Soul food Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣶⢀⡀⣀⢀⣄⣤⡄⢶⡄⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣶⠛⠛⠀⠀⠀⡀⠀⠀⠀⢸⡇⢴⠰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⡏⠀⣿⣿⠀⡟⢸⡏⣼⢣⡿⠀⢸⠃⠒⠂⠀⠀⠀⠀⠀⢜⡼⠀⠀⣿⠀⡞⢹⡆⡾⢸⡆⡾⠘⣿⠀⠈⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⣿⡀⣸⡟⠻⠄⠓⠚⢃⠛⠘⠃⠀⠐⠛⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣇⢸⠇⢧⡸⠃⣇⣸⣟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡃⠈⢉⣿⢃⣴⡶⢤⡈⢉⣉⢙⠛⣩⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⣄⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡩⠀⢀⣾⠏⠈⢸⡇⢸⡇⣾⠁⣿⠀⣿⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⠈⠈⠁⠀⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠟⠁⠀⢠⣾⠀⣼⠃⠻⠟⠻⠀⠙⣾⠇⠀⠀⠀⠀⠀⠀⠀⣷⢻⣺⣦⡞⢠⡖⣿⢰⢠⡟⢀⡶⢸⡞⣹⢰⡟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠊⡡⠂⠈⠉⠉⢉⣽⠟⠲⠀⠀⠀⠀⠀⠀⠀⠿⠸⠸⡽⠧⠸⠧⠿⠸⠜⠧⠘⠧⠾⠁⢧⠜⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣤⡴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡤⣄⠐⠶⠤⠶⠶⠚⠛⠋⠓⠂⢀⡄⣄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⡆⠀⠀⣀⣀⡀⠀⠤⠠⠀⠀⣾⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⢧⠘⠧⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠟⠡⠿⢃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⡤⠤⠤⠄⢠⣿⢤⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣠⠖⠲⣄⢠⡄⠀⠀⣀⠀⢀⣀⡀⢠⡄⠈⡉⠁⠀⠀⠀⠀⠈⠉⠉⣿⡇⢀⠁⣀⠀⣾⠂⢸⡇⠀⠀⢰⡿⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢰⠏⣹⠇⣤⠶⢀⣄⠉⡴⢦⢹⡇⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⢠⡿⠀⠹⣷⣼⡇⠀⠀⠼⠡⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣦⠀⣿⠀⡇⠀⣿⢸⢺⡗⢻⣻⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⢠⣿⠀⢿⡜⠷⠌⠻⠟⠁⠛⠊⠀⠀⠛⠛⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣁⣹⠀⢹⣄⠁⠀⠿⠼⠀⠑⠊⠸⠄⠀⠀⠀⠀⠀⠀⠀⢧⣀⡾⠋⠀⢀⣤⡶⣄⠀⣀⣀⡀⢠⣆⢀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣭⠒⠛⠶⠀⠂⠐⣒⠛⠛⠓⠂⢰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠰⠏⢈⣉⣁⡈⢹⡏⠉⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⢀⡤⢤⠀⣾⠁⣷⠀⣴⠛⣾⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⣨⡿⠀⢠⣿⠉⣿⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⢸⡇⣿⠀⣿⢸⣟⠀⣿⠀⠀⠀⠀⠀⠀⠈⠠⠒⠀⠀⠁⢠⣿⠀⠀⢸⣿⡴⠻⠦⠈⠓⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠇⠾⠁⠘⣚⣁⣀⡛⠂⠙⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠆⠈⠻⣦⠴⠃⣀⣤⠴⠶⠞⠛⠂⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠛⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠃⢸⠀⣤⣀⣇⣹⡩⣟⢾⣬⠢⣄⠀⠀⠀⠗⠚⠒⣿
⠀⢸⣄⣵⣈⣇⢾⠀⣿⢸⢸⠙⢾⣽⡢⣀⢢⣤⣤⣿⠀⠀⠀⠀⠂⠆
⣧⣺⣌⣟⠰⡇⢸⠀⡟⢸⢸⠀⢸⢸⠙⡷⣗⢄⡀⣿⠀⠀⠀⠀⢰⡈
⣿⣿⣿⣿⣶⣇⣸⠀⡆⢸⢸⠀⢸⢸⠀⡅⡟⠻⢿⣿⠀⠀⠀⠀⠈⠣⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠴
⠀⠈⠉⠛⠻⠿⣿⣻⣷⣾⣼⣀⢸⢺⠀⡇⣧⣼⣤⣿⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠈⢡⠀⠀⠂
⠀⠈⠀⠀⠀⠀⠠⠈⠙⠛⠿⢿⣟⣻⣶⣇⣏⢉⢹⣿⠀⠀⠀⠄⠀⠀⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠌⠂⢠⠔
⡀⢀⠠⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢉⠟⠛⠿⠿⠿⣿⠀⠀⠀⠀⠀⠉⠀⠈⢲⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⢀⢤⠑⠉⠄⠂⢸⠖
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠝⢀⡜⡀⣭⣠⣐⣡⣤⣤⣿⠀⠀⠀⠀⠀⠀⠁⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣼⠞⡀⠠⠔⡃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢭⣅⣀⡀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠿⣿⠁⢰⢀⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠜⢁⣸⣿⢰⣻⣃⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠫⠀⡛⠉⢉⣹⠀⠀⠂⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⣏⡇⣸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠁⠀⠀⣹⠀⠀⡤⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠖⠛⢸⣽⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠛⠁⠀⠄⠀⠀⣾⣏⣥⠗
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠋⠉⠀⠀⡀⠀⠀⠀⠀⠈⠙⠒⠀⠠⠀⠀⠐⠀⠀⡽⠛⠓⠂⠀⠤
⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃
⠀⠀⣤⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⣀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⣼⡇⠀⠀⠀⠀⠀⣼⡇⢀⡼⣳⡆⠀⠀⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⢋⡄⠀⣰⠃⡡⣼⣿⠴⠋⢠⡏⢠⡗⡔⢡⡾⠁⣠⠖⢢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⡿⢡⠚⣏⠠⠀⣿⠹⡇⠠⣿⠡⣿⠈⣰⡟⢁⣾⠃⠀⣾⠏⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠔⠘⠧⠊⠀⠀⠀⢠⡄⠀⣨⠀⢀⠀⠀⠐⠿⠘⠉⠓⢈⣼⠟⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠰⡄⣾⠀⠳⣾⠟⢻⡟⠉⣭⡄⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⣤⠀⢃⣶⠀⢰⣿⠀⣾⡇⢡⡿⠀⢰⠆⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢠⣿⢀⢹⡇⠄⣸⡇⠐⠟⠀⢸⡇⣠⠏⠀⠈⠉⢁⡄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⠙⠁⠀⠀⠀⠻⠇⣴⠋⠀⣀⡁⠀⠀⣶⠆⠀⣼⣵⡟⢁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢰⡆⢀⣼⠋⠀⣴⣿⢀⡀⢸⡟⠀⡰⢻⡟⠀⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢁⠔⢶⡀⠀⠉⢸⡏⠀⠐⣿⠀⠏⠀⠸⣇⠔⠁⠘⠧⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⣾⣥⠄⠀⠈⠛⠀⠀⠈⠁⡶⢰⡄⠀⠀⢰⠇⠀⡀⢀⣤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣼⠟⠯⢤⠀⣾⡄⢀⣼⠇⢰⢃⡮⢠⡞⢱⡟⢠⡟⠉⠸⣇⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢐⣽⠋⠀⠀⣿⢀⣿⠉⠃⣿⡰⠁⢾⠃⣾⠠⣿⠁⢿⠀⠀⡀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁⣠⠤⠀⠛⠀⠈⠀⠀⠀⠀⠀⡤⠀⠀⠀⠓⠀⠀⠀⠀⠷⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢀⣾⠃⠀⠀⠀⠀⠐⠛⠛⢛⡒⣾⠓⠀⢩⠍⠉⡭⠁⣐⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⠃⠀⣠⡆⢀⣼⠇⡤⣴⠏⣸⡇⠀⠀⠘⠁⠘⠇⠀⠧⠎⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⣼⣿⠠⠚⡿⠁⠋⠯⠀⠀⠙⢀⡘⠇⠀⠀⠁⠈⠁⠀⠀⠀⠀⢀⡞⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀⠉⠁⠀⢀⣀⠀⣼⠋⠀⠄⣔⡀⠢⠀⣶⠀⣰⡆⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠢⠌⢠⢠⢀⡊⠀⢹⣆⠀⠠⣿⠁⠘⢸⡏⢰⡟⠀⣾⠁⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠈⠀⠀⠀⣘⠈⠀⠂⠀⠠⢻⡇⠀⠛⠀⠀⠀⠁⠈⠁⠀⢿⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠰⢀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣴⢣⡔⣦⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠁⠐⢦⠈⣿⣻⣿⣿⣿⣿⢸⠱⣣⠞⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣰⣿⣹⣿⣿⣿⣿⡆⣠⣵⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⠀⢀⣾⣿⣿⠉⣿⣿⣿⣿⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⡀⢰⣿⣿⣿⢿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣰⣶⣿⣶⣶⢲⣼⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠈⣿⠁⣿⣿⣿⢿⣿⣿⣷⡟⣰⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⣿⠀⣿⣿⣿⢸⣿⠟⠛⠊⠉⠉⢉⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢸⣿⠀⣿⣿⣿⢸⣿⣷⣦⣤⣤⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠘⠻⠀⠿⠿⠿⠊⠿⠿⠿⠻⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣷⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢿⡟⣿⠙⣿⣿⡆⠀⠀⠀⠀⢀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡘⣷⠸⣇⢻⣿⣧⠀⠀⠀⠀⡄⢰⠁⠀⡀⡍⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⢻⡆⢿⡈⣿⣿⡀⠀⠀⠀⢠⢺⡄⠀⣧⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡈⣷⠸⣧⣹⣿⡇⠀⠀⠀⠀⣾⣷⡄⡿⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⢸⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⣹⣿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢀⡤⠤⢤⡀⠀⣿⣿⠀⢀⡤⠤⢤⡀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠃⡄⠀⠀⣷⠀⣿⣿⠀⢼⠀⠀⢠⠘⣶⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠒⠿⣿⠀⢳⣤⣴⣇⣀⣿⣿⣀⣼⣦⣤⡞⠀⣿⠿⠒⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⡶⠀⠀⠈⣷⠋⢀⡤⠄⠈⢻⡟⠁⠠⢤⡀⠙⣾⠁⠀⠀⢦⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⣠⠴⠶⠦⢼⠁⠀⢸⡀⡤⠚⢋⡿⣦⠸⣄⠀⢀⡼⢧⣀⠀⣠⠇⡴⢿⡙⠓⢄⢀⡗⠀⠀⡧⠴⠶⠦⣄
⠀⠀⠀⠀⠀⡞⠁⠴⠲⣄⠈⢧⠀⠈⢹⡗⢾⠉⠀⣸⠀⠈⠉⠉⠀⠀⠉⠉⠁⠀⣇⠀⠙⡷⠺⡟⠁⠀⣸⠁⣠⠖⠦⠈⢳
⠀⠀⠀⠀⠀⢷⡀⠀⣠⠞⠀⠈⠳⣄⣘⣇⠈⠓⠚⠁⢀⡀⠀⣤⠀⠀⣤⠀⢀⡀⠈⠛⠚⠁⣸⣃⣠⠞⠁⠀⠻⣄⠀⢀⡾
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠘⠿⠁⠈⠿⠃⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉
⠀⢠⣶⡶⢦⡄⠀⢀⣴⣶⠶⣦⢰⣆⠀⠀⣴⣴⡄⠀⠀⠀⠀⠀⠀⣴⡶⠶⠶⠶⠶⠀⢀⣴⡶⠶⣆⠀⢀⣴⣶⠶⣦⢠⡄⣠⠶⢶⡀
⠀⠸⣿⣦⣀⠀⢀⣾⡟⠀⠀⢸⣿⣿⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⣿⡷⠶⠶⠶⠆⢀⣿⠏⠀⠀⢹⢀⣾⡏⠀⠀⢸⣾⡿⠁⠀⣼⠁
⠀⠀⠀⠙⢿⣆⢸⣿⠀⠀⠀⣸⢹⣿⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⣸⢸⣿⠀⠀⠀⣸⢹⣇⠀⣰⠏
⠀⢠⠀⠀⢸⣿⢸⣿⠀⠀⢠⠏⢸⣿⡄⠀⡿⢸⣷⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⢠⠇⢸⣿⠀⠀⢠⠏⢸⣿⣰⠏
⠀⠘⠷⣴⠾⠋⠈⠻⣷⡶⠋⠀⠀⠻⣷⠾⠃⠘⣿⠴⠚⠁⠀⠀⠀⢿⠇⠀⠀⠀⠀⠈⠿⣷⡶⠋⠀⠈⠻⣷⡶⠋⠀⠈⣿⠏
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢠⣆⠀⢠⣆⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⡟⠉⠉⢻⡉⠉⢉⡽⠛⣹⠋⢉⣉⡉⠉⠉⠁⠙⠏⠀⠙⠏⠀⠉⠉⢉⣉⡉⠙⣯⠙⠯⡉⠉⢉⡝⠋⠉⠻⡄
⠀⠀⠀⠀⠸⡇⠠⣤⡴⠃⢠⠏⠀⢀⣿⣤⣏⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⣹⣤⣼⡀⠀⠙⣆⠘⢧⣤⠄⢀⡇
⠀⠀⠀⠀⠀⠙⠲⠤⡤⠤⣟⠀⠀⡟⠙⢦⣈⣳⣤⠇⡶⠋⠉⠳⣤⠞⠉⠉⢳⡘⢦⣞⣁⡠⠋⢹⡄⠀⢹⠦⠤⠤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠳⡄⠀⠈⢹⣇⠀⠓⠤⠀⢀⡿⡀⠀⠤⠞⠀⣸⣏⠁⠀⢠⠞⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣠⢴⡏⢀⡽⠶⣶⠒⠋⠀⠉⠓⣶⠶⢾⡁⢹⣦⣤⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠸⠀⠀⢘⡆⠀⠀⠀⠀⡇⠀⠀⠇⣸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠷⣶⣤⣄⡀
⠀⠀⣀⣴⣾⠟⠉⠁⠀⠀⠀⠀⢀⣤⣶⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣤⡀
⠀⣴⣿⣿⢃⣀⣠⣀⡀⢀⣤⡾⣿⣿⣿⠋⠉⢻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⡀
⢰⣿⣿⣿⠋⠉⠙⣿⣿⣿⡋⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢶⣤⡀⠀⠀⠀⠀⠉⠻⣶⣄
⠸⣿⣿⣿⠀⢀⣼⣿⣿⣿⡇⠘⣿⣿⣷⡀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⢀⡈⠻⣷⡀
⠀⠙⢿⣿⣤⣿⣣⣿⡿⠟⠀⠀⠈⠙⠛⠛⠛⢩⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠘⢿⣆
⠀⠀⠀⣸⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣶⠖⠛⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣀⣀⠀⠀⣀⠀⣀⠀⣼⡷⠁⠀⠀⠀⢻⣦
⠀⠀⢰⡿⠁⠀⠀⢀⣀⣀⣀⣀⣀⣚⣛⣋⣉⢰⣿⣿⣇⠀⠀⠀⣿⣿⡷⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⡾⣿⡋⡇⣼⡟⢰⡟⠀⣿⠁⠀⠀⠀⠀⠀⢿⡆
⠀⠀⣾⠇⠀⠀⠀⢸⣿⡿⠿⠿⠿⠿⠿⣿⠏⠀⠻⢿⣿⣿⣶⣼⣟⡋⠁⠀⠀⣼⠿⠃⠀⠀⠀⠀⠀⢰⣿⠀⢸⣇⣈⡿⠛⣿⣀⢾⣡⠜⣿⣠⠞⠀⠀⠀⠀⠸⣿
⠀⠀⣿⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⢀⣾⠃⠀⢠⣴⣾⠏⠙⠻⢿⣿⣿⣦⠀⠀⠸⣆⠀⠀⠀⠀⠀⣠⡾⠃⠀⣀⣉⣁⡀⠀⠈⠁⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⢿⣿⣿⡀⠀⠀⠀⣹⣿⣿⠁⠀⠀⠈⠓⠶⠶⠶⠚⠉⠀⣠⡾⠋⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠈⠙⠻⠷⠦⠤⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣿
⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣇⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⣾⠏
⠀⠀⠀⢹⣧⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠋⠉⣿⡏⠁⣠⣤⡀⠀⣠⣤⣀⠀⢀⣀⣾⡗⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡆⠀⠀⠀⠀⠀⢰⣿⠀⣼⠿⣇⡙⣸⠿⣯⣙⣰⡏⢈⣿⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⠀⣼⠏⠀⠻⡤⠟⠁⠻⣤⠜⠉⠹⠴⠋⠿⠴⠁⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⣶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣠⣴⡆⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠛⠛⣿⣿⢿⣿⣿⣷⣦⣴⣾⠿⠋⠀⠀⠀⠀⢀⣴⣾⣿⡿⠋⠀⠀⠉⠉⠁⠀⢉⣿⣿⣿⣷⣄
⢠⣤⡀⠀⠀⣠⢟⣿⣿⣿⡄⢠⣿⡇⠸⣿⠀⣿⣿⣿⣿⣦⡀⠀⠀⠀⣰⣿⣿⣿⣯⣤⣀⠀⠀⠀⠀⣠⣾⢿⣿⣿⢿⣿⣿⣧
⠀⢿⣷⡀⣼⡟⢸⣿⢹⣿⣷⢸⣿⡇⠀⣿⡇⣿⣿⠈⣻⣿⣿⣦⢀⣼⣿⡿⠋⠀⠀⠀⠈⠁⢀⣴⣾⠟⢁⣾⣿⠃⠈⣿⣿⣿⣇
⠀⠘⣿⣷⣿⡇⣾⡿⠀⣿⣿⠸⣿⡇⠀⠀⠀⣿⣿⡿⠏⢈⣻⣿⣿⠟⢿⣷⣶⣶⡶⠶⢀⣴⣿⠿⢿⣦⣾⣿⠿⢿⡿⣿⣿⣿⣿⠿⢿⣶⡿⠿⣷⡄
⠀⠀⢹⣿⣿⣧⣿⣧⣤⣿⣿⡇⣿⡇⠀⠀⢀⣿⣏⢀⣴⣿⠏⣿⣿⣧⠀⠀⠀⠀⠀⢴⡿⠋⠁⠀⢠⣿⡿⠁⠀⠀⣠⣾⣿⣿⣿⠀⢸⣿⠀⠸⠛⠁
⠀⠀⢸⣿⣿⣿⣿⠋⠉⢹⣿⡇⢻⣷⠀⢀⡟⠻⣿⣿⠟⠁⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠀⠀⢀⣼⡿⣿⣿⣿⡇⢠⣾⣿
⠀⠀⢸⣿⣿⣿⣿⠀⠀⠈⣿⡇⠈⠿⣦⣾⠇⠀⠀⠀⠀⠀⠈⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣠⡿⠏⢰⣿⣿⣿⠃⢠⣿⡏
⢾⡄⢸⣿⢿⣿⣿⡀⠀⠀⠙⠃⠀⡀⠄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⣿⣏⣴⣿⣿⠃
⠀⠻⠟⠃⠘⣿⣿⣷⡄⠀⠀⠀⣎⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⣸⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠈⠉⠙⠳⡆⣠⠞⡷⣠⠖⢠⡞⢀⡞⠁⢈⡟⢉⡴⠻⢆⡴⢻⢆⡴⢋⡽⠁⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣄⠀⢀⡠⠞⠑⠧⠖⠀⠏⠀⠯⠀⠻⠠⠀⡜⠀⠺⠤⠂⠺⠤⠂⠺⠄⠚⢄⣼⣿⠟⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠙⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠶⣾⡿⢠⣶⣶⣶⣶⣤⣄⣤⣤⣄⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠈⠛⢿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣼⣷⣤⣤⣤⣤⣤⣴⡆⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⠀⠀⠉⠙⣿⣿⣧
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⢧⡶⣶⣄⣿⣿⡟
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣶⣤⣀⡀⠀⠀⠀⠉⠙⠛⠿⠿⣿⠿⠿⠛⠛⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡉⠀⠑⠓⠛⠟⡝
⠀⠸⣿⣿⣿⣿⣿⣛⣿⠟⠛⠻⠿⠿⠿⠁⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⢀⣀⡀⣀⣤⡶⠞⠋⠉⠙⢿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣆⡙⠛⢁⡠⠊⠁
⠀⠀⢿⣿⣿⣿⠿⠿⡿⠂⠀⠀⠀⢠⡆⣠⠀⠀⠀⠀⠈⠉⠉⠉⣛⣻⣿⣿⣿⣯⣥⣀⣀⡀⠀⠀⡴⠋⠉⠉⠉⠀⠀⠀⠀⢻⣿⣏⣉⣀⣼⣦⣄
⠀⠀⠘⣿⣿⣿⡧⢠⠴⠶⠒⠲⢶⣾⠅⣯⡀⢀⣀⣤⣤⣶⣾⠿⠛⠁⠀⠉⠁⠀⠀⠉⠉⠛⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⣿⣿⣿⡆⠀⠀⠀⠀⢀⣀⣀⡀⢀⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢙⠁⠀⠀⠀⠀⠰⠀⣾⣿⣿⣠⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠷⠶⠶⠶⠟⠉⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠷⢦⣄⣀⡀⠀⢀⡼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⠀⣀⣀⣀⣀⡀⣀⡀⢀⣀⣀⣀⡀⠀⡀⠀⡀⠀⢀⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⣀⡴⠿⠀⣇⠀⢙⣧⣼⣽⡇⣬⠄⠈⠷⢿⣧⠀⣿⣿⣤⣧⣤⠈⢻⣿⢧⣼⠿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡁⠿⠿⡟⣀⡞⢩⡴⢤⣿⠿⠟⠁⠀⠀⠀⠀⠀⠉⢀⡘⠿⠿⠿⢋⡄⠈⢉⣀⡉⠀⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠁⡛⠉⣉⣥⣈⣁⠀⣉⠀⢀⠂⡐⠀⣀⣴⡖⣶⠈⣩⣶⣶⣦⣉⠁⠒⠀⡃⠈⡳⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣉⠀⣠⣾⣹⣿⣿⣿⣷⡄⢠⠀⠀⠀⠸⣻⣿⢾⣧⢀⣻⣿⣿⡿⢋⠐⢃⡔⠋⠉⣀⠆⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡏⢸⣏⡡⠏⣠⣃⠙⡀⠉⡀⣢⡀⠀⠀⣿⡿⠟⣡⠀⠛⠃⠉⠃⠚⢀⡋⠻⠷⠜⠛⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠓⠘⡿⠀⢽⠽⠏⠠⠘⡈⠁⣛⠀⢓⠂⠐⣀⠂⢀⣠⣴⣰⣶⠂⡀⠀⠈⠑⠐⡒⣠⢿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡈⠀⡾⠲⠶⠖⠄⠀⠀⠀⠛⠀⠛⠃⢘⠁⢠⣿⠟⣩⡟⠛⠃⣥⠠⠀⠤⠈⡧⠿⠟⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡿⣃⣿⣷⣶⣤⡰⠆⠈⣱⠏⠖⢰⣄⠁⠘⢀⣽⣥⣼⣿⣦⢀⣀⡸⠇⠀⠀⠈⠛⠐⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣏⣿⣿⣿⣿⣧⠗⠆⣿⣾⣧⣿⣳⠄⡿⠂⢹⣿⣶⣿⣿⣿⢻⣷⡄⠀⠀⠐⠿⡌⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⢍⡽⣛⢻⡆⠀⣻⣿⠿⠿⠛⠀⠹⠟⠂⠙⠁⢾⣻⣿⣿⠁⢻⠀⠀⠘⠿⠀⠠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠞⠠⠴⠧⣬⣷⣿⢿⣿⣷⣶⠠⠛⡂⢒⣂⠚⠶⠂⠘⣉⠚⠋⠀⠉⠲⠷⠰⠿⠣⡀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠲⠆⢶⣿⣻⣾⣿⣿⣿⣿⡼⠀⣥⣿⣿⡇⠷⣠⠶⠚⢉⣑⠲⡆⠰⢶⣰⣶⢀⣷⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⢻⣿⣿⡿⢫⣾⣿⠄⣰⡛⣿⣟⡄⣶⣁⣠⡶⠮⡉⣀⠘⣶⠚⣥⡼⢦⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣷⣦⠀⢹⡿⢲⣾⠛⣷⠀⢼⣿⣿⣿⠀⣿⡹⡿⣧⣤⣾⠟⢁⣿⡀⢨⣷⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠛⠛⠛⣡⡆⠀⢠⡤⠀⠀⢶⠠⣈⡁⢙⠚⢂⣧⠱⣄⡛⢛⣟⣠⡞⢠⣿⠳⣿⠻⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣴⣟⣿⣧⡄⠀⠉⠈⣄⣀⠗⠀⠀⣤⠲⠞⣿⡻⢦⣀⣤⠀⠍⢀⣤⣶⣤⣠⣀⢠⠄⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⣥⠈⣠⣎⡉⣀⣌⠁⣼⡯⠀⢸⣿⣷⣾⠽⣦⢀⣴⣿⣿⡿⣿⣿⡿⣇⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠀⠉⠑⠉⠠⣉⡛⠓⠊⠁⣬⣿⡇⠀⣿⣿⣿⣿⣟⣯⢸⣷⠔⣋⣰⣧⠈⣄⠀⡄⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣾⣿⠁⡄⠀⠀⠩⢈⣉⡶⣿⣽⣷⣶⣿⣿⣿⣽⣿⣍⣈⠿⠀⠺⠟⠏⠠⠈⡥⠀⣩⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣼⠋⠙⠁⢶⡰⠀⠒⢈⣞⠛⠋⣸⡭⠏⠿⢿⣛⣻⣿⣿⡄⣠⡟⠿⠟⠛⠒⢀⡠⣀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣶⣀⣠⡜⠃⠀⠁⢀⣙⢀⠛⠁⢀⠰⣶⣶⣾⠻⡿⣿⣧⣿⣿⣿⣶⣞⣋⠈⣹⡏⡞⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢿⣿⣯⣿⡿⡄⠀⠀⢈⣛⠆⠀⣄⢠⠈⠉⢋⢍⠀⢸⣿⣿⣿⣿⣿⣿⣷⠛⠃⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠀⠉⠀⠀⠈⠛⠀⠈⠉⠈⠀⠀⠈⠈⠀⠈⠉⠉⠙⠉⠉⠉⠉⠉⠀⠉⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⣿⣿⣿⣿⣦⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣸⡇⢈⣍⡉⣡⣄⢀⡀⣈⡉⣍⣉⠘⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠋⠀⢸⠈⣿⡇⣹⢸⢧⣿⠀⢸⡇⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠚⠋⠓⠛⠘⠘⠋⠀⠘⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢺⣿⣿⠉⠍⣿⡏⢽⣿⣿⣿⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⠿⠿⠦⠵⠿⠧⠭⠿⠿⠿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣟⣋⡁⢻⣄⡾⠃⣋⣻⣷⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣯⣤⡄⠀⣿⠀⠠⣤⣼⡿⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠂⠀⣰⡆⠀⢲⣄⠀⡆⢰⡖⠲⣆⠲⣄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⢰⣯⣽⡄⢸⠙⢶⡏⢸⡇⢀⡿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣍⢡⣭⣀⠀⠃⢘⣀⠀⢋⣈⠋⣉⢀⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⢸⣯⡍⠀⠀⠿⣽⡁⣿⢹⡇⣿⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⠸⠷⠶⢀⡀⠻⠚⠃⢻⣾⠃⠻⠾⠇⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣵⣶⠾⠆⣴⡿⢿⣷⠀⣴⡿⠻⣷⡀⣼⣷⣦⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣤⣤⢰⣿⠀⠀⣿⡇⣿⡇⠀⣿⡇⣿⡇⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠁⡀⢸⣿⠁⠀⠈⢿⣦⣴⡿⠁⢻⣷⣤⣿⠇⣿⣧⣴⡿⠃⠀⠈⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠁⠀⠈⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣰⡶⣦⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⢟⣛⣯⣭⣍⣛⣛⠛⠿⠿⠟⠋⢀⣿⡇⠀⢹⡇⠈⠥
⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⠋⣽⠍⣴⢟⣽⣯⡻⣯⣽⠿⢿⣿⣷⡶⠿⣿⣿⠁⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣀⡀⢸⡇⠀⠙⠄⣿⠈⠉⣿⣧⢻⡏⠀⢠⣿⡿⠀⠀⣿⡏⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠙⣿⠟⢿⡄⠀⠘⡏⠀⠀⣻⣟⢸⡅⠀⢸⣿⡇⠀⢠⣿⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⣧⠀⠸⣿⠏⣾⡇⠀⢸⣿⡄⠀⢸⡿⠀⢰⣿⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⢿⢇⣰⣿⣦⣄⣩⣾⣯⣿⣦⣬⣾⣷⣀⣈⣵⣧⣀⣃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⢋⣥⣤⣤⣤⣤⣈⣉⡉⠛⠛⠿⠿⠿⠿⠿⢛⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠅⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠷⠶⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⣀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⣶⣿⠉⣷⣄⠀⠀⠀⠀⡧⣿⢯⠷⡾⡿⢭⠂⠀⠀⠀⢾⡟⠉⠉⠉⣯⡆⠀⠀⠀⢀⣂⣂⣉⠈
⠀⠀⣿⣤⣿⣻⣏⣸⡆⠀⠀⠀⢈⣿⣯⣤⣼⣿⣁⠀⠀⠀⠀⡱⠆⢸⡷⠀⠶⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠹⢧⣼⣏⣨⠟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⢾⣧⣀⣀⣠⣟⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⣰⠁⠀⢘⡄⠀⠀⠀⢸⠙⠋⠋⢳⠃⠋⠋⢻⡇⠀⠀⣼⣛⣛⣛⣻⡄⠀⠀⠀⡠⠴⠟⠙⠋⠹⢶⣄⡀
⠀⠀⡼⡌⠀⠀⠀⡿⣆⠀⠀⢸⢀⣀⡀⣰⡀⣀⣀⣸⡇⠀⠀⠀⠙⣤⡜⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠘⠚⠒⠒⠒⠒⠚⠚⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⠠⠊⠀⠈⠢⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣀⣀⢀⡀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⣀⡠⠤⣲⣷⠀⠀⠀⣴⠤⣤⢦⡤⢶⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠻⡇⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⣭⣶⣾⣿⣿⣿⠀⠀⠀⢹⠀⣿⢸⡇⣾⠀⠀⠀⠛⢷⣾⢫⡙⣶⠟⠃
⠀⣴⡇⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠋⡟⠻⢿⣿⣿⣿⠀⠀⠀⢸⡆⣿⢸⡇⡿⠀⠀⠀⠀⢀⣿⡿⢿⣧
⠀⠉⠉⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠁⠀⠈⠉⠀⠀⠀⠘⠧⠿⠼⠶⠇⠀⠀⠀⠀⠚⠁⠀⠀⠙

⠀⠀⣀⣤⠤⣄⡀⠀⠀⠀⠀⢠⣺⣭⠷⣠⣚⣯⡷⡄⠀⠀⠀⢀⡤⡤⠤⠤⢤⢤⡀⠀⠀⠀⠀⡀⡀⠄⠄⠀⠂
⠀⣼⠛⣿⣤⡾⠻⡆⠀⠀⠀⠘⠯⣯⠝⠉⢯⣿⠽⠁⠀⠀⠀⠠⣛⠀⢠⣀⠀⣛⡇⠀⠀⠀⢰⣶⣶⣦⣦⣦⣤
⠀⣿⠟⢻⡾⠷⣶⡇⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠐⣭⠀⠘⠉⢨⣭⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠈⠳⠾⠷⠴⠋⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠉⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠛⠛⠿⠿⠿⢿⡟

⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⣬⠀⠀⠀⣣⠀⠀⠀⠀⡇⠁⠁⠁⠑⠁⠁⠁⠁⡇⠀⠀⠠⣯⣭⣭⣭⣽⠄⠀⠀⠀⡤⣶⣿⣁⠍⠠⠿⠷
⢀⣞⡇⠀⠀⠀⢨⢳⡀⠀⠀⡇⡀⡀⡀⡠⡀⡀⡀⡠⡇⠀⠀⠀⠀⢑⣴⡋⠀⠀⠀⠀⠀⢺⣿⣿⣿
⠘⠚⠒⠒⠒⠒⠚⠓⠃⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠔⠁⠀⠉⠢⠀⠀⠀⠀⠓⠒⠒⠂⠉⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣶⠀⠀⠀⢠⡬⣥⡤⣤⡬⣦⠀⠀⠀⠀⠀⠀⢰⣧
⢿⣿⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⢰⣖⣫⣥⣶⣾⣿⣿⠀⠀⠀⠘⡇⢸⡇⣸⠀⣿⠀⠀⠀⠲⣶⣶⠟⡟⢶⣶⠶
⣠⣿⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠘⠻⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⣷⢸⡇⣿⠀⡏⠀⠀⠀⠀⠀⣽⣾⣿⣾⡁
⠛⠛⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠈⠓⠒⠋⠉⠙⠻⠀⠀⠀⠀⣿⣸⣇⣿⣰⡇⠀⠀⠀⠀⠰⠟⠁⠈⠙⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠊⠀⢀⡀⠀⠀⠀⠀⠀⣰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⣹⠇⠀⠀⠀⠀⠀⠀⠀⢦⣤⣾⢃⣠⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠸⣿⠟⠋⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠛⠛⢋⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢱⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢀⡸⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⢠⣿⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣤⣴⣾⣿⡄
⠀⢀⣼⠏⡀⠁⡈⠁⡀⢀⡀⢀⡈⢓⡦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⣸⠋⡄⠁⡄⠁⡄⠁⡄⠁⡄⠁⡄⢁⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇
⢀⠃⠄⠀⠄⠀⠄⠠⠄⠠⠄⠠⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⢸⠂⠀⠂⠀⠂⠀⠂⠐⠂⠐⠂⠐⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇
⠚⣷⡃⡀⠃⣀⣧⣄⠃⡐⠃⡀⠃⡐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠈⠙⠷⣶⠟⠁⠉⠿⣅⡀⢁⡀⢁⣈⣥⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠛⠛⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠇⠈⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢷⠀⠀⠀⠀⠀⠀⠘⠛⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠁⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣦⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⣧⣄⠀⡀⠀⢀⣶⣿
⠀⠀⠀⢠⣴⣾⣿⠿⠛⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⣾⣿⣯⠋⠉⡁⠈⠹⣿⣿⠃⠀⠀⢀⠔⠛⠻⣆⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠀⠀⣿
⠀⠀⠀⠘⢿⣿⡄⠐⠛⠆⢦⡿⠋⠀⠀⠀⠊⢠⡀⢠⣻⠀⠀⢠⣴⡞⠉⠙⠛⠙⠃⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠟⠁
⠀⠀⠀⠀⠀⠉⣷⢉⢦⣼⣥⠀⠀⠀⠀⠘⠀⠀⢤⠿⣸⠀⠀⢺⣿⡇⠀⠀⠀⠀⢀⣿⣿⠆⠀⣀⡤⠤⠤⢦⣄⠀⠀⠀⠀⠠⠖⣨⡿⠉⠟⠃⠀⠈
⠀⠀⠀⠀⢠⣿⣿⣿⣆⠺⣴⣶⣶⣦⡀⠀⠀⠐⠒⠁⠇⠀⠀⠀⠻⠇⢀⡀⣀⠀⠸⠿⠋⠀⣼⠏⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣬⣥⡤⠚⣞⣶
⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠝⣻⣿⣹⣵⢲⡀⠲⣶⡆⠀⢀⡀⠀⡃⠰⡀⣒⠀⡄⠀⠈⠀⡀⣿⠢⢤⠀⢠⠤⠀⠟⠁⠀⣿⡇⣿⣿⢷⡶⣿⣿
⠀⢸⣿⠟⢋⢓⣾⣿⣿⣧⣤⣿⠟⠋⠁⠸⣿⣦⣽⣏⡀⠘⣷⡀⠀⢀⠀⠭⠀⠀⠖⠀⡠⠻⣜⣷⣾⣤⡄⠀⠀⠀⠀⢰⢁⣼⣋⠿⣤⡽⠿⢾⡇
⠀⠈⠛⠳⣤⣿⣿⣿⣻⣿⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⢷⡤⣀⡙⢸⣋⣡⣀⡔⠁⠀⠈⢿⣿⣟⡛⠀⠰⠀⠀⢸⣾⣿⣿⡒⢂⣠⣐⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠁⠀⣄⣄⣰⢿⣿⣽⣿⡿⠿⠋⠉⠀⠀⠀⠙⠁⠁⠀⠀⠀⠀⠺⢿⣻⡿⠿⠀⠀⠐⠈⠁⠀⢹⠿⣿⣿⣿⣿⣿⡿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⡽⠖⠚⡎⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠹⣿⣭⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠰⠀⠐⠀⠆⠄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⠀⠀⠄⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠘⠁
⠀⠀⡈⠀⠀⠀⠀⠀⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠁⠀⡠⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡀⠀⠀⠀⠀⠠⠂
⠀⠀⠐⠂⡀⣄⣤⡄⢠⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢴⡄⠀⠀⠀⣲⠂
⠀⠀⠀⠀⡀⠈⠐⠀⠀⠈⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠉⡔⡁
⠀⠀⠀⠀⠁⠖⣀⠶⢄⡀⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠲⠆⢸⡆⠀⡼⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⢀⠉⠐⠒
⠀⠀⠀⠀⠀⠂⠀⠙⠉⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⡆⢰⠁⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠐⠒⠠⢄⠄⠀⠈
⠀⢰⠋⠃⡇⣔⠀⡀⡀⢤⢠⠀⢆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠆⠀⠙⠂⠀⠉⠁⠀⠻⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣄⠀⡀⠀⠛⠛⣤⣀⠀⣀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠠⠀⢀⢀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⢀⡀⢆⠀⢀⠈⠉⡀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣦⡀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⢿⠀⡀⡞⠀⠉⢠⠸⢃⠗⢠⣀⡴⠀⠀⠀⠀⠀⢸⣷⠒⠋⢸⣧⠈⠒⣲⣿⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠘⢀⡀⠈⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⢐⣞⠠⠯⠬⠅⠡⠌⠋⢅⣲⠚⣄⡠⡴⠃⠀⠀⠀⠀⠀⢻⠙⠀⠀⠀⠀⠀⠀⠈⠀⢣⡀
⣧⣄⣀⠀⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠠⠠⠤⠀⠀⠀⠀⢀⠈⠉⠚⠁⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠄⠠⠠⠀⠀⠄⠀⠱
⠙⢿⣿⣤⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⢀⠁⢂⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣌⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⣄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣊⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠂⠀⠀⠉⠉⠉⠁⠈⠉⠁⠀⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣴⣀⡁⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⣿⣿⠿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢟⣿⣟⣹⣿⣿⣻⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⣿⣯⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣳⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣏⡛⣛⣽⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠈⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⠀⠄⠀⢀⠀⢠⡄⠤⠄⠒⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⢠⣄⣀⣠⣴⣶⣷⣞⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠋⠁⠀⠀⠀⠁⠀⠀⣠⠊
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡄⠤⠛⠉⠀⠀⠀⠀⠀⠈⢧⣄⣀⡀⠀⢀⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠶⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠀⠀⠀⠀⠀⠠⠄⠤⠤⠤⠭⠀⠀⠀⠶⠶⠶⠶⠴⠦⠀⠀⠀⠀⠀⣤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣦⣞⣠
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠐⠒⠒⠒⠒⠒⠒⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⣀⣀⣰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣖⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⣄⣶⡐⠨⠁⠈⠑⠄⠁⡤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⡒⠃⠀⠀⠀⠀⠀⢂⠀⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢠⢈⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠈⠂⠀⠐⠀⠀⡠⠄⠀⠈⡆⠀⠀⢀⠈⠈⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⠠⠪⠀⠀⠀⣠⡁⠀⠀⠈⢑⠀⡀⠠⡇⢀⠔⠁⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⣐⡄⢰⣦⠀⠀⠘⣿⠀⠀⠀⢀⠢⠀⠆⠘⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠈⠿⠃⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠃⠐⠀⢠⠊⢀⠰⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⠀⢉⠠⣥⠒⢁⠌⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠃⢠⠀⠀⢀⣀⠀⠤⠄⠒⠂⠉⠄⣦⣤⡆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⡕⠂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠈⠉⠉⠉⡙⠀⠀⠘⠋⠉⢹⠤⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⢸⠷⠿⠿⢿⠀⡀⢀⠄⠂⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⢠⣷⢶⣤⣤⣼⡆⡀⠌⠳⠤⢔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⠙⠿⢿⠠⢍⣯⣽⣌⢁⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠈⠈⠋⠉⠉⠈⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠁⠚⠊⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠒⠀⠁⢢⣀⡀⠀⠀⢡⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡔⠁⠑⣼⠄⠀⠈⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠬⡶⠃⢀⡇⢀⠥⠀⠊⣡⠤⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⢀⣠⠶⠋⠀⠰⠀⡀⠊⠁⠀⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠉⠀⠀⠀⠀⠀⠁⠈⠈⠀⠉⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣦⡤⣀⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⢀⠀⠀⢤⡤⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠉⠳⣤⣀⠈⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡃⢽⡶⣄⠈⠑⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⡀⠀⠀⠀⠀⠰⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⢯⡛⠶⣿⣯⣌⣲⣤⣄⠲⣴⡆⣀⡀⢤⣤⠤⠀⣀⡀⠀⡠⠀⠀⠈⣊⣤⠎⠳⠠⠄⠀⠙⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠓⠊⢤⣴⡒⠦⣛⣴⣤⣤⣄⡀⠀⠈⠓⣤⣤⣀⠞⠀⠀⡀⠚⢩⡼⠂⠀⠁⠀⣀⠴⢚⠤⣴⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠁⠀⠀⡐⠦⣤⣀⡀⠀⠈⠛⠷⠾⠇⣻⢿⣤⣿⣿⣟⡷⣮⣞⠉⠉⠒⠊⠀⠀⣀⣀⠠⠀⠂⠩⠐⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠠⠄⣸⠍⠙⠻⠻⢏⣹⠷⢋⣙⠛⠛⠁⠀⠀⠠⠖⠋⠉⠀⠀⠀⠒⠀⠁⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠤⡀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠀⠈⠉⠉⠴⠶⠾⠀⠀⠉⠀⠀⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠙⠛⠓⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠊⠳⡈⠳⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠤⠤⠤⠀⠀⠀⠒⠂⠈⠉⠉⠉⠉⠐⣀⠤⠷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⡀⠸⡄⠀⡀⠐⠠⣄⣀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⣖⠴⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠁⠀⣧⣄⣈⣓⠒⠀⠉⠉⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠤⠄⠉⠉⠉⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠼⠴⢦
⠀⠀⠀⠀⠀⠀⠀⡴⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⢉⡁⠁⣦⣄⠶⡄
⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠀⠀⠠⣀⠋
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠁⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣝⡛⣋⡙⢻⡟⣫⣿⢻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣄⡀⢠⡀⠀⣠⡄⠀⠀⠀⠀⠀⣶⡦⢀⠀⠀⠀⠀⠀⢀⣤⣾⣦⣄⠀⠀⠀⠀⠠⠐⠒⣄⡒⠀⠄
⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⣼⣿⡗⣲⡄⠀⠀⠀⠀⠛⠛⢻⠛⠛⠃⠀⠀⠀⢃⢠⡦⢐⣴⡆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣯⠀⠀⠀⠀⠀⣐⣀⣸⣀⣐⡀⠀⠀⠀⠨⢑⡨⠤⢂⡰⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⣾⡟⠛⠛⠛⣿⡆⠀⠀⠀⢸⡏⠉⠉⢹⡇⠀⠀⠀⠀⣴⡺⡽⣖⢄⠠⠀⠀⠀⢀⣤⣤⡄⣤⡤⣄
⠀⠀⡟⠀⠰⡇⠀⠙⡇⠀⠀⠀⢸⡷⠤⠤⢼⡇⠀⠀⠀⢸⢞⢎⢏⣎⣾⠀⠀⠀⠀⢸⣿⣿⣷⣿⣤⣿
⠀⠀⣿⣲⣴⢳⣴⣾⡇⠀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⠈⣯⢗⣷⣮⣎⠀⠀⠀⠀⠻⠟⠃⠀⠈⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉

⠀⠀⣦⣬⣀⣀⣥⣴⡄⠀⠀⠀⢠⣶⣾⣷⠂⠀⠀⠀⠀⠀⠀⢀⣒⣒⡀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⡄
⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠱⢆⣾⣿⠀⠀⠀⠀⢀⣿⡿⣿⣷⠄⠀⠀⠀⢸⣿⡏⣄⡌⣿⣿
⠀⠀⠿⠿⢿⡿⡿⠿⠃⠀⠀⠀⠈⠀⣾⣿⠿⠃⠀⠀⠀⠀⣼⣿⣷⣶⣶⣆⠀⠀⠀⠀⠉⢡⣟⣣⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠉⠃⠀⠀⠀⠀⢠⠖⢻⠛⠲⡄⠀⠀⠀⠀⠾⠮⠴⠧⠷⠇
⠀⠀⠀⢸⡁⠀⠀⢀⡀⠀⠀⠀⠀⠀⣹⠶⠀⠀⠀⠀⠀⠀⡟⠑⣾⣷⠊⣻⠀⠀⠀⢠⠀⢴⠄⢴⠄⢠
⠀⠀⣀⣀⣙⣲⣒⣋⡀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⠾⣅⣨⠶⠃⠀⠀⠀⠈⢶⣾⣶⣾⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡄⣤⢠⢶⡀⡄⡄⢴⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠌⠀⢸⠿⢻⢸⢸⡇⣿⠇⢸⢸⡇⠸⠓⡀⠰⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠢⠔⠀⢁⠀⠀⠆⠈⠠⠀⠠⠉⠁⠒⢠
⠀⠠⣐⣦⣤⣄⡢⡌⠁⡀⠀⠘⠀⠘⠈⠛⠁⠘⠀⠚⠈⠓⠀⠀⠀⠁⠀⠀⠈⠀⠀⠃⠐⢤⠀⠈⠂⠀⠀⡠⠃⠈⠇⠀⠀⢐⡀⣥⠀⣀⠴
⠀⠌⠛⠛⠋⠉⠀⠃⠀⠈⡆⠀⠈⠄⠀⢀⠄⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠆⡠⠃⠀⣬⠆⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⢀⢐⡀⣀
⠀⠄⠀⢿⣿⡗⠀⡬⠀⢂⣀⠀⠀⡼⠰⠄⠀⡀⣀⠀⠀⠃⠀⠀⠠⠞⠀⠀⠀⢀⠑⠐⡂⠡⠄⣀⠀⠀⠣⠀⡔⠉⠢⡀⠀⡰⠊⠁⠀⠀⣄⠑⡄
⠀⠈⠂⠠⠭⠀⠊⠀⡈⣤⣴⣶⣶⣶⣶⣦⣤⠀⠀⠈⠀⠃⠀⠀⢀⢀⡀⠀⠀⠀⡄⠙⠤⢄⠀⣻⠈⢈⠁⠸⠀⠀⠀⠓⡀⣄⠀⢁⠀⠌⠠⢀⠇
⠀⢀⠄⠠⠠⡀⠀⠀⡇⣿⣿⣷⣿⣟⣿⣿⣿⠀⠀⠀⡆⢰⠀⠀⠙⠺⠹⠈⠠⠀⠰⠀⠀⢛⠒⠚⠀⠂⡃⠘⡐⠀⠀⣈⠃⠈⠐⠀⠀⠀⠀⠁
⠀⠊⠀⠀⠀⠈⢂⠀⡇⣿⣿⡟⡿⣿⡿⢿⣿⠀⠀⠀⠆⠀⣤⠆⠂⠐⠒⠒⠒⠒⡖⠀⠀⠸⠀⠀⠀⠨⠁⠀⢱⠀⠀⡄⠀⠀⢠⢴⣯⡀⠀⠈⠢
⠰⣅⣀⣀⢀⣀⠃⠀⠇⠛⠿⠿⠿⠿⠿⠟⠣⠀⠀⢀⠀⠀⠉⠀⢀⡠⠄⠐⠀⠤⡀⠀⠀⠀⠆⠀⠀⡠⠀⠀⠈⠒⠒⠁⠀⠀⠁⠀⠈⢿⣄⠐⡰
⠀⢽⠔⠛⢸⡇⠀⠀⠸⠋⠉⠉⢉⣉⡉⠉⡈⠉⠻⠅⡠⠐⡠⢤⣌⡰⢄⠀⠀⡠⠄⢹⠒⠄⡀⠀⠀⡴⠒⠒⢠⡀⠀⠐⠄⠀⠐⢀⠀⠸⠿⠋
⠀⢺⢤⡄⢾⠀⠀⠀⠀⢸⠉⠀⠀⣠⡤⠀⠃⠀⢀⡐⠀⠠⡀⠀⠀⠀⢀⠀⢸⠀⠀⣘⠢⠱⠈⢄⠀⠀⠀⠒⡆⣶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠙⠲⠧⠟⠂⠀⠀⠀⠈⡄⠀⠠⡤⠛⠀⠸⠀⠑⢄⠀⠖⡱⠆⢩⠀⢊⠐⢚⡁⢎⠠⢊⠜⢀⠒⠀⠢⠄⠤⠬⠤⠤⠤⠊
⠀⠀⠀⢀⣤⣶⣶⣦⣀⠀⢃⠀⠀⠶⠐⠂⠀⡆⠀⠀⠑⠠⢀⠀⠀⠉⠉⠀⠀⠀⠀⢁⠠⠐⠁⠀⠀⠀⠀⢀⠠⢀⠀⠀⣿⣻⠏⣿⡟⣿⡏⡉⣿
⠀⠀⣴⢟⣭⡶⣶⣭⡻⣆⠘⠒⠒⠈⠉⠉⠀⠀⠀⠀⢀⣀⡤⡀⠀⠀⠀⠀⠀⢀⢠⠶⠤⠤⠀⢄⠀⠀⢠⠁⠀⠀⢑⠀⠟⠛⠛⠃⡀⠈⠛⠛⠛
⠀⠰⠿⠟⠁⠀⠈⠙⢳⢿⠀⢠⣴⣶⣶⣶⣶⣶⣶⡄⠈⢥⠜⠁⣀⡤⡄⠀⠼⢁⣄⡀⠀⠘⠃⠃⠀⠀⢸⠀⠀⠐⠘⡄⠀⠀⢘⠀⠉⠈⠈
⠀⢃⣀⡀⠀⠀⠀⠀⣄⣠⠀⢸⡏⠁⠸⠀⡏⠠⢸⡇⢠⣀⢶⡄⢈⣀⠀⠀⠄⠈⠛⢀⠔⠒⠤⣀⡸⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄
⠀⠀⢹⣷⣄⠀⢀⣼⣿⠀⠀⢸⣇⠀⡀⡄⠃⠰⢺⡇⠈⠁⠀⢠⣼⣙⠃⠀⠈⠒⠒⠁⠀⣀⠀⠀⢀⡀⠀⠑⢰⡶⠒⠁⢐⠀⠀⠀⠐⠈⠀⠐
⠐⠂⠘⠋⡻⠀⠘⢋⡙⠀⠀⢸⣿⢾⣷⣿⣾⣤⣾⣿⠀⠀⢀⠀⠈⡉⠀⠀⠀⠀⠀⠀⢺⠁⠋⠙⠛⠛⣿⣆⠘⠷⠇⠀⠺⣶⣿⣛⣓⣚⣻⣷⣾
⠀⠈⣠⣉⠤⡀⠀⠀⣈⡄⠀⣰⣿⠀⡇⡆⢀⠘⢸⣿⠀⢰⠓⠲⠾⠶⢾⠄⢄⠀⠀⠀⠇⠀⣘⢀⡀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢀⠿⠏⢀⡠⣿⣿⠿⠷⠀⠉⢿⣶⡷⠶⠿⠶⠾⠟⠀⢸⠀⠀⠄⠠⠀⠀⠀⠀⢀⡞⠋⡧⠰⠎⠀⡤⠢⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢈⠅⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⡀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠀⢠⠆⠌⠀⠸⡄⠀⡀⠀⠀⠀⠃⠀⢸⠀⠂⠀⠞⣀⣀⡀⠙⠀⠈⠀⠁
⠀⢀⡀⠤⠤⠤⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⠀⠀⢀⣀⡀⠀⠑⠀⠀⠀⠊⠀⠀⠰⠀⠘⠒⠁⠀⠀⠀⠧⠴⠃⠐⠀⠀⢼⣿⣿⣿⡗⠀⡠⠀⠐⠄
⠀⠂⠀⠀⠀⠀⠀⣳⠀⠀⡖⠃⠀⣀⠀⠀⠑⡄⢸⠀⠀⠉⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠄⠀⠀⡄⠀⠀⠙⡍⠉⠀⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠇⠀⠈⠿⢿⠀⠀⠃⠈⡀⠀⠀⠀⠀⠀⡥⠐⠭⠂⠀⠀⠀⢀⠄⠠⣀⠀⠀⣀⠀⢀⠇⠀⠀⢠⠇
⠀⠀⠀⠀⢶⠂⠀⢸⡀⠀⠀⠀⣀⠀⢀⣀⡀⠀⠀⠇⠀⠀⢀⠔⡨⢔⠁⠀⢀⠀⠀⠐⣵⡿⢷⡌⡆⠀⠜⠀⠣⡀⠀⢔⠺⠂⡄⠀⢸⠀⠘⠃
⠀⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⠟⠣⠞⠃⠈⠀⢀⠀⠀⠈⠁⠀⠸⠀⠀⠀⠠⡊⠀⠙⠾⠋⠈⠀⢸⡀⠀⠀⡄⠀⠀⠀⣤⡆⠀⠈⡄
⠀⠑⠚⠚⠛⠛⠛⠋⠀⠀⠑⠆⠀⠀⠀⠀⠀⠐⠃⠀⠉⠑⠒⠒⠢⠤⠆⠀⠀⠀⠈⠢⠠⠊⠀⠀⠀⠈⠑⠀⠊⠁⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢹⠶⠂⠦⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠒⠷⣦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⣿⠖⣤⡜⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠈⣟⢦⣽⣎⣒⢠⣈⡉⢄⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠫⠆⡠⢄⣀⠀⠈⠶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠓⠪⠋⣙⡯⣭⡹⣠⣉⣀⡉⠉⠉⠣⣀⣁⠀⠔⠁⠄⠠⠞⣡⠅⠀⠀⠀⠀⡮⢄⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠑⠀⠀⠐⢤⣄⡀⠀⠈⠛⠷⠼⡏⣻⣯⣽⣿⣷⣶⣼⡭⠙⠂⠒⠀⠀⠀⢁⡀⠀⠐⠃⠅⠂⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠳⣄⠀⠀⠀⠀⠀⡀⠈⣙⠳⢂⣦⣜⣎⡙⠛⠻⣛⣿⢾⣍⢛⡛⠁⠀⠀⠠⠚⠉⠁⠀⠀⠂⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⢤⣀⠀⠀⠀⠀⠀⠙⠒⠀⠈⠀⠀⢈⠐⡓⠺⠛⠃⠙⠁⠠⠤⠀⣀⣤⣅⡀⠀⠈⠀⡘⠋⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⢧⠈⢷⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠒⠒⠂⣀⠈⠉⠉⠀⠀⠈⠀⠀⣤⡐⠛⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢧⠀⡇⠀⢠⣈⠒⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⡗⠃⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠟⠓⠲⠤⠭⠀⠀⠀⠈⠶⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⢄⡀⣀⡈⠁⠉
⠀⠀⠀⠀⠀⠀⡉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠍⠉⠀⡈⠝⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠈⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⣶⡆⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠀⣿⣿⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢠⣿⣿⣿⣶⠀⠀⠀⠈⢻⣿⠿⣿⣿⡟⣱⣷⣶⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣾⡿⣿⣿⣿⡄⠀⠀⠀⠀⢁⣤⣻⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⣶⣿⡇⠋⠀⢸⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠀⣨⣍⡛⢧⡹⣿⣿⣿⣿⣇⡇⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠐⠻⢿⣿⢿⡏⢸⣿⣿⣿⣷⣄⣸⣿⣿⣿⢹⡇⠀⣸⣦⣽⣿⣿⣿⣿⡟⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢘⣯⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⢻⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣷⣿⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣯⣥⣷⣾⣧⣀⠀⣠⢽⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣙⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡽⠖⠀⠀⠘⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣰⣿⣍⠳⣜⠿⣿⠿⣟⣛⣛⡿⣿⣿⡿⣫⡵⢋⣥⣶⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣍⡛⢛⣋⣭⣭⣭⣙⠲⠶⠚⣫⣴⣿⡿⠋⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣠⣤⣴⣿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡄
⠀⢺⣿⣿⠟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⢠⣾⡿⠋⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⡿⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⣿⣿
⠘⣿⠇⠀⠀⢀⣴⣶⣾⣿⣿⣿⣿⣿⡇⠈⠟⠛⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠟⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠠⣄⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⢠⠀⡂⠀⠀⠀⣀⣤⣠⡈⡆⠀⠀⠀⠀⢰⠀⡄⠀⠀⢀⣴⠿⢿⣦⠀⠀⠀⠀⠀⡜⢃⠀⠀⠀⠀⠀⠀⣀
⠀⢸⣿⠻⠏⣿⡇⠀⠀⠀⣈⠀⠶⠀⠀⠀⣿⣿⠛⣿⡆⠀⠀⠐⣻⡏⠁⠁⠀⠀⢰⡇⢸⢀⡇⠀⠀⠘⣿⣤⣴⡿⠀⠀⠀⠀⠋⠠⠋⠀⠀⠀⣿⣫⣿⣻⡇
⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣒⢴⣲⠀⠀⠀⣠⣴⡞⢿⡆⠀⠀⠀⠉⠸⢃⡀⠀⠀⣾⢷⣶⡶⣶⠀⠀⢠⡤⡤⢠⢤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣠⣄⣄⠀⠀⠀⠀⠴⣷⡄
⠀⠀⢶⣿⣾⣿⠀⠀⠀⣷⣴⠿⠟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⣿⣿⣿⣿⠀⠀⢸⡆⡇⢠⣾⠀⠀⠰⣷⠀⠀⣾⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⢰⣿⡇



⠀⠰⠶⠆⠰⠆⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⣀⣠⣞⣟⡷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⢀⠀⠀⡀⠀⠀⢠⠤⠤⠤⠤⢤
⠀⢀⡀⠰⢆⡰⠆⠀⠀⢠⣄⢠⣤⠀⠀⠈⢿⡾⠾⠁⠁⠀⠀⣶⣦⣶⣤⣤⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⢺⣧⣼⠇⠀⠀⠀⢸⢡⡆⡟⠀⠀⢸⠹⠀⠇⠳⢸
⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠁

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣐⡿⢣⣤⡄⠀⠀⠀⠄⠛⣿⡆⠀⠀⣀⣀⣤⣄⡀⠀⠀⠠⠀⠀⢂⠀⠀⠀⠀⠀⢠⣮⠛⠀⠀⢠⠊⡉⣳⣀⡀⠀⠀⠀⢰⣦⡤⠀⠀⠀⣄⣰⡀⡄
⠀⠘⠿⢣⣾⠍⠀⠀⠘⣿⣦⡄⠈⠀⠀⠀⣿⡏⣶⢎⣿⠀⠀⠀⠱⣖⣻⡆⠀⠀⠀⡴⠟⠁⠀⠀⠀⠘⢄⣀⠜⠉⠁⠀⠀⠛⢻⣿⠟⠀⠀⠘⡘⢤⢼⡘
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠈


⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⣼⣿⣿⣧⠀⠀⢸⢾⡯⡭⡿⠇⠀⢀⣾⣶⣶⣾⣷⠀⠀⠠⠤⢤⠤⡄⠀⠀⢠⣼⣟⡷⣤⠀⠀⠀⠀⡖⠿⠀⠀⠀⠀⠀⡠⠚⠁⡀⠀⠀⣤⣶⠀⠀⡀
⠀⠀⠘⠾⠷⠃⠀⠀⠈⠀⠀⠁⠁⠀⠀⠈⠻⠟⠉⠻⠟⠀⠀⠠⠤⠦⠹⠄⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠶⠀⠚⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠛⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠐⠠⠢⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⡄⠀⠀⠀⠀⣿⠁⣿⠀⠀⠀⠀⠘⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄
⠀⢸⣿⡇⠈⠁⠀⠀⢰⣋⣟⣹⣏⡇⠀⠀⠘⠁⠀⠁⠀⠀⠀⠀⡏⠀⢹⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠦⢀⢀⠂
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠈⠁


⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣼⣿⣿⣼⣷⣶⣧⣼⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣷⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⣿⠏⢿⠀⠉⠙⢿⡆
⠀⠀⠀⠸⣿⡇⣿⣿⡟⠘⠋⠋⠅⠀⠀⠀⠉⠀⠈⡇⠀⠀⢀
⠀⡀⠀⢀⣿⣧⣸⣿⡇⠀⠀⠀⡆⠀⠀⠀⠂⠁⠀⡇⠀⠀⡄⠂⡄
⢆⠀⣠⣾⣿⣿⠏⢻⡇⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⢧
⠈⠛⠛⠛⠛⠁⠀⠀⢹⣄⢀⠀⠀⢸⣶⣶⡇⠀⠀⡸⠀⢀⠁⠇
⠀⠀⠀⠨⠐⠄⠀⠀⠘⠮⣅⡀⠀⠈⠁⠁⠀⣀⡜⠓⠆⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠄
⠀⠀⠀⠐⠂⠨⡢⠀⠀⡀⡔⠉⠑⠒⠒⠒⠋⠁⠘⡆⠁⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠂⠉⢲⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠶⠎⠀⠀⠁⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⣤⠤⠤⠶⢲⠾⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠲⣶⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⢀⣀⣴⣏⣀⣾⠄⡼⠀⠀⠀⠀⢸⣿⣭⣭⣍⣉⣹⣿⣿⣿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢑⢦⠞⠉⠉⠁⠀⠀⣠⢣⠎⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠱⡀⠀⠀⠀⠀⠀⠘⠛⠻⠷⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣵
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣴⠂⢠⣤⣤⣄⣀⠀⠀⣰⣧⣬⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣽⣿⣶⣿⣿⣿⣿⣿⣆⡀⣿⣯⣄⢠⣀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠹⠇⠹⢿⣿⣿⣿⣷⠸⡅⣩⠀⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡉⠀⣘⠃⠸⣿⣿⣿⣿⠤⣧⡙⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣦⣁⡴⠀⠻⣿⣿⣿⣶⠟⣿⠟⢀⣾⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠻⢻⠯⣤⡟⠀⠀⣀⣈⣋⠀⠀⠀⠘⣇⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠄⣌⢠⢠⠀⢈⠄⠀⠐⠙⠿⠈⠳⡆⠀⠀⢻⣿⣿⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡾⠃⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢇⠀⠀⢸⣿⣿⡆⠀⢌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣰⣤⣞⠰⣧⠚⣷⣄⣄⠀⠀⠃⠀⢀⣲⡏⢳⣿⠀⢸⢸⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠈⢿⡟⠁⢠⣿⣿⡿⠀⢰⠄⠀⣨⢷⡅⢈⣻⠀⢸⣾⣿⣿⡇⢠⣟⠃⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⣠⠟⠈⢻⡀⣰⠃⠀⣴⠋⣾⣯⣨⣿⠀⢘⣿⣿⣿⡇⠀⠈⢁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠻⠶⢀⠈⠃⠋⠐⠈⣧⠚⠉⠛⢿⡿⢀⣾⠛⠉⢹⡇⠐⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠧⣀⣠⡀⡇⠀⢀⠄⠈⡠⠊⠃⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡛⣡⣤⣴⡾⠁⠀⠀⢀⣴⡟⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⢠⣤⣴⠋⠀⠀⠀⠀⠠⠽⠋⠙⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⢀⠀⣿⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⣰⡏⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠀⠀⠀⢠⠀⠀⠀⠀⠱⡀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣀⢀⡀⠉⠀⣀⠴⠦⠀⠀⠀⠀⠀⠀⠕⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠠⣻⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠇⠀⡟⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣭⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⣗⡆⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣿⣧⡀⢫⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣷⡛⢃⣺⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡟⠉⠀⢠⡤⢠⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠻⠿

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⢀⠤⠒⡤⡀⠀⢀⡠⠤⣀⠀⢀⡀
⠀⠀⢸⠏⢳⣝⣿⣦⣙⣷⣌⠻⣿⣕⡄⠈⣁⠤⠐⠒⠉⠁⢡⡁⡇⠀⠘⠻⠅⠀⡓⢓⣈⣅⢡⠔⠡⡄⢖⡄⠱⡈⠉
⠀⠀⡾⢄⣀⣦⣤⢀⣀⠀⠈⠉⠉⠉⠁⢂⢀⠀⡀⠀⠀⠀⠘⠞⡇⢸⠲⠤⣔⣒⠽⣼⣧⠔⠉⡇⠉⡥⡠⣒⢂⠇
⠀⢠⠁⠉⠙⠃⠶⠾⣛⣩⣵⡶⠦⣤⡄⠀⠉⡏⡝⠉⣀⡒⠒⠓⠁⠘⠚⡲⠢⢌⡉⠑⠺⣿⠒⠸⢦⣭⡡⠴⠊⢀⡀
⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠫⠃⠀⢀⠑⠃⠀⠉⣁⢀⡀⠀⠀⢠⠃⠀⠀⠀⠉⠡⠀⠀⠀⠀⠀⠈⢳⠀⠛⠃
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠽⢿⠃⡤⠂⠉⠀⢀⠈⠉⠢⣌⠒⡦⠤⣀⡀⠀⠀⢀⠀⠀⠀⢀⠎⠉⠁⡹
⠀⢀⣍⠁⠒⠠⠤⢁⣀⠀⠀⠀⠀⡇⠀⠀⢀⠎⠀⠀⢆⠀⠸⠁⢀⡠⠈⢣⠈⠁⡒⢩⡝⡒⠤⢌⡀⠀⣜⡀⠀⢰⠁
⠀⠘⠉⣀⡤⠔⠊⠠⣀⣈⠉⠒⠒⠀⠀⣠⡿⠀⣀⣀⠠⠆⣘⠂⠁⢀⡀⠈⡆⠹⣛⣀⣉⠐⠚⠓⢡⣌⠀⠈⠲⠃⣤
⠀⢠⠊⡀⠀⠐⠑⠂⠀⠌⢳⠀⠲⠖⠛⠁⢠⡀⠀⢀⣠⢴⡀⠺⡁⡡⠁⢀⠇⡴⠇⠤⢈⠓⡄⠀⡠⡔⠂⠀⢲⣄⠉
⠀⢹⣦⠤⣀⣁⣀⣀⣀⣀⣼⠀⢠⠿⠴⣄⢄⢢⡀⠉⠒⠰⠇⠀⠑⠁⢀⠜⠀⣇⢐⡒⢡⡅⡇⢔⠑⠒⠒⣂⡭⡊
⠀⠸⣿⠀⣿⠀⣿⠇⣿⢸⠇⢀⡖⢔⣒⠨⡉⠃⠙⠢⢄⣀⣀⣀⡠⠔⠃⠰⠀⣿⢨⠬⢸⡇⢱⠀⢷⢋⣴⢟⣴⢷
⠀⠀⣿⡄⣿⠀⣿⢰⡏⡞⠀⡾⢁⡨⠙⠃⡉⠀⡀⠖⠠⢀⠶⠰⣖⠀⠉⣿⠀⢫⠃⠫⠄⡧⢸⠀⠘⣟⣵⠟⣡⠾
⠀⣤⠙⠓⠻⠶⠿⠾⠓⠁⣸⠐⢌⠛⣣⡐⠀⡾⠂⡖⠄⡘⠄⠀⣿⠆⠀⢻⡆⠘⢄⡀⣓⣠⠚⢠⡄⠘⣥⢞⣥⡾
⠀⣉⣤⣀⣠⣄⣠⣒⣂⣄⡈⠐⠀⠀⡰⡠⠊⠀⠠⠛⠂⠌⣃⣄⢩⣇⣀⣸⣇⡀⠀⣍⠉⠀⠀⢠⡀⠀⠀⠉⠀⢤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⠀⠘⢠⣤⢄⠀⠀⠀⠀⠉⢉⠾⣿⣴⣟⣻⢆⢀⣸⣧⠰⠆⢠⣀⣀⡀⠀⠀⣠
⠀⠉⠢⠠⠠⠂⠒⠤⠤⠔⠊⠘⠛⠁⠘⠠⠀⠀⠈⠑⡇⢀⠔⠁⢦⢆⠀⣤⠈⣿⠀⠀⢿⡄⢰⣽⡃⠀⠀⠀⡀⣹⠢
⠀⠐⠂⠒⠂⡆⠀⠀⠀⢀⠀⠀⠀⠐⠈⠐⠐⠉⠁⠀⠉⠁⡀⢴⠟⢢⠠⠁⠀⠶⡇⠀⢹⡇⢰⣏⢁⣀⠀⢤⣠⠀⣽
⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⠐⠦⡀⠀⠀⠀⠀⠐⢿⢶⠶⠥⢐⠡⠀⠠⠱⠑⡀⢸⣥⡀⠸⠗⣀⡙⢦⠑⣷⡺⢃⡴⠁
⠀⢰⠀⠀⠐⠀⣸⣿⣷⣿⣬⣀⣵⠄⠃⠀⠀⡄⠈⢢⠣⠀⠀⠰⢐⡂⡂⠱⠝⠀⠀⣠⠚⠁⠐⡵⡌⢻⣟⢻⣟⠐⠗
⠀⢸⣄⡠⠂⠀⠸⣄⡜⢛⣻⣿⠏⠀⠈⢀⣀⡇⠀⠀⢣⠑⡈⠚⣉⠡⠌⣁⠂⠀⢸⡠⠉⢀⢀⡤⣧⠋⡹⢧⡑⢷⡀
⠀⢸⠻⣄⠀⠀⠀⠈⠉⠸⠋⠁⠀⠀⠀⣠⠟⡇⠰⣿⡇⠛⠊⠀⢈⢦⣤⣤⠚⢥⠺⠓⠭⠔⡉⠀⢡⡜⠁⠀⠳⣾
⠀⠈⠓⠚⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠒⠂⠁⠀⠈⠙⠂⠀⠘⠋⠀⠊⠉⠉⠉⠁⠙⠂

⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠛⠛⠛⠻⠗⣀⡀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣤⣾⣿⣷⡀
⠀⠀⠀⠀⠀⣤⣀⣀⣰⣿⠷⠶⠿⠿⢿⡏⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿⣿⣿⣿⡿⠁⠀⢀⣀⣤⣴⡆
⠀⠀⠀⠀⠀⣿⠿⠿⢿⣿⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠈⠙⣻⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⢿⣿⠏⠉⠈⠁⠉⠉⠛⠿⠇
⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠖⠀⣤⣽⣿⣧⡄
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⣯
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢴⠆⢶⠆⢠⣾⣷⣶⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⡀
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀⠀⣾⠇⠀⢹⡇
⠀⠀⠀⠀⠀⠈⠉⢻⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠰⣦⠈⠻⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⢀⣤⠄⣠⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⢤⣶⣾⣿⣿⣿⣿⣿⣿⣷⡦
⠀⠀⠀⠀⠀⢀⠔⢹⠑⢄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠻⣘⡿⠿⠿⢿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠂
⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣶⣶⣶⣶⡆⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⢹⡿⣿⣿⢿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠯⠿⠿⠽⠽⠽⠿⠿⠯⠯⠯⠿⠿⠽⠽⠽⠽⠿⠇
⠀⠀⠀⠀⢸⡁⢀⣀⢈⣿⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣼⣿⣼⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣶⣶⣶⢲⢲⢲⣶⣶⡖⡖⣶⣶⣶⣶⢲⣲⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⣼⢃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣶⡄⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣀⣼⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⢱⣾⣿⣿⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⢠⣤⣶⠟⠋⠁⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠈⢿⠀⠀⣠⣾⣿⣿⠏
⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⣸⣿
⠀⠀⠀⠀⠀⢿⣏⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠈⠙⢶⣤⠀⠀⠀⠀⠀⠀⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢴⡟⠿⠿⣷⡄⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠲⡄⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⣷⡤⠜⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢠⡇⠀⠀⠀⠃⠀⠀⠄
⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣀⠤⠶⠒⠒⢤⣄⡀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠠⣤⣀⠀⠀⠀⣰⠏⠀⠀⢀⠊⠀⠀⠀⠀⠀⡴⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢠⣀⣀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠛⠢⠚⠋⠀⠀⠀⠀⠂⠁⠀⠀⠀⣰⣃⣄⣠⠖⠛⢇
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠂⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⠿⠿⣆⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠤⠤⠄⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣥⣤⣤⣽⡧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⡏⠉⠉⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡹⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣟⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠒⠶⠶⠾⠿⠛⠻⠿⠿⠿⠿⠷⠶⠶⠶⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠁⡇⣿⠀⠀⠀⠀⢾⣿⣿⣦⡄⠀⠀⢰⣾⣷⣿⣶⠀⠀⠐⡀⠐⢆⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣴⣤⣤⣄⣤⡀⠀⠀⡀⠠⠤⢀⡀⠀⠀⠀⠀⣠⣶⡄⠀⠀⢰⡖⣒⣒⢺⣶
⠀⠀⠀⠀⠀⠀⢹⣿⡿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠆⠀⠀⣠⣾⣿⣿⠿⠀⠀⢸⡇⠧⡼⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠁⠀⠀⠓⠀⠀⠘⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠋⠉⠉⠙⠉
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⡀⣄
⠀⠀⠀⠀⠀⠀⢸⣼⣶⣦⣦⡆⠀⠀⠀⠶⠾⠄⠀⠀⠀⣔⣻⢾⣳⡀⠀⠀⠀⢸⡛⠟⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣻⠞⠁⠀⠀⠀⣰⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡏⠉⠉⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠙⢻⠋⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡇⡀⠠⠤⠤⠔⠚⡣⠖⠉⠑⠶⡓⠒⠀⠠⠤⠤⠤⣅⠀⠀⠃
⡇⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠈⠑⠢⠤⢤⠄⠀⢸
⡇⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⠀⣠⡴⠒⠦⣄⡀⠀⠀⡇⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸
⡇⠀⠀⠀⡄⠀⠀⠀⠀⠃⠀⠀⢀⠃⠀⢸⠁⠀⠀⠀⠀⠀⢀⣀⡤⣜⠀⢀⠙⠁⠀⣏⠀⢀⠛⡄⠀⢹⠀⠀⢃⠀⠀⠀⠃⠀⠀⠀⠀⡄
⡇⠀⠀⠀⠇⠀⠀⠀⢠⠀⠀⠀⡘⠀⠀⡎⠀⠀⠀⢀⡴⠊⠉⠀⠀⠈⠉⠁⠙⠢⠴⠫⣑⡆⠀⣻⠀⠈⡄⠀⠘⡀⠀⠀⢠⠀⠀⠀⠀⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢰⠁⠀⢰⠒⠋⡀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡟⠀⠀⢱⠀⠀⠁⠀⠀⠘
⡇⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⢀⡇⠀⠀⢮⡀⣀⠠⠐⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢻⠀⡤⡀⠀⡇⠀⠀⠀⠀⠀⠇⠀⠀⢸
⡇⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠆⠀⡸⠀⠀⠀⠀⢳⠤⠤⠤⣄⣀⠤⠴⠦⠖⢚⡇⠀⠀⠀⠀⢸⡐⠁⢲⠀⠸⠀⠀⠆⠀⠀⢀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⢠⠃⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⢀⠀⣼⡁⠀⡈⠀⠀⢣⠀⠸⠀⠀⠈⠀⠀⠈
⡇⠀⠀⠀⢀⠀⠀⠀⠀⢀⠁⢀⠆⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠘⠀⠀⢸⡀⡴⠚⢣⣾⠕⠀⡐⠀⠀⠀⠀⢆⠀⢁⠀⠀⠀⠀⢀
⡇⠀⠀⠀⢸⠀⠀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠠⠄⠀⠀⠀⠀⠀⢉⣠⡶⠻⠋⠀⡰⠁⠀⠀⠀⠀⠘⡄⠀⡀⠀⠆⠀⢸
⡇⠀⠀⠀⢸⠀⢰⠀⢀⠁⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤⣤⠤⢲⣶⡈⠭⠡⠐⠁⠀⡰⠁⠀⠀⠀⠀⠀⠀⠱⡀⢡⠀⢰⠀⢸
⡇⠀⠀⠀⠀⠀⡄⠀⠂⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⡏⢰⠀⡸⠐⠀⠀⢀⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠂⠀⡄
⡇⠀⠀⠀⡆⢠⠀⡈⡰⠁⣀⠀⣒⢀⢔⠈⠀⠀⠀⠀⠀⡀⠠⡇⠈⠉⠀⠘⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⡀⢠⠀⡆
⡇⠀⠀⠀⠁⠄⠰⡰⠁⠀⠈⠀⠈⢻⠛⡎⠁⠈⠛⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡰⠈⠄⠁
⡇⠀⠀⠸⢀⢀⡞⠁⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠒⠤⠤⠒⠁⠀⠈⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⢀⠸
⡇⠀⢀⢂⣼⠯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⢿⣄⣀
⡷⡏⠉⢹⣳⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠒⠢⠤⢤⣤⢤⠦⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢠⣻⠉⠈⡷
⡇⠑⠲⢾⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁⠀⣠⠔⠚⢹⠉⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢹⠶⠒⠁
⡇⠀⠸⢸⠀⣇⠱⠀⠀⠀⠀⠀⠀⣀⡴⢚⣧⢀⣠⢒⣉⡀⡀⢀⢸⡄⠀⣇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡇⢸⢸
⡇⠀⡆⢸⠀⢹⣀⡇⠀⠀⠀⢀⠚⣃⣀⠤⠐⢛⠿⠂⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡉⠀⠀⠀⠀⠀⠀⣇⣸⠀⢸⠀⡆
⡇⢸⠀⢸⣤⣸⠉⢣⠀⠀⠀⢠⣀⡠⠔⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡀⠴⠀⠀⠀⢠⠋⢹⣠⣼⠀⢰
⡇⡇⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⡴⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡇
⣿⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠰⠶⠀⠈⠀⠀⠀⠀⠀⣟⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢹
⡇⠀⢠⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⢠
⣗⢒⣂⣤⣒⣒⣐⣒⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣈⣑⣒⣐⣒⣠⠤⣒⣒
⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠤⠾⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⣃⡸⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣤⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠁⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡌⡁⠀⠀⠀⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠃⠀⠀⡂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢻⣿⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣽⣿⣿⣿⣶⣶⣦⣶⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⣿⣿⣿⣏⠁⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⣴⠟⣿⠟⣿⣿⣿⣿⠇⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡀⡾⠁⣼⠃⢸⣿⣿⣿⡈⠀⢀⣼⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡀⣸⠃⠀⣿⣿⣿⣿⡇⠀⣼⣿⡿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠑⠃⠀⠀⠁⣼⠏⢸⡇⢠⣿⡿⠃⢻⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣷⢸⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⣼⡏⢸⣿⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⡀⠀⠀⠀⠀⠀⢿⠀⠸⡏⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠸⣇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣶⣿⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠛⠻⠿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⠀⠀⠀⡷⣠⣆⠠⠔⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠐⣒⠀⠀⠘⠻⣿⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡭⠶⣷⢀⡘⠓⣀⠘⠁⠈⢠⠰⠘⠀⢠⡀
⠀⠀⠀⠀⠀⢙⠀⣿⠀⠀⠀⣸⣿⡆⠡⠅⣎⠀⡀⠀⠀⠀⠀⢀⡄⠀⠀⠚⢀⡈⠡⡄⠉⠶⡀⠴⠦⠰⢆⢁⡀⠖⣈⠠⠌⣁⠈
⠀⠀⠀⠀⠒⡰⣴⣿⣧⣤⣴⣿⣿⡞⠈⠁⠀⠀⠀⠉⠒⠀⠀⠠⠄⢤⡤⠶⢀⡐⢃⡀⠛⠄⡤⠘⠀⠀⠀⠙⠳⠴⠮⠰⠦⠁
⠀⠈⠁⠀⡰⠉⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠂⠘⠓⢠⠐⢢⠀⠅⢀⠐⡦⡀
⠀⠀⠐⠈⠀⠀⠀⠀⠹⣿⠿⢿⣻⠅⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠠⣌⣀⢚⡀⠈⣀⠘⠠⡆
⠀⠀⠀⠀⠀⠀⠠⠅⠀⡜⠀⡀⣶⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣶⣶⣾⣶⠂
⠀⠀⠀⠀⠀⠀⠁⠄⠅⣁⠀⠠⠀⠀⠘⠀⡃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⢀⠒⠠⠟⠀⠁⠒⠩⢀⡀⠀⠒⠉⢈⡁⢀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣶⠉⡀⢤⣄⡓⢠⡅⠨⠒⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠉⠁⠀⠑⠄⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⢠⡄⣤⢦⢠⢠⡄⡦⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢢⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠁⠀⡿⡾⡇⡇⢸⠘⣾⠀⡇⢸⠆⠸⠇⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠠⠀⠀⠀⠀⠈⠁⠂⠂⣀
⠀⠀⢀⣀⣀⣀⡠⣀⠉⠀⠀⠀⠃⠀⠃⠙⠊⠀⠋⠀⠓⠘⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠑⢀⠄⢀⡁⠀⠀⢀⠘⠀⠰⠀⢀⡀⣀⠀⣁⠀⣀⠄
⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠁⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⢀⠊⠀⠉⠉⠁⠉⠉⠉⠄⢀⠄⠀⢠⡢⠀⠀⠀⠀⠁
⠀⡀⠀⣶⣶⡷⠀⢰⠄⠀⠀⠀⠀⢀⡄⢠⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠢⡈⢀⠐⠐⡀⠀⠀⡤⠂⠉⠀⠀⠉⠰⡀
⠀⠈⠠⠈⣛⡁⠔⠁⠀⢀⣡⣤⣤⣤⣤⣤⣀⡀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⣀⠀⢽⠁⠀⠀⠀⠌⠀⠀⠀⢆⢀⡀⠀⠀⠀⡀⠁⠀⠅
⠀⠀⠀⢀⠀⠀⠀⠀⢰⢸⣿⣿⣽⣿⢿⣿⣿⣇⠀⠀⠀⠀⢀⠀⠀⠲⢸⢢⠐⢀⠀⢠⠀⠀⠰⠡⠨⠅⠄⠰⠀⠆⠀⠀⠀⠸⠀⠉⠀⠀⠀⠄⠀⠈
⠀⠜⠀⠀⠀⠑⠆⠀⢸⢸⣿⣿⢿⣟⢿⣿⣿⡇⠀⠀⠀⠀⠈⢠⠀⠀⠀⠀⠠⠀⠀⡠⠀⠀⠐⠂⠀⠀⠀⡊⠀⠘⠀⠀⠀⠁⠀⠀⢀⣤⡆⠀⠀⠀⠄
⠀⡂⠀⠀⠀⠀⡔⠀⠘⠸⣿⣵⣾⣾⣿⣶⡿⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⠀⠀⣐⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠣⠀⠨⠀⠀⠀⠂⠈⠻⣢⠀⠀⢠
⠀⢸⡅⣷⢰⡇⠁⠀⠀⡦⠆⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠠⢀⠂⠘⢁⡀⠀⠀⠀⡁⠢⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⢄⠀⠀⠄⠀⠀⢹⣷⠄
⠀⢸⡁⠀⢨⣧⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠡⠀⠀⠈⡠⠁⢀⠁⠉⠐⠈⠈⠀⢰⠁⠀⠀⢇⠨⠑⡀⠀⠈⠀⠀⢀⢋⡄⠀⠀⠀⠀⠀⠈⠀⠉
⠀⢼⡇⣏⢸⡇⠀⠀⠀⠀⠇⠀⠀⢐⠫⡅⠀⠀⠀⢐⠁⠀⡸⠆⡀⠆⢀⠰⠀⠸⠆⠀⠊⡠⢠⠄⢈⠆⢀⠀⠀⠈⠈⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠉⠀⣀⣀⡀⠀⠀⠰⠀⠀⢉⠁⣀⠀⢀⠀⠈⠀⢄⠁⠀⠀⠈⠄⠐⠁⠀⠂⠐⠀⠐⢀⠔⠁⠀⠀⠁⠈⠉⠉⠉⠁⠠⡤⢤⢴⣤⢤⣴⠤⠤⣤
⠀⠀⢀⣴⠿⢛⣛⠻⢷⡄⠀⣄⣀⠈⠤⠤⠄⠘⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠂⡀⠘⣷⣮⣬⠝⠘⢻⣴⣤⣿
⠀⠀⣾⣡⠞⠋⠻⠿⣦⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠲⠖⢡⠄⠀⠀⠀⠀⢀⠄⠀⠋⠁⠩⡄⣈⠂⠀⠀⡅⠀⠀⠀⠄⠀⠀⠀⡁⠀⠄
⠀⡈⠉⠃⠀⠀⠀⠀⠈⠉⠃⠀⣿⠿⠿⡿⢻⡟⠛⣿⡄⠀⠘⡁⠠⡰⠋⠆⠀⠈⢠⣷⠆⠀⣀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠘
⠀⠀⢤⣆⠀⠀⠀⠀⣴⡄⠀⠀⣿⠀⠀⠁⠸⡄⣃⣽⡇⠶⠞⠛⠂⢠⣤⡄⠀⠠⡀⢈⡠⠁⠀⠉⠒⠐⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⣷⡄⠠⣾⢿⡆⠀⠀⣿⡄⣸⢰⡀⡇⠋⣹⡇⠀⠀⠀⠘⠣⣴⠀⠀⠀⠈⠉⠀⢀⠀⡀⠀⠀⡀⠄⡀⠈⢫⠁⠀⠀⠇⠀⢀⡀⠀⢀⣀⡀⢀
⠀⠀⠈⣡⠌⠁⠀⠉⠢⠀⠀⠀⣿⡟⢻⢟⠿⠟⡟⣿⡇⠀⢀⠀⣀⣀⡀⢀⠀⠀⠀⠀⠀⡘⠁⠀⡀⠀⠀⠑⠓⠀⠈⠀⠀⠀⠙⠃
⠀⠀⣰⣤⠐⠀⢀⣀⣠⢶⠀⠠⣿⡇⢾⠘⢀⡄⡇⣿⡧⠀⠨⠉⠉⠋⠉⠙⠂⠠⠀⠀⢠⣁⡀⠈⠙⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⢀⠋⠃⠀⠄⠻⠟⠛⠛⠀⠀⠙⠿⠿⠛⠛⠛⠛⠛⠃⠀⢸⠀⠀⠂⠐⠀⠀⠀⠀⢀⡞⠀⠘⠀⠃⠀⢰⠁⢻⡀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢰⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⠠⡀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⢰⠃⠂⠀⠘⢇⠀⡄⠀⠀⠀⢀⠀⢀⠇⠈⠀⠀⢡⣤⣤⣀⠀⠀⠘⠀⠃
⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠙⠀⠉⠀⠁⠀⠀⠟⣿⣿⠿⠂⢀⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠐⠉⠈⣁⣍⠈⠉⢱⠀⠀⠀⠀⠀⠈⠁⠐⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠖⠀⠀⠰⠄⠀⠀⢱⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⠻⠇⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠴⠈⠕⠁⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⡀⠀⡠⠀⠀⠀⡌
⠀⠀⠀⠀⢻⠇⠀⢸⡁⠀⠀⠀⠀⠀⠀⢀⢠⠀⠃⠈⠀⠀⠀⢀⢒⠥⠞⠀⠀⠀⠀⠀⠀⣱⠿⠻⡦⠡⠀⡠⠀⠈⠄⠀⠰⣀⠓⢀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠜⠛⠐⠘⠀⠀⠀⠇⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠠⣴
⠀⠐⠒⠓⠉⠉⠉⠉⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠘⠀⠈⠉⠑⠀⠒⠀⠤⠂⠀⠀⠀⠈⠂⠠⠀⠀⠀⠀⠀⠉⠂⠀⠁⠀⠀⠀⠀⠈