Ha ha Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣧⢸⡿⣧⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠛⠘⠉⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⢀⣤⡾⠛⠋⠉⣉⠉⠉⠉⠙⠛⢷⣦⡀⠀⠀⠀⢸⣦⣧⢸⠿⡇⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣡⡾⢋⣴⡿⠋⠀⠀⣴⣀⢀⣄⠙⣿⣄⠀⠀⠈⠃⠉⠈⠀⠁⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠘⠃⣰⠋⣴⡿⠋⠀⠀⠀⠀⠛⢃⡾⠙⣧⡘⣿⡆⠀⠀⠀⠀⢸⣦⣇⣼⣿⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⣀⠀⠀⢀⣴⠟⠁⠀⢹⣧⢸⣧⣤⣀⠀⠀⠘⠃⠉⠋⠈⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢸⣿⠀⢻⡿⣀⣴⠟⠁⠀⠀⠀⢸⡿⣼⡇⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢻⣧⡀⠘⠉⣀⣀⣀⣀⣠⣴⢟⣽⡟⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣈⣉⣛⣉⣭⣶⣿⣿⣿⡆⠀⠀⠀⢸⡿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢛⣿⣿⡉⠀⠻⢿⣿⣿⣶⣄⠀⣼⡇⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⢻⣇⠀⠀⣸⣿⣿⣿⣿⣼⡟⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢸⣿⣀⣼⣿⣻⣿⣿⣿⡏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⠛⠉⠈⠉⠈⠙⠿⠷⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠶⠶⠿⢿⣿⠛⠛⣿⡟⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⠀⠀⣿⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⣾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣶⣠⣤⡶⠾⠛⠋⠁⠀⠀⢻⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣷⡶⠟⢻⣏⠁⠀⠠⠊⠀⠀⠀⠀⢸⡟⡇
⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⣧⠀⣀⣠⢤⣶⠿⠟⠋⠉⣿⡄⠀⠈⣿⡔⠁⢠⡄⠀⠀⠀⠀⣿⣷⣇
⠀⠀⠀⠀⠀⠀⢘⣷⡤⣔⣿⡿⠛⢫⠝⠀⠀⠀⠀⠀⠸⣷⠀⠀⣹⣧⠀⣾⣿⣆⠀⠀⠀⣿⣿⣿
⠀⠀⠀⢀⣐⠤⠗⢻⣏⠀⢸⣷⡠⢾⣧⡀⠀⢀⣠⡄⠀⢻⣟⠋⠉⣿⡀⣿⣿⣿⣆⠀⠀⢸⣿⣿
⠀⠀⠀⢻⡄⠀⠀⢈⣿⡶⠾⣿⡇⠸⣿⣿⣄⠉⠀⠀⠀⠈⣿⡄⠀⢻⡇⠿⠃⠘⣿⠆⠀⢸⣿⣿⣀
⠀⠀⠀⠀⢿⡀⢀⠠⢺⣷⠀⢸⣿⠀⣿⡞⢻⣧⡀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣀⣠⡤⠴⠖⠚⠋⠉
⠀⠀⠀⠀⠘⢿⡀⠀⠀⣿⡆⠀⣿⡇⠸⠇⠀⠙⠁⠀⠀⣀⣠⣤⣴⠖⢿⡉⠁
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠘⠋⠀⠈⢁⣀⣠⣤⣶⠶⠟⠛⠋⠉⠁⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠘⣧⣀⣤⣴⣶⣿⣿⣿⣽⣵⣤⣤⣤⣤⡤⠤⢤⣤⣶⣶⣾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢛⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡧⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⡇⣶⡆⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠐⠚⠉⠀⠀⠀⠀⣀⡀⢀⣀⣀⣀⠀⠀⠀⣿⡇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢇⠀⠀⢻⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⢀⣀⠠⠠⠤⣄⠀⢠⣿⠀⠀⠀⠀⠀⠸⠀⠀⢸⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠀⠀⠀⣤⡔⠒⠒⢲⢸⣿⡀⠀⠀⢹⠀⢸⣿⠀⠀⠀⡀⠀⠀⢇⠀⠘⣿⡇⠀⠀⡇
⠀⠀⠀⣀⣀⣀⣀⣀⢸⣿⡉⠉⠉⢹⠠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⠀⣿⡇⠀⠀⢸⠀⢸⡿⠀⠀⢸⣇⠀⠀⠈⡄⢠⢿⣷⠀⠀⡇
⠀⠀⠀⣿⡇⠀⠀⢸⡄⣿⡇⠀⠀⢸⠀⠀⠀⣶⡖⠀⠀⠀⠐⡆⠀⣿⡇⠀⠀⠈⡇⣿⡇⠀⠀⠘⡀⣼⡇⠀⠀⢸⣿⡀⠀⠀⢰⠈⢼⣿⠶⠶⠷⠀⡀
⠀⠀⠀⣿⡇⠀⠀⠈⡇⣿⡇⠀⠀⠸⡄⠀⠀⣿⡇⠀⠀⠀⠀⢱⠀⢻⣷⠀⠀⠀⣇⣹⡿⠀⠀⠀⡇⣿⡇⠀⠀⠈⠉⠀⠀⠀⠀⡆⢸⣿⠀⠀⠀⡇⠁
⠀⠀⠀⢹⣷⠀⠀⠀⣇⢸⣿⠀⠀⠀⡇⠀⢀⣿⠁⠀⠀⠀⠀⠀⠆⢸⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⢣⣿⠇⠀⠀⢀⣀⣀⡀⠀⠀⠰⢸⣿⣀⣀⣀⡟
⠀⠀⠀⢸⣿⠀⠀⠀⠙⠚⠉⠀⠀⠀⢃⠀⢸⣿⠀⠀⠀⡆⠀⠀⠸⡘⣿⡆⠀⠀⢀⣀⣤⡄⠀⠀⢸⣿⠀⠀⠀⢸⠛⣿⣇⠀⠀⠀⢟⠛⠛⠛⠛⠃
⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠀⠀⠀⣿⠀⠀⠀⠣⣿⡇⠀⠀⠀⡟⣿⡇⠀⠀⠘⣿⠀⠀⠀⢸⠀⢸⣿⣶⣶⣶⣾⡄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⡿⣿⡇⠀⠀⠈⡆⣼⡏⠀⠀⠐⠿⠃⠀⠀⠘⣿⣿⠀⠀⠀⢃⢹⣿⠀⠀⠀⣿⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢹⣿⠀⠀⠀⢃⢸⣿⠀⠀⠀⣇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⢸⠸⣿⣄⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠸⣿⡄⠀⠀⢸⠸⣿⡄⠀⠀⢹⣿⡇⠀⠀⢰⣶⣾⡇⠀⠀⠀⣿⣷⣶⣶⣾⡇⠻⠿⠛⠛⠻⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠇
⠀⠀⠀⠀⠀⣿⣇⣀⣀⣨⡆⢿⣷⣶⣶⣾⣿⠁⠀⠀⢸⠀⢹⣿⣀⣀⣀⣨⡉⠉⠉⠀⠀⢀⣀⣀⣤⣤⣤⣶⣶⡾⠿⠿⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠃⣾⣆⠀⠀⢸⣿⣀⣀⣀⣼⠀⠈⠛⠛⠛⠛⠛⠃⠀⣼⠿⠿⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣤⣘⣛⣛⣛⠿⠋⠺⣿⣶⣄⡀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⢈⣳⣥⡀⠱⣄⣠⡬⠟⢶⣤⠜⠀⠸⡁⠀⠀⡟⣄⠤⠄⢮⡢⠤⢿⠉⠉⣿⡉⠉⡇⠀⠀⠘⡧⡀⠀⠘⡄⠀⠘⡈⡆⠀⠘
⠺⠂⠉⡝⢆⠀⢸⠀⢀⠀⢹⠢⡀⠀⢣⠀⠀⢃⢹⠀⠀⢸⠑⡄⢸⠀⠀⡇⢱⠀⡇⠀⣷⡀⠰⡘⡄⠀⢰⠀⠀⡗⡏⠹⢆
⠀⡆⠀⢰⠈⡆⠀⠀⢸⢆⠀⢃⢣⠀⠈⡆⠀⢸⢸⡄⠀⠈⣀⣇⡸⠀⠀⠇⠸⡀⡇⠀⠃⠓⠀⢣⢱⡀⠀⢇⣀⣷⡇⠀⡆
⠔⠃⠀⢸⠀⡇⡇⠀⠈⠉⠀⠘⡆⢆⠀⠸⡤⠚⢾⡇⠀⠀⠁⠀⠀⠀⠀⢰⠀⡇⠃⠀⣀⠤⡀⠀⢣⢣⠀⠈⢆⣥⠗⠀⠧
⠤⡀⠀⠀⡆⢠⡇⠀⢠⡖⢢⠀⠘⡌⡄⠀⢙⡖⢎⢱⠀⠀⣯⡉⠉⡇⠀⠘⡄⢿⠀⠀⠙⢦⢵⠀⠈⢆⢆⠀⢏⢩⣹⡄⢀
⡀⣁⠀⠀⢇⢸⡇⠀⢸⠱⡞⡇⠀⠘⡼⡀⠸⣀⠨⣿⡀⠀⢇⢹⠊⠇⠀⠀⠇⢸⠀⠀⠀⢸⠀⢇⢀⣈⣾⡀⠘⡍⣍⡇⢸
⡇⠸⠀⠀⠸⡀⡇⠀⢸⠸⡇⢸⡤⠤⠺⣧⠀⠣⡀⠽⡇⠀⢸⠀⡄⢸⣀⡀⠼⣼⡆⠒⠲⣸⠀⠘⢆⡀⠬⠃⠀⠈⢏⠀⠸
⠇⠀⣧⠐⠒⠣⣿⠉⠉⢲⡃⠀⠑⠒⠒⠉⠀⠀⠀⠀⠹⡉⠉⢣⣇⡠⡷⣀⡀⠼⡟⠶⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀
⣾⡀⠬⡦⠔⠒⠻⡛⠋⠉⠹⣄⠤⠴⣄⠀⠀⡆⠉⢹⢆⠈⠚⠋⠁⠀⠹⢦⡀⠀⠱⡀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⡈⠣⣀
⠁⠀⠀⠹⡢⡀⠀⠱⡀⠀⢸⢸⠀⠀⢉⢳⠀⠁⠀⠘⠈⠇⢰⠀⠀⣆⠀⢣⢡⠀⠀⢃⠀⠘⣼⠆⠒⣦⠀⠀⡏⠁⢹⢆
⠀⢸⢇⠀⢣⠱⠀⠀⢃⠀⠠⣼⠀⠀⢸⣸⣀⡼⠀⠀⡇⢰⢸⠀⠀⠆⠃⠀⢆⢃⠀⠘⣄⣀⣿⡀⠀⠁⢱⠀⡇⠀⢸⠀⠇
⠀⠘⠒⠃⠀⢆⢣⠀⠘⣄⡠⢾⡄⠀⠀⠁⠀⠀⠀⠀⠃⠸⣸⠀⠀⣀⢤⠀⠘⡌⠆⠀⠙⣄⣼⠇⠀⢸⣸⡀⠄⠀⠀⡆⢸
⠀⠀⡠⠤⠀⠈⠆⢆⠀⠙⢤⠼⡇⠀⠰⣏⠉⢹⠀⠀⢸⠀⣿⠀⠀⡗⣄⣧⠀⠘⡜⡄⠀⡏⠙⣷⡀⠀⠀⠀⡀⠀⠀⢇⠸
⠀⠀⡗⡤⢇⠀⠈⡜⡄⠐⡏⢀⣿⡀⠀⡆⢳⠘⡆⠀⠈⡄⢿⠀⠀⡇⡇⠘⡄⠀⣸⣴⠀⢸⡉⣿⡇⠸⣏⠀⢸⠀⠀⢸
⠀⠀⡇⡇⠘⣄⣀⡸⣵⠀⠹⡁⣹⡇⠀⢡⢸⠀⢡⣀⡀⢥⣸⠤⠔⢧⡇⠀⠹⣅⡠⠼⠃⠀⠉⢹⠀⢈⡤⢿⠛⣦⠀⠈⡄
⠐⠒⢣⡇⠀⠙⡄⠤⠜⢃⣀⣉⠀⢳⡉⢹⢾⡒⠉⣧⣀⣀⡽⠳⠤⡴⠓⢲⡀⠀⠀⠊⠉⠉⢷⣸⠀⠈⣧⢸⠀⢷⢡⠤⠷
⡑⠄⢲⠋⠉⣷⡀⠀⢸⠁⠀⠈⢷⣄⠙⠚⣏⠁⠀⡏⠣⠀⡟⢄⠀⡇⠀⢸⠙⡄⢸⠀⢠⡄⠈⡎⢯⡉⠙⣾⡀⢸⢾⡀⠤
⡙⣆⠈⡀⠀⢁⠱⡀⠈⠀⢰⡀⠘⡌⡆⠀⠘⡄⠀⢹⢀⠀⢀⢸⠀⡇⠀⠈⡀⢇⢸⠀⢸⣹⡄⠸⡘⡍⠉⢹⠀⠀⣼⡇
⡇⣇⣀⡇⠀⢸⠀⡇⡆⠀⠸⠼⠀⠰⡘⡄⠀⢡⠀⣸⣼⠀⠘⠚⠉⠁⠀⠀⡇⢸⢸⠀⠀⠀⠀⠀⠱⡸⡀⠀⢳⠉⢹⡇
⠉⠉⠀⠀⠀⠘⡀⠇⡇⠀⢀⣀⡀⠀⢡⠱⠀⠈⢣⣀⡿⠀⢠⡔⠒⢲⠀⠀⢃⠈⣾⠀⠐⣏⠙⡄⠀⠱⢱⠀⠠⠟⠓⣦
⢲⡈⠉⠇⠀⠀⡇⢸⡇⠀⢸⢦⣸⡄⠀⢣⢣⠀⢰⠉⢻⣆⠸⡙⣤⠼⡀⠀⠸⡀⣿⠀⠀⡆⡏⢱⠀⠀⢡⣃⠀⢧⠒⢻⡆
⢰⠙⡖⢺⠀⠀⢰⠘⡇⠀⢸⠀⠁⢡⠀⠀⣫⡆⠀⠗⢹⣿⠀⡇⢠⠀⡇⠀⠀⣇⢻⣀⣠⡇⡇⠀⢷⠒⠉⣻⡄⠈⠒⠚⡇
⠈⡄⡇⠈⣄⣀⡈⡆⣧⠤⠼⣀⠀⠈⢏⣉⣀⡿⠀⠈⠙⡥⠀⠲⣸⠀⠹⡈⠉⠈⣾⣦⣠⣼⠇⠀⠀⡟⠋⠉⢹⢆⠀⠀⢡

⣿⣄⣀⣾⡇⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⣠⠀⠀⢺⣶⡀⠀⢸⣿⣿⣄
⣿⠟⠻⣿⠇⢀⣼⣿⣿⡀⠀⠀⠀⠀⠀⢻⣷⣶⢿⣿⡆⠀⣿⡿⠟⢿⡇⠀⠀⠀⠀⣾⣇⣀⣼⣧⠀⠀⣴⣧
⠃⠀⠰⠟⠀⣼⠟⠛⣿⡇⠀⠀⠀⠀⠀⠸⣿⡏⠀⠘⡿⠀⠻⠃⠀⠀⠉⠀⠀⠀⠀⣿⡿⠛⢿⡇⠀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠚⠃⢸⠏⠉⠹⡇⠀⠀⣀
⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⣿⣷⣄⡀⠀⠀⢀⡀
⣼⣿⠀⢀⣾⣷⡀⠀⠀⠀⠀⣶⣀⣶⠀⣠⡆⠀⠀⠀⠀⣠⠀⢠⣦⡀⠀⣼⣷⡀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣿⣷⡀⠀⣿⣿⠿⢿⡄⠀⢸⣷
⢻⡏⠀⣾⣿⢿⣧⠀⠀⠀⠘⠟⠉⡟⢰⠿⢿⠀⠀⠀⠀⣿⣶⣾⣿⡇⢠⣿⡿⣿⡆⠀⠀⠀⠀⠀⢹⣿⣿⠟⠻⣧⠀⢹⡇⠀⠀⠁⠀⣿⣿
⠘⠁⠘⠋⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣿⠀⠸⠇⠘⠏⠀⠈⠃⠀⠀⠀⠀⠀⠀⠻⣿⠄⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⢠⣦⠀⠀⠀⣰⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣶⣦⣾⣿⠃⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣦⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠙⣿⠀⢸⣿⠿⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⣿⠀⢠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⡀⠘⠁⠀⠀⠋⠀⠘⠃⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣀⣼⣿⡆⠀⠀⣠⣴⡄⠀⠘⠿⠁⠠⠿⠀⣿⠋⠙⣿
⠀⠀⡀⠀⠀⢠⣿⣦⡀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⠿⢻⢿⣿⠁⠀⣰⣿⣿⣷
⠀⢸⣿⣆⠀⢸⣿⣿⣿⣧⠀⠀⠀⢸⣧⣄⣼⣿⠀⢀⣾⣿⡄⠀⠀⠀⠻⠟⠀⠀⣼⡇⠀⣸⡿⠿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠿⣿⡄⠘⣿⠁⠀⠙⠃⠀⠀⢸⣿⠋⠙⣿⠀⣾⡿⠿⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠟⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⡇⠀⠘⠃⠀⠉⠀⣀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠛⠀⠀⠙
⠈⠁⠀⠀⠀⠀⠀⣼⣧⡀⣰⣶⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⣴⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⣿⠿⠻⣿⡏⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⢸⣧⣤⣿⡇⠀⣼⣿⣆⠀⠀⠀⠀⠀⠀⢰⣿⡿⢿⣿⠃⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠠⠿⠀⣼⡿⢿⣿⡄⠀⠀⠀⠀⠀⠸⣿⠃⢹⡇⢠⡟⠋⢻⡇⠀⠀⠀⠀⠀⠘⠛⠀⢸⠟⢀⣿⠿⢿⣿
⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈⠉⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠏
⠀⣀⡀⠀⠀⣿⡿⣷⣄⡀
⠀⣿⣿⡀⠀⣿⣿⠟⠻⣷⠀⠀⠀⠀⠀⢰⣿⡁⠀⣰⣿⡄⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⣤
⣿⡿⠟⣷⡀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⠃⠀⣠⣿⢿⣷⠀⠀⠀⠀⠀⣠⡀⠀⢺⣿⡄⠀⢸⣿⣻⣷⣄⠀⠀⠀⠀⠀⠀⢻
⣿⡄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠀⢸⣿⠀⢰⣿⠿⠿⣿⡇⠀⠀⠀⠀⢻⣿⣶⣿⣿⣷⠀⢸⣿⠛⠙⢿⡄
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠿⠋⠀⠀⢻⠇⠀⠀⠀⠀⠈⣿⣿⠀⠀⡿⠂⠘⠏
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡏⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠆⠀⠀⠀⠀⠠⣶⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⢿⡇⠀⠀⠀⠀⠀⠀⠀⢈⠀⣷⡘⣤⠃⠀⠀⠀⢴⣶⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⠞⠰⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣿⡇⢀⠀⠀⠀⢴⣯⠄⠻⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢈⣾⡀⠂⠀⠀⠀⠀⠀⠀⢻⣼⡇⢸⣷⣬⣄⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠘⢹⣷⡀⢀⠀⠀⠀⠀⠴⢾⣿⣷⣴⣻⣿⣠⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠸⣿⣏⣿⣄⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⢹⣿⢃⠀⠀⠠⡶⣤⡀⡀⢐⠀⠂⢀⠀⠀⢠⣤⣌⠊⣠⠄⡉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠉⡿⣿⣿⣎⢄⠐⠀⣰⣿⣿⣿⣿⣿⡌⢹⣇⣄⠀⠠⣦⠀⠻⠆⡉⠀⣠⡌⠀⠀⢿⣿⢿⡅⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣣⠂⠀⠠⣿⣿⣿⣾⣴⣿⣿⡿⠿⠿⠿⠟⠷⣶⠾⣻⡟⣰⣿⡿⣃⠀⠛⠙⢿⣿⠀⠸⣀⣷⡶⠐⠦⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⡄⠀⠀⠀⠉⠲⣿⣿⣠⣿⣷⠀⠀⠚⠁⠠⣦⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠈⢛⣽⣿⣿⣿⡌⠻⣿⣿⣏⠁⠀⠀⢀⠀⢄⠀⠹⣿⣿⣿⣿⡿⡄⠀⠀⠀⠨⣤⡄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⣹⢇⣿⣿⣿⣿⣿⠀⠀⠘⣿⣿⣆⠈⠲⣿⠀⢀⣷⣄⠹⣿⣿⣿⣿⣄⣄⠀⢠⠜⠇⠀⡄⠀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠚⠛⣿⣿⡿⣿⣿⣿⣇⠀⠀⠈⠻⠮⢂⣀⠀⣳⣼⣿⣿⣆⢻⡇⠹⣷⠙⢿⣇⠀⠀⠀⢻⡉⢀⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠄⣼⣿⣿⠁⢀⣿⣿⡏⠀⠀⠀⠀⠀⠐⠈⣛⣽⣿⣿⣿⣿⡌⠃⠀⠛⠀⣻⡏⠆⠀⣀⠊⡀⠀⠀⠀⠀⠚⣃⣀⣠
⠀⠀⠀⠀⠀⠀⠀⡼⠏⠂⣴⣿⣿⣿⢀⡼⡟⢿⠁⠀⠀⠀⠀⠀⠀⣸⣿⠿⠝⠋⢻⣿⢷⡀⠀⠀⢠⣁⠀⠀⣶⣿⣦⡁⢀⣀⣄⣀⠰⠿⠛⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣷⡄⠀⢸⠋⠙⠁⠻⠛⠋⠁⠀⠉⣻⣉⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣸⣿⣿⣿⡇⣿⡟⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⡀⣸⠿⠃⠀⠀⢀⡀⠀⠀⠀⠁⠈⠃⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣿⣿⣿⣿⣧⢱⣌⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢸⣿⡗⣟⣴⣶⣶⡖⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢽⣿⣿⣿⣾⡌⢹⡁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⠃⣾⣿⣿⣸⣿⣿⡏⠙⠁⠀⠀⠀⠀⠀⠈⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣰⣿⣿⠛⠛⣱⡄⢀⠀⠀⠀⠀⣠⣾⠇⣠⡞⢰⣿⣿⢧⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⢼⣹⡇⠐⣿⣿⡁⠄⠹⢿⣿⣶⠉⢿⣶⣿⣡⢼⣿⢫⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠸⣇⠛⢷⣄⠈⠁⠀⠀⢀⢋⣿⡏⠀⠀⣿⣿⢃⡼⣣⣿⡟⠀⠀⠀⠀⠀⣠⣴⣾⣿⡟⢟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⣷⢤⡀⠀⠀⠀⠀⠈⠸⣿⣿⠀⡀⣼⣧⢋⣾⡿⠋⠀⠀⠀⣀⣠⣾⣿⣿⣿⣷⡅⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⠘⢢⠄⠀⠀⠀⠀⠀⡇⠙⣽⡻⣧⠙⣤⣼⠏⠀⣠⣴⣶⢿⠇⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆⠀⠀⠃⠀⠀⠀⠀⠐⠲⢦⠄⠿⢷⣦⡀⢻⡝⢠⣾⣿⣿⣧⠄⢠⣿⣿⡿⠛⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⢶⡄⢀⣠⡞⠢⡄⠛⠁⣿⠒⢻⣿⣿⣯⣍⠀⢸⡿⠋⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⣀⠘⠀⣠⣞⣿⣿⠀⠀⠻⣤⢀⡟⠀⠀⠹⣏⠁⠈⢠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣶⡏⠙⠀⢀⣀⠀⠀⢠⣾⠃⠀⠀⠀⢨⣭⣿⣿⡇⠀⠀⠀⠀⡃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⡠⠛⠋⢀⣴⠿⠁⠀⠀⠀⠀⡙⠛⠃⠈⠀⠀⠀⠀⠀⢃⣈⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⡀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠃⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣌⣀⡠⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⢈⣣⣥⣀⠱⣄⣠⡬⠟⢶⣤⠜⠀⠸⡁⠀⠀⡟⣄⠤⠄⢮⡢⠄⢿⠉⠉⣿⡉⠉⡇⠀⠀⠘⡧⡀⠀⠘⡄⠀⠘⡈⡆⠀⠘
⠺⠂⠉⡟⢆⠀⢸⠀⢀⠀⢹⠢⡀⠀⢣⠀⠀⢃⢸⠀⠀⢸⠑⡄⢸⠀⠀⡇⢱⠀⡇⠀⣷⡀⠰⡘⡄⠀⢱⠀⠀⡗⡏⠹⢆
⠀⡇⠀⢰⠈⡆⠀⠀⢸⢆⠀⢃⢣⠀⠈⡆⠀⢸⢸⡀⠀⠘⣀⣇⡸⠀⠀⠇⠸⡀⡇⠀⠣⠓⠀⢣⢱⡀⠀⢇⣀⣷⡇⠀⡆
⠔⠃⠀⢸⠀⡇⡇⠀⠈⠉⠁⠈⡆⢆⠀⠸⡤⠚⢾⡇⠀⠀⠁⠀⠀⠀⠀⢰⠀⡇⠇⠀⣀⠤⡀⠀⢣⢣⠀⠈⢦⣥⠗⠀⠣
⠠⡀⠀⠀⡆⢱⡇⠀⢠⡖⢢⠀⠘⡌⡄⠀⢙⡖⢎⢱⠀⠀⣯⡉⠉⡇⠀⠈⡄⢿⠀⠀⠙⢄⢵⠀⠈⢂⢆⠀⢏⢩⣹⡄⢀
⡀⣁⠀⠀⢇⢸⡇⠀⢸⠱⡖⡇⠀⠘⡼⡀⠸⣀⠨⣿⡀⠀⢇⢹⠂⠇⠀⠀⠇⢸⠀⠀⠀⢸⠀⢇⠀⣈⣾⡀⠘⡍⣍⡇⢸
⡇⠸⠀⠀⠸⡀⡇⠀⢸⠸⡇⢸⡤⠤⠺⣧⠀⠣⡀⠽⡇⠀⢸⠈⡄⢸⣀⡀⠼⣼⡆⠒⠲⣸⠀⠘⢇⡀⠬⠃⠀⠈⢏⠀⠸
⠇⠀⣧⠐⠒⠣⣿⠉⠉⢲⡃⠀⠑⠔⠒⠋⠀⠀⠀⠀⠹⡉⠉⢣⣇⡠⡷⣀⡀⠼⡟⠶⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀
⣾⡀⠬⡦⠐⠒⠻⡛⠋⠉⠹⣄⠤⠴⣄⠀⠀⡎⠉⢹⢆⠈⠚⠋⠁⠀⠹⢦⡀⠀⠱⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⡈⠣⣀
⠁⠀⠀⠹⡢⡀⠀⠱⠀⠀⢸⢸⠀⠀⢉⢳⠀⠃⠀⠘⠈⢇⢰⠀⠐⣆⠀⢣⠱⠀⠀⢃⠀⠈⣼⠆⠒⣦⠀⠀⡏⠁⢹⢆
⠀⠰⢧⠀⢣⠱⠀⠀⢇⠀⠠⣼⠀⠀⢸⣸⣀⡴⠀⠀⡆⢸⢸⠀⠀⠆⠃⠀⢇⢣⠀⠈⣄⣀⣿⡀⠀⠃⢱⠀⡇⠀⢸⠀⠇
⠀⠐⠒⠃⠀⢇⢣⠀⠘⣄⡠⢿⡄⠀⠀⠁⠀⠀⠀⠀⠃⠸⢸⠀⠀⣀⢤⠀⠘⡌⢆⠀⠙⣄⣼⠇⠀⢸⣸⡠⠄⠀⠀⡆⢸
⠀⠀⡠⠤⠀⠈⡎⠆⠀⠙⢤⠼⡇⠀⠰⣏⠉⢹⠀⠀⢸⠀⣿⠀⠀⡗⣄⣇⠀⠘⡜⡄⠀⡏⠉⣷⡀⠀⠀⠀⡀⠀⠀⢇⠸
⠀⠀⡗⡤⢇⠀⠈⡜⡄⠀⡏⢀⣿⡀⠀⡆⢳⠚⡆⠀⠈⡄⢿⠀⠀⡇⡇⠘⡄⠀⣸⣵⠀⢸⡉⢿⡇⠸⢏⠁⢸⠀⠀⢸
⠀⠀⡇⡇⠈⣄⣀⡸⣴⠀⠹⡁⣹⠇⠀⢡⢸⠀⢡⣀⣀⢥⣸⠤⠔⢇⡇⠀⠹⣄⡠⠼⠃⠀⠉⢹⠀⢈⡤⢿⠛⣦⠀⠈⡄
⡐⠒⢣⡇⠀⠙⠄⠤⠜⠃⣀⣉⠀⢳⡉⢹⢾⡒⠉⣧⣀⣠⡽⠳⠤⡴⠓⢲⡀⠀⢀⠊⠉⠉⢷⣸⠀⠈⣧⢸⠀⢿⢡⠤⠷
⡑⠄⢲⠋⠉⣷⡀⠀⢸⠁⠀⠈⢷⣄⠙⠚⢏⠁⠀⡏⠧⠀⡟⢄⠀⡇⠀⢸⠙⡄⢸⠀⢠⡄⠈⡎⢯⡉⠉⣾⡀⢸⢾⣀⠤
⡙⡄⠈⡄⠀⢃⠱⡀⠘⠀⢰⡀⠘⡌⠆⠀⠘⡀⠀⢹⠀⠀⠀⢸⠀⡇⠀⠈⡀⢇⢸⠀⢸⣹⡄⠘⡈⡍⠉⢹⠀⠀⣼⡇
⣇⣇⣀⡇⠀⢸⠀⡇⡇⠀⠸⠴⠀⠰⡘⡄⠀⢡⠀⣸⣘⠀⠘⠚⠉⠁⠀⠀⡇⢸⢸⠀⠀⠀⠀⠀⠱⡸⡀⠀⢳⠉⢹⡇
⠉⠉⠀⠀⠀⠘⡀⠇⡇⠀⢀⣀⡀⠀⢣⠱⠀⠈⢫⣀⡿⠀⢠⡔⠒⢲⠀⠀⢃⠈⣾⠀⠐⣏⠈⡄⠀⠡⢱⠀⢠⠟⠓⣶
⢲⡋⠉⡇⠀⠀⡇⢸⡇⠀⢸⢦⣸⡄⠀⢣⢣⠀⢰⠉⢻⣄⠸⡙⣤⠼⡀⠀⠸⡀⣿⠀⠀⡇⡏⢱⠀⠀⢡⢃⠀⢧⠒⢻⡆
⢸⠙⡖⢺⠀⠀⢰⠘⡇⠀⢸⠀⠁⢡⠀⠀⣫⡆⠀⢗⢹⣿⠀⡇⢀⠀⡇⠀⠀⣇⢻⣀⣠⡇⡇⠀⢷⠒⠉⣻⡄⠈⠒⠚⡇
⠈⡇⡇⠈⣄⣀⡨⡆⣧⠤⠼⣀⠀⠈⢏⣉⣀⡿⠀⠈⠙⡥⠀⠺⣸⠀⠹⡉⠉⠈⣾⣦⣠⣼⠇⠀⠀⡟⠋⠉⢹⢆⠀⠀⢡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣖⠒⠈⠀⢠⣀⣀⠹⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣦⢤⣄⡀⠀⠀⠲⠶⢮⣽⣏⡉⠉⠉⠀⠒⢤⣤⠏⠉⠛⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⠳⣦⣤⣹⡶⠚⠋⠙⠲⢤⠀⠀⠰⢶⣶⢶⣾⣧⣤⣤⣅⣉⠓⠂
⠀⠀⠀⡀⠰⣄⡀⠀⠀⠀⠀⠀⢨⡝⢳⣾⣏⡀⠉⣻⢄⡀⢠⣷⠀⢤⣤⣀⠈⠻⣾⡃⠀⠀⠀⠈⠉⠁
⠀⣀⠀⢹⡄⢿⠟⠲⢤⣀⠀⢦⣰⡟⢧⣀⠉⠻⠆⣿⣸⡇⣼⣸⡆⠀⠈⠛⠷⣶⡋⢳⣄
⠀⠹⣶⠋⠷⢼⣟⢻⡖⠈⢷⠉⢻⡇⣭⣻⣄⢀⠀⣿⢹⣥⠇⢀⡃⢶⣄⠀⢠⡟⠙⢷⣽⣦⡀
⠀⠀⠘⢯⡙⠚⠤⡉⣌⢿⠟⠦⢜⢀⠘⣷⢈⡟⠛⠻⠼⡇⠀⢸⠛⢦⡙⢿⣾⠁⠀⠀⠈⠛⠗
⠀⠀⠀⠀⠀⠀⠹⣦⠾⣾⡇⢲⡀⢈⣶⠘⣿⠀⠀⢠⠀⠀⣆⢸⣀⡤⠟⢶⣍⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢧⠘⠆⠀⠻⣏⠈⢣⣹⡄⠀⢘⣧⠖⠻⣾⡏⠀⠀⠀⢙⡢⠈⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡂⠀⠈⣿⠳⢮⣽⣧⠀⢻⡇⣄⠀⠀⢸⣇⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣠⡿⣆⠀⢹⣇⡴⠋⠻⡷⢾⣄⣿⣀⡤⠴⣿⢰⣏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⠋⠀⠈⠳⡌⣿⡀⠀⠀⠁⠀⠈⢿⡃⠀⠀⢸⣿⠁⢻⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠙⠺⣇⠀⠀⠀⠀⢰⣼⡇⠀⠀⢸⡇⠀⣬⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡀⠀⠀⣿⠀⠀⠀⢈⣿⡇⣼⣷⢸⢧⡄⢸⡄⣿⠿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢷⡀⢸⣿⡄⠀⢿⣤⡴⠞⠋⢹⡇⡿⢻⣀⢸⡷⠻⣇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣠⢷⡀⣿⣹⡄⢸⡇⠀⠀⠀⠀⢿⠷⠛⡇⢸⠃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⢳⣿⠁⠻⢸⡇⠀⠀⠀⠀⠋⠀⠀⣇⢸⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠚⠶⠀⣠⣆⡀⠀⢀⠀⠀⢶⠏⠁⠀⠐⠀⢢⡶⢿⠁⢀⠀⠘⠏⠋⠇⠀⠘⠻⠏⠀⠠⠀⠁⠁⠀⠀⠀⠀⡸⠖⠁⠀⠀⢀
⠀⣄⠈⠁⣻⠕⠀⠀⣀⠀⠙⠉⠀⠜⢦⠄⠀⡈⠀⠀⠈⠛⠂⠀⣄⢀⠀⠄⠀⡀⠐⠆⠀⠀⠀⠈⠀⠠⠀⢠⠀⠀⠃
⣀⡀⠀⢀⠀⠀⢈⠀⠈⠀⠘⠶⠇⢀⠀⢠⠈⣹⠄⠀⣮⡷⢄⠀⠙⠉⠠⠤⣆⠀⠀⢀⣴⣐⡄⠈⠤⣴⠄⠀⠀⠈⠰⣺⡍
⣛⠈⠀⣀⣀⠀⠈⠀⠈⡠⣶⡂⠀⢸⢺⡞⠇⠀⠀⠈⠛⠆⠀⠀⠦⠀⠠⢼⠯⠁⠀⠈⠧⠁⠃⠠⢵⣟⠃⠀⣀⠀⠀⠩⠻
⣀⠀⢀⣰⠿⠄⠘⠷⠇⠘⢻⠖⠃⠀⠀⢀⡀⠀⠰⠂⡈⠀⡰⣤⣀⠀⠂⠀⠀⠰⠦⠆⠀⠐⠀⢤⠀⠀⠀⣔⣬⣟⠂⢀⣠
⠏⠀⠀⠉⠁⢠⡄⠀⠔⠀⢀⠀⠐⠆⠀⠀⢀⣲⠀⢀⠀⠀⢽⣥⠀⠀⢠⡿⠀⢀⡀⠀⠠⠄⠀⣠⣔⣀⠀⡈⠑⠁⠀⠈⠏
⣠⡤⡀⠁⠀⠙⠁⠀⡀⡀⠈⠀⣄⠀⠲⠀⠈⠁⠀⢈⠁⠀⠠⠀⠠⡄⢀⡀⠀⠉⠿⠂⢀⡀⠈⠑⣹⠧⠀⠈⠀⣼⣤⣼
⢨⣽⡏⠀⠠⣬⢶⡈⠛⠙⢸⣼⣞⠧⠐⢀⢨⡶⣄⠀⣆⣦⣠⠀⡀⠀⢀⣥⠀⠀⠰⠂⠀⢀⣀⠀⠀⠀⢠⠀⠀⠀⠉⠘⢀
⣤⠀⠀⡀⠑⠾⠅⠀⠀⠀⠀⠁⠀⠠⠀⠈⠿⠛⠀⠀⠏⠋⠏⢁⢀⠀⠹⢗⡧⠂⠀⠀⠈⠉⣳⡗⠀⢀⠀⠀⣀⣶⡀⠸⠞
⠃⠀⠀⢁⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠖⠀⠄⠀⠂⢀⣀⡄⠀⠙⠋⠀⠀⠈⡀⠀⢺⠟⠂⠈⠉⠁⢀⠀⢀⠐⢾⣗⠈⢀⠄
⡀⣽⡓⠀⠀⠀⠀⢴⡴⠈⠀⣴⣴⣀⠀⠀⢐⡷⠆⠈⠙⠁⠠⢖⣥⡆⠀⠽⠉⢠⠀⢀⠀⠓⠚⠀⠈⠀⢀⠀⠀⢀⠀⢀⣠
⣿⡿⢷⣶⣶⣶⣶⣿⣿⣶⣶⣷⣶⣿⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣾⣿⣾⣿⣶⣶⣶⣶⣾⣶⣾⣶⣶⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣰⣿⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⢰⣿⣿⣿⡀⠀⣰⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢺⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⢸⣿⣿⣿⡇⢰⣿⣿⣿⡟⢿⣿⣿⣿⣷⡄⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣦⠀⠀⠘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣷⡀⠀⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⠻⣿⠿⠏⠘⠛⣻⣿⣦⣄⠀⠀⠀⠻⣿⣿⠟⠁⠀⠘⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣦⣀⠀⠈⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⢿⡿⠿⢻⣶⣿⣿⡆⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣬⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣀⣤⣼⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡧⠀⠀⠀⠘⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⣿⡿⠛⠛⠉⠀⠀⠈⠛⠿⡿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠟⠛⢿⣿⣿⣿⡇⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣴⣶⣷⣶⣄⠀⠀⠀⢹⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠸⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⡀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⣀⡀⠀⠀⢴⣾⣿⣿⡀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣿⣿⣿⣷⡄⠀⠀⣤⣴⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⠟⠀⠙⣿⣿⣿⣿⣆⠀⢻⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢀⣠⣼⣿⣿⣿⣷⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠟⢻⣿⣿⣿⡇⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠻⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠃

⠀⠀⠚⣦⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠔⣶⠀⠀⣀⠀⠀⡠⡤⢰⠤⡀⢀⣀⢀⣀⠄⠀⢀
⠀⠀⠀⠘⡇⠐⢄⠈⢀⠀⠈⠀⠰⠀⠉⠀⠀⡄⠀⣿⠀⠉⠇⡎⠀⠒⠱⡈⠛⠋⠸⢈⠸⠋⠢
⠀⠀⠀⠀⣿⠀⣀⣀⠀⠀⡠⠀⣀⠀⠒⢀⡀⡇⢀⡟⠀⠀⢀⡉⠀⠀⠀⢠⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡏⠈⢐⡄⢳⠀⢠⣬⠌⡇⠀⣾⡟⢠⡼⠃⠐⣶⢺⠤⠀⠀⠐⠾⣿⢿⣤⠀⠘
⠀⠀⠀⣼⠇⠀⢈⠡⠼⠣⠼⠀⣠⠇⢀⣠⠞⠐⢦⠀⠀⠈⠀⠀⠠⢶⠀⠀⠏⠀⠀⠀⢠⠀⠀⠀⠀⠀⠂⠂
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠋⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢸⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⢀
⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⢠⠒⠀⠀⠐⣟⢅⠘⣀⡄⡟⠧⡼⠑⡇
⠀⠀⢀⡀⣠⣠⠀⠀⠀⠀⠹⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⣀⡀⢀⢀⠀⠀⡄⠀⠄⠸⠀⠀⡇⠀⡩⠀⠰⠀⡀⢀⡀⠄⠀⡄⠐⠄⠀⡀⠀⠀⠀⠤⠼
⠐⠀⡨⠀⠀⠃⠀⠘⠚⠀⠀⠀⠁⠁⠈⠘⠂⠀⠑⠀⠁⠀⠀⠀⡀⢐⠀⠸⠀⠁⠀⠀⠰⡀⠀⠀⠀⠒⠃
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⡀⠣⡀⠀⠀⠀⠀⠀⠀⠐⡂⠂
⠈⠃⠀⠠⠰⠉⠀⠀⢠⣄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠠
⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⠀⢀⡀⠀⡀⢀⡀⡀⠀⣄⠀⠀⠀⠀⠂⢠⢰⠀⠐⠁⠀⠀⠀⠘⠋⠀⠀⢀
⠀⡏⠀⠍⠀⣧⡘⡯⡇⠀⠀⠈⠧⠄⠧⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠸⡇⠀⡀⠀⠀⠀⠀⠀⢲⠂⢸⢸⠭
⠀⠁⠀⠁⠈⠀⠈⠁⠈⠀⠠⠄⠀⠀⠀⠀⢠⢀⠀⠀⠂⠀⠀⠲⠀⠀⠀⠀⠀⠁⢀⢀⡴⠀⠀⠈⠉⠈⠀⠁
⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣠⡆⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠨⢇⠛⠉⠀⠀⢠⠀⠆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠠⠀⠀⠜⠀⠀⠀⠸⢔⠋⠁⠀⠀⠀⠄⠐⠀⠀⠂⠀⠀⠀⠀⠀⠗⠈⠈⠤⠘⠂⠄
⠀⠀⠂⠀⠀⠂⠀⠘⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠄⢠⠀⠠⠄⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⣠⠀⠄⡈⠀⡇⠐⠀⢀⠀⠀⠀⠀⠀⢸⠚⠃⠡⠆⠛⠇⠄⠸⠁⠸⠶⡀⠀⠀⠀⠀⠀⠀⠀⢀
⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣀⣀⣐⣀⣀⣀⣀⣊⣈⣁⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⡆
⠀⠀⠀⠀⣼⣿⣿⠀⠀⢰⣿⣿⣿⠀⠀⢠⣾⣿⣿⣿⣇⠀⠀⣴⣿⡇⢀⣾⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⠀⠀⣾⣿⣿⡿⠀⢀⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣇⣸⣿⣿⡇⠀⣼⣿⣿⣏⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣠⣤⣿⣿⣿⡇⠀⣼⣿⣿⠻⣿⣿⣿⡄⢸⣿⣿⡿⠿⣿⣿⡇⢰⣿⣿⡿⠿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⡿⠻⣿⣿⣿⡇⢰⣿⣿⠃⠀⣿⣿⣿⡇⢸⣿⣿⠁⢰⣿⣿⡇⣾⣿⡿⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡆
⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⢃⣿⣿⡏⠀⠀⠹⣿⣿⡇⢸⣿⡿⠀⠘⣿⣿⠏⠻⠟⠁⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃
⠀⠀⠀⢰⣿⣿⣿⠁⠈⣿⣿⣿⠘⠿⠋⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⠀⠙⠛⠀⠀⠀⣀⡀⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⠟⢀⣤⣌⠙⢡⣴⣶⡆⠀⠀⢀⣤⣴⣶⣶⣆⠀⠀⠀⠀⢠⣾⣿⡇⣾⣿⣿⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⣿⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣸⣿⣿⢁⣿⣿⡏⠀⢸⣿⣿⣿⣿⣿⣤⣶⣶⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⢀⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⠘⢿⣿⡿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠉⢹⣿⣿⣿⣸⣿⣿⠟⢿⣿⣿⣿⡀⠀⠀⠀⣿⣿⣿⢹⣿⣿⠃⢘⠛⠻⠋⢹⣿⣿⣷⠀⠀⠀⢀⣶⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⠏⠀⠸⣿⣿⣿⡇⠀⠀⠰⣿⣿⡇⣸⣿⣿⠃⠙⠉⠁⠀⠸⣿⣿⡏⠀⠀⠀⠈⠻⠟
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠸⣿⣿⡿⠈⠁⠀⠀⠀⠉⠛⠛⠀⠀⠀⠀⠛⠋⠀⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢂⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠈⣷⢰⠒⠶⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠛⣧⣀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⢐⢽⢠⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢱⠀⠈⠋⠁⠀⠀⠀⠖⡶⠶⠶⢶⡆⠀⣸⠘⠀⠀⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⣀⢀⣀⡀⡀⠀⠀⠁⠀⠀⠀⢾⡀⠇⡰⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠀⠠⣠⣤⣤⢠⡇⡏⠉⠑⢁⠀⢰⠀⠀⡀⠀⠸⡅⢠⡇⡆⠀⠃
⠀⠀⢠⢠⣤⣤⢤⡇⠋⠉⠹⢱⠴⠚⠉⠀⠀⠀⢀⠀⢠⠀⠀⠀⡇⡁⠃⠀⠠⠾⢀⠰⠀⠀⣧⠀⠀⢳⣌⢿⢰⠀⢀⡆
⠀⠀⠀⢨⠀⠀⡇⡇⠇⠀⠀⣴⠀⠀⢧⠋⠉⠉⠙⣇⢸⢠⠀⠀⠃⡅⢀⠀⠀⡄⡸⡀⠀⠀⣀⡆⠀⠐⣸⠙⢠⠁⠫⣥⣤⡀
⠀⠀⢰⠘⠀⠀⠇⢻⢠⠀⠀⠱⠀⢀⠈⠀⠀⠀⠀⢮⠀⡜⠀⠀⠨⠹⠔⠀⠀⠃⡇⠇⠀⠀⠀⠀⠀⠀⢱⢎⠀⠀⠀⠁⠇
⠀⠀⠀⡈⠀⠀⢰⡻⠼⠀⠀⢠⡆⠸⢘⠀⠀⡆⠀⠘⣠⡄⡆⠀⠀⠀⣀⠀⠀⢰⠃⠄⠀⢰⢂⡌⠆⠀⠈⣼⠤⠁⠀⣡⠁
⠀⠀⠀⠇⡄⠀⠀⠀⢀⠀⠀⢰⠀⠠⠘⠀⠀⠹⠀⠀⢃⣧⠀⠀⠀⡇⡆⠇⠀⠀⠀⠀⠀⢸⠀⠰⣐⠒⠒⣒⣃
⠀⠀⠀⢰⠁⠀⠀⡏⡄⡅⠀⠈⣀⡀⡄⠀⠰⠄⠂⠀⠈⡾⢰⠀⠀⢠⣧⢰⠀⠀⡆⡓⠀⠈⠄⠀⠀⠀⠀⢨⢑
⠀⠀⠀⠐⠘⠀⠀⢁⣽⢠⠀⠀⠋⡇⠇⠀⠀⣀⢀⠀⠀⢡⠈⡄⠀⢰⠸⡀⠆⠄⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⡄⡀⠀⢘⢹⡎⠄⠀⠴⢁⠀⠀⢨⠐⢂⠇⠀⠀⡢⡄⠀⠀⠚⠈⠀⠀⢀⣁⠀⠤⠤⠄⠒⣒⡈⠩⠔
⠀⠀⠀⠀⠱⠭⠭⠭⠼⡙⡁⠀⠈⢸⣀⣀⡸⡇⠈⠬⠤⠥⠥⠇⠠⠒⣂⡀⠩⠡⠤⠐⠒⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡑⠤⠼⠒⢒⣂⠀⠋⡑⠢⣀⠀⠀⡰⠡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠑⠢⡑⠒⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⢀⠠⠤⢄⣀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣀⣀⣀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢹⣂⣴⣷⢖⡟⡛⠾⣙⠲⣖⣶⡿⣛⣾⠿⠦⣼⡿⠤⠙⠋⠁⠀⠀⠈⠀⢐⡴⠒⢂⣀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⣶⡿⣫⡾⠁⣾⣀⣱⡀⢉⢴⣬⡉⠉⢁⡠⠖⠒⠒⠢⠦⣤⣀⣀⣀⣀⡠⠔⠃⣴⣾⠭⠟⢉⡀
⠀⠀⠀⠀⠀⠀⢀⡛⢿⣉⠈⢦⠟⠉⠛⣧⡄⠀⠀⢱⠞⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠳⠶⠤⢤⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠠⣈⢳⡆⢀⣶⡄⠈⢇⢀⡐⠁⠀⣠⣴⣿⣭⣭⣍⡙⠲⠦⣤⣤⠴⢾⠳⢓⡯⢷⣿⣭⣴⠏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣷⣿⣿⣻⣦⠔⠋⢀⡴⠚⣉⣥⣶⣿⢣⢒⠈⢦⣤⣤⣤⣦⣵⣾⠭⠴⣬⣿⣿⡿⢰⠁
⠀⠀⠀⠀⠀⠀⠈⠿⣝⡲⣄⣝⣮⣉⣉⣁⣤⠴⣋⡴⠛⠁⠀⠀⢦⠔⢩⡵⡀⠙⠉⠉⠉⢉⣵⣞⣿⣿⣿⣿⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⠷⠶⣶⣿⣿⣿⡶⠟⠩⠴⠶⢤⣤⣴⣮⣂⣢⠜⣜⢄⠀⣀⣤⢟⡵⣫⡹⣾⣿⠏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣱⡟⠓⠆⢶⢦⣤⣄⣀⣀⣠⣴⠯⠖⢚⣽⣟⡿⢯⠭⣟⣾⣷⣟⡹⣴⣿⣛⣹⡿⠟⠁⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣟⠿⡔⠦⡀⠈⠲⢬⢉⠉⢀⣠⣔⢾⣟⢋⣭⣽⡆⣠⣾⠟⣳⠿⢛⣋⣉⣭⣥⣤⣴⣾⣻⡟⣮⣻
⠀⠀⠀⠀⠀⠀⠀⠦⠀⢵⠀⠀⣶⣴⡞⡉⠙⠛⠳⣤⡉⢿⠔⠈⠋⠙⡿⢡⣾⡷⠚⠋⠛⠙⠒⣶⣾⢟⡗⠟⣻⡿⢹
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠸⡄⠀⡎⢿⣿⣶⣿⣷⡾⣿⣿⣦⢫⠜⢠⢠⠀⣾⠿⡿⡓⣣⢚⡼⠞⣋⣭⢽⢿⠟⡻⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠀⡟⠆⡛⠛⠾⢾⣞⠽⠫⣿⡟⣰⢣⠃⣰⠏⣿⡿⡇⣰⠟⣠⡞⢻⡶⣶⣮⣔⣁⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢧⠐⣷⠤⠬⢭⣿⣦⢹⣞⡳⣼⣇⣧⡏⣰⡿⣥⢈⣶⡿⠋⣰⡿⣫⢚⠷⣾⡿⡋⢙⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⢦⣜⣿⣅⣚⣟⣛⣻⡵⠜⣛⡉⠥⠬⢬⣩⡟⣛⣋⣠⡶⠋⣈⣠⣍⡛⠰⠴⡞⣫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⠻⡙⠛⣻⠿⠶⣦⣽⣤⡶⠐⠒⠚⣼⣷⣯⣬⣥⡶⣟⠉⢺⣼⣯⣿⠻⢛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⣳⣦⣬⣮⢤⢤⣄⠈⣟⠻⠰⡥⣀⢉⣽⠟⡞⠹⢹⢟⢺⡳⢦⣭⡾⣹⣷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⠀⣶⣿⡄⣺⣶⠋⢀⠜⡠⠋⠨⠃⠜⡡⠁⠎⠼⠀⠛⣧⠀⡧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠼⠾⢱⣿⢁⣄⣰⣛⡋⢳⡒⣂⣋⢉⣲⣤⣾⡂⠈⠩⡆⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣮⣿⠁⣵⣬⡙⠮⣝⢀⣀⣉⡉⠍⠚⠉⣻⠽⠇⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣈⣁⣟⠀⠀⢈⡼⢉⠔⣡⠄⡠⠈⣳⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠭⣴⠶⢋⡠⠋⡴⢁⡞⡰⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠁⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⣆⠀⠀⠐⠄⠀⠀⠀⠀⣠⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠠⣄⣀⣀⣤⣿⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⡀⠀⠀⠀⠈⠛⠛⠛⠁⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠦⢄⡀⠀⠀⠀⣠⢊⡈⡑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠰⠦⣀⠈⠐⡄⠀⠘⠦⡅⠰⣔⠀⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⡈⠉⠀⠀⡀⠠⠐⠈⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣄⠀⠇⠀⠀⠄⢠⡄⠀⠘⠀⠀⠀⠙⢢⡀⠂⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢈⠔⢉⠀⠀⠀⠀⢀⠄⠊⣀⢀⡀⠄⠀⠀⠂⡀⡀⠄⠤⡑⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠴⠷⠤⠤⢄⡤⢠⠀⠊⠀⠀⠀⠤⠤⢒⡉⠀⠂⠀⠀⠀⠀⠐⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⢐⣃⠀⠀⡥⡵⠀⣀⠀⠀⠀⠀⢀⣩⠀⠔⢊⠀⠀⠀⢠⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠂⠉⠉⡄⠸⠤⠤⡄⠈⠑⠒⠒⠋⠁⠣⣭⡤⠔⣀⠔⢊⣇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣄⠀⢠⡀⠀⢠⠀⠀⠂⠠⡭⠉⠈⠀⠞⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⣾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣶⣦⣬⣹⣯⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠈⣾⣽⠿⠿⠟⠋⠀⢈⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠐⣿⠅⠀⠀⢸⠀⠐⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡄⠀⠀⠈⠀⠀⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⣾⡇⠀⠀⢠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡈⢹⡇⠀⠀⣸⠀⣸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣴⣁⣼⣇⢀⡤⠿⣶⡇⠀⣤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠄⠀⠠⡆⣈⡹⠉⠉⣉⣹⣿⡟⠂⠀⣄⠀⠀⡀⠸⠟⣻⢀⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⢠⡀⠀⠃⠀⠀⠀⢛⣛⣳⣀⣤⣿⡿⠟⠿⠷⠾⠿⠀⢿⣥⡤⠶⠖⠋⠈⠁⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣠⢀⡀⢀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣴⡶⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠟⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠈⠁⠒⠂⢄⠀⡀⠤⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠠⢀⠀⠀⠄⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠓
⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⢉⢀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠃⢀⡀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⡐⠑⠃
⠀⠀⠀⠀⢁⠀⠀⠈⠋⠀⣌⠈⠁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⣆⠈⠁⠀⢀⠂⠀⠀⠀⠀⠀⢀⠀⢡⠀⠀⠀⠺⢫⠀⠀⠀⠀⠄
⠀⠐⠺⡇⠀⠁⠀⠀⠐⠈⠀⠉⠀⠀⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣉⡀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠩⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠈⡦⢀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠉⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⣀⠠⠊⠁
⠀⠀⠀⠀⠰⡄⠈⠀⠃⠀⠐⠃⠈⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠘⢫⡉⠉⠉⠉⠙⠉⠉⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠐⠒⠂⠀⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠂⠐⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠁⠈⠉⠉⠉⠉⠙⠃


⠀⠀⠀⠀⠀⠀⣠⠶⠶⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠂⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠄⠀⠀⠀⠀⢴⣦⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠤⡀⠀⣀⠠⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⣀⠀⠀⠀⠀⠈⠁
⠀⠀⢀⡠⠀⠐⠛⠛⠂⠀⠀⠀⠐⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⣀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣠⣄⠱⢂⣅⣠⣌⢠
⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡈⠉⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡀⠀⡀⠻⣿⣿⡿⢃⠻⢿⣿⠟⢠⠀⠠⢤
⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠔⠉⠢⠄⠤⠒⠁⠀⠀⠀⠀⠀⢱⠀⠀⠐⠀⠈⠉⠠⠊⠑⠤⠀⠔⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⢊⠡⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⢤⣠⠔⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢒⣀⠒⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⣄
⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⢃⣠⠒⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⡀⠀⠀⠈⠙⠓
⠀⠀⠀⠉⠍⠉⠛⠿⣷⠶⣴⣦⢶⣿⠛⠉⠁⢸⠀⠀⠀⠀⠀⠀⡞⠉⢠⣤⡄⠀⠇⢤⣤⠀⠁⢱⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠈⠲⠊⠀⠀⠀⠠
⠀⠀⠀⠀⠘⢄⠀⠀⠀⣠⠆⠑⢄⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⣀⠦⢀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⢀⠛⠃⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⢀⡠⠊⠒⠤⠀⠤⠊
⠀⠀⠀⠀⠀⠀⣀⡄⠒⠈⡇⠀⠈⠉⠁⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢶⣄⣀
⠀⠀⠀⠀⢀⡞⠐⠒⢲⠐⠃⠀⡎⠁⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⢀⠸⡑⡄⠤⠘⠒⠒⠒⠓⠒⠚⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠻⠆
⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣾⣷⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣼⣿⠁⠀⢹⣿⡏⣿⡟⠉⠉⠉⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣿⠀⠀⢸⣿⡇⣿⠀⠀⣴⡄⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣼⣿⣿⠀⠀⢠⣤⡄⣿⠀⠀⣉⡁⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⠀⠀⣿⣇⠀⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡷⠰⣿⣿⣷⢿⣶⡾⠟⠻⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⢸⣿⡇⠀⣿⠁⣴⡆⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⠉⠁⠀⡇⠀⠛⠃⠀⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠂⠀⢰⣶⡆⠀⡇⢰⣶⣶⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⣀⣼⣿⣇⣸⣧⣸⣿⣿⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⢻⣿⠃⠈⢿⡟⠉⠀⠀⠈⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠸⠿⠀⠀⢸⠀⠀⣴⣷⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢰⣶⠀⠀⢸⠀⠀⣀⣀⡀⠀⢸⣿⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⣸⣿⡀⠀⣼⠀⢀⣿⣿⡇⠀⢸⣿⢃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣇⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠙⢿⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⠀⠸⣿⣿⡟⠀⢀⠀⠻⣿⣿⡀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡆⠀⠻⠿⠃⠀⢹⣿⠇⠀⠉⠀⠀⠈⢿⡏⠙⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠿⣿⣿⡀⠀⣴⣶⡄⠀⢿⠀⢠⣿⣿⣿⣦⣾⣿⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠉⠙⣿⣿⣿⠀⠰⠆⠀⠈⠻⣧⠀⢸⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠉⢻⣿⡷⠀⠈⢿⣿⠀⢀⣤⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⠀⠁⣠⣴⡀⠈⢿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⠀⠹⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠉⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠛⠉⠉⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⣰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢸⡇⢠⡇⠀⠀⠀⠀⠘⣇⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠶⢶⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢸⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢄⣠⠱⠀⠀⠀⠀⢻⡿⣿⣦⣀⠀⠀⢸⠀⠘⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⡇⠈⠻⢿⣷⣦⣬⣄⣥⣴⣿⣷⣄⣀⣀⣠⣴⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠉⠙⠛⠛⠛⠉⠈⠙⠛⠟⠛⠋⣿⣿⠁⠀⣤⠤⠴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣧⣀⠀⢻⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣆⣠⠞⠉⠀⠀⠀⠀⠉⢻⡿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⠀⢀⣿⣇⣀⣀⠀⢠⡶⢶⡀⠀⠀⠀⡏⠀⠘⣿⡅⣴⡾⢛⣻⣷⠶⠿⢶⣿⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣶⣶⡾⠛⠉⠁⠀⠉⠙⢾⣿⡧⠙⢦⡀⢰⡇⠀⠀⠹⣷⣏⠀⢿⠀⠀⠀⠀⢸⣿⣆⣀⣸⡓⠂
⠀⠀⠲⡶⠺⡄⠀⠀⠀⠀⠀⢹⣿⡠⢀⣤⣴⣦⣄⡀⠀⠙⣯⢂⠈⠳⣼⠀⠀⡀⠀⢻⣟⠦⣼⡷⠟⠁⠀⣼⠹⡏⠀⠈⣷⣤⣤⣀⡀
⠀⠀⠸⠓⢴⠆⠀⠀⠀⠀⠀⣾⣿⣏⣾⠋⠀⠀⠉⢷⠀⠀⢸⡷⣄⠀⠈⠀⢠⣧⠀⠀⢿⣄⠀⠀⣀⣤⡾⣣⠾⠷⠶⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣷⡀⠀⠀⠀⣸⠃⠀⢸⣯⣿⣷⡄⠀⢸⠙⣧⣠⣬⡿⠻⠛⠛⠉⠰⡏⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⣀⡤⠶⠾⠿⠿⠿⢿⣿⣿⣯⠻⠦⠤⠞⠁⠀⢀⣾⣿⣿⡈⠻⡶⠟⠀⠉⠉⠁⠀⢄⣑⣄⣀⣀⣹⣄⠀⠀⠀⠠⢎⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⡹⢿⣿⣧⣀⡀⢀⣀⣴⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠳⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣠⠞⠁⠀⢈⠿⠛⠛⠛⠋⠁⠈⠻⣧⠀⠀⠀⢀⡴⠞⠛⠓⠲⣄⡂⠀⠙⢦⠈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣰⠋⠀⣠⠴⠶⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠔⢃⡀⠀⠀⠀⠀⠀⣿⣰⠃⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣃⡀⢰⠊⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠛⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠖⠒⠈⠀⠒⠛⢃⡀⠀⠀⠀⠀⣠⣴⠶⠔⣇
⠀⠀⠀⢀⡶⠦⣦⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡀⠀⠠⠄⠤⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⢀⠘⡄⢀
⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣇⣃⣀⣧⣤⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠖⠚⠛⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠡⠉⠠⠀⠀⠀⠀⠀⠀⣄⠀⠘⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠘⣃⣤⣠⣤⣄⠀⠐⠲⠎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣤
⠀⠀⠀⢀⠀⠀⠠⠠⠀⠀⠀⠀⠀⣴⢀⠖⠉⢀⠀⠀⢡⠈⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡤⣄⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠈⠈⠀⢀⠀⠀⠀⢀⡀⠀⠀⣸⢛⡁⠶⠈⠀⠰⠆⢤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣤⠟
⠀⠀⣤⠴⠂⠛⣡⡴⠦⣭⡁⢰⣿⠇⠀⢹⡄⠀⣠⠀⣴⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠠⣾⠏⠀⠀⠘⠿⠟⠻⣄⣀⣀⣈⠇⠀⠀⠀⡄⠀⠀⠀⢰⡞⢁⡴⢲⡄⠀⠀⠀⠺⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣤⠴⢮⣻⣼⡏
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⠃⠀⠀⠈⠁⠑⠀⣀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠀⠐⠀⠒
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡂⠄⠨⠀⠠⠅⠸⠀⠀⠓⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣭⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠵
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⣀⣠⡤⠠⠀⠀⠀⠆⠰⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠶⠂⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡚⡒⠀⠀⠀⡀⠉⠵⠆⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠁⣈⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠐⠆⠀⢨⣍⡥⠀⠁⠀⢁⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⢀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡤⠤⠀⠈⢙⠉⠀⠋⠀⠀⠤⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠻⠚⠴⢇
⠀⠀⠀⠀⠐⠶⠲⠶⠶⠶⠒⠂⠀⠀⠀⠰⠞⠀⠀⠀⠀⠴⠦⠄⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⢀
⠃⠓⠢⣤⠀⢰⣶⣀⠀⠉⢉⣴⠒⠀⠀⠀⠀⠀⡀⠂⡔⠀⠀⠀⠀⠀⠀⢀⠀⡔⢄⠀⠀⢤⣀⣀⠀⠀⠀⠀⢠⠾⠿⠋⠀⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠁⠀⠀⠀⠀⠰⠶⠀⠐⠈⠔⠂⠀⠀⠀⢀⡀⠹⠋⠠⠄⠀⠀⠀⠀⢠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢛⣿⣯⣥⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡴⠊⠙⠋⠉⠉⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣄⣀⣀⣀⣀⣀⡤⣶⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠠⠐⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠚⠁⠉⠂⢹⠃
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⢉⠳⡀⡇⠀⠀⠀⠀⠀⠤⠤⠭⣕⣆⠀⠀⠀⠀⢀⣴⣂⣀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢣⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠉⠀⠈⠁⡇
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⡴⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠴⡇⠀⠀⠀⠀⠀⠀⢴⣖⠒⠒⠶⠤⢤⣀⣀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⡀⢹⡄⠀⠀⠀⠀⠀⠸⡿⠿⣷⣶⠶⠤⠤⠭⡿⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣋⠀⢀⣱⣄⠀⠀⠀⠀⠀⠹⣄⠈⢻⡀⠀⢀⡼⠁⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠢⣄⠀⠀⠀⠀⠈⠙⠒⠓⠒⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣀⣀⣠⡤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣠⣂⠀⠀⠀⣀⣀⠞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⢳⠀⣤⣀⡀⠀⠒⠒⠋⠀⠀⡀⠀⠢⠎⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡩⠛⠺⣏⠀⠀⣈⠁⠀⠀⠙⢯⡹⠛⠛⠒⠒⠄
⠀⠀⠀⠀⠀⠀⢰⠘⣗⠤⣀⠀⠠⡀⡷⡈⠙⠲⠄⡎⢰⢀⢹⠀⠉⠳⢦⣼⠳⡄
⠀⠀⠀⠀⠈⢦⠊⠧⣽⠒⠆⠙⡆⠱⡇⣈⣃⡀⠀⠏⢿⠈⢀⡁⣦⡀⢠⡏⠳⢼⣦
⠀⠀⠀⠀⠀⠀⠳⠉⠃⡀⢠⢻⠓⠢⢀⠘⣆⡜⠁⠓⠺⠀⢸⠙⢮⡙⢾⡀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⢫⠈⢣⡠⠳⡸⡄⠀⢰⡀⣰⣸⠔⠊⠙⠦⡙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢵⠀⠑⢳⢤⣘⣯⠀⢺⠀⡀⠀⠰⡆⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢈⡷⡀⠸⣇⡼⠛⡷⢬⣸⡇⡀⠠⣧⣸⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⡉⠀⠘⢆⢻⠀⠀⠈⠀⠈⣯⠀⠀⢻⡏⠘⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠈⢃⡄⠀⠀⢸⣽⢀⣄⢸⠀⢰⡀⡟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣶⡀⠈⣇⢀⣤⠞⣟⢸⢻⠈⢸⡠⡇⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⡘⡆⢻⢱⡀⣿⠉⠀⠀⠸⡮⠜⡇⣽⠀⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠈⢾⠁⠣⣿⠀⠀⠀⠐⠁⠀⡇⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁

⣿⠋⠙⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⡿⡏⡌









⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣩⣩⣭⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣭⣭⣭⣭⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣒⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⡿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡿⠛⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠲⠀⠀⠈⠀⠀⠀⠀⠀⠳⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⠄⢀⣤⠀⠀⠀⠀⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠣⣈⡿⠏⠀⠀⢀⠔⢻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠀⢀⡤⢶⠁⠀⠈⡍⠉⠙⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠊⠀⠔⠊⠀⠠⠀⠈⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⡉⠡⠀⠈⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣇⢀⣤⣤⣛⠁⠢⠡⠄⠠⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣀⠅⠀⣽⣿⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⢀⣀⣀⡀⠀⠤⠐⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠐⢐⠒⠒⠒⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡴⡇⠀⠀⠀⠀⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⢁⣘⣿⡷⠴⠇⠀⠀⠀⣠⠀⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣹⣛⣛⣹⣋⣎⣛⣟⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣭⣿⣭⣭⣽⣿⣭⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢖⠻⡉⠉⣙⡛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⣠⠤⠤⠤⠤⠤⣝⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢰⢄⠀⠀⠀⠀⠀⣀⣠⢶⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⣄⠉⠉⠉⠉⠉⠉⣠⡎⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠘⣿⣿⣶⣶⣶⣾⣿⠟⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠻⠿⣿⠿⠟⠁⠀⠀⠀⠀⣼⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣃⠀⠉⠉⠛⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣶⣄⣀⡀⠀⠀⢀⣀⣠⡶⠋⠀⠀⠙⠲⣄⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠉⠉⠉⢉⣩⠟⠁⠈⠙⢦⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢀⠔⠊⠉⣄⠈⠉⣉⠓⠲⠤⢤⣤⠤⠶⠚⡿⠁⠀⣀⣀⣤⠴⠚⠉⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠈⣷⡀
⡞⠲⠧⠴⣇⣀⣸⢧⡤⣾⣀⡀⢰⡖⠶⠶⠖⠒⠛⠛⠋⠉⠑⠄⠀⠀⠀⠀⠀⣠⡼⠋⢀⡠⠔⠋⠀⠀⠀⢹⡄⠀⠀⠤⠚⠀⢷
⠓⠶⠦⠤⠭⢭⣥⣄⣀⣀⣀⠉⠙⢷⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠱⡆⠭⣗⡶⢫⡀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣇⠀⠀⠉⠒⣽⡛⡻⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⢸⡇⢸⠀⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⠀⠀⠀⠀⡇⠈⠳⠞⠁⠀⣀⣀⣀⣀⡠⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠈⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢻⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢸⠇⡼⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⢀⡿⢀⡇⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⢳⣄⡀⠀⠀⠤⠤⣤⣤⣤⡤⠤⠖⠚⠉⠀⠀⠀⢀⡾⣅⣼⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⣰⠋⠀⠙⠳⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠙⠓⠶⠶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠈⢩⠟⠛⠛⠛⠛⠛⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⣠⠤⣖⠒⠶⠧⠿⣤⠖⠛⠲⣿⠀⠀⡀⠀⠀⢀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣠⣼⠶⠋⠁
⠀⠀⠀⠀⠀⠀⡼⠁⣰⠽⣄⠀⠀⡾⠁⣠⢤⡀⢹⡙⠓⠻⠦⠤⠼⠷⠖⠛⠲⠶⠤⣤⣤⣀⣠⠴⠒⠦⣄
⠀⠀⠀⠀⠀⠀⢧⠀⠙⠋⢙⠗⢾⡇⠐⣇⡼⠃⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⡔⢢⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠋⠀⠘⣇⠀⠉⠀⢀⡾⠉⠉⠉⠉⠛⠒⠒⠒⠒⠒⠶⢤⠤⢼⡇⠘⢦⠊⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⣷⣄⣀⣀⣴⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⣠⠶⠛⠉⠉⠉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⣀⡀⠀⠀⣀⣀⣀⠀⠘⣷⠞⠁⣀⣀⠀⠀⣀⣀⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣼⠟⢻⣿⣷⣾⣿⣿⣿⣧⠀⠸⣇⣾⢋⣿⣿⣾⣿⣿⣿⡆⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣆⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣵⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸
⠀⠀⢀⣀⣀⡀⠀⠀⠀⢻⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⡇⠘⠻⣿⣿⣿⣿⡿⠋⠀⠀⢀⡿⠀⠀⠀⠴⠞⢻⠷⣦
⠀⠰⠟⣿⡉⠉⠁⠀⠀⠈⢧⡀⠀⠀⠈⠛⠿⣿⣿⠿⠛⠁⠀⢀⡾⣧⡀⠀⠀⠉⠉⠁⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣼⠀⠈
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠈⠙⠶⣤⣄⣀⣀⣠⣤⠞⠋⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⡛⠛⠛⠛⢛⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⢻⢦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣳⡀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠀⠀⠀⠈⡼⡇⡞⠛⠛⢻⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠙⣷⣄⣠⣴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡇⠀⠀⢸⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡘⠀⠈⠛⠉⠀⠀⠀⠀⠔⣲⠶⠶⠶⢶⢦⠀⢃⡇⢁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠈⡞⡄⢸⢸⢸⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⢁⣀⣀⣀⣀⡀⡏⡿⠿⠿⠏⡇⠀⡇⡇⠀⠀⠀⠀⢸⢳⠘⣼⡸⡀⠀⢸⢿
⠀⠀⠀⠀⠀⢠⢄⣴⣶⣶⠲⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⢸⢸⠛⠛⢻⢹⡇⡇⠀⠀⢸⠃⢠⢁⠀⠀⢸⡆⠀⠀⣇⡆⡏⡇⡇⠀⢸⢸
⡖⡶⠶⠿⡟⣾⠈⠀⠀⠀⢸⡟⠋⠁⡤⣤⣤⣤⣤⢤⡀⢸⢸⠀⠀⠘⢸⢿⢰⠀⠀⢈⢸⢸⢸⠀⠀⢸⢱⠀⠀⠈⡀⣄⣧⢸⣀⣸⢸
⡇⡇⠀⠀⢰⢡⡇⡇⠀⠀⡇⡇⠀⢠⢁⠃⠀⠀⠀⢳⣇⠈⡄⡄⠀⠀⡏⣼⠸⠀⠀⠸⢸⡸⢸⠀⠀⢸⣈⡆⠀⠀⢃⢇⢩⢰⠒⠚⢢⢷⡤
⢃⢣⠀⠀⢸⢸⠇⡇⠀⠀⢡⠇⠀⢸⢸⠀⠀⠀⠀⠈⡞⡄⡇⡇⠀⠀⠣⠻⠴⠃⠀⠀⡇⡷⠙⠀⠀⠀⠀⠀⠀⠀⠈⡞⣼⢸⠀⠀⢸⢸
⢸⢸⠀⠀⠘⡸⢟⣰⠀⠀⢸⢰⠀⢰⢸⠀⠀⣤⠀⠀⢹⢣⡇⢃⠀⠀⠀⠀⠀⠀⠀⠀⢃⠃⡇⠀⠀⡴⢒⡒⡆⠀⠀⢱⢻⣈⣓⣒⠚⡸
⠘⡌⡄⠀⠀⠉⠁⠀⠀⠀⠸⢼⠀⠘⡄⠀⠀⡟⡆⠀⠀⠏⣿⢸⠀⠀⠀⡖⣉⢳⠀⠀⢸⠀⡇⠀⠀⡇⡇⢱⠸⣀⣀⣀⡟⡆⠀⠀⠉⠁
⠀⡇⡇⠀⠀⢠⠤⠄⡄⠀⠀⡇⡆⡇⡇⠀⠀⡇⢱⠀⠀⠸⣹⡜⡂⠀⠀⠇⣿⠸⠀⠀⠈⡠⣄⣀⣀⠇⡇⠀⠓⠒⠒⠒⢶⠗
⠀⢃⢡⠀⠀⢸⢸⡇⡇⠀⠀⢱⢣⡇⡇⠀⠀⠛⠉⠀⠀⠀⢧⠃⡇⠀⠀⢹⢻⡇⡇⠀⠀⣇⡖⠒⠒⠒⠃⠀⠀⠀⠀⠀⢸⢸
⠀⠸⠸⠀⠀⠀⡏⣷⢸⠀⠀⢸⢸⢣⠁⠀⠀⣀⡤⢤⠀⠀⠈⡆⢸⣀⣀⣸⢸⢣⣑⣒⣒⣋⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾
⠀⠀⡄⡄⠀⠀⢡⣿⡌⠦⠤⠤⠇⢰⠀⠀⢀⡡⠒⡌⡆⠀⠀⢱⢰⠂⠒⠒⠒⠃⠀⠀⠀⠀⣀⣀⡠⠤⠤⠐⠒⠒⣉⣉⡡⠞
⠀⠀⢣⣉⣉⠉⠉⢴⠱⡒⠒⠒⢲⢸⠀⠀⢸⢿⠀⢱⣈⣉⣉⣉⣸⠄⢠⠤⠖⠒⢒⣉⣉⡩⠤⠤⠖⠒⠒⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢇⠱⡀⢀⣺⣈⣉⣩⣭⡼⠒⠦⡀⠀⠀⠀⠀⢠⢃⠖⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢌⠥⠤⠤⠒⠒⠒⠈⠉⠢⢌⠑⢤⡀⡰⢣⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣌⣡⠃
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⣾⡟⠻⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠆⢰⣶⣾⣿⣷⣶⣶⣾⣿⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡏⠉⠉⠀⣼⣿⠀⠀⠀⠘⠛⣿⣿⠛⠉⠉⣿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠿⠿⠀⠀⠀⠀⠠⣿⣿⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⡟⠛⠛⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣤⣤⣴⣾⣿⣷⣶⡆⠠⣶⣶⣿⣿⣾⣿⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⠛⠛⠋⣿⣿⠀⠀⠀⠿⠿⣿⣿⠉⠉⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆⠀⠀⠀⢠⣶⠄⠀⠀⠀⠀⠀⣴⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣇⣀⣀⣀⣸⣿⣇⣀⠀⢀⣀⣀⣿⣇⣀⣉⣽⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠿⢿⣿⠟⠛⠃⢸⣿⣿⣿⣿⠿⠿⣿⣿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⡇⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠚⠛⠉⠉⠉⠉⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠂⠀⠀⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠓⣤⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⢀⡞⠁⠀⠂⠁⠀⣱⠏⡴⠃⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⢸⠁⠎⠀⠀⠀⠊⡏⣸⠃⠀⢀⠤⠂⠈⠁⠀⠀⣀⣈⣐⣠⡀⠀⠀⠀⠀⠀⠁⠂⠄⣀⠀⠀⠀⢻
⠀⠀⠀⢸⡌⠀⠀⠀⠀⠀⠻⡇⡠⠂⠁⠀⠀⢀⡠⠖⠋⠉⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄
⠀⠀⠀⠀⢻⡀⠀⠀⠀⡆⠠⡏⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⣀⣀⣀⣠⣤⣤⣀⠀⢸⡇
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠂⠀⣇⠀⡠⠐⠂⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠒⠀⠀⢸⡇⢸⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⠀⢹⡎⠀⠀⠀⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡾
⢀⣀⠀⠀⠀⢸⠀⠀⠀⠁⠀⢸⢷⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡢⠀⢸⡽⠁
⡞⠻⣄⣠⡴⠃⠀⢀⠈⠀⠀⡞⠀⡷⠋⠙⠛⠂⠀⠀⠀⠀⣀⣠⠆⠀⠀⠀⠠⣄⠀⠀⠈⠉⠀⠀⠘⡇
⢳⡀⠀⠀⠤⠀⠂⠀⠀⢀⡞⠁⠸⡇⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠀⠀⠀⠀⣿
⠀⠙⠦⢤⣤⣤⣤⠤⠖⠋⠀⠀⠀⠙⠲⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣀⣠⣤⣴⣾⡆⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⢿⡿⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠇⠖⠒⠋⠀⢀⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠴⠦⢄⣀⣀⣀⣀⣤⡤⠤⠖⠛⢻⠉⢹⡗⠒⠒⠒⠒⠊⢉⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢀⠀⢠⠁⠀⠀⠠⠤⠤⠒⠀⠀⠈⣧⣼⠦⠶⠒⠒⠒⠢⢄⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⢦⠏⢀⡴⣄⣀⣄⠀⠠⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠈⠉⠋⠀⠉⠴⡇⠈⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣉⣙⣲⣌⣿⣁⣀⣤⠤⠤⠴⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⠉⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣈⣹⣏⣁⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠚⠒⢺⡗⠓⠚⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣸⣇⣀⣰⣇⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣗⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣷⣾⢡⡶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠶⡟⣻⣦⣿⣧⣙⣲⣯⠶⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠐⠦⣼⣸⢿⣵⠊⠁⠀⠈⣙⢯⣔⡃⠄⠀⠀⠀⠀⣷⢀⡟⠀⡀
⠀⠀⠀⢀⡀⠈⢷⣠⡟⠀⠀⢸⡛⣦⢼⡿⢋⡀⠀⠀⠀⢊⡥⢄⢻⡿⠗⠀⠀⠠⣀⣸⣾⡶⠋
⠀⠀⠀⠀⠉⢓⣬⡟⢻⡄⠀⠐⠒⣨⡿⠁⢾⣿⠀⠀⠀⡋⣶⠀⠘⣷⠀⠀⠀⠀⠈⣿⡼⠋⠛⠒
⠀⠀⠀⠀⠛⠛⢉⡿⠛⢷⢦⡀⠀⣿⡇⠀⠠⠤⠂⠒⠀⠘⠒⠁⠈⣿⡆⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠣⡱⣄⠹⡅⡄⠀⠀⣶⡟⠿⣷⡄⠀⣼⠿⠁⢀⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠳⣝⢌⡲⣜⡛⠾⠟⢛⣠⡾⢋⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠘⠋⠹⣿⠮⠵⡶⢾⣁⣴⠏⢉⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠀⠘⢧⣼⠁⠀⠙⠃⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠉⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⠀⠉⠉⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⣩⢿⣖⠒⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⣴⠏⠸⣿⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣰⡟⠀⠁⠀⠀⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠢⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣰⣶⣄
⠀⠀⠀⠀⠀⠀⠸⠿⠶⠋⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣏⡁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣦
⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⣴⣿⣿⡇⠀⠀⢀⣴⣾⣿⣿⡆⠀⠀⣠⣴⡄⠀⣴⣶⣆⠀⠀⣰⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⡇⠀⢰⣿⣿⡇⢸⣿⣿⣿⠀⢰⣿⣿⡿⢻⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⡇⠀⣸⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣷⣿⣿⣿⡏⢀⣿⣿⣿⣷⣾⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⠃⢸⣿⣿⣿⡀⢸⣿⣿⠋⠉⣿⣿⡇⣸⣿⣿⠏⠉⠉⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿⣿⡿⢠⣿⣿⠏⠀⠈⣿⣿⣿⡇⢸⣿⣿⠀⢸⣿⣿⡇⣿⣿⠏⠀⠀⠀⠹⠿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⡇⠀⣿⣿⣿⡇⣿⣿⡟⠀⠀⠀⠙⠿⠿⠁⠸⠿⠃⠀⠀⢻⣿⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⠇⠀⠙⢿⣿⠃⣈⣉⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣤⡄⢠⣶⣶⠀⠀⢠⣴⣾⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠙⠛⠋⢠⣿⣿⠀⢠⣿⣿⣿⠀⠀⢠⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⣼⣿⣿⠀⠀⣾⣿⣿⣿⣿⡇⠀⣀⡀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣤⣼⣿⣿⣿⡄⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣥⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⣿⣿⡇⣼⣿⣿⣏⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⡟⠀⣾⣿⣿⠿⣿⣿⣿⠛⠋⠁⠀⠘⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⣿⣿⣿⣧⣿⣿⡟⠉⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⡿⢸⣿⣿⡇⢸⣿⣿⠃⠀⣿⣿⣿⡄⠀⠀⠀⢰⣿⡧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠸⣿⣿⣿⡟⢿⠟⠀⠀⠹⣿⣿⣿⠀⠀⠀⠘⣿⣿⠇⢸⣿⣿⠃⠀⠉⠁⠀⠀⠻⠿⠟⠁⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠸⣿⡿⠟⠀⠀⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠁⠀⠘⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠖⠒⢲⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣠⠖⠋⠉⠙⠢⣼
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡠⠒⠈⠁⠀⠀⠈⠙⠲⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⡤⠤⢷⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣄⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⡄⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣴⣾⣿⣿⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣋⠉⠈⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⡀⠀⠀⣀⣀⣀⠤⠖⠚⡅⠠⡤⠤⠤⠄⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢈⠉⠉⠉⠀⠀⠀⠀⠀⢹⣤⡧⠤⠤⠤⠤⣈⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠲⣞⢀⡴⣄⣀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⡈⣉⠀⢀⢲⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠤⠵⠶⠗⠒⠒⠒⠛⢩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠠⣤⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⠶⠶⣿⠶⠶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⣀⣿⣀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⢀⠄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡈⠉⢁⠀⠏⢠⣋⣀⣀⣀⣤⣶⠊
⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⠛⢻⣕⣶⣢⣧⣶⣷⣶⣶⣿⣿⡿⠋⠉⠉⠁⡀
⠀⢨⡉⠓⠒⣲⣌⣀⣔⣄⣁⠀⡄⠀⠀⠀⣠⣬⢤⣍⣛⣃⣬⣽⣷⣿⣿⣻⣩⣙⣻⣟⣿⡿⠁⠀⠀⠈⠉
⠀⠈⣯⣫⣭⡶⠟⢓⣺⡟⣏⠀⠀⠒⠶⠾⠋⠉⠳⣬⣭⣯⡭⢴⣶⣶⣾⣿⣽⡯⢷⡿⠋⠀⠀⢀⠄⡘
⠀⠀⢛⣫⣟⣽⣟⣑⢎⣽⣮⢳⠂⠤⠤⠤⠦⣤⠀⠀⢨⣿⣿⣿⣿⢷⣶⣾⣽⣿⣋⣤⣄⣤⣶⣅⡠⠓
⠀⠀⠀⠉⠉⢙⣻⣖⣻⣯⢺⢆⠀⠀⠀⢀⣀⣌⡇⠀⢸⣿⡟⠁⣤⡀⠨⣙⣫⣽⣷⢮⡉⠍⠛⢦⣄
⠀⢰⣄⣛⣲⣤⣤⣷⠳⣗⡷⡘⣟⡝⣏⣽⣛⢟⠇⠀⠈⠛⠛⠮⣭⣤⣭⡶⣶⣄⠁⠠⠉⣰⠀⢸⡯⠛⠴⢤
⠀⠈⢮⡋⢓⡙⠘⢻⣧⠈⣿⢿⣓⣋⣩⢥⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⢷⣿⣧⡴⠮⣄⣀⣀⣤⣱⡖
⠀⢀⣄⠈⠀⠈⢻⠧⣿⣷⣌⡳⠭⡭⢶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣛⣻⡵⣋⣝⣪⣉⡉⠙⠛⣃
⠀⠘⢧⣄⠀⢊⣍⣙⣾⣿⣿⣻⣿⣿⣿⣿⣾⣶⠊⠁⠀⠀⠀⠀⠠⢀⣧⣬⣉⣫⣽⣿⣶⣿⠿⠛⠛⠿⠥⠞⠉⣀
⠀⠀⠦⠜⢉⠀⣿⣟⡭⣿⣿⡿⠿⣿⣿⣍⣿⣿⣿⣷⣦⣤⡄⣠⠀⣿⠿⠷⣷⡞⣶⣾⢷⡾⣒⣚⡳⢄⡀⠀⢸⠃
⠀⠀⠉⠙⣶⣿⣻⢏⠞⠛⢙⠯⣁⣲⣬⢭⣿⣻⡿⠛⠛⠋⠀⣿⠂⠙⡟⠷⣿⣟⠿⠿⣿⡿⠭⢍⢻⣤⣥⠄⠁
⠀⠀⠀⣨⠝⠋⠁⠀⠀⠊⠉⠳⠖⢶⣽⣷⣽⣽⡇⠀⠀⠀⠀⣾⣄⠀⣇⣤⣼⡳⣭⣽⠏⠀⠁⠀⣧⣨⣥⠛⠛⠁
⠀⠀⠀⠹⠰⠄⠈⠀⡄⠐⠀⠀⢀⣁⣉⠿⠿⠾⣧⣀⣀⣠⣴⣿⣥⣾⠿⠋⠉⠑⠦⠜⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⠒⠋⠉⠉⠉⠉⠉⠉⢹⡆
⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣷
⠀⠀⠀⣠⠴⠋⠀⠀⠀⢀⣀⣤⠴⠖⠒⠛⠋⠉⠉⠉⢙⠓⠲⢤⣹⡀
⠀⢀⣠⠟⠀⠀⠀⣠⠖⠋⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠹⡇
⣠⣟⠁⠀⠀⢠⡞⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢉⡟⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⡁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡤⠜⠂⠀⡇
⠘⣧⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠹⣆⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠆⠀⠀⠀⠀⠀⠙⣦
⠀⠀⢹⡄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸
⠀⠀⠀⠻⣄⠀⠈⣻⠄⠀⠀⠀⠀⣤⣄⣀⣀⣀⣀⣠⣤⣴⣾⡄⠀⠀⡾
⠀⠀⠀⢰⠏⠉⠛⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⡇
⠀⠀⠀⠘⠷⡤⣦⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⠋⠙⣋⡡⠟⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠧⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠲⣤⣤⡤⠴⠶⠶⠚⠛⠉⠉⠈⢹⣆⠀⠀⡏⠉⠉⠉⠉⠉⠐⠒⠉⠁⢀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠞⠋⠉⠉⠉⠉⠉⠉⠁⠛⠶⣤⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠈⡷⠤⣤⡞⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣿⣁⣀⡀⡴⠃⠱⠖⢊⡦⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⡀⠀⠀⢀⣉⣙⠆⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠈⠒⠒⠤⣩⠇⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⣶⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠰⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⠛⠛⡟⠛⠛⡿⠛⢻⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢸⡇⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢼⡇⠀⠀⣿⠤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣧⣤⣤⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⣤⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⣀⡀⠀⠀⠀⢀⡤⠾⠀⠀⠀⣀⡀
⠀⠋⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠉⠙⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠰⠀⠀⠀⠀⠆⡀⠀⠀⠄⠀⠠⢶⢶⣤⣀⣠⣀⣠⣤⡶⠟⢻⠉⠀⠃⠀⠀⣀⠙⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⠘⠘
⠰⠀⠸⠇⠀⡇⠛⠀⢀⠂⠀⠀⠀⠀⠀⠉⠉⠩⡁⠈⠁⢀⠌⠀⠀⠇⠀⠀⠿⢠⠙⠁⠀⠌⠀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠈
⠀⠑⠀⠀⠔⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠂⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠒⠀⠀⠀⠀⠀⠀⠉⠓⠀⠙⢒⠀⠀⠀⢠⠴⠒⠀⠀⠐⠢
⠀⢀⣠⠾⠛⢁⡐⠳⣄⡀⠀⠀⢀⣤⣤⣀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠠⠂⠀⠀⠐⠂
⠐⡏⠁⣤⠄⠨⠄⡤⠀⠈⡃⠀⠀⠀⠀⠉⢻⡆⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠠
⠀⢳⠀⠀⠀⢠⡄⠀⠀⢠⠁⠀⠀⠖⠒⠬⣆⠀⠣⠘⠃⠀⠄⠀⠀⠡⡀⠀⣠⡄⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠈⠁
⠀⠀⠑⠄⠀⠃⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢀⣀
⠀⠀⠀⠐⠶⠐⠁⠀⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⣀⠴⠂⡘⠛⠦⣄⡀
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠂⠀⠀⠀⠠⢡⣶⢦⡄⠁⣴⣶⠆⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋⠀⠀⠴⠱⠆⠀⠀⡉
⠀⠐⠀⠀⠠⠇⠀⠀⠐⠖⠀⠀⠀⢀⠤⣿⡷⠀⡄⠭⢿⠟⠀⠀⠀⠆⠀⠒⢀⡆⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠂⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⣀
⠀⣰⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠤⠄⡀⠀⠙⢛⡢⠀⠀⠀⢘⠩⠅⢀⠀⠈⠍⢃⠀⠀⠀⠀⠨⠀⠠⠀⠀⠈
⠀⠁⠀⠀⠀⠀⠀⠟⠛⠷⠆⠀⠀⢄⣀⣒⡂⠀⠄⠀⠀⠀⠀⠀⢀⠂⠀⢀⣤⢶⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣀
⠃⠀⠐⠛⠀⠰⠀⠘⠛⠉⣀⠂⠀⢠⠀⢉⡀⠀⣣⣼⡁⣰⡇⠀⠘⡀⠀⠈⠛⠸⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠈⠣⣙⣋⠼⠓⠉⠉⠚⠀⠀⠀⠻⢄⢀⡴⠋⠲⠤⠚⠁⠀⠀⠀⢦⡀

⠀⠀⣄⠀⢠⡀⠀⠀⠀⠀⠀⠀⣤⢿⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⣿⠀⣠⡄⠀⠀⢰⢰⡆⢠⡄
⠸⡇⣿⡄⢸⣿⡄⠀⠀⠀⠀⠀⢻⣻⡇⣟⠷⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⣾⡏⢰⣿⡇⠀⠀⣾⢺⠇⣿⡇
⠐⣿⢻⡇⢸⡟⢷⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⢀⡟⢹⠇⠀⠀⠀⠈⠀⠃⠁
⠀⠉⠘⠋⠈⠃⠀⠀⡄⣶⠀⣀⠀⠀⠀⠀⠀⣠⠜⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡿⢰⣿⡄⠀⠀⠀⠈⠀⠁⠀⢀⡠⠔⣂⡀⠐⠒⠒⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡇⢹⢿
⠀⠀⠀⠀⠀⠀⠀⠘⠸⠇⠼⠹⠃⠀⢀⡀⠤⢀⠤⠊⠠⠄⠀⢀⡀⠀⠀⠢⠄⠀⠀⠈⠑⠢⣄⠀⠀⠀⠘⠋⠗⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣬⠁⠁⣀⡈⢷⠀⠀⠀⠉⠀⠠⢄⠀⠀⠠⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠹⠈⠀⠀⠀⢠⡤⠤⠤⡑⠀⡀⠀⢀⠀⢀⢀⣨⠂
⠀⠀⠀⠀⠀⠀⠂⠢⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢉⠀⠀⠂⠀⠀⠰⠒⠒⠄⠀⠀⠙⠄⠈⠂⠀⠠⡀
⠀⠀⠀⠀⠀⢀⠤⠀⠁⠀⠠⠄⢸⠀⠀⠀⠀⢠⣦⡁⠒⠤⠤⠤⢤⠲⠀⠀⠀⠀⢀⠈⠦⠀⡄⠀⢱⠀⠀⣲⠂
⠀⠀⠀⠀⠀⠌⠁⠂⢈⠖⠀⡇⠸⡄⠀⠀⢠⣿⣿⣿⣿⣷⣶⣶⣿⠀⠀⠀⠰⣼⢁⠆⢰⡄⡀⠀⠈⡆⢠⢏
⠀⠀⠀⠀⠘⣔⠀⠊⠀⠀⣠⠃⠀⠳⡀⠀⢸⣿⡏⠉⠋⢙⣿⣿⠇⠀⠀⠀⠀⠀⠈⣀⡈⠲⠃⠀⢰⠇
⠀⠀⠀⠀⠀⠈⠐⠠⡀⠠⠓⢄⠀⠀⠙⢄⠀⠙⠻⠷⠶⠿⠛⠁⠀⠀⠀⠀⢀⡀⠋⠀⠀⢀⣇⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⢢⡤⠤⠤⠵⠦⣀⣀⡀⠀⠀⣠⠤⠤⡒⠚⠉⠉⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⠤⠤⠰⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⡔⠒⠁⠑⢠⠄⠒⠁⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠡⠀⠀⠀⢀⠀⠀⠀⠀⣀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⠀⠀⣀⢈⠉⢁⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣿⣿⣛⣛⣻⣟⣿⣻⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣠⡾⠛⠉⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣠⡾⠋⠀⠀⢀⣀⣀⣀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣴⡟⠁⠀⣤⣾⣿⣿⣿⣿⡷⠀⠀⠉⠛⠳⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣼⠏⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⡛⠿⢶⡿⠛⠛⠛⠛⠻⠿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣧⠘⣧⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⢷⣀⠀⢀⣀⣄⠀⠀⢀⣠⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠈⠙⠛⠛⠋⠁⢀⣴⠟⠁⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠈⠋⢠⡏⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠻⣦⣀⠀⢀⣀⡀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⢀⣠⣤⣤⣾⠁
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣴⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠞⢛⣉⠀⠈⠹⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣷⣄⠀⠀⠀⠀⠀⠀⣴⡟⠉⠛⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠘⣯⡉⠙⠛⠛⠷⠶⠶⠿⠿⠟⠛⠛⣉⣽⣿⠈⠁⠀⠀⢀⡀⠀⢸⣧⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢿⠙⠳⠶⣤⣤⣤⣤⣤⣴⣶⣶⠟⠋⠉⣿⠀⠀⠀⢀⣿⡇⠐⠛⠁⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⣰⠏⠀⢠⡟⠁⠀⠀⣸⡟⠀⠀⠀⣾⠿⣷⣄⣀⣠⣴⠟⠃
⠀⠁⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⢻⡄⠀⠀⢰⡏⠀⠀⠈⠀⣀⣤⡾⠟⠀⠀⢀⣾⠟⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠙⠶⢦⣼⣷⡶⠶⠾⠛⠋⠉⠀⠀⠀⣠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣤⣄⣀⡀⠀⠀⠀⣀⣀⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠒⠒⠒⠒⠶⢤⣄⡀⠀⠀⠀⠈⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⢸⡟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣁⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣣⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣀⣤⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⡲⠞⣁⡴⠖⠛⠉⠉⠉⠉⠉⠛⠓⠦⣄⡀⠀⠀⠉⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⣠⠖⠉⠀⠀⢀⣾⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⡶⠒⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡴⣻⠁⣴⠷⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⢿⡄⠀⢀⡞⠁⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡰⠋⠀⡇⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢸⠃⠀⠀⠀⢀⡿⢄⡀⠀⠀⠀⠀⢀⡠⣄⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠶⠂⢀⡀⠙⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠙⣦⠀⠀⠀⣾⠁⠈⢧⠀⠷
⠀⠀⠀⠀⠀⠀⠀⢠⠖⣉⠭⢍⡀⠀⠀⢿⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠓⠦⡀⢸⠀⠀⠀⠀⠈⠳⣄⠀⣼⠋⠉⢢⣏⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠙⢦⠀⢸⠀⡴⠋⠀⠀⠙⣆⢀⣤⢤⣄⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⡇⠘⣇⠀⠀⣠⣀⣤⣈⡄⣏⠀⢀⡏⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣷⡀⠀⠸⣇⠤⣇⢧⣠⣤⣤⣄⠀⢾⠀⠀⠘⠃⠀⠠⠴⠖⠛⠛⠛⠿⢿⡷⠀⠙⢦⡜⢡⡏⠀⠈⠁⢉⡒⠋⠀⠀⢀⡜
⠀⢰⡆⢀⡴⠞⠓⢶⠋⠀⢀⠙⠀⠀⣇⠀⢸⠛⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⢸⠁⠈⢳⡖⠓⡆⠘⠃⠀⢠⡴⠋
⡄⠀⠀⢸⠀⠀⢀⣼⡀⠀⢹⡄⢠⠀⠉⠀⡇⠀⠀⢀⠔⠚⠉⠉⠉⣱⠶⠤⢄⣀⡀⢀⣀⡡⠏⠀⠉⠁⠀⠀⠀⣤⠤⠚⢀⡜⠀⠀⠀⠀⢸⠁
⢱⡀⠲⡀⠳⠖⠁⠀⠙⣶⠚⠀⠘⢦⠀⠀⣇⠀⠀⠻⡀⠀⠀⠰⠋⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⠎⠀⠀⠀⠀⠀⡸
⠀⠹⢄⠙⠆⠀⠀⠀⠀⠈⠛⠒⡞⠀⠀⠀⠘⠦⣀⠀⠙⠲⠤⣀⣀⣀⠤⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⣀⠜⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠈⠉⠒⠶⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⣰⠖⠒⠙⠋⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠒⠀⠚⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⢀⣇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣤⣐⢒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣌⠙⠲⠦⢤⣀⣠⠤⠤⠖⠛⠉⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠲⣶⠶⠄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⢤⣀⡀⠀⠀⠀⣘⢻⡀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡏⠉⠛⠶⣄⡟⠘⡇⣠⡴⠶⠖⠲⣞⣸⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠳⣄⠀⠀⡟⠃⠀⠛⠒⣷⠀⠀⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⣤⣤⣬⠦⢤⣄⢸⡇⣸⡳⡄⠀⠀⠀⣷⠶⠚⠛⢛⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⣭⡟⠁⠀⣎⠩⠷⠤⣒⡶⠾⠷⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⠢⣤⡀⡀⠀⠀⠀⠀⣨⠇⣀⣠⠔⣫⠃⠀⠀⢸⣇⢠⡞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢌⣉⣑⣒⣒⣚⣉⣉⠭⠔⠊⠁⠀⠀⠀⠈⢯⡛⠧⣄⣀⠀⠀⠀⢀⣠⠼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⠉⠉⠉⠁⠀⣤⠖⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣀⣀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⡀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀
⢰⣶⢸⠻⡜⡂⠘⠹⠘⢻⠘⠀⢰⣶⢸⠿⡜⠂⠘⠻⠘⢻⠘⠀⢰⣶⢸⠻⡜⡂⠘⠹⠘⢻⠘⠀⢰⣶⢸⠻⡜⠂⠘⠻⠘⢻⠘
⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠆⠀⠀⠀⠀⢦⠀⢠⢷⣆⣼⢀⠆⠀⠀⠀⠀⣦⠀⢰⢷⣆⣴⢀⠆⠀⠀⠀⠀⢦⠀⢰⢷⣆⣼⢀⠆⠀⠀⠀⠀⣦⠀⢰⢧⢆⣼
⠀⣰⣼⣼⢷⢘⡀⠈⠘⠉⠛⠘⠀⣰⣼⣼⢷⢘⡀⠀⠘⠉⠟⠘⠀⣰⣴⣼⢷⢘⡀⠀⠘⠉⠛⠚⠀⣰⣼⢼⢷⢘⡀⠀⠘⠉⠛
⠀⠈⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠘⠁
⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⡀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀
⢰⣶⢸⠻⡜⠂⠘⠻⠘⢻⠘⠀⢰⣶⢸⠻⡜⡂⠘⠻⠘⢻⠘⠀⢰⣶⢸⠿⡜⡂⠘⠻⠘⢻⠘⠀⢰⣶⣸⠻⡜⠂⠘⠻⠘⢻⠘
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠆⠀⠀⠀⠀⢦⠀⢰⢧⢆⣴⢀⠆⠀⠀⠀⠀⣦⠀⢰⢧⣆⣶⢀⠆⠀⠀⠀⠀⢦⠀⢰⢧⣆⣴⢀⠆⠀⠀⠀⠀⣦⠀⢰⢧⣆⣴
⠀⣰⣴⣼⢷⢘⡀⠀⠘⠉⠟⠘⠀⣠⣼⣼⢷⢘⡀⠀⠘⠉⠛⠘⠀⣰⣼⣼⢷⢘⡀⠀⠘⠉⠛⠘⠀⣰⣼⣼⢷⢘⡀⠈⠘⠉⠛
⠀⠈⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠘⠁
⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⡀⡄⢀
⢰⣶⣸⠻⡜⠂⠘⠻⠘⢻⠘⠀⢰⣶⢸⠻⡜⡂⠘⠻⠘⢻⠘⠀⢰⣶⢸⠻⡜⡂⠘⠻⠘⢻⠘⠀⢰⣶⢸⠻⡜⡂⠘⠹⠘⢻⠘
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠆⠀⠀⠀⠀⢦⠀⢰⢧⣆⣴⢀⠆⠀⠀⠀⠀⣦⠀⢰⢷⣆⣶⢀⠆⠀⠀⠀⠀⣦⠀⢰⢷⢆⣴⢀⠆⠀⠀⠀⠀⣦⠀⢰⢧⣆⣶
⠀⣴⣼⣼⢷⢘⡀⠀⠘⠉⠛⠘⠀⣠⣼⣼⢷⢘⡀⠀⠘⠉⠛⠘⠀⣰⣴⣼⢷⢘⡀⠀⠘⠉⠛⠚⠀⣴⣼⣼⢷⢘⡀⠀⠘⠉⠛
⠀⠈⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠘⠁
⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⡀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀⠀⠀⠀⢀⡀⢀⠀⢀⣀⠀⡄⢀
⢰⣶⢸⠿⡜⡂⠘⠹⠘⢻⠘⠀⢰⣶⢸⠻⡜⡂⠘⠻⠘⢻⠘⠀⢰⣶⢸⠻⡜⡂⠘⠹⠘⢻⠘⠀⢰⣶⢸⠻⡜⡂⠘⠹⠘⢻⠘
⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠆⠀⠀⠀⠀⢤⠀⢰⢧⣆⣴⢀⠆⠀⠀⠀⠀⣦⠀⢰⢷⣆⣴⢀⠆⠀⠀⠀⠀⣤⠀⢰⢧⣆⣴⢀⠆⠀⠀⠀⠀⣦⠀⢠⢧⣆⣴
⠀⣴⣼⣼⢷⢘⡀⠀⠘⠉⠛⠘⠀⣠⣴⣼⢷⢘⡀⠀⠘⠉⠛⠚⠀⣴⣼⣼⢷⢘⡀⠀⠘⠉⠛⠘⠀⣴⣼⣼⢷⢘⡀⠀⠘⠉⠛
⠀⠈⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⠀⠀⣾⣿⣷⠀⢠⣿⣿⣿⣧⡀⠀⠀⠀⠀⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⣿⣿⣿⠀⣾⣿⣿⣿⣿⣿⣦⠀⠀⠀⢹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣠⣿⣿⣿⡇⣿⣿⣿⣭⣿⣿⣿⣷⡀⠀⠈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣆⠀⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡍⠙⠿⠟⠃⠛⣻⣷⣤⣀⠀⠘⢿⡿⠋⠀⠈⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣇⣠⣤⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣶⣿⣎⠋⠁⣿⣿⣿⡇⠀⢸⣿⣿⡟⣿⣿⣿⣿⣦⡀⠀⠀⠀⢹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣀⣠⣽⣿⣿⣇⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⠀⠀⠀⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠟⠋⠉⠀⠈⠙⠻⢋⠀⠀⠀⠈⢿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⠉⠙⣿⣿⣿⠄⠀⠉⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡀⠀⠘⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠙⠋⠁⠀⢠⣤⣶⡄⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣄⠀⠀⣀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⢰⣾⣿⡆⠀⢸⣿⣿⣷⠀⠀⢠⣿⣿⣿⠃⠙⣿⣿⣿⣆⠈⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⣾⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣿⣿⡇⣿⣿⣿⠛⠛⠛⠛⠛⠛⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⢸⣿⣿⣧⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠀⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠛⠣⢿⣿⢲
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡎⠌⢡⠀⢒⠲⠟⣫⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠃⠑⠂⠸⠇⠅⣤⣹⣯⡿⢀⣀⡠⣄⣤⣀⡀⠀⠀⢠⡾⣿⡾⢻⣦⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⣯⣍⣒⣤⡤⠀⠛⣿⣽⢛⠛⠀⠀⠀⠙⠻⢿⣷⣠⠾⠟⠛⠙⠯⢄⠙⡿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⠠⡇⠀⢧⣈⡩⠋⠀⢀⠞⠁⠻⢬⠔⠀⢀⣘⢳⡄⠀⡼⣵⡘⠀⡇⢀⡔⠄⠘⡿⣻⢛⣿⣇
⠀⠀⠀⠀⠀⠀⢧⣀⣱⣀⠀⠀⠀⠀⣠⠃⢸⣒⠢⡈⠀⠀⠻⡀⠀⠁⣿⠁⡈⠱⠈⠀⠘⠓⠁⠀⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠑⣦⡀⢠⠃⢠⠟⢻⣷⣌⣢⣰⣄⠀⠀⣤⡿⠘⣷⣒⣒⣒⣢⠗⠒⠂⠈⢹⠋⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠈⢸⠀⠘⠤⠤⠔⠋⠉⠀⠀⠀⠀⡬⢷⠀⢸⠿⠯⡽⠃⠀⠀⠀⢀⣾⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠎⢆⠀⠀⠀⠀⠀⠀⠀⠀⣇⣈⡠⢾⣆⠀⠑⠋⠀⠀⠀⠀⣠⢻⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠣⡀⠀⠀⠀⢀⣠⠞⠉⠁⠀⠰⠋⠑⢦⣀⠀⠀⠀⣰⠃⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢶⣴⠊⢉⡴⠂⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⣀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠻⠿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⠿⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠈⠙⢶⡄⠀⣠⠶⠛⠉⠉⠉⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⡠⢤⣄⠀⠀⠀⢹⢀⠠⣤⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⢀⣀⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⢗⣺⣿⠀⠀⠀⢸⠻⣴⡿⠃⠀⠀⠀⠀⠀⠀⢸⠃⠀⠠⠶⢶⢦⡄
⠀⡴⠛⣏⠉⠃⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣼⠀⠉
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠳⣤⣀⠀⠀⠀⢀⣠⡴⠋⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⡤⠶⠋⠁⠀⠀⠀⠀⠉⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢳⠀⠀⠀⠀⠀⠀⡈⠒⠀⠀⠀⠀⠀⠀⠀⣿⠐⠂⠀⠀⠀⠀⠀⠀⠐⠏⠆
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠆⠐⠐⠀⠐⠠⠀⠀⠁⠀⠁⠁⠀⠀⠡⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢀⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠈⠁⠀⠆⠀⠄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣀⠀⠀⠀⠀⠀⣀⡔⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠆⠀⠀⠀⢀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⠀⠀⠀⠀⠀⠀⠠⠘⠆⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡃⠀⠀⠀⠀⠀⢄⠘⠀⠀⠀⠀⠀⠀⢢⠄⠤⠂⠲⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣠⡀⠨⠃
⠀⠀⠓⠀⠀⠀⠋⠀⠀⠀⠀⠃⡀⠀⣀⡀⠀⠀⠀⢠⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⢀⡀⡀⠅⠀⠀⠀⠀⠁⠀⠀⠝⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠲⡀⠀⠀⠀⠀⠀⠀⡒⢲⡄⠀⠀⡀⣠⡔⠦⡄⣀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⡀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⠀⠠⢤⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠑⠀⣰⠀⠀⠀⠀⡀⢦⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠒⢀⠀⡦
⠀⠀⠀⠙⠀⠈⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⢠⠄⠀⠀⠀⠀⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡀
⠀⠀⠀⡴⠢⠰⠀⠀⠀⠀⠀⠀⠐⠚⠲⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠂⠀⠀⠬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠒⠂⠐⠒
⠀⢀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢤⣤⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠈⠠⠀⠄⠀⠌⠁⠀⠀⠐⠀⠐⠀⠀⠂⠀⠚⠁⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢠⠀⠑⠖⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠢⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠉⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠋⠉⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡦⠀⠾⠿⠿⣷⣄⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠓⠦⢴⡟⠁⠀⠀⠀⠀⣀⡀⠈⠻⡄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠑⠲⠒⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠈⣧⢀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠉⢢⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⣀⣠⠄⠀⠀⠉⢢⣀⠀⠈⠑⠄⠀⠀⠀⠀⠘⢳⡄⠀⠀⢀⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⢻⡃⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠉⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⣀⣀⣀⠀⠀⣀⣠⣴⠞⠋⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢿⠀⠀⠈⠋⠉⠀⠀⢂⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⣶⠤⠴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠘⠀⠀⠀⠀⣀⣠⣤⣾⣿⡇⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣷⣶⣾⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠿⠿⡿⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠉⠘⠋⠀⠀⠀⡼⠁⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠙⠤⣀⣀⣀⣠⣤⠴⠞⢁⡜⠁⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣀⡀⠀⠀⠀⠀⠀⣀⣤⠏⠀⠀⠀⠀⣼⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⡏⠉⠉⠉⠛⠉⠉⠀⢀⡄⠀⠀⣠⠇⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠏⠀⠳⣄⣀⠀⢀⠀⣠⡴⠋⣀⡤⠞⠁⠀⠀⠀⣿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣽⠃⠀⠀⠀⠱⡄⠉⠉⣉⡥⠖⠋⠁⠀⠀⠀⠀⠀⠀⣿⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢸⡏⠀⠀⠀⣠⣶⢹⣤⠞⣩⠄⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⡀⠘⣇⠀⢀⣾⣿⣿⣿⣷⣤⣤⣶⣿⣦⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣼⠇⠀⠈⠳⠾⠉⠻⣿⣿⣿⣿⣿⣿⡿⠟⢣⡀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠉⠉⠁⠀⠀⠀⠉⠲⠦⠤⠟⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠰⠇⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠉⠻⠟⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠂⠊⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡴⠊⠀⠉⠰⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠓⢀⡀⠀⠀⠀⠀⢀⡜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡏⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢠⠀⡀⠀⠀⠀⠀⠀⡀⠈⠂⠀⠀⠀⠄⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡾⠁⠀⠀⠀⠐⠚⠹⠆⠀⠀⠀⣠⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠙⢃⠀⠀⠀⠀⣶⣄⠒⠂⢠⡀⠁⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢀⠟⡀⠀⠀⠀⠹⡙⢿⡆⠒⠚⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡉⠀⠘⢤⡀⠀⠀⠑⠰⠧⠄⠂⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠊⠀⠀⠠⡁⠀⠀⠀⠽⠶⠦⢤⣤⣤⣤⡐⠋
⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠈⠢⢀⣀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠦⠴⠤⠤⠤⠤⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢸⠁
⠀⠀⠀⢀⠸⣄⠀⠀⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠂⢤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⡠⠊⠀⢀⠗⠐⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠰⠁⣀⡔⠁⠀⠀⠀⠃⠀⠀⠀⠀⢀⣤⠄⠀⣀⠀⠀⠀⢠
⡌⠀⠀⠈⠀⠀⠀⠙⠛⠋⠁⠀⠀⠜⠁⠉⠻⣿⣿⠆⠀⠀⠈
⠓⠀⠀⠒⠒⠂⠀⠀⡞⠉⠉⠁⠀⠈⠁⠀⠚⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⡆⢰⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠒⠒⠶⠒⠀⠘⠲⠒⠒⠒⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠘⠀⠀⠀⠀⠀⡆⠘⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠋⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇⣸⡆⠀⠀⠀⠀⠀⠀⠀⣶⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⠑⢄⡀⠀⠀⠀⠀⢠⣌⠙⢩⣶⣶⠆⠀⢴⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⠎⠙⢂⠀⠀⠀⠀⠉⠛⠛⠿⠻⢤⣤⣌⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣀⣀⡚
⣿⣿⣿⣿⠿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣠⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⢠⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠒⠋⠁⠀⠀⣀⠀⠀⠀⣀⠀⠀⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠈⡄⠀⢻⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢀⣀⣀⣀⡀⣶⡂⠀⠰⠀⢸⡿⠀⠀⠀⠀⢡⠀⢸⣷⠀⠀⡇
⣀⣀⣀⣀⢰⣶⠐⠒⢢⣠⠴⠚⠉⠀⠀⠀⠀⢸⣇⠀⠀⠇⣿⡇⠀⠀⡇⢸⡇⠀⠀⡆⠀⠀⡆⠘⣿⡄⠀⡇
⣿⡅⠀⠈⡜⣿⠀⠀⢸⠀⠀⣰⡆⠀⠀⠐⡄⢸⣿⠀⠀⢰⢸⡇⠀⠀⡇⣸⡇⠀⠀⣿⠀⠀⠰⠈⣿⡗⠒⠣⢀
⢿⡇⠀⠀⡇⣿⡀⠀⠸⠀⠀⣿⠃⠀⠀⠀⢠⠈⣿⠀⠀⠸⠼⠟⠀⠀⢡⣿⠇⠀⠀⠀⠀⠀⠀⢃⢿⡇⠀⠀⡇
⢸⣇⠀⠀⠣⠿⠇⠀⠀⡇⠀⣿⠀⠀⢀⠀⠀⠆⣿⡆⠀⠀⠀⢀⠀⠀⢸⣿⠀⠀⢰⣶⣶⠀⠀⠈⡾⠷⣶⣶⠇
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠇⢀⣿⠀⠀⣼⡀⠀⠘⣸⡇⠀⠀⠻⣿⡇⠀⠈⣿⠀⠀⢸⠀⢻⣧⣤⣤⣧
⠀⣿⡀⠀⠀⡿⣿⠀⠀⢸⢸⡟⠀⠀⠛⠃⠀⠀⢻⣿⠀⠀⢸⢸⣇⠀⠀⢿⠶⠶⠾⠀⠀⠀⠀⠀⢰
⠀⢻⡇⠀⠀⡇⣿⡄⠀⠘⣸⡇⠀⠀⣀⣀⡀⠀⠈⣿⣄⣀⣈⡜⣿⣤⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠀⢸⣷⠀⠀⢰⢹⣧⣤⣤⣿⡇⠀⠀⡟⢻⣧⠀⠀⢹⠛⠛⠛⠃⠈⠀⢀⣀⣀⣤⣤⣤⣶⠶⠾⠟⠋
⠀⠈⠛⠛⠛⠛⢸⣯⠉⠉⣿⣇⣀⣀⡇⠈⠛⠛⠛⠛⠂⢠⠶⠾⠟⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⡿⠿⠿⠛⠙⠿⣶⣄⡀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣶⣄⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠒⠒⣦⣀⠀⢀⡖⠉⠉⠉⠙⢿⡻⣦⡀
⠀⠀⠀⠀⡴⠋⣠⠴⠒⠒⠒⠒⠶⢤⣄⠀⠀⠀⠀⠀⠀⢀⠇⠈⠉⠉⠀⠀⠀⠀⠀⠀⡹⣆⠻⡟⢾⡛⠙⠛⠓⢦⣀⡀
⠀⠀⠀⡼⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣆⠹⡄⠹⡄⠀⠀⠀⣏⠙⠳⢦⡀
⠀⠀⢸⣷⠷⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢳⠀⠀⠀⠀⠀⢻⠀⠀⠀⠹⣦
⠀⠀⣿⠃⠀⠀⣿⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣇⠸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠳⣄
⠀⢸⠙⢄⣀⣴⣿⣿⣿⣿⣿⣿⣷⠀⠀⠱⡃⠆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣶⠏⠀⠘⣿⠀⠀⡄⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⢹⢷⡀
⠀⡎⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⣸⠁⠠⠀⠀⢀⣎⠀⠀⠀⠀⢳⠘⠀⢻⡀
⠀⣧⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠀⡄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢰⡏⢠⣧⠤⠤⣤⠞⠉⠉⠳⣤⠤⠀⢸⠀⠃⠈⡇
⠀⢸⡀⠀⠀⠹⣿⣿⣿⣿⣧⣾⢃⣄⣄⡀⢀⡄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⣼⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⠀⠀⠀⡇
⠀⠈⢷⡀⠀⠀⡈⠛⠿⠟⠋⠁⠉⣿⠿⢣⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⠀⢀⢠⡇
⠀⠀⠘⣷⢄⡪⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡞⠠⠃⡾
⠀⠀⠀⠈⢷⡍⠒⠦⠤⠤⠴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠊⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠈⣠⡴⠋⢀⣤⠤⢤⣄⡀⠀⠀⠀⠀⣀⣠⡤⠚⠀⠀⢀⣠⠞
⠀⠁⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠑⠠⠀⠀⠀⠠⢀⠤⠷⠤⠒⠤⣀⣀⣤⠾⠋⢀⡔⠉⠀⡀⠀⠀⠉⠙⠛⠿⠭⠭⠀⠀⠠⣊⡵⠛⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣀⣀⣀⣀⣠⣤⡴⠶⠛⠉⠀⠀⠀⡞⠀⣠⠿⠶⠦⢤⣔⣂⣀⡠⠤⠴⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⠲⢤⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⣾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣶⣠⣤⡶⠾⠛⠉⠁⠀⠀⢹⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣷⠾⠟⢻⣏⠀⢀⠀⠂⠀⠀⠀⠀⢸⡟⡇
⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⣧⠀⣀⡠⣴⣶⠿⠟⠋⠉⢿⡄⠀⠈⣿⡄⠁⢠⣄⠀⠀⠀⠀⣟⣷⣇
⠀⠀⠀⠀⠀⠀⢘⣷⡤⣰⣿⡿⠒⢩⠝⠀⠀⠀⠀⠀⠸⣷⠀⠀⣹⣧⠀⣾⣿⣆⠀⠀⠀⢿⣿⣿
⠀⠀⠀⣀⣀⠬⠓⢻⣏⠀⢸⣿⡠⢾⣧⡀⠀⢀⣠⠄⠀⢻⣟⠉⠉⣿⡀⣿⡿⣿⣆⠀⠀⢸⣿⣿
⠀⠀⠀⢻⡄⠀⠀⢨⣿⡖⠺⣿⡇⠘⣿⣿⣄⠉⠀⠀⠀⠈⣿⡆⠀⢻⡇⠿⠃⠘⣿⠆⠀⢸⣿⣿⣀
⠀⠀⠀⠀⢿⡀⢀⠠⢺⣷⠀⢸⣿⡀⢿⡟⠻⣧⡀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣀⣠⡤⠴⠒⠚⠋⠉
⠀⠀⠀⠀⠈⢿⡀⠀⠀⣿⡇⠀⣿⡇⠸⠇⠀⠉⠁⠀⢀⣀⣤⣤⣶⠖⢿⡉⠁
⠀⠀⠀⠀⠀⠈⣷⡀⠀⠘⠋⠀⠈⢀⣀⣤⣤⡶⠾⠟⠛⠉⠉⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠘⣧⣠⣤⣶⣾⣿⣿⣽⣥⣥⣥⣤⡤⠤⠤⠤⢴⣶⡶⡶⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢉⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁



⣿⡏⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⣘⡅⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠁⠀⠉⠀⠳⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠓⠒⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⣀⡴⠀⠀⠀⣠⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡠⠾⢥⣀⠀⠀⠀⡹⠦⣄⡀⠹⡆⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢳⡄⠤⠄⢀⡧⠚⠀⠀⠀⠙⡆⠀⡾⠁⠀⠀⠙⣦⢹⡖⠒⠲⠚⠁⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡸⡀⠀⠀⠀⠀⠀⢻⡸⠃⠀⠀⠀⠀⢿⠈⣇⠀⠀⠀⢸⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡄⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⢾⣿⠀⠀⠠⢐⣀⣺⡇⣿⠀⠀⠀⣾⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡇⠀⠀⠀⠀⣯⡀⠀⠀⣰⣿⡛⣿⣿⠀⠀⣴⣿⣏⣿⡇⣿⡀⠀⠀⣿⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡇⡇⠀⣰⣿⣿⣿⡿⢸⡆⢰⣿⣿⣿⣿⠃⡿⢣⠀⠀⠏⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡃⠀⠀⢀⡜⢣⢱⡄⢿⣿⣿⣿⣃⠀⢻⣿⣿⣿⣿⡟⢰⠇⠈⢦⡀⠂⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⢀⠔⠊⠀⠘⣄⠻⣿⡟⠟⢁⠈⠀⠀⠙⠛⠿⠟⢡⡟⠀⠀⠎⠩⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡿⠀⠀⠱⡀⠀⠘⣆⠀⠀⠀⣄⣠⣄⡀⠀⠀⠀⣰⠏⠀⠀⢸⠀⠀⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢰⠀⠀⠀⡇⠀⠀⠈⠳⣄⠀⠘⠀⠈⠉⢧⠀⠚⣧⠀⠀⡤⠚⢄⠀⡄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⡆⠀⠀⠗⠈⠑⠆⠀⠈⠳⡇⠀⢀⠀⠀⡇⠀⣿⡤⠶⡀⠀⠐⠀⣿⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⣷⠀⠀⢠⠀⠀⠐⠂⠀⡊⠳⢤⣶⣤⣿⡇⠀⣿⠀⠀⠄⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢴⢹⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠿⣿⣿⡇⢠⡏⠀⠀⠀⠀⠀⠀⣿⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⢣⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⠀⠋⢻⠀⡾⠁⠀⠀⠀⠀⠀⠀⣿⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢸⡀⠀⠀⠀⠀⠀⠀⠀⢈⡄⢀⡴⠃⡼⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⡇⠀⠀⠀⠀⠀⠀⢰⡁⠿⠊⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡰⠀⠀⠈⡄⢧⠀⠀⠀⠀⠀⠀⠀⠑⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣠⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠀⠀⣀⠤⠦⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢀⡈⡠⢀⣈⠀⠳⣄⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⢠⡿⠠⡇⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠈⠘⢁⠈⠙⢧⣄⠈⢧⡜⠀⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⡘⠃⠈⠁⠀⠀⠀⢢⡀⠠
⠀⠀⠀⠀⠀⠀⠀⡖⠉⠳⢶⣄⣉⠳⠄⠁⢀⠃⣇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⠇⢀⠀⠦⠄⠀⠠⠖⠐⣢⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠒⠒⠐⠒⠋⠀⢸⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡞⠀⢸⣀⣀⡀⠀⠀⠙⠉⠁⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⢸⠁⠀⠀⠀⠀⠈⠛⠒⠲⠶⠖⠁
⠀⠀⠀⠀⠀⢀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⠀⠀⡿⠙⠒⢰⡖⡶⠒⠒⠒⠲⠶⠦⣾⠁⠀⠇
⠀⠀⣰⠚⠉⢻⡆⠰⡈⢳⡀⠀⠀⠀⢀⠞⣡⠬⡇⠀⠀⡛⠤⠠⠜⡰⠁⠀⠀⠀⠀⠀⢰⡏⠀⢸
⠀⠰⠃⠀⠀⢠⡇⠀⠩⡄⢳⣀⢀⡰⣡⠎⠀⠀⡶⠀⡼⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢾
⢀⠃⡄⢠⠀⠸⡀⠀⠀⠙⢄⣉⣩⠾⠁⠀⢠⣞⠁⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠻⡀
⠘⠁⠁⣎⠘⣄⡙⠦⣀⡀⠀⠀⠀⠀⠀⠀⣠⠋⠉⠉⠙⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠒⠒⠲⣬
⠀⠀⠀⠉⠀⠈⠙⠓⠉⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⡆⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡇⠀⠀⠈⢳⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣘⣷⣤⣤⣴⣒⣚⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣳⣶⣶⣒⣚⣉⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣦⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣰⠷⣄⠀⣠⠶⣄⠀⠀⣀
⠀⢀⡤⣾⢻⡏⣷⣀⠀⠀⢀⣀⠀⢸⠉⠳⢤⡏⠀⠈⠛⠁⠀⠹⠞⠋⢹⠀⠀⠀⠀⠀⠀⠀⣀⣴⠳⣄⣤⡀
⠀⠸⣄⡈⠀⠀⣉⣹⠆⠀⢸⡍⠙⠛⠀⣀⣀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠘⠛⢹⠇⠀⠀⠀⢸⣍⠛⠀⠋⠼⠷⡄
⠀⠀⠈⢧⣀⠀⠻⣅⠀⢶⠤⠇⠀⢠⢎⠏⣯⢱⠀⠀⠀⠀⡏⣼⢹⢹⠀⠀⠛⢲⠆⠀⠀⣀⡾⠁⢀⣠⠤⠞⠁
⠀⠀⠀⠀⠉⢧⡀⠀⠙⠾⠇⠀⠀⠘⢾⣦⡯⠞⠀⠀⠀⠀⠑⠿⠾⠋⠀⠀⠴⠯⠶⠶⠛⠁⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⡀⠀⠀⠀⢠⠴⣞⡿⠉⠉⠉⠹⠽⠋⠳⡀⠀⠀⠀⣀⣀⣤⠴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⡇⠀⠀⣀⣀⡀⣀⣤⣀⠀⠀⡇⠀⠀⢙⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠀⠀⠀⠳⣄⣞⡁⠀⠉⠁⢀⣈⡦⠞⠁⠀⢘⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠶⢶⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⣀⡀⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡇⠀⢤⣀⡤⣄⣀⡴⢶⠀⠀⣿⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠉⠀⠈⠉⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡇⠀⢸⠀⠀⠀⠀⠀⢸⠀⢀⠟⠛⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⠤⠭⠥⠤⠾⠀⠀⠀⠀⠀⠸⠦⠤⠤⠤⠤⠾⠃

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠹⡗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢊⠝⠉
⠀⢠⣄⢰⣦⡀⠀⠹⡄⡙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣰⠋⠀⣠⠀⣼⡇⢠⣶
⢠⡌⢿⡎⣿⣳⡄⠀⠹⡜⣦⡈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣋⡔⣰⠃⢀⣼⣿⣤⣿⢁⡿⣿
⢸⣿⠟⢿⡻⠇⠉⠂⠀⠹⡘⣿⣶⣌⡓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⢊⣥⠚⡽⢰⠃⠀⢠⡿⠉⣽⠛⡾⠛⣿
⠀⠘⡇⠈⠃⣠⣆⡟⣾⡀⢳⡘⣿⣿⢹⡗⡦⢬⣉⣙⡒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢛⣉⣉⣡⡤⢾⢛⡏⡼⢡⠇⠀⠀⠘⠃⠀⠋⠀⠁⠀⠈
⠀⠀⠀⠀⠀⡿⠹⠛⠉⠃⠀⢣⠘⣿⣇⡇⣇⠀⢿⠀⢹⠋⠉⠉⠙⡟⠉⠉⠉⢹⠉⢉⡇⠀⡇⣞⡜⡸⢡⠏⠀⢠⣤⡶⠋⣤⡾⠃⢀⡀
⠀⡸⣆⣷⡀⠀⢀⡄⣰⡇⣰⠌⢧⠹⣿⡷⣼⣀⢸⡀⢸⡄⠀⠀⠀⣇⠀⠀⠀⢸⠀⣸⠃⣸⣷⣟⣰⢁⡎⢀⡴⠟⢙⣿⡿⣋⣴⣿⠟
⠐⢿⠻⠋⠈⠐⡿⢷⣿⣼⣿⠀⠈⢆⠹⣧⡏⡏⡟⢳⡤⢧⡤⣤⣦⠯⣷⣒⣤⡿⢶⠛⡟⢷⢸⣾⢃⡞⠀⠈⠀⠰⠛⠡⠟⢛⡾⠇
⠀⠀⠀⠀⠀⠸⠁⠘⠀⠁⠘⠀⠀⠘⡆⢻⣾⠇⡇⠸⠀⠼⠀⢸⠇⠀⠸⠀⠸⡇⢸⡄⢿⠸⢾⠇⡼⠀⡄⣤⠀⠀⠀⠀⠀⠘⠁
⠀⠀⢲⣖⡿⣴⠂⠒⠀⣴⣧⠂⣶⡄⠛⡟⢏⢰⡇⢻⠒⢿⠐⠺⡇⠀⢻⠓⢺⠇⢸⡇⣿⢖⠘⡾⢳⠷⣿⠿⠆⢀⣴⣺⢿⣾⠂⠈⠐⠛
⠀⠀⠏⠽⠛⠻⠀⣰⡄⢹⣿⠀⣿⣿⡀⠹⡌⠣⡙⠚⢦⡼⣄⢀⣇⠀⣿⡀⣸⣁⡼⠛⣡⠏⣰⠃⠈⠁⠁⠀⠀⠼⠩⠟⠟⠟
⠀⠀⠀⠀⠀⠀⣀⣿⣧⣾⣿⣀⣿⡾⣷⠂⠹⡄⠈⠓⠲⠤⠬⣍⣀⣉⣀⣉⣁⡤⠴⠚⠁⢠⠇⠀⣀⢰⡇⢰⡆
⠀⠀⠀⠀⠀⠀⠈⣿⠏⠸⣿⠉⡇⠀⠙⠃⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⣠⣿⣼⣇⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠛⠀⠀⠀⢀⡀⣶⢠⡄⠙⠒⠲⠶⠒⠒⠒⠒⠒⠒⠒⠒⢋⡄⡄⠀⢸⡇⢸⠏⠃⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢶⣧⡿⡇⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢼⢿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠁⠀⠶⡿⠇⠀⠀⠞⠿⠇⠀⠀⠘⠈

⠾⡶⡾⠀⢤⡤⢀⠀⠁⠀⠀⠀⢰⣢⡿⣙⠂⠀⠰⠀⠰⣌⡶⡻⡙⠀⠀⠀⠈⣿⠹⠛⡇⠀⠐⠽⢳⣞⠁⠀⡀⠀⠁⠘⠈⠀⠀⠄⠀⠐⣻⡷⠒⠀⠀⠉
⠀⠀⠀⠘⢋⣽⢕⡀⠀⠈⠀⠀⠒⡿⠶⠆⠀⡶⣤⡀⠀⠉⠳⠈⠀⠠⢷⢴⡇⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⣀⠀⠀⢀⠀⠀⠲⠀⢀⠀⠈⠁⠀⠀⠴⠂⠀⠘
⠀⠘⠂⠀⠠⠚⠋⠀⠤⠀⢰⠄⠀⣰⡀⡀⠀⠀⠙⠁⠀⡰⣄⡀⠀⠀⢤⣀⠀⠀⢸⢦⣴⠀⠀⢀⠀⠃⠀⠈⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠛⠀⠀⠄⠀⣀⣠
⣦⣄⡀⠀⣠⠀⠀⠀⣤⠀⠀⡀⠀⠉⠋⠋⠀⣄⠀⢰⡄⠀⠿⠂⢀⢪⡷⢟⠳⠀⠀⠀⠀⠀⠚⢻⢏⡁⠀⠀⣆⣯⣧⣷⠄⠀⠒⢶⡷⠀⠀⢠⠀⠀⢋⢽⡖
⣛⡒⠀⢀⣀⣠⠀⠀⢉⠀⠀⢁⡴⣖⣋⠀⠀⢿⢻⣶⢻⠁⢠⠀⠀⠙⠳⠆⠀⠀⠰⡤⠀⠠⠭⡿⣭⠁⠀⠈⠙⠧⠘⠘⠀⠲⢽⣟⠫⠀⠀⣀⠀⠀⠈⠩⠟
⠉⠉⠀⠠⢭⡿⢍⠀⡾⡦⡦⠀⠲⢽⣤⠖⠀⠈⠀⠉⠀⠀⠀⢠⠄⠀⠒⠀⢤⣀⡀⠀⠀⠄⠀⠀⠀⢠⢧⣰⡀⠀⠀⠄⠀⡀⠀⠈⠁⢀⠠⣈⣿⠧
⣿⡂⠀⠙⠛⠮⠁⠀⠀⠁⠀⡀⠀⠊⠉⠀⣀⡀⠀⠘⠛⢀⣀⠀⠀⠐⠀⠀⢵⡾⠭⠁⠀⠀⢤⡤⠀⠀⠈⠈⠀⠀⠀⠀⠀⠙⢀⠀⠀⠀⠻⢯⠳⠃⠀⠼⣷
⠁⠀⠀⠀⡄⠀⣨⡽⡁⠀⠃⠁⠀⣴⠀⠀⠈⠀⠀⠀⠀⢴⡞⠀⠀⢤⠀⠀⠺⠛⠒⠀⠀⠐⠿⠃⠀⣰⢦⠄⠀⠈⠛⠀⣠⠾⣥⣢⠀⠀⣤⠀⠀⣄⢀⢀⡙
⡴⣶⢒⡀⠀⠀⠈⠁⠀⠀⡄⣠⡀⠀⢀⢠⣀⠀⠙⠂⠀⠀⠀⠀⠀⡀⠀⠀⠰⠀⠀⠰⡄⠀⣄⠀⠀⠀⠘⠋⠀⢀⣄⠀⠀⢉⡼⢷⠊⢀⠀⠀⢲⢧⢾⢼⠄
⢈⣉⣗⡁⠀⢀⠤⣵⣮⡀⠛⠍⠃⢻⣄⣷⡻⡄⠐⠂⠠⣙⡶⣀⠀⢠⡄⣴⢀⠄⠀⠀⠀⢀⣈⣤⠀⠀⠀⠖⠀⠈⠁⠀⣀⠀⢀⡀⢀⡀⠀⠀⠀⠘⠋⠘
⡈⠁⠉⠀⠀⠲⣭⡗⠄⠁⢀⠀⠀⠉⠃⠑⠁⢀⠀⠘⣷⡾⢕⠌⠀⢺⠛⡏⣿⠓⠈⠁⠀⢚⡿⣤⣂⠄⠀⠀⠀⠐⢚⣿⣥⡆⠀⠀⠀⠉⠀⠀⢄⡠⠀⣶⣴
⡟⠂⠀⠰⡆⠀⠈⠈⠁⠀⠀⠀⠶⠀⠀⡀⠀⠈⣀⠀⠁⠉⠀⠀⠀⠈⠀⠀⠁⢰⣦⠾⠀⠈⠊⠞⠋⠀⠀⣄⣤⠀⠠⠶⣿⠄⠀⠀⠃⠀⣐⠯⣟⠛⠆⠀⠈
⠁⣀⡀⠀⢠⠀⠀⠗⠀⠈⠁⠀⢀⠀⠀⠁⠀⠈⠉⠀⠐⠀⡀⠉⠀⣆⣤⡆⠀⠀⢀⡁⠀⠀⢀⣠⣄⠀⠘⠯⠈⠀⢀⠀⣄⠀⢠⡄⠀⡠⠈⠹⠣⠅⠀⠰⠃
⡐⢺⣏⡓⠀⠀⡀⠀⠠⢼⡶⠖⠀⠀⣾⣰⣼⣠⠀⠀⢀⣺⡷⠖⠀⠉⠁⠀⠀⠼⣻⣔⡕⠀⠲⠿⠈⢠⡄⠀⣠⠀⠚⠻⠙⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⢀⣠

⠦⡜⢲⠀⠀⠀⢀⡀⠀⠀⠠⡄⠈⠣⡀⠘⡄⠈⠀⠓⠊⠁⡀⠠⠀⠀⠠⡀⣀⠀⠀⣼⢗⠞⢕⠟⠁⠹⣼⠀⢁⣀⢧
⠀⠁⠀⠐⢂⣀⠀⠀⠀⠰⠆⠀⠀⡀⠈⠢⡘⠀⠀⠀⠖⢨⠅⠖⠈⠁⠠⡄⠰⠶⠸⢈⣇⡸⡘⠀⠀⠁⠀⡄⠀⠁⠠
⠀⠈⢿⣿⣿⣿⠁⠀⠀⠀⠄⠁⠀⠐⠃⠀⠈⠻⠆⠀⠁⠄⠐⠀⠀⠀⠀⠁⠀⠀⠀⠙⠖⠊⠃⠀⠀⣄⡤⢀⡁⠀⡄
⠀⠀⠀⢿⣿⠃⠀⢀⣧⠀⠀⠀⢀⠠⠀⠀⠐⣀⠀⠀⠁⠀⠀⠀⢴⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣸⢋⡉⢛⣓⣓⠿
⠀⠀⢴⡎⠁⠀⠀⠘⠋⣀⣀⣀⣀⣀⡀⠃⠀⡄⠀⠀⠀⠀⠸⢄⠀⠐⠃⠀⠤⠀⣶⠄⢬⠿⢆⡹⠧⠿⠧⣬⣩⡕⠿
⠎⠀⠀⣔⢕⣚⠶⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠴⠚⢡⡆⢰⡇⢠⡀⠀⠀⠀⠐⠛⠀⠀⠀⠛⢋⠈⠛
⠀⠄⠀⢋⢜⠈⡎⡆⠘⣿⣿⣿⣿⣿⡇⠨⠂⠉⣁⡂⠀⠀⢠⠄⠀⢠⡆⢀⠈⢁⠘⠃⠀⠀⠁⠀⠰⠆⠈⠱⠓⣴⡔
⢀⡂⠛⢀⢋⠸⠳⡁⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠰⡇⠈⠁⢺⠇⠙⠀⣤⠀⠀⢀⠀⣠⡀⠀⠀⠀⠁
⠘⢌⣭⠫⡆⣤⠞⠘⠀⠋⠉⠉⠙⠋⣁⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠸⠀⡄⠀⣶⠀⠛⠀⣀⠀⠀⠈⣥⠀⠀⢂⠀⠳
⠀⠀⠁⠀⠈⢀⠀⢠⣆⡃⢠⡄⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⡀⣠⢠⠄⠀⠁⠀⠀⠀⡤⠐⠀⠆⠀⠀⠀⠀⠀⠈⠐⠂
⠀⠀⠀⢰⣆⣠⣶⣿⣿⣿⣿⣿⣾⣥⠆⠀⠀⣶⠄⠀⠀⠤⠯⠑⡖⢙⡖⠀⠀⢀⠀⠀⡀⠈⠌⠠
⠀⠀⠔⠀⣹⣿⣿⣿⣷⡿⣿⣿⣿⣿⢀⡁⠀⠘⠀⠀⠐⠑⡎⣹⣉⠍⠅⢠⣦⠀⠀⠀⠀⠀⠀⠰⠂⢱⠄⡀
⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠃⠀⠀⠀⠀⠀⠈⠨⠁⠘⠀⢀⡀⣀⡀⠠⠆⠘⢄⠐⠀⠀⠘⠒⢉⡁⠄⡀
⡀⠀⠀⣀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠀⠀⣤⡀⣤⠶⣆⠀⠀⠂⠀⢀⡮⠳⠔⠛⠺⠀⠀⠀⢀⠀⠀⣀⠀⢨⠰⠈⠁
⠀⠀⠄⠉⠀⠀⠰⠀⠀⠀⡄⠀⡆⠀⠸⡯⣚⣇⣸⢮⢞⣠⣆⠀⢀⢸⢧⢢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀
⠀⠀⢻⣿⣿⡿⠀⢀⡀⠀⢀⠀⠀⠀⠶⠀⠛⡘⠓⠀⠈⠓⠀⠀⠈⢗⢆⡩⡆⢀⡀⠀⠁⠀⠒⠀⡀⠀⠀⠀⢠⡀⠡
⠂⠀⠀⢻⡿⠙⠛⠟⠀⠀⠸⢷⣄⠀⠀⠙⠏⠁⠀⠛⠀⠀⠀⠀⠛⠈⠈⠉⠠⣿⡿⣠⣾⡧⠀⠀⡀⠀⠀⠀⠄⠃⠐
⢰⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡀⠀⠀⢀⡀⠀⠠⠆⠀⠜⠃⠀⣠⣄⢟⣽⣿⣧⠀⣤⠈⠁⠂⠐⡀
⡿⠧⠠⠠⠸⠂⠀⠀⠀⠀⠀⠀⠀⡌⢡⡀⠀⠀⢈⠁⠠⠁⠜⠂⢤⠀⡄⢿⢿⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡂⢐⡀⠀⠀⢀⠀⠀⠦⠀⠀⠶⠂⠀⠆⠰⠈⠀⠁⠠⠁⠀⠀⠀⠀⡠⠁⠈⠿⣿⣭⡄⠀⢠⡄
⣁⡽⢼⣠⠀⠛⠃⠰⠀⠄⠀⠀⠒⠀⢈⢃⠚⠀⢠⡀⠄⠀⠠⠁⡠⢁⠠⠀⠀⡠⢉⠀⠀⠈⡃⠀⢀⠀⢀⠀⢠⠀⡳
⡼⢤⠼⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠔⠁⠀⡘⢃⠀⡷⠀⣀⢀⡀⠀⠈⠏⠀⠀⠐⠈⠀⡴⠾⠍⡻⢏⢩⡢⠀⣀⡍⢨
⠀⠁⡁

⣿⡿⠿⠿⣿⣿⠿⠿⣿⣿⠿⠿⠿⠿⣿⣿⠿⠿⣿⣿⡿⠿⢿⣿⡿⠿⠿⠿⣿⣿⠿⠿⢿⣿⡿⠿⢿⣿⡿⠿⠿⠿⢿⣿⣿
⣿⡇⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⡀⠀⢿⣿⠀⠀⣿⣿⡇⠀⢸⣿⠁⠀⡀⠀⢸⣿⠀⠀⢸⣿⡇⠀⢸⣿⡇⠀⢀⠀⠸⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⠇⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠷⠀⠈⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠿⠀⠀⣿⣿
⣿⡇⠀⠀⣶⣶⠀⠀⣿⠁⠀⢀⣀⠀⠀⣿⠀⠀⣶⣶⡆⠀⢸⡇⠀⢀⣀⠀⠀⢿⠀⠀⢰⣶⡆⠀⢸⡏⠀⢀⣀⡀⠀⢸⣿
⣿⣧⣤⡤⠿⠿⢤⣤⣿⢤⢤⣿⣿⡤⡤⣽⣤⡤⠿⠿⢧⣤⣼⡤⡤⣾⣿⡧⣤⣼⣤⣤⠼⠿⠧⣤⣼⣧⠤⣼⣿⣧⠤⢬⣿
⣿⣿⡿⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⠀⠀⢸⣿⠀⠀⠀⠀⢻⣿⠀⠀⣿⣿⡇⠀⢸⣿⠇⠀⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⣿
⣿⣿⡇⠀⢸⡆⠀⢹⣿⠀⠀⠉⠉⠀⠀⢸⡟⠀⢠⡇⠀⠸⣿⠀⠀⠉⠉⠁⠀⢸⣿⠀⠀⣷⠀⠈⣿⡆⠀⠈⠉⠁⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠘⣿⠀⠀⣶⣶⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠀⠀⣴⣶⡆⠀⢸⡇⠀⠀⠀⠀⠀⢻⡄⠀⢰⣶⡆⠀⠀⣿
⣿⣿⣀⣀⣿⣿⣀⣀⣿⣀⣀⣿⣿⣄⣀⣸⣀⣀⣿⣿⣄⣀⣹⣀⣀⣿⣿⣇⣀⣸⣇⣀⣼⣿⣇⣀⣸⣇⣀⣸⣿⣧⣀⣀⣿
⣿⡇⠀⠈⣿⣿⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⠃⠀⠀⠀⢹⣿⠀⠀⢹⣿⡇⠀⢸⣿⡇⠀⠀⠀⢸⣿⣿
⣿⡇⠀⠀⠛⠛⠀⠀⣿⡏⠀⢰⡆⠀⢸⣿⠀⠀⠛⠛⠁⠀⢸⣿⠀⠀⣇⠀⠸⣿⠀⠀⠘⠛⠃⠀⢸⣿⠁⠀⣶⠀⠀⣿⣿
⣿⡇⠀⠀⣤⣤⠀⠀⣿⠃⠀⠈⠁⠀⠈⣿⠀⠀⣤⣤⡄⠀⢸⡇⠀⠀⠁⠀⠀⣿⠀⠀⢠⣤⡄⠀⢸⡟⠀⠀⠉⠀⠀⢹⣿
⣿⣇⣀⣀⣿⣿⣀⣀⣿⣀⣀⣶⣶⣀⣀⣿⣀⣀⣿⣿⣇⣀⣸⣁⣀⣴⣶⣆⣀⣸⡀⣀⣸⣿⣇⣀⢸⣇⣀⣰⣶⣆⣀⣘⣿
⣿⣿⣿⠉⠉⠉⠉⣿⣿⠉⠉⣿⣿⠉⠉⢹⣿⠋⠉⠉⠉⢿⣿⠉⠉⣿⣿⡏⠉⢹⣿⡏⠉⠉⠉⢹⣿⠋⠉⢹⣿⡏⠉⠉⣿
⣿⣿⡇⠀⢰⡄⠀⢻⣿⠀⠀⠛⠛⠀⠀⢸⡿⠀⢀⡆⠀⢸⣿⠀⠀⠛⠛⠃⠀⢸⣿⠀⠀⣦⠀⠘⣿⠀⠀⠘⠛⠃⠀⠀⣿
⣿⣿⠃⠀⠈⠁⠀⠸⣿⠀⠀⣀⣀⠀⠀⢸⡇⠀⠈⠁⠀⠀⣿⠀⠀⣀⣀⡀⠀⢸⡟⠀⠀⠉⠀⠀⢿⠁⠀⢀⣀⡀⠀⠀⣿
⣿⡿⠀⠀⣶⣶⠀⠀⣿⠀⠀⣿⣿⠀⠀⢸⠁⠀⣴⣶⡀⠀⢻⠀⠀⣿⣿⡇⠀⢸⠇⠀⢰⣶⡄⠀⢸⡇⠀⢸⣿⡇⠀⠀⣿

⠀⠀⠀⢸⣷⠀⣿⠀⣶⡆⠀⣿⠆⢸⡇⢰⣶⠀⠘⡷⠀⣿⠀⢴⡆⠀⢿⠆⢸⡇⠰⣶⠀⠸⡗⠀⣿⠀⢴⣆⠀⢻⠂⢸⡇⢠⣶⠀⠐⡿⠀⣿⠀⣴⣆
⠀⠀⠀⠀⣿⠐⣿⢀⣏⣿⠀⢸⡗⢺⡇⣰⣹⡇⠀⣿⠒⣿⢀⣎⣿⡀⢸⠗⢺⡇⢰⣙⡇⠀⡷⠒⣿⠀⣎⣿⡀⢸⠗⢺⡇⢸⣘⣇⠀⡿⠒⣿⠀⣏⣻
⠀⠀⠀⠀⠏⠀⢸⠸⠁⠉⡇⠘⠀⠀⣅⠛⠈⢹⠀⠁⠀⠁⡸⠁⠈⡄⠈⠀⠈⠁⡎⠀⢻⠀⠃⠀⠛⢰⠉⠘⡇⠘⠀⠸⠃⡏⠁⠻⠀⠇⠀⠸⢸⠉⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢰⣷⠀⣶⠀⣤⡄⠀⣾⠆⢰⡆⢠⣤⠀⠰⣷⠀⣶⠀⣤⡄⠀⣾⠂⢸⡆⢠⣤⠀⠰⡷⠀⣶⠀⣤⡄⠀⣾⠀⢰⡆⢠⣤⠀⠐⡷⠀⣶⠀⣤⡄
⠀⠀⠀⠀⣿⠠⣿⠀⣟⣿⠀⢸⡆⢼⡇⢘⣛⡇⠀⣿⠀⣿⠀⣜⣳⠀⢹⡆⢼⡇⣨⣛⡆⠀⣷⠠⣿⠀⣏⣻⠀⢸⠦⢼⡇⢸⣹⡇⠀⣷⠠⣿⠀⣏⣻
⠀⠀⠀⠀⡟⠀⢸⢸⠋⠙⡆⠸⠀⠈⡇⡟⠉⢳⠀⠃⠀⠉⠰⠋⠙⡆⠘⠀⠸⠁⡞⠉⢳⠀⠃⠀⠟⢰⠋⠹⡇⠸⠀⠸⠇⡞⠉⢿⠀⡇⠀⢸⢰⠋⠹⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠁⠀⠘⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠆⠀⠀⠀⠈
⠀⠀⠀⢠⣦⠀⣦⠀⣠⡀⠀⣶⡀⢰⡄⢀⣄⠀⢰⣦⠀⣦⠀⣠⡄⠀⣶⡄⢰⡆⢀⣄⠀⢰⣦⠀⣶⠀⣠⡀⠀⢴⠄⢰⡆⢀⣄⠀⠀⣦⠀⣶⠀⣠⡀
⠀⠀⠀⠀⣿⣀⣿⠀⡟⣷⠀⢻⣅⣸⡇⢘⢻⡆⠘⣧⣀⣿⠀⡙⣷⠀⢻⣄⣸⡇⢨⠻⡄⠀⣧⣀⣿⠀⡜⢷⠀⢹⣄⣸⡇⢸⢻⡆⠀⣿⣀⣿⠀⡟⣷
⠀⠀⠀⠀⡏⠀⢹⢰⠛⠻⡄⢸⠁⠘⡇⠾⠛⢷⠀⠯⠀⠿⠰⠏⠻⡆⠸⠁⠸⠃⡹⠛⢷⠀⡏⠀⡿⢠⠟⠹⡇⢸⠀⢸⡇⡜⠛⢷⠀⡏⠀⢹⢠⠛⢻⡆
⠀⠀⠀⠀⠁⠀⠘⠈⠀⠀⠃⠀⠀⠀⠡⠀⠀⠘⠀⠀⠀⠀⠂⠀⠀⠇⠀⠀⠀⠰⠃⠀⠘⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠇⠀⠈⠀⠁⠀⠀⠘⠀⠀⠁
⠀⠀⠀⢠⣄⠀⣤⠀⢀⡀⠀⣤⠀⢠⡄⠀⣀⠀⢠⣄⠀⣤⠀⢀⡀⠀⣤⡀⢠⡄⠀⣀⠀⢠⡆⠀⣤⠀⢀⡀⠀⣴⡀⢠⡄⠀⣀⠀⢀⣦⠀⣤⠀⢀⡀
⠀⠀⠀⠀⣿⣀⣿⠀⡿⣧⠀⢻⣄⣸⡇⠘⢿⡄⠘⣿⣀⣿⠀⡻⣧⠀⢿⣁⣸⡇⢘⢿⡄⠈⣏⣀⣿⠀⡿⣷⠀⢹⣀⣸⡇⢸⢿⡆⠀⣯⣀⣿⠀⡿⣷
⠀⠀⠀⠀⡿⠈⢻⢠⠗⠻⡄⢸⠁⠙⡇⣼⠺⢇⠀⣯⠈⠿⢠⡗⢿⡀⠸⠁⠸⠇⠺⠚⣷⠀⡏⠀⡿⢀⠷⢻⡆⢸⠁⢸⡇⡼⠞⣷⠀⡏⠈⢻⢀⠷⢻⡆
⠀⠀⠀⠀⠁⠀⠘⠘⠀⠀⠇⠈⠀⠀⠡⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠰⠂⠀⠸⠀⠀⠀⠀⠸⠀⠀⠁⠀⠀⠀⠁⠇⠀⠘⠀⠁⠀⠈⠘⠀⠀⠃
⠀⠀⠀⢀⣄⠀⣀⠀⠀⠀⠀⣠⡀⢀⡀⠀⠀⠀⢀⣄⠀⣀⠀⠀⠀⠀⣠⠀⢀⡀⠀⠀⠀⢀⣄⠀⣀⠀⠀⠀⠀⣠⡀⢀⡀⠀⠀⠀⠀⣄⠀⣀
⠀⠀⠀⠘⣿⠀⣿⠀⣿⣧⠀⢿⡃⢸⡇⢸⣿⡀⠘⣿⠀⣿⠀⢿⣇⠀⢿⡃⢸⡇⠘⢿⡀⠘⣏⠀⣿⠀⡻⣧⠀⢸⡃⢸⡇⢸⢿⡄⠀⣟⠀⣿⠀⡿⣧
⠀⠀⠀⠀⣿⠉⢻⢠⡧⢿⡀⢸⠏⠹⡇⣼⠴⣇⠀⡟⠉⣿⢀⡧⢿⠀⢸⠋⢹⡇⢺⠤⣇⠀⡟⠉⣿⠀⡧⢿⡄⢸⠉⢹⡇⣸⠾⣧⠀⡟⠉⢿⢀⡷⢿⡄
⠀⠀⠀⠀⠃⠀⠸⠘⠀⠀⠇⠈⠀⠀⢃⠁⠀⠸⠀⠀⠀⠈⡈⠀⠀⡇⠀⠀⠀⢰⠆⠀⢸⠀⠀⠀⠁⠸⠀⠈⠇⠈⠀⠈⠁⡇⠀⠘⠀⠃⠀⠘⠸⠀⠈⠇
⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠸⣿⠀⣿⠀⣾⣆⠀⢻⡇⢸⡇⢰⣷⡀⠘⣿⠀⣿⠀⢾⡆⠀⢿⠂⢸⡇⠐⣷⡀⠸⡟⠀⣿⠀⣾⣆⠀⢹⡀⢸⡇⢰⣷⡀⠀⣟⠀⣿⠀⣾⣦
⠀⠀⠀⠀⣿⠘⣿⢀⣯⣿⠀⢸⠇⠻⡇⣨⣬⡇⠀⡿⠘⣿⠀⣦⣽⠀⢸⠇⢺⡇⢸⣬⣇⠀⡟⠀⣿⠀⣧⣽⡄⢸⠃⢸⡇⢸⣬⣇⠀⡿⠐⢿⠀⣧⣽⡀
⠀⠀⠀⠀⠏⠀⢸⠘⠀⠀⡇⠘⠀⠀⢇⠋⠀⢹⠀⠀⠀⠈⠈⠁⠈⡆⠈⠀⠀⢀⡋⠀⢹⠀⠁⠀⠋⢸⠁⠘⠇⠘⠀⠘⠁⡇⠀⠹⠀⠇⠀⠘⢸⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠸⣿⠀⣿⠀⣴⡆⠀⢻⠆⢸⡇⢠⣶⠀⠘⣿⠀⣿⠀⣴⡆⠀⣿⠆⢸⡇⢠⣦⠀⢸⡟⠀⣿⠀⢶⣆⠀⢿⠃⢸⡇⢠⣶⡀⠐⣟⠀⣿⠀⣴⣆
⠀⠀⠀⠀⣿⠰⣿⢀⣏⣿⠀⢸⡇⢾⡇⣨⣩⡇⠀⣿⠰⣿⠀⣎⣽⠀⢸⠇⢾⡇⢰⣹⡇⠀⡷⠴⣿⠀⣎⣿⡀⢸⠦⢼⡇⢸⣸⣇⠀⡿⠰⣿⠀⣯⣿⡀
⠀⠀⠀⠀⠏⠀⢸⠸⠃⠈⡇⠘⠀⠀⡇⠛⠀⢱⠀⠁⠀⠈⠘⠃⠘⡆⠘⠀⠈⢁⡍⠀⢻⠀⠃⠀⠋⢰⠁⠘⡇⠘⠀⠘⠇⡎⠁⢻⠀⠇⠀⠸⢰⠉⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠰⣷⠀⣶⠀⣤⡄⠀⣾⠂⢰⡆⢠⣤⠀⠰⣷⠀⣶⠀⣤⡄⠀⣾⠆⢰⡆⢠⣤⠀⢰⡗⠀⣶⠀⣠⡄⠀⢺⠂⢰⡆⢀⣤⠀⠐⣷⠀⣶⠀⣠⡄
⠀⠀⠀⠀⣿⠤⣿⠀⣟⣷⠀⢹⡦⢼⡇⢨⢛⡆⠀⣿⠤⣿⠀⡜⣳⠀⢹⡦⢼⡇⢠⣙⡆⠀⡷⠤⣿⠀⣌⣻⠀⢹⠦⢼⡇⢸⣹⡇⠀⣿⠤⣿⠀⣏⣿
⠀⠀⠀⠀⡟⠀⢸⢸⠋⠙⡆⠸⠂⠈⡇⠟⠉⢳⠀⠷⠀⠛⠰⠏⠙⡆⠘⠀⠘⢃⡘⠉⢻⠀⠃⠀⠟⢰⠋⠹⡇⠸⠀⠸⠇⡞⠉⢿⠀⡇⠀⢸⢰⠋⠹⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠘⠁⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⢠⣦⠀⣤⠀⣀⡀⠀⣴⡄⢰⡄⢀⣄⠀⢠⣦⠀⣦⠀⣀⡀⠀⣶⡄⢰⡄⢀⣀⠀⢠⡆⠀⣦⠀⣀⡀⠀⢰⡄⢰⡄⢀⣀⠀⠀⣦⠀⣤⠀⣀⡀
⠀⠀⠀⠀⣿⣠⣿⠀⡟⣷⠀⢹⡄⣼⡇⢘⠻⡄⠈⣿⢠⣿⠀⡙⣧⠀⢹⣧⣼⡇⢨⠻⡄⠈⣧⣤⣿⠀⡝⣷⠀⢸⣤⣼⡇⢸⢻⡆⠀⣿⣤⣿⠀⡝⢷
⠀⠀⠀⠀⡟⠀⢻⢰⠛⠛⡄⢸⠁⠘⠇⡿⠛⢧⠀⠏⠀⠹⢰⠗⠻⡄⠸⠀⠘⠃⡺⠛⢷⠀⠇⠀⠿⢠⠛⢻⡆⢸⠀⢸⡇⡜⠛⢿⠀⡇⠀⢻⢠⠛⠻⡆
⠀⠀⠀⠀⠁⠀⠈⠈⠀⠀⠃⠀⠀⠀⠐⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⠃⠀⠘⠀⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠇⠀⠈⠀⠁⠀⠈⠘⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣼⣿⠁⠀⢹⣿⡏⣿⡟⠉⠉⠉⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣿⠀⠀⢸⣿⡇⣿⠀⠀⣴⡄⠀⢸⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⣿⣿⠀⠀⢠⣤⡄⣿⠀⠀⣉⡁⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⢸⣿⡇⣿⠀⠀⣿⣇⠀⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡷⠰⣿⣿⣷⢿⣶⡾⠟⠻⢿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⡇⠀⣿⠁⣴⡆⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠈⠉⠁⠀⡇⠀⠛⠃⠀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⢰⣶⡆⠀⡇⢰⣶⣶⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⣀⣼⣿⣇⣸⣧⣸⣿⣿⣤⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠈⢻⣿⠃⠈⢿⡟⠉⠀⠀⠈⠹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠸⠿⠀⠀⢸⠀⠀⣴⣷⡀⠀⢲⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢰⣶⠀⠀⢸⠀⠀⣀⣀⡀⠀⢸⣿⡏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⣸⣿⡀⠀⣼⠀⢀⣿⣿⡇⠀⢸⣿⢃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣇⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠋⠁

⠘⠛⠻⠃⢀⠀⠀⡀⠸⠻⠸⠿⠄⠀⢸⠂⠀⠐⠀⠀⠀⠀⠛⠛⠙⠛⠀⠸⠛⠛⠻⠃⢀⠂⢀⠀⠸⠻⠰⠿⠄⠀⢺⠂⠀⠐⠀⠀⠀⠀⠛⠛⠑⠛
⠀⠆⠀⢠⣤⣴⠀⠀⣤⢠⡄⢀⡶⣦⡀⠛⠐⠃⠀⠀⠀⠀⠀⠂⠐⡟⡖⠀⠂⡄⠀⢰⣶⣰⠀⠀⣤⢠⡄⢀⡶⣦⡈⠙⠓⠓⠀⠀⠀⠀⠀⠀⠐⡟⠓
⠀⠀⠀⠀⠈⠁⠀⠀⠋⢘⠀⠛⠀⠈⠁⠀⣇⡇⢸⡇⠀⠀⠀⠀⠰⠇⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⡋⢘⠀⠙⠀⠈⠁⠀⣇⡇⢸⡇⠀⠀⠀⠀⠰⠇⡄
⠾⠆⠀⠀⢁⠈⠀⠀⠃⠘⠐⠒⢀⣀⠀⠀⡟⡇⣾⢷⠀⢶⣶⠀⠀⠚⠛⠳⠾⠆⠀⠀⢁⠈⠀⠈⠃⠘⠑⠐⢀⡀⠀⠀⡟⡇⣾⢧⠀⢶⣶⠀⠀⠚⠛
⢠⣀⡤⠀⠀⠀⠀⠈⠀⠀⣸⡏⣿⢻⠆⢠⡀⠁⠀⢀⣀⡀⠀⠀⣦⢀⣶⡀⢠⣀⡄⠀⠀⠀⠀⠈⠀⠀⣺⡏⣽⢻⡇⢠⡀⠀⠁⢈⣀⣀⠀⠀⣤⢄⢶
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢱⡆⡿⠃⠀⢸⡷⢲⣄⣼⠓⣿⠀⠀⣉⣈⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢳⡆⡿⠃⠃⢸⡷⢲⣆⣼⠛⣿⠀⠀⣁⣈
⠁⠀⡀⠀⢸⠀⠀⠘⠓⠃⠉⠉⠘⠛⠀⠀⠀⠈⠁⠈⠉⠁⠀⠀⠉⠉⠀⠘⠁⠀⠀⠀⢸⠀⠀⠘⠓⠃⠉⠉⠘⠛⠂⠀⠀⠈⠁⠈⠉⠁⠀⠀⠉⠉⢀
⠁⢀⣉⡀⢸⢱⣎⡇⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⢠⣦⣾⣷⣾⡇⠀⠀⠈⠉⠁⢀⣈⡀⢸⢱⣎⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣦⣾⣧⣾⡇⠀⠀⠈
⠇⠈⠛⠃⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⣿⣿⣷⢸⡟⣸⣏⠇⠘⠛⠃⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⣿⣿⣿⢨⡟⣸
⠄⠘⠛⠘⠙⠀⣈⣀⠀⢸⠙⠀⠙⠀⠸⠿⠰⠛⠄⠉⠉⠉⠈⢉⠐⠛⠊⠶⠆⠘⠛⠘⠙⠀⣀⣀⠀⢸⠙⠈⠙⠀⠸⠿⠸⠛⠄⠉⠉⠉⠈⢉⠘⠛⠘
⠶⠰⠄⠀⠀⣿⣿⣿⡂⠈⣤⡀⡄⠀⠀⠰⢤⡖⠀⣧⡇⢰⣇⢸⣄⠀⡀⠰⠶⠰⠆⠀⠀⣿⣿⣿⡄⠈⣤⡀⡀⠀⠀⠰⢤⡖⠀⣧⣷⢰⣇⢸⣄⠀⡀
⠂⠐⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⣉⢠⡀⢠⠀⠀⠀⠁⠁⠈⠉⠘⠈⠓⠂⠀⠂⠐⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⣋⢠⡀⢠⠀⠀⠀⠁⠉⠈⠉⠘⠈⠓⠂
⢀⡀⣀⡀⢀⠀⠀⠈⠀⠀⠀⠀⣿⢼⣇⣟⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⢼⣇⣟⣇⠀⠀⠀⠀⠀⢀⠁⢀
⣼⣿⣿⡇⠛⠲⠴⠂⢀⣠⠀⣤⠙⠘⠛⠁⠙⠀⠀⠀⠀⠀⣤⡀⣀⣀⠀⣿⣼⣿⣿⡇⠘⠶⠴⠄⢀⢠⠀⣤⠙⠈⠛⠁⠙⠀⠀⠀⠀⠀⣤⠀⣀⡀
⠙⠛⠻⠃⢀⠒⠀⡀⠼⠻⠰⠿⠄⠀⠸⠃⠀⠐⠀⠀⠀⠀⠛⠋⠙⠛⠀⠘⠛⠛⠻⠃⢀⡂⢀⡀⠼⠻⠸⠿⠄⠀⢺⠓⠀⠐⠀⠀⠀⠀⠛⠋⠑⠛
⠂⠆⠀⢠⣤⣴⠀⠀⣤⢠⡄⢀⡴⣦⡀⠉⠐⠓⠀⠀⠠⠀⠀⠂⠐⡟⡗⠠⠂⡄⠀⢰⣶⣰⠀⠀⣄⢠⡄⢀⡴⣦⡈⠙⠑⠃⠀⠀⠀⠀⠀⠀⠐⡟⡓
⠀⠀⠀⠀⠈⠀⠀⢀⠋⢈⠀⠛⠀⠈⠁⠀⣇⡇⢸⡇⠀⠀⠀⠀⠰⠇⡄⠀⠀⠀⠀⠀⠈⠀⠀⢀⡋⢘⠀⠛⠀⠈⠁⠀⣇⡇⢸⡇⠀⠀⠀⠀⠰⠇⡄
⠾⠆⠀⠀⢃⡈⠀⠀⠁⠘⠐⠒⢀⣀⠀⠀⡟⡇⣾⣷⠀⣶⣶⠀⠀⠚⠛⠳⠾⠆⠀⠀⢁⡈⠀⠀⠁⠘⠑⠒⢀⡀⠀⠀⡟⡇⣾⣧⠀⣶⣶⠀⠀⠘⠛
⢠⣀⡄⠀⠀⠀⠀⠈⠀⠀⢺⡏⣿⢻⡄⢀⡁⠀⠀⢈⣀⣀⠀⠀⣦⢀⣶⡀⢠⣀⡄⠀⠀⠀⠀⠀⠀⠀⣺⡏⢿⠻⡇⢀⡀⠀⠁⢈⣀⣀⠀⠀⣤⢀⢶
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢳⡆⡿⠃⠀⢸⡷⢲⣄⣼⠓⣿⠀⠀⣁⣈⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢳⡆⡿⠃⠀⢸⡷⢲⣄⣼⠓⣿⠀⠀⣁⣈
⠁⠀⡀⠀⢸⠀⠀⠘⠓⠃⠉⠉⠘⠛⠀⠀⠀⠈⠁⠈⠉⠁⠀⠀⠉⠉⠀⠘⠁⠀⡀⠀⢸⠀⠀⠘⠓⠃⠉⠉⠘⠛⠀⠀⠀⠈⠁⠉⠉⠉⠀⠀⠉⠉
⠀⢀⣉⡀⢸⢱⣎⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣦⣾⣧⣾⡇⠀⠀⠈⠉⠁⢀⣈⡀⢸⢱⣎⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣦⣾⣧⣾⣇⠀⠀⠈
⠇⠘⠛⠃⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⣿⣿⣷⢸⡟⣸⣏⠇⠘⠛⠃⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⣿⣿⣿⢸⡟⣸
⠀⠘⠛⠘⠙⠀⣀⣀⠀⢸⠙⠀⠉⠀⠸⠿⠸⠻⠄⠉⠉⠉⠈⢉⠘⠛⠈⠶⠆⠘⠛⠘⠙⠀⣀⣀⠀⢸⠙⠀⠙⠀⠸⠿⠸⠛⠄⠉⠉⠉⠈⢉⠐⠛⠘
⠶⠴⠄⠀⠈⣿⣿⣿⡄⢈⣤⡀⡀⠀⠀⠰⢦⡖⠀⣷⡇⢸⣇⢸⣄⠀⡀⠰⠶⠰⠄⠀⠀⣿⣿⣿⡄⠈⣤⡀⡀⠀⠀⠰⢦⡆⠀⣧⣿⢸⣇⢸⣄⠀⡀
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠉⠉⣋⢀⡀⢠⠀⠀⠀⠁⠁⠉⠉⠘⠈⠓⠃⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠈⠙⣋⢀⡀⢠⠀⠀⠀⠁⠉⠈⠉⠘⠈⠓⠂
⢀⡈⣀⡀⢀⠀⠀⠌⠀⠀⠀⠀⣿⢼⡇⣟⣇⠀⠀⠀⠀⠀⢈⠁⢀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⣿⢼⣇⣟⣇⠀⠀⠀⠀⠀⢈
⣼⣿⣿⡇⠛⠲⠴⠄⢠⢠⠀⣤⠙⠈⠟⠁⠙⠀⠀⠀⠀⠀⣤⠀⣀⣀⠀⣿⣼⣿⣿⡇⠘⠲⠰⠄⢀⢠⠀⣄⠙⠈⠛⠁⠙⠀⠀⠀⠀⠀⣤⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⢶⣆⢀⣼⡟⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⣸⡇⠀⣸⣇⣾⠟⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⢰⡏⠙⠷⣤⡀⢀⣿⠁⠀⣿⠿⢋⠶⠶⣶⣤⠙⢿⠄⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⣿⢧⣶⣺⣄⠁⠘⠟⠛⠿⠟⠀⣿⠛⠛⠶⣶⡄⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⠇⠸⣏⣠⡿⠀⠀⠀⠀⠀⠀⠠⣿⣤⣤⣴⡿⠀⠀⠀⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⡇
⠀⠀⠀⢠⣤⡶⣶⡄⣿⡏⠀⠈⠛⠿⣶⣄⠀⠀⠀⠀⢀⣾⠿⠟⠛⣛⡋⠉⠉⠉⠉⠉⡉⢁⠀⠀⠹⣿⣿⣿⣷⣄⠀⠀⡂
⠀⠀⠀⢸⣧⠀⢸⣷⣿⠇⣤⡶⠾⢇⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠉⣀⣈⠁⠀⠀⠀⢀⣠⣄⡁⠀⠀⠈⠻⣿⣿⣿⣦⠀⠃
⠀⠀⠀⠀⣿⡀⠀⣿⡟⠰⣶⠞⠛⢹⣿⠀⠀⠀⠀⠀⡟⠀⠀⠀⡈⠁⠉⠃⠀⠀⠀⠊⠀⠀⠉⠀⠀⠀⠀⠈⢹⣿⣿⣆⣤⣾⣿⣷⣄
⠀⠀⠀⠀⢹⣷⠶⠟⠃⠀⢿⣤⣤⡶⠿⠀⠀⠀⠀⡞⠁⠀⡜⠉⠉⠙⠲⠤⢄⣀⡠⠴⠒⠉⠉⠉⢢⠀⠀⠀⢸⣿⣿⡟⠉⠉⠙⣿⣿⣆
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⢀⠀⠀⠀⠀⠈⡇⠀⠀⡁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠘⠻⢿⣷⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⠀⠀⠙⣄⠀⠣⣀⠤⠐⠒⠚⠛⠓⠠⢤⡀⠀⠀⣠⠏⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠗⢦⣌⡙⠒⠶⠤⠤⠤⠤⠶⠚⣓⣉⣀⣠⡤⣖⠋⠀⠀⢀⠀⠀⠀⢀⣤⣄⠀⠀⣴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣠⠂⠀⠉⠙⠲⡒⠀⠀⢀⣩⠝⠋⠉⠉⠀⣀⠀⠑⣄⠐⣄⠑⠄⢀⡾⠀⣼⣣⡾⠋⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢴⡏⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⢹⢱⠀⢸⠀⠸⡄⠀⣾⣅⣰⠿⢋⢦⣤⡈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣠⠞⠀⠀⢃⡀⠀⢠⡍⢠⡟⠙⢳⡆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⢠⠏⣽⡴⠛⣧⠈⠙⠓⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠤⣤⣀⣀⣀⣀⣀⡠⠤⠤⠤⠤⢤⠤⠤⢴⠇⠀⠀⠀⠛⠲⢋⡿⢷⡊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⡼⠀⠀⠀⠀⠀⠀⠘⠓⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁

⠀⠀⠀⠀⠀⣠⣶⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⣠⠤⠶⠖
⠀⠀⠀⠀⣿⣿⡿⢿⣙⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⢞⣡⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠉⣵⣾⣿⠟⠁⠀⠀⠀⠀⢀⠀⠀⠀⣿⣾⡿⢋⠔⠒⠢⢍⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠘⠻⣶⣄⡘⣿⣷⡧⢊⠭⣑⢄⠑⡜⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣀⣿⣦⣶⠶⠿⠟⠛⠛⢛⣿⠿⠛⠿⢿⣿⠷⣶⣤⣦⡣⠈⠢⡙⢿⣆
⠀⠀⠀⣀⣴⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⣶⠦⢹⡆⠀⠈⠙⠻⣿⣢⡙⢦⢹⣷
⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⣀⣈⣡⡾⠁⠀⠀⠀⠀⠈⢿⣞⢸⢸⣿
⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠄⠀⠀⠀⠀⠀⠀⠈⣿⣿⢸⣟⠣⠜
⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⢸⣿⣧⣿⣦⡀
⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣏⠁⠀⠀⣠⠾⠿⣿⣿⠿⠞
⠀⠀⠀⠉⠛⠿⠶⠶⣶⣦⣤⣤⣶⣶⡶⠶⠶⠀⠀⠀⢀⣴⠋⠀⢿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢀⣀⣠⣤⠶⠛⠁⠀⣠⣾⠀⠀⠀⠺⣶⣶⡿⠋⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢻⡄⠀⣀⣠⣾⠿⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⠻⣿⠟⠋⢀⡼⠃⡀⠀⠀⠀⢸⡏⠀⠀⠀⢴⣿⣶⣾⣿⣾⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠙⠛⠉⣀⣴⠏⠀⠀⠀⣿⠃⠀⠀⠀⠀⢀⣼⡿⣿⠟⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠧⣤⣄⣀⣀⣀⡀⠀⠀⠈⠉⠀⢀⣀⣀⣰⡟⠀⠀⢀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠒⠲⠶⠦⠬⠭⣿⣤⣾⣉⣉⣉⣉⣉⣉⣿⣧⡶⠿⠛⠉
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡇
⠀⣰⠋⠙⡇⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣿⠀⢸⠇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⣠⣿⢀⡞⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠷⠴⠚⠛⠻⠶⣦⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠛⠷⢶⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⣶⠶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠲⢦⣤⣤⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡾
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡆⠀⣸⠀⡾⣄
⠀⠀⠀⠀⡏⡁⡏⢰⣏⠙⣆⠀⠀⠀⠀⠐⢄⠀⠳⣄⠀⢘⣧
⠀⠀⠀⠀⠇⠙⢴⠻⡌⡗⠈⣷⢀⡇⢠⣿⠈⢷⡖⠛⢷⣸⣁⣱⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣬⠂⣄⢱⢤⡏⠀⣷⠋⢼⡀⠈⢷⡄⢀⣿⠀⠀⠈⠳⡀⠈⠳⣄⣀⣝⣧⡠⠄
⠀⠀⠀⠀⠀⠀⣿⠀⡇⡏⡀⠳⠜⠁⢸⢦⡇⠀⠈⣡⠏⣰⠂⣠⢶⠀⠉⠀⠀⢤⡑⠀⠈⠛⠄⠀⠀⡀⠀⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠹⠀⠇⠀⣿⠀⢸⡀⣿⢀⠽⢆⣠⠋⡽⣣⠾⢡⡇⠀⢻⣆⠀⠸⣟⢳⣤⡄⠀⠱⣄⣙⣦⡀⢷⠚⠓⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⢹⠀⡟⠁⠀⠀⠑⢞⠉⠁⣤⠘⣄⠀⠀⠹⣆⣠⣿⠋⠉⠙⢷⣄⠉⢇⠀⠙⢦⡃
⠀⠀⠀⠀⠀⢰⡄⠀⠀⠘⡟⠀⠘⣼⡃⠀⢰⡇⠀⢰⠀⡼⠙⡇⢻⡆⢀⣠⠿⡇⢸⠀⠀⠀⠀⠈⠳⠀⠁
⠀⠀⠀⠀⠀⠀⢷⣤⡤⠴⣇⠀⢠⡿⢳⡀⢾⠗⠒⣧⣼⣥⣤⣽⡈⣿⠟⠁⠀⢹⣼⡇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢹⠀⣼⣇⡤⠿⣿⠀⢸⡿⠁⠀⠀⠀⣧⠸⡆⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠸⡄⡟⠁⠀⠀⡟⣆⠚⣰⠆⠀⠀⢠⡜⠀⢹⡀
⠀⠀⠀⣄⠀⢠⡄⠀⠁⠀⠀⢸⠃⠀⠀⠀⠁⠈⣳⣏⣀⣀⢀⡟⠀⣰⠇⠁
⠀⠀⠀⡇⠀⢸⡇⢠⣿⠀⠀⢰⡟⠀⠀⠀⢠⢀⡟⠀⠀⠀⣽⣡⡞⡟
⠀⠀⠰⠏⠉⢹⢀⡿⢹⠀⢠⣟⣀⣀⡀⢀⣿⡞⠀⠀⠀⣼⠟⠉⢹⠃
⠀⠀⠰⠀⠀⢸⡾⠉⡻⢠⡿⠉⠉⠉⠉⢹⠏⣴⣿⠇⡴⠋⠀⡀⠃⡄
⠀⠀⠀⠀⠀⠞⠀⠀⢡⡟⠀⠀⠀⠀⠀⣯⡞⢡⡏⠈⡱⠁⣸⢃⡼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠞⠉⠉⡝⢁⡼⠓⢻⢏⡞⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠞⠀⢀⣯⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠁⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡟⢲⣾⣾⣶⡄⣶⣶⣶⡆⣶⣶⣶⣶⢶⣦⢰⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⠉⠁⢸⣿⣁⣿⢷⣿⡇⣿⣧⠁⢠⣿⠇⠸⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢸⣿⢿⡇⠀⣿⠶⢿⡇⠀⣼⠇⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣠⡇⢀⣿⣼⣿⣶⣿⣿⣿⣷⣾⣯⣀⡀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠮⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠤⠭⠭⠍⠁⠀⠀⠀⠀⠀⠀⠁⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀⢀⣠⣀⡀⠀⠀⠀⠀⣠⣶⡆⢄⠲⡄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⣴⠀⠿⣿⠏⣆⠀⢀⡀⠙⠛⠁⢸⡇⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⣄⣀⣀⣠⠿⠚⠊⠳⣤⣤⣴⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢹⣿⠿⠛⠁⣴⣰⣆⡄⠈⠻⠿⠿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⡠⠀⠘⠋⠙⠃⠀⠀⣤⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢼⣧⡤⢤⣤⠄⠠⠤⠶⣿⠃⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⣿⣶⠀⠀⠈⠀⠀⢸⣿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢏⠻⠶⢶⢶⢶⠞⠋⠌⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆⠉⠐⠀⠐⠐⠈⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠐⠂⠐⠞⠋