Palm tree Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣷⣶⣤⡀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡉⠉⠉⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠟⠛⠛⢁⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⡟⢻⣿⣿⣿⣦⠀⠘⠻⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡏⠋⣿⣿⡿⠋⠀⢸⣿⣷⠀⠙⣿⣿⣿⣧⠀⠀⠀⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⣿⡿⠀⠀⠀⠘⣿⣿⠀⠀⠈⢽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⢀⣿⣥⣄⣀⠀⠀⣿⣿⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣤⣤⣠⣾⣿⣿⣿⣿⡿⠿⣤⣿⣿⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠏⠈⢿⣆⠙⠻⣿⣷⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⣿⡏⠀⠀⠘⣿⡆⠀⠈⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠻⠀⠀⠀⠀⢹⣿⡀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣞⠱⣆⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠻⠄⢠⠀⡀⠈⡼⣋⠄⠀⠂⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣉⣉⣉⡛⠷⢦⡈⣵⠲⣮⢢⣞⡼⠋⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡒⢼⣋⣬⢿⣾⣲⠅⠒⣝⢾⣷⢳⣿⣋⣴⣆⣽⣥⣤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⡴⠄⣶⣤⣠⠆⡀⠀⠀⠉⠒⠾⣾⣷⢿⣭⣭⣍⡤⢀⣀⣈⠁⢀⠙⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠛⠓⠒⡯⠔⢊⢹⡇⠡⠀⡀⠈⠉⠒⠶⣤⡛⠘⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⣠⡾⣫⣿⠁⠀⠏⠙⠑⠴⠄⣀⠀⠉⠢⡀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢁⡼⢋⡴⣇⡟⡧⠀⢸⠈⡓⠀⠀⠁⠘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠰⢋⣴⡟⢰⢸⠇⣶⠀⠘⢀⡋⠀⠀⠀⠀⠀⠘⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⣠⡟⠉⠀⠆⣿⠀⢹⡀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣤⠋⠀⠀⠀⠘⡿⠀⠋⠷⢀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢰⢰⣷⠀⠀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠻⣷⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⣄⠻⣿⡆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡇⢰⡿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠉⠉⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣽⣦⠀⣿⣡⣴⣿⡿⠿⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣟⣥⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⢿⣿⣿⣿⣿⣟⠛⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣴⠏⠀⣀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠁⣼⣿⠿⡿⠙⣿⡆⠀⠈⠋
⠀⠀⢀⣤⣶⣾⣿⣿⣶⣿⣾⣿⣾⣟⠿⢿⣆⠀⠀⠀⠀⣿⠁⠀⣰⣿⠇⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⢀⣴⠶⠿⣿⣿⣿⡉⠛⢷⡀⠈⠀⠀⠀⠀⠃⢀⡼⢹⠏⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⢰⡟⠁⠀⣼⠛⢿⣿⣷⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠁⠈
⠀⠀⠀⠀⠈⠁⠀⠀⢿⡆⠈⢷⡙⡇⠀⠁⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣾⣷⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣼⣿⣿⣿⣼⣿⣷⣯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠿⠿⠛⠛⠛
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢴⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠠⢶⣾⠿⢿⠉⠁
⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠖⠶⠦⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠑⠾⢟⠛⠛⠃
⠀⠀⠀⢀⣴⣞⡭⢴⣟⣠⠤⢤⡶⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⡜⠰⠿⡛⠛⠃
⠀⠀⠐⠋⠿⠋⠀⠛⠁⠀⡴⠟⠒⠒⣲⠶⠂⠀⠑⣄⠀⠀⢰⠳⢾⣟⠋⠀⢀⣠⠤⠐⠒⠒⠒⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⣉⣷⠶⠌⢣⡀⡆⢠⠞⢁⠴⠊⠁⠠⣤⣄⣀⠘⣶⠦⣄⣰⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣉⡓⠦⡳⣵⢃⠞⠁⣐⣶⣖⠒⠺⢷⡀⠉⠺⠇⠀⠙⣧⠙⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢉⠀⢀⣤⠎⢉⣷⣼⡏⣹⢾⡿⠷⠮⠭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣶⣰⢻⡴⢩⠗⠊⢹⠋⠻⣩⠩⡷⣅⢰⣧⢠⡆⢉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣤⡜⠸⠇⠘⠁⠀⠀⠀⠈⣻⠁⡟⠒⠁⠈⠻⢹⡼⢻⢸⡇⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠈⠀⢸⡎⣧⣿⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣇⠀⠀⠀⠀⠀⠀⠈⠀⢸⢿⣾⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠈⠁⢀⣸⣆⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⢻⠀⠈⠉⠀⠘⣆⠀⡾⡔⣇⠔⠡⢝⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⢆⣣⠈⡧⠴⠖⠚⠁⠈⢣⣧⠃⠻⢰⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠙⠀⣸⠄⠀⠀⠀⠀⣠⠭⠷⠆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣯⣀⣽⣭⣭⣭⣭⣿⣽⣭⣭⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣿⣯⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣾⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣶⣾⣿⣆⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣇⠀⠀⠀⣰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠙⢿⣿⣿⣿⣦⠀⣰⣿⣿⣿⠿⢁⣠⣤⣶⣶⣶⣶⣶⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⠋⠛⠛⠛⠻⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⠀⣡⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣿⡇⠀⠙⣿⣿⣿⣟⠻⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠃⢀⣿⣿⣿⠉⠀⢸⣿⣿⣏⣿⣷⠀⠀⠙⢿⣿⣿⡄⠀⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⢸⣿⣿⠃⣿⣿⠀⠀⠀⠀⠙⠟⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠋⠁⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠿⡿⠿⢿⣿⠿⠿⠿⠿⢿

⠀⠀⠀⠀⣀⢰⣤⡀⣠⣴⠀⡀⠀⠀⠀⠀⠀⠀⢐⣳⣶⡄⢀⣤⡤⠀⠀⠀⠐⠲⣶⣠⣶⣖⠀⠀⢀⣀⣀⣻⣆⠀⣀⣄⣀
⠀⠀⠀⠀⠘⢻⣿⣷⣿⣿⣿⣥⡀⠀⢀⠀⠀⣰⣯⡿⠛⣿⠿⣿⡻⣆⠀⠠⠾⢿⣿⣿⣿⡿⠷⠄⢴⣿⣿⠟⣯⢼⡿⠿⣿⠂
⠀⠀⠀⠀⠒⠛⡿⠁⠙⣿⣍⠁⠀⢠⣾⡿⢶⠿⣟⠣⣼⠃⠀⣸⠇⠋⠀⠀⠐⠛⠁⣿⠙⠀⠀⠀⠘⠹⡏⠀⡇⠈⢿⡆⠈
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠉⠀⠀⠈⠸⡇⠀⢧⠈⢰⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠃
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣄⠀⠀⠀⠀⠀⢠⣤⣤⡀⣠⣶⣖⣀⠀⠀⢀⣤⣶⣦⣀⣠⣴⡦⠀⠀⠀⠀⠀⡀⢠⣶⣦⠄
⠀⠀⠀⠀⣀⠀⣴⢠⣬⣿⣿⣶⣞⣀⡀⠐⣻⣿⣿⣿⡿⠿⣯⡅⠀⠀⣴⢿⣿⣿⣿⣿⣿⣷⡄⠀⢠⢶⣿⣿⣿⣿⣿⠯
⠀⠀⠀⠤⣿⣷⣿⠛⠛⡠⢻⣏⠛⠿⡄⠀⣟⠰⡏⠀⢆⠀⠀⠙⠀⠀⠀⢸⡟⣸⠃⢻⡿⠛⠀⠀⠰⠛⣿⠀⠱⡀⠈⠃
⠀⠀⠀⠸⠋⣿⠀⢳⡾⠁⢰⠟⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠈⠀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⠿⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⡛⠹⣦⡀⠈⠀⠀⣀⣠⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⢿⣿⠿⠲⠇⡆⠀⠀⠙⠓⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠠⣞⡿⠟⠛⢩⠟⠉⠀⠀⢼⡇⢸⡌⠻⣿⡶⣠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠙⠀⡑⢼⣿⡄⠈⠰⢽⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢸⡇⠈⣿⣇⠀⠀⠈⠙⠉
⣀⣀⣀⣀⣀⣀⣀⣀⡼⠀⢀⣀⡀⣀⠘⣀⣈⢇⣀⣿⣷⠀⢀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀
⠉⠉⠉⠉⠉⠉⠙⠉⠇⠀⠺⠛⢋⠦⠉⠙⠷⠶⠇⠸⡿⠀⠈⠉⠉⠉⠛⠛⠛⠛⠟⠋⠉⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣀⣀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠐
⠒⠠⠤⠤⠤⠤⠀⠀⠀⠀⡔⠈⠈⠉⠀⠀⠘⠓⠒⠀⠀⠀⠀⠀⣀⣀⣉⣘⡋⠢⠤⠤⠄⠀⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠓⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲
⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⣦⠈
⠀⠀⠀⠠⡀
⠀⠀⠉⠀⠴⠦⠤⠲⠒⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⢾⣿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣷⣦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⣿⣷⣿⣷⣿⣿⣿⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣿⣿⣿⣿⣿⣿⠖⢿⡟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠈⠻⠿⡛⠋⣿⣿⣿⢀⡀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠓⠀⠛⣿⡿⠙⢹⣿⠏⢹⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠆⠀⠀⠀⣿⡇⠀⠻⠋⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣼⣿⣿⣿⣿⣿⡧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢹⣿⡿⠻⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠘⣿⠀⠀⢸⡏⠁
⠀⠀⠀⠀⠀⢀⣤⣴⣷⣶⣶⣤⡀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢾⣯⡿⣿⣯⡿⠿⠃⠀⠀⠀⠰⡿⠛⢰⡟⠻⣿⠖⠀⢸⡇
⠀⠀⠀⠀⠀⠘⠿⠃⢸⡟⠀⠈⠛⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣿⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠿⠄⠀⠸⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣷⣄⣀⠀⠀⠀⡀⢀⠀⠀⢴⣿⣿⡃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⡿⢿⣿⣿⠟⢡⣴⠦⣵⣤⡰⣿⣰⣿⣿⣿⠀⠀⠱⡀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠈⠉⠉⠰⢾⣿⣿⣷⣺⣿⣿⡿⣿⡿⠃⠀⠀⠀⠎⠀⢈⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣤⣀⢀⡙⣿⣿⣿⣿⣿⣫⠿⢡⣾⣤⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠟⠻⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣃⣾⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣰⣶⣾⣿⣿⣿⣿⣿⣿⣵⣶⣠⣤⣶⣾⡉⠀⠒⠖⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟⣿⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⠻⠛⢁⡜⠙⣠⣿⣿⣿⣿⣿⣿⡟⠻⣿⡿⢿⣿⣿⢿⣿⠄⠀⢄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⢀⣴⡯⢀⣾⢿⣿⠿⠛⣿⡿⣿⣿⣮⣽⣻⠈⠹⣿⣿⣿⣿⡢⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢰⡿⠇⠀⠀⢠⣾⠟⣠⣯⢿⣟⠏⠀⢰⣿⡇⠙⣿⣿⣿⢿⣿⡆⠸⠛⣿⡾⣿⣆
⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⡾⠃⠀⢿⡸⠈⠀⠀⠀⢸⣿⠀⠀⠈⠇⢻⣿⣳⢯⠀⠀⠁⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠸⠁⠀⠀⠀⠀⢸⣻⠀⠀⠀⠀⠈⠛⣾⣗⠄⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠰⣆⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⢻⣦⢰⣿⣿⠏⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⣼⣿⡿⠀⣀
⠀⠰⠟⣻⣿⣷⣌⢻⣿⣿⣵⣾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢛⣿⣿⣦⡘⣷⣿⣯⣴⣿⡃
⠀⠀⠀⣀⣤⣭⣿⣿⣿⣿⣿⣯⣭⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣽⣿⣟⣿⣿⣯⣥⣤⣤⣤⣄⡀
⠀⢠⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡻⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⢿⣟⡿⣿⣯⡟⠛⠉⠙
⠀⣼⣿⡿⠋⣿⣿⡿⠀⢿⣿⣷⡝⢿⣷⠀⠀⠀⢰⣄⠀⣠⠄⢀⣀⠀⠀⠀⢠⣿⡿⠟⢹⣿⣿⠇⠘⡿⣿⣦⠛⢿⡄⠀⠀⠀⣤⡀⢀⡄⠀⣀
⠸⠋⠁⠀⠀⣽⣿⠇⠀⠘⡆⢿⣿⣀⣨⣶⣶⣤⣄⣿⣾⣿⣿⡟⠁⠀⠀⠀⠟⠉⠀⠀⢨⣿⡻⠀⠀⢳⠘⣿⣆⣀⣵⣶⣤⣤⣸⣧⡟⣴⡟⠉
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⣷⢀⣻⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢸⡄⢈⣿⣿⣿⣿⣿⣿⣿⠋⣼⣳⣿⠿⡿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⠉⠉⠉⠉⣉⣿⣿⣿⣿⠻⣿⣿⣦⡝⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠉⠉⣩⣿⣿⣿⡟⠻⣿⣶⣌⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⢴⣿⣿⠏⣿⣿⡇⠈⠉⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡠⣾⣿⡟⢸⣿⣿⠀⠁⠙⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠃⣾⣿⠋⠀⠸⣿⡇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⠞⢠⣿⡏⠁⠀⢿⣿⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡞⠁⠀⠹⠃⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠃⠀⠀⠛⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣯⣞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⣿⣵⣃⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⣤⣤⣄⡉⠉⠙⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣶⣄⠀⣿⣧⠀⠀⠀⢀⣤⣶⡶⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠂⠀⠀⣀⣀⣠⣤⣖⡢⢿⣿⣦⠈⣿⠀⢀⣴⡿⠿⠍⠉⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠉⢁⣴⣾⣿⣯⠛⠟⡻⡫⢿⣷⡝⢿⣇⣽⢠⣿⣟⠃⠀⣠⢄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣰⣿⡿⠛⠀⠀⣀⣀⣀⡀⠉⢴⣿⣆⢿⣿⣿⡟⢡⣴⣾⣿⣿⣿⣟⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⢸⣏⢠⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿⢿⣶⣍⡻⣼⣻⠟⣡⣾⠿⠿⠿⡟⠛⠻⠃⠁⠀⠉⠳⡄
⠀⠀⠀⢠⡶⠛⠉⠛⠻⠿⣿⣦⣄⢿⣼⡟⣰⣿⣼⢻⣿⣿⣿⣶⣬⣦⣅⣭⣿⣶⡦⣬⣕⠿⣿⠿⢿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣰⣦⣬⣝⠻⣿⣿⣇⡿⢋⡯⢾⣟⣛⣻⡿⠏⢩⣿⣿⣿⡟⢿⡎⠻⣿⣮⡳⡀⠉⠙⣿⣿⣦⡀
⠀⠀⠀⢀⣴⣿⣿⡿⣿⣿⠿⣿⣷⡮⣛⣭⣴⣿⣏⡛⣻⠿⣿⣿⣋⣿⡟⢹⡿⠀⠘⣿⡀⠉⢿⣻⣿⣦⡀⠘⠁⡿⣿⡄
⠀⠀⢠⡟⠁⠈⠈⢀⣥⣾⠿⡻⣩⡾⢻⣾⠿⣿⣿⣿⣦⡀⠁⠊⢹⣿⢹⠈⠇⠀⠀⢻⡇⠀⠰⣿⣿⣿⣇⠀⠀⠀⢹⣷
⠀⠀⠈⠀⠀⠀⣰⣿⠏⠁⣠⣴⡿⠁⢸⡇⠀⠉⣷⠀⢻⢿⣆⠀⢸⣿⠆⠁⠀⠀⠀⢸⣷⠀⠀⠸⢹⣿⣯⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⢰⣿⠙⠀⢰⣿⣿⣇⠀⠘⣿⠀⠀⠉⠀⠈⢸⣿⡆⠈⣧⣃⠀⠀⠀⠀⣸⣿⠀⠀⠀⢱⣿⣿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢿⡏⠀⠀⢸⣿⣿⡃⠀⠀⢿⣇⠀⠀⠀⠀⠈⠋⣿⠀⠹⡾⠀⠀⠀⠀⡿⣿⠀⠀⠀⢉⣿⡟
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⣿⣷⡁⠀⠀⠘⣿⡆⠀⠀⠀⠀⠸⢿⠀⠀⠱⠀⠀⠀⠀⡏⣿⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠹⣼⣄⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢰⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⣜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣎⢧⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠳⣄⠀⠀⠀⠀⠀⠀⡾⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣄⡄⠀⡀⠙⣶⡈⢶⣧⢴⢇⣎⣼⢃⣾⣿⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠦⣝⢾⣿⣄⠈⣻⣿⣷⣀⡙⢿⣿⣿⠃⢸⣿⣿⣿⣿⠷⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢙⠛⣿⣿⣿⣶⣾⣬⣻⣿⣧⣄⣽⠃⣀⣿⡿⣿⣿⣟⣉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣧⣽⣿⣿⣝⣯⣅⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣄⠀⣴⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⢛⣻⣷⣿⣿⣿⣿⣋⣁⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢉⣩⣿⣿⣿⣿⣿⣿⣯⣭⣍⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣟⣿⣿⣿⡿⢹⣿⣿⣿⠿⣿⣍⠻⢷⣄⣀⣀⡀⠀⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣟⣽⠧⢼⡿⠃⢸⣿⢿⣿⣧⠈⠙⠧⢀⣹⣧⣬⣹⣶⣾⣿⣿⣛⡛⠒
⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣿⣿⣷⣶⣾⣿⠶⢾⡿⠀⠻⢿⡇⠀⠞⠉⠁⠀⣈⣿⣿⣿⣿⣿⣭⡉⠃
⠀⠀⠀⠀⠀⠈⢡⡴⣿⣿⣿⣿⣿⡿⣿⣏⠃⠈⠇⠀⠀⠈⠟⠀⠀⣠⣴⢟⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢰⠏⡼⢻⣿⣿⣿⣿⣿⣦⠉⠃⠀⠀⠀⠀⡀⠀⠀⠼⠋⢠⠟⢛⣿⡿⣿⡇⢻⡏⠙⠀⠉
⠀⠀⠀⠀⠀⠘⠀⠀⣿⢹⡟⢸⣿⠈⠛⣧⡀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⣿⠟⠀⢻⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠻⡄⠀⠀⠑⡀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢠⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢷⣿⣶⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⣋⣀⣀⣀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⢀⡀⢀⠀⣀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⡙⠻⣶⣌⣷⣶⣿⣶⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⠀⠻⣿⣷⣄⠻⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣶⣽⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⠛⠟⠋⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣴⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⡿⡿⠿⢸⣿⣽⣿⣿⠇⣻⣿⡛⠹⢾⣿⣿⣿⣶⣶⣤⣴⣤
⠀⠀⠀⠀⠀⠠⣄⠻⣷⣼⡇⣠⡄⠀⠀⠀⣠⣶⣿⠿⠟⠋⢁⣾⣿⣿⣧⡀⠀⢾⣿⢻⣿⣿⣿⣿⣇⢀⣀⣀
⠀⠀⠀⣰⣿⡿⣿⣷⣿⣿⣿⡿⢀⣀⡀⣸⠿⠋⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⡿⢿⣿⣬⢻⣿⣿⣿⡿⣟⣻⣿⠟
⠀⠀⠘⠛⠛⡛⣿⣍⠻⣿⣿⣿⣋⡉⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⣿⢻⡿⡷⢀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣿⣯⣭⣭⣿⡟⠛⠛⣯⠙⠲⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣿⠀⠀⠀⠿⠛⢿⣿⣯⡿⢻⣿⣿⣯⣝⣛⣿
⠀⠀⠀⣸⡟⠉⠁⠿⠿⠁⠹⣶⣝⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⢞⣵⣿⣿⣇⢨⣿⣭⡉⠛⢿⣿⡄
⠀⠀⠀⠉⠀⠀⠀⠀⢀⣶⠀⠀⠙⣷⣄⠀⢹⣇⣽⣿⣰⡏⠀⠀⠀⣿⠀⠀⢰⣿⠈⣿⣿⡇⢿⣾⣿⣿⢿⣷⣶⣯⣃
⠀⠀⢸⣷⣶⣦⣴⢟⣿⣷⣄⠀⣀⣈⡙⢿⣄⢿⣿⣿⡿⣢⣤⣤⠀⣿⠀⠀⠸⣏⠀⠛⢹⡇⠈⠘⣿⣿⠀⢹⣇⠉⠉
⠀⢐⣶⣾⣿⣿⣿⣾⣿⣿⣿⡶⠦⣬⣙⢿⣿⣾⡿⢿⣿⣿⣙⣛⠇⣿⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠘⠿⠀⠀⠃
⠀⣿⣛⣉⡙⠛⣿⠁⠴⣿⣷⣦⣴⣾⣿⣿⠿⣿⣧⠸⣏⣉⡉⠛⠓⣿⠀⠀⠀⠀⠀⠀⣿
⠀⣼⠿⠛⣿⣿⢻⣧⡶⢾⡇⠹⠇⠉⠁⢠⣾⣿⠛⢻⣿⡙⠻⢿⠆⣿⠀⠀⠀⠀⠀⢀⣿
⠈⠁⠀⠀⣿⣿⢾⠙⢧⢸⣷⡀⠀⠀⠞⠋⢀⡏⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠛⠁⢸⡄⠈⢹⡈⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⠁⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠂⠘⠛⠛⢻⠷⠶⠶⠶⠶⣶⣶⣾⣿⣶⣦⣤⣤⣤⣿⣿⣤⣤⣤⣤⣤⣤⣼⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄
⣀⣀⣠⣀⣀⣀⣀⣀⣀⣉⣉⣻⣿⣿⣉⣉⣉⣉⣈⣉⣉⣙⣻⣿⣿⣿⣿⣋⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⡍⢽⡟⠛⠛⠛⠛⠛⢛⠻⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢤⡄⢀⣴⠆⠀⠀⠀⠀⣠⣤⣤⣿⣷⣯⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⣦⣴⣂⣀
⠰⠶⢦⣿⣾⣧⣤⡀⠀⠀⠀⠀⣰⠞⣻⣿⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣰⠇⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⣍⠉
⢀⣴⢿⡿⣿⠻⢦⠀⠀⠀⠀⠀⠁⠀⢿⠃⣧⠈⠁⠀⠀⠀⠀⠀⠀⠈⢙⣻⣿⣿⣖⠂⠀⠀⠀⠀⠘⠁⢸⡏⢳⠉⠃
⠈⠁⡼⠀⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣹⠙⣧⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣦⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣠⠖
⢀⣤⣤⣿⣷⣿⡥⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠚⢛⣿⣿⣿⣟⠉⠁
⠀⢠⠾⢻⣿⡿⣷⡄⠀⣀⠀⢀⡄⠀⠀⢀⣠⣹⣦⣾⣁⠀⠀⠀⠰⠋⢸⣿⢻⠙⠷⠀⠀⠀⠀⠀⠀⠀⠐⣦⣠⡶
⠀⠀⠀⠸⠇⠸⡄⠁⠶⢼⣷⣿⣤⡀⠀⢀⣤⣿⣿⡿⣭⠁⠀⠀⠀⠀⠈⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣗⠂
⠀⠀⠀⠀⠀⠀⢻⡄⠶⢻⢻⡟⠳⠀⠀⠈⢁⡎⠸⠇⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⢋⠏⢿⠈⠃
⠀⠀⠀⠀⠀⠀⢸⡇⢰⠃⠈⠃⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⢸⣷⡏⠀⠀⠀⠀⠀⠀⣀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣤⣦⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣤⣄⠀⠹⣿⣿⣇⠀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣦⣐⣺⣿⣿⢀⣿⡿⢂⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⣅⣘⠿⣿⣷⣼⣿⣿⣾⣏⣴⣿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣫⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠀⣠⣶⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠙⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣯⣾⡿⠛⣵⣿⡟⠀⣿⣿⢻⣿⣿⣿⣿⠋
⠀⠀⠀⠀⢀⣀⡀⢀⢱⡇⣰⣴⣶⠦⠀⠀⢠⠟⢁⣾⡿⠛⣡⣾⣿⡿⠀⠀⣿⣿⠈⠘⢻⣿⣿⡄
⠀⠀⠠⢄⣛⣿⣿⣿⣆⣿⣿⣿⠁⠀⠀⢀⠀⠀⠸⠉⠠⣾⣿⣿⡿⠁⠀⠠⣿⣿⠀⠀⠀⣿⡿
⠀⠀⠀⠀⢈⣹⣾⣿⣿⣿⣿⡗⠀⣠⣿⣿⣿⣷⠄⠀⠀⠉⠉⣿⠃⠀⠀⠚⣿⣿⠀⠀⠀⠉
⠀⣠⣤⣴⣾⣿⣻⣿⣿⣿⣿⢇⣼⡿⠟⠉⠉⠉⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠁
⠀⠈⠉⣉⣭⣭⣿⣿⣿⣿⣿⣾⣿⣷⣾⣿⣿⡿⠇⠀⠀⢰⡟
⠀⠀⠺⠟⢋⣻⣿⣿⣿⣿⡿⣿⣿⣿⡿⣿⣷⣧⡀⠀⢀⣿⠁
⠀⠀⢀⣴⠿⠻⢫⣿⣿⣿⣿⠈⣿⠿⣿⣦⡉⠻⠻⡀⣼⡇
⠀⢀⡾⠁⢀⣴⡿⣹⣿⢻⣿⣇⠘⣇⠘⣿⡏⠀⠀⢰⡿
⠀⠈⠀⠀⢸⡿⠱⣿⡿⠈⣿⣿⠄⠘⣆⠉⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠈⠉⠀⠀⢹⡄⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⣿⣾⣿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⣴⣟⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣼⣿⣿⣿⣿⣿⣿⣿⣯⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣄⠀⠀⠀⠀⠀⢀⢀⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⢿⣿⣿⣷⣄⠀⠀⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⢿⣶⣶⣀⠀⠀⢻⣿⣿⣿⡄⣴⣾⣿⣿⠟⢀⡀⣴⣶⣤⢀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠛⠛⣿⣿⣦⡀⢿⣿⣿⣿⣿⣿⢟⣤⣼⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣄⣿⣿⣿⣿⣷⣿⠿⠛⠛⠉⠁⠉⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣶⣶⣾⣷⣶⣦⣤⣬⣻⣿⣿⣿⣭⣴⣶⣶⣦⣶⣶⣄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⠿⡿⢛⣩⣭⣿⣿⠟⢛⠟⣿⢿⣿⣿⣿⣟⡻⠿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣻⣷⣾⠟⢛⣴⡿⠀⢠⠏⠀⢸⣷⡙⠿⣿⣿⣿⡆⠈⠙⠛⠻⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⣺⣷⠀⠀⠀⠀⠀⠋⢁⣾⣿⡿⠋⢠⣿⡿⠀⣰⠏⠀⠀⢨⣿⣷⠀⢻⣿⣿⣿⣆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⣿⣧⠀⣾⡟⠁⠀⢀⣀⣤⡀⢠⣿⣿⣝⠀⠀⣿⣿⡅⣰⠏⠀⠀⠀⢐⣿⣿⣧⠀⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⢿⣿⣦⣿⢁⣴⣿⣿⠿⠋⠀⠻⣿⣯⡁⠀⠀⢻⣿⣱⡏⠀⠀⠀⠀⣼⣿⣿⣋⠀⠀⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⣦⡻⣿⣿⣿⣿⣿⣵⣦⣶⣦⡀⠈⠉⠁⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⢠⣿⣿⣟⠃⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠚⠛⠋⠙⠛⢛⣛⣿⠛⢯⣥⣀⡀⠉⠉⠛⠛⠂⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠋⣡⠇⢸⡆⠙⢿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢠⡏⠀⢸⣧⠀⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣷⠀⠘⣿⣷⡀⠀⠘⣷⡁⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠈⠙⠓⠀⠀⢸⣷⡀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⣦⡀⠀⢀⣀⣀⠀⠀⠀⠀⠴⣶⣄⢀⣤⡶⠆⠀⠀⠀⠀⠀⢲⣄
⠀⠀⠀⠀⠀⢶⣾⣿⣷⣼⣿⣷⣶⠂⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⣴⣿⣿⣦⡀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣀⠀⣹⣿⣿⣿⠿⢂⣾⣿⣿⡷⡄
⠀⠀⠀⠀⠀⣠⣼⣿⡿⠻⣿⡿⠿⠟⠃⠀⢰⣶⣄⣠⣾⣿⡏⢀⡾⠁⠉⣿⡌⡷⠀⠈⠉⣡⡿⠏⣿⢿⠏⠉⠉⠈⣽⣿⡿⠁⢸⠁⢿⣏⠉⠻
⠀⠀⠀⠀⠈⠉⢡⡞⠀⠀⠙⠿⠆⠀⠀⢰⣟⣿⠛⢿⡙⠷⠉⣾⠃⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠘⠇⠀⢾⠀⠈⢿⠆
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠈⣇⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠈
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⣶⣼⣧⣀⣤⠀⠀⠀⣠⣿⣿⣿⣦⣾⣿⣷⠶⠒⠀⠀⢐⣿⣿⣿⣿⣴⣿⣿⣯⡁⠀⠀⠀⣀⣤⣶⣴⣿⣿⣿⡥
⠀⠀⠀⠀⠠⣤⣀⣿⣱⣟⡛⢿⣿⣿⣷⣶⠤⠀⢠⡾⢻⣿⠛⡟⠉⠛⠿⡆⠀⠀⠞⢛⣿⡿⢻⢿⣿⣿⣿⠷⠀⠀⢚⣽⣿⠿⢿⠛⠿⢯⡁
⠀⠀⠀⠐⢺⣿⣿⢿⡉⠉⣱⠏⢹⣇⠉⠛⢦⠀⠸⡇⠸⡇⠀⢹⠀⠀⠀⠁⠀⠀⠀⠸⣿⢀⡟⠀⠹⡿⠉⠀⠀⠀⠘⠁⣿⠀⠀⣇⠀⠀⠁
⠀⠂⠀⠀⠟⠉⣿⠀⠙⣾⠃⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠈⠀⣸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⡄⠀⣠⡄
⠀⠀⠀⠀⠸⣧⣼⣏⣀⣀⣀⠀⠀⠀⠀⠀⢠⡄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢀⣠⠄
⠀⠐⠾⣿⣷⣿⣿⣿⣯⣭⡁⠀⠀⠀⠈⠙⢷⣿⣴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣀⡀⠀⠀⠀⠀⠲⢶⣦⣼⣷⣿⣁⣀
⠀⢠⠾⢛⣿⣿⣿⢿⣦⠉⠉⠀⠀⠀⠚⣻⡿⠿⣿⢿⣍⠁⠀⠀⠀⠐⠚⢛⣷⡿⠿⢯⣍⠀⠀⠀⠠⠾⢿⣿⣿⣿⣿⣯⡉⠁
⠀⠀⠀⢸⠏⣿⢹⠀⠉⠃⠀⠀⠀⠀⠀⠋⠀⠀⢹⠆⠈⠀⠀⠀⠀⠀⠠⠏⣿⠁⠀⠀⠈⠀⠀⠀⠀⢰⠟⣿⠇⢹⣷⠈⠙⠂
⠀⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⢿⡄⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣸⣇⢀⣀⣀⠀⠀⠀⠚⢛⣽⣿⠿⣿⣯⣍⡉⠉⠁⠀⠀⠀⠀⠀⢰⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠀⠀⠀⠀⠠⠶⢶⣿⣿⣿⣿⣯⣅⡀⠀⠀⠀⠚⠋⠀⢈⠈⣛⡉⢿⡄⠀⠀⠀⠈⢛⣻⣿⣿⣿⣧⣤⡀
⠀⠀⠀⣠⣤⣤⣼⣏⣀⠀⠀⠀⠀⠀⡴⠟⣻⡿⢻⣿⣷⡉⠁⠀⠀⠀⠀⠀⠀⡾⠀⠸⠃⠀⠀⠀⠀⠀⠔⠛⢩⡿⠟⠻⢶⡀
⠀⠀⠀⠁⠀⣾⠁⡈⠙⠳⠀⠀⠀⠀⠀⠀⢿⠃⠀⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠃⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⢀⣴⣆
⠀⠀⠀⠀⢀⣀⣀⣀⠀⢿⣧⣼⣿⡿⢁⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⢿⡆⣾⣿⠟⣀⣤
⠀⠀⠀⠀⠛⠋⠿⢿⣿⣆⣻⣿⣿⣾⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠿⢿⣷⣌⣿⣿⣷⣾⣿⠄
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣯⣿⣿⣷⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠻⣿⣿⡿⣿⣯⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⢻⣿⣟⠿⣿⣏⠉⠀⠈
⠀⠀⠀⢠⣾⠿⠋⠑⣿⣿⡟⠀⢿⢿⣿⡌⠿⡧⠀⠀⠀⢷⡆⣰⢆⣤⡤⠀⠀⠀⢠⣿⠿⠉⢸⣿⣿⠃⠀⡟⢿⣷⡉⠻⡆⠀⠀⠀⣷⢀⣴⣂⣤⡤
⠀⠀⠀⠈⠁⠀⠀⠀⣿⡿⠁⠀⢸⡌⢻⣷⣴⣾⣿⣿⣶⣼⣿⣿⣿⣯⣤⣀⡀⠀⠉⠀⠀⠀⠀⣿⡏⠀⠀⢹⠈⢿⣧⣴⣿⣿⣿⣶⣽⡿⣳⣟⣣⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇⠠⠿⠿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⢿⡆⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇⠴⠿⠿⢿⢿⠿⣿⣿⣴⣿⣭⣽⣟⡻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣯⠹⡿⣿⣧⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡄⠹⠻⣿⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⢞⣿⣿⠏⠘⣿⣿⠀⠀⠁⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⢊⣿⡿⠃⠸⣿⣿⠀⠀⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⠁⠸⡿⠃⠀⠀⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡜⠁⢸⡿⠁⠀⠈⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡾⠁⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡞⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⣤⡀⠀⠀⢀⣿⠀⠀⠀⠀⠀⣠⣶⣾⣷⣶⠆
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⣀⣀⠿⣿⣶⣄⢸⣿⡀⠀⢠⣠⣾⠟⣡⣴⣶⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠚⠛⠋⡉⠉⢉⣽⣿⣿⣿⣿⣝⢷⣿⡅⣴⣿⣿⣏⡴⠟⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⣤⣤⣄⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢧⣌⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢶⣾⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣷⣭⣭⡓⠈⠿⣷⡶⢌⠙⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠉⠛⠿⢀⠀⠈⠛⠆⠐⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠟⠙⢸⣿⣿⣿⣿⡙⢻⡟⣷⡄⠀⠀⠀⠩⡷⣤⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢀⣾⢿⠃⡏⣿⠁⠈⣿⣹⣷⠀⠀⠀⠀⠈⢟⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⣧⡏⠀⠀⢻⣟⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠻⠛⠁⠀⠀⣸⠃⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢸⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣠⣠⡀⢀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⢀⢀⢳⣼⣾⣿⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣯⣾⣌⣄⣠⠀⠀⢦⣻⢿⣿⣣⢡⠀⣀⣤⣼⣾⣿⣿⠟⠋⡠⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠻⢿⣿⣿⣿⣷⡄⢨⣿⣿⣿⣧⣦⣶⣿⣿⣿⣿⣻⣥⣦⣼⣽⣾⣿⣿⣾⣷⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣶⣵⣮⣷⣴⣴⣧⣦⣙⢿⣿⣿⣿⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣁⣀⡠⢂⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣔⣠⣦⡰⣌⢻⣹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⣶⣿⣿⣿⣷⣿⣾⣷⣷⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢤⣶⣶⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣯⣹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣟⡻⡟⠿⠛⠿⠿⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⠚⠛⠿⢿⠿⣿⡋⣭⠿⢷⣭⣿⣿⣿⣿⣿⣿⣿⡿⢟⣋⣍⣶⣾⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣼⣿⣿⣿⣿⣿⣯⣙⣭⣴⣿⣾⣮⣿⣽⡳⢎⣁⠁⠈⠛⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⣿⣿⣿⣿⠯⠋⠁⢀⣴⣶⣿⣿⣿⣿⠃⠻⣷⣼⣿⣝⣿⣿⣿⣿⠿⣾⣿⣝⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⣾⣿⣯⡿⠋⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠀⠀⠹⣿⣤⡙⠿⣿⣿⣟⣷⡝⢿⣿⣿⣯⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣹⣿⣟⠂⠘⢿⣿⣿⡋⠀⠙⠻⠿⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠁⠀⠀⠀⠀⠀⠀⢀⣾⡟⠛⠁⣼⣿⠇⠀⠀⠀⣿⠿⠏⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⢀⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣽⣯⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⡀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣾⣿⣿⣿⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣷⣿⣯⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⣩⣽⣿⣿⣿⣿⣿⣍⡁
⠀⠀⠀⠀⠀⠉⠉⣛⣿⣿⣿⣿⣿⣿⡛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢠⣾⠿⢛⡽⣿⣿⣿⣿⠻⣿⣦
⠀⠀⠀⠀⠀⢠⣾⡿⣿⣿⣿⣿⣿⡻⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣴⠋⣸⣿⠏⢿⣿⡄⠀⠙⠇
⠀⠀⠀⠀⠀⠟⠁⠀⣿⣿⠹⣿⣏⠻⣄⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡴⠟⠁⠀⢘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⠛⠦⠘⢦⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣾⣿⣿⣴⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⡠⢀⣤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣧⡅⠢⡀⠐⣿⣦⡀⠀⠠⢊⣶⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣻⣧⠬⠢⡙⣿⡰⠠⢁⣾⠛⢁⢄⣤⡶⠦⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠺⠿⡷⣶⣤⣐⠺⣗⡑⣘⣧⡇⣽⣭⣯⣴⠟⠛⢉⣁⠠⣄⢤⡨⣤⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣈⠍⣉⠁⡛⠻⠿⣵⠢⡘⣯⣅⠟⡵⢋⣰⣦⡙⠧⠙⠳⠙⠃⠙⠈⠑⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣵⢟⡾⣻⠇⡾⢃⡾⣱⡾⡄⠨⣙⢺⣼⣿⠏⠔⢃⣨⣍⣭⣭⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠀⢠⣂⣥⡦⣶⡶⠖⠐⣾⣡⠛⡏⢙⡭⠥⠬⣍⢩⡉⠛⠫⢛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢛⠝⠃⢡⣠⢞⣩⠿⣀⣸⢈⡿⠫⡐⢦⣦⣼⣳⡗⢰⡄⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⡄⠿⢈⣧⣾⢃⡈⠀⡇⡁⢨⡌⢦⡄⠩⠙⠋⠇⠘⢱⣷⡲⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣴⣆⠻⠀⠘⠇⡇⢬⡏⠀⠁⠁⠐⣯⡈⡼⡂⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠸⠉⠀⠀⠀⠀⠡⡸⠍⢀⡄⣀⠠⠞⠀⠘⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠦⠘⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠂⠒⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠦⠶⢔⡋⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣛⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣥⡂⠀⠀⠀⢱⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠇⠀⠀⠀⠀⠀⢠⣾⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠑⠮⣶⣄⠀⡎⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠹⠟⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⣀⡀⠀⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠉⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠍⠀⣀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠺⡗⠒⢻⡟⢛⣷⡾⠿⠶⠶⠶⣶⣺⣿⣿⡀⠀⠀⣽⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⡇⠀⢸⣇⡿⠋⠀⠄⡓⠀⣱⣿⣿⣿⣿⣿⣶⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣤⣧⣤⣼⣿⣆⣀⡄⡊⠯⡐⠌⠙⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣰⠏⣀⣞⢡⠏⢰⠁⣼⠁⡞⢡⡿⠻⣷⡌⠀⢀⡈⠙⠋⠀⠀⣀⡀⠀⠀⠘⢋⡟⠛⢛⡟⠻⡆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⠉⠉⠑⠛⠒⠓⠴⡇⣼⠀⠀⠘⡷⠌⣂⠈⠛⠀⠀⠀⠛⠁⠀⠀⡀⡸⠀⠀⣸⠁⠀⡷⢠⡆⠀⣦⠤⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠀⠀⣿⠛⡟⣹⡧⣠⠄⠠⡄⠐⡒⢾⣄⣇⠀⠀⡟⠀⠀⡇⠈⠉⠉⠉⣀⡠⡇⢸
⠀⠀⠀⠀⠐⣄⠠⣿⠀⣾⠀⠀⠀⣠⡎⠀⠀⠀⢸⠀⠀⠀⢸⣘⣦⣀⣴⠄⣋⡀⠾⣆⠋⢠⠆⠹⠟⠶⡇⠀⠀⡏⠈⠉⠉⠁⠀⢀⠇⢸
⠀⠀⠀⠀⠀⠈⠓⣿⢀⣿⠀⢀⡔⣹⠀⠀⠀⠀⢸⡆⠀⠀⢸⠉⠀⠀⠀⠉⠉⠉⠁⣟⠀⢨⡂⠀⠀⠀⡴⠀⠀⣷⠤⡤⢤⠖⡚⣻⠀⢺⠂⠀⡀
⠀⠀⠀⠀⠀⠉⣷⡟⣷⣿⠀⣾⢷⣏⠄⠀⠀⠀⢸⡇⠀⠀⢸⣆⣀⣤⡤⠤⠤⠶⠶⡟⠃⣀⠓⠛⠛⠻⡆⠀⢸⡇⠚⠐⠒⠘⠉⡯⠀⢀⣀⠼⠁
⠀⠀⠀⠀⠀⣀⣸⡗⣿⠿⠐⢻⡿⠏⠀⠀⠀⠀⢸⡇⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢱⡀⠉⠀⠀⠀⢠⣇⣀⣸⡧⠄⠀⠠⠄⣺
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⣮⣯⣴⣷⣦⣄⡀⠀⢸⡇⠀⠀⢸⣇⠀⣀⣀⣀⣤⡤⠤⢾⡇⣾⠒⠚⠛⠋⠉⡿⢹⠁⠒⠒⠀⠉
⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⠳⡾⣷⠖⠚⠛⠉⠉⠉⠀⠀⠀⠀⠀⢘⠦⢽⣠⣤⣤⢲⡶⡇⣼⡀
⠀⠀⠀⠀⠐⣎⢙⠛⠛⢻⠛⠋⢩⣠⠏⠉⠓⢶⡇⣿⠀⢀⣀⣀⣀⠤⣤⣶⣒⣿⡟⣾⠀⢘⣶⢿⡺⣿⣛⣷⣿⣽⣦⣄
⠀⠀⠀⠀⠀⠈⠛⠶⠶⠾⠶⠾⠛⠁⠀⠤⡤⣶⣧⣿⣿⣛⣥⣿⣍⡾⡿⡲⣟⢟⣫⣹⠀⢸⡿⢿⠻⡟⣏⣻⡹⢬⣆⠳⣿⣂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣟⣏⣯⣷⣶⣷⠿⡟⢿⠻⣏⣿⠹⣇⠸⣟⣸⣧⣽⣷⣬⢿⡶⣟⣟⣿⢯⣻⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣭⠧⣽⡞⢷⣏⣘⣷⣤⣿⡶⢿⢟⢻⣻⡻⣝⣎⣮⣷⣷⢿⣾⠿⣿⣻⣯⣽⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⣟⣿⢻⡙⣟⣦⣳⣽⣼⢾⣶⠿⣿⡻⣯⢻⣦⣹⣷⣿⣿⡿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⢿⣝⡻⣮⣿⣶⣿⣷⣿⠿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⢦⣄⠀⠀⢠⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣌⣻⣷⣴⣿⣥⣴⣾⠿⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢀⣀⣩⣽⣿⣿⣿⣿⣿⣿⣿⣁⣤⣤⣴⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣛⠛⠛⠿⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠦⠄⠀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣷⣉⠻⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠺⣻⣷⢾⣿⠟⢩⣿⣿⠏⢰⣿⣿⣿⣿⣿⡌⠛⢿⣿⣷⡀⠉⠻⣿⣶⠲⠶⣶⣄⣀⠀⢠⣼⢟⣡⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣟⣡⣼⠷⠒⢾⣿⠟⠀⢸⣿⣿⢿⣿⣿⣿⡆⠀⠀⠙⠷⠀⢀⣨⣿⣦⣤⣤⣙⣿⣷⣿⣿⣿⣟⣉⣉⠉⠉⠒
⠀⠀⠀⠀⠀⢛⣷⣿⣿⣿⣿⣏⣠⣤⣤⣾⣿⣦⣄⣸⣿⣿⠀⠨⢿⣿⣿⡆⠀⠀⣴⠟⠛⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣟⡉⠙⠛⠦
⠀⢀⡤⠾⠟⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠉⣿⡏⠀⠐⠀⠙⣿⣧⠀⠘⠁⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣯⣿⣯⣹⣷⣦⡀
⠀⠉⠀⣤⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠁⠀⠘⠇⠀⠀⢀⠀⠘⠿⠀⠀⠀⠀⣠⣾⡿⠟⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⢀⣾⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⠛⢷⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⣾⠟⠉⣰⣿⣿⣿⣿⣿⣿⣿⣧⠙⣿⣿⠻⣿⡀⠙⠷
⠀⣼⠋⠠⠟⢡⣿⠟⣿⣿⢻⣿⣿⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠰⠛⠀⢄⣾⣿⡿⠛⣿⣿⠀⠙⣿⠀⠈⠁
⠀⠻⠀⠀⠀⣼⡟⢰⣿⠇⠘⣿⣿⠀⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⣿⠟⠀⠀⣿⡿⠀⠀⠙
⠀⠀⠀⠀⠀⣿⠃⠀⠟⠀⠀⢻⣿⠀⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢇⢠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠸⡇⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠄⠀⣿⠈⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡅⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣰⣿⣇⣠⣿⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠟⠙⠛⠋⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣤⣤⣀⠀⠐⠋⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⠤⠤⠤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣻⣿⣷⣾⣟⣛⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢤⡀⠀⠀⠀⠀⢀⠤⣠⣒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠷⣌⡒⢄⠐⢿⡷⡄⠀⡐⢡⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⣩⡿⢶⡑⡈⢿⡴⡐⣀⣟⣋⠠⣰⣶⣒⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⡻⣿⣶⣬⣙⣯⡌⢜⣗⡧⢮⣷⣵⠿⠋⣉⢤⣔⢦⣴⣦⡶⣅⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡒⣨⣡⠄⣠⢄⡉⢙⠛⢿⣐⢌⣷⣰⣃⠞⠁⣐⣶⡙⠋⡉⠃⠉⠀⠁⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣠⢧⠟⠽⠻⠋⠘⣋⠾⠭⠟⠂⠐⢬⡹⣾⣿⣱⣋⣥⣴⣶⣶⣶⣦⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⣮⡴⣖⡺⠛⢋⣈⣽⠴⢌⢅⣸⣒⠒⠒⠄⣤⢈⡉⠃⢍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡩⠓⢡⠰⡶⣫⡴⠋⠢⠆⡤⠃⠁⠌⠻⡷⣯⣿⠁⡿⢠⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⢆⠉⠃⡷⠿⠠⣄⠀⠧⠄⠸⡆⡾⣇⠐⠈⠉⠃⠁⠻⣯⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡶⡿⠈⠀⠀⠁⠀⠐⠤⠀⠀⠀⠨⣷⠐⣫⡄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠃⠀⠀⠀⠀⠀⢯⡓⢰⠂⠂⠀⠁⠀⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⣾⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠉⠒⠈⠉⠛⢻⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣤⣮⣴⣾⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⡛⣿⣿⣿⢿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠖⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣁⠖⣛⣿⣿⣷⡀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢬⣿⣿⣿⡄⠀⣼⣿⣿⣟⣷⠶⠌⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣭⣁⣀⣈⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣩⣾⣿⣿⢿⣿⣿⣿⣷⣾⢿⣿⣹⣿⢿⣿⣿⣳⣍⠫⠳⡙⢜⢿⣻⣷⡶⣤⡀
⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⡿⣻⢿⡟⡱⡫⡟⣱⠿⠫⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠄⠈⠁⠀⠀⠈⠀⠈⠈⠈⠇⠈⠇⠹⠹⣷⣄
⠀⠀⠀⣐⣬⣿⢟⣽⡿⢋⠜⡡⢋⠜⠁⠀⠈⢀⣤⣾⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⢠⣾⣿⣿⢏⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣻⠏⠸⠃⢹⣿⠛⠛⠁⡿⡿⣿⢿⣿⣧⣄
⢰⣿⠟⢰⠃⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠀⠉⠀⠀⠀⣸⣿⠀⠀⠀⠃⠁⡿⠘⣿⢻⣿⣷
⠰⡏⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣿⡇
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣧⠁⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡝⠋⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⠟⢎⠃⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢛⣫⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣩⣤⣶⣿⣿⣿⡿⠿⠛⢋⣉⣉⣡⣬⣥⣤⣤⣴⣶⣶⡶⠶⠶⠶⠶⠶⠖⠚⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣈⣴⣾⠿⠛⢋⣭⣿⣭⣴⣶⣿⣿⡿⠿⠟⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣴⠿⠛⠉⠀⣀⣤⡼⠿⠛⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⡰⠞⠋⠀⠀⠀⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠛⠛⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣤⡎⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠹⠁⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒
⠀⠀⠀⠀⠀⢀⣀⣙⣛⣛⣛⣛⣛⣛⣛⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⡿⠉⢹⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡏⠉⢿⡇
⠀⠀⠀⠀⠀⣸⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣇
⠀⠀⠀⠀⠀⣿⠃⠀⣿⠁⠀⠀⠀⠀⠀⠀⢠⣿⠀⣸⡇⠀⢸⡇⠀⠸⣿⠀⠀⠀⠘⣿⠀⠘⣿
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⠃⠀⠸⣷⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⢰⡟⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿⠀⠀⢿⡄⠀⠀⠀⢹⡆⠀⢻⡆
⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⠁⢠⡏⠀⠀⠀⢻⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⣸⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⠀⢸⡇⠀⠘⡇⠀⠀⠀⠀⣇⠀⠈⣇
⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡈⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢹⡅⠀⠀⠀⠀⠀⣀⡴⠖⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⠶⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⣼⠋⣠⡎⠀⠀⠀⢀⡴⠛⢁⣄⣠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣸⠁⠈⢹⡇⠀⢀⡴⠋⠀⠀⠀⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠙⣆⠀⢰⡇⠀⠀⣸⠀⣴⠋⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣛⡛⠛⢛⠛⠲⠦⣼⣧⣶⠖⠀⠀⠘⣇⡼⠁⠀⣠⣿⡼⠃⠀⠀⣤⣀⡼⠃⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣛⣿⣀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠘⣿⠀⠛⠛⡿⠁⠀⠀⠀⣸⣏⠤⠞⠛⠋⠁⣈⣉⣉⡤⠿⠛
⠀⠀⠀⠀⠀⣠⣤⠚⠛⠛⣉⠈⠉⠉⠉⠈⠙⠛⠦⣤⣤⡴⠄⠙⠳⣄⠀⢹⡆⠀⢸⠁⠀⠀⣠⠾⠋⠁⠀⠀⢀⣀⠤⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠳⠾⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠣⢄⡀⠀⠘⢷⡀⢳⠀⡺⠀⣠⠟⠁⠀⠈⣻⡷⠶⠿⠭⠒⠒⠒⠲⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠦⠤⠾⣏⣀⣀⠀⠀⠈⠙⠳⣤⣀⠹⣾⣠⣧⠞⠁⢀⣠⠴⠛⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡌⠉⠛⢢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠜⠛⠛⠋⠉⠉⠙⠓⠚⠛⣻⣿⡿⣿⠰⠿⠿⠥⠤⠤⣤⣀⣀⣀⣹⣧⣀⣀⣀⣀⣠⡼⠟⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⢀⣼⣃⣀⣤⡤⢔⣾⠟⢉⣽⢷⡘⣷⡦⣤⣀⡀⠀⠀⣄⠉⠙⠻⢤⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣶⣤⣤⠔⢛⡿⠟⠋⠁⢀⡴⠋⠁⢀⣾⡇⠀⢻⡞⢷⡄⠉⠙⠓⠤⣿⣆⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠴⠛⠉⠁⠀⣠⡶⠋⠀⠀⠀⣠⠟⠀⠀⢠⡟⢸⡇⠀⠸⣷⡀⠹⣦⡀⠀⠀⠀⠉⠻⣷⢤⣤⣶⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⣶⣴⠋⠀⢿⣤⠟⠀⢸⡇⠀⠀⣿⢣⡀⠘⣿⣄⠀⣠⡄⠀⠈⢳⣄⠉⠛⢦⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣠⣾⠃⠀⠀⣸⡏⠀⠀⢸⡇⠈⠻⣷⠈⣷⠒⢽⣎⠻⣏⠀⠀⠀⠀⠙⣦⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢰⣄⠀⣠⠞⢉⡇⠀⢀⡴⢛⠇⠀⢠⣤⣧⠀⠀⠸⡇⠸⡆⠀⠘⣧⠈⠳⣄⠀⠀⠀⡘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣀⣼⠟⠛⠁⠀⣼⠀⢺⡞⠁⣸⠀⠀⠀⠈⢻⡆⠀⠀⢱⡄⢹⡄⠀⠈⢇⠀⠈⠳⣤⣾⠃⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠖⠉⠀⠀⠀⠀⠀⣿⠀⡾⠀⠀⢹⠀⠀⠀⠀⡎⠹⣆⠰⢿⡇⠀⣿⠒⠠⣼⣧⠀⠀⠀⠙⠲⣤⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⠃⠀⠀⢸⡆⠀⠀⢸⡇⠀⠈⢷⡀⢻⡀⠸⡆⠀⠀⠙⡆⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣇⠈⠻⣾⠃⠀⠀⠀⠙⢾⣧⠀⢳⡀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢰⠃⠀⠀⠀⠀⠀⠀⠈⠀⠘⡷⠶⢤⣄⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠓⠶⢤⣀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠳⠶⢤⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠘⠛⠲⠶⢄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠁⠘⠛⠲⠤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⢄⣀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠙⠛⠲⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠢⠤⣄⣀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⡑⠒⠢⢤⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠿⠿⠿⣿⠿⢿⣿⣿⡿⣿⡿⢿⡿⣿⣿
⣿⣦⣾⣶⣴⣦⣼⣤⣼⣧⣤⣼⣧⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣶⣶⣶⣿⣷⣾⣿⣿⣶⣾⣶⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡄⢀⣤⡾⠛⠙⢿⣦⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⣿⡏⠉⢹⣷⡿⠋⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⠀⠀⠈⠻⢷⣄⡀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⠀⣤⡾⠋⠁⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢉⣿⣅⢀⠀⠀⠀⠀⠀⠙⢷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣿⠀⠀⠀⢀⣘⣁⣀⣠⣴⣿⠿⠿⣿⣿⢸⠀⠀⠀⣿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⣿⣿⣿⣿⣿⠋⢀⣤⣿⣿⠿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣰⣿⠟⠋⣷⠒⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⢠⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⠱⣤⣭⣭⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠛⠿⣿⡛⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠶⠖⠲⠶⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠘⠻⠿⣋⠉⠛⠛
⠀⠀⠀⠀⠀⢀⣴⠞⣋⣥⣶⠆⣀⣀⣤⣤⡄⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢠⠏⢶⣶⠒⠶⠾⠆
⠀⠀⠀⢠⡾⢿⣿⠛⢉⣼⠟⠋⠉⣡⣖⣋⣀⣀⣤⣤⣀⠀⠑⢤⡀⠀⠀⠀⠀⣞⣠⣤⣬⣷⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠛⠁⠀⠀⣠⣾⣯⣭⣀⣀⠀⠙⣄⠀⠀⢸⠁⠉⢻⡶⠀⠀⣀⠴⠖⠊⠉⠀⠀⢀⣀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣤⣟⡛⠂⠈⢣⠀⢻⢀⡴⠋⣠⠔⠋⠀⠀⠐⢶⣶⠤⣀⡀⠻⡝⠲⢤⣈⣷⣎⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⡉⠙⠲⣄⢣⣡⠞⣠⠞⠁⠐⠶⢿⡛⠓⠲⠾⣧⠀⠈⠙⢿⡆⠀⠉⢻⡎⠙⣮⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠉⠉⠉⢉⡉⠙⢲⣤⣑⡟⠺⣧⣶⣮⣭⣍⣛⡛⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠿⠙⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡀⢀⢾⠁⡠⢺⢋⡠⠴⣺⠿⣿⠷⠴⢿⣸⠇⠀⣴⡈⢉⡛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢠⡞⣧⡎⢸⣾⠁⠛⠉⠀⠰⣇⣀⡝⢸⡁⢻⠍⢳⣄⣿⣇⢸⣧⠀⣤⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣷⣼⠀⠻⠀⠈⠁⠀⠀⠀⠀⠀⢈⡟⠒⣿⠉⠉⠀⠀⠙⠃⣿⡞⢹⠀⣿⠀⡀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⣀⣿⠀⠀⠀⠀⠀⠀⠉⠀⢸⣴⢹⡇⣷⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣷⣿⣤⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢹⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠒⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠤⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣀⣠⡼⣦⠀⠀⠀⢀⠀⣰⠇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⣇⠀⠀⠉⠀⠀⠘⣧⠀⢠⣿⣠⢿⠠⢊⠠⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡄⢸⠀⢹⣄⣀⣤⡤⠶⠋⠈⢳⡘⣇⠏⢸⡇⣌⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠺⣇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⡀⠁⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⡾⠓⣀⣀⣀⣀⣀⣴⡞⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⣿⠉⠉⡿⠻⠟⠿⢿⠛⢿⠛⣿⠻⠟⡿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣿⣿⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠰⣴⣦⣴⣧⡶⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⣿⣿⣿⣿⣾⢃⡆⣴⣞⡴⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣨⣿⣿⣿⣿⠛⣿⣽⣿⣿⣾⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⣿⣿⣛⡛⠋⠉⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣟⠩⠀⠀⢀⣀⣀⣤⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣠⣾⡿⢱⣿⣻⣿⣿⣿⣶⣮⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣏⠛⠿⡿⡿⡿⠊⠙⠆
⠀⠀⠀⠀⠈⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠿⠟⠌
⠀⠀⠀⠀⠀⠈⣿⠟⣿⣿⣿⠟⢯⡿⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢀⣤⣾⣿⠛⡠⢿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠻⣿⣿⣿⣏⣿⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣟⣿⣅⠀⣿⠋⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⠀⠟⢸⣿⣿⣿⣯⠅
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡟⠋⢳⣿⣿⣿⢷⣿⠀⢁⣿⣿⡿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠉⠙⠻⠙
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠀⠀⣠⣿⣿⡿⢿⢹⣿⠃⠈⠩⠛⢱⣿⣿⣿⣿⢻⣿⣷⣄
⠀⠀⠀⠀⠀⣼⡿⣿⣿⠋⠀⠀⣾⣿⣿⣿⣿⡀⠀⣿⠀⠀⠀⠀⠀⠉⠿⣿⣆⠈⠋⢿⣿⣆
⠀⠀⠀⠀⠀⠋⠁⠁⠀⠀⠀⢠⣟⣿⣿⠟⠻⠁⠀⣿⡆⠀⠀⠀⠀⠀⠀⠋⠿⠀⠀⠀⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⣟⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠟⠉⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠀⠀⢠⡄⢠⠆⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠌⢇⠀⠀⣷⣿⢰⠀⢠⡟⠀⣠⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣄⠀⠐⠚⢧⡀⣿⣿⡿⠀⡞⣰⡼⠋⠀⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣄⢪⣜⣤⢸⣿⡇⣸⣽⠟⠀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣻⣿⣾⣸⣷⢰⣿⣯⣶⠿⠁⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⢿⣦⡵⡘⣯⠻⢿⣾⣿⡿⠿⣷⣤⡴⠟⠛⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⠁⣸⠓⠋⢰⣙⣻⣾⣷⢬⢫⡏⣻⣾⡷⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⠻⡿⢻⣟⣶⣾⣧⡿⢿⠲⠀⢀⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡤⠶⣟⠛⡟⢫⡿⣿⡏⠘⠋⠛⠛⠻⢶⣽⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠸⠅⢙⠀⠀⠁⠀⠀⠀⠐⠿⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠀⠀⠀⠀⠀⠀⠀⢸⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⡀⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢘⣽⢃⣰⡟⠁⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢻⠁⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡬⠿⢿⣿⣶⣦⡀⠛⣸⡇⢀⠖⣁⠀⢈⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠙⠿⣷⠀⣼⣣⠏⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣭⣭⣶⣦⣬⣵⣟⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣡⣤⣜⣿⣿⣾⣶⡭⢙⣷⣶⡶⠦⣝⣣⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⠿⢿⣿⣿⣯⣾⣟⡟⢩⣿⣿⣦⡘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠸⣿⠋⣿⢛⣿⣿⢸⠈⠉⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢻⠋⡰⠈⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⣤⣏⠀⠀⠀⠀⢀⠀⣀⡀⡀
⠀⠀⠀⠀⣠⣤⡤⣤⣤⣤⣤⣤⡉⣭⣭⣽⡿⠿⠩⠈⣿⠤⢬⣕⣛⠚⢻⠉⠉⠩⠁
⠀⠀⢠⣤⡴⠦⣴⣿⣿⣿⣽⠻⠷⠛⠉⠁⠀⠀⠀⢀⣹⣧⠀⠉⠙⠻⢛⣛⣛⠓⢲⣖⣀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠠⢶⡶⢶⣶⣦⣭⣙⢂⣀⡀⡀⠀⠀⠀⠀⠈⠉⠳⣄⠐⠀⠀⠙⠻⢿⣷⠍⠉⡉⠈⠉⠉⠛⠛
⠀⠀⠀⠀⣤⣤⣶⣿⣶⣬⣭⣾⣶⣿⣿⣿⣧⣈⠓⠒⠓⠈⠀⠈⠳⠄⠀⠀⠀⠴⠾⠒⠿⠿⠶⠆⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠤⠒⠶⠶⣾⣯⣤⣀⡈⠛⠋⠀⠲⠾⠿⠿⠿⠻⠒⠒⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢏⣾⣿⣿⣎⢿⣷⢀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣸⣿⣿⣿⣿⣸⡇⣿⣿⢟⡹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠇⠿⠿⠿⠿⠿⠇⢇⣭⣶⣿⣿⣮⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⣿⣿⣿⣿⣿⣇⣧⡹⣿⣿⣿⣿⢏⣼⣿⣯⣭⡍⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢸⣿⣿⣿⣿⢸⣿⠷⣙⣓⣚⣋⠾⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣙⣛⣃⣛⣛⣛⣃⣉⣚⣛⣙⣛⣛⣋⢺⣷⣝⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡞⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⣼⢹⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⢾⠷⣸⣿⣿⣿⣿⣿⡇⡇⣿⢸⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣧⣿⢸⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣸⢘⢻⢸⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣈⣀⣈⣉⣁⣉⣉⣁⣀




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠉⠉⠻⣗⠀⠀⠀⠀⣠⣾⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⢠⡠⢤⠀⣿⣠⣂⣀⣀⣿⠀⠀⠀⠀⠻⠛⠛⠻⢿⣿⡇
⠀⠀⠀⠀⠀⢸⠈⠉⡀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠀⠠⠈⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⣠⠀⠄⠀⡆⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠈⠀⠙⠆⣹⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣻⡔⠊⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣷⣶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠛⢻⠄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒⠀⠀⠀⠤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⣶⠆⠀⢀⠀⠀⢰⠀⠀⠠⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⣀⣀⡀⣠⠂⢀⣀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣆⠀⠀⠀⣠⢠⣼⣾⣿⣿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣀⣄⣀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡆⢀⣾⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⣿⣿⣿⣶⣤⣆⠀⠀⢿⣿⣿⣿⣷⣾⣿⣟⣯⣿⣇⣰⣶⣴⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣿⣿⣿⣷⣦⣼⣿⣽⣿⣿⣿⣿⣿⣡⣾⣷⣿⣯⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠈⠙⠿⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣥⣤⣴⣴⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⠿⣟⣿⠟⢿⠿⢿⣶⣾⣿⣝⣿⣿⣿⣿⣿⡿⠿⣿⣿⡿⠻⢿⣯⢻⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⣀⠐⠋⣽⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠁⠈⠛⡙⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡏⠀⢈⣵⣿⡿⢿⡟⣿⣿⣿⣿⢿⢿⣿⡟⢿⣿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣷⣦⡀⠀⠀⠀⣰⣿⣿⠋⢀⣴⣿⣿⡿⡝⣿⠀⣿⣿⣿⣿⣎⠟⠹⠋⡌⡿⢻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⢀⣼⣿⣿⠀⢠⣿⣿⢻⡝⠣⠉⠀⠀⣿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠘⠉⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢿⣿⣷⣾⣿⣿⣋⣰⣿⣿⣹⣧⣵⣶⣶⣶⣤⣿⣏⢸⣟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢣
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⡿⣿⣿⣷⣶⣀⡀⢨⣿⣿⣿⣿⡟⢉⣿⣿⣿⣿⣿⠟⠋⠉⠈⠉⣿⣿⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠁⠀⢲⣿⣿⣿⣾⣿⣿⣿⣿⣵⣾⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⣿⣟⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣸⣿⣿⣯⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⣿⡯⠀⠀⠁⠃
⠀⠀⠀⠀⠀⣴⣿⢿⠛⠉⠈⠁⠀⠛⠛⢛⣩⣿⣿⣿⣿⣿⣿⣿⣏⠉⠁⠀⠀⠀⠀⠉⠛⠀⢠⣿⡇
⠀⠀⠀⠀⠰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢹⣿⡟⣿⡿⣿⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⣿⣿⠀⣿⡇⣿⡇⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⢹⡇⠀⢻⣇⢹⣧⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠈⠁⠀⢸⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⢰⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⢀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⣿⣿⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣶⣶⣿⣿⣿⣿⣿⣠⣴⣶⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠉⠉⠀⢈⣛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣟⡛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢀⣠⣴⣶⣵⣾⣿⣿⡿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣠⣿⣿⡿⠿⠿⠟⠋⠀⣴⣿⣿⡿⠛⣿⣿⣿⣿⣿⡟⠻⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠴⣾⣿⣿⣶⣦⣽⣿⣿⣿⣷⣶⣶⣶⣤⣤⣼⣿⢿⡿⠁⠀⣽⣿⡏⢻⣿⣿⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣯⣭⡀⠈⢹⡿⢹⣿⠃⠀⠀⢺⣿⡇⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⢀⣴⢿⠿⣿⣿⣿⣿⣿⢿⣿⣯⡙⠻⣿⣷⣜⢀⣿⠇⠀⠀⠀⠝⣿⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⢠⣿⡿⢻⣿⡇⠈⣿⣿⣷⡀⠀⠉⠉⣾⡟⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢸⠟⠁⢸⣿⡃⠀⠘⣧⠻⡇⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⢻⡆⠁⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⣤⣝⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢋⣤⣶⠄⡈⣿⠂⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢀⣀⠤⣊⡑⢄⠀⢀⠞⠉⠴⢿⣿⠇⣠⣿⠸⣇⠐⣦⣄⡉⠓⠢⣀⡠⠄⡊⠠⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠀⠀⠀⠠⠴⠚⣹⠃⠀⢙⣡⡆⠀⠊⠩⠵⠞⠁⠙⠃⠻⠓⠌⠳⠈⠲⠤⠀⠀⠀⠓⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢶⡟⠛⠒⠀⠀⠀⠁⢀⣄⠉⠀⠛⠀⠀⠀⠀⠀⠀⠾⣿⣷⣤⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠁⢂⡀⢄⠀⠀⠀⠰⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⠀⠀⠀⠀⠑⢄⡀⠄⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠙⠢⣀⠀⠀⠀⠻⢄⠀⠀⡄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠀⠀⠀⠈⠳⡄⠀⠀⠈⢂⠀⠇⠀⠀⢀⠁
⠀⠀⠀⠀⢀⡀⠄⠐⠀⠐⠃⠀⠀⠀⠀⠀⠀⠓⢤⣀⠀⠀⠈⢠⡁⠀⠀⣦⠀⠀⠀⠸
⠀⢀⠄⠂⠁⠀⠀⠠⠀⠀⠀⠐⠂⠒⠂⠀⠀⠀⠀⠉⠢⡀⠀⠀⢧⠀⠀⣼⠀⠀⢀⠃
⠤⠁⠀⢀⣀⣀⡀⠀⣀⠀⢄⡀⠀⢀⣀⡀⠠⠤⠤⠤⠤⠽⢦⣀⣦⠀⠀⢂⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣀⣤⡴⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡊⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠻⢋⠁⢄⡀⠀⠈⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⡠⠔⠚⢧⠀⠃⠈⢢⡀⠙⢦⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⢡
⠀⠀⠀⠀⡔⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⡀⠤⠒⠈⠁⢀⠈⠓⠄⠀⠀⠀⠀⠈⠂⠀⠣⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠄⠂⠁⠀⠀⠀⠀⠠⣀⠉⠃⠀⠀⢸⠀⠀⠀⡀⠀⢄⢡⠀⠑
⠀⠀⠰⠀⠀⣀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⠉⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠱⡆
⠀⠀⠠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠢⠤⠀⠀⠀⠀⠀⡇⠀⠀⠈⡀⠀⠀⠸⡄⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠓⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡉⠓⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⣋⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢸⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠀⡔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠠⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠂⠀⠠⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⠂⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠐⠀⠐⢒⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⠈⠁⠀⢂⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠈⠉⢊⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡔⠁⠀⠈⢂⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠌⡁⠀⡈⢂⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠌⠀⠀⠈⢡⡱
⠀⢀⠀⠀⠀⠀⠀⠀⠀⢐⣀⣀⣀⣀⣀⣀⣘
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣴⣦⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡠⠊⠢⡀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢄⠀⠀⠀⠀⢀⣴⣷⣄
⠀⠀⠀⠠⠊⠀⢌⠆⠈⠢⠀⠀⠐⠀⢰⡆⠀⠀⡀⠀⠀⠠⠊⠀⢈⡀⠀⢐⡀⢀⣴⣿⣯⢩⣿⣷⣄
⠀⠀⠀⠀⠀⣸⣀⣺⡀⠀⠀⠀⠀⢰⣏⣹⡆⠀⠀⠀⠀⠀⠁⢰⣂⣸⡀⠈⠀⠀⢸⣿⢱⣶⢹⣿
⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠐⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋
⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⣠⣄
⠀⠀⣸⣿⣛⣻⠀⠀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⠉⣽⡉⠑⠀⠀⠀⠀⠀⢻⣿⠇⠀⠀⠀⢿⡿
⠀⠀⠃⠿⠤⠾⠈⣾⠀⣾⠀⠀⠀⠀⠘⢿⣿⣋⣀⣿⣄⣀⠀⠀⠀⠀⣠⣾⣿⣷⡄⢀⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠼⠿⠗⠿⠶⠀⠀⠠⠾⠿⠿⠿⠏⠉⠉⠉⠁⠀⠸⠇⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣶⣦⣄⠀⠸⢴⡇⠀⣠⠖⠁⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣷⡀⢸⡇⡴⠁⠐⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣘⣈⣁⣐⣀⡽⣧⣿⣽⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠛⢋⡝⣿⣻⣻⣟⣛⠛⣿⣉⣭⣍⡛⢻⡋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⣳⣷⣿⣿⡿⣻⣿⣼⡖⣿⣿⣬⡙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⠃⠉⠩⣿⡿⢾⣿⣿⣿⡈⠛⠿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡿⠁⢻⣿⠅⡃⠀⠈⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⠃⠐⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣀⣤⣇⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⢠⣤⡴⣦⣤⣄⠠⣤⣄⠤⣤⣤⣿⡿⠖⠀⠈⣻⠦⢤⣔⣂⡐⢋⡍
⠀⠀⢀⣤⣴⠦⣤⣶⣯⣽⣾⡟⠿⠞⠛⠉⠁⠀⠀⠀⢀⣹⣧⠀⠈⠙⠛⠺⣛⣛⡓⠒⣶⣂⡀⠀⣀⣠⣄
⠀⠀⠀⠀⠠⢴⣤⣶⣶⣶⣬⣙⡓⢀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠱⣄⠐⠁⠀⠈⠻⢿⣷⣌⠉⢉⠁⠈⠉⠙⠛⠓
⠀⠀⠀⠀⣠⣤⣴⣶⣧⣬⣭⣥⣷⣼⣿⣿⣿⣄⡙⠒⠖⠒⠂⠀⠈⠳⠄⠀⠀⠀⢠⡼⠷⠶⢿⠿⠦⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠀⠤⠽⢬⣭⣽⣍⣀⡀⠐⠒⠚⠂⠴⠶⡶⣶⠾⠶⠦⠶⠄⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠙⠋

⠀⠀⠀⢀⣄⣤⣤⣶⣔⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⡀
⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣶⣲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢅⣲⣵⣼⣿⣿⣾⣦⣠
⠭⢭⣭⣽⣯⣿⣽⣿⣟⠿⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣴⣿⢿⠟⠛⠛⠛⠿⠿⢿⣷⡄
⠢⡆⠺⣯⣽⣿⣿⢿⣶⣯⣭⡭⠝⠿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠩⠬⢟⣻⣿⣿⣷⣾⣶⡖⣶⣼
⣲⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠭⣼⣷⣿⣿⠿⠟⠛⣩⣾⣿⣿
⢪⡿⢻⣿⣿⣿⣟⡿⡿⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⡿⠛⠁⠀⣠⣾⣿⣿⠿
⠹⢡⢻⣿⣿⣧⣬⣭⣴⡄⠙⠻⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡿⡿⠁⠀⣠⣼⣿⡽⡿⠏
⠀⠀⢻⣿⣿⣿⣯⣿⣛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⣴⣿⣿⢏⢃⠁
⠀⠀⠀⠙⠏⡟⡿⣿⡢⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢟⠜⠌
⠀⠀⣀⣀⣀⣀⡃⢿⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⠁
⢉⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣄⢀⢀
⠀⠀⣿⣽⣿⣿⣿⣿⡸⡿⡿⣿⡯⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣷⣵⣽⣾⣾⣿⣾⣦⡀
⢖⠿⣿⣿⣿⣯⣟⣿⣆⣃⢡⠁⠁⠜⠹⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠛⠛⠻⠿⠿⢿⣿⣿⣿⣷⣦
⠀⡇⣿⢸⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿
⠀⠀⠙⠊⠞⣿⣿⣿⣿⣿⣶⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⠈⠛⠻⠹⡿⠻⣷⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠈⠠⠪⢊⠟⡝⢱⢿⢾⠿⡿⠟⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⠐⠄⡀⠀⡀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⡼⠉⠀⠀⠈⠉⡸⠀⠀⠀⠀⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠑⣀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠑⠦⠄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⡄⠂⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⡀⢀⡇⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠘⠄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠊⠀⠀⠀⠈⠐⢒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⠔⡲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣆⠀⢦⠤⠤⠀⢀⣀⢀⠐⠒⠀⠒⠒⠒⠒⡆⡠⠊⠀⠀⠀⠀⢀⡔⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠈⡄⠀⡄⠀⡾⣿⠋⠀⠈⡶⠠⠤⠤⠤⠔⠋⠀⠀⠀⠀⢀⡠⠊⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠰⠀⠸⡄⠉⠁⠀⠀⠐⠦⠄⢀⣀⣀⣀⣀⣀⡠⠔⠊⠁⠀⠀⠀⠀⠈⠲⢄⣀⠀⠀⠀⠀⠀⣀⡠⠤⠚⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⢠⠛⠉⠉⣩⠛⠁⠒⠒⢦⠤⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⢉⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠓⠓⠒⠒⠒⠛⠓⠛⠛⠿⠿⠷⠶⠶⠆⢤⢤⠤⠄⠀⠀⠀⠤⠤⠄⠒⠉⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡎⠀⠀⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠳⣀⢀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⣀⢀⡀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⣼⡀⠀⠀⢀⣀⣀⣀⣀⠀⠤⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿