Riddle Emojis & Symbols

⠀⠀⠀⠀⠀⠤⣤⣄⡤⠄⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⣤⣄⣀⣀⣤⣤⣴⣀⣴⣶⣶⣤⣀⣀⣀⣄⣀⣀⠀⠠⣀⣀⡀⠄
⠀⠀⠀⠀⠀⢸⣭⢋⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢏⠻⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡣⣼
⠀⠀⠀⠀⠀⠘⣱⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⡉⢹⣴⣷⣾⣯⣤⠿⢻⣿⣿⣿⣿⣧⢘⣱⣬⣷⣼⡗⢀⣽⠋⡽⠿⣿⣿⣿⣿⣿⣿⣷⡈
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣭⠉⣵⣆⢉⢺⡾⣁⡛⢹⢿⣷⣖⠚⣻⣿⡿⣇⣩⣬⢿⡏⠙⣥⣳⡟⣀⣹⡆⣸⠿⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠵⣀⢳⣏⣅⢹⣾⣿⣿⣶⣂⣼⠏⣿⡿⠟⣿⢷⢠⣴⢿⢀⣐⣳⣾⣿⣿⣏⡌⣻⣏⡴⠲⢿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠗⠢⣼⡿⠛⠸⣿⣿⣿⣿⣿⣿⣶⡖⠋⣿⠶⢻⡆⣴⠿⢠⣴⣿⣿⣿⣿⣿⣿⢋⣙⣿⣧⡆⢾⣿⣿⣿⣿⣿⠡
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⢶⣽⣿⠛⣷⣿⣿⣿⣿⣿⣿⣿⠿⠧⠿⣷⣾⣧⣿⡦⠴⢿⣿⣿⣿⣿⣿⣿⣏⡈⠻⣿⡴⠰⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⠟⠦⣿⣵⢰⣼⣿⣿⣿⣿⣿⣿⣿⣿⡾⣶⣶⠶⠶⠖⡞⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⠻⣿⡷⠲⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠞⠲⣿⣣⣤⣽⣿⣿⣿⣿⣿⢡⣶⣌⢻⡟⠿⠿⠿⠿⢿⢋⣴⣶⠘⣿⣿⣿⣿⣷⠃⢻⣿⡖⠐⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡞⠘⢿⣏⣀⣻⣿⣿⣿⣿⣿⡜⣿⣿⡇⠁⠀⠀⠀⠀⢠⣿⣿⡟⢸⣿⣿⣿⣿⣷⠃⢿⣿⡟⠹⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢉⠻⣿⣉⠻⣿⣿⣿⣿⣿⡇⣿⣿⣿⡀⠀⠀⠀⢀⣸⣿⣿⡇⢿⣿⣿⣿⣿⣷⠛⢶⣿⠛⢻⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⢋⠻⣿⠏⠻⣿⣿⣿⣿⣿⣵⣿⣿⣿⣭⣭⣿⣻⣭⣽⣾⣿⣷⣼⣿⣿⣿⣿⡿⠒⣾⡿⠋⢳⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠘⢿⣿⠻⣿⣿⣿⠃⣰⣀⣈⠉⠛⠛⠛⠙⠛⠋⠛⠛⠉⠉⠁⠀⢹⣿⣿⡷⠳⣾⡟⡉⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⡙⢿⣷⣶⣾⣿⣿⠀⢻⣿⣿⣷⡄⠀⠀⠀⢠⠀⠀⣾⡆⠀⠀⠀⢸⣿⣿⡷⠳⣾⣏⣘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⡉⢿⣿⣥⣬⣿⣿⠀⠸⣿⣿⣿⣁⣄⠀⠀⠸⢦⣴⣾⣿⡆⠀⠀⢸⣿⣿⡴⢶⣿⣧⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⢸⣿⣿⣿⣿⣿⣟⣈⢿⣿⣧⢮⣿⣿⡇⠀⠙⣿⣿⣿⣿⠃⠀⠀⠀⢸⣿⣿⣷⠀⠀⣾⣿⣿⡶⠶⣿⡥⢬⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡯⢌⣿⣿⡷⢮⣿⣿⣷⠀⡂⠌⣽⡿⡿⠀⠀⠀⡆⢸⣿⣿⣿⠀⣰⣿⣿⣿⡖⡑⣾⡷⠲⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠖⢮⣿⣿⡷⣾⣿⣿⣿⣧⡙⠼⣿⣖⣳⡀⠀⠀⡇⢸⣿⣿⠉⣰⣿⣿⣿⣿⣿⣩⣻⣿⣋⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠠⢸⣿⣿⣿⣿⣟⢹⣾⣿⣿⠛⣾⣿⣿⣿⣿⣷⣄⣹⣿⣿⡇⠀⠀⢃⢠⣿⣩⣾⣿⣿⣿⣿⣿⣿⣷⠻⣿⣇⡼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣠⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣟⣿⣯⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣶⢛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿
⠀⠀⠀⠀⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⠙⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘
⠀⠀⠀⠀⠀⢰⣐⣶⣚⣷⣆⣶⣆⣲⣾⢰⣿⣀⣿⣏⣺⣾⣝⡿⠿⣽⣽⣿⣾⣿⣿⡿⢟⣯⣶⣒⣶⣖⣶⣾⢸⣷⣘⣿⣛⣿⡏⣾⣇⣲⢸
⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠒⠒⠒⠒⠒⠒⠒⠂⠂⠐⠒⠒⠂⠐⠒⠒⠒⠐⠂⠒⠒⠒⠒⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠿⠂⣿⠿⠶⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⢋⣉⣤⣴⠶⠶⠾⠿⣿⠷⠶⠶⣦⣤⣉⡙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣁⣴⠾⠛⣉⣠⣴⡶⠶⠶⠆⣿⠷⠶⢶⣦⣄⣉⠛⠷⣦⣈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⢤⠾⢋⣠⡶⠟⢋⣡⣤⣴⠶⠶⣾⠿⠷⠶⣦⣤⣈⡙⠻⢶⣄⠙⠷⣦⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⣨⡿⣦⣴⠟⢉⣤⡾⠛⣉⣤⣴⠶⠶⠿⠰⠶⠶⣦⣤⣉⠛⢷⣤⡉⠻⠂⡈⢻⣆⠙⣷⡀
⠀⠀⠀⠀⠀⠀⢠⡿⢁⣾⠋⣰⡟⢁⣴⠟⢁⣴⠞⢋⣡⣤⡶⠶⣶⠰⠶⢶⣤⣌⠙⠳⣦⡈⠻⣦⡈⢻⣆⠙⣷⡈⢿⡄
⠀⠀⠀⠀⠀⢠⡿⢁⣾⠃⣼⠏⣠⡿⢁⣴⠟⢷⡶⠟⢉⣠⣴⠶⠿⠶⠶⣦⣌⡉⠻⠦⢈⣿⣦⡈⢿⣄⠹⣧⠘⣷⡈⢿⡄
⠀⠀⠀⠀⠀⣾⠃⣼⠃⣸⠏⣰⡟⢠⡾⢁⣼⠇⣠⣾⣟⣁⣤⡶⠆⣶⢶⣤⣈⠛⢃⣄⠹⣧⡈⢷⡄⢻⣆⠹⣧⠘⣧⠈⣷
⠀⠀⠀⠀⢸⡏⢰⡟⢰⡿⢀⣿⢀⣿⠁⣾⠃⣴⠟⣀⡙⢿⣤⣴⠶⠿⣦⣄⣉⣴⡟⠻⣆⠘⣷⠈⣿⡀⣿⡄⢿⡆⢻⡆⢹⡇
⠀⠀⠀⠀⣼⡇⣸⡇⣸⡇⢸⡇⢸⡇⢸⡏⢰⡟⢠⡿⢀⡶⠉⠀⠀⠀⠀⠙⢿⡁⢿⡄⢻⡆⢹⡇⢸⡇⢸⡇⢸⣇⢸⣇⢸⣧
⠀⠀⠀⠀⣿⠀⣩⣥⣿⡇⢾⣧⣬⡅⢸⡇⢈⡁⢨⣥⣼⡇⠀⠀⠀⠀⠀⠀⢘⡃⢈⡁⢸⡇⢸⡿⢻⣧⣬⣅⢘⣿⣬⣿⠈⣿
⠀⠀⠀⠀⢻⡇⢻⡇⢹⡇⢸⡇⢹⡇⢸⡇⢸⣇⣸⣧⠘⣷⡀⠀⠀⠀⠀⢀⣾⠃⣼⠇⣸⡇⢸⡇⢸⡏⢸⡇⢸⡏⢸⡏⢸⡟
⠀⠀⠀⠀⢸⣇⢸⣇⠸⣧⠘⣷⠈⣿⡀⢿⡄⢻⣇⠙⠃⣈⢻⡷⠆⠰⠾⠻⣧⣾⣏⠰⠟⢠⡿⢀⣿⠁⣾⠃⣼⠇⣸⡇⣸⡇
⠀⠀⠀⠀⠀⣿⡀⢿⡄⢻⣆⠹⣧⠘⣷⡈⢿⣄⢉⣴⣄⡙⢻⣷⠆⠰⠶⠟⢋⣠⡝⢷⣤⡿⢁⣾⠃⣼⠏⢰⡟⢠⡿⢀⣿
⠀⠀⠀⠀⠀⠘⣧⠈⢷⡀⢻⣆⠹⣧⡈⢿⡾⠛⢿⣥⣉⠛⠿⠷⢶⣶⠶⠾⠛⣉⣤⡾⠛⢷⣿⠁⣼⠏⣰⡟⢀⡿⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠸⣧⡈⢿⣄⠻⣦⡈⢋⣤⡘⠳⣦⣈⠙⠻⠶⢶⡆⠰⡶⠶⠟⠋⣁⣴⠞⢃⣽⡷⢀⣴⠏⣠⡿⢁⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠻⣦⡈⠻⣿⡉⠻⢶⣄⡉⠛⠷⠶⣶⣦⣴⡶⠶⠾⠛⢋⣠⡶⠟⢁⣴⠟⠁⢴⠟⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠻⣦⣌⠛⢷⣤⣉⠙⠻⠶⢶⣦⣤⣤⣴⡶⠶⠟⠋⣉⣤⡾⠛⣡⣴⠿⣦⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠙⠷⣦⣌⡙⠛⠷⠶⢶⣤⣤⢠⣤⡶⠶⠾⠛⢋⣡⣴⠾⠋⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣉⠙⠛⠶⠶⣦⣤⣿⢠⣤⣴⠶⠶⠟⠋⣉⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢶⣦⣤⣤⣤⣤⣴⡶⠶⠟⠛⠉⠁


⡖⠒⢲⠖⠶⠶⠶⠶⡖⠶⠖⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⣶⡶⠶⠶⠶⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠉⠉⠙⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠻⣿⠟⠀⠀⠀⢀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣴⣾⣷⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⣿⣿⣿⠿⠿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏⣼⣿⣿⡘⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠸⣿⣿⣿⡗⣼⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢨⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣬⣭⣭⣾⢟⣩⣝⡻⠇⣸⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⠿⠟⣋⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠒⠒⡖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠖⠒⠒⠒⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠂⠀⠀⠂⠀⡄⠀⠀⠈⠀⠐⠀⠀⠀⠆⠀⠁⠐⠀⠀⠀⡂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⠁⠀⡀⢀⠀⠈⠉⠃⠀⠉⠉⠉⠙⠀⠀⠀⡏⠉⠀⠀⠉⢁⠀⠈⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢉⠀⠀⠀⠀⢈⡀⠀⠀⣀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⣅⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡃⠀⡄⠠⠄⠀⠀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡇⠀⠀⠀⠀⠠⠤⠤⠤⠧⠤⠤⠴⠤⠤⠤⠆⠀⠀⠀⠀⠀⠀⠠⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠄⠤⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄⠀⠆⠐⠀⠰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠐⠚⠀⠀⠀⠁⠀⠀⠀⠂⠒⠀⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠄⠀⡆⠈⠁⠀⠀⠘⠀⠂⠀⠁⠀⠀⠀⠀⠛⠀⡂⠀⠃⠀⠀⠀⠀⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⡇⠀⠉⠉⠉⠁⠀⠉⠉⡏⠉⠀⢀⠀⠀⠀⡇⠀⠉⠉⠉⠉⠉⡃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⡇⠀⠀⠀⠀⠈⠁⠅⠀⡇⠀⠁⠈⠀⠁⠀⠍⠈⠁⠀⠀⠀⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠅⠀⠇⠀⠀⠀⡀⣀⠀⣀⠀⡇⢀⡀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤⠤⠀⠀⠤⠤⠤⠤⠤⠤⠤⠃⠀⠤⠴⠤⠄⠀⠠⠤⠤⠤⠀⠀⠀⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣿⣻⣛⣟⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠲⡞⠉⠉⠉⠀⣀⣀⡀⠉⠉⠀⠉⠉⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣀⣀⣠⠄⠀⠓⠊⠉⠉⠉⠀⡀⠉⠉⠉⠉⠉⠑⠒⠤⣤⣀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢁⣠⠞⠉⣀⣀⣤⠤⠴⠒⠛⠛⠉⠉⠉⠙⠒⠚⢻⠙⠒⠦⢤⣀⠈⠑⢦⡀⠙⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠳⣤⠖⠉⢀⣠⠞⠉⢀⣀⣠⠤⠴⠒⠂⠀⢘⡟⠃⠀⠒⠚⠒⠦⠄⠀⠈⠙⢆⠀⠳⣄⡀⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠁⢀⠞⠉⢀⣠⠞⠙⣄⣀⡠⠤⠴⡆⠀⠘⠓⠒⠶⠶⠒⠶⠤⣀⡴⠳⣄⠈⠃⠀⡀⠙⣆⠀⢳
⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣾⣀⣠⠋⢀⡴⠉⢀⡤⠖⠉⠀⠀⢠⠤⠷⠶⠒⠲⠶⠤⠤⠶⠤⣄⠈⠳⡀⠈⠳⣴⠊⢷⠀⠹⣄⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⡎⠀⣸⠀⢨⠃⠀⡎⠀⣰⠋⠀⠀⠰⢧⣀⠀⠀⣤⣤⣶⣦⣤⡤⠤⢤⡀⠈⠢⡀⠈⢳⡀⠘⣄⠀⠳⣄⠈⢳⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢳⠀⢘⡆⠀⡇⠀⢇⣰⠋⠉⠙⠒⢤⣀⠈⠳⣄⠀⣀⣀⣀⡀⢹⠛⠒⠼⣦⡀⠘⣆⠀⠳⣄⠈⠓⠀⠈⠀⠀⢀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡒⠛⠀⠀⢹⡄⠈⠉⠉⠙⠒⠦⣀⠈⠳⡄⠈⠉⠉⠉⠉⠉⠉⠓⠦⠀⠈⠁⠀⠈⢳⡀⠀⢀⠀⢰⣀⣸⡆⠀⡳⠒⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠐⢆⠀⠙⠒⠚⠛⠒⠦⡀⠈⢣⡀⠙⠒⠋⠉⠁⠀⠘⠓⠦⠄⠀⠐⢦⣀⡔⠉⢀⡴⠚⠳⣤⡇⠀⡇⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠙⠒⠒⠒⠒⢦⡀⠘⣆⠀⠳⠤⠶⠒⠋⠀⠘⠓⡶⢄⠀⠐⢆⠀⡏⠀⡴⠋⢀⡴⠚⠉⠀⢀⠇⠀⣻⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠶⠖⣆⠀⢳⡀⠘⠲⠤⠤⠤⠶⠚⠛⠓⠺⠅⠀⠀⡄⠈⠿⠤⠞⠀⠀⠋⢀⡴⠂⠀⠉⠳⡼⠁⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠙⠲⠤⣤⣠⣤⠤⠖⠒⠲⣄⠀⢠⡀⠘⢦⣀⣤⠤⠴⢆⠀⡞⠀⡰⠋⠉⠉⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣤⣀⣀⣀⣤⠤⢶⡀⠘⢶⠋⠙⢦⣀⣀⣀⣤⠀⠈⠷⠇⠀⡇⠀⣸⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⠀⠙⢦⠀⠉⣀⣀⣸⣦⢤⣀⣠⠞⠁⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠈⠳⠊⠉⠉⠁⣀⣀⣀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠘⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⣴⣶⣦⣄
⠒⠂⠀⠀⠀⠀⠀⠈⠐⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠲⠶⠶⠶⠶⠃⠀⡰⠶⢿⠿⠿⠷

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



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠂⠀⢨⠀⠀⣠⠵⢶⠒⠲⢤⡀⠀⠀⠀⡰⠗⠀⠀⠀⣀⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⣣⠞⠁⠀⠀⠱⢤⣀⣙⣦⡴⠊⠀⠀⠀⣠⠊⠁⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⡴⠁⡃⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣠⠞⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣰⠋⠀⠀⠀⣠⠴⠚⠉⢉⡟⠙⣲⠧⣄⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⢠⠴⠒⠒⠶⢦⣴⡁⠀⠀⢀⣠⡤⠤⠷⡤⠤⢤⣀⠀⣀⣀⡀
⠀⢰⠃⠀⠀⠀⢰⠃⠀⠀⢀⠞⠀⡴⠁⢀⡼⠛⢧⡀⠀⠀⠀⠀⠈⠑⠢⠄⣀⣏⣀⣀⣠⠴⠊⠀⢈⡷⢶⡉⠀⠀⠀⠀⠉⠲⠤⠞⠛⢣⡀⠉⢳⡀
⠀⠘⡆⠀⠀⠀⢸⡀⢀⡴⠋⠀⡼⠀⣰⠋⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡀⠀⠀⣠⠔⠋⠀⠀⠙⣦⡖⠛⠓⢦⡀⠀⠀⠀⠀⢹⠀⠀⢳
⠀⠀⠙⢦⣀⣀⡠⠷⡋⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠳⣤⠴⠚⠛⠓⠲⣄⡀⠀⢙⣶⠚⠁⠀⠀⠀⣠⠞⠁⠙⣄⠀⠀⢹⠀⠀⠀⢀⡾⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠇⠀⠘⣄⠀⠀⠀⠀⢀⠜⠙⢦⠀⠀⠀⠀⣀⡽⢾⡁⢸⠀⠀⠀⢀⡴⠃⠀⠀⠀⠈⠳⣤⡟⠀⢀⣠⠞⠁⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠀⠀⠈⠳⢄⡀⣠⠏⠀⠀⠀⣳⣤⡔⢪⠥⣄⠀⣹⠿⢤⣤⠴⠋⠀⠀⠀⠀⠀⢀⡴⠋⢑⡶⣏⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠣⡀⠀⠀⢀⡽⠋⠛⠛⠉⠉⠀⠀⠉⡟⠒⠚⠻⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠈⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠈⠙⠒⠶⠶⠶⠒⠋⠉⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⢤⠀⠤⠤⠤⠤⢠⠄⠤⠤⠤⡤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠄⠤⠤⠤⢤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⠤⢤⠀⢸⠀⢠⠤⠤⠀⢸⠀⠀⡤⠤⠂⠀⠀⠀⡀⠀⡇⠀⡠⠤⠤⠤⠄⠀⠘⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠘⠀⢸⠀⢸⠤⠼⠀⠀⠤⠼⠀⠀⠀⠀⡤⠤⠄⠀⡇⠀⡇⠀⠂⠀⠠⠤⠤⠤⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠼⠀⢸⠀⢀⠄⠤⠤⠤⠤⠤⠂⠀⡄⠀⠀⠀⡇⠀⡧⠤⠀⠀⠀⠀⠀⠤⠤⠠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠈⠀⢀⠀⠀⠀⢀⡀⠠⠅⠀⠄⠀⡇⠀⠧⠀⠀⠀⠤⠀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢼⠀⢀⠀⠸⠀⢀⠀⠸⠀⢀⠀⠀⡄⠀⠀⠀⡀⠀⠧⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⢀⠀⠠⠀⢀⡀⢨⠀⠀⠄⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⠀⠸⣀⣀⣀⣨⠀⠸⣀⣀⣀⣀⣄⣀⠀⠀⡇⠀⢀⣀⡄⠀⢀⣀⡀⠀⢀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣀⣀⡀⣀⠀⠀⠀⠀⢀⣀⡀⢀⠀⠀⣀⣀⣇⡀⡀⠀⣂⠀⣀⣀⣀⣀⣀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡸⠀⢀⣀⡀⠀⠸⣀⢸⣀⣀⠀⠀⠁⠀⢀⢀⡀⠀⠀⠀⡇⠀⠅⠀⠀⠀⢀⣀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣇⣀⣇⣀⡀⠀⠀⠀⠈⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢸⠀⠀⣀⣀⣀⣀⠀⢸⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⢅⣀⡀⠀⠀⠀⢸⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⠀⢸⠀⠸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⠀⢸⠀⢸⠀⠀⠀⢸⠀⠀⠀⢀⡁⠀⠄⠀⡀⠀⠀⠀⡏⠀⠀⠀⠉⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠀⠁⢈⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⡉⠈⡇⠀⡇⠀⠁⠀⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢸⠀⠀⠀⢸⠁⠈⠀⢸⠁⠀⠀⠀⡁⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠈⠀⡉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⠉⠉⠁⠉⠀⢰⠀⢸⠀⢰⠉⠉⡅⠀⠈⠉⠉⠉⠁⠀⡇⠀⡄⠀⠈⠀⠁⠀⢰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠉⠉⢹⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠀⡆⠀⡇⠀⠈⠉⠁⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠈⠁⠉⠁⠈⠁⠉⠀⠈⠉⠀⠉⠈⠉⠉⠉⠉⠉⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠄⣟⣙⣛⣛⣋⣛⣙⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠸⠀⠀⠀⠠⠀⠀⠀⠦⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠰⠀⠀⠀⢠⠀⠀⠀⠤⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⠀⠀⠀⠄⠀⠀⠀⢠⠄⠀⠀⠄⠀⠀⠀⠠⠄⠀⠀⢤⠀⠀⠀⢠⠄⠀⠀⡄⠀⢀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠠⠀⡆⠀⠤⠆⠘⠀⠤⡄⠀⠀⠂⠆⠠⠀⠤⠄⠀⠀⢰⠀⠐⠀⠠⠀⡅⠀⢲⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡤⠀⠀⠀⢷⠂⠀⠀⠴⠀⠀⠀⢰⠄⠒⠒⣶⡄⠀⠀⢰⠀⠐⠒⣼⣄⠀⠀⢷⠒⠒⠒⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡇⠀⡴⣆⠈⠀⠄⠄⠀⠀⢠⠀⠀⠀⠰⠀⢠⠀⣶⡆⢸⠀⠄⠄⣯⠄⣶⡆⠘⠀⠰⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢷⠒⠒⠒⡶⠀⠀⠀⢴⠀⠀⠀⠶⠄⠀⠀⢾⠖⠒⠒⠾⠀⠀⠀⢴⠂⠐⠒⡴⠄⡀⣀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⢸⠀⠀⠀⡇⠀⠶⠆⠀⠀⠠⠀⠀⠀⢰⠀⠸⠀⡄⡄⠀⠀⠆⠄⢠⠀⡄⡄⡇⠀⢰⣦⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠒⠒⠂⡾⠀⢀⡀⣷⠒⠀⠒⣦⠀⠀⠀⢴⠒⠒⠒⣶⠄⠀⠀⠷⠀⠀⠂⣺⠀⠀⠀⢷⠖⠒⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠦⠀⢸⠀⠠⠀⡇⠀⠦⠶⠸⠇⠰⠀⣻⠀⠰⠀⢀⠀⠆⠄⣹⠀⢰⢀⢨⡇⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢶⠒⠒⠒⡾⠀⠀⠀⢷⠒⠒⠒⠲⠀⠀⠀⠿⠖⠒⠐⢾⠄⡀⠀⢿⠒⠒⠒⢺⠅⣀⡀⢤
⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠤⠀⢸⠀⣠⠀⡇⠀⣦⡆⢨⠀⠆⠄⠀⠀⡶⠆⠀⠀⠀⡆⣸⠀⠴⠂⢸⠀⠄⠆⣼⠀⢶⢾⢸⡇⠀⠀⠂⠶⠆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⡼⠀⠀⠀⢧⠒⠒⠒⠶⠀⠀⠀⢴⠖⠒⠒⢲⣄⡀⢀⢿⠒⠒⠒⣾⠄⡀⠀⢾⠖⠒⠒⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⡴⠄⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⣶⠀⢰⣆⢸⠀⠰⠀⣿⠀⢴⠦⢸⠀⡄⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⢷⠂⠀⠀⣴⢀⠀⣀⣶⠀⠒⠂⢴⢄⣀⣀⣿⡖⠒⠒⢾⣄⣀⣀⣿⡒⠒⠒⣾⣄⣀⣀⣤⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⢸⠀⠤⠀⡇⠀⣴⠀⢸⠀⢰⠀⢙⠐⣰⣆⢘⡃⢰⠀⢸⠁⣁⣀⣨⡁⢠⠀⣩⣿⣿⣷⣾⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠐⠀⠒⣾⣀⣀⡀⣷⠒⠒⠒⣾⣀⣀⣀⣾⠖⠒⠒⢶⣄⣀⣀⣼⠖⠖⠒⣴⣇⣤⣄⣿⡿⠿⠿⢿⠃⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⣶⠄⢰⠀⣴⠀⣧⠀⣦⣦⢸⡀⣤⡄⣿⠀⣶⣆⢸⠀⢰⡀⢽⣖⣶⣶⣺⠀⢰⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣷⠶⠶⠦⣼⣀⣀⣀⣧⠤⠶⠶⢾⣅⣀⣀⣿⠶⠶⠲⣾⣄⣀⣀⣿⡾⠾⠿⢾⣇⣀⣀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣶⠀⢸⠀⣤⠀⣿⡄⣴⣄⣸⠀⡄⡄⣸⢀⣶⣶⣾⡄⢠⠀⣿⣆⣶⣶⣿⡇⡤⡆⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠤⠠⠀⢼⠀⠀⠀⠿⠶⠶⠶⠶⠀⠀⠀⠼⠶⠷⠷⠾⡇⠀⠀⡿⠷⠿⠛⠿⡇⠀⠀⡽⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⢠⡄⠀⠀⢰⠄⠀⠀⢠⠀⠀⠀⣠⠀⠀⠀⢠⠀⠀⠀⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⢈⠀⠀⠀⣠⠀⠀⠀⢠⡄⠀⠀⢠⠀⠀⠀⢨⠀⠀⠀⣼⠀⠀⠀⢸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠐⠂⠀⠂⠒⠒⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣤⠀⠀⠀⠀⠀⣾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⢀⡀⣼⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣇⡀⠀⠀⣀⣽⣾⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠘⡆
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣇⡄⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠂⠀⠀⠀⠀⢱
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡀⣽⣿⣿⣧⣿⣿⡿⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⠁⠈⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⡟⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⠱⡂⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⠈⢻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠠⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⡇
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⠇⠹⣿⣿⡀⠀⠀⠈⠀⠀⠈⠀⢀⠈⠀⠀⠄⠀⡄⠀⠀⠀⢠⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⡀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⢻⣿⣅⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣟⠁⠀⠀⢸⣿⣿⠀⠘⣿⣿⠀⠀⠀⠀⢀⣆⠀⠀⠀⠐⠋⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠙⠻⠶⠀⠀⠀⣿⣿⡀⠀⢸⣿⣄⡀⠀⠀⠀⠀⠀⠀⢰⠒⢀⠆⠀⠴⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⡀⣾⡿⠁⠀⠀⠉⠛⠃⠀⠀⠀⠀⢀⠔⠉⡠⠛⠀⠉⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⡀⠀⠛⠋⠀⠂⠀⠀⠀⠀⠀⠀⢀⡠⠘⠀⢠⠜⠁⠈⢠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣠⠔⠒⠈⢀⡀⠤⠐⠁⠀⣀⠐⠁⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⠀⠀⠀⠀⠰⠄⠐⠊⠉⠀⠀⣀⠔⠊⠁⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠂⠀⠀⠀⢀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠤⠀⠠⠤⠤⠤⠤⠤⠤⠀⠶⠖⠓⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣴⣶⣦⣤⣤⣤⣤⣤⡶⠶⣶⣦⣴⣶⢶⣦⣴⠆⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡮⠶⠻⠿⠿⠻⢶⣿⣿⣯⣿⣿⣏⣩⣿⣾⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣩⣿⣿⣿⣦⠖⢀⣥⣽⣿⣿⣟⡿⣿⡣⡿⣿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢻⣷⣾⣿⣿⣿⣵⣾⡿⢱⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣿⣯⡟⣯⣿⣿⣿⣿⠀⢦⡾⣿⣯⣿⣿⣿⣿⣿⢣⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣿⢳⢾⡿⣿⣿⣿⣿⣿⣿⣏⠀⠈⢛⠈⠂⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣺⣿⣷⡿⣯⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⠆⠀⢸⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⣻⣾⣇⣿⣿⡿⣿⣿⣿⣿⣿⣷⣦⠖⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣻⣿⣿⣿⣹⣿⣭⣻⣿⡟⣡⣦⣦⠀⠻⢿⣽⣿⡿⢿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣿⣿⠟⢛⢉⣾⡟⣿⣿⠿⣷⣶⣤⡴⣀⠉⠀⠐⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⣾⢏⣾⡟⣸⣿⣿⣟⣾⢠⣏⣿⣿⡟⠁⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣈⣿⣷⣿⣷⣽⣛⠛⠺⠧⡿⠛⢁⠄⠀⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣻⣿⣿⡋⣼⣈⣨⣴⣯⠖⣿⣵⠶⣄⢁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢠⣸⣿⣿⣿⣾⠟⠁⠚⣿⠅⣰⣿⡿⣿⣾⣦⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠠⣏⣿⣤⣿⠿⠀⢀⣚⣽⣶⠿⣻⣿⣾⣿⢇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣉⣿⣷⣿⣇⢻⣶⣿⣿⢻⡭⣶⣺⣿⣭⣿⣟⣸⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⢿⣿⣿⣿⣿⣿⣷⡏⠈⣽⣿⠛⠋⠉⢱⣽⣿⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡄⠸⢿⣿⡿⠛⢻⣿⣷⣴⣿⣷⣤⣤⣶⣿⡿⠿⠿⢃⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣇⣀⣸⣿⣿⣿⣷⠿⠿⣫⣿⣿⣿⣿⣿⣿⣯⠴⢿⡿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡛⢀⣠⠴⠿⢿⣿⣿⠟⣳⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠭⣭⣭⣤⣤⣴⣶⣿⡷⣾⣿⣯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣙⡛⠛⠛⠋⠙⢉⣩⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣂⣠⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠒⠋⠉⠉

⠀⠀⠀⠀⠐⠒⠂
⠉⠁⠀⠈⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠁⠀⠈
⠀⠀⢰⠤⡀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⢘⣂⠕⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠀⠀⠀⠀⡀⠀⡇⠀⠈⠆⠒⢄⠀⠀⠀⠀⠀⠀⡼⠀⠀⠘⣄⠀⠀⢀⠖⡄⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⢄⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣈⣦⣤⣸⣀⣼⠖⠋⠉
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡇⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠄⢀⠞⢦⠀⠀⠀⠀⠀⡰⡑⠀⠀⠀⠀⠀⠀⡼⠋⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⠀⢀⣾⠟⠋⢱⡄
⠀⠀⠐⠂⠐⠃⠀⠀⠃⠀⠀⠀⠘⠚⠀⠀⠀⠀⠀⠂⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠿⠀⢀⡼⠁
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣴⠟⠁
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠢⠄⠀⡷⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠧⠔
⠀⠀⢸⠀⡀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠉⠁⠈⠉⠐⠠⡀⢸⠀⠀⠀⠐⠃
⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠲
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢣⠀⠀⠀⠀⢀⠄⠀⠀⠀⠑⡄⢀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠰⠁⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠁⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢘⠀⠀⠀⠀⠀⢀⠈⡀⠀⠀⢀⡆⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠇⠀⠀⠀⠨⠤⠤⠤⢤⠀⠀⠀⠀⡀⠀⠤⠤⠄⠀⠠⠤⢄⠀⠀⠤⢤⡤⠤⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⣀⣀⣤⣀⣀⣀⣀⠀⢸⣄⣠⠀⠀⣅⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⠀⠀⠀⠀⢀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢐⠀⢸⠀⠸⠀⠀⣀⣀⠆⠀⣀⣀⡆⠀⢀⣀⣀⣀⣀⠀⠀⣀⣀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢘⠀⢸⣀⢀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠨⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠰⠀⠀⢀⣸⠀⠀⠀⠀⠅⠀⣀⣀⡀⠀⢸⠀⢸⡀⣘⣀⣀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⡁⠀⠀⠀⡇⠀⢸⠀⢸⠀⠀⠀⠈⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⡇⠀⡏⠀⠉⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠉⠀⠀⠀⠁⠀⢸⠀⢸⠀⢰⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢘⠉⠉⠉⠉⠀⠀⠀⠀⡋⠉⠉⠉⠉⠉⠁⠀⢸⠀⠀⠉⠉⠉⠉⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠁⠀⢰⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢹⠀⠐⠃⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠒⠀⠉⠀⢰⠀⠀⠀⠀⠇⠀⠂⠀⠀⠀⢲⠀⠈⠁⢘⠀⠀⠂⠈⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠚⠓⠒⠒⠒⠒⠒⠃⠀⠈⠀⠀⠒⢺⠀⠀⠒⠒⡓⠒⠃⠀⡄⠀⠘⠒⢲⠀⢸⠀⠀⠀⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠚⠒⠒⠀⠀⠁⠀⠐⠒⠓⠒⢢⠀⢸⠀⠈⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⠂⠀⠰⠒⠒⠒⠒⠀⠀⠒⠒⠒⠒⠖⠒⠒⠒⠚⠀⠘⠒⠲⠖⠒⠒⠒⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡤⠠⠀⠀⢈⠀⠀⠤⢠⠄⠀⠀⠠⠄⠀⠂⠀⡤⠀⠀⠀⠀⠀⠰⠀⠀⠄⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡇⠀⡧⠠⠤⠠⠴⠠⠄⠀⢸⠀⠀⠀⠀⠦⠤⠤⠤⠆⠀⢠⠠⠄⠀⢘⠀⠀⠀⠀⡤⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⠇⠀⡇⠀⠠⠤⠤⠤⠤⠤⢼⠀⠀⠤⠤⠤⠤⡆⠀⡠⠤⠼⠤⠤⠤⢼⠀⠀⠀⠀⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠄⠀⠘⠀⠀⠀⠀⠠⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣸⢀⣀⡀⣀⣄⠀⠀⠀⢀⡀⣸⣀⣀⣀⣀⣀⢠⡄⠀⠀⣀

⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣧⣋⣿⣥⣭⣭⣭⣬⣥⣭⣬⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⢠⣶⠶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⣿⡿⠀⠀⠀⠀⠠⠔⢠⠀⡄⠀⠀⠀⠸⣿⠀⣸⡿⠀⠀⠀⠀⠀⢀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠂⡂⠀⠀⠀⠀⠀⢠⣾⠛⠁⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠿⠗⠀⠀⠀⠀⠀⠀⠀⠥⠃⠀⠀⠀⠀⠀⠰⠿

⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⢀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⢀⣠⢤⣀
⠀⠀⠀⣿⠀⠀⢹⠆⠀⠀⠀⡧⠂⠂⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⣽⠇⠀⠀⠀⠀⣿⠁⠀⢸⡆
⠀⠀⠀⠈⢀⡤⠞⠀⠀⠀⠀⠀⡐⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢰⡟⠉⢻⡄⠀⠀⠀⠀⠚⠋⠙⣧⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢰⠉⠀⢱
⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠁⣠⠟⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⠶⠤⢤⣀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠶⠤⣤⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⡴⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡏⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⣠⠤⡄⠀⣸⠀⢠⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⢧⡹⠴⠇⣠⠇⠀⢈⡇⠀⠀⠀⣼⠃⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⠙⠛⠛⠁⠀⠀⢸⠇⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣀⡴⠋⠀⠀⠀⡸⠀⠀⠀⠀⠀⠐⠓⠲⠦⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠉⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠙⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠁⠈⠳⣄⠀⠀⠀⣠⠀⠀⠀⣷⠤⠤⠤⠤⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠓⣄⡴⠁⠀⠀⠀⣿⠉⠉⢉⣉⣹⠀⠀⠀⠀⠀⢀⡴⠚⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣴⢛⣷⣄⠀⠀⠀⣿⣒⣒⣒⣒⣾⠀⠀⠀⢀⡴⠋⠀⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠉⠉⠛⠪⢍⡐⢲⠇⠀⠀⣠⠀⢹⡄⠀⢠⡞⠀⠀⠀⠀⣼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠷⣄⣠⠖⢦⠴⠚⠉⡏⠀⢀⠞⢁⡄⠸⡇⣰⠋⠀⠀⠀⢀⡞⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠙⠒⠚⠣⢭⣉⣛⠙⢁⡴⠋⠀⢀⡟⠁⠀⠀⠀⣠⠋⠀⣹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠓⠦⣤⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠉⠉⠀⠀⢀⣸⢧⣀⣠⣴⣮⣤⡤⠤⠿⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠓⠚⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠺⠦⠤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠚⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠏⠀⠀⠈⠓⢦⡀⠀⢀⡴⠋⠉⠙⠲⣤⣀⣀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠿⠟⠛⠿⠿⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢸⡅⠀⠀⠀⢸⡇⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⠇⠀⠀⠀⠸⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠿⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠹⣷⡶⠾⠟⠛⠉⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡶⣶⣶⣶⣶⡾⠿⠿⠿⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⣠⣤⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠉
⣼⠟⠁⠀⠀⠀⠀⠉⠉⠛⠻⠷⢶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠾⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠿⠿⠿⠛⠿⠿⠿⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⡤⠊⠉⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⡞⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⠀⠀⠀⢀⡴⠃⢀⠠⢶⠀⠶⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⠳⠶⠒⢋⢰⡇⢨⣘⡾⠀⣦⣹⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠞⠉⠙⠦⠎⠁⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⡀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⢀⠄⢺⠀⠀⠀⠋⠀⠀⠢⠄⢸⡏⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠘⢿⣄⢐⡁⠀⠸⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠉⠛⠷⠶⣦⣤⣴⣶⠶⠾⠛⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠙⠻⠶⣦⣤⣤⣤⡴⠶⠾⠛⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠞⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠉⠛⠛⠛⠛⠉⠉⠁⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⣀⣠⣤⣶⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⠉⠉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⣶⡶⠶⣶⡶⠶⢶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠒⠂⠤⡀⠀⠀⠠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠈⢦⠘⠰⡞⠈⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣀⣅⣀⠇⠀⠀⠀⠀⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠶⠶⠒⠒⠒⠛⠒⠒⠶⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄
⠀⠀⠀⢠⣾⢛⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⣿⠘⠈⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⢿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠠⠖⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠈⠢⠀⢤⡄⠀⠀⢠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡿⠛⠋
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢀⡀⠀⠀⠀⡈⣱⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣸⣤⡴⠞⠋
⠀⠀⠀⠀⣿⣄⣄⣤⣤⣤⡤⠤⠤⠤⠴⠤⠴⠶⠖⠲⠒⠒⠒⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠍⠉⠁⢹⡇
⠀⠀⠀⣴⢿⠀⠀⠀⠀⠀⠀⠒⠤⢀⡀⠀⠀⠀⠀⠀⠈⣤⠄⡜⠁⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠀⢸⡇
⠀⢠⡞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⡀⠀⠀⠇⠀⠠⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇
⢰⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠠⠀⠤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠈⠛⢶⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⠤⠿
⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⢹⡏⠉⠉⠉⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣄⡀⢀⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠋⠉⠁⠀⠀⠀⠀⠉⠛⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢠⢞⣶⣴⣶⣶⣀⣠⣤⣠⣄⣤⣤⣂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠀⠀⠀⠀⠀⠀⡟⠀⠀⠘⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⢀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢠⡀⠀⡇⠀⠀⣼⠁⠀⡼⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⣧⠀⠘⠀⢰⠇⠀⣰⠃⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠸⣆⠻⠿⠿⠃⢀⡟⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠹⡀⠀⠀⠀⣼⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢧⠠⠀⣰⠏⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠸⡄⢀⡟⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻⣼⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠟⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣦⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠟⠛⠛⠛⠿⠿⢶⣶⣤⣀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⢀⣀⣀⣀⣤⣤⡄
⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠈⠙⠛⠋⠉⠁
⠈⠉⠉⠙⠛⠛⠁⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⣶⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⢺⣿⣶⡿⠛⠉⣿⡆⠀⠀⠀⠀⣸⣿⠀⠀⠀⠐⠿⠶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣴⣶⣄⣸⣿⠻⣿⡧⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣿⡏
⠀⢀⣀⣀⣠⣤⡄⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠘⢿⣟⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢰⣿⠃
⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⢸⣿⠀⠀⣸⣿⠀⠀⠀⠀⠀⠙⠿⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠙⢿⣄⠀⠀⠀⣸⣿⣶⡾⢿⠿⢿⣶⡀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⣻⣧⣶⡿⠟⠋⠁⠀⠀⢀⣼⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⢸⣿⣣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠀⠀⠀⢀⣠⣤⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⣤⣴⡾⠿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠣⣈⠉⠁⠼⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣦⣼⡆⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣁⠐⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡴⠾⣉⣛⠲⣄⠀⠀⠀⠀⡰⠛⠁⢠⣤⣌⠙⢦⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣏⣶⣴⣿⣿⡇⠈⢻⡄⠀⣾⢡⣷⣤⣾⣿⢿⠀⠈⣷⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡈⢿⣿⠿⠟⠀⠀⢸⠀⠀⣇⠘⢿⣯⣟⠽⠋⠀⠀⣿⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠈⠧⣀⠀⠀⠀⢀⣠⡿⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢙⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⡎⠀⠀⠈⠙⠒⠚⠋⠁⡎⠀⠀⠀⠈⠓⠦⠤⠤⠶⠚⠁⠀⠀⠀⠀⢈⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣀⣼⡇⣠⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⢰⣧⠨⠄⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀

⠀⠀⡟⠶⢢⡌⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢋⣧
⠀⠀⣿⡀⣾⠀⠀⠀⠀⠀⠀⠀⢠⠟⢦⣄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡤⠔⠂⠀⠉⠉⠁⢀⠴⠊⠙⣆
⠀⠀⠈⣧⢸⡆⠀⠀⠀⠀⠀⡴⠛⠳⢤⣉⠙⠛⠒⠒⠒⠋⠉⠉⢳⡶⣶⠚⠉⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠘⢧
⠀⠀⠀⢹⠀⡅⠀⠀⠀⠀⡴⠛⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⢸⠃⠸⣆⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠈⡇⣿⠀⢀⡤⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠶⢿⣄⣤⣿⠖⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢹⢸⣄⡞⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠘⡏⠻⠃⠀⣀⣤⡇⠀⠀⠀⠠⠾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⣷⢀⣴⠟⠉⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⠀⠀⠀⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⣹⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⣼⣀⣀⣰⣁⣀
⣿⠿⣿⠿⠿⠿⠟⠻⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠛⠛⣿⠻⣿⡟⠿⠿⣿⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡏
⠀⠀⠀⠀⠀⠀⣠⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⣢
⠀⠀⠀⠀⠀⠀⠱⡄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠸⡁⢀⡇⠀⠀⠀⠀⠀⠀⢀⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣀⠀⠀⠀⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠉⠉⠉⠀⠀⠉⠉⠉⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢠⣾⠿⠂⠀⠀⠀⠀⠐⠻⢷⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠘⡡⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡠⠂⠑
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢲⠁⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⠜⠀⢀⡴
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣺⡆⠀⠈⠄⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡴⠾⢀⡔⠉⢱
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠁⠀⢰⠆⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⣇⠀⠠⠠⡔⠉
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠠⡂⠀⠀⠈⠂⠤⠤⠔⠁⠀⠈⠀⠈⠀⠀⠀⡠⠂⠀⠀⠀⢠⡟⠀⠀⠀⢸⣥⣠⠤⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⢠⠏⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠒⠀⢀⡀⠀⢀⡠⠠⠄⠀⠁⠀⠀⠀⠀⠀⢠⠏⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡀⡇⠀⢀⡂⠀⠀⡆⠀⣀⠀⠀⠀⠀⠀⠀⢀⣿⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠹⡍⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠈⠢⣀⠀⡀⠀⠤⠓⣂⠠⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠸⡆⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⡀
⠀⠀⠀⣀⠤⠰⠖⣾⠁⠀⠀⠀⠀⠀⢘⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⡅
⡠⠴⠚⠁⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠸⠓⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⢀⣀⣱
⠓⡲⠃⠀⠀⡴⠒⢄⡈⡱⠀⠀⠀⠀⠈⠗⠒⠒⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉⠉⠉⠉⢹
⠀⠣⠔⢆⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⣶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣩⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣄⣀⣀⣀⡤⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢳⡀⠀⠀⠀⠀⠀⠀⣰⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠳⠶⣢⣤⣄⠲⠿⠃⠀⠀⠛⢦⣄⣄⣀⣴⠾⠃⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⢟⠢⡀⣀⣀⢀⣠⣤⣾⠁
⠀⣄⣀⣀⣀⡠⣤⣄⡲⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠋⠉⢁⣕⠃
⠀⠈⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽
⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⡄
⠀⠀⠀⠀⠨⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠙⠪⣖⣄⡀
⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣿⠿⠒
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠁
⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠴⠄⠀⠼⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢨⢴⠁
⠛⠛⠑⠐⠭⢖⢦⡀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣆
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⡶⠂⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣷⣤⣀
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⠕⠋⠉⠉⠁⠉
⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠈⠀⠀⠈⠂⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇
⠀⠀⠀⠀⠀⠾⣧⢂⣦⢄⠀⠀⠀⠀⠐⠈⠀⠀⠀⢰⡀⠐⡐⡁⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢿⣧
⠀⠀⠀⠀⠞⠁⠀⠀⠈⠳⣵⠀⠀⠀⠀⠀⠀⠀⠀⠺⠐⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣐⠿⠛⠛⠛⠛⠛⢺⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⢀⢀⣀⣐⢄⡀⠀⠸⠀⠀⠘⠀⠀⢐⡢⠀⡀⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡻⠟⠋⠁⠉⠀⡏⡟⢙⠀⣀⣛⠩⢤⣿⠀⠉⠉⠛⠳⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⣛⣙⡉⠀⣀⣭⠄⢠⡶⠀⠀⠀⠀⠀⠈⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⠉⡋⠀⢀⣨⡄⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢉⣙⠁⠀⡥⠄⠴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⣭⣀⣠⠤⠦⣲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣶⣶⡶⠞⠁⠀⠀⢀⣀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠗
⠀⠀⠀⠀⠀⠀⣀⡙⣏⠓⢦⡀⢆⣠⠴⠒⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡴⠋⠉⠈⠹⠀⠀⠟⠀⠁⠀⠸⠖⢒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠘⣩⠵⠄⠀⠀⡄⠀⠈⠀⠀⠀⠀⠀⠃⠀⠀⣀⣠⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠃⡶⠈⡠⠃
⠀⠀⠀⠛⣤⡀⠀⠀⢀⠴⠃⠀⠀⠀⠙⠀⡄⠀⠀⠏⠁⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⢀⡀⠀⠀⠀⠘⣤⣤⣴⠁⠀⠀⠀⡀
⠀⢀⡴⠉⡠⠤⣄⠀⠈⠈⢄⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠘⠋⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠘⠗
⠀⡾⠀⢸⠀⠐⡜⢦⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⡇⣀⣼⠓⣰⡄⠀⠙⠂⣀⠀⠀⠀⠀⠀⣐⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠹⠁⢻⣰⢩⠀⠀⠀⠈⠁⡀⠀⠀⢠⠋⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠛⢸⠀⠀⠀⠀⠀⠈⢢⢀⢐⠄⢚⣦⠴⠒⠊⠉⠉⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⢀⠔⠲⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡰⠁⣠⡞
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⣀⠔⠢⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢰⢋⠑⠲⡇⡸⢄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢘⠮⣉⠈⠻⣤⠜
⠀⠀⠀⠀⠀⢸⠤⠤⠤⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡤⣄⣤⣤⣄⠠⠼⣇⠔⢉⠤⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠇⡀⣀⠀⢀⠀⠀⠀⠀⠐⠠⠁⠀⠀⠀⠊⠀⠼⣁⣽⡦⠋⠀⢣⠒⠁
⠀⢰⠒⠒⠋⠻⠀⡏⠉⠉⡇⠠⡆⠀⠀⠰⠄⠀⠀⠀⠀⠀⣀⡈⠉⣁⡀⠀⠈
⠀⢸⠀⠀⠀⠆⠀⠀⠀⠀⡇⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⣬⠀⠀⠀⡇
⠀⢸⠀⠀⠈⣶⢶⣾⡀⢀⢵⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠚
⠀⢸⡀⢠⠊⠁⠀⠀⢈⣁⣠⠘⢆⠀⢠⢠⠀⡄⡄⠀⠀⠀⠀⠈⠁
⠀⠈⠓⠚⢄⣀⠀⣀⣈⠟⠉⠉⡶⠃⡀⢘
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠐⠌⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣤⣶⣶⣶⣿⣿⣷⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠉⠻⠿⠿⠿⠟⠛⠓⠒⠒