Downloaded Emojis & Symbols

⣿⣿⣦⣀⣉⠞⢾⣋⠚⣴⠈⢵⡛⣿⡿⣿⣿⣿⣽⣯⣯⠉⢀⠸⡃⠶⠈⠷⠈⠃⠙⠻⣷⡦⠟⠀⡞⠁⢸
⣿⣿⣿⣿⢿⣶⠪⣁⡀⠉⠑⠀⠋⡛⣝⣿⣿⣟⣟⡶⡿⡳⠉⢨⣧⣤⣅⠂⠀⠀⠀⠀⢿⠀⣈⠂⡄⠔⢋
⣿⣿⡛⣛⡷⢻⡟⣛⡛⠋⠀⠀⠠⣟⠓⠈⠉⠈⠉⠉⠃⡀⠘⠏⢙⣟⠟⠄⡘⠠⠀⠑⠀⠀⠀⣤⡾⠖⠛
⣿⣿⣿⣿⣷⣿⣛⣫⣵⢾⠣⣤⠽⢁⡀⠀⠀⠀⠀⠀⠀⠁⠠⠎⠈⠁⠀⠲⢀⣄⢀⠒⡗⠀⠀⠘⠁⠀⠒
⣿⣿⣿⣿⣿⣿⣿⣿⠗⡞⠉⠁⠀⠈⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢸⣦⡇⠀⠀⠤
⣿⣿⣿⣿⣿⣿⣿⣧⣴⣷⣿⢃⡀⢀⠀⠀⠀⢀⡠⠤⠀⠀⠀⠀⢠⠀⠀⢟⡹⡳⢿⢟⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠲⠄⠀⠀⠀⠂⢀⠀⠮⠀⠀⢛⡠⢼⠀⠀⠀⠀⠀⢶⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠶⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠖⠣⡄⠀⠀⠀⠀⠀⠀⠚⣫
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣞⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠛⢠⡀⠰⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠂⠀⠀⠈⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⢠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⠛⡷⠞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⠤⢀⠈⠀⠀⠀⣀⡋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⢫⣾⣤⣀⢳⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⣶⡟⢺
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⣠⣤⠀⠸⠇⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⢭⣁⣷⣏⣻⡧⠤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠟⠀⠀⠀⠀⠀⠀⡲⠶⡛⣭⡿⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢃⡤⠍⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣧⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⢸⣄⣈⣳⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣯⣭⣯⣋⣿⡏⣯⢻⣫⡏⡟⣽⣽⡇⠀⠀⠀⠀⠀⠀⠀⣿⣒⣒⣒⣶⡶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣻⠀⠀⠀⠀⣽⣷⣷⣿⣯⣾⣷⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⢹⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠹⡀⠀⠀⠀⠀⠈⡏⠉⠀⠁⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⢸⢙⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣴⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢹
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⡟
⠀⠀⠀⠀⠀⠀⠀⢸⡗⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣷⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣏⢾⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣧⢻⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣸⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣸⡧⣄⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿
⠀⠀⠀⢠⡔⠒⠒⠒⠛⠛⠛⠓⠒⠓⠚⠳⠿⠿⠵⠶⠿⠷⠴⠶⠾⠿⠿⠧⠤⠾⠯⣾⠯⠮⠤⠯⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠑⠒⠒⠒⠂⠲⠶⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠶⠦⠤⠦⠶⠔⠰⠶⠦⠶⠦⠤⠤⠤⠤⠤⠤⠤⡤⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠢⣴⡆⠰⠀⠀⠗⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡄⠀⢀⢠⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠃⠖⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣳⣼⣧⣀⠸⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠂⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤
⠀⠀⢀⣒⠀⠀⡀⠀⠀⠀⠀⠀⠙⣿⣿⣿⢇⠀⣆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢷⡀⡇⣼⣿⠀⠀⠁⢤⣤⣤⠤⣀⣴⠞⠉
⠒⠒⠲⠾⣿⣿⣿⣷⣶⢤⣀⠀⠀⠈⢻⣿⣎⣯⣟⠀⠸⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣷⢸⣿⡏⠀⠀⠀⣠⡿⣡⣞⢋⡠⠜⠁
⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣷⣦⡀⠀⠹⣿⣿⣇⢧⠀⣇⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⢿⣼⣿⡇⢠⣶⣾⣫⠟⣫⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣄⠙⣿⣿⣿⣧⢸⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⢟⡿⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣾⣿⣿⣿⣿⡇⠀⠀⢰⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣡⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⡀⣠⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣇⠀⠀⠀⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⢏⡻⣆⠠⣄⣠⠤⣤⠀⣄⢠⡄⣠⡤⢤⣀⡤⢢⠞⣫⠟⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡗⣷⠜⣧⣿⠿⣰⠆⠘⢩⡄⠲⠴⠀⣭⠛⠀⣷⡹⢿⣾⡏⢶⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣞⣶⡿⠁⣞⣥⠰⠿⣴⣆⠻⠸⢣⣶⡼⠷⢬⣽⠆⠹⣷⣋⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⣷⣦⢀⣀⠚⠇⣾⠋⠖⠐⠌⢿⠰⠟⢀⡀⣠⣾⡟⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡃⠛⣿⠳⡉⢶⢤⡔⠱⠂⠄⠾⢱⣄⢴⠉⡷⢻⡝⠂⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣏⠟⢁⣷⢨⡂⡙⠰⠾⡣⠀⠒⠘⠂⢬⡻⠦⠚⠁⣯⢰⡇⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⢺⣷⢈⡁⠎⠳⣴⡖⢸⠓⠢⠤⠢⠥⠒⢻⠐⣶⡶⠙⠊⣅⢸⡿⢰
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠸⡧⠘⠂⣧⣓⣀⠛⠷⣀⢀⠾⠛⢁⣚⣥⡇⠛⣰⡿⠀⢇⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡻⠄⠻⠆⢸⠾⢋⣀⣠⡼⠿⣤⣀⣘⠳⣞⠀⠾⠃⠾⣿⡟⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⠲⠃⡄⣆⢻⠋⢩⡷⢖⣒⠾⣯⠉⣻⢡⡆⣆⡡⢞⣿⣀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠙⠋⠈⠛⠶⢷⣥⢹⣷⣨⣀⠨⠇⣄⣩⣴⣿⢡⣵⣿⠖⣋⣌⡉⠘⠛⣷⡄
⠀⠀⠀⠀⠀⢠⡿⢋⡴⢶⡦⠸⣟⣧⢧⣿⡟⠶⡁⠠⠦⠀⡱⢟⣿⣮⢋⣛⠉⠻⣅⣹⡷⢠⣮⡁
⠀⠀⠀⠀⠀⣾⡇⠺⠗⢛⣡⣤⠈⢡⡴⢾⡛⠶⣧⣤⣠⣤⡷⠞⡏⢀⠸⠿⠏⢶⠏⠀⠀⣾⡀⣷⣆
⠀⠀⠀⠀⢸⣋⣄⡀⠛⢸⣇⠾⠀⠹⠃⠀⠑⢄⡀⠀⠀⠀⣠⢞⣥⣿⣷⢄⠀⠀⢸⡿⢦⡉⠉⢉⣿
⠀⠀⠀⠀⣼⢻⣏⣿⠀⣠⣅⠀⡿⢀⠌⣼⡇⠀⠈⠉⠉⠉⠀⠀⠈⠀⠐⠶⠉⠲⣆⠻⣾⠃⣿⢩⣿⡀
⠀⠀⠀⠸⣡⣾⠉⠁⠀⣯⢹⡄⢴⠋⠸⠛⣥⡀⠀⠀⠀⠀⠀⠀⠀⣴⣇⣀⣤⣿⣿⣤⣤⡄⠙⣿⣭⣧
⠀⠀⢠⢾⣯⣿⠁⣿⡆⠹⠟⢁⠏⢠⣦⠀⠛⠃⣠⣤⠀⣼⣖⣀⣤⡿⠛⠿⢆⣘⠛⠰⣿⠣⠈⣋⡁⢼⣧
⠀⠰⠿⢀⣥⠹⡷⠘⢧⣶⣶⠄⣶⡄⣼⣆⣠⣾⢿⣟⣿⣿⣿⡏⣹⡟⠸⢗⡈⠁⣴⡀⠲⠆⣀⠛⢫⣤⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⢀⣿⣷⠘⠿⢡⣄⠀⠀⠈⢣⡄⣈⡠⣬⢹⣧⠾⡿⠟⢿⡿⡿⠛⡉⠉⣠⣘⣋⢶⣉⣴⡂⢾⣉⣷⣀⠉⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⠹⠿⠛
⢸⠹⣿⠇⠀⠈⠉⣤⡐⠶⠮⣿⣜⠓⢠⣤⡻⣾⢣⡎⠀⣽⠊⡙⠹⡊⠉⡍⢁⡋⠀⠛⠛⠀⣹⡁⢿⣷⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣄⣀⣩⡉⢰⣿⡿
⠸⣤⢠⣦⡀⠛⠀⠛⢣⣤⠀⠶⢍⡳⣬⣙⠃⢠⡁⠈⠉⡡⠮⠴⢃⡘⢰⠖⢘⣿⡿⢷⣄⠀⠈⠉⣤⣤⢸⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢿⣧⣿⠗⠋⠁
⠀⢻⡃⠙⠓⢰⣿⢂⣤⠠⠿⠂⣀⢩⣠⠿⣳⣌⠛⢠⣤⣄⠀⠰⠊⠉⠁⠀⠘⠋⣼⠟⣿⠟⢒⣒⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠠⣯⡾⢧⡀⡿⠁
⠀⠀⠙⢾⣗⡀⢁⠘⣡⡆⢲⠄⠛⢑⣔⠠⣙⣿⣄⣠⣭⡉⠠⣤⣄⠀⠀⠐⣋⣀⠿⠶⡿⠀⣿⣻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣸⣷⣷
⠀⠀⠀⠀⠈⢗⣾⢇⣬⣠⡼⢛⡜⢣⡙⣜⣩⣌⠉⡈⢹⣶⣆⠨⣧⡄⠀⢀⣉⡡⠀⣀⡀⠀⢙⠋⠹⣏⡉⢹⣷⡀⠀⠀⠀⠀⠀⠸⣬⠉⠋⠸⣆
⠀⠀⠀⠀⠀⠈⢧⣤⣬⡛⢨⠫⠙⠐⣨⠏⠛⢿⡀⠛⠀⢈⡘⠻⠟⠉⣿⡏⠉⡿⠆⠿⠷⢰⣟⡿⢠⡿⡷⣈⡙⠟⣆⠀⠀⠀⠀⠀⡿⢺⡟⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡀⢟⢠⠀⢾⡲⠁⠀⠀⠀⠳⣾⣷⡌⢉⠀⠺⡷⢀⣷⣄⣷⣿⣦⠀⢈⣛⢱⠏⠙⢶⣿⡙⣧⣼⢦⣀⠀⠀⣠⣟⣘⠻⠿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⠶⢶⡤⠝⠂⠀⠀⠀⠀⠈⠻⣄⠻⠗⢠⣤⠀⠉⢤⡀⢹⡶⠄⣉⡭⢾⡀⠀⠀⠙⣿⠿⠛⠛⠛⢽⣿⢋⣽⢋⣴⣦⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠖⡠⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢾⣟⣩⣶⠟⠀⣵⣼⣿⠃⣉⠥⢴⣇⠀⠀⠀⠈⠳⣿⡶⣦⠀⢙⣋⠁⣾⡥⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢷⣦⣼⣿⠦⠉⣥⡁⣾⡄⠀⠀⠀⠀⠈⠙⠛⠓⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣿⣃⢺⠂⡶⣀⠚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⠎⢰⡏⠺⢧⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⡷⢶⢟⡟⣷⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣵⣉⠠⢍⡁⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣍⢡⠈⢈⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠹⣦⠈⠑⢤⠤⠤⠄⠀⠒⠒⠒⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠉⠉⠉⠉⠉⠉⣼⠎⠀⠀⠘⣧⡀⠈⡆⠀⠀⠀⠀⠀⠀⠞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠈⢷⡀⢸⠀⠀⠀⠀⠀⡸⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢀⢎⣤⣤⣤⣤⣤⡀⢀⣾⠃⡴⠒⢲⠖⠒⢲⢺⡛⠀⢇⠀⠀⠀⢠⢃⠀⠘⣧
⠀⠀⠀⠀⠀⣠⠃⠀⡏⠉⠉⡏⡹⢃⣾⠃⠀⣧⠀⢠⡄⣠⡳⡛⢷⡀⠘⡄⠀⠀⡆⠈⠙⢶⢿⡄
⠀⠀⠀⠀⡰⠁⠀⠀⠣⠤⠤⠋⢠⡾⠃⠀⠀⡇⠀⠀⡵⣷⠁⠇⠈⢿⡀⢣⠀⡸⠀⠀⠀⣿⠸⣧⠀⠀⢀
⠀⠀⠀⣜⣁⣀⣀⣀⣀⣀⣀⣀⣠⠃⠀⠀⠀⠈⠉⣹⠟⠁⠀⢠⠀⢸⢻⡌⣦⠁⠀⠈⠛⠛⠀⢿⡀⠀⡞⣦
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⢀⠀⣸⠀⣸⠀⣿⣌⠙⡄⠀⠀⠀⠀⢸⠁⣰⠁⣽
⠀⠀⠀⠀⢸⠀⠀⠀⡔⠒⢲⠒⢲⠒⢲⠒⢲⠀⠉⢹⡭⢭⣛⣛⡻⢽⢻⣿⠉⠉⡭⠄⣀⢀⠀⢸⠀⡇⠀⠨⡆
⠀⠀⠀⠀⢸⠀⠀⠀⣧⠤⢼⠤⢼⠤⢼⠤⢼⠀⠀⢸⠧⢽⠧⠤⢿⠺⠼⢿⠀⠀⡇⠀⢸⠈⡇⢸⠶⠄⠀⠀⡞
⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⢸⠀⢸⠀⢸⠀⢸⠀⠀⢸⠀⢸⠀⠀⢾⠀⠀⢹⠀⠀⡇⠀⢸⠀⡇⢸⠀⠀⠀⠀⢑
⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢸⠀⢸⠀⠀⢸⠀⠀⣸⠀⠀⠉⠉⠉⠈⠁⢸⠀⠀⠀⠀⢨
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠆⢺⡄⠈⠋⠋⢫⠀⢠⠺⠤⠤⠤⠤⠤⠤⠤⢼⠉⠹⠏⠉⠁
⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠚⠛⠛⠛⠛⠛⠒⠚⠒⠒⠒⠒⠒⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀
⠀⠀⠀⠀⢰⣀⣤⠀⠀⢀⡀⠔⣠⠞⠐⣿⠂⠙⣦⡾⠀⣶⡯⢀⠀⢀⣤⣼⣷⡀⢠⣤⣤⣶⣶⣾⣿⠟⠻⣿⣯⣶⣴⣾⣿⣶⣿⡏⣶⣞⣂⡀⠰⣤⡀⣀⠂
⠀⠀⠀⠀⣿⣿⢟⣶⢿⣿⣷⠾⣯⣤⣾⣽⣶⣀⣿⣿⣀⣿⣋⣠⣽⣿⣷⣿⣿⣿⣿⣾⣿⠿⠿⢿⣇⢀⢀⣿⣿⣿⣿⣿⢁⠿⣿⣷⣿⠿⠿⣿⣿⣿⣟⣿⣤⠆
⠀⠀⠀⠀⣿⣿⣿⣥⣤⣝⣥⣤⣤⣽⣿⣿⠻⣿⣿⣿⣿⣾⣿⣿⣿⣄⣸⣿⣿⣧⣌⣿⣿⡀⠐⠂⢹⣾⡏⠀⣸⣿⡿⠻⡉⢀⣿⣏⣿⠷⣶⣿⣿⡋⢀⣸⠋
⠀⠀⠀⠀⢸⣿⠁⠈⠹⣿⣿⡍⠀⠹⣿⠏⠀⠙⡿⠛⠉⠟⠁⠋⣠⡿⣿⣿⣍⠡⣽⣿⣿⡷⠞⣿⣷⣁⢀⣿⣿⣿⣿⣾⣿⣼⣿⣿⠡⠞⣭⣿⡟⢿⡉⠛⣧
⠀⠀⢠⣷⣿⣿⣤⣶⠀⣹⢈⣿⣷⣶⠿⠧⣸⣾⣇⣀⣴⣿⣄⣾⠋⠀⠙⣿⣿⡆⣼⣯⣿⣄⣩⣤⣿⣿⣿⣿⡿⢿⣿⡿⠛⢹⣿⣿⡀⠀⠰⡟⢿⣄⣀⡀⣿⣤⡄
⠀⠀⢀⣷⠌⣋⠁⢽⣧⣤⣾⣿⣿⣦⣄⣀⠉⠛⣿⢄⣬⣿⣿⣿⣄⡀⢀⣿⣿⠟⢛⣿⢿⣿⣿⣾⠙⠿⣿⣿⣄⢀⣹⣧⣴⠿⠿⣿⣇⢶⠀⠃⣸⣿⣿⣿⣿⢷⡇
⠀⠀⢹⡁⡆⠉⣷⣬⡿⠋⠉⠉⢻⣿⣿⣿⣄⠼⠿⠀⠻⢋⣿⣿⢏⣱⠊⢻⣿⣿⣯⣀⣀⣉⣿⣿⡷⠂⣐⣻⣿⠋⠉⢸⡟⠢⣀⣀⣿⣌⢷⣶⣿⢿⣿⣿⣿⣾⡀
⠀⠀⢸⣿⣿⣴⣿⣿⣤⣦⣤⠟⠛⢹⣿⣿⣿⣓⣠⡀⡴⠋⠿⣳⣿⣿⣾⠟⡟⢿⠀⠠⣹⣿⣿⣿⣿⣄⣼⣿⣿⣠⣴⣾⡄⠀⣿⣿⣿⡟⢟⣿⠋⠀⣻⣿⣿⣿⡇
⠀⢰⣏⣿⡿⢻⣿⣿⣟⣽⣿⡀⠀⢀⡏⢻⣿⡛⠛⠻⠀⠀⠸⣿⣇⡾⢯⠀⣀⣼⣷⣄⣸⣿⡏⠙⢻⣿⠿⠟⣿⣿⣿⣿⡿⠚⣻⣿⣿⣷⣿⣯⣀⣴⠿⠛⠛⢿⡇
⠀⠀⢟⡻⢁⣼⣻⣿⣿⣿⣿⣿⣆⣼⣿⣏⢩⣿⣶⡤⣳⣯⣀⣀⣿⠃⢾⡛⠿⠋⠘⢿⣿⣿⢷⣬⣴⣯⣤⣴⣿⣿⣿⣿⠿⢶⣿⡿⠟⠁⠤⣽⣿⣿⡈⠁⣀⣤⠌
⠀⠐⣿⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣸⣻⡆⠀⣩⣏⢹⣷⣠⣶⣾⣿⡐⣦⣀⣿⡛⠀⠀⠉⠛⠿⣿⣯⡊⣻⣫⡿⢦⣈⣿⢷⣶⣶⡾⠫⠙⠋⠉⠙⢿⣿
⠀⠸⢻⡿⠟⠋⣤⣿⣭⢌⣻⣿⣿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠻⣿⠟⠉⣨⡿⢿⣿⣿⠀⠈⣰⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠙⣿⣆⠀⣠⣦⣀⡀⠈⢿⡄
⠀⢰⣸⣦⣴⡞⢿⡀⠁⢈⣿⡿⠋⣴⠛⠻⣿⡿⠛⠛⣿⣼⣿⡿⠟⠓⣿⣿⣟⠛⠉⢻⣦⣽⣿⣧⣾⣿⣿⣿⣈⠹⡛⣻⡿⠟⠛⢿⣾⣇⢳⡾⠟⠿⠿⣿⣿⢻⡅
⠀⠈⣿⣿⣿⡇⢘⣿⣷⡾⣯⣶⣾⣿⣆⣀⣿⣥⣦⣴⣟⣿⣻⣧⣤⣽⣿⠈⢿⡷⣶⣶⣿⣿⣿⣿⣿⣿⡏⠉⡹⠻⠶⠿⣷⣦⡼⢛⢿⣭⣿⣿⣠⠀⠐⠀⠈⠛
⢠⡐⣿⣋⣈⣿⡾⣋⣽⣾⣿⠿⣿⣿⠿⠻⣿⢻⠏⠀⢈⣿⣿⣦⣤⣟⣉⣻⣾⣇⣼⣍⡀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠀⣸⣿⣇⣠⡼⠿⣏⠘⣿⣦⣾⣤⣀⢴
⠈⣡⠈⢻⡿⠟⣱⣿⡉⢻⣷⡦⠾⣷⣀⣴⣿⣄⠀⣼⣿⡟⡴⢛⠻⢿⡟⠉⢻⣿⣿⣅⣨⡿⠛⢻⡉⢿⣿⣿⣿⣧⣾⠷⣿⣿⢻⠟⣀⣽⠿⡿⠻⢤⣴⠉⠉⠛
⠀⣻⡴⢟⣵⣿⣿⣏⣠⣾⡋⢠⣤⣽⡿⠿⡋⠿⠿⣿⣿⣵⣶⣿⣀⣠⡿⣿⣿⠛⣛⢿⣿⡿⢂⣾⡟⢦⣴⣿⣿⡿⡕⠴⠋⠛⠛⠁⠻⠁⠀⠀⠄⠀⠁
⠐⢫⡖⠿⠟⠛⢛⡻⠿⡛⠳⠾⠟⠛⠗⠒⠟⢤⣾⠿⠿⢿⣟⠿⣿⢿⡿⣿⣿⡿⣯⣁⣈⣻⣿⣿⣧⣴⠻⢿⡿⠃⠀⠀⠀⠀⠀⠀⡀⠀⠚⠁
⠀⠀⠠⢐⠂⣀⣠⡄⠊⠁⠀⠐⠂⠀⠀⠀⢀⠘⠀⠀⢠⢘⡟⠶⠀⠘⣧⣫⣼⣆⠀⢹⠯⠍⠉⢈⡿⠁⠁⣀⣆⠀⠀⠀⠀⠸⢷⣴⡧⠀⠀⠀⠀⠀⠀⣰⣄⡀
⠀⠀⠀⠃⢰⠏⠹⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡦⠀⠀⠀⠈⢁⣀⣠⣤⠈⠉⠁⠈⠃⠀⠀⢈⢣⣽⡁⠒⣿⢿⠛⠀⠀⠀⠐⠒⠋⢽⠷⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠈⢉⡿⢷⡛⣍⠀⠀⠀⠀⠀⠘⠸⠇⠁⠀⠐⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠠⣦⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠃⠘⡇⠁⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣴⣿⣁⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⣰⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠿⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⢀⠀⡀⠀⠀⠰⠶⡾⣥⢠⡄⠀⠀⠀⠀⠀⠀⢰⠟⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁
⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡌⡿⣭⠀⠀⠀⠰⠅⠐⠆⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠰⡗⣆⠀⢀⠖⠀⠀⠀⠀⠀⠀⠁⠀⠗⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢈⡷⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠛⠿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠰⡅⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢆⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠲⣾⢥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡤⠀⠀⠋⠀⠀⠀⣀⡀⢀⣠⠏⣀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⡃⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠞⢿⠇⠀⡀⠀⠀⠈⠛⠿⠦⣌⢛⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡴⠃⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⢀⠀⢀⡀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠂⠑⠀⠀⠂⠀⠀⠀⠀⠉⠀⠒⠃⠠⠀⠌⠠⠨⠁⠌⠄⠸⠸⠀⠀⠀⠀⠨⠝⣂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⢌⡠⢄⣆⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠈⠀⢠⡀⠀⢈⠰⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⠔⠠⠔⠀⠀⠀⠀⡂⠈⠐⢠⡄
⠀⠀⠀⠀⠀⡐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠁⢀⠀⠘⣁⣛⠀⠀⡁⠀⠀⠀⠑⢔⡢⠊⠀⠀⢠⡒⠀⠠⢄⡐
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠄⠀⠀⠀⠀⠐⡔⠀⡇⢢⡔⢸⡇⢢⡂⠐⠀⠀⠀⠈⡀⠀⡄⢀⡀⠀⡃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠄⠀⠈⠁⡀
⠀⢀⡀⣀⠀⠂⠀⠀⠀⢲⡂⠂⠒⠒⠲⠀⠐⠐⠀⠃⠂⠐⠘⠂⠂⠂⠀⠤⠀⢸⠀⡇⢠⡤⠈⡀⠀⠁⠀⣲⡆⠀⠀⠀⠀⠀⠀⠸⠁⢀⡄⠘⠛
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠧⠿⠯⡿⢿⡷⠀⠶⡆⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠀⡇⠘⡏⠘⠂
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠈⠈⠉⠉⠉⠐⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⣀⠀⠀⠴⠒⢦⡀⠀⠉⠉⠉⠉⠉⠋⠉⠙⠉⠁⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠃⠁⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣄⠛⣠⠇⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠁⠈⠀⠀⠁⠈⠀⠀⠈⠴⠄⠠⠄⠡⠦⠀⠤⠀⠀⠀⠉⠀⠀⠀⢀⠀⠠⡀⠀⠀⠀⠘⠀⠀⠀⣻⡍
⠀⠰⠠⠠⠆⠆⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⡀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⢴⣴⣴⠄⠀⠀⠀⠀⠴⠂⠠⠀⠲⠠⠄⠠⠀⠀⠄⠠⠀⠀⠠⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠗⠀⠁⠀⠀⠹⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣧⠙⠿⣧⡀⠀⡀⢀
⠀⠀⠀⠀⠀⢀⣀⣴⣶⣯⣶⡦⠀⠀⠘⠳⠀⠛⣯⣱⠖⠿⢤⡀⠀⢀⣴⣦⡀⠀⠀⠀⣴⣦⡀
⠀⠀⠰⡶⣟⠻⣿⠟⢛⣿⣿⡁⠀⠁⠀⠀⢀⣀⠈⠙⠂⠀⠀⠙⠛⠛⠋⠉⣙⣿⡶⡎⠁⠈⠛⢤⣀⣀⣀⡀
⠀⠀⠀⠀⢠⣴⣆⠘⠿⣿⠋⠁⠀⢀⣤⣿⣿⣿⡎⠓⠦⠀⠀⠙⠛⠒⠀⠊⠉⢉⣧⠀⠐⠀⢠⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⠳⢶⣶⣿⡿⣿⢛⠟⢿⣶⣶⣄⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠻⠅⠀⠂⠀⣋⠿⠛⠹⠀⠀⠀⠀⠐⢿⣿⡅⠀⠀⠀⣸⣿⣿⣀⡤⠸⠁
⠀⠀⢸⣿⣷⣤⣄⣀⠀⠀⠀⠀⢠⡀⠀⠈⠠⠀⢁⢠⣿⣶⣿⣦⠀⠀⠀⠀⠘⠿⠟⠂⢀⣿⣿⣿⣯
⠀⠀⠈⠁⠀⢸⣿⣿⣾⣷⣤⣆⣿⣷⢠⣦⠀⠀⠀⠙⠻⢿⣍⡁⠁⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⡅
⠀⠀⠠⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣄⢰⣿⣴⡄⠀⠉⠂⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣷⣿⣤⣶
⠀⠀⠀⠀⠈⠁⠀⠈⠛⠻⠿⠛⠿⠿⢿⠻⠿⣿⣾⠿⣿⣿⣿⡄⣰⣦⠀⠀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠘⠛⠛⠋⠀⠀⠈⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢩⡤⣐⢤⡔⡉⢀⡠⢩⢢⡤⡂⢥⡍⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⣀⣠⣥⡞⢬⣣⢓⣔⣴⢟⠷⣦⣢⡺⣜⡱⢺⣼⣀⣀⣀⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⡯⣯⣭⡭⡤⡬⠨⠨⡭⣟⣿⣾⣟⠕⣸⣅⠨⣻⣶⣿⣻⢭⠅⠄⢥⣤⢭⣭⣽⢽⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡿⣺⣾⠶⠶⠧⠧⠧⣧⣿⡟⢁⢢⢉⡁⡔⡈⢻⣿⢬⢼⠸⠾⠶⠷⣷⣖⢿⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡄⡯⢺⡃⢿⢞⠲⡲⠲⠷⠧⣇⡱⢛⡱⢆⡲⠌⣸⠼⠾⠒⠖⠞⡺⣿⢸⡗⢽⢀⡇
⠀⠀⠀⠀⢀⡠⠄⣾⡄⡇⠽⠇⢸⡢⢕⣵⣧⣆⢐⠰⣩⡞⢽⡫⢳⣍⠆⣆⣟⣬⣮⡪⢐⡇⠸⠭⢸⢈⣧⠠⢀⡀
⠀⠀⠀⠀⠇⡶⡸⣍⣇⢯⠍⡯⢼⡄⠥⢻⡡⣬⡑⢾⣴⡯⣸⣆⣹⣆⡾⢋⣵⢌⡟⣌⢰⡧⣽⠩⡽⣼⡩⢃⢶⢘
⠀⠀⠀⠀⠑⣔⢍⢞⢻⣿⣾⠿⠭⢧⢐⡘⣷⣌⣋⣼⡙⠊⡼⢧⡑⢋⣧⣙⣡⡾⢂⡂⡼⠭⠿⣿⣿⡟⡳⡭⣢⠂
⠀⠀⠀⢀⡔⠭⢐⣽⢟⠝⠡⡐⢡⢊⣣⠾⡶⢿⡳⢈⠯⣯⠤⠤⣼⢽⠁⢞⢷⢦⠷⣜⠐⡪⣂⠌⠫⠻⣯⡂⠭⢢
⠀⠀⠀⢾⠀⡱⣿⡱⠶⢾⠆⠠⡱⢎⡷⡷⠶⣾⠶⣏⠠⡇⣿⣿⢸⠈⣹⠶⡷⠶⢾⢾⡱⢎⠆⢰⡷⡷⢹⣿⡎⠀⡷
⠀⠀⠀⠈⠣⣒⠨⣻⣮⣢⡐⠡⡚⢎⡝⢶⠵⢶⡵⢈⣖⣟⡒⠒⣻⣺⡀⢾⡾⠞⡶⢫⠠⢏⠍⢂⣔⣵⣞⠅⣒⠜
⠀⠀⠀⠀⡠⠫⣚⢮⣾⣿⣿⣶⣒⡞⠨⢡⡿⢋⣍⢻⣡⢄⢳⡞⡡⣌⡟⣩⡙⣗⠌⠅⢳⣒⣶⣿⣿⣧⡥⣓⠝⠄
⠀⠀⠀⠀⡅⢷⢥⣊⡏⣞⣂⣗⢺⠃⡐⣼⡑⢛⡡⣞⢹⢇⢹⡏⣹⠏⢷⣌⡻⢊⣧⢂⠸⡖⣻⣐⣳⢻⣑⠼⠾⢨
⠀⠀⠀⠀⠈⠑⠂⢿⠀⡅⣲⡆⢸⠅⡢⡻⡛⠏⠹⠰⣙⢧⣺⣗⡼⣋⠆⠍⢭⢛⢟⢕⠨⡇⢰⣒⢸⢈⡟⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠃⣗⢼⡅⣿⣮⠴⠴⠴⡶⡖⡏⡑⢬⡱⢎⡥⢊⢹⢲⢶⠤⠮⠦⢵⣯⢸⡧⣻⠨⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⠽⢿⠶⠴⡶⠆⡖⡓⣿⣧⡈⠔⣉⡁⠢⢁⣼⡿⢺⢺⢰⢶⠶⡶⡿⡏⣾⢸⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣟⣟⣛⣓⠓⢓⢒⢐⣓⣯⣿⣿⣯⡢⢹⡋⢐⣽⠿⣿⣝⣚⡒⠒⡚⢚⣚⣛⣻⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠙⡛⢧⢊⡝⡬⠫⠻⣮⡶⠟⡕⢵⢫⡱⠸⢛⠉⠉⠉⠉⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣘⠓⠩⠚⠣⣃⠈⠙⣘⠜⠃⢅⠚⣃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡄⣀⣤⣤⠀⠀⣀⣀⠀⠀⣤⣤⣀⢠⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣼⣿⣿⣇⣀⣾⣡⡌⣷⣀⣸⣿⣿⣧⣿⣮⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣿⣿⣿⣿⣿⡋⠉⠹⣿⣿⠏⠉⢙⣿⣿⣿⣿⣟⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠠⣟⠙⠻⣾⠛⠻⢿⣿⣿⣶⡶⣶⡾⢷⣶⢶⣶⣿⣿⡿⠟⠛⣷⠟⠋⢻⠄
⠀⠀⠀⠀⣀⣴⢄⠀⣻⣤⢾⡗⠀⣲⡿⣿⣿⣿⣿⡯⠔⠢⢽⣫⣿⣿⣿⢿⣖⠀⢾⡷⣤⣟⠀⠰⢦⣀
⠀⠀⠀⣜⣽⣿⣿⣾⣿⡀⢠⣠⡟⣉⣙⡷⠛⣉⣥⣴⢖⡲⣶⣬⣉⡛⠼⣋⣉⢻⡄⡄⢀⣿⣿⣿⣿⣯⢣
⠀⠀⠀⢩⣶⣿⣿⣿⣿⣷⣿⣯⠷⡼⣡⣾⡿⠿⢿⡁⢸⡇⠈⣿⠿⢿⣷⣌⢣⡾⣽⣿⣾⣿⣿⣿⣿⣶⡌
⠀⠀⠀⣿⠿⢿⡿⠻⢻⣿⣿⣿⡟⢠⣿⡏⠿⡧⢾⣿⣷⣶⣿⡷⢼⠿⢹⣿⡆⢻⣿⣿⣿⡟⠟⢿⣿⠿⣿
⠀⠀⠀⠀⣠⣼⣇⡀⠸⣯⡿⣿⢡⣿⠟⠱⣾⣿⣿⠿⣻⣟⠻⣿⣾⣷⠟⠻⣿⡌⣿⢿⣽⡇⢀⣸⣧⣄
⠀⠀⠀⢺⡁⠾⣿⣟⢾⣏⠰⡁⢸⡱⠶⠶⣹⣿⣿⢾⣿⣿⡷⣿⣿⣏⡷⠶⢎⡇⢘⠆⣹⡷⣻⣿⠶⢈⡗
⠀⠀⠀⠀⠙⢻⡏⠁⢰⣟⣷⣳⡘⣿⣦⣴⢿⡿⣿⣶⣽⣯⣴⣿⢿⡿⣦⣴⣿⢃⣾⢾⣻⡇⠈⢹⡟⠋
⠀⠀⠀⣿⣶⣿⣷⣴⣼⣿⣿⣿⣧⠸⣿⣇⣴⡗⢾⣿⡿⢿⣿⡷⢺⣶⣸⣿⠇⣼⣿⣿⣿⣧⣦⣾⣿⣶⣿
⠀⠀⠀⣘⠿⣿⣿⣿⣿⡿⣿⣟⡶⢣⡙⢿⣷⣶⣾⡁⢹⡏⢈⣽⣶⣾⡿⢋⡜⢷⣻⣿⢿⣿⣿⣿⣿⠿⣃
⠀⠀⠀⢳⡻⣿⣿⣿⣿⠁⠘⠙⣧⣘⣩⡷⣬⣙⡛⠻⠮⠵⠿⠛⣉⣥⢾⣅⣋⣼⠋⠃⠈⣿⡿⣿⣿⢿⡟
⠀⠀⠀⠀⠉⢻⠆⠀⣹⠟⢾⡷⠀⠽⣷⣿⣿⣿⣻⣗⠢⠔⣺⣝⣿⣿⣿⣾⠯⠀⢾⡷⠻⣯⠀⠑⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠐⣧⣀⣴⢿⣤⣴⣾⣿⣿⠿⠷⠿⢷⡾⠿⠾⠿⣿⣿⣷⣦⣤⡿⢤⣄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⣿⣿⣿⣿⣿⣅⣀⣰⣿⣾⣆⣀⣨⣿⣿⣿⣿⣿⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⢻⣿⣿⡟⠉⢿⡙⢋⡿⠉⢻⣿⣿⡟⣟⢟⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠂⠉⠛⠛⠀⠀⠙⠉⠀⠀⠛⠛⠉⠘⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠑⠀⠀⡠⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠉⠲⠶⢤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⣠⡾⠻⠿⠋⠉⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣰⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⣠⠞⠉⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⢠⡾⠇⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠞
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠘⢁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⣦
⠀⠀⠀⠀⠀⠱⡀⢀⡄⠀⠈⠀⠀⠀⠉⠙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠛⠛⢦⡀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁
⠀⠀⠀⢠⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣰⠏
⠀⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⢶⡜⠁
⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⢻⡀
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢠⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠈⠳⣤⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠠⠲⠶⠶⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⣾⠃⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠟
⠀⣰⠃⠘⠷⡤⡴⢦⣄⠀⠈⠛⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠁⣄
⢠⡇⠀⠀⠀⠀⠀⠀⠈⢉⠋⠉⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠈⢧⡀
⢸⡇⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠈⠻⡓⠶⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⡁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢸⡇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠈⢷⡄
⢸⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⠳⢤⣀⠀⠀⣀⡀⣀⡼⠋⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠈⢿⡄
⠀⡿⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨⠁⠀⠀⠉⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠂⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠈⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣿
⠀⣷⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⡇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⢹⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢀⡏
⠀⠀⢦⡀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡁⠐⡏⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⠤⠖⠉⠠
⠀⠀⢱⡈⠓⠶⠶⠞⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣿⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⡀⠀⢀⡦⠀⠼
⠀⠀⠈⠳⣄⣀⠀⢀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣠⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠀⠀⠀⠋⢉⡄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⢀⣼⠃⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣈⣢⡄
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣭⣿⣟⣝⣿⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣷⣲⣲⣶⣶⡶⢤⡄
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⡇⠀⠀⠈⠉⢹⣯⡇
⠀⠀⠀⠀⠀⠀⢸⡷⡇⠀⠀⠀⠀⢸⠀⠀⣼⣿⣿⣿⠂⠀⣿⣿⣿⣧⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣧⣧⠀⠀⠀⠀⢸⠀⠀⢿⣿⣿⡛⠁⠀⠛⣻⣿⡿⠀⠀⡇⠀⠀⠀⠀⢸⣻⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢸⠀⠀⠈⢿⣿⣿⣦⣠⣾⣿⡿⠁⠀⠀⡇⠀⠀⠀⠀⣸⣻
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣽⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢾⡇⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣀⣀⡃⠀⠀⠀⢘⣛⡃
⠀⠀⠀⠀⠀⠀⠀⢿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣶⣖⣲⣶⣶⣤⣤⢴⣶⣶⠶⣶⢖⣶⣶⣶⠶⢶⣶⣶⣶⢖⠾⣿
⠀⠀⠀⠺⣉⣁⣀⡀⣀⣈⠉⣉⡉⣉⣉⣉⣉⣉⣉⢉⠉⠉⢉⠉⡉⡉⠉⡙⢛⡛⠛⠛⠛⠋⠀⠁⠈⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢿⡟⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡴⠔⡛⠻⠷⠋⠀⠀⠀⠘⠧⣀⣀⡶⠁⣀⡠
⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⣤⠿⠛⠳⣄⡀⠀⠀⠴⣴⠞⠉⢠⠀⠙⠈⠀⣼⡆⠀⠀⠀⢀⡌⠋⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠈⠳⣌⠑⠂⠓⠂⠀⠀⠀⣾⡆⢰⣿⣯⠀⣠⢔⠿⠋⠄⢠⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡠⠀⠀⠀⠀⠀⠀⣌⣷⡦⠋⠀⠔⠃⠀⣿⣷⣾⣿⣿⡎⠀⠁⠀⡠⠐⣋⣴⡿⠛
⠀⠀⠀⠀⢿⣦⣤⡀⢡⢎⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⢀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠂⡀⠀⠴⠾⢋⣀⣄⣀
⠀⠀⠀⠀⠀⠈⠉⢻⣷⣾⠷⠶⣤⡀⠀⢀⣴⡿⠃⠀⣤⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣺⣿⢠⣿⣦⣼⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠈⠳⣬⡁⠀⠀⠈⠻⢾⣿⣏⣀⢀⣸⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠋⢉⠀⠔
⠀⠀⠀⠀⠀⠀⣀⣶⠀⠈⠙⢶⡀⠀⠀⠀⠀⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢉⣀⣀⠄⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠘⠿⠃⢶⣄⡀⠀⠉⠲⣦⡀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠚⠛⠋⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠳⢶⣠⣄⣙⣷⣿⣿⣿⣿⣿⣿⡿⢿⠿⠟⠁⠀⠀⡀⠀⠀⠀⠀⢀⣤⠾⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠉⠻⢹⣿⣿⣿⣿⡿⠉⠈⠀⠀⡀⠀⢀⣴⣾⡷⠚⠁⠀⠀⠊⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⠋⠍⠁⠀⢀⡄⠀⠈⠘⠿⠛⣲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣃⠤⠒⠂⠀⠀⠈⠉⠀⠀⠀⠐⠨⠾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⢻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⢫⣿⣥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡆⣦⣦⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢇⡾⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣄⣷⣿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⠊⢀⡀⠈⠀⠀⠀⠀⠀⠈⠀⠀⣧⢸⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣇⣼⣄⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠏⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡵⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⡤⢶⣿⡿⠿⠛⡉⣩⣯⣤⣾⣿⣿⣿⡍⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⡆⡀⠀⢀⣼⡃⣽⢋⠃⠀⢸⢃⣿⡿⢻⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣸⢿⣿⡏⠈⠀⠀⠀⣸⣿⣷⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⠟⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⡟⣿⣿⡧⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠝⣿⣿⣿⣷⣹⢿⣿⣿⣭⣽⣷⣮⣿⡿⠿⠃⠀⠀⠀⣀⡛⣳⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠋⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⡷⠡⡤⠈⡙⢃⡖⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠄⠨⠭⠀⠓⣆⡉⢙⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣦⣤⡀⠀⠰⣿⣿⣿⣿⣿⢿⣿⣿⢻⣿⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠻⠿⠻⠛⠛⠿⢿⣿⣿⣭⠭⠉⠉⠉⠁⣈⣈⣄⣿⣿⣿⣿⣽⣿⣷⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣿⣿⣿⣿⣿⣷⠄⠀⠁⠈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⣾⣿⣲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣵⠟⠛⡻⢟⠛⠻⣮⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⣡⣀⣀⣤⣤⠶⣷⣿⣁⢀⣤⣺⣇⣤⡀⣈⣿⣾⠶⣤⣤⣀⣀⣜⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣯⣄⡀⡀⡄⡈⢹⢵⠋⠱⠎⠙⡬⡏⢁⢠⢀⢀⣠⣽⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⢿⣷⠠⣀⣖⣹⣣⠶⠚⠓⠶⣜⣟⣢⣈⡄⣾⡿⠏⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⣧⠀⠬⠔⢰⣯⢟⣲⡟⣡⢞⡭⢭⡳⣌⢻⣖⡻⣽⡖⠢⠥⠀⣼⡧⣀
⠀⠀⠀⠀⠀⠀⠀⢠⢞⣵⠟⢻⣆⣈⣴⣹⣼⠾⠵⠇⠣⢿⡎⢱⡿⠼⠘⠮⠷⣧⣏⣦⣁⣰⡟⠻⣮⡳⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⣴⡵⠓⢩⡞⣡⢞⣭⣆⢪⣶⣆⣰⣶⡕⣸⣭⡳⣌⢳⡌⠚⢮⣦⠀⠈⣿⣽⡄
⠀⠀⠀⠰⠶⠶⢾⣿⣿⢎⢾⣾⡱⠤⢾⠀⡇⣏⢎⣉⢈⣹⣿⣿⣏⡁⣉⡱⣹⢸⠀⡷⠦⢎⡷⡷⡱⣿⣿⣿⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠘⣞⣿⡀⠀⠻⡓⡤⣘⣧⡙⢮⣛⡏⢜⠿⠏⠹⠿⡣⠸⣛⡵⢋⣼⢃⢤⢞⠟⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢮⡻⣦⣼⠏⢉⢻⣹⢻⢶⡲⡄⡒⣾⢇⡸⣷⢢⢠⢖⡶⡟⣏⠛⡉⠹⣧⣴⢟⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢺⡟⠀⢒⠂⠼⣟⣮⠽⣧⡙⢮⣓⣚⡵⢋⣼⠯⣵⣻⠧⠀⡒⠀⢻⡗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣰⣾⡿⠸⠉⠋⣽⡛⠶⢤⡤⠶⢋⣯⠝⢉⠁⢿⣷⣆⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣟⠋⠁⠁⠃⢁⣸⡚⢄⡸⢇⡠⢗⣇⡀⠘⠈⠈⠙⣻⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡝⠉⠉⠛⠛⠶⡿⣿⡉⠈⠛⢽⡯⠛⠁⢉⣿⢿⠶⠟⠛⠉⠉⢫⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡻⣦⣤⣵⣾⣤⣴⢟⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⠽⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⡟⣿⠇⠀⠀⠀⠀⠀⢀⣾⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠻⡇⠋⠀⢄⠀⢘⡿⠿⣿⣿⣿⣿⠟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠬⢀⡀⢀⡔⠂⠉⠞⡸⠎⠀⣶⣤⣀⠙⣿⣷⣤⠀⠌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣦⠈⠂⡌⠀⠠⠀⠂⡀⠈⠄⢌⡙⠛⠋⠏⠉⠉⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣠⡯⠂⣀⡑⠄⠀⠘⡧⣀⠠⢆⡸⢨⣄⠀⠆⠀⠠⢛⣽⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠭⢤⠰⣶⣙⣷⣼⡆⠀⡕⠁⠀⠀⠀⡀⠉⠑⡄⠀⠈⠙⢿⡷⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⢠⣸⠀⠠⢋⠟⢫⣁⠉⢁⠢⡈⠃⣀⣬⠀⡀⡈⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢘⣆⠀⠃⠀⣠⠽⠜⠃⠀⣎⣰⠝⢃⠚⠄⡨⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣆⠸⣄⠈⠋⠈⠁⠰⢃⡠⠈⠀⢀⣀⠻⡫⢰⡔⢈⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣾⠁⠓⠀⣈⠀⠀⡇⠈⠃⠛⠋⠀⢣⠊⠀⢺⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢰⠀⠘⠟⠟⠀⠀⢀⠠⠀⠸⠇⠀⠀⠀⠀⢸⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠏⠉⠉⠉⠉⣉⡉⠉⠉⠹⣿⣿⣿⠋⠉⠉⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢁⣀⡀⠀⠀⣾⣿⣿⡆⠀⠀⠈⠉⠀⠀⢠⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣧⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠅⠀⠀⡀⣀⣴⣶⣶⠄⠄⠊

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣀⣀⣀⡀⣸⡆⠀⡊⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣠⣶⣻⣿⣿⣿⣿⣿⣧⡼⢥⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠺⠄⠀⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠛⠛⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⡙⠋⠁⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⢩⡀⣀⣀⣠⣤⣶⣾⣿⢣⡆⡀⢀⣇⠄⣽⣿
⠀⠀⠀⠀⠀⠀⣼⠀⠀⣴⠀⣀⣸⡄⠀⠂⣤⠀⣀⠢⣔⠺⣿⣿⣿⠿⡿⣿⡿⠟⠁⣼⣇⠀⢸⣷⢈⡉⠉⠁
⠀⠀⠀⠀⠀⠀⣿⡀⣶⠿⠊⢀⠝⠓⠴⠀⠍⠉⣠⣐⡩⠌⠋⠉⣀⠀⢠⠀⠒⠒⠤⠄⣠⠉⠛⠛⢄⡀
⠀⠀⠀⠀⠀⠀⠟⢁⠄⠀⠀⠉⠀⡆⡀⠀⠤⠀⠉⠀⡀⠀⠂⠁⢀⡄⣿⡀⠀⠂⠀⠄⠋⠑⡄⠀⠈
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⡛⠉⠠⡄⠀⣀⢠⣧⢤⡦⠀⠼⠗⠛⠓⠈⠁⠀⠁⠀⠀⠇
⠀⠈⠀⠁⠠⢀⠀⠀⢀⡀⠙⠛⠛⠋⠀⠀⠀⠀⠈⠈⠛⠀⠐⠡⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠙⠻⠷⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠋⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⣾⡿⠁⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠋⠀⠀⠀⢾⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣖⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣆⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠿⡞⣷⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⡄⠀⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣥⣿⣽⣿⡌⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣯⡹⠿⣿⣿⣿⠦⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⣿⡜⢻⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣶⣶⣶⣶⣾⡟⠛⠛⠛⠛⠛⠛⠋⠓⠒⠒⠒⠒⢶⣶⣶⣶⣶⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⢀⠀⠀⠤⠀⠤⠀⠀⠀⠀⠀⠔⢺⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⡀⠄⠀⠀⠀⠀⠀⠀⠀⠢⠠⠬⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠋⠁⠀⠀⠀⠀⠀⣠⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢳⠤⠾⠛⠿⠶⠦⠀⠀⠴⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⠟⠘⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠗⠈⠀⠀⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣄⣀⣤⣄
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠁⠐⠀⢸⣇⠀⠀⣤⣤⠀⠀⠚⠛⠛⠻⡿⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠠⠄⠐⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⡀⣀⢤⢼⣿⢻⡏⠀⠀⠀⠀⠀⢉⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⠀⠀⠀⠸⡶⣾⣻⣿⢿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠋⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠴⠂⠀⠀⠾⢻⡿⠿⠿⠼⢿⣷⠏
⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠤⠂⠀⠀⠀⠀⠈⠁⠄⠁⠀⠀⠀⠀⠐⡂⡄
⠀⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡀⠀⠀⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠠⠔⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠓⠻⠟⠛⠂⠀⠀⠀⠀⠀⠐⠂⠁⠃⠀⢀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠘⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠁⠀⠉⠆⠀⠀⠀⠉⠁⠀⠘⠁
⠀⠀⠈⠀⠀⣴⢶⡀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀⣷⣼⡃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠙⠉⠛⠇
⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⢢
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡀⣀⣼⣿⣿⣿⣤⣀⣀⢀⠀⠀⠀⠀⠠⠤⠤⠴⠶⠦⠤⠄⠀⠀⠀⢴⣶⣿⠋⠻⠿⢦⣄⣀⠀⠀⠀⠀⠀⣤⣄⣀⡀⢀⣀⣈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣤⣀⣀⡀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⣶⡏⣿⣿⣿⣿⠛⠛⣡⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣤⣤⣝⣾⣧⣈⠀⠿⠾⠀⢠⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣧⠙⢻⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⢧⡀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⡟⠿⣿⣷⣄⠀⠉⠛⠻⠿⠿⣿⢻⣷⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡇⠀⣀⠸⠿⣿⣿⣿⣿⣦⣶⣿⣿⣸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⣻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠃⢰⣿⠿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢄⣨⡄⠴⠛⠁⠈⠃⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣻⣿⡖⣶⣿⣶⠠⢄⣀⠀⠀⠀⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠰⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣦⣴⣿⣿⣿⣿⡿⣦⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠀⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⡿⠃⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡿⠿⣿⡿⠿⠻⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣶⣦⠛⠁⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⣙⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣤⡴⠂⣤⣤⠀⡀⠀⠤⣤⣘⣻⣄⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⣤⣀⡀⠀⠸⠏⢤⠀⢰⣯⣿⣿⣿⣄⠃⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⣀⠉⠉⠉⠛⠛⠛⠛⠓⠀⠀⠘⠛⠚⠛⠛⠿⠿⢿⣦⠳⡄⠀⠀⠀⢀⣥⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠄⠠⠿⠿⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠥⠾⠿⢥⢮⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣛⣿⠗⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣺⠀⠀⠀⠀⠉⠉⢿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⡆⠀⠀⢸⠀⠀⠀⠀⠀⠆⢸⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⡷⠀⠀⣿⣿⣿⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⣿⣿⣷⡀⠀⠀⣠⣾⣿⣿⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⣿⣿⣿⣶⣼⣿⣿⡿⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⢗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣼⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣼⡇⡀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⡞⡇⠀⠀⠀⠀⠘⠛⠓⠛⠛⠚⠛⠓⠓⠛⠓⠓⠒⠓⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣾⣿⣽⣿⣛⣴⣶⣖⣲⣲⣲⢖⣖⣖⡶⡒⣺⢛⣻⣿⣶⣶⡶⢒⣶⣲⣲⣶⢖⠾⢓⡇
⠀⠀⠀⠀⣯⡉⠉⠉⠁⠀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠓⠛⠚⠛⠓⠚⠓⠒⠒⢲⡆
⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠛⠛⠓⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠓⠛⠛⠓⠛⠛⠓⠛⠓⠚⠒⠒⠒⠒⠲⠶⠶⠶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⣳⢟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢖⡀⡙⠉⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠈⠁⠹⠏⠒⡦⠔⣼⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⣹⡧⠐⠀⠀⠐⠓⡖⠂⣵⠂⣟⠁⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡆⠀⢸⡧⢍⡧⣼⠗⠂⠀⣼⠋⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⣨⠀⠀⠀⠙⠀⠀⡀⠏⡀⢤⣰⣿⣿⣽⡔⢷⣶⡄⠈⢁⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡇⢌⣛⢾⣷⣿⣿⣿⣿⣿⢧⣄⡬⠳⢟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠗⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠐⠰⣁⡠⣬⡿⠋⣿⣿⣯⠿⣷⣿⣽⣷⣢⠞⣂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡴⠢⠆⢠⡟⣦⢼⡇⠀⠈⣿⣳⣦⣿⡿⣿⣿⡧⡿⣭⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⢀⣦⣍⡁⡦⢠⡛⣽⣻⣿⡇⠀⠈⢻⣿⢾⣿⣷⣿⣿⣛⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣹⠌⠁⠈⠃⠰⠀⢀⠘⠻⣏⢰⣲⣾⣷⣿⣾⠋⠈⠀⠀⡀⠹⢿⣿⣿⣿⣿⣿⠿⠁⠠⠆⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠈⡆⠀⢀⢀⡈⠄⠛⡿⠕⢿⣾⣿⣿⡿⠟⠋⠀⠀⡠⠎⠰⢠⠘⣿⣷⣿⣿⣿⣾⣼⡿⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠂⠀⠰⢱⡆⣠⣚⡟⣷⡄⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠂⠀⠂⠰⡄⢸⣿⣿⣿⣿⣩⢷⡀⠙⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣠⢫⣿⠪⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠐⠀⠀⠤⣷⣂⠀⣿⣿⣿⣿⣿⣿⣹⡡
⠀⠀⠀⠀⠀⠀⠀⢠⣄⡌⡉⣿⣿⠿⢗⣮⣹⣳⠏⠀⠀⠀⠰⡀⠤⠤⠄⠀⠐⠘⢂⡘⠀⠀⠐⢼⣏⣀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣼⣴⣼⣿⣿⣿⡿⢿⣿⡟⠀⠀⠄⠀⠈⡉⠀⠌⡀⠄⠀⠀⠂⠁⠀⣀⠀⢻⡿⢾⠿⢿⡿⠿⣿⣭⡷
⠀⠀⠀⠀⠀⠀⡀⠐⣾⣿⣿⣿⣧⣽⣟⣶⠟⠀⠀⣠⣦⡀⢃⡕⢀⠀⠠⠈⠐⡀⢀⢠⠈⠅⢀⢹⣷⣿⣷⣿⠷⣦⣈⢿⣿⠄
⠀⠀⠀⠀⠀⠀⠙⢀⣻⣿⣿⣿⣿⣿⡏⠁⠀⣠⣾⣿⣯⣽⡀⠚⢠⠌⠀⠁⠀⢂⠉⠀⠀⠖⣻⡶⢁⣿⣿⣶⣼⣿⣟⣧⣟
⠀⠀⠀⠀⠀⠀⢤⡏⡿⢻⣿⣏⣻⣁⣤⣤⣤⣿⣿⣿⣯⣽⣷⣤⣄⢈⠱⠐⢠⠀⢠⠑⣦⣷⣿⣧⣾⣿⣿⣿⢿⣿⡟⣿⣻⣗⢠⣀
⠀⠀⠀⠀⠀⠂⠈⠁⠙⠛⠛⠙⠻⣿⣿⡟⠻⣿⠙⣿⣓⣾⡷⠿⣿⣦⣤⣤⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⠿⣿⠄⢹⡖⡟⠉⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠰⠲⡟⠘⠋⣿⣿⣿⡛⢿⣿⣿⣿⠛⠻⠿⠿⠛⠉⠀⠙⠀⠈⠙⣾⡷⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⠀⢹⡋⠓⢸⣿⡧⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣶⣶⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣠⣄⣿⣿⣥⣾⣿⣶⣶⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠿⠛⠛⠛⠉⠉⠙⠛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⢐⣄⣀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠛⠛⠛⠛⠛⠄⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢐⣿⣿⠋⠀⠀⠀⢀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⣿⠟⠀⠀⢠⣤⢤⣄⡀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠨⣿⣭⠀⠀⢀⣒⣠⣿⣿⢤⣿⣿⢿⣠⣦⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⢹⠇⠀⠀⠛⠟⠘⠋⠛⣿⣁⢦⡄⠀⠀⢰⢸⠀⠀⣿⡇⠀⠀⠀⠉⠉⢻⠛⠂⠙⠃⢨⠙⣿⡷⣄⡟⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣂⢸⣧⡀⠀⠀⠀⠀⣤⣤⡀⠈⠀⠀⠀⠀⢰⠠⠆⠀⢻⣇⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠂⠀⠈⠉⠹⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⢹⣄⣿⣿⣿⣈⣀⣤⡶⡟⢆⠀⠀⠀⠀⠀⢘⡣⢺⡀⠸⣿⣧⣀⣀⣀⡀⣄⠀⠀⠐⠞⠿⢷⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣿⣿⣿⣿⣏⠙⢶⡄⠈⠀⠀⠀⠀⠀⢐⡈⡯⣧⢀⣿⣿⣿⣿⣿⢸⡏⢀⣀⣤⣶⣿⡟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡙⣿⣿⣿⣿⣿⣿⣆⠂⠀⠀⠀⠀⠀⠘⣾⡃⢹⣿⣿⣿⣿⣿⣿⣾⣶⣿⢿⣯⣉⡙⠓⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⣀⠀⠀⠙⣿⣜⢿⣿⣿⢿⡋⠉⠀⠀⠀⠀⠀⠀⠈⠟⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇⡀⠙⢿⣿⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡆⠀⠸⢿⣎⢻⡏⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⡀⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠋⢷⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣟⣷⡌⠻⣿⣿⣿⣿⣿⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣧⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⢘⣿⣷⣆⠹⣿⣿⣿⠃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠀⠀⠀⠀⠀⠸⢿⡧⠀⠀⠈⠘⣿⣿⣆⠹⣿⡏⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣠⣾⣦⣤⣤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢟⣿⣿⣿⣙⣿⢋⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣿⣁⣿⣿⣧⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⣡⣿⣿⣿⣿⣿⢱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢿⣴⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⣵⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⢠⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣣⣾⣿⣿⣿⠟⠁⠀⣿⣿⣿⣿⣿⠰⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢠⣿⣿⣿⣿⣿⢸⡗
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⣿⡟⠃⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⢼⡇
⠀⠀⠀⠀⠀⣰⣿⣏⣉⣵⣿⣿⠋⠀⠀⠀⠀⠀⠀⠐⣿⣿⣹⡏⣿⣾⠃
⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣼⣯⣿⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣿⣿⣻⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⡫⣿⣿⣿⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣾⣿⣿⣿⣿⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢿⣿⣿⣿⢀⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣿⠀⠈⣿⣿⡿⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢿⡀⠀⢸⣿⣷⡀⢺⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣇⣤⣤⣾⡗⢲⣾⣿⡛⣷⣼⡇⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣥⣾⣿⣽⣾⣿⣯⣤⣿⣯⣿⣿⣷⣤⣤⣽⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣭⣭⣯⣿⣿⣿⣿⣷⢶⡿⠿⠷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣾⣿⣿⣿⡿⠿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣧⢻⣧⡙⢿⣆⣻⣷⡘⢷⡌⠙⠿⣶⣶⣤⣬⣿⣿⣿⣿⣷⣿⣿⡏⣠⣾⣿⣽⡾⠟⣩⣾⣯⣴⣾⣿⠟⢀⣼⢟⣴⠟⠀⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡆⢻⣷⡄⠈⠻⣿⣿⣶⣿⣷⣦⣀⠉⠙⠛⢿⣿⡙⢻⣿⣿⣿⣰⣿⣿⢟⣭⡾⠟⣛⣿⣿⣿⣿⣷⣾⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⠀⢻⣿⣆⠀⢹⣿⡟⠛⠻⠿⣿⣿⣦⣄⠈⣿⣧⢰⣿⣿⣿⣿⣿⣿⣿⢋⣴⣿⣿⣿⡿⠿⠛⠛⢻⣿⠏⣴⣿⣿⠟⢫⣿⡏⣿⡿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⡆⢸⣿⢠⡶⠶⣤⡀⠉⠻⣿⣧⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣀⣤⠶⢶⡘⣿⣿⣿⠟⠁⣠⣿⠏⢸⣿⢣⣿⣿
⣿⣿⣿⣿⣯⢻⣿⣧⡀⢻⣿⣿⡏⣼⢲⣶⣂⣙⢷⡀⠀⠹⠿⠛⠋⠉⠉⠉⠉⠉⠙⠻⠿⠋⠀⣠⢞⡉⣦⡕⢺⡇⢿⣿⠃⣠⣾⡿⠃⢀⣿⢃⣾⣿⣿
⣿⣿⡹⣿⡻⣷⡙⣿⣷⡌⣿⣿⡇⣿⢸⠸⢮⣽⣂⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡡⣿⣺⡜⡀⡇⢸⣿⣾⡿⠋⠀⣠⣿⣷⣿⣿⣿⣿
⣿⣿⣧⠹⣷⡙⢿⣮⣿⣿⣾⣿⡇⣿⢸⣷⣯⣭⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣝⣿⣿⠆⡇⣼⣿⠏⣀⣴⣾⣿⣿⠟⣩⣾⣿⣿
⣿⣟⢿⣧⢻⣷⡀⠙⢿⣿⣿⣿⣿⡽⣎⣾⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣾⣗⣼⣿⣿⣿⣾⣿⣿⠿⣋⣵⣾⣿⢟⣿⣿
⣿⡿⣷⣿⣿⣿⣿⣶⣤⣙⣿⣝⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⢛⣻⣿⣿⣷⣿⣿⡿⣋⣴⣿⣿⣿
⣿⠷⠦⠈⠙⠻⢿⣿⣍⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣽⣿⣿⣿⣿⠿⠿⠛⢿
⣿⠷⠛⣛⣛⣻⣿⡿⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⡾⠋⠉⣹⡟⢦⡀⠀⠀⠀⠀⠀⣠⡾⣻⡍⠉⠙⡆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠷⠖⠖⠉⠃⠀⠀⠀⠀⠀⢷⠀⠀⣿⡇⠀⢷⠀⠀⠀⠀⢠⡏⠀⣿⡇⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠖⠶⠿⣿⣿⣿⠿⣿⣿⣷⣿
⣿⡿⢋⣵⣿⣯⣷⣶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢿⠇⢀⡞⠀⠀⠀⠀⠈⢧⡀⢻⡇⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣶⣿⣿⣿⡶⣬⣙⣿
⣿⣴⠿⢋⣽⣿⡟⠁⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠤⡤⢄⠀⠀⠉⠋⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠙⢿⣿⣿⣿⣶⣍⣻
⣿⣧⣾⣿⣿⡟⣠⡶⠛⣩⣷⠿⠛⠋⣻⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡟⠉⠛⠿⣯⡛⠳⢦⡈⢿⣿⡿⣿⣿⣿
⣿⣭⣾⣿⣿⣾⠋⢀⣾⠟⠁⠀⠀⣴⡿⡿⠀⠈⠙⠳⢦⣄⣀⠀⠀⢀⣠⣷⣀⠀⠀⢀⣀⣤⡶⠟⠋⠁⠘⡟⢿⣄⠀⠀⠀⠹⣦⠀⢻⣾⣿⣧⣾⣿⢿
⣿⣿⣿⠟⣿⣿⠀⣾⠃⠀⠀⠠⠚⠁⣠⣷⠀⠀⠀⠀⠀⠈⠉⠉⠙⢧⡼⡟⣦⠟⠉⠉⠉⠀⠀⠀⠀⠀⢰⣷⡀⠉⠳⠀⠀⠀⠈⠃⠀⣿⣿⡟⣿⢃⣾
⣿⣧⣿⠀⢹⣿⠀⠃⠀⠀⠀⠀⠀⠀⢁⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⣇⠹⣆⠀⠀⠀⠀⠀⠀⠀⢀⣦⣧⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⣿⣾⣿
⣿⣿⣿⣇⠀⢻⣇⠀⣆⠀⠀⢀⣀⣴⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⡼⠁⣼⣿⣄⠹⣆⠀⠀⠀⠀⠀⠀⠘⣿⡟⠷⣤⣀⠀⠀⠀⡄⠀⣾⠃⡟⢀⣿⣿⣿
⣿⣿⣿⣿⣦⡀⠻⡄⢿⣶⣄⣉⣁⣠⣾⡿⣿⣰⠀⠀⠀⠀⠀⣼⠃⡼⠁⡇⠹⣆⠹⣆⠀⠀⠀⠀⢸⣦⡿⢿⣦⣄⣀⣀⣤⣾⡇⡸⠋⠀⢀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⣀⣈⣳⣬⣭⣽⠟⠋⠀⢹⣿⢠⠆⠀⠀⣸⢃⡾⠁⠀⡇⠀⠘⢦⠹⡄⠀⠀⢢⢸⣿⠃⠈⠙⢿⣯⣭⣴⣋⣀⣀⣠⣴⣿⣿⣿⣿⣿
⣿⡻⢿⣿⣏⠛⠻⠿⢿⣿⣿⣿⣛⠛⠻⣦⡀⢻⣿⠀⠀⢀⣧⡏⠀⠐⠀⣇⠀⠄⠈⣷⣿⠀⠀⠈⣿⠏⣠⡶⠟⢛⣻⣿⣿⣿⡿⠿⠛⠋⣽⣿⡿⣫⣿
⣿⣿⣆⠻⣿⡆⢀⣾⣿⣿⣿⡿⣿⣿⣦⡘⣷⠀⣿⣄⠀⠈⣿⣷⠀⢀⠈⠛⢀⡀⢀⣿⡿⠀⠀⣰⣿⢠⡿⢠⣾⣿⣿⢿⣿⣿⣿⣦⠀⣼⡿⢋⣴⣿⣿
⣿⣿⣿⡆⠘⣿⣾⣿⣿⢨⣿⣇⣿⣿⢿⣷⣽⣇⣿⠉⢳⡀⢹⣿⡄⠒⠀⣆⠐⠈⢸⣿⠇⣠⠞⠹⣿⣼⣷⣿⢿⣿⡇⣿⡏⢰⣿⣿⣷⡿⠁⣼⣿⣿⣿
⣿⣿⣿⣷⠀⢸⣿⡟⣻⣷⣿⣿⣿⣟⠀⣿⣿⣿⡏⠀⠀⠹⣼⣿⡇⢠⡊⠈⣠⠀⣾⣿⣰⠃⠀⠀⣿⣿⣿⣿⠄⣿⣿⣿⣷⣾⢟⣻⣿⠁⢀⣿⣿⣿⢿
⣿⢿⣿⣿⡄⠈⣿⣧⣃⣿⣿⠁⡻⠿⣿⣿⣿⡟⠀⠀⠀⠀⢻⣿⣷⠈⠀⠀⠀⠀⣿⣿⠏⠀⠀⠠⠙⣿⣿⣿⣿⢿⡇⢹⣿⣗⣠⣿⡟⠀⣸⣿⣿⡇⣸
⣿⡈⢿⣿⣷⡀⠘⢿⣿⣿⣥⣄⣸⣶⣾⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣷⣶⣌⣽⣝⣿⣿⠿⠃⣠⣿⣿⠟⣠⣾
⣿⣿⣷⣿⣿⣿⣷⣤⣭⣝⣛⡻⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣹⡆⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠿⣛⣋⣭⣤⣴⣾⣿⣿⣿⣾⣿⣿

⠀⠀⠀⠀⢀⡠⠋⠉⢱⠤⢄⡀⠀⠀⣤
⠀⠀⠀⢰⠋⢀⡠⠖⠁⠀⠀⢙⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢆
⠀⠀⠀⢸⠎⢁⣀⡤⠔⠊⠉⠀⢡⢠⣾⠟⠛⠛⠛⠛⠛⠟⠛⠛⠛⠛⠻⢶⣄⣪⣀⣀⠷
⠀⠀⠀⢸⡊⠁⠀⠀⠀⣀⡠⠔⢎⠸⢷⡀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠀⠀⣞⣁⣀⣀⡠⠔⠓⢄⠀⢀⣄
⠀⠀⠀⠀⠙⢲⡖⠊⡍⠀⠐⣠⣸⠤⠼⠧⠤⣀⡀⠀⠆⠀⢀⠂⠀⡰⣋⣀⣀⡀⠀⠀⠀⠀⢸⣄⣈⣉
⠀⠀⠀⠀⢠⢃⣾⣄⠀⣰⠞⢁⡔⠒⠐⠒⠑⠄⢈⠑⢄⠀⠀⠀⢰⠋⠀⣀⠀⠀⠉⠉⠉⠉⠁⢸⣦⣤⡉⠢⡀
⠀⠀⠀⠀⡇⢸⣿⠸⡟⢡⠖⢊⠀⠘⠀⠀⠃⠀⠄⠧⡀⢳⠀⠀⢸⠋⠋⠀⠉⠈⠙⠉⠙⠉⠒⣮⣙⢻⣿⡆⢱
⠀⠀⠀⠀⠸⡈⢿⣶⢁⠜⠀⡀⠀⠈⣓⡒⠁⠀⠀⠀⢇⠈⡇⠀⢸⠀⠀⠀⠘⠁⠀⠘⠀⡤⠎⣣⠼⠦⠿⡟⡸
⠀⠀⠀⠀⠀⡙⢤⣹⠀⡇⠀⠀⠀⢸⡀⢈⠂⠄⣀⣀⣸⢠⡷⠤⢼⣄⣀⠀⠐⠤⡤⠄⠀⠫⣴⠃⠀⠓⠀⠈⢣
⠀⠀⠀⠀⠺⠷⠀⠈⡆⠳⡄⠂⠀⠀⡩⠛⣩⢅⣀⣶⣶⣶⣶⣶⣶⣶⣦⣬⣍⠑⠢⡠⠆⠒⠯⣦⡘⠢⠌⠃⢸⠒⣶
⠀⠀⠀⠀⠀⡤⠴⠳⢜⠂⢗⣆⢀⠂⢹⠢⠭⣛⣻⠿⠿⠿⠿⠿⠿⠿⢿⣛⠫⠤⠚⠗⠋⡝⠱⠸⠈⠓⠤⠒⠣⡰⠞
⠀⠀⠀⠀⣔⣁⢁⠎⠁⣀⠀⠹⡅⣑⣺⡀⠀⠀⠀⢀⠉⠉⠉⠉⠉⢁⠀⠀⠀⠀⢸⠒⠊⠁⡰⢰⠂⢸⡷⠂
⠀⠀⠀⠀⢸⠀⠀⢀⡀⠀⢀⠀⢱⠀⠀⢣⠀⠀⠀⠘⠃⠀⠀⠀⠀⠙⠃⠀⠀⢠⠧⠤⠔⣊⠴⠃
⠀⠀⠀⠀⠀⠳⣄⠀⠁⠐⠋⠀⡸⠀⠀⠀⠑⣄⠀⠀⠈⠒⠤⠴⠚⠁⠀⢀⡠⠋⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠒⠶⠤⠤⠤⠤⠶⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠉⠳⣄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⡇⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⢤⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⡠⠚⠛⠛⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⠉⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠀⢀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠘⢿⡿⠃⠀⠀⢀⣀⣼⣄⣀⣀⣧⣀⣀⣸⣇⣀⣀⣼⣀⡀⠀⠀⠀⠈⠻⡿⠃⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⢸⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⡇⠀⠐⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⡇⠁⠉⠉⠁⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣅⣀⣀⣀⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡧⠤⠤⠤⠤⠤⢴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣉⣉⣉⣉⣉⣉⣡⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⡀⠀⠀⠀⠀⠙⠿⢿⠿⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⠿⠟⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⣤⣶⣄⠀⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⣠⠞⠀⠀⣤⣷⣄⠀⢸⡇⠀⠀⠈⠉⠉⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠒⠚⠁⠀⠀⠀⠿⣿⠟⠀⠘⢧⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠇⠀⠀⠠⡄⡀⠀⢠⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠁⠀⠀⠀⡄⠀⣀⠀⠀⠀⠀⢀⢤⣌⡛⢏⡤⢏⣠⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣵⡔⠀⠀⠘⢁⢾⢠⣤⡀⠐⠀⢸⣷⠈⢿⣾⣧⣬⣇⣘⡷⠀⡖⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢮⣿⣷⠀⠠⠈⢿⣿⣿⣿⡷⠀⠀⠀⢋⡑⣚⠷⢾⠋⢋⡉⠠⠛⢩⡏⢹⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢸⣿⢿⣧⠀⠻⡞⢷⣻⣿⣥⠀⠀⠀⣼⣿⣍⣤⣀⠁⠻⠲⠀⠀⢠⡍⢏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠒⠰⠁⠈⠉⣼⢿⣷⣤⡈⠀⠈⢉⣉⡀⠴⠊⠉⠉⠈⠲⣍⣻⡇⢤⡀⡤⠠⢕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣵⡋⣙⡠⢸⠛⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⢦⣳⠐⢉⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢻⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⠀⢀⠈⠀⠆⠀⠆⠀⠀⠀⢀⣀⡀⢀⡆⠀⠸⢧⠀⠀⢐⣀⣌⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠺⠁⠀⠀⠀⢟⠛⠮⠼⢷⠁⠀⠀⠀⠀⠀⢻⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠓⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠈⢠⠄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠋⠀⡀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣀⣄⣀⣀⣠⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠰⠀⠀⠀⢀⡼⠇⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢇⣽⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠻⠀⣼⠀⢦⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠽⣷⡞⢦⡄⠰⠋⠑⠀⣀⠀⠀⠀⠀⠘⢿⣶⡶⠶⠶⠶⠾⢿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡝⠈⣋⢿⡛⠧⠀⣤⡀⠀⠙⢻⡆⢠⣦⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⠶⢷⡈⠿⣆⣠⡼⢋⡄⠀⠈⠁⠀⠋⠛⠛⠿⢷⣄⣀⠀⠀⢀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⡸⠁⢀⠋⡰⠢⣽⠁⠬⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠓⡤⢀⢀⠾⡀⢠⡄⠘⢲⡄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣶⠈⠁⣬⢱⢾⣤⣤⢤⠤⠀⣤⠀⠀⠒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⢈⡧⠀⡤⠈⠓⠄⢀⣈⠷⣀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣨⠇⢠⡄⠰⠚⢠⠽⣭⡴⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠤⠐⠆⡀⢠⡤⠀⠀⢁⠀⠀⢀⠈⠁⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢼⡤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⡾⡃⠀⠀⠈⣔⠑⠃⠈⠀⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⢠⡀⠀⢥⣾⠃⢸⠁⠠⠶⠞⠉⢀⠆⠚⠃⠰⠄⠀⡆⠀⠀⠀⠖⠠⠷⠖⠄⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠀⠚⠋⠀⠀⢠⠀⠄⠀⠘⡇⠀⠀⠀⣨⠠⡄⠀⠀⠰⠂⠰⡷⠲⠶⡧⠀⠀⢰⠆⠲⠾⠁⡆
⠀⠀⠀⠀⠰⠠⠃⠀⠶⣖⣀⠉⠀⠱⢤⠀⠀⠀⠾⣬⠃⠀⠀⠂⢱⠀⠀⠀⠀⠨⠀⣤⠀⢀⣀⡠⢓⠀⠀⠀⠀⣄⣀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⡄⢀⠀⢈⠉⢐⠀⡀⠀⣈⣦⠀⠀⣤⢀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠐⣲⣧⡶⠺⣛⣉⣹⣦⣀⢀⣀⡩⣿⣤⡤⠀⡇
⠀⠀⠀⠀⠀⢁⠠⠤⡁⠀⣆⣩⣹⣯⠭⠅⠙⠿⢿⣿⡿⢶⣂⣶⣄⣀⣉⠒⣤⣾⣿⡛⣱⠾⠋⠉⢀⡼⢿⣄⣀⣙⣿⣋⡤⠖⢀⡉⠁⠦⡀
⠀⠀⠀⠀⠀⡆⠀⡉⠁⢪⡏⠁⠀⠀⠀⠀⣆⡐⠘⠛⣷⣎⢉⡙⠻⣟⠻⣿⣿⡻⣅⡀⠀⢄⠀⣨⣄⣶⡤⣇⠃⠀⢀⠰⠂⠒⠉⠙⠢⣀⠈⠀⢄⡀
⠀⠀⠀⠠⢴⠦⠀⢇⣄⣠⡽⣶⣶⣴⠦⠉⠩⢽⣿⣾⡏⠈⠛⠶⣦⣽⣷⣘⢺⠹⣟⠃⠀⠰⠀⠀⠈⠟⣽⣾⡟⠀⢸⡇⠀⠀⠀⠀⠀⠈⢆⠀⡀⢁
⠀⠀⠀⡈⢀⠀⠀⠚⠿⠻⣤⠉⠛⠋⠀⣅⡀⠀⠀⡹⣠⣄⠒⣠⣤⣈⣉⣀⣹⠗⣿⠰⡶⠦⠄⠀⠀⠊⠛⠻⢃⡆⠸⠁⠀⠀⠀⠀⠀⠀⠈⠀⠿⡆⢠⢠
⠀⠀⠋⠀⠀⠀⠀⠀⢠⣨⠝⠀⠀⠀⠐⠟⠵⠂⠀⢀⣉⠉⣼⠈⠛⠟⠛⠻⣿⡾⢣⡄⠆⠀⠀⣠⡆⠨⠂⢰⠞⢡⣤⣀⠀⠀⢲⡤⣤⣤⣀⣈⡻⢈⡌⡟
⠀⠀⠀⠄⠀⠈⠀⡀⠀⠀⢀⠀⣀⠀⠀⡀⢄⠀⠠⡏⢀⡙⠓⠇⠀⠀⠀⠰⢋⡄⢀⡇⠀⡀⢀⡀⠀⠤⢠⠈⡆⠀⠛⠯⠛⠀⢈⠁⠀⠁⢶⣬⡗⣸⣿⡇
⠀⠀⠀⠀⠀⠀⢀⠀⣀⠠⠔⠀⣶⡼⢬⣅⣭⣩⡖⢊⡁⠀⢀⡖⠁⠀⠀⢠⠟⣾⠀⠀⠈⠉⠩⠤⢤⣿⠃⡠⠃⠀⠀⠀⠀⢠⡆⣰⠄⢻⠄⠰⠶⠝⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠄⠀⠨⢻⣆⣅⣨⠿⠛⠻⠛⢺⣗⣻⣟⢦⠐⠋⠀⢿⠀⠒⠤⡀⠀⢠⡶⠟⠋⠀⠈⠉⠉⠶⠀⠀⠉⠉⠒⠛⢁⡀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⢳⠄⠘⡇⣻⠩⡇⢀⣤⣲⠶⠿⢿⣽⣻⣼⠅⢰⡴⠷⠾⠷⠦⢶⣯⡀⠀⠀⠀⠀⠀⠀⠀⠒⢠⠀⠠⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠀⠀⠈⠉⠓⢊⣿⠞⢉⣁⠀⠀⠀⠀⣈⣁⠓⢤⣃⡐⢒⢢⣀⣤⣴⡿⠀⠀⠀⣀⠀⠠⢄⡀⠀⠈⠁⡆⠀⠚⡿⣁⣀⠀⢂⣠⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⢁⠀⠀⠀⠀⣀⢩⣾⣿⣽⡗⢆⠀⢿⣽⣯⣁⢼⣷⡝⠈⠉⠁⠘⣧⣶⡄⠒⡀⠑⠾⠗⠀⠨⠔⠄⢠⠒⠀⠜⠀⠀⠁⠈⡠⠘⠁⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡆⠀⢀⡉⠀⣻⣏⠛⠁⠀⠀⠀⠙⠛⠉⢸⡿⠃⠀⢑⡶⣿⠛⠀⢀⠸⠄⠀⠀⠀⠀⠀⠘⢀⠖⠰⠞⠂⠀⠀⠀⡸⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣆⣤⡄⡴⠐⠒⢺⣶⠇⠉⣯⡀⠀⢠⣄⣤⠀⠀⢀⡨⢤⠀⠀⠈⠉⢉⠀⠑⠆⠓⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⢀⠀⣄⡳⠆⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡀⠀⠀⠁⠀⠀⠐⢀⡙⡁⢀⡠⢀⡀⠀⠀⠁⠈⠀⠀⠀⠀⠈⠠⣴⣜⣀⠀⡦⠀⠀⠀⠄⡀⠂⠀⢀⡀⠄⢸⠆⠏⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠀⠀⣠⣲⠀⠀⠠⠀⢻⣧⠴⡌⠑⣖⣃⣀⡛⣤⡀⠀⠀⠀⠀⠀⠑⣟⢿⡀⠀⠀⣡⠞⠀⢤⣷⣤⣄⠀⠄⠀⣼⠇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄⠀⠀⡐⣦⡶⠛⠛⠛⠫⠥⡻⣏⣁⠴⣦⣤⠀⠀⠀⢚⡼⡌⣿⢿⣏⠀⠰⢚⠿⠿⠌⠂⣸⢾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⡀⠒⠂⠀⠀⡴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠘⠧⢾⣧⡄⠒⡄⢀⣺⣧⡶⡿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠹⢞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢠⠾⡴⠉⣠⡴⡶⢀⠀⠀⠀⢐⣠⡶⠊⠉⠁⢸⠀⠈⡉⠋⠀⣧⢀⣀⠄⢀⠀⠀⡀⠀⠂⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠐⠉⢶⣧⠀⠈⠛⠓⠢⠙⠀⠀⠈⠉⠋⠀⠀⢀⠘⠛⠀⠀⠀⠀⢹⣷⠈⢀⣶⡶⠤⢡⠄⢰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⣏⡖⢠⠀⠀⡀⠀⠀⠱⠴⣏⣥⢀⣀⣜⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⣄⣀⡀⠀⠀⡄⠀⠀⠰⠋⠓⠂⠫⠉⠃⠀⠀⠀⠀⠘⠃⠓⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⠉⠀⠀⠚⠁⠀⠈⠀⢀⡀⠀⡀

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

⠀⠀⠀⣀⣠⣤⡴⠶⠞⢛⣛⣛⣛⣛⣛⣛⡲⠦⣄⡀
⣴⠾⠛⣋⣩⣤⠶⠟⢛⣉⣭⠵⠖⣒⣛⣯⠭⠭⢚⣙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠
⣴⠶⠛⢋⣡⡴⠶⠛⣋⣥⡴⠾⢛⣩⣥⠶⠞⣋⣭⡵⠶⣛⣆⠳⣌⠳⣄⢠⡀⠀⠀⠀⣀⣤⡴⠶⢛⣋⣩⣭⣤⣤⣤⣤⣤⣉⣉⣉⠙⠛⠛⠻⠿⠿⠟⠛⠛⢉⣁
⣤⠶⠛⣋⣡⡴⠾⢛⣉⣥⠶⠞⣋⣩⡴⠖⢛⣩⡴⠖⣛⣩⠼⣦⣘⣃⣈⣡⠥⠶⢚⣋⣭⠶⠞⢛⣉⣉⣥⣤⣤⣄⣈⣉⡉⠙⠛⠛⠿⢿⣶⣶⣶⣶⣶⣿⠿⠿⠛
⠶⢞⣛⣭⠤⠶⣚⣫⡭⠶⢞⣋⣭⠴⠖⣛⣩⡥⢖⣫⡭⠶⣛⣉⣭⠭⠥⠶⠖⣛⣉⣥⡴⠞⠛⣋⣉⣉⣉⣉⣉⣉⠙⠛⠻⠿⣷⣦⣤⣀⣀⡀⠀⢀⣀⣀⣀⣤⣤
⣋⠭⠵⠶⠭⠭⠷⠖⣚⣋⣩⡥⠶⠞⣛⣭⠴⢚⣩⠵⠚⢛⠉⠉⠛⠷⣟⣛⣋⣉⣭⡴⠶⠚⢛⣉⣉⣉⣉⣉⡙⠛⠻⢷⣶⣤⣀⠉⠛⠻⠿⠿⣿⣿⠿⠿⠿⠿⠟
⠙⠛⠛⠛⠛⠛⠛⣛⣉⣩⣤⠶⠞⣋⣭⠶⣚⡭⠶⠚⠛⠛⠿⣿⣦⠀⢹⡿⢰⠦⠴⠶⠞⢛⣉⣭⣭⣭⣍⣉⡛⠻⢶⣤⣈⠙⠻⣷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠿⣿⣶⠿⠿⠿⠛⠛⣉⣡⡴⠖⣋⡥⢖⣫⠵⠶⠿⠿⣶⣦⡀⠘⣿⠇⣼⠃⡾⣸⢽⣛⣛⣉⣭⠤⠶⠦⢤⣍⡙⠳⣦⣈⠛⢷⣤⡀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣀⣠⣤⣤⣴⡶⠾⢛⣉⡥⢖⣫⢵⣺⣭⠶⠶⣶⣦⡄⠈⣿⡇⢰⡿⢠⣿⠰⣧⠘⠶⣬⠭⠴⣒⣛⡛⠓⠶⣮⣙⠳⣦⡙⢷⣄⠙⢿⣶⣤⣀⡀
⠛⠋⢉⣉⣤⡴⠞⣋⡥⣚⣭⣺⡭⠴⠶⢶⣦⡀⢹⡿⢀⣿⠁⣾⡇⠸⣿⣀⠙⠻⠖⣒⣛⣉⣉⣉⡙⠻⠶⣤⡉⠳⣎⠻⣦⠙⣷⣄⠉⠻⠿⣿⣿⣷⣶⣶⣶⣶⣤
⡾⠿⠛⣋⡥⢖⣫⢕⣫⣻⢽⣖⣚⣛⢶⡄⢻⡇⣸⡇⢸⣿⠀⢿⣧⣀⠙⠛⣛⣛⣭⣭⣥⣬⣭⣉⣛⠻⣦⣌⠻⣧⡈⢷⡌⣷⡈⢻⣷⣤⣀⠀⠉⠉⠛⠛⠻⠿⢿
⡴⠞⣋⡥⣚⢽⣾⠷⠓⠉⠁⠀⠀⠀⠀⡇⣾⠀⣿⡇⠸⣿⣦⣀⠙⢛⣛⣩⡭⠴⠶⠶⠶⠶⠦⣭⡟⠛⢂⠙⠗⣈⢻⡎⠻⡎⠻⣦⡉⠻⢿⣿⣷⣦⣤⣄⣀⡀
⢖⣫⣕⣯⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡀⠻⣷⣄⡈⠙⣛⣛⡭⠵⣒⣺⠭⠭⠭⠭⢭⣓⣲⡍⡲⠦⠛⢦⡻⢧⠻⣇⠹⢧⡙⢿⣦⣄⠉⠙⠻⠿⣿⣿⣿⣿
⣝⠮⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⢷⣤⣈⣉⣛⣩⠭⢖⣺⠭⢗⣚⣫⣭⣭⣭⣝⣒⡻⠿⣾⣷⣾⣷⣿⣮⡻⣜⢳⣜⠻⣦⡙⠻⣿⣶⣤⣀⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠳⣤⣭⣭⡭⠵⢖⣫⡭⠶⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠶⠶⠷⠶⠶⠾⠓⠬⠳⣌⠻⢦⣄⡉⠛⠿⣿⣷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢍⡛⠶⣤⣀⡉⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠍⠛⠷⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⣠⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡷⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣾⣿⣧⡄⠰⠦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣋⣴⡿⠿⠿⠿⠋⠴⠀⠀⠘⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡇⠈⠉⠉⠉⠀⠀⠀⠤⠤⠴⠖⠁⠀⠀⠈⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣾⣦⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⣀⠀⠀⠀⠀⠀⠟⠛⠙⢋⠀⠀⠀⠀⠀⠀⡜⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠉⠀⠀⠀⢀⡀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠚⠁⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠦⠶⠤⠶⣂⠀⢀⠀⠐⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠉⢡⢿⣯⠀⠀⠀⠀⠀⠀⠀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⡈⠀⠀⠀⠀⠀⠲⣼⣧⠄⠀⠀⠀⢀⣠⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣷⠉⠀⠤⠀⠀⢿⣻⡿⠀⠀⠤⠀⠸⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠰⣄⠀⠀⠀⠀⢻⣦⣀⡀⠄⠀⢻⣿⣗⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠁⠀⠸⠏⠻⡄⠀⢶⠻⣿⣿⣧⠀⠀⠀⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣴⡬⣾⣤⣼⣿⣿⠿⠀⠀⢀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢻⣶⣶⣶⣬⣽⣿⣿⣦⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡄⣠⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⠀⣀⣠⡀⣀⣀⡀⣀⣦⠀⣤
⠀⠀⠀⣀⡀⣀⣤⣄⣠⣤⣄⣀⡀⠀⣀⣀⣤⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣽⣉⣈⣽⣛⣋⣼⡹⣿⣿⣯⣶
⠋⢛⣛⡛⠛⢛⡛⠛⢛⣛⣛⣋⣙⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢰⡆⠀⠀⢸⣿⢸⣿⠀⠀⠀⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣿⣴⡆⣿⣿⢸⣿⣿⣶⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⣄⣴⣿⣿⣸⣿⣿⡷⠶⠾⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢿⣏⣽⣿⣯⠿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣰⣿⣼⡟⣿⣩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠿⠿⣺⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣯⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⣷⡖⣻⣿⡇⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡇⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⡇⣿⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡖⣶⣼⡏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠹⣿⣶⣯⣿⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⢸⣏⣻⣿⣟⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡶⠛⠸⣿⣿⢹⣿⣿⡷⠶⢶⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠻⠇⣿⣿⢸⣿⣿⡿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠸⠃⠀⠀⢸⣿⢸⣿⠀⠀⠈⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⢀⣀⣀⣐⡂⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⡤⠠⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⠆⣠⣾⣿⣿⣿⣿⣿⢿⠿⢿⣿⣿⣿⣿⣿⣿⣟⣀⠛⠀⠤⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⢿⣿⠿⢛⣥⣾⣿⣿⣿⣿⡙⠿⡧⠴⠾⠿⠟⠉⠉⠟⠛⠛⠉⠉⠀⠀⠀⠀⠩⠿⣏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⠉⢿⣿⢿⣿⣿⠀⢺⣧⣿⣿⣿⡟⠉⠀⢀⠤⠤⠀⣀⡀⠀⠀⠀⢠⣶⣿⣿⣆⣠⣶⡀⠀⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⣠⣴⣶⣦⣄⢻⣄⠈⠻⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⣿⣶⣾⣿⣿⠀⠹⣿⡦⠀⢐⣶⣴⣿⣿⣿⣿⣷⣶⣶⣤⣄⠀⠀⠀⠀⠉⠻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡆⠀⠸⣿⠿⠛⠁⠀⢴⠿⢃⣠⠘⡛⢹⣿⣿⣻⣿⣿⣺⣿⣿⣿⠃⠀⠀⠀⠋⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢠⣿⠀⣀⠀⢀⣠⣾⣿⣏⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣆⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡏⢸⣿⢦⣿⣿⣿⠂⠈⣘⣀⣼⣿⣿⠿⡿⠿⠸⣿⣿⠇⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣯⠀⠙⢿⣾⣿⡿⠟⠛⡛⢛⠻⣟⠛⠻⠶⣶⣿⣧⣄⡀⠀⠀⠀⠀⠈⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡿⠋⢠⡄⠈⣿⡟⡀⢀⢑⡀⠈⠉⠈⠀⠀⢀⡠⠙⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⣧⠀⢿⣠⣾⠟⠀⡄⠀⠈⠛⠀⢂⠁⠄⠀⠀⢰⠃⢼⣦⣉⠉⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢿⠂⣲⠛⡃⠀⠠⠉⠠⠀⠀⠠⠌⠀⠀⠀⠀⡀⠀⡈⢁⡜⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣶⣗⣶⠊⠏⠐⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠲⠆⠀⠀⠀⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⡆⠀⢾⣶⣆⠀⠀⠀⠁⠀⣀⣀⠀⠀⠀⠀⠐⠀⢀⡀⠀⠐⠆⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠠⣿⡇⠀⢸⣿⡿⠑⢄⠀⠀⠐⠈⠛⠷⢦⣤⣤⠄⠲⣾⣿⢶⡀⠀⠀⠙⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣿⡇⠀⢸⣿⣧⢰⣄⢁⡀⠆⠀⠀⠀⠀⠀⠄⢠⣤⣼⣿⡘⠳⠀⢠⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣏⡀⠁⣸⣿⣟⣁⣙⣾⣷⡿⠟⢢⣀⣀⠀⣀⣨⡟⠛⣿⡇⡀⢠⠃⣜⢸⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡯⣿⢾⢿⣿⣿⣿⣿⣿⣿⠷⠄⠬⠿⠟⢻⣿⣿⣿⣾⣿⣿⡇⢠⡈⣿⢠⠶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣹⠿⣥⣿⣾⣌⣿⣿⠿⣿⣿⣿⣿⣿⡷⠶⠶⣮⣭⣝⣿⣿⣿⣥⣇⠀⢖⡋⣨⡈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⠉⠙⠉⠁⠀⠈⡿⠧⠿⡿⠤⠀⠃⢀⣾⣿⣝⣿⣿⣿⢹⣿⠀⡐⠀⢒⡉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡗⠀⢹⣟⣛⣿⠂⢰⣇⢠⣙⠦⠒⠀⣀⣀⠀⠀⠀⠈⠉⠉⠀⠿⢀⡱⣤⣤⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠈⠉⠉⠉⡠⠋⠙⠃⠉⠉⠀⠀⠉⠉⢹⡆⠀⠀⠈⠀⠀⠀⣩⡇⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣾⣶⣶⡖⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⣺⣶⣤⣠⣤⣤⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡿⠷⠂⠀⠀⠀⠐⠼⢿⣽⣿⠿⠿⡿⢏⡁⠀⢀⡀⠀⠀⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃⠀⠡

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⢀
⠀⠀⠀⠉⠉⠉⠃⠀⠐⠀⠠⠰⠠⠤⠠⠄⢀⡈⠀⠈⠉⠁⠐⠂⠲⠒⠀⠠⠤⡤⢠⢀
⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⣄⣀⠀⠀⠁⠈⠛⠒⠒⠒⠒⠖⠠⠀⠦⠤⣄⢁⠐⠂⢄⢠
⠀⠀⠀⠈⠁⠿⠷⣤⡄⣀⡀⣀⠀⠀⠀⠀⠁⠏⠉⠙⠒⠐⠓⠂⠀⠰⠆⠐⠂⠀⠲⠄⠀⠀⠙⠺⠛⠲⢲⡤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡙⡈⢇⠰⣓⡤⠰⡶⣤⣤⠤⢤⣀⡀⠀⠄⢀⢀⣠⣄⡠⡤⠄⣠⠄⠒⠂⠐⠐⠀⠒⠂⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡲⢿⣾⣖⡍⢷⣰⡆⣹⣶⣶⢦⠿⢌⠨⢣⠬⠍⠞⣡⣄⣧⣜⣿⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠿⣁⡴⢩⡼⠀⢡⡿⡧⢔⠓⢨⣭⢵⡨⣑⣥⠖⠈⢿⢽⡽⠏⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⢶⠆⠀⠀⠳⣆⢛⡟⣍⢥⢘⢷⠉⠀⠀⡐⠛⠈⠈⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠋⠃⠹⢼⠵⠚⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⢄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠒⢰⠤⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠦⡄⣀⠀⢁⠀⠀⠀⠀⠰⡈⠄⠀⠠⠀⡀⠂⠁⠀⠀⡀⠛⢦
⠀⠀⠀⠀⢤⣀⡄⠶⢀⣸⢭⡣⣽⡙⠃⠀⢀⢀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠⡈⠒⢀⡀⠄
⠀⠄⠈⢐⣀⣤⡈⡏⠅⢷⡿⣿⣭⡅⠀⠀⡗⣲⣔⣂⣠⠀⢀⣀⠀⠀⢄⠀⠀⠀⠀⠐⠠⠐⠀⢨⠉⢶⣦⣑⠢⢄⣀⡀
⠀⠂⢨⠔⠂⡈⢻⡚⠫⠿⣟⢋⠦⠀⣀⢹⢼⢰⢙⠨⣇⣽⣿⣭⣠⢀⡸⠆⡀⠀⠠⠀⠂⠄⠐⢮⡆⠀⢩⡙⢢⡐⣍⣛⡡⣤⡀
⠀⠂⠀⠠⠃⠰⠄⡘⣿⢾⢡⡚⠃⠀⠸⠎⠠⡤⠙⠺⠯⡉⢁⣲⢀⡘⢔⠀⠉⢤⠀⠮⡑⠤⠀⠄⠙⠀⠊⡃⠍⢨⡀⠩⠭⣂⡄
⠀⠈⠘⠃⠁⠙⠂⠃⠉⠈⠉⠂⠀⠐⠂⠂⠈⠉⠐⠒⠀⠛⠂⠛⠚⠂⠈⠂⠸⠀⠀⠀⠈⠛⠴⠀⠀⠌⠐⠀⠈⠒⠂⠙⠂⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠃⠀⠐⠀⠠⠀⠂⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠍⠀⠀⠀⠒⠀⢸⠀⠡⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡀
⠀⠀⠀⠀⠀⠀⠔⠂⢉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⠂⠀⠀⠀⡆⢈⠀⠒⢄
⠀⠀⠀⠀⠀⠁⠔⠉⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⡀⠀⠀⢀⠋⠁⠈⠑⠄⠁
⠀⠀⠀⡀⠑⠎⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠈⠖⠁
⠀⢠⠩⠩⠈⡆⠀⠀⠀⠀⠀⠘⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⠊⠀⠀⠀⠀⠀⠀⡞⠈⠉⢢
⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠐⠀⠀⠀⠀⢸⠂⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠓⠐⡃⠀⠀⠀⢘⠂⢺⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⣉⡇⠀⠀⠀⢨⢉⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠈⠑⠀⠀⠠⠊⠀⠈⠉⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⣀⣀⣀⣀⡂⠀⣔⣀⣀⣀⡀⡀⣃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠐⠲⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣿⣧⣄⣀⣿⣆⣀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡅⡠⠀⠁⡤⡲⣦⣀⣠⢔⢢⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠞⠛⠇⡀⠀⣗⠦⣼⢿⣯⡳⢴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣒⡀⣀⣸⠁⠀⠙⠛⠁⠘⠈⠉⠉⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⡇⠀⡀⢰⣗⣶⣼⣼⣭⣵⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡱⣃⣀⡅⠘⠓⢒⣒⣚⣒⣁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠠⢿⣿⣿⣿⣿⣟⣩⡗⠀⠤⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠙⠄⠉⠣⡀⢹⠈⠉⡩⢤⠀⠀⠀⠀⠀⠀⠀⣆⡆⠀⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⡆⢉⠈⠀⠀⡇⢸⠀⠀⠘⠊⣀⣀⣠⣄⣀⣠⣤⡤⡄⠀⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣧⡈⢁⣴⣶⣿⢠⡞⠀⠀⡎⠛⣛⢿⡿⠻⠯⠭⣄⢹⠁⠀⡇⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⢻⣿⣿⣿⡟⣾⢱⠀⠀⡇⠐⣅⣀⠵⠀⠠⠠⠎⢸⡀⠀⡇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⢤⡀⢀⣾⣿⣿⣿⢧⣿⡸⠀⠀⡇⡀⠨⠀⠀⠀⠀⠰⣆⣾⡅⠀⣧⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⡘⢠⠒⡄⣷⣿⣯⣿⣿⣿⣼⣿⢀⠀⠘⡇⠓⠘⡒⢀⠉⠁⡄⠰⢸⡂⠀⣿⡟⠁⠀⠉⠑⠂⢤⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢡⡈⠒⢁⡯⠀⡼⣿⣿⣏⣿⡇⣼⠀⠀⣇⣈⣡⣥⣤⣴⣶⠶⠛⠛⠀⠀⣿⣷⠷⠖⠀⢠⢛⡙⢄⡀⠀⢨⢵
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠟⠇⠀⢸⣿⣿⣿⣿⢸⠇⠀⠀⠈⠉⢰⠋⠁⠀⠀⠈⠀⠀⠀⠀⡇⠈⠁⠒⠤⢼⡐⢂⣼⠿⢏⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⡄⠀⠀⠈⣿⣿⣿⡇⣿⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠙⢅⣀⣁⣰⠮⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠻⡄⠀⠀⢿⢿⣿⣾⡏⢸⡇⠀⠀⠀⠘⣒⣒⣢⣽⣥⣶⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢉⢳⣶⠓⢤⠀⣿⣿⣿⣾⡷⠾⠿⢻⣿⡿⠟⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⣛⣸⡀⠃⠀⡇⢸⣿⣿⠃⠀⠀⠀⠘⡿⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠋⠘⣇⢸⣤⠇⢸⢹⡟⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠉⠉⠀⠀⠀⣼⣇⣄⠀⠀⠀⠀⣏⠹⡗⠚⠋⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡠⡈⠻⠒⠊⠉⠙⠀⣷⠾⠾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢆⡸⠀⣧⡶⠿⢻⡞⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣄⣀⣴⠇⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⢹⠇⠀⠀⠀⢸⠁⠀⠀⠈
⠀⣀⣤⣶⣶⣶⣦⣴⣶⣿⣿⣿⣿⣷⣶⣶⣶⣾⣇⡟⣾⠀⠀⠀⠀⢸⠀⣀⣠⡷⠒⠤⠄⣀
⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⡃⠀⡇⠀⠀⢸⣿⣭⣄⡀⢀⣀⣤⢴⡇
⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣭⣁⡚⠲⢧⠶⠞⠛⠉⠙⠛⢿⡭⠓⣊⠬⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣦⣄⣠⡤⠶⢚⡳⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠛⠻⢷⣿⣽⣟⡻⢿⠇⣐⠠⠵⠚⠁

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

⠀⣤⡄⠠⣤⡄⢠⣤⡄⢠⣤⠀⣴⣴⠀⠀⠀⠀⢻⣟⣛⣛⣻⠃⠀⠛⡟⠛⠛⢻⡟⠀⠘⡟⠛⠛⠛⡟⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⢀⣠⣤⣤
⠀⠉⠁⠈⠉⠁⠈⠉⠁⠈⠉⠁⢙⣛⠀⠀⠀⠀⠈⢿⣿⣿⠟⠀⠀⠀⠳⣶⣶⡜⠀⠀⠀⠹⣄⢀⡼⠁⠀⢀⣾⣿⠛⠛⠿⣿⣷⣤⣾⣿⠟⠋⠁
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠀⠀⠀⠀⠀⡠⠋⠳⡄⠀⠀⠀⣠⢟⡙⣄⠀⠀⠀⢀⢞⣝⢆⠀⠀⠘⣿⣷⣀⣀⣤⣾⣿⠿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⣀⣀⣹⡀⠀⢀⣗⣿⣿⣾⡆⠀⢀⣟⣿⣿⣟⣇⠀⠀⠘⠻⠿⠿⠟⠋⠁⠀⠀⠉⠛⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣤⡄⠸⠿⠀⣶⡄⠀⠀⠀⠀⠠⣦⠀⢿⠁⣰⡦⠀⠀⠀⠀⠀⣤⡄⠸⡇⢀⣴⠄⠀⠀⠀⠀⠀⠺⣆⠀⣿⠀⣠⡀⠀⠀⠀⠀⠐⠻⣿⣿⠆⢰⣄
⠀⣤⠀⠀⠀⠀⠀⠉⣤⡄⠀⠀⢠⣀⠈⠁⠀⠀⠉⣠⣤⠀⠀⢀⣀⡀⠁⠀⠀⠘⣁⣤⡄⠀⠀⠘⠒⠂⠈⠁⠁⡼⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿
⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋


⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⣴⣿⠿⠿⣿⣷⣴⠀⠀⠀⠀⣠⣾⠿⠿⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣷⣄⠀⠀⠀⠀⣴⡦⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⣶⠿⠛⠀⠀⣠⡀
⠀⣿⡟⠁⠀⠀⠐⠛⠛⠀⠀⠀⢸⡿⠁⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⢸⡟⠁⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀
⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣤⣀⣠⣸⡟⠀⠀⠀⠀⠻⣿⣦⠄⣤⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⢰⣶⡆⣶⣶⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⣶⣶⣶
⠀⠈⠉⠁⠉⠉⠈⠉⠁
⠀⢢⣤⡄⣤⣤⢠⣤⡄⣤⣤⢠⣤⡄⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠋⠃⠉⠙⠈⠛⠁⠙⠉⠈⠙⠁⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⢀⣀⡀⣀⣀⢂⣀⡐⣀⣀⢀⣀⡀⣀⣀⢀⣀⡀⣀⣀⢀⣀⡀
⠐⠜⡛⣃⡛⡛⣘⣛⢃⠛⡛⣘⢛⢃⡛⡛⣘⠛⣃⢛⢛⡘⡛⣃⣀⣀⠀⠀⠀⠀⠙⡛⡛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠀⠀⠀⠀⠠⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡤⠀⠀⣐⠀⠀⠀⠀⠀⣴⣢⠀⠀⠀⡄⠀⢠⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⢀⠀⠀⢠⠀⠴⠁⠀⢀⡍⠀⠀⠀⣤⠀⠀⠸⠀⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢨⠀⠀⠸⠢⡆⠀⠀⠀⠀⠁⠀⡠⢺⠇⠀⠘⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠈⠆⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⡀⠇⠀⠀⠀⡄⠀⠀⠄⡀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⢐⠀⠀⠐⠀⢹⡄
⠀⠀⠂⢀⠀⢀⠺⠀⠁⠀⠀⢸⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣴⠿⠶⠒⠂⠀⠀⠾⠀⠀⠀⢌⢠⣯⠀⠀⠀⣴⣄
⠀⠀⠀⢐⣦⣤⡄⠀⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠤⠂⠀⠀⠀⠀⠀⠀⢛⢰⣻⣆⠀⠀⢧
⠀⠀⠀⠘⠙⠿⡙⠯⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣹⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠂⣸⣶⣯⠀⠀⠀⠀⠀⠀⠀⡀⠕⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠘⡀⠀⡀⠐⠈
⠀⠀⠀⠀⠀⠈⠝⡏⣧⠀⠀⠀⠀⠀⠀⠃⠀⣠⠀⠀⠀⠀⠀⠀⢂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠁⢸⡄⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠳⡀⢀⠠⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⠘⣤⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡡⠂⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⢨⠓⢄⠀⠀⠀⠀⠀⠀⢀⢠⢄⣼⡀⠥⠀⠁⠼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠻⢚⠛⠇⠀⡀⠛⢰⠟⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⡁⢉
⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⡁⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢺⠁⠘⠀⠀⠀⠸⠀⠈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠈⢀⡀⢸⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⢀⡆⠐⠂⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⢰⣦⢣⠀⠀⠘⠀⢘⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢸⠀⠀⠀⠀⠀⠀⠀⢰⡦⠘⢀⡃⠀⠰⣆⠀⢰⡀⢧⠀⠀⠀⠀⠀⣤⠁⠀⢡⡇⠉⠀⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⢁⠚⠀⠀⠀⠀⠑⠓⣦⣻⡌⣇⠀⠀⠀⠀⠈⠋⠀⠀⠙⣮⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢊⡁⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⢀⠀⠸⣷⣤⠀⠉⠛⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⢸⡤⠄⠫⠆⠈⢿⠟⠄⠀⠐⠂⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⡠⠤⠤⢄⡀⠀⠀⠀⠀⢀⠤⠤⠤⣄⠀⠀⠀⠀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀
⠀⢀⠎⠀⠚⡇⠀⠙⡄⠀⠀⣰⠁⠘⠉⣷⠈⢣⠀⠀⠀⣰⠁⠚⠉⣳⠈⢣⠀⠀⠀⡰⠁⢠⢾⡇⠈⢧⠀⠀⠀⡜⠁⣾⣉⡁⠈⢆
⠀⠘⡄⠀⠀⡇⠀⢀⠇⠀⠀⢻⠀⢠⡞⠁⠀⡸⠀⠀⠀⢻⠀⣀⠈⣳⠀⡸⠀⠀⠀⢣⠰⠧⢼⡧⠀⡜⠀⠀⠀⢧⠀⣉⠀⣹⠀⡜
⠀⠀⠘⠢⠤⠥⠔⠋⠀⠀⠀⠀⠑⠯⠭⠭⠚⠁⠀⠀⠀⠀⠑⠬⠭⠥⠚⠁⠀⠀⠀⠀⠑⠤⠬⠥⠊⠀⠀⠀⠀⠀⠓⠬⠭⠥⠊
⠀⠀⢀⡠⠤⠤⣄⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣀
⠀⢠⠋⢰⢋⡑⠀⢱⠀⠀⠀⢠⠋⠈⠉⣹⠀⢳⠀⠀⠀⢰⠋⢰⡉⣱⠄⢳⠀⠀⠀⢰⠃⣴⠉⢳⠈⢣⠀⠀⠀⢰⠛⣿⣰⠉⣯⢣
⠀⠸⡀⢸⡁⢹⠆⢰⠀⠀⠀⢸⡀⠀⣰⠃⠀⢸⠀⠀⠀⢸⡀⢴⠉⢹⡄⢸⠀⠀⠀⢸⠀⢘⠒⣻⠀⣸⠀⠀⠀⢸⠀⣿⢿⠀⡿⣸
⠀⠀⠑⠤⠍⠭⠔⠁⠀⠀⠀⠀⠑⠤⠍⠠⠔⠁⠀⠀⠀⠀⠑⠬⠭⠭⠔⠁⠀⠀⠀⠀⠑⠬⠭⠥⠔⠁⠀⠀⠀⠀⠑⠭⠬⠭⠕⠁
⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⣰⣿⣋⠉⣿⣿⣆⠀⠀⠀⢠⣾⣏⣥⡍⣿⣆⠀⠀⠀⢠⣾⣏⣥⡍⣿⣦⠀⠀⠀⢀⣾⣿⠋⠉⣿⣦⠀⠀⠀⢀⣾⡏⢩⣭⣽⣷⡀
⠀⣿⣿⣿⠀⣿⣿⣿⠀⠀⠀⢿⣿⡿⢋⣴⣿⣿⠀⠀⠀⢸⣿⡿⣭⡄⢿⣿⠀⠀⠀⢸⣿⠁⠞⠀⢿⣿⠇⠀⠀⢸⣿⣧⣴⣦⢹⣿⡇
⠀⠘⠿⣿⣤⣿⠿⠃⠀⠀⠀⠈⠻⣤⣬⣥⠿⠃⠀⠀⠀⠈⠻⣧⣬⣴⡿⠋⠀⠀⠀⠀⠻⣿⣿⣤⡿⠋⠀⠀⠀⠀⠹⢷⣬⣥⡾⠟
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⣠⣾⠋⣩⣙⣷⡄⠀⠀⠀⢠⣾⣉⣉⠉⣷⣄⠀⠀⠀⢀⣾⡟⣩⡙⢿⣆⠀⠀⠀⢀⣴⡟⢉⡉⢻⣦⠀⠀⠀⠀⣴⠋⣿⢋⡍⢢⡀
⠀⣿⣿⠀⣥⠙⣿⣿⠀⠀⠀⣾⣿⣿⠏⣰⣿⣿⠀⠀⠀⢸⣿⠇⣨⡀⢿⣿⠀⠀⠀⢸⣿⣧⣘⡃⢸⣿⡇⠀⠀⠰⣿⡇⣿⢸⣿⢸⡇
⠀⠹⣿⣤⣉⣴⡿⠃⠀⠀⠀⠘⢿⣿⣠⣿⡿⠋⠀⠀⠀⠈⢿⣦⣉⣡⣾⠟⠀⠀⠀⠈⠻⣧⣍⣡⣾⠟⠀⠀⠀⠀⠻⣇⣽⣤⣡⡾⠁
⣤⣤⣤⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣥⣤⣤
⣿⣿⣹⣝⣭⣭⣽⣭⣽⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢿⡿⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢻⠳⢤⣖⠉⠀⠠⡇⠀⠉⣲⠤⠚⡟⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⢸⠀⠀⠈⢱⠀⠈⡇⠀⡏⠀⠀⠀⡇⠀⣤⣀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⡇⠀⣿⣿⣿⣦⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⣇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠛⠢⣄⡀⢸⠀⢀⡇⠀⡇⠀⣀⠼⠿⠧⡈⠙⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠔⠊⠀⠀⠀⠀⠀⢉⠿⠀⣨⣏⠰⣷⣉⠀⠀⠀⠀⠀⠑⠠⢄⠁⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢁⠀⠀⠀⠀⢀⡠⠔⠊⠀⣠⠔⠻⠟⠢⣄⠈⠑⠢⣄⡀⠀⠀⠀⠀⡨⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠤⠒⠁⢀⡠⠖⠉⠀⣀⢴⣦⣀⠀⠉⠲⢤⣀⠉⠲⠤⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠄⠊⠁⢀⡠⠔⠈⠀⠐⡇⠈⠙⠢⢄⡀⠈⠑⠦⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⡉⠀⠀⢠⠂⠁⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠉⠲⡄⠀⠀⢙⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢼⠀⠀⠀⡠⠔⠊⠉⠉⠙⠢⢄⡀⠀⠀⡧⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⢀⠠⠐⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠚⠛⠛⠛⠛⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠋⠉⢀⣠⡴⠶⠛⠛⠒⠦⢤⣀⡀⠉⠙⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠉⠀⠀⠠⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣤⣀⡈⠉⠛⠶⢤⣄⡀
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀⡈⠙⠓⠦⣄⡀
⠀⠀⠀⠀⣰⠁⠀⠀⠀⠢⢄⡀⠀⠀⠐⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠦⢄⡀⠉⠙⠢⢤⣀⡀
⢀⡤⠚⠹⣇⠀⠀⠀⠀⠀⠀⠉⠓⠦⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀
⣾⣄⡀⠀⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀
⠈⠛⠿⣷⣤⡀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⣀⡤⠖⠉⠀⠀⠀⢹⡟⠲⣄
⠀⠀⠀⠈⣿⠿⣷⣤⣀⠀⠀⠀⠉⠳⣦⠴⢤⣄⡀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠙⠓⠦⣤⣤⠶⠛⠋⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⢀⣠⠾⠃⠀⢸
⠀⠀⠀⠀⠘⣆⠈⠙⠿⣿⣶⣤⣀⠀⢿⣦⣤⣈⠙⠳⢦⣄⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⢀⣤⠞⠋⠁⢀⣠⡶⠟
⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠉⠛⠿⣿⣶⣬⡛⠿⢿⣶⣶⡿⢄⡀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⢀⣤⡾⠟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠈⠙⠻⢿⣷⣦⣄⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⠀⣀⣴⡾⠛⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠀⠀⣀⣠⡴⠞⠋⠀⢀⣠⣴⡾⠟⠁⠀⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⢀⣤⡶⠟⠋⠁⠀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠈⠙⠻⠿⣶⣤⣤⣀⣀⣀⣤⣶⠾⠛⠉⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠷⣤⣄⣀⠀⠀⠀⣀⣤⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⡟⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠙⠉⢿⣿⣿⣿⣿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣬⣉⡉⠉⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣿⡯⠿⡟⠻⣷⣄⠄⠋⠀⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢺⠛⢹⣈⣿⣧⠥⣹⡆⢱⢻⡖⢲⡄⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⡂⡿⣷⣿⣿⣦⣼⣿⢟⣛⣿⣾⠛⠩⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⣾⣷⣿⣻⣯⣼⣷⣿⣿⣿⣿⢿⡇⠀⠀⣳⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢿⣤⣹⣿⣿⣿⡾⠿⢟⠁⡇⣿⣰⣀⢘⡆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⡟⠛⢫⣙⣿⣧⣴⡾⣶⣿⣿⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣶⣾⣿⣻⣏⡿⠯⢿⠷⠿⠋⠸⣏⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡏⠛⠛⠉⠱⣶⣾⣯⣄⣀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣆⠀⢠⣿⣿⣿⣿⠟⠛⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠈⠛⠋⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣤⣠⣠⣤⣴⣿⣿⠁⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⢿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠴⣶⣿⣿⣿⣶⠦⠤⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣦⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⣯⣤⣄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣶⠀⣠⠀⣠⣶⣦⠈⢲⣤⠹⣿⣿⣿⣍⣿⡗⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡟⢠⡿⠀⣿⠏⠉⣄⢸⣿⣷⣿⣿⣿⣿⣟⢟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⣿⣧⠸⢣⣼⠋⠀⠀⠛⠋⣿⣿⣿⣿⣿⣿⣿⡙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⢠⣶⠾⠋⢉⣻⢿⣿⣿⣿⣟⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⢓⣀⠀⠸⣿⡿⠛⠻⢿⣴⠛⣿⣿⣿⣿⣆⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣾⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣿⣿⠛⢻⣀⡀⢀⠀⠀⠀⠀⠘⠊⠉⣿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⣤⡀⢰⣷⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠙⣿⡇⠀⢹⣿⣿⣾⣶⣾⢿⣿⡟⢿⣿⣷⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣿⣷⣶⣿⣿⣇⣉⡻⡇⢰⣿⣿⠛⣿⣽⣿⣿⣿⣿⠿⢷⣤⣴⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠡⣉⢻⣿⣿⣿⣿⣟⣾⣄⣀⣸⣿⣿⣿⣿⠟⠛⠒⠀⠘⠋⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⣾⡿⠿⠿⠛⠻⠛⠛⠛⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡄⢠⣶⠶⠆⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⡁⠈⠑⠉⠁⠀⠀⣼⣟⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡳⠿⣤⡀⠙⠛⠀⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣄⠈⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠷⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠘⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢠⣰⣷⣿⣿⣰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣿⣾⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⢠⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⢐⣾⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠔⠁⠀⢆⠀⠀⠀⡈⠰⣉⠔⠃⢘⡅

⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⡿⡿⢿⢿⠀⠀⠀⠀⠀⠀⣼⣛⣿⣷⣟⣧⠀⠀⠀⠀⠀⢀⣴⢶⣶⡶⣢⡄⠀⠀⠀⠀⢰⣶⣶⣴⣶⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠋⠀⠀⠀⠀⠀⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⣤⣼⣿⣿⣧⣄⠀⠀⠀⠀⠠⢶⣿⣷⣾⣿⡶⠤⠀⠀⠀⢀⣤⣤⣤⣿⣿⣟⡥⠀⠀⠀⠀⣤⣙⣿⣿⣟⣠⡄
⠀⠀⠀⠈⢩⣿⣿⣿⣿⡝⠁⠀⠀⠀⠘⣿⡿⣟⣛⢿⣿⠋⠀⠀⠀⠩⣾⣿⣿⣏⣡⣿⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠻⠿⣿⣿⡿⠟⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠛⣠⣾⣿⣦⠙⠃
⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⢀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢠⣾⣗⣄⠀⠀⠀⠀⠀⠀⠀⣰⣒⣢⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣷⣶⣦⡄
⠀⠀⠀⠀⢠⠼⡿⢿⠧⡄⠀⠀⠀⠀⠀⣠⣼⡿⢿⣯⣄⠀⠀⠀⠀⠀⢀⣿⡿⢛⣶⢶⡄⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⢇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⢹⣿⣿⣯⣿⡇⠀⠀⠀⢠⣾⣯⣿⠿⠿⠟⠃⠀⠀⠀⠚⢷⣿⡿⢻⣯⡿⠟
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠈⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠀⠀⠀⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⢄⡀⠀⠀⠀⢀⣀⣤⣤⣤⣤⢄⣀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣵⣿⡇⠀⠀⠀⠀⣽⣟⣯⣭⣛⣯⠅
⠀⠀⠀⠠⠼⣿⣿⣿⢿⠷⠄⠀⠀⠀⢢⣿⢿⣿⣿⡿⣟⣕⠀⠀⠀⣀⣿⣿⣿⣿⠿⣫⠖⠀⠀⠀⠀⠈⠻⣿⣿⡿⠟
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠈⠙⠁⠈⠋⠁⠀⠀⠀⠀⠐⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠒⠋⠉⠉⠉⠉⠉⠙⠒⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠐⠀⠀⠀⠘⢢⠐⠀⠀⠀⠂⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡀⠀⠀⠀⠉⠁⠀⠴⡀⠙⠃⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠉⠢⣄⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⣀⠴⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢸⠀⠀⠀⠉⠒⢢⠤⠤⠤⠤⡄⠒⠘⠁⠀⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡀⠔⠁⠀⠀⢸⠁⠀⠀⠀⠀⢠⡄⠒⡄⠀⢰⡏⠉⢲⡀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠈⠁⠐⠒⠒⠒⠒⠃⠉⠁⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⠀⠀⢷⡀⣹⡤⢾⣀⣠⠎⠈⣳⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠈⣧⠴⠚⠁⣳⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢄⡤⠛⡿⠿⠛⠛⢿⡟⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⢀⡟⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⠏⠀⠀⢸⡁⠀⠀⠀⠀⠀⠈⠁⠀⡝⠉⠓⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣑⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⡜⠀⠀⠀⠀⠙⠦⢄⣀⣀⣄⡠⠴⠚⠁⠀⠀⠀⠹⡋⠛⢤⠀⠀⣀⡤⠚⠅⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠉⢸⠁⠀⢠⠃⠀⣠⣴⣤⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣯⠉⠀⢁⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⢀⡷⠚⢧⢀⡏⠀⠀⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⣽⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠋⠀⠀⠀⢹⠁⠀⠀⠘⢿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡴⠃
⠀⠀⠀⠀⠀⣀⡤⠯⣼⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡸⠁⠀⠀⠈⢳⠀⠀⠀⢠⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢀⠴⠚⣉⣧⡀⠀⠀⠀⣼⣄⠀⠀⠸⢇⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⢸⡇
⠹⣤⠞⠁⢠⠛⢲⠶⠻⣄⠘⢦⡀⠀⠀⠘⡋⠲⠦⢤⣄⣀⣀⣀⠘⠂⠀⠀⠀⣀⣀⣀⣠⣤⡴⠖⠊⠁
⠀⠈⠳⢴⡇⠀⢸⠀⠀⠈⠚⠋⠀⠀⠀⠀⣱⠖⠒⠶⢄⠈⠉⠉⠉⠉⠉⢉⡽⠿⠿⢤⡀⢀⠃
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢣⡶⠒⠠⡀⠳⡀⠀⠀⠀⣴⠃⡠⠄⠲⣾⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⣿⠴⠁⠀⠀⠀⢹⣴⣇⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠓⠛⠓⢾⡁⠀⠀⠀⠀⠀⠀⠀⣹⠶⠒⠛⠛⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⣀⣀⣠⠗⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠛⠋⢽⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠛⠩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠚⠛⠒⠒⠤⢄⣧⠀⠀⠀⠀⠀⠀⢠⣇⠤⠄⠒⠚⢓⠶⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢠⠈⠁⡠⠀⠀⠈⠳⣄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠙⣁⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⢤⠤⠤⡤⠤⠤⡶⠴⠤⠤⠤⠤⢾⠀⠀⣾⢠⡤⠤⡤⠤⢤⡤⠤⢤⡤⠤⣤⠄⢾
⣀⣀⣀⣀⣀⣀⣀⣀⣽⣶⣾⣶⣶⣷⣴⣴⣷⣦⣶⣶⣴⣶⣾⣄⣀⣿⣴⣦⣤⣷⣤⣴⣦⣤⣴⣦⣤⣶⣤⣾⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⡀⠀⠀⠀⠰⡆⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢏⠀⡗⠀⠀⡇⠀⢸⠂⢸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠳⡈⢢⠀⡇⡴⠋⡔⠋⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⡔⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣟⡍⣭⢹⣭⡍⣭⣩⣩⡝⣿⣿⣀⣀⣀⣀⣀⡤⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⣀⣀⣀⣀⣿⣿⣯⣥⣭⣬⣭⣥⣭⣭⣬⡅⣿⣿⣀⣀⣀⣀⣀⠔⠉⠉
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠉⠉⠉⠉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠉⠉⠉⠉⠉⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠔⢁⠜⠀⡇⠳⣄⠣⡀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣇⠀⡧⠀⠀⡇⠀⢸⠄⢹⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠁⠀⠀⠀⠰⠇⠀⠀⠀⠈⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠒⠂⠀⠀⠐⠆⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠴⡤⠀⠲⠚⠷⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⡦⡉⢩⣿⡆
⠀⠀⠀⠀⠀⠀⠈⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠆⢀⠀⣹⣥⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡀⠀⢀⠀⠈⠉⠀⠀⠀⣠⡄⠠⠾⠖⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠘⠀⢊⡅⠉⠁
⠀⠀⠀⠀⠀⠴⠦⠆⣤⠀⢺⡄⠸⡖⠀⠀⢀⣀⣀⠚⣁⣴⡖⣹⣠⡼⠃⣀⠀⠀⣧⣆⡀⠀⢀⡧⠚⢃⣠⠤⠚⠉
⠀⠀⠀⠀⠀⠠⡄⠀⠀⠌⠓⣽⡀⠁⠀⢠⢿⣽⣿⣿⢽⠟⠻⣿⣿⠛⢻⠟⡿⢹⣿⣦⣷⠄⣼⠁⠈⠁⠀⠐⠂⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠤⠄⠠⠤⣀⠁⢀⡢⠉⢁⡴⣸⣇⠸⣿⡁⣹⣷⣴⣞⠛⠃⣨⣦⡵⠻⢿⣿⣏⣼⣿⠿⠏⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⢷⡄⣺⢧⣨⣄⣚⡟⠃⢿⡁⢢⣼⣿⣯⢹⡅⠀⢀⣻⣄⣙⣛⣿⣿⣿⣾⣧⣷⡾⠂⡀⢀⡠⠤
⠀⠀⠀⠀⠄⠀⠻⠆⠁⢀⠀⢀⠹⠛⣿⣯⣿⣟⣆⠀⢀⡹⠛⠉⠉⠿⣿⢋⡿⠛⣽⣿⣿⣿⣿⣧⣤⣽⣿⣿⣾⣾⣏⣘
⠀⠀⢀⣠⣴⣦⡄⠂⠐⠀⠁⠇⢧⣈⠿⣿⣿⠋⠸⣷⠈⠗⠒⣴⣧⣬⡿⠀⣠⣾⠿⣿⣿⣽⡿⣹⡿⢿⣿⣿⣿⣋⡉⣽⢃⡁
⠀⢠⣾⠿⠿⢿⡇⠀⢼⣷⣀⣸⣤⡯⣶⣿⣿⠁⠠⡬⠀⠐⢈⢿⣿⣟⣶⣏⠙⠀⢀⣿⠿⠿⠗⢹⣿⣿⣿⡿⢿⢿⣷⢾⡇
⠀⠀⣷⣿⣷⠀⠹⡦⠀⢀⣼⣅⠀⠢⠾⠿⠛⢄⡀⠰⠀⠈⠀⠢⠀⢛⣩⣿⣿⣿⣿⠅⠀⠀⢈⣿⠋⣠⡶⣶⣷⠤⣹⠀⠇
⠀⠀⠈⠉⠀⠂⢸⣷⠻⠿⣿⢏⡀⠂⠀⢦⣤⣄⠙⠆⠀⠀⠀⢀⡻⠟⠁⣼⣷⠿⢿⣧⣀⣀⣴⡟⣶⣿⣤⣾⣿⡧⢸⣤⡾⠃⠀⠈
⠀⠀⢀⠂⢀⣀⠘⣟⠒⠙⣧⣎⢈⠀⠀⣈⣤⡙⠆⠤⡀⠐⠲⣄⡀⣀⣴⠁⠀⣀⣀⣙⡟⢛⣿⣷⣟⡀⢁⠀⢉⣥⣾⣍⣉⠴
⠀⠀⠈⠀⠀⢥⠴⣿⡇⢸⣿⢹⣿⣦⡾⢡⢿⡇⠈⣤⢿⣶⣾⡏⢰⠁⢠⡋⢉⣿⡿⣏⢙⢋⡸⣿⣿⣿⡿⣯⣿⣿⣿⣭⡄⠀⣀
⠀⠀⠀⠀⠀⠀⢄⠋⣄⣿⣧⠆⣉⣛⠸⢻⠘⢀⣿⣽⢋⠙⢻⣷⠄⠰⠊⠉⠀⠀⠀⠉⠉⠈⠙⠻⣿⣿⣴⣿⣿⣿⣿⣷⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡉⢻⡏⢡⣯⡙⠛⣁⠴⠛⣿⠧⠤⡄⠚⠉⠀⠀⠀⠀⣀⡤⣤⣤⣤⣤⣴⣶⣬⣽⣾⣿⣿⣿⠹⠟⠊⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣧⣴⠋⠀⢸⣟⣻⣁⣼⣴⠇⢀⣤⣴⡆⠀⣀⣴⣾⣯⡁⠀⢀⣄⠀⠀⣿⣿⡟⣭⡿⡿⠿⢿⣰⣄⠀⢹⠀⡀
⠀⠀⠀⠀⠀⠔⣨⡿⢿⣿⠄⢀⣾⣟⡚⢻⠟⠁⠀⠀⠀⢉⣵⣾⣿⣿⠉⣟⠓⢶⣿⣿⣷⣤⣽⣿⢺⣿⣷⡶⠁⢸⡿⠿⠷⢿⣄⠅
⠀⠀⠀⠀⠐⢻⡿⢳⠘⢿⣆⡜⢻⣧⠕⠁⠀⠀⠀⣠⡾⠟⣿⡟⢹⣧⣼⣿⣦⣸⣿⣿⣿⣿⣿⣿⡿⠉⢻⣿⣿⣿⣷⣞⣃⣠⠁⡽
⠀⠀⠀⠀⠀⡀⢦⡁⢤⡄⢉⡷⠘⠁⠀⠀⠀⣠⣾⣟⡠⠾⠛⢿⣿⡿⠛⠛⠛⣿⣿⡿⠋⠉⠀⢸⣧⢀⣼⠇⣸⣿⣿⣟⠻⣿⣆⢱
⠀⠀⠀⠁⣀⡶⣸⢐⣆⠔⠊⠀⠀⠀⢀⣤⡿⣿⣏⣍⣁⡉⠘⠀⠓⡆⠐⠉⠉⣻⠣⣤⣠⡦⣤⡟⠃⠀⣽⣾⣿⢉⣿⣿⣷⣼⣿⠚⡄
⠀⠀⠀⠀⠀⠈⠉⠛⠶⢶⣄⡀⢴⡾⠟⢫⡁⠈⠲⣦⣬⡉⠉⣛⣻⣛⣶⠶⢿⣿⣶⡁⣨⡀⣀⣷⠖⠾⣯⣀⣿⣿⣿⣿⣿⣿⣿⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠅⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⣽⣶⣿⠟⠉⢀⠀⠀⠁⠀⢙⣯⡈⢉⣅⠀⣠⣿⠁⠀⣹⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⣤⡤⠮⠙⢫⣥⠀⢩⠀⠀⠀⠈⠀⠀⠀⢀⣴⣿⣿⡇⢠⣿⡏⠀⠀⠀⠀⣸⣿⣿⣿⡉⡉⠉⠁⠀⣾⠛⣧⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⢀⣿⣿⣿⣇⠈⢿⡃⢠⣤⣀⣀⣿⣿⡾⠛⣹⣿⣿⣤⣤⣿⣤⡿⠋⢻⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢦⣤⣶⣾⣃⣴⣿⣿⣿⣿⡿⣿⠿⠣⢤⣬⣿⣿⡿⢿⣿⣷⣾⡿⣏⡙⣷⣤⠞⠓⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠛⠿⠛⠛⡉⡉⠁⠀⠛⠄⠀⣀⣤⣤⠞⠉⢿⠿⠿⠋⠐⠈⠗⠛⠁⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠾⣀⣿⣿⡾⢶⣟⠋⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣄⣤⡄⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣷⡟⡹⠃⠀⠀⢠⣤⣤⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠀⠀⠀⡙⠄⠠⢱⡄⢈⣉⡉⠛⢿⣿⡁⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⠲⢂⠊⠀⡀⠄⠁⠐⠈⠛⠿⡶⢼⠻⠿⠂⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⡏⠄⠘⢄⠀⠀⠖⡀⢀⡄⡍⣁⠀⢠⠀⠀⡾⣻⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⡁⢴⣞⣻⣤⡦⠀⠰⠈⠀⠈⠀⠉⠓⢌⠀⠐⠛⢿⡮⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀⣀⠀⠬⡹⠛⣍⡀⠁⠢⡐⢂⣈⡅⢀⢀⠐⠂⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢘⣄⢀⡀⣀⠜⠛⠋⠀⣎⣸⠛⡑⡃⢄⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⣄⠈⠀⠀⡀⠃⡔⠁⡀⣀⣈⢫⠑⡆⢀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠧⠈⣁⣠⡅⠀⠀⠀⠁⢉⡁⠀⠆⠀⠸⠏⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣭⡀⠉⠉⠁⠀⠰⠐⠂⣘⣁⣠⣀⠀⠨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠀⠀⠀⢠⣴⣦⡀⠀⠘⠻⠿⠃⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⡀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣇⠀⠀⠀⠀⣠⣤⣄⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠉⠀⠀⠀⠀⠉⠛⠿⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣦⣄⣀
⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠈⠋⢹⡇⠀⠀⠀⠀⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷⠀⠀⠀⠀⢸⡏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⢶⣆⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠛⠛⢸⣯⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢠⣤⣤⣤⣼⣷⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠶⠶⠶⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣿⣦⣤⣤⡄⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠄⠀⠀⠀⢸⡯⠀⠀⠀⠀⠠⣶⣶⣦⢸⡇⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣶⠶⠶⣿⣷⣶⣶⢶⠾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⠷⠶⠾⣿⡶⣶⣶⡶⢾⠇




⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⣀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠂⠤⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡊⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠠⣀⣀⡀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⢻⠸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⣿⣾⣾⣷⣶⣄⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣼⡀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣴⣿⣿⣿⡅⠳⢮⣽⣛⠙⠻⠀⠀⠀⠀⠀⠀⠝⢿⣿⣗⣀⡿⢻⠇⢸⣿⢹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⢸⣿⡿⢇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣼⡀⢸⣿⠚⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢋⣼⠁⠀⢸⣿⡇⠈⡄⠀⠀⠀⠀⠀⠀⠰⠀⠀⣠⠀⠀⠀⠀⠀⠀⠃⣿⡄⣾⡟⢼⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠠⢀⡏⢀⣿⠁⠀⢀⡟⣿⣿⠀⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣇⣿⠀⢸⣿⠃⢿⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⡼⠋⠀⠀⢸⡇⢹⣿⡄⠰⢿⣥⡀⠀⠀⠐⠲⢾⠥⠥⠖⠀⠀⠀⣠⠇⣤⣿⣿⠏⠀⠸⡟⠀⢸⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⠀⠀⠀⣸⡇⠘⣿⡇⠀⠈⢻⣿⣦⣄⠀⠀⠈⠁⠀⠀⣀⡴⢻⡟⠘⣿⣿⡏⠀⠂⣀⠃⠀⠀⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠀⠀⠀⢀⣿⣧⠀⢸⡇⠀⠀⢸⣿⣿⡇⠉⠲⢄⣠⠴⠚⠁⠀⢸⣇⣺⣿⣿⠅⠐⢠⡌⠀⠆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡄⠀⡄⣿⣿⡀⢸⡇⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣄⢀⣾⠁⣾⢄⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⠁⣿⣿⡇⢸⠃⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣼⡇⣸⢃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⣾⣧⢀⣿⣿⠀⣼⠀⠀⢸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣧⡿⢰⢯⣿⣿⠷⢄
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⠏⢻⣧⣿⡿⠀⡟⠸⢠⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠙⠻⡧⣼⣿⣿⣧⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⣿⡿⠃⣰⣦⣧⡿⠋⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠋⠀⠀⠀⢸⡇⣾⣿⣿⡿⡀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⣠⣿⡷⠋⠀⠀⠀⠈⠙⠓⠒⠦⠄⠴⠒⠊⠉⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⠀⢰⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⡄⣈⠀⠀⢹
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠸⢷⣸⣿⣿⡿⠋⠁⠀⠀⢸
⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⣿⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⣸
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢁⡾⠀⠀⠀⠀⠀⢠⠀⠀⠀⢰⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⣿⢿⡏⢋⡿⠀⠀⠀⠀⡿
⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠊⢸⣿⢃⡾⠁⠀⠀⠀⣇⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⠀⠀⠀⠘⣇⣸⣃⣾⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⣿⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⣀⡴⠞⡁
⠀⠀⠀⠀⡘⠈⠓⠊⠉⠉⠉⠁⠒⣿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⣿⣿⠁⠉⠀⣠⡾⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢹⣿⣿⠇⠤⠖⠊⡋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠴⠈⠁⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⢸⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⠄⢀⣁⣠⠴⢚⡩⠓⠈⣠⠬⠒⣫⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢀⢏⠀⠐⢹⠁⠀⠀⢐⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠄⠀⠀⢸⠀⣀⣴⠀⠀⢸⠀⠀⣠⠿⠤⠤⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡂⠀⠀⠠⡃
⠀⠀⠉⠁⠀⠁⠀⠀⠈⠛⠛⠛⠀⠀⠸⠶⠏⠀⠈⣡⠰⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆
⠀⠀⠀⠠⠄⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⡇⢀⠴⠧⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡿⠀⠀⢰⠒⠶⠠⢵⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠂
⠀⠀⣀⡀⠤⢶⠀⠀⢘⠀⣀⡥⠀⠀⢸⠀⠀⢀⣹⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⢐⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠘⠛⠭⠇⠀⠀⢸⣴⣚⡛⠁⢂⣡⠔⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⢘
⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⠷⠀⠀⢠⠤⠤⢤⣬⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣠⣾⠀⠀⢸⠀⢀⣠⠆⠀⠀⠀⠀⡀⠀⠴⢺⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⣹⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠞⠛⢒⠲⢤⣤⣴⠴⠋⠁⠀⢂⣀⢰⠉⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠂⣤⠶⠋⠁⠠⢐⡽⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⢒⣒⣛⣋⣉⢁⣈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠭⠉⢉⡽⠋⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠥⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⣾⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⣀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣸⠞⠋⠀⠁⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⢀⢠⡼⣉⠉⠉⣩⣯⣹⣿⣟⡄⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢟⡻⣾⣹⠁⠠⠾⠁⠉⠁⠉⡙⣯⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡛⠛⠃⠈⠀⠾⠃⠀⠀⠀⠀⠀⢀⣮⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠦⠼⠿⡃⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠉⠃⠔⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠰⠀⠈⠂⢀⢚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡐⢲⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡙⢀⡠⠴⡦⡀⠀⠀⠀⠀⢀⠖⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⢱⠀⡻⣭⠣⠀⣠⠔⠉⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠙⡇⠀⠀⠃⠉⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠀⠀⠀⠄⠀⠀⠀⠀⠀⡁⠀⡠⠈⠑⠆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⠉⠀⠀⠀⠀⠀⠰⠀⠀⢠⠂⠀⢠⠃⠀⠙⠆⡰⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡀⠀⡆⠀⠀⠀⠀⡅⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡘⢄⠀⠀⠀⡌⠀⠀⠃⠀⢡⠀⠣⡀⠀⠀⠐⠀⢰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢂⠀⠙⢌⠣⡀⡔⠀⠀⡘⠀⠀⠀⢀⠀⠀⠑⠠⠁⠀⣸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣁⣀⢀⠕⢺⠁⠀⡰⠉⠂⢀⢀⠈⠀⠀⠀⠀⠀⠀⢹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣸⠀⠠⠉⠀⢄⠀⠀⠀⠐⡄⠀⠀⠀⠀⠸⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣄⣄⣀⣠⠈⠆⡀⠠⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠁⠀⠊⠀⠈⠁⠁⠀⠁⠀⠀⠈⠉⠐⠄⡄⠀⠁⣄⠀⡈⠣⡀⠀⠀⠈⠠⠀⠉⠈⢄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⠐⠀⠘⠂⠀⠐⠒⠀⠀⠃⠐⠂⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣄⣀⣀⠀⢀⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢈⡿⣯⡶⠿⢾⣝⢿⠠⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀
⠀⠀⠀⠀⠀⠀⢰⣾⣿⡇⠰⣷⠀⣿⢾⣷⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢈⣧⡿⢦⣤⡼⣿⣾⠁⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠻⣿⠛⠉⣋⡼⣿⡽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⡃⢶⠄⣄⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣷⣶⣾⡿⠂⢄⠀⠀⠙⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠀⠁⠄⠀⠘⢦⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⡇⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⠄⠐⢃⣀⠭⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠔⠚⡈⠁⠀⠐⠢⣶⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠀⠀⠀⠄⠁⠘⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠒⠋⠉⠁⠀⠀⠉⠉⠓⠲⠦⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠦⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠒⠒⠒⢲⠀⠀⠀⠀⠀⢰⡖⠒⠒⢲⠄⠀⠀⠀⠀⠀⡖⠒⠒⢲⡆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡟⣉⣉⣉⣉⣉⣉⣉⢻⠀⣾⠉⠉⠉⠉⠉⠉⠉⢹⡆⢸⠋⠉⠉⠉⠉⠉⠉⠙⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧⣉⣉⣉⣉⣉⣉⣉⣸⠀⣿⠈⠉⠉⠉⠉⠉⠉⢸⡇⢸⠈⠉⠉⠉⠉⠉⠉⠁⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠉⠉⠉⠉⠉⠉⠉⢹⡇⢸⠈⠉⠉⠉⠉⠉⠉⠁⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠘⠛⠛⠛⠛⠛⠛⢸⡇⢸⠘⠛⠛⠛⠛⠛⠛⠁⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠒⠒⠒⠒⠒⠒⠒⢺⡇⢸⠐⠒⠒⠒⠒⠒⠒⠂⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠛⠒⠒⠒⠒⠒⠒⠒⠛⠓⠛⠒⠒⠒⠒⠒⠒⠒⠚⠓⠛⠓⠒⠒⠒⠒⠒⠒⠚⠓⠚⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠄⠠⠀⣀⠀⠀⢀⠀⢠⠀⠠⢠⠀⡀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠉⠁⠀⠁⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠈⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠳⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⣾⠹⠏⣻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⡽⠑⡟⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⡟⠀⠀⡏⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠾⣅⣀⣿⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣠⠖⠲⢦⣀⡇⠀⠀⡇⠀⢀⣀⡀⠙⢦⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠐⣇⠀⠀⢠⣿⡇⠀⢸⡇⡼⠉⠀⠙⣦⠘⣇⠀⠀⠀⠀⠀⠙⡦⠤⣄⣀⡀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣀⣈⣙⣚⣉⣸⣀⡀⣸⠀⠹⢤⣠⡴⠋⠀⣻⠀⠀⠀⠀⠀⣸⠃⠀⠀⢨⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠓⠒⠶⠶⠶⠤⢾⠀⠀⠀⠀⢀⡟⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠐⠒⠒⠒⠀⠠⠤⠤⠤⢄⠀⡰⠀⠀⠀⠀⣸⠁⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢀⡴⠖⠒⣶⠰⢰⣶⠒⠒⠓⠒⠒⠒⠒⠲⠖⠒⠶⠲⠶⠶⠶⠿⠶⠶⣶⢠⡀⢀⡇⠀⠀⠀⡼
⠀⠀⠀⠀⠀⣠⠏⠀⠀⢠⠏⠃⢸⣿⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⣿⠰⠉⡽⠀⠀⠀⣰⠃
⠀⠀⠀⠀⢠⠏⠀⠀⠀⡾⠤⠆⠈⣿⡀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢸⡟⠸⢶⠃⠀⣀⡴⠃
⠀⠀⠀⠀⡞⠀⠀⠀⢰⠇⠀⠀⠀⢹⣧⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢀⣿⠁⢰⠉⠛⠋⠉
⠀⠀⠀⢰⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠹⣧⡀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢀⡾⠀⢠⡾⠃⠀⢸
⠀⠀⠀⡾⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠙⠦⣄⣀⣀⣀⡤⠞⣁⡴⠛⠀⠀⠀⢸
⢀⡴⠚⠷⢤⣄⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣤⣭⣭⡤⠶⠞⠋⠀⠀⠀⠀⠀⢸
⢏⠀⠀⠀⠀⠀⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡄⢠⡦⢤⣄⡀⢀⡗⠀⠀⢠⠀⣀⢠⣄⣤⣤⣤⣀⣤⣀⣀⣀⣀⣀⣠⣄⣠⣤⣤⣄⣀⣠
⠈⣇⠘⡇⢀⡞⢁⡾⠀⠀⠀⠀⠀⠁⠀⠙⢦⡀⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⡴⠋⠀⠁
⠀⠈⠙⠛⠚⠦⠾⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢦⡀⠀⣿⣄⣀⣀⣼⡀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⡤⠤⠤⢤⡉⠙⡇⠀⠈⠀⢸⠉⣽⠧⠤⠤⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠞⠁⠀⠀⠀⠛⢶⣇⠀⠀⠀⣸⠞⠃⠀⠀⠀⠘⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠶⠚⠋⠙⠒⠦⣄⣿⠀⠀⠀⣇⡤⠖⠛⠉⠓⠲⢤⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠈⢻⡀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣀⣀⣀⣀⣀⣀⣀⣀⣨⡇⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽