Rage comic Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⢀⣉⡁⢯⣉⡉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠈⠤⣀⣀⣀⣀⣿⣿⣎⣿⠷⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠴⠚⠉⠉⣉⢹⡍⠩⣝⠀⢠⠰⠿⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠨⡆⠀⠀⠘⠟⣱⠇⠀⢙⣤⣄⣉⠴⠃⣱⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⢽⣶⡤⠖⠉⢀⣀⣠⣤⠤⣤⣶⣶⢦⡙⢷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠀⣠⣶⢾⠟⠋⢟⠉⠉⢹⠀⠀⠇⢀⣷⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡠⢤⡀⢀⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⣶⠁⣼⣿⣤⣀⣱⣀⣈⣦⢤⣤⢦⡴⢶⣼⢿⡇⡃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⡴⠻⠺⠓⣿⠁⡔⣢⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡙⡄⣿⣿⠏⠈⢨⠀⠀⡇⠁⢰⠀⢸⣄⣈⡶⠃⠏⠈⢐⠦⠤⠤⠤⠔⢍⡝⡇⢸⠁⣰⡻⠋⣶⢀⣴⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠦⠍⣉⠒⠤⠾⡤⠴⠗⢒⣋⣩⣭⣤⠶⠖⠋⠀⢰⣁⣀⣀⣀⣀⣰⡄⠉⠀⠈⠄⠁⠠⠞⢥⣌⣑⡛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠀⠀⠈⠑⠒⠶⢾⣛⠋⠉⠁⠀⠇⠀⠀⠀⠀⣿⡿⠁⠀⠀⣀⠤⠜⠁⠀⠠⠒⠀⢀⢠⡊⠙⢩⡙⠁
⠀⠀⠀⠀⠀⠀⢀⠌⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠁⠘⠓⠂⠐⠒⠐⠛⠃⠒⠈⠁⠀⢀⡀⠤⠄⠒⠒⠈⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⣼⣶⠂⡰⠂⠰⠒⠒⠒⠒⠒⠒⠐⠂⠈⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣦⣄⣀⠀⠀⢰⣿⠏⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠺⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⡀

⠀⡆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⡇⠀⠀⠀⠀⠀⠀⢈⣉⣉⣉⣩⣉⣉⣨⣀⡀⠀⠀⠀⠀⣀⣉⣁⣉⡁⠉⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠠⠤⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⡀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠂⠀⠀⡀⠀⢀⡀⡀⡀⠀⠀⠀⠀⡇
⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⠂⠀⠀⠀⠀⠀⠀⡀⡁
⠀⡇⢂⣐⢒⠐⢒⠀⢐⢐⡒⢒⠂⠀⣠⡶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠃⡇
⠀⡇⡏⢠⡃⠘⠀⡜⠣⠠⡜⠄⢣⢀⡟⠀⠈⠈⠙⣿⠂⣷⣿⣶⣶⡦⠀⠀⠻⠿⠿⠈⠄⠀⠀⠤⠀⠀⠀⠤⡇
⠀⡇⠩⠡⠀⠈⠁⠤⠬⠅⠬⠄⠀⠘⢧⠀⠀⠀⢠⡏⠀⠛⠛⠛⠛⢀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡇
⠀⡇⠉⠉⠈⣨⡬⠥⠉⠁⠉⠀⠀⠶⣤⣄⣀⣴⣶⣏⡁⠀⠈⠉⠀⠀⠀⠠⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠙⠻⡇⠀⠀⠀⠀⠈⢬⡥⠼⠅⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠈⠁⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⣀⢀⡀⣀⡇
⠀⣇⣀⣀⣀⣀⣀⣀⣰⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⢀⣀⣂⣀⣀⣀⡀⣀⣛⣘⣋⣛⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠚⠛⠛⠒⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⡁⠀⢠⣶⠶⠶⠒⠂⠂⠀⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠒⢻⡿⠿⠛⠻⠿⣿⠛⠀⠀⠀⠘⣿⡿⠟⠛⠻⢷⠂⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣸⣿⡗⠶⠀⠀⠀⣿⠀⠀⠸⠀⠀⢿⡀⠀⠀⠶⣰⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣶⡿⠁⠀⠀⢸⣇⠀⠈⢿⣷⡶⣿⠍⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠀⠀⠀⠀⠈⠙⠛⠛⠋⣠⣸⣧⣶⣾⡿⣶⣴⡾⡉⠉⠉⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⡌⠀⢀⣀⣠⠤⢖⣒⢶⣿⣿⣿⡯⠭⠭⠻⠤⠤⠙⠛⢻⣶⣶⢦⡄⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠸⣛⠉⠀⠀⠀⠀⠀⠉⠙⠛⢛⣿⣿⣯⡟⠒⠛⠉⠀⠀⢠⡭⢉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠩⠐⠒⡄⠀⠀⠀⠀⠀⠀⠁⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠲⢶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠠⠊⠐⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠒⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⢀⡴⣶⣿⣿⡟⠳⢶⣄⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢉⣡⣤⣤⣄⡉⠀⠛⠛⠛⣩⡝⠛⠳⢦⣼⠗⠀⠀⠰⢶⣿⠿⠛⠛⠛⠋⠁⠉⠀⠀⡐⢌⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢠⡞⠁⠀⣦⣈⠙⠛⠲⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⢤⣤⣶⠛⠛⠳⠈⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡇⠶⠾⣏⠙⠳⢦⣤⣀⡀⠀⠀⠀⠂⡞⠛⣀⣀⡀⠀⠀⠈⣻⣶⣄⠀⠀⠀⢸⣧⠀⠐⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠦⠉⠀⠀⢻⣶⣤⣀⣻⡉⠛⠻⠶⢦⣤⣙⣈⠉⠉⠁⠠⢤⡶⠋⠀⠀⢈⣠⣴⢿⣿⡀⠈⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠹⣦⡙⢿⣿⣶⣤⣄⣠⡟⠉⠉⠙⢻⡿⠓⠲⣶⠶⠚⠛⣿⠉⣹⣈⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠈⠳⣾⡁⠀⠉⠛⣿⠿⣷⣶⣶⣾⣷⣶⣶⣾⣶⣶⣶⣿⣾⣿⣿⣿⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠈⠻⢦⣄⣠⡟⠀⠀⠀⠉⣿⠛⠛⠛⣿⠿⢿⡿⠛⣿⢻⣿⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣐⠠⢀⠀⠄⡈⠛⠳⠶⢤⣤⣤⣿⣀⣀⣰⣇⣀⣼⣧⣼⡷⠾⠛⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣑⠀⠈⠐⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⠠⠂⠀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃

⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡫⠛⠋⣋⡟⣛⢛⠛⣿⣛⣻⣟⣛⣿⢛⡿⣛⣛⢻⢹⣿⣿⣟⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⢻
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠈⢉⢉⣉⣉⣉⣒⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠠⠤⠤⠠⠤⣀⣀
⠀⠀⠀⠁⡠⠚⠁⣠⠔⠚⠋⠁⠀⠈⠃⠀⢄⡉⠑⠢⢍⠓⢄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠅
⠀⠀⢀⠞⠀⡴⠊⢉⠶⠤⣄⠀⠠⠂⠀⠀⠀⢈⠆⢄⠀⠙⢦⠑⣄⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⢠⠃⢀⡾⣄⠀⠎⠀⢀⠀⠑⡄⠀⠒⠀⠀⢀⠁⠀⠱⡀⠀⠱⡈⢦⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⡎⠀⡜⠀⠊⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠈⡆⠠⢄⡇⠀⠀⢣⠈⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⡇⠀⡇⠀⠀⠀⠀⠈⠠⠀⠀⠘⡀⠀⠀⠱⠀⠀⠀⠀⢱⠀⢀⠇⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢣⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠋⠉⠀⠀⢀⣾⠴⠋⠀⠀⡆⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠘⣆⠈⠢⣀⠀⠐⠃⠀⠀⠀⢀⡆⢀⣀⣀⣤⡴⠚⠝⠇⠀⠀⠀⡸⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠈⣦⡀⠀⠈⠉⠉⠉⠉⠉⠉⡉⠉⠀⠒⠀⠀⠀⠀⢀⡀⠀⢰⣁⣀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃
⠀⠀⡤⠒⠃⠀⠠⠤⠴⢶⣖⡲⠻⠁⠀⠁⠐⢆⣐⠺⢙⡴⠁⠀⠘⠀⠀⢳⠀⠀⠀⠉⠲⠤⣀⡀⠀⠀⠀⠀⢀⣀⠤⠚⠁
⠀⠸⡁⠀⠀⡀⠀⠒⠘⠬⠥⠔⢡⠁⠀⠐⢄⠀⠀⠁⠁⠀⠀⠀⠀⡄⣀⠞⠀⠀⠀⠀⠀⠀⠀⢈⠍⡠⠋⠉⠁
⠀⠀⠉⠒⠚⢇⠀⠀⢀⠄⠀⠀⢇⠀⠀⠀⢸⠀⠀⠀⠴⠀⠀⠀⢰⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠥⠊
⠀⠀⠀⠀⠀⠘⡄⠀⠈⠀⠤⡀⢈⢑⠒⠊⣁⠠⠂⠁⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⡈⠀⠀⠉⡀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠲⢤⣀⣀⣀⣀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⠶⣦⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⠀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠉⠉⣭⣭⣭⣭⣭⣭⡭⠤⠄⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣦⣴⣴⣶⣶⣤⣤⣿⣽⣧⠈⠀⠀⠀⢰⣦⣴⣴⣶⣶⣦⣤⣤⣄⠀⠀⠀⠘⣇
⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠛⠋⠉⠋⠛⣟⣿⡋⠁⠀⠀⣠⠀⠀⢸⣿⠟⠉⠉⠉⠉⠻⡏⠁⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⡗⠿⠵⠀⠀⠀⠀⣿⡇⠀⠀⢰⣿⠀⠀⢸⣿⣆⠀⠀⠀⠿⢆⡇⠀⠀⠀⠀⡏
⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣧⣔⣠⣂⣤⣾⢟⠃⠀⠀⠸⣿⡀⠀⠀⠻⣿⣶⣦⣴⣶⡿⠃⠂⠀⠀⢀⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⡟⠓⠉⣠⠀⢀⡘⣿⣷⡀⠀⠀⢿⣿⣿⣿⡿⠗⠀⠀⠀⠀⢸⠇
⠀⢸⡇⠀⠀⢀⡤⠖⠀⠒⠄⠀⠀⠀⠈⠙⠛⠃⠀⣠⣶⣼⣿⣬⣿⣻⣿⡿⢿⣿⣿⠏⣄⠀⠀⠀⠀⠈⠙⠳⠄⢸⠁
⠀⠀⢿⡄⢰⠏⠀⠀⠀⠀⣠⣤⡴⢶⣶⣷⣟⣿⣿⣿⣿⣿⣿⣟⣛⣛⣓⣆⣴⣚⣛⣻⣿⣿⣶⣤⣄⢠⡀⠀⠁⡾
⠀⠀⠈⢷⡘⠀⠀⠀⡾⠷⠾⠉⠀⠉⠉⠁⠀⠉⠛⠿⣿⣿⣶⣶⣶⡾⠷⣶⠶⣦⣴⡶⠶⠛⠋⠉⠉⠙⠛⢻⢸⠇
⠀⠀⠀⠈⢷⣄⠀⠀⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠟⠛⠛⠛⠏⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⢡⠏
⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁

⠀⠀⢀⡠⠠⠔⠒⠉⠁⢀⢨⡉⠙⠦⡀
⠀⡴⠋⠐⠠⠤⠄⣀⢾⣯⣺⡷⠖⠒⠚⣤
⢸⠀⠀⡰⠊⠁⢀⣤⢹⠀⠉⡅⠀⠀⠿⢟⢆
⠘⠀⠀⠃⡀⠀⢘⡻⠋⠀⠀⠹⠶⠤⠴⠃⢈⢣
⠇⠀⠈⠒⠋⠛⢋⣀⡠⢤⡤⢶⡲⠛⢬⠛⣧⣿⡆
⡇⠀⢰⢠⣴⣞⠻⡁⠉⢣⠀⠀⡇⠀⠸⢠⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠠⣔⣚⢢⡠⠒⠒⣄
⢡⠀⢾⣼⣿⣿⡷⠻⠒⠒⡃⠐⡃⠐⡌⠙⢍⠻⠺⢄⣀⠀⠀⠀⠀⣠⠠⣮⠀⡿⠁⣀⣹⣁⠘⠚⠓⡄
⠈⠣⣘⠿⠿⣿⣀⣸⠀⣠⣄⣠⠧⠤⠖⣒⣊⠁⠇⢀⡔⠉⠁⠉⠉⡇⠐⠽⠀⠇⠰⠋⢁⣤⠁⠖⢦⠃
⢀⡴⠛⠋⠐⠢⠭⣉⣉⠥⠄⠒⠒⠈⢩⠁⠀⠀⠀⡜⢒⠖⠒⠒⠒⠋⣢⠀⠀⢈⡠⠀⠉⣡⠷⣠⠤⠃
⠊⢇⠀⠀⠀⠀⠀⠀⠈⠉⢒⠖⠂⠤⠮⠄⠀⠀⠀⠠⠎⠠⠤⠐⠒⠉⠀⢀⡄⠅⠤⠒⠉⠓⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠶⠒⠒⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣄⠈⠙⠿⣆
⠀⠀⠀⠀⠀⣴⠟⠁⢠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⣏⠉⢻⣿⣿⣷⡀⠱⣜⣇
⠀⠀⠀⢀⡾⠋⠀⣠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠈⢣⠀⢻⣿⣿⠟⣆⠙⢿⡀
⠀⠀⣠⡏⠀⣠⣴⣿⣿⡑⠒⢿⡿⢿⣶⣶⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⡀⠀⣸⣿⣿⣿⡟⠀⠈⢇⠈⢷⡄
⠀⢰⣿⠀⠺⠟⠛⣿⣿⠀⠀⠀⡇⠀⣿⡿⠉⠓⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢸⡆⠘⣿⣆
⢸⠈⡟⠀⠀⠀⢰⣿⣿⣦⣤⣴⣷⣶⣿⠃⠀⢀⡇⠀⠀⠀⠀⠀⠀⠙⢿⣛⠛⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⢹⡛⡆
⢸⣾⠁⠀⠀⠀⠈⡿⠿⢿⣿⣿⡿⠟⠃⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⢦⣤⠤⠀⠈⠁⠀⠀⠀⢷⢸⡄
⢸⣿⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠉⣉⠉⠉⠙⢛⡶⠦⡄⠈⣙⡇
⢸⣿⠀⠀⠀⠀⠀⠈⠳⠀⠀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣞⠉⠀⠀⠀⣰⠋⠑⠦⠴⠋⠀⣴⠃⠀⢻⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢀⡟⢷⣄⣀⡴⠃⠀⠀⠀⠀⠀⣰⠃⠀⠀⢸⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠖⢉⣄⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢨⡇
⢹⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⢀⡇⠀⢀⡞⠉⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢸⡇
⠘⡇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢦⣀⣸⠟⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠘⣧
⠀⢷⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢿
⠀⠈⢧⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠃⢸⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣸⠀⠈⠻⣅⡼⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠸⡏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⠿⠶⠤⣄⠀⠀⣠⢤⣄⡏⠉⠙⣆⠀⢀⡟⠁⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⢳⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣇⣀⣀⣨⠗⠋⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠉⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣶⠶⠾⣿⣿⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠈⢩⡟⢲⣴⠏⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣴⡟⠁⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠇⠀⠀⠀⢴⣶⣶⣶⣤⣄⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠉⠉⠁⠀⢈⡿⠋⠛⠻⢷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⠀⠀⣠⡶⠟⠋⠀⢠⡼⠛⢷⣄⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠈⠙⢿⣿⣧⠀⠀⠀⡄⢀⠀⢸⣿⣿⠁⠀⢠⡾⠋⠀⠀⠀⠀⢸⡀⠀⠀⠙⣧⡀⠙⢷⣄
⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⡉⠻⣇⠠⠞⠁⠀⠀⠈⢿⡿⠀⢠⡿⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣤⠟⢷⠀⠈⢻⣆
⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⣠⠞⠋⠉⠉⠈⠉⠉⠳⣌⡀⠀⠀⢆⠀⢣⣀⣁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⢻⣇
⠀⠀⠀⢠⣿⠃⠀⠀⢠⡞⣁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣶⡌⠓⠂⠈⠉⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠈⣿⡄
⠀⠀⢠⣿⠇⠀⠀⠀⣿⡟⠋⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢤⡘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⡇
⠀⠀⣾⡏⠀⠀⠀⠀⢻⣇⣠⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣀⣤⣶⣶⣶⣿⣶⣝⣻⣶⣤⣄⣀⠀⠀⠀⠀⣀⣼⠏⠀⠀⠀⢿⣧
⠀⠀⢻⣧⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⣠⡾⢿⡉⠀⠀⠀⣿⠉⠛⠻⢿⣿⣿⣿⣿⣿⡛⠛⠛⠓⠋⠀⠀⠀⠀⢻⣧
⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣡⣾⠋⠀⠀⢳⣦⡀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣠⣴⣾⡿⠋⣰⣿⣿⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣫⡿⠻⠋⠀⣿⠇⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠄⠀⠀⢿⡇
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⢳⣿⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⡆⠀⢸⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⠀⠀⣿
⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠁⠀⠀⢀⣼⣿⣿⣿⠋⠙⠻⣿⣿⠇⠘⠀⠀⣿
⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣀⠀⢠⣾⠃⠈⢹⣿⠀⠀⢀⣿⠟⠀⠀⠀⠀⣿
⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⣰⡞⠛⠛⠻⠿⠃⢀⣀⣠⣿⣤⡶⠟⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣟⣴⣶⣶⣦⣿⠀⠀⠀⣀⣴⠞⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣼⣿⣿⣿⣿⣿⣿⠿⢫⡿⠁⠀⠀⠙⠛⢀⣤⠞⢋⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠙⢿⣤⡀⠀⠀⠀⠀⠀⠀⣃⣾⣿⣿⣿⣿⡿⠻⣷⣤⠟⠀⠀⠀⣠⡴⠞⠋⢀⠴⠋⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠂⠻⣿⣿⣿⡿⠋⠀⠀⠀⣉⣀⣤⠶⠛⠉⠀⠀⠀⠀⠐⠒⠚⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣄⡀⠀⠀⠀⠉⠛⠛⠻⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠷⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣩⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣷⠀⠀⠤⠤⠄⠂⢀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠖⠛⠙⠉⠈⣀⡁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠙⠃⠂⠀⠜⠀⠀⠀⢀⢄⣀⠤⣼⣿⣿
⠀⢀⡀⠀⠀⠀⢌⢙⡿⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢀⠄⠀⠀⠚⠆⡠⠐⡶⡷⣶⣿⣦⣿⣿⣷
⣰⠏⣉⡳⣄⡀⠀⠀⠉⠠⣿⣿⣿⣿⢻⣿⣟⢻⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⢤⡤⠚⠚⠋⠉⠉⠉⠉⠉⠉⠙
⣧⣾⡿⠟⠋⠉⠙⠂⠀⣴⠟⠛⣿⣧⣬⠿⣧⣼⠀⠀⢀⣿⠉⣻⠁⠀⣟⠉⣃⣴⣿⣿⣶⣄⣀⡜⠀⠠⢤⣄⡀⢀⣔⢶⡶⠄
⣿⣿⠁⠀⠀⠀⠠⠀⢄⠙⠃⠈⠁⢹⣷⣤⣾⣿⣀⠄⠀⢛⣛⣥⣴⠷⣼⡿⠻⢷⠿⠿⣿⣿⣿⡀⢩⠓⠠⡜⠀⣀⢤⠀⣉⡩⢵
⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣴⡿⠿⢭⠾⠁⠀⠉⠙⠿⠛⠊⢳⣖⣈⡒⠢⠟⠉⠙⡇⣿⣟⣖⣺⣓⣖⣹⡯⠴⣷⠏
⠀⢂⣀⠀⠀⠀⠸⠾⠀⢈⣿⠟⢿⣿⣿⣿⣇⡀⠈⠑⢢⠄⠀⠀⠀⠀⠀⠈⠙⠻⢋⡀⠀⠀⠠⡇⠘⠿⢿⣹⣍⣯⡠⠷⠊⢁⣠
⢀⡀⠤⠀⠤⢀⠀⠀⠀⠰⡿⠀⢸⣿⣿⡷⠿⢿⣷⣶⡇⢦⣑⡀⢉⠉⠀⠍⠂⠈⠁⡄⠀⠀⠀⢇⠀⢀⣀⠀⣀⡀⠈⠲
⠈⢀⡐⠀⡄⢻⣀⠀⠀⠀⣿⡀⣸⣿⢣⣤⣾⣿⣯⣿⣯⡂⢿⣄⣈⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢀⣼⣥⡀⠐⠂
⠀⠸⠅⣀⠤⠶⠃⠀⠀⡰⠏⢿⠟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡍⣩⠿⠛⠉⠉⠉⠙⠒⢤⣀⣀⡤⠄⠈⠐⢭⡍⠉⢁⡂⢀
⠀⠠⠀⠀⢀⣀⣀⣐⣦⡌⠣⡀⠘⣿⣿⣭⣯⣉⣴⣿⣿⡷⢈⣿⠥⣤⡀⠀⠀⢀⠤⢤⣄⠈⢦⠒⠀⠀⢰⣔⡟⠒⠚⠙⠏
⠀⠀⠀⠀⠔⠩⠛⣉⠲⠄⣦⣧⣠⠻⡟⠞⠂⠉⠴⠿⠉⠀⡞⡏⠀⠙⢻⠀⠀⡇⠀⠘⢛⡆⠈⣇⠀⠀⢀⠁⢿⠻⠿⡷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣛⠛⠛⠛⠛⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⠿⠿⠿⠿⠿⢿⣿⡟⠛⠳⢦⣄⡀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣦
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣟⢷
⠀⠀⢀⣀⣼⠟⠁⠀⣠⡶⠋⠉⠀⠀⠀⠹⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⢛⣻⣷⡄⠘⠋⢿⣿⡄
⠀⠀⣼⡟⠁⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠉⠙⢷⡀⠀⠀⠙⣿⡄
⠀⢰⣿⠀⠀⠀⣾⣷⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣿⡇⠀⠀⠀⠀⣼⣿⣤⣤⣤⣤⣤⠤⠴⣶⣼⣿⡄⠀⠀⠸⣿⣦
⡇⠛⣿⠀⠀⠀⣿⡛⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⡏⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢹⣿⡇
⡇⣸⠇⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⢿⣁⡄
⡇⡟⠀⠀⠀⠀⠀⠈⠛⢶⣤⣄⣀⣀⣀⣤⡴⠟⠁⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣤⣤⣤⣤⠾⠋⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁
⢸⡞⡇⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⠶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⡶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠘⣇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠹⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⢸⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠘⣇⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⢻⡆⠀⠉⠛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⠛⠛⠛⠛⠛⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⡄⠈⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠹⡄⠈⠄⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢿⠀⠁⡠⠂⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠐⢦⡀⠀⠱⣄⠎⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠌⠂⠂⣻⠓⠀⢉⠢⣤⠶⠋⠠⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠬⠥⠴⢃⠠⠛⢠⠠⡀⠀⡇⣐⢩⣬⣅⠂⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠁⠉⠁⢉⣀⠄⠀⠀⠀⠀⠀⠰⡘⠠⣙⡣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢱⠤⠀⡀⠀⠀⢣⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣀⣀⠀⠈⠀⠠⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠉⢳⣀⣀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⣾⠟⠃⠘⠯⢻⣛⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡹⢁⠴⡋⡠⠟⢢⢹⠏⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⣷⡿⢶⠧⣦⡎⠾⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠭⠖⠟⠸⠀⠁⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠚⠛⠓⠢⠤⠤⠤⢶⡀⠀⠀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠶⣄⠀⠀⠉⠛⠲⢦⣤⣀⣠⡖⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⠶⠛⠁
⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⢲⡶⠶⠶⠒⠛⠋⠉⠁⠀⠀⠀⠀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⣦⡀⢀⡄⢤⠀⡀⠀⠀⠀⠀⣻⣶⣾⡷
⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⣠⣏⣀⣀⣨⡿⢦⣷⢼⣧⣿⡀⢀⣠⠞⠋
⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠖⢛⡿⠋⠉⠉⠉⠀⠀⠀⠙⠳⣤⣭⠶⠋⠁
⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠿⠶⠶⠦⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠚⠛⠛⠒⠒⢲⣿⡶⠿⠍⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠀⡄⢠⠀⡄⢠⠀⡄
⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣀⣀⠀⠙⣦
⠀⠀⠰⢒⡶⠿⢤⣤⣀⡀⠀⠀⠀⢀⣿⣿⠏⢀⠼⠋⠉⠳⣄⠘⣳⡄⠀⠀⠀⠀⠃⠘⠀⠃⠘⠀⠃⠘⠀⠃
⠀⢀⣠⠞⠁⠀⠀⠈⣻⣍⠀⠀⠀⠘⣿⡇⡴⠁⠀⠀⠸⣄⣨⢳⡙⣧⠀⠀⠀⠀⢠⠄⡤⢠⠄⡤⢠⠄⣤
⠀⣼⠃⠀⢠⠔⠋⠉⠉⠙⢷⣄⠀⠀⠋⠀⣇⠀⠀⠀⠀⠀⠀⠀⢻⠘⣧⠀⠀⠀⠀⠀⠀⠈
⡇⡿⠀⠀⡌⢒⡦⠀⠀⠀⠈⢻⠁⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⣸⠀⢸⣳⡀⠀⠀⠀⠀⠇⠸⠀⠇⠰⠸⠸⠘
⣇⠇⠀⠀⢹⠉⠀⠀⠀⠀⣠⠏⡠⢶⡉⠉⣏⣓⡺⢿⣓⠒⡒⠚⠁⠀⠀⢳⣧⠀⠀⠀⠀⡄⡀⠀⢀⠀⢀⢀
⣿⠀⠀⠀⠘⢦⣀⣀⣠⠞⠁⣼⣇⠀⣿⠲⠇⠉⠀⠀⠈⠙⠛⠑⣄⠀⠀⠈⣿⠀⠀⠀⠀⠁⠁⠁⠀⠈⠈⠈
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠡⠟⠙⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠰⠰⠰⠸⠸⠰
⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣠⠤⣤⠞⠁⠙⣦⣠⡤⢄⠈⠀⠀⣿⠀⠀⠀⠀⡀⡀⠀⣀⠀⢀⢀
⢰⢱⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢰⠃⠀⢀⡤⢄⡸⠁⣹⡀⣈⣽⠀⠀⢸⡀⠀⠀⠀⠁⠁⠁⠈⠀⠈⠈
⠈⢯⣇⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⣠⠤⣄⡾⠀⣨⠕⠋⠁⠀⠁⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠢⠰⠰⠰⠰⠰
⠀⠀⢻⡀⠀⠀⠀⠀⢰⢃⡤⠶⣄⡼⠁⢀⣨⠗⠊⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⡀⡀⠀⢀⠀⢀⢀
⠀⠀⢸⡙⠦⣀⠀⠀⠉⠚⠒⠲⠦⠵⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠑⠁⠒⠈⠐⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠁⠀⠀⠀⠀⠈⠑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠠⠠⠤⠤⠄⠒⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡧⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡎⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢧⣀⠀⠀⠀⡄⠀⠀⣀⣀⣀⣀⣤⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⢿⣄⣢⣿⠇⠈⣿⣿⡿⠋⣭⢹⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣌⠙⢻⣧⠀⠘⢩⣙⢷⣄⢄⣾⠞⠁⠈⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡞⣳⠀⣼⠤⠏⢽⡢⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⡘⠾⠁⠀⠑⠀⢱⠘⢠⡞⠁⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡘⠄⢀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣞⠀⠀⠈⠙⠒⠀⠀⠀⢀⡠⠔⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⣿⠀⣴⠟⠛⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣧⣿⠘⣿⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠘⠛⠀⠙⠛⠛⠋⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠈⣅⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⣼⣿⣿⣾⣿⣿⣿⣿⣠⡀⣤⣾⣤⣭⣤⠀⣠⢄⢀⣤⣤⡀⠀⣠⣍⢡⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⡟⣿⢠⣿⣈⣼⣿⣿⡇⢠⣿⠃⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣹⡏⡇⢻⣿⣿⡇⢸⣿⠠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣷⣾⣿⣿⠇⢿⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⢿⣿⢿⣿⠹⣿⣿⣿⣿⣿⣿⠀⠻⣿⣿⣿⣍⠿⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢹⣿⠃⠸⣿⢸⡿⠀⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⠀⠀⠀⣿⣿⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⠀⢀⣿⣿⡷⠒⣿⣿⢻⣿⣿⣧⡤⠀⣿⣿⠹⣿⡇⠀⠀⢸⣿⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⣸⣿⣀⣤⡤⠉⠀⠀⢻⣿⠀⣿⣏⣠⡤⠤⠸⣿⠀⢻⡷⠀⠀⠾⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠟⠉⠛⠋⠉⠁⠀⠀⠀⠠⠾⠟⠉⠉⠉⠀⠀⠀⣰⡿⠶⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉⠁⣠⣄⡀⢷⡄⣄⠈⠑⢄
⠀⠀⠀⠀⡰⠊⠡⣀⡀⠀⠀⠀⢹⣿⣿⡎⣿⣿⡶⠖⠚⠧⡀
⠀⠀⠀⡜⠀⠀⢀⣨⡿⠛⠛⠛⠛⣟⠻⠟⡹⠇⠀⠀⢠⣶⡜⡄
⠀⠀⢰⠁⠀⠠⡏⠀⠀⠀⢠⣶⡆⢸⠂⠈⢳⠀⠀⠘⠤⠍⡱⠻⡄
⠀⠀⡜⠀⠀⠀⢧⡠⠄⠀⠀⣉⡵⠋⠀⠀⠠⠿⠷⠶⠖⠚⠁⢠⣿⡄
⠀⠀⡇⠀⠀⠓⠬⢿⣷⡶⠋⠁⣀⣀⣤⣤⠤⠶⢶⣶⣾⣛⠿⢆⠙⣿⡀
⠀⠀⡇⠀⠀⢠⠄⢀⣤⣶⣾⡿⠟⠱⡞⠉⠉⠉⡇⠀⠀⡇⠀⢸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⠀⢀⡀⢄⡀
⠀⠀⡇⠀⣦⠇⢰⣿⣟⣁⠀⠳⡀⡄⠸⡄⢀⣂⣃⣀⣠⣷⣠⣾⣿⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣋⣩⢿⠵⡢⣜⣷⠃⣠⣆⣸⠆
⠀⠀⠸⡀⢿⠀⣿⣿⣿⡿⠓⠓⡟⠊⠟⡏⠭⢹⡍⠉⢫⠉⠋⠢⣙⡇⡾⠤⢤⣀⠀⠀⠀⠀⠀⣠⠔⢦⣧⠈⢳⠎⢀⠥⣴⣧⣄⠓⠊⢉⢱
⠀⠀⠀⠱⣄⠣⢽⣿⣿⠁⠀⢰⠇⠀⠀⣇⠀⢀⣧⣀⡸⠷⠔⠒⣋⣠⠃⠀⢠⠞⠉⠉⠉⠉⠉⡇⠳⢏⠼⠀⡺⠀⡼⠒⠁⣠⡿⠀⣟⢣⣸
⠀⠀⠀⠀⡸⠓⠒⠤⣌⡉⠒⠾⠷⠖⠚⢋⣉⣩⣥⣤⡶⣾⠿⠛⠉⠀⠀⢠⣧⣤⡤⣤⣤⣤⡤⠼⢄⠀⠀⠀⠱⠂⠀⠀⠺⠥⢚⣆⣨⣥⢉
⠀⠀⢀⢼⠁⠀⠀⠀⠀⠈⠉⠒⠶⠾⣿⡛⠋⠉⠁⠀⠀⡎⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⣀⡤⠖⠁⠀⠀⠠⠚⠉⠀⢀⣤⠋⠘⠲⢌⠙
⠀⣠⠋⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⠙⠒⠒⠒⠃⠤⠤⠤⠤⠤⠿⠿⠤⠔⠒⠋⠉⠀⠀⠀⣀⣀⡠⠤⠔⠒⠋⠁⠀⠉⠙⠂⠉
⢰⠃⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⡤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠔⠒⠊⠉⠁
⢸⠀⠀⠀⠀⠱⣄⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠥⠴⠊⠀⡼⠁
⢸⠀⠀⠀⠀⠀⠙⠿⣷⣦⣤⣀⡀⠀⢸⣿⠇⠀⠀⠀⢰⠇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠐⠶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⡶⠛⠁⠀⠀⠀⡴⠛⠋⠻⠟⠉⠿⠟⣋⣉⣿⣝⣶⣄⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢿⣄⢛⡃⠀⠀⠀⠀⣠⣤⣇⣀⣤⣀⡀⠀⠀⠀⢡⠤⠷⢿⣿⡿⢧⡀⣄⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⢠⣾⢿⣏⠀⠀⠀⠀⠀⣿⢿⣿⣥⣤⣬⢻⡆⠀⠀⢖⣖⣶⣾⣿⣿⡈⢷⠘⠆⠀⠀⠘⣿⡄
⠀⠀⠀⠀⢀⣿⠻⢿⣟⣧⡀⠀⠀⠀⠸⣿⢋⣻⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠾⠇⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⢸⣧⣄⣘⣿⣿⠙⠀⠀⠀⠀⠀⠉⠁⢀⡠⠤⠒⠒⠛⠛⠙⠛⠛⠛⣲⣦⡀⠀⠀⠀⠀⠀⢠⡹⣧
⠀⠀⠀⠀⢸⣿⣬⣿⠿⠟⠀⠀⠀⢀⣀⡤⠖⠋⠁⢀⣀⣀⣤⣴⠶⣶⣶⣿⡉⣽⣿⣿⣦⡀⠀⠀⠀⠀⠻⣿⣇
⠀⠀⠀⠀⢸⡟⠋⢁⣀⣠⣤⠶⠞⣋⣉⣀⣤⠶⠛⢹⣏⠁⢸⣿⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢦⡀⠀⠹⣿⡄
⠀⠀⠀⠀⠈⠻⣿⣉⣩⣥⡴⢶⣿⠉⣼⢿⣇⠀⠀⣸⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢧⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⢻⡀⣸⣷⡀⢸⣿⣷⠟⠈⠻⢷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⢿⣝⠿⣿⣿⣿⣿⠿⠛⠉⠉⠙⠻⡇⢸⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡢⣽⣷⣾⠿⠋⠁⠀⠀⠀⠀⢠⡀⢻⡜⠃⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠙⠻⢷⣦⣄⡀⠀⢀⣤⣾⣧⡿⠟⠋⠁⠀⠀⠀⠀⠀⠠⣄⢲⣿⡆⢹⣀⡇⠐⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣀⡠⣤⣤⢼⣧⣽⣦⣬⣿⠇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣔⠲⣦⣝⣻⣶⣽⣷⣝⣿⣿⣿⣿⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣽⣦⣰⣤⣰⣦⣲⣦⣻⣦⣿⣷⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⣿⣟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⣸⠿⢣⠎⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢹⡆⢀⣿⣿⣿⣿⠟⠛⢿⠟⠉⣷⠞⣁⡴⢋⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⡴⠺⣿⠁⠈⠻⣆⠀⣸⡴⢞⣡⠞⣫⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣷⣤⣽⣴⣶⣶⣛⣩⠵⠚⣩⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣭⣭⣭⣭⣭⣥⣤⣶⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⢯⣶⣀⡀⠶⠶⠄⠠⠎⠉⣹⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⢀⣴⠟⣁⣤⣶⠿⣛⣉⣉⣛⡛⠻⡷⠒⠒⠚⠉⠉⢀⣽⠿⠿⣿⣿⠶
⠀⠀⢠⡞⣡⣾⡿⠋⣠⡞⠋⠉⠉⠉⠻⣆⠀⠀⠀⠀⢀⡾⠋⠁⠀⣴⣿⠟⣧
⠀⢠⡿⠀⠀⠀⠀⢰⡏⢀⣀⣀⠀⠀⠀⢿⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⣿⡄
⠀⣼⠇⠀⠀⢀⡴⢿⣧⡸⡿⠟⠁⠀⢀⣿⠀⠀⠀⠀⠘⢷⣤⣤⣤⣤⣶⣿⣹⡇
⠀⣿⠀⠀⠀⠀⠀⠛⠉⠛⠶⢶⣶⠶⠛⠁⠀⠀⠀⠀⠀⣀⣴⠟⣁⣤⣤⣈⠙⢿⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⣒⣒⣚⡛⢛⣿⠏⣰⣿⣥⣤⣹⣷⠈⣷
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠯⠭⠤⠆⢸⡟⢠⣿⠼⠧⢯⣿⣿⡆⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠓⢸⣇⢸⡇⠀⠀⠀⠀⣿⢹⡇⠀⠀⣴⡆⠀⠀⠀⠀⣠⣶⡶⣶⣦⡀⠀⣴⡆
⠀⢹⡆⠹⡄⢷⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⠀⠀⠀⣸⡇⣾⠁⠀⠀⣿⡇⠀⠀⠀⢸⣿⠁⠀⠀⢹⣿⠀⣿⡇
⠀⠈⣷⠀⢹⣾⡇⠈⢣⡀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⢸⡿⢸⡇⠀⠀⠀⣿⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠸⣿⡀⠀⠀⣸⣿⠀⣿⡇
⠀⠀⠘⣧⠀⢻⣿⡀⠀⢙⠀⠀⠀⠀⢘⣛⠷⣦⠀⠀⢸⡇⣾⣧⣄⣀⠀⢻⡄⢹⡆⠀⠀⠿⠿⠿⠿⠷⠀⠙⠿⠿⠿⠟⠃⠀⠿⠿⠿⠿⠷
⠀⠀⠀⠹⣆⠀⢻⣧⠀⠸⣆⠀⠀⠀⣀⣉⠛⢮⡀⠀⣿⠁⣿⠀⠀⠈⠳⣼⡇⢸⡇
⠀⠀⠀⠀⠹⣆⠀⢻⣷⡀⠈⠣⡀⠀⠀⠉⠛⢦⣍⢰⡟⠀⣿⢻⣟⡟⣟⣻⡇⢸⡇
⠀⠀⠀⠀⠀⠸⣦⠀⠙⢬⣑⢦⣌⠓⠀⠀⠀⠀⠈⢻⣷⠀⢻⣏⣉⣛⣻⠟⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡈⠙⠻⢿⣶⣤⣤⣤⣄⣀⣻⣆⠀⠈⠉⠉⠁⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⣀⠉⠙⠛⠲⠾⠏⠉⠛⣛⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢦⣤⣤⡴⠾⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠈⠐⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠚⣉⡀⢠⡈⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠛⣂⣘⣃⡠⠈⡄⠠⢲⠞⠦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⠛⠛⠛⠭⠋⠀⠸⡆⠀⠀⠱⠁
⠀⠀⠀⠀⢀⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠃
⠀⠀⠀⠀⣶⣿⣿⣟⣿⣸⣏⣹⣀⣯⣍⣿⣿⣿⣦⠀⠀⠀⠀⣐⠁⠈⠐⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠛⡄
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⡸⠀⠉⠢⢀⠀⠀⠈⢵⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣷⣿⣶⣿⡇⠀⢠⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢻⣿⢻⠿⠛⡛⠛⠛⠿⠻⢟⣿⠛⣿⣿⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠹⣷⣾⣾⣶⣿⣶⣷⣷⣷⣾⣶⡿⠁⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⢿⡿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠖⠀⠀⢦⠀⠀⠲⡒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠆⠀⠀⠱⠔⠂⠀⢈⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠄⠚⠁⠀⠀⢘⡄⠀⢀⣤⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⠤⠐⠚⠁⠈⠚⠛⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠛⠉⠉⠉⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠐⡄⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠹⡄⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠢⡃⢀⡔⠁⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠙⣦⡄⢸⢏⣀⣀⣤⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣘⠛⢃⡄⢀⠮⡀⠀⠐⢽⠉⠄⢀⡠⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠁⠀⠀⠀⠀⠘⡘⢄⡻⢟⠄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠒⠛⠉⠀⢀⣀⠀⠀⠀⠩⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣀⡀⠁⠀⠀⠵⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⣦⣀⣀⡔⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢲⣿⠋⢁⢛⠝⢿⣅⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣡⣪⢑⠐⢫⣎⡟⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⠛⡛⢻⡾⡌⠁⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡉⠘⠈⢁⠁⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡁⠀⠙⠳⢦⣄⣀⠀⠀⠀⡠⠀⠠⠊⠀⠀⠀⠈⠉⠉⠉⢳⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠉⠳⣄⠀⠀⠀⠉⠙⠓⠾⠦⠤⢤⣤⣤⣤⣤⡤⠤⠶⠚⠋⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣄⠀⢀⠀⡀⠀⠀⠀⠀⠀⢷⣤⣽⡴
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡼⠁⣀⣈⣷⣼⣧⣿⣼⣄⠀⣀⡴⠋⠀⠉
⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠖⢺⠟⠉⠉⠉⠁⠀⠈⠛⢦⣭⠵⠚⠁
⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠛⠒⠒⠲⠶⠶⠶⠤⠤⠤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣰⠏

⠀⠀⠀⠀⡀⠤⠠⠤⠠⢄⠀⠀⢰⡒⠒⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⡔⠉⢀⡀⠀⠀⠀⣀⠕⠀⠀⠉⠒⠬⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⢀⡱⠀⠀⠀⠀⠀⢀⠔⠊⠄⠀⠀⠀⠈
⠀⡘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⠐⠒⠈⠁⠀⠇⠀⠀⠀⠀⢠⠃⠀⠐⠒⠂⠀⠈⢹
⢀⠃⠀⠀⠀⠄⢀⣀⠀⣸⣂⡒⠒⠶⠶⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⡌
⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣠⠎⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠓⢤⡄⠤⣀⣀⠤⢄⣰
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡰⠊⡎⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⠀⠀⠈⠁⠁⠈⠁⠈⠁
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢀⡀⢀⡔⠋⠀⢸⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠬⠷⠀⠀⠈⠋⠀⠀⠀⠈⠉⠁⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⣤⠽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠠⡴⠶⣆⠀⠀⠀⠀⠀⡀⠀⢀⡏⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢗⠄⠀⠴⠋⡠⠒⠫⣠⢦⡠⣄⡀⠀⠹⡏⠻⣦⣈⢃⠢⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢈⣅⣓⠊⠀⡴⠛⠁⠀⠙⠛⠛⠁⠒⠛⢄⠈⢣⡑⡅⣭⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⠈⠀⣞⣀⣀⣀⣀⣠⠰⣄⣀⣀⣤⣈⢧⠀⠑⣜⢲⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡆⠀⠀⢰⡉⠀⣴⣦⠉⠉⠀⠉⢠⣶⡄⠈⢹⠀⠀⠈⢸⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢹⠀⢀⣴⣀⣀⣀⣀⣰⣄⠀⠀⡞⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢸⠇⡞⠀⣉⠙⠛⠉⠁⠈⡇⠀⡇⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⢀⣠⣶⣏⠀⢴⡯⠭⠍⠉⠩⠭⢿⡄⢀⣿⣦⣄⡀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣰⣿⣿⣿⣿⣷⣄⠀⠀⠒⠒⠒⠀⠀⣠⣾⣿⣿⣿⣿⣦⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠘⠉⠁⠀⠀⠈⠉⠛⠛⠿⠿⢿⣿⣿⣝⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠀⠉⠉⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣴⣦⣤⣤⣀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⢀⣀⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⣄⣰⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣿⢿⡿⠿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠈⠙⠛⡛⠋⠁⣀⣀⣀⣀⣀⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠢⠤⠤⠤⠤⠄⠒⠂⠠


⣶⣶⣶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣽⣶⣤⣿⣵⣿⣽⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠈⠙⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠶⠖⣲⣦⠀⠀⠀⠀⢠⣴⡶⠶⠄⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠟⠙⣿⣿⣿⠃⠀⠫⠄⠸⠗⠀⠀⠀⠪⢅⡩⠷⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⢧⣤⠀⠠⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣦⠀⠀⠀⢰⢂⡀⠀⠀⠀⠀⠀⡀⡔⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠈⠑⠒⠒⠒⠉⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡔⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠑⠬⣒⠒⠒⡚⠕⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⡠⠤⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣋⣉⡁⠀⢠⠞⠙⣇⠈⠑⠒⢹⠉⠉⠀⠀⠀⠠⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡢⣄⠀⢀⡴⠋⠀⢀⣹⣠⠏⠀⡖⠉⠐⣦⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢩⣷⣤⠎⠀⠀⠀⠙⡟⠁⠀⣼⡴⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠈⠳⠤⢀⣀⣠⢭⣟⠀⠀⠀⣠⠞⠁⠀⠰⣻⡥⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠙⠟⡛⠋⠁⠀⠀⠀⠈⠡⠒⠛⠛⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣐⣠⣂⣤⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠍⢀⣀⣀⣀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡽⡬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠸⡇⠀⠀⡇⠀⠀⡏⠉⢱⡖⠤⣄⠀⠀⠀⠀⣠⠔⢉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⡇⠀⠀⡇⠀⢸⠀⠀⢘⣉⠦⠔⣉⡤⠚⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢏⠉⠑⠒⠳⣤⣤⣧⠠⠼⠒⠈⠉⣠⠔⠊⠁⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢛⢿⡖⠊⠋⢍⠁⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀
⠀⠀⠀⠀⢠⠎⡴⢳⡌⣵⠦⣀⠀⠀⠀⢀⣠⠤⣦⣀⣜⠸⡿⠀⠀⠀⠙⠲⢤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠄⡀
⠀⠀⠀⠀⣾⣸⣃⡷⣼⢣⡟⠊⡗⢰⣹⠹⣇⢉⠔⠋⢁⣠⠒⡄⠀⠀⣀⣠⣄⣀⣀⣀⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣴⠃
⠄⠀⠀⠀⠈⠛⠨⢽⣇⣾⣠⠦⠽⢆⢀⠀⠀⢧⢀⡜⠁⣀⠙⠠⡔⠚⢦⠸⣸⠈⣆⠁⡀⠀⣀⠔⠉⠁⠀⣀⡤⠴⠋⠁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠘⠓⣿⠏⠀⠐⠄⠐⡋⢸⡦⢉⠀⢸⠀⣷⣊⣠⡤⠶⠚⠉⠁⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠤⠜⠛⠛⠯⠽⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡴⠤⢄⣸⡇⢴⠂⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠑⢿⣄⢀⣱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⣙⣻⣄⡴⠶⠻⣉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡉⢉⣳⣶⡀⢤⣤⣤⣤⣤⠤⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠀⠤⠄⠀⠤⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣴⠳⣭⠵⠀⠁⢀⣠⠾⣽⣦⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠀⠀⠀⠀⠈⠲⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⡜⠀⢠⠞⠉⠑⠀⠀⠈⠀⠌⠉⠙⣆⠘⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⡀⠀⠈⠛⢤⠋⠀⠀⠀⠀⠘⠠⠟⠁⠀⢀⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠰⠀⠃⠀⠄⢀⡀⠀⡀⠀⠄⠘⠀⠂⢀⠐⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢂⠀⠀⠀⢠⠀⠈⠉⠉⠁⠀⢄⠀⠀⠀⢀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠘⠀⠀⠀⡆⠀⠐⠒⠒⠒⠀⢸⠀⠀⠀⠙⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⢀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣆⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⣰⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢞⡄⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⢀⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡒⠛⠋⠭⠭⠭⢹⠤⣀⣸⣷⣤⣴⣾⢧⣀⡠⣾⣖⣒⠯⠭⠽⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣮⣑⣒⡚⠭⠽⠿⠿⠾⠿⠶⠾⠿⠿⠿⠿⠷⠶⠒⠻⠿⠿⠿⠿⠿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡴⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠘⣟⠆⢈⠈⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠠⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⣯⡁⢾⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣈⣷⣼⠿⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠖⠛⠉⠉⠘⣧⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠁⠀⠄
⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠒⠒⠒⠓⠒⠒⠒⠀⠰⠆⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡯⠤⠀⠤⣄⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⠆⠈⠈⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠂⠀⠚⢀⡼⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢀⡴⠛⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠂⣼⠲⡄⠀⠀⠀⢰⣶⡴⠉
⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⣿⠀⢳⡀⠀⠀⢠⡎⠁
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⣿⠀⠘⣇⠀⠀⣼⠃
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢿⠀⢰⠏⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢦⣼⢷⣤⣶⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡾⣧⡴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡛⠋⠀⠉⠈⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁⠉⠀⠙⢛⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣶⣞⠛⠀⠀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⠀⠛⣳⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡿⠆⠀⠈⠛⠻⠆⠀⠀⢀⣀⣀⡀⠀⠀⠰⠟⠛⠁⠀⠰⢿⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⣀⣴⡶⠄⢀⣴⠞⠋⠉⠉⠙⠳⣦⡀⠠⢶⣦⣀⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⢿⣠⡶⠲⢦⡴⠖⢶⣄⡿⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⢀⣼⠏⠀⠀⢸⡇⠀⠀⠹⣧⡀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⠟⠁⠀⢀⣴⠏⠹⣦⡀⠀⠈⠻⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠋⠀⠀⣠⡞⠁⠀⠀⠈⢳⣄⠀⠀⠙⢷⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣀⣀⣀⣴⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣦⣀⣀⣀⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠉⠙⠃⠈⠉⠉⠉⢉⠖⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠖⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡀⠀⣀⣀⡀⠤⠤⠒⠒⠉⠁⠀⠀⢡⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠑⢄⡲⠉⠀⢀⣐⠲⠒⠀⠀⠀⠘⢋⡤⠤⠤⠈⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠘⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠋⡙⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⣤⣄⣀⠀⠀⠀⣀⣀⣤⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⣈⠒⠀⠐⠁⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣰⣋⣉⣉⣭⣉⣉⣉⣛⣻⡀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠧⢤⡤⢄⠀⠀⢀⠀⣀⡨⠗⠁⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣄⣸⣀⡾⠃⠀⢷⣂⣠⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡇⠀⠀⠀⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⠀⠀⠀⠀⠀⠐⠀⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡏⠉⢹⠉⢩⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣓⣢⡼⣤⣜⣢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠉⠉⠙⠋⢹⠀⠀⠀⠀⠀⠀⢸⠁⠙⠋⠁⣉⣟⠉⡇⠀⠀⠀⠀⠀⡇⠘⠛⠋⠉⠛⠛⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠲⠶⠶⠤⠀⡾⠀⠀⠀⠀⠀⠀⢸⡄⠀⢘⣹⣇⣨⣷⢇⡆⠀⠀⠀⠀⢻⡀⠀⠒⠛⠛⠗⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠰⣤⠻⢤⣀⣀⣠⠞⡥⠀⠀⠀⠀⠀⠀⠀⠙⣦⣬⣷⡼⢷⠋⡾⠀⠀⠀⠀⠀⠀⢙⡶⠤⠤⠤⣶⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⢼⡧⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣏⢸⣇⡟⠈⠛⠁⠀⠀⠀⠀⠀⠀⢺⡀⠰⣶⣶⣟⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡟⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠒⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⣰⠒⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣀⠤⣤⠶⠀⢹⡄⠀⠀⠀⠀⠀⠐⡾⠗⠈⠛⠛⢚⡇⠀⠀⠀⠀⠀⠀⠘⣿⠂⠉⠻⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣩⡁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣇⠠⠄⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣰⠃⣀⣀⣀⣠⡭⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢉⣽⣛⣃⣠⣴⡟⠛⠀⠀⠀⠀⠀⠀⢈⡷⢤⣤⣴⠋⠀⠀⠀⠀⣀⡀⠀⢻⡈⠉⠙⠋⠓⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⢰⠋⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡇⣿⠀⠀⠀⠀⠀⠈⠹⣆⡀⠉⣳⢶⢶⣖⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⢉⣭⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⢸⠀⠀⠀⠛⠶⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠶⢶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠉⠀⠀⠀⠀⠈⠉⠛⠿⣦⣄⠀⠀⢀⣴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⢀⣤⣾⣦⡀⠀⠀⠀⠈⠻⣷⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠿⠋⣿⠉⠻⠂⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢠⣤
⠀⠀⢰⣿⠀⠀⠀⢀⣴⡷⠀⠀⠀⠻⠀⠀⠐⢷⣄⠀⠀⠀⠸⣷⠀⠀⠀⠀⣀⠀⠀⠀⢀⣴⡿⣦⡀⠀⠀⢸⣷⠀⠀⠀⣄
⠀⠀⢸⣇⠀⠀⠀⢿⣿⡿⠿⠿⠿⠿⠿⠿⠿⢿⣿⠗⠀⠀⠀⣿⠀⠀⠀⣰⣿⣆⣠⣴⠟⠋⠀⠙⣷⣄⡀⢸⣿⠀⠀⠀⠙⠃
⠀⠀⠘⣿⡀⠀⠀⠀⠙⠟⠀⠀⠀⣶⠀⠀⠐⠟⠁⠀⠀⠀⢸⡟⠀⠀⣰⡿⠉⠛⠋⠀⠀⠀⠀⠀⠘⢿⡇⢸⡿⠀⠀⠀⠀⠀⢶⡄
⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⢿⣦⣿⣶⡿⠀⠀⠀⠀⠀⣠⡿⠁⠀⢾⣿⣶⡦⠀⠀⠠⣶⣶⣶⠄⠀⣿⠃⣾⠇⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣼⡟⠀⣀⣀⣀⡀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠙⠻⢶⣦⣄⣀⣀⣀⣀⣀⣤⠀⠀⢸⣿⠀⠀⣷⡄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣰⣿⣿⠋⠀⠸⠿⠋⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠉⠙⠛⠋⠉⠙⢷⣤⡈⣿⡀⠀⠈⢿⣦⡀⠀⠺⠛⠛⠿⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠗⠀⠀⠀⠙⠻⣶⣤⣄⣠⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⣦⣀⠀⠉⠉⠉⠁⢀⣠⣴⠿⠿⢶⣦⣄⡀⠀⠛⠛⠀⠀⠀⠀⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠈⠙⠛⠿⠶⠾⠿⠛⠋⠁⠀⠀⠀⠈⠙⠻⣶⣀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇


⠀⠀⣀⠀⠀⢀⠀⢀
⣿⣏⢭⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⣴⠿⠟⠛⠻⠿⠿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠿⠛⠛⠛⠋⠛⠛⠷⣄
⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠒⠒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡶⢿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⣿⣶⣦⣀⡀
⠀⠀⠀⠀⠀⠘⠿⠿⠋⠁⠉⠛⠚⠋⠀⠀⠈⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠙⠛⠚⠋⠀⠀⠈⠛⠻⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣴⣶⣌⠑⢾⡇⠀⠘⣇⢸⡤⢴⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠋⠉⣉⣉⣻⣌⠙⠳⠿⡼⣌⠳⠸⡀⠹⣦⣙⠶⣷⣄⣈⣉⠙⠛⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⢀⡴⠛⢁⣤⠶⠞⢛⡿⠟⠛⠉⣉⡀⠀⠀⣀⣈⣓⠂⠙⠦⣤⡍⠁⠀⠈⠛⠿⣿⣿⣶⣦⣤⣉⡙⠛⠶⣤⣄⡀
⠀⠀⠀⠀⢀⡾⠁⣴⠋⠀⢀⡴⠋⢀⣔⡴⠚⠉⠠⠒⠉⠁⠀⠀⠀⢀⡤⠒⠚⣡⠤⠴⠤⠀⠀⢈⣉⣙⠛⠿⣿⡓⠶⣤⡉⠻⢶⣄
⠀⠀⠀⠀⢸⠁⣸⠃⠀⠠⠋⠀⢠⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠋⠉⠉⠒⠈⠙⣦⡈⠙⠷⣄⠙⢷⡀
⠀⠀⠀⠀⣾⠀⣿⠀⢀⡶⠀⢠⠟⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠛⢦⡀⠈⢷⡈⢿⡄
⠀⠀⠀⠀⣿⢀⡇⢀⡞⠀⠀⢸⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⣷⠀⠈⢷⡘⣷
⠀⠀⠀⠀⡇⢸⡇⠸⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⡇⠀⢸⡇⣿
⠀⠀⠀⠀⡇⣸⠷⠶⠄⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⣧⠀⢸⡇⣿
⠀⠀⠀⢀⣿⠏⠀⠀⢰⠀⣴⠃⠀⠀⠀⢀⣀⣀⣀⣀⠤⠚⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⡟⠀⢸⡇⣿
⠀⢀⣴⠏⣿⠀⠀⠀⢸⠀⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣄⣀⡴⣣⠁⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠑⣦⣰⢈⣇⡀⢸⠇⣿
⢀⡾⠁⠀⣿⠀⠀⠀⢸⠀⢿⠀⠀⠀⢀⡤⠶⠶⠶⠶⠒⠋⠉⠙⣿⠀⠈⠁⠉⠁⠀⠀⠰⣤⣤⣾⢻⠁⣭⠟⢶⢤⣀⠘⡿⠈⡏⠙⢿⣠⡿
⣼⠇⠀⠀⣿⠀⠀⠀⢸⡇⣼⠀⠀⠀⠞⠁⠀⠀⠓⠒⠚⠯⠐⠁⠀⠀⠀⢢⡈⣆⠀⠀⢀⡴⠋⠉⠛⠓⠀⠰⠧⠴⠾⠃⡇⢰⠇⠀⢸⣿⣇
⣿⠀⠀⠀⣿⠀⠀⠀⢸⣇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠟⠀⢠⠋⠀⠈⠓⠶⠶⠶⠖⠀⠀⠀⠀⣧⡾⠀⠀⣾⠀⢻
⣿⡄⠀⠀⢸⡇⠀⠀⢸⡟⠃⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⣤⡖⠁⠀⠀⠐⠋⠀⠀⠀⠈⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⢸⡇⠀⠈
⢹⣇⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⡏⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡿⠀⠀⢀
⠈⢿⣆⠀⡀⣿⠀⠀⠀⣇⠀⢀⡞⠀⠀⠀⢀⡴⠋⠁⠀⠛⠂⠙⠛⠿⠀⠀⠀⠀⢀⣤⣴⣦⠄⣽⡄⠀⠀⠀⠀⠀⣼⠇⠀⠀⣾⠃⠀⠀⢸
⠀⠈⢻⣦⣡⢹⡆⠀⠀⣿⠀⡾⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠈⠁⠀⠀⠈⢹⡇⠀⠀⠀⡀⢸⡏⠀⠀⣼⠃⠀⠀⢀⣾
⠀⠀⠀⠙⠿⣷⣷⡀⠀⢻⣼⠇⠀⠀⠀⠁⠀⠀⣠⣴⣶⡖⠒⠶⣄⡀⢄⣀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣇⡟⠀⠀⣸⠏⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠈⠻⢶⣾⣿⠀⠀⠀⠀⢀⣠⠞⠉⠁⠀⠑⣺⡇⠈⠙⣦⣀⡉⠑⠒⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠃⠀⣰⣟⣀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣴⠋⠀⠀⢀⣴⠾⠛⠋⠓⠤⠄⠿⠈⢉⣽⣿⣶⡄⢀⢰⠇⠀⠀⠀⣾⣏⣀⣴⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⡞⠁⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠈⣿⣿⣌⡞⠀⠀⢀⣼⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠚⠿⠛⠋⡜⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⢀⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠞⠋
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣀⣀⣤⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⢷⣤⣀⠀⠀⠀⠀⣀⣠⡴⠋

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠛⠿⣿⠛⢿⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢈⠙⢿⣦⣀⣴⣾⣿⣿⣟⠛⠃
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣄⠀⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠆
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠙⠻⠿⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣑⡤⣤⣤⣦⣰⣆
⠀⠀⠀⠀⠐⠒⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠉⠉⠉⠉⠙⠋⠉
⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣟⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⢷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣴⢦⣶⣶⣴⣖⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠖⣿⣟⣿⣿⣿⣿⣿⡾⣾⣾⣷⣦⣶⣯⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠐⣾⣥⣴⠟⠛⠉⠙⠿⠿⠿⠿⠿⠷⠿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⡀⢾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠳⠄⠙⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⠟⡕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡝⢿⣿⣿⣯⣏⣉⠛⠛⠛⢛⣛⣿⣾⣿⣿⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠘⢿⣷⣽⣿⣿⣷⣶⣶⣿⣿⣿⠟⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢻⣿⣿⣻⢿⣻⡿⣿⠟⣡⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣩⣴⣏⠬⢫⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⡏⠉⡿⡃⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡓⠒⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠘⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⢀⣀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⡠⢼⣶⣿⣿⡟⣩⢋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠐⠀⡄⠀⠀⠀⠒⠂⠈⠉⠹⣷⠻⢿⣅⣀⠒⠺⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⣴⡀⠀⠀⠀⠄⠂⠈⢘⣿⡌⠉⠉⣀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⣾⠗⠂⠀⠀⣀⡌⣴⠫⠋⠀⠀⠀⠀⠈⠋⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⣡⡀⣀⡤⠚⣭⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠐⣿⠟⡯⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠄⠊⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠔⣠⠖⠀⠀⡠⠒⠒⠒⠦⡄⠀⠀⠀⠀⠺⣷⠉⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣎⠁⠀⢘⡇⠀⠀⠀⠤⣴⢶⣏⠁⢨⠲⠀⠀⠘⡃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠠⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⢹⣿⣿⡀⠀⠀⠀⠀⠀⡶⡄⠀⠒⠶⠖⠄⢒⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⡄⢠⡄⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⢠⣼⠗⠀⠀⠀⠀⠀⡀⠀⢀⣀⣠⠤⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡹⠋⡀⠀⠀⠀⠀⠀⠀⠈⠐⠏⠁⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢀⠀⠀⠀⠀⠀⠁⠠⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠰⠈⢻⣇⣰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠲⠔⠁⠀⠀⠀⠀⠀⠀⣴⢠⠊⠀⠀⡿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠻⠃⠀⠀⠀⠻⠁
⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⣿⣿⡿⠻⡿⠛⡿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣶⠀⡞⠒⠒⠀⠀⡆⠀⠀⠐⢲⠦⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠤⠤⣿⢰⣇⣀⡀⠀⢀⡇⠀⠀⠀⣼⠀⣈⡷⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⢸⣁⣀⣀⠀⢸⣃⣀⣀⠀⡟⠉⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠇⢀⣀⠀⠀⠉⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠤⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⡀⠀⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠦⠄⠀⠄⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠢⢅⠀⠀⢀⠇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠂⠢⣀⠀⠀⠑⠒⠂⠧⡀⠂⠇⠀⠂⡤⠀⠀⠁
⣀⣀⣀⣀⣄⣤⣠⣠⣤⣤⣠⣤⣄⣀⣤⣤⣤⣤⣤⣤⣥⣤⣭⣴⣦⣤⣤⣤⣤⣤⣤⣴⣤⣤⣭⣬⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⣿⣿⣋⢙⣋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⣀⣀⣤⠶⠶⠞⠛⠛⠛⠛⠛⠻⠷⠶⣶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣴⡏⠹⣷⡿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡠⠶⣄⣠⣶⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⣿
⠀⠀⠀⠀⢸⡿⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⢀⣀⠶⢦⣀⣠⡼⠛⢦⣴⠟⠁⠈⣉⣀⣠⣼⡏⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⠛⢶⡶⠉⠉⠙⠛⠁⠀⠀⠘⠋⠀⠀⢠⡇⠀⠀⠀⠀⠹⣿⣿⠇⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢀⣀⣰⣿⣋⣁⡠⠶⠶⢶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⣀⣀⣀⡀⠾⠋⠀⠀⠘⢿⡀
⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠈⠛⣿⣅⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢠
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠋⠑⠒⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡾
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠠⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣴⣦⣀⢠
⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⣍⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⢿⣤⡟⠃⠀⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠘⠛⠛⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠈⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡄⢀⣤⢶⣆⠀⣠⡀⠙⢷⣤⣄⠀⠀⠀⠀⠀⡖⠋⠙⠉⡀⠉⣷⡄⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠻⠿⠉⠻⠿⠟⠉⠙⠷⣦⣀⠀⠀⠘⡇⠀⠻⠟⢀⡘⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠶⣼⣧⣤⣠⣤⠞⠁⠀⢾⡋
⢀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣀⣀⣠⠾⢷⣄⣠⣴⣶⣶⣶⣤⣀⣀
⣿⣏⠉⠉⠙⠛⠻⠷⢾⡏⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⠾⠿⠷⢶⣷⣶⣶⣶⣿⣧⠀⠉⠉⠁⠀⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠷⣤⡀
⠀⠛⣷⡶⣴⡞⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⢈⣿⢿⣄⣠⣶⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠈⢿⣤⡿⢃⣽⠋⢿⡶⠶⠶⠶⠶⠶⢶⣶⣶⣦⣤⣤⣤⣀⣀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣼⠇⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣤⣼⠋⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⢂⡀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣈⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠓⠂⠀⠀⠠⠀⠀⠀⠀⠀⠒⠒⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠒⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣿⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⣿⠆⠘⠓⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠿⠟⠀⠸⠀⠀⠀⠿⠟⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⢻⣇
⢀⣀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⠀⣘⣿⠛⠛⠛⠛⠛⠛⠛⢻⣂⣤⣤⣤⣾⡟⠀⣀⠀⠀⣀⠀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠅⠀⠨⠁⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⠛⠛⠉⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠛⠻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣠⣀⣀⠀⠀⠀⠀⠀⠈⣥⣶⣳⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣉⡉⠭⠅⡄⠀⠀⣆⠀⠈⠉⠉⠻⢿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠘⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⣰⠄⠀⠀⢀⠀⠀⠀⠀⣀⣼⣿⡇⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⢀⣉⣀⠀⠀⢈⣉⠀⠀⠀⣽⣿⣿⣧⠀⠀⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠛⢿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠀⠹⣿⣶⣤⣤⣴⣶⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⢀⢻⣿⠦⠉⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠏⠁⠀⢀⣴⣿⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁


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

⠀⠀⠀⠄⢠⣶⣤⡀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠠⠊⢀⣀⠀⢀⣀⣀
⠀⢉⠀⠀⢀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠆⣠⡄⠐⠲⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠐⠀⠀⠂⣠⡀⢄⠁⢨⠈⢉⠐
⠀⠱⣶⣶⡞⠁⠹⠛⠀⡀⠀⠀⠀⠀⣤⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠟⠂⠀⠀⠀⠀⠸⣿⣆⠀⠀⡼⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢻⣾⢾⠿⠽⠗⡺⠋
⠀⠀⠈⠑⠐⠂⠁⠀⠀⠀⠀⠠⠀⠀⠈⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠚⠁⠀⢀⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠈⢈⠀⢀⠤⠂
⠀⠐⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡠⣤⣤⡀⠙⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣶⠀⡀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢈⡌⢿⡀⢤⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠋
⢤⠀⠀⠀⠀⠐⠀⣀⠀⠀⠀⠀⠈⠋⠀⠲⠀⠀⠀⠀⠀⢠⣶⠞⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⠴⠞⠈⠁⠀⠹⠟⠛⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⣀⣀
⠈⠋⠀⠀⠀⠀⠀⠙⠋⠻⠖⠀⠀⠀⢰⣦⣦⢾⡆⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⢛⡁⠀⠀⢨⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⠊⠁⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠗⠀⣠⠿⠟⣠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠻⡁⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⡄⠏⠀⠙⣷⡼⠁⠀⠈
⠀⣴⠤⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠆⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠈⠀⠀⠀⠀⣹⠇⠀⣀⢀
⠀⢙⣯⣤⣐⣥⠁⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠀⢈⠀⠀⠀⠀⡼⠛⠛⠧⠀⠀⠀⠀⠀⠀⠐⠢⣴⣶⠊⠀⠀⠀⠀⠀⠀⠀⠔⠃⠀⠀⠙⠋
⠀⠀⠙⠓⠈⠒⠄⠀⠀⠀⠀⠐⣲⣄⡀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣅⡀⢠⡆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⣈⣉⠉⠁
⢀⠐⠆⠀⠀⠀⠀⠀⠀⠤⣄⣾⣿⣿⡟⠀⠀⣀⠀⠀⢄⡀⠀⠈⠉⠁⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠍⠂⠀⠋⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢀⣤
⠏⠀⡀⠀⠠⠄⠀⠀⠀⣀⣒⠋⠙⣻⠦⠄⠈⠂⠀⠀⣀⣁⠀⠀⣆⣶⣶⣦⣤⣤⣠⣄⣸⣦⢀⢀⡀⠀⠀⠗⢲⠓⠞⠳⠚⣧⠀⠀⠆⠀⠀⠀⠀⠉⠀⢻⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⣠⠀⠀⠀⠀⠀⠀⡇⢘⠀⠐⣷⣿⣿⣿⣿⣿⣿⡿⣿⡿⣼⣿⠇⠀⠐⠇⡎⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣿⣿⣟⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠉⠈⠉⠙⣿⣯⣼⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢀⣾⣿⣿⣷⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣾⣿⣿⣿⣭⡼⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣭⣭⣍⣀⠾⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣾⣿⣿⣿⣷⣶⣮⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⣛⡉⢙⣛⣛⡛⠛⢭⣭⣬⣿⣿⣿⣿⡿⠟⢿⣿⣟⣿⡿⠿⢷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣺⣽⣶⣿⣿⣿⣿⣿⣿⣿⣤⣶⣶⣌⣉⣿⣿⣉⣡⣶⣶⣄⣿⣿⣿⣿⣿⣿⣶⣾⣭⣓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⠟⠿⠾⢻⣿⠏⢹⣿⡿⠳⠿⠿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⡆⠀⠻⣄⡀⠀⣸⣛⠁⠈⣛⣇⠀⢀⣠⡟⠀⢸⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣭⡄⠀⠈⠿⠛⠁⠀⠈⠳⠖⠁⠀⠈⠛⣿⡁⠀⢠⣽⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡎⠀⢀⡇⢀⣴⠞⠛⠿⠿⠛⠳⣤⡀⢸⡀⠀⢰⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢖⣿⣿⣿⣿⢠⠀⠀⡇⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⢸⠃⠀⡄⣿⣿⣿⣿⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⡽⣿⣿⣿⣿⣎⠀⢀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⡀⠀⢸⣿⣿⣿⣿⣟⣾⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠨⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢆⠀⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣻⣿⣿⣧⢳⠀⡀⠀⠀⠀⠀⡘⠁⠀⠀⢀⠀⡾⣼⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣻⣿⣮⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⣷⣿⣿⣿⡏⠲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⢿⣿⡄⠀⡄⠘⠄⠀⠀⢀⢿⣿⢿⣿⠎⠀⠀⣀⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣿⠟⠻⣆⢘⣆⢀⡎⢠⡟⠻⣿⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢹⠏⠡⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠒⠛⠛⠛⠛⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠶⠿⠯⣥⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⢀⣀⢠⠋⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣀⠠⣌⣳⣌⢻⣀⡀⢷⡸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣠⠴⠾⠃⠀⠉⠉⠣⠄⠱⣄⡙⠲⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢀⣯⡴⠋⡄⡠⠖⠉⠠⠒⠈⠉⠁⠀⡠⠬⠓⣀⠠⠄⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢠⡇⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠸⠋⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢠⡞⠀⡾⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⢻⡆
⠀⠀⠀⠀⢀⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⣸⠁⠀⣴⠁⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⡄⠀⡇⠀⠀⠀⠉⠈⠉⠉⠀⠀⠀⢀⠠⣄⣠⣾⡇⠀⠀⠀⠀⢀⣠⣀⠀⠀⠐⢦⣸⣿⡄⠀⠀⠀⢰⠇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⢀⡴⠒⠒⠚⠛⡉⠉⠻⠇⠀⠀⠉⠀⠀⠐⠦⣶⣏⡅⠼⠛⡶⢤⡈⡇⢸⡇⠀⢰⢇⣿⡄⠀⠀⠀⠀⣿
⠀⢀⣠⣤⣿⡀⠀⡏⠀⠀⠈⠀⠀⠈⠉⠉⠁⠁⠀⠀⠀⢰⣸⡆⠀⡠⠊⢀⣈⠉⠀⠘⠙⠛⠁⡇⣼⠀⣠⣿⢿⡀⢷⡀⠀⠀⠀⢻⡇
⡼⠋⣀⣀⠉⠙⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢀⠜⠀⠁⠀⠁⠀⠀⠈⠉⠉⠀⠀⠀⢀⣿⠷⠿⠿⢯⡈⢷⡈⣧⠀⠀⠀⢸⡇
⠇⠋⠉⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⢁⣴⠶⠶⡄⢹⠈⣧⠸⡄⠀⠀⢸⡇
⠀⡄⠀⠀⠙⡇⠀⠀⣠⠂⠀⠀⢀⡾⠋⠀⠳⠈⠛⠳⠀⠀⠀⠀⣠⣤⣤⢀⡇⠀⠀⠀⠀⠀⠀⢸⠓⠀⠀⠠⠋⠀⢸⡆⠀⠀⠀⢸⡇
⠀⠙⢦⡄⠀⣿⣇⢠⡏⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠂⠁⠀⠀⠈⡇⠀⠀⠀⠀⡆⠠⠞⠀⠔⠊⠀⠀⠀⠀⣧⠀⠀⠀⢸⡇
⠀⠀⠀⢹⡀⠁⢸⣾⠀⠀⠀⠀⠀⣠⡶⠿⣏⢙⠳⣄⠠⠤⣀⡀⠀⠀⠀⢀⡇⠀⠀⢠⣼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠻⠦⠾⣿⠀⠀⢀⡴⠊⠀⠀⣀⣤⠿⣀⠀⣿⠒⠤⣤⣀⠀⠀⢸⠁⠀⠀⣼⡿⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢹⡄⣠⠏⠀⠀⠴⠋⠁⠀⠀⠀⠁⠀⠀⠚⠙⢿⣷⢀⡏⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠲⠿⠋⡞⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠚⣧⡀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⠤⠴⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠈⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⢀⣟⣼

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⡿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣾⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣷⣶⣶⣷⣾⣷⣿⣶⣦⣂⣀⡀
⠀⠀⢀⣐⣾⣿⣿⣿⣿⠿⠛⠿⠟⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠿⠋⠁⠈⠉⠉⠉⠉⠛⠛⠻⠛⠟⠂
⠀⠀⠀⠙⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠪
⠀⠀⠀⠀⠀⠀⠀⠜⠫⠓⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠒⠛⠋⠉⠉⠉⣿⠋⠉⠉⠛⠿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠛⠛⠛⠒⠲⠶⠶⠾⢿⣷⣿⣷⣄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠉⠀⠀⠀⣀⣀⣀⡀⠀⠀⠘⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⣼⡿⠟⠛⠛⢷⣄⠀⠘⠿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⣠⠞⠉⣀⣠⣤⣤⣤⣽⣧⡀⠐⣌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⡾⣫⠴⠛⠉⠀⠀⠀⢸⣿⠉⠳⣄⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⣠⠤⠴⠶⢦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣤⣤⣿⣆⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣠⠞⠉⠀⣀⡤⠴⢶⡞⠛⣿⣦⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠘⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡏⣠⠖⠋⠁⠀⠀⠸⣧⣀⣘⣧⣾⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡇⠀⠘⡿⣦
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⢡⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡓⠒⠒⠒⠒⠛⠛⠉⢉⣼⠃⠀⠀⢹⡘⣧
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠶⠾⠛⠁⠀⠀⠀⠀⢳⢸⡆
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠈⣧⠀⠀⢀⣀⣠⠤⠖⠋⡠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣧
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠘⢿⣍⡉⠀⠀⣀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿
⠀⠀⠀⠀⠀⠀⡆⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡄⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣧⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠘⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⢇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⣼⡏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠉⠉⠉⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⢀⣤⣾⡏⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢶⣤⡀⠈⠛⢿⣦⣀⣀⣀⣀⣀⣤⣴⡾⠟⠁⠀⠀⢀⣠⣶⠿⠛⠉⢿⣆⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠀⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠙⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠻⡿⣿⣿⣿⣿⡿⠿⠛⠛⠁⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡋⠀⢀⡴⠋⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡏⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢿⣿⢻⠏⠳⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠣⠀⠁⠀⠀⠀⢆⢧⢷⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢰⡠⡀⢼⡼⣿⣟⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠈⢧⠸⣇⣷⢸⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠺⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⢷⡀⠘⣿⣿⣿⣏⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣆⡀⢰⡀⣰⣂⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣯⣁⣿⣬⣴⣧⣄⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠛⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠀⠀⠀⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⢀⡄⣀⡶⣿⣿⣏⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⢋⡼⢋⣶⣿⣧⡙⢷⣝⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢡⡟⣴⢏⣴⣿⣟⠻⣦⠉⣷⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡜⠁⡠⠋⡼⢡⣾⣏⣿⣿⣷⣄⠷⣎⠻⣿⣿⣿⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⠀⠀⠸⢁⣿⣿⡿⣿⣿⣿⣿⣆⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡀⢠⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠁⠀⢠⣴⣿⣿⣟⣻⣿⣿⣿⣿⣿⡌⠛⠹⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⠀⠀⣼⣿⣿⣿⣿⣿⣭⣿⣿⣽⣿⣿⣦⠀⠈⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠟⠀⠀⣠⣾⣿⣿⣿⡟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣤⣤⣯⣉⠢⣤⣤⣀⣤⡔⣩⣴⣷⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣤⣾⣿⠋⣉⢭⣭⡍⡉⠉⣿⣿⣿⢉⡤⣶⣶⠂⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠤⠬⡙⠛⢿⣿⣿⣀⠀⣈⣛⣁⣈⣀⣿⣿⣿⣅⣀⣈⣡⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠠⠒⢚⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠿⠿⠿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⠀⢀⢤⡀⢀⡠⢄⠀⡠⠤⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡀⠀⠀⠀⠀⠐⠁⠀⠈⠋⠀⠀⠉⠀⠀⠈⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢿⣿⣿⣿⣶⣶⣶⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⣀⣀⣀⣀⣀⡠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣄⣴⠋⠉⠀⠀⠀⠀⠀⠉⠉⠙⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⡛⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⡎⠀⠀⠀⣠⠂⠀⠀⢠⠂⠀⢀⠀⠀⡀⠀⠀⡆⠀⡄⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣼⠀⠀⠀⢠⠃⠀⠀⢠⠏⠀⠀⡎⠀⠀⡇⠀⠀⡇⠀⣷⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣇⠀⠀⢠⡏⠀⠀⢠⠏⠀⠀⡼⠀⠀⢸⠁⠀⢰⠁⠀⡇⢳⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡎⢿⣀⠔⠹⡇⢀⡴⢻⠀⢀⡴⠁⠀⣠⠏⠀⢀⡞⠤⠞⠀⢸⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⡤⢤⡀⢸⠀⠀⠀⢀⠉⠉⠀⠈⠉⠉⠐⠶⠖⠉⠦⠤⠊⠀⡀⠀⠀⠘⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢧⣐⡌⠚⠁⠀⠀⠀⠨⠕⣶⠆⠀⡀⣀⣀⣀⣀⠀⠲⣾⠭⠤⠄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠈⠙⣄⠀⠀⠀⠀⠐⠉⠀⠀⠈⠉⠁⠉⠉⠉⠁⠀⠈⠑⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⠀⠀⡈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⢿⣄⣴⣧⣀⣤⣈⡑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣻⠶⠶⣏⠳⣄⠀⢒⡶⠲⣟⣫⣭⠦⠾⠦⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⢢⡴⠛⢧⡤⠖⠉⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣠⢼⡀⠀⠀⠀⠀⠀⣸⢄⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⢆⣀⠇⠀⠀⠀⠀⠀⢇⣀⠟⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠀⠈⠉⠉⠁⠉⠙⡇⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⢀⡟⠀⠀⠀⠀⠀⠀⠀⣇⢠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⡛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠲⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠒⠂⠀⠤⠤⠄⠀⠀⠀⠄⠒⠒⠒⠢⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⠀⠀⠠⠤⠐⠒⠒⠒⠦⠀⠀⠤⠐⠒⠒⠢⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢢⡈⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠊⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⠤⠤⠴⠖⠒⠦⢄⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⣭⣽⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⠤⣤⠄⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠛⢛⣛⣒⡒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠯⠥⢽⣀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠉⠁⠀⠈⠁⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠒⠂⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⡰⠋⡉⠁⠈⠧⠤⠀⠒⠂⠀⠠⣤⠏⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡘⢦⡀⠀⠀⠀⠀⠀⠁⠾⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠦⠤⠤⣤⣀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⠀⠀⠀⠉⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠶⠶⠶⣶⠦⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠹⣄⣀⡀
⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⠒⠦
⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢀⠀⠀⢀⠤⠤

⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⢀⠊⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠈⠑⡀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢀⠊⣀⠀⠀⣀⠑⡀
⠀⠀⠀⢀⠀⠘⠀⠀⠃⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢈⠀⠘⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⢈⠉⡁⢈⠉⡁
⠀⠀⠀⠈⢄⡀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠈⢄⠀⠠⠄⠀⡠⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⢀⠊⠀⠀⠠⠀⠑⡀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢀⠊⢀⠠⠄⡀⠑⡀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠑⡀
⠀⠀⠀⢈⠀⠘⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠃⠀⠁⠀⠀⠀⠀⠈⠀⢠⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠈⡠⢄⠁⠀⡁
⠀⠀⠀⠈⢄⡀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠈⢄⠈⠀⠀⠁⡠⠁⠀⠀⠀⠀⠈⢄⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠈⢄⠀⠂⠐⢀⡠⠁
⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⢀⠊⡁⠀⠀⢀⠑⡀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢀⠊⠀⠀⢀⠀⡑⡀⠀⠀⠀⠀⢀⠊⡀⠀⠀⠀⠑⡀
⠀⠀⠀⢈⠤⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠂⡀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠂⠀⠁
⠀⠀⠀⠘⢤⠃⠊⠁⠀⡠⠁⠀⠀⠀⠀⠈⢄⠀⢋⡹⠀⡠⠁⠀⠀⠀⠀⠈⢄⠈⢏⡩⠀⡠⠁⠀⠀⠀⠀⠈⢄⠀⢏⡹⠀⡠⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁

⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⢀⠊⠠⠀⠀⠄⠑⡀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢀⠎⡀⠀⠀⢀⠑⡀⠀⠀⠀⠀⢀⢊⠀⠀⠀⠀⡑⡀
⠀⠀⠀⢀⠀⢀⠥⠬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠆⠀⡁⠀⠀⠀⠀⢈⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠂⠀⠁
⠀⠀⠀⠈⢄⠓⠂⠀⠚⡠⠁⠀⠀⠀⠀⠈⢄⠐⠑⠊⠂⡠⠁⠀⠀⠀⠀⠈⢄⠀⠁⠈⠀⡠⠁⠀⠀⠀⠀⠈⢄⠀⠈⠁⠀⡠⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠉⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣄⡀⠀⠀⠉⠛⠿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⠀⠀⠀⠉⠙⠛⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁






⡿⠿⠿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣟⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠂⠄⡌⠀⠀⠀⠀⠀⠀⠁⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⣆⡀⢘⡄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡸⡹⠉⣧⠀⠀⠀⠀⠀⠀⠀⠸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠁⠀⢿⠁⠀⠸⠀⠀⠐⠤⡀⠀⢠⢄⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⠀⠈⠒⠊⠸⠉⠑⠢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢃⠘⠁⡄⠠⣄⢰⡀⣆⠔⠂⢄⠀⠀⠄⠴⢤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⡘⠛⣀⠈⠦⠈⢁⠤⠤⠈⡄⠀⠀⠀⡀⠹⠃⡀⠀⠀⠀⠀⢀⠂⠁⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡁⠀⠀⠠⡀⠚⠂⠀⡄⠈⡀⠠⠀⠀⠐⠀⠀⠀⠀⢀⡄⢠⠀⢀⠋⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠙⣀⠸⢄⡀⠀⠁⠢⠀⠊⠈⠀⠐⡀⡇⠀⠀⠀⠀⠀⢰⠁⠠⣀⠑⢢⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠢⢠⡁⡀⠀⡃⠀⠀⠀⠀⢀⣀⢈⡀⠈⠀⠀⠀⠀⠀⠀⠀⠑⢢⢀⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠌⠀⡁⠸⡀⠀⠀⠀⠀⠀⡠⢃⠈⠀⠀⠀⡄⡀⠀⠀⠀⠀⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠈⠢⣀⣀⢠⠩⠕⠀⠙⢢⣄⢠⣰⢶⣶⣀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠤⢴⡀⠀⠈⠲⠓⢌⠺⠁⠀⢛⠛⠠⢄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⡀⠀⠀⡠⠏⠻⡿⢿⣾⣧⣴⣷⣼⣷⡿⠄⡀⠀⠀⢀⠠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠑⠠⣷⣤⡀⡀⢠⠠⣈⡁⢀⣉⣤⣤⣤⠴⠦⠀⠁⠀⠀⠀⠀⠀⢀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠠⢤⠔⠁⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⣉⠐⠲⠤⣼⡆⠀⠀⠀⠐⡁⠉⠉⠁⠀⠀⠈⠉⠉⠉⠀⠀⠈⡗⠀⠀⢀⡠⢖⠡⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠈⠛⠲⠦⣄⣀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣱⡤⠖⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠦⠥⠴⠒⠚⠚⠛⠒⠀⠉⠛⠀⠉⠃⠉⠛⠂⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣖⠠⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣛⡿⠅⠀⠀⠀⠀⠀⣈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢴⣷⣤⡤⠄⠀⠰⠀⢠⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠧⡴⠀⠀⠀⠠⣠⠈⣀⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⡶⠛⠁⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠄⠚⠒⠂⢄⡰⢫⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⡼⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢃⠀⠀⠀⠠⢄⡇⠈⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠒⠒⠲⠞⠛⣦⣤⠴⣚⠉⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠀⠀⠀⠀⠙⠫⣈⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡞⢉⢑⠦⣤⣜⣠⡤⡄⠐⠤⣄⣰⠀⠀⢀⣌⡗⠀⠈⢧⠀⢠⠔⣫⡍⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⠒⡏⠁⠈⠛⢑⣞⣢⣀⠀⠉⠉⣉⣩⠑⢒⣏⣧⢀⠓⡃⠚⠉⢁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢈⣤⠼⠯⢍⡉⠁⠛⠃⠤⠀⠁⠈⠯⣁⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡈⡉⠑⠒⠂⠀⠰⡀⠀⢸⠁⠀⠀⠀⠀⠈⠲⠄⢀⠃⠀⠀⢀⣔⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⠉⠉⠓⠒⠂⠐⠲⠦⠷⠀⠘⣦⣀⣀⣀⣀⣀⡠⠤⣾⠀⠀⡠⠋⠀⠀⣠⡔⣉⡳⠶⠖⠋⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⢻⣹⣋⡩⣭⠽⠍⠉⠉⠀⠚⠁⠳⣄⠀⣠⠚⠓⢦⡏⣀⣰⣟⣫⠭⣭⢭⡥⠤⠤⠤⠤⠤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡰⠇⠀⡀⠀⠀⠀⠀⠀⠀⢨⣿⡿⠀⠀⠀⠉⠀⠀⠀⠑⡖⠾⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⢄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠓⠲⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⠉⠙⠓⢲⠖⠶⠶⠒⠒⠒⠚⠛⠉⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⢸⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⣀⣀⡀⣼⠀⡇⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠐⠛⣿⡻⠿⣒⠒⠂⢀⣀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣾⣶⣤⣤⣄⣦⣤⣭⣥⣿⣴⣦⣦⡁⠀⠀⢈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠻⠿⠧⠽⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠠⠤⠀⠄⠀⢠⠠⠠⠀⠀⠠⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠆⠀⠄⠄⠆⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡞⠁⢸⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣹⣆⡙⣇⢀⠸⣆⢳⣘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠓⠀⠈⠉⠑⠤⠘⢦⣈⠓⠊⠙⠳⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⣠⠔⠋⠡⠐⠊⠉⠉⠀⢀⡬⠝⢂⣠⠤⠄⠈⠉⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠠⠋⠀⣰⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠛⠛⠋⠉⠑⠂⠙⢷⡀
⠀⠀⠀⠀⠀⢀⡞⠀⢰⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⢦⡀
⠀⠀⠀⠀⠀⡾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⣧
⠀⠀⠀⠀⠀⡥⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢹⡄
⠀⠀⠀⠀⢰⠃⠀⣠⠃⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢸⠇
⠀⠀⠀⠀⣿⡆⠀⡏⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢀⡀⣀⣀⣠⣧⠂⠀⠀⠀⠀⢀⣄⡀⠀⠀⠐⣄⡀⢸
⠀⠀⠀⠀⣹⠁⠀⢿⠀⠀⠀⡤⠖⠒⠒⠒⠊⠉⠙⠿⠀⠉⠈⠁⠀⠀⠢⢤⣶⣫⣿⣿⠗⠦⢄⠘⡇⢸
⠀⢀⣀⣀⣹⡀⠀⡼⠀⠀⠘⠁⠀⠈⠉⠉⠙⠈⠁⠀⠀⠀⣆⢳⠀⠀⡴⠋⣀⠉⠉⠛⠛⠒⠚⠃⡇⣼
⡴⠋⢉⡉⠉⠙⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⢠⠏⠈⠀⠸⠀⠀⠈⠉⠉⠉⠁⠀⠀⢠⣿⠷⠶⠶⣤
⠇⠚⠉⠙⢳⡄⠃⠀⠀⠀⠀⠁⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠈⢁⣤⠴⢤⡀
⠀⡄⠀⠈⠙⣇⢠⠀⢀⠄⠀⠀⠀⣠⠞⠁⠸⠆⠛⠻⠦⠀⠀⠀⠀⣠⣤⡄⢸⡇⠀⠀⠀⠀⡀⠀⢾⠓⠀⠀⢀
⠀⠙⣦⡄⠀⢹⢸⢀⡞⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠈⠁⠀⠀⢹⡇⠀⠀⠀⢠⠇⣠⠞⢀⠤⠂⠁
⠀⠀⠀⢹⡄⠉⢸⣼⠃⠀⠀⠀⠀⢀⣴⡶⢿⠙⡳⢤⡀⢤⣀⡀⠀⠀⠀⠀⢸⠇⠀⠀⢸⣼⠀⢀
⠀⠀⠀⠀⠳⢤⡬⣿⠀⠀⠀⣠⠔⠋⠀⢀⣈⣽⣇⠀⢹⡶⠤⢈⣉⡀⠀⠀⣼⠀⠀⠀⣿⠷⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡾⠁⠀⢠⠞⠋⠉⠀⠈⠉⠀⠁⠠⠚⠻⣿⡆⢠⠇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡞⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⣶⠿⢋⠏⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠴⣿⡁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣤⣤⠴⠞⠉

⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣦⡀
⢠⡾⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠻⢿⣆
⠋⠀⢀⣀⣠⣴⣦⣶⣾⣿⣿⣟⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⢟⣯⣟⣷⣶⣆⣤⡀⠀⠀⠀⠙
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣥⣀
⠀⠈⠻⣿⣿⣿⣟⣋⣉⣉⣉⡙⣻⣟⠆⠹⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⡍⠰⣿⠟⠋⠁⠈⠈⠉⠁⠙⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠙⠃⠀⠁⠁⠀⠀⠀⠀⠀⠘⠣⠏⠀⠾⠿⣤⣤⣄⣀⣀⣀⣤⣤⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠄⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠂⠀⠀⠬⣷⣿⣿⣿⣡⢋⠠⠀⢀
⠀⠀⠀⠀⠀⠀⢰⠞⠋⠡⠀⠀⠀⠐⠂⠉⠁⠸⣿⡛⢿⣅⣄⠒⠾⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢠⣦⠀⠀⠠⠀⢀⡨⢸⣽⡄⠉⠡⠄⣀⡀⢀
⠀⠀⠀⠀⠀⢀⣠⠊⠀⠀⣸⠟⠂⠀⣀⣴⠝⣵⠩⠃⠀⠀⠀⠀⠀⠙⣤⡀
⠀⠀⠀⠀⢀⢞⠁⠀⠀⠀⢀⣄⣠⡾⢋⣵⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡆
⠀⠀⠀⠀⢠⡴⠀⠀⡀⠀⢸⡟⡼⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟
⠀⠀⠀⠀⢸⠃⠀⢈⠀⠀⠰⡠⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⣀
⠀⠀⠀⠀⢰⠃⣀⠤⠐⣡⠏⠁⠀⠐⠉⢉⣉⡉⠢⡀⠀⠀⢠⡝⠷⠠⠃
⠀⠀⠀⠀⠀⠻⠤⣠⣡⡼⠀⠀⠀⠀⠛⠛⠿⠀⠐⠉⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠇
⠀⠀⠀⠀⠠⠄⠚⣶⣱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣄⡀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⣾⡟⣿⣿⡄⠀⠀⠀⠀⠀⣠⠀⣀⣀⣀⣀⣈⠩⠄⠀⡀
⠀⠀⠀⠀⠀⠂⠸⠀⠉⠹⣷⡀⠀⠀⠀⠀⠉⠑⠒⠀⢀⠀⠀⠈⠀⡈
⠀⠀⠀⠀⠀⠀⠠⡤⠀⢀⠈⠇⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢺⡀⠛⣀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢨⡁⠐⡿⠁⠄⠀⠀⠀⠀⠁⠀⠴⡟⠉⠤⠠⠤⠀⠤⠀⠶⠤⠖⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠙⠺⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠈⠂
⠀⠀⠀⡠⠂⠀⠠⠀⠀⠀⠀⠈⠂
⠀⠠⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠰⠀⠛⣏⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠊⠀⠀⠀⠀⠀⠀⢠⣀⠆⠀⠀⣿⡻⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⡯⢿⠇⠘⠛⠟⠀⠛⠄⠀⠉⠫⠈⣿⠛⠃⠻⠋⠉⠉⠻⢿⣿⠏⣿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠸⠻⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠻⠿⣿⣿⣷⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠛⠙⠛⠛⠿⢿⣿⣿⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⢸⡇
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⢿⣿⣿⣿⣶⡦⠀⠀⠈⠗
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢉⣿⣿⠃⠀⠀⠀⢞
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣶⠿⠛⠉⠉⠉⠉⠉⠻⣦⣀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⠀⠀⣀⠀⣼⣿⡏⠀⠀⠀⠀⠀⡠
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢤⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⣿⣿⣿⣿⠀⠀⠀⠀⢠⣶⣤
⣿⣿⣿⣿⣿⣿⡇⢀⡀⣰⣾⣿⡟⠀⣆⣤⠄⢀⠄⠀⠀⣠⡠⡀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢌⢋⣯
⣿⣿⣿⣿⣿⣿⡏⢸⠁⣿⣿⣿⠇⠀⡁⠀⠀⡿⠃⠀⠀⠀⠈⢁⠀⢸⣿⡏⣿⣿⣿⠀⠀⠀⠀⢠⣟⣿⣿
⣿⣿⣿⣿⣿⣿⡇⣼⢠⣿⣿⣿⠀⢸⠃⠀⡀⠟⠈⠀⠀⢀⠀⠘⣃⣸⢻⣿⣿⣿⡇⠰⠿⣶⠄⠀⠀⠉⠉
⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠟⣁⠟⣠⠎⣠⠴⠦⢄⠀⠈⣦⠀⢁⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡐⢁⣔⠀⣼⠋⠉⠁⠀⠀⣦⡈⠂⠘⠂⠘⢿⣿⠟⠀⠀⠀⠀⠀⠀⡄⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⠁⣼⠿⣀⠀⠀⠀⠀⢨⡄⢸⠀⠀⢀⣾⣿⡄⠀⠀⠀⡀⢐⢒⠀⣼⣿
⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⡀⠀⠀⢿⣷⡘⠿⠁⣼⣷⣿⡇⠀⠀⠀⣾⣿⣿⢿⡀⣧⣿⣤⣾⣽⣦⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿⡇⠈⠄⢸⣿⡿⠁⠀⠀⢠⣿⣿⣿⠿⣿⣾⣿⣿⡿⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⣿⠀⠀⢹⣿⠃⠀⠀⣷⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣯⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣾⣿⣷⣶⣾⡟⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡶⠶⠶⠶⠶⠛⠛⠛⠛⠿⠿⠟⢛⡛⠛⠛⠛⠛⠛⠳⢶⣄
⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠩⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⡑⠢⢄⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⢀⠄⠂⠀⠐⠒⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠈⠐⠂⢍⡢⢄⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⠈⠀⠁⠀⠀⠀⠀⠹⣦
⠀⠀⢀⣴⠟⡁⠤⠤⠤⠄⠾⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⢠⣾⢋⣁⣤⣿⠿⠿⢿⣽⣷⠀⠠⠄⠀⠀⠀⠤⠿⠷⣤⡀
⠀⠀⣸⡇⠊⠔⣠⣤⣤⣄⠀⠀⠀⠀⠀⠉⢻⡏⠁⠀⠀⠀⠙⠛⠉⠀⠀⠘⢶⣤⣀⣀⣠⣴⠶⠛⡛⠛⢷⣄⠈⠊⢷⡄
⠀⠀⢿⡇⠠⠀⠉⠀⣄⠙⠿⠛⠃⠀⢀⣴⠿⠁⠀⠀⠀⠀⣀⣀⡀⡀⠀⠀⠀⠈⠉⠉⠁⣀⣤⡾⣷⣀⠀⢹⡆⠀⠈⡷
⠀⠀⠸⣿⠢⣁⠀⣼⣿⡀⠀⢀⠠⠾⠿⣧⠀⠀⠀⠀⣤⣤⣤⢈⡿⠈⠉⢉⣀⣠⣴⣶⠟⠋⠁⣠⡿⠋⠉⣼⠃⡀⢰⡏
⠀⠀⠀⠹⣧⠀⠀⣿⡿⢻⣶⣤⣀⣀⠀⠈⠻⠶⠃⢀⣀⣀⣠⣬⣵⣶⠟⠛⠉⠁⣠⣿⣤⡴⢾⡿⠃⠀⠀⠀⣊⣴⠟
⠀⠀⠀⠀⣿⠀⠀⣿⣧⣿⡀⢸⡟⠉⠛⢻⡿⠛⠛⢻⡟⠉⠁⠀⠀⣿⣤⣴⣶⡿⠿⣿⠉⣴⠟⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣶⣾⣷⣶⣾⣿⠿⢿⡟⠉⠁⠀⢀⣿⡾⠃⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⣿⠀⠀⢻⣿⣿⢻⣟⠻⣿⠿⠿⣿⠟⠛⠛⢻⡏⠁⠀⠀⠀⢿⣄⣠⡴⠟⠁⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⣿⠀⠀⠀⠙⠷⣦⣿⣤⣹⣧⣀⣸⣇⣀⣀⣸⣧⣠⣤⣤⠶⠞⠛⠉⡀⠄⢂⠠⢐⣠⡶⠛⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢄⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⡀⠄⠐⠈⠅⠐⣈⣤⡶⠟⠉
⠀⠀⠀⠀⣏⠀⠀⠒⢄⡀⠈⠁⠀⠀⠀⠐⠒⠀⠀⠀⠠⠀⠀⠀⠀⢀⣠⣴⠶⠛⠉⠁
⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠈⠛⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠶⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⢀⠀⠀⢸⣇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣿⠀⠀⠀⣴⡇
⠀⠀⠈⣦⡀⠘⠟⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⠀⠀⢸⣿⠀⢠⠀⠀⠀⠀⠀⠀⣇⡘⠃⠀⠀⢸⡟
⠀⠀⠀⠹⣟⡦⣄⡀⠀⢘⡡⠂⠀⠀⠀⠀⠀⠀⢱⡙⠁⠀⠀⢸⡟⢀⡞⠀⠀⠀⠀⠀⠀⢹⣹⢶⡠⣄⡈
⠀⠀⠀⠀⠸⣗⣧⣯⣏⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⣤⠤⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣷⠾⠏
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⣤
⠀⠀⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⢠⣶⡲⡄⠀⡄
⠀⠀⠀⠐⡀⠸⣿⠁⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠈⣡⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⣧⣹⡇⢰⠁
⠀⠀⠀⠀⣧⣀⠀⠀⠀⢿⢏⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠀⠈⠻⠟⠁⡜
⠀⠀⠀⠀⠉⠲⡗⢦⢤⡴⠉⠀⠀⠀⠀⠀⠀⠀⠠⣤⣴⣾⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠤⡤⠦⣄⡠⠊
⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠉⠉⠑⠦⡀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠉⠓⢦⡀
⠀⠀⠀⠀⢀⡴⠛⠉⠀⢈⡇⠀⠀⠀⢀⠎⠀⠀⣠⠴⠒⢦⠀⠀⠘⣆⠀⠀⠀⢠⠏⠀⠀⣠⠴⠒⢦⠀⠀⠙⡄⠀⠀⠀⢠⠋⠀⠀⣠⠴⠒⢦⠀⠀⠹⡄
⠀⠀⠀⠀⢺⠀⣠⢞⣻⢿⠁⠀⠀⠀⢸⠀⠀⠸⢁⣴⣲⣮⠀⠀⠀⢹⠀⠀⠀⣼⠀⠀⠸⢁⣴⡲⡏⠀⠀⠀⢹⠀⠀⠀⡞⠀⠀⠸⢁⣔⡲⡏⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠉⢩⣷⣿⠄⠀⠀⠀⠸⡀⠀⠀⠀⠉⢿⡗⠀⠀⠀⡾⠀⠀⠀⢸⡀⠀⠀⠀⠹⢿⡗⠀⠀⠀⡞⠀⠀⠀⢹⡀⠀⠀⠀⠹⢿⡇⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠄⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠉⠀⢀⠜⠁⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠁⠀⣠⠞⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠁⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠒⠶⠶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⢠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠶⠶⠖⠋⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠛⠛⠓⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀⠀⡴⠁⠀⠀⣠⠤⢤⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⠀⠀⡀⠀⠀⠀⢀⡞⠁⠀⣀⣀⣠⣤⡀⠈⠳⡀
⠀⠀⠀⠀⠀⢠⠞⢁⣀⡽⠀⠀⡜⠀⢸⠁⠀⢠⡎⣠⢤⣼⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⣷⣾⣻⣷⣾⠀⢀⠇⠀⠀⠀⢸⠀⠀⢸⣷⣾⣻⣷⣾⠀⠀⢣
⠀⠀⠀⠀⠀⠈⠐⢷⣯⡇⠀⢠⠇⠀⢸⡀⠀⠀⠀⠛⣿⣿⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢾⣧⣿⡿⣿⣿⠀⣼⠀⠀⠀⠀⢸⠀⠀⢿⣧⣿⡿⣿⡿⠀⠀⡼
⠀⠀⢀⣀⣀⠀⠀⠈⠙⠇⠀⠈⠀⠀⠀⠳⡀⠀⠀⠀⠈⠙⠀⡴⠒⣇⠀⠀⠀⠀⢀⣀⣀⡉⠙⠛⠋⠁⠀⠁⠀⠀⠀⠀⠈⢧⡀⠀⠉⠛⠛⠋⢁⡔⠲⡅
⠀⠀⠀⠀⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣤⣤⡤⠴⠳⠴⢫⢤⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⡤⠜⠳⠴⢣⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⣾⣯⣠⡿⢷⣿⣄⡷⠀⠀⢠⠃⠀⢀⣔⣲⣶⣟⣲⠀⠈⣧⠀⠀⠀⢰⠃⠀⢠⣖⣲⣶⣟⣢⠀⠈⣆⠀⠀⠀⢰⠃⠀⢠⣖⣲⣾⣟⡦⠀⠘⡆
⠀⠀⠀⢠⣿⠛⣿⣷⣺⣿⣾⢳⠀⠀⢸⠀⠀⣸⡟⣿⣾⣿⣿⠀⠀⢸⠀⠀⠀⣾⠀⠀⣼⡟⣿⣾⣿⣿⠀⠀⢸⠀⠀⠀⣏⠀⠀⣼⡛⣿⣾⣿⣷⠀⠀⣷
⠀⠀⠀⢸⣝⢷⣾⣿⠿⣿⢾⡿⠀⠀⠸⡄⠀⠙⠿⢿⣯⡿⠟⠀⢀⡟⠀⠀⠀⠸⡄⠀⠛⠿⢿⣯⡯⠟⠀⢀⠏⠀⠀⠀⠸⡀⠀⠳⠿⣿⣭⡿⠏⠀⢠⠇
⠀⠀⠀⠀⠈⠉⠛⠾⠟⠛⠋⠀⠀⠀⢠⣏⣀⣀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡤⠋⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⢀⣀⣘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⣰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠉⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠁⠂⢀⡀⠄⠂⠀⠈⠀⠈⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠈⠑⠢⡧⠀⠀⠒⠒⠒⠒⠂⠀⠤⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢀⣐⣒⣒⣒⡈⠲⢄⠀⣀⠀⠤⠀⣀⣀⣀⠀⠬⢢⡀
⠀⠀⢀⠔⠘⠁⠀⠀⠀⠀⠀⠠⠄⢒⠡⠐⠉⠁⠀⠀⠀⠀⠀⠉⠘⠙⠂⠀⠉⠀⠀⠀⣀⡀⠉⠁⠚⢆
⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠎⠁⣉⠀⠀⠀⠀⠀⣤⠶⣷⣶⣤⡀⠀⠀⠂⠀⠀⢀⣴⣟⣿⣿⣷⡀⠀⠈
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⣸⣿⣟⣿⣤⣿⠷⠀⡢⠀⠀⠀⢸⣿⣿⡿⠶⠿⠗⢀⠆
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⠨⠭⠄⠀⡀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠉⠀⠀⠀⠀⠈⠒⠤⠔⠂⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⢀⡀⢀⣀⠉⠉⠁⠒⠒⠀⠤⠤⠄⢀⣀⠀⠀⣀⠠⠤⠄⠒⠈⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢄⣀⣀⣀⣀⡀⠉⠉⠁⠒⠒⠐⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠂⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⣀⠀⠤⠊
⠙⠵⡂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊
⠀⠀⠀⠁⠒⠬⢉⣀⠐⠒⠀⠀⠠⠤⠤⠀⠀⢀⣀⣀⣀⡀⠠⠄⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠒⠒⠒⠒⠒⠂⠐⠒⠒⠂⠉⠀⠀⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠍⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⣀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠓
⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠐⠒⠂⢄⠀⠠⠀⣀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠈⠁⢢⠀⠀⠣⠀⠀⠀⠀⠀⢀⠀⠀⣀⠔⠒
⠀⠀⠀⠀⢀⠄⠀⠀⠀⢠⠤⢀⣉⢈⠑⠄⠤⠀⠀⠀⠀⡐⢡⣴⣶⣦⡀⠀⠀⢠⣶⣶⣶⠄⢡⠀⠠⠅⠀⠀⢀⠡⠁⠴⠞⠁⠄
⠀⠀⠀⠀⠀⣀⣶⣢⡴⠋⠀⠀⠙⣷⣵⡀⠀⠀⠀⠀⠀⠀⠈⠭⠤⠭⠀⠐⠢⡀⠰⠶⠒⠀⠀⠡⠀⠀⠀⠐⠓⢂⡰⢃⠔⠁
⠀⠀⠀⠀⢀⠡⠉⣡⡤⠀⠠⠶⠦⠈⣿⠁⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠤⠄⠠⠠⠕⠀⠀⠀⠀⢠⡀⠀⢀⡠⠒⠁⠶⠁⠀⢀
⠀⠀⠀⠀⢠⠑⡆⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⠅⠀⢀⢤⠤⢴⡖⠒⣶⠒⢲⡖⠦⣆⠄⠀⠲⠀⠈⡀⠁⠋⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⢧⠀⠐⠀⠐⠀⢀⣟⠁⠃⠀⠀⠀⠀⠀⡄⠐⠸⣖⣲⣿⠿⣻⢗⡾⢭⣶⡏⠀⠀⠡⠶⠀⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠉⢷⠄⣀⣀⣴⣟⣥⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠙⢏⣳⣠⠼⣭⣶⡿⠋⠀⢀⠂⣄⡀⠙⠋
⠀⠀⠀⠀⠀⡆⠩⡜⠀⠈⠁⠰⢻⠿⠦⣀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠈⠉⠉⠉⠁⢀⣀⡔⠁⠀⠈⢁
⠀⠀⠀⠔⠁⠀⠀⠈⠁⠀⠀⠈⢁⢄⠄⠀⠑⢄⠀⠀⠀⢀⠀⢲⠲⣈⠓⠶⠤⠄⠔⠩⢀⡵⢤⢤⣀⣀
⠀⠀⠂⠀⠠⠉⠠⠪⠀⠪⠢⠪⠀⠀⠠⠂⠆⠀⠂⡠⠀⠋⠠⠘⡇⠀⠈⠑⠢⢤⠐⠂⠁⠀⠈⠠⠙⠌⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠈⡠⠚⠄⢳⠔⠢⠤⡾⠈⢳⡤⠴⠚⠇⡀⠳⡇⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠈⠀⢆⠀⠁⢸⠄⠀⠀⣿⢛⠻⡅⠀⢀⠀⡆⣐⠁⠀⠄⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙⡄⠠⠀⡇⠀⢠⠇⠔⡀⢇⠀⠸⠀⠀⠁⡀⢀⠀⠂⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠁⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣫⣿⡷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⣿⢏⣽⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣯
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣽⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣉⡀⠐⢰⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠲⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠘⣷⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⣾⣿⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣝⡻⣷⡦⣤⣀⠠⠂⠀⠁⠀⠀⠀⠀⢧⠀⢫⣦⣤⣶⢿⣽⣫⣽⡿⠿⢿⣿⣿⠷⢦⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⢸⣿⣿⢠⠾⠛⠋⠁⠀⠀⠀⠀⠀⠉⠙⠛⠿⢯⣿⣷⣀⡔⠀⠀⠀⠀⠀⠀⠉⣿⣿⣽⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢇⣿⢿⣿⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣤⣤⡤⢤⣄⡈⢩⣁⡀⠀⠀⠀⢀⡀⠀⣠⠋⠉⢀⢠⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⣾⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⢁⢸⣿⠀⠀⠀⠰⠺⡛⢛⣿⣿⢿⡿⠻⠗⠚⠛⠋⢻⣄⣁⡀⢀⡈⠉⠐⠋⡟⡀⢶⣷⣋⣠⡟⣿⣿⣧⠙⣻⡿⠃⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⢹⡏⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠀⠀⢱⡑⢦⣤⠀⠀⠀⢐⠋⠟⠃⠀⠀⠐⠭⣙⣻⣟⠛⠉⠁⠀⠀⠀⠀⢻⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢇⣾⣷⣿⡟⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠈⠉⠁⠀⠀⠀⡜⠇⠀⠈⠧⠀⠐⢫⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⡾⣽⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣟⡼⣵⣿⣿⣿⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣳
⠀⠀⠀⠀⠀⠀⢀⣿⡟⣱⡿⢿⣿⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⢋
⠀⠀⠀⠀⠀⠀⣼⡏⡼⣻⢃⢏⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⣯⠎
⠀⠀⠀⠀⠀⢀⡿⣼⢷⢏⣾⡞⣿⣾⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⣠⠶⠋⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣿⣾
⠀⠀⠀⠀⠀⢸⣷⣣⣏⣾⡝⣼⣿⣿⢼⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢀⠀⠀⠉⠒⠲⠤⠴⠚⠁⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⣿⠿
⠀⠀⠀⠀⠀⣸⡟⣿⣸⣿⣿⣿⣿⡟⡾⣸⢷⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣠⣾⣿⣿⣷⣦⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢠⢿⡆⣿⣧⠞
⠀⠀⠀⠀⠀⣿⢳⡇⣿⣷⣿⣿⡟⣵⢡⣇⣿⣷⡄⠀⠀⠀⠀⠀⠜⠀⠀⣴⣿⣿⣅⡈⠙⠛⠿⢿⣿⣿⡿⢿⣿⣦⡀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢠⡟⢨⡷⣿⠏⣴
⠀⠀⠀⠀⠀⢿⢸⢠⡻⡽⣿⡿⠞⡱⢟⣿⣽⣸⢿⣄⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠉⠙⠲⠦⠴⠦⢤⣤⣶⣾⣿⣿⣄⠀⠀⠘⠀⠀⠀⠀⢀⣾⡇⣼⢁⡟⣴⣿
⠀⠀⠀⠀⠀⢸⣿⢰⡅⣷⡟⣡⠞⣣⢟⣽⣡⡟⡼⣿⣦⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢠⣿⣸⢁⠇⣸⢳⢏⡇
⠀⠀⠀⠀⠀⠀⢿⣧⣷⣿⠞⢃⡼⣣⠞⣹⣟⡼⢱⣿⣺⢧⡀⠀⠀⠙⢯⣄⡀⠀⠀⠀⣀⣠⣤⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣟⡾⣼⢃⡿⢸⢧
⠀⠀⠀⠀⠀⠀⠀⣸⣫⠏⣠⢏⣾⣥⣾⢟⡞⢥⠟⣿⣯⡟⣷⡀⠀⠀⠀⠀⠙⠲⠾⢿⣿⣿⣿⣿⣧⠿⠷⠋⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣟⣼⣽⢛⣾⠃⡾⣱
⠀⠀⠀⠀⠀⠀⡼⢣⠇⣸⢃⡞⣼⣿⢫⠟⣰⠏⣼⡿⣿⣷⣇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣿⣷⣿⢯⢟⡿⣷⣻⠃⣰⡿⢋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⡀⠀⠀⠀⢀⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣁⣴⣾⣿⣿⡿⠀⠀⠸⣿⣿⣿⣶⣄⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⠟⠋⠉⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣮⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠛⢛⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⡛⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⡾⠋⣉⣉⣙⣷⡄⠀⠀⠀⢀⣴⣟⣉⣉⠙⢳⣄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣾⡷⠛⢉⣩⡉⠀⣿⠀⠀⠀⢸⡃⣉⣍⠉⠛⠳⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠸⣧⡀⢿⣿⣾⣶⠏⠀⠀⠀⠘⣿⣿⣷⡇⠀⣠⠟⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠿⢿⡟⠀⠀⠀⠀⠈⠛⢷⣶⣶⣤⣴⣶⠞⠛⠻⠿⠟⠛⠻⣶⣶⣤⣴⣶⡾⠟⠁⠀⠀⠀⣤⣽⣿⠿⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⡘⢻⡿⠀⠀⠀⠀⠀⠀⢶⣄⠈⠙⠻⢿⣿⣦⣀⡀⠀⠀⣀⣠⣿⣿⠿⠛⠁⢀⣴⠆⠀⠀⣶⣟⠉⢻⡟⠛⣠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠰⣤⣤⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠉⠙⠛⠛⠛⠛⠉⠁⠀⢀⣠⡴⠛⠁⠀⣨⡿⠏⠉⠀⠀⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⢹⡿⣦⣴⠀⠀⠀⠀⠈⠙⠛⠶⠶⢤⣤⣤⣤⠶⠶⠞⠋⠁⠀⠀⠀⠰⠟⠓⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠘⢛⡿⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣾⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⢻⠿⣻⡿⣿⣿⠟⠉⠉⠀⠀⠈⠉⠉⠛⠿⣿⣿⡍⢻⡻⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⡰⠋⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣆⠀⠈⢷⡀
⠀⠀⠀⠀⠀⢠⣿⢏⠄⠀⡀⡀⠁⡀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣠⢀⢻⡄
⠀⠀⠀⠀⠀⣾⣿⣿⣦⣴⣱⢃⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣧⢷⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣹⣿⠇⢀⣠⣤⣶⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣌⣿⣿⣿⣇
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠴⠋⠉⠀⡉⠉⠉⠉⠉⠙⠁⠀⠀⠀⠘⠛⠛⠛⠋⠉⠛⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣠⣷⠿⠿⠾⣶⣧⡄⠀⠀⠀⠀⠀⠀⣀⣴⣴⣶⣾⣀⣿⣿⣿⡄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⠁⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠻⠿⢿⣿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⠉⠛⢿⣿⢿⣿⣿⣿⣿⣿⣿⢹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢤⣉⣙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢛⠛⠻⠆⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⢈⠙⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠻⠇⢀⠀⠀⠀⠀⢉⡩⠛⢷⠀⠀⠀⠇⣤⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠈⠀⠀⠀⣈⡿⣛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣂⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⣁⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠿⠻⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢿⠞⠛⠿⠋
⣶⣶⣶⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢤⣭⣭⣿⣿⣶⡀⠀⠀⠀⠀⣴⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿⡄⠀⢠⣾⣿⣿⣷⣦⣤⣤⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⣠⣾⠿⣛⣭⣶⣶⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢀⣩⣶⣿⡿⠟⣛⣛⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠉⠉⠉⠉⠛⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⣶⣶⣶⠶⠾⠟⠛⠉



⡟⠉⢻⡟⠿⠿⠿⠿⢿⠻⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠿⠿⣿⣿⠿⠿⠿⢿