Barbecue Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣉⣉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⡆⣿⣹⡆⡾⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠿⣈⡷⡏⣨⡗⢧⡼⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⣦⡀⠀⠀⠠⣤⡤⢠⡄⣤⢀⣤⢡⡤⠀⠀⠀⠦⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡆⠀⠀⣾⠀⣸⢸⣿⡿⣿⣟⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣯⣤⣤⣤⣬⣤⣭⣤⣤⣥⣥⣭⣥⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠉⠉⠛⢻⠛⠋⠉⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣀⣀⣸⣆⣀⣀⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⢻⠟⠛⠛⠛⠛⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⢿⣿⠿⢿⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣮⣶⣦⣴⣧⣾⣯⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⣦⣂⢀⣀⣀⡠⠘⣀⠀⠀⢰⡀⠀⢠⣤⣴⣶⣿⣿⣷⣦⡀⠀⠠⠀⠀⢀⡠⣶⣟⡷⢲⡦⣀
⠀⠀⠘⠏⡠⢨⡡⠰⠴⠞⣋⡄⠀⠀⢧⠀⠐⢍⠻⢿⣿⣿⣿⣷⠇⠀⡤⣢⠄⠀⢀⣏⡟⣵⢏⡾⣻
⠀⠀⠀⠈⠒⠪⠦⠮⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠁⠲⡿⠟⠋⠁⠀⠀⠐⠃⠀⠀⠈⠙⠿⢿⣶⠿⠋
⠀⠀⢀⠀⠄⠀⣀⣀⡀⠀⢈⠀⢀⣀⠀⠀⢀⣤⣀⣀⡀⠀⣤⣄⡀⠀⠀⠠⠀⠀⠀⠀⠄⠀⢀⣀
⠀⠀⠀⠑⠂⠘⠿⢿⠯⠀⣨⣃⠋⠁⠀⠐⠀⠉⠛⠃⣁⣈⡀⠀⠀⠀⠀⡇⢇⡳⠾⠀⡜⠀⠹⠮⠇
⠀⠀⠀⢀⡄⣠⢀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠃⠛⠛⠚⠛⠒⠋⠉⠀⠀⠀⠈⠲⠤⠛⠋⠀⢀
⠀⠀⢴⣫⠎⠴⣫⣬⠇⢠⠀⠀⢴⣩⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠆⠊⠉⠁⠁⡸
⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠯⠂⠀⡠⠐⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⣄⠀⠀⠀⣭⠄
⠀⠀⠀⢀⠔⡺⢔⢢⣤⣤⣀⡀⠀⠀⠀⣠⣤⣶⣾⣁⣠⠄⠒⠉⠀⠀⠀⠀⠀⠱⠴⠫⠛⣓⠔⠚⠁
⠀⠀⠈⢿⡾⣴⣵⣋⡴⠋⣩⠼⠂⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠔
⠀⠀⢀⠀⠈⠙⠛⠝⣋⠿⠁⠀⠀⠀⠀⠘⠻⣟⠛⠛⠛⠛⠛⠉⠀⠠⠤⠶⠂⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠃⠔⠀⣀⠀⠀⠀⠀⢀⣶⣿⣻⣧⠀⠀⢨⠋⠀⠐⠛⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣰⣿⣻⠦⡄⠀⣿⣿⡿⠛⠁⠀⢀⠞⠰⠶⢷⣞⢛⠀⠀⢠⠀⠀⠁⠀⠀⢻⡇⠀⡄⠀⢸
⠀⠀⢀⣜⡿⣭⣻⣷⠁⠀⠈⠁⠀⠀⢀⣀⠎⢀⣀⣄⠸⣿⠟⡄⠀⠀⠀⠀⢰⠰⠀⠈⠀⠀⢣⠀⢠
⠀⠀⠈⠙⠷⣍⠝⠁⠓⢦⠀⠀⠀⠀⠸⣿⠟⠓⠒⠒⠒⠒⠚⠓⠀⠀⠀⠀⢘⡇⠀⠀⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠃⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢉⣹⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⣛⣻⡟
⠀⠀⠀⠀⠀⠀⠀⢹⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⡁⢀⡀⠦⢥⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠋⢉⡄⢀⡶⠀⣿⡾⢡⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠾⠛⠉⠁⠀⠠⠴⠿⠿⠾⠿⠶⠿⠿⠾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⠶⣶⠛⡻⠛⣻⠛⣹⠟⢛⠟⢓⡶⢤⣀⣤
⠀⠀⠀⠀⠀⠘⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⢳⡾⠧⣾⣥⣾⣁⣴⣁⣴⣯⣤⡾⢴⡞⠳⣿
⠀⠀⠀⠀⠀⠀⠹⣧⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢿⣿⣿⣿⣿⣿⡿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢩⣤⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠈⣿⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⡶⣶⠖⡶⢒⣿⢶⡶⢶⠦⣿⣇
⠀⠀⠀⠀⠀⢀⣾⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣯⣞⣡⣞⣠⢋⣿⣋⣴⣣⣾⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠉⠉⠉⠉⠉⠿⠏⠉⠉⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄
⠀⠀⠀⠀⠀⠀⢀⡀⣿⠓⣿⢧⣴⠀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⢰⡄⠀⠀⠀⠀⢀⠈⠲⣄⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢀⣀⣈⣛⣁⣀⣀⣈⣉⣟⣃⣀⡀⠀⠀⠀⠀⣷⡈⣿⣿⣾⣿⠀⠀⠀⠀⠀⠱⣤⣾⡀⠀⠀⠀⢈⣿⣿⡿⠋
⠀⠀⠀⠐⠒⢿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠒⠀⢠⠀⢻⣿⣿⣿⢻⡟⢠⡄⠀⠀⠀⠀⠀⠀⠙⢦⣀⡴⠋
⠀⠀⠀⠀⠀⠘⢷⣹⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢺⣷⣿⡿⠙⠇⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡴⠛⢢⡄
⠀⠀⠀⠀⠀⠀⠀⣹⠻⠿⠿⠿⠟⢿⠁⠀⠀⠀⠀⠈⠻⠁⠉⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⣠⣴⠋⠁⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⡞⠒⠒⠒⠒⠒⠒⠒⠺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠁⠀⠀⢀⠀⠀⠀⢀⡀⠀⠈⠋⠃
⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⣠⡴⣾⣛⣛⣶⢦⣄⠀⠀⠀⠀⠀⠀⢀⣿⣆⠀⢀⣼⣧
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡾⡿⠋⠁⠀⠀⠈⠙⢿⢷⡀⠀⠀⠀⠀⣾⣿⣿⡆⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠀⣾⢿⠁⠀⠀⠀⠀⠀⠀⠈⣿⣷⠐⡆⠀⠀⢻⣿⣿⡇⢸⣿⣿⡇
⠀⠀⢀⡴⢣⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠸⠀⢿⣼⡀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠐⠇⠀⠀⣼⣿⣿⡃⢸⣿⣿⡇
⠀⠀⠚⣴⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣷⣤⡀⠀⠀⢀⡤⣮⡿⠁⠀⠀⠀⠀⠻⠿⠿⠂⠸⠿⠿⠃
⠀⠀⠀⣿⢿⣿⣿⡿⠋⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠿⢿⡿⠿⠞⠋
⠀⠀⠀⢻⡌⢿⡟⠁⠀⠠⡘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠰⠐⠄
⠀⠀⠀⠀⢻⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣤⣤⣤⣤⣴⣶⣿⣿⠟
⠀⠀⠀⠐⠒⢻⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠈⢷⣜⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⣰⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡧
⠀⠀⠀⠀⠀⠀⠀⢹⠛⠿⠿⠿⠟⢻⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡼⠒⠒⠒⠒⠒⠒⠒⠺⡄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⢠⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣟⣋⣁⠀⠉⠙⠒⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠟⠉⠉⠑⠂⠘⠛⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠇⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠘⠆⠀⠀⡀⠀⠀⠀⠐⠋⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⡔⠂⠀⠀⠀⠀⠀⡀⠴⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢤⣄⠰⠞⠁⢠⠁⠀⠀⠀⢀⣤⡞⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⣾⣯⠁⠀⠀⠀⠑⠐⢲⣾⠿⠟⠀⠀⠟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⢀⠠⢈⣿⢀⠀⠀⠀⠀⠜⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠁⠀⠟⠙⠛⢷⡄⠀⠀⢀⠊⣡⠉⠓⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠁⠐⠓⠶⠶⠖⠀⣴⠁⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣷⣾⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⣿⠀⣀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡆⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠒⢤⣀⠀⠀⠀⠀⢀⡠⠤⠀⢤⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣿⣄⠀⠀⠀⢀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠖⣀⠀⣠⣄⠀⠀⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣾⡟⠉⠳⡄⠈⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠁⡀⠀⡈⣉⣅⠔⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⣾⠁⠀⠀⠈⢆⡀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠻⢷⣤⠀⡇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣿⠀⠈⡇⠀⠀⠀⢀⠘⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡇⠀⠀⠀⠀⣀⡀⠀⠀⠁⠀⠀⢸⠀⢸⣧⠰⢀⡴⠁⠀⠀⠀⠀⣰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣦⣀⡿⢰⠎⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣶⣶⡄⠐⠶⠖⠒⠲⠶⠶⠰⠶⡤⢤⣤⢀⣄⡀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡋⢀⡿⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⣠⡴⠞⠛⠃⠀⠀⢿⣿⣿⣿⣿⣿⣿⡶⠒⣶⢶⡶⣶⣶⣷⠿⠿⡇⠀⠈⠁⠈⠛⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣼⣁⠀⢀⣤⠞⠁
⠀⠀⢸⣇⠀⣴⣾⣷⣿⣿⣿⣶⡍⠀⠀⠉⠀⣄⣠⣤⣶⣤⠀⠀⢠⣶⣿⣿⣿⣿⣶⡆⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡁⠈⣿⣿
⠀⠀⢸⠛⠳⠿⣯⣟⣛⡛⠉⠁⠰⣶⠷⠿⠿⠻⠛⠛⠉⠁⠀⠀⠈⠉⠛⠛⢛⣛⣉⠡⠤⢚⡉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠛⠪⠿⢾⡿⠿⣇
⠀⠀⠈⣆⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠚⠶⠶⠶⠶⠶⠶⠶⠗⠚⠚⠚⢛⣋⣭⣭⣿⣶⣿⣿⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠟⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠏⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⣋⠾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠳⣬⡲⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠕⠁⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣝⡻⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣻⡥⠚⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣿⠟⠿⠿⠿⣿⡿⠿⠛⠛⢻⣿⠁⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣀⣀⣀⡤⠤⠾⠗⠀⠀⢀⣀⣸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⣻⣽⣷⡀⠀⠀⠀⠀⠛⠲⣦⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠳⣍⠩⣿⣛⣿⣿⣶⣶⣿⣿⣿⡿⠋⢻⣧⠀⠀⠀⠀⠀⠀⣿⡿⣷⣶⣶⣦⣀⠀⠀⠀⠀⠀⢠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠈⠙⠻⠿⠿⣿⣿⠿⠿⠛⠉⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⢹⡆⠘⠛⠛⢿⣿⣿⣿⣿⣿⣾⠛⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡏⠉⠉⠉⠛⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀⣔⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠿⣛⣫⣭⣭⣥⣭⣭⣭⣛⠻⢿⣿⣿⣷⣴⠞⠋⢺⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣫⣴⠿⠛⣩⡵⠛⠁⣠⠘⠛⠙⣻⣶⣍⠻⣿⣿⣷⣄⠀⠙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢋⣾⠟⣁⣴⠟⠉⣀⣴⠞⢡⢇⣴⠞⢋⢄⣽⢷⣌⢻⣿⣿⣦⡴⠟⠛⠃
⠀⠀⠀⠀⠀⢀⣿⣿⡿⢡⣿⣥⠞⠋⢀⣤⠾⠋⢀⣄⣼⠈⢀⡀⡞⠈⢁⣠⣿⣧⢻⣿⣿⡆
⠀⠀⠀⠀⠀⣸⣿⣿⢃⣿⠋⣱⢯⣙⡒⢧⡠⡶⠛⠁⡙⣷⣶⠞⣡⡴⠛⠁⣠⣿⡆⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⢸⣯⢤⣿⣓⠲⢭⣿⣷⡀⠴⠟⢡⣏⣴⠞⠉⢀⣴⠞⠋⢸⣿⢸⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⢸⣏⢈⡓⠦⢭⣽⠿⠋⠉⢛⠲⣾⣬⣄⣀⡚⠋⠀⣠⠾⢻⡿⢸⣿⣿⠇
⠀⠀⠀⠀⠀⢹⣿⣿⡌⣿⡋⢁⣠⡶⠊⢀⣠⡶⠋⣼⢇⡶⠉⠛⠿⢿⣿⡦⣠⣾⠇⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣷⡘⣷⡟⠁⣠⡴⠟⠁⡀⣸⣿⠀⣀⡴⠟⠁⣀⣼⠞⣽⡟⣼⣿⣿⠇
⠀⠀⠀⣤⢤⡾⠛⢿⣿⣷⣌⢿⣾⡉⢀⣴⠞⢱⣿⡏⠞⠋⢀⣤⠞⠋⣠⡾⢋⣼⣿⣿⠏
⠀⠀⠀⠹⣷⡷⡀⠈⢻⣿⣿⣷⣝⠻⣿⣤⣠⡶⠉⢀⣠⡾⣋⣡⣴⠾⣋⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠘⢿⣿⣄⣴⠟⠻⣿⣿⣿⣶⣭⣝⣛⣛⠛⣛⣛⣛⣭⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠹⣇⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠃⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣒⣒⣒⣒⣒⣒⡲⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⢛⢋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡤⣝⡲⠦⢤⣤⣤⠤⠴⣚⡥⣌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡼⠀⠀⠉⠙⠓⡖⡖⠛⠉⠁⠀⠸⡜⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⢡⡇⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⣷⠹⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⡖⢲⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠐⣦⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣍⠉⠀⠀⠀⠀⠀⣒⡒⠟⠂⠀⠀⠀⠘⠦⣬⡥⠏



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣷⣶⣤⡀
⠀⠀⠀⠀⠀⢀⡴⠿⣿⣾⡟⢻⣷⣆⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠰⢻⣿⣿⣿⣾⣿⣿⣿⣿⠄⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢫⣤⡄⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⠳⠤⠀⠰⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⡿⣿⣿⣿⣿⣿⣯⣿⣛⣻⡿⣟
⠀⠀⠀⠀⠀⢀⠁⣿⣷⡄⠀⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⣿⣷⣾⣭⣿⣻⣿⣿⣿⣿⠏
⠀⠀⠀⢠⠴⢦⡀⠈⠉⠀⠀⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠻⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠈⠢⠾⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠙⠉⢻⠋⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠀⠀⠀⠀⡞⢻⢃⡀
⠀⠀⠀⣀⣄⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⣓⡖⠒⠐⢴⠛⠉⢃
⠀⠀⠀⢻⡟⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⠁⢾⣿⣿⡄⠀⢸⡀⠀⠀⢆
⠀⠀⠀⢨⠁⢰⢰⣿⡊⠕⡏⢝⢫⢹⣿⣶⡆⠈⡇⠀⠀⠀⣀⣀⡆⠀⡈⠛⠋⠀⠀⠐⡇⠀⠀⠈⡆
⠀⠀⠀⢸⡄⠸⢸⣾⢁⢂⣇⣪⡜⣸⣿⠿⠇⠀⡇⠀⠀⢸⡋⠈⣿⡆⠀⠀⠀⠀⠀⠀⢿⠄
⠀⠀⠀⢸⡇⠀⠀⠹⢿⣿⣿⣿⣾⡷⠋⠀⠀⢸⡇⠀⠀⠀⠙⠚⠋⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⠃⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣤⣈⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠰⡟⠘⠃⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢎⢃⡀⠉
⠀⠀⠀⠀⠀⡠⠤⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠸⢄⣰⣦⡤⠂

⠀⠀⠀⠀⠐⢄⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠈⠛⠾⠿⠇⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣆⣹⠄⠤⠀⠀⠀⠀⠀⣾⣟⣧⣬⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢉⢉⣽⣤⣴⣶⣾⣿⡿⡻⢿⣿⢿⣿⡿⣿⠟⠇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠤⣬⡽⣿⣿⡟⢩⡟⠚⠉⢸⡇⣘⣀⣦⠀⠀⠀⠀⠀⣀⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⢸⠀⢀⠁⠈⢘⣧⣬⣷⣼⡿⠿⠛⠋⠉⠘⡄⠀⠀⠀⠘⠿⡿⠁
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⣁⣿⡼⠷⠸⠷⠾⠛⠛⠉⠁⠀⡇⠀⠀⠀⠀⠀⢱
⠀⠀⠀⣶⡄⣧⠀⠀⠀⠀⠀⠀⠀⡾⠙⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⢈⣿⡈⣇⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⢹⣷⣹⡆⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠹⣷⣿⡀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠘⣌⠳⡄⠀⠈⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡵⠶⠶⠶⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⡿⣿⠿⠷⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠿⠿⣿⣗⡂
⠀⠀⠀⠀⠀⣠⡶⣿⠛⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣄⣀
⠀⠀⠀⠀⠘⣿⡿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠦⣼⡏⢹⡿⠧⠾
⠀⠀⠀⠀⡀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠄⠟⠉⠋⠀⠀⢀
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡄⠀⠀⠀⠀⢰⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠲⣤⡀⠀⢠⡞⠀⠀⠳⣄⠀⠀⢀⠏⠀⠙⣄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⢦⣎⠀⠀⠀⠀⠈⠳⣤⠏⠀⠀⠀⠈⢳⡀⠀⢀⢼⡇⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣀⡞⠀⢣⠀⠀⣰⠎⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⢳⡾⠁⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢤⡀⠀⠀⠀⠔⠓⢀⠀⢀⡜⠑⢄⠀⠀⠀⣀⠰⠆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠰⠀⠀⠑⢤⠎⠀⠀⠀⠘⠆⠀⠀⠀⠲⠈⠀⠀⠀⠐⠀⠀⢀⠠⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠀⢠⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢠⣀⠀⠀⢀⡴⠢⣄⠀⠀⣠⠖⠲⢤⡀⠀⢀⣠⣄⠀⠀⠀⢀⡜⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣄⠀⠀⡼⠉⠳⣤⠏⠀⠀⠈⠛⠊⠁⠀⠀⠀⠑⠖⠉⠀⠈⢣⣀⡠⣬⡁⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⢀⣀⣀⣀⡤⠤⠤⠤⠶⠶⠦⠤⠤⣄⣀⣀⡀⠀⠉⠀⠀⠳⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠦⣄
⠀⠀⠀⢀⠔⠋⠁⠲⣤⠴⠊⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣴⠲⣦⡀
⠀⠀⡴⠋⠀⠀⠀⠘⠀⠀⠀⢠⠴⠊⣉⣀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠐⠒⢠⣄⠀⠉⠀⠈⠳⡄
⢀⡾⠁⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠈⠁⠀⠀⠀⠐⠒⠒⠚⠛⠛⠀⠀⠴⠶⠤⠀⠀⠀⠐⠒⠒⠂⢀⣄⠀⠀⠙⠦⠀⠀⠀⢹⡄
⡾⠃⠤⢀⡰⠛⣧⠀⠈⠀⠀⠀⠛⠀⠀⠄⠠⠄⠒⠒⣀⣠⡀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⣦⠤⢸⡇
⠇⣀⡴⠟⠁⠀⢻⢦⠀⠀⠰⠆⢀⡒⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠤⠤⠄⠒⠒⠢⠀⠀⠀⠀⠀⠀⢻⠻⠤⠼⠃
⠀⠀⠀⠀⠀⠀⢿⠀⠑⢄⡀⠀⠀⠀⠀⠙⠃⠉⠉⠋⠀⠀⠀⡤⠀⠀⠀⠠⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢸
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠑⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⠔⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠲⠦⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠐⠂⠉⠀⠀⠀⠀⣸⠃⣰⠋⠉⠑⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⠃⡈⡇⢠⠆⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⡇⣀⡠⠰⠀⣆⠘⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠘⢧⡈⠀⠢⠔⢈⡄⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⢀⡟⠀⣠⣤⣀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡞⢀⡼⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠖⠉⠀⠀⠀⠀⢠⠟⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⡤⠤⣤⠀⢀⡤⣤⣤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⢿⡄⢸⣧⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢠⡏⢸⡇⢸⡟⡄⢹⡄⠀⠀⠀⠀⠀⠀⠀⡾⠁⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣾⠀⢸⠇⢸⡇⢇⠈⢇⠀⠀⠀⠀⠀⠀⢸⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢰⠇⠀⢸⠀⢸⡇⢸⠀⠸⡀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡏⠀⠀⡈⠀⢸⡇⠘⣇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⡿⠀⠀⠀⣿⠀⢸⡇⠀⣿⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⡜⠁⠀⠀⠀⣿⠀⢸⡇⠀⢸⡆⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣰⠁⠀⠀⠀⠀⣿⠀⢸⡇⠀⠈⣧⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣰⠇⠀⠀⠀⠀⠀⣿⠀⠘⡇⠀⠀⠸⡀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⠋⠀⠀⠀⠀⠀⠀⢿⠀⠀⡇⠀⠀⠀⣷⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⡜⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⢸⣆⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣃⣰⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⡿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡟⠉⠙⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠳⣄
⢀⡴⠞⠋⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠏⠀⠀⠀⠀⣿
⣾⠁⠀⠀⠀⠀⠘⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠙
⢻⡀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⣠
⠀⡟⠂⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⠀⠀⠀⠀⠹
⠈⢧⣀⣀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠻⠆
⠀⠀⠉⠹⣧⣤⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠾
⠀⠀⠀⠀⠀⠘⢦⣀⣤⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠧⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡢⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⣠⡖⠉⠉⢙⣏⣠⠔⠒⠛⢳⣈⣀⡤⠤⢴⣅⣁⣀⣀⣀⣀⣐⡥⠵⣖⣁⣀⢀⣀⣀⣴⣋⡀
⠀⠀⠀⠀⣰⣳⠧⠀⠀⡠⢊⡜⢉⠀⠀⣠⠞⡰⠋⠀⢀⣸⣣⡀⢀⣤⣸⠤⡑⣄⠼⢜⣄⡴⠦⡙⢇⠀⠀⢻⡄
⠀⠀⠀⣰⠃⣟⠀⠀⣸⢍⢸⠀⠀⠀⣞⣳⢰⡃⠀⠀⣾⡵⡗⡠⢈⡦⢝⢦⡼⢬⣢⠼⢦⡱⣄⠜⢒⠥⢤⡀⢳⡀
⠀⠀⣰⠃⣰⣙⢒⣒⣫⣟⠌⠧⠤⠜⠛⠑⠈⢦⡤⠴⠋⠉⠀⠀⠸⢄⠼⠢⢃⡧⣍⢦⣀⠧⠼⠀⣸⡢⠤⠇⠀⢧
⠀⣰⢧⠚⠉⠉⠽⠟⢪⣀⠖⠉⠉⠹⠿⠿⠻⡄⣱⠊⠉⠉⠽⠽⠟⠲⣄⠀⠪⡀⡸⠆⢝⠔⠛⣢⢸⠓⠲⡄⠈⡙⣇
⣰⠃⠈⠒⠒⠖⠒⠒⠚⠀⠒⠒⠒⠒⠒⠒⠊⠁⠙⠲⠶⠶⠶⠦⠤⠔⠋⠀⠀⠀⠀⠀⠈⠲⣛⠃⠸⠝⢒⣁⣀⣀⡘
⠛⠛⠳⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠓⠚⠚⠛⠛⠛⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣲⠒
⠀⠀⠀⢧⠀⠀⠀⠮⠭⠭⠭⣭⠭⡽⠂⠀⠀⠀⠀⠰⢦⢰⢲⢠⢶⠀⠀⠀⠀⠀⠸⠭⠭⠭⠭⣭⡽⠀⠀⠀⣰⠃
⠀⠀⠀⠘⡆⠀⠀⢰⣉⣉⣛⣛⣛⣻⠂⠀⠀⠀⠀⠠⠼⠠⠼⠸⠼⠀⠀⠀⠀⠀⠸⣍⣉⣉⣙⣛⣳⠀⠀⢠⠏
⠀⠀⠀⠀⠹⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠏
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⣤⡶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⣤⠤⠶⠖⠒⠒⠚⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡶⠂⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠊⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣽⠀⠀⠀⠔⠁⣠⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠂⣀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤⠀⠀⣚⣻⣿⠀⠀⣄⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡭⠄⠀⡀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢇⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢐⡶⣒⠲⣊⠍⡨⠑⢜⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⣀⣠⣬⣵⣶⣴⣶⠷⠿⠿⠧⣤⣉⡉⠉⠀⢹⣀⣤⡿⢹⣿⣷⣦⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣹⣷⣦⣤⣿⣟⣿⣥⡿⣷⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡻⣿⣿⡿⣿⠶⣶⣶⣶⣿⣭⣷⣶⣾⣯⣻⣛⣿⣿⠿⠾⠛⠝⠙⠁⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢿⢿⣶⣕⢾⣛⣟⠿⡻⣿⢟⣿⠿⢟⠛⠏⠉⠉⣂⠁⠀⡀⠀⢠⣺⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣀⠃⠹⢷⣬⣷⠹⠙⠊⠀⠀⢠⡀⠀⣤⠀⠰⣾⡗⠀⠁⠀⣈⡛⠅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠢⡀⢸⣷⠀⣦⣺⡆⠘⠿⠃⠀⠀⡀⢠⣤⠀⠀⠉⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠘⠟⠀⣈⠛⠡⠀⠂⠀⠀⠀⠀⡀⣿⡀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠨⠿⠀⠀⢀⣀⠤⠤⠔⠒⠉⠈⢹⣇⠈⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣀⣀⣀⠤⠆⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⡀⠈⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡛⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡹⠀⠁⠀⠀⠀⠀⠀⢠⢀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠐⡈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣀⣀⣀⣀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠛⠷⠶⠶⢶⣶⣤⣬⡉⠙⢲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠃⣀⡼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⠀⠀⢀⠤⢒⠩⠐⠈⠉⠀⠀⠀⣠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢙⢿⣿⣷⣦⠀⠀⠀⠀⣀⠀⣴⣾⣿⡿⡋⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣠⠔⠁⠀⠉⠛⠛⠁⡄⠀⣰⡇⠈⠛⠛⠉⠀⠈⠢⣄⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡀⠰⣧⢠⣿⡇⠀⢠⡇⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣤⡇⠀⠁⢸⣿⣷⠀⠸⠇⣰⡇⠀⠀⠀⠀⠀⠈⠳⣄⣀
⠀⠀⠀⠀⠀⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⢿⢸⣿⠃⢠⡀⣾⣿⣿⡇⢀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄
⠀⠀⠀⣴⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣸⣿⣆⣿⣷⣿⣿⣿⣿⣿⢀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣦
⠀⠀⠈⠿⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡟⣛⢻⣿⡉⣿⡏⣭⠝⡏⢭⢍⣏⢩⣽⡟⣭⣹⡏⣿⢻⡟⣛⣻⣿⣀⣀
⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⡇⡥⢘⢇⣭⡘⣇⣶⣘⣇⣚⣂⣟⣘⣻⣇⡻⣻⣇⠿⢸⡇⣭⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣷⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣾⣿⣿⣿⣿⣏⡀
⠀⠀⠀⢀⣴⡿⠿⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⣿⣦⡀
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣯⣽⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠉⠀⠀⠀⣀⠠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣀⢠⣤⡔⠒⣈⣉⡀⠀⣀⣀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣭⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣖⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⣭⣿⣻⣿⣟⣛⣻⣿⣟⣻⣭⣭⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠛⡟⠛⠉⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⡇⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⣀⣀⣀⣇⣀⣀⣀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠛⠦⣄⣯⡤⠖⠛⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⢠⣷⡄⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢛⣛⣛⣉⣉⣛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢻⣿⣷⣶⣶⣟⠀⠈⢳⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠤⠴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢤⣤⠶⢾⢛⣶⣶⣶⣶⣟⠀⠀⢸⣇⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠴⠶⠶⠶⠶
⠀⠀⠀⠀⢀⡴⢞⡿⠛⠁⣠⠴⠋⠀⢀⣼⢛⣶⣶⣶⣶⣟⠀⠀⣼⡽⠋⢀⡴⠋⠀⢉⡽⠓⢦⣄
⠀⠀⠀⠀⣯⡖⠋⢀⡠⠞⠁⢀⣠⠞⠉⣾⣘⣓⣒⣒⣒⣻⣤⠞⠋⢀⡴⠋⠀⢀⡴⠋⢀⡴⠋⣹⡇
⢀⣤⠤⠤⠿⠙⠲⠯⣤⣀⣴⠋⠀⣠⠞⠋⠉⠉⠉⠁⣠⠞⠁⢀⡴⠋⠀⠀⣴⢋⣀⣴⡿⠶⠚⠹⠧⠤⠤⣄⡀
⣏⢰⣖⣒⣶⡆⠀⠀⠀⠀⠉⠉⠉⠛⠛⠒⠒⠒⠒⠚⠓⠒⠚⠛⠒⠚⠛⠋⠉⠉⠁⠀⠀⠀⠠⣶⣖⣒⣲⠄⡷
⠘⢦⣭⡥⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⣬⣥⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣦⠤⣽⠟⠒⠲⠦⣤⡤⠤⢤⣤⠶⠒⠻⢯⠥⢴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡟⠀⠀⠀⠀⠈⣿⠉⢿⠁⠀⠀⠀⠸⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⠃⠀⠀⠀⠀⠀⣿⠀⣾⠀⠀⠀⠀⠀⢷⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⡟⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠸⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢸⠃⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⢣⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠸⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣸⣅⣀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⢀⣀⣷⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣯⣀⡉⠉⠓⠶⢤⣄⣀⣿⠀⣿⣀⣤⠴⠖⠛⠉⣁⣸⡇⠘⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠁⣸⠁⠀⠉⠛⠒⠶⢤⣀⡈⠉⢳⣿⣁⣠⡤⠶⠚⠋⠉⠀⢷⠀⢻
⠀⠀⠀⠀⠀⢠⣴⣿⣶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠋⣿⠉⠀⠀⠀⠀⠀⠀⠀⣸⣷⣾⣧⡄
⠀⠀⠀⠀⠀⣿⣯⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⣹⣿
⠀⠀⠀⠀⠀⠈⠻⠿⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠒⢿⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⡼⠃
⣿⣿⠟⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⠖⠚⠛⠛⠉⠉⠙⠛⠓⠶⣤⡀⠀⠀⠀⠀⠀⣤⠖⠚⠛⠛⠉⠙⠻⣿⠷⠶⣤⡀⠀⠀⠀⠀⠀⢠⡴⣒⠛⣛⡍⢉⡽⢛⡛⠲⢦⣄
⢽⣒⣲⠤⣄⠀⠀⠀⢠⡄⢠⡄⠹⡆⠀⠀⠀⠀⣽⣶⣶⣦⣄⠀⠀⠀⣯⠀⠀⠀⠹⡆⠀⠀⠀⠀⢨⣗⣲⣶⣥⡚⣫⡴⣋⡴⢋⡴⠊
⠀⠉⠉⠙⢿⣷⣄⣀⣀⣉⣉⣠⣼⡇⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣟⣛⣛⣆⣀⣠⣴⡇⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣦⣚⣉⣶⣋⣐⣯
⠀⠀⠀⠀⠀⠙⠻⠿⣿⡿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⡿⠿⠿⠟
⠀⠀⠀⠀⠀⢀⣠⣤⣴⢶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⢀⣤⡾⣿⣛⣷⣽⣼⣿⣽⣽⣏⡝⣷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⣩⣿⣿⣿⠟⠁
⠀⣠⡟⢯⣱⠾⠋⠁⠀⠀⠀⠀⠈⠙⠿⣦⣯⡽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢐⡔⣧⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠁⢀⣾⡀
⠐⣿⣿⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣃⣎⣿⣿⣶⡷⠀⠀⠀⠀⠀⢸⣿⠟⢁⣼⣣⣻⣾⣷
⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠰⣽⣯⣯⣿⣯⣯⣭⣷⠀⠀⠀⠀⠀⠐⢧⣦⣭⣭⣿⣽⣯⣽
⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟
⣤⣠⣶⣶⣦⣤⣴⣤⣤⣤⣤⣤⣤⣴⡟⠛⠛⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠘⡇
⣀⣀⣀⣉⣁⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢿
⡷⠶⠶⠬⠭⠭⣿⣀⣀⣀⣀⣀⣀⣀⣤⣄⣠⣤⣤⡤⢄⡀⠀⠀⠀⠀⠀⣏⢎⡦⠤⠤⠤⢿⠀⠀⠀⠀⠀⠀⠀⢸⡱⡱⠤⠤⠤⢼⡆
⣟⣛⣛⣛⣛⣩⡿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣻⣦⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⡔⣩⣿⣿⣿⡿⠋
⠀⢀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡾⣫⡾⣻⠆⠀⠀⢾⣽⣯⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⡠⣇⡀
⠀⠀⠙⣆⡈⠳⣄⠀⠀⠀⠀⠐⢯⡴⣫⠞⣩⠞⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠸⣿⡿⠋⢠⡼⣔⣷⣿⣴⡄
⠀⠀⠀⠈⠳⠶⣿⡄⠀⠀⠀⢀⠞⠛⠷⠞⠁⠀⠀⠀⠀⠀⠀⠀⢹⠉⠀⠈⣯⠀⠀⠀⢠⣤⣾⡄⢿⣤⣬⣭⣭⣭⣭⣭⣭⡄⣰⣧⣤
⢀⣀⣾⣿⣿⣿⢿⣷⣿⢻⣿⣿⢻⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢹⡄⠀⠀⠀⣿⣿⣿⠈⢿⣿⣿⣿⣿⣿⣿⠟⠀⣿⣿⣟
⠈⣿⣿⡿⠿⠾⢿⣿⠿⠾⢿⣿⠾⠿⠿⠿⢿⣿⣟⠀⠀⠀⠠⡫⢝⠤⠤⠤⠬⣇⠀⠀⠀⠻⣿⠟⢦⣄⢸⠏⠉⠉⢻⠁⣠⡾⣫⣽⠟
⠘⠛⠛⠁⢀⣤⡾⠛⠀⠀⠈⠛⣷⣄⡀⠀⠘⠛⠛⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠳⣆⣽⢻⡷⠶⡶⣾⣿⣹⣵⠞⠁
⠀⠀⢀⡴⣿⠟⠁⠀⠀⠀⠀⠀⠈⠻⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢟⡛⣻⣿⣿⣛⣿⠉
⣤⣤⣼⣮⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣾⣥⣤⣤⣤⣼⣦⣤⣤⣤⣤
⣿⣿⣄⣠⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⠀⠀⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⣆⠀⠀⠀⣠⣿⣿
⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⣰⡟⠀⠀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠈⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⡇⠀⠀⢰⣿⠁⠀⣸⣿⡟
⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⡇⠀⠀⠹⣿⡄⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠙⢷⠀⠀⠀⠈⢳⠀⠀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⡇⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⣛⣿⣿⣯⣽⣧⣴⣯⣤⣿⣤⣼⣧⣼⣤⣼⣧⣤⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠉⠉⠉⠉⠁⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣀⣀⣀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⠋⠰⠟⠂⠳⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠐⠀⠂⠀⠀⠀⠀⠈⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠘⡍⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⣄⡰⠋⠙⢲⠀⠀⠀⣶⢸⠉⠀⠳⡎⠙⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡼⠀⠀⠀⠀⠈⡏⢹⠋⢸⠘⡀⠀⠀⢻⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠃⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⡇⠀⠀⠈⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠇⠀⠀⠀⠀⠀⢀⠁⢸⠀⠀⢣⢳⠀⠀⠀⠸⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡞⠀⠀⠀⠀⠀⠀⢸⠀⠾⠀⠀⢸⠸⡄⠀⠀⠀⢣⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡰⠁⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡜⠃⠉⠉⢦⠀⠘⡄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠸⣄⠀⠀⠀⡸⠀⠀⢳⠀⢳⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡼⢤⡎⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠙⠓⠒⠊⠁⠀⠀⢀⠗⠈⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣄⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢶⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⣎⠡⠞⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠄⠁⠀⠀⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣧⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠠⢣⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠛⠋⢧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢱⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⣀⣀⣀⣸⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣿⣿⠏⠼⠿⠿⠿⠸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣤⡇⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠳⣿⣿⣿⣿⡇⡻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡴⢾⣟⢿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠛⠋⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠂⣿⣿⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⢸⠀⠀⠀⣠⡤⢤⣀⡀
⠀⠀⠀⠀⢀⣤⣾⣾⠛⠋⢁⣼⡿⠃⠀⠀⢀⣠⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡗⠁⠀⠀⠀⣠⠞⠀⠀⠀⣡⠇⠀⠁⠸⡆
⠀⠀⠀⣠⣾⠛⠿⠟⠀⣀⢈⣛⣳⣶⠾⢿⣟⠛⠀⠿⠋⣛⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⠀⠀⠀⠀⠀⠀⠀⠙⡒⠒⠊⠁⠀⠀⠀⠀⠀⠙⠲⡀
⣀⣀⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢩⣷⣿⣿⣿⣿⣏⣿⣿⣷⡟⣸⣇⣤⣤⡄⢀⣀⡈⢨⡇⠁⠐⠉⠚⠉⠉⠀⠡⠉⠑⠆⠀⠁⠀⠘⠈⠀⠐⡔⢀⢁⡠⢂
⠀⠀⢻⡇⠛⢻⣿⣿⠿⠛⠛⠛⠓⠔⠋⠿⡿⠿⠿⠿⢿⣿⠏⠉⢹⡏⠳⠶⠇⠀⠀⠰⡆⠐⠓⠂⠀⡐⠂⠑⠂⠐⠠⠂⠁⡠⠤⠀⠤⠧⣀⠔⠁⠙⠚⠢⠶
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⡇⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⢿⣶⣶⣤⣄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⡠⢔⠒⠂⠉⡉⣭⢍⠩⠚⠲⢶⡦⠤⣀⠀⢰
⠀⠀⢸⡇⣠⣾⣿⣿⣿⣿⣟⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣸⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠝⠉⠐⠌⠤⠀⠀⠀⠄⠒⣒⡘⢃⡀⠀⠑⠀⠱⡘
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣿⣷⡾⢿⣿⣛⣻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠌⢻⢦⣘⠉⣤⡀⠰⠘⢁⠀⢀⡀⠁⣤⠀⢡⡐⠀⢉⣐⠏⠂
⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣷⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠈⠑⠒⠤⠤⣀⣈⣀⣀⣀⣀⣀⠤⠤⠒⠊⡹⠉
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣾⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡘⢲⣤⣀⡇⢀⣀⣀⣀⣰⡴⠞⠁
⠀⠀⠀⠀⠀⠀⢸⡿⢿⣧⣬⣭⣿⣿⣿⣭⣿⡿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠏⣃⠀⠈⡅⣽⠿⠍⢒⡒⠽⠔⡀
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠈⠉⣿⡏⣿⠉⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠌⠀⠀⠈⠁⡃⠟⠋⠉⠀⠀⠀⠘⡔⡀
⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣿⡁⣿⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠘⡔
⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢰⣿⠀⣿⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠈⠰⡀
⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢸⣿⠀⠛⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⡁⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣤⡴⢖⣚⣛⣉⣉⣉⣙⡓⠶⢦⣄⡀
⠀⠀⠀⠀⠀⣠⣴⠟⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⣴⣟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡟
⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⠟⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢋
⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡾⣫⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⣠⡾⠁
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⡾⣻⣼⠟⠁⢀⣴⣶⣶⣶⣦⣄⠀⢰⡏⢠⣾⡿⠁⣠⣴⣶⣿⣿⣿⣷⣦
⢀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡿⣫⣾⠟⠁⠀⢀⣿⣿⡿⠛⠛⠿⣿⣷⡈⢠⡿⠋⣠⣾⣿⣿⣿⠟⠉⠀⠀⠉
⣼⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣵⡿⠋⠁⠀⠀⠀⠈⢿⣿⣧⣠⠀⠀⢹⣿⡇⠘⢁⣾⣿⣿⣿⠟⠁
⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣭⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣸⡟⠀⣠⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣫⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣀⣾⣿⣿⣿⠟⠁⣀⣤⡴⠶⣒⣀⣀
⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢟⣯⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣠⣴⣾⣿⡿⠿⠋⣡⣴⣿⠟⠉⠐⠊⠉⠉⢙⣿
⠈⢿⣿⣿⡿⣟⣋⣭⡶⢟⣻⣵⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠩⢭⣤⣴⡾⠿⠛⠋⠀⠀⠀⠀⠀⠀⠈⠛⠋
⠀⠈⡿⠿⠿⣛⣯⡵⠞⠛⣉⣀⣠⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠉⠛⢋⡩⣴⣶⡿⠿⠛⠛⣩⣟⠛⢁⣤⠖⠀⣠⡞⠀⢠⡾⠠⠀⣶⠀⠈⢯⡉⠉⢿⡟⠿⠿⢷⣦⣤⡀
⠀⠀⠀⠀⣏⢼⡋⠀⠀⣠⡴⠛⠁⢀⡴⠟⠁⠀⣴⠏⠀⠀⣼⠇⠀⠀⣿⡅⠀⠈⢷⡀⠀⠙⣦⡀⠀⠈⠙⢯⡂
⠀⠀⠀⠀⠹⣾⣿⣴⣿⣁⡀⣠⡼⠋⠁⠀⢠⡾⠋⠀⠀⢰⣿⠀⠀⠀⢹⡇⠀⠀⠘⣷⡄⠀⠈⢻⣦⣠⣴⣿⠁
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣷⣶⣦⣤⣾⣧⣤⣤⣤⣾⣷⣶⣶⣶⣾⣿⣿⣿⣿⡿⠟⢛⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣾⣭⣽⣛⣛⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⣾⡇⢸⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡾
⠀⠀⠀⠀⠀⠀⠹⣎⢿⣿⣿⡉⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠻⣿⣿⣦⣬⣭⣭⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢮⣙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠈⠉⠉⢹⣿⡏⠉⠉⠀⠀⠹⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣤⣶⣶⣶⣿⣿⣇⣿⣿⣸⣿⣿⣿⣷⣶⣶⣦⣼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠈⠻⠿⣿⣿⣛⣿⣿⢻⣛⣻⣛⠿⠍⠁⠀⠀⠀⠘⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡅

⠀⠀⠀⠀⠀⢀⡀⢠⠄⣠⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣼⣱⣿⣆⠫⣆⠀⠀⠀⣰⣿⣿⢦⡀⠀⠀⢀⡾⢡⡀⠀⠀⠀⣠⣾⠆⠀⠀⠀⣠⡾⡀
⠀⠀⠀⠀⢿⡿⣮⡈⡼⢢⢟⡆⠀⠰⣏⡻⣴⡾⡷⠀⠀⢼⠿⣆⣿⠀⠀⠘⢿⣏⣠⠇⠀⠀⢿⡱⢹⠆
⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⠖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⢀
⠀⠀⠀⠀⢀⡖⣩⣦⣭⠲⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢷⢀⣹⣆⢾⡄
⠀⠀⠀⠀⠈⢰⣿⣿⣿⣗⠘⠀⠀⠀⠀⠀⢀⣠⣾⣟⣿⣦⣀⠀⠀⠀⠀⠀⠀⢠⣿⢈⡸⢿⢻⢸⣷⣠
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⣰⣿⡿⣿⡿⡿⣿⣿⣷⠀⠀⢀⣀⢀⣟⣻⣎⣻⣆⣾⣾⣹⣟⡁⢀⡀
⠀⠀⠀⠐⣒⠀⠀⠀⠀⠉⣙⣓⠀⠀⠀⣿⣯⡇⢺⡇⢸⢱⢸⣿⡇⠀⠀⠘⠻⡍⢿⢹⣿⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢻⣷⣧⣵⣯⣜⠎⡰⣿⠃⠀⠀⠀⠀⠙⢮⣣⣻⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠤⠠⠩⠉⠉⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢈⠟⠉⠉⠉⠛⡃
⠀⠀⠀⠀⠀⢰⣾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⡜⠒⠒⠲⠶⠒⢳
⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠠⢤⣿⢾⣿⣦⠄⠀⠀⠀⠀⠀⠀⢠⠄⠐⠀⠠⡀⠀⠀⠀⠀⢰⡉⢹⡆⠄⠀⠀⠀⠄⠀⠸⣄
⠀⠀⠀⠀⠀⠈⡿⠿⢿⠁⠀⠀⠀⠀⠀⣠⠔⣡⣶⡶⢶⣦⡈⠢⡀⠀⠀⠀⠉⠉⠀⠀⢀⣀⠀⠀⠀⠀⠉
⠀⠀⠀⡆⠀⠰⢱⣿⡍⠀⠀⢰⠀⠀⢘⠡⣴⣿⣿⣤⣼⣿⣿⣲⠉⠂⠀⠀⠀⠀⠠⡀⢸⣭⢀⣤⡀
⠀⠀⠀⠣⢠⣃⡈⠀⣉⣻⡇⠜⠀⠀⠲⣄⠙⣿⡏⠏⠻⣻⡿⢚⡴⠂⠀⢀⡀⠀⣀⣙⢦⣥⢚⣋⠀⠀⣀
⠀⠀⠀⢰⣰⣮⡅⠄⢸⣅⣦⡦⠀⠀⠀⠈⠀⣈⠛⠛⠛⢋⡠⠊⠀⠀⠀⠈⠉⠉⠉⣩⠞⡟⢺⣍⠉⠉⠉
⠀⠀⠀⠈⠀⠒⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠐⠟⠁⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠇⠀⠙⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⣾⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⠀⠹⣿⣦⡀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡄⠀⢻⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⠋⠀⢀⣼⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⢴⣶⣶⣶⣶⣶⠶⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠉⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠉⠙⠛⠛⠻⠿⠛⠛⠛⠉⠀⢺⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⣿⠏⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⣿⣟⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡘⠛⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠘⠛⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⣄⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢸⠏⠷⣄⠀⣾⡛⠛⠻⠟⠛⠷⣶⣿⣟⢋⣷⠶⠶⢯⡿⢁⠷⢒⢍⣷⡴⠶⣶⡶⣤⣀
⠀⠀⠀⠀⠀⢠⡟⠐⣴⠉⠷⠿⡇⠀⠐⢲⣍⣉⡉⠉⠉⣻⡁⠀⣀⠀⢠⠘⠤⠍⢢⣾⣧⡀⢸⣿⣷⣿⣷⡄
⠀⠀⠀⠀⢠⠟⡀⣒⠠⠶⠂⡈⢤⠀⢝⡩⠙⠓⠚⠿⠛⢛⡀⢈⣁⣤⣪⣿⣲⠶⠻⢯⣹⣿⡿⠿⢻⡴⡀⡿⠹⡆
⠀⠀⢠⡟⢿⣦⡀⠤⠄⠁⠈⣁⠘⣤⠜⠴⠀⠀⠀⠀⠀⠾⠉⠁⠂⡌⠠⠛⣿⡇⣇⣨⡽⢟⣃⠂⣸⢱⡗⠃⢀⣿
⠀⠀⠈⢻⡿⢛⡁⠀⠆⠀⠀⠀⢀⣃⠀⠂⠀⠙⠐⠀⢃⡄⠐⠗⢤⣤⢀⡄⠀⢣⣿⣉⢀⠆⠈⠳⣅⣟⣀⢀⣾⣧⡀
⠀⠀⢰⡏⢠⠈⠘⢆⠀⢒⣀⡴⡤⠽⠂⠀⠀⣄⢀⣠⡴⢷⣤⣄⣀⡀⠀⣀⣀⢺⡿⢆⡤⠀⠀⠀⠀⠠⠀⣨⣟⣾⠁
⠀⠀⣸⠃⣈⠸⠀⡙⠁⠜⡏⠁⡂⡀⢄⡀⠠⣸⣍⡿⠛⠈⠙⠛⠙⠛⠛⠛⣭⣿⣷⣾⢃⡁⠀⠀⠀⠀⢀⣾⢾⣅
⠀⠀⢸⡄⠁⠦⢈⡃⠄⠘⣾⠁⠀⠀⠀⠀⡰⢸⡟⠁⠀⠀⠀⠡⢰⠆⠐⠋⡭⠛⡋⠉⠀⢀⣀⡀⠱⠠⢾⣷⣤⡏
⠀⠀⠈⣷⣤⣥⡈⣅⢀⠞⠂⠑⠁⢀⠀⠀⠲⣼⡄⡀⠀⠀⠀⠀⠂⠁⢠⣎⠀⣀⣤⣶⠿⠛⠉⠀⠀⣿⠆⣿⢯⡄
⠀⠀⢰⣿⣟⢰⣶⠈⠡⡐⠐⡆⢠⠄⣦⠴⠿⣟⠛⠗⠲⠄⣴⠆⣿⣄⠀⠈⡆⠂⢀⡀⠀⠄⠘⠀⠀⢄⣾⣿⣼⣇
⠀⠀⠈⢿⣿⣼⣿⣧⡴⠄⡄⠀⠂⠐⢛⠦⢀⠄⢀⡶⠠⣠⡤⠔⠋⠋⠉⠀⠀⠀⠤⢀⣀⠠⠐⢈⠐⠃⠻⡿⠷⠛
⠀⠀⢠⣻⣿⣷⣧⣀⣷⣄⠢⠐⠆⣸⠂⠀⢀⢈⣿⣇⡔⠹⠲⠂⠀⣠⠄⣀⠴⠆⠀⠮⣄⢀⣶⠿⣤⠀⣱⣷
⠀⠀⠘⣿⠿⠿⠏⠙⠈⣿⡟⠆⢠⣼⣤⠊⠉⠛⢷⠿⠲⢂⡽⠄⠀⠄⠀⠉⠀⠀⡏⢠⣦⠈⣠⡙⢩⠉⣿⣹⡇
⠀⠀⢼⠃⠀⠀⠧⠀⣚⢹⠇⠁⢀⣹⠇⠀⠀⢀⠲⢀⣄⠐⠂⣠⣄⠀⠈⣿⣙⣯⣀⡿⢇⢠⣿⠁⣼⠼⠅⠈⣷
⠀⠀⣸⣧⡠⢀⠬⣀⠠⠤⡧⠂⣾⠅⠙⢦⠯⡏⠀⢻⣿⣦⣴⣿⡿⠀⣰⢿⡟⠓⠀⠰⠠⠤⢥⢀⣧⡀⢐⣠⣿
⠀⢠⡿⠟⣿⠀⠀⠈⠃⠀⢹⠊⡑⢦⢭⣁⠠⣟⣤⡀⠉⠛⠛⠋⢀⡆⠰⠠⠆⠰⠀⣷⣤⠄⢨⣴⡄⠋⠙⣿⠃
⠀⠈⣛⣾⣿⣦⣄⣀⣉⡀⢈⡠⠀⠐⠀⣹⠰⢋⡍⠁⢰⡿⠿⢿⣿⣤⠀⢄⡤⠄⣐⣭⣴⣮⠶⠃⠀⣀⢀⣾⣧
⠀⠘⢧⠄⠚⠁⠈⠟⢁⣴⡿⣩⡾⠒⣃⢹⣶⣋⣴⡿⢼⡧⠦⠀⠰⣦⣾⠟⡿⠿⠿⠛⠛⣡⠀⠿⢂⣽⣿⣿⣟
⠀⠀⠸⣦⣀⡀⠀⣰⣿⣷⠿⡋⠰⠆⠀⢨⣟⠻⠀⠣⣬⡀⠠⠔⡂⠰⣿⡆⠀⠀⠀⠾⠂⠁⢀⡿⢯⠝⢿⣿⣿⡆
⠀⠀⠀⢸⣿⣧⡄⠛⠉⢠⠀⠙⠀⠈⢀⡼⢿⣾⣍⠀⣤⠹⠀⠀⠀⢀⣯⡽⠟⡚⠷⣶⠞⢴⠉⠀⠀⢠⡼⣿⣿⣧
⠀⠀⠀⠀⣿⢟⣡⡌⣃⡀⠀⠈⡠⠈⠁⠀⠈⢳⣹⡄⠘⡐⠁⢠⣿⡿⣽⡧⠄⠀⠠⡇⢈⠘⣶⢛⡊⠍⢓⣛⣩⠿
⠀⠀⠀⠀⣟⠈⠻⣧⠈⣻⡿⠋⠰⠿⣤⣀⣤⠈⣏⠶⣶⡅⠈⢸⣝⣦⡹⠰⠢⠐⠄⣿⡶⣫⢕⠢⡴⢾⣟⣿⣽⠆
⠀⠀⠀⢠⣿⣄⠸⣿⠇⠛⠀⠀⠰⠀⠀⢀⠁⠀⢸⡨⣿⣿⢾⣿⣻⣫⢷⣦⣀⢄⣴⣫⣞⠿⠶⣻⠟⠁⠀⠈⢻⡀
⠀⠀⠀⠸⣭⡿⠗⠒⢯⣄⡀⠀⠀⠀⠀⠈⠀⠀⠈⣇⣿⣿⡐⠗⠦⠚⣂⣿⣿⣷⡟⠁⠈⠇⠀⡡⠳⠘⠢⠀⢸⠇
⠀⠀⠀⠀⠈⠓⢶⣄⡂⠀⠈⠛⠶⠤⣤⣠⣴⠐⠶⠖⠒⢾⡛⣿⣻⣿⣟⣿⣿⣿⣿⣟⣇⣀⣰⢿⣦⣤⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⢤⡴⠶⠛⠋⠉⠳⠶⠤⠴⠶⠚⠁⠀⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠒⠂⠉⠉⠉⠐⠒⠂⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡐⢁⠠⣈⢻⡄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣟⡛⠛⠛⠛⡛⠛⠛⢛⡶⠶⢶⣤⣀⠀⠀⠠⢋⡠⢈⡹⠧⠉⢠⠼⢱⠇
⠀⠀⠀⠀⠀⠀⢿⣯⠀⠀⠀⠀⠀⠘⣍⡉⠻⣌⢉⣉⡥⠴⠚⠁⣨⡿⠇⠀⠀⠸⢄⡸⣀⣤⡄⣸⡀⠁
⠀⠀⠀⠀⣠⣴⣦⠙⠷⣤⡀⢰⠒⠒⠋⠉⠘⠵⠻⣄⠀⣀⣤⠾⠋⠁⢀⣀⣀⠀⠀⠐⢃⡬⠛⣤⢳
⠀⠀⠀⠸⢿⣇⠀⠀⠀⠈⠙⠻⠶⢤⣤⣤⣤⠤⠶⠞⠛⢉⣡⠴⠀⡐⢁⠠⣨⠱⣄⣠⠄⠃⠆⢋⠞
⠀⠀⠀⠀⠈⠙⢷⣄⡀⡎⠙⠃⠀⠀⠠⠀⠠⣄⣀⣠⡾⠛⠁⠀⠀⢀⡹⢠⠸⢡⠏⡤⠦⣄⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⢤⡤⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠈⠟⠋⢹⣷⡌⠓⠄⢛⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢲⣿⠆⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠊



⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠄⣦⢲⠆⠀⠀⠀⠀⠁⠀⠀⠂⠄⠀⠀⠀⠀⠀⢤⡄⡀⠀⠀⠙⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⢄⣀⣓⣠⢂⣘⣀⠂⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠘⢧⡀⠀⠰⠄⠀⠀⠀⢥⠁⡔⠊⢀⠄⠀⠀⠀⠘⣣⡔⠀⠀⣀⢄⡟⠂⣄⠀⠈⠁⠀⢹⡋⠀⠀⡈⠉⠁⠀⢙⡇
⠀⠀⠀⠀⢘⠃⠀⠀⠀⠘⠂⢀⣀⣴⡀⢀⠈⠖⢀⠞⠁⢀⡄⠊⠀⠀⠀⠀⠀⠠⣡⠜⢧⢗⡫⠂⡀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⣼⠁⣀
⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⢀⠌⠈⠈⠁⠀⠀⠐⠦⠀⢀⠎⢠⠞⠆⠀⠀⠀⠠⣔⣄⣶⠨⠍⡠⠖⡧⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠀⠐⢤⡆⠀⢧⠀⠂⠀⠀⠄⠀⡅⢤⣥⠔⠚⢀⡠⠆⠀⠀⠀⠙⠠⠤⠄⠠⠤⠤⠂
⠀⠀⠀⠀⠀⣀⣰⡄⠀⠀⠀⢤⠀⠀⣀⡀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠸⢗⣸⢩⡍⢮⡛⠀⠀⣄⢶⠆⠀⠀⣀⠀⠀⢦⣆⡄⠈
⠀⠀⠀⠀⡶⠚⠁⢃⣀⣀⠀⣀⠀⠀⠘⢡⠾⣼⠀⠀⠀⠀⢀⡀⠀⠀⠀⠦⠀⠀⠈⠉⠛⠃⠉⠀⠀⠷⡉⠀⠀⠀⠀⠁⠀⠀⠀⢊⢱⡆
⠀⠀⠀⠀⠀⠀⡞⠋⢀⡠⠴⠬⢤⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⡦⡀
⠀⠀⠀⠀⠀⠀⠻⣶⠃⠁⠀⠀⠀⠈⠆⠀⠀⣥⠀⡆⡄⢐⢰⠀⡄⢀⠇⠀⠂⢰⠀⠰⣀⠂⡦⢀⠀⠀⠀⠀⠀⠘⢼⣁⠄⡓⣧⢂
⠀⠀⠀⠀⠋⠀⠀⠘⠀⠁⠀⠀⠀⢀⠀⠉⠀⠤⠐⠳⠁⠬⠸⠄⠇⠨⠤⠀⠀⠇⠱⠐⠻⠀⠗⠀⠇⠁⠀⢲⡦⡄⢩⢽⣶⠲⠨⠇⡰⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠠⠀⠀⡈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠉⠹⢾⣤⡜⠿⢭⠘⣧
⠀⠀⠀⠀⣠⠀⠀⠢⡇⡀⣀⠀⣠⠅⠀⠀⠙⣣⡆⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠎⠃⠀⠀⣄⠀⠀⠀⠀⠘⠳⠴
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠂⠀⠀⠚⠃⠀⢀⠀⠀⡠⠠⠎⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡠⠀⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⣄⣀⣄⣀⡀⠀⠀⢠⡄
⠀⠀⠀⢠⠀⡈⠀⠀⠀⢠⡀⢠⠔⠀⠀⠀⢄⠀⠀⠁⠀⠀⠁⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⢻⣿⣧
⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠉⠲⠀⠀⠀⠀⠘⠀⣴⡀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠁⠀⢰⠇⠀⠀⠀⠀⠻⡿⢤⠂⠀⢠⣿⣿⠃⢠
⠀⠀⠀⠀⠀⠘⡀⢀⠄⠎⠁⡀⠀⠰⠄⠀⢡⣹⠓⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣦⣟⠁⠀⠀⠂⠀⡜⠀⠀⠀⠀⠾⠋⠐⠀⡀
⠀⠀⠀⠀⠀⠲⠈⠈⢀⢀⠉⠈⠀⠙⠀⠀⠈⠁⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂

⠀⠀⠀⠀⠀⠀⢀⣄⣠⡦⢀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄
⠀⠀⠀⠀⠀⠰⡼⠋⠙⠹⠿⣴⠀⠀⠀⠀⠀⢠⡈⣿⣧⣽⡄⠀⠀⠀⠰⣄⢱⡄⠀⠀⠀⣾⣿⣿⡿⠋
⠀⠀⠀⠤⣿⠹⣿⣿⣿⣿⣿⣿⣿⡧⠤⠀⠀⢸⣷⣿⣿⣿⠇⡀⠀⠀⠀⠈⠉⠳⣄⢀⡴⠋⠉⠉
⠀⠀⠀⠀⠘⢧⣻⣿⣿⣿⣿⣿⡿⠁⠀⠀⣿⣶⣿⠛⡇⠹⣷⣿⠀⠀⠀⠀⠀⢀⡬⠛⣄
⠀⠀⠀⠀⠀⠀⡟⠛⠿⠿⠛⢏⠀⠀⠀⠀⠘⠏⠈⠀⠀⠀⠘⠃⠀⠀⠀⢀⡴⠋⠀⠀⠈⠳⣤
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠈⠳⡆
⠀⠀⠀⠀⣠⡋⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠈⠀⠀⠀⣰⡀⠀⢀⣆⠀⠀⠈
⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣴⡿⠛⠉⠉⠛⢿⣦⡀⠀⠀⠀⢸⣿⣷⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⠄⣾⡟⠀⠀⠀⠀⠀⠀⣿⣧⢠⡄⠀⢸⣿⣿⠀⣿⣿⡇
⠀⠀⡠⢳⣶⣿⣿⣿⡿⠃⠀⠀⠀⠘⠂⢻⣧⠀⠀⠀⠀⠀⠀⣿⡟⠘⠃⠀⢸⣿⣿⠀⣿⣿⡇
⠀⠀⢱⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣀⣀⣴⣾⠟⠁⠀⠀⠀⠈⠛⠛⠀⠙⠛⠁
⠀⠀⢸⡜⣿⣿⠋⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠄⠄
⠀⠀⠀⢳⡜⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣶⣀⣈⣀⣀⣤⣶⣶⠆
⠀⠀⠀⠂⢻⡉⣿⣿⣿⣿⣿⣿⣿⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠈⠳⣽⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣀⣰⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠆
⠀⠀⠀⠀⠀⠀⡞⠙⠛⠛⠋⢣⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⣸⢀⣀⣀⣀⣀⣈⡆⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⣤⡇⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⣤⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠕⡹⡣⡄
⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠻⠛⠛⢛⠛⡛⠛⠛⠛⠛⠀⠀⠀⢀⡀⠀⡀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢄⠀⢰⡕⡡⡪⢊⠔⠁
⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠘⢿⠿⠿⠿⠶⠶⠤⠶⠾⠿⠿⠁⠀⠀⠸⣦⣄⣀⠀⠀⠀⠀⠀⠀⠁⢐⣦⠀⠀⠀⠀⠀⠀⠐⢣⣴⠛⠮⠞⠁
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⡿⠿⠶⠦⠴⠶⠾⠿⠿⠿⡟⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠓⠖⠛⠛⠛⠁⠀⠀⠀⠀⠀⢀⣴⠏⠉⢶⣄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠓⠛⠞⠓⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⠉⡋⡟⠂⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⢘⠀⠀⠂⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣆⠀⠀⠀⢠⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠈⠲⣶⠖⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⢿⠿⡇⠀⠀⢠⠪⢅⣛⣂⠀⠀⠈⠉⢲⠤⢄⡀⠀⠀⠀⠈⢿⣿⣿⣦⠀⢠⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣿⣻⣯⣿⡭⠷⠿⣶⣿⣿⣿⡧⠀⠀⠈⠛⠶⠦⣤⣭⣭⣭⣽⣥⣤⠴⠟⠀⠀⠀⠀⠈⠻⠿⠛⣷⠛⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠹⡿⠷⠶⠖⠒⠚⠓⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⢀⣀⣀⢀⢀⢀⣀⣀⡀⠀⠀⠀⣼⡟⠛⠛⠛⠛⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡀⠀⢀⣼⣄
⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⢰⣿⣷⣤⣤⣤⣤⣶⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⣿⣿⣿⡿⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣾⡿⠃⠀⠀⠀⠀⠸⠋⠉⠙⢿⠋⠉⠙⡇
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣿⣉⣿⣿⡏⢠⣄⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡠⣶⣼⣿⠿⠋⠀⠀⠀⠀⠀⠀⢸⣶⣴⣾⣿⣷⣶⣶⡇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⣿⠆⣾⣿⣧⣺⢹⣣⣿⡇⠀⠀⠀⠀⣴⣾⣷⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠿⠇⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⣻⠛⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠿⠿⡟⠉
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠹⣿⣿⣴⣦⣙⡛⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣧⠁⠀⠀⢘⡄
⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣶⡎⠻⢻⣿⠆⠀⠀⠀⠀⠀⡜⠌⠉⠉⠉⠁⢱
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣧⠝⠃⠀⠀⠀⣀⣼⣴⡄⠀⠀⢀⡀⠀⢃
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠉⠁⠀⠀⠀⠀⠀⠈⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠉⠙⢻⣿⣆
⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠿⣿⣇⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⠀⠀⣿⣿
⠀⠀⢀⣼⣿⣿⠿⠋⠁⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⢰⣿⡿
⠀⣠⣿⣿⡟⠁⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢻⣿⣏⠁⢹⣿⠀⠀⠀⠀⢀⣾⣿⠃⣰⡾⠛⠿⣷
⠀⠻⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠉⠛⠀⣸⠏⠀⠀⢀⣠⣾⣿⠏⢠⣿⠃⢀⣀⣸
⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣴⠞⢁⣠⣶⣾⡿⠿⠛⠁⣠⣾⡏⠀⣈⠛⠛
⠀⠀⣴⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⡼⢁⣴⠟⢋⡥⠶⠶⠶⠶⠿⠟⠋⠐⠛⣿⠇
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠰⠇⢸⠏⠀⢡⣄⠰⣿⠉⠙⠛⠲⠶⠖⠛⠁
⢰⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠘⠀⣴⡄⢿⣷⣄⠀⣄
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣠⣤⡤⠀⣀⣼⣿⡇⢸⣿⣿⣇⠸⣷⡄
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢀⣾⣿⡟⣠⣾⣿⡿⠛⠁⣸⣿⣿⣿⠀⣿⠇
⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⢀⣴⡏⣼⣿⡿⢠⣿⣿⢏⣴⠃⣰⣿⣿⠟⡿⠀⠉
⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⣠⡴⣿⣿⠃⠿⠋⠀⠸⣿⣿⣿⠃⣼⣿⠟⢁⣼⠇
⠀⢻⣿⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⠿⡇⠀⢿⣇⠀⠾⠋
⠀⠀⢻⣿⣭⣴⣶⣿⡿⠿⠛⠉⢀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠉⠛⠋⠉⠁⢀⣤⣶⣿⣿⣿⡿⢿⣿⠛⣿⡏⢹⣿⠉⣿⡇⢸⣿⠀⣿⡅⢹⣿⠉⣿⡛⢻⣿⠻⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⢻⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣟⠛⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⡷⢀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣤⣿⣇⣸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⢀⣿⣧⣼⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷⣾⣿⣶⣿⣷⣾⣿⣶⣿⣷⣾⣿⣾⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣿⣿⣷⣶⣶⣤⣭⣭⣍⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣭⣥⣴⣶⣶⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀⢠⣤⣤⠀⠸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⢸⣿⣿⠀⠀⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣀⣀⣨⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⠿⠿⠿⠿⢛⣛⠛⠛⠋⠹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⠁⢈⠙⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡜⠷⡾⢁⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣄⠒⣶⢤⠤⡴⢶⢦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⠞⠫⠚⢡⠮⢂⠕⣡⢄⡡⢊⠔⠩⢫⡞⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡵⠏⠀⡀⢐⠍⡠⢀⡠⢀⠔⡠⢀⠄⡀⠐⠀⠐⢀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⠅⡢⢑⠬⢂⠔⡨⢒⠥⡪⡔⠝⡪⠕⠊⠄⢐⠅⡨⠚⡠⠂⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢡⠕⠠⠀⢡⡠⠀⡁⠢⣁⠼⠋⠔⡠⠐⡡⠊⣰⠀⢂⠔⢁⠔⡡⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⢊⢴⠎⢊⠔⡣⢲⡁⠡⠄⠀⢊⠔⠞⠡⠊⡡⠔⡡⢊⠄⢊⠔⠂⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢕⡡⢊⠔⠠⡊⡜⠆⢐⠠⢊⠄⡢⡄⢴⡈⠔⡡⢐⠡⢊⡠⠒⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡁⢈⠁⡠⠊⡔⠱⡑⣤⢈⠔⣡⠔⡹⢆⠑⢎⡐⠁⠔⡁⠒⠁⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡖⠡⠊⢔⡡⣊⡠⢁⢚⡡⢊⠔⠈⢔⡢⢻⡀⢩⢔⡈⡂⠀⠀⠀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⣊⠐⠁⡨⠈⠁⢞⡡⢂⠁⡊⠔⠙⢊⡶⣡⠊⠑⡩⠀⠀⠀⠀⠄⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⣎⢂⠐⡡⢘⠈⡷⠁⢊⠀⠡⢀⠍⢰⡉⠀⡠⠠⠂⠔⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣦⡩⣪⠃⢞⠥⡊⢐⠅⣊⢄⠆⠀⠸⠅⠀⠁⡀⠂⣀⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠉⠙⠿⣤⡀⠹⣊⡐⠁⠊⠁⠁⠁⠀⠀⠀⣀⠠⠀⠀⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⡉⠲⠷⠿⢦⣴⡾⢛⠀⢈⠻⠛⠋⡀⠛⠁⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣐⣂⣭⠟⣁⣤⣤⢶⡲⠟⠿⣧⣒⢚⠓⣶⢾⠜⠓⢚⣱⣟⡖⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡗⣼⣏⡀⠠⠤⠈⢽⣌⠋⠉⠒⠶⠤⠉⠛⠋⢡⠄⠒⣠⣿⢫⡿⣽⣧⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣣⡿⢯⣞⢟⣦⣁⣒⢲⣛⣛⣺⣷⣦⣀⣀⣀⣀⣀⣴⣿⣟⡟⣿⢳⣛⣽⠿⢿⢿⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣸⣻⠿⢞⡭⣘⣶⠋⠿⠿⢻⣿⠏⣛⣩⣿⣛⢟⣯⡽⢿⠿⠟⠘⣃⣋⡩⢥⡲⠍⠩⠍⠱⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠷⡠⠈⠉⠓⠚⠛⠋⠽⡭⠦⠤⠤⢼⠭⡮⢭⠉⠟⠟⠟⠘⠲⠂⠈⠁⡄⣞⣛⣋⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠂⠐⠀⠀⡔⠰⢁⠌⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠁⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⡀⠀⠆⡀⠠⠀⠄⠐⠰⢀⠃⠄⠐⠠⢀⠁⠂⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⡦⣀⡁⠁⠰⣱⠃⠞⠾⠲⠷⢷⣆⣤⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⡟⠁⠀⠉⠐⠗⠀⠲⠒⢢⣄⢸⣼⣧⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⣠⣦⡄⣄⣀⣀⣼⣽⣄⣨⣅⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⣼⢋⠉⠀⠉⣖⠽⠬⡌⠁⢭⡤⠭⡘⣟⡙⠫⢨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢰⡟⢀⠖⠉⢀⠠⠐⠠⠚⠀⠀⠀⠀⡇⢧⢘⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀⠟⡁⢫⠐⠠⠢⢄⠠⠐⠀⠀⠀⠀⠀⢀⠘⣇⢀⣴⣧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡵⢄⡉⠀⠡⠒⠂⠀⠠⠤⠤⠤⠀⠐⠒⠻⢄⡟⠋⣙⣿⡟⢽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢦⢤⡜⢰⠁⠀⠀⠉⣴⣤⣤⠀⠀⢀⣀⣀⣀⣀⣠⢤⡏⣹⣨⣿⠆⠛⠛⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡔⣥⣶⢀⣇⢤⣔⠾⠝⠃⠉⠀⠀⠠⠍⠩⠭⠀⠀⠀⠀⣣⢸⡷⣟⣉⣁⠉⠁⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡣⣾⣧⣬⣬⣭⣥⠖⣆⣒⣒⣄⣤⣥⡬⠭⢭⣭⣭⣁⡀⣽⢐⠞⠁⠠⠛⢆⠐⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣷⣝⣻⣟⢵⡦⠦⠄⢀⣀⣀⣁⠀⠰⠛⠳⠗⠒⠲⠶⠒⣯⣼⢀⣴⡆⣿⠸⠆⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠛⠛⠛⠛⢻⠀⢠⡛⠏⡶⠓⠖⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠳⠞⠛⠛⠉⠁

⠀⠀⠀⢀⣀⣰⣶⣶⣶⣦⣄⠀⠀⠀⠀⠔⠀⠰⡀⠀⠀⠀⠀⢀⣀⣠⣤⣠⣀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⡴⠆⠀⢀⡴⠂⠀⢀⡰⠆⠀⣀
⠀⠀⠐⠛⠿⠿⡿⠟⠛⡋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠈⠠⢈⡯⢻⣷⣧⠀⠀⠀⠈⠉⣷⠀⠀⠀⣀⡀⠀⢁⣀⠀⠀⣀⠀⢀⣈⠀⢀⡈⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠇⠀⠀⠀⠈⠀⠁⠀⠈⣟⣻⣾⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⣷⢺⣾⢟⣷⠒⣿⠻⠶⣖⠛⠛⠷⠲⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠁⠀⠀⠀⠈⢀⡿⠀⠀⠀⠈⠉⠀⠒⠒⠚⠂⠀⠘⠓⠛⠒⠛⠓⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠁⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣄⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠉⠙⠋⠀⠀⢀⢔⣡⣶⣾⠿⠿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣻⣳⣴⣾⣿⣷⣿⣿⡷⠀⠈⠒⠒⠉⢹
⠀⠀⠀⠀⣀⠂⠄⢀⠀⠠⢀⣐⠢⠀⠀⠀⠀⠀⠀⢤⣵⠿⠋⠁⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⡿⠿⠛⠛⠀⠈⠁⠀⠀⠀⠀⠀⠨⡄
⠀⠀⠀⠢⠤⣉⠐⠀⠈⣁⠀⢈⠔⠃⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠈⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢸⠀⢠⠁⠀⢀⡀
⠀⠀⣶⠤⢄⣀⠈⠑⠂⢈⠐⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠋⠀⠀⠀⠀⢘⠀⠄⠀⢰⠁⣿
⠀⠀⠙⠛⠛⢻⣌⣹⠶⠋⠀⠀⠀⠀⠀⣰⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣀⢄⣄⠀⠀⠐⠒⠀⠂⠀⠀⠐⠁⠀⠀⢈⡜⠀⢀⠘⠓⠛⣴
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⢨⡷⠈⠀⠀⢀⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡇⣇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠶⢶⣶⡶⣶⠶⢚⠂⠀⠀⠀⠰⡀⠁⠀⠀⣾⣿⡏⢀⣮⠀⠀⠀⠀⠀⠀⠞⠀⠀⠘⡁⡛⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⢀⡿⠿⠾⠿⠾⡿⠿⢿⠀⠀⠀⠀⠀⡈⣴⠂⠀⠘⠿⠷⠄⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡆⠃⠀⡇
⠀⠀⠀⠀⠀⢤⠦⠄⠀⡄⣠⡀⠀⠀⡠⠾⠂⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠁⠀⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠄⠀⡇⡄⠠⡇
⠀⠀⡀⠀⠀⠀⣰⠏⠀⡔⠉⢧⠙⠖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢸⡇⠀⠀⡀⣀⣴⣴⣶⡆⠀⢀⣀⠀⠿⠆⠀⠀⢣⡅⢸⡇
⠀⠀⠀⠀⠀⠀⠁⢰⠞⠀⠀⠈⠇⠘⣁⠤⠀⠀⠀⠀⠀⣠⣴⢆⡜⢉⠝⠗⠦⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢰⡛⠋⠋⠉⠙⠇⠀⠀⠉⠁⠀⠀⠀⠀⠸⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣴⣽⢿⣶⣭⣏⣷⣄⣬⣵⣤⠀⠰⠀⠀⣠⠋⠀⠀⠘⡧⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣴⣯⣟⡻⢶⣤⡀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⢀⡴⠊⢁⠶⠀⠀⠀⢲⡈⠀⠰⠀⢀⠀⠉⢻⡀⠀⠸⣧⣤⣤⣉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣶⣤⡙⡿⣿⠟⢱⡶⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠂⢀⡎⠀⢠⡾⠁⠀⠑⠦⠈⡻⢟⣁⡿
⠀⠀⠀⠀⠠⣤⣤⡀⠀⠈⠙⢿⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠃⢀⡾⡀⢰⡿⠁
⠀⠀⣼⠀⠀⢸⡏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠤⠀⠂⠀⠀⠀⣰⣶⣺⠟⠀⠀⠀⠀⠀⠌⠀⢠⡿⠁⠀⠀⠀⠀⢤⡂
⠀⠀⣹⠀⠀⢈⡁⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡷⠎⠁⠀⠀⠀⠀⠀⠀⠠⢤⡾⠁⠀⠀⠀⠀⡆⠸⢁⡐⡇
⠀⠀⣿⠀⠀⠈⣿⠄⡄⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⢀⡴⣾⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡄⠀⠀⠀⠀⠀⢀⠃⠸⠀⡇⡇⢄⠔
⠀⠀⣿⠀⠀⠀⠡⡆⠁⠀⠀⠀⠀⠀⠒⠀⠒⠐⠒⠀⠒⠒⠀⠐⠀⠀⠀⢐⣿⡷⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠈⠀⠀⠀⠀⠘⠀⠂⠚⣛⣽⡌
⠀⠀⢿⠀⠀⠸⣷⠀⠈⠀⠀⠀⠀⠀⠠⣀⣤⠀⣄⣀⣀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⡀⢂⠐⡀⣂⠀⠀⠀⠀⠀⠀⠀⢸⣶⠆
⠀⠀⠸⡀⠀⣸⢡⠄⡄⠀⢀⡀⠢⠄⣻⣾⠏⣹⣁⡼⣤⣾⡚⣩⣤⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⡟⡌⠁⠉⡀⢆⠰⡐⢂⠀⠀⠀⠀⠀⠀⠈⣿⡶
⠀⠀⠀⠈⠰⢯⠎⠉⠀⠀⠈⠡⠤⠈⠭⠭⠬⠩⠍⠠⠭⠌⠭⠉⠁⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠉⠉⠁⠉⠈⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣰⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠍
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⣿⣷⣷⣶⣶⣾⣿⡿⢿⣿⣿⡿⠿⠿⠛⠋⠀⠠⠔
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣯⣛⠶⠶⠦⠤⠅⠀⠀⠀⠠⠄⠤⠤⠤⠄⠒⠒⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣦⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⠊⡁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠿⠿⢿⠿⠿⠟⠛⠻⠶⠓⠚⠲⡶⠚⠿⠋⠁⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣖⣄⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣻⡛⠽⠛⠿⢷⣤⣀⣀⣀⣀⣀⣠⠤⠖⠒⠚⠋⠉⠁⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣠⣤⣀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣀⣀⣤⣤⡴⠚⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡶⢶⢶⣶⢿⡿⠉⠁⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠿⣿⣿⣿⣿⣉⣈⠉⠀⢀⠀⡈⣉⣉⢀⣀⣠⣴⡤⠶⢚⡉
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⡁⠪⠽⢛⡛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⠄⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⣄⣀⣀⠀⠀⠀⠈⠀⠀⣀⣀⡤⠴⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⠒⠂⠀⠶⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠂⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠳⠁⠀⠀⢀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣷⠁⠀⠀⠀⢤⡶⠏⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣼⣤⡀⠀⠀⠱⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠂⠠⠤⠭⠀⡄⠀⠁⠀⠑⡄
⠀⠀⠀⠀⠀⠀⣠⢞⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡇⢰⡀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠐⠠⣄⣀⠀⠀⠂⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⡷⣀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⢀⠘⢑⣂⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⡸⠁⠈⠣⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠆⡇⠀⠀⠀⠀⠐⠄⠀⢰⠀⡇⠀⢀⠀⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⣀⡯⡰⠁⠀⠀⡠⠊
⠀⠀⠀⣀⣤⠤⢶⣶⣶⣖⣾⣓⣂⡀⣛⡂⣲⣶⠀⠦⠤⢄⡀⠀⠀⠀⠀⠀⠀⢰⠥⠟⠀⢀⡠⠊
⠀⢰⡏⢡⣶⣶⣶⣯⠛⠋⠛⣁⣈⣭⡍⠉⣩⣿⣶⣦⣤⠀⢀⣦⠀⠀⠀⠀⠀⢸⡆⠐⣶⡉
⠀⠘⠉⠛⠻⠯⢭⣥⣸⣛⣛⣛⣉⣉⣀⣀⣈⣍⢭⢭⣄⣲⣭⣰⠀⠀⠀⠀⠀⠈⠘⠛⠛⣇
⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢧⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⡟
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣹⣿⣿⣿⢯⣿⠇⠀⠀⠀⠀⠀⠀⡀⠀⢰⡇
⠀⠀⠀⠀⠑⢤⣤⣀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠟⠁⠏⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠉⠺⠿⣿⣷⣶⣿⣿⣿⣿⣿⠿⠊⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⡏⠀⠀⠸⣆⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣤⣖⣚⠋⠀⠂⢤⢿⡄⠀⠀⠀⣄⣀⡄⠀⠀⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠛⢝⢻⣿⣿⣦⣶⣶⣶⠟⢷⡀⠀⠀⠀⢿⢷⣶⣤⣀⡀⠀⠀⢀⠀⢿
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠉⠙⠛⡟⠛⠉⠁⠀⠘⣧⠀⠀⠀⢸⠀⠉⠙⢿⠿⠿⠿⠏⠀⢸
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⡄⠀⠀⠘⡆⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⣀⣀⣀⣠⣤⣤⠴⠶⠶⠗⠛⠛⠛⠛⠛⠉⠛⠉⢙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⡿⢛⡉⠩⢥⠀⠀⠉⠁⠐⠂⠀⠒⣂⠈⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⡠⠊⠄⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⢃⣀⡀⠠⠀⠐⠀⠉⠁⢀⣀⠀⠤⠀⠀⠀⠀⠀⠉⠭⠁⠀⣴⣿⣿⣿⠀⠀⠀⠀⢀⠔⠀⢠⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠂⠠⠤⠀⠀⠀⠀⠈⠉⠀⢀⡀⠠⠄⠀⠀⠂⠠⠤⠄⠀⠀⠐⢩⣭⣿⠀⠀⠀⡰⠋⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡶⠀⣉⡁⠀⠀⠉⠉⠄⠀⠀⠀⢀⣐⠐⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⡟⠀⠀⣀⠠⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢟⣋⢉⡀⠀⠀⠤⠄⠀⠀⠤⣀⠡⠤⠄⠀⠈⠉⠐⠒⠒⠀⠀⢻⣿⣿⡇⢀⠄⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠉⠐⠂⣀⠀⠀⠉⠀⠀⠐⠀⠀⠀⣉⣀⣠⣔⣂⠤⠒⠤⢢⣰⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣍⡮⠉⣀⣀⠀⠀⠀⣐⣂⣐⣤⣄⠔⠲⢭⣶⣬⡳⠯⣔⠊⠀⣩⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣴⣤⣾⣷⣶⣿⣿⡿⠿⠛⠛⠛⠛⠲⢦⣼⡄⠀⢀⢀⣿⣤⣾⡿⢃⣿⣿⣿⣷⣖⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣶⢾⣿⣿⣿⣭⣿⢶⡶⣿⣿⡿⣽⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣟⢟⣿⣿⡿⣿⣷⣶⠶⡶⣖⣺⣺⣭⣿⣷⣾⣿⣟⢟⡿⣻⣟⣿⡷⣜⡫⠿⠛⠉⠑⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⣿⣷⣝⡻⣽⡶⢶⠾⣿⢿⡿⣿⢿⣿⣿⣿⢿⠿⢏⣛⠿⠍⠚⠊⠁⠀⠀⢀⡶⣶⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡇⠇⡏⣿⣮⡙⢾⡑⠮⢷⣙⠯⠏⠝⠉⠐⠃⠈⠀⠀⣀⣶⣶⠀⠘⠃⠀⠘⢷⡿⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣦⢇⡌⡏⡟⣾⡟⠉⣀⣄⣀⠀⣴⣻⡆⠀⠘⠃⠀⠘⠿⠏⢀⠀⠄⠄⢴⣖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠓⠧⣀⢿⡇⠀⣿⣼⣿⠀⠙⠛⠁⢀⣀⠠⠄⢲⣶⠁⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡽⠀⠀⠀⠀⠈⠹⡇⠀⣈⡙⠥⠐⠂⠀⠈⠀⠀⠀⠀⣀⣿⣆⡀⠀⠀⠀⠀⢻⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢀⣀⡤⠤⠖⠚⠋⠉⢹⣿⠐⠍⠀⢀⠠⢸⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡜⠀⠀⠀⠀⠀⢀⣀⡄⣷⠶⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢈⠐⢗⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣧⠴⠖⠒⠋⠉⠉⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣃⠀⠀⠀⠀⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠭⣒⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠒⠈⠁⠈⣿⡄⠀⠀⠀⠀⠀⠘⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡸⠀⠀⠀⠉⠒⠤⣁⠒⠄⣴⣠⡠⠄⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠁⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⠃⠀⠀⠀⠀⠀⠀⠀⠈⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⡞⠁⠀⠀⠀⠀⠀⠀⢃⢠⡴⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢂⣁⡗⠢⠤⡀⠄⠒⢢⠤⠒⠧⡀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣠⣎⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠂⢁⡨⠀⢠⠤⠀⠈⠀⠠⠖⢂⠀⢸⡀⠀⡏⠢⠄⠀⠀⢀⢎⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠡⠄⠀⣠⡤⣀⠀⠀⣀⠀⠀⠑⠈⠁⠀⠐⠛⠉⠉⠀⠈⢱⡔⡑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢒⡞⡀⢤⡬⢤⣄⡇⠐⠉⠀⠀⠐⠀⠀⠤⣀⣀⡤⠀⠀⠀⣀⢄⡦⠪⢊⡘⣖⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢾⡓⠐⠒⠒⠒⠀⢘⢣⠀⣰⣓⣱⠀⠀⠀⠀⣄⠀⠀⠠⠾⡠⠥⠤⠖⠐⠁⣈⠆⢀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠈⠢⠄⣀⡀⠴⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠥⠤⠐⠒⠊⠉⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠲⢆⠠⠤⠤⠄⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠠⠤⠤⠄⡴⠖⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠐⠈


⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⢠⣾⡆⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⢠⣿⠏⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⢠⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣠⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣤
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⣴⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣴⣿⣿⣿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣦⡀⠀⢿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣠⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠟⡀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⢠⡶⠶⣦⡀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢠⡶⠶⣦
⠀⠀⠀⢻⣄⣀⣼⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣇⣀⣼
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠁⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⣿⣿⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢿⣿⣦⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠈⢻⣿⣇⠀⠹⣿⣿⡄⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⣿⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠹⣿⣇⠀⢹⣿⡆⠀⠈⣿⣿⠀⠀⠀⣾⡇⠀⣿⣿⠀⢀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠹⣿⣧⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⣿⡟⠀⠈⣿⡇⠀⠀⢹⣿⠀⠀⠘⣿⣧⡀⠹⣿⣧⠈⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⠘⣿⣇⠀⠙⣿⣦⠀⠀⠀⠀⢰⣿⠇⠀⢰⣿⠇⠀⠀⣾⡿⠀⠀⠀⠈⠻⣿⡄⠙⣿⣇⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⢸⣿⠀⠀⢹⣿⠀⠀⠀⢠⡿⠃⠀⠀⣾⡏⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⣹⡇⠀⢸⣿⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⣸⡏⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⣼⡟⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⢠⣿⠁⠀⠼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⢠⡿⠁⠀⠼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠟⠛⠛⠛⠉⠉⠉⣉⣉⣉⣁⣁⡠⣤⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⠙⠛⠛⠻⠷⢶⣦⣤⣀⡀
⠀⠀⠀⠀⢀⣠⣤⡶⠟⠛⠉⣉⣁⡤⣴⠶⢂⣶⣾⡿⠛⠻⣿⡿⠛⢉⣩⣿⠟⠁⣉⡼⠛⢿⡉⢉⣭⡯⠟⠉⢀⣿⡾⠷⠢⣤⣤⣌⡉⠛⠿⣦⣄⡀
⠀⠀⣠⡶⠟⢋⣡⠤⠐⠛⣡⣽⡯⠛⢁⣴⡿⠛⠻⣷⣄⢀⡼⣠⣴⠿⢋⣡⡴⠛⢿⣦⡀⢠⣿⠿⠋⠀⣠⡴⠛⠿⣧⡄⢀⡼⠛⠉⡹⢿⣶⡀⠉⠻⣦
⢠⣾⠋⢀⡴⠋⠁⣀⣤⣾⣽⣧⣴⡞⠉⠛⣷⠆⠀⢀⣤⣿⣿⣿⣿⠛⠛⢻⣷⠀⠀⣉⣼⣟⣡⣴⡚⠛⢻⣷⠄⠀⢈⡴⠋⢀⣤⣾⠟⠁⠀⢱⠀⠀⢸
⣾⠇⠀⠸⣄⣠⣾⠿⠋⣹⠁⠀⠹⡿⠂⠀⣁⣤⣾⣿⢿⠟⠁⠈⢻⠷⠀⠈⣁⣤⡾⠋⠝⠁⠉⢹⡿⠀⠀⣁⡤⠞⠉⢀⣴⡿⠛⠁⢀⣀⠴⠃⢀⣠⣾
⣿⣆⡀⠀⠙⠛⠧⣤⣴⠿⢄⣀⣀⠤⠞⢋⣤⡿⠛⠁⠈⣦⣀⣀⣀⠤⣴⣿⠟⠁⢀⣴⡷⣄⣀⣀⣤⡶⠟⠁⠀⢀⣴⣿⡟⠤⠖⠛⠉⣀⣤⣶⣿⣿⣿
⢻⣿⣿⣷⣦⣄⣀⡈⠈⠙⠛⠛⠣⠴⡾⠿⠃⣀⣀⣤⣾⣋⣁⣀⣤⣾⣏⣁⣠⣾⣟⣁⣀⡀⣴⠿⠿⠤⠶⠐⠚⠛⠋⣁⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⣀⣀⣀⣀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠈⠉⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⠋⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡏⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢹⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢠⣿⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣿⡄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⢻⣿⠛⢻⡿⠻⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢀⣿⠁⣀⣀⣤⡤⠶⠛⠛⠉⠉⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠉⠙⠛⠶⣤⣄⣀⠀⠀⠸⣷⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⣿⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠦⣿⡆⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠇⢀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⣿⠿⢿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⢰⡿⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠘⣷
⠀⠀⠀⠀⠀⠀⣾⠇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢻⣇
⠀⠀⠀⠀⠀⢰⡟⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠈⣿⡄
⠀⠀⠀⠀⠀⣾⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠸⣧
⠀⠀⠀⠀⢰⡟⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢻⣆
⠀⠀⠀⠀⣿⡃⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⣿⡀
⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⣿⣿⣿⣿⢟⣡⠞⠁⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⣿⣿⣿⢟⡵⠋⠀⠀⠀⢸⡃⠸⣄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⣿⣿⡿⢛⡵⠋⠀⠀⠀⠀⠀⢀⡗⢠⠟⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣫⣴⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣼⠋⣿⠉⣿⠙⣇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠇⠀⣿⠀⣿⠀⠹⡆⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⡏⠀⠀⣿⠀⣿⠀⠀⢻⡄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⡞⠀⠀⠀⣿⠀⣿⠀⠀⠀⢷⡀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡼⠁⠀⠀⠀⣿⠀⣿⠀⠀⠀⠈⣧⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠃⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠘⣇⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⢿⣀⣿⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁



⣀⣀⣀⣀⣀⡀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣤⡸⠋⠿⢳⣾⣀⡄⠀⠀⠀⠀⠀⣀⠸⣿⣆⢲⡄⠀⠀⠀⠀⢄⠙⢦⡀⠀⠀⠀⢰⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢠⡴⢼⣦⣤⣤⣤⣤⣿⣤⣤⠀⠀⠀⠀⢿⣦⣿⣿⣿⡿⠀⠀⠀⠀⠈⠳⠞⢇⠀⠀⢀⡼⠿⠿⠋
⠀⠀⠀⠉⠈⣧⢸⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁⢠⣆⣸⣿⣿⡟⢹⣧⣼⡀⠀⠀⠀⠀⠀⠀⢑⣴⠋
⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⣿⡟⠻⠀⠁⠀⠹⡿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣸⠁⠉⠉⠉⠁⢱⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡢
⠀⠀⠀⠀⣠⣮⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⢀⣼⣄⠀⢀⣾⡀
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣰⣿⠟⠋⠁⠈⠙⢻⡿⣄⠀⠀⠀⠀⢸⣿⣿⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡆⢰⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⡄⢴⠀⠀⢸⣿⣿⠀⣿⣿⣿
⠀⠀⢀⠞⣤⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠗⠸⣿⡇⠀⠀⠀⠀⠀⠀⣸⣿⠃⠚⠀⠀⢸⣿⣿⠀⣿⣿⣿
⠀⠀⠛⣾⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⡦⣄⣀⣀⣠⢼⡿⠋⠀⠀⠀⠀⠘⠛⠛⠀⠛⠛⠛
⠀⠀⠸⡏⣿⣿⡿⠋⠀⢂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠟⠛⠋
⠀⠀⠀⢻⣌⡟⠁⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⣀⣻⡶⢲⣶⣶⣶⣶⣶⣶⣶⣶⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣶⣶⣿⣿⡿⠏
⠀⠀⠀⠀⠀⢷⡸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣟⡏⠉⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⣠⣴⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠉⠁⠀⠸⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠧⠤⠤⠤⠤⠤⠤⢷⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠁⠈⠁⠀⠐⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐
⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣠⠴⠐⢁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢀⡠⠀⠤⠂⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠂⠐⠒
⠀⠄⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠀⠀⠆
⠀⠠⠀⠀⠀⠀⠀⠀⠨⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠐⠀⠀⠀⠀⠀⠀⠂⠐⠊⠂
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠀⠀⠀⠀⠴⠏⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠁⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠘⠄⠰⠅
⠀⠀⠀⠀⠀⠀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠐⡀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡤⠢⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄
⠀⠘⠀⠁⠁⠑⠀⠀⠀⠀⢀⠒⠀⠃⠴⠁⠒⢲⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡀⠐⠂⢄
⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠐⠌⠀⠚⠈⠈⠀⠸⠀⠀⠀⠀⠁⠃⠀⠈⠀⠀⠀⠀⠀⠐⠀⠐⠂⠐⠀⠒⢈
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠐⠠⠤⠥⠤⠔
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣽⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢳⣿⢿⣿⠯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⣿⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣄⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠇⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠉⠁⠀⠀⠀⠀⠀⣸⣷⣤⡀⠀⠀⠀⠀⠀⠉⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⣀⠤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠛⠀⠀⠀⣀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠻⣿⣿⡇⠀⠀⠀⣴⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠈⠙⢿⡄⠀⠀⠈⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⠿⠟⠛⢛⣿⠛⠉⠉⣩⡿⠋⠉⢉⡽⠋⠉⢉⡿⠋⠛⢻⡟⠻⠿⢿⣶⣶⣤⣄⣀
⠀⣠⣶⡿⠟⠋⠉⣡⡾⠃⠀⢀⣴⠟⠁⠀⢀⣼⠋⠀⠀⣠⠟⠁⠀⣠⡟⠀⠀⣰⡟⠀⠀⢀⣾⠁⠀⠉⣽⠟⢿⣶⣄
⣼⣿⠋⠀⠀⣠⣾⠋⠀⢀⣴⡿⠉⠀⢀⣴⡟⠁⠀⣠⡾⠃⠀⢀⣶⠃⠀⢀⣴⡏⠀⠀⢀⣿⠋⠀⠀⢠⡟⠀⠀⠙⣿
⢿⣿⣄⣴⣾⠟⠁⢀⣴⣾⠏⠀⢀⣴⡿⠋⠀⢀⣴⠟⠁⠀⣴⡿⠃⠀⢠⣾⡏⠀⠀⢠⣾⡟⠀⠀⢠⣿⠃⠀⠀⣠⣿
⠈⣿⣿⣿⣷⣤⣴⣿⡟⠁⠀⣠⣿⠟⠁⢀⣴⣿⠋⠀⢠⣾⡿⠁⠀⣠⣿⠏⠀⠀⢀⣿⡿⠃⠀⢀⣿⣯⣤⣶⣿⣿⣿
⠰⣿⣏⠻⠿⣛⡛⠿⠿⢿⣿⣿⣷⣤⣴⣿⣿⣅⣀⣴⣿⣏⣀⣀⣴⣿⣯⣤⣤⣤⣾⣿⣷⠶⠿⠟⠛⠛⠉⣉⠀⣽⣿
⠀⢻⣿⡙⠒⢿⣿⣿⣷⣶⣦⣤⣤⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣤⣤⣤⣶⣶⣿⡗⠀⠀⠀⣸⣿⠇
⠀⠀⢿⣿⡆⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⢤⣴⣿⠏
⠀⠀⠀⢻⣿⣷⣶⣤⣬⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⢂⣶⡿⠃
⠀⠀⠀⠀⠹⣿⣿⡇⠀⠀⠹⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⡛⠛⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣄⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣤⣼⣿⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠛⠻⠿⠿⢷⣾⣿⣿⠿⠟⠛⠛⠉⠉⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡿⣿⠃⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣹⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⣴⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢦⡴⠚⠉⠉⢙⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣴⠋⠀⠀⠀⣸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡇⠀⠀⢀⠸⠅⠈⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣠⡎⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣴⣃⣀⣀⣤⠀⣀⠀⡀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣻⣯⣯⣿⡅⠈⢠⣀⢀⣌⡞⡿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⣿⣿⣿⣿⣟⢛⣡⣻⢆⢗⡼⣫⣿⣿⣷⣍⡷⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣻⠿⠷⣿⣿⣟⣵⣿⣿⣿⡿⠽⢛⣯⣞⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣗⠖⠀⠰⠖⠒⠒⠒⠀⠛⠙⣿⡟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣷⣄⣀⠁⠀⠀⠀⢀⣀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⢿⣿⣿⣷⡾⣾⣿⡿⣏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⣿⡟⠛⢁⣻⡿⠤⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠙⠧⣤⣀⡽⠃⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢠⢖⣿⡓⢤⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⠃⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⢀⡤⠖⠋⠛⠿⠛⠙⠓⠤⣀⡀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣦⣽⣷⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⢀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣾⡿⣼⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣛⣛⣟⣹⣛⣟⢛⡿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⠁⠀⠀⠀⠈⠁
⣀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⣶⣦⣴⣶⣤⣿⣦⣼⣿⣴⣿⣷⣼⣷⣤⣷⣦⣼⣷⣥⣤⠀⠀⠀⠘⠛⠀⠀⠐
⣜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⢀⡤⠀⠀⠀⣤⡤⠤⠤⠤⣤⠤⠤⠤⠤⠀⠀⠀⠀⢀⣄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⠀⠰⠇⡶⠀⠀⠠⢰⠆⠤⠸⢇⡿⠀⠀⠺⠐⠇⠀⠀⠀⣀⡀⣀⡈⠻⠘⣀⠀⣀⣄
⠈⣭⡍⣍⣉⠉⠉⠉⠉⠉⠉⢉⣩⣀⣀⣀⠀⣤⠤⠭⣉⣉⡈⣈⢡⣈⣁⠉⣩⣭⠉⣀⣀⣈⣯⡍⠉⠉⠉⠛⠛⠋⠉⠉⠉
⠀⣿⣷⣤⣹⣀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠸⠿⠋⢿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣤⠔⠓⢆⡀⢐⣦⣠⠼⠷⡖⠀⠀⢀⠠⡾⠀⣤⣤⣤⣭⣥⣀⣀⡀⠀⠀⠘⠿⠃
⠶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠶⢶⣮⣷⢶⡚⠙⢯⣀⣈⣶⣤⠀⠀⠀⠀⠀⢱⠀⢒⣒⣒⣿⣿⣿⠿⠇
⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢻⣧⠟⢾⡉⠉⢳⣄⡈⠀⠀⠠⠄⠀⠀⠀⢴⠚⠛⠩⠉
⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠺⠗⠀⠀⠀⠀⠀⣿⠶⠖⠛⠛⠩⡈⠀⠐⡀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣶⢆⣶⠁⢀⣀⠄
⠀⠀⠀⠀⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠰⠷⠀⠀⠰⡦⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⠀⠀⠀⠀⢸⣿⡆⢰⣿⢸⠇⣴⣿⣿⣿⣦⢠⡀
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⡀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡭⠋⠀⠀⠀⠀⠀⢸⣿⡇⠀⢿⣾⡄⢿⣿⣿⣿⡿⢰⡿
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣾⢿⣁⠀⠀⠙⠿⢦⣽⡿⣿⡁⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠀⠀⠀⠈⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠀⠀⠀⢸⣧⠀⠀⣀⣠⣤⣤⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠟⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⢄⣠⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠
⠀⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠚⠻⢸⠾⢡⠻⢓⠀⠀⠀⢀⡀⠔⠒⠋⠱⠤⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⢠
⠀⠧⣄⣀⣀⣀⡠⠜⠀⠀⠀⠀⠀⠀⠘⠈⠈⠁⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠠⠑⠀⠀⠀⠆⠀⠀⠀⡀⠞⠚⠁⣸⠜⠉⠀⡀⣴⠀⠠
⠀⠿⢦⣤⡄⠽⡤⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠘⠚⠀⠈⠓
⠀⠀⠀⠬⠩⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢀⣀⠀⠠⠄⢀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣶⣿⠟⠳⠶⠦⢦⡄⠀⠀⠀⠀⠀⠁⠀⠀⠁
⡔⠀⠁⠄⠄⠀⠒⠀⠲⠂⠀⣈⠁⢂⡠⠀⠀⠀⠰⠒⠀⠲⠶⠛⠉⠉⠂⠀⠀⠀⠈⠉⠻⠥⢀⣀⢤⡤⠴⠂⠀⠀⠀⠀⠀⠄⡀
⠈⠲⠤⠤⢑⣁⣂⠀⡀⠈⠛⢀⠀⠀⠀⠔⠂⠀⠀⠴⢤⣄⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠿⠾⠶⠶⠿⠑⠀⠀⠀⠀⠀⠀⠀⠀⢉⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂
⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⣤
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⡆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠐⠀⠀⠀⠀⠁⡀
⠀⠱⢬⣽⣿⣿⡫⠅⠀⠀⠀⠀⠁⠀⡇⢠⠀⡄⠁⠀⠀⠖⠄⠐⢠⠤⠀⡄⠀⠀⡄⡀⠀⠀⢏⠀⢀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠔⠁⠸⢄⠀⠀⠠⠀⠢⠀⠰⠘⠠⠃⠡⠠⠠⠁⠃⠀⠀⠈⣉⠃⠀⠀⢠⣷⡈⣧⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠾⠋⠁
⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠱⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠁⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⡀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠄⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠈⠂⣐⠂⠀⠀⠉⠓⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⠋⠠⠟⠂⠳⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠐⠀⠂⠀⠀⠀⠀⠈⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢫⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠘⡍⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⣄⡰⠋⠙⢲⠀⠀⠀⣶⢸⠉⠀⠳⡎⠙⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡼⠀⠀⠀⠀⠈⡏⢹⠋⠸⠘⡀⠀⠀⢻⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣰⠃⠀⠀⠀⠀⠀⡇⢸⠀⠀⡇⡇⠀⠀⠈⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠇⠀⠀⠀⠀⠀⢀⠁⢸⠀⠀⢣⢳⠀⠀⠀⠸⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡞⠀⠀⠀⠀⠀⠀⢸⠀⠾⠀⠀⢸⠸⡄⠀⠀⠀⢣⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣰⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡜⠃⠉⠉⢦⠀⠘⡄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠸⣄⠀⠀⠀⡸⠀⠀⢳⠀⢷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡼⢤⡎⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠙⠓⠒⠊⠁⠀⠀⢈⠗⠈⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣤⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠞

⠀⠀⠀⣤⠤⠄⠀⠀⠀⠀⢠⣐⠦⢀⠀⠀⠀⡄⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣤⣄⡀⠀⠀⢀⠀⠀⠀⠀⢀⡤⣴⣶⣤⡤⣄⡀
⠀⠀⠀⣽⡻⠒⠲⠶⢲⢚⠊⠁⣠⡞⠀⠀⠀⢲⡆⠀⢐⡻⢿⣿⣿⣿⡿⣿⣿⣿⣳⠀⠀⠈⠉⠉⠁⠒⠢⣿⢋⣾⢋⣼⠟⣽⢦
⠀⠀⠀⠈⣋⠽⡳⡳⠚⢚⢚⠛⢉⣤⠆⠀⠀⠐⢿⠀⠀⠙⢤⠉⠻⣿⣿⣿⣿⡿⠟⠀⠀⠾⢩⠖⠀⠀⠠⣿⣼⣣⣾⠃⣾⣡⣿
⠀⠀⠀⠀⠈⠙⠚⠲⠷⠯⠞⠚⠋⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠺⣿⠿⠛⠋⠀⠀⠀⠀⠈⠑⠈⠀⠀⠀⠈⠛⠿⢿⣿⠿⠟⠁
⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⡄⠀⠀⠀⢀⣀⣀⣀⣀⢀⢀⣀⣀⢄⣀⡀⠀⠀⡠⢐⠀⠀⠒⢄
⠀⠀⠀⠑⠄⡸⠀⣾⣻⣿⣿⠆⠀⢙⠆⡾⠟⠁⠀⢀⠒⠛⠯⠿⠏⠿⠄⠂⠛⠋⠉⠀⠀⠀⡜⢰⠁⣎⣴⢈⠆⡇⠀⢺⡹⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠫⠶⠀⠀⠀⢀⣤⣄⢠⣠⣤⢠⣶⣞⠗⣆⡠⠤⠀⠀⠀⠹⣌⠓⠨⣍⣡⡼⠁⠀⠀⠉⠉⠁
⠀⠀⠀⠀⣀⠆⡠⠖⣢⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠁⠀⠉⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠉⠀⠀⣀⣀⣀⠀⠠
⠀⠀⠀⣿⢡⠎⠠⠊⣡⣤⠯⢁⡰⠀⢀⢠⢆⣬⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠚⠁⠀⡀⠉⢠⠽
⠀⠀⠀⠈⠉⠛⠚⠋⠁⠀⠀⠀⠀⠀⠘⠚⢻⡙⠀⠀⠀⣠⠔⠋⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣌⠉⠁⠀⢀⡀⠐⠀⠀⢨⣱⡀
⠀⠀⠀⠀⠀⢀⡤⠤⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣀⣠⣤⠄⠂⠀⢈⡀⠽⠃⠀⠀⠀⠀⠀⠙⢄⢀⡤⢺⣧⣇⣀⡀⠼⠋
⠀⠀⠀⣤⣴⢁⡔⣫⢔⡪⠟⣛⡷⠶⢄⡀⠀⠀⠀⠾⣿⣿⣿⣿⣶⣶⣯⣥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠌⠁⠤⠖⠁⠀⠀⣀
⠀⠀⠀⠀⠫⢿⣹⠷⣾⣤⣾⣁⢀⡴⠚⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⣀⢀⠀⠀⠋⠻⠜⣏⡹⠏⠀⠀⠀⠀⠀⠀⠉⠛⢿⡛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠤⠤⠶⠟⠀⠀⠀⠀⠐⠀⠀⠚⠁
⠀⠀⠰⢁⡴⠁⠀⠀⠀⠀⠈⠀⠀⢀⣤⣲⠿⢿⡇⠀⠀⠀⢹⠓⠂⠀⠔⢷
⠀⠀⠀⠀⠀⢀⣼⣷⣦⡀⠀⠀⢠⣶⣿⣿⣿⡿⠃⠀⠀⢠⡗⣐⣀⣤⣥⣼⣦⠀⠀⠀⡄⠀⠀⢰⠀⡀⠀⢠⢴⠀⠐⠂⠀⠀⡆
⠀⠀⠀⠀⢠⣾⣾⢧⣬⡛⡳⠀⠘⢿⠿⠟⠁⠀⠀⠀⢀⠎⠀⠉⠉⠉⣿⣧⣽⠀⠀⠀⠱⠀⠀⠀⡇⠁⠀⠘⡿⠀⠸⣿⠀⠀⠇
⠀⠀⠀⣠⣋⣟⢷⣄⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⡎⢀⡀⠤⠴⣈⡻⠿⠏⣇⠀⠀⠀⠀⠀⠀⢇⡏⠀⠀⢧⠀⢰⠹⠀⠀⡄
⠀⠀⠀⠈⠙⠿⣮⡈⠟⠉⠛⠶⣤⠀⠀⠀⠀⠀⢻⣿⡟⠛⠒⠒⠒⠒⠒⠛⠚⠛⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⠀⠀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠸⠇⠀⠀⠰⠀⠸⠀⠃⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣠⠖⡿⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡤⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡿⠁⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠘⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠔⠀⠀⡠⠊⢀⣄⠀⠀⠀⠀⠀⠰⠦
⠀⠀⢸⠀⠀⠠⡿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠈⠀⠀⠴⠂⠀⣀⠀⢀⡠⠊⠀⠀⣰⡥⠀⠘⠁⠀⠀⠀⠐⢶⠆
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂⠀⢀⡀⠤⠐⠀⣀⣸⠟⠂⠁⠀⠀⠀⠀⠙⡁
⠀⠀⢸⠀⠀⠀⠀⠀⠰⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠐⠓⠂⠀⠀⢴⠆⠀⠈
⠀⠀⠙⠇⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐⠋⠀⠛⠁⠀⢀⣠⡤⣄⠀⢀⣤⣤⣤⣄⣀⢠⣟⣡⠇⡀⠀⠀⣠⢤⠀⠀⠀⠀⠓⢿⡆⠀⠀⢈⠀⠄⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢃⣴⡿⠀⠛⠋⠉⣉⣉⠛⣿⣛⣅⢠⡍⣴⢶⠻⣾⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿⠁⣼⠏⢳⢸⡏⢸⣼⣿⡵⠟⣾⣃⣿⡨⢾⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠉⣸⣿⢦⡟⢻⣉⡟⠹⠏⢻⣦⡬⠵⠶⣄⠘⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣠⠞⠁⠙⠊⣤⣤⣤⣴⣶⠿⠋⠉⠛⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣠⠤⠀⠰⠿⠃
⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⠀⠚⠷⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠀⠛⠦⠀⠀⠀⠀⠀⠀⠀⢠⠞⣤⣤⠔⠒⠒⠢⠄⠈⠀⢀⡤
⠀⠀⠀⡈⠁⠶⠄⠉⠀⠀⠀⣤⡤⠀⠀⠙⠛⠀⠀⠀⠀⠀⡀⠒⠋⠀⠰⠶⠆⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⢻⡟⢁⣤⠀⠀⠒⠀⠀⣀⡀⠀⢀
⠀⠀⠰⣿⡀⠀⢀⣄⢀⣴⣤⠀⠀⣴⣦⡄⠠⢢⠆⠀⠀⡾⠀⠚⠂⠀⠀⠀⠈⠃⠀⠉⠁⠀⠙⠀⠀⠀⠀⢀⢱⣬⠕⠊⠉⡉⠉⠉⠐⠢⡀⣀⠃
⠀⠀⢸⣿⣿⣷⣴⣦⣤⣠⣤⣄⣀⣀⣀⣀⣤⡏⠀⠀⢠⠆⠀⠈⠁⠀⠀⠀⠄⠀⣦⡀⠀⠀⠐⠀⠀⠀⠀⢸⡟⠁⣀⡀⠀⠋⠀⠀⣀⡀⠀⠉
⠀⠀⠘⢫⣭⣌⣡⡄⠘⠛⠋⠉⢉⠉⣽⣷⣠⣾⠀⠀⠈⠃⠀⠐⢂⠐⠀⠀⡀⠀⠉⠀⠀⠘⠀⠀⠀⠀⠀⢨⠄⠀⠉⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢾⠿⢿⠷⠒⠷⠶⠶⠶⡾⠛⠛⠋⠉⠁⣀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠠⠄⠀⠐⠀⢀⠤⣄⠀⠀⢿⡴⠃⠀⠀⠀⠀⠺⠆⠀⠀⢠⡀
⠀⠀⠀⠾⣶⠶⠤⣤⣤⣤⣤⣼⣍⣤⣤⡴⢾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⠄⠤⠀⠀⠀⠀⠀⠀⠘⣇⠀⠺⠆⠀⣀⠀⠀⠀⠓⠈⠁
⠀⠀⢠⣾⣥⣄⣚⡃⠀⠀⣙⣁⣛⣀⣤⡤⠴⠖⠒⠀⠀⠀⠀⠐⠒⠀⠈⠁⠀⣀⠀⠀⠀⠀⢸⠆⠀⡀⠀⠀⠘⢄⡀⠀⠀⠉⢀⣀⠀⠀⣀
⠀⠀⠈⣻⣡⡾⡍⠛⣻⣏⠛⠉⠉⠉⠀⠰⠦⣈⠜⠁⠀⠀⠀⠀⠐⠆⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠉⠀⠲⠤⣤⠉⠐⠋⠁
⠀⠀⠀⠈⠉⠉⠙⠛⠂⠠⠶⠴⠖⠚⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠢⠀⠺⠂⠀⠀⠀⠀⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠟⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⡀⠀⣤⣠⠁⢀⣀⣶⢠⣰⣆⢼⣆⠀⠀⠀⠀⠠⠆
⢀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣤⣤⣤⣝⣦⡬⠓⢖⡉⢻⣄⠁⠀⣽⣿⣷⠀⠩⣽⣿⣿⣿⡯
⠀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⢹⡌⠒⢈⢙⣦⡄⠀⠀⠀⠁⠉⠁⠔⠛⠹⠟
⠀⠀⠈⣿⣷⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠘⠃⠀⠀⠀⢰⡟⠚⠉⠉⠀⠀⠀⡄⠀⠀⠀⠀⢿⡄⠀⣾⣻⠇
⠀⠀⠀⢸⣿⣿⠗⠂⠀⠀⠀⠀⠉⢀⡀⠛⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢴⡟⠀⠀⠀⠀⢸⣷⠀⣿⡟⢸⡅⠀⠀⠀⣧
⠀⠀⠀⠘⠋⠛⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣾⡏⠀⠘⠿⣮⣻⣦⣄⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠛⠁⠀⠀⠈⠁⠉⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠴⣶⣿⣧⣀⣠⣤⡴⠶⠶⠶⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠉⠉⠁


⣶⣶⠶⠶⠶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣶⢶⣿⠿⣿⠿⣿⢿⡿⣿⠿⣿⠿⣿⡶⣶⣶⣶⣶⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⠟⣛⡿⢋⣽⠏⣡⡟⠁⣼⠃⢰⡏⢰⡇⢸⡇⢸⡆⢹⡆⠘⣧⠈⢻⣄⠹⣯⡙⢿⣛⠻⣿⣷⣶⣄⡀
⠀⣀⡀⠀⠀⣾⣟⣡⠟⢁⡼⠋⣠⠟⢁⡼⠋⢀⡾⠁⢠⡟⠀⣼⠁⢸⡇⠈⣧⠀⢻⡄⠘⢷⡀⠙⢧⡈⠻⣄⠙⢧⡈⠻⣌⣻⣷⠀⠀⢀⡀
⣾⣿⣿⣆⠀⣻⢿⣷⣴⣏⣠⡞⠁⣠⠟⠁⢠⡾⠁⠀⡾⠁⢀⡿⠀⢸⡇⠀⢿⡀⠈⢷⠀⠈⢷⡄⠈⠻⣄⠈⢳⣀⣙⣦⣼⡿⡿⢀⣰⣿⣿
⢸⣿⣿⣽⣿⢿⣦⣌⡉⠛⠻⠿⢿⣿⣶⣶⣿⣤⣤⣼⣧⣤⣼⣇⣀⣸⣇⣀⣸⣧⣤⣼⣧⣤⣤⣿⣶⣶⣿⡿⠿⠟⠛⢉⣠⣴⡿⣿⣯⣿⣿
⠘⣿⣿⡧⢻⡀⢻⣿⣿⣿⣶⣶⣤⣤⣄⣀⣉⣉⣉⠉⠉⠙⠙⠛⠛⠛⠛⠛⠛⠋⠋⠉⠉⣉⣉⣉⣀⣠⣤⣤⣶⣶⣿⣿⣿⡟⢀⡟⢾⣿⣿
⠀⠙⣿⠛⢻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠻⣿⠇
⠀⠀⠙⠳⠞⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠳⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⡛⠿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⠿⢛⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠻⣶⣬⣉⠛⠻⢿⣿⡧⣿⣿⣿⣿⢸⣿⡿⠟⠛⣉⣤⣶⠟⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣍⠛⠻⠶⣾⣿⡧⣿⣿⣿⣿⢸⣿⣷⠶⠟⠛⣩⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⢠⡞⣿⣿⣷⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣾⣿⣯⢳⡄
⠀⠀⠀⠀⠀⣾⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⣷
⠀⠀⠀⠀⠀⡇⢸⣿⣿⣟⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣿⣿⡇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣟⣻⣿⣿⡇⢸
⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢸⣿⣿⡇⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⣷⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣼
⠀⠀⠀⠀⠀⠹⡄⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⢠⠇
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠿⠿⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⢈⢉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣤⡀⠀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠉⢿⡇⠀⣿⡇⠀⣿⢸⣟⣸⠇⣴⡆⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠸⡇⠀⢿⣇⣰⠏⣸⢻⡄⢰⡿⣧⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠋⣠⣬⣭⣥⣤⣭⡀⠃⠟⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⢿⣿⣿⣿⣿⣿⠋⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣾⣸⣇⠀⠀⠀⣹⢛⡟⢿⠁⠀⠀⣸⡇⣧⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣹⡏⣿⠆⠀⢠⠻⣿⡿⠟⢇⠀⠀⣿⢹⣿⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠳⠋⠀⢀⡯⠀⠙⠁⠐⣾⣷⢀⡙⠮⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢲⡇⢠⣄⣘⠀⠀⡁⠀⢰⣿⠁⣾⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣼⠇⢸⠀⢸⡇⢸⡇⠀⣿⠃⢰⡿⠁⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣋⣿⠄⣾⠀⣾⠃⣸⡇⢠⣿⠀⣼⡇⢀⡏⣹⣦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠃⠀⠃⠀⣿⢠⠛⠷⠃⠻⠞⠈⠧⠞⠘⢤⢏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⣉⣵⠛⡆⣳⣆⡇⣰⣯⣭⣭⠭⠭⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠙⠛⠛⠉⠋⠹⣠⠇⢽⠹⠇⢹⣟⣛⣓⣒⣒⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠠⡐⠬⡓⠀⠀⠀⠀⠀⠒⠲⠶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠒⠋⠁⠰⡆
⠀⠀⢀⠐⠌⠳⡄⠂⣀⠠⣁⠀⠠⢀⠀⠢⠀⠀⠀⠐⡖⠀⠀⠀⠐⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⠴
⠀⠀⠃⠀⠀⠀⠄⠀⠠⣅⡒⠌⠑⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢁⠀⠀⠀⠀⠀⠱⠀⠀⠠⠀⠠⡇⠀⠀⠀⠂⠀⠀⠀⠀⠤⠔⠂
⠀⠀⠀⠀⠀⠓⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢃⠂⠀⠀⠀⠀⣥⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠘⠀⠀⠀⠀⢸⡉
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡓⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⡠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠢⠜⠀⠀⢀⠄⠠⠐⠒⠀⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠠⠀⠤⠄⢤⢠⡀⠄⠀⠀⢔⠒⠁⠀⠄⠀⢰⠃⠀⣠⠋⠀⠀⠀⠈⣶
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠚⢃⠀⠠⠀⠠⠀⠀⠀⠀⠁⠈⠓⠀⠠⢀⣡⠀⠀⠀⠈
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢀⠀⢼⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃
⠀⠀⠀⠁⠀⠀⠀⠠⠄⠘⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢠⠁⠀⠁⠐⠀⠀⠀⠀⡀⢠⡐⠤⡀⠀⠀⠀⠀⠀⠐⠛⠉⣿⠉⣨⠅⠻⠀⢹⡂⠹⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀⠀⡀⠈
⠀⠀⠀⢠⠂⠳⠀⠀⠀⠀⠀⠄⡐⠨⢑⠬⣑⠦⣕⠢⠀⠀⠀⠐⠇⠀⠉⠘⢰⠄⣌⠀⢸⠄⠛⠘⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠄⠀⠐⠪⣑⠢⢍⡒⠭⡂⠍⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠐⠤⠴⠂⠀⠀⠀⠀⠒⠄⠀⠁⠂⢌⡐⠤⠁⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠁⠠⡀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠈⠀⠀⠀⠄⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠠⠀⠀⠈⠀⠀⠀⠀⠀⠄⠂⠀⢀⣀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⠀⠀⠀⠀⠠⠀⠀⠈⠲⠐⠒⠂⠁⠈⠀⣀⠄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠄⠊⠀⠀⠀⠀⠠⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡆⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠄⠀⠐⠒⠂⠈⠀⠘
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠈⢱⠦⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⡀
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄⠄⠀⢀⠞⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠂⠁⠀⠀⠀⠀⠀⠐⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⢀⡀⠀⠀⠀⢀⠈⠀⠀⢀⢠⡄⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠄⠄⠂⠌⡀⠈⠈⠇⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠠⠀⠐⢈⣀⣥⠴⠒⢚⢨⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠂⠤⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠃
⣀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠢⢀⣀⣀
⠤⠤⠔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢤⠂⣤⠄⠀⠀⠀⠀⠀⠐⠤⠀⠤
⣀⡀⠥⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⢔⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀
⠤⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠵⡪⢔⠁⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠞⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠆⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠀⢸
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠱⡀⠀⠀⠀⠀⠁⠀⠀⢀⣉⣉⣀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁⠀⠀⢸⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠤⠀⠀⠀⠰⠀⠀⠀⠀⠠⢄⣀⡀⠀⠀⠀⣀⡤⠆⠀⠀⠀⠀⠀⢀⡦⠀⢀⠀⠀⠀⠀⠀⡐⠈⠀⠀⢂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤
⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⠀⡄⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠚⠚⠚⠓⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠇
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⢀⣀⠤⠊
⠀⠀⠁⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⢀⣠⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠉
⢚⠀⠀⠀⠀⠀⠀⠐⢄⠈⠉⠉⠉⠉⠁⣀⡠⠔⡀⠀⠀⠀⠀⠀⠈⠂⠤⠤⢀⣀⣀⡠⠔⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣢⠄⡀⠀⠀⠀⠀⠀⠀⠈⠩⠭⠭⠭⠭⠠⠐⢈⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠔⢁⠃⠀⠀⠀⠀⠀⡀⠀⠐⠒⠒⠒⠚⠛⠋⠁⡠⠀⠀⠀⠀⠀⠀⠰⣀⣀⣄⣀⣀⣌⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠒⠛⠛⠓⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠒⠈⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⡈⠀⠐⠀⡀⠁⠸⡂
⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠁⡂⠂⠀⠁⢧⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⣠⣤⣀⣀⣀⢀⣀⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠆⠊⠉⠡⡯⠜⠁⠀⡀⠀⠀⠣⠼⠋⠉⠉⠻⠇⠒⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠁⠊⠀⠀⠀⠰⠌⠀⠰⢂⡀⠀⣢⠀⠐⠊⠀⠳⠾⠈⢑⡲⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡥⠞⠁⠀⠰⡽⠋⠕⠀⠀⠀⠀⠀⠀⢤⠒⠀⠀⠀⠣⠂⠨⢥⠀⠀⠀⠀⢠⠀⢀⠨⡹⠀⡭⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⠁⠐⠴⡄⠀⠀⠑⠴⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠒⠂⠐⡲⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⢃⡀⠀⢀⢄⠀⢘⣳
⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠠⣒⡄⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠐⠂⠀⠘⠼⡓⡄⠉⡄
⠀⠀⠀⠀⡠⠚⠂⠄⠀⠀⠀⠠⠔⠀⠀⠑⠃⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠈⠁⠀⠐
⠀⠀⠀⠀⣣⣤⣄⣥⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠠⠀⢄⣠⡀
⠀⠀⠀⢎⢾⣿⣿⣿⠃⣾⣤⠖⣄⢀⡔⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠛⠃⠀⣁⠀⢸⣿⢈⣦
⠀⠀⠀⠈⠺⢿⣻⣅⡀⠉⠻⠁⠙⢻⣅⣰⣦⣤⣄⡤⣀⣀⣀⡀⣀⠀⣀⢀⡀⢀⣶⠢⠤⠐⡦⠀⣀⠤⣀⣀⣤⠂⣰⡶⠞⢻⣿⠎⠉⢹⠃
⠀⠀⠀⠀⠀⢿⣿⣷⡷⠶⠛⠓⠦⠚⣉⣉⣛⣿⣄⡴⠏⠈⢿⣆⣸⢛⣷⣤⣯⣁⣽⠀⣰⡿⣿⠉⣿⣠⡎⠉⢨⣆⡙⠿⠋⢠⣾⣷⡀⠀⠱
⠀⠀⠀⠀⠀⡤⡙⠻⠷⢬⣤⣤⣤⣤⣤⣤⡿⢿⡟⠁⠀⠀⠀⣿⣀⣉⣠⣿⣿⣿⣭⣽⣷⣾⡁⠀⢈⣿⣿⡿⠽⣿⣷⣤⣴⣿⣿⣿⠳⡎⠁
⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣶⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠉⠉⠁⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣧⠄
⠀⠀⠀⠀⠀⣿⣿⡇⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣽⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⡿⠿⠿⠿⣿⣿⣿⣿⡟⢛⠄
⠀⠀⠀⠀⣿⣌⢻⣽⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⣹⣿⠻⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣉⣥⣤⡶⢶⣶⣿⣿⠉⢹⣿⣧⣼
⠀⠀⠀⠀⠈⢧⣈⣿⡆⣹⣅⣰⡗⠒⠠⠶⢲⣾⣿⡿⢿⡉⢹⡷⠦⣤⣤⣤⡤⢤⣾⠞⣿⣿⡏⠀⠈⠿⣿⠁⢺⣿⡿⠋⠀⠘⣿⣥⣎⢀
⠀⠀⠀⠀⠀⢸⣯⣤⡌⠙⣻⣏⣀⣶⣶⢀⡀⠙⠋⠀⠾⣧⣶⡶⠀⠙⠿⠛⠧⠀⣵⡀⠍⠩⠶⢠⣾⡛⣸⢃⣀⣈⠐⠿⣿⣶⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⢄⠀⠙⠋⠉⠉⠉⠉⠛⠻⣿⡯⠀⢺⣷⣾⣿⡁⢰⣶⣇⣴⣶⣦⣬⡗⣷⣶⣶⣾⠿⠷⠿⠟⠻⠿⠷⠛⠋⠁⣸⡟
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠊⠁⠈⠛⠻⠛⠉⠉⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣬⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⢀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⡀⠬⠓⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⣯⣭⣄⡀⠈⣉⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠀⠀⠀⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠉⠁⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣄⠀⠀⠀⠀⠀⠀⠾⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠦⠀⠈⠁⠀⢀⢠⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢤⣀⠰⠊⠀⡈⠀⠀⠀⣀⣴⠋⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⠀⠈⠀⢺⣿⠟⠃⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡠⠐⣠⣧⣤⡀⠀⠀⠈⠹⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⠢⠄⢁⣈⣈⣓⡀⠀⡐⠀⠞⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠉⠀⢸⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⣤⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢹⡄⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠢⢄⡀⠀⠀⠀⢀⠤⠀⠠⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⣿⡄⠀⠀⢀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠊⡤⠠⡴⣄⣀⠈⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢾⡏⠈⠳⡀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠄⡤⣤⣖⠊⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢠⡟⠀⠀⠀⠈⣤⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠂⡇⠀⠀⠀⠀⠀⠈⠒⠀⠀⢸⡆⢠⡇⢀⠀⡠⠂⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⣇⠈⣟⢠⠞⠁⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⣤⡄⠠⠤⠤⠤⢤⢤⠠⣤⠀⣀⡀⣀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋⡷⠈⠀⠀⠀⣠⠞⠁
⠀⠀⢀⣠⠶⠚⠃⠈⠘⣿⣿⣿⣿⣿⣷⡦⢰⣶⣶⣶⣶⣶⠿⠿⠈⠉⠉⠘⠳⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣏⣸⣁⠀⢀⡴⠋⠁
⠀⠀⣿⣄⢴⣿⣿⣿⣿⣿⡮⠁⠀⢉⣀⣄⣤⣴⣦⠀⠀⢠⣾⣿⣿⣿⣷⡆⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⢸⠿⡇⠈⣿⣧
⠀⠀⢿⠉⠛⠻⠯⣭⣍⣁⣀⣻⣛⠛⠛⠛⠉⠁⠁⡀⢀⣀⣉⣉⣉⡭⣥⣐⣒⣭⢠⡇⠀⠀⠀⠀⠀⠀⠈⠁⠛⠻⠟⢻⡄
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉⢉⣤⣶⣾⣿⣿⣿⡟⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⣱⣿⠃⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣤⣤⣾⣿⣿⣿⡟⣵⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠳⣔⢤⣀⡀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⢟⡳⠋⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣛⣷⣶⣶⣤⣴⣾⣿⣿⣿⣿⣿⣟⣫⠕⠋⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠛⠛⠻⣿⠟⠛⠋⢻⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣶⣞⣉⠉⠁⠀⠐⠲⡾⣿⡀⠀⠀⠀⠀⣄⣀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⡛⠿⣿⢿⣿⣦⣤⣤⣤⣴⣾⠿⣧⠀⠀⠀⠀⠀⢸⣿⣧⣤⣄⣀⠀⠀⠀⠀⠀⢁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠙⠢⢿⣿⣿⣿⣿⣿⠿⠛⠁⠀⢹⣇⠀⠀⠀⠀⠈⣏⠹⠿⠿⣿⣷⣶⣶⣶⣤⠾⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⣿⠀⠀⠀⠈⢿⠛⠙⠛⠛⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⢸⡀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄