PlANET Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡟⠁⠘⠗⠐⣲⣧⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠛⠙⠉⠀⠀⠀⠀⣴⠿⠁⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⣛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⡀⢴⠃⠀⠀⠀⠀⠀⠀⠈⠁⢠⡾⣡
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠃⠀⣠⢏⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠁⠀⠀⠐⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣣⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣈⣶⠔⠀⢀⣴⣶⠖⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢞⡼⠻⠋⣰⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢈⣀⣠⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠴⠋⠀⢀⣴⡷⠟⠀⢀⣹⡿⠟⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⢀⡴⣭⠟⠀⠀⢀⡜⠋⠀⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠹⣿⢄⡀⠀⠀⢀⣤⣶⡟⢁⣀⡴⣫⡾⠁⠀⢀⡴⠏⠁⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠸⣿⣿⣶⣿⣿⣿⣃⣼⡿⣫⣾⠟⠀⢀⣤⠞⠁⠀⢀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣾⠟⣫⣾⣿⣡⣴⣶⡟⠁⢀⣠⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢟⣵⣾⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠿⠿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠑⠂⠐⠂⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂

⠀⠀⠀⠀⠀⣴⣾⣷⣦⠀⠀⠀⠀⠀⣠⢴⠆⠠⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀
⠀⠀⠀⢀⣸⣭⡖⠀⠀⡂⠁⠀⠀⢸⡷⠎⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣤⠀⠀⠀⠀⠀⢨⢭⠉⠉⠁
⠀⠀⠀⠈⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠀⠀⠀⠀⠀⠀⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠻⠷⠶⠊
⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⣀⣤⠄⡀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠄⠀⠀⠀⠀⠀⠀⣤⡶⠒
⠀⠀⠀⠀⣼⣿⡇⠀⠈⠀⠀⠀⠀⢸⣿⡟⠀⠀⢠⠀⠀⠀⢀⣾⣿⠖⠚⠋⣻⠀⠀⠀⢸⣿⡀⠤⠂
⠀⠀⠀⠀⠙⢿⣷⣶⠞⠀⠀⠀⠀⠘⢧⣴⣄⡀⠀⠀⠀⠀⠻⠽⢿⣦⡄⠀⠁⠀⠀⠀⠀⠙⠿⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⠀⠀⢀⣀⠀⣠⣀⡤⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⠀⠀⠀⢀⣠⡤⠄
⠀⠀⠀⠀⢰⣛⣿⠣⢐⠁⠀⠀⠀⢡⡌⠀⡉⣉⡀⠀⠀⠀⠀⠀⠋⣠⠚⣹⠎⠀⠀⠀⣾⣿⠓⠀⠐
⠀⠀⠀⠀⠈⠿⠿⣉⡁⠀⠀⠀⠀⣼⠇⠀⢣⠀⠹⠆⠀⠀⠀⠀⣰⠟⠿⠕⠁⠀⠀⠀⠘⠿⠿⠷⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠂⠀⠀⠒⠤⣂⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⢉⠉⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⢘⠀⢠⠄⠂⠀⢀⣾⢱⠀⠀⠀⠀⠀⠀⠀⣼⠇⠠⠞⠁⠀⠀⠀⢈⣧⣄⣀
⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⡗⠐⠀⠀⢀⢑⣡⢂⣾⠀⠀⠀⠀⠀⠀⠀⣧⠀⣀⠀⢀⡀⠀⠠⠈⢹⠄
⠀⠀⠀⠀⠀⠀⡅⠠⣀⠀⣀⣀⣤⠶⢟⡞⠁⣼⠏⠀⠀⠀⠀⠀⠁⠀⢻⡍⠀⠒⠋⠀⠀⢀⢈⡤⠀⠐⠂
⠀⠀⠀⠀⠀⢄⠷⣄⢉⣉⡥⣜⣶⡾⠋⢀⠾⣉⡰⠂⠀⠀⠀⠀⠉⠀⠀⠘⠶⢭⣈⣬⣥⠴⡋
⠀⠀⠀⠀⠀⡇⢀⠈⠉⠓⠺⠟⠉⠀⢠⠋⠌⠹⣿⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠣⠈⠃⠀⠈⠀⠀⢀⠔⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠁⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠄⠤⠦⡀⠀⢀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠰⠂⠀⠀⠀⠂⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠠⣿⡼⡧⠀⠀⠠⠛⠓⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⡄⢀⠕⣄⡠⠖⠰⠀⠀⣀⢤⠃
⠀⠀⠀⠀⠀⠉⠀⠯⠵⣅⣤⠴⠀⠐⠒⠠⠡⠄⠀⠀⠀⠀⠀⠀⠀⠘⠎⠠⠄⠀⡇⢀⠒⠫⣺⠏
⠀⠀⠀⠀⠀⠃⠀⠠⠒⠀⠀⠲⠀⠒⠂⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠠⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠱⢤⡀⣀⠀⢈⠁⣁⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠄⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⠠⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡉⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠜⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠁⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠀⡀⢘⡃⠠⠀⠐⠄⣠⠐⠇⠀⠀⠀⠀⠀⠫⢤⢧⣠⣤⣽⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢤⠁⠈⢰⠀⠀⡀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠤⠀⠙⠿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠥⣀⣀⠹⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣠⡴⠶⣚⣛⠋⣁⠐⢢⢱⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠁⠲⣿⠿⠿⠛⠋⠁⢠⠈⣆⠀⣬⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⢜⡜⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⢿⣿⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠛⡅
⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠉⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⠋⠁⠀⠐
⠀⠀⠀⠀⢀⡴⣫⣾⠟⠁⠀⠀⠈⢀⠀⠀⣀⣠⣴⣾⡿⠛⠉⠀⠀⠀⠀⠐⠁
⠀⠀⢀⡴⡁⠀⡍⠸⣀⣀⠀⣀⣤⣴⣷⣿⡿⠛⠉⠁⠀⠀⠀⠀⢀⠄⠊
⠀⠠⢱⠰⡀⠐⠀⠒⣒⣒⣭⠿⠟⠛⠉⠀⠀⠁⠀⠐⠒⠂⠀⠈
⠀⠐⠠⠅⠤⠉⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠒⠸⢿⣷⣶⣦⣄⡀⠀⢀⣠⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠶⠋⠀⠀⠀⣺⠟⣩⣿⣿⣿⣿⣟⠛⠛⠻⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢁⣾⠋⠁⢘⣿⣿⣿⣧⡀⣰⢇⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠋⠀⠐⠉⠁⠀⣰⣿⣿⣿⣿⣿⡷⣫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⣾⠿⣋⣿⣿⡿⢋⠜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⢁⣴⣿⡿⣋⠔⣡⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠤⠊⠁⠀⠀⣾⡿⠟⡡⢊⣥⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⣡⠔⣉⣴⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢒⣩⣖⣤⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⢤⣀⣀⣠⡬⠥⠖⣚⣩⣴⣾⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠈⠀⠃⠈⠃⠈




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣠⠖⠛⢋⣉⠙⠓⠦⣄⠀⠀⠀⢀⣆⠀⠀⠀⢀⡤⠶⡟⢹⠋⠛⠲⢤⡀⠀⠀⢤⡞⣦⠤⠀⠀⣠⡴⡺⢛⠟⢉⠗⢶⣄
⠀⠀⢠⠞⡁⠶⠀⠻⠞⠀⠀⣶⠈⢷⡀⠙⣯⣨⡟⠁⣰⢛⢒⢒⠁⠘⠤⠤⠤⠤⠽⢆⠀⣼⠛⠻⠀⢀⡾⠉⢁⠀⠄⠒⠁⡰⠁⣨⠷⡀
⠀⠀⡟⢠⠔⠦⠀⠘⠂⠆⢠⢤⠐⠀⣧⠘⠋⠈⠓⢰⠏⠉⠈⠀⢉⡇⢠⣦⠠⣖⣒⣛⡆⠀⠀⠀⠀⣾⡤⠊⢁⠔⠂⠈⢉⠤⠊⣀⠴⢻
⠀⠀⡇⠘⠲⠚⠀⢠⠚⢲⠈⠉⠀⠀⣿⠀⣀⣀⡀⢸⣋⣉⡉⠉⣉⠀⣀⠤⠤⠤⠤⢤⡇⢀⠤⢄⠀⣿⠔⣒⠥⠐⠒⠬⠅⢒⣊⢅⡮⣿
⠀⠀⢻⡄⣞⡆⠀⡈⠛⠋⠀⠰⠆⣰⠇⢰⠋⠬⢳⠀⢷⡐⠋⡈⠋⠀⠑⠒⠒⠒⢒⡾⠁⠺⣘⡺⠀⠘⣯⣊⠕⡀⠬⠄⠉⣀⠠⡀⢭⡟
⠀⠀⠀⠙⢦⣀⠀⠁⠀⠰⢂⣠⠾⠃⠠⡈⠓⠒⠋⠀⠀⠻⢭⣭⠭⠭⠭⠝⢀⣯⠟⠁⠀⠀⠀⠀⢄⠀⠈⠳⣏⡴⢊⠩⠤⠀⣂⡴⠋
⠀⠀⠀⡰⠀⠈⠙⠛⠚⠛⠋⠁⠐⠄⠀⠀⠄⢀⣤⢠⣄⠀⠀⢉⠙⠛⠛⠛⠉⠀⠜⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⠛⠛⢋⡁
⠀⠉⢊⠁⣉⠈⠀⠀⠀⠀⣴⢶⡄⠐⠉⠐⠀⣾⢤⣻⢾⠀⠢⠀⠀⠀⠀⠀⠳⡈⠀⠈⡀⠒⠂⠠⠀⡒⢀⠀⠠⢿⡿⠆⠀⠻⠟⠠⠶
⠀⠀⠄⠉⠑⠄⣀⣀⣀⣀⡈⠛⠁⠀⠀⠀⠀⠈⠛⠛⠋⠀⠐⠀⣀⣀⣀⡀⠀⠤⠒⠄⡇⠀⠐⠂⢿⡽⢀⠀⠀⢉⣋⣀⣀⡀
⠀⠀⠀⢀⡴⠾⢉⡐⠀⠈⠉⣳⣤⡀⠀⢠⠂⡡⠐⠶⢶⣶⡶⠛⠩⠭⠭⠟⠻⢶⣄⠀⠈⠀⠀⠘⠀⠂⢀⡴⠞⠉⠉⣉⠉⣉⠓⢦⡀
⠀⠀⣰⠋⠙⠢⢀⡀⠀⠀⠀⡔⡤⠳⡄⠸⡀⢆⠡⡀⠻⡛⠒⠒⠦⠤⠤⠤⠤⠖⠚⢧⠀⠀⠺⠒⠀⢠⣞⡀⡈⠁⠈⡐⠯⣊⠂⣶⠹⣆
⠀⠀⡿⠤⣀⡀⠀⠈⠉⠒⠒⠒⠒⠒⣷⠀⠑⢄⠑⢬⣦⣈⠙⠶⣒⣒⣒⣒⣒⣉⣉⣹⣧⡀⠀⠀⠀⣾⠘⠭⠀⠀⠶⠀⠀⡀⢀⣤⠀⢹
⠀⠀⣇⢠⣶⡄⠉⠉⠀⠒⢂⣀⡉⠉⡿⠀⠀⠀⠑⢤⡉⠋⠭⡦⢄⣉⠙⠲⢄⣈⡀⢠⣿⢿⣷⡄⠀⢿⠀⢠⠫⠕⡄⠀⠀⣁⠀⠠⠄⣸
⠀⠀⠹⣄⠉⠄⠒⠈⣀⠀⠀⣤⠄⣼⠃⠀⠀⠀⡀⠀⠻⡑⠦⣌⡙⠂⠌⠐⡢⠤⢀⣈⢁⡴⢈⠜⡆⠘⣧⠰⠉⠊⠁⠀⡎⠡⢱⠄⣰⠏
⠀⠀⠀⠈⠳⣆⣉⡀⠆⢀⣉⡶⠞⠁⠀⢋⠐⢨⠁⢠⠀⠙⠷⣤⣛⡓⠦⣤⣄⣈⡉⠁⠀⠀⢁⡠⠃⠀⠈⠳⢤⣀⣛⠀⢈⣁⣥⠞⠁
⠀⠘⠃⠠⠆⠀⠉⠉⠉⠉⣁⠔⢀⠀⠠⠆⠒⠲⠆⠀⠀⠄⠀⠀⢈⡉⠉⠉⠡⠄⠀⠈⠉⠉⢠⣲⡀⠺⡗⠀⠀⠈⠉⠉⠉⠁⠀⠀⣴⡄
⠀⠀⠀⡁⠈⠐⠀⠀⠀⠈⠂⢀⠠⠁⠀⠀⡜⢢⠀⠈⡀⠀⠀⠐⠄⡐⠀⠘⢄⡀⠓⠠⠄⡤⠒⠁⠓⠠⠠⠄⠐⣶⠆⠀⠀⠀⢠⠀⠉⠁
⠀⠀⠀⠘⠀⢀⣠⣤⣤⣤⣈⡀⠈⠠⡔⠊⠀⠀⠑⣠⠀⠀⠀⣀⣨⣤⣤⣄⣀⠠⢶⠀⠀⢀⠀⡀⠀⠐⠁⠀⢀⣠⣤⣤⣤⣀⡀⠀⠺⠂
⠀⠀⠀⣠⠞⠉⠓⠒⢱⠄⠀⢹⢦⡀⠀⠑⠄⠠⠋⠀⠀⣠⠞⡉⢃⠵⠸⣄⢉⠿⣦⡀⠀⠆⠁⠐⠢⠠⣠⣞⣛⣀⣀⣒⣊⣠⠝⢳⣄
⠀⠀⣰⡇⠀⣀⣠⠔⠚⠀⢀⣻⣂⣿⡄⠀⠘⠁⠀⢀⣾⡁⠀⢠⢖⢠⡐⠋⢼⢰⡉⢳⡀⠀⠀⠀⠀⣰⡇⠒⠤⣄⣀⣀⣀⠤⠒⠁⢘⣆
⠀⠀⡇⠑⠌⣓⠤⠤⣀⠀⣏⣀⠀⠈⣿⢀⡖⢦⠀⢸⣅⠸⠤⢌⡢⠥⠖⢲⠀⣇⢉⣹⡇⠀⠈⠀⠀⡿⢭⣙⡒⠒⠰⠶⠶⣒⣒⣿⣗⣻
⠀⠀⣧⠀⠀⠘⡄⠀⠀⡑⠀⠈⡇⠀⡟⠀⠙⡋⠀⢸⡄⢹⡆⢤⠃⡀⠀⠘⠤⠬⠅⢾⠇⠀⠀⠀⠀⢿⡒⠲⠮⢭⡽⢿⣛⣉⡭⠖⢋⣿
⠀⠀⠘⢦⡀⠀⢸⢀⡔⠁⠀⠀⢹⡜⠁⣴⢋⡍⣷⠀⠻⣬⠥⠤⠤⠃⠠⡄⢒⠴⣴⠏⠀⢠⣼⣧⡄⠈⢷⡩⠍⣂⠒⠤⠤⠤⢆⣈⡽⠃
⠀⠀⠀⠈⠙⠦⣬⣚⣀⣀⡤⠖⠋⠀⠀⠙⢶⡴⠟⠀⠀⠈⠲⢶⣄⣐⣤⣹⠾⠛⠁⠀⠀⠀⠙⠋⠀⠀⠀⠙⠷⢦⣐⣒⣂⣴⠶⠋

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

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⠖⠋⢩⢭⠉⠙⠲⣄⠀⣀⣀⢇⣀⡀⢀⡴⠚⡯⢹⠉⠉⠓⢦⡀⠀⠲⣎⡶⠂⠀⣠⡶⠛⠋⠍⡩⢛⠶⣄
⠀⠀⡞⠡⠈⠁⢈⡋⠀⠐⠃⠈⣇⠀⡵⢼⡍⢠⠯⠤⠬⠤⡈⠒⠒⠒⣒⣻⡄⠜⠁⠙⠀⡼⢃⡠⠀⣂⠉⠤⠎⡠⠊⣧
⠀⢸⡇⢎⣉⠆⠀⣀⣁⠺⠗⠀⢸⠀⠀⠀⠀⣾⠤⠤⠄⠤⠊⠘⠑⠘⠐⠒⣷⠀⠀⠀⠀⡗⣁⡠⠊⣀⠠⠐⣉⠤⢚⢽⡇
⠀⠘⣇⢠⢤⠀⠘⠦⠞⠀⣤⠀⣼⢀⡶⡲⠆⠸⣖⠲⠀⠶⠀⠦⠉⠉⠭⢭⡇⢰⢩⢵⠀⢯⡴⢜⠡⠐⠋⠤⠐⠊⠜⣺⠁
⠀⠀⠘⢮⡉⠀⠃⠀⢠⠀⣠⡼⠁⠈⠧⠥⠆⠀⠹⣖⣒⣒⣒⣒⡦⢠⣲⠞⠀⠀⠁⢁⠀⠈⠳⣕⢪⠔⢒⡀⠉⢀⡴⠃
⠀⠀⠀⡄⠉⠓⠒⠲⠒⠛⠁⠂⠁⠈⠀⢀⣠⢤⡀⠀⠉⠓⠒⠒⠚⠋⠁⢆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠒⠒⢛⠉
⠀⠁⢊⢈⡀⠀⠀⠀⠀⣴⣦⠀⠂⠀⠀⣾⢼⡻⠯⠀⠀⠀⠀⠀⠐⠂⡁⠈⠀⠔⠂⠠⢀⡂⡀⠀⢾⡿⠆⠀⠻⠃⠰⠄
⠀⠀⠀⠀⠃⣀⣠⢤⣀⣉⠉⠀⠀⠀⠀⠈⠛⠛⠁⠀⢀⣀⣤⣄⣀⡐⠒⠂⢴⠀⠐⠂⠻⠟⡀⠀⣈⣉⣤⣄⣀
⠀⠀⢀⣴⡛⠀⠀⠀⠀⠨⠷⢦⠀⢠⠋⠔⡈⢛⣿⣟⠉⠁⠒⠒⠉⠙⠳⣄⠀⠀⢀⡈⠀⠁⡴⠊⣅⠀⠄⣠⢌⠙⢦⡀
⠀⢀⡏⠀⠉⠐⠤⣀⣀⣐⣩⣂⣷⠀⢆⠡⠐⢄⠙⢬⣉⣉⣛⣛⣋⣉⣩⠹⣆⠀⠙⠁⠀⡾⡰⠄⠀⠀⠨⠩⠄⠘⠃⢳
⠀⢸⡉⢑⡒⠠⠤⠀⠀⠀⠠⠤⢼⠀⠀⠑⢄⠙⠷⠢⣈⠒⠶⢶⣒⠒⠖⠒⣿⣶⣄⠀⠀⡇⠈⡡⠤⡈⠀⠐⠂⠘⠃⢸⡇
⠀⠀⢧⠘⢋⠠⠀⠀⠐⢒⡒⢂⡞⠀⠀⠀⠀⠙⡦⢌⡑⠺⢖⡀⠤⢉⡑⠂⠛⢈⠟⠳⡀⢳⡀⡑⠥⠂⠀⡔⡒⢄⠉⡼⠁
⠀⠀⠈⠻⣤⡒⠀⠌⠀⢢⡥⠞⠀⠒⠠⢐⠃⣀⠈⠲⣌⡳⠦⢤⣀⡀⠀⠛⠉⠁⠊⣀⠇⠀⠳⢤⣀⠐⠀⠑⢒⣨⠞⠁
⠀⠘⠀⠠⠀⠉⠙⠛⠉⠉⠆⠀⠀⡼⠐⠪⡄⠀⠠⠀⠀⠉⡙⠛⠉⠩⠉⠈⠁⠁⢉⣢⠀⢾⠆⠀⠉⠉⠛⠋⠉⠀⢠⣤
⠀⠐⠈⠀⠁⠂⠀⠀⠈⡀⡀⡈⠀⠀⡜⢢⠀⢁⠀⠀⠀⠂⡐⠀⠀⢄⠘⠀⠄⡤⠒⠉⠃⠄⠄⠀⠾⠆⠀⠀⠀⠄⠈⠁
⠀⠀⠀⠀⣀⡤⠴⠶⠤⢤⡀⠀⠴⡉⠀⠀⣁⠦⠀⠀⣠⡤⡴⢦⠤⣄⡸⠇⠀⠠⡀⠀⠀⠈⠀⣀⡤⠴⠶⢦⢤⣀⠈⠃
⠀⠀⢠⠞⠁⠈⠉⢸⠀⢀⡞⢳⡀⠀⢂⡜⠀⠀⡰⠛⠁⢁⢊⣘⡦⡼⣻⢦⠀⠓⠀⠈⠑⢢⠾⠭⠤⠤⠬⠤⠒⣩⠷⡄
⠀⢠⡟⡀⢴⡒⠉⠀⢀⡴⠛⠛⢷⠀⢀⡀⠀⢸⠳⡄⠐⣇⠖⣀⣀⢣⠳⠬⡇⠀⠠⠀⠀⡿⠬⣉⣓⢒⣒⣒⣋⣀⣤⣻⡄
⠀⢸⡄⠈⠐⡈⠉⠒⠄⠓⢢⠀⢸⠀⠣⠜⠀⢸⠳⣌⢉⡢⠈⠀⢇⠘⠒⢒⡟⠀⠀⠀⠈⡯⢕⣒⣂⣤⣬⠵⠖⢚⠽⢺⡇
⠀⠀⢳⡀⠀⢰⠀⡠⠃⠀⠐⣇⠏⢠⡶⡲⣄⠘⣦⣓⣈⣀⠇⢀⠀⢬⣅⡼⠃⢀⣰⣄⠀⢻⡔⠒⠀⠩⣈⣉⣉⠅⢒⡟
⠀⠀⠀⠙⠦⣄⣒⣁⣀⣠⠔⠋⠀⠘⢦⣥⠟⠀⠈⠳⢤⣀⣒⣄⣳⡽⠚⠁⠀⠈⠹⠋⠀⠀⠙⠶⣤⣐⣒⣂⣤⠼⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣿⣿⠛⢿⠛⠿⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⣤⣀
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠉

⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⠿⠛⣛⠫⠭⠉⡀⢶⠀⠀⠀⠀⣼⣏⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠶⠶⡿⢀
⠀⠀⠀⠀⢠⡖⣶⣿⣿⠀⠀⠀⠀⠗⠂⠀⠀⠀⠀⢿⣟⢻⠀⡀⠀⠆⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡞⠄⠀⠀⠀⠀⠀⠀⠹⢞⡖⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠉⠙⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠰⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠄⢀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡟⠉⠐⠠
⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⢡⠀⠀⠀⠀⠀⢠⣾⣿⣿⠇⠀⠀⠐⡄⠀⠀⠀⠀⠀⢸⣿⣭⡴⠶⠒⠛⢻⡆⠀⠀⠀⠀⢸⣿⣿⠀⣀⡤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣀⣠⡾⠀⠀⠀⠀⠀⠸⣿⡛⢉⡀⠀⠀⠈⡇⠀⠀⠀⠀⣴⢿⣿⣟⡀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠘⢿⣿⣦⡀⢰⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠷⣿⣷⣦⡤⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⡤⠀⠀⠀⠀⠀⠀⢀⣄⣠⠄⢠⣤⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠛⣻⢿⣿⠀⠀⠀⠀⢀⣤⣶⣖⡒⠄
⠀⠀⠀⠀⠀⠀⠸⠿⢾⣶⣋⠐⠚⠀⠀⠀⠀⠀⠂⣠⡝⠀⠘⠛⣃⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⣴⠎⢻⡶⠃⠀⠀⠀⠀⣾⣿⡿⠖⠈⠂⢠
⠀⠀⠀⠀⠀⠀⠻⣿⣟⣳⣦⠶⠒⠀⠀⠀⠀⠀⠀⣿⡀⠀⣰⠀⠛⢿⣦⠀⠀⠀⠀⠀⠀⠁⢠⢻⣧⠶⢛⡕⠀⠀⠀⠀⠀⢻⣿⣷⣬⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠶⠖⠀⠀⠀⠀⠀⠀⠸⠏⠁⠀⠁⠰⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⢎⠓⡚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠩⠁⠀⠀⠉⠉⠁⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⡀⠀⠠⠣
⠀⠔⠂⢈⠭⠍⠩⠥⠴⠆⢐⡖⠀⡀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⢣
⠀⠑⢄⠈⠢⢄⠀⠀⠀⠀⢀⠅⠈⢀⠁⠀⠀⠈⠪⠿⠁⠈⠉⠁⠻⠧⠃⠀⠀⡀⠀⠀⠀⡇
⠀⠀⠀⠁⠢⢄⡉⠒⠤⣀⢸⠂⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠂⠀⠖⠀⠠⠁⠀⠀⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡈⠑⠂⠤⣄⡠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⡧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒⠠⢄⣈⠁⠒⠢⠄⣀⡀⠀⠀⠊⠀⠈⢀⠀⠀⠀⠀⠰⠁⠒⠭⣒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠐⠂⠀⠉⠒⠂⠤⣄⣈⠉⠙⠛⠠⠄⣀⡀⠀⠁⡰⠃⠀⠀⠀⠀⠉⠒⢅⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠠⠄⠀⠤⢀⠀⠈⠛⠒⠒⠠⢤⣀⣉⠉⠑⠒⠂⠠⠤⠤⠀⠀⠀⠕⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⡀⠀⠀⠀⠤⠄⠀⣀⠤⠊⠁⠀⠉⠁⠀⠐⠒⠒⠀⠀⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠁

⠀⠀⠀⠀⡠⠖⠚⠛⢻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⡓⣦⣄⠀⠀⠀⠀⠀⠀⠀⣰⣒⠫⠛⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣄⡀
⠀⠀⠀⢈⠁⠀⠀⠀⠀⢲⢹⣿⣆⠀⠀⠀⠀⠀⠀⠐⠀⠘⠗⠛⣿⣷⡀⠀⠀⠀⢠⠏⠉⠛⠁⢄⠈⣙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⢿⣿⡄
⠀⠀⢸⠌⠀⣀⠀⠂⡀⠉⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⣭⠸⠇⢔⣽⣿⡇⠀⠀⠀⢷⣀⡈⠀⠀⠀⣹⣿⣿⣿⡄⠀⠀⠀⠀⣀⣄⣐⣦⣤⣠⣾⣿⣿
⠀⠀⠰⠀⠀⠉⠀⠀⠉⠧⣨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⡈⣵⣯⣿⣿⠇⠀⠀⠀⠘⠿⣿⡇⠀⢰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⣠⢍⣍⣿⣯⣽⣿⡟
⠀⠀⠀⠁⢂⠀⠐⣠⣤⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠆⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠐⢻⣧⣤⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠆⠀⢘⡋⣡⣿⠟
⠀⠀⠀⠀⠀⠁⠁⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⢲⢶⣤⣄⣴⣶⣶⡀⠀⠀⠀⠀⠐⠂⠂⠲⣄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⣷⡄⠀⠀⠀⠀⠀⠀⠀⠔⠡⠋⣹⣿⣦⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠐⠚⠛⠛⠛⠛⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⡿⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⣿⣷
⠀⠀⠀⠀⠒⠶⢶⣶⡖⢶⣟⣿⡿⠀⠀⢀⠀⠀⠀⠀⠈⣠⠞⢋⣴⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢠⣠⣨⣵⡿⠁⠀⢠⠀⠀⠀⠀⠀⣠⣤⣴⣿⣿⠏⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠐⠂⠉⢛⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠁⠀⠀⠀⠀⠁⠈⠉⠀⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⡿⠟⠉⣩⣷⢶⠚⣉⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠿⠿⠿⠋⠛⠩⠝⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⣀⣴⠾⠋⢀⣤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡐⣀⣈⣁⣀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡴⠾⠛⠋⢀⡤⢞⣫⠞⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⠿⠛⠛⠛⠋⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⢃⣠⡴⣚⡭⠖⢋⣥⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣆⠐⠀⠀⠐⠂⠀⠀⣀⣠⠌⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡴⠞⠋⠙⠫⣩⣤⣶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⠳⢭⣽⣁⡬⢩⣥⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠉⣹⣳⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣢⠑⠊⠑⠁⠓⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣄⠀⢀⣴⡟⣱⣦⠀⢣⠀⢀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠠⠂⣀⡀⠀⡀⠀⠠⡀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡣⠘⠚⢶⣿⣿⡆⠀⡇⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⢄⠃⠀⠈⠠⡀⡁⠘⠀⠀⢆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡉⠤⡄⠀⠈⣟⡻⠗⣦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠃⢂⠈⠢⠀⠠⠊⢀⠂⡍⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣄⣰⣿⣦⣜⣡⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠆⡑⠀⠀⠀⠐⢠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠊⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠸⡠⠑⠊⠋⠢⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡠⠊⠁⠠⠒⠁⠈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⠁⠀⠐⠨⡝⠳⣄
⠀⠀⠀⠀⢐⡩⠄⠀⠈⠛⠓⠀⡼⠀⠔⠐⠚⠀⠀⠀⢁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠇⠀⠀⠀⠀⠀⠐⠘⠌⢧
⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⠀⡇⠒⡀⠀⡀⠂⠉⠂⢈⠆⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠕⢄⢤⠀⠀⠀⠀⠀⠀⠀⣨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠈⠀⠈⠊⠉⠁⠈⠙⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⢘⡆⠀⠀⠀⢠⠈⠉⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣐⠒⠁⠑⠠⢄⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡬⢀⠀⠀⡴⠊⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⢤⣤⡤⠄⢀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠁⠀⢀⠀⢸⣟⣀⣮⣿⣿⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⢀⣀⡀⠐⠷⠶⠼⣟⣉⣽⣿⣿⣿⣿⣿⣿⢷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢡⣀⡄⠀⠈⢒⡿⠝⣁⣀⠄⣌⠛⣿⡾⠦⣿⣿⣿⣿⣿⣷⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⢴⣿⣷⠞⠀⠸⢿⢲⡆⠸⠿⠎⠀⠀⠙⠅⠘⠛⠏⠾⢿⣿⡿⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣍⣊⣽⣛⣁⠑⣠⢄⣴⣿⠇⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠉⣉⠑⢪⣿⣤⣀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⢨⣿⣷⢷⣿⣿⣿⣾⣞⣽⣿⣱⠂⠑⢀⣴⡴⣠⠇⠂⠀⠀⠘⣋⠀⠐⣿⣹⣿⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⡌⠃⣟⠋⢀⣿⣿⡿⢛⣻⣿⣟⡏⠀⡀⠀⠘⠟⠐⠂⠀⠀⠀⠰⠊⠀⠀⢀⣝⠛⡿⢿⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⠿⢷⣿⣿⣶⣿⣟⠋⠀⠘⠀⠀⣀⠈⠀⠀⣁⠀⠉⠀⣀⡐⠀⢸⡇⠠⠀⠨⣿⠆
⠀⠀⠀⠀⠀⠀⠀⡄⢢⣸⣦⣰⣞⣿⣿⣿⣿⡟⣦⠀⢀⣀⠼⢿⣷⣾⡿⢡⠄⣤⠃⠀⠀⠀⠠⠁⠀⠨⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣷⠈⢻⡏⢤⢘⢯⣛⣿⣿⣿⣳⣏⣿⣶⣾⣿⣿⡁⠁⢮⣅⠀⠀⠀⠀⣄⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⢸⢻⢆⣾⣠⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣇⣼⣿⣿⣦⡄⠀⠈⣿⣶⣀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠁⠀⠀⠈⢛⣿⣟⣻⣿⣿⣿⠟⠛⠛⠿⣿⣿⣯⢯⡝⠋⠁⠀⠀⠀⠏⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣏⠁⠀⠀⠃⣘⡿⡿⣿⠃⠒⠠⠀⠀⠘⣿⡿⠌⠠⠆⠤⠀⣀⠀⠀⣻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡔⠂⠘⠻⠡⠺⢿⣆⠀⠀⠀⠠⣤⣿⣥⡠⢄⡀⠀⠄⣀⣴⠾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⢤⣀⠀⠠⣨⢛⣂⠆⢸⣿⣿⣿⣿⣾⣿⣞⣿⣿⣿⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠻⢊⣙⢿⠿⢯⣼⣛⣿⣿⢚⣻⣽⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠓⠛⠛⠒⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⠶⠾⠿⠿⠛⠻⠿⠿⠷⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠋⠁⠈⠙⠛⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠁⠀⠀⠀⠀⢀⣤⣶⠶⠿⠛⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣠⡾⠟⠉⢀⣠⣤⡶⠾⠟⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢀⣄⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣠⡾⠋⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⣴⡿⠃⣼⡇⠸⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⣠⡾⠋⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡄
⠀⠀⠀⢀⣼⠟⠀⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⡾⠟⠁⠀⣠⣾⠏⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠈⢿⣆
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠛⠉⠉⠁⠀⠀⠀⢀⣴⠟⠁⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠁⠀⠀⠀⠀⢻⣆
⠀⠀⣾⠃⠀⠀⠀⢀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣸⡏⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠿⠋⢀⣀⣤⡾⠋⠀⠀⠀⠀⢀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡀
⢀⡿⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⢉⣩⣴⣶⠿⠟⠋⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⣀⣤⡶⠾⠷⣦⠀⠀⠀⠀⢠⣾⠏⠘⣧
⢸⣧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⢠⣿⠁⠀⠀⢠⡿⠃⠀⠀⢿
⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣴⡿⠁⠀⠀⣰⡿⠁⠀⠀⢀⣾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣰⡟⠁⠀⠀⢀⣴⡿⠋⠀⠀⢀⣼⠟⠀⠀⠀⣠⡿⢻
⣿⠀⠀⣀⣤⣶⠶⠾⠿⠿⠛⠁⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⣿⣀⣀⣤⣶⠟⠋⠀⠀⠀⣠⣾⠋⠀⠀⠀⣴⡟⠁⢸
⣿⣠⣾⠟⠁⠀⣠⣤⣶⣶⣦⣤⣄⣀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠈⠛⠋⠉⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⣠⣾⠋⠀⢠⣿
⢹⡟⠁⠀⣠⡾⠋⠁⠀⠀⠀⠈⠉⠛⠿⢶⣶⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣴⠟⠁⠀⣠⡿⣿
⠘⣧⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢀⣴⠟⠁⠀⠀⣴⡟⢁⡿
⠀⢻⣄⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⣠⣶⠟⠁⠀⠀⣠⣾⠋⠀⣼⠃
⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠁⠀⢀⣤⡾⠛⠁⠀⠀⣠⡾⠟⠁⠀⣰⡏
⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠛⠁⠀⣀⣤⡾⠟⠉⠀⠀⣠⣴⠿⠋⠀⠀⠀⣰⡟
⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠟⠛⠉⠀⣀⣤⣶⠿⠛⠉⠀⢀⣤⣶⠿⠋⠁⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠁⠀⠀⣀⣴⡶⠟⠋⠁⠀⣀⣤⣶⠾⠛⠉⠀⢠⡀⣠⡄⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⢀⣿⠃⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⢀⣠⣶⠿⠛⠉⠀⠀⢠⣦⢠⣿⠱⠿⢁⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣾⡇⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⣿⠃⠈⠁⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⣼⡏⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄⣀⠀⠀⠀⣰⡿⠃⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⢾⣿⣤⣤⣤⣤⣿⣥⣤⣤⣤⣤⣶⡶⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣥⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⠿⠀⠀⠀⠈⢉⣲⣤⡀
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⣤⡀⠀⠈⠛⠂⢱⣤⠔⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢰⣧⢀⠀⠒⠀⠈⠀⠀⠀⡔⣰⠄⠀⢱⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡠⢾⣿⡄⠉⠀⢰⠉⠙⣷⠀⠀⠀⠀⣆⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠁
⠀⠀⣴⠟⠁⠸⣿⣿⣂⣀⡈⠃⡚⢃⣤⣶⣤⣿⠿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⢘⠉⢄⠀⠀⠛⢛⣛⣩⣭⡲⠖⠛⠋⠉⢱⡄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀
⠀⠀⠀⠋⠉⠉⠉⠛⠿⣿⣿⣿⣿⣤⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡥⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠄⠀⣠⣤⠀⠰⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⠿⠃⣀⣴⣿⠁⠲⣄⡀
⠀⠀⠀⠀⠀⠀⣀⠀⣠⠄⠀⠀⢀⣤⣶⣿⣿⣿⣿⣯⠓⡀⠉
⠀⠀⠀⠀⢃⡐⠙⠀⢿⣶⣿⣷⣿⣿⣿⣿⡉⠀⢉⣄⡀⠁⠀⠀⢠
⠀⠀⠀⢀⡄⠀⠀⠐⢿⣿⣿⣿⠹⢿⣿⠟⠛⠂⠈⠛⠃⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣾⢠⣶⡀⠀⠈⠙⢻⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⣾⣿⣿⣷⣠⣤⢈⣿⠉⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠘⠀⢿⣿⣿⣿⣿⠙⠟⠹⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠈⠐⢀⡻⣿⡏⠀⠀⠀⠈⠀⠀⠒⠒⣻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⣾⣅⠀⢳⠤⠀⠀⠀⠀⠳⣾⠣⠟⣹⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠛⢿⣷⣤⣤⣤⣾⣶⡤⠖⢃⣄⠉⠒⠀⠂
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⡿⠟⠓⠄⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⡄⠠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣁⠾⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠠⡤⠄⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠴⢀⣀
⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣤⠴⠾⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠀⠴⠀⣀⣢⣄⣄⡀⠀⠀⠀⠈⠘⠇
⠀⠀⠀⠀⠀⠀⢀⣽⡏⠉⡀⠀⢀⣨⢿⣶⣄⣤⡤⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠖⠒⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢈⡟⠙⢦⣤⡄⢻⠇⠡⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣀⣀⠀⠀⠂⠀⠀⠀⠀⠘⢦⠀⡀
⠀⠀⠀⠀⠀⢠⣼⡃⠀⣿⠉⠀⠀⣷⣄⡀⠀⣨⣿⣷⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣚⡆⢉⠠⠤⣈⡳⠾⢧⡀⡀⠀⠘⢂⠀⠀⠀⠰⡃
⠀⠀⠀⠀⠀⠀⠈⢻⣦⣸⡶⡄⣤⣼⠁⠉⠻⣯⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠰⠀⠀⠑⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠳⣤⡀⠻⢄⣀⣀⣿⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡐⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⠉⣷⠀⠀⠘⡿⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠁⠠⡀⠉⠿⣀⠀⠀⠀⠀⠀⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠘⢏⡀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⠆⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⢴⢲⠖⠦⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠢⢤⡀
⠀⠀⠀⠀⠀⡜⡁⠂⠘⠛⠀⠰⠌⢣⠀⠀⠀⠀⢠⡋⠀⢈⡘⠠⠤⠤⠽⡄⠀⠀⠀⢀⡾⢉⠀⠀⢂⡡⠂⡘⢦
⠀⠀⠀⠀⢸⠁⣊⡀⠀⣁⡀⠶⠎⠀⡇⠀⠀⠀⣧⠀⠀⠠⠌⠐⠂⠪⠁⢿⠀⠀⠀⢸⠆⡁⠀⠁⠠⠐⡁⠔⣪⡇
⠀⠀⠀⠀⠘⣆⡠⡄⠀⠣⠞⠀⠄⢠⠇⠀⠀⠀⢳⡴⠆⠒⠀⠊⠉⠡⠀⡟⠀⠀⠀⠘⣦⢂⠀⠁⠀⠒⢀⠈⣺⠃
⠀⠀⠀⠀⠀⠘⠮⣀⠈⠀⠒⣠⠴⠃⠀⠀⠀⠀⠀⠻⢭⡭⠭⠤⢇⡰⠞⠀⠀⠀⠀⠀⠘⠷⣤⣂⠁⢀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⢀⡴⠆⠁⢉⠉⡓⢦⡀⠀⠔⠀⠠⠶⣶⠖⠛⠋⠙⠓⠦⣄⠀⠀⠀⠀⠀⢀⡴⢚⠉⠉⠉⠒⢤⡀
⠀⠀⠀⠀⢀⡏⠈⠒⠄⣀⡀⠀⠀⢹⡀⢂⠂⠠⡘⠫⣙⣒⣒⣒⣒⣂⢉⣧⠀⠀⠀⢠⠏⡤⠀⠀⠘⠓⠁⠶⢳⡀
⠀⠀⠀⠀⢸⠉⣒⠀⠀⠤⠠⠤⠄⠠⡇⠀⠑⢄⠛⠖⣨⡁⠠⢄⡀⠀⠒⢺⣷⣄⠀⢸⠀⠨⣠⠈⠀⠐⠀⢃⠀⡇
⠀⠀⠀⠀⠈⢇⡉⠀⠀⠀⠀⠠⠄⡾⠁⠀⠀⠀⠹⡆⠬⡐⠋⠀⠀⠈⢁⡈⠡⠉⠱⠈⢆⠜⠂⠂⠀⡪⠐⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠑⠦⣤⣀⣠⠵⠊⠁⠀⠀⠀⠀⠀⠈⠳⠮⢝⣲⡤⠄⠈⠁⠀⠠⠔⠀⠈⠓⠦⣬⣀⣤⠴⠊

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣠⠚⠉⠀⢱⠂⢈⠗⣄⠀⠀⠀⠀⢀⡴⠛⠋⠐⢈⡌⠝⣦⡀⠀⠀⠀⠀⣠⠎⠥⠔⠂⠥⠙⡳⣄
⠀⠀⠀⠀⢠⠣⡀⢄⠂⠁⢀⠜⠃⠻⡆⠀⠀⠀⡼⢀⠀⢎⢐⡀⡘⡎⠢⣷⠀⠀⠀⢰⠧⢅⠐⠒⣐⣂⣉⣤⣸⡆
⠀⠀⠀⠀⢸⡀⠀⢂⠀⠑⡂⠁⠢⢀⡇⠀⠀⠀⣏⢲⠁⡑⠀⠀⠃⣙⡂⣿⠀⠀⠀⢸⡊⠴⠂⣠⠴⠒⣋⠕⢺⡇
⠀⠀⠀⠀⠀⠳⣀⠀⡆⡔⠀⠀⢸⠞⠀⠀⠀⠀⠘⢮⠀⠀⠂⠰⡀⣄⡴⠃⠀⠀⠀⠀⠳⣀⠀⠀⠀⠉⠠⣨⠟
⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠎⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠤⠔⠛⠁


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⣡⡿⠒⣩⠖⠋⠀⠀⠀⠀⠀⠀⠀⡴⠋⠛⡛⠉⠙⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣁⣤⠶⠛⣁⢴⡺⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⣤⠶⠶⠶⠖⠒⠲⠆
⠀⠀⠀⠀⠀⠀⢀⠔⢃⣠⣔⡯⠗⣫⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢀⡠⠁
⠀⠀⠀⠀⠀⠰⠗⠚⠉⠉⠓⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠷⡦⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢐⣶⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠊⠊⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡄⢰⣾⣹⣗⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠂⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢋⡀⠈⢻⠿⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣠⣷⣤⣫⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⢀⠀⠁⠀⠁⠉⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠈⠩⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⡃⠀⠀⠀⠀⠀⢄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠁⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠐⠀⠂⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠒⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠂⣄⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⡀⠀⣔⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠹⣄⡀⠈⠓⠀⠈⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⢰⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢸⠆⠉⠀⡐⠲⡦⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣰⠚⢷⠀⠀⠀⠈⢝⠆⠐⠆
⠀⠀⠀⠀⠀⢀⣼⣿⣷⢤⠘⠥⠒⠀⣉⠈⣀⡨⣀⡴⠞⠟⣻⣷⡄⠀⠀⠓⠀⠈⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣮⣿⣷⣶⣟⢗⣯⣥⣶⣿⠀⠀⠀⢸⡿⠁⠀⠂⠀⠀⢀⣀⠀⠀⠀⠀⠀⠿⣧
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣤⣧⣽⣷⡍⣢⠤⢶⣦⠀⠈⠀⠀⠀⡼⠛⢻⣷⠀⠀⠀⢆⠀⠘
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠿⣿⣶⣦⡄⡰⡄⣰⣴⡶⠀⠀⢃⡀⠀⠉⠀⠀⠀⠀⠑⠊⠀⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⡀⣀⢁⣀⣤⣀⣀⢀⠉⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠸⣿⣿⡙⢿⢿⣿⣿⣿⣿⣈⠿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠰⠄⠀⡌⠹⠏
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠁⡀⣴⣿⡷
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣦⡙⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣈⣉⣤⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣛⣩⣭⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⡿⢿⣿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠤⢀⡉⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠒⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⡍⠀⢀⢀⡀⠀⠈⢓⡧⡈⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⡠⠖⠈⠅⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⢠⠃⠀⠈⠁⠀⠄⡠⠚⢇⡟⠀⠀⠀⠀⠀⠀⠀⢰⡏⠈⠈⠁⠀⠀⠀⡠⠀⠖⣿⠓⠒⠄
⠀⠀⠀⠀⠀⠀⢠⠅⠀⠀⠥⠸⠈⠁⠀⢀⣥⣪⡴⠁⣼⡇⠀⠀⠀⠀⠀⡀⠄⢺⣇⣀⠤⢀⣠⠄⠁⠀⠑⡀⠹⠒⢀⠀⠂
⠀⠀⠀⠀⠀⠀⢸⡄⠐⣂⣀⣀⣤⡴⠞⢛⣫⠟⠀⣼⡟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿⠀⠈⡉⢀⢀⣀⠀⠄⣰⠆⠀⠀⠃
⠀⠀⠀⠀⠀⠰⡤⠳⣤⡀⣌⡤⢶⣛⣾⠟⠁⢀⡼⣋⣀⠛⠀⠀⠀⠀⠀⠈⢈⠁⠀⠙⠻⢭⣥⣤⣤⠴⢞⠁
⠀⠀⠀⠀⠀⢰⠁⠀⠈⠉⠓⠺⠿⠟⠁⠀⢠⠊⠈⠉⣿⡳⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠘⠦⠈⠧⠄⠂⠁⠀⠀⢀⠔⠁⠀⠀⠑⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠤⣀⣀⡀⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠈⠂⠒⠛⠢⠁⠂⢌⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡆⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠐⠞⠂⠀⠀⠀⠈⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣿⡼⢧⠀⠀⠀⠈⠫⠛⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡠⢃⣄⡠⠾⠰⠆⠀⠀⡤⢶⠃
⠀⠀⠀⠀⠀⠈⠁⠈⣭⣭⣍⣠⣤⣄⠀⠰⠖⠢⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⢀⠈⠁⡇⢀⠠⠞⡧⣾⠏
⠀⠀⠀⠀⠀⠀⠆⠀⢀⡴⠀⠈⠠⡆⠀⠦⠌⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⢀⠁⠀⢁⠤⠜⠁
⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠁⠴⠐⠂⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠾⢦⣄⣀⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⠉⠁⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⣀⠀⠄
⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⡐⠁⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠠⡀⠀⠀⠑⠀⠀⠀⠨⡁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⠀⠐⠊
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⢀⡈⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⠀⠇⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⢐⠀⠈⡗⠠⡤⠕⠰⠀⢀⡀⡄⠀⠀⠀⠀⠀⠀⢭⣀⣱⣀⣀⣔⣻⣾⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠁⡀⠂⠑⠂⡇⠀⠘⠀⠀⠀⠉⡱⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠤⣤⡔⠃⠐⠐⢆⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠴⣶⡖⠀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠸⢿⣤⣿⣿⡟⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣤⣄⣀⠛⠓⢚⣯⡠⣾⠿⣿⣿⣿⣿⣟⢟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣦⠔⡄⠀⣈⡟⡒⢠⣤⣂⡦⠉⣿⡟⢺⣿⡿⣿⣿⣿⡿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣴⣿⣿⢏⠡⠈⠓⣫⡇⠈⠛⠁⠀⠀⠈⠀⠈⠉⠀⠉⡿⢿⣛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⢬⡾⢯⣦⣮⣥⣮⣾⣿⣻⡀⢀⢆⠀⠀⢀⠈⡈⠀⠄⠀⢠⠤⠀⣾⡻⣶⡴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠧⣾⠿⢻⣿⣿⣿⣿⣿⣾⣿⠚⠃⠈⢰⣿⢋⠚⠀⠁⠀⢀⠄⠆⠀⠸⣶⣿⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠃⠘⠇⣠⣾⣿⣿⣝⣾⣿⡿⠇⢀⠀⠀⠀⠡⠐⠀⡄⠀⠄⠉⠀⠀⠀⣶⠂⠘⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡐⢆⠈⣙⣿⣿⣿⣿⣿⡄⠀⠀⠀⢠⣶⣄⣠⣴⠆⠀⢠⡔⠒⠀⠀⠻⠀⠁⢤⣿⡇
⠀⠀⠀⠀⠀⠀⠠⣧⡟⢿⣿⠟⠚⣿⢿⣿⣿⣾⡄⡴⢶⣍⣹⣿⣿⠃⠌⡰⠇⠀⠀⠀⠀⠁⠀⠀⣹⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣯⡷⡄⣿⣬⢣⠎⣳⣾⣿⣿⣷⡿⣿⣿⣿⣿⣿⡎⢠⣿⣧⣀⠀⠀⢼⣇⡄⠈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⡓⠀⠁⠋⠮⢿⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⡟⣿⠟⠋⠀⠀⢘⢿⣿⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠂⠀⠀⠻⠹⣿⣯⣿⡟⡤⠀⠀⠈⠻⣿⣿⠘⢁⠀⡈⠀⠀⠀⠸⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠤⠀⠿⡗⡼⣿⣇⠀⠀⠀⢀⣀⣿⣃⢀⠀⠀⠁⡈⢁⣤⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⢀⡀⠀⠉⣙⡲⠆⠄⢰⣿⣿⣿⣷⣿⣦⢴⣶⣿⣿⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⡆⡃⢿⣿⣿⣴⠞⣿⣿⠝⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠂⠋⠿⠿⠕⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⢈⠉⠈⠉⠉⠛⠒⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠠⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠙⠂⠀⢀⠱⡀
⠀⡠⠤⠐⣒⣒⣒⣒⣀⡤⠤⢤⡌⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠰⡀
⠀⢢⡀⠈⢄⡀⠀⠀⠀⠀⠈⢹⠀⠊⠐⠀⠀⠀⠰⡱⣾⠂⠐⠒⠂⢾⡶⡙⠀⠁⠀⠀⠀⠀⢵
⠀⠀⠉⠢⢄⠈⠒⠤⣀⠀⠀⡇⠀⠀⢀⡐⠀⠀⢀⡠⠀⠀⠠⠤⠀⡀⠄⢀⡀⠂⠀⠅⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠒⠤⣀⠉⠒⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢢⠄⣀⠉⠑⠢⠤⣄⠄⠀⠚⠀⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⠐⡺⢅⡒⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣉⠐⠂⢤⣀⡈⠉⠒⠢⠤⢤⣠⠄⠀⠐⠀⠀⠄⠀⡠⠁⠀⠀⠁⠒⠅⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠄⠙⠒⠒⠤⣄⣀⡈⠁⠒⠂⠤⠤⢴⣁⡀⠀⠀⠀⠀⠀⠈⠑⢌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡚⠁⠀⠉⠒⠀⠀⠀⠀⠀⠉⠑⢒⠶⠠⠤⠄⢀⣉⡉⠐⠒⠒⠒⠒⠁⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⢤⣀⣀⣀⣑⣂⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠛⠂⠀⠀⠀⠒⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢀⡀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠕⠈⠀⠈⠁⠂⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠠⠤⠤⠥
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⡀⠀⠀⠀⠑⢌⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡁⠀⠡⠀⠀⠀⠀⢂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⡦⠀⢀⡉⠉⠐⠠⠄⢀⠀⠀⠀⠀⢳⠀⠀⠑⠄⠠⠀⠀⠀⠀⠀⡆⠇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠔⠂⠀⠁
⠀⠀⠀⠉⠢⡀⠀⠉⠀⠐⠂⠄⢈⡁⠒⠠⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠐⠂⠀⠀⡁⠠⠀⠤⠤⠤⠀⡄
⠀⠀⠀⢠⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠉⠐⠠⢌⠳⣄⠀⠀⠀⠀⠀⠀⠀⡄⡈⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⢀⡠⠔⡠⢁⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠉⠁⠀⠀⠀⠀⢀⡀⠄⠐⠂⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢊⡠⠐⠂⠉⠀⢈⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠒⠒⠊⠉⠀⡠⠔⠁⢀⠔⠁⠀⠀⢀⠠⠐⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠈⠂⠐⠒⠈⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⢔⠒⠠⠄⢀⣀⣀⣀⠠⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠷⣦⡀⠀⠐⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠟⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚⠋⢠⣧⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⡀⢸⠋⢻⠇⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠰⠷⣦⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠀⠐⠂⢾⡃⠀⠀⠀⣸⠉⢻⡷⠀⡀⠀⠂⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣼⠋⠙⣿⠄⠀⠀⠀⠀⠲⠬⠃⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⡤⡁⠸⢭⡴⠂⠀⠈⠑⠃⠀⢐⡡⢉⣡⡾⠿⠿⢿⣿⣧⠄⠀⠀⠘⠛⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣦⢿⣲⣦⣤⣖⠶⡾⡱⠞⠋⣩⣰⡟⠁⠀⠀⠊⢫⣿⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣿⣷⡉⢾⠻⣿⣷⢻⣇⠀⠀⠀⠀⠈⠟⠥⢠⠀⠀⠁⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠏⠙⡇
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣏⠠⡿⣿⣿⣦⣽⣦⣼⣿⣷⢌⣱⡶⠒⢻⠿⠤⠀⠁⠀⠀⠀⠀⡼⠛⠉⠻⣿⡇⠀⠀⠀⠐⢳⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⣶⣤⡀⠄⢦⡀⠀⢤⣤⢲⡄⠀⠀⠷⠀⠀⠀⠙⠁⠂⠸⠀⠀⠀⠑⠤⠎⠀⢿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢁⣴⣿⣿⣿⣿⣿⣎⢃⡑⠺⠃⠉⠉⠀⠀⠀⠀⠛⠲
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣤⣣⣄⣴⣶⣾⣷⣴⣶⣆⠆⠀⠀⠀⢀⡀⢀⣴⣶⡄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡈⠻⡿⣿⣿⣿⣿⣿⣿⣆⠘⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢘⠇⠀⠀⣌⠀⠹⠃⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡆⠀⠈⠋⠀⠀⣠⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣱⣰⢦⣰⣶⣼⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣛⣻⣿⣿⣿⣿⣿⣿⣷⣄⠹⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⣉⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⢀⠤⠶⠚⠓⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣖⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡖⢲⠒⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⣄⡀
⠀⠀⠀⠀⠁⠀⢀⠀⠀⠱⠎⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠄⠅⠾⠾⢻⣿⣆⠀⠀⠀⠀⢠⠞⠙⠛⠓⢀⠀⠛⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠺⢻⣿⣿⣆
⠀⠀⢰⡉⠀⠀⠀⠠⠀⠐⠃⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⢂⠂⡾⢀⢈⣿⣿⡄⠀⠀⠀⣎⠀⠀⠁⠀⠀⢛⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⡀⠠⣄⢀⢉⣼⣿⣿⡄
⠀⠀⢨⠁⠀⠘⠂⠀⠘⢲⡀⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⢘⠁⢓⣴⣻⣿⣿⠇⠀⠀⠀⠹⣿⣿⡦⠀⢠⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⠉⢉⡛⡛⣿⣟⣻⣿⣿⠃
⠀⠀⠀⠃⡤⠀⠀⡀⠈⢀⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣀⢘⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠨⣿⣇⠀⣸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠘⡍⠈⠳⠟⠛⣽⣿⠏
⠀⠀⠀⠀⠀⠒⠤⢸⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢨⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⣤⠷⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠸⠛⢛⣳⣦⡀⠀⠀⠀⠀⠀⠀⠰⠟⠉⠸⢟⣿⣶⣶⠛⢿⣷⠀⠀⠀⠀⠐⠈⠁⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢶⣄
⠀⠀⠀⠀⠀⠀⣀⢀⣀⣈⣉⣙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠒⠑⠋⣠⣿⣿⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣧
⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉⠋⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣻⡿⠋⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⣿⡆
⠀⠀⠀⠀⠘⠛⠿⡿⣿⠛⣿⡟⣿⡏⠀⠀⢠⠄⠀⠀⠀⠀⡠⠞⠋⣠⣾⡿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣼⠟⠀⠀⢠⠀⠀⠀⠀⠀⣠⣤⣴⣾⣿⠟⠁⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⣠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢙⣻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⠉⠀⠀⠀⠀⠀⠉⠈⠉⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠾⠻⠓⠈⠠⢅⢢⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠈⠁⠒⢤⣴⣶⣿⣭⣷⠖⠎⢉⠁⢪⠑⠀⡘⢌⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡁⠀⠀⠀⠀⢀⠇⡼⢂⣼⡯⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⡠⣢⢞⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⡾⣫⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⢫⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠟⠉⠀⠀⡐
⠀⠀⠀⠀⠀⢀⡴⣫⣿⡿⠋⠀⠀⠀⠡⡀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⡔
⠀⠀⠀⢀⡴⡫⠪⡟⢱⠁⠀⠀⠀⠀⢀⣈⣦⣶⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⡐⡟⡐⠀⢅⠧⣈⣐⣒⡤⢼⣞⣻⡿⠿⠛⠙⠠⠀⢀⣀⣀⡀⠠⠤⠒⠁
⠀⢰⠀⢇⡑⠠⠤⢬⣤⣤⠶⠟⠛⠉⠁
⠀⠀⠁⠒⠐⠒⠈⠁

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠦⠤⣤⡀
⠀⠀⠀⠀⠀⣰⠋⠤⠀⠯⠃⠀⡌⠳⡄⠀⠀⠀⠀⣰⠋⠐⠃⠣⠤⠀⠬⠷⡀⠀⠀⠀⠀⣴⠋⡀⠀⠐⢈⡔⢉⢧⡀
⠀⠀⠀⠀⢰⡇⡔⢂⠀⠉⠐⢠⣦⠀⢹⠀⠀⠀⢰⡃⢀⠀⣈⠇⠴⠄⠖⠀⢷⠀⠀⠀⢸⠕⠈⠠⠂⠉⠡⠐⡡⠔⣧
⠀⠀⠀⠀⠘⡇⠈⡁⠀⢮⡹⠂⢀⠀⡼⠀⠀⠀⠘⣧⣠⠀⠤⠠⡒⢒⣂⢀⡾⠀⠀⠀⠸⣍⠥⡂⠁⠐⠨⠄⠂⠯⡟
⠀⠀⠀⠀⠀⠙⢖⡃⠐⠂⢠⠄⣀⡴⠁⠀⠀⠀⠀⠙⢶⣒⣒⣒⣠⠄⣤⠖⠁⠀⠀⠀⠀⠹⣮⣀⠤⠂⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠋⠁

⠀⠀⠀⠀⠀⠀⢀⣀⠄⠐⠲⠤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠖⠢⠤⣀
⠀⠀⠀⠀⠀⡰⠛⢄⡁⠀⠀⠀⠨⠳⡄⢈⠠⠀⠁⢼⠯⠤⢄⣀⣀⣀⠨⠷⡄⠀⠀⠀⠀⡴⠋⠐⠀⠢⡯⡂⣨⢳⡀
⠀⠀⠀⠀⢠⠧⠄⢀⠈⠁⠒⠂⠀⠀⣳⠀⠢⡀⠠⣦⣑⠲⠒⣒⠒⠒⡂⣈⣿⣄⠀⠀⢸⠁⠋⠀⠠⠀⢀⡀⣬⠀⣧
⠀⠀⠀⠀⠘⡇⠶⠆⠀⠉⠁⠩⠉⢀⡽⠀⠀⠈⠲⣌⡀⠓⣠⠌⠐⠂⠠⠄⠼⠛⠷⢄⠸⡄⠠⡑⡁⠀⡀⠄⠀⠂⡟
⠀⠀⠀⠀⠀⠙⢆⡀⠠⠀⠀⠤⣃⡼⠁⠀⠀⠀⠀⠙⢮⣑⢦⣄⣀⠀⠀⠰⠂⠊⠀⢈⠀⠱⣌⡀⠠⠀⠢⠁⣣⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠁⠐⠀⠐⠂⠁⠀⠀⠀⠉⠓⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⢀⣠⡴⣒⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡖⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⡶⢤⣀
⠀⠀⠀⠀⠀⣰⠋⠀⢀⠠⠇⠀⣞⢱⡄⠀⠀⠀⠀⡰⠋⠀⡁⠁⠰⢲⢫⠳⡄⠀⠀⠀⠀⡼⡓⡒⠒⠀⠒⣈⠝⢳⡀
⠀⠀⠀⠀⢰⠋⠄⠲⠅⣀⠀⣖⠉⠈⢻⠀⠀⠀⢰⡏⠢⢈⠢⠨⠔⠌⣎⠒⣷⠀⠀⠀⢸⢗⡒⠀⠭⠬⠭⢄⣶⠮⣷
⠀⠀⠀⠀⠘⡆⠀⠘⠄⠀⡱⠀⠘⠀⡼⠀⠀⠀⠘⡎⣓⠠⠂⡀⠈⠢⠬⢁⡟⠀⠀⠀⠸⡇⠚⠁⠴⠖⣉⡡⠔⢉⡟
⠀⠀⠀⠀⠀⠘⢦⡀⠐⠰⠁⠀⣀⠟⠁⠀⠀⠀⠀⠙⢆⣀⠐⡀⠺⡰⣠⠞⠁⠀⠀⠀⠀⠹⢆⡀⠀⣀⡂⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⠉⠤⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡫⠒⠉⠀⠉⠐⠢⣉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠀⠀⢀⢸
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠁⠀⠀⠀⠀⠀⠀⠀⠑⢌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠉⠑⠄⠀⠀⠀⠈⢢⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢘⠁⠒⠂⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠘⣄⠀⢈⠀⠀⠀⠀⠀⢃⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴
⠀⠀⠀⢸⢅⠒⠒⠀⠤⢀⡈⠉⠒⠂⠤⣀⠀⠀⠘⣆⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⣀⡀⠠⠄⠒⠒⠈⠁
⠀⠀⠀⢸⠀⠑⢄⠀⠀⠀⠀⠉⠁⠒⠠⠄⣉⠁⠂⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠖⠂⠈⠉⠁⢀⡀⠤⠐⠒⠀⠉⠉⠁⠀⢺
⠀⠀⠀⠀⡆⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢌⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠇⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣀⠀⠀⡠⠔⣡⢎⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠂⠀⠀⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⢉⡠⠔⠒⠂⠉⢑⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠤⠤⠤⠤⠴⠒⠀⠀⣀⠔⠊⠀⡠⠊⠁⠀⠀⠀⣀⠴⠋⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠸⢄⡀⠠⠤⠐⠊⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡉⠁⠒⠒⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⠄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠾⠛⠛⠛⠛⠛⠛⢳⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠀⠈⠙⣛⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢀⣤⡶⠟⠋⢉⣉⣽⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⣴⠟⢁⣤⡶⠟⠛⠉⠁⠀⠈⠙⢷⣄
⠀⠀⠀⠀⢀⣾⠏⣴⠆⣿⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⢀⣴⠋⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡄
⠀⠀⠀⣠⡿⠁⠰⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡾⠛⠀⢀⣴⠟⢁⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠈⢻⣆
⠀⠀⣰⡟⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⠛⠛⠉⠉⠁⠀⠀⢀⣴⠟⠁⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠛⠁⠀⠀⠀⠻⣆
⠀⢰⡟⠀⠀⠀⣠⣴⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢀⣴⠟⠁⠀⠀⠀⢀⣠⣤⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⣿⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠶⠟⣋⣠⣤⠶⠛⠁⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣠⡿⢿
⢸⢇⣴⠟⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⣠⡾⠛⠋⠉⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢀⣴⠾⠋⠉⠉⣿⠀⠀⠀⣰⡟⠀⠸
⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⡾⠃⠀⠀⣼⠏⠀⠀⢀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢠⡿⠁⠀⠀⣠⣶⠟⠁⠀⢀⡾⠃⠀⠀⣠⡿
⣿⠀⢀⣤⡶⠶⠿⠿⠛⠋⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⢿⣅⣠⣴⠾⠋⠁⠀⠀⣰⡟⠁⠀⢀⣴⠟
⣿⣴⠟⠁⢀⣤⠶⠶⠶⠶⣦⣤⣀⡀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⣠⡾⠋⠀⠀⣠⡾⠃⠀⣼
⢸⡇⠀⢠⡟⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣠⡾⠋⠀⢀⣼⢋
⠈⣷⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣠⡾⠋⠁⠀⣠⡾⠁⣼
⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⠀⢀⣤⡾⠋⠀⠀⣠⡾⠋⠀⣰⡏
⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠞⠋⠀⣀⣤⡶⠟⠁⠀⣀⣴⠾⠋⠀⠀⣠⡟
⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠟⠋⠉⣀⣤⡶⠟⠛⠁⢀⣠⣴⠞⠋⠁⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠙⣷⣄⠀⠀⢀⣾⠃⠀⠀⠀⠀⢀⣠⡶⠞⠛⠉⠀⠀⢀⣤⡶⠛⠉⠁⢀⣠⡴⠞⠛⠉⠀⣠⡄⣴⠆⢀⣾⠏
⠀⠀⠀⠀⠀⠈⠻⣦⣀⣼⠃⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⣴⠾⠋⠁⠀⠀⢀⣾⠀⠿⠈⢋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣄⡀⠀⣰⡟⠁⠀⠀⠀⠀⠀⣴⠟⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠘⠃⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣿⣀⡀⠀⠀⠀⢠⡾⠃⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣶⣿⣥⣀⣀⣼⣇⣀⣀⣤⣤⣴⡶⠾⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠖⠐⢶⠆⠠⢤⣾⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⢿⠿⠟⠁⠀⠀⠉⠀⠀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⠏⠁⠈⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠛⠀⠀⠀⠀⠀⠀⠀⢛⡱⢦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⡮⠍⠀⠀⠀⠀⠀⠀⠀⢀⠘⠃⢀⣠⡟⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⣼⢟⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣡⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡏⠀⠀⠀⠀⠈⠀⠀⢤⠚⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣰⢏⣴⣿⣿⣿⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣁⣶⠄⠂⠀⢀⣰⣶⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣡⡿⢿⠏⠁⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠋⠁⠀⣀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⣰⣮⡾⠏⠀⠀⠳⣾⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠈⠁⠀⠀⡠⢞⡿⠋⠀⠀⠀⢰⣿⠟⠉⢠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⣠⢞⣵⠛⠁⠀⠀⠀⣴⡏⠁⠀⠀⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡍⠹⣷⡤⢀⠀⠀⠀⠀⣀⣴⣾⣿⠛⢀⣠⣰⢟⣵⣿⠋⠀⠀⢀⣴⠟⠉⠀⠀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠛⠄⢰⣾⣿⣷⣶⣾⣾⣿⣿⡏⣁⢾⣿⢟⣡⣿⠟⠀⠀⠀⣤⠬⠃⠀⠀⠀⣀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣽⣿⣿⣿⣿⣿⣟⣻⣬⣾⢟⣵⣿⡿⠋⣀⣠⣴⠾⠋⠀⠀⣀⣠⣾⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣷⣾⣿⣿⢿⡀⠠⣠⣼⣿⣿⡿⠊
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠟⣩⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⠿⠽⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢢⡀⠉⠉⠁⢀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁
⠀⠀⠀⠀⢠⠀⠙⠁⠀⠀⢤⡦⡀
⠀⠀⠀⢀⡇⡀⠄⠐⠃⠀⣀⡀⠘⡅⠉⣷⠄⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⡠⢺⣷⡈⠀⡊⣹⠀⠀⢀⣾⣿⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠞⡁⠀⠿⢗⣳⣤⠴⠟⠛⡛⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠉⠉⠛⠿⣿⣷⣤⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣡⣴⣯⣐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠆⢺⣥⣤⣼⣿⣟⠛⢛⡀⠂⠀⡀
⠀⠀⡠⠀⠀⠻⣿⡿⠙⠿⠋⠁⠈⠃⠀⠀⢈
⠀⠀⠣⣿⣶⣀⡀⢳⠃
⠀⠈⠘⢿⣿⠿⠙⠙⠂⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⡞⠛⡄⠀⠀⠠⣤⠼⢿⠆
⠀⠀⠀⠙⢾⣦⣦⣾⣶⠂⢠⡌
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣵⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⢤⣤⠤⠖⠻⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠤⣤⠄⠀⠀⠁⠃
⠀⠀⠀⠀⢸⠷⣄⡀⣴⢋⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⢀⡀⠈
⠀⠀⠀⠠⢾⡀⢏⠁⠸⡦⣀⣠⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠬⠛⠳⠀⠀⠐⠀⠀⠐⡀
⠀⠀⠀⠀⠀⢻⠾⢁⠺⣄⠀⣹⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⠀⠀⠈⢠⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠋⠀⠈⡇⠀⠹⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢠⠀⢣⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⡿⠿⢿⠛⠿⣿⣿⣷⡶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⢿⣃⡾⠀⡐⠌⠐⠋⠈⠀⠙⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡿⢛⡛⣉⣉⣁⣄⣀⣤⣀⣀⣀⣀⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⢻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣬⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⠛⠛⠃⠒⠟⠛⠹⠟⠟⠻⠿⠟⠻⠟⠻⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠹⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡤⣤⣤⣤⣄⠀⠀⠀⠀⢀⢛⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠝⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⣿⣿⣿⣿⣷⣾⣿⣿⣧⡄⠀⠀⡤⢈⢩⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣉⠛⠂⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⢎⣉⣉⡿⠿⠷⠾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣘⣛⣿⣷⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡠⡀⣀⢀⣤⢀⣄⡄⣠⠾⠆⠤⠐⠐⠒⠊⠁⠆⠀⠀⠀⠉⠛⡿⠉⠋⢭⣿⣿⣧⣍⢋⡉⠹⣿⣿⣷⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⠟⠙⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠈⠙⠧⡄⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣋⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣏⣀⡀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣶⣾⣿⣿⣭⣤⣴⣤⣶⣶⣶⣶⣶⣾⣷⣶⣪⣴⣶⣶⣆⠴⣦⡶⣦⣤⣄⣀⣐⣠⣤⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠋⣨⣴⣿⣿⣿⣿⣿⣿⠿⡛⠛⠙⠉⠋⠉⠉⠉⠉⠛⠉⠀⠁⠀⠘⠻⠻⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⣡⢀⣂⣤⣠⣤⣴⣶⣶⣶⣤⣤⣴⣤⣀⣀⠀⠀⠀⠀⣹⢿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣹⢻⣿⣿⣷⣾⣷⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡛⠏⢛⣿⣛⡛⠻⠙⢟⢿⣿⣿⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣽⣀⡆⠠⠦⡌⠠⡝⢛⡚⢢⣮⣾⣿⣿⣟⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣶⣥⣶⣷⣿⣿⣷⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⢀⠀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣀⡴⣔⡁⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⢃⠀⠀⠄⠀⢀⠠⠀⠀⠀⠀⠀⠀⠔⠖⠚⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⡀⠂⠃⠀⠀⠁⢢⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢐
⢀⠑⠚⠰⠦⠖⠁⠲⡤⢮⡆⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⢀⠰⣠⠃
⠘⠈⠰⠐⠠⢀⠠⢶⠄⠄⠋⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡉⠰⠂⠂⠈⠒⠀⡈
⠸⡷⠄⠄⠀⠀⢲⣦⡄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠛⠀⡄⠊⠠⠔⠁
⠀⠘⢤⡠⠔⠂⠀⢤⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⡄⠒⡀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠖⠀⠀⠀⠂⡀⢀⠱⡄⠒⠄⠤⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢰⠀⠁⠀⡠⠏⠀⠒⠀⠈⡠⣜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡤⠔⠀⠡
⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠁⣐⢠⠀⠠⣅⣉⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀
⢀⠀⠀⠄⠀⠀⠀⠉⠉⠉⠀⠃⠀⠀⠀⠀⠉⠔⠆⠀⠘⠄⠀⠈⣁⠋⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠔⠃
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣖⣯⣼⣟⢲⣦⣽⣤⡀⢠⠀⠀⠈⠀⣠⣦⡙⣅⠀⠙⠷⣦⡀⠀⠀⠀⠀⣠⡴⠖⣲⢤⡀
⠀⠀⠀⠀⣰⣶⣯⡿⣿⣿⣿⣿⣿⣿⣦⣼⣿⡌⠄⣄⠀⠐⢅⠀⠑⢤⡐⢄⡀⠈⢑⡀⠀⠀⠐⠋⡀⠈⢁⣼⣿⡀
⠀⠀⠀⠀⣿⢄⣽⣷⡌⠻⠿⢿⣿⠭⣭⣁⣿⣷⡠⠏⠀⠀⠀⠑⢄⠀⠉⠲⢌⡑⠺⡇⠀⠀⠘⣁⠀⣠⠔⡻⣿⠁
⠀⠀⢀⣈⡟⢻⡿⣛⣿⣿⣷⣾⣧⡴⣿⣿⡟⡿⠃⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⣨⡿⠀⠀⠀⠀⠈⠛⠿⠷⠚⠁
⠀⢠⡼⢃⣀⣘⣿⡏⠙⣋⠈⠛⢋⡄⠈⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠵⠈
⠀⠀⠈⠑⠻⢏⠙⣻⣿⣧⣦⣿⣼⡳⢾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠉⠉⢉⡿⠿⣿⠟⠋⠑⠁⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠂⣐⣦⣤⡀⠀⠀⣤⣄⡰⣧⢠⡇
⠀⠀⣤⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣚⣃⣀⡀⠐⣒⣀⡀⣘⣻⣦⠀⠀⠲⠥⠤⠚⠁
⠀⠸⣏⣉⠉⢉⠀⠀⠀⢀⣴⣯⣤⠀⡟⣳⣦⡀⠀⠀⠉⠉⠙⠇⠈⠈⠉⠉⠛⢨⠙⠩⡇⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠛⠛⠋⠀⠀⠀⢶⣶⠿⣏⠛⣉⡿⢿⣷⠀⢰⣶⣦⣤⡤⣤⣶⣄⠠⢤⣤⣤⣼⡧⠀⠀⣤⡾⠿⠿⠿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣽⣷⣾⣿⡀⣠⡟⠀⠈⠋⠛⡛⠿⠿⠓⠛⠛⠙⠉⠉⢿⠇⠀⢸⣏⠤⠴⠛⠿⠶⣿⡆
⠀⠀⠀⠀⣴⣞⢦⠀⠀⠀⠉⠉⣉⣿⣿⣿⠟⠀⠀⠀⠈⠺⣉⣛⡛⡛⢛⣛⣛⣿⡿⠋⠀⠀⠘⣷⣶⣶⣶⣖⣲⡾⠁
⠀⠀⠀⠀⠘⠻⠛⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠛⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⡀⠈⠈⠙⠂⠀⠙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⠁⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠘⠳⡄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠰⠀⠉⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⣠⠀⠈⠏⠀⠀⠀⠀⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡀⠀⠄⠀⠄⠒⢁⠀⠀⠀⠐⠊⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄
⠀⠀⠀⠀⠀⠐⠔⠀⠤⠋⠀⠀⠊⠙⡇⠀⠐⠰⣦⠸⡄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⡠⡤⣄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢎⠀⠀⠀⠠⡄⣀⠀⠈⠃⠀⠜⠒⠃⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠱⡀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⣈⣁⠙⠃⠀⠀⠀⡠⠀⠀⠀⢤⡆⠀⠀⠀⡀⠒⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠘
⠀⠀⠀⠀⠀⠘⣦⠀⠐⠁⠈⢧⠀⠀⠀⢰⠇⠀⠀⠈⠁⢿⡄⠀⠀⠀⣀⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⢸⡇⠀⢻⣀⡀⠀⠀⢀⡴⢚⠁⠀⠔⠋⠀⠈⠉⠻⣻⣄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠈⡑⠂⡊⠀⠢⠟⠫⠉⠁⠊⠐⠻⠁⠀⠀⠀⠀⠀⠁⠀⠀⠻⣿⠇⠀⠀⠀⠀⠀⢀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⡀⠆⠀⠀⠉⠛⠃⠠⣤⡐⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⣁⠀⠈⣀⠀⠠⣀⠈⠂⠀⠀⠀⢀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⢸⡉⠙⢿⢥⡀⠀⢀⣀⣀⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡉⠀⠀⢙⠟⠀⠐⠠⠉⠝⠀⠀⠀⠀⠀⠀⠀⠀⠉⡹⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⡄⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠀⠑⠛⠃⠀⠀⠀⣀⠄⠃⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⡠⠔⠚⠭⢭⡉⠓⠦⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠁⠀⠀⠀⢀⠾⢷⣴⡤⣀⠐⠈⢑⠢⣌⢢⠀⠀⢳⡤⠚⢲⡀⠒⢄⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⡀⠰⠁⠀⠁⠄⠀⣶⣦⣼⣿⣿⠂⢀⡵⠬⠍⠱⡀⢨⣀⠀⠀⠉⠓⠿⠷⣄⡁⠢⠙⡇⠀⠌⠀⠀⠀⠙⢦⢀⡣⠀⠰⠁⠀⢠⣭⣳⡀⢠⣏⣀⣋⣽⡄
⠀⠀⠤⠾⠁⡇⠴⢄⠀⡘⠀⣿⣿⣏⣽⣿⠇⠸⣄⠀⠀⡀⠀⢸⠿⣿⢿⣷⣶⣤⣀⠈⠙⠦⣌⡇⠀⢃⠀⠀⠀⠀⠈⡟⡞⠀⠸⣀⠀⣿⣿⣿⠃⠐⠈⠓⠊⣉⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠙⠛⠛⠉⠀⠀⠈⢡⡌⠀⠀⠈⢆⠀⠀⠛⠻⢿⣿⣷⣦⣀⡜⠀⠀⠀⠳⠄⣢⣀⣾⡛⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣦⣀⣀⣈⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣶⣷⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⠯
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⢿⠿⠿⢿⢟⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣛⣻⣛⣿⣟⣛⣿⣟⣛⣻⣿

⠈⠓⠂⠀⠀⠛⡯⠀⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⢠⠈⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠀⣀⣀⡀⢠⡤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀⡀⠀⠀⠀⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠀⠀⠈⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢢⠀⠀⠐⠂⠄
⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡀
⡀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠦⠤⠄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠒⠂⠀⠒⠀⠀⡀
⠀⡀⠀⣀⡀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⡡⣤⡀⠈⠉⠉⢠⠉⠳⠀⠀⠀⠀⠀⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠫⢟
⣥⣰⣀⣉⣁⣀⣞⣋⣲⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣐⣁⣀⣀⣀⣀⣀⣀⣀⣿⣲⣐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠛⠛⠛⠛⢻⡿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⠁⠀⢀⣠⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣜⣿⠿⠟⠋⠁⠀⢀⣠⣴⠶⢋⣁⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢺⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠿⠛⠉⠁⠀⢀⣠⣴⠖⠛⣉⣤⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣾⣦⣤⡴⠷⠛⠉⠁⠀⠀⢀⣠⡴⠞⠛⣉⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⢹⣿⠿⠟⠛⠉⠀⠀⠀⣀⣠⣤⠖⠚⢉⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠒⠋⢉⣀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣁⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

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

⣏⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⢹
⣿
⣿⠀⠀⣠⣴⣶⣦⣠⣀⡀⠀⢀⣀⣀⣀⣀⣀⡀⢀⣀⠀⠀⢀⢀⡐
⣿⠀⢺⣿⣿⣿⣿⣿⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁
⣿⠀⣼⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣄⣴⣿⢵⣦⡈⢳⣤⠤⣤⣄⡀
⣿⠀⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢾⣿⣿⡄⢡⣼⠁⠀⣹⣆⠠⠀⠀⢀
⣿⠀⣿⣿⣿⣿⣿⣿⡆⢘⣿⣿⣿⡏⠀⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⠇⠀⠙⠷⢶⣿⣿⡀⠀⠀⢸
⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⡤⣿⣿⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣯⣥⣤⣤⣽⣧⠀⡆⢸
⣿⠀⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣀⣿⣿⣧⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡇⢸
⣿⠀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠏⠉⠉⠙⢿⣾⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⢸
⣿⠀⣿⣿⣿⣯⣿⣿⣷⣶⡿⠿⢿⣿⣏⠀⢠⣶⠃⠈⣿⡆⠱⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢸
⣿⠀⡌⢻⣿⣿⣿⣿⣯⡝⠀⠀⠀⢻⣿⣆⠁⠀⠔⠀⣹⣿⣷⡁⣾⢟⠛⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⢸
⣿⠀⣿⠉⣉⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣷⡂⡘⣿⣿⣷⠃⣨⡧⠸⣿⣿⣿⣦⣌⢿⢿⣿⣿⣿⡇⢿⢸
⣿⠀⣿⣧⡻⣿⣿⣿⣿⣿⣷⣶⣶⣋⣻⣿⣿⣿⣭⣯⣧⣈⣻⣂⡌⢻⣇⠀⣿⣿⣿⣿⣿⣺⣿⣿⣿⠛⠀⢸⢸
⣿⠀⠁⢺⣿⣿⣿⣿⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣘⠿⣿⣿⣿⣿⣿⣿⣿⣦⡄⢸⢸
⣿⠀⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢸

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⢤⡀⠀⠀⠀⠄⠐⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣽⣿⠂⠀⠀⠀⣰⡄⠀⠀⢰⠁⠀⠀⠀⠀⢹⠀⠀⠀⡤⠀⢀⢠⡜
⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠉⠁⠀⠀⠘⡀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠃⠓⠋⠁
⠀⠀⢀⢀⡀⠀⠁⠀⠀⠀⠀⣀⢘⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠒⠲⠖⠊
⠀⠀⠼⣿⠷⠀⠀⠀⠀⠀⢨⡀⢰⠹⡄⠀⠀⠀⠃⢐⡄⠀⠀⢤⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢻⣖⠚⠖⠓⠉⠀⠀⠀⠸⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠀⠀⠀⠈⠁⠄⠀⠀⢀⠀⠀⠀⠀⠈⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢽⡿⠄
⠀⠨⠄⠀⠀⠀⠀⠆⠀⠈⠛⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠐⢤⠀⠁⠀⠀⠰⠀⠀⠀⠀⠁
⠀⠀⠐⠀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠃⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣄⡐⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⢹⠀⠀⠀⠀⠘⣄⠀⠀⠀⡀⠀⢀⣄⠀⠀⣿⡟⠡⣾⣿⣷
⠀⠀⠀⣼⣿⣅⠀⢀⠄⠀⠀⠀⠀⣀⡖⠁⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠈⠙⠁⠀⠱⣦⣄⠀⡉⠁
⠀⠀⡜⠘⠁⠀⢰⠁⠐⣄⣀⡤⠚⡡⠀⠀⣤⡤⠀⠀⠀⠀⠀⡄⠀⢸⠉⠐⢢⣤⡀⠀⠀⠈⠀⠀⡀
⠀⠀⡂⠀⢂⠀⠈⠓⠒⠋⠉⠈⠁⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⢸⣠⠖⡋⢀⠙⢄⠀⠀⠀⠿⠃
⠀⠀⠠⠀⡂⠀⠀⠀⠀⠀⡔⠉⠈⡁⣐⡀⠀⠀⠀⠈⠀⠀⠀⣠⣀⠈⠣⡀⠀⠊⠀⡈⠢⣀⣀⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠐⠀⡀⡀⠀⠀⠀⠰⠆⠀⠀⠛⠇⠀⠀⠙⢆⠈⠢⢃⣔⠁⠈⢢⡘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⡨⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠚⠹⡀⠙⣄⡠⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢶⣾⣄⠀⠀⢰⠉⠢⡀⢈⠦⠜⡆
⠀⠀⠀⠐⠦⣠⡠⠔⠁⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠃⠀⠀⠀⠑⠢⢬⣣

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢠⠤⠒⠀⠐⠢⣤⡀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡀⠀⣠⡤⠒⠀⠒⠂⢤
⠀⠀⠀⠀⠐⠁⡰⠂⠀⠀⠀⠀⠉⠑⠀⠀⠀⠁⡀⠀⠀⡀⢠⠀⠀⠀⠀⠤⠀⠀⠠⠐⠉⠁⠀⠀⠀⠀⠲⡀⠑
⠀⠀⠀⡇⠆⢰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠣⡀⠤⠂⡠⣽⢊⢸⡥⠀⠪⠄⡐⠊⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠇⡇
⠀⠀⠀⣷⠀⡄⠀⠀⠀⠀⠀⢗⠂⠤⢤⣄⡀⠈⠆⠀⢰⣴⠊⢶⣴⠀⠐⠎⠀⣀⣤⠤⠄⢂⠇⠀⠀⠀⠀⠀⡄⢰⡇
⠀⠀⠀⢹⡇⡇⠀⠀⠀⠀⠀⠘⢆⠀⠀⢻⣿⠾⠺⠯⡅⠻⠞⠾⠃⡼⠿⠲⢾⣿⠃⠀⢠⠞⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠈⣇⠃⠀⠀⠀⠀⠀⠀⠀⠳⢄⣀⢁⣀⡀⠀⠑⣦⣀⣴⡞⠁⢀⣀⡀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⢃⡏
⠀⠀⠀⠀⠸⣴⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠀⠉⠙⠓⠀⢹⣧⣿⠁⠀⠛⠉⠁⢸⣷⠄⠀⠀⠀⠀⠀⠀⠀⢰⡼
⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠊⣷⡀⠈⠁⠀⢀⣸⡿⣿⣀⠀⠀⠉⠀⣸⡏⠂⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⢀⡤⣟⣷⡄⠀⠀⠀⠘⡃⠛⠀⠀⠀⠀⣾⣽⠇⣆⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠂⠀⢨⢟⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢘⣿⠀⠀⠒⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢸⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⢛⠜⣿⣿⠂⠀⠀⠀⠀⠀⠀⢺⣿⡟⢝⠃⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⢛⣍⣿⡿⠉⠀⠀⠀⠀⠀⠈⠸⣿⡏⣝⠣⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⢿⣷⡇⠀⢠⣤⣤⠀⠀⣷⣿⠿⠿⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢁⢀⡿⣹⣿⢷⡈⢿⠏⣰⢿⣿⡽⣇⢀⠁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠕⠋⠞⠠⠿⢿⣿⡴⠈⠰⣼⣿⡿⠧⠙⠎⠓⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢀⡇⡀⠘⢸⠀⠤⠀⢨⠘⠀⠀⡅⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⢠⡄⣤⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠠⠀⠘⠂⠚⠁⠀⠀⠀⠁⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠋⠑⣶⣶⠀⠀⠈⠀⠀⣀⣴⣆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡽⠃⠀⡼⠛⠃⠀⠀⠀⢀⣬⣽⣿⣍⣉⣀⠛⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣶⣾⠇⣶⠃⠀⠀⠀⠀⠀⢸⣮⣿⣿⡿⢾⣿⣿⣿⣿⣿⣦⣌⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣯⣿⡷⠃⠀⠀⠀⢀⣀⣴⣿⡟⢻⢝⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣨⣼⣿⣿⡟⠃⠀⠀⠀⠀⣰⣾⣿⣿⡏⢻⣠⣈⠾⠂⠄⣸⣿⣿⣿⣿⣿⣿⡟⠶
⠀⠀⠀⠀⠀⠀⣸⡿⠛⢻⠇⠀⠀⠀⠀⠀⡾⠿⣟⣻⣏⠡⠄⠠⠍⠀⠀⢤⣸⣿⣿⣿⣿⣿⣿⣿⣦⡁
⠀⠀⠀⠀⠀⢠⣿⡤⠄⠂⠀⠀⠀⠀⠀⠀⠳⣤⣤⣌⣈⡁⣀⣈⣀⡄⣁⠘⠿⠿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢘⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡴⡇⢨⠕⠂⢻⣿⣿⣿⢿⣿⣿⢃⡆
⠀⠀⠀⠀⠀⢰⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣿⠄⠀⠀⢹⡷⠀⢸⣿⠇⠈⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣟⢷⠆⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⣿⠻⣅⠀⠀⠀⢸⠇⠀⠀⣿⡇⢠
⠀⠀⠀⠀⠀⠀⢿⣿⡯⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⡟⡳⠃⠀⠀⣀⠀⠀⠀⠀⠈⢀⡌
⠀⠀⠀⠀⠀⠀⠈⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡞⠁⠀⠀⠀⠏⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⠠⣦⠀⢀⠀⠀⠀⠀⢠⡄⠀⣀⣀⠀⠀⠠⣤
⠀⠀⠀⠀⠀⠀⠀⢿⣥⣿⠈⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⡡⣿⠅⠘⠋⣼⣯⣉⢠⣤⣿⠘⠃⠈⢉⡿⣡⣤⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠶⠶⠟⠰⠿⠶⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⠇⣿⠀⠀⠀⠻⣧⡿⢻⣤⡿⠀⠀⠀⣼⠃⢬⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⡀⠀⠀⢀⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⣤⣠⣄⣠⣤⣄⠀⣤⣠⣄⠀⣻⡃⣤⠀⢠⡄⢠⣠⣤⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⣿⡋⠁⣭⡤⣿⠀⣿⠁⢻⡇⣿⡇⣿⠀⢸⡇⢸⡏⢹⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠾⠟⠀⠿⠂⠈⠿⠶⠿⠀⠿⠀⠺⠇⠿⠇⠻⠷⠿⠇⠸⠇⠸⠟⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢀⣤⣄⢀⣤⣄⠀⠀⣠⣤⡀⣠⣤⡀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠶⣿⢘⡷⣿⡀⢰⡏⢸⡇⢀⡼⠃⠿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠘⠓⠛⠘⠳⠛⠙⠃⠛⠞⠁⠛⠛⠂⠳⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠂⠀⠀⠈⠑⢦⡄⠂⠀⠀⠀⠀⠀⠀⣴⠊⢉⡠⠊⠉⠳⣄
⠀⠀⠀⠀⠀⢀⠔⡁⠀⡴⣀⠾⠉⠠⣀⠾⢹⠂⠀⠀⠀⠀⠀⢸⠃⠂⠁⠐⠀⠠⠠⢼⡖⠦⠄
⠀⠀⠀⠀⠀⡌⠀⠐⠃⠋⠁⢀⣨⣖⡵⢁⣿⠀⠀⠀⠀⠠⠔⢻⡤⠖⣀⡔⠀⠀⠑⠄⠓⢀⡀
⠀⠀⠀⠠⠄⢲⠀⠑⠴⠒⣺⣉⡴⠊⢀⡿⢁⡀⠀⠀⠀⠠⠤⠘⠣⣤⡤⠄⠰⢀⣠⠏
⠀⠀⠀⠀⢨⠁⠙⠺⠮⣵⡿⠋⠀⡠⢋⠺⣶⠀⠀⠀⠀⠀⠐⠈⠀⠨⢉⠛⠋⠍
⠀⠀⠀⠀⠸⠀⠳⠀⠐⠀⠀⢀⠔⠀⠈⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠃⠲⠷⡔⠀⠄⠹⡄
⠀⠀⠀⠀⠀⢀⢠⢠⡇⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⠀⠀⡀⠁⢀⠈⠀⣁
⠀⠀⠀⠀⠠⠠⢿⢿⠏⠀⠀⢊⣉⡀⢗⠃⠀⠀⠀⠀⠀⠀⠸⡄⠏⠵⢾⡏⠙⣀⣴⣾⠇
⠀⠀⠀⠀⢠⠄⠛⢉⠑⠛⡍⠀⢉⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⡃⠘⠃⠂⢀⡼⠋
⠀⠀⠀⠀⠀⠲⣀⠀⠀⠐⠡⠄⠀⢨⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠇⠦⠤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⣀
⠀⠀⠀⠀⠀⢠⠒⠁⠀⠀⡀⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠀⡄
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠓⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠀⠐⠊
⠀⠀⠀⠀⢰⠀⠄⠌⢤⡁⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⢠⡄⠇⠀⠀⣀⢴⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠀⠜⠀⢸⠃⠳⠀⠐⠠⠆⠃⠀⠀⠀⠀⠈⠳⠶⢶⣶⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠐⢄⣀⡸⠀⠀⠆⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆
⠀⠀⠀⢀⢀⣰⡄⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⡀⠐⣶⣤⣦⣷⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡀⣛
⠀⠀⠀⣌⣸⣿⣿⣦⡜⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢠⣤⣖⣒⡲⣤⣀⣀⡀⣰⣿⣿⡿⠓⠧
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣷⡝⣿⣿⡿⠛⢿⣿⣷⡤⣤
⠀⠀⣴⣿⣿⣿⣿⡄⠙⢿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⣛⣿⣿⡜⢿⣧⣀⣼⣿⣿⡇⡄
⠀⠀⣿⣿⣿⣿⣿⣷⣤⡘⢿⣿⣿⣄⢠⣿⣿⠋⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣟⠛⣡⣬⣤⠭⠟⠻⢿⣿⠁⡟
⠀⠀⣿⣿⣿⣿⣿⣿⡿⢿⣾⣿⣿⡿⠸⣿⣿⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣦⣸⣿⣿⣿⣷⣴⠿⠿⠷⣤⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣻⣿⣿⣿⣿⣿⣷⡇
⠀⠀⣿⣿⠿⠿⣿⡿⢉⡛⣿⣿⣿⣿⡏⠀⠀⢀⠀⢻⣿⠋⢉⢻⣿⣿⣿⣿⣿⣿⣿⣿⢹⣆⢷⣿⣿⣿⣇⡇
⠀⠀⢿⣿⣿⣿⣿⡶⠺⠟⠉⠉⠙⣿⣇⠀⠐⠋⠀⠀⣿⣆⡘⠏⢻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⡄⠙⠙⠛⠛⠾⣶⠀⠀⠀⠀⢹⣿⣦⢀⡀⠁⠀⢸⣿⣷⣀⠎⠀⡀⠙⣿⣿⣿⠛⠉⣿⠛⣿⢿⣿
⠀⠀⠀⠀⢠⣹⡄⡀⠞⣆⠀⠀⢀⠼⣫⣭⣉⡇⠰⠀⠀⠻⣟⠋⠀⢴⡇⠈⣿⣽⣿⣷⣦⢩⣙⣿⣿⣿⡃⠀⢠
⠀⠀⠛⠂⢈⡿⠃⠓⢀⣀⣉⣉⣀⡀⠈⠹⠙⠇⠲⠀⠀⠀⠀⠀⠀⠸⣇⠀⠹⣦⣹⡿⢿⣼⣿⢾⣿⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠉⠛⠀⠐⠮⠀⠀⠛⠠⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠖⠂⠂⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢒⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠚⠛⠡⠤⠴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠉⠛⠳⠶⠤⠤⠜⠛⠲⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠠⡄⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠠⢀⣀⣀⠒⠉⠉⠀⠀⠀⠀⠁⠐⠩⢭⣶⣀⣀⣀⠄
⠀⠀⠀⡈⢙⡛⠛⠯⠐⠀⠁⠀⠀⠈⠐⠠⠴⠋⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠄⠀⠠⢀⠀⢀⡀⢀⣀⣀⡀⢀⡀⢀⣠⠤⠶⠤⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠠⠤⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⠄⠀⠀⠤⠴⠟⠛⠂⠀⠀⠀⠀⠀⠀⠀⠠⠴⠚⠉⠉⠉⠂⠅⠀⠁⠈⠐⠋⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠁⡤⠶⠶⠶⡌⣠⠶⠶⠶⢤⣘⣮⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠤⠐⠠⠤⡤⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠲⠾⠶⠚⠁⠀⠀⠀⠠⠄⠂⠀⠋⠀⠀⠀⠀⠀⠀⠀⠳⢤⡄⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⠲⠦⡤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣄⡀⠀⠀⠀⡀⠀⡀
⠀⢄⣀⣀⣤⠒⠺⠉⠉⠂⠀⡀⠀⠄⠐⠉⠉⠓⠲⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⢉⣿⡷⢶⣯⣂⠀⠈
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠁⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠨⢍⠉⠲⢄⡀⠲⣂⡰⠀⠈⢄⡀⠐⢀⡤⠖⠉⡩⠉⢠⠀⠀⠀⠀⢠⡐⠁⣀⡤⠤⠈⠁⠤⢤⣀⡀⢀⣀
⠀⠑⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠁⠁⠁⠀⠠⠄⠊⠑⠒⠉⠑⠤⠄⠀⠀⠁⠀⠀⠀⠈⠈⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⡰⠋⠀⠈⠉⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⡄⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠂⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠂⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠁⠐⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⠀⢀⣀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡇⠘⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢴⡀⠀⠀⠈⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠁⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⢨⠀⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠚⠀⢰⠶⠂⡇
⠀⠀⠀⠀⠀⠀⠘⢦⡀⡀⠐⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣄⣄⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⢀⡠⢔⢢⠉⢤⣒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣄⠰⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠠⣀
⠀⠀⠀⠀⠀⡣⠗⠁⠀⠀⠀⠀⠱⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⡇⡅⠀⠀⠀⠀⠀⠀⡃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢉⣇⠀⠀⠀⠠⠀⠀⣍⠹
⠀⠀⠀⠀⠀⠰⡙⢄⠠⠀⠀⣰⣙⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⢀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠰⠎⠒⠥⠤⠍⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⢀⡠⢠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀⠀⠯⠇
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣐⠞⠁⠀⠀⠈⢱⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢹⠃⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠁⠀⠀⢀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⣀⠼⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠱⣆⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⣄⠤⠛⠛⠄⣀⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⣠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠐⠒⠒⠂⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢞⠅

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⠃⠀⠀⠀⠈⠑⡴⠂
⠀⠀⠀⠀⠀⠞⣿⣤⡄⢀⡠⠀⣤⣼⡯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢽⢄⡀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⢀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠓⢢⡴⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁

⠀⠀⡠⠒⠈⠉⠉⠀⠐⠄⡀⠀⠀⠀⠀⠀⢀⠄⠂⠊⠉⠉⠐⠒⢄⠀⠀⠀⠀⠀⠀⡠⠔⠀⠈⠉⠁⠀⠠⢀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠉⠉⠁⠐⠤⡀
⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⣠⠃⠀⠀⠐⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁
⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢐⠜⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠐⠂⠤⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠤⠤⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⠂⠠⠤⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠤⠤⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣀⠤⠐⠒⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠐⠦⣔⡬⠔⠒⢳⢀⠀⠀⠀⠠⠀⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⢀
⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠠⠁⠀⠀⡠⣐⠵⠋⠁⠓⡀⣠⠯⠂⢀⠔⠁⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⡐⠊⠀⠀⠀⠀⠀⠀⠈⠢
⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠁⢀⢔⡡⠚⠁⠀⠀⠀⠀⢸⠕⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈
⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣖⡵⠋⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀
⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⡡⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠂⠄⣀⡀⣀⠠⠔⠊⠀⠀⠈⡞⠁⠀⣰⠦⣀⡀⠀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠉⠢⢀⠀⠀⠀⢀⡠⠐⠁⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⣿⣗⢷⣿⣡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⢫⣾⣿⣷⣷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠟⢀⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣽⢿⣿⣿⣿⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣮⠟⣩⣿⣿⣿⣿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠗⣩⣾⣿⣿⣿⣿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣐⣰⣿⣾⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⣶⡴⠾⠓⡈⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⡿⢻⣿⣿⣿⣿⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⢭⣕⡚⣢⣰⣤⣤⣶⣚⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⡿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⠿⢟⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠈⠉⠁⣉⠩⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠂⠀⢂⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠷⠶⠲⢒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⠤⣖⡶⠽⠽⠿⠷⣒⡤⢄⡀⠀⠀⠀⢼⠫⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡪⡒⠝⠂⠉⠉⢈⠈⠉⠁⠚⢕⡪⡳⣄⠀⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣠⣤⡴⣫⡪⠊⠀⠀⠀⠀⢼⡉⡻⠄⠀⠀⠀⠈⠪⡪⣣⣤⣤⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⣏⢿⣿⠻⢛⣋⣹⡱⡕⠁⠀⠐⠲⠤⣤⡌⠘⠈⣤⡤⠤⠂⠀⠀⠱⡱⣻⡙⠻⣿⠋⢻⣗⡦⢄⣀
⠀⠀⠀⠀⠀⠀⡠⢚⡵⠊⣡⠞⠉⢀⠔⠉⠋⣧⣷⠁⠀⠤⠦⢭⠵⢤⠹⠀⡌⣠⠦⢭⢥⠦⠄⠀⢁⣣⡇⠉⠲⣵⠛⠓⢌⠑⢮⡑⡶⠳⣆
⠀⠀⠀⢀⡶⠛⣷⡏⠀⠐⣅⡀⣄⣸⡀⠀⢸⣿⠸⠀⠀⠀⠈⡓⠂⠁⠀⡇⡇⠀⠀⠒⡋⠀⠀⠀⠸⢨⣷⠀⠀⡘⠀⠀⣨⣇⠀⢹⠉⣿⠁
⠀⠀⠀⠀⠛⡶⢧⡱⢄⡀⠽⣏⠎⡳⠌⠒⠬⢿⣾⡀⠀⠀⣏⣹⠀⠀⠠⣇⣧⠀⠀⢸⣩⠇⠀⠀⣸⣾⠧⠔⠉⠀⣀⠴⠋⢁⡠⠋⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢭⣚⠯⣯⣙⡓⠒⠤⢤⣀⣉⣉⠉⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠋⣉⣉⣀⡤⣤⢒⣟⣉⡤⠴⣚⡩⠔⠋
⠀⠀⠀⢀⢴⠖⠀⠀⠀⠀⠈⠉⠓⠒⠯⠭⣷⣶⠶⣶⠤⠭⠭⠭⢭⣭⣭⣭⣭⣭⡭⠭⠭⠭⠤⢖⣒⣶⣿⡋⠌⣻⠾⠉⠁
⠀⠀⠀⠀⢈⡀⣵⡋⠀⠀⠀⣀⡀⠀⠀⠀⠀⣻⣄⣼⠻⡻⣝⡿⣛⠛⠛⠻⠛⠛⢛⡹⢟⡽⡫⠏⠁⠀⠜⠛⡞⠛⠄
⠀⠀⠀⡎⠔⠉⠈⢷⣒⡲⣬⠐⠠⠠⡄⠀⠀⠀⠈⠀⠀⠈⠓⠯⢖⣢⣭⣡⣉⣯⣒⠮⠗⠋
⠀⠀⠀⠉⠀⠀⠀⠀⡰⢼⡞⡄⢀⠇⠐⠄⠀⠀⢠⣀⣠⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⡊⡈⠛⢶⣄⠀⢲⡟⣩⡝⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠲⠾⠛⠚⢷⣬⣵⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣲⣯⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠠⢄⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡤⠀⠤⠉⠠⠀⠀⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⡁⠀⠀⠀⢻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣴⣶⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠙⠀⠀⠸⠆⠰⠀⠀⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠐⠀⢠⣶
⠀⠀⣴⣶⣲⣦⠀⠀⠀⠂⠀⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠚⠓⠂
⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠴⠒⠒⠀⠀⠀⢰⠛⠋⢲⠄
⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠂⠀⠀⢀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⢿⠀⠀⠛
⠀⠀⢰⣦⣙⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀
⠀⠀⠳⠭⣭⣭⠇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠽⠃
⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⡇⠀⠀⢀⠴⣿⣛⣹⣬⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠉⠉⠁⠈⠉⠉
⠀⠀⢠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣺⡿⢶⣄
⠀⠀⠙⠉⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣡⣴⠿⢻⡇
⠀⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣥⣼⠟⠁

⠀⠀⠀⠀⠀⠀⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⡇⠀⢀⣄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣧⣏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⠟⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣈⣉⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⢠⣄⠀⣄⣠⣀⣂⢀⣀⣄⣀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⡟⣿⠻⢿⠿⡿⠿⢿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠊⠈⠈⠋⠁⠉⠉⠛⠉⠈⠈⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣾⣶⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠃⠯⠽⠅⠺⠅⠹⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣺⣇⣇⣾⣇⣮⣇⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⡂
⠀⠀⠀⠀⠀⠐⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⠈
⠀⠀⠈⠀⠀⢠⡀⣠⠇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠁⠠⠖⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠄⠀⠒⠀⠀⠀⠀⠀⡀⠐⠐⢲⢤⡀⠀⠀⠀⠀⠀⠔⠀⠀⠤⠒⠖⠉⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠚⠶⠆⠚⠛⠷⠛⡀⠀⠀⠀⢁⠄⠈⠀⠀⣠⢼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢿⣶⣾⠷⠹⠞⢻⠁⠀⠀⡠⠁⣀⡤⡲⠋⠁⡘
⠀⠈⠀⠈⢀⠄⠁⠈⠀⠀⠈⠫⠭⠭⠭⠟⠃⠀⠠⠊⠀⡢⠕⠂⠒⠐⠈⠀⠀⠀⠈⡌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⡀⢴⣒⣶⣤⣄⠀⠀⣀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⢀⡤⠖⠒⠂⢄
⠀⠀⠀⠀⢀⠉⠉⠉⢐⣓⣏⣉⡤⠂⠄⠀⠀⠀⠀⠀⠀⡀⠰⠓⠰⠂⠀⠀⠀⢀
⠀⣀⠤⢦⢂⣴⣾⣾⠭⣟⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⡞⠉⠈⠈⠂⡀⠂
⠨⠗⠒⠛⠻⡏⠁⠀⣀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠲⠀⢀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⣤⡴⠆⠀⠀⠀⠀⠀⠀⡴⠋⢭⣭⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢲⡄⠄⠀⠀⠀⠀⠀⢻⢙⣶⣋⡇
⣀⡀⠀⢸⠁⢨⠳⣤⡶⠂⠀⠀⠀⢸⡇⣤⡸⢇⣄⣘⡇⠀⠀⠀⠀⠀⠀⣀⣤⣻⠷⠤⠔⠀⠀⠀⠀⠀⢠⠊⢀⣴⡿⢃⢀⡀⠀⠀⢠⣊⢉⣏⠎⣿⣉
⠀⠈⠢⣸⣦⣁⣁⡼⠃⠀⠀⠀⠀⠈⠳⣝⡁⢈⣻⠞⠁⠀⠀⠀⠀⠰⠾⠋⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣟⡽⠻⣍⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀
⠀⠀⣠⣤⣶⣤⡄⠀⠀⠀⠀⠀⠀⠘⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⢶⡄⠀⠀⠀⠀⢀⠞⠁⢀⡈⠑⠄⠀⠀⠀⠀⠀⠀⠀⢁⣷⣦⡀
⠀⠀⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠿⠀⠀⠀⠀⠀⠀⠀⢸⢠⡶⣶⢶⣸⡇⠀⠀⠀⠀⢞⠀⢨⣳⣷⣤⡆⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡅
⠀⠀⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⠛⠛⢹⡇⠀⠀⠀⠀⠘⠦⠙⠻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠙⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠦⢄
⠀⠀⣤⣶⣾⣷⣶⣤⠀⠀⠀⠀⠀⠀⠀⢩⣭⣭⡁⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⡄⠀⠀⠀⠀⠀⠀⠒⠐⠿⠿⣿⡇⠀⠀⠀⠀⠀⠄⠀⠛⢷⠾⡆⠆
⠀⠀⠉⠙⣿⣿⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⣿⣧⡀⠀⠀⠀⠀⠀⣦⢀⡨⢅⣈⡧⠀⠀⠀⠀⢠⠀⣇⣀⡹⣉⣸⡇
⠀⠈⠀⠐⢿⡿⠄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢸⣿⣸⣁⣏⣸⡇⠀⠀⠀⠀⠀⡀⠈⣥⣬⣿⣇⠀⠀⠀⠀⡁⠀⡄⢨⣤⣼⣿⡇
⠀⠀⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣤⠤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠠⠆⠌⠛⠀⠀⢠⠀⠀⠀⠀⣀⢀⡀⠀⠒⠒⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⣀⣤⣴⣶⣶⣶⣶⣿⣾⣽⣒⡂⠃⠀⠒⠓
⠀⠀⠀⠀⢔⣲⣺⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣄⣤⣄
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠻⠿⠿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣥⣲⣿⣿⣿⣿⣿⣿⣧⣾⣷⡿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠙⢻⣿⣦⡀
⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⡿⣿⣿⡿⣿⡿⠛⠉⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⣀⠙⢿⣿⣶⣀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠈⠙⢛⡛⠉⢁⣉⣋⣽⣿⣀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⣩⣭⡇⠀⠙⢷⣄⡙⠿⣿⣾⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⢸⣯⠿⢿⣿⣿⠂⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣴⣶⣿⣻⠿⣦⣀⡙⠿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣭⣉⣁⡚⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡿⠿⠿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡁⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠶⠞⠛⠛⠛⠛⠛⢛⣷⣶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⠀⣈⣽⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣠⡶⠛⢉⣠⣤⠶⠿⠻⣦⣄
⠀⠀⠀⠀⢀⣴⢟⡁⣤⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⠞⢉⣴⠞⠋⠁⠀⠀⠀⠀⠈⠙⣷⡀
⠀⠀⠀⣰⡟⠁⣿⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⣠⡾⢃⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣆
⠀⠀⣰⠏⠀⠀⠁⠀⠀⣀⣤⡴⠶⠞⠛⠛⠋⠉⠀⣠⡾⠋⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠹⣦
⠀⣰⠏⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⢀⣴⠟⠀⠀⠀⠀⣀⣤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠸⣆
⢀⡟⠀⣠⡾⠋⠀⠀⠀⠀⠀⢀⣠⣤⠶⠞⣛⣡⣤⠶⠛⠁⠀⠀⢀⡴⠛⠉⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⢀⡾⢻
⣸⣡⡾⠁⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⣴⠟⠉⠁⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⢀⣤⠾⠋⠁⢈⡿⠀⠀⢠⡿⠁
⣿⠋⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣠⠟⠁⠀⠀⣠⡞⠁⠀⣠⠟⠀⠀⣠
⡇⠀⠀⢀⣀⣠⣤⣤⠾⠋⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⢰⡏⠀⢀⣤⠾⠋⠀⢀⣴⠋⠀⠀⣴⠏
⣷⣠⡾⠋⢉⣠⣤⣤⣄⣀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠘⠓⠛⠋⠁⠀⠀⣠⠞⠁⠀⢀⡾⠃⢀
⢻⠋⠀⣰⠟⠁⠀⠀⠈⠉⠛⠷⠶⠋⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣴⠏⠀⢠⡟
⠘⡇⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⢀⣴⠟⠁⢀⣴⠏⢰
⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⣠⡶⠋⠁⢀⣴⠟⠁⢠⡟
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠉⢀⣠⡴⠟⠉⢀⣠⡶⠛⠁⠀⢠⡾
⠀⠀⠀⠻⣆⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠛⠉⣀⣤⠶⠞⠋⢁⣠⣤⠾⠛⠁⢀⠀⠀⣠⡟
⠀⠀⠀⠀⠙⢷⣄⠀⣰⠏⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⢀⣴⠟⠉⠀⣠⡴⠾⠛⠉⢀⡄⣰⠇⡾⢁⣾⠋
⠀⠀⠀⠀⠀⠀⠙⢷⣏⠀⠀⠀⣴⠋⠀⠀⠀⠀⢀⣴⠋⠀⣀⡴⠟⠉⠀⠀⠀⠀⠾⠁⠈⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣼⡃⠀⠀⠀⠀⣠⡟⠁⠀⣴⠋⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢦⣴⣏⣀⣀⣸⣇⣀⣀⣠⣤⣤⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⡄⠀⠃⠀⠀⡀⠀⠀⠀⠐⠐⠀⠀⠠⠀⠀⠀⠀⡄⠀⠀⠙⢆⠀⠀⠀⠀⠀⡴⠋⡂⠔⠸⠀⠀⠤⠼⢦⠀⠿⠃⠀⠀⠀⠀⠈⣀⡶⠒⢡⡲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⣤⠀⠀⠀⠀⠀⠀⠤⠀⠒⠀⠀⠰⠀⠀⠈⠃⠀⢐⠀⡸⠏⠀⠀⠀⠀⠀⠀⢠⡤⠀⣶⣶⠐⠿⠂⠀⠀⢯⡈⢇⠀⣠⡏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⡀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⢰⡇⠀⠀⠀⠀⠀⠀⠀⠰⠂⣤⠈⠀⣦⠀⠀⠀⠀⠙⠵⡎⡘⡳⠈
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡄⠀⢨⠀⠀⢀⡀⠀⠀⢃⠀⠁⠀⠓⠀⡠⠀⠀⠀⠁⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠖⠈⠀⠀⠀⠀⢠⡀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠃⢀⠀⠀⠇⠸⠃⠀⠀⠀⠑⠤⢀⢀⣀⣀⠤⠂⠀⠀⠀⠀⠀⡈⡠⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠰⠄⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣰⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠆⠀⠘⢰
⠀⠀⠀⠀⠠⠀⠀⠠⠐⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⡀⠀⠀⠀⢀⠃⠁⣟⡀⠈⠀⠀⠀⠀⢀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠠
⠀⠀⠀⠀⠄⠠⠀⠀⡀⡄⠀⠀⠀⠀⢆⠄⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠉⠄⠀⠀⠈⠁⢸⣏⡀⠀⠀⠀⣀⠀⡀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠤⠀⢐⢤⠼⠔⠉⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⢀⠀⠀⢀⡀⢰⠀⠀⠀⠀⣶⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⠄⠠⢄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠐⠈⠈⠀⠀⠈⢁⡏⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⠀⠀⠀⢇⢒⠆⠀⢱⠀⠀⡈
⠀⠀⠀⠁⠀⠀⠀⠀⡄⢠⡀⠃⠀⠀⠀⠀⠀⣇⠀⠀⠄⠀⠳⠀⠄⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢳⡄⠀⡠⠃⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢀⡀⠀⠈⠫⡀⢀⣠⡰⡶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠄⠁⠀⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠰⢁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢠⠄⠘⢋⣉⠘⠑⠢⡀⠀⠀⠀⠀⠀⠤⠈⠀⡀⠄⠋⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠘⠛⡠⠀⢀⠜⠀⠀⠀⠀⣀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠔⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠦⠴⠖⠚⠁⠀⠀⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠰⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠐
⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠞⠁⣈⡙⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠚⠀⠄⠰⠀⠀⠄⡡⠆⠀⠀⠀⠀⠀⠀⣤⠀⠈⠒⠀⠀⠑⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠚⠐⠂⢀⠈
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠉⠑⠲⢼⡀⠀⠀⣆⠲⠀⡠⠠⢄⠀⠀⠀⠰⠞⠀⠀⢰⣤⣼⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠘⠄⡃⠀⠚⠃⣀⠨⠵⠤⣀⠉⠀⡟⠀⢶⡸⠀⠀⠀⠀⠀⠀⠘⣿⣭⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠀⠀⠑⢆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⣀⠀⢇⠀⠲⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⢀⠀⠱⣄⠊⠀⠘⢀⡤⠀⠀⠀⠀⠀⠀⡸⢁⣀⠀⠀⠱⢸⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠢⣌⣁⣄⢸⣇⣀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠰⢈⡁⠀⠀⠀⣿⡰⠊⢁⠑⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠈⠙⠷⢶⡷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠐⢣⠃⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠂⠀⠀⠒⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⣀⠀⠀⠀⠤⠤⠄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⠀⢀⡄⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢡⠤⠤⢀⡀⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢇⡀⠔⠁⠀⢀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⠉⢀⡀⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⣁⡆⡂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠈⠁⣀⠠⠐⡎⠁
⠀⠀⠀⢀⡠⠒⠁⠀⡔⠊⠀⠡⠀⠀⠀⣀⣀⠠⠤⠐⠒⠈⠉⣀⠠⠄⠒⠈⠁⠀⠀⠰⠁
⠀⠀⠔⠁⠀⠀⠀⠀⠉⠀⠀⠈⠉⠉⠁⢀⣀⠠⠄⠐⠒⠋⠡⠁⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠑⠂⠠⠤⠤⠄⠀⠐⠒⠒⠈⠉⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⣀⡀⠀⠀⣀⡀⠤⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣼⣿⣷⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣳⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⣾⣿⣿⣿⡿⠁⢠⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣵⣿⣿⣿⣿⣿⠃⢠⣿⣿⡇⢸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣪⣾⣹⢿⣿⢿⣿⡿⢀⣿⣏⣼⣿⢸⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣵⢿⣿⣿⣿⣿⣽⣿⡇⣼⣿⣿⣿⣿⠀⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠉⠀⠿⣿⣿⣿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠻⣿⣷⣾⡏⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠊⣿⣿⠏⠀⠀⠀⠀⠀⢀⣠⢦⠠⠒⣦⡃⢸⡧⠀⠀⠘⣿⣧⣴⣟⢳⡄
⠀⠀⠀⠀⠀⠀⢀⣾⡋⠙⣿⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠘⠀⠀⠀⠀⠸⣿⠿⠟⣇⣨⣦⡀
⠀⠀⠀⠀⠀⢴⣿⣥⣷⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢀⣽⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠈⠻⣧⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣍⣿⣿⣿⢏
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣟⣿⣷⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⠟⡑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⢹⠿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⣿⣿⣿⡿⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⣀⣴⣿⣿⣿⢟⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣾⣿⣿⣿⣿⡆⢀⣀⣀⣀⠀⠀⣘⣠⣴⣾⣿⣿⣿⡟⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠻⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⣿⣿⣿⠿⣿⡿⢫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⢿⣿⠂⣿⡾⣿⣿⠇⣸⣿⣼⢛⣦⢞⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡻⡆⢸⣷⣿⠏⣠⣿⣿⣿⡿⡣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡀⠙⠉⠜⣾⣿⣿⢫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡠⢊⣾⣿⢟⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠻⡣⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿