⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠀⠀⠀⠀⠀⢰⡤⠂⠀⠀⠀⠀⠀
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣴⣦⡀⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠀⠀⠀⠀⠀⠨⡷⠀⠀⠀⠀⠀⠀
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⢀⣠⣶⠿⢋⢙⠿⣶⣄⡄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠀⠀⠀⢀⣠⣴⣿⣶⣄⠀⠀⠀⠀
⢤⣤⣄⣄⣄⣤⣤⣦⣶⠿⠟⠫⠡⢑⢐⢐⠨⡨⢙⠻⢷⣶⣦⣤⣤⣄⣄⣤⣤⡤ ⠀⢠⣤⣚⣽⣿⣿⣿⣿⣦⣴⠀⠀
⢽⣯⠩⠩⠩⠩⠩⠨⢐⠨⠨⠸⢷⣷⠾⠻⠛⡛⣷⡮⠄⡂⢌⠩⠉⠍⠍⠍⣽⡯ ⠀⠈⠋⢻⣿⣿⣿⣿⣿⡏⠙⠀⠀
⢹⣷⠨⠨⠨⠨⠨⢐⠡⣰⣥⣥⢾⣿⠷⠷⠗⣿⢯⣤⡧⠂⠢⠨⠨⠨⠨⢐⣽⡗ ⠀⠀⠀⠈⠙⠻⣿⡟⠋⠀⠀⠀⠀
⢘⣿⡅⠅⠅⠅⡊⡐⢨⣸⣿⢵⢞⣿⡟⠳⠳⢷⡿⣵⣤⣥⠅⠅⠅⠅⠅⣢⣿⠣ ⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⠀⠀
⠄⢿⣧⢑⠨⢐⢰⣼⠟⣙⣾⡇⢸⣿⠷⢾⣾⠈⠿⢈⢻⣕⣨⡨⠨⠨⠐⣼⡟⠄ ⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠀
⠄⠘⣿⡶⠺⢶⣿⢗⠶⢶⣿⠾⢾⣾⡻⣻⠷⠷⠳⠖⠶⠖⢗⠶⠵⠺⣺⣿⠁⠄ ⠀⠀⠀⠀⢀⣼⣿⣇⠀⠀⠀⠀⠀
⠄⠄⠸⣿⡎⡈⡻⣷⣔⣸⣿⢁⢪⣿⡢⢈⢓⠡⢡⣡⣵⣾⢛⠻⢋⢰⣿⠣⠄⠄ ⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀
⠄⠄⠄⢚⢿⣆⢂⠌⡙⣽⡿⠶⣾⣿⢶⢶⠾⡛⠫⡉⠍⠡⠂⠌⣲⣿⠣⠄⠄⠄ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀
⠄⠄⠄⠄⠈⢿⣧⡂⡚⠟⢷⡥⣾⣿⣇⡐⠨⠠⡁⡂⠅⠅⢅⣽⡟⠁⠄⠄⠄⠄ ⠀⢸⡗⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠄⠄⠄⠄⠄⠄⢙⢿⣦⡑⡐⠸⢯⢉⠛⠳⠧⠥⢂⠂⢅⣵⡿⠫⠄⠄⠄⠄⠄⠄ ⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠄⠄⠄⠄⠄⠄⠄⠐⠙⢿⣦⡡⠂⡂⠌⢌⢐⠨⣐⣼⡿⠋⠈⠄⠄⠄⠄⠄⠄⠄ ⠀⢸⡗⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠙⠿⣷⣔⡁⣂⣢⣾⠟⠍⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠈⠙⠿⢟⠋⠁⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀
⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄⠄ ⠀⠛⠛⠿⠿⠿⠿⠿⠿⠿⠟⠋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⣿⣯⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀