⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠛⠋⠀⠀⣤⣶⣾⠿⠿⢦⣿⣷⡶⠶⠾⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣁⡀⠀⠀⠛⠛⣻⣶⣶⣿⣿⣿⣷⣤⣄⣈⡿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣽⣇⠀⠀⠀⠀⣾⣿⣿⠛⠛⠛⢿⣿⣿⣿⡇⠀⢠⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⣿⣿⣦⣤⠄⠘⣿⣿⣿⣦⣤⣶⣾⣿⣿⣿⣧⢀⣰⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡿⠿⠇⠀⣸⠛⠛⠿⠿⠿⢿⣿⣿⣿⡏⢸⣿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠘⣿⠀⠠⣤⣴⣶⣦⣼⣿⡿⠇⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣠⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣠⡄⠀ ⠘⠛⣿⠀⠀⠀⠀⠀⣾⠋⠀⢹⡇⠀⠀⠀⢰⡟⠁⠘⣿⠀⠀⠀⠀⠀⣰⢿⡇⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⢻⣆⣀⣼⡇⠀⠀⠀⠀⣿⡶⣾⡏⠀⠀⠀⠀⣴⠏⢸⡇⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠉⣹⠇⠀⠀⠀⢸⡏⠀⠀⣿⠀⠀⠀⠸⠿⠶⢾⡷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⣶⠆⣷⣷⢤⣤⡀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⢟⣿⣿⡟⠃⠁⠀⠏⣿⣿⣷⣿⡏⠙⠷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣫⣭⣴⠊⠀⢸⢹⣿⣿⣿⣿⣷⠀⠀⠈⠈⠒⠦⡀
⠀⠀⠀⡠⢤⠀⠀⣀⡤⠚⠉⠹⣿⣿⣿⣿⢞⣿⣂⣐⠽⣾⣿⣿⣿⣿⣿⢄⣠⣿⢄⣀⠀⠈⢢⡀
⠀⠀⠀⡇⢸⡀⡠⠁⠈⢳⣄⡁⢻⣿⣯⣿⣿⠾⣿⣶⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠱⣀⡀⠀⠀⠑⢄
⡠⠒⢶⣿⣿⡟⢄⠀⠀⢸⣿⡷⠞⣿⣿⣿⣿⣿⣜⣿⣿⣯⣿⣷⣿⣿⣿⡇⠀⠀⠀⠈⠫⢦⡀⠀⠈⣳⣄⡀
⠇⢚⣿⣿⠿⡇⠀⡠⣊⡿⠋⠀⠀⢹⣿⣿⣿⣿⣿⣿⣷⡿⡽⣝⡟⡿⢿⠿⡄⠀⠀⠀⠀⠀⠙⢦⣼⣿⠻⣿⣦⡤⣀
⠈⣿⣡⠠⢴⢃⡹⠉⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⢿⣿⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⢷⡄⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠯⢹⣟⡉⢛⣿⡟⠽⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠤⣶⣶⣶⣾⣿⣧⠀⠀⠀⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣠⣤⣾⠟⠛⠛⠛⠛⣧⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣾⡿⣧⠀⠀⠀⠀⠀⠀⢸⡍⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡯⠟⢀⣼⣷⠄⠀⠀⠀⠀⢰⡿⠀⢠⠴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣠⣿⣭⣯⠀⠀⠀⠀⠀⠘⠳⣷⣾⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣿⠿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠸⢷⣾⣿⣿⡆

⠀⣰⠃⠀⠀⠿⣿⣧
⢠⡇⠀⠀⠀⠀⢻⣿⣦
⠸⣇⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠤⣤⠿⣿⣷⣶⡄
⠀⢻⡄⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡈⣁⢜⣉⢿⣿⣿⠀⠀⣔⣉⠵⣳⣆
⠀⠈⠹⡀⠀⠀⠀⠀⠀⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⣛⡟⠛⣿⣿⡇⠀⢿⡲⣾⣟⡁⣔⣹⣷⣀⣠⠤⠒⢒⣤
⠀⠀⠀⢻⡀⠀⠀⠀⠀⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡻⡶⠞⢀⡖⠉⣿⠃⠀⠈⣿⣿⣿⣯⣭⣿⣿⣍⣤⡖⢩⣿⣿⣷
⠀⠀⠀⠀⢻⡄⠀⢀⣾⣿⣿⣿⣿⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡿⡿⠏⠀⢀⠟⣶⢤⣞⣁⡛⠛⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠈⢻⡄⠀⡿⣿⣿⡟⠻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣠⣾⠋⣰⠏⢠⣿⣉⠙⢫⣭⣽⣺⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠻⠎⣴⠿⣿⠿⡶⠋⢑⣦⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠟⠁⡰⡟⠀⣾⣿⣿⠟⠉⠉⠙⠻⢷⡆⠹⣿⣿⣿⣿⣿⣿⠟⠳

⠀⠀⠀⠀⠀⠀⠸⣷⣿⢷⣶⣿⣿⣿⣏⡀⠀⠀⠙⢄⠀⠀⠀⠀⣿⠉⠑⠋⠒⠤⣠⣿⡏⠀⠀⠀⠀⡴⢺⠩⡗⡄⢸⡄⢈⣿⣿⣿⣿⣿⣷⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⢻⣿⣿⣿⣿⣿⡄⢠⠎⠀⣀⠄⣴⣿⡆⠀⠀⢾⡷⠀⣿⡇⢀⠀⠀⠸⡟⡧⡀⡤⢿⢸⣿⡿⠿⠻⣿⣿⡿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠿⠁⣠⠖⠁⠀⣠⠼⣿⡀⠀⠀⠀⠀⢿⣇⠘⢾⡀⠀⠛⠢⠭⠥⠞⢸⠿⢷⣴⡞⠁⠈⣷⣽⡿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠯⡀⠀⠀⠁⠀⣠⠊⢁⠀⣇⠃⠀⠀⣀⡀⠘⣿⣖⠀⢣⠀⠀⠀⠀⠀⠀⠘⡆⠀⠈⢷⡈⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁⠀⠀⠀⢹⡆⠀⠀⠛⠟⠀⠈⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⢿⣄⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣇⡇⢀⣸⡧⠜⠒⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠀⣀⣼⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⣰⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⣠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣷⣄⡀⠙⣿⣿⣿⣿⣿⣿⣇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⣷⣿⠛⣿⡏⠉⠉⠁⠁⠉⠛⢦⣹⣿⣿⣿⣿⣿⣿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⢱