Eternal love Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⡶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠹⣆⣼⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠙⠃⠀⢀⣾⠇⠀⢀⣤⡴⠶⠟⠛⠛⠛⠉⠉⠉⠛⠛⠛⠷⣦⣄
⠀⠀⠀⠀⢀⣤⡶⠟⠛⠛⠛⠛⠛⠛⠲⠶⢤⣀⡀⠀⠀⠈⠢⠄⠀⣠⡾⠃⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⣀⣴⡾⠋⠀⢰⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠙⠲⠤⣀⠀⠙⠲⠶⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣤⣤⣤⣤⣴⣶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠤⠄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢀⣀⣠⣤⣤⣤⣀⣀⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣶⣶⣦⣀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⡘⠃⡄⢿⣿⣿⡻⣿⣿⢟⣭⡝⣿⢻⣿⣿⢻⣏⣻⣟⢟⣿⡏⣛⡻⣿⢛⡛⣇⢋⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⡿⠾⣷⢸⡿⡿⣅⣿⣿⢸⣿⣾⣿⢸⣿⣏⢻⣾⣿⡟⣸⣿⣇⣿⡇⣿⢸⠇⢿⢸⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠾⠾⣟⣾⣤⣷⣆⣾⣿⣿⣦⣭⣵⣿⣷⣾⣿⣶⣶⣿⣿⣶⣾⣿⣿⣷⣿⣷⣿⣾⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣵⣿⡇⣿⣿⣿⣿⣿⣷⣿⣹⣿⣿⢹⣣⣿⣿⣿⣿⣿⣿⠟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣿⣿⣿⣿⣷⣙⣛⣿⣯⣛⣫⣿⣃⣿⣿⣙⣫⣿⣿⣿⠿⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠲⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣟⣿⣿⣯⣽⣿⡿⠟⠁⠀⠀⠀⠘⠃⠀⠀⠁⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⠀⢀⠁⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡟⠁⠀⠀⠀⠈⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃





⣿⢿⠿⡿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣟⣻⣿⣿⡿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⢈⣡⢾⣿⢷⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣽⣷⣿⣿⣯⣼⡆
⠀⠀⠀⠀⠀⠀⣷⡻⣮⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣗⣾⠃
⠀⠀⠀⠀⠀⢐⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠹⣟⢵⣿
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠻⣜⢄⣰⣀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠲⠦⣤⡀⢤⣤⣾⢀⣾⣉⠩⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡙⠁⠀⢸⣿⡭⠇⢰⡶⢄⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢭⢹⣧⠀⣼⣿⣗⣷⣠⣤⣬⡇⠀⠀⠀⠀⣠⣤⡄⡐
⠀⠀⠀⠀⠀⠰⢦⡀⠀⠀⠀⢠⡾⢡⠘⣼⠇⢰⠟⠋⠉⠙⠻⢿⣿⡿⠀⠀⠀⠈⢓⣟⡯⢹
⠀⠀⠀⠀⠀⠀⡔⠏⠆⡀⠀⠈⢳⡀⡄⢹⢀⡟⠀⠂⡠⠀⠀⠀⠈⢀⠀⠀⠀⠘⠛⡟⡖⢺
⠀⠀⠀⠀⠀⠀⡮⠍⡠⠅⠀⠀⠀⠙⠺⣴⡞⢀⠎⠻⠀⠀⠀⢀⠀⢸⡄⠀⠀⠀⠛⡿⣾⢸
⠀⠀⠀⠀⠀⠀⣤⣛⡄⠀⠀⠀⠀⠰⡊⣻⣷⣌⣀⢀⠀⠀⣠⠈⠇⠎⠀⠀⠀⠀⠹⣷⣿⢼
⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠈⢸⠏⢹⠉⠈⠙⠛⠀⠤⢭⠃⠀⠀⠀⠀⠻⢿⠊⠻
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠎⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⡦⣄⠀⠀⠀⠀⠀⠀⠐⠻⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠂
⠀⠀⠀⠀⠀⠀⡿⠖⠃⡤⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣿⣗⣷⡧⡀
⠀⠀⠀⠀⠀⠀⣿⣽⣯⣿⣯⡇⠀⢀⣀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠑⠂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣾⣿⣾⠆⠀⠀⠉⠙⣒⠒⣊⡓⠲⠤⠴⠒⠉⠀⠀⠀⢀⣀⣶⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠙⠛⢻⣿⣿⣿⣿⣿⣿⣟⠋⠉⠉⣻⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣷⡀
⠀⠀⠀⢀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢿⣿⣿⣿⣷⣄⣾⣿⣿⣿⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄
⠀⠀⠀⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠁⠀⠙⢿⣿⣿⣿⣯⣿⡿⠋⠀⠀⠻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡄
⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡅⠀⠀⠀⠀⡹⣿⣿⣿⣷⠀⠀⠀⠀⠀⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇
⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢰⣿⣾⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠈⢿⣿⣿⣿⡿⠃⠀⠀⠀⢠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣤⡀⠀⠀⣠⣴⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⢀⣩⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣷⣄⣠⣶⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣷⣦⣀⣴⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢟⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣝⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢄⡀⣤⠀⡠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣤⣤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠌⢢⣾⣿⣿⣿⣿⣷⣿⣾⣤⣴⣮⣄⣬⣶⣶⣶⣾⣿⣿⣿⡿⣿⣿⡿⣿⣿⣷⣿⡁⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢍⣤⠙⠛⢉⣾⣿⣿⣍⣥⣤⠌⣙⠛⢮⣿⣿⣿⣧⡉
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⡵⣜⣿⣿⣿⠁⠠⡄⠀⣤⣦⡬⣳⢼⣿⣿⣿⣇⢧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡛⣻⣫⡽⠛⣹⣿⣿⣬⣾⣯⡞⠙⠇⣈⣑⣻⣿⣿⣿⣿⣿⡏⠧⠨
⠀⠀⠀⠀⠀⠀⠀⢠⠻⣿⣿⣿⣿⣿⣿⣯⣽⢉⠞⠀⣠⣿⣿⢿⠀⠊⠃⢰⣦⣼⣿⣿⣿⣿⣿⡍⠛⣿⣿⣀⠎
⠀⠀⠀⠀⠀⠀⠰⣬⣶⣿⣯⣿⢿⣿⣾⣏⣵⡏⢠⠟⣻⢿⡏⣠⢶⣺⡗⣿⣿⣿⣿⡏⣿⣿⣿⠇⣾⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣿⣿⣿⣷⣿⣿⣇⣀⣯⡞⠾⢻⣿⡿⣡⣿⣯⣹⣄⣴⣿⣿⢏⣼⣏⣸⡆⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢚⣿⣿⣿⣿⣿⣿⣿⡟⢁⣉⣿⣿⣷⠸⡾⠉⢸⣿⡿⣸⣿⢿⣿⡏⣽⣿⠙⢿⣾⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡠⢛⣿⣿⣿⣿⣿⣿⠿⠉⣼⣿⡿⢿⣿⣿⡓⢧⣼⠉⣴⣿⠇⢸⣿⣧⡻⠿⣿⣿⠑⣿
⠀⠀⠀⠀⠀⠀⠀⢢⣼⣯⣿⣿⣿⣿⣿⣶⣮⡉⠁⠀⣽⣿⡷⡄⢀⣿⣾⣿⣿⡄⠸⣿⡿⠿⣶⣿⣯⣾⣽⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣽⣿⡿⣿⣿⣿⣦⣤⣬⡿⣿⣷⡏⢺⣿⣿⣿⡻⣠⢸⡁⠶⣿⠿⢟⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⢙⠿⣿⣿⣿⣋⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠝⡧⣔⡻⢿⠟⢱⢳⡏⢿⣿⢁⠑⢰⢹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣫⣿⣿⡿⢿⣿⣿⣻⠏⠐⣿⡟⡰⠋⢠⠏⢸⣷⡀⠙⠛⠷⢼⣿⠂⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣼⢿⣽⣿⣿⣿⣿⣿⣡⣴⢶⣿⣿⣿⣦⡘⢏⡜⠁⢠⠏⠀⠨⣿⣷⣤⣤⡀⣾⣿⡼⠷⠂
⠀⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⠄⡿⠋⣱⣿⣟⠉⠉⠻⢧⡞⠀⢠⠏⠀⡀⠀⣈⢿⡿⣿⣶⠷⠛⣇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣷⣤⣀⠀⠇⢰⣯⣤⣄⣀⠀⡽⢏⣿⣿⣿⣧⣿⠎⡆
⠀⠀⠀⠀⠀⠀⠀⡟⣋⣿⣿⣿⣿⣿⣿⣷⣸⣿⣿⣿⣿⣧⣿⣿⠖⡁⠀⠙⠋⠉⣡⣐⠁⣽⣿⣿⣿⣿⣅⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⢿⣧⢈⣿⣶⣔⢶⡠⣿⡾⠿⣫⣿⢿⣿⣿⡿⠙⡆
⠀⠀⠀⠀⠀⠀⠐⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣽⣿⣮⣿⣿⣿⣟⣯⣶⣟⣻⣿⣹⣿⣿⡇⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠟⠋⠉⣝⡿⠯⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠽⠿⠟⠟⣛⡩⠟⠫⠭⠙⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣍⠀⠤⠠⠀⢈⣡⠛⠰⢢⠀⠀⢀⡀⠀⠛⣄⡁⠀⠀⠄⠂⣨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⠈⠉⠙⠳⢬⡐⢄⡗⠀⢞⡡⢊⡥⠞⠉⠉⠀⣀⠶⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠤⠀⠈⠐⣏⡿⠀⠀⠈⢿⣽⠂⠀⠀⢤⠆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠦⠎⠗⠀⠀⠀⢨⡱⠼⠂⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠂⠋⠁⠉⠙⠋⠉⠛⠉⠀⠉⠓⠒⠶⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢀⡀⠀⣔⡆⢲⢼⢠⡿⡀⣇⡀⠀⢰⠁⢠⢦⣠⠀⡀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⢀⠄⠺⡄⢣⠄⠛⠘⠈⠀⠁⠀⠀⠩⠅⠀⠈⠉⠙⠋⠀⠞⢡⠟⠂⠀⠀⢑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠈⠧⠂⠁⢀⡠⠤⠒⠒⠎⠟⡙⢙⠉⡉⠫⠱⠖⠒⠬⢅⣀⠀⠉⠀⠃⠀⠀⠑⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⣀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⡀⠀⠈⠉⠢⢄⠀⠀⠀⣀⡠⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⠤⠤⠤⣀⣠⡊⠀⠀⠀⠀⠀⡊⢠⣱⠀⠠⢤⠀⠀⢀⣖⠄⠀⢧⠄⡇⠀⠀⠀⢠⣗⣤⠞⠁⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠈⡱⠏⠀⣀⣠⠤⡄⣁⡢⠄⢰⠲⣛⣠⢧⣘⡨⠲⢀⣠⠮⠤⠤⠄⣀⡀⠳⠤⡀⠀⠀⢱⢄⡙⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠯⠔⠚⡇⠀⡴⠋⢀⠔⠊⠁⠀⡀⠀⠀⠀⠙⠻⣀⢸⠃⠈⢋⢀⡼⠋⠀⢀⣀⢀⡀⠀⠈⠒⢄⠈⢦⣀⣸⡀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⣥⠞⠁⢀⠊⠀⠠⠖⠋⠁⠉⠀⠀⠀⠀⠈⢿⠀⡆⢸⠏⠀⠠⠘⠉⠁⠈⠁⠀⠀⠀⠈⠆⠀⠈⠉⠃⢀⠠⠟⠄
⠀⠀⠀⠀⠀⠀⢀⠧⡆⠈⠃⠲⢅⠀⠀⠌⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣷⠃⠀⠀⡔⠈⠀⠀⠀⠀⠀⣄⠀⡀⠸⠀⠀⠔⠋⠉⣀⠆⢺
⠀⠀⠀⠀⠀⠀⠘⠁⠘⢆⡀⠀⠌⣴⠒⠶⠰⣎⣩⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⠠⢅⡱⠃⠚⠙⢾⡀⠀⣠⠛⠀⡸
⠀⠀⠀⠀⠀⢠⣄⣙⡤⢀⣷⠐⡎⠀⠠⠄⡀⡟⠀⠀⠉⢰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠈⢧⢀⠠⠀⠀⣱⢈⠧⠀⠾⠤⢴
⠀⠀⠀⠀⠀⠀⡃⢄⠀⠀⢈⠛⠛⠢⣠⣤⡧⢷⡄⠉⠀⢈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠉⢪⡛⠲⣶⡭⠊⠉⠙⣄⠀⢀⡄⡠
⠀⠀⠀⠀⠀⠀⠘⢮⡑⢲⡋⠀⠠⠀⣽⡀⠀⢈⣿⠆⠛⠛⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡴⠛⠋⠡⣟⣁⠀⣨⣗⠐⠂⠀⣸⢋⡡⠞
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠡⢸⣄⣀⡤⢊⡝⠻⣿⠡⠐⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠐⠊⠌⡵⠛⠫⠝⢦⣄⣴⣆⠀⠀⠤⢄⡀
⠀⠀⠀⠀⠠⠂⠁⢀⠠⡾⠻⢍⣽⡁⠀⠀⠀⠈⡷⣄⠠⢾⡉⠢⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠥⢉⣿⠦⢠⣾⠁⠀⠐⠀⡠⣷⡄⠎⠻⠂⠤⣀⣈⠂
⠀⠀⠀⠀⠀⠉⠉⠀⡐⢁⠔⣚⢻⡜⢣⡴⠂⢲⢅⡅⠀⠀⢙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠔⢡⡃⠀⠐⣤⡗⠒⠲⡎⠱⣿⠏⡒⢄⠑⣄⡀
⠀⠀⠀⠀⠀⠰⠠⠋⢠⠂⢨⠔⡍⢓⡠⠀⠀⣰⠢⡀⠛⣥⠌⢇⠀⠑⢦⡀⠀⠀⠀⠀⠐⢠⠚⠁⠀⠞⢠⡤⢋⠔⢣⠀⠀⠫⣼⠸⠐⠔⠈⢂⠈⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⡰⠀⠈⢆⡠⠞⠉⡆⠬⣶⣦⡹⣬⣷⡀⠀⠙⢦⡀⠀⢀⡔⠁⠀⢠⣾⠄⣧⣶⠄⢒⡇⢹⢢⣴⠃⠀⠡⣀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠀⠈⠁⠘⠄⠹⠑⠎⡄⠑⣄⢣⠈⢂⣀⠀⠙⢤⠎⢀⡔⠋⠰⢡⠎⠀⠛⠆⠌⢀⠆⠀⠁⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠀⠐⢤⡌⢼⣀⠘⢤⠇⠀⠈⠀⠠⠜⢀⣤⢈⡤⠈⠀⠟⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⡠⠄⠂⠈⠉⠑⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⢀⡠⠔⠈⠀⠀⠀⠄⡀⠀⠀⡀⠀⠀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⢀⣀⡀⠀⠀⠉⠲⢄⠀⠀⡠⠖⠉⠀⠀⢀⣀⡀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⡴⠋⠀⢀⡤⠒⠉⠉⠉⠉⠉⠒⢤⡀⠀⠳⠎⠀⢀⡤⠒⠉⠉⠉⠉⠉⠒⢤⡀⠀⠙⢦
⠀⠀⠀⠀⡜⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠈⢣
⠀⠀⠀⣸⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⣇
⠀⠀⠀⡏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹
⠀⠀⠀⣧⠀⠀⡇⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠛⠲⢤⡀⢀⡤⠖⠛⠉⠉⠓⠲⢤⡀⠀⠀⠀⠀⢸⠀⠀⣼
⠀⠀⠀⢸⡀⠀⢳⠀⠀⠀⡴⠋⠀⢀⡤⠴⠦⢤⡀⠀⠙⢏⠀⢀⡤⠴⠦⢤⡀⠀⠙⢦⠀⠀⠀⡞⠀⢀⡇
⠀⠀⠀⠀⢣⠀⠀⢣⡀⡼⠀⠀⡴⠁⠀⠀⠀⠀⠈⣦⠀⠈⣶⠁⠀⠀⠀⠀⠈⢦⠀⠀⢧⠀⡼⠁⠀⡼
⠀⠀⠀⠀⠈⢣⡀⠀⠳⡇⠀⢸⠁⠀⠀⠀⠀⠀⡴⠉⢇⠀⠘⣆⠀⠀⠀⠀⠀⠈⡇⠀⢸⡞⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠱⣄⠀⠘⢦⣸⡄⠀⠀⢀⡠⠞⠀⢀⡼⢦⠀⠈⠳⣄⠀⠀⠀⢠⠇⠀⢸⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠈⠙⠒⠚⠉⠀⢀⡴⠊⠀⠀⠓⢄⡀⠀⠙⠒⢒⠞⠀⢀⣏⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡦⠤⠤⣤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠙⠲⢤⡤⠋⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⢦⡀⠀⠀⢀⡴⠋⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠙⢆⡰⠋⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⡴⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠠⠊⠀⠐⠄⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⡠⡔⣲⢠⠎⠀⠀⠀⠀⠀⠀⠄⠰⣆⢴⣲⠆⡸⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣽⡰⠃⠏⠛⢀⡠⠊⠀⠀⠀⠀⠀⠈⠢⣀⠉⠘⠊⠧⣽⣌⡑⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠤⠀⠋⠝⠂⠤⡠⣖⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⢶⡰⠀⠙⠈⠃⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡴⠒⣀⠤⠔⠛⠛⠉⠁⢀⠀⣀⠀⡀⠀⠀⠀⠉⠉⠋⠙⠒⠦⢌⡸⠇⢤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠤⠒⠉⢀⢠⡤⠐⣮⡆⢛⢾⢐⠟⠄⣇⡀⠀⢰⣃⣰⠞⡄⠄⣠⢀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⣤⠀⠹⡀⠳⠂⠁⠈⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠈⢉⡀⠛⠡⣏⠁⡀⠀⠨⣑⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡄⠈⠖⠁⢀⡠⠤⠖⠒⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠐⠒⠤⢤⡀⠀⠀⠉⠀⠀⠈⠁⠑⡄
⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠑⠦⣀⠀⠀⣀⡤⠴⡁
⠀⠀⠀⠀⠀⠀⢈⠗⠦⠤⠦⣄⣴⡁⠀⠀⠀⠀⠀⡃⠠⡸⠀⠠⢦⠀⠀⢀⣖⡆⠀⠧⠆⡸⠀⠀⠀⠀⣮⡧⠔⠁⠀⠀⠈⢦
⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢈⡻⠃⢀⣀⠤⠤⠤⢍⡒⢄⣘⠺⣉⣥⠃⣌⡠⢺⢀⣤⠮⠤⠤⠤⢄⣀⠙⠢⢄⠀⠀⠈⡦⣀⠓⢤⣤
⠀⠀⠀⠐⠚⠑⠚⠙⡄⢀⡔⠁⢀⠖⠉⠀⢀⡀⠀⠀⠀⠉⠻⣄⣘⠃⠀⢏⣀⡼⠋⠁⢀⣀⠀⡀⠀⠀⠑⢆⠀⠳⣄⣈⣄⠀⠉⠁
⠀⠀⠀⢴⣄⠀⠀⠀⡧⠋⠀⢠⠃⠀⠠⠚⠉⠁⠉⠀⠀⠀⠀⠈⢻⡀⡆⢸⠏⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠉⢀⣀⠼⠣
⠀⠀⢸⢤⡄⡙⠳⠦⡁⠀⠀⡆⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣧⠃⠀⠀⡰⠊⠀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠀⡠⠚⠍⢃⠸⢚⡇
⠀⠀⢸⠐⠺⢀⠂⠀⢸⡔⠲⠇⠠⣇⣡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⣆⣸⠒⠒⠋⠳⡅⠀⢀⡜⠉⢀⠇
⠀⢠⡈⣳⣄⡈⡗⢲⡃⠀⢠⠀⠀⡟⠀⠀⠉⣲⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⢻⢀⠀⠄⠀⢨⡎⡩⠤⠴⠧⢤⡆
⠀⢸⠣⡀⠀⠀⠸⠊⠓⠤⣢⢦⠴⣇⡔⡁⠀⢘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠈⢢⣝⠷⢾⣬⢐⠋⠉⢣⠀⠀⡠⢂⠇
⠀⠀⠳⣌⠒⢶⡃⠀⠤⠀⣽⡁⠀⢹⣷⡖⠚⠛⡤⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢤⠟⠓⠲⢾⣅⠀⢀⣧⠀⠐⠀⢈⣟⣉⡴⠋
⠀⠀⢀⡈⠩⠍⣧⡀⣀⡼⢛⠾⢿⣟⠍⠰⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠂⠠⣹⡛⠓⡍⠣⣄⣀⣼⠠⠄⠄⠄⡀
⠠⠊⠁⢀⠠⡖⣻⣉⣿⠀⠀⠄⠈⢸⣦⣀⡠⣖⠛⠢⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡪⠚⣲⣦⣀⣴⡇⠀⠐⠀⢀⣽⣤⠵⠙⡆⠤⣀⡈
⠈⠒⠈⢁⠜⢀⢔⣿⣇⠟⣆⠤⠄⢾⣁⡇⠀⠈⢳⢤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢊⡠⠊⡎⠀⠈⣄⡵⠂⠲⣴⠋⣎⡟⣗⢄⠘⢄
⠀⢖⡰⠋⠠⠃⣎⠜⡘⡔⡊⠀⠀⣸⢌⠉⠦⣐⠨⢆⠈⠒⢄⠀⠀⠀⠀⠀⠠⢂⡴⠋⠀⡸⠅⣀⠖⡩⢺⡀⠀⠨⣕⡞⡜⠬⠀⠣⡀⠫⠼
⠀⠀⠀⢀⠁⠀⡀⡰⠀⠩⡀⣠⡖⢹⠤⢑⣤⣍⣲⣨⣦⠀⠀⠑⢄⠀⠀⠀⡠⠋⠀⠀⣴⡄⣖⣩⡈⠄⠼⠑⠦⣀⡜⠀⠱⡀⠀⠀⠁
⠀⠀⠀⠘⢄⡠⠜⠁⠀⠀⠙⠁⢡⠀⢗⠢⠟⡈⠢⡉⢏⠑⠢⡀⠀⠱⣄⡜⠁⣠⠒⢁⠋⡴⠉⡜⡗⢘⠃⡸⠀⠉⠀⠀⠀⠈⠚⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⣴⠀⠣⣀⡗⢜⡀⠸⣉⡆⠀⠈⠀⢎⣹⠀⣈⠜⣇⡰⠁⠶⠦⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡖⠁⠀⣀⣀⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡏⣠⣴⣿⣿⣿⣿⠟⣋⣁⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣰⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣆⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠓
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿
⢀⣴⣿⣿⣿⣿⣶⣿⡏⠀⠀⣀⣠⣄⣀⠀⠀⠀⠈⠻⠋⠀⠀⠀⢀⣀⣤⣀⠀⠀⠈⣿⣷⣾⣿⣿⣿⣷⣄
⣾⣿⠋⠀⢀⣈⠙⣿⡇⠀⢰⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣷⠀⢀⣿⡟⢉⣀⠀⠈⢻⣿
⣿⡇⠀⢰⣿⡟⠁⣾⣿⡀⠸⣿⣿⠁⣴⡏⢻⣿⣿⣿⣿⣿⣿⠛⣷⡄⢹⣿⡿⠀⣸⣿⡆⠙⢿⣷⠀⠀⣿
⢹⣧⠀⠸⣿⡄⠀⣿⣿⣷⡀⠙⢿⣦⣼⣿⣿⡿⠟⠉⠙⠿⣿⣿⣿⣤⡾⠟⠁⣰⣿⣿⡇⠀⣸⡿⠀⢠⣿
⠀⢻⣦⠀⠙⢧⡀⠘⣿⣿⣷⣄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣴⣿⣿⡿⠁⣠⠟⠁⢠⣾⠃
⠀⠀⠙⢷⣄⡀⠁⠀⠈⣿⣿⣿⣿⣦⡄⠀⠀⢾⣷⡆⣶⣿⠆⠀⠀⣴⣾⣿⣿⣿⡏⠀⠀⠁⣀⣴⠟⠁
⠀⠀⠀⠀⠉⠛⠛⢀⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣆⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠻⠿⠿⠿⣶⣶⣶⣶⣶⣶⣶⡾⠿⠿⠿⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠙⢿⣿⣶⣤⣤⣄⣀⣀⣤⣤⣴⣾⣿⠟⠁⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠋⠉⠉⠉⠛⠻⢿⣦⡀⠀⠀⢀⣴⡿⠟⠛⠉⠉⠉⠙⠛⢿⣷⣄
⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⣿⡇⣠⣶⡿⠿⠿⠿⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠿⠿⠿⢿⣶⡄⣸⣿
⠀⠀⠀⠀⠀⢈⣾⡿⠋⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⡀⠀⠀⢀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠙⣱⣿⠃
⠀⠀⠀⠀⠀⣸⣿⢰⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣣⣆
⠀⠀⠀⠀⠀⢿⣿⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⣀⣼⡿⢿⣧⣀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⣿⡿
⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠙⢿⣷⣄⠀⢀⣠⣾⡿⠋⠀⠀⠙⢿⣷⣄⡀⠀⣠⣾⡿⠋⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣀⣙⢿⣷⣝⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣭⣍⣀⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⡷⠈⠉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠋⠉⠙⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⣀⣠⠴⠖⠚⠛⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⠉⠉⠙⠲⢤⣈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⣠⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡑⠦⣀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡑⠢⣄⢀⣠⠴⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⡕⠾⣉⠑⠮⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉⠁⠀⠀⠀⠉⠐⠤⢌⣑⠲⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣊⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠉⠉⠀⠀⠀⠒⠛⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣶⣦⣤⣀⣠⣤⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛⠿⠛⠛⠁⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣿⣿⡟⠉⠀⣰⣶⣿⣿⣿⣿⣿⣦⣤⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⢀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⣼⣿⣿⡿⠀⠀⠀⡿⠟⠛⠋⠙⠛⠻⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⢀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠟⠁⢀⣀⣀⣀⣀⡀⠀⠈⠉⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣁⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠋⠁⣠⣴⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⢿⣿⣿⣿⣿⣯⣥⣴⣶⣾⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣀⣙⡻⣿⣧⡉⠉⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣄⣀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣶⣶⣶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⡿⠉⠈⢹⣿⣿⣯⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠉⠓⠦⣄
⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⢸⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣉⣲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⢸⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠟⠁

⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣿⣿
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣻⡝⢀⠁⠢⣀⡂⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠨⡀⢂⡄⡁⣸⠇⣀⡴⠶⡷⣍⠠⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⡢⠄⠟⢾⠢⡀⣿⣀⡿⢄⡷⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠰⣁⡀⠈⡱⣤⣸⡿⢣⡇⠀⢨⣴⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠌⢳⠦⣍⣀⣸⣿⠿⠃⢠⡞⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠹⣿⣿⣠⣬⠞⢁⣠⡀⠀⠀⠀⠐⠒⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠻⣿⡵⠃⠘⣷⠉⠀⠀⠀⢀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⢈⣼⣷⠴⠚⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢈⣯⠰⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⣿⣿⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠀⠀⠠⣰⠾⣿⣾⣿⣿⣿⢿⡿⢿⣦⡀⠀⠀⡀⠁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠠⠞⠁⣾⡟⠙⢯⠀⠀⠈⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠂⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣦⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠾⠟⠛⠛⠳⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⢀⣴⠾⠓⢶⡄⠀⠀⠀⠀⠉⠻⢿⣿⣶⣤⣴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⡾⠁⠀⠐⠾⠟⠀⠀⠀⠀⠀⢀⣠⠿⠛⠿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⢿⣿⣿⣿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠓⠦⡄⠀⠀⠀⠀⣀⣤⡤⠶⠶⠛⠛⠻⠿⢶⣄
⠀⠀⠀⠀⣾⡿⠋⠀⠀⠀⠀⠀⡤⠶⠶⠶⠦⣤⣀⠀⠀⣀⣠⠴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡇
⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡭⠟⠿⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⡿⠃
⠀⠀⠀⠀⠀⠙⠳⠤⢤⣤⣤⡤⠴⠶⠚⠛⠉⠀⠀⠀⠀⠀⠉⠙⠛⠷⠶⠶⠶⠶⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠉⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠿⠛⠉⠉⠉⠙⠻⣿⣷⡀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠚⠛⠛⠛⠒⠶⢦⣄⣀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⣴⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠟⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠛⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣤⣤⣤⣤⣴⣶⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣤⣄⣀⣀⣀⣤⣤⣶⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣣⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣿⣿⣿⣿⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣐⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⣀⣚⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣂
⠀⠀⠀⠀⠀⠀⣬⣭⣭⣭⣭⠭⠉⠉⠉⠉⢭⣭⣭⣭⣭⣥⣌⠩⢭⣭⣭⡿⠉⠉⠉⠉⠭⣭⣭⣭⣭⣥
⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠐⢒⣒⣶⣶⣶⣶⣄⠐⠂⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠠⠄⠙⠿⠿⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⢛⣛⣛⣛⣛⣒⣀⣀⣀⣀⣚⣛⣛⣓⣂⡙⢛⣛⣛⣛⣛⣓⣀⣀⣀⣀⣒⣛⣛⣛⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠉⠀⠀⠉⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣯⡏⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠛⠋⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠉⠁⠀⠀⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣀⣴⣶⡿⠿⠗⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣠⡾⠋⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠑⢦⣀⣀⠀⣀⣀⡤⠖⠋⢀⣠⣶⣿⠟⠁⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣉⣉⣉⣠⣤⣴⣾⡿⠟⠋⠀⠀⠀⠀⠈⠛⠶⣦⣤⣤⣤⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁


⣿⣯⢹⣟⠻⣿⣟⢟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠛⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⢸⣿⠟⠋⠉⠉⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠛⠛⠛⠛⠿⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⢙⣿⣿⣶⣶⣶⣤⣤⣀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⣤⣴⡾⠛⠉⠙⠿⣷⣦⣤⣤⣽⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⣀⣽⡿⢿⣿⣶⣤⣀⠀⠀⠀⠉⠉⠉⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠛⠁⠀⣀⣤⣶⠿⠋⠁⠀⠀⠈⠛⠿⣿⣿⣿⣶⣶⣶⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣀⣀⣀⣠⣤⣴⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠀⠀⠉⠉⠙⠲⡄⠀⠀⠀⢀⣠⣴⡾⠟⠛⠋⠉⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣤⣤⣤⣶⣶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠁⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠶⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣶⣶⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣶⣾⣶⣿⣿⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣟⣿⣿⣯⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣧⣼⣿⣷⣾⣿⣿⣿⣽⡻⣃⣲⡄
⠀⠀⠀⠀⠀⢀⣼⣿⠏⣻⡿⠋⠁⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣷⣄⡀⠀⠀⣀⣴⣾⣿⣿⣿⠟⠛⠉⠁⠀⠀⠀⠉⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⣾⣿⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⢀⣼⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡆
⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢁⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣷
⠀⠀⠀⠀⠸⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠛⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⢛⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠏⢡⣞⣿⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⢿⣿⣷⣄⢀⡀⠀⠀⣀⣠⣴⣾⣿⣿⣿⡿⠟⠀⠀⠀⠙⠻⣿⣼⣏⢨⣤⣠⣀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣤⣿⣶⣶⣶⣶⣶⣶⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣷⡾⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣰⡄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠋⠛⠲⣾⠀⣰⠃⢳⡀⠘⣶⠚⠋⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣰⠚⣲⣄⠈⠻⣇⠀⢀⡷⣄⠈⠳⡞⢲⡀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⡽⠞⠁⣨⠷⣄⢈⡿⠋⢀⡼⢦⡀⣨⠟⠁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠉⢀⡠⠞⢧⣀⡼⠋⢀⡴⠻⣄⣠⠟⠁⢀⡴⠛⠲⢤⣀⡀
⠀⠀⢀⣀⣠⣤⠤⠶⠖⠚⠋⠉⢀⣠⡤⠞⠉⠳⣄⠀⠙⢦⡴⠋⠳⣄⠈⠳⣤⡴⠋⠙⠲⢤⣀⠈⠉⠙⠓⠒⠶⠤⣤⣄⣀
⠀⠀⠀⠉⠉⠙⠓⠒⠶⠦⣤⣀⡀⠉⠓⠦⣄⡴⠋⢳⣄⠀⠙⣦⠖⠉⢳⣄⠈⠳⣤⡴⠚⠉⢀⣀⡤⠴⠶⠒⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡴⠋⢀⣴⡋⠈⣳⠞⠁⢀⣴⡋⢈⡷⠚⠁⣀⣴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣰⢯⡀⠙⢾⡁⢀⡴⣏⠀⠙⢯⡀⡠⢾⡁⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠙⠶⠟⢦⠀⠹⡏⠀⢈⡷⣄⠀⠙⠶⠞⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠞⢧⡀⠹⣄⡞⠀⣸⠓⠦⠤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠙⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢀⡀⠀⢸⡇⠀⢀⡀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⣀⡀⠘⣿⡀⠸⡿⠀⠸⠇⠀⢿⠇⢀⣿⠃⢀⣀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠙⠷⠀⠈⣁⣠⣤⣤⣤⣤⣤⣤⣄⣈⠁⠀⠾⠋⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠙⠛⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠛⠋⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣶⣤⣀⠙⠛⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠋⠙⠿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠛⠋⢀⣤⣶⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡗⣀⣀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠂⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠐⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⣶⣦⡄⠀⣾⣿⣿⣿⡿⠋⣁⣤⣤⣌⠙⢿⣿⣿⡿⠋⣡⣤⣤⣈⠙⢿⣿⣿⣿⣷⠀⢠⣴⣶⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣿⣿⣿⣿⠁⣴⣿⣿⣿⣿⣷⣄⠙⢿⣦⣾⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠘⣿⣿⣿⣿⡀⢻⣿⣿⣿⣿⡿⠻⣷⣄⠙⢿⣿⣿⣿⣿⡟⢀⣿⣿⣿⣿⠃⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠾⠿⠃⠀⢿⣿⣿⣿⣷⣄⠙⠛⠛⠋⣠⣾⣿⣿⣷⣄⠙⠛⠛⠋⣠⣾⣿⣿⣿⡿⠀⠘⠿⠷⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠄⠘⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠃⠠⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠉⢀⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⡦⢀⡀⢴⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⡀⠉⠛⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣠⣄⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⣠⡄⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢠⡶⠀⢈⠉⠛⠛⠛⠿⠿⠛⠛⠛⠉⡀⠀⢶⡄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠉⠁⢠⣿⠃⢰⣶⠀⢰⡆⠀⣶⡆⠈⣿⡄⠈⠉⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠈⠁⠀⢸⡇⠀⠈⠁⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃





⣿⣿⣷⣾⣷⡿⢾⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣾⣿⢷⢾⠿⠿⠿⠷⣶⠿⠷⠶⠶⠶⣶⢿