Watering can Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠀⠀⠀⠈⠙⣝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⠆⠀⠀⠀⠀⠀⠈⢆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣼⠀⠀⠀⠀⠀⠀⠀⠈⠆⠣
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⣿⣿⠶⠿⢿⣿⣿⣿⣿⣶⣷⠀⣦⣤⣄⡀⠀⠠⠤⣄⣀
⠀⠀⠀⠀⠀⣠⡾⢟⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠉⠁⠀⠀⠀⠐⠀⠀⠈⠉⠛⠿⢿⣿⡀⣿⣿⣿⣿⣿⡖⠀⠀⠉⡷⡄
⠀⠀⠀⢀⣼⣯⣷⢟⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⠻⢿⣟⢿⠁⠀⠀⠀⡄⣿
⠀⠀⠀⣼⣟⣯⠷⣿⣬⠓⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠐⠂⠉⢉⡙⠻⠤⠈⠁⠘⠛⠛⠻⠿⠿⠿⠦⢽⠋⠉⠉⠹⡏⢸⠀⠀⠀⢠⠀⠇
⠀⠀⠀⠀⠈⠀⠀⠀⠑⠄⠀⠈⢢⡀⠄⢐⣂⣀⣠⣤⣴⣶⣶⠾⡯⠧⢴⣤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣷⢸⠀⠀⣠⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠻⣛⠉⠉⠉⠀⠀⠀⠀⠀⢘⠲⢼⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡿⢾⠀⡰⠁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢉⠑⢻⣥⣉⡉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠉⢉⣀⡠⠴⠿⡾⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠳⢤⡀⠀⠀⠀⢸⠙⢻⠧⣄⠉⠉⠁⠒⠒⠒⠒⠒⠒⠚⠉⠉⢉⣀⣤⣴⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠘⠦⣄⠀⢸⠀⡼⠀⠀⠀⠉⠉⠐⠒⠒⠒⠒⠒⠒⠈⠉⠁⠀⠀⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠺⣝⣾⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠈⠛⢿⣧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢚⣛⣛⣛⡛⠲⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣩⠶⠛⠋⠉⠉⠉⠉⠛⠳⢦⣝⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣷⠀⠀⠀⠀⠀⠻⣎⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠞⣻⣿⣇⡄⠀⠀⠀⠹⣦⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠞⣡⡾⢋⡴⠛⢷⣄⠀⠀⠀⠹⣆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡇⠀⠀⠀⠀⠀⢀⣴⠟⣡⠾⣩⡾⢋⡴⠋⠀⠀⠀⠙⢷⣄⠀⠀⢻⡜⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣇⠀⠀⠀⢀⣴⠋⣠⠞⣡⡾⣋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠸⣇⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢀⣴⠟⣡⠞⣫⡾⢫⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣸⣷⠟⣡⠞⣡⡾⢫⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⣡⠞⣡⡾⢫⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣧⡾⢫⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠟⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠞⢁⡴⠋⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠞⢁⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⣴⠿⢦⣬⣍⣉⠉⠛⠛⠛⠶⠶⠶⠦⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠞⢁⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠋⠁⠀⠀⠀⠉⠉⠛⠳⠶⣤⣄⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣡⠞⢁⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣤⣤⣀⡙⢦⡀⠀⠀⢀⣴⠟⣱⠞⢁⡴⠋⣠⠞⠁
⠀⠀⠀⣴⡶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣦⣴⠟⣡⠞⢁⡴⠋⣠⠞⠁
⠀⠀⠈⣿⡿⣦⣸⡟⢷⡀⠀⠀⠀⠀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢹⢿⣁⡴⠋⣠⠞⠁
⠀⠀⠀⠹⣧⡈⠻⣧⣼⢇⡀⢠⣴⡟⢉⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠞⠁
⠀⠀⠀⠀⠈⠛⠓⠛⠻⣾⡇⣿⣸⡷⠛⢉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡼⠿⣤⡴⠟⠁
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣸⣏⣀⣀⣀⣀⣀⣀⣀⡀
⣼⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⣷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠘⠳⣶⠒⠒⠒⠒⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⣶⠞⠋
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⣀⣀⣀⣈⣳⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡟⣍⣽⠟⠻⠿⠟⠛⠛⠻⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⢉⣉⡉⠉⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣀⡴⠚⠋⠉⠉⠉⠉⠓⠶⣄⡀⠈⠛⢦⡀
⠀⠀⠀⡶⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⣼⠁⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠳⡄
⠀⠀⠀⠛⠒⠶⢤⣀⠀⠉⠳⢤⡀⠀⠀⢰⠇⢠⣞⣀⣤⣤⠤⠤⣤⣤⣀⣀⣀⠀⠀⠀⠀⢳⡄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠳⣄⠀⣼⢦⣈⠉⠀⠀⠀⠀⢠⠖⠒⠒⠒⢯⡝⢦⠀⠀⠀⣧⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠘⣆⣿⠀⠉⠙⠒⠶⠤⣤⣈⣙⣒⣒⣒⣺⠷⢻⡇⠀⠀⣿⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡟⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢰⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢠⠏⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠏⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⡠⠬⠥⣀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⣄⠀⠀⣀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠋⠀⠀⠀⠀⢀⣽⣶⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢐⠀⠐⠁⡀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠠⠀⠀⠀⢀⠀⠂⠒⠀⠐⠂⡀⠀⠀⠀⢀⢸⠀⠀⢀⢠⣺⣿⡵⢊⢈⠀⠀⠑⠆⡀
⠀⠀⠀⠀⠠⠄⠀⢀⠈⢁⠔⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠉⠀⠒⠀⠀⠀⢂⠣⡔⣷⣻⠟⡉⠔⠁⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣑⠯⠉⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡜⠁⠑⠄⡀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠠⠀⠘⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠂⠚⢀⣈⣠⡤⠬⠦⡀⠂⠂⠀⠀⠂⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠄⡈⠂⠀⠄⠀⠠⠀⠊⢀⠌⠐⠅⡀⠀⠀⠀⠀⢠⢆⠂⠁⢣⡤⠴⠖⠚⠉⠁⠄⠀⠀⠀⠀⠈⠐⠥⠄⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠂⠠⠤⠤⠄⠊⠄⠀⠀⠀⠀⠀⠀⡀⠋⠆⠑⢍⢷⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⡘⠁⠖⡈⠰⢠⣉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⢠⠘⠁⡴⣄⠁⠆⡌⠁⠀⠀⠀⠀⣀⡂⡠⠀⠀⠈⠐⠐⠈⠉⠂
⠀⠀⠀⠀⠀⠈⠁⠤⠤⠬⠁⠄⠉⠁⠁⠄⠤⠲⠀⠀⠀⠀⠠⠠⣠⣾⣿⡉⠴⢠⠀⠇⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠐⡟⠁⠣⣤⣲⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⣿⠈⢀⡿⡗⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠪⢧⣹⡴⠋⣀⠁⡀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠀⢰⠐⡆⠴⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡀⠸⠂⡇⠀⠈⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠄⢀⣀⢀⣀⢀⣤⢀⠄⠀⠘⠿⡛⣠⡇⠘⣰⡟⠃⠀⡀⠀⢀⠀⠀⠀⠀⢀⠀⠄⢀⠀⢀⠐⠒⠈⢁⡀
⠀⠀⠀⠀⠂⠀⠒⠀⠠⠀⢂⠀⠠⠐⡒⢢⠄⠎⠀⠀⠀⢀⡀⠀⠀⡀⠊⢁⠈⠀⠂⠠⠾⠃⢾⠵⠀⡠⠤⠄⠔⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠛⠀⠁⠈⠁⠀⠀⠈⠀⠈⠘⠁⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠉⠁⠁⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡀⠀⢀
⠀⠀⠀⣀⢴⣾⠉⠋⠓⠒⢤⠀⠐⡠⠀⣀⢀⡀⣀⣀⣀⣠⣀⣀⣀⣀
⠀⢀⡜⢁⠯⠁⠀⠀⠀⠀⠀⠁⢶⣶⡿⠋⡰⠋⠍⡱⡍⢹⡻⠋⢙⢝⣝⢝⢝⢹⠟⢖⣦⣅
⢠⡮⢨⡆⠃⠀⠀⠀⠀⠀⠀⠀⠠⠍⠓⠚⠓⠶⠴⠴⠭⠾⠥⠤⠴⠷⠴⠵⠼⠵⠗⠛⠉⠑⠂
⢼⠭⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⡫⠤⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠺⡗⡸⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠄⠐⠀⠠⠁⠂⠄
⠀⡟⠪⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠆⠀⠐⠀⠠⠄⠃⠀⠠
⠀⠜⡄⠀⢧⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠆⠁⠈⠠⠄⠀⡄⠁⠀⢄
⠀⠈⠻⡆⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠂⡠⠈⠀⠀⡀⠠⠀⠒
⠀⠀⠀⠳⡄⠆⢧⠀⠀⠀⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⢀⠐⠂⠀⡀⠁⡈
⠀⠀⠀⠀⠘⣆⠀⢱⡀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠠⠤⠖
⠀⠀⠀⠀⠀⠈⠆⠁⠛⠦⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡀⠁⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⢆⢁⡙⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠊⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡾⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠠⠋⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠐⠶⣤⡀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠐⠀⠔
⠀⠀⠀⠀⠀⠀⠈⠳⣕⢀⡇⠀⠀⠀⢀⣁⠀⠀⢀⢱⠀⠐⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠈⢧⡁⠀⠀⠉⢀⣹⣧⡂⠘⢸⡇⡆⠔⠂⠀⠂⣠⣾⠃⡂⠀⠀⠀⠀⠀⠈⠔⠁
⠀⠈⠛⠻⠷⠶⠶⠶⣾⣜⣽⡖⢪⡶⢳⡞⠯⢵⡘⠆⣜⠣⢄⠀⣰⣾⣿⡿⠟⢀⡠⠄
⠀⠀⠀⠀⠀⠀⢀⣠⠌⣯⣓⣬⠚⣷⠷⢯⠜⣒⣱⣶⠉⠙⣸⡄⠛⣿⠩⢆⣔⣯⡒⣏⣤⣦⣏⠀⠈⡠
⠀⠀⠀⠀⠀⡰⢗⡲⠣⠚⢶⣊⡟⣷⡽⠇⡀⠁⣌⠙⢆⢀⡙⠀⠈⣉⣫⣴⣿⣏⣛⣽⡿⢇⣿⣶⡼⠁⠀⢠⡔⠁
⠀⠀⠀⠀⠀⠈⠠⢤⣴⣶⣦⣭⡝⠛⠶⢶⣷⣤⢬⠅⢞⠉⢘⠒⣉⢉⡱⢲⣎⢹⣇⣨⡧⢈⢛⡛⣁⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠔⣺⣀⣨⣤⣶⡚⠙⡉⢀⣤⠖⢉⡏⢹⢦⡈⠻⠁⣕⣳⣿⣩⣯⡒⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠐⠉⠊⢁⠴⢲⣿⣄⠜⠲⠂⠀⠀⠹⠱⡏⣾⣼⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠈⠐⠀⠊⠀⠀⠀⠀⠀⠐⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠹⡌⢳⣄⣀⠀⠀⠀⣴⡶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠖⠻⡄⢻⡉⠛⣆⡜⡟⠀⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢿⠀⠀⢻⡈⣧⡴⠋⠻⡁⠀⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠈⠳⣦⣼⠟⠋⠀⠀⠀⠙⢾⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⢳⡇
⠀⠀⠀⠀⠀⠀⣤⠤⣈⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⢰⠃⡏⠠⣤⣄⣀⣀⣀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠸⣴⣇⡠⠖⠤⠤⣈⡉⠉⠉⠛⠚⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⢠⠞⢀⠀⢠⠂⢠⢠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣌⣧⠀⠀⠀⠀⠀⢀⣠⡴⠋
⠀⠀⠀⢺⠀⠈⠀⡏⠀⠈⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠁⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠒




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⣋⣉⣍⣍⣍⣖⣒⡢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⡴⠞⠋⠉⠀⠀⠀⠀⠀⠉⠉⠛⠶⢭⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⡼⠉⠀⠀⠀⣀⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢠⡟⠀⠀⠀⣠⢊⣴⣶⣎⢋⠉⢒⠦⢤⣀⠀⠀⠀⢸⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡾⠀⠀⠀⣰⣵⢿⣿⣟⡿⡎⠀⠀⠈⠘⠘⠹⣗⠢⢼⣇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⢰⠡⣿⣿⣿⣻⢱⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠘⣄⠀⡎⠀⠀⠉⠛⣣⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⠲⣄⠀⠀⠀⡰⢃⢎⣜⣔⠄⡔⡀⡠⡀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡤⠟⣩⢞⢕⡡⡪⣪⣪⢎⠜⡔⡠⢁⢂⠎⡔⠠⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢷⣥⣮⣾⣛⢕⡡⣊⢜⡴⡡⢂⢞⣔⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠀⠀⣉⣽⢾⣷⠯⢮⣔⣵⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣽⢁⡤⢊⣡⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⠟⣁⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⠔⣓⡯⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⠳⡄⢴⡶⡠⢢⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⡈⠋⠑⣹⣄⢜⢌⢿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡂⡪⠀⠴⢀⠔⡀⠉⢦⣈⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡄⡄⠀⠄⠀⠄⢀⠀⠃⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡈⡀⠀⡄⠀⡀⠀⠀⠆⠈
⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⢀⠁⡀⢠⠀⠀⡁⠀⡁⠃⠈⡀
⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠈⠀⠀⢈⠀⠃⠀⢀⠂⠀⡁
⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠃⠈⠀⠀⠈⠀⠃⠀⠈⠸⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⠀⢰⡆⡁⠐⠀⠀⠆⠃⠀⠀⡁⠀⠃⣴⡄⣰⠀⢈⠀⠀⢠⣼⣷⡄
⠀⠀⠘⢷⣾⢇⡁⠖⠦⠤⡄⢣⣄⡤⣵⠲⠡⠺⣯⡟⠆⠄⢠⢄⢸⣿⡣⠎
⣠⠔⠉⠛⣡⣤⣄⣤⠤⠶⠔⣠⠖⠾⡎⡶⡌⣴⣦⡅⡀⣤⣀⣠⣁⣈⣃⣲⢋⣑⠢⠀⠤⢀⢄⡔⡢⣒⢔⡢⣒⢔⡠⢖⠤⡢⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠮⢍⠉⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⡰⠉⠑⡀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢠⠁⠀⠀⢱⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡈⠀⠀⠀⠈⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠓⠒⠀⠈⡝⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣠⠆⠁⢀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⠤⠄⠀⠠⠤⢀⡀
⠀⢀⢊⠐⠀⢀⠎⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⣀⡀⠀⠀⠤⠤⠤⠤⠤⠤⠤⡅⠀⠀⠀⣏⣈⣉⣀⡲⠊⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⠠⠁⠀⢀⠔⠁⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⠇⠀⠀⠀⢠⠀⡠⠒⠉⠀⠉⠑⠢⡀⠀⠈⢆
⢇⣀⠐⠁⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠎⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠈⠉⠐⠒⢢⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠉⠢⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠔⠁⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡠⠃⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⠊⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡰⠁⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢉⡐⠂⠤⠤⠄⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⠀⠤⠤⠔⠒⣉⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠛⠛⠒⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢀⡴⠒⠚⠛⠛⠲⠶⢤⣀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡇⠀⢀⡠⠖⠒⣒⣶⠶⣶⣦⡤⢿⡄⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⡄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣸⠀⢀⣾⣤⣀⡘⠳⠶⠶⠖⠊⠀⠸⠇⠀⠘⠐⠒⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣥⠀⠰⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡏⠈⠙⠛⠛⠛⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⢻⡄⡄⠀⠖⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⣿⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠞⢋⡾⠷⠾⣧⡰⠆⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣦⣤⡤⣤⡾⠁⢠⡞⠁⠀⠀⠀⠉⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⢉⡽⠋⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⢷⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢀⡴⠋⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠊⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠷⠶⠦⣤⣤⣤⣤⠴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡠⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠉⢊⠊⢻⣆
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢢⢀⢿⡆
⠀⠀⠀⣠⣾⣟⠟⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠈⡚⣾⣿
⠀⠀⣾⣿⡿⠙⣢⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣷⣷⢷⢿⣧⣤⣀⣀⣠⢤⣶⣶⣶⣄⡀
⠀⠀⠻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠎⠉⠀⠉⠛⠛⠻⠿⠿⢿⣻⣼⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⣿⣆
⠀⠀⠀⠀⠈⠉⠉⢻⣿⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠻⣿⣽⣟⠁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡝⣆⠀⠀⠀⠀⠀⠀⣠⣴⢿⣷⣶⣭⣉⣉⣋⣃⡀⢀⡀⣈⣈⣟⣋⣿⠤⠴⢒⣿⣿⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣌⢧⡀⠀⣠⣴⣿⣭⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡍⡏⠁⠠⠿⠔⠛⠀⠀⠀⣽⣿⢀⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⢳⣾⣿⣥⡾⣯⢛⣿⣿⣿⣿⣿⣿⣿⣿⣫⣴⠂⢀⠄⠀⠀⠀⠀⠀⢈⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⠙⢯⣧⣿⡽⣹⢿⣿⣿⣿⣿⣿⣿⣟⣿⣶⠿⢈⠀⠍⠀⠀⠀⠀⠐⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡜⢿⣽⣿⣿⢻⣿⣿⣿⣟⣿⢿⡿⠿⠭⠤⠠⠤⠤⠐⢐⣀⣬⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⠾⠿⠛⠛⠚⠉⠉⢁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡘⣿⢾⣿⣿⣿⣿⣿⣿⣿⣱⣡⠀⠀⠀⠀⠀⠀⠀⠀⠂⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡞⠫⣿⣿⣿⣿⣿⣿⣟⠟⡒⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣿⣿⣿⣿⣿⣿⣿⣧⡰⡅⠄⠀⠀⠀⠀⠀⠀⢸⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⡅⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢿⣝⡇⡃⠀⠀⠀⠀⠀⠀⢠⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⢿⡎⠇⠀⠀⠀⠀⣀⣀⠤⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣄⢀⣾⠟⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⠋⠁⠀⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣏⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣵⣿⣿⣿⣷⣦⣀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⢿⣷⡶⠾⠛⠛⠉⠉⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠀⠀⠈⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠆⠀⠀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⠀⡄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⡄⣴⢣⣀⢰⠀⡇⢢⠀⡄⣸⡈⡄⡈⣆⣀⣆⢰⡆⣂⣦⠐⡀⣷⣇⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠦


⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣀⠀⡴⠘⡄⢀⠄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⡀⢸⠁⢧⢰⠁⠹⡀⠀⣷⠃⢰⣣⠖⠁⡤⠖⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡀⠈⠺⡄⠈⢿⠀⠀⠹⡄⢹⠀⡼⠁⠀⢰⠀⢀⣾⠤⠖⣲⠶
⠀⠀⠀⠀⠀⢠⡀⠀⢃⠀⠉⠒⢤⣙⢦⣸⡄⠠⠀⢻⣼⡾⠁⠀⠀⡼⢀⡞⠁⣠⣞⣁⡀
⠀⠀⠀⠀⠀⠈⢏⠓⠮⣷⡀⠑⢄⠈⠻⣿⣧⣠⣧⣼⣿⣧⣴⣇⣰⣷⣯⠴⠚⠉⠀⢀⣆⣀
⠀⠀⠀⠀⠀⡤⢬⣷⣄⣀⡙⢦⡀⠙⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣠⠔⠈⣀⠔⠁⠀⣀⠵
⠀⠀⠀⠀⠀⠱⣄⡠⠤⠬⠭⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣞⣁⠤⠖⠛⠳⢤⡀
⠀⠀⠀⠀⠀⠊⢄⡀⠀⠀⠤⠤⢴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠙⠓⠒⠶⢶⣒⠒⠋
⠀⠀⠀⠀⣤⠤⠤⠭⠟⠒⠶⢦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠉⠁⠀⠀⣀⡈⠕
⠀⠀⠀⠀⠈⠓⢦⣤⠴⢚⡽⠛⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣭⣉⡉⠉⠀⠙⢆
⠀⠀⠀⠀⠀⢖⡉⢀⠔⠉⠠⠔⠊⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠧⡀⠙⣎⡉⠙⢿⡓⠚
⠀⠀⠀⠀⠀⠀⠉⠁⠀⡠⢤⡶⠋⣡⣾⠃⢸⠛⢻⣿⠟⢿⠋⢻⢿⠦⣄⠈⠂⠈⢻⡲⢤⣱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡼⢁⡇⠀⠂⢠⠏⡟⡆⠈⡀⢸⡌⠳⣌⠑⠢⢄⣀⢳⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠶⠯⠖⠚⡿⠁⢸⠀⠀⡰⡟⠀⣇⠹⡀⠀⢸⠷⡀⠘⡶⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⠴⠚⠠⠊⢠⠇⢠⢿⠀⠑⡀⡸⠀⢳⢀⡇⠈⠢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠁⠸⡆⠞⠀⠁⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⡟⢿⣿⡿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡇⣠⡅⢰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠛⣿⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠋⠐⢉⠉⠉⠀⠀⠈⠻⣿⠉⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠈⠀⠀⠀⠀⠦⠀⠀⠀⠀⣽⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡇⠹⣄⠀⠠⢀⣀⠀⠀⠀⠀⠀⠀⡹⢻⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡟⠉⠀⠀⠈⠓⣤⣀⣀⠀⠀⣀⣀⣴⡚⠁⠸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⣠⠴⠒⠉⠁⣸⣭⠽⠛⠉⠁⠀⠈⢦⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣾⡉⠀⣀⣀⡤⢯⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡼⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡱⣴⣏⢷⡫⠵⠚⠛⠉⢁⣀⣀⣸⣆⣀⣠⠤⠶⠒⠚⠹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⡽⣭⡽⣀⣴⣶⣒⣿⡉⠉⡽⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣰⣿⡿⠧⠋⠉⠁⢀⡿⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠉⠉⠙⠓⣲⠶⠋⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣳⡤⠴⠒⠋⠁⠀⠀⠀⠀⠹⣖⠒⠒⠒⢒⣖⡒⠒⢖⣒⠖⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠳⣄⠀⠀⠀⠀⠈⣣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠘⠴⠃⠀⠀⣀⣄⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⢶⣄⣠⣴⣿⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⡔⢦⠀⠀⠀⠳⠜⠁⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⣇⣸⠟⠛⠒⠲⠤⢭⣍⣙⡛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡙⠉⠀⠀⣏⣳⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠊⢀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣟⠀⠀⠀⠀⠀⣀⡴⠯⢤⡯⠼⠦⢤⠤⠬⢤⠴⠿⠦⠿
⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠴⠖⠋⠁⡇⠀⢸⠃⠀⠀⢸⡆⠀⢸
⠀⠀⠀⠀⠀⠐⠁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⣾⠀⠀⠀⠸⡇⠀⢸
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⡴⠒⢶⣋⣉⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣼⠁⠀⡇⢀⣀⣀⣀⡏⠉⢹
⠀⠀⠀⠀⣨⠤⢤⡖⠒⣲⣵⠒⠙⣒⠋⢰⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⢀⣀⣠⠤⠴⢺⡟⠉⠉⢀⣀⣀⡤⠼⠃
⠀⠀⠀⠀⢱⠦⠘⠭⠜⠩⡭⠟⠉⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠈⠓⠚⠉⠉⠁
⠀⠀⠀⠀⠈⠒⠒⠉⠓⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢷⡄⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⡄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢳⠂⠀⠀⠀⠀⠀⠀⠡⡀⢲⡀⣰⢀⡅⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣙⠢⣑⣘⣜⡐⠉⠴⠂
⠀⠀⠀⠀⠠⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢒⣽⢿⢿⠒⣒⠒⠂
⠀⠀⠀⠀⠀⠢⠆⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢻⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⡰⢃⠂⡇⠑⡌⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⣠⡄⠀⠀⣏⠰⢿⣇⠀⠀⠠⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠂⠉⢓⠋⠁⠐⠀⠀⠀⣿⣿⠏⠀⣀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠨⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠂⠀⠈⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⣀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠠⠀⠉⠢⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠄⠀⠀⠀⠛⠀⠀⠀⢀⡍⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠍⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⢸⡀⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠐⠄⠀⡀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⣰⠀⠀⢸⡇⠀⠀⠈⢸
⠀⠀⠀⠀⢶⣦⡂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢧⠆⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢪⠉⠀⠄⢸⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠇⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⣀⣭⡆⠀⡄⠂⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠰⠂⠈⣄⡀⠀⢸⡇⠀⠀⢀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⣶⠆⠀⠀⠀⠠⡝⢻⡇⠀⠀⠆⠣⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣁⠀⢸⡇⠀⢀⠄⢠⣤
⠀⠀⠠⠀⠐⠠⠀⢀⡀⠀⠀⠀⠘⠀⠰⡿⠂⠀⠀⠀⠀⠀⠀⠀⠁⠉⠃⠀⠀⣆⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⠹⣄⣿⡇⢀⡎⠀⠀⠙
⠀⠀⠀⠂⠀⠀⠁⢸⠃⠀⠒⡠⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠻⣿⣇⡞
⠀⠀⠀⠀⠀⠀⠐⠚⠐⠂⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠀⠂⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡶⣆⣠⡴⣦⡴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⣤⡷⢦⣀⡾⠁⣼⠋⠀⢸⠀⣿⠖⡷⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣦⣄⣿⠀⡈⣧⠀⠙⢧⣾⠃⠀⠀⣼⡾⠁⢠⡿⠋⣿⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣦⡐⢽⡌⠛⢦⣱⣿⠀⢀⠈⣿⠀⡀⣸⡟⡀⣴⠋⠀⠀⡟⠉⢉⣟⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠉⠉⠛⠻⣄⢀⠙⢿⣧⠸⣆⣿⢠⣇⣿⣵⣾⠁⠀⠀⢀⡷⠞⠋⠉⣩⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡉⠉⠓⠦⣤⡀⡈⢿⡳⣤⣻⣦⣿⣿⣿⣿⣿⣿⣧⢀⡜⢀⣞⣀⣀⣠⣾⣋⡉⢉⡟
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠽⠦⣄⡀⠀⣿⣿⣴⣿⣿⣯⢽⢽⣺⣷⣟⣟⢿⣿⣫⠶⢛⡉⠉⠉⠉⣩⣟⣡⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠧⣄⡀⠀⠈⠉⠛⣛⣿⣿⢯⣿⣬⣽⣮⡯⣷⣗⡯⣯⣿⣗⣊⣁⣀⣤⠴⠛⠁⠀⢈⡭⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠛⠛⢛⣻⣿⣿⣿⣳⡿⣽⣲⣻⣟⣿⣯⣟⣿⡻⣿⣿⡿⠿⢿⣶⡶⠶⠶⢯⣄
⠀⠀⠀⠀⠀⠀⠈⣛⣶⠶⠖⠚⢋⣩⣿⣿⣿⣷⣞⣟⢛⡜⣿⢯⣷⣿⣻⡾⣹⣿⣿⣒⡒⠂⣈⣻⣷⢦⣀⣼⠛
⠀⠀⠀⠀⠀⠀⠀⣩⠟⠛⢛⡿⠋⠀⣀⣀⣤⣿⣿⣽⣟⡾⡯⣟⣟⣯⣿⣿⡏⠀⠘⣷⣾⡋⠉⠀⣀⡤⣿⡯⠿⠆
⠀⠀⠀⠀⠀⠀⠚⠓⠒⣶⠟⠒⢛⣉⣭⠟⠉⢁⣸⣏⠙⠻⣷⣿⣿⣟⠉⠉⢳⣾⠿⠿⣤⣉⠛⢿⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⡞⠋⢩⡟⠁⠀⠉⠁⠀⢙⣷⡶⢿⠋⢻⢻⣿⡶⠦⠿⣗⠒⠦⡈⠛⣦⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⠋⠉⣙⣛⣛⣿⡏⠸⠁⣿⠀⢸⢸⡇⠳⣄⠀⢿⣤⣤⣤⣤⣬⣟⠋⠁
⢠⣤⣤⣤⠤⠤⠶⠶⠶⠤⠤⢭⣿⣍⣉⠉⠉⠀⠈⢧⡀⠀⣿⠀⠎⢸⠗⢦⣌⠀⠸⡆⠀⠀⠀⠀⠉
⠀⠙⢦⡀⠀⠙⠛⠒⠶⢦⣤⣄⣀⠈⡍⠛⠶⣄⡀⠈⠛⠶⣿⠀⠀⣾⠀⠀⠈⠙⠓⠿
⠀⠀⠀⠙⢦⣄⠀⠀⠀⠉⠉⠉⠙⠛⢷⣦⣀⠈⢳⡄⠀⠀⠘⣦⣀⣿
⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠈⠛⠉⠉⠉⠈⠙⢷⣄⢻⣄⠀⠀⣿⠻⣿⠀⠀⠀⠀⢀⣠⠶⠛⠛⠛⢛⡛⠛⠛⠓⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⣀⣨⣿⠟⢧⡀⢸⠀⢻⠀⠀⠀⣰⠟⠁⠀⠀⣠⣞⣩⣤⠤⠴⠤⠀⠀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠁⠙⢷⣄⠻⣾⠃⢸⡆⠀⢰⠏⠀⣠⣴⡞⠋⠉⠛⠓⠂⠀⠀⠀⠀⢀⣠⡤⠶⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠙⠀⢸⣇⣤⣿⡴⠟⠁⠈⠉⠙⠒⠂⠀⠀⠀⢀⣤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⠋⣡⡿⠷⢦⣄⣀⡀⠀⠀⣀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⡴⠋⠀⠀⠀⠈⠉⠉⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠛⠿⠛⡿⠻⡿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠋⢠⠀⢀⠆⠀⢹⠁⠀⡠⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠓⠦⣴⠁⠙⢢⡆⠀⠀⠘⣦⠎⠀⠀⠀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠓⡄⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⣰⠔⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢃⠀⠀⠀⠈⡄⢰⠀⠀⠀⠋⠀⠀⠀⡰⠁⠀⢠⠃⠀⢀⡠⠤⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠠⡒⠉⠉⠉⠳⡡⡀⠀⠀⢸⠀⢣⠀⠀⢰⠀⢀⡞⠀⠀⡰⠁⢀⠴⠋⠈⠁⠀⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣈⡢⣀⠀⠀⠘⢌⡢⡀⣀⡳⠰⠷⠖⠈⡗⠛⢇⡴⠊⡠⠊⠁
⠀⠀⠀⠀⠀⣠⠔⠉⠁⠀⠀⠑⠢⢄⡀⢹⠛⠉⠀⠀⠈⠀⠀⠀⠀⠀⠰⣴⢁⣤⠶⠒⠒⠚⠉⡨⠁
⠀⠀⠀⢀⣚⠢⢤⡤⢀⣀⡀⠀⠒⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡏⣀⣀⡀⠀⢀⡔⠉⠂
⠀⠀⠀⠘⡀⠉⠁⠀⠀⠀⠈⠙⠒⠚⡧⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⠀⠀⣹⠉⠀⠀⠈⡱⠛⢍⠑⠢⠥
⠀⠀⠀⠀⠈⠑⠢⣀⣀⠠⠤⠀⠀⢤⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢨⣯⣠⠤⠖⠉⠲⡄
⠀⠀⠀⠀⠀⠀⣴⡾⠒⠂⠈⠉⠉⣉⡭⡷⣠⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠑⢄⡀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⣼⠟⠀⠀⢀⡠⠖⣉⡤⠚⠋⢉⡽⠖⠶⣤⠴⣴⠖⢇⠀⠀⠀⠈⡻⠙⡁⠀⠐⠒
⠀⠀⠀⠀⠀⡋⢀⡤⡖⠉⡠⢊⠍⠀⠀⣠⠋⠀⢀⡾⠁⠀⠁⠀⢸⠉⠉⠉⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠛⠁⢰⣧⠋⢀⠎⠀⢠⠊⡇⠀⢀⠏⠆⠀⠀⠸⠀⠈⡧⣀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠸⠀⡰⠁⠀⢹⠀⡈⠀⠘⡀⠀⢠⠀⠀⢃⠀⠉⠑⠀⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠰⠁⠄⢠⠋⢦⡇⠀⠀⡜⢢⠘⡧⡀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠁⠀⠀⠱⡀⡸⠀⠀⠉⠁⠈⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠈⠻⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡿⣛⣿⠏⠀⠀⠂⠀⠀⠈⠉⢸⣿⠁
⠀⠀⠀⠀⠀⠀⢧⠉⠈⠀⠀⠐⠇⠀⠀⣀⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⠜⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⠀⢀⣀⡴⠖⠁
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠘⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢰⣿⣿⣿⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣶⣶⣤⡂
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⢸⣿⣿⣿⣿⡯⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠈⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣿⣿⣿⣿⠃⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢰⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣾⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⢰⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠋
⠀⣾⣿⣿⣿⡏⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠿⠟⣿⠻⡿⠿⠿⠟⠁
⢠⣿⣿⣿⣿⠃⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏
⣼⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣷⣦⡀⠘⠛⠛⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄
⠂⠀⠌⠙⠻⠿⠿⠿⠆⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⠇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢠⡄⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐
⠀⠀⣻⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠙⠁⠀⠀⠀⠀⠋⠠⡥⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⡤⠄
⠀⠀⠻⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠀⠀⢀⣀⣀⠀⡀⠓⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⣀⠀⠈⠰⠦
⠀⠀⠰⡀⠀⢠⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠨⣿⣿⣿⡿⠿⠟⠻⢿⣿⣦⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠃
⣦⠀⠴⠄⠀⠈⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠙⠀⢀⣄⣀⠄⠀⠙⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁
⣿⠙⠒⣦⠀⡘⠀⠀⣬⠀⠈⠆⠀⠀⠠⠀⠀⠀⢀⡀⠘⠀⠀⠀⠀⠉⠁⠀⠀⠀⠜⠢⠀⠰⠀⠀⠀⠐⠀⢠⠀⠀⠐⠀⠀⠤⢀⠆⠠
⢻⢀⠀⠈⠀⠃⠀⠀⣽⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⣷⣺⣶⠃⠀⠀⠀⠀⠀⢀⠄⠀⠀⠄⠀⠇⠀⠀⠀⠄⠀⢀⠀⠀⠰⠤⠇⡉
⠀⢯⣠⡀⠈⠁⠀⠀⣽⠀⠈⣠⡀⠀⠀⠀⠀⠀⠀⠘⣿⡽⢀⡠⡶⢀⠀⠊⠍⠀⠀⠀⣔⠀⢠⣰⣿⡀⠀⠀⠀⠠⣄⠠⠇⣀⣄⠘⠃
⠃⠉⢀⠙⠄⠰⡆⠀⢺⣁⣼⠀⠀⠀⠀⠀⠀⠀⠠⠄⠙⣇⠬⠴⠃⠸⢂⠀⠀⢀⡞⢡⠘⠚⠀⣏⡣⠀⠀⠀⠁⠀⠈⠶⣌⠉⠀⠀⢴
⠀⣰⠏⢳⡀⠀⠆⠀⣽⠛⣿⣧⠀⡀⠀⠀⠀⠀⠀⡘⢀⠃⠒⠚⢃⣸⠏⣰⣤⣻⠂⣻⠀⢦⢠⣿⠃⠀⣄⠀⠀⠀⠀⠀⠈⠚⢁⠊
⠀⠁⠀⠀⣷⢀⣶⠄⣿⠀⡟⢹⣏⠁⠀⠀⢀⠄⣾⠇⣼⠆⠀⠀⢎⢈⠓⠈⠠⣨⡁⠚⣥⠜⠮⠝⠂⠀⠈⢢⠄⡀⠀⣀⠀⣀⠈⠐⠆
⡴⡄⠀⠓⠮⠋⠦⠀⣼⠰⠁⠙⣿⠳⡄⢀⠌⢠⡟⠀⠀⠓⢦⡇⡠⠈⡀⠀⠀⠀⠁⣞⣾⣷⣄⣠⠀⠐⢀⡰⢠⢴⠐⠣⠠⠘
⠀⢸⣦⣆⣠⡠⡾⠿⣿⠦⠃⢨⣟⠀⢶⠀⢰⡾⡶⠄⡄⠤⣭⢜⣓⢺⡏⠉⢀⡠⠀⠘⣺⣏⡀⡦⠀⢀⣉⡀⣼⡜⡙⠃⠀⠁⠀⠶⡀
⠆⠈⣥⣄⠐⢛⣿⣀⣿⡀⠐⠢⡌⠀⡈⠰⢦⣞⠁⢠⠓⠂⠀⠀⠀⢾⣁⣠⡜⠱⢾⡠⠝⠛⠛⣰⠆⡙⠛⠁⠛⠁⠒⣤⡳⢄⣤⣤⠙
⠻⢎⣿⣿⣡⣬⣭⡙⣿⢛⠀⠀⠸⠀⣷⣶⣾⣿⣷⣷⣶⠌⢀⠀⢴⡟⡱⠾⢆⣟⣻⣀⣗⠘⠋⠝⢨⡅⠀⠀⢀⣄⣀⠬⠁⣹⠘⠓⠶
⡖⠺⣟⡽⠿⢋⣙⣫⠁⡀⠀⢤⡄⢨⣯⣾⠽⠿⢿⡿⠀⠒⠤⠀⠘⣝⠿⢛⠈⢻⠿⢿⠏⠉⢰⠓⠃⢩⠑⢂⣼⠾⢻⣤⣺⣭⠶⣄
⠉⠴⣿⣂⢶⡄⢀⣤⢞⣿⣿⠶⣲⢹⣏⡈⢥⣣⠛⣟⣀⣤⡗⢠⣦⣯⡟⣁⢀⠘⠸⡏⠃⢀⠘⡁⠻⢻⠄⠛⢣⢛⣜⣷⢷⢿⡙⠿

⠀⠀⠀⠀⠀⠀⣟⡆⠀⠀⠀⠀⠀⣸⣧⠀⢀⣿⡇⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⡇⠸⡆⠀⠀⣀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣀⠀⠀⠀⠀⠀⠉
⠀⡠⡄⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠻⠟⠀⠀⠉⠀⠀⠀⢸⢦⠀⠀⠀⠀⠀⠀⠙⠤⠃⠀⢰⣿⡆⠀⠛⠀⠀⠀⠀⠀⠀⢿⡷⠀⢠⠛⡆⠀⠀⠀⢀⡆
⠰⣧⠇⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠳⠼⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⡜⡄⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣆⠀⠀⠿⠇⠀⢀⡄⠀⢸⠁⡽⠀⠀⠈⠛⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠶⡄⠀⠀⠀⣿⡄⠀⠀⢀⠀⠀⠘⣿⡇⠀⠀⢰⣷⠀⠀⣰⡄
⠀⢾⡿⠀⠀⠀⠀⠀⣾⣷⠀⠘⠞⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⡄⠀⠈⠳⠃⠀⠀⠈⠿⠇⠀⢀⡞⡆⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⢿⡷
⡄⠀⠀⢀⡀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⣶⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣸⠀⡟⠀⠀⠀⣿⠀⠀⠀⢠⡀⠀⠀⠀⠀⣼
⡟⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⢰⣷⠀⠀⠀⢸⣿⡆⠀⠘⠚⠁⠀⢀⡀⠁⠀⠀⠀⢮⡳⠀⠀⠀⠀⠸
⠀⠀⠘⠿⠟⠀⠀⢠⡀⠀⠀⣸⣧⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⡞⢆⠀⠀⠀⠀⠘⠟⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⡏⣇⠀⠀⠛⠋⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⣇⢸⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠁⠀⢠⡀⠀⠀⠀⠀⠸⠟
⣶⡀⠀⢀⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⡎⢣⠀⠀⠀⢠⠀⠀⠈⠛⠀⠀⠀⡞⢡⠀⠀⠀⣼⡀⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠸⠇⠀⢠⡆
⠿⠇⠀⢸⣿⠀⠀⣄⠀⠀⠀⠀⣴⡄⠀⠙⠋⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠧⠜⠀⠀⠰⣿⠇⠀⠀⠈⠉⠀⠀⠀⣰⣄⠀⠀⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠈⠉⠀⢰⠉⡆⠀⠀⠀⣿⠇⠀⠀⠀⢠⡀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⠿⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⣦⠀⠀⠸⣄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⡀⠀⠀⢼⢹⠀⠀⣼⡆⠀⠀⠀⢀⠜⡄⠀⠀⠀⡇⡳⠀⠀⠀⠀⢠⢶⠀⠀⠀⠀⠈⠋⠀⢀
⠃⠀⠀⠿⠇⠀⠀⠈⠁⠀⠀⠀⡔⣇⠀⠀⠀⡄⠀⠀⢰⣿⠀⠀⠈⠉⠀⠀⠻⠏⠀⠀⠀⣮⠀⡇⠀⠀⠀⠉⠁⠀⠀⠀⢠⡇⢸⠀⠀⠀⢀⠀⠀⠀⠸
⠀⠀⢀⠀⠀⠀⠀⣰⡆⠀⠀⣼⠀⡇⠀⠀⣰⣿⡀⠀⠈⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⢀⣦⠀⠀⠀⠀⡀⠀⠈⠧⠞⠀⠀⢰⢡⡄
⠀⢀⠟⡆⠀⠀⠀⠿⠇⠀⠀⠘⠚⠁⠀⠀⢻⣿⡇⠀⢀⡄⠀⠀⣸⣷⠀⠀⢰⡆⠀⢰⡀⠀⠀⠀⠸⠿⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢻⡴⠇⠀⣠
⠀⣾⢀⡇⠀⢠⡀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠉⠀⢀⠇⡇⠀⠀⠘⠛⠀⠀⠘⠁⠀⡎⢹⡀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣿⣧
⠀⠈⠋⠀⠀⢿⡇⠀⠀⠀⢸⡇⠀⠀⣾⡆⠀⠀⠀⠘⠶⠋⠀⠀⢠⠀⠀⠀⠀⠀⠀⢳⣈⡇⠀⣰⡆⠀⠐⡿⠀⠀⠀⠀⠀⠀⡎⣇⠀⢀⣷⡀⠈⠻⠟
⠀⣤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠋⠁⠀⢠⡀⠀⠀⠀⠀⢀⣿⡆⠀⠀⢠⡀⠀⠀⠉⠀⢠⣿⣷⠀⠀⠀⠀⢀⠴⡀⠀⠀⠙⠃⠀⠘⠿⠇⠀⢀
⢸⣿⠆⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⣤⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠛⠁⠀⠀⢯⠇⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠸⣼⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⡞⡆
⠀⠁⠀⠀⢸⢦⠀⠀⠀⠀⠀⠀⢼⣸⠀⠀⠀⠈⠁⢠⣾⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⢠⣷⠀⠀⠀⠀⢠⣷⠀⠀⣰⣿⠀⠀⠀⠳⠃
⠀⣀⠀⠀⠻⠜⠀⠀⢀⡼⡀⠀⠈⠁⠀⢀⣤⠀⠀⠘⠟⠀⠀⣠⠀⠸⠏⠀⠀⠀⠀⠀⠸⣿⠆⠀⣤⠀⠘⠿⠁⠀⠀⠀⠘⠿⠁⠀⣿⣿⠇⠀⠀⣀
⢰⣿⡆⠀⠀⠀⠀⠀⡞⠀⡇⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⢠⡇⢣⠀⠀⠀⢀⣾⡆⠀⠀⠀⠀⢸⣸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢸⣿
⠈⠛⠁⠀⡀⠀⠀⠀⠹⠴⠁⠀⠀⢀⡀⠀⠁⠀⡜⡇⠀⠀⠈⢧⡸⠂⠀⠀⠈⠿⠃⠀⣠⡄⠀⠀⠉⠀⠀⣾⣿⠀⠀⢀⢼⡄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⢸⠁⡼⠀⠀⡄⠀⠀⠀⠀⣶⡄⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠈⠁⠀⠀⡎⢀⡇⠀⠀⡤⠀⠀⣾⣇
⠀⠀⢸⣿⡟⠀⠀⠀⠀⣿⡄⠀⠀⠻⠿⠃⠀⠈⠚⠁⠀⢸⣷⠀⠀⠀⠀⠻⠃⠀⠀⠀⠈⠀⠀⣰⡆⠀⠀⠀⣄⠀⠀⠹⠞⠁⠀⣸⠘⡇⠀⠙⠋⠀⡰
⠀⠀⠀⠉⠀⠀⢀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⢠⡄⠀⠀⠀⠸⢆⠀⠀⠀⠀⠷⠇⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⢰⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣲⡦⠀⠀⠀⠀⠀⢀⣀⣠⠈⣐⠖⠀⠀⠀⠀⠀⠀⠀⣀⣔⣾⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡿⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣋⣿⣥⡿⠯⠀⠐⣀⣰⣦⣤⣈⣿⡍⠈⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⢠⣼⣿⣶⣶⣶⡆⠀⠀⠾⠿⠿⠋⠋⣰⣤⣿⣿⣧⣤⣀
⠀⠀⠀⠀⠀⣀⡄⣠⣀⡉⠛⠋⡟⠉⠉⠀⠀⣺⣿⣿⡻⣟⣷⣻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡤⣮⣿⣿⣿⣿⣾⣿⣷⡀⠀⠀⠀⠀⣲⣿⣿⢿⣷⣿⣿⣿⣿⡁
⠀⠀⠀⠐⣰⣿⣛⣷⣽⣿⡆⠀⠃⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣷⣿⣿⠷⠀⠀⠀⠀⠀⢀⣾⣵⣿⣿⢿⣿⣿⣿⣿⣿⣿⠂⠀⠀⣩⣿⣯⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⢀⢿⣿⣶⣿⣷⣿⣿⣶⡄⠀⠀⠰⢹⣻⣿⡏⢈⣿⣯⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠰⣿⣿⡿⠷⣟⡽⠛⣯⣿⡏⠋⠀⠀⢸⡣⢿⣿⣿⣿⠿⣿⣻⣿⣷⡆
⠀⠀⠀⡾⣿⣯⣝⣏⣯⣿⡿⠀⡇⠀⠀⠉⠛⣿⡆⡆⢀⣽⣷⣾⠿⠟⠉⠀⠀⠀⠀⠀⠀⢀⡹⣀⠀⢸⠀⠀⠿⣿⡇⠀⠀⠀⢸⠈⠀⠙⢹⡇⠀⠈⠉⠋⠉
⠀⠀⠀⠙⢿⠟⢸⡁⠀⠉⡿⢿⣿⣶⠀⠀⠀⠉⠁⡇⢸⠙⣿⡇⠀⠀⠀⣀⣀⡀⠀⠀⠀⠻⢹⣿⡇⢸⠀⠀⠀⠀⠀⠀⣀⣤⣼⣄⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡅⢩⣉⣿⠀⠀⠀⠀⠀⡛⠈⠓⠛⠓⢠⣶⣿⣿⣿⣿⣷⣶⡀⠛⠹⠿⠦⢾⠤⠤⠤⠤⠤⠠⠨⠹⣿⣿⡇⠀⢨
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠓⠛⠿⠷⣾⣿⣿⢷⣶⢿⣤⣀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⡤⣿⣶⣿⣷⣿⣦⠀⢰⡴⣿⣿⣀⣀⣸⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⣀⢀⡀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡿⣃⣶⣶⣽⣲⣶⣿⣯⡿⣟⡡⠊⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡟⠁⡰⠄⣿⣿⣿⣿⣿⣦⣽⣿⣿⣍⣉⣿⣾⡯⣥⣴⣶⡶⣶⣶⣶⣿⣿⣷⣾⣶⣄
⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠳⣀⠉⢻⣩⠽⣉⡿⠬⠏⣀⠇⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷
⠀⠀⠀⠀⣿⣟⣿⣿⣿⠟⠛⠛⠛⢛⣛⣩⣭⣵⣾⣿⣿⣿⣿⣿⣿⣷⣷⣶⣿⣶⣒⣻⣥⣾⣿⣿⣿⣿⣿⣷⣿⣿⢥⣟⣛⣻⣿⢿⣏⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠸⠯⠿⠿⠿⠤⢤⣴⣾⣿⣿⣿⣿⡿⠿⣿⣿⣿⡟⣻⢿⣛⣿⣹⡽⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡟⣿⣶⣦⣌⠉⠙⢻⡇⣹⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡛⢚⣿⣿⣿⣿⣷⣿⣯⣿⣿⢿⣿⣿⣿⣿⣟⣿⡄⢹⣿⣿⣿⣟⣿⣿⣿⢿⡆⠀⠀⠁⠙⠛⠛⠛⠛⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⡆⢹⣿⣿⣿⠷⠮⣿⣽⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠿⢿⣿⣯⣽⣿⣿⡽⠟⠋⠈⠓⠛⠛⠛⠛⠛⠒⠒⠒⠚⠛⠒⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣯⣍⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠸⢄⢢⡅⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠉⠙⠿⣿⣇⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⢞⢚⠿⡻⢆⠂⡀⠀⠀⠀⠀⠀⢀⠀⢀⢶⣀⠀⠐⠠⡀⠀⠀⠀⠀⠘⠂⠘⠀⢈⣻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⠏⢘⢣⣧⡡⢾⡈⠓⠌⠤⡚⠀⠀⠎⡊⣀⣀⢤⡈⡉⡁⠠⡀⠁⠂⣄⠀⠰⢤⡀⠀⢺⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⣟⠽⣀⠿⡗⡇⠀⡰⢆⠀⠀⡠⠚⠉⠀⠀⠀⢱⡛⠋⠂⠌⡐⠄⣼⠀⠀⠿⠀⠀⣩⡄⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⢸⠅⠀⠪⠿⢦⡀⠉⠉⠢⢉⠁⠀⠀⠀⠀⠀⠀⡗⠂⠄⡀⠀⠀⠐⠀⠯⡧⠙⠉⠀⡀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⢦⠀⣀⠀⠔⠊⠀⠀⠀⠀⠈⠐⠠⢀⠀⡆⠀⠀⠀⣀⠄⠀⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⢀⡀⢙⠁⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠈⠁⢀⠀⠙⠀⢰⡞⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠘⠃⡠⠈⠀⢘⠃⠸⡗⢮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠀⠰⠂⠀⡌⠀⢿⠯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠉⠀⠀⠆⠀⠀⠀⠸⣆
⠀⠀⠐⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠂⠀⢀⡄⠀⢺⠀⠀⠒⠉
⠀⠀⠀⣉⣻⣿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣦⡤⣴⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢠⠗⠀⠘⠀⠀⠀⠀⡆⠀⠀⠐
⠀⠀⢀⡀⢛⢽⡆⠈⣸⡆⠀⢰⡦⣠⠊⠀⠀⠀⠀⠀⢀⠀⠀⠈⠄⢉⣱⡵⡆⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠦⠀⠖⠀⢘⠂
⠀⢀⡈⠱⠸⢟⡿⣏⢺⡔⢀⣏⡼⢋⠈⣰⣴⡖⠘⠂⠈⠷⠈⢀⢤⢄⢼⡿⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠂
⠀⢀⡹⣦⣀⣿⣿⣃⠰⢶⣼⣾⡟⢃⣴⠟⠡⣐⠖⠀⠆⢈⠴⠄⡀⠋⣻⠹⠿⠁⠡⠀⠈⠁⠀⠀⠀⠀⠀⠣⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠴⠋⠈⢪⢿⣿⣿⣿⣶⣿⣿⣿⡾⣯⣶⣔⢾⣄⠠⣀⡷⠀⠰⠈⠉⠀⢹⠰⠆⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⣀⣹⡉⠉⠉⠉⣯⣴⣾⣷⡄
⠀⠀⠠⢡⠋⠛⣻⣷⣷⡻⠛⠻⡗⡞⡿⣯⣟⠃⣀⡨⣮⢊⠐⠷⢀⣧⣞⣤⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠹⣿⣿⣿⣿
⠀⠀⡴⠀⠀⠀⢻⠏⠈⠺⠿⠷⠳⠘⣰⠌⠀⠀⠈⠀⣻⡌⠃⠀⠀⢡⣤⣤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⠇⠀⠀⠀⠀⣽⣿⣿⡿
⠀⠀⠃⠀⠘⡄⠋⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠃⡠⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢶⡶⠶⣶⣶⣦⡤⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢂⠀⢀
⠀⠀⠀⠀⢰⢁⢂⠐⢀⣤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣘⣀⡀⠐
⠀⠀⠀⠉⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠉⢠⣶⣿⠛⢃⠅
⠀⠀⠀⠀⠀⠀⠐⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣐⠐⠂⡀⡀⠀⢀⠁⡈⢿⠯⡁⢘⡙⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠤⠀⠀⠀⠀⠄⠤⣀⣨⣤⣤⣄⡁⠘⢄⠀⠁⠱⠠⠌⠋⠿⣇
⠀⠀⠀⠀⠀⡀⠀⢻⡀⠈⢀⣀⡁⠀⢈⡄⠢⡾⣽⣿⣷⣿⣷⠬⠨⡂⠀⠀⠀⠀⠀⠀⢻⠀⢀⡀⠀⠀⡀
⠀⢀⠐⠀⠀⡒⠀⣸⠁⠀⠀⠀⠀⠀⠀⠂⡸⢿⣿⣿⣿⣿⣿⠀⡀⠄⠀⠀⠀⠀⠄⠀⠘⡶⠁⠐⠠⠀⠂
⠀⠀⠈⠉⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠂⡤⠔⠟⠛⠛⠉⠀⠱⠀⠀⠠⢀⣀⡀⠌⠀⣰⡇
⠀⠀⠀⠀⠀⠠⠀⢸⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠀⢠⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡠⠂⠀⠀⠀⡀⠀⠀⠀⠠⡂⠀⠇⠀⡢
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⠀⠀⡿⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣉⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠉⠀⠀⢀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠸⠇⠀⠀⣀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠁⠀⠀⢸⡆⠀⠀⠘⠟
⣧⠀⠀⠀⠸⠂⠀⠀⠉⠀⠀⣸⡄⠀⠀⡀⠀⠀⠀⠰⠇⠀⠀⡄⠀⠀⣠⠀⠀⠀⠀⠉⠀⠀⠀⠶⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⡄
⠉⠀⠀⢀⠀⠀⠀⠀⢠⡀⠀⠈⠀⠀⠠⠷⠀⠀⠀⡀⠀⠀⠸⠇⠀⠀⠉⠀⠀⠀⢸⡄⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠃
⠀⠀⠀⠈⠀⠀⠀⠀⠘⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⢀⠀⠀⠀⣷⠀⠈⠁⠀⠠⠷⠀⠀⠘⠁⠀⢀⣆⠀⠀⠀⠀⠀⣄⠀⠀⢠
⠀⣠⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⣷⠀⠀⠀⠾⠀⠀⠀⢀⠀⠀⠀⠸⠆⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠁⠀⣴⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠸⠂⠀⡀⠀⠀⠀⠀⢰⡆⠀⠀⠛⠀⠀⠀⠙⠀⠀⢠⣷⠀⠀⠈⠃⠀⠀⠀⠀⠀⣼
⠀⠀⡀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣸⠄⠀⠀⠀⢠⣧⠀⠀⡀⠀⠘⠃⢰⡄⠀⠀⣰⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠸⠇
⠀⠘⠃⠀⠈⠋⠀⠀⠀⠀⠿⠀⠀⠀⣄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠃⠀⠀⠀⠘⠃⠀⠀⠙⠁⠀⠀⠛⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣰⠀⠀⠻⠂⠀⠀⢀⡄⠀⠀⣰⠀⠀⠀⣤⠀⠀⢀⡄⠀⠀⢠⡀⠀⠀⠀⠀⠀⠺⠀⠀⢀
⠀⠀⣿⠀⠀⠀⠉⠁⠀⠀⠀⠀⣾⠄⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠘⠃⠀⠀⣼⠀⠀⠀⠀⠀⠸⠇
⡆⠀⠀⠀⠀⣆⠀⠀⢰⡆⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢰⠄⠀⠰⠆⠀⠀⣾⡄⠀⠀⢾⠀⠀⣄⠀⠀⠷⠀⠀⡀⠀⠀⠉⠀⠀⢰⡆
⠁⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⢰⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠿⠀⠀⠀⡀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⢸⠆⠀⠀⢠⣧⠀⠀⠀⠙⠃⠀⣠⡀⠀⢸⡆⠀⠀⠀⠿⠀⠀⢰⡆⠀⠀⠛⠀⠀⣦⠀⠀⠀⠀⠸⠇⠀⠀⠀⣴⠀⠀⠃⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠉⠀⠀⠀⣆⠀⠀⠀⡄⠀⠉⠀⠀⠀⠀⣾⡀
⢰⡄⠀⠀⢰⠆⠀⠀⠀⠘⠛⠀⠀⣧⠀⠀⠀⣆⠀⠀⠿⠀⠀⠘⠃⠀⠀⠀⠁⠀⡀⠀⢠⡄⠀⠈⠋⠀⠀⠈⠉⠀⠀⠀⢰⡆⠀⠉⠀⠀⠘
⠀⠀⢀⠀⠀⠀⢰⡆⠀⠀⢠⡀⠀⠉⠀⠀⠈⠉⠀⠀⠀⠀⡆⠀⠀⠀⢰⡆⠀⠀⣷⠀⠀⠀⢀⠀⠀⠀⡄⠀⠀⢰⡆⠀⠀⠀⠀⢀⣆
⠀⠀⢸⡇⠀⠀⠈⠁⠀⠀⠘⠃⠀⠀⠀⠀⣰⠀⠀⢠⠀⠈⠛⠀⢰⠀⠈⠉⠀⠀⠀⠀⠀⠀⠼⠇⠀⠀⠁⠀⠀⠀⠀⠀⢸⡄⠀⠈⠉
⠰⠄⠀⠀⢠⡆⠀⠀⠀⢠⠀⠀⠀⣸⡆⠀⠈⠀⠀⠸⠇⠀⠀⠀⡀⠀⠀⠀⣴⠀⠀⣦⠀⠀⠀⠀⠀⣤⠀⠀⢸⣇⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⣷⠀⠀⠀⠉⠀⠀⠉⠀⠀⣶⠀⠀⠛⠀⠀⠀⠁⠀⢀⡄⠀⠀⠉⠀⠀⣦
⠀⠰⠇⠀⠀⠀⠿⠀⢀⠀⠀⢰⠄⠀⢀⡄⠀⠉⠁⠀⠀⣾⠄⠀⠀⠀⢀⣇⠀⠀⠀⣠⠀⠀⠀⢀⠀⠀⠀⢴⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠉
⠀⠀⠀⢰⡆⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⡿
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠸⠗⠀⠀⢀⣇⠀⠘⠁⠀⠀⢠⡧⠀⢠⡄⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠋⠀⢀⠀⠀⠀⣄
⠀⠛⠀⠀⠀⢸⡆⠀⠀⢰⠀⠀⡀⠀⠀⢠⡆⠀⠀⢀⡀⠀⠉⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠁⠀⢠⡆⠀⠀⢼⠆⠀⠀⠿
⠀⠀⢀⡄⠀⠈⠀⠀⡀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠀⠙⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠘⠃⠀⢀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡄⠀⠀⠻⠃⠀⠀⢠⡇⠀⠀⠉⠁⠀⠠⠇⠀⠀⠈⠁⠀⠀⠀⠺⠀⠀⠀⠿⠀⠀⠸
⠀⣴⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⡀⠀⠀⠘⠗⠀⠀⢀⠀⠀⠀⢠⠁⠀⠀⠀⣶⠀⠀⠀⠀⣆⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠶⡭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢠⣁⣤⡁⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠁⠈⢿⡁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⡒⠀⠋⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⠀⠀⠁⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡄⠀⡠⠎⠹⣷⣦⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠒⠓⡒⣾⡅⠤⠄⠒⣨⢋⠳⢤⡀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢚⠋⠀⠀⠀⠀⠶⣀⡎⠸⠀⠀⠀⢀⡜⠃⠀⠀⠀⢷⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠞⠐⠒⠒⠒⠊⠉⢙⢁⡀⠆⠀⣠⠏⠸⠂⠀⠀⠀⢸⠀⢀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⠀⠻⠤⠚⠁⢠⠃⠀⠀⠀⢠⡟⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⢀⡌⠀⠀⠀⠀⣼⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⡖⠉⢛⣦⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠤⠁⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿⢣⡤⠈⠀⠘⠀⠒⠲⠖⠒⠛⠛⠛⠛⠃⠀⠀⠀⠐⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢸⠤⠴⢶⡉⠉⠙⠒⠶⢤⣄⣀⡀⠀⠀⠀⢀⠀⠀⢸⡄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠁⠿⠀⠀⢸⠆⠀⠀⠀⠀⢰⠆⠉⠉⠛⠛⠛⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈⠂⠚⠁⠖⢀⡀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⢸⡀⡠⠞⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢸⠙⠳⠶⠶⠶⠞⠛⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠉⢷⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⡠⠤⠀⠀⠀⠀⠀⣿
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⢩⡅⠀⠀⠀⠀⠀⠀⣸
⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⢸⡇⠀⠀⠀⠀⢀⡟⠀⠀⠒
⠈⠓⠀⢀⡀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⠀⠀⠀⡼⠁
⢀⠈⠀⠸⠈⢆⠀⢸⠃⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢸⡇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠐⠓⠚⢅⠸⠂⠀⣇⢀⠠⠐⠀⠂⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡀⠀⠀⡇⠀⣀⠤⢤⡀⠀⠀⣠⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠾⠀⠀⠀⠀⢧
⠀⠀⠐⠉⠈⠉⠉⠰⠋⠀⠀⠀⣹⠪⡁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⡀⠀⠀⠀⢸
⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣠⡼⠃⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⠀⢸⠆
⠀⠈⠀⠀⢃⠀⢀⠃⠀⡜⠃⠀⠀⠀⠀⠀⣠⡴⠛⠙⢳⠄⢠⠀⠀⠀⢠⠏⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⠂⠈⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠒⣤⡄⠀⠉⠉⠉⠉⠈⠁⣼⠃⠀⢀⡰⠏⠀⠘⠀⠀⠀⡎⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣀⠀⠠⡎
⣀⠀⠀⢀⡀⠘⠀⠈⣂⠀⠀⠠⠀⠀⢰⠇⣠⠖⠋⠀⠠⠀⠛⠛⠓⣤⠁⠋⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠰⠁⠀⠈⠁⠀⠛⠊⠀⠀⠐⠃⠜⠁⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁⠀⠀⣀⠠⡤⠴⠊⠁⠀⢀⣠⡤⠞⠁⠀⠀⠀⡇⠀⠀⡝
⠀⠀⢤⡠⠔⠂⢀⠔⠓⡀⠤⠀⠀⠁⠀⠀⢀⠤⠒⠛⠓⠈⠁⠀⡄⢀⠔⠋⠉⡢⢀⣠⠖⠈⣷⣉⣁⣀⣀⠠⣴⡶⣾⠁⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⡁⠀⡠⠖⠒⠲⠦⢠⡀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠉⠀⢾⠁⢀⡴⠛⢦⣤⠀⠌⠉⠀⣰⠏⠀⠀⠈⣿⠀⠀⠀⠀⠀⢀⠴⢄
⠤⠤⢄⣀⠀⠀⡄⠀⠀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠔⠁⠀⢱⠀⠀⡰⠋⠀⠀⢀⡾⠟⣀⠤⣄⠀⢰⡏⠀⢸
⠀⠀⠀⠉⠙⠂⠶⡀⠀⠀⠈⠳⠤⢄⡀⠤⠶⠚⠀⡔⠀⠀⠠⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠜⠀⢀⡴⠃⠀⢸⢆⡠⠦⣰⠞⡡⠊⠁⢀⣼⠃⠀⠀⢀⡞
⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣭⣴⣤⣤⣤⣭⣭⣭⣤⣮⣤⣴⣶⣿⣮⣥⣤⣴⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⢰⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠙⢆⠀⠀⠀⠀⠀⠸⣤⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣆⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠸⣄⡼⠀⠀⡰⢶⡀⠀⠀⠀⠀⠳⢄⣠⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡆⠀⠀⣸⠁⢳⡀⠀⠀⠰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠘⢦⠴⠃⠀⠀⡇⠀⠀⢣⠀⠀⠀⠑
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⣸
⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠃
⠳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠹⡀⠀⠀⠀⠀⠀⠉⠒⠒⠁⠀⠀⠀⡸⠉⠳⣄⠀⠀⠀⠀⢸⠀⢳
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡄⠀⠀⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠖⠃⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣳⣼⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⠈⣷⣿⣿⣷⣿⡴⠂⠀⠀⢀⠼⡽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠷⢦⣄⡀⢿⣷⣾⣿⣿⣿⣿⣷⣴⣶⡤⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣂⡀⠑⠲⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢠⠿⠟⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣭⣤⡤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡨⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠿⠉⠀⢀⠔⠫⠟⣿⣿⠿⣿⡟⣿⣿⡏⠛⣗⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠲⣿⠃⠀⠀⣴⡟⠀⢸⣧⠀⠈⠻⢇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠛⠁⠀⠀⠻⢃⠀⣾⡀⠱⠄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠘⠀⠉⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠄⣡⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣸⡇⠀⠀⣀⠀⠙⣿⡗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣿⣿⣿⣧⡀⠊⠀⠀⠠⣝⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢀⣉⡆⠙⠟⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⠃⠀⠐⢠⣬⣿⣦⢲⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⠟⠲⢄⡀⠙⠛⠋⢸⡟⡆⠀⠀⢀⣴⣾⢿⢿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠲⢄⠀⢸⣧⡇⠀⠀⣬⣿⣷⣦⣄⢀⠙⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⠀⠀⠁⢸⡏⠀⠀⠀⠛⠻⢿⣉⡙⠫⣦⣄⡰⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡝⠛⠛⠛⠓⠀⠀⢺⡗⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡻⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣦⣿⣤⠿⠷⠺⠷⠿⣶⣼⣿⠀⢀⣀⣀⠀⠀⠀⠀⠀⠙⠻⢶⣟⣿⣿⣷⣄⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠋⠁⠀⠀⠀⠀⠀⠀⠈⢹⣿⠐⢬⡍⠛⣷⣆⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠛⠶⠀⠰⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣫⠀⠀⠀⢣⠀⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡶⡀⠀⠀⠀⢨⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣼⣿⣷⡄⠈⢷⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠛⠆⠳⣝⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⢛⣛⣛⣛⣛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣥⠶⠛⠉⠉⠉⠉⠉⠛⠶⣮⣙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣎⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣹⣇⢀⠀⠀⠀⠘⢷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡴⢋⡿⢿⣤⠀⠀⠀⠈⢻⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡶⢋⡴⢋⡴⠋⠙⢶⣄⠀⠀⠈⢷⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⣠⠞⢡⡼⢋⡴⢋⡴⠛⠀⠀⠀⠀⠙⢧⣀⠀⠸⡇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⣠⠞⣁⡶⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⢿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢹⡄⣠⠞⢁⡼⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣬⠟⢁⡴⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⡼⢋⡴⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡿⣯⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣻⣗⠲⠶⠶⢦⣤⣤⣤⣀⣀⣈⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⠞⠉⠉⠛⠳⠶⢤⣄⣀⡀⠈⠉⠉⠉⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢦⣤⣀⡀⠀⠙⣦⡀⠀⠀⠀⠀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⣿⣦⡀⣠⡾⣫⡾⢋⣴⠟⣡⡾⠋
⠀⠀⢰⣿⣯⡉⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣯⡾⢋⣴⠟⣡⡾⠋
⠀⠀⠀⢿⡉⠙⢿⡀⣿⠀⠀⢀⣤⠶⢛⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⣡⡾⠋
⠀⠀⠀⠀⠻⢦⣤⠿⢧⣾⢠⡟⣿⣴⠿⢷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣷⣟⣁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠈⠉
⣴⠞⠓⠚⠛⠛⠛⠓⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⢶⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠙⠶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠟⠁
⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠲⠄⡈⠓⢄⠀⠀⡀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣇⠀⠈⠢⣠⠇⠀⠀⠟⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⠀⡤⣑⢦⣸⣷⣦⣀⣀⣦⠎⢻⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠚⠇⠘⠛⢬⣯⠈⢿⣿⠇⠘⢿⡟⠁⠀⢠⢀⣤⠌⠀⠀⠀⠀⠀⠀⢠⣀⠀⠴⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠘⠀⠀⣹⠀⠀⠘⠀⠀⢠⣾⠟⠃⠀⠀⠀⠀⠀⢀⡖⢸⢃⠀⠀⠴⠛
⠀⠀⠀⣀⣀⣀⢡⡀⠈⠀⠁⠀⠠⣧⣃⡟⠀⢀⣄⣠⡶⠏⠁⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠏⠰⠀⠐⣯
⠀⠠⠟⡉⠉⠉⠉⠉⠓⠐⠢⠤⣤⣤⣼⠷⠶⣿⠷⠤⠤⡀⠀⠠⠴⠂⠀⠀⠀⠀⣻⣴⢣⡆⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠂⠄⢂⡤⢦⡴⠎⠁⠀⠀⠐⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢾⣷⣶⡯⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣀⠀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⢨⠋⠀⠀⠀⡀⠂⠀⠀⠀⠀⠄⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣴⠃⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠚⠀⠖⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣴⠀⠀⠀⠃⠀⠀⠀⢀⠀⢢⠀⡀⠂⢀⡤⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⠇⠀⠀⠀⠀⠀⠀⠀⠐⠩⡶⢿⣷⣱⣶⣴⠦⠀⠀⠚⠂⠀⠀⠀⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⡄⠂⠀⠀⠀⠘⠁⠶⠺⢧⠩⡭⣝⠀⠠⠀⠐⠖⠶⠤⢄⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠃⠃⠀⠐⢤⠀⠀⢀⣒⠐⠂⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠉⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢸⠀⠀⠀⠻⣟⠣⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠄⠀⠀⠀⠈⠙⠲⢴⣶⣆⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⢁⠀⠀⠰⢂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣿⠃⠀⠈⠉⠉⠋⠚⠛⠲⠤⠬⠦⠤⠵⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠠⡇⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⡘⠃⠀⠀⠀⣰⡏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣁⣀⣀⣀⣀⣠⣆⣀⣀⣀⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠀⠃⠀⡆⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄
⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⣇⢄⢀⣡⣤⣤⣤⣷⣀⡅⣴⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠢⠀⠀⠀⠈⠲⣬⣿⣿⣯⣿⣿⡯⣿⣿⣿⣿⡀⡀⠄
⠀⠀⠀⠈⡤⠀⠤⠀⠀⠀⠀⣀⠀⠀⠢⣴⣿⣿⣿⣿⣿⣿⣾⣿⣿⡹⣿⣷⡄⡀
⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⣯⢠⠔⠚⠁⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢯⣽⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⡟⠒⠀⠀⠀⠒⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠿⣙⠂⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠈⠀⠀⠀⠊⢀⠿⣿⣾⣿⣿⣾⣿⡿⢿⠛⠀⠀⠉⠑⠀⠀⠀⠀⠠⠄⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⡀⠈⠈⢸⠏⠉⠛⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⡤⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⡰⢄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⣾⣿⣿⣿⡗⠒⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⢿⣿⣿⣿⠆⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣷⡄⠀⠀⠀⠀⢀⣾⣷⡆⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠙⣿⠏
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢁⣤⠀⠀⠀⢾⣿⢿⣄⠀⠙⠇⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠾⠟⢀⠀⠀⠈⠁⠈⢙⢄⠀⠀⠁⠀⠀⠄⠱⢤⡀⠀⣤⡀⠀⢸⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢡⣀⠀⠀⢸⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⣆⠈⢀⣾⣿⣿⠀⢸⠀⠀⢀⡟
⠀⣀⡀⣶⣾⣿⠷⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠘⡄⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣨⡿⢿⣿⣿⠃⢸⠀⠀⠀⠁
⠀⠀⠂⣿⣿⣿⡟⠋⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⢱⡹⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⡇⠐⠈⠙⡏⠀⢸
⠀⠀⠀⠹⡟⠑⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⣷⠀⠰⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⢀⠀⠀⡇⠀⣀⠀⠀⠰⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⢸⡆⠀⠀⣙⣷⠀⠀⠀⠀⠀⠰⠀⠀⢸⡇⢆⠀⡃⠀⢾⣀⠀⠀⠀⠀⢀⠾⠁⣹⢿⡆
⠀⢸⡄⠀⣇⣰⣿⡆⠀⠀⠈⢉⡛⠆⠀⠀⠀⠀⠀⣀⣀⣴⣧⣾⣿⠁⣷⠀⢀⠿⠀⣴⠀⢾⠀⠀⠀⠀⠀⠈⣧⠘⡆⢿⠀⢼⠈⠳⡄⠀⠀⠀⠀⠀⡉
⠀⠈⣧⣸⡿⣿⣿⣇⣠⣴⣤⡾⠃⠀⠀⠀⠐⠴⣾⣿⢿⠟⣿⡛⠉⣧⠸⣆⡡⠐⢠⡇⠀⠈⠀⢀⣶⡚⠀⠀⣿⠀⢹⣼⡀⣺⠐⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢸⢿⡇⢤⣿⡿⣿⣭⢿⡇⠀⠀⠀⡆⠀⠀⠈⢳⣄⠀⠘⡇⠀⠸⡆⣿⠅⠀⣼⠃⠀⢐⠀⠈⠀⠁⠀⠀⢹⡇⠈⣿⡇⣿⠀⡇⢀⠻⡆⠀⠀⠀⠀⠀⣰⠃
⠀⠀⢸⠀⣇⢸⣯⣤⣴⣾⣿⣧⣤⣤⢦⣇⢀⣠⠀⠘⣿⣦⡀⣿⠀⠀⢿⢸⡄⠀⡟⠀⠀⢸⠀⠀⢠⠆⠀⠐⣼⡷⣤⣼⣿⣿⠀⣿⡎⠀⢻⡀⠀⠀⣠⣾⠇
⠀⠀⣾⡄⣿⡾⢻⣿⡛⢿⣿⣿⣦⡁⣾⣿⣿⣿⣿⡀⢿⣿⣷⣿⠀⠀⠸⡿⣇⢸⡇⠀⠀⡼⠀⠀⡼⠀⣠⠀⢸⣷⡀⠈⣿⣿⠀⢻⠋⡄⠈⣧⡀⠀⢻⣿
⠀⠀⡟⡇⡏⡇⠈⡏⣇⠘⣍⠙⢿⣛⠹⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⣷⣿⢸⠇⠀⢠⢑⠰⣾⣧⡾⠋⠀⣼⡏⢳⢰⣿⣿⢀⣸⡀⢣⠀⢻⠀⠀⣼⡏⠄
⠀⢰⡧⣇⣷⣿⣠⣷⢸⡆⠘⣧⠸⡇⠀⣿⠿⣿⣿⠇⢸⣿⡿⢿⡇⢰⠀⣿⣼⣾⠀⣀⣼⣸⣶⣿⣉⢷⡀⡼⢸⡇⢨⣿⠀⣿⢻⣿⣆⡸⡆⢸⡇⣷⣿⠀⠸
⠀⣸⠀⣯⡿⣿⡉⣿⡀⣷⣿⣿⣧⣿⣴⣿⣷⡏⣿⠀⠸⣯⡇⠘⡇⢸⠀⢸⣿⣿⣿⣿⡟⣿⣿⠛⣻⠛⢰⠃⠘⡇⢀⣿⡄⣿⢸⡇⡇⠙⣧⡈⣿⡇⣿⠀⠀⡇
⠀⣿⠀⢿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⢿⡀⠀⣿⡇⠀⡇⢸⠀⢸⣿⣿⣿⠈⣷⢸⡏⣰⠃⠀⡿⠀⢀⣧⠦⣿⣇⣿⣾⡇⡇⠀⢹⢻⣿⡗⡏⡁⠀⢹
⠀⣿⠀⢼⣧⣾⡟⢻⣿⣿⣿⣿⣿⡇⣿⣿⣿⡇⢸⡇⢰⡿⡇⠀⡇⢸⠂⢸⡿⣟⣷⣤⣇⣸⢧⡏⢀⢰⣇⡴⢛⡟⠀⣿⣿⣿⣿⣧⡇⠀⢸⣈⣿⣧⡏⣿⠀⢸⡀
⠀⣿⠀⣾⣿⠨⡇⢸⡿⣿⣿⣿⣿⣿⣿⣿⡇⢣⣸⡇⡼⣷⣷⠀⣧⣼⡇⢸⠆⣿⣿⣿⢻⣿⣾⣷⣾⣾⠟⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⠴⢻⡅⣿⣿⡇⢹⠀⠸⡇
⠀⣿⣴⣿⣿⠀⡇⢸⡇⢻⣿⣿⠟⢹⡿⣿⡷⣿⣿⣿⣷⣿⣿⣷⣿⣿⣿⢸⠀⡿⠹⣿⢸⣿⣿⣿⣸⡿⠶⡀⢸⠃⢀⠹⣿⣿⣿⡿⣷⡄⢸⡇⣿⣿⡇⢸⡇⠀⡇
⠀⢿⡟⢹⣿⣆⡇⢸⣷⣾⣿⣿⣧⣾⣧⣿⠇⢸⢻⣿⡏⡟⠀⡏⢿⢻⠈⣿⠀⡇⠀⣿⣼⣿⣿⣿⣿⡇⠀⠀⣿⠀⢸⢀⣿⣿⣿⡇⢹⡇⢸⡇⣿⣿⡇⠘⡇⠀⡇
⠀⣿⠃⠈⣿⣟⣷⣿⣿⠿⣿⠙⡟⢿⡏⣿⠀⢸⣾⣿⠀⡇⡆⣇⣿⢸⠀⣿⡆⡇⠀⣿⡿⣿⠏⡟⢸⣇⣀⣀⣿⠀⣼⡞⢿⣿⣯⡇⠀⠀⠈⡇⣿⣿⣧⠀⡇⠀⣿
⠀⣿⠀⢸⣿⡿⡏⠈⡿⣧⣸⠀⡇⢸⡇⣿⠀⢸⣿⣿⠀⢧⠃⢻⣿⠸⠀⣻⣿⡇⠀⢻⡇⡇⢸⣿⣿⣿⡉⢩⣿⠀⣿⠇⢸⣿⡏⠁⠀⠀⠀⡇⣿⣿⢹⠀⡇⠀⣿
⠀⢸⠀⢸⣿⡇⡇⣦⡇⠀⢹⠀⡇⠀⡇⣿⠀⢸⡟⣿⠀⢸⡀⢸⣿⠀⠀⣿⣿⡇⠀⢸⠁⡇⣼⠋⢸⠈⠛⢸⣿⠀⣿⠀⢸⣿⠀⠀⠀⠀⠀⡇⠛⣿⢸⠀⣷⠀⣿

⠀⠀⠀⠀⠆
⡀⠀⢠⠂⡇⠀⠀⢀
⡝⢀⢇⣇⢣⠀⢀⠎⢦
⠀⢺⢸⣿⣸⠀⡼⠸⠂⠳⡀⠀⠀⡴⡇⠀⡠⡎
⠀⠈⢺⣿⠃⠀⢡⠀⡀⠀⠹⣀⠞⠀⣧⠞⠀⠁⢀
⡀⠀⠈⡏⠀⠀⠀⡄⢻⣤⣶⠋⠀⠀⣯⣼⠀⡇⡸⠄⠀⠀⡔
⠀⢀⣸⠁⠀⠀⠆⢣⢸⡿⠁⠀⠀⠀⣿⣯⢀⡽⠁⡱⠊⢰⠁⢀⡤
⢀⢸⠏⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⣼⡷⢋⡴⠋⠀⠀⣿⡊⢠⢀⠰⠂⠀⣠⠂
⢸⡼⢀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⣿⡴⠋⠀⠀⠀⢠⡿⠗⠋⠀⠀⡥⠎⡅
⠸⣷⢸⠀⠀⠀⠀⣄⣷⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⡷⡹⠁⠀⢀
⣟⣿⣼⣦⣸⢂⣰⣿⣧⠀⢀⡃⠀⣼⡄⡠⠀⠀⠀⣼⣤⠄⠄⣀⡠⠞⠛⠁⣠⢖⠥⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣟⡕⡡⡠⢡⣾⡿⠟⢛⡉⠀⠀⠀⣠⢞⣑⡁
⢿⣿⣫⣻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣟⣕⡴⣋⡥⢔⣠⠔⠀⠀⢀⡞⡉⢉⡌⠀⠰⠊
⣟⣎⣳⡗⣿⣿⣟⣏⣥⣿⢿⣿⣿⣿⣿⣿⣿⡿⢚⠉⠀⠀⣀⡴⠛⠛⠂⠉⢉⠬⠋⠁
⣾⣿⣿⣿⣿⣿⣶⡷⣯⣞⣿⢺⢿⣿⣿⣿⠿⠟⣋⣡⣴⣾⣧⣀⣀⣀⣤⣾⣁⣀⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⣭⣾⣿⣿⣿⡟⣛⣩⠍⠉⠉⠉⠉⢁⣀⡈⠉⠉⠉⣉⣩⣭⠖⢊⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⡷⣿⣿⣿⣿⣿⣛⣃⡩⠍⢀⡈⠄⠀⣀⣴⡾⠖⠂⠔⠂⠀⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣫⣿⣻⢿⣿⣿⠿⠿⠧⠒⢒⣈⣡⣤⣶⣉⣉⣉⠒⠚⠤⠆⠒⠒⡨⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣯⡼⣹⣿⣿⣷⣶⣾⣿⣿⡢⠬⠍⣙⠓⠶⣔⣒⣂⣀⠤⠒⠉

⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⣜⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡻⣿⡧
⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄
⠀⠀⠀⠀⠀⢾⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡝⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢿⡷
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀
⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢰⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠻⣘⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣻⠏

⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⣼⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣿⣧
⠀⠀⠀⠀⠀⠙⠬⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠬⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠽⠋
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠐⠦⠀⢚⠀⢨⠀⢾⢃⢀⠈⠀⠀⢲⡆⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠘⢇⠈⠃⠀⠀⠀⠀⣀⢀⠀⢈⣿⣷⠀⢀⣼⠿⡷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣠⠴⠂⠁⠀⣀⡀⣠⣴⠼⠛⠁⢠⣼⡟⠋⢠⡄⢹⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠶⡶⠿⠿⠛⠋⣉⣀⣠⣴⣾⣿⡏⣿⡄⠸⢧⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠂⣿⣿⣵⣶⣴⣶⣶⣦⣿⠿⠿⠿⣿⣭⡉⠀⢈⣁⣄⡹⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⣷⠟⢀⣈⣽⣿⡛⠉⢹⣯⣵⡄⣼⡟⠉⠉⠣⡀⠈⠉⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠰⠞⠋⣬⡶⠃⠘⡋⠉⢻⣤⠞⠋⢿⠁⠈⢻⠷⢤⡀⠹⣿⡅⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠛⠁⠤⠼⣇⡀⢻⠿⠆⠀⢩⡰⣄⣼⣿⣜⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠀⠠⡆⠰⡇⠋⠾⠻⡏⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⢶⣶⡀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠷⠶⣦⣤⡘⣳⠀⠀⠀⣿⣿⠀⠀⠀⠀⢠⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣋⣼⣷⣶⣶⣦⡤⠭⠭⢥⣀⠀⢨⣿⠀⠀⠀⠀⢣⡞⠉⣀⠄⢊⣠⣶⡿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⣋⡉⠝⠋⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⣿⡇⠀⢠⣾⣿⣿⣷⠶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇⠀⣼⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠂⣀⠀⡀⢀⣼⠟⠁⢼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢒⣠⡿⠟⠛⠛⢿⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣵⠞⠝⠁⠀⠀⠀⠀⠘⣆⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣁⣠⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠙⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠻⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡿⢿⡿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠛⠶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⢦⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⡞⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠛⠻⢦⣀
⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⡾⠛⠉⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⢀⣤⠿⠶⠶⢾⠏⠀⠀⠀⠀⠀⠀⠹⡷⠶⠶⠶⣤⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠋⠉⠉⠉⠙⢷⡄⠀⠀⠀⠀⠹⣆
⠀⢠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠻⠞⠛⠛⠷⣦⣿⡄
⠀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡅
⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠉⠛⢻⡛⠛⠛⠛⠛⠛⠛⠛⠻⣟⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⣠⣴⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠋
⢠⡾⠋⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣏⠉⠁
⠘⣧⣀⣀⣼⠃⠀⠀⠀⠀⠀⣴⠟⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣆⠀⠀⠀⣠⡴⠟⢻⡄
⠀⠈⠉⠉⠁⠀⠀⠀⣤⠀⠸⣏⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⣿⠀⠀⣾⠋⠀⠀⣾⠁
⠀⠀⠀⠀⠀⢀⣤⡾⢻⡇⠀⠙⠛⠛⠋⠀⠀⠀⢀⣼⣧⠀⢸⡏⠀⠀⣸⡏⠀⠀⢻⣤⣤⣼⠏
⠀⠀⠀⠀⣰⡟⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⣿⠀⠈⠻⠶⠾⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠹⣦⣀⣠⡿⠁⠀⠀⠀⠀⠀⠰⣟⠀⠀⢠⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡞⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢀
⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⣦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⡶⠀⠈⠄⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⣠⣾⣆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣶⠇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣯⡵⣤⣴⡾⡅
⠀⠀⢀⠀⠀⠀⠀⠠⠂⣰⠿⣿⣿⣿⣿⢷⣶⣤⣤⣀⡣⣍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⢹⡟⠀⠀⢀⠀⠀⠀⠀⢼⣧⠀⠀⠋⠀⢉⠙⠀⡅
⠀⠀⢈⠀⠀⣼⠀⡆⣼⣇⢾⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⠀⡄⠻⡇⠀⠀⠀⠀⢰⠀⣀⣿⣿⣦⠀⠀⠀⡏⣠⠈⡇
⠀⠀⠀⢳⠠⢿⣆⣴⠿⠻⣿⣿⡿⠿⣿⣿⢟⠾⠛⣿⣿⣿⣿⡄⠀⠀⠘⠀⢀⡀⠀⠀⣦⠀⠀⠀⠀⡀⡇⢘⡇⠀⠀⠀⣠⣿⣦⣿⣿⡛⠿⣷⡆⠀⠈⠀⠀⡁
⠀⠀⢀⡸⣷⣸⣿⣧⢿⣾⣿⣿⣧⣤⣽⣿⡟⠿⢿⣿⣿⡿⢿⣷⡄⠀⢨⠀⡌⠀⠀⠀⣿⠀⢀⢄⠀⢻⠁⣯⡇⠀⠀⣲⣿⡟⣅⢱⣀⣠⡀⢈⠻⠀⠈⠿⠁⠑
⠀⠀⠀⢢⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⡤⠀⢀⡏⠉⢉⣻⣿⣶⣶⣤⣄⡀⠀⠊⠉⣿⡄⠫⠘⢨⠋⣷⣏⣧⡼⣴⣿⣟⡙⢻⣶⣾⣻⣆⣿⣾⣂⠠⠄⠀⠁
⠀⠀⠈⡈⣿⣻⣿⣿⣿⣿⣿⣿⣿⠿⢹⣿⣟⣻⣦⣶⠐⢲⣾⣿⣿⣿⣯⣿⣿⣷⣶⣶⣿⣺⣦⡶⣾⢻⣿⣿⡿⣇⣦⣼⣇⠀⢀⣹⡉⣿⣿⣿⡿⣿⠀⡀
⠀⠀⠀⠁⢿⣾⣿⣿⠛⣿⣿⣿⣿⣶⣿⣯⡽⣝⣿⣿⣄⡈⣿⣿⣿⣿⡿⢻⣿⣿⢿⣿⣿⢿⢿⡿⠿⢾⣿⣻⣿⣿⠿⣿⡿⣴⣾⡿⢃⡷⡯⣝⣯⣝⣻⣿
⠀⠀⠀⠒⣼⡿⣟⣼⣷⣿⣿⡥⠸⣏⠉⢙⣿⢾⣯⡇⢸⣈⡿⢿⣷⣶⡟⣾⣷⠷⣶⣿⣿⣾⣟⣿⣅⣸⣿⠟⠻⣾⠞⣣⣿⠟⣻⣿⠿⢷⣾⣭⣽⣾⣟⣿⠀⠈⠃
⢠⡦⠀⠀⠀⠿⣡⣾⡟⣛⣻⡵⢶⣿⣿⣿⠿⡷⡼⣻⣿⣱⣆⣲⢿⣿⣻⣿⠛⢹⣿⣿⣿⣿⣧⣼⣎⣿⣿⣽⣇⢷⡼⣯⣧⠂⠉⢘⣿⣏⣣⣿⣿⡿⢷⣟⠀⢷⠂
⠈⠡⣀⡆⠘⣰⡧⢿⠛⣡⡿⣏⢛⡟⣇⣁⡃⣠⠜⢡⡀⣽⣩⢟⣘⠻⣿⣏⢈⣈⣻⣿⣿⣿⣿⣯⣿⢿⡿⣿⣏⠻⣿⡛⣿⡄⠀⣀⣿⣿⣿⢛⡿⣧⣾⣿⠀⠨
⠀⠙⢻⡁⡼⠁⠀⣂⡼⣿⣤⢫⢿⣿⣈⡯⢷⣅⣮⢠⡿⠇⣹⣤⣾⢕⣿⣿⣳⣿⡟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣭⣹⣿⣿⣟⣻⣿⣿⣿⠻⣟⣹⡿⢿⣽⡿⡇⢸
⠀⠀⠀⢣⣠⡆⣼⢿⣷⣟⣿⠰⢚⡽⢿⡿⢦⡋⡵⠾⠂⢶⣧⢹⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣿⣼⣷⣿⡙⠿⣿⢷⣾⣷⣿⣿⢻⣧⣼⣻⣿⣫⣠⣿⡇⢠
⠀⠀⠀⠀⠧⢸⢧⣸⣿⣾⣧⣷⣤⣾⡏⣳⢼⣿⣷⣿⣿⣿⣿⣸⣿⠟⡻⠛⢿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⠒⠤⣤⡌⢶⣿⣿⣯⣻⣏⣈⣇⣹⣿⣿⣿⣿⣧⠘
⠀⠀⠀⠀⠘⣾⣾⢿⣿⣏⣉⣉⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⡼⣀⣰⣿⡿⢻⣿⠿⣼⠁⠉⢊⡁⠀⠻⠿⠷⡶⣿⣿⡏⢹⣿⣧⣿⢟⡿⠏⡹⣷⣶⡇⠉⡹⠘
⠀⡞⣁⡉⡑⣾⣇⣘⣿⣿⣿⣿⣷⣽⠹⣿⣿⣿⣿⣿⣿⣿⡗⣣⡿⢻⣿⣷⣾⣿⣦⡼⣀⣸⠋⣁⣸⣠⣄⣿⠀⣨⣾⣿⣾⣿⣿⠿⣏⡁⠘⣤⣌⣷⡏⢿⡦⠖⠋
⠈⠋⠀⠈⠹⣿⣦⡉⣿⣿⣿⣿⣟⠿⣦⡼⣿⣿⣿⣿⣟⣿⣾⣿⣦⣿⣿⣟⣻⣿⣿⣿⣿⣿⢿⡟⡄⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⢍⣢⠈⠁⣿⢷⣷⣤
⠀⠀⠀⠀⠀⢸⣿⣹⣿⣿⣿⠋⠀⢠⣿⣿⢶⣽⣿⣿⣿⣿⣿⣿⢡⣟⣽⣿⣻⣏⣭⣿⡗⢻⣾⡦⢶⣿⡻⡏⢛⠋⣿⢙⠀⣿⡏⣲⣾⣿⣿⣿⢶⣟⢌⣿⠋
⠀⠀⠀⠀⠀⢸⣿⣻⡟⣿⢣⡄⣰⣿⣿⣿⣞⣿⣿⣿⣿⣯⣻⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣼⣿⣵⣾⣿⡅⢠⡊⠀⣿⣭⣿⣿⣽⡁⠩⠏⢙⠀⠀⢹⣿⣿⡗
⠀⠀⠀⠀⠀⠀⢻⡇⠹⣿⠸⡰⠟⠃⠟⠻⡟⢿⣿⡿⡿⠟⣿⡿⣿⠻⠿⢿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⣷⣤⣶⣾⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠻⠈⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠉⠉⠀⠙⠁⠉⠉⠈⠉⠈⠉⠀⠀⠀⠈⠃⠋⠙⠙⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢐⡪⡆⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠠⢪⣵⠗⡄⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠈⠿⡿⠀⠀⠀⣸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⣿⣿⡇⠀⠀⠀⠀⠀⠘⢴⠴⡺⠁⠀⠀⠀⠀⣸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣷⢿⣿⣷⠀⠀⠀⠀⠀⡰⡈⡎⢌⢎⠁⠀⠀⠀⣬⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢻⣟⣿⣿⠀⠀⠀⠀⢐⢘⢰⢩⢣⢂⣣⡄⠀⠀⠹⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⣟⣿⣿⣿⠀⠀⠀⠀⢘⠂⠡⢮⢎⠒⢘⡀⠀⠀⠀⠀⠉⠁⠀⠀⣴⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⣿⡿⠏⠀⠀⠀⠀⠀⠨⢈⡔⡆⡌⠹⠂⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠚⠈⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⠀⠀⠹⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⠀⠀⣾⣷⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠈⠛⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⣧⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠘⠿⠿⠿⠋⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠏⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣷⠀⠀⠀⢹⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⡽⣤⡇⠀⠀⠀⠉⠋⠁⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣳⣶⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣷⠶⠞⣣⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⢀⣽⡛⠞⢉⣧⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⣻⣿⣾⣯⣋⡆⠀⠀⠀⠀⢸⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢿⣿⣿⠀⠀⠀⣼⢿⣿⡇⠀⠀⢰⣿⣽⠿⣮⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠀⠀⠀⠹⣿⣿⡇⠀⠀⠀⢿⣝⣶⢏⣿⠀⠀⠀⠀⠀⠀⠙⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠉⠙⠊

⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⣍⢢⡀⢀⡤⢒⡦⣄
⠀⠀⠀⣠⢴⣶⢤⠸⡄⠸⠤⠴⠃⢸⠀⠻⣍⡼⣀⠤⣄
⠀⠀⢰⡃⠸⠬⠼⠀⡨⠗⠒⠋⠉⠙⠓⠢⢄⣸⠁⡴⢦⢳
⠀⠀⠀⠳⠤⡤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠘⠂⠋
⢀⡔⡺⢲⠀⢰⠁⠀⠀⠀⠠⡄⠀⠀⠈⠀⠀⠀⠈⢄⠔⢒⡲⡄
⠸⡀⠑⠋⢀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⡇⠟⣹
⠀⠉⠓⠊⠁⠘⡀⠀⢀⣀⡀⠀⠀⠀⢀⣀⡤⠞⢀⡞⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠉⠉⠉⠉⠉⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡶⠶⠶⠖⠒⠚⠉⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⡠⡖⠉⣀⣉⣩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡘⣽⠀⠀⠀⠀⠀⠀⠀⠀⢷⠙⠒⠤⠄⠊⠁⠈⠖⠛⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠠⠁⡉⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⡠⠊⠑⠒⠂⠄⣸⠀⠀⢀⣄⡄⠠⠆⠀⠦⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈⢢⠤⠜⠹⠄⠀⠐⠀⠠⠀⠀⢀
⠀⠀⠀⢀⡴⠒⠻⡄⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠤⠚⠤⠆⠀⠠⠀⠀⠀⠂⠀⡀
⠀⠀⠀⢯⡠⠾⠴⢣⣧⡄⠀⣤⣄⠀⣠⠀⠰⠆⠀⠉⠘⡆⠀⠙⠲⠤⠤⣀⣀⣀⣠⠆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠉
⠀⠀⠀⠀⠀⠀⠰⣇⠤⠤⠄⠐⡶⠒⠊⠉⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠉⢳⠀⠀⢠⠖⢢⡤⠠⣡⡖⠲⡶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⡜⢲⡏⠉⡞⠙⢣⠚⢄⢤⣧⠗⡔⢢⠴⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⡍⠈⣻⠑⡖⠈⣠⣁⡴⠻⣄⡽⠋⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡄⠀⠀⢀⡼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⡟⠋⠁⠀⠙⠚⣷⠀⠀⠀⠀⠙⡖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠘⢆⠀⠘⢆⠈⠑⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡼⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠰⠂⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡛⠙⠻⣧⣄⣤⣀⠤⠂⠘⢇⠀⠀⠀⢿⣶⣦⠀⢀⣼⣾⡇⢁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠈⠁
⠀⠀⠀⠀⠀⣠⡌⡵⠇⠀⠘⣿⣿⣮⣿⡦⢻⣁⡘⢷⣦⣠⣤⠟⠃⣼⠟⠛⠛⠁⠘⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠖⠃
⠀⠀⠀⣰⣰⣿⠟⠃⠀⠀⠀⠉⠀⠈⡀⠀⠚⠋⠁⠈⢋⡫⡀⠀⠾⣝⣴⣾⠿⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠨⠉⠁⠀⠀⠀⣠⠀⠀⠀⠀⢠⣶⡄⠀⠀⣸⡁⢀⣷⣦⣶⣿⣿⣿⣿⣀⠀⢿⣷⣶⡦⠀⢰⣁⠆⠀⢀⠰⡲⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠄⢂⢀⡚⠮⢿⣦⣀⠀⠨⠉⠛⣷⣶⣿⠃⡄⢀⣽⣥⣿⣿⡿⣻⣷⣄⣼⣿⢀⣬⡻⠽⢯⠄⡀⣀⠉⠀⠤⣄⠀⠄⠀⡀
⠀⠀⠀⢀⡀⢠⠼⠮⠛⠀⢨⣧⢈⣠⢀⣀⡁⠨⢁⣍⢓⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣷⣿⠋⢀⣟⢁⣤⣙⣿⣿⣧⣖⣶⣫⢀⡐⢠
⠀⠀⠀⠀⣽⠀⡐⠒⠶⠀⠀⣿⡽⢿⣿⣿⡦⣠⣾⣀⣷⣿⡿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢿⡿⠻⣛⣻⣿⣿⣾⣷⣮⣠⢡⡏⠄⠁
⠀⠀⡄⠀⡉⠀⡇⠀⠀⠀⢀⣿⠀⢸⣿⠿⠇⢁⠛⠛⣿⣿⣧⣾⣿⣿⣿⣿⣿⣷⣽⣿⣿⡟⠀⣿⡏⠘⠙⣿⣿⣿⠛⣻⣉⠿⠦⡤⠄
⠀⢀⡇⢀⣡⢨⡇⠀⠀⠀⢸⣿⡇⣸⡏⣠⣶⣾⣤⣀⣽⣿⣿⣿⣿⡿⢿⣿⣿⣿⣻⢿⣿⣷⣶⣿⣇⢀⣴⣿⣿⣿⣾⣿⣷⣿⡟⠐⠀⣀
⠀⠈⡇⠠⡦⢸⣷⣴⣾⢳⣿⣿⣇⣸⣷⣿⣿⣧⡿⢯⣽⣿⣿⣿⣾⣽⡿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⣿⣿⣷⣾⡿⠿⠿⠋
⠀⢘⣇⣀⠀⢸⡇⠉⠁⠶⠖⢺⣇⢸⡷⣾⣛⣗⣬⣵⣚⣿⣿⣿⡿⢿⣿⡏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣧⣿⣿⢋⣼⡥⠚⠲⠁
⠀⠺⣿⣿⢀⠘⡏⠀⠀⠀⢠⣻⣗⣸⣇⢉⣉⣿⠛⠉⠙⢛⣿⣿⣿⣛⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠄
⠐⢶⣝⡧⠊⠈⠍⠀⠀⠶⡈⢻⣿⣽⣇⠀⠀⣟⢀⣠⣤⠄⠩⠤⣽⣿⣿⣄⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⡘⢴⠞⠀⠀⠀⠀⢀⣘⣾⡿⠿⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠐⣉⣩⣽⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡄
⠀⠷⣿⠇⠀⠀⠀⠀⠀⠈⠹⠿⣶⠂⡐⠀⠀⠿⠃⠀⠀⠀⢀⣀⣶⠤⠭⢿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡟⠁⠁⠀⠀⠀⣀⣀⣀⡀
⠀⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠀⠀⠢⠲⠂⠀⠀⠀⠘⠋⠃⠀⠀⠀⠁⠤⠈⠉⠉⠈⠉⠹⠤⠀⠉⠙⠿⠦⠁⠀⠀⠀⠈⠀⠉⠉

⠙⢹⡏⠉⠏⠀⠀⠀⠀⠀⠙⠁⢰⣬⣿⣿⣿⣿⢿⣿⣻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⠃⠊⠉
⠀⣼⠁⠀⢀⡀⠀⠀⠀⠀⠀⢠⡼⠗⣹⣿⣿⣿⣿⣿⣻⣻⣧⣾⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣯⣹⣿⣏⠳⠰⠆
⠀⢹⡀⠀⠘⠙⢿⡶⠄⣴⢰⣯⣦⣿⣋⡼⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⣿⠟⢶⣀⠁
⠀⠈⠁⢀⣶⣶⡏⢿⣻⢋⣉⣙⣿⣯⣿⣠⣾⣿⣿⣿⣷⣿⣇⣀⠙⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠂⣿⡍⡆
⠀⠀⠀⠙⢣⡙⠗⢽⡉⠇⠈⢻⠟⠛⣟⡿⡟⠛⠛⠛⠻⣿⢿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠑⠉⠈⠹⣀⠑
⢀⠀⣍⣽⡇⠀⠀⢠⣉⣓⠶⣶⡶⣟⡽⡀⢀⠀⠀⠀⣤⣧⣀⣉⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠦⣶⣾⡍⠤
⠀⠛⣿⣿⣿⣿⣧⡶⢦⠋⠹⣿⣿⣿⢀⣁⠀⠒⠂⠙⠛⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⢉⣸⡿⠉⠐⡀
⠀⠀⣇⢹⣷⣿⣿⣷⡆⢳⣿⣿⣷⣿⢟⡉⠤⣿⣖⣀⣀⣀⣬⣷⣿⣿⣿⢿⠚⣻⣿⣾⣿⣿⣯⣼⡷⡆⠀⠀⠁
⠀⡄⢽⢹⡇⢻⣿⣿⡑⠀⠑⡻⣿⣿⡟⢱⢴⢾⠿⠧⠀⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠷⠃⡅
⠀⠻⣿⢺⡧⣞⣿⣿⣅⣤⣶⣦⣿⣿⣻⣿⣻⣤⣴⣶⣶⣿⣿⣿⡿⢧⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡀⡇
⠀⠀⢿⣿⣇⠈⠋⣿⡛⢋⣀⢀⡩⣍⠛⢟⣛⣿⣿⣥⣿⣿⣿⣋⣵⠾⠟⠛⡉⣛⣽⣿⣿⣿⣿⣽⠃
⠀⠀⠂⣼⣿⣿⢇⣾⣇⠀⠙⠻⠻⠛⠾⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠁⠲⠭⢍⠁⠌⠉⢉⣻⣭⣀⠄
⠀⠀⠀⠈⠋⠁⠀⠁⠈⠀⠄⠀⠀⠀⠀⠁⢠⣿⣿⣿⡿⠀⠀⢀⠀⠀⢀⡈⡉⠛⣏⣠⣄⣻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠙⠷⠧⢾⣯⣻⣿⡟⣷⢶⡄⡴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠊⠛⢋⣛⡯⣓⣹⣦⣄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠉⠛⠛⠻⣯⠁⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⡆⠀⠀⢀⡞⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡞⠀⠀⠈⢷⡀⠀⡠⠢⠀⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠹⣆⠑⠚⠁⠀⠐⣇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡠⠀⠀⠀⠀⣰⣫⠖⠀⠀⣄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣏⢀⡆⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⡴⠃⠠⡤⠀⠀⠀⠀⡔⡄⠀⠀⠀⠀⠀⡠⠀⠀⠈⢧⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠑⠁⠀⠈⠌⢧⠀⠈⠁
⠀⠀⠀⠀⠀⢸⠁⣱⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠈⠉⠁⠀⢠⠇⠀⠀⠀⠚⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡙⠂⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠠⢤⣾⣿⡟⠑⡄⠀⠀⠀⠀⠀⣰⣿⣿⠉⢢⠖⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠈⠉⠉⠁⠀⢠⠀⠀⢠⡄⠀⠉⠉⠉⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡟⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠓⠲⠶⠤⠤⠤⠤⢤⠤⠤⠴⠖⠒⠋⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠈⠻⣷⣦⣤⣀⣀⣀⣀⣀⣠⣤⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠀⠈⠁⠉⠁⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠄⠤⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⢠⠀⠋⢐⡀⠁⠀⠀⠀⠘⡄⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⡀⠀⠙⣄⠲⡆⠀⠁⠀⠀⠀⠆⠀⠀⠇⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢀⠀⠀⠀⠁⠀⠀⠈⠳⢄⣀⣀⣀⠠⠊⠀⣀⠄⠸⡀⠀⢛
⠀⠀⠀⠀⠀⢔⠢⠀⢒⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⠀⠀⢬⡉⠁⠀⠈⠉⠈⡄⠀⢧⠀⢸⡄
⠀⠀⠀⠀⢀⠈⠠⠐⠀⠀⠀⢠⣐⠀⠀⠒⠀⠀⠀⠀⠀⡀⠠⡈⠁⠑⠀⡀⠀⠸⢻⡀⠸⡄⠈⡇
⠀⠀⠀⠀⠀⠘⠀⠀⢡⡠⠂⠰⠇⠔⠁⠀⠤⠀⢀⠞⠀⠁⠀⠹⡟⠀⠀⠁⢠⡏⠀⢧⠀⢳⡀⢹⡀
⠀⠀⠀⠐⠀⠑⠀⠀⣄⡃⡆⢠⡤⠃⠴⠂⠀⠀⣊⠉⠀⠀⠀⠀⠑⠌⠄⠀⠊⠐⠀⠈⢂⠀⢷⡀⢇
⠀⠀⠀⠀⠐⠁⠀⢦⠈⠁⠛⠀⠀⠀⢠⠠⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠘⠄⠀⢀⠀⢠⠘⡤⢄⠳⣌⢆
⠀⠀⠀⠀⢀⠔⠀⠈⠥⠴⠤⠠⠤⠤⡄⠀⠢⡃⠀⠀⠈⠢⡀⡠⠀⠀⠀⠘⠉⠸⠀⠈⠉⢡⠀⠉⠀⠈
⠀⠀⠀⠀⠘⠀⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠁
⠀⠀⠀⣠⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠧⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠂⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠠⠤⠀⠀⠀⠒⢒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢱⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣬⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠐⠂⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢄⠀⠀⠎⠈⠄⠀⠉⠃⢀⠀⠀⢨⠔⠁⠀⠀⡀⠄⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡁⠀⠀⡆⠀⠀⠇⠀⠀⠀⠀⠀⢠⠈⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠂⠁⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠂⠄⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠄⠊⠀⠀⠀⠀⡐⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⡄⢆⠀⢀⣀⣀⡇⠀⠀⠀⡰⠃⠀⠀⠀⠀⡀⠴⠐⠂⠈⡐
⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⣀⢠⡀⠠⠀⠀⠀⠐⣠⣴⠞⠛⠯⡙⠉⡛⢻⢦⣰⠁⠀⠀⠀⠐⠉⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠱⡀⠁⡀⠀⠀⠀⠈⠢⣀⠀⢲⡾⠇⢐⠁⠠⡐⠉⡀⠀⠔⢐⣂⣷⣄⠀⠀⠀⠒⠈⠀⠀⠈⠉⠉⠒⠠
⠀⠀⠀⠀⠀⠀⠈⠂⠀⣀⠀⣀⣀⣄⣈⡁⡾⠡⠀⡉⣈⠱⢤⠈⣢⡈⡁⠶⢠⠇⠛⣧⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠁
⠀⠀⠀⠀⢀⠠⠤⠄⠂⠈⠁⠀⠐⠂⠠⢬⡧⠆⠆⣤⣡⡉⡎⠲⢤⠢⣄⡵⢆⠐⣏⢙⡆⠂⠉⠉⠀⠀⠚⠂⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠢⢄⡀⠀⠀⠀⢠⠄⠀⢸⡧⠆⢈⠶⢁⡏⣈⡹⢏⠹⡤⢓⠀⣉⣍⢙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠠⠒⠈⠀⠀⠀⠀⣀⠀⠀⠠⣧⠴⣀⡁⠟⢠⠽⠒⢼⠂⠈⠻⡀⠆⢀⣱⡇⠂⠀⠀⠀⠀⠀⠉⠒⠤⢀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⣀⠤⠒⠋⡹⢶⠁⡥⠒⠘⡄⠛⠀⡙⢠⣀⠉⠂⣴⢟⠲⢔⠒⠤⣀⡀⡀⢀⣀⠠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⡠⠊⡠⠚⢉⠓⢮⣥⣆⣐⣅⣵⡤⠦⠖⠋⠀⡀⠓⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠄⠀⢀⠌⠀⠊⠀⠀⠀⠀⠈⠀⠭⠁⢈⠀⠁⠀⡀⠀⠀⠐⠀⠀⠀⠀⡄⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢰⣥⣤⠁⠀⢠⠆⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠦⣀⠀⠀⠁⠀⠤⢀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⡄⠀⠀⠆⠀⠉⠢⣀⡆⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠈⠀⠀⠀⠄⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢰⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣰⠤⠊⢁⡔⠉⠀⡀⡰⢄⠀⠀⠀⠈⢢⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠀⠀⣠⡗⠁⠀⠢⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠢⠐⠀⠀⠀⠀⢀⡀⠐
⡀⠀⠀⠀⠀⣀⠀⠀⢀⠀⢨⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡤⣀⣀⣀⡀⠀⠀⢀⡐⠠⠒⠚⠉⠀⠀⠈⠉⠙⢃⠀⠿⠂⠠⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠴⠤⠤⠤⠆⠀⠈⠑⢢⣤⣠⡄⣀⡀⠀⠀⠀⠠⡀⢀⠘⣧⡀⠀⠘⠐⠉
⠀⠀⠀⠀⠤⡄⠀⠚⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠁⠈⠛⠚⠋⠁⠀⠀⠀⠛⠉⠑
⣀⣀⠐⠃⠉⣀⣤⣠⣤⣰⣤⣴⠜⠂⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠂
⣄⠴⠿⠒⠛⠋⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢄⠤⠰⣄⠀⣤⡴⠤
⠀⠀⠀⠀⠀⣀⡄⣠⠀⠘⠃⢀⡀⠀⡀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠙⠠⠦⠄⠈⠉⠁
⠀⠀⠀⠘⢳⠀⣤⣀⠠⠄⠀⠀⠀⠀⠀⠀⠁⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠄
⠀⠀⠀⡿⠿⡶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠀⢠⡄
⠂⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⡠⠶⠶⣶⣦⡀⠀⢠⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶
⠀⠀⠀⠀⠀⠈⠁⣠⣴⠞⠋⡋⠀⠀⠀⠀⠷⣤⡀⠛⣇⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣠⠮
⠀⠉⠀⠹⣆⠀⠀⠙⠏⢠⡜⢀⡄⠀⠀⣵⡀⢙⣿⣆⠸⠋⠓⣤⢻⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠌⠚
⡄⢠⣤⠈⣿⣄⠐⣷⣦⣼⠀⣼⡇⠀⠀⠻⣖⠄⢚⣿⠡⡎⠇⢠⣾⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴

⣿⣆⠀⠀⠀⠀⢰⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⡄⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⣠
⣿⠟⠀⠀⠀⠀⠘⠿⣿⠿⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⠿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠀⠀⠰⣿⣷⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣿⡄⠀⠀⠀⠀⠀⣰⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣾⣷
⠀⢠⣾⣿⡆⠀⠀⠈⠀⠀⠀⢀⣼⣷⡀⠀⠀⠸⣿⣿⡗⠀⠀⠀⢠⣾⣿⣿⣷⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⢻⣿⣿⠇
⠀⠘⠻⠿⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⢿⣿⣿⠿⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀
⡄⠀⠀⠀⢰⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⣠⣾⣿⡆⠀⠀⠀⠀⡀⠀⠀⢀
⠟⠀⠀⠀⠀⠉⠁⠀⠀⢠⣶⡀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⣾⣿⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠉⠉⠀⠀⣠⣾⣧⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠈⠁
⠀⠀⢀⣴⡄⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿
⠀⠀⣾⣿⣷⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧
⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⢀⣼⣿⡄⠀⠀⠀⠀⠀⢠⣾⣿⣿⣇⠀⠀⠀⠀⣠⣆⠀⠀⢾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠇⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠀⠀⠀⠘⠿⠿⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠃⠀⠠⣀⠂⠸⣧⠐⠄⠀⠄⠀⢢⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠘⠁⠱⠉⠾⡀⠀⢠⠃⠀⠀⣿⠀⠘⠁⠀⠀⠈⡆⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠁⠠⠀⡇⠀⠀⠃⠀⠐⡄⠈⠀⠀⠀⣿⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢄⠀⢁⠀⠀⠀⠀⢃⠀⠀⠸⠀⠀⠀⡆⠀⠀⠀⠋⠀⢀⡔⠁⠀⠀⠀⠀⠠⠄⠒⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠉⠀⠓⠄⢀⠈⠄⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⠄⠄⠀⠀⣀⣠⣅⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠥⠀⢀⠀⠀⠀⠀⠑⠰⣄⠀⠀⠀⠀⢸⣆⢧⢀⡀⣸⠀⡀⠀⢀⣴⢋⣬⠔⠊⠁⠀⢀⡤⠖⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠱⡀⠹⣦⡀⠀⠀⠀⠈⢧⡀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣿⣶⢟⡡⠋⠁⠀⠀⠀⠀⠀⠀⠀⡴⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⢀⣈⠢⣈⠛⢦⣄⣀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠈⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠐⡒⠒⠈⠁⠀⠀⠀⠀⠈⠉⣒⠬⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣠⣤⠤⠴⠖⠉⠀⢀⣠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡤⠤⠄⡀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡀⠀⠀⠤⠤⠤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒⠤⠀⠀⠀⠀⠀⠀⠀⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢒⠶⠶⠖⠒⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠦⠤⠤⠤⣄⠂⠀⠀⠀⠐⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠬⠄⠀⠤⡠⠐⠉⠀⠀⠀⠀⠀⢀⠤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠔⠂⠀⠀⠀⠀⠀⠈⢀⠴⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠠⣌⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡤⠀⠀⠀⠀⠰⠊⠀⠀⢀⣼⠇⢈⡟⢻⠿⠿⡿⣿⣿⡛⢏⠀⠀⠀⠀⠈⠳⡤⠄⣀⠀⠐⠢⠦⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠠⠁⠀⠀⣠⠟⠁⢠⠏⠀⠀⠀⢦⠁⣿⠉⢻⣟⣆⠀⢀⠀⠀⠀⠐⠄⠀⠈⠉⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠄⠀⠀⠠⠤⠁⠀⠐⠋⠀⠀⣠⠋⠀⠀⠀⠀⢸⠀⠛⠀⠀⢿⠸⡄⠈⣦⠀⠀⠱⡌⡄⠐⢤⣀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠄⠊⡀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠘⠀⣬⠀⠈⢷⣄⠀⣿⡄⠈⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣊⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⢿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡀⠠⠠⠷⠀⢠⡇⡠⠆⠀⠀⠈⢢⣀⠀⢀⠃⢦⠀⠀⣘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡾⠂⠀⠈⢢⡄⣶⠈⠈⠑⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠧⠾⠃
⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡼⣦⡀⠀⠀⢸⣀⣼⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠘⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⢣⠀⠀⠀⠉⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣸⡞⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠲⠛⠃
⡄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⢀
⢹⠀⠀⠀⠀⠀⠀⣠⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⡇⠀⠀⠀⠀⠀⣸
⠾⠀⠀⠀⠀⠀⠠⣿⠁⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠈⢷⣴⠇⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣧⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣸⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⢰⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⣄
⡀⠀⠀⠀⢸⣿⡟⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀⢀⡟
⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⢷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅
⠀⠀⣿⣇⠀⠀⠀⠀⠀⢰⢳⡄⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄
⠀⠸⣿⣿⠀⠀⠀⠀⠀⣌⠀⣿⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠛⠛
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠸⣦⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⠟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⠀⠀⡿⠀⢃⡆
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⠀⠀⠀⠙⢶⡿⠁⠀⠀⠀⠀⣶⡀
⠀⠀⠀⠀⠀⠀⡾⣷⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢷
⣀⠀⠀⠀⠀⠰⣁⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣼⠃
⣿⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⢀
⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⢀⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠀⠀⠀⠀⠀⠀⣸⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢰⡇⠈⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⢀⠄⠢⠀⠀⡠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠢⣀⠆⠀⠈⠇⠀⠀⣧⠊⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠠⠤⣸⠀⠀⠀⠈⡀⠀⢸⠀⠀⢠⠃⠀⠀⣠⠞⠏⣉⣿⠆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⡀⠀⠈⢣⡀⠀⠀⢣⠀⢸⠀⠀⡌⠀⠀⠀⢡⡴⡶⠏⠁⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠔⠊⠉⠉⠉⠒⠦⣄⡑⢄⠀⠈⢆⠘⣆⠀⡇⠀⠀⣰⠉⠀⡠⠔⠊⠉⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠙⠢⣕⣤⣼⣿⣿⣶⣿⣦⣶⠃⡠⠊⠀⢀⡀⠤⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠚⠛⠒⠤⠤⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠒⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢤⠔⠒⠒⠒⠒⠒⠶⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠠⠤⠒⠒⠒⠒⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢀⡤⢚⣿⣿⣿⣿⣿⣿⣿⣿⣟⠳⣀⠀⠉⠐⠒⠠⢤⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠰⢀⣀⣀⣀⡠⠤⠖⠊⠁⡠⠊⢉⠟⠛⢿⣿⠿⠛⢣⠀⠀⠀⠉⠢⢄⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢠⠎⠀⢠⠃⠀⠀⢸⠂⠀⠀⠀⠳⡀⠀⠀⠀⠀⠑⠖⠠⠤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡴⠁⠀⢠⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⢦⡀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠹⠁⠀⠀⡎⠀⠀⠀⠀⡎⠀⡄⠀⠀⠀⠸⠀⠈⠒⠄⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠤⠐⠈⠃⠀⠀⠀⡼⣿⠀⠀⡀
⠀⠀⠀⠀⠒⠒⠒⠀⠤⠀⣀⡀⠀⠀⠀⠀⠀⠡⣠⠤⠊⠀⡏⣆⠀⠘⠦⡀⢠
⠀⠀⠀⠀⠀⠀⢦⠐⠂⠀⠀⠀⠉⠐⠢⣄⠀⣀⣀⠀⠀⠀⡇⢘⠳⡮⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠓⠂⡐⠀⠠⠀⡀⠀⠀⠑⠄⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⠬⣀⡀⢰⠀⠀⠃⠸⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⡄⠀⠀⠆⡠⠂⠁⠀⠀⠀⢀⡀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠀⣿⡀⠀⡀⣠⠄⠀⠀⠀⣀⠤⠒⠒⠂⠀⠉⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢱⡾⠋⠀⠒⠒⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⡺⠀⠀⠄⠀⢀⠈⠤⣩⡇⠀⠀⢀⣙⠅⡀⠀⢠⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠀⠀⢀⢀⡀⠀⠀⠀⠆⠀⣧⠤⣴⣆⠀⠀⣃
⢉⠁⢷⠀⢀⠀⡾⠀⠀⠉⠀⠀⠘⠿⠇⢀⠋⠀⠈⠀⠀⠀⠀⣦⣿⣦⣄⡀⠀⠐⠀⠀⠀⠀⠋⣼⡿⠓⠀⠀⠀⠳⡋⢣⣉⣁⠀⠺⠛
⢀⣶⠙⠁⠀⠀⠈⠀⠀⠀⢀⡀⠀⠤⠀⠀⢀⣤⣀⠀⠀⠀⢾⣿⣮⣿⢿⡆⠀⠀⢰⣶⠆⠀⠘⠁⠁⠀⠀⠀⠈⠀⢻⣩⣏⠁
⡐⠧⡨⠀⠀⠠⠀⠀⠀⠀⣏⣴⣳⠀⠀⠀⠛⢻⣿⠀⠀⠀⠐⡟⠉⠻⣯⡇⠀⠀⠀⡀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠿⠷⠀⠀⠀⠀⠠⢿
⠩⣴⡤⠄⠀⢀⡀⠰⠀⣾⣏⣿⣿⠀⠀⠀⣠⣌⡉⠁⠀⠀⠙⠋⢹⠋⠁⠀⠀⠀⢀⡈⠒⠂⠀⠑⣀⠁⠀⠀⠀⡀⠀⠀⣀⣤⣤⡀
⠀⡬⠀⠀⠀⠀⠙⠀⢤⡀⢬⠀⠁⢠⠀⠀⠹⠿⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⢀⣈⣈⡙⣶⣠⡠⠊⠀⠀⠰⠟⠿⣿⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠈⢳⡄⠀⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⠋⠀⣴⣿⣷⡄⠀⠀⠇⠀⢀
⠀⠀⠀⠀⢀⠀⠐⠶⠆⠀⢻⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠿⠁⠀⠀⠘⠀⢸
⠀⢸⠀⠀⠉⠠⣶⡆⠰⠄⠈⣿⠀⠀⠀⠫⠄⠃⠛⠸⠛⠃⠙⠆⠸⠈⠃⠋⠛⠿⠘⠀⠛⠘⠂⠀⠠⢤⡄⠀⠀⠘⠀⠀⠀⠀⡄⠀⠘
⠀⠸⠀⢰⣶⠀⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠄⠀⠀⠐⣄⢰
⢀⠟⠀⠀⠀⣀⡉⡎⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠀⠀⠀⡀⠀⠀⠀⠨⢿⣄⡆
⡼⠀⠀⠀⠀⢋⢺⠄⠀⠠⠀⢀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠰⡆⠀⠀⠀⠀⠠⠌⠁⠀⠀⠐⡇⠀⠀⢻⣷
⠁⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠋⠀⠀⠀⠠⠆⢉⣠⠀⠀⠀⠀⢭⣶⣮⣅⠀⠀⠀⠀⠀⠀⠀⢠⠀⠪⣧⠀⠀⢸⡆
⢀⡰⠆⡤⠀⠀⠃⠀⠀⠀⠀⣂⠀⠀⢠⣜⣇⢖⣔⡆⠀⠀⣾⣿⣭⣶⣿⠄⠀⠀⠐⠙⠛⢟⠀⠀⢀⣤⣤⣤⡄⠈⠀⢭⣯⠀⠀⠈⠣
⡄⠰⠲⠉⠀⠀⠈⠑⠀⠀⠀⠈⠁⠀⠀⠈⠋⠈⠙⠁⠀⠀⠈⠉⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡿⢷⠀⠀⠍⣭⠀⢠⣾⡆
⣧⠀⢀⠄⠀⠀⠶⢲⠄⠀⠀⣠⣿⣦⣀⠀⢀⡄⢀⠘⠃⠀⠀⢠⣶⡄⠀⢀⣡⣠⣤⡀⠀⣠⣤⠀⠉⠈⠇⠴⠂⠀⠀⣚⣶⠀⠈⠿⠇