⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⠀⠀⠀⠀⢠⣾⣷⣄⡀⠀⠀⢀⣴⣿⣷⣄⠀⠀⠀⢀⣴⣾⣷⣄⠀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠛⢿⣿⣷⡄⠀⣴⣿⣟⢿⣿⡿⠀⣿⣿⣿⢿⣿⣷⠀⣶⣿⣿⠙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⣿⣿⣿⠀⠉⠀⠀⢸⣿⡇⠀⠀⣿⣿⠀⣿⣿⣿⠀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⢸⣿⣷⣤⣴⣿⣿⠀⣿⣿⣿⣾⣿⣟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⡇⠀⣿⣿⣿⠀⢀⠀⠀⢸⣿⡿⠿⠿⣿⣿⠀⣿⣿⣿⠟⢿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⣿⣿⡇⠀⣿⣿⣏⣴⣿⡷⠀⣸⣿⣧⠀⣠⣿⣿⡀⢻⣿⣿⢀⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⠗⠘⢿⣿⡿⠀⠻⣿⣿⠟⠁⠀⠀⠙⢿⠟⠁⠙⢿⡿⠋⠻⣿⣿⣿⣿⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⣠⣤⢶⣻⣿⣻⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⣼⣺⢷⣻⣽⣾⣿⢿⣿⣷⣿⣿⢿⣿⣿⣿⣇
⠀⠠⡍⢾⣺⢽⡳⣻⡺⣽⢝⢗⢯⣻⢽⣻⣿⣿⣿⢿⡄
⡨⣖⢹⠜⢅⢫⢊⢎⠜⢌⠣⢑⠡⣹⡸⣜⣯⣿⢿⣻⣷
⢜⢔⡹⡭⣪⢼⠽⠷⠧⣳⢘⢔⡝⠾⠽⢿⣷⣿⣟⢷⣟
⢸⢘⢼⠿⠟⠁⠀⠀⠀⡀⠃⠑⡌⠀⠀⠀⠈⠙⠿⣷⢽⣻
⢌⠂⠅⠀⠀⠀⠀⠀⠀⡀⣲⣢⢂⠀⠀⠀⠀⠀⠀⠈⣯⠏
⠐⠨⡂⠀⠀⠀⠀⠀⡀⡔⠋⢻⣤⡀⠀⠀⠀⠀⠀⢸⣯⠇
⠈⣕⠝⠒⠀⠀⠒⢉⠪⠀⠀⠀⢿⠜⠑⠢⠠⡒⡺⣿⠖
⠀⠐⠅⠁⡀⠀⠐⢔⠁⠀⠀⠀⢀⢇⢌⠀⠀⠀⠸⠕
⠀⠀⠂⠀⠀⠨⣔⡝⠼⡄⠂⣦⡆⣿⣲⠐⠑⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠃⢫⢛⣙⡊⣜⣏⡝⣝⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠁⠈⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣀⣄⣤⣠⣤⣤⡤⠤⠤⢤⣀⣤⡀⠀ ⣰⠀⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⣿⣿⣿⠿⠧⠴⠛⠛⠒⠛⠉⠉⠋⠉⠉⠉⠉
⢸⣿⣿⠿⠏⠉⠁⠀⢰⣿⠁⠀⠉⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⣠⣤⢶⣻⣿⣻⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⣼⣺⢷⣻⣽⣾⣿⢿⣿⣷⣿⣿⢿⣿⣿⣿⣇
⠀⠠⡍⢾⣺⢽⡳⣻⡺⣽⢝⢗⢯⣻⢽⣻⣿⣿⣿⢿⡄
⡨⣖⢹⠜⢅⢫⢊⢎⠜⢌⠣⢑⠡⣹⡸⣜⣯⣿⢿⣻⣷
⢜⢔⡹⡭⣪⢼⠽⠷⠧⣳⢘⢔⡝⠾⠽⢿⣷⣿⣟⢷⣟
⢸⢘⢼⠿⠟⠁⠀⠀⠀⡀⠃⠑⡌⠀⠀⠀⠈⠙⠿⣷⢽⣻
⢌⠂⠅⠀⠀⠀⠀⠀⠀⡀⣲⣢⢂⠀⠀⠀⠀⠀⠀⠈⣯⠏
⠐⠨⡂⠀⠀⠀⠀⠀⡀⡔⠋⢻⣤⡀⠀⠀⠀⠀⠀⢸⣯⠇
⠈⣕⠝⠒⠀⠀⠒⢉⠪⠀⠀⠀⢿⠜⠑⠢⠠⡒⡺⣿⠖
⠀⠐⠅⠁⡀⠀⠐⢔⠁⠀⠀⠀⢀⢇⢌⠀⠀⠀⠸⠕
⠀⠀⠂⠀⠀⠨⣔⡝⠼⡄⠂⣦⡆⣿⣲⠐⠑⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠃⢫⢛⣙⡊⣜⣏⡝⣝⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠁⠈⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣀⣄⣤⣠⣤⣤⡤⠤⠤⢤⣀⣤⡀⠀ ⣰⠀⠀
⢰⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⣿⣿⣿⠿⠧⠴⠛⠛⠒⠛⠉⠉⠋⠉⠉⠉⠉
⢸⣿⣿⠿⠏⠉⠁⠀⢰⣿⠁⠀⠉⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⣠⣤⢶⣻⣿⣻⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⣼⣺⢷⣻⣽⣾⣿⢿⣿⣷⣿⣿⢿⣿⣿⣿⣇
⠀⠠⡍⢾⣺⢽⡳⣻⡺⣽⢝⢗⢯⣻⢽⣻⣿⣿⣿⢿⡄
⡨⣖⢹⠜⢅⢫⢊⢎⠜⢌⠣⢑⠡⣹⡸⣜⣯⣿⢿⣻⣷
⢜⢔⡹⡭⣪⢼⠽⠷⠧⣳⢘⢔⡝⠾⠽⢿⣷⣿⣟⢷⣟
⢸⢘⢼⠿⠟⠁⠀⠀⠀⡀⠃⠑⡌⠀⠀⠀⠈⠙⠿⣷⢽⣻
⢌⠂⠅⠀⠀⠀⠀⠀⠀⡀⣲⣢⢂⠀⠀⠀⠀⠀⠀⠈⣯⠏
⠐⠨⡂⠀⠀⠀⠀⠀⡀⡔⠋⢻⣤⡀⠀⠀⠀⠀⠀⢸⣯⠇
⠈⣕⠝⠒⠀⠀⠒⢉⠪⠀⠀⠀⢿⠜⠑⠢⠠⡒⡺⣿⠖
⠀⠐⠅⠁⡀⠀⠐⢔⠁⠀⠀⠀⢀⢇⢌⠀⠀⠀⠸⠕
⠀⠀⠂⠀⠀⠨⣔⡝⠼⡄⠂⣦⡆⣿⣲⠐⠑⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠃⢫⢛⣙⡊⣜⣏⡝⣝⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠁⠈⠈⠊