Floral Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⠀⣿⣿⣇⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣴⠂⠀⠠⠈⠀⣼⣿⡟⢋⣁⡈⠻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠙⣏⠀⠀⠆⠀⠀⢈⣭⡖⠚⠿⠃⢨⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣄⠀⠀⢸⣿⠃⢸⡿⠀⠀⠃⠀⠀⠙⢿⡿⢣⣶⣾⡝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣋⠉⠙⣆⠀⠈⢿⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡂⠜⠀⠀⠀⠀⠘⠄⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢺⣿⣿⣿⣠⣶⣦⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠛⢄⣁⠈⠹⢿⣿⠇⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢛⡧⠀⠾⣿⡗⠀⣻⣦⣄⠀⠀⠀⠀⡍⠀⠀⠀⠋⠙⢋⣈⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⡔⢀⣀⣤⣿⣿⡟⠀⠀⠀⢠⠉⠀⠀⠚⠀⠲⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢿⣿⣿⡷⠀⠉⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡜⠀⢠⠆⠀⠀⣼⣷⣿⣷⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡠⠃⣴⣶⣤⣹⠿⠿⢻⡥⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠄⠀⢾⣿⣿⡿⠈⢣⣄⣌⠀⠙⣻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠐⠀⠀⢉⣩⡖⠒⠺⠿⣷⠀⢉⣽⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠰⣿⣿⣿⣆⣴⢀⣀⣰⢼⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡀⠀⠀⠀⡀⠂⠘⠿⠟⠉⢼⣿⣿⣿⡇⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠔⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠈⠛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⢿⣶⣄⠀⡘⡏⠀⠀⠁⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣄⣀⣈⡀⠙⠛⢠⡿⠁⠀⠀⢀⠖⠉⠛⠛⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠛⠿⠷⠒⠐⢮⠃⡄⠀⠀⠉⠀⠐⢶⣶⡄⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡥⠀⠀⠀⠀⠀⠀⠈⠻⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢳⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠳⣄⠀⠙⠳⠤⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⠿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡔⣀⣀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠀⢀⡠⢊⣀⡠⠂⡀⠀⠀⣚⡫⣇⣤⣠⣄⠨⠄⠀⣃⡀⠀⢀⣀⣀⣀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⢦⡐⠖⡉⠛⣷⠀⠀⠻⣅⠈⠩⢅⠈⠓⠲⠌⠉⠀⠈⠙⠀⣞⠁⠀⠂⠀⢍⠲⠭⠉⠉⠉⠩⢏⠂⠋⡇
⠀⠀⠀⠀⠀⢀⠉⠀⠉⠐⠒⠁⡀⠀⠘⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠠⠃⣀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠨⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠄⢁⠀⢘⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠈⠀⠠⣀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠬⢥⠴⠤⠤⠤⠮⠤⠤⠴⡿⠄⠀⣶⣾⡆⠀⠀⠤⠤⢒⠒⡶⢐⠿⣄⠀⠀⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠀⡐⠀⠀⠀⠠⠔⠉⠐⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡌⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⢀⡹⠁⠄⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠠⠀⠈⡟⠁⡀⠐⡤⠀⠠⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⣉⠀⡌⠁⠀⢳⡥⡞⠀⡥⢠⠆⠀⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⢤⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠠⡱⣇⣅⣂⢴⠡⣀⢄⣠⠄⠐⢈⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠘⠀⠀⠀⠀⠅⣠⠖⠉⠀⠀⢹⠟⠉⠉⠙⡄⢈⠋⠠⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⠁⡀⢀⣡⡄⠀⠀⡞⠁⠀⠀⠀⢀⠃⠀⠀⠀⠀⠙⡅⠰⠂⠀⠠⠀⠀⢤⢀⠀⠄⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠛⠁⠀⠀⣰⠷⠓⠂⢄⡀⠀⢸⠀⠀⡀⢠⣀⠴⠁⠀⠁⢂⠀⣰⠰⠟⠓⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠃⡠⠤⠀⡜⠁⠀⠀⠀⠀⣤⢖⠟⠙⠛⠫⡙⢥⣀⠀⠀⠀⠘⡌⠉⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢀⡄⠄⠀⠐⢉⠁⠀⡀⠀⠀⢸⣷⠁⡠⠀⡀⠀⠀⢂⢳⠠⣀⣠⠴⢧⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠒⠘⠓⠚⠀⠀⠀⢼⣀⠀⠐⠂⠈⠐⢀⣼⣿⠚⠁⠀⠀⡼⠀⡐⠈⠐⠲⢤⣂⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⢀⡲⢆⠀⠀⠀⠎⢿⣶⡤⣄⢠⣤⡾⠏⠀⠈⠐⠒⣹⠰⣂⡀⢀⠂⠀⢢⠀⠙⠉⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣤⣄⣆⢴⠁⠀⢀⡥⣖⠀⠀⠀⠀⠩⠋⠙⠈⠀⠀⠀⢹⠒⠊⠪⠼⣆⣲⠋⣘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠜⠃⠚⢆⠀⠈⠀⠈⢄⡀⢀⣠⠂⠀⠀⠀⢀⣀⣠⣼⠳⣷⣞⠁⠈⠇⠋⠱⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠈⡄⠀⠁⠀⠄⠐⢩⡆⠠⠀⠐⠂⠀⠈⠁⠁⢠⡖⠒⢲⠉⢽⠅⡛⠀⣿⢫⠩⠁⠶⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠀⠀⡤⠈⠀⢀⠣⣌⡾⢀⠤⢀⡠⡀⠀⠑⣷⡖⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠐⠀⢀⡀⠀⠁⠀⠛⢻⠀⠀⠀⠀⠇⠒⠀⠀⣳⣀⠠⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠈⠛⠂⠀⠀⠀⠐⠀⠀⠀⣆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⠀⠀⠀⠀⠀⠀⣳⠘⠁⠀⠀⠠⠂⢠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠀⠀⠀⠑⠀⠀⠀⣷⣶⣾⡓⠀⠀⢡
⠀⠀⡀⠄⠀⠀⠛⢀⡌⠀⡴⢁⠔⠉⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⢂⡀⠀⠴⠖⠈⠈⢹⡿⠏
⠀⠀⠀⠀⣘⣿⣀⠀⠀⠈⠐⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⣸⠃
⠀⠀⠀⠀⣿⠟⠻⡁⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠈⡇⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣐⣿⣧
⡀⠀⢀⣌⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙
⠿⣿⣿⣍⠀⠀⠘
⠀⢨⡿⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠤⣄⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠲⣀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣈⡂⢇
⠀⣴⣄⢀⡠⠄⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈
⠉⢹⣿⣿⠉⠀⢤⠀⠀⠀⣀⠔⢁⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⣶⣤⣴⠯
⣠⡾⠋⠁⠀⠀⠐⠁⢀⡔⠡⠠⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠙⣿⣿⠆
⠁⠀⠀⠀⠀⠂⣺⣶⣾⡋⠁⠉⢖⠒⠂⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠉⠁⠀⢹⡟⠁⠀⠀⡀⠀⢀⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⣶⣶⡆⢀⡀⠀⠁

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠊⠀⢴⣾⣿⣿⡄⠈⠂⠙⠛⠀⠀⠐⠀⠀⠀⠀⠎⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠒⠋⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣐⣀⣀⠀⠀⠀⠀⠀⠀⠋⡿⠃⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣼
⠀⡠⠒⠃⠀⠒⢀⠀⠀⠀⠀⠀⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⢀⣾⣟
⠞⠀⠀⠀⠀⠀⠈⠁⡄⠀⠀⠀⠉⠉⠤⠤⠤⠄⢀⡴⠒⠒⠒⠠⡀⠀⠀⠈⠃⡀⠀⠀⠀⠄⠠⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⣀⣶⣿⡟⢉
⠂⠒⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⣄⡀⢈⢢⠤⢤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣷⣷⣿⣿⣷⣾⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠐⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠉⠩⢯⣿⣿⢿⣿⣿⣯
⠷⠄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⠀⡠⠒⠀⠀⠐⢉⣿⡿⠄⠉⠏⠛
⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢵⣤⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠰⢄⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣿⣆⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣶⠇
⠀⠀⠀⠀⠈⡟⠒⠠⠀⠀⠀⠣⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠉⠉⠙⠧⠀⢀⠀⠀⠀⠒⠤⢤⣿⣿⣿⡇⠀⣿⣇⣠⣴⢅⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠠⣤⡼⣿⣿⣿⣸⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⢈⡄⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡿⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠠⠀⠀⠀⠑⠀⢀⡎⠀⠄⠺⠃
⠀⠚⠀⢤⡀⠀⠀⠀⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢔⣾⠿⠛⢿⡇⠐⠦⠀⠀⢀⣀⡀⠀⠀⠀⠃⠀⠀⠤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠈⠐⠛⢧⡀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠄⣀⣀⣀⡀⠤⢰⠞⠋⡠⠀⡀⠀⠙⣄⠀⠀⠀⠀⠀⠉⠁⠀⠊⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠁⠀⠀⠀⠀⠀⠀⠀⠸⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠖⠒⠻⣷⢶⣷⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠔⠋⠀⠀⠀⠀⠀⠀⠀⠂⠣⣄⣀⡄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠄⠀⠀⠀⠀⠀⠁⠉⠉⠉⠚⢆⠀⠀⠀⠀⢀⠀⠀⠀⣠
⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠉⠘⠈⠁⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⢸⣇⣸⣀⣠⣾⠿
⠀⠀⠀⢀⡇⠉⠉⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢱⣄⣆⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⣽⣧⣾⣿⣿⡿⠿⠃
⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⢿⣿⣆⡀⠀⡜⠁⠀⠀⢀⣴⣞⡥⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⡏⡁⠀⠀⠀⠐
⠀⠀⠀⡀⠠⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⢤⣀⠀⠀⠀⠀⢻⣿⣷⣀⣠⡄⠀⣤⣿⣿⠟⢀⡀⠀⠀⠀⠀⠢⡄⢀⠍⠀⠂⠉⠷⣁⠂⠤
⠒⠀⡉⠁⠀⠈⠀⠀⠐⠄⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠈⠙⢿⣿⡛⠃⢰⣿⣿⣩⠆⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠓⠒
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣿⣿⣶⣶⣉⡄⠓⢦⣹⣿⣡⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠁⠀⠀⠀⠒⠋⠉⠉⠈⠞⠛⠙⠋⢻⡿⢿⠅⣠⣆⠋⣼⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣊⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣼⣃⠖⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡿⠩⠂⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡗⠵⠀⠀⠀⠀⣄⡀⠀⢾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣹⡄⡠⠀⠀⠀⠀⡄⠈⠆⢸⠛⡡⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠥⡄⠀⠀⣷⣤⠐⢄⣰⢃⡼⠀⠔⠃⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡨⡄⠀⠀⠻⣿⡇⠀⡹⢁⣤⣤⠀⠀⡀⠄⠚⠅⣀⠄⠒⡩⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠣⢄⡀⠛⡄⠀⠀⠀⢠⢿⡂⢅⠀⠀⠠⢌⠣⣀⢣⣿⣿⠏⠀⠌⢡⠀⢰⢊⡀⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠌⣦⡘⡄⢰⣶⠀⣐⣗⠧⠀⠀⠐⡄⢱⣸⠼⠛⠁⠀⡐⠀⢀⡴⠋⠁⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠑⣆⠀⠁⠀⠃⣿⢎⠄⠀⢀⠜⠁⠀⠀⠉⠐⠒⠇⣀⣼⠤⠐⢒⠞⠀⢀⠤⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠤⠀⣈⣤⡀⠘⡟⠪⣷⣂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡔⠋⠀⢠⠁⢀⠌⢀⡠⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢧⠀⡷⠊⠀⠇⠀⠀⠀⠀⠀⢀⠄⠒⠒⠄⡀⠀⠀⠈⠐⠤⣴⠖⠃⠒⠮⣀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠠⠄⡉⠒⠤⠄⡤⠋⠀⠀⠀⡀⠤⠤⠤⠄⣀⡎⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠈⢋⢣⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠥⣦⠊⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢀⣠⠊⠀⠈⠢⠀⠀⡤⢀⡀⠀⠀⠸⠄⣉⣁⡉
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠄⣀⢰⠖⢹⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡔⠉⠉⠑⠄⠀⠀⡄⢀⡅⠀⠈⠢⡀⣰⠢⡘⠦⠈⠆
⠀⠀⢀⡤⠒⠫⡀⠀⠀⠱⡄⠀⠈⠑⠺⡀⠀⠀⠀⢨⠀⠀⠀⠀⠀⢣⠀⠀⠶⠂⠀⢠⠗⠈⢡⠀⠀⠀⠘⡅⠣⣈⠄
⠀⡴⢋⡠⠄⠒⠒⠓⣒⣦⠬⠶⣄⣀⡀⢡⡀⠀⠀⠈⠄⠀⠀⠀⠀⡠⠥⡀⠀⣀⠔⠁⠀⠀⡘⠀⠀⠀⠀⢰
⣰⣀⠁⠀⢀⡔⠊⠉⠀⠀⢀⠠⠂⠉⠉⠀⡱⣄⠀⠀⠈⡶⠠⠄⠚⢄⠀⠈⠈⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⠃⢀⣠⡟
⠁⠀⠀⠀⠀⠀⠁⠒⠂⠴⠥⠄⠤⠄⠒⡨⢤⣫⠶⢆⠈⠀⠀⠀⠀⠀⠑⠤⣀⣀⣀⡤⠊⠁⠀⠀⠀⢀⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⣬⢛⡡⠑⠉⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⠀⠐⠒⠂⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡾⢏⠢⠀⠀⢀⠔⠊⠱⢄⠀⠀⠀⢀⠠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡽⡟⠌⠊⠀⢀⠜⢁⣀⠤⣴⠋⠉⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡸⡗⡌⠀⠀⢀⠊⠉⠀⢀⠔⡇⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⣔⣾⠣⠈⠁⠀⠀⣈⠀⡀⢴⠏⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⣆⣽⢣⠉⠀⠀⠀⠀⡏⠁⠀⠎⠀⠀⡄⠔⠁
⠀⠀⠀⠀⠀⠀⠮⣽⣉⡍⠀⠀⠀⠀⠀⢀⠀⠐⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠰⡰⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢩⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⣂⠐⢁⣰⠐⡐⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡮⠿⣧⠟⡈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠲⠊⠁⠘⠠⠢⠄⡖⠒⠆⢹⠊⠁⠈
⠀⠀⠰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⣄⠘⠓⢂⠀⠀⢀⡀⣾⣗⠦⢀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⢀⡴⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠐⠀⠀⠀⠀⠘⣏⠑⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣰⡦⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠉
⠀⠀⠀⠀⠀⣀⠩⠉⠀⣀⡿⡄⠀⠠⣤⡄⠀⠀⢀⣄⠀⠀⣀⠀⠀⠀⠀⢠⣄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠤⠛⣿⡆⠀⣤⣾⣷⠟⡴⢾⣿⢀⣠⠾⠋⣠⠁⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⢈⣀⠀⠀⢀⡀⠂⠺⢃⡈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠊⠁⠀⠘⡂⠈⠡⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢠⡆⣤⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡛⢀⠔⠀⠀⠀⠀⢤⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢄⠀⠐⠁⠀⠀⠘⠁⡀⠀⠒⠲⢄⢀⠠⠀⠀⡥
⠀⠀⠀⠀⠀⠀⠣⣀⠂⠠⠆⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠡⠈⣿⣵⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠳⢄⠤⣤⣀⣁⠐⠤⠀⠐⢞⣻⠎⡁⠀⢭⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠠⠅⠀⣼⣿⡿⠀⠒⢄⠀⠀⠉⡆⠈⠀⠀⠉⠸
⠀⠀⠀⠀⢀⠄⠀⠀⠼⠀⠀⠀⠐⢇⠀⠋⠹⠁⠀⠀⠀⠑⠀⠁
⠀⠀⠀⠀⠂⠀⠀⢀⡜⠒⢀⣤⡂⠀⠀⠀⢰⡀
⠀⠀⠀⠁⠀⠀⠁⢁⣤⣴⠊⢨⠀⠀⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠁⡾⠆⢀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠲⠀⠈⠀⠰⠀⠀⠀⠀⢰⠄⡃⠰
⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠈⠂⠤⣤⣷⣠⠀⠀⠀⢐⠂⡀⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠃⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⢠⠰⠆⠀⠀⢀⢿⣾⡯⠓⠒⢀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡐⠀⡀⢈⠠⠁⠀⡏⡐⠒⠠⢀⣰⠿⡐⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠈⠆⢘⠀⠳⡀⠀⣰⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢢⠀⠀⠀⠴⠐⠀⢠⠃⠀⡬⣿⣹⠶⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠈⠀⠁⠢⣤⡷⠛⣮⣀⠤⠚⡁⢀⡄⠀⠀⠻⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠰⠄⠱⠤⢴⣀⡀⠠⢽⣷⣤⡿⣇⠀⠀⠀⢨⠃⢶⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢁⡄⠒⠁⣘⢹⡀⢀⠀⠀⡘⠙⠀⠘⢆⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠆⣀⠠⢶⠻⠠⠂⣡⠀⡛⠰⠀⠈⢃⡀⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢠⡏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠀⠀⠸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠰⠦⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⣉⣄⣠⡀⠁⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣼⡏⠉⠉⠛⣷⡄⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣀⢻⣦⣤⠄⠀⠘⣧⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⢀⡿⢀⣴⠾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⣟⠐⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠾⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣶⢶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢰⡿⠋⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢷⣄⠀⣿⠁⠀⠘⠦⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡁⢙⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢠⣶⠿⠿⢾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢻⣏⠀⠀⢀⠹⣷⠀⠀⠀⠀⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⣈⠙⠛⠁⡰⠂⣿⠀⠀⠀⣠⡤⠞⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠟⢰⡇⠓⠀⢀⡿⠀⣠⠟⣩⠖⠛⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠁⠂⠀⣾⠃⣼⣣⠞⡕⢺⠇⣧⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢀⠖⠁⠀⠈⠛⠀⠀⠈⣸⣾⣏
⠀⠀⠀⠀⣀⣀⣤⠤⠤⠶⠦⠶⣤⣄⡀⠀⠀⠀⠙⣶⣦⣴⡿⠀⠀⠀⠀⠘⢃⣼⠟⠉⠀⠈⠳⢄
⠀⠀⠀⠀⠙⢿⣄⠰⣖⢛⡿⣶⢶⣬⣇⠀⠀⢀⣀⣽⣿⣿⡷⢦⣤⠶⠖⠋⠛⢿⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠛⣷⡈⠫⡻⣄⡈⠉⢛⡷⠀⠉⠁⠉⢻⡏⠁⣾⠁⠀⠀⠐⠀⢼⣿⣆⣤⣤⣶⠷⠚⠓⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⣌⠊⠗⣦⣌⠀⠀⠀⠀⠀⣈⡳⠂⠉⠀⠂⣤⣤⣴⣾⣿⣏⣹⣿⡿⠂⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠆⠉⠘⢦⡀⠀⡀⣤⡿⠁⠀⠀⠀⠀⠁⠈⠙⠛⣻⣿⣿⣿⣷⣄⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⢿⣿⣂⠠⠤⠤⢤⡁⢀⠊⠉⠁⠀⠙⢯⡀⠙⢣⣤⣜⣓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢚⣿⠶⣿⣏⡿⠀⠀⠀⠀⠙⢬⡄⠀⠀⠀⠀⠀⠉⠀⠀⠛⢉⠻⢿⠦⡙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⢻⣌⡇⠀⠀⠀⠈⠀⣸⣷⠀⠀⠀⣀⡀⠂⠠⣶⣁⠦⠤⠴⠴⠙⣣⡘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⣿⠗⣀⡀⣤⣤⣤⣼⣿⡷⢿⣾⠉⠀⠀⠀⠀⢩⣤⣥⣉⣉⣉⣉⣥⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⢻⡄⠀⠀⠀⣠⣳⠞⠉⠁⠀⠀⢀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢡⠉⠈⠉⠁⠉⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢁⡼⣻⠟⠁⡋⢃⡤⡆⠀⠀⠀⠀⠀⠀⢸⡿⠁⢻⠿⣦⡀⠀⠀⠀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⡿⢱⣯⣴⠶⠟⡫⠜⣣⡀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠀⠈⠟⡹⢿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣿⠧⠖⠒⠒⣉⣡⣴⠞⠛⠁⠉⠒⠀⠂⠹⠀⠀⠀⠀⠀⠀⠈⡅⠉⢋⢷⡹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣠⣤⣴⡶⠾⠿⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⣀⠀⢀⣤⣾⡓⢦⣈⡌⣧⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠙⢷⣝⠦⣍⡃⣿⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣮⣙⠛⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠁⠀⢤⣧⣤⣀⡀⠀⠤⡃⠀⠿⣿⡷
⠀⠀⠀⠀⠀⠉⠿⢿⡿⠏⠀⠀⠐⠚⠁⠀⢸⡇
⠀⠠⡄⠰⡂⣠⠀⠀⠀⠀⠀⠈⠙
⠀⠈⠹⠀⠀⠨⠀⢰⡀⠆⠀⠉
⠀⢀⣰⣀⡀⠀⠀⢀⡡
⠐⢲⣿⣿⣿⠉⠀⠀⠸
⠀⠀⠀⠉⠀⠀⠀⠒⠆⢀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣤⣾⣇
⠀⡇⠀⡄⢠⡀⠐⠒⢀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠛⡆⠀⠀⣀⠄⠉⢻⡏
⠀⠀⠀⠉⠈⠠⢦⣀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠎⠀⢀⡀⠸⠃
⠸⣿⣶⠯⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠀⠈⠛
⢀⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⣠⣀
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣾⡃⠀⠈⢐⣆⠘⡀⢴⡀⠠⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢀⠄⠉⢻⡇⠀⠀⠀⠸⠀⠀⠈⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣄⠀⠀⠀⠸⠃⠈⠀⠠⣼⣤⣀⠀⠀⠠⢕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢀⡀⢄⠀⠀⠀⠈⢹⡿⣿⠿⠉⠀⠀⠘⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡟⡗⠂⠀⠀⠀⠀⢠⣤⣿⣶⣿⣶⣾⣤⡄
⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⠿⠁⠀⠀⠀⠀⠀⠀⠠⠤⣷⡇⢸⡇⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁


⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠈⢛⣿⣻⣟⣿⡛⠁⠀⠀⠀⠀⠀⠛⠛⣿⣧⠀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣄⠠⣶⠀⣴⠄
⠀⠀⠀⠈⣿⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠾⢿⣯⠿⠻⠛⠓⠀⠀⠀⠀⠀⢀⣿⣧⣤⣼⣿⡆⠀⠀⠀⠀⣠⣌⡻⣧⣿⣾⣏⣴⠿
⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠉⠉⠛⠻⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⣴⡏⢡⡄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⢼⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠫⣽⣿⣿⡿⠂⠀⠀⠀⠀⠀⢤⣦⠄⠷⣿⣿⡿⠁
⠀⠀⠸⣿⣿⡟⢻⣿⢀⠄⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⠿⠗⡂⠀⠀⠀⠀⠲⣾⠿⠶⠶⠾⠿⠶⡶⠖
⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠛⠉⠁


⠀⠀⠀⠀⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀
⠀⠀⠀⢀⣈⡷⢾⣁⣀⡀⠀⠀⠀⠀⢠⣿⣿⣏⠻⣽⣿⣿⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⡤⠀⠀⠀⠀⠀⠀⣀⢠⢰⡂⡆⣲⢠⢀⡀
⠀⠀⠀⠉⢉⡷⠺⣅⠁⠀⠀⠀⠀⠀⠈⣿⣿⣿⣀⣿⣿⣿⠀⠀⠀⠀⠀⠠⣤⣾⣶⣷⣧⡤⠄⠀⠀⠀⠀⣧⠾⠞⠛⠛⠛⠾⢦⡇
⠀⠀⠀⠀⠘⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠏⠇⠭⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣡⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡛⠉⡁⠀⠀⠸⣿⣿⣿⠀⠀⢀⣴⣶⡶⣄⠀⠀⠀⣰⣷⡀⠀⢠⣯⡭⡷⢙⣧
⠀⠀⠀⠀⠀⠀⢀⡃⠀⣃⠀⠀⠀⣿⣿⡟⠀⢀⣾⣤⡀⠀⣹⣆⢀⣸⣿⣿⣿⣀⠈⢯⣫⣾⣯⠟
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠴⠾⠿⠷⠄⠀⠈⠉⠉⠉⠉⠀⠙⠙⠋⠁⠙⠋⠁⠀⠈⠉⠁⡄
⠀⠀⢠⠶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⣤⣤⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠘⢄⣸⣿⣿⣿⣿⠇⠀⢀⣤⣤⣶⠾⡃⠀⣸⡶⢾⣿⠉⠑⢸⡿⢿⡿⠧⢤⣠⠖⣛⣛⣛⣛⣛⣛⣛
⠀⠀⠀⠀⠭⣽⣿⣿⡯⠍⠂⠾⠻⠯⠿⠛⠀⠀⠁⠃⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⠿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠒
⠀⠀⠀⠀⠀⠀⢹⣠⠀⡇⠀⠀⣠⠞⠉⢲⡀⠀⢠⣸⣾⣧⢖⡀⢾⡛⠃⠘⠙⣷⠆⣴⣾⣿⣤⡆
⠀⠀⠀⠀⠀⠀⡆⢠⡀⡇⠀⠴⠿⠶⠰⠼⠿⠄⠀⠈⠙⠉⠉⠁⠀⣿⣀⣄⣸⡅⠀⢹⠏⠹⡇⠈
⠀⠀⠀⠀⠀⠀⠃⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠉⠁⠈⠉⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣷⠀⠀⣠⣶⣿⡿⠿⣿⣶⣤⠀⣰⣿⣿⣷⡀⢠⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠴⠶⠶⠶⠶⠐⣿⣿⠍⢶⡦⠩⣿⣿⠈⠻⠿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠻⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠚⠛⠛⠃⠀⠀⠀⠀⠤⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⣅⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⠀⠀⠀⡐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠛⠀⠀⠉⠁⠀⠀⡸⠓⠈⠀⠈⢷⡄⠀⠀⠀⠀⡀⠐⠤⢈⠈⠀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⣖⡓⠀⣤⠀⠸⠆⠀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠞⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠞⠓
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣤⠴⠶⣗⣃⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣦⣦⣦⣤⠶⠤⣄⡀
⠀⠀⠀⢀⣀⠀⢰⣿⣧⡀⠀⠀⠚⣛⡟⠉⠉⢛⣛⣇⡀⠀⢸⣟⣟⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⢠⣾⣿⣆⢿⡇⡈⠃⢀⣄⣶⣯⣍⣲⡆⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠰⠉⠉⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠸⠇⠀⠿⠀⠀⠑⠀⠀⠀⠀⠀⠀⡘⣿⡆⠀⠀⠀⠀⠀⠙⠛⠋⠀⣶⣴⣶⣶⣶⣤⡆⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋
⠀⠀⠀⠀⠒⠀⠀⠐⠀⠀⠀⠀⠠⣿⣿⣿⣷⣿⣿⣦⠀⢉⣙⣋⠀⠀⠀⠙⠿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣽⣿⣽⣽⣽⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽⣿⣿⣿⣿⣿⣯⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠴⠶⠦⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⣀⣠⡤⠴⠶⠚⠿⠛⠋⠙⠉⠉⠉⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣭⣒⣠⣤⣤⣴⣶⠶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠂⠀⠤⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⡿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢐⣂⣥⡴⠶⠛⠋⠉⠉⡏⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢒⣩⡴⠾⠿⠭⣄⡀⠀⠀⠀⠀⠀⠁⡿⠛⠉
⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠀⢀⣠⠔⣫⡵⠚⠉⠀⠐⠲⠿⠟⠢⠁⠀⢀⡬⢤
⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡼⢖⣩⣶⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⢀⣀⣠⠴⣊⣴⣿⣡⣶⣿⠻⣌⣉
⠀⠀⠀⠀⠈⠛⢿⣶⣦⣭⣭⣭⣭⣶⣾⣿⣿⡿⠛⣿⣿⣦⣈⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠉⠁⢸⣧⣀⠘⢿⣌⢉⡙⠉⢠⠀⠀⠀⠀⠀⠀⠙⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢠⠈⠛⢷⣽⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣮⠷⠒⠀⠉⢛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⢶⠶⠀⠀⠹⣮⡝⣦⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⠀⠀⠀⢻⢻⣾⡗⣦⡀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠛⢈⡿⠁⠘⣿⡄⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡏⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣥⠆⠁⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣻⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣭⣽⣿⣽⣯⣿⣿⣽⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⣀⣴⡦⢴⣯⡉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⢴⣿⣿⢗⣺⣿⣿⡄⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠻⣿⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿
⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣿⡟⠀⢹⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠘⡿⠁⡄⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢻⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡄⠀⣾⣿⣿⣿⠀⢶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣀⣴⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠿⠏⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣦⣄⡀⠀⠁⠀⠀⣁⣴⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢀⣤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠐⠛⠉⠛⠠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢠⣸⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣿⡇⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣈⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⢁⡐⠀⠀⠀⠀⠀⠀⠀⠛⠠⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⢧⣼⣧⠀⠀⠀⠀⠀⣰⡟⣀⣼⣡⣴⣟⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣾⣿⣬⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠛⣉⣩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⣉⠉⠉⠙⠛⠛⠻⣿⣿⣿⣷⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⡻⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠛⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⣿⣿⠀⣀⣀⣤⣤⡤⣶⠊⠻⢿⣯⣙⠃⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⠋⠉⠉⠉⠋⠀⠈⢳⣄⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡐⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣝⣿⣋⣈⣿⠀⠀⠀⠀⠀⠀⣰⣿⠿⠛⠛⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢄⣀⣤⣀⣀⡀⠀⠀⠀⣀⣤⣴⠶⠂⠀⠀⣻⡆⠀⠀⠀⠀⠀⠀⢄⠀⣶⠤⠀⠀⠀⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣿⣿⣿⣿⣷⣦⣾⣿⣿⣿⣿⣿⣿⣟⠛⠀⠀⠀⠀⠀⠀⢴⢸⡷⢻⣿⡏⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⣿⡿⣿⠏⠛⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⢾⣋⣿⠟⠁⠀⢰⣶⣶⣆⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⠋⠁⠀⠋⠰⠋⠀⠀⠂⠹⠋⠀⠉⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⡟⣿⣿⣤⡴⠋⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣴⠶⣶⣶⣶⠀⠀⢴⣶⣄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣸⠇⢸⣿⣯⠀⣴⡟
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⠀⠈⠃⠀⠀⠀⠀⠀⣴⣀⣀⣠⣿⠋⢠⣶⠋⠀⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠓⠚⣿⠾⠛⠋⠁⠀⠈⠙⠿⢿⡀⣿⠃⠀⣾⣽⣿⣿⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠁⢀⣾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⢀⣿⣿⣿⣯⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣾⡿⣽⡇⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣶⣿⡟⠁
⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡴⠶⠒⠛⠀⠀⠀⠀⠀⣀⣤⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⠟⠛⠛⣋⠁
⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⢀⣤⣶⣶⣾⡿⠷⢄⠀⠀⢀⣤⢿⣴⠀⠀⠀⠀⠀⠀⠀⢀⡴⠄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠻⣿⣶⡀⠀⢠⣾⠿⠟⢻⣿⣿⣿⣧⠀⠀⢠⣿⠏⣴⡏⠀⠀⠀⠀⠀⠀⠀⡤⠀⣶⣡⠶⡄⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⣀⣴⣿⣿⣿⣿⣿⣧⣐⣟⡁⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⢙⡢⣿⠉⠢⠄⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⢿⣿⣿⡿⢿⣿⡛⠿⣿⡯⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣡⣴⡿⠋⠙⠁⢺⠙⣷⠀⣤⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⣁
⠀⠀⠀⠀⠀⠀⠀⠠⠴⠾⠛⠉⠀⠀⠀⠀⠸⡇⢹⣇⠀⠁⣤⡾⠂⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢠⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢿⡄⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⣿⠇⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⡀⠀⠀⠀⠀⢈⣉⣽⣿⣶⠆⣤⣀⣀⣀⣤⠶⠋⠀⢠⡾⠋⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣷⡀⠀⠀⠐⢛⣻⣿⡿⠋⠚⠛⠛⠉⢉⣴⣾⣦⣌⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣴⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⢸⢿⣿⠃⠿⠀⠀⠀⠀⠀⢸⡏⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⠾⠿⢿⡟⠳⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⢀⠟⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠤⠀⡀⠀⠀⠀⠀⠤⢄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡀⠒⠐⢂⡉⠉⢄⠉⠐⡆⠤⣀
⠀⠀⠀⠀⠄⣄⣠⣀⣀⣀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢅⡀⠀⣤⠀⠘⣖⠀⣸⣆⡀⣸⠄⢻⠲⡀
⠀⠀⠀⢁⠚⢸⡃⡩⡆⠀⡗⠁⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⢰⠎⠉⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⡀⠈⠳⡂⠸⠒⠈⠉⠐⠀⠈⠁⠈⠑⢇⣰⠅
⠀⠀⠀⣖⣂⡯⠀⢴⡁⣨⣧⠀⢸⠀⠀⠀⠀⠀⠀⠀⢲⡀⢂⡸⠀⢘⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠅⠀⠠⠄⠀⠀⠀⠀⠐⠂⢈⠈⠋
⠀⠀⠀⢠⡠⠕⢞⡷⣿⡿⢾⡀⢨⠀⠀⠀⠀⠀⡆⢃⠡⠴⠀⠘⠾⠇⠀⠉⠛⠢⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠐⠂⠀⠀⠐⠀⠀⠄⠆
⠀⠀⢠⠈⠲⠆⠘⠉⠻⠛⠉⠠⢀⠠⠀⠀⠀⣜⠩⠀⠾⣀⣀⡀⠀⠀⠀⠎⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡁⢀⠀⠀⠀⠉⣿⠀⠀⡌⠱⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠇⠈⢰⡯⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂⠘⠉⢁⢈⠁⢈⢐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢄⣹⢤⠛⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠜⠁⡌⡄⠘⠈⠢⠈⢸⣄⢀⡸⠀⠀⣸⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠙⡅⠀⠀⡴⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢦⠀⢇⠀⡨⠤⠄⠉⠀⠀⡘⠉⠙⢀⠙⠷⠺⢍⡔⠠⢤⡀
⠀⠀⠀⠠⡎⠀⠰⠃⠀⡠⠁⠀⡴⠁⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠘⠉⠉⢃⠐⠀⠀⠡⠂⠀⠴⠂⠈⠀⠐⠀⠀⠀⠙⢦⣀⡴⠆
⠀⠀⣿⠀⠉⡒⠚⠁⠒⠓⠄⣠⠃⠀⡞⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣾⡀⢠⠄⡘⢤⣶⢀⡄⢹⢀⠜⢁⡼⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠙⡀⠘⠀⡹⠂⢠⠚⠃⠘⡧⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠁⠐⢤⢱⠈⠰⡤⠠⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⣘⠁⠀⠀⢸⡇⠀⠐⠉⠂⠖⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣌⠁⠀⠀⠀⠀⠀⠀⠐⢄⣀⡀⠀⡇⠀⠀⠀⢸⠤⠬⠿⠻⠃⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠗⠛⠛⠛⠂⠹⢻⠀⠀⠀⢸⠙⠈⠳⠚⢃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢺⠤⢮⠹⢟⣂⣀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⠀⣄⠀⠨⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⣴⠩⠗⣈⡑⢦⠈⢂⡬⡀⡎⢹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣀⠂⠈⠱⡀⠀⠀⠀⠀⠀⠅⠈⠚⠤⠝⠘⠏⠹⠀⠎⠐⠑
⠀⠀⢀⢀⠀⣁⣉⠉⠙⣏⣩⡟⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣄⡄⠀⡀⢠⡄⠀⣴⢀⢠⡄⡀⢀⡖⠲⢰⡆⠢
⠀⠀⢸⠀⠀⠉⢠⣷⣋⠉⠁⣀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⡹⣿⠞⣋⡉⢶⠄⢉⣴⠒⣁⣤⠉⠀⠄⣊⢨⠟
⠀⠀⠀⠀⠀⠰⢸⡥⠐⠙⠿⠍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠄⠘⠆⠀⠀⡜⠀⠀⢰⠈⠘⡆⢵⢀⢰⠃⠛
⠀⢀⠀⠀⠠⠀⠉⠀⠈⠀⠀⠀⠀⠰⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠄⠱⠀⡴⠀⠀⠀⠃⠀⣠⠃⠀⠐⡀⠀⢟⠃⢸⠂
⠀⠀⠂⠄⠀⠀⠀⠄⠀⠀⠀⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠰⠁⡴⠁⠀⡔⠁⣠⠀⠁⣀⠊⣼⡅⡠⠴⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣠⠶⠚⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣘⡛⠛⠛⢛⣛⣿⣄
⠀⠀⠀⠀⠀⡀⠽⣿⣖⣶⡿⠇⠈⢀⢀⠻⠃⢀⣴⣾⣿⣷⣄⠀⠀⠀⠀⣀⣈⡉⠉⢩⡽⡷⣶⣄⡉⠩
⠀⠀⠀⢠⣬⣽⣳⠮⠿⠿⢥⡉⠀⣀⠋⣢⣶⣿⣿⣿⣿⣿⣿⣷⣤⣜⣛⣯⣭⣽⣥⣀⢀⢀⠆⠉⠋⣗
⠀⠀⠀⠀⠀⠉⢿⠟⠛⠙⣁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣖⠚⠿⠿⡛⣷⣱⣾⣿⣷⣦
⠀⠀⠀⠘⠛⠒⣄⣠⣶⣿⣿⣿⣿⣷⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⣤⣼⣿⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠋⠀⠙⠛⠿⠿⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⢡⠐⠟⠋⠀⠙⠃⠉⠻⢿⣿⣿⠵⠚⠁⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠙⠟⠋⠉⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣤⠤⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠀⢀⣀⠟⠁⣱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠜⢩⠁⢠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⣫⣷⡏⠀⠀⠐⢻⣭⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠿⠟⠡⠺⠃⣴⠎⠉
⠀⠀⠀⢤⠴⢖⣿⣷⢾⠲⢤⣂⡄⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⢀⣀⣙⣿⡽⠾⣛⠀⠀⠘⠉
⠀⠀⠀⠙⠽⡶⡞⣏⣿⠀⠀⠰⠆⠈
⠀⠀⠘⢷⣾⣿⣯⡵⣖⠀⠀⢀⣠⡴⠂
⠀⠀⢤⣤⣬⣧⣷⣷⣫⠀⠀⠀⢁⣀⠄
⠀⠀⠀⠉⢻⢻⢻⡏⡇⠀⠀⠀⠙⠁
⠀⠀⠰⢶⡿⣿⢻⡟⡿⠊⠄⠀⢀⡀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢤⡀
⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣦⣔⣦⣤⣤⣤⣀⣀⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⡀

⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠈⠀⢹⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠰⣆⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⢶⣷⡦
⣰⠄⠀⠀⠀⠠⣿⣆⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠙⢇⠘⠁⠀⠀⠀⠀⠀⠀⠀⣤⣥⠀⠀⠀⣤
⡈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠁⠀⠀⠠⣤⠈⠾⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠟⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⣼⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠈⡛⠋⠀⠀⠀⠀⠀⠈⠀⣄⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣀⣊⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠘⠀⠘⠁
⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡮⠀⠀⠀⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢠⡏⠀⠀⠀⠠⡠⠀⠄⠐
⠈⠇⠀⠀⠀⠀⠀⠈⢰⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⠆⠘⠁⠀⠀⠀⣸⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⣠⡘⡀⠈⠒⠒⡈⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠂⢠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⢦⡀⣠⣿⢿⣧⡤⠤⣤⣀⡀⠚⣾⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣴⢃⡀⠀⠀⢧⢿⠟⠉⢀⡀⠀⣰⢋⠁⠀⣻⠖⠋⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣻⣾⣷⠠⠀⠘⠀⣠⣶⣯⡤⡴⠃⣼⡆⡀⣵⡃⠠⢋⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣁⡈⠻⡟⣆⣀⣴⡿⠟⠋⠈⢀⣀⢿⡿⣿⣿⣀⡐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠉⠀⢀⣠⣄⣤⣔⣉⣤⡿⢠⡤⠀⢀⣀⠈⣿⣵⡟⠉⣡⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠸⢷⣤⣠⣼⣿⣿⣛⣬⢭⡍⠉⢠⣛⡶⠤⢴⣾⠿⢿⣛⣤⣦⡸⡇⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣽⣿⣿⣿⠸⠀⠀⢸⣿⡟⠀⠠⢶⣞⣟⠛⠛⠿⣿⠃⠀⣸⠇⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⣻⣟⣃⣀⡜⠀⣐⡿⠶⡆⣦⠈⠙⢷⡔⡄⡟⣠⡧⠏⣻⡭⠿⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⣤⣭⣁⡈⠻⠿⠟⡴⡋⣵⠞⠓⣿⢹⣇⠀⣠⣝⠘⡟⢻⣤⡾⠛⠉⠁⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠀⡀⠀⠉⠂⠀⠘⣾⡟⠁⠀⠀⡿⣼⠇⢸⡿⢋⡤⣜⡻⠯⣟⠛⠷⣤⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣶⣜⡿⣾⣷⣝⢦⣠⠀⠸⢯⡞⠀⢀⣼⣷⣯⣾⠏⣧⠟⠓⠉⢹⢰⣮⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡮⠺⢿⣿⣿⢫⠖⠛⠲⡝⢖⣉⣉⣤⡽⣁⠀⢧⣀⣠⡴⣻⣮⡻⣅⠀⣸
⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣟⣦⣶⡶⢂⠸⣦⣤⣴⡇⣾⣍⣉⡽⠿⠿⠷⡌⠉⠁⠀⠹⢿⣿⠻⣄⡟
⠀⠀⠀⠀⠀⠉⠛⠛⢻⣏⣨⡭⠋⠕⢉⣷⢨⣭⣉⡜⠿⣄⣀⠀⠀⣀⡠⣿⣤⡶⠀⠀⢀⠙⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠋⠀⠀⢀⣾⣣⡟⠘⣿⣿⡆⡼⣯⣭⠿⠃⠸⠿⢽⣧⣤⡴⣾
⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠤⠶⠚⢹⣿⡿⡇⠀⠀⠏⣿⡆⢩⣅⣀⣀⣀⣤⣤⠟⠃⣰⢧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠙⢄⠀⠀⢻⠃⠀⠙⠻⢯⡉⠉⠀⣠⠼⠓⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠳⣶⠏⠀⠀⠀⠀⠉⠙⠛⠉⠁

⠀⡁⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠁⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⢀⣀⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⢦⣀
⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣤⣶⣶⣾⠯⠟⠓⠒⠒⠒⣂⡈⢳
⠀⢸⢇⠀⠀⠀⠀⢀⡠⠔⣒⠭⠕⢒⣉⠽⣿⣿⣿⣿⣍⣉⠩⠭⠭⠤⠤⠌⡷⣄
⠀⠈⢎⢣⡀⠀⠀⣿⡈⠩⠴⠒⣉⣩⠤⠒⢊⣻⣿⣿⣿⡶⠒⠒⢒⡒⣒⠊⢹⠈⠣⡀
⠀⠀⠈⢣⡱⡄⠀⢰⠈⠓⠢⠬⠥⠒⠒⢩⡍⢸⣿⣿⠿⣇⠀⢈⠥⠭⣍⢁⣼⣄⡀⠈⠢⡀
⠀⠀⠀⠀⠱⡜⢆⠸⡀⠐⠒⠒⠀⠀⠀⢀⣠⡚⢻⠀⠀⠀⣟⣇⠀⠀⢈⡇⠀⠀⢸⠉⠙⢿⢦
⠀⠀⠀⠀⠀⠘⢎⢣⣧⡀⠀⠀⠤⠆⢰⠁⢠⠝⠚⠢⣤⡞⠉⠈⣷⠊⠉⠳⣶⠖⠋⠳⣄⡸⠉⡗⢄
⠀⠀⠀⠀⠀⠀⠈⢢⠱⡉⠓⠒⠒⠚⣿⣦⣧⣀⠀⠀⣸⢳⡤⠤⠻⣀⠀⣠⢧⣀⣀⣴⣿⣤⣶⡇⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡙⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢦⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⢛⡿⣟⠓⠒⠒⠤⢤⣈⢦⣤⣤⡤⢒⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠳⡀⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢡⠖⢉⡥⣀⠉⠲⠼⠃⢸⠀⠀⠀⠀⠀⠈⣗⣉⠶⣍⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡑⣄⠉⠛⠻⠿⣻⠟⢋⢄⠀⠀⢸⢀⠋⠀⠀⠉⠑⢒⣒⣁⠀⠀⠀⣀⣀⣀⢟⠛⠛⠋⢟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⢆⠀⡴⠋⠀⠀⠸⣌⠲⠤⠞⣸⠀⢀⡠⠔⠊⠉⢀⠀⠀⠀⠀⠀⢀⠀⠘⡄⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢣⣧⠀⠀⠀⠀⠈⠉⣛⡩⠕⠚⠉⠀⠰⠒⠒⠉⠁⠀⠀⠀⢠⠋⠀⢰⠁⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠹⡗⠤⠤⠔⢒⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣠⠔⠁⠀⠀⠀⢀⣠⠤⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⢾⡄⠀⠈⠙⠓⠀⠀⠀⠀⣀⣀⣤⠤⠤⠖⠒⠉⠉⠀⠀⠀⣀⡤⠖⠊⠁⣀⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢫⡳⠤⠴⠖⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⢀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠁⣀⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⢆⠀⠀⠀⣀⡠⠔⠚⠉⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⢳⠒⠉⠁⣀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠤⠒⠉⠁

⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠸⣿⣿⡷⠀⠀⠀⠀⠀⣀⠤⣀⠀⠀⠀⠀⠀⢀⣺⣄⠀⠀⠀⠀⢠⡤⠏⠻⢤⣄⠀⠀⠀⢠⣶⣷⣦
⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⣴⣇⢀⣸⣦⠀⠀⠀⣀⣼⣿⣿⣄⡀⠀⠀⠈⣷⢀⡀⣾⠃⠀⠀⠐⢻⣿⣿⣿⠛
⠀⠀⠐⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠙⠋⠙⠛⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣤⣾⠿⣷⣤⠀⠀⠀⠀⢀⣠⣀⡀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⢀⣠⣋⣉⣃⡀⠀⠀⠈⣿⣇⢛⣸⡿⠀⠀⠀⠐⠿⢿⠿⠟⠀⠀⠀⠸⠿⠻⠿⠶⠆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠟⠃

⠀⠀⠀⣾⠿⡆⠀⠀⠀⠀⠀⡏⠉⢱⠀⠀⠀⠀⣀⣠⣤⣤⡄⠀⠀⠀⢀⡶⠿⡛⣶⡄⠀⠀⠀⢀⣤⣤⡄⣄
⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⠁⠁⠉⠀⠀⠀⠀⠁⠽⣿⣿⠇⠀⠀⠀⢸⢿⡕⣋⣴⣿⠀⠀⠀⢿⡿⠿⣿⠹
⠀⠀⠰⣥⣤⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠲⠶⠿⠞⠁⠀⠀⠀⠘⠁⠈⠃

⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠⣆
⠀⠠⢴⣦⣦⣶⣦⠀⠀⠀⠀⢔⠉⡂⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⢀⣼⣿⣤
⠀⠐⢚⣿⣿⣿⡋⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠰⣿⠇⠀⠀⠀⠀⠀⠀⠸⠋⠓⠀⠀⠀⠀⢀⣾⣿⣿⣾⣤


⠀⠀⠀⣀⣀⣤⠀⠀⠀⠀⣶⣄⣿⡿⠷⠀⠀⠀⢴⣷⣶⣷⣀⠀⠀⠀⢀⣔⣆⣗⡴⡀⠀⠀⠀⣰⠻⠿⢳⡄
⠀⢰⣿⣿⣿⠗⠀⠀⠀⠀⠛⠃⠛⠃⠀⠀⠀⠀⠙⠉⠉⠉⠙⠁⠀⠀⠀⠈⠙⠋⠋⠁⠀⠀⠐⠻⠷⠤⠴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣄⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠻⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣤⣤⣄⣀⡀⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣀⣠⣤⣶⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣬⣭⣻⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣷⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣲⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠙⠛⠿⣿⣿⣿⠀⠀⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠿⠟⠛⢻⡟⠛⠿⣿⣿⣿⣿⠟⠉⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⡄⠀⠉⠙⠉⠉⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⢻⣿⠃⠀⠀⠀⠉⠉⠉⠓⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠛⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⠁⠀⢠⡄⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠶⠂⠘⠋⠀⠀⠀⠀⠀⠒
⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢠⠀⠺⠁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠰⠆⠀⠈⢠⠀⠀⠀⠀⠀⢀⣠⣦⡀
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⡄⠀⠒⠀⠈⠀⠀⠀⢀⣴⣿⣿⣿⣿⣄
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠁⢀⡠⠟⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣆
⠀⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠁⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠈⠉⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⠀⢀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠰⠀⡀⠀⠀⠀⠀⠀⠂⡀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠉⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁
⠰⠉⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢍⠆
⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠐⠤⠐⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⣠⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠌⠈⢿⣿⣿⣿⣿⣿⣯⡀⠈⢐⠀⠀⠀⠀⠀⠀⡀⢆⢀
⠃⠀⠡⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄

⠀⠀⠀⢀⣤⣤⡀⠀⠀⢀⣤⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣠⣀
⠀⠀⠀⢿⣿⣿⡷⠀⢀⣹⣟⠁⠀⠀⣠⣼⡿⠃⠀⠀⠘⡿⠃⠀⠀⢰⣿⠁⠀⠀⠻⣿⣿⡦⠀⠈⢻⣿⡍
⠀⠀⠀⠀⣽⣿⠀⠀⠈⢛⣿⣄⠀⠀⠙⢛⣿⣤⡄⠀⢸⣿⠄⠀⠀⠿⣿⣃⠀⠀⠀⣴⡿⠀⠀⠀⣰⣿⣧
⠀⠀⠀⠠⣾⣷⡆⠀⣠⣼⣿⣏⠀⠀⢀⣿⣟⡋⠁⠀⢠⣿⣶⠄⠀⢸⣿⠿⠃⠀⣀⣾⠿⠂⠀⠀⠻⣿⠟
⠀⠀⠀⢠⣾⡿⠀⠀⠻⢿⣿⣿⠇⠀⠿⣿⣿⡋⠀⠀⣼⣿⣅⠀⠀⣿⡛⠂⠀⠀⢿⣿⣷⡄⠀⠀⢺⣿⣆⡀
⠀⠀⣠⣿⣿⣤⣄⠀⣴⣿⣿⣷⡄⠀⢠⣿⣿⣿⡆⢀⣬⣿⣯⣄⠀⣼⣿⣧⣄⢀⣤⣭⣭⣤⡄⠀⣶⣿⣿⣿
⠀⠀⠙⢿⣿⣿⡿⠃⠙⠿⣿⠿⠃⠀⠘⢿⠿⠋⠀⠘⠿⣿⡿⠟⠀⠻⢿⠿⠋⠈⠿⣿⣿⡿⠇⠀⢿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠒⠒⠒⠚⠛⠒⠒⢒⣶⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠐⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⠀⠀⠀⠀⠈⢻⣿⢿⣿⣿⠿⠟⠁⡀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣦⣀⣀⠀⠙⡶⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⢿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠉⠉⠉⠙⠛⠛⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠤⠀⠁⠐⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠹⣶⣶⡄⠀⠀⠀⠀⠀⠰⠅⠨⠴⢥⣀⣼⣴⣦⣥⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣷⣈⣿⡧⢖⣩⠀⠀⠀⠀⠠⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣻⠏⠉⠉⠻⣷⠀⠉⡒⡈⣭⠈⣰⢟⣩⣤⡉⠉⠻⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣿⣧⠀⠈⠻⡏⠙⢶⠀⢠⢶⣦⡀⠀⣁⠈⠰⣿⣻⢿⣿⣾⣧⠀⠀⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡤⠘⣿⣆⠈⠂⠁⠀⣤⠀⠘⠜⠟⢃⠀⣰⡷⠻⢹⠛⣧⠹⠃⢻⣶⡀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡈⠻⢷⣄⣈⠀⠶⠈⣀⣿⠗⠀⠀⠋⣤⣤⣀⠀⠈⡔⠛⠢⠘⠛⠰⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⢦⣉⠘⠈⣁⢿⡼⣇⣢⣿⠇⠘⡆⣠⡏⠀⠀⠈⠛⠻⣯⣥⡤⠀⠹⠶⠯⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠍⠈⠁⠀⢘⣷⣿⡿⢡⠀⢂⠳⠽⡇⠀⠀⠈⡀⠂⠀⠙⢻⣀⣀⠀⣤⢷⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⢸⠀⠀⢰⡦⢄⢉⣗⡬⠃⠀⠀⠀⠀⠀⠙⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⢸⡆⠀⠀⢻⠠⠞⠷⣟⢣⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡆⠆⠻⡄⠀⠹⠰⣶⣤⡜⢯⣝⣧⣒⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣄⣂⠀⠀⠀⠀⠙⣯⣿⣶⣿⣯⢹⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⡀⣹⢻⣿⣿⣡⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢂⣟⢺⡏⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣡⠛⢸⡇⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢅⣿⣀⡾⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠈⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣶⣾⣿⣿⢿⣟⣿⣯⣭⣿⣟⢯⡻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣯⣿⣶⣛⣛⡲⢮⣳⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠈⠉⣋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣮⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣟⡿⢿⣟⡿⣟⡿⢿⡳⣽⣿⣿⣷⡏⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢃⠀⢀⣻⣿⣻⣿⡿⡿⢯⣽⣛⣚⣭⣵⣚⡦⣿⣻⣺⣿⣿⡇⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⠿⢿⣿⣇⠉⢉⣽⣻⢭⣝⣿⣷⣶⡶⢯⢟⡿⣿⣻⣟⣧⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣿⡇⠀⠈⣿⣿⠀⣾⡽⢱⣫⢿⣿⡿⠿⠿⣿⣿⣻⣵⣻⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣤⣀⣀⣀⣀⣀⡴⢃⣴⣿⣷⡀⠀⢹⣿⠀⡟⡇⢸⣿⣿⣴⣿⢿⣿⣿⣿⣿⢿⣿⠵⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠿⠷⠶⠄⠚⢿⣿⣿⣧⠀⢸⣧⠀⣧⡇⣿⣷⡿⡇⣿⣿⣲⡼⣭⣭⣽⠶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⣿⡀⢿⣇⢙⢿⣧⣇⣿⣿⣽⣤⣤⣴⣶⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡇⠀⣿⣿⣾⣿⢸⣸⢿⡳⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿⣿⣿⣯⣧⣳⣷⢿⣿⣟⣿⣿⣿⣟⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⣿⣿⣿⠈⠛⠿⣯⡽⠿⠭⠭⠽⠿⣽⣿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢶⡒⣘⣻⣿⡀⣀⣿⣿⣿⠁⠀⢀⣤⡦⣒⡲⠶⠶⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⢺⣿⣽⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠀⢸⢸⡿⣿⡿⣿⣿⡿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⢸⣳⣿⡇⣿⣿⣶⣶⣶⣾⣾⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣷⢸⠸⢸⢻⣯⣳⠿⡿⣿⣿⣛⡻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⣯⣟⢮⣛⣛⣛⣻⡽⣝⣮⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠸⣿⣿⣿⡿⠿⠿⠿⠿⠚⠯⠭⠥⠜⣿⣿⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⢩⣤⡀⠀⢶⣿⣿⡇⠘⣯⣽⣭⣍⣛⣋⣛⣙⣛⣛⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⢸⣅⠀⠀⠀⠀⠀⠀⠈⠿⣿⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠹⣿⣿⣿⣛⣋⣉⣁⣼⡿⠋⠁⢀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠸⠋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠓⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⢿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⣿⢸⣿⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡟⣿⢸⡙⣇⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣼⠁⡟⢸⡇⢻⡄⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠲⠄⠀⠀⠀⠀⠀⠀⠜⠁⠀⡰⠁⢰⡇⠀⡇⠀⢳⡀⠀⠈⠛⠿⣿⣿⣿⢟⠥⠒⠁⠀⠀⢉⢻⣿⣿⣿⣿⣿
⠀⠀⣀⠠⠤⠤⢀⡈⠢⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢡⠀⠀⠑⠀⠀⠀⠀⠀⣈⡵⠃⠀⠀⠀⣀⣤⠾⢠⣿⣿⣿⣿⣿
⣴⠟⠁⠀⠀⠀⠀⠈⢰⡞⠈⠉⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠂⠤⡀⠀⠀⠴⠋⠥⡐⢾⣿⣿⣿⣿⣿⣿
⠉⠋⠒⠒⠀⠄⠀⠀⠘⠧⠀⠀⢀⠐⠖⠶⢬⠑⡄⠔⠒⠢⠀⠀⢠⡤⠀⠀⠠⠀⢀⠞⠉⠁⠀⠭⠂⡣⠤⢤⠀⠀⠀⠀⠘⠟⡟⠉⠉⠉⠛
⠀⠀⠀⠀⢀⠠⠤⠀⠀⣤⠀⠤⡤⠇⠀⠀⣠⠋⢰⠀⡀⠠⠑⢄⣀⢠⡀⡆⠀⠈⣱⢆⡄⠑⡄⠀⠀⠈⠀⠀⢀⠖⠀⠀⠀⠀⠄
⠀⠀⠀⡐⠁⠀⠀⠀⠀⠈⠣⠤⡀⠀⢊⠀⠑⠐⠚⠀⠈⠄⠙⢄⠉⠉⣠⠜⠀⠘⢧⡌⠴⠚⠀⠀⠀⠑⠀⠃⠀⠠⠂⠀⠀⠀⢾⣦⣤⣤⣴
⠀⠀⠀⠱⣄⠀⠀⠀⣀⠀⠀⠀⠈⠂⠤⡀⠀⠉⠀⠀⠐⠁⠀⠀⠁⠈⣤⠀⠀⢢⡄⠀⠀⠀⠀⡄⠀⠐⠀⡆⠀⠀⠑⠀⢀⣰⠿⣭⢿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠁⠙⠶⠤⠤⢤⣤⣄⣈⠂⠤⠀⠐⢦⡀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠑⢄⠀⠀⢈⡵⠀⠀⢈⣉⠁⢉⣉⣭⡤⠾⢏⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠄⠀⠀⠀⠀⢀⣀⣤⣤⣤⡄⡃⠀⠀⠀⢉⣉⠉⡤⠤⢐⣥⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠛⠉⠁⢽⣿⣿⣧⡐⠦⠴⢚⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣸⣲⣶⣧⡶⠖⠈⠂⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣯⣿⣿⠿⠛⠛⠛⢿⣿⣿⣿⣶⣮⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⣴⣿⢟⣉⣤⠞⠛⢻⣿⣿⣿⠛⠛⠛⠛⠻⢧⡍⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣟⣻⣭⣽⣿⣿⣿⣿⠻⣿⣷⣾⡶⠶⢀⡀⠙⠲⢤⡈⠹⣷⣦
⠀⠀⠀⠀⠀⠀⡐⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⠿⢿⣶⣿⣿⣯⣀⣜⣿⣦⠀⠈⣿⣆⣩⣿⠇
⠀⠀⠀⠀⠀⢈⣴⡄⣽⣿⣿⣿⡏⣿⣿⣿⡿⠛⣁⣼⣿⣮⣽⣿⡿⢧⣍⠙⠻⣿⣿⡆⢸⣿⡻⣿⡟
⠀⠀⠀⠀⣰⣿⣿⣷⣿⣿⣿⣿⠀⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣿⣷⣼⣿⣷⡀⣿⣿⡇⢸⣿⡇⢸⡇
⠀⠀⠀⠀⣿⠟⣿⣿⣧⣿⣿⠏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣽⠉⢿⣇⣸⣿⣷⠀⢷
⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣏⡀⠀⣿⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣿⡏⠀⣀⣿⣿⣿⡇⠀⠈⢧⡀
⠀⠀⠀⠀⠁⠀⢿⣿⣿⡿⣿⣿⣷⢬⣶⣌⠙⢛⣛⣻⣿⣿⣷⣶⣶⠴⣶⠟⢀⣾⣿⢹⣿⡿⠃⠀⢀⡤⠁
⠀⠀⠀⠈⡀⠀⠈⢿⣿⣧⠈⠛⢿⣧⡙⠉⠻⢯⣍⣿⣿⣿⠟⠉⢁⣤⣥⣶⣿⣿⡿⠸⡿⠃⠀⢀⠞
⠀⠀⠀⠀⠙⢦⣀⠈⠻⣿⡆⠀⠀⠙⠻⠆⠀⠀⠉⠉⠙⠢⣄⣰⣿⣿⣿⣿⡿⠟⠃⡐⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢧⡀⠀⠀⠀⠐⠀⠀⠂⣶⣯⣉⣉⡉⣙⣛⣻⣫⣴⣶⣯⠔⠒⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠢⣄⣀⣒⣶⣦⡆⢀⣀⣛⠉⠉⠓⠫⠉⠉⠉⣽⡿⠋⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⠟⠿⢿⣿⣿⣧⣀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣻⠟⠋⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣠⠀⡀
⠀⠀⠀⠀⠀⢀⡠⣴⣿⣷⣶⣄⢀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⢷⣶⣧⣼⡀⢠⠆
⠀⠀⠀⠀⠔⠃⠀⠀⢸⠋⢹⡿⣿⣷⣄⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠐⣿⠀⣿⢸⡏⢹⡟⢻⣦⡾⠂
⠀⠀⠀⠀⠤⠒⠒⠤⢤⣀⠸⣇⣿⣿⣿⣷⡀⠀⢸⡀⠀⠀⠀⠀⠀⠐⠁⠰⠃⡼⢃⣠⠇⣺⡷⡿⠚⠯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣿⣿⣿⣿⣿⣷⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠿⣄⣁⣦⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠟⠃
⠀⠀⠀⠀⠀⢀⣤⠤⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⣴⣾⣷⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⢤⣀⠀⠀⠀⢀⣴⣿⣿⠟⠀⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⠀⢰⣿⢯⣾⢻⣷⣤⣄⣀
⠀⠀⠀⠀⠈⢓⡦⣴⣟⣿⠟⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⢸⣷⣿⣖⣿⣿⣿⣿⣿⣿⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡗⣤⣀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠞⡀⢠⡖⠀⠀⡀⠈⠁⠀⡼⠂⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠉⠠⠐⠄⠋⠒⠤⢽⠠⠐⡂⠀⠀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⡰⠒⠀⢀⡀⠀⣴⡶⠄⠠⠃⠆⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠒⠀⠀⠀⠩⠝⡁⠐⠂⢀⡀
⠀⠀⠀⠀⠀⠀⢰⠿⠗⠀⠠⠀⠀⠀⠐⠀⠀⠘⠁⠈
⠀⠀⠀⠀⠀⠀⡸⠠⢤⣠⡀
⠀⠀⠀⠀⠀⠀⠩⠗⠜⠋⡌⠡⠠⠶⠂
⠀⠀⠄⣠⡤⠈⠁⢴⠘⠐⠂⡰⠖⠂
⠀⠀⠹⠙⠀⠀⠀⠐⡄⣠⡤
⠀⠀⠀⠰⡄⠀⠀⠀⢹⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⢴
⠀⠀⠀⠀⠑⣤⡄⠀⠌⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠢⡄⠿
⠀⠀⠀⠀⢒⡖⠰⣗⣯⠘⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠄⠛⠃⠁⢀
⠀⠀⠀⠀⠀⡋⠽⡢⢇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠁⣶⠊⠀⣠⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠠⠄⠀⠀⠠⣤⠤⠀⢀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠼⢃⣄⣀⣤⣤⣀⣠⠶⢾⠀⢀⠃⠀⠀⡀⠐⠀⠶⢦⠄⠀⡀⢀⠔⠋⠲⢰
⠀⠀⠀⠀⠀⢀⡞⠁⣮⠙⠁⣯⡠⢬⢇⢉⠃⠘⡖⢤⣠⠁⠀⠀⠀⢀⠀⠄⠀⠀⠈⠋⠂⠀⠌
⠀⠀⠀⠀⠀⢸⡃⠀⠈⠀⢄⡼⠰⠂⣰⣯⡐⠀⠛⠀⡆⢿⣠⠀⠀⠀⠲⠲⢢⡅⠀⢶⡦⠊
⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠠⡾⠀⠠⣀⣂⣰⡤⠤⠠⢧⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠓
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⢤⡀⢀⣤⣄⡤⢤⡀
⠀⠀⠀⠀⠀⠐⣿⣦⣰⣶⡀⣄⠀⠀⠀⠀⠀⠘⢦⣀⢺⣿⣰⡮⢾⣦⠳⣄
⠀⠀⠀⠀⠰⠟⠑⠟⠑⠿⠋⣿⣇⣤⠀⠀⠀⠀⠀⠀⢿⠁⢿⣸⣿⣿⢣⡾⣤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⢿⣴⡄⠀⠀⠀⠀⠀⠙⣏⢛⡻⢭⡼⠓⢤⣤⠬⠷
⠀⣄⠀⠀⠀⠀⠀⠀⠿⣆⠀⠀⠀⠀⢾⣧⣄⠐⣿⡿⠷⣆⢸⠉⢀⡤⣆⣠⣂⣤⡀⠀⣰⡆
⠀⢏⠙⢆⠀⠀⠀⠀⢷⣽⠆⠀⣠⠔⡆⢼⡟⠀⠈⠛⠲⢬⣿⣴⢟⣉⡉⣊⡵⣿⡆⣄⣈⣦⡀⢠⣴⠆
⠀⠈⢳⡾⠲⠶⡛⢦⡈⠿⠀⠴⣇⠔⠁⠀⢹⣧⣄⣀⠀⠀⡻⠋⠀⠈⠉⠉⢠⣏⣀⢿⠿⠿⢏⣤⣄⢀⣀
⠀⠀⡼⢧⡿⢻⣿⣮⠙⡆⢀⠤⠖⢷⡀⡼⠋⠉⣀⡉⠳⣔⣁⣀⡀⠀⢠⣤⢻⡿⠷⣷⣤⣴⡎⣿⠿⣉⠉
⠀⠈⢧⣸⢷⣽⣿⡇⢾⠑⠓⠒⠒⣁⣼⡇⣴⠋⠉⣝⣶⣭⣤⡀⠙⢧⠀⣝⣀⢀⠜⠻⣿⠯⢿⣤⡌⠉
⠀⣠⣾⡿⢦⡥⠛⠒⠃⠀⠀⢀⡾⠁⣠⠞⢳⡔⣫⠭⣍⠳⡄⢹⡆⢸⡗⠻⠟⢺⣴⣷⡀⠀⡻⠿⠛⠀⠛
⢸⣤⠿⠁⠀⠀⢀⣀⠀⠀⣀⣸⡇⠀⣏⢀⣾⠰⡱⣿⠆⡇⣷⣼⣡⠞⢹⡢⠀⣏⣛⠻⣃⡉⠙⠮⠗
⠋⠁⠀⠀⣠⣞⠿⠒⢁⡠⠊⠈⠻⣄⣘⣶⡿⢧⣑⣒⣚⣵⠏⣻⠈⣦⠀⠉⠌⣻⣿⡶⠙⠒⠋
⠀⠀⣤⣾⣯⣥⣤⣴⠟⠀⠀⠀⠀⠀⣽⠈⢷⡈⠋⣉⣯⣠⡴⠏⢀⡿⠀⠰⢀⡮⠉⠁⠀⠀⢀⣠⣤⠄
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢠⢻⡄⠀⠸⣦⣀⠉⠛⣉⣿⣤⣤⡴⠟⠁⢀⡇⠀⢀⣀⣠⣤⣤⠏⢀⡜
⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⠸⠟⣤⣤⡄⠈⠙⠛⠛⢉⠃⣠⣤⣴⡶⢾⣿⠁⢰⣏⣤⡥⣶⡸⢾⡉
⠀⠀⠀⠀⠀⠀⠀⠿⣿⠿⠂⠲⢿⣿⠷⠀⡤⠒⡿⣤⡞⠋⠀⣀⡴⠋⡐⠀⡏⠹⣏⣾⣿⡿⣠⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⠟⣼⣥⡀⠸⠫⠔⢡⡏⠀⠂⠁⠀⣠⠌⠄⠂⠉⢻⡙⢟⣯⣁⡼⢌⡀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠁⠺⣿⣿⡦⠃⠀⠀⠀⠁⣀⢄⡂⠡⠀⠐⠂⠀⠤⢄⡉⣉⣤⣄⡀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⡀⠀⠀⣰⠿⢾⣍⡉⠉⠉⠐⠢⡀⠀⠀⢸⠻⡠⣶⣮⣝⣲⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⢳⠆⠀⢤⢀⡾⠃⠀⢆⡁⢳⠀⠀⠀⠀⠈⣢⡀⠈⢧⢿⡛⣃⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠈⣿⠁⠀⠀⠀⠉⠛⠃⠀⠀⢠⡎⣻⡙⢆⠈⢳⣱⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠞⢻⢻⡾⣆⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠛⠳⠞⠙⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛


⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠈⣿⣿⣤⣤⣤⣤⠎
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠉⢉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡰⠹
⠀⠀⠀⠀⠢⠀⣀⣤⣦⣿⡀⠀⠀⠀⢣⣄⡀⠀⣀⣤⠂⠀⠀⠄⡐⢀⠃⠀⠀⠀⢀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠉⠻⣾⠟⠁⠀⠀⠀⡘⠁⠄⠀⠀⠀⣰⠃⡀
⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⡇⠀⢀⠀⠀⣸⢃⡄⠀⠀⢀⢀⠏
⠀⠀⠀⠀⠀⠈⠡⡀⢄⠀⠀⠀⠹⡄⠀⠀⠀⠁⠀⡎⠀⡴⢁⠌⠀⠀⡠⡢⠃
⠀⠀⠀⠀⠀⢠⠀⠘⠄⠀⠀⠀⠀⣇⠀⠀⡀⠀⡸⡃⡼⢡⠏⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⢸⠀⠀⠃⠀⠃⢹⡴⠃⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⡀⠀⠀⠀⠀⢸⠁⠀⡤⠀⠀⠀⠀⠀⠀⠐⠀⢀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡇⠀⠀⡈⠀⢸⠀⡈⠃⠀⠀⠀⢀⠀⠀⠀⠐⠁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠒⠀⠀⡆⡼⠁⠀⠀⠀⠀⠀⠀⠀⠁⢀⠂⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⡇⢸⠡⠀⢰⢱⠇⠀⠀⢀⣠⣥⠦⠁⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⢧⢸⠀⢱⠃⢸⠀⢀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡘⣰⢣⠀⣿⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⣧⡏⠸⠀⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⣿⡇⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢳⣄⡏⢱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠠⣤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⢠⠄⠴⠄⢠⠠⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠠⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠉⠉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⡏⢉⡀⢀⢀⠀⡀⡀⢀⡀⢀⠀⢀⣀⡀⡀⡀⠀⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠄⡄⠀⣀⡷⣏⢸⢸⢸⢧⡁⡆⡄⠀⢾⠐⠛⢣⣼⡇⠛⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡀⠀⠀⠁⢀⣉⡁⠈⠉⠘⠉⠀⠉⠁⠀⠀⠈⠉⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣧⡀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⠌⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈
⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠉⠀⠘⠀⢀⡀
⠀⠀⠋⠀⠀⠘⠃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⢀⡠⠤⠄⡀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡜⠁⠀⣀⠀⠙⣆⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡇⠀⢘⠿⡄⠀⣹⠀⠀⠒
⠀⠠⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⠀⠀⠀⠤⠀⠀⠘⣤⣂⢀⣠⡜⠃⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡄⢠⠃⠈⠈⠀⠹⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⠋⠆⠀⠆⠀⠲⠑⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣵⣤⣤⣤⣤⣬⣬⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣏⣿⣿⣧⡇⣤⣰⣾⣿⣶⣤⣤⣀⠀⣀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⣿⣿⡷⢿⠳⢻⣿⣿⣯⣭⣽⣷⣕⢬⠑⢤⡀⢀⠎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣷⠶⣷⡊⠈⠊⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⣰⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣷⣼⣆⣀⣼⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣼⠏⢠⣿⡇⢀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠶⠤⡘⣿⣿⣿⣽⡷⢊⣯⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡏⠀⠈⣿⡟⠉⢽⣿⡗⠀⠀⣾⡿⣿⣿⣿⡿⠋⢹⣿⣿⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢇⠀⠀⠸⡇⠺⠿⠟⠁⠀⢸⠏⠀⠀⠉⠉⠀⠀⣠⣿⣿⣿⡿⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠒⠇⠀⠀⠀⠀⢀⣨⣧⡀⠀⠀⠀⠀⣺⣿⣿⣻⠿⡣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⣉⠁⠀⠀⠀⠈⣃⣿⣿⡷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠰⢞⣛⣛⣿⠖⠀⠀⠀⢡⠟⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⢀⡀⣀⣡⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣄⣠⣴⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠉⠙⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠙⣷⢦⠀⠀⠀⠉⠛⠏⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⠿⠋⠀⠀⠘⢷⠀⠢⣿⡀⠀⠀⣷⣿⣧⡀⠀⠠⡤⠴⠒⠋⠉⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⡀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⣿⡆⢸⡟⣿⣿⣝⠶⣤⣤⣤⣤⣤⣄⣠⠶⠊⠁
⠀⠀⠀⠀⠀⠀⣰⠛⡡⠔⠪⠭⠿⠿⣿⣿⣭⣿⣿⣯⡭⠹⠟⠻⠷⠶⢾⣿⢸⣿⣿⠿⠿⠛⣳⣛⠿⢿⣻⢏⠟⣆
⠀⠀⠀⠀⠀⢰⠁⠈⠀⠀⠀⠀⣠⢼⡵⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠑⠈⠉⢀⠡⢖⣫⠟⠁⠘⢀⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡩⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⢀⡀⠔⠋⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠁⠀⠀⠐⠈⠀⠀⠀⡀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⣀⣤⣴⡶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⣲⣶⣄⠀⠀⠀⢀⢤⠄⠶⠀⠖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⢀⣉⡉⢉⡉⠉⢢⠀⠀⡁⠀⠀⠀⠀⠀⢠⡴⣏⣤⣾⣿⢟⠋⠹⠃⠀⠀⣧⣿⣶⡾⠛⠛⣋⡙⢻⣆⠀⠀⠀⠀⠀⣰⡷⠺⣿⣯⡭⣿⣆
⠀⠀⠀⢸⣿⢶⢻⣽⠀⢸⣷⣾⡇⠀⠀⠀⢀⣴⣛⢠⣶⣿⡟⠁⠰⠈⠀⠀⠀⠀⠈⠉⠙⢀⢰⣿⣻⣿⠀⠃⠀⠀⠀⢀⣾⠏⠀⢂⢬⣿⣷⡄⠾⣧
⠀⠀⢠⠐⣯⣿⣷⣿⡆⢼⣿⣿⠇⠀⠀⢠⣾⣓⣮⣿⣽⢟⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠗⠉⠀⠀⡀⠀⠀⢠⣿⠟⠰⠤⠜⡷⠬⣿⣷⢶⡿⠃
⠀⠀⠈⠢⠀⠀⠈⠉⠠⠞⠋⠁⠀⠀⠀⠉⠲⠾⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠁⠠⠒⠃⠀⠀⠈⠛⠒⠒⠂⠀⠀⠀⠼⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⢠⠄
⠀⠀⠀⠀⠀⢀⣠⡶⠞⠓⠀⡀⠀⠀⠀⠀⠀⣴⡚⢫⡭⣭⡬⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⣧⣅⣼⠦⡀⠀⠀⠀⠀⣀⢠⠒⢠⠀⠀⢶⣶⢂⡄
⠀⠀⠀⢰⠋⠀⠀⠑⢈⡧⢤⣴⣪⠄⠀⠀⠀⣟⢷⡈⠙⠛⠁⠠⠄⢳⠀⠀⠀⠀⠀⠜⠁⣀⠄⠀⠈⠹⣠⣧⠀⠀⠀⠀⡏⠨⠁⠀⠀⠀⠲⣿⡿⡇
⠀⠀⠀⣅⠡⠶⠒⠀⠘⢃⠘⢁⢼⠂⠀⠀⠀⢃⠈⠿⢶⣆⣴⡴⡶⢤⡆⠀⠀⠀⢀⠀⣸⡭⡳⣆⠀⢸⡏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⡗
⠀⠀⠀⢶⡒⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣤⣈⡉⠈⠃⠀⣸⠇⠀⠀⠀⠘⠀⢿⣿⣎⢯⡇⠈⣷⠏⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣷⡿⠃
⠀⠀⠀⠘⠓⠒⠒⠚⠃⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠓⠛⠃⠁⠀⠀⠀⠀⠀⠦⡀⠉⠉⣩⢅⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣄⠂⢀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠑⢂⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠰⣾⠿⠁⡆
⠀⠀⣀⢈⡉⠀⠈⠱⢿⣄⣤⡷⠗⠋⠍⠀⠀⢀⠀⢠⡄⠴⣖⡫⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣶⡞⠁⠀⠀⠀⠀⠀⣾⣁⠎⣁⣹⣥⣿⣾⡇
⠀⠀⠑⠫⠤⠆⠐⠟⣽⠿⠟⠋⠀⠀⠀⠀⠀⠈⠀⠀⠉⠇⠸⠟⠁⠀⡐⠀⠀⠈⠁⠀⠤⠠⠄⣰⣇⢸⡗⠈⠀⠐⠀⠀⠀⡿⢘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠛⠃⠐⠈⠀⠀⠀⠀⣇⢸⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⣠⠔⠄⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠰⠀⠒⠰⠆⠀⠀⠀⠀⠀⠀⡀⠐⡠⠒
⠀⠀⠀⠀⢠⠀⠄⠄⠀⠄⢰⡆⠆⠀⠀⠀⠀⢰⠤⠀⠒⠐⠒⣀⣈⣀⣀⠀⠀⠀⠀⠀⣤⠈⠀⠀⡀⣀⣤⠽⠞⠛⠀⠀⢰⠁⠀⠑⠀⣄⡀⠀⢀
⠀⠀⠀⠀⢸⣄⡀⣀⣀⣰⠀⣿⣤⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢀⡜⢁⡠⠴⠞⠋⠁⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢉⡐⢀⠀⢰
⠀⠀⠀⠀⢀⠁⠀⣿⣿⣿⠀⣿⡿⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠘⠳⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣀⠐⠁⠐⣈⣴⡿
⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠰⠋⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤⠼⠿⠿⠟⠃⠀⠀⠸⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠄⠀⠀⠠⠿⠛

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢈⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠚⠻⣦
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⢸⣿⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠐⠋
⠀⠀⠀⠀⠀⠀⠀⣾⡁⠁⣹⡆⠉⠈⢥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠠⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣷⣷⣷⣶⣾⣓⣲⣤⣄⡀⠀⠃⠀⠀⠀⠀⠀⣀⣀⣤⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠾⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠒⢀⡀⠀⠀⡿⣿⠷⡇⠀⠀⡀⠐⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡿⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡷⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢠⠖⠒⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡧⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⣶⣶⡷⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⡀⠈⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣷⡘⢿⡡⠂⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⣆⢸⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣉⣙⡙⠻⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⡿⠆⠙⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠈⠉⠁

⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣃⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⢀⣀⣤⣀⣾⣿⠿⠛⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣠⣴⠟⢣⣠⠟⠀⠀⠀⠀⠀⠀⠉⢨⡛⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡟⠻⠿⠟⠻⣋⣠⡤⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⡍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠠⣇⢀⣀⡀⢀⣿⡇⠀⠀⡤⠋⠀⣴⣶⣷⣦⡾⠟⠂⠀⢀⡐⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⣿⣿⣷⣁⣿⣇⣤⣴⣿⢂⣤⣾⠟⠛⡛⠛⡀⢀⡀⠌⠙⢀⣇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⣿⠿⠿⢛⣿⢿⡏⠀⠺⣿⣿⣷⣦⣤⣶⣿⢃⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⡿⣿⠸⡆⢹⠀⡆⣬⣴⢾⣿⣶⣇⠸⣿⣿⣿⣿⣿⣟⠂⢀
⠀⠀⠀⠀⠠⠄⠦⢤⡀⣧⠀⠀⢸⣰⠃⠀⠀⠋⢀⡏⢸⡿⡹⣏⢀⣼⡇⠻⠙⣣⠀⣿⣻⣿⣿⣿⡀⠋
⠀⠀⠀⠀⠀⠈⠒⠀⠀⢿⡆⠀⢋⡌⠀⠀⠀⠂⠀⢷⠀⢿⡇⣿⣿⣽⣇⠀⢀⣾⡄⣿⣿⣿⡭⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣄⢾⣿⣤⠀⠀⠀⠀⠀⢠⡀⠻⣭⣙⠿⢿⡜⣿⢷⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠁⠉⣠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠄⠀⠀⣉⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠋⠂⠸⠎⠁⠀⠀⠀⠀⠀⠀⣦⣸⡿⣿⣿⣿⡛⠓⠒⢀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡧⠤⠀⢠⠤⠀⠀⠀⠀⠀⠀⠙⠟⣿⡟⢻⣿⣵⣿⣿⢏⠛⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⢠⠁⢀⣿⣦⣤⡦⠤⠄⠀⠀⠀⠀⠀⠀⠀⡾⠛⢯⣘⠝⢋⣿⣓⣠⠶⠞⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⢠⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⢀⡀⠿⠿⢻⠻⣯⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠈⠀⠙⠂
⠀⠀⠀⠀⠀⡀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡦⢝⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠂⡀⠸⡆⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠄⠀⠀⠀⠀⠡⡀⠀⠀⠉⢧⡀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠂⠤⠀⠀⠳⠆⠤⠀⢀⡀⠀⠀⠙⠦⠀⠀⠀⢳⡀⠀⠀⢰⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⡀⡄⢀⠄⠊⠉⠁⠃
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠰⡌⢠⡀⠒⠉⠠⠀⠀⠀⠀⠂⠀⠀⠀⠈⠳⢤⡀⢳⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠁⣠⡞
⠀⠀⠀⠀⠒⠀⠀⢀⠈⢁⡄⢸⠃⠀⠀⠀⠈⠀⠀⠀⠤⠤⠤⠒⠀⠀⠀⠉⢻⣧⣰⡄⣠⠴⠚⠻⠛⠒⠒⢤⠀⠀⢀⣿⡘⠟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠠⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣴⠃⠀⢲⠈⠀⠀⠀⠀⠐⠶⢾⣷⣤⣀⣀⣀⣀⣀⡜⢋⡀
⠀⠀⠀⠁⠀⠀⢠⡶⠟⡆⠀⠀⢂⡀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣭⣭⣭⠛⠃⠈
⠀⠀⠀⠀⠀⠀⠈⡂⠈⢱⠄⠀⠈⢣⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡿⢿⣝⢁
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠻
⠀⠀⠀⠀⠀⠀⠈⠁⡀⠈⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⢦⡀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢼⣿⡧⠄⠀⠐⠊⠃
⠀⠀⠀⠠⣒⣁⠰⠃⢀⡠⠄⠀⠀⠀⠀⠀⠀⠄⠀⠸⣿⣇⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⠆⠀⢤⡀
⠀⠀⠀⠀⠋⠈⠉⠁⠲⢄⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⡎⣿⣿⡀⠈⠀⠀⢪⠉⣲⡄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠻⣿⣧⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⡀⡀⠀⠈⠲⡏⠀⠀⠙⢿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄⠀⠀⠠⠈⡀⠀⠀⠀⠐⠂⠈
⠠⢴⠀⢰⠒⠰⠢⣀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⣾⣿⣿⣿⣷⣶⣶⣿⠃
⡲⠚⠛⠉⠐⠒⣄⠉⠒⠀⠀⠀⠈⠉⠉⠉⠁⠁⠀⠀⠙⢿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠠⠄⠀⠖⠠⢠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢠⠈⠀⡰⠁⠈⠙⠀⡀
⠀⠀⠀⠀⠀⠀⡾⢭⠹⢸⡁⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋⠉⠁⠐⠓⠠⢆⠀⠠⢐⡀
⠀⠀⠀⠀⠀⣾⢿⣕⣐⣨⣿⣿⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⣀⢤⣀⠤⠤⡀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢳⣀⠠
⡿⠊⠀⠀⠀⠙⠷⣦⠴⠶⣿⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⡴⡎⣀⣄⣄⣵⣬⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⢿⣷⣤⠤⠀⠀⠀⠀⠀⢀⡽⠛⠉⠉⠉⠙⠛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛
⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢾⡀⢠⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⡀⠂⣀⣀⣤⡾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠒⠂⠉⠁⠙⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢀⡀⢀⠄
⠀⠀⠄⠤⠤⠤⠤⢤⣀⣀⠀⠀⠰⠀⠀⠀⠀⠀⠺⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⠊⡁⠁⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⠿⠿⣿⣿⣿⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⠿⠟⠛⢋⣩⣵⠶⠟⠛⠛⠛⠛⠷⠶⣤⣀⠀⠀⠉⠉⠙⠛⠻⠿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠛⠋⠁⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⠀⠀⠀⠀⠈⠙⠷⢦⣤⣀⣀⣀⣀⣀⣠⣤⡶⠟⠋⣀⣠⣤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⠶⠶⠤⣤⣤⣤⣭⣭⣭⣭⡭⠷⠶⠶⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⢤⣴⣤⢦⣄⡀⠀⠀⢀⣠⡿⢧⠈⡷⣠⠟⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⣿⡟⣾⣇⣿⢦⣍⣵⠀⢠⣿⢻⣏⠦⣈⠀⣾⣀⣉⣀⡀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠌⠑⠢⡀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⢰⠙⠋⠉⠉⠀⠀⠻⣿⣿⡀⠘⣿⣦⡉⠛⠶⢾⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⣷⣄⣑⠂⠄⠀⠀⠃⣠⡇⠀⠀⢸⡿⢿⢻⢛⣿⢿⢿⠅
⠀⠀⠀⠀⠒⠀⠀⠀⣀⠄⢱⠀⢸⣼⠃⠀⡰⠛⠛⠻⠿⣿⣿⡿⠤⠤⠄⠀⠀⠊⠂⠀⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⠀⠀⣾⡗⣚⡂⢼⣿⣼⣇
⠀⠀⠀⠀⢘⠀⠀⡈⢰⠁⡮⠀⢸⣿⠇⠀⡁⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣧⣼⣥⣤⣽⣿⣾
⠀⠀⠀⠀⠘⢀⣀⠀⡈⠈⢀⠠⠾⠋⠀⠀⠁⠠⠄⣀⠀⡈⣿⣿⣧⣀⣤⠀⠄⠊⠀⠀⠙⠿⣿⣿⣿⣿⣿⡿⠛⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣽⡿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠚⣡⠠⡿⢥⣿⣿⣟⡀⠀⡲⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠋⠉⠀⠂⠀⠀⠉⢿⣿⡇⠀⠀⢸⠀⠈⠀⢀⠠⣾⣿⣿⠄⠀⠎⠩⢀⡀⠙⡤
⠀⠀⠀⠀⠀⢰⠤⠴⠖⣿⣿⣿⠒⠒⠒⠒⠒⠒⠋⠛⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠘⣿⡇⠀⠀⠘⢶⠞⠁⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠘⡇⠑⢄⠂
⠀⠀⠀⠀⠀⢸⡀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⢄⠀⠀⢔⢀⠌⣼⡟⠀⠀⠀⠀⠸⡀⠀⠀⠀⠹⣿⣿⣇⠀⠀⠀⠀⡰⠁⠘⢼⡖
⠀⠀⠀⠀⠀⠈⠓⠠⠀⠈⣿⣿⣧⣀⠀⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠓⠀⠦⠀⠹⠿⠿⠆⠀⠐⠈

⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣶⡄⠀⠀⠀⠙⠻⠿⣿⣿⣿⣶⡀⠀⠀⠙⠻⠿⢿⣿⣶⡀⠀⠀⠀⠀⢠⣾⣆⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠇⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠾⣿⡿⠄⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⠀⠀⣠⣤⠄⠀⠀⠀⠀⢀⠀⠀⢀⣤⡤⠀⠀⠀⠀⠀⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⣤⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠈⠙⣿⡿⢥⣄⣀⡄⠀⠀⠀⠈⢻⣿⠯⢤⡀⠀⠀⠀⠀⠈⢹⣿⠿⠿⣿⣿⡆⠀⠀⠀⠈⠙⣿⡿⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣀
⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣐⣖⡸⢶⡶⡇⠀⠀⠀⠀⠀⠀⣀⡈⠹⣿⣧
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⠿⡿⣷⣯⣵⡆⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉


⣿⣿⢟⠿⠛⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡔⠀⣀⠄⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⠈⠀⠐⠂⠃⠀⢀⠠⠄⠐⠤⠄⠈⠡⠂⠠⠀⠂⠀⠀⢠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠴⡤⠈⠁⠀⡀⠢⡀⠀⢠⡀⢈⠀⠀⠀⠰⠀⠀⠄⠐⠀⠁⠀⢤⠁⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠱⠄⡔⠀⢠⠀⢀⠤⠆⠀⢰⡈⢂⠈⠉⠀⠂⢀⠄⠈⠀⠀⠀⡀⠀⠀⡀⠁⠀⢀⣦⠠⠈⠂⠄⠐⠁⠀⠀⡅
⠀⠀⠀⠀⠐⠂⢰⠀⠀⠤⠬⠤⡀⢀⠒⠪⠀⠁⣐⡀⠁⣀⠤⠀⡠⠀⢈⡉⠈⠃⠀⣠⢀⠀⠈⠀⠐⠒⠗⠒⠀⢈
⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠰⠀⠁⢀⡀⣄⠀⠚⠙⡁⠀⠀⣐⣖⢈⠀⢄⠊⠑⠂⠙⠉⠃⢠⠀⠀⠀⠀⠶⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⣔⡁⠔⠈⡂⢐⠀⠀⠀⠉⠀⠁⠀⠀⠈⣄⠀⠀⠀⠀⠀⠺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⢀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⢀⠀⢀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡀⠸⠀⡄⠀⠀⠀⠀⡀⠐⠀⠐⠀⠀⠀⠐⠒⠂⠄⢀⡀⠀⠀⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢇⠀⠒⠀⠀⠐⠄⠀⠀⢀⠖⠀⠠⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠄⠀⠂

⣿⣿⣦⣀⣈⡧⢳⣟⠓⢧⠆⠉⣾⠻⣷⣿⣿⣿⣷⣽⣯⣯⠉⠀⠸⠏⠰⠀⠻⠈⠛⠈⠋⢿⣶⠼⠃⠀⡟⠀⢸
⣿⣿⣿⣿⣿⣶⠮⢍⡀⠈⠙⠆⠸⠛⠻⣚⣻⣿⣟⣝⡶⢿⣳⠉⠁⣯⣤⣀⠒⠀⠀⠀⠀⠈⡏⠀⠘⠠⡄⠔⢋
⣿⣿⠟⠛⣳⢾⣿⢸⢟⠖⠂⠀⠁⢸⡟⠯⠉⠛⠉⠉⠛⠃⠀⠰⠏⠛⡿⡻⡡⢀⠂⠄⠀⠢⠠⠀⢁⣠⡷⠖⠛
⣿⣿⣿⣿⣧⣼⡿⣛⣋⣴⠶⢀⣘⡓⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⡞⠀⠋⠁⠰⠆⣠⠀⠑⢰⡄⠠⠀⠸⠁⠀⠰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢤⠟⠘⠁⠀⠙⣓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡅⣿⢸⠃⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣁⣼⣴⡶⠀⠀⠀⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⣶⠞⡿⣵⣿⢿⡇⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣴⣷⠀⠀⠀⠈⣅⡀⠀⠀⠀⠄⠈⠁⢄⠒⠋⠸⡆⠉⡟⠁⢀⠀⠀⢀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣭⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⢀⣄⢤⠋⠁⠃⠀⠀⠀⠀⠀⡽⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⡴⣢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⠴⠠⠄⠀⠀⣀⠀⠀⠚
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⣾⠁⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠀⠈⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣧⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⣰⣿⣅⣸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠏⣡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣬
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡶⡟⠃⣄⡀⠀⠀⠀⡶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠗⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⠿⠶⠀⣷⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⠏⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣰⢉⣶⣴⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠰⢤⣼⣿⣭⣿⡗
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⠀⠀⠀⠀⠀⠀⣨⠚⢻⣣⣾⠿⠅
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⡠⠬⠍⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠙⢻⡛⠫⠭⡄⠀⠉⠉⠛⢦⡀⠀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣶⡏
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠳⢄⢀⣀⣀⡀⠙⣔⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⡴⣫⠽⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠸⣄⠹⡉⠉⠳⠏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣰⣯⠞⠃⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠈⣹⠧⠤⠀⠀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠠⠟⠁⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣹⣾⡧⠤⠶⠊⠉⠳⢌⡢⣀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠠⠤⠵⣌⠣⣰⠋⠀⠀⠈⣦⢊⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠠⠤⢤⡄⣀⠀⠀⠀⠈⢳⡹⡀⠀⠀⠀⣡⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡄⠀⠱⡣⠀⠀⢱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢳⢃⠀⣯⡀⠀⠀⠀⠀⠀⢀⣀⠴⠞⢩⡄
⠀⠀⠠⢖⡈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠂⠀⠤⠤⣀⠀⠘⣆⠀⠆⢷⠀⠀⠀⠀⠀⣀⡤⠉⠁⠀⠀⠈⣧
⠀⠀⠀⠀⠉⠓⠺⢏⡉⠚⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠘⡄⠸⢰⡄⠀⠀⢀⡴⠉⠀⠀⢀⡤⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢷⣄⡀⡀⠀⠀⠀⠀⠀⢀⣄⣀⠑⣷⠀⠀⡁⠀⣰⠊⠀⠀⢰⣠⠋⠀⠀⠀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠶⠦⡴⠶⠚⠉⠁⠀⠀⠈⠑⣆⠃⢠⠇⠀⠐⣄⠜⠁⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠚⠺⣄⣀⣀⣘⠁⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⠋⠀⢀⣀⣀⠀⠀⠉⠁⠉⠙⠳⣄⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠉⠉⢲⠓⠿⠖⠛⠉⠉⠉⠙⢲⣀⡠⠤⠤⠤⢈⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠞⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⠉⠀⢀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⡠⠦⢤⣇⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⢸⠀⠀⠀⣀⡀⠀⠀⠀⣼⢡⡗⢪⡥⠰⣭⡏⡀⢀⡠⠆⠀⠀⢠⣴⡃
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠸⡄⠀⣠⠇⠉⠳⣤⡾⢻⣄⠳⢮⣁⡶⠋⠻⡴⠋⠀⠀⠀⠀⠀⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣼⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣆⠿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⢧⢀⠠⠄⠐⠦⣼⠁⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠖⠒⢶⣄⠀⠀⣠⠤⠶⠃
⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠛⣀⡴⠋⢀⡴⠛⢇⠀⠀⢸⠋⠓⢦⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⠀⠀⣠⠽⠛⡶⠚⠉⠉⠀⠀⣠⠏⠀⠀⠀⠉⠚⠃⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠑⠦⠤⠤⣄⣀⠀⠀⠀⠀⠈⣹⡟⠁⠀⢈⡴⡶⠦⠤⠖⢛⠣⢄⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠙⠒⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣀⣀⣤⠞⠩⠭⠭⢭⡷⢦⣄⣀⣀⣀⣠⠴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡃⠀⠀⠀⠀⠈⠢⠁⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢲⣤⣄⡀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠂⡕⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡠⠀⠙⢿⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣧⠀⢀⠄⠁⠀⠀⡇⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡐⢀⣙⣬⢿⡾⠂⠀⠀⠀⡻⠀⠂⠐⠓⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣜⣩⢁⣄⠈⠁⢤⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠡⡄⠀⠉⠓⠲⡞⠁⠂⢀⠈⠲⠀⠤⣄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⡀⠀⠘⠢⣄⠀⠀⠉⢢⡀⠈⠐⠄⠀⠀⠈⡏⠀⠀⠀⠀⠞⠀⠀⠀⠆⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠀⠀⠀⠃⠐⠀⠀⠉⢀⠀⠀⠙⢧⠀⢀⠰⢐⡀⠀⢠⠀⠀⠀⣘⢼⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠥⠃⠀⠀⠀⠐⢖⠒⠀⠈⢂⠀⠀⠀⠀⠀⠱⡋⢴⡀⢠⠀⡀⠐⠚⠂⢀⠀⡀⠈⠀⠠⣆
⠀⠀⠀⠀⠀⠀⠄⠀⢀⠄⠀⠐⠂⠀⠀⠀⠀⠡⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⠈⠙⢿⠀⠁⠀⠀⠄⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠔⣚⠈⣠⣘⠖⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠄⣈⠂⣀⣀⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⢉⡩⣬⠅⠚⡂⠀⠁⠀⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡿⠧
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠺⠈⠉⠉⠁⣀⣤⠴⠖⠒⠒⠚⢱⣄⠀⠀⠀⠀⡶⢲⣤⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠊⠀⠀⠀⣠⠄⠀⠀⠉⠙⠂⠤⠀⠀⠇⠺⠊⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠊⠀⠀⠀⠀⠐⢱⠃⠘⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡴⠐⢢⡆⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠚⡁⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠉⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠟⠶⢯⠁⠒⠀⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠠⡀⠑⠊⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⢬⠃⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠡⠄⢠⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠠⠀⠦⠠⠴⠤⣁⠀⠀⠀⠀⠀⢀⠤⡆⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢻⡉⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇⠀⢸⡗⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠐⢄⠘⡇⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡿⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠆⠀⠘⢷⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠉⢠⠏⠀⢀⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠐⢀⠀⠸⣇⠀⠀⠀⠀⡀⣿⡄⠀⠀⠀⠀⠀⣤⣶⠿⢉⠀⠀⡎⠀⠔⠋⢀⡄
⠘⣷⠶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠁⠢⢻⡇⠀⠀⢀⠀⠈⡇⠀⠀⠀⢠⠈⠐⠁⡠⠂⠀⢰⡇⠀⢀⡠⠊⠇
⠀⠘⣷⡀⠙⢿⣍⠀⠈⠓⠖⠦⢄⣀⠀⠀⠀⢷⣣⡡⡀⠀⠈⠻⣶⠀⡜⠀⠀⡇⠀⠀⢀⠇⠀⠀⢀⠁⠀⡀⣟⠀⠒⠁⠀⠀⠃
⠀⠀⠿⣷⠀⠀⠙⢿⠂⠀⠀⠁⠢⡈⠳⣄⠀⠈⢳⣄⠱⡀⠀⠀⠘⣴⡇⠀⢀⠃⠀⠀⣸⢀⠀⡠⠘⢀⣰⡞⠁⢀⠄⢀⠀⡜
⠀⠀⠀⠻⡄⠀⠀⠀⢷⡀⠀⠀⠀⠈⢢⡈⠳⣄⠀⠙⢿⡌⠂⢢⡀⢹⣤⠀⡎⠀⠀⠀⢣⢸⣠⡇⣰⣿⠏⢀⠐⢃⡴⣫⠞
⠀⠀⠀⢂⠈⢆⠀⠈⠉⠳⣄⠀⠀⠀⠀⠱⡀⠙⢦⠀⠀⠙⢆⡚⠢⣼⣿⡼⠀⠀⠀⠀⠘⣿⣿⣿⡿⢛⣩⠴⠞⢋⡔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠈⣧⠀⠑⢄⡀⠀⠙⣦⠀⠀⠀⠀⢧⠀⠀⢣⠀⠀⠀⠉⠓⢾⣿⠇⠀⠀⠀⠀⠀⣸⠿⠿⠿⠷⠖⠒⠊⠁⠀⠀⠀⠀⢀⣀⡠⠤⠤⣤⣶⡶⢛⣿⠋
⠀⠀⠀⠀⠸⡆⠀⠀⠉⠑⠀⠀⢳⣄⠀⠀⢸⠀⠀⠈⡇⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⢊⠅⠀⠈⠀⣠⣶⠟⠉⢠⡾⠃
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢸⡇⠀⠀⢻⠀⠀⠀⠀⠀⢸⡆⠀⢀⡾⠋⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⣠⠔⠁⠀⠀⠐⣩⠟⠀⠀⠀⢾⡏
⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⢄⠀⠀⠀⠀⠈⠳⣿⣄⠀⢸⠀⠀⠀⠀⠀⢸⡇⣰⠟⠀⠀⠀⠀⠀⣠⡴⠏⠁⠀⢀⡜⠁⠀⠀⠀⢀⡾⠃⠀⠀⡠⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠈⠶⣄⠢⣝⢦⣄⠠⢤⣤⡝⣿⣾⣖⡄⠀⠀⠀⠀⢸⡷⠃⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⡎⠀⠀⠀⢀⡴⠛⠂⠀⠒⠉⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠁⠪⠉⠓⠶⢤⣭⣙⣿⣧⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⣸⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⠔⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠙⠒⠶⠤⠤⠶⠒⠛⠛⠿⣷⡀⠀⠀⢸⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣾⣀⠞⠛⠀⠤⠤⠤⠤⠔⠚⠡⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢸⠀⠀⠀⠀⠀⡧⢸⠆⡴⢀⣤⣤⠿⠋⠀⠀⠀⠀⠀⢀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢸⠀⠀⠀⠀⠀⣇⢘⣶⣿⣾⣿⡥⣄⣀⣠⣀⣄⠤⠖⢁⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡆⠙⢿⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⡆⠀⠀⠀⠀⠘⣾⣿⣿⣯⣤⣖⠀⠀⠀⠐⠂⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡀⠈⠳⣄⠑⠝⠳⣶⣤⣄⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⢀⣾⠟⠁⠀⠀⠈⠉⠛⠒⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠸⣦⠀⠑⠀⠈⠋⠑⢄⠀⠀⠀⢸⡇⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠘⢷⣄⢀⠀⠀⠀⠈⢆⠀⠀⢸⡇⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠒⠤⣀⣤⠝⢿⣶⡀⠀⢶⡜⡄⠀⢸⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⡀⠀⠀⠀⢹⣿⣷⣿⣿⡇⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢯⡛⠛⠒⢩⠾⠛⠛⠷⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣿⠀⢹⠀⠰⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡏⡻⠇⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣃⣁⣠⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠛⠋⠀⠀⠀⠙⠦⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⡀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⠂⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣿⣿⣇⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢿⣿⣦⡀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⣿⢿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⢿⡌⣿⡋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⢸⣧⢸⣷⢃⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⢸⣿⢸⣿⢸⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢸⣿⣸⡟⣸⣯⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣸⣿⣿⢇⣿⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⣿⡇⢿⣸⣧⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⢿⡈⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠟⣿⣿⣈⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⣿⣏⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣿⣿⣿⡿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⣿⣿⣿⣿⣹⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢹⣿⢿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⢯⣿⠿⣿⣿⣿⢿⡏⣿⣜⢿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⣱⣿⠏⣾⣿⢸⣿⣿⣿⢸⣷⠘⣿⣏⢻⣿⣿⣿⡿⣿⣿⣿⣿⣷⣤⣀⡀
⠀⠀⠀⣤⣤⢀⣤⣤⣴⣦⣶⣾⣿⣿⡿⢛⣥⣾⣿⠏⣼⣿⡏⣾⣿⣿⣿⡄⢿⣧⠸⣿⣷⡹⢿⣿⣿⣯⣻⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄
⠀⣴⣶⣿⣶⢾⣿⣿⣿⠿⠿⠟⢋⣭⣶⣿⣿⣿⠋⣼⣿⣿⠇⣿⣿⢻⣿⣇⠸⣿⣆⠹⣿⣿⣦⡻⣿⣿⣿⣾⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣀⣤⣦
⠀⠉⠛⠛⢿⣿⡿⢿⣿⣤⣶⣾⣿⣿⣿⣿⡿⢃⣾⣿⣿⡿⢸⣿⣿⢸⣿⣿⡀⢿⣿⣆⠹⣿⣿⣷⣌⡻⣿⣿⣿⣿⣮⣻⢿⣿⣿⣿⣿⢿⣷⣟⢧⣄⡀
⠀⠀⠀⠀⣾⡿⢷⣤⡉⠛⠟⠋⠉⠑⠈⠟⣡⣿⣿⣿⣿⠇⣾⣿⣿⢸⣿⣿⡇⠘⣿⣿⡄⠸⣿⣿⣿⣷⣬⡻⣿⡟⣩⣿⣦⣬⢿⣿⣥⣿⣿⡟⠀⣹⠃
⠀⠀⠀⠀⢻⣧⡄⠙⠿⣷⣶⢿⣶⠀⢠⣾⣿⣿⣿⣿⣿⢰⣿⣿⣿⠘⣿⣿⣿⠀⢹⣿⣿⡄⠘⣿⣿⣿⣿⣿⣯⠘⣿⣟⢠⣶⣆⠀⠀⠘⣿⡆⠺⠟
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠙⢻⣦⣄⢀⣼⢿⣿⣿⣿⣿⡇⣾⣿⣿⠿⡀⣿⣿⣿⣇⠀⢿⣿⣿⡄⠘⢿⣿⣿⣿⣿⡇⣿⣿⠀⢉⣿⡟⠛⠛⢛⣡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢇⣈⣿⣦⣭⣛⣻⡟⢘⣿⡿⠝⢢⣤⡄⢠⣶⣏⠀⠈⣿⣿⣿⡄⠈⢿⣿⠿⠟⢠⣿⡿⠀⠿⣯⣽⣆⣠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣯⣝⠻⠿⠿⠿⠛⢉⣤⣤⡾⠿⢷⣎⠉⣛⣿⣿⣿⠉⠛⢷⣄⠠⠿⠐⠾⢷⣤⣀⣤⣾⡟⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠻⢿⣶⣾⣿⠿⣿⡿⠿⠄⠀⠻⠿⠿⢛⣻⣏⡉⣀⣠⣤⣠⣄⣀⣠⣴⣾⡧⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠋⠁⠙⠛⠻⠟⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢋⡤⠒⠂⢀⠀⠀⢙⡆⠀⠀⠀⠀⢀⣠⠔⠚⢉⠀⠀⠀⡉⠉⢑⠀⠀⠀⠀⢀⣤⣴⣶⣮⣍⣉⠉⠒⢤
⠀⠀⠀⠀⠀⢀⠎⣀⠈⠁⠀⢀⢀⣨⠇⠔⡊⢠⠀⠀⣠⡖⢩⠀⠀⠀⠀⡨⠖⠈⠀⠀⠁⠀⠀⡠⠂⠉⠉⠉⢛⠤⣀⣀⣱⡆⠈⢱
⠀⠀⠀⠀⣠⣧⡊⢀⡰⠆⠒⡉⡠⠀⣀⠬⠐⠁⠀⢰⡡⠄⠒⠒⡠⠔⠉⠀⠀⢀⣁⠔⠀⠀⢸⡁⠀⠀⢀⠔⣡⠤⠺⣿⣿⣿⠔⠉
⠀⠀⠀⡜⠘⣡⠞⠲⠤⣌⠭⠉⠒⠉⠀⠀⠀⠀⠀⠸⣉⠒⠒⠩⠄⠀⢐⡮⠔⠁⠀⠀⠀⠀⠘⢆⠉⠀⡉⠉⠀⢀⡘⠿⠛⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠛⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠤⣞⣩⠊⣙⣯⠵⡤⢄⠀⠀⠀⠀⠀⢀⡴⢉⡯⢥⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠠⠤⢤⣴⣀⡀
⠀⠀⠀⠀⠀⡴⢳⡴⣏⡠⢏⣀⡽⢤⠚⠚⡄⠀⠀⠀⠠⣾⠀⠊⣀⣠⢥⡴⡗⠲⠦⡀⠀⠀⠀⢀⣤⡄⡀⢠⣙⣃⠨⡀⠽⣃⢠
⠀⠀⠀⠀⠀⠑⣾⣀⣸⣀⣀⣽⣄⣠⠶⡞⠀⠀⠀⠀⢠⠛⡚⠿⢸⢉⣳⡾⠢⢤⡈⠀⠀⠀⠀⢀⠝⣶⣾⣵⣮⣷⣬⣥⢲⣮⠞⠳
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠄⠀⠇⠀⠀⠀⠈⣈⠂⡘⠦⠊⣎⣠⠓⢀⡾⠁⢠⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⡄⠸
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⣀⠀⠀⠀⠀⠀⠈⠁⢧⡐⠀⠓⠛⠉⣁⡤⠒⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢴⡶⣿⣿⣿⣟⣿⣿⡶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⢻⣾⣿⣿⣿⣾⣿⣿⣧⣶⣿⣿⣿⣤⣦⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣽⣧⡀
⠀⠀⠀⠀⠀⣴⢺⡗⢊⣻⣻⣷⡋⡭⡝⣿⡎⣿⣿⣿⣿⢸⣿⢫⣶⣾⣿⣿⢿⣷⣥⣦⠙⠲⡄
⠀⠀⠀⠀⣠⣯⣿⣷⣮⠽⢩⡻⢷⡩⣶⣿⣷⣸⣭⣿⣿⣿⣿⣌⣛⣿⡿⣡⣿⣿⢙⣿⣷⣖⠘⡆
⠀⠀⠀⢀⣼⣿⣿⡿⢿⣜⢶⣿⣶⡿⣿⣿⣿⣿⣿⣽⣿⣿⣟⣿⣻⣿⣿⣿⣿⣵⣿⡿⣿⠿⣿⣷⣆
⠀⠀⢀⣿⣿⠫⡿⠿⢦⣙⣿⣿⡿⢿⣿⣿⣝⣿⣙⣽⣽⣯⣿⣿⣽⣿⣿⣿⣿⠿⣟⣙⣿⣿⣿⣽⣏
⠀⠀⡸⣻⣿⣷⣶⠿⣂⣿⣿⣟⣿⣿⣿⣿⠛⠛⢻⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡆
⠀⠰⣿⠹⠟⣹⣿⠟⠿⡟⣻⣿⡻⡤⢾⣿⡇⠀⣿⣿⣯⠀⠰⣷⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣍⣟⣛⡧
⠀⠀⠈⠉⠓⠈⠀⠈⠹⠚⠏⠃⡐⠀⣸⣿⡇⠀⣿⣿⣿⣿⢶⣄⠙⢿⡇⠀⠘⠏⠉⠙⠙⠛⠋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡋⠉⠣⠿⠀⢸⡇
⠀⠀⠀⠐⣁⣀⣰⣖⣒⢑⡐⠒⣲⡷⠋⠃⢠⡤⠼⠙⠿⢦⣄⡠⣴⣛⣟⣤⣤⠤⢠⣀⣀⡀⠀⠀⢀
⠀⠀⠀⡂⢇⡀⠀⠀⢠⢸⠉⠀⡵⠀⢖⣒⠈⠘⠀⣔⠒⠊⠸⠀⠤⢌⢀⠀⢁⠖⢆⠁⢹⠑⣄⡰⠁
⠀⠀⠀⠇⡰⠒⠃⠀⢀⠀⣀⢰⠁⡀⡤⠐⠀⠀⡀⣠⠌⠀⠈⠀⡀⢈⠄⠄⠈⠀⠸⢀⠀⢰⣈⣤
⠀⠀⠀⡀⠠⠀⠀⠀⢐⢐⠀⠄⡆⣀⠘⠒⢂⠀⡇⠑⠂⠀⢰⠀⠓⢊⠀⠐⢄⠀⢁⠄⡀⡸⠈⢐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⣁⡀⠀⢀⡀⠀⠰⠤⠀⠁⠀⡤⠀⠐⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⣠⠆⣸⡟⠁⠄⠀⣨⡀⠉⠂⢄⣀⠶⠛⠁⠁⠀⢀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠐⠋⢀⠀⠼⡀⠛⠁⠶⢢⣄⣻⠠⡤⠶⠂⠋⣒⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⡡⣠⢈⠀⠀⠀⠄⠀⠀⠈⣆⣀⠐⠃⢠⡆⣀⠉⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⡖⠁⠉⠀⠀⣤⠌⣁⣰⢿⣏⢛⢂⡐⢉⠈⠉⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡠⠚⠛⠉⠂⠶⠀⠁⢨⡺⡏⠀⠘⠆⠑⢀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⣾⣿⣤⠈⠁⢠⠃⠀⠀⠀⠀⢘⠀⠀⠀⣢⠟⡤⠳⠄⠁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠛⠂⠀⠀⠘⠀⠀⠀⣀⢀⡉⠀⠀⠀⠑⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠷⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⣦⠄⣸⠿⣍⠛⢢⡀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡈⠉⡟⡄⡆⢸⠀⠀⡛⡉⢬⠁
⠀⠀⠠⣖⣀⡾⡵⠊⠀⠀⢰⣇⠑⠈⠲⠀⣠⠿⠛⠁
⠀⠀⠀⢺⡞⢱⠁⠀⠀⠀⠈⣧⠀⠀⢀⡐⠁
⠀⠀⠀⠈⠁⢸⠀⠀⠀⠀⠀⢸⣆⡼⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⢀⠃⢳⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠀⡀⠠⠄⢈⠓⣾⠄
⠀⠀⠀⠀⠀⠀⠹⡄⢀⡀⠀⢀⠌⢷⡇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡤⢤⣀⣀⣸⣯
⠀⠀⠀⠀⠀⢀⣀⣉⠙⠖⣤⢸⡤⢻⣷⠂⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠴⠂⠖⣭⣤⠉⣀
⠀⠀⠀⠀⠀⠈⠉⣿⠁⡙⣿⣝⡧⠊⢹⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠙⠉⠀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠠⠞⣛⣿⠧⣥⡅⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⣄
⠀⠀⠀⠀⠀⠠⠖⢘⣉⣠⠖⠀⠙⣼⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠉⠽⠥⡰⠄⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⣀⢀⠀⠀⠘⠓⡆⠀⠀⠀⠀⢿⣟⠚⠇⠄⢀⠤⠢⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡟⠁⣀⣀⣀⣠⣠⣄⡀⠀⣠⢤⢾⡗⠤⠒⠘⠃⠀⠀⠀⡀⠁⠃⠠⠴⠧⣦⡄⠈⣀⠀⠀⢀⡤⠚⣉⡳⠄⡦⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠕⠂⡟⠓⣹⠌⣶⢫⡉⠈⣟⠛⠲⢤⠜⢠⣊⡡⠐⠃⢘⢆⠏⠀⠀⠠⠀⠀⠀⠁⠈⠉⠁⠑⠻⡦⢤⠤⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠈⢷⠘⣡⠀⢻⡆⠉⡻⠟⢦⣠⠖⠙⠀⣫⡁⠳⡾⢆⡉⠄⠀⠀⠀⠀⣞⠀⠃⠀⠀⡠⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⢡⣀⡼⣅⡹⠏⢁⠽⢷⣌⠒⠈⠓⠉⠀⡃⠺⣯⣀⡔⢀⠀⠀⠈⠳⠚⠟⢧⡄⢀⢀⡵⣾⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠋⠉⠉⠁⠀⠀⠄⢘⣤⠇⠠⡊⠡⢄⠀⢡⡀⢀⠂⢀⣠⡇⠐⠤⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠉⠲⠤⠬⢵⡟⠣⠋⡈⠉⠹⡄⣀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢀⡀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⢠⣾⡞⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⢿⡟⢷⠀⠀⠠⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣈⡄⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⠄⠀⠀⠰⡾⢯⡭⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠛⠠⠤⠶⠶⠂⠶⠶⠶⠦⠶⠆⠰⠶⠦⠄⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⢀⣐⠀⠀⠀⠄⠀⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠢⡂⠀⠀⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠱⣄⠀⠳⠀⠃
⠀⠀⠀⠄⠀⠀⠀⠉⠢⣤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠑⣴⣿⣿⡄
⠀⠀⠀⠀⠀⣴⣶⣖⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣺⡘⠁⠀⡿⠃⠀⠀⠀⠀⠠⠉⠛⢛⠁
⠀⣀⣀⣀⠀⠌⠉⡇⡸⠀⡔⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣤⡄⣤⠶⠚⠂⠂⠃
⠀⠁⠀⠉⠳⣄⠀⠑⠀⠀⢀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠄⠀⠸⠀⠀⠀⠠⠀⠙⠛⡟⠁⠀⠈
⠀⠀⠀⠀⠀⠈⠃⠄⠠⡅⠘⠁⠀⡃⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⠈⠀⠁⠀⠂⠠⣇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠠⠄⠚⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⡀⠿⠿⠂⠘⠀⠈⢻⠦⢀⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠎⠊⠈⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠠⠜⠐⠀⠈⠐⠂⠀⠀⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⡀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢿⣿⡆⠀⠰⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⢃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠⠃⠀⢠⠂⡀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⠀⠀⡄⠀⠀⠀⡄⠈⠀⠀⠀⠇⢀⡇⠀⠟⠄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠂⠀⠀⠀⠃⠀⢀⢊⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠢⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣼⡟⠀⠀⣠⣤⣷⡃⠁⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠚⡿⠻⠎⠁⠀⠀⠀⠀⠀⠀⠀⠴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⣁⡄⠀⢰⠁⠀⠐⠰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠿⢳⣦⠞⠁⠀⠀⢴⠛⠟⣾⡏⠀⢠⠆⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣽⣿⠟⠛⠀⠀⠀⢸⣦⣤⡤⠁⣴⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠚⠛⠛⠁⠀⠀⡜⢛⡟⢣⣀⣇⠀⠀⡞⠛⠉⠁⠸⠿⠛⠇⠀⠀⠀⠀⡀⣠⣆⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⢻⣋⠀⣼⠃⠀⠀⡼⠀⠀⢰⠀⠀⠀⠀⣰⣿⣿⠟⠻⣄⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠃⠀⠀⣼⠁⠀⠀⣾⠀⠀⢠⣿⣿⠿⡗⠀⠀⢸⣧⠀⠄⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣿⠀⠀⠛⠟⠁⢁⣀⣰⠀⠀⠡⠀⠀⠀⣈⠈⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢠⡀⠛⠆⠀⢀⡤⣚⣤⠄⠀⠀⠀⠀⢀⠃⠘⠋⠀⠀⠀⠀⢠⢀⣼⣿⠀⠀⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⣯⠀⠛⠃⠀⠀⠠⣏⠂⠈⠀⠀⠀⠀⠀⠀⢊⠛⠃⣠⣤⣼⣏⠻⠆
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢤⠐⢾⡆⠀⠀⣼⣦⢀⡀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠊⠀⠀⠀⣟⠈⠁
⠀⠀⠀⠀⠀⠀⠃⡐⠀⠀⠀⠀⠀⠀⠀⡄⠒⠾⡇⠀⠰⠏⠃⠸⡇⢤⣴⣧⣤⠶⠁⠀⠀⠀⠀⠀⠴⠀⠀⠀⣉
⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠰⣄⡇⠀⠀⡷⢂⡿⢋⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⢿⡀⠀⣧⡞⠁⠈⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⣿⡄⠿⠀⣼⣿⣧⠀⠀⠀⠀⠙⠀⣤⣤⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢤⠀⢸⢰⠀⡇⠉⣤⠀⣿⡿⢃⡀⢀⢛⡀⠀⠈⠻⠛⠛⠁⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣼⣟⠀⣧⠀⠉⠀⠘⡇⠘⣧⡾⢻⢻⠇⠀⣀⣠⠖⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢤⠀⠀⠀⠀⠀⠀⢻⡟⠂⣿⠃⠀⠀⠀⠃⣸⣀⣤⡘⣃⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣧⠀⣸⠄⡄⢀⣼⣾⡿⠻⠟⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⢿⢀⣿⣾⣿⡿⠟⠋⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠏⠛⠉⠉⠀⠀⢸⣼⢹⣯⣡⣶⣾⣷⣽⣻⣤⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢟⣀⠀⠀⠀⠀⠀⠐⠈⣿⢠⣿⠆⡈⣻⣿⣿⣿⣿⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁⠀⠈⠙⢶⣄⠀⠀⠀⢾⡏⢸⣿⡟⣹⣿⣿⣿⢹⡷⠾⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠙⢿⣆⠀⢸⣿⣩⡟⠀⠀⠀⠀⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢸⣿⠻⡇⠀⠀⣀⣀⣀⠙⠀⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣇⣤⣿⡿⠟⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠻⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣒⣒⠀⠀⠀⠀⢁⣴⣾⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⣾⠯⠛⠒⠑⠋⠛⠀⢰⡿⣩⣴⠶⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡋⠛⠀⠁⠀⠀⠀⠀⠀⠀⣠⠎⣔⣿⣭⣁⣼⣷⣄⡧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠈⠉⠀⢀⣠⠾⠵⠁⠂⡎⠉⠀⠀⠀⠈⠉⣷⣶⣯⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⡈⠉⡉⠉⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⢸⡐⠈⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣾⠗⢋⡔⠑⢂⣀⢀⣀⠨⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢙⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡔⢀⡴⠛⣠⣶⡿⢫⠀⢀⠀⠀⠀⠀⠢⠄⠀⠠⣖⣀⢁⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⠔⠫⠂⢜⡵⠃⠤⠂⠶⠻⠇⠀⠀⠀⠀⠘⠛⠃⠛⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠊⡀⠨⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡔⠳⠀⠀⠀⠀⠀⠠⠀⠤⠤⠂⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⢀⠰⠌⢠⠀⠐⠤⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠀⣦⢠⠐⠂⠀⠀⠂⠁⠛⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣤⡈⠈⠿⠀⠉⠋⠁⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠃⢠⠆⠄⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠋
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠄⣠⠾⠃
⠀⠀⠀⠀⠀⠠⠀⠃⡄⠀⠀⣧⠀⠀⠀⠀⠀⢈⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠘⠀⠀⠀⡀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⡧⠀⠀⢤⡖⢬⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿
⠀⠀⠀⠀⢹⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣷⣷⣦⠀⠀⠀⣀⡀⠰⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠁⢠⣤⠀⠀⠀⠉⠻⠿⢿⣿⣿⡧⠀⣶⣮⣅⢨⣅⢈⣃⡄⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠈
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠲⡠⣄⠛⠿⣿⣷⣶⣿⡿⠃⠀⠀⠘⠁⠀⠀⠀⠘⠋
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠆⠀⠈⠛⠛⠁⠠⠆⠀⠀⠀⠀⠀⠀⠀⣀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆
⠀⢼⣿⣿⠟⢠⡐⠶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢠⡄⠀⠀⠀⠐⠀⠀⠻⠛⠋
⠀⠘⠋⠁⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠠⡀⠀⠀⠂⠀⠄⢀⠀⠀⠀⠀⠀⠘⣿⣧⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⣦⣈⡈
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠚⡀⣀⠿⣿⣿⣿
⠋⢁⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣰⣿⣾⣿⣿⣷⣄⠀⠀⠂⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠘⠀⣀⠌⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⢀⣤⣭⣽⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢀
⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠈⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠂⡠⠤
⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠀⠀⠈⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠻⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⢴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⠓⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠰⣷⣤⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢞⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⡫⢶⣉⡟⣿⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣥⠚⣷⣾⣿⣷⠿⠖⠛⣭⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣏⣽⣿⡿⠟⠫⡥⠀⠛⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣰⢟⡱⢻⣴⣿⠟⣩⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⢀⡾⣫⣾⣿⡿⣋⠰⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠁⠀⠀⠀⣰⡟⣵⣿⡿⢫⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⣴⢏⣾⡿⠋⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢸⠀⠀⣼⢏⣾⢏⠘⠃⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣶⣶⣤⡀⠀⠀⢠⣿⡶⢷⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣆⣰⡏⡾⣃⠘⠃⠀⠀⠀⠀⠀⣾⡟⠉⠉⢻⣿⣏⠉⠻⣿⣿⣦⢀⣾⣿⣷⠾⡞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣛⡼⣿⢸⠃⠉⠁⠀⠀⠀⠀⠀⠀⢿⣷⣤⣤⣾⣿⠏⠀⠀⢿⣿⣿⣿⣿⣿⣿⠺⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣄⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⣾⢳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠉⢿⣭⡀⠈⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⣷⡎⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⢯⣭⣀⣶⢮⣝⢶⣤⣄⣀⣀⠀⢀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⠻⣶⢏⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⢻⣿⣿⣶⣝⠳⣮⣛⠿⣿⡛⣿⡿⢿⣿⠿⣿⢿⣿⠟⣿⣭⡿⢚⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣄⠙⠻⠶⣯⣝⣛⣚⡿⠶⠿⣶⣛⣛⣯⡵⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠟⠁

⠟⠿⡆⠀⢠⣿⣿⣿⣗⠐⠛⠻⢻⣿⣿⣿⣯⣀⣀⠀⣿⣿⢯⣿⡀⠀⠀⠀⠀⢸⢿⣻⣿⡷⣿⣼⣵⣤⣤⣀⣠⣀⠄⠀⢠⠈
⠀⠀⠈⢲⣿⡟⡍⠂⢈⠀⢀⡀⠈⠻⣿⣿⣏⡣⣈⣿⣿⣿⣿⣿⡇⡀⠀⣀⣠⣿⢛⣿⣿⣴⣿⣿⣿⣿⣿⠻⠙⣷⣶⢖⠳⣴⣐
⣤⣀⡀⢈⢙⣗⣶⣍⡠⠚⡁⢉⠁⣰⣿⣿⣿⣿⣿⠋⠛⠛⢪⣻⣇⠀⠀⠀⠙⣿⣿⣿⣿⣿⡝⠄⠛⢻⠙⠲⣶⣬⣿⣮⠠⠈⢿
⣿⣿⣿⣧⣾⣿⣿⣿⣶⣶⣄⣠⡷⡛⣛⡍⣇⠈⣿⠀⠀⠀⠈⢣⡏⠙⣷⠁⢤⠛⠿⡟⢩⡤⠀⢺⠃⠸⠛⠘⠀⡯⠾⡄⠞⣬⣹
⠛⠛⢉⣻⣿⡿⣿⢿⣿⣮⢿⡛⢿⣿⣍⣴⢿⣴⣿⣆⠀⠀⡸⠋⣁⠒⣬⣄⠊⡃⠀⣈⣄⠠⣄⠘⡄⠐⡄⠀⠘⢥⠋⠓⡶⢻⢾
⠀⠀⡄⢹⠀⠹⠘⣾⢿⣿⣞⣷⡘⡉⠉⢰⡾⡟⢣⡙⠠⠞⠇⠀⢠⣰⠽⠤⠼⡏⠫⣿⠛⡛⢯⣕⢥⣶⣹⣄⣿⣤⣎⣩⡡⢷⣤
⢷⢠⣏⠿⢷⠠⢧⣸⢧⠠⢹⢐⡄⠛⠃⢘⡛⣏⢫⣿⣘⠓⣿⣿⣷⣀⡾⠃⢤⡀⡀⠘⠀⣉⠿⠻⠟⠿⣿⣿⠇⣿⠃⠉⠀⠀⠉
⣀⣀⣹⠖⠿⢷⣶⠟⠋⣛⢮⣶⣴⠒⣀⢸⣦⣁⠸⠿⠛⠖⠳⢾⣿⣇⡀⠘⢳⣦⣗⣀⡶⠤⠀⢀⣤⢀⣀⣽⣿⡇⠀⠀⠀⣠⣄
⠛⠋⠁⠀⠀⠈⠁⠀⠀⠃⠛⢙⣇⠙⢧⡶⡤⠉⠀⠀⠀⠀⠀⠀⠉⠻⣇⣥⣾⣿⣿⣿⣿⠁⠀⢶⣽⣿⡟⣷⠛⣇⠀⠀⢲⠏⢉
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⣾⣿⣄⡀⠐⠂⠐⠁⠀⣄⢀⣰⣿⡟⠛⠙⠻⠿⡿⢖⣾⣿⠿⣿⠿⢿⡓⡿⠂⢬⠇⠀⣴
⠓⠦⣄⠀⠀⠀⣰⠀⠆⡀⠶⡾⢫⣀⠠⢹⡇⠀⠀⠀⠀⠀⠀⣿⠏⠁⠀⠀⡀⠂⢀⠀⢸⣿⠟⠀⠀⠙⠀⠀⡄⠀⠀⠘⠀⢐⠏
⠀⠀⠈⠻⣶⣥⣿⣿⡴⠟⠀⠸⠁⠀⣀⢰⣇⠀⠀⠀⠀⠀⠀⡏⢰⡶⠒⠋⠙⠀⠠⠴⠾⢿⡀⢀⠀⢀⠆⣰⣇⠀⠀⠀⢀⡐
⣠⠖⠀⢀⣽⣿⣿⡿⠀⠀⠀⢰⡇⠀⠉⠀⠈⢢⡀⠀⠀⢰⣧⣾⠟⢀⡀⠀⠀⠺⠶⣤⠀⣀⡘⢿⠞⠁⠼⠋⠙⠀⣀⠀⣘⠿⢀
⠛⠀⠀⠍⠁⠀⢀⣃⠀⣠⡴⢿⡇⠀⢄⠁⠛⢛⡻⡢⡲⣖⢵⡯⡻⠋⢀⠀⠀⠀⠀⠀⢀⡀⠀⡦⣠⣾⡿⠂⠀⠀⠘⠛⠋⠆
⡀⠀⠀⢁⣴⣤⣾⡄⠉⠀⠀⠀⠘⢶⣬⣷⡀⠀⠀⠀⠉⡑⠽⣬⡬⡭⠄⠀⢤⣰⡌⠁⠜⠁⠀⣸⣿⣏⠀⠀⠀⣀⣀⡀⠀⠀⠉
⣥⡿⣯⣭⣵⣸⡿⢿⣦⣤⡀⣠⠖⠉⠋⠀⠈⠻⠷⠆⠀⡨⠉⢩⠤⣤⣤⠠⣴⣭⣥⣶⣂⣤⣴⣿⠏⡉⠁⣶⣾⣿⣿⣷⡀⠀⠈
⣾⠏⠹⢟⣷⠏⠀⠀⠙⣿⣿⠇⠀⢀⣀⠀⠀⠀⣀⣠⡤⠷⢄⡀⠀⠀⠀⠀⢀⠄⠈⠹⣟⢝⢩⠈⡝⢧⠀⣿⣿⠉⠙⠻⣽⡖⢠
⠭⠀⡆⠒⠁⠟⢠⡄⠠⠯⡄⢀⡀⠀⠀⢀⣠⣼⡟⠁⠀⠀⠀⠉⠓⢶⡤⠶⠯⠁⠀⠀⠀⣾⣷⣷⣾⣿⣦⣿⠁⠂⢤⢠⡼⠻⠦
⠀⠰⣇⣟⠺⡉⠷⣵⡄⠠⠃⠈⠀⠒⠀⢩⠿⣿⡅⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢿⣮⣧⠉⠙⠿⣿⠃⣄⢰⠎⠛⢦⠃
⢱⣴⠫⠅⣠⠐⣦⣿⡡⠚⢁⣀⠐⠃⠄⣠⣾⣿⠧⠀⠀⠀⠀⠀⢀⣿⣃⠀⠀⠀⠀⠀⣠⠞⣿⣏⣂⣁⣀⠀⠀⡸⣿⠀⣆⠐
⢂⣨⣷⡶⠟⣡⣿⡷⣘⢛⡁⠀⠈⠓⢀⣼⣿⠇⠢⠀⢠⣤⣤⡤⠸⠿⡇⠀⠀⠐⠚⠝⠀⣼⢏⣻⣯⣭⣷⣦⣄⣰⣿⣿⢗⣀⡖
⠁⠀⣈⡿⠺⡟⠇⢀⠠⠎⠉⠀⠐⣶⠋⢸⣿⣶⣤⣤⣾⡿⠉⠀⠀⠠⣧⢀⣀⡤⢀⡴⠈⠉⠀⠈⢩⣽⣿⡿⠋⠀⠀⠁⠀⠍⢣
⠀⠈⠉⠀⣀⡄⠀⠁⢀⠀⠀⠀⠠⠀⠀⢈⣿⣿⣿⣿⣿⣷⣾⣴⠖⢢⣼⣾⠋⢻⣴⣀⠀⠀⠀⢀⢸⣮⣿⡇⠐⣄⠐⠀⠀⠀⠂
⠀⢠⡆⠈⢁⣼⠀⠀⠀⣄⠢⡀⠀⣁⣀⡾⠿⠿⠿⠟⠿⢄⡻⣼⣧⣞⣡⣩⣩⣞⠛⡛⠃⡄⠀⠈⣲⢏⣻⠇⠚⠻⠄⠀⠀⣤⡀

⠀⠀⠀⠀⠀⠀⠒⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠲⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡔
⠀⠀⠀⠀⢀⠀⠀⠐⣀⡀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⢿⡿⠿⠿⢿⣿⠿⠿⢿⡿⠛⠛
⠀⠀⠀⠐⠚⠁⠀⠀⠀⠀⠀⠺⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⡿⠛⠛⠛⠛⠛⠛⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠀⠀⠀⠀⠀⢀⣀⡠⢠⣆⣴⢰⣆⣤⣄⣢⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⢀⣴⣿⣿⣿⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣟⣦⣄⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠿⢿⣹⣿⠿⠞⡿⢻⣿⣻⣿⣿⣻⣿⠿⢿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣛⣿⣷⡐⢠⠀⠀⠐⠘⠻⠃⠀⠐⠂⠋⠙⠛⠛⠻⠛⠉⠉⠀⠀⠙⠁⠀⠀⠈⠉⠉⠉⠉⠉⠑
⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⠿⢿⡿⢿⣿⣿⣷⠀⠀⠠⡆⢀⠠⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠃
⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠈⣻⣿⡟⠀⠀⠀⡛⠁⠀⠀⣠⣤⡉⠒⠀⢲⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⡇⠀⠀⠀⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠄⡀⠀⠀⠄⠀⠀⠀⠀⠁⠶⣿⣿⣿⣶⣤⣀⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠏⠀⠀⠀⠀⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⠀⠀⠈⠻⠿⣿⢿⣄⠀⠆⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠄⠊⠉⠙⠉⠩⠒⠀⠀⠀⠀⠀⣤⣤⡜⠁⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠄⠀⠀⠀⠀⠀⠠⠌⠡⡀⠀⠀⠀⠀⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠢⠀⠀⠀⡀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⣄⣛⣃⣀⡄
⠀⠀⠀⠀⠀⢸⣿⡶⠀⠚⠐⠪⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢂⠔⠀⠀⠀⠁⠀⠐⠂⡐⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠰⡎⣁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠲⠨⡀⡘⡀⠈⠠⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣠⠁⠈⠀⠀⠀⠀⠀⠐⠄⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢤⡄
⠀⠀⠀⠀⠀⠀⠸⠳⢶⠶⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⡀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⡀⠀⣀⣠⡤⠶⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠃⠀⡠⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠼⠛⠋⠉⠉⠛⠛⠓⠲⠶⠶⠀⣤⡀
⠀⠀⠀⠀⠀⣴⠀⠀⠀⢗⣐⡈⢰⣆⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠈⢨⣦⡀⠑⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢀⢀⠀⣀⡄⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠘⣿⠀⠀⢗⠀⠀⠈⠀⢿⡆⠀⠀⠐⣀⠈⢉⣠⠃⠀⠀⠀⠑⣴⠄⠈⠛⢦⡀⠀⠀⠀⠀⠀⢀⠀⠶⠖⢀⣾⣷⣬⣭⣥⠆⠀⣷⣬⣭⣥⡾
⠀⠀⠀⠀⠀⠁⣀⣤⣬⠦⠤⢄⣀⡺⠀⠀⠀⢠⣌⣉⣉⣡⡾⠀⠀⠀⠀⠈⠚⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⡿⠀⠀⠿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁⠙⠃⠈⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢀⠄⠂⡀⠄⠼⢉⣀⠀⢂⠀⠀⠀⠐⠛⠛⠀⠐⣅⠉⡔⠀⠆⠘⠛⠛⠂⠀⠀⠀⡠⠀⠀⠐⣄⣀⢀⠤⡀
⠀⠀⠀⠀⡠⠂⡤⢠⠇⢀⡏⠶⢭⡄⢞⡀⠐⢦⣄⠀⠻⠇⠀⠈⠉⠙⠀⠀⠻⠃⢀⣤⠶⢀⣀⢇⣀⣋⡅⣗⠀⢉⢀⡈⠄⡀
⠀⠀⠀⢰⠀⢚⣣⡄⢰⡆⠈⠚⠃⡱⢠⣽⢿⡶⢈⣳⠒⠀⠀⠀⠀⠀⠀⠀⠀⠲⣏⡑⢾⠿⣥⠀⡎⠱⠤⠋⢢⡌⣇⡿⡆⠠
⠀⠀⠀⠈⠁⣀⣩⡀⡻⠃⠤⠤⠊⣱⠟⢡⡞⠱⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊⢷⡈⠻⡟⢦⣀⡀⠿⠗⠬⡛⠁⠲
⠀⠀⠀⠀⠉⣭⣒⡏⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣻⢝⣛⠺
⠀⠀⠀⠐⠤⠈⠴⠒⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠽⢘⣋⣀
⠀⠀⠀⠀⠀⢰⣄⡾⢋⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⢷⣆⣤
⠀⠀⠀⠀⢰⣄⢻⠗⣫⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⠶⣿⢃⡴
⠀⢠⣾⠀⠀⠙⢆⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠞⠁⠀⢰⣤
⠀⠈⠛⠀⠿⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠴⡆⠘⠋
⡂⠈⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄
⠗⢂⡄⢋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢔⡋⠰
⠁⠂⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄
⠀⢠⣶⠀⠿⠃⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠺⠇⢠⣄
⠀⠈⠻⠀⠀⣴⢏⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢋⢷⡄⠀⠸⠛
⠀⠀⠀⠀⠘⠁⣾⣟⢾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠶⣿⣄⠛
⠀⠀⠀⠀⣀⣘⠁⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⡾⠯⠛
⠀⠀⠀⠀⢀⣴⢸⡅⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠑⣶⣠⡈⠐
⠀⠀⠀⢠⠲⠶⣩⠧⠎⠀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠘⣀⣗⢪⣭⣄
⠀⠀⠀⠸⠆⠴⣶⡐⣿⡆⠀⠈⠳⣿⣦⡙⣦⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣴⢟⣤⠞⡠⠞⠉⠁⣼⠤⢨⣍⢀⣼
⠀⠀⠀⠈⡀⢻⣆⢥⠉⢢⡔⣛⣦⡇⢚⣽⡿⢓⣨⠵⠆⠀⠀⠀⠀⠀⠀⠀⠐⠺⣥⡐⠻⣿⣝⠰⣄⠴⠦⣀⠟⢀⠋⣵⠂⠘
⠀⠀⠀⠀⠀⢁⡀⢠⢄⢀⡃⠡⠆⠀⡉⠀⠰⠛⠁⠀⢶⡆⠀⠠⡤⣄⠀⠀⡶⠄⠈⠛⠓⠀⢠⠂⢉⡝⢃⠏⠀⡋⠘⢁⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠑⠀⠤⠐⠁⠀⠀⠀⢲⣶⡶⠀⠒⠠⢓⡄⡓⠀⢰⣶⡦⠂⠀⠀⠀⠃⢀⡀⠤⠃⠈⠁⠒⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣁⣀⣴⣄⣈⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣉⣭⣶⣶⢶⣦⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣿⣿⣿⣿⣿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⡟⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠀⡁⣀⣀⢄⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⢀⠅⣀⡀⠀⠀⠋⠀⠀⢈⡉⠚⠠⡌
⠀⠀⠀⠀⠀⠀⠏⠀⠠⠄⡀⠡⠒⠈⠉⠉⠈⠑⠠⡈⠓⣀⠠⠲⠤⡀
⠀⠀⠀⠀⠀⠀⢥⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠠⡄⠘⠤⠁⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⢀⡂⠈⠀⢄⠀⢠⡄⠀⢱⠀⠀⠀⠀⠉⡠⠔⠛⠦⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠘⡇⠀⠀⠈⠆⠀⡁⠀⠀⢣⠀⠀⠀⠸⠶⠤⣀⠀⠈⠠⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢃⠀⢸⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠓⠲⠆⠄⣙⠓⠶⢌⣢⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠸⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠐⠢⣄⣀⠀⠀⠈⠁⠒⠤⠈⡅⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠈⠀⣈⠀⢦⡀⠀⠀⠙⣠⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢠⠁⠂⠀⠫⠟⢝⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠐⠁⠀⠻⠀⠀⠉⢡⠡⠀⠠⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠈⠢⠠⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⠀⠆⠣⠀⠰⡈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⢀⣀⠔⠀⠀⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠡⡘⠄⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢻⠀⠀⠀⠀⠀⡡⠔⡡⢀⠎⠁⠀⠀⡄⠀⠀⠀⠀⠡⠀⠄⠡⠈⢦⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠀⢋⠀⠊⠀⠁⡀⠀⠈⠀⡅⠀⠀⠀⠀⠀⣁⢈⠄⢡⠘
⠀⠀⠀⠀⠀⠰⠊⡀⠀⠀⢠⠀⠀⠰⠖⠁⢀⠀⠀⠐⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠄⢠⠂⠄⠃
⠀⠀⠀⠀⢸⠀⠀⢡⠀⠀⠀⣅⣀⡤⠤⠒⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⢀⡠⠚⠁
⠀⠀⠀⠀⠈⠀⠀⢀⠂⠀⠀⠈⠁⣀⠔⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠉⢀⠤⠒⠁
⠀⠀⠀⠀⢀⠀⠀⠀⢢⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠓⠀⢀⠀⠀⠀⠀⡀⠴⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⢀⡔⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠳⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣧⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠵⡶⠾⠑⠦⠐⣶⡎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠶⣦⣬⣤⣴⣶⣂⠀⠶⠶⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣤⣭⣭⣥⣶⠟⢛⣫⡍⠛⠛⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣿⣿⣿⣿⣿⣧⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⣤⣀⠉⠙⠛⠛⠛⠉⣿⣿⣿⣿⣿⣿⣇⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣠⣶⣶⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣶⣤⣄⣀⠈⠉⠉⠉⠉⠁⠘⠿⠿⠛⠉⢹⣿⡇⣀⣴⣷⣾⣿⡿⠛⢹⣿⠀⢀⣴⠀⣀⣤⣴⡆
⠀⠀⠀⠀⠀⠀⢀⡀⢤⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠛⠿⢿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠋⢀⣀⡼⠿⣶⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠘⠻⢤⣄⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠠⠂⠀⠀⢀⣠⣴⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⣍⡓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣶⣦⣤⣴⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢬⣉⠓⠶⢤⣄⡀⠀⣀⡀⠀⠀⠀⠀⢸⡿⠛⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⠄⣽⣯⣟⡻⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣰⣿⠀⠀⣨⠔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⡧⣶⠛⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⣿⠀⢀⣴⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣷⠠⠗⠀⠀⠀⡀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⡄⣋⡀⠰⠊⠁⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠜⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠛⠛⠛⣉⠉⠀⠀⠀⠀⢀⣀⣤⣴⣾⣾⡏⣄⠀⠀⠀⢰⡄⣠⠐⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣄⠀⠀⠀⠀⢀⡀⠀⣂⣀⣠⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⠟⢠⣿⡈⠒⠂⣾⡇⠀⡼⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⠀⢀⢤⣠⣷⠀⠀⠁⠀⣦⡀⣠⠤⠰⢦⣈⡙⣿⣿⣿⡿⣟⠿⡿⠿⣿⡟⠛⠀⠀⢼⣿⡆⠁⠋⣿⣷⠠⣤⠇⢀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣧⣿⠶⠃⠀⣩⠗⠮⣂⠄⠘⡥⠈⠁⡄⢰⠈⣉⠭⠛⠩⠑⢊⠀⠊⢠⠈⠂⠒⠥⣢⡠⣀⠀⡌⠛⠜⠛⠿⡂⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠧⠊⠁⠠⠀⡠⢞⡄⢠⠀⠀⠁⡀⠀⠉⠀⠟⠃⠋⠀⠀⣀⡠⠂⠨⠂⠀⣾⡆⠐⢄⡀⠈⠉⠈⢸⠷⣦⠀⢂⠂⢘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢃⠤⢊⠁⠀⢀⠰⠀⡀⢸⡀⣆⠀⠙⠒⠁⠀⠀⠀⢠⠀⠂⠀⠀⠄⠀⣿⢠⣿⣇⠀⠂⠀⡀⠀⣁⠤⠊⠀⣦⢸⠀⢸
⠀⠀⢰⠐⡀⠄⠀⠀⡀⠀⠀⠀⠀⠁⠈⣁⣀⣀⡛⠗⠉⠀⣠⡠⠄⠀⡀⠀⣾⡆⠤⣌⣀⣀⠼⠿⠾⠟⠛⠋⠉⡉⠔⠈⠀⠀⠐⠀⡏⢸⠀⠘
⠀⠀⠸⠀⠤⡌⠒⠠⠄⠀⠉⠑⠂⠀⠿⢿⣿⡭⠿⠇⠀⠀⠂⠀⠀⠈⠝⠐⠿⠧⡈⢁⡠⠂⠅⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠈⠤⢆⡀⠰⢠⣦⣤⣄⡀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⠿⠃⠒⠀⠀⣤⣀⢀⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠭⢃⣆⠶⠀⠀⠀⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢀⡄⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⠟⠻⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣄⣼⡃⠀⢀⣤⣴⡀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠋⠛⠻⢿⣷⣏⠁⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠺⠛⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠾⣋⣄⡀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⣠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠈⠿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠙⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢿⣷⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣄⣀⠀⢻⣆⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣦⣤⣤⣴⣶⣾⣿⣿⠿⠿⠿⠿⠿⢿⣿⣦⣿⡄⠀⢹⣿⡆
⠀⠀⠀⠀⢰⡄⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠘⣷⡀⠀⠀⣀⠈⠙⠛⠷⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢸⣿⡇⠀⢸⣿⡗
⠀⠀⠀⠀⠀⠈⢿⣄⠀⠉⠻⠶⠦⠀⠀⠀⠉⠙⠛⠛⠛⠓⠒⠒⠀⠀⠀⠀⠀⣀⣤⣶⠟⠉⠀⠀⠀⠀⣼⡿⠀⠀⣸⣿⡇
⠀⠀⠀⢠⠀⠠⢄⣉⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⡿⠟⠉⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⢠⣿⣿
⠀⠀⠀⠘⣦⠀⠀⠉⠛⠻⠿⢿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⢤⣤⣤⣀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠆⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⡿⠟⠋⠀⣀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢦⡤⠀⠀⢀⣀⣀⣤⣤⣶⣾⣿⣿⠿⠟⠋⠁⠀⢀⣴⡾⠃⠀⠀⠀⠀⢀⣼⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⢀⣤⣾⡿⠋⠀⠀⠀⠀⢀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠠⠶⠾⠋⠀⠀⢀⣠⣴⣾⣿⠿⠋⠀⠀⠀⠀⠀⢀⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣤⣤⣄⣀⣀⣠⣴⣶⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⢀⣠⡴⠂⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⠶⠛⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⢀⣀⣤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀
⠀⠀⢉⡐⠢⢵⢇⣨⣿⣿⣶⣄⠀⠀⠀⠀⠀⣼⣿⣯⣽⣙⣺⣯⡿⢯⠾⡿⣶⠀⠀⢀⡴⡚⠉⠉⠄⢋⠽⠓⠢⣄
⠀⠀⠈⠋⠉⢱⣿⣿⣿⠛⠁⢈⠶⡄⠀⠀⢀⣿⣽⣿⣿⣿⣿⣯⣿⣿⣿⣿⣽⠀⠀⠈⣷⢆⡙⣖⣢⣄⠠⠂⠉⠉⣙⣦⡀
⠀⠀⠀⠱⡂⢸⣿⣿⡏⠳⢦⣈⣥⣻⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠳⠐⠀⠌⠁⠒⠿⣆⠀⠉⡀⠀⡇
⠀⠀⠀⠀⠈⠛⠛⠻⢇⣀⣀⣉⣍⡼⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠈⠂⠠⢤⠁⠂⠘⠶⣔⣤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠚⠊⠉
⠀⠀⠀⠀⣠⡤⠴⠶⠶⠦⠤⣀⡀⠀⠀⠀⠀⠀⢠⠖⣯⠭⣝⣒⡶⣦⣄⡀⠀⠀⠀⠀⠀⢀⣤⠶⣦⣤⣤⣤⣠⣄⡀
⠀⠀⢠⡿⠷⠤⠴⠂⣀⡀⠠⠜⠛⠳⣄⠀⠀⠀⢀⡴⠁⣠⣾⣿⣿⣿⡿⣛⠢⡀⠀⠀⠀⣚⠤⢤⣿⣾⣿⣿⣿⣤⢿⣶⣦⡄
⠀⠀⠸⠴⠖⠚⠛⢒⠦⢍⡓⠦⣠⠤⠤⢷⣦⠀⠸⡦⠀⣿⣿⣿⣿⠟⠲⢭⣙⣌⣷⣄⠀⣟⠓⢶⣿⣶⣿⣿⣯⣏⣭⣽⣣⡿
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠬⠳⣟⣄⢀⣬⡿⠀⠀⠑⠢⣿⣿⣿⣿⢀⠀⡀⢹⣍⣻⡝⡇⠹⢶⣸⣿⣿⣿⡟⠶⠦⠯⠥⠖⡗
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠄⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠐⠒⠈⠻⣼⠞⠃⠀⠀⠉⠙⠛⠻⠧⡼⠦⠶⠖⠋⠁

⠀⠀⠀⠀⣀⣠⡤⠶⢤⡤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠴⠖⠲⠶⠤⣄⣀⠀⠀⠀⠀⢀⣤⡾⣎⡻⣭⡿⣿⣦
⠀⠀⣴⢯⣅⣀⣴⣾⣿⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⡞⠃⠀⣤⣴⡯⠽⢃⣶⠀⢈⠳⡀⠀⠀⣶⠘⠓⢞⣹⣞⣯⡽⠖⢣
⠀⠀⠸⠋⡓⣿⣿⣿⣿⣿⡉⠀⠀⠀⠙⠢⡀⠀⠀⠀⣧⣄⠄⠀⠈⠟⠀⠻⠁⣀⣠⠴⣇⠀⠀⡏⢻⣮⣤⣬⣤⣤⣵⣶⣿
⠀⠀⠀⠢⢰⣿⣿⣿⣿⢙⠮⡳⣄⠀⠀⠀⠈⢢⡀⠀⣿⣿⣿⣶⣶⣶⣷⣾⣿⣿⣷⣶⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠙⠿⠿⡇⢀⡂⠈⠺⣷⣄⡤⠖⠋⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠘⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⢀⣤⠀⠀⢄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠛⠛⢻⣆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠂⠀⠀⠉⠀⠀⠤⠶⠀⠀⠀⠀⠀⠤⢤⠀⠈⠢⠤⠤⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⢤⣤⡀⠀⠀⠀⣠⣠⠄⠀⠀⠠⠶⠆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠀⠀⣤⡀⢸⣚⣋⡇⠀⠀⢸⣣⣼⡟⠀⠀⠀⠀⠀⠀⣾⣿⣦⡶
⠀⠀⠀⠠⢤⡄⠀⠨⠒⠀⠀⠀⠀⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⣀⡀⠀⠉⠀⠻⠆⠀⠀⠀⠀⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢀⡾⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⡴⠀⢀⠀⠀⢠⠀⠀⢠⠀⠈⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡀⠀⠀⠀⠐⡀⠀⠐⠤
⠀⠀⠀⠀⠀⠑⡤⠐⢹⡃⠀⠀⠑⠂⠀⠀⠀⢇⣀⣥⠀⠀⠀⠐⠂⠀⠀⠲⢆⠝⠁⠀⠀⠀⠉
⠀⠀⣠⠇⢠⣁⠂⢠⠟⠀⠀⠀⠀⣀⡀⠀⠀⠈⠝⠁⠀⠀⠀⢀⣀⣤⣀⣀⣀⣀⠂⠀⠙⠏⠺⠒⢐⠂⠑⠀⡀
⠀⠊⠁⠀⠈⠉⠀⠘⠀⠀⠺⣕⢦⡈⠀⠔⠀⠀⡀⠀⠀⠲⠾⠿⠿⠿⠿⠿⠿⠿⠿⠷⠂⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⠃⠀⠈⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⡃⠀⡾⠆⠀⠀⠀⠰⠀⠀⠀⠈⠲⠒⠲⢒⢞⠁⢈⣧⣥⡀
⠀⠀⢀⣀⡀⠀⠀⠀⠚⠘⠂⠀⠐⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢸⠵⢾⠀⠀⠀⠠⠀⠀⠀⠄⠀⠟⣽⣄⢻
⠀⢀⣄⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⢡⠃⠸⡈
⠀⠀⠀⠀⠀⠀⠂⠤⠄⠂⠆⠀⠀⠀⠉⠀⠀⠀⠀⠀⣲⡄⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠠⢄⣀⠈⠋⠙
⠀⠀⠀⠕⠂⠀⠀⠶⠤⠆⠀⠠⡶⠀⡄⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣀⡋⣨⣭⣧⣤⡉⣫⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠆⡀⠐⠐⠀⠡⠅⢤⠼⠿⢤⠄⠥⠅⠸⡉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⣤⡀
⠀⠀⠙⠂⠀⠀⠀⠈⣺⡧⠂⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢦⠘⢃
⠀⠀⠀⠄⠀⠀⠀⠀⠌⠁⠀⠀⠀⢀⠀⠤⢀⠀⢸⠀⠀⢈⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠻⠿⠇⠐⡆
⠀⠀⢈⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢰⡀⡽⢔⣷⠀⠀⢄⣁⣀⠀⠀⢀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠀⢠⡇⠀⠀⠀⠈⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠈⣷⡀⠀⠀⠀⠀⢿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠹⣧⠀⠀⠀⠀⠸⣿⣿⣿⣿⣧⡀
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⣄⢻⣷⣄⠀⠀⠀⠙⢿⣿⣿⣿⣿⡄⠠⡀
⠀⠀⠀⠈⠙⠻⣷⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⣿⣧⠻⣿⣷⣄⠀⠀⠀⠙⢿⣿⣿⣿⡄⢿⡄
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⢿⣿⣇⠹⣿⣿⣷⣄⠀⠀⠀⠙⢻⣿⣿⡜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣄⠘⢻⡆⠹⣿⣿⣿⣷⣄⠀⠀⠀⠙⣿⣷⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⠙⠀⠘⢿⣿⣿⣿⣧⡀⣷⡀⠘⢿⡇⢣⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣦⣄⠀⠀⠀⠀⠀⠻⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣷⣿⣷⡀⠈⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣉⠛⠦⣄⠀⠀⠀⠀⠙⠻⣿⣄⠀⢀⡘⢿⣿⣿⣿⣿⣷⡀⠈⠀⢰⡇⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣬⡑⠀⡀⠀⠀⠐⣌⠻⣆⠀⢳⡄⠹⣿⣿⣿⣿⣧⠀⠀⣾⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡀⠀⠀⠘⣷⡀⠂⠀⢿⣦⡘⣿⣿⣿⣿⡆⠀⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢹⣿⡀⠀⠈⣿⣷⡜⣿⣿⣿⡇⠀⣿⡟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⠀⠀⢻⡇⠀⢰⠸⣿⣿⣞⣿⣿⡇⠀⣿⢳⡟⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⡿⠟⠛⠛⢋⣉⣭⣿⣿⣿⣧⠀⠘⡇⠀⢸⡇⣿⣿⣿⢻⣿⡇⢸⢧⡟⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣧⣴⣶⣬⡙⢿⣿⣿⣿⣿⣿⠀⠀⠇⠀⢸⡇⣿⣿⣿⣸⣿⠁⠰⢋⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠶⠾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⢣⣿⣿⢇⣿⠏⠀⣠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⡀⢰⢯⣾⣿⢏⡾⠁⢀⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⡼⢀⣵⡿⠛⠑⠋⢀⣴⣿⣿⣿⠟⣁⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⡼⠁⢛⣥⠞⣁⣤⡶⣿⣟⣛⣭⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠁⠀⠀⣠⠞⢁⣴⠿⢓⣫⣭⣶⣾⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠈⠁⢀⣩⣴⣾⣿⣿⣿⣿⠿⠿⢛⣉⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠀⠀⠀⣀⣤⡴⠾⠟⢛⠛⠯⠭⣽⣶⣶⣾⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⣉⣁⣀⣀⣀⣤⣤⣶⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⡆⣀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠚⠻⠟⢀⣿⣿⣿⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣿⠖⠒⣿⡅⣰⠂⠐⣦⡼⠋⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⡏⠉⠙⢧⣀⣴⣋⣹⣮⣴⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⣉⣹⡿⢿⣶⡖⠛⢣⡀⠈⣿⣯⣭⠅⠴⢾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣾⣿⣿⠛⠛⠆⢰⣿⣧⣤⣾⣿⠟⣿⣿⣿⣛⠄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣄⢀⣾⣿⣿⡿⣿⡷⠂⢘⠋⢹⡟⠻⣨⡧⠴⣿⡿⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⣿⣿⣿⣿⣿⣷⣶⣿⣷⣿⣿⡿⠉⢰⣄⣸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡈⣻⡁⠉⣿⠀⢹⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠶⣿⣿⣷⡤⠷⠶⠾⣿⣿⡟⠛⣿⡿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠈⣻⣿⣿⣷⡄⣠⣿⣿⠿⢄⣯⣶⠟⣠⠿⠛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠛⠿⠿⠛⠀⣿⣿⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⢠⠃⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣀⡴⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣻⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⣀⠜⢋⣉⣽⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠋⠈⠛⠿⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠒⠀⠤⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⠠⠀⣀⣤⣤⣶⣶⣶⣦⣤⣀⡀⠠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣾⣿⣿⣿⣿⣿⠟⣻⢿⣿⣿⣶⡐⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣬⡟⠻⣬⣶⢳⣿⣿⣿⣿⡸⣷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣀⠀⢸⣿⣿⣿⣿⣿⡷⢠⣼⡿⣻⣿⣿⣿⣿⠇⢨⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⠆⡼⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⡿⠀⠼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⣷⡹⣿⠟⢛⣉⠉⠉⠯⠉⠛⠻⢿⡿⣣⢷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⣏⣅⡀⠉⠀⠈⠁⠀⠀⠙⠛⠂⠒⠉⠀⠈⠙⢉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡙⢿⣿⠓⠶⣤⣀⣀⠀⠀⠀⢀⣀⣂⣴⠴⢾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠂⣬⣿⣶⣶⣦⣬⣭⣤⣤⣬⣥⣤⣶⣾⣿⡁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠧⠤⠌⠻⠋⠅⠈⣿⣿⣿⣿⣿⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣄⠀⠻⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠇⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⢸⠃
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠇⠀⠀⠀⠀⠀⠘⠛⠋⠛⠛⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠹⠟⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠁⠀⠙

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⡄⠀⠀⠰⠂⠀⠀⡀⠠⠜⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠊⠈⠀⠀⢀⠄⠀⠠⠄⠀⠒⠀⠈⠐
⠀⠀⠁⠀⠀⠀⠉⠀⢠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠄⠀⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⠿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣻⣿⣏⡷
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠐⢠⣶⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⡀
⠀⠀⠀⠀⣀⣀⡀⠰⡟⠀⠀⠀⠀⠀⣰⣿⠛⠛⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⡀
⠀⠠⣾⣯⣽⣿⡿⠂⢳⠀⠀⠀⠀⠀⠈⠁⠉⠀⠈⠀⠋⠀⢀⠚⠀⠀⠀⠀⠈⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⣠⢞⣿⡯⠟⠀⠀⠀⠀⠐⠄⠰⠀⠀⠀⢨⣄⠀⢀⣤⣤⣤⣤⣄⣀
⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠘⠂⠀⠁⠀⠘⠻⠿⠿⢿⣥⡽⠇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡴⠶⠶⣤⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢿⣷⣾⠇⠀⢀⠀⠀⠀⠀⠋⠀⠀⠈⠀⠛⠀⠀⠀⠀⣿⡘⠀⠰⢈⣧⠀⠐⣃⠘⠃
⠀⠀⢀⡠⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⣠⣐⣀⣀⣒⣀⣀⣀⡀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠈
⠀⠤⠀⠁⠋⠀⠀⠀⠀⠀⠀⢠⣿⡯⡽⠋⣿⢩⡟⡙⡿⡙⣽⡇⠀⠀⠉⠉⠉
⠀⠀⠘⠃⠀⠀⠀⠀⠀⡀⠀⠈⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠛⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠒⠒⠒⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠿⠶⣶
⠀⢠⣶⣖⣛⣟⣟⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠻⠾⢂⠀⢀⣤⠀⠀⠀⠀⢀⣀⠀⠁
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣯⣥⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⡛⠻⢟⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠢⠜⢀⢌⠛⠁⣤⠄⠀⠈⠛⠻⢫⣶⡍⢋⣥⡀⠀⠃⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠠⠡⣎⣹⣧⠀⠀⠉⣷⡄⠀⠀⢠⡦⠀⠀⠀⣡⣄⣠⠈⣀⠀⣿⠄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢋⡴⣦⢸⣿⣿⣀⣤⣶⠖⠤⠀⠀⠹⣿⣿⣄⣬⡀⠻⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣀⡙⠃⠘⠟⠛⣿⣿⠟⢴⡶⠠⠐⠀⠘⢷⠘⠛⠁⣩⣤⠀⡀⣠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣶⣾⣷⣽⡥⠀⠀⣀⡀⠈⠁⠀⠀⠀⠐⠠⠀⠁⢀⣀⡀⢠⣬⣯⣶⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠃⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⠀⠒⠋⠁⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠠⢶⡿⣿⣷⢄⠀⠀⠀⠀⠀⠀⠠⣾⡿⢿⡶⠼⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢷⠀⠀⠀⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠛⠣⡀⠀⠀⠀⠀⢀⣤⣤⡤⢤⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⢻⣄⠀⠀⠀⠙⠏⡴⠂⠿⠃⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢆⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣆⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢸⡇⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠘⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠰⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⢿⣿⣿⠟⠋⠉⠙⠛⠿⢿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠛⠿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⣠⣘⣧⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄⠠⣄⠈⠛⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠉⣀⣀⡀⠀⠘⠃⠘⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠻⠳⢆⠀⠀⠀⣿⣿⣩⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣄⣈⣀⣀⠀⠀⠀⣀⣾⣿⣿⠛⠂⠀⠐⣰⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣤⣤⣾⣿⣿⣿⣿⡿⡿⠟⠛⢉⣵⣖⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠐⢤⣀⠀⠙⣿⣿⡟⠋⠁⠁⠀⠙⠻⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠤⣶⠁⠈⠳⣄⡀⠐⠊⢹⠂⠘⠻⠀⠶⣶⠖⠘⠒⠲⠌⠻⢿⣿⣿⣿⣿⣿⣽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣿⡄⠀⠀⠈⠳⣤⣔⢃⠀⠀⢾⠀⠀⠘⠷⣤⣀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⣠⡀⠀⠀⠀⠹⠁⠀⠀⠀⣸⣇⠀⠀⠀⠈⠛⠙⠁⠀⠀⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠶⠶⢦⣤⣴⣀⣀⣀⣾⣿⣧⣀⢀⠀⠀⠀⠀⠤⠀⠈⠉⢀⡀⠉⢛⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄⠄⣀⠐⠲⠶⠶⠤⣀⣀⣈⣉⡉⠉⠉⠙⠉⠙⠋⠁⢀⣈⡉⠠⠠⠲⠆⠒⠂⠀⣉⡀⠀⣈⡐⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠕⠺⢭⣒⠤⣀⡀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠂⣀⠀⠉⠁⠀⣀⡒⠆⣀⣀⣤⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠑⠢⢍⡓⢦⣄⡀⠀⠀⠀⠀⠀⢼⣷⣾⣿⣧⡄⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠀⠈⠀⠀⠀⠀⠉⠓⠮⣝⡳⢦⣀⠀⠀⣴⣿⣿⡿⠋⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠈⠙⠲⢭⣛⠶⣬⣻⠿⣿⣷⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⡀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣽⣻⢦⣝⡢⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠮⣝⡳⢯⣛⠻⠿⠿⠿⠛⠛⠽⠷⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠒⠀⠉⠀⠀⠀⠉⠓⠬⣛⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁