Bloom Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡴⠂⢠⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠄⠀⠀⠀⠈⠁⠀⢀⠠⠀⠀⠴⠆⠈⠐⠀⢀⠘⠀⠀⠀⠖
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠠⠧⠀⠁⠀⠀⣐⡄⠀⢠⠄⢈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⡌⡀⠀⠀⢀⠀⠀⣂⡀
⠀⠀⠀⠀⠑⠀⠆⠀⠠⠀⡄⠚⠀⠀⠧⡀⠄⠁⠀⢀⠀⠂⠀⠀⠀⢀⡀⢀⠀⠌⠀⠀⠬⡆⠠⠀⢐⠀⠃⠀⠄⠆
⠀⠀⠀⠀⢉⠀⠬⠀⠐⠒⠒⢢⠀⠄⠉⠂⠀⣠⡁⠀⠤⠐⠈⢐⠀⠠⢄⡀⠁⣀⣆⠠⠀⠀⠀⠉⠙⠁⠁⠀⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠃⠀⢀⠤⢰⡀⠈⠀⠄⠀⢀⠬⠯⠠⠀⢢⠀⠈⠁⡋⠈⠁⣂⣀⠀⠀⠘⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠅⠂⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠈⠀⠀⠄⠠⠤⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⡕⠀⠀⡀⠀⢀⠀⠀⢀⠀⠀⠀⠉⡀⠀⠈⢲⠂⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣃⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⢸⡟⡼⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣽⢿⣟⠐⠂⢴⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡎⣿⠁⠷⣟⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡶⠚⠙⠻⢇⣴⣛⣯⣭⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⣰⣿⡿⣿⠇⡄⠀⢡⡌⠉⠛⠻⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠄⢠⣿⣯⡗⠀⣹⣄⣓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢧⡟⠀⢀⠟⠋⣴⣶⡿⡷⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄⠀⠀⣶⣆⡾⠶⠷⠄⠛⠋⣐⣘⣉⣀⠈⠉⠹⣿⣿⣶⣯⡻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⣿⣹⣷⠆⣿⣟⡈⣚⠀⡈⠁⡀⠙⣿⣿⣭⣛⣷⣄⠀⠙⠻⠿⢿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢀⡀⣶⠿⠋⠤⢀⣹⡷⠋⠉⢀⣀⡘⣇⢯⣀⢀⣰⡅⠀⠈⠻⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣛⠛⢆⡀⠂⠀⣧⠀⢻⣿⣦⣿⣦⣟⣿⣯⠝⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⠿⠿⠸⢎⣷⣴⢖⠏⠀⠀⠈⠉⠈⠻⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣭⠻⢏⡤⠶⣚⣿⣯⠿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⣻⣿⠿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⠀⣴⣶⠿⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡠⣴⠛⣥⡟⠁⠀⠀⠀⠈⠁⣟⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢹⠏⠛⠋⢫⡤⠒⠀⢈⠂⢀⢀⡀⢀⣀⠀⠸⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣦⣶⣆⢘⣿⣀⣰⡅⢀⣿⠿⠿⠏⠁⠀⠐⠮⢩
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠹⣿⣿⡿⣿⠿⠿⣷⢿⡋⠀⢶⣶⣧⣥⣤⡶⡙⢢
⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⢀⠀⠟⡏⢰⢸⣄⣤⡷⢚⣿⣿⡜⠿⣿⣿⣿⡟⢀
⠀⠀⠀⠈⠉⡙⠂⣧⠀⠸⠞⠀⠀⠀⢸⡀⣿⡸⣦⣾⡅⠁⢸⠐⣿⣿⢿⠷
⠀⠀⠀⠀⠀⠀⠀⢹⣆⣰⣇⡀⠀⠀⠀⢁⡘⢷⡛⣿⣧⢰⢿⣷⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠉⠉⡄⠀⠀⠀⠀⠀⢀⣀⣴⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡠⠄⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⢀⣿⣇⡀⠈⡁⠀⠀⠀⠀⠠⣽⣿⠿⣿⣻⣦⣴⠾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⣀⢀⣹⣤⡴⠤⠄⠀⠀⠀⠀⠀⣴⠻⢖⡻⣫⣟⣁⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣰⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⠠⠘⠛⠻⠻⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢀⠹⡏⠉⠳⡀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠡⡀⠀⠈⢦⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠙⠀⠀⠠⢀⠀⠈⠀⣀⠀⢣⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠
⠀⠀⠀⠤⠐⠀⠐⢈⠈⠇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠙⠢⣧⣠⠁⣀⠴⠦⠤⠄⣀⠀⠀⣶⢴⠏
⠀⠀⠀⢀⠄⠈⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡞⠁⢠⠀⠀⠀⠀⠢⠾⣷⣄⣀⣀⣀⣐⢛
⠀⠀⠈⠀⠀⣶⢋⡄⠀⢠⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠂⠀⠀⠀⠀⠀⠀⠀⠈⡿⣿⣷⣾⠮⠋
⠀⠀⠀⠀⠀⠠⠀⠩⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢷⠐
⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠑⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠶⢦⡴⢶⣖⣛⠛⠉⠙⠛⠛⠳⢦⣄⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠹⡆⠀⠀⠀⠀⠀⠉⢷⡀⢠⠾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣩⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠙⢣⠠⢤⣤⣤⣄⡀⢻⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣴⡟⣹⠞⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠸⣄⡀⢿⠀⠀⠙⠾⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⣾⣥⠟⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⠙⣻⣇⣀⡀⠀⠸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣼⠏⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⣤⡾⠋⣀⣠⣤⠖⠲⣌⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⠛⠉⠉⠉⠀⠀⠀⠈⠙⢦⡙⢦⡀⠀⣠⠄⠀⠀⠠⡄⢀⡼⣡⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠾⠻⣦⠱⣴⠃⠀⠀⠀⠀⢹⠏⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⢴⠤⣤⣤⣀⡀⠀⠀⠀⠀⠈⢳⡉⡄⠀⠀⠀⠀⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⣀⠀⠀⢻⡜⡄⠀⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⡀⠀⢿⣰⠀⠀⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⡇
⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⢀⠀⣤⣄⣀⣀⠀⠀⠈⠀⠀⠀⠀⠈⢣⡀⠀⢇⢇⡀⠻⠒⠂⠀⠀⠀⠀⠀⠀⣠⡶⠊⠉⠀⠀⣿
⠀⠀⠀⠚⢏⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠂⠈⠉⠀⢀⠀⠛⠒⢤⣀⠀⠈⢷⡀⠸⡘⢻⠆⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠉⠓⢿⣍⡉⠙⠳⣤⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠓⢦⠘⣧⠀⠇⢸⡄⠀⠀⠀⢀⣤⠋⠀⠀⠀⠀⣠⡄⠀⠀⢠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣼⡄⢸⠈⡃⠀⠀⣤⠎⠁⠀⠀⢀⢀⠞⠁⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⠐⣦⣀⣀⠀⣤⣀⣰⡶⠛⠛⠉⠀⠙⠷⣄⡀⢳⠀⢰⡇⠀⠀⡀⠀⣸⠋⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⡀⣿⠀⠀⠀⠹⣮⠃⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠉⠉⠙⠿⣄⣀⣀⣠⣉⡀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠙⠳⣄⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⠙⢦⣸⢦⣷⣤⠶⠞⠛⠛⠙⠛⠶⣄⠀⢀⣀⣀⣀⣀⠈⢳⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠛⠉⠉⠉⠉⠉⠉⠛⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡴⠞⠁⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠁⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢤⣰⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣴⠤⣝⣋⠩⣙⣻⠇⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⡇⠀⠀⠀⣴⠒⢦⣄⠀⠀⣰⣿⠀⣿⡀⠿⠃⢀⣼⢿⣔⢇⡦⠞⠁⠀⠀⠀⠀⠛⠷⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠻⣄⣀⣴⡟⠀⠀⠈⣳⡾⠃⠹⣧⣌⠙⠳⣤⡏⠁⠀⠹⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⠀⠀⣼⠋⠀⠀⠀⠀⠙⢷⣄⠟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣀⠠⠤⠤⣀⣾⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⡴⠶⠤⠶⢤⡀⠀⠀⢀⣤⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠋⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠘⡇⠀⢀⣴⠏⠀⣠⡴⢶⠉⠉⠀⢀⡿⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣠⡤⠤⠤⠚⠋⠁⢀⡼⠋⠀⠘⠳⢄⣀⡼⠃⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠷⢦⣄⣀⣀⣴⠞⠉⢩⠟⠁⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠦⣄⣀⠀⠀⠀⠀⠀⠀⢈⣽⠟⠁⠀⠀⣠⡶⣿⠖⠴⠶⠛⠛⡉⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠀⠋⠉⡜⠁⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠷⣤⣀⣀⣀⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⠉⠉⠉⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⣀⣀⣠⡶⠏⠥⠤⠤⢤⣬⡽⢶⣤⣀⣀⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣋⡙⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⡶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡙⢿⣡⣌⣷⡀⠀⠀⠀⣤⣤⣤⣸⣿⠀⠀⠀⠈⠉⢨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣁⣨⣿⣿⢠⡴⣞⠭⠃⠁⠀⢁⣀⣠⣶⣿⣿⣿⣿⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⡿⢿⣇⠀⢀⣀⠤⣾⣿⢿⡟⠿⣯⣿⣿⣇⠀⣿⣍⣿⣛⣡⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡀⠘⡇⢰⣿⣿⣟⣡⣾⣿⣽⡟⠙⠷⠿⣿⣿⣿⡟⢠⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⡿⠛⠟⢿⠛⢿⣿⣿⣿⢏⣡⣤⣄⠘⢿⣿⣿⣿⣿⣿⣿⡐⠰⠄⠀⠘⠙⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣼⣿⢿⣿⣿⣩⣦⠀⢘⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠿⠛⠛⣻⠟⠉⠙⠻⠿⠿⠿⠿⢿⣾⣿⣿⣿⠃⠀⢀⡀⣀⣠⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠚⠃⣁⣠⣀⠀⠀⢀⠀⠀⠶⠶⢾⣿⣷⣿⣿⣄⡀⢈⠁⠈⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠏⡙⠛⢷⡾⣟⢿⠷⣦⣄⠀⣿⣿⣿⣿⣿⠓⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠦⠀⠀⠀⠀⡀⠉⣀⡀⡉⣿⣿⡟⠉⡿⢻⣏⠙⢦⣤⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⠀⠘⠀⠀⠀⣠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠛⠆⠀⠀⠀⠀⣀⡤⠶⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣉⣉⠑⠦⢄⠀⣼⣿⡏⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣴⡾⠋⣰⠟⢀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⡉⠁⠀⣠⠴⠀⣿⣿⣷⣾⠏⣿⣿⣇⣤⣤⡶⠂⠀⣿⣿⡇⠀⠸⠇⡀⢨⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⠀⠀⢸⡿⠀⢀⣿⣿⣟⣳⣷⣿⣿⣿⠋⠉⠁⠀⢸⣿⢇⠀⢰⠏⣼⢡⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠈⣧⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⢸⣿⠷⡀⣼⡗⣋⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡏⢹⣷⣥⡂⢙⣿⣎⣻⣿⣿⣿⣿⡿⣿⠿⣧⠹⣿⡄⠸⣿⡎⠠⣿⡶⣅⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣿⢷⣄⣸⣿⣷⣿⡧⠾⣿⣿⣿⣿⣿⡟⠀⣿⠀⠈⠀⠹⣿⡆⠙⣿⣼⣿⣷⣿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣾⣿⣿⣿⣿⣿⠿⠿⠏⠉⠉⠁⠀⠀⠀⢀⣶⡢⢰⣿⣿⣤⡸⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡿⠿⠟⠋⠹⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣾⣿⣿⡇⢸⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣭⡙⠻⠦⣄⡀⠉⠿⠿⢿⣿⣧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣶⣄⠈⠙⢿⢶⣄⠀⣿⠙⢿⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⡌⠹⣷⡀⠀⠀⢹⣧⠀⠀⠀⠙⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡂⠈⢻⣶⠀⠀⢸⡆⠀⠀⠀⠈⣿⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣄⡘⣿⣿⡄⠀⢯⠀⠀⠀⠀⢹⡷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⡈⠻⣿⣄⢸⣆⠀⠀⠀⢸⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣯⣿⣿⣿⣦⡀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟⠉⠙⠻⢿⣷⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⡬⠀⠠⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⡼⠧⣀⠀⡵⡖⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣐⠂
⠀⠀⢠⠄⣄⠀⠀⠀⠈⠀⢀⡀⠁⠰⢒⠀⠀⠀⠀⠀⠀⠀⡱⠁⢈⠃⠒⡄⣹⣤⡗⠋⠦⡂⠀⠀⠀⠀⣠⠀⠀⠀⡠⢤⠧⣄⡡⠔⠋⠙⢺⣄
⠀⢐⣁⢠⠀⢄⠀⠀⠀⠸⣸⣁⡎⠀⡸⠀⡐⠀⠒⢀⠀⢸⡇⠀⢀⠀⢰⣾⠋⡎⠹⣄⡠⠇⠤⢢⠀⠃⠁⠀⢂⣸⠀⠀⠀⢸⠃⠀⠀⠀⠀⣸⠀⡀
⠀⠣⡑⠄⢁⡢⣄⠀⣀⣶⢿⣥⣇⡠⠀⠀⢂⠀⠘⢄⠀⠈⢳⣀⣠⡤⠺⢃⠌⣀⣤⡞⣆⠀⠀⢨⠀⠀⠐⢸⠟⠁⠀⠀⢔⠸⡄⠀⠀⠀⢰⣁⠚
⠀⠀⢿⡃⠶⢽⣣⣲⣷⠾⠶⠒⠊⢀⠀⠀⠂⠀⠀⠀⠑⠂⠈⠻⣵⣷⣴⣯⡔⠋⠁⠴⠁⣀⠔⠁⠀⠀⠀⠀⡳⣌⡢⣤⣘⢦⠀⢀⣄⣠⡾⠁⡀
⠀⠀⢀⡀⠄⠀⠜⣿⢿⢄⠀⠀⣢⡄⠅⠠⠀⠀⠀⠀⠀⢀⣤⢾⠛⣽⠛⡟⠿⠻⡟⢧⡁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⢲⡿⠟⢿⡿⠿⠥
⠀⠀⠀⠁⠀⠾⣠⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⡇⠀⠈⠉⠙⠋⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⡸⠋⠋⠁⠀⠈⡇⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠁⠀⠀⠀⠀⠀⢀⠐⠀⢀⡀⠈⠁⠀⢀⢿⡒⣒⠉⠀⠀⠀⡖⡄⠠⡇
⠀⠀⠀⠀⠀⢀⠀⢀⣀⠰⢤⣶⡄⠈⠀⣦⠞⠁⠶⠶⠏⠠⣦⣀⠀⠶⠶⠋⠲⠿⠛⠻⠦⠙⠀⡀⠶⠶⢄⠠⡶⠶⠶⠶⠶⣶⢆⠰⢶⡄
⠀⠀⠀⠀⠀⠀⠓⣄⠉⠠⡀⠙⠻⡀⠀⠈⠻⡄⠀⠘⢦⠀⠀⠉⠁⠂⠀⠀⠀⠀⠁⡟⣅⠀⠀⠀⠀⠐⠊⠁⢃⠀⡀⠀⠈⠉⠆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠋⠣⠀⠀⠈⠀⠣⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠙⠛⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠀⡤⠄⢁⠀⠀⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢈⠀⠀⣁⡀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣘⣃⣰⣀⣀⣈⣁⣖⣀⣀⣁⣼⣇⠀⠀⣴⣶⡄⠀⠀⠀⣀⣐⠲⠤⢤⡄⠬⣦⡀⠀⠀⠘⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠿⠿⠟⠀⠠⠌⠀⠀⠀⠀⢉⠤⠇⣠⠋⠄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠐⠁⠀⠀⠀⠐⠁⠀⠐⠁⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⡠⣱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠤⣀⣶⣾⣾⡅⡲⠇⢀⣀⡴⠀⡠⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠒⡹⢿⣿⠿⠋⠐⠀⠀⠙⠀⡜⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⣀⡴⠉⢧⡖⠘⠂⠀⠀⠔⠀⢳⣀⣤⡤⠂
⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⣀⠀⡎⠀⠀⠀⠀⠘⢄⣀⠀⠀⠃⢀⡜⠁⠀⠀⠀⢀⡀⠀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠐⢄⠎⠈⠑⢌⠀⠀⣀⣀⠀⠘⠘⣆⢀⠔⠋⠀⠠⣎⠀⠀⠀⠀⠨⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠁⠀⠀⠀⠀⠈⠓⠒
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⢰⢇⠀⠣⢀⡴⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠋⠙⠄⡑⢺⠁⢠⡀⠀⡴⠀⢠⠎⠁⠀⠀⠀⠀⠀⠊⠡
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠢⣄⡨⠓⠠⢀⡉⠁⠀⣰⠋⠀⠠⢄⠀⠀⠀⠀⠠⠀⠐⡠⠒⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠈⠁⢋⡏⠀⠔⠠⢪⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠈⠦⣠⠄⠼⡤⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⡀⠀⠀⠐⠀⠀⠀⢳⡀⠐⠤⣸⡴⢀⠀⠒⠛⠴⡒⠓⠆⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⣠⠞⣡⠐⠀⠀⠂⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠁⠀⠀⠀⠀⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢐⡀⠀⠁⠐⡦⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣸⣯⡜⣓⡺⢷⣦⣫⣶⣦⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣶⣿⠿⠋⠉⠙⢾⡷⠛⠿⡄⡴⣁⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠏⠀⠀⢀⠔⣰⣤⣠⣤⣂⣞⣿⠟⠈⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡰⢶⣶⣴⠷⠾⣟⣿⣿⣿⣿⠟⣡⠶⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⣀⣈⣛⣻⣿⣿⣿⡟⢏⡋⠉⠀⢠⣞⣥⠖⠀⠀⣠⣠⢄⣴⣷⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠳⢦⣘⠋⠉⠉⢀⡼⠟⠽⢦⣉⡉⠓⠈⠙⢀⣀⣀⡈⠛⠁⠈⠉⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⣤⣀⣀⣀⣤⣀⡀⠈⢧⠀⠀⠀⠘⢿⣷⢂⣤⠞⠉⠁⣠⣴⠴⠒⣲⠖⠋⠁
⠀⠀⠀⠀⠴⠛⠛⠛⠿⠭⣴⡆⠀⠀⠀⠀⠈⠙⠺⢦⡀⠀⢀⣼⣿⣋⣁⣤⡒⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣶⣶⡶⡞⠚⠙⠻⡟⠉⠁⠀⠈⠉⠁⠀⠀⠈⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠉⣞⡥⠞⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣃⠴⠚⠁⠀⠀⠀⠀⠀⡰⠀⢀⣀⣠⣠⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⡠⠷⠛⠛⠛⠋⠉⠁⠉⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠢⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠰⣾⢿⠃⢠⡈⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠠⠤⢄
⠀⠀⠀⠀⠀⠂⠀⠀⠇⠀⢧⠀⠀⠠⠈⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⠖⠒⠢⠄⣤⡁⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠓⠐⣆⠀⠀⢀⡀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠶⠀⠀⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠃⠀⡀
⠀⠐⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡴⠀⠐⠂⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⢄⠊⠄⠚⡑⠀⠀⢤⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢸⡄⢠⡀⢀⣐⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⡒⠑⠤⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⣀⠀⠀⢄⡀⣀⠀⠸⣿⣿⣿⣦⠄
⠀⠀⠀⠀⣀⣀⣤⠂⠤⡀⠀⠀⠀⡀⢀⡀⢘⡿⠀⠀⠀⠀⠀⡀⠀⠁⠑⠉⠻⣿⣶⣶⣷⣦⡗⣶⢦⡤⣾⣦⡂⢤⢄⣠⣠⢤⣤⣤⡐⣤⣤⣤⣄⡤⣴⣶⣿
⣿⣾⣿⣿⣿⣿⣿⣯⣖⣤⣷⣶⣤⣶⢾⣿⢾⣗⣿⣷⣶⣶⣿⣿⣶⡦⣮⣿⣟⣝⣿⣿⣿⣿⣰⣮⡿⢽⣿⣿⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣧⣜⠿⣿⣿⡿⠿⣋⣙⣻⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠛⣻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣴⣿⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣇⠹⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⣋⣭⣍⠀⠀⠈⢿⣆⠀⠻⣶⡟⣄⣴⣾⣄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣠⣀⣤⣴⣷⣿⣿⣿⣿⣿⣿⡌⠑⠦⠀⠀⠀⠀⠀⠘⠿⣮⡁⠈⠉⠙⢦⣤⣴⣿⠿⠷⣶⢤⡀⣀⡼⠛⠛⢷⠄
⠀⠀⠀⠙⠋⠳⠈⠻⠿⢉⣤⣿⣿⣷⠀⠀⠀⠀⢀⣠⣤⣴⡆⣄⡀⠁⠐⠂⢠⣌⣀⡁⠀⠀⣠⡶⣿⣿⠙⠄⠀⠀⠀⠙⠓⠤⠴⠶⠶⣤⡀
⠀⠀⠀⠀⠀⢴⣶⠿⣆⠈⠻⢿⡏⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡊⠛⠷⠀⠀⠀⠉⠉⠉⠁⠈⠁⠀⢀⣾⠀⠀⠘⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠙⠷⣶⣶⣿⣿⣿⣿⢛⠽⢿⣷⣾⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠙⢿⣟⠈⠁⠎⠀⠼⢻⣿⠿⢻⡃⠀⠀⠀⠀⠠⣴⣿⣿⡙⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠰⡚⠀⠈
⠀⠀⠀⣶⣤⣄⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠶⠀⠀⡴⠃⠀⣤⣀⣠⣄⠀⠀⠀⠀⠀⠙⢫⣷⣤⣄⠀⠀⣿⣿⣿⣿⡞⠉⠈⠁
⠀⠀⠀⢿⡿⠿⠷⣿⣶⣦⣀⣄⠀⠀⠀⣼⣧⠀⠀⠀⠈⠀⠠⢖⣼⣿⣿⢯⡿⠷⡀⠀⠀⠀⠀⠀⠉⠙⠀⠀⣴⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢄⠀⣿⣿⣿⣿⣿⣷⣾⣦⣿⣿⣆⣾⣦⠀⠀⠀⠀⡈⠙⠻⠧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⠆⣀
⠀⠀⠀⢤⣤⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡴⣄⠀⣾⣿⣴⣆⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣴⣶
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠙⠿⢿⣿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣦⣿⣿⣿⣿⣴⣦⠀⢠⣄⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣯⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠁⠈⠙⠛⠛⠛⠶⠿⠿⠅⠀⠀⠰⢷⣴⠿⠟⠋⠙⠛⠻⠿⠿⠟⠉

⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢳⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣾⣿⣿⣶⣶⣶⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽
⠀⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⣸⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢠⡿⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣶⣾⣿⣿⠿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⠁⡼⡄⠀⠀⠀⠶⣶⣶⣶⣿⣟⠉⢿⣿⣏⠁⡀⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣦⡀
⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠉⡁⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠿⡿⠿⠟⠉⠙⢹⣷⣴⣄⣤⣄⡀
⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠟⠁⠀⠀⠉⢻⣿⣿⣶⣤⣶⣾⣦⣶⣶⣿⣿⣿⠛⠉
⣤⡿⠜⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣽⠟⣿⣶⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⠋⠘⣿⡏⠙⢻⣿⣿⣿⣄⣠⢾⣿⣦⣴⡿⣿⣿⣿⣿⡿⠛⠿⣿⡳⣿⣿⡇⠀⠀⠀⠀⠰⣼⠆
⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠛⢳⣿⣷⣦⣬⣿⢤⣞⢻⡿⣹⡿⡷⣴⣿⣶⠿⣸⣽⣿⣛⣿⣤⡰⣴⣾⣹⠾⣟⠅⠀⠀⠀⠀⠘⣿⣦
⣊⠀⠐⡇⠀⠀⠀⠀⠀⠀⠈⣀⣄⣤⣿⡿⣿⡯⢿⠛⠿⢾⣿⣾⣄⠠⣽⣻⣯⣿⡿⠟⢫⣮⣻⡿⠟⣽⠿⠶⣷⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀
⡟⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⡿⠼⣿⠳⢦⣤⣀⣘⣻⣿⣿⣿⣿⡿⣿⣵⣰⣾⣿⠿⠩⣦⡴⢿⡾⡘⢻⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⢗⡉⢱⣂⣯⣵⣶⣽⡿⠿⠟⣻⣿⣿⣭⣍⣛⠛⠿⣷⣿⣖⣛⣿⣉⣹⣓⡋⢹⡷⠀⠀⠀⠀⠀⠀⠀⠘⢿
⠀⣾⣿⡇⠀⣤⠀⠀⠀⠐⢿⣷⣿⠷⠟⢫⡭⡟⠁⢤⣶⠖⠀⠻⠿⣿⣿⣿⣯⣤⡀⠀⠉⠉⣿⣿⣻⣿⣿⣷⣾⣷⡦⠀⠀⠀⠀⠀⠀⠀⠈
⢰⣿⣿⢂⣾⣿⠀⠀⠀⠀⠘⠿⢿⣷⢶⣿⣿⣥⣤⣜⠋⣴⣶⣾⣿⣿⣿⣿⣯⣿⡿⠈⢻⠲⠛⠚⠊⢻⣼⣿⠿⠟⠂
⣼⣿⡿⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⣿⣯⡻⣧⣶⣿⣿⣿⣿⣿⠏⠉⠉⢀⣀⣀⣈⣁⣶⣶⣷⠟⢟⣡⡀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⣿⢿⡟⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⣾⠯⢽⡿⢫⣷⣿⠟⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⣄⣿⡄
⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠉⠀⠶⠀⠀⣿⠀⠛⣿⡿⣻⣿⠋⡘⣿⢿⠉⣿⣧⣶⣞⠋⣿⣿⣿⠀⠚⠉⠰⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇
⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠿⠆⠀⠠⠄⣿⠀⣠⣼⣿⣿⣿⣧⣇⢸⠈⠀⣿⣿⣿⣿⡟⠋⢸⣯⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⣙⠴⠿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⠓⠀⢸⡿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⢠⠁⠀⣾⣿⡇⠀⢸⣿⣿⣿⠹⣿⣿⡀⣻⣿⠟⠁⠈⠀⠀⢸⡇⠈⠉⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣯⣿
⣿⣿⣿⣿⣀⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠛⣀⠀⢸⣿⣿⣿⠀⢽⣿⣿⡿⣧⣀⣀⡤⠀⠀⣸⠇⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸⣿⣿⣿⠀⢺⡏⠋⠀⣿⣿⣿⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⠈⠛⠛⠻⠀⠘⠇⠀⠀⠈⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣰⣿⠀⠀⣨⠔⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢀⣴⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡤⡧⣶⠛⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⣿⠀⢀⣴⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣷⠠⠗⠀⠀⠀⡀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡏⡄⣋⡀⠰⠊⠁⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠜⠋⠉⢹⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠁⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠛⠛⠛⣉⠉⠀⠀⠀⠀⢀⣀⣤⣴⣾⣾⡏⣄⠀⠀⠀⢰⡄⣠⠐⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣄⠀⠀⠀⠀⢀⡀⠀⣂⣀⣠⣿⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⠟⢠⣿⡈⠒⠂⣾⡇⠀⡼⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣿⠀⢀⢤⣠⣷⠀⠀⠁⠀⣦⡀⣠⠤⠰⢦⣈⡙⣿⣿⣿⡿⣟⠿⡿⠿⣿⡟⠛⠀⠀⢼⣿⡆⠁⠋⣿⣷⠠⣤⠇⢀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢰⣧⣿⠶⠃⠀⣩⠗⠮⣂⠄⠘⡥⠈⠁⡄⢰⠈⣉⠭⠛⠩⠑⢊⠀⠊⢠⠈⠂⠒⠥⣢⡠⣀⠀⡌⠛⠜⠛⠿⡂⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠧⠊⠁⠠⠀⡠⢞⡄⢠⠀⠀⠁⡀⠀⠉⠀⠟⠃⠋⠀⠀⣀⡠⠂⠨⠂⠀⣾⡆⠐⢄⡀⠈⠉⠈⢸⠷⣦⠀⢂⠂⢘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢃⠤⢊⠁⠀⢀⠰⠀⡀⢸⡀⣆⠀⠙⠒⠁⠀⠀⠀⢠⠀⠂⠀⠀⠄⠀⣿⢠⣿⣇⠀⠂⠀⡀⠀⣁⠤⠊⠀⣦⢸⠀⢸
⠀⠀⢰⠐⡀⠄⠀⠀⡀⠀⠀⠀⠀⠁⠈⣁⣀⣀⡛⠗⠉⠀⣠⡠⠄⠀⡀⠀⣾⡆⠤⣌⣀⣀⠼⠿⠾⠟⠛⠋⠉⡉⠔⠈⠀⠀⠐⠀⡏⢸⠀⠘
⠀⠀⠸⠀⠤⡌⠒⠠⠄⠀⠉⠑⠂⠀⠿⢿⣿⡭⠿⠇⠀⠀⠂⠀⠀⠈⠝⠐⠿⠧⡈⢁⡠⠂⠅⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠀⠈⠤⢆⡀⠰⢠⣦⣤⣄⡀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠛⠿⠃⠒⠀⠀⣤⣀⢀⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠭⢃⣆⠶⠀⠀⠀⠐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢿⠏⠩⠁⠀⠀⠀⠀⠤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⢠⠄⡄⠀⠂⠈⣄⡉⠉⠫⠿⠫⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡠⠄⠰⢏⣟⣯⣒⣂⣀⡀⠘⠃⠤⢠⣤⡤⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠒⠊⠉⢠⠤⣞⣠⢟⣎⣞⣿⣶⡶⢄⠂⣠⠀⢀⠀⠀⠌⡀⠹⢎⣳⡽⢂⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢀⣀⠐⠄⠿⠟⣻⡿⡿⡿⢿⣞⢴⣏⠀⢣⢀⡒⣆⢠⢦⠁⢀⠀⢁⡵⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢠⣾⣽⣿⣷⡁⢪⢼⡟⣙⣗⣯⣿⣄⠛⢀⡀⢾⠘⠢⠌⠻⣃⠂⢉⠟⠒⣚⢁⢀⣠⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣭⣾⣼⣿⢾⡿⠿⣷⡽⢃⢋⡟⣉⡤⢻⠧⠈⢳⣄⣠⡀⣥⡄⠁⠀⠀⣁⣠⢿⠁⢐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⡹⡾⣿⣾⣏⣯⠸⣿⣣⢁⣸⡟⠡⠆⠀⠲⡀⢸⠛⠾⣛⠚⣷⢀⡀⢦⠘⣧⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⡿⣷⣿⣷⡿⣳⣾⢋⡔⢁⣀⠤⠒⠒⠒⠶⣭⣿⠀⣃⣼⣙⣿⠟⢦⣈⡿⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣭⢷⣺⢹⠟⣷⣿⡷⣯⣴⣿⠁⠀⠀⠀⠀⠀⠘⣷⣦⣮⡘⠺⣏⡔⡐⣾⣛⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡭⢽⣋⠿⣬⣻⠿⣿⣽⡿⠀⠒⠀⠀⠀⠀⠀⢻⢋⣢⡑⢾⡋⠞⢻⠯⣁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⣿⢿⣿⣿⠾⣾⢽⡼⣿⡏⠁⠀⠁⠀⠀⠀⠀⢀⣿⡘⠷⣻⠮⢯⡟⢛⠒⣅⣐⣋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣟⣿⣟⣛⡾⢺⣿⠇⠀⠀⠀⠀⠀⠀⣀⣼⡿⠉⣻⠆⡜⣦⣌⡿⢉⠀⢿⣧⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣤⠀⠀⠟⡷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣼⡅⢾⣷⢄⣿⡷⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠿⣾⡇⢆⣱⢸⣿⠀⠀⠀⠀⠀⡠⠂⠀⠐⠿⢿⣿⣾⣻⡫⠫⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢹⢟⢻⡄⠀⠀⠀⠈⠀⠀⠀⠀⠘⣷⡿⣿⣧⠧⢘⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⠸⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣏⣔⣁⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣉⣻⡟⠦⣄⣀⠀⠀⠀⢀⣷⡀⣀⠔⢹⢹⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢄⡿⣉⣙⣿⣙⡿⢋⣻⣿⠤⠧⢜⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⡟⠁⣠⠸⢿⡮⣌⠈⠑⣦⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼⠁⠄⣮⡀⠁⠳⢄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠁⠀⠉⠒⠒⠚⠛

⠀⠀⠀⠀⠀⠀⠐⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⣶⠀⢀⢈⠀⣠⣾⡇⠀⠀⢀⡀⠘⠠⠖⠁⠤⠒⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣴⣶⠆
⠀⠀⠀⠀⠐⣆⠀⠀⠀⢹⡟⠀⠐⡆⠈⠙⠁⠀⣠⢈⣇⣉⡉⠁⠁⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⣘⠠⠴⠾⠛⠁
⠀⠀⠀⠀⠀⠻⣷⣮⣤⡞⠉⣶⠀⠀⠀⠰⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁⣦⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⢩⠒⢲⠈⠁⠀⠘⢀⠋⠀⠐⠢⠄⠀⠀⣀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠂⠈⠓⠋⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠓⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠉⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠑⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣂⣀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠠⣤⡀⡀⠀⠈⡆⠀⠀⠀⠀⠠⠂⠀⢀⢰⢃⣊⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢴⠠⣤⣤⣠⠀⢰⣿⠃⠀⠀⠀⠀⠀⠘⣳⣷⣦⡀⠘⠀⠀⠀⠀⠈⠀⠰⠈⣼⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠐⣻⡿⠷⣇⠀⠀⠀⠀⠄⠀⠀⠰⠃⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣿⠀⠁⠀⠐⣴⣿⣦⠄⠁
⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⢀⣠⣴⠶⠶⠒⠂⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠁⠀⠀⠀⠀⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠐⣴⣦⠀⠀⠰⠂⣀
⠀⠀⠀⠀⠈⠈⠂⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠼⠖⠀⠈⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠙⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡇⠈⠉⠀⢠⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⣄⠀⣿⣿⣏⡄⠀⠀⣾⣿⣿⣿⣿⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢀⢻⣦⣿⡏⣽⡇⣴⡷⣽⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣌⠿⣷⣴⣝⠿⡟⣭⣿⡟⢡⣷⣮⠻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢩⢔⣿⡾⠿⣷⣿⣿⣿⣿⣇⢹⣷⣿⢦⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡉⢙⣷⣿⡿⠿⣿⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣜⣀⣀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣟⣴⣾⣾⣿⣻⣿⣿⣿⣿⠏⠉⠉⢻⡀⠀⠀⠁⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⡿⣿⢿⣟⣿⣏⣾⣿⣿⣿⠀⠀⠀⢸⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⠀⢠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣿⣄⠉⠙⢿⣿⣿⣿⡿⠋⠙⣠⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⠟⠛⣶⣧⣹⣿⣿⡤⣷⠞⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⣿⠏⠉⠉⠀⠈

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠀⢲⣾⣿⣿⠀⠙⠈⠙⠃⠀⠐⠂⠀⠀⠐⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠂⠉⣼⣿⠷⠠⡀
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠀⠁⠏⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣿
⢠⠆⠁⠀⠈⠁⠆⠀⠀⠀⠀⠶⢆⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠂⠤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡘⣠⣾⡯
⡉⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠐⠒⠂⠰⠉⠀⠀⠈⠢⠀⠀⠀⠀⠢⠀⠀⠀⠂⠉⠀⠐⠀⠀⢀⡀⢀⣤⣀⣰⣤⣤⣀⣴⣿⣿⣏
⠀⠀⠀⠀⡁⠀⠀⢀⠀⡀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠓⢦⡔⠙⠉⠃⠀⠀⣀⡀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⢿⣿⣿⣿⣥⣤
⣄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠘⠖⠦⠀⠀⠀⢀⡀⠀⠀⠠⢿⣿⡏⠻⡿⢿
⠀⠁⠀⠀⠀⠐⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠁⠀⠀⠀⢀⣿⡏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⣄⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠠⠄⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣿⣧⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡆
⠀⠀⠀⠀⢸⠒⠤⠤⠀⠀⠡⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡆⠀⣸⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠊⠉⠹⠦⠠⠀⠀⠀⠀⠠⠤⣼⣿⣿⡇⠀⣿⣅⣠⡤⡀⠐⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⢤⡼⠿⢿⣿⣼⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⢡⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠈⠃
⠀⢁⠀⣦⠀⠀⠀⠀⠀⠒⡄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⣒⡾⠛⠋⠿⣇⠐⠂⠀⠀⠠⢤⡀⠀⠀⠅⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠉⠉⠷⠀⢀⠐⠁⠀⠀⠀⠀⠀⠂⠤⠤⠤⠐⢢⠟⠉⠔⠃⠄⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠓⡄⠀⠀⠀⠀⣀⣠⣀⡀⡃⠀⠀⠀⠀⢀
⢀⡤⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠉⠉⠛⠿⠿⠤⢄⣀
⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠑⠒⠣⢤⠠⠤⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⠀⣤⠀⠆⠀⣠⣶
⠀⠀⠀⠐⠆⠢⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠸⣧⢀⣽⣶⣶⣾⡟⠋
⠴⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠰⠃⠀⠀⢀⣠⠎⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠉⠁⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢀⣀⠀⠀⠀⠈⢻⣿⣧⢘⢀⠀⢀⣠⣿⣿⠋⠀⠀⠀⠀⠀⢀⠀⢐⠟⠩⠙⢢⡀⠄⢀
⠤⠀⠐⠁⠀⠃⠀⠀⢄⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠈⠙⠢⡀⠀⠈⠻⣿⣿⠻⠀⣸⣿⣟⡡⠊⠁⠀⠀⠀⠀⠀⠁⠌⠀⠀⠀⠀⠈⠑⠒⠠
⠀⠀⠑⠀⠀⠀⠀⠀⠀⠰⠀⠀⡁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣶⣶⣬⣉⡀⠢⢜⣿⣟⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠁⠀⠀⠀⠒⠋⠉⠉⠹⠛⠛⠛⢻⡿⢿⠁⣠⡔⢫⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⡴⢶⡽⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠄⢀⡀⠀⠀⠀⢀⣠⣠⣀⡀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠀⢀⣼⢇⡄
⠀⠀⠀⠀⠨⠵⢞⣳⡟⠻⠂⠀⠀⠀⣠⣀⣤⡀⠀⠀⠀⠈⢢⣄⣠⡄⠃⠀⠀⠀⣿⣿⡟⠁⠀⣀⣾⣿⢋⠈⠀⠀⠀⠀⠀⠀⠐⣯⠁⡄
⠀⠀⠀⠀⠀⠀⠁⢻⠀⠀⠀⠀⠀⠰⣿⠿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡇⠠⠔
⠀⠀⠀⠀⠀⠀⠀⡎⠰⠃⠀⠀⠀⠈⢾⣿⣽⡞⡗⠀⠀⠀⠀⢲⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⢀⠀⠀⠀⠀⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠉⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⣤⠀⢘⣦⠾⠁⠀⠠⠐⣦⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⢠⣤⢞⠀⠀⢀⠈⡄⢠⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠔⠋⠀⠊⠀⠀⠀⠀⠀⠀⠅⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡟⠋⠉⠁⠀⠀⠈⠀⢑⡺⡍⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡇⠀⠀⠀⠀⠀⠈⠰⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⢀⡄⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣨⠁⣉⠀⠀⠀⣶⡶⠀⠀⠀⡇⠀⡿⠋⠁⠀⠀⠀⠀⠀⠀⡀⢉⠀⠀⠀⠀⠆
⠀⠄⠀⠀⠀⠀⣀⠀⡦⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⡃⡿⣃⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣿⠀⠀⠀⠾⡷⠄
⠀⠂⠀⠀⠀⠀⠈⢰⡖⠚⠀⠀⠸⠿⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠉⠳⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣾⠆⠄
⠀⠂⠀⠀⠀⠀⠀⠘⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉
⠀⡂
⠀⠁
⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⠀⠀⠀⠀⠀⣤⣤⣀⣀⠀⠀⠀⠀⣶⣶⢦⣤⣤⣄⡀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡆⠀⠀⠀⢀⣀⠀⠉⠻⣿⡄⠀⢰⣿⡏⠀⠙⣿⣿⣿⣦⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡿⠂⢛⣿⣮⡛⢿⣆⠀⢸⣿⠀⣾⠟⠀⢀⡀⠹⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣛⣴⣿⣿⣿⣿⡁⠀⠉⠳⡸⣿⢸⠏⣴⣿⣿⢿⣆⢿⣿⣿⢏⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣿⣿⣿⣿⣿⡿⠁⠰⣶⣦⣜⣿⡼⢀⣿⠋⠉⣸⠟⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣹⡿⠟⢋⣀⣀⣀⣿⣿⣿⣿⡇⣼⣿⣧⣸⡏⠀⣼⠟⠛⠛⠛⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠘⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢀⡴⠋⠛⣆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣠⣤⣴⠻⣿⣿⣿⣿⢿⣿⣛⣿⣿⣿⣦⣄⠀⣸⡧⢀⠐⣿⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠞⣿⣿⣦⣀⣴⣄⠀⣸⣿⠟⣿⣿⢿⣿⣿⣿⡇⠰⢿⣿⣿⠙⣦⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠙⣿⣿⣿⣿⣿⣷⡜⣿⠀⢻⣿⣿⣿⡟⠃⢉⠶⢦⡉⢀⣸⣿⣟⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣻⣷⣼⣿⣿⣿⣿⡏⢿⡏⠀⠀⢠⣤⣤⣄⡀⠀⠀⡈⣙⠹⠛⠛⠁⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⣿⣿⣿⣿⡇⠘⢷⣞⠛⢿⡝⢿⣿⣿⣦⣼⣿⣥⡘⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠋⠉⢻⣾⣿⣿⢃⣴⣿⣿⣤⣬⢧⣤⣽⣿⣿⣿⡿⣿⣿⣦⠙⠇⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣦⣤⡈⣿⣿⣿⣿⡻⣧⡠⣥⡼⠈⠻⣿⣿⣿⠿⣿⣻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣻⣾⡿⣿⣿⣿⣿⣿⣧⠀⠀⠡⣤⣤⣤⣼⣿⣿⣿⣎⣿⣿⡿⣿⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣷⣾⣟⠿⣿⣿⢿⣿⣿⡆⠀⠀⢬⣝⡛⠿⢿⣿⣿⣿⣿⡟⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⡜⣿⠄⣿⡿⠁⢀⣴⡟⠹⣿⣦⣄⠀⠉⢻⡿⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⠛⢿⣿⣿⡟⠀⠛⣵⣾⣿⣿⠃⠀⠘⢿⣿⣇⠀⠀⣇⢸⣿⣿⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠄⠀⠈⠻⠏⠼⠿⠿⠿⠟⠃⠀⠀⠀⠀⠻⠿⠀⢸⠧⡾⢿⠿⠇⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠻⠻⠿⢩⣵⠿⡏⡟⠀⡇⢹⡏⢛⣦⠉⠙⠌⠛⠿⠟⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⠿⡻⠁⠐⠀⣰⣿⠹⣴⣗⡇⢼⣇⡟⢀⡿⠛⣿⡟⠠⠀⠀⠀⠔⠈⠟⡿⣿⣯⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⣋⣿⣿⡟⠋⠁⠀⠀⠀⠀⣟⣿⣼⣿⣹⣧⣟⡼⢁⡿⢃⣴⡿⡿⣄⠀⠀⠄⠀⠀⠀⠀⠉⢛⣿⣿⣯⡛⢛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣼⢯⠉⠀⠀⠀⢀⠀⠂⠁⠀⣿⣿⣿⣧⣿⣟⡞⣡⠟⣠⡾⠫⣺⣿⡏⠀⠀⠀⠀⠙⠦⢀⠀⠀⠀⠈⣹⢿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠙⠈⢈⠿⠋⠉⠀⠀⠈⢦⡀⠀⠀⢠⣿⣿⣿⣿⣿⣫⡾⣣⡼⣣⣾⣿⡿⢋⣷⣤⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠻⢏⠀⠐⢙⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠛⠂⣠⠴⡄⠠⠤⠤⠤⢤⣤⣤⣌⣙⣿⣿⣿⣝⢷⣾⣿⣿⣿⣯⣼⣛⣯⣾⣿⠿⢿⡇⠀⠄⡀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠨⠷⢠⡀⠙⠿⣿⣿⣿⣿
⣿⣿⣿⡧⡁⣠⣾⡉⠀⠀⠀⠠⠀⠀⠀⠀⠈⢹⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠚⢺⣿⠷⢨⣿⣿⣷⣦⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣹⣦⠀⣡⣿⣿⣿
⣿⣿⠿⠋⠡⠝⠉⠉⠀⠠⠃⠀⠀⠀⠀⠀⠀⠈⢃⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣼⠁⢀⣸⡏⠸⣿⣿⣿⣦⣀⠀⠀⠀⠀⠣⠀⠈⠈⠋⢥⡉⠹⣿⣿
⠿⢿⣤⣾⣅⡀⣀⠔⠃⠀⠰⣦⣠⣄⠠⢮⡦⠐⣿⣿⣿⣿⣿⣿⣿⡿⢿⢟⣿⣿⣿⡟⣻⠏⠁⠀⢀⣿⡇⢰⣿⣧⣋⡻⣿⣷⣄⠀⠀⠀⠈⠓⣄⠀⣀⣿⣤⣾⠿
⢀⠊⠉⠙⠓⠻⠟⠅⠀⠀⠀⠸⢿⡿⠀⠈⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⠀⢀⣰⣾⣿⠁⣼⣿⠟⣿⣯⣦⣬⣿⣷⣤⡀⠀⠀⠙⠽⠒⠛⠉⠉⢀
⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣼⡆⠠⠀⣀⣤⣶⣿⡆⢿⣿⣿⣿⣿⣾⣿⣿⣷⢿⣿⣾⠏⠀⢸⣿⣿⢟⣾⣿⣿⣿⡿⠋⠉⠉⠛⠻⣿⣻⣶⣄⠀⠀⠐
⠁⢒⠠⠄⣀⠀⠀⠀⣠⣶⠟⣁⣤⣶⣿⣿⢿⢿⣿⣿⠈⠁⠀⠀⢉⣿⣿⣿⣿⣯⣿⣿⡀⡀⢸⣿⠋⢈⣿⣿⡏⠉⠀⢀⠀⣤⣴⣄⣿⣿⠿⡻⠷⡄⠀⠀⠤⡐⠊
⠀⠀⠀⠀⠀⣀⣴⣿⣽⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣧⠀⠀⠀⠸⣿⣿⣿⣿⣿⣾⣿⣷⣷⣟⣋⣴⣿⣿⣿⣷⣶⣧⢯⣝⣿⣿⣯⣿⣿⣼⡶⠂⢿⡆
⠀⠀⢀⣤⣾⠿⠟⠛⠛⠋⠉⠉⠉⢩⣿⠛⠛⠻⠿⣿⣿⠀⠀⠀⠀⢹⡿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣣⣯⣿⣿⣿⣿⠿⢁⣶⣶⠿⣿⠀⠀⢀
⠀⢸⠙⠥⠧⠤⠤⠠⢄⠂⠀⠀⠀⢸⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟⣁⣴⣾
⠀⠘⣇⢠⡶⡶⠶⣞⣛⣲⣒⣂⢀⠔⠛⢿⣿⡽⣷⡄⠀⠀⠀⠀⠀⠘⣯⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣿⠋⣻⣿⣿⣿⡧⡀
⠀⠀⣿⣷⣶⣿⠾⠟⠿⣿⣿⣭⣤⣤⣿⠃⠀⠀⢸⣿⡄⠀⠀⢀⣤⣾⣿⣿⣿⡁⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣴⣾⣷⣿⣿⣿⣿⣿⣾⣼⣦⣤
⠀⣠⡻⣯⣿⣧⣀⣀⣀⣾⣟⣉⣬⣿⣿⠀⠀⠀⠈⢿⢿⡄⠀⢿⣻⣾⣿⣿⣿⢃⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣤⣶⣷⣿⣿⣿⣿⣿⡿⠿⣿⣿⠿⠿⠛
⠀⠙⢿⣗⣚⣒⣒⣚⣛⣓⣒⣒⣒⣚⣶⣦⠀⠀⠀⠈⠃⠈⠀⠀⠈⠉⠉⣱⣷⣯⣯⣽⣿⣿⡇⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠻⠾⠿⠿⠿⠁⠀⠀⠀⠀⠀⠉⠛⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⡀⢰⡄⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠳⢇⠄⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⢸⣧⡀⠴⣿⡿⠚⠚⣛⡯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣌⠂⠀⠀⠀⠀⠀⢁
⠀⠀⠀⣿⣿⡧⢤⡼⡂⢽⠯⢅⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⣲⠆⠀⠀⠀⠀⠀⠀⠛⠳
⠀⠀⠀⣿⠿⣷⣿⣿⣧⠻⢷⠿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⡀
⠀⠀⠀⠘⣆⠙⠋⣿⣜⢳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠐⢀⠀⠀⠠⠈⠗⡄⠀⠔
⠀⠀⠀⣴⣿⡷⣤⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⣄⠀⢀⣴⣾⣤⡿⢠⣥⠇
⠀⠀⣾⣿⣧⡉⢲⣼⣇⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⣀⠈⠉⠻⠿⠗⠰⠛⠐⠊
⠀⠀⣿⣿⣿⣿⡌⢻⣇⢻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⢉⣠⠤⢤⣤⣶⡖⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢈⠻⣿⣷⣦⢬⣋⠈⡀⠐⡄
⠀⠀⢿⠿⠿⣿⣿⠿⡿⣿⠿⠿⠿⠿⠿⠿⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠃⠀⠰⠀⠘⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠠⡐⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤⠀⠀⠀⠀⡶⠀⠀⣠⠖⠒⠁⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣀⠀⠠⠔⠂⠂⠄⢠⠆⠀⠀⠀⠀⠁⢣⠴⠋⠁⠀⠀⠀⠀⠀⠀⣠⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠲⢠⡄⠂⠀⠈⣀⡀⢀⡤⣄⠀⠁⠀⡀⢀⡀⡀⢀⡐⠀⠂⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⡇⠉⠲⠐⠀⠆⠈⠀⠠⠘⠒⠃⢄⣀⡀⠀⠈⠁⠚⣍⠙⠒⠊⠄⢈
⠀⠀⠀⠀⠀⠀⡰⠁⠉⠒⠀⠀⠀⠀⠀⠀⠈⠃⠀⠁⢸⡴⠷⠖⠀⠀⠊⠀⠀⠀⠍⠙⠲⢄⣐⠀⠰⠀⡆⠀⢄⠀⠈⠑⢆⠁
⠀⠀⠀⠀⠀⠀⠦⠀⠀⢀⠀⠀⠠⠀⢀⠀⠐⠀⠀⠀⠔⠃⠐⠀⠢⢄⠈⠀⠈⠀⠀⠀⠀⠀⠙⠀⠀⡜⠀⠀⠀⠀⠀⠀⠠⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠶⠀⠀⠀⠁⢀⡁⠔⠖⠃⠊⠀⠀⠡⠀⠀⢐⠤⣖⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢐⣀⠄⠀⠀⠀⢠⢿⡤⠓⠀⠀⠂⠁⠀⠀⠀⠀⠀⠁⠆⠃⠀⠀⠀⠀⠀⠀⡀⡄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠃⠀⠠⠄⠀⠘⠙⠀⠀⠀⡀⠤⠂⠀⠀⠢⠀⣨⠄⠈⠀⠀⠀⠀⠀⠀⡰⡠⢠⡜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠂⣤⠃⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⢣
⠀⠀⠄⠀⠀⠀⡀⠚⡓⢂⠀⢶⠀⠀⢸⣆⡤⠖⠚⠉⠣⠄⠀⠐⡱
⠀⠀⠈⡄⠀⠂⠀⠀⠀⠈⠖⠈⡤⠀⡜⠉⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡦
⠀⠀⠀⠘⢄⠀⠁⢀⠀⠈⠀⠔⠀⡘⠀⠀⢀⡠⠖⠋⠉⠐⠀⠂⠀⠀⠐⠳⣄
⠀⠀⠀⠀⠈⠁⢀⠀⠑⠀⢐⢀⠆⠀⢀⣴⣭⢀⡁⠉⠐⠄⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⢠⡊⠁⠀⠠⠀⠸⡌⠀⠇⢠⠋⠀⠀⠠⠄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢗⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠹⣆⢀⡇⠀⠀⠀⠀⠀⠀⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠆⠀⠀⢀⣀⠀⠀⠀⡀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠈⠀⣈⢰⠦⢶⠋⣱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⣀⠀⢀⠁⣾⢀⡴⢋⢀⠀⠠⠀⠐⣮⠛⢶⣦⣿⡉⢿⠁⢸⣇⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⢿⣿⠀⠀⠀⢰⣾⣱⣸⣿⣆⠀⠀⠘⢿⢦⣈⣿⣛⣿⢯⡵⠎⠉⣤⠥⡼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣇⠀⢡⣌⣿⡻⣿⣿⠏⠀⠀⠀⢘⣦⣴⡎⠉⢳⠀⣖⡀⠈⠀⠸⠯⣬⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠨⡭⠝⣻⣦⡀⠓⠌⠛⠾⠿⠿⠀⠀⣠⣾⢿⠷⢾⠲⣦⣤⠃⠋⠀⠀⠰⢇⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢈⠀⠀⢀⡴⢋⣿⡟⠦⣄⣀⣀⣠⠤⠔⠚⠁⠀⠀⠀⠀⢱⢦⣿⡆⢳⡀⠗⣀⡪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢴⣍⣠⡤⣂⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡽⠈⢠⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠉⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⣀⡈⠁⠐⢁⡐⠃⠀⠀⠀⣀⣀⣀⠀⣶⠀⠀⠻⠇⠀⠀⢘⣤⣬⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠏⠀⠀⠀⠀⢏⠙⠦⠴⠿⠉⠀⠀⠀⠀⠀⠀⢷⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⢁⡄⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠞⡀⢀⣀⣀⠀⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⣠⣾⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡏⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠀⠀⠀⢰⠋⢠⡎⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣦⣨⣄⠘⠁⣊⠳⣄⠀⠀⠀⠀⠀⠀⠹⣦⣤⣀⣀⣀⣀⣀⣤⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠩⠿⢳⣽⡷⠀⠁⠄⠀⠐⢶⣤⠀⠀⣀⠀⠘⠛⠋⠁⠈⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢻⣥⡀⣖⢘⣧⣉⠁⠘⢷⡄⠀⡀⢹⠀⠘⡿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠿⠋⢹⠆⠊⢻⡶⠺⠫⣴⠀⣤⡤⠀⠀⠀⠀⠀⠉⠙⠛⠶⠤⢠⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠌⠀⠀⢄⠸⠋⠑⠆⡐⠂⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⣱⠂⡤⠠⢣⠀⠲⠀⠈⠘⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⡾⠁⠀⢰⠀⡿⡷⠦⠖⢶⠦⠀⠴⡀⠀⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣤⡆⣼⠆⠠⠆⠈⠉⠄⣀⣨⠟⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣈⡝⠀⣤⠄⠴⠛⢤⠻⣥⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣮⡍⣠⠶⠂⠲⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣯⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⢳⠗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣾⠛⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣿⣿⢶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰⣦⠠⠷⡎⠿⡂⠿⠷⢆⢠⡦⢄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢫⡟⢐⠀⠀⠀⠀⠀⠀⠀⠀⢰⡡⣿⣿⣿⢷⣇⠘⠂⠑⠀⠀⠈⠡⠐⠏⢳⠀⠀⠀⠀⠀⠀⠀⠊⠖⠘⢿⡆
⠀⠀⠀⠀⠀⠀⠠⣠⣿⣿⣿⡇⡽⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣽⣿⣿⡟⠈⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣀⠀⠀⠀⠀⠀⠀⣀⡀⠸⣵
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣼⠃⠈⠀⠀⠀⠀⠀⠀⠀⣼⣿⠙⣿⣿⣿⣟⣦⡞⠗⢀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠄⠈⣽
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⠐⣿⣽⣿⣿⡻⣷⢊⠊⠇⠠⠀⠀⠀⠀⠀⠀⠀⡴⡇⠀⠀⠀⠀⠀⠀⠘⠂⠝
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⣿⣰⡿⣿⣿⣿⣟⡻⣦⠈⠠⠶⢀⡖⠂⠀⠈⢀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⢉⡛⣿⣿⡀⠑⠙⡿⣏⣿⣿⣍⢷⣀⣦⡀⣠⠀⡃⢀⣾⣯⠅
⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣼⡇⠄⠀⠀⠀⠀⠀⠠⢠⣿⣶⣿⣿⣦⠀⠷⢮⣽⣿⣿⣿⣿⣷⣿⠃⣠⣷⣾⡿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣾⢿⣿⣷⣄⡘⠿⠿⠿⠻⠻⠿⠿⢿⠿⢾⡧⠖⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢰⣟⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣻⣝⢿⣿⣿⣷⣷⣶⣶⣶⣶⣶⠶⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰
⠀⠀⠀⣻⣧⣿⣿⣿⣿⣧⣿⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣈⠻⠾⣳⣼⡟⠻⣿⡋⢻⠅⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠎⠇⠀⠐⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⣿
⠀⠀⠀⢿⣯⣵⣿⣿⣿⣿⣿⣖⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣺⡏
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢼⡏⠁
⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣝⠢⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣳⣄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣷⠶⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣝⢠⣀⡀⣀⠀⠄⠀⢀⣀⠀⠀⠀⠀⢀⣀⣈⣴⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣉⣷⡶⠀⠈⣁⣀⣶⣶⣾⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠚⠻⠟⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⠋⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣙⣛⣓⣃⣐⣋⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⣿⣿⣿⣿⡏⣿⣎⠻⣧⣹⣷⣌⢷⣌⠛⠿⣶⣦⣤⣽⣿⣿⣿⣿⣿⣿⠏⣠⣾⣿⣷⠟⣋⣵⣿⣴⣾⣿⠟⣀⣾⣫⡾⠋⢀⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠘⢿⣦⠀⠙⣿⣿⣷⣿⣷⣦⣄⠈⠉⠻⣿⣏⠛⣿⣿⣿⣸⣿⣿⣫⣶⠟⣋⣭⣿⣿⣿⣷⣿⣿⣿⠋⣀⣴⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣇⠘⢿⣷⡀⢸⣿⡏⠉⠛⠻⢿⣿⣦⡄⢹⣿⢀⣿⣿⣿⣿⣿⣿⡟⣡⣿⣿⣿⠿⠛⠛⠉⢻⣿⣣⣾⣿⠿⢋⣾⡟⣸⡿⣿⣿
⣿⣿⣿⣿⢿⣿⣆⠈⢿⣧⣸⣿⢰⠟⠓⢶⣄⠈⠛⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⣠⠶⢛⢻⡜⣿⣿⡿⠁⣠⣾⠟⢠⣿⢣⣿⣿
⣿⣿⣿⣿⣯⠻⣿⣦⠘⣿⣿⡇⣾⢹⢿⠴⣬⠳⡄⠀⠙⠉⠀⠀⠀⠀⠀⠀⠈⠉⠋⠀⣠⠏⢥⣾⢆⠙⡇⣿⡿⣠⣾⡟⠉⢀⣾⣣⣾⣿⣿
⣿⣿⡜⣿⡙⣷⣝⢿⣷⣹⣿⡇⣿⢸⣌⠽⠎⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣔⠽⣯⡯⡄⡇⣼⣿⡿⠋⢀⣴⣿⣿⡿⣿⣿⣿
⣿⣿⣷⡸⣷⡈⠻⣿⣿⣿⣿⣷⢻⡸⣫⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣚⣟⢡⣧⣿⣿⣤⣾⣿⣿⠟⣫⣼⣿⣿⣿
⣿⣷⣽⣷⣿⣿⣤⡈⠻⣿⡿⢿⠿⠳⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠞⢿⠿⢿⣿⣿⣯⣵⣿⣿⢟⣵⣿⣿
⣿⣯⡙⠛⠿⣿⣿⣟⠛⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠛⣿⣿⣿⣶⣿⣿⣿⣿
⣿⡤⠶⠶⠶⣶⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⡾⠛⠛⣷⢦⡀⠀⠀⠀⠀⠀⢀⡴⣾⠛⠛⣦⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣷⣶⣦⣼
⣿⣶⣾⣿⣿⣿⣷⣶⠶⠭⠙⠂⠀⠀⠀⠀⠘⡇⠀⢸⣿⠀⢳⠀⠀⠀⠀⢠⠏⠀⣿⡀⠀⣸⠀⠀⠀⠀⠀⠀⠩⠽⠿⣿⣿⣿⣿⣿⣿⣶⣿
⣿⡿⢛⣽⣿⣯⣥⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢸⡿⠀⣸⠀⠀⠀⠀⠸⣆⠀⣿⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠐⠲⣶⣭⣿⣷⡦⣍⣛⣿
⣿⣴⠿⣫⣿⣿⠋⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠓⠋⠁⠀⠠⡤⢄⠀⠈⠑⠛⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠈⠻⣿⣿⣿⣶⣍⣻
⣿⣵⣾⣿⣿⢃⡴⠞⣩⣵⠿⠛⠋⣻⣷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣟⠉⠛⠿⣯⡛⠳⣤⡹⣿⣿⢿⣿⣿
⣿⣵⣿⣿⣿⡟⠁⣴⠟⠁⠀⢀⣴⠟⡟⠀⠈⠙⠳⢦⣄⣀⣀⣀⣴⣿⣄⣀⣀⣀⣤⠶⠟⠋⠁⠀⣟⠻⣆⠀⠀⠈⠻⣆⠈⣷⣿⣿⣾⣿⢿
⣿⡿⣿⠉⣿⡇⢸⠏⠀⠀⠀⠋⠀⣴⣷⠀⠀⠀⠀⠀⠀⠈⠉⠓⡞⡟⣶⠋⠉⠁⠀⠀⠀⠀⠀⠀⡿⡄⠈⠑⠀⠀⠀⠈⠀⢸⣿⣿⣾⢃⣾
⣿⣷⣿⠀⢻⣧⠈⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⡾⢀⣧⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣾⢿⡏⣿⣿⣿
⣿⣿⣿⣧⠈⢻⡆⢸⣄⠀⠤⠴⠞⢫⣿⡇⠀⠀⠀⠀⠀⠀⡼⢁⡾⡟⢧⠙⣆⠀⠀⠀⠀⠀⡀⣿⣯⡙⠓⠦⠀⠀⣰⡇⣸⠏⠚⢀⣿⣿⣿
⣿⣿⣿⣿⣷⣀⠙⠘⣿⠳⠶⢴⣶⡿⠋⣷⡇⠀⠀⠀⠀⡼⢁⡞⠀⡇⠈⢧⡘⣆⠀⠀⢀⠀⣷⡿⠹⢿⣶⠤⠶⢚⡿⠐⠋⠀⣠⣾⣿⣿⣿
⣿⣿⣿⣿⠿⣿⣷⣶⣾⣿⣾⣿⣥⣤⡀⠸⣧⡜⠀⠀⣸⣡⠏⠀⠀⡇⢀⠈⠳⡼⡆⠀⠀⣧⣿⠃⣀⣤⣽⣿⣿⣿⣶⣶⣶⣿⢿⣿⣿⣿⣿
⣿⣮⡛⣿⣧⠀⢈⣽⣿⣿⣿⣷⣦⡈⢻⣆⢹⣇⠀⠀⣿⣿⠀⠀⠠⡷⠀⠁⢠⣿⡇⠀⠀⣼⠃⣴⠏⣡⣴⣾⣿⣿⣿⣭⠁⠀⣾⡿⢋⣾⣿
⣿⣿⣷⠈⢿⣦⣾⣿⡏⣿⣏⢻⣿⣿⣆⣿⢸⡟⢦⡀⢸⣿⡆⠄⠄⡄⠈⡀⢸⣿⠃⣠⠞⣿⣰⣏⣼⣿⣿⡏⣾⡟⢹⣿⣧⣼⡟⢠⣿⣿⣿
⣿⣿⣿⡇⠈⣿⣿⢿⣷⣽⣿⣾⡿⠘⣿⣿⣿⠇⠀⠹⣄⣿⣧⠀⠐⠙⢀⠀⣿⡟⣴⠃⠀⢹⣿⣿⣿⡉⣿⣷⣿⣧⣾⠿⣿⡟⠀⣸⣿⣿⣿
⣿⣿⣿⣷⠀⢸⣿⡘⢹⣿⡏⢻⣿⣾⣿⣿⡟⠀⠀⠀⠹⣿⣿⠀⠉⠀⠑⢠⣿⣿⠃⠀⠀⡈⢿⣿⣿⣶⡿⡯⢻⣿⡇⣹⣿⠇⢀⣿⣿⡟⢸
⣿⡘⢿⣿⣆⠈⢿⣿⣿⣫⣄⣱⣦⣾⣿⣿⡇⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⢸⣿⣿⣷⣮⣐⣮⣹⣿⣿⠟⢀⣼⣿⡿⢁⣼
⣿⣿⣾⣿⣿⣷⣦⣭⣝⣛⡻⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣿⣿⣿⣿⡿⠿⣛⣋⣭⣤⣴⣿⣿⣿⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣴⣾⣿⣿⣷⣦⠀⣠⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠒⢎⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⠂⠊⣘⣿⡿⣶⣦⣄
⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣶⣶⣀⠀⠀⠀⢈⣛⡛⠋⠹⠿⠿⠿⠿⠿⠿⠿⢿⣿⡸⡇⠴⠀⠋⠻⠀⠼⠟⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡄⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠻⢀⣴⣶⣶⣄⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣿⣾⣶⣾⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣾⣷⠀⠀⠰⠀⠀⠀⠀⠀⠀⣿⡯⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠻⣿⣿⣟⠁⠉⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣴⣶⣼⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⠈⠙⠛⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⠀⠀⣨⣤⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣾⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠯⢧
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣳⣖⠒⠚⠛⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⢐⢈
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠸⡄⢀⡼⣾⢿⣋⣤⣀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣤⣶⣶⣶⣶⣿⣭⣍⣛⠿⢃⣠⣴⣶⣤⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠛⠛⣿⣿⡇⢰⡆⣄
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⢿⣿⣿⣻⣿⣿⣿⣿⣿⣷⠟⠉⠀⣀⠈⠛⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣃⣀⣀⣿⣿⡇⠀⠁⢸⣦
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣾⣿⡇⣿⣿⣿⣿⣿⡿⠋⢀⣶⣿⣿⣿⣦⠈⢿⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⡀⠘⣿⣧⡀
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠉⠋⠀⠻⠟⠻⢃⠙⠁⢠⣿⣿⣿⣿⣿⣿⣧⠀⢠⡄⠀⠀⠁⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠃⠀⠁⠀⠸⢋⡄⠀⠁
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡄⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣾⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠘
⠀⢰⣶⣶⣶⣶⡆⠀⠀⠀⠀⠀⣿⣿⣶⣾⡏⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣴⣶⣶⣾⣿⣿
⠀⢸⡿⢿⠿⢿⠁⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⢠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠈⣿⡄⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣷⠀⠀⠠⣾⣿⣿⣿⣿⠃⠀⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⡀⢹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠋⠀⠀⠙
⠀⠀⠀⠀⠈⠉⠉⠀⠁⠀⠉⠉⠉⠉⠉⠀⠀⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠆⠀⠀⠀⠀⠀⢀⠀⡈⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠛⡀⠛⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠤⣤⡁⠠⠊⠀⠀⠀⠀⠀⠒⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢦⣀⠀⠊⠀⠀⠀⠀⠁⠀⠀⠀⠓⠀⢢⢀⢐⠠⠀⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠩⣀⠐⠂⢠⡄⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡤⠈⢕⣣⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠄⠀⠀⠈⠲⣄⠀⢀⡠⠀⠐⠀⢀⡀⠀⣠⣤⠵⣧⡔⠋⠉⢉⡓⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠘⠁⠀⠀⠈⠊⠁⢹⣿⣶⡗⠠⡀⠀⠀⠀⠐⠏⡀⢲⠀⠀⠁⠄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⢩⡀⢀⣾⣿⠿⠁⠀⠈⠒⣄⠀⠠⠔⠇⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⠃⠀⠀⠀⠀⠘⡧⠈⠈⠀⠃⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⠛⠙⠀⣤⣞⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠐⠀⠀⠀⠒⠉⣀⣀⣠⠞⠁⡉⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣮⠇⢀⠈⢠⠀⢠⠦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠈⠆⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠈⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠈⢆⠀⠀⠀⢦⠀⠠⠀⠀⠀⠀⣄⠀⠈⡄⠇⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⢃⠐⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠉⢷⡛⣷⣦⠀⠀⠀⠀⠊⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⡅⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠰⠀⠋⠀⠀⠀⡰⠻⢿⣿⠛⠉⠉⢀⠀⢀⡠⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⡘⢠⠚⠂⠠⠀⣰⡾⠇⠈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠄⠀⢀⠹⠆⠘⠁⠘⢆⠀⠀⢠⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠣⡀⠀⠠⠀⠀⡌⠄⠀⠀⡷⠀⢀⣑⣶⠻⣦⡤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠐⠤⢄⠀⢙⣄⣶⣠⠈⠀⠀⡠⠎⠀⠀⠈⠉⠙⣿⡅⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠈⠀⠄⠄⠀⠙⣿⡋⠅⣽⡧⠒⠉⠐⠂⠠⢶⠀⠀⠐⠈⠇⠀⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠘⠂⠀⠳⢐⣻⠤⠤⠀⠐⢿⣿⣾⠟⢿⡀⠂⠀⠀⠀⡆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠄⠀⠈⠁⡌⢽⡀⢀⡠⠀⠀⡟⠈⢀⠀⠙⢄⠐⠂⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⢠⠴⠾⡃⡠⠂⡆⠀⠸⠀⠦⠀⠈⢃⡀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠒⠂⠀⠉⢀⡞⠀⠀⠀⠀⠉⠐⠈⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⠏⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠁⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠦⡀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠉⢠⣄⣀⠀⠀⠀⠀⢱⣼⣷⣾⠄⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣤⡀⢤⣚⣿⢿⡟⠀⠀⠀⠈⠀⠀⠀⠑⠄⠀⠀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠑⠤⣄⡀⠀⠀⠀⠀⠀⢈⡄⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠊⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⣿⣿⣻⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣤⡠⡀⠀⠀⠂⠄⠐⠰⢄⣀⢀⡠⠀⠠⠉⠀⠐⠀⠀⢹⢿⣿⡿⠄
⠀⠀⠀⠀⠀⠸⠅⠀⠀⢀⠄⠉⠀⠀⢰⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠏⠃⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠁⠀⠀⠀⠸⡺⣄⠀⡀⠀⠀⢃⠀⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠤⠄⣀⠈⠻⢿⣾⣷⡤⠂⠁⠀⠀⠸⠁⠀⣤⣀⠀⢀⡀
⠀⠀⠀⠈⠀⠀⠀⡠⢮⡿⠁⡀⠀⠠⠬⠿⢻⣿⣿⢷⡦⠤⠖⠚⠁⠙⢷⡏⠿⠛⠀⠀⡁⠀⠐
⠀⠀⠀⠾⠁⠉⠀⠀⠈⠁⠀⠀⡄⢀⣨⠶⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⡀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠜⠃⢨⠀⣠⠀⠀⠂⠀⠀⠀⠀⠀⠀⣰⠌⠀⢀⡏⢓⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠀⠀⠀⠀⠠⣿⡃⠀⠀⠑⠒⠀⠒⠂⠁⠀⠀⠀⠩⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣏
⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠢
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠤⢼⠃⠀⠀⠀⠀⠙⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⢦⣀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠉⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⠐⠀⠀⣸⡆⠹⣷⡄⠀⠀⠀⢤⢠⣼⣬⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠹⠇⠈⠉⠁⠀⠀⠀⠘⢟⠋⠉⡁⠀⠀⠠⣴⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣦⠀⠐⢆⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡈⢧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⣴⣴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠓⠀⠀⢠⣤⣦⣴⠀⠀⠀⠀⠶⠶⠶⠦⢬⣿⣾⣧⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠄⠨⠅⠀⠘⠃⠀⠀⠀⠀⠀⢀⣀⠈⠙⠿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠈⠀⢀⣀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣴⡂⠀⠀⠀⠱⠏⠀⠀⢤⣦⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⣤⠁⠀⠀⠀⢰⣶⣧⠄⢀⡀⢀⠀⠀⣺⣿⠛⠁⣶⣄⠀⠀⡀⠀⣠⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠋⠁⠀⠀⠙⠃⠀⠀⠙⠁⠦⣈⠺⣿⣷⡀⠘⡄⢸⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀⠶⣄⠀⠀⣶⠀⠀⠐⣄⡀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣆⢱⢸⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠉⠛⢶⣀⠹⡀⢹⡰⠿⠇⠀⠀⠀⣠⣤⡄⠀⠀⠈⠛⢿⣷⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠢⠄⣙⣳⣷⣀⠀⠀⠀⠀⠀⠀⠉⠋⢁⡆⠈⠉⠙⠒⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣠⣭⠿⠿⠦⠀⣀⣤⡤⠀⠀⠘⠛⠀⠀⠀⠀⠀⢤⣬⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⣰⣿⠋⡐⢆⠀⠀⠀⣴⡿⠗⠃⠀⠀⠀⠉⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢷⣾⣷⣄⠀⢆⠀⢂⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢠⡀⠀⢀⡉⠻⠿⣷⣼⡄⠸⡆⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠘⠀⠀⢠⠤⠭⠴⠿⠿⣿⣶⣿⣄⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⣶⠀⠠⠤⠒⠒⠋⠉⠉⠉⠛⠛⠷⠶⣦⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⡰⠿⣆⠀⠀⢀⣠⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣴⣿⣾⣿⡷⢡⢰⡿⢆⣰⣿⡿⡿⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠲⣶⣤⣄⠀⣿⣴⡼⠛⠟⠛⠳⢧⠀⡾⠋⠉⠉⠛⠛⣧⣿⠀⣴⠇
⠀⠀⠀⠀⢲⣶⣖⣦⣽⣯⣿⣿⣟⠁⠀⠀⠀⣀⣀⣘⣿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣃⡖⣶⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠳⣿⡿⠟⠉⠉⠉⠉⠒⣤⣶⠟⠋⠉⠉⢻⡷⠶⠿⠷⣦⣀⣴⠋⠉⠙⠛⢿⣿⡛⠋
⠀⠀⢀⣀⣀⣀⠙⣇⠀⠀⠀⠀⡠⠎⠁⠁⠀⠀⠀⡀⠸⠁⠀⠀⠀⠈⢿⣏⡀⠀⠀⠀⠀⣙⣀⣀⣀⣀⡀
⠐⠻⣿⣭⣿⠿⠿⠛⠓⠤⣤⣾⠁⠀⠀⠀⠀⡀⢀⣀⣔⣠⣀⣀⠀⡴⠋⠛⠻⣷⣄⣠⠖⠉⠙⣿⡿⣿⣿⠟
⠀⠀⠈⢿⠁⠀⠀⠀⠀⠀⣽⠿⣆⠀⢀⢠⣼⣿⡿⣟⣻⡟⢻⣷⣮⣐⡀⠀⠀⢈⣿⠁⠀⠀⠀⠈⢻⠾⠃
⠀⠀⢀⡰⣤⡀⠀⠀⠀⢺⣟⠀⠀⠁⢢⣿⡿⡳⢎⡶⠋⢾⣼⣯⣿⣿⣧⠤⠒⠛⠛⢷⣤⣤⡤⠴⠛⠄
⠐⠾⣿⣅⠀⣉⣳⡶⠤⠼⢯⣁⡀⠀⢼⣿⢿⢧⣪⠀⣶⠀⠱⡿⣿⣿⡿⠀⠀⠀⠀⠀⣿⣯⣀⠀⢠⣶⡞⣷⣦
⠀⠀⠈⣉⡽⠃⠀⠀⠀⠀⣼⠟⠋⠉⢹⣿⣖⣿⣋⠒⡄⠠⡞⣽⣟⣿⡇⠀⠀⠀⠀⢀⡏⠀⠙⢿⣿⠏⠈⠉⠁
⠀⢀⣾⣿⠅⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⢹⣿⣿⣵⡿⣿⣾⣿⣟⣿⠏⠉⠙⠓⠶⡶⠞⠁⠀⠀⠀⠿⢉⠲⣄
⠰⠿⠿⣯⣄⣀⡀⣀⣠⠼⣿⡀⠀⠀⢀⡔⠈⠙⠙⠿⠿⠟⠛⠉⢱⡄⠀⠀⠀⣸⠷⠦⡀⠀⠀⠀⢤⣿⣿⣾⣧
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠸⢷⣦⠤⢾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⡠⠞⠁⠀⠀⠈⣦⡀⠠⠶⠛⠋⠉
⠀⠀⠀⠀⠀⣔⠄⠀⠀⠀⠀⣼⠃⠀⠀⠉⠳⣦⣄⣀⣧⣀⣀⡤⠞⠁⠙⡆⠀⠀⠀⢀⣠⠷⡄
⠀⠀⠀⠀⠺⠓⠖⠒⠶⠚⢛⣿⠀⠀⠀⠀⠀⠀⢸⢿⣿⠉⠀⠀⠀⠀⠀⠘⣷⠤⠶⣊⠳⣷⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡽⢧⣤⣤⣀⣤⣤⡏⠈⠛⢳⣄⡀⠀⣀⣀⡴⢟⡀⠀⠀⠈⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣏⣿⣛⣽⣿⣿⡇⠀⠀⠀⢸⠟⡟⣿⡏⣷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠟⠁⢽⡋⣿⠟⣄⠀⣠⠋⠀⠹⣜⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠈⠿⠃⠀⠀⠀⠙⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⢀⣤⣄⠀⠀⠀⠀⠀⠐⠄⠀⠀⠒⠺⠷⣼⢵⣶⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠦⠈⠀⢀⣶⣆⠀⠀⠀⣁⠸⢆⠀⠀⢀⡦⡽⣷⣤⣄⠀⠘⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠀⠀⣗⠒⠖⠈⠛⠋⣤⣀⡀⢀⠀⠀⠑⢄⠀⠀⠀⠉⠖⠀⢉⠀⠶⠆⠀⠀⠠⡀⠀⠀⢼⡷⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠈⣀⣀⣰⢛⣛⣁⣬⣈⣳⣶⠶⠿⠦⠤⠶⠲⢴⠿⣿⠦⠴⠿⠶⢤⣽⣤⢤⣀⡀⢀⣴⠆
⠀⠀⠀⠀⠀⢀⣀⠤⠔⠂⠉⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠒⠒⠂⠛⢷⣌⠉⠉⠛⣦
⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⠂⢠⣤⣄⠘⠀⠀⠈⠾⠀⠀⠔⡆⠀⠀⠀⢀⣀⠰⡆⠀⠀⠀⢀⣀⣹⣶⣦⣾⠗⠢⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⢛⠛⠁⠀⠐⢀⡂⠂⠒⠚⠒⠶⢦⡄⣘⠟⠗⠐⢃⡬⠛⠉⠁⢀⣠⡤⠶⠋⠙⠒⢦⣌⡂⠀⠀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡰⠇⠀⠀⠀⠈⠁⠀⠰⢷⠄⠀⠋⠐⠊⠡⠄⠚⢩⣄⡤⠒⠈⣉⠋⠀⠀⠀⠀⠀⣀⣼⠿⠶⣌⡑⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠊⢩⣥⡄⠀⠚⠢⠀⠀⠀⠀⠴⢾⠉⠀⠀⠀⠀⠉⠲⣌⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠐⠿⠋⠰⣦⡄⠀⠁⠀⣦⡀⠛⠋⠀⠀⠀⠀⢀⡴⣿⠀⢰⣿⡇⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⣆⡙⣃⠀⣼⠟⠠⠂⢰⡉⠛⠀⠀⠀⠤⠀⠀⠀⣴⡤⣔⠾⠋⣱⡌⠳⢀⣥⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠐⠀⠀⠉⠀⠀⠈⢤⠄⠀⠀⠀⠀⢀⠤⠔⠊⣻⠿⠁⠀⠀⠀⠀⠛⠸⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣀⢠⣿⠀⠈⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣤⣆⠀⠀⠀⠀⠐⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉


⠀⠅


⠀⡄
⠀⠄
⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢠⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⡄⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠁⢠⠀⡀⢠⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠤⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠠⠃⠈⠑⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡶⠀⠀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡻⠻⠆⠀⠀⠀⠀⠀⠀⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢀⠀⠀⢀⣠⣆⣠⠀⠀⠃⠀⢀⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣽⡿⠁⠀⢠⡋⠉⠹⢃⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠶⠆⠂⠀⠺⢿⢇⡀⡀⠀⡸⠿⠛⢀⡿⢶⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⢻⡃⢠⠇⠀⢠⠂⠀⠠⠀⠀⠀⣴⣿⠟⠲⣄⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢠⠏⠀⠀⡇⠀⢠⣿⠟⠻⠀⠀⢹⠆⠀⠀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⢠⣄⠀⠘⢀⡄⠀⠃⠀⠉⠉⠀⡴⠞⠀⠀⠀⠀⢠⡆⠈⢢⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠈⠀⠀⠀⠞⢷⡛⠱⠄⠀⠀⡴⠀⠀⠀⠀⠀⠀⠐⠿⠃⣀⣸⡟⠦
⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⡄⢲⡆⠀⢠⣷⢀⡀⠀⠀⠉⠀⠀⠀⠀⠀⠐⠀⠀⢸⡋⠁
⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡎⠑⠇⠀⢘⠉⠘⡇⢢⣿⡶⠊⠀⠀⠀⠀⠐⠂⠀⠀⠁
⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠃⠀⠠⡘⢾⡄⠀⣏⡼⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠀⣷⡄⡟⢀⣶⣇⠀⠀⠀⠲⢀⣄⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⡀⢠⡄⢱⠙⡄⢸⣿⢋⡀⣘⣀⠀⠘⠛⠛⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠱⣾⡇⢸⡄⠁⠀⡇⢈⠷⠛⡟⢃⣠⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢸⡇⢸⡇⠀⢀⣤⣾⣶⡷⠴⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠀⠈⡇⣸⣷⣷⡿⠟⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⢳⡏⣿⠥⣶⣶⣽⣿⡴⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠠⣄⡀⠀⠀⠀⣸⠇⣿⣠⣨⣿⣿⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠈⠙⢦⡀⠀⣿⡔⡿⠃⠛⠛⢿⣼⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢿⡆⢿⡿⡇⠀⢀⣀⡀⠋⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣤⣿⠾⠃⠀⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⣄⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⠷⡀⠻⠣⠸⠀⣹⠞⠑⢶⠖⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⠀⠀⡹⠟⠛⠛⠻⢄⠀⠀⠘⠄⠈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⣤⡀⠀⠀⠈⢿⣷⠦⣸⡀⠠⡗⠀⠀⠀⠀⠈⠧⠀⠀⡀⠀⢠⠟⠛⠙⢶⡤⢤⣤⠖⠚⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⠓⢦⡀⠀⢱⣤⣈⣷⣦⣿⡆⠀⢀⣀⠀⠀⠀⣦⣷⣴⡇⠀⠀⠀⢈⣀⣈⣿⣦⡞⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⣄⣿⣿⣾⠉⠛⢻⣿⢿⠟⢳⣤⣇⠈⠑⣆⢀⡀⠉⠹⣿⣆⣠⠞⠉⠉⠉⠙⣿⡉⠉⢙⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡃⠀⠀⠀⣸⠁⠀⣠⠾⠿⣶⠀⠀⠈⢓⡟⢻⠦⣾⠿⢿⡀⢀⡦⠤⣴⣿⠤⠞⠋⢁⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⠷⡄⠀⠀⠛⠀⠴⠁⠀⢠⠟⠛⣏⣸⣋⡉⠻⡄⠀⠀⠀⢹⡟⠀⠀⠘⠹⢓⣦⣾⡉⠁⣹⠟⠉
⠀⠀⠀⠀⠀⠀⣀⣤⡔⢲⣧⠀⠀⠀⠀⠀⠉⠐⠛⡀⠀⢄⡠⠴⠿⣄⢀⡏⠁⠈⠉⢳⡘⣆⠀⠀⣰⠀⠀⡤⠂⠀⠈⠉⠛⣇⠴⠃
⠀⠀⠀⠀⠀⠀⠉⠉⣑⣺⣧⣀⣀⡠⠲⣤⣬⣐⣛⣋⣡⠾⠇⠀⠀⡼⠋⣱⣤⠶⣤⣸⣧⣿⣷⣿⣷⡄⠀⠀⣀⣤⣄⣄⣴⣧⣤⣀⡀
⠀⠀⠀⠀⣀⣤⣶⡊⣉⣩⠿⠟⠛⢧⡀⢠⠞⠉⠀⠀⠀⠀⠀⢠⡞⠀⠀⠻⣤⣤⡄⡈⠋⠰⣶⣤⡻⣿⠋⠉⠉⠀⠈⠹⣿⣟⠀⠀⠉⠱⣦⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠓⠳⠶⢦⣠⠞⠛⠓⠖⠋⠀⠀⠀⠀⠀⠻⠦⢤⡤⠤⠀⢉⣁⣾⡀⠀⢀⠀⠀⠀⠈⣻⣿⣿⠟⠉⠉⠛⢳⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⢬⣿⣏⡀⠀⠀⢹⡆⠀⠀⣿⣿⣟⠻⢷⡶⠶⠤⠚⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣾⣃⣀⣤⣿⣿⣿⡅⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠹⣿⡓⠢⠤⢤⣙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠁⠈⢣⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⣶⣶⣦⣄⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢿⣳⣤⣖⡿⠿⠛⠉⠉⠉⠀⠐⠒⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠙⢷⣄⡀⠀⠐⢶⣶⣶⣶⣶⡿⠿⠓⠻⠷⠶⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢦⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠁⠀⠀⠀⢀⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⢦⡀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠈⠙⠺⠿⠶⣶⠶⠶⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢧⣀⣀⠀⠀⠀⠈⢻⡧⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠟⠛⢦⡀⠲⠀⠀⠃⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣤⣤⢶⣻⠗⠁⠀⠀⠀⠙⢦⠀⠈⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡆⠀⠀⠀⠀⠀⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢀⣶⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡜⣿⣰⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠁⠀⠹⡘⢰⣃⡤⠶⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡟⠁⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⡀⣟⡾⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⢸⢻⡄⠀⠀⠀⣀⡀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠻⣧⢻⣄⠀⠀⡿⠛⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠘⠳⣝⢷⡼⠁⠀⠀⠀⠀⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢻⣿⡄⠀⠀⠀⣸⣳⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⢘⠹⣿⡀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⢿⣇⠘⠂⢹⡇⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣄⡻⣷⣧⠀⢣⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢦⣉⠃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢉⠣⠁⠀⢀⣴⣶⡿⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣒⣯⠽⠛⠉⠉⠉⠓⢌⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠁⠤⡤
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠓⢘⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⣦⠀⠈⠛⠃⠀⠉⠁⠸⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢦⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⡒⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠄⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠄⠀⢀⣀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠐⢰⡆
⠀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠂⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠙⠀⠀⠀⠀⠀⠻⠀⠀⡀⠀⠀⠀⠀⠈⠋⠀⢀⠀⠊⠁
⠀⠁⠀⢄⡀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⢂⣠⡀⠁
⠀⠂⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣀⠀⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠁⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⣀⡄⢀⠈⢠⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠈⠓⣦⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠡⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢰⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢦⠀⠈⠀⢠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠻⣾⣷⣷⡆⢃⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡄⣸⡄⠀⠀⠀⠀⠀⠀⢀⣠⠖
⠤⠤⣴⣦⣴⣦⣤⣀⠀⠀⠘⢿⣿⣷⣼⠀⢸⠀⠀⠀⠀⠀⠀⠈⠀⠀⣷⢰⣿⡇⠀⠀⢙⡿⣩⠟⢋⠤
⠀⠀⠀⠉⠉⠛⠿⣿⣿⣦⡀⠀⢻⣿⣿⣣⠘⡄⠀⠀⠀⢀⠌⠀⠀⠀⢸⣿⣿⡁⣠⣴⣫⢞⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣷⣤⡹⣿⣿⣧⣃⠀⠀⠀⡆⠀⠀⠀⠀⣦⣿⣿⣿⢟⣿⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⡀⠀⡜⠀⠀⠀⠀⠀⣿⣿⣿⣣⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡎⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⠀⠀⠀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣇⠀⠀⠀⣠⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇⠀⠀⠀⠀⠈⠡⠀⢷⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣤⣦⣤⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠢⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢏⡜⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠂⠈⠙⡆⠈⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⡼⣄⣀⡂⠀⠀⠀⣇⠀⠀⠠⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣡⠤⠶⠚⣟⠁⠀⠀⢠⠝⠀⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠾⠵⠒⠶⣅⣀⢸⡆⡀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠁⠈⢣⡀⠀⢰⠀⠈⠉⠑⢢⡤⠂⠀⠀⠀⡤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠚⢦⡤⠀⠀⢀⠀⡀⠈⠳⡀⠀⠀⢸⡆⠀⠀⢁⢀⠀⠀⠇⠀⠀⠀⡔⡠⠀⠀⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣠⠀⠀⠀⠀⣀⣀⡀⠐⠄⠀⠀⠙⠀⠐⢌⡴⢂⠀⠀⠀⠀⣐⣎⠋⠀⠉⠂⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠈⠢⠀⠀⠸⡄⠀⠐⠀⠀⠈⢢⠹⢦⣾⠠⠂⠀⠀⠠⠀⠐⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠁⢀⡊⠀⠀⡄⠤⠆⠀⣤⡀⠁⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⠀⢠⡀⠀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠓⠁⠠⠶⠂⠒⡻⢆⠀⠤⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠂⣷⡋⠂
⠀⠀⠀⠀⠀⠀⠰⠀⠀⡇⠐⠚⠞⠁⠀⣈⣀⠤⠤⠬⢶⡀⠀⠀⠀⠀⣤⢤⡀⠀⠀⠀⠀⠆⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⢀⣀⡤⠂⠉⠁⠀⡀⠠⠀⠐⠳⠆⣀⠀⠀⡇⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⠀⠈⢀⠄⡜⠱⠶⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢄⡄⠤⣠⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠖⠉⢶⠞⠁⠀⠀⠀⠀⠀⠀⠡⡀⠀⠙⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢨⠦⣴⡟⠠⠄
⠀⠀⠀⠀⢀⠀⠂⢚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠆⠀⠀⠁⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⡈⣤⠀⣤⣄⡂⠀⠀⠀⠀⠀⢀⢤⠔⠳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⡀⠀⠀⢠⣰⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⢀⡀⠈⠷⣄⣀⣿⡇⠀⠀⢀⣴⣾⣿⡇⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠉⠳⣤⣹⣿⣿⣷⡄⢠⣿⣿⣿⣿⡇⠀⠀⣠⠔⠺⠏⠀⠀⠸⢿⣿⣿⣯⣿⣦
⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⠋⠁⠘⠯⡍⠉⢻⣀⠀⡼⠁⠀⠀⠀⣀⣀⡀⠀⠹⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢀⠼⠋⠀⠀⠀⠀⠀⢰⡄⠈⣿⣧⠀⠀⣀⣴⡿⠿⠛⠁⠀⢀⣾⠟⠿⠋⣿⣿
⠀⠀⠀⠀⠀⠀⡧⠤⠀⠀⠀⢸⣦⡀⠈⢿⠀⠘⢻⡇⠀⣿⠏⠀⠀⠀⠀⠖⠋⠀⠀⠀⠘⠉⣿⣇
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢈⣿⣷⠀⠈⠀⠀⠈⣧⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿
⠀⠀⠀⠀⠀⠘⡷⠀⠐⣶⣦⣧⠈⢻⡀⠀⢀⣀⣴⣉⢀⣿⣵⣠⡖⠁⠀⠀⠀⠀⠀⠀⢀⠾⢛⡃
⠀⠀⠀⠀⠀⠀⣧⡀⠀⢹⣯⣷⠀⠀⢻⣾⣿⣿⣿⣯⣯⣦⣿⣿⣿⣶⣆⡀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣦
⠀⠀⠀⠀⠀⠀⢸⣌⡀⠀⢿⣷⣦⣀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣠⣤⡶⠚⠋⠉⠉⠉⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡨⢿⡀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣳⣦⣤⠤⠤⣶⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠀⠤⣶⣮⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⠋⠀⠀⠀⠈⠛⣯⣿⢯⣷⣽⣺⣷⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⡀⢤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠏⠻⢆⡀⠀⠀⠀⢀⡀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣢⢄⡌⠀⠀⢿⣿⣿⣥⣍⠁⠈⠉⠀⠀⠀⠈⠀⠉⠓⠲⣤⣸⣿⡿⠿⣿⠏
⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠙⠻⠿⣿⣕⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⢰⣧⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠶⣶⣶⣿⣷⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣦⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣄⠀⠀⢠⡆⠠⢿⣯⣿⠟⠁⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⡏

⠀⠀⠀⠀⢰⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣷
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⡔⠉⠀⠀⠙⡆⠠⡀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⠄⠀⠀⢀⣤⣶⣦⠐⠁⠀⡠⠂⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠄⠀⠀⠐⠿⣿⣿⡗⡠⠄⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠂⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠸⣄⠀⢆⠀⠀⠀⢀⡁⠀⠠⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠈⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠈⠑⠶⠷⢶⡖⠋⠀⠀⠂⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⢈⠍⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡦⠚⠀⠐⠒⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡇⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿
⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⠀⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠐⠀⠀⠀⠉⠂⢄⠀⠀⢠⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⠀⠀⠰⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣏⠘⡀⢰⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠁⠀⠀⠀⠀⠢⢠⣬⣾⠅⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⡻⣄⠱⣄⣄⠀⣐⣰⠏⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠒⠀⠒⢉⠟⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠐⠮⠻⠶⠞⢻⡋⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⠀⣠⠆⠹⡄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠰⠛⠈⠁⠀⠀⠙⣆⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢰⠀⠹⠀⢀⡀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠓⢄⣰⠊⠁⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⠀⠀⠀⢸⠇⠀⠀⠀⡰⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠐⢼⣤⣆⡠⠖⠓⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠩⡷⣤⢏⠒⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⠀⣠⠃⠈⠀⠹⠒⠤⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠄⠀⠈⠉⠁⡨⠋⢹⠀⠀⠀⠀⡗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠑⠀⣰⠁⠀⡀⢧⠀⠀⡜⡟⠲⡄⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⢀⣧⠀⡈⡐⠀⠑⠊⣀⣇⢀⡞⠁⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠈⠈⠙⣆⠀⡁⠀⠰⣉⠀⢈⡿⢽⠊⠉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠙⢧⣇⠀⠀⠀⢉⣟⠀⢨⠓⠒⢒⣃⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠘⠛⢄⡀⠀⢸⡘⠖⠁⡠⠊⠁⠀⠉⠲⣟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡇⣿⣄⠾⠟⠁⠀⠀⠀⢀⣟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣇⢙⣧⣶⠖⡀⠠⣤⠄⠀⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⠈⠉⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠛⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⡀⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⡉⠘⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠄⠰⢿⡇⠠⡀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⡈⠂⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⠠⠀⢀⢝⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⣶⣆⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠉⠂⠀⠡
⠀⠀⠀⠀⠀⠀⠌⠉⠁⠀⠀⠂⠀⠀⠀⠀⠙⠿⠇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⣾⣿⠄⠀⠀⠐⠀⠀⢀⢤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⢴⣥⠀⠁⠠⠀⣤
⠀⠀⠀⢀⣄⠀⢦⠀⡀⠀⠈
⠀⠀⠀⠀⠘⠂⠈⠒⠠⣄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢀⣀⣠⡆⠀⠀⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣿⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠀⠀⠈⠻⠏⠁⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠁⠀⠀⠀⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠛⠳⢦⣄
⠀⠀⠀⠀⣠⡶⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⣸⡷⠂⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠲⣯⡀
⠀⠀⠀⠀⢹⡟⠃⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠘⢿⡁⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣴⡇⠀⠀⠀⠀⠀⠀⢸⣦⣤⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠦⠶⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠦⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⡀⠀⣀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠉⠈⠉⢳⡞⠉⠁⠉⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠀⠀⠉⢻⣾⠋⠀⠀⠈⠙⠳⣤⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⣹⣦⡀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⠀⠀⢀⣴⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣶⠤⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⢴⣾⡋
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠙⢷⣄⣀⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠀⣠⣷⡀⠀⠀⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⠞⠋⠈⠛⠶⠶⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁

⣶⣶⣶⣾⣶⡷⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⡿⢷⡿⠿⠿⠷⣶⣶⠶⠶⠶⠶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠐⡀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠴
⠀⠀⠀⠀⢀⠀⠀⠀⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⢀⡠⠄
⠀⠀⠀⠀⠈⠂⠠⠀⠍⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⡁
⠀⠀⠀⠀⠀⡄⠅⠂⠦⠩⠒⡐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠞⠀⠂
⠀⠀⠀⠀⠁⠸⠀⠠⠉⠓⣄⠸⠃⠨⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠚⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣱⡆⢀⠄⠐⠂⡄⢠⠀⣉⠀⠀⠀⠀⠀⡀⠁⠁⠀⠢⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⢟⠙⠀⠀⠀⠀⠹⠞⣀⡉⠄⣀⣠⣤⠜⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠊⠈⢦⡀⠀⢀⡁⠐⠀⠤⠔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣧⣀⠀⢉⣣⢳⣜⡓⠚⣧⠆⠍⣳⠽⢿⣽⣿⣯⣿⣿⣎⣻⣯⢭⡝⠁⠀⢹⠋⢰⠀⠹⡇⠈⠻⠈⠛⢿⣵⣆⡼⠃⠈⡾⠃⠀⣛
⣿⣿⣿⣿⣿⣿⣤⣄⣛⠃⠀⠘⠲⡄⠘⡷⣼⠟⠾⠷⣿⣿⢿⣻⣭⣟⣧⡖⠙⢐⡗⡀⠐⠠⡄⠀⠀⠀⠀⠀⣿⠃⠀⠰⠄⡑⣀⡤⠻
⣿⣿⣿⣿⣿⣍⣻⣷⡄⣿⣆⣤⡄⠀⠌⠀⣴⣼⡛⠻⢿⠟⠾⢳⢯⣎⠐⠁⣰⠼⣿⣿⣿⡇⠀⢠⡄⠀⠀⣄⠘⠀⠠⠂⠀⢻⣁⣠⣷
⣿⣿⣥⣄⣤⡟⢹⣿⣡⣯⡴⠁⣀⠄⠀⣀⡻⠄⠉⠀⠀⠀⠀⠀⠀⠀⣄⠀⠈⣂⢀⡟⡜⠘⠁⠖⠐⠃⠄⠀⡁⠁⠀⠐⢺⡟⠉⠈
⣿⣿⣿⣿⣿⣷⣿⣟⣭⣥⣾⡿⣛⢢⡬⠽⠅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠃⠀⠀⠀⠀⠛⠂⣶⣀⢀⠁⣿⠂⠐⠀⠘⠀⠀⠈⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢲⠛⠈⠀⠀⠀⠉⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⡦⢽⣔⡏⠀⠀⠀⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣀⣾⣰⣶⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢺⢻⣥⡿⡽⡽⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣦⣴⡆⠀⠀⠀⠀⢚⠉⠉⠀⠀⠀⢀⠀⠈⠃⢀⠤⠚⠋⢸⡅⠊⢱⠛⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⢠⡀⠈⠃⠀⠀⡈⠥⠖⡿⠀⠀⠁⠀⠀⠀⠛⣷⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠾⢛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠗⠙⢤⠀⠀⠀⡀⠀⠀⠀⠀⠘⢉⣱
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⡾⣫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠁⠛⠀⣀⠀⢤⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣾⡅⠀⠀⠀⠀⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⡆⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⡨⣾⣯⣀⣣
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⢁⣹⠋⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣶⣄⠀⠀⠁⠀⠀⠀⢀⢘⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠳⠀⢱⡶⣂⣂⠀⠀⢺⠹⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⢡⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠺⠟⣒⢰⡇⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢁⣽
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡜⢁⡦⣤⠀⠘⠇⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢂⣈⣉⣁⣧⣿⢙⢾⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢥⣠⣭⢿⠛⣚⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡄⠀⠀⠀⠀⠀⠀⠠⢾⠈⠹⠧⣽⡟⠉⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠠⢞⡒⠂⠈⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠭⢍⣒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⠑⣲⢄⡀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡹⠀⠀⠀⠀⠉⠊⠀⠐⠆⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢀⡀⢠⠃⠀⢠⠇⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠤⡀⠙⣄⠐⠎⢁⠆⣄⣴⠧⠒⠉⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠓⠀⣈⣢⣬⣟⣦⡞⠃⡰⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⣠⡒⠋⠩⠭⠑⣯⣯⡛⣿⣿⣿⢥⡄⣨⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⢀⣀⠈⠀⠀⡠⠘⠌⠠⣠⣨⣄⡀⠀⠀⠀⢀⠤⠖⠊⡰⠁
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠈⠁⠀⠀⠐⠁⡟⠀⠀⣈⠈⠙⠻⠶⣤⠮⠥⠖⠒⠋
⠀⠀⠠⠂⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠈⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢉⠂⠀⠀⠠⢄⣱⣄⡀⠀⣀⠀⠀⢀⡔⠁⢸⡀⠀⠀⠀⠀⠀⠀⣀⠼
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠈⠙⠯⣁⡤⠖⠁⠀⠀⠀⢣⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠟⠛⠛⠻⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠶⡻⢟⢛⣻⢿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⣠⠶⣒⣿⣴⠿⠟⠻⢷⣼⣯⣛⢦⡀
⠀⠀⠀⠀⠀⢰⣿⣀⡀⠈⠁⠀⢴⣿⣿⣿⣿⣿⣷⣥⡥⣿⣧⠀⠀⠀⣼⢃⣾⠋⣡⡿⣶⢶⣗⡾⠷⣤⠙⣷⢻
⠀⠀⠀⠀⠀⠈⣷⡠⣤⣴⣤⣀⣼⣿⣿⣿⣿⣿⣭⣤⣜⣩⠏⠀⠀⠀⣿⣼⠇⣼⡟⢠⠊⠉⠉⠙⣦⣸⣧⣼⣿
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣧⡀⠀⠀⠀⣼⠛⣻⡋⢻⣣⠀⠈⠀⠀⡼⣽⢸⣿⠘⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⢻⡄⠘⢷⣌⣷⡛⠲⡖⠋⣹⡷⣾⣋⣴⠇
⠀⠀⠀⠀⠀⠀⠹⣿⣟⢽⣿⣿⣿⣻⢧⣿⣿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠳⣤⣠⠿⣌⣙⠛⡷⠛⠉⣠⢏⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠻⣧⡺⢿⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣉⣉⡿⣾⣛⡭⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⡁⠠⠀⡍⡳⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⡾⠛⠛⢦⣼⡄⣷⣄⢸⡶⠋⠀⠈⢹⡄⠀⠀⠀⠀⢠⡞⠉⠀⠀⠙⢦⡀⠀⢂⣿⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠐⣴⣼⣿⣿⣿⣿⣶⣶⠀⢀⣼⠃⠀⠀⠀⠀⢼⣠⡤⠤⢤⡀⣸⣇⣀⣼⠋⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣈⣱⣤⣼⣿⡿⣻⡛⣿⣿⣷⠶⠿⢥⡀⠀⠀⠀⠀⡼⠡⢘⠌⡐⣽⠉⠀⠈⢳⣀⣄⣤⠟⠹⣆
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠐⣾⣿⣷⣬⣵⣿⣿⡿⠓⠀⠀⢹⡄⠀⠀⠀⡇⠄⠀⣨⠷⠿⣄⣀⣀⣾⠫⣀⠀⠐⣀⡿
⠀⠀⠀⠀⠀⠀⠹⢦⣀⣀⣤⢾⣿⣿⣿⣿⡏⠳⡶⠤⠶⠟⠀⠀⠀⠀⠙⢆⣰⠁⠀⠀⣸⠫⠍⠙⢦⣠⣅⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠘⠟⢹⡏⠋⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢹⡔⠐⠀⠀⠘⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣰⠃⠙⢤⡀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠟⠶⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⣻⣿⣭⣟⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣵⣾⠟⢻⢿⡿⡟⠻⢷⣮⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣲⢄⠀⠀⠀⢀⣀⣀⣰⣋⣾⠏⠀⠀⢈⣲⣖⡁⠀⠀⠹⣷⣹⣆⣀⣀⡀⠀⠀⠀⡠⣖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⣦⣶⡿⠟⠛⡛⠛⠛⠿⣷⣤⠺⡱⡟⢻⢎⠗⣤⣾⠿⠛⠛⢛⠛⠻⢷⣶⣴⠗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢻⣶⡢⡀⢃⢸⠀⠀⢸⣳⠏⠀⢎⡱⠀⠹⣞⡇⠀⠀⡆⡘⢀⢔⣶⡟⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⠪⣿⣿⡘⡈⣠⣜⣰⣯⡴⠞⠛⠛⠳⢦⣽⣆⣣⣀⢁⢇⣿⣿⠕⠁⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠈⣁⣐⡒⠪⡽⣻⠥⢭⣿⢏⣤⠲⣛⣛⠶⣤⡹⣿⡭⠬⣝⣿⠅⢒⣒⣉⠁⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣫⣽⣿⡄⠀⠀⣀⢾⡅⣇⣯⢟⡇⠿⠱⢏⡡⢌⡹⠎⠿⢸⡻⢿⣸⢨⡷⣀⠀⠀⢠⣿⣯⣝⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣱⣿⠋⠁⠙⣿⢶⣲⡴⣾⡿⢟⣩⡍⡆⠉⡉⢸⠀⠀⡇⢉⠉⢠⢩⣭⡻⢿⣶⢦⣖⡶⣿⠋⠀⠙⣿⣎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣳⣿⣁⡀⢀⢞⡢⠋⠁⣰⠏⢠⣟⡵⢦⣃⣈⣮⣿⡦⢴⣿⣷⡁⣘⡰⢮⣛⡄⠹⣆⠈⠙⢔⡳⡀⢀⣈⣿⣞⣧
⠀⠀⠀⠀⠶⡷⡷⠶⡷⣾⣿⡷⣸⢾⣿⣉⢎⡱⣿⠀⣿⢺⡁⢎⠀⠀⢈⣏⢾⡷⣹⡁⠀⠀⡱⢈⡇⣿⠀⣿⢆⡱⣋⣷⡷⡏⢾⣿⣿⢾⠶⢾⠾⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⣿⡉⠁⠈⢮⠕⣄⡀⠹⣆⠘⣭⡳⠎⡍⣉⢿⣿⠗⠺⣿⡿⡉⢩⠳⢞⣭⠃⣰⠟⢀⣠⠮⡵⠁⠈⢉⣿⢯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⣿⣄⡀⣠⣿⠾⠽⢳⢿⣷⣮⣛⣃⠃⣀⣁⢸⠀⠀⣇⣈⣀⡘⣸⣛⣵⣾⠿⠞⠯⠷⣿⣄⠀⣠⣾⢏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣝⣻⣿⠃⠀⠄⠉⢾⡃⡏⣟⣎⡇⣶⡰⣎⡑⢊⣱⢆⣶⢸⣱⣻⢹⢘⡷⠉⠀⠀⠘⣿⣟⢫⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢀⣉⠩⠥⢔⣷⣽⡒⣚⣿⣎⠛⠼⣭⣭⠧⠛⣱⣿⣓⢒⣫⣾⡢⠬⠍⢉⡀⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⢀⢔⣿⣿⢱⢁⠙⢫⠸⣟⠳⢦⣤⣤⣴⠞⣻⠏⡝⠋⡈⡎⣿⣿⡢⡀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼⠿⠕⠁⡎⠸⠀⠀⢸⡽⣆⠀⢌⡱⠀⣰⢯⡇⠀⠀⡇⢁⠈⠪⠿⣧⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠟⠿⢷⣦⣤⣥⣤⣤⣶⠿⠛⢴⡱⣧⣽⢎⡦⠛⢿⣶⣤⣤⣬⣤⣴⡾⠿⠻⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽⠊⠀⠀⠀⠈⠉⠉⠹⣍⢿⣄⠀⠀⢈⡽⠯⡁⠀⠀⣠⡿⣹⠏⠉⠉⠁⠀⠀⠀⠑⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡻⢷⣦⣼⣾⣷⣧⣴⡾⢟⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣽⣹⣟⣯⠷⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡴⠠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀
⠀⠀⠀⠀⠀⠈⠟⠁⠀⡔⡡⠀⢸⢀⠄⢈⡀⡴⣸⢁⣄⡄⠀⡴⢣⢀⠇⣰⢣⠆⡤
⠀⠀⠀⠀⠀⣀⠀⠁⠀⠁⠁⠀⡜⢸⢀⡎⡸⣱⠇⢊⡞⠀⠀⠁⢎⡞⢰⢃⡎⣰⠃⠠⠤⢤⡀
⠀⠀⠀⠀⠀⢈⡟⠃⠀⣄⣀⠐⠀⠀⠘⠀⠃⠋⠰⡌⠀⠀⠂⢀⠈⠁⠉⡞⠐⠁⠀⠀⠁⠀⠃⢀⠂
⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⣤⠀⠀⠀⣶⠀⠉⠓⠂⣀⣍⣂⣀⣘⣁⣤⣴⡇⠀⢀⢰⢜⠒
⠀⠀⠀⠀⠀⠆⠴⢠⣄⣑⡀⡀⠀⡇⠀⢤⣴⠏⢢⡀⢺⣯⢻⣙⣹⣏⣿⣻⣏⡿⠟⠰⡌⢒⡄⠀⢀⠐
⠀⠀⠀⠠⠄⠀⠘⠏⠱⠈⠛⠁⢠⡾⠂⠀⠀⠀⣠⡗⢸⡿⠋⠉⠉⠉⠉⠠⣤⣶⠖⣰⣤⣾⣇⠘⠶
⠀⠀⠀⠀⠋⢂⣹⠆⢠⠁⠀⠀⣿⠛⠷⠀⠈⢻⠛⠁⢀⣤⠤⣶⢶⢶⢻⣿⡟⢓⡠⣄⠀⠄⠙⠛
⠀⠀⠀⠀⠀⠀⠈⠋⣾⣆⡀⠀⣿⠀⠀⠀⢀⠨⠁⠆⢸⣿⣇⣿⢼⣼⣶⡿⠀⠉⡰⢀⡈⠢⢹⠁
⠀⠀⠀⣀⢀⠈⡉⠀⠈⣩⡇⢲⣬⣥⣤⣾⣺⠶⢤⠇⠀⠉⠉⠑⢤⣄⡈⠻⠀⢄⠄⢻⠃⡖⠀⢆⣠⣶⠶⠆
⠀⠀⠀⠈⠛⠿⣧⣾⣦⣿⡟⣨⢯⡀⠒⡄⢉⢀⡀⡶⢠⡀⣴⠛⣬⡏⣜⠃⠘⠢⠤⠄⡉⢊⡹⠉⣉
⠀⠀⠀⠀⠀⠀⣛⠟⢛⠭⡄⢶⡄⡇⣿⡇⢸⢸⡇⡟⢸⠃⣿⡀⣿⡇⣿⡇⣾⢰⢰⠐⢷⣏⡀⣞⠋
⠀⠀⠀⠀⠀⠰⠁⠐⠋⢸⡇⢸⡇⣷⠘⡇⢘⣼⠃⡗⢀⢾⣇⡇⢻⡇⣿⡇⣿⢸⢸⠀⢿⢸⠇⠛⢷⡄
⠀⠀⠀⠀⠀⠈⠄⠀⠀⢸⡇⣆⢀⡿⠇⣇⣸⣿⠀⠏⠸⠈⠛⠿⠸⢇⣿⡇⣿⢸⢸⢡⡄⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢢⠀⢱⠀⢸⣇⣿⣴⣿⡿⠟⠛⠀⣠⣤⣴⣶⣶⣤⣤⠀⢿⣿⣿⣤⣼⣘⣇⠀⡘⠀⠰
⠀⠀⠀⠀⠀⠀⠀⣈⡁⠾⠟⠙⠊⠼⢧⠀⢰⠀⠀⠈⠉⠉⠉⠀⠀⠀⠈⢹⡯⠡⠈⠽⠗⢀⣥⡴⠁
⠀⠀⠀⠀⠀⠐⠠⠭⠿⣦⠀⠛⠠⠀⠈⠐⠿⢄⠀⠀⠀⠀⠀⠀⠀⠀⣦⡞⢭⠠⠚⡁⢶⠾⠧⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠴⠚⠋⠸⠠⣦⠒⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡰⠃⠀⠋⢰⡆⠘⠘⠓⠲
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠴⡶⣤⣤⣠⡄⠀⠈⠁⠘⠳⣄⣠⣆⠀⠀⠀⢀⣀⡦⣴⠾⣆⢴⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠈⠰⢧⡤⢣⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣋⠝⢃⠂⡀⠀⣀⣀⢴⡠⠀⠠
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠤⠤⠀⠁⠀⠈⣴⢤⡀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⡠⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠱⡛⠣⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠠⣉⣤⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠊⠁
⠀⠀⠀⠀⢀⠈⠉⠀⣬⠧⠀⠀⢤⡄⠀⠀⣠⡄⠀⢀⡀⠀⡀⠀⢤⡄⡄
⠀⠀⠀⠀⠀⠀⠔⠂⠉⢷⡀⠢⠾⠷⠫⠞⠿⠅⣤⢛⠉⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠤⣄⣠⠴⠈⡈⠀⠄⠲⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⡈⠁⠈⠀⠀⠀⠀⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠞⠋⡁⠉⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⢰⠀⠀⠀⣶⣞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⡐⠄⠀⠂⠀⠀⠳⠄⢄⡄⢠⣎⣥⡶⣬⡀⠠⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣰⣦⡴⠟⡽⣾⠟⣧⣰⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠲⡄⠀⣼⠁⣹⣇⣐⡈⠀⢀⡄⠵⠀⢸⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡀⢀⠰⣟⢫⣿⠏⠹⠆⠀⣿⡀⠘⠃⣆⠉⠀⠈⠁⠀⠀⣿⣸⠇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⣀⠀⢁⣾⡀⠂⠀⠀⠀⡄⠀⢤⠀⠙⢆⢠⡏⠀⠀⠀⣰⡆⣠⠛⡟⠀⢁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠐⣿⠾⠂⠀⠀⠀⠀⠀⠀⠀⠐⠦⠼⠖⣿⠿⠥⣀⠀⠀⠀⠈⢦⣤⣀⣀⡆⡺⣶⣤⣿⣿⡿⢿⣡⠄⠀⣠⣋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡧⠈⠀⢀⠃⠀⡠⠄⠄⠀⣠⣄⡀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠠⡈⠁⠨⣽⠿⠻⠿⢷⡾⠀⠀⠀⠀⠀⠉⢱⣾⡻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠚⠀⠰⡀⠀⠠⠊⠀⠐⠂⠄⠀⣨⡹⢢⡀⠀⠀⣦⣀⠀⠀⠀⠀⡠⣶⣞⣾⡤⢤⣄⠐⠂⢠⣴⣦⡀⠀⠀⠗⠀⠀⠉⠀⠭
⠀⠀⠀⠀⠀⣀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠁⣶⣄⠈⠙⠀⣰⣶⣆⣼⠅⠀⢻⠀⢐⣿⡏⣀⣰⣦⡋⣡⣾⠨⣛⠳⣦⠈⠳⢦⠀⠘⣻⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠨⠷⡄⡀⠈⣿⣿⣿⣧⡀⠀⢸⡋⠣⣦⡰⠀⠠⣅⠀⠀⠀⣸⡆⢀⣹⢋⡅⣭⣭⣷⡛⢟⡉⣤⣰⣎⠘⠐⠈⢡⠀⠈⡘⢹⣿⣷
⠀⠀⠀⣠⡄⠠⠄⣶⠥⠀⢻⣿⣿⣿⣟⣁⠂⢻⡲⠆⠈⠁⠀⠙⠷⣴⡖⢋⠃⢨⣵⣎⣿⠇⣸⣾⠃⣠⣿⣝⡁⣩⠄⠐⡦⣿⡀⠀⠀⠙⡿⠋
⠀⠀⠀⠹⠀⠀⠺⣧⣰⣷⣌⠛⠻⣿⣿⡯⠀⠀⣦⣄⣀⣦⣤⣀⠘⠭⠿⣽⣧⡹⡏⢿⣿⣌⡥⣾⠞⠋⡰⠋⠀⠀⠠⢀⣡⠟⠳⠀⣶⡀
⠀⠀⠀⠘⠀⢄⢀⣴⠹⠃⠈⠉⢺⣿⠋⢠⡷⠀⠹⡄⠉⠀⠈⠉⠐⣻⣿⠏⢸⣧⣵⢿⣭⢬⣿⣁⣠⡆⠀⠀⡀⣰⠗⢻⡷⠂⠀⣼⡟⠁
⠀⠀⠀⠉⠉⠉⠋⠀⠀⠀⠀⠐⣿⠁⠀⢻⣴⠄⠀⣤⣾⡿⠻⣿⢿⢹⣵⣯⣾⣿⢫⡲⡦⣴⡀⠈⠉⢄⣀⠸⠛⠿⠀⡼⢁⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠁⠙⠀⠰⠃⠈⣠⣿⡷⣿⡟⠠⣝⡷⠾⠿⢶⡶⠛⠉⠀⠀⣰⠞⠀⣿⣿⣿⣿⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠔⠀⠀⢰⣿⣿⣿⠻⠁⠀⠉⠃⠀⠀⠂⢤⠿⠗⠋⠙⠁⠀⠀⠀⢨⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣶⣯⠀⠀⠀⣽⠿⠛⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡔⠀⢈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣤⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣅⣀⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⠿⣯⢧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣮⣵⣶⣿⣛⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⢛⣽⣿⣿⣿⠟⣿⡿⠿⢿⣿⣯⣿⣿⣿⣿⠋⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣵⣿⣿⣇⣠⣼⣿⣿⣿⣿⣿⣯⣍⣉⣓⣲⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠉⠉⠉⠙⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⣿⣫⣿⣿⣿⣹⣽⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⢻⡟⠛⠉⠙⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⠁⠀⠀⠋⠁⠀⠜⠓⣿⢿⣿⡟⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠈⠁⠈⠁⠁⠘⢿⣿⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠃⠹⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⡀⠄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠧⠓⡐
⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠠⠂⠀⠰⠂⠀⠠⠄⡀⠀⠉⠀⢘⡀
⠀⠀⠀⠀⠀⠂⡀⠀⠄⢈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢢⠔⣶⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠳⡠⠤⣤⣈⡐⠄⠀⠲⣻⠆⡁⠈⠍⢲
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢐⡀⢠⣿⡿⠀⠁⢄⡀⠀⠖⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠂⠀⠀⣁⡀⠀⠀⠃
⠀⠀⠠⠀⠀⠄⠈⡀⡠⠛⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠈⡿⠀⠈⠄⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠐⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⡸⠀⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠠⢤⣵⣠⠀⠀⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠼⢿⠟⠁⠁⠄⢠⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠄⠀⠀⠀⢄⠀⠄⣎⠁⠀⣰⠛⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠰⠀⣈⠈⠀⡆⠈⣢⡴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣱⡶⣄⢀⡠⠂⠀⡀⠉⠹⡇⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠦⠙⢤⣤⣀⠀⠨⣿⣤⣿⡄⠀⠀⠈⠃⠖⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠈⠨⠹⠀⣠⠀⠘⠉⡀⠙⠄⣀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠠⠐⣿⠁⠂⠰⠀⠍⠁⠀⠀⠢⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⠻⣿⣿⣿⣿⠿⠿⠛⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣋⣉⡹⢦⣿⡄⠛⠫⣿⣼⠇⠀⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣾⣿⣿⠽⢿⣿⣿⣶⣆⣀⡁⢀⣼⣿⣿⣿⣷⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣧⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠓⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⣿⣻⣿⣷⡄⠀⠙⠿⣿⣿⣿⣿⣿⢿⣯⣳⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⢋⠘⠹⣿⣿⣦⣠⣀⣠⡉⢉⣉⣿⣏⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠟⠀⠠⠄⠛⣹⡿⣿⣿⣿⣷⣿⣿⣟⣦⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣵⣿⡝⠿⣿⣿⣯⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⠁⢸⠿⠿⢿⣿⠿⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡃⠀⢤⣨⡄⠰⠛⠁⠀⠈⠠⢀⣠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠎⢈⣿⣿⠶⣶⣿⣷⠀⢄⣀⠀⠀⠀⠀⠈⢿⣿
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠲⠀⠀⠀⠂⠀⠀⠀⠈⠁⢿⣿⣿⣷⣤⣬⣿⣿⣾⣿⣿⢧⡄⠀⠀⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣿⢷⣽⡿⡀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠀⢸⣿⣿⣿⣿⣿⢿⠟⠊⠁⠀⠙⠰⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢨⣤⣈⡿⠁⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣼⡽⠃⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠼⣿⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣷⠂⠀⢀⡑⠀⠀⠀⠄⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡅⡁⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠖⠛⠋⠘⠒⠶⡤⠆⠀⠘⢻⣾⣥⣿⣆⠠⡀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⢀⣐⣄⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣷⣶⣤⣀⡀⠚⠓⠲⣄⠠⣿⣾⣿⣿⣿⣆⠡⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣤⠀⠀⠀⣤⡄⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠙⠉⠙⠛⠛⠛⢿⣦⡻⠆⠀⠀⠀⢀⣴⣶⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠤⠀⠾⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠰⡒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠿⣽⣾⣷⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠛⠍⢙⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⡀⣰⢀⠁⠁⠘⢧⠴⢦⣀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣤⠟⣄⠠⠁⢠⠀⣠⠃⠀⠙⣴⣯⣾⣷⣡⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⣽⠷⠾⠓⠠⠼⣋⣁⣁⠠⠔⠉⠹⢿⠛⠭⡛⠛⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡉⢀⠄⣀⡀⠀⣻⣗⣀⡈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠱⡐⠋⠉⠠⠆⠉⠿⢿⣃⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⢿⣀⠀⠈⣁⣠⡶⣶⣶⣏⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢻⡽⠿⠋⠻⣽⣟⣽⣠⢠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠲⣤⣶⠘⠟⣧⣷⣚⠁⠈⠁
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⡿⣭⣀⡀⠀⠀⠈⢻⡄⠆⢹⡟⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠄⣈⡁⠒⢦⣆⣻⠈⠀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠛⣷⣰⣿⣷⠶⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣈⣽⣿⡽⠐⡏⠉⠃⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡻⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡰⠋⠈⡇
⠀⠀⠀⠀⢀⠐⠂⢄⠀⠀⠀⠸⠁⠀⠀⠈⢁⠀⠀⠀⠀⠠⠔⠈⠁⠀⡠⠠⡀
⠀⠀⠀⠀⠀⢢⡀⠀⠁⠐⢴⣧⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⡇
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡽⢷⠟⠀⠀⠀⡱⢠⠀⠐⢄⠀⠀⡰⠁⠀⠀⠀⠈⠒⡄
⠀⠀⠀⠀⠀⠈⠀⠀⡠⠊⠀⠈⣧⡀⠐⢎⢠⠊⠀⠀⠀⠙⢶⣷⡤⠶⢂⣈⠈
⠀⠀⠀⠀⠀⠀⠀⡊⣀⣀⠀⠀⡈⠹⡄⠄⠀⠑⠒⣲⠶⠋⠁⢻⡀⠀⠀⠀⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠳⠔⠁⠀⠙⢆⠀⠀⣞⣁⠀⠀⠀⢸⢰⠀⠀⡴⡊⠁⡀
⠀⠀⠀⠀⠀⢀⠠⢄⠀⠀⠀⠀⠀⠀⠈⠠⠑⢄⠀⠉⠙⢆⣠⠇⠀⠣⠠⠇⠙⣄⠈⢳⣄
⠀⠀⠀⠄⠤⠇⠀⠈⡄⡰⠋⠉⠣⡀⠀⠀⠐⢄⠙⠢⣄⠀⠀⠀⠀⠀⡄⠀⠀⠈⢦⠈⠎⠳⡀
⠀⠀⠀⡄⠀⠀⠀⠀⡇⡇⠀⠀⠀⠉⠁⢢⠀⠄⠐⠀⡈⠑⠦⣀⠀⠀⠀⠀⢀⠀⠈⢧⠘⡄⠘⢆
⢠⠀⠐⠈⢦⡀⠀⠀⢱⡇⠀⠀⢀⡠⠔⠊⠀⠀⠢⡀⠀⠁⠂⠌⡑⢦⡀⠠⠀⠑⢄⠈⣇⢐⠀⠈⢆
⠀⢂⠀⠀⠀⠉⠢⢄⣸⣇⣤⠊⠥⠄⢀⣀⠀⠀⠀⠈⠢⠀⠀⡀⠈⠑⠍⠢⣵⡀⠀⠣⢸⡈⡀⠀⠈
⠀⡼⠁⠀⠀⠀⢀⡤⠻⢾⡂⠀⠀⠀⠀⠀⣱⠤⣀⡀⠀⠀⠐⢄⠀⠀⠀⠀⠪⡳⡄⠀⠸⡇⡇⠀⠸
⠀⠣⠤⠔⠒⠍⠁⠀⠀⠀⡁⢀⠀⠀⢠⠊⡁⠀⠀⠈⠉⠒⠢⠤⣉⣢⣀⠀⠀⠈⢌⠂⠀⠃⠃⠀⠃
⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⢀⠀⠀⠀⣠⠂⠈⠃⠒⠒⠒⠒⠒⠒⠒⠊⠛⠿⢦⣄⡀⠑⡅⠐⡆⠸
⠀⠀⠀⠀⠀⠈⠀⠈⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⢀⠉⠒⢬⣆⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣀⡀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⢉⡴⠋⠸⠉⠣⣾⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣤⣀⠄⠀⢠⡎⠀⠀⠀⠀⠀⠸⠆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⢆⠀⠤⢄⢠⡏⢀⠈⣻⠛⠁⠀⠀⡆⠀⠀⠠⠦⠤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⢄⠀⠀⠀⠈⠁⠀⢳⡷⠀⠀⠀⠀⠀⠀⢊⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⠂⠀⠀⢠⠀⠀⡐⠀⠀⠀⢠⡎⢧⣀⠀⠀⠀⢀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠰⣸⣂⣾⣁⠀⠀⠀⠀⠃⡌⢳⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠽⢏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠐⢾⡿⠟⠃⠀⠀⢤⣰⡴⠁⠘⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣢⣿⣿⠏⠀⠀⠀⠹⣄⠀⠀⠀⠘⣿⡇⣀⠄⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠢⡀⠀⠀⢀⡈⣳⣤⣄⡀⠘⢓⢁⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠈⢓⡄⠘⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢄⠜⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡲⠚⠉⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠞⠁⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠁⠀⠀⠁⠀⠀⠀⣤⠀⠂⢰⡆⠀⠛⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢄⢠⠁⠀⠐⠘⢣⣄⡀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠑⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠠⠋⠀⠘⠲⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣠⠀⡠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣶⣿⣿⡿⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠃⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⠟⠛⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠙⣿⡟⠁⠈⢂⠰⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠞⠀⠀⠀⠀⢀⡼⠋⠻⠀⠀⠹⠓⢄⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡴⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢀⠀⠉⠀⠀⠀⠐⢄⠀⠀⠀⠀⢀⡠⠴⠒⠢⡀⢀⠔⠒⠦⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠹⡆⠀⠀⠀⠀⡔⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⣎⠀⠀⠀⠀⡇
⠀⢀⡀⠤⠤⢤⣀⣀⠀⠀⢇⠀⠀⠀⠀⢐⣿⣾⣤⣴⡋⠉⡁⠈⠒⠄⢰⣀⣀⣀⣈⣿⣿⣶⣠⣤⣴⣃⡀
⠀⠈⠉⠉⠛⠛⠒⠺⠿⢷⣾⣶⣦⡤⣶⡿⣿⣿⣿⣧⡀⠀⠀⠀⢀⡶⠋⠉⠉⠙⠿⣿⣧⣾⣿⠛⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠋⠀⣿⠋⠇⠀⠙⢦⡀⡠⠌⡗⠀⠀⠀⠀⢀⡼⠋⠻⠿⣧⡀⠀⠀⡼⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⣃⠀⠀⠓⠶⢤⣀⠴⡻⠁⠀⠀⠀⠈⣷⠢⢞⡧⠁⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠤⠊⠠⣀⠀⠀⠀⡠⠋⠙⠛⣖⠶⡮⠤⣤⣼⣄⡀⠀⠀⣤⣃⢰⣿⡥⠤⠄⠚⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠀⠀⠀⠀⣺⣿⣷⣚⠒⠂⠀⠽⡦⠊⠀⠀⠙⠙⢧⡀⠀⠀⠠⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢿⡟⠫⠈⠑⢦⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠄⠀⡀⠀⠀⠀⠀⢱⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢣⣀⣀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠤⠊



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