Quill Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣴⣶⣿⣿⣿⠿⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢿⣿⠓⠺⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢋⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢹⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢀⣶⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠸⣿⣼⣿⡿⣹⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⣿⣿⣯⡿⢦⡀⠀⠀⠀⠀⣿⣿⠷⢿⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⣿⣿⣿⡋⠀⢸⣧⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⣿⣿⣿⣧⠀⢈⣿⡄⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠛⠿⠿⠇⠐⠊⠋⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠠⠄⠀⠀⠀⣤⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠿⢷⣼⡶⠶⠦⣴⠤⣭⣕⣀⠀⠉⠀⠝⠓⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⢃⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠀⠉⠙⢙⣂⣀⠀⠀⠀⠀⠀⠈⠻⡳⠶⣄
⠀⠀⠀⠀⢀⣀⣤⣶⡶⠶⣾⣿⣛⢿⣷⣦⣟⠂⠄⢀⠀⠀⠀⠤⠀⠀⠀⠈⠁⠻⠿⢦⣀⠀⠀⠀⣳⣼⣿⠀⠄
⠀⠀⠀⣠⣿⣿⣿⡛⢱⣾⣿⣿⣿⣿⡷⠛⢉⣩⣄⡀⠒⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⡮⠳⢄⣿⣿⣿⣿⠀⠀⠀⠀⡀
⠀⠀⢰⣿⣿⣿⣇⣼⣿⣿⣿⣿⡿⠛⠀⠀⠀⠈⠉⠙⠛⠳⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣴⣾⣶⣟⣿⣿⣿⡀⠀⠀⠱⢹
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡⣖⢶⣿⣿⣿⣿⣿⠿⠟⠛⠿⢿⣟⢿⣇⠀⠀⠀⢸⣇⡇
⠀⠀⠀⠻⢿⡿⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢲⣿⠆⠀⠉⠁⠈⠁⠒⠻⠃⠙⢦⡀⠀⢸⣿⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣷⣤⢀⠀⠀⠀⠀⠀⠀⢈⢮⠻⣤⣸⣯⢠⡶⠋⠀⢞⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠦⠂⠀⡀⠀⠀⠀⠀⠳⡝⣿⣿⣿⠂⣀⠠⢁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠶⣦⣬⣀⣀⡀⠀⠀⠁⠺⣎⢿⡇⢰⢁⡴⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⣿⣿⣿⣿⣶⣶⣤⣸⣆⢻⣿⣮⠀⣡⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⠏⣿⣿⣿⣿⣿⣧⢻⣧⣾⠿⠛⠉⠲⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠔⠂⢀⣸⣿⣿⣿⣿⣦⢿⡏⣤⠤⠀⠱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣼⠟⠉⠀⠀⠀⠹⣿⣎⣿⡥⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠰⡀⠀⠀⠠⠀⠠⠘⣿⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠈⠀⠀⠁⠀⠀⠀⠈⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⡀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣾⣿⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⢿⣯⣸⣽⣥⣿⣷⣿⡿⠟⢋⣩⡵⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡥⠤⣼⣽⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣾⣿⣿⣿⣿⣿⡷⠟⢛⣻⣿⡿⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⣿⢿⣹⣿⣿⣵⠟⠂⢵⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣿⣿⢸⣿⣫⡿⠅⣤⣼⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣽⣿⠃⣹⣿⣿⡽⠿⣳⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣿⡇⠻⢘⣿⢯⣾⣷⣶⣿⣿⣟⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⣧⣰⡿⣵⣋⣉⣉⣛⣛⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣇⢠⣼⢟⣾⣿⣛⣛⣛⣻⣿⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣛⠢⣿⣾⣫⣿⡋⢩⣍⣉⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⣯⣷⣿⣿⡟⣋⣀⣴⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⣿⠟⣧⣶⣿⣿⡅
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡄⠤⠠⣿⣿⣟⠽⠝⠛⢻⠟⠁
⠀⠀⠀⠀⢀⣸⣟⠻⠿⠿⡿⢧⣴⣿⢟⣇
⠀⠀⡐⢕⠻⢿⡿⠗⠚⢿⣿⣿⢿⣯⢍⣿⣤⣾⣦
⠀⠀⣿⡎⠳⠤⠀⠓⣛⣛⣻⣿⣿⣿⣿⣷⡀⠀⣶⡀
⠀⢠⣿⡟⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣯⠄⢸⣿⣡
⠀⣿⣿⡟⠀⠀⠀⠀⠴⣾⣿⣿⣿⣿⣿⡿⠃⠸⢿⣧⠆
⡐⣿⣿⡇⠀⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣀⠀⢸⣷⠐
⠻⣾⡛⠷⡀⠀⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣷⠀⠸⣿⡷
⠀⠈⠙⠓⠂⠲⣄⣀⣦⣭⣽⣿⣿⣿⣿⠿⠷⠒⠊⠁
⣿⣿⠛⢛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢆⠀⠳⣤⠰⣎⠑⠾⠄⠙⠿⣆⠢⡀⢄
⠀⠀⠀⠀⠀⠀⡀⣤⡘⠒⠀⢙⣀⣈⣅⣨⣀⢀⠀⠀⠀⠈⠡⠹⡄⠑⡀⡀
⠀⠀⠀⠀⠀⠀⠐⢄⢁⡤⠂⠉⢉⡉⢉⠙⠛⠶⠯⣕⡠⢤⠀⠀⠀⠀⠰⠃⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠛⠍⠐⠡⠖⠂⡀⠀⠀⠙⠓⢥⡃⣃⢐⠀⠀⠃⠀⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠋⡀⠀⠀⠉⠳⣜⢦⡀⠀⡀⠈⡇⢹⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣷⣟⣫⡤⠬⠉⠓⢮⡳⢤⡄⠁⡈⠀⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠛⠈⠀⠀⠀⠛⢦⡑⢦⠁⠈⠰⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣛⣋⣹⡶⠏⠀⠀⠙⢦⡙⢆⡀⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢑⠪⢐⠤⢀⡀⠈⠙⢦⡙⢆⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠂⠐⠀⠛⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⡠⠤⠔⠂⠈⠀⣠⠞⠛⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⠔⠊⠀⠀⠂⠀⠀⠂⠀⣀⣠⣠⣄⠒⠁⠀⠀⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡠⠀⢊⠋⠜⠁⠀⠀⢀⠀⡀⠀⠔⠓⠂⠀⠈⠀⠀⠀⠉⠁⠀⠔⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠀⠀⢘⣀⣠⡤⠔⠒⠭⠈⠀⠀⠀⠀⠐⠶⣶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣤⡴⠺⢻⡉⠁⠈⠳⠦⠠⠤⠄⠠⠬⠀⠊⠉
⠀⠀⠀⠀⠀⢀⠠⠺⡥⠉⡉⠠⢄⠀⠈⠳⠄⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠂⠅⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣾⡿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⡿⢟⣫⣽⣶⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣴⣿⣿⣿⣿⣿⠿⣻⣵⣾⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⣾⣿⣿⣿⡿⣋⣵⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⡯⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣰⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣄⢠⡈⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⡟⢡⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠳⢾⣿⡟⣰⣿⣿⡟⠛⠁⠀⢀⡤⠐⠒⠀⠀⠉⠉⠁⠀⠁⠀⠀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣰⠹⡟⠙⠂⠀⠀⠀⠻⢄⣀⣀⣀⡀⡀⢀⠠⠴⠃⠀⠀⠀⠀⠀⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠶⠚⠋
⢀⡤⠄⠀⠐⠀⠀⢰⣷⠟⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠻⢤⣀⣀⣀⣀⣀⣿⠋

⠀⠀⢀⠀⠀⠀⡀⢀⣄⣤⣿⣿⣷⣶⣤⣤⣤⣤⣴⣼⣦⣤⣀
⠀⠀⠘⣄⣸⣿⣿⣿⣿⣿⣿⣻⣿⣽⣿⣿⣿⣷⣽⣿⣿⣿⣿⢷⡄
⠀⠀⠀⠙⠿⣯⣉⣉⣛⣛⠟⠛⣛⣛⣻⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣴⡄⢰⣦
⠀⠀⠀⠀⠓⠲⠿⣿⣿⣿⠷⠋⠙⢿⣿⣿⣛⠋⠛⢻⣯⣻⣿⣿⣿⡏⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣶⡤⠈⠛⣷⣝⣿⣧⣻⣿⡇⢿⣿⢰⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⣿⠿⢯⡻⣿⣶⡄⢻⠹⣿⢿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⣾⣿⣷⣝⢷⣤⣀⡇⠈⢸⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⠿⣛⣠⣴⣾⣷⣽⡻⣷⣤⢸⣿⢻⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣛⣋⣉⣠⣾⡿⢿⣮⣻⢾⣿⢁⣼⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣟⣿⣿⣋⠩⠛⠿⣷⣽⣿⣦⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡿⠿⠛⢻⣿⣯⣦⣝⣛⣿⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠛⠛⠌⠛⠛⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⡴⢖⣿⠿⠷⠶⣶⣶⡶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⣠⠟⠙⠁⢚⡩⠄⠀⢀⣀⣀⣀⣀⣀⣀⣈⣑⠢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⡠⠀⠈⠁⢀⣴⡾⢵⣶⠿⢿⡿⠿⠟⠛⠛⠛⠛⠛⠓⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⠎⡡⠂⠀⢀⠞⢁⣠⠴⣚⡭⠗⠊⠉⢶⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢃⠜⢁⡜⠁⠀⣰⣯⠞⣫⠵⠾⠗⠒⠀⣠⠶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⣧⠃⢀⡞⠀⣠⠶⣋⡴⠋⢁⣀⣤⡴⠾⠛⠛⡩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣿⠁⠀⣼⣤⠞⣡⠞⣉⣀⣀⠨⠄⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢰⠃⠀⣰⠟⣡⡾⠟⠉⠁⠀⠀⠀⠀⣠⡴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢀⢤⠏⡀⠀⠀⠀⣠⡾⣡⠞⠁⠀⠀⠀⣀⣤⠴⠖⠋⢁⡞
⠀⠀⠀⠀⠀⠀⢀⣾⡞⣸⠀⠀⢀⣴⢋⡼⠃⢀⣀⠒⠚⠉⠉⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⢠⠏⣾⠀⡏⠀⢠⡾⣡⡿⠞⠋⠁⠀⠀⠀⠀⣀⡤⢖⡋
⠀⠀⠀⠀⢠⠏⠀⠇⠀⣷⣠⡟⡴⠋⣀⣀⣀⣠⣤⠴⠚⠛⢋⡽⠋
⠀⠀⠀⠀⣼⠀⠀⢰⠀⣸⢏⡼⠁⠛⠉⠉⠁⠀⠀⠒⣒⡾⠉
⠀⠀⠀⢶⣿⠀⠀⠈⣷⢏⡾⠁⠀⠀⠀⠀⠀⠐⣊⡽⠋
⠀⠀⠀⢸⢻⡀⡇⢠⡟⡾⠁⢀⡀⢀⣀⣤⣶⣯⠥
⠀⠀⠀⠀⢇⠁⣷⡿⣼⢁⡴⠋⠀⣉⡴⠚⠁
⠀⠀⠀⠀⢛⠂⣿⢳⣷⠋⠀⣠⠞⠁
⠀⠀⠀⢰⣻⣰⡏⡟⠁⣤⣾⠅
⠀⠀⠀⠈⠈⣿⢸⢷
⠀⠀⠀⠀⢰⡏⡞
⠀⠀⠀⠀⢼⠁⡇
⠀⠀⠀⠀⠈⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠉⣛⣄⣼⡇⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠉⠋⠉⣽⢷⣎⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣻⠀⠀⠀⢀⡀⠀⢀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣚⣿⡇⠀⠀⢠⠀⠀⠉⠻⣿⣿⣿⡿⢿⣧⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⢱⣶⡿⠻⠆⠐⠈⠁⠀⠈⢙⡂⠀⠁⠙⢎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠛⠉⠛⠓⠶⣤⣀⡀⠤⠀⠀⢈⣤⠶⠠⠀⠈⠳⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠤⠀⡀⠀⠀⠀⠀⠀⠈⠀⠔⢘⣧⡤⠔⠒⠘⠁⠀⠀⠀⠀⠀⠀⠛⢆⠀⠀⣼
⠀⠀⠀⠀⠀⠀⡀⠀⣨⣗⠀⣀⠀⢂⣷⠠⠶⠿⠷⣶⣾⣿⣷⣶⠀⠀⠀⠀⠀⠀⡀⠼⡿⠛⠃
⠀⠀⠀⠀⠀⠑⠚⠿⠿⠿⠋⠉⠀⠀⠘⣀⠀⠀⠀⢈⡉⠙⠋⠙⠳⡂⢄⠀⠀⣀⣿⣴⣿⣿⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠉⠀⠈⠛⠁⠙⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠘⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⢃⣴⠟⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⣾⠟⣠⠖⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⣼⢏⣷⠟⠁⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡟⣩⡾⠁⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢀⣿⠟⣁⣠⣴⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠏⠀⠀⣸⡿⠋⣀⣤⣴⠋
⠀⠀⠀⠀⠀⠀⣠⠎⠹⠇⢀⣴⡿⠋⠀⠉⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠿⠀⢠⣾⠏⠀⠈⠁⣰⠋
⠀⠀⠀⠀⠀⣰⠃⠀⠀⣰⣿⠟⢀⣠⣤⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢀⣴⡟⠁⢀⣤⣴⠚⠁
⠀⠀⠀⠀⢠⡇⠀⣠⣾⡟⠁⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡰⣻⠋⠀⠀⠀⣰⠃
⠀⠀⠀⠀⢸⣇⡴⣻⠏⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⢞⡝⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⢸⢟⣼⣁⣠⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣣⣋⣀⣠⠴⠊⠁
⠀⠀⠀⡴⣣⠋⠀⣁⣠⠤⠤⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡼⠁⢈⣀⡤⠤⠦⢤
⠀⢀⣞⡴⣡⠖⠋⠁⠀⠀⢀⡰⠃⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⢎⡴⠚⠉⠀⠀⠀⣀⠞⠀⠀⣀⣀
⠀⠘⢿⠞⠁⠀⠀⣀⡤⠖⠋⢀⡴⠚⠉⢁⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡷⠋⠀⠀⢀⣠⠴⠚⠁⣠⠖⠋⠉⣸⣃⡀
⠀⠀⠈⠀⠀⠀⠐⠧⣤⡤⠖⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⢤⣤⠴⠊⠁⠀⠀⠀⠉⠁


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⠿⠃⠛⠛⢛⣩⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠛⠋⢉⢀⣤⣤⣦⣶⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠁⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠋⠁⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠾⠛⠟⠀⠀⠀⠀⢠⣷⣾⣿⣿⣿⣿⣿⠿⣛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⢀⢠⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢉⠀⠀⠘⣌⣤⣼⣶⣿⣿⣿⣿⣿⣿⣯⣶⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣜⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠃⢀⠀⣄⣴⣼⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⠀⠀⠠⢀⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢸⡄⠀⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⣹⣿⣿⡿⣷⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⣀⣽⣿⣿⣾⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠤⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⣿⢿⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠁⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠭⣀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⠀⠀⠀⢀⣤⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⢀⣴⣷⡿⠛⡛⠛⠛⠛⠛⣿⣿⣧⣷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠀⣠⣿⣀⣀⣀⣤⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠐⠆⠀⠀⣸⣿⣾⣡⣶⠿⠿⠿⠿⠟⠋⠉
⠀⠀⠀⠀⢠⠘⠁⢀⣴⡿⠋⠉⠐⢄
⠀⠀⠀⠀⠘⠶⠶⡟⣿⠁⠀⠀⠀⣘⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⣠⠿⣷⣶⠶⠶⢯⠤⠶⣶⣾⣿⠉⠈⠉⠉⠉⠉⠛⠧⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⣰⣯⡼⠟⠁⠀⠀⣸⠀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣶⣶⣦⣠⣤⠤⠾⣭⣀⣀⣀
⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠈
⠀⠀⣠⣤⠞⠁
⢠⡿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢻⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⡄⠀⢸⣿⠐⢁⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠛⡄⠙⣄⢸⡟⠀⣸⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⠀⠙⣿⣇⠰⣿⣿⣿⡟⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠙⠋⠻⢶⣌⣿⡙⢿⣿⣝⢣⣿⣟⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣙⠳⣤⠀⠠⡈⠰⣿⡞⠋⢿⣼⣿⣿⡞⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣎⡑⢤⣛⠠⠈⠁⠸⣧⠁⢄⢻⢿⣿⢷⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣙⢯⡙⠶⣾⣙⢦⣄⡀⠘⡷⠀⠀⢸⣿⢸⣇⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣍⠻⣿⣶⣈⠙⠳⢾⣤⠈⠉⠆⠀⠀⣿⢰⣟⠀⠀⢰⣿⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣬⡞⠹⢦⣄⡊⠼⠟⠤⡬⠀⠀⢸⢰⣏⠀⠀⢸⡿⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡝⠛⠿⣵⣬⣻⠶⣄⡀⠠⠀⠀⠈⢸⡏⠀⠀⣸⡇⢸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠑⠉⠷⣬⡙⠀⠊⠐⢂⠘⠅⠀⢀⡇⢀⣿⣿⡟⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⠀⠀⠀⠙⠚⡤⠠⠈⠀⢠⠃⣼⠁⢸⣿⢹⡇⠟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣧⣄⠀⢄⠀⢂⡀⠀⠀⡠⠏⠰⠇⠰⣆⡿⢸⡇⢰⣞⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡝⠷⣌⠑⠢⡀⠃⠄⠀⠘⡀⠀⢀⣿⠁⣼⠃⢸⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⡉⠳⣦⡈⠑⠀⠀⠀⠀⠀⠘⠁⢀⡿⠀⣌⠡⢸⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠙⢧⡴⡈⠀⠆⠀⠀⠀⡈⠀⣠⠟⡀⢸⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣔⠠⠈⠓⠀⠀⠀⠂⠀⠀⢂⡽⢠⠁⣾⢁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡼⢻⣅⠀⠁⢄⡀⠀⠰⠂⡰⠚⢤⠃⢰⡿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣬⠁⡀⠀⠀⠁⠀⢰⠀⣸⠇⣠⠟⠷⣌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣬⣆⡐⠀⠁⠀⡔⠉⢀⠓⣸⢲⡟⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣀⢀⠀⠈⠙⢯⣙⠓⢀⠀⠁⠰⠋⣸⣯⠟⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⡗⠶⣶⣤⠉⢰⡢⠀⠸⠃⣠⡿⣏⢷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢌⡲⢄⣀⠀⠀⠙⠂⠀⣠⠋⢵⣩⡿⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠼⡳⢦⡀⠃⠀⠼⢀⣼⣟⠤⢚⠡⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡙⠆⠀⠘⠠⠛⣤⣶⠄⡰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢈⠲⡀⣃⠀⢀⢰⠾⠷⢉⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⣙⢾⡧⠀⠈⠀⣀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣄⠻⡉⠊⡛⠀⠘⠛⠁⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣷⣄⠀⡁⠀⢀⢀⡀⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠿⣅⡁⠀⠈⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠠⡟⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠐⠟⠐⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣶⣴⢀⣧⣦⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣴⢿⢻⡿⡟⢸⢻⣽⡇⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠆⢸⡟⠸⠈⠁⠁⠈⣸⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢸⠀⢸⡇⠀⠀⠀⠀⠀⣿⡟⢀⢻⡇⠀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡟⢸⠀⠀⠁⠀⠀⠀⠀⢸⢻⠇⠈⢸⠃⢰⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⡄⢸⠈⣧⢹⠀⠀⠀⠀⠀⠀⢀⡿⡾⠀⠀⡜⠀⣸⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⡇⡎⠀⣿⢼⡄⠀⠀⠀⠀⣇⣾⣻⠃⡀⠀⠀⠀⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⠇⠇⠈⡇⡇⠀⢹⣸⡇⠀⠀⠀⠀⢹⢧⣯⠞⠀⠀⠀⣰⢏⢔⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣷⢡⠀⠈⣇⢷⠀⢡⠀⢠⣟⡾⢋⡠⠊⣠⣾⠟⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠸⡼⠀⠀⠸⡈⠀⠀⢷⣟⡾⠖⢋⣴⡿⠛⢁⡴⣣⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⡏⠀⠀⠁⠀⠀⠀⠀⢱⠀⠀⠀⠃⠀⢀⣾⡟⠀⠀⠉⢁⣠⢶⣯⠞⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣿⠏⢀⡠⣴⣶⠿⡿⠏⠁⠜⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣠⣿⠟⠠⠖⡻⠭⠒⠉⠀⠠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢻⡸⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⢳⣿⡀⠀⢠⡀⠀⠀⠀⢙⣿⣿⡤⠖⠒⠁⠀⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢕⢤⣸⠀⠀⠀⠀⠱⣳⡀⠀⠱⣦⡀⣰⣿⣋⣀⠀⠀⠀⢀⣀⠴⡞⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢹⠀⠀⠀⠀⠀⠈⠳⠄⠀⢀⣿⡟⠁⢠⣤⣶⣶⣿⣿⡮⠗⢈⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢄⠀⠈⢶⡀⢸⠘⡄⠀⠀⠰⣄⠀⠀⢀⣴⡿⠋⠈⠉⠉⠉⠉⠉⠁⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠱⡄⠀⢿⣼⠀⠁⠀⠀⠀⠙⣦⣴⡿⠋⠉⠁⠈⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠙⢦⠀⠘⠀⠘⠻⠀⠀⠀⠀⢀⣤⣿⣏⡀⠀⠀⠀⠀⠀⠀⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⢄⠀⢳⡀⠀⠀⡀⠀⡄⢀⣴⡿⠋⠀⠀⠀⢀⣤⣤⣐⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢅⣉⠓⢦⡱⡀⠧⠀⠀⠀⣠⣿⠿⠋⠀⠀⠀⠤⠤⠴⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣆⠁⡇⠀⣀⡴⣪⣕⠁⠀⠀⢀⠀⠀⢄⡀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠓⠲⣌⡀⠔⠊⠵⠦⠄⠀⠀⢄⡀⠀⠙⡶⢦⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⠈⠤⢤⡄⠤⠔⠢⢄⡈⢦⠀⠘⡆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠠⠴⠃⠀⠁⠀⠀⠀⠀⠙⠸⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣠⣴⣶⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢠⣶⣾⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣶⣼⣿⣿⣼⣿⣿⣿⣿⣿⡿⢟⣫⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⠉⠀⠀⣷⣿⣿⣿⣿⣿⣿⡿⠟⣩⣶⣿⣿⣿⣿⣿⣟⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⢻⠀⠀⠀⣿⣿⣿⣿⣿⠟⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡇⠀⠀⠈⠀⠀⠀⣿⣿⡿⠋⣡⣾⣿⣿⣿⣿⣿⣿⣛⣛⣋⣩⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡇⠀⠀⠀⠀⠀⢀⠿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⢻⠀⠀⠀⢀⠔⠁⣠⣾⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣯⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⡌⡇⠀⠀⠀⠀⠘⠀⢀⡔⠁⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢻⡇⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠘⣧⠀⠀⠀⡴⠋⢀⡴⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⢤⡞⠁
⠀⠀⠀⠀⠀⠀⣰⣇⠀⠀⠀⠀⠀⠙⠀⣠⠎⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⢀⡏⢸⠀⠀⠀⠀⠀⢀⠞⠁⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⢸⠁⠸⠀⠀⠀⠀⡴⠋⣠⠞⠁⠀⠀⠀⣀⣀⣀⣠⣤⠤⠤⠶⠒⠒⠚⠋
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⢀⠞⢁⡴⠃⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⡩⠛
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠋⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⡇⠀⢀⡞⢁⡜⠁⠀⠀⠀⠀⢀⣀⠤⠤⠤⠶⢒⡶⠚⠁
⠀⠀⠀⠀⠀⡇⣠⠏⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉
⠀⠀⠀⠀⠀⡷⢃⡼⠁⠀⠀⠀⠀⣀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⢀⡞⢡⠞⠛⠓⠛⠛⠋⠉⠉
⠀⠀⢠⠏⡴⠃
⠀⣰⢋⡞⠁
⢰⢣⠎
⣿⠋
⣿⣿⡾⢿⡿⢿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠢⡀⣀⡤⢄⡀
⠀⠀⠀⠀⢠⣈⠳⣦⣤⠾⢃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠛⠁⠀⠀⡗⠀⠀⠀⡠⢄⠀⢀
⠀⠀⠀⠀⠀⠙⡇⠀⠀⢠⡞⠁⠀⢀⡐⢦⣀⠀⣠⡖⣀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⢜⠁⠀⠀⢸⠀⠀⠋⠉⢙
⠀⠀⠀⠀⢠⡞⢁⣤⣤⡀⠳⣤⠀⠈⠻⣦⠉⠉⢁⡾⠋⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⠀⣠⣀⠤⠃⠀⡎⠉⠀⠀⠀⠀⠛⠲⡄
⠀⠀⠀⠀⠀⠐⠋⠀⠀⠙⠆⠀⠀⠀⣠⠟⣀⣀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠔⠉⢆⢡⠀⠀⠀⠀⠈⢑⣆⢴⠀⠀⡤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠞⠉⠉⠛⠦⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠘⠃⠀⠓⠚
⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠔⠉⠈⡉⠉⠑⢄⠀⠀⠀⣰⠒⠲⢾⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠈⡉⠉⠑⢄⠀⠀⠀⣴⠒⠶⢶⣶⣦⡀
⠀⠀⢀⠎⠀⣀⠔⠙⢦⡀⠈⢇⠀⠀⢉⠏⢉⡉⢉⡀⠹⡄⠀⠀⠀⠀⠀⢀⠇⠀⣠⠜⠑⢄⡀⠈⣆⠀⠀⢩⠏⢍⡉⢉⡠⢹⡀
⠀⠀⠸⡤⡏⠀⡖⠀⣦⠈⡷⣸⠀⠀⢽⡀⠘⠠⠈⠃⢀⡯⠀⠀⠀⠀⠀⢸⡴⡏⢠⡆⠀⣦⠉⡧⣼⠀⠀⢽⡀⠘⢀⠐⠃⢠⡯
⠀⠀⠀⢏⠻⣄⢠⠁⢀⡼⢋⠏⠀⠀⠀⠳⣀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠈⢏⠻⣄⠠⠅⢀⡼⢋⠇⠀⠀⠀⠣⡀⠀⠀⢀⠞
⠀⠀⠀⠀⠳⣬⠟⡛⢯⡠⠊⠀⠀⠀⠀⠀⣼⢻⡟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⠟⡛⢯⡴⠋⠀⠀⠀⠀⠀⣼⢻⡟⣧
⠀⠀⠀⠀⢠⠏⠂⠑⠊⢧⠀⠀⠀⠀⠀⡸⠁⠁⠈⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠂⠑⠊⢧⠀⠀⠀⠀⠀⡼⠀⠁⠈⠀⢣
⠀⠀⠀⠀⡎⠈⢂⠀⠌⠈⡆⠀⠀⠀⢠⠇⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢀⡏⠈⠄⢀⠂⠈⡄⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⡆
⠀⠀⠀⢸⠁⠀⠀⠃⠀⠀⢹⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠃⠀⠀⢱⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⢸⠀⠀⠀⠀⠀⢸⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢲⡝⠃⠀⠀⠀⠀⢀⣷⠏⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠛⠣⡈⠇⠀⠀⠀⠀⡀⣦⠁⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⠀⠀⠀⠈⠑⣆⠀⠀⡰⠳⠈⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡼⠋⠀⠀⠀⠀⠀⠈⣦⢂⣵⣦⠒⠈⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡧⠁⠀⠀⠀⠀⠀⢠⣟⣼⣻⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣇⠸⡏⠀⠀⠀⠀⠀⠀⡴⣏⣟⢻⡁⠄⠐⢤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡌⠀⠹⠀⠀⠀⠀⠀⡄⣠⠎⠉⢀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡿⠁⠀⠀⢷⠀⠀⠀⡞⠹⠋⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣥⠻⠀⠀⠀⠀⠈⡇⣀⠘⣠⡶⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣾⣿⠱⡆⠀⠀⠀⠀⢸⡟⣤⣋⣠⡴⠖⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⠇⠀⠘⣄⠀⠀⠠⠈⡾⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡄⢻⡏⠀⠀⠀⠀⠆⣴⠟⣠⡑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠙⠄⢃⠀⠀⠀⠀⠸⠏⣸⠟⠁⠀⠀⠒⠋⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠘⣇⠀⠀⢀⠀⠐⠁⠀⠀⠀⣠⣄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠀⠸⣄⢠⠌⣤⣴⡤⠤⠤⠊⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⢠⣿⡾⣾⣿⡩⠄⠐⠒⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢸⡇⣰⠏⠀⠀⢀⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⢱⡿⠦⠐⠚⣻⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣡⡟⠟⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⣤⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠹⣷⣿⣿⡿⠾⠿⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣶⣿⣷⣶⣶⣶⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢈⣴⣿⠟⠉⢹⣿⣷⢻⢯⣉⣹⣿⣿⣿⣿⡙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣶⣶⣾⣿⣯⠟⣾⢋⣻⣿⣻⣿⣽⣿⡈⣷
⠀⠀⠀⠀⠀⠀⠀⣱⣭⣝⣻⣿⠿⢛⣡⠞⠉⠉⠉⠀⣀⣀⣼⣿⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⣿⡿⢟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡗⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡧⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣤⣄⣀⣀⣀⣀⣼⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠟⠿⠿⠟⠛⠛⠋⠁

⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣠⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠀⠀⢀⣶⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣸⠟⠛⠂⠰⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⠛⠿⣦⣰⣿⣇⠀⠀⠴⠘⣿⠟⢠⡀⢠⡇⠠⠀⠂⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠲⡤⠤⡀⢀⣴⡞⠁⠀⠈⠁⠒⠶⣤⠀⠀⣼⡧⠸⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⣁⣂⡰⣖⢶⣼⣿⣯⣶⠆⠶⠆⠀⠀⠀⠈⢳⡤⢾⣻⣶⠖⠤⢦⢴⣶⣾⣶⣶⡶⠶⠶⠶⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢿⣿⣿⣿⢻⣷⡿⣯⣿⣿⣽⠆⠒⠀⠀⠀⠔⠀⠘⣇⣠⣿⣷⣿⣿⣿⣷⣶⣾⣿⠿⠷⠦⠤⠦⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡟⢷⣿⣽⣦⣿⡿⠋⣻⢶⡄⠝⠁⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⢋⣹⢻⡇⣏⣿⡧⠀⣷⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠊⠁⠀⠀⠀⠀⣨⡿⠛⠒⠳⢁⠈⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⢿⣬⣽⣸⣿⡗⣿⡇⠀⣿⡇⠈⢦⣄
⠀⠀⠀⠀⣀⣠⣶⣿⣿⣿⣶⣶⣤⣠⣾⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡌⣧⣷⣻⣇⣰⣿⣿⠷⡾⣿⡀
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⡠⠀⠂⠀⢀⣼⢿⣟⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠿⠿⠿⠿⠾⠿⠿⠃
⠀⠀⠈⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣅⠁⠀⣠⠞⣙⣆⢹⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⠒⠒⠛⠛⠃
⠀⠀⠈⠉⣿⣏⣉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⠟⠋⠉⠻⣾⣿⣿⣿⣿⣿⣟⣿⠛⢿⡿⠿⠿⠛⠿⠿⠿⠟⠀⢀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠈⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⢹⡏⣻⡃⠀⠀⠀⠀⠀⠀⠀⣆⢚⡇
⠀⠀⠀⠀⣿⣷⡤⠀⠀⢀⡀⠀⠀⠈⠛⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠀⣿⢘⡙
⠀⠀⠀⠀⠙⠛⠉⠙⠉⠋⠉⠙⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣀⣀⡀⣀⡀⣀⣈⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⢟⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄⣿⣿⡿⣿⣿⣿⢟⣵⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡟⣼⣿⣿⣳⣿⣿⣿⣛⣿⣿⡿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⡿⣿⢿⣿⣿⠟⣫⣿⣯⣶⣶⣿⡿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⣿⠋⢺⣠⣿⣿⢟⣵⣾⢟⣛⣛⠛⠿⢿⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢺⡇⡇⡇⢀⣿⠾⣫⣴⣿⣿⣾⣿⣍⣙⣿⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣸⣿⢃⣿⢿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠸⣿⣿⣿⣿⢓⣿⠿⠶⠶⢾⣿⣿⣛⠿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⢿⣴⣿⣟⣥⣾⣿⣿⣿⣿⣿⣟⡶⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣤⣿⣷⣟⣿⣃⣼⣿⣿⣿⣯⣍⣻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⡿⣿⣿⡟⣡⣤⣀⣠⢬⢻⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢬⡿⢫⣷⠤⠛⠶⠿⣟⣩⣾⠄⣄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡿⠀⠀⠛⠤⠤⠤⠌⠡⣊⠃⠞⢉⣠⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⡴⠋⠰⣶⣀⠀⠀⠀⠀⠛⠋⣁⣤⠶⡋⠀⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⡴⠋⠀⠀⠈⣿⣿⣿⣴⡄⠀⠠⠞⣫⠔⠃⠀⠶⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢤⡾⠋⠀⠀⠀⠀⠀⠘⢿⣿⣿⡇⡿⠓⠈⢀⠀⣈⣥⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣭⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠥⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠸⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠



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

⡄⠀⠀⡀⠀⠀⢀⡀⡀⣠⣤⣄⡀
⢻⣄⣸⣿⣿⣶⣼⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⢠⡀
⠘⢿⣟⡿⠿⢿⣿⣿⣿⣯⣽⣿⣟⣿⣿⣿⣿⣿⢿⣿⣿⣿⣦⣀
⠐⢤⣝⣻⣶⣤⡤⣭⠛⠛⠻⠿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠈⠛⢿⣿⣿⡷⠶⠚⠛⣿⣿⣿⣿⣿⣾⣟⢿⣿⢻⣿⣿⣿⣹⣧⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⣍⢉⡛⠳⣽⠻⣿⣿⣿⡿⣿⢹⣆⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⠄⡉⠛⣷⣝⢿⣿⣷⣿⢸⣿⣷⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⣥⣄⠀⢽⣷⡽⣿⣧⢼⣿⣿⢹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣷⣦⣾⣿⣮⢻⣾⣿⢛⠸⣉⣿⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣤⣽⣷⡝⢿⣿⠆⢹⠇⣿⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣿⣿⣿⣿⣿⠿⠿⣮⡻⣧⣬⠀⡟⠛⠿⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣭⣭⣭⣤⣴⣶⣾⣷⣝⢿⣶⡇⠀⠀⣾⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⣛⢉⣉⣭⣿⣿⣦⡻⣷⡖⢰⣯⠟⣿⣿⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣝⣿⣿⡷⠊⣩⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⠃⠀⠘⠻⢿⣿⣻⣷⣞⢛⣽⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠃⠛⠉⢹⣿⢖⣂⡙⢿⣿⣿⣎⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣟⣻⣷⡬⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠹⡏⠉⠉⠉⠓⠺⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡿⢿⣿⣷⣤⡀⢨⣽⢲⣦⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣜⣿⣎⣉⣉⣉⣭⣽⣷⣿⣿⣯⣼⠆⠀⢀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⣎⡙⠻⡿⢿⣉⠉⢻⣿⣿⣿⣻⡷⠆⣽⣧⡴⣿⣆⡄⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠈⠻⢀⣀⠘⠾⠟⠛⢻⣿⣿⣿⣿⣿⣷⣆⠀⠐⣶⠂⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡷⠀⠀⠀⠀⠀⠉⠽⣿⣿⣿⣿⣿⣿⣿⣋⠀⢐⣿⡏⡄⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡦⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡐⢸⣿⣿⢡⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠓⠀⠀⠀⠀⢈⣉⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠈⢹⣿⡎⡀⠀⠀⠀⠀⠀⠘⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⢿⣿⣿⠆⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣄⠀⢸⣿⣇⢁⠀⠀⠀⠀⠀⠀⠘⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠻⡷⠀⠀⠀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⢿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠤⣥⣤⣄⣀⣰⣄⣙⣛⣿⣿⣿⣿⣿⣿⣭⣭⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢉⣉⣁⣀⣀⣀⠀⠀⠠⠤⠤⠤⠀⠒⠒⠂⠀⠈⠉
⣶⣶⡶⢶⡶⢶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣶⣦⣶⣶⠶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣿⣷⣦⣼⣯⣿⣿⡟⣱⡟⡟⠛⢭⡻⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢄⡣⠂⡈⢹⣿⣿⣿⣿⣿⣿⣿⣿⢏⢶⣿⣿⠷⣧⣿⣿⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠉⡷⢋⠴⣊⣶⠉⠙⣿⣿⡿⣟⢣⣴⣿⣾⠤⡵⣿⠀⣿⣯⠀⠞⡝⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠅⠀⢴⡁⠊⠔⠡⢖⡭⢠⣿⣿⢿⣼⠟⣉⠳⢬⣽⣧⡴⠿⢟⠋⡟⣼⣯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠒⠒⡄⢻⣤⠔⡵⠁⣠⢋⠎⢹⣌⣻⣶⣻⣤⣴⣦⣬⣛⡛⠺⣇⣷⡽⠛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⢻⡤⠂⢀⣶⠛⢾⣀⠔⢔⡕⣡⠜⣱⣿⣽⡿⢋⣁⣠⣀⠉⡛⠿⣷⣄⠋⣵⣮⠏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢠⠎⡠⢂⠉⣏⡱⠀⣏⠴⠋⢰⠟⡟⢠⢟⣼⡇⣿⣿⣿⢿⣟⣿⣷⡈⢿⣧⡈⠻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡏⠘⠁⠄⣰⠁⠈⣠⡼⠃⣠⠟⢰⣁⡏⣾⢊⣿⣿⢿⣧⡼⠛⣸⣿⣿⣀⠙⠷⣦⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⠷⠄⠾⡀⠄⠚⠛⠉⡐⢊⣁⣠⡤⢻⣷⡟⣿⣿⠏⠘⣿⣰⠋⣍⠹⣿⣿⣷⡄⠘⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣟⠘⡆⠃⣀⣖⣛⠛⣳⠀⣿⣿⣿⡃⢸⣿⣗⣿⡇⠀⠀⣿⠛⢸⡟⣤⣿⣿⣿⠁⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣼⡟⣹⣿⣿⣿⣿⣿⡏⠄⣿⣿⡝⢧⢈⣿⣟⣿⡿⣤⣤⣽⣷⣿⡟⣿⣿⣿⡇⠀⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢃⣼⣿⣟⣿⣿⣿⣿⣥⣄⠀⢹⣿⣾⡇⣿⣿⣿⣝⣿⡿⣿⢿⣿⣿⣿⣿⣿⠀⢸⣿⡟⠃
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣃⣿⠧⣿⣿⡷⠿⢻⣿⠻⢿⡄⠠⣌⠛⠣⣿⣿⣿⣝⣛⢻⡛⢿⡿⣻⣶⠿⡅⢠⣿⣽⠇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⢿⣾⣿⡋⠀⠀⣀⢛⣲⡷⣄⠂⣡⡐⠸⣿⣿⣿⢿⡿⣴⣽⣟⣿⣏⣿⢀⣵⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣯⣿⣿⣿⣏⢸⣿⣿⡜⣿⣁⣼⠀⡀⢨⣬⡿⣿⣿⠈⡄⢱⠘⡝⢿⠻⠿⣶⣿⣿⡻
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣻⠿⣿⡉⢿⣿⣷⣈⣷⡏⡘⠁⣼⡀⢠⣿⣿⡀⠓⢀⠁⡉⠀⠀⠉⠐⣤⢿⡕
⠀⠀⠀⠀⠀⠀⠀⠈⣇⣿⣿⣽⠎⣿⣷⣟⠋⠛⢉⣿⡿⠁⣰⡟⢁⣰⣮⡙⣿⠖⢮⣤⣦⣴⣤⣦⣴⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣬⣄⠙⠳⣿⣿⣿⣾⣷⣿⠟⢁⡴⢏⣴⣿⠃⢸⣿⡏⠸⡸⢷⡘⢦⠻⡜⢿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠝⢰⠶⣛⡻⠟⠛⠋⠀⣤⠊⣠⡾⠃⡏⠀⢨⡗⢶⠀⡇⠀⡇⠠⡄⣦⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣍⢓⣲⡀⢄⠊⣴⡾⠋⣀⣠⡋⠀⠛⠃⢸⠄⠹⠄⠑⠄⠀⠈⠀⠀⠲⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠺⠲⠛⠁⠉⣀⡴⣋⠉⠳⣌⠉⢿⣶⠈⠣⣄⠈⠘⢷⡀⢠⡀⠈⠦⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣴⢶⡶⡿⣧⣄⠉⢷⠀⣿⡇⣸⢻⣇⠀⠹⠆⠀⠘⢣⡈⢣⣀⠐⡘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣸⢡⣞⣴⡏⣹⣄⣘⢗⠉⠉⠉⢩⠉⠙⠲⣧⡳⣄⠀⢷⡀⢠⠃⢱⡀⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣻⣿⣿⣿⣯⡀⠈⢳⠏⢠⡞⠉⠙⠿⠂⠀⠀⠀⠀⠀⢈⠳⡌⢶⡀⠱⣌⠂⠈⠓⠠⢷
⠀⠀⠀⠀⠀⣀⣠⠐⢪⣿⣿⣿⣿⣿⣿⣿⣇⠘⡱⠉⣂⠀⠀⠠⠀⠀⠀⠀⠀⠐⣄⠀⠙⢟⣶⡅⠀⢿⣄⣾⠑⢲⠹
⠀⣠⣴⡄⢋⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⠃⠀⠉⢂⠀⠀⡀⣠⡄⠀⠐⠀⠊⠢⠀⡈⣹⠀⠐⠀⣽⣻⣧⠈⠠
⢰⣡⡟⠀⢸⠦⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⡿⠀⠀⠀⣿⠁⣨⣿⣿⣿⡇⠀⡃⠈⣵⡆⠁⢿⣄⠀⢰⣿⡇⣯⠀⣤
⢨⣿⠓⠀⣈⡶⠸⣿⣧⡤⠘⣍⠉⠙⣿⠇⢸⠃⠀⠀⠘⣇⠀⠁⢿⣿⣿⠇⣠⠁⡴⠛⠀⠀⢻⠀⢀⣿⡿⢡⠃⠀⡍
⠘⡀⣀⠐⢱⡇⠀⡛⡍⠁⡄⠈⣠⠟⢁⠀⢸⡀⠀⠀⠠⠈⠳⢤⠀⠀⠡⠚⠡⠒⠁⠀⠇⡠⣸⣶⣾⣿⣱⠏⠀⠈
⠀⠻⠟⢷⣞⡀⢠⠋⠘⠒⠁⠚⢡⣖⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠂⣠⡞⣐⣫⣚⡉⠉⠁⢰⠞
⠀⠀⠀⠈⠛⠁⠢⡀⠀⠀⠄⠀⠈⠉⠀⣸⠧⣕⢶⡤⠄⠀⣤⠀⣿⡇⠀⣀⣀⡴⠟⣩⠶⠈⠟⠙⠹⠄⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠆⠀⠘⠂⢀⡿⡦⠙⠟⠀⠀⠀⠀⠀⢫⡀⠙⠃⢠⠦⠊⣹⡀⠓⠄

⣿⣿⡼⢗⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠟⠻⠛⣿⠉⠉⠩⠁⠐⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠈⣿⡇
⡿⢿⠀⠀⢤⣤⣄⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⣿⣶⡶⠖⠒⢲⣶⣶⣿⡇
⣷⠠⢀⠀⠋⠻⣿⠀⠀⠀⠀⠸⡦⠤⠴⠶⠶⠄⠿⠤⠴⠶⠤⡞⠀⠀⠀⣶⣦⣉⡉⠉⠁⠀⠀⠘⠻⢿⣿⣇⣀⣀⡀
⡿⢈⡀⠻⡅⢀⢹⣤⣤⣤⡤⠤⢄⠒⠀⠀⠀⠀⣖⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠙⠻⢷⣦⣄⡀⠀⠀⠀⠈⠙⠻⣿⡇
⠁⢀⣷⠀⠩⠘⣆⠻⣿⠿⠒⢄⠀⠀⠀⠀⠀⠀⣿⠀⠀⣤⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⣿⡇⢁⡀⡂⠀⠀⠀⢸⡇
⠀⠸⠯⠠⢤⡵⠈⣇⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⣿⠀⠰⢿⣇⣨⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⡂⠁⠀⠀⠀⢰⣶
⠠⢄⡀⣀⡀⠂⠀⣿⣢⠄⠈⠉⠲⡀⠑⡄⡀⠄⡻⠄⠀⠈⠩⠍⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠅⠀⠀⠀⢸⣿
⠔⢛⣿⣿⣆⠀⠀⠸⠯⢄⠀⠀⠀⢧⠞⠁⣤⣮⣥⣤⣤⣤⣤⡭⠀⠀⠀⣿⣿⣶⣶⣶⣶⣿⡇⠀⠀⠅⠀⠀⠀⢸⣿
⠀⠀⠁⢀⠌⡇⠀⢠⣤⣾⣧⠀⠀⠸⡄⠊⠀⠀⠀⠀⢉⣿⣿⣿⠀⠀⠀⣿⡟⠉⠉⠉⢱⣿⡇⠉⠉⠁⠀⠀⠀⢸⣿
⠂⠀⡔⠁⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⢷⠀⠀⠀⠀⠀⠚⠛⠛⠛⠀⠀⠠⠻⢷⣤⣀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⣠⣾⣄⠀⣀⢤⣴⣿⣿⣿⣿⡧⠖⠚⠷⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣾⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡿⠟⠹⣽⣷⣽⠟⠋⠉⠀⠐⠒⠓⠒⠒⠂⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠃⡀⠀⠀⠀⠀⠘⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣾⣿⣿⣿⠾⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⣿⡿⠁⠷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣿⣿⡿⣡⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢯⣿⣿⣻⣾⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡉⣣⣾⣿⣽⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣛⣿⣿⠿⣷⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣶⣟⣛⣦⣀⠀⠀⠀⠀⠀⣻⣿⣿⣵⣞⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⣿⣿⡿⠊⠁⢺⡇⠀⠀⠀⢀⠟⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⣿⣿⣷⡂⠀⢸⣿⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⣿⣿⣿⣿⡃⣀⠸⠿⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢄⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⣿⣿⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡏⢧⣠
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠃⣸⣿⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢻⡜⢿⣿⣿⣿⠀⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣙⢿⣿⢈⣽⣿⣿⡏⣿⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡳⢿⡿⣿⣿⣿⣧⡇⢸⣿⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣟⡇⣼⣿⡇⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⢿⣿⣿⣿⣿⣿⣵⡿⣿⣧⣻⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢭⣛⣿⣿⣿⣟⢹⣿⣇⡟⠃⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠈⠙⠛⠿⣮⣻⣿⡯⡇⢸⣻⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⣂⠀⠀⠥⣽⣧⣿⠸⢹⠀⣿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣤⣤⣽⣭⡳⣾⡀⣿⠀⠀⣼⢀⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣝⡛⠿⢿⣿⣿⣮⡑⢿⡀⠀⣿⣼⣿⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣶⣶⣑⣾⣿⣷⣕⠀⣿⣿⣿⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢯⠍⠙⠛⢻⣿⣽⣷⣮⡻⣿⣟⣿⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠤⠬⠁⣈⣩⣮⣝⢿⣳⠀⠇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⡿⠁⠀⠀⠉⠛⠲⢝⢠⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⡾⠷⣌⠻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣵⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡟⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⡿⣼⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢱⣿⣿⣭⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣇⣿⣿⣭⣭⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⡿⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢧⣿⣿⡿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢸⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣾⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣭⣿⣿⣿⣿⣿⣿⣿⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣠⡤⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⣸⣿⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡄⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢸⡇⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⡀⠃⠀⠀⠀⡴⠃⠀⠀⠀⣀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣇⠀⠀⠀⠀⠀⠠⡌⠈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢘⡇⡰⠀⠀⡀⣴⠟⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢠⢎⠀⠀⡞⠀⠁⣀⣤⣜⡁⠀⣀⢀⠤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣾⢺⠆⠀⠀⠄⢼⡿⠿⠿⠛⠓⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⡌⣿⣡⣄⣶⠾⠟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣼⡳⠛⠛⠛⠏⠁



⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⢠⠄⠺⠃⠀⡄⠰⠟⠀⡤⠐⠟⠀⢠⠀⠾⠁⢠⠀⠺⠃⠀⠀⢠⠄⠺⠃
⠀⢠⡄⠀⠀⢠⡤⠀⠀⠀⣤⠀⠀⠀⣤⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⢀⣀⣀
⢀⣿⣷⡀⠀⣿⣿⡇⠀⣼⣿⡆⠀⢸⣿⣿⠀⢠⣿⣷⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠾⢿⠿⣿⡿⣿⣿⣿⡃
⠘⣿⡿⠃⠀⢻⣿⠃⠀⢿⣿⠟⠀⠘⣿⡟⠀⠸⣿⡿⠃⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠰⠿⡿⠏⠉⠉
⠀⠿⠇⠀⠀⠸⠿⠀⠀⠸⠿⠀⠀⠀⠿⠇⠀⠀⠿⠇⠀⠀⠀⠀⠿⠇

⠀⣤⣤⠀⠀⠈⢃⠀⠀⢘⠃⠀⠀⠠⡤⡄⠀⠀⢘⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠐⠰⠋⠂⠀⠀⠞⠁⠀⠐⠟⠀⠀⠃⠺⠓⠀⠀⠰⠟⠀⠀⠀⠐⠸⠛⠂⠀⠀⠀⣠⣶⣦⡴⠿⠿⠇
⠀⣼⣇⠀⠀⣼⣯⡄⠀⢠⣿⡀⠀⢠⣿⣄⠀⠀⣼⣇⠀⠀⠀⢀⣼⣧⠀⠀⠀⠀⠈⠉⠉⣡⣀⡀
⢰⣿⣿⡆⠀⣿⣿⡇⠀⣿⣿⣧⠀⢸⣿⣿⠀⢸⣿⣿⡄⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢀⡘⠛⠟⠛⠀⠴⢿⡿⠆
⠀⣿⡏⣠⣤⢸⣿⠀⠀⢹⣿⢁⣠⡄⣿⡇⣀⡬⣿⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠰⠿⡿⠗⠀⠀⣴⣷⣶
⠀⠉⠁⠀⠀⠈⠉⠀⠀⠈⠉⠈⠈⠀⠉⠁⠁⠁⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣦⣷⢀⡀
⡦⠤⣠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⠟⠛⠛⠙⠛⠋⠿⣿⣸⣷
⡀⡀⣈⡁⠁⠀⠲⠆⢄⠀⣀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿
⡙⣿⣿⠿⠿⠎⠦⠢⢤⣀⡉⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⣼⣸⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠂⠀⠀⠂
⠉⠂⠀⠀⡀⠀⣤⣄⣀⢠⠙⢦⡀⠉⠓⠶⢠⢠⣀⡀⠠⢠⠀⣀⣸⡇⡏⢸⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠋⠙⠚⡾⠊⠉⠀⠀⠀⢀⡢⢌⢲⡈⠉⠙⠀⡀⠈⠈⠿⢿⡇⡇⣿⡇
⠀⢀⣀⣤⠄⠀⠀⢀⠀⠀⠀⣠⣶⡾⠷⠞⠁⠀⠀⠀⠁⠈⡀⠀⠀⠁⠃⢻⣷
⠴⠛⠛⠁⠠⣴⣜⠟⠃⠀⣀⡶⠖⢒⡒⠀⠁⠐⠶⣶⡜⢦⡱⣶⠀⠀⠀⠀⡟
⣠⠦⠙⠁⢾⢾⡧⠀⡀⠠⣰⣖⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠴⠁
⠀⡀⠐⠋⠀⠀⣠⠸⠁⠚⠋⠡⠊⠁⠀⠀⠀⠀⢠⡄⢰⠢⠀⠑⢴⢦⡀⠀⠁⠦⣀
⠒⠀⡠⣔⢾⣦⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⣿⡜⡇⠀⠢⠀⠻⡻⡼⣆⠀⠀⠠⢄⡀
⠀⠺⣿⣾⣕⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠁⢀⢠⠀⠀⠃⠀⠘⠀⠂⠀⠀⠀⠦⠄
⠀⠸⢦⡈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡔⣬⠇⠇⢠⠀⠆⠀⠀⠀⠀⢤⠀⠘⠷⡄
⣌⢲⣄⡉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠀⢀⠀⠀⠘⠀⠀⢀⡟⠀⠀⢀⠀⠶⣆⠙⢦⡀
⣬⣐⠈⠙⠃⠀⠀⠐⣆⠀⠀⢰⡄⢦⡀⠀⠀⠀⡏⠀⠀⠀⣞⡄⠀⠀⠀⠀⢸⠇⠀⢠⠀⠀⡀⠙⠀⡀⠚⣤⡀
⠶⠍⠑⠂⠀⠀⠀⣴⡈⣦⠸⡿⣿⣌⢷⡜⣦⢀⠈⠢⠀⠀⠹⠇⠀⠀⠀⠀⡜⠀⠀⠀⠆⠀⠹⡄⠀⠀⠀⠀⢶⡇
⠀⠀⠀⠀⠀⠠⣄⠻⣷⡌⢷⠈⠀⠀⠀⠀⠈⠘⠂⠀⠡⠀⠀⠂⡾⠀⠀⠀⠀⢰⠀⠀⠂⠀⠀⠀⠑⠃⠁⠀⠸⢿⣆⡄
⠀⠀⠀⠀⠀⡙⢿⣷⣦⡙⢦⡁⢀⣀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠘⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢸⣿⠁
⠀⠀⠀⠀⣀⣿⣷⠝⠛⠛⠀⠙⢻⣿⠟⠛⢉⣉⡉⠉⠹⡆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣶⣿⣿⠟⠊
⠀⠀⠀⠀⣻⠏⠁⠀⢐⡶⠀⠠⠀⢱⡀⠀⠸⠿⠿⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣼⡄
⠀⠀⠀⡀⠆⠀⠀⠀⢨⣭⡀⠀⠀⠄⠳⣄⠀⠀⠀⢀⣤⢿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⡇⢱⡀
⠀⠀⠀⠿⠀⠀⠀⠀⠐⣤⡁⠀⠀⠀⠄⠈⠛⠷⣿⡿⢿⣿⡿⠻⠿⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡿⢳⠈⡅
⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠘⠦⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣱⠋⠀⣯

⠀⠀⠀⠀⠀⠀⡠⠄⠀⠄⡀⠀⣀⠄⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⣶⡦
⠀⠀⠀⠀⠠⣼⠷⠀⠀⢠⠷⠒⠯⡀⠀⠀⣿⣄⠀⠀⠀⠰⠤⠀⠀⠀⠺⣿⠷⠀⠀⠀⠠⠴⠀⠀⠀⠀⣄⣀⣀⣮⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣦⡀⠉⢊⡉⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣄⣳⠀⠀⠉⠀⣼⠂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠣⣿⠆⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢻⡉
⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⣤⠦⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠀⠀⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣠⠐⠶⠖⠒⠖⠒⠒⠒⠲⠀⠀⠀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣀⣀⣀⣤⣀⣀⣀⣀⣀⣸⡆⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠻⣇⣀⣀⣠⣠⣄⣀⣀⣠⣀⣀⣀⣄⣠⡀⠆⠀⠀⠀⠘⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢻⣶
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣦⣠⣤⣭⣿⣿
⠀⠀⠀⠀⠀⢠⠜⠡⠤⠄⠀⠰⠶⠄⠠⠤⠤⠶⠶⠤⠿⠀⠀⠀⠀⠀⠡⠀⠄⠀⠀⠀⠀⠰⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡤⠀⠄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣴⣶⣶⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠐⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠤⠿⠿⠿⠿⠿⠯⠭⠭⠽⠿⢿⣿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠾⠛⠇⠀⠀⠠⠀⠄⠀⠠⠤⠀⠀⠀⠠⠀⠀⠀⠀⠠⠆


⣿⣾⠿⠿⣾⣿⣿⣶⣿⣾⣿⣿⣷⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣶⣷⣶⣶⣾⣶⣾⣷⣿⣿
⣿⣷⣏⣹⣧⣤⣤⣤⣤⣦⣤⣮⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⠌⠀⠀⠀⠀⡠⢀⠁
⠀⠀⠀⢠⣬⣿⣿⣿⣿⣿⣿⣿⣇⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢰⡏⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡅⠀⠸⠁⠀⠁
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢹⡇⠀⠀⡰⠁⠀⠠⠀⠁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠃⠀⠁⠀⠰⠁⠀⠠⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⢠⡏⡄⠀⠀⠀⡘⠀⠀⠀⢀⡴⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⠀⠘⠀⠀⢀⠃⠀⠀⠔⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⡟⠠⠀⠀⠀⢸⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣧⠀⠡⠀⠀⠀⠀⠀⠔⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣇⠀⠉⠀⠀⢰⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠁⠀⢸⡎⢦⡀⠀⠀⠸⡀⠀⠀⠈⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠁⠀⠙⠂⠀⠀⣇⠀⠀⠀⡅⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠱⠀⠀⠀⠀⠀⠀⢸⡀⠀⢘
⠀⠀⠀⠀⠀⢀⣤⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⠀⠀⠀⣇⠑⢶⣄⡀⠀⠀⢧⠀⠀⠀⠀⠀⡀⠈⠂
⠀⠀⠀⠀⠀⡾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶⠏⠀⠀⠀⠘⠆⠀⠀⠉⠀⠀⠘⡆⠀⠀⡴⠋⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⡀⠀⠘⡄⠀⢠⠊⠁⠁
⠀⠀⠀⠀⢀⠤⠤⢤⡀⠀⣿⣿⣿⡿⠟⠛⠛⠻⠏⠀⠀⠀⠀⠀⠀⠀⢈⠠⠐⠒⠂⠀⣀⣹⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⠟⠁⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠋

⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⣿⠿⠷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣿⠇⠀⠀⠀⢻⣷⣤⡀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⢠⣿⡁⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠀⠘⠻⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⡀
⠀⠀⢸⡿⠀⠀⠀⠀⠀⠙⠻⠿⣿⣷⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁
⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠠⣴⣄⠀⠀⠀⠀⠀⢀⣶⡿⠃⠀⠀⢀⣠⣿⠁
⠀⠀⠀⢻⣿⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⣠⣾⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡆⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⣤⣿⣿⣦⡤
⠀⠀⠀⠀⢻⡆⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⣼⠃⠀⠀⢀⠿⠟⠁⠀⠀⠀⠀⠰⣶⣦⡄⠀⢨⣻⣿⠇⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠘⣿⣿⡧
⠀⠀⠀⠀⠈⠉⠐⠀⠀⠀⠈⠻⠀⠀⠀⣼⡏⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣆⣨⣿⣿⠄⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠘⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣯⡀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⢷⠆
⠀⠀⠀⠘⣿⠟⠀⠀⠀⡄⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠾⠟⠿⣷⣦⣀⢀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⣿⡄⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣿⣿⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠗
⠀⠀⠀⢤⣿⣷⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣤⣤⣤⣤⣤⣶⡿⡇⠈
⠀⠀⠀⠀⠸⢿⡄⠀⠀⠀⠘⠟⠙⠓⠶⠦⣤⣤⣤⣾⠋⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⣴⣶⣿⣷⣦⠀⠀⠀⠀⠉⠉⠉⠉⠃⠉⠉⠘⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣠⠖⡒⢲⣶⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⣠⡶⣾⣿⣝⣾⣿⠹⢿⣧⣿⣿⣏⣿⣿⣿⠶⣦⣴⢇⡹⠂⠉
⠀⠀⠀⠀⠀⠀⠤⣬⠷⣟⣟⣯⣿⠙⣿⢾⣋⠿⠾⠿⣿⠃⠉⣿⢷⡿⢋⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢰⣿⣿⡻⣾⣿⣿⣤⣿⣽⣽⣿⢀⣕⢶⡈⠙⠳⠤⠼⠛⣈⢎⣽⣯⣭⣯⣇⣕⣠⡀
⠀⠀⠀⠠⣿⣿⣿⣷⣻⣿⣿⢿⣿⣿⢿⣶⣾⣿⣷⢹⣖⣤⣴⣰⣶⢿⡿⢡⠯⢂⣹⠀⡩⢿⣧
⠀⠀⠀⠋⢸⢷⣶⣶⣷⠻⣋⠾⣿⣿⡀⠀⠁⠉⠐⠺⠟⠇⢠⠛⣷⣿⡇⣈⣬⣿⡟⢿⣥⠐⠛⣆⡀
⠀⠀⠀⠀⣜⣇⣿⠝⠿⣾⢧⣷⣿⣮⡃⠀⠀⠀⠀⠀⠀⡀⠀⣀⠶⣝⢺⠘⢿⠛⣆⠀⠃⠸⣿⢞⠰⡀
⠀⠀⠀⠀⠸⣳⣿⠆⡰⣾⣹⣇⣿⢧⠀⠀⠀⠀⠀⠀⠀⠠⠶⠟⡿⠦⠛⠰⠜⢀⠛⡂⠰⡴⢿⡟⠀⡠⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠐⣿⣿⠧⢿⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⢨⢕⣦⣀⠠⠀⢀⠈⡡⠀⠼⠤⠘⡃⢀⡺⣆⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠐⠂⠀⠀⠨⠀⠀⠂⠃⣄⣧⢈⠲⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡏⠀⠀⠀⢀⠺⠀⠀⠙⠖⢛⡟⠓⢃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠴⡄⠠⡄⠒⡘⠀⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⠄⣆⠀⢀⣠⠠⠐⠟⡁⠀⠈⠛⠈⡀⠀⠈⣳⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⢀
⠀⠀⠀⢲⣆⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠰⣻⡿⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢠⡧⠂⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢠⣿⠆⠀⠀⠀⠀⠀⣽⣧
⠀⠀⠀⠙⢿⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⡿⠏
⠀⠀⠀⠀⠈
⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⢀⣾
⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣽⡆⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣗⣠⣦⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⢼⣯⠉⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⠹⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠛⢋⣄⡀⠀⠀⠀⣀⠀⠀⠀⣤⡄⠀⠛⠀⠀⠠⠖⠀⢀⡀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⢸⣿⣿⣿⡷⠀⠈⠀⠀⠀⠛⠁⠀⣀⠀⠐⢠⠄⣲⠈⠓⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡤⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⣀⣾⣧⠀⠍⠛⢻⣯⣤⣤⣴⣿⣖⣸⡄⠀⠛⠁⠀⠀⠠⠍⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⡶⢠⣤⣿⣿⠏⠙⣻⣶⣦⣀⠠⣭⣭⡉⠉⠛⠉⡹⠇⠀⠀⠘⠃⣶⣆⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠂⠀⣨⣿⣿⣯⣸⣿⣿⣿⡟⠇⠻⣿⣿⡇⠀⠀⠠⠀⠀⠀⡤⢛⣥⠈⢁⣾⡶⢦⣶⡄⠡
⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣯⠉⠀⠙⢫⣿⣷⡄⠀⢈⠹⠏⠀⠀⠀⠀⠠⠈⠫⠠⠀⣠⣼⣿⣿⣾⠟⠁
⠀⠀⠀⠉⠀⣀⠙⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠈⠙⢿⣿⡇⢴⡿⠲⣿⣿⣿⣆⣤⠀⣰⡄⠀⠀⡤⠴⢀⣾⣖⡃⣿⣿⣿⣿⡇⢰⣿⠃
⠀⠀⠀⠀⣠⡙⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⢁⣶⣿⠗⠀⢺⣆⡀⣀⡀⢻⣿⡅⠿⠿⠉⠙⠉⠀⠀⠰⢶⢼⣿⣿⣿⡿⠿⠿⠋⠁
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠀⠀⠉⠀⠀⠀⠬⠀⠀⠀⣠⣍⣃⡀⢀⡹⠿⠏⠛⠃⠐⠖⠀⣰⣿⡷⣃⠀⠶⢀⠀⠀⡶⣿⣿⣇⠐⢰⣶⣂⠀⣀⣶⣤
⠀⠀⢀⣠⡀⠂⢠⣶⡄⠀⠘⠀⠀⠀⠀⠀⢠⠄⠀⠀⠸⣿⣿⡏⢁⣛⣿⣴⣦⣾⣿⣷⣆⣠⣿⣿⣷⣻⣄⠀⢀⡠⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠛⠻⣿
⠀⠀⢸⣿⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢨⣤⠀⠈⠛⠉⢻⣿⡿⠛⠉⣙⣿⣯⢉⣌⢰⣶⢦⠘⠋⠈⠻⣿⣿⣯⠿⣿⣿⣿⣧⣦⡀⢠
⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢰⣦⢀⣤⣄⠀⠀⠈⢉⡀⠀⠀⠀⠀⠋⠁⠀⠈⢛⢹⡷⣻⣯⠚⣛⠀⠀⠀⠀⠀⢉⡁⣉⠀⠉⠀⠀⠈⠉⠉⠃
⠐⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⣠⣴⣶⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠉⠀⠀⠛⠁⢰⣿⣷⡄⣺⣟⠛⠂⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⣿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⣷⠘⣼⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢳⡄⢹⢠⣿⣿⣿⠟⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣷⡌⠳⣄⠹⡔⡗⣿⡏⢀⡴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⡟⡏⠀⠸⡆⣙⣷⣿⡶⣫⠜⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠇⣇⠀⠀⢱⢹⣿⠟⠋⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⢠⠀⠈⠀⠀⢸⣞⡯⠖⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠁⠀⢠⠀⣼⠀⠀⠀⢠⠟⠉⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢸⡈⠀⠀⠈⠄⢸⡈⡇⡰⠃⡀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣇⠠⠀⠀⢣⠈⣧⡿⠋⡁⠠⠀⣀⣠⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⢸⣟⡿⡆⢃⠀⠀⡵⣛⣀⡤⠶⠒⠍⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⠀⠹⣾⣿⠈⣶⣾⣻⡯⠝⠀⠀⠀⠀⣠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆⠀⠀⢹⣿⡿⠿⠋⠁⠀⠀⠀⠀⢀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣀⣾⣯⣴⣶⣚⠉⠉⠉⢐⣚⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⣶⡀⢤⡀⠀⢸⣟⣼⡿⠿⠿⠿⡿⠭⣽⣿⣟⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⢂⠃⠘⣆⣼⠟⠁⠀⠒⠒⠚⠃⣀⡀⣉⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣀⡈⠹⢿⣆⠈⢣⡶⠛⠁⠀⠀⠀⠀⠀⠠⠦⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠦⠤⠦⠀⠀⠙⢷⣦⣻⡾⠛⠉⠉⢠⣤⣀⣀⣀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣧⠀⣸⣿⣯⠤⠀⠒⠀⠀⠀⠐⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠀⢀⣿⣾⣿⠷⠔⠶⠤⠀⠲⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣷⠿⠯⠉⠉⠉⠀⠚⠛⠛⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉
⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠋⠁

⣿⣿⣿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⢈⠀⠀⣼⣷⣶⡄
⣿⣿⣿⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠸⡆⢘⣶⣿⣿⣿⣿⡁⠀⠀⠀⣤⠆⣠⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀
⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠉⢿⡟⣿⣿⣿⣿⡏⠀⠀⠀⢘⣷⠞⠁⣆⠀⡀⠀⠸⣿⣿⠆⢸⣿
⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡶⣤⣘⡖⠁⠀⠈⣿⢿⠀⢸⣿
⣿⣿⣇⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡆⢸⣿⣿⢩⣿⣿⣧⡄⠀⠀⢸⣿⣇⣏⣿⡇⠀⠀⠀⠀⠀⠀⠺⠿
⣟⣟⡉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠋⠉⠉
⠿⠿⠧⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⠿⠷⠿⣿⠿⠿⠿⠟⠛⠁⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⡀⠀⢀⣀⡀
⣿⣿⢰⣶⣶⣶⣶⣶⣶⣶⢹⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢨⠃⣤⣾⣟⢷⣾⣷⢰⡄
⣿⣿⢸⣿⣿⣿⢿⣿⡯⢿⢸⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠨⠇⢿⣿⣿⣽⣿⡿⣿⠇
⣿⣿⢸⣿⣿⣿⣿⣿⣿⣟⢸⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣄⠈⣽⠛⣿⣿⢣⡝
⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠋⠀⣿⣿⣿⣿⣧⡬
⣿⣿⢸⣿⣿⡿⢿⣿⣿⡿⢸⣿⣿⡇⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⢠⠆⠀⣿⣿⣿⣿⠏
⣿⣿⣦⣤⣤⣤⣤⣤⣴⣴⣾⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⠀⠐⠀⠀⠛⠛⠛⠁⠀⠐⠀⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠆⠀⠀⣠⠔⠃⠀⠀⠀⠀⠀⠀⠀⡙⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⠧⡄⣤⣦⣄⠀⠀⠀⠀⠃⠆⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠼⠿⣦⣀⣾⣆⠀⠀⣬⢿⣿⠀⡀⢠⡆⢀⠠⠄⠈⣆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠠⣤⢄⡀⣠⣾⠋⠉⠉⠀⠲⢦⡌⠁⢰⣷⠸⠁⠀⠀⠀⠀⡿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣉⣰⣶⡗⠆⠾⣟⠠⠖⠲⠆⠀⠀⠀⠙⡆⢼⡛⣷⡞⠴⠦⣶⣶⣷⣶⣶⠶⠶⠶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢛⣿⠿⣿⣻⣷⠞⠁⢰⢀⠖⠀⠀⠀⠀⠀⠀⠁⣠⣤⣿⣿⣿⣿⣿⣿⣿⠟⡟⠒⠲⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠟⠟⠿⠿⣿⣾⣟⡣⠈⡃⠀⠀⠀⠀⠀⠀⠀⢀⣄⣾⣋⣀⣿⠯⣽⢿⣽⣿⡿⠀⣿⡄⣄⡀
⠀⠀⠀⠀⠀⢀⣠⣾⣅⣀⡀⠀⢀⣴⠟⠉⠈⠉⠐⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣽⣜⣝⣿⣿⢸⣿⣿⣿⠀⣼⣧⣘⣷⣆
⠀⠀⢠⣤⣶⣿⣿⣿⣿⣿⣿⣷⣿⣷⣦⣀⠀⠀⠀⢀⠄⠐⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠁⠀⠀⣰⠿⡍⢷⣿⣿⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⡤⠤⠷⠄
⠀⠀⠰⣿⣿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⣾⠗⠚⢿⣼⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠙⠛⠻⣗⣻⡍⠀⠀⠀⠀⠀⠀⡄⢾⠆
⠀⠀⠀⢸⣿⣦⠀⠀⢀⡀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠐⠀⣿⢛⡗
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢿⣿⡧⠤⠤⠤⣀⣠⣤⠗⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣫⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣂⣀⣘⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣁⠙⠿⣿⣿⣿⢟⣱⣤
⢀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣦⡤⠟⠋⠓⢿⣯⠝
⢉⠙⠈⣦⠀⠐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠊⠁⠀⣀⣤⣾⠟⢁⠼⠛⠻⢯⡀⠀⠀⠀⠀⠘⢷
⣔⣭⣦⡼⠟⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂⣤⡀⠀⠀⢀⡴⠷⠀⢀⡛⠉⠉⠃⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀
⠛⠧⣒⠰⠢⠀⠐⠲⠤⣀⠒⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡝⠂⢀⣴⠟⠁⠀⢰⠟⠀⠀⠀⠀⠀⢀⣀⠀⠀⣠⣤⣠⡀⠹⣦⡀
⠀⠀⠈⠙⠳⢤⣤⡐⠾⣿⣿⠶⢦⡤⢤⣤⢐⣿⣿⠟⠁⠀⢠⠞⠁⠀⠀⢀⣀⣜⠃⡔⢲⣆⡒⢤⣍⠉⣁⡬⠽⠧⣤⣤⠈⢻⣆
⠑⢤⡀⠀⠀⠀⠉⠙⠛⠒⠬⢅⣀⣶⡿⢳⡿⣏⣤⣤⣦⢀⣠⣄⣀⣀⣹⣿⣦⣭⣹⣷⣿⣍⣍⣁⣀⣐⣈⣓⣒⣂⣤⣶⣾⣿⡿
⠦⡿⢻⣄⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⡷⠿⣿⣭⣭⣯⣉⡛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣦
⠋⢱⢣⡍⡄⠀⠀⠀⠀⠴⣿⡿⡿⡜⠁⠀⠀⠉⠉⠙⠛⠻⠿⠿⠷⠶⣿⣯⣶⣶⣶⣄⣄⣉⣿⣿⣿⣶⣾⡿⠿⠟⠛⠉⠁⠉
⠀⠀⡹⠀⠈⢆⠀⠀⠀⠈⠙⣿⣐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠁⠀⠀⢘⠀⠀⠀⠀⠰⡟⡾⢳
⠀⠀⠴⠁⠀⡄⠀⠀⠀⣠⣾⠋⠀⠉
⠀⠀⠀⠐⠀⠇⢀⣤⣾⠟⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⢰⣝⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢋⣴⡇⠀⠀⠀⢄⠙⣿⡻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣟⣿⡁⠀⠀⠀⠀⠱⣌⢛⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢦⣿⣿⣿⣟⡿
⠀⠀⠀⠀⠀⠀⠿⠋⢸⣿⠿⠿⠿⠃⠀⠀⠀⠀⠐⠮⣭⣿⣿⢩⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢆⣠⢴⠂⠀⠀⠀⠀⠰⢵⣮⣽⣿⡄⢰⠦⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣗⡃
⠀⠀⠀⠀⠀⠐⠄⠀⣽⣿⠟⣑⡿⠀⠀⠀⠀⢘⣢⣶⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣟⠂
⠀⠀⠀⠀⠀⠈⠀⠀⢸⣃⠉⠠⠒⠀⠀⠀⠀⠀⠦⢿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠴⠞⠀⠀⠀⠀⠀⠈⣿⣿⣝⣿⡗⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠐⠀⠀⢸⣯⢄⣿⠄⠀⠀⠀⠀⠀⠀⠈⢮⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠕⠀⠀⠀⠀⠀⠀⠀⠘⣄⣹⣿⣯⠀⠀⠀⠀⠀⠀⣬⣿⡿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⡧⠀⠀⠀⠀⠀⠀⠙⣿⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡙⢻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣾⣭⠿⣹⠆⠀⢰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡻⣿⡟⢷⡄⠐⠁⠸⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠈⠁⠀⠰⣄⠀⠀⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢹⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠐⡄⠘⠹⣯⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣤⠀⠀⠀⠀⠰⠀⠀⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡎⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⢁⠀⠸⣿⠃⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡇⠀⠀⠀⠀⠀⠘⡀⠀⠿⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢰⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠏⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⢿⣿⡤⠀⠀⠀⢸⡇⠀⠀⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡌⠻⡇⠀⠀⠀⢸⡇⠀⠀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢸⡇⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇⠀⠀⠀⠀⣸⠁⠀⠀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⣿⠀⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠘⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⣿⢟⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⡾⠀⢋⣵⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⣼⠁⢸⡿⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⡿⠀⣤⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⢸⠇⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣟⣹⣏⣹⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⢿⠿⣟⣻⡇
⠀⠀⠀⠀⠀⢠⣤⡀⠂⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⢰⣶⡄⠙⠛⠁⠀⠀⢠⣶⡄⢹⣻⡆
⠀⠀⠀⠀⣠⣼⣷⣦⣀⣀⠀⠀⠀⢤⢾⣯⣯⣄⠀⠀⠀⠀⢠⣾⢩⣤⠀⠀⠀⠀⢀⣿⣿⣤⠀⠀⠀⠀⠀⣨⣿⣶⣦⡁
⠀⠀⠀⠀⠉⣿⣿⡏⠉⠁⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠻⣿⣾⣿⡇⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠛⢻⣿⣿⠁
⠀⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠠⣿⣿⡏⠃⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠋⠈⠃⠀⠀⠀⠀⠀⠀⠘⠉⠃⠀⠀⠀⠀⠀⠀⠛⠙⠃⠀⠀⠀⠀⠀⠙⠙⠃⠀⠀⠀⠀⠀⠀⠘⠋⠋

⠀⠀⠀⣦⠀⠀⠀⣰⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠳
⠀⠀⠀⢧⣼⣻⢄⡟⠀⠀⠀⢀⣻⣟⡀⠀⠀⠀⠀⠀⠐⠀⠀⢰⣿⢇⣙⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣟⡀⠘⠧
⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡄⠀⠀⡴⢯⣗⣀⢀⣀⠀⢀⣀⡿⣿⣿⣿⣄⡀
⠀⠀⠀⢾⣿⣏⠀⠀⠀⠀⠀⠿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⡿⠇⠀⠀⠉⢡⣿⣿⠹⠿⠃⠀⠀⠀⣿⢿⡇
⠀⠀⠀⢈⣿⢻⡇⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⣿⣿⡇⠀⠀⠀⢀⣙⣿⣿⣿⠀⠀⠀⠀⢸⡿⢸⡇
⠀⠀⠀⠸⠇⠸⠇⠀⠀⠀⠀⠀⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠿⠻⠇⠀⠀⠀⠸⠿⠿⠼⠏⠀⠀⠀⠀⠸⠇⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠀⠀⠀⠀⠀⠰⠖⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⣶⣦⠀⠀⠀⠀⣀⣀⠈⠀⠀⠀⠀⠀⢀⣤⡀⢠⣶⣤⣦⠀⣠⣄⡀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠶⣰⣠⣄
⠀⠀⠀⠀⣠⣝⣩⠆⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⣠⣬⣿⡁⢨⣿⣭⣯⠀⢹⣯⡽⠃⠀⠀⠀⢰⣿⣿⣄⡀⠀⠀⠻⣿⣿⣿⠄
⠀⠀⠀⠀⣿⡟⠻⠦⡴⠛⠲⢿⣿⣿⠀⠀⠀⠀⢹⣿⣿⢷⣈⣿⣿⣟⣠⢿⣿⣿⡀⠀⠀⠀⢸⣿⣿⡈⠙⠦⠀⠀⠈⣿⠆
⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠸⣿⣿⣄⠉⣿⢻⡏⢁⣴⣿⡿⠁⠀⠀⠀⢸⡏⣿⡋⢾⠆⢰⡄⡀⠙
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⢠⣿⠁⣿⠀⣿⢸⣿⢸⡏⠸⣧⠀⠀⠀⠀⣸⡇⢿⡇⠀⢸⡚⠙⡇
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠘⠃⠀⠛⠀⠛⠈⠛⠘⠃⠀⠙⠃⠀⠀⠀⠙⠁⠘⠁⠀⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣶⣶⣾⣿⣧⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣿⣿⣿⣽⣿⣿⣿⣿⣿⡿⠿⡿⠿⢿⣿⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⢿⣿⣿⣿⡿⠟⣋⣩⣼⣿⠿⠉⠒⠿⣿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠟⡟⢋⣼⣟⣿⣛⣿⣷⣶⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡿⢻⣃⣤⣿⣿⣿⣍⡻⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣷⣼⣿⣿⠟⣿⣮⣭⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⣻⣥⣶⡶⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠉⠉⠉⠹⠟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⢀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠂⣷⢰⡿⢮⣁
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠈⣼⣷⡀⠀⢿
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢽⣿⣏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⡀⣽⣿⣷⡀⠠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢦⡀
⠀⠀⠀⠀⠀⢀⡀⠀⡰⠀⠂⠀⠀⠀⠀⠀⠀⠘⠋⢴⡤⠈⢂⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠑⠀⠇⠀⡤⠀⠀⠀⠀⠀⠀⢇⠀⠙⢋⢀⠄⡄⠀⠀⠀⠀⠀⠐⠀⢉⢀⢀
⠀⠀⠀⠀⠀⠈⠀⠀⠠⠊⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⠈⡴⠁⠀⠀⠀⠀⠀⣿⠀⠀⣠⠎
⠀⠀⠀⢀⠓⠦⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⡠⠠⠀⢠⢞⡤⣰⠀⠀⠀⠀⠀⠸⡀⠘⣁⠀⠀⠂
⠀⠀⠀⠘⠢⡀⠀⠀⠈⢀⡀⡴⠀⠀⠀⠀⠘⡔⠕⡀⢡⣋⢞⡵⠀⠀⠀⠀⠀⠄⠙⢤⡀⠀⠀⢀
⠀⠀⠀⠠⣄⠑⢆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠠⠳⣀⢸⣫⢟⡡⠂⠀⠀⠀⠀⠲⡀⠄⠀⠁⡀⢀⠜
⠀⠀⠀⠀⠈⠁⠈⠐⠀⣠⠖⠀⠀⠀⠀⠀⠘⢆⠈⢲⠕⠉⠀⠀⠀⠀⠀⠀⠀⠈⠢⡁⠀⣴⠋⠂
⠀⠀⠀⠀⠀⠢⡀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢺⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠐
⠀⠀⠀⠀⠀⠀⠈⢩⠀⡀⠀⠀⠀⠀⠀⠀⠀⡖⡂⢈⣾⣀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠠⣰⠐
⠀⠀⠀⠀⠀⠀⠀⠘⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⣟⠁⡠⠈⠀⠀⠀⠀⠀⠀⠈⢦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⡟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸

⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣸⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣧⣠⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢺⣿⣿⣿⣿
⡋⢻⠟⠛⠛⠻⣿⣿⠋⢹⣿⣿⣿⡟⠉⣿⠟⠋⢹⣿⣿⣿⠀⢸⡿⠻⣿⣿⣿⡛⢻⠟⠛⠛⠻⣿⣿⠋⢹⣿⣿⣿⡟⠉⣿⠟⠉⢹⣿⣿⣿⠁⢸⡿⠻⣿⣿
⣿⣿⣿⣿⣶⣶⣿⠉⠀⢸⣿⣿⡟⠁⠀⠏⠀⠀⢸⣿⡿⠃⠀⣚⣀⣼⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⠁⠀⢸⣿⣿⡟⠁⠀⠏⠀⠀⢸⣿⡿⠃⠀⡘⣀⣴⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⡆⢸⡿⠋⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⡿⠋⠀⠀⠀⠀⠀⠀⠸⠛⠁⠀⠙⢿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠈⢿⣿⣿⣿
⣿⣿⣿⣿⠿⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⡀⢈⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⡀⢈⣿⣿⣿
⢹⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢹⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⢹⣿⣿⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣇⠀⢹⣿⣿⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠆⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿
⣿⣿⣿⡟⠉⡉⠙⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⠀⠀⣠⡆⠀⠠⢤⣤⣤⣿⣿⣿⣿⣿⣿⡟⠉⡉⠉⠂⠀⠀⠀⠀⠀⠀⢠⠿⠋⠀⠀⣠⡆⠀⠠⢤⣤⣤⣿⣿
⣿⣿⣿⣷⣾⡇⢠⣿⣦⣄⠀⠀⠀⠀⣧⣀⣤⣶⣿⣿⣧⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣾⠇⢠⣿⣦⣀⠀⠀⠀⠀⣦⣀⣤⣶⣿⣿⣧⠀⠀⠀⣹⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⡇⠀⣿⣿⣿⣿⣿⣿⢿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⡇⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⡇⠀⣿⣿⣿⣿⣿⣿⢷⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⡇⠀⣿⣿⣾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣏⣿⣾⣧⣟⣿⣿⣿⣿⣿⣿⡇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣿⣿⠿⢿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⠿⣿⣿⡿⢿⣿⣿⣿⠃⢸⣿⣿⣿⣿
⣧⣼⣥⣄⣀⣈⣿⠟⠀⢸⣿⣿⣿⠇⠀⡿⠃⠀⢸⣿⣿⡟⠀⣸⠋⢠⣿⣿⣿⣦⣼⣥⣤⣀⣈⣿⠟⠀⢸⣿⣿⣿⠇⠀⡿⠃⠀⢸⣿⣿⡟⠀⢸⠋⢨⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣤⡀⢸⣿⡿⠃⠀⠀⠁⠀⠀⢸⣿⠏⠀⢤⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⢸⣿⡿⠃⠀⠀⠁⠀⠀⢸⣿⠏⠀⢤⣦⣶⣿⣿⣿
⣿⣿⣿⣿⠛⠛⠛⠛⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠛⠃⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿
⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣄⠀⠹⣿⣿⣿
⢿⣿⣿⣿⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠐⠿⠿⠿⠿⢿⣿⣿⣿⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠰⠿⠿⠿
⣼⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣼⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠛⢿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠛⢿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⣤⣾⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣤⣼⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⣿⣿⣿⣿⠿⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠀⠀⠀⡀⠀⠀⠈⠉⠛⣿⣿⣿⣿⣿⣿⣿⠿⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠈⠉⠛⣿⣿
⣿⣿⣿⣇⣠⡆⠀⣤⡀⠀⠀⠀⠀⠀⠘⠉⠀⣀⣤⣾⡇⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣇⣠⡆⠀⣤⡀⠀⠀⠀⠀⠀⡜⠉⠀⣀⣤⣾⣇⠀⠈⠙⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⣸⣿⣿⣶⣤⣤⡄⠀⣿⣶⣿⣿⣿⣿⣿⣄⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣶⣤⣤⡄⠀⣿⣶⣿⣿⣿⣿⣿⣄⣀⣠⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠶⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⣻⡏⠁⣀⠄⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⣫⠁⣰⡟⠁⣠⡾⠋⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⣴⠏⣼⠋⢀⣼⠋⠀⣠⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢰⡆⢠⡟⢠⠃⢠⡞⢁⡄⢰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⡀⠀⣿⠀⢸⠃⠈⢠⡟⢀⡿⢁⡿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⣶⢀⣷⢸⡟⠀⢸⠀⠀⠎⢠⡾⢁⡾⠁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⣿⢸⣿⢸⡇⠀⠈⠀⠀⠠⠋⣠⠞⣡⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢸⡆⠀⣿⠀⣿⠀⡇⠀⠀⠀⠀⠀⠊⣡⡾⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢸⣇⣠⢻⡄⢻⡀⠃⠀⠀⠆⠀⢀⡴⠋⣀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢁⡄⠘⣿⢿⡸⡇⠘⠃⠀⢀⡼⠀⠔⠋⣠⠞⣡⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢸⣇⡆⢿⢸⡇⠸⠀⠀⠀⣼⠃⢀⣴⠞⣡⡾⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣷⠸⡇⣿⠀⠂⠀⣼⠃⠚⢋⣥⠞⣩⠖⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡄⠘⣿⢻⡆⢣⠈⡄⢀⣼⠇⠀⠐⣩⣴⣾⡷⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣷⡄⣿⠘⣇⠈⠀⢀⣼⠏⣠⡴⢟⣫⠾⢋⡄⢀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⣿⠙⡀⠛⠀⢀⣾⠏⠀⡡⠴⠋⣡⡾⢋⣠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢿⢿⡀⠇⠀⢁⣾⠃⠀⠀⢀⣠⠾⣫⡾⢣⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠸⡇⠀⢠⡾⠁⠀⣠⠶⢋⣵⠾⠋⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⠀⠈⠀⠀⣰⡟⠁⠀⢁⣠⠶⠋⠁⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠋⠉⠉⠉⠉⠀⠀⠀⣴⠏⠀⣤⠶⠋⠁⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠁⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡾⠃⠀⠀⠀⢀⣠⠴⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠚⠛⠋⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠆⣠⣄⡀⠀⢀⢀⣀⣀⣀⣤⣤⡶⠾⠛⣿⡀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⢀⠃⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⢿⡄
⢀⡙⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠐⠀⠈⠙⠶⣄⡀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠸⠇⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⢿⡆
⡆⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠃⠀⠀⠀⠀⠀⠀⢸⡇
⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠶⠦⠤⠤⠴⠶⠶⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⠦⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠶⠶⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠾⠛⠉⠀⠀⠄⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠔⠈⠛⠉⠀⠀⠀⠀⣠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠞⠉⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠆⠈⠁⠀⠀⠀⠀⡀⠤⠂⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣖⣚⠛⠋⠁⠀⠀⠀⡀⠀⡠⠖⣊⣤⡶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣯⣙⠀⠀⠀⢠⣴⢾⣿⢉⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣞⣿⣿⣿⣿⢿⣻⣤⣾⣷⠘⣿⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠿⠿⣷⣮⣻⣟⣭⣶⣿⣿⣧⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠀⢀⣠⠾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣴⢟⣵⣿⣿⣿⡿⠋⠁
⠀⠀⢀⠀⠀⠀⠀⢤⣤⣤⣤⣬⣵⠿⢿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣼⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⣿⣿⣿⣿⣿⡿⠟⠛⣉⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⣿⣿⣿⣟⣛⣉⣩⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣟⣛⣩⣭⣵⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⢹⣿⣿⣿⣯⣥⣤⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⢿⣼⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣧⢹⣿⣿⣿⣿⡷⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⣹⣷⡟⢿⡊⠭⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢬⣿⣿⡝⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡈⠣
⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⠶⢲⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠋⣉⠕⣂⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠁⣠⡞⠹⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠿⠄⢀⡴⠋⠰⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⣠⠟⠠⣶⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡅⠈⣴⠏⢰⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⢛⡾⢃⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣬⣿⣯⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢞⣻⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿⣷⢸⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⢸⣿⢈⣍⢻⣿⠘⣋⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⣿⡿⠸⣏⣼⣿⠸⣇⣴⣜⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠀⣠⠤⣀⠀⠀⠀⠀⠀⢠⠲⡀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⡀⠀⠀⠀⢀⡠⠤⣷⠦⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠙⠁⠀⠈⡆⠀⣤⠤⠐⠃⠀⠑⠦⠤⣤⠀⡠⠃⠀⠀⠀⠀⠘⢄⠀⢠⠃⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⠀⡰⠁⠀⠈⠲⡄⠀⠀⠀⢠⠞⠁⠀⠱⡀⠀⠀⠀⠀⢀⠞⠀⠸⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⣶⣿⡴⠁⠀⠀⠀⢠⢁⣀⣤⣄⣀⡆⠀⠀⠀⠙⣤⣤⣴⣦⠊⠀⠀⠀⠳⢄⣀⣠⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⡇⠀⠀⠀⠀⠀⠈⠙⡿⢻⠛⠉⠁⠀⠀⠀⠀⠹⠉⣿⠉⠀⠀⠀⠀⠀⢸⢻⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠈⢢⠀⠀⡀⠄⠐⠀⠃⠰⠀⡠⠀⠀⣬⠇⢤⠒⠉⠭⢒⣀⠀⣿⠀⠀⣼⠈⠈⠉⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⣀⣀⣀⡰⢀⠀⠀⢀⠔⡏⣠⡌⢓⠢⡀⠐⠀⠨⢘⠁⡡⣿⡆⠀⠅⡃⠛⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⣈⣩⣭⣠⠂⠀⠀⠀⢡⣆⣉⣀⣰⠊⠀⠀⠀⠀⠘⢔⣈⣒⣀⣁⡰⠁⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⢹⡟⠀⠀⠀⠀⠸⠿⢻⠙⡟⠃⠀⠀⠀⠀⠀⠀⠿⢿⠙⡟⠀⠀⠀⠀⠀⠸⠀⢠⠄⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠟⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠠⠶⠰⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⢀⣀⠤⡀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⢀⡠⠀⠀⢀⡴⠖⠀⠀⠶⣦⣤⡀⠘⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⣿⣧⠀⢴⣿⡏⠀⣼⠏⣡⣀⣽⣿⣶⣬⣿⣧⣴⣀⢸⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⡀⠰⡄⢸⣦⡶⠾⠿⠟⠋⠉⣿⣿⡿⣷⡘⣿⣾⠟⣠⠖⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠉⠈⢩⡙⠶⠦⠤⢤⣴⣿⣿⣡⣽⡿⢛⣡⣾⣿⣷⡄⠀⠴⠒⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⡉⠐⠀⢀⣿⣤⠀⠀⠀⠀⠀⡤⠀⠸⠦⣬⣿⡀⠀⠀⢠⣈⣛⣛⠛⢻⣷⣿⣏⣾⣟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣷⣶⣾⣿⣿⡀⠀⠀⠀⠀⠘⠶⣄⢲⣦⡙⠛⠛⠻⠿⢿⣿⣿⣿⣾⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡙⠿⣿⣿⣿⣷⣶⡄⠀⠀⠀⠹⣷⣿⣿⣶⣾⣿⣦⣶⣮⣉⣻⣿⣿⣷⡿⠃⣀⣀⣀⣠⣴⠞⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⢤⣈⠙⣻⣿⣿⣀⠀⢀⣠⣌⣙⡻⣿⣿⣿⣿⣏⣩⣿⣿⣿⣿⣷⣶⣿⣿⣏⠙⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢽⣿⣿⢿⣿⡿⣿⣿⣿⠟⠉⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⢻⣧⡏⠀⠙⠛⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠈⠃⠈⠛⠒⠾⠟⠁⠀⠀⠉⢹⡿⠶⠛⠉⢹⣿⣿⣿⣹⣆⠀⠀⠘⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣾⣷⣄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠏⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⢰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡉⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢯⣷⢤⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⠿⣿⣦⡄⠀⠀⠀⠀⠀⠀⡾⢋⣸⡿⢸⣿⣿⣯⣤⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣾⡿⠿⣤⣄⠀⠀⠀⠰⡀⢾⣿⢷⣾⣿⣿⣿⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣤⣄⠀⠈⠫⣁⡀⠀⢬⣻⣶⣤⣶⠀⠀⣾⣿⣄⣿⣿⣛⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣶⣮⣭⣿⣶⣿⣿⡿⣿⣷⡀⢹⣿⠁⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠈⠈⠉⠋⠉⢹⠟⢠⠏⠀⠙⣶⣼⠆⠀⠀⠀⢀⣤⣦⠀⠀⢀⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠠⠛⠀⠀⢠⣿⠃⠀⠀⢠⣾⣿⣿⣿⡄⢠⣾⣷⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠀⢀⠚⠁⣠⣤⣴⣿⣿⠟⣡⠈⣽⡿⡿⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⠞⠀⣼⣿⣿⣿⠿⢧⠀⢹⣴⣿⠛⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⢺⣿⣿⣿⣿⡂⣤⣠⣼⣿⡿⠴⠦⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⣸⡿⢿⣿⣿⣿⣿⣿⣿⣿⢷⡀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣉⣴⣶⣤⣤⣬⡛⡻⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠒⠉⠉⢹⣿⠿⣯⣾⡿⠋⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠈⠓⠋⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑