Irish language Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢟⡛⣿⢻⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣑⣽⣽⣞⣹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⣏⢻⡿⣷⣦⣝⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠿⠿⠿⠿⠿⠿⢻⣿⣬⣷⣼⣛⡇⣻⣿⣿⣷⣌⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⠀⠀⠀⠀⣠⣶⣿⣶⣾⣿⣿⣿⣿⣿⣷⣮⣿⣿⣧⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢉⡏⣊⢍⢺⣿⣿
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠹⡆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⣶⣾⡿⠟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠸⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠛⠛⣛⣻⢟⣟⢿⣿⣿⣿⣿⣿⢧⣿⡇⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⡿⣿⠿⠄⠀⠈⢻⡇⢿⢮⣿⡿⠿⢿⡟⢻⡄⣿⣷⢸⡇⠀⠀⠀⠀⠀⠀⢠⣶⠶⠶⠶⠶⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠘⠛⠿⣟⡉⠁⠀⢠⣷⣸⣇⠛⢠⠘⣧⡀⢸⡇⣸⠃⣿⡿⢸⡇⠀⠀⠀⠀⠀⠀⢿⣿⡘⣘⣀⡃⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢄⠀⠒⠀⣴⣿⣿⡏⠙⡿⣧⣴⣿⣿⡾⢡⡟⢰⣿⡇⣾⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠶⠿⡙⠓⠤⣴⣿⡇⠘⠘⣴⢡⢹⣿⣿⣿⢡⡞⢡⣿⡿⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢿⣿⣶⣤⣄⡐⠉⢿⡄⣰⡟⢊⣾⣿⣿⣿⣮⡳⣿⡿⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠻⠛⠻⢿⣿⣿⣷
⠄⠀⠂⠠⠀⠀⠀⠀⠀⣀⣴⠏⢠⠟⠟⣡⠏⠉⠹⣦⣸⢣⣏⣚⣼⣿⣿⣿⣿⣿⣿⣮⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⣦⣮⣽⣿⡿
⠀⠀⠀⠀⠄⠀⠀⠀⣀⣿⠗⣣⠏⣴⠟⠁⢀⡄⢀⡾⢣⠞⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠁⠄⠀⠁⠀⠀⠀⣼⣟⣵⠏⣠⢠⠏⣠⢰⠟⣱⡟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⡭⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡴⣤⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣦⣿⣇⣿⣾⢁⣠⣴⣷⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣄⠰⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣿⣴⣶⡽⣿⣿⣿⣿⣿⣿⣿⣯⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠷⠿⠿⠿⠿⠿⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠆⠀⠃⠀⠚⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡿⠓⠉⠁⠀⠀⠀⠐⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣷⡀⠰⢶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣩⣻⠏⢡⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⣤⣤⢠⣀⣐⣿⣿⣿⡇⣀⠀⢴⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⢴⣿⣿⡷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣯⢿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠻⢿⣿⢿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠽⠿⠿⢿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣿⣿⣿⣿⣿⣤⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣛⣿⣿⣿⣿⣿⣿⣿⡟⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⡹⠾⣿⠿⠟⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⡠⡌⣼⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⣡⢾⣪⠺⠿⠷⠿⣆⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢑⠴⠻⠩⣦⡸⢶⣦⢵⣦⢉⡿⠝⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⡀⠀⠀⠉⢸⣤⣭⢧⣻⣕⣋⣥⡋⠉⠃⠒⠀⡠⢤⣄
⠀⠀⠊⠛⣂⡀⠀⠀⣔⠫⡕⠀⢱⣷⠀⠲⡆⣸⣍⡛⠙⢉⣩⠇⠐⣶⡆⣶⡀⠉⣰⠟⢁⡄⠐⣦⢠⠔⠙⠃
⠀⢴⣀⢈⡾⠑⠠⠰⣿⣷⠈⠛⢾⠽⠀⣶⡟⣏⢩⡿⠯⢯⡏⠨⠫⡝⣇⡛⣥⠛⢻⢤⣿⡇⢀⢼⢁⠔⠀⣜⡀
⠠⢘⡵⢂⣽⢛⢀⠂⠙⠈⠊⠛⢶⣶⣮⡉⢰⡜⢸⠄⠀⠀⠇⠰⡦⠈⠚⠛⣃⣴⡗⡁⠏⠁⠀⡘⡉⣁⣌⡟⠂
⠈⠒⠾⣯⣿⣗⡿⣛⣔⠳⡟⢆⠉⣹⠙⠛⣟⠇⠺⠆⠀⠐⢳⠰⣶⠋⠉⣉⠻⠻⣿⠿⢀⣐⢴⢿⠾⣽⣯⠙⠆
⡴⣒⠲⢮⠻⣼⢰⢑⣾⡇⡀⢠⡧⣷⣷⡄⢹⣸⣯⢭⢭⠵⢻⣧⣏⠤⡾⢁⣤⣾⡇⢴⣫⡌⡣⣿⡳⣩⠴⠤⣄
⠻⠞⠀⡠⠱⣽⡜⡀⢉⢔⣀⡾⠃⢙⡿⠈⣇⡞⡳⣶⡜⣧⣒⠺⣹⠀⠂⢻⠈⠟⠿⣌⡉⢁⢇⣏⠜⣅⠀⢎⣮
⠀⠀⠀⠙⠋⠙⠶⢜⠄⢻⠁⡼⠗⢼⣇⡀⣦⣌⢙⣿⣛⣯⣧⡸⣲⢀⠀⡺⠶⢴⢈⣛⣣⣮⣟⠞⠈⠛
⠀⠀⠀⠀⠀⢶⡗⠲⣷⣿⣷⣯⢄⣛⣧⡤⢀⡭⡫⡅⠀⢨⣿⠫⡅⠀⢙⠁⣠⣚⡰⣯⣛⡵⢯⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣩⣍⠉⠉⣽⠻⠓⢦⠀⢤⠀⣀⠁⢔⡘⣿⣍⠉⠉⠉⠹⡍⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢀⣀⡏⢅⠈⠚⠈⠧⣀⣄⡀⠐⠃⣈⣹⡦⣄⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣅⠘⡳⠐⠋⣛⡖⠁⡶⢄⠙⡽⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⢿⡉⢾⠉⡐⠇⠼⡷⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠁⡙⣿⢂⡘⠃⠈⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣵⣛⣦⣝⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⣠⣄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⣤⠀⠀⠀⠠⠄⠠
⠀⠀⠀⠀⠀⠀⣴⣭⣤⠀⠀⠀⠀⣴⠇⠀⠀⡀⠟⠙⠋⠀⠀⢀⠀⡀⠀⠀⡟⠻⠙⠄⠀⠀⠃⠃⢲⣄
⠀⠀⠀⠀⠀⠀⠈⡙⠁⠂⠀⠀⠀⠀⠁⡄⠀⠃⠐⠀⠈⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣰⢣⠀⠀⠀⢸⣏⣱⠀⠀⢰⠋⠉⠂⠀⠀⢸⠉⢳⡀⠀⢸⣉⡁⠀⠀⠀⣏⣉
⠀⠀⠀⠀⠀⠀⠀⠋⠉⠃⠀⠀⠸⠆⠼⠀⠀⠘⠦⠴⠂⠀⠀⠸⠤⠞⠁⠀⠸⠤⠄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠠⠀⠀⢂⣠⣤⠀⠀⠀⠀⠀⠀⡠⢴⠀⠀⠀⠀⣀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠑⠀⠁⠩⣦⠀⠀⠘⠟⠃⠀⠀⠀⠙⠙⠆⠀⢸⡇⠤⠐⣉⡂⣵⠶⡄⠀⠈⠃⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠘⠷⠶⠆⠁⢠⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠁⠠⡅⠀⠀⠀⡷⠀⢾⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡶⡏
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠃⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠚⠁⠀⠀⠀⠈⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠔⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡔⢐⣦⢄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠘⠉⠐⠀⠀⠈⠄⠐⠄⠀⠀⠀⠀⠘⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡆⠀⠀⠀⠀⠀⠑⣸⡄⠀⠀⠄⠈⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣤⠉⠀⠀⠀⠀⠀⣄⠀⢩⠀⠀⠀⢀⠤⢄⠀⠀⠀⢠⠤⢄
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⢣⡐⣿⠀⠀⠀⠀⠀⠀⡏⠳⣼⠀⠀⠀⢇⠀⢨⠇⠀⠀⢸⠂⠚
⠀⠀⠀⠀⠀⠀⠈⢉⠁⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⡁⠀⠉⠀⠀⠀⠈⣁⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠀⡈⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⡠⢐⣄⠸⠀⠀⠀⠀⡀⡈⠹⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠄⠉⠋⠀⠃⠀⠀⠐⠛⠏⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠄⠠⡄⠀⠀⠀⠘⠐⠀⠌⠀⠀⠀⠀⡖⠀⠐
⠀⠀⠀⠀⠀⠀⢠⠂⠦⡀⠀⠀⠀⡖⠒⣦⠀⠀⠀⠀⣴⠒⠆⠀⠀⠀⠀⠐⢲⠂⠀⠀⠀⠀⡄⠀⡄
⠀⠀⠀⠀⠀⠀⢷⣀⣠⠃⠀⠀⠀⡏⠙⢆⠀⠀⠀⠀⢤⣉⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⣄⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣌⡠⠅⠀⠀⠀⣸⠺⡆⠀⠀⠀⠀⢉⡛⠀⠀⠀⠈⡒⡖⠠⣤⠒⠀⠈⣤⣜⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠓⠀⠀⠀⠀⠛⠓⠶⠀⠀⠀⠏⣁⣹⣤⡇⠀⠀⡌⠻⠛⢁⠂⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠢⠀⠴⠀⠀⠀⠈⠚⠺⠇⠀⠀⠀⠸⠀⠐⠇⠀⠀⠀⠀⠄⠘
⠀⠀⠀⠀⠀⠀⠐⡄⢀⠆⠀⠀⢰⠀⡴⡄⡖⠀⠀⠀⠀⢆⡰⠀⠀⠀⠀⢦⣠⠆⠀⠀⠀⠀⠈⣱⠆
⠀⠀⠀⠀⠀⠀⠀⠹⠎⠀⠀⠀⠀⠷⠀⠹⠃⠀⠀⠀⢀⠞⠣⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠴⠥⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣉⣻⣋⣙⢛⣟⣋⣿⢻⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⢻⡍⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢶⡉⠉⢳⡅⠀⠀⠀⡠⠌⠠⠄⠲⠉⠈⠉⠀⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠓⠁⡄⠀⡤⠄⣰⡇⠀⢀⡮⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠄⡀⠰⠋⠀⠀⠀⠐⠀⠒⠒⠐⠂⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠙⠓⠰⠀⠈⠁⠀⠐⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠉⠀⠀⠀⠀⢰⠢⢀⠄⠀⠀⢀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠰⠶⠚⡶⠃⠀⠀⠀⠂⠉⠀⠀⠁⠄⠐⠀⠀⠀⠀⡜⠀⡸⠀⠀⠀⠈⠁⢠⡄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠚⠢⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠃⠀⠀⠀⠀⠀⠀⢻⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⢠⡄⠤⠤⠤⠤⣄⠀⢀⣀⠀⠀⢎⡀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢋⠐⢀⠐⠀⠠⢾⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣇⣤⠋⠁⠀⠀⠀⠀⠈⠷⠃⠀⠉⠉⠲⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡶⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠠⣛⢠⡶⠠⠤⢀⠀⣀⢀⣠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠸⠊⡁⢩⡦⠀⠀⢀⣡⠐⠀⠁⠌⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠤⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠆⠒⣰⠋⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠠⠊⠑⡀⠀⠀⠀⠀⠰⠀⠒⠀⠀⠀⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠒⠐⠒⠂⠈⠀⠀⠠⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⢀⡀⣤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⡎⠑⢠⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⢈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠑⠀⢐⠀⠘⡟⠀⠁⣄⠈⠀⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠈⠑⠒⢶⠀⢠⡼⢉⠡⠀⠀⠀⠰⠀⠆⠀⠂⠦⠂⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠣⡘⣀⣀⡠⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠄⠀⠀⠀⠀⠀⠰⡀⠀⠌⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠤⠖⠞⠁⠀⠀⠀⠀⠀⠀⡠⢎⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⠐⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡂⢀⠀⠀⡀⣀⠎⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⢀⠔⢂⠴⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⢀⡔⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢃⣄⡀⢀⣀⣠⢊⠳⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠊⠉⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠄⠀⠀⠘⠀⠀⠀⠘⠐⢇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⢠⡤⠶⣠⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⠀⢠⠀⠀⠀⠀⠀⠶⡊
⠀⠀⠀⢛⣁⣀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠠⠀⠀⠁⠀⠁⠉⠛⣦⢰⠦⢤⣀⣀⣨⠂
⠀⠀⠀⠉⢀⣀⣅⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⣂⣬⡔⢛⠂⠉⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⠎⠀⠀⠀⠂⠀⠂⠐⠂⠂⠀⠀⠠⠀⠀⠐⠀⠄⠀⠀⠀⠐⢀⠀⠀⡆⡠⠌⣨⣭⣭⣥⡸⠉⣆⠋⣙⠁⢈⡉⠈⠁⠎⠠⣀
⠀⠀⠀⠉⠰⠆⠀⡀⣀⣤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡒⢀⡠⠜⠃⠀⣾⣯⣥⣤⣽⣿⡈⣿⡇⣻⡟⠛⢻⣧⠀⣰⣞⣛⣻⣶⡀
⠀⠀⠀⠀⠀⢀⡆⠚⠈⠁⢤⣔⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠘⠀⠈⠀⠀⠀⠀⢿⣇⠀⠁⠀⣀⠀⣿⡇⢽⡷⢶⣾⡋⠀⣿⡙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠐⠁⠀⠙⢏⡤⠖⢀⠀⠀⢀⣀⣀⡰⠆⠵⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋⠀⠻⠃⠻⠃⠀⠙⠻⠏⠈⠻⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠉⠛⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢲⡶⣠⠀⠀⠀⠀⢀⢀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⢦⠀⡄⣀⠀⠀⠀⠐⡬⠉⢀⠉⠁⠀⠀⠀⢠⣄⠀⠺⠟⣿⣽⣿⠟⠇⠀⢰⡆⠀⠀⢀⣤⣄⠐⠲⢿⣧⣶⣆⡴⢸⡈⡟⠽⠴⠶
⠀⠀⠀⠀⠀⠀⠉⣡⠾⡁⣧⢹⠏⡷⢾⠩⡀⠠⣮⡜⢧⠀⠀⣾⢵⠀⣠⣾⣯⣿⣿⣻⣦⡐⣿⣿⣃⣀⢸⣛⠿⠃⢤⣾⣽⣯⣿⣿⣾⣷⣏⠟⠋⠀⢀⡀
⠀⠀⠀⣠⣤⡄⠀⠀⠚⣿⣻⣿⡿⡟⠿⣿⡻⠂⡠⡶⣗⡲⠶⠿⣿⡚⢿⣿⢵⡤⣾⣿⡾⢻⣿⠝⠉⢉⢽⣿⣷⣄⡸⠿⣮⣿⣿⣿⣿⣿⢿⡄⠀⢴⣯⣿
⠀⠀⠀⢿⣮⣁⣀⣀⠘⢿⣯⣷⢟⣻⣻⠁⣵⡿⠋⠉⣽⣿⠆⣀⠈⢻⡾⣿⣄⢷⢿⣿⡅⣾⢡⣤⡄⠙⠾⢇⢀⣙⣳⡄⣿⣿⣿⡟⢃⣻⣯⠶⣶⣶⣾⣯⣀
⠀⠀⢀⡤⢾⣯⠞⢉⣽⢲⣤⣌⢻⣵⠼⡴⢿⢲⠆⣠⣬⡁⢺⡷⣧⡺⢂⣻⣿⣷⣯⣇⣀⡻⣿⡼⠇⢠⠶⣾⡌⠋⣽⣿⣿⣿⣯⣴⡿⢻⣿⣶⢀⣻⣿⠈⢿⣦
⠀⢰⠿⠅⢘⣛⠂⠸⣦⡗⢀⣹⣿⣾⣯⢽⣿⣥⠘⠷⢶⣿⠀⣩⣿⢟⣻⣽⣿⣿⣯⣯⣭⣻⡻⣦⣄⣿⣿⠻⠃⠲⣿⢿⣾⣿⣿⣿⣦⠈⢉⣉⢀⣤⣶⡄⠾⣿⣤
⠶⢾⠐⠀⣽⠝⢳⡐⠒⠀⠉⢫⠟⢹⠗⢸⠉⠳⢤⡤⠾⣫⡞⣫⣾⡿⢿⣿⣿⣿⡝⠷⠶⠶⠶⣶⣍⢻⣯⢻⠛⢛⣡⣸⣿⣿⡈⠉⢁⡤⣘⠉⠫⣿⣝⣡⡴⣿⠁
⠀⠀⢻⡒⢢⠴⣛⠁⢰⢋⣿⠂⠀⣼⠏⡿⠞⠛⢶⢀⣾⢫⣿⣿⣿⡟⡏⠉⠁⣿⡏⢒⣲⣶⠾⠿⠏⠿⣽⣿⣰⢯⣤⠉⢿⣹⣷⣄⣛⣿⣿⠇⢶⣻⡏⢩⡟⠁⡀
⢀⡤⡀⡙⡄⢾⡌⠃⠘⠿⣧⠴⣻⣧⠟⠁⠸⣟⡻⣾⢷⡟⣿⣿⣿⠟⢇⠶⠦⣿⡇⠀⠀⢀⡄⠀⣈⠛⠛⢺⣿⠛⢋⣀⠀⣹⡏⠿⣿⣿⣫⣤⣤⣚⠃⢺⡕⠺⣟
⠸⣆⠀⣒⠃⢈⠟⠛⠛⠒⢺⡮⢉⡖⢂⡴⢻⣷⢰⣟⡿⣿⣿⣿⣺⣿⢦⣧⢆⡟⠁⠀⢰⣛⢛⡧⢿⠀⢀⣽⢿⣴⣿⡍⢻⣥⣿⡾⣿⡇⢀⡀⢹⡿⢷⡀⠙⠛⠛
⠀⠈⠉⠀⢰⠋⠚⣴⠖⢦⠣⠞⣙⢻⣾⡄⣘⠚⢻⣇⠀⣿⣿⣿⣮⣿⣶⣫⣿⣶⡆⣠⣔⡒⣒⣳⣼⣶⣿⣿⢸⡇⠉⣤⣼⢿⢿⡦⡍⢱⢯⣟⡇⣠⣸⣇⣤
⠀⠀⠀⣄⣉⢐⡆⠻⠶⢼⠇⠸⣴⠁⢲⡛⣾⣠⣼⣇⢲⣿⣿⣿⣿⣧⡿⣷⣴⣼⡕⢃⡍⠹⠿⣿⣿⡿⣿⣿⣾⢶⢦⡿⢕⡏⣈⣛⣄⠘⣷⣄⣀⣉⣿⠉⠛⠁
⠀⠀⠀⠈⠈⠻⢦⡴⠼⠉⣰⠖⠚⠒⡆⣇⢻⣽⣍⢻⣎⢿⣿⢧⣿⡿⡿⣧⣸⡿⣎⣠⣷⣴⣶⣾⡝⣷⡟⣿⠏⣼⢫⣿⣿⣿⠅⣠⡈⣷⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠼⣛⡆⠚⠹⣾⣷⣟⣰⣟⣷⣙⢿⡿⣝⣣⣟⣻⣿⣿⣧⣽⣿⣾⣿⣿⣏⡾⣿⣶⡽⣾⣿⢋⣀⠈⡻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣉⣆⠘⣦⡿⣿⡽⣿⣟⣷⣿⠿⣛⡿⣷⣿⣽⣯⣻⣽⣷⣾⢿⣫⣷⣿⡿⣿⣿⣻⢾⣿⣿⡗⠺⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣔⣿⣩⣿⣿⣿⣷⣿⣿⣷⠿⢿⣷⣾⡿⣯⣭⡽⣿⠾⣟⠻⠿⣶⣿⣿⣷⣪⣙⡜⣈⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠈⠋⢉⣉⢻⣿⣿⡇⣴⣦⠸⣟⡿⢳⣿⣿⣾⡳⠽⠋⢰⣶⢨⣿⣽⣟⣥⢬⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠏⠱⣿⣟⣷⣼⣧⣤⣤⣾⣯⣭⣥⣭⣽⣦⣤⣶⣧⣾⣿⣻⠟⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣟⣿⣿⣻⣙⣿⣿⠋⠈⢻⣿⣿⣽⣯⣿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠈⠙⠯⠀⢸⣧⣖⣞⣳⣿⠀⠈⠟⠀⠀⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣯⣬⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣁⣉⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠉⠉⠙⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⣠⣾⣿⠇⠀⣿⡇⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⠀⣴⣿⠟⠉⠙⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⢀⣼⣿⣿⠏⠀⢠⣿⠇⠀⠀⠀⠀⣾⡿⠛⠉⠉⢻⣿⣄⣀⠀⣼⣿⠃⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⢸⣿⣿⠋⠀⢠⣿⣿⣶⣤⣶⣶⣾⣿⣧⣀⣤⣾⣿⠿⠛⢿⣿⣿⠃⠀⢠⣾⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣿⣿⠃⠀⢠⣿⠃⠀⣹⠟⠉⠀⣿⠏⠀⢈⣿⠋⢀⡶⠀⢀⣿⠇⠀⢠⡿⢋⡁⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⢀⣾⠇⠀⠀⢀⠀⠀⢰⡏⠀⢀⣾⣯⠀⢾⣁⣠⣾⡟⠀⠀⠋⣴⡟⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⣼⡿⠀⠀⢠⣿⣷⣶⣿⠀⠀⢸⡟⠘⠷⣶⣌⠙⣿⠁⠀⠀⣾⣿⠁⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣄⣀⣸⣿⠀⣿⣿⡀⠀⢸⣿⣄⠀⠀⠀⢀⣿⣄⠀⢸⣿⣿⡀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣀⣨⣿⡏⠛⠻⠟⠋⠀⠘⠻⠿⡿⠿⠟⠻⢿⣿⣿⠿⠟⠻⠿⠿⠛⠻⠿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠋



⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣤⣤⣀
⠀⠀⠀⠀⠀⣀⣤⣤⣄⣰⡿⠁⠀⠀⠉⠁⢹⡄⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠐⢀⣾⣿⢾⣿⣿⣿⣧⡀⠀⢀⡴⠖⠛⠛⢿⣶⡀⠀⠀⣴⠟⠛⠋⢿⣿⡆
⠀⠀⢾⣿⠃⠈⠉⠀⠀⢻⣿⣄⠀⠀⡀⠾⣾⡇⠀⠀⠈⠉⢻⣿⠀⣾⠀⠀⠀⠀⠀⢻⣿⡄⠸⠃⠀⠀⢀⠀⠸⣇
⠀⠀⠻⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠃⡀⠀⠈⠀⠀⠛⠃⣿⠈⠀⠀⠁⠀⠈⣿⣷
⠀⠀⠀⠀⠀⡄⢠⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠨⣿⣿⣆⠀⠀⠀⢀⡄⠠⡀
⠀⠀⠀⠀⠀⠃⠼⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⡰⠀⠃⢰⠀⠸⣿⡆⣶⣤⠀⠘⡇⠘⣿⣆⠀⠠⣿⢸⣁⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⡀⠈⠀⠀⣿⠃⣿⡿⠀⠀⠁⠀⢸⣿⡆⠀⡆⠼⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢻⠀⠋⣠⠄⠀⠀⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢣⡂⡀⡦
⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠢⡈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞
⠀⠉⠉⠉⠉⠋⠋⠛⠛⠛⠿⠾⠶⢦⣬⣤⣶⣤⣴⣶⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠲⠟⠋⠁

⠀⠀⠀⡀⠀⢀⣀⡀
⠀⠀⠘⣅⠀⢾⠛⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡴⣿⠖⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣶⣷⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣿⣿⡿⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠞⠿⠛⠛⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠒⠠⡀⠀⠀⠀⠀⢀⡤⠒⠠⠀⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⢀⣀⠄⡀
⠀⠀⠀⠀⠈⠀⠀⠀⢰⡆⢀⠀⠀⠀⠀⠀⡀⠠⠀⠈⢀⠀⠈⠆⠀⠠⠀⡞⠠⠀⠈⠀⠀⢉⡉⣠⣅⢠⡄⠀⠀⡔⢎⠀⢸⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠅⣾⠀⠀⠀⠀⠀⠀⠍⢠⡌⢡⡄⠀⠀⠀⠻⣬⠑⡯⠃
⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠅⠀⢠⠀⠀⠡⡈⠀⠘⠀⠄⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢁⠉⠀⠀⠀⠈⠀⠀⠀⠒⠊⠀⠀⠀⠀⢀⠐⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠃⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠚⡆⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⢀⡈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠐⠀⠀⠀⠁⢸⣏⠀⠀⠀⡀⢀⠀⢑⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠆⠐⠤⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⡀⢰⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⠀⠐⢄⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠆⠀⢀⡁⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠘⠈⠃⠀⡂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠄⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠠⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⡀⠀⠱⣀⢀⣀⣤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⠔⠁
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡠⠂⠉⣩⠉⠑⠠⡀⠀⠀⠀⠰⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⢄⢀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠉⣐⣀⠔⠁⠀⠀⠠⢄⠈⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠔⠉⡑⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⣃⠀⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⡆⠀⠑⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠃⠂⢀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠊⡀⠀⣀⠈⠳⣄⠀⠰⠌⡤⠂⡐⡄⠀⠀⠛⠀⢠⡷⢾⡇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠉⠁⠢⠀⡇⠈⠋⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠇⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠁
⠀⠀⠀⢠⡀⠢⡈⠀⠀⠰⠂⠀⠀⠀⠀⠐⢁⡄⠀⠑⡈⠀⡠⠁⠀⠀⠀⠀⠀⢀⠀⢠
⠀⠀⠈⠒⠴⣦⣿⣔⡾⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡷⠈⠀⡌⡆⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⢀⣤⠖⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡆⠀⠀⣤
⠀⠀⠀⠀⢠⣿⡇⠐⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠃⠀⠀⠀⠀⢀⢠⡀⡄⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠙⠶⠞⠃
⠀⠀⠀⠀⣾⣿⠓⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠾⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣷
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢀⠀⠀⠀⠀⠀⢈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣸⢀⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠅
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠻⣦⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠿⠿⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢾⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠉⠉


⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⡿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⡿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣯⣽⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉⠉⠉


⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⣿⣷⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⣿⣶⡷⢿⣾⣿⡿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣷⡾⠿⠿⠶⡿⠷⣶⡿⠷⢾⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠐⢒⠺⠓⠢⠒⠘⠏⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⣀⡀⠀⠀⡰⣴⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠰⡤⠤⠀⠤⡴⠀⠀⢠⠂⠁⠀⢀⠔⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡛⠚⠒⠐⠢⠐⠚⠁⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠔⠛⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⠠⠇⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠛⠀⠀⠷⠀⠀⠀⢀⣠⠖⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠂⢠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢳⣶⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠠⡴⠿⠁⠙⠉⠁⠀⠀⠀⠩⠆⠀⠀⠀⠀⠒⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠙⠉⠃
⠀⠀⠀⠀⠀⠀⢐⠀⢓⠀⠀⠀⠀⠀⠘⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠜⡁⡐⠲⠂⠀⠀⠀⠈⠇⢀⣄⠀⠀⠀⠀⠀⠀⢰⡶⣶
⠀⠀⠀⠀⠀⠀⠈⢤⠀⠀⠀⠀⠀⠀⡀⣈⠙⠀⠀⢐⣖⣶⡞⠆⠀⠀⠀⠀⢤⠚⣁⡚⣠⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⢀⠌⣄⡀⠀⠈⠉⠈⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠯⣣⠅⠀⠀⠀⠀⠀⠀⠀⣩⠃
⠀⠀⠀⠀⠀⠈⠛⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⡴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠰⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⢺⠠⠄⠀⠀⠀⠁⢀⣦⢤⣤⡤⣤⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠜⠀⠀⣠⠰⠿⠒⠛⠋⡉⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢤⡘⡛⡀⠜⠁
⠀⠀⠀⠀⠤⠴⠦⣐⡀⠁⣠⠦⠤⢀⣀⡸⠂⠘⠀⠙⠤⠖⠀⠀⠀⠛⠋⠙⠁⠀⠀⠀⢀⡀⠀⣴⠀⠀⠀⠀⢀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢐⡀⠀⠀⠆⣄⠈⠀⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⢿⡀⠀⠀⠀⠀⠙⣃⠅⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠁⠀⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠑⡐⠋⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠄⠀⠀⠀⠀⣤⢘⠃⠀⡀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡄⠀⠀⠀⠀⠠⣶⢈⠀⣠⢫⠄⠀⠀⠀⠀⠒⠤⢄⣀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⡌⠰⠀⠀⠀⠀⠀⠲⢿⡆⣀⡌⠀⠀⠀⠀⠀⠀⠐⠘⠛⡀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⣁⢴⡂⠀⠀⠀⠀⠀⢭⣿⠋⠁⠀⠀⠀⠀⠀⢀⡤⠤⣤⠤⡀⠀⠀⠀⠀⠀⠀⠠⢴⣶⠄⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠀⠁⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⣘⠉⠀⣚⠀⠛⣄⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠃⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣶⣶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢸⣣⣼⣦⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠿⡿⢿⠟⠿⠆
⠀⠀⠀⠀⠀⢠⣶⣿⠞⢹⢻⣿⡦⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣠
⡀⠀⠀⠀⢀⣟⠛⠀⠀⢰⠀⠋⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⢂
⢿⠀⠀⠀⠾⣿⡆⠂⣄⣸⠀⠈⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠓
⣿⡆⠀⠀⢸⣿⣃⠀⠙⠛⠀⠀⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣡⣴⠀⠀⠀⠀⠀⣼⣾⣷⣆⢠
⢿⠃⠀⠀⠀⠼⢿⣶⣶⣖⣦⣼⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣿⠟
⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣶⣶⣶⢰⣶⣶⠎
⠀⠀⣀⡀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠃⠀⢻⡟⠀⠀⠀⠀⠀⠀⠠⣄⠠⣶⠖⣀⠂
⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠈⢣⣶⣦
⠀⠀⠀⠀⠠⠶⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠠⣽⢹⣿
⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣿⡮⣭
⠀⠀⠀⠀⢀⠀⡀⠀⠄⠇⠀⠀⠀⠀⣀⣀⠔⠒⣒⠒⠠⣄⣄⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⢏⢀⠀⢐⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢰⣿⡷⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣿⣷⣾⡧
⠀⠀⠀⠶⢤⣤⡤⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠛⠛⠛⣿⣷⣿⠆
⠀⠀⠀⠀⠸⢿⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⣰⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⡏⠀⠀⠀⣿⣿⣧⠄
⠀⠀⠀⡖⢢⣤⣴⠐⡇⠀⠀⠀⠀⠀⠀⠀⠓⠒⠉⠉⠖⠚⠀⠀⠀⠀⠀⢨⣿⣿⡇⠀⣶⠄⢿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢲⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠈⢄⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠄⠀⠀⠀⡻⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡄⠁⠀⠁⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠤⠤⣾⣿⣟⣶⣃⠀⠊⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠠
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠆⠑⣤⡟⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡿⢿⣿⠁⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠈⣷⡄⠀⠀⣤⡏⠀⣼⠇⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠁⢸⣦⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⣀⡄⠘
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⠋⠀⣴⣿⠃⠀⠀⠀⠁⠀⠀⠀⠘⡿⢽⡢⢄⡀⠀⣀⡆⠸⣿⣷⣷⣼⠋⠀⠀⠀⠀⡄⠀⠀⢣⠀⠸⠇⠤⣿
⠀⠀⠀⠀⠀⠀⠀⡻⣦⡀⠘⣶⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠀⠘
⠀⠀⠀⠀⠀⣎⢰⡇⢸⣿⡆⢹⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠁⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⢸⣯⠀⡘⠉⣷⡀⢹⡄⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡀⠄
⠀⠀⠀⠀⠀⠈⠁⠘⠁⠈⠙⠳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⠀⠀⠀⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⡀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣰⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⠶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⣷⣴⡿⠇⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠒⠶⠶⠶⠶⠾⠑⠛⠁⠀⠀⠀⠠⠒⠛⠹⠉⠃⠁⠙⠁⠀⠀⢢⠄⠋⠉
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣹⣄⠀⠼⣿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠀⠀⠀⠀⡀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⢸⡦⣤⠀⢠⣤⠿⠛⢿⠀⢹⠀⡁⠀⠀⠀⢀⡌⣠⣦⠀⠂⢸⠤⠀⡀⣴⠆⢀⡴⠀⠀⠀⠀⢠⣿⠀⣰⠟⠦⠀⠀⠔⠃
⠀⠀⠀⢠⠊⢀⡾⠀⠈⠀⠀⠀⠀⠀⠈⣆⢘⣴⠃⠀⠀⢀⣼⣴⠋⡰⠃⠀⠀⠀⠀⠀⠀⠀⠎⠇⠀⠀⠀⠀⠘⠁⣼⠁⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⣼⣠⡏⣇⠀⡂⠀⠀⠀⠀⠀⠀⢻⣸⡟⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠸⣁
⠀⠀⠀⢽⣿⡄⠛⠛⠛⠁⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠞⣶⣢⠀⠀⠀⠀⠀⢰⣢⠔⠒⠒⠒⠒⠒⠲⢖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢿⠀⠠⠌⠳⣄⠀⠀⠀⠀⢸⠀⠛⢠⣌⡆⠘⠀⠣⣤⠤⢤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⠈⢧⡀⠀⠀⣨⣦⡀⠀⠀⠈⢆⠀⠠⠛⠄⠀⠀⣀⠀⣤⠀⠉⠀⠾⠇⠙⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣶⣿⣿⡉⠳⣄⠹⣦⣴⣿⣾⠇⠀⠀⠀⠀⠙⣶⡖⢒⣌⠀⠉⢀⡀⠀⠛⠃⢠⣄⠛⠃⢸⣦⡀
⠀⠀⠀⠀⢀⣤⠚⠹⡇⠀⢿⠀⠹⡆⠈⠳⡄⠈⠳⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⢩⡀⣈⠉⢠⡄⠈⢃⡀⠿⠂⣀⡀⢰⡶⠀⡦⣍⣒⠒⣶⣶⡦
⠀⠀⠀⣰⡏⠸⣆⠀⢻⡀⠘⣧⠀⠹⣆⠀⠙⢦⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠉⡷⢠⠊⠉⠉⠉⠉⠑⢻⡁⡎⢑⠸⠃⠀⠀⠈⠉
⠀⠀⢰⠃⡿⣄⡙⢦⡀⢷⡀⠈⣧⣀⠈⠷⣤⢄⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⠀⢰⣼⠀⠀⠀⠀⠀⠀⠀⣷⡇⠸⣶
⠀⠀⠀⢰⣆⢹⢹⡈⡟⠉⠁⠀⠀⠈⢷⡀⡇⠸⢦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣀⣀⣀⣄⣀⣀⡤⣈⣤⡀⢉⡴⠶⢄⡀
⠀⠀⠀⠀⡟⡿⢨⣹⠇⠀⠀⠀⠀⠀⢨⣙⠇⢸⣤⡇⠀⠀⠀⢀⣀⣤⣤⣲⣶⠶⠭⠿⠽⠷⠚⠓⠛⠚⠓⠛⠀⠉⠀⠉⠉⠀⠀⠀⠉⠉⠑⠒⠒⠒⣤
⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠈⣉⣀⣀⠉⠀⠀⡤⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣋⣹⣉⢭⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠁⠉⠉⠓⢦⡉⠙⠒⠒⠒⠒⠒⠢⠤⣄⡀⠀⣀⠀⢀⠤⠤⠤⠤⠤⠤⠤⣄⠀⣤⡀⢠⠴⠖⠒⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣀⢀⣀⣀⠀⣀⣀⡀⢀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣼⠉⢦⠏⠀⠀⠀⠀⠀⠀⠀⠘⠴⠁⠣⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠈⢳⠁⢤⢀⠒⠀⣤⠈⡟⠁⢻⠀⠀⠀⢀⡄⢀⡄⠀⠀⠀⠀⠀⠀⠠⡋⠑⠒⠒⠒⠲⢤⡤⢤
⠀⠀⠀⣠⠔⠚⠋⠉⠉⢹⡄⠀⠸⡀⠀⠘⣿⠃⠀⢠⠃⠀⣸⠀⠀⣀⠴⢛⠛⣆⠀⠀⠀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⠀⠨⣴⣁⣀⣀
⠀⣰⢿⠁⠀⠀⠀⠀⠀⠀⠳⣀⠀⠑⠦⢄⣀⡡⠴⠋⠀⡰⠃⠀⣞⣉⡀⠀⠀⢸⡿⡄⠀⢠⢊⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠉⠑⠢⣄⢀⡀
⣰⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠙⣦⠶⠀⣿⣧⠀⢲⠈⠁⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠏
⠀⠀⢸⢀⡶⡄⢠⡤⠤⠤⠤⠤⠤⣄⠀⠴⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢰⣿⠾⡆⠈⠳⢄⣀⡀⣀⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⢸⠀⡇⡿⠀⠀⠀⠀⠀⠀⢹⢸⠀⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⣟⣿⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⠞⠀⠳⠃⠀⠀⠀⠀⠀⠀⠘⠞⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢻⠽⡄⠀⠀⠀⢸⠀⠀⣠⡀⠀⢠⠖⠒⠒⠲⡄⠀⢠⡀⠀⢸
⠀⠀⠀⢀⡤⠤⢤⣀⣠⣤⣄⣀⡀⣠⠴⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣴⡼⡗⢶⠀⠀⠀⠸⡀⣀⡇⡇⠀⣸⠀⠀⠀⠀⣇⣀⡾⡇⠀⡸
⠀⠀⣰⠃⠀⢀⠞⠁⠀⠀⠀⠀⠹⡅⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢯⣹⣄⣀⣀⣀⡀⣀⣀⣉⣉⣁⡀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⡇⠀⠀⣜⡀⠀⠀⠀⣀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠿⠿⠁⢉⣴⣤⠀⠀⠉⠉⠉⢿⠿⠋⠲⢤
⠀⠀⠹⣄⡀⢫⠁⠀⠀⠈⠉⠁⠀⠘⠤⣀⣀⡠⠎⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⢸⡿⠃⠀⢠⣤⡀⠈⠛⠋⠀⢰⣿⠆⠀⠀⢰⣿⡆⠈⣇
⠀⠀⢀⣀⠉⠙⣇⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠈⣇⠀⠀⠙⠛⠃⠀⢸⣿⠆⠀⠀⠀⢾⡷⠀⠉⠀⡴⢻
⠀⠀⠘⢌⠙⠒⠃⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣿⢸⢳⠰⡿⠳⠶⠖⠒⠒⠒⠒⠛⠉⢳⢠⢿⢠⠇⢸⡀
⠀⠀⠀⠀⠉⠓⠒⠒⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⡇⢸⠘⡇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⢸⢸⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡄⠀⠀⡤⠤⠤⠤⠤⢤⡀⠀⢀⠀⠀⣿⠀⠀⠀⠀⡇⣾⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢻⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⢸⡆⠀⣿⠀⠀⠀⠀⣇⡿⠀⢸⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡸⢸⡀⢀⠇⠀⠀⠀⠀⠀⢇⠀⡼⡇⠀⡟⠀⠀⠀⠀⢿⡇⠀⠘⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⢇⡾⢸⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⢫⣧⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⣠⡇⠐⠙⢿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣥⣴⣾⠋⠀⠰⠷⠈⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⣋⣭⣵⣾⣯⡐⠷⠀⠀⡀⠀⣿⣿⣿⣿⣦⡀⠀⠘⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠛⠛⠉⣿⣦⣄⠈⠁⠀⠀⠉⠛⠿⣿⣿⣶⣶⢟⣿⠇⠀⠲⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠅⠈⠀⠃⡸⠋⡣⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣏⣀⣠⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣫⣿⠃⢀⠀⠐⠜⠂⠆⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣽⣿⡿⢛⡛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠠⠀⠤⠜⠀⢀⡠⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⢹⡿⣷⣌⢻⣿⣿⣿⠿⠿⢿⣦⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⡀⠀⠀⠐⠀⠀⠠⠄⠅⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣾⣿⡟⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠵⡀⢄⣴⣶⣿⣿⠥⢀⠀⠄⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿⡿⣏⣿⡇⠀⠀⣀⣠⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣴⢬⣿⣿⣝⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⢰⣿⣿⠀⠻⣾⣿⣦⡀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⠋⠈⢿⣝⡻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⣟⢇⠀⠀⠉⠉⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠉⠛⣿⣷⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠰⠿⠟⢻⣮⡓⠦⡤⣶⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠⣴⡿⠟⠿⣶⡀⠙⠻⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣾⣿⠃⣴⢿⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠹⠦⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⢀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⢠⣾⡿⠙⣷⠀⣀⣤⣤⡴⠶⢦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⣴⣿⠟⠀⢀⣿⣿⣿⠟⠁⢀⣤⣾⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣝⡲⠶⢶⣶⣶⠿⠟⠋⠀⢀⣠⣾⡿⠋⠀⣠⣾⣿⠟⠁⣠⣶⣿⣿⡿⠛⠁⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠳⣝⡶⣤⣤⣤⣤⣤⣴⣶⡿⠟⠋⣠⣴⣿⠿⠋⢁⣴⣾⣿⣿⠟⠋⠀⢀⣴⠶⠶⢤⡈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣛⠶⣯⣭⣍⣉⣩⣥⣤⡶⠿⠛⠉⢁⣤⣾⣿⡿⠟⠉⠀⠀⠀⠀⣾⡇⢰⣆⣼⡇⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣍⣉⣉⣁⣀⣤⣤⣶⣾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣉⣉⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠄⠠⠀⠀⠀⠀⡠⠐⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠤⣀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⣀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠊⠀⠀⠀⠒⠲⣄⠀⠀⠀⠀⠀⠀⡀⠀⠓⠠⠀⠨⠄⠂
⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠠
⠀⠀⠀⠀⡠⠒⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⡀⠤⠀⠀⠈⠐⠀⠀⠈⠉⠉⠀⣀⡀
⠀⠀⠀⠀⠂⠀⠁⠉⠉⠀⡀⠠⠔⣈⡀⠀⡀⠀⠠⠄⢂⢠⠀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠨⡠⠤⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⢾⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠄⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠨⠤⢄⣤⣬⣥⣤⠄⠀⠀⠀⠀⢀⡀⠀⠀⠠⢔⣽⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠄⣀⠀⠉⠐⠒⠀⠄⠠⠤⠀⠀⠀⠀⠤⠄⠐⠷⢤⣤⣀⣀⣀⣀⣐⣐⣨⡧⢀⠠⣊⠔⠒⠉⠉⠉⠙⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠒⠒⠠⠄⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢁⠀⡀⠀⡴⠃⢀⠠⠀⠀⠄⠠⢌⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⢧⡔⡥⠚⠉⠉⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⠀⠀⠀⠀⠠⠀⠐⡀⠔⡯⠥⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣟⠒⠤⠤⣤⠭⢤⣴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣌⡀⠉⠉⠙⠛⠛⠛⠛⠛⢑⣂⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠲⠶⠖⠒⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠄⠠⠈⠠⠀⠀⠠⠂⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⡀⠀⣠⣤⣤⣄⡀⠙⠏⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⢀⣸⣧⡀⠙⠛⠛⠛⠁⠈⠋⠀⣀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠈⢻⡟⠉⠀⠀⠀⠰⠶⠀⠀⠀⠙⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠇⠀⠃⠀⠈⠁⢀⣤⣶⣷⣦⣄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣠⡀⠀⠀⠉⠉⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⡀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⠁⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠉⠁⠉⠀⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣤⠀⠈⠋⠀⢰⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠰⣿⣿⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣟⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡀⣀⣤⣤⣄⣤⠤⠀⠀⠀⣀⠄⠘⠛⠉⠹⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡾⠟⠋⠀⠀⠀⠀⠀⠈⠛⠟⠀⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠷⣀⠀⠀⢀⠉⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⡜⣻⠀⠀⣹⡆⠀⠐⣀⠘⠃⣐⠃⠀⠀⢠⡆⠀⢱⠒⢛⢳⠦⠐
⠀⠀⠀⠀⠊⠀⠐⢬⣒⢥⡬⣟⠁⠀⠉⠁⠀⠀⠈⠘⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠨⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠐⠠⠀⠀⠀⠀⠀⠀⢸⣀⠆
⠀⠀⠀⠀⠀⠀⠖⠰⠆⠀⠒⠘⠃⠀⠀⠀⠀⠀⠀⡼⣆⠀⠠⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢈⠀⠀⠀⠀⢄⠂⠓⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡴⡒⢃⠈⡐⠀⠀⠀⠠⡄⡄⠀⠁⠀⠀⠀⠀⠀⠄⠎⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⣀⠥⢀⡐⡀⠐⣀⠈⡀⠀⠀⠀⢡⡄⠀⠀⠀⠀⠀⠀⠀⢔⠁⡔⠀⠀⢀
⠀⠀⠀⠀⠀⠒⠒⢀⠃⢐⡈⠀⢩⡀⢡⡄⠀⠀⠀⡆⠀⣤⡆⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣀⠀⡘⢃⡄⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠈⡋⠈⠃⠀⡀⠀⠀⠀⠂⠀⠰⠄
⠀⠀⠀⠀⡠⠋⠈⠒⠋⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠐⠙⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠖⠒⠚⠉⠛⠋⠋⠋⠀⠠⠦⠤⠆⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢤⡀⠋⠶⠴⠴⣄⡄⠀⠀⠧⢀⠀⡀⠑⢖⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠒⠂⢠⢀⣤⠀⠀⣰⠀⠘⣧⡄⠐⠛⠁⠛⠄⠀⣅⠂⠬⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠠⡔⡖⢻⢀⠠⠒⣄⢼⠝⠏⠋⠀⠀⠶⠋⠑⠒⠚⠷⠂⢀⣀⠀⠂⠰⣌⣆⠀⡀⠈⢹⣄⡄
⠀⠀⠀⠀⠀⠀⢠⠹⣦⣼⣧⣶⡿⠟⠉⠀⢓⡳⠂⠡⣄⠀⠀⠀⠀⠘⣧⠀⠀⢉⡧⢀⠀⢹⡦⣀⠀⠈⢿⡇⠀⡀
⠀⠀⠀⡀⢸⠀⠎⢀⣸⣿⢳⣏⣤⠤⠚⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⢇⣆⣷⢀⠁⠘⡧⢸⣦⡀⠎⢷⡴⢻⡆
⠀⠀⠀⣧⠀⡆⠀⡸⢋⡿⣾⣉⣆⢠⢠⡠⣴⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢿⠳⠷⣧⡄⣣⡑⡄⢼⣷⣾⠁
⠀⠀⢀⠸⡔⡉⢶⡟⣹⣱⡟⠓⠁⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠵⠂⠳⣄⣏⠘⠻⢷⣿⣀⣿⡃⣨
⠀⢳⠈⡦⢻⣦⡟⣿⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⢸⣿⡝⣿⡷⡴⠂
⠀⠈⢷⡄⠈⢿⣾⢃⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠳⣿⡇⢻⣇⢽⠄
⣄⠀⣸⢿⣆⣼⣟⣱⣿⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡑⢻⡷⣼⣿⣷
⠘⣧⡽⣎⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢟⣸⣿⣼⣿⠏
⠀⠘⣧⣿⢸⣿⣿⢀⣄⠀⢠⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⡏
⠀⢀⢹⣾⢾⣿⣿⣨⠋⠡⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣷⣀⠀⡓⢾⣿⣿⢳
⠐⢾⡤⣿⣤⣿⣿⡄⠀⢸⣿⣫⡀⠀⢠⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣟⡻⡟⣾⣿⣿⢸⠇
⠀⠸⣿⢏⢿⣿⣿⣧⠀⢒⢸⣟⡆⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⡇⢈⣿⣿⡇⢸⠀⠠
⠀⠀⢹⡥⡂⢻⣿⣿⣧⠀⢖⣿⢩⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣛⣿⠥⣼⣿⣿⣇⡏⠀⠏
⠀⠀⠀⠘⢷⡈⣿⣿⣿⣷⡨⣯⣾⣿⢘⣠⣀⡆⠀⠀⠀⠀⠀⠀⠀⢶⣷⣆⡀⠀⠈⢀⣤⡸⣿⣏⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣾⣿⣛⠛⣿⣻⣿⣶⣄⢀⠀⢀⠀⠀⠘⢝⢯⣇⢆⣇⡞⣿⠩⢿⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠛⠻⣿⣷⣾⠼⠿⠿⠿⠯⣄⣠⣤⡄⢠⠴⠓⢉⣩⣍⠙⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠓⠦⠤⣼⣿⣥⠤⠄⣨⡤⠐⠀⠀⢈⠗⣅⠀⣲⣊⣹⣥⣾⣿⣿⣿⣿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡏⠉⢻⣿⣟⣩⣹⣷⣶⣊⣠⠶⢻⣯⠟⠉⠀⠀⢤⣤⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠿⠏⠀⠊⠁⠐⢤⠞⠂⠀⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⡀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡀
⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⠐⡇⡾⣫⠾⣧⢤⡄⠀⢠⢞⠿⣷⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠛⠋⠉⠓⢡⣠⠁
⠀⠀⠀⠀⠈⣷⡀⠀⢳⡀⠀⣀⢿⡟⠡⡎⠀⡄⡇⠀⢸⡘⠆⠈⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠀⠀⠉⢀⣤⠞⠿⠃
⠀⣀⠄⠂⢀⣿⣿⡆⠉⢷⣶⡏⢉⢧⠀⢻⠓⢣⠇⠀⣾⣿⠆⠀⠀⠀⠀⠀⢰⣀⠀⠀⢀⢁⡀⢹⣄⠠⡟
⠸⡿⠀⠀⡏⠉⠈⢷⠀⠀⠈⠻⡌⣧⢳⣀⡴⠃⠀⣰⡿⢿⠂⠀⢠⣶⣶⣶⠇⠈⠂⠀⣸⠉⠉⢐⠨⢧⣀
⠀⠀⠀⠀⠀⠠⠀⠈⠇⠀⢀⣴⡷⠸⠋⠁⠀⢀⡼⣯⣟⡞⠀⠀⠀⠀⢸⡟⠁⠀⠀⢸⣇⠀⢰⡏⠀⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠁⠀⠀⠀⣔⣭⣿⣮⣛⠁⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠉⠳⠚⠷⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⢎⠟⡟⡝⣿⡇⠀⠀⢢⠴⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡍⢲⢊⠂⡓⡬⢷⡩⣇⠀⡠⠿⠅⢾⣙⣿⣇⢀⣀⣀⣀⣤⣤⠴⣆⣀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢇⡍⡦⢚⣣⠋⠠⢽⡇⠘⠿⠋⠁⠿⡿⢻⢳⣋⢟⣿⢴⢫⢗⡭⡛⢒⠏⠑⠢⠴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⢂⡁⣀⡕⠀⠀⡹⠢⠾⡛⣀⠀⠀⠀⠀⠻⠅⢋⡫⣿⢻⣸⠛⠘⣋⣵⡆⠁
⠀⠀⠀⠀⠀⢀⣶⡦⠀⢀⢋⠁⢑⠀⠀⠀⠀⠇⠃⠀⠀⠑⡁⠀⠀⠀⠀⠀⠁⡰⠟⠀⠛⠂⠀⠈⠁⠍⠂
⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠸⠇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⢀⠠⠀⠀⠀⠀⡀⢀⣧⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠤⠶⠚⢀⡜⢡⣠⣼⣡⣴⡄⣐⣼⣿⣿⣿⠇⠀⠀⢰
⠀⠀⠀⣦⣴⠎⠁⠐⠖⠀⠀⠀⠀⠀⠀⠠⡀⠀⠹⣆⡽⢭⠉⠹⠿⣿⣿⣿⣿⡿⠁⠀⠀⢠⣾⡀⢠⣤⡷⣄
⢰⠀⠀⢸⡿⠀⢀⠀⠀⠐⣧⣆⠀⠀⠐⢰⣷⠀⣦⠹⢄⠨⠀⠀⢠⣿⠿⣿⣿⣿⣦⣤⣴⣿⣿⣧⣿⣿⠇⠘⡇
⠘⣆⠲⣼⠁⠀⢸⣿⣶⣶⣿⣿⣶⣶⣾⣿⣟⣾⢯⡀⠀⠀⠀⢀⠎⣀⡴⠛⢿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣆⠀⠙⠶⠄
⠀⠈⣿⡇⠀⠐⠛⢿⣿⣿⡿⠿⠿⠛⢹⣿⣻⣿⠀⠀⠀⠀⢰⣴⡞⠋⠀⠀⠘⠿⣿⠀⠀⠀⣿⣿⡏⢻⡋
⠀⠀⠈⠁⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⣸⣿⣹⣿⠀⠀⠀⠀⠘⠻⠟⠀⠀⠀⠀⠠⠙⠆⠀⣰⣿⡏⠀⣸⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠁⠈⠙⠛⠁⠀⠈⠉⠁

⠀⠀⠀⠤⠀⠀⠠⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⡠⡤⢠⡄⠀⠀⠀⢀⡀⠶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⡤⡄⢀⠁⠀⢠⡄⠀⠀⡂⡀⠀⠀⠀⠀⠀⢀⢡⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠇⣀⠀⠀⢠⠢⠀⢄⠕⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⠀⠀⢀⠀⠀⠀⡈⣠⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠤⠄⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠸⠰⢳⣦⠁⠀⠉⠀⠁⠈⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠠⠌⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡂⠀⡀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠇⢀⡀
⠀⠐⠐⠀⠉⠛⠒⠆⠀⠀⢠⠀⠀⠀⠀⠈⠀⠘⠈⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⠀⠀⠠⠄⠐⠛⠀⠀⠐⠒⢀⡄⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠
⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⠀⠎⠄⠅⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢔⠄⠑⠀⠁⠀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠⠀⠉⠁⠀⠀⠀⠀⠀⠒⡀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠠⠄⠂⠀⠐⠠⠀⠀⠠⠤
⠀⠀⠀⠐⠀⢀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠐⠐⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡕⡂⠀⢠⠅⠀⠀⠀⠀⠀⠄⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠖⠐⠾⠣
⠀⠀⠀⠐⠂⠀⠑⠀⠄⠀⠀⠁⠀⠋⠃⠀⠀⠘⠉⠀⠀⠀⠐⠀⠀⠋⠀⠀⠀⠀⠐⠀⠀⠀⠠⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠀⠄
⠀⠀⣤⡄⠡⠄⠀⠀⠀⠀⠀⠀⠂⠀⠐⡐⠂⠀⠀⠀⠈⠀⠐⠀⠀⠀⠒⠲⠒⠐⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⠤⣤⠄
⠀⠀⠀⠀⡄⣅⡀⠀⠀⠠⠦⠄⠀⠀⠀⠰⠀⠀⠀⠈⠥⠖⠀⠀⣔⠠⠀⠀⠐⠡⢐⠄⠀⠀⠀⠀⠂⠠⠀⠁⠀⠀⠂⠀⠀⠒
⠀⠀⣀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠈⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠂⠒⠀⠀⠐⠂
⠀⠀⠁⠀⠂⠂⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠀⠀⠀⠀⠀⠀⠈⠀⠐⡃⠀⠀⠸⠂⠀⠐⠆⢀⡀⢆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠧⠀⠀⠠⠄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡈⠀⠉⠈⠀⠱⠎⢠⠃⠈⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠰⣄⡀⠀⠀⠀⢈⠀⠀⠁⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠘
⠀⠀⠀⠀⠐⠀⠂⠀⠀⠒⠀⠀⠄⠀⠀⠀⠂⠀⠔⠀⠀⠈⠉⠀⠀⠀⠂⠄⠰⠀⠀⠀⠀⠀⠀⢈⠈⠀⠉⡀⠸⠀⠀⠀⠀⠨⠀⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠘⠐⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠈⠘⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⢦⣼⠀⡌⣿⣿⡆⢻⡰⣴⣃⡶⠋⠹⢲⡼⠀⢠⡸⠀⠀⢸⡄⢴⠥⣰⣷⡞⢻⡈⢸⣿⣿⣧⢸⣿⣀⢼⢿
⣛⣿⣇⡿⣿⣿⣷⠋⣷⠋⢸⠀⣥⠟⡼⠓⠂⢩⡤⣰⠀⠈⢷⡘⠮⢼⡞⣷⠀⢻⣾⣿⣿⣿⣾⣿⣸⣽⣿
⠘⢧⣸⣧⣿⣿⣿⣼⠉⣧⡯⣂⡴⠚⠁⠀⢐⠘⠆⣬⡳⢦⡈⢷⡤⣉⣿⡜⣄⡄⠹⣿⣿⣿⣿⣿⢉⣿⣿
⡦⣹⡟⠈⣿⣿⣿⣇⣾⣿⡞⠉⠀⢬⠌⣠⠀⠤⠄⠰⠭⠵⢿⣿⣷⣌⣐⠿⣎⠻⣄⣿⣿⣿⣿⣿⣼⣿⡷
⣷⣼⣷⣞⣿⣿⣿⠞⢡⡿⢀⣤⣉⣤⣞⠚⠯⠀⠀⠉⠊⠀⠀⠀⠉⠻⢾⣝⠾⣿⡟⣿⣿⣿⣿⣿⣿⣯⣏
⠸⣏⣿⣿⣿⣿⣿⢸⡿⣷⣩⣠⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣿⣿⣿⣿⣿⣿⣦⣾
⠀⢹⣏⣸⣿⣿⣿⣿⣋⡽⠯⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⢹
⢀⡾⠙⣿⣿⣿⣿⣏⠿⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⢸
⣼⠁⢰⣿⣿⣿⣿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣿⣿⣿⣿⣿⡇⢸
⣏⢀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⣿⣿⣿⣿⣿⣧⢠
⣿⡟⢰⣿⣿⣿⣿⢾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠤⢻⣿⣿⣿⣿⣿⣿
⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣿⣿⣿⣿⣿⡏
⣿⣇⢸⣿⣿⣿⣿⣧⡀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⡇⠉⣿⣿⣿⣿⣿⣿⡇
⠘⣿⣾⣿⣿⣿⣿⣿⡘⣌⠂⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡇⣴⣿⣿⣿⣿⣿⣿⣇
⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⣰⡿⣝⡞⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢰⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡃⢸⡷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢹⣸⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿
⢋⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⡕⠀⠀⡀⢀⣀⣀⣠⣤⣤⡤⣶⣷⣿⣿⡟⢻⣿⣿⣆⣿⣿⣧⢻⣿
⣾⠃⣸⣾⢻⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣦⣴⡷⠛⢋⣭⢿⣉⣴⢿⣿⣿⣿⡿⣠⣾⣧⢻⣇⠟⣿⣞⣷⣻
⡟⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⣷⡟⢣⣾⣱⣷⣟⣿⣿⣿⢇⣿⣿⣿⣾⣿⣷⣻⣿⡟⣿
⣷⠀⣿⡟⢸⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⣿⣷⣿⣿⣿⣿⡏⣽⣿⣿⠸⣿⣿⣿⢣⣿⢹⣿⣿⣿⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⠂⡸⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⡝⠻⢧⣄⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⡏⢠⡎⠹⡆⠀⠀⠋⠒⢤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠡⡘⢷⣠⡇⡀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣼⠸⣿⡀⠀⠈⡢⣝⠛⠧⢀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠙⠷⠾⠮⣅⣉⡒⣤⣀⠁⠓⠺⢅⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣤⠞⠟⠓⣲⣦⣤⣄⡀⠈⠙⠺⣟⡲⣦⡂⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠁⠀⢀⣽⡿⠛⠉⠈⠹⣆⠀⠀⠀⠹⡄⠙⢦⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⣸⣟⠂⠀⠀⠀⢠⡿⠀⠀⠀⠀⡇⠈⠈⢷⣁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢠⡋⠉⠙⢻⠒⢤⣾⡟⠁⠀⠀⣠⠞⠀⢀⠀⢸⣿⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢄⡈⢿⡻⠶⠃⠀⠃⢈⢿⠿⢷⣿⣅⡀⠀⠈⢀⣾⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⢦⢹⡿⢽⣶⣄⣀⠀⠈⠁⠀⠀⠀⠈⠉⠓⠶⢮⣈⡴⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠆⠙⣿⠁⠄⠈⠹⣿⣭⡒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢻⣦⡀⠀⠀⠻⣷⡙⢦⡉⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣀⠀⠀⠀⠀⠀⢈⡄⠀⠈⡆⠉⢳⠢⠄⡘⢷⡼⠟⠋⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢤⣝⢦⠈⠳⢤⣀⠀⠀⠀⢇⡀⠀⢱⣀⣨⠦⠖⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⡀⠀⠀⠈⠓⢄⣀⠼⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⠶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⢀⠴⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠄⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⡗⣊⣉⣦⢠⠤⠤⠤⠀⠛⠚⠉⠙⠛⠓⠒⠠⠤⠤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣭⣭⡵⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⠐⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀
⠀⠀⢰⠆⠳⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⠃⠀⠀⠀⠀⠀⢤⢰⠀⠀⠀⠀⠀⠀⠀⠂⡘
⠀⢀⡎⠠⠀⢸⡁⠀⠀⠀⠀⠀⣄⠀⠺⢢⠚⠃⢀⡄⠀⠀⠀⠲⠀⣀⣀⠐⠃⠀⠀⠀⠠⠴⠀⣀⠄⠀⠀⠤⠀⠒⠂⠀⠀⠀⠈⡟⢻⠀⢐
⠀⠀⢶⣶⠟⡇⡏⠀⠀⠀⠀⠀⠘⡗⣬⣿⡹⡄⡯⠁⠀⢀⣐⠀⠃⢴⣄⠘⡁⢂⡀⠀⣰⣦⠀⣤⠟⠀⠚⡴⠂⠈⠀⠀⠀⠑⢘⣓⣘⡣⠊
⠀⠀⠨⣐⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠗⠉⠀⠀⠀⠀⠀⠠⠧⣙⣁⠴⠑⠂⠀⠈⠘⠁⠀⠀⠉⣀⡘⠁⠀⠀⠀⢠⠀⠀⠀⠏⠹⠄⠀⠀⢀⡀
⠀⠀⠀⢿⡵⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠘⠖⠀⠀⠀⡀⠀⠀⠀⠀⢭⡥⠀⠀⠀⠀⣡⢣⠀⠀⢀⣀⠀⢠⠌⠙⠆
⠀⠀⠀⣘⢠⠀⠀⠀⢀⡷⢯⡀⠀⠀⠀⢀⢀⠀⠀⣀⠤⠄⡄⡀⠀⠸⠗⠀⠀⡀⠠⠀⡁⠠⠀⠀⠀⢰⡆⠀⢀⠀⡘⠔⢥⡏⠀⠨⠍⠀⢰⢚⠀⠈⠀⠀⡀
⠀⠀⠀⢸⡖⠀⠠⣁⠁⣷⣯⡇⠀⠤⠀⠘⢉⠀⠮⢰⡶⠳⣶⠹⡄⠀⡂⠀⠀⠀⠛⠀⡅⠘⠃⠀⠀⠈⣷⠒⠋⠀⠀⣄⣢⠀⠀⢀⣆⠀⠀⠙⠶⣀⡈⠟⠁
⠀⠀⠀⢰⢺⠀⢄⡅⢰⢾⠿⡇⠤⠄⠀⠸⠚⠀⣇⢹⣦⣤⣟⢁⠃⠈⠋⠀⠠⠀⣀⠈⠂⢀⣀⠈⠀⠀⢸⠀⠀⠀⠀⠰⠖⠀⠀⠘⡞⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⢬⡷⣾⠔⠡⠀⠀⢰⣠⠀⠀⠃⠠⡅⠄⠋⠀⠀⠀⠀⠀⠐⠁⠀⡀⠸⠁⠂⠀⠀⡟⠀⠀⠀⠀⠈⡏⠀⠀⢀⢦⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⣴⠄⠀⢐⣸⠀⠐⠀⠀⢠⠀⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠰⠇⠀⠀⠀⡏⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢐⠀⠀⠀⠘⠿⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠁⠀⠀⠀⠘⠦⠆⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠠⡄⡄⠀⠀⠀⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⡆⠀⠀⢠⠉⠄⠀⠀⠀⠘
⠀⠀⠀⢸⢉⠀⠀⠀⠖⠐⢠⠁⠀⠀⠀⠀⠇⠁⠀⠀⠀⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠷⡆⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢦⡆⠀⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢐⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠁⠀⠀⠀⠀⠈⠀⠀⡀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡞⠰⠀⢠⢠⠄⢄⠄⠀⠀⠀⠀⠀⠀⢠⢠⠄⠀⢀⠄
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠄⠰⠒⠚⠀⠀⠀⠀⠀⠞⠀⠐⠀⠰⠠⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠴⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠓⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠿⠻⣦⡀⠀⠀⡀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠂⠀⣀
⠀⠀⠀⠈⠙⠛⢻⣿⣦⣄⠀⠀⠀⠀⢸⡴⠚⠛⠀⠠⠷⠦⠤⠄⡀⢰⠀⠀⢸⣿⡌⢀⢁⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠶⠀⠘⣿⣿⠀⠈⢢⣤⡄⠘⢤⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣾⣿⠃⠀⠀⠀⠀⢀⣄⠀⠀⣠⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣴⠟⠀⠀⠀⠀⠀⠀⠑⠀⠀⢤⣴⠀⠀⠀⠀⠀⠀⠈⡿⠛⠻⠁⠀⠀⠀⠀⠀⠸⠃⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⠀⡨⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⢲⡇
⠀⠀⠀⠐⠀⠐⠃⠀⠀⠀⠀⢀⠀⠲⢠⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣦⡦⠀⠀⡰⡿⠀⠀⢿⢦
⠀⢀⠀⠠⠀⠀⡀⠀⢰⡀⠀⢀⡀⠀⢾⡆⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⠛⠻⣿⣿⣧⠀⠈⠀⡇⠀⠀⢸⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⢰⠈⠁⠀⠘⠻⣆⠀⠈⣧⣤⣤⠆⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢴⠀⠀⠐⠄⠀⠀⠀⢩⣮⢧⣀⠀⠀⢸⣴⠆⠀⠀⢸⠁⠀⠀⠀⣿⡿⠀⠀⠀⠀⢀⣀⣀⣾⠿⠋⠀⠀⠀⠀⠐⠂⠐⠒
⠀⠀⠒⠀⠀⠀⡄⠀⠺⠁⠃⠀⠀⠀⠰⣼⣭⡯⣷⡆⠀⠀⠀⠀⠀⠘⠃⠀⠰⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣀⠤⣄⣀⠀⠀⢤⡀
⠀⠀⢸⣶⡄⠀⣿⣦⣤⣴⡆⠀⠀⠀⠘⠎⠐⢾⡟⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠚⠉
⠀⠀⠘⣿⣿⠿⠻⣿⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⢻⣿⡿⢶⣶⣶⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⡀⠀⣄⡀⢀⡀⠸⠦⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠃⠀⠆⠈⠀⠂⠀⠀⠰⠚⢁⡀⠀⠸⠿⣿⣿⡿⠟⢿⣿⠛⠛⠛⠳⠄⠀⠘⠀⠀⠀⠹⠃
⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⢰⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠸⠟⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⢸⡓⠃⠀⠀⠸⠀⠛⢃⢀⡀⢀⠀⠀⠀⠀⢠⠶⢦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣾⡧⣦⠀⠀⠀⠁⢀⠸⠹⠂⡀⢈⠇⢳⠆⢀⣤⣿⣶⡟⠂⠀⢀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣿⣿⣿⡿⠊
⠀⠀⠀⠀⣠⣿⣿⣇⢲⡄⠀⠀⢀⣦⠇⠀⠀⠷⢐⠀⠀⠀⢸⡟⠠⣉⣿⣷⠀⠈⠀⠀⠀⢾⣄⡀⠀⣀⣀⣄⠀⢀⡇⠀⠀⠀⠙⢟⢿⠃
⠀⠀⠀⣠⣿⣿⣿⣷⡋⠀⠀⠰⠁⠈⠀⢀⠞⠀⠆⠀⠀⠀⠘⡇⠀⠸⣇⢿⡀⠀⠀⠀⠀⠀⣿⠁⠀⠉⣿⠏⠀⢸⠀⠀⠀⠀⠀⡀
⠀⠘⠋⠉⠀⠛⠛⠛⠉⠀⠀⠀⠀⠂⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⠋⠒⠊⠀⠉⠀⠁⠉⠀⠀⠀⠀⠀⠑
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣽⣭⣯⣮⣭⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿⣿⣾⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡋⢙⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣤⣀⠀⠀⠀⠀⠀⣾⣿⣿⣏⣹⣿⣿⣿⣿⣯⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣽⣿⣷⣄⠀⠀⠀⠘⠛⠛⠛⠛⢿⠟⠛⢻⡟⠉⠉⠉⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢿⣿⣿⣿⣿⢿⣿⣦⠀⠀⠀⠀⣀⣀⡀⣼⠀⠀⢸⡇⢀⣴⣿⡿⠟⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣷⣾⣿⣿⠀⢀⣴⣿⠟⣿⣿⣿⡀⠀⢸⣧⣾⣿⣿⣿⣦⣿⣿⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⡍⠙⡏⠉⠉⠀⣴⣿⣿⣷⣦⣾⣿⣿⣿⡄⣾⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢦⣄⠀⠈⡇⠀⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣷⣼⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣾⣿⣦⠀⣷⠀⢻⠀⣼⣿⣿⣿⣿⣯⡸⣿⣿⣿⣿⣿⡇⡿⠛⠛⣻⠛⠛⠛⡟⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣙⣿⣟⣡⣿⣿⣷⡰⡇⠘⠀⠘⠛⠛⠛⠻⡿⠿⠿⣿⠿⠿⠟⢡⡇⠀⠀⡏⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠹⠉⠉⠀⣃⣄⣀⣾⠂⠀⠀⠀⠀⡇⠀⠀⡟⠀⠀⠠⢸⠇⠀⢸⠱⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠀⠁⢣⠀⠙⡆⠀⠀⠀⢰⡇⠀⢠⡇⠀⢀⡀⣾⠀⢀⡏⠁⢀⣴⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⣴⣶⣦⡘⡆⠀⢸⡀⠀⠀⢸⠀⠀⠘⣡⡾⣿⣿⡆⠀⡼⠀⢠⣾⣟⣿⣅⣽⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⣿⣿⣿⣷⠀⠈⡇⠀⠀⡞⠀⢰⣾⣿⣿⡿⣿⣿⡌⠁⠀⠘⣻⠛⠿⠿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠿⣿⠿⡟⠋⡇⠀⢸⣶⣶⡇⠀⢸⡟⣻⠛⢻⠿⢿⠇⠀⠀⢠⠇⡌⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢹⡀⢹⡄⢹⢀⣿⣧⣿⣿⠆⢸⠁⠇⠀⣾⡴⠃⠀⠀⢠⠏⣸⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣄⢧⠘⢷⡘⡆⠀⡏⢸⠁⠀⣿⡜⠀⣴⠋⠀⠀⡠⣠⢳⣌⠁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣼⣟⠈⢆⠀⢳⣇⠀⡇⢸⠀⢠⡿⠁⢰⡏⠀⣠⢞⡴⠇⡁⠈⢳⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣆⠈⢦⠘⣆⠀⠙⣄⡷⢸⠀⡼⠁⢀⡞⠀⡪⣐⢩⠴⠊⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣄⠀⠀⠈⠣⡈⠧⠈⢧⠀⠈⠃⠘⠋⠀⠀⠚⠋⠉⠈⠀⠀⣠⠔⠋⠀⠀⢠⡤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠆⠀⢸⣿⣷⡄⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⢀⣾⣿⡇⠀⠰⠀⠈⠛⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⠀⡀⠀⣼⣿⣿⣿⣿⣷⠀⢀⠀⠸⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⡶⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⣄⣠⣤⣀⣀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣶⣦⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⣴⣧⠛⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠠⣾⣏⢉⣭⡉⠉⢹⣿⣿⣿⣤⣭⣿⣶
⠀⠀⠀⠀⢸⣿⣷⣄⡟⠀⠀⠀⠰⣲⡆⠀⠈⠙⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠆⠀⠀⠀⢻⣿⡋⠿⣿⣶⣼⣿⣯⣿⠟⠻⠛⠻⠆
⠀⠀⠀⠀⣸⣿⣿⢿⣁⣤⠀⠀⠐⠁⠐⠀⠀⠀⠀⠀⠘⣿⣿⣧⣿⠛⠛⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⢸⡿⠁
⠀⢀⠤⡴⠛⠷⠿⠋⠙⠁⠀⢘⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣿⠀⠀⢸⣿⠋⢿⣿⡇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢨⣑⠀⠀⠀⠀⠀⠀⠀⠶⠟⠁⠚⠋⠀⠀⠚⠋⠀⠐⠞⠃⠀⠀⠀⠀⢯⣇⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢮⡅⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢿⢗⡅⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⢀⡇⠒⠙⠛⠳⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢾⡱⠎⠀⠀⠀⠀⠀⠀⢸⡄⠀⠙⠄⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠉⡆⠀⠀⢀⣀⣠⣤⣶⣶⣷⣿⡿⠷⠒
⠀⠀⠀⢀⣠⣤⣶⣿⣻⣿⡷⢠⡃⠀⠀⠀⠀⠀⠀⢹⡇⠐⠂⠄⠿⠄⠀⢸⣿⣿⠞⠁⠀⠀⠀⠀⢀⡞⠁⠘⣲⣿⡿⣿⣿⣿⠿⢿⡉⠁
⠀⠀⠀⢺⣿⡿⠏⣷⡛⡝⣿⡎⠷⠀⠀⠀⣴⣶⣤⣼⠁⠀⠀⠆⠀⠀⠀⢸⣯⣬⠶⠖⠃⠀⠀⠀⠀⠛⠿⠿⠛⣩⠟⠉⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢸⣷⠀⠀⠿⠈⠄⢹⠃⠀⠀⠀⢀⣥⣿⣿⣷⡀⠀⠀⠀⠀⠀⠐⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦
⠀⠀⠀⣤⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⣸⢛⠟⣋⠽⠷⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⣤⣾⡗⠀⠁⠀⠀⠀⢀⡀⠀⣴⣿⣿⣿⠋
⠀⠀⠐⡿⢸⠁⠀⠀⠀⠀⠀⡄⠀⠀⠘⠁⢰⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠃⠀⠈⢉⣿⣿⣿⣿⣿⡖⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠙⠛⠂⠀⠀⠀⠀⠀⠀⡘⠻⡟⠋⠁⠀⠀⠈⠛⣇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢣⡀⠀⠀⠀⠀⠆⠀⢄⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣴⡾⢷⣜⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠉⠁⠀⠀⠻⡿⠻⣿⣦⣄⣀⣀⣀⣠⣄⣀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠋
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣼⣿⣿⣽⣿⣆⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠀⠈⢃⠙⠋⠙⣿⠲⣄⠉⠉⠙⠋⠉
⠀⠀⢹⣿⣿⣿⡿⠈⠻⣿⣿⣿⣼⣿⣿⣿⢿⣏⠋⡟⠋⢿⡆⠀⠀⠀⠐⣿⠿⢿⣤⣤⣤⠾⢧⢦⣰⡿⠀⣿⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⣨⣿⣿⡿⠛⠁⠚⠛⠛⠙⡿⣹⡏⠀⠀⠀⠁⠙⠒⠛⠁⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⠀⠋⠀⠀⠀⡶⢿⣿⣽⣿⣷⣿⣿⡄
⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠥⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⠀⠀⠀⠀⠀⠀⠺⡟⠛⠛⠛⠛⢿⠁
⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢀⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣴⣿⣿⢤⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣁⣀⢀⣤⣶⣿⣿⣿⠇⢸⠳⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⠟⣛⣥⣶⠟⣿⡟⢩⡿⣫⢀⠘⣇⠀⠀⠀⠑⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢢⡤⠖⣪⡅⣰⡿⠟⠫⢀⣠⢾⡿⠐⠛⢱⣿⠘⠄⠻⠣⡄⠀⠀⢀⣙⢮⠁⠐⠦⣄⡀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇⠘⠋⢠⠖⠀⢀⣠⢴⣿⠏⡄⠀⣀⣴⣿⣿⡆⠰⣀⡀⠀⣷⢄⡀⠹⠄⢀⡀⠀⢈⣙⠓⣿⣼
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡵⣆⣥⡶⠞⢁⣴⣿⠟⣾⠁⡼⠿⠋⢀⡝⠻⣄⠀⠁⣠⣀⠓⠈⡀⢀⡆⠙⢰⣴⡠⣃⣏⣻⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣻⠋⠸⢋⣥⡶⠾⣿⡿⠋⠰⢃⠾⠁⢷⠀⢿⠁⠑⡹⠀⠀⠀⠹⠀⠸⡇⠸⡇⡀⣿⣿⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠁⢀⣨⠉⢁⣤⡆⠉⠀⠀⣴⡟⠀⢰⡈⠀⣼⢠⠄⠃⡈⠣⠀⡇⢀⣆⣧⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠛⠶⠾⠛⠛⠛⠓⠻⠛⠛⢿⣄⢠⡀⠁⠘⢠⣾⡷⢐⣿⣸⣠⡀⣇⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢳⢸⡇⣰⢀⣨⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣇⠀⣶⠀⣤⣼⣠⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢿⣇⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠛⠻⣿⣿⣿⣿⣾⣿⣿⣿⡷⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣤⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⣿⣿⣿⣿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠹⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠁⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠟⠁⠀⠀⣠⣶⣶⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋

⠀⠀⠀⠀⣠⣤⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡄⠘⡄⢠⢃⡨⠛⠧⣽⡤⠃⠠⠿⠄⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣧⡟⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠛⠯⠤⠤⠔⠊⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠰⢿⠀⠀⠀⣄⠫⠑⠀⡀⠀⠀⠀⠠⠀⠀⠈⠇⠒⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟
⠀⠀⠀⠀⠀⢀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⢿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠐⠐⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠀⠉⠉
⠀⠀⠄⠀⠀⠀⠀⠾⠆⢿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠄⢀⣴⣿⠟⠁
⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠁⠤⢘⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠘⠀⡒⠈⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⡀⠀⠀⠀⣾⡇⠀⠀⢠⡶⣆⠀⠀⠀⠛⠛⠛
⠀⠐⠂⠀⠀⠀⠀⠳⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠋⠀⠀⠀⠈⠀⠀⠀⢸⣽⣿⡇⠀⢀⢀
⠀⠀⠀⠀⠀⣀⡀⠳⠆⠀⠀⠀⠈⠀⠁⠀⠀⠀⡀⠀⠀⣠⣶⡧⠀⠀⠀⠀⠀⠻⠓⠀⠙⠛
⠠⠀⠀⠀⠀⢙⡃⠀⠀⠀⠐⠂⠀⢠⣤⡄⠀⠻⡟⠀⠀⠘⠁⠀⠀⡀⠀⢀⡴⡶⢢⠀⢀⣦⡀⠀⠀⠀⠀⢴⡷
⠀⠐⠢⠀⢰⣏⣷⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣤⣤⡄⠀⣾⠿⠀⠘⢷⣏⡿⠁⠈⠰
⠀⢈⠡⠀⠹⣾⡿⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠑⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠾⠮⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠛⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠆⠀⢰⠀⠀⠆⠀⠀⠈⠀⢀⡤⠒⡻⣏⠑⠢⣄⠀⠀⠀⠀⢒⠀⠗⠀⣀
⣐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⣏⣤⣤⡧⠼⣦⠤⢬⣇⠀⠀⠠⠈⠀⠀⠀⠐⠀⠀⢀⠠
⠀⠅⠀⠂⠀⢲⡶⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠉⠲⣾⣀⠀⣹⡖⠉⢸⠀⠀⠙⠀⠀⠀⠁⣰⣰⡀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⢸⣽⣶⣿⣿⣿⣶⣯⡆⠀⠀⠀⠀⠀⣠⣤⣶⣦⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠨⠄⡸⠀⣀⡀
⠀⠀⣾⣿⣿⡟⣩⠹⣿⣿⡷⠀⠀⠀⠀⣼⣿⣶⡀⣴⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠙⠋⠶⠈⣡⠈⠛⠁
⠀⠀⠞⣿⣿⡄⠀⠀⣿⣿⡛⠀⠀⠀⢠⡟⠛⠋⠐⠉⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠈⠁⢿⠇⠀⠀⠿⠙⠃⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⡀⣄⣤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠉⠛⠛⠻⠿⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⣩⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠓⠒⠒⠛⠛⠁⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠘⠂⠀⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡟⠛⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⢩⡥⠀⠀⠀⢔⢀⡆⢀⣶⠠⡆⡆⣴⠀⣤⢰⢤⡄⣰⡄⣆⠀⡆⢀⣦⢰⣄⡆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠣⠆
⠀⠀⠀⠀⠀⣲⣾⡮⠄⠀⠈⠛⠒⠀⠀⠀⠀⠘⠊⠃⠈⠹⠀⠃⠃⠛⠀⠛⠘⠘⠀⠙⠃⠛⠀⠃⠈⠛⠘⠛⠃⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠊⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠦⠤⠴⠦⠴⠸⠠⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠸⢆⡄⠀⠀⣠⠾
⠀⠀⠀⢰⣄⢀⣀⡀⢠⡦⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⢿⣿⡄
⠀⠀⠀⠀⠁⠈⠉⠁⠈⠁⠀⠀⢰⣦⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠐⢿⡶⠛⠚⠛⢷⡿⠆⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣿⡇⠻⠃⣿⡇
⠀⠀⠀⠀⣤⡤⠀⣀⣠⡄⠀⠀⠘⣿⡆⠀⠀⠀⢸⣿⠃⠀⠀⢸⢿⣶⠁⠀⠒⠀⠈⢷⣾⠇⠀⠀⠀⠀⠀⠿⢿⢤⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⣂⣀⣀⡩⢭⠅⠀⠀⠀⠘⠇⠀⠀⠀⠸⠃⠀⠀⠀⢰⣶⣿⠀⠀⠀⠀⢀⣼⣶⡆⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⣿⠃
⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠉⣴⣿⢲⣶⣾⢻⣷⠈⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣶⣶⠁
⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠺⢉⠟⠈⠁⠀⠀⠀⢠⣤⣤⠆⠀⢙⣻⣃⠀⠐⣶⣶⡆⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠈⠉⠁⠀⢠⣿⣿⣿⡆⠀⠀⠉⠀⠀⠀⢸⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⡀⠀⠀⠚⠏⠀⠀⠀⣄⣀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠛⠿⣶⣄⠀⠀⠀⠚⠻⠁⠀⠀⠠⠴⢿⡟
⠀⠀⣠⡾⠛⠉⠀⠀⢀⣠⡤⠶⠚⠛⣋⣉⣩⣭⣭⣭⣛⣦⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠁
⢠⣾⠋⠀⠀⢀⡴⠞⠉⢀⡤⢖⣪⠭⠒⠒⢋⣩⡭⠿⠛⠉⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣼⣿⠏
⣿⠃⡎⣖⡆⡞⠀⢠⠞⡡⠚⠁⢀⣠⠶⠛⠉⠀⠀⠀⠀⢀⣀⣠⣤⣶⠟⠁⠀⠀⢀⡾⣻⠏
⣿⡄⢣⠳⠃⠳⢤⣏⣞⣀⡤⠞⠋⠀⠀⠀⠀⣀⣤⣶⠟⢛⣿⠉⠁⠀⠀⠀⠀⢀⡞⣰⠃
⠘⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠿⠛⠁⣠⢎⣿⡄⠀⠀⠀⠀⢠⡞⣴⠃⢀⣸⣦⠄
⠀⠈⠻⢷⣤⣀⣀⠀⠀⢀⣀⣠⣴⡾⠛⠉⢀⣠⠴⢊⡵⢋⠘⣧⠀⠀⠀⢠⠟⡼⠃⠀⠀⠀⠙
⠀⠀⠀⠀⠈⠉⠛⣿⣛⠿⠿⠯⠗⢒⣒⣉⠥⠔⠊⡥⢖⡡⠂⠹⣆⠀⢠⠏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠐⡩⠔⣡⠀⢻⣴⢏⡾⠁
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡴⣢⣴⢃⡞
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠚⣵⢣⡞
⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⢡⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣀⣀⣠⣤⡴⠶⠛⡿⢡⠏⠀⠀⣰⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⢀⣾⣿⠏⠀⠀⠈⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⠀⠈⡟⠛⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡋⢣⠀⠀⠀⢹⠠⡇⠀⢠⣿⠟⠉⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠣⠤⠒⠚⠀⠙⠢⢾⡏⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣦⣄⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠈⢙⡏⠀⠀⣀⠀⠀⠀⠀⠀⢀⡆⢙⣮⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠦⠀⠶⠛⡇⣸⣀⣽⣧⠀⠀⠀⠀⠘⣿⣿⣿⠇⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠹⣿⣿⠏⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⠤⠤⣤⠤⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⢴⡊⠁⠀⠀⠀⠀⠀⠀⠰⣿⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠁⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡲⠤⣀⡀⠀⠀⠀⣀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⣀⠉⠉⢹⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠘⠛⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠠⣾⣷⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠈⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡀⠀⠀⣾⣷⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠿⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⢹⣶⣦⠀⠀⠀⢀⡀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠉⠙⢿⠇⠀⠀⠀⠉⠁⠀⠀⠀⠻⠟⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠙⠿⠃⠀⣠⣄⠀⠀⢾⣿⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡰⢡⠿⠿⠀⣀⡀⠈⠻⠟⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢰⢠⣧⣄⠀⠾⣿⡟⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⡌⡏⠛⠋⠀⠀⣀⡀⠐⠿⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⣠⡳⠀⡾⠆⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠇
⠀⠀⣴⣶⣾⡗⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠀⠀⢸⡇
⢀⣸⣿⣿⣿⠃⠀⠀⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡾⠀⡇⠀⠀⠀⠀⡆⢰⡄⠀⠀⠀⢰
⠀⠉⠉⠉⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⢠⡇⠀⡇⠀⠀⠀⠀⠇⠘⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡌⠀⠀⠀⠀⠸⠀⠀⢣⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠃⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡜⠀⠀⣷⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⢸⠀⠀⢰⠁⠀⠀⢸⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣠⡅⠀⣼⣤⣤⣼⠀⠀⠀⠜⠀⠀⢠⠁⠀⠀⣿⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⣿⣿⣿⣿⡄⠀⠀⣿⣶⣶⣾⠀⠀⠀⣿⣶⣶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠀⠛⠛⠛⠛⠃⠀⠀⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠀⠠⡄⠀⣀⡀
⠀⠀⠀⢀⡀⡴⠂⠀⠀⠀⣤⣴⣶⣦⡄⠀⢠⡤⠀⠲⠀⠄⠀⠠⠀⠀⢀⠀⠀⢰⢸⠄⠂⠽⠀⠓⠀⠀⠀⠒⣀⢀⡀
⠀⠀⠀⠉⣰⠀⠀⠀⠁⠀⣿⣌⡹⢿⠷⢄⢀⠀⠘⠜⠀⠀⠈⠀⠀⡸⠂⠘⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⡆⠑
⠀⠀⠀⢀⠋⠀⠀⠀⠀⠠⠿⠿⢿⣆⡀⠀⢀⠀⢘⢂⠀⠀⢘⠐⠀⠁⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢬⡟⠂⠀⠠⡤⠀⡀⠀⠀⠂⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠉⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡄⠀⠰⠂⠠⠀⡴⠒⠀⣠⠀⠀⣠⣿⣆
⠀⠀⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠂⠀⠄⠀⠄⠀⢸⣷⣤⣴⣿⣿⡿⣿⠿⣿⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠒⠀⠀⠀⠀⠀⢹⡿⠿⠁⢹⠟⠀⠈⠀⠟
⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠊⠀⠀⠀⠂⢠⠀⠀⠈⠃⠀⠀⠉⡰⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠠⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡐⠀⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢲⠁⡆⠀⣠⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡤⠀⠖⠅⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡈⠀⠂⢴⣶⣦⣄⣀⣤⡴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣀⠀⢀⡄⢀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⠀⠀⠤⠄⠀⢄⠘⠉⠉⢻⣿⠛⠛⣿⠋⠉⣛⣩⠄⠀⠀⠄⠀⠀⠀⠀⠌⠀⠊⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⣜⣿⣶⣔⠆⠀⠁⠉⠀⠀⣠⣤⣶⣦⣄⠀⠀⠀⠀⢀⡀
⠀⠈⠃⣻⠏⡀⠀⠀⠀⣀⠀⢽⣟⣻⠟⠈⠑⠶⢶⡦⠈⠀⠀⠈⠉⠩⣥⡬⢿⣿⣭⡧⣦⠀⠀⠀⠀⠠⠀⠤⠀⠀⣰⣠⣌⣄⣀⠠⢤⣦⣽⣥⣔⠄
⠀⠀⠀⠈⡷⠀⠀⠀⠀⠉⠑⠀⣿⡏⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠉⠑⠈⠀⠀⠀⠉⠙⠿⣷⣶
⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⣸⣇⣿⣿⣿⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢻⣷⡆
⠀⠀⢸⣦⣶⡖⠀⢀⣠⣾⣿⡿⢻⣿⣿⣿⣿⣿⣴⡶⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣄⠱⣲⣄⠀⡠⡇⠀⢻⡇
⠀⠀⠈⠛⠛⠛⠛⠻⣿⣿⣿⢷⠋⠸⣿⣿⣿⣿⣿⠀⠀⢀⠄⠉⣷⣄⢠⣄⠀⠀⢀⠄⠐⣀⠀⠀⣤⠀⠀⠀⠀⠀⢀⣿⣿⡿⡣⡚⠑⣿⣿⢽⡧⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣂⣠⠙⣿⣿⣿⡗⣂⣷⣾⡆⠀⠈⠻⣿⣿⣶⣄⣸⣿⣧⣿⣼⣴⣿⣇⣼⣡⠄⣴⣿⣿⣿⣿⣔⡡⣀⠀⡁⠀⠀⢈⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠁⠙⠻⢿⡟⣿⣿⣿⣿⣷⣿⣶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣤⢂⣤⠈⣄⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⢀⡘⣿⣿⣿⣿⣏⠉⠿⣿⢿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠀⠉⠿⢿⣿⣿⣿⣿⣽⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠀⡀⠈⣿⣿⡏⢿⣿⣷⣿⠃⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠛⡟⠿⡶⠶⣿⠿⡟⢲⣭⣿⣿⣿⣿⣿⡕⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣽⠾⢎⣻⣿⣾⣿⡯⢿⠶⠚⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⣃⠧⠀⠚⠉⠀⠀⢻⣿⣷⣶⡟⠌⢻⡆⠀⢼⣿⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣽⣿⣿⣿⣿⣿⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⡄⠀⠹⣿⣿⣿⢱⣾⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⣿⣿⣿⣢⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠿⠆⠀⠀⠘⣿⣿⣀⢸⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣻⣿⡏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⠄⠀⠀⠀⠀⠘⣿⣟⠳⣇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⢹⠛⠄⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣏⡷⣿⡅⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⢶⣮⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢀⡶⢤⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣿⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡾⠟⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⣀⣤⣤⣤⣤⣤⣶⡶⠶⠿⠿⣿⠉⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣤⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢁⣴⠂⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠛⠛⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐⠶⠆⠘⠒⠂⠀⠀⠀⠀⠀⠀⢀⣾⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡤⠀⠀⠸⠿⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧⣄⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠋⠀⠀⠘⠿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡆⠀⠀⢠⠎
⠀⠀⠀⠀⡄⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⢀⡀
⠀⠀⠀⣰⡇⠀⣾⣿⣿⣴⡿⠂⠘⣷⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⠏⢀⣠⣄⠀⠀⠀⠀⠀⠀⠘⣿⡍⠐⠂⠐⠺⠗
⠀⠀⠀⢻⣷⣀⠘⣿⣿⣿⣧⣶⣆⣼⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡌⠐⠃⠀⢲⠆
⠀⠀⠀⢸⣿⣿⣶⡼⣿⣿⣿⣿⡟⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⠁⠛⡃
⠀⠀⠀⠸⣿⣿⣿⠃⢿⣿⣿⣿⠁⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⠽⠒⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠆⠋⢰⢀⠃
⠀⠀⠀⠀⠿⠿⠷⠀⢸⣿⣿⣿⢠⣿⣿⡇⠀⠀⠀⠀⠀⠴⠡⡁⣠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠠⡄⡄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠁⠀⠀⠀⠀⡾⣧⢸⣶⡿⢛⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢠⡆⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⡸⣾⣶⣤⣀⠀⣠⣤⢻⡏⣜⣤⠰⢁⢋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⠈⢰⡞⠄⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣿⣨⣿⡟⣕⣿⣿⣧⣽⣷⣿⣿⡆⠀⠹⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡄⠀⠀⢨⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⢌⢷⠸⣇⡿⢸⢸⣹⣽⣿⢿⣹⠿⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣄⠉⢀⡄⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣲⡈⢇⣿⣷⢸⡾⣞⡛⢞⠳⣭⣉⡡⠇⠀⠀⠀⠀⠀⠀⣰⣶⢶⣾⣇⠀⠀⠀⠀⠠⡄⠀⠻⠟⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠹⣯⠘⢾⠏⢧⣑⣷⣂⠀⠑⠦⠈⠀⠀⠀⠀⠀⠀⠀⠰⠋⣀⣤⣷⣮⠷⣦⡀⠀⠀⠀⢄⡀⠀⣀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣜⠃⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠁⠀⠀⠀⠀⡺⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠁⠀⢀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢄⠀⠀⠀⠃⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⢀⣴⣿⡀⠀⢹⡆⣦⢴⡖⣶⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡄⠘⠓⠀⠐⠀⠀⠀⠀⠰⣀⡀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠛⢻⡏⠡⠴⠚⠓⠿⠸⠇⠿⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠉⠁