Lychee Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⡀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣧⢸⠀⢀⠄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠈⢿⢀⡎⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠈⠢⡀⣸⠞⠀⡔⠀⠀⢸⠀⠀⠀⣀⣀⠤⠴⠒⠚⡉⠉⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⡼⠀⠀⠀⢄⠀⠀⢸⡇⠀⢸⠆⠀⠀⢸⡤⠖⠋⠉⠀⡀⠀⡠⠊⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢋⠙⠀⠀⠀⠀⠀⠉⠉⠙⣷⡀⠀⠀⠈⠳⣄⣸⢁⡴⠋⠀⡠⠖⠉⠀⠀⡀⠀⠠⣡⠾⠠⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠉⠁⠀⠈⠃⠀⠀⠀⠰⣿⣷⠀⠠⡄⠉⢶⣀⣄⣀⣠⣏⣀⣀⣠⠊⠀⠀⠀⡆⠐⡅⢀⠜⠁⣀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠖⠋⠉⠀⠀⣄⣈⡉⠛⠣⣄⠀⠈⠒⢧⡀⣱⠟⠂⠉⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠐⠒⠀⠀⠀⢢⠀⠀⠐⠂⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠙⠢⣀⠀⣷⠡⢴⣉⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠘⠢⠀⠀⠀⢠⡀⠀⠀⠀⠉⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢱⡄⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⢼⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⣳⣠⠞
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠐⢄⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠁⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠹⣇⡀⢄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠁⡀⠀⠀⠔⠀⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠰⠄⠀⠀⠀⠀⠐⠖⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠋⠁⠀⠀⠊⠁⠀⡀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢶⣄⠀⠒⠦⠀⠀⠠⠄⣸⠶⠲⠖⠒⠒⠚⠁⠀⣀⠄⠀⠀⠠⠄⠀⠀⠋⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠖⠾⠷⠟⠋⠳⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣠⠄⢀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣊⠁⠀⣠⠀⠀⠒⠋⠀⠀⢀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠶⠶⠖⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⢧⠃⣏⠀⠏⠗⢮⠗⢾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡴⠀⠁⠚⠂⠐⠒⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠃⠀⢀⠁⠰⡀⠀⠀⠀⠀⠀⠠⠈⠈⢀⠀⠳⡈⠐⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠘⡄⠈⠀⠀⠀⠀⠀⡠⠔⢀⡐⠀⠀⠀⢆⠠⠈⠑⢄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡀⢡⠀⠃⢠⠊⡀⠀⠀⠀⠈⡆⠀⠀⠀⠑⡀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡘⡀⠰⠁⠐⠁⠀⠀⠀⠀⡰⠄⠤⠄⠀⠁⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢂⠀⠀⠀⢱⠃⡈⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⡄⢘⡀⡠⠂⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⢠⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣸⡧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡘⣩⠙⠋⡜⢠⢭⢋⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⣙⠺⠉⢈⢿⣥⡄⠸⣎⠛⢹⠏⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡔⠀⠀⢀⣠⠅⠶⡤⠿⠂⣁⡬⢿⣴⠛⣏⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡈⠛⢸⡟⢠⣅⢴⠖⢦⡷⠂⠊⣳⠼⢁⣿⣯⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣂⠹⡧⠠⡍⠈⢃⠰⣦⠎⢷⠚⡏⢡⡴⢾⣇⣼⣣⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠉⣐⡙⡤⠘⡞⢸⡄⠈⠶⠚⡟⢠⡍⣼⢺⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡋⠠⠇⣰⠄⠙⡛⡓⡆⣘⢘⣽⡜⣅⣽⢫⣿⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣩⢲⣾⣤⣷⡞⡹⣅⣿⣏⡿⣾⡧⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡽⣇⣬⠵⣾⡿⡙⣧⣽⣯⣵⣿⣶⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡙⣞⣷⣾⣹⣿⢶⣯⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢣⣯⢖⠌⡀⠎⡼⢣⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⢼⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠤⠶⠖⠲⠦⠶⣼⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠋⠠⠆⠀⠘⠀⠀⣀⠴⠊⢸⠀⢝⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⢠⠀⠀⠤⠄⢠⠒⠊⠀⠀⢠⠃⢀⠈⠀⠙⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠄⢀⠀⠀⣠⠖⢡⠂⡀⠀⢀⢻⠐⠄⠀⢀⡀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠉⢀⠎⢀⡔⢁⠞⠀⢀⠆⠇⠀⠀⡀⠤⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠁⠀⡞⠁⢠⠎⢀⠎⠀⢀⠎⢠⠃⠄⠀⠁⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠠⢀⠴⡇⢀⠏⢀⠎⠀⢠⠊⢀⡜⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡸⢁⡇⠸⠀⡎⠀⡠⠃⡔⢹⠀⠈⠀⠀⠑⠃⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠟⣇⢀⡘⢀⠜⡡⢊⣠⠟⠀⠰⠄⡀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠾⢶⡉⢸⠀⠦⠀⣀⣥⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⠒⠛⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡠⠒⠀⡀⠂⠂⠐⠠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⡁⠀⠂⠤⠈⠉⡀⠀⠘⢡⠰⠆⠀⡬⢀⢀
⠀⠀⠀⣀⣈⣿⠐⠃⡄⠃⠀⢶⠉⢊⡁⠐⢀⠊⢀⡀⠸⠇⢐⠐⢂⡀
⠀⠀⠰⠲⠿⠂⠼⠁⠀⠂⠀⢄⠐⢈⡀⠀⠋⢠⠤⠀⣀⠁⠀⡖⠘⣁⣓⡄⠀⠀⠀⠀⢀⠀⠀⠀⠄⡀⠄⡠⡤⣀⡄
⠀⠐⠀⡤⠀⠃⣀⠈⠐⠓⠀⠀⠃⠈⠁⠉⠁⠀⠐⡗⠁⠴⢀⣰⠚⣩⣟⣃⢆⠀⡠⠀⠊⠠⡇⠘⠂⠘⠂⠓⣠⠀⠀⠗⣣⣀
⠀⢢⢠⣤⠞⣄⠈⢀⠀⡈⠐⠀⠠⠌⠀⣤⡟⠀⠘⠋⠀⢲⡝⠉⣰⢋⣯⡿⠈⠄⠐⢀⠋⠁⠀⠀⠁⢀⠂⠀⠖⠈⣁⠀⢠⡉⣰⠤⡀
⠀⠉⠈⠁⠀⠉⣀⠉⢁⠛⠀⠛⠀⠟⠀⡰⠆⣰⠷⠀⡾⢀⣼⡛⣿⠟⠁⢀⠉⠀⠀⠄⠀⢰⠀⠀⠀⠙⢡⠀⠛⣢⣈⣁⠆⢁⢀⣀⠣⢠
⢀⡀⠆⢠⣦⠀⢉⡀⠉⠓⢀⠲⠀⢠⣄⡑⠚⢛⡄⢠⡄⢀⢺⡿⠚⠁⠑⠀⠀⡠⠀⠀⠶⠀⠜⠁⠀⡷⠄⠁⠢⡌⠠⣄⣀⣛⠀⡀⠀⠠⢅
⠉⡤⢦⡚⠀⣧⡉⠟⠛⠃⡐⠔⠂⢠⡤⠉⣰⡍⡤⣀⣸⣟⡾⠆⡀⠀⠀⠀⠀⢁⠀⠲⡄⠴⡤⠶⠨⠀⣄⠴⠈⠵⢆⢈⠍⡙⠰⠉⢁⡴⢤⡀
⠘⢇⡆⠉⠰⠀⠧⢰⡦⢠⢋⣷⣀⠊⣴⡐⣈⣴⡟⢿⣵⡿⢀⠐⢙⠦⠠⡈⢠⡄⠐⠃⠴⣠⠄⠀⠚⠃⠰⠒⠲⠆⠲⡦⣠⠄⣠⠀⡜⡸⣼⡿⠖
⠀⠀⠽⡤⣞⡋⢟⠃⠀⠛⠛⠄⠘⠂⠉⠉⠁⠈⠀⠀⠀⠓⠲⠤⡉⠀⡀⢁⠈⠀⢈⠀⢶⠀⠁⢄⠰⠇⢀⣤⣀⠀⡖⠠⣴⢀⡈⠠⠀⡘⠡⢙⡀
⠀⠀⠙⡣⣼⣁⣈⠁⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠁⠋⠘⠂⡆⢚⠁⣨⣄⠲⣿⠹⢆⡀⠀⢶⠆⣤⠉⠱⣚⠃⢤⠀⡃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⡀⠇⢡⠀⠾⠁⢀⠘⡿⣬⠀⠀⣰⡄⠸⠱⠄⡆⠴⣶⠈⣧⢃⠠⠊⢐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠐⠒⠒⠈⠫⣿⣯⣅⡀⢯⣱⡚⣀⡉⣀⠛⢅⢰⣴⣋⠀⢶⠥⠴⠻⢀⠸⢆⣄⣎⠵⠁⡜
⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠈⠀⢈⢽⣫⡈⠋⢰⡜⣩⣄⣛⢡⡄⠴⠦⢀⡞⢄⣞⠓⡁⠃⡆⠁
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠈⠁⠀⠀⠀⠀⠀⠸⢺⡁⡔⠈⠿⠉⠉⡁⣆⣀⡸⠟⡠⢶⡷⣏⠛⠒⡃⠆⠁
⠐⠁⠀⠀⠀⢸⡄⡴⠁⠀⡀⠀⠀⠀⠀⢀⠀⠂⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⣷⡸⣷⡲⢿⠘⠋⠫⠺⠿⣥⠞⠃⢠⡹⠺⠀⠁
⠀⠀⠀⠀⠀⠈⠁⠀⡡⠈⠀⠀⢀⣄⣤⠕⡲⠯⠗⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠐⣿⡮⠾⠿⡍⣭⠙⠀⠀⠤⠄⠀⠒⠁⠈
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⢈⣠⡀⠁⠀⠀⠀⠀⠀⠈
⠀⠐⡒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⢠⠖
⠀⠀⠱⣬⢂⡰⢤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⢄⡄⢱⠊⠁
⠀⠀⠀⠈⠩⠅⢌⠡⠜⠆⡀⠂⢠⡔⡀⣀⠀⠧⠄⢀⢤⣼⡠⢋⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠯⣈⢣⡌⣣⠄⠵⢂⠊⡖⡱⠆⠐⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣡⣍⣿⣏⣅⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣠
⣿⣿⣏⣉⣩⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⢀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⡀⠢⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣼⢿⣚⠳⡀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠈⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣿⣽⡇⠖⠷⡀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠡⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⣿⡗⣙⠎⣘⢧⣄⡀⠀⢀⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠴⠤⠄⠠⠤⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⠰⠬⡄⣑⡱⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣽⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⡂⡑⠈⠔⡙⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡟⡆⠯⠉⠀⠀⢀⠀⠀⢛⣿⡄⠀⠀⠀⠀⠀⢀⣠⠶⠚⠉⠉⠀⠀⣀⣀⣀⠁⠙⠆
⠀⠀⠀⠀⠀⢠⣷⡗⠯⠀⠀⠄⠀⠀⠀⠀⠀⢡⡿⣿⡀⠀⠀⢀⡔⠋⠀⠀⢀⣤⣶⠾⠟⠛⢛⣿⣷⠀⠀⡂
⠀⠀⠀⠀⠐⡿⢦⠁⠠⠀⠀⠀⠐⠂⠀⢁⢀⢲⡛⢿⠇⠀⠀⣞⠀⠀⢀⣼⡟⠋⠁⠀⢀⠔⣺⣿⠟⠀⢰⠇
⠀⠀⠀⠀⣸⡵⣠⠀⠐⠀⠀⠠⡀⠐⡀⠡⠦⣜⣭⡏⠀⠀⠀⣿⠄⠐⢾⣿⣷⣤⣤⣶⣿⣾⠿⠃⠀⡀⠁
⠀⠀⠀⠀⢸⣟⣦⠃⡬⢀⡩⢩⠤⣨⣓⣿⣻⡾⠋⠀⠀⠀⠀⢻⣷⣄⠈⠻⠿⠿⠿⠟⠋⠁⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠛⢾⣷⣿⣮⣿⣿⣯⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠘⠻⣿⡶⠀⡀⠀⠀⠀⠀⣠⡶⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠶⠶⠚⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠒⠢⠤⠤⠤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠈⠂⠀⠀⠀⠀⠠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠂⠀⠀⠀⠀⠆⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⢀⠀⠀⠀⡀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠊⠀⠀⠀⠀⠀⡓⠀⠀⠀⠀⠂⠂⡀⠀⠀⠀⠀⠀⡎⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠘⡄⠀⠀⠀⠀⡄⠀⠀⠁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠠⡅⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⢦⣔⣐⣠⡴⢣⣀⠁⠀⠀⠀⡀⠀⡀⠀⠀⠀⡄⠀⠤
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠰⠐⠂⠀⠀⠀⠒⠀⠀⣠⠁⠀⠀⠀⠀⠙⠒⠱⠴⠊⠀⠀⠀⠀⠀⠀⠇⠀⠐
⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⢠⠀⠠⠀⠀⠀⠀⡜⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⠂⠀⠀⠀⠀⠀⠀⠠⡀⠱
⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠸⡂⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠂
⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠐⠒⠲⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠑⢔⣈⣀⡀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⢀⡎⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⠄⠀⠀⠀⡀⠂⢸⠄⠀⠀⠀⠀⠀⠀⠐⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠇⠠⠄⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠓⠉⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣁⣂⡤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣈⢀⠀⠐⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢦⣄⣄⠴⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⣉⣛⣉⣝⣙⣯⣏⣿⣫⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣤⣀
⠀⠀⠀⠀⡴⠉⠀⠈⣩⣌⡀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⡇⠀⠀⡎⠀⠀⢻⠀⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⣇⠀⠀⠃⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡼⢄⢠⢀⡀
⠀⠀⠀⠀⢺⠀⠀⠄⠀⠀⠁⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⡀⢤⣟⡅⠖⠚⢶⣍⠆
⠀⠀⠀⠀⠸⣄⠀⠐⢄⡠⠂⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠕⡄⣐⠆⠀⢂⠈⢡⣤
⠀⠀⠀⠀⠀⠀⠑⠢⠄⠤⠞⠁⠀⠀⠀⠀⠘⠂⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢆⠾⣏⣁⠀⣌⠡⠄⠰⣆⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢆⡰⢽⡬⠇⢌⡁⢂⣀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪⠍⠅⠊⠈⠛⠇⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣰⡏⠉⠈⡑⠊⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⠄⠦⠐⢄⣀⡤⠤⢀
⠀⠀⠀⢀⣲⣽⡧⠀⢨⠀⠀⠀⠸⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠠⠀⠀⠉⠙⠇⠀⠀⠁
⠀⠀⠀⢈⡝⠳⠉⣷⣀⡙⠒⠃⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⢀⡸⠋⠀⠀⠀⠀⡀⠀⠀⢄⠠
⠀⠀⠀⠀⠀⡐⠠⠈⡹⠯⠱⢶⣶⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⡏⠀⠀⠀⠀⠀⢀⠂⠘⠠⠎⡰
⠀⠀⠀⠀⠙⠦⠒⣠⡰⠔⣲⡳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣇⠀⢀⣀⠀⠀⢸⠛⡀⣜⠘
⠀⠀⠀⠀⠀⠀⠉⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠻⠤⠄⠘⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠄⠈⠀⢐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠂⠀⠀⠠⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠖⡫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠔⢀⠀⠀⡄⠈⠀⡀⠀⠁⡠⠀⠀⠠⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⣄⡐⠀⠀⠀⢀⠂⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠠⠄⠁⠀⠤⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢤⡃⣦⣤⡀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡟⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠆⠄⠁⠐⠀⢀⠀⢀⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⡦⠀⠉⠐⠀⠀⢁⠀⠀⠁⠁⠂⠄⠀⠀⠀⠀⠀⢀⠠⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣀⠁⠈⣀⠀⠉⠐⣧⠀⠀⡀⠀⢠⢀⠂⠀⠀⠀⠀⠄⠀⠠⠀⠈⠀⠀⠒⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠠⠔⠒⠈⠉⠒⠀⠀⠴⠀⠀⠀⠀⠩⢦⡄⠀⠀⠀⠀⠂⠁⠀⡄⡐⠈⠀⢀⠀⡀⠀⠀⢀⡄⠁
⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠠⠀⠀⠁⢀⡀⠀⢀⡀⠀⢀⣧⠻⢁⡀⠂⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⣰⢆⠂
⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⡠⠀⠁⠀⠠⠄⠀⠀⠀⢀⣣⢚⠋⢳⠡⠀⠐⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⡀⢬⠏
⠀⠀⠀⠀⢀⠀⢀⠀⠆⠀⠀⠀⠀⠠⠄⠀⢁⠀⠐⣫⢧⠉⠀⠈⢻⢂⣂⠀⡁⠀⠐⠀⠐⢀⢀⠠⠴⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠂⠀⠐⢀⠀⠀⣤⠬⠁⠀⠀⠀⠀⠀⠚⠈⠾⢌⣀⠰⠧⠈⠒⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠁⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣤⣄⢶⣴⣥⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣯⡏⣿⡻⡯⣿⡷⢴⠳⣬⢷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⣦⠧⠶⠶⢾⢆⡷⠃⡀⠰⣶⠑⡞⢱⢬⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡝⢷⠚⠖⠙⣖⢻⠞⠀⠀⠀⠰⡋⣏⢩⠛⡴⠟⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡱⠟⠘⠶⠙⡎⢩⠏⠀⠀⠀⠀⠀⠏⣈⡟⣹⣉⠲⡉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣞⢷⡋⡳⠚⣧⢘⠏⠀⠀⠀⠀⠀⠀⡧⣇⠈⣏⣼⢢⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡤⠏⢹⡖⠈⡻⠀⠀⠀⠀⠀⠀⠀⣇⢸⠗⣮⣰⠏⢹⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⣤⠛⣇⣴⡾⠃⠀⠀⠀⠀⠀⠀⠀⣅⠘⠚⣄⡰⢌⣻⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣉⣇⢱⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡛⢨⠐⣇⢸⣌⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣯⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠿⣈⢶⣫⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⢷⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣻⣿⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠲⢤⣀⣈⣀⣀⡠⢶⣿⣿⣽⠟⠁⠀⠀⢀⡏⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⡞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⢣⡏⡞⣢⢃⢡⡏⡰⠟⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣸⠂⠛⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠚⠉⡁⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠔⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠾⣷
⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣰⡿⠆
⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡆
⠀⠈⠀⠘⠂⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢹⣼⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⣮⣾⠁
⠀⠀⠃⠀⠀⠉⠣⡀⠀⠀⠀⠀⠈⣳⡶⠚⠟⠛⠳⠿⠤⣆⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⣦⣴⣷⡷⠟
⠀⠀⠈⠄⠀⠀⠀⠙⣷⣖⠀⠶⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠦⢤⡆⠀⠊⠀⠀⠐⣍⣴⣼⡶⠋⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠢⡀⠀⣴⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣗⣾⣷⣿⡾⠁⠀⡠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠀⠀⠀⠀⠀⠈⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⠟⠉⠀⠀⠀⠀⠀⠉⠉⠓⠴⣎⢀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⢀⡉
⠀⠀⠀⠀⢠⣟⡴⠀⠸⠂⠀⠀⢀⡀⠀⠀⠀⠀⢠⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣖⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠖⡶⠚⠛
⠀⠀⠀⠀⢸⣿⢹⡀⠀⠄⠀⠄⠀⠀⢀⠀⠁⠈⣾⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡏⠀⠀⣠⠀⠀⢠⡤⠀⡰⠃⣼⣵
⠀⠀⠀⠀⠀⢿⣏⠓⡄⠘⠷⡀⠀⠀⠀⠀⠀⢰⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠤⠊⠁⣀⠐⠀⠀⠰⢳⣿⡼⠃
⠀⠀⠀⠀⠀⠈⢻⣦⠞⠀⠀⠀⢀⣀⠀⠀⠀⢘⣿⡆⠀⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡤⠀⠀⠀⠷⡆⠠⣺⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⡛⢦⡀⠉⠀⠲⠄⠻⣿⣿⠁⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⡦⣀⠤⣚⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣯⣉⣓⣤⠤⣶⠾⣿⣿⢀⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠿⠶⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠛⠋⠻⠦⣴⡀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢾⣉⣡⡒⢀⣤⣀⣀⣀⣀⣤⣾⠟⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣽⣿⣵⣿⣿⣿⣽⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠺⣰⠀⡀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠠⡀⢹⡔⠀⠀⠀⡇⠀⠀⠀⠀⣀⣀⠤⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀⠀⠀⠄⠀⠀⠀⠀⠐⡎⠀⡬⠀⠀⣀⡠⠔⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠂⢩⠁⠀⠀⠀⣈⠉⠙⢧⡀⠀⠈⠢⣀⡃⠔⠁⡠⠊⠁⠀⡀⠀⢠⠴⠁⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠁⠀⠀⠙⠻⠀⠐⢄⣸⠷⠦⠠⠮⠤⣤⠊⠀⠄⣸⠀⢇⣰⡁⠄⠀⠀⡞
⠀⠀⠀⠀⠀⢀⡎⠠⠄⠀⠀⣀⠀⠠⠄⠀⠀⠀⡠⠋⠀⠀⠀⠈⠑⠂⠀⠉⠢⢄⠈⢡⡞⣠⠐⠀⠀⢰⠁
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢎⡀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⣏⢀⠈⠂⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠘⡀⠀⡰⠁
⠀⠀⠀⠀⠀⣿⠈⠃⠀⠀⡀⠀⠀⠀⠒⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠠⠀⢳⠊
⠀⠀⠀⠀⠀⠙⣦⠀⡀⠀⠉⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠂⠀⠀⠠⠀⢺
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠠⠀⠀⠀⠀⠒⠀⠘⡀⠀⠀⠀⠀⣀⠤⠴⠊⠁⠀⠀⠁⣀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣌⣉⣂⣀⣐⣶⣟⡁⠁⠁⠈⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠻⣄⡠⠄⠀⠀⠀⠠⠔⠀⠀⢈⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⠥⠶⠶⠦⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠟⠙⠀⠁⠋⠊⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣀⡄⠀⢸⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠉⣡⡜⠳⣄⣠⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⡿⠀⠀⠈⣾⡀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠃⠀⠀⣸⠁⣶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⢠⣇⣠⢿⡇⣠⠖⠈⠐⠚⠻⡗⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⠀⠈⠀⠀⠃⣸⣇⠀⠀⠒⠄⠀⠀⠈⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣺⣅⠀⠀⠀⢸⣾⡏⢹⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⢹⡍⢧⡄⠀⠸⣿⠁⢸⣷⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠹⡀⠘⣿⣮⣟⣤⣼⣿⡂⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⠿⠒⠈⠁⠐⢋⣙⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠘⢿⣦⠀⢸⠀⠀⠀⣦⢀⠀⡠⠀⠤⣦⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠠⢄⣼⣿⠀⢸⠀⠀⠀⡇⠌⠓⠠⡀⠀⠐⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡆⣤⣼⣿⡠⢀⣀⠀⠄⢠⣾⣿⡟⠀⢲⡇⠀⡼⢠⡀⠀⠀⠀⠀⠀⣼⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣷⣿⣾⣿⡏⠠⠒⠛⠛⠲⠧⡘⣧⠀⠀⠀⣠⣂⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠈⠉⢿⡟⠀⠀⠀⠀⠀⠀⠀⣸⡼⢿⠿⢿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⢀⡀⣿⡁⠀⠀⢠⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠙⣆⠀⠀⠀⢀⣾⣷⡀⠀⠀⠀⠀⢈⠀⣴⣿⡇⠀⠀⠀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢷⣢⣴⣾⣿⡿⣿⣞⣶⣦⣤⣴⣾⣿⣿⡃⠀⢀⢀⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣹⡕⠀⠉⠿⣷⣿⣿⣿⣿⣿⣿⣖⣻⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⣀⢂⢾⣿⡿⠛⠛⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣄⢀⡀⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿⣛⣿⣿⣿⣿⣿⣿⡟⣯⣻⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣽⡿⢣⣾⣯⡟⡽⢻⢟⣝⢫⠼⣿⡿⢿⣿⠿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣟⢛⡰⢿⣿⢿⡾⢁⣇⢿⣫⢞⣾⢣⣶⡞⢡⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣻⣵⣿⣿⣿⣿⣷⣿⣷⣿⣿⣾⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣙⣋⣈⣉⣹⣝⣩⣟⣙⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠈⠀⠀⠂⠀⠐⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠹⠿⠿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⢨⣇⠤⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⣾⡄⠀⠀⠀⠀⠀⠁⠘⠋⠰⠃⣀
⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠁⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⣸⣆⣴⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⡿⠀⢲⠈⠹
⠀⠀⠀⠀⠀⠀⠉⠀⢠⡾⣿⡿⢷⠌⢀⣼⠁⠀⠀⠀⢸⢠⣼⣿⣿⡿⠟⠛⢻⠿⡁⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⢧⣾⣶⣬⣿⢦⠀⣀⣤⣿⢸⣿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡇⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠴⠀⣴⣿⡿⠟⣻⣴⠂⠀⠉⠁⠟⠛⣾⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠻⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠉⡀⠠⠿⠶⠛⠿⣿⣿⣳⠆⣾⡆⢠⠀⠈⠁⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⢂⡀⢾⣧⣤⣤⡟⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⣤⣀⡈⡁⠀⢀⣿⡃⡀⢀⡀⠀⠀⢠⢇⣸⣤⣰⣶⣦⡿⠘⠿⢿⡒⠀⠉⠉⠀⢠⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⡭⠈⣴⣷⠖⢈⡛⠻⠾⢷⡆⠞⠋⠙⠟⠉⠉⠩⠉⠁⣄⢼⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠉⠀⠭⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠰⠋⠀⣰⣶⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣾⣧⣂⠄⡀⠀⠁⣀⠀⢾⡆⢸⣿⢷⢽⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⢿⣖⠴⠆⣤⡹⡏⠀⠣⣸⠿⠍⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⢊⠱⡟⠠⣤⣵⡇⣼⣠⠜⡓⠚⠁⣂⠡⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠟⠛⣬⢙⢏⠃⡄⣽⣿⢰⡟⡡⢆⣠⣀⠺⠙⠉
⠀⠀⠀⠀⠀⠀⣤⣠⣸⡋⠴⠶⢦⣷⣦⣳⢲⡈⢿⣿⣾⣣⡖⠁⠉⢀⠀⡠⠦⠤⡤
⠀⠀⠀⠀⢤⣷⠀⢿⣧⣠⠂⠬⠭⢟⡋⡙⢿⡇⣴⢮⡱⣏⣠⠞⠡⡽⠋
⠀⠀⢀⣶⣦⣌⣷⣿⡿⡿⡦⠶⠀⢻⡏⠊⠘⢿⣿⣿⡷⠸⢟⣊⠔
⠀⠀⠟⠋⣻⡷⣾⣯⣽⠟⠀⠄⠲⠄⢣⢑⣴⣼⢉⣿⡧⣟⢀⡺⢮⣁⣀⠄
⠀⠀⠀⠀⢶⡿⠿⢿⡿⡴⠒⠀⠀⠀⠀⢹⠟⢿⣸⣦⠙⠚⢋⣠⠆⠘⠁
⠀⠀⠀⠀⢲⠿⣶⢫⣿⣦⠃⠀⠀⠀⢈⢇⣿⣸⣿⢻⣇⣣⡹⣻⡂⣠⣆
⠀⠀⠀⠘⣾⣸⣿⣼⣿⢻⣋⠁⠀⠀⠈⠣⣸⣷⣯⠀⢻⡿⣷⣯⣎⠙⠃
⠀⠀⠀⣴⡿⡿⣷⣽⣿⣿⣯⢀⣀⣠⡞⠩⡷⢿⣿⡕⣾⣿⠟⢏⣽⠇
⠀⢠⡾⠿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠈⠉⢛⣿⣶⣿⣿⢸⣿⠘⠌⣽⣀⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢴⣍⡏⣿⣿⡿⣻⡆⠘⣸⠀⢿⡏⠡⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⢲⠇⣿⡟⣽⣤⢸⢱⡆⠁⣷⣙⣧⡄⣀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⡾⡖⡿⡃⢹⢿⠄⢾⡇⢜⢹⣿⢿⣷⣿⣼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠈⣸⡿⣶⣧⡿⣈⢀⣻⣼⡏⡟⡞⣿⣿⢟⡍⢿⢿⡀
⠀⠀⠀⢀⢄⣀⡀⢀⠤⣤⣄⡴⣿⣇⣿⣿⢱⣿⣦⣘⢿⣷⣿⣇⣿⡟⣾⣷⣾⣾⡧
⠀⠀⠀⠀⢾⡎⠄⡴⢂⡘⠳⢿⢟⠻⡳⣷⣿⢸⣿⣿⢨⢟⡿⢿⣿⣿⣿⣿⣿⣿⠷⠓⠒⠶⢶⣶⢷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄
⠀⠀⠀⠀⠸⣿⡞⢰⠏⠀⠀⣸⢨⡇⣰⢸⣏⠙⢿⣿⣾⡾⣬⡘⣿⢻⠹⣿⣿⠋⢠⠄⢀⠆⠀⠈⡏⢃⠉⠙⡆⠀⠀⠀⠀⠀⡀⠀⡔
⠀⠀⠀⠐⠀⠉⢅⣽⠀⣰⡾⠟⠚⠛⢳⠏⠱⣦⣴⣆⢛⣿⢻⣿⣝⣷⣿⣿⣿⡄⣼⢀⡆⠀⠀⣼⠃⣼⢸⣧⣿⢀⣶⣤⣴⡯⠈⣶⣼
⠀⠀⠀⠀⢀⣴⡶⣿⠗⢯⡶⠛⠃⣄⠁⢆⠠⠿⠛⠽⡟⠟⠢⠹⣿⣻⠹⢏⡭⡝⠛⠁⣥⡾⠿⢉⣾⣿⣿⣿⣋⢙⣓⠑⢤⢻⡇
⠀⠀⠀⠀⠀⠛⠲⠁⡄⢼⠀⡄⠀⠈⣧⣸⣿⡿⠓⠲⠲⠤⡆⢤⣤⣁⢚⡻⠆⠀⠉⠁⠻⡂⣬⠙⣽⣝⣉⣝⠛⠓⠛⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢆⠷⣼⣦⡘⢶⡶⠿⣦⢸⡿⣧⡴⠞⠓⠛⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠛⠙⠀⠘⠛⠞⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⢀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⡀⠀⢀⣿⣄⣀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣐⠶⠤⠤⡀⠀⠈⠁⠐⠄⠀⡀
⠛⠓⠣⠼⢀⣹⣿⡆⠀⠀⣿⣻⡧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⠄⠈⣏⠉⠉⠉⠙⠓⠀⠀⣴⠀⠀⡄⠐⠄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠀⠉⠙⠓⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⠀⠨⠀⠀⢤⡀⠙⢮⣷⣿⠀⠀⣿⠀⣆
⠀⢀⡀⠠⠄⡄⠀⠀⠀⢄⠀⠀⠄⢐⠠⠀⡀⠀⠀⠉⠉⠋⠿⣷⣶⣤⣄⡀⠀⢀⠀⠀⠀⠀⠄⠀⠀⣷⡀⠀⢻⣦⠈⢿⡇⠀⣸⣿⠀⣿⠐⢒⠒⠚⠓
⢀⠀⡀⠄⠀⠄⠀⠀⠀⢀⡉⠒⢄⡀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⣷⢾⡇⠀⠀⢸⡂⠀⠀⢹⣷⠀⠈⣿⡇⢸⡏⢠⣿⡏⣸⡏⠀⠀⠂⢁
⠡⠐⠂⡂⠂⠅⠏⣠⡒⢆⠀⢀⠄⠉⠢⣄⠀⠈⠀⣀⣠⠤⠶⠒⠛⠉⠉⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⠘⣿⡇⠀⢹⣿⢸⠟⠋⠙⠲⠟⣀⣠⡀⠀⠈
⠁⠐⠠⢅⠁⢎⠐⠢⠁⠬⠡⠃⢴⣃⣤⠼⠗⠛⠉⠁⠐⠀⡀⠒⠀⡀⠀⠠⣴⣆⠘⡄⠀⠀⢻⠀⠀⠀⢾⣧⠰⠈⠉⢻⡆⠀⠀⠈⠺⠿⠋⠀⠀⠠
⠸⢁⡇⠀⠐⠂⡠⠚⣀⣤⠷⠚⠋⠡⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⢴⡁⠐⠖⠒⠶⢤⣌⣦⡀⠈⠦⠀⠀⠺⣿⣥⠄⠀⠀⠠⠀⠀⠤⠀⡀⠀⠈⠀⣀⠐
⢤⢉⠹⢐⣪⡴⠞⠋⠁⠠⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠁⠐⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠀⠀⠉⠅⠀⠂⠠⠖⠀⠀⠀⠀⠋⠁⠀⠀⠀⠁
⣠⡵⠞⠋⠁⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⡀⠀⠹⠶⠷⠿⠶⠄⠀⢀⠀⠀⠀⠁⠀⠤⠀⠀⢀⡔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠹⣿⣿⣷⣼⣾⣼⣾⣇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠀⢀⡀⠱⠜⣾⣿⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡇⢀⠀⠀⠙⠪⢢⣎⣿⣿⣿⣿⣿⣿⣿⣏⠵⠓
⠀⠀⠀⠀⠀⠀⢤⣿⣩⣴⣷⣿⡷⢄⣿⠅⣀⠇⢽⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⢘⠿⣿⣿⣿⣿⣤⣤⡁⢠⣐⢄⣸⣿⣿⣽⣽⣯⡇⠐⣄⠉⠀⣠⡄⢐⡤⠛⠛⠁⡂
⠀⠀⠀⠀⠀⠀⠄⠓⠿⢻⢯⣉⣹⠟⠿⡟⢻⢾⣿⣿⣿⣿⣿⣿⣄⢀⣈⣠⠄⣈⠉⠁⠀⣱⣸⡔⡇
⠀⠀⠀⠀⠀⠰⣤⣤⣀⣀⣾⣿⣿⣿⣄⣉⠘⣽⣿⣿⣿⣾⢻⣿⣿⡉⣍⠉⠉⡉⢩⣾⣺⣴⢿⣻⣶⣷⡀
⠀⠀⠀⠀⠀⢢⣸⣿⣿⡿⣿⣿⣿⡌⣿⣿⣴⣿⣿⣽⣿⣿⣿⣿⣿⣧⢀⣿⣿⣷⣷⣿⢿⣻⣿⣟⣿⢽⣿
⠀⠀⠀⠀⡀⠘⣽⣿⣿⣿⣿⣿⡏⠙⢿⣿⣽⣿⡟⡛⢿⠿⠛⠟⠛⠛⠐⠿⣿⣿⣿⣿⣯⢻⣞⣿⣾⣿⢿⣃⡄
⠀⠀⠀⣌⢱⣼⣾⣿⣿⣿⠿⡿⠛⡠⠿⠿⠿⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠙⠁
⠀⠀⠀⠉⠀⠉⠉⠉⠁

⡂⠙⠿⠧⠤⠀⠤⢠⣀⢹⠇⢀⠡⠀⡈⠑⠀⠐⠀⢀⠈⠱⣧⠀⠄
⠀⠔⢤⠀⠜⠳⡄⠈⣿⠢⠂⠈⠑⠁⣄⠀⠀⠀⠀⠉⢄⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢸⣧⣨⢤⠐⠊⠙⣆⢫⡴⢂⡀⠀⡀⠈⢿⡇⠀⠀⠀⠀⠠
⠨⠋⠀⢸⡇⡐⢾⡟⠀⠀⠀⡉⠢⣌⡐⠊⠁
⠀⠀⠀⠘⠃⠘⠀⠈⠀⠀⠀⠀⠀⣿⡇⠂⠀⠀⠀⠌
⠀⠐⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⠠⣠⡾⠿⡚⢿⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⡄⢴⡆⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⠀⠘⡏⠀⢰⣿⠂⠀⣛⣿⠀⢀⣿
⠀⢸⡇⣤⡄⢽⠀⠀⣾⡿⢿⣇⣬⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⢐⠀⠀⠚⡟⠒⡟⢫⡟⣤⠊⣏⡄⢀⣀⣀
⠀⠀⠀⠘⠃⠀⠀⠀⠉⠁⠈⠁⠀⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠁⠀⠁⢘⣿⣿⣿⣧⠈⠉⠉⠉
⡒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⢄⡢⣀⢄⡠⣀⣁⣰⠦⠴⠒⠛⠋⡸⠀⠀⠀⠀⠁⠀⡇⢸⡇⣿⢸
⠭⣓⡪⢭⣒⠦⢄⡀⠀⠀⠀⠀⠀⠀⢈⣳⡽⠶⠓⠋⠉⠀⠀⠀⠀⠠⠘⠁⢡⡀⠀⠀⠀⠀⠀⡇⢸⢠⡇⣿⠄⡄⡠
⠭⣒⡫⢵⣒⠭⣓⡪⠅⣂⣠⠴⠒⠋⠉⠀⠀⠀⠀⠒⢷⣆⠀⠀⠠⡤⠀⠁⠠⡿⠀⠀⠀⠀⠀⠁⣉⣿⠋⠙⣘⠟⠣⢀
⣯⢕⣚⡭⢖⣫⠵⠒⠋⠅⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠋⢉⠿⡀⢠⡿⢡⡀
⢞⣫⠵⠚⠉⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠐⠞⠃⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠃
⣿⣷⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶

⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠹⣿⡇
⠀⠟⠋⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡙⢿⡀⠠⣂⠀⡀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠵⠼⣍⠁⡇
⠀⢇⡵⠆⠉⢀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡉⠳⠄⡖⣠⠖⠚⠁⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠦⢬⣎⣳⡇
⠀⣯⠴⣖⠋⠉⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠑⠓⢤⡄⣿⣡⠶⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠊⠈⢹⡇
⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣼⣿⣿⣿⡇⣿⣿⣷⣦⣄⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⠀⢁⣀⣀⣠⣤⣤⠀⣤⣤⣴⣤⣤⣈⣵⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣸⡇
⠀⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⣾⣿⠀⣿⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐⠀⠀⠀⠀⠀⠀⣀⣀⣠⣥⣤⣴⣶⣾⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢣⢳⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣅⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⢢⠣⣀⠿⡂⠀⠀⠄⡰⠀⠀⡀⠎⠀⠀⠁⠀⠀⠀⠚⡄⢸⢀⠆
⠀⠀⠀⠀⠀⠀⠐⢢⡓⠏⠒⠀⣈⠁⠟⠉⠁⠉⠢⠀⠀⣀⠆⠐⠐⠂⠕⠲⢎⠑⠤
⠀⠀⠀⠀⠀⢐⠤⠒⠒⠒⡲⣤⢂⣿⣀⠀⠀⠀⠀⡁⢀⠁⠀⠀⠀⠀⢸⣀⢢⠄⣠⢣⡄
⠀⠀⠀⠀⡔⠁⠀⠊⠀⢀⠀⠉⠉⠉⠀⢌⢑⡴⠉⠀⡠⠛⠉⠀⠑⣎⠁⠀⠈⠺⢉⡔⠉⠧⢲⢀⠀⠀⠀⠀⠀⠀⡀⡀⠤⢀⠄
⠀⠀⠀⠀⠁⠌⠀⠀⢀⠁⠀⠀⠀⠁⠀⢰⠁⠀⢠⠈⠐⠆⠀⠀⠁⣀⡍⢂⡠⠊⠁⠹⢄⠤⣜⣉⠠⠤⢐⡀⠨⠅⠒⢀⣉⠀⠀⡀
⠀⠀⠀⢀⣦⡀⠀⢀⣨⢀⠀⠀⣀⣠⠀⣀⣦⡀⠀⠀⢠⣴⢀⣩⣬⡴⢃⣨⡅⠀⢠⠇⣊⠥⠴⢖⣚⢊⡀⠨⠭⠀⠁⠐⠒⠀⠉
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠠⠄⠀⠲⡖⠀⠈⠁
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠠⠄⠈⠡⠤⠀⠄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡰
⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠀⠁⠐⠒⠒⠘⠋⠉⠁⠒⡚
⠀⠀⠀⠀⠀⠀⢀⡾⢻⣍⠹⣇⠀⢀⠀⣀⠀⠠⠤⠠⠀⠀⠒⠂⠀⠀⠀⢩⢸
⠀⠀⠀⠀⠀⠀⠘⣯⡈⡛⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢰⣦⣄⠀⣶⣴⣆⣰⣷⠀⣤⣾⡆⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⢿⣷⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⠁⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿⠿⣿⣿⣿⣿⡿⣿⢿⣻⡟⡯⣿⣿⣛⣿⣿⣻⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣻⣿⠿⡿⣿⡻⢟⡟⣪⣿⣿⣿⣿⣾⣟⣇⣷⣟⣶⣾⢾⣿⡿⢻⣿⣯⠿⣾⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠿⠿⠛⠋⠋⠙⠳⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣟⣯⠵⠛⠙⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⣽⣶⣔⡦⢴⣶⣦⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣷⣦⠔⠒⢶⠖⣍⠉⠙⢤⠀⢜⣿⣿⣌⠟⠛⠻⣿⣿⣿⣿⣿⡿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢹⡏⠀⠀⠀⢺⣿⡒⠋⠊⠀⠙⠋⣵⠉⠀⠀⢸⣿⡇⡄⢀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡦⠄⠀⣈⢣⠀⠀⠀⣿⣿⠃⠀⣀⣤⣿⡇⣿⡇⠀⠀⣸⣿⠇⢻⣿⣿⣿⠿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⡇⠀⠧⠀⠁⠛⠉⠙⡍⠉⠉⢩⠉⠉⣹⡟⠁⣴⡆⠈⡧⢸⣸⣿⣿⠁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣖⠚⠀⠀⠀⠀⠀⠇⠀⠀⠼⠀⣠⣿⣷⣶⣿⣷⣾⠻⢉⠸⠿⠯⠀⠚⠋⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠷⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣫⣉⠛⢛⡟⠛⠛⠛⠤⠀⣀⠀⠀⠈⣧⠀⠀⠻⣦⠘⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡄⠀⠀⠀⠀⣏⠀⠀⡿⠋⠉⠀⠀⠈⠳⡐⠀⠀⠀⠀⣈⢁⠀⠀⢼⣧⠀⠀⢻⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠙⣦⡀⠈⢷⡗⠀⢸⣿⡆⠀⠘⣿⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣂⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠄⠀⠀⠀⣿⡄⠀⠘⣿⣆⠈⣿⡄⠸⣿⣷⠀⠀⣿⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠛⠀⠀⠀⠀⠒⢿⠀⠀⠀⢀⡶⠀⠀⠀⢸⣿⡀⠀⢻⣿⡀⢸⡇⠐⣿⣿⠀⠀⣿⣿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡶⠤⠀⢀⠀⠀⠀⠸⡄⠀⠀⠈⣧⠀⠀⠀⠸⣿⡇⠀⠸⣿⡇⢸⠃⠀⢸⣿⠀⠀⣿⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⡀⠀⠀⢻⠀⠀⠀⠀⣽⡇⠀⠀⣿⠇⡜⠀⠀⢸⡟⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⣇⠀⠀⠀⢸⡇⠀⠀⠿⠋⠒⠒⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠘⠓⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡤
⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀⠀⠄⣁⢌⡠⡀⢸⠀⡀⢅⡤⠀⠞⠠⠂⡠⡸⡮⢁⠀⠀⡀⢂⣤⡄
⠀⠀⠈⠁⠘⠛⠙⠲⡾⠷⣮⢾⣀⣀⡧⠙⠚⠱⢿⣾⢀⠀⠀⠊⠛⠁⠀⠀⠀⠀⠉⠚⠐⠉⠀⠘⠋⠉⠙⣯⣦⣆
⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣤⣷⣀⡀⠀⠸⣿⡇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠌
⠀⠀⠀⠈⠙⠛⠛⠂⠀⠀⠀⣐⣿⣿⣿⣿⣕⣀⠀⠈⡧⠀⠀⠀⠆⠀⠀⠀⠀⠈⢂⠐⠀⡀⠀⠀⠐⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⢻⣯⣿⣖⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⡏⡰⠈⠠⠀⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡯⠄⠇⠄⠀⠀⠀⠀⠀⠀⠘⠀⣾⠀⡄⢠⡤
⠀⠀⠀⠀⢀⢄⠀⠀⠀⠒⣿⣿⣿⣿⣿⣻⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠐⠢⡇⠀⡇⠠⢀⠌⠒⠀⠀⠀⠀⠀⢀
⠀⣴⣖⣤⣿⡿⠁⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠘⠀⠀⠀⠀⢄⠀⠈⢆⣇⡜⠤⠀⠠⠀⠀⠀⠈⠚⠁
⠀⠉⠉⠉⢻⣿⡗⠀⠐⣼⣻⣿⣿⣿⣿⣯⢋⡽⢻⡗⢀⣈⠀⠀⠀⠀⠀⢹⠀⠀⡏⢀⠀⡴⠋
⠀⠀⠀⠀⠀⠉⠰⡄⢙⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⢺⠀⠀⠀⠀⠁⠀⠳⠐⡇⠈⡠⠀⠀⠄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣭⣿⣿⣿⣿⠛⠹⢿⣿⣟⣦⠖⠈⠀⠀⠀⠈⠂⣰⠀⢰⡇⠸⠁⣸⠟⠉⠓
⠀⠀⢀⣠⠄⡀⠀⠀⢹⣿⢿⣿⣿⡿⡼⢂⣿⣿⣿⣷⡄⢀⡄⢀⠀⠀⡀⢈⠡⡈⣷⠗⣈⠀⢰⠆⠁⠀⠀⠀⠁
⢠⠼⠠⣴⡿⠃⠀⠀⠉⢺⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠁⢸⠃⠀⠀⠀⠀⠀⠄⠘⡇⢰⡀⠴⠡⠈⠁
⠀⠀⠀⠉⢺⣅⠐⡀⢠⢿⣿⣿⣿⣿⣹⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⢀⠀⠘⢆⣧⠌⠀⢄⢀⡀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠘⣿⠟⠀⢠⢿⣿⣿⡿⢻⡃⢿⣿⣿⠇⡠⠃⠠⠀⢴⡄⠀⠨⢦⠁⠘⣿⠀⢀⠴⠈⠀⠀⠀⠘⠙⠀⠠⠆
⠀⡐⠀⠀⠄⠀⠀⠀⠀⠊⠹⠛⠳⣼⣆⠔⠙⠛⣠⣴⣗⠐⠀⠀⠁⠀⠀⠀⠑⢤⣏⡴⢋⠐⣆⣀⣀⣀⣀
⢀⣷⣶⣦⠶⣿⡏⠀⠀⣠⣶⣀⠆⢹⡇⣤⡼⠛⠛⠉⠉⢛⡀⣠⣤⣄⣠⡾⣁⠸⣏⣰⡵⠾⠟⠋⠉⠙⠛⠶⠾⠷
⢨⣽⣵⣭⣭⣾⣧⠶⠾⠛⡁⠙⣻⣸⡏⣁⣴⣿⣄⣻⣶⣾⣽⡿⠿⠟⠋⠙⢳⠐⣿⠍⣀⣼⣷⣦⣤⣤⡀⠙⢶⣤⡄
⠈⠀⠚⠉⢉⣡⣤⡶⠋⡴⢀⡀⠈⢹⡷⣿⣶⣷⣿⣾⣶⣏⢀⣤⠖⢡⠦⠤⠈⠑⣿⣠⣤⢠⣤⣤⣤⣤⡁⢈⣀⣉⣙
⠀⣠⡄⠳⠿⠛⠋⠀⠆⠀⠸⣿⣿⣼⣇⣬⣉⠻⣿⣿⣿⡏⠛⠉⢴⠋⠀⢀⡌⡣⣿⢈⣉⡛⣷⣿⣿⣿⢿⠿⡛⠛⠛
⢀⣿⠆⠶⠦⠖⠀⣿⣯⡷⠈⠉⡉⢹⡏⢛⠛⠺⠿⢍⠀⢀⠠⠤⠀⠒⠒⠚⠛⠓⣿⠘⠛⠻⠿⠿⠾⢭⡅⢀⣿⣄
⢠⣴⣴⣤⣤⣤⠼⢴⣹⡶⠒⠛⠋⢸⡟⠛⠛⠛⠛⠓⠀⢠⢀⣴⣶⡿⠿⠶⠷⠀⣿⠶⠶⠾⠷⠲⠶⠦⠄⠸⣦⣿⡀
⠘⠛⣉⣭⠥⠀⠀⣦⢹⡇⠀⠀⠀⣾⡇⠀⠲⠀⠀⠀⠀⣾⠀⢉⠐⠀⢀⣠⣴⣾⣿⣶⣦⣄⠀⠀⠀⠀⠀⢸⣎⣿
⠀⠐⠄⠂⠀⠀⠀⣼⣿⠀⠀⠀⣰⣿⣧⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⣸⢫⡏
⠀⠀⠂⠀⠀⠀⢀⠟⡿⠀⠀⠀⣿⣿⠿⠧⠀⠀⠀⠀⠀⠈⡆⠶⠀⠙⠿⢿⠿⣿⠿⠟⠿⠟⠿⠄⠐⠒⢠⠏⡼⠋
⠀⠀⠀⠀⠀⣰⣯⡾⠀⠀⠀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠄⠀⣠⡾⠃⠀⠀⠠⠀⠀⠀⠀⢠⣿⣼⠅
⠀⠀⠀⠀⢰⣿⡟⠁⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣰⠟⠀⠀⠈⠀⠁⠀⠈⠀⢁⣾⡿⠁
⠀⠀⠊⠀⠈⠉⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⣴⣿⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣐⣾⣷⡆⢀⠀⠀⠀⠖⢙⡀⠀⠈⠃⠁⠀⡴⠶⠀⠀⠀⢰⠶⠶⣤⠀⣀
⠀⠀⠀⠻⠿⠛⠟⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⢀⣬⣿⣿⣷⣢⡔⠂⠀⠀⣿⣾⡞⢧⡄⠀⣄⠙⠆⠀⠀⠀⠈⢁⡄⠉⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢠⣚⢄⣹⡇⠸⢄⠀⠀⠀⠀⠀⠀⠀⠴⠇⣰⣋⠀⠀⠀⠀⠀⣿⠋⠀⠰⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠀⠀⠀⠀⢺⣹⢺⡛⣇⡐⢘⣤⡄⠀⠀⠀⢰⡕⠐⢲⠀⠹⠇⠀⠀⠀⠀⠀⠀⣰⠂⡌⠛⠁
⠀⠀⠀⠈⣛⡦⣀⣤⣄⠙⢿⠛⠙⠀⠀⠀⠀⠈⢕⢺⢯⡝⢩⣽⣿⡃⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⢀⠀⠀⠀⣨⣶⠉⠆
⠀⠀⠀⠹⣿⣷⢾⣿⡾⠀⠀⠀⠀⠀⢠⡄⠀⠀⣟⡻⢶⣿⣿⠋⠙⠁⠀⠀⣤⡄⠀⠀⠀⠙⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢸⣿⢾⡋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢫⣼⣿⠉⠛⠀⠀⠀⣠⡶⠿⣷⣶⣄⠀⠀⠀⠀⠤⠀⢰⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠙⠛⠁⠀⢺⣿⢻⠀⠀⠀⠀⠀⠀⠀⠔⢿⠆⠀⠀⠀⠀⣷⣷⠾⣾⣿⣿⠀⠀⠀⠘⠁⣆⣿⠀⠀⠀⠀⠐⠾⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⣧⣿⣿⡿⠟⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠲⣴⣿⣟⡷
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠈⣩⡟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠰⠃
⠀⠀⢠⣿⣻⣿⣿⣿⡆⠀⠀⠀⣰⢾⣿⣧⡀⠀⠰⠟⠀⠛⠀⠀⠀⠀⠀⢀⡤⣤⡀⠉⠇⠀⠀⠀⠀⠋⠀⠀⡀
⠀⠀⠘⠿⢟⢿⣿⣿⠇⠀⠀⠀⡉⠀⠈⠙⢻⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⣬⡾⣿⠀⢠⣄⠀⠀⠀⠘⠻⠿⠐⠁⠀⠀⣠⣴⡆
⠀⠀⠀⠀⠛⠻⠛⠋⠀⠀⠀⠸⡿⣄⣀⣤⣼⠇⠀⠀⢀⣠⠐⣀⠀⠀⠀⠻⠅⣠⢸⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⢄⠀⠀⠀⡀⠂⣀⠈⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⣲⣀⠙⠲⠍⠀⠈⠀⠠⡴⡎⢠⠜⠉⠢⠠⡒⢠⠖⠂⠠⠄⢀⡄
⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠰⠂⠚⢀⢀⠐⠀⢄⡄⠀⠀⠀⠀⠀⠀⠂⠞⠁⠈⠀⢠⣞⣅⢰⡚⠐⡠⠄⠉⠁⠉
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣔⠀⠀⡘⠉⠀⠀⠀⢑⣀⠀⠀⠈⠂⠀⠀⢂⣠⠔⠚⠀⠉⠂⣀⡁⠮⠗⢚⢦⣈⣻⠔⠾⢁⡀
⠀⠀⠀⠈⠃⠀⠂⠀⠀⡀⢂⠀⢈⠵⠀⢠⣴⣞⠹⣯⠰⠁⠀⠀⠀⠀⠙⠁⠀⠐⣈⡼⠗⢨⣈⠉⢉⡜⢍⣣⣨⠖⣚⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠨⠲⠤⢿⡿⣿⣾⠉⠁⠀⠀⠀⠀⠀⠀⠆⠊⠁⢦⡴⣰⣛⡓⠨⢷⡾⠟⠛⢧⡑⣍⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⣺⡀⠀⠀⠠⠀⠀⡁⠀⠀⠀⠄⠀⠀⠀⠀⡦⠖⠉⠉⡓⣀⠀⢀⠜⠛⠟⠘⠋⣋⠩⠓⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠠⢔⠠⠐⠄⠀⠀⠙⢄⣠⡤⠐⠀⠀⠀⠀⠀⡀⠆⠋⠀⠈⠉⠑⢂⣄⠘⠒⠓⠂⠀⠤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⢳⣆⠈⠒⢀⣄⡠⢻⣯⣹⣆⡈⠀⢀⠢⢠⠀⠀⠀⠀⠀⠀⠶⠏⠀⠁⠀⠈⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠨⠷⠦⡄⠡⢠⠀⠀⡀⣠⣷⣠⠋⠀⠑⠡⠂⠘⠉⠉⢋⣴⠽⠮⣙⡛⠓⠒⠒⠒⠫⠤⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣤⡄⠀⠀⠈⠂⠈⠉⢹⠋⠄⢠⡀⠀⠈⠀⣀⡴⠃⠁⠀⠀⠀⠉⢏⠐⣤⣖⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠛⠷⢶⡠⠴⠤⡗⠸⠃⠐⠸⠷⠃⠀⡔⣀⣤⠤⢤⡆⠀⠒⠪⣙⣄⣀⣉⡠⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠂⠉⠀⠈⠃⠐⠁⠈⠑⠢⡀⠒⠈⢺⠀⠋⠁⠐⠀⠀⠁⠀⠀⠀⠈⠉⠹⠆⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠀⠈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡤⠀⣀⡀⠀⠀⣠⠀⠴⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠀⣦⡋⠰⢿⡂⢸⣠⡄⢻⣠⡷⢸⡃⠀⢹⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⠀⠀⠠⠆⡀⠀⠹⡀⢀⠀⣅⢼⠈⠹⣠⢿⠀⠸⠇⠀⠼⠄⠐⠆⠀⠀⣀⠈⠀⠐⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡘⠄⠀⠀⠴⠀⠐⠀⠄⠰⠅⢄⠐⠐⠀⠀⠈⠁

⠀⠙⠿⠀⠀⠰⢠⣄⠹⠀⡀⠀⠈⠁⠀⠀⠀⠀⠁⣷
⢀⡒⠂⠀⠙⣆⠀⡿⠐⠀⠀⠁⠦⣀⡀⠀⠀⠀⠀⠋
⠸⡷⠊⣄⠀⢀⣧⠐⠀⠠⠀⠀⠀⡻⠃
⠈⠀⠀⠯⠀⠈⠁⠀⠀⠀⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢤⠻⠂⢻⣦⠀⢀
⠀⢀⠀⠀⢀⠀⠀⢰⣟⣷⠐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣼⡇⢀⣬⣲⠀⢸⡇
⠀⠹⠒⡶⠚⠀⠀⢿⠉⠿⠶⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠸⠀⠨⠱⣏⣴⣰⠄⠤⠤⠶
⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠌⠁⠀⠀⠀⠀⠀⢰⡖⡟⣻
⣞⠴⣑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠑⢮⣪⡵⠵⠚⠚⠉⠉⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢸⠃⡇⡏
⡮⣝⡢⢍⡲⢌⡂⠄⣀⡠⠤⠒⠊⠁⠀⠀⠀⠰⣄⠀⠀⢀⡄⠀⠀⠵⠀⠀⠀⠀⠀⢘⡺⠃⠓⡺⠏
⡭⣗⡯⢕⣪⠵⠒⠩⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢈⠐⠀⢰⠟⣤
⣫⠵⠚⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⣾⡆⠚⠘⠿⢙⠃⠰⠆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡌⠋⠸⠟⠘⠃⠰⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠘⣛⠹⣿⡇⠰⠂⠿⠇⠘⠛⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠆⠙⡋⢻⣿⡆⠶⠐⠿⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣥⣤⢈⡁⠰⠆⢠⣤⢾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⣥⣄⢉⠁⢰⡷⢠⣄⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠸⢛⡛⢈⢹⠀⣴⠀⣭⡤⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠆⠸⢛⡋⢈⢸⠀⡔⢈⣭⡰⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⠟⠀⢻⡿⠣⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠈⢿⡟⠁⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠰⣿⠲⠆⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⠟⠟⢻⣿⠇⠛⠙⢿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠛⠟⢱⣿⡆⢠⠄⣶⡆⠰⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡎⢓⡛⣴⢗⣦⠾⠆⢿⣿⠚⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⣠⣀⠙⠃⡄⠀⢀⣀⣶⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⡝⣣⣈⠛⠁⣾⣷⢀⡀⣾⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⠹⠿⠟⠘⢱⠀⣠⠈⣛⣨⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣌⢿⡾⠇⢰⠀⡴⢘⣋⢨⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⡗⠈⢾⣶⠇⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣾⣷⠘⣾⡾⠃⠻⠿⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡇⠀⠀⠀⢀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢸⠶⠒⠋⠉⠉⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⢠⡤⠤⠔⠒⠒⠒⠒⠒⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣠⡮⠤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⢰⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠉⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡏⠀⠀⠀⠀⢠⠎⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠰⠃⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠆⣀⣀⣸⣩⣧⣤⣶⣾⣷⣶⢶⣤⡀⠀⢀⣀⣠⡤⠴⣚⣉⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣻⢿⡿⣿⣽⡿⢟⣎⣹⣹⣟⣿⢧⡿⣆⠉⠀⣠⣴⠾⠛⠉⠉⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣎⡿⢍⡟⣹⢷⢤⠗⢾⡇⢱⣌⣏⣉⡷⣟⣿⣶⢿⠋⠀⠀⠀⠀⢀⡤⣖⠒⠲⡄⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣷⢬⠋⢻⠼⣆⣧⣞⢹⡁⣹⢄⣹⢷⢮⣻⣿⣿⡆⡀⠀⢀⡔⠁⠈⠀⠀⢠⠇⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢛⡧⣧⠞⣷⢿⢠⣇⣇⣸⠹⡉⣳⢼⡉⣾⢦⢧⣿⣟⠳⣌⠑⣏⠀⠀⠀⠀⠀⡞⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣃⣏⣳⠿⣴⣏⣭⣨⠟⣶⣿⡛⢦⡟⢣⣾⢾⣿⠞⣞⣁⠿⢾⢽⣲⣦⣤⠾⠥⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⣦⣿⡶⣧⠾⣌⡏⣹⣀⣽⣽⠷⣽⣯⣿⣻⣿⢾⣁⣾⠒⡻⣞⡭⢓⡿⣷⣒⣶⣶⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣹⣛⡾⣏⣹⠙⣞⣧⣜⡶⢧⡼⣧⣿⣿⣿⣧⡜⠺⡵⣛⣶⣻⣞⣉⣏⡷⣟⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⣯⣽⠾⣉⡿⣩⣃⣿⣽⡮⣙⣿⠁⠨⣟⣿⣿⣿⣯⣭⡿⢺⣥⣿⣿⣛⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣳⣯⣽⣯⢿⣻⣽⣶⠟⠁⠀⠀⠈⠁⠙⢿⣶⣷⣟⣯⣾⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠾⠽⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⠠⡌⢸⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠕⢧⡖⠁⠀⠀⠀⠀⠀⠀⠀⣠⣔⠂⠉⣉⣁⣠⣈⡙⠲⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢸⢠⠊⡀⠀⠀⠀⠛⠀⠒⠒⠒⠒⡰⠋⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⢻⣆⡙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢠⡿⣿⣿⣿⣿⣿⣿⠛⠻⠛⢘⠿⢿⢦⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇⠀⠁⠀⠀⠀⠀⠀⠀⡘⠁⢠⣿⣿⠁⠐⠛⠻⢿⡇⠀⠀⠀⠀⠀⣘⡀⠈⠋⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⣿⣿⣧⡥⠤⢄⠀⢡⠀⠀⢀⣀⠠⡈⠓⠀⢑⢆⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⢰⡎⣠⠿⠏⠀⢀⠀⡀⢀⣃⣀⠧⣤⡅⡯⡤⢷⡀⠰⣌⢊⢢⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡇⠀⠀⠀⢸⠎⠀⠀⠀⠈⢀⠀⠀⡆⠹⠐⠳⠄⠀⠰⠎⠛⠈⢹⣯⣭⣿⣿⣦⠴⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⠀⢰⠀⡇⠀⠀⠠⣤⠤⣾⡞⠚⢆⡁⢀⠀⠀⠀⠀⢠⠔⢚⡁⠐⠰⠀⠈⠷⣄⠀⠀⣰⠇⢀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡇⠇⠈⠑⠀⢸⠷⣨⢇⠀⠄⣱⠊⠳⡀⠀⢠⠃⢰⠏⠀⠀⠀⠀⠀⠀⠈⠑⢣⡀⠋⢃⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⡌⠒⢶⠒⢻⣿⣿⡄⡀⠀⡏⠀⣦⣑⠀⢰⡆⠄⠀⠀⠀⠀⠀⠐⡤⠀⢀⡜⠀⠀⠀⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⣄⠈⢆⢰⠘⢿⣧⣇⣀⠙⡀⡽⠛⠛⠻⠗⠒⢦⡀⠈⠢⡀⣰⡃⣀⣽⣠⡦⣀⡰⣄⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡻⠿⠋⠉⢠⡨⢧⣺⠁⠀⠀⠀⢀⡄⠀⡟⠋⠁⠉⠉⠉⠉⠁⠀⡀⣀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠰⠃⢰⠉⠱⡄⠟⣣⡀⠀⠀⢾⣷⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⡌⠀⢺⠀⠐⡄⢠⠟⢳⠦⠔⠃⠘⠻⠢⣄⣀⣠⣤⣤⣶⢶⣭⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢫⠀⡴⠁⢀⠯⣅⠀⠀⠀⠀⠀⠀⢸⡭⣏⠼⡁⢯⣜⣧⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠺⢄⠼⠢⠄⣀⢀⡀⠴⠋⠈⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠔⡒⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠋⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠃⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠉⢄⠠⠀⠀⠀⠀⠋⠈⠐⠄⠤⠀⠀⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠁
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠣⠄⢄⠀⠀⠀⡴⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⡤⠀⠀⠀⠀⠀⠀⠘⡀⢀⠀⠀⠀⠀⠀⠀⠈⠪⠀⠟⠋⠉⢦⡀⠄⠀⣀⠂⠄⠒⠀⠀⠀⡇⠀⠀⠀⢀
⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⡀⠀⠀⠁⠀⠈⠢⠀⠁
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠐⠀⠀⠃⠀⠁⠀⠀⠀⡈⠘⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠄⣀
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢨⣒⣀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠱⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢄⡠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠄⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠑⠛⠓⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢲⠀⡀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⢄⠤⠔⠂⠀⢪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣈⠀⢀⠀⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⡀⠀⠠⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢦⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⡀⣀⢀⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠐⠒⠮⣉⡽⢁⠜⣰⠋⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⢞⠀⡞⠀⠉⣆⠀⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⢀⠤⠒⠀⠉⢙⠗⢖⠋⠁⠀⠀⠀⠀⠢⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢀⠂⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡄⡰⡀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡖⠁⠀⠀⠉⡰⠖⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢷⠻⣕⣲⠔⠓⠒⠉⠉⠉⠉⠉⠘⠁⠀⠀⠒⠂⠤⠤⠤⠄⠀⣀⣠⡀⠀⠀⠁⠀⡄⠀⠳⡶⠶⡏⠈⣶⠓⢄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢲⣼⡦⢬⣷⣀⢰⠀⢤⣀⣀⡀⠀⣀⣠⣤⣤⣤⠤⠴⣖⠈⠉⠀⠀⠀⠀⠀⠀⢠⣔⠁⠀⢠⠛⡋⠙⣏⠁⡿⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡏⢲⠤⡀⠀⠀⠉⠙⢦⡈⠁⠉⠉⠡⠉⠐⠀⠉⠉⠒⢤⣈⠁⠐⠂⠀⠀⣀⡀⠸⠊⣸⠦⣾⠓⡋⢻⡉⢹⣦⣼⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡈⠲⣄⠀⠀⠀⠈⠳⢤⡀⠠⠀⠀⠀⢀⠀⠄⠀⠈⠛⢿⡃⠀⠀⠀⣠⠖⠛⠛⠒⣿⡂⠙⠳⢾⣉⣤⣼⣉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠀⠀⠐⣄⠀⡙⢲⠤⣄⠀⠀⠑⣦⣄⣀⠀⠀⠈⡀⠀⠄⠀⠂⠙⢦⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡧⣀⣯⠉⡤⡀
⠀⠀⠀⠀⠀⢀⡤⠶⠒⠂⢾⡖⠓⠒⠒⢾⡀⢈⠂⠐⢈⠉⠒⢤⡈⠳⡉⠓⠦⣤⢀⡤⢤⣬⣠⣐⡠⣳⡞⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠦⢿⠄⡟⢢⡆
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠻⡗⠤⢄⣄⠨⠻⣷⠶⠶⠶⣛⡯⠭⠤⣼⣾⡇⠤⠤⣀⠀⠀⢀⡞⠁⠀⠈⠓⣏⣹
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡊⠀⢀⠂⡁⠀⠈⢳⣄⣉⠁⠀⠈⢧⠀⡜⠁⠀⠀⠀⠀⠿⠄⠀⠀⠀⢱⣴⠟
⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⢧⡙⢦⣄⡀⠀⠀⠀⢀⠻⣟⠛⠳⠶⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠓⠤⣌⠳⣌⠛⢶⣀⣠⠂⢁⠈⣆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣤⠤⣤⠴⠛⠁⠀⠀⠀⠙⠲⠼⣆⠀⠉⠙⠛⠶⠖⠞⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⡀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢠⡀⡇⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⢱⡇⡜⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠈⢢⣸⠎⠀⠄⠀⠀⡇⠀⢀⣀⠤⠔⠒⠋⡩⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠢⢄⣀⣠⠁⠀⠀⢢⡀⠀⡿⠀⡰⠃⠀⣀⠷⠊⠁⠀⢠⠀⡠⠊⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠎⠁⠰⡀⠀⠀⢀⣤⣄⠀⠘⠳⣄⠀⠀⠙⢢⠇⠊⠁⡠⠊⠀⡀⠀⡄⠀⡰⠚⠈⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠘⣀⠼⠛⠓⠒⠛⠒⠶⢎⠀⠀⠠⢧⠀⢣⡼⠅⠖⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⣸⠁⠤⠄⠀⠀⢄⠀⠀⠤⠀⠀⠀⢀⠜⠁⠀⠀⠀⠈⠉⠑⠀⠄⠉⠢⣄⠀⢱⣊⣤⠂⠀⠀⢀⠇
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢏⡀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⢸⡃⡀⠙⠀⠀⠀⠢⠀⠀⠀⠈⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠎⠙⡀⠀⣠⠊
⠀⠀⠀⠀⠀⢸⡇⠙⠄⠀⠀⠀⠀⠀⠀⠢⠄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠠⠀⢻⠐⠁
⠀⠀⠀⠀⠀⠘⢧⡄⠀⠀⠀⠑⠀⠀⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠃⠀⠀⢀⠀⢴
⠀⠀⠀⠀⠀⠀⠈⢻⣄⠂⣀⠀⠀⠀⠀⢄⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⣀⡴⠘⠁⠀⠐⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠐⠤⠄⠀⠠⢀⣸⠶⠤⠤⠐⠒⠊⠉⣀⠀⠀⢀⠄⠀⠐⠃⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠲⠷⠞⠛⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠠⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢬⣀⠀⠄⢀⠐⠉⠀⣀⡠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⣠⡠⠀⡦⣄⡤⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠃⠉⠀⠁⠁⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠂⣤⣶⣤⢲⣶⣷⣴⣶⣡⣾⣿⣿⡏⠤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣰⣿⠽⠫⣶⣾⣿⣿⣿⣿⡙⣿⣷⣿⣿⣿⣇⣠⣦⣴⣿⣿⣿⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⢶⣶⣟⠵⣿⣥⣿⣿⣧⣿⢻⣾⣷⣿⣿⣤⣍⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⠀⡀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡉⣰⣿⢟⣼⣓⡿⣿⣯⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⠹⣿⣿⡟⡛⣿⣿⣿⣷⣞⠢⣿⣿⢉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡇⢸⣿⣧⣿⣿⣼⠿⠻⣿⣿⣶⣿⣿⣿⢿⡿⠁⢻⣏⢩⣟⠹⣿⣟⣃⡑⢾⡍⢲⡙⣿⣧⠸⣿⣿⣤⣶
⠀⠀⠀⠀⠀⠀⠀⣠⡘⢿⣷⣿⣿⣿⣿⣿⢛⣶⣿⡿⢿⣿⣿⣿⣿⠀⠐⠆⣿⣿⣶⣽⠇⠀⠉⠉⠻⣏⠐⣧⣵⣹⣦⣀⣹⣷⢿⠆
⠀⠀⠀⠀⠀⠀⠀⣴⣆⣸⣿⢟⣹⢿⣿⣷⣿⣿⣾⣷⣬⣿⣿⣿⡛⠀⠰⠚⢻⣿⣿⠃⠀⣀⣤⠀⣴⣯⣹⣿⣿⣿⣾⣿⣿⣧⣾⡐⢦⡀
⠀⠀⠀⠀⠀⠀⡶⡄⢸⣿⣿⣿⢹⣯⣿⣿⡿⢿⣿⣿⣯⣍⠹⣿⣷⡄⠈⢙⡿⠟⣉⣉⣁⣻⠿⠿⣌⣿⡿⣿⠝⢭⣭⣹⣿⣫⡿⣦⣨⡧
⠀⠀⠀⠀⠀⢠⡿⠟⣶⣿⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⠀⠎⢠⣾⡋⣿⣿⣿⣶⣶⣬⣬⣋⣩⣴⣾⣷⢽⣿⢯⣷⡾⠿⠇
⠀⠀⠀⠀⠀⠈⢹⣷⣾⣿⣿⣿⠿⢷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁⠆⠐⠌⢋⣡⣤⣬⣝⢿⣿⣿⣿⣿⣿⣭⣿⠿⣿⣶⣟⡟⣧⠆⡙
⠀⠀⠀⠀⢠⡴⣷⣤⣽⣿⣿⠁⠀⠀⣿⡆⠈⣿⡿⠛⢛⠟⢻⣿⡆⣀⠃⡀⠒⣾⣿⣿⣿⣿⣷⣿⡿⣿⣟⠠⢓⣭⣀⣠⣄⠫⣘⣿⣿⡟
⠀⠀⠀⠀⠈⢁⣴⣯⣽⣿⣿⣦⣠⢲⣿⣷⣶⡏⣰⣷⣾⡷⣆⠘⢄⣭⢺⣅⢠⣿⣿⣛⣿⡿⡿⢿⣿⣿⣿⠗⣿⠻⣟⠙⠛⣷⣿⢿⣿⠟
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣏⡻⢷⡹⠿⣠⣿⡿⢋⣰⣿⢃⡈⠱⢿⣿⣼⣿⠏⠛⠋⠄⠀⢬⣿⣏⣿⣿⢿⠷⣼⣷⣟⠿⣽⣿⠟
⠀⠀⠀⠀⠀⢂⠘⢿⣿⣿⣿⣿⣿⣷⣾⣷⡞⣿⣿⣇⣙⣫⣥⣀⣱⣤⡌⡛⢹⣿⣤⠀⢠⡶⠖⢺⣿⣿⢨⣿⣿⣆⣹⣾⣿⣷⡏⣱⣀⣤
⠀⠀⠀⠀⠀⠘⢀⠈⢿⡟⣟⡙⠛⢟⣻⣿⣇⠻⣿⣟⣿⣤⣸⡟⣽⣿⣧⣇⣾⣿⢿⣶⣿⣵⣄⢉⣽⣿⣦⣿⡟⣿⡻⣭⢿⣷⣿⢾⣿⣉⣀⡄
⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⣿⣿⣷⣌⣻⣿⣿⣷⣬⣅⠙⢻⣿⣿⣿⠇⣿⣙⣿⣿⣦⡈⠙⠹⣿⣿⣿⡌⢿⣁⠛⠻⣧⠘⠛⣿⣿⡀⠈⠝⣿⠓⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣉⠙⢿⣿⣿⠿⢿⣿⣿⣿⣶⣀⣈⠛⠁⣸⣿⠿⠿⣿⣷⡌⣻⣷⣜⣿⣿⠹⣾⡟⢛⠁⢛⠟⠹⢿⣿⣷⠾⢿⣿⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠿⣷⣎⣹⣹⣷⣹⣾⣿⣿⣿⣿⣿⣷⡅⡟⠀⢠⣾⣿⣿⣧⢻⣄⡿⢿⣿⣶⡟⢹⡟⣉⡽⢳⣿⣿⣿⡟⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⡿⣁⢻⣿⢻⣿⣿⣿⣿⣿⡧⣽⠃⣧⡀⠈⣿⠋⠙⠟⡀⠘⠟⠂⣼⡟⠏⣿⢿⠿⢃⣙⢡⢷⡼⡟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣃⢿⣬⣿⣾⡿⠿⣿⣿⣿⠇⢘⠆⢿⣿⣟⠋⠀⠀⢀⣿⣷⡆⠀⣿⡉⢇⣴⢻⡴⠛⠉⣧⡾⣿⣬⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣶⣿⣿⣿⣷⣶⡿⠟⠋⢀⣍⣸⡆⠡⡻⣧⣠⠀⠿⠿⠟⠋⠀⣻⡵⢛⣷⣿⠛⠾⠛⠟⣧⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣶⣿⠉⠀⣴⣶⠏⢹⣿⡇⠘⠿⣮⣿⣧⣀⢀⣾⣿⣶⣿⣷⠺⣷⣿⣟⡛⠓⢶⣿⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡀⠹⣏⣩⡾⠟⣛⣉⠁⣠⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠏⣩⣶⣬⠙⣮⣛⡻⢦⣟⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢹⣷⣛⣛⣿⣆⠙⠛⢻⣷⣞⣿⣇⢀⣄⢸⣿⣿⠝⣿⣿⣿⢶⡶⠟⢿⡿⣇⠿⣻⡛⢦⣹⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢻⣿⡏⢹⡛⠛⠃⢠⣿⡿⣿⣹⡏⢻⡟⢻⣟⣿⣀⣿⠙⢿⣾⠃⠀⠀⠀⠀⠈⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣠⣼⡿⣾⡇⠀⢰⡄⢸⣇⣠⠙⣯⡾⢿⣿⣟⣿⣯⣯⣤⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⣻⠿⣀⣙⣷⣄⣠⣿⠖⣸⣷⣄⡸⢇⣄⠛⠻⣿⣭⡍⣿⡤⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⣈⣷⣾⣿⡅⠀⠛⢹⡿⠸⠛⣿⣿⠀⠘⠟⣴⣾⣿⣿⣿⢁⣷⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢿⣿⣿⡟⣫⣵⣀⣶⡟⠁⢤⣯⡙⠟⣠⣞⢶⣟⠻⣿⣿⡇⣀⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⠉⠻⠛⠙⠟⠛⢋⣠⣆⠀⢀⣡⣾⣿⡛⢱⣤⡿⣧⠀⣿⣷⣾⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠆⠟⣸⠟⣉⠷⠛⡼⠿⣿⣷⣽⣿⡿⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣗⣾⢳⣄⣿⢿⣿⢿⣟⠋⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⢻⡟⠸⣿⣼⣯⣿⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣵⠁⠈⢹⣿⡷⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢣⣄⠲⠻⢷⣿⢧⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣶⣋⠙⠂⠰⠾⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⣀⠀⠀⠀⠀⢯⣊⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠷⠀⠂⠛⠃
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠦⠁⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⢀⡤⣲⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠥⠖⠁
⠀⠀⠀⠀⠀⠀⠀⣠⢶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠁⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣿⠄⠀⠀⠎⠀⠀⠀⠀⠖⠈⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣿⣿⣿⣷⣶⠀⠀⠀⠀⠸⠇⢠⠞⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⠛⢿⣽⡿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⡄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣤⣿⣿⣿⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠊⠀⠀⠀⢸⣷⣿⡇⠁⢰⣾⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⣿⠋⠀⠀⣴⠒⣷⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠀⠀⢾⣿⣿⣷⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠟⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠏⠀⠀⠀⠀⠆⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⣀⠀⠐⢄⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠤⠀⠀⣀⠰⠀⠀⠀⡢⠀⠀⠦⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠄⠀⠀⠀⠀⠁⠀⠀⠃⠀⠈⢠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠈⠀⠀⠉⠀⢈⠧⠀⠊⠀⠚⠁⠄⠀⠀⠂⡄⢓⠀⠀⠀⠀⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⠤⠤⠴⣀⣄⡀⠴⢌⣢⠱⠄⠐⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢨⢑⡰⡆⢀⠘⠃⢠⠀⠀⠀⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠁⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢁⡐⣩⠃⠀⠀⠈⠊⠁⠰⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠲⠋⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⣥⠟⠀⠈⢢⠀⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣠⠓⠈⡇⠀⠀⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⡄⠀⢀⠀⠀⠀⠀⠲⠁⠘⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠐⣠⢉⡄⠤⠁⣠⠊⠀⠀⣁⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣚⣰⠋⠀⠐⠁⠀⡔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢄⣀⡀⠀⣤⠉⠢⣄⡤⠁⠀⢀⠃⠀⣄⠀⠀⠀⠀⣰⡘⠁⠀⠈⠉⠡⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠃⠈⢃⠀⠀⢾⡀⢰⡆⡀⠛⡤⠰⢤⠀⠀⠀⠶⠅⠈⠀⠐⠀⠀⠞⠉⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⡄⢸⠉⠀⠸⢅⡈⠃⠐⢃⠀⠠⡀⠀⢸⠁⠀⠰⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢀⠀⠁⠀⠰⠀⠀⠀⡋⠀⠀⠧⠀⠀⠖⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣳⢷⡢⢈⠸⠰⠣⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢸⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⠀⠾⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣄⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢊⣩⠿⡿⠋⠀⣸⡏⠀⢸⡷⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠐⠉⠈⠁⠈⠀⠀⣘⢁⠃⠀⠘⠘⣦⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠁⠀⠀⠀⠀⢠⡾⠁⠀⠸⢀⠀⠁⠘⢧⡀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠀⠀⠀⠀⢸⠀⠀⠀⠘⣿⡄⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⢤⠠⣤⣀⠁⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠨⠙⣄⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡯⣙⢫⢨⠙⠃⡺⣝⢷⣄⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠘⣦⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣖⢡⡕⢎⣩⠀⡎⠅⢺⣵⢻⣷⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠈⡇⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣽⣷⢈⡴⢩⠴⠄⢁⠴⢤⣱⣜⣳⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢰⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡼⡦⢟⠼⢃⡄⢲⢉⣲⣏⡷⢾⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣻⣷⡸⣈⡶⣏⢽⡩⠾⠃⠾⣃⣽⣿⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡾⡕⢯⢿⢚⠾⣉⣟⣸⢾⣹⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡩⣻⢾⣿⣾⣿⡿⣾⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⠿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠀⣀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣤⣾⣿⣷⣤⣿⣿⡋⢹⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠻⠃⠀⠀⠛⠃⠀⢰⣦⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢻⣿⣀⣿⣿⡟⢻⣿⣉⣿⣿⣿⣷⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣤⠀⠾⠇⠀⢠⣤⠀⢶⠆⠀⠀⠀⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣷⣾⣿⡿⠻⣿⣷⣿⣿⣿⣏⣈⣿⡿⡃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡇⠉⠀⠀⣤⡀⠀⠁⠀⠀⠀⠿⠂⢀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⣹⣇⣸⣷⣶⡿⣿⣿⣀⣿⡿⠿⣿⡄⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⣠⣿⠗⠘⠿⠀⠉⢁⡀⠀⠾⠇⠀⣠⡀⢛⣯⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣶⣶⣶⡶⠾⠏⢻⡿⠿⣿⣤⣾⣿⡿⠿⣷⠶⠏⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⠉⠉⢉⣉⣠⣧⠀⣠⡀⠛⠃⠀⠀⣀⡀⢉⣅⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠻⣿⣿⠀⠀⠀⠀⠑⠖⡻⢿⢹⣏⠷⢴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡅⢰⠀⠀⣸⣿⣿⣿⣷⣋⡥⣀⠆⠀⢂⡙⣥⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⢱⣿⣿⡄⠀⠀⢀⠀⡀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣼⠀⠀⠹⣿⣿⣿⢿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⣿⠹⣿⠀⢠⣬⣥⣥⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢰⠀⢹⣿⠛⠚⠛⢻⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⠀⣿⡆⠈⣿⣿⣿⡇⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⡆⢸⣿⠀⠀⠀⢸⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠉⠉⠉⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣷⣾⣿⣷⣶⣶⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠥⠤⠠⠠⠤⠦⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣭⣬⣽⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣾⠟⣀⣀⣀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⢠⣄⡀⠀⣼⣿⠀⠀⠀⢀⣤⣤⣄⣽⠁⢈⣛⡋⠁⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢋⣠⣤⡦⠈⢿⣿⣦⠟⠃⢀⣀⣀⡏⠀⠀⠀⠙⣆⠘⠿⠿⣦⡀⠀⣿⠟⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣷⣦⣶⡿⢟⣋⣤⣤⣀⡀⢹⡀⠰⠿⠟⠋⢱⡄⠀⠀⠀⢸⡌⣳⣞⡉⠉⢻⡁⢠⡄⠀⣴⣿⠁⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⢀⣽⠟⠉⠉⠉⢉⠙⠛⠿⣦⣤⣀⠀⢾⣿⠀⠀⠀⣸⠿⣿⣿⡿⠀⣼⠃⠀⠙⢶⠟⠃⠀⠀⣾⡿⢀⡀
⠀⠀⢲⣦⡀⠀⢀⣾⣿⣿⠏⠀⠀⢸⠇⢠⣤⣤⣀⣻⢀⡴⠚⠓⠪⠙⢿⣮⡛⠀⠀⣰⠟⠀⣙⠛⢁⣼⣧⡤⣤⣤⠈⢠⣶⣦⣄⣿⠃⠘⣿⠀⠀⣀⣀
⠀⠀⠀⠙⢧⠀⢾⠿⠛⠁⠀⠀⠀⢸⣇⠀⠉⠛⠛⣻⢺⠀⠻⠟⢻⣦⡀⠹⣿⣦⣴⠃⠀⠘⢻⣷⠟⠁⣴⡇⠀⣈⣷⣦⠎⠉⠀⠘⠀⣀⠜⠚⢿⣿⡿⠟
⠀⠀⠀⠀⡆⢀⣤⣤⣤⠄⠀⣠⣾⡿⠉⠳⢦⣴⠞⠁⠘⣷⡀⠀⠘⢿⡇⠀⠸⣿⣇⢀⣠⣾⠟⣁⢸⣾⠟⠀⠀⣿⣿⣿⡇⣠⡴⢎⣁⢠⡖
⠲⣿⣿⡶⢷⡛⠿⠛⠁⠀⠠⠿⠛⠁⣠⡞⠉⠉⠉⠂⠀⠘⣷⣀⣠⣤⣄⡀⠀⢿⣿⣿⡿⠁⣀⣻⣆⠀⣤⣶⣄⠘⠛⢋⡞⠁⠀⢈⣽⣯⣄
⠀⠀⠀⠀⠈⠙⠶⠶⣶⣶⠶⠶⠶⣴⣿⠀⠻⢶⣤⡄⠀⣰⡿⠋⢀⣄⠀⠉⢧⣸⣿⣿⢃⣪⣷⡍⢻⡄⠻⠿⠏⠀⢀⡼⠁⣄⠀⠸⣿⣿⡟
⠀⠀⠀⣠⣶⣾⣶⣤⢮⣤⣤⡀⠀⢀⠹⣧⡀⠀⢰⠀⢠⡿⠀⠀⢸⣿⡆⠀⢸⢻⣿⣿⠀⣹⠛⠃⢸⡇⣀⣀⣤⠶⠋⠁⢸⣿⣆⡤⠈⠉
⠀⠀⠀⠉⠙⠉⠁⣴⣶⣿⠙⠋⠀⣿⠇⠈⠙⢻⠾⠷⢾⣿⡀⠀⠀⠙⠳⠀⠀⣾⣿⣿⠀⠛⣠⡶⠟⠛⠛⠛⠲⠦⣄⡀⠀⠛⢿⣃⠀⠀⠀⣿⣿⡧
⠀⠀⠀⠀⢀⣀⢀⡹⠿⠟⠲⣦⣄⣋⣴⡾⠀⠸⣷⢀⣤⠌⠻⣦⣄⣀⣀⣠⣾⣿⣿⣿⣶⡾⠉⠀⠀⠠⣿⣿⠇⢀⣠⣭⣭⣁⠀⠉⠁⠀⠀⠐⠙⠁⢠⣦⣦
⠀⠀⠀⢠⣿⣿⣿⣿⡆⠀⠀⠀⠨⡍⠉⢰⣿⣶⠱⠛⠁⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢙⢣⡿⠋⠀⠀⠀⠈⠻⣦⣄⣀⣀⣠⣮⣀⠘⠟⠏
⠀⣤⣤⣸⢿⣿⣾⣿⡿⠀⣀⡴⠶⠿⠶⢤⣭⣥⠴⠷⠦⠤⣤⣤⣤⣀⠀⠘⣿⣿⣿⣿⡿⠷⠶⠤⠤⠖⢡⡿⠁⠀⣀⠀⠀⣰⣾⣶⠀⠉⠁⠀⠀⠀⣙
⠀⠀⠉⠉⢩⣛⣋⣤⡶⣾⠋⣠⠀⠀⠀⣴⠞⠉⠉⣿⣆⠀⠀⠀⠉⠻⣷⣶⣿⣿⣿⣿⠇⠀⠀⠀⢀⣴⡟⠁⠀⢾⣿⣿⠀⢘⠛⠉⠀⠀⠀⠰⣌⣧⣟⣤
⠀⠀⠀⢠⣿⣧⠀⠀⣠⣼⣞⠋⠀⠀⢰⡇⠀⠀⣰⣾⣿⣍⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣧⣀⣤⣶⣿⣋⣀⠀⢀⣨⠟⠀⣐⣢⣿⠤⡀⠀⠀⠓⣹⢿⡻⠆⠁
⠀⠀⠀⢸⣿⡟⠀⠐⢿⣿⣿⠀⠀⠀⠸⣇⠀⠸⣿⣿⣿⣿⠀⠀⣀⣠⣤⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠿⠿⣯⣀⠀⠐⠥⢻⢿⣓⠀⠀⠀⠀⠉⠊⠁
⠀⠀⠀⠈⠋⠀⠀⠀⠈⠁⠹⣦⡠⠒⠓⠻⣷⣤⣽⣿⣹⣯⣶⠿⠿⠿⢿⣿⣿⣿⣿⣿⡿⠋⠀⣰⣿⣶⠀⠀⢠⡙⡳⣦⡜⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣶⣶⡄⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠁⠀⠀⠘⠛⠋⠀⡪⣿⣿⡳⠈⢷⠀⣶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠀⠀⠈

⠀⠀⠀⠀⣀⣀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠘⡄⠮⠐⠥⠣⣅⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠂⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⠀⠚⠉⡝⠁⢀⠀⠀⠀⠈⠷⢨⠇⠀⠀⠀⠀⠸⣴⠀⠀⠀⠀⠀⠑⡄⢤⠀⠀⠀⠀⣰⣿⣿⣿⣿⣇
⠀⠈⣀⡇⠐⠀⠀⠀⠐⠂⠘⠦⣄⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦
⠀⠸⣐⣛⢄⠀⠀⠀⠀⢠⠮⣤⠆⠀⠀⠀⠀⠉⠙⣇⠀⠀⠀⠀⠠⠽⠂⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢘⠿⠒⠓⣘⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠇⠋⠉⠻⡧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠸⡌⠉
⠀⠀⠀⠀⠈⠙⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⢛⠳⣦⡞⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢦⣀⣤⢶⠂⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣆⣘⣗⡶⠄
⠀⣠⠴⢼⣶⠞⠛⠛⠷⣿⠚⠛⣦⠀⠀⠀⢰⡶⢶⣾⠟⡛⠛⠶⣾⣄⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡄⠀⠀⠀⠀⢐⡷⣤⣟⢻⣆⣏⡽⢇⣦
⠀⢧⣅⣾⠃⠈⠀⠀⢀⠘⣷⣴⠋⠀⠀⠀⠀⢹⣾⠁⠀⠀⠀⠀⠸⣯⡽⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠛⠙⠯⠼⣿⠛⢻⡶⠟⣺⠗
⠀⣰⠛⢿⡄⠀⡀⡀⠈⢠⡟⠩⣳⠀⠀⢀⣴⣋⣿⡄⠀⠀⠀⠀⣰⡟⣄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⠟⣻⡷⣿⡻⣭⣿⣶⠆
⠀⠙⢦⠶⣿⡶⣦⣤⢶⡻⣟⠛⠋⠀⠀⠀⠀⠀⢹⡟⢶⣦⣶⢾⡟⠚⠛⠃⠀⠀⠀⠻⣿⠿⢿⠿⡿⠟⠀⠀⠀⠀⠈⢁⡹⢦⡧⣸⡵⡧⠀⠛
⠀⠀⠀⠀⢷⣤⡼⠛⠧⡷⠏⠀⠀⠀⠀⠀⠀⠀⠸⠟⠋⠈⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠘⠉⠿⠂⠉

⠀⠀⠀⠀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢘⠀⠈⣲⡃⠀⢘⡀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢣⣠⠔⠙⠁⠀⠀⠀⠀⠀⠀⠀⡤⢺⢻⠀⠀⠀⠀⠀⠀⠀⠀⣀⡰⢦⣈⢝⡺⠂
⠀⡔⠛⠛⡶⠊⠉⠉⠑⢾⠁⠈⢱⠀⠀⠀⠸⡂⢚⡟⠈⠉⠉⠑⢶⠤⠤⣀⠀⠀⠀⢠⠊⢀⡇⠈⡆⠀⠀⠀⠀⣀⠟⢤⢏⠢⣄⡇⡌⢃⢲
⠀⠣⣀⣼⠀⠀⠀⠀⠀⠀⡷⠶⡁⠀⠀⠀⠀⡸⠞⠀⠀⠀⠀⠀⠀⣃⠔⠉⠀⠀⢀⡇⠀⠀⠁⠀⠘⡄⠀⠀⠀⠙⢙⠧⢀⢽⠊⠙⡬⣑⣮⠗
⠀⡘⠁⠘⣄⠀⠀⠀⠀⣠⡃⠀⣈⠀⠀⠠⠮⢀⣸⡄⠀⠀⠀⠀⡠⠋⢢⠀⠀⠀⠸⡇⠀⠐⠇⠀⠀⢸⠀⠀⠀⠀⢑⣪⠒⡙⡵⠞⡑⣤⣝⢪⠓
⠀⠈⠒⠒⡏⠑⠒⡶⠊⠉⢏⠈⠁⠀⠀⠀⠀⠀⠠⠈⣑⢶⡒⠊⠇⠈⠈⠁⠀⠀⠀⠑⠤⠔⢻⠢⠤⠊⠀⠀⠀⠀⠀⢁⠹⢢⠧⣜⠬⠦⠀⠛
⠀⠀⠀⠀⠳⠤⠔⠉⠢⠔⠃⠀⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠙⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⣛⣻⣿⢟⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣙⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡝⠟⢿⣿⣿
⣿⣿⢿⠿⣿⡿⣇⣻⢿⡟⣻⣛⢿⣿⣿⣿⡿⡿⣿⠧⠿⣯⣙⢷⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⢳⣗⣿⣿⣿⣿⣿⣿⢻⣿⢩⢵⣮⢭⣎⢱⠿⣿⣿
⣿⢵⣿⡷⣴⣿⣿⣿⣿⣮⢿⣿⢧⣿⣿⣿⣷⡻⡟⣴⣿⣿⣿⣿⣆⣭⣭⢛⣿⣿⣿⢧⣿⣿⣾⣿⣜⣿⣿⣿⣿⣫⣚⢢⣮⡓⣎⡝⣟⡫⢇⢻⣿
⣿⡶⣛⡑⣿⣿⣿⣿⣿⣿⢤⣤⡻⣿⣿⣿⡿⣫⡼⣿⣿⣿⣿⣿⣿⡘⣵⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⡫⣞⢿⡖⡿⡟⡶⣿⣋⢿⢻
⣿⡷⣿⣿⠝⢿⣿⣿⡿⣋⠻⠿⣏⣿⣿⣿⣬⣽⡇⣻⢿⣿⣿⡿⢫⣿⡮⢿⣿⣿⣿⡻⣿⡿⠙⢿⣿⢇⣿⣿⣿⣿⣯⣹⡛⢽⣾⡞⣽⣯⣮⢓⣿
⣿⣿⣾⣶⢾⣿⣶⣰⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡯⠿⣻⣤⣲⡿⣼⣿⣿⣿⣿⣿⣿⣿⣶⣾⣇⢻⣶⣿⣿⣿⣿⣿⣿⣏⣓⠣⣶⣌⣾⣾⣿⣿⣿
⣿⣿⣿⣿⣷⣭⣷⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠤⢤⣦⣶⣴⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡀⠀⠀⠈⢀⣠⠶⠶⣦⠈⠙⠻⠏⡟⣾⡆⠀⠀⠀⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡲⠋⠽⠁⠀⠀⠈⠀⠀⣀⡄⣀⣀⡀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣦⣁⣴⣷⣾⣿⣵⣶⣦⠀⢠⣤⣿⣿⣿⣿⣿⠀⠀⠈⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠘⣿⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠙⠛⣿⣷⣽⣿⣿⣿⠛⠛⠁⠀⠀⠉⠉⠀⠈⠀⠀⢀⣤⣼⣤⡘⢿⠇⣴⣿⣿⣦
⠀⠀⠀⠀⣰⣧⣼⣷⣤⣀⠙⠛⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠃⣄⠀⠻⢿⣿⠟
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⡀⣀⠀⠀⢀⢀⢀⠀⠀⡀⠀⠀⢀⡀⠀⠀⢰⠿⠀⠀⢰⣇
⠀⠀⠀⠀⠙⢿⣿⠇⠀⣩⠀⠀⠀⠀⠀⠇⠿⠀⠳⠸⠺⠈⠇⠨⠇⠈⠳⠀⠇⠀⢠⢯⠇⣀⣴⣿⣿⣷⣤
⠀⠀⠀⠀⠀⣸⠟⢰⣾⣿⣿⡆⣠⡀⠀⠀⠀⠀⢠⡄⣤⢠⡀⡄⣤⠀⠀⠀⠀⠀⢈⠁⢸⣿⡿⠛⣿⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡋⠱⠟⠃⠀⠀⠀⠀⠘⠁⠛⠀⠁⠃⠛⠀⠀⠀⠀⠀⠌⢀⣼⣥⣠⣦⢈
⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢎⣤⣸⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⠿⠛⠘⣿⣿⣿⢿⣿⢿⣿⣿⣤
⠀⠀⠀⠀⠀⠛⠿⣧⡻⣿⣿⣿⣟⣫⡿⠋⢀⣤⣶⠆⠀⠀⠀⠀⠙⠛⠉⠀⣰⡁⠈⠙⠻⡀⠉⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠛⠋⠉⣩⣴⣾⣿⡿⠋⠀⠀⣄⠀⣆⠀⠀⠀⢠⣿⣷⠀⣿⠀⠡⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⠁⠀⠈⠀⠀⠀⢉⡧⢀⣤⣿⣿⣿⠀⢯⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠙⠛⠁⠀⠉⣓⠀⣀⠠⣶⠁⠀⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠋⠀⠀⠀⠀⠈⠙⠛⠁

⣿⡿⢿⣿⠿⣿⣿⠿⠿⠿⠛⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⢿⠿⠻⠿⢿⡿⠿⠿⢿⠿⠿⠿⠿⠿⠿⠿⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿
⣿⡏⠂⢙⠻⣿⠿⠶⠒⠊⡞⣿⠄⣉⣅⠀⠀⠿⠇⢀⠀⠈⡆⠀⢀⡄⠠⠃⠀⠀⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⢀⡁⡔⠂⠙⡴⢷⡈⠀⠀⠘⣿⣷⡤⢁⠀⠀⠘⠋⣀⡀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢸
⣿⡇⣜⠋⠉⠑⠤⡄⠀⠘⠛⢦⠀⠀⠸⣿⠁⡏⠀⠢⠀⠀⠀⠉⢹⢶⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⣿⣿⡉⡧⣀⠁⠴⠴⠛⠻⢧⠀⠲⡗⢠⠷⠀⠐⠢⠀⢠⠀⠀⠈⢿⣷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡆⢻⣿⡗⡁⣸⣆⠠⠀⠀⢄⣿⣿⡴⠙⢏⠂⠀⢾⡄⡀⠀⢃⡀⣀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⣬⡉⠁⠀⢹⣿⡇⠀⠐⢻⣿⡏⠀⡀⠈⠀⠀⠀⣀⠙⣦⣋⠈⠩⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡁⠀⠂⡀⠀⢸⣏⠈⠙⡥⠀⠄⠣⠀⠀⠀⠀⠀⠙⠁⠀⠀⣼⣿⢠⠢⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡇⠀⠒⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠠⠌⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⢰⡀⢀⣐⡿⢿⡞⠋⠛⣿⣷⣦⠀⠀⠀⡄
⣿⡄⠈⠀⠀⡄⡀⠀⠀⡀⠀⠈⢀⣾⠟⢿⣷⠀⢰⡶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠹⣿⠎⠀⠈⠛⣹⣆⣀⣈⡍⠀⣬⡿⠿⠖⠀⠀⠳⣦⡄⠀⠀⠀⠀⢰
⣿⣤⡴⠀⠈⠀⠘⢦⣤⠁⠀⢀⣼⣿⣶⣾⣿⡧⠈⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⡀⠀⠀⢀⣿⣿⠈⠀⠀⢀⣁⡐⡧⠀⠀⠀⣼⣿⡇⡀
⣿⡇⢱⣶⣝⣿⡤⠾⠠⠀⠆⠬⣿⡏⠙⠉⣿⣇⣤⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡋⢴⠂⠤⠄⠤⢀⣀⣼⣿⣯⣀⣠⣴⣿⣿⠱⠷⠄⠀⠀⣝⡛⢪⠀⠀⠀⠀⢸
⣿⡇⠈⠁⢈⡏⠀⠀⠀⠀⠀⠘⠛⠃⠘⠀⠛⠃⠉⠉⠉⠛⠛⠳⠄⠄⢀⡀⠀⠀⠷⣮⣆⣀⡇⠀⠀⠀⠀⢸⠂⠀⠀⣾⠀⢠⣾⠂⢨⣿⢀⣸⣧⠄⠂⢀⣠⣤⣾
⣿⣇⣀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠉⠐⣆⣿⣿⠁⠀⠀⠀⠀⠁⠈⠁⠀⠈⠉⠁⠛⡟⣿⣿⣿⣿⡯⠇⢀⠈⠉⠉⡉⠈
⣿⣗⣤⠬⠥⣀⣐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣍⠲⢬⡒⢬⣑⠢⣕⡲⣅⣚⠙⢛⠁⢶⠀⠀⠄⠀⢠⡄⠀⠀⣤⠄⢴⣶⠟⢿⡟⠛⣿⠹⠉⠀⠀⠀⠀⢰
⣿⠗⣒⣉⡭⠥⠔⠒⣊⣉⠠⠤⠀⠂⢀⡀⠀⠀⠀⢀⣈⣳⣦⠽⠶⠞⠛⠋⠉⠩⠁⡀⡘⠀⠸⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⢸⣿⠀⣸⡇⢠⡏⠀⠁⠐⠀⠀⠀⠈
⣿⣏⣥⠤⠶⠒⣋⣩⡥⠴⠖⢒⣉⣩⣤⠴⠶⠚⠛⠉⢁⠠⠄⠀⠈⠉⠁⣠⠐⡶⠚⢣⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠀⣿⠇⢸⡇⠀⠀⢀⠀⠀⠀⠘
⣿⣧⠴⠖⠛⣋⣩⣤⠶⠖⠛⠋⠉⠀⢀⠀⠒⠁⠀⠀⢠⠴⠀⠘⠁⢀⡐⠃⠘⠃⠀⠸⢤⣅⠀⡀⠀⠀⠀⠀⡀⠀⠀⡇⠀⢸⡏⠀⣿⢀⣼⣠⠼⢠⣇⠄⠀⠀⢈
⣿⣧⠶⠞⠛⠉⠁⡀⠤⠀⠀⠀⠀⠀⠀⠛⢛⣿⣦⡀⠀⠀⠀⠀⢈⠀⢀⡀⡀⠀⠂⠠⣘⣿⠄⠀⠀⠁⠀⠀⠁⠀⠈⠉⠒⠋⣹⣿⠛⠉⠿⠇⠰⣿⠿⣄⡀⠀⢰
⣿⡇⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⢠⢤⡀⠀⠌⠛⠛⠁⠀⠀⠀⠄⠈⠿⠛⢂⠀⠀⠀⠀⡄⠀⠀⣤⣀⣦⣴⡇⠀⠀⠀⣸⣷⢨⠀⠀⡀⠐⠋
⣿⡇⠀⢀⡠⠀⠀⠀⠀⠀⠐⣦⣷⡤⠀⠀⠀⠀⣄⡀⡁⠀⠀⠀⠀⠀⢀⠔⢒⣁⡀⠀⠀⠀⠀⠂⠀⠈⠀⠀⣉⠀⡰⠏⠀⢀⡼⢧⠀⠀⢠⣿⡿⣣⣆⡀⠀⠀⢠
⣿⡇⠀⠀⠀⠀⠀⠀⠰⠊⠉⠉⠓⠀⢀⡄⠀⠀⠀⠀⠀⠀⠠⠀⠈⢀⣬⠒⠁⠂⠀⠉⠂⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⠀⠟⠀⠀⠁⠀⠚⢋⠁⠉⠉⠁⠀⣠⠘
⣿⡇⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠈⢰
⣿⣧⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⠿⠿⣿⡿⠿⢿

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⣪⣿⣿⣿⣷⣴⣦⡀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣶⣶⣰⣀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣾⣶⣆⣖⡀
⠀⠀⣀⢀⣄⣬⣿⣿⣿⣿⣿⣿⣧⠤⠀⠀⠀⠀⡄⣈⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⢀⠀⣹⣿⣿⣿⡷⣜⡾
⠀⠀⢐⣚⣽⣾⣿⣿⣿⣿⣿⣿⣿⣶⡖⠀⢐⠚⣥⢼⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢉⡤⣶⣿⣿⣿⣿⣷⣷⣦⠄
⠀⠀⠩⠟⢟⢿⣿⣿⣿⣿⣿⣿⣷⣾⠀⠀⢩⡟⢏⢿⣿⣿⣿⣯⣯⣿⠧⣭⠀⠈⢩⠻⠊⢿⣿⣿⣿⣼⣾⡾⢂⡅
⠀⠀⠐⠀⠙⢻⡛⣻⣿⣿⣛⣿⠓⠍⠀⠀⠀⠀⠉⠾⡿⣿⣿⣿⢟⡷⠲⠉⠀⠀⠀⠀⠁⠟⠿⣿⣿⡙⠋⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⢠⣤⣀⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀
⠀⠀⠀⠀⠀⠐⢒⢻⣷⣽⡪⢂⠀⠀⠀⠀⠀⠀⠀⠐⢀⢰⣷⡜⡂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠐⠠⠀⢰⣭⡾⣟⣿⡔⢢⡄⠀⠀⠀⠀⠀⠀⠑⣭⡽⡟⢯⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗
⠀⠀⠀⡠⣌⢲⣌⣳⣿⠟⡏⠂⡆⠁⠀⠀⠀⠠⡄⠐⣀⣒⣻⠉⣇⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⢀
⠀⠀⠀⠁⠀⢠⣭⢿⣿⡖⢉⠎⠁⠀⠀⠀⠀⠀⠀⢀⠉⠽⣿⠄⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠐⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿