Pumpkin Pie Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠊⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠸⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠒⠂⠉⠉⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⠐⠂⠠⠄⣀
⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⡀⠤⠄⠒⢒⡦⠀⠀⠈⠂⠤⢀⣀⡀⢀⣀⡀⠠⠔⠊⠁⠀⠀⠐⢍⡁⠒⠢⠤⢈⠐⠠⣀
⠀⠀⠀⢀⠔⠋⠀⠀⠀⢎⣁⣀⠠⠔⠊⠁⠀⣀⠔⡹⠀⠀⠀⠀⢀⠒⡄⠀⠀⠀⠐⡑⠢⡀⠀⠀⠈⠑⠢⠄⣀⣨⠂⠀⠑⢄
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⡔⠁⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠈⢆⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⢄⡈⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃
⠀⠀⠀⠈⢗⠂⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠤⠻
⠀⠀⠀⠀⠈⢆⠀⠀⠈⠉⠙⠢⠤⠴⢄⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡠⢀⣀⠠⠂⠀⠈⠁⡀⠀⢠⠃
⠀⠀⠀⠀⠀⠈⢆⠘⡀⠀⢠⠀⠀⠀⡀⠀⠁⠀⠉⠒⠒⠉⠉⠐⠒⠊⠉⠑⠒⠊⠁⠈⠉⠉⠀⠀⠀⠀⢰⠀⠀⠀⠃⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠑⠳⠤⣀⣆⠀⠀⠃⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠒⠠⠤⠦⠀⠀⠀⣄⠀⣀⢀⣸⠀⠀⠀⠠⠥⠤⠐⠚⠃⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠒⢋⡉⠙⠛⠦⠤⠦⠤⠤⠞⠙⠛⠒⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⢀⡴⠚⡽⠁⠀⠀⢠⠿⡄⠀⠀⠀⠻⡓⢦⡀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⢀⣀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠈⠉⠚⠀⠀⠀⠀⠯⠤⠽⠀⠀⠀⠀⠳⠶⠛⠀⠀⠀⠀⠀⠀⠈⠳⣤⠴⠶⠤⣄
⠀⠀⣠⠖⠋⠉⠉⠙⠂⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⢳⡀
⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠑⠦⣀⣠⠤⠤⠤⠤⠖⠉⠉⠉⠉⠑⠢⣄⠀⣀⠤⠖⠚⠛⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠈⠓⢦⡤⢤⡄⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⢤⣀⣠⠤⠚⠁
⠀⠀⠀⠀⠈⢧⠀⠀⠀⢠⠈⠑⠂⠤⠖⡖⠉⠑⠢⠴⠚⡏⠑⠂⠁⠀⠉⡟⠋⠁⠈⠑⢢⠤⠤⠤⠤⠒⡟⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠘⣆⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠇⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠘⠦⠤⠼⠦⠤⠤⠤⠤⠷⠤⠤⠤⠤⠴⠷⠴⠶⠦⠤⠴⠧⠤⠤⠤⠤⠾⠤⠤⠤⠤⠾⠴⠦⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠁⠀⢀⣀⣼⣟⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠁⠀⠀⠓⠦⠉⠉⠉⠉⠉⠉⠉⠛⠻⣶⡄
⠀⢀⣠⣤⣤⣤⣤⡶⠶⠦⣶⠾⠛⠲⠶⣶⡶⠶⠶⣶⡶⠲⠶⠿⢛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⢀⣿⠋⠀⠀⠀⠈⠙⠂⠀⠀⠁⠀⢦⡀⠈⠑⠀⠀⠀⠁⠀⣴⠾⠋⠙⠦⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠄⣠⡾⠛⠳⣦
⠈⣿⣄⠀⠀⠀⡀⠀⠐⣤⣠⣄⣤⣤⡷⠴⠦⠶⠶⠾⠶⢾⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠉⠁⠀⠀⠀⢹⣧
⠀⠙⢿⣷⣦⠀⠨⣾⡿⣯⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⡀
⠀⠀⠀⠉⠻⣧⠀⠸⣿⣳⣿⣽⣿⣷⣶⣦⣤⣤⣄⣀⣀⣀⠀⠙⠻⠶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡶⠟⠉⠈⠙⠳⢦⣄⣀
⠀⠀⠀⠀⠀⢹⣧⠀⠸⣷⢿⣿⣿⡿⣿⣷⣶⣾⣿⣿⣿⣽⣿⣻⠶⣦⣤⣬⣍⣉⣙⣛⣛⣛⣛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢻⡆⠀⢹⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣾⣭⣽⣭⣭⣭⣭⣿⣛⣟⣻⠶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡶⢶⢿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢿⡼⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣿⣾⣷⣿⣷⣯⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠸⣿⢿⣾⣿⣿⣯⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢹⣏⢿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠛⠻⢿⣿⣿⣽⣟⣿⡿⣿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⢤⣤⣌⣁⣈⠉⠙⠛⠛⠛⠿⣷⣾⣯⣿⣟⣻⣟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠶⠶⣤⣤⣀⣉⡉⠉⠉⠛⠛⠻⠷⣶⣶⣿⣿⣿⣽⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣧⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠲⠶⢦⣤⣤⣀⣀⡀⠈⠉⠛⠛⠿⠶⣾⣿⣿⣿⣽⣟⣿⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠓⠶⠶⢦⣤⣤⣉⣀⠈⠉⠙⠛⠛⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠳⠶⠶⣾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡕⠁⠀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡘⠠⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣏⠀⠀⠈⢘⣦⣤⣀⣀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⢉⡽⠋⠁⠀⠀⡿⠋⠙⢯⠀⠀⠀⠉⠳⣄⠀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡰⣻⠋⠀⠀⢠⠏⠀⠀⠀⠀⡼⠁⠀⠀⠈⡇⠀⠀⠀⠀⠈⢧⠀⠀⠀⠻⡷⡄
⠀⠀⠀⠀⠀⠀⡞⢱⠃⠀⠀⠀⡏⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢱⣹⡀
⠀⠀⠀⠀⠀⡼⠀⡞⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣇⣇
⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⢹
⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⣼
⠀⠀⠀⠀⣴⣿⣿⣧⡀⢀⣤⣾⣷⣶⣄⢀⠀⣈⣷⣶⣶⣦⣄⠀⣿⣠⣴⣶⣶⣦⣀⣹⡀⣀⣴⣾⣿⡄
⠀⠀⠀⠀⢻⡃⠈⠻⠿⠿⠟⠁⠀⠙⠿⢿⠿⠿⠋⠀⠀⠙⠿⣿⡿⠟⠋⠀⠈⠙⠿⢿⣿⠿⠋⠁⠹⡿
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠳⠤⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠚⠛⠛⠛⠛⠛⠛⠛⠓⠶⠶⢦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⢉⣀⣤⣤⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣦⣤⣄⣈⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⢁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠻⣦⡀
⠀⠀⠀⠀⠀⢀⡼⠋⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠻⣄
⠀⠀⠀⠀⣠⡟⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠘⣧⡀
⠀⠀⠀⣰⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢷⡀
⠀⠀⣰⠏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠠⢄⡐⠒⠒⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢷⡀
⠀⢰⡏⠀⣾⣿⣿⣿⣿⡿⠿⢿⣿⠿⠿⢿⣿⠿⠿⣿⡿⠿⠿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⣷
⠀⣿⠀⣼⣿⠋⠀⠀⠀⠉⠂⠀⠈⠀⠠⡄⠈⠃⠀⠀⠁⢀⡴⠋⠉⠳⠀⠀⠀⠀⠀⠀⣀⣀⡀⢄⣠⠾⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⡇
⢸⡇⢠⣿⣿⣆⠀⠀⠀⣀⣀⠤⠴⠶⠶⠞⠚⠒⠒⠛⠛⢻⡁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿
⣾⠁⢸⣿⣿⣿⣷⣧⠀⠙⡍⠑⠲⠤⣀⣀⠀⠀⠀⠀⠀⠀⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢹
⣿⠀⣾⣿⣿⣿⣿⣿⣧⠀⠹⡄⠀⠀⠀⠉⠉⠉⠙⠓⠒⠲⠦⠤⣈⣙⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠉⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸
⣿⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⢳⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠐⠒⠒⠒⠤⠤⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠭⢿⣿⣿⣿⣿⣿⣿⡄⢸
⣿⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠃⢸
⢻⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠸⡆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠀⣼
⠸⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢳⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⡿
⠀⢿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣈⡉⠛⠓⠒⠶⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠁⣸⠇
⠀⠘⣧⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣈⣉⠛⠛⠛⠓⠒⠶⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠃⢠⡟
⠀⠀⠘⣦⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣀⣀⠉⠉⠛⠲⠶⢤⣤⣤⣀⣀⡀⠀⣿⣿⣿⣿⣿⠃⢠⡟
⠀⠀⠀⠘⣧⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⣈⡉⠉⠛⢹⣿⣿⡿⠃⢠⡟
⠀⠀⠀⠀⠈⢷⡄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣴⠏
⠀⠀⠀⠀⠀⠀⠹⣦⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢁⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⣁⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⡉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠛⠛⠛⠋⠉⣁⣠⣤⠶⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣲⣶⣶⣶⣶⣶⣶⣶⣶⣚⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠐⠒⠒⠚⠁⠀⠈⢉⡉⠉⠉⣉⣅⡀⠀⠀⣛⠉⠉⠉⠳⠶⠦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠋⣠⠦⣶⣤⠾⠛⠒⠛⠋⠉⠛⠛⢉⡀⠉⠛⠛⠉⠑⠲⠿⠶⠦⣍⠋⠉⠁⠹⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠉⣴⠶⠞⠋⠄⠐⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠙⠳⣄⣀⠀⠈⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⣶⠛⠁⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠈⠙⠻⢄⠀⠀⠈⢳
⠀⠀⠀⠀⣠⣴⣶⡟⠇⢠⣴⠟⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡤⠘⢷⡄
⠀⢀⣴⣿⣿⣿⣿⡇⡄⠀⢱⠀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢶⢮⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠀⠀⠰⡀⠀⢹
⣰⣿⣿⣿⣿⣿⣿⡇⢿⣦⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⠻⣰⠇⡇⣽⢙⡗⣶⢤⣤⣀⣀⠀⠀⠀⠈⠁⣠⠗⠀⡸
⣿⣿⣿⣿⣿⣿⣿⣿⡈⢿⣀⠀⠹⣄⡀⠁⠀⡀⠀⠠⠄⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠑⠽⣼⠇⡟⢸⠃⡏⢸⠀⡏⢸⠉⡟⢲⠲⣤⠋⠁⠀⠙
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣷⠀⠀⠙⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠌⢿⣗⣺⣤⣇⣸⠀⡇⣼⠀⡇⣾⢀⣯⠦⣶⡏
⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡷⣌⡛⢷⣦⣄⠀⠈⠷⠴⠤⣄⠀⢀⣀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠹⣯⢽⣓⣾⢯⣷⣯⢼⣧⠿⢋⣠⡾⠋
⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣌⠙⣶⣭⣛⠷⣶⣶⣄⡀⠀⠉⠀⠈⣉⠷⠤⠒⠒⣦⡠⠤⢤⡀⠐⠦⢼⠯⠔⢮⠭⠔⢚⡩⠄⡘⠟⢉⡠⣾⠇
⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣧⡈⢿⣏⠛⠶⢭⣝⣛⠿⠿⣷⣤⣀⣠⣤⣄⣁⣠⣄⣀⣀⣤⣄⣠⣤⣶⣤⣾⡷⠭⠔⣂⣡⠴⠚⢁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣷⣝⣧⡀⠀⠀⠉⠙⠓⢶⠶⣬⣭⣭⣭⣛⣛⣛⣛⣛⣛⣛⣩⣭⡭⠥⠴⠒⠚⠉⣁⣠⣤⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣤⣄⡀⠀⠀⠈⡄⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣾⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠶⠶⠼⣤⣿⣄⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣤⠯⠟⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢱⣀⣀⡠⠤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠑⠤⠄⠈⠀⠉⣷⠲⠀⢦⢆⢄⠍⢙⢒⠢⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠲⠤⠄⠀⠀⠀⠀⠒⠛⢲⠒⠲⠤⣌⣀⡃⠫⢪⠖⢈⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠼⣅⣀⣀⣀⠤⠤⢄⣀⣀⡠⠤⠞⠀⠀⠀⢀⣀⣉⣹⣶⣰⠋
⠀⠀⠀⠀⢀⣠⠤⠖⠒⠋⣭⣽⣋⣁⣀⣀⣠⠤⠤⠄⠀⠀⠒⠒⠒⠒⠒⠒⠚⠉⠉⠉⠀⠀⡴⡵⠧⢤⣀
⠀⠀⡴⠊⠁⠀⠀⠀⢀⠤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣞⠀⠀⠀⠀⠙⠢⡄
⠀⠸⡅⠀⠀⢀⣤⣾⣷⢶⣴⣇⣀⣀⣀⣀⣀⠤⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⢾⠏⠀⠙⡄⠀⠀⠀⠀⡿
⠀⠀⠈⠲⢤⣀⠙⠯⣗⡯⠖⠉⠀⣀⡯⠕⠒⠒⠒⠒⠒⠲⠤⢬⣉⡉⠉⠉⠙⠛⠓⢶⡁⣀⠤⠚⠀⢀⣠⠴⠊
⠀⠀⠀⠀⠀⠈⠉⠑⠶⣮⡭⠭⣝⣓⣒⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣶⣶⣤⣤⡴⢯⣤⡶⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠬⠭⢭⣭⣭⣭⣭⣭⡭⠭⠭⠤⠴⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣠⠶⢠⠞⠲⢲⣶⠒⠦⣤⣠⡴⡤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠰⡾⠉⠘⡏⠉⡂⢋⠀⠀⡀⢀⣐⣁⣀⣐⣋⠀⡀⢀⠿⠉⠉⢛⡦⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⡆⢉⠻⣂⣀⣻⣭⣦⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⡏⠈⠀⢀⠒⠤⠄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⣻⣶⣾⣿⣿⣿⣿⣿⣿⣿⡟⠛⠯⠽⢛⡿⣶⠽⠷⣎⢿⣿⣿⠿⣿⣿⣿⣿⣷⣾⣧⡀⠀⠀⡴⢢⣄
⠀⠀⠀⠀⠀⠀⣖⢠⣿⣿⣿⣿⣿⣿⡿⣽⢏⡿⣭⠉⠛⠋⠐⠁⠀⠈⠋⠀⠀⠒⠡⠞⠕⠛⠛⡻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣽⣯⣨⣇
⠀⠀⠀⠀⠀⣼⡿⠉⣿⣿⣿⣿⣿⣿⢿⠃⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠊⠀⠁⠘⢿⡻⣿⣟⣿⣿⣿⣿⣿⣏⢉⣄
⠀⠀⠀⠀⢠⣿⣷⡖⠉⠻⣿⣿⣣⡴⠜⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡠⠢⢶⣔⣿⣿⣿⣿⣿⣿⠃⢨⣿⡀
⠀⠀⠀⠀⠀⢿⣿⣃⣤⡤⢿⣿⣿⣫⡄⠢⠂⣀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⣻⣿⣿⣿⣿⣿⡟⢿⣷⣼⣿⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣿⡶⠀⢈⡽⠿⣿⣧⣨⣵⣁⣴⣢⡄⣀⠀⢀⠀⢀⡀⠀⠀⠀⣠⣄⣠⠠⢶⣶⣶⣾⣿⣿⣿⡿⠿⣯⠀⢀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣀⣴⠾⠉⠉⢻⡿⠿⢿⣯⣿⣷⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠿⢿⠛⣻⣿⡋⠀⠀⣿⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣭⣻⠷⣤⣴⣿⡄⠀⣠⡿⠁⠈⠛⠉⠉⣿⠛⠛⢻⡫⠉⢹⣿⠉⣁⡀⣀⣨⣿⡷⢶⣻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣮⣭⣏⣛⣛⡷⠲⠶⡶⠶⢾⡿⡶⠤⠾⠱⠶⠟⢓⢚⣛⣯⣭⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣛⠗⣲⠖⠒⠒⢲⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠿⠿⠿⠧⠄⠰⠶⠶⠾⠿⠿⠛⠛⠋⠉⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠢⠂⠄⠢⠀⠀⠢⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⢧⠀⠈⣆⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢆⠀⠀⠀⢳⠀⢸⠀⠀⡰⢋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢳⡀⠀⢸⢠⠏⢀⡞⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢀⡇⠀⠾⠁⠀⢸⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠞⠀⠀⠀⠀⠀⠀⠳⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠴⠶⠶⠤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⢛⠟⣻⠁⠀⣠⠀⠀⢀⡀⠀⠀⣄⠀⠈⢏⢻⡓⠲⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠉⠀⠀⠀⠈⠙⠁⠀⢞⣠⠁⠀⡞⢱⠀⠀⣇⣱⠀⠈⠉⠀⠀⠀⠀⠉⠙⠓⠦⣤⣀
⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⡴⠒⠒⠟⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠛⠚⠓
⢳⡀⠀⢀⡀⠀⠈⠉⠙⠒⠒⠦⠤⠤⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠤⠴⠒⠒⠒⠋⠉⠉⠀⢀⣀⠀⠀⣠
⠀⠉⠉⢻⠉⠳⣄⣀⣤⡴⠦⣄⠀⠀⠀⣀⣀⣀⠀⠀⠀⠉⠉⠉⣉⡉⠉⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⣠⠶⡖⠦⣄⣀⡴⠋⣽⠉⠉⠁
⠀⠀⠀⠘⡇⠀⠀⠀⠀⡇⠀⠈⠓⠒⠛⠉⢸⠈⠛⠦⠤⠤⠖⠋⢹⠉⠛⠦⢤⡤⠖⠋⠀⡇⠈⠙⠲⠶⠞⠁⠀⡇⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢻⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠈⠓⠲⠤⣄⣸⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⣁⣀⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠶⠦⠧⠤⣤⣤⣤⣀⣀⣸⣄⣀⣀⣀⣠⣤⣤⡼⠤⠤⠶⠶⠒⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⣿⣶⣶⡄
⠀⠀⠀⠀⢀⣠⡴⠶⢿⣿⣿⣿⣯⣿⣿⡻⣿⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣝⢹⣿⣹⣷⣤⣀
⠀⠀⠀⣀⣻⣿⣡⣄⡘⣿⡿⠟⠁⠛⠿⠿⠋⠀⣝⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠈⠛⠋⣁⣬⡏⠈
⠀⠀⢸⡏⠹⣿⣿⡮⡿⠂⠀⠀⠀⠀⠀⠀⠐⣿⣋⣿⡿⢧⡀⠀⠀⠀⠀⢀⡞⢁⣀⣤⣤⡶⡶⠟⠛⠋⢻
⠀⠀⣾⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⣿⠀⠀⠀⢰⣿⠿⠛⠋⠉⠁⠀⢀⣀⡴⠄⠚
⠀⠈⢿⡀⣠⣶⡦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢳⣤⢸⣿⠀⠀⠀⢸⡥⠤⠴⠒⠛⠉⠉⠁
⠀⠀⢿⡏⢻⣷⡿⠛⠀⠀⣄⠀⠀⠀⠀⠀⠀⠘⠿⠾⣃⣰⠆⠀⠀⠀⠀⣀⣀⣀⣤⣤⣴⣦⣤⣤⣀⣀⡀
⠀⠀⠁⣙⣯⡀⠀⠀⣶⣞⣿⣯⡿⢠⣞⣩⣷⡆⢀⣞⣽⣷⠀⢠⣦⣶⣶⣿⠋⠛⠻⠛⠁⠘⠛⢛⣉⣭⠿⡧
⠀⠀⠀⠹⣿⡷⠦⢶⣬⡛⠛⠛⠁⠈⠻⢿⡯⣤⣾⣾⡿⠋⠀⣨⣿⠘⣫⣍⡀⠀⠀⠀⠀⠒⠺⢯⣅⣀⡤⠇
⠀⠀⠀⠀⠈⠻⢷⣿⣷⣝⣓⣻⣿⣿⣞⣫⣼⡿⠿⠋⠀⠀⠀⢷⣝⣿⣿⣞⣁⣴⣶⡄⢀⣴⢶⣄⣀⣉⣷⣶⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⣮⣻⢟⣉⣑⡬⢫⣭⣝⣫⣶⣾⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⢻⢻⢻⣹⣿⣿⣽⢹⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠛⠛⠛⠛⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠐⠶⠶⠶⠶⠶⠒⠒⢲⡤⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠋⣠⣤⣠⠶⠤⠴⠒⠲⠖⠛⠓⠶⠖⠲⠤⣤⡬⣙⠛⠛⢓⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⡴⠶⠊⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢉⠛⢦⣀⠀⠱⠦⣀
⠀⠀⠀⠀⢀⣀⡄⠁⢸⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠑⢦⣀⠀⢣⡀
⠀⢀⣴⣾⣿⡟⠀⠘⡏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢁⠀⠱
⣰⣿⣿⣿⣿⣧⢱⣄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡍⡏⡟⢲⢢⢤⣄⣀⡀⠁⠀⠁⣨⠆⢀
⣿⣿⣿⣿⣿⣿⣎⢻⣄⠘⠦⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣇⡇⡎⢸⢸⢸⢀⠏⡏⡖⣲⠉⢀⡈
⠹⣿⣿⣿⣿⣿⣿⣷⣝⢦⣄⡘⠒⠢⣄⣀⡀⠀⠀⠀⠀⠀⢈⠀⠂⠀⠀⠘⢿⣷⣷⣾⣼⣸⢀⠇⡧⠟⣩⠟
⠀⠙⢿⣿⣿⣿⣿⣿⣯⠓⣬⣛⠶⣬⣤⡀⠈⠒⠀⠒⣦⠀⠤⢤⡀⠠⣀⠠⢌⣷⠫⢝⠻⠽⠛⠉⠴⠟⡁⣴
⠀⠀⠀⠉⠻⢿⣿⣿⣿⣷⣌⢿⡝⠲⠭⣝⣛⡿⠷⣤⣤⣤⣬⣤⣤⣀⣤⣤⣤⣴⣦⡾⠶⢁⣀⠤⠒⢉⣼⠏
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣿⣆⠀⠀⠈⠉⢛⠳⡖⠒⠺⠿⠯⠭⠽⠿⠒⠒⠒⠊⣉⣡⣤⣶⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⠦⣤⣌⣄⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠙⠷⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⠉⠱⠓⠒⠀⢈⣿⣦⣀⡀
⠀⠀⠀⠀⠀⣀⠔⠁⠙⠛⠛⠀⠀⣴⡶⠾⠋⠉⠉⠉⠙⠓⠦⣀
⠀⠀⠀⢀⡸⠐⠿⠉⠉⠀⢀⣤⣶⠿⠀⢀⡴⠒⠒⠲⢤⡤⣀⡈⠓⠲⣄
⠀⢀⠞⠷⢿⣟⠓⠂⠀⠀⣾⠃⠀⠀⠀⣸⡄⠀⠘⢯⠑⣿⠀⠉⡦⡀⠉⠓⠦⢄⡀
⠠⢊⣴⣦⣤⠄⠀⢠⠞⠛⠋⠀⠀⠀⢸⠀⠙⠦⢤⣤⡿⠟⢀⡔⣁⡼⠄⠀⠀⠀⠈⠙⠲⢤⣀
⡔⣀⣀⣀⠀⠀⡴⠟⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⣀⣀⣠⠔⢋⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀
⠏⠀⠀⠉⠙⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣒⣉⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⢤⣽
⠈⠙⠢⠀⡄⠀⢳⣤⡤⠤⠴⠶⠶⠖⠒⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠳⡄⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠹⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠶⠒⣒⠩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⣼⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡇⠀⢰⣯⣉⡁
⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⢻⡁⠸⣇⠀⣿⠈⢉⣹⡟⠛⠲⢦⣀
⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢹⠟⠋⠛⣿⡾⠋⠀⠑⣄⠀⠀⠙⢷⣄
⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⡇⠀⠀⠀⠘⣧⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⢰⡟⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠘⡆⠀⠀⠀⢻⡄⠀⠀⠀⠀⢀⣠⣤⡏⢠⣾⡁
⠀⣿⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣷⢀⡤⠞⠋⠙⢳⣼⢥⣿⠞⠛⠓⢶⣤⡀
⢸⡇⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢹⡟⠁⠀⠀⣴⠋⠀⠀⠈⢷⠀⠀⠀⠙⣷⡄
⢸⠃⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⡇⠀⠀⢸⠃⠀⠀⠀⠀⢸⡆⠀⠀⠀⠘⣿⡀
⢸⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣸⣧⠶⠶⠾⣇⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣻⡇
⢸⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⣟⣀⣤⡴⠞⠛⠋⢁⣀⣤⡴⠚⠋⠙⠲⣼⣄⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⣿⡇
⠀⢿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣠⠴⠞⠛⠉⢀⣀⣠⡴⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⣀⡿⠀⠀⠀⠀⣰⣿⠁
⠀⠘⣷⡀⠀⠀⠀⠘⣿⡀⠀⡴⠋⠁⠀⢀⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣴⠟⠁
⠀⠀⠈⠻⣦⡀⠀⠀⠹⣷⡸⣷⣶⡒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠈⠙⠳⢦⣤⣙⣿⣿⠉⠙⠛⠶⠶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠓⠶⠶⠦⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠛⠛⠲⠶⠶⠶⠶⠶⠶⠶⢾⡇
⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⣀
⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠈⠉⠛⢶⣄
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠙⣷
⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⡿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠈⠛⠒⠲⠶⠶⠶⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠞⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋
⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠶⢶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠶⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠒⠒⠒⠚⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢀⠀⠀⣽⠛⠓⡤⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⣈⣀⣰⡇⠀⠀⠠⠃⠀⠉⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⣶⣄⣠⠀⠀⠐⢐⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⣿⡿⠳⡸⣩⡆⣿⠈⢿⣻⣿⣿⣿⣷⣿⣯⣄⢠⣿⣯⡏⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠛⣋⡴⠱⠇⣴⠂⣝⡟⠛⡀⣠⢿⣟⣹⣻⣿⡿⢿⠿⣿⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⣟⡉⢁⢀⡄⡰⢃⣠⣿⣟⡷⠿⠮⢞⣻⣛⣬⣭⣤⣶⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠾⠌⣿⣋⣘⣋⣭⣭⣽⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣴⣿⣯⣭⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠻⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠿⠻⠛⠛⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠈⠣⣱⡄⢀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⢤⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢌⢂⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢷⡟⢻⡛⢲⣄⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠙⠋⠉⠙⢿⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⣸⠃⣨⠁⢸⡇⠑⡄⠀⠀⠉⠓⠢⣄⡀⠀⠀⠀⠀⠀⢸⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣏⠀⣾⠃⢠⠇⠀⠈⢧⠀⡸⠀⠀⠀⠀⠀⠀⠉⠑⠢⢤⣄⣀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠙⢤⣿⣆⣈⣳⣄⣀⡼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⠇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠶⠛⠻⢿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠴⠶⠖⠒⠛⠫⠉⠁⠀⠀⣄⠠⠄⣸⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠶⠖⠖⢒⡛⠛⣉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢆⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢀⠁⠉⠀⠠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠈⠀⣸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠀⠠⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠰⡤⣣⠟⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠬⠥⠤⠤⠴⠤⠴⠦⠤⠤⠤⠀⠀⠀⠀⠴⠤⠤⠤⠤⠤⠴⠴⠶⠶⠶⠒⣚⣋⣁⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⡼⠁⡤⢀⡀⢠⡀⣀⢠⡤⢰⣇⣠⠀⣿⡠⣤⠀⣤⠀⡄⢠⡄⠀⠀⠀⠀⣾⣠⡄⠀⡤⠀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠀⢸⡇⢸⠃⣸⡦⣿⢸⡇⢸⡇⢹⠃⣿⢴⡋⣠⡇⢠⣇⢾⠁⠀⠀⠀⠀⣿⠁⡿⢸⡇⢰⡧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠘⠓⠈⠃⠹⠁⠛⠈⠛⢹⡗⠋⠀⠛⠈⠉⠁⠉⠙⠏⠘⠋⠀⠀⠀⠀⣿⠚⠁⠀⠉⠈⠳⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠠⣠⢀⣤⣄⡤⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣄⣂⣵⣀⣀⢩⠉⢀⡧⠴⠃⠐⠻⠶⠒⠋⠉⠻⠿⠗⠚⠷⣦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⡱⢛⡩⠤⢤⣈⣉⠀⡞⠀⢸⠆⢺⠀⠈⣯⠉⠁⢄⠀⠸⡆⠐⠂⠐⣦⢰⡈⠳⡄⡀
⠀⠀⠀⠀⠀⠀⢠⠉⢴⣇⢡⠀⠀⣼⣁⣀⣀⠥⠠⠾⠦⠼⠀⠀⡿⠶⠶⠞⠒⠒⠳⠦⠴⠀⠸⡶⠓⠂⠉⠈⡄
⠀⠀⠀⠀⠀⠀⠈⣇⢶⡤⠇⠀⢰⡁⡉⠥⠤⠒⠀⢠⠄⢰⠀⠀⣇⠀⠠⠴⠈⠑⠢⣤⠀⣀⠀⢱⣤⠇⠘⡴⠁
⠀⠀⠀⠀⠀⠀⢸⣿⡗⠽⣄⣀⡈⠉⠙⠓⠊⠀⠀⠿⠶⠒⠉⠉⠙⠓⠒⠂⠆⠀⠀⣯⣩⠴⠖⠀⣀⣴⣾⣧
⠀⠀⠀⠀⢀⠀⠀⠻⣷⡀⠀⠉⠉⠛⠓⠲⢤⣁⣐⡳⠶⠼⠯⠭⠿⠷⠒⣂⣠⣤⠭⠤⠖⠖⠛⠋⣭⣾⣿⡏
⠀⠀⠀⠀⠀⢤⠀⠀⠈⠻⢷⣤⣄⡀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠛⠋⠉⠉⠀⠀⠀⠀⢀⣠⣴⣶⡿⠟⠉⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠙⠛⠻⠶⠦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣴⠤⣶⠾⠛⠛⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠭⠈⠁⠀⠀⠐⠀⠀⠀⠄⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠈⠉⠉⠉⠉⠉⠉⠉⠉⠐⠒⠢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⠈⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⡀⠀⠀⠀⢻⢗⠠⡀
⠀⠀⠀⠀⢀⠔⠉⠗⠁⠀⠀⡮⠃⠀⠀⢀⠻⠀⠀⠀⠨⡃⠀⠀⠀⠫⠆⠀⠀⠀⠉⠀⠀⠑⢄
⠀⠀⢀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢄⠀⠀⠀⠀⠀⠀⢀
⠀⠉⠀⠲⡈⠉⠀⠀⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠀⠒⠒⠒⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⢰⠂⠈⠁
⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣶⠞⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠕⠉⠀⠀⣼⣻⠀⠀⣴⣦⠀⠀⣟⣦⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡵⠁⠀⠀⠀⠀⠉⠁⠀⠀⠙⠋⠀⠀⠈⠉⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠴⠾⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠷⠦⢤⡀
⠀⠀⠀⠀⠀⣴⡣⠀⠀⠀⠀⠈⠉⠁⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠒⠒⠀⠀⠈⠉⠁⠀⠀⠀⠀⠑⡜⣆
⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡽
⠀⠀⠀⠀⠀⠈⠳⣅⣈⣉⡭⣶⣤⣐⣒⣩⠖⢦⣀⣀⣠⠴⠦⣄⣀⣀⡴⠲⣄⣀⣀⡤⠶⢶⣂⣆⣺⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⠈⠀⠉⠛⠃⠉⠀⠐⠒⠒⠒⠁⠀⠒⠒⠒⠊⠀⠒⠤⠤⠐⠂⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠛⣦⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⡴⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⣠⠏⢀⣤⣤⠤⣤⣧⣤⣤⣤⣤⣾⣤⣤⣀⣀⣀⣼⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢤⣿⠶⠞⠉⠀⠻⠆⠀⠀⠀⣿⠷⠀⠈⠉⢹⠁⠀⠈⠉⢩⡏⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⣰⠏⠀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⡇⠀⣴⠏⠀⢰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡅⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢘⣷⠞⠁⠀⠀⢸⣧⠞⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⡇⠀⢀⣠⠞⠛⣧⣀⣠⡴⠋⢷⣀⣀⣴⠟⠹⣦⣀⣀⡴⠟⢷⣄⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⡟⠛⠓⠶⢦⣿⣾⣯⡥⠀⠀⠈⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣤⣤⣄⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣠⠀⠀⣤⣤⣤⣤⣤⣴⠀⠀⣤⠀⢀⣀⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠙⠃⠀⠀⢰⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠈⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⢀⣄⠀⠀⢿⡄⠀⠀⠀⣼⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣤⣤⣶⠟⠁⠀⠀⠈⢿⣦⣤⡾⠏⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⢹⣧⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡞⠁⠉⣷⠀⠀⠀⠶⠀⠀⠀⠀⣿⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⣿⠀⣀⣴⡆⠀⠀⠀⢀⣿⡋⠁⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣥⡽⠛⠋⠉⠀⢷⣀⣤⠾⠋⠈⠳⠶⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⡄⠈⢦⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⠀⠀⠘⢄⠀⠃⠀⠀⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠣⡀⠀⢸⢀⠆⢀⠔⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⡁⠀⡸⠊⠀⠌⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠃⠀⠀⠀⠀⠘⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠶⠒⠒⠒⠒⠶⠤⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠋⠩⣋⠏⠀⡰⡆⠀⢠⡄⠀⢰⢦⠀⠹⣉⠏⠙⠲⠤⣄⣀
⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠦⠃⠀⢢⡸⠀⠈⠲⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⣠⠤⢤⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤
⢧⠀⠀⠀⠈⠉⠐⠒⠢⠤⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠤⠤⠤⠐⠒⠒⠈⠉⠁⠀⠀⢀
⠀⠙⠛⡏⠓⣄⣀⣤⡤⢤⡀⠀⠀⢀⣀⣉⠉⠉⠉⠉⠉⣉⡉⠉⠉⠉⠉⠉⣀⣤⣀⠀⠀⠀⢀⡤⢶⠦⣄⣠⠔⢫⡏⠛⠉
⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⠈⠓⠚⠉⢸⠈⠙⠶⠤⠖⠋⠉⠉⠙⠲⠤⠴⠋⠁⡇⠈⠙⠒⠒⠋⠀⡞⠀⠀⠀⠀⣸
⠀⠀⠀⠈⣇⠀⠀⠀⢣⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠉⠓⠒⠾⠤⣄⣀⣀⡀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣀⣤⠧⠴⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⡀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠂⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠈⠑⣄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠊⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘⢦⡀⠈⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⠤⠖⠂⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠙⠶⣀⡀⠉⠲⢦⣄⡁
⠀⠀⣴⠂⡀⠠⠆⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠄⢤⣠⡀⢀⡀⠀⠀⠀⠀⢀
⢠⡎⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⡄⠀⠀⠀⢠
⣿⡁⠀⠀⠀⠀⠁⠈⠉⠀⠀⢄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠘⢷⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠈⢁⣈⠚⠉⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⣠⡀⣀⣀⠀⠁
⠀⠀⠀⠈⢿⠃⠀⠈⠿⣤⢄⣀⣀⣤⣄⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠁⡨
⠀⠀⠀⠀⠈⢷⣷⡀⠀⠀⠙⠉⠿⠛⠉⠀⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡴⠶⠶⠶⠶⠶⠦⠔⠁⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣄⡤⠶⠒⠛⠒⠰⢦⣀⠀⠀⠀⠀⠀⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠱⣷⠶⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⡃⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣃⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⢿⣿⣷⣦⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢐⠀⠀⢰⣮⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠓⠶⠾⠿⠶⠶⠚⢻⠷⠶⠶⢶⡻⠾⣤⡤⠶⠾⠛⠛⠉⠉⠁
⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠀⠀⠀⢰⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣁⣤⠃⠀⡄⢰⡟⢁⡟⢃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠉⣰⠟⠿⠴⠄⣀⣼⣧⡽⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣤⣭⡀⠄⣠⣭⣁⣀⠀⠀⠈⣙⡿⠁⠁⠀⠀⣴⠋⠀⡈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠚⠁⣰⡛⣀⠀⠀⠀⠈⡇⠈⠙⢻⣶⣤⡙⠀⠀⡠⣴⠿⣿⣄⢈⡰⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠦⠽⠲⠖⠶⠺⢿⡶⠒⠢⣥⣄⡐⠀⠀⠀⣬⡀⠈⠀⠀⠀⣼⣁⢀⣤⣿⡏⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣥⣿⣥⣀⣀⣀⢀⠀⠠⠜⠁⠀⠀⣽⣿⣇⣀⣀⣰⣿⣿⣶⣶⣾⣿⣿⣋⡿⢿⡿⣿⢲⠇
⠀⠀⠀⠀⠀⢀⣴⠏⢀⣺⣿⣿⣧⣫⣿⣥⣿⣿⣶⣦⣿⣶⣿⣿⢿⣻⣿⠿⠿⡿⠟⠿⣷⣶⣤⠄⠙⣿⣟⣶⣿⡹
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⢿⣿⣿⡿⠿⣿⢛⡟⢋⣡⡴⢛⠋⠬⠊⢀⣡⣴⣾⣿⣏⡛⠑⣡⡗⡿⠅⣿⠘
⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⣿⠾⠟⠛⢻⣿⣿⣷⣺⣿⣷⢿⣗⣂⣉⣥⣶⠾⠛⠉⣀⡄⠀⢈⣿⠟⠛⠁⣠⣾⡿⣼
⠀⠀⠀⠀⠀⣿⣿⣿⣯⣦⣵⣶⠟⣛⡭⠿⠛⡛⠋⠀⢤⡆⠀⢹⣟⡋⠽⠏⣀⣀⣀⣤⣤⣼⠶⠶⢾⡟⢛⣋⠵⠃
⠀⠀⠀⠀⠀⣿⢿⣿⠛⠶⠘⣩⣾⣫⡵⣗⣣⣤⣤⣴⣶⠶⠶⠾⠟⠛⠋⠋⠋⠉⠭⠵⠁⠒⠒⠉⠉
⠀⠀⠀⠀⠀⣷⢿⠿⡶⠛⠟⠛⠛⠛⠛⠹⠉⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠉⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂

⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠘⠟⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠀⠀⢀⡄⢀⡄⢠⡠⢤⠄⡀⠀⠻⠗⠀⠀⠀⠂⠀⠀⠀⠠⠀⠐⢾⠇⠀⠀⠀⠘⠟⠉⠈⠆
⠀⠀⠀⠀⠃⠀⠀⢀⡀⢗⢢⡄⡀⠀⠀⠀⠀⣭⣄⣈⣀⣈⣀⣀⣁⠠⢤⡼⠀⠀⢀⠀⠀⠆⠐⢀⢀⣠⠁⠀⠀⠀⠀⣠⠀⠀⠀⠐⠐⡗⠂⠰
⠀⠀⠀⠀⡄⠀⠀⢨⠉⢯⣕⠿⣚⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠠⠀⠺⠙⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⡀⣃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⢀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠰⠄
⠀⠀⠀⠀⣆⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠗⡿⠻⠞⠷⠮⠍⠶⠛⢛⡝⠀⠀⢀⢒⠀⠀⠀⠀⣤⢄⠀⠀⢁⡠⠃
⠀⠀⠀⠀⣸⠀⠸⣠⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⣆⠐⠀⠀⠀⠀⠀⠀⠘⠠⠆⢰⡀⣦⢰⡀⠦⠼⠚⠀⠀⠀⠘⠊⠀⠀⠀⠈⠀⠁⠁⠈
⠀⠀⠀⢀⡸⠀⠀⡟⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠉⠐⠂⠀⠀⠀⠀⢐⠀⠀⠀⠄
⠀⠀⠀⢿⣇⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡄⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⣔⣠⣬⡧⡴⣶⣾
⠀⠀⠀⠘⠋⠀⠀⠃⠀⠀⠐⠆⠀⠀⠂⠤⡤⠄⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠁⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣒⠺⠿⠿⠛⠉⠂
⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢸⣿⣶⠔⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⠊⠀⠤⡑
⠀⠀⠀⠀⠐⣡⡴⣶⢶⠂⠀⣀⠀⠀⠈⠉⢿⠛⠁⠀⠀⠀⠀⡈⠐⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠉⠙⠀⠀⠀⠀⠀⠘⢀⠀⠀⠼⢀⣠⣀
⠀⠀⠀⠰⢰⡿⠾⣿⣾⣤⣾⠇⡀⠀⠀⠀⠀⡀⡀⣠⡀⠄⠀⠀⠀⡠⢆⡀⠊⠁⠀⠛⡀⠈⠉⢡⠴⠤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠛⠋
⠀⠀⠀⠈⢘⣶⠾⣛⣩⣽⠾⣺⠃⠀⠀⣠⣞⡧⢤⡄⠀⠀⠀⠄⠀⠈⠣⢖⠈⠁⠐⠈⠈⠀⠀⢑⠜⠁⠀⠀⠀⠀⠠⠖⣠⡍⢋⡒⠶⣤⡀
⠀⠀⠀⠀⠀⠬⠸⠟⠯⠶⠚⠁⠀⠀⠰⠭⠟⠋⠉⠀⠀⠀⢀⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠙⡏⣚⡄⡀⠉⣋⡘⣂⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠆⠀⠒⠓⠠⠰⠀⠓⠂⠛⠃
⠀⠀⠀⠀⠰⠖⣠⠀⠀⣔⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠐⠊⠀⠀⠀⠀⣀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠀⢀⡄⠴⣢⣾⠟⣡⡲⠆⣤⡐⠀⠀⠀⠀⠀⡺⢿⣿⢿⡿⡇⠀⠀⠉⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠸
⠀⠀⠠⠄⣀⡀⠐⠀⠀⠆⠤⠀⠂⠀⠀⠠⡝⠰⠿⠡⣾⡽⠡⠶⠏⢀⠄⠀⠀⠳⠀⠉⠁⠀⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⣀⢠⡄⠀⣤⣄⣀⡀⠀⠀⠀⠀⢀⡜⢋⡂⢃⠣⣄
⠀⠀⠀⠀⠀⠤⠂⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⡆⢽⡎⣘⠿⢠⣮⣘⣛⡁⠀⠀⠄⠀⡉⠀⢈⠀⠈⡁⠈⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠈⠉⠙⠓⠂⠀⠀⠀⠀⠀⠀⣿⢣⢷⢄⡻⠇⣾⣜⠋⠉⡄⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢀⡀⠶⠀⠀⠀⣀⠀⢀⠀⠀⠀⡀⠠⡤⠀⠀⠀⠸⠜⠷⠘⢿⢠⣍⠋⠿⠃⠀⠀⠀⠀⠠⠤⣀⣀⣀⣀⣐⡦
⠀⠀⠀⠺⣀⣉⣿⣿⣿⡶⠒⠶⠦⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠁⠀⠦⠀⠀⠀⠀⠑⠠⠀⢀⢀⣀⠠⠀⠀⠀⠀⠣⢀⣀⠀⠀⢀⣈⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠰⠄⠀⠀⡀⠈⢅⡀⠀⠀⠈⠀⣀⠔⣀⠰⡷⠂⠀⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⢸⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⡤⠐⠁⠀⠘⠒⡉⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡰⠃⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⡃⡠⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⣀⢄⡠⠀⠀⠀⠡⡀
⠀⠰⡀⠀⠀⠀⠀⣸⡀⠀⠈⠀⠀⠀⠐⠤⠌⠀⠀⠂⠀⡠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⡀⠂⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠈⠐⠢⠄
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⡀
⠠⠀⠀⢀⠀⢀⠀⠀⠀⠈⢄⠀⠀⠀⠀⢀⡄⠀⠌⠀⠀⠀⠴⠀⠀⢀⠀⢒⣄⠀⡀⠀⠀⠂⠈⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⡀
⠀⠰⠠⠌⠀⠈⠂⠀⢀⠀⡀⠁⠀⠀⠀⠉⠀⠀⢇⣈⣉⠰⠀⠀⠀⢈⠀⠀⢈⠀⠂⢀⠈⡠⠏⠀⠆⠢⠀⠀⠀⠄⠈⠁⠀⠀⢠⣢⠀⠀⠋⠁⠀⠀⠐
⠀⠐⠀⠂⠀⠀⢃⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣄⠀⠀⠃⠀⠀⠀⠀⠀⡄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠀⠀⠙⠀⢐⠀⠰⠈⠀⠘
⠀⠜⡀⡀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠋⢳⠀⠶⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠧⠈⠂⠠⢀
⠐⠁⠀⠀⠀⢏⠀⡠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠤⠁⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⣀
⢇⠀⠀⠀⠀⠀⠆⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠄⠀⢀⠀⣀⠾⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈
⠀⠁⡀⠀⠀⠁⠀⠤⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢀⡀⢀⡠⠤⠄⠤⢀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠐⠂
⠀⠀⠁⠀⠘⠀⢊⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂⠀⡠⢽⡏⢀⠠⠷⡉⠁⠂⢄⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁
⠀⠀⠐⠄⠀⠀⢀⡃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠡⡀⠀⠁⠀⠰⡀⠀⠀⠀⠀⠂⠀⠂⠐⠆⠀⣀
⠀⠀⠀⠢⡔⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠇⠀⠀⠀⠱⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠨⠡
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⢀⠁⡄⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⢀⡄
⠀⠠⠀⠀⠀⠀⣀⠠⠐⠉⠀⠀⠁⠀⠀⠀⢐⠀⠀⠢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡰⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠱⡀⠀⢠⠈⢀
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠑⠀⠀⠀⠀⠆⢀⣀⡀⡀⠠⠇⠀⠀⠀⠀⠻⠂⢀⡤⠠⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠈⠛
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣶⠄⠀⢀⠀⢤⡀
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⠀⠂⠀⠀⠈
⠀⠞⢲⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠤⠁⡂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠍⠴⠉⠀⠀⠀⡀⠀⠨⠀⠀⠀⠰
⢀⡠⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢄⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠃⠀⠀⠘⢀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢠⣤⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣱⠊⠀⠒⢤⡄⠀⣴⡄⠀⠀⠀⡀⠀⠐⠊⠁⠀⠀⠀⡠⠅⠀⠀⠈⠁⠒⠢⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠇⠀⠀⢀⠀⠀⠀⣀⣠⡶⠀⠀⣠⠀⠀⠀⠀⠀⠂⠁⠀⢈⠉⠀⣠⠒⠚⠀⠀⡀⠤⢀⠀⠀⢀⠤⣀⠀⠀⠤⠀⠔⠀⠀⠀⠆⠀⠚⠆⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠁⠀⠀⠐⠊⠀⠀⠀⠃⠀⠀⠄⠑⠄⠀⢈⠠⠀⠀⠑⠂⠄⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠠⠠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⡄⠂⣀⣀⡀⠀⠔⠀⠂⠀⠀⠀⠀⠀⠀⠘⠈⠁⠀⠀⠁⠢⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀
⢉⣣⠃⠀⢸⣄⠚⠀⢀⠀⠀⠙⢄⠀⠀⠁⠀⠁⠀⠀⢇⡘⠀⠐⢀⠰⠂⢠⠀⠀⠀⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⣐⣥⢠⠋⠀⠀⠀⠀⠴⠖
⠁⠉⠒⠉⠀⠀⢣⠀⠀⠑⠄⠀⠈⠂⠀⠀⢀⠆⠀⠀⠈⠀⡀⠁⠇⠀⠀⡘⠀⠀⠀⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠒⠁⠀⠀⡀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣤⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⠓⣤⠄⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣠⣮⣀⣠⡄⠀⠀⡕⠀⠀⠂⡅⠀⠀⠀⠀⡍⠑⠢⡀⢀⡔⢄⠀⠀⠀⠀⠀⡠⠖⠒⢦⡜⠀⣳⡯⣅⡙⢆
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⡀⣸⡋⠀⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠀⠡⡀⠆⠈⠃⡀⠘⠀⠀⠀⠀⡖⢠⠊⢩⠏⠉⠉⠀⠙⡄⠈⡆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠉⠘⠀⠀⠀⠄⠀⠀⠘⡄⠀⠀⢆⠁⠉⡉⠀⠀⡀⠁⣨⡀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⠇⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡈⢠⠀⠀⠀⠀⠀⠀⠈⢑⡶⠀⡠⣶⠤⣄⡠⠀⠀⠀⠀⢡⣀⠀⠀⡆⠀⠀⠀⢰⠀⠀⣁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠘⠀⠀⠀⢷⠘⡄⠀⠀⢦⠁⠀⠀⠈⠐⠚⠋⠀⢦⡀⠀⠀⢤⣶⠀⠀⠈⠦⠀⣡⠀⠀⠀⣀⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠈⠲⠷⠴⠶⠋⠀⠀⠠⠤⠀⠀⠀⠀⠀⠳⠀⠀⠈⢊⢢⢢⡀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣠⠾⠁⠾⠡⠗⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡥⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢠⡇⠐⢀⠂⠀⠀⠂⠈⡇⠀⠀⠀⢀⠤⠐⠒⠀⠉⠉⠉⢩⠉⠉⣐⢲⣖⡤⢀⡀⠀⠀⠀⠀⢀⠠⠐⠒⠈⠀⠐⢠⡄
⠀⠀⠀⠀⠀⠈⣇⠀⠈⠀⠀⠀⠈⢠⠃⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡡⢿⢾⢟⡦⠑⡄⠀⢀⡔⢁⡠⠀⠀⠀⠁⠀⠉⠭⡟
⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⡀⠅⠁⠀⠀⠀⠸⡆⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠷⠐⣩⢒⠶⠃⠀⢸⡞⠁⠀⠀⠀⠀⣀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⠆⠀⠀⠀⢰⠀⠉⠉⠀⠀⠐⠒⠒⠒⠂⠀⠀⠉⠁⢀⠃⠀⠀⠈⠳⡤⠄⠀⠒⠉⢀⠄
⠀⠀⠀⠀⠀⠀⠀⡠⠤⠠⡐⠲⣄⡦⢤⡀⠀⠀⠀⠑⠠⠤⣀⠤⠄⠀⠀⠀⠀⢀⣀⠤⠐⠊⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢀⡞⢀⡴⠂⠉⡫⠤⢟⠙⠲⡌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠘⣆⣸⠀⠀⢸⠁⠀⠀⠆⠀⢹⣠⠇⠀⠀⠀⠐⠁⠀⠇⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⢈⡔⠀⣴⠀⠊⣀⠈⠀⠉⠒⠒⢶
⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣸⣄⢀⣠⣤⡤⠏⠁⠀⠀⢀⣀⠀⠀⠀⣀⢀⣀⡄⠀⣤⠀⠀⠀⠀⠀⠲⡇⠀⠀⠹⠷⣤⡇⡀⠀⠐⠉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡀⠀⠀⢸⠉⠈⠱⣤⠉⣥⡴⠟⠀⢠⢁⠀⠀⠀⠀⡄⠀⣀⣀⣀⡀⠠⢺⡏⠐⠦⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⣀⡤⢐⡺⠿⡷⠄⠀⠘⡇⣀⠀⠀⠀⠀⠀⠀⡐⡡⠂⠀⠀⠀⣰⡴⣋⣀⡀⣀⡀⠀⠘⢿⣦⣀⣤⠶⠃
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣳⣞⠥⠂⠉⠀⠀⠀⠀⠀⠁⠓⠤⠠⠶⠶⠟⠊⠀⠀⠀⠒⠛⠉⠁⠀⠀⠋⠀⠹⠊⠁⠶⠻⠍⡄
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠈⢆⠈⢢⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠈⢆⠀⠆⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠆⠀⢸⠜⠀⠎⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠄⠀⠋⠀⠀⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠊⣝⡹⠀⡠⡄⠀⢠⡀⠀⡤⡀⠸⣙⠟⠒⠦⢤⣀
⠀⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠣⠃⠀⢇⠇⠀⠳⠂⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀
⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄
⡴⠒⠾⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠙⠒⠲
⠳⣄⣀⣀⡀⠀⠉⠁⠒⠒⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠀⠒⠒⠒⠀⠉⠉⠀⢀⣠⣀⣀⠴
⠀⠀⠘⡆⠙⠒⠒⡏⠑⢦⣀⣠⠴⡶⢤⣀⠀⢀⡠⢤⠤⣄⠀⠀⣠⠴⡖⠢⣄⣀⣀⠔⢉⠉⠓⠖⠋⢸⠁
⠀⠀⠀⢳⠀⠀⠀⢠⠀⠀⠀⠀⠀⠃⠀⠈⠉⠁⠀⢸⠀⠀⠉⠉⠁⠀⡇⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⡎
⠀⠀⠀⠈⠒⠦⢤⣸⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⣀⣠⠤⠖⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠈⠉⠀⢀⣀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠀⡤⢄⣈⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⣀⠤⠔⠒⠉⢉⡡⠔⠁⠀⢀⣀⠉⠑⠂⠤⠤⠤⠤⠤⠒⠊⠉⢀⣀⠀⠀⠀⠑⠦⣄⠉⠉⠒⠤⢌⠑⠦⡀
⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠧⠤⠤⠒⠊⠁⠀⠀⣠⠔⢁⠜⠀⠀⠀⠀⠀⡎⣧⠀⠀⠀⠀⠘⣌⠑⢄⠀⠀⠀⠀⠉⠑⠢⠤⠜⠀⠀⠈⠳⡄
⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⡠⠊⠀⠀⠀⠀⠀⢰⠀⢰⠀⠀⠀⠀⠀⠈⠢⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣠⠜⠁⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥
⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⢻⠒⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣀⠠⢺⠃
⠀⠀⠀⠀⠀⢣⠀⠀⠈⠉⠈⠑⠤⣀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠔⠒⠒⠊⠁⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢣⡀⢧⠀⠀⢠⠀⠀⠀⠀⠉⠉⠉⠉⠒⠦⠖⠊⠑⠢⠤⠔⠊⠒⠲⠴⠒⠉⠑⠒⠊⠁⠈⠉⠁⠀⡄⠀⠀⢠⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠑⠬⣆⡀⠈⡆⠀⠀⢳⠀⠀⠀⢰⠀⠀⠀⠀⡆⠀⠀⠀⠀⡄⠀⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⢀⠁⠀⣀⡼⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠢⠤⠼⣄⣀⠀⢈⡄⠀⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⢀⣀⣠⠧⠤⠖⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠓⢦⡀⠀⡠⠂⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⣠⣶⠆⠀⠀⠀⢀⡀⠀⠤⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⢸⣿⠀⡁⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⣰⣿⡏⠠⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⣠⣿⣿⠃⠀⠀⠀⠀⠀⣼⣿⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰⣿⡟⠀⠀⣀⣯⣟⡶⠀⠀⠀⠀⠀⠀⠀⣀⡟
⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠉⠿⠟⠋⠀⢀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⢠⣾⡿⠀⢠⣿⡇⠀⠀⢀⣾⡿⠀⢠⣾⡟⢁⠌
⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⡠⢻⣿⠃⢀⢾⣿⠀⠀⠀⣼⣿⠃⠀⣿⡟
⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡠⣈⣻⡧⠚⠀⠘⠿⠤⠊⡘⣿⠀⠀⡀⠹⣇⡠⠁⠘⠷⡄⠀⠀⠁
⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠰⣿⣿⢟⢝⣾⣿⣿⣯⣿⣶⣄⠀⢺⣿⣿⣮⣫⣬⠄⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣦
⠀⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⢙⢕⣵⣿⡟⠉⠉⢻⣿⣿⣿⡆⠀⢿⣿⣿⣿⠃⠀⠀⠀⢹⣿⣿⣿⡿⠋⠉⠙⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠓⠶⠤⠖⠚⠁⣿⣿⣿⣷⣤⣤⣾⣿⣿⣿⠇⠀⢸⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣧⣤⣶⡆⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠿⠟⠁⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⡟⠛⢿⠇⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⣿⣿⣷⣄⣀⣤⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⡠⠃⡇⠙⢇⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂
⠀⠀⠀⠀⠀⣠⠖⠋⡀⡠⠊⠀⡼⠃⠀⣠⠀⠈⠛⠉⠢⢀⣀⣀⠀⠀⠀⠇⡠⠃⠀⢀⠀⡠⡀⢢⡦⢂⠂⡆⠘
⠀⠀⠀⠀⢸⡇⠀⠀⢠⠁⠀⢰⠁⠀⠀⠀⠀⢀⠆⡠⢟⡡⠆⠮⡱⡄⠀⠃⣥⢼⠸⠚⠉⡟⠐⠉⠈⠉⠀⠁
⠀⠀⠀⠀⠈⠧⣀⠀⠈⠀⠀⠈⠀⠀⠀⢀⡠⠄⠊⠀⣨⠀⠀⠀⡇⡅⠘⠀⠀⡜⠰⠠⠀⢇⡀⠔⠠⠂
⠀⠀⠀⠀⠀⠃⠈⠉⠐⠒⠒⠚⠈⠁⡉⠤⡀⠀⠀⠀⣹⠀⢀⡜⡰⠃⠀⠀⠀⠈⢄⢸⠠⠺⠼⠄⢋⠔
⠀⠀⠀⠀⠀⢰⠀⠀⢀⠀⡔⠢⣄⡜⠀⠀⡸⠀⠀⠀⢸⠴⣫⠜⠁⠀⠀⠀⠀⠡⠈⠿
⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠣⡀⠈⠀⠀⡴⠁⠀⠀⠀⢸⠉⠀⠀⠂⠀⠀⠀⠐⠂⠀⠀⠀⢀⠀⡀⠀⠠⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠢⣠⠎⠀⠀⠀⢀⡠⠏⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⢀⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⡀⠤⣒⠥⠊⠀⠀⠀⠀⠀⠀⠀⠘⠄⡄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠱⠶⠒⠛⠓⠉⠉⠀⠒⢤⠀⠀⠀⠈⠀⠀⠠⠀⠀⠀⠀⡀⠬⡑⠢⣀
⠀⠀⠀⠀⠀⠀⠊⡇⠀⠀⢀⠀⠀⡀⠀⠀⠀⠃⠈⢆⡇⠀⠀⣠⠔⡠⠀⠎⠒⠂⢄⠀⠀⠀⠢⡀⠃
⠀⠀⠀⠀⢀⡀⡐⠀⠀⠀⢈⠐⣶⡕⣠⡦⠒⠀⠂⠈⡇⠀⠘⠄⠘⠀⢰⠀⠀⠀⠀⡆⠀⠀⠀⠈⠢⡈⠣
⠀⠀⠀⠀⣼⠊⣰⢰⠾⠏⡼⠊⠈⠈⠀⠀⠀⠀⠀⠀⠀⠂⠑⠄⡀⡀⠀⠂⣀⠖⠊⠀⠀⢀⣀⠠⠄⠸⠀⠂
⠀⠀⠀⠀⠿⠘⠉⢀⠤⠀⠃⠔⠱⠀⠀⠀⠀⡀⠀⠁⣀⣀⣀⣀⣀⠀⠤⠀⠀⠐⠂⠉⠀⠀⠀⠀⠀⠀⡇⡄
⠀⠀⠀⠀⠀⠰⠀⠁⡄⠀⠸⣀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡃
⠀⠀⠀⠀⠀⢠⠀⠊⠀⠀⠘⠁⠠⠁⠀⠀⠀⢀⣀⡀⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠒⠒⠂⠈⠀⠀⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⢸⡀⢀⣀⣀⣀⢀⣀⠀⠀⠤⠀⠤⠤⠤⠤⠀⠀⠀⠐⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠒⠒⠒⠒⠂⠒⠂⠈⠁


⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣛⣿⣿⣿⣛⣛

⠀⠀⠀⠀⠀⠀⣿⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠸⡀⠈⢣⡀⢀⡀⠀⠀⠀⣀⠴⠚⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢳⡜⠑⠀⣠⠞⠁⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⣻⠀⢰⠃⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⡆⢼⠊⠁⡀⠄⠐⠂⠀⠐⠃⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢈⠠⠄⢹⢀⡄⢀⣀⡠⠄⠀⢀⠞⠚⠉⠉⠉⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢵⡄⢦⠸⠒⠉⠉⢀⣀⠔⠡⠐⠲⢴⠀⠀⠀⠀⠀⢀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⣀⡤⠖⢋⠤⠤⠿⡾⠲⠛⠓⠩⠂⠄⠀⠰⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⡀
⠀⠀⣀⣤⠶⠛⠁⠀⡴⠁⠀⡠⢺⠓⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⡆⠈⠲⣄
⣠⣞⣉⡀⠠⠓⠄⣼⠇⠀⠊⢠⡀⠀⠀⠀⠀⡄⠀⢐⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡛⠦⢤⣀
⡏⠀⠉⠉⢻⠒⠦⢬⡀⠀⠀⠀⠁⠀⠀⠀⢠⠄⡀⠂⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠈⢳⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢀⡴⠺⠦⣤⣤⣄⣀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣠⠞⠁⠀⠀⠀⢸⠀⠈⢙⡿⠓⠋⠉⠙⠓⢦⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠈⠳⣄
⢸⡏⠻⢶⣄⣠⡤⢀⠀⠀⠈⢧⡞⠁⠀⠀⠀⠀⠀⠈⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠳⣤⡀
⠀⡇⢀⠂⠤⡀⠉⠲⣥⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠄⠀⠐⠀⠀⠂⡀⠈⠀⠀⠶⠂⢤⣁⣀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠈⣻⡦⡀
⠀⣿⠈⣻⡡⠂⠤⢀⠀⠙⠛⠲⠖⠢⠀⠤⠥⢦⡲⡀⠈⢧⡀⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢉⣙⡓⠲⣤⣄⣀⠀⠈⠀⠀⢨⡇⠈⠢⣀
⠀⣿⠀⠈⢓⢢⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠦⢄⣳⣤⣀⡀⠄⡀⢈⠀⠐⠠⠀⠀⠀⠀⣰⠋⠉⠉⠉⠁⠈⠙⢮⠀⠀⠀⠀⠶⣅⠀⠀⠀⠑⢄
⠀⠈⠳⢤⣄⡑⠂⠑⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠚⠙⢦⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠀⠀⠘⠛⠛⠲⠷
⠀⠀⠀⠀⠀⠉⠓⠦⣄⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠶⠶⠒⠾⣇⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⣀⣀⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠖⠋⠉⠉⠀⠈⠙⠓⠲⢤⣤⡀⠀⠀⠰⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠩⢁⢐⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠈⠌⡘⡂⠂⠆⠡⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠦⢤⣄⣀⡀⠀⠈⠈⠉⠀⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⢤⣤⣀⣀⡼⠁
⣿⣿⡟⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡄⢤⣧⠀⣤⠶⣦⡀⠀⠀⣲⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣾⡆⠹⣿⠀⠸⣿⠸⣿⡛⠛⠁⠀⢰⣿⡁⣸⣷⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠄⠈⢻⣧⠘⣿⣄⠻⠿⠛⠛⠃⠙⠛⠛⠀⠠⣿⣏⠉⠛⠁⣸⣶⠁
⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⡈⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣴⡿⠁⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠹⣿⣦⣤⡾⠃⠀⠀⠀⠀⠠⠊⠹⣄⣀⡀⠀⠀⠀⠠⠊⢲⣀⠀⠈⠃⢰⣿⠳⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⣹⠤⠒⠒⠓⢄⠀⠠⠇⡄⠀⠀⠙⠦⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⡁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠣⡀⠈⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠅⣀⣀⣙⣒⠒⠒⠒⠊⠁⠀⢀⣀⣀⡀⢧⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢴⣲⣄⠈⠉⠉⣹⣽⡂⠀⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⣾⣿⣿⡇⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠈⠛⠋⣠⠀⣀⠉⠋⠁⠀⠀⠀⢠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⠠⠤⠎⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓⠒⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⡻⠃⠀⠀⢀⢴⠆⠀⠀⠀⠀⡤⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⣗⢄⠀⠀⠀⠀⠳⠵⠈⠓⢄⡀
⠀⠀⠀⠀⠀⣠⠔⠉⠈⠋⠀⠀⠀⠀⠺⠎⠀⠀⠀⠀⣜⡇⠀⠀⠀⠀⠸⡸⠀⠀⠀⠀⠈⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⡇
⢣⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠉⠒⠒⢲⡒⠊⠉⠁⠈⠉⠁⠒⠒⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⡶⠒⠊⠉
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋

⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⣇⡞⠀⠀⢀⠀⠀⠸⡇⢀⠀⡀⠀⢀⡀⠀⢸⡇⡙⢶⠀⢰⣦⡄⢿⢌⡈⢷⣀⠘⢀⣾⢂⡄⢸⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⠀⠂
⠀⠀⠀⠀⠐⠁⡘⠀⠀⠉⡇⠀⠀⠓⠉⠘⠃⠚⠈⠃⠀⠈⡇⠀⠺⣄⠘⡇⠀⢾⠘⠁⢸⠻⠄⠈⣧⠘⡧⠺⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠠⠄⠀⠀⠤⠀⠂⠀⠀⠐⣆⠆⠐⣀⠰⠀⠀⠀⢠⡆⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡠⠄⡤⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠄⢀⠀⠐⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⢣⡆⠀⠸⣦⡇⠘⠂⡾⠀⠸⣤⡀⠀⠘⣖⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⡀
⠀⠀⠀⢀⠐⢁⠐⠁⠀⠀⠀⠀⠋⠂⠀⠀⠀⠀⠀⠀⠃⠀⠰⠀⠁⠀⠚⠀⠻⠀⠐⠘⠇⠀⠉⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠅⠀⠀⠀⠀⠈⠁⠠⠄
⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠠⠘⠀⠈⠀⠠⠛⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠁⠀⡀⢄⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠈⠁⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠀⠀⠘⠇⢸⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠐⢆⡀⠄⠀⠀⣄⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣀⠀⠀⠀⢀⠀⢈⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡁⠀⠢⣭⠀⠀⠀⠠⠀⠀⠋⠀⠀⠀⠀⠀⠀⠉⠀⠰⠇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀⡁⠀⢤⡀⠀⠐⠀⣤⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠈⠑⠦⣈⡁⡆⠛⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠐⠄⢀⠀⢀⡀⠙⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡬⠀⠀⠀⢀⠀⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠛⣠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠋⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠂⠁⠉⢠
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠂⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠁⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠃⠀⠄⠀⠀⢠⠀⠀⠀⠤⠀⠀⠰⡄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⡀⣀⢀⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠒⠀⠒⠊⠑⠂⠁⠊⠁⠀⠉⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡠⠄⡒⠀⠐⣠⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠤⠄⠀⢀⣀⠀⢀⣀⣀⡀⠀⠤⠤⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢋⠠⢼⠃⠀⡠
⠀⠀⠀⠀⠀⣃⠀⠀⠀⠉⢀⡀⢠⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠺⡁⠀⠈⠀⠀⠀⠈⣠⠄⠀⠀⠀⠀⢠⠈⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠰⠄⠀⣤⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠧⠘⠃⠀⠛⡄⠀⠀⠀⠀⠀⠀⠠⠒⠖⠂⠐⠒⠒⢂⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠃⠀⠘⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠶⠀⢠⠆⠀⠀⠀⠀⡄⠁⠀⡄⠀⠀⠀⠀⠇⠀⡅⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⢀⣄⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠙⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⠀⠀⠀⢀⠁⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣔⠀⢤⣄⡀⠀⠀⠀⠀⠈⠐⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈
⠀⠀⠀⠀⠀⡀⠈⠂⠀⠀⠀⠀⠃⠈⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠡⠀⢀⠀⠀⠀⠀⢠⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚
⠀⠀⠀⠀⠘⡄⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢾⠀⠁⣋⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠀⠠⠛⠓
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⠀⠐⠋⠉⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠂⠐⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡴⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠲⠆⣰⣄⠀⠀⠀⠀⣤⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠒⠂⢠⡀⠀⠀⠀⣠⢀⠀⠊⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠂⠀⠀⠀⠀⡀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⣸⠇⢀⣀⣀⣀⣶⣀⣀⣀⣀⣰⣀⡀⠀⠀⠀⣴⡋⠉⠉⣷
⠀⠀⠀⠠⣤⣤⣿⡤⠖⠋⠰⠯⠍⠉⠉⣽⢿⠍⠉⠉⢻⠋⠉⠉⠉⢹⡏⠁⠀⢀⡟
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⢀⡼⠁⢠⡤⣤
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡄⠀⠀⠀⢹⠀⠀⠀⠀⢸⡄⠀⠀⠀⢸⡀⣠⠞⠁⠀⣿⢀⡼⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠀⠀⠀⢀⣼⡇⠀⠀⢀⣼⣇⠀⠀⢀⣼⣟⠁⠀⠀⣀⣿⠋⠁⠀⣠⡶
⠀⠀⠀⠀⣠⢴⡷⢤⣄⣀⡸⣦⣤⢶⡋⠀⠙⠶⠖⠋⠀⠙⠶⠶⠋⠁⠘⠳⠶⠞⠉⠈⠓⠶⠚⠉
⠀⠀⠀⠀⠙⣛⣁⣀⡀⠈⠉⠉⢉⡉⠁⠀⠀⠀⢀⠀⠀⣀⣀⣀⣀⣀⣀⠀⢀⡀⠀⠀⣀⣀⣀
⠀⠀⠀⢠⡾⠋⠉⠉⠻⠀⠀⠀⣾⡇⠀⠀⠀⠀⢻⡇⠀⠉⠉⣿⡏⠉⠁⠀⢸⡇⠀⢻⡏⠉⠉
⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⣼⡇⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠸⣧
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⢀⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⣿⣀⣀
⠀⠀⠀⠸⣷⡀⠀⠀⣀⣶⠆⠀⠘⣷⡀⠀⢀⣾⠃⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡇⠀⠀⢸⣏⠉
⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠈⠙⠛⠛⣅⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠘⠃⣠⠤⣌⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠛⠛⣦⠀⠀⠀⡄⠀⠀⠀⢸⡇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⣀⣀⣿⠀⣀⣴⡆⠀⠀⠀⣸⡗⠋⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⠧⠼⠋⠉⠉⠘⢧⣤⠴⠛⠁⠙⠲⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⣒⣦⡈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡁⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⡞⠙⠦⠤⠤⠤⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠗⣰⠋⠸⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠃⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣦⡀⡀⠀⠀⢠⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣒⣚⣋⣉⣙⣒⣒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠐⠉⢉⠈⡌⣄⣦⣤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠿⢿⣿⣿⣿⣿⣿⠿⠿⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⣄⡆⠀⠀⠉⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣸⣚⣛⡓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡄⠀⠤⢤⣠⡠⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⣴⡶⣿⢷⠲⣄⠀⠀⡏⠀⢀⠇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣲⣦⡗⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⢸⣿⢸⡇⣿⠀⢠⣧⠔⡫⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠹⠁⠁⠱⠈⡆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠻⠶⣿⡿⠿⠋⠀⡼⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢀⠰⡀⢆⢀⣀⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠥⣟⡩⠭⠥⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⢰⡦⠒⣦⣶⠀⣦⣶⡀⣰⣶⣦⠖⣦⣴⢀⠖⢲⠂⣦⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⣈⢿⠲⣄
⠀⠀⠀⢸⡧⠔⠃⢿⠀⡟⡟⣷⢿⣿⡧⠴⠋⣸⡏⠀⢸⠀⡟⣿⠀⠀⠀⠀⠀⠀⢠⠖⣉⠥⢒⢤⡯⢋⣄⡏⡗⢦
⠀⠀⠀⠈⠁⠀⠀⠈⠉⠁⠁⠈⠈⠉⠁⠀⠀⠉⠉⠁⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⢳⣰⡁⠀⢡⠋⠰⣻⠋⣰⣁⣼
⠀⠀⠀⠀⠀⠀⠀⢴⡋⠓⣷⠞⢹⠞⡏⣴⠋⠇⣾⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠉⠉⠉⠉⠉⠉⠀⠀⣾⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢈⣝⡦⣿⠒⠋⢀⣇⢿⣀⡴⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣸⣷⡼⠂⠀⢰⠗⠲⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠊⡎⢠⠁⢡⠙⡄⢸⠀⣠⠇⡼
⠀⠀⠀⠀⠀⢰⡇⠀⢠⡖⣾⡖⢆⠸⡆⡴⣾⣙⠃⣷⠚⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⢇⠘⡀⣸⣠⠃⢸⣉⡥⠞
⠀⠀⠀⠀⠀⢸⡇⠀⢸⣇⣿⣼⣼⠀⢿⡇⣿⠀⠀⡷⢖⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠉⠉⠉⠉⠁⢈⡞
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠀⠈⠀⠈⠉⠁⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣄⠀⣠⡤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⢘⡿⠁⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣀⣀⣠⣤⡟⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣞⣀⣀⣤⣤⣤⠤⠴⠶⠶⠖⠒⠛⠛⠛⠉⠉⠉⠉⠀⠀⢰⡇⠀⠀⠀⠀⢠⡟
⠀⠀⠀⢠⡤⠴⠶⠶⠶⠾⠿⠓⠒⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⡟
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⠟
⠀⠀⠀⠘⡇⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠶⠀⠀⠀⠀⢀⣄⠀⠀⠀⠤⠀⠀⢠⡇⠀⠀⢠⡟
⠀⠀⠀⠀⣷⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡾
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠿⠇⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠃
⠀⠀⠀⠀⢸⡄⠀⢀⡀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡟
⠀⠀⠀⠀⢸⡇⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢸⠇⠀⢸⡇
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⣾⠀⠀⣸
⠀⠀⠀⠀⣠⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠀⠀⡿
⠀⠀⠀⠀⠙⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠒⣲⠤⠴⢶⠶⣉⠉⠓⢶⡶⠦⣤⠤⣴⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠾⠥⢤⣀⠉⠓⢤⣠⠎⠀⢈⠗⢄⠀⠙⢾⠁⠀⢈⠷⣄⠙⢦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⡴⠒⢮⡡⠋⢡⠎⠀⢠⠋⠓⣄⠀⠙⣄⢀⠏⠀⠀⣳⡄⠀⢳⡰⠃⠀⠈⢆⢈⣇⣙⣦⠽⠲⡄
⠀⠀⠀⠀⡼⠛⠉⠉⢳⡤⠮⠤⢤⣇⠠⠤⢼⣇⣀⣈⣿⣀⢀⣰⣃⣹⡤⠤⠷⣤⠐⠲⢯⣭⠤⠈⣇⢀⣠⠏
⠀⠀⠀⠀⠳⣄⣐⣾⠁⠀⠀⠀⣠⠟⠄⠀⠀⣽⠤⠀⠀⠈⡷⠀⠀⢹⠎⠀⣠⣟⣀⣀⣤⠧⠴⠊⢁⡏
⠀⠀⠀⠀⠀⠀⠘⡎⠓⠖⢲⡛⠖⠶⠶⡖⠛⠶⠴⠒⠒⠛⡶⠒⢲⠋⠚⠋⠁⠈⡸⠀⠈⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣶⠾⣿⣡⣿⣿⠿⠿⡤⠿⣽⠿⣿⣝⣵⣦⡤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⠛⣧⣤⠿⢿⡋⠹⣣⣼⡾⣿⣯⡙⠻⢯⡉⣉⣡⡴⢶⣏⣸⡟⢢⣄⡀
⠀⠀⠀⠀⢀⣴⣾⣿⣾⡷⠈⠁⢀⣤⣾⡿⠂⠐⣠⠶⣶⣿⣿⡷⠶⠞⠛⠿⢇⡓⠟⠙⠻⣿⣀⡉⣲⣄⡀
⠀⠀⠀⢰⣈⣿⣵⣊⣹⠷⠞⢻⣏⠉⠀⢣⣶⠿⠛⣳⡄⠀⠙⢆⣀⣠⣤⣤⣤⣼⡴⠆⠠⠞⠛⢿⣿⠟⠁
⠀⠀⠀⣿⠋⢻⢿⣟⡀⠀⣀⣋⣽⣦⠞⠃⠁⠀⣠⣴⣶⣧⡴⠞⠛⠙⢿⡏⠀⠙⠧⣄⣀⣀⣀⣿⡯⣌⣿⡀
⠀⠀⠀⣿⣷⠞⠿⣿⣾⣻⡁⠙⠿⢧⡤⢀⣠⠾⠇⠉⠛⣁⠀⠀⣀⣀⣨⣿⣄⠀⠀⠻⠛⣛⣵⡿⠧⢨⢽⠁
⠀⠀⠀⠈⢿⣞⣁⡀⠉⡩⠟⢳⣶⡒⠛⠉⠙⠷⠦⢀⡀⠀⠀⡻⠿⡿⣵⠀⠙⢻⡶⢔⢋⣩⣙⢄⡦⢣⠏
⠀⠀⠀⠀⠀⠀⢩⣻⣿⣤⣴⣀⢀⡟⠁⢙⣳⣶⠒⠛⠷⠦⠯⠐⠶⠒⢋⡐⠆⠀⠀⣰⢇⠷⢚⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣾⣋⡹⢿⣿⣶⣬⣿⣹⣧⣀⣀⣘⣀⠀⢀⠼⠾⠁⠒⣈⣉⣥⣴⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⠗⣲⣶⠿⠱⠤⠾⠶⠷⠾⠶⠶⡿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃⠀⠠⠴⠤⠄⠠⠄⠠⠄⠘⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠟⠛⠉⠉⠁
⠀⠀⢀⣴⣶⡄⠀⠀⠀⢀⣠⣴⣶⣶⣦⣤⣤⣤⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡏
⠀⠀⣿⡏⠀⠀⠀⢀⣴⡿⠋⠀⣴⡿⠋⢿⡏⠙⢿⣦⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢻⣧⣀⣠⣴⡿⠋⠀⠀⠀⣶⣆⢀⣴⡅⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠰⠿⠿⠿⠿⠿⠿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣶⣤⣀⡉⠛⠀⠀⠀⣀⣤⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡿⠁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠃⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡯⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣧⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣼⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣀⣀⣀⣠⡤⠒⠲⠤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⠉⠓⠲⣅⠀⢀⠞⠈⠓⣤⡀⠈⠢⡤⠋⠁⠙⣦⡉⠲⣄⠀⡀
⠀⠀⠀⠀⠀⢀⣀⣤⠒⣲⠞⢩⠂⠈⣹⠶⣄⠀⠑⢎⠀⢀⡞⠀⠙⢆⠀⠙⣆⢀⠞⠁⠙⡄⠘⣟⠻⣖⢲⣄⡀
⠀⠀⠀⠀⢀⡯⠤⠬⢿⡀⣠⣃⠀⢰⠃⠀⡈⢣⠀⠈⠳⡜⠀⠀⢠⠎⢧⠀⣘⣏⠀⣀⣀⡼⠖⠚⠒⢾⠁⠀⢹
⠀⠀⠀⠀⢾⠀⠀⢠⡴⠋⠉⠉⠉⢹⠎⠉⠉⠙⣇⠚⠉⠙⠲⡔⠛⠒⢮⡩⠉⠉⣿⠀⠀⠉⣟⢉⣠⠞⢰⠚⠉
⠀⠀⠀⠀⠈⠙⠲⡘⢦⣀⣀⣤⣞⣋⣁⣀⣠⣜⣋⣁⣀⣠⣴⣃⣀⣠⠼⠤⠤⠞⠳⢲⠞⢻⠁⠙⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⠈⢣⠈⠉⠉⠩⠀⠀⠉⠉⠀⠀⢠⡇⠀⠙⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣀⡠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠖⠒⠚⠛⠉⠉




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

⠀⠀⠀⠀⠀⡠⠀⡟⡠⠊⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡼⠁⢰⡟⠀⣰⢃⠀⢀⠀⠀⢀⡀⢠⡄⣀⠀⠀⡀⢀⣄⢀⡞⢠⡆⢀⡄⠀⡴⠀⢰⠄⠀⠀⢰⠀⢤⠀⡅⢀⡴⠆
⠀⠀⠀⠀⣷⠄⢸⠋⠋⢁⡟⠀⣿⠀⠀⣿⠀⣸⠃⡼⠀⢠⡇⢰⠃⣾⣥⠊⠀⡿⠀⢸⡇⢀⡏⢠⠀⠀⣾⠀⣾⢸⡇⣾⠂
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠸⣇⠄⠻⠄⠁⢿⠠⠏⠀⠧⠀⢸⠁⠘⠀⠇⠻⠖⠘⠇⠀⠸⠀⠸⠤⠞⠀⠀⢿⠀⠧⠘⠗⠙⠳⠊
⠀⠀⠀⠀⠀⠀⠀⠁⢰⡆⠀⣤⠀⣤⢈⡄⢀⡤⠄⣤⢦⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣿⠀⡟⣼⠁⣼⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⢑⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠐⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠇⣿⠘⠇⠹⠄⠹⠤⠉⠳⠔⠂⠀⠀⠀⠖⠀⠲⠈⠀⠙⡃⠀⠀⠀⠙⠁⢀⠀⢀⠁⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢀⠀⠀⢀⠀⠀⣀⠃⠀⠀⢿⠇⠀⠿⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⡀⠈⠁⠀⠀⠈⠁⠈⠀⠀⠀⠡⠰⡀⠀⠛⠠⠆⠒⡄⠀⠀⠀⠀⢰⠢⠀⡀⠰⠶⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠠⠂⠐⡀⠀⠀⠀⢀⢠⠁⠉⠀⠂⠡⠄⠄⠁⠀⢀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠊⠈⢆⠀⠈⢤⠀⠂⢆⠀⠀⠉⠁⠈⠁⡄⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠣⠀⠀⠑⠠⠤⠆⣀⣀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠒⠐⢄⠀⠀⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠊⠀⠀⠀⢀⠀⠀⠀⣀⡠⠀⠤⢤
⠀⠀⠀⠀⠀⠀⢰⣢⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠍⢘⠀⠀⠀⠀⠀⠀⡷⠰⢴⠤⠤⠖⣤⠃⠀⢠⣎⠜⣴⣳⡤⢚⡆
⠀⠀⠀⠀⠀⠠⠉⠀⢀⠈⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠈⠲⠶⠢⠐⠈⠁⠀⠀⠘⠳⠛⠈⢰⣷⡿⠃
⠀⠀⠀⠀⠀⠚⠀⢀⡂⠀⠀⠀⢀⡔⠣⡄⠀⠀⠀⠰⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡐⡀⠉⠋⠀⠀⠀⠀⠈⠺⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠃⠀⡗⠀⠀⠀⠀⠄⡲⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠒⣊⠄⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⢿⡿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⡿⢿⢿⣿⣿⣿⡿⣿⣿⡿⣿⠿⣿⠿⡿⢿⡿⢿⣿⢿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿
⣿⣿⣿⣿⣠⣷⣈⣦⣦⣄⣨⣤⣼⣼⣴⣼⣧⣾⣬⣠⣧⣤⣿⣦⣦⣤⣔⣣⣿⣴⣮⣧⣜⣧⣘⣜⣸⣿⣺⣿⣩⣌⣠⣅⣸⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠐⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠉⠀⣈⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡬⢄⡤⡖
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠒⠋⠰⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠈⠀⠐⠀⠤⠀⠤⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⢇⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⣀⢀⡀⣀
⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠖⡵⢿⣳⣢
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⢀⡠⢡⡉⡀⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡶⠾⠿⠉⣉⣉⣀⡒⢒⠖⠂⠒⣢⣄⣀
⠀⠀⠀⠀⠀⢀⡀⢤⣴⣭⣄⣀⣀⣀⠔⠋⠀⠀⣠⠖⠛⠒⠈⠿⢅⣀⣤⠾⠧⢤⣤⣄⣉⣑⠢⣤⣄
⠀⠀⠀⠀⢠⡋⡶⠋⠀⣠⣞⢁⡜⠁⠀⠀⣠⠿⠷⠶⡦⠤⣤⣀⡀⠀⠉⠒⡶⠊⠀⣠⡼⠛⠓⢾⠄⢇
⠀⠀⠀⠀⢮⠀⠈⠑⢾⠤⣀⠉⠉⠉⠑⠚⠣⠤⢤⠎⠀⢀⡴⠋⠉⠓⡲⠊⠀⢀⣾⣋⣉⠭⠖⢋⣠⠊
⠀⠀⠀⠀⠀⢹⠉⢹⣦⣄⡀⠉⠛⠛⡓⠲⠦⡴⠤⠤⠤⠿⡵⠖⠒⠒⠥⠒⠒⣉⣁⣀⣀⣠⢼⠏⡎
⠀⠀⠀⠀⠀⠈⡇⠀⣿⡇⠈⠉⢻⡏⢹⠒⠒⠀⢶⠶⠖⠒⠒⠠⣴⡖⠋⠉⢹⡟⠃⠀⣿⠃⡌⢸
⠀⠀⠀⠀⠀⠀⢱⡀⠘⠃⠀⠀⠐⠁⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡇⠀⠀⠀⢸⠃⠀⢠⡇⢀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⣄⣀⢄⣀⠀⠀⠀⣀⡃⠀⠀⠀⢀⣀⡀⠀⣀⠴⠦⠔⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠒⠒⠉⠁⠀⠈⠉

⠀⠀⣀⠁⠀⠀⡀⠀⠀⢈⠁⠈⠋⡀⣌⡂⠂⠀⠀⠀⡁⠀⠠⢀⠇⠁⢀⠀⢀⠇⠀⠀⠀⠀⠈⠐⡠⠲⢦⡆⠡⡀⠀⣀⡀⠀⠁⠀⠀⠀⠀⠂⠀⢠⣄
⠀⠀⣀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⡈⠈⠁⠐⡀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠁⠑⠀⠤⠀⠀⠀⠀⢅⠀⠀⡀⠘⠀⠀⠀⡆⠀⠉⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⡋⠁⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠄⠁⣶⡆
⣠⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠈⠈⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣠⡀⠡⠰⠢⠀⢀⠀⠐⡂⠀⠀⠀⠘
⠙⠆⠨⠈⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⠿⠀⠀⠀⠀⠘⠳⠦⣄⣤⠄⠀⠀⠈⠀⠀⠀⡂⠄⠀⣄⡴⠀⠀⠀⠀⠀⠀⢀
⠂⢀⡸⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⢾⠄⠀⢡⢀⠉⢡⠀⠀⠀⠀⢄⡀⠲⠉⣥
⠀⠀⠀⠀⠄⠀⠦⡀⠀⠳⠀⢀⠀⠙⠁⠀⠀⠀⠉⠁⣮⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠤⠀⠀⠈⠁⠀⢠⣶⠀⠓⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠤⠀⠀⠀⠰⠀⠀⠀⣏⣩⠀⡀⠀⠀⠂⠀⠀⠈⠀⠀⠀⡈⠀⠀⠄⠀⠀⠀⣀⠀⠀⠈⠉⠉⠀⠐⠶⠀⢀⠀⡄⠀⠀⠀⠀⠀⡤⡆⠀⠆⠀⡀
⠈⠐⠀⠐⢄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠂⡀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠊⠬⠀⢘⡗⡀⠠⡘⢢⡀⠘⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⡄⠀⠀⠀⢀⠁⠀⠃⠀⠈⠠⢀⠀⠀⠀⠈⠀⠚⠁⠀⠐⠀⠀⠂⠐⠦⠀⠠⠀⠀⠲⡀⣨⠸⠁⣈⠄⠉⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⠘⠠⠂⠀⠀⠃
⠀⡐⠀⢀⠂⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠒⡀⠀⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠂⠒⠁⠀⠠⠆⠀⢸⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠊⠀⠀⠀⠀⢠⠉⢀⡀⢀⠀⠀⠂⠀⠀⠀⠂⠐⡀⠢⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⠀⠀⠀⠐⠀⠀⠀⠨⠁⠈⠋⠑⠆⠀⣂⡀⠀⢀⠆⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠒⠂⠀⡀⡈⠗⠠⠄⠀⠸⡀⠀⠀⠀⠀⠀⠐⠄⠄⠀⣀⠄
⠐⠂⠐⠀⠀⢀⠀⠁⡀⠀⠀⠀⠀⠀⠡⠉⠀⣁⡀⠀⠀⡀⠠⠄⡀⠀⣠⣄⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠠⠄⡀⠀⣥⠀⠀⠸⠀⠀⠀⡤⠐⡐⢁⡄
⠀⠀⠀⠀⠰⣦⢐⠀⠀⠀⠀⡘⠈⠂⡀⡨⠀⠛⠃⠀⢪⠀⠘⠁⠛⠀⠙⢁⠰⠀⠁⠀⠀⠀⠉⠀⠀⠂⡰⢦⡈⢀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠀⡞
⡐⠦⢒⣀⡤⠁⠄⠀⠀⠉⠀⠃⠀⠀⠀⠠⠀⠀⠀⢀⠀⠲⠶⢠⠆⠀⠀⢄⠀⡀⠀⢄⠀⢠⠀⠈⠀⠠⡑⡀⠘⠈⠀⠀⠀⠀⡃⠴⠰⡃⠠⢀⠊⠀⡀
⠀⠠⠄⠀⠀⣶⠀⠀⠀⢠⠂⠠⠀⠀⠀⠀⠀⠀⠀⠈⠘⠄⠐⠀⣤⡄⠀⠈⠂⠁⠀⠀⠀⡀⠆⠀⠂⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⣀⠀⠈⠀⠀⠤
⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠆⠀⠀⠉⠁⠀⠀⠀⠀⠠⠀⠻⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠘⠛⠀⠄⠀⠠⠐
⣀⢀⢄⡀⠇⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠅⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⡀⠀⣤⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡞⢑⠂⠀⠂⠠⢀⠈
⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⢂⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠌⠔⡂⣄⡐⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⣀⡖⠉⠂⠀⠀⠈⠀⠀⠔⠐⠊⠂
⠀⠠⡀⠀⠀⠀⠀⠢⠤⠉⠒⠦⡀⠀⠀⢀⠀⠀⢀⣘⠳⠖⠀⠀⠀⠀⠀⠀⢀⡠⡷⠄⠀⠀⠀⠉⠀⠀⡄⠙⠓⠛⠉⠀⠀⠀⠀⠀⠀⡠⠰⡀
⠀⠀⣉⠀⠁⠒⠄⠀⠀⠀⠀⡔⠈⠀⠠⢎⣹⠄⢁⡀⠀⠀⡀⢀⡀⠀⠀⠐⠀⠠⠄⠌⠀⠀⠠⠀⠈⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠂⠈⠂
⠀⠀⡀⠐⠃⢤⠀⠀⠈⠃⠤⠄⠄⠠⢰⠄⠁⠐⠡⠄⠌⠑⠈⢁⠀⠀⠠⣀⠀⠀⢀⠴⠈⢅⠀⠢⠀⠫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣠⡄
⠀⡰⠀⠀⠀⠀⠈⢁⠀⢀⡀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢀⡀⠀⠁⠁⠠⠀⠀⢀⡰⠀⠀⠀⠀⠘⠦⡀⠀⠀⠐⠀⢀⠄⠀⠉⠁⠀⠀⣭
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⢀⡠⠈⠀⠁⠐⠊⠀⠀⠘⢁⡤⠂⡠⠒⠂⠠⡈⢰⢄⠀⢀⣈⠀⢀⡃⢀⠴⠁⠶
⠀⣶⡆⠀⠐⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠰⠶⠄⠀⡀⠀⠂⠀⠀⠀⡁⠀⠀⠀⠀⡀⠒⠀⠘⣀⣄⠀⠀⠀⠀⢀⠀⠰⣀⠃⠨⠁⠖⠃⠀⢹⠄⠀⠒⡈
⠀⠀⢀⡒⡀⠒⠒⠀⣀⠉⠀⠐⠊⠁⢀⣀⠀⠀⠈⢀⠀⢀⠐⠀⢈⠂⣀⠀⠀⡠⠁⢀⢀⠈⠨⠉⠁⠀⠠⠄⠉⣠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠘⢁
⠀⠀⠠⡘⠷⠀⠀⠀⠈⠓⠀⢁⠴⠁⠀⠀⠆⠀⠀⠁⢀⠅⠐⠀⠉⠉⠀⠈⠁⠀⠀⠘⠋⠀⠀⡠⠄⠀⣀⠀⠀⠉⠁⠈⠀⠀⡠⠙⠛⠃⢀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡤⠀⠀⠀⠀⣠⠶⣾⠠⡞⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡍⣇⠀⠀⠀⠐⣧⠞⢹⡄⣹⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢦⠈⣧⠏⡼⢦⠇⠀⠀⠀⠀⠀⢁⡬⠥⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡸⣾⢰⡏⠓⠁⠀⠀⣠⠖⠋⠉⠙⠋⠀⠀⠀⠈⢳⣰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⢶⡿⠈⠉⠀⡠⠒⠋⠙⠃⠀⠀⠀⠀⠀⠀⣀⣀⣀⣨⡟⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢾⣁⣀⣝⠛⠃⣀⡤⠼⠁⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⢉⡴⠚⠁⠀⠀⣠⠷⣄
⠀⠀⠀⠀⠀⠀⠈⠉⠈⠛⢃⡞⠁⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⢀⡼⢧⡀⠀⠀⠈⠁⠀⢈⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠉⠀⠀⠀⠀⠚⠉⢈⠏⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⣞⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠤⠤⠴⠖⠚⠁⠀⠀⠀⠈⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡏⠉⠉⠉⠛⠛⠒⠲⠶⠶⠤⠤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣈⣉⣉⣉⠉⠛⠛⠓⠒⠒⠶⠶⠦⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀⠉⠉⠉⠉⠙⠛⠛⠒⠒⠒⠲⠶⠦⠤⠤⢤⣤⣤⣄⣀⣈⣉⣉⣉⣉⣉⣉⣉⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢋⡿⣴⢀⣴⢠⣄⣄⢀⣶⢀⡀⢀⠀⡏⢀⡄⠀⠀⠀⠀⠀⢀⠀⣀⢐⡂⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠓⠋⠰⡧⢾⡇⣾⠏⣿⠏⡟⢸⡟⢹⢿⣇⣾⡗⣧⡞⣷⠀⠀⢸⣷⢹⡿⡇⣿⠜⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠃⠋⠀⠁⢸⡇⣿⠴⠋⢸⡿⢬⡇⡿⠀⡿⠀⠀⠸⡧⠞⠁⠷⠻⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⢿⢛⠟⠀⠀⠀⡤⡞⠀⠀⠀⠀⣴⠀⠀⠀⠀⠸⡄⠀⠀⠀⠘⡗⡄⠀⠀⠀⠈⠪⠆⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠋⠀⠈⠁⠀⠀⠀⠘⠞⠀⠀⠀⠀⢸⡜⠀⠀⠀⠀⠘⠜⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿
⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿
⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣷⣄⣀⡀⢀⣀⣀⡠⠤⠤⢀⣀⣀⣀⣀⣀⣀⡀⠤⠒⠊⠉⠉⠢⢄⣀⡀⠀⠀⠀⠀⢀⣀⠠⠔⠊⠁⠀⠙⠢⢄⣀⡀⠀⠀⢀⣀⣠⣾
⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠔⠒⠂⠉⢉⡋⣉⠉⠽⠍⢉⠉⠁⠒⠒⠤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠒⢁⢀⢀⣠⡤⣶⢒⠖⠉⢀⡼⣿⡟⠳⣮⠉⡌⠉⣦⣤⣀⡀⢄⠑⠢⠄⣀
⠀⠀⠀⠀⢀⡠⠶⠏⣀⣠⣶⣊⣿⣿⠹⣆⡹⠃⠀⢠⡾⢻⡌⢹⣄⠎⠀⢀⡾⠻⡇⠈⣏⡟⠓⢤⡀⢈⠓⢦⡀
⠀⠀⠀⣴⠋⠄⠠⠔⠉⠁⠠⠀⠈⠉⠉⡹⢁⠀⡰⠋⠉⠙⠓⠚⠛⢒⠒⠛⠂⠾⠧⠴⡟⠀⠀⣾⡙⠶⣍⢠⡎⢢⡀
⠀⠀⢰⠗⠂⣰⣷⡖⠉⢉⣷⣶⣶⣶⡶⠁⠠⢀⣧⣤⣤⢴⣶⠤⠤⢄⣀⣀⣠⣄⣀⠎⠀⠁⡰⠁⠀⠙⠃⠲⡀⠀⣿
⠀⠀⢸⠅⢸⡿⢿⢁⠄⣼⡿⣿⠁⢹⠃⠀⢠⢿⣿⠇⣿⢨⠃⡀⢀⣾⢻⡿⠟⣿⠏⠀⢀⣾⠛⢿⣶⠤⠤⣄⣤⡀⣿
⠀⠀⠸⣧⠈⣷⠁⠀⠾⠯⠭⢿⡤⠧⠤⣴⣏⣩⣇⣰⠧⡞⠀⢠⡟⠛⣽⠁⠀⡿⠀⠀⣾⣟⠀⢠⠏⠀⣸⠋⡝⢢⡾
⠀⠀⠀⣷⣖⣙⣄⢸⣀⣀⠀⠐⠀⠀⣀⣀⡀⠀⠀⢀⡜⠁⢉⡜⠑⠲⠯⠤⠒⠛⠒⠚⠻⠿⢦⠃⠀⡼⣃⠔⣑⣮⠇
⠀⠀⠀⠸⡜⡃⣦⠙⠿⣿⡋⡙⠉⢡⡿⠋⢹⡟⣿⠋⠠⠀⣾⣶⣤⣤⣀⣀⠤⠤⣄⣀⣀⣀⡌⢀⡸⠒⢡⣤⠇⣿
⠀⠀⠀⠀⢳⢠⢡⠸⡗⢠⡍⢑⠢⠼⢧⣀⣼⢀⠇⠀⠀⣼⠏⢹⡟⢹⡿⠁⠀⣰⣿⡯⠿⣛⠋⣥⣠⡇⠀⣿⢰⡇
⠀⠀⠀⠀⠈⠃⡘⡆⢧⠘⣿⠀⢷⠐⣦⠤⣌⢉⡉⢒⡚⠛⢒⠚⠒⡚⠓⠉⣉⠍⢤⢶⠒⣹⡧⢾⣿⡇⢸⣃⠟
⠀⠀⠀⠀⠀⠀⠐⠷⠸⡄⢹⡆⢸⡇⢿⠀⣯⠀⣿⡁⣿⡎⢸⣼⡎⣶⡅⢶⡎⠀⠀⣿⠂⣻⣃⣿⣿⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠘⢿⡈⣿⢸⡆⢻⠀⠹⡃⢬⠃⢀⢙⡇⢼⡇⣾⡇⡆⠀⡶⣁⢁⡦⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⠘⢆⠀⣇⠘⡇⢘⣘⣇⢘⣧⠤⠧⠃⠞⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠈⠻⢦⠴⠒⢦⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⣤⢠⡖⠀⠀⠀⠀⠁⠀⠉⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠉⠛⠁⠻⣤⣤⣤⣶⣦⡀⠀⠀⠈⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠛⠓⠶⠶⢤⠀⠀⣀⡀⠀⠁⠸⣧⡴⣦⠀⣀⣤⡄⠉⠙⠳⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠐⠂⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣀⣀⠈⠛⠋⠀⠉⠀⣴⠀⠀⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⡀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀⠀⠀⠛⢻⣆⠀⠀⠀⠀⠉⠛⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⡉⠛⢧⠆⠀⠀⠀⡀⠿⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⢀⣽⠆⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠳⣄⠀⠙⢷⡄⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡀⠀⠁⠀⠀⠙⢧⡀⠿⣤⡄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⣠⡴⠓⢀⡴⠃⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠞⠛⠉⠉⠁⢀⡴⠋⠀⣀⣤⣤⣤⡴⠛⠁
⠀⠀⠀⠀⠀⠀⣰⠟⠀⠒⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡤⠶⠶⠶⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⣴⠏⠀⣠⠞⠉
⠀⠀⠀⠀⢀⡾⠁⠀⠃⠀⠉⢀⣀⣤⣤⠴⠶⠶⠒⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁
⠀⠀⠀⠀⢸⡇⢤⣤⠴⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⡄⠀⠀⣠⡾⠁⢀⡼⠋
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠄⠀⣀⡼⠋⠀⣴⠟
⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⠴⠞⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠤⠀⠀⠃⠀⠀⠀⠀⣀⣀⣀⣠⣤⡤⠶⠞⠛⠉⠉⠀⠀⠀⠀⣀⣠⠴⠛⠁
⠀⠀⠀⠀⠀⣉⣀⣤⣤⡤⠶⠶⠒⠛⠛⠛⠋⠉⠉⠉⣀⣀⣠⣤⡴⠶⠖⠚⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠘⣯⡀⠀⣀⣀⣀⣠⣤⣤⠴⠶⠚⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁



⣿⢿⠿⡿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣿⣛⣟⣿⣿⣿⣿⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠐⡁⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⠀⠀⢀⠀⡀⠊⠀⡪⠋⢁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠉⠀⠈⠁⠀⠈⠀⠀⠀⣤⠈
⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠈⠁
⠀⠀⠀⠈⠈⠀⠀⠂⠀⠀⠀⡄⢀⣈⣰⢀⢓⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡌⠀⠸⣉⡠⠎⠊⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠
⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠈⠀⠀⣀⠀⠂⠠⠀⡀⠈⠠⠂⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⢀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠈⠉⠉⠓⠒⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠠⠀⢀⡀⠀⠔⠈⠀⠂⠚⠂⠐⠀⢠⠄⠀⠀⠁⡀⠈⠀⠀⠈⠀⢀⠀⡀⠍⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⢠⠔⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠠⡄⠅
⠀⠀⠀⠀⠀⠀⡀⠠⠒⠀⠀⠔⠂⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠼⠀⠀⠀⠀⠁⠀⠐⠰⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⢶⣤⡀
⠀⠀⠀⠀⠀⢀⣼⣿⠋⣴⢸⡇⠀⠀⠀⠀⣤⣴⣷⠶⠶⠶⠄⠀⠀⠀⠀⢀⣴⡿⣻⡅⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⣼⣿⠇⠀⠛⠞⠁⠀⠀⠀⠀⠀⣼⠇⠶⠀⠀⠀⠀⠀⠀⠀⠸⠋⢠⣿⠃⠀⠀⠀⣠⣿⠇⠶
⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⣴⢠⣿⠂⢠⣿⢠⣿⣰⡆⢰⣾⡗⢀⠀⠀⠀⠀⠀⣾⣿⠀⢀⣠⣴⣿⠏⣰⡆⢠⣾⡗⢀
⠀⠀⠀⠀⢸⣿⡏⠀⠀⢠⡿⠘⢿⡴⠛⠿⣾⡏⠹⠷⠛⠻⠖⠃⠀⠀⠀⠀⢻⣿⣿⣾⣿⠿⠋⠁⠀⠹⠷⠛⠳⠖⠃
⠀⠀⠀⠀⠘⢿⣧⠀⣠⡿⠃⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠁⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣼⣿⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠟⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡶⠛⠉⠀⠀⠀⠉⠉⠛⠷⢦⣄⡀
⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⣀⣰⡾⠛⠛⠷⣦⡉⠻⣦⡀
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⢿⣤⡀⠀⠀⢘⣷⠀⠘⣷
⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠸⣧⡈⠛⠷⢦⣼⣧⣤⡾⠋
⠀⠀⠀⠀⠀⠈⣷⠈⠻⣦⡀⠀⠈⠻⠶⣦⣤⣤⡾⠛
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠈⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠈⠙⠻⠶⣦⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠶⠿⠿⠶⠶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⣦⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⠶⠾⠟⠛⠻⢶⣤⣤⣤⠴⠦⣤⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⣠⡞⣀⠀⠀⠀⠀⠀⠀⠀⢠⢶⡀⠉⠓⠄⠀⣀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠘⠉⠸⠋⢠⠀⡀⠀⠀⠀⠀⠘⠈⠣⠀⠀⠀⠀⠈⠳⣄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠉⣠⠀⣠⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣤⠖⠀⠀⠰⠛⠁⠼⠃⠀⠀⠀⠀⣰⢆⡆⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⣜⡳⢶⣤⡙⠷⣦⣀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠸⠋⠞⠁⠀⠀⠀⠀⠈⢿⡿⠄⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠀⠀⠀⠈⠙⠂
⠀⠀⠀⢀⣀⣀⣿⠀⠘⠃⢀⣀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⢸⡀
⠀⠀⢸⣏⠉⠁⠈⠁⠠⠞⠋⠉⠙⠛⠶⣄⣀⣠⣤⣤⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡳⠃⠀⠀⢀⣀⡾⠞⠀⣧⣀⡀
⢀⡾⢛⡉⠀⠀⢀⡀⠀⢀⣀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⠤⠞⠛⠻⢦⣄⠀⠀⣠⡴⣦⣀⠀⠠⠞⠉⠙⠳⣦⣴⠟⠉⠙⠓⠦⣌⠉⠙⢷⡄
⠘⠷⠶⠛⢶⣴⣾⡙⢷⣼⣏⣿⣇⠀⠀⠀⠀⠀⡆⣸⠀⠀⠀⠀⠀⠀⠀⠀⡈⡅⠈⠀⠀⠀⠙⠳⠄⢰⡄⠀⠀⠀⠁⠀⠰⡄⠀⠀⠀⠁⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣭⣉⡁⠈⠳⢤⣤⡤⠞⠻⢷⣄⠀⣀⣤⣄⡀⠀⢀⣷⣿⣄⠀⠀⠀⣀⣤⣄⡾⣿⠀⠀⣀⣀⣀⣸⢿⠀⠀⣠⣦⣄⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣶⣤⣀⠀⠀⠀⠀⠙⠛⠋⠁⠉⡟⣿⡟⠉⠀⠉⠻⠶⠟⠋⠀⠈⡟⡿⢶⠊⠁⣠⣾⠛⢾⣥⠾⠋⠀⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⠶⠶⣶⣦⣤⣤⣼⣷⣿⣁⣀⣀⣀⣀⣀⣀⣀⣠⣴⣷⡿⠿⠾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣄⡀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⡻⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⣼⣿⣾⣿⣿⣿⣿⠉⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⢿⣿⢿⡁⣿⠀⣿⠀⣾⡇⣿⠁⠶⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⣽⣾⣷⣭⣤⣿⣷⣭⣧⣿⣦⣭⣾⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣛⢻⡟⢺⡟⣛⣻⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠸⠿⢠⡇⢸⡀⠭⢾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⢶⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⠔⢡⠟⠀⠀⣶⡶⣶⣶⣤⣀⠀⠀⢠⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⣼⣷⡥⠖⠉⠀⠄⠀⠀⠑⠲⠬⠭⠿⠃⠐⢻⣾⢷⠋⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠈⣎⣣⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣴⣟⠉⠉⠉⠁⠀⠀⣀⣀⣀⣀⣤⡽⣿⠀⠈⠁⢀⣹⣞⢳⣄⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢠⣾⢿⡀⠀⠀⠀⠘⣇⣿⢉⡟⣻⠉⣟⢹⡏⣹⢈⣇⢸⣧⡟⠀⠀⠀⠈⡹⢻⠯⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⡛⠋⣇⠀⢠⡄⠀⢈⡿⠋⠙⠉⠛⣛⣛⣛⣛⡉⠉⠉⣍⢧⡀⠀⠀⠸⣡⠋⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡳⣄⢳⣠⣿⡶⠀⠀⢠⢏⣴⣀⠔⠓⠋⠉⠉⠉⠀⠉⠓⠒⠺⢷⣿⠀⠀⠀⢀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣾⣾⣕⡵⡇⠀⠀⢸⣿⣀⣂⣈⣀⣁⣀⣀⣀⣀⣀⣀⣄⣠⣼⣿⡆⠀⡴⢺⡆⡤⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣯⡽⡿⣿⣟⠻⢷⣄⠀⢸⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⢸⡇⠀⣵⣾⡯⣁⠲⠄
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠈⠀⠰⡇⣿⠈⣏⢻⡁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⢀⠀⢸⡇⠀⠀⠈⠀⠀⠉⠀⣀⠀⠀⠛⠀⠰⠆
⠀⠀⠀⠀⠀⣠⣿⡟⢷⢆⡀⠃⠀⠀⠿⠋⠀⢸⡄⢇⠀⢸⠀⣏⠖⠦⠆⠛⠛⠆⡿⠋⠗⠀⠚⠋⠀⢸⡇⠀⣤⡀
⠀⠀⠀⠀⠀⠘⢎⡀⠀⠳⢝⢦⡀⠀⠀⣦⠀⠀⢷⠸⡄⢸⠃⠇⠀⠀⢀⡀⠀⠀⠋⢀⡀⢀⣤⣄⠀⢸⡇⠀⠉⢀⡴⡲⢋⠏⡽⡛⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠙⠿⣦⣄⠀⠀⠀⠈⣇⣱⢸⡇⠀⠯⣅⢸⣙⡇⣿⠀⣏⣀⠸⣗⣋⠀⢸⡇⠀⠀⡞⠈⠜⡱⣊⠜⡰⢩⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠙⠲⣄⡈⠛⢷⣤⡀⠀⠀⠁⢸⡆⠀⠛⠋⢸⠁⠀⠀⠀⠀⠁⠀⠈⠉⠀⠈⡇⠀⢸⣦⠈⠎⡠⠇⠜⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣉⠻⢶⣄⠀⢸⣇⣀⡀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣼⡇⠀⠀⠓⠾⠤⠧⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⠙⠦⣝⡆⢸⡿⣟⠟⠻⠛⠿⠿⠿⠟⠛⠛⠛⠛⢛⣻⢿⡇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣶⣶⣾⣷⣶⣶⣶⣶⣚⣛⣿⣭⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠷⠷⡖⢷⠏⠀⠀⠀⠀⠀⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⣿⣸⡿⢓⡿⠁⠀⢸⠟⠳⠛⠀⠀⠀⠀⣡⠃⠀⠀⠏
⢤⣈⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠿⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠫⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠖⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠤⣀⢀⣄⡀⠀⠀⢎⠑
⠤⣤⡄⠀⠀⠀⠀⢸⣿⣇⠈⡰⠨⣷⠀⠀⠀⠀⠀⠀⠀⠰⠒⡄⠀⠀⠀⠀⠀⠀⠀⣀⡎⠁⠀⠁⣨⠋⠀⠀⠈⠑⢄⢂⣀
⠂⠐⡇⠀⠀⠀⠀⠘⣿⣿⣧⣶⣿⡟⠀⠀⠀⠀⠀⢀⠞⠀⢀⠦⠀⠀⠀⠀⢀⠀⠼⠂⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⣷
⠤⠔⠁⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠐⣯⠉⠂⠀⢰⣦⠶⣄⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠉⠋⠀⠀⢀⡺⢠⠞⠁⠀⡇
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⣀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠐⢘⠓⠢⣤⡄⢈⠃⢸⠀⠀⣨⠇⠀⠀⢀⢢⣬⣳⡀⢀
⣻⠀⠀⠀⠀⠀⢀⠎⠰⠀⢋⣯⡀⠈⡿⠉⢳⡄⠀⠀⠀⠀⠻⣄⣈⣼⠓⠀⠀⠠⡇⠀⠈⠤⠖⠁⠀⠀⠀⠀⠛⠷⠚⢠⣯
⠁⠀⠀⠀⠀⠀⠘⣀⣀⠜⡸⠉⠀⣼⡿⢄⡾⣏⠑⣦⠀⠀⠀⠀⠀⠁⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣀⣤⣄⡀⠀⠀⠀⠈⠛⠋⠳⣶⣯⣟⣁⣜⣿⠋⢠⣿⠆⠀⠀⠀⠀⠉⠛⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠁⠃⠈⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣼⡄⡀⠀⠀⠀⢠
⣶⢓⣤⡾⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣄⠔⠀⠀⠀⠀⡈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠘
⠙⠛⠉⠀⣾⣝⢪⠀⠌⠷⡄⠀⠀⠀⠀⠀⠀⠀⠋⠙⣽⠃⠀⠀⢀⠛⠑⠬⣦⡀⠑⢄⠀⠀⠀⠀⠀⡀
⣤⣄⣀⠀⢿⣿⣌⣤⣴⣷⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠻⢤⣄⡀⠨⡛⢦⣀⠹⢷⣀⡄⢰⠁
⠓⠊⢉⣑⡈⠛⠿⠿⠿⠋⠀⠀⠀⢀⣔⠴⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣤⡂⠌⣷⣾⣿⡟⠦⡀⠀⠀⠀⠀⠀⢀⣾
⠀⠄⠀⠀⡅⠀⠀⠀⠀⠀⠀⢀⠔⠑⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣝⣶⣿⡟⠬⡙⠢⢌⡲⢄⡀⠀⠀⠘⣿
⠷⠄⠤⠈⠀⠀⠀⠀⠀⢀⢴⠅⠀⠠⠖⠀⣰⠎⡇⠀⠀⠀⢀⣤⣄⣤⠀⠀⠀⠀⠈⠻⢽⡻⣦⣼⡌⢲⣽⣦⣉⣦⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⢐⠕⠃⡠⠂⠀⢀⢎⠟⡴⠁⠀⠀⠀⢠⡇⠈⣋⠀⠀⠀⠀⠀⠀⠀⠙⠫⡉⢙⠻⣿⣿⣿⣿⡗
⠀⠀⠀⠀⢀⡀⡪⠆⢀⡴⠊⠀⠀⢠⢂⡞⢠⠁⠀⠀⠀⡠⡋⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣿⡿⢿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⡶⠋⠀⠀⠀⡠⢓⠌⢠⠃⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠙⠋
⡦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡴⢡⠟⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣶⡿⢹⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠁⠀⠀⢀⢀⣰⠄⠀⠀⠀⣾⣴⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⣠⣿⣣⠟⡙⠻⣾⣽⠇⠠⣏⡋⢷⡀⠀⠀⠀⢰⠰⠄⠠⠔⣡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠔⠀⠀⠀⠈⡇⠀⠀⠈⢦⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠤⠂⠀⠀⠘⠋⠁⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠑⠦⡀⠑⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⢠⠔⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⢤⠰⠄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣆⣠⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠰⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⢷⣀⡀⠀⣀⣀⣀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠈⠛⠛⠋⠉⠉⠉⠓⢆⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠖⠶⠶⠖⠃⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠉⠀⠀⠙⠦⢄⣤⣀⣤⠜⠉⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣰⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠟⠛⠒⠛⠟⠓⠺⠿⠿⠶⠞⠛⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⣀⣀⣴⣟⣡⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢀⣤⠀⠀⣴⣆⣤⡀⠀⢀⣾⠏⠁⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⢸⣧⢶⡎⣿⠆⣸⢹⡏⢹⣷⢤⣾⠋⣷⠄⢀⣤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⡇⢸⣿⢸⡇⣿⢠⠃⣼⡇⣼⡟⣼⡿⢽⠏⠀⣼⡿⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⢴⣄⣴⢦⣸⣿⡄⡘⣷⠞⣿⠘⠃⣿⡏⠐⣿⠇⠈⠀⡿⢠⡟⠀⣰⣿⣣⢞⣿⠿⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⣿⡘⢷⠇⠀⠀⠀⠀⠀⠛⠀⡄⡿⠀⠀⠀⠀⣾⣁⠞⠁⠉⢠⡿⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠳⠃⠀⠀⣀⣄⡀⠀⠀⠀⠀⠈⠁⢀⣤⠀⠀⠉⠁⠀⠀⢀⡀⠀⢿⣠⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡀⠀⠀⢸⣿⡁⢁⡠⣤⡄⠀⠀⠀⢈⣋⠀⢀⣴⢦⠀⣰⣟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇⠀⢀⡠⣿⡏⠁⢠⣿⠗⢳⣦⠔⣿⡏⢀⣿⡇⠀⠀⢻⣿⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢏⣀⣿⠇⢀⣾⣿⠀⢸⡇⠀⣿⣡⠏⢻⣷⣤⡴⠋⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⢀⠀⠉⠀⢀⡞⣼⡇⠈⠛⠁⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⢀⡀⢠⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢡⢲⠀⡘⢠⡿⠀⣠⠄⣄⡄⣴⠀⣦⡦⠠⠆⢸⡇⡷⠯⠎⢉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⡀⠀⠀⠀⠈⠉⠀⠀⠙⠂⠘⠀⠉⠀⠀⠉⠀⠀⠀⡀⠀⠀⢀⣸⣷⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣿⠛⠀⢀⢶⣧⢠⣤⠀⠀⠀⠸⠇⠀⢀⣤⠤⠀⢠⣿⡫⠃⠀⠈⠹⡿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠊⢸⣿⠁⣿⡇⠀⢠⣿⠀⢀⣾⡏⠀⠀⣿⣟⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⣿⠁⢠⠺⣿⡴⠋⢿⣷⡤⠊⠙⢿⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡴⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣴⡿⠃⠀⠉⠻⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣤⡾⠟⠛⢻⣿⠟⠁⠀⠀⠀⠀⠀⠈⣿⡟⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣴⡿⠋⠁⠀⠈⠉⠀⣀⣀⣼⣧⣄⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣁⠀⠀⠀⠉⠁⠀⠀⠀⢀⣴⠿⠛⠉⠉⠉⠉⠙⠷⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡿
⠀⠀⠀⠀⣠⡿⠋⠁⠀⠀⠈⠛⠃⠀⠀⠀⠀⢀⣀⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣧
⠀⠀⠀⢰⡿⠀⠀⣀⡀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠁⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⢸⡇⠀⠀⠙⠻⣷⡀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠿⢿⣄
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠘⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠶⠶⠶⠶⠶⠶⠾⠿⠿⠛⠛⠋⠉⠀⠀⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠙⢷⣤⣄⠀⢀⣿⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⢻⡍⠉⠉⠉⠉⠛⠛⠛⠛⠛⠻⠿⢷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⣷⡀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠉⢻⣧⠀⠀⠀⠀⠈⠉⠉⠉⢉⠉⠛⠛⠛⠛⠛⠻⠿⠶⠶⠶⠾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠘⣧⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⢀⣤⡶⠟⠁⣀⠀⠀⠀⠀⢠⣤⣴⣿⣥⡸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠘⣧⠀⠀⠀⢠⣿⠁⠀⠀⠀⠈⠁⠀⢀⣼⠟⠀⣠⣾⠃⣠⣿⠋⢠⣾⠀⢀⣤⡶⢶⣤⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠘⣧⡀⠀⠀⢻⣧⣀⠀⠀⢀⣠⣴⣿⠏⣀⣼⣿⠃⣰⡿⠁⣰⡿⠁⣰⣿⣧⣴⠾⠟⣠⡄⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠈⠻⠶⠶⢶⣾⣿⣿⣿⣿⣭⣄⣻⣿⣛⣙⣿⡾⠻⢷⠾⠿⢷⠾⠻⢷⣤⣤⣤⠾⠛⠁⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⢶⣶⣤⣤⣤⣤⣄⣀⣉⣉⣉⡉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠶⠶⠶⠶⣶⣶⣦⣤⣤⣤⣤⣄⣀⣀⣀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠷⠶⠶⠶⢶⣦⣤⣤⣤⣤⣀⣀⣀⣀⡈⠉⠉⠉⠉⠉⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠷⠶⠿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡶⠟⠻⠶⠟⡋⣉⠛⢛⣋⣉⡙⠓⠞⡛⠛⠳⣤⡶⠶⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠞⠛⢛⣁⠠⠩⣉⣀⣐⣛⣛⡛⠀⠱⠶⠷⣶⣶⠒⢒⣤⣭⣍⣑⡀⠀⠶⠤⠍⢩⢩⠙⠷⣤⡦⣄
⠀⠀⠀⠀⠀⢀⡤⠴⠏⠉⡁⠒⠺⠛⠛⠰⠿⣿⣿⣿⠟⢉⣭⣿⣷⣦⣤⠀⢁⡴⣋⣙⣛⡛⠛⠁⠰⣿⣿⣶⡶⢒⣶⣥⣄⠀⠈⠛⠳⣄
⠀⠀⠀⠀⣠⣏⡓⠀⠌⠛⠻⠛⣩⣿⣶⣶⣤⣤⠀⢀⣔⣉⣉⣉⣉⣉⣀⠀⠘⠿⣿⣿⡿⠋⣽⣿⣶⣤⣄⠈⢠⢎⣙⡛⠻⣷⣿⣶⣦⡸⠷⣦
⠀⠀⠀⢰⡿⡤⠤⠐⠚⠟⠀⣾⣶⣶⣶⡤⢤⣄⣀⡃⠘⠛⠟⠿⠁⣈⣽⣿⣳⣶⣤⠈⢠⢎⣈⣭⣭⣉⣉⣁⠁⠛⠿⠿⠂⣠⣭⡍⠛⢐⡛⢯⡀
⠀⠀⠀⠸⣧⠙⠻⣕⣆⡠⣄⢉⣽⣋⡉⠁⠠⠾⠿⠿⢿⡷⠂⢀⣾⣥⣤⣬⣤⣤⣍⣀⣀⠙⠻⠿⠟⠁⡰⢿⣿⢿⣶⠄⠐⠁⣀⣠⠄⣻⠾⢸⡇
⠀⠀⠀⠀⠘⢷⡦⢌⡉⠙⠶⠶⢮⣛⣓⡲⢴⣲⣶⣲⢶⠦⢤⣄⣉⠛⠳⠿⠟⠋⠼⢽⠿⠿⠷⠂⠀⠚⠀⢀⣉⢀⡠⢖⣷⣋⡴⠛⠛⣁⣴⠟
⠀⠀⠀⠀⠀⠀⢻⣗⢮⣕⣲⠤⣄⡉⠉⠉⠓⠒⠒⢮⣕⣾⠯⣽⣻⣖⣛⣓⠶⣖⣛⣲⠶⣶⣿⣒⣋⡭⢭⣭⡴⠓⠶⠛⢁⣉⠥⣖⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣟⢿⣿⠝⢗⠾⢭⣽⣒⣀⣀⠀⠀⢀⣀⣀⣉⣉⣀⣈⠙⡋⢁⠉⠉⠉⠀⠉⠉⠀⠀⢠⣔⣲⣾⣭⡗⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣕⣕⢕⠵⢵⢝⢝⠝⢝⢟⢗⠖⡖⠶⠶⠶⢶⠶⢶⢶⢶⢶⢖⣛⢛⣛⢏⢝⢝⢕⣴⣟⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠷⠵⣥⣵⣅⣅⣅⣁⣁⠑⠐⠀⢐⢐⢐⣐⣑⣑⣓⣑⣵⣵⠴⠖⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣠⡀⠀⠀⣀⣠⣤⣤⣤⣤⣀⠀⠀⢀⣀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⢠⣾⠟⠛⢿⣦⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⢻⣿⠛⠉⠁⠀⠀⢸⣿⠀⠀⢸⣿⡟⠛⠛⠋
⠀⠀⣾⡟⠀⠀⠘⣿⡆⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⡇
⠀⠀⣿⡇⠀⠀⠀⠻⠃⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣷⣶⣦
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡏
⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⣼⡿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠙⠻⠿⠿⠿⠃⠀⠀⠀⠘⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⠀⠀⣶⣶⣶⣤⣀⠀⠀⠀⢰⣦⠀⠀⢠⣶⣶⣶⣶⣶⠀⠀⣴⣶⣶⡄
⠀⠀⣴⣶⣶⣄⣸⣿⣿⡿⠀⠀⣿⡇⠈⠙⣿⣆⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣇⣠⣶⣶⣦
⠀⠀⠹⢿⣿⣿⣿⣿⡿⠁⠀⠀⣿⡇⢀⣠⣿⡏⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠉⠻⢿⡿⠁⠀⠀⠀⣿⡿⠿⠛⠋⠀⠀⠀⢸⣿⠀⠀⢸⣿⡿⠿⠟⠀⠀⠀⠀⠘⢿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣧⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠉⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⡤⠂⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠈⡿⡄⠀⠀⣠⡗⠋⠉⠳⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣼⡧⠤⡀⢸⡇⢘⠀⣼⠃⡇⢀⡴⢶⠧⢤⡀
⠀⠀⠀⠀⠀⡇⠙⠀⠀⣠⠔⠋⠁⠀⠙⠶⠇⠈⠓⠊⠀⠻⠞⠁⠘⠤⠊⠀⠀⠍⠳⢄⠀⠀⠸⠉⡇
⠀⠀⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⣠⡄⢰⣶⣆⢰⣿⣇⢸⣿⣶⡄⢰⣶⡆⢠⣤⢀⡀⠀⠙⠂⠤⠘⠁
⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⣿⠀⣿⣷⢸⣿⣿⣿⣿⣿⢸⣿⢹⣿⢸⣿⣣⣿⡟⣸⡟⢰⣶⠀⢀⡀
⠀⠀⠀⠀⠀⠸⣿⡻⣿⣼⣿⡄⢹⣿⢸⣿⡟⣿⢹⣿⢸⣿⣼⡿⢸⣿⣿⠋⠀⣿⡇⣿⣿⡇⣾⡿
⠀⠀⠀⠀⠀⠀⣿⣇⣿⠃⣿⡇⢸⣿⠘⣿⡇⠀⢸⣿⢸⣿⠟⠁⣸⣿⣿⠀⢀⣝⠁⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠹⣿⣼⡿⠀⣿⣧⠀⢸⣿⢸⣿⠀⠀⣿⡟⢿⣷⣾⡟⢸⣿⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠈⢋⣥⣄⠈⣥⡄⣠⡁⣀⡁⠀⣠⢬⡁⣀⣉⣉⠀⠘⠛⠀⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠇⣿⡏⢹⡇⣿⡇⣼⡇⠀⠃⣿⣧⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠹⣷⡀⣿⡧⠼⠁⣿⡇⣿⡇⠀⡄⣿⡇⠀⠀⢻⡷⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠸⡄⣸⠇⣿⠇⠀⠀⣿⡇⠹⣧⠜⠁⢿⠧⠤⠀⣶⣤⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢡⠀⠈⠁⠀⠀⠀⠀⠀⢰⣶⠀⠀⣀⣄⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠐⠁⠀⢀⣠⣤⡴⠛⣷⡀⢰⣶⠀⣸⣿⣩⠃⡔⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠖⠋⢸⣿⢁⢠⣿⠇⢻⡏⢀⢻⣿⠀⠀⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢆⣼⠟⠀⠸⠷⠃⠀⠻⢦⣀⡀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡴⠒⡂⣻⣟⠀⠀⠀⠀⣂⠔⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢔⠀⣿⢋⣙⠶⢴⣊⡁⠀⠠⠀⠀⠀⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⣫⠤⠤⢤⣤⣌⠉⠛⠒⠶⠶⠤⠴⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠔⠊⢀⣈⡻⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣆⠻⠿⠿⠻⢾⣻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶⣶⣶⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⣴⠞⠛⢻⠞⠉⠀⠀⠀⠀⢻⡟⠛⢦⡀
⠀⠀⠀⠀⠀⣀⣀⣴⠟⠛⠛⠿⠁⠀⠀⢀⣤⠶⠿⠶⢶⣄⠀⠀⠀⠸⠃⠀⢈⡇
⠀⠀⠀⣰⠟⠉⠉⠙⠳⠀⠀⠀⢀⣀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢷⡄
⠀⠀⢰⡇⠀⣤⣄⠀⠀⣀⡴⠞⠋⠁⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⢸⡇⠀⠀⠙⣷⠞⠉⠀⠀⠀⠀⠀⠙⠳⠦⣤⣤⣤⣤⣤⣤⣤⡤⠶⠞⠛⠉⠻⣦⡀
⠀⠀⠀⠹⢦⣄⠀⣿⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀
⠀⠀⠀⠀⠀⠸⡆⠹⡆⠀⠀⠉⠉⠉⠉⣉⣽⠿⠿⣟⠛⠒⠲⠶⠶⠶⠶⢤⣤⣤⣤⣄⣀⣀⣙⣷⣄
⠀⠀⠀⠀⠀⠀⢻⡄⢹⡄⠀⠀⠀⣠⡞⠋⠀⣀⣤⠟⠀⠀⠀⠀⢀⣠⣶⣀⠶⠀⠀⠀⠀⠉⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢻⡄⢳⡀⠀⠀⣿⠀⠀⠀⠉⠀⣰⠟⢀⣼⠃⣼⠏⣰⠇⣠⡴⠶⣦⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠳⣤⣀⣙⣷⣦⣤⡶⠻⣯⡴⢿⣧⣾⣇⣼⣏⣴⣟⣛⣛⣡⠶⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⢤⣭⣭⣭⣉⣉⣉⣛⣛⠛⠛⠒⠷⠶⠾⠶⠮⠭⣭⣥⣤⣤⣄⣀⣀⣘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠓⠒⠶⠶⠶⠤⢤⣤⣤⣤⣀⣉⣉⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡂⢀⠖⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠊⠲⠃⠈⠀⢀⠜⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠴⢚⣣⣴⣶⠖⠀⢀⠀⠀⢤⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡄⠐⠲⠀⢁⠊⠉⡖⡀⣅⠒⠀⢢⣄⠀⠀⠀⣴⠊⠀⠀⠀⠉⠉⣉⡴⠶⠄⠘⠦⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠒⠉⠉⠀⣀⠀⠀⠂⡃⠀⣀⡤⠀⠒⣃⣴⣲⣦⡌⠀⠀⠀⣻⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣶⣶⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡀⠀⠐⠀⠘⠶⠀⣤⡙⠷⠀⠾⠃⠶⢋⣰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠐⠀⠀⠙⠛⠷⠶⠦⠀⠉⢀⠐⣄⢀⣴⣿⠿⠿⠿⠿⠿⠿⠟⣀⡤⢤⠀⣀⢄⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠟⠁
⠀⠀⠀⠀⠀⠀⣌⠀⠈⠂⠸⠖⠀⣀⣀⣉⣛⠁⠀⠀⠈⠛⣁⠀⠀⣄⣀⡐⠶⣶⣶⡤⠄⠀⠁⠊⠉⠀⢀
⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠠⠴⠿⠛⠋⢀⣴⠟⢡⡆⠀⣿⡆⢡⣤⡙⠛⠂⠀⡀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠀⣿⡷⠀⠉⠁⠈⠛⠷⡄⠀⠘⠞⠀⠀⠀⠀⣠⠴⢸
⠀⠀⠀⠀⠀⠀⠀⠙⣦⣤⠀⠀⠐⠄⠋⠀⠀⠀⠘⠋⠀⠀⠘⠒⠃⢀⠀⠀⠀⠀⢀⣀⣠⡾⢫⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⠟⢶⠚⢦⣤⡀⢀⡁⢀⠀⠀⣀⡀⣀⣀⣀⡄⠀⠐⠒⠋⠉⠀⢁⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠈⠁⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠄⠀⠀⣠⣀⣄⣤⠤⠤⠀⠒⠈⠉