Fall leaf Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠒⠛⠋⠉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣇⠀⠀⠀⠄⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢶⠒⠋⠉⠡⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⣀⣬⡷⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹⣇⢀⣠⡤⠶⠚⠋⠉⠁
⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⡠⠋⠁⠉⠀⠀⠀⠴⠀⠄⣀⠀⠀⠛⠛⠳⠶⢦⣄
⠀⠶⢾⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠉⠙⠓⠒⢚⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠄⠀⡀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣓⣲⡶⠖⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠢⡄⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡰⠋⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣿⠛⠲⡿
⠀⠀⠀⣠⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠑⠢⠀⠀⠀⠀⣸
⠀⠀⠀⠀⣩⠽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⡜⠁⠀⠀⠀⢀⠀⢀⡄⠀⠀⠀⠀⠀⠘⠀⠀⢀⣾⠁⠀⡀⠀⠀⠀⠀⠀⢰⠏⠓⢦⠇
⠀⠀⡜⠀⠀⠀⠈⠀⠀⠀⠀⠇⠀⠀⢀⣄⠀⠀⢀⣴⠏⣿⣠⠞⣇⠀⢀⠀⠀⠀⡞
⠀⠚⠤⣤⠀⠀⠀⠀⠀⠀⠀⠇⠀⢠⡞⠘⣆⡴⠋⠁⠀⠉⠀⠀⣿⠀⠁⠀⢀⠞⠁
⠀⠀⣰⠁⠀⢀⠐⠁⠀⠀⠀⠀⣠⠟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⢀⡴⠋
⠀⢠⠃⠀⠀⠀⠀⢀⡴⣆⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠏
⣶⣷⣶⣶⣶⣶⣞⣥⣤⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠾⣆⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢄⢀⠇⠀⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⢠⠤⠊⠀⠈⠾⡄⡰⠂⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠦⣀⡀⠀⢸⡡⠃⠀⠀⠉⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠙⠲⣼⢷⠥⠜⠞⠷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠉⠎⡨⢀⠄⠂⢼⠑⢉⣉⠚⢪⢟⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢤⣤⣄⣀⡤⡖⠄⣀⡤⠖⡀⠀⠀⠀⠀⠀⠀⠈⣯⠂⠐⠀⠀⠀⣻⢸⢆⡸⡳⢃⢎⡞⠀⠀⠀⠀⢰⡦⣀⣀⠘⠢⢤⣄⠀⣀⣤⠖⠂
⠀⠀⠀⠀⠐⠖⢦⣕⡢⠀⠀⠀⠰⠈⠢⠤⢤⠀⢀⢄⠀⡴⠈⢀⠴⠃⠀⡹⢸⡠⠃⠀⣋⣾⠀⠀⣀⢀⠴⡏⢱⠈⢀⡊⠀⠴⠒⠈⡠
⠀⠀⠀⠀⠀⢘⣷⣞⣱⠳⢄⡀⠀⠧⠀⠀⠸⣫⡍⡦⠕⠋⠐⡸⣀⠀⠀⣷⠊⣠⠚⣰⢛⠼⣤⠞⢠⠀⢠⠅⡰⠠⠊⠁⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠈⠉⠀⠀⣂⡄⢀⠈⢻⠀⠱⡔⡄⣾⢶⡟⣟⠔⣡⡎⠈⠉⠉⢺⡆⣟⣠⣌⠔⠛⠄⠁⠉⠘⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⣟⡳⠀⢄⠀⡄⠤⠰⠃⠙⠲⢀⣈⣇⠈⠏⢰⠡⡜⠀⣿⡠⠏⢰⠂⠈⠀⢸⡗⠋⢸⣥⡔⠉⠁⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠂⠠⢄⡀⠀⠀⡀⠂⠀⠐⠰⢊⣩⣝⠷⣆⠘⢄⠹⡀⢿⡄⠀⠀⠀⣀⠶⢟⠠⠀⠈⠪⠄⠀⡬⣼⡧⣄⣀⠈⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⢦⠀⢇⢀⠞⠉⢶⢧⠤⢬⢱⣄⡑⠙⠾⠀⠀⢠⠶⠚⠊⠐⣿⡄⣷⠐⣖⣮⣵⢋⣰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣃⢞⠨⡐⠐⣽⣖⣋⣠⣉⣙⣷⣉⣇⡶⢛⡂⢀⡀⠘⠈⢶⣍⠈⠈⠈⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⣰⣬⡏⡖⠋⠇⠉⠺⠉⡞⠜⢱⠞⣻⠟⠙⠳⣄⠐⠋⠁⠰⠽⡆⠙⢶⣲⣾⣊⣓⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣥⠖⠋⢑⠎⠐⡇⠘⣐⠀⠀⡀⡐⠞⣤⡿⠃⠀⠀⠀⠈⠳⣤⠴⢃⣠⢤⡌⣼⣈⣓⡾⠭⠑⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋⠉⠉⠡⠤⠶⠦⣈⡐⢛⣐⣈⢾⣣⠙⠉⠀⠀⢠⡆⠀⠀⠀⠈⣇⢡⠶⠓⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⢻⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠘⡌⠳⣄⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠼⠀⠀⠘⡄⠀⠀⠧⢤⠀⠀⠀⠀⠀⠀⣠⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡐⢤⡀⠀⠱⡀⡇⠀⠸⡀⠀⣠⠋⠒⠊⡸⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣗⠀⠈⠲⣄⢳⡇⠀⠀⠳⠖⠁⠀⠀⢰⠃⠘⠧⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠈⠙⢧⠀⠀⠀⠀⠀⢰⣧⠇⠀⠀⢰⡋
⠀⠀⠀⠀⠀⢰⣶⠒⠒⠒⠚⠉⠉⠛⠙⠒⠚⠀⠀⠀⠀⠈⡆⠀⣰⠁⠀⢰⠏⣀⠄⠀⡠⠛
⠀⠀⠀⠀⠀⠀⢧⠉⠢⢄⡀⠀⠀⠀⠐⡄⠀⠀⠀⠀⢦⠀⢸⡴⠃⠀⣠⠗⠋⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠑⠲⠤⢄⣈⣦⡀⠀⠀⠀⠱⣄⣧⠀⢰⠃⠀⠀⠀⠈⠒⠒⠊⠉⣇⡀
⠀⠀⠀⠀⠀⠀⠰⢧⣀⣀⠀⠀⠀⠀⢀⣨⠝⠛⠲⠤⣄⣀⠈⠹⣤⠃⠀⣀⣤⣴⣎⠤⠤⠒⠒⢒⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠈⢉⣶⣷⣶⣉⠉⠀⠀⢀⡤⠤⠤⠤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠒⠒⠒⠤⡀⠀⠀⠐⢒⡶⢋⡏⡸⣗⢌⠙⠢⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⢀⡴⠋⠀⡸⠀⡇⢻⠀⠳⠎⠐⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⠀⢀⡤⠊⡠⢦⡄⠃⡤⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠐⠋⠀⡔⠁⠀⠸⠜⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡟⢄⣠⡄⠀⠀⠀⠀⣄⠀⢀⣠⡶⠔⠂⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠁⠀⠀⣇⣴⡇⠀⢰⣿⠋⠉⠘⠁⠀⠀⠘⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⢇⠀⢀⠀⠀⠀⠈⡇⢰⠏⡇⠀⠀⡇⠀⠀⠀⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢜⠀⠀⠀⠀⢱⡏⠀⠃⠀⠀⠁⠈⠀⢀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠘⠀⠀⠀⠀⠘⠁⠀⣸⠂⠀⠀⠀⠠⢶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠖⠶⠞⠀⠀⠀⠈⡇⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⣀⠔⢋⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⢄⠀⠀⠀⠐⢦⣀⠀⣰⢁⡔⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠹⣋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⠢⣄⡀⡀⠙⣄⡷⠋⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠚⠋⣻⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣈⣉⣙⣷⣿⣷⠶⠶⠒⠐⢦⡀⠀⠚⠒⠄⠀⠀⠀⠀⢈⠍⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢹⡎⠢⣄⡀⠀⠀⠉⠓⠒⠂⠀⠀⡠⠀⠤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⢿⡀⠀⠉⢢⣀⠀⢸⡉⠉⠒⠒⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠙⠲⢦⣪⢿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣲⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡰⢻⠇⠀⠀⠀⠀⠀⠀⢠⡞⠶⠤⠶⠋⢰⠃
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠏⠳⠞⢉⠂⢧⡀⠀⠀⢠⠟⠷⠖⠋⠀⠆⠀⡠⢀⡏
⠀⠀⠀⠀⠀⢸⠳⣄⠀⠀⠀⠀⠀⠀⠀⡜⢙⠃⢠⠀⠀⢸⠀⠰⣇⣀⡴⠋⠀⢀⠎⠀⡰⢀⡴⠁⠈⡷
⠀⠀⠀⠀⠀⢸⠀⠈⠓⢦⡀⠀⠀⢀⠎⠀⢸⠀⢸⠀⢀⣆⡠⠂⠈⡁⠀⠀⢠⠁⠀⣀⠷⠯⠄⠀⣸⠁
⠀⠀⠀⠀⢠⡼⠀⢰⠀⠀⠉⠲⡄⣸⠀⡄⢸⠀⠀⢆⡞⠉⠀⢠⢠⡇⠀⢠⡃⠴⠊⠉⠁⠀⠀⠀⢧⡀
⠀⠀⠀⠀⢸⡆⠀⠀⣇⠀⠀⢠⠉⠁⠀⠃⠸⡀⢠⠎⠀⢀⠔⠁⢸⣠⣔⣋⡠⠤⠤⠖⠀⠀⢠⡔⠋⠁
⠀⠀⠀⢀⡼⠃⠐⠤⣘⡄⠀⢰⠂⠀⠈⡄⠀⢱⠯⠖⠒⠁⡆⢀⣞⣁⣀⠤⠄⠀⠀⠀⠀⣴⣋⣀
⠀⠀⠀⠀⣷⠠⡄⠀⠀⠘⢆⡎⠀⡀⠀⣇⢀⣟⡤⠒⠋⢸⣠⣊⡀⠀⠀⠀⠀⠀⡠⠀⡼⠉⠉⠉⠉⣷
⠀⠀⠀⢀⡿⠀⠈⠢⠄⣀⣀⣣⣀⠇⠀⠈⡾⠀⠀⣀⠴⠛⠁⠈⠀⢀⠊⠁⢀⡜⠁⠀⠀⣠⠴⠊⠀⠈⠓⠶⠶⣤⡀
⠀⠘⢯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣸⠁⡠⠊⠁⠀⠀⠀⠀⣰⣁⣀⡤⠞⠒⠚⠻⣉⡉⠉⠛⠒⠒⠛⠀⣀⣤⠿
⠀⠀⠀⠈⠓⠦⠤⢤⣬⠉⣁⣀⣀⡤⣤⣯⣾⠴⠒⠒⠚⠓⠛⠻⣍⠁⠈⠑⠦⢤⣀⠀⠈⠉⠉⠒⠦⢀⡤⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠌⠳⣄⠀⠀⠀⠀⠀⠈⠓⠶⣤⣄⡀⠈⠙⠓⠒⣂⣤⣤⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⢹⠃⡌⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢿⠀⠙⠲⠶⠶⠾⠇
⠀⠀⠀⠀⢀⡤⣖⡿⠟⠋⠉⠀⠀⠀⠘⡆⠇⠀⠀⢸⠳⡚⠉⠉⠀⠀⠀⠈⠳⢦⡀
⠀⠀⣠⢖⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠠⠀⠀⢠⠀⢸⠢⣤⠔⠒⠀⠀⠀⢺⡁
⠀⣴⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢀⡈⠀⠈⠆⠈⠑⠒⠤⢤⡀⠀⠳⣄⡀
⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡼⠛⠦⠤⣤⣤⡤⠖⠶⠶⠶⠖⠖⠚⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢻⣶⣤⠀⠀⢦⣼⣿⣿⣤⠆⠀⣠⣴⡿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣿⣷⣷⣘⣿⣿⣿⡏⣼⣶⣿⠿⠁⠀⠀⠀⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣿⣿⣿⣿⠿⠛⠂⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⡿⠗⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠇⠿⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠀⠀⠀⠉⠈⠙⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣷⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣹⣿⣿⣿⡿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡍⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⢰⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠈⠀⠀⠀⠀⠀⢀⠄⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠘
⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⢄⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠊⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠄⠀⡠⠊⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢸⣀⠄⠀⠀⠀⠀⢀⠌⠁⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠬⢦⡀⠀⠀⢸⠀⠀⠀⠀⡰⠥⠤⠀⠀⠀⠀⠀⠀⠁⠀⢀⠠⠖
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢸⠀⠀⢀⠞⠀⠀⠀⡀⣀⠀⠀⠀⠀⡠⠂⠁
⠀⢤⣤⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠤⣀⣀⣀⡈⠣⣸⡇⣴⣋⡤⠖⠒⠉⠁⠈⠀⠠⠤⠤
⠀⠀⠀⠀⠀⠁⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⢻⡟⡉⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠐⠀⠀⠀⠀⠄⠂⠀⠈⡇⠀⠀⠐⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⠐⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠉⠀⠀⠈⢛
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠠⡂⠀⠌⠀⠓⢶⠂
⠀⠀⠀⠀⠀⠀⠀⢧⠉⠙⠒⠚⠳⣄⠀⠀⡞⠀⠀⠀⠀⠀⠄⠀⠀⡇⠀⢀⢠⣀⠤⠤⣤⠴⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⠐⠀⠀⠈⠓⠦⠇⠀⠀⢀⠀⠀⠀⠀⠈⢧⡴⠋⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⢠⡀⠁⠐⠂⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⡀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠠⠄⠀⠠⠀⠀⠀⢄⠈⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⡳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢠⠀⠀⠀⠀⠄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⣀⣀⠤⠞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⢇⡀
⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠔⠈⠂⠀⠆⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠉⠑⣲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⢌⡁⠀⠂⠀⠈⢀⣀⡀⣀⠀⠈⠀⠀⠠⠐⠀⡁⢀⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⣀⡴⠴⠚⠉⠀⣿⠀⠑⠢⠤⣤⣸⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣟⣿⣿⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣦⢀⠀⠀⠀⠀⠀⠀⠀⣀⣭⢤⣄⣀⠀⠈⢇⠐
⠀⠀⠀⠀⠀⠀⣾⣿⣿⢀⠄⠠⡀⠀⠀⣴⠻⣿⣿⢿⢾⣽⣳⣲⢄⣖⡀
⠀⠀⠀⠀⠀⢷⣿⠙⢸⠁⠀⠀⠀⠀⡜⠾⢩⢿⠷⠦⢴⡯⣛⠿⣿⡿⠛⢷⣿⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢠⣷⡴⢩⣵⠛⡷⢾⢦⡏⣹⣏⢫⣶⣾⣿⣿⣷⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠈⠲⠧⠀⠀⠀⠀⠘⡟⠞⠋⢠⠒⡇⢺⠉⢠⣶⡼⢹⣟⣿⣿⣷⡿⣿⢿⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⠁⡞⠐⡇⣯⠀⢶⢀⣜⢻⡦⣽⣟⣿⣿⡿⣾⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠬⢀⡿⡗⠀⣤⠈⠁⡻⠿⢷⣬⠛⣿⣿⣿⣿⣇⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡂⢸⡇⢰⠄⢍⠁⢨⣉⣟⢠⡜⠓⢻⢻⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣼⣂⣸⣁⣼⣿⣮⣤⣹⡗⢿⠈⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣋⢪⡿⣿⣏⠉⠃⢸⡇⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠁⢢⠀⠀⠀⠀⠀⠺⣿⠋⠙⢻⣿⣿⣾⣾⣷⣤⣼⣧⣼⢿⡿⣿⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⡰⠃⠈⢢⣀⣘⣀⡀⣤⡀⠀⠀⣿⡀⠀⠀⢹⣿⢿⣿⣿⣿⣿⣿⣿⣆⢷⡹⣧⡘⣿⡀
⠀⠀⠀⠀⠀⠀⡠⠋⠡⠄⠀⠀⠛⢉⣿⡗⠈⠁⠈⠉⠉⠁⠀⠀⠀⡟⠈⠻⣿⣿⣿⣿⣿⣾⣎⢳⣜⢿⣿⣇
⠀⠀⠀⠀⡔⠉⠀⠀⠀⡀⠂⣀⡴⠛⠛⠃⠀⠀⠀⠀⠀⠐⠀⠠⣸⠃⠀⣼⣿⠻⣝⣿⣿⣿⣿⣷⣿⣿⣿⣿
⠀⠀⠀⠀⠡⠄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠠⢤⣄⣀⠀⣀⠘⢦⣴⠁⠀⠀⣘⣇⠀⠀⠈⣿⠋⠻⣿⢿⣿⣿⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⣠⣶⣶⣾⣾⣿⣿⣿⣤⣾⣿⣿⡇⡀⡤⢿⣤⣶⣤⣿⡀⠀⠘⢷⡈⠘⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣙⡛⠉⠙⠛⡛⢛⠿⢿⣿⣿⣷⣷⣧⢸⣿⣿⣿⣿⡇⠀⠀⠈⢹⡆⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠏⠳⠦⠤⠀⠀⠴⣿⣿⣿⣿⣿⠘⢿⣿⢁⣿⠁⠀⠀⠀⠀⠗⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⠀⢘⣿⢀⡿⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠀⠌⠈⠚⠁

⠀⠀⢀⠀⣀⡀⣀⡄⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠁⠈⠛⠡⠯⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢆⡀⠀⠀⠀⢀⠤
⠀⠤⠠⠈⠈⠲⠇⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢈⠁⠀⠀⢀⡤⠒⢉⠖⠰⠄
⠄⣁⠀⠩⠅⣀⡄⠣⠑⡀⠀⢀⢁⠀⠀⠐⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⣴⡤⠤⣤⠀⣄⠀⣀⠀⣀⡰⢋⠀⣴⠁⠀⠰⠁⡀⠠⠘
⠐⣤⢠⠄⣰⠞⣷⣄⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠃⠹⠿⠟⠿⠶⠒⠀⠀⠃⠓⠉⠐⠠
⠀⠁⠀⠀⠠⠞⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⡐⠢⠀⠀⠀⠀⠀⢠⡀⢀⠀⠰
⠀⡀⠘⠀⡥⠘⠆⠀⠀⠀⠀⠀⠀⠒⠑⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠁⠸⠁⣤⠀⠀⠂⠀⠀⡁⠀⠂
⡎⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠡⠀⠠⠃⠀⡼⠀⠀⠀⢀⠆
⠀⠀⠀⢠⠙⢄⡈⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⢴⣏⡅⠠⠀⣀
⠚⠉⠁⠘⠂⠈⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⡾⠺⡾⠉
⠀⠀⠀⠀⠀⠀⠘⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠃⠀⠁⠀⢀⠐⠊⠠
⠀⠀⠀⠀⡀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠳⡄⠀⠈⣀⠀⠀⢶
⠀⡠⠂⠀⠈⡰⣾⠫⠀⠀⠀⠬⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣄⠀⠉⠂⠠⣄
⠒⠁⠀⠒⢁⠔⢉⡗⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⡀⠀⠀⠀⠀⠀⠈⠙
⠀⠠⠴⠛⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡦⠀⠂
⠆⠁⠀⢰⠋⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⣀⡠⠔
⠐⠀⠀⢸⠖⡆⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠈
⠀⠀⠀⠞⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡤⢀⡕⠛⠃⠀⠀⠉⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠉⠈⠁⠈
⢠⣾⠾⡏⠉⢀⠀⠀⠈⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣿⡀
⢠⡿⠈⠋⠉⠀⠀⠀⠃⠄⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⢤⡆
⠏⠐⠒⠂⠀⠀⠀⠀⠀⠃⠉⠠⠀⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠶⡶⡴⣥⠓⢠⡄⠀⠙⢲⠄
⠀⢄⠀⠠⢀⣀⡘⣶⠛⠓⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤
⠀⠀⠠⠂⡼⠉⠀⠇⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⡀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡄⠀⠀⠀⡄⢀⡀⠀⠀⠀⠈⠉⢀⠀⡀⠀⠀⠈⠠⢤
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠠⠄⢀⠀⠚⠁⣀⠀⠀⠀⠒⠀⠤⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⠀⠀⡤⠀⠀⠘⡂⢤⣀⣄⠀⠚⠀⠀⠐⣀⢀⠀⠈
⠚⠳⡶⠀⠀⠀⠐⠄⢀⠀⠀⠀⠀⠀⠤⡎⠒⠁⠀⠀⠀⠉⠑⢯⣄⣀⡀⣀⡀⡠⠀⠞⣁⠀⠀⠀⠀⠀⠣⠔⠀⠀⠀⡐⠁⡀⠈⡬⢿⢦⣄⡀⠘⠋⠀⠣⡀
⠀⠘⠓⢤⣀⠀⠀⠄⠀⠃⠀⠀⠛⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⣻⡅⠛⢇⠉⠀⠤⡼⣤⠄⠀⠀⠀⠀⠀⠰⠀⠀⣥⡄⠃⠀⡖⠺⢶⡒⠚⠙⠛⠃⠒⠥
⠀⠀⠀⠁⠐⠀⢘⡞⠀⠀⠀⠀⢴⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⠮⠁⠀⢀⠜⠙⢷⠤⢀⡐⢰⠃⠀⠀⠀⡀⠀⠁⠚⠩⠇⠀⠁⠨⠀⣤⠁⡄⠀⠀⠀⠀⠈
⠤⠀⠀⠀⠀⠄⠁⢦⠔⢀⣀⠀⠈⢤⣑⠀⠀⠀⠀⠀⠀⠀⣠⠏⢃⡀⠀⢠⠐⠁⠀⠀⠀⢉⠙⠀⠀⠀⠀⠀⢄⠰⠆⠐⠀⠀⠀⠀⠀⠀⠀⠉⠃⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⢾⣽⣿⣿⣿⣿⣯⡗⠀⠀⠀⠀⢀⣤⠴⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠇⣀⠁⣀⣀
⠀⠀⢿⣿⡿⠁⠎⢻⣿⡿⠀⠀⠀⠀⣾⣿⣷⠰⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠉⠘⠃⠨⠄⠉⠁
⠀⠀⢫⢿⣿⠀⠀⢸⣿⣍⠁⠀⠀⢸⣏⠉⠀⠁⠈⠉⣽⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠘⣿⣤⣤⣼⡇⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⡖⣴⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⡄
⠀⠀⠀⠀⣀⣈⣉⣩⡅⠀⠀⠠⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⣿⣶⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠄⠀⠀⠀⡀⢀⡀⢀⡀⣀⢀⢀⠀⢀⢀⢀⠀⣀⢀⠀⢀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣀
⠀⠀⠀⠀⠀⣔⣆⠆⠀⠀⢶⣌⠉⠀⠀⠀⣱⢸⠀⠺⡇⣿⢾⢸⠇⢿⢸⢹⠀⢿⠈⡇⢸⠀⢻⡇⡟⡇⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠘⢹⠛⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣤⠄
⠀⠀⠀⣀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢀⣾⣶⣶⣿⡎
⠀⠀⠀⠙⠁⠙⠛⠈⠋⠀⠀⢠⣤⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢶⣦⠿⠚⠿⣧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠱⠶⣿⡇
⠀⠀⠀⢠⣤⡀⢀⣀⡄⠀⠀⠈⣿⡆⠀⠀⠀⣸⡟⠀⠀⠀⣷⣶⠇⠀⠐⠀⠘⣷⣶⠀⠀⠀⠀⠀⢿⣿⡤⡀⠀⠁⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⢐⣂⣀⣉⣭⡅⠀⠀⠀⠘⠇⠀⠀⠀⠿⠁⠀⠀⠀⣶⣾⡀⠀⠀⠀⢀⣿⣶⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⢿⠀⠀⣿⠇
⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⢰⣿⢲⣶⣾⢿⡧⠉⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠈⣷⣶⡇
⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⣉⡛⠈⠀⠀⠀⠀⣴⣶⡖⠀⣨⣭⣅⠀⠐⣶⣶⠆⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠀⢠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠛⢿⣄⠄⠀⢤⡤⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⡶⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠸⣽⣷⣦⣀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢂⣶⣿⣷⣾⣿⣷⣦⠠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠁⢀⢤⣽⣿⣿⣷⡄⠀⠀⠀⡇⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⡟⠻⣷⣒⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⡿⣏⠋⢹⡇⠀⠀⠀⡇⠀⢸⠀⠀⢸⠋⣿⣪⡟⢸⡇⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⠀⣃⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠉⠁⠉⠉⠐⠟⠉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡃⠀⢘⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣚⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣴⣆⣴⣤⣄⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠄⢀⡀⠴⠂⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⣿⢿⡏⢛⡻⣿⣗⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⣠⣯⣥⣬⠆⠀⠀⠀⠀⡇
⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣿⣿⣍⣃⡈⢠⣿⣿⣦⠄⠀⡇⠀⢸⠀⠀⢀⣀⢂⣩⣟⣻⣝⡁⠁⠀⠀⠀⡇
⠀⢀⣻⠁⠀⠛⢿⡇⠀⠀⠀⠀⢸⡇⠀⠀⢹⣿⣿⣶⣾⣿⣿⡟⠀⠀⠀⡇⠀⢸⠀⠀⠀⠈⠁⢿⢹⡯⡟⠐⠓⠁⠀⠀⡇
⣾⡿⠋⠤⠠⠀⢤⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⢿⢺⡿⠿⠋⠁⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢀⣷⣶⠄⠀⠀⠀⠀⠀⡇
⠉⠃⠈⣶⣿⣤⡷⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⡇
⣧⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⣶⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠇

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠂⢄⠀⠘⠒⠶⠀⠸⠇⠀⠀⠀⠈⠁⠀⢸⡀⠀⠐⢀⡀⠀⠙⠃⣤⡄⠁⠌⠁⠠⠀⠀⠀⠙⠂⠀⠒⠊⠀⠈⠠⠀⢀⠐⠂⣀⡀⠀⠉
⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠰⠆⠀⠀⠄⢀⣀⠀⠉⠁⠉⠀⣀⡄⠘⠦⡷⢛⣀⠀⠀⠀⠙⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠋⠁⠀⠀⠠
⠀⠀⠀⠀⠀⣶⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠯⠀⠘⠗⠀⠺⠿⠀⠀⠀⠀⠀⠀⣠⠈⠈⠀⠀⠛⠀⡐⠀⠀⠀⢀⡀⠀⠠⣄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠬⡙⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⢐⠣⠀⡆⠀⣀⡰⢶⣶⡀⠀⠀⠑⠀⢀⠠⠀⠦⡀⠀⣠⡦⠀⠀⠀⠀⠀⠀⣠⠄⠀⡉
⠀⠀⠀⠀⠉⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢛⣁⠼⠏⠀⠀⠤⠄⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⠄⠀⠈⠉⠀⠈⠉⠁⢀⣂⠒⣤⠀⠀⠀⠠⠀⠀⠀⠤⠾⠀⠸⠀⠀⠀⠀⣀⠀⠐⠂⠴⠆⠀⠠
⠀⠀⠀⠂⠒⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠀⠀⡺⣿⡿⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠒⠀⠈⠀⠀⠠⠆⠀⠀⠀⠀⠀⠦⠀⠀⠛⣾⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠂
⠀⠀⠀⢀⠄⡀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠈⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣀⠀⠀⡆
⠀⠀⠀⠀⣀⡀⠀⠀⠤⠤⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⣠⣿⣿⡿⢿⠿⠿⠿⢿⢿⣿⣧⡀⠀⠀⠀⢰⡲⡀
⠀⠀⠀⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠙⠋
⠀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠉⠀⠀⠀⠀⢠⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠠⠀⠂⠻⠀⣀⠈⠀⠀⢀
⠀⠀⠀⠀⠤⠀⢁⡀⠀⠀⠀⠀⠀⠀⠰⠀⣤⣴⡇⠀⠀⠀⠻⣿⣤⣬⣧⣬⣥⣤⣧⣤⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂⣠⡈⡀
⠀⠀⠀⠘⡀⠀⠀⠠⣷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠆⠀⠘⠓⠓⠀⠀⠀⠀⠁⣈⡁
⠀⠀⠀⠀⠴⡀⠀⠀⢘⣻⣿⠩⣬⠀⠀⠉⠀⠀⠀⠉⣸⠏⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠰⠆⠀⠛⠈⠶⠆⢐⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡇⠀⠠⠠⠀⠀⠀⠰⠒⠚⠀⠐⠁⠀⠛⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠈⠀⠄⢠⡄⠀⠀⠶⠐⠀⡴⡆⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠠⠤⠴⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠆⠀⢸⠀⢨⡀⠛⠀⠀⢰⠛⣆
⠀⠀⠀⡀⠀⠀⠀⡀⠄⠀⠀⠀⠔⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠐⠀⠘⠐⠂⠀⠀⠑⠉⠀⠀⠉⠉⠂⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠂⠀⠀⠲⢷⣤⣶⠟⠀⣀⢀⠀⠈⠠⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢠⡀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⣀⠈⠉⠀⠈⠀⠸⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠄⠀⠀⢤⢰⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⠀⠀⡀⡀⠀⠈⠁
⠀⠀⠀⠠⠀⠐⠂⠀⠀⠀⠀⠈⠈⠉⠀⣠⠈⠉⠀⢤⣰⠔⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡠⠀⠀⠀⠀⠉⠁⠀⠉⠈⣀⠈⠉⠁⠀⠈
⠀⠀⠀⠀⠀⢀⣀⣀⠆⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠥⠠⠀⠀⠀⠄⢈⠀⠀⠀⠐⠀⠀⢀⠌⡉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠢⠀⠁⠉⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠄⠲⣄⠀⣨⠀⠀⡠⠀⠀⠀⠈⠂⠁⠂⠀⠀⠀⠀⠁⠀⢀⠀⠀⠠⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠀⠐⠀⠀⠈⠃⠃⠀⠴⠆⠀⠶⠀⠀⠀⠂⠉⠀⠰⠆⠈⠛⠀⠀⠀⠘⠐

⡿⠿⠀⠀⠀⠀⢉⡛⣿⣿⣿⣿⣿⡿⠋⠀⠀⣩⣭⢹⣷⡄⠉⠀⠀⠸⣿⣿⣿⡿⣽⣿⣁⣀⠀⠀⠀⠀⢶⣿⣿⣿⣿
⠁⠀⠀⠀⠠⣶⣿⣿⣿⣿⣿⡏⢉⠁⠀⠀⠀⢿⡏⠀⠙⠓⠀⠀⠀⠀⣤⣶⣾⣿⢿⡏⣿⣟⠃⠀⠀⠀⣾⣿⣿⣿⣿
⢀⣤⢀⣴⠀⠈⠙⠉⣹⠿⠋⠁⢀⠀⠀⠀⠀⠈⢀⠀⢀⣤⣶⡇⠀⠀⠻⢿⠟⣱⣿⣿⠻⣿⠇⠀⠀⠀⠛⠛⠻⠟⢠
⣸⣿⣼⣿⣶⡾⠂⠀⠀⠀⠀⠀⢹⣿⣷⣦⠀⠠⣾⣷⣾⣿⣿⣷⣶⣴⣦⡄⠀⠻⠿⠟⠀⠀⣠⣤⡄⠀⠀⠀⢶⡄⣿
⠸⣧⣙⢿⣶⡄⠀⢠⣶⣶⣦⠄⠘⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⢠⣄⣀⠀⠀⠀⠿⠿⠁⠀⠰⣤⡘⣿⠸
⣷⣝⠻⢧⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⡠⠘⣿⣿⣿⣿⣿⣿⣤⡀⠀⢾⣿⣿⣷⡄⠀⠀⠀⠀⠙⠷⣝⢷⡘⣷
⠈⠙⠀⠀⣠⣶⠀⠀⠀⣾⣿⣶⢠⣶⣶⡄⠈⠀⠠⠟⢿⣿⣿⠿⡿⠛⠁⠀⠸⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠿⠈⢿⠘
⠀⢀⡀⠈⠛⠁⢠⣶⣦⡹⣿⣿⢹⣿⣟⣁⠀⠀⠀⠀⠘⠻⠏⠀⠀⠀⢠⣤⣀⠀⢀⠠⣄⠀⣾⡇⣴⣟⡀⠀⣤⣄⡀
⣿⣿⣷⡄⠀⠀⠘⠿⢿⡿⣮⣿⣾⣽⣿⡿⠃⠀⠀⣀⡄⢀⡄⠀⣀⠀⠈⠙⠋⠀⠘⠿⠟⡀⣨⣤⣌⠉⠁⢀⣿⣿⣿
⣿⣿⣿⡶⠃⠀⠀⢴⣿⡿⢿⡿⠙⠿⠷⠀⠀⠀⣰⠟⣴⡿⣡⣾⣿⣴⡖⢀⣀⠀⠀⢠⠋⠀⠙⠻⠄⢠⣴⣤⣙⣿⣿
⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⡀⠀⠀⢸⢇⣾⢅⣼⠛⣹⠿⣻⣾⣿⣥⠄⠀⠀⠀⠀⠀⠀⢀⣄⠈⠙⢻⣿⣿
⢀⣀⣀⠀⠀⡀⠀⣰⣄⠀⠀⣴⣼⣿⡇⠀⠀⠀⢸⠟⣼⣿⢸⣷⢠⣿⣵⣿⣷⣶⣶⡤⠀⠀⢶⣿⣾⣿⣤⠀⠈⠉⠉
⠿⣿⣿⣧⠀⠁⠀⣿⣿⣿⡄⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⠏⢸⣿⠀⢿⡇⠙⢿⡀⠀⠀⠀⣠⣶⣿⣿⣿⣷⡈
⠀⠀⠉⠉⠀⠀⢀⣈⣿⣿⣿⣿⣿⣯⣴⣶⣶⡤⠀⠀⠀⠀⠀⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⠿⡿
⣆⢠⣷⠀⢠⡄⠀⠙⢿⣿⠿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣤⣾⣀⣤⣀⡀⠀⠀⢠⣾⣿⣦⠀⠉⠈⠀⠀⠀⣀⣀⡀
⡿⢸⣿⢠⣿⡇⣠⣶⠀⠀⠆⠙⠻⢿⣦⠀⠀⠀⠀⠠⠀⢿⣿⣿⣿⣿⡿⠋⠀⠀⣾⠿⠿⠋⠀⡀⠀⠀⠀⠀⠈⠻⢿
⣷⡾⣁⣺⠟⣼⣿⢃⣤⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣥⣤⡀⠀⠀⠀⠀⠀⢀⣾⣿⣦⠀⠀⠀⠀⠘⣻
⣿⣿⣿⣥⡴⠛⣱⡿⢃⠀⠀⠀⢻⣿⣷⡀⠀⠀⢰⠿⢻⣿⣿⡻⣿⣿⣿⣷⠀⠀⠀⣿⣷⣼⣿⣿⣿⣠⣴⣶⠀⠀⠉
⠰⠿⠛⣫⣶⠿⣉⡴⠏⠀⠀⠸⢿⢿⡿⠇⠀⣀⣀⠀⠘⢿⣿⠇⠈⠋⠉⠉⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡿⠄
⠀⢀⠈⠉⠁⠞⠋⠀⠀⠀⠀⣀⠀⠋⠀⠀⠀⠙⠻⠃⠀⠈⠛⠀⠀⣰⣾⣶⣦⠀⠴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⠀⠀⠀⢠⣤⣄⣄⠀⣰⣿⣆⠀⠀⠀⡀⠀⣤⣤⡀⠀⠀⠀⢸⡿⠟⠛⢁⣀⠀⠉⠉⠿⠛⠙⢻⡟⠙⠋⠀⠀⣤
⣿⡟⠀⠀⠀⢘⣿⣿⣿⣧⣹⣿⣿⢁⣀⠀⢻⣿⣮⡛⡛⢿⣆⠀⠈⠀⣠⣄⣸⣿⣧⣴⡄⠀⠀⠇⠀⠀⠀⠲⣿⣿⣿
⠀⠁⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠈⠢⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢁⣀⠄
⠀⠀⠀⠀⠈⠢⡀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡤⠞⠪⢊⠛⠒⣂⠄⡆
⠀⠀⠀⠀⠀⠀⠈⠲⣴⡧⠤⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠙⠌⣀⢸⣷⡬⠼⠃⠀⠀⠀⠂⢾⣙⢠⡏⢸⢸⠇⠘
⠀⠀⠀⠀⠄⠀⢀⡀⢻⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠉⠻⠥⣢⡈⠛⡩⢁⠀⢀⠀⠀⠀⠀⠢⠬⠿⢹⠼⠬⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⣀⢠⣤⡀⠉⢱⠛⠋⠅⠭⠅⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣔⡀⡙⠛⢙⠢⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠉⡙⢷⡀⠉⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠠⠺⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠋⠛⠂⠀⠀⠀⠀⠠⠀⠀⠄⠑⠠⢌⡞⢁⡄⠁⠀⡀
⠀⠀⠀⠀⠀⠠⠢⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⡀⢀⡀⠀⠀⠀⠀⠀⠒⢤⣀⢀⢰⠉⡠⢁⣤⠘⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⣠⣰⠲⠆⠬⢶⡾⣿⠀⠀⠀⠀⠀⠀⢀⡐⠉⠑⣯⣦⡷⠃⠄⠁⠁
⠀⠀⠀⠨⢄⠶⢐⠀⠉⠁⠆⠀⠀⠀⠀⠀⠀⣠⠤⠲⢌⣳⣶⢞⣻⣿⣝⠄⠀⠀⠀⠠⠐⢄⠀⣶⡼⣿⢿⠓
⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣈⡺⢿⠋⠤⡟⡀⠿⠀⠀⠀⠀⠀⠀⠐⠡⠈⡡⠼⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠄⠋⡬⠹⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣭⣴⣭⣯⣽⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⢟⣭⣭⡉⢙⣛⣉⠉⠻⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣟⠻⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠛⠛⣿⣿⣷⣿⣾⡄⠈⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣤⡀⣀⢼⣿⣿⣭⣴⣾⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣷⣄⢈⣿⣿⣿⣿⣷⠈⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⠍⠡⣨⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣇⢸⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⠃⣹⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣯⣶⣾⣶⣾⡀⠙⣿⣼⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⡀⢪⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⠦⢹⣏⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⢾⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⢹⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠙⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠏⠀⠉⠠⠈
⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⢄
⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠴⠒⠉
⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢹⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠈⠢⡀⠀⠀⢀⠀⠀⡌⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⣷⠄⠈⠁⠀⠀⠀⠀⢠⣤⣤⠐⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠁⠀⢿⣄⡛⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠄⠀⠀⠀⠀⢈⢿⣶⢷⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡀⠀⠣⢤⣀⡀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡈⢧⡈⠓⠶⠶⠄⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⠹⡀⡔⣠⠀⡟⢂⠂⡄⢰⠴⣠⢦⢰⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠈⠀⠉⠀⠉⠁⠈⠀⠁⠈⠈⡄⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⠀⣸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢄⠀⠀⡇⠀⢀⡠⠊⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⢠⠇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⣀⠱⣴⣡⠔⠉⠀⠀⠀⠑⠤⣀⠀⠀⢳⠀⠀⢠⠏⠀⠀⠀⢀⡤⠂⠁
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⠈⠻⡿⢉⠉⠁⠉⠀⠀⠀⠈⠙⢦⣘⡇⢠⠏⠀⢀⡤⠞⠁⠀⠀⢀
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⣿⣿⣴⣞⡉
⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠁⠉⠉⡉⠑⠒⠤⡀
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠿⠒⣴⠞⣴⠛⣱⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢹⣿⡏⣀⠁⡐⢃⡴⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣫⠔⠚⠘⣿⠿⢆⣿⣴⢳⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣈⣴⣿⣦⠀⣘⠙⠿⣟⠻⠈⣾⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣤⣤⢾⣴⣫⣍⡻⡎⣶⡕⢸⡿⢼⣟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠋⣾⣏⠙⢓⣣⣿⣷⢈⣽⠀⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⢿⣦⣭⣭⣿⣧⣤⡰⣾⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣷⣮⣽⣿⡟⠁⠘⣷⠘⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⠛⣋⡾⣮⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠉⠉⠙⣿⣿⣿⣿⠟⠳⣬⢳⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⡀⠀⠸⣿⣿⡇⠀⡄⠘⣷⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣇⠀⣠⣿⣿⣿⣶⣿⣆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⢻⡟⠛⠉⣿⠏⠉⠙⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⢻⣦⡀⣿⡆⠀⠀⡿⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⢿⣾⣷⡀⠐⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒
⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣟⣿⣟

⠀⠀⠀⠀⠀⠀⣴⠀⠝⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣯⡤⠀⠴⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⣠⠀⠀⠈⠃⣴⠃⣴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢿⡿⣿⠏⠀⠀⠀⣄
⠀⠀⠀⠀⠈⣷⠀⠀⣤⠃⣰⡇⠀⠀⢠⠀⠀⠀⣀⣀⠀⠀⠀⠈⠁⣿⣄⡀⢀⡴⠊⠀⠀⠀⠀⠀⠀⣀⠀⣠⠆⠃
⠀⠀⠀⠀⠀⠸⣆⠀⢁⣠⢿⠁⠀⠀⠀⠀⠀⠀⠙⠙⠗⠀⠀⠠⠆⠹⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢻
⠀⠀⠀⠀⡄⣰⠹⣶⡈⣧⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠂
⠀⠀⠀⠀⢱⡏⠐⠋⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠈⠁⠁⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⣆⣠⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⠤⠄⠀⠀⠀⢀⠤⢴⠲⠶⠶⠛⠉⠃⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⢿⡟⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⡿⢦⠄⠤⠼⠛⢻⠀⠇⣠⠀⠀⠀⡈⣠⢆⠀⠈⠇⠀⠤⠆⢠⡖⠀⠀⠀⢸⡇⣠⠛⠢⠀⠐⠁⢀
⠀⠀⢠⠃⣰⡇⠀⠀⠀⠀⠀⠀⣇⣼⠇⠀⢀⣴⠿⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢰⠃⠀⠀⠀⠀⠀⣸
⠀⠀⢸⣾⡁⠧⠶⠄⠀⠀⠀⠀⠸⠿⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢎⡟⣄⡀⠀⠀⠀⠀⠀⢀⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡄⠀⠀⠀⠀⠀⠀⠀⣸⠛⣄⢨⢽⣻⠃⠀⠀⠀⢀⡴⠋⢠⠷⣤⣄⣤⡴⣋⣱⢶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢇⢳⣄⡀⠀⠀⠀⠀⢠⡟⠀⠨⢹⡼⡽⣇⠀⠀⡠⠫⠒⡫⠨⢍⠢⣢⣴⠾⢙⡼⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡴⠃⢸⡀⢻⡇⠀⠀⠀⠀⣾⢷⠀⠉⠀⣧⡎⠙⡷⡞⡡⠻⢷⣅⢎⣦⠿⣯⡤⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢢⠸⡇⢠⠹⡄⠀⠀⢸⢭⠂⠑⣄⠀⡇⣧⠅⢭⡚⡐⠉⣦⣾⠛⠁⠣⢈⡿⢯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣹⢂⣿⡔⠀⢙⢦⣠⡏⠀⢆⠀⠈⢦⢻⡇⠉⠙⢇⣨⡶⠛⠍⠈⣷⠴⢿⣽⣢⡧⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡜⣀⣯⠀⠀⠀⢙⢣⠀⠀⢂⠀⠈⣶⠃⢀⣤⠟⡉⢊⢶⡊⢴⡟⣱⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠫⠎⠕⣻⡄⠀⡀⡞⠀⠇⠠⢤⡂⠀⢹⡧⠟⡁⠀⠈⡆⣸⠃⠤⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠀⣿⠚⠘⠀⢈⢧⡙⠁⠀⠀⣎⠀⠀⡸⠞⠛⠑⠿⠶⣥⣔⣲⠇⡠⣀⢛⠷⠒⢦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⡌⠓⠤⣀⡿⠀⠀⢠⡀⢸⣧⠀⢀⠼⣠⣥⣞⠓⡄⢢⡀⢀⠤⠚⠉⢩⠝⣃⠶⠟⠧⠶⣶⣶⣑⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⣻⡄⠀⢀⠁⡀⠀⢀⡇⠸⣯⣄⠈⠂⠌⠁⠈⠑⢾⡟⠊⢁⣀⣀⣱⡯⠎⠀⠀⠀⠀⠀⣬⡥⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⢣⠀⠀⠀⢰⠀⣸⢁⠌⠸⣫⣄⣀⡀⠀⠀⠀⢠⠞⠉⠀⠀⢩⡯⠶⠒⠛⠋⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡽⠀⢀⠆⠀⠀⢰⣤⣯⡿⣀⠾⠿⣻⠞⢛⡓⠶⠶⣁⠀⠄⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠁⠀⠈⠐⠦⢢⣾⡿⣩⠞⠋⠓⢀⣀⠀⠀⠈⡑⢦⡈⢑⠖⢦⣤⣄⣀⠀⠉⠛⠓⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠂⠀⠈⡿⣫⢶⣑⣂⠀⠀⠀⠀⢈⠑⠆⠀⠀⡠⠊⢠⠔⠻⡌⠉⠋⡐⠂⣀⣬⣷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢆⢂⠔⠓⠒⠒⠉⢭⣐⠀⠀⠀⠀⢠⡶⠶⠿⠒⠛⠛⠒⠚⠓⠶⢅⣜⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣰⠃⠀⡅⠀⠐⠂⠁⠨⠉⢓⢦⣄⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠋⠉⠙⠓⠦⢄⣄⣀⠸⡷⢄⣛⣁⡌⠻⣦⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠉⠙⠻⠞⠛⠷⠄
⠀⠀⠀⠀⠀⢀⠠⢐⠨⠒⠁
⠀⠀⠀⠀⢀⠕⠂⠁
⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣄⡈⠙⠲⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣴⣶⣶⣶⣒⣴⣧⡀⠀⠙⣿⣷⡄⢹⡎⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣮⣿⣿⣿⢷⣄⠀⠈⣿⣧⡀⠁⠂⠹⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣋⣾⠁⣿⣷⣶⣦⣾⣿⠍⠀⠠⠄⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣤⡛⠿⣿⣿⡟⠛⠀⠀⠀⢀⣴⠀⠵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡧⢀⠀⣀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠻⢻⣿⠛⠻⣤⠉⠛⢠⠈⠁⠈⠉⠁⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢠⣿⣿⣿⣷⣾⣦⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣼⣿⡿⠋⢉⣿⡿⣷⣀⣀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣄⣾⡿⠃⠸⠛⠛⠋⢻⣿⡶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⠁⠉⠛⠛⠛⠉⠉⠀⡀⠀⠀⠀⠘⢿⠀⠀⠘⣦⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⡤⠄⠀⠀⢀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⢰⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⡔⠃⠀⠀⠈⠉⣉⣱⡦⠶⠆⠀⢀⣴⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢀⡀⢁⡠⢔⣰⣿⣿⣏⣴⣶⣶⡾⠟⠛⠁⠀⠀⠀⠀⠃⠀⠀⠀⡄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⠿⣬⣶⣼⣿⣿⣿⣿⠟⠛⠁⠀⠰⣤⣄⠂⠀⠀⠀⠄⠀⠀⠀⠀⢀⣷⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣶⣶⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠘⠋⠀⢠⣰⠂⠀⠀⠀⢂⣤⣿⣿⣿⣧⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⣀⣤⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣶⣾⣯⣧⣿⣿⢻⠛⣿⠁⡉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⡄⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⠀⣆⠒⠁
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡰⠄⢄⡈⠐⠁⠆⠀⠀⠉⠋⠐⠐⢦⣀⠄⠀⠀⠀⡘⠶⣀⡔⠉⠀⠀⢩⡀⠄⢠⠔⠲⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⣀⢀⠑⢤⠀⢈⡀⠉⠖⠃⠀⠀⠀⠀⠆⠀⢀⠀⡉⠘⠁⠀⠐⡀⠁⢸⠁⠀⠀⠀⠀⡿⣯⠀⢀⡀⠈⡄⣀⠄
⠀⠀⠀⠀⠀⠀⢄⠈⠊⠄⠀⠂⠈⡃⠀⠀⠀⠀⠈⠢⡨⠄⠀⠹⠀⠀⠀⠀⠐⠁⣹⣠⣼⠀⢀⣠⡤⠞⣅⡇⠀⢨⠀⢸⠙⠁⠠
⠀⠀⠄⠄⠲⠤⠀⠙⠊⠁⡄⠀⠀⠳⠂⠀⠀⠀⠀⠀⠘⠂⠀⠐⠂⠑⠒⠐⠀⠀⠛⠟⠛⠻⠁⠀⠀⠀⠀⠑⠰⠂⠠⢆⠐⠚⠀⠀⠂⠴
⠀⠀⠀⠀⠐⣀⡀⠀⠀⠑⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠈⠀⠀⠈
⠀⠀⠀⢉⠁⠀⠈⢲⡋⡖⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⣆⢁⠠⠀⠄⠤
⠀⠀⠀⠈⢄⡀⠀⠀⢿⣺⡇⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠂⡠⢀⠄⡰⢠⢀⢆⡄⠔⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠘⣺⠞⠀⠀⠀⡆
⠀⠀⡜⠁⠀⠉⠛⠚⢾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⠌⠀⠀⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣏⣀⣀⡤⠆⠤⡀
⠀⠐⠀⠀⠀⠀⢀⣴⡋⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠜⠁⠁⢀⠈⡤⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠁⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⢩⣃⠒⡀⠅⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠁⠇⠐⠁⠏⠸⠀⠃⠺⠰⠇⠊⠇⠼⠀⠁⠀⠀⠀⠀⠀⠀⣽⢫⠀⠱⡄⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠐⠉⡈⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠊⠉⠇⠃⡈
⠀⠀⢀⣀⣁⠀⡀⢀⡀⢥⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⡀⠈⢠⡌⠀⠠
⠀⠀⠀⠀⠀⠀⡠⠋⠁⡂⠀⠉⠀⠙⠦⣠⡤⠴⠞⠋⣿⠿⢽⠈⠁⢁⠉⡉⠀⡀⠀⠨⠏⢄⠀⠀⠀⠀⠀⠙⡀⢀⠀⠐⢁⠙⠠
⠀⠀⠀⠀⠀⠀⢀⠔⠱⡃⠀⠃⠀⠷⡼⠁⠀⣀⠀⠀⡇⠀⠹⠒⠁⢀⠐⠀⠀⠁⠀⢐⠂⠈⠃⠀⠀⢀⡀⠘⠆⠀⡦⡀⠈⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠃⣐⡠⠄⠪⡟⡄⠀⠀⠀⣸⠷⣼⡐⠀⠀⠈⢁⠳⣤⣌⡀⠀⠀⠀⠀⢀⠘⡈⠒⠢⢐⡔⠀⠈⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠈⢁⡤⡈⠁⠀⠀⠀⠀⠀⠌⠀⠀⠈⠘⠀⠀⠀⠐⠙⠢⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠀⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣌⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣌⠻⣿⣧⡀⠀⠀⠀⠀⢀⣾⡿⢱⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡙⣿⣷⡀⠀⠀⠀⣾⣿⢃⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣌⢿⣇⠀⠀⢰⣿⡟⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣶⣦⣤⣀⡀⠀⠈⠻⣿⣦⢿⡄⠀⢸⣿⠇⣿⣿⠏⠀⠀⠀⠀⠀⠀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣮⣭⣛⠻⠿⣿⣷⣦⡀⠀⠙⠿⣧⠀⠘⣿⢸⣿⡏⠀⠀⠀⠀⣠⣴⡿⣻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⣦⣍⡛⢿⣦⡀⠀⠘⣷⡀⡿⣾⠟⠀⠀⠀⣠⣾⡿⢋⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⢿⣷⣮⣿⣦⡀⠘⣧⣼⠋⠀⠀⠀⣴⣿⠟⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⡀⠀⠀⠀⠈⠉⠉⠉⠓⢾⡏⠀⠀⠀⣼⣿⠏⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣝⡻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⢿⡀⠀⢠⣿⢏⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣌⡻⢿⣿⣦⡀⠀⠀⠀⢸⡇⠀⢸⣏⣾⡿⠋⠀⠀⠀⢀⣀⣤⣴⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⡙⢿⣷⡄⠀⠀⠀⣿⠀⣬⡿⠋⠀⠀⢀⣠⣶⡿⢛⣵⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⣙⢿⡄⠀⠀⢻⡾⠋⠀⠀⠀⣴⣿⡿⢋⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣀⡀⠀⠀⠀⠉⠛⠿⣦⣿⡄⠀⢸⡇⠀⠀⢠⣾⣿⢋⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣯⣙⠿⣿⣦⣄⠀⠀⠀⠀⠉⠛⢦⣸⡇⠀⢀⣿⡟⣡⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣮⡛⢿⣷⣦⠀⠀⠀⠀⠀⢹⡇⠀⣸⢟⣼⣿⠟⠋⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡙⢿⣷⡄⠀⠀⠀⢸⡇⢠⣿⡾⠟⠁⣀⣴⣾⢟⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣦⡻⣿⡀⠀⠀⢸⣷⠟⠁⠀⣠⣾⡿⢋⣵⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⢦⣄⡀⠀⠈⠛⠿⣷⣜⢷⡀⠀⢸⡇⠀⢀⣾⣿⠟⣵⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡝⢿⣶⣄⠀⠀⠈⠙⠻⢧⡀⢸⡇⢀⣾⡿⣡⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡹⣿⣷⡄⠀⠀⠀⠀⠙⣿⠁⣸⡟⣴⣿⡿⠋⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⡌⢿⣿⡄⠀⠀⠀⠀⣿⢀⣿⣾⠟⠋⢀⣤⣶⣾⠿⣻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣎⢻⣿⡄⠀⠀⢠⣿⠞⠋⠁⣠⣶⣿⠿⣋⣵⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⢻⡇⠀⠀⢸⡏⠀⢀⣼⣿⠟⣡⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣎⣿⠀⠀⣿⠀⢀⣾⢟⣥⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⢠⡏⢀⣾⣣⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣡⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⡀⠀⠀⡠⠔⠒⠒⠒⠢⢤⡀⠀⠀⠀⢹⠉⢃⠒⠦⣀⠀⠀⠀⠀⢠⡧⣀⡀
⠙⠦⡍⠐⠂⠶⠄⣌⣂⡐⠌⢢⠀⠀⡞⢀⠀⡆⠀⠈⠳⡀⠀⡰⠁⣄⠄⡈⢂
⠀⠀⠈⢦⡀⠀⠀⠄⠐⠙⡛⢮⣇⠀⢣⠀⠀⠹⣆⡠⠀⢧⠀⠃⠐⢧⠀⠀⠀⠃
⠀⠀⠀⠀⠈⠓⠤⠤⠬⠤⠒⠉⠈⠙⠲⢕⣦⣘⠛⢦⡀⠇⠀⠡⣀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠀⢒⠀⢄⣤⠞⠓⢬⣍⣻⡄⠀⠀⠈⠂⠤⠻⣄⠁
⠀⠀⠀⠀⠀⠀⢀⠜⢀⢀⣈⠖⠒⠋⠉⡸⠀⠀⠀⠀⠈⠉⠓⠒⠦⢄⣀⡀⠈⣧⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠠⢞⠀⠀⠂⢀⡴⠁⠀⠀⡀⠔⠊⠉⠁⣒⢺⠉⠈⠉⠉⠉⠉⠀⠀⠉⠉⠉⠓⠦⣤
⠀⠀⠀⠀⠀⠀⠈⢄⠐⢀⡠⠤⠔⠉⠀⠀⢀⡎⠀⠀⠀⢒⠴⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⡸⠁⠤⠤⠛⠋⢘⡴⠃

⠛⣁⣀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠀⢴⣁⠀⠀⡀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡈⠉⡃⠀⠉⠑⠓⠄⠀⠀⡀⠀⠰⠶
⠈⠛⠊⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⣤⠂⢀⠀⠀⠀⠐⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢀⠀⢈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢠⠀⠀⠈⠊⠂⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠈⢤⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣀⣀⠀⠠⠄⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡀⠀⠈⠁⠤⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣈⣀⠈⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠆⠀⠀⠀⠤⠀⠀⠀⣀⣉⣉⣂⣄⠀⠠⠴⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠃⣁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡄
⠀⢀⠤⠀⠀⠀⡰⠖⠋⠀⠀⠀⠈⠛⢉⡀⢀⠀⠀⠀⠀⠀⡀⢌⢀⡀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠈⢻⣿⠋
⠀⠀⠀⠀⠀⠁⠀⠠⠔⠂⠀⠰⡅⠀⠲⠇⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠚⠶⠤⣄⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⠙⠐⠒⠤⢈⣢⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠇⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⣀⠀⠀⡀⠀⠀⣀⠠⠀⠀⠀⣀⣀⡀⠀⢠⠏⢠⡀⡜
⠀⠀⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠃⠘⠁⠀⠀⠀⠀⡃⠤⣀⡉⠢⣠⢸⠘⠿⠁⡠⠔⢒⡂
⠀⠴⢀⡄⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠐⣀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⣨⣙⣓⣼⣷⣴⣇⠠⠔⢀⡰⠁
⠀⠀⠀⠀⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⡘⠟⠈⣠⡾⢁⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢠⠆⠘⠉⢉⠉⢛⣿⣿⣿⠟⠋⡉⠉⠉⠑
⠁⠀⠀⠀⠹⠒⢤⡄⠀⡠⠀⠀⠀⢀⠈⢁⣷⠟⣁⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢠⣧⡴⠺⠋⠈⡴⠫⠟⠻⢍⢠⣄⠀⠈⠁⢀⠈⠂
⠀⠁⠀⠀⢠⠐⠢⠀⠀⠀⠀⠀⠀⢀⡶⠏⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠠⠠⠖⠈⠀⠘⠀⡴⠘⣤⠌⢆⠉⠁
⢄⠀⡄⠒⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀
⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠁⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠘⡀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⡠⢔⠀⠀⠀⠀⣤⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢠⠂⢰⠀⠀⠇⡗⠀⡦⠊⠉⡁⠀⠀⠀⠀⠀⠠⠌⣡⡟⠀⠀⠀⠀⠠⠀⠄⢐⣾⣧⡀
⢀⠀⠀⠀⠀⡀⢀⠀⠀⠰⠅⠀⠹⠂⣁⠴⠋⠀⠀⠀⠀⣶⡞⠁⠁⠀⠀⠀⠀⠀⠀⢀⠁⠁⠈⠁
⡆⢸⠀⠀⢘⠀⠜⠀⠀⠀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠴⠄⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠇⣸⠀⠀⠀⠀⠀⠀⠀⠘⠀⠴⠤⠆⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠂
⠁⠠⠔⠁⣀⣄⣈⠉⠀⠂⠑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠐⠃⠀⠈
⠀⠀⠀⠤⠲⢄⣀⣈⠉⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠀⣥⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢠⡄
⠐⠲⠂⠒⠀⢀⠈⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠖⠁⠀⠐⠀⢁⡀⠀⠀⠇⠀⠀⠀⠉⠒⢦⣀⠁⠀⢱⠆⣀⣧⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠁⠉⠀⠀⠀⠀⢠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⠩⢷⣤⡀⠠⠈⡉⠦⡃⡀
⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠷⠆⠈⠙⠻⢧⣶⣀⠁⠡⡄
⣥⣷⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣐⣂⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣈⣐⣚⣁⣈⣉⣙⣂⣀⣀⣀⣀⣀⣀⣀⣀⣐
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣠⡄⠂⠀⢀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⣰⣿⢀⡆⠀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣼⠋⠀⠘⠄⠙⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⠀⠀⠀⡼⠛⠿⠟⠋⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡄⠀⠀⣀⣠⣤⣾⣿⣯⣷⣞⡿⣿⠀⠀⠐⣡⠀⠀⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⠀⣴⣏⠀⣴⣾⣷⣾⡿⣿⠛⠻⣿⡿⣁⣿⣆⠀⣎⠀⠀⠀⠀⠘⠀⠀⣼⣻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣷⣿⢿⣼⣿⣿⣿⣿⠋⠋⠒⠶⠿⠟⠛⠋⢹⠀⠹⡄⠐⣄⢳⢁⣼⠏⠙⢿⣜⡇
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡿⢿⠟⣾⣿⣿⣿⡟⣿⠘⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠸⡆⢸⡎⢈⠃⠀⠀⠀⣿⠁
⠀⠀⠀⠀⣴⠟⠻⣿⣉⣿⣿⣿⣿⣷⣿⡿⢻⡟⢻⣿⣭⠿⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠗⠉⠀⡀⢀⡀⣿
⠀⠀⠀⢸⣿⠀⠀⢹⣿⣿⡿⠿⠟⡛⣋⣀⠟⢁⣸⣿⣿⠀⠘⣦⢻⡿⠓⠿⢳⡶⠆⠀⠀⡆⠀⠘⢆⡀⢠⠁⠀⠀⣿
⠀⠀⠀⠸⣿⣦⣶⣿⣿⣿⣷⣤⣤⡿⠯⡉⣀⣾⠈⠻⣿⣔⣛⡁⠈⠐⢦⣆⣈⣧⠀⠀⢤⣷⠐⠂⢨⣿⣿⠂⠆⢰⣿
⠀⠀⠀⠀⣸⣹⣹⣿⠿⠥⠾⠷⠦⠶⣾⣿⣌⡙⠛⠚⠚⠛⠛⠓⠒⠂⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠘⡆⠀⠀⣠⠤⠖⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⢀⠞⠁⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠓⣄⠀⠀⠀⠀⠀⠰⣶⠦⡘⢆⣠⠃⣼⣀⣠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡄⢀⡤⠒⠛⡇⠈⠒⠼⠾⣯⠞⣁⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢀⣠⠃⡟⠀⠀⢀⡇⠀⠀⣠⠞⠳⢏⡁⠀⠀⠀⠀⠈⣱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠤⠤⣀⠙⣄⣇⠀⣠⠞⠀⡠⠚⠁⢀⣀⣀⣉⡒⠤⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⣦⠸⡟⠉⠀⣠⣾⣖⠒⠺⣏⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣈⠉⠉⠳⣇⣠⠞⠁⡏⠀⠈⢳⠈⠑⠒⠒⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⠀⢰⠋⢣⠀⢀⡟⠁⠀⠀⢣⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⡄⠀⠀⠀⠘⢆⣸⢠⣯⠖⠋⠉⣹⠂⠈⠑⠒⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⣼⠀⣠⠞⡇⠀⢻⡿⢇⣀⠠⠔⢁⡤⠤⠀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠦⣌⠑⢾⢸⡇⠀⢰⢀⡏⠀⠀⡞⢦⢠⠏⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⠀⢈⡹⠮⣿⣇⠀⡘⢸⠀⢀⣤⠳⣼⡾⠤⠤⣔⣊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⠒⢾⣿⡶⠃⣿⠀⡏⠈⢧⠈⢇⣠⠋⠁⠀⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠚⠻⠾⣿⣧⡀⢿⠀⡇⠀⢸⣸⠏⠙⠢⠤⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢨⠏⠉⢻⠀⠸⡄⣼⡟⢀⠔⠊⠉⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⠔⢚⣁⣀⡀⠈⣇⠀⠘⣿⡵⠃⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠉⣳⠼⣦⠞⠉⠓⠢⠤⠄⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠶⠶⠒⠊⣡⣦⠈⢦⡀⠀⠀⣰⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠈⢆⠀⠑⢄⠀⣇⠀⢘⢀⡤⢴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠲⢤⡳⣀⣸⢀⣖⣚⡷⢮⡲⣼⣏⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢄⣀⣀⣀⡠⠟⠪⣿⠼⠗⠛⠒⠒⠛⠛⠦⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⣤⠴⢚⣧⡀⠀⠀⡠⠚⠛⠓⠒⡶⠋⠉⠙⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣠⠃⠀⡞⠀⠙⣆⠀⡇⠀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⠞⠁⠀⠀⠧⡀⠀⡼⠀⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⢦⡇

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⠶⠶⣶⢶⣶⡶⢶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠰⣄⠀⠀⢃⠀⠀⠀⠈⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠲⣶⣾⣿⣿⣿⣿⣧⠀⠀⠀⠉⠀⠀⠐⠲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡦⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⣴⣄⡀
⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠐⠋⠀⢸⡖⡄⣸⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⣴⣦⡀⠀⠀⠀⠘⣿⣷⣦⡄
⠴⠖⠀⠀⠀⠀⠘⠛⢠⠀⢀⣠⣤⣄⡀⣱⣿⣯⣶⣾⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⣶⣔⡄⠀⠈⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣁⡉⠉⠙⠛⠛⠻⢿⣿⠿⠿⠿⠷⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣿⣿⣿⡛⠂⠀⠀⠀⠀⠀⢀⣶⡀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣷⣶⣦⣤⣶⣾⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆
⠀⠀⠀⠀⠀⠲⢶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠏⠉⠉⠉⠉⠁⠈⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠛⢿⣿⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠉⠻⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠽⠞⠋⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡐⠀⠀⠀⡠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡀⡀⠃
⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⢠⡄⡀⠀⠀⠀⠀⡠⠀⠀⠀⣈⠁⡄⠀⠀⠀⠘⠠⠈⠀⠀⠐⠿⢩⣝⡢
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⡀⠁⠀⠠⠄⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⠮⣶⠀⢹⠅
⠀⠀⠀⠀⠀⠠⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠖⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠢⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡅⡆⠀⢀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡜⠠⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠀⡀⠀⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠁⠀⠰⠆⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⣶⣈⣃⡀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⢀⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⢡⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⡀
⠀⠀⠉⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⠀⠀⠔⠀⠀⠀⠀⠀⣠⢐⠐⠀⠄⠀⠀⡠⠤⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⠁⠀⢀⠂
⠀⠀⠂⡙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠄⠒⣾⠪⠀⠀⠀⠀⠀⡀⠇⠀⠙⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡂⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠠⢀⡄⣠⢔⣒⠰⢱⣦⣄⢄⠀⠀⠀⡐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡄⣴⣾⣿⣿⣦⣼⣿⣷⣿⣿⣿⣦⡀⠀⠀⠈⡈⠉⠂⠄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣦⣾⠇⠀⠂⠀⠈⠐⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⢨
⠀⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠈⠙⢿⣿⣏⡀⡀⠀⠁⠀⠀⣇⠀⠀⠀⡰⠀⠀⣀⠀⣠⢀⢀⡀⠀⠀⠀⠀⢀
⠀⠈⠢⣠⠸⣿⣿⠋⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠿⠿⣿⠀⠀⢄⠀⠸⡄⡀⢠⠃⠀⣠⡔⢊⣤⠲⣪⣍⢊⣿⣿⣿⣿⡑
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⠀⠀⠀⠀⠀⣤⣾⣿⡂⢀⣀⣀⠀⠘⣆⢇⡤⠞⠁⣃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠃⠀⠀⠀⠀⠹⠿⠛⠁⠀⠀⠀⡠⢁⠿⠇⠀⣀⠔⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢠⣄⣧⡼⢸⡤⠿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⠀⠈⠢⢄⠀⢀⠔⠁⠀⠀⠀⠀⠀⠘⠂⢙⠛⢦⣒⣒⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠄⢹⠇⠀⠂⠀⠠⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣿⣿⣿⣿⣿⠀⠀⠉⠛⠛⠁
⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠂⠀⢰⠀⠀⠀⠈⢳⡄⠀⠀⠀⢀⣠⣿⡿⣿⣿⡿⠻⠿⠿⠷
⠀⠀⠀⠀⠈⠁⠀⠁⠀⠊⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢹⡿⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡆⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠁⢀⣴⣿⣿⡛⠁⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⡄⠀⠀⢀
⠀⠀⠀⠀⠀⣶⡄⠀⠀⢸⣧⠴⠚⠉⢿⣿⣦⣍⠉⠛⠿⣿⡿⠿⠛⠉⠀⢀⠀⠀⠀⠀⢀⠀⠠⠍⣿⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣿⡇⠀⢠⠎⠻⣿⣷⣦⠀⠙⠻⠿⢷⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠚⢆⠀⠀⠀⠁⢀
⠀⠀⠀⣀⠀⠈⠻⢦⠇⠀⠀⠈⠛⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠹⠂⠀⠀⠀⠀⠄
⠀⠀⠀⠹⣿⣦⠀⢸⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠥
⠀⠀⠀⠀⠙⠛⠷⠾⣾⠉⠉⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢒⡂⠀⠀⠀⠔⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⣼⡿⠏⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣮⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠐⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠓⠂⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠠⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠐⣀⢂⢻⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠖⠉⢈⡇⠀⠀⠀⠀⠀⠐⠀⢍⢻⡋⠕⠩⠀⠀⠀⠀⠀⠘⣷⣄⢸⡀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢳⡀⠀⡟⠀⣠⠞⠀⠀⠀⠀⠀⠀⡀⠈⡀⢻⠃⠁⠒⠀⠀⠀⠀⠀⠀⠈⢻⡜⡇⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⡇⢠⣥⠞⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⡈⢺⠓⡢⠑⡆⠀⠀⠀⠀⢠⣄⠀⠙⣷⠎
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢧⢠⣇⠞⣡⠤⠤⠶⣶⠀⠀⠀⠀⠠⠒⠂⠈⢺⠃⢀⠨⠠⠀⠀⠀⠀⠀⠻⣇⠀⢹⠀⢠⣾⠃
⠀⠀⠀⠀⠀⢸⠙⢦⡀⠈⣿⣷⣎⣁⣀⡤⠞⠁⠀⠀⠀⠀⠠⠠⠀⠘⢺⠓⠂⠀⠤⡄⠀⠀⠀⠀⠀⠈⢦⣸⠀⡾⠃
⠀⠀⠀⠀⠀⢸⡀⠀⢳⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⠀⠂⢻⠋⠐⠀⠀⡁⠀⠀⠀⠀⣦⡀⠀⢻⡞⠁
⠀⠀⠀⠀⠀⠀⠳⣄⣾⡥⠖⠉⠉⢉⡿⠂⠀⠀⠀⠀⠀⠀⠅⠦⠀⠈⢻⠃⠁⠀⠀⠁⠀⠀⠀⠀⠙⢷⡀⢸⠀⠀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠁⢾⠦⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢳⣜⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢺⠖⠀⠀⠒⡄⠀⠀⠀⠀⠀⠀⢀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠐⡆⠀⠀⠀⠀⢀⣰⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢡⠎⠀⠀⠀⠀⠀⣾⡏⢸⠁⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠗⠁⠀⠀⠀⠀⠀⢸⣿⢀⠇⢠⣾⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠀⣠⣤⡄⠀⠀⠀⣾⣿⡞⠀⣾⢇⠎⠀⠀⢀⣀⠀⡠⠚⠉⢀⡤⠖⠂⣩⠟⡿
⢀⣤⣄⡠⡀⠀⠀⠁⢹⣿⠞⣴⣿⠁⣀⡀⠀⢻⣿⠀⢸⣿⠏⠀⠀⡆⠙⣿⡿⠀⠀⡴⠃⠀⣠⠞⠁⢠⡇
⢠⠿⠣⣅⠓⢰⣀⣀⠈⠉⢰⣿⠇⣼⡏⡼⢀⡞⠻⡤⢾⣿⠀⠀⡼⢧⣠⡿⠃⠀⠀⣳⢶⠊⠀⠀⢀⡜
⠈⢹⠓⠈⠳⢌⡁⢠⡇⠀⢸⣿⠀⣿⣏⣠⠊⠀⠀⠀⢸⣿⣠⠞⠁⠀⠀⠀⠀⠠⠊⠁⠀⠑⠒⠛⣉
⠀⠀⢡⡏⠀⣨⣹⠲⢍⡀⠀⠉⠉⠈⠉⠁⢠⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠒⡏⠁⠀⠳⣤⡀
⠀⠀⠀⠉⠛⠁⠁⠀⠀⢉⣀⣀⣀⣀⣀⣀⣿⡏⠀⠀⣀⣀⡤⠤⠈⠁⢠⣤⠊⢹⣿⠁⣿⡇⠀⠈⠒⠒⠋⠺⠃
⠀⢠⣶⠛⢢⡀⠀⠀⠐⠉⠀⠀⠈⠉⠉⣻⣿⠛⠋⠉⠉⠁⠀⠀⠀⠀⣾⡏⠀⣼⡇⢰⣿⠃⠀⣀⡀
⢠⣿⢁⣴⣿⠁⠀⣰⣦⠀⠀⣴⡆⠀⠀⣿⡏⠀⢀⣾⠂⠀⣠⡀⠀⠀⡿⠃⠀⠈⠀⢸⣿⠀⠀⣿⡟⠉⢉⣷
⠘⠟⠋⣽⡟⠀⣰⣿⠇⢀⣼⣿⠇⠀⡰⢻⣷⣠⢾⣿⠀⢰⣿⡇⠀⡼⠁⠀⠀⠀⠀⢸⣿⠀⢸⣿⠇⠀⣰⣿
⠀⠀⠀⢿⣇⡼⠉⢿⠴⠋⣼⣿⠀⡼⠁⠀⠉⠀⠘⢿⡴⠚⣿⠀⡼⠃⠀⠀⠀⠀⠀⠐⢿⣀⠼⠟⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠴

⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⠀⡀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠄
⠀⠀⠀⠀⢀⠀⣴⠦⠀⢀⠂⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠳
⠀⠀⠀⠉⠊⠐⢋⠃⠂⠉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡐⠀⠈⡀⠀⠀⠤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⠠⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠀⠠⠐⠀⠀⠂⢰⠀⠀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠀⠀⣡⠘
⡳⠉⠔⠆⠀⠢⠐⠁⠀⠁⠉⠙⠀⠀⠄⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⠁⠀⠊⠁⠀⠠⡀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠠⠒⠉⠂⠀⠐⢤⠀⠀⠄⠀⠀⠈
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠘⠀⠈⠀⠂⠠⠀⢀⣠⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⢁⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂⠀⠈⣀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠰
⠄⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠄⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠄⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢠⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡀⢈⠁
⠐⠀⠀⠈⠁⠀⠀⠀⠈⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡀⠄⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⢁⠀⠠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢸⠂⠀⠒⠐⠄
⠀⠀⠰⠀⠀⠀⠀⠀⢠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠⣠
⠀⠃⣄⠘⠂⡀⠀⠄⢨⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠉⠀⠀⣰
⠀⠀⠈⠀⠀⠑⠐⠄⢌⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣤⡀⢠⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⣆⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⢀⠇⠘⢀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠱⠄⠀⠁⠀⠀⠀⡀
⠀⠀⢴⣒⢆⢱⢝⡆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡈⠀⠀⠈⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠙⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠘⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡟⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣟⠳⣦⣀⠀⠀⠀⡠⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣤⡀⠀⠀⢶⠀⠀⠀⠀⠐⣼⠀⠀⠀⡠⠔⠙⢛⣿⣄⠀⠀⢈⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⣷⠀⠈⠀⠀⠀⠀⠀⠁⠀⢰⠉⢃⠀⠰⠎⣸⠏⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣀⠄⢹⣿⣷⣖⢾⢺⣿⣛⡆⠀⠀⠀⠀⡀⠀⢀⠈⡆⠈⢤⠄⡀⣇⡃⠾⠹⠂
⠀⠀⠀⠀⠀⠁⣠⣤⣿⣿⣯⣮⣿⠿⢟⡿⢠⡿⡄⠀⢸⣧⠀⣌⣀⠱⣀⣘⡀⣻⢻⣇⠀⣠⡤⠖
⠀⠀⠀⠀⠀⠈⠁⢿⣿⣿⠜⠟⠉⠠⠏⠁⣼⠁⠣⠀⠎⢿⠀⠙⠛⣧⣤⣭⣴⢏⡼⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠁⠀⢹⣤⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠐⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠈⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⢄⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠊⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢄⠀⡠⠊⠀⠀⠀⠀⠀⢁⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁
⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢸⣀⠄⠀⠀⠀⠀⢀⠌⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠬⢦⡀⠀⠀⢸⠀⠀⠀⠀⡰⠥⠤⠀⠀⠀⠀⠀⠀⠁⠂⢀⠠⠖
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢸⠀⠀⢀⠞⠀⠀⠀⡀⣀⠀⠀⠀⠀⡠⠂
⠀⠤⢤⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⣄⣈⠣⣸⣇⣴⣋⡤⠖⠂⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢻⡟⠉⠀⠀⠀⠀⡀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠈⡇⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠡⠐⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⣀
⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⣠⠞⢀⠀⠀⠀⠄⢁⠀⠀⠀⠀⠀⠀⣬⣿⣼⡿⣃⡀
⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⣴⣦⣸⣋⣀⠀⠀⠀⢢⠀⢸⠃⣠⠏⠀⠀⠀⠀⠉⢣⡶⠀⠀⠀⠀⠙⣿⣭⣾⡿⢃
⠀⠀⢶⣦⣤⡈⢻⢠⣶⣿⠇⠀⠀⢀⣬⡉⡟⣻⡟⠀⠀⠀⢸⡆⡴⠞⢃⡄⠀⠀⠀⠠⠀⣄⣇⠀⠀⠀⠀⠀⢉⣭⣭⣶⡿⠃
⠀⠀⠀⠙⠻⠿⠾⠟⠛⣁⡄⠀⠀⢈⣛⢻⡟⠻⠛⠀⠀⢸⡄⠙⠂⣠⡞⠀⠀⠀⠀⠀⠀⠀⢹⣠⠄⠀⠀⠀⠈⣭⣍⣧⣶⡷
⠀⠀⠻⣿⣶⣄⢀⣴⣿⡿⠁⠀⠀⠻⠿⢿⠿⢿⡿⠀⠐⣄⢿⣄⠋⠁⣴⠃⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣹⣛⣋⣡⣤⡀
⠀⠀⣀⣈⣙⠛⢻⠉⣁⣠⣤⡄⠀⣾⣷⣾⣥⣶⣶⡄⠀⠸⣆⠈⡤⠞⣡⠎⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⠀⠀⠀⣙⣛⣛⣩⣭⡀
⠀⠀⠙⠿⠿⠷⠾⠾⠿⠟⠋⠀⠀⠉⠉⠁⡏⠙⠋⠀⠀⠀⠈⠓⣀⡴⠋⠀⠀⠀⠀⠀⠀⣀⠸⠛⠀⠀⠀⠀⠈⣛⡛⣟⣻⣭
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠀⠀⠀⠀⠀⠈⠻⠟⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⡆⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢀⠀⣇⣿⣰⠏⠀⠀⠀⠀⠀⡀⠀⠠⢎⢞⡇⠀⠀⠀⠀⢸⢀⠞⠉⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡠
⠀⠀⠀⠈⣧⢿⣿⣫⡶⠟⠁⠀⠀⠀⢝⢯⣢⡿⠚⣤⡄⠀⢸⠃⢠⢃⡰⠇⠀⠀⠀⢠⡙⢿⢃⣴⡗⠀⠀⢀⡀⠀⣀⠀⠀⢀
⠀⠀⢀⢳⣼⣿⣯⣴⣾⣛⡁⠀⠀⣤⡤⢅⣸⡫⠍⣊⠀⠀⠘⢄⡞⠉⢀⡀⠀⠀⠀⠸⣿⣦⠿⠟⣁⠀⠀⠀⠁⠂⣬⡄⠀⠉
⠀⠀⣈⢷⣝⢿⣛⣿⣯⠵⠂⠀⢀⣈⡊⠽⡿⢒⠭⠋⠀⣀⠀⢨⠃⡠⠊⠁⠀⠀⠸⣦⣌⢹⣶⣿⠏⠀⠀⠐⠆⠀⣈⡀⠀⠞
⠀⠀⣌⡳⣝⠢⠥⢶⣞⣛⡁⠀⠙⣕⠮⢵⡖⡭⢽⡿⠀⠙⣄⢸⠉⠀⠀⠀⠀⠀⢠⣙⠻⢟⣩⣶⡏⠀⠀⢠⡀⠀⠙⠃⢀⡄
⠀⠐⢮⣝⡾⣝⣛⣻⣭⡥⠄⠀⢶⢖⡋⢭⡭⢛⣃⣤⠠⣦⠀⢹⣀⡼⠋⠀⠀⠀⢈⠿⣷⡞⣛⣭⣴⠀⠀⠀⠀⠀⠲⠗⠁
⠀⠀⠀⠉⠛⠺⠵⠶⠟⠛⠁⠀⠈⠑⠎⠹⠋⠍⠚⠁⠀⠈⠢⣼⠁⠀⠀⠀⠀⠀⠘⢿⣶⣼⠛⠛⠁⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠣⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢍⣀⣀⠆
⠀⠀⢀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⡄⠐⠄⠀⠀⠀⠀⠙⠇⢠⠏⠁⠀⢠
⠀⠀⠀⠠⠀⠀⠈⠢⠄⠀⢀⠀⠀⠀⢠⡇⠀⠀⠀⢀⡷⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣡⠀⠴⠴⣏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠈⢡⠃⠀⠀⠈⠁⠀⠳⠒⠲⠀⢵⠞⠉⠂⠚⠃⠀⠀⢐⠀⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠼⠀⢰⡀⠠⠗⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⡀⠠⠄⠀⠀⠀⠉⠘⠈⠱⠤⡴⠶⠶⠚⠿⢹⠗⠄⠀⠀⠀⠀⠀⠐⡄⢀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠻⠴⣄⠀⠀⠀⠀⠀⢡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⣰⡀⠘⡄⣸⡄⠀⠘⠛⠏⢃⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⣀⣀⢠⡀⠀⠄⠀⠀⠀⢠⡀⢀⠀⠇
⠀⠀⠀⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠈⠑⠀⠂⠀⠀⠀⠀⢙⠘⠻
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠺⠀⠀⠄

⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡚⠄⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠂⠀⠀⠀⠈⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣄⠂⠀⠀⡀⢉⠉⡡⠆⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢰⠃⣀⠈⠢⡄
⠀⠀⠀⠀⣄⠢⢀⢸⣏⢛⠂⠤⠀⠀⠌⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠉⠀⠀⠀⠠⠀⠀⠀⠄⠀⠤⠆⠀⠀⠀⠘⠀⠀⠀⢀⡄⠀⠀⠀⠂⠀⠈⡀⠀⠁
⠀⠀⠀⠀⣈⠁⠈⠁⠀⠀⠓⡄⠀⠀⡀⠀⢀⠀⠀⠘⠃⠀⠀⢀⠀⠄⠁⠁⠠⠀⠁⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⢀⠀⠀⠀⠑⠢⠀⠀⢀⠀⠀⢁⠀⢰
⠀⠀⠄⠀⠀⠘⠀⠠⢀⠓⠀⠀⠁⡄⡄⠀⢀⡀⠀⠐⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⠁⠀⢠⡄⠃
⡲⠍⢇⢲⡀⠈⢢⠄⠊⠀⠈⠁⠉⠙⠃⠀⠀⣀⠀⠀⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡘⠁⠀⠐⠉⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠁⠁⠘⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠒⠀⠀⠀⠉⠀⠀⠠⠖⢰⠀⠀⠙⢄⣀⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠰⠂⠁⠀⠀⠀⠀⠀⠦⠀⡰⠀⠀⠄⡈⠀⠀⠀⠈⢉⠀⠀⠁
⠈⠁⠀⠀⡄⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠆⠀⠜⠀⠀⠀⠀⠀⠀⠀⠠⠆⠃⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠁⠠⠀⠺⠁⣀⠀⠤
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⢀⠄⠀⢦⡀⠀⢠⡄⠀⠀⠀⠀⠀⡀⠂⠀⠀⠈⠁⠈⠉⠀⡀⠀⠔⠀⠀⢉
⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⡀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡄⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠄⠀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠄⠀⢠⠀⠀⠰⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠈
⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠸⠀⠀⠸⠀⠀⠐⠈⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⡀⠀⠑⠂⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠠⠄⠀⡄
⠠⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠀⠀⠀⠄⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠴⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠂⠐⠆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⡀⠀⢀⠆
⠀⢠⠀⠀⣀⠀⠀⠈⠀⠀⠺⠀⠀⠀⠂⠀⠀⠀⡄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢠⠀⠀⠩⠿
⠀⠀⠺⡄⠁⠑⢤⠀⠘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⠃
⠀⠀⠀⡀⠀⠀⠀⠁⠒⠠⢅⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⢀⠀⠠⠀⠄⠀⠠⠀⡠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣐⣤⣀⠀⡠⠄⠀⡀⠀⢀⠀⠈⠁
⠀⠀⠀⠀⠀⠆⠀⢠⢲⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢁⠏⢹⠍⠀⠁⠀⠒⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡀⠈⠑⠂
⠀⠀⠀⣀⣀⡘⢦⢾⡙⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠩⠀⠁⠀⡌⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠉⠈⠁⠀⠀⠀⠀⠓
⠀⠀⠘⠳⠜⣷⢸⣪⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠔⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤⠄
⡀⢀⣀⢀⣀⣉⣀⣉⣀⣀⢀⢀⣀⣀⢀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⡀⣀⣌⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠂⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⢓⣄⡀⠀⠀⠀⠀⢀⣔⠀⡀⠀⠀⠀⡐⠁⣼⢡⣯⠤⠄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⣷⠀⣟⠀⢁⠀⠀⠀⠀⠀⠀⢀⠷⠀⠀⠀⠀⠀⠀⠀⠹⣦⠄⠠⠾⡿⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢲⠃⠁⠀⠁⠀⢸⡄⠙⣴⠋⠉⠁⠀⡎⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠷⣤⡙⠖⠂⠈⠀⠀⢙⠁⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⢿⣿⡿⠷⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠶⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠗⠀⠀⠀⠀⠀⠐
⡐⠒⠲⠄⣀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⡰⠊⠀⠀⠀⠀⢠⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠸⡄⠳⠊⠀⠀⠀⠀⠀⠀⠀⠙⠏⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⡄⣠⠜⠀⠀⠰⠀⠀⠀⢠⣿⠆⢀⠈⠀⠀⠀⠈⢦⡑⠙⢁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠠⣄⣠⡄⠀⠀⢃⢀⠀⣧⡍⠀⠀⠀⠀⠀⣀⣾⣿⣿⠆⠀⠀⠀⠀⠀⡈⠄⢿⣧⠴⢊⠀⠀⠀⠀⠀⠀⢹⡔⠀⠀⢀⡀
⠀⠀⠀⠀⠠⠤⠀⠬⠹⡄⠀⠀⠀⣾⢆⠋⠀⠀⠀⠀⠀⠀⠈⡻⠛⠁⠀⠀⠀⠀⠀⠀⢛⣄⣞⠠⢀⡀⠀⠀⠀⠀⠀⠀⠘⠳⡄⠊⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠉
⠀⠀⠀⠀⠐⣷⠀⢂⡀⢀⠉⠀⠀⡋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠹⠈⢻⡇⢈⡇⠀⢠⠁⢀⡀⠀⠀⢀⣀⡤⠀⡰⠀⠀⡠⢾⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⣿⣟⡴⡾⠿⡏⠀⠔⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡸⢁⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠃⢀⠀⠈⠄⠀⠀⢀⡤⠂
⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠈⠛⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠛⠷⣬⠀⡄⡰⠋⢀⠀⠁
⠀⠙⢛⢷⡶⠂⠀⢀⠀⠀⠀⠀⠀⡏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⣶⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⢄⠠⠀⢂⠙⠛⠂⠂
⠀⠀⠀⠉⠋⠐⠂⢀⡻⢦⡀⠀⠀⠄⠐⣾⡋⢻⡄⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠂⣀⣠⠀⠉⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡀⠙⡆⠀⠙⢛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣁⣈⣠⣉⡛⠍⠉⡋⠉⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠇⠸⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⡉⠳⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠛⠛⠉⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠂⠀⣰⢷⠀⢹⣯⡹⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣢⣶⠜⠋⠁⠀⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⡏⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠉⠀⠒⢦⣴⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠀⣠⣆⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣇⣧⣴⣿⣷⣽⡟⢦⡐⠓⠀⠚⠘⡛
⣂⣀⠤⠆⠀⠀⠀⠀⣀⣀⡀⠀⣀⡀⢀⣤⣶⡶⠖⠈⠉⠉⠀⠸⠛⠛⠛⠛⢛⣿⣿⣿⣿⡿⣿⣧⣸⣿⠷⢿⣿⣷⣾⡷⢄⠰⣬⡼⣽
⣿⣿⣿⣿⣶⣿⣿⣿⣾⣷⣥⣭⣤⣸⣿⣿⣿⣶⣂⣤⣄⣀⣀⢀⣠⣤⣴⣴⣿⣿⣿⣿⣞⣏⡀⣹⣿⣿⣷⣿⣿⣿⣿⣿⣷⣽⣛⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢡⠀⠀⠀⣀⢀⡀⠤⠤⡀⠀⠀⢀⠐⠈⠉⠆⠀⠀⠀⠀⢀⠋⡍⠁⠀⠂⢄⡀⠀⠀⠤⡤⠂⠃⠀⠀⠄⠂⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠂⠉⠀⠀⢨⡇⠀⠐⠋⠀⠀⡌⠀⢠⠀⠀⢀⠀⠀⠀⢸⠀⠈⠢⡀⠀⠀⠙⡄⠀⠀⠀⡘⠀⠀⠀⡄⢀⠔⠁⠄
⠀⠀⠀⠀⠀⣤⠀⠀⠉⠀⠀⡃⠀⠀⠈⠀⠀⠀⠀⠀⢠⠊⠀⠀⢘⠀⡀⠈⠑⠀⠀⠀⠆⠀⠀⠐⢄⠀⠀⢰⠀⠀⠠⠜⠀⠀⠀⠘⠇⠄⠊
⠀⠀⠀⡰⠈⠿⠀⠀⠀⠐⠀⠅⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⢮⡔⠁⠀⠀⠉⠄⠀⠈⠢⠀⠀⠀⠑⢀⡘⠀⠀⠀⠀⠀⢀⠔⡀
⠀⠀⠰⠀⡘⠀⠐⣀⣀⠀⠀⠀⠀⠀⠐⠭⠁⠀⠀⡀⠀⠀⢄⠀⢸⠀⠀⡠⠂⠀⠤⠀⠀⠀⠈⠁⠀⠂⠈⠡⠀⠀⠀⠀⠐⠀⢀⠐
⠀⠀⠠⠊⠀⠀⡌⠀⠀⠀⠁⠆⡀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠂⣸⡀⠊⠀⠀⡐⠀⠀⠰⣅⠈⠰⡄⠀⠀⠀⠀⠀⠀⠰⠀⠐⠀⣡⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠈⠐⠂⠠⡭⠤⠀⠒⠈⠀⠀⠀⠇⠀⠉⠂⡼⠀⠀⠀⠀⠀⠀⣇⣀⡈⠠⠭⠛⠐⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠐⡢⠄⠁⠀⡠⠶⢄⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠃⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠏⠁⠁⠀⠀⡌⠁⢰⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⢠⠈⢁⠛⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⡄⠀⠀⠀⣀⠀⠘⠤⡇⠀⠀⡄⠂⠀⠀⠀⡀⠂⡰⠀⠀⠀⠀⠀⠈⠖⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢆⠀⠀⡆⠀⢀⠃⠀⠀⠘⠄⠒⠀⠠⠈⣄⠀⠈⠃⠀⠀⠈⠛⠈⠀⠀⠀⠔⠓⠀⠀⠀⠀⠀⡇⠑
⠀⠀⠀⠀⡠⠐⠀⡀⠀⠀⢀⡠⠛⠄⠀⠀⠑⢄⣁⡀⠂⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⡐⠤⣘⡀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠱
⠀⠀⢀⠊⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠃⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠉⠂⣄⠀⠀⠀⠀⠀⢈⠉⠁⠀⠀⠡⠀⠀⠰
⠀⠀⢸⡀⠤⠐⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠁⠢⢄⡀⠀⠀⠑⠀⠄⣀⡀⢉⡄⠂
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⠰⢠⠀⠀⠇⠀⠀⠸⠀⠀⣄⠀⠲⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⡠⠂⠀⠀⠀⠀⡄⠀⠈⠛⠀⠀⠀⠀⠋⠁⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣉⡉⠱⡦⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠠⠀⠀⠀⢀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⢀⠀⠒⠀⠀⢠⠂⢂⡠⠂⠉⠂
⠀⠀⠀⠀⠰⡁⠀⢌⡐⠢⢄⠀⠀⠀⠀⣄⠒⠈⠉⠀⠀⠀⣠⡄⠀⠀⠈⠉⠁⠒⢠⠀⠀⠀⠀⢠⠉⢂⡀⠀⠀⠀⢠⠊⢰⠄⠀⠀⠀⠀⣀⠂
⠀⠀⠀⢀⣀⡈⠢⠀⠀⠂⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⢐⠉⠀⠀⠀⣠⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠃⡀⠀⠀⡀⠀⠀⠀⠵⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠷⠀⠀⠠⠈⠃⠀⠀⠀⠁⠄⠀⡀⠀⠀⡠⠊⠀⠀⣤⡐⠁
⠀⠀⠀⢀⠠⠀⠀⢀⠀⢛⠀⠀⠁⡀⢁⠀⠀⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠠⠊⢠⠀⢰⠀⠀⠈⠂⡀⠆⠀⠜⠀⠀⢃⡠⠊⠀⠀⠀⠀⡠⠄
⠀⠀⠐⠁⠀⡠⠒⠁⠀⢸⠀⢤⠀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⢀⡠⠊⠁⠐⠂⠀⠈⠁
⠀⠀⠇⠀⠀⠀⡠⠂⢂⠀⠀⠀⠀⡀⡠⠀⠀⠀⣤⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⡷⠁⢠⠀⠀⠀⠀⠀⠀⠰⠔⠈⠀⠀⠀⠀⠀⠀⢀⣀⡔⠢
⠀⠀⠈⠁⠀⠉⠀⠀⠀⠉⠉⠀⠀⠈⠀⠀⠀⠀⠈⠢⠈⠐⡄⠀⠀⠀⡀⠀⢦⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠀⠁⠀⡆
⠀⠀⠀⠀⢀⡀⠤⠠⣀⠤⠤⢀⡀⠀⠀⠀⠀⠀⡄⠀⠡⣠⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⢰⠀⠢⡌⠈⠆⠀⠱⠀⠀⠀⠈⠢⢄⡀⠀⠇
⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⢡⠀⠈⠻⡄⠀⢠⠀⠀⠰⡶⠃⠀⠀⠀⠠⠄⠲⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠹
⠀⠀⠣⡀⠐⢀⠀⠇⠀⠘⠀⡐⠀⢀⠜⠀⠀⠀⠀⠂⠀⠐⠰⣦⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠁⠀⠆⠀⠐⢢⡠⡀⠀⠀⠀⢁
⠀⠀⠀⠈⠢⠀⠢⣀⠀⠀⠌⢀⠔⠁⠀⠀⠶⡄⢠⡀⠈⠒⢀⠀⢢⡀⠀⠀⠀⡠⠀⠀⠀⣄⠀⠀⠁⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠋⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠽⣶⠧⠐⠁⠀⠀⠀⠀⣀⠐⢄⠁⡀⠀⠀⠈⠈⠑⡀⠀⠀⠃⠀⡠⠊⡸⠀⠀⢀⢀⠀⠈⢃⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠣⠈⠶⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠃⡀⠖⠁⠀⠘⢦⡀⠀⠂⣤⣤⠀⠀⠀⠆⠁
⠀⠀⠀⢠⠲⠀⠀⠀⠀⠀⠀⠘⠁⠀⢉⠐⠢⢄⠀⠀⢀⠐⠈⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠣⣀⠁⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣰⡆⠔⡠⠞⠀⠀⡌⠡⢀⢀⡴⠚⠀⠀⠀⠠⠐⠃⠐⠺⠀⠀⠀⢀⡀⢴⠀⠀⠀⠁⠀⣀⠀⠌⣰⡄⠀⣤
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠁⠀⠀⡙⠉⠁⠀⠀⠀⠘⣧⠀⠙⠁⠀⣠⠀⠀⠀⠓⢄⠀⠀⠀⢈⠀⢠⠉⢠⠁⡆⠀⠀⠀⠀⠈⢁⠈⠛⠀⠈
⠀⠀⢀⠂⠀⠉⠀⠐⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠱⣄⠄⢀⠇⠀⠀⠀⠀⠀⠁⢂⠤⠁⠀⠘⣠⣄⠔⠁⠀⠀⡟⠀⠐⣼⠦⠐⠒⡰⠆
⠀⠀⠰⠀⠀⠀⠀⢀⠀⠀⠰⠀⠀⠀⢠⠪⠀⠘⠢⠀⠀⠄⡁⢀⠌⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠃⠀⡀⠋⠉⠉
⠀⠀⠀⠱⢀⠀⢀⠂⠀⢠⠆⠀⠀⠀⠘⢆⠘⠃⣄⠓⡀⠈⡷⠁⠀⠠⠐⠃⡰⠆⠀⠀⣀⠄⠻⢄⠀⠀⢰⢂⠐⠀⠠⠀⠾⠇⣀⠀⠀⠶
⠀⠀⠀⠀⠀⠁⠪⠀⠒⠁⠈⠀⡀⠀⠄⠀⠉⠓⠈⠰⠆⠀⠇⠀⠠⢇⡰⠟⠰⠆⠀⢰⡀⠀⠀⠀⡆⠀⢰⠈⡀⠰⣤⠎⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠐⡣⠀⠀⠀⠀⠀⠀⠑⡇⢀⣦⠋⠴⠚⠁⠀⠀⠀⡄⠀⢀⡘⠁⠀⠀⣄⣀⠘⠉⠒⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠆⢀⣀⠙⠀⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠀⠀⠀⠀⠘⠛⠒⠀⣀⡀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⡄⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠂⠀⠖⡉⠑⠀⡀⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠢⣰⠂⠈⠁⠋⢶⠀⠚⢰⡀⣊⣀⡬⠤⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠢⡄⠈⡆⠀⣏⠠⠂⠀⠀⠸⠀⠀⢀⡟⠉⠀⠀⡄⠀⠀⠀⢨⠏⠈⠆⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠡⡀⡸⠀⣇⠀⠀⠀⠀⠀⣇⡴⢋⡶⢈⠁⢤⠀⠀⠀⣸⠃⢂⡆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠀⡴⢠⠀⠱⢇⠀⢹⠀⠀⠀⡦⢠⣏⡤⢋⠆⠸⠀⠀⠀⠀⠀⣅⠤⠚⠉⠩⠀⠑⠂⠀⠀⠊⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡆⠀⡀⠁⠀⢆⠀⠈⢧⠀⡇⣄⠐⣁⣾⡏⠀⠴⠀⠀⢇⠈⡀⣀⡴⠃⠀⠋⠀⠀⠆⠀⠆⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡹⠣⡀⢸⠀⢰⠈⢻⡇⠀⣠⠏⠈⣷⠀⠀⠀⠀⠈⡤⠴⠚⣤⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⠀⠙⢾⠀⠀⡀⠀⣿⡞⠁⠀⠀⢸⡆⠀⠀⣠⠚⠀⠁⠂⠠⠀⣰⡄⠀⢠⡄⠊⠀⠀⠀⠀⢀⠀⠀⠀⡅
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠒⠒⢾⡀⠀⠈⢧⠀⢡⠀⠸⣧⠀⠀⠀⠀⢻⣦⠚⠁⠉⠀⠀⠈⣀⠠⠢⣄⠀⢈⠁⠀⠀⠀⢀⠄⠛⠀⢦⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠳⡀⠀⠈⠓⣎⠀⠀⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣰⠁⠠⠀⠀⣀⡜⠒⠒⠖⠒⠣⢄⣴⠡⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠃⣠⠙⠲⣤⡀⠸⡄⠀⠙⢷⠀⠀⠘⡛⠀⠁⠀⠀⠀⣸⢁⣠⡾⠛⠋⠉⠀⠀⠀⠀⠀⣤⠄⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⣀⠞⠚⠶⣿⣦⡀⡀⢀⠀⢰⣷⠀⠀⣀⣤⣦⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠓⠁⠀⠀⠀⠀⠈⠙⠻⣿⢷⡸⣿⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠙⠞⣹⣿⣿⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡾⣿⣽⣿⣟⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡇
⠀⠀⣠⠀⡀⣄⣠⣀⡀⢀⣀⣀⡀⢀⣠⣠⣾⡿⣿⢿⣿⣿⡿⣿⣿⣾⣾⣿⣿⣷⣶⣄⠉⣁⡀⠀⣀⢀⣀⣀⣀⣠⡀⠀⢠⣀⣀⣀⣀⠀⠃
⠀⠀⣿⣿⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣷⣟⣽⣟⢸⣯⣽⣿⣯⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡎⣿⣿⣿⣞⣿⣷⣽⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠈⠀⠀⠈⠈⠀⠀⠁⠀⠁⠈⠁⠀⠁⠈⠀⠈⠀⠀⠀⠉⠁⠀⠀⠉⠀⠉⠀⠀⠁⠉⠈⠁⠀⠀⠁⠀⠈⠀⠀⠈⠁⠀⠈⠀⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣄
⠀⠀⠀⠀⠀⠀⣟⡇⠀⠀⣠⡤⠀⠀⠒⢶⣶⡀⣿⡇⣾⠟⢁⡀⠀⠀⠀⠀⡿⢶⣤⢠⣾⡯⠅⣀⣄⠀⠀⠀⠀⠀⠐⢶⡟⠉⣴⠆
⠠⢤⣤⣤⣀⠀⠛⠁⣰⡿⠋⠀⢀⡄⠀⢲⣌⠁⠈⠋⠛⠟⠋⠁⠀⢀⣀⣀⣈⠳⠛⠻⠋⣩⣿⡯⡟⠀⠀⠀⠀⠶⢦⣤⠬⠔⢳⡄⠀⠀⣀⢠⡄
⠀⠀⠀⣉⣭⡄⠀⠠⣦⣲⣦⣤⠘⣿⣄⢸⣿⡗⠃⠀⣠⡤⠀⢀⡄⠘⢯⡝⡟⠛⠀⠀⡐⠉⣀⣥⡀⠀⠀⢀⡀⠰⣟⣁⡀⠀⠀⢀⣹⣤⡘⠋⣙⡓
⠀⠠⠾⠛⢩⣶⠆⡷⣦⣄⡀⠀⠀⣠⣿⡗⠛⠁⠀⣼⣿⡇⢠⣾⡇⠀⠀⠸⣿⡶⣄⡀⣷⢿⡻⠝⠁⠠⣄⣿⠰⣗⣋⢿⠃⠀⠐⣻⡌⠈⠉⣼⠉
⠀⠀⠀⢠⡿⠃⠐⡇⠈⠙⠻⠆⠀⢹⠋⠀⠀⠀⠃⢹⡿⢴⣯⣉⠀⠀⠀⠀⠉⠚⠙⢹⡇⢀⣀⠀⠀⠀⣩⡿⠄⣨⠉⠁⠀⠀⠀⠉⠀⠀⠀⢀⡄⣤
⠀⠀⠀⠈⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠻⠿⠷⠂⠀⢀⣀⣀⣀⣀⠟⣟⣟⣿⠇⠀⠀⣠⣼⣇⠀⡀⠄⡀⠀⠀⠁⠘⢻⠚⠁⣿⣤
⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠘⠯⡝⡟⢻⠀⠀⠀⠀⠀⠀⠀⠉⠘⠇⣾⠻⠦⠄⠀⠢⠀⠀⢹⡆⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠞⢻⣦⡿⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⠀⠈⠙⠦⣦⣀⠀⢹⡄⠀⠀⣀⢀⣀⣀⡀⠀⠀⢀⢔⡵⣚⣯⡿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣀⡀⠀⠀⠀⣼⣊⡥⠄⠀⠀⠀⠀⠘⠹⡆⠀⠀⠀⠾⠑⠋⠉⠁⠀⠀⠀⣾⡿⣪⣖⣵⡾⢟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠒⡒⠒⠄⠀⣸⣫⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡿⠍⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⡀
⠀⠈⠩⠭⢭⣍⡀⠟⠀⢀⠤⠮⢍⡉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⡃⠀⠀⠀⠀⣼⣿
⠀⠀⠐⠲⠲⠲⠽⢀⡼⡩⠭⠍⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⣀⣀⡠⠀⠀⠀⠀⠀⠀⠀⢢⣄⠈⠱⠤⣤⣛⠂⠀⡠⢊⣦⣶⣶⠁⠀⠀⣠⡾⣯⣿⡆
⠀⠀⠀⠀⠀⠀⢰⠶⠶⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠜⠉⠁⠀⠀⠀⠀⠀⠀⢀⣴⢄⢠⣉⣱⣲⠶⠀⢠⠞⡻⣡⡖⡡⠃⠀⢠⣾⢹⣧⠿⣻⠇
⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣷⠲⠚⠉⠀⠀⣴⣷⣿⠟⠋⠋⠀⠀⠠⣯⣿⣞⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⡀⠀⠀⠀⠀⢴⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠈⢿⣿⡗⠀⠀⠀⠀⢤⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⠄⠀⠀⠀⣸⢹⣷⣾⠀⠘⢿⣶⡧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠀⠀⠀⠀⠸⣾⣿⡏⣀⡀⢸⣿⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣯⠀⢰⣄⣆⣠⣿⣿⣧⠻⠇⠠⣽⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣄⠈⣿⣿⣿⣿⣿⣿⣶⣢⣾⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢃⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉⠙⢿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⡿⠟⠛⠻⣟⣽⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⢿⣿⣿⣿⣯⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠚⠈⠀⠀⠀⠀⣫⣽⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠘⢫⣽⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠟⠀⠀⠀⠀⠀⠀⠀⠈⠏⠻⠏⠙⠅⠀⠀⠀⠀⠀⠀⠀⠀⠁