Cute flower Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠂⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠈⠀⠀⠀⠀⢀⠄⡀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠔⠈⡡⠐⠒⠒⠊⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠨
⠀⠀⠀⠀⠀⠆⠀⡈⠀⠀⠀⢀⡀⠀⠀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠅⡐⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠡⠄⠀⠀⠐⡀⠀⠀⠀⠀⠀⣀⡈⠊⠐⢄⠀⠀⠀⣀⣀⢀⣠⡤⣐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠢⣡⠀⠘⡀⠈⠀⠀⠉⠍⠇⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠂⠠⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠰⠀⢠⡂⠀⠀⡯⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⡠⡤⢄⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡂⡀⠐⢃⠃⠀⠀⠅⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⣌⡞⠰⢁⠖⠉⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢤⢨⣉⠀⢀⠐⣲⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⢳⠎⠀⠐⡀⡠⠂⠙⢂⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⠀⡐⠄⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠿⣥⡀⠀⠡⡀⠈⠀⠀⠀⣀⢱⠃⠀⠐⣨⠖⠂⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠆⢁⠀⠀⠀⠀⠠⠄⠢⡀⠈⠻⠀⢀⠀⠁⠀⢀⣼⠤⠬⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠒⠚⠓⠄⠄⠁⠀⠀⠉⢂⠀⠀⠀⠀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⡀⢀⢀⡀⡼⢠⡑⣆⣏⢞⡇⠒⠲⢯⡉⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⠤⠋⠉⢀⢄⡀⠻⠵⣯⣜⠞⢅⠀⠀⠀⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠔⢁⠈⠀⠄⠀⣤⠀⠁⠈⡍⠒⠤⠤⠤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣂⠀⠀⠀⠀⠀⠀⠑⠒⢖⢻⠃⠀⠈⠅⡰⠱⠀⠀⠀⢁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠶⢿⠠⢨⠍⠀⢰⢡⠐⠀⠈⡀⢀⣠⡾⡀⢀⠓⢄⠀⡀⢈⢂⡀⠀⠀⠀⡄⡐⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠑⠏⢼⡏⢀⣣⠄⢤⠉⢠⡄⠀⠈⠀⣿⠅⢈⠡⠰⡠⠩⠄⢅⢶⣰⢂⠀⠀⠱⢶⡀⠀⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠁⣵⠐⣮⠅⠘⠗⠀⠟⠀⠠⠐⢯⡂⠀⠻⡄⠁⠐⠀⡠⠝⢴⠊⠍⣛⣬⠒⠀⣢⢭⣵⣈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⣶⠅⠀⠙⠺⡇⡷⠂⠀⠀⠟⠁⠀⢿⠾⠛⠹⠋⠀⠿⠊⠋⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⣰⠋⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠙⣧⠀⣿⢀⢀⡼⢁⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣤⡼⠀⠘⡿⠛⢱⠏⠁⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⡄⢰⠇⣀⡼⢿⣥⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠛⠉
⠀⠀⠀⠀⠀⠀⢰⠏⠉⠳⣤⡏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠸⣆⠀⣀⡟⢧⣤⣴⠇⠀⠀⠀⠀⠀⠀⠀⢸⡏⢷⡀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⣀⣈⠛⠻⣧⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢷⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣠⡴⢻⠆
⠀⠀⠀⠀⢠⠟⠉⢉⣽⣦⣬⡿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣧⠀⠀⢸⠃⠀⠀⢀⡴⠛⠁⢀⡟
⠀⠀⠀⠀⠘⢦⣤⣤⠞⠃⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠸⡆⠀⡿⠀⢀⡴⠋⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢿⢸⢇⡴⠋⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠹⣆⠀⠀⢸⣿⠟⠁⠀⠀⣀⡴⠋⠀⣠⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣤⡀⠹⣄⠀⠀⠀⠀⠈⠷⣄⣸⣯⣤⡤⠶⠚⠉⠀⣠⠞⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⠳⣄⠹⣆⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⢀⡴⠋⠀⢰⠇⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢶⠀⠀⢿⡀⠀⠈⢷⡹⡄⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣠⠟⠀⠀⢠⡟⠀⠀⠀⠀⣾⡁⣠⡟
⠀⠀⠀⠀⠀⠀⣠⢤⣄⠀⢧⣶⡾⠀⠀⠈⢧⡀⠀⠀⠻⣿⡄⠀⠀⠀⠀⣿⠀⠀⢀⡴⠃⠀⠀⢀⡾⠀⠀⠀⠀⢠⡟⢛⡿⠚⠳⡄
⠀⠀⠀⠀⠀⠸⣇⠀⢼⣧⣀⠘⣇⠀⠀⠀⠈⠳⣄⠀⠀⠙⣷⠀⠀⠀⠀⡟⠀⢠⡞⠁⠀⠀⢀⡾⠁⠀⠀⣀⣠⢾⡶⠞⠿⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠉⢛⣯⣥⣉⡽⠟⠶⢦⣄⡀⠀⠈⠳⢦⣄⣘⣧⠀⠀⠀⡇⣰⠏⠀⠀⠀⢠⡞⠀⣀⡴⠚⢉⠀⠀⢻⣿⠍⠛⡆
⠀⠀⠀⠀⠀⠀⢰⡏⢘⣹⠃⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠉⢹⡆⠀⢨⣷⠏⠀⠀⢀⡴⠋⣠⠞⣩⡴⠞⣿⠀⠀⠀⠙⠲⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢠⡶⠶⢤⣀⡀⠙⢦⡀⠀⠀⢷⠀⢸⣟⣀⣠⠴⠋⢁⡼⣣⠞⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠙⠲⣤⡹⣆⠀⠸⡇⢸⡏⠉⠀⠀⢀⡞⡼⠃⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣙⣻⣆⠀⠻⠘⠇⠀⠀⠀⠛⣼⣥⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⢀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⠄⠤⡀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⣀⡠⠀⠀⠤⠀⠀⠀⠀⠀⢇⠀⠀⢸⠔⠂⢢⠀⠀⠀⠀⠈⠂⠀⠘⡄⣐⣁⡀⠜
⠀⠀⢀⠤⢄⡁⠀⠁⠉⣇⣜⠉⠀⠑⠢⠤⠐⠀⠀⠰⡉⠁⠘⠶⠒⢪⡀⣀⣀⠅⠀⠀⠀⠀⠀⢠⢄⣰⠁
⠀⠀⡜⠀⠀⠑⡤⠤⡴⠋⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢤⠞⠒⢪⠀⠈⢉⠆⠀⠀⠀⠀⡈⠁⠀⡧⠄⠄
⠀⠀⠓⡤⠤⠒⢄⣀⠜⠤⡄⠨⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢆⢀⡀⢸⠓⠐⠁⠀⠀⠀⠂⠀⠉⠒⠚⡀⠀⢐
⠀⠀⠸⠄⡀⠀⢀⡇⠀⠀⣈⠆⠀⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⢀⠖⠉⢺⠉⠉⢡
⠀⠀⠀⠀⠈⠢⠊⠏⠐⠁⠀⠀⠀⠀⠀⠑⡆⠀⢠⠀⠒⠉⢆⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣸⠣⠄⠁
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⣣⣀⡀⣟⠀⠀⣈⠇⠀⠀⠀⠀⠀⠀⢀⣀⠀⡈
⠀⠀⠀⠀⢀⠔⠈⡩⢷⣐⠂⠄⠀⠀⠀⠀⠐⢥⠀⠀⢸⠄⢸⠉⠉⠁⣢⠀⠀⠀⠀⠀⠀⠥⠤⢘⠣⡈⢰
⠀⠀⠀⠀⠰⠤⠔⠁⠘⠢⡁⠁⠀⠀⠀⠀⠀⠀⠣⠐⡏⠀⠀⠳⠤⠜⠀⠀⠀⠀⠀⠀⠀⢠⠐⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠁⠈⠈⢰⠋⠙⠄⠀⠀⠀⢀⠊⠀⠀⢈⢠⣤⡠⠒⠉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⡀⠸⠀⠃⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠁⡰⠋⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠋⠉⠀⠸⢅⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠸⠀⠀⠀⢀⠈⠀⠀⠀⠐⠁⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡀⠀⢰⠀⠘⠇⢀⡇⠀⠀⢠⠂⠀⠀⢀⠄⠀⠀⠀⠀⠐⠉⠀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠳⡰⡄⠀⣇⢰⡄⣸⠀⠀⣤⠏⠀⠀⡠⠃⠀⢀⠔⠋⠁⠀⠀⢀⣀⠔⠁
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠁⢢⣀⠀⠀⠈⢧⡠⣳⣹⣾⣿⢾⡿⢿⣷⣾⡏⠀⣠⠞⠁⡠⠖⠁⠀⢀⡠⠔⠂⠈⠉⡷
⠀⠀⠀⢀⡤⠷⠒⠒⠒⠲⠤⢄⣈⠑⢦⣀⠈⢿⣷⠟⠹⠈⠈⠙⠁⠉⠉⢻⣾⣿⣔⣋⣠⡴⠖⠋⠁⠀⠀⡀⠴⠊
⠀⠀⠀⠻⢄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢬⣻⡿⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⢿⣿⣯⣁⣂⣤⡤⠶⠞⠛⠀⠀⠀⠐⠒⠠⢄
⠀⠀⢀⡠⠐⠊⠉⠀⠒⠢⠤⣤⣄⣀⣀⣸⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣋⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠈
⠀⠀⠻⣆⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣺⣿⣯⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⡿⠉⠉⠉⠉⠉⠉⠉⠉⠒⠲⠭⣁
⠀⠀⠀⠀⠀⡠⠈⠁⠈⣉⠭⠽⠟⠛⠛⠛⣻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠿⠶⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⢈⠗
⠀⠀⠀⠀⠸⣁⠴⠚⠉⠀⠀⠀⢀⣠⣴⠾⠟⢻⣦⡋⠠⣀⠀⠀⡀⠬⣐⣶⣟⠳⢄⡀⠀⠀⠀⠀⠉⠛⠋⢉⠉⠉
⠀⠀⠀⢀⡼⠁⠀⣀⡤⠴⠒⡩⠐⠈⠀⢀⣰⠏⢸⣿⢿⡶⢷⣷⣾⣿⣏⡇⠘⣧⠀⠈⠐⠠⣀⠀⠀⠀⠀⠀⠙⠢⣦
⠀⠀⠀⠀⠉⡾⠋⠁⣀⣠⠊⠀⠀⢀⡴⠛⠁⢠⠏⠀⢨⠃⢸⡏⠈⠹⡏⣷⠀⠈⠣⡀⠀⠀⠈⠢⡀⠀⠠⠤⠄⢤⠜
⠀⠀⠀⠀⠀⠉⠉⠉⢀⠀⠀⣠⠖⠉⠀⠀⢠⠏⠀⠀⡌⠀⢸⡇⠀⠀⠹⡘⡄⠀⠀⠘⢦⡀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠊⡝⠀⠀⠀⣠⠃⠀⠀⣰⠃⠀⢸⢻⠀⠀⠀⢁⢱⠀⠀⠀⠈⠈⠢⣄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠀⢀⡴⡇⠀⠀⢰⠇⠀⠀⢸⡌⡄⠀⠀⠸⡈⢧⠀⠀⠀⠠⠀⠀⠑⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠒⠁⠉⢻⣄⣡⠋⡀⠀⠀⢸⡇⠱⡀⠀⠀⣧⣈⣧⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢱⡀⠀⢸⡃⠀⠳⡀⠀⣿⠀⠈⠛⢦⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠞⠉⠁⠀⠈⠲⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠰⠀⠹⣤⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣼⣿⣧⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠃⠀⠀⠈⣿⡿⢆⠀⠈⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⢀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡴⠁⠀⢀⡜⢀⡀⠀⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⡄⠉⠀⠀⠀⠾⠀⢸⡇⠀⠟⢦⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠢⠀⠀⠀⠀⠇⠀⠀⡠⠃⠄⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠀⠱⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣀⣶⡆⠀⠀⠀⡀⣦⡴⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⣹⣿⣿⣧⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⡏⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⡀⠀⠀⠀⠀⣠⣾⡇⣠⡶⠂⠀⡘⠀⠀⠀⢀⣻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⡛⢻⣿⠞⠁⠀⠀⡀⢺⠉⠛⢻⡿⠁⠀⢴⠇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⢿⣿⠟⠉⠀⠀⠀⠀⢻⣶⣤⣤⠈⢠⡞⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠶⠿⠛⠂⠁⠀⢀⠛⢺⡟⢧⡀⣰⠀⠀⢠⡟⠛⠉⠁⠀⡿⠿⢻⠁⠀⠀⠀⠀⠀⠄⢀⡆⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠈⢻⠿⠀⢀⣿⠂⠀⠀⣠⠆⠀⠀⣸⠀⠀⠀⠀⠀⣼⣾⣿⡿⢶⡄⠀⠀⠘⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠁⣼⠃⠀⠀⢰⠏⠀⠀⢀⡇⠀⠀⠀⣦⢾⣻⣿⡇⠀⠀⢹⣦⠀⠀⡈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⡇⠀⠀⣼⣿⡟⠡⠙⠆⢐⠀⠀⢿⠀⠈⠀⠀⠼⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⢠⣀⠀⠀⠸⠃⢀⡀⠀⠸⠇⠀⠀⠉⠉⢀⠀⣰⣶⠞⠀⠀⠈⠀⠀⠀⢠⣦⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠐⠆⠈⠙⠀⠀⣠⣶⣨⣶⠖⣁⠀⠀⠀⠀⢠⠈⠀⠉⠁⠀⠀⠈⠀⠠⠆⣤⣿⡿⠀⠀⠸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣷⠂⠈⠋⠁⠀⠀⠠⣎⠑⠀⠀⠀⠀⠀⠀⠀⠀⡘⠨⠛⠁⣴⣦⣤⢿⡉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠾⠃⠀⠀⠀⠀⠀⠀⠀⢠⡄⠲⣿⠀⠀⠀⣸⣷⡄⢀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⣟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠏⠀⡄⠀⠀⠀⠀⠀⠀⠀⢨⠰⢦⣽⠀⠀⢠⡟⠻⠀⢿⡇⣀⣠⣦⣄⣠⡞⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⢠⡀⣥⠀⠀⢸⣥⠌⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⡈⠻⣿⡀⠀⢸⡇⣼⠏⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⣧⡀⢸⡿⠃⢀⣤⡇⠀⠀⠀⠀⠀⢤⡀⠀⠤⠄⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡟⢷⣀⠇⠀⣾⣿⣿⠆⠀⠀⡀⠀⠀⠀⣼⣷⣦⣄⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢸⣸⠀⣻⠀⠁⡆⠀⣿⡿⠁⣄⠀⡀⣁⣀⠀⠀⠙⠛⠛⠁⠀⠀⣿⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣸⣿⠀⢹⣀⠀⠃⠀⠘⡇⠀⢿⣴⠟⣿⢹⠇⠀⢀⣀⡴⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⣤⠀⠀⠀⠀⠀⠀⠈⢻⡟⠆⢸⡟⠀⠀⠀⠀⠇⢰⡇⣀⣄⠹⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⢀⠀⠀⣸⣴⣿⣿⣿⡿⠐⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣇⣼⣧⣾⣿⡿⠋⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣾⣿⠷⠆⠀⠀⢸⢆⡿⣿⠿⠟⢋⣁⣄⢸⣿⡆⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠃⠀⠀⠀⠀⠀⠀⠸⣿⡇⣿⡷⠞⢿⣿⣿⣿⣿⣿⡾⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠧⢤⣀⠀⠀⠀⠀⠀⠈⠀⣹⠃⣾⡿⢀⢀⣹⣿⣿⣿⣿⠿⣟⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⢺⣿⢀⣿⣿⠏⣾⣿⣿⣿⡏⣿⠟⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⢸⣿⢏⣽⠃⠀⠀⠀⠀⠻⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⡆⢸⣿⠿⣿⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣼⣿⠀⣸⣧⣤⡦⠙⠛⠛⠓⠀⠐⠓⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣷⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠀⠒⠠⡄⠀⠀⢀⠄⠒⠀⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠈⠀⠈⢂⣰⠅⠀⠀⠀⠈⠠⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⡀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠰⢰⡖⠈⠠⠀⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠈⠉⠲⢿⡄⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠆⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⣘⣐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⣀⡀⠴⠤⠤⠀⣀⡀⠀⡰⠃⠀⠀⣀⠤⠚⠛⠉⠉⠩⢉⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠉⢠⡄⠀⡄⠘⠂⠀⠈⠙⡧⣀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⠉⠉⠐⠂⠤⠀⣀⠀⠔⠁⠀⠀⠀⠤⠀⠀⠛⠀⠈⠀⠈⠁⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠰⠄⠰⠂⠀⢃⠈⠀⠀⠀⠘⣂⠀⠀⠀⠀⠀⠀⠀⣠⣡⡎
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⢩⡤⠤⠄⠀⠒⠒⠉⠁⠠⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⣀⠀⠀⢀⣀⠠⠤⠦⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⠟⠋⠀⠀⠀⠀⠐⠀⠀⢠⠄⢢⠀⢖⠀⠐⠐⠦⠀⣠⡀⠀⠀⠀⠘⠈⠉⠀⠒⢤⣀⠀⠀⠀⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠑⠒⠊⠀⠀⠥⠌⠀⠀⡜⠀⠀⠀⠀⠀⠀⠈⠛⠦⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠢⠀⠀⠀⠀⢀⣠⠴⠊⠀⠀⠈⠁⡶⠤⠤⠄⠤⠤⠐⡖⠉⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠴⠶⠾⠋⠁⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠁⢤⣀⣀⣀⠀⠄⠁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⡉⢻⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⡀⠀⠀⠀⡀⣰⢿⡀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⢀⠀⠞⠁⠘⡀⠀⠀⠀⠀⢀⠐⡙⠈⠳⣁⠀⠀⠈⠀⠄⠁⠀⠀⠀⢀⠀⠂⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠀⢀⡠⠔⠁⠀⠀⠀⠉⠁⠉⢁⠀⠤⠄⠒⠉⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⡠⠆⠁⠀⠀⠀⠀⡆⢀⣴⠯⠄⠀⠃
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡰⠊⠀⠀⠠⠀⣸⠃⣰⡴⠏⠤⢤⠄⠘
⠀⠀⠀⠀⠀⠀⠈⡅⠘⠃⠠⠤⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡐⢁⡆⠀⡴⠃⣠⣥⠞⠋⠀⠀⠀⠀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⣄⠀⠀⠀⠀⢻⠀⠀⠀⠀⡇⢸⠀⣠⣴⠞⠋⠀⠈⠉⠉⠉⠁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢒⡀⠀⠙⠦⣄⢸⠀⠀⢰⠀⠐⡄⠀⡀⠑⢄⠀⠀⢻⠀⠀⠀⠀⢃⡼⠞⣉⣀⣁⠐⠒⠒⠒⠂⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠋⠉⠙⠳⢤⣀⣃⠀⠸⠀⠹⡆⠀⠆⠀⢸⠀⠀⢀⡴⠋⠑⠄⢀⣀⣀⣀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠠⠤⠄⠒⠒⠉⠙⠳⣦⣇⡀⠸⠀⠀⠀⢸⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠴⠞⠃⠀⠈⣙⠷⣄⡀⠀⢸⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠤⠀⠀⠈⠉⠀⢠⠜⠳⣄⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡄⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⡇⠐⠀⢺⢀⠔⠁
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠒⢤⡇⠀⠈⠿⠃⠀⢰⠠⠔⠲
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⠀⠀⠠⠤⠤⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠒⢒⣒⣛⠋⠉⠁⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣴⠟⠉⠉⠉⠛⠶⣤⣀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣠⠾⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⣻⡶⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡄⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣿⠁⠀⠀⠀⠀⢀⣤⠴⠶⠶⣤⣀⠀⠀⠀⠀⠀⣀⣀⠀⢠⡟⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢰⡏⠀⠀⠀⠀⢰⡟⠁⠀⠀⣠⡴⠟⠛⠶⢶⣟⠋⠉⠉⠙⠛⠳⣤⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢠⡟⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⠟⠶⠦⣄⡀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠹⣆⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢿⡄⠀⠀⠈⣷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡆⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠻⢦⣤⣴⠟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣹⠷⣄⡀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢰⡏⠀⠈⠙⠛⠶⣤⣄⡀⣼⠛⠶⣤⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⣿⠤⠶⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣿⠀⠀⠀⠀⠀⠀⠈⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠋⠁⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢳⣶⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⣀⣤⣤⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣦⠀⠀⠀⠀⣼⠏⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡏⣿⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣸⠃⣿⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⠀⣿⠀⢀⣿⠃⠀⠀⠀⣀⣀⣤⣤⣤⡤⠤⠤⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣿⠀⣿⢀⣿⢃⣠⠴⠚⠋⠉⢁⣀⣠⣤⡴⠶⠚⢛⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢸⡄⣿⣾⠟⣋⣠⡤⠶⠚⠛⠉⠉⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⣿⣿⡟⣛⣉⣁⣀⣀⣀⣀⣤⠤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⠶⣤⡟⠁⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠙⢦⣤⠞⠋⠉⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⣸⡧⠤⣄⠀⠀⣸⠇
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⡾⠁⠀⠀⠈⣿⠙⠛⢦⡀
⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣀⡤⠾⠤⣤⣠⠴⠖⠾⢦⣄⠀⠀⠀⠀⠀⠀⠈⠓⡶⠶⠻⣤⣀⣀⡴⠋⠀⠀⠈⡧
⠀⠀⠀⠀⡴⠚⠉⠙⠒⣾⠁⠀⠀⠀⠀⠹⡆⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣠⠾⣇⠀⠀⠀⠈⠳⣄⠀⠀⢀⡴⠃
⠀⠀⠀⣸⠁⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣸⠀⠀⠀⢠⡞⠁⠀⠈⠳⢤⣤⡤⠞⠉⠉⠉⠉
⠀⠀⠀⠸⣄⠀⠀⠀⠀⡾⠉⠓⠶⠖⠻⣥⣀⡀⣀⣀⡴⠃⠀⠀⣰⠋
⠀⠀⠀⠀⠈⠓⠶⠶⠞⣧⠀⠀⠀⠀⠀⠀⡿⠻⣏⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⣀⡤⠶⠒⠛⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣠⡤⠞⠁⠀⠘⣧⠀⠀⢰⠇⠀⠀⣀⡴⠋⠁⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠦⢤⣄⡀⠀⠀⠘⣧⠀⡿⠀⢠⡞⠁⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠘⠧⢤⣀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⢸⣆⡇⣴⠋⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⠀⠀⠙⢶⣿⡿⠁⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠶⠶⠶⠒⢻⡧⠶⠶⠖⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢳⣿⣾⣧⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣿⣿⣿⣿⢫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠔⠛⠉⠻⠀⠀⠀⠀⠀⠀⠎⢁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠁⠀⠀⠢⢾⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀⢀⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠈⠻⠿⣄⠀⠀⠀⠀⣀⣀⡀⠀⢠⣀⠈⣣⠀⠀⠀⠀⠈⠿⠟⠓⠖
⠀⠀⠀⠀⠠⢲⣿⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠠⢼⣿⣴⣿⣿⡧⠄⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠈⠙⢛⡏⠁⠀⠀⠴⠶⠯⣳⣄⣼⠀⠀⠀⠀⠀⠀⠒⠿⡿⣿⣻⡷⠒⠀⠀⠀⣀⢠⣀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⢀⠔⠂⠀⣿⣿⣤⠀⠙⠏⠀⠀⠀⢤⡄⠀⠈⠐⠀⠈⢃⠀⠀⠀⠄⢸⢋⡘⣡
⠀⠀⠀⠀⣄⣠⠤⠄⡟⠀⠞⠀⠛⠛⠿⡇⠀⠀⢀⣴⠆⠀⠁⠀⠀⢰⡴⠟⣳⠂⠀⠀⢀⡴⠋⢉⡥
⠀⠀⠀⠈⡽⠿⠀⠀⠀⣀⠀⠀⣀⣤⢠⣆⠀⠰⠿⠋⠀⠶⠲⢤⣄⣬⡶⠛⠁⠀⢠⡄⠤⠀⠒⠊⠀⠠⣴⣿⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⠐⠌⠃⠙⠘⠀⢀⣀⣤⣄⠘⠻⢶⡜⠃⣀⡀⠰⢤⠈⠁⢀⡀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⢘⢦⣄⢂⢤⡀⡟⠠⡀⠀⢀⣤⣸⡟⠒⠁⠰⡀⠀⠨⡷⠛⠋⣉⠀⠘⠀⠀⣨⣿⠿⣅⠀⠀⢿⡄⠀⢀⡤
⠀⠀⣤⡀⠀⠻⠈⣱⡾⠿⠇⠀⠈⣉⠉⠁⠿⡃⠀⠀⠀⣈⡦⣠⣤⣤⡞⠁⢀⣀⠀⢠⡴⣡⢤⠀⠄⠀⠀⠁⢠⣾⠃
⠀⠀⠈⠛⠿⠀⢸⣋⢤⣤⡀⠀⠀⠹⣷⡀⠀⠀⠀⠀⣴⠛⠁⢈⡀⠭⠭⠍⠛⠃⠀⠀⢤⡁⡤⠀⠃⠸⢷⡦⠈⠁
⠀⠀⠀⣠⠶⠶⠆⠈⠁⠸⠿⠀⠀⠀⠹⠃⠀⠀⠀⢸⠇⠁⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⣴⡶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠻⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡆⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⣴⠶⠛⠛⠛⠛⠛⠛⠷⠶⣤⡀⠀⠀⠈⠻⢄⠀⠀⠀⡧⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⢀⣠⡀
⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⣧⠀⠸⡀⠀⠀⠀⠀⡇⠀⠀⣾⠀⠀⠀⠀⢀⣼⠿⣿⡇
⠀⠀⠹⣿⣿⣄⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠈⠻⣆⠘⣷⡀⢛⡀⠀⠀⠀⡇⠀⢀⡏⠀⠀⣠⡾⠋⠁
⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⢷⡘⢷⡀⠡⠀⠀⠀⠀⠀⣼⠃⣠⠞⠁⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣀⠀⠀⠀⠀⢠⣬⠛⠀⠀⠹⢆⢻⡄⠀⠀⠀⠀⠰⢋⡼⠁⣠⣤⡾⠟⠛⠉⠉⠉⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣤⣀⣈⠉⠀⠙⠲⡄⠀⠘⠃⣐⠛⠶⣤⣴⡿⠀⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢷⣦⡄⠀⢀⣀⠀⣿⠀⠀⠈⣿⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠴⠶⠶⠶⠶⠿⠿⠿⠿⠋⢰⡆⠙⠛⠉⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡿⠿⠈⢿⣄⠀⠀⣀⣴⡿⠃⠀⢶⣤⣤⣀⣀⣀⣀⣠⣤⣴⣶⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠟⠋⠀⢀⣴⠃⢀⣿⠿⠟⠛⠉⠀⠠⡀⠰⢄⡙⠛⠛⠛⠛⠉⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠟⠁⠀⠀⢀⣴⠟⠁⣴⡟⠁⣰⣾⠃⠀⠀⠀⠀⢀⡀⠙⢶⣄⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠋⠀⠀⠀⢀⣰⠟⠁⢀⣾⠟⠀⠐⣿⡟⠀⠀⠀⠀⠀⠈⡀⠀⠀⠈⠓⠄⠀⠀⠀⢹⡇
⠀⠀⠀⠀⣰⣿⣿⡿⠃⠀⠀⢀⣠⣴⠞⠁⠀⣠⣿⠋⠀⢀⠿⣿⠇⠀⠀⠀⠀⠀⠀⠃⠀⣴⣦⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠿⡿⠋⠀⣀⣼⡟⠁⠀⢀⡜⠀⢻⠆⠀⠀⠆⠀⠀⠀⢸⡄⠙⠛⠋⠀⠀⠀⠀⣿⠃⢸⣿⣠⣤
⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠿⠷⠶⣶⡿⠡⣤⡘⠀⠀⣤⣤⡀⠀⠀⢸⡇⠀⣸⡆⠀⠀⠀⣸⡟⠀⢠⠟⠙⠛
⠀⠀⣾⣿⣿⠀⠀⠀⣀⣀⣤⣶⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠈⢿⣿⡟⠀⠀⢸⡇⠀⣿⠁⠀⠀⢠⡿⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠛⠛⠛⠷⠶⣦⣄⡀
⠀⠀⢿⣿⡟⠻⠿⠿⠿⠟⠋⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⢹⠀⠀⢀⣿⣧⡼⠁⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦
⠀⠀⠀⠀⠈⠉⠑⠒⠀⠀⠀⠀⠈⠿⣷⣄⠀⠀⠀⠈⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⢠⡿⠁⠠⣾⣤⣤⣾⡿⠋⣰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣀⠀⠀⠀⠀⢀⠀⠀⠙⢷⣦⣴⠟⠁⠀⠀⢀⠀⠉⠻⣇⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠛⠁⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⣦⣤⣤⣤⣤⣄⡀⠈⠀⠀⡀⠀⣀⡀⠙⠆⠀⢹⡇⠰⠶⠶⠶⠶⠞⠛⠿⠷⠀⠀⠀⠀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⣉⠠⢶⣷⠀⢿⡀⠈⠃⠶⠆⠀⢸⡇⠀⣀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢃⣀⠤⠤⠚⠋⢀⣀⠠⠄⠹⣧⡈⠻⢦⣤⠀⢀⣴⠟⠠⢦⣼⣟⣛⣛⢛⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠀⣠⠴⠛⠁⠀⠀⠀⣤⠈⠛⠷⠶⠶⠾⠛⠁⠀⠤⢄⣀⠉⠙⠿⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣄⢀⡾⠁⠀⣴⠂⣾⣶⡄⠸⣦⡀⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⠉⠸⠇⢀⣾⡟⠀⣿⠻⣷⠀⢉⠳⣄⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⣿⡆⠹⣧⡈⢠⣬⠸⠇⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠁⠀⠀⠀⣹⡇⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣤⣴⣾⠿⠋⠁⠀⠀⠀⢠⣤⣾⣦⡀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠻⠇⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣄⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁


⣿⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠁⠈⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣾⣶⣶⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣄⣄⡀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠂⠀⠀⠀⠀⠀⠀⠸⠎⠁⡄⠉⠻⡃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠂⣠⣸⡇⠀⠀⡁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠢⠉⠀⠠⠟⠐⣄⣞⠁⠀⠀⢀⠀⢀⠀⢉⠙⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠰⠀⠀⡎⠀⠀⠀⡰⣄⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣘⠀⠀⠀⠀⡀⠀⠀⠀⠀⣷⠀⠀⢀⣰⢀⡔⠀⠀⠀⠀⡗⠘⡖⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣿⡆⠀⠀⠈⠀⠀⠀⠀⣿⣶⠀⢨⣿⣿⠿⠃⠀⢀⣠⣤⠎⠀⠀⠀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⡀⢀⡀⢀⣸⣿⡟⠀⠀⠘⢧⡀⠀⠀⠈⣿⡟⠀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⢤⡀⠀⠀⠀⠑⣆⣄⡀⠘⢣⢋⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠙⣠⠘⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠜⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠉⠁⢀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠉⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠈⠁⠀⠀⠀⠀⠸⠂⠉⢩⡇⠀⠁⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⣹⠖⢆⣀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠈⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣤⡀⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⣸⣤⣤⡜⠂⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢽⣿⣿⠿⠭⠤⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⠏⡠⡀⢀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠋⠀⠀⠀⣠⠀⠀⠀⠀⢀⣠⢻⡟⠀⠸⠿⡀⠀⠈⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠈⠠⠀⠀⠀⠈⠁⠄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠢⡀⠀⡀⠀⠀⠀⠀⠀⢀⠇⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠈⢂⢡⠀⡆⡄⠀⠠⡂⠐⠉⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⡀⠀⢡⣆⣁⠀⣴⠋⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠐⠈⢠⠊⠄⠠⠌⠇⠀⠀⠒⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⢒⡒⠖⠚⢄⠐⠃⣀⠾⡐⠂⠤⢀⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡠⢂⠀⢰⡏⠉⠀⡀⠀⠁⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⡇⠀⠂⠈⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⡠⠒⠠⡀⠀⠀⠀⠈⡀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠢⠀⠀⠀⠈⠂⡀⠀⢠⠃⡇⠂⠀⠀⠀⠀⠀⢀⠠⠊⡠⠂⡁⠀⢀⠔
⠀⠀⠀⠀⠀⠡⡀⠀⢀⠀⠑⡀⠀⠀⠀⠈⠉⠁⠀⠐⠈⢄⣀⡀⠄⠂⠁⡠⢊⠀⠊⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠱⡀⠈⢂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠎⡠⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠢⡀⠑⡄⠀⠀⠀⠀⢡⠀⠀⠀⠀⡠⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠌⡀⠀⠢⡀⠀⠀⠃⡄⠀⠀⠜⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠤⡈⠢⡀⠰⠠⠀⡌⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣐⠆⢞⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣧⠀⠀⠀⢀⡀⢰⠇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠰⡆⢽⢿⢀⣀⡀⢸⠅⡿⠀⡿⠀⠀⠀⢀⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣆⢠⣀⡄⢻⢸⣿⣸⣿⣯⣾⢰⠃⢰⣇⣤⣦⢄⣾⡟⣠
⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⣟⣎⣻⣾⣿⣤⡏⣿⣿⣿⢷⡎⣶⣼⣿⣿⣯⢞⢟⡼⠁⠀⠀⠀⢀⡄
⠀⠀⢀⣶⣄⡀⢀⣤⢆⣷⣜⣎⢻⣿⣿⡜⡇⢸⣿⡟⡿⢠⡇⣸⣿⣿⠏⣼⣾⣶⣷⡶⣠⣴⣯⠞
⠀⠀⠀⡙⠻⣝⡮⣝⣿⣿⣿⡻⣇⠹⣿⠇⢣⠸⠉⠀⠃⠸⠁⠜⣿⢃⡞⣽⣿⣿⣯⢞⡵⢋⣡⠆
⠀⠀⠀⠉⠓⢦⣙⠮⣙⠿⣿⣿⡊⢦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠸⣿⠟⠫⢖⣥⣶⣩⣀
⠀⠀⠀⢀⣼⣶⣿⣿⣟⡦⣌⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣤⣾⣿⣿⡿⢛⣀⣤⣴⣶
⠶⢤⣶⣶⣬⣽⣿⣿⣿⣿⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠿⠿⣛⣻⠭⠿⠚⣋⣉
⠀⠰⠦⠤⢭⣭⣉⡛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣏⡍⠁
⠀⠀⠀⢰⣾⣿⣿⣿⣿⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣿⣿⣿⣿⠿⠿
⣀⣀⣠⣬⠭⢽⣿⣿⣿⣿⡻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⣶⠦⢶⡗⠞⠯⠽⢿⣿⣿
⠹⠶⠛⣛⣋⡭⣵⣿⣽⣶⣷⣦⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⢿⣿⣿⣿⣿⣏⡛⠒⠲
⠀⠀⠈⠉⠀⢲⣿⣿⣿⡿⣋⣠⢖⣡⣀⢄⠀⠀⠀⠀⠀⠀⠀⡄⠠⣄⣬⣝⢦⣬⣛⠿⣛⠿⠇
⠀⠀⠀⠀⠀⣈⡵⣾⠵⣪⣿⣵⣿⣿⢫⢎⣰⣴⣀⡄⡇⢲⣠⣜⢦⠘⢿⣿⣷⣿⣦⣝⠻⣽⣲⣄⣀
⠀⠀⠀⠴⣿⠷⢋⣥⠞⣹⣻⣿⣿⢷⣯⣾⣿⣼⣿⣧⢷⠘⣿⣿⣯⣿⢮⢿⡿⣿⡷⠈⠳⠆⠉⠛⠉
⠀⠀⠀⠀⠁⠀⠉⠀⠀⠘⠟⣴⢋⡾⣿⣿⢇⣿⣿⣿⣿⢦⢻⣿⣿⡿⣦⠳⣵⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢡⡟⠀⠻⡿⢸⢼⣿⡟⢻⠸⡿⡜⡿⠛⠈⢧⡙⢮⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⣿⠈⠁⠀⢸⡄⢷⣷⠀⠀⠀⠀⠀⠈⠁⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣏⣀⣀⣀⣀⣀⣸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣶⡄⢠⣶⡆⠀⣴⣄⣤⠀⢀⠀⠀⠀⠀⠰⠊⠉⠀⠀⠀⠈⠉⠀⠀⣀⠄⠊⠁⠀⠀⢸⠋⠉⠉⡁⣻
⠀⠀⡍⠀⠉⢹⡇⠀⢿⣿⠟⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⡟⠀⢀⢀⠁⣿
⠀⠀⣧⢀⣀⠈⣧⠀⠀⠀⠀⠀⠨⠀⠠⠀⠀⢀⣤⣶⣿⢟⡴⠋⠀⣤⡤⣤⣤⣀⠀⠀⢰⣷⢣⣾⣷⠀⣿⡄
⠀⠀⣿⠈⠁⠀⣿⠀⠀⢰⠀⠀⡄⠀⠐⠀⠀⠭⢭⡿⠞⠋⠀⠀⢰⠋⠀⠛⠛⣿⣷⠀⢸⠙⠿⠿⠿⢰⣿⡇
⠀⠀⡟⠀⠀⢘⡇⠀⢀⣿⠂⠒⢀⠠⠀⡀⠀⠀⠀⠀⣴⠂⠀⠀⢈⠀⠀⠀⠀⢸⢿⠀⠸⠄⠀⠀⠁⠼⡿⠗
⠀⠀⠥⣀⣀⡠⠏⠀⠘⠿⠤⠦⠀⠀⠠⢀⡀⠀⠀⠘⠋⠉⠁⠀⠈⢤⡀⠀⢀⣾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠰⢃⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⣤⡤⠤⠄⠄
⠀⠀⠀⠄⠀⠀⠀⠀⠀⢈⡀⠈⠠⣄⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠰⠥⠜
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⡁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠂⠠⣶⣶⣤⣤⡀
⠀⠀⣆⠈⠡⠀⠀⢀⡆⠀⢘⠁⠚⠉⠀⠈⠀⠀⠀⠀⠀⢻⣦⣀⣀⣀⣶⣿⠀⠘⣦⡤⠤⠤⠶⠿⣿⡿⢯⡇
⠀⠀⠘⢀⡀⠀⣐⡟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⠁⠘⠿⠿⢻⣿⠀⠀⠹⣆⠀⠀⠀⠀⠉⢀⡞
⠀⠀⠀⠀⠥⠹⣏⠀⠀⠀⠀⢠⣴⣦⣾⣿⣿⣷⣦⡀⠀⢿⣄⣰⣶⣶⣾⣿⠤⠀⠀⠸⠷⠤⣤⣶⣶⡿⠶
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠋⠉⠉⠉⠀⠀⠀⠈⠈⠉⠉⠉⠁

⠀⠀⠀⠀⢀⣤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣆⠂⡀⠄
⠀⡀⠠⠶⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣸⣿⠼⡄
⠛⠱⠟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣷⠕⠿⣆⣦⣤⣄
⠀⠒⡀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⡰⣦⣿⡟⣟⠋
⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡶⢷⠉⠁⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡎⣀⡏⣿⣿⣾⣾⣷⣾⣷⡴⠂⠴⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢂⠀⠶⠮⠁⠀⠀⢻⣿⣿⣿⠛⣻⣿⣿⠃⠀⠀⡉⠉⣴⣶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠚⠏⠁⣿⣇⣶⣿⢷⣿⠝⠀⠀⠀⠁⠀⠀⠈⠉⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⢈⣻⡆⠀⣀⠉⠀⠀⠉⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠐⠀⠀⠀⠒⠊⠥⣦⣾⠅⠀⠀⠀⠠⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣆
⠊⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⡀⠙⣹⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠁


⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣣⠽⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣣⠟⢠⠟⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡡⢼⡈⠎⣂⡰⣏⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠇⡑⠚⣧⠀⠄⣸⢯⣀⣏⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡗⠉⠑⢈⠤⠿⠈⢉⠵⡂⠠⣹⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⡋⡲⠎⣼⡁⡑⠎⢻⣉⣅⣁⢜⡑⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡱⣨⠁⢀⣌⠉⣱⠓⠟⠡⠀⡷⢰⠧⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢌⡓⠂⢐⠟⢋⡶⠛⠛⠾⠥⡵⠖⠋⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠯⠤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⠝⣋⡭⠭⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡆⠊⡡⠈⢲⣉⠮⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣉⣥⡀⣽⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣻⡓⢙⣶⣎⣃⠀⣸⠨⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣽⣫⢼⣀⡵⠔⠳⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢈⡳⢜⣃⠜⡑⠰⣀⡓⢊⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢡⡁⡤⢸⢇⡀⠒⢹⣦⣀⣀⠀⠀⠀⠀⠀⠀⡤⣞⠑⠈⡗⢦⣗⡈⡟⣉⡉⢉⣛⢲⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠼⣦⢱⣏⣣⡴⠋⣱⣤⣤⣧⠌⣹⠶⣄⠀⠀⢸⠗⢇⠗⢶⠋⡻⠼⢎⣷⡥⢞⠐⠒⡖⢙⡞⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⢤⡾⠶⢎⢁⡋⡎⠰⣶⠀⣜⡙⢌⠢⣈⣇⠀⠘⢦⣜⠳⣙⣦⣒⣡⠛⣀⣯⡽⠶⠚⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠺⣄⡱⢀⡟⠣⣑⡴⠿⡃⠈⠃⣸⠀⣇⡟⠀⠀⠀⠉⠙⠛⠚⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣼⣧⡨⢇⠆⢀⣾⠋⠂⡔⠁⠑⡟⢲⢊⡝⣰⠟⠁
⠀⠀⠀⠀⠀⠀⣰⠧⣠⣧⠮⡖⠻⠤⡟⢩⠑⢢⣴⣫⣾⠿⠚⠁
⠀⠀⠀⠀⢀⣴⡷⠾⠗⠒⠛⠛⠛⠛⠋⠉⠉⠉⠉
⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠿⠛⠉⠉⠁⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⢿⣧⡀⠀⠀⣸⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠉⠙⠳⠦⣄⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠿⠷⣄⡀⠀⠀⠙⠲⢄⡀⠀⠀⢿⣇⠀⢀⣴⣶⡄
⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣶⣦⣤⣄⡀⠉⠢⣄⠈⢿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠷⣤⡈⠑⢄⠻⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣙⠳⣄⠳⡝⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⢀⣴⣿⡿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣷⣮⣦⡈⢮⠻⣿⣷
⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣄⢣⡙⣿⣇
⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠣⠈⢻⣆
⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣀⣀⣠⣤⣶⡿⠋⠀⠀⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠙⣿⣆⢃⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡷⠈⠻⣆⠀⠀⠀⠀⠀⠈⣿⡎⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡅⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⢹⡆⠀⠀⠀⠀⠀⢸⣿⡀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⣠⣾⣿⠟⠛⠉⠉⠙⠻⣆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡇
⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣼⠇
⠀⢠⣿⣿⣯⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠒⠀⠀⢰⠇⠀⣸⡇
⠀⢹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠞⠀⢠⡿
⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠹⢿⣿⡿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⢀⣠⡼⠋
⠀⠀⠀⠀⠻⣿⣷⣄⠀⢰⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠙⠿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠿⠟⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡄⣠⣶⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣠⣾⣫⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡟⢀⣾⣿⣿⣽⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⢉⣽⣿⠏⢀⣾⣿⣿⢷⣿⣟⣿⣿⢡⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⣾⣿⣿⣿⢸⡟⣼⣿⢃⣿⣿⣿⣿⣿⣿⣿⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⢱⣿⠃⣾⣿⣿⡟⣿⣿⣿⡿⠀⣾
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢀⠀⠀⣧⢹⣿⣿⣿⣿⣿⠏⣼⣿⣿⢋⣾⣿⣿⡿⢡⠀⣿⡆
⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⣾⠀⠀⣿⣆⢿⣿⣿⣿⡟⣼⣿⢟⣵⣿⣿⡿⢋⣴⡟⠀⣿⡇
⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⣿⠀⠀⢿⣿⣎⢿⣿⣿⢰⣿⣷⣿⠿⢛⣡⣶⡿⢋⡀⠀⣿⡗
⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⢿⣷⡀⢻⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣵⣾⣿⠟⣋⣴⠟⠀⣰⣿⡇
⠀⠀⠀⣄⠸⣿⣿⣆⠀⠀⠀⠀⠀⢻⣿⣜⣷⡀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣟⣭⣶⣿⠟⠁⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⣠⡶⠁
⠀⠀⠀⠸⣆⢹⣿⣿⣷⡀⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠿⠋⠁⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⢀⣴⣾⠟
⠀⠀⠀⠀⣿⡄⢿⣿⣿⣿⡄⣄⠀⠀⠀⠈⢻⣿⣧⠠⡀⠀⢻⣿⣿⠿⠋⠁⠀⢀⣴⣿⠟⠁⠀⢀⣀⣤⠄⣠⣾⣿⣿⠏⣠
⠀⠀⠀⠀⢻⣿⡜⣿⣿⣿⣿⡌⢧⡀⠀⠀⠀⠻⣿⣧⠹⣦⣼⡟⠁⠀⠀⠀⢠⣾⠟⣡⣴⣶⠿⠛⠉⣠⣾⣿⣿⣿⠃⣼⠃
⠀⠀⠀⠀⢸⣿⣿⡜⣿⣿⡏⠛⠈⢷⡄⠀⠀⠀⢹⣿⣧⠘⣿⡇⠀⠀⠀⢀⣾⣣⣾⡿⠋⠁⣠⠞⣴⣿⣿⣿⣿⢏⣾⡇
⠀⠀⠀⢠⠀⢿⣿⣿⣎⢿⣿⣄⠀⠈⢿⣄⠀⠀⠀⢻⣿⣆⢻⡇⠀⠀⠀⣸⣿⡿⠋⠀⢀⡾⠋⠀⠁⣿⣿⡿⢣⣾⣿⠁
⠀⠀⠀⠘⣷⣜⣿⣿⣿⣷⡙⢿⣦⡀⠘⣿⡄⠀⠀⠈⣿⣿⣿⡇⠀⠀⢀⣿⡟⠀⠀⣰⡿⠁⠀⢀⣾⣿⢟⣵⣿⣿⡿
⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⢿⣮⠻⣿⣄⢹⣿⡀⠀⠀⢹⣿⣿⡇⠀⠀⢸⡿⠀⠀⣰⡿⠁⢀⣴⡿⢟⣵⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⣀⠀⠘⢿⣦⣿⣇⠀⠀⠈⣿⣿⡇⠀⠀⣾⡇⠀⢰⣿⢃⣴⡿⠋⠐⠛⣛⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣷⡄⠈⢿⣿⣿⡀⠀⠀⢿⣿⡇⠀⢀⣿⠀⢀⣿⣿⣿⠟⠁⣠⣴⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠆⠘⣿⣿⡇⠀⠀⢸⣿⣿⠀⢸⣿⠀⣼⣿⣿⠃⢀⣾⠿⠛⠋⠉⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠘⠛⠶⣶⣦⣤⣄⣀⠤⣤⡀⠀⠀⠀⢶⣌⠻⣿⠀⠀⢸⣿⣿⠀⣾⡇⢠⣿⣿⠇⠰⠋⠀⣀⣤⣶⣾⣿⣿⣿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⢭⣿⣿⣿⣿⣶⣧⣄⡐⢤⡈⢻⣷⣌⠀⠀⢸⣿⣿⠀⣿⡇⣸⣿⡿⠀⣠⣴⣿⣿⠿⣿⣿⡿⠋
⠐⢦⣤⣤⣤⣤⣤⣽⣿⣿⣿⣟⢿⣿⣷⣌⠢⣿⣿⣆⠀⠘⣿⣿⢸⣿⠃⣿⠟⣱⣾⣿⣿⠟⣡⣾⣿⠟⣠⠞
⠀⠀⠈⠙⠿⢿⣿⣿⣿⠟⠻⣿⣷⣍⠻⣿⣷⣼⣿⣿⣧⠀⣿⣿⢸⣿⠐⢃⣾⣿⣿⠟⣡⣾⣿⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⡈⠻⣿⣿⣿⣿⣆⣿⣿⣿⣿⣰⣿⣿⡿⢁⣾⣿⢟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡿⢋⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣤⠴⠖⢦⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡏⠀⠀⠀⠀⠙⡆⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⣠⡀⡄⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠳⣄⠀⢀⠚⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣦⢾⡇⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⠶⠶⠶⠾⠛⠛⠛⠛⠶⠶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⢀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠲⠶⣤⡀⠠⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⡞⠛⢲⣶⣌⠙⢦⡀⠀⠀⢀⡞⣉⠀⠀⣶⣶⣦⠀⠹⣦⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣾⢼⣿⣿⣿⣿⡿⠀⠀⣿⠀⠀⣿⢰⣿⣷⣾⣿⣿⣿⠀⠀⣿⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⠈⠷⠿⠿⠛⠁⠀⠀⣾⠀⠀⣧⠈⠻⢿⣭⡭⠟⠁⠀⠀⣾⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⠘⢧⡀⠀⠀⠀⠀⣀⣼⡏⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢋⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣨⠁⠀⠀⠉⠛⠶⠶⠟⠋⢠⡇⠀⠀⠀⠈⠻⠦⣤⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⣉⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⣠⠶⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠰⣷⡆⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀
⠀⠀⢻⠓⠓⣠⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠟⢉⣧
⠀⠀⢸⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠂⠀⠉⠉⠉⠀⢀⠔⠋⠹⣆
⠀⠀⠈⢻⡈⣷⠀⠀⠀⠀⠀⠀⢠⡶⠛⢦⣈⡙⠛⠒⠲⠦⠶⠖⠊⠉⠙⢲⣦⣤⡴⠚⠁⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠘⡅⢘⠀⠀⠀⠀⠀⢀⡼⠄⠀⠀⠈⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⢸⠇⠘⣦⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢷⠀⡇⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣤⣄⣀⣾⡁⠀⢹⣆⣀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠸⡆⣧⠀⣴⠋⠉⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣷⢸⣴⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠸⡀⠛⠀⢀⣤⡶⢿⠀⠀⠀⠀⠒⠛⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⡇⢠⡴⠋⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠳⠋⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠂⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠅⠀⠀⡸
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣴⣿⣾⣶⣶⣴⣷⣶⣶
⣿⣛⣻⣛⣛⣛⣛⣃⣙⣛⣿⣛⣛⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣭⣭⣭⣽⣿⣯⣭⣭⣽⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⢀⣼⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠀⠀⢠⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⡟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⢰⣿⣿⡿⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣿⣶⣤⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⡇⢸⣿⡿⢡⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠃⣿⣿⣿⠃⣼⣿⢃⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⡀⠀⣷⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⣿⣏⣾⣿⠟⠁⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡀⢿⡆⠀⣼⣷⡀⠀⠘⣿⣿⢠⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣇⢸⣿⡀⣿⣿⣷⡀⠀⣿⡇⣸⣿⠟⠀⠀⠀⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣆⢿⣧⠹⢿⣿⡇⠀⣿⣧⣿⠏⠀⠀⢠⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡈⠙⢿⣿⣿⣧⢸⣿⡇⠀⣿⣿⡟⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣦⡄⠈⢿⣿⣇⠹⡿⠀⣿⣿⠃⠀⣸⣿⣿⡿⣹⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣧⠀⡄⠀⠀⢀⣴⣿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣤⡀⠙⣿⣆⠀⠀⣿⡿⠀⢰⣿⣿⣿⢡⣿⣿⣿⠏⠀⠀⠀⠀⠀⢻⣿⣿⡏⢰⡇⠀⢠⣾⣿⣿⣿⣿⠇
⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣦⡘⢿⣆⠀⣿⡇⠀⣿⣿⣿⢃⣿⣿⣿⠏⠀⢰⣄⠀⠀⠀⠘⣿⣿⣇⣿⠁⣰⣿⣿⣿⣿⡿⠃
⢸⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣆⣿⡇⢀⣿⣿⠇⣼⣿⡿⠃⠀⠀⣼⣿⣧⠀⠀⠀⠘⣿⡿⠃⣰⣿⣿⣿⠿⠋
⠈⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠐⣶⣶⣤⣤⣄⣀⠀⠀⠀⠹⣿⣿⡇⢸⣿⡟⣸⣿⡟⠁⠀⠀⠀⣿⣿⣿⠀⠀⠀⣴⠟⣡⣾⣿⠿⠋⠁⠀⠀⠀⣀⣠⡀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢿⣿⣿⣿⣿⣷⣦⡀⠀⢻⣿⡇⢸⣿⣷⣿⠏⠀⠀⣤⡀⠀⣿⡿⠃⠀⣠⣾⣷⡾⠟⢉⣀⣤⣴⣶⣾⣿⣿⣿⠏
⠀⠀⠘⢿⣿⣿⣿⣿⢿⣿⣿⣷⡄⠀⠻⣿⣿⣿⣿⣿⣷⣄⠘⣿⡇⢸⣿⣿⠃⠀⠀⠀⢿⣿⡔⠟⠁⢀⣾⡿⠟⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠈⠻⣿⣿⣿⣷⣍⡻⢿⣿⣦⠀⠙⣿⣿⣿⣿⣿⣿⡆⢻⡇⢸⣿⡇⣀⠀⠀⠀⠘⣿⠇⢀⣴⡿⠋⣠⣾⠿⣛⣯⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦⣝⢻⣷⣄⠈⠻⣿⣿⣿⣿⣿⣼⡇⢸⣿⡆⣿⣷⡀⠀⠀⣟⣰⡿⠋⣤⠞⣩⣴⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣷⣄⠈⢿⣿⣮⡻⣿⣿⠈⣿⡇⠘⢿⣷⠀⣰⣿⠏⠀⢪⣴⣿⣿⠟⠛⠉
⢤⣴⣶⣶⣾⣷⣶⣶⣶⣶⣤⣤⣀⡉⠙⠻⢿⣿⣷⣄⠙⢿⣿⣿⣿⡇⢻⣿⠀⠈⠻⢠⡿⠁⢀⣴⣿⠟⠉
⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡉⠻⣿⣷⣄⠙⢿⣿⣿⡘⣿⡆⠀⠀⣿⠁⣰⣿⠟⠁
⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣭⣝⣋⣛⠛⠻⠿⢶⣌⠹⣿⣧⡀⢻⣿⣧⢹⣷⠀⢸⠃⣴⡿⠁⢀⣤⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿
⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠀⠀⠈⠻⣿⣄⢻⣿⡄⢿⡀⡏⣰⡟⠀⠴⠿⠿⠛⠁⢀⣴⣶⣿⠟⠀⣀⠔⢀⣴⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠹⣿⡆⢿⣷⠸⣷⣱⣏⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣁⠴⠚⠁⠶⠿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣤⡀⠹⣿⡘⣿⠀⣿⣿⠋⠀⠀⠀⣀⣤⣴⣿⡿⠭⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣷⣿⣇⢻⣶⣿⠃⠀⣠⣴⠿⠛⠉⠁⠀⠀⠀⠀⢺⣿⣿⣄⠙⠓⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⢸⣿⠇⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢴
⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⣄⠁
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠡⠀⠀⠀⠀⢹⡀⠀⠀⠐⠂⠀⠀⢀⡀⠀⠸⡋⠁⠋
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠠⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠉⠃⠀⠘⠠⠤⢀⠄
⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⢀⡄⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⢠⡞⠃⠀⠀⠤
⠰⠒⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠮⠒⠃⠀⠀⠀⠁⠀⠀⠀⢰⣞⣵⣋⣒⠀⠈
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⡔⠊⠙⡐⠀⢰⡗⠞⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡤⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⣶⢖⡶⠶⠶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⡄⢀⠀⣠⣀⡆⠀⠀⠀⠀⠰⠶⣶⣄⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣄⠈⠠⣌⠉⠀⠀⠀⠀⠀⠀⠀⠸⢿⡏⠓⢐⠀⠹⠃⠀⠀⠀⠒⠀⣠⣯⣀⣤⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⢢
⠀⠀⠀⠀⢀⡀⠹⣦⠺⠟⠀⠀⠀⠀⠀⠴⢲⡆⠀⠈⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡿⡿⠟⢿⣿⠇⠀⠀⠀⠰⠃⠀⠀⠀⠀⢠⠐⠄
⠀⠀⠠⣾⡟⠻⡷⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢀⣾⣿⡄⠀⠀⠀⠀⠡⠆⡀⠐⠂⠀⠀⠄
⠀⠀⠈⠣⡁⠴⠁⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠈⠁⠀⠈⢳⠀⠀⠀⠀⠀⣠⣶⣾⣿⠿⠿⠿⠃⠀⠀⠂⠀⢠⣌⡤⠀⠀⠀⢠
⠀⠀⠀⢀⡀⠀⣰⣿⠿⢿⡷⣄⠀⠀⠀⠀⠊⠁⠀⣸⣀⠰⠴⠞⠀⠀⠀⠀⢰⢟⣵⡿⠷⡄⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠠⠾⠀⢀⡆
⠀⠀⠀⠀⠁⢸⡟⣥⠀⠸⢃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠘⢸⣿⠃⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠀⠈⠓⠒⠛⠁⢀⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇
⠀⠀⠀⢀⠠⠤⠄⠀⠀⠀⠀⡠⠄⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢲⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢦⣤⡀
⠀⠀⠀⠃⣶⣦⠀⠀⠀⠀⠸⣴⣦⡾⠃⠀⠀⠀⠀⠀⠀⠀⢰⣯⠤⡀⠻⠉⠙⣷⠀⠀⠀⠀⢤⡤⢄⠀⠀⠀⠀⢸⡀⠀⠀⠉⠙⠂
⠀⠀⠀⠀⠈⠘⠀⠤⠀⠀⠀⠀⠀⠀⡇⠀⣴⣄⠀⠀⠀⠀⠏⣠⠄⠰⠞⠀⠀⠿⠀⠀⠀⠃⠻⠷⠞⠀⠀⠀⠀⠀⣩⠤⠴⠉⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⢳⡅⠀⣤⣄⠀⠀⠀⠀⠀⠀⠃⠀⠸⠻⠂⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣠⠄⢠⣄⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠸⠃⠀⠐⠋⠛⠀⠀⢀⡀⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⣤⠀⠀⠀⣠⠶⠟⠛⠛⣿⡿⠶⡀
⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⢀⣼⣿⠷⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠀⠀⠀⠻⡀⠀⠀⠀⠀⠡⡴⠂⠀⠀⠠⠚⠁⠀⠀⠀⠀⠚⠁⠀⠉⡄
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⣼⠟⠁⢀⣤⡄⠀⠀⠀⣰⠶⣄⢀⣼⠀⣀⠀⠀⠈⠢⣀⣀⣤⠶⠃⢀⡠⠀⠀⢲⣶⣄⢠⡾⠛⢷⠀⠀⠀⠁
⠀⠀⠀⠂⠀⠀⠀⢀⣴⠟⠁⣀⠈⡾⠍⠡⠀⠀⠀⠃⣀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠙⠿⠈⢄⣀⠀⠀⣀⠴
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⣤⢀⣴⣿⢋⡉⠀⠀⠉⠀⠀⠀⠀⢀⣤⠶⠄⠀⠀⠀⠀⠀⢘⣧⣄⡀⠀⠀⠀⠀⠀⣠⢴⣦⣤⡀
⠀⠀⠀⠠⡄⠀⠘⠈⢿⣼⣿⠂⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⡍⠀⠀⠀⠀⠀⠀⠠⠿⠿⣿⠠⡀⠠⠀⢀⡴⠀⠀⢀
⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⡀⢳⣶⡶⠂⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠿⠲⣄⣉⣁⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠉⠠⡀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠸⣆⣀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠇⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠘⡻⠋⡀
⠀⠀⠀⢀⡀⠀⠈⢀⠙⢤⠘⠿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⡦⠀⠀⠀⢀⡀⠀⠀⢦⡀⠻⠃⠀⠀⠀⠀⠀⠀⣀⣁⣹⣦⣄⠈⠁
⠀⠀⠀⠉⠉⠀⠀⠈⢡⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠈⣡⣴⣶⣤⡙⡄⠀⢐⣦⡀⠀⢠⠞⠉⠉⠉⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⠊⠀⠀⠀⠀⢸⣿⣥⣌⠻⣿⣿⠀⠉⠋⠀⠀⠇⠠⣾⣶⠀⡀⠄⠀⠁⡄
⠀⠀⠀⠀⢀⣀⠀⠀⣼⣴⢃⠀⠀⢀⠀⠀⠀⢠⢋⡴⢁⠀⢄⡀⠀⠀⠀⠛⢛⡃⠀⣿⣏⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠢⡀⣠⣇
⠀⠀⠀⠀⠘⠛⣠⣼⢿⡋⠀⠀⢠⡄⠀⠀⠀⣿⡟⠏⠀⢠⡀⣸⠀⣠⡤⢄⠈⢁⣶⡟⣉⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⢧⠠⠄
⠀⠀⠀⠀⠀⣰⡟⢡⠁⢹⡄⠀⠀⠁⠀⠀⢠⣿⡁⠀⠀⠀⠀⠁⠀⠻⠶⠀⣰⣿⣿⡿⠿⣿⣷⣞⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠐⣠⣄
⠀⠀⠀⠀⠀⣿⡇⣮⠀⢸⡷⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⣀⢀⣿⣿⠋⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⣿⡇⠀⠐⠆⡐⠹⠿⠁
⠀⠀⠀⠀⠀⢿⣧⣻⣀⣾⠃⠀⠀⠀⠀⠀⠈⢿⣷⡙⢷⣦⣀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠹⣷⣄⡠
⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣽⣿⣿⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⢿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡄
⠀⠀⠀⢢⡄
⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢙⠀⠀⣀⠄⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠐⣄⢺⠀⡃
⠀⠡⣠⠀⣶⢢⠜⡾⠀⠀⠀⢀⣶⣼⣿⠟⠀⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠳⡌⠣⡐⢁⠠
⠀⠀⠈⡹⢮⣧⡷⠁⠀⡄⠰⠾⢁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠒⢠⣘⣃⡿⠀⣒
⣄⠀⢀⢻⣷⡿⣿⠀⠈⡿⢋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠒⠀⢀
⡻⣆⠈⢿⣿⢿⣿⣿⣴⠗⠁⠀⠀⠀⡀⢠⣠⣄⡀⠲⠶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠘⠘⠀⡰⣬
⣻⣿⣧⣘⣿⠀⣽⣿⠃⠀⠀⣠⣴⣂⠁⠚⠋⣉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄
⣿⠟⠛⠿⢿⣷⣼⣷⣤⣖⣾⡋⠉⠁⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⠀⠀⡇⠀⢸⠇
⡏⣶⢿⡽⣢⠈⠻⢿⣿⠯⠋⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⠀⠘⠤⠆
⠀⠄⠾⣯⣿⣿⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠢⡈⠙⢣⣄⠺⡇
⠂⠀⠠⣿⣿⡏⠙⠮⠙⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠐⠉⠀⡅⠁
⠀⠀⠃⠺⢻⢁⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣍⠀⠀⠻⠄⠀⠳⡀⠀⡇
⠀⠀⠀⠀⠸⣦⠁⠦⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠹⠀⡃
⠀⠀⠀⠠⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢆⠀⠀⠇
⠀⠀⠀⠐⠆⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉⠀⠟⣼
⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠐⢮⠘
⠀⠀⠀⠀⠈⠁⠀⠀⢰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠖⠈⠀⠀⢀⡀⠀⠀⠀⠀⢺⡆
⠀⠆⠀⠠⠀⣎⠀⠀⢺⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⢢⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⡜⠁⠀⠀⠋⠂⠀⠹⡉⠢⣄⠀⢘⡷
⠀⢾⠀⠀⢰⡟⠀⢀⣿⣷⠟⠀⠀⠀⠈⠁⠀⠀⡀⠀⠲⠤⠈⡆⢋⠞⠡⠄⢀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠁⠈⠑⣧⠐⠄⣀⠀⠀⠀⠀⡀⠘⡀⠀⠁⠈⠛
⠀⠸⠀⠀⢼⡇⢠⣿⠏⣀⠀⠀⡀⡀⠀⠀⠀⢀⡴⠶⠀⡱⠀⠷⠿⣄⠉⠀⠈⠁⠀⠀⠐⠀⠀⢀⡀⠃⠀⠀⠀⠀⠇⠀⠀⠙⢆⣀⠀⠀⠀⢂⠈⣄⠀⠂
⠀⠀⠀⠀⣸⣡⠟⠁⣾⠁⢀⡠⠊⠉⠁⠀⠀⣡⠆⠉⢁⡀⠀⢀⠁⠀⢉⠁⠊⠀⠤⡀⠁⠀⠀⠈⡘⠁⣠⠞⠀⢀⡀⠀⠀⠀⡤⠹⣤⡀⡀⠙⠁⠀⠀⠀⣀
⠀⠀⡀⠀⢸⠃⠤⢦⠈⣴⠠⠀⠀⠀⠐⠂⠉⠀⡀⠀⠀⡖⠂⠈⠈⠀⠘⠄⠀⠀⠀⠙⢆⠀⠀⠐⠃⠰⢃⡀⡔⣈⠁⠀⢈⠰⢀⡞⠀⢙⣳⡀⠀⢠⣤⣄⡈
⠀⠀⡇⢠⠁⠀⠀⢀⡾⠋⠀⡀⠀⠀⠀⠐⠀⡈⠁⠀⡔⠀⠀⣴⡂⠂⠀⠀⠀⢀⣠⡄⠀⠃⠀⠀⠀⠀⠀⠙⠄⠁⠀⢠⣈⠀⡈⠁⠈⠒⢀⡛⠛⠀⠉⢺⡀
⠀⠀⠏⣸⢸⡆⢀⠂⠀⢀⡮⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⡀⠀⢨⠊⣰⠁⠀⢌⠁⢻⠐⠂⠠⡀⠀⠀⠀⠁⠀⠁⠉⠇⣤⠀⠀⠁⠈⢀⠀⢼⡷
⠀⠀⢸⣿⡜⣇⠆⠀⢠⠏⠀⠤⠈⢾⣀⠐⠃⠀⠀⠀⠀⠀⠀⡉⠀⠾⣓⠀⠁⠸⠄⢄⠀⠈⠀⠺⠶⣂⠔⠀⠌⠀⢈⠀⠀⠀⠀⠀⠻⢧⣴⠀⠀⣸
⠀⡤⠽⠛⠀⢱⣄⢸⡋⡠⠤⠴⣶⣌⠉⠀⠀⠀⠀⠀⠀⠀⠠⢃⠤⠄⢈⡴⠀⠄⢀⣂⠈⠄⠀⠀⠀⡙⠀⠀⠐⢤⣦⠅⠀⠀⠀⠀⠀⠙⠳⠎⠂⠁⠎
⠀⠀⡀⠀⠀⠀⠘⠉⠁⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⡀⠄⠈⠎⠀⡊⡏⠑⠠⠬⡙⠋⠀⠀⠀⠀⢠⡐⠄⠈⠃⠴⠀⠀⠀⠀⠀⠀⠴⢾⠂⠀⠀⠆
⣶⣿⣿⣷⣾⡿⣿⣷⣷⣶⣾⣷⣶⣶⣶⣶⣶⣾⣶⣿⣷⣿⣿⣷⣷⣿⣾⣿⣿⣶⣶⣾⣿⣾⣷⣾⣾⣿⣾⣷⣶⣶⣶⣶⣾⢿⡿⠿⣶⠷⢶⣿⡿⠿⠿⠿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠳⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠂
⠀⠀⠀⠀⠀⠲⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⣌⠢⡀⠀⠀⡾⢶⣤⡀⠀⢸⠀⠀⠀⠀⠀⡠⠔⠈⢠⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣍⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⡇⠚⢉⣁⡀⠈⣢⣞⣀⣠⢤⣁⣀⠀⠣⣀⠠⠐⠁⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠉⠙⠒⠢⠤⠤⢃⡜⠉⠀⠀⠉⠳⣴⠋⠀⠀⠀⠈⢻⡙⠒⢤⡀⠀⠀⢠⠃⠀⠀⠀⣀⠤⠐⠒⠈⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⢀⡴⢻⠁⠀⠀⠀⠀⠀⠘⡄⢀⣀⠀⠀⠀⢣⠀⠀⠈⠳⣄⠺⠤⠐⠂⠉⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢠⠎⠀⢸⡀⠀⠀⣖⣆⠀⠀⢳⢰⣿⡆⠀⠀⢸⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠕⢠⠇⠀⠀⠀⢣⡀⠀⢿⡿⠀⠀⣾⡀⠛⠁⠀⣀⠞⠀⠀⠀⠀⠀⡄⢣⠀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠲⠶⣒⡈⠉⠁⠀⠀⡸⠀⢤⠀⠀⠀⠙⠦⣤⣤⠴⠚⠀⠈⠙⠋⠉⠁⠀⠀⠀⠀⢀⠘⠀⠀⡇⠑⠢⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢤⡀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢸⠀⠀⠀⢀⣀⠬⠵⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠇⢡⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⠀⠀⢸⢠⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠸⡀⠀⠀⠸⡀⠀⠒⠀⠤⠤⠠⠤⠀⠐⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠖⠉⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⣀⠔⠊⠁⢀⣀⣀⠤⠤⠤⠀⠒⣦⠈⢧⠀⠀⠀⠀⠀⠁⠀⠦⠀⣀⡀⠴⠔⠊⠁⠀⠀⠀⠀⠀⢀⡴⢁⠤⠀⣀⡀⠀⠀⠀⠀⠑⠢⣀
⠀⠰⠞⠒⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠘⢆⠀⠀⠀⠉⠉⠁⠒⠂⠤⠤⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⣀⠠⠄⠒⢌⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⢁⡤⢄⣀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠗⠊⠉⠀⠀⠀⠀⡆⠀⠀⠈⠉⠓⣒⠲⠲⠶⠖⠒⣋⡉⠀⠀⠀⠀⡁⠀⠀⠉⠒⠤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡴⠋⠀⢇⠀⠀⢀⠜⠀⠙⣄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡴⠋⠀⠀⠀⠘⡀⢀⠎⠀⠀⠀⠈⢢⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡠⠊⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⠀⠀⠀⠀⠱⡀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠐⢀⡀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠐⠀⠞⠁⠈⠀⣀⠀⠀⡴⣌⠂⢄⡈⡙⠛⠋⠉⠉⠀⠀⠠⣄⣀⠈⠀⠈⠉⠒⠒⠀⠀⣔⠒⢄⠀⡀⠀⢀
⠀⠀⢠⠀⠳⣬⡛⠻⢋⢙⡁⣌⠀⠀⠀⢰⠀⢂⣠⠭⠤⠆⢀⠐⠉⢠⠀⣀⠩⢀⢀⠀⠄⠀⠁⠀⢠⡀⠀⡀
⢀⠀⠺⠷⣥⣤⠔⠊⢱⡟⠀⢸⡌⠲⢤⣴⣾⢯⣤⣦⡤⠄⠐⠒⠒⢄⠱⡝⠳⣤⣒⡉⠀⢀⠈⠀⠀⡁⠐⡄
⠸⣮⣧⣀⠋⢡⠊⠀⢸⢰⡇⠀⢿⡄⠀⠲⣭⣇⡘⢯⠙⣷⣦⠠⣀⠰⡦⣬⣀⠀⠉⣉⣃⣠⠤⠖⠖
⠀⢀⡵⡣⠠⢷⠆⢠⠾⢸⣷⡀⠈⢻⡄⠀⠀⢉⠻⣮⠁⠘⠇⢷⠄⠑⡞⣦⠉⣙⠳⢌⠓⠦⣤⣉⠉⠉⠉⠆
⠀⠋⢠⡇⠀⣿⡄⢸⡄⢸⡯⣷⠀⢠⣷⠈⢀⠀⠁⠏⡄⢀⠀⠸⠠⠀⠛⠈⢧⡈⠁⠂⠄⠀⠀⠨⠛⢦⡀
⠐⠀⠘⡇⠙⢸⡇⠸⣷⡈⣧⢻⠀⢘⡍⠀⠠⠀⠀⠠⢧⡀⠈⢄⡀⠀⢠⣌⣀⠹⠦⠀⠘⠀⠀⠜⠀⠀⠑⡄
⠀⢠⠃⣇⡜⢸⠃⡄⠌⡅⢻⠀⠀⢈⡇⠀⠀⠀⠀⠂⣸⠃⢤⠀⠀⣄⠚⢮⡙⠓⢦⡀⠐⠤⠤⣤⡀⠐⠀⠁
⠀⠀⠀⠻⡀⠀⠐⠘⠀⠈⠞⠘⠀⢸⢣⡄⠀⠂⠀⠀⢻⡐⠈⠂⠀⡟⠓⢤⡛⣦⠀⠁⢀⡂⠐⠀⠙⢆
⠀⠀⠂⠄⠀⢠⠘⡆⢸⠆⠘⡄⡼⠀⡜⣧⢀⠀⠀⠀⠠⠀⠄⢡⠸⡧⡄⠈⠉⠈⢳⡀⢠⡀⠀⠘⠀⠁
⠀⠀⠁⠀⠀⠀⣼⠃⠈⡀⢀⣼⢃⡜⢅⢹⡄⠉⠩⣭⣶⣀⡒⠈⠀⠁⢷⠄⠘⠆⠢⠹⠀⠝⢧⡀⡀
⠀⠁⢀⣀⣀⡴⡿⢠⠀⠁⡄⠈⢈⢀⡏⢸⡇⣶⣄⠀⠤⡈⠙⠀⢀⠀⠈⠂⠀⠀⠀⠀⠀⠐⡁⢷
⠀⠒⠀⣈⣉⠔⠁⢸⡄⠄⢁⡠⡺⣸⠃⢸⣧⡇⢙⣦⠀⠀⢀⠀⡈⢷⣤⡀⠀⠀⡀⢠⠇⠀⠺⡌
⠀⡀⠀⠁⠀⠀⡴⢸⠁⢘⡿⢠⠃⢰⠇⡿⠛⠀⢈⢎⠀⠠⡄⠀⠙⢸⣇⠙⡆⠀⢀⡾⢰⡀⢀⠈
⠀⠁⠄⠀⠀⢸⠃⠂⠰⠛⢠⠃⢠⣼⠘⢡⠶⡄⠀⠸⡄⠄⠀⠀⠀⣾⡙⡇⠀⠀⣼⢇
⠀⠀⠠⠀⠀⠏⡂⠀⣂⠔⡁⣠⢘⠘⢠⡏⠠⢿⠀⠠⢠⡠⡄⠀⠀⠹⣇⠀⠠⠀⣿⠀⠂
⠀⠀⠀⠀⣢⢞⠀⠀⢡⠊⡇⠸⠃⠄⠘⣇⠐⠈⠀⡀⢸⣇⠈⠈⠀⠀⠉⠀⠀⠀⢿⡀
⠀⠐⣠⣶⠏⢈⠀⠠⢡⣰⣿⠀⠀⠐⣀⠘⢆⠐⣼⠃⢦⡘⣧⡑⢶⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡿⡏⠀⢞⠀⠀⡀⢹⡌⠇⢄⣴⣧⢠⠀⣼⢃⠀⠀⢭⣿⡝⠒⠆⢀
⠀⠀⠀⢷⠀⠘⠀⠀⠃⢸⠁⢠⡞⢹⢹⣆⠠⡟⢸⣷⡀⠀⠬⠙⣧
⠀⠀⠀⠈⠃⠀⠰⠀⠀⠀⠂⡏⠂⢘⠀⠹⠀⠇⠈⣯⣷⠠⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠔⠆⠀⠀⠀⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢢⠀⠀⢢⠘⠀⠃⠿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡰⣀⣾⣰⣰⣴⣂⣂⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣄⠷⣧⣅⣻⣯⠿⣞⣫⣻⠶⢃⡀
⠀⠀⠀⠀⠀⠐⠀⢄⡀⣅⢠⡀⡀⠠⡊⣾⣽⣿⣳⣿⣿⣿⡻⣽⣷⠗⣂⠀⢀⡀
⠀⠀⠀⠀⠤⢀⠠⣿⣳⣤⡧⣝⣶⢞⣥⣵⣶⣿⣿⡿⣿⣿⣿⢿⣿⣶⣷⣷⡄⢲⣰⡏⡤
⠀⠀⠀⠀⠀⢘⣾⡦⢘⢪⣷⣿⣿⣿⡿⡻⢿⣿⡷⠇⣋⡭⢾⣿⣻⣾⣿⣽⣿⣿⣿⣬⣤
⠀⠀⠀⠀⠀⠒⠋⠉⢟⣿⣿⣿⣿⢽⣷⣿⣿⣿⡿⡿⣩⣵⣿⣽⡿⠿⣿⣿⣿⣿⣿⣯⠾⠳⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣹⣞⢻⠿⣿⣿⣻⡴⣏⣿⣿⣿⣟⢿⣾⣿⣟⣿⣿⣿⣯⣀⣿⡥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⠻⣽⣧⣷⡉⢟⠻⡿⠃⡿⠿⠟⣿⣿⣿⣿⢿⣿⣿⠟⡾⢟⠉⣒⡶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢜⢶⣴⡿⣞⢛⣃⠳⣘⠐⣢⡤⢶⠾⠣⣾⣿⡧⣻⢿⢗⣡⣾⡗⠗⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⣿⣇⢹⡆⣾⠀⠿⠎⣾⣿⢿⠟⡃⡻⣾⣮⡿⣘⡳⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⢄⣰⡓⠀⠐⣋⣻⡯⡐⠁⡘⠇⠘⠿⢟⡫⠰⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⠀⠿⠛⠳⠡⠫⠅⣬⠗⡀⠐⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠂⠀⠂




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠠⠴⠶⢶⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣷⣄⠀⠈⢿⣿⣿⣄⠀⠀⠀⠀⢀⣴⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣷⡀⠘⣿⣿⣿⡄⠀⠀⢀⣾⣿⣿⡟⠀⠀⠀⠀⣠⣴⣾⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡄⠈⣿⣿⣷⠀⢀⣾⣿⣿⡟⠀⠀⠀⣠⣾⣿⣿⣿⠏
⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣶⣄⡀⠹⣿⣿⣿⣷⠀⠸⣿⣿⡄⣼⣿⣿⡟⠀⠀⢠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⡆⠀⢿⣿⣧⣿⣿⡟⠀⠀⣠⣿⣿⣿⣿⣿⣿⠇⠀⡄
⠀⠀⢸⣿⣿⡿⠋⠁⠀⠈⠉⠛⢿⣿⣿⣆⠘⣿⣿⡇⠀⢸⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋⠀⣰⡇
⠀⠀⠸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⠸⣿⣧⠀⠈⣿⣿⣿⠃⠀⠀⣿⣿⣿⣿⣿⠟⠁⢀⣴⣿⡇
⠀⠀⠀⠹⡇⠀⠐⠒⠲⠶⠶⣶⣶⣤⣀⠙⢿⡄⠹⣿⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⡿⠋⣠⡄⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣌⠻⡄⢻⡇⠀⣿⣿⡇⢰⡄⢸⣿⣿⡟⢠⣾⡟⢡⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⠙⠳⣼⡄⢻⡄⢸⣿⣧⢸⡇⠈⣿⣿⢠⣿⠋⣠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣄⢳⠸⣿⣿⢸⣇⠀⢹⣿⢸⠇⣴⣿⡿⠃⢀⣴⣶⣶⣶⣄
⠀⠀⠀⠀⠀⢠⣿⡿⠟⠋⠉⠉⠉⠉⠉⠙⠻⢿⣿⣦⡙⢧⡀⢿⣿⡀⣿⡀⠀⢿⠀⣸⣿⡟⠁⠀⠸⠟⠉⠈⠉⢻⣧
⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣄⡈⠛⢿⣎⢳⡘⣿⡇⠸⣧⠀⠀⠂⣿⡟⠀⣦⡀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠘⠁⠀⠀⠀⣴⣿⣿⡿⠿⠿⠿⣿⣿⣿⣷⣄⠙⣷⡅⢹⣿⡀⢿⡆⠀⠀⣿⠁⠀⣿⣷⣤⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣌⢻⣄⢻⣧⠘⣿⡄⢤⡈⠀⠀⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⣀⣾⣿⣷⡄⠀⠀⠈⢻⣿⣿⣧⡹⡎⢿⡆⢹⣷⠸⣇⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⢿⣿⣷⣿⠘⣿⡀⢿⡇⢿⡄⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡇⢻⣇⢸⣿⢸⣇⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣤⣀⠈⢻⣿⡘⣿⠀⣿⠘⣿⠀⠈⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⢁⣉⠉⠻⢷⣄⠹⣧⣿⡀⣿⡄⣿⠀⠀⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢰⣿⣿⣿⣶⡄⠻⣷⢹⣿⡇⣿⠀⣿⠀⢠⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⣀⠉⢉⣿⣿⡿⠀⢹⣧⣿⡇⣿⢸⡿⠀⣾⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠿⠁⠀⠀⣿⣿⣷⣿⣾⠃⣼⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⢹⣿⣿⣿⡏⣼⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⡜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠛⠛⢶⡏⠀⠀⠀⠈⣧
⠀⠀⠀⠀⢀⡞⠉⠀⠀⠈⠱⡞⠉⠀⠀⠉⢳⡀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⡼⠓⠒⢦⣀⣠⡟
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣿⠀⠀⠀⢨⡇⠀⠙⢦
⠀⠀⠀⠀⣈⡧⠤⣤⣠⠖⠋⠉⠉⠳⣏⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⢀⣽⠉⠈⠙⠲⣖⠋⠀⠀⠀⡼
⠀⠀⠀⡼⠁⠀⠀⠀⢸⡀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢹⠀⠀⠀⢀⡴⠋⠘⢦⣀⠀⣀⡼⠓⠶⠶⠚⠁
⠀⠀⠀⢧⠀⠀⠀⠀⣰⠓⠦⣤⡤⢾⡁⠀⠀⠀⣠⠞⠀⠀⣰⠋⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠈⠓⠦⠤⠴⢿⠀⠀⠀⠀⠀⢹⠟⣟⠋⠁⠀⠀⣼⠃⠀⠀⠀⢀⣀⡤⠴⠖⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣄⣀⣀⡴⠋⠀⠈⢧⠀⠀⢰⠃⠀⠀⣠⠖⠋⠁⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠤⢤⣀⠀⠀⠈⢧⠀⡿⠀⣠⠞⠁⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠛⠦⣤⣀⠀⠀⠀⠀⠈⠙⠲⣄⠸⣶⣇⡼⠁⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠈⠳⣿⡟⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠹⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣨⢀⣠⠄⠀⡠⠒⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣓⣷⣿⣵⠏⠀⣦⢳⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⢠⠤⡀⢈⡍⢀⡄⣎⣳⢋⠤⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡁⠃⠀⠀⠀⠀⠣⣈⠎⠁⠚⠁⠈⠛⠘⠶⣧⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢮⣙⢢⠁⢡⠶⠶⣶⡆⠀⡠⠊⢻⠈⠇⣄⡏⠷⠳⡺⡦⡀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡵⢲⢾⠒⠉⢁⡸⠶⡴⠋⠹⠆⠀⠙⠋⠀⣠⠌⠛⠁⣔⡡⡿
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠈⢧⠃⠘⡔⢳⠸⡇⡤⠠⠋⠀⢸⣲⢄⠀⡎⡹⠀⣠⡀⠁⠉⣚⡻⠜⠁
⠀⠀⠀⢠⢤⣀⢸⠀⠳⣄⠀⢸⡃⢱⡎⠀⠈⣀⠀⢞⣒⣄⠻⣶⢂⢭⣄⡀⠙⣐⡀⢍⠿⠁
⠀⠀⠀⠈⠦⣤⣹⠻⣦⠋⠁⢰⡱⢈⢙⢆⢘⡽⠁⢀⠤⠉⢠⡿⠒⢒⠚⢱⣆⠉⣥⠠⠶
⠀⠀⠀⠑⠢⢤⠛⠳⡄⢠⢞⠇⠁⠈⠛⠎⠉⣠⢀⡁⠀⠰⠲⢄⢠⢏⣴⣏⣯⢤⢡⠞⠽⢻⣧⣤⣤⠄
⠀⠀⠀⠔⢪⢋⢏⡖⡏⠀⡈⠀⠛⣿⠶⠄⢀⠙⠻⠬⠆⠑⢄⡓⢿⣼⢁⠃⠉⣡⠶⣅⠾⡢⣗⠊⠁
⠀⠀⠀⠓⠊⠁⢈⣻⡤⣸⡇⠠⣁⠬⢪⢲⠁⡾⡳⠀⢀⠻⠀⢈⡼⣽⢠⠐⠋⢸⢾⠏⠷⡞⠜
⠀⠀⠀⠀⠀⠈⠋⠁⢞⠐⠁⠀⠀⠀⠘⠎⠐⠖⠁⠀⠈⠁⠸⠎⠀⠀⠀⠀⠀⠈⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠀⠀⢒⠤⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡜⠁⠀⠀⠐⣄⠀⠈⠈⢦⠀⠀⡜⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⢱⡦⠊⠀⠉⠉⠙⠛⠛⠛⠳⣦⣸⡆⢸⡀⡈⣧⠞⠀⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⡌⢠⡀⣆⡞⡕⠁⠀⠀⠀⠀⠠⡀⠀⣄⠀⡙⣿⡜⡇⣷⡏⡼⢸⠃⡆⢸⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⣿⠸⠀⠀⠀⢢⠀⠱⡄⠹⡄⠸⡆⢹⡜⣿⣿⣿⣰⣧⣿⣼⣧⠇⣀⠔⠉⡜
⠀⠀⠀⠀⠀⠀⠀⢰⠈⣷⡇⠇⠀⠀⠀⡌⢧⠀⢻⡀⢻⡀⣿⣼⣷⣿⣿⡿⠿⡛⠋⠉⠉⢾⣥⠞⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠹⣇⠀⠀⠀⢢⠘⣌⢳⡀⢷⣸⠿⠋⠉⠙⠐⠒⠈⠁⠀⡴⠃⠀⠀⢻⡴⠃
⠀⠀⠀⠀⢀⠤⠴⠶⠞⠛⢿⡀⠀⠐⣄⠳⣌⢷⣽⣿⠋⠀⢠⠄⣠⠎⣠⠞⣠⠞⢀⡴⢁⡠⠀⣧⠀⢀⠔⡆
⠀⠀⠀⠀⠈⠒⢤⡀⢤⣀⠪⣿⣤⡑⢌⡳⣬⣻⣿⣿⢀⣴⣃⣴⣡⣾⣥⣞⣁⣠⣊⣴⣫⣴⠞⢁⡴⢋⠜
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡻⠶⣽⣿⣿⣿⣿⣿⣿⡿⣿⠻⡟⢿⠛⡿⢿⣿⠿⠿⠛⡿⠯⠤⣒⡭⢖⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢒⡶⢾⡟⢋⠞⣸⠃⠸⠀⡟⠈⠃⠀⢸⡏⢳⣀⣞⠔⢊⣉⡤⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠊⠀⠋⡴⠁⠠⠃⠐⠁⣀⡤⠖⠉⢻⡆⢻⡗⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢤⣀⢈⣤⠶⠶⠒⠛⣩⠕⡪⠝⢋⡉⢿⡄⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠠⢎⡡⢊⠴⠔⠁⠀⠀⢻⡄⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡠⠋⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡘⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⢝⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⡀⠈⡄⠀⠀⠠⠀⡠⠆⢀⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠄⠀⠀⠀⠀⠈⠊⠀⠘⠁⠐⠀⠀⠀⢈⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡖⠠⠤⠀⠠⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠢⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠡⡀⠘⠂⣾⣿⣿⣿⣿⣿⣶⠀⠂⢂⣤⣤⣤⣀⡒⠀⠀⢁⠂⠄⡀⠀⠘⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⡠⠲⣹⣿⣿⣿⣿⣿⡿⣠⡀⣾⣿⣿⣿⣿⣿⣿⣶⢀⡟⠀⠌⠂⡀⠀⠀⠀⡠⢁
⠀⠀⠀⠀⠀⠀⠒⡂⠀⠂⠀⠠⠊⠀⠀⠙⠿⣿⣿⡟⠉⠀⠁⠁⠻⣿⣿⣿⣿⣿⣿⢋⠞⠙⠢⢄⡀⠈⠁⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠠⠈⠀⠀⠉⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠮⠭⠿⠭⠖⠁⠀⠀⠀⠀⠉⠲⢄⣀⣤⠁⠀⣀
⠀⠀⠀⠀⠀⠐⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠁⠋
⠀⠀⠠⢆⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠐⢄⠀⡀
⠀⠀⠄⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⢂⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄
⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⢠⠊⠀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠠⠄
⠀⠀⠠⠀⠁⠀⢀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠑⠀⢀⠃⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⢀⠀⢨⠀⠀⠠⠌⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢠⠀⠀⠀⢀⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⡀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠂⢀⠠⠇⠀⠠⠒⡀⠀⠀⠜⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠁⠀⠈⠐⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠇⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⢀⡴⠞⢁⣠⠖⠋⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⢧⣀⣠⠞⣉⣤⠶⠋⣡⡶⢋⠭⠥⠤⠤⣄⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⡥⠴⠚⠉⠉⠉⠉⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠺⡂⢀⠀⠀⠊⠉⠀⠉⠉⠓⠦⣄⣉⡳⢤⣚⣩⠥⠒⣶⠠⠀⠀⢀⡤⢲⠆⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠃⠀⠀⠀⠐⠀⢀⣀⠤⠒⢉⣻⠶⣍⡙⠒⠋⠁⢀⡀⠀⠈⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠤⠴⠒⠉⠀⠀⠀⠈⠉⠓⠚⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣤⡂⠀⠀⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡞⠀⠉⠑⠂⠠⡴⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠠⡤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⢤⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⢙⡶⣁⠠⠂⠉⠁⠒⠦⣀
⡠⠄⠀⠀⠀⠀⡔⠀⡀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣼⠀⠈⠙⠀⠀⠀⠀⢀⠈⠳⣅⠀⠀⠀⠀⠀⠀⠀⢀
⠃⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⠀⠀⣠⠎
⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀⣀⣀⣉
⣿⣿⡋⣋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢰⠀⣤⠀⣤⡄⢀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦⡘⣷⣼⣷⣿⣾⣿⣴⣿⣴⢾⣠⢆⡤⢀⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡈⢶⣷⣌⠛⣿⠿⣿⠛⣿⣿⢿⣿⣿⣾⣥⣾⣥⣾⡴⠂⣀
⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣌⣻⡿⢭⣝⣛⣠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣭⣭⡶⠟⢃⡀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⢦⣼⣋⣽⣶⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣭⡤
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣡⡀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣫⣿⣿⣿⣿⣷⣤⣀⣙⠀⡏⠺⣿⣿⣿⣿⡻⣿⡿⠿⣿⠤
⢀⣶⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠛⣿⣿⣿⣿⣵⠿⢿⣿⣿⣿⣟⣛⡏⠀⣿⣀⣾⣿⣷⣿⣷⣿⣿⣶⣶⡶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠈⣹⣿⣿⣿⣿⠁⠠⠈⠉⠿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⣿⣿⣆
⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣸⣿⣿⣷⣿⣦⣶⣤⡄⢤⣿⣧⣼⣭⣼⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡯
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠉⠉⠻⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⣿⣿⣿⡟⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⢈⣳⣶⣿⣻⣿⢿⣿⣿⣿⣿⣿⣷⣿⣿⡖⠿⣿⣿⡯⠷⠀⣈⣍⠁⣁⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢄⣹⣿⣿⣿⣾⣿⠛⣻⣿⣿⢿⣃⠉⣝⠿⠛⠋⠙⢠⣴⣾⣿⣿⣾⣭⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⢶⣿⣿⣿⣿⣿⣧⣶⣿⠝⠻⣻⣿⠃⠢⠀⢀⡴⣱⣾⣿⣿⣿⣿⣿⣿⣯
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠐⢋⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠁⠙⠇⠀⢸⠁⠀⠘⠛⠿⠟⣿⣿⣿⣿⡃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠉⣼⣿⣿⣿⣿⣿⠟⠂⠀⠀⡄⠀⢲⠀⠀⠀⡀⠀⠀⠀⠛⢿⣿⣟⠃
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠑⠀⡄⠀⢀⡌⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠎
⣿⣿⡿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠶⠈⠁
⣻⣽⣏⢹⣿⣿⣿⣿⡇⢸⣿⣿⢿⣿⣿⣿⣥⣴⣶⣀⣂⣀⣤⡀⠀⣄⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠄
⣯⣹⣿⣷⣿⣿⣿⣿⡇⢺⣿⣷⣶⣿⣏⣹⣿⣉⣹⣿⣿⣻⡟⠁⢠⣿⡄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⣠
⣿⢿⣾⡿⣿⣻⢩⣿⡇⢸⣭⣿⣿⡿⣯⣼⣽⣹⣿⣉⣉⣙⣿⠀⢸⣿⡇⠘⠛⠃⢀⠀⠀⠀⣾⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿
⣿⣷⣿⣷⣿⣿⣼⣿⡇⢸⣟⣻⣦⣴⣿⣿⣿⣿⠿⢋⣙⡿⣿⣧⣴⣦⡤⢛⣿⣵⣧⠀⣗⣄⣿⣧⣀⢀⠀⠀⠀⠀⢠⡞⠀⠀⢸⣿⣿
⡿⢿⢿⣿⠟⣿⣿⣿⢋⣤⣿⡿⢾⣿⣿⣿⣿⣷⠖⢻⣿⣷⣶⣾⣶⠣⣥⡷⣉⣙⣽⣿⣟⣥⡉⠛⡃⢸⣷⣄⣀⠀⠸⠀⠀⢰⣾⣿⣿
⣶⢾⣿⣽⣿⣧⣿⣿⡿⣿⣛⣿⠻⣿⣿⣤⡿⠿⣼⣾⣿⣿⣦⣍⠳⠾⢴⣷⡟⣻⠻⢷⡿⠿⣿⣿⡇⢸⣇⣺⡿⢀⠀⠀⣦⣾⣿⣿⣿
⣛⢀⣽⣿⣭⣿⣿⣋⣿⣿⢭⡿⠛⣿⣱⣿⡷⣶⡝⢟⣼⣿⡓⢶⡞⣛⠃⣶⣽⡟⡳⣦⣷⠶⠒⢻⡇⢸⣯⡭⢁⣾⣶⠀⣿⣿⣿⣿⣿
⡿⢧⡟⣻⣯⡿⣾⣋⣽⣯⣽⢿⣶⣮⣤⣙⣰⣟⣛⣛⢷⣪⣿⢛⣿⡋⣲⣀⢻⣾⢃⣼⡛⢸⣿⣿⡇⢸⣿⡇⣿⣿⣇⠀⣿⣿⣿⣿⣿
⣋⣼⣧⣦⣼⣿⣿⣿⢻⣯⣿⣿⣿⣿⡟⠛⣻⡿⠗⢸⣻⠻⡿⣿⡴⢽⣋⡿⢬⡷⢿⣍⢹⣏⡿⣿⡇⢸⣿⣷⣿⣿⡿⠀⣿⣿⣿⣿⣿
⣿⡾⣿⣭⣿⣤⣿⣩⣾⣿⣶⢳⣿⣿⣋⣷⣿⣵⢿⠋⣻⣴⠋⣽⣻⡏⣛⣹⢿⣷⣿⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⣿⣷⣯⣍⣹⣶⣬⣿⣿⣡⣿⣿⣟⣩⣽⣽⣿⣇⣴⣆⣿⣯⣤⣄⣴⣧⣽⣧⣰⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢠⡆⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⣾⡇⠀⠀⣾⡇⠀⢠⣿⠀⠀⢠⣾⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠸⣿⡄⠀⢻⢿⡄⠀⣟⣧⠀⡼⣿⠀⢀⣿⡏⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⢢⣄⠀⠀⠹⣿⣄⠀⢹⣟⠢⡈⣯⠹⢦⡏⠈⠿⠡⣏⡴⠏⡿⠁⣠⣾⡿⠀⠀⣠⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣀⠙⣿⠙⠢⣯⣠⣼⣷⣶⣿⣷⣷⣶⣶⣿⣤⣹⡷⠊⢡⡞⣀⣤⣾⡿⠁
⠀⠀⠀⠀⠐⣦⣄⡀⠀⠈⠾⣯⠉⢻⣦⣾⣿⣿⡿⢿⡿⠟⠏⠿⠙⢻⠿⡿⣿⣿⣷⣾⡉⢠⡴⠋⠀⣀⣴⣾⠋
⠀⠀⠀⠀⠀⠈⠻⠿⣖⡶⠂⢹⣶⣿⡿⠟⠉⠁⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠈⠋⠻⣿⣿⣾⡓⠙⣋⡽⠛⠁⠀⣀⣀
⠀⠀⠈⠻⣷⣦⣤⣤⠌⢻⣤⣿⣿⠿⠀⠀⣴⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣆⠀⠀⠛⣿⣿⣾⠃⠴⠶⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠉⠛⠷⣆⣰⣿⡿⠟⠀⢠⠎⠁⣀⣀⣀⠀⠀⠠⠈⠀⠀⠀⣀⡀⠈⢱⡄⠀⠻⣿⣿⣦⡞⠋⠁⠀⠀⣀⣀⡀
⠀⠘⠻⢿⣶⣶⣖⠋⠉⣿⣿⠟⠀⠀⢈⣾⣟⣿⣿⣿⣿⣦⡀⢀⣴⣿⣿⣭⣍⠛⢦⠁⠀⠀⠿⣿⣿⡀⣯⣽⡿⠿⠛⠁
⠀⠀⠀⠀⠀⢀⣉⠝⢾⣿⠏⠀⠀⠀⢸⣿⣿⣗⣚⣶⣿⣿⡇⢸⡿⣟⣶⣲⣻⡷⠀⠀⠀⠀⠀⢻⣿⡟⠓⢤⣄⣀⣀⣀⣀
⠐⠒⠿⢿⡿⠿⠯⣤⣸⣿⡇⠀⠀⠀⢨⣿⡋⠛⠛⠋⢹⣿⠇⢸⡇⠈⠁⠉⠉⠀⣀⡀⠂⠀⠀⢹⣿⡧⣾⠓⠛⠟⠛⠋⠉
⠀⠀⠀⠀⠀⣠⡴⢊⠹⣿⣷⡀⠀⢑⠐⢿⣷⡄⠀⢀⣼⠛⣄⠈⠛⡆⠀⠀⢀⣘⡿⠀⠈⠀⣠⣾⣿⣃⣀⡙⣦⣤⣤⣀⡀
⠀⠐⠚⠿⠿⠟⠛⢙⠟⢿⣿⣿⣦⠀⠀⠀⠀⠀⣴⠟⠉⠓⣿⠛⠒⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠉⢦⡈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⣀⣠⣴⣧⡴⢬⣿⣿⣿⡄⠀⠀⠀⠰⣧⣶⡶⠿⠿⠿⠗⣖⣴⡄⠀⠀⠀⠀⢠⣿⣿⡿⠷⠖⠦⣿⣶⣤⣄⡀
⠀⠀⠐⠛⠛⠛⠉⠁⣠⣇⣈⣻⣿⣿⣆⠀⠀⠰⠀⠀⠿⠷⠖⠲⠾⠿⠀⠀⠆⠀⠀⣴⣿⣿⣿⣥⣄⣷⣄⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⢡⡋⢘⣿⣿⣧⡀⠀⠀⠀⣠⡤⡶⠲⠤⡀⠀⠀⠀⣀⣾⣿⣿⣅⡈⣧⠈⠛⠿⢷⣦⡀
⠀⠀⠀⠀⠐⠉⠉⠀⠀⣠⣾⡷⠋⡍⡈⣙⡿⣿⣦⣀⠀⠀⠁⠀⠀⢀⣀⣴⣿⠿⣿⣁⠘⡆⠳⣾⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠋⠀⢠⣗⡞⠉⣧⣄⡼⡏⢙⣿⠛⡛⡿⣏⠉⡿⣄⠄⡇⠙⣦⣧⡀⠀⠉⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣰⣿⠋⠀⢀⣿⡟⠀⢷⣾⠁⢷⣹⡇⢹⣰⠇⠈⣷⣷⠀⠈⠻⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⢀⣾⠟⠀⠀⣸⣿⠀⢸⣿⡇⠸⣿⡄⠀⠈⠻⣧⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⣿⠃⠀⠸⡿⠀⠀⠙⡇⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠑⠀⠀⠀⠘⠉⠃⠛⠘⠐⠃⠘⠚⠐⠂⠀⠁⠀⠐⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢸⠀⡏⢠⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠁⣀⣀⣀⡀⠀⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠊⠀⠀⠀⠈⢢⠀⢁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢸⠀⠀⣀⡀⠀⡸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠉⠑⠤⠤⡑⠤⠤⠤⠖⠁⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⡀⠀⠀⠀⠀⢀⠤⠠⢀⠔⠚⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⠢⠖⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠲⢤⠞⠁⣀⠴⠒⠒⠒⠲⢀⡴⠚⠉⠀⠈⠉⠓⢄⠱⠤⠠⠤⣄⠀⠀⡀⠠⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠊⠀⠐⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠁⠉
⠀⠀⠀⢀⡴⠒⠒⠀⠀⢀⡤⣖⠋⠩⡍⠉⠉⠓⠲⣤⡀⢀⠔⠋⠁⠀⠀⠈⠙⠦⣄
⠀⠀⢠⠏⠀⠂⠀⠀⡰⠋⠀⠃⠘⠐⣇⠀⠀⠀⣍⠁⠛⣎⠀⠀⢀⠄⠚⢆⡀⠀⠘⣦
⠀⠀⢸⠀⠀⠀⠀⠰⠁⠀⠀⠐⠐⠉⠁⠀⠀⠀⠀⠓⠀⢸⡀⠀⠈⠢⣉⠔⠁⢀⠀⢸
⠀⠀⠸⡄⠀⠀⠀⢀⠀⠀⣀⠀⡀⠀⠸⡄⡄⠀⡀⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⡼
⠀⠀⠀⠙⢦⣄⡀⠸⡄⠀⡆⢂⡑⠀⠀⠣⠂⠈⠁⠀⠀⡼⠀⢤⣀⣀⣘⣑⣠⡶⠚⠁
⠀⠀⠀⠀⠀⠀⣄⠀⡙⢦⡙⠃⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⡀⢰⠀⢈⡭⠁
⠀⠀⠀⠀⠀⠀⠘⡆⠃⡴⠈⣝⠒⠒⠒⠒⠂⡀⠀⠀⠀⠀⢱⠈⢠⡎
⠀⠀⠀⠀⠀⠀⢀⡇⢰⡇⠀⠈⢦⠀⡏⢠⠞⠀⠀⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⡸⠀⢸⠇⠀⠀⢸⠀⢰⠋⠀⠀⠀⠀⠀⠀⢰⠃⢸
⠀⠀⠀⠀⡤⠖⠒⠒⠶⢄⠀⠀⢸⠀⢸⢀⣄⣀⡀⢀⡤⠤⡼⠀⢸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡟⠀⢸⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠃⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⣀⣀⡈⠛⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣰⣿⣿⣿⣿⣿⡷⡀⠙⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢿⠟⠉⣀⣀⠀⠉⠻⡆⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠀⣰⢿⣻⣻⡿⣆⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡶⠷⣿⣷⣴⣝⣳⣦⣄⠀⠀⠀⠀⠙⠣⠿⠆⠀⠻⠽⠇⠈⣮⣽⡆⢸⠀⢠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢀⠀⠙⢿⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⢃⡟⢀⣾⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⢀⠀⠈⢿⣿⣿⣿⡇⠀⠀⢀⣤⣶⣶⡶⢦⣾⣿⣿⣿⠟⣡⠞⣠⣾⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠸⣿⣿⣿⡇⠀⢠⣾⣿⣿⣿⣗⣾⣿⡿⠛⣡⢞⣡⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⣿⣿⣿⠃⣴⢟⣿⢟⣿⠿⠚⠋⠁⣀⣭⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⣿⣿⡟⢰⣿⠨⠟⠋⠁⣀⢰⣶⣿⣿⣿⡿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢰⣿⡿⢀⡿⠋⢀⡤⣖⣻⡿⣾⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠏⣼⡿⠁⣨⢤⢾⣽⣿⣿⣛⣳⣿⣟⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣤⡀⠙⢷⡀⢰⡟⣡⠾⠛⠉⠉⠁⠀⠀⣀⣬⣍⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠻⠟⠀⠈⠃⣿⠜⠁⠀⠀⠀⠤⠒⠚⠳⠿⠟⠵⣿⣿⣻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢀⣀⣠⣤⣶⣶⣦⣤⡀⠀⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠉⠉⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⣿⠃⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⡀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⣾⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡟⠀⠀⠀⠀⠀⠀⠀⠿⣿⣛⣻⢿⣿⣿⣟⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡇⠀⠀⣠⣤⠤⢤⣄⠀⠙⠿⠿⣬⣿⣿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢱⠀⣾⠋⠀⡠⣤⣉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢺⡆⠀⠈⢾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⢄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠉⠓⠀⠘⠀⠃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢉⣶⠟⠛⠻⢷⣆⡠⠀⠝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠸⣿⡀⠀⡀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡟⠛⠛⠀⠀⠀⣿⠀⢀⣠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣴⠟⡉⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣱⣷⣄⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⣼⠏⠀⢀⠀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⢷⡄⢰⡿⠀⠀⠈⠷⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣍⠀⣹⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡆⣠⣶⠿⠷⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⢸⣿⠃⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⡄⠛⠷⠶⠂⣬⠀⣿⠀⠀⠀⠀⣀⣴⠶⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢸⡇⢴⠠⡄⠃⢀⣿⠀⢀⣴⠟⣉⠴⢶⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠘⠀⠀⠀⣼⠇⢰⡟⣡⢞⡡⡦⢸⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⠀⠻⣾⠃⠋⠰⢃⣞⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣀⡀⠀⣀⣌⠁⠀⠀⠀⢠⡄⢀⣤⣶⠟⠛⢤⡀
⠀⠀⠀⠀⢴⣤⠾⠛⣛⣋⣉⣙⣛⠳⢷⣄⠀⠀⠀⠀⢹⣿⣿⣿⣋⠀⠀⠀⣀⣬⣤⣾⡋⠀⠀⠀⠀⠉⡦
⠀⠀⠀⠀⠀⠙⢷⣄⠹⣇⣴⡛⠟⡻⡷⣶⣄⠀⣠⠤⠾⣿⣿⣿⠛⣻⠞⠉⠉⠀⠈⢹⣧⡀⠀⠀⠀⢀⡇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⣷⣌⠡⡙⢦⡄⠂⢈⠟⠁⠀⠀⠀⠈⣿⠀⢸⣏⠀⠀⠀⠈⠁⠺⣿⣷⣴⣶⣾⡟⠃⠉⠉⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣄⡁⠛⣳⣶⠀⠀⠀⠀⠀⢀⣬⠛⠀⠀⠈⠰⣶⣶⣶⣾⣿⣯⣠⣿⣿⠛⠁⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠀⠈⠳⣄⠀⣀⢠⣼⠇⠀⠀⠀⠀⠀⡁⠀⠉⣛⣫⡿⣿⣿⣿⣷⣄⠀⠀⠀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢻⣿⣷⣀⠤⠤⠤⢆⡁⢀⠚⠁⠁⠀⠈⠻⣄⠀⠙⢦⣤⣞⣓⠶⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢚⣿⣷⣾⣿⣩⡇⠀⠀⡀⠀⠙⢬⡅⠀⠀⠀⠀⠀⠈⠁⠀⠀⠏⣉⠿⣿⡦⡉⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠙⣧⣹⠀⠀⠀⠀⠉⠂⢸⣷⡀⠀⠀⠀⣀⠐⠀⢠⣞⢡⡤⠄⣤⠴⠙⢃⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢸⣿⠄⡀⢀⣀⣀⣀⣸⣿⣷⣾⣶⣞⠉⠀⠀⠀⠈⢣⣀⣀⣒⣒⣋⣉⣉⣈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⡀⠀⠀⠀⠀⡸⣥⠞⠛⠀⠉⠉⠉⣿⣿⣿⣾⣟⠁⠀⠀⠀⠀⠀⠈⡉⠛⠉⠛⠋⠙⠋⠙⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣠⣾⡷⠖⠦⠶⢈⣩⡅⠀⠀⠀⠀⠀⠈⢙⣿⠟⢹⣿⣆⡀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⣾⢋⡿⣁⣀⣶⡴⢚⢽⠂⠀⠀⠀⠀⠀⠀⡾⠃⠀⠘⠃⠙⢷⠶⣤⣤⣶⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣼⢃⣘⣛⣋⠭⠤⠚⣡⣴⡟⠂⠦⣀⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠶⠠⢿⣿⡝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠘⠛⠉⣁⣀⣤⣴⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⢀⣼⣀⠀⡶⢹⡌⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⡶⠿⠿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠤⢶⣿⡳⣍⠳⣼⡀⣷⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣬⡳⢦⣄⣿⢸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣬⡁⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⢀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠂⠤⢂⣀⣠⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠈⠠⠀⠀⠀⠄⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⣠⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠒⠂⠐⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠦⡄
⠀⠀⠉⠉⠀⠀⠀⠃⠀⠀⠀⠀⠋⠧⠠⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟⠉⠀⠀⠈⠙⣿⣿⣿⣿⠿⡁⠺⣷⡖⢻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠀⢿⣿⠸⣴⡆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠂
⠠⡄⠠⠄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠀⠀⠀⠀⣴⠛⠉⠀⠸⣿⣿⣇⣀⢈⣥⣭⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢢
⢄⡀⠀⠄⠋⠈⠀⢀⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣠⣤⠀⠀⠀⠁⢤⠴⠃⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠈⠀⠀⠀⠀⠀⠀⣠⠄⠠⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⠀⢀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠁⠀⠀⠘⠀⢎⠉⠀⣠⣶⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⡀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠠
⠀⠀⠀⣓⢀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠄⠈⠉⠛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣧⠀⠈⠁⠀⣀⣀⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠻⠿⣦⣄⠀⠀⠀⠀⢀⠐
⠀⠀⣀⠉⠨⠗⠀⡀⠀⠀⠀⠘⢿⣄⠀⠀⠀⢀⡾⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠰⡟⠉⠉⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠙⢳⡄
⠀⡇⢈⡇⠀⠀⠚⠋⠀⠀⠀⠀⠀⠙⢷⣄⠀⠈⠳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣇⠀⠄
⠀⠁⠀⡙⠀⠐⠀⠀⢀⠀⠀⠀⠀⢀⠈⣿⠁⠔⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆⠀⠀⠀⠀⠀⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠐
⠀⠰⠀⢀⡐⠆⠂⠐⡃⢮⣱⣟⠻⠿⠟⠿⢀⣈⣤⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣿⣿⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠁
⠀⠀⠀⡈⡄⠂⠀⠙⡋⠸⠋⣿⠇⠘⣢⣶⣿⠛⣻⡿⠋⠀⠈⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢿⣏⠀⠘⢿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿
⢀⠈⠰⠏⠓⠀⠉⣀⡠⠀⠊⠁⠤⠰⣿⡏⢀⣼⢋⡴⠶⢆⠀⠀⠀⠀⠶⠖⢚⣩⣿⣿⣿⣻⠟⠉⠀⠀⠀⠀⠀⠀⠘⣿⣦⣀⣴⠏⠉⠉⠀⠘⠻⠿⣿⠟⠛⢻⣧
⠀⡀⢠⣤⠈⡀⠀⠁⠀⠄⠀⡠⠀⠀⠈⢿⣿⠟⣯⠞⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢠⠎⠀⢸⠀⠀⠀⠀⠀⢹
⠀⠄⠘⠋⣀⠀⠀⠀⠀⠘⢢⢷⣾⣦⡄⠈⣻⠿⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣏⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠁⠀⠀⠈⠀⠀⠀⠀⢠⢸
⠀⠂⠀⠀⠈⠂⠀⠀⠀⠂⠰⣿⣿⣿⠉⠂⠉⠘⠿⢂⡾⢀⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⣾⡄⠀⠀⠀⠀⠀⠀⠀⠘⢸
⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⣾⢲⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣴⠃⠀⠀⠀⠀⠀⠀⣀⡤⣾⠃⡏⠀⣹⠀⢀⠘⠀⠀⠀⠀⠀⢠⡿
⠀⠀⢀⡐⢐⠀⠈⠠⠀⡀⠀⠐⠀⠘⡁⢂⠀⠐⣴⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠉⠻⣶⢴⣤⣦⢴⣾⣏⡿⡃⣿⢠⠁⡆⣿⠀⢸⡀⠀⠀⠀⠀⠂⠞⡗
⠀⠖⠉⡄⠀⠀⠀⠀⢈⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠈⠻⣿⣿⢸⣿⣟⡟⣷⣿⠈⣤⡞⢉⡄⢸⡇⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⢀⠂⠁⠁⠀⠿⠏⠀⠰⠤⠄⢀⠐⡀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣧⣦⣭⣙⣷⠀⠀⠀⠀⠀⠀⣙⢻⣿⣯⣿⣧⣿⢸⠀⡿⡇⢀⠃⢸⢇⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠒⠈⠀⠀⡀⢄⠀⠀⢡⡀⠀⠸⠄⠀⠄⠀⠀⠀⠀⣀⠀⠠⠀⠿⡝⠛⠻⢿⣷⣦⣄⠀⣀⣠⡐⠙⢿⣿⠰⠾⣿⣿⡌⣾⠃⠀⣾⠀⢸⠸⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⢀⠀⠄⠀⠈⢻⣿⣤⡹⣴⣀⡀⠞⠁⢰⣌⢣⢹⡇⣯⡀⢤⠃⠀⣸⠀⠀⠀⠀⠀⢿⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣷⣤⠗⠀⠀⣠⣿⡏⣹⣊⡉⠀⡄⣿⠘⡏⢸⡜⣿⣿⡻⢾⠀⠀⢻⠀⠀⠀⠀⠀⢘⠆
⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⠈⢶⣭⣰⡷⠶⠞⠛⢋⠑⡀⡏⣿⡏⡇⢹⠀⣿⢸⠇⠀⠙⣷⣸⠀⠈⠈⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢠⠀⣀⠄⠀⠀⠀⠐⠀⠀⠚⢯⡀⠀⠀⡀⣴⠆⠀⢱⣿⣟⠁⢸⡇⢸⡇⠀⠈⠀⠹⡇⡆⡄⡀⠀⠀⠀⢀⠔⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠈⠀⠠⠀⠈⠵⡤⠀⠀⠀⠊⠀⠀⠀⠀⠀⠉⠀⠀⠀⠢⡁⠀⠻⣿⠈⣇⠁⣾⡇⠀⠀⠀⠀⠀⡇⡇⠇⠀⠀⢀⠸⠀⠈
⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⠀⠂⠀⠀⠚⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠈⠀⣳⣇⣛⣀⣻⣁⣀⣘⣀⣀⡀⢓⢐⠂⣀⢀⢘⣀⣆⣀⡀⢀
⣿⡟⣉⡻⠟⠿⠿⠿⠿⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⡆⠀⠀⠀⢻⣿⣿⣇⠀⠀⠘⣿⣿⣇⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⠁⢀⣿⣿⡟⠀⠀⠀⣰⣿⣿⠏⠀⠀⣠⣾⣿⣿⠟⠋⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿
⣿⣿⡀⠀⠀⠈⣿⣿⣿⡀⠀⠀⢻⣿⣿⠀⠀⠘⣿⣿⡇⠀⠀⣾⣿⡏⠀⣼⣿⡟⠀⠀⠀⣰⣿⡿⠃⠀⣠⣾⣿⡿⠋⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⠿⠟⠛⠋
⣿⣿⣧⠀⠀⠀⠘⣿⣿⣧⠀⠀⠘⣿⣿⡆⠀⠀⣿⣿⡇⠀⠀⣿⣿⠇⢀⣿⣿⠁⠀⠀⣰⣿⡿⠁⢀⣾⣿⡿⠋⠀⠀⢀⣤⣾⣿⣿⡿⠟⠋⠁⠀⠀⠀⣀⣠
⢿⣿⣿⣧⠀⠀⠀⠸⣿⣿⣆⠀⠀⢹⣿⣷⠀⠀⢻⣿⡇⠀⠀⣿⣿⠀⢸⣿⡇⠀⠀⢰⣿⡟⠀⣠⣿⡿⠋⠀⠀⣠⣾⣿⡿⠟⠋⠁⠀⠀⣀⣤⣴⣾⣿⣿⣿
⠀⢻⣿⣿⣧⠀⠀⠀⠙⣿⣿⡆⠀⠀⢿⣿⡆⠀⠘⣿⣇⠀⠀⣿⣿⠀⣼⣿⠀⠀⢀⣿⡟⠀⣴⣿⠟⠀⠀⣠⣾⡿⠟⠉⠀⠀⣀⣤⣶⣿⣿⣿⠿⠟⠛⠋⠉
⠀⠀⠹⣿⣿⣧⡀⠀⠀⠘⣿⣿⣆⠀⠈⢿⣿⡀⠀⢻⣿⠀⠀⣿⣿⠀⣿⡟⠀⠀⣼⡿⠁⣼⣿⠃⠀⣠⣾⡿⠋⠀⠀⣠⣴⣾⣿⠿⠛⠉⠁
⣄⠀⠀⠈⢿⣿⣷⡄⠀⠀⠈⢿⣿⣆⠀⠈⢿⣷⠀⠘⣿⡇⠀⢹⣿⠀⣿⡇⠀⢠⣿⠃⣸⡿⠁⢀⣾⡿⠋⠀⢀⣴⣾⡿⠟⠉⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿
⣿⣧⡀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠹⣿⣧⡀⠈⢿⣧⠀⠹⣿⡀⠸⣿⠀⣿⡇⠀⢸⡟⢠⡿⠁⣠⡿⠋⠀⣀⣴⡿⠛⠁⠀⠀⣀⣠⣴⣾⣿⣿⡿⠿⠿⠛⠛⠛
⢿⣿⣿⣦⡀⠀⠀⠙⢿⣷⣄⠀⠀⠈⢻⣷⣄⠀⢻⣧⡀⢻⣧⠀⢿⡆⢹⡇⠀⣿⠁⣿⠁⣴⠟⠁⢀⣼⠟⠉⠀⢀⣠⣶⣿⠿⠟⠛⠉⠁⠀⢀⣀⣀⣀⣀⣀
⣀⠉⠻⣿⣿⣦⡀⠀⠀⠙⢿⣷⣄⡀⠀⠙⢿⣦⡀⠙⣷⡄⢻⣆⠸⣇⢸⡇⠀⡟⣸⠇⣼⠏⢀⣴⠟⠁⢀⣤⡾⠟⠋⢉⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣤⡈⠛⢿⣿⣶⣄⠀⠀⠉⠻⢿⣦⣀⠀⠙⠻⣦⡈⠻⣆⠹⣆⢻⡀⣇⠀⡇⡟⣸⠃⣠⠟⢁⣠⠾⢛⣩⣴⡶⠿⠛⠛⠋⠉⠉
⠙⠿⣿⣿⣶⣤⡈⠛⠿⣿⣦⣄⡀⠀⠉⠻⢷⣤⣀⠈⠻⢦⡈⢷⡜⢦⢳⢹⠀⣿⢱⢃⡼⢁⡴⣋⡥⠾⢛⣩⣤⣤⣶⡶⠾⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⣉⠛⠿⣷⣦⣄⣀⠈⠙⠳⢦⣄⡙⠲⢌⡪⡣⡷⡀⣻⠁⢊⣴⣿⣪⠵⠖⢛⣉⣉⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⠛
⣤⣄⡀⠀⠀⠀⠀⠉⠙⠻⠿⢿⣶⣦⣤⣍⣙⠛⠶⠶⢤⣤⣉⣙⡒⠍⠊⠐⣥⣇⡴⠋⠊⢑⣒⣛⣉⣉⣉⠉⠉⠉⠉⠉⠛⠛⠻⠿⢿⣿⣶⣶⣤⣄⣀
⠿⣿⣿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠒⠒⠒⠛⢛⣛⠊⢉⠴⢛⠉⠒⠶⠶⣤⣭⣭⣉⣉⠙⠛⠛⠷⢶⣶⣤⣄⣀⠀⠀⠉⠙⠻⠿⣿⣿⣶
⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⣿⣿⣶⣶⣶⣶⣶⠶⠶⠶⠶⠒⠛⣉⡥⣒⣾⠏⡔⠀⡇⣦⡢⣍⠲⢍⡙⠻⣯⣛⠷⢶⣤⣀⡀⠉⠛⠻⢿⣷⣦⣄⡀⠀⠀⠉⠻
⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠖⢛⡥⢞⡕⣡⢣⠃⡇⣿⠰⡹⣌⠳⣄⠙⠷⣄⠉⠻⢶⣬⡙⠻⣷⣦⣄⡀⠈⠙⠿⣿⣷⣦⣄
⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⠿⠿⠛⠛⢉⣡⣴⠞⣫⡴⢋⡴⢃⡟⢰⠇⣿⡆⢳⠘⣦⠘⢷⡀⠈⢳⣦⡀⠙⠻⣷⣄⠙⠻⣿⣶⣄⡀⠈⠙⠿⣿⣿
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣤⣤⣶⠿⠛⣉⣴⠞⠋⣠⡟⢁⡾⠁⣾⠀⣿⣿⠘⣧⠘⣧⠀⢻⣦⠀⠙⢿⣆⠀⠈⠻⣿⣦⡈⠙⢿⣿⣦⣄⠀⠈⠻
⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⡿⠿⠟⠛⢉⣠⣴⡿⠛⠁⣠⡾⠋⢠⡿⠁⢰⡏⠀⣿⣿⡀⢿⡄⠹⣧⠀⠻⣧⡀⠈⢻⣷⡄⠀⠈⢿⣿⣦⠀⠙⢿⣿⣷⣄
⠛⠛⠛⠛⠛⠛⠉⠉⠉⢁⣀⣠⣤⣶⣿⠿⠛⠁⠀⣠⣾⠟⠁⣰⡿⠁⢀⣿⠁⢰⡟⣼⡇⢸⣧⠀⢻⣧⠀⢻⣷⡀⠀⠹⣿⣆⠀⠀⠙⣿⣷⣄⠀⠙⢿⣿⣷
⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⡿⠟⠛⠉⠀⠀⣀⣴⣿⠟⠁⣠⣾⠟⠀⢀⣾⠇⠀⣾⡇⣿⡇⢸⣿⠀⠈⣿⡆⠀⢿⣷⡀⠀⠹⣿⣧⠀⠀⠈⢿⣿⣦⠀⠀⠻⣿
⣿⣿⡿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⣀⣴⣾⡿⠛⠁⢀⣴⡿⠋⠀⢀⣾⡏⠀⣰⣿⠀⣿⡇⠘⣿⡆⠀⢹⣿⡀⠘⣿⣧⠀⠀⠹⣿⣧⠀⠀⠈⢻⣿⣷⡄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⠟⠉⠀⣠⣶⣿⠟⠁⠀⣠⣿⡟⠀⢠⣿⡇⢸⣿⠇⢰⣿⡇⠀⠈⣿⣇⠀⢹⣿⡆⠀⠀⢻⣿⣧⠀⠀⠀⢻⣿⣿⡄
⣀⣀⣀⣤⣤⣴⣶⣿⣿⣿⡿⠛⠉⠀⢀⣴⣾⣿⠟⠁⠀⢀⣴⣿⠏⠀⢠⣿⡟⠀⣾⣿⠀⢸⣿⡇⠀⠀⣿⣿⠀⠸⣿⣷⠀⠀⠈⣿⣿⣇⠀⠀⠀⢿⣿⣿⡄
⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⣀⣴⣾⣿⡿⠛⠁⠀⠀⣠⣾⣿⠋⠀⢠⣾⣿⠁⢠⣿⡟⠀⣸⣿⡇⠀⠀⢻⣿⡇⠀⣿⣿⡇⠀⠀⢸⣿⣿⡄⠀⠀⠈⣿⣿⣿
⠛⠛⠉⠁⠀⠀⠀⣀⣤⣶⣿⣿⣿⠟⠋⠀⠀⠀⣠⣾⣿⡟⠁⠀⣠⣿⣿⠃⠀⣾⣿⠃⠀⣿⣿⠃⠀⠀⢸⣿⡇⠀⣿⣿⣧⠀⠀⠀⣿⣿⣷⠀⠀⠀⠸⣿⣿
⠀⢀⣀⣤⣴⣾⣿⣿⣿⡿⠟⠋⠀⠀⠀⢀⣠⣾⣿⡿⠋⠀⢀⣴⣿⡿⠃⠀⣼⣿⡟⠀⢸⣿⣿⠀⠀⠀⣾⣿⡇⠀⢹⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢻⣿
⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⣠⣴⣿⣿⡿⠋⠀⠀⣠⣾⣿⡟⠁⠀⣰⣿⣿⠁⠀⣾⣿⡟⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿⡀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠘⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢢⡀⠀⠀⠀⢀⠇⠸⡀⠀⠀⠀⢀⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⢄⠀⠀⡼⠀⠀⢧⠀⠀⡰⠋⠀⡇
⠀⠀⠀⠀⠀⠀⢻⡒⠤⣀⠀⠀⠸⠀⠀⠈⠳⣠⠃⠀⠀⠘⣤⠎⠀⠀⢠⠁⠀⠀⣀⠤⢒⡟
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠙⠢⢄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠔⠋⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢀⠤⠒⠊⠉⠉⠉⠉⠑⠒⠤⡀⠀⠀⠀⠀⢀⠎
⠀⠘⠳⣒⠒⠒⠒⠂⠤⠵⠀⠀⣠⠞⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠮⠔⠒⠒⠒⠒⣨⠟⠁
⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⡔⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⢘⣢⠀⠀⣸⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣔⡁
⣀⡠⠤⠒⠒⠉⠁⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠒⠒⠤⢄
⠈⠉⠑⠒⠤⢤⣀⡀⠀⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠛⢄
⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠱⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠔⠥⠤⠤⠒⠒⠒⡲⠀⠀⠈⠢⣑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢖⠒⠒⠒⠒⠤⠬⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡀⠈⠑⠲⠭⠍⣉⣀⠠⠤⠖⠊⠁⢀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⡜⠀⣀⡤⠒⠉⡇⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠉⠒⢤⣀⠀⢣
⠀⠀⠀⠀⠀⠀⡼⠔⠊⠁⠀⠀⢠⠁⠀⢀⡔⠙⡄⠀⠀⢠⠋⠢⡀⠀⠀⡆⠀⠀⠈⠑⠢⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠋⠀⠀⢱⠀⠀⡎⠀⠀⠙⢆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠜⠁⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠱⣤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠖⡀⠀⠐⠂⠤⡀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡏⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠑⠄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠉⠁⠀⠀⠈⠁⠀⠓⠠⢤⠂⠀⠈⠁⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⡐
⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⡠⠋⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠑⢄⠔
⢀⠔⠈⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⡰⠟⠛⠛⠛⠀⠀⠀⠀⠙⠛⠛⠻⢦⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡀
⠃⠂⠉⠁⠢⡀⠀⠀⠌⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⡀⠀⣠⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⢡⠀⠁⠂⠀⠀⠊⢀
⠀⠀⠀⠀⠀⠱⡀⠈⠀⠀⠀⣤⣾⣿⢫⠃⣰⣿⣿⣿⣿⡟⠙⣿⣿⣿⣿⣿⡏⡏⢉⣷⣦⡀⠀⠀⠃⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠈⢻⣏⠇⢠⣿⣿⣿⣿⣿⠇⠀⣿⣿⣿⣿⡿⡜⠀⣾⣿⠉⠀⠀⠀⢠⠀⢀⠠⠐⠁
⠀⠀⠀⠀⢀⠠⠄⡇⠀⠀⠀⠀⠈⠻⣄⣾⣿⣿⣿⡿⠋⠀⠀⠈⠿⣿⣿⣹⠁⣼⡿⠃⠀⠀⠀⠀⠸⠉
⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⢂
⠀⡔⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠰⣶⣦⡐⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⠒⣠⣶⡞⠀⠀⠀⠀⢀⠂⠀⠡
⠈⢀⠂⠈⠁⠐⠢⠀⢱⡀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣶⡶⠶⠶⠶⢶⣶⣾⣿⠿⠋⠀⠀⠀⠀⢀⠎⠀⠀⠀⠑⠂⠄⠐
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠉⠛⠡⠤⠀⠀⠠⠤⠘⠋⠁⠀⠀⠀⠀⠀⢠⠮⢀⡀⠀⠀⢀⠠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠊⠁⢀
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⠤⠀⠀⠂⠁⠉⠐⠂⠀⠠⠤⠤⠄⠠⠀⠐⢅
⠀⠀⠀⠀⠀⠀⠀⠈⡄⢠⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠑⢄⠀⠀⠀⠢⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠜⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠘⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣬⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⡀⠀⠀⠀⠀⠀⠄⡀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠘⡀⠂⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠲⠀⠂⢀⣀⠀⠀⠓⠀⠐
⠀⠀⠀⠀⠀⠦⠀⠄⢀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡐⣤⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠳⡄⣀⣀⡀⠂⢠⡀⠠⢤⢾⡄⠋⠙⡒⢤
⠀⠀⠀⠀⠀⠀⠀⡐⠈⠀⠀⠌⠁⣸⣿⡿⠀⢂⠀⠀⠙⡄⠁⠀⠀⠪⡇
⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⢺⡀⠛⠙⠁⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠞⠉⣠⣶⠀⠀⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠠⣲⡞⠁⢄⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡐⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⡏⠁⠃⡈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠠⡀⠁⠠⡀⠀⠀⠀⢀⠀⠰⡰⠀⠁
⠀⠀⠀⠀⠀⠀⠘⠡⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠀⠀⢉⣿⣷⣧⣀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠁⠀⠀⠀⠊⠉⠛⠤⠀⠘⢠⣞⠄⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠐⠄⠊⠸⢄⠀⢠⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢘⠀⠰⠀⠀⡘⠂⢠⢿⣻⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⢢⣼⠟⢻⡤⠔⠪⠀⣠⠀⠀⠙⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠀⠃⢈⢒⣶⠤⠀⠐⠿⣶⡟⢧⡀⠀⠀⠈⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠘⣀⡴⠀⠰⠀⢠⢀⠑⢨⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠍⠐⢈⡽⠀⠉⠐⠂⠀⠈⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠃

⡄⠀⠀⣌⠀⢘⠉⠒⠋⠒⠊⢓⠀⢀⡄⠀⢀⣄⠀⠀⢠⠁⠐⠋⠑⠊⠑⠊⠙⠂⠈⡄⠀⠀⣠⡀⠀⢠⡀⠠⡚⠑⠒⠙⠒⠉⡣⠀⣠
⡿⡧⠀⠌⠲⠞⠀⢠⣄⡤⠀⠐⠶⠉⠄⠨⢿⣿⠯⠀⡀⠑⠶⠁⠀⣄⣠⠀⠈⠲⠎⠀⠀⡽⣿⡻⡅⠠⠉⠶⠂⠀⢤⣠⡄⠀⠳⠖⠡⡀⠼
⠿⠀⠀⣠⡀⠠⠨⣭⣿⣫⠅⠠⠀⣠⡀⠀⠽⠻⠇⠀⣀⣄⠠⠀⢭⣻⣟⡭⠐⠄⣀⣀⠀⠸⠟⠯⠀⢀⣄⠀⡄⠩⡝⣿⣬⠅⠄⢀⣄
⢀⡀⢐⡀⠘⠦⠀⠛⠿⠋⠂⠠⠎⠀⡂⠀⣀⠀⣀⠀⡃⠀⠳⠀⠈⠻⠟⠓⠀⠞⠀⢘⠀⣀⠀⣀⠀⢐⠀⠱⠄⠐⠙⠿⠛⠀⠴⠃⢠⡂⢀
⢇⠸⠻⠄⠐⠀⠀⠀⢀⠀⠀⠀⠒⠀⡽⠫⡠⠯⡠⠛⠅⠀⠂⠀⠀⢀⡀⠀⠀⠐⠀⠨⠟⢄⠿⢄⠝⢯⠀⠒⠀⠀⠀⡀⠀⠀⠀⠂⢠⠝⠇
⢀⠀⠀⣁⡔⠋⠀⣲⣿⣷⡂⢈⠳⣄⡅⠀⢀⠀⠀⠀⢎⡤⢋⠀⢰⣾⣷⡆⠀⠙⢨⡱⠀⠀⠀⡀⠀⢠⣠⠚⡁⢐⡾⣿⣔⠀⠙⢂⣈⠄
⡿⣒⠀⠀⠀⠈⠀⢱⣿⣞⠁⠈⠀⠀⡀⢐⣺⣿⢗⠂⡀⠀⠀⠀⠉⣾⣷⠉⠀⠀⠀⢀⠐⡺⣿⣗⡂⢀⠀⠀⠁⠈⣹⣿⡊⠀⠁⠀⠀⠀⣒
⡿⠧⠄⡰⠈⠱⠀⠀⠀⠁⠀⢘⠙⢤⡀⠬⠿⣿⠯⠄⣠⠌⠉⠆⠀⠁⠈⠀⠰⠉⠡⣄⠤⠝⣿⠿⠥⢀⡤⠋⠃⠀⠈⠀⠀⠀⠎⠁⢎⠀⠼
⠁⠀⠀⠠⠀⢙⡦⠊⣶⠋⡢⣞⠀⠄⠀⠀⠀⠁⠀⠀⠀⠄⢘⣢⡆⢱⡎⢱⣔⠃⠠⠀⠀⠀⠈⠀⠀⠀⠠⠀⣳⢔⠑⣖⠑⣴⡃⠠⠄
⣦⡤⠄⢢⠀⢨⠀⠈⠀⠉⠀⠈⠂⠴⠂⠤⣤⣷⣤⠄⠲⡄⠚⡅⠈⠁⠈⠁⢀⠂⢠⠖⠠⣤⣾⣄⠤⠐⢦⠐⠁⠀⠁⠀⠁⠀⡕⠀⡔⠠⢤
⣯⡓⠀⠀⠉⠁⠀⢰⣶⣖⠀⠈⠉⠀⠂⢐⣫⣿⣟⠀⠂⠈⠉⠀⢀⣶⣶⠀⡀⠉⠁⠐⢀⣻⣿⣝⡂⠐⠀⠉⠁⠀⣲⣶⡆⠀⠉⠉⠐⠀⢚
⠙⠀⢀⠶⢆⠈⠀⣳⣿⣵⡃⠐⣀⠖⠄⠀⠚⠙⠃⠀⠔⠦⡐⠁⣺⣾⣷⣗⠈⢂⠴⢢⠀⠘⠋⠓⠀⠠⠲⣀⠃⢘⣮⣿⣞⠀⠁⡰⠖⠄
⡤⢄⣠⠅⢈⠁⠀⠀⠙⠁⠀⠘⡁⠀⢥⡠⠤⣠⠤⣀⠅⠀⡙⠀⠀⠘⠃⠀⠀⢋⠀⠨⣀⠄⢤⠤⢄⡬⠀⢈⠃⠀⠈⠋⠀⠀⠘⡀⠨⣄⡠
⠑⠊⠙⠂⢀⡤⠀⡀⣠⡀⡀⢠⡀⠀⡚⠑⠒⠙⠒⠉⡃⠀⣠⠀⣀⣠⣄⣀⠀⣄⠀⢘⠉⠒⠊⠒⠊⢓⠀⢀⡄⢀⢀⣤⢀⠀⢤⡀⠐⠋⠑
⣤⠀⠈⠲⠊⠠⠠⠽⣿⡻⠅⠠⠉⠶⠂⠀⢤⣠⠄⠀⠳⠖⠡⡀⠼⢿⡿⠧⢀⠌⠲⠜⠀⢠⣄⡤⠀⠐⠶⠉⠄⠨⢟⣿⠯⠀⡀⠑⠖
⣿⡥⠀⠄⣠⣄⠈⠹⠟⠯⠁⢀⣄⠀⠄⠡⣝⣿⡥⠀⠀⢀⣄⠈⠉⠿⠿⠉⠁⣠⡀⠀⠀⣭⣿⣫⠌⠠⠀⣤⡀⠀⠴⠻⠏⠁⣠⣄⠠⠈⢬
⠏⠑⠀⠞⠀⢜⠀⣀⠀⣀⡀⣐⠀⠹⠄⠐⠙⠿⠉⠂⠴⠃⢠⡃⢀⡀⢀⡀⢘⡄⠘⠦⠐⠋⠿⠋⠒⠠⠏⠠⡂⠀⣀⠀⣀⠀⡣⠀⠳⠀⠚
⡀⠀⠀⡐⠀⠨⠛⠄⠽⠤⠝⠯⠀⠊⡀⠀⠀⡀⠀⠀⠀⠂⢠⠟⠣⠼⠧⠜⠻⡄⠐⠀⠀⠀⢀⠀⠀⢀⠐⠀⡽⠫⠠⠿⠠⠛⠅⠀⢂
⣷⣖⠀⡹⢠⡸⠀⢀⡀⡀⠀⠪⣠⠚⠁⢐⡾⣿⣖⠂⠈⢢⣀⠆⠀⡀⢀⠀⠰⣠⡔⠁⠀⣲⣿⢷⡂⠈⠓⣄⠅⠀⢀⢀⡀⠀⢆⡤⢋⠐⣲
⣷⠭⠀⠀⠀⢀⢀⣺⣿⢏⡂⢀⠀⠀⠀⠨⣾⣿⡮⠀⠁⠀⠀⠀⣐⢿⡿⣐⠀⠀⠀⠀⠠⢵⣿⣿⠅⠈⠀⠀⡀⢐⡹⣿⣗⡀⡀⠀⠀⠀⠭
⠀⠀⠰⣉⠱⣄⠀⠝⣿⡿⠄⢈⡴⢉⠁⠀⠀⠀⠀⠀⢌⠉⢎⠀⠸⢿⡿⠧⠀⡰⠉⡱⠀⠀⠀⠀⠀⠈⡉⢦⡁⠠⠻⣿⠫⠀⣠⠎⣉⠂
⡎⢱⢔⡃⠠⠀⠀⠀⠈⠀⠀⠀⠤⠀⣳⢔⠁⣖⢑⣴⡃⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⢘⡶⡊⣲⠉⡢⣞⠀⠤⠀⠀⠀⠁⠀⠀⠀⠄⢐⡢⡎
⠈⠁⠠⠁⢠⠖⠀⣤⣾⣤⠄⠐⠦⠀⡅⠀⠉⠀⠉⠀⡅⠀⠔⠀⢤⣴⣦⡤⠀⠢⠀⢨⠀⠈⠀⠉⠀⠨⠀⠴⠂⠠⣤⣷⣤⠀⠲⡄⠘⠀⠈
⣶⠠⠀⠉⠁⠐⢐⣻⣿⣜⡂⠜⠀⠉⠁⠠⢲⣶⡢⠄⠉⠉⠀⠀⣚⣽⣯⣓⠀⠀⠉⠉⠠⢴⣶⡖⠄⠈⠉⠀⠣⢐⣳⣿⢟⡂⠂⠈⠉⠀⠄
⣷⡟⠀⢂⠴⢢⠀⠘⠋⠋⠀⠠⠲⣀⠁⢘⣾⣿⣞⠀⠀⡰⠖⡄⠀⠋⠙⠀⢠⠲⢆⠈⠀⣳⣿⣷⡃⠈⣀⠖⠄⠀⠙⠙⠃⠀⡔⠆⡐⠀⣻
⠃⠀⠀⢋⠀⠨⣀⠔⢤⠔⢄⡬⠀⠈⠁⠀⠈⠋⠀⠀⠈⡀⠠⣄⡠⢢⡴⢄⣠⠄⢀⠁⠀⠀⠙⠁⠀⠘⢁⠀⢥⡠⠢⡤⠢⣀⠅⠀⡙
⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣥⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⢀⣤⠴⣤⠿⠿⠛⠉⠻⢆⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣠⠄⠶⠏⡉⢶⠏⠀⠀⠀⠀⠀⠀⠀⢾⡕⢤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠉⡏⠙⠉⠉⢡⣤⠚⠃⠀⣠⠀⢀⣀⣀⠀⣠⣀⡀⠀⠿⣗⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠈⣧⣴⣴⡄⢜⣿⠀⠀⣼⡅⠀⣻⣿⣿⣿⡏⠈⠀⠀⠶⡌⣭
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸⣿⣿⣷⣾⣿⣿⣿⣿⣵⣿⡟⠁⣠⣦⣴⣆⡊⣈⣠⡴⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⡟⣯⠙⡇⠉⢰⣋⣼⣷⣤⡎⢿⣿⣿⣿⣿⣿⢯⢣⠈
⠀⠀⠀⠀⣀⣠⣀⡀⢸⠀⠀⢠⣠⠆⠈⠉⠇⢸⠆⣷⡖⣿⠉⢰⡏⢿⠿⣎⢙⡿⣿⣿⣿⡂⠔
⠀⠀⠀⠀⠀⠰⠄⠁⢸⣆⠀⠚⡙⠀⠀⠀⠄⠸⡆⢹⣧⢸⣷⣻⡇⠀⠀⣿⠸⣿⣿⣟⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣼⣷⣀⠀⠀⠀⠀⠀⣀⠹⣎⡙⠿⢿⡰⡿⣿⣷⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠉⠉⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢈⣁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠋⠀⠸⠋⠀⠀⠀⠀⠀⠀⢶⣼⣿⣷⣿⣿⡉⢁⣀⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠸⣿⠗⠂⠀⠰⠒⠀⠀⠀⠀⠀⠈⠛⣻⡏⢹⣿⣾⣿⡿⠌⠁⡟⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⢠⣄⣠⣼⠷⠶⠓⠒⠂⠀⠀⠀⠀⠀⠀⣾⠉⠻⣭⣋⣵⣯⣥⣞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠠⠀⠋⠋⠟⠙⡖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠀⠒⣟⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠐⠀⠹⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⢀⠀⠀⢤⡀⡀⠀⠀⠀⠀⠑⢄⠀⠀⠘⢆⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠔⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠂⡀⠀⠀⠙⠠⠀⠀⠀⠐⢤⡀⠈⢆⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⣠⠆
⠀⠀⠀⠠⠄⠈⠀⠈⠃⣉⠘⠇⠀⠀⠈⠀⠀⠤⢀⣀⣀⠠⠀⠀⠈⠓⢾⣆⣤⠀⣀⠴⠶⠶⠤⠤⢀⠀⠀⢀⣧⠼⠟
⠀⠀⠀⠀⢀⡄⠊⠁⠀⠀⠀⡀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣏⡼⠁⠠⡄⠁⠀⠀⠀⠐⢤⣾⣯⣀⠀⡀⠀⠀⡰⠞⡀
⠀⠀⠀⠂⠁⠀⣠⡶⢂⠀⠀⢀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣯⣭⣭⡻⠟⠈⠁
⠀⠀⠀⠀⠀⠂⢑⠀⠹⡆⠀⠈⢣⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⠿⣯⡋⡀⠁
⠀⠀⠀⠀⠀⠀⣈⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠈⠣⢄⡸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡆⢹⣿⣿⣿⠠⠏⢀⣼⣿⣡⠏⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⣿⣿⣿⣿⠃⠀⣾⣿⠘⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⢸⡇⢸⣽⣿⡏⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⡠⣾⡟⠀⠀⣿⣿⣿⠏⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣳⠀⡇⠈⣿⣿⠀⠀⢺⣿⡏⠀⠀⠀⠀⠀⠀⣠⠞⣱⡟⠀⠀⠀⣟⠻⠏⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⢇⢂⣿⣿⡄⢀⠀⢸⡆⠀⠀⠀⠀⠀⣰⡏⣾⣿⡅⠀⠀⠀⠈⠀⠀⠀⠀⢸⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⡜⢿⣿⣄⢢⠀⠣⠀⠀⠀⠀⠀⢿⡅⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣻⣷⠘⢮⡻⣿⣦⡱⡄⠁⠀⠀⠀⠀⠸⣧⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠿⠟⠃⠀⠳⣌⠻⣿⣾⢆⠀⠀⠀⠀⠀⢿⣾⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣂⣷⠀⠀⠀⠀⠀⠀⢹⡄⠈⢻⣯⢆⠀⠀⠀⠀⣸⣿⣿⣿⣯⢷⡕⢤⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣿⣼⠀⠀⠀⢀⣿⣿⣿⣿⣿⣷⡙⠷⣝⡢⡀⠀⠀⠀⠀⠙⢿⣷⠦⢄⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⢀⡜⠀⠀⠀⣿⣟⠀⠀⢀⣾⣿⣿⣿⡿⢻⣿⣿⣷⡈⠹⢮⣦⡀⠀⠀⠀⠀⠙⢄⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⠞⠀⠀⠀⢠⣿⡆⠀⢠⣿⣿⣵⣿⣯⣤⣌⢿⣿⣿⣇⣀⣈⢿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⢠⣿⡟⠀⠀⣾⣯⣾⣿⣿⣷⣄⠙⣮⢿⣿⣿⣿⣿⣿⣷⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠉⠀⠀⠀⠀⠀⣰⢟⡿⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧⠘⡎⢿⣿⣿⣿⣿⣿⡿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⣀⣠⣴⣾⡿⠟⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠈⢿⣿⣿⡁⠀⠁⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣀⣤⣴⣶⡾⠿⠿⠛⠛⠋⠉⠀⠀⠀⣠⣾⠟⣿⠋⠀⠈⠉⠛⣿⣿⣿⠀⠀⠈⣿⣿⣿⢀⠀⠻⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣴⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⣋⣙⣻⣤⣶⣲⢶⣦⡀⠘⣿⣿⡇⠀⠀⠘⣿⡇⠀⠀⢠⠈⠉⠈⠙⡄
⠀⠀⠀⠀⠀⣰⠟⢁⣼⣿⣿⠟⠉⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⡇⠀⠀⢠⣿⣶⣷⡀
⠀⢀⠀⠀⣰⡏⢠⣿⣿⠟⠁⠀⠀⠀⠀⣠⣶⡿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠇⠀⠀⠀⣿⣿⣿⣿⡆
⠀⡘⠀⢰⡟⢠⣿⣿⠃⠀⠀⠀⢀⣠⣾⢟⣩⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠙⣿⣿⣿⣿⡇⢠⡿⠀⠀⠀⠀⠙⠛⣻⠆⠛
⠀⡇⠀⣿⠃⣼⣿⠇⠀⠀⢀⣴⡿⢛⣵⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⡼⠃⠀⠀⠀⠀⠀⠀⠛
⠀⡇⠀⣿⠀⣿⣿⠀⠀⣰⣿⠟⢡⣾⣿⣿⣿⣿⣿⣿⠟⣁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡇⠀⣿⢸⣿⣿⠀⢸⣿⠏⢀⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⡴⠀⠀⣀⡀⠀⠀⠀⣀⠀⢸
⠀⡇⠀⡏⢸⣿⣿⠀⣼⡇⠀⣸⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⡟⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⢎⣤⠞⠋⠉⢻⣴⣶⣯⢽⣤⡼
⣴⠃⢰⠇⠀⣿⣿⡄⣿⠀⢀⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠇⠀⣠⡾⠟⠛⢻⡄⠘⣿⣿⠏⠁⠀⠀⠀⠈⠉⠉⠀⠀⣿⠏
⠏⠀⠸⠀⠀⢹⣿⡇⣿⠀⣸⣿⣿⣿⣿⣿⣿⡿⠘⣿⣿⡿⠀⡾⠋⠀⠀⠀⢸⣿⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⠛⠃⣸⣇⠀⠀⠀⠀⠀⠉⠻⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⡀⠀⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀⠀⣿⣻⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⣴⢻⣿⣧⣿⣿⡏⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢀⠈⣜⣾⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⢺⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡊⠒⠉⠈⡆⣀⠤⡀⠀⠀⠀⠀⠀⠣⣀⠀⠑⡄⠀⡠⠊⠉⢑
⠀⠀⠀⠀⠀⢀⠔⠢⠤⠤⢤⠀⣸⡠⠔⢎⡁⠀⠀⢱⠀⠀⠀⣀⠀⣀⣱⡀⣀⣠⠏⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡰⠓⠒⠂⠁
⠀⠀⠀⡎⠑⠺⡄⠀⠀⠀⢸⡴⠭⡀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠢⡀⠀⠀⢹⠀⢈⠦⠤⢤⣄⠊⠀⠀⠀⠀⠀⣀⡰⠑⣸⠇
⠀⠀⡰⠁⠀⠀⠘⡦⠐⢴⠋⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠠⢴⠋⠉⠹⡄⠀⠀⡨⠇⠀⠀⠀⣀⢘⣀⠀⠀⣿⠔⠒⡆
⠀⠀⠑⠢⡤⠴⠚⢄⣀⡸⠳⢤⡄⠨⠂⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣇⢀⡀⠀⡟⠢⠞⠀⠀⠀⠀⠘⠀⠀⠈⠓⠚⢃⠀⠀⢱
⠀⠀⠀⣏⠀⠀⠀⠀⡏⠀⠀⠀⠑⡀⠀⠀⠀⢸⠁⢸⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠐⠤⢤⠔⠛⢲⡉⠉⠙⢄
⠀⠀⠀⠀⠉⠢⣀⠔⡛⠦⠤⠊⠉⠀⠀⠀⠀⠘⢄⡏⠀⠀⣀⣠⠔⠢⡀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⢨⡧⠀⡐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⢇⠀⠀⠀⡷⠁⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢊⠅⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠵⠶⠷⡔⠒⢣⣀⣤⣤⡊⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠤⣼⢀⣀
⠀⠀⠀⠀⠀⡰⠋⠀⡠⠛⡧⣉⠑⢆⠀⠀⠀⠀⠀⠘⠲⡀⠀⢀⡷⠠⠺⡀⠀⠀⣈⠇⠀⠀⠀⠀⠀⠀⠘⠂⠒⢩⠙⢄⣀⡅
⠀⠀⠀⠀⠀⠱⠤⠚⠁⠀⠓⢦⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠔⢹⠀⠀⠀⢳⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⢸⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⣴⣿⣿⣿⣿⣷⣦⡈⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣾⣿⡿⠟⠛⠛⠻⢿⣿⣆⠈⢿⡇
⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠻⢋⣴⣾⣿⣿⣶⣄⠹⣿⡆⠈⣧
⢠⣾⣿⣿⣿⣿⣿⣦⣠⣴⣦⣤⡀⠀⠀⠀⠀⠘⢿⣿⣶⣄⠀⣾⣿⣿⡿⣿⣿⣿⡆⢹⡇⠀⣿
⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠙⠛⠛⠀⠘⠛⠛⠁⣸⣿⣿⡇⣸⠇⢀⡏⠀⣴⡀⠠
⠻⣿⣿⣆⣀⡤⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣶⣿⣿⡟⢡⠟⢀⣾⣶⣾⣿⠇
⠀⠈⠛⠛⠋⢁⣤⣀⠀⢻⣿⣿⣿⣿⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⡴⢋⣴⣿⣿⣿⣿⡟⠀⠠
⠀⠀⠀⠀⠀⢿⣿⣿⣧⠈⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⠴⣋⣴⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠈⢿⣿⣿⠀⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⠿⠛⠁⢀⣨⣴⣾⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣿⣿⣿⠁⣼⣿⣿⡿⠟⠉⣀⣤⣶⣾⣿⣿⣿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⣿⢀⣿⣿⠃⣸⡿⠛⣡⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⣿⠏⠐⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⢀⡶⠋⠉⠙⢶⣄⠀⢀⣿⢏⣤⣾⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢸⣤⣿⣿⡆⠀⢹⡄⣼⣷⡿⠛⠁⠀⠀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠙⠛⠋⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠉⠉⢉⣉⡉⠉⠙⠛⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⣠⣴⡾⠿⠿⠿⠿⠿⣿⣷⣦⣄⠀⠈⠉⠁
⠀⠀⠀⠀⠀⣴⠃⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⣸⠏⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⡀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣿⠀⢰⡿⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡄⠀⢈⣿⣿⡄
⠀⠀⠀⢸⡇⢀⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠃
⠀⠀⠀⣾⡇⢸⡿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⢻⡇⢸⡇⠀⠀⢀⣠⣤⣤⣄⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⢸⡇⠘⣿⠀⣴⠟⠁⣠⣄⡙⣷⡀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣿⡀⢹⣿⡏⠀⠸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠘⣷⡀⢻⣧⠀⠀⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠘⢿⣦⡹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠈⠐⠄⠀⡀⠂⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡶⠁⠀⠀⠀⠀⠀⣠⠐⢂⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠈⠑⢾⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⣀⣠⣤⠧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⢑⠤⠐⠈⠉⢡⠀⠂⠤⡌⠀⡠⠐⠉⠈⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⣀⠄⠂⠘⠓⠀⠀⡀⠀⠀⠔⠁⠀⠈⡀⠀⠰⠀⠀⠐⠊⠪⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠴⠐⠂⠐⣀⠁⠀⠀⢁⠀⠀⠀⠀⠀⢀⣤⠔
⠀⠀⠀⠀⠀⠘⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠁⠀⣀⠀⠀⠀⠀⠒⠐⠀⠀⠉⠀⠀⠠⠐⡄
⠀⠀⠀⠀⠀⠀⠈⠐⠡⣲⠤⠐⠂⠉⠉⠄⠀⡀⢀⠁⡄⠀⠀⡀⠙⠁⠀⠀⠀⠆⠤⢀⡀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⠠⡀⠁⠈⠀⠑⠀⠐⠀⠰⠠⠀⢀⠄⠀⠀⠀⠀⠙⠲⢤⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠠⡀⠀⠀⠀⠀⠀⠀⢀⠔⢂⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⣀⣠⠴⠊⠁⠀⠀⠀⠍⠐⠂⠀⠂⠘⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠙⠳⡆⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠿⡀⠀⠀⠀⠀⢀⣷⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠀⠀⠐⠁⠈⡄⠀⠀⠀⠀⢠⠁⠑⠄⡀⠀⠠⠊⠀⠀⠀⠀⠂⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠂⠁⠀⠀⠀⢀⠠⠐⠀⠀⢀⠀⢀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠖⠁⢀⠀⡰⠀⣬⡞⣉⡀⢠
⠀⠀⠀⠀⠀⢩⠁⠂⠠⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠃⠄⠠⠂⣠⡵⢚⣁⡀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⢂⠐⠦⣀⠀⢀⠀⠀⠀⠀⠈⠒⢄⠀⠀⢸⡇⠀⠀⢸⢸⣠⠶⠋⢁⣀⣈⠉⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠬⠵⠾⣄⠀⠣⠈⡆⠰⡄⠳⠀⢸⡇⠀⢀⡴⢯⣑⠒⠒⠦⣤⣤⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡀⠀⠤⠙⠛⢦⣤⡀⢱⠀⠤⠠⠄⣠⠎⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠐⠂⠁⢀⡩⠷⢦⡆⢰⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠠⠄⠐⠊⠑⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠁⢸⠇⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡇⠀⠻⠃⠀⡤⠄⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠀⠀⠀⠀⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣔⣞⠻⠗⠾⠖⠀⠒⢦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢪⣼⠟⠉⣉⣀⣀⡀⣀⣤⣤⣿⠘⠿⠴⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⣦⣿⡿⣿⣿⠛⠋⠙⠹⢙⠉⢁⣱⣀⣀⡀⡈⠉⠛⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠙⠋⣁⢨⣄⣠⣠⣼⣧⣶⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣦⣦⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⣰⣶⣿⣿⠿⡙⠋⢡⡁⠙⠋⠛⠁⠀⢢⠛⡁⣽⠍⡻⣿⣷⣶⡦⠊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣯⡝⡇⠀⠠⣀⣀⠁⠄⡄⠀⠄⢀⢠⡔⣠⠇⠀⢢⠞⣿⣿⣷⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣵⣀⠀⢈⠙⡀⣶⡄⡜⣰⣧⣿⢟⣉⡡⠤⠊⠹⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣷⣷⣿⣿⣷⣿⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡸⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⢀⣀⣼⣿⣷⡝⣿⣿⣿⣿⣯⣷⣶⣶⡄⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠽⠛⠉⠙⠉⠉⠉⠟⠓⠶⠤⠈⠁


⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⣾⣿⡿⢋⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣴⣿⣿⡟⣰⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⡀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⣼⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⢿⣿⡀⠀⠀⠀⢀⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⠈⢻⣇⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⡿⠛⠉⠀⠀⠀⠀⣀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠀⠀⠀⢳⡄⠀⠀⠀⢿⣿⣧⠀⠹⠆⠀⠀⣾⣿⣿⡀⠀⣿⣿⡇⢻⣿⣾⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⣿⣿⣿⣇⠀⣿⣿⡇⠸⣿⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣇⠀⠀⢸⣿⣿⣿⡆⠀⠀⠀⣿⣿⣿⣿⡀⣿⣿⡇⠀⣿⣿⣿⠀⠀⠀⠀⣀⣤⣶⠶⠒⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⡇⢹⣿⡇⠀⣿⣿⣿⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢠⣿⡟⠀⠀⣾⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡇⣼⣿⡇⢀⣿⣿⡏⠀⢠⣿⡟
⠀⠀⠀⠀⢀⣴⣿⣿⡟⣱⣿⣿⣿⠃⠀⠀⠀⢠⣾⣿⡇⠀⣼⣿⣿⣿⣿⣿⠀⠀⣾⣿⣿⣿⣿⠀⣿⣿⠁⢸⣿⣿⠃⠀⣾⣿⠇
⠀⠀⠀⢠⣾⣿⣿⢏⣼⢟⣿⣿⠇⠀⠀⠀⣴⣿⣿⠟⢀⣾⣿⣻⣿⣿⣿⠃⠀⣰⣿⣿⣿⣿⠇⣸⣿⡏⠀⣿⣿⠇⠀⣼⣿⣿
⠀⠀⣰⣿⣿⣿⢏⣾⠏⣾⣿⡏⠀⠀⢀⣾⣿⣿⠋⣰⣿⡟⣱⣿⣿⡿⠁⢀⣴⣿⣿⣧⣿⡟⢠⣿⡿⠀⣸⣿⠋⠀⣼⣿⣿⠇
⠀⢰⣿⣿⣿⣯⣿⠏⣼⣿⡿⠀⠀⢠⣾⣿⡟⢡⣾⣿⢋⣼⣿⡿⠋⠀⣠⣾⣿⣿⣿⣾⡟⢠⣿⡿⠁⢀⡟⠁⢠⣾⣿⣿⡏
⢀⣿⣿⣿⣿⣿⡿⢸⣿⣿⡇⠀⠀⣾⣿⡟⢠⣿⡿⢡⣾⣿⠏⠀⣠⣾⣿⣿⣿⣿⣿⣟⣴⣿⡟⠁⠀⠈⢀⣴⣿⣿⣿⡟
⣸⣿⣿⣿⣿⣿⡇⣾⣿⣿⠀⠀⢸⣿⣿⢣⣿⡿⣱⣿⡿⠁⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⢀⣴⣿⣿⣿⣿⡟
⣿⣿⣿⠀⣿⣿⣇⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣱⣿⡟⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠀⣷⡀
⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⣶⣿⠿⣻⣿⣿⣿⠏⠀⣰⠀⣿⣧
⣿⣿⣿⡀⢿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⠇⠀⣸⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⣾⣿⠟⣡⣾⣿⣿⡿⠃⢀⣼⣿⠀⣿⣿⡇
⢹⣿⣿⣇⠈⢿⣿⣿⣿⣿⣿⡀⠈⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⠟⠀⣠⣾⣿⠟⣡⣾⣿⣿⣿⠏⠀⣠⣿⣿⣿⠀⣿⣿⣿
⠈⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣧⡀⢹⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⠋⠀⣴⣿⠟⣡⣾⣿⣿⣿⠟⠁⢠⣾⣿⣿⣿⡏⠀⣿⣿⣿⡇
⠀⠘⢿⣿⣿⣧⡀⠙⢿⣿⣿⣿⣷⡀⢻⣿⣿⣿⠀⢸⣿⣿⣿⣿⠇⠀⣼⣿⢋⣾⣿⣿⣿⠟⠁⢀⣴⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⡇
⠀⠀⠈⢻⣿⣿⣿⣶⣄⠙⢿⣿⣿⣿⣦⣿⣿⣿⠀⠀⣿⣿⣿⡏⠀⢰⣿⣧⣿⣿⡿⠟⠁⣀⣴⡿⢟⣵⣿⣿⣿⡟⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣦⣙⠻⣿⣿⣿⣿⣿⡄⠀⣿⣿⣿⠁⠀⣿⣿⣿⡿⠋⠀⣠⣾⠿⣫⣶⣿⣿⣿⣿⠟⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⡇⠀⢻⣿⡿⠀⢠⣿⡿⠋⢀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣴⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⠀⠸⣿⡇⠀⠸⠏⠀⣰⣾⠟⣩⡾⠟⠛⠋⠉⢁⣀⣠⣴⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡆⠀⣿⡇⠀⠀⠀⣼⠟⠁⠈⢁⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⢹⡇⠀⠀⣼⠃⠀⣠⣾⣿⣛⣭⣭⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠘⡇⠀⠀⠃⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⡇⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⣼⣿⡿⠛⠉⠁⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠘⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣷⣶⣾⢿⣿⣿⣷⣿⣿⣯⠓⠄⠈⠣⠄
⣿⣿⣿⣛⠀⠋⠍⠙⢿⣿⣿⠿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣇⣠⡝⠿⠟⠙⣿⡟⠀⠀⠀⢠⣤
⣿⣿⣿⣯⠀⠀⠘⠃⠀⠉⠛⢷⣎⠉⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠹⠹⢿⣦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠀⣰⠆⠻⠁⠀⢀⡼⠛⣻⡆
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠙⠻⠿⢿⣶⣤⣀⡠⢄⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠘⠇⢰⣾⠋⠀⠃⠀⠀⠿⠇⠈⠿⠁
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣷⣤⠀⠀⠀⠙⠿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣾⣿⡷⠀⠀⠀⣠⡀
⣿⣿⣿⣿⣿⣇⢠⣶⠟⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠋⠈⠉⠙⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠀⠀⢠⣿⣿⡃⠀⡀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣮⣻⣿⠟⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣿⣿⠉⢻⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⡷⣦⣤⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⢸⣿⣿⣷⠾⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣍⠻⣷⣌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣾⡟⠁
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢿⣷⣶⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⢸⣿⣿⣿⣿⣿⣿⣿⡟⢛⣿⣿⣧⠀⠹⣿⣿⠿⠶⠤⣤⡀⠀⠀⠀⢠⡀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀
⠀⢿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⠀⠀⠘⢟⢷⣄⠀⠀⠀⠀⠢⠀⠀⠃⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠉⠙⠛⢷⡄⠉⠀⠀⢸⡿⣿⣷⣦⣄⠈⢆⠙⠳⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠀⠈⢿⣿⣿⣷⡄⠣⡀⠀⠈⠑⠉⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡴⣠⣿⡿⠃
⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⣾⣵⣿⣯⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⣿⣿⣿⣿⣿⣿⠛⢿⡄⠀⠀⠀⠀⠀⠀⠂⠀⣠⣾⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⢻⣿⣿⡇⠈⣿⠀⠀⠀⠀⠀⠀⠇⣴⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣾⣿⣿⣟⣿⡇⣸⣿⣿⢃⣼⠋⠀⠀⠀⠀⠀⣸⣸⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⢀⣴⣄⣴⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⠷⠟⠓⠈⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⡿⢿⣿⢃⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣏⡡⠄⠀⠀⠀⠀⠀⠀⢤⣶⣶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠟⠿⠖⠀⠀⠀⠀⠒⠀⠀⠹⠃⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠦⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠙⢦⡘⢶⣦⡀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠲⣄⠀⠀⠀⢳⡀⢻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⣠⡿⠀⠀⠀⠘⡇⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⢀⡇⢈⣴⡾⢿⣿⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡀⠰⡄⠀⢀⣧⠀⠀⣸⠃⣨⠴⠶⠾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠤⠋⢀⣿⢀⣿⡟⠀⣰⢃⡠⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⢠⡀⠀⠀⠀⣠⣿⣿⣿⠃⠀⠀⢀⣿⠏⡸⠛⣠⠞⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢤⣀⠀⠀⠀⠀⢰⣌⠉⠁⣼⡇⠀⠀⣰⣿⢟⣿⠏⠀⠀⢀⠾⢋⣠⠴⢛⣡⣶⣿⣿⣿⡶⠖⠈
⠀⠀⠀⠀⣿⣷⡄⠀⠀⣼⣿⡀⠀⢸⠇⠀⣰⠟⠵⠋⠁⠠⠴⠖⠒⠊⠩⠤⠶⢛⣋⣽⣿⡿⠋
⠀⠀⠀⠀⢿⣿⣿⡆⠀⣿⣿⠁⠀⢋⣀⣤⣴⣶⣾⡿⠿⠛⠒⠶⢤⣀⠀⠀⠉⠉⠉⠉⠉
⢀⣇⠀⠀⠸⣿⡿⣷⠀⢹⢋⣠⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠳⣄⠹⣿⣶⣶⣶⣦⣄⡀⣀
⢸⣿⣷⣄⡀⢹⣧⡇⠀⣠⣿⡿⠟⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠈⠙⠛⠛⠿⠟⠋⠁
⠸⣿⣿⣿⣷⠀⡟⢠⣾⢟⣥⣶⣿⠟⠓⠶⣄⠀⠀⠀⠀⠀⠀⢠⠄⠄⠀⠀⠈⡇⠲⣄⣀⣀⣀
⠀⠙⣿⣎⢿⡇⢀⣿⡿⠛⠛⠀⠀⠀⠄⠄⠈⡀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⡇⠀⠈⠙⠻⠿⠷⠤⠄
⠀⠀⠈⢿⡜⡇⣿⠃⠀⠀⠀⠀⠀⠁⣀⣀⡰⠁⠀⠈⣿⡇⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠈⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⠶⠋
⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡞⣻⣶⣤⣴⣾⣷⣄⣤⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⣾⡏⣻⢹⡏⣿⣿⣹⢫⡟⣿⣿⢿⣧⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⡾⢻⡏⣿⢹⡘⣇⣿⣿⣸⡼⣇⣿⣿⣿⢸⣼⣿⢣⢏⡼⣫⣿⣶⣾⣇⣀⡀
⠀⠀⠀⠀⠀⠀⣧⠘⣧⠹⡌⢧⡹⣎⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠘⣦⣘⣧⣹⡮⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣯⣞⣭⣾⣿⣮⣧⣀
⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣟⡞⣡⠞⠋⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣠⡾⢫⣞⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣥⣶⣯⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣟⢿⣿⡿⣻⣟⣽⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢶⡺⣏⠻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣽⣿⣿⣿⢿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⡟⢯⠻⡌⢷⠘⣆⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⢿⣿⡿⣫⢏⡾⣹⣿⣿⢹⣿⣿⡏⣯⢷⢻⣿⡌⣇⢻⢸⣇⣿⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠞⠻⠿⣿⣴⣿⣏⣿⣼⣻⢿⡇⣿⢸⣀⣿⣧⣿⣾⡿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⠴⠛⢿⣿⣿⠟⢻⣟⣋⡿⠿⠞⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢶⣤⣄⣀⣀⣀⣀⣀⡤⣺⠜⠀⠘⢿⣦⡀⠀⠀⠀⢀⣠⡾⠃⢱⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣡⠀⠀⠉⠁⠚⠛⠓⠊⠉⠀⠀⠀⠀⠀⠉⠛⠼⠿⠯⠟⠈⠀⠀⠀⢿⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣍⡒⠠⡤⣤⣤⡶⠿⣽⠃
⠀⢦⡠⣤⣤⣤⣠⣴⣖⠜⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠀⢀⣎⡃
⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢸
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⣄
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣳⣄⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠺⣳⣦⣤
⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⠟⠉
⠀⠀⠀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⢋⠃
⢀⣴⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠄⠀⠔⠗⠠⠤⠚⠃⠤⠤⡄⠀⠀⠀⠀⠀⢀⠨⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⣟
⠋⠛⠓⠂⠊⠭⣓⠢⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠡⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡼⡄
⠀⠀⠀⠀⠀⠀⠀⢳⢱⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠡⠀⠀⢤⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢖⡽⠟⠋⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠠⠗⠀⠉⠰⠄⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡽⠁
⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠄⠀⠀⠀⠠⠸⠀⠠⠀⡄⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇
⠀⠀⠀⠀⠀⢐⣛⣧⠫⠮⣕⢦⡀⠀⠀⠀⠀⠑⠀⠅⠀⠀⠀⡥⠄⠩⠌⠄⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⡠⣴⣤⣤⣤⣀⢻⣿⡄
⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠈⢣⢳⠀⠀⠀⠀⠀⡀⠁⠀⠀⠘⠃⠀⠰⠀⢰⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⣚⡛⠋⠉⠉⠉⠛⠛⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⣀⣀⠱⣄⠀⠀⠀⠇⠀⠀⠘⢨⠀⠀⢔⡐⠀⡀⠀⠀⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢗⡮⠕⠒⠐⠋⠈⣿⢲⠒⠆⠀⠐⠖⢊⣀⣸⡿⠀⠋⠓⠛⠵⣦⣀⡯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠉⠀⠀⠀⠀⠀⠀⡷⠖⠖⠂⠈⠉⠛⠁⠀⣉⡥⠀⠀⠀⠀⠀⠈⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⢶⢶⠆⠐⠂⠿⠁⠀⢋⣢⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⣤⣤⠀⠤⠶⠒⠈⢛⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⣀⣤⣀⠠⠤⠖⠆⠘⢟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣭⣤⣄⡀⠤⠶⠶⢚⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⣶⣦⣶⠞⠃⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠢⡀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⡠⠊⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⢦⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⢠⠎⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠴⠊⠀⣀⠤⠒⠒⠒⠒⠒⠢⢤⡀⠈⠢⠔⠁
⠀⠀⠀⠀⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠈⠉⠒⠬⣉⠉⠙⠒⠢⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⡠⠒⠚⠉⢉⡩⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠔⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠓⠤⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠓⡄⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡔⠉⠒⠤⣀
⠀⠀⠀⠀⣀⡤⠖⣊⣁⠤⠤⠶⠚⠁⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠙⠲⠦⠤⢄⣉⡒⠦⣄⡀
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢦⠀⠈⠑⠒⠶⠄⠴⠖⠒⠉⠀⢠⠖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⣠⠊⠀⠀⠀⠀⢠⠤⢤⠀⠀⠀⠀⠈⢢⡀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⠞⠁⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠙⢦⡘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠜⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢀⡀⣀
⠀⠀⠀⠈⠊⠀⠀⠂⠀⠐⠀⠐⠠⠔⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠊⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠰⡁⠀⠀⠀⠃⠰⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⠲⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠆⠸⠁⠐⠀⠸⠀⠆⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⢀⡠
⠀⠀⠀⠈
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠐⠂⠀⠂⠉⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠄⠀⠀⠣⠀⠀⠜⠓⠒⠃⠀⠀⠀⠀⠑⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠤⠤⠀⠂⠁⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠠⡀⢨⠀⠀⠀⠀⢠⠆⠒

⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠄⠐⠒⠀⠀⠀⠀⠀⠀⠠⠀⠂⠉⠙⠲⠀⣄⠀⠀⠀⠀⢀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠀⠀⠀⠐⠌⠓⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠐⠀⠀⠑⠦⠀⠀⠀⠔⠩⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠠⠄⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢈⠀⠀⠑⠀⠀⠀⠀⠀⠀⢈⡖⠐⡂⠐⠄⠀⠀⠀⠀⠀⠀⢀⡀⢐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⡟⠻⠿⠇⠿⠿⠛⣿⣿⣿⣿⡿⣫⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣌⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⢋⣼⣿⣿⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⠹⡿⠁⠀⠀⠀⠀⠀⠀⠹⡿⢡⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⠿⢻⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠙⠿⣿⣿⣿⡟⠿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠻⠿⢿⡿⠟⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣧⣽⣽⣿⣿⣿⡿⣿⣾⣿⣛⣷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣾⣿⣷⣾⣿⣿⣿⣿⣿⣷⣾⣿⣹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⡿⣻⡿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢤⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⠀⢶⠉⣩⠿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠈⠙⢿⣿⣿⣿⣷⣤⣉⠛⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠇⣤⡀⠠⡐⢌⠢⠀⠀⠀⠙⠲⣄⡀⠀⠀⠙⠯⣿⣿⣿⣶⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣴⣿⣿⣆⠙⢆⠑⢄⠢⣀⠀⠀⠙⠻⣧⣶⣤⠂⣌⡙⠿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣧⡈⠳⠀⠱⣌⢷⣄⠀⠀⠈⠻⣿⣿⣿⣿⣷⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⣄⠈⢦⡈⠳⣝⠓⣄⡀⠹⡞⢋⣳⣿⢿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠻⣦⡈⠳⣝⢿⣦⡈⠛⢻⣿⣾⣿⣟⣿⣻⡯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⢿⠓⢝⢷⣝⢻⣶⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⣷⡙⢷⣝⢿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⢽⣿⣮⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⢿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿⣿⣆⠀⢸⡄⠀⢀⣴⡟⠁⣼⡏⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⣿⣿⣿⣆⠈⣷⣠⣿⠋⠀⣸⣿⠁⠀⠀⠀⢀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⡀⢿⣿⣿⣿⠀⢿⡿⠁⠀⣰⣿⡏⠀⠀⣠⣴⡿⠋⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢸⣿⣿⣷⣌⢿⣿⣿⠀⢸⡇⠀⢠⣿⣿⠁⣰⣾⡿⠋⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢿⣿⣿⣿⡎⠿⠋⠀⣼⡇⢀⣿⣿⠇⣴⣿⠟⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡟⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠓⠈⢻⣿⣿⣿⡀⠀⢠⣿⠀⣾⣿⣿⣾⡿⢃⣾⣿⠋⢀
⠀⠀⠀⠀⠀⠀⢠⣿⠇⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠈⢦⡀⠀⠀⠈⠻⣿⡇⠀⣼⠃⣼⣿⣿⣿⢟⣴⣿⡿⠁⣠⠏
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⢻⣦⠀⠀⠀⣿⡇⢰⠏⣰⣿⣿⣿⣿⣿⣿⠟⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣿⣿⡀⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢻⣷⡀⠀⣿⡇⠏⣰⣿⣿⣿⣿⣿⡿⢃⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡌⢿⣷⣠⡿⠀⣰⣿⣿⣿⣿⠟⢁⣴⠟⠁
⡆⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠙⠛⠀⠀⠀⠀⠀⣄⠀⠀⠀⣸⣿⣷⠘⣿⣿⠇⣰⣿⣿⠟⢋⣠⠾⢋⡀
⣇⠀⠀⠀⠀⠀⠘⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⣿⣿⠀⣿⡟⢠⣿⡿⢁⡴⠛⣡⣾⠏
⣿⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣄⠀⠀⠀⠀⠀⢠⣿⣧⠀⢸⣿⡟⢻⠀⣿⠃⣾⠟⠠⠋⣠⣾⣿⠟
⢹⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⠀⠀⠀⠀⠸⣿⣿⡇⣸⣿⡇⠘⢠⡟⢸⡏⠀⢀⣾⣿⡿⠋⣠⡆
⠈⣿⣷⣄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡄⠀⠀⠀⢿⣿⣿⣿⣿⠁⠀⢸⡇⡟⠀⠀⣸⠿⣫⣴⣿⡿⠁⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠈⠻⣿⣿⣶⣤⣀⠀⠀⠘⢿⣿⣿⣿⣦⠀⠀⠀⠻⣿⣿⣿⠀⠀⣿⠀⠀⠀⡴⠃⣾⣿⠿⢋⣠⡴⠖⠛⠋⠉⠉⠉⠉⠉⠙⡛⠶⣄
⠀⠀⠀⠈⠙⠻⣿⣿⣿⣦⣄⠀⠻⣿⣿⡻⣷⡀⠀⠀⠘⣿⣿⠀⠀⡿⠀⢀⡞⠁⠀⢀⣤⠞⠋⠁⣀⣀⣀⣀⣀⣀⣀⣠⣴⡾⠃⠀⢨⡙⣦
⠀⠀⠀⠀⢠⣄⠈⠻⣿⣿⣿⣷⣄⠈⠻⣿⣝⢿⣄⠀⠀⣿⣿⠀⢸⡇⠀⡼⠀⢀⡴⠋⣀⡴⠞⠛⣉⣩⣤⣿⣿⣿⣿⣿⠉⠀⠀⠀⠘⣿⡌⢳⡀
⠀⠐⣦⡀⠀⢻⣷⣦⣈⠻⣿⣿⣿⣷⣄⠙⢿⣦⡹⣆⠀⢸⣿⡀⢸⠃⢰⠁⣰⠋⣠⠞⠉⣠⣶⣿⣿⠿⠛⠉⠀⠀⠈⢿⣷⡀⠀⠀⠀⠙⡇⠀⢧
⠀⠀⠘⣿⣷⣦⣍⡻⢿⣧⡘⢿⣿⣿⣿⣷⡄⠙⢷⡈⠀⢸⣿⡇⢸⠀⡇⡼⢁⡾⢁⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⢶⡈⣿⣇⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠻⣿⣿⣿⣷⣯⡁⠀⠻⣿⣿⣿⣿⣦⡈⠻⡄⠀⣿⣇⢸⢸⡼⢡⠟⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢸⣿
⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣦⡀⠈⢿⣿⣿⣿⣷⡄⠁⠀⢻⣿⣾⣾⢃⡏⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⡿⢸⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠙⣿⣿⣿⣿⣆⠀⠸⣿⣿⡿⣸⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⣰⣿⢇⡿⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⠀⣿⣿⣷⣧⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⣡⣾⣿⠏⣼⠃⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣇⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⠲⣄⠀⣾⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⢀⢸⠆⠻⣶⠞⣱⠚⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡄⢰⠇⣀⣷⣂⣠⠼⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠛⠁
⠀⠀⠀⠀⠀⢰⠋⠉⢳⣏⠀⢀⡇⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠘⢦⣠⣼⠙⣶⠞⠁⠀⠀⠀⠀⠀⠀⡟⠘⣆⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣠⠶⠶⢤⡙⣦⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡆⠀⠀⡾⠀⠀⠀⣠⠴⠋⣸⠁
⠀⠀⠀⠘⣇⣀⣈⡽⠋⠉⠙⠦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⡀⢰⠇⠀⣠⠞⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⢻⠀⠀⠀⣇⡾⣠⠞⠁⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⢧⡀⠀⢻⡿⠁⠀⢀⣠⠞⠁⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠓⣄⠘⢦⠀⠀⠀⠀⠙⠦⣼⠷⠖⠚⠉⠀⢠⠞⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠸⡄⠈⠳⣌⢧⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠋⠀⣰⠃⠀⠀⢀⡴⠒⡆
⠀⠀⠀⠀⠀⢀⣀⠀⢸⣡⣸⠀⠀⢳⡀⠀⠘⢾⣇⠀⠀⠀⠀⡏⠀⠀⢠⠞⠁⠀⢠⠏⠀⠀⠀⢸⠷⣾⠥⢤
⠀⠀⠀⠀⠠⡏⠉⣷⣀⠙⣇⠀⠀⠀⠳⣄⠀⠈⢻⡆⠀⠀⠀⡇⠀⡴⠋⠀⠀⢠⠏⠀⠀⢀⣠⣯⠴⠷⣤⠼⠁
⠀⠀⠀⠀⠀⠉⣻⣯⣍⡽⠟⠲⠤⣄⡀⠈⠳⢤⣀⣻⡀⠀⢸⡇⡼⠁⠀⠀⣠⠏⢀⡤⠞⣉⠀⠘⣾⠏⠓⡆
⠀⠀⠀⠀⠀⠸⣇⣩⠏⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠈⣧⠀⢸⡿⠁⠀⢀⡼⢁⡴⣫⠴⠋⡟⠀⠀⠈⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠓⠲⢤⣈⠳⣄⠀⠸⡄⢸⡧⠴⠚⠁⣠⢫⠞⠁⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠈⠓⢾⣆⠀⢷⢸⡇⠀⠀⠰⣣⢏⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠛⠀⠈⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⡄
⠀⠀⠀⠀⠀⠀⠸⣅⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⠄⠀⠀⠀⠀⠀⠀⠀⠘⠤⠔⠃⠀⠀⠀⠀⠀⠀⠠⠊⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⠤⢤⣤⣀⣀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⣾⠿⠓⠀⠀⠀⠀⠀⠘⠛⠿⠄⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠈⡡⠂⠀⠀⠢⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⡠⠚⠉⢳
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠈⡎⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡔⠁⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢐⣷⠀⠀⢰⠠⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣠⠾⣀⡠⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠛⠀⠀⡸⡀⠁⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠸⡇⠀⣀⠱⡠⠖⠙
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢀⠄⠀⠀⠘⠦⢀⣀⣀⠔⠁⠈⠐⠀⠂⠁⠀⠀⠀⡐⠀⠀⠀⠀⢠⡟⠀⠀⠀⢹⣂⠀⣀⣱⠖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣴⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⡈⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠁⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠠⠀⠀⠀⠈⡛⠀⠀⢐⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣏⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢣⠦⠤⠤⠦⠤⠤⠼⢤⠄⠂⠀⠀⠀⠀⠀⠀⢀⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠳⡀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢷⡀⠀⠈⠲⣄⣠⠂⠉⣃⡀⠷⠐⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⣻⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠾⣄
⠀⠀⠀⢀⠤⠐⠚⠹⡏⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⣀⣤
⣠⠖⠚⠁⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⣀⣀⠆
⠓⣲⠃⠀⠀⢠⠔⠢⣀⠉⡷⠀⠀⠀⠀⠀⡷⠒⠖⠒⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠉⠉⠉⡆
⠀⢧⡠⢦⠀⡸⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠣⠤⣤⠤⠤⠤⠤⠤⠒⠒⠒⠒⠒⠒⢒⡶⠋⠉
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⢀⣀⡤⠖⠋

⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⣶⣶⣄⠀⠀⠀⠁⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶
⠛⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻
⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣶⡀
⠁⠀⠀⠀⣀⡀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⣀⡀⠀⠀⠀⢿⣿⣿⡿⠃⠀⠀⠀⣀⡀⠀⠀⠀⢻⣿⣿⣿⠇
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠹⢿⡀⠀⠀⠀⠈⠉
⣀⣀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠝⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⢀⣀
⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿
⠀⠙⠋⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣄⣀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⣀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡳⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢞⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠉⠛⢶⣤⠀⠀⠀⠀⣀⣠⣤⣴⣶⡶⢶⣶⣦⣤⣄⣀⠀⠀⠀⠀⣤⡶⠛⠉⠁⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⡴⠛⠁⢀⣤⡶⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢶⣤⡀⠈⠛⢦⡀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠟⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠻⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⣀⣠⣤⣶⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⣶⣤⣀⡀
⣀⣤⡴⠶⠛⠋⠁⢠⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⡄⠈⠙⠛⠶⢦⣤
⠉⠙⠳⠶⣤⣄⣀⠘⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠃⢀⣠⣤⠶⠞⠛
⠀⠀⠀⠀⠀⠈⠉⠛⠻⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣦⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⣴⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠈⠳⣤⡀⠈⠙⠿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⠛⠁⢀⣤⠞⠁⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⢀⣀⣤⠾⠛⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠛⠷⣤⣄⡀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡵⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢮⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠉⠉⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟