Norwegian Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢠⣰⡖⣠⢸⣿⢇⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⣴⣿⡟⢠⣿⣾⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢠⣤⣥⣿⣿⣿⣇⣼⣿⡿⠟⠛⠿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⢿⣿⣿⣿⣿⡿⠿⠀⠹⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣧⣾⣿⣿⣿⣿⡟⠀⠀⠀⠈⠙⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠟⣛⣿⣿⣿⡇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⢠⣾⣿⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣆⣼⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠀⠛⡿⠁
⠀⠙⢿⣿⣿⣿⣿⣿⠟⠉

⠀⠀⠀⠀⠀⠐⠀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠑⠀⠄⠀⠀⠀⡀⠈⠍⠲⢀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁
⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠘⠈⠑⡦⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠈⠲⣇⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠇⠶⢀⡀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠁⠳⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠲⠎⢹
⠀⠀⠀⠀⠉⠠⠀⠀⠄⠀⠀⠀⠀⠂⠀⠂⠀⠘⠂⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠈⠀⠁⢰⠇⠀⡀⠀⠀⠀⠀⠀⠀⠰⣄⠤⡔⢶⢗⣲⡻⢽⡴⠾⠇⠖⠃
⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⣶⠘⡶⠐⣞⢧⠀⠀⠉⠍⠂⠀⠊⠀⢀⣠⡶⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠀⠀⠀⠋⠀⠐⠀⠈⠑⣿⠙⣙⠃⢡⠘⠀⡞⠀⠈⠆⠀⠀⠮⢥⡟⠑⠁⠀⠀⠉⠀⠄
⠀⠀⠀⠀⢂⠀⠀⠁⠈⠁⠀⠁⠁⠉⠀⠀⠁⠀⠈⠐⠉⠀⠀⠀⠐⠛⢨⡅⠀⠂⠀⠀⠀⠊
⠀⠅⠀⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠄⡀⠀⡀
⠀⠁⠀⢂⠘⡀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠠⠈⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡅
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⠄⠼⠅⠀⠀⠀⠀⡢⠤
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠠⠆⠧⢱⢿⠂⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠉⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠎⢀⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃⡀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢠⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⡄⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⣰⣿⣿⣿⡿⣫⣥⣤⡀⠀⣀⣀⣤⣤⣀⣀⠀⣠⣤⣬⣝⢿⣿⣿⣿⣆⠡⠄
⠀⠀⠀⠀⠀⠠⣄⠧⢼⣠⠀⠘⢠⣿⣿⣿⢋⣾⣿⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣇⢿⣿⣿⣿⣷⡹⣿⣿⣿⡄⠃⠀⣄⡷⢼⣠⠄
⠀⠀⠀⠀⠀⣓⡇⡶⡂⢱⣫⠀⣸⣿⣿⢇⣾⣿⣿⡿⢋⣥⣬⡝⣿⣿⣿⣿⢫⣥⣬⡙⢿⣿⣿⣷⠸⣿⣿⣇⠀⣝⡎⢰⢴⢸⣞
⠀⠀⠀⠀⠀⠀⠈⠉⠀⣶⣶⡀⢹⣿⣿⢸⣿⣿⡿⣱⣿⣿⣿⢇⣿⣿⣿⣿⡸⣿⣿⣿⡎⢿⣿⣿⡇⣿⣿⡇⢐⣾⣶⠀⠉⠁
⠀⠀⠀⠀⡎⣠⠑⡀⠀⠸⢿⣇⠘⣿⣿⢸⣿⣿⡇⣿⣿⣿⢏⡾⠛⢋⡙⠛⢷⡹⣿⣿⣿⢸⣿⣿⡇⣿⣿⠃⣸⠿⠗⠀⢀⠊⣅⢱
⠀⠀⠀⠀⢠⣿⡶⠴⡄⠈⣹⣽⠂⠹⣿⣇⢿⣿⡇⣿⣿⡏⣾⢁⢔⢕⡪⡪⡈⣧⢹⣿⣿⢸⣿⡿⣸⣿⠏⠐⣯⣏⠁⢠⠦⢴⣿⡄
⠀⠀⠀⠀⠀⢁⠿⠟⠛⣣⣴⣶⣶⣦⡘⢿⣮⠻⣷⡹⣿⣇⢿⡘⡣⡪⢔⢜⢁⡿⣸⣿⢏⣾⠟⣴⡿⢃⣴⣶⣶⣦⣜⠛⠻⠿⡈
⠀⠀⠀⠀⢠⣬⠲⠂⢰⣿⣿⣿⣿⣿⣿⣦⣉⠳⢬⡳⢝⢿⣮⡳⢦⣬⣥⡴⢛⣵⠿⡫⢞⡥⠞⣉⣴⣿⣿⣿⣿⣿⣿⡆⠀⠞⣥⡄
⠀⠀⢀⣀⣴⡌⠀⠀⠈⢿⣿⣿⣿⡿⠿⠿⠿⣷⣦⣄⣀⣀⣈⣉⠂⠈⠁⠐⣋⣁⣀⣀⣠⣴⣾⠿⠿⠿⢿⣿⣿⣿⡿⠁⠀⠀⢡⣦⣀⡀
⠀⠠⣴⣿⣿⣿⢰⡆⢠⡄⠙⠻⢫⣾⣿⣿⣷⣶⣭⣭⣉⣭⡭⢖⣠⡇⢸⣄⡲⢭⣭⣩⣭⣭⣶⣾⣿⣿⣷⡝⠟⠋⢠⡄⢰⡆⣿⣿⣿⣦⠄
⠀⠀⠈⠛⢛⣥⡾⠅⢈⡻⠄⠤⠸⣿⣿⣿⡿⣫⣵⣶⣶⣶⣾⣿⡟⠀⠀⢻⣿⣷⣶⣶⣶⣮⣝⢿⣿⣿⣿⠇⠤⠠⢟⠁⠨⢷⣬⡛⠛⠁
⠀⠀⠀⠀⠉⠉⠀⡔⢁⡆⠘⠳⠃⠈⠛⠛⠃⣿⣿⣿⣿⣿⠿⠋⢠⣶⣶⡄⠙⠿⣿⣿⣿⣿⣿⠘⠛⠋⠁⠘⠞⠃⢰⡈⢢⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠑⣪⣄⠈⣁⡊⢠⣾⣿⣦⠈⣉⡉⠉⠀⣀⣤⣹⢯⡽⣏⣤⡀⠀⠉⢉⣉⠁⣴⣿⣷⡆⢑⣈⠁⣠⣅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⠿⠿⠿⣫⣭⡛⠿⠿⢿⡆⠀⣿⢻⣿⢆⡰⣿⡟⣿⠀⢠⡿⠿⠿⢟⣭⣝⠻⠿⠿⣷⠀⠈
⠀⠀⠀⠀⠀⠀⢠⢐⣀⡀⠀⢾⣿⣶⡿⠿⣷⣾⣿⠇⠀⢀⣈⠉⣡⢬⣥⣌⠉⣁⣀⠀⠰⣿⣷⣾⠿⢿⣷⣿⡿⠀⠀⣀⡂⠄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣀⠉⠱⠾⠿⠶⠈⢁⣠⣾⣿⣿⡷⠁⡘⢃⠈⢸⣿⣿⣷⣄⡈⠉⠶⠿⠷⠆⠉⣀⣴⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣫⣭⣛⣫⡄⠀⣬⣛⣋⣭⡛⠛⠋⠠⡯⠇⢸⢭⠄⡉⠛⢛⣭⣝⣛⣥⠀⠠⣝⣛⣭⣝⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠙⠛⠛⢁⢰⠙⠃⡐⠀⠀⢂⠘⠋⡆⡈⠛⠛⠋⠁⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣤⡞⢳⣤⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣾⣱⣷⣿⣟⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣴⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⠟⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡤⢤⡿⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣷⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢼⣿⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⣀⡀⠀⣀⡀⠀⣠⣀⣀⣀⣀⣤⣤⣤⣤⣴⣿⣶⣦⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤
⢴⣤⡤⢿⣶⣦⣙⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣉⣉⣿⣿⣶⣿⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡏⢠⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢁⡈⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣹⣿⣿⣿⣿⣿⣿⣿⣯⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⡀⢠⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣈⣭⢲⣷⣿⣫⣾⣷⣿⣿⣾⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣾⣧⣖⣶⣷⣿⣿⣿⣿⣿⣿⡟⠉⠁⠈⠙⣻⡦⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⢴⣬⣾⡿⠿⢿⡏⠉⠀⠈⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⣾⣾⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⡿⣯⣿⠟⠉⠉
⠀⠀⠀⠀⠀⡤⣤⣾⣿⣿⣿⣿⣿
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢸⣽⣿⣿⣿⣿⣿⣿⡿⣿⡟⠁
⠀⠀⠈⣼⣿⣿⣿⣿⡿⠛⠁⠉⠃
⠀⠀⠀⠀⠙⠛⠛⠁


⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣰⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠳⣤⣤⣀⣀⣠⣴
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⢻⣿⣼⡽⢋⣠⡤⠂
⠀⢛⠍⣱⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣷⡿⠈⣖⣷⢶⣤⣿⣿⣦
⠀⠀⠀⠐⢻⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⠑⡆⠈⢛⣿⣿⣟⣿⣿⣧
⠀⠀⠀⠀⠀⡴⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⡟⠙⠂⠀⠀⠀⠈⠙⠛⢻⣿⣿⢧
⠀⠀⠀⠀⠈⠵⠛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡟⣅⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠂
⠀⠀⠀⠀⠀⠀⠈⠉⢉⠀⠖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⡈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣟⣿⣿⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⢣⣞⣿⣿⣿⣿⡿⣿⠿⠐⠀⡙⠆⢀⡄⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⡷⠀⢀⣶⣧⠘⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⡛⠐⠁⠻⢿⠟⠐⠛⠙⢿⠿⠿⠛⢛⠁⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠞⢛⠛⠋⠀⢙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣿⡄⠄⠀⠀⠀⠀⠀⢀⡼⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠑⢸⣿⣿⣄⢦⠀⠀⠀⡠⠋⡄⣻⣿⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡶⢭⣸⣿⣦⣄⣀⠀⠀⠀⠀⡴⢫⠖⡂⠸⣿⣿⣿⣿⣷⣮⠭⠀⠊⠐⣱⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠬⠷⠛⢉⣜⣧⡝⡻⢦⣀⢀⡠⠃⠃⠀⠄⠘⢿⣿⣿⣼⣿⠁⠀⠀⠀⣴⡛⠋⢛⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⠞⣉⣩⣍⢻⣦⣿⡟⠀⢠⡄⠀⠀⠀⠀⣿⣿⣿⣿⣧⡞⠋⠛⠁⠁⠘⠉⣿⣿⣿⣿⣵⣳⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠒⢲⡃⠨⢻⣷⠟⣻⠁⠀⠠⠿⣦⣀⠤⢤⣤⣿⣷⣿⣿⣿⣆⣀⠁⠐⠊⠄⡛⢿⣿⣿⣿⣿⣷⣿⣿⡄
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠀⢐⠝⠉⣰⡏⣠⡄⢀⡀⠀⠨⢑⠤⡀⠉⠉⠙⢹⣿⣿⣷⣤⡄⠀⠀⠀⠀⠉⠒⠻⣿⣿⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠐⠁⠀⠀⠁⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⣺⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⣐⣿⣷⣾⣿⣯⠅
⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⢀⣠⠄⡀⠀⠀⣀⠀⠰⠿⠛⡛⠓⠸⠯⠿⠽⠓⠒⠖⠻⡍⠛⠉⠉⠁⠐⠚⠒⠱⠶⠦⠆⠲⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⢀⡉⢀⢀⡀⠀⠁⠀⠉⠁⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠲⠂


⣿⣾⡾⠿⠾⠾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣾
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⡀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⣧⣾⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡠
⠛⠻⠿⠿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣹⣧⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠞⠉⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣀
⡄⠀⠠⡤⠀⢉⠁⣀⠀⠙⢧⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢨⡷⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⡆⠀⠀⠀⠀⠀⠀⢠⣷⢠⣦
⣷⡀⠀⢁⡤⠀⣀⣿⡀⠀⠀⠀⣸⣧⠀⣰⡀⠀⣀⣠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠾⠱⠦⠀⠀⠀⠁⠀⠀⠀⢠⡜⠃⠀⠀⠁⠘⢦⠀⢀⠀⠀⢸⣿⣿⣿
⣿⣇⠀⠸⠁⣰⣿⣿⣖⠀⠀⠀⠿⠿⢦⣿⡅⠠⣿⡍⠀⣞⠋⠘⠃⠀⢠⡀⠀⠸⠃⠤⠀⠀⠀⠀⢀⠀⢡⣀⠀⡴⠣⢀⡖⠀⠦⠐⠀⣄⢀⠀⠚⠀⠀⠀⠀⠿⠟
⠉⠀⡀⠀⠀⣿⣿⠇⠀⠀⠈⠁⠀⠀⠸⠿⠛⠀⠈⠁⠈⠉⠀⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠒⠛⠠⠆⢨⣤⣵⣄⣠⣄⣆⠰⠇⢱⣿⠈⢠⠂⣴⠀⢀⠀⣤
⢀⡼⠀⡀⢸⣿⣿⡡⠀⠀⠀⠀⠀⠢⣄⢠⣶⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠛⠁⠀⢰⣿⣢⣿⠀⠻⡆
⡜⠁⢠⣿⠀⢀⡀⠀⠀⠛⠷⠖⠆⠤⠀⠈⠛⠓⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠠⠄⠀⠙⠛⣿⣿⡧⠈⠡
⠀⠀⣿⠭⣅⠀⠹⠅⠀⢀⠀⠀⠀⣄⡀⠀⠀⠀⠀⢄⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣤⣀⡁⠲⠤⠀⠀⠀⢤⡄⠀⠀⠀⢒⡀
⠀⢠⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⡀⢀⠀⠀⢤⣀⡀⠈⣿⣄⣀⡀⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠋⠀⠉⢭⣦⣀⣁⣴⣶⣶⢾⡇⠀⠀⠤⢀⣄
⠀⠬⠭⠍⠉⠀⠀⠀⣀⣤⣄⣀⣠⣤⣾⣷⠶⠴⠖⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠲⠿⢳⣤⣄⣀⠉⠀⠦
⠀⠀⡀⠀⠀⠀⠁⢀⣀⣤⡾⣟⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠶
⢀⣀⣤⣤⣤⣶⠿⠿⠟⠟⠛
⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⢻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠘⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⣾⣦⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⠁⠀⠹⣿⣿⣶⣄⠀⠀⠀⠀⢿⣿⣿⠟⠁⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⡿⠃⠀⠀⠀⠁⠹⣿⣿⣦⣀⠀⠀⠈⠛⠁⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄⠀⠀⠀⠀⠀⠉⢿⣿⣷⡀⠀⠀⠀⠀⠀⣘⣿⣿⣁⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠀⠀⠀⠀⠀⠈⠿⢿⣿⣦⣄⠀⠀⢨⣿⣿⣿⣯⣈⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠧⠀⣤⣽⣿⣿⣥⣼⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣤⣆⣿⣷⣾⣾⣶⣿⣿⣷⣷⣷⣦⣶⣶⣾⣷⣶⣦⣤⣤⣶⣤⣤⣦⣤⣤⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢒⣲⣖⣒⣲⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠄⠈⠀⢀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⡀⠀⠀⠐⡀⢀⣠⠀⠀⠀⠰⡷⡄⠀⡀⢦⡀⠆⠠⠆⢈⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⡄⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠁⠀⠀⠘⠃⢤⠍⢧⣿⣧⠉⢻⡄⠀⠶⣿⡿⠈⢣⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠒⠲⢛⡃⠒⠠⣄⠀⣺⡿⠂⠘⢧⣼⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠘⢯⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣳⣄⠈⠙⣿⣧⠱⣄⠈⣿⣀⠀⢠
⠀⠀⠀⠀⢀⣤⣾⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⢈⠁⠀⣀⡀⠈⠂⠂⠖⠈⠉⠑⢻⣿⣄⣿⡀⢹⡶⢠⡯
⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣪⣌⣑⣈⣃⡀⠀⠀⠀⠀⢀⣀⣴⣿⣿⡙⢷⣈⣿⣼⣧⠖
⠀⠀⠀⢹⣿⡿⠟⠁⠐⠿⢷⣮⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⢀⡽⠛⣶⡶⠾⣿⣿⣄⣿⣿⠁⢀⣿⣿⣿⠗⠂
⠀⠀⠀⢸⡟⠀⢀⠀⠀⠀⢠⣿⣷⡀⢸⣽⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡟⡄⡩⠴⡞⠋⡀⠀⡀⠀⠈⢹⣿⣧⠈⣿⣿⡟
⠀⠀⠀⠿⠶⠒⣿⣧⣾⣿⣿⣿⠿⠇⠜⠻⡄⠀⠿⣿⠟⢿⡿⠿⣿⠿⢛⠛⠻⠋⠊⠟⠀⠂⠒⢿⡐⠛⣺⡟⢿⢀⡏⠑
⠀⠀⠀⠀⠀⠀⢀⣿⣶⣦⣬⢀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠛⠚⠛⠛⠛⠉⠋⠉⠁⠀⠀⠀⢀⣸⣿⣿⣿⡧⠀⢻⠶
⠀⠀⠀⠀⠀⣀⣄⣤⠛⢉⣈⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣠⣄⣀⣶⣿⣿⣿⠿⠟⣿⠋
⠀⠀⠀⠀⠀⠈⠉⠛⠛⣛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠉⣉⢉⢛⠛⠛⠛⠛⠛⠋⠉

⠑⠦⣴⡞⣳⠄
⠀⠀⢿⠽⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣤⣀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⡀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⡿⠿⢿⣿⣿⣦⣤⣾⣿⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣀⣈⠙⠛⠻⢿⣿⣿⣿⢶⣶⣶⡲⣤⡢⣤⣀⠀⠈⠻⣿⢹⣿⡟⠻⢌⣛⣻⣿
⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣭⣗⣄⡀⠀⠻⠿⣿⣕⡮⠿⣿⣿⣿⣿⣿⣷⣦⣴⠿⣾⡟⠋⠀⠀⠛⣿⡇
⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣳⣦⣤⣀⠙⠿⣷⣗⡻⡛⠻⢿⣿⣏⠁⠀⠈⠉⠓⠦⡴⠞⠉
⠀⠀⠀⠀⠀⠈⠙⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣷⣝⣷⣦⣄⣹⣿⣿⣷⣤⣉⠙⠻⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣾⡿⠿⠭⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣾⣿⢿⣿⣻⣿⣿⠟⠁⠀⠈⠙⠻⢦⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣄⡀⠀⠀⠀⢀⣤⢖⣫⣙⠛⢿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢶⣶⣿⣷⣾⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡉⠛⠷⣦⣤⡤⠤⠄
⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣾⣵⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠐⠂⠙⠂
⠀⠀⠀⠀⠀⠀⠒⠒⠻⠼⡁
⠀⠀⠀⠀⠀⠘⡂⢀⡄⠈⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠻⠤⠄⢶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠠⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡨⠆
⠀⠀⠀⡀⠀⣠⠂⠀⠶⢷⡝⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢀⣀⠴⠶⢤
⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣵⣄⣤⣶
⠀⠀⠀⠶⠠⣰⠆⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡁⠀⢄
⠀⠀⠀⠀⠔⠁⠀⠒⣀⠀⠶⣀⡀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠛⠁⢀
⠀⠐⠧⠄⡤⠀⠀⢀⠙⣀⡀⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣘⢀⠤⠚⠐⠾
⠀⠀⠀⠀⠸⠇⠂⠉⡀⢀⡉⠹⠄⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠐⠪⣭⣋⠠⣤⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣤⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣶⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠓⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⣠⠒⠋⠭⠭⠅⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠈⠁⠂⣀⣀⠀⠉⠙⠒⠢⣤⣀⡀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⡐⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⠒⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚
⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⣀⠤⠔⠒⠊⢳⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠒⠒⢤
⡎⠁⠀⠀⠀⠄⠀⢀⣉⠉⠉⠉⠉⠉⠓⠋⠀⠀⠘⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠀⣤⣤⡤⢄⣀⠗⠂⠀⢀⡠
⠈⠓⠢⠤⢄⣀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠂⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣒⡤⠦⠤⠭⠖⠒⠚⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⣿⣿⣟⣦⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣆⡀⠀⢰⣷
⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⣾⣿⣿⣟⠉⠻⢿⣗⣦⡀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣧⠀⣤⣾⣿⣿⣿⣿⣿⣿⣦⣾⣿⣼⡇⢀
⠀⠀⠀⠀⣧⣿⣧⣦⣾⣿⣻⣛⣽⡿⢷⣄⣀⣰⣼⣿⣷⣾⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡿⠾⣿⣭⣉⡙⠛⠿⠟⠙⢺⣿⣿⣷⣿
⠀⠀⠠⣤⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠈⠉⠛⠛⠿⣿⣽⣿⣿⡷⠦⠀⠀⠀⢀⣚⣏⣽⣿⠿⠿⠿⠿⠷⠶⠤⠤⣤⡤⢤⠴⠶⠿⠿⠿⠿⠿⠿⢦



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣄⣀⣴⣿⣿⣿⣿⣿⣿⣦
⠀⠀⢀⣠⡀⢀⣴⣷⣦⣤⣤⣴⣿⣵⣾⣿⣿⣿⣦⣀⡀⣀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣄
⠀⠐⠛⢿⣿⣿⠉⠙⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠉⠋⣹⣿⣿⣿⣷⠴⠀⠀⠀⢀⣾⣷⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⣷⣄
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⡠⠔⣁⣻⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣄⣠⠏⠱⣴⢦⡀⠀⠀⠀⠀⠀⠀⣀⡴⠃⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣛⣋⣳⣄⠀⠀⠀⠔⠋⠹⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠹⡶⡀⠀⠀⠀⠀⠀⠘⠁⠀⠂⠀⠀⡠
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄
⠀⠀⠶⠀⠠⠞⠃⠀⠰⠧⠄⠀⠀⠀⠀⠀⢀⠀⢀⣀⣴⣂⢀⣤⣄⣀⣀⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠈⠑⠂⠂⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠖⠢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣤⣄⢀⣀⡀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠻⠿⠿⣿⠿⠃⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠶⣶⣶⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣄⠀⠀⠉⣩⠟⠛⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢡⣶⡿⠀⠹⣾⣿⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⢀⣀⣄⡀⠀⢸⣿⡿⣶⡄⠙⣿⣿⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠷⠒⠀⠀⠀⠀⢽⣿⣿⣿⣿⡇⠀⠙⠛⠛⠁⠀⠈⠻⠿⠷⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⡇⠀⠀⠀⠈⠿⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢴⠂⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠀⠀⠀⣸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠠⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣀⠀⠀⠙⢟⠛⢋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⡳⠀⠀⠀⢤⣄⠀⠈⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⢀⣀⣿⣿⣧⠀⢿⣿⠏⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁⢻⣿⣿⣿⠏⠀⠈⠙⠀⠀⠖⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⠴⠋⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠶⡤⠀⠀⣀⣠⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⡀⠤⠐⠂⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⡎⢇⠀⠀⢒⠄
⠀⠀⠀⡠⠔⠒⠒⢢⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠡⡀⠀⠀⢀⠜⠀⠈⢆⠀⠀⠀⣀⠤⣀
⠀⠀⠀⡱⠀⠀⠀⠘⢲⠶⡏⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⢊⠀⠐⢳⠂⠁⠐⠲⡛⠀⠰⠁⠀⠈
⠀⠀⠈⢳⠀⠀⠀⠀⠀⡆⢣⣴⠃⠀⡄⠀⡠⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠀⠀⠐⣷⣖⡁⠀⠀⠀⠀⣑⣤⠀⠁⠒⠈
⠀⢠⠤⠶⠀⠈⠁⠈⠄⠉⠁⠈⡆⠰⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⡡⠤⠀⠄⣀⣀⡤⠋⠀⠀⠀⠀⠀⠈⠢⢄⡀
⠀⢇⠀⢀⡁⠀⠀⠀⠐⠀⠀⢐⡍⡂⠀⠐⠀⣊⠀⠀⠀⠀⠀⢊⠤⠀⠀⠀⠀⢈⠽⠋⠙⠀⠂⠠⠐⠀⠛⢍
⠀⢰⠁⠀⠀⠐⠀⠁⠀⠀⠀⠀⡇⠀⠀⠠⠀⠀⠒⠀⠀⠀⠒⠁⠀⠀⠠⠀⢌⢑⡶⠀⠀⠀⠀⠀⠀⠀⠴⣖⠉
⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠄⠀⠠⠤⠤⢤⠤⠀⠀⠤⠵⠂
⢹⠀⠀⠒⠒⠒⠁⠀⠈⠉⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠤⠀⢀⣀⡀⠀⢀⣀⠀⠀⠀⠀⠚⠀⠀⠀⡇⠀⡀⢀
⠀⠀⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠃⠀⠀⠀⢀⠀⠀⣀⣀⠤⠀⢀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⢸⠀⠀⠁
⠀⢧⣀⠄⠀⠀⢣⣀⠄⠀⠀⠀⠳⠤⠂⠘⠦⠄⠀⠘⠦⠔⠀⠈⠳⠤⠤⠂⠈⠳⠤⠤⠔⠊⠀⠳⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⢤⠄⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣞⠛⣳⠄⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⢁⣠⣎⣉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢯⣁⠡⠝⠃⠀⠀⠀⠀⣐⠲⣤⠤⠀⠒⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣩⣤⡤⣀⡀⠀⠀⣀⣀⡀⠤⠤⠐⠒⠂⠉⠉⠈⢁⣀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣡⡼⣇⠈⢊⡾⠋⠉⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⢠⠞⠻⠮⡺⣝⢷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣯⠀⠀⢘⡩⣲⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⣞⣳⠄⠀⡀⠀⠀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣴⡟⢫⡄⠐⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⠀⠀⠀⠀⢀⡞⠛⠥⣀⡝⢵⡄⠀⠀⠘⠀⠀⠀⠈⠈⠑⠈⠁⠀⠀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢆⠦⠀⠘⣧⡀⠀⠀⢊⡼⠁⠀⠀⠀⢰⠒⣦⠀⠀⠀⠀⠀⠀⠀⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠋⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠴⠒⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠒⠒⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡺⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡇⣿⠑⠰⢭⣽⣷⣴⣶⣤⣤⣄⢀⣀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣮⠳⠀⠚⠋⠉⠉⠉⠉⠉⠁⠀⡿⠿⣿⠂
⠀⠹⠟⠦⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠟⣩⠀⣿⣿⡄⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠉⠑⠀⢤⣄⣀⠀⠀⠀⣠⣄⠀⠀⢸⠛⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⠿⠂⠀⠈⠑⠯⠄⠀⠀⠀⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⣀⡭⠵⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣤⣶⣶⡤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣼⣿⡿⣿⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣰⣾⣿⣿⣿⠾⠃⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠤⢖⡂⠠⣿⣯⡿⠐⢯⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣿⣟⡳⣿⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣤⣤⣄⣀⠐⠀⠤⠤⣀⣠⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣷⣦⣤⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉



⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣻⣿⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⢷⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⣟⣘⡾⠾⣼⣼⣰⢢⢄⠀⠀⠀⠀⠀⠈⡈⠁⠀⠄⠀⠠⠀⠁⠀⠐⢀
⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⠀⠀⢀⠈⠻⡇⢠⣴⠀⠈⠉⠛⠺⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠷⠶⢤⣄⣑⡆⠙⠂⠕⠚⣣⡰⠟⣠⠋⠀⠀⠀⠀⠰⠁⠀⠄⠀⠀⡀⡐⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠉⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠐⢠⡄⠀⠀⡁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠐⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⢸⠃⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠜⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡇⠀⠘⠆
⠀⠀⠀⠀⠀⢈⠀⠀⠀⡄⠓⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡈
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠈⡐⠒⠅⠀⠀⡒⠲⡁⠈⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠴⠦⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠜⠒⠶⠶⠶⢤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⡤⠶⢤⡀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠍⠀⠀⠀⠈⠳⠤⠔⠁⠀⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠈⢁⡴⠒⢲⣤⠤⠤⠴⠖⠂⠀⠃⠀⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠷⠖⠒⠒⠋⠉⠉⠳⠤⠼⠁⠀⠀⠀⢀⠤⢤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢠⠖⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠐⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡋⠁⠉⢻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠟⢛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠿⠿⠟⠁⠀⠀⢩⣭⣭⣴⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⠋⠙⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢄⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡀⠉⠲⢄⠑⠀⠐⠚⠛⠛⠛⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣤⣼⣧⠤⠤
⠀⠀⠀⠀⠁⠒⠢⢤⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠔⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⢰⣦⣀⣀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠆⠰⣄
⠹⡿⠋⠉⠁⠀⢀⣀⣴⠀⠀⠀⠀⢀⣄⠀⠀⠉⢻⠃⠀⠉⣤⣠⠖⠿⢦⡀
⠀⠀⠀⠀⠀⠀⢸⠿⡿⢀⠀⣀⠀⠀⡌⣆⠀⠀⠀⠀⠀⢀⡉⠛
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⣀⣴⡿⠟⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣈⡠⠀⠀⠀⠀⠍⢃
⢸⣿⠀⠀⠲⢶⣶⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢨
⢠⣤⣠⡀⠀⠸⠿⣦⣤⡄⠀⠀⠻⠁⠀⢀⣀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢴⣌⡙⢁⠀⠀⠀⠀⠀⠛⢠⡄⢀⣠⠀⠈⠙⣿⡶⣦⠀⠀⠙⠛⠀⠀⠀⣀⢀⡀⢸⠙⠀⢰⡆⠀⠀⠀⠀⠸⠦
⠀⠙⣿⢾⡇⠀⠀⠀⢀⣀⠈⠁⠀⢂⣤⡀⢸⠇⢀⡤⠀⠀⠀⠀⠀⠀⠀⠛⠘⣇⠀⠒⠀⢨⠷⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠋⣙⣢⡴⢶⣤⡈⠇⢀⠆⢸⣀⣈⠞⠷⠁⠀⠀⠀⠀⠀⣀⣀⢀⡀⢰⣦⠀⢶⣶⣶⣆⠀⠀⠀⠀⠀⢾
⣰⣦⣄⠀⠀⠁⠀⠀⠸⣿⠃⠀⠀⠈⠉⠉⡇⠀⢷⠀⠀⠐⠛⢿⡝⣧⣀⠁⠰⠟⠧⣀⡍⠋⠙⠇
⢸⣿⣏⠀⢀⡀⠀⠀⣠⣿⡆⣴⣤⡄⠀⢀⠁⠀⠀⣇⠀⠀⣤⠼⢷⣿⣟⢀⣄⠀⠸⠃⡷⣀⠈⣁
⣾⣿⣿⠀⠀⣵⣤⡶⢿⡻⢿⣿⣿⢿⣯⡝⠀⠀⣰⣿⠀⢠⣿⣿⣿⣿⣿⣿⣷⣾⠁⠀⢠⣿⣀⣸⠇⠀⠀⣤⡶
⠺⠿⠟⠀⠀⠉⠏⠀⠀⢰⣦⡌⠁⠀⠀⠀⠀⠀⢰⣿⠀⣼⣿⡿⠋⠉⠙⠿⠿⣿⠀⡀⠀⠲⢮⠁⠀⠀⠸⣿⡄
⣠⣤⣤⣤⣄⠀⠰⣄⢀⣼⣿⣶⡖⠀⠀⠀⠀⠀⠈⠉⠀⢨⠇⠀⢀⠐⠀⠀⠀⠸⢣⣿⣄⠀⠀⣗⠀⡿⠀⠿⣷
⢸⣿⣿⣿⣿⣷⣆⠙⣿⣿⣿⣿⣿⣶⠂⠀⠀⠀⠀⠀⠀⠈⢴⢯⣽⢷⣄⠀⠀⠀⣾⣿⣿⣶⣌⢿⠀⠀⠀⠀⠹
⠘⢿⣿⣿⣿⣿⣿⡄⠸⣿⣿⠿⡿⣿⣠⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠜⢁⣠⣭⡈⠛⠋⡴⢨⣿⣿⣶⡦⡄⠀⡀
⠀⠀⠈⠀⢹⣿⡟⠀⠀⠙⠛⠓⠂⢸⣿⣿⣿⠟⠼⠛⠁⠛⠀⢀⠀⠀⠙⠋⠀⠁⠀⢀⣀⣼⣿⣿⣿⡁⠀⠀⡤
⠀⡆⠶⠂⠀⠉⠀⠀⢠⠤⠀⢤⡀⢸⣿⣿⠟⠀⠀⠄⠀⠀⠀⠈⠃⠀⠀⠀⠀⢀⣴⣦⢉⡟⠻⠿⠿⢧⣀⡀
⣺⣧⣤⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠉⠉⠉⣠⣄⣤⡰⢶⣤⠤⣀⠀⠀⠀⠀⠠⠛⠁⣾⣷⠀⢶⣶⣿⡿⠟⠛
⠈⠻⣿⣄⠀⠀⠀⠀⠀⢲⣿⡏⠈⣯⠀⠀⢠⣇⠀⢻⠑⠟⠧⠀⠉⣀⣴⣷⠲⡆⠀⢠⣷⣾⡀⢘⣉⣿⣧⣴⣶
⢐⣁⣠⣿⠀⠀⠀⠀⠀⠈⣽⡇⠀⠉⠀⣠⣤⣀⠀⢀⡀⢰⣶⣶⡾⢻⣿⣯⣰⡧⠞⣿⣿⣯⢷⣿⣿⣿⣿⣿⡿
⢻⣿⣿⣿⣷⣶⣶⣦⣤⣤⣿⣷⣴⣾⣿⣧⡌⢙⣿⣿⣷⣀⣿⣏⠐⢾⣿⣿⣟⣃⠈⢯⣉⣉⣈⣿⣿⣿⡿⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⢶⣶⣒⣒⡲⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠀⠀⠀⠀⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠂⢤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡏⠀⠀⠀⠀⠈⠉⠒⡤⣄⡀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁⠂⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡂⠀⠀⠀⠁⠒⢤⡜⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢀⣀⠀⠀⠀⠘⠓⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⣇⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⡇⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⡇⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⣷⠀⠀⠀⠀⡀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠰⠀⠀⠀⡀⠀⠀⠉⠀⡤⠀⠀⠀⠀⠀⠀⢧⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⢈⠂⢄⠀⠀⠾⠃⠀⠀⠀⠀⠐⠀⡄⠀⠠⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⠇⡇⠀⠀⢠⠃
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⣤⣀⣀⠀⠈⠙⠓⠤⣐⡠⠐⢶⡄⠀⠀⠀⣣⠀⡠⠃
⠀⠠⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⣠⣼⣿⠔⠁
⠀⠀⣿⣿⣿⣏⣿⣣⣃⣕⣩⣼⣿⣿⣿⠇
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠀⡤⠀⣀⣀⠀⡀⣤⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⢻⡀⣀⠄⢻⡟⡼⠀⠀⢠⢸⠁⠘⠁⢀⠀⠀⠐⠌⠀⣷⠀⡏⢆⠰⡅⣿⠘⠇⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢣⢈⡎⣧⠇⠀⢸⣧⠀⡐⠋⠀⡘⠀⠀⢠⠎⠀⠀⠀⠘⣀⣷⡟⡁⠁⠀⢠⣿⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠀⢹⠀⠀⢸⣿⠀⠁⠀⠀⣧⡤⠰⠋⠀⠀⠀⠀⠀⠀⣷⠰⠀⠀⠀⠀⢹⠆⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣆⠀⢸⣿⠠⠈⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣿⠻⠀⠀⠀⠀⠘⣋⣠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢽⠀⠀⡀⠀⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⡷⣴⠒⠛⠁⠀⠀⠀⠀⢀⣠⣶⣶⣄⣸⣠⡾⣶⣦⡀⢰⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⠇⠀⠀⠀⠀⢀⣠⡶⢿⣿⣿⣿⣿⣿⡛⣅⠉⠙⠃⢸⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⡇⠀⠂⢀⣠⡶⠟⠉⠀⠀⠙⠻⣿⣿⣿⡇⢸⣿⣦⡀⠘⡇⢏⣀⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⠉⠷⣿⣿⣇⣤⠞⠋⠅⠈⠀⢀⠀⠀⢠⠠⡄⡙⢿⡟⢸⣿⣿⣿⣷⣧⡇⠸⡿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⢀⣠⢼⣿⠛⡇⠀⢀⡶⠒⠲⠓⠐⠁⠀⠀⡗⣱⢾⣏⡼⣿⣿⣿⣿⣿⣿⠦⣀⣤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⣠⠖⠋⠡⢼⡿⠀⢃⡴⠻⣤⠀⠀⢠⠀⠀⠀⠀⠀⢹⣾⡇⠃⠀⢙⣿⡟⣿⢶⣟⣿⡄⠆
⠀⠀⠀⠀⠀⠀⣤⡴⢞⠋⠀⠠⡄⡀⢸⣷⠓⡟⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠈⣿⡿⢀⣴⣿⣿⣿⡟⢸⣿⡟⡃⡄
⠀⠀⠀⠀⠀⠀⠈⠀⢻⠀⠂⠐⠛⠙⢾⣿⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⡇⢾⣿⣿⣿⡏⡧⢸⡽⡆⢳⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠀⢸⣿⠇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡟⢹⣿⣿⣿⡇⣷⢸⠇⣣⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠆⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⣠⣾⣿⣷⡺⢿⣿⣿⣧⡏⠘⡇⣏⢸
⠀⠀⣤⣄⠴⣶⣼⣿⣾⠀⠀⠀⠂⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⣾⣿⣿⣿⡟⡁⣾⣿⣿⢿⡇⣠⠃⣿⢸⣦
⠀⢸⣿⣿⡿⣿⣟⣿⣿⠀⠀⠀⠀⠁⢸⣿⣿⣅⠀⠀⠀⠀⠀⡄⠀⣰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⢸⡗⣿⠀⡏⢸⡷
⠀⢸⣿⠿⠷⡯⠿⡿⠿⠀⠀⠀⠀⠀⢸⣿⣇⠋⠀⠀⠀⠀⠀⠁⠚⠻⡿⡻⠛⠟⢿⣧⠊⠟⠿⠿⢸⣷⡿⠟⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠀⠀⠘⠛⠁⠀⠀⠀⢸⠋⠁⠀⠀⢰⡇
⠀⢀⠀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣄⡤⠼⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠚⡇
⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠯⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⣀⠀⠉⢳⠢⠄⠄⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠚⠋⠙⢷⣌⣀⣀⣀⣤⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡒⡪⢊⠍⢠⠋⠀⠀⠈⠛⠲⣒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡖⢳⡀⠘⢄⠀⠀⠀⠀⠀⡀⠑⢍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⢄⡋⠒⠄⣉⠉⠉⠁⠐⠢⡄⠈⠆⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠙⠒⠤⢄⡉⢴⢤⠔⠒⠓⠒⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡄⠀⠀⠘⢣⣼⠞⠴⠐⢺⣝⡀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠁⣠⠞⠀⠀⡰⠡⠊⡌⠀⠀⡻⡏⠉⢹⡤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⠏⠁⠀⠀⠀⡰⠱⠁⢰⠀⡠⠊⠀⠈⠁⠊⠀⠀⠀⠉⠉⠉⠙⠛⠒⠈⠋⠓⠲⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠰⠁⡇⢀⠆⠀⠣⡀⠀⠀⠀⠀⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡇⠀⠐⣎⠀⠀⠀⠈⠂⣄⠤⠊⣁⠔⠊⠀⠀⢀⡠⠔⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠃⠀⡘⠀⠑⢢⣤⠔⢉⡠⢓⣍⠀⠀⣀⠴⠊⣁⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠀⠀⣃⡠⠒⣁⠤⠛⠓⣶⠋⣨⠖⢉⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠀⠀⠀⠀⢠⢾⣶⠾⣁⠔⠊⠁⠀⢀⡮⢓⣽⠡⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢀⡰⠟⡫⠕⠈⠀⠀⠀⡠⠒⣁⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⡡⠔⠉⠀⠀⠀⡠⠒⣩⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⣁⠔⠉⠀⠀⢀⡠⠐⡩⠔⠉
⠀⠀⠀⠀⠀⢠⠒⠐⠂⣁⠔⠊⠀⠀⢀⡠⠒⢁⠔⠊
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠨⣁⣈⡡⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⣀⡀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢃⡈⢉⠈⠀⠀⢄⠀⢱⣆⣐⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢢⣌⠀⠀⠀⢋⣁⠼⠒⡉⠤⠖⠨⡑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⢁⠀⠀⢰⡈⠠⡴⠂⠉⢀⠀⠀⠈⠙⠳⡤⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂⠀⠀⢠⣔⣢⡄⢈⠁⢩⠀⠀⠀⢆⠀⠅
⠀⠀⠀⠀⠀⠔⠀⡀⠀⠀⠀⠀⠀⣄⠀⠠⠀⠀⠐⠁⠈⡀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠂⠐⠒⠒⠂⠒⠀⠂
⠀⠀⠀⠀⠐⠠⠀⢀⠀⠀⣀⡔⠀⢈⠂⠀⠀⡠⠈⠁⠀⠀⠈⠠⡄
⠀⠀⠀⠀⠀⠀⢠⠏⠈⣀⠉⠀⣈⠈⠹⠀⡴⠁⡂⠀⠀⠀⢀⡀⠘⡄
⠀⠀⠀⠀⠀⢣⡈⠀⠀⠉⡀⡀⠉⠀⠉⠀⠆⢊⠐⠋⡂⠀⠈⠒⠀⠅⠀⠀⢀⠄⠀⠤⡀
⠀⠀⠀⠀⠀⡀⢱⢔⣄⣀⣀⡀⠀⠀⠀⠀⢃⠀⠀⠈⠃⠀⠰⠆⠀⠀⠀⣰⠃⠀⠀⠀⢈⡄⡀
⠀⠀⠀⠾⠀⠀⠤⠱⠤⡄⢼⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠍⠀⠀⡰⢃⠊⢐⡀⠠⠁⠂⡍⠂⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⢋⣖⠀⠀⠀⠀⠀⠰⠨⠬⠉⣂⢝⠡⡄⠸⣄⡐⠭⠔⢀⣀⠂⠀⢀⠀⠀⠄
⠀⠀⠀⣠⢀⠅⠄⠉⠈⠗⡧⡅⠀⠀⠀⠀⢀⣣⠁⠀⠤⢄⢀⢑⣷⡴⠤⠈⠀⢠⠤⠤⢆⡠⠶⠤⠘
⠀⠀⠰⠧⠀⠀⠑⠂⠈⠠⠁⣈⣄⠀⠀⠀⠀⠉⡄⠀⠀⠊⡀⠀⠈⠀⠀⠐⣠⢦⡤⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠂⠀⠀⠀⠀⠀⢨⡉⣩⣉⡅⠀⠠⡀⠀⠁⠀⠉⣕⣾⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠿⠄⠇⠀⠀⢀⢠⠀⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠸⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⢹⠀⡄⠀⢀⣏⣼⠁⠀⢀⡄
⠀⢀⠀⢀⠀⠀⠙⢇⡂⢄⠰⣆⢸⣄⠁⣶⢾⢾⠇⢀⠔⠙
⠀⠘⣆⠀⠳⣄⡀⠀⠙⢆⢄⢰⣿⢸⠄⠁⡾⡟⢀⠎⠈⠀⠀⢸
⠀⠀⢙⢦⡀⠀⢽⡦⣄⠘⡌⢾⢹⠈⠀⠀⢣⠁⡌⡀⡤⠀⠀⠘
⠀⠀⠀⠱⡙⢆⣀⡱⢄⡑⢺⡌⢄⠀⢀⡆⣜⡜⢰⡇⡃
⠀⠀⠀⠀⢙⠊⢈⠴⣁⠈⢂⠑⣌⣶⢸⡰⠋⠄⡽⠚⣍⠉⠆
⠀⠀⠀⢠⢂⣴⡋⠀⡈⠳⣄⠳⡈⣇⠸⠁⠈⡰⠁⠐⡠⠓⢬⡑⠄
⠀⠀⣴⠗⠁⠀⠙⢿⣦⠀⠙⢧⡱⣿⠀⠀⢠⢣⢂⠔⠁⠀⠀⠈⡉⠒⠦
⠀⠈⠀⠈⠳⡤⢄⡀⠑⣅⢄⣀⠃⣿⠀⢰⢱⣧⠞⡀⠀⢴⠶⠛⠁
⠀⠀⠀⠀⠀⠈⠐⠚⣍⠈⠡⠘⢇⢧⠀⣈⢸⡟⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠈⠒⠶⠆⠜⠡⠎⢁⣈⠳⢦⠘⡎⣾⠄⠃⢈⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣳⡀
⠀⠀⠀⣀⠔⠀⠀⠀⠀⠙⢾⣧⠘⣸⣟⠂⠛⡎⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣤⣄⣸⣋⣳⣤⣤⣄⣀
⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⣿⡀⢰⠁⠀⠀⠀⠀⣠⠏⡞⠀⠀⠀⠀⢠⠞⠉⠀⠀⢀⠀⠈⠀⠀⠁⠀⠉⠙⠝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳⣁⠀⢸⡆⣠⠖⡪⠙⠃⠈⠙⠉⠁⠑⢲⡏⢀⠂⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠔⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣶⣾⡿⠁⠌⠀⠂⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠳⠋⢠⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠈⢿⢛⡋⢐⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⡆⢀⣧⠐⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠤⠾⣷⣿⣿⣿⡄⠄⠀⢆⠀⠀⠀⠀⠘⠀⢀⣜⣻⣷⡔⢸⡀⠀⠀⠀⠀⠀⢰⡿⢀⣞⣵⢿⢯⣿⣿⣷⣒⡒⠒⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢐⣶⠾⠋⠀⠰⡏⠉⠉⠻⢦⣨⣤⡀⢀⣠⣿⠾⡟⢾⣽⣿⣿⣿⣿⣄⣀⣀⣀⣠⣟⣱⣛⣛⣷⡄⣙⣻⣿⡻⣿⣷⣤⣈⡀
⠀⠀⠀⠀⠀⠀⠀⢶⠛⠺⠍⠀⠀⠀⠀⠀⢙⣦⠀⠀⢠⢯⣼⣥⣤⣤⣀⣄⠀⠠⢬⡙⣹⣝⣉⣉⣉⣉⣩⠉⣯⢦⠛⢡⡿⡿⠁⠘⠃⠀⣀⠘⠛⠋⠛⢝
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠩⠀⠀⢠⣀⣀⣤⡞⠁⠄⠀⢸⠀⣧⠀⠀⠀⠀⠀⣀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⢸⣄⠱⢄⡐⡖⠒⠁⠀⠀⠀⠉⣽
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠀⠀⠀⠙⠋⠉⠉⠠⡀⠀⣸⡆⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢸⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠁⠀⠀⢤⢦⠀⢸⠳⠃⠀⠀⡇⣄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⣀⣀⡇⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢼⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⠱⠎⠀⠀⠀⢀⡇⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢚⡇⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠃⠀⠀⠀⠀⠀⠒⠀⠀⢀⣀⡇⢾⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡇⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣈⣻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠧⠤⠴⠶⠒⠚⠛⠛⠉⠉⠉⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠓⠚⠻⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢰⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⢊⣿⣦⣀⠀⣠⣤⣴⠏⠁⠠⣟⣿⣿⠟⣦⠤⢤⣀⡠⠚⠛⢩⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢐⣩⣿⣯⣭⠿⠗⢃⣀⣠⣤⣄⠈⠻⠿⠅⠀⣠⣿⣿⣟⡢⠀⠻⡿⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠛⠋⠉⠀⠀⠐⠋⠉⢠⣾⣿⠧⠀⠀⠀⠘⠻⠿⣏⣻⡯⠀⢀⠀⠀⣾⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⢶⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢷⠜⠂⠁⠀⠘⠿⣿⣿⣟⠛⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣆⣀⣠⣠⣠⣀⣠⣸⠀⠀⢀⣠⣤⣄⣀⣠⣤⣀⣀⣀⣀⣀⢀⣰⣷⣀⠀⠀⡀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠉⠉⠉⠹⠯⠭⠭⠽⣛⣛⣿⠿⣟⡛⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠯⠭⠭⢝⣓⡚⠻⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⣒⠒⠪⠭⠭⣛⡳⠦⢄⡀⠀⠀⢈⣉⡉⠉⢉⣍⣑⣒⡂⠤⠄⣀⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠉⠹⠗⠶⠎⠉⠒⠀⠀⠀⠈⠉⠉⠉⠛⠛⠭⠍⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡘⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣄⠀⢀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠙⠒⠶⠤⣄⣤⣤⣶⣶⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣭⣭⣛⡻⠟⠛⠋⠉⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⡿⠋⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠨⣽⣛⣲⠦⣤⣄⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡒⠤⢭⣙⣛⠻⠟⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠾⢿⣿⣛⡶⠦⣤⣀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣍⣀⠐⠤⢌⣙⡛⠿⠿⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠾⢭⡽⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣭⣍⣒⣒⣹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡲⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢰⠏⠂
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠂⠀⠀⠠⠒⠀⠚⠀⠀⢀⡠⠀⠂⠃⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⢸⡆⣰⣧⣆⠒
⣴⣧⣿⣇⡆⠀⠀⠘⣯⠐⠂⠀⠀⢲⡄⠀⠀⠂⠻⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢰⢷⠀⢠⣾⢷⣭⠌⠛⢶⠒⢠⡆
⣻⡟⢫⣿⣧⣷⣏⡠⠀⠔⠐⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⡔⢯⡀⢘⡁⢂⠪⡦⠴⡘⢦⣝⢳
⠚⣯⡶⢹⣿⣿⠋⠂⠀⠂⠐⡈⢺⣶⣆⣤⣀⣤⢀⠀⠀⠀⢀⡀⣤⢀⣠⡊⠃⣴⠞⠃⢜⡺⠤⠉⠱⣿⠀⠈⠀⠙⢿
⢈⠁⠖⢸⣉⡤⠎⣠⠆⠀⠀⠐⠲⣿⣿⡿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡿⠈⠈⠺⣂⠘⣯⡤⠒⣀⡠⣜⡀⠀⠈⠶⢾
⠸⠄⢠⣟⡉⠠⠠⠶⢀⣰⢿⠑⢠⣙⣯⢓⣹⣭⠟⣋⡁⠀⠀⠀⠙⢿⠀⠈⠙⠳⣎⢢⡟⠒⠉⠈⠣⠌⡂⠀⠠⡀
⠀⠀⢠⡏⠠⢰⠂⢠⠊⠙⢄⣯⡀⠀⠉⠁⠀⢄⣪⣷⣻⣓⣦⣴⡶⠂⠀⡀⠁⣌⠚⢿⣗⠄⣇⠀⢰⡆⠈⠲⡀⡀⠑
⠀⡰⠋⠀⢀⡬⣟⠀⠀⠀⢣⣀⠧⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠉⡋⠀⠀⠉⠐⠉⠄⠀⠁⢿⡁⣀
⠀⠀⠀⠈⠀⠀⠀⠙⠊⠀⠊⠁⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⠘⠉⠀⠄⠐⠤⠦⠀⠽⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠶⠒⠚⠋⠉⠉⣡⠞⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠴⠶⠶⠶⠒⠚⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢸⡿⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢦⣤⣄⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣞⣱⠆⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠲⠶⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣤⣤⣀⣀⣀⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋⣷⡖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠓⠚⠉⠁⠀⠀⠀⡄⠂⣈⠽⠟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣟⣿⣿⣿⣿⣻⣿⣿⣿⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡉⡀⠠⠀⠤⣶⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⢿⣿⣿⣿⣿⡿⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⢠⠉⠾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣨⢉⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⣤⠈⢒
⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⢯⠄⢀⠀⠀⠀⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠼⠟⠄⠒⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢻⠹⠄⠀⠀⠀⢀⣤⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠋⠀⠐⡢
⠙⠙⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⣾⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠻⠛⠛⠃⠀⠀⠐⠁⠀⠀⠀⠀⠘⠉⠠⡾⠊⠀⢀⣴⠡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣴⠟⢠⡄⠀⣰⣶⣆⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⢀⡀⠀⠀⠀⠀⠀⠴⠃⠈⠉⠀⠈⢁⢩⠛⢟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠁⢩⠿⣿⣿⣿⢿⣷⠀⠈⠝⠲⠆⣠⠀⠣⢄⣥⣤⣾⣴⣿⣟⡷⣮⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠃⠀⠈⢻⣿⡾⣿⣔⣂⠀⠰⠂⣀⣘⣧⣬⣽⣶⣿⣿⣿⣿⣿⣿⣋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⡀⠀⠀⠀⢀⣹⣷⣽⣿⣿⣷⣿⠿⠟⠛⠛⢻⢿⠋⣿⣿⣻⡿⣿⡛⣷⣿
⠀⠀⠀⠀⠀⢐⣀⠀⠀⠀⠀⠀⠀⢖⡞⣨⣤⣶⠶⠿⣛⣿⣿⢿⡛⠛⠉⠁⠨⢧⠀⠚⠺⠤⣧⠰⣿⣞⣽⣄⣽⣯⣿
⠀⠀⠀⠀⣀⡻⢿⣤⣤⠃⣀⣀⣀⡮⢸⣙⣯⠿⠿⠛⠋⠁⠀⠈⠃⠀⠀⠄⠀⠀⠀⠀⡀⠤⢤⣄⠙⣭⢿⣿⣿⠏⢁
⠀⠀⠀⠀⠉⠁⠂⣀⡠⠔⢛⡠⠁⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠐⠚⠂⠤⣬⡯⠟⣻⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣀⡀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⠀⢀⠀⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆
⠀⠀⠀⢀⣀⣉⡉⠉⠉⠀⣸⡄⣴⣶⣾⡶⢿⣦⠾⢶⣿⣷⣶⣶⣶⣶⣶⣶⣶⡒⣢⣤⣸⣾⣿⣿⣿⣶⣾⠢⠀⠀⢀
⠀⠀⠀⠘⣿⡿⠀⠀⠀⠀⠀⢹⣀⣀⣍⣀⣀⡁⠀⣤⡗⠚⠛⡛⠛⠛⠛⠋⠙⠉⢛⣿⡛⠛⠛⠋⠛⢻⣿⡖⠀⠀⠘⠇
⠀⠀⠀⠀⢠⠇⠀⠀⠀⢠⣠⣠⠱⡟⠋⠁⠄⠐⣖⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠄⠥⠀⣀⡴⠖⠛⠀⠱⡀⠠⢤⣶⢀⣶⡀
⠀⣀⢨⣄⠉⠀⠀⢀⡀⠀⠈⡈⠀⢣⠀⠀⠀⣸⣿⣀⡀⠀⠀⠂⠀⠈⠁⠛⠠⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⢿⣷⡀
⠀⠀⠘⣇⠀⠀⠀⠀⠁⣁⢀⡀⣀⢸⠀⠀⠀⠈⢉⠉⠁⠁⠀⠀⠀⠀⣀⣦⡀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣷
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⢤⡤⠅⠨⠀⠀⠀⠀⣚⣛⡃⣸⣻⢛⢅⣴⣿⣿⣷⠄⢀⣤⣄⠀⠀⠀⠀⠀⠀⢰⣶⣤⣻⡿⣴⣿⡦
⢀⠂⢀⠀⣠⠤⠤⠀⢠⣤⣬⣥⣤⣤⠀⠀⢤⣬⠀⢀⣅⣈⠉⢴⣦⣝⣷⡬⢿⡅⠉⡟⠩⠀⠀⠀⠀⣉⠇⣚⠻⢩⣿⣶⣾⢿⣷
⠈⠴⠠⢀⣄⠀⠀⠀⠀⠟⠘⣿⢻⠗⠀⠀⠁⠀⠀⠈⠳⠟⠀⠘⠙⠛⠛⠑⠰⠂⠂⠁⠠⠾⠇⠿⠖⠻⠚⠹⠏⠸⠯⠿⠿⠻⠿
⠀⣠⣇⠀⢩⣆⢀⠀⠠⢤⠀⠉⢀⣄⡀
⠈⠉⠉⠞⠳⠋⠁⠀⠐⠿⠷⣀⣿⣿⣷
⠀⠀⠀⣄⣤⠇⡤⠀⠀⢀⣴⠿⠛⢻⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣠⠤⠀⠀⠀⠀⢀⡀⠁⠃⠀⠀⢸⠉⠉⠒⣄⣁⠰⠖⠲⠒⠲⠶⠶⠶⢶⣶⠶⠆⠀⠔⠀⠀⠂⠀⠶⢦⣶⢦⡖⠲⠖⠶⠖⡀
⠀⠠⠄⠀⠀⠀⠁⠀⠗⠧⠆⠠⠰⠞⠀⢤⣴⣿⣿⣤⣤⢀⢀⣤⣤⣀⢄⣸⣿⣧⢤⣤⣤⣤⣤⣤⣤⣤⣾⢹⣦⣤⣤⣤⣤⡌
⠀⠀⣤⣶⣄⠻⡴⢇⠀⣸⢇⠴⢥⣤⣿⣿⣿⣯⣒⠀⠀⣿⠙⣧⡤⢈⠋⢹⣾⠗⢼⣏⣿⣏⣬⣩⣽⣿⣏⣬⡋⢻⣯⠈⣀⣤
⠀⠀⠈⠉⠉⠀⠀⠀⠺⡿⢻⡃⠀⠀⠁⠠⢩⣽⣿⣧⢸⣿⡋⣁⣀⢺⡆⣿⣻⡀⢸⡏⣿⣿⣿⣿⣦⣆⣿⠛⠛⢋⣽⣸⠨⠁⠞
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠘⣷⣤⡤⢤⠰⠿⣿⣿⣿⣾⣿⠀⠀⢙⣿⢁⣿⠘⠀⡿⠇⣽⡿⡙⠿⣷⣿⣿⣰⣶⣾⠿⠈⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠈⠀⠀⡟⡿⠉⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠁⠁⠀⢩⢽⡇⠉⠀⠁

⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⢀⣨⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣫⠄
⠀⠀⠀⠀⢠⣄⢀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⣩⢧⠶⠂
⠀⠀⠀⠀⣄⣈⣱⣆⣠⠤⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣤⣩⣿⣦⣶⠛
⠀⠀⠀⢠⡌⠉⢡⣎⣁⣀⡄⠀⣠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣉⣤⣾⣥⡼⠳⠶⠾⠃⢀⠀⣠⠄
⠀⠀⠀⠀⠓⠚⣯⠉⢉⢁⣠⠀⠋⡀⠀⠀⠀⠀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠉⠀⢰⠀⡞⠀⠀⠀⢰⠃⠁⢺⣤⠿⢶⣧⡾⢿⣶⠶⠾⠋⠊⠀⠟
⠀⠦⠐⠶⡴⠾⢛⡓⠟⠉⠁⠀⠀⣧⠀⡀⢀⡀⠀⠈⢧⡄⠠⢠⠆⠀⠐⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠶⢾⣟⣫⡿⠶⢟⡿⠶⠶⠂
⠀⠀⠶⣦⣀⣴⠞⠛⣶⣄⣼⠻⠇⠘⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣳⣫⣿⣭⣿⣟⣻⡷⢶⡾⠇
⠀⢀⣤⣬⣡⣂⣴⣾⣇⠈⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣋⣽⠶⠖⠺⢛⣿⣷⣤⣤⣶⠄
⠀⠉⠉⠉⠙⡉⠉⣹⡋⠛⠋⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠛⠶⠼⠿⠿⣿⣧⣤⣤⡤⠆
⢀⡝⠛⢿⣍⣠⠾⠻⡿⢷⠆⣦⠆
⠈⣿⠏⣉⣈⠈⣀⢾⣧⣀⠀⡾⠟
⠀⠀⠀⠀⠿⠋⠏⠈⠙⠛⠋⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡀⠀⣰⠲⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⡁⢄⠀⣠⡄⢠⠀⢀⠀⠀⢰⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣘⣟⣀⣀⣠⣟⣤⣀⣀⣤⣹⡃⡀⢀⣀⠀⠀⠠⠃⡀⠈⡁⢈⠐⠀⠀⠀⠀⠀⠀⢰⢸⢀⢸⠰⠸⢠⣺⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠛⣿⠭⠭⠍⠌⠍⠰⠐⠒⢲⡇⠀⠈⠸⠧⠃⠀⠀⠀⢰⢁⠇⠆⠘⠙⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣚⣿⣫⣩⡡⠉⣍⣍⢏⢭⣅⠄⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠩⠙⣯⣧⡽⢺⢼⡗⠓⠁⣉⠈⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀
⠀⠀⠀⠀⠀⠀⢰⠼⠀⠀⡞⡆⠘⣜⣮⣉⢞⣴⠀⢸⠙⡄⠀⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡖⣾⣿⠬⣿⣷⢒⣶⠞
⠀⠀⠀⠀⠀⠀⡽⣞⠀⠀⢣⠇⠀⢽⡿⠽⣿⠐⠀⠘⣶⠁⠀⢳⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢐⣸⠒⣇⡐⠻⠋⠀⠀⡂
⠀⠀⠀⠀⠧⢩⠤⢮⡤⠀⣼⠀⢀⠞⠿⡟⠛⠳⠀⠀⣿⠀⣐⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⡠⠄⢳
⠀⠀⠀⠾⡇⠰⠆⠐⣶⣶⡛⡦⣨⠖⠡⠐⠍⠱⢿⠶⣛⡛⢿⠧⠇⠀⠀⠀⢸⢠⠀⡄⢜⡀⢲⠀⠀⠀⠀⠀⠀⡄⠀⢑⠀⠀⠅⢀⠀⢠
⠀⠀⠀⠂⠁⠀⠀⠠⡉⠻⠟⡽⣧⣦⠤⠴⡤⠴⠾⠃⡙⢁⠀⠀⡄⠀⠀⢰⠀⢁⠡⠃⠈⠄⠈⠀⠀⠀⠀⠀⢠⠁⣀⠞⠀⡀⠄⠘⠆⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠧⡥⠴⠲⡛⢛⣟⠛⣳⡖⠦⠬⡄⠀⠀⠀⠀⢽⠀⠈⠀⠁⢻⠐⠁⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠤⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠆⢰⡇⢸⣿⠀⠙⣓⡀⠀⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⣇⠈⡇⢸⣾⡄⢀⡏⣧⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡗⣻⡄⠀⠀⣟⡷⠀⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣄⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣿⣿⡇⠀⢸⣿⣣⡀⠀⠀⠀⠀⣀⠀⠀⢠⠀⣿⠀⢸⡄⠀⠀⠀⣽⢁⢀⢄⢠⢠⠀⡖⡀⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⣧⡌⣀⡄⢸⣿⠃⠱⠀⠀⠀⠘⠻⠀⠀⠀⠀⡏⠀⢸⢳⡁⢾⠀⡇⠸⠘⠘⠘⠊⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢽⡇⠘⢿⡿⣿⣿⠃⣀⡄⠀⠀⠀⠀⠀⠀⠀⠃⠠⠋⠀⠁⠀⢰⠧⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⢻⣅⡀⢾⡿⠙⢯⣦⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠈⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢧⡀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⣴⡿⠖⠃⠀⠀⠀⣤⡄
⠀⣠⣴⡾⠳⢂⡘⢻⡛⠁⣠⣆⣘⡳⣶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⣴⣿⣿⠟⡄⠀⠀⠀⠻⠇⠀⠀⠀⢀⣀
⠀⠀⠀⠶⠛⡻⠛⠛⠛⠀⠀⠀⠈⠃⠊⠁⠀⠀⠀⠀⣠⡄⠰⣏⠼⢛⣱⣿⣿⢿⡟⢀⡖⠀⠀⠀⠀⠀⠀⠠⣶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⡟⠁⡀⠀⠈⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣞⠀⣸⡿⠞⢀⠀⠀⢠⣤⠂
⠀⠀⠀⠀⠀⠀⣰⡟⠟⣴⣿⡷⠷⡄⠀⠀⠀⠙⢇⠀⠸⠅⠀⣸⣆⣴⣤
⠀⣠⠄⢴⠇⠞⣛⣵⣿⣿⣿⠇⢠⠀⠀⠀⢠⠀⡀⠶⢤⣰⣄⡿⠟⡏⣀⠀⠀⠀⠀⠀⢀⡠⠢
⠀⣀⠀⡆⠀⢠⢿⠋⠀⠐⠁⠀⣼⣇⢰⣦⣿⣦⣿⣿⣤⠿⠿⠷⣾⡿⠋⠀⠀⠀⠀⢠⠃⠀⠀⢁
⢀⣿⣴⣷⡄⢀⣄⣼⣧⣦⣾⣷⣿⡿⠻⠿⠟⠋⠉⠀⠀⠴⠟⠛⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⢆
⠈⠉⠉⠙⠓⠪⢥⣀⡀⡐⢨⡉⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠃⠀⠀⠀⠀⠀⠈⢢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠺⠷⠤⠿⢷⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠁⠀⠀⠀⠀⠀⢂⠤⠊⠀⠀⠀⠀⠀⠀⠈⠑⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⠿⡄⢀⠀⠀⠀⠀⠀⣴⣆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣾⣿⠟⣿⣇⠀⠈⠲⠈⠁⠀⠴⣾⣿⢻⣿⣦⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠋⣿⣿⢸⣿⣿⣆⠀⢀⠀⠀⠀⠀⠀⠘⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠈⠃⠀⠀⢺⣷⠀⡏⢹⣿⡿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⣴⣿⠟⠇⠀⠀⠀⠀⠁⠀⠀⢾⢟⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠹⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣨⣶⣿⣿⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣾⡟⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡄⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠚⠏⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣯⣿⣿⣿⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠣⢿⣿⣿⣿⠋⠛⠿⣿⣿⣿⣿⣷⣤⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣟⠀⠀⠀⢿⣇⡄⠀⠀⠀⠈⠉⠉⠛⠛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣽⣲⣶⣦⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣵⣿⣿⣟⣽⣯⣿⣄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⠻⡿⣿⣆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠻⣿⣿⣿⣷⣽⣯⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠈⠻⣿⣿⣻⣯⣟⣿⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣄⣀⠀⠀⣿⣿⣿⣷⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣶⣿⣿⣿⣿⣎⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣯⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢽⣿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣷⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣃⣴⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣾⣿⣫⣿⣿⣟⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣟⠉⠉⠉⠛⢻⣿⣿⣿⣿⣿⣿⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⡻⣿⣀
⣿⣷⣶⣦⣤⣀⣀⣉⣀⣀⣀⣈⣙⣷⣶⣦⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⢿⡾⣿
⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉
⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠿⠿⠿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠦⠠⢤⣴⣶⣶⣶⡦⠀⠀⠀⠀⠀⢠
⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢀⣴⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠔⠚⠝⠉⠉⠙⠓⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠁⠀⡘⠀⠀⠀⠐⠀⠀⠑⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⢛⣉⣩⡤⠤⠤⠤⠤⠠⠤⠤⠍⣹⣛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠒⠫⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢂⠀⠀⠁⠀⠀⠀⠈⠀⢀⠀⡠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⠠⡁⠀⠀⡀⠀⢠⠁⡠⡣⠊⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠈⠳⠚⠒⠒⢋⠁⠀⢠⠁
⠀⠀⠀⠀⠀⡴⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡶⢤⡀⠀⠀⠀⠸⠀⢀⠆
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⣀⡅⠀⠀⠀⠀⣇⡎⠀⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠃⠈⠂⠐⠀⠒⠀⠁⠈⠁⠀⡄⢉⡀⢀⡀⢀⡀⣀⠅⠀⠀⣤
⠀⠀⠀⢀⠌⠀⡘⠀⢀⠀⠀⠀⢀⠀⠃⠀⢠⠀⠀⣨⠇⠸⠇⠸⠂⠺⠂⠀⢼⣿⡧⡀
⠀⢀⠔⠁⢀⠔⠀⠀⠂⠀⠀⠀⠘⠀⠀⡀⠀⠡⠀⠈⠢⡄⠀⠀⠀⠐⠠⠂⠳⠙⠙
⠺⠷⠶⠲⠷⠶⠖⡾⠲⠶⠷⠖⠶⠷⠖⠾⠖⠶⠺⠖⠶⠶⠷⠀⢀⠔⡠⢀⠁⠀⠐⡀⠄⠢⡀
⠀⠀⡀⠀⡆⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⠀⢀⠁⡀⠐⠁⠔⠁⠄⢀⠀⠀⠀⠈⠂⠈⠂⢀
⠀⠀⢁⠀⢀⠀⠀⢰⣲⠚⠓⣦⡞⠓⢒⣾⠀⠀⠰⠀⢰⣉⣀⣤⣎⣀⣬⣠⣬⣀⣤⣄⣥⣀⣱⣤⣀⣁⣦
⠀⠀⠘⠀⠈⠀⠀⢸⡿⠀⢀⣿⡇⠀⠀⡇⠀⠀⡀⠀⡀⠀⠄⠰⠀⠀⡀⠀⡃⠀⢀⠀⢠⠀⠀⠃⠐
⠀⠀⠀⡄⠀⠀⠀⢸⡟⢰⣸⣿⣧⣴⠀⡇⠀⠀⠇⠀⠁⠀⠰⠀⠆⠀⢸⡏⠉⣿⡋⠙⡏⠀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣿⣿⣿⣿⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⣿⣧⡀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⢻⣿⣿⣿⣟⠧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣿⣿⣿⣷⡇
⣶⣶⡶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣷⣾⣶⣶⣶⣷⣿⣶⣾⣿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡾⠻⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣡⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⠁⠀⣀⡀⢴⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣤⣴⣾⡒⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡹⠞⠀⠋⠁⡆⡀⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗⠀⠀⠂⠀⢬⣥⣤⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠆⠀⠀⠀⠀⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⢐⣶⣾⣯⠈⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢹⠾⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠠⡤⢄⣀⡀⠀⠀⠀⠀⠀⠄⠙⠶⣤⣀⠀⠀⢸⡃⢨⣐⣛⣉⣭⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠯⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠋⠁⣀⣬⣥⡊⠠⠤⠞⢻⣶⢶⣤⠧⠉⠀⢀⣀⠈⠛⣿⣦⢼⣿⣯⣿⣓⣿⣖⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡴⠶⠟⠛⠛⠈⢹⠏⢰⡆⣾⠀⠘⠋⢾⡇⠀⣹⡇⢸⣯⠀⠀⠸⣷⣈⣽⣿⣿⣿⣿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠠⠀⠀⢰⠀⠀⠀⢸⡧⠿⠆⠀⠠⠎⠀⠀⠉⠀⡎⠁⠀⠀⠀⠈⣿⣿⣟⣿⣯⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣀⣄⣲⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡀⣈⡄⠀⢤⣤⣴⣶⣶⡆⠀⠀⢠⣤⠀⣴⡇⠰⠶⠆⠀⠀⠻⠿⠓⠛⠒⠛⠚⠛⠋⠉⠉
⠀⠀⠘⣿⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣋⠉⠁⢸⠀⠀⢸⣠⣷⣽⣯⡇⠀⠀⢸⣿⠀⠛⡇⢸⣿⡇⠀⠘⠛⠻⠟⠛⠛⠛⠛⠛
⠀⠀⠀⠿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠘⠛⠛⠛⠛⠃⡀⠀⢸⣭⣤⡄⡁⠀⠈⠀⠀⠿⠤⠀⠀⠤
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣦⣀⡀⣀⣀⡀⠀⠀⢀⣀⠀⠀⢶⡆⠀⠀⢠⣀⣀⣶⣶⣶⣶⣶⣶⣷⣖⣨⣧⣿⢣⣮⣴⣦⣀⣀⡀⠀⡀⠀⣀⡀
⠀⠀⠀⢉⣉⣉⣭⡉⠉⠉⠈⠁⠙⠋⠁⠧⠳⠛⠛⠗⢀⣸⣟⡃⣀⢱⡄⠿⢻⣛⣿⡿⣿⠻⣿⢾⠋⣿⣷⡏⠏⣻⡏⣿⢛⣿⢻⡿⣿⣿⠿⣿⠿⣿⣿⣿⣿
⠀⠀⢠⣾⣿⣿⣿⣶⢦⣴⣶⣦⣀⣀⣀⣀⣀⣸⣀⣀⣀⡿⠟⠿⣿⣶⣦⣀⣼⣿⣯⣷⣿⣿⣿⣧⣸⡿⢿⠘⠨⣿⡇⠙⠛⣿⣾⣇⣾⣿⣿⣿⠀⣿⢹⣿⣿
⢰⣿⣽⣿⣿⣭⣽⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠗⠀⠀⠈⠀⠁⠈⢉⣻⣿⡟⣭⣯⣭⡟⣿⣥⣿⡷⢿⡿⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣤⢻⣿⣿⣿
⣿⠿⠿⣿⣿⣿⣿⣻⣿⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠠⠦⢴⣦⣤⣶⣶⡖⣻⣿⣿⣿⣷⣿⠀⢠⣠⣧⢠⠀⣀⣸⢀⡿⠁⢸⡉⠉⠙⠛⠙⠛⠾⡿⠾⠿⣯⡅
⢀⣤⣀⡽⣿⣿⡿⠟⠛⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢰⣿⣏⡀⣿⣿⣅⣿⡏⢉⣰⡿⠿⠿⠀⠀⠃⠛⠘⠃⠀⢸⣧⡄⠠⡶⠀⠀⠀⡀⠀⡀
⠉⠀⠀⢠⣼⣿⣷⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠇⠸⠿⠁⠟⠁⠘⠛⠃⠀⠀⠐⢿⣿⠄⢼⣷⣀⠸⣿⣷⣤⣴⣾⣷⣤⣤⣄⣀⣀
⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠤⣀⣼⠄⠉⢸⣿⣿⣿⣟⣛⣿⣟⣉⣉⠛⠉
⠀⠀⠀⢰⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣛⡓⢨⡉⠁⠀⠐⣿⣿⣿⣿⣃⣿⣻⣯⣭⣿⣿⣿⠄
⠀⠀⠀⢙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⢀⠄⠒⠀⠁⠀⠠⠿⠿⠟⠁⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣥⡌⠉⠁
⠀⠀⠀⢨⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠉⠓⠀⠀⢀⣀⠀⢈⣿⠿⣿⠿⠛⢉⣽⣟⠉⠙⠁
⠀⠀⠀⠀⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠱⣯⣼⣿⣿⣿⣧⣄⡹⣿⣶⣶⡾⠂
⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡖⠋⠁⠀⠀⢴⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⡗⠂
⣶⡀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠀⠈⠀⠀⠀⠀⠀⠤⠀⠒⢶⣤⣀⠠⠄⠀⠀⠀⠀⠀⢀⣀⠶⠟⠌⠉⠛⠳⢦⣤⠄⢀⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁
⣿⣿⣦⣤⣤⡦⠀⠈⠉⠁⠀⠀⣀⣠⡠⠖⠂⠁⠀⠀⠀⠀⣈⡽⠻⣷⣤⣄⣠⣴⠶⠋⠉⠀⠀⠀⢀⣠⡶⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡃
⣿⡿⠛⠁⠀⠀⠉⢠⣤⠠⠤⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣷⡾⠋⠁⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣠⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⣀⠀⠉⠛⠶⢤⣀
⠀⠀⡇⠈⠉⠓⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣽⠗⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠙⣳⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠛⠶⣄⡀
⠀⠀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠖⠒⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣽⠒⠒⠒⠲⠶⠦⠤⠤⢽⡇
⠀⠀⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠁
⠀⠀⡇⠀⠀⠀⢀⡴⠛⠉⠳⡄⠀⠀⠀⠀⠸⣄⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡏
⠀⠀⡇⠀⠀⢰⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⣿⠀⠀⠈⠳⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡏
⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠓⠶⠤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠃⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠿⣅⣀⡀⠈⠉⠳⡄⠀⠀⠀⡀⠀⠀⠙⢦⣄⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣿⣀⡀⠈⠛⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣀⢸⠀⠀⠀⠯⠭⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠃

⣿⣿⣿⣻⣛⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣻⣿⣻⣟⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠉⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠤⠤⠤⠤⠀⡀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠔⠙⣇⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣁⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠢⠀⠀⢀⠃⠀⠀⠈⠙⠓⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠤⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⢴⠚⠛⡏⠉⠉⠙⠒⠒⠦⢤⣀⠀⠀⠈⠑⠄⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢴⡇⢈⣀⠀⢈⢦⣀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⢿⡖⡢⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢾⡇⠃⡸⡿⠓⠢⢄⣀⡀⠀⠀⠀⠱⡀⡠⠃⢀⠤⠒⠈⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠻⣾⠗⣒⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠳⡀⠁⠀⠀⢀⠤⠹⠆⠀⠀⠈⠑⢦⠀⠙⠤⢄⣁⣀⡀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠚⠛⠛⠒⠚⠟⠛⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠙⢦⡀⠒⠴⠾⠇⠂⠀⠀⢀⣴⠋⠡⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠫⢁⠀⠀⠀⠀⠀⢀⠄⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⣈⡑⡖⠢⠤⠤⠶⠞⠋⠀⠀⠀⢙⡦⡀⠀⠀⠀⣀⠀⠀⣀⣀⡀⠀⠉⠐⠂⠄⠊⠀⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢀⡠⠤⠒⠋⠁⠀⠀⠑⠢⢤⡄⢀⣀⣀⠀⠈⠉⠒⠠⠤⢠⡤⢞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠘⠋⠉⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠳⣄⠤⢀⠑⠄⣀⡠⠄⠀⠀⣁⡠⡃⡧⠀⣀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣳⡀⠀⠀⢹⡳⣖⠨⠥⠐⢖⡉⠈⠀⠉⠲⠖⠁⢈⢤⡁⢊⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡴⠁⣡⠄⠀⡤⠓⠂⢀⠰⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⣨⠧⠬⢤⠤⠴⠦⢒⠒⠂⠀⠀⡠⠀⠙⡈⠀⢜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡒⠈⠙⠊⡉⠷⠚⠒⢊⠇⠀⢣⢢⣄⣀⠀⣀⣀⡠⠴⠒⠋⠁⠀⠀⠈⢆⠀⠀⠀⠈⠀⠒⠈⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⡥⠤⡖⠒⠈⠁⠀⣀⣤⡁⠈⠡⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⠙⠒⠖⠒⢋⠁⢀⣡⠶⠚⠉⠉⠉⠉⠉⠙⠒⠒⠲⠦⡤⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⡉⣡⣖⠐⠋⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⢀⠀⢷⢄⣀⡠⠎⠀⠀⠤⡔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡎⠀⠀⠑⢠⡀⠀⠀⠀⢀⣈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⢄⣀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠲⣀⠀⠀⠑⠢⡉⠁⠀⠀⠈⠲⣀⢀⠠⠄⠀⠀⣁⠠⠄⠒⠀⠁⠀⢀⣀⠬⠗
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⢠⠀⠄⠄⠒⠁⠀⠀⠀⠈⢦⠄⠂⠉⠁⣀⣀⡤⠤⠒⠚⠉⠁
⠻⣍⠒⠢⠤⠤⠤⠄⠀⠀⠀⠠⠤⠄⠐⠒⢒⣘⡦⠤⣤⠊⠀⠐⠂⢈⣁⣠⡤⠤⣔⣢⡥⠴⠒⠚⠉⠉
⠀⣌⠛⠒⠶⠶⠶⠶⠶⠒⠒⠒⣚⣋⠩⠭⠔⠒⠒⠀⣉⣉⣉⠭⠭⠷⠒⠚⠋⠉⠁
⠀⠙⠦⣍⡉⠐⠒⠈⢉⣉⣉⣉⣠⡤⠤⠴⠒⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣻⣿⣷⣖
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣍⣚⣿⣯⣥⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣚⣿⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⢿⣿⣿⡷⢞⣫
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⡷⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠠⣄⣛⣿⣿⣿⣿⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠠⣙⣻⣿⣿⣟⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠢⡀⠀⠀⠀⠀⠀⡉⣽⣿⣿⣿⣿⣿⣏⣡⣤⠄
⠀⠀⠀⠀⠀⠀⠠⣭⣿⣿⣿⣿⣯⠔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⣌⠛⢷⣿⣿⣿⣿⣿⣿⠟⢁⣀
⠀⠀⠀⠀⠀⢀⣄⣾⣿⣿⣿⣏⣥⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣞⡉⠻⣶⣿⣿⣿⣿⣿⣿⡿⠛⣩⡀
⠀⠀⠀⠀⠀⢠⣭⣿⣿⣿⣿⣷⣦⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠬⣿⣿⠾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣷⠶⠛⠓⠛⠒⠒⠐⠒⠒⠛⠉⠀⢀⣄⣰⣷⣿⣷⣞⣙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⡥
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣯⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠩⣽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃
⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣽⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠤⠴⢾⢿⣿⣿⣿⣿⣿⣶⣤⡤⠖⠀⠀⣆⠀⡄⠀⠀⠀⡄⢰⣇⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⣯⣍⡀⠀⠀⢰⡗⢠⡇⠀⡗⠀⣯⢸⣷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⣤⣿⢀⣟⣾⣿⣭⣷⣿⣿⣤⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣇⣸⣏⣟⣿⣫⣋⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠈⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠚⡆
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠉⠉⡩⠓⠦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠚⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠊⠲⡄⠀⠀⠸⡄⠀⢀⡗⠀⠀⠀⠀⢠⠊⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⢄⡤⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠈⠉⠢⡀⢰⠁⠀⠀⢳⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠢⠤⠤⠃⠀⠀⡔⠉⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡴⠒⠀⠒⢦⡀⠀⣉⣒⣋⣀⠤⠤⠤⠃
⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣀⣀⠠⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠘⠒⠒⠂⠉⠉⠉⠁

⠀⠀⠀⠀⡀⠀⠀⡀⠀⣀⠀⠀⡀
⠀⠀⢀⡾⠙⣄⢿⣿⣷⣶⣶⡤⠠⠥
⠀⣠⠎⠀⠀⠈⢿⣿⣿⣿⣿⣇⢀⡤⡄
⠀⠁⠀⠀⠀⠀⠈⢿⣿⣿⠟⠋⡀
⠀⠀⠀⢀⠀⠀⠀⢈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⡀⠈⠋⠉⠀⠀⠄⠂⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⡟⢺⡟⠀⠌
⠀⠠⡀⠀⠀⠀⢸⠀⠀⠀⢤⡀⠀⢨⡄⢠⡄⠼⠀⠀⠂⢀⠆⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⣠⣄⡼⢀⣿⣿⣦⡄
⢠⠦⠁⠀⠀⢀⣹⠀⠀⢐⡋⠀⢀⣿⡷⢃⣀⠐⠀⠀⠈⠁⠀⠀⣺⣟⠁⠀⠀⠀⠀⠀⠈⠛⠛⣧⣾⣻⣿⡟⠄
⠀⠀⣀⡤⠔⠊⠻⢦⠀⠀⢹⡆⢠⢬⡅⠀⢈⡇⠀⣶⠀⠀⠀⢪⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠘⣿⠒
⠀⣈⠍⠀⠀⠀⠀⠀⠀⠂⣼⡇⢰⣌⣿⠀⢘⠓⠀⢨⡅⠀⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⢠⡽⠀⠀⠀⠀⠀⠀⠀⠙⡿⢿⣞⢻⠁⠀⠸⠀⠈⢛⡅⣀⢹⣿⢛⣷⣿⣏⠀⠀⠀⠀⠀⢀⡀⡠⠀⠀⠀⡹
⠸⠀⠸⣷⣞⡿⠆⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⢘⣼⡇⢡⠀⡀⡀⠈⣿⣿⡄⠄⠠⠀⢀⠘⠤⠷⠈⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⢰⣾⣿⣷⠀⢀⠀⠀⠈⢫⣵⣾⣦⣷⣷⣟⣿⣿⣷⠄⠀⠠⠿⢿⠂⠀⠀⠀⠀⠀⢠
⠰⣶⣷⣄⣀⠀⠀⠀⠇⡀⠈⣿⡿⠙⠀⠈⠷⣾⣠⣿⣿⣻⣟⣿⣿⣿⣿⣿⣿⣻⠀⠀⣴⣿⣿⣦⣀⡀⠀⠀⠈
⢰⣶⣤⣭⣿⡏⣵⣤⣀⣥⣀⣙⣄⣀⡠⠤⠤⠀⢻⣿⠛⢻⣿⣿⡿⣿⣿⡿⣿⣿⡀⣴⣿⣿⣿⣿⣿⣿⣦⣀⣀
⠀⠉⠉⠛⠿⠿⠶⠋⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠛⠋⠀⢀⢝⠂⢾⣇⣀⠈⠉⠉⠿⠿⠿⠿⠿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠅⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣼⣿⡿⢠⠀⠿⣿⣿⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠑⢀⣾⣿⡁⣽⣿⡇⠀⠠⠀⠈⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠃⠀⢠⣿⣿⣿⣶⣿⣿⣧⠀⠀⠖⠀⠀⡀⠀⠀⠀⣤⣶⣯⠀⠀⢀⡀⣠⣴⡾⠋⠀⠆
⠀⠀⠀⠀⠀⠀⣀⣴⠀⡀⠀⠀⣠⡞⠀⠰⣦⣾⣿⣿⣿⠃⣴⣿⣿⡿⣿⣿⣽⣿⣿⣦⣀⠀⠀⠀⡀⢀⠀⢀⣼⣯⠏⠀⠀⠋⠈⢹⡾⠃⠀⠐
⠀⠀⠀⠀⢰⢿⣿⣇⠀⢀⣴⣿⣿⡟⠀⠀⠀⠙⣿⢻⣿⡖⠻⣻⡿⡃⠛⠋⡵⢟⠿⢿⣿⣿⣶⡀⠀⠀⣀⡈⠼⠟⢠⢤⡼⠁⢀⠘⠃⠀⣰⡄
⠀⠀⠀⠀⢙⢿⠟⠻⢠⣾⣻⢹⣋⡷⢸⢁⢸⡆⠘⣇⠹⠏⢤⡁⠠⣸⡄⢀⠀⠀⠀⠈⠁⠛⠹⣿⢶⣦⣌⢁⠋⣰⡎⣸⣯⡀⢸⣧⢰⣦⢼⣿⣀
⠀⠀⠀⠀⢀⣆⣶⣶⣿⣿⣶⣾⣷⣷⣿⣾⣼⣷⣶⣿⣧⣿⣿⣧⠀⣽⣿⢠⡆⠀⠀⠀⠀⠀⢀⣀⣴⣹⣇⣨⣤⣿⣇⣸⣿⣧⣶⣿⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣀⣁⡒⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡋⡿⣿⣿⣿⢿⣿⣯⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⠀⠀⠈⠙⢻⣿⣿⣾⣯⢻⢹⢸⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣾⣿⣿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠉⢀⣄⠀⢀⠀⣷⣸⢫⠻⢿⣄⣾⣌⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣿⣡⣿⢿⡿⢻⣟⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⡄⠀⠀⠀⠀⠀⣰⡀⣸⣿⣦⣴⣇⣿⢾⣷⡦⠊⠉⢡⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣏⢹⢸⣷⠋⣿⣿⣿⣿⣯⡀⠀⣾⣆⠀⠀⢼⣯⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣇⣤⣽⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣸⠉⢾⣬⣿⣿⣿⣭⣠⠌⣿⢗⡀⢈⣾⣿⣞⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣶⣦⣝⣿⣿⣿⣋⡥⢒⣿⡿⠃⡀⣹⣟⣯⡆⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢃⣿⣿⣯⣶⣃⡄⠀⠀⠀⣾⣟⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣦⠀⠰⣶⣿⣿⣵⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠴⠲⣾⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣷⣆⣹⣾⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈

⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠠⢟⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡄
⠀⡼⣤⢻⡏⠱⣾⣶⣶⢩⣶⠞⢢⣤⣀⠺⢢⢀⡀⢸⠥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⣾⣷⣯⡷⠶⢠⡄⣀⣀⠬⡀⣀⣰⢸⡇⢰⡀
⠀⠾⣋⠴⡏⠲⣿⣿⠗⢏⠋⢘⡋⣻⠕⣇⠟⣿⠷⠞⣎⣘⡆⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⣼⢆⣸⡳⡔⢊⡅⣳⡓⣜⢸⣿⡿⡟⠠⡧⠽⣏⡙⢧⣽⣇
⠀⣟⠹⣤⣑⡾⣱⠹⡆⣵⡤⠾⡀⢟⡅⢻⢆⣋⣄⣨⢥⡭⠌⣿⣾⢶⡎⠿⣶⣶⡟⣿⣿⢴⡾⢇⢺⡃⢩⡁⣨⣿⡙⢤⣽⣷⠔⡳⢈⠲⣯⠤⣾⣦⡽
⠀⠑⠀⣾⡹⢆⣯⢀⣿⣇⡓⢛⣀⣋⢱⢾⣯⠔⡰⢣⡜⢻⠳⢼⢷⣸⠗⢂⠸⣿⢏⢹⢇⢚⣝⠺⣿⢳⡏⢻⠀⢇⠑⣤⡈⡛⠁⢤⠘⡄⢼⡐⡗⡸⢧
⠈⠀⠈⠻⠁⠴⣏⠹⠬⠘⠁⠛⠋⡔⢦⠟⣃⠹⢤⠎⠱⡌⢳⠦⡛⠇⠨⠤⠀⠘⠉⠋⠑⠃⠔⠬⠿⠞⠳⣼⡓⠢⣥⠆⡸⠙⡆⣨⠀⢰⢀⠛⡥⢁⠲
⠀⠀⢀⡆⠠⡆⡀⠓⢌⡁⠀⠀⠀⠀⠀⠀⠋⠁⠉⠓⠀⠘⠛⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢷⠀⢦⠈⠈⢶⢌⠛⡛⠒⠀⠀⠀⠀⠈⠉⠂⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠉⠉⠐⠈⠂⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠒⠤⢄⣀⠀⠀⢰⡒⢲⣿⠉⠛⠟⠛⢃⢻⡇⠀⠀⠀⡠⢠⡀⠀⢀
⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⣿⠛⠿⢤⡃⠉⢰⡦⡀⠄⠊⠀⡀⡀⡰⡡⡑⡡⡡⢁
⠀⠀⠈⠃⠉⠢⣀⠀⠐⢤⣆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣀⠶⢉⠍⡸⠀⠀⠀⠀⠜⡐⠑⡔⢉⠜⠔⢠⢃
⠀⠀⠀⠲⢄⠀⠈⣈⠂⠈⠀⠉⠒⠤⣀⣸⣿⣿⣿⣿⣇⢨⣟⡳⠈⠀⠀⠀⢀⠎⠈⢈⢎⢀⢊⠎⡠⠁⠢
⠀⠀⠀⠰⢄⡈⠂⠁⠑⠀⠢⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣏⡇⠀⠀⠀⠀⠠⠂⠂⠀⣁⣀⡀⠔⡠⡑⡡
⠀⠀⠀⠀⠀⠈⠓⠆⢄⠐⠀⢄⢠⣠⣴⣾⣿⣿⠏⠙⢿⣿⣿⣷⡀⢀⣀⠤⠤⠤⠖⠋⠁⠀⠉⠒⠥⣴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠝⠛⠛⠋⡉⢀⣼⣿⣿⠿⢿⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡉⠲⢤⣀⠘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⣛⠶⢥⣄⣀⡀⠀⠀⠀⠠⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠠⡈⠉⠠⣄⣀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠲⢄⠉⠉⢍⡁⠀⠘⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠈⠲⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠉⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⠀⠀⠀⠀⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣇⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⣆⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⢁⡈⢿⣆
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢛⠉⢆⠀⠈⡴⠉⡛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢿⣶⣤⣤⣀⣀⣀⣀⣀⢀⣀⣀⣀⣤⡴⢖⠾⡉⣿⣗⠐⠤⡌⠀⠀⢡⢤⠂⣺⣿⢉⠷⡶⢤⣤⣀⣀⣀⣀⡀⣀⣀⣀⣀⣤⣤⣶⡯
⠀⠀⠀⠀⠈⢿⣿⠒⠭⡋⠉⠛⣽⠻⡝⠃⣤⠊⢀⡾⣛⢻⡌⠻⣷⣌⠡⠆⠰⠌⣡⣾⠟⢡⡟⣛⢷⡀⠑⣤⠘⢫⠟⣯⠛⠉⢛⠭⠚⣿⡿⠁
⠀⠀⠀⠀⠀⠈⢿⣟⣹⣯⣂⠤⠘⡀⠀⠀⡑⠲⠟⢰⡿⣤⠇⣠⣄⡝⠷⣆⣰⠾⢫⣠⣄⠸⣤⢿⡆⠻⡶⢎⠀⠈⢀⠃⠤⣐⣿⣏⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢻⡟⠋⣫⢟⢓⢦⡑⠀⢈⠛⢤⡴⠟⠂⣼⢫⣿⠃⠀⠸⠗⠀⠘⣿⡟⣧⠐⣺⢦⡠⠋⠃⠠⢊⣵⡿⡿⣍⠙⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⢧⠯⠈⠳⢿⠀⠀⣁⠀⠀⠀⣀⠙⠿⣿⠀⡀⢀⡀⢀⠀⣿⠿⠋⣀⠀⠀⠀⣈⠀⠀⣿⠞⠁⠝⡼⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⡀⢐⡏⡇⠈⠟⣰⣷⠄⣀⢤⣼⡛⢦⡳⣏⣹⢞⡴⢛⣧⡤⣀⠠⣿⣆⠻⠀⢸⢻⡀⠀⣦⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣜⡏⡇⠀⠀⢫⠋⠀⠧⠞⢀⡟⢸⣿⡎⢱⣿⡇⢻⡀⠣⠼⠀⠙⡝⠀⠀⢸⢹⣣⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣇⠀⠀⠘⢠⣫⠀⠀⣾⡇⡏⠀⠀⠀⠀⢹⢸⣧⠀⠀⣝⡄⠃⠀⠀⣸⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣘⣦⠿⣟⠻⢷⣷⠀⠀⠀⠀⣾⡾⠟⣻⠿⣴⣃⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢾⢤⣞⣻⣳⣄⣠⣞⣟⣳⡤⡷⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⡠⠀⠀⠑⠀⠀⠀⠘⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⢀⡈⠐⠀⠀⠀⡀⠀⠀⢀⡁⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠄⠀⠀⢰⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠢⢄⠀⠁⠂⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⠀⠀⠠⠊⠀⠀⠀⠀⠑⠀⠒⠀⡀⠀⠀⠐⠆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠘⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⡁⠀⠀⠀⠀⠑⢒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⡀⠀⠸⠀⠀⠀⣀⠰⠀⠈⠀⠀⠀⡇⠀⠀⠀⠙⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠱⡁⠉⠀⠀⠀⠀⠁⠀⠐⠀⠀⡀⢠⠀⢀⡉⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⢀⢀⠀⠀⠀⣀⠀⢀⠀⠣⡈⠓⠢⠤⠤⠤⢐⡙⠀⠒⠉⢀⡌⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠈⠰⠁⠀⠀⠈⠁⠀⠂⠒⠚⡉⠀⡑⢲⠒⠍⠀⠀⠀⠀⠀⢙⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠠⡀⢈⠢⠄⣀⣀⣰⠀⠀⠀⠈⠣⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠌⢰⡀⢀⣀⡀⠀⣄⡀⠠⡄⠈⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠁⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠠⠀⠀⠢⡀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢣⡀⣙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⣰⡟⠻⡌⢳⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣫⣝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⡰⠋⠀⠀⠈⠀⠙⣿⣿⣿⣿⣦⣄⠀⢀⣤⡾⠛⠕⠊⠁⠈⢀⣙⣷⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠹⣯⠻⢿⡿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠙⢦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠉⠙⠻⢶⣄⡀
⠀⠀⠀⠀⢀⠴⠋⠀⠀⣦⠀⣾⣆⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠁⠀⣀⣠⡴⠿⠞⢛⣋⣉⣉⣉⣭⣤⣀⣀⣀⣀⣈⠉⠉⠉⠙⠛⠛⠿⠷⢶⣤⣼⣿⣄⣾⡀⠀⠀⣿⡧⢰⡄⠀⠀⠀⣦⠀⣾⡀⠀⠀⠀⢀
⠀⠀⢀⠤⠖⢋⠭⠴⠒⠛⠋⠉⠉⣭⣴⠶⠿⠿⠭⠭⠉⡉⠉⠙⠛⠓⠶⠤⣄⣀⠀⠀⠀⠉⠉⠛⠛⠻⠶⢾⣿⣿⣿⣧⣀⣀⣰⣿⣴⣿⣧⡤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠐⠒⠦⢤⣄⣀⣀⡈⠉⠉⠉⠉⠉⠉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠷⠤⣄⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⣎⣀⣤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⣀⣠⠤⠴⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠚⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠚⠉⠉⠀⠀⠙⢤⣀⡤⠋⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⣀⡤⠤⠶⠒⠊⡟⠉⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡶⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠳⠤⠖⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡴⠋⠙⢦⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠁⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠹⢤⣠⣞⣠⠇
⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠣⣀⣀⡰⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢹⠀⣀⣀⡤⠤⠒⠚⠉⠉
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠿⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⡇⠀⣀⣀⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⠟⠁⠀⠀⠀⠀⢀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⢸⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⣠⠖⠀⠺⠁⠀⠀⢀⡀⠔⢂⠋⠀⠀⠀⠀⠀⢤⠀⠀⠀⣄⠀⠀⠀⣿⠀⣚⣡⣔⠲⠄
⢠⣦⠔⡧⢰⡄⠀⠀⠐⢚⡁⢦⠀⠀⠠⢤⡄⠠⠀⠔⠒⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⣰⣿⣆⣙⡹⠿⣦⢤⡆⣠
⣿⢗⣍⣰⢾⣧⣤⡶⠂⡉⣰⠄⣁⡀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⣸⡄⠀⢸⣼⠇⠠⡟⣱⠈⣹⣄⣤⠘⣇⡈⢻⣆
⣿⣋⢥⡼⡃⢽⣿⠟⣁⠀⣩⣀⡀⢷⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⣀⠀⣰⢿⠒⣀⣡⣌⠳⡄⢉⣠⡷⢤⢿⡏⠱⠄⠙⣷⣿
⠉⡱⢾⣅⣿⠞⠛⡡⠈⢋⣀⣈⡛⢦⣽⣾⣾⣦⣾⣴⣐⣿⣓⣶⣼⣶⡿⣿⣿⣿⡇⣤⢤⣻⡡⢦⣸⠔⠁⣈⠳⡌⢳⣿⡗⠣⣄⠈⣿
⢻⡆⢸⣇⣷⠾⠋⠙⢶⠋⠹⢶⣧⡈⠙⣿⣿⣿⣿⣿⠄⠹⠈⢿⣿⣿⣡⠻⣿⡿⠋⣱⣄⣈⢰⡄⢱⠒⣀⡸⣧⠛⠻⡿⠷⠀⠈⠙⢿
⠁⣼⡟⣿⣥⠔⠋⣸⠋⢠⠠⠋⠁⠙⠲⣽⣿⡟⣾⣗⠕⢱⣀⠞⣿⡫⠡⠒⢻⠇⠂⢈⣠⡈⠻⣷⡏⠉⢁⠀⠸⡗⠢⢽⡀⠈⠣⢀
⣾⣉⣿⣿⠁⠐⢚⡁⣠⠏⠠⡀⠘⢦⠀⡈⣹⢿⡋⠀⢘⠁⡏⠀⠈⡖⠀⠤⡋⢀⣠⡏⢨⣌⠙⢻⣿⠔⢻⡄⠀⡟⢦⣀⠹⣆⡄⠈⢻
⠈⢉⠟⠀⠀⣠⠤⠋⠉⠀⠀⠙⣆⣸⠟⠛⠚⠀⠓⠐⠈⠛⠓⠂⠀⠈⠀⠀⠈⠀⠀⠁⠁⠀⠛⣋⠄⠀⢈⠙⠚⠁⠀⠈⠙⢿⣅⢀⣀
⠀⠀⠀⠀⠈⠀⠀⠀⠙⠂⠀⠀⠈⠛⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠰⠛⠲⠤⠀⠰⠤⠧⠄⠹⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⢸⣿⡄⢰⣿⡄⠀⣤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⢹⣿⣄⢸⣿⣿⡼⣿⣷⣠⣿⡄⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠈⣿⣿⡎⣿⣿⣿⣹⣿⣿⣿⡇⣾⣿
⠀⠀⠀⠀⠀⠀⠈⢷⣤⡀⢻⣿⣷⣿⣿⣷⢿⣿⣿⣧⢿⣿⣿⢷⣿⣿⣴⣾⡿⠛⣉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣻⣿⣿⣿⣿⣼⣿⣿⣿⡞⣿⣿⣾⣿⣿⣿⣟⣴⣿⣿⠿⠛⠛⠛⠂
⠀⠀⢀⣤⣶⣿⣿⣿⣮⣻⣿⣿⣮⡻⣿⣿⣷⢿⣿⣿⣿⢿⡏⣿⣿⣿⢸⣿⣿⣟⣥⣶⣾⣿⣶⣦⡀
⠀⠀⠉⣁⣤⣤⣭⣝⣿⣷⡻⣿⣿⣿⣮⣻⣿⣯⢿⣿⣿⣸⡇⣿⣿⣿⣼⣿⣿⣿⠿⠛⠋⠉⠙⠻⢿⣆
⠀⣴⣿⣿⡿⢿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣷⡽⣿⣯⢻⣿⣿⣧⣿⣿⣧⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⡄
⡼⠋⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣜⠿⢷⣙⣥⣭⣾⣷⣶⣶⣶⡅
⢀⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣏⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⡟⢁⣾⣿⠿⠋⠉⠀⠀⠉⠻⢟⣽⣾⣿⣿⣿⣿⡿⢿⣛⣯⣭⣷⣶⣶⣶⣆
⠙⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⣛⣭⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣥⠤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠋⠛⠿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢴⣶⣷⣶⣽⡳⣦⣄⠀⠀⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣿⣿⣿⣿⣷⣻⣿⣦⣀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣧⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡉⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⡞⣻⠿⣿⡿⣻⡿⢟⣵⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣟⢿⣿⣿⣶⣦⣭⡙⣿⣿⡿⠿⣟⣫⣥⠻⣿⣛⣯⣷⣾⠿⣫⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣟⣿⠿⠾⡿⠷⠾⢿⣿⣰⣷⢰⣷⡝⣿⠿⢫⣟⠛⣿⣽⠷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⡿⢿⢿⣿⣿⠿⢿⣛⢘⣟⢸⣿⣿⡔⣿⣮⡻⣿⣦⣿⢸⣿⣝⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣻⣿⣿⢛⣿⣿⡿⣍⣾⣿⢸⣿⣿⣿⡜⣿⣇⣛⣛⣈⣹⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠿⣳⣿⣞⠿⣽⣇⢿⣿⢜⠻⣿⡟⢡⣯⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠿⠿⠿⠞⠋⣾⣷⣵⣿⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠈⠉⠛⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⢋⣼⡉⠢⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠇⠀⠀⠀⠀⠀⣩⠿⠋⡀⣠⡿⠟⠁⠀⡀⠀⠀⠀⠹⣇⠀⠀⣀⣀⣠⣴⢾⡁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡿⠿⠛⡦⠀⠀⢂⣴⣫⣵⣶⣿⠁⠈⠳⢤⠀⠀⠸⣶⠀⠀⠀⠈⠳⣀⠙⠙⢿⠟⠀⠷⣄⡀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⡿⠿⠋⠻⣦⣄⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⣀⣀⣈⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⣿⡿⠈⠻⣿⣿⣦⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡃⠀⠀⠈⠉⠛⠟⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⢀⣼⣿⣿⡿⣻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⢀⣾⣿⣿⡏⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⣿⣿⣿⡟⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⣿⠛⠛⠛⠛⠃⠠⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⣰⣿⡿⠁⠀⠀⠀⠀⢀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⢠⣾⣷
⡀⣸⠆⠀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⣠⣞⡿⠃⢰⣿⡇⠀⠀⣦⠀⠀⠀⢀⡁⠀⠀⢸⣿⠀⠀⢀⣠⡀⢀⡉
⣇⣿⠀⣰⠄⢀⢻⣧⠀⠠⠀⠐⠃⠀⣿⡿⣀⣴⣾⣏⠁⠀⠀⠹⠀⠀⠀⠀⢠⣷⠀⠞⠁⣠⠔⠛⠟⠛⠀⠡
⢮⣿⠐⢿⣐⣯⢀⠹⣷⡄⠀⠠⠀⠀⠘⠻⠿⠟⡿⠛⠛⡆⠀⡀⠀⢀⣴⠀⠀⠀⠀⠀⠈⢀⡆⠀⢠⡇⡀⣼⢰
⣿⣿⡀⣸⣷⣇⢺⠀⠈⢀⢰⣄⢄⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠃⠀⢈⣀⣀⣢⡆⣾⣴⣶⣼⠧⣿⣾⣿⣧⣿⢸
⠉⠉⠉⠙⠻⢿⣾⣶⠿⠺⠲⠟⠛⠀⠘⠃⠀⠘⠙⠛⠛⠛⠿⠂⠀⠛⠿⠿⣿⣿⡿⠿⢿⣿⡄⠿⠿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠉⣀⣲⣶⠂⠀⠀⠀⠀⠀⣀⣀⠀⠂⠤⠀⣀⣀⣤⣤⣄⣀⣀⠀⠀⠀⢉⣁⣀⣴⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⢤⣤⣄⠀⠀⠀⠀⠉⠁⠀⠀⠀⣀⣀⠀⠉⠉⠉⠉⠉⠹⠿⠏⠉⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠔⠒⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⠀⠀⠀⢠⣄⡀⠙⣿⣦⣄⣤⣼⣿⣤⣀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂
⠀⠀⠀⢀⣼⣶⣤⣽⣿⣿⣿⣿⠟⠛⠻⢿⣿⣿⡛⠉⠁⠀⠀⣤⣦⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒
⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣬⣿⣷⣤⣤⣤⣤⣬⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡀⠀⣀⠃⠀⠀⠗⢾⠭⠟⠀⠀⠀⠙⢉⠀⠀⢠⠴⠖⠀⠃⢉⠀⠈⠀⠘⠀⠡⠀⠀⠂⠄⠀⠚⠀⠀⣀⠀⣿
⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠈⠉⠀⣿
⢀⠀⠀⠀⠀⠀⡈⠱⣤⡀⣄⠃⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠⣴⣴⣿⠀⠀⠀⠀⠀⢀⣿

⠀⠀⠀⠀⣀⣀⠤⠤⠐⠒⠒⠊⠉⠉⠉⡉⣉⢉⠉⡉⠉⢒⠒⠒⠠⠤⢄⣀⡀
⢀⢶⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠕⠘⠚⠻⠲⠀⠀⡹⡆
⢸⠏⠑⠫⢔⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡧
⣿⠀⠀⠀⠀⠈⣑⠊⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⢟⡸⣧
⢻⡄⢀⡀⠀⢸⡹⡷⡀⠀⠉⠑⠫⠖⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀⡠⣻⡿⡆⣡⣿
⠀⡇⠘⠗⠀⠈⠧⣀⡅⠀⠀⠀⠀⣠⡀⠉⠑⠛⠵⣖⡤⣀⡀⡰⣵⣝⣷⡛⣿⣿
⢀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠙⠁⠀⣠⢲⡶⣄⠈⠙⠺⣻⡇⢹⡿⢁⡿⣿
⢸⡆⠀⣠⣤⡀⠀⠀⣾⣹⠼⠟⡆⠀⠀⢸⣷⠅⠀⢈⠀⠀⠀⣿⣼⡎⠟⢛⢳⣿⡶⢶⣖⠒⠂⠠⠤⠤
⢸⡇⢸⣿⡟⠚⡆⠀⠙⢇⣀⠰⠁⠀⠀⠀⠙⠤⠴⠊⠀⣠⠶⡿⠙⡕⡀⣸⠛⣿⡛⢉⣉⠉⣉⣉⣈⡁⠉
⢸⡧⡀⠙⠢⠤⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠠⣷⣵⠂⢸⣷⡟⣏⣿⡿⠔⠀⠤⠦⠤⠔⠂
⠀⠙⠪⣕⡤⣀⠀⠀⠀⣴⢦⠀⠀⠀⣾⣶⡵⠛⠆⠀⠀⠉⠓⣔⣳⣿⣷⣿⣿⣃⣉⣉⣉⣭⡭
⠀⠀⠀⠀⠙⠳⢽⣦⣀⠈⠊⠀⠀⠀⠙⢏⡀⣀⠇⠀⠀⠀⠀⣿⠄⠦⢶⡿⠷⠺⠿⠖⢳⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣿⢿⡏⣿⠍⠉⠉⠉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣒⣄⡀⠀⠀⢠⡶⡄⠰⣷⢁⣼⣽⡯⠍⠉⠉⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣗⣤⡀⠉⠀⠀⠈⡿⣿⣟⣓⣒⣐⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⣦⢄⡀⠀⣧⡯⠌⠥⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣶⣿⣿⠛⠛⡏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣠⣿⠀⢈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡶⠲⠄⣠⠞⢁⡼⠉⢈⡇⠀⠀⠙⢄⠀⠀⠀⠀⣠⡴⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡫⢻⠅⢀⡼⡯⠒⠛⢁⡤⢾⠁⠀⠂⠸⡀⠑⣄⡤⣞⣡⢷⣄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢰⠒⠉⠊⠰⠃⠐⡩⠊⠀⠀⣀⡟⠀⣸⠃⠀⢐⠀⠁⠄⠈⠻⡑⠁⢠⣿⡀⠃⠉⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀⢸⡂⠀⠀⠀⠀⠀⠀⢀⡴⡋⠋⣠⢜⠃⠀⠀⢘⠳⠄⠀⠀⠀⠈⠂⠼⠁⠁⠀⠀⠀⠀⢀⣾⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⢰⣿⡀⣽⡀⣿⡇⢸⡀⠀⠀⠀⠀⠁⠀⢀⠔⠁⢸⠀⠀⠀⠀⠢⠈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⡀⢰⣿⡂⣸⣇
⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⣻⣿⣗⣿⢧⣿⣟⣾⡆⠀⠠⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⠠⣿⣇⣽⡿⠷⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠚⠛⠚⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣸⣿⣇⠀⣸⣿⣅⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢐⡆⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠦⠿⠿⠦⠤⠤⠀⡀⠀⠀⠀⠀⢀⡆⢀⣾⡆⢀⣿⣿⡷⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡝⣲⠂⠒⠚⠛⠊⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣚⠥⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠏⡀⢀⣿⡇⠀⡠⠔⠒⡢⠎⡩⠔⠊⠉⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⢀⣻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⡑⠢⢬⡦⣘⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠀⢐⣿⡂⠀⠀⡅⠀⠀⠀⢠⣿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠂⠙⢮⡙⠒⢤⡀⠀⠤⢀⣰⣾⣿⡄⠀⠀⢾⣿⡥⠀⢠⣷⠀⠀⢀⣿⣿⣿⠧⠔⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⡽⠀⠀⠙⢆⠀⠀⠀⠈⠉⠉⠒⠞⠿⠿⠿⠆⠾⠿⠗⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⢀⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⡠⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⣄⡸⠃⡞⠀⠀⡰⠁⠏⠈⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⢠⠀⡀⢀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡱⠁⠜⠆⢶⠠⠳⠞⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⢺⠀⠠⠈⠈⠱⡇⠁⠀⠀⢀⠀⠐⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⣰⠋⠀⡔⠀⠘⢡⢀⠔⠀⠠⡀⠀⢠⠆⠀⠀⠀⠀⠀⠀⢴⣤⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣟⢀⣰⣆⣘⣽⡆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⠀⣰⠃⠀⣸⠑⠀⢀⠎⠀⠀⠀⢀⠃⢠⠋⠀⠀⠀⠀⢛⡛⢻⣾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⣿⣿⠿⢿⢭⣹⡀⠈⠋
⠀⠀⠀⢠⡄⡀⠀⠀⠐⠃⠀⠘⠙⠘⢃⡞⠘⠓⠚⠓⠈⠒⠂⠂⠀⠀⠀⠀⠀⠋⠘⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⣿⣗⣿⠏⢩⠑
⠀⠀⢀⣾⣿⣇⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠐⠒⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢺⠃⢸⡅⢸⡿⣿⠁⢠⠃⢸⠆
⠀⠀⣼⠋⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠛⣹⣿⣧⡀⠀⠀⠀⠀⣠⡇⡔⣳⣸⣅⡾⠹⠉⣇⣸⣤⣾
⠀⠀⠈⠚⢁⣠⣤⠴⠶⠟⠛⠛⢛⣛⡳⣦⡀⠀⠀⠀⠸⠀⠀⠀⠀⢀⣔⣨⣿⣿⣿⣿⣿⢹⣧⠀⠀⠀⠀⠀⠁⠀⠜⣳⣾⣷⣰⣦⣾⠫⠃
⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣀⣤⠀⠀⠀⠉⢹⣿⣿⣿⠟⠻⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⣾⢩⠁⡏⠸⡍⠙⣤
⠀⠀⠀⠀⠀⠘⣶⣮⣯⡿⢿⠿⣟⣿⣭⣵⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⣠⣾⣿⣿⣿⣀⣼⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⢄⣽⡄⠀⢿⡀⣿⠈⠁
⠀⠀⠀⠀⠀⠀⠹⢶⣿⡃⢿⢸⣻⣧⡼⠃⠀⠀⠀⠀⣂⣀⠀⣠⣴⣾⣿⣿⣿⡿⠛⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⠆⢸⣷⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠘⠒⠁⠀⠀⠀⢩⣤⡀⠈⠀⢰⣿⣿⣿⡿⠻⣿⣇⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠲⣾⣷⢄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣀⣠⡌⠀⠻⠿⠦⠤⠶⠟⠛⠿⠿⠿⠿⠋⠀⠀⠀⡄⠀⠀⠀⠚⠀⠀⠷⠘⠏⠹⠎⠁
⠀⠀⠀⠀⢀⠀⢐⡄⡀⣠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠹⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠐⠁⡀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⡄⢰⡀⠀⠀⢠⠄⠀⠀⠀⠀⡀⢐⢂⠀⠀⠀⠀⢠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠋⠀⠘⠈⠁⠀⠀⠀⠀⠘⠀⡇⢨⣇⠀⡄⢸⢠⠞⠄⠅⠄⠃⠛⠈⠀⠀⠀⠀⠀⠐⠃⠈⠉⢁⠠⠈⠀⠀⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠜⠉⠀⠀⡼⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⡀
⠀⠀⠀⠀⠀⠆⡀⡄⡄⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣖⡶⢖⣶⣿⣮⣩⡾⣷⣶⠶⣖⣶⡞
⠀⠀⠀⠀⡄⠉⢉⠇⢈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘⢿⣿⡬⣋⢹⣇⣅⣿⢙⡫⣾⣿⠏
⠀⠀⠀⠰⠗⠨⠃⠁⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⢁⠈⠀⠈⠀⠀⠀⠀⠀⠈⠁⡀⠀⠁⠉⠁⠀⠀⠀⠙⢅⣡⣽⣏⢉⣿⣥⡁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣡⣤⣤⣀⠀⠈⠉⠑⢲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⢸⣵⣿⣿⣿⢇⠀⢰⢰⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⣤⣤⡀⠀⠉⠹⠿⠗⠃⠀⠘⣞⢷⣝⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⢴⣶⣤⡀⠈⠉⠁⢀⣤⠶⠶⠶⢦⣄⠀⠈⠙⠚⠭⠉⠉⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠘⠻⣿⡿⠏⠀⠀⢰⣿⣶⣿⣿⣿⣿⣿⣷⠒⠒⢒⣛⡉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⣠⠔⣋⣀⣀⣀⣤⠤⠤⠴⠖⠒⠒⠋⠉⠉⠻⢿⣿⣿⣿⣿⠿⣫⠂⠀⢿⣿⣷⡄⠀⢸
⠀⠀⠀⠀⠀⣾⠉⠉⣽⣂⡀⠀⠀⣠⢖⣒⣒⡂⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠋⠀⠀⠀⠈⠙⠋⣀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠸⠿⠇⠀⠘⣱⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⢔⣂⡀⠀⠀⢀⡴⣫⢷⣶⣿
⠀⠀⠀⠀⠀⣿⣀⣀⡠⢄⡀⠀⠀⢿⣿⣿⣿⢿⡟⠀⢀⡤⢤⠤⠀⠀⠀⣿⣿⣿⡆⠀⡞⡾⣱⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⢶⣝⢦⠀⠀⠙⠛⠚⠋⠀⠀⠋⣾⣿⣿⣷⡀⠀⠙⠒⠋⠀⠀⡜⣇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⢻⣆⢧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣛⡿⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⠿⠿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⢀⣀⣀⣀⡤⠬⠥⠤⠶⠒⠒⠚⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢿⣿⡿⠿⠿⠿⠓⠒⠒⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣼⣿⡧⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠄⠀⠀⠀⣰⣏⠙⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢨⣿⡂⠀⠀⣰⣿⣿⠀⠘⢻⣿⣿⣿⣿⣷⠀⠀⢀⡀⠀⢠⡀⣼⡅
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣼⣿⣿⣿⠆⠀⠀⠳⣝⣯⣻⣿⣷⣶⣴⣿⣾⣾⣿⣿⣇⢀⡀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⣩⣿⣧⣾⣿⣿⣿⣿⠀⠀⠀⠀⠈⡳⢽⣿⣿⣿⣿⣿⣯⠻⢿⣿⣿⣾⡇⢸⣧
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⣟⠳⡄⠀⠀⠐⢻⣿⣾⣿⣿⣿⡟⣫⣟⣻⣿⣿⣿⣿⣿⣿⢀
⠀⠀⠀⠀⠀⠀⣄⣸⣿⣿⣿⣿⠟⠦⣬⠿⣶⣵⠛⢛⣿⣿⣿⣿⡿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣼⡇
⠀⠀⠀⠀⣾⢠⣿⣿⣿⣿⣿⣿⣷⣾⣜⣃⠻⣿⣗⡾⣿⣿⡏⣹⣾⣿⣿⣁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣸⣏⣷⡞⢻⣿⣿⡿⠛⠿⣿⣿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣷⣦⢠⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡖⠛⢿⣿⣿⣛⠻⣿⣿⣿⣿⣯⣶⣾⠟⣟⣙⣿⣿⣿⣿⣿⣇
⠀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢼⣿⣿⣽⣿⣆⣙⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⣭⣿⡿⠿⣿⢻⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⠿⠛⢉⣤⣶⣿⣯⣍⣩⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠐⣤⣾⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠈⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠃⢸⣿⣿⣯⣤⣤⣌⣉⣛⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣯⣄⠂⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣷⣦⣜⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⣿⡿⠛⠀⠀⠉⠉
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠈
⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏
⣿⣿⣿⣿⠆
⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⠀⣀⢌⣳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣀⠴⡁⠈⠀⠠⢗⠎⠱⣄⢀⡤⠤⠔⠒⠦⢴⣁⠀⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠳⣤⡀⠀⠀⠈⢉⣹⡃⠀⠀⠠⡈⠄⡀⢌⠋⠀⠀⠀⢀⠀⢴⠖⠈⣠⢙⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠂⠀⠈⠻⣅⣀⠠⠶⢭⡤⠃⢀⡠⠒⣐⠖⠀⣤⠀⢀⡐⠀⠁⠈⠐⡀⠀⠠⡌⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⡅⠂⠀⠈⠁⢶⣉⣠⡖⠋⠀⠀⣀⣀⣐⢁⠀⠀⣈⠳⢼⣅⡀⠀⢀⣰⠇⠀⢀⡈⠯⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⡴⠀⠀⠀⠰⠉⠁⠀⠡⠐⠂⢄⠀⡈⠙⡁⣀⡀⠈⠁⣻⣾⣉⣉⡅⣬⢧⣀⡄⠀⡒⢶⡏⠤⠄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠉⠉⠁⡇⡠⠊⠀⠀⠄⢀⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣇⠀⠀⢄
⠀⠀⠀⠀⠠⠒⠀⠀⠀⢂⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⢺⠀⠄⠁⠬⡅⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⢹⢰⡂
⠀⠀⠀⠀⠀⠈⣒⠀⠀⠀⢣⠠⠤⠤⠤⠐⠰⠂⠀⠚⠀⠀⠀⢂⡄⠀⠀⠀⠀⠀⠀⢀⣀⡤⡖⠁⠀⠀⠀⢜⡚⠈⠁⠁
⠀⠀⠀⢀⠀⠀⠑⣄⠀⠐⠀⠀⠀⠃⠀⠀⠐⡀⠀⠀⠀⠀⠏⣀⠀⡀⠉⠤⠀⠀⢠⠏⠀⠀⠛⡄⠀⠀⠈⠀⠈⠠
⠀⠀⠀⡆⢀⠐⢄⡤⠤⠀⠀⠀⠀⠰⠰⠀⠀⠀⠢⢄⣀⠤⣄⠁⡩⠈⠓⠈⠀⣠⠃⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢲⠀⢰⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⠉⠀⣠⣀⠠⠚⠁⠀⠀⠀⢰⠀⠀⠀⠠⡀⠀⠀⢀⠃⠀⠀⠀⡀
⠀⠀⢀⣀⠀⠀⠀⠀⠠⢸⣀⠜⠂⢒⣀⡀⣀⣀⣸⣀⠐⠒⠻⣚⠿⠍⠀⠀⠐⠀⢀⢂⣀⣈⢅⠐⢲⢴⡹⠡⣄⣀⡁⡱
⠀⠀⠀⠂⠐⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⢀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⢄⡨⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠢⠔⠚⠑⠰⢁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⡀⠒⠃⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⢂⠀⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢄⡀⠈⠠⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠘⠉⠂⠉⠉⠉⠑⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠂⢀⣀⠙⠢⣄⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣀⠀⠀⣀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡤⠜⠁⠀⠐⠁⠨⡇⠀⠀⠱⢀⠀⠑⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⠤⠄⡀⠈⠋⠉⠉⠐⠁⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣁⣀⠀⠀⠈⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠁⠀⠀⣠⠄⠀⡀⠀⠀⠀⠀⠀⠂⢀⠀⠐⠒⢀⠀⢀⠐⠛⠉⠙⡃⠶⠔⠛⠉⠀⠀⢉⣤⣴⣦⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠁⠀⠀⠀⠀⠈⠈⠀⠐⠁⠅⠀⠀⠀⠀⠑⠺⠄⡛⠀⢙⠛⠀⡀⠀⠒⠀⠐⠋⠁⠀⠉⠛⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠠⠀⣀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠀⠀⠀⠁⢘⠏⠉⠀⠀⣛⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⡅⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⡠⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢠⠢⠀⣸⠀⠢⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠸⡄⠂⠀⣿⠀⠄⢀⡎⡀⠒⠀⡠⠀⠁⠀⠀⠀⠀⠀⢀⡠⠤⠒⠋⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⠲⣌⠊⠀⢱⡘⡄⣿⢸⢀⡞⡰⠄⣠⠞⡁⢄⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠢⢄⡁⠀⠂⢈⠳⣝⢆⢳⣧⣿⡇⣼⡵⣡⠞⣁⠠⠀⢁⣀⡠⠆⠂⢀⣜⠉⠢⣄⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠲⠬⣕⣮⣿⣷⣿⣿⣿⣿⣿⢕⣋⡤⠖⠚⠉⠀⡀⠀⢠⣾⣿⣿⡃⢨⣱⡦⣄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣈⣀⣀⣀⣒⣒⣦⣯⣿⣿⣿⠿⣿⣿⣿⣿⣗⣒⣂⣁⣀⣀⣀⡰⠃⠘⠛⠉⠁⠻⡤⢓⣀⣩⠒⡦⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⢤⣶⡿⣿⣿⣿⣿⣿⣿⣿⣟⣓⠢⠄⢀⠀⠠⡼⠗⣇⠀⠐⡖⠻⣄⠀⢨⣿⣿⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⡤⠴⠚⣉⡵⣺⢟⣿⢿⣿⣿⡿⣿⣝⠯⣙⠒⠤⣤⠽⠧⣄⡞⠃⠘⠓⠶⠁⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠁⡠⢀⠌⣠⠞⡡⢊⡏⡘⣯⢋⢷⠙⢌⠳⣌⠂⣰⢿⣤⡤⠈⠀⢀⣀⣤⠀⠀⣹⡩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠞⠁⢀⠀⡞⢀⠃⣿⠘⡌⢧⠐⠑⠈⡳⠛⢻⡿⠷⠀⠀⢨⣿⣿⠆⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠢⠀⡼⠀⡀⡀⣿⠀⠀⠈⠆⠈⣾⢓⡇⠀⠁⡴⠤⡤⠀⠀⣅⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠒⠀⢹⠀⠐⠀⢨⠞⠈⠋⠀⠀⠈⢣⡤⠷⠀⢻⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣸⠀⠀⢀⡿⠤⡀⠀⣰⣶⡆⠀⢀⣀⡀⡸⠃⣾⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣌⠛⠯⣏⠁⠀⠺⣤⡟⠅⠀⣿⠀⠆⠀⡜⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠙⡦⢄⡙⠦⣀⡞⢳⡘⡀⣿⢰⠀⡼⠁⡉⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡞⠀⠠⠙⠚⢧⡐⣄⢧⣣⣿⡎⣼⣣⢋⡴⠋⠐⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⠋⠈⠘⠲⠦⣕⣲⣝⣾⣦⣿⣿⣷⣿⣵⡯⢖⣁⡤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡰⠃⠀⠀⠂⠁⠐⠲⣭⣽⣿⣿⣿⣿⣿⣿⣿⣾⠿⠣⠀⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡜⠁⠈⠉⠉⡉⠉⠩⡩⢽⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⠏⣉⠉⢉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⠎⠀⠀⠀⠀⢀⣁⡠⠴⠚⣩⢴⡿⣿⣿⣿⣿⣿⣿⡻⢟⡲⠦⣄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⣠⠋⠀⠀⠀⠀⠈⠂⠁⠠⠢⢉⡴⢋⢞⡟⠸⣿⢛⢧⠹⡝⢦⡑⠁⠄⠉⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡐⠉⡼⠁⠇⣿⠘⡈⣧⠐⡂⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡸⠁⠸⠀⣿⠀⠄⠘⡄⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⣿⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⣾⠉⣤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣈⡽⠉⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡛⣿⣿⣶⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣠⣤⣿⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢻⣿⣉⠻⣿⣿⣿⣿⣴⠶⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⢶⣶⣿⣿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣆⡀⠀⢀⣠⣤⣤⣤⣼⣿⣿⣿⣿⣡⣤⣤⣤⣶⣦⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢀⣟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⠙⣿⠿⠿⣿⣿⣿⣿⣶⠤⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⡦⣄⣤⣤⣰⣿⣦⡹⣄⠀⠈⠙⠿⠿⣿⣦⠀⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣷⣿⢿⡿⠋⢻⣿⣴⣶⣦⣄⣹⣷⣆⠀⣄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠧⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠛⢃⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡙⠓⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠿⠛⢧⣴⣟⣿⣿⣿⣿⣿⣿⣿⣷⣭⣀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⣤⡶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣆⠉⢿⣷⢿⣿⠶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠋⠁⢠⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣷⡀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⣿⣿⣿⣶⠾⣷⣴⣿⠟⣻⣿⡇⠀⢾⡿⠿⣿⢷⣿⠉⢠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠋⠀⠀⣛⣹⣾⣿⣿⣷⣶⣾⣷⣦⣤⡄⠀⠁⠀⠀⠀⠀⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣆⠀⣰⣢⣴⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀⠐⠶⠟⠛⠛⠁⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠉⠿⠻⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠟⣛⣶⣌⡀⠰⣄⣸⣿⣿⢿⣿⣿⣿⣿⡿⠿⣿⣿⣏⣀⣀⣤⢀⠈⠋⠙⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣇⠄⠙⠻⢿⣿⣠⣄⡤⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣴⣿⣿⣿⣿⣿⡿⠛⢋⣯⣤⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠻⢿⡾⠏⣬⣶⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠨⠛⠻⠻⣿⠛⠋⣡⣀⣼⣿⠟⠙⠀⢾⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⡿⠛⠛⠁⠀⠀⢠⡞⠡⣿⣿⣿⣿⣿⣿⣿⠻⣶⣾⣷⡖⣾⡷⢶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⢠⣶⣶⣾⣯⣿⠿⠁⢠⡀⠂⣄⠐⣿⠀⡀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣄⣈⠉⠉⠀⠀⠀⢈⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠛⠋⣁⣤⣷⣾⣿⣷⣿⡾⣃⡸⣿⣿⣿⣿⣿⣟⡛⠛⠛⠟⠛⠋⢧⣀⣾⣷⣿⠛⠉⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣋⣴⣾⣿⣿⣶⣿⣧⣀⣼⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⠐⣁⣴⣿⣿⣯⣠⢶⡀⠀⠁
⠀⠀⠀⠀⠀⢠⡼⢿⣿⣿⡿⠛⠟⢙⣿⠛⣛⣿⣿⣿⣿⣿⣿⣿⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠧⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡌⠉⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣤⣤⣤⣴⣾⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠉⠛⢿⣿⣿⣯⣝⠿⢿⣿⣿⣷⣿⣯⣽⠛⠴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠋⠛⡿⣩⣦⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣶⣦⡄⠙⣿⣿⣽⣦⣤⠈⠉⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⠻⣼⣿⣿⣿⣿⣿⣷⣏⣠⣌⠙⠛⠿⢿⣷⣤⡀⢀⡠⠂
⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣆⠈⠻⣿⣿⣿⣿⣿⣾⣿⣯⣠⡿⡶⠈⠉⠀⠛⡆
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠘⠃⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣶⣭⣿⣿⣿⣿⣿⣷⡔⠶⣤⠲⣦⠁⠰⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣉⣻⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠟⠋⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣤⠀⠀⠀⠀⣠⣶⠆
⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣿⡄⠀⢈⣿⣿⣿⣧⡉⠛⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⣙⣀⣡⣴⡿⠏
⠀⠀⠀⠈⠉⠁⠿⠛⠛⠃⠀⡹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⣀⣀⡀⠈⠛⠻⠿⠟⠛⠛⡿⠟⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⠿⠛⠙⠿⠛⠛⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠛⠛⠿⠿⣶⠛⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠖⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠤⢀⠢⠈⠂⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀⡑⣠⣴⣿⣴⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⣿⠏⠁⣠⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢡⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⢀⣠⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣾⣿⣿⣿⡿⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⠟⠋⣠⣾⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠛⠉⠁⢠⣼⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠛⠁⠀⢀⣤⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡿⠛⠁⠀⢀⣤⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣿⠿⠛⠁⠀⣀⣤⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⢀⣠⣴⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠓⠛⠒⠛⠒⠛⠚⠓⠑⠛⠃⠙⠒⠛⠂⠚⠻⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠘⡿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⡞⠀⠀⣀⣿⣚⣳⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠰⣗⣒⣒⣒⣛⣦⠀⠀⣀⠀⠀⠀⠀⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⡀⣠⠞⠁⠀⠀⠀⠀⠘⠳⣖⠒⠒⠈⢳⡾⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢹⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⡴⠋⠀⠸⣏⡽⣆
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢠⡞⠀⠀⠀⢸⡯⠷⣄⠀⠀⠀⠀⠀⠀⣠⣶⢶⠟⠀⠀⠀⢠⡄⠻⡙⠛⢷⡀⠀⠀⢀⣦⠀⢠⡄
⠀⠀⠀⠀⠀⠀⢨⣿⣇⠀⣰⠏⠀⢀⣴⡀⠈⠻⢯⣭⡭⠽⢦⣀⢀⡼⠁⠈⠁⠀⣀⠀⠀⣸⣇⠀⠀⣶⠀⠹⣆⠀⢸⣿⠄⢸⣗
⠀⠀⠀⠐⠒⠒⠲⠿⣤⡾⠁⠀⠀⢠⣿⡅⠀⠀⠀⠀⠙⣯⠭⠭⠿⢄⡀⠀⠀⠀⣿⡇⠀⣽⣯⡄⠠⣿⡆⠀⠙⣦⣘⣿⣃⣭⣯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⠀⢾⣿⠆⠀⢠⣄⠀⠀⠘⢷⣒⣒⠀⠁⣤⠀⠠⣿⡗⠀⠾⡟⠂⣈⣿⡥⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡓⠀⢼⡷⠀⠀⠀⠘⠇⠀⠀⢐⣿⠀⠘⢻⣉⡤⠴⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣫⣿⣍⠀⢽⣿⠀⣀⠀⠀⠀⠀⢀⣨⡿⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠈⠀⠀⠁⠀⠈⠙⠓⠶⢿⡿⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⢀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠙⠤⠙⠓⠒⠒⠒⠲⠶⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁