⣇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⢤⣜⡧⠤⣤⣤⣀⡀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠉⢧⡀⠈⠓⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠻⢤⡀⠀⠀⠀⢠⠇⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡇⠀⢀⡴⠋⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⡀⠀⠙⠚⢉⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⣁⡢⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣇⠀⠀⠀⠀⠀⠀⠀⡵⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠷⠀⠀⠀⠼⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⡀⠀⠁⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠟⠀⠀⡀⠻⠀⡈⠀⠀⡓⠐⠴⠆⠙⠀⠸⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⡈⡂
⠀⠀⠐⢰⢂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡯⠋⣾
⠀⠀⠈⠲⡞⡉⠛⠑⠶⣄⢄⡀⠀⠀⠀⠐⠂⠤⠄⠀⣀⣀⣂⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⢀⡤⠊⠀⢔⠏
⠀⠀⠀⠀⠘⢎⠂⠀⠀⠀⠉⠚⠶⣤⡤⠀⠀⠀⠀⠀⠘⠻⠛⠻⠄⠄⠠⠤⠠⣀⣀⡤⠔⠁⠀⢀⢀⡜
⠀⠀⠀⠀⠀⠀⠑⢕⠀⠀⠀⠀⠀⡞⠀⠩⠂⢸⠩⠅⠀⠀⠀⠀⠂⠀⣀⡀⣠⡌⠺⠁⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⢄⠀⠀⠃⠀⠭⠂⢸⠀⠀⠀⢀⠀⠂⠀⠀⠶⠬⠰⠂⠀⣀⡠⣔⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠤⣀⠀⠬⠄⠸⣀⣐⣒⠓⡦⠒⣀⠀⣉⠥⢜⡁⠀⡇⠱⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠒⢽⠀⢆⠄⠀⢠⣤⣤⣤⣄⠀⠀⠀⠴⢝⡡⠄⠸⠆⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣦⢸⠀⠀⠀⠀⠀⠁⠹⠀⡇⠀⠀⠀⠙⠁⠘⠁⠠⢌⣑⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠭⢱⣐⠀⠀⠀⠀⠘⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⠟⠚⠮⠥⠭⠭⠽⢏⣽⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠉⠀⡉⠲⡀⠀⠀⠀⠠⠒⠈⠉⠓⠢⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠀⠒⠼⣀⣀⣂⣁⣧⡵⠃⠀⠀⠀⠳⢬⣐⡀⠠⠀⠈⡷⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠁⠈⠉⠉⠁⠀⠈⠀⠀⠁⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠚⠛⠛⠛⠛⠓⠶⠶⣤⣄⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣞⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣫⡿⠖⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒⠶⠶⠦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠓⣾⠋⢰⡾⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣤⠾⢻⡇
⠀⠀⠀⠀⠀⠀⣿⠀⡏⠉⠉⠉⠉⠉⠉⠛⠓⠒⡆⠀⣿⠀⢸⠀⠀⢀⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠉⣙⣛⣛⡓⠒⠒⠒⠒⠒⠃⢀⡏⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢻⠀⠀⠀⣿⠀⠀⣾⣿⣦
⠀⠀⠀⠀⠀⠀⣿⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⢸⡇⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢰⡇⠀⠀⡿⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢸⠃⠀⣿⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⠇⠀⢰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⢀⡏
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡟⠀⠀⣾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠓⠒⠒⠚⠛⠛⠀⠀⢀⡟⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⢀⡟⠀⣾
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⢿⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠁⠀⢸⣇⡴⠇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡖⢲⠀⠀⠀⠀⣸⠃⠀⢀⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠩⠉⠉⢩⠉⠉⠉⠛⠛⠛⠛⠛⠀⠀⡿⠀⣠⡿⠉
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣿⣀⡴⠋⠈⠉⠉⠉⠛⡟⢛⡿⠛⠓⣷⡒⠶⠶⠶⠶⢶⣦⢤⣤⣤⣤⣤⣴⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠲⠶⠶⠶⠶⠶⠶⠶⠿⠋⠀⠀⠀⠀⣠⠖⠚⠁⢾⣇⡀⠀⠈⠙⠛⠓⠒⠒⠛⠁⠀⣠⡿⠀⠈⠣⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣧⣀⣀⣀⠈⠻⠯⣿⣶⣶⣶⣶⣶⣒⣒⣾⡽⠟⠁⠀⠀⠀⠀⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⡤⠤⡤⢤⡤⠤⣤⢤⣤⣄⣈⣉⣉⣉⡉⠙⠛⠛⠛⠷⠾⠯⢭⣭⣥⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠋⡿⠓⡾⠓⣲⠓⡶⠧⢤⠧⢤⡯⣤⣽⣉⡟⢀⡖⢲⠖⢦⠤⢤⡀⠀⢩⠟⣇⠀⠀⠀⠀⣠⡴⢶⢞⡿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢸⣉⡽⠉⣹⠛⢲⠟⢲⠓⢲⠿⢤⡾⠤⣼⢥⣼⠁⡜⢉⡟⢒⠟⠒⡾⠁⡰⠋⣴⠏⠀⠀⣠⣞⣁⣠⣧⠋⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠤⠤⠬⣉⣉⣉⣙⣛⣒⠛⠒⠛⠲⠾⠤⠴⠧⠴⠃⢸⣉⣽⣉⡟⠓⡾⢀⡜⣡⠞⠁⠀⠀⣰⠋⠀⠀⠀⠈⠉⠲⢄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠓⠒⠶⠶⠶⠯⠭⣭⣭⣉⣓⣒⣒⣒⠒⠒⠦⠤⠤⢭⣭⣉⣠⢋⡼⠃⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠓⠲⠶⠶⠶⠿⠟⠀⠀⠀⠀⠀⠀⠘⢿⣶⣶⣴⣲⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⣀⣤⠀⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⣤⣄⡀
⠀⠀⠀⢀⡘⣿⡙⠷⠟⢸⣧⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡾⠋⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⣿⣙⠛⢡⡶⠶⣦⠉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⣨⡾⠛⠛⠛⢷⣄⠀⠀⢹⣆⡀
⠀⠀⠀⣩⡽⠇⠸⣧⣤⠿⢀⣙⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⠻⣆
⠀⠀⠀⠹⡷⠞⣷⢀⣴⣄⢻⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠁⠀⠀⠸⣧⠀⢤⣴⡄⠀⣼⠃⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠘⠻⠾⠃⠹⠛⠁⣶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⣿⢰⡞⠁⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣦⣀⣿⠀⢀⣿⣠⡾⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⢰⡾⠷⠿⠾⣷⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠉⠁⠀⠀⠉⠋⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣭⡛⢿⡄⠀⠀⠀⠘⠿⣾⠿⡷⠟⠀⣼⠛⠛⠉
⠀⠀⠀⠀⠀⢠⣤⣤⣴⠟⠀⢠⡾⠛⠛⢶⡄⠈⢿⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⣨⡗⠈⠻⢶⣤⡴⣦⣀⡀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⢸⣇⣀⣀⡀⠀⢿⡄⠀⠀⢸⡇⠀⢀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⣩⡷⠀⠈⠛⠶⠾⠋⠀⠀⣿⡉⠉⠉⠀⠀⣀⣀⣀⣀⡀⠀⠻⠶⠟
⠀⠀⠀⠀⠀⠀⠀⢾⣏⠀⣠⡶⣤⠀⠀⣴⢦⣄⠈⣻⡦⣠⡶⠛⠉⠉⠉⠉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⣿⠀⢀⣿⠀⠙⠿⠋⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠰⠟⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣠⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢠⡞⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣀⣤⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣄
⠀⠀⠀⠀⠀⢠⣄⢀⡤⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢸⡇⠀⣀⣀⡀⣠⣤⡀⠀⠀⠀⣴⠶⠾⠋
⠀⠀⠀⠀⠀⢀⡭⢨⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⢸⡏⠉⠿⠋⢀⣿⠆⠀⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⣨⡿⠃⠀⠀⠘⣧⣀⡼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠻⣦⡀⠀⠀⠀⠀⠉⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣷⠄⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠈⠻⣦⡀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣧⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣄⣼⡇⠀⠀⠀⠈⠻⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⢰⠒⠒⠒⠒⠒⠒⡆⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⢹
⠀⢸⠀⠀⠀⠀⠀⠀⡇⢘⣀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠸⠤⠤⣤⣤⠤⠤⠏⢸⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠘⠛⠛⠀⣤⡀⠀⠀⢀⣀⣠⠖⠒⠢⣤⣄⡀⠀⠀⠀⠀⣠⠄⠀⢸⣦⣤⣤⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⠏⢀⠔⠒⠉⠑⠒⢤⡙⠲⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡜⠀⠀⠀⠀⠀⠀⢳⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⠬⠭⠭⠭⠭⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⣀⣠⡤⣤
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⠀⠴⠃⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⡷⠒⠚⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣮⣿⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣧⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⣠⣤⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠟⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⢸⣿⠃⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣸⣿⣷⣤⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣾⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠉⠉⠉⠉⠉⠻⣿⣶⣶⣾⡿
⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢀⣤⣶⣶⣦⣄
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠋⠉⠹⣿⡇
⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣷⣄⣀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠿⣿⡿⠿⠿⠿⠿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠙⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⠀⠻⣿⣦⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣀
⢀⣴⣶⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠿⠟⠛⠉⠉⠉⠉⠙⠻⢿⣿⣶⣦⣄⡀⢀⣀
⣿⣿⠉⠉⠙⠛⠻⠿⢿⣿⣷⣶⣦⣤⣄⣀⠀⠀⠀⢀⣴⣶⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣶⣤
⠹⢿⣷⣶⣤⣀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⣿⣿⣶⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⣠⡌⢹⣿
⠀⠀⠉⠛⠿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠈⢡⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣷⣶⣿⡟⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣤⣀⣀⣀⣠⣤⣴⣶⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠉⣿⣿⣧⣄⣀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⡿⠃
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⣠⣴⣶⡿⠿⠿⢿⣶⣦⣄⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠉⠀⣀⡀⢀⠀⠀⠉⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⢰⡶⣛⣛⢿⣥⡀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⢰⣿⠁⠀⠀⢿⡗⣿⣿⢇⣿⡅⠀⠀⠀⠈⣿⡆⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⢸⣿⠀⠀⢀⣜⣟⣶⡶⢿⢽⠞⣓⢷⡄⠀⣿⡇⠀⠀⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠠⡏⣶⢝⡇⣠⣤⣹⣮⣋⡼⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠙⠖⠛⠙⢿⣻⠇⠈⠁⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡷⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⢾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣿⣶⣶⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣿⣿⣿⣿⡯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋



⡿⢿⠿⠿⡿⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⡄⠠⠤⠀⠄⠠⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡘
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠒⠀⠉⠀⠁⠀⠀⠐⠒⠚⠛⠁⠉⠉⠙⠒⡠⠤⢄⣤⡭⠖⠦⠀⠀⠀⠀⠀⠀⠀⠠⠈⢁⠞
⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⠀⠀⡀⠁⠀⡀⠀⠀⠀⠀⠀⠛⠠⡀⠀⠐⠀⠀⠀⠈⠂⠀⢀⣈⠀⠀⠒⠤⠤⡀⡄⠂⠀⠀⡠⠃
⠀⠀⠀⠀⠤⢀⣀⣈⣡⣴⣢⠀⠂⠄⠀⠁⠀⠀⠄⠒⠐⠒⣀⠀⠀⠀⠀⠀⠀⣀⠏⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠴⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠈⠃⠒⠀⠨⠄⠤⡄⠠⠀⠀⠐⠖⢈⡀⠀⠠⠐⠤⣄⣂⡱⠖⠃⠀⠘⠻⣋⣀⠀⠀⠀⠀⠉⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠄⣐⠒⠒⠀⠀⢠⡄⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢐⠦⢛⡀⢓⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣘⣁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠁⢠⢾⡉⠓⡄⢀
⢇⠀⠀⡠⠄⠀⠀⡀⡄⢚⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠱⠆⠀⠀⠀⠀⡖⠄⡁⠀⠀⠀⠀⠸⠤⠤⠴⠁⠀⢁
⢸⣷⡞⠀⠀⠂⠑⠁⠀⠀⠀⣈⣉⣀⠖⠀⠀⠀⠀⠀⠀⠀⠠⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡎⠀⠄
⠀⠀⢅⠀⠀⠀⠈⠈⠛⠻⣿⡩⠍⠀⠀⠀⠀⢀⡰⢆⡄⠀⠠⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠒⠒⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⢧⡀
⠀⠀⠀⠀⠀⠀⠃⠤⠖⠒⢦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢹⠀⠀⢠⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠄⢀⣀⣀⣸⠀⠇⠀⠀⠀⠀⠀⠂⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⢸⠀⠀⣀⣶⡀⠀⠀⠀⡇
⠀⠨⠀⣠⣤⣤⡁⠀⢀⣤⣤⡀⡀⠀⠀⢀⡴⠀⠀⠙⠃⠀⠈⢀⣄⠀⡀⠀⠀⡀⠀⠀⠀⡟⠀⠀⢸⠀⠀⠉⠿⠉⠀⠀⠀⣇
⠀⠰⠄⠺⣘⡪⠷⠴⢯⣒⡾⠳⠂⠀⠀⠘⠄⠀⠰⣾⡧⠈⠠⠃⣺⡧⠂⠀⠠⠀⠀⠀⠀⠒⠀⡢⣬⡐⡄⠀⣴⣩⡑⡤⠤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠓⠀⠀⠀⠻⠃⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠓
⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣇⣀
⣄⣀⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⢀⠀⡁⠀⢄⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⠀⡖⠀⠐⠄⣀
⠈⣸⠷⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠠⢌⠁⢈⡇⠀⢀⡎⠉⢱⠄⠀⠆⠀⠀⠀⣠⢐⣛⣛⠁⠀⠖⠁⣀⣈⡀⠈
⠐⠈⠓⠶⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠀⠋⠉⠀⠀⠀⠉⠒⠉⢠⣶⠀⠀⠀⣖⣋⡿⢽⡌⣷⣀⣠⣿⢹⡬⢽⣄
⠀⠀⠀⠀⠀⠀⠑⠠⠀⠉⠉⠈⠉⠗⠂⠀⠀⠀⠀⠀⠁⠒⠂⠀⠀⠀⠖⠚⢿⡎⠇⠀⠀⠀⠀⠙⠳⠚⠁⠀⠀⠈⠓⠓⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠎⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠴⡶⠀⠀⢀⣴⡄⣠⣤⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠃⠀⢸⠀⠀⠀⣀⡄⠀⢀⡀⡄⢀⣀⣀⣀⣀⠀⠀⠈⠉⠉⠀⠘⠻⠄
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⢸⠀⠀⠍⡏⢱⣠⣴⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣴⠄⣠⣄
⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⡀⠸⢻⠀⠀⠀⡇⢸⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠀⣠⣶⠷⣾⠿⠻⠿⠄⠘⠛⠛⢻⣿⡿⠿⠿⠿⠿⡿⠿⠶⠼⠷⢤⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠛⠛⢰⡏⠁⠐⣶⣦⣄⠀⠀⠀⠀⠀⠀⡀⠠⠀⢀⣠⣤⣤⣌⣛⣛⣀⣀⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⡧⠴⠶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡄⣿⢀⣄⠀⢸⡇⠐⠒⣿⣿⡧⠿⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⡄⣤⣿⡇⣿⠘⠛⠀⠘⣷⠶⡾⠋⠀⠀⠀⠠⠄⠀⠁⠂⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈
⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣶⣶⣿⣧⣻⣶⣶⣶⣶⣶⡞⣰⣿⣿⣷⡀⠀⢰⡟⠛⣿⠛⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣻⡟⣶
⠀⠀⠀⠀⠰⢾⣿⣿⣯⠻⣿⣿⣿⠋⢻⡯⠭⣭⣿⣿⣿⣰⡿⣋⣉⣻⣷⠀⠈⠁⠛⠛⠛⠉⠀⠸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠸⡇⣿⡃⣿⣿⣿⣿⣄⣸⣇⣀⣏⠀⢼⣿⣿⣿⠿⠟⣿⡟⣷⠒⠒⠒⠒⠒⠒⠛⠒⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠙⠛⠻⠷
⠀⠀⠀⠀⠀⠤⠿⠿⣷⣿⣿⣿⣿⣿⣿⣭⣍⣛⣻⣿⣿⣿⣿⣷⣆⠤⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠿⠿⣿⣿⣿⣿⣿⣿⠿⣡⣦⡇⣾⣤⣤⣤⣤⣤⣤⣤⠄⠀⠐⠀⠒⠒⣶⣶⣶⣶⣶⣶⣿⣿⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠻⢻⡿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⣿⣷⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠐⢊⣉⣽⣁⣀⣀⣀⣀⣀⣀⣠⣤⣒⣉⣀⣀⣀⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠶⠾⠭⣼⣿⣋⠀⢀⣴⡶⠛⠉⢉⣹⠿⠿⣤⠤⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⡿⠛⠛⣯⣤⠴⠞⠋⣁⠄⢒⣡⡶⠈⢢⡀⠀⠀⠀⠀⠀⠀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣋⡷⢟⡋⣁⣠⣶⣛⣭⣥⣤⣥⣼⣷⠶⣶⣾⣶⣾⣿⣾⣷⣄⡠⠐⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠟⢉⣼⣿⣿⡿⠟⠛⢋⣉⣽⣿⣿⣿⠿⠷⠛⠋⠉⠑⢠⣴⡛⢁⣠⠞⠁⡠⠈
⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⣠⣴⣾⣿⡿⠿⠛⠻⣿⣠⡴⠶⢿⣿⣿⡴⠛⣁⠀⠹⠋⠁⠀⠤⣀⠈⢿⣽⠿⠋⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠢⣠⣴⡿⠿⠛⠉⣁⣤⣶⠶⠛⠉⠁⠀⠀⠘⢩⣄⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣏⣠⣤⡾⡷⣬⣗⡮⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠁⠀⠉⠁⠠⠄⠉⠛⠻⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠒⢚⠒⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⡀⠀⢉⡉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠐⠛⠉⠀⠀⠘⠛⠶⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⠀⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣿⡀⠀⠀⠸⠾⠇⠀⠸⠾⠇⠀⢠⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣦⣄⣀⡀⠀⠀⢀⣀⣠⣴⣿⡿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠘⠿⣿⡿⠛⠛⠛⠛⠻⣿⣿⡿⠋⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠉⠛⠲⠶⠤⢤⣤⣀⣀⡀⠠⠤⠄⠐⠋⠀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡂⠀⠉⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠁⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⡴⠂⠀⠀⠐⠁⠀⠀⠀⠀⢸⠀⠀⢸⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣏⠘⣧⠞⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⢈⡆⢰⡿⠁⢈⠀⠀⠀⠐⠆⢸⠀⢀⡞⢦⣼⠉⣷
⠀⠀⠀⠀⠀⠀⢠⡇⢨⡟⠁⠀⠈⠙⢶⠀⠀⠠⠄⠀⠀⠀⠀⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠋⠀⠀⠙⣞⠁⣇
⠀⠀⠀⠀⢀⡠⠼⢬⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠊⠀⠠⠀⠀⠄⠀⠠⠀⠲⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⢸⣆⣹⣀
⠀⠀⠀⣀⡎⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢠⡞⠁⠀⠈⢳⡄
⣠⠖⢋⡩⢧⡀⠀⠀⣰⢧⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡼⣇⠀⠀⠀⣰⡗⠲⢄
⠙⢦⡏⠀⡜⠉⢻⠉⠳⡄⣙⠆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⠀⢰⡋⢀⡜⠓⡖⠚⣇⠙⢦⣀
⠀⠀⠉⠺⣧⣀⣼⠀⠀⠉⠁⠀⠀⠀⠘⠢⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠁⠀⠀⠀⠈⠉⠀⠀⣇⠀⣸⡤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠈⡟⠋⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⣅⡐⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡙⠻⠾⠿⠯⠒⠉⠐⢄⠀⡤⠒⡛⣶⠭⡤⠭⠒⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡐⠉⠀⠀⠘⢦⠀⠀⠀⠀⠀⢹⡔⠉⠀⠀⠳⡄⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⡀⠀⠀⠱⣀⣀⡀⠠⢤⠂⠀⠀⠀⠀⠈⢆⣀⣀⣀⡀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⡇⠈⠀⠀⠀⠁⠀⠀⠀⢸⠀⣰⠁⠑⠀⠀⠀⡄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⣇⡀⠀⠀⠀⡆⠀⠀⠀⢸⠀⠹⡀⡀⠀⠀⢀⠁⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⢀⡆⠀⠀⠈⠀⠀⠀⡜⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡀⢀⣀⠜⠁⠀⠀⠐⠁⠈⢦⡀⠀⢀⣠⠎⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢸⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠘⡇⠀⠀⠘⠀⠀⠀⡟⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⣀⡴⠖⠛⠛⠛⠓⠶⣄⡀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡀⠀⣠⠞⠁⣀⡀⣰⡖⣶⡀⣀⡀⠙⢦⡀⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠏⠀⠸⣏⠙⣩⠤⢬⡙⢉⡿⠀⠈⢷⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⡀⣿⠀⢰⠞⠃⡞⠁⠀⠀⠙⡆⠓⢦⠀⢸⡇⣠⣤⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⠳⣆⠳⡀⠀⠀⡰⢃⡶⠋⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠘⣧⠀⠸⣧⡴⢬⠉⢩⡴⣤⡿⠀⢠⡟⠰⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣈⢳⡀⠀⠀⠘⠓⠛⠀⠀⠀⣴⢋⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⣼⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣛⣛⣛⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣙⣛⣋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠰⠦⢀⡀
⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣤⣬⣥⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⠀⢉⣳⣿⣷⢦⣄⡤⠤⠤⢤⣀
⠀⠀⠎⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠟⠀⣼⡟⠉⠹⡆⠀⠉⠛⠻⢅⣈⠙⠢⢄⡀
⠀⠀⣦⡏⠀⠀⢀⡟⡿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⢠⠀⠈⠐⠢⢤⣀⠀⠈⠉⠒⠶⣤⣷⣦
⠀⠈⠛⠃⠀⠀⢸⡌⡇⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⢹⣷⡆⠀⠀⠘⡌⠉⠒⡦⠤⣀⠈⠙⠂⠤⡀
⠀⠀⠀⠀⠀⠀⡿⡇⡇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⢸⢿⡇⠀⠀⠀⣧⠀⠀⢸⠀⠈⡇⠑⡖⢤⣬
⠀⠀⠀⠀⠀⢀⣦⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣄⠘⡇⠤⠄⣀⣈⣀⡀⠈⡄⠀⠠⠀⢸⠀⢙⡄
⠀⠀⠀⠀⠀⢸⠃⠀⠙⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⢸⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⡀⠀⠈⢤⣿⡇
⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⣀⠀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠘⡀⡇⠀⠀⠀⠀⠀⠀⠠⠆⣠⡀⠀⠠⠾⣿⡇
⠀⠀⠀⠀⠀⢸⣤⣀⣠⣤⣬⣤⣤⣤⠄⣤⡤⠠⠶⢶⡶⠶⣀⣀⣠⣤⣴⣶⣿⡀⠀⠇⡇⢂⣀⣀⡤⠤⠤⠤⠶⠶⠒⠚⠛⠻⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠃⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣔⣏⣿
⠀⠀⠀⠀⠀⢠⣘⣀⣀⠀⠨⣯⣄⠀⠀⠀⠀⠀⣰⣶⣶⠆⠀⢀⣀⣀⣀⣠⡤⢄⠀⠀⣿⣴⣿⣿⡆⠀⠀⢀⡀⠤⠀⠀⣿⡏⠉⠅
⠀⠀⠀⠀⠀⢈⣿⣿⣯⡄⠀⢺⣷⡂⠀⢤⡄⠀⣤⣽⠓⠀⢠⣿⣿⣿⣿⣿⣇⡨⠀⣀⢿⣿⣿⣿⣇⠈⠀⠀⠀⣀⣠⣴⣿⠁
⠀⠀⠀⠀⠀⢿⣿⣿⣿⡅⣀⢒⣶⣲⡶⠶⠶⠶⣶⠶⠶⠂⣐⣒⣒⣒⠒⠒⠒⢂⠀⠁⢸⣿⣿⣿⠏⠀⣤⣤⣼⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠘⠿⠿⠿⠍⠉⣉⣽⣋⣀⣀⣀⠀⠈⠁⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⡏⠀⢀⣵⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣟⣂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠿⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡇⠀⠀⢀⢀⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠖⠞⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣀⠀⠀⠀⢀⡀⠀⣀⡀⠀⣀⡀⢀⣀⡀⠀⣀⡀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⢀⣬⠉⢠⣭⠁⠤⠤⠀⠤⠄⠀⠤⠤⠀⠰⠦⠀⠒⠂⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠒⠂⠀⠐⠒⠀⠒⢀⣄⣚⣃⣀⣈⠉⠀⠈⠉⠀⠈⠉⠁⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⣼⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣶⣶⣶⣶⡾⠧⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⠤⣤⣤⡷
⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⠉⠙⠛⠻⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢀⣠⣴⣶⣶⣶⣾⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡇⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⣼⣏⣴⣿⣿⡿⠀⠀⠀⠀⠈⣿⣿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⣤⣤⣄⠀⠀⢆⠀⣿⣿⣿⡿⠛⢒⣲⣾⣶⣶⣿⣿⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠸⣿⣽⣿⠆⠀⢸⠀⢿⣿⣿⣥⡈⠉⠀⢉⠟⢁⡀⠹⣿⡆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠚⠉⠉⠀⢀⡾⠂⢼⣿⣿⣿⣿⣦⣤⣄⠀⠛⠷⣾⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣶⣤⣶⣿⣧⣤⣾⣿⣿⣿⣿⣿⣿⣿⣗⠤⣒⣻⣿⣷⡄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⢻⣿⣿⣿⣿⣿⣿⡋⠀⠹⢿⣿⣿⣿⣿⣷⣬⠘⠉⣽⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⢀⣼⣿⣽⣿⣿⣿⣿⣷⣤⣀⡀⠈⠉⠛⠿⠿⣿⣿⣿⣿⠿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⣴⣿⣿⣿⣽⣻⣿⣿⣿⣿⣿⣿⣯⣑⠒⠤⠤⢀⣀⣀⣀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣯⣍⣙⠻⣿⠿⣝⠿⣝⡻⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠓⠾⢭⣉⠻⣾⡞⣻⣮⡳⢬⣻⣾⣿⣿⣿⣿⣯⣭⣽⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⠀⠀⠈⠉⢈⠻⣿⡍⢻⣷⣬⣝⡻⠿⣿⣏⣻⣿⣷⠟⣫⣤⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡏⣴⣶⡆⠀⠀⠀⠀⠀⠈⢷⡘⣷⣞⢻⣿⣿⣿⣿⣛⢿⣿⡿⢿⠏⠈⣿⠷⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠏⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣏⣥⡈⠙⠻⠿⠧⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⣷⡘⣿⣽⣷⡀⠀⠀⠀⠀⠀⠰⡆⠀⡂⣿⣿⡷⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⢀⠘⣿⣧⠘⣿⡇⣻⡇⠈⠀⠀⠀⠀⣿⣀⣸⠿⡅⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢸⣿⠀⢸⣿⣿⣧⣀⣠⣤⠴⠀⠈⠉⠁⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠞⠁⠀⠀⢿⡿⣿⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠐⢀⣠⡄⠀⢀⠤⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣼⣿⣦⣄⣀⣼⢠⠁⣠⠛⠒⠪⣕⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠸⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⠀⡆⠀⠀⢸⠹⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⠐⣾⣿⣿⡯⠿⣿⣿⣿⣿⡟⠀⢤⠃⠀⠀⠚⢴⠃⠀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢰⣿⣿⣿⠀⠀⣿⣿⣿⣿⣧⠤⠼⠧⠀⠀⠀⢸⠀⠈⠹⡾⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠳⠧⣀⣸⣿⣿⣿⠀⠀⣯⣿⡿⠛⡇⠀⠀⠀⠔⠚⠋⠉⠓⢄⠀⢷⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣷⣦⠄⠠⠬⣍⣛⡟⠀⠀⣿⣿⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⢹⡄
⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠁⠙⠊⡌⠣⡀⢀⣿⣿⡇⢸⡷⠖⠒⠒⠮⠀⠀⡀⢀⡦⠴⠃⣰⠞⢳
⠀⠀⠀⠀⠀⠀⢸⣯⢁⠎⠀⠐⠄⠀⠀⠀⢘⡞⠛⢻⡇⢸⡇⠀⠀⠀⠀⠀⢀⡍⠉⠁⠀⠀⠻⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠌⠙⢀⠔⠈⠀⠀⠀⠘⣷⠀⠈⡇⢸⡇⠀⠀⠀⢰⡴⠊⠀⠀⠴⠒⠢⡄⠀⢼⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢄⠤⠐⠀⠀⠀⠹⡄⠀⠃⢸⣷⠶⠶⠶⣏⠀⠀⠀⠀⢀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⣽⠀⠀⠀⠀⣤⣤⡇⢀⠄⠀⠁⠀⠀⢸⡇⠀⠀⢀⠈⠙⠒⠒⠒⠋⠀⣶⠋⣸⣸⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣷⣷⡇⠈⠒⠀⢈⠀⠀⢸⡇⠀⠀⣸⠷⠤⠤⠾⠦⠤⠤⠻⣦⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠧⣍⡇⠀⠄⠀⢸⣴⣷⣼⡇⠀⣰⠏⠀⢰⣄⣠⠖⠒⢦⡀⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⣦⢬⡑⣴⠁⣠⠂⢀⡏⢻⣿⣿⣧⠾⠯⡤⠔⠋⠈⣷⠀⠀⢀⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡙⣧⡰⢋⣴⣾⣷⣿⣿⣿⡇⠀⠀⢤⣄⣴⠾⠋⢀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⣿⣿⣿⣿⠏⡷⠶⠛⡋⠉⢀⣆⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠋⠀⠘⠦⠶⠿⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠀⣀⠀⢀⣔⡁⣸⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠤⢀⡠⠠⢄⡀
⠀⠀⠀⠀⢠⠉⠈⠀⠀⠀⢀⢍⠱⡀⠈⠉⢳⠀⠀⠀⡋⠀⢀⠤⠬⠤⠤⡀⠈⡇⠀⠀⠀⠀⢠⠀⠀⠀⠈⠑⠢⢈⠆
⠀⠀⠀⣀⠬⢉⡂⠆⠀⢠⠤⣭⠚⠀⡠⠤⠤⠃⠀⠀⣉⠉⢹⠀⣤⠞⢸⠉⠉⡇⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠰⠽⠑⢢
⠀⢘⠉⠁⠀⠀⠘⠦⠔⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡉⠉⠑⠒⠒⠂⠘⠁⠉⡇⠀⠀⠀⡀⢀⡠⠓⠒⠤⣄⣀⠤⠀⠴⣀⣀⡀
⠀⠀⠁⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣠⠤⠀⠀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠀⠀⠎⡠⠤⠈⠄
⠀⠀⠀⢀⠁⠀⠀⠀⠀⢸⠈⠊⡊⢂⠀⠀⠀⠀⠀⠀⢎⠉⠁⢺⠧⠀⠀⢀⡨⠂⠀⠀⠀⠀⠀⠀⡐⠘⠄⠠⠀⠣⠤⠁⡇
⠀⠀⠀⠸⡀⠀⠀⠀⠀⢸⡄⠁⠁⢸⠀⠀⠀⠀⠀⠀⠀⠑⠤⣌⢸⢅⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢀⡠⢀⠀⡇
⠀⠀⠀⠈⠉⡟⠛⠟⠛⠛⢲⠒⠲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣄⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂⢲⠤⢎⠀⢀⠟
⠀⠀⠀⢂⣀⡈⠋⠀⠀⡀⠂⠛⡃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⡟⠃⡆⠀⡟⠋⠖⠒⡄
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉


⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀
⠀⠀⢰⠁⠆⠆⡔⠒⠀⠒⡆⣴⠉⢪⢂⠀⠀⠀⠀⠀⠀⠀⡐⡟⠁⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢔⠿⠓⠢⡰⠒⠒⡕⡄
⠀⠀⢠⠀⠑⠁⠈⠊⠀⠑⠁⠈⠂⠊⢸⠀⠀⠀⠀⠀⠀⣔⡀⢇⣀⣘⠀⠈⡆⠀⠀⠀⠀⠀⠀⡌⠀⡘⠂⠐⠊⠐⠂⣒⠁⡀
⠀⠀⠈⠂⢼⣀⡷⠀⠀⠀⠀⢎⣀⡗⠊⠀⠀⠀⠀⠀⠀⣇⣈⠖⠀⠐⣖⣒⠇⠀⠀⠀⠀⠀⠀⠈⢏⣀⡧⠤⠤⠤⢎⡀⡙
⠀⠀⠈⠭⠉⠍⠉⠭⠭⠭⠉⠩⠭⠭⠉⠀⠀⠀⠀⠈⠩⠭⠉⠉⠭⠭⠍⠉⠭⠍⠀⠀⠀⠀⠈⠩⠭⠍⠉⠩⠭⠉⠉⠭⠭⠍
⠀⠀⠉⠀⠀⠀⠉⠁⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠁⠈⠁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉⠉⠙⣧⠀⠀⠀⠀⢹⠋⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣧⠀⠀⠀⠀⢺⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡎⠙⡾⠃⠀⠀⠀⠀⠙⣷⠀⢶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⠀⠀⠀⠀⠀⠀⡿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⠾⠷⠶⠷⠶⠶⠶⠶⠶⠶⠿⠶⠾⠶⠶⠶⠶⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢸⡇⠀⠀⡟⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠙⡗⠀⠀⢸⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⡏⠀⠀⠀⢸⡇⠀⢀⣤⣤⠀⠀⢸⡇⠀⠀⠀⡿⠀⠀⢸⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠛⠶⠖⠲⠚⠃⠀⢸⣤⣬⠀⠀⠘⠳⠖⠶⠖⠃⠀⠀⢸⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⠏⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣧⣀⣀⣀⣀⣀⣀⣀⡀
⠀⢼⠁⠀⠀⠀⠀⠀⠀⣻⠀⠀⢠⡄⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⣤⠤⡤⣤⡀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠈⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢀⠀⡀⠀⡀⠀⠀⢀⡀⠀⠀⡀⠀⠀⢀⠀⠀⠀⣀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢻⠁⠉⠉⢻⠀⠀⢸⠋⠉⠉⢹⡇⠀⢸⠉⠉⠉⢹⠁⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⡀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⢀⣇
⡶⠛⠓⠒⠒⠒⠒⠒⠒⢿⠀⠀⢸⠀⠀⠺⠤⠤⠤⠾⠀⠀⠸⠧⠤⠤⠼⠃⠀⠸⠤⢤⠄⠼⠀⠀⢸⡇⠀⠀⡿⠉⠉⠉⠉⠉⠉⠉⠉
⣷⢤⡤⢤⡤⠤⢤⣤⠤⣿⠀⠀⢸⡀⢀⡀⠀⢀⣀⣀⡀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⡀⢀⡀⠀⠀⣸⡇⠀⠀⣿⠠⠦⠤⠤⠤⠤⠴⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡆⠀⠀⣷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢉⠀⢀⡀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⢀⠀⠀⢀⡀⠀⡀⠀⢸⡇⠀⠀⡿
⠿⠀⠶⠠⠶⠐⠲⠖⠶⣿⠀⠀⠘⠀⢸⡏⠀⠉⠀⠀⡏⠁⠉⢻⠀⠀⡏⠈⢸⡇⠀⢸⠁⠈⠙⠀⢸⡇⠀⠀⣿⠲⠒⠶⠶⠶⠶⠖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠘⠗⠒⠚⠂⠀⠛⠒⠒⠛⠀⠀⠛⠒⠚⠃⠀⠚⠒⠒⠛⠀⢸⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣏⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠙⡇⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠒⠒⠒⠒⠒⠒⠒⠒⠺⡟⠀⠀⢸⡗⠒⠒⠒⠒⠒⠒⠒⠒⠚⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠹⡇⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠒⠒⠒⠒⠒⠒⠒⠒⠚⡇⠀⠀⢸⡗⠒⠒⠒⠒⠒⠒⠒⠒⠒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠉⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣠⠖⠀⣀⣤⠞⠋⠉⠉⠉⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⣿⣿⡦⠀⢸⠁⠀⠀⠀⠀⠀⠁⠈⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢹⡌⣧⣷⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣾⣧⣿⡾⠰⣧⣅⠀⢀⣨⣭⡶⡄⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣏⣀⣿⣇⠀⠀⠉⠛⠉⠀⠸⣷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠻⡄⠀⠀⠀⠀⠀⢀⡀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄⠀⠀⠀⠀⠀⣀⣤⣼⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣁⣿⢿⣷⣶⣂⠀⠀⠀⠲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣿⣿⣿⣿⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⡉⠻⠟⢿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠻⢶⡶⢸⠿⣿⣟⣿⣿⣿⣿⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢂⣀⠕⠀⠙⢮⠻⢿⣿⣿⣿⣿⣷⣷⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⣀⠹⣿⣿⡿⠿⠿⠿⠿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⢠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⡒⢦⠀⠀⠀⠀⡇⠂⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡧⠄⠠⠀⠀⠀⠀⢬
⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣧⠄⠀⠀⠠⠤⠤⢨
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⠀⠀⠀⠀⣷⡀⠀⢀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠁⠀⠇⠉⠐⠀⠀⠀⠀⠀⠊⠁⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠃⠀⠐⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⡀⣀⣀⣀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠚⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⠤⠤⠤⠤⠈
⠀⠀⡀⠀⠀⢀⠀⢀⠀⡀⠀⡀⠀⠀⢀⠀⣀⠀⣀⡀⡀⠀⠀⢀⠀⣀⠀⠀⠀⡀⠀⠀⢠⠈⡥⣄⠀⢆
⠀⢰⠁⠒⠒⠒⠒⠂⠐⠀⢒⡐⡒⢀⡒⠒⢂⠐⠒⠐⠀⠒⠒⣒⣁⠂⠂⠀⠂⠘⠀⡀⠈⠉⠑⠚⠒⠊
⠀⠈⠉⠉⠉⠀⠉⠉⠈⠉⠉⠉⠉⠉⠉⠁⠉⠉⠁⠉⠉⠉⠀⠁⠉⠁⠉⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⢶
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡏⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠁⢸
⠀⠀⠀⠀⠀⠀⠀⢀⣹⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⣏⡀
⠀⠀⠀⠀⠀⢀⡼⢋⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡙⢦⡀
⠀⠀⠀⢀⡴⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠙⢦⡀
⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⣈⢁⠈⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠎⠘⠓⠆⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶
⠀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉
⠀⠀⠀⠘⣷⣾⢻⢘⡢⡾⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡄⡄⣄⢤⠔⠂⡤⠰⡄
⠀⠀⠀⠀⠘⠃⠈⠈⠁⠁⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣻⣮⢻⣽⡟⣟⣸⣿⣟⣽⣧⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠛⠛⠛⠻⠛⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡼⢡
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠊⢐⡞⠀⡀
⠀⢸⡒⡆⢰⣄⠰⡔⡇⢙⢵⢴⡆⢠⡆⠀⠀⠀⠀⠀⠀⠸⣷⡿⠑⠂⠀⠀⠀⠀⠀⠀⠀⣄⡄⡄⡀⣠⢤⡀⡄⠲⢀⣤⣰⡀
⠀⠈⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠝⢓⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠃⠉⠉⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣰⢶⠐⡠⢲⠂⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠉⠁⠁⠈⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⡄⣀⣀⡀⡠⠤⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠄⠈⢉⠇⡃⠈⠉⠁⠀⠒⢒⢒⡗⠢⠤⠤⣤⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠠⠤⠾⠓⠒⠚⠽⠒⠛⠒⠓⡟⠫⡀⠉⠀⠙⢷⠈⢹⡌⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣁⠀⠉⠉⠤⣠⡽⠟⠂⠀⣀⣀⣀⠀⠠⢤⠀⢢⣦⡶⣿⣶⠀⠶⢾⡟⢻⠇⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢠⢐⠐⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⣿⡕⢺⣿⠀⢠⣠⡀⠴⠟⠛⠹⢻⠂⠀⢸⠇⢺⡠⠊
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠠⠄⣋⠀⠀⠀⠠⣀⣤⡽⠇⣈⡃⠈⠁⠀⠀⠀⠠⠀⢰⢾⠀⢀⣿⡴⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣉⣱⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢈⣤⣾⠿⠋
⠀⠀⠀⠀⠀⠀⢀⡠⣀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣟⠕⠁
⠀⠀⠀⠀⠀⠀⠸⢶⡼⠂⠀⠀⠀⠀⠀⠀⡆⡉⡦⠀⢀⢀⠀⢀⣦⣾⡿⠿⠛⠟⠃
⠀⠀⠀⠀⠀⠀⡠⠁⡒⠂⢀⣀⠠⠤⠄⠀⠈⠻⠉⠀⢨⣴⣿⣿⣿⠿⡗⠒⠂
⠀⠀⠀⠀⠀⠀⠑⢲⣧⡤⣟⣛⣿⣿⣄⠀⠠⢙⣀⣠⣯⣿⠿⠋⠁⠁
⠀⠀⠀⠀⠀⠀⢀⡩⠗⠋⠉⠉⠉⠒⠚⠒⠻⠿⢟⣭⣛⠁
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊

⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠳⣆
⠀⠀⠀⠀⢠⡞⠉⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠚⢻⡄⠀⣿
⠀⠀⠀⠀⡟⣷⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹
⠀⠀⠀⠀⣿⢹⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⢻⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⢸⡜⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸
⠀⠀⠀⠀⢸⡇⣷⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⢸⡇⢿⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡆
⠀⠀⠀⠀⠀⣇⢸⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠸⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡄⣧⠀⢸⡆⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠤⠴⠶⠶⠶⠶⠶⠖⠒⠒⠛⠛⠛⠛⠋⠀⢸⡇
⠀⠀⠀⠀⠀⠸⡇⢻⠀⠈⠛⠋⠉⠉⠉⢉⣉⣉⣁⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠤⠶⠶⠶⠶⠖⠒⠒⡚⠛⠛⣧
⠀⠀⠀⠀⠀⠀⣧⣼⡶⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⠤⠤⡤⠬⡤⠤⡤⠤⡀⠘⣧
⠀⠀⠀⠀⠀⠀⢻⡀⢷⡀⠀⢠⡤⠤⠴⡖⠒⢲⠒⠺⡍⠉⣏⠉⢻⣀⣸⣄⣀⣱⣤⡬⣦⠤⢷⠤⠷⡤⢷⠶⠳⡀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⢷⠈⢧⠀⠀⢻⡤⠤⠷⡖⠚⢷⠒⠻⡉⠹⡍⠉⢣⣀⣹⣄⣀⣧⠤⠼⡦⠐⢷⠒⢳⠚⢷⠚⢳⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⢷⠀⠀⢳⡤⠤⢷⠤⠞⢷⠚⢻⠉⠹⡉⠉⢇⠀⢱⡀⠈⣆⣀⣘⣄⣘⣆⠬⢧⠬⡦⠴⢧⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⢷⡀⠈⢷⣀⣀⣧⣀⡸⣦⠤⢧⠄⢷⠒⠚⣏⠋⢿⠉⠉⡏⠀⠹⡀⣹⣀⣈⣆⣼⣤⠬⠇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⢷⡀⠈⢯⣁⣈⣇⣀⣨⣦⣬⡦⠼⠧⠤⠾⠶⠾⠗⠒⠛⠛⠋⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠈⣧⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠖⠒⠚⠛⠋⠉⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢀⣀⣀⣀⡀⠤⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠭⠭⠭⠥⠻⠒⠒⠒⠒⠚⣁⣀⣀⣠⣤⣤⣴⣶⣒⣛⣯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠘⢧⡀⠀⢀⣀⣀⣀⣠⣤⣤⠤⠤⠶⠶⠶⢒⣒⣛⣛⣿⣭⡭⠭⠿⠶⠚⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢯⣭⣭⠭⠭⠽⠶⠶⠒⠒⠛⠛⠛⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣀⣀⡀⣈⣉⣍⠁⠐⢃⣤⢤⣄⡠⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠚⡉⠁⣀⠽⠛⠛⠉⠉⢩⡟⠉⣉⣏⠤⠄⠚⠛⢀⢄
⠀⠀⠀⠀⠀⠀⣐⡿⠿⠥⠄⠒⠒⠉⠁⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⢿⣁⣀⣀⣀⣀⡀⣀⡠⠤⣤⣤⣶⡶⠿⠿⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⠂⠂⢤⡄⠔⠂⠉⠁⠀⠀⡠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⣀⠴⠄⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⣸⣿⠯⠤⠄⣼⣆⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣥⢠⠀⠀⡠⡖⠲⣤⣤⢲⠲⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠞⠉⠑⡀⠀⢧⣳⣴⢻⢿⣘⣶⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣡⢀⣤⠃⠀⠈⠉⠁⠈⠀⡉⡁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣻⠀⠀⢸⢿⠽⠾⢾⠶⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠅⢧⣤⣤⣈⣩⣭⣭⣭⠭⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡲⠶⣶⠀⠠⡘⡿⠿⠿⠿⠿⠶⠎⠈⠒⠒⢒⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠤⡀⠀⠈⢃⠀⡇⠀⢐⡐⠄⠀⠀⠀⠀⠀⠀⠧⠃⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠘⠤⠆⢀⣀⡜⠀⡇⠀⢀⣤⣤⣴⣶⣶⡶⠶⠿⢯⠆⠀⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⢷⣤⣴⣿⣿⢇⡏⡇⠀⣿⠀⡴⠚⢏⠉⠉⠉⠳⢸⠀⠀⡆⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠀⠀⢀⣿⣿⣿⣿⣸⡇⡇⠀⣿⠀⠑⠔⠈⠁⠈⠀⡁⣸⠆⠀⡄⠈⣄
⠀⠀⠀⠀⠀⠀⠀⡰⢋⣈⠳⣀⣾⢿⣿⣿⣏⣿⠇⠁⠀⣿⢸⠠⡁⡀⠤⠤⠀⢓⢻⡃⠀⣿⡤⠈⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⡸⠀⡟⠛⣿⣿⣿⢿⡿⠀⡇⠀⣿⠀⠆⠒⠐⢀⣁⣁⣬⡼⠂⠀⣿⣧⣤⣄⡀⣀⠬⢿⠒⠒⢐⠢
⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⣾⠁⠈⣾⣿⣿⣿⡇⣾⠃⠀⠙⠒⠚⡿⠛⠛⠛⠹⠀⠀⠀⠀⡟⠫⠍⣁⡀⡏⢀⠄⣷⣶⠤⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠀⠀⠀⢻⣿⣿⣿⢱⡇⡆⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠙⢶⠚⠛⠉⢙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣦⠀⠀⢸⣿⣿⣯⣾⠃⣇⠀⠀⠀⠀⠆⣤⠀⣠⣞⣠⠠⠤⠚⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡜⠲⣤⡤⢍⡉⢹⣿⣶⣯⣦⣤⣶⣶⣾⣿⡿⠟⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠆⣌⠑⠀⢱⠈⣿⣿⡏⠉⠀⠀⠀⣿⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠏⢹⠀⣇⡼⠀⡟⣿⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠚⠋⠉⠁⠀⢁⣿⣀⠀⠀⠀⠀⢿⠲⡦⠖⠒⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⣈⠹⡆⠒⠒⠙⠂⣷⣶⠾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢂⢈⠆⣳⣶⠾⢿⡶⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⣁⣠⡏⠀⠀⢘⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⢰⡏⡏⠀⠀⠀⢸⡇⠀⠀⠈
⢀⣠⣤⣶⣶⣶⣦⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣿⣼⢸⠃⠀⠀⠀⢸⣇⣀⣤⡾⠒⠠⠄⣀
⠈⠩⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠌⠀⠀⠀⠀⢘⣿⣯⣤⡀⣀⣤⠴⢾⡇
⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣭⣐⣛⠷⠶⠚⠋⠉⠉⠙⠻⠯⣒⡈⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⢿⣿⣿⣿⣻⡿⣿⣿⣿⣷⣦⣤⠶⠒⡋⠽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢾⣯⣟⣻⣇⠨⠅⠒⠈

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⢸
⠀⠀⠄⣡⠆⠐⢄⠠⠀⠀⠀⠀⠄⡥⠂⣄⣀⡀⠀⠀⠠⢀⡴⠶⢦⡅⠄⠀⠀⠀⠠⢀⢔⠀⡢⡀⠄⠀⠀⠀⠰⢉⠞⠒⣷⣈⠂⠀⢸
⠀⠀⠐⡃⠀⠀⢀⠀⠂⠀⠀⠐⠀⡀⠀⢈⣿⠁⠀⠀⠂⢸⡁⠀⢀⡂⠐⠀⠀⠀⠂⢀⢆⡋⡠⡀⠐⠀⠀⠰⣈⢀⠀⠀⠀⡇⣁⠆⢸
⠀⠀⠀⠑⣀⣠⠃⠀⠀⠀⠀⠀⠀⠱⣀⠟⠉⠁⠀⠀⠀⠀⢩⣙⡙⠁⠀⠀⠀⠀⠀⠀⢃⣿⡘⠀⠀⠀⠀⠀⢠⡀⢂⣀⡜⣀⡆⠀⢸
⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢸
⣿⣿⠟⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⡶⣷⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣾⡻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣯⣿⣿⣿⣿⣿⡿⠛⠿⢿⣟⠙⢿⣿⡉⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⣿⡿⠛⠒⠂⠚⢾⣷⡾⣿⢳⡿⠟⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠈⣿⡟⠋⠁⣀⡠⠤⠀⠈⣿⢹⣡⠏⢠⣴⣶⣿⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⣿⣿⣷⠈⢻⣿⡶⠆⠀⣿⣿⣿⣆⣿⣯⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏⠀⡀⠀⠀⠀⣸⣽⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣋⡁⠀⠀⠀⠈⠉⢨⣿⣿⣿⣟⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣤⠤⠯⠵⠀⠀⠀⣀⣴⡟⢹⣿⣿⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣿⢁⡠⠛⢁⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠛⠁⡤⠒⣩⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⡏⠉⠀⠀⡠⢸⢥⣾⣽⣿⣿⣿⣿⣲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣾⣿⣦⣷⢠⠔⠋⣐⣿⣷⣿⣿⣿⣷⣦⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⣿⣿⣬⣿⠛⢒⢾⣿⣿⣿⣿⣯⡏⣉⠀⠈⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢟⣿⣿⣿⡿⢾⣥⣿⣿⣿⣿⡿⢫⠀⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⣿⠏⠘⣿⣿⠏⠠⠋⣸⡿⠋⣽⠏⠁⠁⠀⠀⠀⣠⣄⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⢠⡟⠁⠀⠒⠼⠛⠁⠂⠁⠀⠀⠀⠀⠀⠀⠉⠁⠁⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠉⠙⠛⠓⠒⠶⠶⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢰⠋⠉⠉⠛⠒⠒⠦⠤⢀⣀⣀⡈⠉⠙⠳⢤⡀
⣠⢤⠞⢻⢹⣧⠶⣆⠀⠀⠀⠀⠀⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⡄⠈⠟⠳⣄
⠙⢦⠱⡴⢾⢃⡼⠃⠀⠀⠀⠀⢸⠃⢰⠁⠀⠀⠀⣴⡆⠀⠀⢀⡄⠀⠀⠀⠀⠀⡇⢰⠀⠀⠈⠳⡄
⠀⠈⣗⣋⡉⢽⡄⠀⠀⠀⠀⠀⡟⠀⡎⠀⠀⠀⠰⠤⠤⣄⣀⣈⡁⠀⠀⠀⠀⢠⠁⠃⠀⠀⠀⢠⡇
⠀⠀⡏⠀⠀⢸⡁⠀⠀⠀⠀⢰⠃⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡎⢸⠀⠀⠀⠀⣸
⠀⠀⣧⠤⠀⠀⢧⠀⠀⠀⠀⣾⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡎⠀⠀⠀⠀⡏
⠀⠀⣇⠀⢀⡀⠘⡆⠀⠀⠀⣏⠀⠳⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⠁⠀⠀⠀⢸⠃
⠀⠀⠸⡏⠉⠀⠀⠹⣄⠀⠀⠙⠲⢤⣀⣀⡈⠉⠉⠓⠒⠲⠤⢤⣀⣀⣀⡰⠃⡼⠀⠀⠀⣠⠏
⠀⠀⠀⢳⡠⠖⠁⠀⠈⠲⣄⡀⣠⡞⠁⠀⠉⠙⠓⠒⠶⠤⢤⣀⣀⡀⠀⢀⣠⠥⣶⠚⠉⠁
⠀⠀⠀⠀⠱⣄⢀⡔⠀⠀⡀⠉⣳⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡀⠀⢸⣆⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠻⢤⣀⡴⠀⢀⠏⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠟⢺⠉⠉⢹⠁⠈⢩⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡿⠚⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⢀⣀⣈⡀⠀⠋⠀⠀⣠⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠿⠋⠉⡏⠉⠙⠓⠦⣄⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⠴⠶⠶⠶⠤⢤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣦⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠶⠀⠀⠀⠀⠀⠀⠈⢉⠓⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡇⠀⠀⡠⠀⠀⢠⡇⠀⠀⠀⠀⣀⣟⣒⡒⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠰⣞⣋⣭⡾⣥⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣼⠀⠀⠀⠉⠁⡼⢁⢀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡗
⢶⠶⢄⣀⣠⣠⠞⠻⡁⠀⢣⠈⠙⠓⠒⣶⠦⠤⠤⠤⠤⠤⢤⡤⠾⠶⠖⠒⢶⠚⠁
⠈⢧⠀⠙⢆⠘⣄⠀⠑⠀⠀⢀⠀⣠⠴⠏⠀⠀⠀⠀⠀⠀⣼⠀⠀⣀⠀⠀⡈⠋⠛⠛⣆⡀
⠀⠈⢧⠀⢈⡆⠈⢀⡴⠶⠶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠀⠀⡰⠁⢀⠆⡰⠋⣷
⠀⠀⠈⠷⠞⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⣰⡀⣀⣌⣰⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠁⣿⣠⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣴⡿⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣤⣤⣶⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣿⣇⣀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⠀⠀⠀⣸⣿⠛⠋⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⣿⠃⠀⠀⣰⣶⣶⣶⣶⣶⣿⣏⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⢠⣿⠃⠀⠀⠀⠀⠈⠛⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⣁⣈⣁⣉⣉⣉⣉⣉⣉⣠⣾⠟⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣄⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⣶⣆⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠉⠉⠛⢿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⣼⡟⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⢿⣶⡾⠟






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡤⠤⢤⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠤⠤⠤⠭⠭⠍⢉⣉⣉⣛⣛⡛⠛⠛⠛⠛⠿⠷⠶⠶⠶⠶⢶⣶⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠒⠒⠒⠂⠠⠤⠤⠬⠍⢹⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⢀⠀⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡠⠚⠀⠀⠀⠀⢸⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠨⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⡉⠐⡒⠢⠤⠭⢉⣁⣒⠒⠠⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠡⢄⠘⢠⠆⠊⠠⠔⣀⡀⠄⢀⠬⠍⣑⠒⠒⠲⠠⠭⢉⣐⣒⡒⠂⠤⠤⢀⣀⣀⡀⠀⠀⠀⢸⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⡐⠢⠉⠔⢂⡠⠀⠁⡂⠀⠃⠠⠆⢒⡠⠉⣁⠄⠮⣈⠡⠒⠀⢀⡄⠡⢉⠉⠐⠒⠂⠬⠭⠍⣉⣒⠚⢸⣀⡇
⠀⠀⠀⠀⠀⣀⡤⠚⠁⡠⠤⠉⡀⠐⠉⠠⠂⠐⡠⠁⡈⡀⠘⠃⠨⠔⠀⡤⠒⠉⡄⠀⠁⠀⠰⠄⢀⠰⠀⠁⡀⠀⠰⠤⠀⠰⠀⢀⡠⣼⣏⣡⠇
⠀⠀⠀⠀⠀⡏⠉⠑⠒⠒⠤⠭⠄⣚⣀⠈⠒⠀⢔⣈⠀⠀⠀⠀⠉⠀⠒⠀⡤⠀⡀⠀⠘⡀⠀⠘⠀⣤⠀⠈⡅⠒⠊⢀⡠⠔⢊⣵⠶⠚⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠢⠤⠤⣄⣀⣉⠉⠙⠒⠒⠤⠤⢤⣀⣐⡂⠂⠡⠔⠀⢤⠄⢈⢀⠒⠠⠀⠖⠀⢁⡠⠔⠊⣁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠲⠤⠤⣀⣀⡈⠉⠑⠒⠒⠦⠤⠥⣀⣀⣁⡠⠔⠊⣁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠢⠤⠤⣄⣀⣏⡤⠖⠋⠁

⠀⠀⠀⢠⡀⢀⣀⠀⠀⠀⠀⠀⠀⢠⠂⠐⠤⠀⣀⠄⠂⡆⠀⠀⠀⠀⠔⠛⠉⠛⠢⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⢐⠌⠉⢈⠁⠔⡀⠀⠀⠀⠀⠀⠙⠒⢠⠔⠁⡠⡊⠀⠀⠀⠀⠐⠨⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠩⢉⠩⠋⠍⢂
⠀⠀⠈⠀⠀⠀⠀⠈⠑⠂⣤⠀⠀⠰⢒⡠⠀⡠⠊⠡⠡⠀⠀⠀⠀⠀⠑⣴⣀⣤⠆⠀⠀⠀⠀⣿⠄⠠⠁⠠⠀⠀⠀⡁
⠀⠀⠓⢅⠎⠦⠤⠴⡰⡱⠉⠀⠀⠀⠨⠴⡈⡀⠀⢧⢘⠁⠀⠀⠀⠀⠀⢸⠛⡃⠀⠀⠀⠀⠀⣨⣤⡤⡤⠀⢤⢤⢤⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠈⠑⠁

⠀⠀⠀⠀⢀⠀⠀⠀⣀⢀⠀⠀⠀⢀⠠⠤⠤⠤⠤⠄⡀⠀⠀⠀⠀⠀⢀⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋
⠀⠀⠴⠒⠞⢋⠉⢡⠷⠠⡀⠀⠀⠃⠄⠀⢀⠰⠀⡆⠀⠀⠀⠀⢀⠠⠟⠿⠿⠤⣒⠀⡰⠀⠀⢀⢀⡌⠖⡀⢁⠈⡐⢀
⠀⠀⢇⠈⢐⠛⠋⠠⡀⠀⡘⠀⠀⡧⠥⠤⠥⠔⠀⡧⠤⠀⠀⠀⢘⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠛⠤⡘⠊⠓⠉⠚⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠵⠵⠀⠈⠀⠑⠓⠖⠀⠀⠀⠈⠁⠈⠀⠉⠈⠁⠈⠀⠀⠀⠀⠐⠁⠉⠉⠉⠉

⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡅⠀⢸⠀⠀⠛⢯⠇⠀⠀⠀⠀⠀⣿⠰⠉⠂⣆⠀⠀⠀⠀⢠⣄⢀⣤⡀⢸⢀⠀⠀⠀⠀⣏⠀⠀⠁⠀⠾⠇⠀⡁
⠀⠀⠁⠒⣚⡚⢂⣀⠨⠤⠀⠀⠀⢀⡉⣀⡆⠀⠀⡇⢑⡀⠀⠀⡀⡩⠨⡉⠉⢉⠀⢀⢿⠀⠀⠀⠀⠀⢂⠤⠠⣈⠀⣰
⠀⠀⠀⠃⣒⠐⠐⠂⠃⣛⠀⠀⠀⠈⠁⠙⢦⢀⠤⠋⠉⠀⠀⠀⠈⠁⠁⠉⠛⠉⠈⠐⠀⠀⠀⠀⠀⠀⢈⣓⣄⢠⣘⡡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆
⠀⠀⡄⠀⠀⠀⠀⠀⠒⠒⠒⠂⢄⠀⠀⠀⠀⢠⠤⠤⠤⠾⠭⠽⠦⣖⠲⢤⡀⠀⠀⠀⠀⠛⡉⠉⢉⠛⠀⢶⢲
⠀⠀⣏⠉⣭⠉⣍⠉⣭⡋⢩⡋⡍⡀⠀⠀⠀⠮⠥⠕⠥⠴⠪⠨⠎⠉⠱⡉⣣⠀⠀⠀⠀⢀⣂⣒⣐⣐⣀⣘⣘⣰⠄
⠀⠀⣃⡀⣀⡄⡀⠤⠤⠤⠤⢄⣠⢈⡀⠀⠀⢅⠉⡩⣅⠉⠉⠉⢀⢀⢀⣠⢄⡀⠀⠀⢸⡏⢠⣾⡄⢀⡀⢀⡀⢨⣳⡀
⠀⠀⠀⠁⠑⠑⠁⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠈⠈⠓⠛⠁⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠈⠈⠛⠋⠙⠛⠙⠋⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡤⠤⠤⠤⠄⠀⠀⠀⠠⠤⠶⠶⠶⠤⡤⠀⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⢒⣀⡈⠉⠁⠤⠄⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠀⠀⠚⠛⠓⠚⠚⠚⡘⡙⠋⠙⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⢁⠂⢡⢂⡕⠐⠌⠠⠰⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⠂⠂⠀⢢⠁⡐⡀⠠⢡⠞⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠂⠌⠀⠜⠠⠡⠐⠠⢁⡞⡐⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡐⡀⢈⢈⠀⠁⠀⢁⡞⣠⠊⣷⣫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡐⠐⡜⢠⠂⠀⠀⢀⠁⡾⢠⠇⢌⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠐⡁⢠⠇⠈⠄⢀⠂⡼⢡⠏⠀⠂⢴⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⢀⠎⠀⠌⠀⠀⡼⠁⡟⡄⠀⢤⢾⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠡⠠⠠⡊⠐⠀⢄⠄⣸⢁⠞⡐⡐⢔⢣⢺⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢠⠱⢡⡑⠀⡐⠀⠂⡰⢃⡎⠌⡐⢈⠀⠢⢻⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠂⠠⠠⡐⠀⠄⠌⢘⠃⡜⠙⠐⠖⠀⠈⠦⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠂⠃⠰⠡⠠⠔⠌⠀⠦⠮⠘⠀⠌⠌⠄⠂⠞⢼⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡂⣐⣆⣀⣀⣉⣉⣉⣁⣀⣀⣀⣀⣒⣒⣒⣒⣒⣓⣒⣓⣒⣒⣒⣒⣒⣓⣓⣒⣒⣒⣶⣾⣿⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠄⠁⠠⠤⠤⠤⢀⠀⢀⡀⢀⣉⡙⣿⠍⢭⡮⠍⢭⠭⠨⠭⡉⠭⠭⠭⠭⠭⠭⠬⠭⠵⢤⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠊⠀⠀⠀⠠⠤⠤⣤⠤⢥⠤⠮⡤⠤⠤⡤⠼⠀⡁⠥⢴⠦⠧⠈⢀⠵⠤⠭⡬⠦⠄⠤⠤⠀⢥⠀⠻⣄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡌⡠⠁⠀⠀⠀⢀⣀⣀⣰⢀⡀⠬⣀⠠⠆⢤⠤⠤⠤⠤⠧⢠⠀⠦⠨⡩⠈⢦⠳⢂⡑⡄⣀⣀⠀⢀⡀⢦⠓⠘⢦⠱⡀
⠀⠀⠀⠀⠀⠀⡜⡐⠁⠀⠠⠤⠄⠤⠬⢠⠄⠜⠀⠀⠦⠀⠠⠼⠤⠤⠠⠄⠠⠠⠤⠤⠤⠬⠬⠦⢁⠤⠵⠶⠬⣦⣄⠋⠢⠤⢤⣥⢌⢷⣳⡀
⠀⠀⠀⠀⠀⡜⠀⠤⠀⠀⠀⠀⠀⠠⠤⠶⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠤⠤⠠⠀⠷⠂⢈⠨⣟⢮⣠⢥⣬⠢⢥⠤⣴⣏⢣
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⠉⠈⢣⠀⠀⠀⠀⠀⠁⠢⢅⡂⢔⡨⢑⠢⣌⢀⠈⡀⢣
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡒⢅⠢⢐⠡⢀⠌⠆
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣅⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠬⣀⠬⡂⠅⠘
⠀⠀⠳⡤⠠⢤⢄⣀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣊⣱⡾
⠀⠀⠀⠀⠉⠉⠛⠓⠛⠛⠚⠚⠛⠐⠂⠲⠂⠊⠴⠳⠳⠓⠣⠞⠞⠞⠰⠳⠷⠓⠒⠲⠾⠶⠾⠂⠎⠖⠰⠛⠴⠣⠳⠶⠛⠂⠋⠒⠚⠚⠛⠛⠉
⠀⠀⠀⢀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠠⢀⠠⣀⠠⣀⠀⡀⠀⢀⠠⣠⠤⢀⠠⠀⠀⠀⡂⠄⢐⠀⠀⡀⠀⣀⠠⢐⠠⢀⠠⢀⠠⠀⡀⠀⡀⢀
⠀⠀⠀⠀⠁⠉⠂⠉⠀⠀⠁⠀⠩⠀⠈⠀⠠⠀⠀⠐⠈⠀⠀⠐⠉⠐⠨⠀⠈⠀⠂⠁⠐⠨⠀⠊⠅⠂⠡⠐⠠⠐⠀⠄⠀⠅⠂⠡⠂⠁⠂⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣷⣶⣄

⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⠀⠀⣿⣿⠋⠉⠉⢻⣿⡆
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣄⠀⢀⣼⣿⡇
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣿⣿⠟⠁⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣴⣿⡿⠛⠛⢿⣿
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣿⡿
⣠⣤⣶⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⢀⣤⣴⣦⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⡿⠛⠛⢿⣿⣆
⠉⠙⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⡿
⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣦⣀⣀⡀
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠈⢻⣿⣿⡿⠿⣿⣷⣄
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⡏⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠸⣿⣷⣤⣤⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠿⠿⠿⠿⠷⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣤⠀⠀⠀⣿⠉⠉⠉⣿⠀⠀⢀⣤⡀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⢀⣴⠟⠙⢿⡶⠿⠛⠀⠀⠀⠛⠿⣶⡿⠋⠻⣦⡀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣼⠟⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⣴⠿⠛⠛⠛⠿⣦⡀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣾⡟⠛⠛⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠛⠛⢻⡇⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠙⠛⠻⣷⡀⠀⠀⢻⣦⡀⠀⠀⠀⢀⣴⠟⠀⠀⢀⣿⠛⠛⠃⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡷⠀⠀⠀⠉⠛⠷⠶⠿⠛⠁⠀⠀⠀⢾⣇⡀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡀⠀⣀⣄⡀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢀⣽⠗⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠟⠙⠛⣷⠀⠀⠀⣿⠛⠉⠻⣶⠟⠁⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠐⠿⢷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠘⠛⠿⠶⢶⣶⣶⠶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢨⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠉⠉⡇⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⡀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⣿⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠃⢿⡟⠀⠀⠀⠀⣿⣷⡅⠀⠀⠀⠀⣿⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⢀⠀⠀⠀⠉⢀⡀⠀⠡⠀⣿⠀⠀⠀⠘⠋⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠰⠀⠀⠀⠀⣀⣀⠠⡠⠚⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⠀⠠⠤⠀⠀⠀⠀⠄⠀⠐⠂⢀⡇⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⡇⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠀⠀⠀⠠⠶⠀⠀⠀⠀⢠⠄⠀⠀⠀⣤⠀⠀⠀⠀⠀⣰⠤⢅⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢢⢥⠘⠂⠤⠤⠤⢄⣀⣀⣀⣀⣀⣀⣈⣀⣀⡁⣀⣀⠀⠠⠞⠁⠀⠀⠉⠚⡤⢾⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡐⠂⠰⠥⠮⠼⠀⠀⠐⠃⠀⠤⠤⠤⠤⠤⠤⠤⠤⠄⠴⠀⠀⠀⠄⣶⣰⠆⠂⢀⠔⡇⡇⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⢀⣀⣈⣈⡀⣀⣀⣁⣉⡉⣀⣀⣀⣀⣂⡀⢀⣒⣀⣀⠀⠀⠀⠐⠒⢂⣀⡇⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢹⠇⠀⡼⣧⠽⣬⢷⡭⢦⡵⣮⠷⣭⢦⡽⢮⠿⣎⢷⡘⠀⢰⡿⠹⡄⠀⠀⢸⣁⠕⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⡜⣡⠋⢸⣧⢻⡜⣯⡝⣮⢻⣭⢳⡽⣮⢽⣭⢷⡽⢯⡽⡮⠷⠀⣼⠇⠀⢸⠀⢐⠸⢁⠎⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡜⠰⠃⢤⢤⠾⠤⠤⠴⠷⠴⠷⠠⠾⢠⡄⠀⠾⠇⠼⠇⠮⠇⠼⠅⠿⢀⠀⢠⠂⢀⡳⣷⣤⡀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⡌⠀⠁⠀⠘⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡠⠋⠉⠉⠁⠀⠉⠉⠁⠀⠈⠈
⠀⠀⠀⠀⠀⠂⠠⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⡁⠀⣀⣤⡀⠀⠐⠀⠀⠀⠀⣠⣄⡀⠐⠂⠀⠀⠀⠛⠀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⢧⣀⡿⠀⠀⠀⠀⠀⠘⣇⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠙⠛⠛⠋⠛⠋⠛⠋⠛⠉⠙⠛⠓
⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠠⣶⡦⠘⠀⠀⠀⢠⣾⣦⣶⡦⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠆⠀⠰⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠰⣛⡖⠐⠒⠂⠐⠐⠂⢞⣳⠰⣛⡆

⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⡆
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⣿⡀⠀⣤⡀⠃
⠀⠀⠀⠁⢰⡞⢳⡆⠀⠓⠓⠛⠛⠋⣴⠋⢳⡄⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢉⣥⡀
⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠴⠋⠉⠙⠦⠋

⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠓⠒⠛⠚⠚⠛⠛⠓⠀⠀⠀⠀⠐⠛⠛⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠠⠤⠤⠤⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠈⠀⠂
⠀⠀⠀⠉⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠀⢀⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡄⢀⣤⣖⣒⣒⣒⡒⣒⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⠠⠤⡀⠀⣈⡉⡇⠀⢸⠀⠀⠀⠀⠀⠀⢠⢒⡆⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡇⠂⠔⠁⠸⠄⠝⡇⠀⠘⡇⠀⠀⠀⠀⠀⣎⠐⣅⡠⢛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠤⣄⣀⡠⡤⡀⢿⠀⠀⡇⠀⠀⠀⠀⠀⣼⠲⣄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠙⠒⠧⠦⠓⠃⢸⢸⣠⠟⠀⠀⠀⠀⡼⠣⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⡟⢻⠛⠓⠛⠋⠀⠀⠀⠀⢀⡞⢤⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠔⠒⠛⠧⠾⠛⠓⠒⠒⢲⣤⣄⡴⠫⣹⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⡅⠈⠉⠉⠉⠉⠓⠒⠒⡖⠉⣯⢺⠹⣬⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢤⡇⠀⠒⡂⡒⠒⠒⢲⠀⡇⠀⣙⣺⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⢤⣷⠀⠟⠲⠃⠀⠀⢸⡗⣷⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢤⣸⢹⠀⢰⣞⡳⠀⠀⢸⣷⣿⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣀⡼⢸⡄⠘⠒⠒⠒⠒⠚⠁⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣤⡇⠈⡇⠀⠀⣤⣤⣤⣤⣤⣿⠔⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢧⣤⠗⡄⠓⣒⢲⡖⠒⠒⠒⠲⡿⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡎⠀⢇⣸⠀⣍⣹⠀⠀⠀⠀⠀⡷⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠘⠉⠀⠆⢾⠀⠀⠀⠀⠀⣏⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⡟⠀⠀⠀⠀⠀⢹⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⣇⠀⠀⠀⠀⢠⢾⠚⡧⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠘⠒⠃⡇⠀⠀⠀⢻⣈⡉⠀⠀⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣓⠒⣒⣒⡭⠃⠀⠀⠀⠈⠒⠬⠭⡩⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣀⡤⠚⠃⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠚⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠑⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠲⠆⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⢀⡀⠄⣀⡀⠀⠀⠀⢀⡠⠄⣀⡀⠀⠀⠀⠀⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠀⢀⠋⢠⣤⠉⢿⡆⠀⠰⠋⣠⣄⠙⣿⡄⠀⢠⡶⠙⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠰⠄⠈⢦⡈⠋⣠⣾⠇⠀⠸⣆⡙⠋⣠⡿⠁⠀⠉⡇⠀⠀⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣤⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠙⣧⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⣀⡀⢀⡀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣯⢸⣿⡅⣿⣧⣸⡇⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠈⠉⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠟⠛⠻⣿⠛⠛⠛⠛⠻⣿⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⢢⣤⡐⠒⢺⣇⠀⣘⣿⠗⢺⣆⠀⣘⣿⠒⠒⠒⠒⠲⡶⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢠⣶⡟⠉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠛⠛⠛⠉⠉⠉⠉⠙⡿⠀⣰⣶⡄⠙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣀⠘⠿⡇⢸⠇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢹⠂⣷⡀⠛⠟⠃⣠⡿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡌⢶⠉⢶⠶⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣟⠁⢶⢶⡖⠉⣤⢡⡄
⠀⠀⠀⠀⠀⠀⠀⢇⡸⠀⢠⡎⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣯⠀⠸⠀⢱⡄⠀⠆⠱
⠀⠀⠀⠀⠀⢀⠻⡜⠃⢀⠏⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣏⠀⢰⠀⠀⠱⠀⠘⢃⠾⡀
⠀⠀⠀⠀⢠⡌⣶⠁⢠⠟⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⢸⡆⣿⠀⢸⠀⠀⠀⠻⡀⠈⣤⢃⡄
⠀⠀⠀⠠⣆⡸⠀⢠⡎⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⣿⠀⢸⠀⠀⠀⠀⢡⡄⠈⢎⣱⡀
⠀⢀⡰⠛⠉⠓⢲⡆⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⢱⡖⠊⠉⠛⢦⡀
⠀⠘⠁⣴⣿⣦⠀⠃⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠈⠀⣶⣿⡆⠈⠃
⠀⠘⣆⡈⠛⠋⡠⠇⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠰⣄⠙⠛⢁⣴⠃
⠀⠀⢹⠉⠀⢻⠁⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠀⠙⠏⠀⠉⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣧⠘⠓⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠀⣏⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⡿⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣸⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣇
⠀⢘⣋⣉⣉⣉⣉⣱⠀⠀⠀⠀⠀⠀⢀⡴⢛⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠁⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⣎⣉⣉⣉⣉⣹⠇
⢀⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⢸⠁⢠⣿⣆⡀⠀⠀⠀⠀⠀⠀⡇⠀⣾⣿⣷⠀⢈⡆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣧
⣾⣿⠿⠋⠉⠉⠙⠻⣿⣧⠀⠀⠀⣰⠿⣆⡈⠛⠛⠉⠶⠆⠀⠀⠰⠾⢿⡀⠙⠛⠋⢀⣼⢷⡄⠀⠀⠀⣾⣿⠟⠋⠉⠉⠙⠻⣿
⣿⣿⡄⠀⠀⠀⠀⠀⢻⡿⠀⠀⣠⡿⠟⠛⣻⣶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠙⠃⢶⣶⣟⠛⠻⣿⡀⠀⠀⢿⡏⠀⠀⠀⠀⠀⢠⣿
⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣡⡶⢋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠻⣦⣈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⢉⡴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣌⡙⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⠾⢋⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠻⢦⣜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠛⠳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡿⠛⠛⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⣴⣶⡄⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⣤⣶⣆⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠘⠿⠿⠃⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⠻⠿⠟⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⣤⣤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣤⣤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠟⢯⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣭⡟⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣤⣴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⠉⣡⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢾⡍⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠋⣸⡇
⠀⠀⠀⠀⠀⠀⣴⠚⠛⠛⠛⠚⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠛⠚⠛⠛⠛⠻⠂
⠀⠀⠀⠀⠀⣴⣿⣶⣶⣶⣶⣶⣶⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣶⣶⣾⣶⣶⣿⣷⡆
⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀
⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠛⠛⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⡇⢎⣏⠇⢎⣏⠆⣷⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠷⠶⠶⠶⠶⠶⠶⠿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠀⡔⠶⢲⢲⢲⠲⠖⡄⢰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣤⡺⡱⣱⠀⠉⠉⠉⡭⡍⠉⠉⠁⢰⡱⡹⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠐⠆⢹⠊⠁⠀⣀⢄⣀⡨⣀⣀⢄⡀⠀⠈⢺⠁⠐⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠌⠀⠀⠀⠑⠚⠀⠂⠂⠸⠒⠁⠀⠀⠈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠤⢤⠤⢤⠤⠤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣻⠀⢸⣃⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠒⢾⠀⢸⠖⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⣽⠀⢸⡍⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⣀⡁⣇⣀⣀⣈