Baked Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠶⠶⠶⠶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⣾⡿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠻⠛⠛⠛⠛⠛⠿⠿⠿⠿⠟⠛⣿⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⡇⠀⠀⠀⣠⠀⢠⡶⠛⢷⣆⠀⢀⡀⣴⠞⠳⣆⠀⠀⠀⣰⠞⠳⣦⠀⠠⠄⠀⠀⠀⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠛⠃⠘⢷⣤⡾⠃⠀⠘⠃⠻⣦⣴⠟⠀⠀⠀⠻⣦⣴⠟⠀⠙⠁⠀⠀⠀⣾⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⢛⡿⠟⠉⡀⠀⠐⠀⠄⢉⡿⠛⠋⠉⠍⠉⠙⠻⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡁⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⣹⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠜⠁⢀⡴⠃⠀⠀⠔⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⣿⣿⣿⡿⠋⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠶⠶⠶⠶⣶⡶⢶⣾⠇⠙⠻⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠛⠛⠉⠙⠛⠛⠋⠉⠉⠉⢹⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⣠⣿⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣈⣻⣷⡄
⠀⠀⠀⠀⠀⠀⣿⣟⣛⣛⣛⣛⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣭⣭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⣭⠭⠭⠭⠽⠿⠿⣭⣿⡇
⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠇



⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⠿⠻⠿⠛⠿⢿⠿⢻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢠⡄⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠈⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⠀⠀⠀⠠⣈⣸⢿⣂⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⢀⣄⠀⠒⠀⠐⢰⠈⠀⠁⠀⡅⠄⢀⢠⠀⠀⠀⠀⠀⠅⠀⠘⠙⡂⢸⡈⡃
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠁⢀⠈⠂⡀⠀⠃⠁⠉⠋⠉⠀⠉⠀⠐⢀⡀⠘⠈⠂⠈⠊⠁
⠙⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠒⢛⠃⠁⠀⠀⠀⠐⠂⠀⠀⠀⡈⠀⠀⠀⠀⠀⠠⠴⠈⠀⠀⠀⠀⠀⠀⡀⠀⠆
⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢐⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⠐⣀⠂⢀⡀⠤⠀⢀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡿⠴⠆⠀⠀⠀⠀⢀⡀⠀⠤⣴⣶⣤⠄⣂⠀⠂⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⡔⠀⠀⢀⣀⣀⠖⠈⠀⠀⠀⠀⠂⠉⢿⡌⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠀⠀⢀⡈⠛⣃⢀⠀⠀⢁⠀⢀⢀⢸⠇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠙⢌⡀⠀⢐⠢⢀⡿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠑
⠀⠀⠀⠀⣴⣿⣿⣿⠀⠈⠁⠀⢀⢀⡌⠀⠀⢀⠞⣀⠀⠄⠐⠒⡦⠓⠛⠁⠐
⠀⠀⠀⣼⣿⣿⡿⠿⠣⠄⢲⢾⣏⠊⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡐⠠
⠀⠀⠀⢈⣟⣿⣗⠠⠀⠐⠁⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠀⠀⠓
⠀⠀⠐⢸⢿⣿⡟⡎⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⢀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⣿⣿⣿⠏⠀⢚⠁⠀⠀⣀⠀⠀⠀⠹⠀⠀⠐⠂⠢⣀⠖⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⢤⡠⠆⠀⠁⡀
⢀⢿⣿⣿⠋⠀⠀⠈⠤⠀⣴⠀⠀⠀⢀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠛⠆⠀⠌⠀⠱⠒⠫⠈⠁⠀⢀⣰⣤⣰⡇
⠐⣾⣿⠇⠀⠀⠀⠀⠀⠀⠐⠱⠤⠀⠙⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⡿⣿⡇
⢸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⡀⠓⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿⣽⣿⠁
⠘⠳⣆⢦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢱⠆⠀⠀⠑⠀⠀⠀⠀⠀⠂⠀⢀⡈⣌⠗⠀⠀⠀⠀⠺⠛⣿⣿
⠀⠀⠀⠜⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠄⠀⠀⠀⠂⠀⠀⠠⢎⡁⠜⠀⠀⠀⠀⠀⠀⠀⠜⠻⠟
⠀⠀⠀⠁⠀⢻⡓⢲⣦⡤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⡉⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠓⡺⠒⠐
⠀⠀⠀⠀⠀⢀⢐⣬⡿⠁⠀⡄⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠀⠀⠀⠈⡍⠁⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⢨⡛⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠈
⠀⠀⠀⠀⠀⣮⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⡄⠰⠀⠀⠠⠄
⠀⠀⠀⠀⠘⠝⠿⠁⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠂⠀⠸⡏⠁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠄⣢⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⡀⠀⠀⠘⠀⠀⡀⠀⠀⠀⢀⡀⠀⠀⢀⣀⢂⣠⢀⡀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠰⠄⠀⠀⠀⢠⠀⡔⠈⠀⠄⠀⠀⠀⠘⡳⡔⠀⠀⢀⢀⡟⠂⣄⠀⠈⠁⠀⢠⡃⠀⠀⡈⠁⠁⠀⠙⡖
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠂⢀⣀⣴⡀⢀⠈⠂⠀⠖⠁⠀⡄⠊⠀⠀⠀⠀⠀⠠⢡⠜⠣⢗⡫⠂⡀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⢸⠁⣀
⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⢀⠈⠀⠈⠁⠀⠀⠐⠦⠀⢀⠎⢠⠞⠆⠀⠀⠀⠀⣔⡄⣴⠨⠌⠠⠔⡧⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠆⠀⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢠⠀⠀⢤⡄⠀⢧⠀⠂⠀⠀⠄⠀⠅⠠⣤⠔⠚⢀⡠⠆⠀⠀⠀⠙⠀⠤⠄⠠⠤⠤⠂
⠀⠀⠀⠀⠀⣀⢰⡄⠀⠀⠀⢠⠀⠀⢀⡀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠸⢓⣸⠭⡅⢎⡑⠀⠀⣄⢶⠖⠀⠀⣀⠀⠀⢦⣆⡀⠈
⠀⠀⠀⠀⡶⠈⠁⢁⡀⡀⠀⣀⠀⠀⠘⢁⠾⣸⠀⠀⠀⠀⢀⡀⠀⠀⠀⠦⠀⠀⠈⠉⠛⠃⠉⠀⠀⠴⡉⠀⠀⠀⠀⠁⠀⠀⠀⠈⢱⡄
⠀⠀⠀⠀⠀⠀⡔⠋⢀⡠⠴⠨⢄⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠠⡤⡀
⠀⠀⠀⠀⠀⠀⠹⠶⠃⠁⠀⠀⠀⠈⠆⠀⠀⣥⠀⡆⡔⢰⢰⠀⡄⢀⠇⠀⠀⢰⠠⠰⠄⠂⣦⠀⠀⠀⠀⠀⠀⠘⢸⣁⠄⡓⣧⢆
⠀⠀⠀⠀⠃⠀⠀⠘⠀⠁⠀⠀⠀⢀⠀⠉⠀⠤⠐⠣⠁⠬⠘⠄⠇⠈⠤⠀⠀⠃⠱⠐⠢⠀⠇⠀⠄⠁⠀⠰⡦⡄⢉⠭⠶⠒⠈⠆⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠉⠸⠖⣠⡀⠟⢬⠘⣣
⠀⠀⠀⠀⣠⠀⠀⠢⡆⡀⢀⠀⣠⠄⠀⠀⠙⣣⡆⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⢀⡱⠎⠁⠀⠀⣀⠀⠀⠀⠀⠐⠳⠴
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠂⠀⠀⠚⠃⠀⢀⠀⠀⡠⠄⠆⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⣄⣀⣄⣀⡀⠀⠀⠠⡄
⠀⠀⠀⢠⠀⠈⠀⠀⠀⢠⡀⠠⠔⠀⠀⠀⢠⠀⠀⠁⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⠻⣿⣧⡀
⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠁⠲⠀⠀⠀⠀⠘⠀⣴⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠻⡿⠄⠀⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠘⡀⢀⠄⠄⠁⡀⠀⠰⠀⠀⠡⣰⠃⠀⠀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢢⣟⠁⠀⠀⠀⠀⠜⠀⠀⠀⠀⠾⠃
⠀⠀⠀⠀⠀⠲⠈⠈⢀⢀⠉⠈⠀⠈⠀⠀⠈⠁⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠆

⠀⠀⠀⠀⠀⢀⡠⠔⠒⠀⠀⠐⠒⠤⣀
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⢀⠎⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡄⠀⠀⠦⣀⠀⠀⠀⠀⠀⠀⠀⢻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀
⠀⠀⡘⠀⠀⠐⢤⢀⠆⠀⠀⣴⢀⠀⢤⢀⢀⠘⠀⠀⠀⠀⠀⢼⠃⢀⣀⡀⠻⣷⣄⠀⠀⠀⣠⡀⠘⣯⠀⠀⠀⠀⠀⠀⠀⠈⢀⡏⢮⡁⠄⢰⣣⡀⠰⣀⣠
⠀⠀⢃⠀⠀⢀⡎⢈⡶⠈⠆⠚⠒⠀⠈⢩⠃⢀⠀⠀⠀⠀⠀⢿⡀⠘⠛⠀⢀⠈⠻⣷⣄⠀⠛⠁⠀⡯⠀⠀⠀⠀⠀⠀⠀⠤⠎⠐⠊⠉⠉⠁⠉⠀⠀⠀⠃
⠀⠀⠘⡄⠘⠊⠀⠁⠀⠀⠠⠐⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠹⢇⠀⠀⠔⠃⠀⠀⠈⠙⠦⠀⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠦
⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠑⠦⢄⣀⠀⠀⢀⣀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⣠⣾⠟
⠀⠀⠀⠀⡀⠀⠀⠈⢿⣦⡀⣠⣾⠇⠀⠀⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣛⣸⣷
⠀⠀⠀⢨⡇⠀⠀⠀⢠⣿⣑⣿⡇⠀⠀⠀⠘⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣷⣾⣿⣧
⠀⠀⠀⢾⡆⠀⠀⠠⢾⣿⣷⣿⣷⠄⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦
⠀⠀⠀⢘⣧⠀⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⢬⠃⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠈⠿⣷⣄⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⢠⡤⣄⠸⠿⢿⠏⢹⡿⠿⠀⡀⢤
⠀⠀⠀⠀⠘⠁⠀⠘⠿⣿⠛⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠈⠻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⣻⢳⢳⢻⡟⡟⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠿⠿⠴⢦⢾⡼⠷⠷⠿⠿⠈⠁


⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢰⠂⢠⡄⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠘⠒⠚⠓⠸⠇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⡌⠀⠀⢠⣶⣿⣿⣷⣿⣿⣷⣦⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⡀⠀⣀⢀⡄⣀⠀⠀⡀⠀⢀⡀⣀⡀⣀⣀⡀
⠀⠀⠀⠀⢿⡀⠀⠈⠉⠛⠛⠛⠛⠛⠋⡉⠀⠀⢠⠇⠀⠀⠀⠀⣤⣴⣶⣦⣤⣾⡟⣿⡇⠛⢸⡇⡆⣿⠈⢡⣿⠘⢻⣿⠸⢃⣿⡘⣸⣿⢛⣷⣦⣤⣶⣶⣤
⠀⠀⠀⠀⠈⠁⠀⠀⠃⠃⠁⠨⠬⠘⠇⠧⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠙⠿⠿⠇⠛⠸⠇⠶⠸⠸⠧⠻⠜⠋⠿⠰⠌⠿⠇⠿⠿⠿⠏⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠐⢧⣰⠒⣶⣲⣙⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠁⠉⠁⠉

⠀⠀⠀⠀⠀⣀⠄⡤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠐⡠⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠁⢂⡄
⠀⠀⠀⠀⡔⣕⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⠁⠀⠀⢀⠄⠀⠀⠉⠱⣀⢀
⠀⠀⠀⠀⠁⣍⡑⠒⠂⠀⠤⠔⠒⢂⡀⠀⠀⠀⠀⣁⠁⠈⠀⠘⠀⠀⠆⠀⠑⣉⡔⠀⠀⠘⣦⡠⢄⣠⠴⠋⠀⠀⠀⣄
⠀⠀⠀⠀⢸⡡⣄⣀⣀⣀⡭⠭⣉⣋⠌⢳⠀⠀⢀⢘⠫⠀⠀⠀⠀⠐⢒⣋⠭⠚⠈⠀⠀⠀⢹⣼⣨⣭⣧⣠⢄⣠⢄⡜
⠀⠀⠀⠈⠒⠭⠤⠀⣀⣀⣐⡚⠩⠅⠂⠁⠀⠀⠈⠒⠤⢄⣀⣀⣀⣀⣀⡠⠤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠘⣏⣭⣭⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠀⠠⠒⠀⢲⡀⠀⠀⠀⠀⠀⠀⢀⠤⣢⣄⠀⢀
⠀⠀⠀⠄⠓⠤⢤⣄⣀⣀⣀⣀⡀⠼⠖⠵⠀⠀⠀⠀⠀⠀⠌⠀⠈⠈⠀⠀⠀⢸⠃⠀⠀⠀⢀⡠⠒⡁⠀⠂⠂⠢⢊⡩⠈⡀
⠀⠀⠄⠰⢤⣤⣀⣀⣀⡀⢀⣀⣀⣠⣴⠆⠀⠀⠀⣠⣖⠀⠠⠀⠀⡀⠀⢄⡰⠃⠀⠀⢀⠴⠈⠐⢠⠀⠁⠐⡁⣀⠄⠀⠄
⠀⠀⢃⠀⠀⡉⠈⠉⠙⠋⠉⠉⢉⡨⠋⠀⢀⠀⠀⠈⢍⠳⣇⠁⠐⣀⡴⠋⠀⠀⠀⠈⠪⢧⡄⠘⠊⠐⠀⠀⡂
⠀⠀⠀⠑⠊⣀⣤⡅⢐⡒⠒⠚⠉⠀⠀⠀⠁⠀⠀⠀⠀⠐⢹⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢄⠉⠉⠄⡀
⠀⠀⠀⠀⠀⠳⠄⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢱⠀⠀⠀⠀⠐⠉⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡀⠀⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠎⡅⠤⠤⠄⠒⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠈⣀⣤⠞⡫⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢻⣆⢀⣼⢢⡇
⠀⠀⠀⠀⢀⠀⠈⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠟⠋⠁⠈⠱⡘⢄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠻⡿⠃⢈⠇
⠀⠀⠀⡠⢰⢄⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⣿⣿⠳⡄⠀⠀⠀⢠⠚⠀⠀⡏⣽⠶⠾⢸
⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣳⠷⠁⠀⠀⠀⠀⠁⠚⠂⠀⠐⠒⠊⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⣤⠖⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣠⠄⠀⠰⠆⠀⠀⠰⠶⠂⠀⠀⡐⠀⠀⢠⠖
⠀⠀⢠⠋⠀⢀⣀⡀⠀⠻⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠠⠆⠀⢀⠀⠀⠀⠀⠀⢟⠊⠀⠀⠔⠀⣴⠶⠀⠀⠀⣀⡀⠙
⠀⠀⡆⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠒⠀⠀⠀⢀⠋⠀⣰⣆⡠⠔⠉⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠆⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⠶⠭⠤⠴⠖⠊⠁⠀⠀⠀⠀⠀⠀⣗⠀⠀⠀⠀⣠⣄⠀⠀⢀⣀
⠀⠀⢿⡄⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣀⡀⠀⠘⠁
⠀⠀⠀⠐⠀⠐⠻⠀⠀⠀⠀⡶⠀⡾⠃⠀⠀⣀⣀⠀⠀⢀⣀⣀⠀⠀⢀⡾⢹⠀⠀⠀⠀⣀⠀⠀⠀⠁⢤⣤⠀⠀⠙⠃⢀⡠⠶⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢋⣼⠇⠸⠟⠛⠛⠛⠿⣿⢟⡋⣘⢂⣤⡼⣧⠃⠀⠀⠀⠀⠈⠁⠐⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⣿⡏⢠⡶⢲⢰⡟⢹⣸⣿⣡⠏⣿⢸⡗⡡⣋⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠈⢁⣿⡧⣼⢻⣏⡞⠻⠏⢷⣄⡭⠤⢥⡈⠣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⡴⠋⠈⠓⢡⣤⣤⣴⡶⠞⠋⠙⠓⠶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠴⠆⠀⠚⠛
⠀⠀⠀⢠⠄⠀⢀⡄⠀⠀⠈⠛⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⢠⠤⠶⠒⠒⠈⠛⠢⠀⠀⠀⠀⠀⠀⣠⣏⣶⠶⠂⠉⠑⠂⠀⠁⠀⠶
⠀⠀⢀⡄⠘⠳⠀⠀⠀⠀⠴⠖⠀⠀⠉⠉⠀⠀⠀⠀⡠⢈⡋⠀⠐⠛⢂⠀⠀⣤⠀⢠⡄⠀⠀⠀⠹⠏⢠⡦⢀⣀⣃⣠⣠⠄⠀⠠⡄
⠀⠀⢸⣷⣄⡀⠶⠆⠺⠷⠀⠀⠾⠳⠆⠊⡜⠀⠀⢼⠁⢨⣅⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠖⠋⠀⢠⡄⠀⠀⠉⠂⢴
⠀⠀⢿⡿⠿⠿⠿⠿⣦⣯⠷⠶⠶⢶⣖⠛⣀⠀⠀⢏⠀⢀⡀⢀⠀⠠⠀⠈⠷⠀⠀⡀⠁⠀⠀⠀⠸⠏⠁⠶⠄⠀⠀⠀⠐⠦
⠀⠀⠀⣽⣿⣶⣛⣠⣀⣀⣀⣠⣤⣿⠿⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⠀⣸⢀⡄⠀⠀⠀⢀⣄
⠀⠀⢀⣭⣍⡉⠁⢈⣉⡉⣩⠿⠀⢀⣀⣤⣴⠂⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠁⠀⠀⠀⠊⠙⠀⠀⢸⡇⠀⣤⡀⠀⠀⠉⠀⢠⠈⠇
⠀⠀⢈⣜⡋⠩⠿⠉⠉⠹⠏⠿⠉⢉⢉⣉⡥⡄⠀⠀⠀⠠⠤⡀⠰⠂⠁⠂⠈⠀⠁⠀⣄⠀⠀⠀⠀⠻⡀⠈⠁⠐⠂⠀⠀⠀⠀⢀
⠀⠀⠺⡿⣩⣟⠻⢶⣶⠲⠓⠓⠚⠋⣩⡄⢐⡴⠀⠀⠀⠀⠀⡄⠀⠀⠀⠿⠖⠀⠀⠀⠁⢠⡆⠀⠀⠀⠙⠒⠠⢄⣀⡘⠃⠔⠒⠁
⠀⠀⠀⠙⠛⠛⠲⠮⠉⢤⣤⠤⠶⠤⠶⠚⠉⠀⠀⠀⠀⠀⠤⠀⠴⠄⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡇⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⣀⠤⠤⠴⠒⠒⠉⠀⠀⠀⠨⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡟⢠⠁⠀⣀⣤⣠⣇⣡⣴⠀⢱
⠀⢀⠐⠂⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢀⠁⠀⢀⠄⢀⢤⠀⣴⣿⣖⣽⠇⠈⠀⡸⠇⠳⢃⠿⠗⠛⠀⣼
⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠁⠀⠠⠁⣰⣇⣼⢀⢾⣭⢯⠜⠀⠁⠀⠹⣶⠶⠤⠤⠤⠖⠋⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⢠⠃⣔⣟⡮⢙⢛⡻⠋⠀⡠⠊
⠀⠀⠀⠀⣀⡤⠤⠴⠶⢤⢄⡀⠀⠀⠀⠀⡎⢀⡿⠗⠃⠉⡁⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠴⠋⠁⠀⠀⠠⠀⡎⠀⠀⠑⠀⠀⢸⠀⡀⠠⠐⠂⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢲⡖⠁⠈⠍
⢠⠃⠀⠀⠀⠀⠀⠀⢀⢷⡄⠀⠀⠀⠁⠙⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⠀⠙⠍⠀⠀⠀⠁⠀⡀⠄
⠚⠉⠀⠑⣦⡀⠤⠒⠁⢘⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠔⠀⠀⠀⠒⠀⠀⠀⠀⠄
⢰⡠⠀⠈⠉⠒⠂⠄⠀⠀⠀⠀⣀⣀⠄⠈⠺⡇⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⡀
⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⣲⣤⠖⠁⠈⣿⠜⠉⠁⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⡿⠁⠀⢠⠟⠁⠀⠀⣰⣫⠌⠛
⠀⠀⠀⠀⡀⠄⣀⣄⡀⠤⣀⠀⠀⠠⠀⠀⣀⣈⣁⡀⠐⠀⢄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⣀⠔⠁⠤⠤⢤⣍⠉⣛⡼⠀⠎⠀⠾⢭⡤⠧⠌⣩⡽⡳⠀⠁⠈⠕⠂⠤⠀⣀⣀⣀⣀⣠⠤⠤⠐⠒⣹
⡼⣁⣬⠙⡓⠲⢀⠼⠊⠁⠀⠀⠀⠀⠀⠈⠓⠒⠒⠓⢉⠀⠀⡀⠀⢰⡀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⣰⠃
⠙⠉⠛⠛⠃⠖⠁⠀⠀⠀⠀⠀⠐⠦⣀⡀⠀⠀⠀⣀⣀⠔⠊⠀⠀⠀⠉⠓⠢⠤⠥⠥⠥⠬⠤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⣀⡀⠀⢀⣄⠀⢤⠞⠀⢀⡎⠀⠀⢘⣦⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⡎⠀⠀⠘⠁⠀⠂⠠⠟⠀⠈
⠀⠀⠀⢨⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⢀⡀⠀⠠⢀⡼⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠺⠧⠴⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⣠⢀⣠⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠤⠐
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢷⠀⠀⠉⠇⠀⠈⠀⠀⠁
⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⢀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠶⠷⠠⠆⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⡇
⠀⠀⠀⠈⠛⠈⠁⠀⠀⠀⠀⢀⠀⠀⡠⠄⠀⠠⡁⠀⠠⠀⣀⡀⠅⠀⠀⠀⠀⣀⠁⠀⢠⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠠⠀⠈⠟⠃⠀⠤⢶⠄⠀⠀⠀⠀⠀⠀⠐⠳⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⣀⣀⣄⣀⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠓⠒⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠣⠰⠀⠘⠂⠀⠀⠀⠀⠀⠃⠤
⠀⠀⣿⡿⠿⢿⣿⡿⣿⠿⣿⣿⡇⠈⢢⡄⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠒⠲⠂⠤⠤⢴⠅
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠙⠿⠿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠑⠤⠄⠀⠤⠖⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡋⠻⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⣻⣿⣷⠏⠁⢶⡷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣸⡂⢀⣤⣾⣷⢠⣤⢤⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣿⣿⣾⣿⣿⣿⡷⣌⣁⣉⣼⠟⠛⢩⢛⣳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡀⠈⠉⠉⠁⠈⠻⠏⠀⠀⠀⢠⣜⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠿⠟⠻⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢦⣄⡀⠀⠠⠀⠀⠀⣄⣠⣴⣾⠿⠟⠉⠉⠁⠀⠀⢤⣄⠀⢰⣴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠙⠙⠛⠚⠘⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠏⠆⠚⠋⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⡟⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠉⠁⠐⠒⠐⠦⠤⢦⡤⣤⣤⣤⢶⠶⠶⠞⠛⣋⠉⠳⣤⣧⢉⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢄⣄⡀⢀⡀⠀⢀⠀⠀⢀⡀⠄⠉⣤⢸⣷⣦⣄⢇⡉⣰⣖⣼⣿⣶⠻⢿⣿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⡯⠵⠛⣯⣫⠾⠛⢦⣤⢶⠄⣰⠟⣿⢿⠋⠛⢾⣿⣿⡀⠙⠻⣿⠆⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠁⠀⡞⠚⠁⣼⠒⠁⠀⠈⠛⣶⠀⠀⠉⣿⡇⠀⣰⣿⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣷⠀⢰⡆⠀⠀⠀⠀⠀⣿⠀⣤⡀⠀⢰⣿⠐⠀⢸⣿⡧⠀⣿⡏⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠸⣷⠀⠀⣷⠀⠀⣿⣸⣷⣵⠀⢸⣿⣣⠀⣾⣿⠇⣀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⡆⢡⣼⣀⢠⣿⣿⣿⡿⠀⣿⣿⡏⢀⣿⣿⡇⢸⡿⣿⣿⣷⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣾⣇⣸⣿⣿⡸⣿⢮⣿⣧⢈⣿⣿⡃⢰⣿⣿⡆⣿⣻⣿⣿⡧⣞⣶⣾⠭⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⣿⣿⢰⣿⣿⡆⢿⣿⣿⣿⣾⣿⣿⡇⢹⣿⣿⡁⣷⣿⣿⣿⣷⣶⣴⢶⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠤⠿⣿⣅⣍⣽⣷⣏⣘⣿⣾⣧⣽⣿⠽⣿⣿⣿⡿⣿⣷⡿⣿⣷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⢿⠿⠿⢿⡿⠿⠷⠛⠒⠛⠛⠁⠤




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠠⠈⠄⠀⠀⠀⠀⢀⠀⠂⠈⠥⠀⠤⠀⠀⠀⡰⢆
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠑⢄⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⢆⣀⠠⠤⠴⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⡆⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠉⠐⠢⣄⠀⠀⠘⣄⠀⠀⣷⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠁⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠒⠲⠤⠤⠵⠤⠴⠤⠴⠶⠾⠖⠒⠒⠒⠒⠂⠄⠀⠀⠠⠀⡀⠐⠂⠀⢄⠄⠐⠀⠈⠀⠀⠀⠀⠀⣀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⢰⠬⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⢄⢀⣀⣤⣤⣤⣴⡾⠿⠛⠉⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠒⠀⡀⠀⠀⢀⠀⢀⡀⣀⢀⣀⠉⢆⠀⠉⠭⣉⠉⠉⠀⠀⠀⠀⢀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠁⠈⠀⡀⢠⣁⣀⣀⣤⠈⠳⣄⣂⡀⠁⠀⠄⠐⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠉⠁⠀⠀⢄⡀⠀⠀⠀⠀⠠⣘⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣙⣹⣭⠄⠀⠉⠉⢩⢭⣤⠀⡀⠬⠶⢶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠁⠀⠀⠀⠐
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⣶⠄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠚⠛⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠋⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣸⠃⣿⣿⡟⠁⠀⠀⢀⣴⣷⠀⠀⢀⡾⠀⡟⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⢿⠀⠁⠈⠁⠀⠀⠀⡼⠛⠛⠀⣠⠞⠀⠀⡇⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢠⡏⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁⠀⠀⢰⡇⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⢺⡇⠀⢸⡇⠀⠀⠀⠀⢀⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⢠⡞⢀⣴⣄⠀⠀⡿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢸⡇⠀⠘⣧⠀⠀⠀⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠿⠿⠁⠀⣸⠃⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠘⣇⠀⠀⠈⠳⢦⣀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⣀⣈⠳⣄⡀⠀⠀⠈⠙⠛⠒⠶⠶⠶⠖⠚⠋⠉⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⢰⣿⣯⠀⠈⠙⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣷⣄⡀⠁⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠶⠶⠒⢒⡒⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⡴⠚⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣿⠀⢻⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡏⠀⠀⠀⠀⠀⣀⣤⡴⠚⣹⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢸⡆⢸⡆⠈⡇⠉⣿⠓⣶⠦⢤⣤⣤⣀⣀⣀⣀⣀⣬⣥⡤⣤⠶⢶⡟⢙⡏⢀⡇⠀⡿⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⡇⠘⡇⠀⣇⠀⢸⠀⣿⠀⢸⡇⠀⣿⠀⢸⠀⡏⠀⣾⠀⣾⠀⢸⡇⢸⡇⢸⠃⢰⡇⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢻⠀⣿⠀⢿⠀⢸⡄⢸⠀⠈⡇⠀⣿⠀⢸⠀⡇⠀⣿⠀⣿⠀⣸⠀⢸⠁⣸⠀⣸⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡆⢹⡀⢸⠀⠸⡇⢸⡇⠀⡇⠀⣿⠀⣾⢰⡇⠀⡇⠀⡏⠀⣿⠀⣿⠀⡟⠀⡿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣧⢸⡇⢸⡇⠀⡇⠸⡇⠀⣿⠀⣿⠀⣿⢸⡇⠀⡇⠀⡇⠀⡟⠀⡏⢰⡇⢰⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢻⠀⣇⠘⡇⠀⣷⠀⡇⠀⣿⠀⣿⠀⣿⢸⡇⢀⡇⢸⡇⢠⡇⢰⡇⢸⠃⢸⠁⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⡇⢻⠀⣷⠀⢻⠀⣿⠀⣿⠀⣿⠀⡏⢸⡇⢸⡇⢸⡇⢸⡇⢸⠃⣿⠀⡿⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣷⢸⡄⢿⠀⢸⠀⢿⠀⢻⠀⣿⠀⡇⢸⡇⢸⠇⢸⠀⢸⠀⣼⠀⡏⢠⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢹⡈⡇⢸⡀⢸⡇⢸⠀⢸⠀⣿⠀⡇⢸⡇⢸⠀⣾⠀⣾⠀⡟⢸⡇⢸⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⣇⣷⢸⡇⠘⡇⢸⡇⢸⡇⣿⢠⡇⢸⡇⢸⠀⣿⠀⡿⢀⡇⢸⢁⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⠤⣧⣨⣇⣸⣇⣟⢸⡇⢸⡇⣿⣀⣟⣀⣧⣼⠷⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⡟⡏⢣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⢀⣴⣄⣸⢿⡀⣾⡇⣤⡻⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠉⠁⣙⣻⠛⠙⠹⠟⢸⣟⡿⠇⢰⣿⣧⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⠞⠋⠉⠁⠀⠀⢀⡆⠞⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣀⣠⣶⡊⠀⢀⣠⣤⡶⠿⡟⣛⣉⣽⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⢠⣌⠁⣀⣀⣠⠞⠁⠀⠠⣦⣼⣷⣿⣿⣿⡟⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣤⣶⣿⣿⣿⣭⠟⠁⠀⠀⠘⡑⣿⣿⠟⣭⣿⣿⡷⠼⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡞⠉⠀⣀⢭⣟⣯⡅⣤⣄⡴⠗⢊⡽⢋⣡⣾⣟⣡⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⣼⣿⣦⣽⣿⡓⠻⠁⢀⣴⢟⣴⣿⣿⣟⠋⠉⣀⣴⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⣿⣿⣿⡟⠁⠀⠀⣰⡟⢁⣾⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣭⠙⠿⢿⣷⣶⣤⣾⠿⠴⠿⠿⠻⠿⣿⣿⡿⣿⣿⣿⡷⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣭⢿⣿⡀⣀⡈⢴⠑⢯⡉⠁⠀⢦⣿⣶⠷⣆⣿⣡⣿⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣻⣿⣿⠳⢦⣤⣤⠁⠧⠀⢳⠟⢷⣴⣆⣿⣿⣯⣿⣿⣿⡛⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡉⠹⣿⣤⣿⣿⣿⢸⠀⢰⣾⣶⣼⣿⣿⡝⢿⣿⣿⣿⣯⠘⣿⡟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠀⢻⣿⠉⢿⣿⡀⣦⣿⣿⣿⢿⣿⣿⣧⠈⢿⣿⣿⠁⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⣧⠈⣿⡇⡀⠀⣾⣿⠀⠈⣿⣏⠀⢰⣿⡯⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢹⣿⡄⣿⡇⣷⠀⣿⡿⠀⢰⣿⡇⠀⣿⣿⠇⣼⣿⣿⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣿⡇⢸⡿⣿⢠⣿⡇⠀⣸⣿⡆⣸⣿⣿⣰⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠈⢳⢻⢸⣿⣧⠀⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣼⣏⣈⣿⣟⣀⣻⣿⣼⣿⣿⣿⣿⣿⣿⣿⣆⣦⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠀⠤⠅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠄



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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⢞⢉⣎⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠈⠁⠀⠘⠉⠀⠀⠲⠄⠄⠀⠀⠀⠀⠀⠐⠄⠴⢧
⠀⠀⠀⠀⠀⠁⣧⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢖⠀⡄⠀⢀⠀⠀⢀⠀⢠⢀⣦⡀⡁⠀⠀⡔⠁⠀⠀⠀⠈⢑⠄⠠
⠀⠀⠀⠀⠀⠀⡧⢌⡉⠁⠀⠒⠒⣊⣉⣹⠤⡀⠀⠀⠀⠀⢢⣀⠀⠀⠂⠈⠀⠀⠘⠐⢀⣀⣤⣞⠀⠀⠀⢸⡶⣐⢢⣤⣒⠋⠄⠂⠄⠀⢤⡀
⠀⠀⠀⢐⠀⣾⡠⣤⣤⣤⣤⣤⣭⡭⣅⣋⡰⠈⡇⠀⠀⢀⢰⠓⠬⢁⠀⠀⠐⠒⣒⣉⡭⠴⢛⠆⡂⠀⠀⠀⢧⣵⣸⣸⣸⣤⠤⢄⣤⢴⣼⠁
⠀⠀⠀⠀⠑⠦⠭⣖⣀⡀⠀⠀⠲⣒⣋⠩⠀⠈⠀⠀⠀⠈⠓⠭⣄⣀⠀⠀⠀⠀⠀⣀⣀⣠⠥⠚⠁⠀⠀⠀⠀⠀⠉⠁⠀⣻⣹⢹⣹⣫⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠔⢡⡀⢀⠠⠀⠒⠒⠀⠀⠒⠒⠬⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠰⠄⡐⠅⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⡠⠖⠩⠙⢥⠒⣀⣤⣀⢀
⠀⠀⠀⠐⠎⠑⠚⠶⠤⠤⠤⠤⠤⠤⠀⠘⠒⠙⡆⠀⠀⠀⠀⠀⠀⠰⠁⡀⠀⠀⠐⠐⠈⠄⡸⠁⠀⠀⠀⠀⢠⠔⠋⠀⠀⢨⠁⣀⠰⠄⡤⠀⢀
⠀⠀⢠⠀⠶⣤⣤⣀⣀⣀⠀⠀⢀⣈⣀⣠⣤⡾⠀⠀⠀⠀⢠⣔⡊⠀⠡⠀⠀⠀⠡⠀⢐⡔⠁⠀⠀⠀⡠⠚⡀⠀⠐⡀⠉⠁⢎⡀⣀⠆⠀⡠⠁
⠀⠀⠸⠀⠀⠈⣉⠉⠛⠛⠛⠛⠋⠙⠛⢉⡼⠁⠀⠀⠀⠀⠈⢋⠻⢔⡂⠁⠀⠐⣀⠜⠉⠀⠀⠀⠈⠣⢕⡀⠁⠀⠂⠡⠊⠁⠐⡄⠀⠀⠄
⠀⠀⠀⠑⠲⠖⠁⢀⡂⠀⠤⠤⠴⠶⢚⠁⠀⠀⠐⠃⠀⠀⠀⠀⠑⠌⣳⣴⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢄⡀⠑⠒⠊⡠⢀⠂
⠀⠀⠀⠀⠀⠀⣟⠉⢁⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠬⠭⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⢀⠵⠀⠀⠀⠀⠀⠉⠀⠱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⢀⣁⠀⠤⠀⠀⠐⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠎⡥⠤⠀⠴⠖⠒⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⡐⠐⠀⠃⢀⣠⡶⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⣧⠀⢀⣼⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡅⣀⣴⠶⠛⠁⠐⠣⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠈⠀⢹⣷⣿⠏⠀⡇
⠀⠀⠀⠀⠀⢐⠀⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠁⠀⠀⠀⠀⠀⠘⡮⣧⢦⣄⠀⠀⠀⠀⠀⠀⠼⠀⠀⠰⠦⣬⣉⣠⢠⡇
⠀⠀⠀⢴⢈⠜⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⡳⡌⠇⠀⠀⠀⠀⠘⢀⢠⡄⠰⠘⠛⣙⣉⡼
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠉⠀⠀⠒⠂⠠⠌⠋⠙⠫⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠋⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⢀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢶⣶⣤⣴⣄⣄
⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⠀⠀⠐⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢛⣿⣿⣿⣿⣇⠀⠤⠸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣯⣿⣿⣿⣿⡀⠀⠀⠿⡿⠇⢠⣤⣶⠀⠀⠀⠀⠀⠀⢀⣀⡺⣿⣿⣿⠯⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠉⠙⠙⠿⠃⢀⣀⢤⣤⣤⣾⣿⠿⠁⠀⠀⠀⣠⣰⠋⢙⣿⣽⣿⠟⣀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣾⠛⠉⣽⣿⣿⠁⠀⠀⠀⠀⣠⣌⣻⡟⠲⠆⠉⠈⠻⠟⢯⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠈⣹⣿⡇⠀⠀⠀⠀⣉⣙⠋⠳⠀⠀⢠⠀⠀⠀⡉⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⠀⠀⠀⠀⠙⠛⡠⠦⠀⠀⠈⢳⡄⢾⡿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣤⣄⢁⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⢾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢋⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⡆⠀⠀⠀⠀⠀⠈⠐⣶⡄⠀⠀⠀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣿⣿⣷⠀⠀⢀⡀⠀⠀⠺⠿⠀⠀⠀⠀⠀⠉⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡧⣿⣿⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⢻⣿⣧⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⢹⣿⣿⡆⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⣿⣿⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠶⡰⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⢺⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡟⡑⢿⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢧⣼⠟⣻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣆⢹⠆⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡡⢚⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠠⠖⠿⢗⠀⠀⡐⠀⠂⠀⠀⠀⠀⠈⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⡴⠄⠀⠀⠀⠤⠀⢀⠀⢀⠀⠀⠀⠀⠀⠂⢀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠠⠀⡀⠀⠀⠕⡆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠁⠈⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⢀⠀⠀⠈⢀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡸⠄
⠀⠀⠀⠣⡀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠤⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠟⠃
⠀⠀⠀⢆⠈⠂⠤⣀⠀⠀⠀⠉⠐⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠬⠌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠆⠊⠁
⠀⠀⠀⠀⠑⠢⣄⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠈⠐⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⢤⠖⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⠀⠈⠁⠐⠂⠀⠀⠀⠐⠂⠀⠀⠀⢀⣠⡤⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠦⠤⣤⣤⠤⢤⣄⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶
⠀⣀⣠⣤⡴⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠉⠀⣿
⠀⣿⠉⠉⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂⠂⠀⠀⠀⠤⠤⠄⠤⠤⠤⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠠⠔⠊⠁⠀⠀⠀⠀⠀⣿
⠀⣿⠁⠉⠉⠁⠀⠀⠀⠐⠒⠀⠀⠒⠀⠀⠀⠀⠀⠠⠤⠄⠠⠀⠀⠤⠤⣀⣀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣇⣀⣀⣀⣀⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⣴⣿⠟⠋⢉⠉⠉⠀⠀⠀⠀⠖⡶⠒⠀⣄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⢻⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⣿⠇⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⠀⠀⢀⡀⠀⣿⣿⣿⣏⣹⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠽⡅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠁⣘⠀⣿⠛⢻⣧⣼⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⣯⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠤⠤⠤⢼⠀⠀⢸⠀⡇⠀⣿⠿⢿⡧⢼⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⡥⡃⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠀⡠⢺⠀⢀⠼⠀⢧⡀⣿⣦⣼⡗⢺⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠳⣕⠒⠒⠠⠤⢦⣤⣄⣔⣀⣀⣰⣋⠀⢸⠀⠘⢦⣠⡴⠃⣸⣿⣿⡗⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⡗⢺⣿⢰⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⣿⣏⣁⡒⠒⠒⠂⠤⠤⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣾⣿⠸⠀⠀⠀⢀⣴⠟⠁
⠀⠉⠉⠙⠿⠛⠛⠿⠷⢶⣶⣦⣤⣤⣤⣀⣀⣉⣁⠀⠂⠒⠒⠀⠤⠤⠤⠼⣤⣀⣀⣀⠀⢘⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠿⠶⠶⢶⣶⣤⣤⣤⣄⣀⣀⣈⠉⢉⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⠟⠛⠁

⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠂⢂⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠞⡠⠂⠾⠰⡄⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠒⢉⠀⠄⠀⠀⢑⣤⡚⠳
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⢀⢴⣾⣙⡏⠀⠓⡄
⢂⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⢀⢴⣿⣭⠞⠒⡛⠉⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀
⠄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠓⠉⠉⠙⠋⠁⠀⠀⡴⠀⡇⠀⠁⠠⡠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠐
⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠈⠀⠀⠐⠀⠀⡂⠙⠧⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢂
⣖⠂⠤⠄⣀⣀⣀⠀⠀⠀⠀⢀⡌⠘⣥⠀⠀⢀⢄⠀⣀⣀⠂⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠻⡄⠀⣠⡀⠀⠀⠀⠀⠀⠈
⡇⠈⢩⣥⠴⠒⠒⠉⠁⠀⠐⠁⢴⡄⢈⣀⠮⠁⢈⢂⠐⠛⣦⣀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠄⠙⠁⠀⣐⣋⣂⣀⣁⣀
⣟⣋⣒⠀⠤⠤⠄⣀⡀⠑⢬⠕⠀⢥⠀⣃⠘⡇⠘⠗⡀⠀⠠⠉⠀⠀⠀⠀⠀⡰⠒⠒⠒⠛⠢⠀⡄⠄⠊⠉⠁
⣓⣒⣢⠤⠕⢛⠭⠀⠀⠀⢐⠈⠢⣰⡦⢴⡀⠛⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠄⠀⠀⠀⠐⡄⢀
⡋⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⡴
⠃⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⡄
⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠄
⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠐⠠⠀⢠⠄⠆

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠐⡃⢀⡬⠑⣦⠀⠀⠀⠀⠀⠐⠐⣀
⠀⠀⠀⢦⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠅⠀⠇⡡⠀⠀⡀⠀⠠⠤⠖⠁⠈
⠀⠀⠀⠀⠉⠛⠛⠿⠧⠀⠀⠄⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⡀⠀⠠⣀⠾⠂⠡⣮⡭⠝⢃⡐⠷⠦⠀⣀⡁⠀⠀⠀⢀⠀⠠⠄
⠀⠀⠀⠨⠵⢦⣄⣠⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠓⢠⣀⠀⠐⠛⠻⠁⠴⠦⠬⠍⠉⠴⠖⠂⠁⠠⠀⠀⠄⠀⠢⠦
⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠿⠀⠘
⠀⠀⠀⠀⠰⠠⠀⠲⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⡀⠀⢂⠀⠀⠀⠐⠦⠤⠄⠀⠀⠀⠀⠀⠁⢀⡤⠀⠀⠀⠠⠐
⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠠⠤⣀⠀⠀⠀⠀⠸⠈⣁⠀⠀⠄⠇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠆⠀⠀⠄⡀⢀
⠀⠀⠀⠠⣄⠀⠑⠀⠀⠀⠢⡅⠠⠐⢀⢄⠀⠀⠑⠖⢂⣈⣀⠴⠁⢴⣿⣿⣿⢿⣾⣶⣄⠀⠀⠀⠈⠉⠓⠂⠀⠄⠀⠤⠀⠜
⠀⠀⢠⠀⣈⠉⠓⠦⡀⠀⠀⠈⠂⠀⠀⠀⠠⠒⠢⠀⠀⠀⠀⠀⠀⠈⡙⣿⣿⣶⣿⣏⣿⠆
⠀⠀⠸⠀⠀⠀⠀⢀⡐⠄⠀⠀⠀⠀⠀⠑⠤⣄⡉⠉⠡⠦⢄⠀⠀⠀⠈⠁⠀⠠⠬⠙⠉⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠉⠒⠦⣀⠀⠈⠑⢄⠀⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠑⠀⠈⠳⡤⠀⠈⠉⠒⠠⠀⠀⠀⠀⠐⠃⢀⠀⠀⠀⠀⠀⡈⠀⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⡇⡘⢀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠖⠁⢀⠀⠀⢰⠀⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠁⠀⠀⠀⠀⠀⠙⠛⠋⠉⠙⠛⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⣠⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠂⠊⠉⡍⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⢠⡴⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠙⠛⠓⣦
⠀⠀⠀⡟⠀⢠⠖⣚⣛⣛⣛⣛⣛⣉⣉⣉⣉⣉⣭⣭⣭⣭⣭⡭⣭⣭⣭⣭⡉⢳⠀⠀⠀⠀⣿⠀⢀⣠⣤⣄⠀⢸⡆
⠀⠀⠀⡇⠀⣾⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡆⠀⠀⠀⣿⢠⣿⡜⠓⢞⢷⢸⡇
⠀⠀⠀⡇⠀⣿⢸⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠀⠀⢸⢸⣇⡶⠲⡆⡟⠸⣿⢦⡠⢛⡾⠘⡇
⠀⠀⠀⣿⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠈⢳⡄⡇⡇⠀⠈⠛⠛⠉⠀⠀⡇
⠀⠀⠀⣿⠀⣿⢸⠀⠀⢠⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠀⠀⢸⢸⠀⢸⠁⡇⡇⠀⡴⢶⡖⢦⡀⠀⡇
⠀⠀⠀⣿⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⢸⡇⡇⣸⣿⠁⠈⢻⣿⠀⡇
⠀⠀⠀⣿⠀⢹⢸⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡄⠀⠀⡸⢸⠀⣾⢸⡇⡇⠸⣟⣢⣔⣻⠏⢸⡇
⠀⠀⠀⢻⠀⢸⡼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣿⢸⠃⡇⠀⢈⣉⣉⡁⠀⢸⡇
⠀⠀⠀⢸⠀⢸⡇⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡇⢸⢰⠋⣸⠀⡇⠐⣏⡏⣹⣹⠀⣸
⠀⠀⠀⢸⠀⠈⡇⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⡇⢸⠈⠛⠛⠀⡇⠀⣉⣉⣉⡁⠀⣿
⠀⠀⠀⢸⡇⠀⣿⡳⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇⣾⠀⠀⠀⠀⡇⠰⣿⡉⣏⡷⠀⡏
⠀⠀⠀⠸⣇⣀⣈⣙⣻⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣿⣥⣤⣤⣤⣤⣧⣤⣭⣭⣭⣥⣴⡇
⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠙⣶⣒⣒⡶⠒⠒⠲⠶⠶⠶⠶⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⣶⠒⢛⡿⠋
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⢻⣿⣿⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⣼⡿⠋⠀⣾⣿⠿⠎⣹⣿⣿⡇⠘⡿⣿⣟⠈⠻⡿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢠⣾⠿⠁⠀⣴⣿⠃⠀⢀⣿⣿⡏⠉⢹⣿⣿⣿⠀⠀⢻⣿⣿⡁⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⣶⣿⠟⠀⢀⣼⣿⡏⠀⠀⣾⣿⣿⠁⠀⢠⣿⣿⣿⠀⠀⢸⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠂⢾⣿⡟⠀⠠⣾⣿⡿⠀⠀⢸⣿⣿⡟⠀⠀⢸⣿⣿⣿⡄⠀⠈⣿⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⢠⣿⣿⠁⠀⢲⠋⣻⠗⠀⠀⣼⣿⣿⡇⠀⠀⢸⣿⣿⣿⡇⠀⠀⢻⣿⣿⡆⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡗⠀⣿⣿⡇⠀⢠⣿⣤⣿⠀⠀⠀⣿⣿⣿⠄⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣾⡇⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⢠⣿⣿⠇⠀⣸⣿⣾⣏⠀⠀⢈⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠨⣯⣿⡧⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⣿⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢈⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢐⣿⣿⠄⢸⣿⣿⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⢼⣿⣿⣿⡗⠀⠀⢰⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠘⣿⣿⠀⠀⢿⣿⣿⣇⠀⠀⢘⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡗⠀⣿⣿⡄⠀⢸⣿⣿⣧⠀⠀⠀⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣾⣿⣷⠦⠨⣿⣿⣿⡀⠀⠀⢸⣿⣿⡆⠀⠀⠸⣿⣿⣿⡇⠀⢀⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡶⢿⣿⣿⣿⠀⠀⠈⣿⣿⣿⠀⠀⠐⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⠚⣿⣿⣿⣧⢀⣀⣾⣿⣿⣦⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⣃⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢦⡈⡄⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠐⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢹⣿⡟⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠸⣿⡇⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣤⣿⣥⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠄⠀⠀⡄⢀⡄⣠⣠⣤⣄⣀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡄⠀⠀⣿⣿⣧⣽⣿⣿⣿⡿⣆⠈⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠀⠀⠈⠻⠿⠿⠿⠿⠏⠀⠈⠀⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⢠⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠠⠀⠀⠀⠠⠄⠛⠧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡤⡀⠠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠃⠀⠐⠀⠀⠄⠀⠀⠜⠁⠤⠶⠂⠠⠀⠠⠈⠀⠤⠠⠓⠄⠃⠢
⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⠂⠐⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠄⠀⠀⠠⠀⠀⠀⠀⠀⡀⢄⠠⠀⠀⠠⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡯⠰⠀⠀⠀⠀⠀⡀⠀⠄⣴⣦⡤⢐⡉⠂⠀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⠀⠀⡔⠀⠀⢀⣀⠐⠈⠀⠀⠀⠀⠀⠹⣷⠉⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⢠⠌⢩⠄⠀⠀⠠⠀⠀⡀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠁⠄⠠⠨⠁⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⢀⢐⠊⠙⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⢀⠀⠂⠀⡀⢚⠋⡀⠰⣦⡇⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣯⡷⣰⡾⠁⢀⡈⠁⢲⣄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠻⢗⠏⡀⠰⣿⣆⠄⠉⣉⣿⣷⡶⠃⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⡇⠀⠀⠀⣹⠀⠈⠘⢁⡒⠿⠛⠉⠀⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⡢⡝⢼⡲⡠⢞⡵⠖⢲⡟⣷⣀⠀⡴⠁⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣗⡠⢳⡸⠸⣵⡇⢿⠃⠈⠻⣙⠇⢹⠉⣠⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡓⢉⣠⠷⢹⣿⡜⢦⣤⣄⣈⡼⣴⠈⠛⠤⡤⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠞⠘⠁⠨⣼⣧⡀⠂⢈⣉⠙⢈⡉⢀⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⢠⠀⠈⠠⠖⢍⠒⠿⠙⠉⠀⠀⠀⠀⠠⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠄⡀⢡⡴⠬⣾⠦⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣞⢔⣫⣽⡓⣮⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣍⠨⣿⣟⡵⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠏⠸⣥⣴⣄⣀⣀⣀⠀⡄⡀⣺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢀⣼⣿⣥⣾⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠿⢿⣿⠿⠛⠁


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢦
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠞⠛⢲⡄⠀⠀⠀⠀⡴⠛⠛⢦⠀⠀⠀⠀⢠⡖⠛⠓⣆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣀⣀⣰⠇⠀⠀⠀⠀⢧⣀⣀⡼⠀⠀⠀⠀⠸⣆⣀⣀⡎⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣀⣀⣀⣀⣀⣉⣉⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡗⠒⠂⠀⠀⠀⠀⠀⠀⠘⣆⠀⠐⢦⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠒⢺⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣸⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡟⠛⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⡴⠃⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠛⢻⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⠉⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠘⠂⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠙⠲⢶⠶⠶⠶⠶⢶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡶⠶⠶⠶⠶⡶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⡆⣲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡖
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⢀⣀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⢀⡀⢀⣀⢀⡀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⢘⠘⠀⠁⢠⠹⡀⡇⠇⠀⠀⡷⠀⠀⠓⣄⠈⠁⠨⢼⢸⠀⢹⢸⢎⢰⠆
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣷⣷⣾⣶⣾⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣾⣶⣶⣷⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠐⠂⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⢀⡠⠚⠉⠉⠑⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⣀⠠⠃⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⡀⠀⠀⢀⣤⣴⣿⣆
⠀⠀⠀⠀⠀⠑⠤⠤⠀⠠⠄⠀⠀⠁⣀⡀⠀⡴⠶⠀⠈⠀⠀⠹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠁⠒⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡍⠀⠀⠀⠀⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠒⠀⠉⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠋⠉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢀⣠⠴⢚⢻⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣡⠔⢋⢄⡺⠛⢂⣼⠋⡠⠂⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⢀⠁⠀⠈⠀⠀⡀⢀⡴⠛⣧⡠⢙⠦⢇⣴⠟⢁⡼⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡴⢋⠀⡌⢠⠏⣀⣴⠟⡁⠴⠋⠀⠀⣀⠄⠀⠀⠠⢦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣼⣠⠿⣊⣭⡾⠫⢉⣀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠰⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣔⣤⣵⡾⠛⢁⣴⣷⠟⠁⠀⠀⢠⣾⣿⣿⠃⠀⠀⣆⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⠀⠀⢀⣀⡀⠀⠀⠁⠀⠀⠀⠈⠉⠛⢥⣴⣾⣿⣿⣯⣴⣤⣦⣶⣿⣿⡿⠋⠀⠀⠀⠛⣟⠚⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⣀⣀⣱⣽⣁⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⢛⡃⠀⠀⠀⣀⠀⠠⣦⣴⠤⠴⠀⡛⠂⠀⢀⣠⣤⠌⣉⣋⣉⣉⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣯⣥⣭⣅⠀⣀⣠⣭⣽⣿⣷⣖⣪⣉⣛⣺⡷⢾⣟⣄⣀⣛⣻⣿⣿⣟⣀⡀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⢽⠙⠫⡍⢙⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠀⢺⢐⡆⡈⣇⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⠶⠛⠀⢀⣂⣩⣜⠈⣰⡇⡈⠡⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⢧⣀⢀⣀⣀⣠⣤⣿⠟⣿⣰⣿⣇⣸⠖⡴⢡⣾⠳⡄
⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⣀⣈⣂⡀⠉⠁⠈⠉⠉⠈⠛⠀⠉⣿⣿⣿⣾⡿⣡⣾⣯⠂⡁
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠙⠙⠙⠻⠿⡿⣷⣶⣶⠤⣤⢄⣠⣤⢰⣿⣿⣿⡟⣼⢿⣿⠄⠀⢸
⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣠⣤⣶⣿⣿⣿⣽⣿⣿⣿⠟⠁⠈⣿⣧⡀⠈⠓⢄⣀
⠀⠀⠀⢠⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⠏⠁⠀⠀⠀⠘⠿⣧⣇⡄⣀⣈⠑⡦⠄
⠀⠀⣠⣀⣀⡁⠀⠀⠀⠙⠻⠿⠛⠛⣻⣿⣿⣿⣿⡏⢿⠫⣿⣿⣿⣿⣧⣀⠀⢂⡦⣄⡀⠀⠀⠉⠛⠿⠇⠎⣑⣷⠶⣄⡀
⠀⢰⣿⡟⡁⠀⠀⠤⢤⡀⠀⠀⣠⠞⡿⠉⠁⠔⠋⣠⣶⠾⡛⠿⣿⣿⣽⣇⣀⡀⠀⡈⠻⠶⡄⠀⠀⠀⠀⢸⣏⡥⢲⠯⠴⢻⡏⠀⠆⣠
⢠⣿⣿⠿⠷⠂⢀⡀⡀⠀⢠⣾⣡⠀⠀⢶⣶⣶⡿⢋⠀⣀⣶⡟⠉⠉⠉⠛⠛⢓⣦⠀⠀⠀⡀⠀⠀⠀⠀⢉⠁⣀⣀⡀⢠⣿⣿⣀⣄⣯⠇
⣾⣽⠏⠀⠀⠀⠘⢷⣿⣦⣌⣙⡙⣗⣿⡿⠛⠁⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠉⠈⢥⠻⣿⠿⠟⠋
⢻⠟⠀⠀⠀⠰⣄⡀⠈⠙⠻⢿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠈⠀⠀⠀⠀⠀⠀⢀⡼⠷⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡟⠻⣿⣦⡀⠀⡀⢤⣤⣤⣠⣤⣀⣴⠦⡀⠀⠀⠀⠀⢀⣼⡇⠏⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣤⣀⣀⠉⠀⣀⣺⡿⣿⠾⣿⠢⡝⣯⠰⣿⣷⡧⢘⣃⠀⠀⠀⢀⣾⣽⠃⢀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⡁
⠀⠀⠈⠉⠀⠘⠃⠉⠛⠙⠒⠂⢹⣷⣿⠾⣥⣟⠛⠜⠏⠋⠀⠀⠀⠾⣏⣐⣷⠞⠁⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢧⣍⡛⠛⠒⠦⠄⠀⠀⢸⣿⣿⣿⣽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠖⠛⠁⠁⠀⠄⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣶⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⠲⠖⠐⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠈⠉⠉⠀⠀⠒⢌⢀⡠⣖⡁⠀⠀⢀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣈⣿⡽⠳⡶⣮⠀⠐⢆⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠈⢀⢀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠇⠉⠉⠁⠀⠀⠀⠀⠀⡬⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢽⠀⠀⠄⠀⠀⠈⠀⠀⠀⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠀⠀⢠⠄⠐⠂⢤⢺⡀⠀⠐⠂⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢢⣌⢦⢤⡀⢀⣸⣳⣤⣀⡀⠀⢀⢀⠶⠥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⢱⡁⠀⠈⢣⡁⡉⣘⢈⡀⣀⠀⣀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠐⠢
⠀⠀⠀⠀⠀⡐⠉⠉⠛⠓⠂⠠⠤⢧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠂⠉⠀⠀⠖⠁⠂⠐⠔⠂⠘⢆⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⠀⡎
⠀⠀⠰⠿⠉⠑⡄⠚⠂⡤⠒⢦⠤⠂⣾⠿⠄⣀⡀⠀⠀⠀⠀⠀⢈⡤⣀⠀⠀⢀⣠⠷⠀⠀⢀⠂
⠀⠀⠀⠑⣄⡼⠁⠀⠀⠐⣤⠇⡄⢠⠇⠀⠀⠀⠀⠈⠈⠉⣉⡉⠁⠤⠤⠨⢉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠸⠷⠷⠶⠶⠶⠿⠶⠶⠎⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠐⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⠀⠀⠀⠀⣀⡀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣾⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⣻⣿⣿⡿⣟⣿⣿⣿⢋⣉⣻⠟⠉⠛⢛⡟⠉⠙⢛⠛⠻⣟⠛⠿⢿⣟⠛⠻⣷⣄⡀
⠀⠀⠀⠀⠀⢾⠿⡿⠿⣿⠿⠿⢿⣿⣷⡿⠿⣿⣷⣶⣷⣿⣶⣶⣶⣿⣽⣶⣶⣬⣦⣤⣤⣵⣤⣤⣽⣦⣤⣤⣬⣿⣦
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠑⣄⢀⠀⠹⣄⠀⠀⠹⡅⠈⠈⠀⠀⡇⢸⢹⠀⠠⢀⠋⠀⢀⡼⣋⠵⣊⠝⠋⠁⠀⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠠⡉⠻⠿⣆⠀⠀⢱⠄⠀⠂⠀⡇⠀⡈⠀⠀⡰⠢⢐⣟⡪⠕⠊⠁⢀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⢄⠀⠈⠛⢦⡌⠂⠀⡃⠀⣧⠀⡆⣠⣾⢱⢾⠟⠉⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣿⢤⣿⣾⡿⠟⠋⠀⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⢨⡝⡿⣍⠀⠀⢀⠂⠀⣠⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠠⡀⡾⢲⠷⣿⡀⠠⠁⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⣿⣾⣳⣎⣿⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣖⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠉⠉⠉⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⣴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠳⢤⣀⡀⣀⣀⣀⠀⣀⣀⣀⢄⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠉⣿⠀⠙⠉⠉⠉⠉⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⡀⠀⠀⠀⢀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠉⠙⠛⠛⠛⠙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡻⠟⠻⢿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠛⠀⠀⠀⠀⠀⠀⠀⠘⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⢀⣀⡀⠀⠀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣭⣛⣫⣬⣛⣽⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠶⠿⠛⠻⠶⢺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡦⣄⣀⣠⣴⡏
⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣦⡄⠀⢀⣠⣤⠤⠤⣶⠚⢧⡀⠉⢁⡼⠓⣶⠦⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⠁⠀⠀⠀⠈⣳⠄⢙⡶⢋⡴⠛⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣮⣝⣛⣥⣮⣛⣛⣵⣯⣿⣿⡇⠀⣿⠀⠀⠀⡀⠈⠻⣄⣿⠖⠋⠀⠀⠀⢀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣿⣽⣿⣿⣿⣽⣿⣿⣯⣿⡇⠀⣿⠀⠀⠀⡇⠀⠀⢸⡇⠆⠀⠀⠀⠀⢸⠅⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⢿⣤⣤⣤⣧⣤⣤⣼⣧⣧⣤⣤⣤⣤⣼⣤⣤⣤⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡤⠀⢉⡀⠀⢀⡀⠀⠡⡀⠀⠁⠀⠀⠀⠂⠀⠀⠩⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠒⠀⠀⠀⠀⢠⡌⠁⠀⠈⠁⠀⠈⠷⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⢲⠞⠁⠀⠀⠉⠀⠀⢀⠀⠓⠖⠒⠚⠿⠛⠀⠀⠀⠀⠀⠀⡀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠦⠀⠺⠂⠀⠀⠀⠐⠈⠀⠀⠟⠀⠠⠆⠀⠀⠊⣰⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⠔⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣠⡄⠀⢀⣀⠀⠀⢴⠆⠀⠀⠀⠀⠔⠀⣠⣏⢃⠀⠀⠀⡌⢎⠀⠀⡠⠒⠊⡀⠔⡁⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠉⠀⠀⠀⠀⢀⡠⠒⠁⢀⠴⠯⢤⣈⣁⣉⣈⣁⣁⡈⠥⠄⠐⠈⠀⠀⣀⣀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠑⢒⠀⠀⣀⣀⠀⡀⠠⠔⠈⠁⢀⠠⢞⠃⠀⠒⠠⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠁⠀⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠀⠠⠤⠐⠂⠈⠀⠀⠀⠉⠒⠤⢀⡈⠀⠈⠉⠀⠉⠉⠒⠂⡀⠠⠄⠂⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣀⣀⣠⡤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠒⠒⠒⠒⠂⠠⠤⠤⠀⠐⠒⠒⠒⠒⠒⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠯⠋⠁⠀⠀⠀⠈⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡇⠀⠀⢀⣀⠀⣀⡀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⢻⣠⠎⡅⠀⠀⡀⢀⠱⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠃⠠⠲⢏⠃⠐⠇⢀⠀⣆⣠⠃⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠃⡀⠀⢀⠾⠁⠀⠀⠀⠀⠀⠀⢄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡐⠃⢀⣤⡟⡀⠀⠀⠒⠀⠀⢤⠊⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠶⠊⠉⢉⠤⠀⢹⡀⢄⠀⠠⠄⣀⠜⠒⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⢁⠀⠞⠁⠐⠂⠀⠀⡑⡌⠛⠒⠛⡂⢃⠏⠀⠀⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡔⠃⠈⠻⣀⠀⠀⠐⠆⠀⠘⠈⠄⢀⣼⠀⢸⠀⢀⠀⣈⣿⢯
⠀⠀⠀⠀⠀⣀⡠⢧⡀⠀⢒⡏⡿⠒⠸⠴⢲⠊⠀⠈⠁⠀⢀⠷⠤⢼⡾⠋⠁⠀⠱⢄⡀
⠀⠀⠰⢖⠉⠀⠀⣀⠍⠋⠩⠳⢧⠀⠀⠀⢸⠀⠀⠀⠀⢀⠎⠀⠀⠀⠙⢦⡀⠈⠀⠀⠙⢦⡀
⠀⠀⠠⠮⠤⡴⠊⠀⠂⠀⡀⠀⠻⠀⠀⠀⠈⠳⡘⠋⠛⢧⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠑⡄
⠀⠀⠀⢠⠎⠀⠀⣀⠀⠀⣀⠀⠀⢳⡀⠀⠀⠀⠙⣄⠀⠘⡄⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠘⠆⡀
⠀⠀⢠⡣⠐⠊⢁⡠⠔⠂⢹⠀⢀⣀⣱⣄⠀⠀⠀⠘⢤⣤⠇⠒⠒⣒⣒⣊⡉⠭⠭⠥⠟⠒⢆⠀⡀⠈⣂⡀
⠀⠀⡚⠒⠂⠁⠀⠀⠀⠀⢸⠉⠀⠀⣀⣈⡑⠤⣀⠀⠀⠀⠀⠙⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠊⠁⠈⠉⠂
⠀⠀⢰⠀⠀⠀⠟⢂⠀⠀⠸⠀⠸⣍⡀⠀⠀⠀⠀⢆⣲⠦⠧⠣⣎⣤⠤⠤⠤⠴⠒⠒⠒⠊⠉⠂⡍⠉⠒⠢⠤⢄
⠀⠀⢸⠄⠀⣀⡀⠸⣰⠀⣒⠀⠀⠀⠈⠉⠒⠢⠤⣀⡈⠑⠒⠤⠤⣠⠒⢄⠀⠀⠀⠀⠀⠀⠀⢀⣨⢤⢄⠀⠐⣀⠅
⠀⠀⠈⡃⠈⠓⢤⡉⠂⢄⡺⠀⢀⣀⣀⠀⠀⠀⠀⠀⢈⣑⣒⠤⢄⣈⠣⡀⢫⠁⠂⢒⢰⠛⠂⠐⠚⢳⠘⠒⠉
⠀⠀⠀⠉⠉⠉⠀⠉⠑⠢⣄⡊⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣮⠉⠛⡾⠯⠥⠤⠜⢻⠉⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠛⠒⠓⠤⠤⠤⠤⠤⠤⠔⠒⠒⠊⢉⡇⠀⠀⡇⠲⠴⠶⠆⢸⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠜⠀⠀⠀⡇⠀⠀⠀⠀⠈⡇⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣤⡄⠀⠀⠀⣀⣀⣤⠖⠁⠀⠀⠀⠀⢇⠀⠀⠀⢀⣠⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡀
⠀⠀⠀⠀⠀⢀⡆⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠛⠃⠀⠀⠀⠀⠀⠀⢸⡔⠀⠀⠀⠀⠀⡠⠔⠀⢰
⠀⠀⠀⠀⠀⠸⠃⠀⠈⠖⠀⢺⠀⠀⠀⠁⠀⡰⠂⠀⣀⠀⠸⣆⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠀⠀⣀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⠀⢸⡇⠀⡄⠀⠘⠁⠀⠀⠉⠀⠀⠈⡇⠀⠀⠀⠀⣷⠞⠁⠀⠀⡀⢠⠔⠉
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠄⠀⠈⠁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⢁⠁⢀⡠⠄⢰
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠲⠂⠀⠘⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠀⠀⠀⢹⡶⠃⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡄⠀⠀⠀⠀⠀⠈⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠴⠀⠀⠈⣿⣴⠂⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠔⠒⠂⠐⠚⠁⠀⠒⠠⠔⠉
⠀⠀⠀⠀⠀⠀⣔⠅⠂⠀⠈⣂⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⡀⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠘⠂⠒⠂⠐⠃⠀⠀⠀⠈⠛⠓⠐⠂⠐⠀⠀⠒⠒

⣶⣶⡶⣶⠶⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠲⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡀⣤⣋⡷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⠤⠞⣻⡥⣤⡷⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⠦⣤⠴⠚⠉⠉⡇
⠀⠀⢀⡼⢣⡤⣼⣆⠀⠀⠙⠢⣄⣀⠀⠀⣀⠀⠀⠀⢸⣡⢇⣴⣏⣭⣷⢯⡽⠛⡆⠀⠀⠀⠀⠀⠸⣅⠀⠀⢀⡤⠶⠦⣄⠀⢳⣀
⠀⠐⠛⠲⡏⠀⠀⠉⠳⣄⡀⠀⠀⠈⠉⣻⣹⠀⠀⠀⢾⠻⠿⢾⣁⣄⣽⡞⠁⠀⢻⠀⠀⠀⠀⠀⠀⠈⡷⠀⡏⠀⠀⠀⢸⡆⠀⠈⢳⡀
⠀⠀⠀⠀⠹⣄⠀⠀⠀⠈⠙⠛⠻⠿⣏⣁⡍⠀⠀⠀⠘⣆⠀⠐⠂⢠⠏⠐⠀⠀⠈⣇⠀⠀⠀⠀⣠⠞⠁⠀⠳⣄⣀⣀⡼⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⣀⣀⣀⣼⣁⡇⠀⠀⠀⠀⠘⢦⠀⢠⠏⠀⠀⠰⠀⠀⠸⡄⠀⠀⠀⡇⠀⠀⠀⠀⣀⣉⣁⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠈⢳⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⠲⠶⠒⠋⠉⠁⠉⠉⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡀⠀⠘⠀⠀⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠹⣄⡀⠀⣄⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡽⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⠧⣽⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢦⢠⡤⣼⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢳⡀⠀⠀⢠⡞⣠⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⢳⡼⠛⢦⡼⢾⠙⢶⣳
⠀⠀⠀⣠⠶⠶⠶⠖⠛⠛⠒⠒⠒⠒⣦⠀⠀⠀⠀⠀⣾⣛⣚⣛⣛⡇⠀⠘⣇⢳⢀⣤⣄⣴⡿⠋⠀⠀⢸⣛⡛⠳⣴⡋⡇⣾⢧⠈⢻⡀
⠀⠀⠀⠙⣟⠉⠉⠉⠉⠉⠉⠉⠉⡿⠉⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠓⢦⠀⠟⣀⣻⡀⠈⢿⠄⠀⠀⠀⠈⣠⣸⣳⡀⠙⣧⡏⣸⣇⣠⣷⠆
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡞⠉⠙⢿⠳⠛⠀⠀⠀⠀⠀⠘⣏⠉⠉⠛⠋⠉⠉⠁⠀⡟
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠶⢿⡶⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣠⡤⣤⣷⣠⣁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣹⠀⠀⠰⣇⠐⠀⠙⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠚⠛⠛⠓⠛
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⡿⠲⠵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⡤⣤⠤⣀⣠⣀⣠⣀⠀⠀⠀⠀⠀⠀⠰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⣠⠟⠛⠉⠛⠲⢤⡿⠶⣿⣶⠦⣄⠀⠀⠀⠀⠀⠀⣠⠶⡛⠉⠉⠯⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⢸⠾⠧⣤⣠⠆⠀⠀⠉⠳⣄
⠀⠀⠀⣼⠁⠀⠀⠀⠰⠀⠀⠙⢾⠓⣼⡧⣌⢧⠀⠀⠀⠀⡾⢡⠆⠙⠀⠛⠀⠘⢁⣤⠹⡄⠀⠀⠀⠀⠀⣼⠹⢦⠀⢈⡙⠲⢦⡀⢀⡀⠳⣄
⠀⠀⠀⠹⣄⠂⠀⣤⠀⠀⠈⠀⣌⢳⡘⢾⣻⣸⠄⠀⠀⠀⢹⡦⠤⠤⢤⣼⣭⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⣿⣃⡾⢀⡴⡒⣒⡶⣝⢻⣄⡤⠿
⠀⠀⠀⠀⠈⠳⢤⣀⠀⠠⠆⠀⠀⠀⢧⣸⣹⣾⠀⠀⠀⠀⢼⡳⠒⠛⣲⣶⣖⣛⣓⣶⣞⣹⠆⠀⠀⠀⠀⣟⠡⠀⣟⢾⣹⣽⠽⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠃⠀⢸⡏⡽⠃⠀⠀⠀⠀⠈⢿⡛⠉⠉⠉⠛⠯⣍⠉⢉⡟⠀⠀⠀⠀⠀⡏⣙⡦⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠚⠛⠋⠀⠀⠀⠀⠀⠀⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣶⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠉⠐⠺⣝⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⡁⠰⠀⣙⢷⡀⠀⠀⢀⣀⣀⣰⣏⣀⣀⣀⣀⣀⣀⣀⣙⣎⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡄⠀⢠⠞⠀⡄⣷⠀⠠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱
⠀⠀⠀⠀⢀⣀⡤⠤⠶⠾⠧⣤⡄⢀⠀⣤⡤⠷⠶⠦⢽⣶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⡖⠋
⣀⣀⣀⣠⡏⢁⣀⣤⣤⣤⣄⣀⠙⢿⠋⣁⣠⣤⣤⣤⣄⣸⠀⠀⠀⠀⣠⠖⠛⠛⠲⣤⠤⣄⠀⠀⣇⣀⣀⣀⣀
⣿⣿⣿⢸⡇⣉⣤⠤⠤⠤⠤⣌⡁⢸⠀⠉⠀⠀⠀⠀⠀⢹⠀⠀⠀⢸⠃⠀⠀⢀⠞⠁⢀⡞⠀⠀⣿⣿⣿⣿⣿
⣿⣿⣿⢸⡇⢀⣀⣠⣤⣤⣄⣀⠀⢸⠀⣀⡤⠴⠶⠒⠒⠛⠓⠒⠒⢚⡒⢒⡶⢋⡤⣾⠃⠀⠀⠀⣿⡻⣿⣿⣿
⣿⣿⣿⢺⡇⠉⣁⣀⣀⣀⣀⡈⠁⢸⢾⣵⡚⠉⠉⠓⠦⠤⠴⠚⠉⠉⠉⢿⠴⠯⣤⣬⡆⠀⠀⠀⠙⣯⢻⣿⣿
⣿⣿⣿⣽⣗⣋⣉⣀⣀⣀⣈⣉⣳⣬⣾⡄⠉⠙⠓⠒⠲⠶⠶⠶⠶⠶⠒⠒⠚⠋⠉⢠⣷⣶⣶⣤⣤⣼⣷⣿⣟
⣿⣷⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⣿⣻⣻⣯⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣤⣤⣤⣴⣾⣿⣼⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠤⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡐⠒⢒⡶⣒⢲⠖⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡧⣖⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣧⣴⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣤⣈⣉⣀⣀⠀⠀⠉⠉⠉⠅⠀⣇⡬⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠛⠛⠛⠛⠛⠿⠿⠿⠿⡇⠀⡇⣩⡁⢸⠀⣀⣤⡶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⣁⣀⠀⠐⠒⠒⠀⠀⠀⠤⠤⠅⠀⠫⣑⡡⢸⠛⠋⣉⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠒⠒⠀⠀⠀⢤⣼⣴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⡠⣶⣶⣿⣍⠉⠐⠒⠂⠤⣄
⠀⠀⠀⠀⠀⡀⠀⠈⠙⢿⣿⣿⣶⣦⣐⢀⡤⣠⠀⡄⠀⠀⠀⠄
⠀⠀⠀⠀⡒⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠒⠒⠒⠒⠆⠀⡀
⠀⠀⠀⣔⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠈⠩⠐⣂⡲⠆
⠀⠀⠀⢪⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣠⣤⢾⣿⡿⠃
⠀⠀⠀⠸⡀⠀⠀⠀⠐⠐⠒⠂⠀⢽⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⠟
⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢀⣄⠂⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠟⠁
⠀⠀⠀⠀⠈⢦⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣼⣻⡅⡮⣀⢘⢏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣿⣛⡾⣿⡽⡒⡋⠀⡃⠀⠀⠀⠀⠀⡠⠞⠉⠈
⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣀⣀⣀⣠⣄⣀⠉⠓⢾⢿⣿⣜⠧⢶⡠⠓⢠⠟⠀⠀⠄⣀⣀⣠⠄⠀⠂
⠀⠀⠀⠀⠀⠉⠉⠉⠻⠿⢿⣿⣿⣿⣿⠿⠛⠒⣾⣿⣿⣿⣿⣛⣁⣤⠟
⠀⠀⣰⡇⠀⠁⠂⢀⣤⣴⣾⣿⣿⡟⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⢸⣆
⠀⢰⣿⣃⣠⣴⣾⣿⣿⣿⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⢸⣿⣿⣿⣿⡿⠟⠋⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠱⡀⠈⠙⠲⠀⠀⠀⢀⣀⡀⠤⠤⠀⠚
⠀⠘⠟⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠂⣬⡶⠿⡏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡄⠀⠀⠀⠐⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛

⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡿⠆
⠀⠘⢿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠺⢎⡀⠀⠀⠁⠀⠀⠀⠀⢰⣷⣾⣿⣿⣾
⠀⠀⠀⠈⠋⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⡀⠴⠀⠀⠀⣿⣿⣿⣀⣿⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⢠⣤⣿⣿⡿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣧⡄⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⣶⡄⠀⠀⠀⠀⠀⢀⢀⠖⢂⢠
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣏⠀⠀⢨⣿⡄⠀⠀⠀⠀⠈⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡈⠠⠄⠀⠀⠀⠀⠀⠀⣾⠁⠀⡟⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢃⠌⡖
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠋⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠸⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠿⡿⠛⠛⠋⠉
⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⣀⡀⡊⠙⠢⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⡄⠀⠙⢄⠠⠀⢁⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⣀⣀⡇⠀⠀⠙⢤⣀⣀⡏⠒⠂⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⢠⢻⡟⣄⠀⠀⠀⠀⠈⠉⠧⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⠿⢿⣧
⠀⠀⠀⣀⠆⣸⢸⡌⣦⡀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣿⣿⣌⣆⣺⣿⡀
⠀⠀⠸⡏⠀⣿⠘⠷⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠠⠀⠀⠠⠀⠐⠄⠀⠰⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⢀⠆⠰⠂⠄⠀⡴⠀⠲⣄⠀⠀⢀⣰⣶⡆⠀⠀⡿⣿⡷⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⡀⠘⠲⢶⡐⢠⡄⢀⢚⠁⠹⣵⣾⡍⢯⠀⢤⡀⠳⠛⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠊⠀⠀⢠⠀⠂⠀⠀⠀⠀⠐⢄⡾⢧⠀⠀⠈⠛⢧⠀⠀⠀⠹⠇⠻⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠒⠆⠀⠈⠁⠀⡄⣃⢉⣤⣄⡀⢀⡤⠓⢁⠀⢠⡄⠀⠀⢀⠀⠘⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢰⣻⠰⣷⣴⣤⠀⠨⠰⠀⢸⡿⠉⠉⠙⡆⠀⠀⡀⠛⠎⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠛⠛⠃⠀⠀⠀⠀⡨⠁⠄⠂⠀⠁⡀⠀⠈⢻⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠑⠀⠁⠀⠀⠀⠀⢠⡀⠀⠐⠲⠀⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠃⠻⠦⡄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⣠⡤⠀⠀⢀
⠀⠀⠀⠀⢀⣶⡠⢤⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠉⠢⡀⠀⡿⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⣼⡏⠀⣾⠇⠀⠀⠀⠀⣾⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢃⡀⠀⢠⠴⠒⠲⣦⣴⠊⠁⠀⠠⣀⠈⡆
⠀⠀⠀⠀⣿⠓⠚⣏⢠⠞⢳⡧⢠⣿⢶⡅⢀⡾⢁⠆⡞⣶⠇⢰⡇⢰⡿⠀⠀⠀⠸⣸⡇⣰⠋⠀⠀⠀⠈⡿⠀⠀⠀⠀⠸⡞⡇
⠀⠀⠀⠀⡿⠀⢀⣿⢿⡠⢸⣇⣼⠇⢸⣇⢸⠁⡠⠊⢸⡏⣠⣾⡧⣾⠇⠀⠀⠀⠀⠣⣸⠡⣀⠀⠀⠀⠀⣿⠠⠀⢀⡤⢀⡿⠃⠀⠀⡸⡓⠂⣰⠧
⠀⠀⠀⠰⢤⣤⠾⠃⠀⠀⠈⣡⠏⠀⠈⠁⠀⠉⠀⠀⠈⠉⠁⠈⣰⠏⠀⠀⠀⠀⠀⠀⠉⠀⣈⠳⠶⢬⠀⣿⡔⢋⣩⠕⠋⠀⣴⠥⢠⠞⠁⠀⢳⡀⢨⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠚⠉⠁⠀⠀⠀⠀⠈⡌⠠⡉⣥⠁⡄⢩⠉⣭⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠐⠀⣰⣿⠟⠁⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠸⡄⢃⡘⠀⠇⠜⢀⢧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⠁⢠⡟⠁⠀⠀⢠⠟⠁⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣁⣀⣀⡈⠨⠘
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢂⠁⠀⠀⠁⠒⣄⠀⠀⠀⠌⡀⠀⠀⠀⠊⠀⠀⠀⠀⠃⢤⣀⣀⠀⠐⠃⠀⠄⢂⡄
⠀⠀⠀⠀⠀⠀⢀⠎⢠⢀⡤⠄⠀⠀⠀⠈⢧⠀⠈⠀⠠⣀⣀⣀⣀⣠⡤⠀⢘⡉⠉⠀⡐⠒⣒⠒⠈⠩⠭⠊⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⢦⠠⣤⠇
⠀⠀⠀⠀⡴⠊⡝⢀⠀⢸⠀⣀⠈⣶⡄⠈⣾⣇⠀⠀⠀⠀⠀⠨⠄⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠊⠉⠁⠀⠀⠠⠈⢃
⠀⠀⠀⣼⠁⠀⣇⠀⠀⣾⣧⠈⢛⡟⢸⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢌⡙⠛⠳⢶⠽⢭⣤⣭⣁⣀⣀⣀⣤
⠀⠀⠰⡇⠀⠀⠻⡄⠤⢏⣿⠀⠀⡰⠃⠰⢣⡏⠀⠀⠀⠀⠀⠀⣴⣿⣟⠩⣶⠲⣦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⣤⣤⣶⣡⣄⡈⠁⠈⠁⢍⠩⢉⣛
⠀⠀⠀⢣⠀⠀⠁⢈⠙⠛⣁⠴⠊⠀⡀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣷⠬⢗⠲⠶⠶⠞⠀⠀⣠⡀⠀⠀⠀⠀⠀⢉⡀⠒⠀⠈⠛⠶⠼⠷⠶⠶⣶⠇
⠀⠀⠀⠈⠃⠀⢄⣀⡈⣉⣠⠴⠖⣋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠓⠒⠒⣶⣤⣦⠟⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠤⠔⠊⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠐⠒⠒⠂⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠙⢿⡄⠈⢣⠀⡀
⠀⠀⠀⠀⠀⠀⣀⡤⢶⣬⣍⡉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢈⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠻⣷⡄⠀⠀⠀⠄⠘⣇⠀⣸⠀⠈⢢
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠰⢀⠠⠀⠁⠂⢀⠀⠀⣀⣀⣤⡴⠶⠿⠛⣓⣼⡇⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠈⠷⠘⡆⠀⢈⠁⠁⠁⠛⢘⠔⠊
⠀⠀⠀⠀⠀⠀⡞⠀⠄⠀⢀⡀⢁⠀⢠⠠⠇⣈⣉⣤⠴⠶⠶⠛⢛⣉⢹⠀⠀⠀⠀⠀⠀⡄⢠⡀⢀⡶⠂⠀⠰⢷⠈⠨⠂
⠀⠀⠀⠀⠀⢸⡇⠁⠀⢃⠀⠀⠈⠀⠀⠂⢀⣀⣠⡤⠤⠀⡠⠾⠛⠁⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⢸⢠⡀⠀⠀⠀⡆⠀⠃⠀⠀⠈⣿⠀⠀⠀⠀⢀⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⡄⠤⣤⠄⠀⠰⢶⠐⣴⠶⡆⠶⢶⡒⠤⢄
⠀⠀⠀⠀⠀⠸⠈⠁⠆⢂⠀⡀⠃⡤⠀⠀⠀⠟⠀⠀⢀⣀⣘⡭⠶⢂⠇⠀⢀⣤⠄⠒⠒⠻⣯⠘⠀⢙⡆⠚⠀⢈⡇⠉⠀⣨⡇⠁⠠⠿⠀⠶⠃⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠃⠆⡤⠀⡇⠐⠿⢖⣿⠙⣿⡃⠤⠒⠁⠀⠐⠁⠀⣀⣁⣀⣀⠛⠀⣀⣈⣁⣀⠀⠈⠡⠤⠤⠒⣀⣐⣠⠴⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡼⠤⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠈⠉⠉⠉⢉⠙⠋⠙⠛⠛⠣⠛⠋⠉⠉⠿⠚⡻⠓⠶⠶⠶⠢⢴⠦⠶⠶⠶⡤⠶⢴⠶⣶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣦⠀⠐⢲⣶⣦⡄⠐⠲⣶⣶⣤⠀⠒⢶⣶⣦⡀⠐⠲⣶⣶⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⠟⠀⠀⢰⣿⣿⠇⠀⠐⣾⣿⡟⠀⠀⣾⣿⡿⠃⠀⢰⣿⣿⠟⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠐⠂⠒⠒⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠀⠐⠒⠁⠈⠙⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⡒⠒⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠈⢉⣉⣉⣉⢉⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣭⢍⡉⢉⢩⡁⣉⢉⡁⣀⢀⡀⣀⢀⡀⣀⣀⢀⣀⢽⢶⣶⣾⣤⡄⠀⠠⣽⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⡺⣷⣽⣾⣷⣽⣮⣷⣽⣾⣷⣵⣮⣾⣷⣿⣺⣷⣿⣿⣿⣿⣷⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⡿⢿⡿⢿⡾⡝⠿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⣿⢿⣿⣿⣿⠿⣿⢿⡿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣀⣀⣈⣙⠋⣁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣴⣦⣦⣴⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣄⢤⡀⠀⠀⠀⠀⠀⣰⠨⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠊⠒⠐⠂⠒⠐⠘⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣈⣉⣀⣀⡀⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⠈⠉⠉⠀⠈⠉⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠤⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠒⠒⠂⠀⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠐⠠
⠀⠀⠀⢀⣤⣤⠖⠠⠀⠀⠀⠐⠁⠀⡠⠀⠀⠀⢀⣀⢤⠀⡀
⠀⠀⢠⣿⣿⡿⠦⠀⣤⣖⠞⠁⠀⠒⠀⠀⠀⠀⠈⠁⠀⠀⡀
⠀⠀⢈⣿⣿⣂⠆⠘⠁⠈⠃⣀⠀⠀⠀⠀⠀⠰⠚⠁⠀⠂
⠀⢀⣼⣿⡿⢁⠀⠀⠀⠀⠀⠸⡆⠀⢀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⣾⣿⡟⠀⠘⠀⢀⡐⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡄⠐⠀⢀⠠⠐⠒⠙⠉⣀⢠⡆
⢰⣿⡏⠀⠀⠀⠀⠀⠑⠤⠀⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣻⠃
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠠⠄⠀⠉⠀⠂⠀⠠⡀⠀⠀⠀⣸⣿⣿
⠀⠉⢺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢀⡄⢒⠆⠁⠀⠀⠀⢉⢽⣿
⠀⠀⠈⠀⢶⠦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠘⠒⢒⡒⠒⠶⠶⠲⣶⠦
⠀⠀⠀⠀⣁⣤⡿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⡍⠀⢈⡭⠉⠭⠭⠿⠿⣿⣟⠀⠀⠁
⠀⠀⠀⠀⣼⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠸⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠂⠀⢹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢈⡏⢀⣤⣤⣤⡀⠀⠰⣄⠀⠀⠛⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡇⠺⣿⣿⠏⠀⠀⠀⡿⠀⡔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠘⠿⠀⠀⠀⡄⠀⢆⡜⠀⣀⣀⡁⡼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠛⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣦⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠘⠉⠉⠓⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣶⡀⠀⠀⠀⠀⠀⠀⢠⣧⣴⡄⠀⠙⠻⡿⠷⢄⠀⢠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣓⡀⠀⢀⣾⡿⢛⣉⣏⠀⠁⠿⠿⣦⢀⡀⠀⠒⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⠿⠻⠗⠊⠁⣾⡋⣽⣿⣤⠄⠀⠀⢈⠀⠀⠁⠀⠒⠉⠓⠈
⠀⠀⠀⠠⣤⠶⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠈⠉⢉⣿⣿⡏⠀⣀⣠⢴⡄⠀⠐⠀⢠⡄
⠀⠀⠀⠀⠙⠳⢤⣆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣨⠗⠩⣤⢾⢯⣤⠈⠁⠀⠂⠀⠸⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡼⠀⠀⠚⠈⠄⣻⠁⠀⠋⢹⣷⡆⢠⣀⣲⡔⠛⠛⠻⢦
⠀⠀⠀⠀⠀⠐⠶⠛⠉⠁⠀⠀⠉⠁⠀⠀⢀⢘⣶⡆⡍⠀⠀⠀⠈⠻⡇⠀⠉⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⣀⢀⣰⣾⣯⡉⢰⡇⠀⣴⣤⣄⣤⠀⠀⢀⡀
⠀⠀⠀⠀⣀⣠⣤⣤⡄⠀⠀⠹⣿⣿⡍⢿⣷⡻⡇⡞⢻⡄⠂⠈⣿⠿⠀⢸⠛⠏⣡⣴⡶⣦⡴⠤⠄
⠀⠀⠀⠚⠉⠁⠀⠈⠠⠿⠛⠛⠛⣻⣧⠤⠈⢄⠀⡇⠈⣿⡠⢀⡭⣤⣤⣤⣤⣄⠀⠉⠛⠿⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠂⠀⠀⠀⠰⠀⠈⡅⢀⣀⣤⣗⡏⡟⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠒⠆⡘⠀⠈⠉⠛⠛⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠚⠉⠙⠛⠫⠉⠉⠉⠛⡚⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠙⡄⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢛⠖⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⡳⡀⠀⠀⠐⡘⡀⠀⠀⢸⡔⠀⠀⠀⡄⠀⠀⠀⠀⠠⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠈⠚⣤⠀⠀⡈⠇⣰⣤⣾⣿⣿⣶⣾⣷⣤⣄⣀⡔⠀⠀⠀⠀⡠⠊⠛⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠑⠄⠀⠀⠀⢈⠓⠉⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣠⡶⠊⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠘⠶⡔⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠄⢀⡹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⡤⠤⠐⣒⠋⠉⣩⣯⣭⡭⠉⠉⠉⡩⢯⣭⣿⣟⡛⠻⠿⢿⣿⣿⣿⣿⣶⠀⠐⠈⠁⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠒⠒⠛⠛⣺⠁⠐⠀⠀⣎⡁⠒⠻⠘⣻⣷⣶⣿⣶⣷⣦⣿⣻⣝⢀⣿⣸⡆⠙⡿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⠀⠀⠀⠀⠀⠘⢕⣄⡈⠻⣿⡿⠛⠂⠁⠉⣿⣛⣛⣘⠿⢿⠿⠛⡰⠌⠽⠞⣀⣴⠃⠀⠙⣿⡷⠴⠶⠒⠀⠬⠽⡅
⠀⠀⢰⣿⣿⣿⣿⣿⡖⣒⡚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠢⠥⣦⣀⡠⠄⠄⠈⠋⠉⠉⠉⣈⡉⠤⢥⣀⡤⠬⠝⠋⠁⢀⣠⣶⣿⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣋⣭⠭⠥⠶⠶⠖⠒⠒⠒⠶⠮⢌⣐⡤⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠛⠛⠓⠂⢉⣉⣁⡤⠤⠄⢒⡚⠭⠶⠿⠿⣿⣧⣀⣀⣀⠀⠠⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠿⠶⣽⣂⣂⣀⣀⣂⣀⣈⣽⡯⠭⡭⠭⠭⠤⠐⠒⠋⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠲⠦⠤⠤⠤⠤⠼⠻⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠓⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣴⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⢴⡟⠛⣌⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣴⠞⢫⠝⠀⢸⡇⠀⢹⡄⠀⠹⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡶⠟⠓⠄⠒⠁⠒⠖⠿⣿⣶⣿⠃⠀⠀⣿⡆⠙⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠘⠛⠒⠶⠶⠶⠶⠒⣋⣥⠞⠁⠀⠀⣰⡿⠁⢀⣿⣷⣬⡙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⣀⣀⣤⣤⢤⣴⣶⡒⠚⠋⠉⠁⣀⣀⣠⡴⠞⠋⠀⣠⠞⠉⣿⡿⣿⣷⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⣤⡶⠶⠟⠛⠉⠉⠀⠀⠀⠀⠈⠙⠻⢿⣿⣯⣍⣩⣤⣤⣤⣶⣮⣥⣴⣾⣿⠇⠈⢻⡇⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠶⠞⠛⠉⠉⠀⠀⠀⠀⠀⠉⠉⢛⣿⠏⠀⢀⡾⠁⢀⣾⠁⠹⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠶⣤⣤⣤⣤⣤⠤⠲⠚⠊⠉⠁⠀⠀⢀⣀⣀⣤⣤⡤⠶⠶⠾⠓⠒⠉⣉⣀⣴⡾⠋⠀⣠⣾⡟⠀⠀⣿⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣤⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠚⠋⠉⠉⠉⠉⠉⠛⠛⠒⠒⠒⠚⠛⠋⠉⢀⣀⣤⣾⣿⠏⠀⠀⣠⣿⡆⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠼⠿⠛⠋⠉⢉⣽⠋⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣠⣤⣠⡤⠶⠶⠶⢶⣿⣿⣿⡟⠋⠀⢀⣠⠞⣹⠟⠀⠀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣷⠶⠶⠖⠒⠊⠉⠉⠙⣟⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠉⠉⠻⢷⣤⣄⣀⠀⠀⠀⢈⣹⣿⡿⠟⠋⣠⡾⠋⠀⠀⢀⣾⣿
⠀⠀⠀⠀⠀⣤⣖⣋⡉⠁⠀⠀⠀⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣼⣿⡿⠿⠿⠛⠛⠉⠁⣠⡴⠟⠉⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢈⣩⡟⠛⠛⠛⠛⠋⠁⠉⠀⠀⠀⢀⣠⣤⣚⣋⡉⠉⠁⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⢀⣠⠴⠞⠛⠉⣀⣀⣤⣶⣿⣿⣿⠿⣿⠷⡄
⠀⠀⠀⠀⢠⣶⢻⣿⣦⣤⣤⣄⣀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣶⣶⣶⣾⣿⣷⣶⣶⣶⡿⡿⢟⣿⠙⣏⠳⡄⢍⠺⠛⡤⣿⡀
⠀⠀⢀⡠⣞⠫⣵⠍⣿⡟⢋⡉⠻⣭⢉⡿⣛⠏⠛⡿⢙⠟⡛⣩⠉⠛⠙⠛⢛⢏⡹⣹⣙⣏⠙⡏⢩⡈⠁⠈⢦⡔⢠⠀⠈⠙⢀⠈⡄⢁⠀⠄⢤⣑⢮⡄⢻⡀
⠀⣰⣟⡄⠹⠀⠇⠘⣡⠷⠈⡯⠆⠉⠌⠃⠉⡰⠀⢤⠃⠛⠸⢀⠋⠀⠋⠛⠈⠈⠁⠱⠉⡭⠀⡐⠃⠁⠀⠀⡘⠀⠂⣰⡄⠰⡆⠀⡿⠀⢱⠆⢠⡏⠐⠀⣼⣷⣦
⢨⡀⢟⠛⣴⡷⠶⠄⣹⠀⠘⠁⡼⠁⠀⠀⠰⠃⠀⢰⠂⡴⠀⢹⠀⢠⠂⠰⣀⠀⡄⠀⠶⠀⣠⡀⠈⢠⠀⠀⢰⡇⣀⣾⣀⣴⢀⣤⡇⣠⡟⡴⠟⠻⠧⣿⣾⠃
⠀⠳⠈⢄⢹⡀⠀⠘⡉⡴⠛⠉⠸⣆⣰⣦⣤⠷⠒⡴⢀⣡⠼⠚⠳⡄⢠⡖⠉⠈⠓⢤⣤⡊⠉⠉⠳⡄⢷⡏⠀⠈⠙⠏⠙⠀⠈⢙⠃⠀⢙⡎⠀⠀⢠⣸⠆⠀⣼
⠀⠀⢣⠘⣿⣡⠀⠀⢡⢀⡀⠀⠀⢫⣽⣮⠁⠀⠀⢻⣼⠁⠀⠀⠀⣿⡎⠁⠀⠀⠀⣶⣿⠁⠀⠀⠀⣷⡌⠀⠀⠀⢸⣼⠃⠀⠀⡟⠀⠀⡾⠀⠀⠀⣾⠋⠀⡰
⠀⠀⠈⠆⠘⣻⡄⠀⠀⣾⣧⠀⠀⠸⠟⢻⡄⠀⠀⢸⣥⡆⠀⠀⠀⢉⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⢀⣄⣤⠀⠀⠀⣈⡇⠀⠀⠸⠃⠀⣴⠁⠀⢀⣿⡏⠀⢠⠃
⠀⠀⠀⠐⡀⢡⣹⡆⠀⠸⣿⡄⠀⠀⡟⢸⡇⠀⠀⠀⣄⣿⠀⠀⠀⢸⠗⠄⠀⠀⠀⣿⢿⠀⠀⠀⢸⣿⠁⠀⠀⢰⣟⠇⠀⠀⡆⠀⢠⠏⠀⠀⡜⢣⠁⢀⠎
⠀⠀⠀⠀⠙⡀⣤⣷⠀⠀⢸⣣⠀⠀⢸⠤⣷⠀⠀⠀⢩⣽⠄⠀⠀⢸⣆⡶⠀⠀⠀⣵⣿⠀⠀⠀⠺⣿⠀⠀⠀⣠⡻⠀⠀⢀⠁⠀⡜⠀⠀⢰⣱⡆⢀⠟
⠀⠀⠀⠀⠀⢡⢠⡙⡇⠀⠈⣿⡄⠀⠀⣆⠹⡆⠀⠀⠈⢿⡀⠀⠀⢸⣽⣷⠀⠀⠐⠛⡛⠀⠀⠀⣾⡍⠀⠀⠀⣹⡏⠀⠀⠘⠀⢠⠃⠀⢀⠟⡷⠀⡜
⠀⠀⠀⠀⠀⠈⡄⢀⠸⠀⠀⢸⣧⠀⠀⢹⡾⣇⠀⠀⠀⢾⡇⠀⠀⢸⣀⣿⠀⠀⢸⢀⣿⠀⠀⠀⣷⡇⠀⠀⢠⣿⡅⠀⠀⡇⢀⡙⠀⠀⡞⣰⠀⢰⠁
⠀⠀⠀⠀⠀⠀⢡⠌⡀⠧⠀⠀⣿⠆⠀⠀⣿⢿⠀⠀⠀⠸⣿⠀⠀⢸⣿⣯⠀⠀⠈⢘⡏⠀⠀⠰⠟⠀⠀⠀⢸⣿⠀⠀⢠⠀⣬⠁⠀⡜⠀⠇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢰⢁⠐⡄⠀⢸⣧⠀⠀⢹⢘⡁⠀⠀⠀⣾⠀⠀⠸⣹⣿⠀⠀⠀⢸⡇⠀⠀⢀⣾⠀⠀⠀⣦⡟⠀⠀⠉⢠⠃⠀⢰⠁⣴⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠂⠀⠀⣷⡀⠀⠀⣿⣿⠀⠀⠀⢿⡀⠀⠀⣼⣿⠀⠀⠀⣾⡇⠀⠀⢘⡿⠀⠀⠀⣿⠇⠀⠀⢠⡟⠀⠀⠗⢸⠃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠸⣇⠀⠀⢻⠍⡀⠀⠀⠘⡇⠀⠀⠃⣸⠀⠀⠀⠟⠁⠀⠀⢉⠁⠀⠀⢸⠈⠀⠀⠀⣿⠁⠀⡾⠀⠆⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢹⠀⠀⠈⢀⠃⠀⠀⠀⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠘⡆⠀⠀⢀⠉⠀⠀⠁⠸⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡆⠀⠀⣀⣠⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠒⠒⠢⠤⠤⡤⠄⠀⠀⣀⣀⡀⣀⣀⣀⣀⠀⠠⠤⣤⠤⠤⠤⠒⠒⠒⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠚⠉⠒⡶⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠊⠲⢶⣦⣤⣤⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣠⣾⣷⡿⠂⠀⠀⠀⠉⠋⠛⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⣠⡴⣦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢸⡿⠾⠛⠀⠀⠐⠛⠛⠆⠀⠀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠓⠘⠀⠀⠀⠘⢋⡥⠀⠀⡤⠤⢬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⢀⡓⠂⠀⠀⠀⠀⠀⠀⠀⠇⠛⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡰⢊⡴⠋⢋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣕⡀⠙⣿⣷⡀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡇⠀⠀⠀⠀⡠⠋⠄⠚⠡⠀⡀⠀⠀⠘⣰⠋⠀⣀⠤⠛⠖⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣴⣄⠈⣽⠆⠰⠋⠰⣄⠀⠀⠀⠀⢾⣿⠀⣼⠀⠀⠀⠀⡀⠀⢀⢈⠂⠀⠉⠜⣁⠠⠳⠁⠐⡛⢁⣠⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣛⣿⡏⢻⣷⣾⡇⠀⠙⠳⢦⣀⠀⠈⢁⣾⠟⣄⠀⠀⡰⠐⢀⠏⢂⠀⣰⣿⣿⣶⣶⣤⣄⣀⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⣰⣿⣿⣾⣿⣿⣾⣡⠇⡰⠁⡠⢎⢀⠂⣼⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠛⠻⣁⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣷⣿⠟⡀⡀⡰⠁⢀⡆⣼⣿⣿⣿⣿⣿⡟⣸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠴⠋⣷⡄⠀⠈⠲⣄⠀⠀⠀⠀⠅⠀⠀⡘⢿⠉⠁⡘⡀⡐⠁⢀⡼⣽⣿⣿⣿⣿⣿⡟⢰⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⢸⡇⠉⠾⠋⢄⠁⡀⠈⢆⠈⢆⠀⠀⠀⠉⠒⣤⣄⣀⡀⢸⡆⢀⢀⡜⠐⠀⡰⠀⢜⣿⣿⣿⣿⣿⡟⠳⣤⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣼⣿⠿⣷⣤⠺⢗⠈⠀⠈⢢⢛⠳⣤⣀⣴⠂⠀⢠⣽⠟⠎⠀⢾⠞⠀⠀⠀⢀⢎⣾⣿⣿⣿⣟⠃⠑⣄⢹⣿⡿⠟
⠀⠀⠀⠀⠀⢹⣤⣟⢾⣿⡄⠀⠱⣿⡄⠀⢡⢢⣌⠉⠑⢀⣤⡀⠉⣤⣶⣄⠸⠙⠓⢶⡀⢮⣿⣿⣿⣿⣿⡏⠰⢂⣇⠜⠉
⠀⠀⠀⠀⠀⣼⢿⣿⠀⠈⢳⣶⠄⢨⠙⣆⠀⢳⡉⣠⠖⡋⠉⠁⠀⠐⠀⢤⣅⠄⣄⡸⠎⢟⡛⠛⣻⠛⡛⠃⠞⢈⠃⠀⠀⠀⠀⠀⣤⣠
⠀⠀⠀⠀⠀⢿⣮⡙⢠⣶⠁⠁⠪⣾⣄⠙⡆⠀⠣⠉⠀⠀⠀⠀⢀⡴⠋⠀⢱⣶⠀⡇⠀⠘⠿⣴⡏⠠⠀⠀⠀⠎⠀⠀⠀⠀⢀⣼⣫⡕⣡⠄
⠀⠀⠀⠀⠀⠀⠻⣿⠆⠉⠂⣠⣬⠟⠣⣠⣧⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠤⠄⠊⡉⢿⣂⣀⣽⠁⠸⠇⠀⡜⠀⠀⠀⠀⠀⠙⠻⢛⠄⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡖⠒⠴⣍⢻⣦⣄⠉⢻⠀⢀⡠⠖⠉⠁⠀⢀⣴⡧⠒⢲⠀⡀⢰⡏⠁⠀⢠⡄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠐⢋⡀⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⣿⣫⠴⠚⠋⠁⠀⠀⣠⠞⠉⠉⠁⠀⠀⠘⣶⡇⢸⣇⢀⡴⠋⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⢂⠉⠤
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠚⠉⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢠⠐⡇⢸⠉⢻⣬⣤⣷⠄⢠⡏⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠚⣡⠖⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⢠⠃⠀⢣⢬⠔⠁⢃⠀⠁⢠⠞⠀⠀⠀⠀⠀⢿⣤⡼⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⢀⣀⣤⠶⣿⠀⠀⣴⠃⠀⠀⠀⠀⠀⠸⡄⠀⠸⣀⡀⠀⣼⣀⣴⠋⠀⠀⠀⠀⠀⠀⡼⠀⢠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠋⣉⠀⠀⢿⡗⠐⠛⠓⠒⠲⠦⠂⠀⠂⠙⡶⠦⢭⡦⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢃⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠆⢸⣷⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡇⠀⣿⡻⡁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠓⠊⠁⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢧⣤⡴⠛⠁⢀⡼⠃⠀⠀⠀⠀⠉⠉⠉⠁⡀⢀⠐⢀⣇⣗⣱⡀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣶⣆⣀⣉⣀⡈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠸⣧⣄⠀⣤⣤⡄⠤⠤⣤⣄⣀⢤⡤⠤⠤⠤⠤⢀⠆⠀⣿⡇⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠉⠉⠉⠒⠋⠀⠀⠀⠀⠀⠁⠀⠀⠰⣿⠀⠀⣿⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣿⡆⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⠀⠀⣿⡆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠘⣿⣄⠈⠻⠆⠀⠀⠀⠀⠀⠀⣠⡎⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣇⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠈⢻⡗⣲⣄⠒⠒⠒⠒⠲⣟⠋⠀⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠊⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢙⢀⣄⡤⠀⠀⠠⠀⣤⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⠀⠀⠀⠀⠀⠀⠛⡟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⠀⠀⠀⠀⠀⠀⠀⢠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡖⠀⠀⠀⠀⠈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠛⠃⣴⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡀⠠⠤⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠤⠂⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢿⣿⣷⣼⣦⣴⣾⣿⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠛⠛⠉⠉⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣆⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢾⣿⠇⣿⣿⡀⢀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⡖⠀⢠⡀⠈⣧⠀⠀⠀⠀⠀⠀⣿⣿⠀⢹⣿⠆⣇⡞
⠀⠀⠀⠀⠀⠀⢸⠡⢜⡲⢽⣶⢻⠀⠀⠀⠀⠀⠀⠘⠁⠀⠸⡏⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠙⣺⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡭⢬⡍
⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠘⣮
⠀⣀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠔⠛⠁
⠀⠻⠦⠘⣷⠖⠤⠤⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡐⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠈⠉⠉⠑⠒⠒⠲⢤⣠⣤⣤⠤⢤⣄⣀⣀⣀⣀⠀⠀⠀⢠⠁⠶⢛⣃⡈⠛⣁⡒⢠⡤⠉⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠁⢸⡀⠚⢦⡬⠀⠀⠩⠡⠄⠂⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⢦⣄⡀⠂⠝⠛⠀⠘⠛⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⢤⣄⣀⣀⣉⡛⠓⠶⠶⠦⠤⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣠⠿⠂⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣿⡛⠛⣈⣉⣷⣹⡇⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢿⣿⣿⣿⣿⣿⣧⡀⠀⣴⠀⠱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣷⣽⡿⠿⠿⣿⣿⣿⣿⣶⣦⣦⡰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⡚
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⢻⡏⠝⢿⣿⣿⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡷⡾⣿⠿⠓⢶⣧⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣶⣴⣿⡿⢦⣄⣤⠈⣤⣬⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣧⡜⢃⣤⠿⠉⠀⠈⠉⠒⢦⢁⣤⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣷⡾⣧⡞⠁⠀⠀⠀⢠⣤⡀⠛⣠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣽⢿⣏⠀⠾⠋⠀⠀⠀⠀⢸⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⡿⢿⣾⢿⣆⠀⠀⠀⡄⠀⠀⡸⠋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣠⢟⣭⣿⣦⠀⠀⠀⠀⠰⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠙⢶⡿⠇⠀⠀⠀⠀⠀⠛⣫⠀⠚⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠉⠀⢀⡀⠾⠶⠉⠠⡀⠀⠀⠀⠀⢯⠂⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠋⠀⠐⠂⢠⣠⡶⠀⠁⠈⠀⠀⠀⠀⠈⢟⠀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⠀⠁⠲⣤⠐⢶⣆⡀⠀⠐⢧⡄⠀⠀⢘⡇⢈⡂⢋⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣤⣤⣤⣠⡀⠑⠦⢈⠓⠀⠀⠹⣷⣄⠂⣨⣷⣿⣧⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣦⡀⠉⢶⡀⠀⠀⢿⡟⢳⣉⣿⣦⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣽⡆⠀⠘⡅⣸⣿⡿⣿⣿⣿⢿⣿⢧⡀
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠏⠀⠖⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⠟⠀⠈⣷⣾⣭⣿⣧⣴⣶⠄
⠀⠀⠀⠀⠀⠐⠀⠀⠘⢓⣤⣤⣵⡟⡛⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⠟⠁⠀⠀⠀⢺⣿⠿⠁⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡾⠋⣠⣭⣿⣶⣿⣾⣿⣇⣬⣿⡿⢿⣿⣿⣟⢁⠀⠀⠀⠀⠀⠈⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣿⣿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠙⠻⣿⣿⣶⣄⣀⣤⡤⠤⠶⠲⡿⢶⠒⠀⢀
⠀⠀⠀⢠⠀⠀⠀⢀⣾⣿⣿⡇⣴⣿⣿⣿⢿⡿⣿⣇⡀⠀⢶⡄⠀⠙⠫⣍⣉⣉⣤⣤⣶⣟⡾⣿⡇⠀⠀⠑
⠀⠀⠀⡌⠀⠀⢠⡜⣿⣿⣿⣼⣿⣿⢻⣿⡀⣤⣿⣿⣿⣶⣌⣱⠶⠦⠀⠈⠙⢦⣀⡒⡩⠋⢀⣾⠂⠀⠀⢀
⠀⠀⠀⠆⠀⠀⣾⣷⣿⣿⣿⣿⣿⣥⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠈⠙⠃⠴⡾⣆⠃⣀⢡⡞
⠀⠀⠀⠠⠀⢼⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢉⡅
⠀⠀⣀⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢱⣶⣿⣆⣾⡿⠓⢾⡄
⠀⢰⠟⠉⡻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣆⠀⡀⠸⣿⣿⠙⣻⡇⠀⠀⢶⠶⠲⠶
⠀⣶⣶⣾⣿⣿⣿⣿⣿⢳⡟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣦⠀⠀⣿⡿⠀⣿⡇⠀⣠⣂⡀⣀⣀⡀
⠀⠹⢿⣿⣿⣿⠻⢻⣿⣈⣛⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⣾⣿⡇⠀⢹⡇⠀⠈⣿⣿⣿⣿⡍
⠀⠀⢰⣿⣿⣯⠀⢨⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠹⣯⠀⢸⣷⠀⠀⣿⣿⣿⣿⣿⣷
⠀⢠⣾⡿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡄⠹⡄⠰⣿⠀⠀⣿⣿⣿⣿⣿⡟
⠀⠘⣿⣿⣿⣏⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⣴⠀⣼⠀⠰⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⣿⡿⠦⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠀⢻⡇⠘⠀⠀⢻⣿⣻⣿⣿⣏⠇
⠀⠀⢴⠿⣿⡇⠀⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡄⢁⡀⣸⣿⣿⣿⣿⠏⡆
⠀⠀⢠⣀⣽⡇⠀⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢈⣷⣿⠃⢹⣿⣿⡏⠑⢾⡟
⠀⠀⣸⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣉⣤⣯⣥⠀⡄⢸⣿⣿⣿⣿⡿
⠀⠀⢹⡿⢿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠦⠀⠀⣴⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠃⠀⣽⡟⣿⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠶⠂⠀⢸⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣭⡿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠛⢿⠻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣿⣿⣿⡿⣿⣿⣾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠸⠃⠠⢿⠹⣧⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠙⠛⠛⠛⠛⠛⠻⠿⣿⢿⣯⡴⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠂⠧⠤⠚⠉⠀⢀⠤⡄⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉
⠀⠠⠔⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠶⠚⠈⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡄⠠⠔⠀⠀⢀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠤⠄
⠀⠀⠀⠀⠀⠐⠋⢁⣀⡤⠄⠂⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⠀⢀⠀⢂
⠀⠘⠀⠑⠀⠠⠀⢒⠉⠀⠀⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠀⠆⠃⠠⠀⠀⠀⢸⠀⠀⠓⠂⠉⠂⠉⢀
⠀⠀⠀⠉⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠁⠊⠀⢸⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡀⠀⡀⢀⠀⠀⠀⢈⡤⠤⠀⠀⠀⠀⢀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠤⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀⢠⠡⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠀⠐⠈⠘⠒⠘⠻
⠀⠀⠀⡀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠄
⠀⠀⡰⠤⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠤⠀⠀⠀⠀⠀⣀
⠀⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠀⢀⡀⠈⠐⠀⠀⢰⠀⠀⠀⠀⠀⢀⡴⠒⢢⣄⠀⠀⠨⠀⠀⠀⠀⠀⣀⡀⡀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠃⣈⠁⠉⣈⠌⠀⠸⠀⠀⠀⡐⠢⠄⠭⠭⠬⠥⠔⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⢀⠤⠐⠒⠀⡒⠤⢄⡀
⠀⠀⠀⠠⢀⠀⠄⠀⠀⠀⠀⠀⠀⢃⠐⡠⠰⠄⠒⠐⡠⢀⡇⠀⠀⠀⠀⠘⠢⢃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⡈⢀⠀⣄⠄⢰
⠀⢀⠀⠀⠘⠑⠀⠀⠀⢰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠴⠄⠀⠀⢀⠞
⠀⠀⡀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠑⠒⠒⠒⠉⠁⣠
⠀⠀⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠀⠀⠁⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠓⠒⠋⠀⠀⠤⠢⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠦
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠊⠁⡀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠋⠉⠤⢈⠀⠀⠀⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠐⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠤⠤⠀⠒⠃⡈⠡⠀⠀⠐⠚⠋⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⢉⡉⠁⠁
⠀⠄⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⡀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢰⠆
⠀⢠⠀⠤⠀⠀⠠⠄⠀⠀⡍⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⣠⠐⠀⠀⠀⠀⠀⠀⠀⠦⠐⠲⠐
⠀⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡠⠐⠀⠀⢀⠀⠀⠀⠈⠀⣠⡾⠀⠀⠀⠐⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠁⠀⠈⠁⢀⠀⣀⢀⠀⠀⠀⢨⡤⠄⠀⠀⠀⠀⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⡠⠠⠦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⡀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠂⠀⠂⠁⠑⠀⠛
⠀⠀⠠⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⠀⠀⠀⠀⠀⠉⠀⠒
⠀⠀⠚⠒⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡀⠉⠉⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠰⠐⠀⠁⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢘
⠀⠰⡄⠰⠠⠄⢄⠀⠀⠀⠀⠀⠀⣀⠘⡣⢄⡛⣂⣠⡌⠀⠀⠀⠀⠀⠒⠐⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠁⠀⢀⠁⠀⠀⠀⠀⠀⡇⠠⢀⣀⠩⠄⠄⠀⡇⠀⠀⠀⠀⠠⢠⠀⠐⠶⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⠂⠀⠀⢈⢡
⠀⠀⠀⠈⠗⠄⠀⠀⠠⠀⠀⠀⠘⠀⠁⠁⠀⠁⠉⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠉⠉⣤⠁⠈⠈⡸
⠀⢀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠐⠢⠴⠶⠒⠈⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⢀⠀⠀⠈⠈⢁⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣖⣉⣉⣁⣬⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠉⠉⠛⡇⠀⠀⠀⠀⠠⢤⣀⡀⠉⠛⠦⡀⠀⠈⠂⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣤⣤⣀⡀⠀⠈⠓⠦⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡄⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠞⠀⠈⢧⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⣀⠤⠀⠠⠠⡄
⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⢈⡅
⠀⠀⠀⠀⠈⠙⠻⠷⣠⣤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠢⠀⠀⡀⠀⠀⡐⠉⠁⣴⠀⠀⠀⢸⠃
⠀⠀⠿⣶⣄⡀⣀⠀⢀⣍⣉⣉⣵⠖⠂⠀⠀⠀⠀⠤⡀⠈⠑⠀⠀⠀⡀⠤⠒⠉⠀⡠⠶⢃⡀⡠⠉⠀⠀⢀⡿
⠀⠱⣦⣄⣈⠁⠙⠃⢠⠇⠀⠈⠀⠀⣀⡀⠐⠒⠂⠀⠀⣀⡠⠐⠂⠁⠀⠀⠀⠀⢸⠀⠀⠈⡘⠃⠀⠀⣠⡎
⠀⠀⠀⠉⠉⠈⠛⠃⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠔⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⠛⣧⢠⡎⠁⠀⠀⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠖⠒⠁⠀⠀⠀⠀⡀⠀⢄⣀⠀⠀⠀⠀⠀⠸⢀⣿⠖⠀⠀⠰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⠁⠀⠀⠀⠀⠈⠉⠐⠄⠀⠀⠀⠙⠿⣤⡤⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢻⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠉⠛⠿⣶⣬⣛⠶⠂⠈⢀⣠⠞⠀⠀⠀⡀⢀⠚⠉⠉⠉⠙⣄⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠋⠁⠀⠀⠀⠀⡌⠀⠀⠽⠖⣶⠦⡔⠉⠹⡄
⠀⠀⠐⣄⣀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⡄⠀⠀⠙⡾⠃⠀⢰⠇
⠀⠀⠀⠈⠙⠛⠻⠥⠬⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⢀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣠⣀⠶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢀⣤⣤⣤⣴⠀⠀⠀⢀⣤⣴⣶⣶⠀⠀⠀⢠⣶⣶⣶⣶⠀⠀⠀⢀⣴⣶⣶⣶⡆⢀⣀⣠⣶⣶⣿⣿⡆⠀⠀⣠⣴⣶⣶⣶⣾⣿
⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⢹⣿

⠀⠀⠀⠀⠐⠀⠒⠒⠶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠿⣿⣿⣷⣦⣤⡀⣠⣶⡺⣷⣶⣦⣤⠠⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠽⢿⣿⣿⣿⡿⢋⣵⣿⣿⣿⣿⢹⣿⣿⡇⢸⢫⣆⢹⡿⠛⠻⣷⠗
⠀⠀⠀⠀⠀⠀⠉⠿⢿⣿⣿⠟⢋⣶⣿⣿⣿⣿⣿⢯⣹⡿⠋⠇⠈⠳⠶⠊⠀⢠⣯⣁⣀
⠀⠀⠀⠀⠀⠐⠛⣛⣽⡿⢃⣴⣿⣿⣿⣿⣿⣿⣏⠀⢫⡅⠀⠀⠀⠢⡀⠀⠀⡀⠀⢀⠋
⠀⠀⠀⠀⠐⠒⠿⣿⠟⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠠⡄⠀⠀⠀⢆⡀⠀⣢⠔⠁
⠀⠀⠀⠀⡠⠶⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣦⡀⠀⠐⠍⠑⢦⠬⠛⠁
⠀⠀⠀⠀⢀⣤⡟⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣷⠀⠈⠉⠗
⠀⠀⠀⠀⢉⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠙⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣀⢀⣀⣶⣶⠎⠁⠁
⠀⠀⠀⠠⠾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢼⣿⣿⣻⠝⣰⣿⣾⡿⠟⠁
⠀⠀⠀⠀⠰⢿⢸⣿⣿⣿⣿⣿⣿⣟⠫⡍⠻⣧⣥⣝⠟⠋
⠀⠀⠀⠀⠀⣼⡎⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠂⠀⠷⠹⣿⣿⣿⣿⣿⣷⢢⠁⠀⠀⠀⠀⠀⢠⡶⠟⠛⠛⠛⠻⢮⣿⣽⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢟
⠀⠀⠀⠀⠀⢿⡀⢧⣹⣿⣿⣿⣿⣿⢫⣖⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢮⠛⢻⣽⣄⠀⠀⠀⠀⠀⠀⣾⡃
⠀⠀⠀⠀⠀⠘⢳⡌⢠⣻⣿⣿⣿⣿⣯⣧⡂⠀⠀⣠⣶⡶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠆⠀⢹⣿⡄⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠫⣾⡇⣝⢿⣿⣿⣿⣿⣯⡄⠙⠿⠟⠐⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠼⣿⣆⣀⣤⣤⣾⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⢣⢹⣧⣙⠿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⠡⢌⣿⠎⠙⠿⣿⣿⣿⣿⣦⣀⡀⡀⠀⠀⠀⣠⡔⠁⢀⣴⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠶⠶⣤⣬⣙⣛⣛⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠈⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠑
⠀⠡⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠥
⠀⠀⠀⢸⢹⠻⡟⢿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⠴⠶⠾⢿⠿⠿⢿⡿⠶⠶⠀⠀⠀⣉⢿⣿⡇⢸
⠀⠀⠀⢸⠀⡆⠙⣦⡇⠀⢦⣐⣖⣀⠞⠓⠒⠒⠒⠂⠐⠀⠐⠒⠒⠒⠒⠒⠂⠀⠀⠐⠒⠒⠒⠂⠐⢀⣴⡶⣆⣠⣶⣄⠘⠛⢼⢹⡑⢸
⠀⠀⠀⢸⠀⡟⠢⣾⡇⠐⠂⠒⠀⠂⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠠⠰⠢⠄⠀⠙⠋⠁⠈⠛⠋⠀⠀⣸⣸⠀⡄
⠀⠀⠀⠸⠀⡇⠀⣿⡿⠟⠿⠿⠿⠿⠿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠿⠿⠿⠿⠿⣇⣿⠀⠃
⠀⠀⠀⠀⠀⡇⠀⣿⡇⠀⠀⠀⠀⠠⣟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠻⠷⢦⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⡄⡀⠀⣿⡇⠀⠀⠀⠀⠀⠈⢉⣉⣉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠻⠿⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⡇⡏
⠀⠀⠀⠀⡇⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⠶⠶⠶⠶⠶⠭⠭⠭⠭⣭⣭⣭⣭⣭⣭⣭⣬⣤⣤⣽⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⡇⢁⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣷⣮⡼⠀⠀⠀⠀⠀⠀⢰⢳⡇
⠀⠀⠀⠀⡇⢸⠀⣿⡇⠀⠀⠀⠀⠀⠀⣯⣽⣿⣯⡽⣯⡽⣯⣻⣭⣯⣽⣌⣭⡽⣭⣽⣭⣷⡽⣯⣟⣷⡆⠀⠀⠀⠀⠀⠀⢸⣻⡇
⠀⠀⠀⠀⡇⢸⠀⣿⡇⠀⠀⠀⠀⠀⠀⢻⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⣏⡋⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⡇⢸⠀⣿⣷⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⢸⡷⣭⣅⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⡇⢸⠀⢿⣿⠀⠀⠀⠀⠀⠀⢸⠿⣯⡿⠿⠿⠿⠿⠿⠾⡷⡛⠛⣛⡻⣿⣿⡿⡓⡒⠚⠓⢧⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⢰⠇
⠀⠀⠀⠀⡇⢸⡆⢸⣿⠀⠀⠀⠀⠀⠀⠘⣷⣼⣷⡿⠧⠿⠷⠿⠿⠤⢼⣓⣀⣚⣣⣶⣿⣥⣬⣭⣿⣅⡍⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸
⠀⠀⠀⠀⣷⢸⡇⢸⢿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣸⢸⡇
⠀⠀⠀⠀⣿⠸⡇⢸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢺⣷⢀
⠀⠀⠀⠀⢹⠀⣑⣼⣟⣦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣿⠶⠚⠱⢸
⠀⠀⠀⠀⢸⠸⠏⠙⡿⠿⠿⠿⢿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⢹⠉⠉⠉⢙⡦⠃⣸
⠀⠀⣀⣠⣼⣼⡇⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣟⣛⣁⣤⡀
⠚⠉⠉⠛⠋⠉⠓⠤⣇⣀⣀⣀⣸⣇⣀⣀⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠿⠤⠤⠤⠼⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣠⠞⠛⠉⠉⠉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⢹⡏⠉⠉⠉⠉⠙⢳⡀
⠀⠀⢠⡏⠀⣶⢛⠭⠭⠭⠭⠭⠭⠭⠭⠭⠥⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⡉⣷⠀⠀⠀⢸⡇⢀⡤⡶⢦⡀⠸⡇
⠀⠀⢨⡇⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⢸⠁⡿⡖⠉⢹⢹⡄⡇
⠀⠀⠀⡇⠀⡏⢸⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠛⠛⠋⠀⠀⡇⣿⢸⡉⢻⢸⠀⠻⣗⣶⣫⠟⠀⣧
⠀⠀⠀⣇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠈⣿⢸⢸⠀⠀⢈⣉⡀⠀⠀⣿
⠀⠀⠀⣿⠀⡇⢸⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⡇⣿⠀⡟⢸⢸⠀⣼⡫⠯⢽⣦⠀⣿
⠀⠀⠀⣿⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⡇⣿⣸⠸⣿⣄⢀⡸⣽⠀⡏
⠀⠀⠀⣿⠀⣿⢸⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠂⠀⠀⡇⣿⠀⡇⣿⢹⠀⠙⠶⠿⠞⠃⢀⡇
⠀⠀⠀⣿⠀⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⣰⠇⡏⢸⠀⣴⢶⢲⢶⡄⢸⡇
⠀⠀⠀⣿⠀⢸⣼⠀⠀⠐⠒⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⡇⡇⠿⠴⠇⢸⠀⠙⠿⠾⠞⠁⢸⠁
⠀⠀⠀⢸⠀⠸⡏⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠇⡟⠀⠀⠀⢸⠀⣴⡖⠲⢲⠀⣿
⠀⠀⠀⢸⡆⠀⠙⠶⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠶⠶⠃⠀⠀⡀⣸⣀⣙⣛⣛⣋⣀⡏
⠀⠀⠀⠘⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢩⡇
⠀⠀⠀⠀⠳⡴⠶⢶⡶⠶⠦⠤⠤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠶⠶⣶⠚⠁
⠀⠀⠀⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⣿⡿⠿⠿⠻⠿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠄⠀⠠⠀⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⠤⠆⠀⠀⠶⠖⠛⠘⠛⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠒⠒⢾⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣆⣶⠀⠀⠀⠀⢶⠸⠆⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣄⣤⣀⣶⠀⠀⠀⠀⠲⠶⠾⠙⠇⠹⠒⠛⠃⠋⠈⠁⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠙⠛⠘⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⡀⠀⣀⢰⡄⠀⠀⢠⡔⢦⣐⣴⣆⣿⠁⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⣀⡤⠤⢰⡖⢺⡺⡆⢾⣈⠈⠧⠷⠻⠘⠃⠲⠀⠈⠁⠈⠁⠀⣀⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠚⠉⠛⠀⠈⠁⠈⠀⠀⡀⠀⠀⠀⠀⣀⣀⢀⣤⣶⢠⡇⠀⠀⠀⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⣄⣄⣤⣰⢦⣶⢶⣶⣶⣖⡺⣿⡁⠃⠀⠾⠵⠟⠛⢚⠻⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠟⠿⠋⠛⠛⠋⠈⠙⠋⠁⠈⠉⠀⠀⠀⠀⠀⠐⣀⠁⠀⠀⠀⣤⡄⣤⠠⣦⢰⣖⣖⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣤⣠⣤⡄⣶⠀⣿⢰⡏⢻⡜⣧⣿⣄⡄⠀⠀⠋⠛⠉⠓⠉⠘⠿⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠾⠟⠓⠋⠋⠉⠁⠉⠁⠁⠀⠀⠛⠀⠁⠀⠀⣀⣀⠀⣀⣀⣠⡆⢠⣤⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⣀⣀⣤⣠⣤⡦⣾⡇⠀⢰⣿⣸⣿⠹⠟⠿⠁⠸⠇⠘⠃⠙⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⢿⡷⣿⠄⠛⠿⠋⠙⠛⠀⠉⠁⠀⠈⠁⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣦⣤⣤⡄⣠⣤⣶⡶⣶⣶⡆⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⣿⣶⣶⣶⣿⠀⠀⠰⣿⣿⠿⠟⠛⠛⠋⠈⠋⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⣠⠄⠄⢀⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡠⠨⠍⠁⠤⠈⠀⠀⢀⣀⡴⡐⡄⠀⠈⡀⠰⠄⡀⠈⠂⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠛⢂⠆⠀⠀⠀⠀⠁⠀⠃⠀⠀⠰⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠀⠀⠀⠀⢠⣤⠄⡄⣠⣤⢠⣤⣤⡀⡤⠄⠀⠀⢤⠀⢾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⢁⡀
⠀⠀⠀⠀⠘⢦⣤⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠠⠀⠂⠀⠀⠀⠀⠀⢤⠀⠀⢨⣐⣀⠂
⠀⠀⠀⠀⡀⠀⠑⠄⠠⠄⠈⠒⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢴⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉⠐⠀⠀⠀⠀⠠⠀⠛⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠠⡀⠀⠀⠀⠐⠀⠀⠀⢀⢤⣀⣀⠀⡀⠀⠀⠄⢸⡆⠀⠀⠀⠀⠀⣀⠀⠈⠱⠀⠀⠀⡀⣲⣴⠀⠈⡐⠦⠠⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢴⠾⠥⠺⠏⠀⠀⠀⠀⠈⠉⠋⠉⠊⠀⠀⠀⠀⠉⠀⠀⠀⠈⠣⠌⢢⡀⠀⠘⠀⠈⠟⠅⠁⠀⠀⠘⠳⢤⣚⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⠀⠀⠠⠀⠀⠈⠀⢀⡼⠋⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠂⠀⠀⡟⠀⠀⠁⠀⠀⣀⣀⡾⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⣀⡴⢛⢡⡙⣦⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡞⠉⠙⢿⡋⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠰⣏⠰⣌⢧⡹⣜⣧⠀⢂⠀⠀⠀⡇⠀⠀⣴⠏⠀⠀⢀⡼⠃⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⢷⡙⢦⡻⠍⠘⡇⠀⠂⠀⠀⣿⢠⡾⠁⠀⠀⢢⡞⠁⢀⠔⠁⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠒⠄⡀⠀⠙⠶⣤⣤⣾⡃⠀⠀⠀⠀⣿⠏⠀⠀⠀⣵⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⢀⡾⠃⠀⠀⢀⡾⠁⠀⢀⣀⣠⣤⣤⣄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠶⠦⠶⠶⠶⠶⠖⠛⠛⣛⣉⣷⡄⠀⠀⠹⣦⠟⣀⣀⣠⣴⡿⠶⠞⡛⢉⣭⠤⡄⠀⢹⡀⣀⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣠⠶⠟⢛⣉⣁⣸⣧⡤⠶⠞⠛⠛⢉⠉⣤⠶⣆⢸⣏⠁⠈⠓⠶⣤⠀⢸⡟⠉⠉⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⣼⠷⠞⢛⣛⣉⠉⢠⡴⠂⢠⡞⠙⠃⣸⠀⣿⣴⠏⢸⣯⡤⠀⠓⠞⠋⠀⢸⡇⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⣿⠀⠀⣿⠁⣹⠇⢸⣧⠀⢸⣇⣠⡆⠻⠀⠋⠀⠀⢄⣐⣠⣤⠴⠶⠖⠒⣾⠇⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣁⣀⣤⣤⣿⠀⠀⣿⠚⢯⡀⠸⡧⠶⠀⠉⠉⣀⣠⣤⣴⡶⠛⠋⢹⡇⣀⣤⡶⠶⠛⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢸⡇⠀⠉⠀⠀⠀⣀⣠⣤⣶⣾⠛⠉⠁⣿⠀⢻⡄⠀⢸⡟⠉⠀⠀⣀⣀⣤⡤⠶⠶⠒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠈⠷⠴⠶⠖⣿⠛⠉⠀⢠⡾⠁⠀⠀⠀⣿⠀⠀⢻⣆⠈⠓⠖⠛⠛⠉⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⠀⠀⢠⡞⠁⠀⠀⣺⠟⠀⠀⠀⠀⠀⣿⠀⠀⡀⢻⣷⡄⠀⠀⠠⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢿⣝⡳⣄⣴⠋⢀⣤⠶⠚⠛⢓⣿⠀⠀⠐⠈⢷⡙⣦⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⠷⠟⠁⠀⣿⣤⡴⠶⠟⢋⣿⠀⠀⠀⠡⠀⠻⠾⠇⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣾⠃⠀⠀⠠⠀⠸⣆⠀⠀⣀⣼⠇⠀⠀⠀⠀⠄⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠾⠋⠀⠀⠠⠁⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢤⠤⠀⠐⠒⠲⠋⠀⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠾⠤⣤⡄⠀⠀⠀⠀⠀⠇⠀⠁⣀⣀⣀⡀⣠⠤⠠⠤⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠋⠀⠀⢀⣬⣷⣶⠀⠀⠀⢠⠒⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣦⣄⣀⣀⣀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⣙⡖⠁⠙⡷⡄⠀⠀⠰⠁⠤⠈⡿⡁⢀⣀⠬⠶⠯⣤⣀⠀⠀⠀⠀⠀⠐⠀⠈⣶⣮⣍⠉⠛⠒⠒⠞⠷⢾⡄
⠀⠀⠀⠀⣀⣴⣶⣽⣿⣇⠠⢀⣷⣧⠀⠀⠰⡀⠀⣠⣿⣿⣷⣾⣿⣾⣿⣼⣿⣿⣦⣀⠀⢰⠃⠀⢲⣽⣿⡘⡆⠀⠀⠀⡰⠋⢺⣿⡄
⠀⠀⠀⣾⣿⡛⣿⣿⡍⢿⡿⢿⣿⣿⠀⠀⢀⣽⣿⣻⣿⠟⠉⣠⡿⠿⠛⠛⠿⣿⣿⣿⣷⣽⡀⢠⣼⣿⣿⠆⡇⠐⠀⢰⣇⠀⣾⣿⣷
⠀⠀⠀⠉⠠⠞⣿⣿⣧⣾⣿⣿⣿⣿⠀⢠⣌⣷⣿⣿⣿⣾⣿⠋⠀⠀⣰⢮⣑⠊⢻⣿⣿⣿⣧⢸⣿⡙⠃⢀⣧⣴⣦⣶⣿⣶⣿⣿⠟
⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣤⣌⣻⣿⣿⣿⣿⣿⠁⠀⠀⢎⣤⡶⣻⢥⠀⣿⣿⣿⣿⣷⣿⢧⣄⣽⣿⡿⠿⠛⢛⣻⣿⣹
⠀⠀⠀⡄⠀⠀⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢈⣟⣽⣶⣵⢸⢠⡽⠋⠉⠉⠙⠛⠿⣿⣯⠤⠖⠊⠉⠀⢿⣿⡿
⠀⠀⠀⢁⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⠃⠀⠀⢨⣽⣿⣏⣼⠃⠈⡆
⠀⠀⠀⠈⢄⠀⠈⠻⢟⣻⣿⣿⡿⠛⠻⠿⠿⠿⠿⠿⠿⡄⠀⠀⠈⡖⡻⡟⠛⠀⠈⠃
⠀⠀⠀⠀⠀⠑⠠⠅⠠⠤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⡳⡧⠤⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⡀⠑⢌⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠻⠾⠻⠴⠶⠶⠶⠦⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠉⠉⠁⠀⠀⠐⠒⠂⠐⠒⠀⠠⠤⠬⠭⠍⠉⢉⠉⣛⣛⣛⣛⠓⡖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠀⢘⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡠⠂⠀⠀⠀⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡋⠀⢒⠂⠀⠭⠍⣐⣒⡐⠀⠤⠄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⡐⠀⠡⠃⡀⠐⢪⠄⠒⠠⠐⣀⠌⢉⠐⡒⠒⠠⠭⠥⢐⣐⠂⠠⠤⠄⢀⣀⠀⡄⡀⢸
⠀⠀⠀⠀⠀⠀⣠⠔⠊⠡⠀⠈⠅⠀⠁⠐⠀⠠⠀⣀⠀⢃⡀⠘⠠⠖⠈⠴⠀⢁⠀⠐⠀⠄⠂⠈⢉⠉⠁⡒⠂⠊⣥⠧⢾
⠀⠀⠀⠀⡴⠯⠤⠔⣂⡀⠂⠤⠀⠩⠄⢈⠁⠂⠀⠂⠀⠁⠀⠉⡀⠊⠀⠠⠄⢈⠄⠀⢁⠠⠂⠀⠆⠀⣈⡤⢶⣍⠿⠒⠁
⠀⠀⠀⠀⠑⠒⠒⠠⠤⢀⣉⣉⠁⠒⠒⠠⠤⢀⣀⣀⠀⠄⠀⢂⡀⠈⣁⠀⠃⠤⠀⠨⠅⠀⢁⡠⠔⣊⡥⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠂⠤⠤⢄⣈⡉⠙⠒⠒⠤⠤⠼⣀⣐⣂⡠⠔⢊⡡⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠤⠤⢀⡧⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⡈⣿⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⠁⠠⣴⠀⠂
⠀⠀⢀⠀⠈⣁⠻⣿⠏⠀⠠⠀⠈
⠀⠀⠈⣹⠀⠁⠋⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠈⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡤⡶⠈⡝⢿⠀⠀⠀⠀⠀⠀⠻⡄⠩⠉⢻⣿⠇
⠀⠀⠀⠀⠘⠗⡀⠀⠀⠀⣀⠤⣀⢀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡏⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠆
⠀⠀⠀⠀⠀⠀⠁⡶⠀⠆⣸⠖⢋⡹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠎⠀⣆⠀⠀⠀⢀⠺⡡⣄⢀⠀⠀⠟⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡱⠈⢽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣤⣀⣀⢶⣾⣥⡾⠀⠀⠀⠀⠀⠐⠁⠛⠀⠀⠠⣶⡜⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢘⡃⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙⠹⡿⢻⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⠈⢿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣸⠄⠰⠆⠈⣀⣤⣤⣤⡘⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠴⠚⢋⢿⡟⣿⣿⡇⠀⠀⠉⠅⠓⠆⢀⠀⠀⠀⢀⠈⠀⠀⠉⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠟⠀⣼⠁⢠⡎⠀⡿⣿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢀⠰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠐⠏⠀⣿⡇⠀⣷⡟⠀⠀⠀⠐⠀⠀⠆⠀⠀⡄⠱⣤⠀⠀⠀⠚⡥⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⣰⣿⠇⣸⣿⠁⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⣿⡗⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡟⢻⣿⣿⡾⣹⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⢋⡇⠀⠀⠀⢠⠄⡠
⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠓⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠢⠀⠂⠀⠀⠀⠽⣃⠠⠀⠀⢞⡆
⠀⠀⠀⠀⠀⠘⠞⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⣿⣽⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡗⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣿⣿⣿⡿⠀⠀⠠⢿⣶⠀⠀⣽⠇⠀⠀⠀⠀⢈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠾⣿⣼⠃⠀⢀⡤⠚⠁⠤⠀⠍⣤⣆⠠⠘⠦⠈⠳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡿⢲⣿⠀⠐⠉⠁⠀⠀⠀⠀⠀⠘⠋⠀⠸⣷⣦⣤⠀⢔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠹⠟⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠉⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠂⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠤⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠄⣤⣄⡀⠀⠀⢀⡠⠊⠀⠀⠀⢀⠔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⠫⠀⢻⣻⡟⣼⠈⡷⣴⣯⣤⣀⢀⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐⠂⠀⣸⣿⢀⠉⠈⣯⠘⢃⣾⣏⡽⣿⣯⡖⡽⣏⠉⠑⠠⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠆⠀⠀⠀⠀⢻⠈⣆⠂⠀⠘⣦⡎⠱⠛⣱⡿⢾⣿⡇⢻⠀⠀⢀⢄⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣥⣀⠀⠀⠈⠷⠮⠧⠤⢴⠌⠧⠤⠧⠿⠋⠽⠿⠶⣞⢧⡄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣆⠀⠀⠈⠙⢯⣍⢀⠀⠈⠁⠈⠈⡁⣄⠀⣠⣼⣿⠆⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣻⣿⠤⠀⠀⠈⠓⠀⠀⠀⠀⠀⠠⡾⠏⢐⣽⣿⠋⣠⠟⠛⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠬⠈⢍⡋⢁⠀⠀⠀⠀⠀⠀⠐⠞⠂⢠⣬⠥⠳⠋⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡚⠇⠀⠀⢀⢬⠉⠁⠀⠈⣠⠶⠋⢈⠙⢃⠀⠀⠀⠀⠀⠁⠀⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠴⣿⡆⠀⢀⣀⡉⠀⠀⠠⠮⠞⡀⠀⠀⠔⠁⠠⢂⠠⠀⠀⠀⠀⠀⠀⠀⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠛⠃⠉⠀⠻⣽⡆⠂⠀⠀⣁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⢀⡀⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⣀⠀⠐⠀⢀⠀⠀⡀⠀⠀⠒⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡴⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠪⠉⠁⠈⠁⠀⠀⠀⠀⡠⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠃⠘⠾⠁⢆⡒⠐⡆⡄⢄⡀⡎⠂⠂⠀⠂⠐⠈⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⢂⠃⠀⡉⡁⠀⠶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⣤⠐⠀⠂⡉⠀⠀⠤⠀⠀⠀⠀⠐⠁⠈⠉⠁⠄⠤⠀⡀⠀⠀⠀⠀⡎⠀⠀⠐⢀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡀⠧⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⢂⡀⠀⠄⠀⠀⠀⠆⠀⠀⠀⣿⣻⡟⣿⣿⣿⡇⠀⠀⠀⡀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣿⣫⣵⣽⣿⣿⠇⠀⢠⠀⠀⡠⠀⠃⠀⠰⠀⠈⢀⡀⠀⠀⠠⠄⠀⠀⠀⠀⡀
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠄⡀⠀⠀⠀⠀⠀⠀⣿⠙⠛⠛⠋⢉⠀⠀⠘⠉⠀⠉⠀⠘⠅⠀⢀⠄⠀⢁⡀⠰⡂⠀⢠⠀⢈⡠
⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠁⠀⠀⠀⠀⠰⠞⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⡄⠀⠀⠀⠀⠀⠘⠀⡀⣰⠂⠉⠠⠀⡇
⠀⠀⠀⠄⠀⠀⠀⡾⠃⢈⣢⡤⠄⠂⠨⠁⠠⠐⢧⡠⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⠀⠀⢀⠜⣠⣇⠀⠀⠀⠀⠀⠉⠂⠠⠤⢀⠀⠀⠀⠀⠠⣴⠄
⠀⢆⠀⠀⠀⠀⠀⣄⠁⠈⠁⠀⡋⠈⠀⠀⠐⠀⠁⠀⠀⠀⠎⠀⡀⠀⠀⠀⡀⠰⡆⠀⠈⢲⠓⠑⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⢁⠀⠀⠂⠀⠀⠀⠀⠀⠃⠈⢁⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⣀⠀⠀⠀⠀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠱⢀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠀⡀⠂⢀⠀⠁⠀⡀⠈⠀⠀⠀⠠⠀⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠠⠠⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠁⠀⠀⣀⣀⣤⠠⡀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⠀⠀⠀⠀⢀⠀⠤⠃⠀⠀⠀⠀⢀⣲⡄⢛⢄⠣⡜⢡⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠒⠃⡤⠀⠀⠀⠀⠀⠀⠀⣼⡿⠏⠀⠀⠀⢌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣥⠈⢣⠌⢱⡜⢣⠄
⠀⢀⣀⣠⠀⠀⠀⠀⣧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠊⠤⠐⠀⠃⠈⠀⠀⡀⠀⠀⠀⠀⢠⠤⡄⠀⠀⠀⠐⢀⡢⢠⡀⠛⣠⠚⢡⠘⠻
⠀⠀⠈⠀⠀⠀⠀⢹⢸⣞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠍⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⣄⠰⢆⡀⠦⣀⠶⣀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⢱⡇⠀⠀⠀⠠⠶⠤⠀⠀⠀⠤⠀⡀⢀⠔⠊⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠤⠈⢡⡔⢁⠔⠉⡦
⠀⠀⠀⠇⠀⠀⠐⠺⣙⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠊⠁⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⠀⠀⠀⢀⣠⡇⠀⠀⠀⠹⣄⠘⣀⠜⢃⡐⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⢂⣀⣤⣄⡀⠂⡠⠀⠀⠀⢀⣄⡀⠀⠀⢈⡄⠀⠀⠀⢨⠉⠀⠀⠀⠀⡙⣈⠖⣀⠲⠀⠠⢴
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣻⣿⣿⠁⠀⠀⠀⢐⡀⠃⠀⠀⠀⠂⠀⠠⠩⠀⠈⠁⣸⡧⠄
⠀⠀⠀⣀⠤⣒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⣹⣯⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣠⡗⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠉⠀⠀⠀⠀⠀⣇⠐⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⡀
⢰⢎⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⢲⠀⠀⠀⠈⠀⢀⠀⠀⠀⡀⠌⠀⠄
⢸⠀⠀⠰⠄⢀⡀⠠⢆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠂⢀⠠⠖⠁⠘
⢸⠀⠀⠀⠀⠈⡠⠑⠣⠀⠀⠀⠀⢨⠁⠀⣀⣀⣠⣤⣤⣤⣤⣴⡄⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠀⡀⠀⠈⠀⠀⠀⢰
⢸⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⣿⣟⣿⣿⣟⣻⢿⣽⠻⣿⣧⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡄⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠉⢀⠀⠀⠀⠀⠀⣿⣧⣿⣝⣿⣿⣿⣿⣿⡿⠿⠀⠀⠀⠀⠀⠰⠀⠀⠄⠀⡤⠤⠀⠀⠀⠀⠈⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠸⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⡇⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠈
⠀⢇⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⢀⠀⠀⠂⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠑⢄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡇⠈⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⢄⡠⡀⠀⠀⠀⠉⠀⠀⠀⠐⠚⠒⠢⠀⠠⠤⠆⠤⠄⠀⠀⣴⣿⣿⡆⢀⡟⢹⢹⠀⢴⣶⣶⣶⠄⠀⠀⠠⠀⠁⠑⡀
⠀⠀⠀⠀⠀⠀⣠⣮⡄⢀⣦⣹⡏⠀⠀⠀⠸⠀⡆⠀⠀⠀⠀⠀⠀⣆⣄⣀⣀⣸⡀⠀⠙⢿⡿⠃⠀⢯⣼⡼⠀⢸⣿⣿⣿⠀⠀⠀⠤⠀⠀⠀⠠
⠀⠀⠀⠀⣠⠞⢾⡟⡿⢿⣿⣋⣱⡀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠛⣿⣷⡗⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠸⣷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣠⠞⠁⢀⡼⣧⣶⠿⣿⢿⣿⠃⢰⣿⣷⣿⡆⠀⠀⢲⡎⠀⢸⣿⢋⠄⢙⢿⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠘⡟⠀⠀⠀⠁
⠀⢸⣿⣤⢴⣿⡾⢋⡵⠊⠙⠛⣿⣦⡄⠛⠿⠛⠀⠀⠀⢼⡧⠀⢸⣧⡠⠖⠉⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠻⢿⡟⢁⢀⣥⣒⣦⡄⠀⠘⣿⣛⢉⠂⠀⠀⠀⠀⢸⡇⠀⢸⣇⠀⡀⠀⣸⡇⠀⠀⢈⣁⠀⡀⢀⣁⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠉⡇⠆⣿⣿⡇⣴⣿⣿⣿⣿⣿⣿⣿⡦⠀⢸⡇⠀⢸⣿⣦⣤⣴⣿⡇⢀⡐⣿⣿⠀⠃⢸⣿⡷⢀⠀⢸⢹
⠀⠀⠀⠀⠀⠀⡇⠸⣿⣿⣷⣽⣿⡇⠁⡇⢸⣿⣿⡇⠀⣞⣳⠀⠘⠾⢿⣿⡿⠿⠃⢸⣧⣹⣿⣆⢀⣾⣿⣡⣾⠀⠀⠁
⠀⠀⠀⠀⠀⢰⡇⡇⣿⣿⣿⣿⣿⡇⠀⡇⢸⣿⡿⠁⠀⠈⣡⣤⣶⣦⣤⡀⠀⠀⠀⠈⢿⣿⡿⠉⠀⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⡠⠞⠁⢃⣿⣿⣿⣿⣿⣿⣦⣧⣼⠛⠂⣄⠀⣾⣿⡽⠛⠲⣜⢿⣆⠀⠀⠀⠀⠈⠛⠐⠀⠘⠉⠁⠀⣴⢤⣤⣤⣤⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠘⠷⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⢸⣿⢸⡁⠀⠀⣸⢺⣿⢀⡠⡀⢠⡄⠠⣀⠄⢠⡤⠀⣰⣿⣿⣿⣿⣯⣆⠀⠀⡀⣿⢸⡇⡷
⠀⠀⠀⠀⠀⣠⢐⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣂⡄⠀⠀⠻⣷⣝⣒⣚⣹⡾⠃⢸⣗⡣⡿⢿⠸⠿⡆⢤⣓⠀⣿⣿⣀⣀⣀⣻⣿⠀⠰⡇⢹⢸⢣⡇⣶
⠀⠀⠀⣰⡾⢿⣿⣿⡿⢿⣟⡩⠉⢉⣭⢍⠉⣰⠁⠀⣠⠤⠈⢉⠙⠉⢁⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⢀⣷⠿⠿⠿⠿⠿⣼⠂⢀⣇⢸⣸⡾⣇⣿
⠀⠀⠀⠹⣧⣀⢹⣿⣿⣇⣿⠀⠀⣼⠇⠀⡟⠄⠀⠀⠐⠀⣠⣽⣶⣶⣤⣌⣉⣲⢈⣉⣀⣙⠾⣯⣩⠟⠀⢰⣿⠀⠀⠀⠀⠀⢻⡆⢰⡼⣸⢧⣇⡿⣼
⠀⠀⠀⠀⠈⠙⢿⡿⢿⣿⢿⡀⢀⣿⢀⡼⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠁⠉⠀⠀⠀⢸⠿⢿⣿⣶⣾⣿⣿⡇⢻⡇⣿⢸⡅⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠯⠉⠭⠟⠀⠀⠀⠀⠀⠀⢮⡤⢾⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⠶⢬⡵⠀⠸⢤⣴⣿⣿⣿⣿⠿⠇⠘⠇⠿⠸⠇⠇⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣠⠀⣰⠛⠁⡠⠒⠒⠄⠀⠀⠀⠀⠀⠚⠋⠟⠳⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢁⠠⠤⠀⠀⠀⠀⠀⢀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠁⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠠⠓⠂⢀⢘⡄⠀⡄⠀⢀⣤⠉⠦⣤⠴⠙⠀⡀
⠀⠀⠀⠘⠁⠐⠄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠂⠀⠢⠀⠋⠒⠒⠂⠈⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠒⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⡐⠾⠃⡡⢤⣭⡝⠋⣀⠶⠶⡦⠀⣀⡀⠠
⠀⠀⠀⠠⠀⠄⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⢀⠀⠁⠛⠛⠻⠶⠄⠠⢾⣽⡻⢋⢀⡶⠾⠁⣀⠀⠀⠀⠀⠢⣀⣴⣐⣆
⠀⠀⠀⠀⠐⢀⣹⠛⠟⠛⠓⠈⠀⠀⠀⢤⡀⠀⠀⠈⣠⠀⠀⠀⠈⠳⠒⠒⠠⠄⠀⠀⡀⣀⣀⡀⠀⠀⠤⡀⠀⠁⠀⠀⠀⠁⠤⣼⡿⠽⠞
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠠⠀⠋⠀⢂⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⡀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⢹⣿⣿⡄⠀⠉⠉⠉⠛⠻⠷⠀⠀⠀⠆⠀⠀⢠⠆⠌⠁⠉⣴⣎⣀⠀⠹
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠃⡢⠤⡀⠀⠀⠀⠨⣹⣿⣿⣷⣾⣿⣿⠃⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠰⠒⠠⢴⡄⠀⠀⠀⠈⠀⠠⠑⠌
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢒⣀⣄⡀⠈⠉⠀⠭⠋⠛⠁⠀⣼⣿⣿⣿⢿⣶⣔⣄⠀⠀⠀⢀⠀⠈⠀⠈⠙⠛⠃⠠⠀⠃⠎
⠀⠀⠀⠀⠀⢀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠠⠀⠂⠢⡀⠀⠀⠀⠀⠀⠛⢻⣿⣿⣶⣶⣟⣻⡇⠀⠀⠈⡼⠎⢒⡀⢲⡄⠰⢼⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡁⠤⢠⡀⠀⠀⠀⠉⠉⠍⠩⠽⠛⠁⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠁⠀⠁
⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠀⠐⠒⢓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠂⣄⡀⠀⠀⠀⠐⠠⠀⡈⠀⠀⠀⠀⠀⢀⠀⠂⠀⢠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠢⠀⡈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠄⠐⠁⠀⠀⠀⠄⠀⠀⠈⠚⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠁⠈⠁⠋⠠⠀⠀⠀⠀⣰⣶⣠⣤⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠈⠀⠀⠀⠀⠀⠰⠂⠠⠀⠀⠀⠈⠈⡁⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠖⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠄⠀⠁⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⣠⢈⡄⡤⠠⠆⠿⡄⠁⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠖⠒⠈⢁⡠⠶⠪⢤⠏⠄⠀⠀⠉⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠐⠂⠀⠀⠀⠀⠀⠐⠞⠉⠁⠁⠈


⣿⠿⠿⠿⡿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿

⠀⠀⠀⠀⣀⠔⠂⠉⠈⠉⠉⠒⠤⡀
⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⡌⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢰⠃⠀⠈⢳⣦⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠀⢀⡆⠀⢀
⠀⠀⡇⠀⠁⡸⠒⣄⢠⠸⠧⠄⠈⢲⠂⠀⠀⠀⠀⠀⣿⠀⠺⠇⠀⠙⢿⣦⡀⠸⠇⠀⣿⠀⠀⠀⠀⠀⠀⣀⠜⠠⠓⠼⠊⠛⠀⠈⠹⠁
⠀⠀⢃⠀⠒⠃⠈⠀⠀⠠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢻⣄⠀⢠⠞⠁⠀⠙⠳⡄⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⡄
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠒⠤⠄⣀⡀⠠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⣠⡦
⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⣠⡆⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⢸⣯
⠀⠀⠀⡺⠀⠀⠀⢨⣟⣺⣯⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣽⣿⣆
⠀⠀⠠⣧⠀⠀⠠⢾⣿⣾⣿⠆⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣆
⠀⠀⠀⢽⡄⠀⢠⣿⣿⣿⣿⡇⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣷⣄⠀⠀⠈⠈⠀⠀⠀⠀⠀⢰⣖⣄⣛⣻⣏⣸⣟⣛⣠⣐⡆
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠈⠛⠣⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⡍⠋⢙⢽⡏⣏⣿⡿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⡄⠀⡖⠀⡄⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠂
⠀⠀⠀⠀⡀⠀⠀⠃⡀⣛⣘⣛⡘⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⢸⠀⠀⠰⣿⣿⣿⣿⣿⣿⡷⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⢠⡀⣦⠀⣦⢰⢄⡄⣄⣤⢠⣰⡄⡦⣰⣶⣄
⠀⠀⠀⠈⠇⠀⢠⡤⠠⠀⠀⠄⡄⡄⠀⠀⠎⠀⠀⠀⠀⠛⠿⠿⠛⢿⣯⣿⢠⡄⡟⣓⢻⢠⡸⡇⣬⣿⢈⢸⣿⢰⣿⣯⡿⠟⠻⠿⠟⠃
⠀⠀⠀⠀⠀⠀⢠⠄⢠⡀⡄⣥⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠁⠉⠈⠈⠁⠁⠀⠈⠈⠁⠉⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠓⠃⠚⠋⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⡀⠀⠀⠀⠰⠠⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⢀⡀
⠀⣵⣄⣶⡀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠁⢳⡀⠀⠀⠀⠀⡄⢢⢄⣀⠀⠀⣰⠀⠀⠀⣷⡄⠀⣿⡀⣿⠀⠡⠀⣶⠚⠓⣶⣄
⠷⣿⣿⣸⣷⣇⣠⣦⣰⣧⣸⣧⣿⠀⢸⣼⡇⠀⠀⠀⣤⣷⢸⣿⡿⠞⠛⠛⠉⠉⠁⠉⠛⠛⢿⣇⣾⣧⣖⡇⣻⣶⣤⣼⣇
⠀⠛⠃⠉⠉⠉⠉⠉⠛⠿⠿⣿⣯⣤⣿⣿⣿⣦⠴⢛⣛⢯⡿⠋⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠻⣿⡧⠿⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⠻⣿⡟⢡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣽⣦⣬⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠇⡈⠀⣀⣤⠶⠚⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠀⠤⢄⡉⠉⡄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠦⣄⢀⡀⠇⢰⠃⠁⣨⠉⣅⡌⡙⠌⠹⣔⢒⣀⣀⣾⠏⠀⣠⢴⡖⣦⢄⠈⢢⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⡆⠝⡂⠷⣿⡆⠠⠇⢾⣥⣿⡲⢼⡀⣿⠿⠿⢿⡏⠀⠰⠛⣻⣛⣧⡚⠀⠸⠿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠻⢶⣬⣨⣿⣧⠀⠡⡄⢹⠉⣨⡿⢀⠋⠀⠀⠘⣿⠀⠘⢁⠀⠛⠋⡩⢀⡘⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⣷⣤⣌⣉⣉⣉⣴⣾⣶⣾⣿⣿⣿⠷⣤⡈⢁⠊⠈⣠⣼⣥⣶⣶⣿⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠐⠺⠀⢅⡢⢀⠀⠀⣬⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢀⠈⠉⠁⠲⢥⠀⠛⠛⠁⠀⠤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⢀⠳⠅⠶⠶⠂⠀⠀⠈⠐⠀⠀⠂⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠠⣟⡁⠀⠀⠘⣿⠀⡄⠀⠀⢠⡄⠀⢀⣶⢶⡦⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣘⠀⠀⢠⡜⠁⠐⠒⢀⠛⠂⠀⢤⣸⠿⠀⠀⡷⢙⣌⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠾⢢⣿⣀⡿⠃⠀⠀⠾⠀⠀⠰⢾⡍⠀⠙⡄⠈⠉⠉⡉⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⡠⠐⠒⠒⢦⣈⠁⠈⠛⠀⢀⢀⢠⣆⡩⠘⠟⠂⠀⠀⣧⠆⢀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠐⠀⠠⠴⠊⢀⣠⠼⣄⠔⠞⠁⠀⢳⠦⡀⠀⠀⠤⣼⡅⠀⡀⠀⠀⠘⢔⣿⢠⠀⣦⠂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⣀⣰⣉⡀⠀⠁⠀⠀⠀⠀⢘⢀⠇⠀⠀⠀⠀⢰⡅⠁⠀⠰⢄⠀⣤⢿⡇⠸⠎⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⠀⠁⠀⠀⠉⠲⡄⠀⠀⠀⠀⣌⡞⠀⠐⢒⠀⠀⠘⠁⢠⠂⠁⠺⣥⠠⡈⠉⠓⣭⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢠⡀⠀⡛⢆⠀⠀⠀⠀⠀⠙⡄⢀⡀⠼⠋⡐⠄⠹⢂⠙⠵⣦⠀⠛⠀⠀⠘⠇⠀⠳⣦⢈⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣬⡳⠽⡆⠣⢄⡑⠂⠀⢀⡤⣖⠊⠁⠀⢰⠀⠠⣿⠀⢷⡇⠀⢀⡘⠁⡉⢍⣑⡄⠠⣄⠀⠟⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠢⣤⣄⠀⠀⠉⠉⠉⠁⠀⠈⠁⠒⢂⠀⠀⡈⠃⠈⢀⠀⠇⠉⠋⠀⠀⠈⠉⡦⢄⣧⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣊⣁⠀⡠⣄⢠⣄⠘⠂⠀⡸⣆⡄⢣⣊⠈⠀⢻⡖⣀⠸⡀⠀⠀⠀⠀⠀⡆⠀⠀⡇⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⠀⠀⢀⣀⡉⠀⢹⠁⠈⢇⠈⡷⠀⢰⡄⠗⠁⠈⢷⠊⢀⠀⢀⣠⠀⠙⠲⢴⡤⢀⣌⡤⠔⠊⢞⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⡀⠏⠀⠉⠑⠲⣄⠀⠈⡆⣳⠀⠀⠀⡀⢀⢀⡘⡄⠃⣱⡈⢟⠀⠀⡀⠀⠏⠉⢀⣄⠀⠀⠈⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠂⠀⠰⢼⠁⢿⣄⠀⠀⠀⠈⠳⣀⣼⠃⠀⣌⣿⠅⠐⠤⠻⣿⡀⢀⣈⠹⠀⠀⢯⡞⠀⢀⠀⠙⢀⣕⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣬⣾⣠⠀⢀⡀⣀⡈⠒⠵⢤⣄⢴⣚⢥⡴⠀⠐⣮⡯⠁⠀⣴⡄⠀⢷⡫⢀⢿⡮⠁⢨⡇⣰⢀⡀⠒⠖⢣⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢳⣾⡈⠂⠐⠾⢗⠀⠀⠀⠀⠀⠀⢳⡀⣘⡟⠂⠀⡀⢉⣽⠃⠸⠗⠋⡼⠠⢄⡎⠁⣤⠀⢿⣶⡐⠴⢆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢨⢤⣅⠀⢀⡴⠟⠁⣄⠀⢦⠤⣀⠀⢳⣿⡯⡠⠊⡇⠀⡹⠢⢄⡇⢵⡗⠌⢺⡇⠿⠂⠀⠦⡚⠇⠠⠬⢦⠇
⠀⠀⠀⠀⠀⠐⣾⣦⣀⢉⢆⠉⢥⢠⠀⠀⠀⢘⣻⡅⠈⠳⢷⣿⣿⡟⢠⠡⢲⠃⣀⢘⣄⢪⣷⠀⢣⣶⢨⡗⠈⣣⣠⡁⠈⢆⠀⠀⠶⠃
⠀⠀⠀⠀⠀⠠⡄⠘⣻⣾⠻⠂⢴⡄⠛⢧⡄⠀⢾⣿⡄⠀⠠⡿⠯⢧⠸⠗⠁⠀⢱⡫⢱⡄⢹⠀⠸⠃⠸⠁⠈⣰⡇⠐⠜⣌⠄⠀⢠⢏