See More
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⠟⢣⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣊⡩⠿⠃⠂⠀⠹⠿⣉⢒⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⢳⡀⠀⠘⠀⠀⢠⢞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢱⠀⠀⠀⢠⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡆⠀⠀⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⢫⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠇⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢦⠀⠀⠀⠀
⠀⠀⠀⣠⣿⡾⠻⢏⡓⠢⠤⢤⣀⣀⣀⣀⣀⣸⣇⠄⡀⠀⢸⣿⣀⣀⣀⣀⣀⣠⠤⠴⣺⡽⠟⠻⣮⣧⡀⠀⠀
⢀⣤⠞⡿⠟⠁⠉⠀⠉⠀⠀⠒⠂⠀⠀⠀⠛⠛⠛⠁⣇⠀⠘⠓⠒⠒⠒⠒⠒⠚⠋⠉⠀⠀⠀⠠⣝⠻⣉⢳⡄
⠸⢿⡿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠛⠛⣁⠀⠀⠀⠀⠀⠀⠄⣀⣀⠀⠀⠀⠀⢀⡴⢿⡿⠃
⠀⠀⠉⠲⡿⢧⣀⣠⡔⣂⠤⠤⠀⠐⠒⠒⠒⢲⣾⠁⠂⠀⣿⣶⠒⠒⠒⠒⠒⠒⠒⠪⢍⣳⣤⣠⢿⡖⠋⠀⠀
⠀⠀⠀⠀⢳⣨⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠀⠀⠀⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⠞⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃⠀⠀⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆⠀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠁⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⡇⠀⢠⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⠁⡇⠀⠘⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠋⠘⠁⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⣱⣭⡝⢷⠀⢀⡤⣾⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣌⣦⡴⢿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
🍆🍆🍆🍆🍆🍆
🍆🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍑🍑🍆🍆🍆🍆🍆🍆
🍆🍑🍑🍑🍆🍌🍌🍌🍌🍌🍌🍆
🍆🍑🍑🍆🍌🍌🍌🍌🍌🍌🍌🍌🍆
🍆🍆🍆🍑🍑🍆🍌🍌🍌🍌🍌🍌🍌🍌🍆
🍆🍑🍑🍆🍑🍑🍆🍌🍌🍌🍌🍌🍌🍌🍌🍆
🍆🍑🍑🍆🍑🍑🍑🍆🍌🍌🍌🍌🍌🍌🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍆🍆🍆🍆🍆🍆🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍆🍆🍑🍑🍑🍑🍑🍑🍑🍑🍑🍑🍆
🍆🍑🍑🍑🍆🍆🍆🍆🍑🍑🍑🍆
🍆🍑🍑🍑🍆 🍆🍑🍑🍑🍆
🍆🍑🍑🍑🍆 🍆🍑🍑🍑🍆
🍆🍆🍆 🍆🍆🍆
♥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⠀⠀⠀⠀⢀⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢻⡿⣦⠀⠀⢰⣿⡿⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠹⠷⠾⠟⠻⠛⠲⠿⢿⣤⣼⡯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡟⠀⣠⣶⣄⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡿⠏⠀⣀⠀⠀⢸⣿⣿⠇⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠾⠿⣷⡄⠀⠉⠁⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣄⣀⣀⡀⠀⠀⢀⣀⣠⣴⠞⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢻⣏⣉⣛⣽⡿⠛⣿⡇⣀⣀⣛⣷⣤⡭⠟⢶⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣴⢻⣿⣳⣄⣾⠟⠛⢻⣯⢀⣀⣿⡿⠟⠉⠉⠉⢳⡄⠀⠀⠙⢧⡀⠀⠀⠀
⠀⠀⠀⢀⡾⠁⠈⠛⢻⠟⢋⣠⠀⠘⠿⣿⡿⠟⠀⠀⢀⡀⠀⠀⢻⡀⠀⠀⠈⢷⠀⠀⠀
⠀⠀⠀⣸⠃⠀⠀⢀⡟⣴⢞⣽⣷⠀⠀⢸⠃⠀⠀⢠⣟⣿⣦⡀⠀⣧⠀⠀⠀⢸⡇⠀⠀
⠀⠀⠀⡟⠀⠀⠀⢸⢿⣡⣿⣿⣿⡇⠀⣾⡀⠀⢠⡟⣾⣿⣿⣿⡆⢸⠀⠀⠀⠀⣿⠀⠀
⠀⠀⠀⣧⠀⠀⠀⢸⠀⠉⠉⠉⠉⢡⡾⣿⣷⡄⠈⠛⠛⠛⠛⠉⠁⢸⠀⠀⢀⣴⡇⠀⠀
⠀⠀⠀⢻⡀⠒⠤⢼⠀⢰⣶⣶⡄⠈⣛⣿⣛⣁⡀⠀⣶⣿⡆⠀⠀⣼⠠⠖⠉⣽⣁⡀⠀
⠀⣠⣴⣾⣷⡀⠀⠸⣇⠸⣿⣿⣷⣶⣿⣿⣿⣿⣷⣾⣿⡿⠃⢀⣤⣿⠾⢷⣾⢟⣉⣿⠆
⠀⣻⣷⡟⢻⣿⣦⣄⣹⣆⠈⠛⠻⠿⠿⠿⣿⡿⠿⠟⠋⠁⢰⡟⠙⠏⣸⣀⡵⠛⡾⣿⣄
⢸⣏⣻⣿⣯⣵⢋⣍⡭⣹⠷⢤⣄⣀⣀⣤⠼⠷⣤⣤⣤⡤⢿⡀⣠⡴⠟⢻⣿⣿⣿⡿⠃
⠈⠉⠉⠁⠛⠓⠛⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠷⣬⣙⡓⢒⣹⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣤⣿⣤⣨⣿⡀⠀⠀⠉⠙⠷⣤⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠋⠉⠉⠉⠉⠉⠛⠒⠦⣤⡀⠀⠈⢻⣆⠀⠹
⠀⠀⠀⣴⢶⣶⡶⠖⢋⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣾⣿⣠⡤
⠀⠀⠀⣻⠦⢀⣠⣴⡿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀
⠀⠀⠉⠀⢰⣿⣿⣿⣇⠀⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠘⣷
⢧⣀⠀⠀⢸⣿⡿⠟⢋⣴⠋⣸⠁⠀⠀⠀⠀⠀⠀⣴⢻⡶⡄⠀⠀⠀⠀⠀⠀⠘
⠀⢨⠃⠀⡿⠋⢀⡴⠋⠀⢀⡟⠀⡀⠀⠀⠀⣹⣾⣅⠈⣇⡇⠀⠀⠀⠀⠀⠀⠀
⣾⠃⠀⠀⠀⣰⠏⣀⡀⠀⢸⢷⡾⠁⣀⣤⠾⠋⠀⠀⠀⢹⣇⠀⠀⠀⠀⠁⠀⠀
⡇⠀⠀⠀⣰⠏⣾⣿⣿⠀⠀⠘⠓⠛⠉⠁⢀⣴⣶⣄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⡟⠀⠙⠛⠋⠀⠀⠀⠀⠀⢀⠀⠺⣿⣿⡿⠂⠀⡟⠁⠀⠀⠀⠀⢠⠀
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠸⠶⠶⡶⣾⠋⠀⠀⠈⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⣍⣻⣶⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⡇
⠀⢰⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣶⣿⠏⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠈⢿⣷⣦⣿⣿⣿⣿⣿⣿⣿⠟⠙⠿⠋⠈⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⡞⠀
⠀⢠⣦⣤⣴⣖⣒⠶⢤⠀⣔⣒⣻⣭⣻⣻⣻⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢸⣻⣻⣻⣻⠏⣩⣴⠟⢛⣻⣭⣻⣻⣻⣻⣻⣻⣻⣻⠛⠡⢐⣒⣻⣻⣻⣶⣦
⠀⢸⣻⣻⡿⠡⠞⢋⣤⣾⣻⣻⠟⣛⣻⣻⣻⡻⣻⠋⣰⣶⣻⡻⠁⣠⣠⣲⣻⣻
⠀⢸⣻⠋⣰⠃⠀⡨⡿⣻⡟⢫⣾⣻⣻⣻⣻⡃⣻⢰⣻⣻⣻⣲⡀⢹⣻⣻⣻⣻
⠀⢸⠃⣸⠃⣸⣻⣻⣶⠟⣰⣟⣻⡿⢻⣻⣻⠇⠹⢸⣻⢻⣻⣻⣻⡂⣹⣻⣻⡇
⠀⢀⣺⠃⣸⣻⣻⣻⡏⣼⣻⣻⣻⣷⠿⠟⠓⠒⠤⣻⣾⢸⢻⣻⣻⣻⣻⣻⡿⠀
⠀⣺⡏⣼⣻⣻⣻⣻⢸⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⢸⣻⢸⢸⣻⣻⣻⣻⡿⠁⠀
⠀⠇⢃⣻⣻⣏⣁⣋⡁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⡼⣾⣻⣻⣻⡟⡇⠀⠀
⠀⠀⠸⣻⣹⣻⠙⠉⠙⠳⠀⡠⠀⠀⠈⠴⠿⠷⣦⣤⢤⣳⣻⢻⣻⣻⡇⡇⠀⠀
⠀⠀⠀⣻⣻⣻⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣸⣷⣻⠃⣺⣻⣻⣷⡇⠀⠀
⠀⠀⠀⣻⣻⣻⣧⠀⠀⠀⢱⡶⠶⠶⡶⠀⠀⠐⠻⢻⣻⢫⣺⠋⣸⣻⣻⣷⠀⠀
⠀⠀⢠⢣⣻⣪⡹⢻⣦⣀⠀⠈⠂⠒⠁⠀⣀⣤⣾⣻⢡⣻⣻⢸⣻⣻⣻⣼⡀⠀
⠀⢀⣏⣫⢹⣢⡻⣲⣩⡛⣻⣷⣶⣖⣫⣭⣶⣻⣻⣻⣢⡙⢻⣈⢻⣻⣻⣯⣧⠀
⠀⣼⣼⣻⣃⢻⣻⣈⢻⠧⠸⣻⣻⢿⢿⡿⠛⠋⠛⠛⠿⠿⣢⣻⣢⢹⣻⣻⣾⡆
⣿⠿⠿⠿⢿⣿⡿⠿⢿⣿⣿⠟⣫⣾⣿⣿⣿⣿⣤⡾⠛⠉⠉⠉⠴⠖⠀⠀⠀⢀⣬⠟⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠙⠿⣷⡶⠯⠭⢽⣭⣿⣟⣿⢿⣿⣿⣿⣿⣿⣿
⢄⠀⠾⢛⣩⣽⠟⠛⠛⠿⣶⣾⣿⠻⣿⣿⣿⣴⣿⠀⠀⠺⣷⠀⠀⣴⢰⠄⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡉⠉⠉⠙⠻⠿⠟⠻⢶⣭⣛⠿⣿⣿
⣧⣴⡿⠛⠛⠀⠀⠀⠀⠀⣸⣿⣇⣄⢹⣿⡿⢫⣤⠄⠀⠀⠀⡀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⣀⣀⠀⠀⠀⠙⣿⣄⠀⠀⢀⣠⣤⡶⣦⣬⣉⠛⢾⣝
⠉⢀⠔⠂⠀⣀⣀⣀⡀⣰⣿⣿⣿⣿⣿⣿⡇⢸⣿⡀⠲⢶⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠟⠛⠋⠉⠉⠛⢷⣦⣷⠀⠘⣿⠷⠞⠋⠁⠀⣠⣴⣮⣭⣤⣤⡍
⠀⠈⣠⡀⠸⡟⠁⠉⠙⢻⠟⠉⠉⠉⠛⠿⢷⣤⣜⠿⠷⠆⣴⣾⣦⠀⠀⠤⠀⠷⠄⠀⣀⣤⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣤⣿⠀⠀⠀⢀⣼⡿⣿⣿⡿⠉⠁⠀
⠄⠀⠈⠻⠦⢻⣆⠀⢠⡞⠃⠀⣀⠀⠀⠀⠀⠀⠙⠳⣤⣴⣆⠁⠀⠐⣀⣡⣤⣴⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⣹⡇⠀⠀⢠⣿⣏⣾⠟⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠹⣦⡾⠁⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⢸⣿⣿⠃⠀⢀⣿⣿⡟⣗⠀⠀⠀⠴⠀⠀
⠀⠀⠀⠀⠀⠀⣐⣿⣄⠀⢠⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⠛⠁⠀⢸⣿⡟⠀⣠⣾⡿⠋⢰⠟⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣴⣾⣿⣿⣿⣿⣇⠈⢻⣿⣷⣶⣦⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⠿⠿⢿⣿⣿⣿⡿⠁⠀⠀⢠⣿⣿⠁⣴⡿⠋⡄⢠⣿⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣭⣭⣍⣛⢻⣿⣿⣿⣿⣿⣯⣵⣶⣶⣶⣾⣶⣶⣶⣤⡀⠀⠀⢸⣿⣿⠃⠀⠀⢀⣾⣿⠃⣼⣿⡵⠟⠀⣾⠟⠰⡄⠹⣦⡀⠀⠀
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⠟⠉⠉⣽⣿⣿⣛⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣭⣵⡄⠈⠙⣿⣶⣄⣸⣿⠃⠀⣠⣶⠿⠿⠷⣴⠟⠁⠀⠀⣰⡏⠸⢦⣽⣦⡘⢿⣤⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠀⠘⣿⣿⡄⠀⠀⠻⢿⣿⣿⡿⠁⠉⣿⣿⣇⠀⠀⠘⠿⠿⠿⠿⠁⠀⠀⣼⣿⣿⠟⠁⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠠⣾⣿⣧⣤⣄⣉⢋⠁⠀⠹⣦
⣿⣿⣿⣿⣿⣿⠟⠁⠉⠙⠶⠶⣄⣈⣻⣿⣦⣀⠀⣀⣀⣀⡴⠶⠞⠛⠋⠙⠛⠶⠶⠶⠦⢄⣤⣀⣤⡾⠿⠛⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⠟⠋⠉⠁⠀⠀⠀
⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⢉⣀⠀⠀⠀⠀⠀⠀⣀⣭⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣶⣤⣀⣧⣴⣶⣤⣴
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠟⠳⠀⠀⠀⠀⠘⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢠⣿⣿⣿⣿⣿⣿⣯⣀⡈⣹
⣿⣿⣿⣿⣿⣿⡀⠈⠙⢶⡀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢠⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿
⣿⣿⣿⣿⡿⠛⢡⡄⠀⠈⢷⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠃⢠⠚⣷⡀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢀⡾⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡀⢺⠀⠹⣿⡄⠀⢽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⣠⠟⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⢸⣆⠀⠸⣿⣄⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⢉⣴⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣿⣿⡄⡝⠀⠀⠹⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠋⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠻⣿⣿⣿⠖⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⡿⠟⠛⠁⢀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢈⡛⠛⠿⠿⣿⣿⡷⠶⣶⣶⣶⣦⣤⣴⣶⣶⣶⣾⣿⠿⠟⠛⠉⠉⠀⠀⢀⣤⡶⣛⣵⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠙⠷⣤⡄⠈⠉⠉⠓⠦⠤⠤⠖⠛⠛⠒⠋⠉⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⣁⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠙⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⡿⠛⠉⢁⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⠉⠛⢻⣿⣶⣶⣶⣶⣶⣿⣟⡛⣻⣿⣿⣿⣤⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠋⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷⣾⣿⠃⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠿⠿⠟⠛⣋⡙⠛⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠀⠛⠎⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠲⠦⣤⣮⡻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀
⠀⣠⣞⡷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣥⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡎⢷⡄
⣼⡿⢻⣿⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣾⣿⣿⣿⣿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⡿⠿⠿⠿⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⡾⠋⣿⣿⡇⠀⢿
⣿⡗⣦⣿⢇⣿⣷⣄⠀⠀⠀⠀⠀⢠⣿⡿⠋⠉⠀⠈⠉⠀⠈⠙⠻⢿⡀⠀⠀⠀⠀⢰⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⢀⡴⠿⠛⢢⣿⣻⣤⣼⣿
⢿⣿⣿⣷⣾⣿⣄⠙⠳⢦⣄⣀⣠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣀⣾⡅⢠⣤⣀⣄⠀⠀⠀⠀⠀⠘⣿⣿⣦⣤⣾⣯⣁⣤⠶⠛⠛⠛⠉⠉⠀
⠀⠀⠀⠉⠉⠉⠙⠳⣶⣢⠈⠛⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠘⠃⠀⠀⢿⣿⣿⣾⡿⢏⣋⣅⣀⣀⣠⠄⣾⣿⣿⡜⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⠍⠀⠀⡀⢀⣴⡶⢶⣿⣿⡿⣶⣯⡀⠀⠀⠀⠀⠰⣿⣿⣿⣶⠿⣿⣿⣿⠙⢿⣷⣶⣿⣿⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠛⠿⣄⣼⣿⣿⣿⣼⡟⠛⠀⠀⠀⠀⠀⠈⠙⣿⡿⣶⣿⣿⣿⣿⣿⡿⠟⠃⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠒⠶⠾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⣤⣴⣤⣀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣦⣤⣤⣀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢀⣤⣿⡿⠛⠁⠀⠉⠉⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡍⡉⠛⢿⠀⠀⣤⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣿⣿⡆⠸⣇⠀⢯⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣶⣿⣿⣿⣿⠀⣿⡄⠈⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⣻⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣿⡇⢻⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠛⠈⠻⣯⡉⢹⣏⠉⢹⡟⠉⠉⢹⠟⠁⠈⢻⡀⣾⣿⣿⣿⠟⢁⣾⣿⡧⣿⡇⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣷⣶⣶⣾⣷⣶⣶⣿⣿⣿⡿⠛⢁⣰⣿⠏⣿⣧⣿⣇⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠯⣽⠻⠧⠤⠤⠞⠋⣀⣤⣶⠟⢫⣿⠆⢉⣿⠋⠙⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠤⠶⠾⠿⣿⣟⣁⣤⣾⣥⠀⢘⡿⠀⣸⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⠿⢿⣿⠃⠀⢸⣇⢰⢸⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⡤⣽⠀⠀⣈⢍⣽⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣇⣘⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣤⣀⣀⡀⣀⣀⣤⣤⣤⣴⣾⣿⣽⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀