Eat Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠖⠊⠁⠁⠀⠀⠈⡆
⠀⠀⠀⠀⠀⣠⠒⠉⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠐⢄
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠱⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⢖⡆
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡤⠒⠀⠀⠈⠈⡇⠀⠀⠀⠀⠀⠀⡀⠔⠓⠛⢮⣟⠹⣤⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠁⠀⠀⠀⠀⠀⢙⡆⢀⡀⠄⠂⠁⠀⠀⠀⢀⣀⡹⣦⠴⠃
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⡤⠤⠊⠀⡏⠉⠉⠉⠉⠉⡻⢻⠉⠀⣾⠳⡀
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⣦⢧⡄⠤⣄⣀⣠⠃⢸⣤⣼⠏⠀⡇
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⠉⠉⠉⠀⡇⠀⠈⠋⠁⠀⠀⡇
⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠲⢤⣀⡀⡸⠀⠀⠀⠀⠀⠀⡞⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠉⠉⠉⠙⠒⠒⠼⢧⣀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⢲⡀⣠⠎⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⠃⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠈⠑⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⢄⣀⡀⠀⠀⣇⣀⡀⠀⠀⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡧⠤⠤⠄⠠⠤⢄⡀⣼⠉⠉⣦⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⣩⣴⡞⠉⢱⠖⠊⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠚⠙⡟⠙⡅⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⢾⡀⠀⠈⢲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⠁⢀⡇⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠙⣦⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡋⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠤⠤⠴⢢⣀⡤⠦⢤⣄⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠓⣦⠀⠀⡇⠀⠀⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⣀⠀⠀⠀⡇⠀⠀⢰⡅⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠻⣄⡀⡇⠀⠀⠀⢰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣠⣄⢳⣴⠋⠉⠀⠀⠘⠁⠈⠁⠀⠀⠀⠀⠋⠀⠘⠂⠀⠀⢹⡇⢀⣠⠤⠊⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠙⠲⠿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠀⠀⠀⠀⠀⠀⣀⡼⠛⠁⠀⠀⠀⢠⢿⣰⣏⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⢦⠀⠀⠀⣀⣀⣠⡤⣈⣧⠀⠀⠀⠀⠰⡄⠀⠀⠀⣖⡦⠀⠀⠀⢰⣡⠴⠤⠤⣤⠄⠀⡎⠸⠃⡿⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⢀⡼⢦⡀⠀⠀⠀⠈⠓⠶⠖⠋⠀⠀⠀⣠⠎⢹⡄⠀⠀⡟⠀⠀⣇⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⡄⢾⠁⠀⠀⠘⣄⠀⠀⡎⠀⠀⠉⠒⠦⢄⡀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢸⠿⢦⡰⠃⠀⠀⢈⠇⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⡧⢤⠀⠀⠈⠳⣴⠷⢄⡀⠀⠀⠀⠀⠈⠁⠒⠒⠋⠁⠀⠀⠀⣠⠏⠀⠈⡇⠀⢀⠤⠾⣼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣁⡤⠞⣆⠀⠀⠀⢸⠀⠀⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣸⠀⢠⡞⠳⠶⢤⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠶⠚⢩⠇⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢰⠛⠒⠶⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⠒⣩⡇⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢼⡓⠶⢶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢧⠘⡆⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⣸⢹⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⢧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⡠⠖⠉⣤⡺⠭⢝⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣁⣀⠤⠒⠉⠀⠀⠀⢸⣽⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡟⠴⠞⠂⠀⠚⠒⢃⠞⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠇⠠⠆⠀⠀⠠⠀⠹⢋⠁
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢢⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠈⢄⠀⠉⠀⡨⠁⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠤⠀⡄⢄⢀⠀⠀⠐⠀⠀⠀⠀⠃⠠
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢱⡄⢀⠷⠀⠀⠀⠀⠀⢀⡜⡀⡸⢀⠀⠉⢀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢘⡾⠄⠀⡀⠀⠀⢸⠀⠠⠀⣠⣴⣶⣦⠀⠐⠀⢫⠉⠂⠂⠚⠓⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠂⡀⠀⢀⠬⡤⣞⣒⣒⡺⢮⣠⣿⣇⢈⠖⠁⠀⠀⡀⠀⠀⠀⠀⠀⠄⠄⠈⠁⠄
⠀⠀⠀⠴⢳⠀⠀⠀⠐⡁⢘⣶⡄⣶⣶⣶⡄⠉⠉⠉⠀⠀⠈⠀⠄⠀⠀⡀⠀⡀⣉⠀⠀⠄⠁⠀⠘⢦⡀
⠀⠀⠂⠒⠺⠷⠀⠤⠀⠰⠏⠻⣿⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠧⠉⠉⠀⠀⠀⠰⠃⠞
⠀⠀⠀⠀⠀⠀⠰⢴⢒⣲⡂⠀⠉⠛⠛⢁⣀⣀⣀⡤⡤⣤⣀⣀⣀⠠⠤
⠀⠀⠀⠀⠀⢰⣶⣿⠫⠈⢱⡆⠐⢸⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡷⠁⠄⡀
⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠙⢦⡄⡘⠉⠉⠉⠋⠋⠋⠋⠉⠉⢉⣁⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠃⠢⠬⠤⠥⠜⠉⠉⠛⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢉⣴⣶⡦⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⣠⣶⣿⣿⠟⣴⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⢿⡿⠟⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⣀⣀⠀⠀⠀⠟⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠈⠁⠄⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢀⠀⠀⠀⠀⠀⠀⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⠲⣤⡴⠂⠀⠀⣠⢿⠞⠀⠐⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠉⠀⢿⣇⠀⠀⢀⣰⣞⠅⠀⠀⣰⠃⠀⠈⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠙⢻⠁⣉⣶⡁⠀⠀⡰⠃⠀⠀⠀⠀⠀⠈⢳⠤⣄
⠀⠀⠀⠀⠀⠀⠠⢤⣄⣀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⡟⢱⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢠⢀⣵⠖⠗⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠰⡄⢚⣧⡈⡆⠀⠨⠳⣄⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠃⠈⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣴⣛⣁⣠⡽⡇⠈⠳⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠉⠁⠀⠀⢧⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣦⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⢀⠂⢸⡆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇
⣀⣀⣀⣀⣀⣀⠀⣸⣿⣿⣶⣦⣴⣿⣿⣷⣬⣵⡼⢠⠀⢿⣿⣿⣿⡇⢀⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣠⣇⣀⣀
⠀⠀⠀⠀⠀⠀⣤⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣷⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⠋⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠉⠀⠀⠀⠀⠀⡀⠀⠈⠻⣿⠿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣾⣿⣿⡀
⠀⠀⠀⠀⢀⠀⠀⠀⣠⠔⢂⣀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⣐⠀⠀⠀⠈⠺⠠⠖⣀⡀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣄
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠸⡀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⢤⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠀⠀⠠⠀⡀
⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸
⠀⠀⠘⠹⠷⠾⠉⠆⠀⠀⢀⣠⡀⠀⠀⠀⣀⠸⣀⣀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣶⣶⣿⣿⣿⣿⣶⣾⣿⣿⣿⠇⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⢄⠀⢀⠴⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠉⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠤⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⠊⠁⠀⠀⠀⠀⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠊⠂⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠦⣀⠉⠂⠤⣀⣈⣉⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠄⠒⠃⠑⠂⠠⠈⡑⡲⠤⠤⢤⠄⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠔⠈⠙⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠒⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢰⢅⠀⠐⡤⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠰⠘
⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠹⡻⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠘⡖⠄⡀⠀⠀⠀⠀⠀⠀⠉⠛⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⡠⠁⠈⠑⢀⠣⢲⠢⡀⠀⡤⣦⡂⠁⠀⠀⠀⠀⠀⡠⠒⠒⠀⠀⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠑⠒⠚⠊⠀⠁⠠⡀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠓⠒⠐⠐⠂⠄⡀⠀⠀⠀⠀⣠⠀⣀⠀⠀⠐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠄⠈⠀⠀⢀⠔⠃⠀⠂⡀
⠀⠀⠀⠀⢠⡇⢰⠡⠣⠀⠀⠈⠑⠈⠁⢈⡀⠀⠀⠀⠀⠐⠄⣀⠀⠀⠀⠀⣀⣀⠀⠠⠄⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠁⠘⠃⠘⠀⠀⠀⠀⠀⠀⣆⠀⠀⠈⠢⢀⠀⠀⠀⠀⠄⠂⠠⠀⠀⠀⠀⠀⠀⠁⠈
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠑⠀⠤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⠀⠀⠐⡁⠀⠁⠀⠀⠘⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠤⠌⠣⣀⡀⠀⠀⠀⠀⢀⠠⠀⠁⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⠞⠀⠀⠉⠁⠀⠀⠀⠀⢀⡀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉
⡂⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⡀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣛⣿⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣛⣿⣟⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠴⠶⠈⠉⠛⠛⠋⠁⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⡇⠀⠘⡇⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢠⡖⠻⡄⠀⣧⠀⠀⠀⣇⠀⠀⢸⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⣰⠋⠀⠀⣧⠀⠹⡄⠀⠀⠸⡆⠀⠈⣧⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢰⠏⠀⠀⠀⠹⡆⠀⢳⡄⠀⠀⢿⡀⠀⠘⢧⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⠀⠀⠀⣧⠀⠀⠀⠀⠀⠸⣄⠀⠹⣤⠀⠀⠻⣄⠀⠈⠳⣄⠀⠀⠀⠉⠳⠆⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⠆⠈⠛⠶⠄⠈⠙⠂⠀⠈⠛⠶⣄⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢇⠀⠀⠀⠚⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠛⠀⠀⠀⡇⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⡄⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⡗⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢸⡇⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠀⠀⠀⣧⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠻⣆⠀⠀⠀⠀⢠⡄⠤⠤⠤⠄⠤⢠⡄⠀⠀⠀⠀⢀⡼⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠳⣄⠀⠀⠈⢷⣄⠀⠀⠀⣠⡾⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠈⠳⢦⣀⠀⠈⠙⠛⠋⠀⠀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡿⠛⠢⢤⠤⡤⠤⠖⠛⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⠶⠚⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣛⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠠⠤⣀⣀⡠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠛⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠀⠈⠓⠒⠢⣬⣹⠧⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⡰⠖⠀⠈⣡⠔⠂⢉⣩⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠰⠆⠉⣀⡀⠀⠈⣷⠦⢤⣀⡠⣶⣎⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠚⢋⠀⠈⠳⠤⠛⠐⢦⣀⢄⣀⣀⣀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠙⠛⠫⠭⠭⠜⠃⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⣤⣄⡘⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠳⢄⣀⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣴⠀⠀⠀⠀⠈⠙⠛⠛⠛⡿⠀⠀⠀⡠⠖⠛⠋⣠⠤⠤⠤⠤⠤⠤⠦⠤⣈⡉⠛⠲⣏⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣰⠁⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⡟⠠⣶⣏⣁⠀⠀⠀⠀⠀⠐⠓⢀⣈⡹⠶⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⡟⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠹⣆⠀⠈⠉⠑⠒⠚⠛⠛⠒⠒⠈⠉⠀⠀⡸⠣⣄⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⣼⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⣸⠇⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢳⣆⣀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠋⠀⠀⠀⢃⠠⣄⠀⠀⠀⠀⠀⠀⣷
⠀⠀⣠⠇⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣤⣉⣙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠘⢀⡼⠃⣄⠀⠀⠀⠀⠸⡇
⠀⢠⡟⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠙⠓⢦⣄⡀⠀⠀⠀⣠⡞⠁⠀⠘⢧⡀⠀⠀⠀⢸
⢀⡜⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠙⣆⣠⠖⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⣧
⡘⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⡖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠹⡀
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠳⣄⠀⠀⠀⠀⠀⣠⠾⠉
⠀⠀⠀⠈⠳⠦⠀⠠⠤⠶⠚⠋⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⠙⠶⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠶⠚⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠠⠄
⠀⠀⠀⠀⢀⠔⠀⠖⠒⠉⠉⠒⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⡠⠠⠈⢀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀
⠀⠠⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠂⠀⠀⠀⠄⠀⠀⠀⢦⡀⠀⠀⠀⠠⢤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠀⠀⠄⡀⡀⠠⡄⠘⠒⠀⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⡀⠀⡀
⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡌⠠⠁
⠀⠀⠌⠏⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡸⢎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠤⠄⠀⠀⠀⠀⠀⠀⡘⠋
⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠙⡶⠃⠀⠀⠀⠀⠈⠘⢝⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⢤⠀⡠⠃
⠀⠂⠀⠀⠀⡢⢮⠁⠃⡀⢀⣶⠐⠀⠀⠀⠀⠀⠀⠀⣀⡀⠐⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⡴⠉⠱⠶⠠⠂⠐⠢⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠀⠳⠢⠄⠀⠄⠀⠀⠀⠠⠖⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠑⠄⠀⠈⢀⠀⢀⠀⠀⢀⠀⡈⢀⡴⡢⢄⢀⣀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡂⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠂⠀⡀⠈⠁⠀⠒⠦⢀⠀⠁⢰⠀⠀⠀⢀⢖⠅⠈⠠⠐⠒⠂⡛⠱⠌⠁⠼⠀⠀⠂⠀⠐⢀⠀⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⠆⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠁


⡂
⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣟⣿⣿⣻⣋⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣻⣿⣟⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠶⠶⠟⠙⠳⠟⠉⠛⠶⠛⠛⠳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⣤⣤⠞⠛⠛⠛⠉⠀⠉⠉⠈⠛⠒⠶⠞⠻⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⣠⡶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠶⣄⣀⣠⡼⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⣇⣀⣼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⡼⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠀⠀⠀⢠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣼
⠀⠀⠀⠀⠀⠀⢸⡃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣀⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁
⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⢤⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⣄⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡶⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⢸⣷⣭⣭⡭⠵⣺⡇⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⣀⣀⣸⠘⠛⠛⠛⠛⠋⡇⢀⣀⣤⠴⢶⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣼⣧⣉⣙⣦⡀⠀⠀⢀⡼⠋⠉⠁⣀⣠⣼⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⣿⠀⠈⠉⠙⠛⡆⢰⠟⠒⠒⠛⠋⠉⠁⠀⢿⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⣀⣾⠀⣠⣤⠶⠞⠻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠉⠉⣿⠃⠀⠀⠀⠀⠿⠞⢳⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠶⠛⢛⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⣾⣿⣅⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣶⠦⣤⣼⢦⣤⠶⠶⣤⡴⣿⠀⠀⢘⣧⣤⣤⣤⣤⣄⣀⠀⢿⠀⣠⠞⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢠⡶⢦⣴⣯⣤⠴⣶⠾⣇⠀⠀⢸⡆⠙⠶⠶⠞⠁⢀⡾⠛⠛⢧⠉⠻⣿⣿⣅⣠⡟⢹⣆⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⡟⠉⠉⢉⣩⠿⠿⣶⠿⣽⣷⠛⠁⠀⠙⠓⠚⠋⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⡼⠀⠀⠈⣿⠟⣿⣟⠻⠿⣍⡉⠉⠉⠉⢷⡀
⠀⠀⠀⠀⢠⡟⠀⢀⡴⠋⠁⠀⣴⣾⣷⠛⢻⣄⣠⡴⠞⣦⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⣩⣭⣄⣀⡶⠛⢁⣰⣯⡿⠶⣦⠈⠙⢦⡀⠀⠈⣧
⠀⠀⠀⢀⡾⠀⠀⣾⠁⠀⠀⠀⣿⠛⢿⣝⡛⠷⠴⣶⣿⣿⣦⣤⣶⣯⣭⡽⠿⠶⠶⠞⠋⠁⠈⣉⣥⠶⠛⣹⢿⣤⠶⠋⠀⠀⢈⡧⠀⠀⠘⣇
⠀⠀⠀⡾⠁⠀⠀⠘⢷⣄⠀⠀⠈⠳⣤⣈⠉⠛⠲⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠛⠛⢉⣀⡴⠞⠻⢦⣿⠀⠀⠀⣠⡾⠁⠀⠀⠀⠹⣆
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠉⠛⠳⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠶⠛⠋⠉⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⢹⡄
⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⢤⣤⣤⣄⣉⣉⣉⣉⣉⣁⣀⣀⣀⣠⣤⣤⡤⠴⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣷⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠿⠿⠿⠿⠿⠟⠁⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⢠⠆⠀⠀⠀⠦⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⡀⠀⠠⢀⡀⠀⢳⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⠋⡝⢿⡄⠀⠀⠈⢀⠀⢸⠀⠀⠀⢸⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⡆⠀⠀⣠⡇⠀⠉⠋⠀⡀⠀⣸⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⣤⡒⠒⠢⢿⡄⠀⠀⠈⠓⠒⠒⠊⠁⢀⡏⠀⠀⠀⣧⢄
⠀⠀⠀⠀⠀⠀⣤⡊⢙⡶⠏⡟⢶⣄⡀⠀⠀⠦⣀⣠⡎⠀⠀⠀⢸⡿⢾⡀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡟⣁⡂⠇⠀⢈⡏⢻⠙⢏⠙⠆⢟⢦⡀⠀⢊⡻⠄⣩⠆
⠀⠀⠀⠀⠀⠀⡼⠝⡏⠉⡟⣧⣠⡟⠀⠂⠀⠈⡰⡄⡜⢇⣓⡄⠀⡇⡎
⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⡇⡇⣿⠀⠀⠸⡡⠔⠘⢑⡇⡈⢫⡀⢠⠃⢡
⠀⠀⠀⠀⢠⡇⡇⣧⠀⠀⣇⣤⡾⠃⠀⡆⡇⠀⣠⠴⠊⠀⢸⣇⡎⠀⢸
⠀⠀⠀⠀⣸⡇⡇⡟⣧⣶⡋⠀⠸⡤⢼⣳⢃⣾⣤⢾⡟⢯⡁⠈⢁⢀⣮⡀
⠀⠀⠀⠀⣽⠃⡇⡇⡇⡏⣷⡀⠀⢻⠞⠁⣜⢰⢸⣿⠀⠀⢹⠊⠥⠄⠀⢈⡁⢒⣤⣄⣀⡀
⠀⠀⠀⠀⢸⠷⢷⣧⣧⣅⣆⣷⡄⠀⠀⢰⣃⣸⣼⣏⣤⣴⠾⡍⠀⠂⠉⠁⠀⡸⢻⣿⣿⣿⣿⣶⣶⣤⣤⡀
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠉⠉⠙⢦⣴⣯⣿⣿⣿⣿⣿⣿⣄⣈⠒⠐⠐⠒⢉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠉⠉⠛⠓⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠙⠻⣍⠛⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣀⣀⣤⣼⣿⣀⠀⠀⠈⢧⡀⣿⢉⣿⣿⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠳⣄⠀⠀⣳⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣷⣾⣿⣿⡿⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣫⣶⣦⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠹⢿⣿⡿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡴⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠀⠀⠀⢠⣤⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠇⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢿⡟⠋⠉⢻⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠶⢶⠟⠛⠳⠟⠉⠛⠶⠛⠛⠳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⣤⣤⠞⠛⠛⠛⠉⠀⠉⠉⠈⠛⠒⠶⠞⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢠⡶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠶⣄⣀⣠⡼⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣇⣀⣼⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢷⡀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⡼⢁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠀⠀⠀⢠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣼
⠀⠀⠀⠀⠀⠀⢸⡃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣀⣀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁
⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢰⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⢤⡤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣄⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡶⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⢸⣷⣭⣭⡭⠵⣺⡇⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⣀⣀⣸⠘⠛⠛⠛⠛⠋⡇⢀⣀⣤⠴⢶⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣼⣧⣍⡙⣦⡀⠀⠀⢀⡼⠋⠉⠁⢀⣀⣼⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⣿⠀⠈⠉⠙⠛⡆⢰⠟⠒⠒⠛⠋⠉⠁⠀⢿⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢰⡇⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⣀⣿⠀⣠⣤⠶⠞⠻⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠉⠉⣻⠃⠀⠀⠀⠀⠿⠞⢳⡆⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠶⠟⢛⡆⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⣶⢦⣤⣼⣦⣤⠶⠶⣤⡴⣿⠀⠀⢘⣧⣤⣤⣤⣤⣄⣀⠀⢿⠀⣠⠞⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢠⡶⢦⣴⣧⣤⡴⣶⠾⣇⠀⠀⢸⡆⠙⠶⠶⠞⠁⢀⡾⠛⠛⢧⠉⠻⣿⣿⣅⣠⡟⢹⣆⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⢠⡟⠉⠉⢉⣭⠿⠿⣶⠿⣽⣷⠛⠁⠀⠙⠓⠚⠋⠀⠀⠀⠀⠀⠀⠘⣧⣀⣀⡼⠀⠀⠈⣿⠟⣿⣟⠻⠿⣍⡉⠉⠉⠉⢷⡀
⠀⠀⠀⠀⢠⡟⠀⢀⡴⠋⠀⠀⣴⣼⣷⠛⢻⣄⣠⡴⠞⣦⠀⠀⠀⣀⣤⣤⡀⠀⠀⠈⣩⣭⣄⣀⡶⠛⢁⣰⣯⡿⠶⣦⠈⠙⢦⡀⠀⠈⣧
⠀⠀⠀⢀⡾⠀⠀⣾⠁⠀⠀⠀⣿⠛⠿⣝⡻⠷⠴⣶⣿⣿⣤⣤⣾⣯⣭⠽⠿⠶⠶⠞⠋⠁⠈⣉⣥⠶⠛⣹⢿⣤⠶⠋⠀⠀⢈⡧⠀⠀⠘⣇
⠀⠀⠀⡾⠁⠀⠀⠘⢷⣄⠀⠀⠈⠳⣤⣈⠉⠛⠲⠶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠛⠛⢉⣀⡴⠞⠻⢦⣿⠀⠀⠀⣠⡾⠁⠀⠀⠀⠹⣆
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⡀⠉⠛⠳⠶⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠶⠛⠋⠉⠀⠀⠀⢀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⢹⡄
⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⢤⣤⣤⣌⣉⣉⣉⣉⣉⣁⣀⣀⣀⣠⣤⣤⡤⠴⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣦⡀⣀⣤⣴⣦⡀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⡀⠈⠛⠛⠛⠛⠛⠛⠓⠒⠀⠀⠀⠀⠀⠀⣀⠀⠒⠒⠶⠶⠶⠶⠾⠟⠛⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠈⠀⠀⠀⠀⠀⠾⠗⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⠗⠀⠀⠀⠀⠀⠐⠂⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠸⣧⣀⡀⢀⣠⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⢉⣉⢉⡁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠉⠙⠋⠉⠉⠙⠀⣾⠁⠀⠀⢀⣠⣴⡶⠶⠟⢉⣉⣓⣒⡒⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⢀⡴⠋⣰⢏⣴⠶⢛⠉⣉⣉⡉⢩⠙⠓⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⣠⣿⡟⠁⣠⡴⣿⣉⡉⠉⠛⠳⢦⣄⡿
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠉⠛⠲⠦⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣿⢰⡏⢡⡟⠐⠀⣷⣄⣀⠈⠙⠳⢦⣀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⡇⣸⠃⠀⠘⣧⡈⠉⠻⢦⣄⠀⠉⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⠃⣿⠀⠛⠀⠈⠙⣦⡀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⣿⡀⠀⠀⠀⢸⡏⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡜⢧⡀⠉⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣙⡓⠶⠶⢶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠠⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢸⠀⡇⢀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⣸⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢈⠀⠣⠈⡃⠀⠀⠘⡄⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡾⢠⡁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣜⠀⢼⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠢⣽⠀⠀⠀⢰⠀⠀⠀⠀⡆⠀⠀⠀⡀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⡀⠀⢠⠀⠇⠀⠀⠈⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡠⠀⡠⠂⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⠀⠀⠂⠀⠆⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⠁⠈⢄⠀⠀⠀⠀⠀⣇⠦⡴⠼⠀⠀⠀⠀⠈⡰⠀⠻⢶⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⢸⡀⠀⠀⠀⠀⡁⠁⢸⢛⠀⠀⠀⠀⠈⠁⠘⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣠⠞⠂⠀⠀⠀⠀⠛⠀⠁⠉⠁⠀⠀⠀⣨⣦⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⢠⠂⢸⠀⠀⠀⠀⢀⠀⠘⠁⢀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⡀⡀⠀⠀⣀⠀⠀⠈⠓⠄⡟⡀⠈⠀⠀⠀⠀⠘⣥⠠⠒⠁⠀⣀⢀⡀⢀⠀⢀⢀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠷⡀⠀⠀⠀⢰⢁⠁⠀⠀⠀⠀⢀⣀⣡⠀⠀⠀⠐⠉⠋⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠤⢀⡤⠤⠀⢠⣄⣐⡂⠠⣴⠦⠀⠈⠲⡂⣀⡈⡛⠀⠀⠀⠀⠀⠉⠈⠉⣠⣄⠔⠀⠀⠄⢰⠆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠈⠉⠐⢅⡀⠀⠙⠇⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⡠⠖⠀⠀⠀⠑⠀⠛⠦⠀⠄⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠶⠷⡇⠀⠀⠀⠐⢸⠀⠀⠀⠀⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠸⠖⠂⠀⠀⠻⠀⠰⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠆⠀⠀⠒⠂⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠊⠀⠀⠀⠀⠀⠀⠀⣤⠒⠰⢷⣄⣴⠂⠠⢤⣀⡀⠾⠀⢀⣄⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⠀⠀⢸⠄⠋⠀⠀⠀⠀⢠⠃⠄⠑⠀⠠⠀⠀⠀⠀⠈⠑⠀⣠⠀⠀⠀⠀⠀⠘⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢠⣀⠁⡀⠀⠀⠀⠀⠀⠈⠂⢆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢃⡀⠀⠐⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡠⠈⡁⠄⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢻⠡⢀⠁⠰⠀⠈⠈⠱⢤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠃⠀⣽⠠⠄⠠⠄⠀⢠⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠠⠀⠸⠄⣀⡀⠤⠤⠤⠘⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⠒⠞⠛⠓⡖⠒⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠈⠢⠄⣁⣉⠠⠔⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠒⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠀⠀⢰⠁⠀⠀⠀⣰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠐⢪⠀⠀⠸⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠇⠀⠀⢇⠀⠈⠛⠋⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠢⢀⠀⠀⢀⣠⠃⡠⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⠴⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠒⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⢀⣀⠀⠀⠈⠢⠬⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⡠⢋⡆
⠀⠀⠀⠀⠀⠀⢣⠭⠅⢀⠀⠀⣠⠤⢄⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠒⠂⠉⠁⠀⠐⣀⣀⠠⠄⠂⠀⠉⢧⣀⠅⡆
⠀⠀⠀⠀⠀⠀⠀⠒⠮⡠⠔⠊⠀⠀⠀⠈⠁⠐⡄⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠀⠀⡀⠄⠂⠑⠒⠚⢶⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠀⠐⠒⠒⠀⠤⠄⢀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢦⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⢀⠔⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠈⢣⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠀⠀⠑⡔⠁⠀⠀⠀⢀⣀⣱⣀⡠⠒⢤⣄⢀⣐⣀⠀⠀⠀⠀⠀⢣⠎⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⢀⣔⠉⠡⢭⡖⠚⠋⠉⠁⠀⠙⢛⢤⣬⡠⠍⠑⡄⠀⠈⠀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡘⠀⠉⠐⠖⠂⠠⠤⠤⠤⠤⠤⠤⠀⠐⡖⠈⠁⠈⢆⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠤⠀⠀⠀⠀⠀⠀⠠⠀⠔⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⢶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠤⠄⠄⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡑⠢⠍⠭⢽⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⣶⣿⡇⠀⣼⣿⡆⠀⢀⣠⣬⣿⣷⣾⠻⠿⣿⣿⣾⣿⣿⣿⣷⣄⣀⣄
⠀⠀⠀⠀⠀⣾⢏⣿⣿⣾⣿⣿⠅⠀⢺⠋⠉⠙⢿⣴⣤⣄⣈⣿⣿⣿⣿⣿⣿⣿⣼⣿⣧⣦⣄
⠀⠀⠀⠀⠀⠋⠀⠃⣿⣿⣿⣿⡄⠀⠈⢇⢰⡿⣳⣿⡿⣟⣿⣍⣉⠍⠉⠙⠻⢿⣿⣿⣿⣿⡟⣧
⠀⠀⠀⠀⠸⠆⠀⢸⣿⣿⣿⣿⠁⠀⠀⣾⡟⢿⣷⣭⣼⣿⡿⣻⣿⡷⣦⣄⠀⠀⢹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⠙⠁⢀⣤⣤⣙⣳⣴⠟⠙⣛⣿⣾⣿⠏⣼⣿⢿⣿⣷⣾⣿⣿⡟⢹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣤⣾⡟⣻⣭⢠⣾⣿⣿⣿⣿⣿⠿⢞⡾⠟⠛⢿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣷⣿⣅⣻⣿⣷⡀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠙⠻⣧⣤⣷⣿⣿⣿⣭⣭⠇⡼⣦⣿⠁⠀⠀⢰⡏⠹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⡛⠤⠀⠀⣾⠀⠀⢸⡇⢙⣉⠻⠟⣿⢻⣿⣿⣿⣶⣿⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠿⢂⣠⣾⠠⠄⡀⢀⡀⠠⠀⣿⠿⢿⣿⣿⣿⡟⢻⣷⣤⣤⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡟⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⢒⡿⠉⡁⡀⠈⡆⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣮⣿⠽⣛⠿⢛⠀⠀⠀⠙⣄⠄⣶⢀⡇⠟⠾⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⣀⡀⢀⣞⡩⠽⣿⣷⡟⠁⠀⠀⡀⠁⣨⣥⣿⡤⠁⣼⣁⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢣⠋⠙⠉⠈⣹⣿⣷⠟⠁⠀⣀⡼⠟⣆⠀⣚⣴⣿⣟⢛⣩⣷⣾⣿⣏⣄⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢻⣧⢀⣿⣤⣴⡲⠾⢿⣿⠇⠀⠠⠾⣩⣤⣿⣿⣿⡟⠟⣷⣴⣿⡟⠛⠒⠛⢺⡻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣴⣿⠿⠸⠛⠉⠁⠀⢀⣘⠟⠀⡤⠀⣲⣿⣻⣿⣿⣧⣿⡾⠿⢿⡿⠓⠒⠲⡞⠀⡟⠃
⠀⠀⠀⠀⠀⠀⠀⡴⢿⢏⠁⢀⡴⠾⣿⡏⠀⠀⠀⠀⠀⠀⣬⠧⠀⢼⡆⠈⣟⡉⣭⣼⣿⡿⡛⢲⣤⠀⠀⠉⣿⡴⠧⣼⠁
⠀⠀⠀⠀⠀⠀⣼⣿⠇⣠⣿⣿⡇⢀⣿⠃⠀⠰⡀⠀⠀⣐⠛⡤⣥⣤⣶⠋⠉⠁⠈⣿⣿⡍⠀⠈⣻⡆⣠⣢⣟⣀⣴⠃
⠀⠀⠀⠀⠀⢠⣿⣿⣰⣿⠁⠀⣧⣾⠏⠀⠀⠀⠘⢓⣾⣯⣾⠏⠉⠉⠁⠀⠀⠀⠀⠀⠻⣿⣀⠨⣦⡟⠙⠁⠈⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⡤⠖⠁⠀⠀⠀⠀⡴⢋⡞⠁⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡼⢿⢿⣿⣇⡤⠔⠒⠠
⠀⠀⠀⠀⠀⠀⠹⣯⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢸⠀⠀⠈⠱⣤⣤⣖⡲⢛⡹⠶⠛⠛⠙⠁⢨⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣉⣉⣋⣙⣿⠛⠁⠀⠀⠀⣀⣴⡿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⠛⠛⠉⢉⡽⠟⣀⠀⠀⣠⣶⣽⡟⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⢤⡀⠀⠀⠀⡀⠤⠐⠀⠈⠃⢀⣩⣿⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠵⣤⣴⣦⣤⣦⣤⣴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⢿⡟⢿⢿⡿⡿⢿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣷⣿⣶⣷⣷⣿⣷⣿⣼⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣯⣭⣽⣧⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠶⠉⠉⠴⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⢀⡀⢀⡀⠀⡀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⣤⣼⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠄⢀⠀⠀⠀⠀⠀⠀⡇⠀⠄⡀⠠
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡇⣿⣷⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⣀⠸⠀⠀⠀⠀⠀⠀⠇⡭⢶⠠
⠀⠀⠀⠀⠀⠀⢹⣿⡿⠟⠀⢸⣿⣿⣿⣿⣿⣷⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠇⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣿⠟⠙⠉⠋⠻⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠂⠀⠁⠐⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠁⠀⠀⠀⠀⠀⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣤⣄⢀⣿⣿⣿⡀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠃⠘⠃⠀⠀⠀⠀⠀⠀⠸⠃⠘⠃⢀⠠⠄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠁⠀⠀⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠈⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠶⠀⠀⢨⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⢡⠀⠈⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⠁⠀⡀⠀⠀⠀⠈⠉⠀⠀⠈⠑⠀⠀⠀⠀⠀⠙⠒⠀⢻⠂⠀⠸⢠⡀
⠀⠀⠀⠀⠀⡒⠠⠀⠈⡍⠹⣤⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⣹⡏⠀⠠⠖⢠⠇
⠀⠀⠀⠘⠀⠘⣆⡠⢀⠑⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⢀⡔⠀⢀
⠀⠀⠀⠐⠂⠀⠈⠢⢤⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠴⠋⠠⢀⠉
⠀⠀⠀⠀⠀⣀⠀⢀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣂⣂⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠈⠀⠤⠵⠆⠀⠴⠶⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣵⣖⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠠⠔⠚⠋⢱⣄⣀⠀⠀⠀⠀⣀⣠⣤⢾⡑⠀⠀⠉⠉⠛⠓⠦⡂
⠀⠀⠀⠀⠀⠀⠀⢀⠰⠊⠀⠀⠀⡶⠛⠉⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠙⠓⠞⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠆⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣶⣶⢿⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⢿⣷⡦⣄
⠀⠀⠀⠀⠀⠀⢠⡾⣁⣴⠏⣵⠋⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣇⠘⡏⣻⡌⢳
⠀⠀⠀⠀⠀⣰⣿⣴⡟⢠⡞⢀⡔⢃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠨⣆⢸⡄⢻⡎⣧
⠀⠀⠀⠀⢠⣿⣯⠴⠄⢸⡖⣋⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣈⣾⡅⣘⢻⣿⡀
⠀⠀⠀⠀⣾⡿⠄⠀⠻⣮⠛⣛⣿⡋⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣯⡉⣽⠖⠀⢛⣿⡇
⠀⠀⠀⢸⣿⠿⠤⠋⠉⠈⢸⣿⣿⡇⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⣠⠖⠈⠀⠀⠀⣹⣿⣿⠁⠙⠉⣄⣹⣿⡇
⠀⠀⠀⠸⡹⣮⠀⡡⢰⣶⣿⣿⡯⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⠢⡈⠄⣠⢿⠇
⠀⠀⠀⠀⢿⣿⡟⠻⢿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠟⢳⣾⡷⠁
⠀⠀⠀⠀⠀⢻⣷⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠏⠁⣾⡏
⠀⠀⠀⠀⠀⠘⢿⡂⢼⣟⣿⣿⣶⣀⣴⠾⢻⣦⠀⠀⣿⣿⠀⠀⣴⡟⠷⣦⣀⣶⣿⢿⣓⡷⢐⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠺⣭⣉⡽⣻⣿⣧⣀⠀⢻⣷⡾⢿⡿⠿⢾⡟⠀⣀⣼⣿⣟⢫⣉⡭⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣷⣿⣿⣿⣶⣿⡅⣼⠀⢁⡻⣶⣿⣿⣿⣼⣿⡾⠋
⠀⠀⠀⢀⡀⠠⢤⣤⣤⡤⢄⣸⡃⠀⠉⠙⢿⣿⣟⣥⠁⠀⢠⣻⣿⡿⠋⠉⠀⢘⣇⡠⢄⣤⣤⡤⠄⢀⡀
⠀⢀⣴⣿⠟⠛⠋⠉⠙⠛⢿⣿⣵⣢⣀⠀⠀⣿⣿⣧⡟⢤⣼⣿⣿⠀⠀⣀⣀⣾⣿⡿⠛⠋⠉⠛⠛⠻⣿⣦⡀
⣰⣿⢋⣠⣴⣲⣶⣿⣯⣵⣾⡧⣄⡉⠛⢿⣶⠟⣫⠭⢭⡭⠭⢛⢿⣶⡿⠋⠉⣠⢼⣗⣪⣽⣷⣶⣖⣦⣄⡙⣿
⠉⣑⣭⡿⠋⠉⠀⠀⠉⠙⢻⡿⠶⢮⣷⣄⡽⣸⣿⡀⢸⠀⢀⠆⣄⣯⣰⣾⡽⠶⢻⡿⠋⠉⠀⠀⠉⠙⢿⣭⣊
⠞⠽⠋⠀⠀⠀⢀⢀⣠⣤⣿⣦⣤⣄⣈⣙⡇⣿⠃⢱⠠⠀⡆⠀⠿⢻⣋⣀⣠⣤⣴⣷⣤⣄⣀⡀⠀⠀⠀⠙⠯
⠀⠀⠀⠀⢀⣾⣷⠟⠋⠉⣿⠉⠉⠉⠉⠙⡇⠆⠀⠀⠀⠀⠀⠀⠐⣸⠋⠉⠉⠉⠙⣿⠉⠙⠻⢿⣷⡀
⠀⠀⠀⢠⣾⡟⠁⠀⠀⣠⣿⣶⣾⠶⠾⠻⣷⢨⣖⣀⣀⣀⣀⣀⠅⣿⠟⠶⠶⣿⣶⣿⣄⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠋⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⢸⡿⣿⣿⠟⠛⠻⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⢻⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡇⠀⠀⠀⠀⠀⠠⣿⣿⣟⣀⣀⣽⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣉⡉⣿⣿⣏⠀⠀⠀⠀⠀⠀⢸⡇
⠤⠤⠤⠤⠤⠤⠤⢄⠤⣾⠇⠠⠤⢠⠤⠀⠄⣿⣿⣟⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷
⠁⡀⠀⠀⠀⠀⠀⢀⢀⣇⡀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻
⣉⠀⣀⢀⡀⣀⣀⣀⢨⡇⣀⢀⣀⡀⣀⠁⣂⢻⣿⡷⠶⢶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⡀⠀⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡠⢶⣿⢿⣿⡉⠛⣿⡿⣿⣷⢄⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠞⢁⣿⠁⠈⣿⣧⢰⣿⠀⠈⣿⡀⠳⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⣧⣾⣿⣴⣶⡿⣿⣿⠿⣶⣦⣿⣷⣼⠀⠀⠀⠀⠀⠀⠀⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢠⣶⣶⡄⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡆⣈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣌⣻⣟⣁⣼⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣛⣃⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠉⠀⠀⠠⠀⠀⠀⠀⠠⢶⣦⡀⣰⣮⣭⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣯⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣴⣶⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠸⠋⠏⠹⠟⠀⣿⡇⠀⠸⠏⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇⣿⠉⡏⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠻⡟⢿⡛⠛⠛⣻⣿⡛⠛⠛⠐⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⢸⣿⣆⠀⣠⣦⠀⠀⠀⠀⠀⠀⠀⣸⡇⣴⡆⡇⠀⠹⣆⠀⢻⣿⠁⣀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣀⣬⣭⣄⠀⠀⠀⢀⣠⣴⣿⣷⣾⣷⣧⣀⣀⣘⣿⣿⣿⣿⣷⣿⣀⣀⣀⣈⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢹⡇⣾⠉⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠉⠀⣿⣿⡇⠀⠀⠀⠘⠿⣯⣇⣹⣿⡿⠿⠿⣇⣇⣿⣿⡿⠿⠿⠿⠿⠿⡿⢿⣿⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠘⠃⠀⠀⠛⠙⠁⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡞⠉⢹⡄⠀⠀⠀⠀⠀⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⢙⢛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠛⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣭⣤⣄⢠⣤⣤⡄⠀⠀⠀⢠⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣭⣥⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣄⣀⣀⣀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⠀⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⣿⢸⣿⠀⡇⠀⠀⠀⠀⠀⠛⢻⣿⣀⢀⡂⢀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠉⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⡀⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠘⢻⣿⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⣿⠟⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⢺⠉⠗⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡌⢿⣿⣆⠀⠀⠀⣸⣿⡀⠀⠀⠀⣼⣿⠏⣸
⠀⠀⠀⠀⠄⠢⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠰⠂⠄⠀⠀⠀⠀⠘⣆⠛⣦⡹⢿⣿⣦⣼⣿⣿⣿⣦⣶⣿⠿⢋⡼⢋⡼
⠀⠈⠀⠀⠁⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠘⣀⡀⠀⠁⠀⠂⠀⠀⠰⣌⠳⣬⡙⠶⣬⣹⣿⣿⣿⣿⣿⣉⡥⠞⣋⡴⢛⣱⠂
⠀⠀⠀⠀⠁⠐⠤⢀⣀⠀⠀⠀⠀⠀⢐⡀⠤⠔⠀⠡⠀⠀⠀⠀⠀⠙⠳⢦⣍⣓⠶⢼⣿⣿⣿⣿⣿⠷⢖⣛⣩⠶⠛⠁
⠀⠁⠀⠀⠄⠈⠁⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠲⣤⣄⣀⣀⣉⣉⣽⣿⣿⣿⣿⣿⣍⣉⣉⣀⣀⣤⡤⠞
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣿⣿⣿⣿⡇⠀⠈⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣽⣿⣿⣿⣵⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠟⠻⠿⠛⠿⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⣠⠀⠀⠀⣠⣄⢠⠀⠀⡀⠀⣀⢠⡄⠀⣠⢲⡄
⠀⠀⠀⠀⠀⠀⢀⣶⣼⣿⣿⢰⢄⡇⣠⢂⡟⢸⠀⣶⡇⣿⢰⠀⣾⠁⣴⢧⠄⣷⢸⡇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣿⡜⢋⣿⠁⢸⣇⡾⡷⠻⠺⣿⡾⠞⣿⡼⠿⠊⠸⡧⠚⠃⢿⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⡏⢸⠇⠀⢉⠀⠀⠀⠀⠉⠁⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠠⠔⣾⠆⢀⡀⠀⠀⣴⡾⣷⢻⠇⣷⣸⣧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⣇⣿⠀⣾⠏⠀⠀⠸⠇⠛⢸⡼⢉⡝⣻
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠆⠀⠀⠀⠉⠉⠛⢻⣧⠋⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⢠⣟⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣮⢰⠄⢠⣏⠀⠀⣀⢀⢄⠀⢀⢄⢀⡀⠀⢰⡆⣠⣏⡰⣏⠀⢸⡟⡤
⠀⠀⠀⠀⠀⠀⠠⣿⡇⣾⢠⡟⠹⢲⡟⣿⠇⣾⢀⣿⠞⣸⡇⣿⢈⢻⡏⠨⠁⣼⠃⣼⣿⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠻⠇⣿⠸⢧⠄⢸⡇⣿⠄⣿⣘⠙⠚⠉⠛⠙⠋⠈⠛⠁⠀⣿⠜⠀⠛⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠈⠁





⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠤⠒⠀⢄⣀⣀⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠈⠁⠀⠁⠀⠒⠴⠀⠁⠀⠀⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠴⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⠀⠐⣚⢀⠀⠀⠀⠀⣈⠘⠁⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⣀⠀⠀⢠⢤⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⣀⠀⠉⣀⡀⠀⠄⠈⡇
⠀⠀⠀⠀⣀⣀⣀⣀⣠⡔⠂⠈⡉⢤⠀⠀⠀⠀⠀⣀⣉⢀⢀⠀⣄⡀⠈⠆⡘⢄
⠀⠀⠀⠐⠈⠤⠶⠶⠄⠤⠀⠉⠀⠀⠲⠂⠀⠀⠀⠉⠀⠈⠁⠀⠀⠁⠁⠤⠁⠀⠦⠨⠽⠯⠩⠴⠆⠀⠰⠀⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢻⣿⠷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⣼⠏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⣇⠛⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠈⠩⠀⠐⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⡀⠘⠃⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢈⡁⢀⠀⡜⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠁⠀⠸⡰⣦⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣀⠀⣻⣞⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⡷⣻⢛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠃⠛⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣀⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡆⠀⡘⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣀⣰⣿⢃⡀⠀⠾⠀⠀⠀⠀⢀⠀⣄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠘⣣⣷⠀⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⣿⠿⠟⣁⠈⠟⠊⠀⠀⠀⠀⠀⠘⣂⠘⠣⣔⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⣟⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣇⠈⠀⠉⠙⢀⡀⠀⠀⠀⠀⠀⢐⣏⠀⠀⣩⡀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠠⣤⣿⣟⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⠖⢤⡤⣀⠀⢨⡅⠀⠀⠨⢋⣶⡀⠀⣄⣀⣌⢿⣿⣿⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠘⢿⡷⠞⠛⠋⠀⠈⣷⠿⣦⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣧⣽⣿⠿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠀⠀⢀⣧⣀⠀⠑⢤⣸⡏⠀⢹⡄⠀⠀⠀⠀⢨⣿⡟⣾⣿⡿⠟⠋⠉⠀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡷⠆⠀⠀⠃⡙⠳⣄⡀⠉⡁⠀⣸⠀⠀⠀⠀⠀⣸⣿⡇⣿⣧⣤⡄⣠⣶⡴⢛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠒⣄⠈⠑⠊⠉⣿⠃⠀⢸⡀⢀⡀⡄⣰⣿⣿⡟⣿⣿⠿⠟⠋⢁⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠬⣻⢦⣀⠀⠈⡆⠀⠸⣷⣶⣾⣧⣿⣿⡿⣱⣿⣿⣄⠀⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠉⠀⠭⠿⣿⡇⠀⠀⠙⠋⠙⢫⠉⠋⣼⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⠀⠀⠀⠀⣀⣤⣤⣤⡶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠢⠤⠀⢀⡀⣟⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⡟⠀⢀⣰⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠿⠉⣿⣠⣤⣤⣤⣀⣤⣿⣿⣿⣿⣿⣷⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⣻⣿⠋⠉⢉⣙⣛⣉⣭⣿⣿⣿⣿⣅⣴⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠁⠉⠉⢉⡟⠁⠈⠉⠉⠉⠉⢿⣿⣿⣿⡟⠉⠉⠀⠸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⢀⣰⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠈⠉⠉⠉⣹⣿⣿⣿⣿⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢨⣦⡄⢠⣤⣀⣀⣤⣿⣿⣿⣿⣇⠀⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠤⠤⣤⣠⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠒⠛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⣨⣿⣿⣿⣟⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣿⡿⢿⣶⣿⣿⣿⣿⡟⢧⣌⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⡀⢸⣷⣾⣧⣄⣸⣿⣟⣀⣼⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠛⠉⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣉⡉⡛⢿⣙⣠⡆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⣠⠶⠛⠉⠀⠙⢀⣁⣒⣤⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣿⣽⣿⡆
⠀⠀⠀⠀⠀⠀⣴⣿⠀⢠⠾⠋⠨⠛⣤⠀⠀⠀⠁⣸⠛⢻⢿⢿⣎⢥⢴⣶⣶⣦⣤⣀⠈⠛⢿⣿⢛⡟⠂⠔⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢰⣿⣉⣴⣿⠀⠀⢀⣤⠛⣷⠀⢻⡀⠛⣶⣿⣫⣬⠘⢾⡌⠉⠀⠀⠈⠙⢻⠒⣤⣽⣿⣿⡆⠀⠀⠀⠀⢰⣧
⠀⠀⠀⠀⠀⣿⡇⢿⣿⣿⣤⠴⣫⣀⣶⣼⠻⢮⠇⢈⣽⣿⣿⣷⡀⣨⡷⡀⠀⠀⠀⠓⢀⢤⡟⠈⠻⣿⣿⡄⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⢸⣿⡬⣿⣿⠇⣄⣽⣿⣿⣿⢆⣈⣰⣦⠙⣿⣿⣿⠗⠎⠀⢨⣿⣧⡤⠀⠐⠮⡿⣴⠃⠈⠿⡧⠀⢀⡾⢘⠇
⠀⡤⠀⠀⠀⠀⢹⣧⡘⠷⢶⣾⣿⣿⣿⣧⣶⣿⠛⢀⣴⠟⠛⢿⣿⣄⣴⣿⣿⣿⡿⠀⠦⠀⠈⢫⠙⡋⠀⡰⢂⣾⢣⠈
⠀⢳⣾⣦⣤⣄⠀⠈⠻⡖⢶⣿⣿⣿⣿⣟⠛⠧⠸⠟⠁⡄⢠⣿⣿⠛⠙⣿⢿⣟⠛⢷⡀⠀⠀⠀⠀⠀⠀⣠⠾⠡⠎⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠹⣿⣿⣿⡷⠤⢠⣦⣀⣿⣿⣿⣿⣿⣞⠀⠀⠀⠀⠀⢸⣿⠘⠀⣾⢻⣼⡿⠀⠈⠀⠀⠀⠀⠁⢠⣄⠘⢂⣠⡔⠒⢈⣩⠄⠀⠀⠀⠁
⠀⠀⠀⠈⠛⠾⠿⣶⣤⣼⣿⠻⣶⣿⣛⠙⠇⢗⡤⠀⠀⠀⠛⢠⡄⠀⢸⠂⠙⡿⢶⡀⠀⠀⠀⢈⣡⢶⢿⡟⡋⠉⠄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣭⣿⡟⠻⠿⠿⣿⣿⣦⡋⠁⠁⠀⠀⡀⣸⡇⠀⠾⠀⠀⠀⠁⠈⣀⣴⡾⠯⠄⡍⣌
⠀⠀⠀⠀⢠⠴⢋⣩⣤⡞⢡⣴⣦⣤⣄⣹⣿⣿⣄⣀⣠⠤⠉⠀⠀⠀⠄⢀⣀⣀⣠⣞⣋⣀⣴⡖⠚⠓⠛⢶⣌⠒⣄⡀
⠀⠀⠀⣴⠟⠚⠋⠁⠀⠀⣠⠰⠙⠉⠉⠛⢛⣏⣯⣻⠽⣿⣿⢿⣭⣿⣽⢿⣿⣾⣿⡀⠉⣩⣉⣛⣷⢆⠀⠀⠈⠓⠪⣱⣄
⠀⠀⠀⡷⠀⠀⠀⢀⣤⠾⠋⠛⠀⠀⠐⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠙⠓⠌⠉⠉⠛⢧⠱⠄⠀⠀⠀⠀⢬⣃
⠀⠀⠀⠀⠀⢀⢤⡿⠉⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡉⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣠⠿⠟⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀⠒⠋⠐⠄⠤⡄⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⠁⠀⠀⠐⠎⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠠⠀⠀⠀⠀⠀⠒⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⢀⡐⠒⠀⠀⠀⠒⠀⠀⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠀⠈⢠⡄⠀⠀⠀⠒⣀⠀⠀⠁⠇
⠀⠀⠀⢀⡀⣀⣀⣠⠂⠀⢈⠠⠀⠀⠀⠀⢀⣉⠀⣀⠀⣄⠀⠱⣘⠄
⠀⠀⠀⠓⠑⠒⠒⠀⠀⠈⠁⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠛⠃⠐⠒⠈⠒⠐⠒

⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⢛⡯⠉⢉⣉⠉⢩⡍⠉⠛⠲⢦⣄⠀⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠒⠂⣀⣠⣤⠤⠤⣤⡀⠀⠀⠀⠀⠒⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠘⠃⠀⡴⠛⣉⡤⠴⠶⠶⣶⠟⠘⠂⠀⢠⠄⠀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⣴⠃⠐⠃⠤⠀⠀⠀⠙⠻⠷⠶⠖⠚⠋⠁⢠⠀⠀⠀⠀⠀⡞⠉⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠀⠀⠀⢶⠀⠀⠀⠀⠴⠆⠀⠀⠀⢀⣠⣀⣀⣀⣼⡃⠀⠀⢸⡇⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡖⠒⣦⠀⢀⡀⠀⢀⣠⣤⣄⡀⠀⠀⣰⠋⠐⠁⠒⠒⠉⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠈⠳⣬⣠⣴⠋⠀⠀⠒⠭⠿⠯⠕⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠳⠦⣤⣀⣀⣀⣀⣀⣀⣀⣁⣤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⡿⣠⡶⠛⣦⢰⡾⠛⢷⡰⡇⠀⢸⡆⢺⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠶⠛⠁⢿⣄⣀⡼⠻⡇⠀⢸⡇⢿⣀⣾⣇⠘⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠉⠀⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⠛⠛⠛⠛⠛⠛⠋⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠀⠀⢠⡶⠀⠀⠀⠀⠶⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠿⣿⡏⠀⠀⠀⠐⠋⠀⠀⢸⠈⠉⠀⠀⢸⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢷⡙⠿⠀⠀⠀⢀⠀⠢⣄⣼⠀⠀⠀⠀⢸⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢷⠀⠀⠀⠴⢿⡀⠀⠀⠁⠀⣠⠀⠀⡾⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⢠⣴⡓⠛⠲⠼⣧⡀⠀⠀⠀⠉⠓⠒⠒⠋⠁⠀⢠⠇⠀⠀⠀⢸⣗⢦
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠛⣶⡾⢻⠛⣦⡀⠀⠀⠠⠀⡆⠄⢀⣴⠋⠀⠀⠀⢔⢺⡿⢾⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠉⢑⡾⠏⠀⢸⠀⠀⠙⣿⠲⡶⠶⡖⠛⢏⢻⠷⡄⠀⠀⢠⠺⣔⡈⠱⣣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⠦⠗⢶⣬⠀⠀⣼⠏⢠⠃⠀⢵⢀⠈⠈⢧⡙⣦⡀⠀⢱⠈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡙⢸⠀⡇⣿⢘⠷⣼⠋⠀⠀⡤⡀⠀⢎⡷⠹⡎⢧⣧⠟⠀⢸⠀⣷
⠀⠀⠀⠀⠀⠀⡘⡟⢇⢸⠀⡇⣿⢸⠀⣿⡀⠀⠀⢳⠱⠞⠈⠁⣱⠥⡄⠱⡄⠀⡞⠀⢸
⠀⠀⠀⠀⠀⢠⡇⣗⢸⣮⠀⡃⣿⢨⣤⡾⠃⠀⣼⢈⡇⠀⣀⡤⠖⠋⠀⢠⣇⢰⠁⠀⢸
⠀⠀⠀⠀⠀⢸⡇⣿⢸⢻⣄⣥⡟⠋⠀⢳⣀⣠⡿⣶⠁⣼⣁⣠⢾⠻⣖⠋⠈⠛⠀⠀⣼
⠀⠀⠀⠀⠀⣿⡇⢿⢸⢸⡏⡟⢷⡀⠀⠘⣧⣁⡟⠁⡸⢹⢹⢱⡟⠀⠈⠳⡤⠔⠊⠈⠉⠓⠒⠠⣄
⠀⠀⠀⠀⠀⢻⣇⢸⢸⢸⠇⡇⠘⢷⡀⠀⠘⠋⠀⢰⡇⢸⢸⣼⠇⠀⠀⣰⢥⣉⣉⡉⠤⠬⠒⠈⢸⣿⣷⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⢸⡟⠛⠿⠾⠶⣦⣼⣬⣿⣄⠀⠀⢀⣯⣤⣼⣾⣿⣴⣾⣿⠋⢧⡀⠀⠀⠀⠀⢀⣠⠏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣦⣀⠉⠓⠒⠒⠊⠉⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠠⠖⠺⠷⠶⢤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠛⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠻⣦⠈⠙⣿⣿⣿⣿⣿⣿⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⢦⣤⣤⣤⣤⣤⣿⣧⣀⡀⠀⠀⠈⢳⡀⢹⣀⣨⣿⣿⠋⠁⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠛⢦⡀⠀⠀⢻⣾⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⢻⣄⣴⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⣿⡿⢛⣛⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠘⢿⣿⣶⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢸⡀⢸⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⠀⢸⠀⣸⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠳⠜⠀⠈⠃⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠋⠀⢘⠴⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⢀⡀⠀⠊⠀⠀⠀⠂⠄⠀⣀⠀⠀⢠⠎⠀⠀⠈⠃⠀⣀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠘⠐⠏⠀⠀⠀⠀⠀⠀⢀⣀⣔⣻⡄⠈⣜⠀⠀⠀⠀⠀⠀⠈⠗⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠠⠀⠀⢐⠔⠹⠃⠿⠘⠃⠀⠀⠀⠀⠀⠈⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠊⠁⠀⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠂⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠃⠀⠀⠠⠤⡞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠀⠀⢊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠈⣁⠀⠀⠀⠀⠀⠀⠀⢈⡁⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠊⠉⡄⠀⠀⠀⠀⠀⢀⡌⠉⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠠⠁⠀⠀⠀⠀⠁⠨⠂⠀⠠⠀⠠⠆⠈⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠲⠀⠸⠤⠄⠤⠄⠀⣄⠀⠰⠣⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢄⡀⠀⠀⠀⠀⢀⠄⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠓⠀⠤⣤⡤⠄⢊⠀⠀⠀⠀⠀⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠠⠠⠄⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠀⠄⠀⠀⠀⠤⠽⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠐⠳⠄⠺⠤⠤⠤⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠀⠀⠀⢈⠉⠙⣳⣶⡤⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠰⢿⣶⠶⠂⠀⠀⠀⠈⠓⠦⣄⡉⢣⡀⡤⠋⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠑⢐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠉⠁⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⡦⠊⠀⠀⠀⠀⠀⢀⡀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣠⣀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⢰⠀⠶⠏⠀⠀⠀⠀⠀⠂⠀⢠⠄⠃⠘⠈⢳⣬⡆⠀⠀⠀⠀⠀⠀⡄⠈⠉⠁⠻⣧
⠀⠀⠀⠀⣄⠀⢀⠀⠀⠀⢠⣶⡆⠁⠀⠀⠀⠈⠀⠀⠀⠀⠐⣿⡧⠠⣄⡀⠁⢠⢶⠆⠀⠀⠀⣠⡇⢀
⠀⠀⠀⠀⢻⡄⠈⢆⡀⠀⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠄⠈⡷⢀⣼⣿⠀⠀⣠⡾⠏⠀⡞
⠀⠀⠀⠀⠀⠡⣄⠀⠈⠀⠐⠯⡙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠛⠉⠉⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⠤⣤⣀⡈⠩⢷⣄⣀⡀⣦⣄⣀⣦⣀⣤⣾⡿⠏⢀⣀⣐⡦⠀⠀⠋
⠀⠀⣠⣤⣤⣄⠀⣐⡀⠠⢧⠤⠤⠤⠄⢾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣧⣤⠤⠄⢠⡬⠁⢐⠂⠀⢠⣤⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠰⡠⠴⡂⢀⣀⠀⠗⠁⠀⠀⠈⠁⠀⠲⠀⣀⣀⢁⠶⠴⠆⠀⠲⠄
⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠼⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠦⠀⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣤⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⢿⣿⣿⣿⣿⣿⣶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢛⣻⣏⢠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠟⠛⠛⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⡀⠀⠀⠀⣴⠾⠛⢁⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⡀⠀⠀⠀⣴⡾⠿⣿⣷⣄⠀⠀⠀⠈⣿⣿⣿⠿⠛⠻⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢲⡿⠀⠀⠀⠘⠏⠀⠘⠛⠛⠁⠀⠀⠀⠀⠿⡿⠋⣴⡻⠆⢹⡿⣣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠃⢀⠮⠟⠁⣠⡾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⣠⣶⣶⣿⣿⣿⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢈⠁⢀⡉⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠰⣟⠛⠛⠛⠳⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠀⣀⣼⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⡃⠀⠈⠉⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢐⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢍⣉⡭⠔⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⡑⠀⠀⠀⠀⠘⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⢻⣤⢦⣄⡄⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡻⠁⠘⠁⠀⠀⠀⠀⠀⠈⢿⡁
⠀⠀⠀⠀⠈⡾⢿⣿⣊⣿⣞⣾⣇⠀⠀⠀⠀⠠⣤⣀⣀⣤⣤⣶⣶⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠉⠀⠹⠟⠋⠙⠋⣁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡴⢒⣟⢡⡀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⣠⣞⠋⠁⣩⢏⠛⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣀⣀
⠀⠀⠀⠀⢠⠞⠋⠈⢻⣾⣓⡾⢀⡟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠁⠀⠀⣠⣾⡿⣍⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⡀⠚⠏⢥⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡾⠟⠃
⠀⠀⠀⠁⠀⠙⠀⡤⠟⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠿⣿⣿⣿⣿⠋⢉
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⡀⠖⠁⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠹⡆

⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡤⠄⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⣠⠶⠖⢿⠉⠉⢹⡏⠀⢸⡿⠉⠉⠉⠁⠀⠸⣁⠀⣀⠄⠀⠀⣲⠍⢁⣉⡁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⣠⣾⠋⢀⡤⠇⠀⠀⠉⠷⢴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⢤⡾⡯⠀⠓⠚⠛⠒⠀⠉⠉⠀⠀⠀⠁⠐⠂⠄⠀⠘
⠀⢸⢇⢨⡟⠯⡀⢑⣀⡀⠀⠀⠸⣟⠡⢀⠀⠀⠀⠀⠀⢀⣠⡀⣠⣿⢋⡇⣢⠴⠖⠒⠂⠀⣀⡀⠂⣶⣋⣽⣿⡯⠯⢽⢀⣠
⠀⢸⡈⠙⠒⣤⠾⠍⠡⡄⢸⠆⠀⠉⢿⠓⢾⠶⣾⠒⠲⣛⣪⢹⡛⠿⠽⠥⠾⢥⣤⠔⢲⣾⡟⠀⠀⠀⠉⠁⠁⠒⠒⢈⡡⠃
⠀⠘⣿⠃⠘⠃⠉⠚⠂⠙⠀⠀⠀⠀⠀⠂⠈⠦⠈⡛⡄⢠⡉⠉⣓⡐⠒⠒⠒⠚⠲⠾⠿⠓⠿⠯⠶⠶⠶⠶⠶⠞⠊⠇
⠀⠀⠈⠣⣄⠀⠐⠒⠠⢤⡀⢠⡀⠀⠀⠀⠸⣆⠀⠨⢷⡈⠐⢦⡉⠙⠁⣢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠘⢦⣀⠀⠀⣸⠃⠘⠀⠀⠀⠀⠀⠘⠀⠀⠈⡇⠀⠀⠙⣶⢄⠀⠐⢽⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⣀⠀⠀⠀⠀⠈⢣⣷⡀⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⠋⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠈⢻⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⠃⠀⢀⣠⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣤⣀⠀⠀⢻⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⠉⠁⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠉⢩⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠘⣿⣿⣿⣟⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⢘⣿⣿⣿⡟⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠹⢿⣿⣧⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢠⣿⣿⠿⠃⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⢿⣿⣷⣶⣶⣶⢞⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⢶⣶⣶⣶⣿⡿⠟⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣤⣄⣀⣉⣉⣭⣶⡿⠃⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠻⣷⣮⣭⣉⣁⣀⣠⣴⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⠿⠿⣫⣴⣶⣶⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣬⡻⠿⢿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢛⣿⡿⠋⠁⠀⠙⠻⠿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠈⠻⣿⣟⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠟



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣥⠠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⣠⠄⠘⠦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢺⣁⣦
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠂⢀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠉⠀⠀⠘⡅⠉⠁⠉⠀⠀⢀⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⢴⡟⠃⠀⡀⡀⠀⠀⠰⠌⠢⡀⠀⢦⣤⣾⣯⣿⣿⣿⣿⣾⣄⠀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⡾⠗⣤⣤⢄⡸⠀⢀⣠⠀⠀⠈⣶⣾⣿⣿⣿⣿⣿⡿⣿⣿⣝⠙⠻⠾⢶⡷⠄
⠀⢠⡀⠀⠀⢛⠩⠽⠿⢤⣽⣿⡟⠛⠃⠀⢀⣱⣟⣿⣭⣽⣿⣿⣿⠘⣏⣷⣤⡆⠀⠈⠃
⠀⠸⠷⣀⡴⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⢉⣉⣉⡙⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣠⣤⣾
⠀⠀⢠⠟⠂⣄⠀⠀⠀⠀⠀⠀⠀⣰⣠⠤⠤⢴⣿⣷⣭⣤⠤⠾⠿⠿⠿⣿⣿⣷⠀⠀⠀⠀⢻⣿⣿⣿⡄
⠀⢴⣄⣀⣠⣿⡇⠀⠀⠀⠀⠀⠀⣾⣛⡋⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣼⣯⡁⡀⠄⠀⠘⣿⣿⣿⠁
⠀⠘⣻⣿⣿⣿⣿⣤⣀⣀⣤⣤⡀⠾⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣹⡏⠀⠀⠀⠀⣽⣿⡟
⠀⠀⢐⣨⣽⠏⠜⠀⡟⠈⠉⠀⠀⠀⠁⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠛⠻⣇⠙⠿⣷⡄⠀⠀⠀⠛⠉
⠀⠀⣿⣿⡿⠀⠀⣰⠀⠀⡠⠂⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣷⣶⣿⠃⠠
⠀⠀⣿⣿⣇⠀⢸⣿⣀⠴⠁⠀⠀⠀⠀⢀⡜⢀⣾⣿⣿⣿⣿⣿⣿⣧⠀⣿⡏⠙⠙⠓
⠀⠀⣿⠋⣈⠉⠛⠛⠿⠲⠲⠂⠰⠒⠛⣉⢩⢸⣿⣿⣿⣿⣿⣿⣿⢟⣠⣿⣿⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢿⠃⢹⣷⣶⣶⣷⣶⣶⣶⠖⣳⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠸⠋⠋⠛⠍⠋⠉⠉⠈⠉⠁
⠀⠀⢸⠆⢸⣿⣿⣿⣿⣿⣿⡧⢀⠘⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡄
⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣤⣿⠇⠀⠠⣟⢻⣿⠿⡻⠻⠿⠿⠿⠓⠂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠂⠀⡝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢫⠀⠐⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢈⠀⡰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢂⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⡖⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢲⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠸⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠇⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⡀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠤⢀⡀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢊⠁⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⠱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠈⡄⠀⠀⠀⢆⠀⠀⠀⠀⢀⡴⠺⠚⠻⡖⢦⡀⠀⠀⠀⠀⡰⠀⠀⠀⢠⠁⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢃⠱⡈⢄⠀⠀⢀⡦⢄⠀⣠⠎⡠⠋⠉⠉⠛⢄⠱⣄⠀⡠⢶⡀⠀⠀⡰⢁⠎⡘⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⡈⢢⡬⠲⣗⡉⠉⠀⠀⡝⠃⠌⠀⠀⠀⠀⠀⠀⢣⠘⢫⠀⠀⠉⢉⣺⠔⢅⡔⢁⠊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠡⡈⢢⣕⢄⡈⠪⣕⢠⣎⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⢱⡄⣪⠕⢁⡠⣪⡐⢁⠜⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠢⣘⠯⡀⠑⠬⣺⣀⡍⠒⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠒⢩⡀⣗⠥⠊⢀⠽⣃⠔⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡱⠦⢕⠤⣋⡙⠐⠠⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠄⠀⢋⣙⠤⡂⠱⢎⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠑⠠⠀⢈⡸⠋⠖⠲⢴⡅⠀⠀⠀⠀⠀⠀⠀⠀⢨⡦⠔⠲⠙⢇⡁⠀⠄⠊⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠂⠄⠀⣀⡀⠀⠈⠉⠐⠒⠒⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠒⠒⠀⠉⠀⠀⣀⣀⠀⠤⠐⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠼⣀⣈⣉⣉⣋⡁⠠⠄⠲⡀⣀⣀⣀⣀⣀⢀⣀⠖⠠⠄⢉⣹⣉⣉⣁⣀⠧⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠤⠤⠤⠤⠤⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠒⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⣀⣀⣀⡀⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⡦⠤⠄⠀⠀⠠⠤⣖⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⢀⠎⠱⠀⠀⠀⠀⠀⢀⠉⢢⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠼⡀⠀⣣⡀⠀⠀⣠⡎⠀⢀⠦⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠈⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀
⠀⠀⠀⣀⣴⣬⡽⠿⠲⣷⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢂⠀⠀⡠⣄⠀⠀⣀⢀⢀⠀⠀⠀⢠⣤⣤⡀
⠀⠀⢨⣏⠙⠒⠂⠉⢁⢹⡆⠀⢀⠞⠁⠀⠀⠀⠀⠀⠢⡑⠄⠀⠀⠀⡠⢤⠤⡀⠀⠀⢨⠀⣯⠀⡎⠀⠹⡇⠀⢟⣏⡮⠁⠀⠀⢸⠁⢩
⠀⠀⠀⣾⠐⢒⣈⡉⠤⠄⣿⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠇⡘⠀⢀⠎⠀⠀⠱⣑⡀⠀⠈⠄⢸⠀⠘⠢⡔⠁⠀⢣⢠⠚⠀⠀⠀⢸⠀⢸
⠀⠀⠀⢹⡁⠤⠤⠐⢒⡀⢸⡀⠀⠘⠢⠤⠤⢤⠤⡤⠤⠊⠀⢠⠃⠀⠱⠓⠀⠈⢷⡀⠀⠇⣨⡇⠀⠆⡇⠀⠀⡆⡈⠀⠀⠀⡠⠃⠀⠀⣷⡄
⠀⠀⠀⠀⡷⠖⠬⠵⢂⣒⠭⠇⠀⠀⠀⣇⣂⣈⣀⣁⣀⠀⠀⠧⢤⣦⣤⣤⣤⡤⠬⠇⠀⠀⢐⣠⠀⢁⡇⠀⠀⢇⠇⠀⠀⠀⠧⠤⠤⠤⠬⠬
⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⠀⠀⢸⠀⠠⡤⡂⠀⠈
⠀⠀⠀⠀⠀⣀⠤⠄⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠉⡉⣿⣻⣉⢉⣉⢉⣏⣟⣉⡉⠉⠉⠀⠀⢸⠄⢈⣀⣀⡀⢤
⠀⠀⠀⡠⢊⡤⠊⠉⠉⠁⠢⡑⢄⠀⠀⠀⠀⣠⣖⠉⡄⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠉⢁⣴⠞⠛⢶⡌⠉⢳⡇⠀⠀⠀⠀⠈⣄⣀⠀⠀⣀⡄
⠀⠀⢰⢁⢋⠔⢲⡄⣀⢀⢀⠘⡘⡄⠀⠀⡐⠕⠁⣼⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢸⣵⣶⢠⣤⣯⠀⢸⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⠘⣇⠀⢸⠅⣋⣿⣸⢀⢃⠃⢀⠤⠥⠤⠤⡤⠤⠶⠶⠶⠶⠶⠼⠤⡀⠀⠀⠀⠀⢻⡧⠤⣿⠃⠀⢸⡇⠀⡆⡶⡆⣖⢆⡶⡠⡆⢒⡞⡄
⠀⠀⠀⠣⣩⢲⠉⠀⠳⡄⡵⢋⠜⠀⠈⠋⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠁⠀⠂⠓⠒⠀⠁⠀⠈⠀⠒⠃⠇⠀⠥⠥⠥⠭⠭⠤⠥⠥⠭⠗⠃
⠀⠀⠀⠀⡄⡸⠭⠉⠘⠃⡆⠁⣠⡎⣙⢢⠀⠀⠀⢀⣀⣀⣀⠠⠤⢒⠒⡄⠀⠀⢠⠒⠒⠂⢐⣒⡦⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠳⠁⠀⠀⠀⣄⠃⠀⢟⢲⠲⢽⠂⠀⠐⠁⡜⡐⢠⢰⠀⠓⢁⡿⠀⠀⢨⣠⡤⠤⣤⣤⡄⠀⠀⣠⣴⣡⣤⣤⣤⣤⣤⣤⣤⣼⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠈⠀⡌⠀⠀⢻⣄⣀⠃⠘⣀⡡⢴⡩⠎⠀⠀⠘⡇⢀⣰⣿⢷⡇⠀⠀⠇⠊⣠⠤⣄⡤⣤⡤⢠⣄⡌⢱⠈
⠀⠀⠀⣀⠤⠤⠤⠠⣄⠀⠀⠈⠙⠋⠙⠁⠀⠀⠈⠑⠣⠷⠾⠐⠋⠉⠀⠀⠀⠀⠀⣷⠻⠿⠀⣸⡃⠀⠀⡏⢇⢙⠖⢋⢋⡘⠧⠘⠘⢃⡼⢋
⠀⠀⠀⡗⠒⢀⡀⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⠋⠉⠙⠋⠀⠀⠀⠁⠂⠐⠀⠂⠀⠂⠀⠀⠒⠀⠒⠁
⠀⠀⢠⢸⠟⠂⢒⠘⡇⡀⠀⠀⡏⡇⠤⠤⠤⠤⠴⠥⠭⠽⠥⠵⠤⠤⠤⠤⢄⢈⢸⠀⠀⠠⠒⠊⣑⣒⣉⣓⠒⠤⢦⡠⡀⠀⠀⠀⣀⣀⡀
⠀⠀⠈⢌⢆⡀⢀⠰⡱⠁⠀⠀⡇⡇⠉⠉⠉⠉⠉⠉⠛⠙⡏⠉⠉⠉⢉⠉⠁⡀⢸⠀⠀⡸⢊⠉⡇⢂⢠⢠⠈⡑⠤⣰⠗⡂⠀⠮⠄⠄⠽⡀
⠀⠀⠀⠀⠑⠲⡖⠈⠀⠀⠀⠀⡇⡤⠤⠤⠈⡆⠀⠀⠀⠀⡇⠀⠀⢸⢠⠀⠀⠄⢸⠀⠀⡣⣀⠀⡇⠸⠸⠸⠀⣃⡴⠳⡀⠅⠀⡟⢻⠙⠋⡅
⠀⠀⠀⠀⠀⣨⣇⡀⠀⠀⠀⠀⡇⡇⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢸⢸⠀⠀⠀⢸⠀⠀⠉⠢⠽⢓⡒⣒⡲⠩⠔⠁⠀⠈⠁⠀⣆⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠁⠀⠀⠈⠈⠁⠀⡴⢌⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⠊
⠀⠀⢠⢰⠰⣠⠤⠤⢤⡴⠖⠚⠛⠉⠀⠀⢀⠤⣒⠒⠀⡰⠖⠉⢳⠁⠀⠀⠀⠀⠀⠀⠀⢴⣶⡖⢲⠮⠅⠒⠀⠀⠀⠀⠀⠀⣀⢴⣂
⠀⠀⡬⠤⠤⠤⠥⠬⠭⠤⢤⠀⠀⠀⠀⡴⢁⠞⡝⠀⠀⡁⠀⣁⠎⢡⠀⠀⠀⠀⠀⠀⠀⠨⣿⠗⠃⠀⠀⠀⠀⠀⠀⠀⢀⠏⠙⠒⢋⣉⢶
⠀⠀⢇⢆⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⡇⠘⡄⠙⢦⠀⠈⢉⠡⢂⠜⠀⠀⠀⠀⡠⣺⣟⣻⣻⣿⣛⢷⢦⠀⠀⠀⠀⠀⡼⠔⢚⣉⡡⠤⠚
⠀⠀⢠⡓⠕⠀⠀⠠⠤⢺⡄⠀⠀⠐⢄⣉⣀⣈⣉⣉⣀⣀⣁⣈⣉⡰⠂⠠⡆⠐⠓⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⡤⠀⠀⣇⣐⣁⠬⠤⠒⠋
⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡎⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀⠈⡆⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄⠼⠤⠚⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⠢⠼⠤⠼⡄
⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡜⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠘⡄⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⢰⠁⠀⢀⠞⠀⠀⠀⠀⢶⠆⠀⣀⣀⣀⡀⠀⢶⠆⠀⠀⠀⠘⢆⠀⠀⢱⠀⠀⠀⠀⠀⣏⡇
⠀⠀⠀⠀⢻⡉⢢⡀⠀⠀⣏⢉⡶⠯⣄⠀⢀⡠⠔⡊⠉⠉⠀⠀⠀⠈⠉⠉⠒⠤⣀⠀⢀⡬⠷⣎⢉⡇⠀⠀⣠⠊⡹⠃
⠀⠀⠀⠀⠀⠙⢄⡱⢄⡀⠈⠫⣀⡁⢊⠗⠩⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢏⠀⣁⡨⠋⠀⣀⠴⣁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠑⠤⣹⠒⠒⠢⠽⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠅⠒⠒⢺⡡⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣉⣉⣓⣒⣒⣛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣓⣒⣒⣋⣉⣉⣀⡀
⠀⠀⠀⠀⠀⢀⠴⢺⡥⠼⠦⠤⠤⠤⣤⡤⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦⣤⡤⠤⠤⠤⠾⠤⣽⠢⢄
⠀⠀⠀⠀⠀⣷⠞⠁⠀⣀⠴⣋⣉⣉⣁⣠⠤⢜⣲⣄⣀⠀⠀⠀⠀⠀⢄⣂⣴⣛⡤⢤⣀⣉⣉⣉⡳⢄⡀⠀⠙⢶⡇
⠀⠀⠀⠀⠀⢿⠀⠀⢰⢧⠞⠁⠀⠀⡶⢿⡭⠥⠬⠷⠚⠋⠉⠉⠉⠉⠛⠲⠯⠤⠬⣭⢷⡄⠀⠀⠑⢦⢷⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠘⠇⠀⣼⢸⠀⠀⠀⠀⢱⠔⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠓⢴⠁⠀⠀⠀⢸⢸⡄⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢭⣢⣄⠀⠀⠀⠑⠮⠤⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠬⠖⠁⠀⠀⢀⣤⣪⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣀⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⠿⣿⡟⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⣰⡿⠋⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡟⠈⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠉⠛⠻⠷⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⡐⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢲⣄⠀⠘⣬⡀⠀⠀⠀⠀⠈⠣⡀⠀⣠⣤⣤⠄⠶⠤⠠⠠⠀⠠⢄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠓⠛⠒⢢⣌⠙⢶⡀⢹⠧⠀⠀⠀⠀⣀⣤⣹⣾⠋⢴⢉⠑⠁⠀⠁⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠘⢋⣉⣉⣉⣑⣄⣀⣈⣧⣀⣷⡀⢾⡀⠀⣠⣒⠞⢛⣡⠻⡖⢦⡥⣀⣐⡂⣨⣄⡉⠈⠉⠛⠀⠀⠀⠀⣿⠃
⠀⠀⣰⣶⣶⣢⣀⣠⣤⣴⣶⣗⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣿⠷⣶⣾⣘⡶⠚⠁⠀⢱⠀⠈⢀⠌⠈⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⣸⠷⠆⣛⠱⠽⠟⢯⠿⠉⡟⠘⢏⠉⣸⠏⢙⡞⢹⡿⠿⢛⣿⠿⣿⠟⢿⣷⣾⣭⣿⣿⣶⣶⡿⣀⣴⠡⠐⡚⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⢣⡤⠁⢤⣤⡶⡦⠈⣇⠀⣮⠀⢸⡀⢠⡇⠁⢧⣾⠟⠠⣀⠁⠈⠹⠈⠈⢿⣻⣿⣿⣿⣩⣿⣿⡭⠤⠒⠊⡠⣠⣞⡍⡡⢂⠔⠀⠀⠀⠀⣿
⠀⠘⢷⣀⡀⠊⢹⡝⠴⠻⠄⠙⠷⠈⠓⠚⠷⣄⣼⡟⠀⠐⠀⠂⠀⠀⠀⠀⠀⣿⡿⣛⡩⣿⣟⡟⡏⠑⠒⠨⣴⣯⠫⣜⠐⠁⠀⠠⠀⠀⠀⣿
⠀⠀⠘⣟⢃⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣥⣀⣀⣀⣀⣀⣀⣠⡶⠟⠛⠛⠉⠻⡏⢿⠇⠀⠰⠀⠀⠙⢷⣭⡆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣶⡆⡟⢺⠯⡙⣄⢀⡨⠛⣤⠀⢩⣞⠁⠀⠂⠀⠀⠠⣻⢯⣥⡆⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠊⠁⢙⣾⣯⠝⣿⠙⢾⣧⣤⡂⣠⠏⠀⠀⠀⠀⠀⣠⣶⡡⠮⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣴⡶⠊⠁⢀⣤⣾⢽⡿⠁⣸⡇⠀⠀⠀⠘⢻⠯⠌⠻⠲⡠⠰⠂⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠖⠋⡽⣇⡞⠁⠀⣽⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⣼⣿⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡬⢼⠋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⣁⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠢⣄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠱⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠐⣇⢀⡎⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣄⣠⣸⣶⠞⡵
⠀⠀⠀⠀⢠⠃⠀⠈⠙⠓⣅⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠈⠀⠫⠇
⠀⠀⠀⢀⡇⠀⠀⠀⠀⣀⡌⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢈⣰
⠀⠀⠄⢸⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⣺⣻⠿⠓⠐⠻⠚⠻⢟⣻⡀⠀⠀⠀⠀⠀⠹⠇⠀⢄⣘⣿
⠀⢠⠀⢿⣶⠔⢀⡛⠟⠁⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⢠⡇⠀⠐⠀⣬⡇⠀⠀⢰
⠀⢸⠆⢸⡇⠀⠀⠀⡴⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢡⠀⠸⡅⠀⠀⠀⢰⠀⠀⠀⠈
⠀⠘⡄⢻⡅⠀⠀⠉⡇⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡄⣷⠐⠀⢤⡞⠀⠀⠰⡞
⡇⠀⠘⣼⢿⣄⡀⢀⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣯⣴⣟⠀⠀⠀⣰⠃
⢧⡀⠀⠘⢜⢿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣭⠎⠀⢤⡴⠃
⠈⢇⠀⠀⠈⠢⡙⣿⡿⠿⣧⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⣿⡿⠟⡁⠈⣠⠞
⠀⠈⢳⡴⠤⠀⠉⠻⢶⣶⣾⣷⢴⣶⡆⣄⡀⠀⣢⠀⣴⡤⢦⡀⠀⠀⡀⢀⣠⡂⣼⠖⢲⣮⠴⠋
⠀⠀⠀⠙⠒⠒⠒⠒⠛⠓⠶⠾⣿⣿⣿⣧⣦⡟⠁⠀⢻⠇⠀⠑⣰⣾⣿⢻⣷⠞⠛⠛⠋⣡⠀⠀⠀⠀⣠⣤⠎
⠀⠀⠀⠀⠀⠀⠀⣠⣧⣬⣄⣀⣀⣬⣿⣿⣿⡄⣀⣁⣈⣁⠀⣠⣾⡿⣳⣿⡛⠉⠉⠉⣛⡍⠛⠒⠛⠋⠁
⠀⠀⠀⠀⣰⣦⡴⠋⠀⣠⣄⠈⠉⣉⣙⣻⣿⣻⢿⣿⣿⡿⢿⣿⣻⣽⣿⠛⠋⠉⣙⣿⠛⠷⡀
⠀⠀⠀⢐⣨⡟⠀⢀⡞⢹⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉⠛⠉⠉⠉⠻⣆⠀⠈⣶⠆
⠀⠀⠐⣿⡋⠀⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢶⠀⠹⣄⡀
⠀⠀⠀⠈⠳⡀⠀⠈⣇⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠙⠀⠀⠘⠿⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢻⡿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣧⠇⠀⢈⣦⡤⠤⠖⠒⠒⠒⠒⠲⠦⠾⣅⣀⠀⢳⣷⣀⡀
⠀⠀⠀⠀⢀⡴⠚⠉⣽⠻⣧⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠶⡟⢹⣍⣓⢦⡀
⠀⠀⠀⢠⣿⣖⣺⠽⠛⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠙⠪⠭⣿⡆
⠀⠀⠀⢸⠘⢧⠀⠀⡼⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⡴⠃⣿
⠀⠀⠀⢸⠀⠀⠑⣶⠃⠀⠀⠀⠀⢸⠳⣄⡀⠀⠦⣄⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⣏⠀⠀⡿
⠀⠀⠀⠸⡆⣀⡴⠃⠀⠀⠀⠀⣠⠏⠀⠀⠉⢙⣛⠉⠉⣛⡒⠒⠚⠉⠓⢤⣀⠀⠀⠀⢈⡽⢠⡇
⠀⠀⠀⠀⢳⠘⣶⡤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠉⣤⠀⠀⣤⠉⠀⠀⠀⠀⠀⠈⠉⠛⠻⡏⣇⡼
⠀⠀⠀⠀⠘⣿⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣼⡇
⠀⠀⠀⠀⠀⡇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⡄
⠀⠀⣦⠤⠞⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠳⠤⣤⠄
⠀⠀⠈⠳⣄⡀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⢰⣖⣶⣶⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠒⠶⠶⠛⠳⣄⡀⠀⠀⠀⣸⣟⣛⣿⢽⡇⠀⠀⠀⠀⠀⣀⡴⠚⠲⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡦⠤⣇⠛⠛⠛⠋⣇⣀⣤⠤⢶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢚⡟⠲⠼⢦⡀⢠⣞⣡⣤⠤⠶⠻⡗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⣸⠁⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⢧⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣤⣏⣠⠤⠖⠚⡇⣇⠀⠀⠀⠀⠀⠀⠸⡄⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢨⡇⠀⠀⠀⠉⣩⣷⡀⠀⠀⠀⠀⠀⢧⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣤⣴⣃⠀⠀⠀⠀⠀⢸⡄⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣶⠦⠤⢧⣤⠶⢦⡴⡏⠀⢸⣧⣤⣤⣤⣤⡀⣧⣠⠞⣿⡄
⠀⠀⠀⠀⢠⡤⠤⠤⣤⣟⣳⣿⣖⡾⠏⢧⣀⣸⠇⠉⠛⠉⠀⣾⠉⠉⡇⠉⢿⣷⣴⣧⣿⡤⠤⠤⠤⣄
⠀⠀⠀⢠⠏⠀⡠⠞⠉⣈⣿⡽⢯⣀⣀⡤⡄⠀⠀⢀⣀⡀⠀⠈⢓⣚⡁⣠⠼⢃⣾⣷⢬⡙⠲⡄⠀⠹⡄
⠀⠀⢀⡞⠀⢸⡁⠀⠀⣟⠻⢿⣛⠯⠵⠾⣷⣤⠴⠯⠭⠿⠶⠖⠋⢉⣉⣥⠖⢫⠿⡤⠞⠀⠀⢹⠀⠀⢹⡀
⠀⠀⡾⠀⠀⠀⠳⢤⣀⠈⠓⠦⣬⣉⡛⠒⠒⠶⠶⠶⠶⠖⠒⠚⢛⣉⣡⠴⠚⠉⠳⠇⠀⣠⠴⠋⠀⠀⠀⢳
⠀⡼⠁⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣬⣉⣙⣛⣒⣒⠒⠒⠚⢛⣋⣉⣁⣀⣠⡤⠤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠈⢧
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣄⠀⠀⠀⠀⠀⣀⣀⣤⣀⣀⠀⠀⠀⢀⡴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣀⣈⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣏⣀⣨⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠹⢷⠙⢿⣿⡝⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⢁⡀⠀⠀⠀⠀⠀⣀⡉⠀⠀⣿⡿⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢁⠟⣧⠀⠘⠁⠈⠀⠀⠀⠀⠈⠀⠙⠀⢀⣟⢣⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠠⠾⠟⣿⣿⡿⠘⢤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡼⠀⢸⣿⣿⡛⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⠀⠀⣿⠳⣄⠀⠀⠸⣋⠙⣙⠟⠀⠀⡰⢻⡿⠀⠀⢸⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢿⣓⣦⠿⣄⡈⠓⠤⣀⣈⠉⣁⣀⠤⠊⠀⢸⠇⠀⠀⠸⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠒⠶⢶⣿⣦⣖⡛⠒⠟⠒⠛⠢⣀⣀⣈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠨⠭⣽⡿⠉⠛⠻⢷⣦⡤⠖⡋⠭⠉⠉⠙⢿⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠤⠤⣼⡋⢰⠃⠀⠀⠀⠀⢸⢠⠊⠀⠀⠀⠀⠀⠀⠻⢭⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⢸⠁⡞⠀⠀⠀⠀⠀⠈⠳⣤⣄⣀⣀⣀⣀⣤⡴⣋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣀⠞⠊⠓⠒⠒⠒⠒⠒⠒⠒⠚⠓⠬⠭⣥⣴⣞⣚⡥⠊

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⡇⡟⡝⠉⣫⡏⡯⡏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⣷⢇⢇⣀⣷⣗⡷⣇⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⡴⠋⠁⠀⠀⠙
⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⡄⠅⠀⢼⡦⠚⡤⢄⣠⠞⣛⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⡀⠀⠄⠂⠀⠀⠄⠈⠀⢇⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣷⣿⢷⣶⣦⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⠁⠀⠀⠈⠀⢀⠤⢴⡾⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⢠⢂⠀⠰⠀⠀⠀⡀⡀⣄⡞⠈⠳⣤⣀⣀⣠⣤⡴⢾⠀⠀⠀⣀⣤⠤⠤⣮⣭⣉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠺⢤⣹⣦⣾⡐⠊⠈⠉⠀⠀⣀⣾⣲⡶⠈⠻⣍⠀⠑⠀⢿⠟⠁⠀⠐⠐⠂⠉⠻⡆⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⡆⠀⣀⡴⠚⠍⠉⣿⠅⠀⠀⠊⠙⠳⠦⡈⠳⣄⠀⠀⠀⠰⠀⠈⠳⡶⠶⠒⠒⠒⠒⠒⠢⡄
⠀⠀⠀⠀⠀⢸⠃⢐⣾⣿⠿⠿⠛⠀⢐⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠁⢿⠀⠈⠙⠶⣤⣀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠛⠖⠊⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠉⠙⠲⠶⠤⣤⣀⣀⣁⣀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⢚⣳⠶⠂⠀⠀⠀⠀⠐⠶⣟⡓⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⢀⡴⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⢦⡀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠁⠀⠀⢀⡴⠋⢀⡞⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡀⠙⢦⡀⠀⠀⠈⠳⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢻⡁⠀⠀⠀⢀⡞⠀⣠⠟⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠻⣄⠀⢳⡀⠀⠀⠀⢀⠟⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠈⠁⠀⠀⠘⠷⠞⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠳⠾⠃⠀⠀⠈⠁⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢯⡖⠒⢦⡀⠀⠀⠀⠀⢀⡴⠒⢲⡽⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡀
⠀⠀⠀⠀⠀⠀⡿⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⢸⠀⢀⣼⠃⠀⠀⠀⠀⠘⣧⡀⠀⡇⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢻
⠀⠀⠀⠀⠀⠀⡇⠀⠈⠒⠀⠀⠀⠀⣀⣤⠶⠋⠀⠀⢸⡆⣸⠃⠀⠀⠀⠀⠀⠀⠘⣇⢰⡇⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠐⠁⠀⢸
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣾⠉⠁⠀⠀⠀⠀⣀⣀⣷⡼⠤⠶⠶⠶⠶⠶⠶⠦⠯⣾⣀⣀⠀⠀⠀⠀⠈⠉⣷⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⠀⠀⡽⣄⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣀⠀⣠⠏⠀⠀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠈⢻⠏⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠹⡟⠁⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠚⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠓⠒⠦⣤⣀
⠀⠀⠀⠀⣠⠞⢉⡴⠷⠶⢶⣶⣶⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⣶⣶⡶⠶⠾⢦⡉⠳⣄
⠀⠀⢀⡞⢁⡴⠋⣀⡴⠚⠉⠁⣀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄⣀⠈⠉⠓⢦⣀⠙⢦⡈⢳⡀
⠀⠀⣿⣹⠋⢀⡾⢋⡾⠓⠛⣩⡽⠋⠉⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠉⠙⢯⣍⠛⠒⢷⡙⢷⡀⠙⣏⣻
⠀⠀⢿⠏⢠⠟⢀⡞⠁⢠⠞⣁⣠⢴⡾⠋⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡋⠙⢷⡦⣄⣈⠳⡄⠈⢳⡄⢻⡄⠹⡿
⠀⠀⠀⠀⡾⣴⠏⠀⣴⠋⢠⡏⢠⡞⣥⠖⠋⠈⠳⣶⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⠞⠁⠙⠲⣬⠳⡄⢹⡄⠙⣦⠀⠹⣦⢷
⠀⠀⠀⠀⢷⣿⠀⡼⣃⡴⠋⢠⡏⢀⡟⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠒⠒⠚⠛⠋⠉⠁⠀⠀⠀⠀⠀⢻⡀⢹⡄⠙⢦⡘⢧⠀⣿⡾
⠀⠀⠀⠀⠈⠃⠀⣧⣸⠀⠀⡾⢤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⢷⠀⠀⣇⣼⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠻⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠟⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⣶⠷⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢿⢶⡦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⣴⠏⣱⠏⢀⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢣⠈⣇⢹⡌⢳
⠀⠀⠀⠀⠀⠀⢀⣾⣵⡟⢁⡾⢁⡔⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢇⠸⡄⢻⡊⣇
⠀⠀⠀⠀⠀⢀⣾⡿⠔⠆⢰⣟⣉⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣌⣶⠄⣤⢻⣿
⠀⠀⠀⠀⠀⣼⣿⠲⢀⣘⡧⠉⣩⣿⡁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣈⣵⠚⠀⣩⣿⡀
⠀⠀⠀⠀⢀⣿⡟⠓⢀⠈⠀⢨⣿⣿⠇⠀⠀⠀⠈⠄⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⢨⣿⣿⡀⠈⠀⣤⣽⣿⡇
⠀⠀⠀⠀⠀⢣⣷⣌⣠⣀⣷⣿⡿⠟⠀⠀⠀⠀⠀⠈⡀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣀⡀⢂⡴⡻
⠀⠀⠀⠀⠀⠘⢿⣿⠉⣛⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⠉⢹⣿⠟
⠀⠀⠀⠀⠀⠀⠈⣿⠃⢈⣻⣿⣆⠀⠀⠀⢀⣀⠀⠀⢸⣄⣼⠀⠀⢀⣀⠀⠀⠀⣠⣾⡟⡉⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣘⡿⣿⣿⣿⣴⡿⠋⠹⣧⠀⣸⣿⣿⡀⣰⡟⠉⠻⣦⣼⣿⣿⣭⣟⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣾⣸⡟⣿⣦⣄⢹⣿⠉⣿⠛⢹⡟⢁⣤⣾⡿⣿⣸⡶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠻⠿⣿⣿⣿⣷⠠⠏⠀⢠⣽⣿⣿⡿⠿⠿⣯
⠀⠀⠀⠀⣠⣴⣤⣤⡿⢿⣧⣴⣾⣇⠀⠀⠈⢹⣿⣵⢃⡀⠀⢶⣿⣿⠁⠀⠀⢀⣿⣆⣤⣿⠷⣦⣤⣴⣄⡀
⠀⠀⢀⣼⠷⢋⡀⢀⣠⣤⠨⣹⡟⠛⠾⣶⣤⣘⣿⠿⢿⣥⣻⢿⣿⡇⣠⣴⠾⠟⢛⣯⡭⢤⣤⣀⡀⣈⠻⢷⣄
⠀⠐⠿⠣⢶⣿⠷⠛⠛⠻⠷⣿⣯⣅⣢⣄⠙⣿⢡⡖⠀⠙⠀⠀⠈⠻⠟⣁⣄⣪⣽⣿⡶⠿⠛⠛⠶⢿⣷⢌⠻⠃
⠀⢀⡖⣾⠟⠁⠀⠀⠀⠀⣀⣸⣇⠉⠙⠛⢿⡇⡿⡟⡄⢠⢀⠀⢨⣾⡷⠟⠛⠉⣁⣯⣀⡀⠀⠀⠀⠀⠙⢿⡷⣄
⠀⠀⠈⠁⠀⠀⢀⣴⣬⡾⠟⣿⠿⠿⠿⠷⢶⡇⠁⠀⠃⠀⠈⠀⠀⠐⡷⠶⠿⠿⠿⣿⠟⠷⣮⣶⣄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣠⣾⠏⠁⠀⠀⣿⣄⣀⣀⣤⣼⡇⢀⡠⠀⠀⠀⠀⠀⢸⣧⣤⣄⣤⣀⣿⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠰⠋⠉⠀⠀⣴⣾⣿⠋⠉⠉⠀⠀⢿⣾⣿⣿⡿⠿⣿⣶⣾⠁⠀⠈⠉⠉⢻⣿⣦⡀⠀⠈⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⣿⠀⠀⠀⠀⠀⢸⣿⣿⣣⣄⣀⣼⣿⡿⠀⠀⠀⠀⠀⢸⡍⠻⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡟⠀⠀⠀⠀⠀⢨⣿⣿⡟⠉⠉⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠈⣿⣿⡟⠛⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠶⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢺⣿⡧⠤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣀⠀⢈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡠⣶⡿⢿⣏⠉⢻⣿⢿⣶⠦⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠞⢀⡿⠀⠘⣿⡄⣼⡏⠀⢹⡇⠙⡀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣦⣾⡷⠶⠾⠿⠿⠿⠿⠶⠾⣿⣦⠇⠀⠀⠀⠀⠀⠀⠣
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣌⣉⡉⣈⠁⢈⣁⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠀⡈⠩⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⢶⣴⢮⢬⠧⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠉⡙⣿⡄⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⣡⠟⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣾⣾⣦⣄⠘⠒⠒⠒⠚⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠘⡏⡀⠓⠀⣀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣵⠿⠋⢉⡍⠁⠉⠐⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠁⠀⠀⠛⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢏⠀⢄⠐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⠀⡇⢀⣀⣤⣤⣼⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠘⠛⠻⠿⣿⠿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃⠠⠄⠁⠻⠛⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⡴⠇⢠⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣿⣿⣿⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁⣀⣠⠀⠀⠀⠀⣀⢓⡼⠛⣞⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⡀⠂⢀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⡴⠖⠻⠟⠉⠉⠣⢤⣀⠀⠀⠀⠈⠀⠐⢐⡀⠀⠀⠀⠀⠀⠁⣠⣖⠓⢮⢀⠀⠀⢃⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠿⠀⠀⠘⠀⠀⡀⠀⠀⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠰⠥⠊⠁⢄⡀
⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠁⠀⠀⠇⠀⠀⠀⠀⠈⠃⠘⠆⠀⠀⠀⠂⠒⠄⠀⠀⠀⠀⠀⠀⡐⠁⠂⠀⢔⠀⢾⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠸⠄⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣸⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠰⠓⢀⢀⡀⠳⠋⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠰⢳⢄⡀⢀⠀⠋⠁⢣
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢹⡗⣶⠦⡤⠠⣄⠀⢠⠾⡅⡸⢄⡠⠛⠠⣄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠘⠀⢩⢁⠔⣷⠀⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣯⡠⡟⠁⣿⠬⢺⠟⠈⠉⡄⠀⠀⢀⠘⠀⠀⡀⢨⠀⠀⠀⠀⠀⠀⠀⠚⢻⠷⢴⠀⠀⠈⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⣷⠀⡧⠀⣾⠁⠀⠀⡇⠀⢀⡈⠀⠀⠀⡇⠈⠀⠀⠀⠀⠠⣄⠟⠈⠁⠀⢘⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠇⠿⠺⠧⠸⠯⠠⠖⠊⠙⠆⠈⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠐⠂⠀⠀⠐⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣦⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⣠⣴⠀⣷⢀⡀⠀⢠⣤⣰⠇⣤⠤⠤⠤⣤⣬⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣤⠖⠋⠁⣸⠀⣼⠟⠓⠒⠒⠙⢿⣄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡟⠞⠁⠀⠀⠀⠀⠀⠀⠙⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣠⡀⡒⢀⣤⡄⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠔⠋⣴⠏⠁⠀⡀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠉⡡⠁⡌⠙⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡼⠁⠀⠀⠀⡀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢸⠇⠀⠂⠀⠁⠀⠀⠀⠀⠀⢸⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⢾⠀⣠⡴⠞⠛⠉⠛⠓⠶⣤⣿⠈⠁⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠘⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⣿⣿⣿⣿⣶⣮⣭⣿⡆⠀⡀⣿⠤⠤⠒⢋⣝⣁⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⣻⠂⠀⠀⠰⢤⣷⡆⠀⠀⢠⡃⠀⠘⠛⠉⠸⣿⡿⠉⠛⠋⠀⠀⠁⠀⠀⠀⠀⠈⠁⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⣿⠀⠀⠀⠀⠀⠈⠉⠙⣲⠦⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠙⢿⠀⠀⠀⡏⠉⠉⠁⠀⠀⢀⠈⢄⣀⠀⢴⠘⣡⠋⠀⠂⢠⢀⣠⣉⡀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠒⠂⠉⠀⠀⠀⠀⠑⢀⡜⠠⠴⡀⡀⢀⠁⠀⠀⠄⣻⡓⠚⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢀⠀⠈⡄⠀⠠⠀⠀⠀⠀⠀⠀⣀⠘⡁⠀⠤⠐⠈⠤⠄⠀⠀⠀⠈⠉⠃⠒⣢⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⢀⠀⠘⠁⠀⠀⠀⠀⠀⠀⡰⠉⠀⠛⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⡠⠴⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢢⠀⠀⠀⠀⠀⠘⠀⠰⠁⠀⠀⢨⡄⢘⣀⠀⢀⣀⡔⠒⠊⢁⡀⠈⠈⡳⣦⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⣸⢷⡆⠀⠀⠉⠀⠰⠇⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⣀⠋⠀⠀⣴⠙⢮⡻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣭
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣠⠞⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠁⠃⡀⠘⠉⣀⠈⠁⠀⠀⣀⢃⡀⠀⠀⠈⣿⡿⠿⢿⡿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣠⡴⢚⠡⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠂⢀⠉⠀⠊⠀⠉⠈⠀⣼⠋⠈⠁⢤⡤⠾⠁⣤⠀⠀⠀⠈⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠆⠀⠀⠙⠓⠒⠂⠂⠀⠀⠀⠈⠦⡀⠀⠀⣠⡇⠀⠘⠦⢤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣤⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠠⠤⠤⣀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⡤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣠⣤⠀⣀⣸⠏⠨⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡁⠠⠀⠀⠀⣀⡤⠖⠚⠉⢁⠀⠈⠁⠁⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈


⠟⠂⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⣤⣤⡄⠄⠀⠰⡆⠰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣶⣀⣄⡰⠋⠀⢦⠀⣀⣤⢤⠒⠶⠉⠈⠁⠁⠀⠰⡄⠀⠀⠀⣧⠀⢀⡋⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⢁⣠⣼⣿⣿⣿⣿⡦⣠⡾⠟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⣾⣥⣄⢻⣿⡌⣷⡆⣏⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠁⢀⣰⣾⣿⣿⡿⢠⠛⣥⠞⡹⠁⠀⠀⠀⠀⠐⠈⢦⣄⡶⣦⣿⣿⣷⣝⣿⣯⣸⣿⣧⡿⣣⣟⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⢠⣤⢿⣿⣿⡿⠟⠁⠐⢸⠟⡔⣡⣼⣔⠁⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣻⣧⣶⣶⣭⣾⣿⠟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢠⣶⠟⣡⣿⣿⠏⠀⠀⠀⠀⣁⣼⡁⠍⣥⣡⣬⢲⣆⠀⢠⣿⣿⣿⣿⡿⢿⡉⠋⢉⡽⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣾⡟⢡⣾⣿⡟⠁⠀⠀⠀⠰⣊⣿⣿⣟⣽⣿⣿⣿⡿⣿⡳⡾⢿⣿⡋⠉⢶⣄⠹⠆⠸⣧⡈⢙⡭⠋
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⣴⣿⡿⠋⠀⠐⠒⠒⠒⢺⡿⠿⠟⠛⠉⠛⠛⡛⠚⣛⣻⣧⠀⠙⣇⠀⢈⡿⢈⡇⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡟⢣⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡆⢠⡏⠀⣸⠇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢿⠴⠛⠁⠀⠀⠀⣀⣀⣀⣀⠀⠁⠀⣤⡀⣰⠄⣤⠀⣶⣶⣿⣿⣿⣿⠃⢸⠇⢠⡅⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⠙⢉⠉⠛⠻⣿⣿⡿⠀⠀⠀⠀⠀⠙⢿⣯⢻⣿⠟⢠⠟⠀⡸⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣩⣥⣶⣶⣶⣶⣷⣿⣿⣿⣿⠿⠛⠁⢠⣀⣠⡤⡲⠏⠘⡿⠟⠉⡴⠋⠀⠀⠁
⠀⠀⠀⣤⢀⠀⠟⣉⢉⡁⠠⠄⠻⠭⠬⠛⠛⠋⠁⢀⣤⣿⣿⣿⣿⡟⠷⠎⣸⠃⠀⠃
⠀⠄⠀⢿⣄⣁⠈⠁⣀⢀⢀⣀⣄⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⡿⢃⢁⣠⠞⠁
⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡽⠧⠴⠚⠉
⠀⠀⠀⠀⠈⠛⠟⣻⢿⣿⣿⣿⣿⣿⣻⡛⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠋⠉⠉⠉⠉⠉⠙⠛⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢤⡀⠀⠠⡀⠀⡀⠀⡀⠀⢀⡀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⡏⠑⠦⡹⣄⣳⢄⠈⢳⢄⠻⢺⣆⠀⠈⣌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡅⠀⠀⠈⠇⠈⠁⠑⢌⡄⠙⠆⠉⢆⡇⢸⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⠃⢀⣀⣀⡀⠀⠀⠀⠘⠁⠀⠀⠀⠸⡇⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⢤⡀⢀⠞⠁⠀⠁⠀⠈⠙⠀⠀⠀⠀⠀⠚⠉⠉⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⠶⡌⠋⠀⠀⠀⢀⡠⠤⢄⠀⠀⠀⠀⠀⠠⡒⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⡙⠀⠀⠀⠀⠉⠴⠿⠆⠀⠀⠀⠀⠠⠶⠿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠤⠤⢄⣀⣱⡄⠀⠀⠀⠀⠢⣀⡀⢀⣉⣁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢒⣫⡭⢥⣶⡒⡒⣒⣲⠖⠒⠲⢦⣽⢲⣄⡀⠀⠀⠘⠪⠉⠙⠁⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠖⠉⠀⠀⠀⠀⠈⠉⠁⠀⢀⡴⠞⠁⢸⡄⠹⣍⠛⠲⠤⣤⠤⡶⣞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠒⢄⠀⢇⠀⢈⡑⢦⣀⠎⠤⣱⡀⠱⣀⡐⢀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⣆⠸⣄⡞⠀⠀⠏⢀⠤⢚⣓⡺⠿⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠸⡄⠋⠀⠀⠀⡠⢁⠔⡩⠌⢠⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢠⢷⠀⠀⠀⠀⢀⣠⢤⣽⠤⠔⠒⠉⠀⠀⠈⠀⠀⣸⠠⠤⢬⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡆⠀⠀⠀⠀⠀⡜⠈⣆⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠖⠃⠀⠀⠀⢇⠀⠀⣀⣀⣠⡤⠤⠔⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⡇⠀⠀⠀⠀⢠⠃⠀⠘⣤⠷⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠀⠀⠀⠀⠀⠀⠀⡸⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡇⠀⠀⠀⠀⡸⠀⠀⠀⣘⣓⣻⣦⣀⣀⣀⣤⠴⢋⡀⠀⠀⢀⣀⣀⣠⣤⣒⡊⢀⣀⣀⠀⠀⣀⣀⡀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣧⠤⠤⠴⠖⠛⠚⠉⠉⠁⠀⠀⠀⠀⠘⣎⡡⢔⣁⠔⠒⡺⠓⠋⢉⣀⠠⠐⠐⠀⠀⣉⠀⣁⠦⠖⠀⢛⠛⠓⢤⡀
⡤⠤⠤⠔⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⡤⠊⠀⠀⠀⠁⠐⠊⠋⡏⠀⠀⠀⠀⠉⢙⣤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢄⡀⠊⠀⠓⠀⠒⠒⠀⠀⠋⣀⡽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠓⠒⠒⠒⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⡟⠟⢻⣷⣿⠃⠀⠀⣀⣀⣀⣀⣤⣤⣤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡉⠉⠉⠉⠁⠀⠀⠀⠺⠋⠉⠀⠀⠀⠀⣴⣶⣶⣶⠞⠁⠀⠙⠻⣋⣍⠁⢸⠿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣿⣿⠓⠶⠂⠀⠀⠀⠀⠔⠀⠀⣠⣿⢀⡄⠀⣰⠟⠛⠉⢄⠀⠀⠀⠀⠁⠀⠶⠦⢷⡄⡀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠯⠽⠿⠿⢭⣟⣿⣿⣿⣿⢻⣷⣤⣤⣤⣤⣤⣊⣀⣴⣿⠿⣷⡿⠓⠉⢀⣀⣠⡴⠿⠤⠤⠤⢄⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢀⣔⣾⣁⠇⠀⠀⠀⠀⢀⣾⣿⣿⠿⢣⠿⠟⠈⠓⠂⣩⠇⣀⣀⣴⣇⣤⣠⣦⣠⠾⠋⠉⠁⠐⠒⠒⠛⠓⢺⣿
⠀⠀⠀⠀⢠⡟⢁⣿⡏⠀⠀⠀⠀⠀⢈⡿⠛⢹⣿⣷⣾⡻⢋⡽⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠈⠀⠸⣿⠁⠀⠀⠀⠀⣠⣿⡄⢰⣺⣿⣿⡤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣰⣿⠛⣧⣸⠛⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠃⠀⠈⣻⡀⠀⡟⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⠟⢆⠘⢦⡙⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡄⠀⠁⠒⠚⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣙⡛⣉⣙⢛⣟⣋⡿⢻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⠠⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠁⡠⠐⠒⠒⠀⢀⠄⠀⡠⠊⠁⠙⢦
⠀⠀⠀⠀⣠⠤⠼⡠⠴⢀⠔⠀⡀⠀⡂⠨⢰⠀⠸⣄⠀⠀⠉⡒⠢⡀
⠀⠀⢀⡞⢁⠤⠒⣁⠠⢃⡠⠊⢀⡠⠀⠀⠀⠳⢤⣈⣀⠠⣀⠈⠂⢑
⠀⠀⠘⣤⠃⡐⠋⠀⠀⠉⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠙⠆⠀⠆
⠀⠀⡘⠑⢀⠀⠀⠉⠈⠉⠁⠀⢠⠖⠀⠀⠀⠀⢀⡀⠀⠀⠈⢳⠐⠀⠱
⠀⠀⢱⣎⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠛⠁⠀⠀⠀⠈⠂⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡔⢱⠖⣄⣄
⠀⠀⠈⡄⠘⡀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠻⡸⣅⣻⣞⡇⠾⣶⣀⠠⣂
⠀⠀⠀⠳⠀⢳⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⢿⣤
⠀⠀⡔⠀⠑⠀⠹⢦⡀⠀⠀⠑⠦⠤⠀⠤⠔⠊⠀⠀⠀⠀⣠⢞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦
⠀⠀⠐⠂⠀⠒⠢⠐⠉⠲⠤⢀⣀⠀⠀⠀⠀⢀⣀⠠⣔⢊⠁⣓⣂⠆⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠀⢪⠽⣍⡩⢋⡇⡀⠀⠈⠉⠁⠁⠀⠀⢀⠤⢤⡀⠀⠀⠀⢰⠈⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠁⠠⠀⡠⠊⠀⢸⠃⠉⠔⠲⢋⠀⡇⠀⠀⠀⢾⢄⠀⠀⠃⠀⠀⠑⡀⠀⠀⠀⢷⠤⠤⠚⠁⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⡄⣄⣃⢀⣀⡀⡲⠄⡄⠀⠐⠸⠀⣧⠀⠀⢠⡆⠉⠀⠀⢄⠄⡀⠀⠇⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⢀⡅⠈⡈⡀⠈⠁⢀⠀⠁⠀⠀⠀⡇⢱⠀⠀⡼⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣀⣀⣠⣤⠤⠚⣉
⠀⠀⠀⠄⢯⠀⢀⠐⠃⠀⠀⠉⠀⠤⠤⠤⠤⠴⠤⠷⠞⠀⠀⠐⠒⠒⠒⠂⡄⠀⠠⡤⠀⣀⣀⣀⣀⣀⠀⢤⡴⠁⠀⠅⠃⡠⠋⠀⢱
⠀⠀⠀⠀⠀⠁⢍⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠹⡣⢈⣉⣉⣁⠀⢠⠃⠀⢀⠀⠀⠘⢁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⢀⠆⠠⣀⠡⣄⣦⠀⠀⠀⠀⡠⠐⠀⠀⠤⠀⠒⠃⡓⠢⡀⠴⠉⠠⠴⠤⠰⣟⣀⠔⢁⣀⣀⣰⡏⠀⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠉⠐⠀⠀⢀⠸⡀⠰⡃⠐⠀⠠⠁⠀⠈⠇⣸⠀⠐⣻⣀⣛⣍⣉⣀⣀⣀⣈⣀⣞⣀⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠰⠦⣈⠀⠂⠨⠅⠨⠥⠀⡠⠊⠀⢄⡠⣈⣁⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢨⢄⠀⠈⠀⠀⠈⠉⠀⠀⠀⠈⣶⠀⠀⡌⢀⠯⢀⡀⠤⠖⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣘⣂⣐⡃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡛⠀⡼⠠⠤⠤⠤⠤⢠⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠐⠒⠒⠀⠀⢄⡰⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠚⡁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⡇⠀⠰⡆⠀⠀⠰⠉⡸⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⡿⢿⠿⠿⠿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢉⣘⠉⠀⠛⢉⣁⠘⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⠈⣀⠀⢀⡀⢀⣀⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠚⢂⠋⢣⠚⠂⣸⣿⠏⢹
⠀⠀⠀⠀⠀⠀⢸⣿⠏⡈⢿⣿⣿⣿⣿⣿⣿⣿⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠆⠀⠀⠀⠈⢩⣤⠋
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠉⠉⠙⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠤⠄⠒⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠶⠀⠀⠀⠶⠀⠀⠈⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⣤⠤⠤⠴⠖⣺⡁
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢀⡀⡀⠀⠀⢀⣶⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⡿⡿⣏⢳⣶⠋⠉⣀⣽⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠦⣄⣈⣀⣠⡴⠋⢹⣿⣿⣿⠇⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⣿⣅⠠⠚⠈⡟⠹⠶⢊⣽⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⡍⠉⠉⠛⢳⠸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣠⣶⣶⣶⣶⣿⣾⣼⣿⣿⣧⠀⠀⣧⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⣿⣷⡀⣤⠴⠞⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢸⡹⣿⣿⡟⢷⠁⢸⡇⠀⠀⢠⣿⢿⡿⢋⡿⠋⣿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠙⣿⡟⠀⠸⣆⡼⣇⠀⢠⡿⣿⠀⠀⠁⠀⠀⠀⠈⠀⠈⣿⣿⠋⠑⠁⠀⠉⠉⠻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⡟⣇⠀⠀⣿⠀⢹⣤⡟⢸⡙⡆⠀⠖⠀⠀⠀⠶⠀⢀⣿⢹⠀⠤⠄⠀⠀⠠⠤⠀⠀⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡇⢹⡆⠀⢸⡄⠀⢿⠀⢠⣿⢇⠀⢴⣐⣒⣐⡆⠀⢈⣿⣿⡀⠀⢠⣤⣤⣄⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⢷⠀⠀⣰⠏⣿⣴⣿⣾⣿⣯⣵⠒⠚⢯⡀⢉⣿⣶⣾⣿⣭⣥⠤⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠗⢻⡇⠀⠀⠈⠳⠴⠀⣠⢿⣿⣿⡟⠹⡏⠀⠀⠀⠀⣱⣿⣿⣿⡟⢿⠋⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠻⣟⣻⢿⠣⣤⠷⠤⠴⠂⢀⣷⠾⣿⡿⣄⣸⢦⣀⡤⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠴⠤⠤⠦⠶⠒⠛⢶⠋⠀⠙⠲⠤⠤⠔⠋⡏⠯⣵⠃⠈⠣⢤⣀⣠⠴⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⢤⣤⣤⣤⣤⠤⠴⠇⠀⠻⠤⣤⣤⣤⣤⠤⠴⠃

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡧
⠀⠀⠀⠀⠈⣛⣟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⣻⣟⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠈⠻⣿⣶⣼⣿⣿⡧
⠀⠀⠀⢲⢸⣿⣿⣿⢿⣿⡿⢿⣀⣐⣿⣿⣗⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣻⣋⣠⣀⣻⡿⠿⠟⣿⣿⣿⣯⡶
⠀⠀⠀⢸⡸⣿⣿⣿⣶⣾⣦⡀⡏⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣴⣶⣶⣿⣿⣿⡟⡇
⠀⠀⠀⠈⠛⠟⠉⢛⠋⢻⣿⣿⡇⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣿⣿⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⡈⠀⠀⠀⡀⢸⣿⣿⣿⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⣿⣿⣿⠀⠁⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠈⠁



⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣘⡿⠿⢟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⣀⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣬⣀⣠⣶⣿⣷⡄
⠀⠀⠀⢶⠀⣼⣿⣿⡿⠛⢿⣿⣿⣂⣐⣖⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣐⣾⣆⣈⣙⡻⢛⣻⣿⣿⣿⣆⠀⡶
⠀⠀⠀⢸⡘⣿⣿⣿⣷⣷⣶⡄⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⡄⠀⠀⠸⣿⣿⣿⣿⣿⡿⢀⡇
⠀⠀⠀⠈⠛⠚⠛⠛⠋⣿⣿⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢹⡀⠀⣸⣿⣿⣿⡟⠛⠓⠛⠁
⠀⠀⠀⠀⡈⠀⠀⠀⠀⣿⣿⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢣⢠⣿⡟⠙⢿⣿⡆⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠉⠉⠁⠀⠰⢄⣀
⠀⠀⠀⠀⢀⢠⠄⠁⠲⠚⠋⢉⡉⠁⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⢀⡀⠠⠒⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⢰⠉⠀⠀⠰⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⡀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠑⢠⢀⡀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⣀⣀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⠀⠀⠈⠁⠐⠀⠀⠑⢤⡄
⠀⡀⠠⠀⠀⠀⠀⠀⠋⠂⠀⠀⠀⠙⢆⠠⠀⠀⠄⠨⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡁⠈⠐⠒⠒⠈⠓⡂⠁⠀⠈⠲⠀⠐
⠀⠠⠀⠈⠄⠀⠀⠀⢸⠀⠀⠀⢠⡌⠀⠀⠀⠀⠐⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠂⠀⠀⠄
⠀⠀⠑⡀⡠⠀⠀⢀⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠄⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠠⣶⢀⠊
⠀⠀⡐⠹⠇⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⡛⢎⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠢⣤⠴⠂⠀⠀⠀⠀⠀⠀⠀⣀⠙
⠀⠐⠀⠀⠈⠰⡄⠀⠀⠀⠀⠀⠀⠀⠙⢶⠾⠀⠈⠀⠀⠀⠀⠑⠣⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⣀⣠⠀⣊⠔
⠀⠀⠀⠀⠀⠀⣄⣀⠂⠀⠀⠀⠠⣤⠤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢇⣤⡄⡡⠁⠀⠄
⠀⠐⠤⠈⢄⡔⠁⠈⠑⠑⠨⠤⠚⠉⣦⣌⡀⠒⢒⡒⢂⠀⠀⢀⢉⣥⣴⠄⠂⠀⠉⠁⠀⠂⠄⡀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠔⠁⠀⠀⢡
⠀⠀⠀⠀⠉⢁⠀⠀⠀⠀⠢⡀⠀⠀⠰⠀⠀⠀⠈⠂⠀⠀⠀⠒⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠐⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⢘⠂⠀⠀⠀⠀⢸⡀⠀⠀⠰⠤⠐⠦⡐⢀⠰⠄⠐⠂⠠⠡⡄⢠⢄⡖⠦⣤⠄⣠⠤⢘⡠⠦⡠⠀⠀⢀⠧⢀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⢸⠀⠐⢄⠤⠊⠀⠀⠀⠉⠛⠂⠄⠀⠀⠹⠀⠀⠀⣀⠼⠭⡂⠀⠁⠀⠛⠉⢈⠍⠉⠁⠀⠒⠈⠀⠀⠉⠀⠀⢁⠦⠤⠀⡇
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠐⠂⠠⡤⠄⢀⠀⠀⠀⠴⠃⠉⠀⠀⠀⠀⠀⠂⠠⠤⠬⢂⡀⠀⢀⠠⢤⠤⠤⠀⠀⠐⠀⠁⠀⢀⠀⠁
⡀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠄⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⡂
⠃

⣷⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⣠⢋⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠰⡄⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⡣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢆⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢀⡿⢁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⣰⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢼⣥⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⡄⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⢀⠀⢾⡇⠀⡀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⣇⣠⠒⡎⠁⠀⠀⣔⡁⠀⡔⠛⣦⡄⢠⡶⠛⡄⠀⠀⢶⡄⠀⠑⠦⠤⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠈⠂⢠⡞⡟⢀⠎⠀⠸⠿⠀⠸⠟⡄⠈⠆⠀⠈⢻⡽⠀⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⢀⣿⣤⠊⠀⢰⠀⠀⠀⠀⠀⠘⡀⠈⣦⠴⣏⣀⢀⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣋⣠⠃⠑⢤⡇⠀⠀⠀⠀⠀⠀⣷⠂⠉⢆⣈⣹⠏⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣹⠟⠦⠤⢼⠣⠀⠀⠀⠀⠀⢀⢻⠦⠀⠞⣯⠃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠄⣾⠀⠙⠇⠀⠀⠛⠁⢸⡶⠀⠀⢀⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⡄⠀⠠⠴⣾⠀⠀⠀⠀⠀⠀⠀⢸⠷⠠⢒⠜⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠆⣀⠀⠀⠠⢾⡄⠀⠀⠀⠀⠀⠀⣸⠦⠐⡁⠚⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠘⠀⢈⡒⠀⠠⠶⢷⣶⠒⠒⠒⢾⣿⠿⠒⠀⠀⠀⠉⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠁⠀⠈⠁⠀⠀⠀⢰⡿⠦⠌⠉⠿⣿⠀⠀⠀⠀⢀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⢸⣄⣀⡀⠀⣠⣼⠃⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⢸⡉⠉⠀⠀⠀⣱⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠂⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣤⣳⣆⡀⢀⣴⣧⡄⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⠂⠀⢹⡈⠉⠁⣘⠁⠀⢢⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣄⣀⣀⣧⣄⣠⣇⣀⣠⠼⠛⠚⠁

⠀⠀⠀⠀⠀⢀⣠⠤⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢼⣏⠀⠀⠀⠀⢀⣠⣾⣾⣿⣿⣶⡴⣖⣠⣴⣾⢧⣍⣩⣭⣿⡿⣿⣿⣦⣄⡀⠀⠈⠳⣦
⠀⠀⠀⣠⡼⢿⡆⠀⢠⢰⣿⣿⣿⣿⣿⣿⣿⣝⢿⣷⣿⣿⣿⡿⠉⣹⣿⡟⣻⣿⣿⣿⣿⣷⡤⡔⣾⢤⡀
⠀⠀⠀⢹⣧⢞⢿⣴⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⢿⣿⡞⣿⣿⣾⣿⣼⡅⣼⡟
⠀⠀⠀⠀⣽⣧⣃⡹⣿⣿⣿⣼⣿⣾⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⣽⣿⣿⣇⣴⣯
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣟⣿⣞⠁
⠀⠀⠀⠀⢀⣀⣤⣤⣼⣯⣿⡧⣭⡲⣝⡻⣿⣷⡙⢟⣿⣟⡛⣣⣿⣿⡿⣋⢻⣏⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⣴⣿⣿⡿⠻⠿⠛⠁⠀⠻⠿⢾⢶⣾⢿⣿⣿⣿⣿⣿⣿⣿⢟⣴⣽⠿⠟⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠟
⠀⠀⠰⠟⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡶⠤⡀⠀⠀⣖⣚⣻⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠛⠃⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣰⣿⡿⣿⣿⣿⠟⠁⢀⣀⣀⣀⣀⠀⢀⠄⠀⠙⠿⣿⣯⣷⣷⡄⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⢿⣿⣳⣭⣥⢀⣤⣶⣾⣿⣿⣯⣿⣿⣿⣾⣦⣀⣤⣴⣶⡿⡿⠃⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡹⣿⣿⣟⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣠⣶⠿⠋
⠀⢀⡴⠾⠿⠿⠒⠾⠷⠶⣭⣟⣷⣿⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⣟⣻⣥⣷⣶⠾⠗⠿⠷⠶⢦⡄
⠀⠈⠀⠀⠀⣀⣤⣤⣴⣶⠴⣦⣭⣽⣟⣛⡿⣿⣿⣻⣼⣿⣏⣿⣿⣿⣿⣯⣾⣿⣿⣿⡿⠶⠶⣦⣤⣄⡀⠀⠀⠙
⠀⠀⠀⠀⢸⠋⠉⠀⠀⣀⣤⢰⣶⣦⣿⣯⣥⣅⠾⠟⣿⡿⣿⡟⠩⢶⣿⣿⣿⡿⢿⣠⣴⣤⣀⠀⠙⠻⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡿⠷⠋⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠛⠿⣿⣿⣇⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡤⢛⣽⡿⢻⡏⠈⢹⠁⠈⢈⣿⣷⢶⠤⢄⣴⡵⡗⣠⠀⢀⣴⣾⠟⣳⠤⢤⣀
⠀⠀⠀⠀⠀⣠⣺⠟⢿⠋⢡⠀⣡⡀⣼⠀⠀⣾⠟⠁⠊⠁⠀⠈⠀⢿⣟⡷⢉⢙⣈⡴⢯⡄⠀⠈⠑⠢⡀
⠀⠀⠀⠀⢀⡿⠋⡤⣒⣀⠿⣿⣿⢻⡛⣦⣾⠇⠁⠀⠀⠀⠀⠀⢠⠄⠉⠳⢾⠿⡋⠀⠈⢻⣦⣄⠀⢀⡈⠢⡀
⠀⠀⠀⠀⢺⠖⠊⣠⠏⠀⠀⠋⠘⠈⠃⢸⣿⡀⠀⠀⠀⠀⠀⢰⡃⢆⠀⠀⠀⠙⠪⡀⠀⠀⠈⠛⢤⣮⠻⣦⡘⣦
⠀⠀⠀⠀⠀⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⣳⡀⠀⠀⠀⠙⢧⣄⡁⠀⢰⢆⣠⣿⣤⣤⠀⠀⠀⠉⠳⣝⣝⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣪⠏⣹⠖⢲⡤⠀⠠⢤⣍⡲⠤⠥⣈⢿⠿⢿⣷⣄⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⣴⣷⣊⢤⢴⣿⠤⠾⡿⡚⠛⠛⢿⡛⠻⡓⠛⢋⣉⣀⣀⣉⣤⣤⡤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⢸⢿⠀⠀⢀⣧⠀⠀⠸⣷⠀⢈⣙⣃⠉⠀⠀⠀⠳⠶⠖⠐⠉⠃⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⣾⠀⠀⠈⢘⣄⠀⠀⠙⢇⣯⣁⣀⡄⣄⣒⡁⣀⡀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠒⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡔⠸⠁⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠐⠘⠀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⠀⠀⠀⠃⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠞⡁⠠⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⢀⡆⠀⠉⠛⠁⠀⠀⠙
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠁⣠⠀⠀⠜⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄⠀⠀⠀⢠⠀⠀⢀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⠠⠀⠀⠄⠀⠀⠀⡀⠀⠀⢰⠂⠀⠢⠤⠤⠀⠀⠀⠀⢁⣨⠿⠷⠶⠕⠀⠘⣦⢣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡏⠀⠀⢀⠀⠐⠀⠈⠙⠚⠉⠁⠀⠀⠀⠀⠀⠠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠂⠀⡀⢩⢀⠀⣐⡹⠒⠆⠀⠤⠀⠊⠒⠂⠖⠀⠀⠀⣀⣈⡄
⠀⠀⠀⠀⠀⠄⠒⠒⠒⠁⠂⠀⠐⠈⠑⠋⠀⠈⠛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣾⠉⡧⢀⡴⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢧⣤⡇⠀⡿⢻⠃⠀⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⢠⢃⡞⠁⣧⠀⡿⣿⠀⣰⠏⢿⡏⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⢤⡶⠦⠤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠉⠉⠀⠀⠀⠈⠉⠛⠛⠿⠶⠶⠿⠾⠷⣯⣼⠃⠀⣿⢦⣤⣤⡽⢦
⠀⠀⠀⠀⠀⠀⢀⣴⣋⣽⠦⠶⠚⠛⠲⢶⡏⠳⣄⢀⣠⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⣧⢀⡞⠉⣷⣀⠙⢳⣄⣧
⠀⠀⠀⠀⣀⣤⡿⠭⣶⠶⠶⠦⠤⢤⣀⠀⢳⡀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢻⡏⢀⣰⢁⠈⠳⣟⠉⢻
⠀⠀⣠⠾⣇⣀⣀⣠⠼⠲⠶⠶⠶⢶⡏⠛⢦⡙⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⡿⠋⠉⠉⠉⢻⣿⣄
⣠⢎⡴⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠉⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡇⠀⠀⠀⢀⡞⠀⠙⣿
⠿⠋⠀⠀⠀⠀⠀⣀⣤⢤⡶⠒⠒⠶⠶⠶⠮⠿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡈⠓⡾⠳⠶⠶⣶⠋⠀⠀⠀⣸
⠀⠀⠀⠀⢀⡴⠋⠁⣠⠜⠓⠒⠒⣶⣶⣶⣶⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢜⣭⣿⣿⣤⡠⣄⣉⡿⠁⠀⠀⢠⡟⠲⠶⠒⢺⡏
⠀⠀⣀⡴⠚⢓⡶⠋⠁⣠⡴⠚⠋⠉⣉⣉⣭⠏⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣽⣿⣥⣼⢿⣿⡿⠃⣷⡼⠋⠀⠀⠀⠀⡟⠀⠀⠀⠀⣸⠃
⠀⣴⠁⣠⡾⠋⠀⠀⣰⠋⠉⡟⠉⠉⠉⠀⣸⠷⣴⠋⠀⡴⠀⢀⠀⢀⠀⠀⡀⢠⡿⣿⣿⠟⢹⡧⣄⣠⡴⠋⠀⢀⣠⠴⠒⡻⠛⢤⣀⠀⣰⠏
⠀⡟⢹⡇⠀⠀⠀⢠⡇⢀⡼⠀⠀⠀⠀⢰⠃⠀⠈⠻⢾⣥⣴⣏⣀⣸⡀⣀⣇⣈⣳⣤⣀⣠⣾⣷⠶⢿⡷⣀⠴⣫⡤⠖⣾⠇⠀⠀⢩⠟⠁
⠀⡇⢸⡅⠀⠀⠀⢸⠛⠉⡇⠀⠀⠀⠀⢸⠀⠀⢀⣀⣼⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠙⠟⠀⠀⠴⠟⠋⠁⢀⡾⠃⠀⠀⣠⠏
⠀⠹⣜⡇⠀⠀⠀⠘⣆⢰⡇⠀⠀⠀⠀⠘⡟⠋⠉⠀⠈⢳⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣛⣠⠤⠖⠋⠁
⠀⠀⠘⠧⠀⠀⠀⠀⠘⣏⠙⢆⠀⠀⠀⠀⢿⡀⠀⠀⢀⡼⠉⠉⠉⠛⠲⠦⣤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣙⣦⣀⠀⠀⠛⠒⢾⠉⠀⠀⠀⠀⠀⠀⠴⣶⣦⡤⣶⠾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠓⠤⣤⣄⣀⣀⣀⣀⣠⡤⠤⠖⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠋⠁⣸⣿⣿⣷⣾⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢁⣠⣴⣿⣿⣿⡟⣡⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣤⣾⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠿⠟⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡿⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⠶⢦⠀⠠⠴⠖⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠁⠀⠀⠐⠆⠈⠁⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣭⠁⠀⢀⡀⠄⠀⠀⠀⣰⡟⣸⠃⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣾⣷⡈⠻⠿⠛⠀⠀⠀⣠⡾⠋⠜⠁⠀⢀⠄⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠋⠁⠀⠙⣿⣧⠀⠀⠀⠀⣠⡾⣛⡴⠂⠀⠀⢠⡞⠀⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⠀⠛⢭⡞⠋⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⣿⣿⡿⣄⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠶⢶⣤⠶⠓⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢂⣠⡷⠞⢿⠲⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⣡⢷⡀⠈⣆⠀⠀⠉⡳⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠾⢛⣧⡼⠃⠀⢤⣡⠈⢳⣄⡀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣯⣩⣤⣤⡶⠾⢻⠀⠀⠙⠃⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⢄⠁⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠦⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣶⡶⣿⣥⡀⢀⣠⣦⣽⣿⣇⠰⢮⡁⣦⠀⡀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠶⠶⠶⠶⠶⠶⠶⠶⠆⠐⠾⠾⠿⠿⠿⠷⠿⠿⠿⠿⠿⠛⠟⠺⠟⠛⠒⠂⢘⣿⣿⣿⣿⣿⣧⣠⣤⣤⣤⣤⣤⣤⣤⡤⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠐⣶⣮⣷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠗⠶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠋⢕⡢⢄⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡉⠒⢑⣤⠀⠈⠻⢶⡄
⠀⠀⣶⠀⢲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣿⣿⣶⣄⠀⠙⣦⡀
⠀⢸⣿⠀⢸⣿⡀⠀⠀⠠⡀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣌⣻⡄
⠀⣿⡗⠀⢸⡿⡇⠀⠀⠀⠈⠢⢄⠙⢆⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⠋⠑⢦
⢸⡿⢇⠀⣾⠃⡇⠀⠀⠀⠀⠀⠈⠑⢌⢳⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠈⡇
⢸⡇⠘⠀⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⣟⢤⣄⣠⣄⣀⠀⠀⠀⠀⠀⣿⣿⣄⣀⡠⢓⠰⣶
⣼⡇⠈⢸⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⡆⠹⣯⠖⠻⠿⣦⢄⡀⢠⣿⠿⠉⠉⢡⠟⡄⢸⢧
⣿⡇⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⣴⡡⠞⢲⣿⣆⠘⢿⡦⣄⡀⠉⠉⣻⣿⡇⠀⢀⣿⠀⢷⠀⣸⡀
⣿⡇⠀⠀⠘⡽⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢸⡸⣿⠀⠈⠻⣮⠙⠦⣠⣿⡿⠛⠷⣮⣴⠀⠺⡀⣿⡅
⣿⣧⠀⠀⠀⣷⠀⠀⠀⠀⠀⢰⡳⠁⠀⠀⣿⣿⢿⡇⠀⠀⠘⠷⡀⢾⢿⣧⡀⡐⠈⣿⠲⣦⡇⣸⡇
⢹⣿⡀⠀⢰⢳⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⡿⣿⠈⢿⡄⠀⠀⠀⡇⢸⡎⣯⠛⢅⣨⡏⠀⣹⠛⣷⣇⡀
⠈⣿⣿⣷⣮⣦⣠⣤⠀⢀⣮⠃⠀⠀⠀⠀⢻⡹⣧⡌⠑⠶⠶⠚⣰⠟⣰⠋⢳⠀⠹⣄⣼⠏⡘⡾⠀⣙⠳⢤⣄⣤⠔⠛⠶⠂
⠀⠈⠻⣿⠋⠈⠉⠈⢳⣦⣥⣤⣤⣶⣤⣤⣤⣵⣝⠻⢶⣶⡶⢟⣫⡞⠁⠀⢸⡄⠀⠘⠏⡰⣡⠇⣼⠛⠉⠉⠈⠉⠓⠒
⠀⠀⠀⠙⠻⢶⣤⣤⣾⡿⠀⠀⠀⠀⣠⡤⣸⣿⣿⣿⣷⣶⣿⣿⣿⣧⠀⠀⠈⣧⣀⠀⢘⣿⢋⣾⠏
⠀⠀⠀⠀⠀⠀⢀⣽⠿⠿⣿⡿⠟⣿⣗⣛⠿⣿⣽⣿⡄⠈⠛⢿⣮⡻⣧⣄⡀⢘⣿⣷⣾⡧⣿⠃
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠊⢁⣴⠶⣿⠊⠙⢿⡶⢭⣽⣿⣄⠀⠈⢻⣷⣹⣿⣿⣿⣷⣿⣿⢿⠁
⠀⠀⠀⠀⢠⠞⠁⠀⣠⠶⠋⠀⣠⠇⠀⠀⠀⠈⠁⠊⠛⢻⣷⣄⣀⣿⣿⣿⣿⡿⠿⠟⠛⠛⡄
⠀⠀⠀⣴⠋⠀⠀⠀⠋⠀⠀⠀⠋⢀⣤⣀⣠⣶⣶⣾⣿⣿⣿⠿⣿⣿⢟⣽⠋⣠⡔⠂⢉⣴⣿⡆
⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣰⡽⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣫⣿⡩⠔⠚⠁⠠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣩⣤⠖⠊⠀⢀⣽⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⡋⠁⠤⠂⠀⠈⣹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡦⣀⡀⠴⠊⠛⣻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⡠⠔⠊⠙⢙⣷⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣀⣠⣴⡏⠙⢿⣿⣭⡋⠋⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⠹⠀⠀⢻⠋⠳⣄⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⣿⡟⣿⣿⠁⠀⠀⢸⡶⠾⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠸⡇⠘⡿⣤⣤⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⣾⠿⠛⠃⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣛⣻⣏⣌⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣿⣭⣽⣿⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢻⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠇⠈⠙⢦⡀⠀⢀⣀⣀⣀⣤⣤⣄⣀⣀⣀⡀⣠⠞⠁⠀⠘⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠤⣼⣷⠏⠀⣀⣤⠶⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⣤⣀⠘⢿⣧⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠋⢀⣠⡞⠛⢻⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⡁⣹⣦⣌⣙⢳⣄
⠀⠀⠀⠀⠀⣾⣷⠶⣛⣫⠿⠻⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠙⠶⣭⣝⣿⣦
⠀⠀⠀⠀⢸⠏⢿⡋⠉⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢠⡟⢹⡆
⠀⠀⠀⠀⢸⡀⠈⠻⣄⠀⢸⠇⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡴⠋⠀⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⢸⡏⠻⢦⣄⣀⠈⠻⣦⣄⡀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠀⢸⠇
⠀⠀⠀⠀⠀⣧⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠈⠉⢛⣛⠋⠉⠙⣛⡛⠓⠚⠛⠋⠙⠷⣄⡀⠀⠀⠀⠀⠀⢉⡽⠁⣿
⠀⠀⠀⠀⠀⢹⡌⠻⣤⣀⣀⣀⣀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠘⠋⡉⠀⠀⠀⢉⠻⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⡞⢻⡁⢸⠇
⠀⠀⠀⠀⠀⠀⣷⣰⢿⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⣷⡿
⠀⠀⠀⠀⠀⠀⢸⡿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠙⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢿⠇
⠀⠀⠀⠀⠀⠀⢸⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡀
⠀⠀⢠⣀⣀⣠⠟⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣤⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⢷⣄⣀⣠⡀
⠀⠀⠈⠻⣍⠁⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢈⣽⠏
⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡵⣶⣾⣿⣯⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠖⠋⠛⢦⣄⠀⠀⠀⠀⠀⢸⣿⣝⣛⣭⡭⢿⡇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠛⠒⠒⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⣺⠹⠿⠶⠶⠾⠟⡇⠀⠀⣀⣠⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣇⣈⠙⣆⠀⠀⠀⢀⡼⠛⠛⠉⠉⣁⣸⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣿⠁⠉⠙⠛⠳⡄⣰⠿⠶⠶⠖⠛⠋⠉⠀⣿⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⢰⡏⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⣀⣾⠁⣀⣤⡴⠶⢾⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⠉⠛⣿⠋⠀⠀⠀⠐⠷⠾⢷⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠶⠿⢻⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣴⣶⣿⣁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣦⣤⣤⣽⣦⣤⣤⣤⣤⣤⣿⠁⠀⢙⣧⣀⣀⣤⣤⣀⣀⠀⣿⠀⣠⠶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⣰⣯⣤⣤⣴⠾⣏⠀⠀⢸⡇⠙⠶⠶⠞⠁⢉⡿⠛⠛⣯⠙⠳⣾⣿⣏⣠⡟⢹⡆
⠀⠀⠀⠀⠀⢠⡟⠛⠛⢛⣹⡿⢷⣾⠿⣿⣷⠞⠋⠀⠙⠷⠶⠛⠀⠀⠀⠀⠀⠀⠸⣧⣀⣀⣼⠃⠀⠘⣿⠟⣿⣟⠻⢿⣟⡛⠛⠛⠛⢷⡀
⠀⠀⠀⠀⢠⡟⠀⢀⡴⠋⠁⠀⣤⣼⣷⠟⢿⣄⣠⣴⠶⣦⠀⠀⠀⣀⣤⣤⡀⠀⠀⠈⣉⣭⣅⣀⡶⠞⠃⣰⣯⡿⠶⣦⠈⠛⢦⡀⠀⠘⣧
⠀⠀⠀⢀⡾⠁⠀⣾⠁⠀⠀⠀⣿⠛⢿⣟⡻⠯⣥⣶⣾⣿⣤⣤⣴⣯⣭⣽⠿⠶⠶⠞⠋⠉⠉⣉⣡⡴⠟⣹⣿⣤⡴⠋⠀⠀⢈⡧⠀⠀⠘⣇
⠀⠀⠀⣾⠁⠀⠀⠘⢧⣀⠀⠀⠘⠷⣤⣈⠙⠓⠶⠦⣤⣤⣤⣤⣀⣀⣀⣤⣤⣤⣤⡶⠶⠞⠛⠉⣁⣤⠾⠻⣮⣿⠀⠀⠀⣠⡾⠃⠀⠀⠀⢹⡆
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⡀⠉⠛⠳⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠞⠛⠉⠀⠀⠀⢀⣁⣤⡴⠞⠉⠀⠀⠀⠀⠀⠀⢻⡄
⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⢦⣤⣤⣤⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣤⣤⣤⠴⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⡆⠀⢀⡤⡀
⠀⠀⠀⢀⠞⠳⣄⠀⢰⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⡠⠖⠂⠉⠐⠲⢄⣠⠖⢉⣀⡀⠉⠓⣄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢰⠀⡴⠋⠀⢱
⠀⠀⠀⢸⠀⠀⠈⠣⣸⠀⠀⠀⠈⢆⠀⠀⠀⠀⡘⠀⢀⣾⣿⣿⣦⢀⠃⢰⣿⡿⣿⣆⠀⠈⡆⠀⠀⠀⠀⡰⠁⠀⠀⠀⠸⠊⠀⠀⠀⡸
⠀⠀⠀⠘⡄⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⢣⠀⠘⣿⣧⣸⣿⠀⣆⢸⣿⣧⣼⡿⠀⢠⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠳⢄⡙⠻⠟⣋⠔⠉⠲⢝⡛⣛⡡⠔⠁⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⣀⠀⠈⠣⣀⠀⠀⠀⠀⠀⢀⣈⠤⠏⠈⠒⠒⠒⠋⠀⠑⠒⠂⠤⢄⡀⠀⠀⡠⠃⠀⢀⠖⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠈⠑⠦⣀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠁⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠀⠀⠀⠀⠀⢎⠀⠀⠀⢀⡤⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠋⢀⣈⠙⠲⠤⣀⡏⠀⠀⠀⠀⠀⢀⣀⢤⡤⡴⢶⠒⡏⢩⣈⡖⣯⠃⠀⠀⠀⠀⠀⠈⠦⠔⠊⣁⠤⢦⠀⠙⢄
⠀⠀⠀⠀⠀⢠⠎⠀⢠⠊⠀⠉⢲⣤⣄⠀⠀⠀⠀⠀⠀⠈⠻⡖⠧⢶⠴⡶⢺⠈⣇⡷⠁⠀⠀⠀⠀⠀⠀⢀⣤⠶⢯⡀⠀⠀⢣⡀⠈⢣
⠀⠀⠀⠀⢠⠃⠀⡰⠃⠀⢀⡔⠁⣠⣉⡛⠀⠀⠀⠀⠀⠀⠀⠈⠛⠬⢦⣥⠴⠗⠉⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠢⡀⠱⡄⠀⠀⢱⡀⣀⠇
⠀⠀⠀⠀⠈⠂⠜⠁⠀⢀⠎⠀⡸⠁⠀⢩⠵⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢧⠀⠀⠀⢣⠀⠘⡄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⡴⠁⠀⠀⡏⠀⡆⠐⠒⠒⠒⠂⠤⠤⠤⠄⠀⠤⠤⠤⠔⠒⠈⠉⠉⠉⡇⠈⡀⠀⠀⠀⠧⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⢦⣤⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⣼⣿⣿⠉⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣵⣦⠀⠀⠀⢸⣿⣿⣧⡀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⣾⣿⠻⢿⣿⡿⠂⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⣄⠀⣼⣿⣇⣄⣠⢀⠀⠀⠀⠀⠀⣀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀⢰⣦⣤⣴⣿⣷⣿⣿⡀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠘⠛⣛⠿⠿⠿⠿⠿⠿⠿⠂⠁⠀⠛⠿⢿⣿⣿⣿⣿⣧⣿⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠏⢸⣿⣻⣷⣾⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠛⣿⡦⠀⠀⠀⠀⠀⠐⣽⡖⠀⠀⠀⠀⠘⠇⢸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠟⢻⣿⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣄⢤⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⡤⠤⠤⢤⠄⠀⠀⠀⠀⢠⣿⣿⡭⣽⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣦⣀⠀⠀⠀⠚⠛⠁⠀⠀⠀⣀⡴⠛⣿⣿⣦⣾⣿⣿⣿⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣞⠛⠖⠒⠂⠠⠶⠶⡟⠋⠉⠻⠿⠟⠋⠛⠶⠤⣀⣀⣀⠠⠐⠛⠉⠀⢠⠏⠙⣿⣿⡿⠟⣉⣤⡾⡿⣉⠿⣄
⠀⠀⠀⠀⠀⠀⣸⣧⠟⢂⡜⠙⠒⠒⠚⠁⠀⠓⠲⣤⡴⠊⠉⠉⠀⣤⠀⠀⠀⠀⠀⡀⠔⠁⠂⠀⠀⠀⠀⠀⡇⢈⡷⢤⡈⠑⠾⣦
⠀⠀⠀⠀⠀⠀⣿⣇⡀⢻⠀⠀⠀⠠⠤⠂⠀⡠⠆⠘⠦⣥⠤⠖⠊⠠⣄⢐⡒⣩⠥⠀⠀⠀⠀⠀⠀⠀⢀⠜⣀⣹⠗⢀⣌⠛⢢⢞⣷⡀
⠀⠀⠀⠀⠀⠀⢻⣿⣉⡿⠀⠀⣀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⠀⠠⢱⢀⣷⠹⡀⠀⠀⠀⠀⠀⠃⡖⠛⠤⣬⠋⠠⠦⢀⣘⣣⣶⣻⡇
⠀⠀⠀⠀⠀⠀⠈⣿⠟⠁⠀⠠⡈⠳⠄⠀⢀⡔⣃⠀⠀⠀⠀⠀⠐⡡⢸⠆⣸⣧⠱⡀⠀⠀⢀⢜⣼⣡⠛⢶⣿⣹⢷⣤⣞⣿⠿⢤⣿⠁
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢾⣦⣤⡴⣯⠛⢻⣷⣵⣒⣒⣫⠞⡷⡇⢘⠿⢿⣷⣬⣁⣩⣵⠟⡶⢉⣱⣿⣿⠉⣾⠇⣸⠛⢠⢾⣏
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣌⡹⠷⣷⡋⢱⠿⣤⡟⠛⣽⣋⣾⢧⡇⠈⣺⠮⣀⠟⢫⡼⢉⠾⢤⡌⠙⣿⣧⡟⠃⣤⣁⡴⠧⣼⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣜⣿⣶⣿⣿⠓⣤⡀⢈⣿⠏⠁⠉⠙⠦⢼⠁⣴⡉⢱⠆⢤⡋⡲⢦⣀⠛⢺⣿⡴⠛⣤⡟⢙⡶⣇⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢳⣯⠟⠻⣿⣿⣿⡶⢔⠛⠛⠃⠀⠀⠀⠀⠀⠀⢣⡄⣠⣤⠀⠁⠺⣓⡶⠅⣱⢿⡾⠷⣶⣿⡟⠩⠑⠂⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡔⢳⡿⠋⠀⠀⢹⣿⣿⣷⣬⣉⠉⠁⠐⠛⠛⢴⡋⣈⣉⠠⠤⠀⠀⠀⠀⠈⠳⠴⣍⣩⣥⠤⠴⠟⠓⠂⠀⠈⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⠞⣴⠋⠀⠀⠀⠀⠀⢻⣿⣿⣦⣝⠓⡶⣶⣶⣶⡦⢠⣤⣤⣤⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⣀⣈⣈⣁⣀⠀⠀⠀⠀⠀⢈⡿⠿⠛⠚⠛⣒⡀⢤⣼⠆⠚⠂⢸⣛⣋⣩⠤⣄⣀⣀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠁⠀⠀⠀⠰⣏⣀⡀⠀⢈⣀⣈⣱⠂⠈⠀⠀⢰⠿⠷⠿⠿⠶⠦⠭⠿⠿⠷⠶⠤⠤⠤⣤⣤⡾⣥⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣄⣀⣀⡈⠉⠉⠉⠉⠉⢀⣀⣠⣤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂⠐⠂⠀⠀⠀⠂⠀⠂⠂⠁⠂⠁⠀⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢩⠞⠁⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠈⠳⡍⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠔⠋⡠⠶⢺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠕⠶⢄⠉⠢⡈⠓⣄
⠀⠀⠀⠀⠀⠀⢀⡜⠁⢠⠞⡰⠚⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠓⢆⠳⡄⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠡⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠓⠂⠀⠐⢖⠋⠁⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠈⠙⡳⠂⠀⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⣀⡠⠒⠜⠳⠞⠡⠐⢄⣀⣠⠛
⠀⠀⠀⠀⠀⠢⠀⠀⠂⠉⠙⠋⠢⠤⣀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⣀⠤⠔⠙⠋⠉⠐⠀⠀⠔
⠀⠀⠀⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⢀
⠀⠀⠉⠇⠀⠀⠀⠙⠢⢀⣰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⡀⠔⠋⠀⠀⠀⠘⠉
⠀⠀⠀⣠⠦⠀⠀⠀⣀⡎⠁⠀⠀⠀⠀⢀⡠⠐⠒⢦⡀⠀⠀⠀⠀⠀⢀⡴⠒⠂⢄⠀⠀⠀⠀⠈⢱⣀⠀⠀⠀⠴⣄
⠀⠀⠀⠈⠁⠐⠠⢰⡅⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⢨⡆⠄⠀⠀⠁
⠀⠀⠀⢀⣀⣀⣠⠔⠀⠀⠢⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠔⠀⠢⢄⣀⣀⡀
⠀⠀⠀⠉⠛⠳⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠛⠉
⠀⠀⠑⠀⠀⠀⠠⠚⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠃⠄⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⣨⡓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⢚⣅⠀⠀⠀⢀⠔⠀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠉⠀⠂⠈⠉⠉⠉⠁⠀⠐⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠐⠀⠉⠀⡄⠀⠀⠀⢀⠀⡀
⠀⠀⠀⢨⣠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢉⡝⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠤⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠰⠆⣣⣤⡼⠃⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⠀⣱
⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠠⢀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⠒⠀⠀⠀⠀⠀⡐
⠀⠀⠀⡀⠀⠢⠀⠀⠐⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢁⣠⣤⣆⠏⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠈
⠀⠀⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠀⠀⠔⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠁⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠀⠐⠄⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⣠⠤⠀⠒⠁⢀⡀⠠⠤⠤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠆
⠀⠀⠀⠈⠂⠈⠉⣉⢀⣠⡤⠆⠂⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠐⠐⠀⠀⠀⠀⢀
⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠖⠀⠉⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⢀⠴⠂⢀⠀⠀⡆⠀⠀⠙⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠂
⠀⠈⠆⠁⠆⠀⠤⠄⡔⠂⠉⠁⡤⣀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠔⠁⢠⡄⠃⠀⠀⠅⠀⠀⡇⠀⠀⠒⠂⠙⠋⠘⠃⠁
⠀⠀⠈⠐⠓⠄⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠠⠐⠀⠔⠀⢐⠀⡇⠀⠀⠁⠀⢠⣴⠇⠀⠀⠀⠀⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠅⠌⠀⠀⠢⠀⠠⢍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠐⠀⠀⠤⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠠⠀⠀⠘⠀⠐⠊⠉⠀⠀⠠⠤⠄⠐⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠂⠚⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⠀⠀⠀⡇⡁⢇⡡
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠁⠀⠉⠁⠘⠓
⠀⠀⠀⡄⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠓
⠀⠀⢠⠦⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇
⠀⢠⠁⠀⠀⠈⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⡀⠠⠤⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⢀⠀⠀⠤⠤⠤⠀⠀⠀⠀⡀
⠀⠐⠀⠀⠁⠀⡀⠀⠀⠀⠈⠀⠀⠀⠳⠠⠄⠀⠀⠀⠀⠀⠀⠀⠐⠅⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠂⠀⠀⠀⠀⠀⠀⠀⠉
⠀⢀⠀⠤⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⡀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⢆⠀⠾⠡⠄⠆⡱⠀⠀⠀⠀⠀⠀⢀⡀⠘⠃⠤⠤⠛⠀⣀⣥⠀⠀⠀⠀⠀⠀⠐⠛⠐⠘⠉⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠐⠂⠀⠐⠒⠁⠀⠀⠀⠀⠀⢰⠀⢈⠈⠉⠉⣉⢉⡉⠀⢹⠀⠀⠀⠀⠀⠀⡀⢠⠀⠐⢬⡀⠀⠀⠘⠀⠀⠀⠀⢀⠚⠉⠀⠀⠆⠔⠀⠁⠓⣄
⠀⠀⠀⠀⠥⣬⠈⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠊⠜⠃⠨⠀⠄⠂⢼⠀⠀⠀⠀⠀⠀⠁⠋⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠒⠂⠀⠆⠐⠔⠂⣸
⠀⢰⠀⠀⢀⠁⠉⢀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⣉⡁⠘⠋⠁⢀⣀⠔⠁
⠀⠈⢄⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⡀⠃⠀⢂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⢰⣄⢀⡉⠉⠉⠉⠉⢁⣀⡴
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠉⡀⠀⠀⠀⠀⠀⠁⠢⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠉⠈⠉⠉⣓⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠉⢩⡝⢤⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣰⢪⡉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠋⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠷⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢠⡺⡀
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠑⠄⠐⡀⠔⠻⠀⠙
⠀⠀⠀⠀⢡⢄⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⢀⡶⠦⠀⠒⠀⠀⠀⠀⠉⠉⠁⠐⠂⠄⡀⠀⠀⠀⠀⠀⠰⠶⡞
⠀⠀⠀⠀⠇⠙⠗⠠⠬⠄⠀⠀⠀⢀⠤⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣎⠀⠀⠀⡠⠊
⠀⠀⠀⠀⢢⡤⠦⠀⠀⠀⠀⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠃⢀⣁⠤⠒⢒⡆
⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠠⠤⡶⠋
⠀⠀⠀⠀⠀⡤⠠⠤⠤⠤⠤⢼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠗⠒⠒⠚⣚⠆
⠀⠀⠀⠀⠀⠉⠲⣦⠶⠂⠀⢉⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣿⡒⠪⠿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠟⣉⣉⣠⣀⠽⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠈⠛⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣏⣁⡼⠋⠀⠉⠂⠤⢀⢀⣀⡀⡀⠠⠄⠐⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠔⠀⠀⠀⠀⠀⣤⡀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠄⠀⠀⠀⣀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠚⠣⠬⠁⣀⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠚⠒⠋⠉⠉⠉⠉⠀⠀⠈⠁⠛⢀⡂⠒⠁⠀⠐⠊⠁⠨⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡙⠀⠀⠀⠀⡀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠤⡀⠀⠀⠈⢣⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⣠⠀⠠⠔⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢅⠀⠀⠈⠆⠀⠀⠀⣿⢁⠁⠀⠀⠀⢀⡠⠔⠉⠁⠤⠤⢤⠀⠀⢠⠊⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣀⠀⠈⢢⠀⠐⢄⠀⠀⠻⣘⣄⣠⡴⠚⡃⠀⠀⠀⠐⠠⣀⠀⠀⠀⢹⡄⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢃⠀⠸⡀⠀⠈⠃⠀⠀⠀⠉⠘⠜⠐⠀⡀⠀⠀⠤⠀⠈⠁⠠⠤⠊⠤⠐⠚⠉
⠀⠀⠠⠰⠂⢀⡎⠀⠑⢄⡀⠈⠦⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⢀⠔⠁⢘⠖⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⡇⢀⠔⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠥⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡛⠿⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠑⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠇
⠀⠀⢀⣾⠿⠳⡀⠀⠀⠀⢀⡀⠀⠰⠁⠊⠗⠢⠐⠈⠹⡄⠀⢀⣰⠁⠀⢗⡀⠀⣀⠀⠀⠈⢁⢀⡠⢦⡀
⠀⠀⠀⣹⠀⢀⢦⠀⠀⠀⠉⠃⡰⠁⡤⠀⠀⠀⠀⠀⡀⢻⢠⣿⣯⡣⠥⣺⣿⠘⢡⠁⠀⠀⢀⡸⠀⢤⣳
⠀⣠⣾⠁⠑⠘⠈⡃⢠⢂⠊⠘⠤⠶⠑⠄⠀⠀⠐⣲⠀⡼⢀⠃⣉⠩⢛⠉⢹⠀⠀⠚⢳⣀⠀⠁⠀⣸⠸⣦⡀
⣼⣿⡇⠀⣤⣴⡿⣅⠁⡜⠒⠃⠄⢌⠤⢗⣒⡶⢖⠓⠒⠓⠺⡀⠘⡢⠮⢤⡘⠤⠤⢰⠈⠏⡀⠀⠀⣿⠀⣿⣿
⢻⣿⠧⠀⣟⠋⡴⣇⣽⡶⡀⠀⠀⠣⣛⡟⠽⣛⡠⠐⢻⠀⠀⠀⣙⠝⠚⠃⠈⡔⣡⣔⢓⠰⡧⠄⢰⡏⠀⣿⣿
⠀⢻⣆⠈⠋⢛⠡⢥⠋⡙⠀⠀⠀⠀⡀⣈⣉⡀⢀⠀⠉⠀⠺⣯⠭⢭⡟⠀⠀⠣⣋⠩⣨⠋⣀⣤⡏⣀⣠⣿⡟
⠀⠈⢟⠟⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⠏⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⡺⠁⡈⠊⠉⠀⠘⢿⡿⣿
⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣭⣤⣤⣤⣤⣤⣤⣽⣎
⠀⠀⣷⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣼⣿⣯⣿⣿⣿⢿⣯⣿⣿⣯⣿⣿⣽⣿⣛⣿⣏⣽⣿⣿⣿⣿⣏⣿⣿
⠀⢀⣀⡠⠬⢭⠉⠉⠉⠉⣉⣉⣭⠉⠉⠉⠉⠉⣉⣉⠉⠉⠛⠛⢛⣛⡛⠛⠛⠛⠛⠛⢛⣛⡛⠉⠉⠛⠉⢙
⠀⣮⣀⣀⣀⣙⠒⠒⠚⠉⠁⠀⠻⠤⠴⠒⠚⠉⠁⠻⠤⠴⠖⠋⠉⠰⢇⣠⡤⠴⠒⠋⠁⠐⠧⠤⠤⠖⠋⠙
⠀⠙⠚⠓⠿⠿⠽⠯⢿⣽⣿⣿⣿⣿⣖⣶⣲⣖⣾⣲⣲⣖⣶⣲⣶⣖⣶⣲⣖⣶⣲⣶⣖⣶⣲⣖⣖⣿⣿⡿⠆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⢀⠇⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡵⢀⡠⠐⠁⡀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⡔⠊⠁⠀⣠⢊⠁⣤⠀⠀⠀⠀⠀⠀⠀⠄⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠌⠁⣰⠂⠁⠀⢀⢠⣄⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠽⠟⠋⢈⠀⠀⠀⠀⣀⠀⠀⢈⡧⠀⠀⠀⠀⠀⠒⠒⠉⠉⠉⠉⠙⠓⠒⠂⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⢀⡔⠚⠀⠀⠀⠀⠀⡀⢴⠀⠀⠀⠀⠀⣀⠀⡆⠀⠏⠀⡀⠀⠊⡠⠊⢁⡠⠊⣵
⠀⠀⠢⡀⡔⠡⢄⠀⠀⠀⠈⠂⡀⢈⡇⡼⠤⠄⠖⠛⣩⠃⠸⡄⠂⠉⠉⠀⠀⠛⠈⠁⠀⠀⡠⠸
⡀⠀⡙⠛⠀⠀⠀⠡⠀⠀⡇⠀⠂⠊⠀⠀⡀⢀⡀⡄⠴⠀⠀⠈⠚⠳⠤⠤⠀⠀⠁
⠣⡈⠀⠀⠰⠒⢴⠀⠁⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⢒⠤⢢⡀
⠀⠠⡀⠀⡀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠐⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⠀⢀⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⢱⠀⢠⡞⠀⢀⣤⠴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢙⡀⠁⠀⠙⡆⢠⣄⣌⠁⡜⠀⠀⣐⢉⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠛⡆⠀⠀⡷⠞⠀⠈⣿⣇⠀⣠⠛⠉⠻⣿⡄⠀⢀⠀⠀⠰⠆⠀⠉⠒⠆
⠀⠀⠀⠀⠀⠀⠐⠋⠁⠉⠀⠀⠀⠿⡓⠦⣀⣿⠃⠀⠀⠸⠰⠞⢸⠧⠀⠴⢿⠈⢉⣛⠀⠀⠀⢹⣿⡄⠊⠀⠠⠄⠀⠀⠀⠴⠦⠄⡀
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀⣲⣀⠀⢀⡐⣿⡟⠀⠀⠀⡘⠳⠏⠀⠶⠀⠒⠀⠛⠋⠉⠀⠀⠐⠀⣿⣟⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠤⠒⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⢠⣿⠅⠀⠀⣀⣇⡀⠀⡀⠄⠀⠡⣀⣠⡤⢿⣀⠀⠀⠐⢹⣯⠀⠖⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⢀⠀⢤⡐⠀⠀⢹⠉⠂⣼⠏⠢⡀⠄⣿⠉⠋⡁⠀⠀⠀⠀⢀⠀⢀⠘⡿⠁⠂⠀⠰⣿⠐⠀⠀⠐⠊⠉⠉⠀⠒⣠⡄
⠀⢀⣤⣖⡈⠉⠀⠀⠀⠉⠀⠈⠈⠁⢰⡟⠢⠀⠈⢴⡏⠀⠀⠈⠳⢀⣤⡜⠋⠀⠈⠀⢿⡗⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘
⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠑⢌⢠⣼⡁⠈⠀⠀⠀⠆⠀⠠⠀⠐⠀⠀⣯⡖⠀⠀⠀⢿⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⡛⢻⠗⠠⢀⠀⠘⢻⡇⠀⠀⠀⠀⢀⠀⣄⠀⠀⢀⢴⡴⠋⣀⠀⠀⢻⡇⣀⡹⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⣠⠛⡿⠀⠂⠤⢉⠒⣾⡇⠀⠃⠠⠀⢉⠀⠨⡴⠀⠈⢸⣷⡫⠔⠂⠁⢸⡇⠈⠱⣄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠟⠁⢰⠇⠀⠀⠀⠀⠈⠙⢷⠈⠀⠀⣀⡉⢀⡠⠀⣀⠀⡾⠋⠀⠀⠀⠀⠈⡇⠀⠀⠀⠻⡑⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠆⠊⠀⠀⣸⠀⠀⠀⠀⠀⣠⠚⣇⣤⠚⠀⠀⠒⠂⠀⠬⠛⣾⣠⡟⢦⠀⠀⠀⠀⣇⠀⠀⠀⠀⠙⠈⣆
⠀⠀⠀⠀⠀⠀⢠⡇⡌⠀⠀⠀⡏⠀⠀⠀⡠⠊⡠⠊⠁⠈⢧⠀⠤⠤⠤⠤⠤⣴⠇⠀⠈⢦⠳⣄⠀⠀⢿⠀⠀⠀⠀⠀⠐⢿
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢰⡇⠀⢀⠞⠡⠊⠀⠀⠀⠀⣵⠀⠀⠂⠀⠀⠀⢲⠀⠀⠀⠀⠣⣈⣆⠀⢸⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⢸⠇⠀⠚⠞⠁⠀⠀⠀⠀⠐⣬⢓⡚⠃⠀⣛⡫⢥⡛⠀⠀⠀⠀⠈⢦⣧⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡷⡎⠀⠀⠀⠀⠀⠀⠐⢩⡓⠤⣤⠀⡤⠞⣥⠓⠀⠀⠀⠀⠀⠘⡀⠇⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠃⠃⠀⠀⠀⠀⠀⠀⢠⡓⢮⡓⠦⠤⠒⢉⡄⣃⠀⠀⠀⠀⠀⠀⢱⡾⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⢾⠀⠀⠀⠀⠀⠀⠀⢀⠿⣕⢬⣁⡀⡉⣵⢹⡌⠀⠀⠀⠀⠀⠀⠸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠦⠀⠀⠀⠀⠀⠀⠀⠈⡡⠮⡓⠀⠀⢚⡵⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡳⠌⠁⠉⣩⣴⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⡈⢒⠀⠀⠛⡉⠲⠦⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⢀⠴⠋⠀⢀⠜⠁⠈⠀⠀⠘⠇⠈⢢⡀⠑⠢⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠋⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⣴⠀⠀⠀⢢⠀⢐⣄⠀⠀⠀⣤⠀⠀⠄⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣶⣶⣶⣤⣶⣧⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣋⣙⣋⣸⣋⣹⣝⣨⣟⣻⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣠⢶⠒⡀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢰⡏⣽⢒⠛⢛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠶⣦⠀⠀⠀⣠⣶⡟⠉⣩⡉⢷⡄
⠀⠀⠀⠀⠀⠀⣰⠃⣆⠈⢁⣈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡆⠾⠞⠻⣇⠀⠀⢹⠁⢲⣟⠉⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢻⣶⣾⠶⢬⡾⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣃⠂⢀⠁⡞⠀⠀⢸⡗⢀⡹⢀⡀⣼⠁
⠀⠀⠀⠀⠀⢠⣴⠛⡇⠓⣤⣧⣵⢠⠙⢆⠀⠀⠀⠀⠀⠀⠀⣈⠷⣛⡾⢤⣄⡀⠈⢧⣰⣤⣔⣒⣛⣷⣤⣤⣄
⠀⠀⠀⠀⢀⡏⢘⡤⠷⢾⣤⣅⠈⠘⡆⠈⠀⣀⣠⠤⣤⣀⣼⣹⣀⠀⠀⡼⠀⠱⣠⠶⠚⠋⠁⠈⢳⠀⠀⠀⢈⢳⡀
⠀⠀⠀⠀⠸⣇⡏⠀⠀⢠⣰⣿⠇⠤⠒⢺⡉⠁⠀⢀⠀⠲⠀⠀⠀⡉⠉⠉⢲⢺⡇⠈⣇⠀⠀⠀⠈⡇⠀⠀⠈⡆⢳⠲⣦
⠀⠀⠀⠀⠀⣏⣂⣔⣔⢈⡷⡇⠠⠤⢔⡎⡠⢰⠓⠒⠒⢠⢀⠂⠀⠁⠀⢀⣯⣼⡇⠀⡝⠢⣀⣠⡤⠴⠖⠒⠒⠻⢿⠶⣿
⠀⠀⠀⠀⣠⣽⡿⠿⢟⣯⠜⠁⠀⠀⠀⠀⠐⠈⠑⠀⢀⡈⠀⠂⠀⢀⡀⣿⠀⣟⠀⢸⠓⢺⠋⠁⠀⢀⣀⣠⣤⣀⡞⢀⡇
⢠⣤⣄⣾⠃⠐⢋⣉⠛⢧⡤⢤⣀⣡⣌⠉⠆⠀⠀⠠⠁⠀⠀⠠⠄⠀⠀⢿⡀⣟⠀⣼⠀⢸⠴⠚⠉⠉⠀⠀⣀⣟⠀⢸⠁
⢁⠀⠀⠙⢦⣀⣄⣸⣦⢀⠀⢀⣿⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣈⣷⡀⠀⣿⠀⢸⠀⢤⡴⠦⠍⠓⠒⢘⠇⣸
⠘⡦⢄⡀⠀⠹⡏⠉⡟⢦⣜⡠⢧⢀⡟⠀⠐⠒⠤⢤⣀⡀⠀⠤⠖⠚⠉⠁⠈⠳⠤⣿⠀⡟⠈⢀⣀⡤⠴⠒⠋⠉⠀⣿
⠀⣃⠀⠈⠑⠢⣧⠀⢣⢸⠟⠦⠴⠛⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⣿⠀⡷⠊⠉⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠙⠓⢦⣄⡀⢸⠀⢸⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣀⡀⠀⠉⠻⡆⠈⣇⣠⠤⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⡀
⠀⠀⠁⠈⠙⠒⠀⠧⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⡀