Electric motor Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣦⣤⣤⣤⠀⠀⠀⠀⠀⠀⣸⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣦⣤⣤⣤⡀
⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣿⣿⢛⡻⣿⣷⠀⠀⠀⢀⣤⣼⣿⣿⡏⠀⠀⢹⣿⣿⣇
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣮⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣷⣦⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠉⠭⠿⠿⠿⠿⠿⠍⠉⠁⠀⠀⠀⠀⠀⠼⠋⠛⠋⠻⠦⠀⠀⠀⠀⠀⠀⠈⠽⠿⠿⠿⠿⠏⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⢀⣤⣤⣤⣴⣦⣤⣤⣤⣤⡄⠀⠀⠀⠀⢠⣤⣼⣿⣿⣿⣤⣤⡀⠀⠀⠀⠀⢀⣤⣼⣿⣿⣿⣤⣤
⠀⠀⢀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⠍⠉⠁⠀⠀⠀⠀⠈⠩⠿⠿⠿⠿⠯⠉⠀⠀⠀⠀⠀⠀⠉⠽⠿⠿⠿⠯⠁


⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣤⣤
⠀⠀⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⠀⠀⠀⢀⣾⣟⢿⣿⣼⣽⣻⣿⡄⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡄⠀⢸⣿⣲⣿⣿⣿⣿⣗⣺⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⠀⠀⠸⣿⡽⣻⢿⣿⢟⢷⣽⡟⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠀⠀⠀⠀⠙⠿⣿⣿⣾⣾⡿⠋⠀⠀⠀⠀⠀⣨⣿⠻⡿⠿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠
⠀⠀⠀⣀⣤⣀⣸⣿⣿⣿⣀⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⢿⣿⡄⠀⠀⠀⠀⢰⣷⣶⣾⣿⣿⣶⣦⣄
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠉⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠙⠛⠀⠀⠛⠋⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠘⠛⠿⠏⠉⠹⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠐⢐⢚⣿⣿⣿⣿⣿⣿⣗⠂⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢨⣩⣿⣿⣿⣿⣿⣿⣏⡹⠿⠆⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠘⠛⣿⡿⠿⠿⢿⡿⠛⠁⠀⠀⠀⠀⠈⡈⠴⣿⣿⣿⣿⣿⣿⡧⠄⠀⠀⠀⠀⠀⠛⣿⡟⠃
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣯⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⣤⣔⣚⣛⠤⠤⢟⡻⠓⠠⠅⠒⢠⣴⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⠉⠀⠀⠀⠺⠕⠒⠙⠂⠀⠀⠈⠁⠒⠤⡀⠰⠿⢛⡏⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⣢⡄⠑⣄⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⡠⠞⡒⠂⠠⠤⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠤⠔⠒⢈⡁⠄⡇⢐⠂⠄⢸
⠀⠀⠀⠀⠀⢀⠎⠉⠘⠉⠉⠀⠀⠀⠈⠉⠒⠢⢄⠀⣠⠠⢀⡡⠤⠐⠂⡉⡀⠀⠠⠐⡈⡾⠐⢨⡇⠠⠋⡂⢸
⠀⠀⠀⠀⠀⡈⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡑⠄⢈⣡⡀⠀⡄⡑⡐⢄⠠⠢⠀⣰⢃⢁⣱⠁⢘⡂⠄⢸
⠀⠀⠀⠀⠀⡇⢀⠴⠛⠛⠒⣿⡿⢧⡲⡀⠀⠀⢈⠀⠘⣞⣿⣏⡞⡕⢌⢌⠂⡠⠡⡑⠇⠄⢜⣽⠀⠠⣉⡀⡘
⠀⠀⠀⠀⠀⠅⢰⠃⣼⣿⣷⡀⣛⣹⣷⡇⠀⠀⢐⠕⡀⡗⣩⢟⢈⢊⢊⡢⡑⠠⡑⡍⡄⠜⡞⢳⠄⣸⣽⠀⠃
⠀⠀⠀⠀⠀⠰⢈⠀⠻⣿⡻⢡⣾⣿⣿⡟⠀⠀⢔⢠⠂⡇⣣⠕⡑⡁⡕⡐⣀⡕⡌⣜⢌⣸⣼⡾⠀⣛⡭⠚
⠀⠀⠀⠀⠀⠀⠪⡙⣄⣤⣠⣶⣿⡻⡣⡨⠂⠨⠓⠕⢰⠩⣢⡮⢪⢊⢔⢌⢉⢀⡈⣨⣬⡍⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠻⠭⣝⠊⢊⡈⢔⡨⡐⡥⢫⣾⣿⠕⢕⣕⣵⠷⠖⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠬⠤⠾⠵⠕⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⡠⢀⠀⠀⢄⠄⡂⢂⢔⠔⡠⢊⢔⠕⠕⠑⠕⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠄⠠⢂⠄⡂⢀⠅⡊⢐⠁⠊⠐⡡⢊⠔⡡⢊⠔⡡⢊⠔⠁⠡⠊⠐⠑⠁⠈⠈
⠀⠀⠀⠀⠀⠀⠂⠐⠁⠊⠔⠡⠂⠅⠊⠔⠡⠊⠐⠁⠊⠀⠊⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄
⠀⠀⠀⠀⠀⠀⢠⣤⣦⣴⣿⣿⣿⣿⣧⣴⣤⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢼⣿⣿⡿⠿⣿⣿⣯⠄⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⠋⠉⠉⢹⣿⣿⣿⣇
⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣽⣿⣿⡘⠗⣸⣿⣿⠅⠀⠀⠀⠀⠛⠛⢻⣿⣿⣿⣄⡀⢀⣸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠉⠉⠉⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⣶⡆
⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡆⠀⠀⠀⠀⠀⢀⣶⣶⣾⣿⣿⣿⣷⣶⣶⣦⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣾⣶⡄
⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⢀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⠒⠒⢒⣖⠒⠒⠒⠒⢛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣑⣒⣀⣀⣀⣴⣾⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢶⣾⣞⣿⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⡇⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢹⡇⠀⣯⠕⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡇⢸⡇⠀⣗⡫⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢸⡇⡇⢸⡇⠀⡧⠖⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣸⣗⣒⣒⣺⣄⣀⣀⣀⣈⡇⡇⢸⡇⠀⣏⣭⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⣗⣒⣒⣺⣀⣀⣀⣀⣀⡇⡇⢸⡇⠀⣗⣒⣿⢶⠶⠶⠶⠶⠶⡶⠶⠶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢹⣷⣶⣷⣾⠉⠉⠉⠉⢉⡇⡇⢸⡇⠀⡧⣭⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⡇⠀⠀⠀⠀⠀⠀⢰⡄⡇
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⢸⣧⡇⢸⡇⠀⣟⡲⣿⠬⠥⠤⠬⠭⠤⠭⠥⠬⠭⠤⠭⠤⠤⠤⠬⠭⠤⠬⠭⠤⠭⠭⠤⠭⠥⠬⢽⡇⠀⠀⠀⠀⠀⠀⣼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⢸⡇⠀⣷⣝⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇⠀⠀⠀⠀⠀⣰⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⣇⣀⡿⡻⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⡇⣠⣤⣤⣴⣾⣿⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣮⣿⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣺⡇⣿⣿⣿⣿⣿⣿⠏⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣧⣭⣭⣭⣭⣭⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠾⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠷⢾⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣽⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢉⠀⠀⠁⢀⣀⣤⣤⣼⣤⣤⣤⣀⠀⢠⡦⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠟⠉⠉⠈⠁⠁⠁⠉⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁⠐⠊⠁⠀⠀⠀⠀⠀⠈⠁⠐⠄⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠨⠕⠀⢀⠀⣴⠿⠃⠀⠀⠀⠀⡀⣄⡪⢆⠢⢆⡠⠄⠀⠀⠀⢄⠀⠀⠀⠀⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠀⠀⠀⠀⠠⡵⠈⠀⠀⠰⠀⠀⠈⠠⡎⠆⠀⠀⢃⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠮⠄⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠶⠆⠀⠀⠀⠀⠀⢠⡄⠀⠠⠇⠠⠄⢠⠀⠄⠀⡷⡢⠄⠄⡇⠠⠀⠀⠠⡇⠀⠐⣎⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣤⠀⠀⠘⠋⠀⠀⠈⠃⠂⠀⠀⠀⠐⠒⣂⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠊⠐⠠⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⢴⠆⠀⡀⡐⠻⠀⠀⠀⠀⠀⢀⠔⠁⠰⠀⠀⠘⠀⠠⢀⡀⠀⢁⠈⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⠀⠀⠀⠀⣀⠰⠈⠀⠀⠊⢀⠀⠀⠀⠀⠘⡿⠧⢀⡄⠀⣀⣍⡆⢀⡀
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠐⣄⠀⣰⡦⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⡀⠀⠂⠀⠠⠑⠃⠀⠀⠘⠀⠀⢀⠄⠀⢙⡿⡜⡴⠮⠁
⠀⠀⠀⠀⡻⠁⠠⡄⠀⠀⠈⢣⡈⠀⠀⠀⠀⢠⡄⠈⠀⠀⠀⠈⠀⠀⠠⠘⠋⠀⠀⠀⠀⠀⠀⠁⠀⠠⢄⣈⠚⣹⠳⠧⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢄⠑⢄⠀⠀⠀⠋⠀⠀⠘⠀⢀⣄⠀⠀⡖⢈⡀⠄⠀⠀⠘⠂⠀⠀⠀⠀⠀⢡⡀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠈⠀⠀⠀⠁⠐⠀⠠⠀⠸⡿⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡞⠉⠂⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣳⣕⣀⣲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⡛⢛⢛⣋⠯⠽⠞⠛⠛⠓⠒⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠉⠀⠀⠀⠛⡡⠞⠉⣠⣴⣶⣤⣄⠉⠻⣷⣆⠀⢢⣜⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠃⠀⠀⠀⣠⢰⡆⣠⣤⣤⣀⠀⠙⠾⡿⠀⠀⠈⠁⠀⠈⠛⠁⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠀⠀⠀⠀⢀⡼⠋⠀⠙⠛⠪⢿⣿⡇⠀⠀⠀⠀⣴⣿⣽⣿⣷⣶⡄⠀⠙⠋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⠀⢀⡎⠀⣠⣦⣤⣄⡀⠀⠀⢀⣤⣦⠀⠀⠱⠶⠭⣝⣿⣿⠇⠀⠀⠀⠸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⠎⠀⠐⠻⠼⢻⠝⣻⠀⢠⣿⣿⣿⡆⠀⠀⢿⣢⣌⡿⠁⠀⢠⣾⣷⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⢈⠃⢀⣀⣀⠀⠀⠀⠀⢠⡿⣿⡜⣿⣧⠀⠀⠈⠛⠉⢀⡀⢴⢿⣿⣿⣧⠤⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⡎⠀⣾⣿⢹⡽⢷⡄⠀⣯⡉⢿⣿⡟⣩⠜⢏⠀⠀⡹⠋⠀⠈⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⢰⢸⠉⣿⠉⠙⠛⠋⠁⠀⠉⠉⠉⠉⠛⠨⠧⢠⠆⠰⠁⠀⠀⠀⠀⠀⣰⠻⢯⣿⣤⣟⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⢸⠨⢴⣿⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⡇⠀⠀⠀⠀⠀⢈⣇⠀⠎⠀⠠⡜⡏⠁⠂⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⢸⣏⣷⣡⢡⡿⠀⢰⣥⢿⣿⣿⣯⠵⣦⣉⣭⣷⣤⣤⡄⢀⡀⢸⣿⣿⠀⠇⠠⢀⠇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⡇⠀⠦⠩⡍⠀⠀⠀⠸⣿⣙⣥⣿⠏⡼⠙⠿⣾⣿⡉⠉⠉⠛⠻⢿⣽⠿⢷⣤⣔⣁⣀⡀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠠⠀⢰⣶⣷⢲⣲⣦⠀⠻⣿⣿⡏⡼⠁⠀⣠⣻⡍⢿⢤⣤⣄⡀⠀⠻⣁⠸⠄⢩⡖⠉⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣷⠀⠀⠀⠀⠅⠀⠉⢿⣿⠟⠁⠀⠀⠳⡞⡼⠁⠀⣼⣋⡴⣿⡌⢇⠀⠙⣿⡿⠓⢲⠶⠤⠤⠗⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣹⣀⠀⠀⢀⠈⢆⠈⣠⣦⣤⣤⣶⣦⠀⠀⠀⠀⣸⣧⣾⣾⢿⣿⠘⠂⠀⠀⠀⡴⠊
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣷⣶⣤⡉⡱⢆⡆⠠⡀⢸⠃⠩⣿⣿⡿⠃⠀⢀⡀⠀⠙⠚⠸⠧⠾⠗⠀⠀⢀⣠⠜
⠀⠀⠀⢀⠤⣚⣿⣿⠛⢙⠋⠸⢤⣄⣀⡀⠼⠮⠧⠀⢈⣠⣈⣢⣄⠘⠻⠶⠾⢿⡿⠀⢀⣤⡄⠀⢠⣤⣀⡴⢋⡡⠂⠤⡶⢖⠢⣀⣀⣀⡀
⠀⣤⣒⣳⣶⣿⣷⣖⠀⢸⣶⣶⣆⠀⠈⠉⠒⠀⠤⣠⠬⠭⠭⠉⠛⢿⠶⣬⣙⣛⠛⠓⠛⠹⢷⣿⣿⣮⣍⣀⠀⠉⠐⢠⠒⠀⠚⠉⢙⠉⠁
⠀⢕⠽⢁⠈⢹⠀⢸⡤⢼⡂⠛⠉⢙⡠⠤⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠄⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠁⠚⠯⣤⡀⠠⡞⠀⠀⠀⠀⠘⠉⠒⠶⡄
⠀⠘⡒⠴⠮⠭⣀⠘⠇⢀⡈⠁⠐⣤⠈⠒⠒⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⢀⣬⠶⣦⣤⡄⡀⠤⠤⠀⠄⠀⠀⠀⠐⠚⠛⠛⢲⠄⠀⠀⠒⠒⠚⣿⡄
⠀⠀⠀⠀⠀⠀⣤⣍⣀⠀⣄⣀⠀⢻⡄⠐⠒⠒⠐⠀⠀⠀⠀⠀⠉⠀⠉⠈⠙⠛⠛⠳⠤⠤⠤⠒⠒⠒⠒⠒⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠒⠒⠒
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡸⣿⢾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⣀⣀⣘⣛⣛⣛⣛⣛⣚⣛⣛⣛⣛⣛⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⡇⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⡇⣿⣿⣿⣛⣛⣛⣛⣻⣋⣛⣙⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⡀⣿⣿⢸⣿⣿⡇⣿⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⡇⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠙⠛⠉⠉⠛⠃⣿⣿⣿⣿⣿⡇⣿⣿⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠛⠛⣿⣿⣿⡇⣿⣿⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠙⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠃⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⢱⣀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣪⣸⡵⢎⠧⣽⢷⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠛⠛⠛⢻⠃
⠀⠀⠀⣠⠴⠶⢶⡶⠶⠶⣶⣿⣶⣶⣶⣶⡶⣿⠈⡇⠀⠀⠀⠀⠀⡰⣱⣽⣧⢻⣏⢿⢭⡿⢫⣿⣮⡳⡀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⢋⣭⠙⠶⢼⡄
⠀⠀⠞⡇⠀⠯⢾⠍⠩⠉⠍⠉⠉⠩⠭⠭⠅⣿⠀⡇⠀⠀⠀⠀⢰⢫⢵⣮⣽⡫⠊⠉⠑⠪⣻⣭⣾⣥⢡⠀⠀⠀⠀⠀⠀⣴⠟⢗⠄⠀⠉⠀⠰⡾⠻⣦
⠀⢸⠀⡇⠀⣛⢻⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣿⠀⡏⠉⢲⠀⠀⠀⣚⣾⠶⣗⠀⢰⡻⡳⠀⣔⡷⢾⣞⡊⠀⠀⠀⠀⠀⢸⣛⣄⠀⢾⢫⠉⡝⡦⠀⣤⣿⡃
⠀⠈⡄⡇⠀⣳⣹⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⣿⠀⡏⠉⠁⠀⠀⠸⣼⣾⡶⢫⡳⢄⣈⡀⢴⣴⠻⣾⡾⡼⠀⠀⠀⠀⠀⢸⣯⠉⠀⠘⢌⣒⡡⠃⠀⠉⣽⡅
⠀⠀⠈⠣⣀⣭⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⢣⡹⣺⡿⣹⡗⣶⡚⣿⡹⣻⡺⡡⠁⠀⠀⠀⠀⠀⠀⠹⣦⡿⠂⢀⣉⠀⠐⢷⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠙⠪⣝⠼⠯⣟⡯⠿⣘⠭⠊⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢨⠷⡦⣶⢴⡾⡅⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠛⠁⠀⠀⠀⠀⠀⠈⠛⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡴⢖⣲⠛⣖⡢⣦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠤⣤⠤⢤
⠀⠀⠀⠀⠀⢀⡀⢀⠀⢸⠀⠀⣶⠄⠐⡏⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡙⢾⣟⣿⣶⣟⣿⡟⢉⣷⡇⠀⠀⠀⠀⠀⠀⢠⡾⠈⡷⠤⠞⠤⠿⠤⠾⠤⠤⢤⣀
⠀⠀⠀⢠⠞⠁⠀⠀⡯⠭⠭⠭⠭⠭⠭⢽⢹⢲⠀⠀⠀⠀⠀⢠⠳⣾⡿⡟⢣⣀⠤⣀⠜⢿⢿⣯⢾⡄⠀⠀⠀⠀⣀⢸⣷⠀⡯⠭⠭⠍⠍⠭⠭⠩⠭⠩⠍⢧
⠀⠀⠀⡌⠀⠀⠀⠀⡯⠤⠭⠭⠭⠭⠤⢽⢸⢸⢲⠄⠤⡄⠀⢸⣋⣙⣿⠆⢼⠱⣒⢌⠆⢴⣿⣋⣹⡆⠀⣾⠟⢿⡆⠀⣿⠀⣗⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⢃⠀⠀⠀⠀⡯⠭⠭⠭⠭⠭⠭⢽⢸⢸⠚⠀⠀⠁⠀⠸⡡⣿⣧⣧⡔⠓⠖⠚⢢⣼⣼⡟⣼⠂⠀⠉⠉⠙⠦⢠⡿⠀⣿⠶⠶⣶⠶⠶⠶⠶⠶⢶⡶⣾
⠀⠀⠀⠈⠣⣄⡀⢀⡯⠬⡭⠭⠭⢭⠥⢿⣸⠞⠀⠀⠀⠀⠀⠀⢿⣾⣁⣽⣿⣵⣿⣮⣿⣯⣙⣮⡎⠀⠀⠀⠀⠀⠀⢸⣗⠀⡯⠭⠭⠭⠭⠭⠭⠭⠭⣭⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠃⠀⠀⠘⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠿⠦⣟⣻⣠⣟⡯⠴⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠯⠭⠍⠉⠉⠹⠭⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇
⠀⠀⠀⠀⢀⡴⣮⡟⣹⣗⣒⣒⣒⡒⣿⡇⣻⣷⣤⠀⠀⠀⠀⠀⠀⠀⣶⣽⣆⣼⠀⣹⠷⠶⠶⠶⠶⠶⡇⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⣴⢾⢾⣷⡷⣶
⠀⠀⣀⢀⣟⣒⣒⡇⢺⠧⠠⠤⠤⠤⣾⡇⣕⣒⣚⣧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠉⣠⣤⣤⣤⣤⣤⣤⡈⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⡏⡄⠀⠀⡆⣿
⠀⠘⠯⢠⡯⠭⠭⡇⣼⣿⣿⣭⣭⣯⣿⡇⡪⠭⠭⣯⠯⠼⠃⠀⠀⠀⣿⣿⣷⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢙⡆⠀⠀⠀⠀⢀⠃⡇⡁⠀⣿
⠀⠀⠀⠀⢿⣛⣛⡧⣹⣓⠒⠒⠒⠒⣿⡇⢝⣛⣻⠏⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⠉⠻⣿⡿⠿⣿⡿⠿⠟⢹⣿⡗⠒⠊⠁⠀⠀⠀⠀⢸⢀⣀⣁⣠⣻
⠀⠀⠀⠀⠀⠙⠓⢷⠽⢧⡄⠤⠤⢤⡾⠧⡖⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢿⠛⢶⣤⣀⣄⣀⣀⣤⡖⢻⡿⠇⠀⠀⠀⠀⠀⠀⠀⠙⢹⣉⣉⡟⠙
⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠀⠀⠀⠈⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠦⠚⠉⠉⠉⠉⠉⠉⠃⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣫⣝⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢀⣘⣿⣿⣿⣿⣮⣵⣿⣿⣿⣿⣃⣀⣀⡀⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢨⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡅⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢀⣀⣀⣀⣀⣠⣶⣾⣿⣽⣿⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠸⠿⠿⠿⠿⢿⣿⣿⣿⢸⣿⢸⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⣿⠸⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⠇⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠷⠒

⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠀⠀⣠⠴⠒⠒⠒⠂⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠳⠀⠀⠀⠀⠀⠀⢠⠆⠠⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣤⣀⠀⠀⠈⠀⠀⠀⢠⠊⠀⠀⠀⠁⠀⠀⣽⣿⣿⣴⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⢀⡀⠀⣼⠉⠉⠁⡉⠙⠲⣤⣀⠀⠀⠀⠄⠀⠀⣀⣈⣤⡾⠿⠛⠋⠉⣁⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢠⠖⠋⠁⠐⠢⡀⠈⠑⢄⢸⣿⣷⣶⡶⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⣀⠠⠜⣿⡀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⢢⡀⠀⢻⣿⠁⠀⠀⠘⢢⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⢶⣞⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠡⠀⠀⠠⠤⠒⢊⣀⣤⣴⠶⣟⣻⡭⠿⣖⣿⣭⢿⣒⣿⣷⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠐⠀⢦⣲⣞⣻⡭⢿⣒⣻⡯⢵⣖⣿⠿⣗⣺⡿⢽⣒⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄⠀⠸⣿⢿⣖⣻⠭⣕⣚⡯⢽⣗⣿⣯⢷⣚⣿⠿⣗⣛⣿⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⢃⠀⠀⠃⠀⠀⣿⣽⣗⣺⡭⢿⣒⣿⡭⢿⣚⣻⡭⣷⣚⣿⢽⣿⣿⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠐⠀⠀⠀⠀⠀⠠⣶⡀⢀⠇⡸⠀⠀⢰⠀⠀⣿⠭⠷⣖⣻⡭⢵⣖⣿⠭⣷⣺⣯⢽⣗⣿⣭⣿⡏⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠈⠀⠀⠀⠀⠀⠱⡌⠁⣠⠇⠀⠀⡀⠀⠀⣿⣿⡭⢿⣒⣯⠽⣷⣻⡯⣿⣒⣯⢽⠷⠛⠋⡹⢁⣀⣤⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠇⠀⢸⣟⣛⡯⠽⣖⣻⣭⠷⠞⠛⠉⠁⠀⣀⡤⠤⠚⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢀⠎⠀⢰⣷⠶⠶⠛⠛⠉⠀⢀⣀⠤⠴⠒⠋⠉⠀⠀⠀⠐⠀⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠁⠀⡀⠀⠁⠀⠀⠀⠀⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠐⢒⡉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⢂⡀⠤⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠁⠄⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢨⣨⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⣀⣀⣀⣀⣸⠄⡀⠀⠀⠀⠀⠀⢠⢖⡱⣚⡚⣷⢓⣟⣎⡲⣄⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣉⣉⣉⠉⡏
⠀⠀⣠⠂⢙⣛⡗⣒⣒⣒⣛⣚⣚⡓⣓⢺⠀⡇⠀⠀⠀⠀⢐⠥⡓⢷⡼⢗⡛⣺⢧⡾⣟⡮⣆⠀⠀⠀⠀⠀⠀⣠⣿⠋⠁⠷⠈⢙⣿⣄
⠀⢰⠀⠀⢸⢬⡇⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⡦⠤⠄⠀⠀⡨⣏⣟⡿⠎⢀⣤⠄⠑⣿⣛⡸⡍⠀⠀⠀⠀⠀⢴⠇⠈⢡⡤⠀⢤⡈⠁⠹⡦
⠀⢸⠀⠀⠸⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡖⠒⠂⠀⠀⢝⣯⣯⣧⢂⠈⠛⠁⡠⡿⣭⢱⣋⠀⠀⠀⠀⠀⣿⠃⠂⠸⡘⠤⢀⠃⠐⠓⣟
⠀⠀⠳⣀⢘⢙⡇⠉⠉⠈⠉⠉⠉⠉⠉⢸⠀⡇⠀⠀⠀⠀⠨⡚⡥⠾⣳⡷⣶⢺⣞⠷⣮⠗⠆⠀⠀⠀⠀⠀⠙⣆⣴⠄⠈⡛⠁⠠⣤⣼⠋
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠘⠒⠃⠀⠀⠀⠀⠀⠈⠪⣑⠯⢥⣟⡮⠽⣊⠕⠋⠀⠀⠀⠀⠀⠀⢀⠎⠈⢶⣄⣿⣠⢶⠁⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠋⠀⠀⠀⠀⠀⠙⠃⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣲⣷⣿⢙⣷⣯⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠰⠀⢩⠉⠂
⠀⠀⠀⠀⡀⠤⠠⣄⣨⣀⣨⣽⣀⣸⡤⡀⠀⠀⠀⠀⠀⢐⢟⣧⣹⡿⠝⡟⠫⣿⣧⣼⣻⡀⠀⠀⠀⠀⠀⣾⡇⢸⠉⠉⠙⠉⠉⠀⠉⠓⢢⡄
⠀⠀⠀⡎⠀⠀⠀⣗⡒⣒⣒⡒⣒⣒⡇⠉⣀⠀⠀⠀⠀⣎⠾⣿⡉⠁⠖⢋⠲⡉⣫⣿⢼⣅⠀⣀⣀⣤⠂⢹⡇⢸⠥⠤⠤⠤⠤⠤⠤⠬⠥⠽⡄
⠀⠀⠀⡇⠀⠀⠀⣗⣒⣒⣒⣒⣒⣒⡇⠄⣨⠭⠭⠃⠀⢟⢶⣿⣋⢀⠄⣀⠄⠉⣝⣷⢶⡋⠀⠹⠶⢾⠀⢸⡇⢸⠭⠉⠉⠉⠉⠉⠉⠉⠩⢩⡇
⠀⠀⠀⠣⡀⠀⠀⣗⣒⣒⣒⣒⣒⣒⡇⡤⠀⠀⠀⠀⠀⠘⣮⡟⣻⣷⣤⣧⣴⣿⡛⢯⣳⠁⠀⠀⠀⠀⠉⣿⡇⢸⣶⣶⣶⣶⣖⣶⣶⣒⣲⠟
⠀⠀⠀⠀⠈⠁⠀⠃⠀⠇⠀⠀⠃⠀⠏⠀⠀⠀⠀⠀⠀⠀⠙⠿⠭⣛⢿⣩⢿⣻⠽⠿⠋⠀⠀⠀⠀⠀⠀⠘⠇⢼⣂⡒⠐⠀⢖⣀⡒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣹⠄
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣄⠀⠀⠀⠀⢀⡠⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣈⢈⡁
⠀⠀⠀⢀⣞⣛⡫⢸⣗⣒⣒⣒⣸⣷⢸⣛⣳⡄⠀⠀⠀⠀⠀⣾⣿⣷⣾⡤⠟⠉⠉⠉⠉⠙⠣⢸⣷⡆⠀⠀⠀⠀⠀⠀⢸⠻⡛⡟⢛⡇
⠀⢠⡆⢺⢭⡭⣍⢸⡃⠀⠀⠀⢰⣷⢸⣭⡭⣿⣦⢠⠀⠀⠀⣿⣿⣿⣻⣤⣾⣿⣿⣿⣿⣿⣶⣼⣿⡇⠀⣄⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇
⠀⠀⠁⠹⣖⣶⣓⢸⡇⠄⠤⠤⠸⣿⢐⣖⣒⡟⠁⠀⠀⠀⠀⣿⣿⣿⣻⠿⣿⣽⣿⣿⣿⣿⡿⢿⣿⡧⠤⠟⠀⠀⠀⠀⢠⠀⢠⠀⠀⡇
⠀⠀⠀⠀⠙⠿⢭⣸⣇⡀⠀⠀⣸⣿⣨⠿⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⠦⣌⣉⣉⣉⣉⣉⡤⢾⣿⠇⠀⠀⠀⠀⠀⠀⠘⢾⠚⢺⡟⠃
⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠸⠄⠟⠉⠉⠉⠉⠙⠣⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠒⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣤⣼⣧⡄⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡧⢸⡟⢻⣿⣛⣋⣛⣙⣋⣋⣉⣉⣉⣉⣙⣛⣛⣛⣛⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣶⣿⢸⣿⣿⠛⣿⣿⡇⢸⡟⢻⣿⣭⡭⣭⣭⣭⣭⣭⣭⣭⣥⣬⣭⣭⣭⣭⣽⣿⡟⠻⣿⢸⣿⣶⣾⣿⣿
⠀⠀⠀⠀⢠⣀⣠⠀⠀⣶⣽⣾⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⡷⢾⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣿⣿⣿⣿⢰⣿⣟⣻⣿⣿⢸⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⠀⠀⡿⣿⣿⣿⢸⣿⣿⢸⣿⣿⠛⣿⣿⡇⢸⡷⢾⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⡟⢻⣿⠸⣿⣿⣿⣿⣿⢸⣿⣿⣇
⠀⠀⠀⣶⣾⣿⣿⣶⡌⡯⠿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⡇⢸⣧⣼⣿⣥⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢸⣿⣿⣷
⠀⠀⠀⠀⢸⣿⣿⠀⠈⡿⠿⣿⣿⢸⣿⣿⢸⣿⣿⡋⣻⣿⡗⢸⣧⣼⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣿⡟⢙⣿⢰⣿⣯⣽⣿⣿⢸⣿⣿⡟
⠀⠀⠀⠀⢸⠿⢿⠀⠈⡿⣿⣿⣿⢸⣿⣿⢸⣿⣿⣿⣿⣿⡗⢸⣇⣸⣿⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⢰⣿⡿⢿⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠹⢸⣿⣿⢸⣿⣿⡋⣿⣿⡇⢸⣏⢹⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣟⢙⣿⢸⣿⣿⣿⣿⣿⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢸⣿⣿⣿⣿⣿⡇⢸⡟⢻⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣿⣿⣿⣿⢸⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠟⠋⠘⠿⠋⠉⠉⠁









⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢀⣾⣿⣿⣿⡷⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡀
⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⢀⣀⣀⡀
⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⢸⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠟
⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣻⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠛⠿⠿⠿⠟⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣘⣛⣛⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣛⣛⣛⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣄⡘⠄⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⠤⢄⣡⠀⣄⠀⠈⢩⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⢀⣀⣀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠠⠤⠀⠀⠈⢣⠈⣴⠆⡜
⠀⠀⠀⠀⠀⠖⠢⠄⡀⢯⣀⣀⠀⠀⠈⠀⠉⠉⠉⠉⠉⢀⠇⣀⣀⠠⠭⢄⣀⠀⠀⠀⣀⡗⡈⠀⡄
⠀⠀⠀⠀⠀⣠⡵⠋⢀⣤⣶⠾⠗⠂⠠⠎⠉⠉⠉⠉⠀⣄⢈⠉⠡⣄⠀⡉⠍⠑⠀⡟⠘⠀⡆⠀⠙⠀⠐⠶⠶⠆⢀
⠀⠀⠀⠀⠠⠋⠀⡰⠋⠁⢀⡀⠀⢀⠀⠙⢂⡲⡒⠂⠈⢁⡼⡸⢤⠄⣠⠤⠤⠤⡆⡐⢆⠀⣡⣢⠈⠂⢧⠀⠤⣀⡀⠙⢦⡀
⠀⠀⠀⠐⠁⠀⡜⠀⣤⣚⡙⠀⢰⠃⠲⡄⡾⠳⠈⠛⠓⢫⣥⣤⠔⠀⠘⢦⠄⠀⢡⠘⢸⠀⠛⠁⡰⣌⢮⡆⠸⢻⣝⢦⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠷⣤⣀⣀⣉⠉⠓⠒⠦⠴⣖⣒⠛⢯⡥⢀⠀⠠⠠⠄⠠⣬⠥⣠⡷⣠⠀⢠⡇⢸⢱⡇⠀⠋⡀⠀⣸⡞⡇⠀⡇
⠀⠀⠀⠀⠀⠀⡆⠀⢢⠀⠉⠉⠉⠒⠒⠤⠤⢌⣉⠁⠛⠛⠀⠶⠒⠀⠒⠒⠚⣩⠞⠁⠀⠀⣇⠘⣆⠫⣄⡀⢀⣠⡞⢠⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠙⠢⠤⠤⠖⠃⠀⣠⠀⠀⠈⠁⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘⢆⠈⠲⢬⣉⣉⡡⠔⠁⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢄⡀⠤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⢀⣀⠠⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣧⣤⣤⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣷⣶⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢍⠙⡶⠊⣀⡤⠬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣶⣿⣷⡟⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⠉⠘⢶⣟⣺⣿⢦⣴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⢉⣿⠞⣹⠮⠿⠟⠂⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⣠⢽⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⣷⠞⢉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠂⠖⠻⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠌⣿⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠺⠻⠿⣯⣟⢻⣿⣾⣿⣤⣊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⠀⠀⠀⠘⠛⠽⣿⢿⣽⣗⣖⣠⢄⣀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣄⣀⣀⣀⣀⣀⣰⣧⣤⣿⣥⣤⣭⣭⣋⣉⣀⣀⣰⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣝⣛⣩⣛⣻⣟⣽⣟⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⢄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠦⠀⠀⠀⢀⣀⡂⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠀⠀⠀⠀⡾⣛⣻⢿⡖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢻⣇⣬⡴⢾⡇
⠀⠀⠀⠀⣀⣄⠸⣿⣿⣿⣿⣶⣶⣿⣷⣦⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣏⢽⡿⠫⡥⠏
⠀⠀⠀⢾⠋⠀⣀⣀⡀⠀⠉⠙⢿⣿⣿⣿⣶⣾⡿⠦⣤⠀⠀⢠⡶⢶⣿⣿⣏⠇⠀⢁
⠀⠀⠀⠀⣠⡿⠋⠉⠉⠑⢠⣬⠛⠛⠉⠉⢹⣿⣶⣶⣿⣤⣤⣾⣦⣤⣿⢏⡿⣿⡄⠀⣀⣀
⠀⠀⠀⢠⣿⡀⠠⠴⣤⣉⡉⢀⠰⣶⣶⣶⣾⢟⣽⣿⣿⣿⣿⣿⢏⣿⣟⡟⠀⢸⣷⠀⠸⣿⠀⠲⣤⣤
⠀⠀⠀⠸⣿⠐⠠⠤⠄⠠⢌⣉⣙⣿⣛⣛⣥⣾⠟⠛⠛⠟⠻⣿⣾⣿⠟⢀⡴⠀⢿⣧⣤⡈⠣⠀⢹⣿⣧
⠀⠀⠀⠀⢻⣧⣀⠢⠀⣀⡁⠛⠛⠿⠿⣿⣿⣧⠀⠀⣀⣤⣄⣹⣿⡟⣼⣿⣇⠀⠸⣾⣿⠇⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠻⠽⣛⣒⣓⠲⠶⠶⢦⣙⠻⠿⠛⡉⠐⠉⠸⣿⣄⠀⠈⠁⠀⠀⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠤⠍⣉⣋⡁⠀⠒⠂⠻⣿⣷⣤⣤⣤⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠚⠲⠽⢛⣻⣿⡛⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡾⡧⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⡷⣥⡀
⠀⠙⠋⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣽⣯⡧⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⠠⡷⠷⢚⠆⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⣟⠐⠀⠀⠀⣀⠀⠀⠀⣴⣖⣉⡁
⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡷⡿⠉⠀⠠⠤⠴⠦⠄⠀⠗⡆⣖⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠤⠰⠀⠀⠀⢛⣻⣿⠒⠒⠒⠒⠶⠒⠂⠈⢷⡥⢶⠛
⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⡤⠄⠀⠀⢀⠀⠀⠀⡼⠓⢘⡆⠀⠀⠀⣶⣾⠄⠼⢾⡗⢀⣸⡄
⠀⠀⠀⠀⠀⠀⢀⠀⠰⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠨⠇⠀⠀⠈⢉⠀⠀⠰⠛⠃⡠⠷⠀⠀⠀⣟⠻⠀⡈⢿⡅⠸⠁⣇
⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠘⢶⡀⠀⠀⢀⡤⢾⠭⣧⢀⠀⣂⣀⡀⡰⠛⢠⣤⣼⣉⢛⣿⢻⠄⠀⢀⡇⠀⣧⠁⡞⣇⠐⡟⣿⠒
⠀⠀⠀⡇⠀⣼⣠⣸⣧⣷⣶⣶⣿⢶⠶⠿⠿⢷⣛⣛⣛⡙⠯⠭⢿⣷⢰⣾⠿⠻⣿⡿⣿⡟⣷⣾⣿⣴⣦⣻⣶⣯⣿⣅⣿⣿⣷⡆
⠀⠀⣠⣧⣸⡭⣟⣹⣿⣻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠛⠓⠦⠬⢭⣍⣀⣚⠛⠾⠿⢿⣷⣿⣿⣿⣿⠍⣿⣿⣿⣷⡽⠿⣷⠃
⠀⢠⠤⣗⣨⠶⣫⠽⠋⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⢠⡀⠀⠀⠀⠀⠉⠉⠙⠓⠒⢶⣤⣤⣥⣉⡛⠺⠿⠿⣿⣿⣷⣶⣾
⠀⠀⢘⣩⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢯⣷⣦⣤⣄⡉⠁
⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣠⢞⡥⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢠⡖⢋⣩⡼⠷⡄⠀⠀⠀⠀⠀⠀⢠⢞⡭⠂⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⡞⢡⠘⣿⡆
⠀⠀⠀⠀⣏⢸⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣼⠛⣉⣥⠴⠾⡇⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⡇
⠀⠀⠀⠀⠹⣌⠆⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢼⣋⠉⣤⠶⡟⠁⠀⠀⠀⠀⠀⠀⣧⢣⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡧⢸⠀⣿⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣤⣿⣤⣧⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⣯⣼⣤⣿⡇
⠀⠀⠀⠀⠀⠈⣳⣶⣶⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣶⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠐⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿

⠀⠀⠀⠀⠀⣀⢀⣤⢠⣄⢀⡀⠀⠀⠀⠀⠀⠀⢠⠖⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣠⣤⣶⣤⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⣰⣞⠛⣶⡀
⠀⠀⠀⢀⣘⠋⢾⡏⠉⡽⠎⢛⣀⠀⠀⠀⠀⠀⠙⠦⣀⣬⣬⡃⣤⠀⠀⠀⠀⠀⠀⠀⡇⣼⣿⡿⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡙⠿⠾⠏⡁
⠀⠀⠀⠾⠿⠸⡿⠀⠀⢛⡿⠸⠿⠆⠀⠀⠀⠀⠀⢠⣿⣿⡸⢞⣵⢟⣀⠀⠀⠀⠀⠀⣧⣿⣿⡇⠀⠘⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⡸⠁
⠀⠀⠀⢶⣶⠰⣿⡶⢠⣾⡷⢰⣶⠆⠀⠀⠀⠀⠀⠘⣿⣿⣧⣌⠡⠿⡋⠀⠀⠀⠀⠀⠹⣿⣿⣷⡗⣰⣿⣿⠇⠀⠀⠀⠀⠀⣠⠀⣾⣮⣩⣶⡆⢠⡀
⠀⠀⠀⠈⢩⣄⢶⣷⢻⣶⢆⣬⠉⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢻⡂⢯⡀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⠀⠿⠿⠿⠿⠇⢸⣿
⠀⠀⠀⠀⠀⠈⠀⠛⠘⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠑⠻⢦⡀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⣀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⡀
⠀⠀⠀⣿⣿⣷⣿⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⢸⠟⢉⣉⠛⣿⠀⢠⢀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠻⣿⣿⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠳⣄
⠀⢀⡄⣿⣿⣿⣿⢰⣀⣠⣶⢾⣿⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⣴⣴⠀⠀⠀⠀⠀⣿⣿⡈⠀⢁⣿⣿⠀⠀⠀⠀⠀⡞⠀⢠⡀⢙⣶⣄⠀⠀⠸⡆
⠀⠘⠇⣿⣿⣿⣿⢸⣿⠶⠶⢸⣿⠀⠀⠀⠀⠀⠀⣿⣶⣷⣾⣷⣿⠀⢿⢿⠀⠀⠀⠀⠀⣿⣿⠟⠛⠛⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠸⣿⣿⣿⠀⠀⢀⡇
⠀⠀⠀⣿⣿⣿⣿⠸⣿⠛⢻⢸⣿⠀⠀⠀⠀⠀⠀⠙⠿⣿⢿⠿⠟⠀⢸⢸⠄⠀⠀⠀⠀⣿⣿⣈⣠⣀⣿⣿⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠉⠉⡇⢀⡼⠁
⠀⠀⠀⠛⠋⠩⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⣄⣀⣠⣎⡞⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⣤⠼⠃⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡄⠀⠀⠀⠀⢼⠄
⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⢫⣻⠇⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⢀⠰⠚⠋⠁⠸⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠟⠀⠀⠀⣾⣭⣶⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⣤⡤⢸⠩⣭⣭⡭⢻⠠⣤⡀
⠀⠀⠀⠉⠛⠗⣶⣶⣤⣀⡀⡶⠒⢦⠀⠀⠀⠀⠀⠀⢨⡿⢿⡅⠀⣴⡟⠉⢻⣆⠀⠀⠀⣶⡆⠀⢬⡥⠀⢠⣥⠀⠀⠀⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡆
⠀⠀⢠⣶⣶⣴⣬⣿⣿⣿⣿⣿⣾⣿⣷⣦⣄⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⡇⠀⣾⣧⠀⢸⣷⠀⠀⠀⠿⠟⣵⡎⠿⠿⠿⠿⠏⣶⠹⠿⠃
⠀⠀⠘⠿⣟⢙⡿⠿⠿⠿⠿⠿⢿⡟⢙⡿⠿⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⠀⡟⠀⠀⠀⣿⡇⠀⣿⣿⠀⢸⣿⠀⠀⠀⢸⣿⣮⣴⣿⣿⣿⣿⣷⣭⣾⣿
⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠉⠀⠀⠉⠀⠉⠀⠀⠀⠃⠀⠀⠀⠙⠁⠀⠙⠋⠀⠈⠋⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⠀⢀
⠀⠀⠀⠀⠤⣴⠚⢹⣱⠆⠈⠉⠡⠿⠄⢀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⣤⠀⠀⠑⠢⡀
⠀⠀⠀⡀⠀⠁⠑⠤⠅⡀⠠⠀⠠⠂⠀⠟⠉⡀⠘⠂⠀⠀⠀⠀⠀⠁⠤⠊⠀⢸⠀⠀⠠⠀⢄⠀⠀⣐⠗⠆⠐
⠀⠀⠀⠑⢴⣿⠀⠀⠂⠀⠙⠓⠒⠑⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⢤⠀⠀⠐⠀⠀⠖⠒⠊⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠒⠄⠀⠀⣠⠖⢄⠀⠀⠀⠀⠀⠀⠀⣠⢺⠅⠀⠀⠙⣾⠇⡇⠀⠀⢀⡤⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣐⠈⡀⠀⠇⠺⠀⠸⢟⣉⠵⠀⠀⠀⠀⠈⠛⠃⠀⠀⣿⣷⠀⠀⠲⠆⠂⠐⠶⠿⣋⣤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⠀⠀⠁⠀⠀⠶⠶⠞⠋⠉

⠀⠀⠀⢀⠠⠤⠤⡄⠐⠒⠄⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠛⠀⠱⢖⠒⠚⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⡄⠀⠀⠀⢀⣀
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠠⠀⠠⠧⠄⡀⠀⢀⠀⢀⣀⠠⠐
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⡀⠤⠂⢁⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⣠⣄⡆
⠀⠀⠑⠒⠂⠀⠌⠑⠤⡆⠁⠈⠁⠀⠀⠂⠁⣠⠀⠀⠀⠀⠀⠀⠄⠁⠳⠶⠶⠤⢤⡀⠀⠀⢀⣄⠀⠀⠀⢀⣰⡿⡟
⠳⠴⠀⠀⢀⠀⣠⢀⡀⠀⠀⠐⠞⡢⠀⣤⢾⠋⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⠁⠀⠀⠀⢿⡜⡇⠘⠁⠀⠙⠋⠁
⠐⠂⠾⢟⣳⠎⠉⠉⣀⠤⠀⢸⠠⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠁⠐⢯⣾⡉
⠀⠀⠈⠀⠀⠐⠀⠀⠠⠀⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠫⠉⠁⠀⠀⠈⠉⠙⠉⠉⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠷⣦⣀⠀⠐⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⢀⠌⣤⢇⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⢔⡏⠅⠠⡀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡔⢦⡖⠀⠀⠀⡤⠂⢠⡴⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢱⣿⣀⡦⣤⠬⠶⠾⠿⢋⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⢨⡄⠀⡀⡌⠷⠎⢀⣾⢻⡆⢠⢂⣤⡄⠀⠀⠀⠀⠀⣰⠟⠩⡍⡽⣄⢿⡅⣿⣀⣀⣠⠄⢴⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣶⠇⡆⠃⠑⢤⣴⣿⡿⡾⠃⢁⣾⣇⡏⠀⠀⠀⠀⠀⡟⠜⠀⣿⣇⠀⠼⠋⢻⣄⡉⣤⢋⠾⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⠀⠀⠀⢾⡿⣼⠀⠙⠛⠉⠉⠋⠀⠀⠀⠀⠀⠀⢻⡘⠾⠤⠋⠀⠀⠀⠀⠈⠀⠈⠢

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠐⠒⠊⠉⠉⠸⣿⢿⢄
⠀⠀⠀⠀⠀⢀⡏⢴⠶⣶⡀⠀⠈⠉⢐⣒⣄⠀⢀⣶⣶⡺⣀⣀⠠⠤⠤⠤⠤⠐⠒⠒⠲⡁⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢻⠈⠓⠋⡇⠀⠀⠀⠻⣼⡟⠀⣳⡒⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢀⣱⣄
⠀⠀⠀⠀⠀⢀⢼⠤⠀⠤⣿⡍⠉⠹⡏⠈⡇⢰⡏⠈⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣏⣽⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⡇⠈⠳⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢉⠏
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣟⡛⣛⣛⢛⢛⡛⣟⠀⠀⠀⠀⠀⠀⠀⠀⡠⣧⡤⣀⡎
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡀⢸⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡇⠀⠀⠀⠀⠀⠀⢸⣿⡉⢹⣾
⠀⠀⠀⠀⣼⢭⣬⣭⣭⣭⡭⡭⢷⠀⠀⠀⠈⠁⡅⠀⠈⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⡘⠛⠽⠝⢻
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠢⠃⠐⠜⠀⠢⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢘⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⠤⠤⠤⠷⠶⠶⠾⠾⠧⠤⡄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡶⣖⣶⡚⣲⣖⠒⣲⣖⠒⣲⣖⠒⣲⣖⠒⣲⣞⠓⣶⣶⢶⡄
⠀⠀⠀⠮⠥⠤⠤⠤⠤⠤⠤⠤⠤⠥⢶⠀⠀⠀⠀⢺⡐⣿⣽⡿⣿⣽⡿⣯⣽⡿⣯⣽⠿⣯⣽⢿⣯⣽⢿⣯⣽⢇⡗
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠛⠺⠻⠲⠺⠻⠶⠞⠿⠖⠞⠟⠖⠟⠷⠖⠿⠷⠶⠻⠳⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡠⠶⠒⠛⠉⠉⠉⠉⠛⠒⠶⢤⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⠋
⠀⠀⠀⠀⣰⠋⡠⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠟⠀⢴⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠆
⠀⠀⠀⣰⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡄⠀⠔⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⣠⠉⢠⡀⠀⠀⠠⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⢂⡀⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⢠⡀⡀⠀⠀⡰⡛⠁⠀⠀⠀⠀⠀⠀⢘⡄⣀⣡
⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢆⠀⢁⠜⡝⠁⠀⠀⠀⠀⠀⢀⠤⠚⠛⠛⠋⠀⠀⠀⠀⡀⠀⠀⠱
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣿⢠⠃⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠑⠚⠋⠀⠀⠀⠐⠀⠀⠂⠁⠀⠀⠀⡀⠠⠀⠀⠒⠂⠀⠀⠀⡔
⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⡇⡞⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢀⣤⣴⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⣜⠣⢄⡀⣼⣸⠁⠀⠁⣀⡖⠋⠁⠀⠀⠀⡴⠋⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠤⠂⠈⠁⠀⠁
⠀⠀⠀⠀⠀⣍⠳⠄⢀⠀⠈⠉⠉⠉⢑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⡡⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢸
⠀⠀⠀⠀⠈⠆⠉⠒⠢⠄⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⣀⡤⠔⠂⠀⡄⢪⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠑⠢⠤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢢⣄⣀⣀⣀⠀⢀⠔⠒⠀⠀⠀⠀⠀⢐⣉⣶⠆⠀⣀⢬⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⣠⠴⠛⠉⢀⡤⣚⡭⠟⠀⠀⠀⣰⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⡠⢚⡥⠋⠁⠀⠀⠀⠀⠐⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢢⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠛⣓⡶⠀⠀⠈⠑⣣⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠐⢁⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣸⠞⠁⠀⠀⢀⠔⠋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡰⠂⠀⠰⠤⠀⠀⠠⠂⠀⠀⠀⣠⠛⡀
⠀⠀⠀⠀⠚⠢⠀⠈⠁⠀⢀⡴⠊⠁⠀⠀⡠⠚⢁⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⣤⡄⠀⠀⢯⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠙⠲⠶⠶⠖⠒⠋⠁⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡴⠋⠀⠀⠀⣀⠬⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⡠⠔⠊⠁⢰⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⣀⠀⠀⡀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⢀⠞⠁⡠⠔⠉⠀⢀⡴⠒⠁⠀⠀⠀⠀⠀⠀⢰⠀⠈⠂⠐⠋⢹⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⣰⣫⠖⠉⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⣀⣀⠀⢨⠀⠀⠠⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⢀⡾⠋⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠉⡄⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢲⡀⠀⠂⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠤⠤⠴⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⠤⠤⢤⠉⣤⠤⠤⢤⠩⣤⠤⠤⢼⢇⣯⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠵⣦⣶⣦⣤⣵⣶⣶⣦⣤⣵⣶⠔⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠽⠯⢯⡭⣿⣭⠯⢽⡿⡗⢶⡁⢒⡄
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣂⢄⡀⠀⠀⠠⣽⠀⣠⠤⠀⢠⡎⣾⡿⢷⡟⣄⠚⣿⠁⢀⡠⣐⣶⣶⣤⡀
⠀⠀⠀⠀⢠⢏⢣⡀⠀⠻⣍⠛⠷⠶⢦⣼⣷⣷⣴⣿⣿⣧⣻⡶⣿⣷⣯⡼⢿⠶⠛⣩⠟⠀⠀⡜⡹⡄
⠀⠀⠀⠀⢸⠊⠉⠑⠀⠰⡾⠷⣶⢄⠘⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠠⣶⠾⢷⠆⠀⠊⠉⠑⡃
⠀⠀⠀⣾⣿⡳⡀⢰⡦⢘⣷⣾⣶⣷⣷⣷⣿⣿⠛⠿⢿⣿⠿⡿⣿⢿⣿⠶⣿⣿⣷⣾⡃⢴⡆⣀⢞⣾⣷
⠀⠀⠀⠘⢿⣿⢞⣡⣼⣿⣿⣿⠟⡉⣾⣿⠿⣔⢶⢺⣿⠈⠉⢁⣀⣨⣁⣰⠈⠻⣿⣿⣿⣧⣌⡳⣿⡿⠃
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⣸⡿⢫⠭⠙⣭⣿⡿⢿⣬⣿⣿⣿⣿⣿⣿⣾⣇⠸⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣏⣴⣿⣿⣿⣀⢀⣢⣿⡏⢙⡿⢷⣤⣌⠋⣿⣿⣿⣿⣿⣿⣦⣹⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣟⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⡇⠀⣿⠉⠀⣿⣸⣿⣿⣿⣿⣿⣿⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⢻⣿⣤⣾⡿⠟⡛⠿⢾⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣿⡿⣿⡿⣿⣿⢡⢀⣠⣭⣤⣶⣿⢻⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠚⢉⣿⡟⣿⣶⣿⣟⣛⡻⣿⡟⠉⣻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣇⠛⣿⢹⣿⣿⣿⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣟⣹⠟⢿⣿⣮⣫⣩⣽⣿⣿⣵⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⣷⣽⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⢿⠈⠉⠙⢿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠬⠀⠀⠀⣀⡀
⠀⠀⢠⣄⣾⣦⡀⣠⠤⡹⠻⣆
⠀⢀⣠⣼⣿⢿⠄⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠖⠓⠘⠛⣿⢰⡄⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣧⣿⣞⣋⠉⠈⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⠾⢻⡙⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⣿⡃⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸
⠁⠀⠸⢳⣿⢳⡦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⢙⢹⣧⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⠒⢰⣾⣖
⠀⣀⣴⣶⣿⠻⠇⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⠯⠅⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢈⣽⡟⠙⠢
⠛⠁⢘⠹⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠰⢸⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠘⠀⠉⠨⣿⣿⣤⡀
⠀⠀⡝⢂⣿⠄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⢴⣾⣟⠇⠀⠙⠆⠀⠀⡠⠖⡀⣠⣤⠀⠀⠀⠀⢀⣤⢤⣾⡶⠀⠈
⠀⠀⡄⠘⣿⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⢹⡏⠃⠀⠀⠀⠀⠀⠀⣀⡀⣹⡿⠲⢄⡀⠀⠁⠀⢘⣽⡿⠖⡤
⠀⠰⠈⢤⣿⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡇⠃⠀⠀⠀⠀⠀⠘⠉⠉⢿⣿⣤⡀⠀⠀⠀⠀⢀⢸⡇⠂
⠀⠐⠀⢸⣿⡂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⡇⠤⠀⠀⠀⠀⠀⠀⡠⠀⢺⡏⠀⠈⠀⠀⠀⠀⡀⢼⡇
⠀⠁⠈⣺⢿⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⡇⢈⡀⠀⠀⠀⠀⠀⠀⠀⢾⡟⡉⠂⠀⠀⠀⠀⠁⣸⡇⠰
⢸⣳⣄⢼⣾⡧⣀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⣭⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⢊⡇⠀⠀⠀⠀⠀⠠⠁⣼⡇⢀⡄
⣻⣀⣈⣻⣻⣃⣉⣹⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣏⣈⣿⣗⣉⣵⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣸⣉⣻⣟⣉⣇
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣥⣄⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢫⣟⣽⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣸⣅⣌⣥⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣾⣼⣿⣧⣾⣯⠉⠙⠻⠷⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⣿⣶⣦⣄⠀⣀⠀⠀⠘⣱⠿⠿⠿⡿⠟⠉⣿⣷⣦⣄⠀⠀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣮⠙⣲⣿⡇⢀⡀⠀⠀⠀⢠⣷⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⢀⠴⣒⣦⣶⣶⣤⣄⡀⠀⠀⡨⢋⣾⡝⣿⡟⢉⣁⣀⣀⠀⠾⠿⠿⠿⠯⠀⠀⠂
⠀⠀⠀⠀⠀⡐⢡⠞⠁⠐⠂⠒⠢⢝⠻⡦⠉⣷⣷⣹⣷⢿⣳⠀⡈⠋⠀⠀⠀⠀⠐⠂⢀⡈⠉
⠀⠀⠀⠀⠠⠁⡏⠈⠀⢄⣠⠄⠬⡈⠋⣀⢾⣻⣿⣇⣿⡮⢱⢧⣿⡶⣤⠠⠈⢆⠀⠠⠎
⠀⠀⠀⠀⢸⣾⡇⠀⠠⢸⡇⣾⣟⣦⣀⠁⠘⣿⠻⠛⣤⢹⣮⢿⣿⣷⡻⡀⠀⠈⠿⢦⣄
⠀⠀⠀⠀⠀⢿⣷⡀⠀⠜⠳⣌⣙⠡⠁⠀⠀⣿⡄⢺⣿⡇⢿⢼⣻⡷⣶⠀⠀⠀⠀⠀⠈⠙⠢
⠀⠀⠀⠀⠀⠈⢿⣷⣄⢀⠐⠀⠐⠀⠀⡈⢠⡿⠈⡞⠛⠛⣓⢫⡟⣿⣿⡇⠀⠁⠀⣀⣀⠀⠶⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣬⣀⣀⣀⣨⣴⡿⠁⠀⠁⠞⠛⠸⢾⣿⢿⡾⢟⣀⣀⣤⣿⣿⣧⡀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠻⠟⠛⠉⠀⠀⠀⠀⠈⠀⠀⠀⢙⣮⣿⣾⣿⣛⠿⠟⠛⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⣇⠀⢠⡤⢄⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣷⣦⡈⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠙⠿⣧⠈⠂⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠉⠓⠐⠃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⣀⣠⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⣷⣶⣶⣶⣷⣴⣮⣴⣼⣶⡿⠛⠓⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣿⣿⣿⠿⣿⣿⣿⣿⡟⠀⠀⠂⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢃⠀⠀⠀⠶⠶⢿⣷⣶⣶⣷⣿⣿⣿⠶⠶⢶⡂⠐⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠃⠀⠀⡘⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣀⣠⣀⡄⠰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⠀⠀⠈⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⡟⢛⢉⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡨⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠶⠟⠟⠛⠛⡿⠛⠿⠿⠿⠿⠟⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⣀⠤⠐⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣊⣉⣉⣠⣈⠙⠁⢀⠀⢍⡲⣌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⠋⠉⠉⢀⠀⠄⠀⠉⠀⠆⢇⣀⣈⠗⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⡭⠀⠀⠀⠂⠀⠀⣀⠤⢚⡿⠁⠸⠒⠤⠤⠚⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠒⢀⣰⡏⠀⠛⠁⠀⠀⡀⠄⠒⡊⠠⠂⠀⠀⠠⠖⠋⠛⡛⠻⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠨⠾⠛⠒⢦⠤⠒⠈⠁⠀⠀⡀⠠⠒⠁⠀⠀⠀⠀⢀⠤⠂⠀⠀⠀⡀⢰⠃⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡗⢀⡀⠀⠀⠁⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠂⢰⠃⡾⠟⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠥⠿⠂⠠⢄⡀⠀⠀⠀⡠⣾⠇⠀⠀⠈⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡟⢸⡷⠚⠁⢠⠢⣀⣠⠤⢶⡾⠠⠄
⠀⠀⠀⠀⠀⠀⠔⡁⠀⠒⠂⢀⠂⠤⡈⠢⣀⠀⠈⠉⠁⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⡇⢀⠠⠰⡏⣿⠋⠀⠀⠈⣴⢶⠇
⠀⠀⠀⠀⠠⠀⠀⠔⠁⠀⠀⢠⠌⠢⡀⠑⡈⠳⢄⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢂⢹⡀⠀⠀⢿⣾⡖⡤⠖⠛
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⣰⠯⠄⠀⠐⠀⠹⠀⠀⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡀⠤⠜⣸⢼⠷⠒⠋⠁⠉⠙⠃
⠀⠀⠀⠀⠀⢀⠡⡀⠀⡼⠁⠀⠀⠀⢀⢆⡧⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⢷⠻⠷⠁
⠀⠀⠀⠀⠀⠈⠢⣌⠒⠀⠤⠀⢠⣂⠔⠝⠁⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠑⠄⠀⠉⠑⠂⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡰
⠀⠀⠀⠀⠀⠀⠀⣨⠌⠉⠉⠭⠭⠭⠭⠡⠭⠭⠭⠭⢭⠬⣭⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠀⠀⠐⠀⠐⠈⠁⠉⠉⠉⠋⠋⠍⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠲⠦⠶⠶⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀
⠀⠀⠀⠀⠐⠀⠀⠚⠋⠉⠉⠉⠉⠉⠙⠛⠚⠉⠛⠚⠋⠋⠋⠉⠀⠁⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠁⠀⠈⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠐⢀⠄⠂⠈⠁⠈⠉⠀⠢⢄⠀⠈⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢠⠀⣆⣔⠀⠀⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠎⠁⠀⢈⠆⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠄⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠴⠠⠀⠀⠀⠊⠄⠀⠀⠀⠐⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠂⠀⢸⠀⠠⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣽⠟⢻⣏⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⢁⢠⢴⠊⠐⢀⣨⠉⠕⡢⢦⢬⡉⠁⠀⢁⠅⢤⣀⠀⢂⢤⣄
⠀⠀⠀⠀⠀⢀⠌⢠⠔⠚⣉⡀⠀⢠⡖⠗⢒⣦⣐⣂⣁⢄⣩⡆⣤⢷⠖⠢⡆⣐⣀⢌⠑⢿⣆
⠀⠀⠀⠀⠀⡈⠀⣎⠀⠞⣁⡅⢀⠏⠘⢠⠋⠀⠀⠀⠀⠀⠀⠀⡉⠉⢹⡇⢡⠀⢈⠽⠂⢈⠈
⠀⠀⠀⠀⠀⠠⡀⠈⠓⠤⠤⣉⣀⢤⣀⡆⡄⠉⠙⠀⠀⠀⠐⢡⡴⠾⢼⡧⣤⣭⢥⣤⣴⣶⣷
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠠⠀⠼⠯⣈⡻⠓⠲⣒⠲⠶⠴⠲⢾⠷⠶⠊⡀⠤⠄⠰⠼⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠐⠉⠠⠾⠅⠠⠀⠀⠢⠸⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠄⠂⠐⢀⠀⢠⠀⠀⡐⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⠈⠀⠌⡂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠀⢁⣀⡔⢐⠨⡀⠐⠒⠑⠀⢸⠀⣀⡄⠄⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠉⠚⠛⠉⠄⠂⠔⠨⢘⠳⡦⠄⡠⠐⠜⠡⢐⠠⠀⠁⠈⠪⠐⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡿⠿⠿⠿⠿⠿⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠉⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⣤⣤⡄⠀⣿⣿⠀⣤⣤⡄⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠇⠀⠿⠟⠀⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡆⣸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣠⣴⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⠾⠿⠟⠋⠉




⣿⣿⣿⣻⣟⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⣛⣿⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⣚⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣙⣳⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣾⣫⣼⣤⡴⠶⠶⠶⠶⣾⣿⣷⣶⣄⠀⠀⠀⢻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡆⠀⠀⠈⢿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢟⣯⣽⣶⣶⣶⣤⣒⠤⣀⣽⣿⣿⣿⣿⢀⣄⢀⡄⠈⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣫⣾⣿⣿⣯⣿⣶⣾⣟⣿⣷⡌⠻⣿⣿⢟⡽⠛⠉⠈⠽⡄⠘⣿⣿⣿⣿⣳⡀
⠀⠀⠀⠀⠀⣄⠲⣿⠽⠟⠿⣿⣿⣿⣿⣿⣿⣿⣀⡛⣿⣧⠘⣷⠉⣀⣤⣶⣿⡟⣿⡄⠘⣯⣀⣉⣙⢧
⠀⠀⠀⠀⢀⣿⠟⠉⣀⣀⠁⠀⠉⠉⠉⠉⠻⣿⣿⣿⡌⠙⣤⢺⣿⣭⡾⠟⠻⣿⡛⠁⠀⠘⣿⣿⣿⣾⣧⡄
⠀⠀⠀⠀⠘⠁⣴⣿⣿⣿⣷⣄⠀⠀⢴⡷⢶⡿⣿⣿⣴⠚⢫⡈⡞⣧⠀⠀⠀⣹⣧⠀⠀⠀⠸⣿⣿⣿⡟⠛
⠀⠀⢀⡀⣀⣰⣻⣿⡿⠿⣿⣿⡆⠀⠈⢿⣿⣿⣿⣷⣿⡇⢸⡇⢧⣿⣧⣿⣿⣿⣿⣇⣀⡀⠀⢻⣿⣿⣷⣾⣆
⠀⠀⢻⣇⣀⣀⣀⣀⣰⢀⣀⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣧⢸⡇⢸⣿⢻⣿⣿⣿⡿⠉⠉⠉⣶⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠘⠛⡟⢻⢿⣿⣿⣿⣿⣿⡇⢀⠀⠀⠀⠀⢸⣿⣩⡇⣠⡄⣼⣿⣟⡿⠛⣛⣂⣤⢠⣤⡿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢰⣷⠈⠄⠹⣿⣿⣯⡽⠁⡀⡴⣾⣶⣷⣾⣿⣿⢲⣿⠃⣿⣿⢫⣦⠞⠉⠙⠃⠈⠉⢁⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⢸⣇⠀⠐⠽⠟⠋⢀⢜⣹⣿⠿⠿⡟⢟⣙⠿⠁⠏⣸⣿⣿⢏⠀⠀⢀⡀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⣿⣷⣤⡀⢀⣒⣡⣾⣿⣿⣶⣿⣿⣿⢟⢵⡆⢰⣿⣿⣿⣿⣧⣴⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⠟⢁⢈⡿⣿⣿⣿⣿⣿⠃⠀⠀⣾⣿⣿⣿⣿⣟⠉
⠀⠀⠀⠀⢽⠿⠿⣿⣿⢭⡿⣿⣿⣹⣿⣿⣿⣷⡿⢃⣴⣶⠘⣿⣾⣿⣿⣿⠏⠀⠀⠀⢻⣿⣿⣿⢿⣿
⠀⠀⣇⢸⣿⢶⣶⠸⣯⣾⣿⣶⣭⣙⡛⣋⣩⣥⣾⣿⣿⣿⡇⢹⣿⡟⡿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣾⣯⣧⣀
⠀⠀⡟⡞⣿⣼⣿⡆⢻⣿⣿⣻⢿⡏⢱⣿⡏⠉⠉⢻⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢩⣭⣤⣤⣤⣤⣤⢰
⠀⠀⡏⢡⠸⣿⡿⣇⠈⣿⣿⣿⣿⣆⢸⣿⣷⣦⣶⡾⡿⠿⠿⢆⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⡏⠁⢾
⠀⠀⠛⠣⠄⢹⣿⡷⠶⠾⠿⠏⠿⣿⣿⣿⣿⣶⣿⡿⣟⡻⣿⣏⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢡⡗⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠛⠛⠟⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣽⣥⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣰⡶⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡿⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣯⠀⠀⠀⢹⣇⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠟⠛⠉⠉⠀⢻⡆⠀⠀⣀⣿⣦⣀⡾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⢷⣿⠛⠉⠁⠀⠀⠀⣀⣠⣴⠾⠛⠿⠾⠛⠿⣧⣌⡉⣱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣰⡶⢶⡄⢹⣇⢀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠙⠷⠾⠃⣸⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣴⠾⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⢀⣠⣤⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡟⠉⠀⢀⠀⠈⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢀⣾⠛⢻⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠻⠶⠾⠃⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢷⣤⣀⣀⣀⣠⡾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⠉⠙⠉⠉⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿

⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⢉⠙⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠒⠂⠀⠀⠘⠒⠀⠤⡀
⠀⠀⠀⢀⣠⡤⠟⠓⠛⠉⠁⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⢀⡠⠒⠉⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⡞⠀⠀⠀⣀⠤⠴⣶⣻⡯⠥⠼⠥⠀⠀⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⢧⠀⣀⡤⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢠⠟⠁⠀⠀⠀⢀⣀⣤⡤⠤⠐⠒⠐⣒⡛⠩⠤⣄⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⣿⠀⠀⠀⢰⣼⡿⠷⠖⠒⠚⠉⠉⠉⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⡖⠀⠂⠄⡄⠀⠀⠲⠀⠀⠻
⠘⡷⠖⠋⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡴⠋⠀⠀⠀⠀⠀⠀⢸
⣾⠁⠀⠀⣀⣠⠤⠶⣖⣛⣫⣭⠥⠦⠔⠂⠀⠈⠑⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠺⡈⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⢻⡀⠀⠊⢉⡴⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣹⢗⣽⠋⠀⠀⢀⣀⣤⠤⠶⠶⣲⠾⠿⠯⢥⡀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠃⢸⠇⠀⠀⢰⢟⠉⠈⠙⠻⣼⠃⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡰⠁
⢸⠀⠈⠢⠤⠴⠋⢸⡀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠐⢤⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣼⠄⠒⠚⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠁
⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠤⠤⠤⠄⠀⠀⠤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⢀⠇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡸
⠀⠙⢆⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⣀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠂⠒⠀⠚⠀⠀⠀⠀⠤⠧⠠⠴⠒⡶⠁
⠀⠀⠀⢻⠛⠉⠉⠛⠉⠉⠙⠯⠉⠙⠯⠉⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣙⣓⠀⡇
⠀⠀⠀⢸⡆⠀⠀⠤⠤⠤⠤⠤⠤⠀⠄⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡁⠀⠠⠤⠤⠤⠤⢤⣤⠶⡶⠶⠀⡇
⠀⠀⠀⠺⡉⠀⠰⠶⠶⠶⠒⣒⣒⣛⡫⠁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠁⠀⠀⠀⠀⠠⠤⠤⠴⣶⣾⣿⠀⡆
⠀⠀⠀⢺⡅⠐⠶⠶⠶⠚⠛⣛⣚⣓⡭⠁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠁⠀⠀⣀⣀⣀⣀⣠⣵⣶⣶⢶⠀⡇
⠀⠀⠀⢾⡅⠀⠶⠶⠶⠒⠚⢛⣒⣛⠻⠁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⣤⣤⡶⣶⡃⣠⠇
⠀⠀⠀⠈⠳⣄⡀⠒⠒⠒⢚⣓⣛⣾⣥⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠈⠉⠭⠋⠔⠁
⠀⠀⠀⠀⠀⠀⠻⡍⠉⠉⠉⡭⢉⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣛⣛⣿⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣧⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏⠉⠉⡷⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠁⠉⠉⠀⠀⢸⡇⠀⠀⡇⠀⠀⢀⣉⡿⠆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢾⣇⣀⣠⡷⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⢀⣀⣤⠴⠖⠋⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢀⣈⣷⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣠⠞⠋⢁⣀⡈⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢠⠞⠉⠉⠉⠳⣄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⠀⠀⠀⠀⠀⢹⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠙⣦⡀⠀⢀⣠⠏⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠁⠉⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡶⠶⠿⠿⠿⠶⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣴⡾⠟⠉⢁⠤⢖⣒⣒⠒⠦⣄⣀⡀⠈⠙⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢾⠟⠛⠛⠻⣿⣾⣿⣅⣀⠀⡰⠁⠀⠀⢀⣽⠿⠿⠿⣿⣿⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣄⣀⢀⣼⠟⠁⠈⠉⠙⠽⡇⠀⢀⣴⡏⠀⠠⡶⢦⠺⠁⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠈⢉⠛⢦⠀⠀⠀⠀⠀⢻⢇⡞⡻⠇⠀⠀⠀⠀⠺⣇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣿⠷⣦⣄⠀⠀⠀⠺⣷⣤⣄⠀⠀⠀⠀⠉⢿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⢱⠀⠈⠻⣏⡽⢷⣦⣼⣀⠈⠑⠶⣶⢶⠖⠋⠀⠈⠻⣕⢄⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⡜⠀⠀⠀⣻⣿⠿⣿⣿⣿⣶⣮⣐⠾⣿⡗⠢⠄⣀⠻⠟⠒⠛⠐⠆⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠃⠀⢠⠎⣿⣿⠀⠈⠻⣿⣿⣿⣿⣿⣦⣝⡻⢶⣾⣷⣾⠀⠀⠀⠸⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠠⠀⡞⠀⢻⣿⣦⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⣶⣿⢻⣿⣯⣤⢄⠀⢣⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢿⣿⡿⣿⢿⣿⣷⣄⠀⢸⣿⣿⢿⣿⣿⣿⣿⠉⠻⢿⣿⣿⠘⣷⠈⣆⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⡉⠻⣮⢣⢻⣿⣿⣦⣸⣿⣿⡀⠉⠻⣿⣿⣷⣄⠀⠉⠻⢧⣿⡀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠃⠀⢻⣇⣸⢏⣿⣿⣿⡉⠻⣿⣦⡀⠈⠙⢿⣿⣷⣦⡰⠎⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⡀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠟⣻⣿⣷⣄⣿⣧⣙⢦⡰⠆⢹⣿⣿⣿⣶⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢇⠀⠀⠀⠀⣠⣿⣿⠿⡇⠀⠈⢽⣿⣿⣿⣿⣿⣷⣝⠶⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣠⠴⠚⠛⢷⣦⣄⣧⣀⡈⠒⠺⠿⣿⣿⣿⣿⣿⣷⣌⣀⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠁⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡠⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠣⢠⠀⠀⠚⠓⠀⣠⠴⠒⠊⠉⠉⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢶⠔⠀⠺⣢⣄⡈⠉⠜⠁⠀⣀⡠⠄⠒⠉⠁⠀⠙⠄⠀⠀⠀⠀⠀⢀⡠⠖⠋⢉⣉⠥⠔⣢⠟⣀⡀
⠀⠀⠀⠀⠀⠀⢀⠃⠎⠀⠀⣀⡀⠀⠀⠀⠀⠒⠶⣶⠬⣉⡉⠁⠒⠢⠄⠐⠒⠒⠒⠒⠉⣁⡤⠒⠊⢁⡠⠖⠋⠑⠦⠐⢆
⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⡁⠀⠀⠀⠀⠀⢤⠔⠒⢒⡂⠀⠪⠅⡂⢀⠀⣀⠒⠦⠤⠒⣉⣀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⣐⣒⠒⠀⠋⠁⠂⠀⡀⠈⠑⠲⢴⣊⠱⠆⡀⠀⠁⠠⢇⠈⢠⠶⣣⠄⢀⡀⠠⠂⠈⠉⠁⠒⠤⣀⠀⠈⠃
⠀⠀⠀⠀⡠⠂⡠⠀⠀⠃⡄⠀⠆⠀⢦⢌⠑⠢⠄⠀⢀⣠⠀⡇⠘⢆⠀⠀⠀⣘⡛⠠⣵⣦⡀⢠⢰⠀⠀⠲⠖⢄⠈⠣⡀⠀⠈
⠀⠀⠀⡰⠡⢪⣪⠗⠀⡼⡔⠐⠂⠜⠌⠂⠑⠀⠀⢀⠵⠒⢤⢸⣁⠘⠀⡴⣠⠭⠙⠃⢀⣬⠅⠁⢄⡄⠰⠶⣟⠛⣷⠀⢡
⠀⠀⠀⠃⠀⠀⡇⡎⠀⠑⠁⠸⠆⢚⠀⠀⡆⢠⡗⠹⣀⢀⣠⢈⡥⣤⣈⢑⣒⣄⠀⠀⠐⠠⠬⠉⠀⠙⠓⣀⢸⠂⠚⡁
⠀⠀⠀⢂⠀⠰⣧⠑⠤⠤⢚⡶⢠⠈⢀⠇⠃⣀⣀⡀⠈⢉⣀⣀⣉⠢⠄⢒⣋⣭⡥⠄⢄⠑⠒⠦⠤⠀⣤⡩⠞⡠⡰⠁⡘
⠀⠀⠀⠈⢢⡑⠄⡀⠤⠲⠉⠀⠁⢀⠎⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠑⠜⠒⠂⢀⠨⠊⢀⠔⠁
⠀⠀⠀⠀⠀⠉⠂⠤⠄⠀⠠⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⠀⠠⠄⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⡞⡛⠳⡤⢄⡤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⡇⢧⢃⣀⠇⠀⠀⡏⠀⢻⠐⠒⠒⠘⢿⠉⠙⡍⠉⠉⠉⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠦⠙⠦⣥⡥⣤⣤⣀⠁⠀⣼⣶⣤⣤⣀⣼⠃⢀⡇⠀⢀⡔⠐⠀⣼⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢗⡶⣄⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠉⠉⠒⢿⡷⢦⣼⠀⢠⠸⢿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡏⠛⠳⢿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠉⠀⢀⣿⣦⡜⠁
⠀⠀⠀⠀⠀⠠⠖⣾⠿⠗⠿⣿⣶⣤⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡆⠀⣼⣿⡿
⠀⠀⠀⠀⠀⣄⣸⠀⠀⠀⠀⠀⠈⠉⠻⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⢀⡔⠁⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠣⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠐⠁⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠂⢀⣴⠦⠦⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⠀⡆⣰⣽⠃⢠⠄⠈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⡇⢿⠃⠀⢿⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠸⡄⠳⠘⢆⠀⠀⠀⡠⠋⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣵⣄⠀⠤⣤⣴⡏⠀⠀⠀⠈⠙⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠻⣿⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠄⢀⡀⠀⢀⣀⣠⣬⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣖⠈⠉⠙⠁⠀⠐⣶⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣏⠙⠿⠯⠗⣶⣶⣒⣲⣾⠯⠙⢛⣽⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⣿⠿⠿⣿⢿⠦⠤⠤⢤⣤⡤⠤⠤⠤⢤⣤⡼⠿⠿⢿⣻⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡂⠁⠐⠒⠒⠚⠛⠓⠒⠒⠒⠚⠃⠁⠀⢰⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠧⠤⠤⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠼⠿⠟⠛⠛⠉

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠶⢦⣤⣄⣀⡀⠀⠘⡇⠈⡏⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣀⠉⠙⠛⠲⠮⢽⣿⣛⣺⡷⠶⣧⣤⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡷⢲⣦⣤⣄⣀⡈⠩⢿⡟⠲⠶⢭⣭⣛⡓⠶⠦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠿⠞⠃⣼⣿⣭⡽⢻⡶⢲⡦⣤⣄⣀⡈⠉⠙⠓⠲⢬⡟⣿⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⢀⡾⠁⠈⠉⠀⢸⡇⢸⡇⣸⣿⣏⢉⣿⣷⡶⢶⣼⣷⠟⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣤⣀⣀⣠⣤⠴⠞⠋⠁⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⢸⡇⣨⡟⢹⡏⠛⠋⣠⠿⣿⣶⠟⠉⠓⠶⠦⢤⣤⣤⣤⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢛⣁⣀⡀⠀⠀⠀⠀⠀⣸⡟⢹⡇⢸⡇⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉⠁⣿⠫⢭⣉⡉⠛⠲⣦⣴⣏⣹⡇⢸⡇⢸⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣄⣠⡽⠟⠿⢧⣤⣈⡉⠙⣻⡷⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠙⣷⣈⣽⠟⣷⣦⣤⣄⣉⣽⣟⠿⢶⣤⣌⣉⠛⠻⠶⣤⣄⣀
⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⢀⡿⢷⣤⠿⠛⣷⡾⣤⣄⣀⠈⠉⠙⠓⠶⢤⣌⣉⡽⣷⠀⠀⠀⢀⡀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣿⠀⢸⡏⢹⣿⡶⢦⣤⣤⣀⡀⣹⣀⣿⠖⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣧⢾⡟⠛⠋⠻⣿⣏⣽⠿⢯⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶⠶⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡶⢻⡇⢸⡇⠀⢀⡾⠁⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⣿⠀⢸⡇⢸⣧⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠶⠶⠖⠒⠋⠉⠀⠀⠀⠀⣿⠀⣸⡧⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⣿⠋⢹⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢻⠄⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣼⠶⠛

⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⢰⡟⢹⡆⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠙⠋⢀⡼⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⣠⡶⣏⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⢾⣍⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠙⢦⡀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁⠀⠀⠀⠈⠙⣦⠀⢀⣴⠞⠁⠀⠀⠀⠀⠈⠻⣄⠀⠀⠈⣳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣴⠒⢦⠀⠀⢸⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣴⠋⣡⣤⡉⢳⡶⠖⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠙⠶⠋⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⢯⣠⡗⢀⡟⠛⢷⡈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⣀⡴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⣤⣤⡴⠞⠀⠀⠀⠙⣦⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠛⠉⠉⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⡇⠀⠀⠀⠀⠀⠀⢰⠇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠙⣦⠀⠀⠀⠀⠀⠻⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣌⣙⣉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣠⣤⣤⣼⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠀⢀⣀⠀⠈⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠰⣏⢙⡇⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠒⠒⠒⠒⠒⠒⠒⠒⠒⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠛⠙⠋⠛⠛⠋⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



⣏⣹⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡒⢰⠒⠲⡄⡆⠒⡖⠂⡴⡆⢰⣆⡲⢰⠀⠀⣖⣒⠀⠠⣒⠂⠒⡖⠂⡖⢲⢠⡖⠒⣦⢰⡠⠂⣶⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣁⢸⣀⡠⠃⡇⠀⡇⢰⠋⢻⢸⣏⡹⢸⣀⡀⣏⣉⠀⢀⣈⡷⠀⡇⠀⡏⢹⡘⢆⣀⠟⢸⠙⣄⣿⣉
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⣶⣶⡶⠶⠶⠶⠷⠾⠷⠶⢶⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣿⢹⡇⠀⢸⡟⣿⡆⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣿⢸⡇⠀⢸⡇⣿⡇⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣼⡇⠀⠸⠷⠿⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⣀⠀⠀⠀⠀⠀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢿⣿⢻⡿⠀⠀⠀⠀⠙⣿⠟⠁⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⠀⠀⣠⡿⣱⡟⠁⢀⣼⢿⣶⣾⠛⣿⡄⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢿⣯⣙⠻⣶⣟⣼⠟⠻⣶⡾⣣⣿⣷⣿⣿⣿⣷⣶⣶⣶⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠉⠛⢿⣿⣿⠻⢶⣴⡟⣵⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠈⠛⢷⣾⣿⣾⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣹⣿⣿⣿⡛⠛⣛⣛⡛⠛⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⣿⡇⠀⣿⣿⡇⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣿⡇⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠿⠷⡿⠃⠀⠛⠛⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠙⠻⣦⣄⣀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡷⣦⣀⠀⠀⢀⣽⠟⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠈⣻⣟⠁⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢀⣼⢿⡿⢶⡿⠃⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⢸⣏⣹⣧⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⡾⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠶⠶⠶⠿⠿⠿⠿⠶⠶⠶⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⣠⡾⠋⠀⠀⠘⢷⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⣠⡾⠋⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⢀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⢀⣤⡾⠛⠁
⣠⣤⣤⣶⠶⠟⠛⠉⢀⣠⣴⠾⠛⠁
⠉⠁⣀⣀⣠⣤⡶⠾⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⣳⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⠌⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠉⠛⠷⢦⡴⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⣠⣾⣷⣤⣌⡹⣋⠻⣿⣿⣿⣿
⠀⠀⠀⠀⣴⠿⢷⡝⠟⠁⠀⠀⠀⠀⢀⡾⠛⠳⣄⠀⠀⠀⠀⣿⣿⣿⣿⠋⣀⡉⢳⣴⣾⣿⣿⣿⣿⡿⢻⣮⣞⠻⣿⣿⣿
⠀⠀⠀⠀⠿⣶⡾⣃⠀⠀⠀⠀⠀⠀⠙⠆⠀⢀⠞⠀⠀⠀⠀⣿⣿⣿⣿⣄⠙⢁⡼⣿⣿⣿⣿⣿⣿⣧⣻⣿⣿⣱⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡁⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢿⡿⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⢀⡬⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣟⣛⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠃⠠⠦⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛




⠀⠀⢀⠄⠀⠰
⠀⠀⠐⠕⢦⡀
⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠙⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠶⣦⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠰⠦⣄⡀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠘⣧
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠛⠉⠉⠉⠉⠛⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠘⠇⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⡟⠁⠙⠞⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠙⣧⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠾⠃⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⣠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣿⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⣷⢄⣼⠟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣤⣤⣴⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣧⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠘⢷⣌⠳⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡶⠶⠚⠉⠁⠻⢷⢶⡀
⠀⠸⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⠁⢀⠀⢀⡤⠀⠀⠈⠷⠳⣌⠀⢈⠇
⠀⠀⣆⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣥⣴⣲⣯⡽⠶⠞⢄⠑⡜⢭⠽⠃
⠀⢀⣧⣀⡚⠆⠀⠀⣀⠀⠀⢀⣠⣤⣶⢻⡛⠋⠉⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡀
⢀⠈⢫⢙⣿⣾⢢⣠⣴⠖⢿⣿⣻⡉⠉⠨⠏⠉⠂⡄⠀⠀⠀⠜⠁⠀⠀⠀⠀⢀⢤⡈⡦⡀
⣀⢀⣾⠷⠹⢿⡏⣿⣷⡀⠘⣫⠟⢠⠥⣴⢫⣦⠖⠎⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⡀⢀⣄⠀⠀⢀⣀⣀⡀
⢻⡀⠖⣦⢈⢸⡧⢛⠥⠖⢚⢫⣥⠭⢬⣉⢉⣉⠴⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⠰⠉⠠⢺⠿⠿⢿⣿⣶⡄
⠀⠳⣤⣉⣴⣷⣆⣐⠈⢷⣶⣼⣿⣀⢠⢤⢼⡺⡟⠡⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡐⢖⠇⡈⡀⠀⠉⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠩⠞⠳⠄⠖⠑⠂⠢⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⢀⠻⣈⠀⠀⠰⠂⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠡⢼⠄⠊⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠠⠈⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣤⣶⣴⣾⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠁⠀⠀⠈⠉⠙⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣤⡀⣰⣄⣠⣄⢀⡦⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢻⠛⠃⠙⠋⠙⢻⡇⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢸⡆⠀⠀⠀⠀⢸⠇⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠈⣧⠀⠀⠀⠀⣾⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢿⠀⠀⠀⠀⡟⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡆⠀⠀⢠⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣇⠀⠀⢸⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣛⣛⣛⣛⣛⣛⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣭⣭⣭⣭⣭⣭⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠶⠶⠶⠶⠶⠶⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⣛⣛⣻⠟⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠂⣀⠳⣄⠀⠀⠀⠀⠤⠐⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⡁⡼⠋⠉⠙⣜⡢⠬⠔⠚⠃⠀⠉⡁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⣔⠢⣸⡘⢿⠁⢾⡷⢠⣇⡠⠔⢊⡩⠬⠭⣽⠈⠈⠉⠉⢻⡗
⠀⠀⠀⠀⠀⢀⠊⠈⡇⡇⠉⠻⣦⠄⢒⣉⡤⠶⠮⠥⠤⣤⣀⡀⠉⠉⠉⠒⠤⠃
⠀⠀⠀⠀⠀⢸⠀⡰⢱⠃⠀⠀⣸⠋⡏⠀⠀⠀⠤⣄⠀⠀⠀⠉⠛⢭⡓⢦⣀⠀⠀⢀⣀⡤⠖⠚⠛⠲⣄
⠀⠀⠀⠀⠀⠸⠭⠴⠧⠤⡴⣞⠇⣸⠀⠀⠀⠀⡰⡹⡆⠀⠀⠀⠀⠀⠙⢦⡉⠯⡉⠉⠀⠀⠀⠀⠀⣀⠏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡽⢠⣧⣀⣠⣤⣺⣷⣕⣃⣀⣀⣀⣀⣠⣤⡴⢛⢦⣌⠑⠒⠒⠒⠒⠋⠁⢀⡼
⠀⠀⣀⡤⠔⠒⠒⠊⠐⠛⢳⠃⣾⢽⣌⢣⣏⢉⣩⠝⢛⣻⠥⣄⣀⡀⠀⢨⠋⡀⠉⠙⠲⣦⡤⠴⢶⠚⠫⠤⣄⡀
⣠⠞⠁⠀⠀⢠⢔⢞⠟⢋⡏⢸⠛⠦⣬⡳⡙⢆⢹⡐⠉⠉⡇⠀⠈⢫⢩⡇⠀⠁⣠⢔⠩⠂⠉⠁⠈⠉⠉⠓⢦⡙⢦⣀⣀⣀⣀
⠳⢤⣤⡤⠴⢳⢡⠃⠀⡼⢀⡏⠀⠔⠻⣧⠜⣎⠳⡳⣕⣚⣁⡤⠔⢃⡏⠓⠒⡶⠡⠋⢀⣄⣀⡤⠤⠴⠒⠒⠛⠉⠉⠁⠀⣿⡆
⠀⡎⠀⠀⠀⡇⢂⠀⠰⣇⣸⠀⠀⠀⢀⣿⡇⡇⠱⣌⠢⠐⡇⢀⣀⣼⠥⠤⠖⠓⠋⢉⣉⣀⣀⣠⠤⠤⠤⠤⠖⠒⠒⠒⠛⢉⣿
⠀⡇⠀⠀⠀⢱⠸⣀⠄⠀⠀⠀⢀⢀⡰⣻⣧⠆⠀⠈⠳⠼⢉⣀⣐⣒⣒⣈⣉⣉⣉⣉⣀⣀⣠⣤⢤⡤⠤⠤⠤⢤⠤⢤⠤⠼⠿
⠀⠸⡄⠀⠀⠀⠱⢜⠢⢠⣀⣀⡠⢞⡵⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢠⠇
⠀⠀⠈⠢⣄⡀⠀⠀⠉⠒⠒⠒⣊⡥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣉⠓⠤⠤⠤⠤⠔⢋⣠⠔⠃
⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⡩⠛⠉⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡜⠀⢀⣴⣶⣄⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠙⢿⠇⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⢠⠞⠁⠀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⡛⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⣴⣿⣿⡆⠀⠀⠆
⠀⠀⠀⠀⠀⢰⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣄⡀⠀⠀⠀⠙⠿⠿⠃⠀⡰
⠀⠀⠀⢀⣠⣾⠠⣶⡆⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⣄⡀⠀⠀⢀⡠⠊
⠀⠀⠐⡿⢿⣿⡤⠈⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉
⠀⠀⠀⠰⢿⡟⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠉⠻⣿⣿⡿⠋
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣠⣾⣷⣄⠀⠀⠀⠀⠙⢄⡀
⣿⣿⠀⣤⣶⠀⠀⠀⠀⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠛⠋⠀⣿⡏⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀
⠀⠀⠘⣿⡇⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⡀⠀⠀⠀⠙⠛⠛⠀⢀⠏⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⢀⡀⠔⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⣤⣤⣤⣤⣄⣀⣠⡤⠖⠦⡄⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⢹⣖⣒⣶⣖⣶⠀⠀⠀⠀⠀⠀⠀⢘⣜⡣⠛⠛⠛⠛⠉⠉⠛⠳⠦⠖⠂⠀⠀⠀⠀⠹⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣩⡷⠋⠁⠀⠀⠹⣽⡀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⢎⡇
⠀⠀⠀⠀⠀⣠⠶⠿⣧⡾⠋⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⡞⣡⡍⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⢰⣧⣘⣃⣿⡀⠀⠀⠀⠀⠀⠀⠀⣻⣏⡀⠀⠀⠀⠀⠱⢬⣥⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠸⣅⢠⠇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣗⣼⠂
⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣟⣯⣄
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢡⣬⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⣼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⠥⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣶⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣇⡟⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠛⠀⠀⠀⠀⠀⠸⢿⠿⣿⣿⠿⡿⠟⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠈⢳⠌⠡⡞⠁⠀⠀⠀⠀⠀⠀⣿⣿⢭⢹⣿⣿⣿⣶⣶⣶⢶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⠰⢠⣄⡀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣬⣥⠇⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠛⠛⠛⠛⠛⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠠⢾⣿⠟⠁⠉⠻⢿⡖⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄
⠀⠀⠀⠀⢀⣛⡘⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢛⢻⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣻⡬⠼⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡄
⠀⠀⠀⣴⡿⠛⠿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⣹⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣛⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⣶
⠀⠀⢸⣿⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠻⢶⠞⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠷⣄⠟
⠀⠀⠈⠿⣷⣦⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⠉⢨⡗⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠄⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠈⣀⠀⠐⡦⡀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣖⣀⣀⠧⠌⠀⣈⠁⠹⣆
⠀⠀⠀⠀⠀⢩⡉⠲⠬⠉⠉⠓⠒⠲⢤⣀⣀⠀⠀⠀⡄⠈⠁⠀⠀⠀⠀⠈⠳⠄⠀⢯⣣⠀⠈
⠀⠀⠀⠀⠀⠀⢑⣤⠐⣄⠉⠙⠲⢄⣀⡀⠀⠀⢀⡴⣃⣠⣤⣄⣀⠀⠀⠀⢀⡀⣀⣈⠁
⠀⠀⠀⠀⠀⡸⢋⠟⠁⠀⢉⡓⠒⠒⠒⠉⡛⠫⠭⠤⠊⣀⠤⠂⢀⠍⠙⠋⢽⠆⠀⠸⠂⣧⡀⠤⠤⠄⡀
⠀⠀⠀⠀⠐⠕⠃⡠⠒⠉⠀⡀⠀⠀⠀⢠⡹⡓⢤⡀⢰⠁⠀⢰⠀⠈⠀⣀⡈⠀⢠⠊⢀⠘⠉⠠⢞⡉⠀⠠⡀
⠀⠀⠀⠀⠀⢀⠎⠀⠤⢮⣁⡀⠀⠀⠸⠦⢅⣀⣤⣀⡀⠃⠀⠤⡤⣄⣀⢹⡇⠀⠇⡴⠁⠀⠰⡔⡀⣀⠀⢆⠈⢆
⠀⠀⠀⠀⠀⢸⠀⢄⣀⡀⠀⠉⠉⠀⢐⠤⡐⠚⡷⠄⠈⠠⣀⣼⠁⣹⣿⢋⠃⠀⠘⠀⡇⠀⠓⠂⠀⢀⢱⡀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⡀⠭⢭⡄⠐⠯⠥⠤⢬⠥⠄⢤⣶⣶⣤⢒⣏⢁⡵⠃⠀⠀⢠⠀⠀⠀⠠⣀⠀⢀⡜⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠣⡀⠙⠢⢤⣁⡤⠔⠁⢀⠞⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠈⢣⡀⠐⠤⠈⠉⠀⠐⠁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⣀⣀⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⠠⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢉⣉⣙⣓⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⣾⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡍⢻⠉⠩⠍⣿⣛⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣰⠏⠉⠉⠉⠁⣿⡀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣰⠃⠀⠀⠀⠀⠀⠈⠻⣦⡙⢛⣛⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡁⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢩⠙⢿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⡽⠷⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡏⣴⠛⠙⢦⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠳⣄⣠⡼⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣼⣧⣤⣤⣤⣤⣼⣧⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇

⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿