Grocer Emojis & Symbols

⠀⠀⠀⣼⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠠⠆⠀⠀⠀⣀⠠⠐⠂⢩⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣥
⠀⠀⠀⠀⠈⢳⠀⣠⡾⠀⠀⠻⢦⡀⠀⡀⠀⠀⠈⠲⢤⣤⠤⠂⠉⠀⠀⠀⠈⣿⠈⢳⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣤⠜⠛⠸⡟⠁
⠀⠀⠢⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠙⢾⣅⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⢤⣴⡿⢀⢸⣿⣦⡀⠀⠠⠋⠉⠀⡾⠿⣿⣇⡀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣨⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⢠⠀⠁⢠⠀⢀⣀⣼⣿⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠈⠳⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢸⡁⢀⡀⠀⠀⠀⢠⡀⠀⠀⢀⣼⣿⡟⠀⠀⠠⠃⠀⠀⠘⠀⠈⠻⢿⣿⡀⠀⠀⢸⡿⠛⠀⠀⠀⠄⠀⠀⠀⢀⣼⣿⠃⠀⠀⠀⠀⠺⣦
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣿⢿⣧⣾⣿⡏⠀⠀⠰⠁⠀⢠⢠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠰⠀⠀⠘⠉⠀⠀⢀⠠⠾⠗⠀⠈⠷⠀⠀⠹⡆
⠀⠀⢀⡆⢀⣠⠄⠀⠀⠘⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠘⠉⠀⠘⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠈⡳⠚⣻⠶⡖⠠⣾⣤⡀⠀⠀⠈⠁⠀⠀⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢰⠀⠀⠺⣿⡶⠀⠀⠀⠀⠀⡀⠤⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⣤⡯⠀⠉⠀⢻⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢘⠀⠀⣶⣿⠓⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣾⣶⠀⠤⡤
⠀⠀⠀⠛⠘⠃⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢁⣻⣧⣆⣀⠀⠀⠀⠻⠆⠀⠀⠹⣇⠀⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⣰
⠀⠀⠀⠀⣀⡀⠀⠀⠀⣸⣷⠸⡇⠀⠀⠷⠔⡇⣤⣽⡿⢿⣯⠳⡄⠀⠀⠀⠀⠤⠠⣿⣷⡄⠀⠀⠀⠀⣠⣄⡈⣀⡀⠉⠀⠀⠀⣀⣀⠀⢀⠀⡀⠀⣀⡀
⠀⠀⠀⠀⣿⡁⠀⠀⠀⠘⠿⠄⠀⠀⠀⠠⠄⠙⡁⠁⠀⠀⠙⣷⢹⡄⠀⠀⠈⠀⠀⢸⣿⣿⡄⠀⠀⣠⣻⣿⢹⣿⣿⠀⠀⠀⠀⠈⠻⠷⠎⢘⠿⠚⠃
⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⢀⣲⠔⠀⣴⠂⠁⠀⠀⠀⠀⣿⡞⠁⠀⠀⠀⠀⠀⢸⠿⠟⠀⢀⡀⠘⠿⣿⡆⢿⡿⠀⣀⣀⠀⠀⠀⢀⠰⠃⣴⡶⣶⣶⣆
⠀⠀⠀⠀⠉⠀⠀⢀⣀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣰⠉⡷⡈⢿⡀⠀⢿⣷⣤⢡⣇⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠠⠀⣤⣠⣤⡴⠀⠀⠀⣀⣀⣀⣀⣤⠀⠀⣀⡄⠀⠀⠘⣧⣑⢼⡾⠁⢰⣮⣿⣿⡗⠙⠉⠛⠁
⠀⠀⢀⣀⣤⡴⠖⡁⠀⠀⠀⠻⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢠⡀⠈⠉⠉⠀⠀⠀⠀⢹⡟⡶⠭⠛⣚⣟⣿⡄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠉⠻⠟⠀⠀⢀⡄
⠀⠀⠀⠀⠉⠀⣠⣡⡶⠠⢤⡤⠦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣿⡆⠀⠀⠀⣐⣦⠀⠈⠐⠫⠔⠃⠉⠉⢿⠓⣀⡀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢠⣽⡿⢿⡔⠋⠁⠀⠀⢠⣀⡀⠀⠀⠈⣷⠀⠀⠈⠋⢀⣤⣾⣫⠏⠀⠀⠀⣠⠇⠀⠀⠄⠈⠸⠏⠀⠀⠀⠀⠀⢠⠀⠀⠈⢀⠇⠀⠀⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⣧⣼⠇⠀⠀⠀⢀⡴⠋⠉⠙⢷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⢛⡿⣿⡿⣿⡀⠀⠀⠀⠀⠀⣀⡤⠚⠃⠈⠳⣄⠀⠀⠀⠀⠀⠀⢀⣿⢇⣿⢿⠀⠀⠀⠀⣸⠃⣼⠛⢦⣀⣉⣉⡙⢷
⠀⠀⠀⠀⠀⢀⡶⢋⡵⠒⢉⣡⢾⣿⣧⠘⣷⠀⠀⠀⡰⠊⠀⠁⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⡾⡼⣸⡿⢸⡤⠀⠀⣰⠟⡴⠃⠀⠀⠉⠀⠈⡷⢸⡇
⠀⠀⠀⠀⠀⣿⠁⡼⠀⡔⢉⠔⣿⡏⡏⣇⠸⡇⠀⢰⣅⠀⠀⠀⠀⠀⠀⠀⠤⠴⣧⠀⠀⠀⢰⠇⡇⠹⠃⢿⡇⠀⢰⢣⡞⠀⠀⠀⠀⠀⢀⡼⢃⡞
⠀⠀⠀⠀⠀⣿⠀⢿⠘⡇⣿⢰⣳⢃⡇⡿⢀⡇⠀⢸⡀⠀⠐⠤⠀⠀⠀⠀⠀⣀⡟⠀⠀⠀⣼⢸⡀⠀⠀⣸⠁⠀⢸⡌⠳⠤⠶⣄⠀⠀⣸⢣⡏
⠀⠀⠀⠀⠀⠹⣧⡈⢧⢱⣿⣾⣫⢞⡴⢃⣼⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢈⡽⠃⠀⠀⠀⡏⠸⠇⠀⢠⠇⠀⠀⠀⠙⠛⠲⡆⠈⠓⠚⠋⣼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣿⣟⣛⣉⣤⠞⠁⠀⠀⠀⠀⠈⠳⡄⣰⠖⠚⠛⠉⠀⠀⠀⠀⠀⣧⣀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠈⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣷⡀⠀⠀⠀⠀⠀⠀⡾⠀⠘⠓⠒⢺⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⢰⠃⠀⣤⠀⠀⡼⠀⠀⠀⠀⢀⡴⡖⠉⠉⡇⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣘⣧⡴⠋⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⢀⣧⣀⠀⡀⠀⢀⠇⠀⠀⢀⡾⠋⠀⢿⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠁⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣼⠁⠈⢉⣩⣤⡞⠀⠀⠀⡟⠃⠀⠀⠀⠀⠀⠀⠀⢹⣄⡴⠃
⠀⠀⠀⠀⠀⡾⠀⠀⢀⠀⢠⣄⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢰⢟⡆⠀⠀⠀⠀⢠⡷⢤⣀⠀⠀⡜⠀⠀⠀⠈⣇⠀⠀⠆⠀⣄⠀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⢷⠀⠀⣾⠆⠘⠿⠀⠀⠀⣿⣿⠃⠀⠀⠀⢰⡟⢠⠃⠀⠀⠀⠀⣼⠀⠀⠠⢤⡾⠁⠀⠀⠀⠀⠙⢦⣀⡀⣀⣸⠟⠁
⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⠀⡿⢿⢸⠀⠀⠀⠀⢠⡇⠀⠠⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⣀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠹⣄⡀⣀⣤⣤⣴⣾⡿⠟⠀⠀⠀⠀⠀⣿⢸⡏⠀⠀⠀⠀⢸⠋⠂⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢞⣩⡤⡤⣄⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⣤⣀⠀⠀⢸⡀⣠⠏⠀⠀⠀⢀⣤⠶⠒⠶⣄⠀⠀⠀⣼⣳⠏⡁⢸⡵⣀⡹⣆⢹⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡇⠀⠈⢣⡉⢧⡀⠈⠛⠁⠀⠀⠀⡴⢋⡴⠛⠛⢦⢹⡆⠀⠀⣿⣿⢺⡽⣠⣄⠳⠆⣿⢸⡇
⠀⠀⠀⠀⢠⡞⠉⢠⡇⠀⠀⢹⡿⢦⡀⠀⠀⢠⡏⠀⠸⠁⠀⠀⠀⠃⠈⡇⠀⠀⠀⠀⣀⡼⢡⡿⠀⠀⠀⣸⠀⣧⠀⠀⢻⡜⢦⡀⠳⠞⢀⣴⢃⡼⠁
⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠘⠀⠈⢻⡀⠀⢼⠀⢠⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡼⠋⡴⠋⠀⢀⡀⠀⠙⣦⠘⡆⠀⠀⠙⠶⣭⣙⣛⣩⡵⠞⠁
⠀⠀⠀⠀⠈⢻⣶⠀⢀⡴⠀⠀⢀⠀⣼⠁⠀⠘⣧⠘⣆⠀⠀⢸⣀⣠⡟⠁⠀⠀⢸⡃⠸⣇⣀⡴⠛⢷⡀⠀⣸⠀⡿⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠿⢧⣤⡤⠾⠞⠁⠀⠀⠀⠈⠳⠿⣦⣄⣼⣿⠉⠀⠀⠀⠀⠘⠷⣤⣬⣥⠴⠶⣌⠓⠚⢁⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⡬⣥
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠔⠄⡈⠁⠠⡤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⠘⠁⢤⠁⠀⠀⠀⣓⠀⠀⠀⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠐⢨⣖⠋⠠⠤⠄⠀⠀⠈⠓⠉⠁⠀⠀⠀⠉⠑⠌⠀⠀⠀⠀⠀⠉⢐⠢⠠⠀⠄⠀⡀
⠀⠀⠀⠀⢀⠀⣠⣆⠀⡈⠛⠀⠀⢰⠑⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠝⣶⡀
⠀⠀⠀⠀⡁⡨⠋⠀⠐⠤⠀⠀⠀⠈⠀⠀⠀⢠⠄⢀⣴⢆⡴⣊⡉⣉⡀⢀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠇⢀⠸⡣
⠀⠀⠀⠀⡜⡀⣠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠧⣿⠼⠵⣿⢧⢿⡿⡼⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡜⡞⠈⣄⠒⠀⠀⠀⠀⢠⡖⢰⢲⣷⠞⣉⡁⣀⡉⣸⣢⡇⢀⣘⡀⡆⣚⣁⢆⣀⠀⣀⡀⠀⠀⠀⠀⢠
⠀⠀⢰⠋⠀⠀⠉⠀⠊⠂⠀⠀⠀⢀⡟⠞⠿⠾⠼⠿⠹⠷⠛⣦⠿⢿⣼⠿⠿⠝⠿⠟⠹⠾⣵⠇⠀⠀⠀⡰⠋
⠀⣆⠨⠀⢆⢀⣚⣐⠒⢤⠀⢀⢐⠮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠁⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣰⠃
⠀⢹⢰⠀⣴⠥⠒⠒⠂⠊⠂⡀⠡⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠊⠁
⠀⢸⡄⢈⡵⣊⠠⠀⠀⠀⠀⣉⢄⠤⠀⠄⠀⠀⠀⢠
⠀⠈⠾⢯⢚⡥⠀⠀⢀⡠⠚⠁⣠⣞⠛⠉⠻⢿⣕⠓⠢⢤⣁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⢀
⠀⠀⢸⢣⠊⠀⠀⠠⠂⡴⠯⡢⡀⠀⠑⠄⠀⠀⠈⠳⣄⠀⠈⠳⣈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡘
⠀⠀⢈⠆⡐⢀⠌⠠⠊⠰⠒⠆⠪⠲⠒⠀⠑⠀⠀⠈⠳⠡⠀⠀⢉⣶⠇⠀⠀⠀⠀⠀⢆⠀⣀⠀⡇⢀⠀⢠
⠀⠀⢸⠀⠁⠘⠀⢁⠈⡒⠙⢂⠨⢎⠰⡄⠀⠁⠀⠀⠠⠱⢀⡀⠂⠀⡄⢄⠀⢀⡀⠀⠈⠡⢩⢀⠂⢈⠰⠋
⠀⠀⠈⠰⠀⡗⠾⢀⠀⠀⠀⠘⠒⠺⠐⠳⡞⠃⠒⢅⠈⠰⡮⢙⠂⠻⠋⡘⢕⣁⡖⠈⢠⡀⠒⠐⠂
⠀⠀⠀⠰⣇⡦⠽⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠀⠀⠀⢁⡀⢀⡴⠀⣀⡇⢸⠨⣤⡌⢻⣠⣶⡤⣤⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⣿⠭⡀⠀⠀⠀⠀⡆⠀⠀⠀⢸⠁⠀⠀⢸⢇⣼⣻⣀⣒⠶⡌⣤⣈⣁⣠⢃⡰⠓⠦⠒⠁⢄⣄⣂⠤⠄
⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⡇⠀⠀⠀⢸⠆⠀⢰⢡⠏⢠⡏⠀⢹⡄⠘⡆⢋⠏⢛⡔⢿⣗⠤⠂⠔⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⣄⠀⢁⠀⠀⠀⣸⠀⠘⣩⠙⡆⠸⡇⠀⢸⠇⠀⡗⡁⢲⡰⠆⠶⢿⠿⠆⠚⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠺⣀⠴⡰⢮⡁⠈⠍⠀⠻⠆⠷⠀⠼⠁⠼⠃⠹⢄⢈⠡⡶⠊⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠃⠀⠄⣦⢲⠆⠀⠀⠀⠀⠁⠀⠀⠂⠄⠀⠀⠀⠀⠀⢤⡄⡀⠀⠀⠙⠀⠠⡀⠀⠀⠀⢀⡀⠀⠀⢄⣀⣓⣠⢂⣘⣀⠂⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠘⢧⡀⠀⠰⠄⠀⠀⠀⢥⠁⡔⠊⢀⠄⠀⠀⠀⠘⣣⡔⠀⠀⣀⢄⡟⠂⣄⠀⠈⠁⠀⢹⡋⠀⠀⡈⠉⠁⠀⢙⡇
⠀⠀⠀⠀⢘⠃⠀⠀⠀⠘⠂⢀⣀⣴⡀⢀⠈⠖⢀⠞⠁⢀⡄⠊⠀⠀⠀⠀⠀⠠⣡⠜⢧⢗⡫⠂⡀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⣼⠁⣀
⠀⠀⠀⠀⠀⢠⠁⠀⠈⠀⢀⠌⠈⠈⠁⠀⠀⠐⠦⠀⢀⠎⢠⠞⠆⠀⠀⠀⠠⣔⣄⣶⠨⠍⡠⠖⡧⠀⠒⠀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢠⠀⠐⢤⡆⠀⢧⠀⠂⠀⠀⠄⠀⡅⢤⣥⠔⠚⢀⡠⠆⠀⠀⠀⠙⠠⠤⠄⠠⠤⠤⠂
⠀⠀⠀⠀⠀⣀⣰⡄⠀⠀⠀⢤⠀⠀⣀⡀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠸⢗⣸⢩⡍⢮⡛⠀⠀⣄⢶⠆⠀⠀⣀⠀⠀⢦⣆⡄⠈
⠀⠀⠀⠀⡶⠚⠁⢃⣀⣀⠀⣀⠀⠀⠘⢡⠾⣼⠀⠀⠀⠀⢀⡀⠀⠀⠀⠦⠀⠀⠈⠉⠛⠃⠉⠀⠀⠷⡉⠀⠀⠀⠀⠁⠀⠀⠀⢊⢱⡆
⠀⠀⠀⠀⠀⠀⡞⠋⢀⡠⠴⠬⢤⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⡦⡀
⠀⠀⠀⠀⠀⠀⠻⣶⠃⠁⠀⠀⠀⠈⠆⠀⠀⣥⠀⡆⡄⢐⢰⠀⡄⢀⠇⠀⠂⢰⠀⠰⣀⠂⡦⢀⠀⠀⠀⠀⠀⠘⢼⣁⠄⡓⣧⢂
⠀⠀⠀⠀⠋⠀⠀⠘⠀⠁⠀⠀⠀⢀⠀⠉⠀⠤⠐⠳⠁⠬⠸⠄⠇⠨⠤⠀⠀⠇⠱⠐⠻⠀⠗⠀⠇⠁⠀⢲⡦⡄⢩⢽⣶⠲⠨⠇⡰⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠠⠀⠀⡈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡀⢀⠀⠀⠉⠹⢾⣤⡜⠿⢭⠘⣧
⠀⠀⠀⠀⣠⠀⠀⠢⡇⡀⣀⠀⣠⠅⠀⠀⠙⣣⡆⣀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠎⠃⠀⠀⣄⠀⠀⠀⠀⠘⠳⠴
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡀⠀⠀⠀⠂⠀⠀⠚⠃⠀⢀⠀⠀⡠⠠⠎⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⡠⠀⠄⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⣠⣄⣀⣄⣀⡀⠀⠀⢠⡄
⠀⠀⠀⢠⠀⡈⠀⠀⠀⢠⡀⢠⠔⠀⠀⠀⢄⠀⠀⠁⠀⠀⠁⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠛⠛⢻⣿⣧
⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠉⠲⠀⠀⠀⠀⠘⠀⣴⡀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠁⠀⢰⠇⠀⠀⠀⠀⠻⡿⢤⠂⠀⢠⣿⣿⠃⢠
⠀⠀⠀⠀⠀⠘⡀⢀⠄⠎⠁⡀⠀⠰⠄⠀⢡⣹⠓⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣦⣟⠁⠀⠀⠂⠀⡜⠀⠀⠀⠀⠾⠋⠐⠀⡀
⠀⠀⠀⠀⠀⠲⠈⠈⢀⢀⠉⠈⠀⠙⠀⠀⠈⠁⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠂

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⡠⣤⠀⠀⠀⠴⣤⡀
⠀⠀⠀⠈⠦⣤⠈⢁⡆⠐⢀⠀⠠⠷⠬⠠⠠⠄⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠰⠞⠀⠸⡷⣶⣡⣂⡼
⠀⠀⠀⠰⡶⢦⣷⣞⠁⠉⠁⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠑⢤
⠀⠀⠀⠈⡦⠂⢻⡟⠛⠋⠉⠁⠀⣀⠀⠀⠀⠐⠒⠒⠒⠂⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⡀⠛⠀⡿⠑⢳⣃⡀⠬⢁⠀⠀⢆
⠀⠀⠀⠀⢉⡼⣿⡏⠡⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⠒⠠⠤⠄⠀⠀⠀⠒⠀⠠⡤⠀⠐⠂⠉⠳⠤⠀⠲⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⢶⠾⠏⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣠⣁⣰⡶⡻⠖⠠⠆⢐⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠉⠙⠁⠀⠀⠀⠁⠈⠉⠉⠁⠈⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⡀⣏⡺⢦⣤⡤⠤⠤⠤⠄⠄⠀⢀⡀⠀⠀⠀⠾⠤⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣾⡆⠀⠀⢃
⠀⠀⠀⢀⡀⢠⡴⠟⢷⣄⠀⠉⠀⠀⠒⣀⠀⠠⡤⠔⠀⠀⠐⠆⢄⠰⡂⠀⡁⠐⣤⠴⡄⠲⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣄⠆⡮
⠀⠀⠀⠀⠉⠛⣇⢠⡈⠉⢻⣦⣀⠀⠀⣨⢓⠘⢠⠀⡈⠻⡳⣄⡏⠘⡉⠄⠸⠋⠀⢡⡠⡛⣀⠄⠒⠀⣼⣻⣿⣿⣿⣿⣿⠠⠁
⠀⠀⠀⠀⠀⠀⢉⡐⢁⣄⣀⣭⢿⣧⠉⡅⠀⠀⠈⠁⢠⠎⠁⠿⡿⠋⠀⠀⠀⣠⣐⠦⣽⣾⡫⠤⢃⠢⠛⢒⣎⣛⠛⠻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠀⠐⣈⢁⣤⠧⠇⠈⠀⢀⢋⠜⣃⣼⡷⠃⠒⣤⡾⠟⢁⡄⣸⡉⠁⢈⠺⣀⡀⠓⠈⡙⢮⡰⣊⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠧⠰⠀⠏⠀⠂⠁⡉⣽⢢⡴⢌⠃⠂⠉⠉⠑⣦⣐⣹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⠀⠀⠀⠀⠁⠀⠀⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠛⠛⠛⠶⣦⡘⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⠻⣿⠉⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠲⠶⠶⣶⣶⠿⠿⠿⠿⠿⠿⠿⣷⣦⣄⠀⠋⠀⠀⣿⣇⣀⣤⣶⠶⠶⠶⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠛⠒⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠈⠙⣿⣆⠀⢠⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⢙⣷⡦⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡉⠁⠀⠀⠤⠤⠤⠶⠒⠛⠛⠉⠉⠉⠉⠉⠛⠳⢦⣄⢘⣿⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣛⣿⣃⣀⣀⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣽⡿⠋⣍⣿⣤⣴⡶⠾⠿⠿⠶⣶⣤⣄⡀⠀⠀⠀⠉⠉⢉⣩⣽⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣦⣄⡐⠼⠶⠶⠛⣋⣡⡴⠶⠛⢋⣩⡿⠟⣿⠗⣨⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⣩⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⢟⣋⣥⣶⣶⣿⠟⠁⢀⣾⠃⣰⣿⣿⣯⢠⣤⠤⣂⡤⠄⠀⠀⢀⣠⣤⣤⣤⣤⣤⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠛⣻⡿⠛⠁⣠⣶⣿⡏⢰⣿⠉⠻⣿⣦⣝⡛⠛⠛⢉⣀⣀⣠⣤⣤⣭⣝⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠁⠀⢀⣼⠟⠀⣠⣾⠟⠉⣾⠃⢸⡇⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠛⠋⠉⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣾⣏⡀⠀⠀⢠⡾⠁⢀⣼⠟⠁⠀⠀⣿⠀⢸⠁
⠀⠀⠀⠀⣠⣾⡿⠟⠋⡉⠉⢩⡿⠟⠛⠿⠿⣶⡿⠁⣠⡟⠁⠀⠀⠀⠀⣿⠀⢸
⠀⠀⢠⣾⡿⠋⠀⠀⠀⠻⣦⣈⣤⠆⠀⠀⠀⡿⠁⣰⣿⡀⠀⠀⠀⠀⠀⣹⡄⢸⣄⣀⣀⣀⡀
⠀⢠⣿⠏⠀⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣸⠃⣰⡏⢿⣷⠀⠀⣠⣶⣿⣿⣧⠈⣿⠿⠿⠿⣿⣿⣷⣤⡀
⠀⢸⣿⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡟⠀⢸⣿⣧⣾⣿⠟⠉⠀⠘⣦⠘⣦⡴⠀⠀⠀⠉⠙⢿⣷⡄
⠀⢸⣿⡀⠸⣿⠀⠀⠀⠀⢀⣀⣤⣤⣴⣾⡇⣼⣥⣤⣾⣿⣿⡿⠁⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⢿⣷⣄⠈⠃⢀⣴⣾⡿⠟⠋⠉⠉⢹⡃⡏⠉⠉⠛⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠈⠻⣿⣦⣴⣿⠟⠉⠀⠀⠀⠈⢷⣼⣅⣧⣤⠞⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣿⡇
⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⣸⣿⠃
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⢀⣴⣿⠏
⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢠⣿⡿⠻⢿⣶⣶⣶⣶⣶⣾⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠠⢤⣤⣤⣤⣤⣶⣿⠟⠁⢀⣴⣿⡿⠁⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣶⣤⣬⣍⣉⣉⣉⣤⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⠿⠿⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠁⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠆⠁⠤⠐⠇⠂⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠀⢠⠅⠀⠠⠁⠀⠈⠄⠀⠀⠀⠀⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠀⠄⠀⠀⠀⠸⠀⠀⡃⠀⢀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠐⠂⠀⠀⠀⢸⣅⠠⠖⠀⠐⠂⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⡀⠀⠣⠀⠐⠂⢀⡤⠐⠂⠒⠁⠚⠒⠂⠤⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⠀⢱⠀⠚⠀⠄⠃⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⣸⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠜⡄⠀⠁⢀⠃⠀⠀⠀⠀⢪⠜⣁⠀⡠⢲⠏⠘⠨⡇⠘⠣⣸⣆⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠲⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠈⠁⠁⢠⣿⢯⡵⢚⠏
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣝⣦⣄⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⢴⡿⠵⠪⠚⠻⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣨⣤⠄⣤⣤⣤⡤⠀⠘⠻⠀⠀⠀⠀⠀⢠⢠⠐⠖⠁⠀⠁⠀⡄⠦⠀⢠⡀⠀⠈
⠀⠀⠀⠀⠀⢀⡞⠛⣉⡴⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⡸⠘⡇⠀⠤⠀⡀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣣⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠓⠞⡄⠐⣖⠀⡃⠰⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠰⠄⠀⠀⠈⠘⠀⠀⠀⠐⠢⢉⡐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠠⠄⠔⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⢉⣉⣉⣉⣉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠖⠉⠈⣠⢀⣠⠨⠝⠑⢢⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⢾⠀⠘⠢⠄⠀⠀⠀⠀⠀⠠⠤⠊⠀⢸⠶⠦⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠸⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⣹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣹⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⠀⣠⠿⣄⠀⠀⢀⡼⢧⡀⠀⠀⣠⠿⣄⠀⠀⢀⡼⢧⡀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠀⠀⠈⠉⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠀⠀⠀⠀⡖⠒⠒⠒⠒⠒⢲⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠚⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠚⠒⠛⠒⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠠⢐⣀⣰⠆⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡤⠶⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⡀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠄⠀⠀⠁⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠
⠀⠀⠀⠀⠈⠉⠠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⢀⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡀⠀⡀⡀⠈
⠈⠀⢈⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠁⠀⠀⠀⠀⠀⠀⠀⣉⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠠⠤⠀⠠⠀⠰⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡲⠀⠀⠀⢆⡀⣠⠄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⢠⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠠⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠐⠄⠘⠑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣉⣀⣈⡉⠤⢴⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⢀⠀⠀⠀⠇⠀⠠⠄⠀⠀⠤⢀
⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢰⠀⢂⢀⡄⢲⠐⠀⢀⡇⠀⠀⠀⠀⠆⡐⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⡈⢀⢀⠈
⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⠀⠀⡠
⠀⠀⠀⠁⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠉⠒⠒⠓⠒⠉⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠀⠠⠦⠒⠂⠀⠐⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⣠⡇⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⢀⠀⡀⠀⠀⠠⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣢⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠐⠀⠁⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠒⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠒⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠁⠀⠀⢸⠂⠀⢀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠊⠀⠁⠀⠀⠀⠀⠰⠤⠀⠔⠃⠀⠐⢄⠀⣀⡀⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀
⣿⣟⣙⣋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠚⠿⠅⠀⠠⠀⠀⠀⢀⠀⠀⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⣂⠀⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠠⠄⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠄⡀⠀⠨⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⣔⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⡄⠀⠀⠀⠢⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡠⠠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⣶⠏
⠀⠀⠀⡁⠤⡀⠀⠀⠉⠒⠠⠄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⡀⠀⠤⠄⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠓⢄⠀⠑⠂⠄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠈⠂⠤⣀⠈⠑⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⠠⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀⡀⠈⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⢀⣀⡤⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⠄⣀⢀⠀⢀⣀⣀⣀⣠⠤⠦⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠓⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣉⣹⣆⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⢲⣤⣶⣶⣶⣠⣶⣯⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠆⡆⠀⠀⢴⡾⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡩⠀⠀⠀⠀⠀⠀⠁⠀⠠⠤⢿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢄⡟⠀⠀⣔⣀⠉⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⢀⡿⠁⠈⠀⠁⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠠⣤⣼⠄⠤⠴⠤⢄⡀⠀⠀⠀⠀⣴⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⢛⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠓⠛⠚⠛⠛⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⡇
⡖⠈⠭⠭⠭⠭⠭⠭⠥⠤⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⢀⣀⣀⣀⡀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠀⢀⡠⠄⠂⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡔⠀⠉⢀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠆⠀⠀⠀⠀⠀⠀⠀⢰⠃⢰⠀⠀⠀⠁⠀⠀⡄⠰⠀⠀⢃⠀⠀⢠⠀⢰⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢸⠸⠀⢸⠀⠀⠀⠸⠀⠀⡸⠃
⠀⢦⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠈⠆⠀⠀⢀⠀⠀⠀⠀⠀⠘⠘⣾⣾⠾⠬⠽⠴⠄⠚⢊⣉⣀⣐⡀⢲
⠀⠸⣄⣀⣀⠀⢤⠏⠀⠀⠀⠀⠀⠸⡀⠀⠊⠀⠀⠀⠀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠠⡈⢉⣩⡋⢻⣽⣇⣳
⠀⠀⠀⠈⠉⠉⠍⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡷⠀⠀⠀⢀⡓⠠⡟⢙⣿⣀⣻⡭⠇
⠀⠀⠀⠀⠀⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠙⠂⠛⢯⢉⡤⠛
⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⡀⠀⠀⠈⢇⠀⣀⠤⠒⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣐⣒⣒⣂⣮⣁⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣄⡀
⠀⢠⣾⣿⣿⣿⣦⠀⠀⢠⣿⣿⣿⣿⣷⡀⠀⢀⣀⣀⣴⣷⣦⣤⡀⠀⢠⣤⣆⣶⣿⡄⠀⠀⠀⣄⡀
⠀⣸⣿⣿⣿⣿⡿⠀⠀⠘⣿⣿⣿⣿⣿⢃⣤⣿⣿⣿⣿⣿⣿⣿⡿⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⣾⣿⡧⠄
⠀⢻⣿⣿⠿⠋⠁⠀⠀⠀⠈⢿⣿⡿⠁⠈⢿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠙⢿⣿⡿⠁⠀⠀⠀⢨⠁
⠀⠀⠈⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣄⢉
⠀⠀⠀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣦⠀⠀⢠⣾⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣼⣿⣿⣿⣿⣿⡏
⠀⠀⠸⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡶⠀⠀⠀⢿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠁⣀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⡀⢈⣀⣠⣤⣤⣀⠀⠀⢀⣠⣀⣾⣿⣿⣧⣠⣄⡀⠀⣾⣿⣿⣶⡀⠀⣴⠿⣿⣿⡃⠀⠰⣶⣾⣿⣿⠆
⠀⢸⣗⣾⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠘⠛⠛⠛⠛⠓⠀⢻⣶⣴⣿⠗⠀⠈⠉⠛
⠀⠈⠻⣿⣽⣿⣿⠿⠋⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠁⠀⢠⣤⣤⡦⠀⠀⠈⠿⠿⠇
⠀⠀⢀⣠⣤⣆⣤⡀⠀⠀⠀⠀⢀⣀⢈⡙⠛⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣤⣤⣄⡀
⠀⠀⣽⣿⣿⣿⣿⣯⡀⠀⠀⣺⣿⣿⣿⣿⡀⠀⠀⣶⣦⣶⣶⣦⠀⢀⣾⡹⣼⣏⢿⣷⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠛⠉⠋⠋⠋⠛⠃⠀⠸⣿⣿⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⡇⠘⣿⣷⣽⠿⣸⣿
⠀⠀⢠⣤⣤⣤⣤⡤⠀⠀⠀⠻⣿⣿⣿⡿⠁⠀⠘⢿⣿⣿⣿⠟⠁⠀⠈⠻⠿⣿⡿⠇
⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⠀⠙⠛⠋⠀⡀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢀⡤⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⣿⣿⣧⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣛⣛⣁⣀⣀⣀
⣿⣟⣛⣟⣙⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠲⢤⡀
⠀⠀⠀⡌⡀⠝⠲⢍⣀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣈⣄⣡
⠀⠀⠀⢣⠄⠈⡠⢘⠇⠀⠀⠐⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢄⠤⠜⠉⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⠐⠚⠛⠙⠟⠋⠛⠂⡀
⠀⠀⢰⠊⢾⡤⠤⢾⡶⠤⠤⠤⠾⠙⢷⡀⠀⠀⠀⠀⠀⢢⣠⡠⣆⣎⠐⢲⡀⣶⡟⠀⠀⠀⠀⠀⠀⠀⢢⠄⣀⣠⠀⠀⠂⠀⡶⠓
⠀⠀⢣⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⠀⠀⠀⠀⡰⠛⠛⠣⢛⠀⠀⠉⠃⠻⠦⠀⠀⠀⠀⠀⠀⠠⢈⠀⠈⠁⠀⠀⠀⠀⠘⠃
⠀⠀⠞⠚⠒⠴⠧⠶⠤⠐⠲⠒⠚⠊⠀⠀⠀⠀⠀⠀⣱⡖⡐⣀⠀⠀⠀⠲⢶⣤⣖⠀⠀⠀⠀⠀⠀⠾⠯⠀⠀⠀⠀⠀⠀⢀⣀⡰⠶
⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠐⠻⡝⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢨⠁⠈⠁⠀⠀⠀⠈⠉⠀⢹⠃⠀⠀⠀⠀⠳⠤⠤⢦⣀⡄⠠⡤⢀⠄⠰⠴⠆⠀⠀⠀⠀⠓⠤⡤⠒⠀⠢⡄⠀⠈⠀⠀⠖⠀⠁
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⢣⠀⠄⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠐⠴⠄⡆⠀⡀⠀⠠⠼⠃⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠰⢅⠀⠀⢠⠀⢀⠀⠅
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠘⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠻⣄
⠀⠀⠀⠀⢀⡽⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠀⣠⣧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⢈⡀⣀⠐⠓⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⣆⣻⡀⠀⢶⢾⣏⣛⡈⠈⠢⠀⠀⠀⠀⠀⠀⠊⠉⠁⠠⢶⠖⠚⠉⠉⠱
⠀⠀⠀⢀⢌⡩⠁⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣀⡀⠀⣀⢀⣀⣀⣴⡄
⠀⠀⢀⡁⠂⠂⢠⡀⠀⠀⠀⠁⠀⠙⠂⠀⠀⠀⠀⠆⠀⢠⠀⡄⢀⠀⠄⠀⠀⡀⠀⠒⠀⠀⠀⠀⠈⠑⠄⠈⠀⠉⠋⠙⠻⠉⢄⠀⠘⡀
⠀⠀⠠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠈⣄⣄⡐⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠂⠀⠀⠈⣠⠀⡀
⠀⠀⢸⠷⠄⠚⠣⠀⠂⠠⠒⠀⠒⠰⠶⠀⠀⠀⠀⠃⠀⠁⠉⠂⠰⠶⠒⠂⠘⠋⠉⡝⠁⠀⠀⠀⠸⠖⠠⠷⠤⠀⡠⢦⡄⠀⢠⠷⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠰⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⠶⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠈⠀⠠⠤⡤⠦⠤⠦⠶⠢⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⢀⡀⣀⣀⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡
⠀⢠⡈⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠛⠉⠈⠁⠁⡀⠀⠀⠀⢀⣏⠉⠛⠑⠛⠒⠖⠒⠛⠛⠓⠐⢛⣇
⠀⠀⠷⠒⠦⢀⠀⢀⣀⣀⡠⡄⠀⠤⠊⡁⠀⠀⠀⠀⣤⣀⣤⠤⠄⠀⠀⠤⠤⣴⠞⡀⠀⠀⠀⠀⣟⣛⠛⠛⢓⠒⠒⡒⠲⢚⣛⣫⣛⡇
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠘⠁⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢉⠀⠁⠀⠈⠉⠋⠙⠀⠉⠉⢘⠅
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠲⠂⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠊⠀⠁

⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⡼⠒⠒⠠⢩⣶⠘⠟⠒⠈⠤⠒⠀⠖⠆⡶⠂⠧⠖⠗⠴⠐⠀⠂⠆⠃⢠⣮⠡⠐⠒⠻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠁⠈⠆⠀⠀⠀⠀⠀⠁⠶⠀⣀⡀⠀⠀⠀⢮⣧⠞⠀⢬⡷⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬
⠀⠠⠀⠠⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠐⣿⠆⠀⠐⢷⠖
⠀⠀⠈⠀⣿⠦⠀⠀⠀⢀⠄⠒⠇⡈⠃⠀⠀⠀⠀⠀⠛⠀⠀⠀⠚⢀⠀⠀⢀⣀⠀⠀⠀⣀⢠⣤⣤⡤
⠀⠀⠄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠈⠀⡀⠀⠀⡄⣠⣄⠀⠀⠙⠀⠀⠁⠠
⠀⠀⠀⠀⠰⠀⠀⠀⣀⡀⠀⠀⠀⠤⠉⠰⠄⢂⠀⠈⠀⠀⠀⠸⠀⠂⠀⢰⠇⠋⢸⠀⠀⠀⠖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠀⠐⠀⠀⠀⠀⠘⠀⠈⠄⠀⠀⠀⠄⠁⠀⢸⠁⠀⠘⠀⠀⠀⠀⠘⠷
⠀⠐⡾⠚⠀⠀⠓⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠈⠂⠠⠤⠄⠀⠈⠀⣰⠓⠀⠀⠀⠀⠀⠀⠚⠶⢷⠚⠃⢐⡄⠀⠀⠀⡸⠀⠀⠁⠀⠀⠀⢰⡷⠝⣇
⠀⢠⣄⡀⠀⠀⠀⠐⠟⠛⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⡠⠄⠀⡀⠤⡁⠀⠀⠈⠁
⠀⠀⣠⡷⠻⠃⠀⠀⠀⠠⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⡴⠔⠀⠀⢆⠀⠀⡄⠀⠀⠀⠀⠀⢠
⠀⠀⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀⠈⠉⠁⠀⠀⠀⠈⠁⠀⢀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠰⠈⠃⠀⠀⠀⠂⢠⠀⠠⠀⠀⢀⣀⣴⣴⠀⠀⢰⣿⡀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⣤⠀⠀⠁⠀⣿⣿⣿⠀⠀⠸⣿⠃⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠘⠀⡘
⠀⠀⠀⡡⠂⣢⢬⡳⡄⠀⠀⠸⠟⠀⠀⠀⠉⣷⣿⣿⡤⠀⠀⢻⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠉
⠀⠀⣄⠣⠀⠠⠄⠂⠇⡖⠀⣈⣡⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠛⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠠
⠀⠀⠈⠀⠀⠀⠀⣀⠜⠀⠀⠈⠃⠀⠀⠀⠀⣿⣿⣽⠃⠀⠢⣤⠄⠀⠀⠁⠤⠤⣤⣄⠀⠀⠀⠤⠖
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠖⠈⢳
⠀⠀⠀⠀⢀⣠⡀⡅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠞⠉⠁
⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠤
⠀⠀⠀⠀⠀⠐⠊⢃⠀⠀⣤⠙⢂⡦⣆⡈⠀⢀⠁⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⢴⠁⠇⠈⠁⠄⠂
⠀⠀⠀⣆⠀⠀⢀⡀⢤⠆⠘⣗⡣⠜⢡⡜⡠⢬⠀⣡⠀⠀⣭⠁⠂⠈⢀⠄⠀⠀⠀⠉⠊⡈⠙⠠⠊⢉⡐
⣠⠖⡰⠞⠛⠓⠚⢅⠈⠀⠀⠈⠳⢎⡡⠄⢁⠶⠀⠹⠢⡐⠀⢈⠖⠉⠀⠈⠐⠀⠀⠀⠀⠈⠄⠀⠘⡁⠀⠑⡀
⠁⠀⠡⠀⠀⠀⠀⣢⠀⠐⠦⡀⠄⠈⠳⢖⣁⠾⡄⠀⠔⠁⠀⠃⠀⠀⠀⠀⠀⠀⠑⠀⠀⠄⠚⠒⠂⠌⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⢤⢀⣀⣀⠀⠈⠠⡀⠒⠶⡿⡀⠉⡎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠉⢈⠃⠰⠂⠢⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠉⢂
⠀⠀⠀⠀⠀⠔⠁⡏⠀⠀⠈⢶⡠⡄⠦⠈⠌⢦⡙⠇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⡀⠀⠀⠰⠤⡀⢠⠀⠁⠑⢄⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠄⣳⢐⡀⠀⠀⠀⠡⡀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⢢⣀⠀⠈⡊⠀⠀⠀⠈⠁⠑⢤⠀⡀⠤⠞⠁⢄⠐⠀⠈
⠀⠀⠀⠀⠢⠀⠠⢠⡶⠤⢀⡔⠄⠀⡀⠀⠠⢂⠔⣆⠑⠤⠀⠀⠀⠘⠢⡀⢀⠔⠀⠀⠀⠀⠀⠀⡈⠀⠑⡤⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠀⠑⠀⢡
⠀⠀⠀⠀⠀⣸⢢⠀⠉⠑⢐⠁⠀⡈⢱⡄⠀⠈⠻⠀⠀⠁⠀⠘⠂⠀⡀⠋⠀⠀⠀⠀⠀⠀⢀⠈⠐⡀⢀⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠘⠈⠃⠀⠀⠢⣁⠀⢁⢀⡄⠐⢀⠀⠀⠀⣆⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⣐⠁⠢⡀⣈⠃⠀⠠⠀⠀⠀⠄⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠖⠁
⠀⠀⠀⠀⠀⠀⠡⡀⠀⡠⠐⢣⣈⠾⠌⠑⡸⠤⣍⣘⠁⡐⠉⠐⠓⠊⠣⣄⣀⣀⣠⠔⠆⠘⢄⠀⠈⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠠⠁⠀⣐⠠⠊
⠀⠀⠀⠀⠀⠀⠀⡸⠡⡌⠈⡣⢈⠦⡚⠎⠀⠀⠘⠃⠀⠈⠂⠀⠀⠀⠀⡤⠀⠎⢀⠀⠀⢀⠠⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠠⠊⠀⡠⠁⡀
⠀⠀⠀⠀⠀⠤⠅⠓⡤⢍⠈⡤⡔⠢⠞⠂⠀⠀⠀⠀⠀⠀⢠⠤⠠⡡⢾⣥⡀⡀⠀⡐⠐⠀⠀⠀⠔⠁⠀⡠⠀⠀⠀⡀⠄⠀⠠⠊⠁⠁
⠀⠀⠀⠀⠁⠠⢃⠤⠢⠾⠙⠀⠒⠐⠁⠑⠤⢀⡀⣀⡤⠚⠁⠀⠀⡸⢈⠳⠀⠘⠃⠀⠀⠀⠊⠀⠀⠐⠉⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠁⡀⠀⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣶⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠒⠒⠠⠤⣀⡀⠀⠀⠀⠀⢀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠳⠶⠂⠚⠚⠀⠀⠀⣨⡍⢐⢢⣤⠈⠓⠁⡔⠒⠒⠒⠒⠒⡄⠀⠰⡉⣁⠀⠀⢀⠸⠥⠤⠼⢇⡀
⠀⠀⠀⠀⠀⠀⢀⠤⠊⠻⠜⠂⢦⠭⢛⡀⠀⣴⠂⡰⠂⠈⠀⠀⢸⠀⠀⣠⠋⡜⠻⣆⠀⣠⠛⡀⠀⠈⠁⣠⠔⠁⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⣀⢔⡎⢡⡤⠤⠐⢒⠶⠫⣁⣤⡀⠀⠀⠉⠀⠀⠺⠀⠀⢘⠀⢰⠧⠤⠼⠾⠧⢴⠧⠤⠶⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⢘⠉⠙⠶⠚⠙⡄⠀⠘⠤⠔⣇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠉⠢⡀⠇
⠀⠀⠘⠘⡀⠘⠒⠊⠀⠀⠀⠀⠀⢥⡠⠇⡠⣠⢤⣄⣀⠤⠔⠒⠊⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠇⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠔⠓⠉⠈⠁⠀⡔⠒⠒⠢⡀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠸⣼⣀⠠⠄⠒⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⢀⡴⠁⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣤⣄⠀⠒⠒⠒⠀⠀⠀⠐⠒⠒⠀⢀⣤⡀⠈⠉⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢀⡠⠃⡄
⠀⠀⠀⠀⠀⢸⠀⠈⢉⢍⣑⣒⣒⣒⠒⠀⠈⠉⠉⠀⠀⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠸⢿⣃⣠⣮⢿⠀⠀⠀⠀⠀⠀⠀⡏⠲⢄⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⡇⢰⣦⣶⢰⢴⠀⣤⡴⠀⢽⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠈⠱⣄⠀⠀⠀⠀⠀⠀⣇⡰⠋⠉⡆⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⢇⠈⠁⠉⠈⠙⠓⠉⠙⠀⣸⠀⡇
⠀⠀⠀⠀⢀⠎⠁⠒⠒⠀⢴⡦⠤⠤⠤⠷⢤⠀⠒⠂⠉⠏⠀⠀⡰⠁⢸⡀⠀⣀⠀⡀⣸⠀⢀⣀⠀⠈⠢⣈⡉⣉⣉⣉⣉⣉⣉⣉⢉⣁⠔⠁
⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠑⢄⠀⣞⡂⢂⡴⠁⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠋⢃⠀⢠⠤⢄⠀⢙⣂⣀⣐⡃⠀⠀⠈⣇⣀⣀⣺⠁⠀⠀⢹⣂⣀⣐⡃
⠀⠀⢸⡀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠑⠁⠀⣈⣉⣉⣉⡁⠀⠀⠀⣏⣉⣉⣹⠀⠀⠀⢨⣉⣉⣉⡇
⠀⠀⠀⠈⠑⠒⠠⢤⣇⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠠⠤⠒⠊⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⢡⠀⠀⡘⠀⠀⠀⠀⡆⠀⠀⡎⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡜⠀⠀⠀⠀⠀⣆⣠⠇⠀⠀⠀⠀⢱⣀⡘⠀⠀⠀⠀⠀⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠃⠀⠀⠀⠀⠀⠘⢸⠀⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠀⠀⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠊⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠐⠒⠚⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢠⡄⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠠⠠⣤⡄⠄⠀⠀⠀⠀⢠⠄⠇
⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⢀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣸⣀⡀
⠀⠀⠀⠀⠀⠉⠒⠒⠢⠤⠤⠀⠤⠤⠤⠠⠀⠤⠤⠐⠒⠉⠀⠀⠀⠀⠯⠠⠀⠄⠄⠀⠀⠀⠀⠠⠀⠀⠤⠀⠄⠄⠀⠠⠄⠠⠀⠀⠀⠀⠠⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣂⠈⡉⣱⠦⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⠀⠀⠀⠀⠀⡤⠜⠉⠉⠀⠉⠉⠓⢦⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⢺⣋⡵
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⢠⡾⠁⠀⠀⡴⠋⠉⠉⠁⠂⠀⣴⠏⠉
⠀⠀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠁⠀⠀⠸⡏⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⢐⣲⠆⣀⠀⣰⠶⠚⢹⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣠⠴⣦⠴⠦⣬⡑⠚⠋⠉⠒⠮⡙⠍⢂⡀⢸⠀⠀⠀⠀⠀⠀⠈⠟⢌⣀⣀⣠⡾⠁
⠠⠚⣅⡀⠁⠀⠀⠈⢻⡄⠀⠀⠀⠀⠘⢆⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣴⠓⢄
⡂⢦⠏⡋⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⢣⡀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⡆⢱⡤⢤⡀
⣀⠚⠉⠃⠀⠀⠀⠀⠘⢿⣄⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠋⡷⠊⠙⠺⢿⠛⠙⠲
⠘⣇⠀⠀⠒⠤⠄⣠⠴⠦⠽⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⣏⡐⢲⣦⣄⡀⠀⠀⠀⣼⠀⢰⠃⠀⠀⠀⠀⠇
⠀⠈⠳⠤⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠵⢒⣿⣿⠴⠋⠀⠈⠹⣆⠀⠀⣿⠀⡜
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡇⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⢀⣴⠾⢯⣍⠉⢧⡉⠒⢦⡀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡇⠸⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⢀⡴⠋⠂⠀⠁⠳⠈⠀⠙⣆⠐⠿⣦⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠋
⢠⡾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣬⣇⠀⠀⠙⠢⠤⢄⣠⣤⠴⠞⠁⠀⠀⠀⠙⠲⠤⣤⣀⣠⣇⠴⠃
⢸⠀⠛⡆⠀⠀⠀⠀⠖⢠⡊⠰⠤⣤⣼⠎⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⢀
⣿⠀⠀⠳⠦⣀⣰⠧⠬⠀⠀⢀⡎⢀⠇⡆⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠴⠃
⠹⣄⡇⠈⠲⢶⠶⣄⠀⠀⢀⢞⡔⠁⠀⡇⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠉⠀⠴⠛⠁⠚⠋⠉⠉
⠀⠘⢧⠆⠀⠨⣄⠈⠙⢯⣴⣂⠀⢀⡞⢁⣸⠃⠀⠀⣀⡤⠴⠒⠋⠁⠀⠀⠀⢀⠀⢀⣶⠀⢦⡉⠉⠙⠒⠤
⠀⠀⠘⢧⣀⣀⣈⠓⠙⢓⣺⡿⣻⠋⡰⠋⠀⢠⣶⣉⣀⣠⣀⣠⣤⣤⡶⠴⠶⠾⠛⠛⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠛⠷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠋⠙⠻⣦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⡌⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠛⠛⠛⠳⠶⢦⣤⡐⠃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿
⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠹⡇
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣀⣠⣤⠶⠶⠶⠶⠶⠶⠶⢦⣭⣀⢹⡄
⠀⠀⠀⠀⢰⠏⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣆
⠀⠀⠀⢀⡿⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠹⣦
⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣴⣞⣿⣉⣹⡇⣠⡴⣮⡉⠛⣷⣤⠼⢷⣄⠀⠀⣠⡤⠶⢺⡿⠀⠀⢀⣠⠄
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣾⡋⢼⡋⢹⣿⣿⠶⣿⣄⣼⠇⣼⠋⠀⠀⠀⢙⣷⠟⠁⠀⢠⣾⣁⡀⠐⠋⠁
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⣟⠈⣿⠈⣿⠋⠁⠀⠀⠀⠈⢳⡄⢿⡀⠀⢀⣴⠟⣡⡾⠋⠀⢈⣉⣭⡿⠃
⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡏⠙⢻⣏⣸⡇⠀⠀⠀⠀⠀⣠⠾⠛⠛⠛⠛⠿⣧⡞⠋⠀⢀⠐⠿⣯⣄⡀⠀⢀⣤⣤⡤
⠀⠀⠀⠈⣿⠀⠀⠀⠀⣾⠻⢶⡾⠋⠉⣷⡀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠘⣷⠶⠟⠋⠁⠀⠀⣨⠟
⠀⠀⠀⠀⣹⣧⡴⠶⠶⠿⢦⣼⣇⠀⠀⠈⠳⢦⣤⣤⣿⡁⠀⠀⢀⠀⠀⣸⠇⣿⠶⢦⡾⠛⠛⠻⠷⣤⡀
⠤⣤⣄⠀⠻⢷⣄⡀⠀⠰⢤⣤⣙⢻⣦⠀⠀⠀⣼⠀⠘⢷⣤⡾⠛⠴⠾⣋⣼⠇⠀⢸⡇⠀⠀⠀⣠⡌⣻
⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠀⠀⠙⢷⣽⡷⠶⠛⠻⢦⣄⢰⡟⠛⠓⣶⡟⠋⣡⡴⠶⠚⠛⠻⠶⣬⣭⠾⠋
⠀⠀⠀⠀⠀⣴⡏⠀⠒⠒⠓⠀⠀⣼⠋⠀⠀⠀⠀⠀⠙⣿⠶⠛⠛⠛⠻⣾⡉⠀⠀⠀⢸⣇⠶⢘⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠛⠛⣻⡟⣀⣠⣴⡏⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣠⡘⣧⠀⣠⣤⠄⢛⣷⡾⠁⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢿⣍⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⣤⠶⠶⣾⠛⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢙⣿⢷⣄⣀⣠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠛⢠⡿⠀⣴⠛⠛⣷⣤⠾⣧
⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠘⣧⣀⣽⠿⣏⠀⠻⣄⠀⠀⢤⣤⣴⠖⣠⡾⠻⣦⡿⣦⣤⠾⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⣿⠀⢹⡷⢶⣿⠛⠶⠦⠤⠴⠞⠋⠀⠀⠻⣤⣼⠷⢦⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠋⠀⠸⣶⣋⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⡐⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠉⠀⠀⠀⠠⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠉⠁⣲⠐⢎⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠃⠀⠀⠱⠄⠀⠀⠀⠀⢠⣾⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠻⣿⡿⠏⠀⣀⣀⣤

⠀⠀⠀⠀⠀⠀⠢⡀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⡄
⠀⠀⠀⠀⠀⠀⢠⠄⠈⢄⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠛⠫
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠐⠀⠀⠴⠋⠀⠠⠀⠀⠀⠠⠄⠤⠄⠻⣿⣿⣿⡇⡀⠀⠀⠀⣀⣤⣶
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠑⠀⢄⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠛⠉⠡⠂⠁⠀⠀⢰⣿⣿⣿⠃
⠀⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢹⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⠒⠊⠁⠠⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⢲⠁⣘⠀⠀⣀⣀⣠⡇⢉⣭⡄⠸⡄
⠀⢀⠠⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⢐⠠⠀⠀⠜⠀⠀⢀⠀⠀⣀⢈⣤⡖⡦⢖⡞⠀⠇⠀⣾⠙⢯⠏⣿⣯⠽⠁⢠⣷
⠀⠈⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⡐⠁⠀⡰⠁⢰⠏⣽⠀⣽⣛⣿⢈⠃⠘⠀⠀⣧⣤⣄⣈⣀⣀⣠⠴⠫⠃
⠀⠀⠀⠀⠈⠐⠀⠂⠠⠂⠄⠀⠠⠂⠒⠀⠀⠀⢰⠁⣰⣏⡓⠯⠿⢼⡿⠐⠁⢠⠂⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⣷⣂⡃⠴⠔⠋⢀⡠⠒⠁
⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⡝⠓⠢⢀⠀⠀⠀⡜⠀⠜⠉⢁⡀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⠤⠠⡤⠆⠀⠀⠠
⠀⡠⠊⠁⠀⠀⠀⠀⠀⢰⡃⠀⠀⠈⠀⢌⢠⠇⡐⠂⠉⠁⠀⠀⠀⠀⠀⠀⡀⢠⣀⡆⠀⠀⠹⠅⠀⠀⠉⠀⠀⠁
⢰⣁⠀⣀⠀⠀⠀⠀⢈⡸⢻⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠃⠀⠀⠑⠀⠀⠀⠀⡀⠠⠄⠂
⠙⠀⠀⠀⣱⠤⠔⠊⠁⠀⢊⠀⠐⠁⠀⠀⠀⠀⢀⠄⠒⢖⡃⠀⠀⠀⠈⠀⠀⣀
⠰⡄⠀⠀⠉⠉⠁⠲⠀⠀⠀⠀⠀⡀⣀⠆⠀⠙⠽⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠁⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⡠⢐⣦⡴⠊⠀⡈⣯⠝⠉⠀⢈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢸⠟⠁⠀⢸⠟⠁⠀⠀⢠⣟⠭⠛⠳
⠀⠀⠀⠀⠀⣀⠠⠤⠤⠀⢀⠀⠀⠀⢀⠠⠀⢒⣀⢀⡐⠒⠀⠄⡀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢀
⠀⠀⡠⠔⢁⣄⣈⣉⠙⠻⠦⣹⠀⡔⠁⢰⢚⣋⣸⣁⠋⣛⣻⢦⠈⠂⠈⡓⠤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠒⡏
⣠⡊⣐⡶⠦⢤⣌⠉⣳⠔⠋⠁⠀⠀⠀⠀⠀⠿⠠⣤⡤⠭⠓⠁⠀⠀⠀⢠⡁⠀⠀⠩⠉⠉⠉⠉⠉⠁⠄⠀⢀⡼
⢇⠶⠶⢶⡏⢢⡴⠊⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠈⠊⣀⠔⠁⠀⠀⠳⢮⣀⣀⠀⠀⠀⠀⠐⠀⣐⣨⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢻⡿⠋⠉⣿⠋⠀⠀⣠⡴⠟⠶⢦⣄⡀
⠀⠀⠀⠀⣠⡴⠿⠍⣳⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣻⡟⠁⢸⠃⠀⣸⡇⠀⣀⡾⠋⠀⣀⣤⠶⠾⠿⣦⣄
⠀⠀⠀⣠⠿⠄⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠇⠠⣿⠀⠀⣿⣧⠖⠛⠛⠋⠉⠙⠓⠛⠛⠷⣤⣤⣤⣤⣝⣧
⠀⠀⣾⣃⠀⠖⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣿⠀⠀⣿⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠈⠙⠳⣄
⠀⣰⠟⢡⠄⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣇⠀⢹⣇⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣤⣹⣇
⠀⢿⡶⢂⡀⠺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⡀⣸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠉⢳⡄
⢠⣿⠀⠀⢀⡰⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠷⠦⣵
⠈⣿⡟⠀⠉⠀⠀⡽⠳⣦⣀⣀⠀⢀⣀⣤⣤⣴⡾⡿⠉⡏⠘⣧⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠈⢷
⠀⣿⠀⢀⡀⠒⠃⠀⢀⠚⠋⠉⣻⠋⠀⢠⠏⠀⠀⠁⠀⣧⠀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⢦⣸⠇
⠀⠹⣧⣾⠁⠀⠀⢠⠟⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢦⣄⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⢹
⠀⠀⠈⣿⠀⠀⣠⠀⠀⠀⢰⠇⠀⢀⡾⠀⠀⠀⠀⡀⠀⢿⡄⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢷⡄⢸⡆
⠀⠀⠀⠻⣦⢰⣿⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢡⠀⢸⡿⢦⣤⣹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⢻⡞
⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠘⣧⠀⢷⡀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠙⣷⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢻⣆⠀⢠⡀⠀⠀⣴⠀⠀⣿⠀⠸⡇⠹⣆⠀⠛⢶⣤⡤⣬⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠻⣷⠀⢸⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣼⣇⠀⠀⢻⡄⠀⢻⡆⠀⣿⠀⠹⣆⠀⠀⠻⣦⡀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠃⠀⣿⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠘⣷⡀⠘⣷⡀⠘⣇⠀⠹⣦⠀⠀⠈⢹⡷⠦⠴⠿⠶⢤⣀⣀⣀⡀⠀⠀⢀⣀⣠⡴⣿⠃⠀⢹⡇⠀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣦⣽⣷⡄⠹⣷⡀⠹⣆⠀⠘⢷⣄⠀⠀⠙⢦⣤⣀⣠⡴⠟⠉⠉⣽⠟⠉⢉⡿⠁⠀⣿⠀⢠⣿⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣦⣽⣷⡀⠹⣧⡀⠀⠙⢶⣄⠀⠀⠙⠻⢦⣤⣀⣤⠞⠁⠀⠀⣼⠇⠀⣰⣏⣰⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣦⣈⣿⣦⣀⣀⣹⠷⣦⣄⣀⣠⡴⠛⠳⢶⣤⠶⠞⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢩⡄⠀⡄⠈⣀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠁⠀⠀⣠⠆⠀⠠⠄⠀⠈⣄⣀⢀⣤⡴⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠄⠀⠀⠀⠀⠁⠶⠀⣠⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢠⡄⠀⣠⠀⠀⠖⠀⠀⠀⠄⢀⡾⢂⢀⡀⡀⡂⠀⠠⠒⡁⠐⠀⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠚⠀⠀⠀⡀⠠⠈⢀⡔⠛⡒⠒⠀⠐⠀⠀⠒⠀⠀⢀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀⠑⠀⠐⠂⠐⠠⠄⠀⠁⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⣀⠀⠗⡀⠈⠀⠀⠀⠀⠀⠠⣠⣤⣤⢦⡠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡤⡄
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢐⠓⠊⠨⠁⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠄⠠⠀⠀⠀⠀⢎⠰⠈⡟⠉⡵⡄⠀⠀⠀⠀⠀⠀⠀⠃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⡔⠀⠀⠀⠀⠀⠈⠢⣤⠤⠔⠉⠀⡀⠀⠀⠀⠂⠟⢳⡋⠛⣲⣾⠁⠀⠀⠀⢠⠊⠵⠇⢪⠓⠂⢑
⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠎⠀⠀⠀⠀⠀⠀⠑⠂⠤⣀⡀⠤⠊⠀⠀⠀⠀⠀⠲⠦⠉⠙⠀⠁⠀⠀⠀⠀⠈⠂⠤⠠⠛⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⢀⠀⠀⠀⠀⠀⠀⠀⣁⢓⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠈⠉⠀⠐⢄⠀⠀⠀⠀⠈⠤⠀⢀⡦
⠀⠀⠀⠀⠀⠈⡸⠶⡇⠀⠀⠀⠀⠀⠀⠢⠜⠫⠙⣉⣃⠖⠀⠀⠀⠀⠀⠀⠘⢃⡀⣄⣀⠀⠀⠀⠀⠦⠊⠀⠉⡉⢢⣀⡠⠀⠀⠀⠰⠃⠀⠀⠈⣄⡀
⠀⠀⠀⠀⠓⢺⠀⠀⠐⠂⠀⠀⠀⠀⠈⢈⠃⡉⢰⡈⡐⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠂⣸⠉⠀⠀⠀⠀⢠⡀⠀⣠⡟⡠⢤⡱
⠀⠀⠀⠀⠀⠀⠁⠐⢀⡠⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠬⠉⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⠿⠃⠀⠀⠀⠈⠓⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠣⡊⣉⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀
⠀⠀⠀⠀⢀⡜⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⡰⣿⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠐⠶⠀⠀⠀⠀⠀⠀⣠⣆⠀⠀⠀⣀
⠀⠀⠀⠐⠁⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⠀⠀⡡⠀⠀⠀⠀⢺⠮⣿⢿⠆⠀⠀⠀⠀⠀⠀⣢⣄⡏⠀⠀⠀⠀⢀⠀⠀⠀⠀⣼⢛⣬⣇⣐⣨⣻
⠀⠀⠀⠠⡀⠀⣠⠶⠲⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢜⢎⣷⡦⠀⠠⠀⠀⠀⠀⢰⣿⣿⣳⣦⣀⠴⠋⠀⠀⠀⡈⣿⢫⠞⢁⠏⡠⡅
⠀⠀⠀⠀⠈⠉⠛⢄⡑⠖⠊⠀⠀⠀⠀⠀⢀⣦⣄⡀⡠⠃⠀⠀⠀⠀⠀⠣⣳⢟⡅⠨⠀⡀⠀⠀⠀⠀⠑⢿⣿⣿⠿⠒⠀⠀⠀⠀⠀⠈⠻⠴⠚⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠜⢂⠍⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⠾⣷⣶⣤⠀⠀⠀⠈⢢⡀⠀⠀⠀⣤
⠀⠀⠀⠀⢆⣤⣶⣶⣆⡘⠂⠀⠀⠀⢠⡄⢠⣀⣀⣠⣿⣀⡀⠀⠀⠀⠀⢘⠉⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣬⡻⣿⣇⠀⠀⢀⡀⠃⠐⢓⠚⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⡿⠁⠀⠀⠀⢀⠄⠀⠀⠹⡀⠀⠀⠀⠀⢀⣀⣀⣠⡬⣿⠿⣿⡾⠏⠀⠀⠘⡀⠀⠁⣴⠋⠉⠲
⠀⠀⠀⠻⣿⡿⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠠⣠⣀⣠⣀⠇⠀⠀⠀⠀⠈⠈⢷⣼⣀⣼⡷⠃⠀⠀⠀⠀⠀⠀⠒⠚⠻⣄⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⠿⣿⠿⢿⢿⡿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣦⣶⣶⣶⣷⣶⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡶⠛⠛⠉⠉⠑⠢⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠒⠒⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠁⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢙⣛⣷⡆
⠀⠀⢀⡏⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⡁⠐⠶⣿⣧⣤⣤⣤⣤⣤⡤⠤⠤⠄⣿⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠛⠛⠛⠛⠶⣄
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠑⢄⠈⢷
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⡆⠘
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡇⢠
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⣼⢃⡞
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⣠⠀⡄⡄⡄⠀⣤⠀⣿⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⣴⠟⢁⠎
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⣿⠀⠊⠒⠑⠃⠁⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠛⠷⣦⣤⣄⣀⣀⣠⣤⣴⠶⠛⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠿⠛⠁
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠸⣧⣀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠘⢿⣷⣤⣤⣄⣀⣠⣤⣴⣾⡿⠃⠀⠀⠀⠈⠙⢷⣄⣀⢀⣀⣠⣤⣶⡶⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂⠐⠋⠉⠀⠉⠳⣦⣄⡀
⠀⠀⠈⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁
⠀⠀⢀⣀⣤⣴⣶⣛⠉⠉⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿
⠀⣴⠟⠉⠉⠉⠉⠉⠉⠒⠂⠄⢸⣧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⣀⡤⣀⠀⠉⠙⠒⠶⣤⣀⠀⠀⣿⠀⠀⠙⠻⢶⣤⣀⣤⡴⠚⠋⠉⢹⡇
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠙⠛⠚⠀⣀⣠⠶⢢⠀⢹⡇⠀⢸⠀⠀⠀⠀⠀⠋⠉⠙⠀⠀⠀⠀⢸⠃
⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠛⢸⣿⠀⠀⠀⢀⡴⠋⠀⣀⣀⣤⣤⠶⠶⠛⠋⠉⠈⠙⠁⠀⢸⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⢸⡇⠀⢰⠆⢠⠀⠀⠀⠀⡎⠀⢸⡟⠀⢀⣴⣿⠶⠿⠛⠋⠉⠁⠀⠀⠀⠀⣰⡏⣠⡇⠀⠀⣼⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠈⣿⡀⠈⠁⠀⠳⠂⠀⠀⢝⠂⠸⡇⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⣾⣋⣰⠆⠘⠛⠋⠀⠀⠀⣿⠇⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠞⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠉⠓⠦⣄⣀⠀⠀⠀⠀⡇⠀⠀⢻⣾⣛⠂⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠄⠀⠀⠀⠀⠈⠈⠉⢀⣀⣤⠞⠓⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⠛⠉⠉⠉⠉⠉⠙⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣦⣄⣀⠀⣿⣿⣷⣾⣿⣿⠿⠿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄
⠀⠀⠀⠀⠀⣾⣿⠋⢀⣿⠉⠛⠻⢿⣿⣿⣿⡿⠛⠁⣀⣤⣤⣄⣈⠙⠻⢿⣿⣶⣄⠀⠀⠀⠀⠀⠘⢿⣿⣧⡀
⠀⠀⠀⠀⠀⢻⣿⣾⣏⡁⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠿⠟⠛⠻⢿⣷⣦⡀⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣦⡀⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠈⢻⣿⣷⡀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠹⣿⣿⣄
⠀⠀⠀⣠⣾⣿⡿⠛⠉⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⠈⢿⣿⣷⡀
⠀⢀⣾⣿⡿⠉⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠙⢿⣿⣦⡀
⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠙⢿⣿⣦⡀
⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠙⢿⣿⣦⡀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠻⣿⣿⣄
⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠈⢿⣿⣧⡀
⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠙⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⡀⠀⠀⢀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣠⣤⣶⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⡀⢜⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⣄⡐⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⢀⢸⢴⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠞⡑⢁⠊⣯⢺⢻⠟⠉⠃⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡴⣞⣯⣯⣯⣮⣾⣖⣻⣐⠓⢿⣜⣄⣀⣥⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣧⣿⣿⠿⠋⠁⠀⠀⠸⠈⠙⠻⢯⣢⡄⠨⣿⣿⣿⣿⣇
⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣻⣿⡿⠇⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠳⡳⠸⠿⠋⣿⡿⠟⠁
⢻⣿⡿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⢻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⣿⣤⠀⣿⣃
⠈⢙⢿⡐⠒⠀⠀⠀⠀⠀⠠⢀⣤⣦⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⡧
⠀⠁⠀⣨⣥⣐⣶⠐⠀⠀⠀⡼⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⢀⡿⡛⠹⢿⣿⠃
⠀⠀⠀⣽⣿⣿⠅⠀⠀⠀⠀⠠⠂⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⢈⠠⣳⠄⢆⠄⠀⠀⠀⠰⣿⢡⠅
⠀⠀⠸⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⡏⠀⢤⠆⢒⡣⠽⠁⠀⢈⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢸⠠⠙⢉⠒⠀⠄⠙⢺⠉⡃⠂
⠀⢀⣀⣤⣤⣤⠄⣠⢤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠀⠀⠀⠁⠉⠁
⠀⠉⠉⠉⠉⠀⠊⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⠖⡒⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⡈⡆⠍⠁⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠂⠉⠁⠀⠄⠐⡀⠀⠀⠀⠀⢀⡊⠐⠁⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠄⠀⠸⠀⠀⠀⠠⠈⡉⠰⠃⠰⠆⠘⠂⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠐⠘⠁⢰⠂⠀⠱⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⣀⣀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠞⠀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠘
⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠂⠀⠀⣁⣀⣀⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⣯⡀⢋⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡘⢱⡖⠂⢀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⢰⠀⠙⣄⠁⠀⠀⠘⠦⠀⠀⠀⠀⠀⠀⠰⠙⢘⡠⢇⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠈⠅⠘⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠀⠀⠈⠷⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⡄⠠⢀⠹⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠘⠁⠝⠀⠒⠂⢈⡉⠀⠀⠈⠀⠀⠠
⠀⠀⠀⠀⡀⢒⣾⠀⢤⡀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠠⠐⠂⠌⡐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠸⠀⠀⠀⠀⢀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⡉⠤⠈⡁⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⣀⡀⠄⢀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠐⠂⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠓⠠⡀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢼⡤⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠉⠄⠡⣄⡗⠋⢤⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡐⠀⠛⠛⠈⠀⠐⡽⠦⣀⣀⡀⠀⡀⠈⣃⢀⠊⢉⢧⡀⢁⠨⠧⡀⠀⡀⠈⠀⠀⠀⠀⢀⠀⠀⣾⠛⠂⢤⡠⢴⡀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠉⣈⠀⠀⠿⠀⠀⠐⠲⠀⢀⠀⠐⢌⠂⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠂⡂⢀⡍⠀⠠⠋⠈⢠⠠⡂⠌⠐⠀⠀⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠨⠁⠀⢐⠡⠀⠐⠁⠄⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡜⠀⠀⠀⠀⠂⢀⣀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡠⠒⢒⡄⠈⡄⠀⠀⠀⠀⠀⠴⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠓⠒⠉⢀⠄⢰⠀⠀⠀⠀⠀⠠⠀⠀⠅⡀⠀⡀⠀⠀⠀⡀⠀⢊⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢅⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠡⡑⠀⡀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠀⣀⣀⡀⠄⠀⠈

⠀⠀⢀⣰⠟
⠀⢠⣿⡝
⢀⣿⣯⢧
⢸⣏⣹⡌⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡐⣒⣒⣶⣖⠒⡶⠤
⢸⣏⠀⠹⢾⣵⣄⠀⠀⠀⣀⣠⡄⢃⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⡀⠄
⣿⡾⣦⠰⣻⣷⣏⠿⣿⢿⣿⡏⣰⠟⠉⠀⠀⠀⠀⢀⢙⣙⣿⡇⢈⡞⠀⠀⠀⢠⡄
⠛⣀⠙⣶⡘⣳⣿⣿⣿⡾⣿⡠⡏⠈⠀⠀⠀⠀⠀⠐⢋⣡⡑⢷⣸⢀⣀⣴⠶⣺⢀
⠈⡿⢿⠋⡿⢧⣀⣽⡇⡇⣼⢉⡧⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠈⣷⣯⠚⢁⣴⣿⢸⣀⣠⣤⠤
⠀⠐⣼⢧⡠⠀⡾⡻⢧⣧⣾⡅⢣⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣠⠟⣟⣁⣟⠫⢉⡀
⠀⠀⠈⠎⢸⢠⣄⠀⠘⠈⠈⣇⣸⠠⠀⢀⠄⠀⠀⠀⠀⠀⠁⢰⢇⠹⡏⠄⡼⣵⠚⣦⣜⣴⣾⣷⣷⣶⣶⣤⣀⠀⡀
⠀⠀⠀⠘⠦⣨⣿⣧⣄⣄⣾⠏⠀⠀⠀⠋⠀⠀⠀⣠⠾⠄⣌⢆⡓⠊⡰⢼⣹⢟⣣⣿⣿⣿⡿⠟⠹⠟⣿⣿⣿⣿⣋
⠀⠀⡀⠀⠀⢈⠋⠀⠀⢹⣿⠀⠀⠀⠀⠘⠅⠀⠌⠃⠀⠃⢘⣳⠛⣖⢻⣟⢷⡶⣋⣛⣙⣛⣇⠀⠀⠀⠛⠛⠛⠉⠋
⠀⠀⠁⠀⠀⢠⣦⠀⣠⡼⢟⢀⠀⠀⠀⠀⡀⠁⠀⢈⡀⠀⠜⠄⠈⠛⠐⠉⠌⠃⠙⠉⠁⠈⠈⠁
⠀⠀⠀⠀⠀⢀⡀⠊⠀⠀⡾⢃⠤⠤⠄⠚⢛⠋⠁⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠌⣨⡴⠀⠀⠀⠀⠀⠀⠀⢀⠉⠂

⠀⠀⠀⠀⠴⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠁⠀⠊⠀⠀⠤⠀⠀⠀⠀⠐⠀⠾⡀
⠀⠀⠀⠀⣱⠢⠄⠀⠀⠀⠤⡄⠀⠀⠀⠀⠊⠀⠂⠠⠀⠠⠀⠂⠐⡠⠀⠀⣅⡀⠀⢀⡰⠂
⠀⠀⠀⢠⡏⣈⣀⣀⣀⣀⣐⣋⠑⠀⠀⠀⡻⠔⠀⠀⠀⠀⣒⡢⠽⠁⠀⠀⠸⣵⣈⣷⣄⢤⣠⢤⡅
⠀⠀⠀⠑⠛⠠⠤⠀⠐⠊⠉⠀⠀⠀⠀⠈⠒⠤⠄⣀⣀⡀⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⢹⣭⣭⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠠⣀⣀⠀⠀⠀⠈⠉⣀⢢⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⢸⠂⠀⠀⠀⢀⠠⠊⠀⠙⢈⠖⠂⠠
⠀⢀⠀⢤⣀⣀⣉⠉⠁⢀⣀⣠⡴⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⢠⠎⠀⠀⡠⠀⠁⠀⠐⠀⠂⢀⠌⠁⠂
⠀⠀⢀⠀⡩⠉⠉⠉⠉⠉⣉⠔⠁⢀⠀⠀⠘⠙⢦⠀⢀⡠⠚⠁⠀⠀⠑⠑⠀⠀⠀⢀⠀⡰
⠀⠀⠀⠉⣤⠒⠀⡄⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⢀⣐⠔
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠘⢧⠜⡀⠀⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⢩⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⢷⣀⡼⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⡶⠛⠉⠀⠀⠁⣱⣄⣀⠀⠀⠀⠀⢸⠀⠀⣈⡻⢃⢸
⠀⠀⢄⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣝⠆⠀⠀⠀⠃⢠⠐⠘⡋⣋⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣲⠀⠀⠄⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⠂⠀⠒⠒
⠀⠀⠸⣍⡴⠂⠀⠀⢀⠐⢚⠫⡍⢉⣤⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⣉⢁⡤⠐⠂⠉⡇⠀⠀⠀⠀⠀⠀⣠⣌⠿⣿⣿⣿⡄⠉⢀
⠀⠀⠀⣸⠂⡧⠀⢀⠟⠦⠄⠀⠛⢂⣉⠄⠀⠁⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⡍⢀⣤⣴⡴⠃⡇⠀⠀⠀⠀⠀⠀⠀⠹⢿⡄⠠⡴⠒⠾⠉
⠀⠀⠘⠯⠴⠇⠀⠠⠄⠰⠖⠚⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣅⡌⠛⢃⣩⣴⠖⠃⠀⠀⠀⠀⠀⠀⠀⡄⠈⠥⠀⠀⠤⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢐⣊⣁⣋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⢶⠖⢦⢴⠈⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠴⠖⠒⡊⠉⠉⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡒⠶⠶⢒⣂⡴⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣉⠡⢤⡠⠀⠐⢒⣈⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⠤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⣠⡀⠀⠀⠤⠉⠭⠥⠴⠖⠚⠉⠁⠀⠀⠀⣀⠠⣠⡔⢒⠏⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⢤⠤⠤⠄⠀⠀⡀
⠀⠀⢈⡿⣆⡀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠚⣿⠋⠀⡰⢿⣠⠎⠀⠀⠀⠀⠀⢸⠀⠀⠢⢽⡿⠟⢁⣶⠆⠀⡀⠀⠀⡟⠛⢛⠛⣓⣒⣒⡒⢒⠀⠁
⠀⠀⠀⢇⣹⡙⠓⠚⢋⣿⠉⠀⡸⢯⠠⠎⠛⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠰⠋⣴⣸⠿⠋⠀⠀⡇⠀⠀⡿⠀⠸⠛⠙⠛⠋⠃⢀⠀⠸⡄
⠀⠀⠀⠀⠈⠳⠦⠴⠋⠙⠛⠋⠁⢀⣀⣠⡤⠤⠶⠶⠒⠒⠲⠤⣀⠀⠀⠀⢸⠇⠰⣤⡼⢓⣯⣚⣅⠀⢰⡇⠀⢰⠁⠀⣴⡏⠀⠒⠂⠒⠉⢧⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣄⡀⠀⠀⢀⣀⣀⣠⣤⡀⠀⠀⠀⠀⣿⡆⠘⢁⣾⣽⠿⠋⠉⠀⢸⡇⠀⣸⠀⢠⠀⠁⠀⠀⠀⠀⠀⠠⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠳⠯⠶⠾⠿⡿⠛⠛⠋⠡⠀⠀⠀⠀⣿⡅⢀⣉⣁⣀⣀⣀⣀⡀⢸⡇⠀⣿⠀⣇⠀⠠⣤⣤⣤⣤⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⠀⡄⢖⠉⢈⣓⣂⠀⠐⠀⠀⠀⠀⠈⠀⠚⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⢻⡆⢠⠄⢀⠀⡍⢉⠩⢠⠀⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢱⠈⠂⠀⡈⢈⡀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡸⠇⠸⠀⡇⠈⡶⠸⠎⠀⠇
⠀⠀⠀⢠⠖⣒⣂⠀⢰⣲⡄⠀⠀⠀⠱⠄⠀⠀⠆⠀⠐⣉⡙⠂⠁⠀⠀⠀⠀⠀⠀⢠⣩⣭⣭⡅⠀⠀⠀⠀⠀⣖⣿⣀⣀⣀⡀
⠀⠀⠀⢈⠉⠉⠉⠉⠉⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠿⢭⠍⠗⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⠀⠀⢠⡎⠤⠀⠀⠀⠄⣼⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⣾⢁⠀⣤⣤⣄⠀⣏⠄⡇⠀⠀⢰⣖⣋⡉⠉⠉⠉⠉⠉⠉⠑⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢠⡄⢻⠀⠀⢰⣿⡿⠿⠿⠿⠿⠯⠍⠽⡗
⠀⠀⡇⢀⠈⠭⠭⣭⣉⠉⠀⡏⠀⠀⢠⣯⡿⠛⢛⣛⣛⠉⠙⣛⠈⠀⠀⠀⠀⣿⠀⠀⠠⠴⠦⠤⡀⢻⢸⠘⡇⠀⢰⣌⣙⣛⠛⠛⠒⠚⠛⠃⢡
⠀⠀⣿⡅⠀⠄⠀⠀⢹⣷⠀⡇⠀⠀⢸⡟⠃⠰⠿⠧⡼⠇⠀⠀⢠⡇⠀⠀⠀⠉⠀⠐⠀⠘⠁⠀⠐⢸⡾⣰⠁⠀⣿⡏⢉⣡⣤⣤⣀⣁⣀⠀⠈⡇
⠀⠀⢻⠘⢷⡶⠶⣒⠋⣿⠀⡇⠀⠀⢸⡇⢉⠙⢛⠛⢛⠛⠉⠁⢸⡇⠀⠀⠀⢇⢠⠀⡧⠀⠶⣀⢀⠀⠻⠃⠀⠀⣿⣰⠋⠤⠤⠄⠠⠤⠄⠙⢦⡇
⠀⠀⢸⠀⢲⡿⠻⣀⡄⣿⠀⡀⠀⠀⠸⡇⠨⠴⠒⠆⠘⠀⠠⢀⢼⡇⠀⠀⠀⢸⣞⠋⠁⠀⠈⠁⢸⠀⢠⠀⠀⠀⣿⡧⠀⠂⠂⠀⠀⠀⢂⠠⢸⡇
⠀⠀⢸⣄⣁⣀⡐⣛⣁⣿⡶⠇⠀⠀⠈⡧⠙⢓⣒⡶⠶⠶⠖⢚⢹⡇⠀⠀⠀⢸⠙⠀⣁⠀⡀⢀⡞⢀⣿⠀⠀⠀⣿⠘⢦⣐⡲⠦⠰⠚⣉⠴⢚
⠀⠀⠀⢧⡈⠉⠉⠩⠉⠅⠠⠁⠀⠀⠐⣇⣀⠙⠻⢯⣭⡽⠂⠀⠸⠃⠀⠀⠀⠀⢷⣆⣀⣋⣉⡁⢀⣠⠏⠀⠀⠀⠈⢧⣄⣈⣉⣉⣉⣉⣠⢄⣻⠆
⠀⠀⠀⠀⠉⠙⠛⠓⠂⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠲⠤⠤⢄⡀
⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⣄⣤⡴⠴⠦⢤⣹⢢
⠀⠀⠀⠀⡴⠋⠀⠀⢠⠞⠁⠀⠀⢠⡆⣨⠇⡘
⠀⠀⢀⡞⠁⠀⠀⠀⢹⡆⠀⠀⠀⠈⠛⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⣆
⠀⢀⣾⠀⠀⠀⠀⠀⠈⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢱⡋
⠀⣸⠁⠀⠀⠀⠀⠀⠐⠀⠘⠉⠓⠲⢴⢦⠄⠠⠄⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢻⡟⢻⠄
⠀⣿⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣦⣤⣈⡙⣲⡤⠴⠖⢒⡾⣃⣾⣷⠒⠢⠤⣀
⠀⣿⡸⠁⠀⠀⠀⠄⠀⠀⣠⠶⢿⣛⣻⠿⠻⢿⡿⠉⠉⠀⢨⠟⠁⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠙⢆
⠀⢷⢄⣴⠀⠀⠀⠀⠀⡴⠁⠀⣠⠏⠀⣈⣠⡧⠤⣤⡈⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠸⣾⡃⠄⠀⠀⠀⢸⠃⠀⢾⣿⣻⣾⣟⣛⠋⠛⠻⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⣠⣄
⠀⠀⣿⡧⡣⡄⢸⠁⣺⡄⠀⣾⣿⣯⡛⢷⣄⡉⠻⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠤⢿⠘⠛⢷⡆
⠀⠀⠙⣷⣷⡧⢸⡦⠸⡟⠂⠛⠻⣿⣷⣤⣌⣿⣷⠞⠛⠻⣧⣀⣤⡀⠀⠀⢠⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠀⣼
⠀⠀⠀⠈⣿⣿⣮⣿⡦⣿⡥⣀⣀⠾⣿⠟⢿⡿⠟⠲⢤⡎⠁⠀⠀⠈⢳⠴⠒⠚⠒⠖⠐⣧⣤⣄⠀⠀⠀⡻⠓⠀⠀⠀⠰⡻
⠀⠀⠀⠀⠈⠙⠿⣿⣿⡿⡄⠀⠃⢰⢧⠀⠀⠃⠀⢀⠌⠁⠈⠐⡄⠀⣸⣀⣀⡀⡐⠀⠀⠀⠉⠈⠉⠉⠙⠲⠒⠤⢤⡥⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠻⢧⠣⣀⠀⢘⡌⢆⡀⠀⠀⡄⠀⠀⠀⠀⠘⠈⠻⣯⠙⢹⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠕⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠉⠈⠓⠚⠒⠚⠳⠦⡀⢀⢤⣀⣀⢠⣿⣤⣠⡽⢻⡿⠛⠛⠓⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠃⠀⠈⠉⠙⠙⠛⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠃⠀⣠⠀⣀⣀⠀⠀⠘⠀⠀⠨⠀⠊⠉⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡤⠀⠀⠀⠀⠔⠃⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⢴⡄
⠀⠀⠀⠀⠀⠀⠠⣀⢀⠀⠀⠀⠀⠀⠀⢀⣴⠁⠀⣀⠠⣤⣄⠀⠶⡄
⠀⠀⠀⠈⣇⣠⡉⡾⠛⢧⣦⡄⠀⠀⠀⠀⠀⣠⠀⠠⢀⢄⠀⠈⠛⡘⢷⣄⡀
⠀⠀⠀⠏⠛⠑⠀⠁⠀⠸⡏⢰⣤⣇⠁⢴⣦⢾⣾⠁⠀⠈⢁⣠⣀⡀⢀⠻⠿⡏⠑⠂⠀⠀⠓⠭⠒⠤⢀⡀
⠀⠀⢧⠀⡠⠀⠐⠀⠀⠀⢸⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠉⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⣮⢶⣄⠈⠙⠢
⠀⠀⠐⢄⡀⣀⣀⣠⢴⣾⣿⣿⣿⣿⣯⣿⣿⠛⠑⢷⠄⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⡆⠙⢎⠳⣽⠷⡆
⠀⠀⠀⠈⠛⠉⠸⠗⠛⠛⠻⠿⣿⣿⣿⡟⠁⠀⣸⣿⡖⠀⠀⢢⣠⠀⣞⠉⠁⢀⠀⢀⠚⠛⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡏⠀⠀⢀⠀⠀⢀⠀⠚⢻⡄⠙⠃⠴⢛⡅⠝⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡀⠂⠀⠀⠀⣀⠁⠀⣀⠀⠐⠉⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠴⠛⠁⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠁⢀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠠
⠀⠀⠀⢤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠛⠛⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⡀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠴⠀⠒⡁⠀⠀⠤⠤⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠐⠒
⠀⡀⠀⠀⠀⠈⠤⠠⠴⠒⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠉⠁⠀⠀⠀⣤
⠀⢁⠀⠀⠀⠀⠀⢀⡀⠄⠠⠀⠀⢉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠔⠈⢀⡂⠀⠀⠀⠀⡅⠀⢀⡀⢀⡤⢠⠠⠀⠁
⠀⠈⠀⠬⠀⠈⠀⠃⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠘⡀⠀⠁⠀⠀⠀⠇⠀⢀⣤⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠛⠁⠀⠀⠄⠀⣙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠂⠀⠀⠀⢛⠉⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⢀⡀⠀⣁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢨⢀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠁⠈⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠄⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠲⠠⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠘⠆⠘⠃⠂⢂⠄⠀⠀⠀⠀⠀⠤⠄⢙⣐⣒⣉⠠⠤⡆⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⡀⠀⠀⠀⠀⣀⠤⠀⠀⠠⠤⢀
⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠸⡀⢆⢀⣄⠲⠀⢂⠀⡇⠀⠀⠀⠀⠰⢠⠂⠈⠲⠂⠀⠀⠀⠀⠀⢀⠈⠀⣀⡀⠁⡁⣀⣀⢱
⠀⠀⠀⠀⠛⠄⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⢀⠜
⠀⠀⠀⠀⠁⠀⠈⠠⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠒⠒⠒⠒⠁⣀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⡠⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠕⠆
⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠒⠀⠀⠚⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠐⠀⠀⠣⣄⠀⠀⠐⠠⣾⣡⣀⡤⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠤⠈⠀⢳⣦⡵⡈⠉⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠷
⠀⠀⠀⠀⠐⠀⠃⣀⠗⠁⢤⡍⡉⠋⠁⢀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⢰⣄⠐⠠⠄
⠀⠀⠀⠀⠀⣈⠋⠉⠢⣨⠂⠁⠁⠤⠐⠈⠑⠐⠀⠀⠀⠀⠀⠃⢀⡀⢀⣀⡤⠚⠙⠚⠀⢀⠃
⠀⠀⠀⠀⠀⠋⠀⠀⠈⠁⠇⠀⠀⢀⣴⠀⠐⠒⠀⠀⠀⠀⠀⠀⠈⠉⠙⠇⠀⠀⢀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠤⢤⡀⠘⡤⠠
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣬⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠁⠀⠀⠈⣿⣗⣼⠏⠉
⠀⠀⠀⠀⠀⠀⢀⢈⣄⠨⠇⠠⢏⡀⠕⠀⠀⠀⠀⠀⢠⠂⠀⠀⡀⠀⠖⢤⢐⡯⠁
⠀⠀⠀⠀⠀⠐⠏⠀⢙⠉⢢⡌⠈⢱⡄⠀⠀⠀⠀⠀⠈⠁⠀⠄⣠⠚⠁⠉
⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠴⠛⠦⠀⠀⠀⠀⠐⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣅⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠠⠄⠀⠀⢀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠄⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠄⠂⣠⣦⡀⠠⠀⠀⢀⠀⠀⠀⠀⠂⢠⣤⢴⠵⡀
⠀⠘⣄⠀⠄⠀⡿⠀⠀⠀⠀⠠⡀⠀⠀⠀⡊⠀⠀⠀⢄⠙⠮⣙⠒⠂⠀⠀⠀⠀⠈⠐⢺⠋⠑⠀⠑⠂⠀⠒⠉⠀⠀⠀⠀⣤⣲⡭⣆⣼⣽⣄
⠀⠀⠈⠓⠺⠀⠘⠆⠀⠀⣀⡴⠃⠀⠀⠀⣧⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠈⠃⠻⠜⡰⢡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⡀
⠀⠀⠀⠘⠠⠟⠄⠐⢂⣠⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠤⠬⣳⡤
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠈⠄⠀⠀⢠⠀⡜⢀⡴⠒⠀⣄⠀⠀⠀⢰⠀⠃⣀⣸⢼⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡠⠩⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠒⠈⢠⠀⠐⠄⢠⠈⠀⠀⠀⠈⠦⡴⠒⠁⠈⠣⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⢰⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢸⡄⣀⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠉⠓⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠉⠁⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⠀⢀⢭⠘⠶
⠀⠻⠶⠄⠀⠁⠒⠦⢄⣀⠀⠠⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⢀⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠉⠓⠒⠂⠀⠀⠰⢄⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⣤⡤⣦⡤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠖⠤⢺⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠐⠒⠛⠃⠈⠀⠀⠀⠀⠤⠀⠠⠜⠀⠃

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⡄⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣥⣖⢦⡀⠠⠄⡂⣤⡇⠂⠀⠀⠀⠀⢀⡠⠄⠂⠀⠀⠀⠀⡠
⠀⠐⠄⠑⡀⠐⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠀⠀⠀⡿⣹⠃⠀⠀⢀⠴⠋⠀⠠⡔⠀⠀⠀⠈⠁⠠⠂⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠒⡈⠆⠐⡀⠀⠛⢠⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠁⠁⠃⠀⠀⠐⡀⠀⠀⠀⠀⠀⡠⠴⠁⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⠈⠆⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢧⡀⣀⠀⠀⠀⠀⠀⣀⠈⠀⠀⠀⠀⠃⠀⠀⠀⡄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⡾⠋⠉⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣼⠛⠭⠀⡀⠀⣀⣀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣾⣤⡀⣠⠞⠃⠀⠉⣉⣉⣉⣀⣤⣿⣦⠀⠀⠀⠀⠠⠀⠀⠙⠿⣎⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⣠⠀⠀⢠⣿⠀⠀⠀⠙⠷⠌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣿⣦⣤⣾⣿⣿⣿⣟⣻⣟⠂⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣾⣿⣷⠤⢀⠆⢀⠀⠸
⠀⠀⠀⠀⠀⠀⢠⠴⣶⣿⣤⣤⣾⠛⣻⠿⠿⠧⠞⠛⠈⣥⡤⠾⠷⠶⠿⠿⠿⠿⠿⠿⣿⣿⣷⣶⣾⣿⣿⣿⡶⠛⣶⡟⠀⡀
⠀⠀⠀⠀⠀⠸⡄⢀⣾⣿⣿⣿⣿⡄⠀⠀⣀⣀⣴⣶⣾⣿⣄⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠛⣿⠟⣷⣸⣷⣿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⢻⡟⢫⣷⢩⣿⣿⡿⣦⣸⢿⣍⣭⣽⣿⣿⣿⣏⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠿⠗⠒⠒⠿⣿⣿⣿⣤⣠⣶⣄
⠀⠀⠀⠀⠀⡄⣠⣽⣧⣼⣿⣯⡥⣿⣾⣿⣧⣿⣿⣿⣿⠟⠛⠟⢷⣶⣤⣶⣶⠂⠀⠀⢀⠀⠀⠲⠀⠠⠙⢀⣸⣶⣶⣿⣿⣿⡛⠛⠛⠛
⠀⠀⠀⠀⠘⢿⡿⠿⠛⠿⠿⠿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣧⣸⣿⣿⣿⣶⣶⣿⣷⣄⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠉⠉⠙⠻⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠉⠉

⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡗⠀⢀⣀⡀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⢷⣤⣙⣷⡀⠻⡟⢠⢄⠙⢅⢤⣞⢀⡷⠾⠯⣭⣬⣙⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢁⡚⢉⠀⣈⡑⢿⠿⡿⠃⣙⣍⡷⣿⣤⠀⠀⠈⢹⣿⡆⠸⡇
⠀⠀⠀⢀⣤⣴⡾⡟⠛⣩⡍⠋⣀⣐⡀⢒⢒⠎⠿⡛⡋⢁⣍⢱⠫⣿⠉⠑⢦⣦⠟⠀⣖⠁
⠀⠀⠀⣉⣁⣀⣠⢤⣟⡉⣭⡭⣭⣭⢝⣗⣳⣏⣾⣷⣴⢴⣬⣽⣦⣼⣉⣺⡿⢋⣀⣷⡿⡄
⣴⠾⠛⠙⠉⣉⢵⡾⢋⡩⠞⣁⣋⢳⣹⣾⣼⡏⠠⣏⣤⣄⣠⠈⣻⡍⠟⠉⣤⣼⠻⣅⠳⡘⠆
⠀⠀⠀⠀⠘⠁⠈⠀⠊⠔⠋⢹⠟⠒⣅⣠⠌⡷⣄⣤⣽⣿⣿⡇⢡⣤⡿⠺⣯⡙⠢⡈⠳⠌⡢⣷⣢⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠸⢱⢯⢧⡏⠳⠉⠉⠉⠉⠛⠳⢦⣍⠓⣬⢴⣪⣷⠾⣿⣦⣄⣀⠀⠀⠀⠀⠀⡨⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⣿⣾⣗⣦⢭⣞⣿⣿⣿⣿⣿⣛⣽⡷⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⢉⣭⣍⢩⣭⣭⣭⣝⠓⠲⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⣐⣿⢷⣿⣿⣿⣟⣿⣽⣿⡧⣿⣿⣶⢆⣉⡓⠦⣄⡀
⠀⠀⠀⠀⠀⢀⣾⠁⣼⣿⣟⣿⣿⣷⣾⣿⡿⣿⣼⡿⣷⢷⣿⣿⣞⣯⣻⣷⣦⠍⠲⣄
⠀⠀⠀⠀⠀⣼⣿⡆⠸⣿⣿⢿⣿⣿⣷⣾⣿⣾⣿⡋⠀⠀⢭⣻⣋⣽⣿⡷⣿⣿⡷⣈⠱⣄
⠀⠀⠀⠀⢠⣿⣿⣿⣄⠀⢶⣿⣿⡷⣿⣿⣿⣿⣿⣾⣷⣞⣿⣯⡿⠾⢷⣾⣭⣽⣚⣲⠷⠘⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠙⠿⣿⣿⢟⣽⣾⣿⣿⣿⢿⠿⢁⣼⣮⣄⠱⠀⢉⠝⢿⣷⠀⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⣘⣽⣿⣿⣿⣿⣍⠀⣥⣽⣿⣿⠆⠀⠀⠂⠀⠉⢾⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⡟⠁⠀⠡⠄⠀⢀⣠⣷⣶⣾⣿⠿⠷⢶⣦⣄
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡵⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⠶⡒⠀⣉⣻⣷⣾⡀
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣷⣭⠲⠆⣘⡃⠂⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⡿⣽⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣽⢏⣌⣭⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⢶⡝⠷⣿⣿⣿⣿⣿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⡦⠀⢠⣴⣶⠒⡄⠙⣿⡿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡦⠀⠀⠀⠈⢠⠀⠀⠀⡏⠁⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣄⡀⠀⡀⣠⢾⠈⠃⠀⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡭⣙⠙⠻⢿⣿⣿⣿⣽⣿⡴⠃⠀⢀⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠉⠻⣿⣿⢟⣣⣞⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⡿⢟⢿⠿⢿⣿⣿⢿⣿⣾⣤⣀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡋⠀⡁⠐⠀⠄⢀⢀⡉⠁⠙⣿⣿⣧⣄⣤⣤⣠⣀⠙⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠠⠈⡀⢈⠠⠀⢀⣤⣤⡘⢿⣿⣿⣿⡿⢥⡉⣃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣰⣆⣤⣴⣾⣿⣏⠠⣶⢽⣿⣿⣿⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢰⠋⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⡾⠥⠽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⠞⣳⠀⠀⠀⠀⠀⠀⢀⡾⠂⠳⣄
⠀⢸⡑⠦⣄⣀⣠⠴⠋⠉⢻⠁⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⢳⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣖⡿⢈⢂⡟⠀⠀⠀⠀⠀⡴⡫⠀⢠⠀⢊⠑⣄
⠀⠀⠙⠦⣀⣀⠀⣀⣠⠔⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢹⡔⠙⡇⠋⢣⠁⣴⠟⠀⠀⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠲⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⠦⣧⣀⣠⣤⡠⠧⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⣀⠀⠀⣀⣰⠞⢛⢶
⠀⠀⠀⠀⠀⣀⣤⣾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠯⡏⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣮⣷⠶⡒⠦⣄⠀⠀⢰⣉⢊⣠⠌⣳⣴⢣⣊⣰⠒⠊
⠀⠀⠀⢠⠞⡽⢪⡽⢧⠙⣄⠀⠀⠀⠀⠀⠀⢀⣯⣭⡯⣿⣇⠀⠀⠀⠀⠀⢀⡞⢁⠊⠀⠂⠀⢂⠀⠱⡈⣇⠀⠀⠈⠉⠘⠦⠚⢿⡷⠃
⠀⠀⠀⣜⠀⠀⠈⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠿⣯⣿⠛⣿⣇⠀⠀⠀⠀⢸⠀⠈⠀⠀⠀⠀⠈⠀⠀⡇⣿⠀⠀⠀⠀⠀⣰⢞⠉⠑⢢⡀
⠀⠀⠀⠘⢆⣀⣀⣀⣀⡤⠋⠀⠀⠀⠀⠀⠀⠘⡇⣿⣿⣇⠸⣟⠂⠀⠀⠀⠘⣆⠰⡀⠸⠀⠀⢀⠀⠰⣠⠇⠀⠀⠀⠀⠀⢣⡀⠀⢀⣸⠃
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⡏⠉⠛⠁⠀⠀⠀⠀⠈⠓⠚⠒⠓⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣿⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣤⡀⠀⠀⠀⠀⠀⢀⣤⠞⠒⠋⠙⠲⢤
⠀⠀⠀⠀⠀⢠⠟⠁⠉⣯⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⡻⣗⢤⡀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⣼⠀⠢⢠⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⢠⠃⠀⠀⢰⠇⠀⠀⠀⠀⠀⢠⣼⢛⠹⣻⡻⡛⣗⠝⡄⠀⠀⠀⠀⣾⠀⣀⣀⣀⠀⢤⣤⣄⣹⠀⠀⠀⠸⣇⣑⡄⣀⠀⠂⠠⠴⡤⠃
⠀⠀⠀⠀⣼⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⢸⡇⢃⠰⠸⣏⢸⢸⢰⣹⡀⠀⠀⠀⠘⠶⠯⢿⡇⠀⠸⡟⠋⠁⠀⠀⠀⠀⠀⢸⠃⡀⠀⠀⠀⣾⠁
⠀⠀⠀⢠⡇⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢷⡐⠵⢬⣿⣃⡯⣂⡿⠁⠀⠀⠀⠀⠀⠀⠐⣧⣄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠸⣀⡇⢀⣀⢀⡟
⠀⠀⠀⠘⠧⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⣠⠤⠖⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⣋⣩⢤⢤⣽⣄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠲⠦⣄
⠀⢀⡞⠁⠀⠀⣀⡠⠷⠒⠒⠒⢦⡀⠀⠀⠀⡴⣫⠝⠿⢍⡑⢢⠀⠀⠀⠀⢸⡥⠒⠋⠉⠙⡆⠀⠀⠀⠙⡆⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠈⠳⣀
⠀⡟⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⡀⠀⠀⠀⡄⢸⡇⠀⠀⠀⢺⠀⠀⠀⣀⣾⣳⣤⣤⣄⣀⡇⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⡇⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢻⣠⠀⠀⢠⠁⡸⠀⠀⠀⠀⠈⠓⠒⠺⡻⠃⠁⠈⣼⠀⠉⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⣠⠎
⠀⠙⠢⠤⠼⠦⢄⣄⠤⠤⠖⠊⠀⠀⠀⠀⠀⠀⠻⠤⠤⠤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠄⠀⣻⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢀⣀
⠀⠀⠀⢀⠔⠈⠹⣁⣀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠢⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠔⠀⢈⠚⠁⠀⠀⡢⢄
⠀⠀⠘⠁⠤⣀⣀⡀⠀⣈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠀⠃⠀⠀⡌⠀⠀⠀⠐⠀⠀⠀⢄⠀⢠⠋⠉⡆
⠀⠀⡸⢄⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⢀⠃
⠀⢰⠒⢘⠁⠹⠉⠉⢃⠀⢹⠀⠀⠀⠀⠀⢄⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠁⠀⡎⣛⣟⢓
⠀⠀⢆⠈⡀⠀⡄⠀⠸⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⠉⠉⡁
⠀⠀⠈⠢⣐⡀⠰⡀⢰⢀⣃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠦⠀⣀⣀⣈⠑⣶⣻⠤⠔⠀⣉⣁⣀⠀⠈⠑⢢⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠐⠀⠀⠈⠐⠀⠠⡀⠀⠀⠀⠀⠀⠓⠋⠣⡐⠢⠄⣀⠀⠀⠀⠉⠰⢆⠀⠀⠉⠀⠀⠀⠀⡇
⠀⠀⢀⢀⡠⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢄⡀⠈⢁⠰⠃⠁⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⡂⠀⠈⠺⢤⠔⠊⠀⠀⠑⢄⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⡠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣀⣀⠇
⠀⠀⠘⣉⠀⠚⠾⠀⠀⡀⠄⠒⠈⠑⢄⠀⠀⠀⠢⠀⠄⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠶⠷⠆
⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⠀⠀⠀⣱⢲⡀⠀⠀⠀⠲⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡰⡟⠂⣈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠰⣷⠏⣈⡰⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⡰⠆⠛⠈⢩⠉⢶⠠⡄⠀⠀⠀⠀⠀⠀⠣⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⢓⡈⣅⠠⣆⡒⠃⠁⢠⡴⠂⢄
⠀⠀⡤⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠢⡀⠀⠀⠀⠀⠀⠀⢰⠂⠏⠙⣀⢠⡔⠁⠈⠛⠋⠀⡡⠱⠣⣽⢁
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⢠⢄⢀⣀⠀⠘⡆⠀⠀⠀⠀⠀⠰⣇⢙⡁⣡⡌⢀⢤⡔⢲⠎⣉⠝⠃⢜⢘⠀⠆
⠀⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠵⠯⠴⠮⠬⠭⠄⠄⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠁⠀⡴⠇⡨⠓⢤⡌⢱⠎⣠⠋⢃⠸
⠀⠙⠒⠲⠒⠒⠒⢲⠒⠒⠒⠒⠒⠒⢲⠖⢲⠶⠶⠒⠒⠤⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣴⣉⡰⢆⣨⢓⣤⠩⠵⠞⠢⠃
⠀⠀⠀⠀⠀⠀⠆⠸⠀⠀⠀⠀⠀⠀⣸⣿⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⡀⠤⠀⠠⠄⡀
⠀⠀⠀⢰⠀⢠⠀⡇⠀⢰⡖⢒⣒⣒⣛⣛⣓⣚⣒⣒⣒⣦⠀⢰⣲⣒⣒⣒⣒⣒⣒⣒⣲⣒⣀⣀⢀⠈⡇⠀⡰⢁⠀⠂⠀⠀⠠⠀⠑⠄
⠀⠀⠀⣸⠀⢸⠀⢇⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⠈⠓⠲⡀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠐⠸⠀⠄⢠⠂⠉⠁⠢⠀⠀⠈⡀
⠀⠀⢠⠃⠀⢸⠀⠘⡄⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢣⠀⠀⠑⠎⠙⢄⠌⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠇
⠀⣴⠣⠤⠤⠼⠤⠤⠽⠤⠤⠤⠭⠶⠤⠤⠤⠴⠮⠥⠤⠤⡄⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠈⠄⠈⠈⡐⠀⢒⠤⣀⠎⡘
⠀⠱⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠔⠁⠀⠀⠀⠈⠢⢄⣀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠑⠎⠀⠁⠁⠀⠄⠊
⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣷⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⡿⣟⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣛⣿⣿⣿⣺⣿⣿⣿⣿⡯⢝⡲⢝⢮⣾⣷⡿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⡻⢟⢯⣦⡳⡽⣿⡭⣺⣝⣟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣲⣵⣿⡷⣝⡶⣝⢮⡻⣯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡻⠿⣿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⢝⣮⣳⢱⣻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠄⢍⡋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⣧⡹⣿⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣯⣏⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠀⠈⠂⠝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣽⣿⣿⡿⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠒⢦⡀⠈⠎⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⢻⣟⣟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⣸⠇⠀⢐⡼⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣽⡜⣾⡟
⠀⠀⠀⠀⠀⠀⢸⢸⣽⣻⣿⣿⣿⣿⣿⡿⠉⠀⣠⠼⠿⣿⠛⠛⢶⣞⣠⣟⠋⢉⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⢇⣿⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠷⠦⣼⣇⡀⢀⣸⠀⣀⡾⠿⠧⣤⠜⠃⢄⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢸⣽⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣟⣿⣿⣿⠟⠛⠛⠓⣆⢀⣼⠏⠉⠉⠉⣿⡯⠤⣄⣠⣿⣆⠀⠀⢣⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡿
⠀⠀⠀⠀⠀⢰⡿⣿⣿⣿⣿⣦⣀⣠⠴⠿⡿⠛⠳⣤⡶⠶⣿⠀⠀⢸⡿⠃⠈⢳⡄⠀⠀⣧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠁
⠀⠀⠀⣀⣀⣠⣧⣿⣿⣋⣁⣈⣿⠁⠀⢀⣿⣀⣀⡾⠀⠀⢹⠦⠴⠋⢻⣤⣤⣾⣧⠀⠃⢿⡿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠏
⠀⣠⡾⠛⠉⠉⠙⠿⠿⠋⠉⠉⠛⠿⣶⡋⠉⢻⡿⠋⠉⠉⢿⣄⣀⣴⣿⣿⣿⣿⣿⣿⠘⠈⣿⣿⣿⣿⣿⣿⣿⣿⣽⠁
⣰⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣾⣇⡀⣀⣤⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⣿⣿⣯⣤⣤⣄⣀⣀⡀
⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣭⣉⡁⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣾⣿⠿⠿⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢻⡽⣷⠿⣿⢿⣿⣿⣶⣶⣤⣥⣤⣤⣤⣤⣤⣶⠶⠿⠛⢻⠟⠛⠋⠉⣀⣴⡾⠋
⠘⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣭⣵⡞⢧⠟⢿⣻⣿⣿⣟⣻⣿⣿⣿⣿⠟⠋⠉⢁⣤⠤⠤⠴⠋⣠⣤⣶⣿⠿⠋
⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠈⠙⢿⣿⣿⣿⣶⠾⠿⠿⠛⠛⠛⠉⠡⠤⠤⠤⠴⠞⠋⢀⣠⣴⣾⡿⠿⠛⠉
⠀⠀⠀⠉⠛⠻⠿⠛⠻⠶⠾⠛⠉⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣾⣿⣷⣦⣤⣤⣶⣶⣶⠶⠶⠶⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢒⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠁⠞⠉⠙⣳
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠀⠀⠀⠀⠀⠀⠰⡾⠷⠀⠀⠀⠀⠀⠀⠀⣿⢧⡀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢧⠀⠀⠀⣠⡴⢦
⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠂⠀⠀⠀⠀⠀⠀⢷⣿⠀⠰⠐⠀⡁⠂⠀⠠⡀⠀⠀⠀⠀⠀⠠⢬⣁⠀⠀⠀⠀⠊⠀⣸
⠀⠀⠀⠀⠀⠿⡄⠀⠀⢀⠔⠀⠀⠀⢀⡰⣲⣿⠀⠀⠀⠀⠀⣠⡾⣯⣻⠂⠀⠈⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠏⠉⠙⠚⠃⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠈⠉⢉⢻⣿⠀⠀⠀⠀⢠⣿⣇⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢀⠀⠈⠀⢀⣀
⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠀⠀⠀⢀⡎⣼⡿⠀⠀⠀⠀⢸⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠇⠀⠀⠀⣾⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠟⠁⠀⠀⠀⠀⠈⠻⣷⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠸⡀⠠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠘⠃

⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢄⡀⢤⠄⡀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠠⠄⢀⠀⠀⠀⠀⡠⠀⠤⢄⠀⠀⠠⡴⠒⠠⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠠⠀⢠⠋⠀⠀⠀⠈⢂⠀⢠⠂⠉⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠑⠀⠒⠁⠀⠈⠀⠇⠀⠀⠰⠀⠈⢃⠘⠁⠉⠠⡘⠀⠀⠀⡔⠉⠀⠙⠆
⢠⠀⠀⠘⡀⠀⠀⠀⠀⠈⢄⠀⢏⠑⠀⠒⠒⠒⠂⠈⠁⢀⠆⠀⠀⠀⠀⢀⠄⠀⠀⠢⡀⠈⢢⣄⠜⠀⠀⠈⠀⠀⠥⠈⢁⣀⠀⠀⡇⠀⠀⠀⡅
⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⡃⠈⠢⠄⡀⠀⠀⣀⣀⠠⠊⠀⠀⠀⠀⠠⠁⠈⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠈⡠⡉⠡⡀⠦⡀⠙⠢⠤⠚
⠀⢄⠄⠒⠒⠂⠌⡁⠒⠀⠂⠁⠀⢀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢀⠨⡀⠽⠂⠠⠀⠀⠀⠠⠀⠀⠘⠂⠁⠀⣠⠤⠠⠄
⠀⠸⡀⠀⠀⠀⠀⠤⠁⠢⡀⠀⠀⠉⠀⠁⠀⢀⣴⣤⣄⣀⢀⠀⢰⠃⡀⠀⠀⠀⡆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡱⠌⠐⠀⠀⡎⠡⣀⢀⡌
⠀⠀⠑⠄⡀⠀⠀⠀⢀⠔⠁⠀⠈⠐⠂⠁⠀⠘⢿⣿⢿⣿⣿⠇⠀⠑⠂⠁⠬⠀⠃⢀⠶⠀⠀⠢⡀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠑⠤⠄⠋
⠀⠀⠀⠀⣀⠨⠤⠬⠀⢀⣀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡂
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠃⢠⠤⡀⠀⢔⠒⠂⠤⠤⠐⠈⠀⠀⠀⡔⠀⢐⠀⢱⠀⠀⡤⠀⡃⠀⠀⠰⠉⠀⠀⠀⠂⠹⣌⠉
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠀⠀⠰⠀⠈⢆⠀⠀⠤⢀⡀⢀⣀⠀⠄⠊⠀⠀⠈⠀⠁⠀⠈⠀⠊⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⡆
⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠂⠁⠀⠀⠀⠂⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠑⠠⣀⣀⣀⠤⠐⠈⠀⠀⠀⠀⠀⠀⢀⡀⠤⣤⠀⠰⠇⠣⡀⠀⠀⠀⢠⠂⠆⢄⠀⠀⠀⠀⠀⠀⠐⠊⢀⣀⣀⡀⠀⠑⠲⠄⠠⠄⠊
⢀⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠐⠎⢦⠀⢸⡆⠐⠀⠀⠀⠘⠄⢀⡌⠈⢁⠄⠀⠀⠄⠀⡔⠋⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠣⠜⠀⠀⠀⠀⡠⠀⠲⠆⠁⠐⢄⠀⠀⢀⠈⠀⢀⢣⠀⡇⠀⠀⠀⠀⠀⠑⠒⠉⠀⠀⠈⠁⠰⠀⠀⠀⠀⠀⠐⠀⢀⣀⢄⠄⠀⠁⠂
⠀⠀⠠⡄⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠱⡠⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡠⠄⠀⠤⠅⡔⠊⣃
⠀⠀⠀⠀⠀⠠⣀⡀⢀⠈⠄⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠦⠼⠦⢀
⠀⠀⠀⠀⠑⠠⠄⢃⠜⠀⠈⠂⠤⠔⠒⠒⠁⣠⠄⠒⢦⣼⣁⠀⠀⠀⣠⣾⣿⡳⣷⣶⣶⣶⣶⣾⣶⡄⠀⠀⢠⠀⢄⠀⠀⠀⡎⠀⠀⠀⠀⠈⠆
⠀⠀⠰⢢⣀⡀⠐⠀⠀⢞⠉⠑⠄⠀⠀⠀⣸⠁⠀⠀⠈⠀⠈⣣⢠⣾⣿⣿⣿⡗⠟⠿⠋⠿⠹⠿⠿⠇⠀⠀⠀⠓⠤⠀⠀⠀⠅⠀⠀⠀⠀⠀⠸
⠀⠀⣺⣉⣱⣿⣷⣦⡀⠀⠍⠀⠙⠈⠁⠀⠹⣄⣀⠀⠀⣀⠔⡋⠈⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠘
⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠍⠉⠠⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⢀⣀⡀⡠⠊
⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠲⡄
⠀⠀⠙⠛⠿⠿⠟⠟⠀⠀⢠⠊⠁⠱⣄⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⠀⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢂⠱⠀⠀⣐⡀⠎⠀⠈⠂⠒⠁⠀⠀⠲⠒⠁⠀⠀⠀⠈⠁⠀⠀⠀⠠⠒⠑⢄⠀⠀⠀⢀⠀⠂⠢⠦⢄
⠀⠀⣴⠂⠉⠁⠀⠀⠀⠘⠀⠁⠀⠀⠈⡄⢃⠀⡇⠀⠀⠐⠀⠀⠀⠀⢀⠄⠒⠂⠈⠑⢄⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠀⠀⢠⠁⠀⠀⠀⠀⠀⠱
⠀⢸⣿⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠇⡘⠀⠄⠀⠀⠀⠀⢡⠀⠀⠁⠀⠀⠀⠠⠀⠈⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⡄⠀⠘
⠀⠈⢿⣿⣦⣂⣀⠕⠀⠐⢄⠀⢀⡠⢊⠐⠀⠀⠣⡀⠀⠀⠀⠸⠀⠀⢂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠑⢄⡀⠀⠀⡀⠈
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠑⠄⠀⠀⠔⠁⠀⠀⠀⠀⠀⠑⠠⠠⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠇⠀⠉⠁⠒⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠉⠑⠒⠤⠤⠀⡀⠎⠠⠚⢠⠐⠒⠒⠚⠛⠩⠭⠭⠼⠛⢲⠂
⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⢰⠀⠆⠀⠆⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠠⠀⠐⠀⠀⢸⠀⠀⠀⡇⠀⢀⠀⢺⡀⠐⠒⠒⠒⠂⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⢸⡇⠐⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠓⠀⠁⢓⠲⠤⠤⠤⣤⣄⣤⠤⠤⠎
⠀⠀⠀⠀⠀⠀⢸⡇⠢⡠⠂⠀⠀⠀⢸⠀⠀⢠⡇⠀⠰⣿⣶⣼⠀⢠⠆⠀⠀⠀⠀⠄⢸⠀⠀⠀⢀⡄⠐⠒⠶⠶⠤⢤⣄⣀⡀
⢀⠀⠀⠀⠀⠒⠂⣇⠀⠀⠀⠀⠘⠀⢸⠀⠀⢸⠃⠐⠷⠿⠿⠇⡄⢮⢀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠸⠀⠀⠀⠀⠈⠀⠐⠂⠈⠉⠛⢲
⢛⠒⠒⠒⠂⠀⠀⣿⢠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠈⠀⠀⡤⠄⠞⢰⠃⣠⡶⣞⡓⠶⠞⠉⠙⢦⠀⠀⠀⠀⠀⢸⡄
⠀⠙⠒⠒⠀⠀⠀⢹⠀⠀⠉⠉⠉⠋⠀⢰⠀⠀⠀⠀⠀⠀⢀⡇⢰⠀⡴⠀⠈⠀⠀⢨⠾⡋⠀⠈⠻⣄⠀⢀⣀⠀⢳⠀⠀⠀⠀⣿⢇⣀
⠀⠈⡀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢸⢸⠁⠀⠀⠀⡅⣸⠁⠀⡀⠢⠀⠀⠀⢀⡅⠀⠉⠀⠀⠀⢿⣀⠀⠁⠀⠐⠀⢀⣀⠀⠇⠨⠉⢙⠛⠛⠶⠦
⠀⠀⠑⠤⢤⡤⠤⠀⣀⠶⢠⠀⡄⢀⠀⠀⡎⠀⠀⠀⠀⢡⠇⠀⠀⠈⠒⣢⢀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠙⣧⠀⣄⡀⢳⠀⣀⠀⠉⠐⠒⠂⠼⢃⡴⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠐⠨⠀⠂⢱⠃⠀⠀⠀⡾⠀⠀⠀⠀⣎⠀⠀⠒⠶⢶⣤⣄⣉⡀⠀⠀⠀⠘⠇⠈⠁⣀⡇⢀⡉⠁⠀⠀⠀⢰⡯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠃⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠉⠙⠛⠷⢦⣤⡀⠐⡤⠊⠁⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣶⣤⣤⣤⣀⣀⣉⣀⣀⣤⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠤⢁⡀⠈⠁
⠀⠀⠀⠃⠀⠀⢀⡀⠀⣄⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠀⠈⠠⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠠⠆⠉⡵⠀⠆⠒⡲
⣤⡄⠀⠀⠆⠀⠈⠆⠰⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⡏⠁⠀⠐⣆⠠⣞⣤
⠘⡷⠂⠀⠀⠀⢀⡉⠀⠀⢀⠀⢐⡂⡀⢀⡤⠀⠀⠀⠀⠁⠀⠑⡀⠃⠀⠠⠀⠀⠀⠐⡀⠀⢀⢀⠀⠀⠂⠀⠀⠀⠀⡇⢤⠀⠴⠹⠀⠍⠉
⠀⠱⣄⠀⠀⠀⠀⠳⡴⠋⠁⠀⠀⠀⠄⠆⠀⠀⠉⠀⠀⠀⠐⡀⢠⡤⡀⠀⣀⡀⠀⠐⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠐⠠⠕
⠀⠀⠈⠑⠂⢰⠀⠈⠀⣤⣄⠠⠞⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⢠⠈⠰⠶⡀⢤⡇⢀⠎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣿⠆⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⢀⠀⠀⠀⠰⢃⠈⢩⠀⠀⠀⠭⠿⡀⢉⠀⠙⠋⡄⡎⠙⠀⠀⠀⢄⡁⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⡇⠀⠙⠒⠜⠁⠁⠀⠀⠀⠁⢀⠀⠙⠂⣀⠀⠀⡤⠤⠞⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠹⣮⡵⠀⢀⠄⠀⠀⣄⠀⠀⠀⠀⠀⡄⠀⢁⡀⠀⠀⠻⠥⠔⠁⠀⡠⠢⡄⠀⢀⣤⡊
⠀⠀⠀⠀⠀⠀⢀⡖⠀⠐⢖⠊⠀⠈⣲⠖⠁⠂⠀⢖⠁⠀⠀⢀⡴⠋⠉⠁⠲⣄⠁⠘⢄⠀⠂⠄⠀⢉⡀⠄⠊⠀⢼⡁⠀⠁⠀⢱
⠀⠀⠀⠀⠀⣠⣬⣵⡄⢠⣞⣀⡀⣀⣳⣤⠀⠀⢠⣞⣀⡀⢀⣀⣙⣦⠀⢀⣴⣁⣈⠛⠛⠁⠀⠀⠀⣀⣼⡂⠀⢀⣀⣙⣦⠀⢀⣞⣀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠞⠻⠛⠓⢆
⠀⠀⠀⠀⠀⠀⠰⠛⠉⠓⣦⣷⠾⢣⢀⡀
⠀⠀⠀⠀⠀⣰⡖⢀⣠⣤⣾⡅⠀⠘⠋
⠀⠀⠀⠀⠀⣿⣰⠟⠁⠀⣠⡤⠶⠦⠀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⠇⠀⣰⠟⠁⠀⣠⠴⠛⠉⣠⡴⠞⢋⡉⠭⠤⠤⠤⠭⠭⢉⣛⠲⢦⣄
⠀⠀⠀⠀⠀⢹⠀⣼⠃⠀⠀⡴⠁⠀⢠⠞⡡⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⡓⢄
⠀⠀⠀⠀⠀⢸⣰⠇⠀⠀⡘⠀⠀⣰⢃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠄⠃
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠁⠀⢰⠁⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠉⠀⠀⠀⠀⠈⠀⣀⣀⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠂⠀⣀⠘⠀⠀⠀⠀⠶⣷⠀⣉⡀⢰⡏⠠⠤⠖⠢
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠊⠝⠠⡄⠀⠀⠒⠒⠢⠀⠀⠉⠀⢀⢀⡴⠚⠋⣷⠟⠉⢉⡥⢧⡴⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢧⠄⠀⠀⠀⠀⠓⣂⠀⠀⢀⣀⠀⠀⢀⡀⠙⠀⠀⣰⠃⡾⠁⠀⣼⠁⠀⢠⡏⠀⠀⢿⠀⢲⡈⠂
⠀⠀⠀⠀⠀⢲⣤⢈⣠⣀⡀⠛⠀⠉⠀⠙⠋⠀⠉⠉⠉⠙⠭⡀⠀⢰⡇⠀⡇⠀⠀⡇⠀⠀⣾⠀⠀⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠑⣘⢏⡖⠛⢑⠀⠠⡄⠐⢦⠀⠀⠀⢀⠌⠴⠩⠛⢺⡇⠀⡇⠀⠀⡇⠀⠀⡟⠀⠀⠀⢸⠁⠀⡇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢀⠊⠉⠉⠀⢀⠀⠁⠀⠀⠀⠐⢚⠷⠿⠷⠫⢔⡡⢊⠹⣇⠀⠹⡀⠀⠇⠀⠀⡇⠀⠀⠀⡿⠀⢸⠇⠀⡎⢀⣀⣑
⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠆⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣤⣅⣀⢻⡄⠀⢣⠀⠀⠀⠀⣷⠀⠀⢰⠇⢀⡾⠀⣰⣃⠉⠁⠉⠂
⠀⠀⠀⠀⠀⢄⣳⡈⠀⠀⠀⠸⠻⠖⠋⠀⠈⠁⠀⠀⠐⠉⠀⠀⠀⠑⠈⣿⣄⠀⠁⠀⠀⠀⢸⡀⢀⡟⢀⣾⣅⣴⠃⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⢤⣤⣀⠀⠀⠀⢀⡜⠛⠳⠲⢀⡀⠀⠀⠁⢠⣴⣿⠁⠀⠈⠓⠀⠐⠂
⠀⠀⠀⠀⠀⠀⣤⣤⣄⣷⠤⢄⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠑⠂⠀⠠⢀⣠⠛⠉⠒⢀⠤⠀⠀⠀⠀⠀⣄⠀⠀⢀⣠⣤⡀⢀⣡⠤⠂
⠀⠀⠀⠀⠀⠀⢹⣿⡿⠿⠂⢊⣩⠖⣢⠟⠒⠒⠶⣤⠀⠀⠀⢀⠌⠑⠒⢢⡈⠙⢋⡀⠖⠀⣔⢒⣖⣉⣨⡉⠉⠉⠀⠀⠁⠀⠈⠙⠄
⠀⠀⠀⠀⠀⢴⣿⣿⣟⣩⣵⣮⠔⠈⠀⠀⠀⠀⠀⠀⠁⢀⠔⠁⢈⠉⠒⢢⡌⠓⠒⠤⠀⠀⠸⡿⠉⣿⣅⢰⠄⠀⠀⠀⠀⠀⣀⠠
⠀⠀⠀⠀⠐⠿⠟⠛⠻⠿⠋⠁⠀⠀⢀⠀⠀⠀⢀⡠⠂⠁⠀⠀⢈⣉⠭⡑⠶⠏⠉⠀⠀⠀⠀⠨⣏⠁⠈⡅⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠒⢉⡕⠒⠀⠀⠀⠀⠀⠀⠑⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢌⡁

⣶⣶⣷⢶⣶⠶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣷⣷⣾⣶⣾⣶⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠆⠐⡐⠖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠣⢄⢣⡰⠂⣙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠣⣠⠳⠀⢠⡸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⢄⡀⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠁⠢⡛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠈⠢⣄⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⡀⠀⠑⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠈⢢⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢃⠀⠡⡀⠀⠱⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣺⣯⠭⠭⣑⠢⣆⠀⠑⠄⠀⠐⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⣡⣴⣶⣿⣿⣿⣶⣤⡉⠢⣖⡊⠁⠑⢄⠁⠀⠀⡄⠀⢧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⡥⠘⢻⢿⣾⢿⣿⣿⡿⠿⠛⢄⠑⣀⠔⣊⠉⢢⠀⠀⠘⡰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⠇⠮⢇⢈⣀⠓⠈⣿⠐⢿⣿⠀⠀⢸⡄⢹⠛⣁⡤⠾⡇⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣀⡾⣼⡴⠈⢿⡇⣤⠀⠀⠀⠈⡿⡗⢰⣿⡇⠀⣜⡥⠔⢉⠁⠀⢰⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣌⠢⡍⠀⠹⠀⣺⣑⣄⠀⣰⢆⡺⢴⠍⢂⣦⡧⠀⠈⣤⠖⢛⢁⣁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⢈⠋⠀⠀⠸⣜⣃⣿⠻⡴⣽⢯⠟⠞⢧⣴⣼⡏⠰⣘⣤⣢⡬⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠼⠃⣂⣾⡀⡀⢀⢊⠄⡡⢈⡏⡟⣯⣿⢬⠠⣼⡣⠸⠃⠀⡩⠚⠁
⠀⠀⠀⠀⠀⢐⠂⠂⠀⠈⣿⣻⣿⣾⡘⢠⠁⢰⠁⡇⢸⢿⠿⢽⣛⣄⢀⢶⠈
⠀⠀⠤⣶⡝⡌⣇⣰⡀⣸⣚⣚⣻⣯⣳⣼⣄⠎⢠⢁⣾⣳⠀⠸⢹⢏⠝⠀⠁
⢀⣀⠀⢀⠀⠊⠘⢹⣭⢳⣻⡊⠈⢉⣹⡼⡏⣞⣯⣿⣿⣿⡄⠈⠰⠊
⢨⠀⠁⠂⠁⠀⢘⣾⢈⡈⢙⣿⢤⣀⢀⡞⠸⡻⢹⣭⠩⠄⠳⡄⠀⠄
⠈⠑⠒⠊⠁⠐⠘⠺⠛⠁⠘⣹⡿⠁⠀⠁⠀⠀⠈⠀⠀⠀⠀⠈⠓⠻⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠖⠋⠉⠁⠀⣏⣉⣙⣛⠳⣶⣴⡏⠁⢤⡁⠛⢲⣤⠖⠋⢉⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⡇⣼⠁⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⢛⡎⣇⠁⣢⣀⣧⣾⣄⠁⠈⠀⢸⡇⠒⠤⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡗⢠⣼⣿⣶⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣭⣍⡑⣛⣹⣷⣿⡟⢦⣀⠀⣸⣧⠀⠠⠼⢏⠦⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⢸⣿⣷⣋⣉⢻⡿⣟⣳⢄⣀⠀⠀⠠⢤⣴⣫⣾⡟⡏⢯⠹⡇⢹⠈⡇⡟⠀⠈⠉⠛⠁⠀⠀⠵⢤⡼⠗⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣼⣟⣴⢻⡿⠿⠟⠀⠸⠽⢿⣍⠓⢯⣽⣋⣟⢻⣿⡻⣿⣷⣱⠸⡀⢦⠀⡄⠀⢻⡶⠒⢢⡄⠀⣤⠤⣤⣤⠤⢦⣄⣀⣈⣿⣛⡷
⠀⠀⠀⠀⠀⢀⠟⠛⣹⣧⠟⣹⣿⣽⣝⣓⣒⢦⣹⣷⠻⠿⣠⠮⠽⢿⣮⣽⣿⢦⢳⠸⡀⠇⢸⢸⣧⡄⠤⠷⣈⡷⠀⢤⣤⠤⠄⣤⡤⠍⣿⣶⠧⡀
⠀⠀⠀⠀⠠⠋⡰⢾⡟⣡⡞⠉⠀⠀⠈⠉⡻⠉⠉⣿⣛⣿⣿⠾⣟⡟⢋⡿⠿⠷⣷⣧⣇⣠⣸⠞⠻⣦⠤⠎⢵⡷⠴⠋⣌⣷⣾⣄⣵⣮⣼⣗⣶⡿⠷
⠀⠀⠀⣤⣾⣋⡹⠯⢾⣉⡩⣶⣄⠀⠀⣠⢶⡀⢸⡿⠿⠷⠶⠤⠚⠛⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠹⣦⣤⣤⠖⢶⣤⣯⣭⡀⡟⠀⠀⠉⠉⠛⠲⠾⢄⡀
⠀⠠⠞⠉⠛⠓⠒⠛⠻⠋⠉⠛⢙⡇⢠⣏⣾⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠾⡗⠛⠛⡇⡿⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⢷⠒⠲⠶⠶⠶⠶⠖⠚⠚⢿⡇⠀⠈⠁⡞⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠂⢀⡤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢰⣦⢿⣷⠀⠀⠀⣰⠀⠀⢀⡞⠁⣤⡀
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡸⠁⠀⢀⣴⠖⠙⠋⠂⠀⠀⠀⣼⠃⠀⡾⢁⠂⢀⡀⠀⠀⣀⠀⠀⠀⠀⠈⡄⠹⡎⣿⡀⢀⡔⠋⠓⠒⠶⣷⣚⠅⡇
⠀⠀⢈⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣷⣤⡤⠃⠀⣰⡟⠁⠀⠀⠀⠀⠀⣀⢰⣯⠀⣸⡗⠂⢰⠏⠀⠀⡾⠁⠀⠀⠀⠀⠀⠹⠨⠡⣹⠟⠀⠕⠒⠀⠂⠀⠚⠻⣏
⠀⠀⢸⡋⠉⠉⠉⠉⡉⠩⢿⡀⡟⣿⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣴⠏⠉⢹⢁⠀⣿⠀⠀⠹⠀⠀⠸⡇⠀⠔⠁⠀⠀⠀⠀⣇⣴⡗⠀⠂⢀⠈⠀⠈⠀⠀⣶⣿
⠀⠀⢸⡇⠀⠀⢀⣀⣀⣀⣼⣯⣵⡏⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠛⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⣀⣀⡴⢦⡾⠻⣦⡿⠘⡇
⠀⠀⠘⣷⠖⠛⠉⣋⠀⠀⠈⠀⠈⠉⠓⠦⡄⠀⠀⠀⠀⠀⢀⣶⢹⡄⠀⠀⠁⠀⠁⢀⡾⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣍⡩⣴⣞⡶⣤⣪⠔⠠⣿
⠀⢠⡞⠀⢀⣀⣨⠤⠴⠒⠲⠒⠢⣤⡄⠀⠈⡄⠀⠀⠀⠀⢸⣿⠛⠀⠀⠀⠀⠀⢀⣾⠁⢀⡴⠁⠃⡀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢉⠟⠛⣆⡸⢝⣡⡷⠞⠁
⠀⢾⠀⠐⠀⠙⡛⠒⢚⣛⡛⠛⠉⠁⠀⢀⠴⡇⠀⠀⠀⡠⠼⣿⢀⡤⠀⠀⠀⠀⣼⠇⢀⡿⠀⠀⢸⡑⣿⠀⠀⠀⠀⠀⠀⣠⡆⣀⣀⣬⠁⠀⢼⡿⠋⣡⠖⢛⣷
⠀⠀⢷⠒⠉⠒⠦⠚⠉⠀⠉⠢⠐⠉⠑⢎⣼⡀⠀⠀⡞⠁⢀⣿⡞⠁⠀⠀⠀⢠⡟⠀⠈⠿⠄⠀⠀⠀⢧⠀⠀⠀⠀⢠⠯⢿⡏⠁⠒⠛⠓⠛⡿⢁⣜⣻⣦⠴⠃
⠀⣠⣼⢷⡤⣄⣠⣤⣶⣶⣶⣲⣶⣶⣖⣋⢏⡽⡀⠀⠁⠀⠉⠻⠃⠀⠀⠀⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⣾⣦⣤⣄⣀⣀⣸⣧⣾⣾⠥⠴⣶⡆
⠀⠙⠈⠙⢿⠿⠿⠿⠟⠛⠛⠁⠈⣃⢨⡿⠛⠙⢯⡖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢰⣄⠀⠀⠀⠀⠀⠀⡀⣠⣟⣇⢠⡟⢭⠉⣿⠟⡾⣏⠑⣶⠋⠁
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢰⣿⣾⣴⠓⢒⣿⢑⣾⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠟⠞⠣⣈⡲⢿⠛⠃⡔⠑⠓⠶⠿⢿⡿⢦⣾⡿⣸⢣⡌⢟⡅
⠀⠀⠀⠀⠀⣨⢶⡄⢀⣀⣠⡴⢚⣙⣥⡿⠉⠭⠉⠉⠻⡖⣰⡆⣶⡍⠲⡄⢠⡦⠵⣿⠓⢺⠒⢺⠃⠹⠃⢸⠄⡸⠁⠀⠦⠀⢀⣼⡧⠈⡼⢁⣿⡿⠖⠉
⠀⠀⠀⠀⠀⠳⠌⠠⠤⢻⣷⠞⠛⢉⣸⠃⠀⠀⠀⠀⠀⢷⢌⣀⣘⢰⠀⢙⣼⠻⡇⠈⡆⠘⠀⠀⠆⠀⡄⢸⡔⠀⢀⣄⠀⠀⡘⣹⠟⠊⠛⠛⢯
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠛⠉⢈⣄⣦⠀⠀⠀⣠⠖⠉⣹⠀⣌⣽⠶⠛⠛⠛⠻⢦⡸⢤⣧⣀⣤⣤⣷⣿⣁⡀⠀⠀⠀⡄⠀⡿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠰⠷⠛⠉⡟⠀⢹⠰⡟⠰⠂⠀⢉⡰⠿⠁⠀⠀⠀⠀⠠⠶⠷⣾⣯⢩⠁⣤⠰⡟⢣⣤⡙⢛⣚⣯⠺⠁⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⣼⡀⣀⠷⠊⢀⡇⠑⡶⠂⣹⡿⢁⡗⠀⠀⠀⡠⠀⠀⠀⠀⠈⡇⠀⠀⢰⠀⢸⡀⠿⢠⡏⠝⢩⡗⠠⠤⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣁⣀⣀⠾⠢⠤⠌⠒⣸⢏⠘⣀⣃⠀⠀⣰⠁⣀⣤⡴⠒⠛⣧⠈⠀⠘⡀⠀⣡⠈⠀⠛⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠀⠀⠀⠈⠣⡀⡟⣿⣻⠟⢶⡛⠛⠋⠉⠛⠣⣀⡼⠟⠓⠘⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠉⠁⠀⠀⠐⠒⠒⠉
⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⠤⠶⠶⠶⠖⠒⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠶⠒⠒⠒⠛⠛⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠥⣀⣀⠀⠀⠳⡀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⡇⠀⠀⠀⠈⠁⠒⢻⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢯⣟⣯⡇⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⢀⡄⡇
⠀⠀⠀⠀⠀⢀⠔⠁⠈⠀⢜⠧⣄⠀⠀⠀⠀⠀⢸⢀⡄⢠⡤⡆⡖⠀⣹⣯⡀⡇
⠀⠀⠀⢀⠞⠁⡔⠀⢠⠀⠀⠑⡈⠙⢦⠀⠀⠀⢸⠀⣿⠛⠇⠇⠛⠛⠉⠁⠀⡇
⠀⠀⠀⡏⠀⠈⠀⠀⠈⠀⠀⠀⠈⠀⠈⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠣⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⡴⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡀
⠀⠀⠀⠀⢹⡌⠉⠉⠉⠉⠉⠉⠀⡼⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠻⠿⠓⠤⣀
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠰⠾⠿⣀⠀⢠⣶⣿⠒⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠋⠛⢒⣒⠒⠒⠚⠛⠳⠦⠤⠤⠤⠬⠯⠭⣷⡄
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢠⣇⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠙⠿⠷⠀⢰⣾⣷⡀⠀⠀⠀⠙⢷⡄⠀⡇
⠀⠀⠀⠀⠀⣠⣤⠟⠀⠀⠀⢸⣦⡍⠓⠦⣄⡀⢸⠀⠀⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠛⠿⠧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢿⣿⣶⣶⣶⣶⣿⣿⠏⠀⠀⠀⠉⠛⠶⠒⠚⠉⠉⢸⠀⠀⠀⠀⢰⣶⣶⠄⠠⣤⣄⠀⠘⠻⠟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠒⠒⠓⠶⠶⠦⠭⠿⠥⢤⣤⣀⣀⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠤⠂⠀⠀⡀⢠⠒⠤⠠⡀⠀⠀⠀⠀⠀⠐⠄⠀⡀⠄⠀⠴⠀⠀⠀⠀⠀⠠⠀⡀⢐⠀⠀⠠⠀⠀⠀⠀⠀⡐⠘⠉⠙⠐⠀⠀⠀⠀⠰⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠁⡄⠀⠀⠂⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠃⢠⠈⠀⣀⠀⠀⠡⠀⠀⠀⠐⠀⢀⠀⣜⠀⣎⠄
⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢀⠈⠂⠀⡐⠐⠀⠰⠈⢠⠠⠄⠁⠀⠀⠈⠣⠃⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠋⠇⠠⠃
⠀⠀⠀⠹⠄⠀⠀⠈⠢⠀⠀⠀⠃⠀⠀⠀⠈⠂⢄⡀⡐⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⡷⠋⠂⢄⠀⠠⠀⠀⠀⠂⡠⠾⢟⡃⠀⠀⣸⠂
⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡃⠈⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉⠀⠀⠈⠇⠀⠀⠁⠐⠛⢂⠤⠐⠂
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⢀⠀⠁⠂⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠄⠀⠄⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠄⠀⣠⡾⡇⠀⠀⡀⡀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡀
⠀⠀⠰⠎⠀⠀⠀⠀⠀⠒⠁⠄⠀⠀⠀⠀⠀⠄⠀⠄⡀⠀⠀⠀⠙⠀⣠⠣⢈⡆⠀⠀⠀⠸⣡⢀⢀⠀⠄⠈⠀⠀⢀⣀⢀⣀⡀⠀⠀⣠⠀⠀⠀⢀⠅
⠀⠟⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠭⢙⡚⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⣾⡉⣠⣊⢔⠝⡄
⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠿⠉⡅⠀⠀⣞⢮⣱⠆⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢀⡀⠀⣈⢁⠌⠙⠛⠛⠁⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠠⠟⠀⠀⠀⠀⣠⣞⠗⠁⠀⠀⠒⠀⠀⠘⢓⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠛⢦⠤⢬⠃⠀⠀⠁
⠀⠀⠀⠐⠀⠤⠈⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠂⠀⠀⠀⠀⠂



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠗⣒⢒⢈⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠁⠀⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢆⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⠀⢀⠜⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠠⠄⡆⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡄⢀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀
⠀⠀⠀⠀⠀⠁⠘⠄⠁⠀⠀⠃⠄⠀⡀⠀⠀⠀⢀⡤⠂⠉⠀⠀⠀⠀⠀⠈⠁⠢
⠀⠀⠀⠀⠀⠃⠄⡀⠀⠀⠀⡀⠄⠈⠁⠀⠀⠀⡎⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠢⠁⠀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠂⠤⣀⣀⣀⡠⠄⠀⠀⠀⠐⢀⠀⡟⡉⠚⠀⠀⠈⠀⠀⠀⠀⠐⢈⠀⠀⠀⠸⡉⠒⠀⠀⠀⠀⠀⠂⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢀⡁⠀⠀⠀⠀⠀⠲⡢⠂⠀⠀⠀⠀⠑⢔⠀⠀⠀⠀⢀⣄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣄⡀⠁⠀⢀⡄⠀⠀⢤⠀⠀⠂⢒⠀⢀⠀⠀⠈⠉⠈⠀⠀⠀⢀⠀⠒⠂⢀⠄
⠀⠀⠀⠀⠀⠀⡀⠋⠀⠀⠁⢀⠀⠀⠀⠀⠀⡏⣉⠁⠉⠹⠂⠀⠀⢸⠀⠀⠠⠈⠄⠀⠀⠀⡄⡀⠰⠪⠀⠀⠼⠆⠀⠀⠐⠅
⠀⠀⠀⠀⢀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢐⠄⢀⠤⠀⠀⠀⡀⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠡⣀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠿⠀⠀⠀⢸⠀⢀⢀⢐⠂⠃⡃⠠⠀⠀⠈⠆⠯⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠉⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠂⠀⠀⠀⠂⠀⠀⠠⠄⠀⠀⠒⠒⠂⠂⠒⠒⠒⠒⠒⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⡉⠀⠂
⠀⠀⠀⠀⠀⠀⡄⠀⢈
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⣠⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣯⣷⡶⢦⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡽⢿⡿⠛⠀⣌⡀⢠⡆⢀⣤⢀⠀⠀⠹⠇⠢⣄⣶⠀⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡋⠹⣿⡄⠈⣢⠌⢀⡔⠉⢣⣠⣤⠴⠖⠄⠀⢰⣿⣿⣶⣝⣼⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡿⠓⢸⠃⠀⡀⢻⡔⠻⣷⣄⠈⠗⠈⣤⠀⢰⣿⣞⣿⣿⣷⠶⠛⠛⠻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⠃⣸⣿⠿⣧⣼⡿⠟⠿⠀⢠⡿⢋⣙⣻⣿⢏⣻⠏⠀⠀⠀⠀⠀⣿⣲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣄⠘⠿⣿⠋⠻⢅⣤⢤⣜⠻⠴⢿⣿⣿⠿⣄⡉⠢⡒⠀⠤⡄⠀⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣼⠟⠛⠛⡇⠀⣠⡄⠁⠀⠀⠀⠀⠠⠍⠁⠀⠛⠉⠹⡆⠀⠀⡟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⢃⡀⠀⠀⠁⠠⣄⠈⠙⠂⠀⠀⠀⢀⡀⠈⢀⣼⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠔⡡⣿⣦⣀⡠⠀⠉⠉⢳⣄⠀⠀⠄⢸⣟⣓⣉⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢧⣼⣷⡿⠿⠛⢧⠀⡀⢸⡿⣀⡀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠠⠀⢻⠏⠀⠀⠀⢀⡞⠠⠂⣀⠁⠉⢠⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠒⠸⠂⣤⣄⣀⣿⡀⠀⢐⡠⠀⢠⡌⠁⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠞⠀⠀⠁⠆⢸⣿⣇⣠⣤⣤⣢⠖⠚⠁⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⣠⣦⣿⣿⣿⣿⣿⣿⣿⣶⣦⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠟⢯⣿⣿⣿⣿⣿⣿⣥⣤⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⠻⠟⠋

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣠⣒⡟⢛⣶⡀⠀⠀⠀⠀⠀⡜⠀⠘⡀⠀⠀⠀⠀⠀⠀⡜⠉⠱⡀⠀⠀⠀⠀⠀⣰⣚⡛⠛⡳⡀
⠀⢸⠁⠀⠈⠁⠀⢱⠀⠀⠀⠀⢰⠁⠀⠀⢣⠀⠀⠀⠀⠀⡸⠀⠀⠀⠣⡀⠀⠀⠀⠘⠀⠀⠉⠉⠀⢸
⠀⠘⣄⠀⠀⠀⢀⡜⠀⠀⠀⠀⠘⢄⠀⢀⠎⠀⠀⠀⠀⠀⡅⢀⡀⢀⣀⡅⠀⠀⠀⠘⢄⠀⠀⠀⢀⠜
⠀⠀⠈⠑⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⢴⡂⠀⠀⠀⠀⠀⠀⠀⣀⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⣠⣤⣶⡀
⠀⠀⢠⡛⡛⢫⡵⣀⠀⠀⠀⡰⠋⠀⠙⠁⠈⠳⡀⠀⠀⠀⠀⠀⠀⡎⠉⢢⠀⠀⠀⠀⠸⢿⣿⣿⠆
⠀⢨⣓⠁⠄⠰⡈⡕⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⠇⠀⠀⠀⢰⢏⡟⡽⣷
⠀⠐⣟⣄⠀⢠⢮⠟⠀⠀⠀⠙⢄⣀⠀⠀⣀⠜⠀⠀⠀⢠⠖⠒⠊⠀⢀⠞⠀⠀⠀⠀⢻⣽⣜⣾⣾
⠀⠀⠈⠛⠓⠚⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠓⠲⠒⠚⠁⠀⠀⠀⠀⠀⠀⠙⠓⠛⠁
⠀⠀⢀⠤⠶⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡆⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢤⡀
⠀⠀⡇⠀⠀⠀⠀⢃⠀⠀⠀⠀⡠⠊⠉⠑⠲⡄⠀⠀⠀⠀⣴⠋⠉⠋⠛⡄⠀⠀⠀⡎⡀⠃⠀⠀⠀⠘⡆
⠀⠀⢇⠀⠀⠀⠀⡘⠀⠀⠀⠀⡇⠀⠀⠀⠀⡘⠀⠀⠀⢸⡅⠐⠂⠀⠀⣿⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡆
⠀⠀⢘⠆⠀⠀⡠⠃⠀⠀⠀⠀⠘⠦⠤⠤⠞⠁⠀⠀⠀⠸⣦⢀⠀⠀⢠⠇⠀⠀⠀⢣⡡⠀⠀⠀⣠⡴⠁
⠀⠀⠈⠒⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠛⠁⠀⠀⠀⠀⠀⠉⠛⠚⠚⠋
⠀⠀⠀⠀⡲⠂⡄⠀⠀⠀⠀⠀⠀⠴⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⡂
⠀⠀⠀⠀⢱⠀⠐⠀⠀⠀⠀⢀⡔⠂⠋⣗⡦⢄⠀⠀⠀⢀⡰⢻⠈⠙⢁⣸⠇⠀⠀⠀⠀⣤⡾⢣⠟⣣
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⣾⡖⠈⡱⠌⠁⢮⡆⠀⢀⠏⢁⡨⠶⠀⠁⡞⠀⠀⠀⢀⢼⡥⢿⣡⣏⣽
⠀⠀⡠⠐⠁⢀⠞⠀⠀⠀⠀⢣⠐⡂⡅⠀⡉⡤⠁⠀⠈⢆⠁⠠⠃⢒⠞⠁⠀⠀⠀⠑⡞⢲⠚⣦⡞⠊
⠀⠀⠑⠒⠈⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠒⠋⠀⠀⠀⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠉⠉⠊⠁

⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠂⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢂⠀⠀⡠⢀⢀⠀⠀⠀⠈⠂⠠⠀⠒⠀⠒
⠀⠀⠀⠀⠀⠸⢀⠀⠄⠈⠁⢈⠀⠀⠀⠀⠀⠀⠄⠤⠄⡀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢐⠀⠀⠈⠑⠄⢀⠀⠁⠀⠀⠀⠂⠠
⠀⠀⠀⠱⠀⠀⢠⠀⠄⠀⠀⠁⠀⠀⠈⠁⠀⠐⠚⠀⢀⢀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠅⠀⠀⢠⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⡀⢳⡴⣎⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠸⠏⢁⠀⠀⠀⠊⠀⠀⣀⡁⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠠⠀⠀⠀⠀⠀⢈⣧⣂⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡀⠀⠀⠀⠀⠀⠉
⠀⠀⢀⠄⠀⢀⠀⠀⠀⠀⠂⠀⣜⠉⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⣀⠀⠂⠡⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠎⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⠄⠀⠒⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠁⠀⠂⠀⠄⠀⠃⠨⠌⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡠⠈
⠀⢀⡀⠦⠀⠀⠀⡐⠠⠀⠠⠀⠀⠈⠀⢰⠀⠀⠀⠀⢃⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡀⠁⡀⢒⠀⡈⠀⡀⢆⠈⡀⠀⠀⠀⠘⠀⢘⠁⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⢁⠐⠄⡠⠀⡀⠢⠀⡌⠀⠀⠀⠀⠳⠆⢀⠘⢀⠆⡠⠞⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⠴⠺⠀⠀⢀
⠀⠀⠁⠄⠀⠀⠈⠡⠠⠀⠀⠀⠀⠀⠀⠲⠆⡴⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠉⠂
⠀⠀⠇⠁⡄⠀⠸⠈⢠⠀⠀⠀⠀⠀⠀⠀⢠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⡀⠀⠀⠐⠂
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢡⡜⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠠⠀⢐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢄⠰⠀⠀⠉⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠴⠀⢈⡴⡀⠛⡤⠀⢄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠠⣁⠆⠀⠀⠀⡀⠀⡀⠀⠁⠀⠀⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠠⡄⠀⠀⠀⠀⠐⠢⢘⠀⠀⠀⠈⠀⠀⠀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠃⠀⠀⠀⠠⡀⠂⠂⠀⠀⠀⠀⡀
⠀⠀⢸⠄⠀⠰⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠐⣄⠀⠐⣁⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⠶⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠄⣲⣶⠀⠀⠀⠀⠀⠀⠀⠂⠄⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠄⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠉⠄⠈⠉⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠐⠈⠁⣀⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⢃⣄⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣠⠄⠁⠀⠷⠂
⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢈⡀⠠⣶⠄⠀⠸⠏
⠀⠀⢠⣀⣤⣀⣀⣀⣀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡋⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠈⠀⠀⠀⠈⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈

⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠂⠁⠀⠀⠀⠀⠀⠈⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠒⠚⠉⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠟⠛⢻⢿⡏⠀⠀⠀⠀⠀⣀⠀⠀⠀⠲⠦⣄⠀⠈⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⠉⠁⠢⢤⡀⠈⠑⠀⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡇⠀⡀⠊⠛⠿⠶⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣰⠁⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠤⠖⠋⠁⠀⠀⠙⠦⣤⣄⣀⣀⣀⣤⣤⣤⠶⠾⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣠⠖⠂⠀⠊⢹⡆
⠀⠀⠀⠀⢀⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠃⠀⠀⠀⠀⢴⡄
⠀⠀⡀⠀⠀⠀⠉⠛⠿⣴⣤⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠑⠂⠀⢀⠆⠀⠀⡜⠀⠀⣰⡇⠀⠀⠀⣽
⠀⠀⠿⣷⣦⣄⢀⣀⠀⢠⣄⣉⣉⣽⡟⠃⠀⠀⠀⠀⠠⢤⡀⠈⠑⠀⠀⠀⣀⠤⠒⠋⠁⢀⡴⠇⢣⡀⣠⠈⠀⠀⠀⢨⠏
⠀⠱⣦⣄⣀⠉⠈⠛⠁⣼⠅⠀⠈⠁⠀⢀⣀⠐⠒⠒⠄⠀⠀⢀⡀⠀⠒⠉⠀⠀⠀⠀⠀⢸⠀⠀⠠⠑⠇⠀⠀⢀⣠⠁
⠀⠀⠀⠉⠉⠂⠛⠶⠀⠋⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠻⣆⢠⡞⠉⠀⠀⠀⡸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢇⢀⣿⡬⠁⠀⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈⠁⠀⠈⠙⠒⠠⢀⠀⠀⠀⠀⢺⣿⠀⢀⣀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣤⣠⡄⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢢⠀⠀⠀⠻⠿⣿⣯⣛⠲⢤⣀⡀⠠⠀⠀⢉⡇⠀⠀⠀⠀⠀⣠⠤⠠⠄⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠉⠛⠿⢶⣏⢁⣤⠤⠒⠋⠁⠀⠀⠠⠂⠀⢤⣀⡀⠀⠀⣸⠶⣄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢠⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠚⠉⠹⣛⣿⠁⠀⢸⠄
⠀⠀⠈⠳⣤⣤⣀⣀⠀⣀⣀⣀⣀⣴⠎⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⡆⠀⠀⠀⢸⠃⠀⢀⡾
⠀⠀⠀⠀⠀⠉⠙⠛⠒⠂⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠦⢠⡀⠄⠀⠁⠀⠀⠀⠀⠀⠈⠳⢠⣀⣤⣤⠝⠛⠉

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀
⠀⠀⠀⠰⠼⠏⠀⠙⣀⠀⠀⠀⠀⣂⠀⠀⠀⠠⠀⠀⢀⢶⣅⠀⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠞⠉⠁
⠀⠀⠀⠇⠀⠀⠀⠀⠋⠀⠀⠂⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠒⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⠀⠀⠀⠁⠃⠘⠒⠂⠀⠀⠚⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⣠⠀⠀⠀⠀⠧⠀⠀⠀⠆⠀⠰⠀⠀⠁⠀⠀⢀⣤⣶⣶⡀⠀⣸⡄
⠀⠀⠀⠀⢀⠘⢒⠦⡀⠀⡀⠀⠀⠀⠉⠉⣤⡀⠀⣠⠀⡄⢀⢠⠀⠀⡤⢀⢠⡀⠀⠀⠀⠈⠁⠀⠀⠀⢤⠉⠓⠂
⠀⠀⠀⠀⠿⠤⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⣇⡗⢰⣻⡆⣧⠎⢸⣤⠄⣇⣸⠸⣆⠆⣠⡤⠀⠀⠀⠠⢄⡀⠀⠀⠙⠂
⠀⠀⠀⠀⠄⠤⠤⠒⠈⠁⠀⠀⠀⠀⠼⠀⡇⢹⢼⢸⡇⡏⣇⢸⠀⠀⡏⢳⠀⣿⠀⢻⣄⠀⠀⠀⠀⠒⠭⠔⠒⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠭⠤⠤⠧⠥⠬⠬⠭⠤⠥⠬⠤⠄⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠉⠉⡲⠈⠁
⠀⠀⠀⠠⠀⠂⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠄⠂⠀⠄⠀⠀⠠⠄⠒⠂⠄
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠉
⠀⠀⠀⢀⡠⣤⣀⣀⡁⠀⠒⠀⠀⠀⠀⠀⠠⠊⠀⠀⡀⠐⠒⠈⠀⠐⠤⡀⠀⠈⠁⠒⠒⠀⠠⠤⠀⠂⠀⠀⠀⡀
⠀⠀⠀⠋⠀⠘⠋⠁⠿⢿⠿⠊⡴⠤⠤⢤⠀⠀⡠⠎⠉⠉⠉⠐⢄⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠒⠔⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠠⠄⠤⠤⠐⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠟⠛⢿⢻⣿⣦
⠀⠀⠀⠀⠀⢠⣾⡿⠛⠁⠀⢠⣿⡿⠛⣽⣿⠃
⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⣠⡽⠷⣶⣤⠀⢀⡀
⠀⠀⠀⣰⣿⣥⠀⠀⣠⣤⣡⣟⣷⣶⣿⣿⣶⣾⣿⣐⣠⡀
⠀⠀⠀⣿⣿⣷⢃⡈⣸⣯⡉⠛⣿⠿⢻⣿⣿⣿⠟⣿⣿⡏⢤⣀⣰
⠀⠀⢠⣿⣿⣧⠛⣟⠏⠉⠀⠀⠀⠀⠈⠙⠀⠉⠀⠈⠁⠀⠀⠙⠛⠛⠁⠀⡀⠀⣀⣀⣀⢀⣀⡀
⠀⠀⠸⣿⣿⣷⣶⣷⠖⠂⡀⠀⠀⠀⠀⠀⣠⡦⣾⠃⠀⠀⠎⠀⠀⠀⠸⡀⠀⠱⡌⢻⣿⣿⣿⣿⣶⡀
⠀⠀⠀⢻⣿⣇⣸⡇⠠⠖⠑⠂⠀⠀⢀⣦⡎⢿⡝⠀⠀⠀⠠⠀⡀⠀⠀⠁⡀⠀⢹⠈⣿⣿⡉⣿⣾⣿⡄
⠀⠀⠀⠈⢉⢻⡟⢻⡄⠀⠀⠈⢱⠰⣯⢱⡛⠚⠰⠀⠦⠀⢀⠀⣇⠀⢠⡄⠀⠀⠘⢷⣿⣿⣿⣿⡿⢿⡇
⠀⠀⠀⠀⠰⠈⠂⠀⠀⠀⠀⠀⠀⡀⡟⠃⠙⠿⣦⣤⣀⣂⣰⣦⣈⡈⢸⠁⠀⠀⡰⠀⠿⢺⣿⣿⣿⣪⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⣬⣤⠀⠀⠀⠈⠙⠻⣿⣨⡁⠄⢯⠀⠀⠀⠁⠈⠀⠈⠙⠻⠿⠿⠉
⠀⠀⠀⠰⣆⣀⢀⢴⣥⡎⢡⣁⠀⢬⡛⠿⣷⡆⣀⡄⢀⡠⠈⣭⣥⡞⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠌⢉⡤⠞⠁⠱⢟⠁⠑⠤⠹⣦⠤⠂⠈⠀⠈⢧⠀⠈⢈⣧⣀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠒⠐
⠀⠀⠀⠀⠀⠉⠀⠀⢀⢴⡎⢡⠷⠈⠂⢌⠃⣀⠀⠀⣀⡾⢤⣤⠆⠀⠙⠳⢤⣀⠂⡀
⠀⠀⠀⠀⠀⠀⠸⠷⣯⡆⠁⠀⠀⠀⠀⠀⠉⠙⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⡿⡿⠆⠀⢀

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⣎⠀⢀⡠⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢤⠀⠀⠀⠀⠕⠀⡀⢽⠀⠀⠀⡀⠀⣠⠌⢂⡔
⠀⠀⠊⠳⠘⠈⠀⠀⣀⠴⡆⠠⢄⠀⠐⠀⠀⠀⡀⠗⣤⣄⠂⠀⠀⠀⠀⠀⡞⢅⡻⣦⢰⡾⠇⠀⠈
⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⠈⣧⠈⡧⠀⠀⠈⠢⠆⠺⠇⠩⠀⠀⠀⠀⠀⠀⡏⠸⠈⠠⠀⡇⠀⠀⠀⢰⠧
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠠⠀⠀⠀⠀⠀⠀⠀⢸⢈
⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠤⡶⠄⠀⠨⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠲⠴⠂⠀⠀⠢⠤⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⡀⡀⣼⠀⡦⠀⡔⠁⠀⢀⠄⠁⡠⠀⠈⠁⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⣀⠤⠂⠴⠆⡀⠀⠈⠻⣤⢿⣬⢡⡞⠁⠂⠀⠈⢆⠀⢗⣻⠂⢠⡀⠀⠀⠀⢀⠀⠀⠁⠀⡀⠊
⠀⠀⠀⢈⡁⠒⢅⢐⠘⡄⠀⠀⠀⠈⠙⣧⡋⠀⠀⠀⠀⠀⢠⢰⢌⠽⠛⠁⠀⠀⠀⠀⠀⢉⠀⠉⡶⠁⠘⡧
⠀⠀⠀⠀⢈⡁⡁⠂⡇⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠰⢿⡟⠉⡆⠘⠀⠀⠀⠀⡠⢠⠄⠀⠁⠀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠃⠀⠀⠀⠀⠀⠀⠰⠛⠁⠱⡀⢄⠀⢀⡆
⠀⠀⠀⠋⠀⠀⠀⢀⣠⡀⣀⣀⠀⠀⢀⡶⠀⠁⠀⣤⣶⡄⠀⠀⠀⠀⠀⣲⠆⢀⣀⠐⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠀⠀⠀⠸⠿⠅⠀⠀⠀⠉⠉⠁⠒⠓⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣒⣶⡿⠋⠙⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⠶⢛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣤⣴⣍⡀⠀⣠⠮⠀⠐⠛⠛⠓⠒⠀⣈⣷⣄⠀⠀⠀⠀⠀⡈⠀⠐⢶⣦⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡾⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡆⠀⡀⠀⠀⢰⡆⠀⠀⠈⢷⣆⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣀⢀⣠⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣷⡞⠀⠀⢠⣿⣿⣀⠀⠀⡀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠉⢉⣿⣿⢿⣛⣯⣟⣓⣿⠚⠛⠂⠀⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣠⣾⣿⣿⣯⣤⣥⣠⣶⠀⠈
⠀⠀⠀⠀⠀⠀⡌⠉⢙⣿⣿⣿⣿⣏⠀⠛⠉⠉⠉⢀⣀⡀⣼⠏⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⣿⣿⢛⣻⣿⣿⡁⣴⣽⣄⣠⣦
⠀⠀⠀⠀⠀⠀⢳⣤⣶⢿⣹⢿⣿⣿⣆⠀⢠⣄⠶⠾⢻⣿⣿⣷⣦⡤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣼⣿⣘⠛⠺⢿⣿⣿⣿⠓⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⣤⠺⢧⣾⡿⠻⡏⢳⣾⡵⣷⣽⣿⣿⣿⣿⣿⣔⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠩⠽⡉⠁⢄⣉⢉⣿⣿⣿⣾⣶⣿⣷⡄
⠀⠀⠀⠀⠀⣚⣤⣷⣷⣭⣾⣿⣿⡛⣿⣿⣿⣿⣿⣯⣿⣿⡏⠁⣐⣍⣽⠷⢿⣿⣯⡄⠀⠀⣠⣄⠀⠈⠁⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⠇⠈⠉
⠀⠀⠀⠀⠀⠙⠟⠋⠉⠉⠉⠉⠻⢶⣿⣿⣿⣿⣿⣿⠿⠿⣷⣶⣿⣿⣿⣧⣾⣿⣿⠿⠿⠿⠿⠿⢦⣴⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⢠⠤⢄⠀⠀⠀⠀⠀⠀⠸⡉⢢⠀⠀⠀⠀⠀⠀⡤⢄⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡶⡀
⠀⠀⠀⠀⠀⢀⠱⢤⣗⢀⡀⠀⠀⠀⠀⡨⠛⢣⠀⠀⠀⠀⢀⡽⠂⠿⠥⡎⠀⠀⠀⠀⠀⠀⠀⡇⠈⢢
⠀⠀⠀⠀⢰⡱⠀⠀⠀⠀⠈⡆⠀⠀⡰⠁⠀⠀⢇⠀⠀⠀⢸⢐⢈⢀⠀⡏⠀⠀⠀⠀⠀⣀⠜⠀⡀⢸
⠀⠀⠀⠀⠈⡗⠀⠀⠀⠀⢀⠇⠀⠰⢡⠀⠀⠀⠈⢆⠀⠀⠈⢢⡨⠠⡰⠁⠀⣠⠄⣒⣊⣁⠤⠊⢀⠞
⠀⠀⠀⠀⠀⠘⢆⢀⣀⡠⠎⠀⠀⠘⢼⠀⠀⠀⠀⡸⠀⠀⠀⠀⠉⠉⠁⠀⠀⠙⠢⠤⠤⠄⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢉⠆
⠀⠀⠀⠀⠀⠀⢀⠖⠚⠺⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⡇⢱⠀⠀⠀⠀⠀⡔⡮⠉⠛⡏⠢⡄
⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠈⠑⡄⠀⠀⠀⠀⣠⡎⠙⡞⠉⠙⣾⣉⣑⠆⠀⢸⢸⠀⠀⠀⡸⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣸⡤⣵⠊⠑⡤⠾⡏⠉⡆⠀⠀⠈⢎⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⢀⡠⠃⠀⠀⢠⠛⢞⠁⣱⠄⠧⠤⠋⠈⠀⠀⠀⠀⠀⡉⣒⢒⣈⣁⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠈⠁⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⢸⢹⠠⠀⠄⠀⠀⠀⠐⠀⢄⠀⢄⠏⡇
⠀⠀⠀⠀⠀⠀⣤⡀⡜⢆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣦⡐⢀⠈⠀⠂⠀⠂⡀⠀⡜⡰⠁
⠀⠀⠀⠀⠀⠀⡼⣝⣧⠜⡡⡇⠀⠀⠀⢀⡤⠤⢤⠀⢀⠀⠀⠀⠀⠀⠀⠙⠿⣢⠤⣀⣀⣈⣀⠤⡪⠞
⠀⠀⠀⠀⠀⠀⣹⠤⢷⠞⢴⡃⠀⠀⠀⠪⠤⢔⡟⠉⠉⠉⠑⢦⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠊⠉
⠀⠀⠀⠀⠀⡞⠣⣠⠎⠑⡼⣙⡄⠀⠀⠀⠀⡎⡎⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⡠⠔⣒⡂⠤⢄⣀
⠀⠀⠀⠀⢸⠷⢎⠉⡢⢎⡀⡜⡇⠀⠀⠀⠀⠳⡁⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡰⠋⠀⠁⠀⠈⠁⠀⡔⠁
⠀⠀⠀⠀⠈⣦⢴⡛⠣⣤⣏⡱⠁⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠁⠀⠀⠀⠀⠰⣁⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠈⠢⣝⣛⡧⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⠤⣌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠤⠤⣄⡙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠷⠶⠦⢤⡀⠙⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠶⢴⣶⠶⣞⡻⠭⣉⠙⠲⢤⡀⠉⢢⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⡀⠀⠀⠀⠀⠈⠳⡄⠙⢦⡀⠙⢆⠀⠙⣄⠀⢳⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠈⢳⢹⠀⠀⠀⠀⠀⠀⠙⡄⠀⢳⡀⠈⢧⠀⠸⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣼⡤⣴⣫⣸⡦⣤⡤⣄⡀⠀⠀⢹⠀⠀⡇⠀⢸⡄⠀⡇⣼
⠀⠀⠀⠀⠀⠘⠯⣽⣦⠖⠀⢀⡞⢁⠞⠁⣰⠋⠀⠈⢳⡀⠙⣆⠙⣄⣄⢸⠀⠀⣿⠀⠀⡇⢠⣷⠃
⠀⠀⠀⠀⢠⠞⠉⠙⠛⠋⠉⢻⡀⣼⠤⣴⢧⡀⢀⠖⠀⣇⠀⢸⡄⢸⣾⣼⠀⠀⡟⠀⢸⠃⣼⠃
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣷⠛⣶⠛⣾⠙⡏⠀⠀⡿⠀⢸⢇⡜⠁⢻⠀⢠⠇⢀⣞⡜⠁
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣸⣏⣹⣉⣿⣉⣿⣹⠆⣰⠇⢀⣾⠞⠀⢠⠏⣠⢋⣠⠞⠉
⠀⠀⠀⠀⠀⠈⠳⠤⠶⠤⠞⢧⣸⢧⡽⣧⠯⣤⡷⠶⠓⠚⠋⠀⣀⡴⠿⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠶⠖⠋⠁