Tiger salamander Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⣤⠴⢶⣶⡶⠒⢶⣶⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣋⣍⠿⡶⢿⣿⡎⣯⢰⣿⡎⠿⣰⡆⢼⠟⢹⣿⢖⠦⣤⣀⠀⠀⢀⣤⡀⠀⣠⣄⣀
⠀⠀⠀⠀⠀⢀⡴⠻⠿⠇⠺⠟⠀⠀⠺⣛⠘⠀⠈⠉⣶⡆⡿⢃⣶⠀⠿⡡⠿⢃⣭⡍⢹⣷⡿⣇⣾⢭⣠⣽⠷
⠀⠀⠀⠀⢠⠿⠋⠛⢠⣴⣇⣶⣀⣴⣤⠈⣷⣄⣤⣀⡉⠀⠀⢀⣀⠀⠀⠁⠀⠘⠋⢠⣤⣄⠰⠏⡛⢛⡹⢿⣿⡗⢲⣦⡀
⠀⠀⠀⢠⡏⠀⠀⢰⣟⡟⠉⠀⠈⡟⣿⠁⡏⠉⠉⠙⠓⠲⠯⠿⠿⢷⣶⣶⣦⢤⣶⡿⠋⠁⠀⠈⠉⠀⠀⠀⣘⣿⠙⣻⡱⡄
⠀⠀⠀⢸⠀⠀⠠⣾⣿⠀⠀⠀⠀⡇⣿⠸⣥⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠉⣀⣠⣴⣶⣴⣆⡠⠀⣀⡄⢴⣶⠀⠈⠉⢸
⠀⠀⠀⠸⡄⡀⠀⡛⠸⡀⠀⠀⠀⠙⠺⣟⣾⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣷⠀⠀⠀⠉⠉⠑⠲⢿⣿⣦⠤⠴⠶⠒⠁
⠀⠀⠀⠀⢻⡓⣄⠀⠀⠙⠦⣀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣆⣄
⠀⠀⠀⠀⠀⠙⢿⣾⣄⣀⣀⣈⠉⠓⠒⠲⠶⠤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣶⣾⣿⣿⡿⠿⠿⠷⠾⠿⢭⣷⣤⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠤⠀⠄⠀⠁⠀⢀⠆⠈⠀⠀⠐⠋⠀⠀⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠆⠑⣤⣀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠁⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢐⠂⠈⠀⠀⠀⠠⠄⠼⠂⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠊
⠀⠀⠠⠀⠈⠋⢨⡀⡄⠂⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⣱⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥
⠀⠀⠀⡄⠀⢀⣂⣔⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠁
⠀⠀⠠⠀⠀⠺⣿⣿⠇⠋⠀⠀⠀⠀⡄⣀⠀⠀⠀⠒⠁⠀⠀⠓⠂⠒⢀⡠⠶⠂⠄⢠⡤⠄⢏⢳⡆⠂⠠⠀⠦⠤⠄⠤⡀⢀⠄⠒⠆⠐⠀⠜⢩⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⠀⠀⢞⡄⠠⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠐⠎⠠⠀⠀⠀⠂⠂⠀⠑⠣⠀⡀⠀⠁⢨⠠⡘⠂⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠁⠡⠀⠁⠀⠀⡀⢡⠀⠐⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⢅⡀⠀⠠⠔⠠⠄⠁⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠀⠈⠀⠀⣄⠠⠠⠀⠉⠈⢰⠉⠀⢠⠂⠈⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠠⣄⠚⠂⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠁⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣉⠉⠉⠉⣭⣍⡩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠌⠉⠀⠀⠀⠢⠊
⠀⠀⠀⠀⠀⠀⠀⠐⡁⠐⠀⠀⠀⠀⡔⠂
⠀⠀⠀⠀⠀⡠⣏⠐⠀⠀⠀⠈⡠
⠀⠀⠀⠀⠈⠴⣇⠀⠀⠈⡠⠊
⠀⣠⠀⠀⠁⠀⣀⠈⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠶
⡧⠄⠀⠀⡀⠨⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⣤⣴⢒⣲⣶⣾⣿⣧⣀⣀⣽⣿⣿⠛⠋⢠⣄⡀
⡇⠀⠀⠈⡔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⢐⣾⣿⣯⣿⣿⣿⠉⠀⢸⡿⠛⢿⣿⠋⠙⢻⣶⣾⠿⠛⠛⣻⣿⣅⠀⠐
⡇⢀⡠⠀⠀⡀⠀⠀⠀⢀⡀⣀⣄⡀⠀⠀⠀⢛⣋⠴⠾⣿⣿⣿⡟⠉⠈⣿⡏⠉⣿⣧⣄⣾⣷⠀⣿⣿⣆⣄⣿⣿⣿⡇⠀⣴⣿⣿⠿⣷⡀⠀⣀⣠
⡃⠂⠀⢐⠇⢀⣀⣛⡛⠿⣟⣿⣽⡟⣨⣤⣶⣋⣵⣶⣶⣿⠿⣿⠿⠢⣠⣾⣷⠀⢹⣏⣿⣟⣿⣷⠟⢹⣿⣿⣿⣿⣿⣧⣼⣿⠋⠀⣠⣼⣷⡀⠉⠁
⠁⠀⠈⠁⣀⣈⣩⣴⣷⠛⣿⣶⡟⢿⣿⣿⡿⢿⣿⣿⡏⠀⠀⠈⣿⠀⢸⡿⣿⣦⣾⣿⣿⣿⢿⣷⡄⢸⣿⣿⠟⢉⠀⠈⠉⠛⢶⣾⢿⣯⣹⣷
⠀⠀⢀⡴⠛⠛⢿⣿⣿⠛⠻⢿⣧⣀⣹⣿⡁⠀⢹⣆⣷⣀⣰⣾⣿⣷⣿⣿⣿⡿⠟⠛⠁⠀⢨⣍⣁⣈⣿⠇⠈⠉⠀⠀⠀⠀⠀⢷⡿⢛⣹⣿⠄
⠀⠰⠛⠱⠟⠷⠞⣋⣹⣦⣀⣼⣿⡿⠿⣿⣇⣠⣾⣿⣻⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⡰⣶⢚⡯⠟⣿⠏⠀⠀⠀⠀⢀⡀⠀⠀⢸⣇⣩⣼⣿⡇
⠀⠈⢧⡐⠶⠀⠘⢷⣾⣿⠻⠿⠿⢷⣤⣾⣛⣿⡋⠉⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣟⣻⣣⠞⠁⠀⠀⠀⠠⣤⠟⠁⠀⠀⣸⣿⣿⣿⣿⠀⠛⠃
⠀⠀⠀⠉⠙⠓⠶⢿⣿⣿⣶⣿⣾⣿⠿⠿⠛⠛⠻⢀⣻⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⢛⣿⣿⡿
⠀⠀⠀⠘⠃⠀⠀⠀⠈⠉⠙⠋⡉⠀⠀⠀⠴⠀⠀⠈⣩⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⣠⣿⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁⠀⠀⠀⣠⡄⠶⣾⢿⡟⠁⠀⠀⠂⠀⠀⠀⠈⠉⠀⠀⠀⣀⠀⠀⠀⠀⠰⠆⠀⠀⢀⠼⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢂⠿⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣽⣿⡿⠟⠉⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣄⣀⠀⡀⠀⠀⢀⣴⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣠⣼⣿⡿⠋⠁⡀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠁⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⡞⠛⠛⠙⠛⢙⠛⠓⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠑⣄⠀⠈⢢⠀⠀⠀⠈⠀⠀⡇⠀⠀⠫⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣟⠉⠢⡀⠀⠀⠀⠘⡀⠀⢀⣄⣤⡤⠶⠶⠶⠷⠶⠶⢦⣤⣀⡨⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠡⡀⠈⢣⠀⠀⣠⡼⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠫⠤⣀⠀⠀⠀⠈⢢⢸⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠒⠤⣀⡱⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣴⢛⠀⠀⠀⠀⠀⢀⣀⡀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠳⣄⡼⠓⠊⠀⡀⡀⠀⠀⠊⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢖⣛⡁⠀⠀⢀⡾⠁⠀⠀⢸⠀⠸⠀⠀⠈⠑⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠟⣁⡄⢀⣾⠀⠀⠀⠀⢸⠀⢰⠀⠀⠀⢦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣡⠞⣹⢣⡟⡰⠀⠀⠀⠀⢈⣀⠎⠀⠀⠀⠀⠙⠳⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠟⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠲⣄⡀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡯⠤⡀⠀⠀⠀⢪⠈⠑⢄⣀⣀⢀⣸⡏⠻⣗⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡀⠆⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⡿⢀⣴⠋⠀⠀⢀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣸⢣⣞⣵⡦⢠⡄⢸⠻⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⠤⢄⠀⠀⠀⠠⠂⢄⠀⠐⢄⣰⠏⠈⠉⢰⡇⣾⢷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠘⢄⡀⠑⡄⠀⠘⢄⠘⡀⠀⢠⡟⠀⠀⠀⠸⡶⠇⠘⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠙⢆⠸⠀⠀⠈⡆⠙⢢⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⣀⣀⠀⠛⠀⠀⠀⠃⢀⡞
⠀⠀⠀⣀⣤⡤⢴⣶⠞⠁⠀⠀⠀⠀⢸⠀⠈⡆⠀⠀⠀⠀⢸⠟
⠀⠀⣼⠋⣠⣴⠋⢁⡈⠉⠑⠢⡀⠀⠘⡀⠀⢣⠀⠀⢤⣴⣯⣤⣄
⠀⢠⣇⡾⠉⠀⠉⠀⠀⠉⠢⣀⡅⠀⠀⠁⠒⠊⠀⠀⠀⠀⠀⠀⠈⢳
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡞⠁⠀⠀⣼⠁
⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⣆⠀⣿⡴⠞⠋⣡⠟⠀⠀⢀⡼⠃
⣧⠀⠀⠀⠀⡴⣛⢲⠀⠀⠀⠸⠀⣤⠞⠁⠀⣶⣛⡁⠀⠀⢀⡞
⢸⠀⠀⠀⠀⠳⠭⠞⠀⠀⠀⢠⡶⠃⠀⠀⢀⡴⢋⡀⠀⠀⡞
⣾⠀⠀⢠⡀⠀⠀⢀⡠⢊⡴⠋⠀⠀⠀⠀⣯⡴⡿⢡⣿⢸⠇
⢸⣄⠀⠀⢁⡤⠖⣩⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⣥⠟⠻⠟
⠀⠙⠷⠥⠶⠖⠛⠁
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠁⠁⠀⠀⠀⠁⠈⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠁⠀⠁⠀⠀⠀⠈⠁

⠀⠀⠀⠀⢀⡤
⠀⠔⠈⠉⡡⠻⠇⡖⠂⠄⡀
⠀⢌⠓⠀⢋⠨⢱⢐⠀⠀⠙⢅⠂⢤⢀⡀⠀⠀⠀⢀⡀⠀⠠⠤⠀⠀⢠⠤⡤⠄⠀⠀⢀
⠀⠑⢕⡠⠀⠭⠌⠃⠠⠐⠀⠀⠁⠨⠀⣀⠈⠉⠡⠀⠀⠂⠀⡄⠠⡀⠣⡀⠈⠄⠀⠀⠤⠀⠠⢄⠀⠄⢀⡀
⠀⠀⠀⠈⠉⠀⠛⠢⡈⠀⠀⠀⠥⠊⢰⢸⠀⠄⠀⡄⠀⡆⢀⠁⠐⢂⢄⠈⡀⠃⠀⠄⡓⠁⠄⠀⢱⠀⠀⠄⢢⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡔⠒⣁⠤⠋⠤⠀⠀⢇⠜⠀⠐⠠⠘⡠⠀⢸⢠⡠⢃⡦⠐⢖⠓⡂⠪⡢⠌⠀⠈⠀⡇⢀⠤⣱
⠀⠀⠀⠀⠀⣀⡀⠀⢤⠊⢲⢅⡐⢇⣠⠂⢲⠠⠊⢀⡔⡠⠊⣠⣦⢈⡉⠵⡁⠈⢰⠘⢀⡠⠄⠌⠀⠀⢰⣠⡡⠁⠎⢄
⠀⠀⠀⠀⠀⠤⠊⣡⠄⠬⠚⠉⠀⠉⠱⠧⠘⠘⠁⠈⠁⢀⡟⠓⣂⠀⠑⢒⠡⠔⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠰⡀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡤⠂⠃⢈⡦⠂⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠡⠀⠀⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠹⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠴⠈⠀⠠⢁⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠀⠐⡀⠈⢱⠀⢀⡀⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠤⠁⠀⠀⠀⠈⠒⠚⠊⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢛⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⣖⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⡦⠈⠛⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣿⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣲⡖⠉⢰⡒⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⡼⢧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠽⣥⢋⣀⠭⢷⠖⣖⣲⡌⠍⠤⢭⠷⠴⠖⠶⠶⠿⣿⠓⡍⠦⠜⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⢟⢁⡧⠖⠋⠉⠯⡐⠢⡄⠐⡏⢦⠀⡔⢢⠀⡔⠁⢺⣀⣠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡛⠐⢉⠔⢹⣊⣉⠙⣦⡀⢈⡖⠚⠛⠉⠉⠛⠓⠚⠓⠓⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢈⡶⣟⠉⠳⣀⠈⡭⢢⠑⢺⡃
⠀⠀⠀⠀⠀⠀⠀⢠⠟⠊⢉⡟⠀⠀⠁⢆⠀⣧⣷⡏⢀⠔⢿⢳⢦
⠀⠀⠀⠀⠀⠀⠀⡟⠋⢉⡞⡤⠒⠤⢄⣀⡷⢫⣔⣛⠉⠲⣚⣋⣨⡇
⠀⠀⠀⠀⠀⠀⢰⣧⠴⢺⠃⠁⠐⢢⡀⡸⠁⢀⣵⡫⣶⢠⡄⢰⡌⡇
⠀⠀⠀⠀⠀⠀⢸⡇⣀⢸⠀⢀⡠⠤⢼⡇⠀⠀⠉⢠⣧⠋⢧⡿⠙
⠀⡴⢻⠋⠒⢤⣸⣁⡈⢻⠀⠓⠒⠢⣼⠁⠀⠀⠀⠀⠁⠀⠈⠁
⣸⠉⠓⠤⢀⣞⡼⠁⠈⢹⠀⠀⠀⠀⢹⢤⣀⣀⣀⣀
⡇⣀⡀⡦⣜⢿⠀⡀⠀⡟⢀⡤⠖⢢⡀⠈⠒⠉⠀⢯⠹⣆
⣧⠇⢳⣹⠈⢹⠾⠍⠇⠐⠧⠔⠒⡭⢴⠋⠉⠉⠓⣆⣴⠛⣆
⠁⠀⠀⠁⣰⢋⠄⠠⡄⠀⠀⡤⠠⠍⠚⡆⠀⠀⠀⢹⠀⡵⢹⡀
⠀⠀⠀⠀⣿⠃⣠⢀⣇⡤⠦⣌⠆⢤⣐⣿⠀⠀⢀⠞⠀⠉⠙⠣⣄
⠀⠀⠀⠀⢻⣹⠯⡑⡜⠒⠒⢩⢖⢶⡌⡟⠀⠸⠗⣻⢀⢶⢸⠛⢮⡧
⠀⠀⠀⠀⠀⢿⡳⠟⡻⠉⠤⣘⣷⠞⡽⠁⠀⠀⠠⡧⠋⠘⣾⠇
⠀⠀⠀⠀⠀⠀⠙⢾⣁⠀⠀⢀⡸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⣤⠍⠉⠉⠍⡉⠋
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢐⡀⠁⠀⠀⠠⠊
⠀⠀⠀⠀⠁⢀⠀⠠
⡄⠀⠀⠀⢔⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣶⡶⣶⣶⣷⠾⠿⣶⣿⣷⠷⡶⢦⢀⣀
⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣠⣶⣶⣿⣿⣿⢿⣿⣿⣿⣿⣟⠛⢹⡿⢿⡿⠛⢿⣶⡾⠿⢻⣿⣿⣿⣦
⡇⠠⠂⠀⠀⣀⣀⣰⣾⣿⣿⢿⣿⣿⣿⢛⣿⣿⣿⡉⠸⣏⠉⣿⣦⣿⡇⣼⣿⣤⣾⣿⡧⢠⣾⡿⠿⣿⣿⣇
⠃⠀⢀⣴⣾⣷⣾⢨⣷⣾⣿⣾⣿⣷⣿⣿⠛⠉⢿⡅⣾⣿⣄⣽⣿⣿⣿⡃⢸⣿⣿⣿⣿⣿⣯⣠⣾⡟⣿⣿⡇
⠀⠀⢠⡾⣻⢿⣿⡟⠿⣿⣌⣻⣿⠀⢻⣽⣄⣰⣾⣷⣿⣿⣿⣿⣿⣹⣏⣁⣸⣿⣿⣿⣶⣿⣾⣿⡾⣛⣿⣿⡇
⠀⠀⣟⢛⡛⢛⣭⣿⣤⣿⣿⠛⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣽⢋⣿⣿⡟⠛⢻⣿⣿⢿⣤⣶⣿⣿⡇
⠀⠀⠙⠾⣥⣤⣽⣿⣭⣭⣭⣿⣷⣾⣆⢨⣿⣿⠚⣿⣿⣿⠟⣿⣿⠗⣷⠛⣾⡏⣥⣻⣿⢛⣏⣿⢿⣿⣿⡯
⠀⠀⠀⠚⠋⠟⠉⠛⠛⢛⣿⣯⣤⣶⡜⢉⣿⣿⠀⠉⠹⠛⠀⣀⠀⠀⠐⠋⠼⠿⠛⣿⣏⢁⣼⣿⣾⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠈⠹⡎⢱⡟⡟⠁⠠⠉⠀⠀⠊⠡⣦⡤⠆⠀⠀⠐⢿⠟⣡⣿⣿⣿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⠔⠻⠁⢠⡾⢧⡀⠀⢀⣨⡉⠀⠀⠀⠀⢀⣐⣿⣿⡿⠋⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡋⣩⣵⣶⠞⢧⣀⣈⡟⢃⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠊⢉⣴⣿⠿⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁

⠀⠀⠀⠀⢀⡄⠀⠀⢀⣠⣶⣶⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀
⠀⠀⠀⠀⠭⡀⠀⠀⢿⣿⣯⣿⣿⣷⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⡀⢤⡄⠀⡀⠀⠀⠠
⠀⠀⠀⠀⡠⣉⣰⣀⠀⠙⢿⣇⣐⣛⣿⣿⣿⠿⣿⣿⣷⣶⣦⣶⣦⣶⣶⣤⣤⣤⣤⣴⣶⣦⣄⠀⠀⢀⢳⠸⡿⠱⢷⢆⣆⢀
⠀⠀⠀⠀⣼⣿⣿⣿⡷⣷⣤⠍⠻⣿⣿⠻⣿⣦⣀⡈⢉⠉⢉⠉⣉⣿⠛⢛⣿⠋⢉⣛⣿⡿⠿⣷⣾⣿⣷⣦⣵⠀⢂⣨⡤⠼⠂
⠀⠀⠀⠈⠛⢧⣯⣿⡿⣻⣿⣄⠂⡉⠻⣦⣸⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠛⣻⣿⣿⣶⣶⣾⡟⠻⢿⣶⣄⡀⠀⢴⣴⠄
⠀⠀⠀⠀⠀⠉⠘⠟⢱⣺⠟⠋⠋⣀⣴⣞⣻⣟⣛⣿⣿⣿⣿⣷⣾⣾⣿⣷⣾⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⡟⣿⣦⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠚⠛⠛⢛⡛⠋⣁⣬⠄⠀⠈⠉⠉⠙⠉⢩⣾⣯⣿⣷⣴⠦⠀⠀⠀⠀⠈⠉⠛⡿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⠻⠛⠋⠉⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠿⠟⠛⠛⠉

⠀⠀⣀⣠⡀
⠀⢧⣿⣿⣽⣷⣶⢶⣿⠗⣦⣄⡀
⠀⠀⠙⠳⢯⣭⣥⣤⣀⣀⣠⢘⣉⡑⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⣉⣋⣈⣩⣓⢾⢝⠷⡇⣸⣹⠟⣿⣶⣢⣤⣀
⠀⠀⠀⠀⠀⠘⠻⠟⠋⠱⢾⡟⠈⣿⣏⣻⠾⣆⢇⣸⣇⣩⡏⠛⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⡙⠂⠈⠉⠚⠛⠎⣀⡽⢛⠛⢷⣎⣉⠉⠙⣷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠃⠀⠀⠀⠀⠀⠀⠘⠁⠉⠙⠼⣦⠀⡉⠠⣠⣿⣬⠹⠇⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⢿⡟⣤⣌⣿⠿⣤⣼⣿⡛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣤⣤⣿⠋⠉⠉⠀⢻⡏⠁⣰⣿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⣹⣝⣶⢶⣿⢿⣿⣉⣥⡴⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢻⡿⣿⠋⠍⠉⠉⠻⣏⠻⣃⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⢻⣎⠉⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⣻⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⣯⣤⣾⣿⣧⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⡾⠫⢡⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠙⠛⠓⠒⠊⠉⠁
⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢛⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⡌⠙⠃⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠯⠧⣤⠔⠂⡤⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣏⡁⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣟⣰⠂⠈⣲⣥⣤⠄⢤⠀⠀⠀⠀⣤⣠⡤⢤⣤⣴⣺⡯⡞⢇⣠⠇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣼⡗⢚⢉⡤⠞⢲⡏⠩⢉⠁⢡⠒⡄⠀⣠⢍⠀⣠⠞⢰⠃⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠽⢂⡵⣪⠥⠀⠤⡀⠉⢢⣤⠵⠤⠦⠷⠤⠧⠼⠦⠧⠤⠴⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⢢⣴⠥⠤⡙⠒⠒⣒⡳⠄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡡⠆⢠⠎⠘⠂⢄⠉⠢⠐⣁⡏⠀⣙⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡯⠤⣤⠎⣀⡀⠀⠀⢣⣰⠟⣻⡤⠼⣁⣧⠮⢹⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠀⣀⡞⠺⢁⣀⠉⠒⡾⠁⠻⢑⠖⣀⠙⠐⢒⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡷⠋⠁⠇⠀⠀⠈⠓⣴⠃⠀⠰⠗⢫⢏⡜⡇⡿⢤⠁
⠀⢀⣀⣄⡀⠀⢀⡧⠠⣼⠀⢠⠖⠒⠒⡿⠀⠀⠀⠀⠸⠞⠀⠳⠇
⢀⠏⣰⠁⠈⢱⢾⡧⠤⢸⡄⠀⠉⠈⠳⡇
⡼⠀⠈⠐⢢⣮⠞⠀⠀⢰⠀⠀⠀⠀⠀⠗⢶⢲⠶⠦⣤⣀
⡇⡤⣄⢿⠪⣹⡄⣠⡀⠘⢀⠔⠊⣉⡷⢀⣈⣁⣀⠀⠃⠚⣇
⡷⠃⠸⣼⠀⢸⠟⠒⠞⠀⠛⠒⠉⢱⡒⡎⠀⠀⠈⠙⡆⢏⠙⡆
⠀⠀⠀⠀⢰⢣⠐⠒⣢⠀⠀⢰⡒⠒⠈⢹⡀⠀⠀⠀⣷⠀⡇⢹
⠀⠀⠀⠀⣿⡃⣠⠤⠵⡰⠒⢢⠙⠠⠤⣹⡇⠀⢀⡴⠃⠀⠀⠈⡳⣄
⠀⠀⠀⠀⠸⡍⡟⢍⣦⠑⠛⠉⣔⡤⣦⢸⠃⠀⠓⠊⡟⣰⢦⢸⠙⠮⡇
⠀⠀⠀⠀⠀⠻⡕⠚⣫⠉⠰⢄⣛⡖⢫⠏⠀⠀⠀⠸⠴⠁⠸⣼
⠀⠀⠀⠀⠀⠀⠘⠶⣅⠀⠀⢀⣀⠟⠁

⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣠⣾⣿⣦⣾⣦⣄⣀⣀⣀⡀⢀⣀⣠⣤⢤⣠⣠⣶⣶⣶⣤⣤⣤⣄⡀
⠀⠀⠹⣯⣶⠆⠛⠛⠟⢉⣿⡿⠛⠿⠿⠐⢳⣶⣟⣉⣙⣿⣋⡙⠛⠻⠿⣷⣤⣻⣶⣄
⠀⠀⠀⠈⠙⠻⣿⣿⣤⣿⠿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣻⠿⢿⣿⣿⣿⣶⣴⣿⣙⣻⡿⢿⠶⣀
⠀⠀⠉⠉⠀⠘⠛⠟⠛⠛⢿⣾⠿⠿⠿⠿⠿⠛⠛⠛⠛⠿⠿⢿⡿⢤⣿⣿⡿⠿⠿⠿⣿⣷⠛⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡲⢿⠟⠁⠀⠠⢀⠀⠀⠀⠠⠤⠀⠀⢀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠀⠀⠀⠀⠫⠿⠿⠋⠀⠀⠀⠒⠒⠒⠂⠀⢸⣟⣌⠃
⠀⠀⠀⠀⠀⠐⠗⠺⠷⠲⡖⠴⠖⢶⠶⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⡀⠀⣸⠯⡉
⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠶⣶⠶⣶⣶⣦⠄⠠⢶⡖⣶⣶⣛⣿⣿⠛⢛⠛⠉⠙⠉⣁⣤⢛⣽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣠⣴⣶⣺⣿⣽⡿⠟⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣥⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⢐⣶⣭⣏⠁⢉⠉⠉⣉⡍⣝⠛⠃⣭⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣠⣴⠛⣳⡤⣔⣋⣀⢀⠠⠚⠻⣦⠉⠃⠙⠉⣧⠙⠉⠉⠃⠒⠻⢜⢀⣭⣶⣤⣄⡀
⠀⠀⠰⠊⠑⣞⠿⣿⣿⡿⢾⣿⠋⠉⠀⢀⠀⡄⢸⠀⣦⣰⡆⣾⣈⣴⢲⡶⣶⣀⣜⣿⠈⠉⢿⣿⢎⣓⢄⡀
⠀⠀⡴⣴⣾⠷⠛⠻⠿⠓⠉⠈⠳⡿⣮⣽⡾⣇⠈⣎⣿⢹⣧⣠⣧⣷⣸⣷⣿⣿⡿⠿⡷⢀⢰⢧⡞⠋⠀⢿⣦
⠀⡘⠀⠙⠃⣶⣻⣷⢥⣴⣶⣾⣿⡿⠿⣿⣿⣟⣘⣉⣉⢁⡹⠿⠅⣛⣉⣾⠉⢁⣘⣤⣤⣜⣚⢸⣷⣷⠀⢸⣟⢷⡀
⠀⠐⠴⣿⣿⣮⣽⣷⠿⠭⠚⠛⠿⠷⣄⣠⡜⢻⡄⠀⠀⠀⠀⣀⣠⣤⢤⡿⠀⢉⣿⠛⠋⠀⠈⠉⠛⠛⢿⡞⠁⢙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⣨⡇⠀⠀⠀⠈⣉⡩⡆⡐⠃⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣷⣻⢲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡔⠛⣁⣠⡠⠋⠀⠀⠀⠀⠘⠛⠛⣏⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣫⠄⢠⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠏⠲⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠪⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⠋⢐⣀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⡄⠀⢀⣄⡄⡄⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣀⠀⡞⢷⠀⠀⠀⣡⢔⣶⢥⠴⠒⠛⠛⠓⠤⢿⢻⡿⡿⢻⢿⣿⣿⣭⣗⣿⣤⣐⣠⢀⡀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣈⣣⠘⠶⢣⣾⣡⣴⣿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⡄⠿⢷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣬⣶⣦⣤⣔⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢢⠝⠒⠚⠚⠛⠉⠹⠟⣼⣥⣤⡀⢀⣀⣀⣶⣾⣿⣷⣆⠘⡷⠶⣭⣉⣙⡛⠿⠛⠻⠻⣿⣿⢿⠛⠛⠿⠛⢻⣿⡿⠛
⠀⠀⠀⠀⠀⠉⠄⣰⠃⠀⢀⣀⡄⠀⠀⢀⠘⣋⣡⣾⢤⣿⣿⣿⣿⠿⡋⠉⠉⠢⠷⠀⠠⠈⠈⠉⠁⠀⠒⠐⠀⠀⠤⠀⠤⠀⠀⠈⠉
⠀⠀⢠⡖⠀⠀⢸⡃⠀⠁⠢⢀⠀⠀⠀⣼⣌⠻⢿⢏⢅⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠊⠂⠀⠀⠀⡀⠐⢢⡄⢀⣠⠤⠀⠄⠦⠀⣀
⠀⠀⡈⠄⠀⠀⠀⠉⠲⠦⠤⠴⠿⠿⠛⠟⠛⠛⠛⠱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠴⠾⢤⣔⣨⢼⣁⣀⡠⠶⠒⠈⢁⠐⡇
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣀⣠⠤⠴⠒⠒⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⢐⣬⠞
⠀⠀⠸⡎⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣊⡴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣦⣴⣷⡿⢏
⠀⠀⠀⠘⢦⡑⠦⡀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠐⢈⣀⣄⣤⣠⠼⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⢠⣤⣤⡟⣨⣿⠿⠃
⠀⠀⠀⠀⠀⠙⠦⣄⠑⠒⠤⣄⣀⣀⡁⡠⠴⠿⠛⠛⠉⠉⠀⠀⠀⠀⢠⡶⠒⠒⠲⢄⣰⣷⣧⣿⣿⣿⣿⡟⠀⡾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣄⣀⠀⢀⡀⢀⢀⣀⣀⠀⢀⣀⣀⣤⣼⣷⣶⣶⣄⠈⠻⠟⣛⠛⠉⠉⠀⢃⠀⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠈⠣⢄⣀⡈⠐⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣤⡄⢀⣴⡶⢆⣄⣠⣤⣤⡴⠀⣤⣤⣀
⠀⠀⠀⠀⠀⣰⣦⡀⠘⣿⣧⠸⣿⡇⢸⢹⢃⣾⣿⢯⣾⣿⠛⣿⣿⣿⠿⠿⠛⠢
⠀⠀⠀⣠⣄⠘⣿⣷⣄⠘⣿⣷⣿⣿⠾⠊⢸⢿⡟⣾⣿⢃⣾⣿⠋⢀⣠⣤⣶⣶⡦
⠀⠀⣀⡘⠻⣷⡼⠟⠛⠉⠁⣠⣤⣄⠀⠀⠀⢸⣷⣿⡟⢸⣿⡇⢰⣿⠟⢋⣥⣶⣮⣤⣄⠀⢀⡀
⠀⠀⠉⠻⡄⠈⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⠀⠀⠙⠻⣿⣄⠻⡇⠸⠏⢠⣿⣿⡟⣋⣩⣭⡠⣿⠇⠀⡀
⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢿⣄⠀⢸⣿⡿⣛⣭⣿⣿⣟⠈⠀⠊⠁
⠀⠀⠀⠈⠻⠷⠀⠰⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠠⠀⢿⣾⠿⠿⠛⠛⠋⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⡤⠒⣒⠒⠊⢉⠚⠋⠓⠒⡒⠚⠛⠶⠶⣯⣉⣒⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⢀⡤⠖⠊⠉⠋⠂⠒⡴⡝⢺⢷⡀⢀⣶⠤⣠⡢⣦⣥⣼⣣⠨⣀⠺⣿⢛⠿⠷⢤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣻⣎⢀⣹⡶⡺⢭⣥⣀⣀⠠⠴⠝⠉⠈⢻⡎⠈⠉⠀⠁⠀⢹⡆⢀⠀⠀⠈⠉⠉⠈⠙⢼⠁⣈⣶⣺⣷⣶⣦⣄⡀
⠀⢠⠖⠛⠓⢶⠛⡭⣽⡿⣿⣿⡤⣿⣿⠋⠉⠁⠀⠀⡀⢀⡀⠈⠧⠀⣶⡀⢖⡃⢤⣞⠈⣸⡰⣶⡴⣶⠦⡀⣄⢷⠏⠉⠉⠹⣿⣋⡢⢉⡲⢄
⠀⢸⠀⣀⣴⣿⣥⣴⣿⣞⣿⣦⠾⠉⢻⣤⣤⣞⡠⠾⣧⣼⡇⠀⢢⡘⣽⡷⠾⡷⠈⢸⡝⣯⡆⢸⡏⣿⣟⢷⣶⣿⣯⣤⡀⠀⢹⡯⢰⣿⠿⠁⣙⣦⡀
⢠⠞⣻⣿⡿⠋⢉⣀⡈⣉⠉⠁⠀⠐⣀⣈⢻⣽⣿⣾⣿⣿⣿⢀⡨⣇⣿⣇⢵⣳⢓⣾⡭⢹⣧⣾⢿⣿⣿⡟⢏⠉⠙⠚⠁⡄⣼⢱⣗⢀⡠⠀⠈⣿⣿⣆
⡏⠀⠈⠉⠁⣾⣏⣯⣿⠂⠄⣰⣿⣷⣿⣿⣿⠿⠿⢿⣽⣟⢛⣈⣁⣀⣉⣡⣀⡭⠭⠭⢤⣉⣁⣉⣿⠁⠀⣄⣌⣷⣤⣴⣴⣛⡃⠀⠙⢻⠸⠁⠀⢽⢎⠛⣧
⠣⣠⣾⣿⣿⣬⣛⣯⣥⡾⣛⣋⡽⠿⣿⣿⣿⡄⠀⠀⢈⠏⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣟⠀⠘⢫⣿⠿⠿⠛⠁⠈⠉⠚⠛⠾⠿⣶⣶⠞⠉⠱⡽
⠀⠈⠉⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⢛⡿⠀⠀⣿⠀⠀⠀⠀⠀⠰⡯⠭⢭⡛⠉⠝⠇⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣢⣈⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠟⠀⠢⣴⡏⠀⠀⠀⠀⠀⢀⠠⠤⣒⢷⢤⠈⠁⣸⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢏⡁⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⠔⠓⠋⢀⡐⢀⡤⠛⠀⠀⠀⠀⠀⠀⠑⠚⠛⠛⣟⣠⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⠊⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⠷⠌⠈⠉⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠧⣆⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⠞⢛⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡔⠋⠈⠉⣠⣬⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠈⣁⣤⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠡⠈⢠⣠⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⢐⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠈⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠃
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠘⡿⡿⠿⠛⠛⠛⠛⠿⣿⣿⣿⣿⡆⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣆⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠦⣤⣄⡀⠀⠐⠂⡄⠀⠴⢄⡀⠀⠀⢻⣿⣿⣿⣆
⠀⠀⠀⣠⠶⠒⠟⠛⠛⠻⢦⣄⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣀⡀⠀⠀⠠⢄⣠⣄⡠⠀⢻⣿⣿⣿⡄
⠀⠀⠚⠀⠀⠨⠦⣴⣤⠤⠄⠈⠙⠢⠀⠀⠀⠀⠐⠂⠀⠩⠭⠉⠙⠛⠳⢲⣆⣤⡄⣀⠀⠀⠙⢿⣿⣷⣤⡀
⠀⠀⠀⠉⠙⠒⠒⠢⠭⠝⠓⠦⢤⣀⠀⠀⠀⠀⠀⠀⣀⣉⣄⣀⣀⠀⠀⢉⣉⣉⣟⣳⣦⣀⣀⡀⠈⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⣠⣤⡰⢻⡉⢁⡠⣤⢨⣄⣠⡄⠙⠳⠶
⠀⠀⣠⣖⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⠛⢋⠉⣡⠆⠲⢛⣹⡥⣽⣶⣿⣶⣾⣿⣴⣎⢷⣴⡆⢑⡄
⠀⠋⠀⠉⢩⣿⣿⡻⠶⢀⠀⠀⠀⠀⠀⠀⣀⣠⣭⠅⣠⣶⠟⠘⣓⣹⣃⡙⠻⡊⠁⠀⠀⠀⠀⠀⠀⠈⠐⠫⢘⣧⣤⢶⠄
⠀⠀⠐⠦⠞⠻⠟⠋⣶⢿⡡⣦⢄⠀⠀⠄⠻⢯⠦⢶⠏⢀⣠⣾⣿⣿⣯⣿⣼⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡌⣁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠁⠛⣠⡟⣷⠷⠿⠻⠉⣠⢶⣿⡿⠿⡿⠓⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡟⠴
⠀⠀⠀⠀⠀⠀⠀⠠⠏⠗⠠⣀⢩⠃⣬⣄⣠⣴⣾⡟⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⡤⠴⠂⠀⠀⢀⣠⣣⠥
⠀⠀⠀⠀⠀⠀⠀⣉⣜⠠⡛⠂⣍⢧⣈⢻⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠚⣵⠍⠁
⠀⠀⠀⠀⠀⠀⠀⡛⢯⡆⠉⠀⠁⠁⠙⣠⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⡀⠀⢀⣥⡷⠞⠁
⠀⠀⠀⠀⠀⠐⣀⣋⠸⡦⠀⠀⠀⠀⠀⡏⢺⠀⠀⠀⠀⡤⠤⡄⠆⠀⠀⠀⠀⠐⠈⠋⠁⠈⢀⣠⠴⣟⣛⠉⠁
⠀⠀⠀⠀⠀⠀⠹⠋⠱⠂⠓⠀⠀⠀⡀⢷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣾⠟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠞⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠚⣆⠀⠀⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⡠⠋⠀⠀⠀⠉⠃⡀⠀⢀⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠁⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⣿⠿⢛⣯⣽⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⢀⣀⣀⣤⣶⠿⣟⣭⣶⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣾⣻⣿⡿⠿⠟⢻⣫⣽⣿⣿⣿⢿⣿⣋⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⡿⠿⠻⠛⡙⣋⣉⣩⣭⣶⣶⣿⣿⣿⣿⣿⡿⠛⠙⠿⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣤⣾⣿⠟⣙⣫⣴⣶⣾⣿⣿⣿⢿⡿⣿⠿⣿⣟⡿⠿⠞⠋⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣷⣿⠟⣉⣴⣿⣿⣿⣟⡿⠿⠌⠁⠊⠓⠐⠋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠓⣾⣿⣿⣷⣟⣻⣷⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣿⡿⠋⠉⠀⠈⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⠀⠀⠀⠀⠘⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠀⠤⠾⠟⠟⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢹⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠄⠀⠀⠀⠀⠀⠈⠉⠒⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠧⠶⣤⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣿⣿⣿⠿⠛⠁
⠀⢀⣴⣾⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉
⢠⣾⠟⠁
⣾⠃
⣿
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣯⣟⣻⣻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⣾⣁⣀⣴⡓⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣽⣿⣿⣿⣿⣿⣿⣿⠏⣁⣼⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣀⣿⣿⣿⠿⠿⠛⠛⠛⠛⠿⣼⣿⡿⠋⢸⣿⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣹⠋⢠⣴⡿⣿⠃⣿⡀⢀
⠀⠀⠀⠀⠀⢰⣤⣾⣯⠟⠁⠀⠀⢀⣾⣤⣾⠁⠀⢰⡾⠟⢀⣿⠿⢿⠷⣤⣯⣤⣿⣷⣤⣀
⠀⠀⠀⠀⠀⣾⣿⢻⠃⠀⠀⠀⠀⠈⣿⣝⣿⣿⡟⠁⠀⣠⡞⠃⣸⠇⢠⣿⣿⠟⢿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⠀⢀⣼⣿⠟⠋⠀⡀⢐⣽⠯⠀⠞⠀⣿⣿⣿⡟⠀⠀⢻⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠘⢻⣿⣿⠋⠀⣦⣾⣷⣿⠋⠐⠀⢐⡾⢿⣿⣿⡇⢠⣤⣿⣿⣿⣿⣻⡿⠓⠂
⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠴⠚⣿⢁⠔⣴⢷⡿⢟⠃⢤⣤⡾⠭⠛⣿⣿⣿⠁⠀⡴⠜⠙⡿⠛⠻⣆
⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⢠⢣⣯⡼⢣⣾⡕⠀⠀⣀⠀⠈⢀⣤⣾⣿⡟⠀⠀⠀⠀⠀⠇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠀⡎⢸⣱⡏⣺⡋⠁⠀⣼⣿⠛⠛⢿⣿⣟⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣼⢿⣷⣿⣤⠀⠀⠛⠉⠀⢠⣻⣿⣿⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⣻⣆⠻⣞⣷⢖⠿⠟⣳⢶⣶⣿⣿⠁⠀⣿⣿⣷⣀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠘⡏⢿⠶⠀⠀⡸⠛⠾⣿⠁⠀⠀⠙⢿⣿⠛⠛⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠰⢘⠀⠀⢈⠀⠀⠀⠀⠀⠐⠋⢀⡈⠙⠲⢶⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆⠀⠀⡀⠀⠐⠂⠀⢠⣶⣶⣴⢷⠾⡿⠿⣦⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⣿⡿⠖⠂⠐⠣⡍⠻⢷⣷⢀⣀⡀⠘⠄⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣄⣴⠆⠀⠉⢲⣿⠊⠐⡉⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⢻⣿⣿⣌⠹⠄⠀⡄⢻⣿⣶⠀⢁⣤⣶⡂⡐⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⢹⣿⣷⡶⠿⠛⠉⠉⠁⠈⠀⠐⠿⡏⠀⣙⣻⣿⣿⣿⡽⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗⠛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠟⢻⡿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢠⣆⡾⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣄⡀
⢠⡖⣄⣶⣦⢾⣿⡟⣻⣟⣛⣛⣛⠛⢋⣉⣩⣭⣭⣤⣤⣤⣬⣍⠉⠛⠿⢿⣦⣄⡀
⢸⠟⣻⣯⣴⣿⣥⣤⡆⣽⣿⣿⣿⣿⣿⣟⣹⡟⣿⣽⣛⣏⡿⣿⣿⣿⣶⣶⣬⡛⢿⣦⣤⣤⣄⡀
⠘⢿⣿⣿⣿⠿⢿⣿⣿⠛⠉⢿⣛⡿⣟⣩⣛⣿⣿⣟⣛⣻⢛⣾⡟⠛⢛⣿⢿⣷⣌⠛⠿⢿⣿⣿⣦⡀
⢠⣶⣶⣿⣿⣶⣾⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣯⣿⣿⣤⣽⣿⣶⣿⣦⣾⣿⣿⣷⡀
⠈⣭⣭⣭⣭⣽⣛⣍⣍⣩⠏⣿⣿⣿⣿⣿⣿⣿⢿⣽⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠸⠟⠛⠛⢻⣿⣿⠿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠛⠛⠛⠻⠿⠿⠟⠛⠛⠉⠋⠙⠃⠘⢠⣀⣀⣀⣛⣉⣭⣹⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣯⠉⣩⣙⣛⣹⣯⣿⣿⣯⣼⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣍⣈⠉⢋⣹⣽⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⣀⠀⠀⢀⣀⣴⣿⣾⠛⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣾⣿⣧⣤⣿⣅⠀⠘⡟⠛⣿⣿⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠋⠉⠉⠁⠀⠉⠙⢿⡏⠉⠉⠛
⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⡶⠒⢲⢰⡒⠒⠢⠠⢄⣀⠀⠀⠰⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⢠⣄⠹⣧⠀⣿⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣿⣻⣿⣇⡀⢰⠇⠰⠮⣜⣓⠦⣄⣴⠉⠉⡿⠶⣩⣉⠉⣿
⠈⠻⣆⢻⡆⢿⠀⣸⡟⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣠⣾⣿⢟⣵⢯⡿⠙⢿⣷⣦⣀⠈⠀⣀⣀⣀⣀⣤⣐⣿⢚⡟⠻⠨⣿⠆
⣀⣀⠈⢷⣿⣾⣶⡿⠀⠀⣠⣾⣿⣿⣿⣧⠀⠀⣼⠿⡿⢶⣻⡵⢻⣦⣀⣠⣳⡶⣾⢿⡿⣿⢿⠿⣿⣟⡟⢻⣿⠿⡿⠶⠏⣤⠞⣍⣹⢿⡇⢒⢶⠀⢀⡀
⠉⠛⠿⣶⣿⣿⠛⢣⠔⣻⢻⣿⣿⣿⣿⣿⠀⡜⢩⣿⠛⢹⣯⣠⣼⢿⣻⡯⣿⡟⣯⠜⣲⠋⠼⣿⠁⣼⢛⣭⣾⣭⡳⣿⣠⡋⡻⠢⡜⢻⡽⠛⣶⠿⠛⠿⣆
⠀⠀⠀⠈⢻⣿⡓⢛⣿⠯⠘⠻⡾⣟⡿⣏⢠⠄⣼⣟⣠⣴⣿⣿⡟⣻⡻⣶⣯⣿⢿⣟⣻⣱⣆⣴⣨⣽⠺⣿⣯⣿⣷⠋⠀⢹⠁⣦⢼⠉⣊⠰⠏⣴⣇⢐⣾⣧
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣶⣿⣃⢾⡐⡾⣯⣼⣻⡾⢧⠙⣋⣻⣽⣿⣷⠷⢿⣯⢿⣽⣷⣧⣐⣾⡯⣝⢷⣽⡟⠀⠀⠈⡟⢯⣿⠟⠛⠲⢿⣜⣿⣻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⠇⣷⣿⠾⢿⠆⣾⠄⢛⣻⢾⡿⢯⠝⠛⣙⣿⣿⣷⣻⠓⠁⠟⣺⠧⡴⠁⠀⠀⠀⠱⣼⡇⢺⣄⣸⣿⣧⡙⢿⡻⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣞⢿⠟⠞⢠⠾⡗⣯⠈⣽⠚⣿⣿⡇⢚⠗⢻⡿⠋⠀⠀⠀⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠻⣮⣻⣹⣿⣿⠑⡬⢏⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⣿⢯⣬⣟⣴⠟⣿⢷⡌⠰⣂⠴⠾⢻⣿⡿⠖⠀⠁⠀⠀⠀⠀⠀⢹⣿⣿⠟⡀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢏⣁⣸⢧⣼⠫⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣯⣜⣷⡟⣾⣵⣷⡿⣼⢷⡉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠏⣡⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡖⣸⣿⣿⡇⢷⣹⣻⡾⠋⢀⣾⣃⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣉⣴⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⠙⢃⡈⠍⠉⠀⡄⢉⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣴⣿⣿⣻⠎⠀⠀⠀⠀⠀⠈⣿⣻⣽⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡿⢿⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢻⣿⡏⢙⠀⠀⠀⠀⠀⣠⠜⣹⡿⠟⠋⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⠇⠘⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢶⣿⡛⣿⡀⠀⠀⠀⣼⣷⠒⣯⣤⣴⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⡶⢲⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⣿⡏⣹⣧⠀⠀⠀⢿⣠⣿⣿⣿⣿⠻⠶⠿⢷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⡬⠗⠛⠓⠛⢾⡛⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢿⣏⣙⣙⣆⠀⠀⠀⠉⢻⣿⠿⣯⡛⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣳⠊⠀⠀⠀⠀⠀⠠⡘⢦⡾⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⣿⣤⠼⢿⣆⠀⠀⠀⠀⢻⣧⠈⠻⣶⡌⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⠃⠀⠀⠀⠀⠀⡀⠀⢱⠈⣿⣶⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠹⣟⠀⠶⣸⣧⠀⠀⠀⠀⠛⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣽⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⡿⠿⡙⢻⠞⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⣄⠀⠀⠀⠀⠀⠀⢠⡟⢀⣿⠝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠿⣿⣆⣠⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢵⡤⣤⣤⡤⠞⠋⢀⣾⣧⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⣿⡅⢉⡿⢉⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣼⣟⡷⠛⣻⠋⣹⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⢉⣿⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⠞⠻⠛⡟⠛⣽⣿⡖⢶⣤⣤⣤⡤⠤⣤⣤⣤⠶⠶⢾⣿⡁⠀⢻⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠾⣿⣟⠈⢲⣌⣥⠉⢻⡿⣗⠀⣺⡟⠙⢻⣶⣶⣿⣥⡼⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢩⠍⠉⢉⣍⢩⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠍⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢀⠀⢀⠆
⠀⠀⠀⠀⠠⣺⠄⠀⠀⡀⠀⠔⠁
⠀⠀⡀⠀⠀⠘⠂⡀⢈⠕⠁
⡄⠂⠀⠀⠀⡴⢂⠚
⡏⠀⠀⠀⠂⠑⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⣀
⡇⣤⣶⠖⢀⣤⣄⣠⣾⣿⡟⠻⣿⠛⠟⠛⠛⠛⠛⠋⠉⠉⠉⢉⡁⣀⣀⣀⣀⣀⢀⡉⠉⠙⠛⠿⣿⣶⣄⡀
⡇⣿⣡⡼⣿⠛⠉⣠⡙⠋⠁⣀⠙⣷⣿⣶⠶⣶⣤⣴⣶⡿⢻⣿⠿⣿⠻⡟⣿⠛⡿⢿⣶⣤⣶⣀⣀⡈⠙⠿⣷⣦⣀
⠁⣯⡁⣴⣿⡿⣿⣿⣿⣾⣿⣿⣰⣿⡿⢿⣾⣿⣿⣿⣿⣧⣼⣷⣠⣿⣶⣧⣼⣦⣏⠹⣿⣿⣿⣿⣿⣿⣶⣆⠈⢻⣿⣷⣤⡀
⠀⠙⠿⢿⣿⣷⣿⠿⠛⠯⢉⡙⠋⠉⠀⠠⠀⠙⠛⠟⠁⠠⠉⢉⠋⣸⠉⣉⠉⠙⠉⢿⣿⠋⠉⠉⣀⣿⠻⣿⣤⡄⠈⠙⠛⠿⣄
⠀⢀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⡷⠚⠛⠛⠛⢻⡛⠛⠿⠛⠓⣿⡿⠿⣿⠋⢹⣿⣧⠀⠙⢿⣷⣦⣖⣠⣀⣼⣷⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠁⠀⠀⠀⣀⠈⣃⠀⣀⣀⣴⣿⣦⣾⠟⠉⠉⠉⠙⠓⠒⠚⠛⣿⢿⣿⣿⣿⣿⣷
⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢐⢀⣸⣿⠿⠃⠀⠀⠀⠈⣤⠄⠬⠟⢹⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠹⣿⠿⠛⡟⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠔⠛⢿⣿⠟⠃⠀⠀⠀⣲⠀⠀⠀⠰⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣅⣀⣤⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠒⠒⢢⠟⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⠀⠀⣀⣠⣤⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⡀⣠⣤⣤⣤⠄⠀⠀⢺⣷⣾⣤⡶⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⢿⣿⣴⡾⠟⠛⣿⣿⣿⣶⣾⡿⣿⣯⣀⣠⣴⣿⣶⣤⣤⡤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠄⢀⣠⣴⣏⣤⣼⠿⠿⣿⡿⢿⣿⣇⠀⢀⣿⡁⠈⣿⣧⠀⠀⣽⣿⣿⡏⠁⢀⣼⣿⣿⣤⡀
⠀⠀⠀⠀⣀⠰⠀⢀⣀⣀⣤⣤⣶⣶⣄⢀⠀⠀⣠⣴⠚⢉⣻⣿⣿⣿⣅⠀⠀⢿⡇⠀⢿⣿⣷⣾⣿⣇⣸⣿⣿⣶⣶⣿⣿⣿⡇⠀⣾⣿⠿⠛⠻⣧⡀⠀⠤⠾
⠀⠀⠀⡠⠃⠀⣤⡤⢯⠉⣻⣯⠿⣿⣇⣴⣷⣿⣧⣾⣿⣿⡿⠋⠙⣿⣋⠑⣶⣿⣿⡀⠈⣷⣽⣷⣿⣿⠟⠁⢹⣿⣿⣿⡿⠿⠷⣿⣿⡃⢀⣴⣶⡿⣷⡀
⠀⠀⠀⠀⣠⣤⣤⣶⣿⣏⣹⣿⣿⡏⠻⣿⣿⡿⠛⣿⡿⣿⠀⠀⠀⢸⣿⠀⣾⣟⣿⣿⣿⣿⣿⠿⠛⣿⣷⠄⣾⣿⡿⢋⣠⠀⠀⠀⠉⠻⣿⢟⣿⣦⣹⣇
⠀⠀⢀⡴⢋⡉⠛⣿⣿⡏⠉⠛⢿⣷⣤⣸⣿⣇⠀⢈⣷⣼⣦⣀⣾⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⣤⣤⣀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⢛⣭⣿⣿
⠀⠀⠛⠐⠟⠛⠓⢋⣩⣿⣆⣠⣾⣿⡟⠛⣿⣿⣀⣾⣿⣏⣿⣿⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⣐⢶⣟⣿⠾⢩⡿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⣷⣬⣤⣿⣿
⠀⠈⢷⣀⠿⠀⠀⠻⣶⣿⡟⠻⠿⠿⢷⣤⣾⣛⣹⡛⠉⠙⣿⣿⠃⠀⠀⠀⠀⠂⠀⠀⠀⠉⣉⣿⣛⣟⡴⠋⠀⠀⠀⠀⠤⣤⠟⠁⠀⠀⢐⣿⣿⣿⣿⣿⠀⠛⠃
⠀⠀⠀⠈⠙⠓⠶⢾⣿⣿⣿⣾⣿⣾⣿⣿⠿⠟⠛⠛⠆⢘⣿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⢻⣿⣿⠇
⠀⠀⠀⠐⠓⠀⠀⠀⠈⠉⠛⠛⠋⡉⠁⠀⠀⠠⠀⠀⠀⠉⣹⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣵⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠁⠀⠀⠀⣀⡀⢤⣤⣿⣿⠟⠁⠀⠠⠄⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⠿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⡄⢸⣇⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡴⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⠟⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠦⠐⠁⢀⣤⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣶⣦⣤⣤⣶⣶⣄⣀⣀⣤⣄⠀⡀
⠀⠀⠀⠀⢀⣄⡀⣠⣤⣴⠿⠟⣛⡛⣿⣏⣌⣹⣏⠛⣛⣿⠿⠷⣮⣅⡛⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⢜⣡⣾⡿⣿⣷⣾⣿⣿⣷⣾⣿⣿⣿⣿⣷⣿⣿⣿⣶⣼⡙⠻⣶⣄⠀⠀⠀⠀⠀⠙⠛⢲⣄
⠀⠀⢀⢰⣿⡿⢏⣴⣾⣿⣏⣾⣿⣿⡿⢿⣿⣿⡿⣯⠟⣿⣿⣿⣿⣿⣶⣌⠁⣤⠀⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⢤⣼⣏⣴⣿⣹⢿⣻⠿⠋⢣⠜⠃⠀⠀⢀⣔⢺⣿⠟⠋⠉⠉⠉⠻⣿⣷⣉⠱⣄⡀⠀⠀⠀⠔⣿⡇
⠀⠀⠈⠿⠿⠟⣻⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠁⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣍⣿⣷⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⣼⣷
⠀⣼⣿⠇
⢰⣿⡿
⣿⣿⣧
⢿⣿⣿⣦⡀
⠈⢿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣿⣿⠋⠙⢿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣴⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣀⢀⣸⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠋⠙⢿⣿⣿⣄⣀⣀⣀⣤⣴⣾⣿⣿⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣼⠟⢿⣇⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠉⠁⠀⠀⠁⠀⠈⢿⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢻⡿⢿⡟⠛⠿⠿⢿⣿⣷⣤⣤⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢸⡇⠘⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠃⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣛⣋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⢈⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⣿⣿⣿⡿⠟⠻⣿⣟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⡿⠶⣀⣙⠿⢟⢿⡃⠀⠀⠀⢉⣀⣤⣤⣤⣤⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠋⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠋⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣄⠀⠀⠀⢨⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠛⠿⢿⣿⣿⣿⣿⣦⣀⣟⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣠⣴⣿⣿⣿⣿⣦⣄⣀⣤⣴⣿⣿⣿⣿⡿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⠇⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣹⣿⣿⣿⣿⡇⠀⠈⠻⠿⣿⣿⣿⠿⠿⠛⠛⠚⠗⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣏⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣏⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠙⢷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠈⡱⠖⠀⣠⠿⢯⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡤⠛⢻⡻⢟⣹⣷⠀⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣲⢠⣤⢿⣷⣿⣿⣿⣶⠛⣉⠜⢊⢿⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠹⣸⣡⣿⣿⢻⣿⢹⡟⠷⣵⢾⡇⠈⣲⣮⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄⠸⣇⠀⢈⣶⣿⣿⣙⡛⠈⢉⣀⠤⣊⡈⠮⠛⠿⣿⣽⢻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⡴⢉⣶⣿⡟⣫⠴⣝⣿⠉⠁⠀⠀⡏⢇⡐⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢰⠁⣠⣿⡟⡣⣾⠻⣿⡯⣁⣤⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠀⣸⣾⣿⠥⠊⠿⠿⠛⢺⣿⡿⠥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣨⣾⡿⠊⠁⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡠⣾⠟⢋⣥⠀⠀⠀⠀⠚⠨⠇⣴⣄⢀⣀⡀
⠀⠀⠀⠰⣟⡩⠟⠺⠜⢰⣉⣒⡶⠀⠀⠀⠀⠀⠰⠋⠋⠻⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠒⠊⠙⠃⠲⢲⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡐⣀⡦⡆⡇⡠⠆⠾⡤⣀⠈⠘⢷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡋⢠⢱⡶⠛⠋⠉⠉⠉⠙⠲⣴⠟⠰⠆⣄⢌⠋⠛⢏⡲⢄
⠀⠀⠀⠀⠀⠀⢠⡇⣜⡳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠈⣷⡉⢆⡠⠀⡄⢳⡀⡓⢶⠄
⠀⠀⠀⠀⠀⣠⣏⠳⡼⠃⠠⣄⡀⠀⠀⠀⠀⠀⠀⡰⠃⡜⠓⡅⠸⠂⠀⠁⠠⠷⠒⠇⠁
⠀⠀⠀⢀⡴⣡⣎⠋⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⢀⡏⣰⢧⣄⡈⣏⠃⣈⠁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖⠐⡦⠄
⠀⠀⢠⠟⡥⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡦⡀⠚⠙⢟⡞⠛⠻⡅⣤⠩⣤⣿⠀⠀⠀⠀⢀⣠⣴⣄⠘⢏⢠⣤⣥⠀⡀⠂
⠀⠀⢸⡥⢂⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣆⠀⠀⠀⠀⠀⠅⠆⠐⢀⢹⡖⠠⠔⣋⠊⣭⣀⡍⠰⠛⡀⢀⣠⠈⠁
⠀⠀⠸⡶⣲⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⡘⠀⠀⠀⠀⠀⠈⢧⣳⠄⢀⡸⠃⠀⠉⠤⠰⠆⠐⢀⣬⠑⠊
⠀⠀⠀⠙⢯⣀⡤⡈⠲⠤⠀⢀⣀⢀⠠⡔⠛⣠⠃⠀⠀⠀⠀⠀⠀⠀⣁⢺⡆⣭⡘⢓⣀⣒⠤⠐⠚⠡⠬⣉⠁⢲⠤⠄
⠀⠀⠀⠀⠀⠙⠛⠧⣟⣤⠖⢠⡇⣸⣀⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⣚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⢷⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣞⠁⠀⠀⣀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉⠉⠀⢀⣿⣿⣭⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⣤⣶⣿⣿⣿⣿⣿⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣽⣿⣿⡿⢿⣿⣿⠟⠋⠁⠠⣦⣏⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⣿⣿⣿⡄⠀⠀⣴⡟⠙⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⣻⣿⣿⣿⣿⣿⡿⠡⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⣀⣤⣀⣀⣿⣿⣿⣯⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⢷⣷⣾⣯⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣟⣟⣿⣿⣿⡟⠁⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣯⣄⡀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠈⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢩⣟⣛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣀⣀⣀⢀⡀⠀⠀⠀⠀⢿⣤⢗⣀
⡎⢀⣀⣀⡈⠲⢌⡲⣄⠀⠘⠧⡀⠈⢝
⠱⡈⣯⡑⡼⡄⠀⠉⠚⠷⡀⠀⠙⣄⠈⠣⡀
⠀⠙⢜⠫⢅⡱⣀⠀⠀⠀⠈⠲⠤⣼⡀⠀⢸
⠀⠀⠀⠉⠲⢝⢮⠉⠑⢦⡀⠀⠀⠀⠀⠹⠭⣉⣉⣡⠖⠲⡤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠱⡑⠒⠒⠙⠀⡤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠉⠓⠒⠤⣀⣀⠄⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⡑⠢⠤⢄⡈⠙⡆⡠⠂⠤⠤⠤⢀⣀⠀⠀⠀⠀⠈⢿⡢⢄⡀⠑⢄⠀⣠⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠘⡀⠀⠀⠉⠉⠀⠓⠤⠄⠠⠤⠤⠤⠓⠀⢰⡃⠐⠒⡌⠛⠋⠑⠲⠽⣉⡑⣿⣇
⠀⠀⠀⢀⣤⡹⠕⠒⠉⠁⢀⡠⠔⠑⠒⠤⢄⣀⣀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠉⠑⠒⠼⠀⠀⠠⣤⠤⠄⣈⣉⣉⠒⠒⠢⠤⣀⡀
⠀⠀⠀⠀⢠⡾⠄⠢⣲⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⣏⠀⠀⠀⢀⣀⠤⠶⠥⠤⢤⣀⣀⣉⣉⣐⣒⣒⣙⠂⠀⠀⣔⠪⣝⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠐⠲⠭⣙⠗⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢦⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠟⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡞⠥⠰⣆⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢣

⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠐⢿⣇⣀⣿⡏⠀⢀⣀⡀⠀⠀⠀⠀⢠⣤⣀⣼⣷⣄⡰⣶⠀⠀⠀⠀⠀⠀⢴⣶⠀⢸⣿⠀⢠⣶⠂
⠀⠀⠉⢹⣿⡟⠒⠛⠛⠀⠀⠀⠀⠀⠈⠉⠈⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢿⣿⡶⠞⠉
⠀⠀⣶⣼⣿⣥⣤⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⢻⡿⠛⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⢰⢿⠏⠈⣿⠁⣷⣦⠀⠀⠀⠀⠀⠀⠈⠃⠀⣸⠃⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⣦
⠀⠀⠀⠀⡇⠀⠈⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠚⠟⠋⢰⡟⠐⢿⣶⡀
⠀⠀⠀⠀⣷⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠈⠳⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡆⠀⠘⣿⠃⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣀⠀⣀⣀⠀⠀⠀⠀⠀⠙⠓⢺⣿⠗⠖⠞⠻⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢺⣿⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣸⠋⢹⡿⠉⢷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣆⣴⡄⠀⠀⠀⠀⠀⠀⠈⠙⠒⣿⣿⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠋⠀⢸⡇⠀⠘⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠹⣿⢹⣧⠀⠀⠀⠀⠀⠀⢀⣤⡞⢹⣿⠛⢶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⣿⠀⠉⠀⠀⠀⠀⠀⠀⠈⠋⠀⣿⠃⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠖⠋⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⣀⣠⠟

⠀⠀⠀⠀⡀⠀⠀⢠⣤⣀
⠀⠀⠀⠈⡀⠀⢾⣿⣽⣿⣶⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⢀⡄
⠀⠀⠀⢀⣤⣦⣀⠙⠿⣤⣽⣿⣿⡟⠻⢿⣿⢶⡶⣾⣷⣶⣶⣦⣾⣿⣦⣀⢀⣈⠃⠟⠘⠗⡴⢀
⠀⠀⠀⣿⣟⣿⣯⢿⡇⠈⠻⣯⠙⣿⣶⣦⣤⣴⣤⣾⣧⣴⣧⣤⣾⣿⣍⣛⣿⣿⣿⣛⠀⠐⢋⣉
⠀⠀⠀⠀⠊⠿⢣⣾⠻⠒⢀⣬⢻⡿⠿⣿⣿⣿⣯⣽⣿⣯⣽⡷⣾⣿⣿⣿⣿⣷⣮⣿⡿⣦⡈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⡛⠋⠠⠅⠈⠉⠉⠉⠉⣼⣿⣽⣧⠶⠂⠀⠀⠈⠉⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⣠⣤⣤⣶⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⣤⣤⣤⣶⣶⣤⣤⣤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣶⣿⣿⣿⣷⣝⡻⣿⣿⣿⣿⣿⢟⣽⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠾⠙⠛⢻⣽⣿⣿⣇⠊⢙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡰⡿⣿⣱⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⡀⣷⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡛⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⢠⡤⢟⣼⣿⣿⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣾⣿⣿⣿⡇⣠⣠⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠒⣴⣿⣿⣿⣿⡿⠇⡙⣿⣿⣇⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣶⣦⣴⢰⣿⣿⣯⣕⣒⣒⣟⣛⡾⠛⣿⣿⣿⣿⣿⣿⣛⣟⣭⣿⣿⣿⣿⣧⣢
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⡛⢿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣽⣾⣻⣿⣿⣿⣿⠟⠙⣿⣿⣷⣤⡀
⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣝⢿⣿⣿⣏⣿⣿⣶⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠈⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣶⡶⡿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠠⠶⢛⣿⣿⢿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠦⣽⣛⣿⣿⠿⠿⠶⠾⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠁⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⣫⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠿⠟⠛⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣠⣤⣴⣿⣿⣶⠿⠿⢿⣿⡶⠶⣶⣶⣤⣀⣀⣀⠀⣤⡀⠀⠀⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠠⣚⣵⣾⠿⢿⠋⠉⢀⣿⣀⣤⣾⡏⢠⣶⣶⣦⣌⣻⣿⠿⣶⣀⠛⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣁⣤⣴⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣯⡟⢿⣿⣧⣄⠙⢿⣿⣷⡄⡀
⠀⠀⡠⠴⠞⠁⠀⠀⠀⠀⠀⠀⣾⠟⢁⣴⣿⣿⣽⣿⡿⡿⢿⣿⣿⣿⣿⣿⣿⡯⢿⣿⣾⣿⣿⣿⢷⣦⣉⢻⣷⣠
⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣴⣿⣿⣿⣿⣿⣿⣷⣤⣤⢄⣉⠉⠉⠉⠹⠷⠞⠏⠛⠻⢿⣿⣿⣿⣿⣿⣿⡍
⠈⢿⡀⠀⠀⠀⠀⠀⠀⣀⠘⢁⣾⣿⠟⠁⠀⠀⠀⠀⠉⠻⢧⠼⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡍⠉⠉
⠀⢿⣯⣒⣀⠀⣀⡠⠞⢁⣴⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠿⠇
⠀⠀⠙⠿⢿⣾⣿⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣬⣶⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⢿⣿⣿⠿⢿⣾⣿⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⢻⣟⣥⢝⡛⡛⢉⣿⣟⣉⣙⣙⣭⣽⣷⣶⣾⣿⣿⣿⣦⣶⣼⣯⣭⣿⣿⣿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣾⣟⣻⣿⣿⣿⣹⣿⣷⣶⣶⣿⢿⢿⡿⠿⠛⠉⠁⠈⠉⠙⠻⣏⣵⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣁⣬⣽⡿⠁⠉⠉⠉⠀⠀⠀⠀⠀⣬⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⣶⣯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⡿⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢘⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢨⢊⠀⢀⡰⠂⠈⠁⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠨⠀⠠⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠇⠀⠁⠈⠉⢀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠈⠄⣀⠀⢀⠔⡡⠀⠀⠀⠀⠈⠐⠂⠌⡁⠀⠂⢠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠠⠐⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠁⢄⠀⠀⠀⠀⠑⡄⠀⠈⠐⠐⠌⠫⡍
⠀⠀⠀⠀⠀⠀⡠⠄⠡⠐⠠⠂⠐⠄⠀⠀⠠⠄⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠈⠢⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠠⠊⢀⠄⠒⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠠⢀⠰⠀⠀⡀⠠⠁⠀⠀⠤⠐⠀⠀⢄⣀⢀⠆⣠⠀⡀⠀⠠⠤⢀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣠
⠀⠀⠀⠐⢡⠉⠁⠀⢀⠠⠔⠁⠀⡀⠀⠀⠀⠀⢈⡀⠬⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⢁⠠⠄⡀⠈⠁⠀⠙⠛⠁⠐⢀
⠀⠀⠰⠀⠈⠂⠀⠠⠂⠀⠀⡀⠠⠤⣀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⢀⠔⠁⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠁⠄
⠀⠀⠘⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠈⡄⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⡀⠀⠄⠀⠀⡁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠘⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠃⠈⢠⠀⢤
⠀⠀⠀⠁⡀⠀⠒⠀⠰⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠄⢒⣓⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠐⡄⠀⠂
⠀⠀⠀⠀⠑⣀⠀⠂⠂⠌⠦⡀⠀⠀⠀⠀⠈⠀⠀⠉⠂⢈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠃
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠂⠨⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠄⠀⠀⠀⠀⠉⠓⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⢾⣛⢰⡖⢶⣰⠞⣦⠚⣿⠓⢻⡟⣴⣶⠆⣴⠛⣿⠀⠀⠀⣾⡓⢰⠞⣶⢸⢃⡶⢳⠆⡷⢷⢲⡆⡴⢲⡆⣷⢻⣦⡞⢻⡇⣶⡷⠆⡶⠺
⠀⠀⠀⠀⠒⠛⢸⡗⠛⠘⠒⠋⠀⠃⠀⠘⠃⠙⠓⠒⠙⠒⠛⠀⠀⠐⠲⠛⠘⠒⠛⠘⠋⠓⠚⠃⠃⠸⠀⠃⠛⠚⠃⠋⠘⠋⠓⠚⠃⠛⠒⠂⠃
⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢨⠍⠉⢩⡭⡭⠉
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⡠⠂⠊⠀⠀⠀⠀⠈
⠀⠀⠀⠠⡪⡇⠀⠀⠀⡂⠊
⠀⡀⠂⠀⠀⠈⠐⡀⠈
⡆⠀⠀⠀⠀⡧⠊
⡇⠀⠀⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣢⣄⣀
⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⠿⣿⣿⣙⣦⡀⠀⠀⠀⢀⣀⠠⠀⠀⠄
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣿⡿⠒⠂⠙⣿⣽⣶⣶⣿⣿⣷⣭⣶⣦⣤⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠀⢀⣻⣿⣿⣿⠛⠛⠋⠛⠛⠛⠻⣿⣿⣿⣿⣲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠰⢤⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⣫⡄⣤⣶⣿⣿⡿⠋⠉⠻⣮⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠰
⠀⠀⠀⠀⠀⠤⣀⣀⣀⣠⣤⣤⡀⠀⠀⢀⡠⠶⠛⠁⣠⣶⣾⣿⣿⡿⠋⠀⠀⠀⠀⢹⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣰
⠀⠀⠀⠀⠒⠒⡻⠙⠛⠛⣿⡷⣧⡔⠈⢋⣀⣼⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣀⢠⡾⢼⣻⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣵⠇
⠀⠀⣤⣶⣤⣤⣴⠖⣦⠶⣛⣭⣥⣴⣶⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠠⠃⣄⡘⢬⠀⠀⠀⠀⠀⣀⣤⠞⣋⣤⡾⠃
⠀⣼⡿⣿⣯⣿⡽⣊⣴⣿⣿⣿⣿⣿⣿⣫⣯⡩⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣀⡤⠔⢒⣭⣵⣶⠾⠛⠁
⠀⢽⣿⠿⣿⣿⡿⠿⠿⠛⠋⠛⠉⠍⣙⢻⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⠿⠿⠾⠟⠛⠛⠉⠁
⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠈⠁

⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⠀⢀⣾⡿⣿⣿⣦⣍⡲⢄⠀⠀⠲⣷⣷⣆
⠀⠀⠈⢿⣶⡓⠝⢿⣿⣿⣦⣱⡄⠀⠙⠄⣹⣦⡀
⠀⠀⠀⠈⢻⣍⣅⠈⣿⣿⣿⣿⣿⣦⣀⠀⡿⢿⣷
⠀⠀⠀⠀⠀⠈⠛⢷⣌⡙⠛⠻⣿⣿⣷⣿⣿⣿⣯⣀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣦⣬⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠛⠻⣿⣶⣤⣄⡈⠙⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣦⣄⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠙⣿⣿⣿⣿⣿⣿⣄⣠⣄⣀⣀⣀⣀⣨⣿⣧⡀⠉⠙⢿⣿⣿⣿⣿⣦⣷⣟⣲⡒
⠀⠀⠀⠀⠀⠀⠀⢈⣷⣤⡖⣺⣿⣿⠿⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣿⣶⣤⣀⣽⣿⣿⣿⠋⠉⠉⢳⣶⢤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠾⠻⢿⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⢻⣯⣤⣴⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣭⣿⡂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠙⠛⠻⣿⣷⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣿⡏⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⣚⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠟⢻⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠆⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⡏⠑⣅⠀⠁⠀⠀⠀⡂⠀⠀⠀⠘⠆⣸⠀⢻⠀⠌⠀⠈⣠⠁⠀⠀⠀⠀⠀⠰⡄⢰⢿⣤⠀⣸⠂
⠀⠀⠀⠀⡤⠆⠀⠀⠀⢀⣿⡤⠀⠆⠀⡀⡄⠀⠀⠀⠀⢰⡇⠀⣿⠀⠀⠤⠀⡈⠟⡀⠀⠀⠀⠀⡟⡄⣿⠀⠴⡄⢠⠛⣄⠀⡶⠀⠀⠀⠀⠁⣸⠀⣿⡂⠁
⠀⠀⠀⠀⣷⠆⢀⡴⠋⠈⠁⢀⡄⠀⠀⠀⠡⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠐⢀⡇⠀⣏⠤⠁⠀⢰⡇⡃⣿⠀⠀⠃⣸⠀⢹⠐⠃⠀⠀⠀⠀⠀⣥⡀⣿⡇
⠀⠀⠀⠀⠀⠐⣾⠁⠀⠀⠀⣴⠆⠀⢈⠙⠀⠀⠀⢦⣀⡈⣗⠀⡟⢀⣀⠀⢸⠃⡄⣿⠀⣀⣀⡈⣧⠁⣽⡀⣠⠀⣿⢀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠇⣿⠁
⠀⠀⠀⠀⠀⣰⠃⠀⢀⠀⠠⡯⠂⠀⠸⠃⠀⠀⠀⠈⠉⠀⠛⠐⠃⠈⠁⠀⢸⡅⡇⣿⠀⠀⠁⠀⠉⠛⠈⠉⡉⠀⣿⠈⢸⠇⠀⠀⠀⠘⠳⠖⠢⠀⣿⠀⠆⠉
⠀⠀⠀⠀⢠⡧⠀⠸⠇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⢷⡤⢸⡇⠃⡏⣤⣤⠄⠀⠀⠁⠀⠘⠷⠒⣼⡦⣿⠰⠴⣶⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⢸⠂⠀⢀⡄⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠆⠎⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⢸⡶⠀⢸⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢰⠀⠀⠸⠇⠀⠀⡜⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⢰
⠀⠀⠀⢠⡜⣷⠀⠀⣗⠀⣰⠁⣤⡤⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⢄⢺⡁⣈⣅⠀⡏⠀⢋⣀⠈⠁
⠀⠀⠘⠃⠀⠙⠛⠀⢠⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣟⠂⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⢀⣘⣏⡀⠀⡦⠀⠀⣀⡀⠴⣿⠠⢀⣤⠀⠀⠀⠀⢶⠀⣾⣯⡆⢀⡶⠀⠀⠀⠀⠀⣿⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡇⠚⠁⠀⠀⠙⠷⣿⣿⣷⠰⠏⠀⠀⠀⠀⠈⠃⣾⣿⡟⠈⠁⠀⠀⠰⣇⣰⣼⢷⣀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡇⠀⠀⠀⠀⠀⠀⣞⣿⢻⡆⠀⠀⠀⠀⠀⠀⢠⣷⣿⣿⠀⠀⠀⠀⠀⠀⣸⣸⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣇⡇⠀⠀⠀⠀⠀⠀⡟⣿⢾⡇⠀⠀⠀⠀⠀⠀⢸⣿⣇⣿⠀⠀⠀⠀⠀⠀⣿⣸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠷⢧⡤⢹⢸⣶⡧⣤⣶⠀⣴⣄⡀⣷⢿⢿⢃⡀⣤⡄⠀⠿⡶⠶⣟⣿⡯⠶⠾⠆⠀⠀⠀⢿⢻⣽⠇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣬⠊⠀⠀⠀⠀⠈⠉⠉⠛⣻⡞⠈⠉⠉⠁⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠚⠶⠒⠸⣾⢹⠆⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⣄⠀⠀⠀⣴⡄⡄⠀⠀⠀⠀⢀
⠀⠀⣤⣤⣤⡗⡖⠀⣘⣃⣠⣶⣄⠸⣿⣖⣀⡀⢀⣈⣥⡦⠤⠶⠶⣿⠟⠻⠂⣠⡶⢤⡇
⠀⣾⣿⡿⠿⠗⠢⠤⠞⠿⠿⠟⠿⠚⠛⠛⠛⠉⠻⠿⣿⣿⣷⣶⣥⣀⠀⠀⠂⣀⡀⡈⠑⢀⠀⠀⣄⡀⠀⠀⠐⠯
⢐⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⠀⠀⣠⠞⠀⠀⢈⣁⡉⣛⣷⡶⢞⣯⠜⢷⣿⣿⣿⠲⡀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣴⣶⣛⣿⡿⣿⢤⣤⠤⡄⣴⠖⣻⣿⠾⢟⣡⣾⣾⣿⣶⠀⠈⠿⠉⢿⡧⢤⠀⠀⠀⠀⡀
⠀⢀⠆⠀⠀⠀⠀⢹⣿⣿⣽⠟⢹⣿⣛⣛⣃⣿⠿⠿⢿⣿⣫⣡⣴⣯⢹⣿⣿⡿⠛⠒⠀⠒⠰⢷⣿⡞⣷⡀⠈⣱⣞⣀
⢀⡀⢻⣄⠀⠐⡒⢾⣿⣿⣿⣷⣿⣿⣹⣿⣿⣿⢻⣿⣿⣉⣽⣿⣿⡟⠿⣜⣿⣏⠀⠀⠀⣀⣠⡴⠛⠿⢿⣧⣤
⢸⣿⣠⣿⠀⠵⡄⡰⠀⠋⠙⢿⣿⣩⣿⠟⠛⠛⠿⠿⠛⠛⠋⠉⠻⢷⣴⣿⡿⠛⠛⣶⣾⣿⢁⣠⣤⣄
⠈⠉⠛⠀⢤⣤⡞⠀⠀⠀⠀⠈⠛⠟⠁⠀⣤⣤⡂⠈⠀⠀⠠⠠⢀⠀⢉⢣⣄⠀⠈⠙⠹⠛⠟⠻⢿⡷⣴⠶⠆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣤⣥⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⢛⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣶⣾⣿⣿⣿⢿⠟⣻⢻⣟⣿⣉⣛⣛⣛⣉⣋⡉⠉⣉⣉⠉⣩⣏⣉⣤⡾⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⢛⣻⣿⣭⣿⣾⣷⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣯⠷⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⢟⢻⣼⣶⣿⣿⣿⣿⣟⣛⣏⣩⣁⣍⣈⣁⣦⣆⣶⣾⣾⡛⢁⣠⣿⣿⣾⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⡟⣶⣾⣿⣿⣿⣷⣦⣭⣿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⢿⣿⢿⡏⠁⠈⠙⠛⠙⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⣝⣷⡾⠿⠿⠿⠛⢋⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣹⡶⢶⣄⡀
⠀⠀⠀⠀⠀⠀⣠⡾⣿⣶⠟⠉⠀⠀⠀⠀⠀⣼⣿⣟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠓⠂
⠀⠀⠀⠀⠀⣰⣿⣹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢯⣍⣴⡷⠥
⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⣸⣿⣿⠃
⠀⠀⢠⡿⣿⠃
⠀⠀⣾⣻⠏
⠀⢰⣿⡟
⠀⣸⣿
⠀⣿⡟
⢠⣿⡇
⠸⣿⠁
⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡠⠄⢄
⡠⠊⣁⠀⠀⠀⠑⢄⡀
⢣⠈⠿⠿⠀⠀⠀⠀⠙⠒⠦⢄⡠⠀⠀⠤⠄⠔⠒⠒⠙⠉⠉⠉⠉⠁⠀⠀⠐⠒
⠀⠑⢄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤
⠀⠀⠀⠈⠑⠂⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⢳⡤⠀⣤⠀⠀⠀⠀⠀⠠⠀⠀⠞⠩⣿⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀
⠀⠀⠀⠀⠀⡀⣴⡤⠉⡀⠊⠁⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠵⠦⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣅⠂
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠉⠕




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣻⣿⣏⣿⣿⡟⣭⣝⣿⣿⣙⠿⢷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢻⣿⣝⢿⣟⣿⣿⣧⣿⣾⣿⣿⣙⢻⣿⡗⣿⢟⣸⣿⢿⣿⣷⣦⣤⣀⡀⣠⣶⢦⣄⣤⣶⣦⡦
⠀⠀⠀⠀⠀⠀⣠⣞⣻⡿⣟⣿⣿⣻⣿⣛⡻⣿⣿⣵⣾⣯⣿⣿⢿⣿⣿⣿⣯⡿⣿⣿⡿⣤⣶⣆⣿⣿⡿⢿⣿⣿⣯⣿⣿⡗
⠀⠀⠀⠀⠀⣼⠿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣽⣞⣿⣻⣯⣵⣿⣯⣶⣿⣻⣿⣯⢿⣿⣿⣿⣷⣶⡄
⠀⠀⠀⠀⣼⢳⣿⣿⣿⣿⡿⠋⠁⠀⢹⣿⣿⣿⡏⠉⠉⠙⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣮⣟⣯⣽⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣿⣿⣿⣃⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⡻⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡏⠉⠉⠙⠛⠛⠻⢿⣿⣿⣿⣿⣿⣷⣿⣿⠟⠃
⠀⠀⠀⠀⢹⣿⣿⣻⣿⣿⣷⡀⠀⠀⠀⠀⠈⠙⠿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣤⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡛
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣭⣭⣽⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⠻⠏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⢷⣄





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣶⣤⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣿⣿⣿⣦⣤⣿⠿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⢿⣿⣿⣿⣿⣷⣶⣄⠛⢿⣦⡀⠀⠀⠀⣴⣦⣄⣯⣤⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⢿⡇⠀⠀⠀⠀⠁⠹⣧⣈⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⡿⡀⢺⡇⠀⠀⠀⠀⠀⢠⣿⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷⠀⠀⡀⠘⣿⡔⠙⡻⠟⠙⣿⣿⣿⣀⣉⣸⣇⠀⠀⠀⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣦⣠⣿⢤⣾⠟⠀⠈⠛⠿⣦⣉⢸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⣤⣾⣷⡀⠀⠀⠀⠀⣸⣿⡀⠛⢿⣿⣿⣿⣿⣿⣿⣧⠩⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠏⠀⠈⠻⡿⢷⡄⠀⣠⡾⣿⣿⣿⣶⣿⣿⣿⣿⡋⢹⣿⣿⡛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⣿⣾⣷⣄⣿⣿⣿⠛⢹⣿⣿⣿⡟⠀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠟⠋⣹⣿⡇⠈⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠑⣱⣿⣿⣿⣿⣇⡘⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠃⢿⣿⣿⣿⣿⣿⡿⠰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⠃⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡉⠙⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣿⢟⢻⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⣾⣿⣿⠿⠃⣽⣿⣿⣿⣿⣿⣿⣿⢈⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⠀⣸⣿⣿⢁⢠⣿⣿⣿⣿⣿⣿⣿⠟⠡⣸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣦⣿⣿⣿⠈⣸⣿⣿⣿⣿⣿⣿⠽⢏⣾⣿⣿⣿⠃
⠀⠀⠀⠀⣾⣿⠄⢠⣿⡿⢛⣿⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢉⣴⣿⣿⣿⡟⠁
⣶⣷⣦⡀⢹⣿⢀⣾⡟⠁⢸⣿⣷⣿⣿⠁⠸⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠏
⠀⠉⠛⠿⣾⣿⣿⡟⠀⠀⢸⣿⣿⣿⢛⣠⣼⣿⣿⣿⣿⠿⢋⣿⣿⣿⣿⣿⣷⣦⣄
⢀⣤⣤⣴⡿⢿⣿⠀⠀⠀⢸⣿⣿⠣⣼⣿⣿⣿⣿⣿⣿⣜⣉⣿⣿⣿⣿⡿⠟⢻⣿⣆
⠘⠿⠋⠁⠀⠀⢻⣷⡄⢀⣼⣿⠇⢰⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠟⠃⣼⣿⣿⣤⣾⣿⣿⣿⢏⣠⣿⣿⣿⠿⠛⠋⠉⠀⠀⠈⢻⡟⢿⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡋⢔⣤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠃⣹⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣴⣿⠋⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠧⢸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠿⠿⠿⣩⣿⠄
⠀⠀⠀⠀⠀⠀⢰⡿⢀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠛⠁⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣾⡇⣌⣻⣿⠛⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠂
⠀⠀⠀⠀⠀⢠⣿⠃⠠⣿⢡⣾⡏
⠀⠀⠀⠀⠀⢸⣿⣶⣶⣦⣼⡿
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣧⣼⣿
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀⣿
⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣶⣤⣄⡀