Drinks Emojis & Symbols

⣞⣟⣉⣉⣉⣉⣉⠉⠉⠉⠙⣶⣶⡄
⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⡏⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⣛⣙⣿⣻⠿⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣟⠋⢹⣏⠉⢉⣿⠳⣮⣛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⣿⠀⣼⠃⣠⠞⠛⣯⡻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⠤⠤⠤⠼⠦⠼⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠧⠿⠶⠧⠾⣧⣤⡴⠛⣷⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣥⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢦⣄⣀⠀⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢠⡞⠁⠙⣿⣦⡈⠙⢻⡿⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡴⠋⠀⠀⠀⠈⢧⣙⣶⢟⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣰⠎⠀⠀⠀⠀⠀⠀⠀⠻⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢿⣿⣿⣿⣿⡿⠋⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠛⠛⠛⠛⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣠⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⠀⠀⣿⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠉⠉⠉⠀⠀⢹⡀⢀⣿⠀⠀⠉⠉⠉⠙⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⣄⣀⣀⡀⠀⠀⠈⠉⠉⠁⠀⠀⠀⣀⣀⣀⣤⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉
⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣄⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣛⣛⠃
⠀⠀⠀⠀⠀⠀⡌⣁⣈⡈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠰⣜⣟⣿⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⡷
⠀⠀⠀⠀⠀⠀⠈⣹⣿⡉⣀⣈⠿⠿⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⢟⣇⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠰⢒⣒⣒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣍
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠘⣍⣉⣏⠌⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣶⣿
⠀⠀⠀⠀⠀⠀⣧⡉⠐⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠆
⠀⠀⠀⠀⠀⠀⣬⣤⣤⣬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠂
⠀⠀⠀⠀⠀⠀⠙⢿⣿⢟⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠈⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠾⠿⠖⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠾⠿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠘⠿⠇⠀⠀⠀⠀⠀⠀⠀⠠⠾⠷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠈⢩⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣶⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣭⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡾⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣰⣃⣠⡄
⠀⠀⠀⠀⠶⣿⡄⢈⣏⠰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠀⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣿⣿⡷⢄
⠀⠀⠀⠀⠀⠈⠁⠉⠉⠁⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠙⠋⠁

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

⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⢀⡀⠀⠀⠀⢠⠀⣥⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢰⣧⣄⣷⣶⠀⠀⠀⠀⠀⠁⠐⠂⠜⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠀⠠⣤⣄
⠀⠀⠀⠀⠀⠈⠀⠑⠒⣿⠀⠀⠀⠀⠀⠆⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠛⠀⠀⠀⠀⢰⠀⠀⠀⠀⠹⣶
⠀⠀⠀⠀⠀⢠⠀⠀⠀⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠰⠀⠓⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠐⠦⠈⠾⠃⠀⠀⠀⠀⠀⠣⠀⠠⠾⠃⠀⠀⠀⠸⠆⠀⠶⠃⠀⠀⠀⠀⠠⠄⠠⠶⠀⠀⠀⠀⠀⠘⠦⠀⠀⠀⠴⠟

⠀⠀⠀⠀⣀⡀⠀⢠⣰⢄⡀⠀⠀⠀⡤⠄⠀⠠⠀⢤⠀⠀⢠⠂⠐⠒⠂⢲⡄⠀⠀⣠⡤⢀⠀⣤⣤⣄
⠀⠀⠀⠀⠹⡄⠀⠈⢹⠟⠀⠀⠀⠀⢂⠀⠀⠀⠀⠘⠀⠀⠀⢂⠀⠀⢀⠞⠀⠀⠀⠣⠀⠀⠀⠀⠀⠉⠀⠀⢠⢀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠄⠀⠀⠀⠀⠈⠈⠀⠀⠙⢻⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣁⡟
⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⢀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠸⠋
⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠘⠀⠀⠀⠐⠋

⠀⠀⠀⠀⣀⡀⠤⠄⠀⢀⡀⠀⠀⠀⠀⡀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⡄⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⢏⠀⡀⢀⡀⢻⡇⠀⠀⠀⠘⠓⠛⠛⢛⡗⠀⠀⠀⠂⠀⠈⠀⡶⠀⠀⠀⠀⠃⠀⠀⢹⡇⠀⠀⠀⠐⠗⢒⣆⣰⠛⣿
⠀⠀⠀⠀⠘⡀⠀⣀⢀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠀⠀⢄⡋⢿⢛⡇⣿
⠀⠀⠀⠀⠀⢟⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠁⠀⠀⠀⢀⠐⠀⢀⡀⠀⠀⠀⠀⢸⠀⠀⠐⡇⠀⠀⠀⢀⡁⠀⠒⠊⠀⡁
⠀⠀⠀⠀⠀⠘⠃⠀⠚⠃⠀⠀⠀⠀⠀⠙⠀⠒⠛⠀⠀⠀⠀⠘⠀⠐⠛⠁⠀⠀⠀⠀⠀⠂⠀⠚⠀⠀⠀⠀⠈⠓⠂⠀⠈⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠶⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡔⠂⠐⡄⠀⠀⣿⡣⠄⠙⠀⠈⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⢘⣃⡀⡀⠀⠀⢘⣖⣟⡠⠂⠀⠀⣿⡠⢄⠀⠲⢘⠀⠀⠀⠀⠀⠻⣷⠄⢀⡉⠁⠟
⠀⠀⠀⠀⢸⣥⣅⢛⣄⠀⠈⣼⠋⠀⠀⠀⠀⢸⠟⢢⠒⠂⠈⠀⠀⠀⠀⠀⠀⠘⣷⠄⡒⠊
⠀⠀⠀⠀⠀⣿⡯⠉⢩⡙⠡⠸⠀⠀⠀⠀⠀⢿⣦⠿⠰⡏⢰⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢹⣷⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠿⠓⢄⠘⢸⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠸⠙⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡦⢠⠛⢸⠀⠀⠀⠀⠀⠀⢄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠢⠴⠰⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⢀⣷⡀⠀⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠖⠀⠁⣄⠁⠈
⠀⠀⠀⠀⠀⠀⢸⣿⢧⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠐⣠⠶⣌⣶
⠀⠀⠀⠀⠀⠀⢸⣿⣾⣦⠤⠦⣻⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣭⡏⠀⠩⠃
⠀⠀⠀⠀⠀⠀⠘⠛⠿⢀⡀⠀⠀⠀⠀⠀⠀⣯⣁⠌⠂⠒⢙⠀⠀⠀⠀⠀⠀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⣿⣧⢄⠀⢀⢘⠀⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢁⢨⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⠀⠀⡀⠀⠀⠀⠀⣿⠟⠶⠄⠛⠛⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡍⡜⠻⠄
⠀⠀⠀⠀⠠⠔⠀⠐⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⢀⣤⣶⡆⠀⠀⠀⠀⠀⠀⣴⡴⠂⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠸⢀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⡼⡿⠿⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠸⢰⣿⡿⣿⡤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⠄⠒⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣾⠟⠏⠈⢣⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣤⣯⠤⡀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣰⠃
⠀⠀⠀⠀⢀⡙⠻⠿⠷⠾⠿⣫⡄⠀⠀⠀⠀⠀⠀⠈⠲⢼⡷⠀⠀⠀⢠⠀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⢤⠇
⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣁⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠒⠂⠒⠚⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠘⠢⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⡇⠀⠛⣿⡿⢃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠲⠤⡌⣉⠀⡤⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⣼⡄⠀⠀⠘⠙⠓⠒⠒⣒⣲⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠺⣿⣧⡠⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⢻⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⣷⣂⡀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣿⠧⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⣿⣷⣦⠀⣡⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣥
⠀⠀⠀⠀⠀⢀⣿⣻⣛⡓⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠇⠀⠀⠀⠀⠀⠀⠀⠲⠤⠭⠭⠙⠂⠈⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠀⠀⣀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠴⠦⠄⠀⠀⠀⠀⠁⠀⡟⠀⠀⠸⠀⠀⠀⠀⠒⠒⠒⠒⠒⠶⠶⠶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⠋⠁⠀⢀⣠⠴⠒⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⣤⣄⡀⠀⢀⣀⡀⠀⠉⠛⠻⣦⡀
⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠠⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⣳⡄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡶⠶⠶⠞⠋⠀⠀⠀⢀⣀⣤⣶⠿⢃
⠀⢀⠙⠳⣶⣶⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⠶⠶⠾⣿⠟⠛⠉⠀⠀⠈
⠀⠈⠉⢉⠱⠿⢤⣭⣉⣉⣙⠛⢛⣛⢛⠓⠛⠛⠋⠀⠀⣓⠒⣛⠛⠛⠛⠛⠛⠋⣉⠉⠉⠉⠁⢀⡄⠀⠀⠀⠈⠀⠀⠀⢀⣀⡠⠄
⠀⠀⠀⣾⠀⣀⠀⠂⠈⠉⠉⠘⠛⠛⠛⠛⠋⠉⠁⢀⠛⠉⠉⠉⠀⠀⠀⠀⠔⠊⠉⠑⠀⠀⠀⠀⣀⣀⣤⣤⡤⠶⠚⠛⠋⢹
⠀⠀⠀⠸⠀⠈⠙⠛⠓⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠾⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢠⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠘⣧⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠶⢀⢸⡇
⠀⠀⠀⠀⠀⣿⣎⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠀⠀⠀⠀⠀⣠⡴⠶⠾⠶⢤⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⢻⡏⠓⠤⠄⠀⢀⡎⠀⠀⠀⠀⠀⠀⠠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠈⠀⠀⢐⡒⣤⠶⢷⣦⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⠖⠒⠒⠉⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠠⠖⠋⠁⠀⠀⠀⠀⠈⠃⠌⠉⣉⠝⠋⠉⠉⠉⣉⡉⠉⠙⠛⠒⢤⡀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⡼⠃⠀⠀⠤⠀⠀⠈⠉⢄⡀⠀⠀⠀⠉⠆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣷⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢻⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡀⠀⠀⡀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠸⠀⠀⠀⣧⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⣤⣤⡤⠐⠂⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠙⠀⠀⠀⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⢀⡠⠤⠐⠛⠀⣀⣉⠤⠤⠤⠤⡴⠒⠓⠀⠀⠀⠠⠠⠀⠈⢁⡈⠁⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⠀⠀⠀⠀⢾⣋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠷⣶⣄⣀⠀⠈⠛⠂⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠘⠷⣤⣤⣀⣉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠦⠤⢠⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠰⠀⠀⠠⠤⠀⣀⡀⠀⠀⠀⣀⣤⣌⠁
⠀⠀⠀⢀⠀⠀⠾⣦⣤⡤⠈⣿⠁⠀⠀⠧⠈⠓⠈⣿⣾⠀⢸⣾⠁⠀⣦⣰⡆⠀⢁⣄⣠⠀⠀⢙⡋⠉
⠀⠀⠀⠈⠁⠀⠀⠘⠟⠀⠰⣿⡆⠀⢸⣿⣿⡇⠀⢻⡿⠆⠀⣿⠀⠀⡿⢽⡇⢀⣿⣿⣿⣷⠀⠯⡿
⠀⠀⠀⠠⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠈⠿⠿⠁⠀⠀⠀⠀⠀⠛⠀⠀⠿⠿⠇⠀⠻⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢀⣀⣀⣀⢰⣿⣿⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡇⠀⣾⣿⡇⢸⣿⡏⢡⣤⣤⠉⠠⠖⣶⣿⠆
⠀⠈⠿⡿⠞⢸⣿⣿⠘⠰⣶⡦⠂⢸⠂⢠⡀⠠⡄⣿⣿⣿⡆⠀⣿⣿⡇⠀⣿⠃⢸⣿⣿⠀⠀⣯⡆⡇
⠀⠀⠀⠀⠀⠘⠛⠛⠂⠀⠀⠀⠀⠐⠀⠈⠉⠉⠀⠻⠿⠟⠃⠀⠛⠛⠃⠀⠈⠀⠈⠛⠛⠀⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣀⣼⠟⠰⠶⠶⠶⠆⠦⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠐⣿⣿⠇⠿⠿⠿⠿⠇⠺⠀⠀⠀⠀⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠁⡄⢠⡄⠀⠄⠀⢸⣇
⠀⠀⠈⠁⠀⣿⣿⣿⣿⡷⢸⠇⣤⣤⡄⣿⣿⠀⣶⣶⡂⠀⢰⠀⠀⠀⡇⢸⡇⠀⠀⢀⣯⣹⠀⢤⣤⣤⠄
⠀⠀⠀⠀⠐⠾⠿⠿⠷⠇⠸⠀⠙⠛⠁⣿⣿⠀⠈⠋⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⢸⣿⣿⡇⠀⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠋⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢠⠅⠁⢠⠤⢐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡐⠉⢢⠢⠰⠈⢀⡠⠓⢌⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠰⠤⠄⠤⠥⠉⠐⣡⠊⠀⠀⡊⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠮⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢀⠈⠉⣰⣂⡴⡄⢦⠠⠬⠴⡅⠇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠐⠒⠒⠒⠒⠒⠒⠂⠀⠀⠒⠒⠒⠒⠚⠆⠋⠍⠁⠐⡏⠢⢠⠀⡐⣠
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢄⣇⠠⠔⣉⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠗⠒⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠘⡇⡠⢄⣀⣀⡀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡃⡇⠀⠀⠀⢀⠠⠐⠈⠉⠉⠒⠢⠤⠐⠊⠁⠀⠀⠀⠀⠀⢡⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡷⠇⠀⠀⢠⠁⡀⠔⠂⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⣘⠠⠀⠀⠀⢄⠀⠀⠀⠀⠀⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠀⠀⠀⠡⠀⠀⠀⠀⠠⢹⠀⢠⡀⠀⠀⠑⢄⠀⠀⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⠀⠀⠑⠀⠀⠁⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⠀⠘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢡⠀⠀⠀⠀⢀⠄⠁⠂⠌⣶⡀⠀⠀⠀⠰⢸⠀⠀⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠂⠀⡀⠢⢀⠀⡉⠀⠀⠀⠀⠁⠀⢀⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡆⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠁⠒⠐⠁⠀⠀⠀⠀⠀⠀⢰⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢦⣙⠲⠤⠤⣤⣤⣤⠤⠤⠐⣊⡡⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠉⠒⠒⠒⠂⠒⠒⠂⠉⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠤⠤⠤⠐⠒⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣛⣛⣛⣋⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⡀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣾⣿⣷
⠀⢰⠂⠀⠀⠀⠀⠀⠻⣿⠀⠀⠄⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⢰⠆⠀⠀⠀⠀⠐⠰⣶⡿
⠀⠘⢦⡀⠀⠀⠀⢀⡴⠋⠀⠀⠈⢄⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⣀⡈⡸⠃⠀⠈⢧⣀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠉⠻⠶⠞⠋⠀⠀⠀⠀⠀⠈⢳⣾⠟⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠻⡿⡟⠁⠀⠀⠀⠀⠉⠛⠶⠶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⢈⠀⢀⣤⡈⡁⠁⢃⡀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠻⢿⠃⠙⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡄⠀⠁⠀⣨
⠀⠀⢀⠀⠀⠒⠓⠠⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠦⠾⢿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠐⠒⠠⢀
⠀⠀⠀⠈⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠂⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢻⡟⠋⠁⠀⠈⠉⠉⠀⡢⠄⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⡐⠶⠀⠀⠀⠉⠁⠀⠀⠀⡧⠤⠐⠒⠀⠀⠀⠀⠠⠴⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠞⠁⠀⠀⠀⠀⠂⠀⢠⠔⠐⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠀⢸⡆⠀⠒⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠐⠖⡁⠀⢸⠇⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠀⠀⠳⠀⠐⢤⡀⠐⠀⢀⣤⠖⠚⠛⠒⠂⠀⠀⠴⠆⠐⠒⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⢸⠁⠉⠉⠒⠒⠒⠒⠒⠈⠉⠉⠁⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⠒⠐⠛⠉⠀⠠⠀⠁⠠⠄⠐⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠄⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⢠⠀⠀⠀⠀⠠⠊⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠒⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠄⠀⠠⠄⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣇⡇⠀⠀⠀⠀⠈⠀⢠⠇⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⠤⠤⠤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣿⡇⠀⠀⠀⠀⠂⠀⠁⠀⠀⠘⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠤⠠⠄⠀⢀⡼⠷⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠠⠄⠀⠐⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢸⠀⠘⠍⠃⠘⠠⠘⡏⠉⠁⠉⠀⠀⣀⠄⠀⠀⡿⡇⠀⠀⠀⡁⠐⠀⠀⠀⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠓⠁⠀⠐⢀⡆⠀⠀⠈⡄⠸⡀⠀⢳⠶⠖⠒⠚⠋⠁⠀⠀⠀⡇⢰⡀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠸
⠀⠀⠀⠀⠀⠀⠀⡎⠇⠐⠀⢀⠞⠀⠀⠀⢠⡇⠀⠇⠀⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠛⠒⠢⠤⠤⠤⠴⠒⠁⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠱⣀⡠⠐⠉⠀⠀⢀⠠⠐⠓⠒⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣄⣀⣀⣀⣤⠤⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⢶⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡚⠛⠉⢁⣠⣶⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⣀⠈⠙⢷⣶⣿⣿⣿⣿⣿⣿⡏⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡇⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣡⣤⣤⣤⣤⣤⣤⣤⣼⣏⣈⣿⠦⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⣥⣄⣀⣸⣀⣀⣀⣴⣿⣭⣽⣿⡇⠈⠻⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠩⠍⠉⠉⠉⢹⡿⠁⠀⠈⣿⠃⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣶⣛⡛⠛⣻⢻⣿⠛⢛⣶⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⡞⢹⠏⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢰⡓⣶⣬⣷⣯⡾⢚⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣟⣻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⢮⣟⣷⣧⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣯⣭⣭⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⢷⡤⠤⢤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢴⣶⠒⢛⡿⣿⡟⣿⣯⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⢋⣾⣿⣿⣿⠈⢳⡌⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣹⣞⣭⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠉⠛⣛⣛⡛⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣭⣭⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣊⣭⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⢻⣿⠀⣿⠿⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⠉⠃⠛⢋⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣈⠁⠀⣉⣀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⣧⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡼⠃⣴⠂⠂⢠⠏⢠⣇⡴⠒⢺⠋⢠⢷⠀⢲⡖⠀⡷⠀⠀⠀⡖⠈⡇⡸⣇⢰⣦⡻⠘⢻⠉⢹⣠⢸⠃⠀⢠⣆⠭⡀⠰⢷⠀⣧⡸
⠀⠀⠀⠀⠀⠀⣇⠀⢻⣀⡄⢸⡀⠈⡿⡄⠀⠸⠀⡟⢺⣀⣸⣀⡀⣧⣤⠀⠀⡟⠀⠠⠋⢻⠨⡟⢇⠀⠸⠀⠀⡕⡺⠀⠀⠸⠁⡪⠁⠟⢻⠀⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡈⠡⢤⠤⠉⡒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠞⠉⢔⢆⡈⠄⢀⢜⠢⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣒⠀⠀⠈⠆⠁⠋⡔⣁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢰⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⢉⣱⣢⢶⡐⠖⠀⠀⠩⢠
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠳⠛⠟⠋⠉⠀⢸⠑⢌⢄⢀⠎⠌
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡄⠠⢋⡡⠊
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠋
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡆⡤⢄⣀⣀⠠⠤⠀⠤⣀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠀⠀⠀⠀⠀⠂⠁⠙⠍⠒⠀⠀⠒⠉⠀⠀⠀⠀⠀⠈⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣦⡇⠀⠀⠐⠀⠠⠐⠣⡀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⢩⢡⠀⠀⢂⠀⠀⠀⠀⠁⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠀⠠⠀⠀⠀⡀⠄⠁⠀⢠⠤⠤⠄⠑⠀⠀⠀⡤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⡄⠀⠀⠀⠁⠁⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀⠀⢀⠀⠈⠐⠠⣴⡀⠀⠀⠀⠐⠀⠀⠀⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⠀⠀⠠⠁⢀⠜⠂⠄⠀⡅⠀⠀⠀⠀⠀⠀⢸⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⡄⠀⠀⠰⠂⠈⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇⠀⠀⠀⠣⢀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⢠⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠊⠊⠀⠀⠀⠀⠀⠀⠀⡈⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠢⣉⠓⠲⠦⠤⠤⠤⠶⠒⣋⡡⠔⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠉⠉⠐⠒⠒⠒⠈⠉⠀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠒⠒⠒⠋⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡄⢰⣿⣦⠀⣰⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠚⠛⣿⣛⣿⣿⣿⡿⣿⣿⣿⣿⣿⡟⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠶⠤⠤⠂⠀⠲⣟⠻⣿⡿⠿⣉⠐⠒⢦⣝⢿⣿⣿⣿⢸⣿⠇⠳⡄
⠀⠀⠀⠀⠀⠀⠒⢲⠠⣀⣀⣀⠀⠀⠀⠈⠉⠉⠉⡁⠉⠀⢨⣉⠉⠉⠙⠟⠿⠏⢛⢣⣤⣠⣿
⠀⠀⠀⠀⠀⣿⠀⠸⣄⡙⠟⠛⢿⣧⣄⢠⣄⣠⣼⠇⠈⠁⠀⠈⠳⢦⣤⢽⣔⡄⠈⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠛⠶⠾⠻⠛⢋⠲⣌⠻⠿⢞⡉⠉⠀⠀⠀⠈⣿⠶⠖⠀⢸⣿⣷⠈⡽⣹⣿⠇
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠑⠌⠛⠛⢋⣠⣤⡀⠀⠀⠀⠈⢑⣠⡄⣼⣿⣿⡆⢸⣿⡟⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠘⣤⠲⣦⠀⠀⠀⠀⠀⠘⠛⠁⠈⠉⠀⠀⠀⠉⢉⠉⡰⠃⣽⣿⠇⠸⣿⣧⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢯⣀⣤⡀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠻⠞⠧⡴⢛⣿⠈⠳⣌⣹⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡿⢱⣿⠀⠀⠀⠀⠀⠁⣿⡿⠆⠀⠀⠀⠀⠀⡟⠁⣿⣾⠇⠙⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⡽⠃⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠿⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠙⠆⠐⠆⠑⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣤⢾⣋
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠃⣀⣤⣤⣄⣀⣀⡤⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠈⣧⡀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠘⠿⠿⠋⠀⠀⠀⢠⡔⠒⠉⠉⠉⠉⢉⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⣹⠉⠙⠛⠛⠛⠋⠉⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠠⠶⠶⣏⠘⠀⠀⠀⠀⠀⣀⠀⠀⠗⠚⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠈⢻⡅⣀⣙⠀⠏⣩⡟⣁⢀⡴⠋⠁⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⡆⠀⣖⡚⠇⢹⣿⣇⠀⠁⣛⡟⢃⡴⢊⡴⢧⠀⢀⣠⠞⣩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡾⠁⠀⠀⠙⣿⣾⣿⣿⡆⠘⣻⣶⣫⡴⢋⣤⡾⠶⣫⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣦⡄⢀⡾⠁⣿⠀⠀⠀⠀⠀⢨⣿⣿⣭⠀⣀⠀⣻⣟⠶⠋⣡⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡇⢹⡾⠁⠾⣧⣀⡀⠀⠀⠀⠈⣟⣛⣋⠀⡈⢙⡛⡋⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⠀⠀⠠⣬⣭⣿⡄⠀⠀⠈⣿⣿⠾⠿⠓⠾⢷⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠰⢤⣈⣹⠀⠀⠀⠙⠿⠶⠶⠶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣀⣀⣀⣈⠉⣳
⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣰⡏⠀⢈⣥⠞⠋
⠀⠀⠀⠀⣿⠃⠀⠀⠀⢀⣴⠟⠀⠀⠈
⠀⠀⣴⢶⣯⠀⠀⠀⢶⡟⠁
⠀⠀⢰⡞⣻⣷⣀⠀⠘⠃⣶⡄
⠀⠀⠀⠉⣅⣻⡿⣿⢋⣼⣏⠁
⠀⠀⠀⠀⠙⠉⢠⣿⡆⠙⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠴⠒⠀⠲⠄⠀⠀⠀⢰⠄⠀⠀⠀⠂⠀⠾⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⣰
⠀⠀⠀⠀⢀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢠⣀⠁⠀⣀⣀⣤⠄
⠀⠀⠀⠀⢸⠄⠄⠋⠈⢷⡆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⡟⠋
⠀⠀⠀⠀⢸⣶⠀⠀⠔⣻⡇⠀⠀⢠⣾⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⢶⣿⠀⠀⠀⠀⠀⠀⠀⠈⢛⡛⠁⠀⠀⠀⠐⢶⣀⢀⣠⡿⠂
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠚⠁⠀⠀⠘⣿⣿⣿⡾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⢠⣾⡄⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠁⠀⠀⠀⠀⡈⡀⠀⢀⣾⣖⣺⣿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠠⠀⠀⠀⠀⢡⠀⠀⠀⠉⠉⠀⣐⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠴⠦
⠀⠀⠀⠀⠘⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠐⠲⠀⠀⠀⢐⣲⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠦⢶⠄
⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠀⠀⠀⢹⢿⣶⣶⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠆⠀⠁⠀⠀⠀⠀⠠⠄⣀⠤⠒⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢟⣻⠿⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠀⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠃
⠀⠀⠀⢀⠀⠀⠾⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠁⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠠⣤⠀⢀⣀⠀⠀⠀⢀⢠⣬⡁
⠀⠀⠀⠀⠀⠀⠴⣶⣀⣀⠀⢻⡏⠀⠀⠸⡄⠘⠂⠘⣷⡶⠀⢰⣾⠁⠀⣤⣀⡄⠀⢉⣀⣀⡀⠀⠸⠿⠉⠁
⠀⠀⠀⢈⠃⠀⠀⠘⠿⠃⠀⣿⣧⠀⠀⣰⣶⣶⠀⠘⢿⣧⠀⢸⣿⠀⠀⣿⣹⡇⠀⣿⣿⣿⣷⠀⢸⣹⡆
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠹⣿⡿⠀⠀⠈⠀⠀⠸⠟⠀⠀⣷⣾⡇⠀⢿⣿⣿⡟⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⡀⠀⣤⣤⢄⢰⣶⡾⠓⠀⢀⠲⠀⣠⢤⣤⣤
⠀⠰⣶⣶⣲⠀⣿⣿⣿⢀⣀⣀⣀⠀⣤⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⠀⠘⣿⡇⠀⣿⣿⡇⠀⢧⢾⢸⠁
⠀⠀⠈⠉⠁⠀⣿⣿⣿⠀⠉⠋⠁⠀⡁⠀⠷⠦⠭⢀⣿⣿⣿⡆⠀⣿⣿⡤⠀⠙⠃⠀⡿⠿⠇⠀⠸⠿⠞

⠀⠀⠀⢠⣤⠀⣀⣀⣀⡀⢀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⢀⣤
⠀⢀⣴⣾⣇⣸⣛⣛⣛⣃⢘⡂⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠻⡿⠃⣭⣭⣭⣭⣭⠈⣅⠀⠀⠀⢸⣿⡟⠀⣀⣀⠀⠀⠀⠀⠀⠈⡆⢰⡆⠀⢰⠀⣰⢿⡄
⠀⠀⠀⠂⠀⣛⣛⣛⣛⣛⠐⡋⢲⣶⣶⢸⣿⡇⠀⢿⡯⠀⠀⠘⠀⠀⠀⡇⢸⡇⠀⠈⠀⣿⣶⡇⠘⠿⡿⠖
⠀⠀⠀⠀⠀⢹⣛⣛⣛⣛⢘⡃⠀⠉⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⡁⠆⠀⠀⠀⠀⠀⠠⢄⡠⢀⡨⠄⠲⠆⡲⠀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠁⠶⠀⠚⠛⠛⠀⢀⡠⠗⠀⠀⠀⠀⠐⠃⠚⠒⠛⠓⠀⠀⠀⠀⠀⠀⠈
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠔⠁⠀⠀⡀⠀⣁⡀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠈⢁⡄⢢
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠⣒⠒⠂⠀⠀⠀⠀⠀⠀⠈⠸⠀⠒⠀⠄⠀⠐⠀⠀⠀⠀⢀⣀⠞⠀⣠⠔⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠞⠁⠀⠀⠀⠑⠀⠀⠹⠦⡤⠀⠀⠀⠀⠠⠀⠀⠀⠀⢒⠆⡴⠁⠠⠺⠗⠀⠀⢈⣆⠆⠀⠀⠀⠁⠀⠀⠰⣛
⠐⣤⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⢄⠀⠀⠀⠈⣇⠀⠀⠀⢠⠀⠤⠴⠿⠊⠀⠀⠀⠀⠀⣇⠀⠀⠹⠀⠀⠐
⠀⢸⠀⠀⠀⠔⢀⡐⢢⠄⠑⠀⠐⠚⠃⠀⠀⠀⠀⠀⡅⠀⠀⠀⢰⠀⠒⠳⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠉⠀⠠⠘⠀⠀⠰
⠀⠸⠀⠀⠀⠀⢀⠃⠀⠀⠀⠂⠒⠒⠀⠐⢄⠀⠘⠂⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⢶⠀⠀⠀⠀⠀⡒⠤⣄⣀
⠂⡄⠀⠀⠀⠀⣸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠙⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⡇⠀⠀⠀⠀⠸⡈⠁
⠄⠁⠀⠀⠀⠐⠓⢦⡀⠀⠈⠁⠀⠀⠀⠒⠋⡀⠀⠀⠹⠆⠀⢀⡀⠘⠇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣆⠄⠀⠂⡄⠀⠀⢣⠀⠀⠈⠀⠀⠀⠀⠊⠀⠀⠀⢠⡄⠀⠀⠡⠗⠢⠄⢀⣠⠤⠂⠀⠀⠀⠀⠀⠈⣗⠰⡀⠀⢰⣶⡂⠀⠀⠀⠊⠶⠀⠀⢄
⣀⠀⠀⠀⠈⠉⠀⠐⠀⠀⢠⠆⠀⠀⠀⡆⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠸⠒⠉⠀⠀⣀⢀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠈⠃⠉⠀⠀⠀⠀⣤
⠙⠒⠄⠀⣀⣀⣀⣀⠀⡴⠃⠀⠀⠀⠀⠐⣝⠦⠀⡀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⣄⠂⠨⠛⠀⠐⡄⠢⠀⠀⠖⠋⡠
⠀⠀⠀⠀⠁⠈⠁⠀⢳⠁⠀⠀⠀⠀⠀⠀⠈⠐⠉⠁⠀⠀⠀⠀⠀⠈⠠⠒⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠃
⠤⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣰⣁⠐⠄⣀⠀⠈⠒⠬⠭⠒⠐⠈⠁⡔⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠐⢄⠦
⠑⠙⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡤⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠡⢄⠉⠲⠤⠀⠀⠀⠀⠀⠊⠀⠀⠠⠀⠀⠀⠀⠂⠀⢰⣧⠀⠀⠈
⡀⠀⠀⠀⠀⠀⠏⣀⠀⠤⠶⠼⡄⠀⠠⡦⠀⠀⡀⠠⢂⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠉⢧
⠀⡠⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠂⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠙⠶⡔⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠘⢟⡦⡀⠄⠞
⠀⠀⠀⠀⠄⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⡪⠀⠀⠀⠀⠀⠀⠀⠀⣰⠈⠥⠔⠃⠒⠂⠀⠀⠀⡤⢤⡤⠒⡀⠞⠀⠀⠀⣀⡀⠀⠀⠑
⠀⠀⠀⠞⠀⠀⠈⠀⠀⢡⡀⠀⠀⠀⠓⠁⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢀⠀⠀⠀⠻⠆⡀⠀⠀⠀⠀⠙⠀⠀⠄⠠⠄⠁⠀⠀⠀⠀⠀⣀⠀⠰
⢀⣠⠄⠀⠀⠀⠀⠀⠀⢀⠩⠀⠀⢰⣤⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠂⠒⠊⠉⠀⠈
⠀⠀⠀⠁⠀⢸⡆⠀⣀⠀⠀⠀⠀⠉⠋⠁⠀⠐⢄⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⢄⣀⣀⠀⡔⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⡻⠶⢦⡀⠀⢠⣀
⠀⠀⠀⠀⠀⠀⠁⠀⢿⡄⠀⠀⢀⣀⡀⠀⠀⡀⠀⠀⡀⠀⡀⠐⠚⠳⣄⠀⠈⠐⠛⠢⡸⠀⠀⠀⠀⠘⠉⠂⠀⠀⠀⠀⡀⠀⠀⢀⠀⠈⠂⢈⡄
⠀⠀⢰⢀⠀⠀⢐⠀⠀⠀⠀⡰⠋⠀⠐⢄⠄⠀⠀⠀⠀⠀⠑⠠⡀⠀⠈⠳⡀⠀⠀⠀⠀⠐⠀⠁⠀⢀⢀⠀⠀⠀⠀⠀⠑⠺⠀⠀⠀⠈⠂
⠀⠀⠈⠛⠓⠢⠎⠀⠀⠀⠞⠟⠀⠀⣠⣿⠆⢀⠀⠀⠀⠀⠀⠀⣀⠙⠲⢄⠘⠢⠀⠀⠀⢀⡄⠀⠔⠋⠀⠃⠀⠲⠞⢃⠤⠂⠀⠀⠀⠀⠀⠐
⠂⠀⠀⠄⠈⠢⠠⠀⠀⠀⠀⠠⠄⠊⠉⠁⠀⠹⡟⠀⠀⠀⠀⢀⡽⠀⠀⠀⠉⠰⠐⠠⡔⠀⠑⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠘⣆⠀⠀⠐
⠀⡀⠀⠀⠀⠀⠀⠛⠀⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠀⢀⠀⠀⠁⠀⠀⠣⡀⠈⠉⠁⠀⣠⡾⠟
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠈⠋⠢⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⠂⠀⢠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⢀⣴⣿⣿⣿⣿⣿⡀⠀⣹⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣆⠂⣼⣿⣿⣿⣿⣿⡯⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⡟⣡⣼⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⢿⡆
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⠋⣙⠻⣿⣿⣿⣿⠟⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⠁⠉⠛⠋⠀⠀⠀⠀⠀⠈⡙⢂⠆
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣧⣈⡀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠈⠉⠉⠉⠀⠀⠀⣿⠿⠿⠋⠉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠂⢐⡴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⣐⡞⢤⡤⠶⠀⠀⠀⠀⢸⢇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⢄⡀⠀⣀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢱⣦⣄⣀⣠⡴⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠋⠉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠧⠀⠀⠒⠂⠀⠒⠀⠄⡀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⡄⠀⢀⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⣠⣿⡿⠀⠀⠸⣿⣿⡇⠀⠀⠀⢤⢾⣧⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡅⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠿⣿⡿⠀⢀⣴⣦⡄⠀⣴⣶⡄⢠⣄⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡙⢣⣤⣄⡀⠀⠀⠀⠈⠻⠿⠟⠀⠻⡿⠇⠘⢿⡇⠀⠐⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣼⠿⠿⠃⠒⠈⠀⠈⠋⢠⡄⠀⠀⢠⣶⣄⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠋⣆⣰⡎⠀⠀⠀⠀⠀⠀⢸⣧⣄⠀⠸⣿⠟⠀⣾⣿⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⢠⣴⣤⠀⠙⠁⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠻⠿⠟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⢀⣤⡶⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⣰⡄⠉⠁⠀⠈⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠿⠇⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣦⣶⣴⣶⣦⣴⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶
⣿⣿⣏⣀⣁⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⢀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣗⡀
⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⢠⠄⠀⠀⠙⢶⣄⠀⢀⠀⠀⠀⠀⡁⠀⠀⠀⠈⠉⠙⣿
⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠸⠀⠀⠀⠀⢸⡞⠀⢸⣤⣄⠛⢻⡇⠀⠀⠀⠀⠀⠀⡏⠀⢠⣄⠀⢀⢠⡄
⠀⠀⠀⠸⠿⠿⠿⠿⠃⠀⠀⠀⢂⠀⠀⠀⡾⠁⠀⠈⣇⣀⣄⣨⠁⠀⠀⠀⠀⠀⢠⡇⠀⠸⣿⣀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠙⠛⠁⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⠈⠉⠉⠁⠀⠀⠑⠛⠛⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠉⠁⠀⠀⠈⠁⠒⠤⡀
⠀⠀⠀⢀⣀⡀⠀⡠⠊⣁⣀⣀⠀⠐⠒⠤⠤⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡀
⠀⠀⠀⡥⠄⡶⠉⠀⠢⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢉⠄⠀⠀⠀⠈⠑⢍⠁⠒⠠⣀
⠀⠀⠀⠀⠰⢡⠀⠀⠀⠙⡆⠀⡗⠒⠠⠴⠤⠤⠤⠤⠽⠉⠐⢶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠖⠠⠃⠀⣴⠂⠀⠀⠀⠀⠑⡀⠀⠈⢳⣄⣀
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠙⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣂⢀⡁⢀⡌⡇⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠈⢯⠉⢆
⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈⠁⠀⢀⠖⠒⠒⠀⠓⠀⠉⡏⢑⡄⠀⠀⠀⠀⡍⠉⠀⠀⠀⠀⠈⠙⠃⠒⠀⢤⢀⣸⠀⠀⠀⠀⣼⠀⢨
⠀⠀⠀⠀⠈⠆⠀⠀⡜⠉⠱⠉⠀⠀⠀⠀⠀⠀⡀⢼⠀⠐⣆⠀⡤⠴⠾⣏⡁⠁⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⠰⢄⠀⠀⠀⠀⢠⠀⠈
⠀⠀⠀⠀⠀⠈⢆⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠣⣼⣆⠬⠁⣰⡇⠙⠢⠴⡖⠁⠀⠀⠀⠘⠈⠀⡄⠀⠀⠀⠓⠀⠀⠀⠀⠘⠤⠀⢄⠀⠀⠀⡌⢰
⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢚⡩⠋⠉⡆⠀⠸⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠜⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠂⡄⠀⠀⠲⡒⠉⡇⠀⢀⠜⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⢄⡠⠐⠈⠉⢘⠅⠀⠀⠀⠀⠀⠀⠀⢈⠦⠻⠀⠀⠈⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠒⠀⢤⣿⡦⣤⠴⠋⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠎⠀⡠⠶⣶⢻⠀⠀⠀⣀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠒⠢⠼⠛⠉⠱⡀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠈⡎⠉⣿⠁⠀⠀⣸⠦⡀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢰⠁⠀⠀⠀⠀⠀⡸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⣇⠀⠘⠳⠶⠚⠋⠀⠈⢢⠀⠀⠀⠑⢄⡀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⠄⠀⠀⠒⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⣼⠀⠀⠀⠀⣀⣀⠀⠀⢡⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⣂⡀⢰⡀⣀⠤⠚⡅⠀⠀⡠⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣟⠀⠁⠀⠀⠀⠀⣀⠬⠦⠞⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡨⠋⠉⠘⠃⠉⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠲⠶⣐⣂⣙⢲⣖⣖⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠈⠀⠔⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠒⠀⢠⢠⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⣉⣉⡉⠈⠉⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠸⠖⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⢀⣀⢀⣀⣀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⣈⢉⣉⣀⡀⠬⢥⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠸⠀⠀⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⠀⠀⢆⡀⣙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠤⠴⠃⠀⠀⡗⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠄⠤⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⠀⣠⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠸⠀⠟⠰⠋⠐⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠻⣿⣇⠀⢈⣀⣤⣴⣤⣤⣤⣤⣴⣶⣶⣤⣄⣁⠀⠀⠀⠀⣤⣦
⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣿⣯⡿⠀⠀⠀⣼⡟⡿
⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⣿⡟⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣴⠆⣿⣷⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⠇⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⣸⡿⠀⢿⣇
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠘⠛⢠⣤⠀⢀⡀⢀⡀⠉⢻⡿⠀⠀⠀⠀⢠⢀⣿⠃⢠⢻⣿⠈⠁
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣿⢸⢇⡟⡽⢸⢇⡄⢸⣇⣀⣴⣦⠀⡖⢸⡇⢠⠃⠀⣿⣦⠶⠄
⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⣸⡟⣾⢼⡇⠁⣼⡟⠑⣿⠉⣼⢣⣿⠾⡷⢻⡴⠃⣠⢾⣿
⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⢠⡟⠷⠃⠘⢧⡴⣿⢧⡴⠻⠴⠋⠁⠁⠀⠐⠀⠀⣸⠋⢸⡿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⠋⢠⣀⡴⢶⡀⠀⠃⣴⡄⠶⢺⡟⣡⠀⢠⣾⠂⠀⣏⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠀⢸⣧⡞⣷⢈⣻⢃⣾⢀⣿⠔⣹⣿⠴⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣠⡟⢸⡟⢻⠎⠻⠊⠛⠋⣵⠋⣿⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⢀⡴⢠⡆⣄⠀⠰⣇⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⢿⡇⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⢀⢋⠀⠰⠄
⠀⠀⠀⠀⠀⠀⢀⡀⢤⠐⢒⠊⠁⠀⢡⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠴⠒⠴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⢁⡈⡒⠀⠠
⠀⠀⠀⢠⠊⢹⠀⠀⣈⠠⠼⠐⠲⠄⠤⠆⠀⠀⠀⠀⠀⠑⠀⢀⠀⠂⠀⠀⡀⠀⠀⠀⠙⠲⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠛⠉⡟⠀⢀⠈
⠀⠀⠀⠈⠒⠊⠉⠁⠀⠀⠀⠀⠀⠧⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠈⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣖⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢤⠅⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣩⠀⠙⡤⠤⡤⠤⠤⡤⠤⠤⠄⢀⡀⣀⠀⠀⠠⠠⠤⠄⠐⠒⢌⡀⠀⠀⡀⠄⠀⠀⠠⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠨⠏⠌⠙⠒⠏⠉⢳⠉⠁⠈⠁⠉⠁⠐⠒⠒⠘⠋⠥⠹⠗⡠⢄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⣧⢝⡐⠒⠒⠂⢀⠼⠦⠴⠦⡤⠤⠤⡤⠤⠤⠤⠶⡂⠐⠒⠒⣂⠯⡼⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠐⠢⣔⠁⠀⠀⠀⠀⣈⠗⢏⡀⠀⠀⠀⠀⠈⣢⠒⠉⠀⠀⠘⡇⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠄⡀⠀⠠⠊⠀⠉⠢⢄⡠⠊⠁⠀⠀⠉⠢⡀⡠⠔⠉⠀⠑⢄⠀⠀⣀⡆⠀⠀⠀⠀⢄⠀⠀⠀⡄⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⡑⠣⣀⠀⠀⢀⠊⠑⠦⡀⠀⠀⢀⠴⠋⠢⡀⠀⠀⢀⡨⢶⠉⠀⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⠀⠀⠑⣔⠁⠀⠀⠀⠈⢢⣔⠁⠀⠀⠀⢙⣤⡔⠁⠀⠀⢣⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠈⡶⢄⠀⠀⢀⠊⠀⠑⢄⡀⠀⡔⠁⠀⠱⡀⢀⠔⠁⠀⠑⡄⠀⠀⡠⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠉⢢⡃⠀⠀⠀⠀⡝⠪⡀⠀⠀⢀⠜⢣⠀⠀⠀⠀⢘⡔⠈⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠃⠈⠒⢄⢀⠌⠀⠀⠈⢢⡔⠁⠀⠀⠱⡀⣠⠞⠁⢡⢀⠜⢃⠀⡀⠀⠀⠀⠀⠀⠀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⡳⡀⠀⠀⠀⠜⠢⠀⠀⠀⢀⣽⠀⠀⣀⠔⠁⠀⠈⠅⠂⠅⠀⠀⠀⠨⠅⠂⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠀⠬⠦⢀⣎⣀⣀⣱⡀⠠⠎⠄⠓⠉⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠐⠁


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢠⡟⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠤⠤⡞
⢀⠔⠁⠁⠀⠉⠁⠀⠉⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⡄⠀⠀⠀⠀⢀⠞⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡇
⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⡇⠀⠀⠀⠀⣾⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠀⡇
⠀⠀⡏⠉⠑⠀⠚⠒⠊⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠙⣆⠀⠀⠀⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣷⡆⠀⡇
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⡓⡄⢣⠀⠀⠀⠀⠀⠀⢸⢠⣤⣤⣤⣤⢸⠀⠀⠀⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⢿⡇⠀⢧
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⣂⠇⡸⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣿⣿⢸⠀⠀⠀⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⡞⣸⠁⠀⠸⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣡⠔⠁⠀⠀⠀⠀⠀⠀⠘⡟⠻⠿⠿⠛⡟⠀⠀⠀⣿⠉⠉⠁⠀⢸⠀⠀⠀⠀⠀⢀⡼⣰⢃⠀⠀⠠⡹⡄
⠀⠀⣇⠀⠀⠀⠀⠀⠀⢨⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⡇⠀⠀⠀⢿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡞⢰⠇⠎⠀⠀⠀⢱⠘
⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣇⣾⢸⠀⠀⣀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣰⣶⣦⡀⠀⠀⡆⢀⣀⣀⣀⣀⣀⠀⡆⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⠠⠤⠄⠠⠤⠄⠇⠀⠀⠈⢿⣟⣏⠁⠀⠉⠙⣿⡿⠀⠀⢃⢸⣯⣟⣿⣿⣿⢀⠇⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠻⣿⣦⣤⣤⠎⠙⠁⠀⠀⠈⠢⡙⢿⣿⠟⡡⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⡖⠉⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⢸
⡇⠐⠒⠀⢨⠀⠀⢸⠀⠀⡤⠚⠀⣼⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠐⣾⣿⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⣿⠈⡇⠀⠀⠀⢸
⠀⠀⠀⣠⡇⠀⠀⠀⡀⠀⣠⣾⣿⣿⠀⠀⠀⠀⢀⣀⣤⣼⣤⣄⣀⠀⠀⠀⠀⠀⡠⠴⠶⡷⠶⠤⡀⠀⠀⠀⡧⠺⢶⣄⣀⡤⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⢸⣿⡿⢛⣫⣻⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢠⠿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡋
⠀⣹⣷⡄⠀⠀⠀⠀⠀⠧⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡀⠀⡇
⠀⠘⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢳⡀⢂
⠀⠀⠈⠛⠁⠀⠀⠀⠻⣶⣶⠏⠀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠳⠀⢣⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣴⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠾⠿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣀⣳⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠉⠁⠀⠀⣸⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡀⠀⢀⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣇⠀⣼⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣰⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠙⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⢁⡀⠀⠙⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠿⠂⠀⠀⠙⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠹⠿⠃
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢐⣤⣤⣤
⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠛⠉⠙⠋
⣿⠿⠿⠿⢿⢟⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣛⣛⣻⣿⣛⣛⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⢟⣋⠬⠭⠶⠒⠒⠒⠒⠒⠒⠮⠭⢭⣛⡻⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢟⡫⠖⠊⠁⠀⠀⠀⢀⡀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠉⠛⠲⢝⡻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣫⠞⠉⠀⠀⡀⠠⢶⡟⠀⣯⣽⡆⢺⠀⡾⠀⠀⠀⢠⡶⢦⠀⠀⠀⠉⠳⢍⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⡱⠊⠀⠀⣀⠐⣆⣧⣄⠀⢷⠀⠿⠀⠃⠘⠀⠛⠒⠀⠀⡟⠛⢉⣴⡒⡆⠀⠀⠀⠑⢎⠻⣥⡀
⠀⠀⠀⠀⠀⠀⣰⡿⣫⠞⠀⠀⠀⢾⡁⠀⡘⠧⠉⠀⠀⣀⡤⠤⠄⣐⡒⠦⠤⠄⣀⡀⠀⠘⠁⡽⢃⣴⠓⣄⠀⠀⠳⣝⢿⣆
⠀⠀⠀⠀⠀⣼⡿⡱⠃⠀⢠⡖⠲⣬⡛⠒⠁⢀⡤⢚⣭⡶⠞⠋⠛⠙⠛⠛⠛⠷⢶⣭⣓⢤⡀⠀⠋⣸⠋⠁⢤⣄⠀⠘⢎⢻⣧
⠀⠀⠀⠀⣸⡿⡸⠁⠀⣠⡀⠻⢦⡾⠁⢀⡔⣩⡾⠋⠁⠐⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣅⠂⡀⠀⢠⠖⠋⠙⣀⠀⠈⣇⢻⣧
⠀⠀⠀⢰⣿⢱⠃⠀⠀⢷⣄⣠⡇⠀⣠⢫⡾⠋⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⢀⡀⣀⡀⠀⠀⠘⢷⡙⡄⠀⢀⣀⣼⣋⡀⠀⠘⡎⣿⡆
⠀⠀⠀⣾⡇⡏⠀⠀⠀⠀⠈⠉⠀⢰⢣⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣤⣟⠯⢿⣧⡆⠀⠀⠈⢿⡜⡆⠀⠁⠀⠉⠀⠀⠀⢹⢸⣷
⠀⠀⢠⣿⢹⠃⠀⠀⠀⠀⠀⠀⠀⡆⣾⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣟⣿⣷⡚⣿⠅⠀⠀⠀⠘⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⡊⣯⡀
⠀⠀⢸⢿⢸⠀⠀⢤⣴⣀⠀⠀⢰⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠙⠋⠀⠀⠀⠀⠀⠀⣿⡘⡄⠀⠀⣀⣦⡤⠀⠀⡇⣿⡇
⠀⠀⢸⣿⢸⠀⠀⠚⠻⠉⠀⠀⠸⡜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢣⠁⠀⠀⠉⠟⠓⠀⠀⡇⣿⡇
⠀⠀⠈⣿⣸⡄⠀⠀⠀⠀⠀⠀⠀⣇⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣸⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⠃
⠀⠀⠀⢿⣇⣇⠀⠀⠀⢀⣀⣀⠀⠸⡜⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⠇⠀⣀⠀⠀⠀⠀⠀⣸⢸⡿
⠀⠀⠀⠸⣿⡸⡄⠀⠀⣟⠁⠨⠇⠀⠙⣜⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡾⣣⠋⠀⣄⣙⣆⡀⠀⠀⢠⢇⣿⠇
⠀⠀⠀⠀⢻⣧⢻⡀⠀⠈⢠⠖⠛⣷⠀⠈⠣⣙⢷⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⣠⡾⣋⠜⠁⢀⣾⡁⠁⠈⠁⠀⢀⡞⣾⡟
⠀⠀⠀⠀⠀⢻⣷⡱⡄⠀⠘⠧⠞⣡⠴⢦⡀⠈⠓⢭⣛⠷⢦⣤⣤⣄⣉⣥⣤⡴⠾⣛⡥⠚⠁⢀⡴⣌⠀⠙⠲⠀⠀⢠⠎⠄⠛
⠀⠀⠀⠀⠀⠀⠹⣷⣜⢄⠀⠀⠀⣯⡀⠈⣴⣃⡤⣀⠈⠉⠓⠒⠲⠍⠀⠐⠒⠚⠉⠁⠀⢠⢤⡈⢷⡟⠲⠄⠀⠀⡠⣡⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡱⢄⠀⠀⠀⠾⢩⡇⠀⣩⠛⢂⡴⣄⢀⡄⢠⡄⠀⠀⢺⣋⡇⢸⡞⠻⠆⠉⠀⠀⡠⢊⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣕⠦⣀⠀⠈⠀⠐⠏⠀⡿⠓⡶⢸⡇⢸⠀⠀⠀⠈⣯⠀⠀⠉⠀⠀⣀⡴⣫⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣮⣕⠦⣤⣀⠀⠀⠀⠈⠁⠈⠁⠈⠉⠁⠀⠀⠀⠀⣀⣠⢴⣪⣵⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣮⣭⣓⣒⡲⠤⠤⠤⠤⠤⠤⢶⣒⣊⣭⣵⡔⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠆⠀⠀⠰⠀⠀⡌⠉⠉⠉⠉⠉⠉⠉⠉⣱⠀⠁⠀⠀⠀⠀⢗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠚⠴⠿
⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢨⠁⠂⠀⢠⡇⠀⠀⠀⠀⠡⠀⠀⠲⢦⠄⠀⠀⠀⠀⠶⣾
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠎⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⠀⠀⠘⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠂⠀⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠌⠀⠀⠀⠑⠀⢀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠄⠄⠐⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄
⠀⠀⠀⠀⠰⠀⣀⣄⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡝⠃⠀⠀⡀⠰⠂⢀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⠃⠄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠸⠁⠆⠀⠀⠠⠄⠟⠀⠀⠀⠀⠀⠀⠀⢩⠄⠀⠠⡝⠓⡐⠀⠀⠀⠀⠀⠀⠖⠄⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⣤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⡦⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉
⣿⣿⣿⠿⣿⠿⢿⣿⣿⡿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣷⣮⣶⣷⣶⣿⣶⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠻⠀⠀⠀⠀⠀⣀⡩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠉⠁⠟⠀⠀⠀⠘⠠⢤⣤⢤⠜⠃⠀⠀⠙⠃⠀⢠⠴⣯⠈
⠀⠀⠀⠀⠀⠈⢆⠀⡬⠁⠀⠀⠀⢰⡦⠤⠀⠀⠄⣴⠀⠀⢀⠀⠀⠀⠘⡆⠀⠀⠀⢻⡾⠿⣀⠀⠀⠀⠀⠀⠈⠂⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⠀⠀⠘⠇⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠼⠀⠀⠀⠀⠐⠺⠉⠀⠀⠀⠀⠧⡀⣈
⠀⠀⠀⠀⠀⠀⠀⢐⠂⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⠖⠀⠀⠀⠀⠀⣓⡀⠀⠀⠀⠀⠷⠆⢀⠀⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⢩⠙⢢
⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠊⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⢏⡇
⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠶⠿⠶⠦⣴⡀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠀⠀⠈⢄⠀⠀⠀⢠⣴⠃
⠀⠀⠀⠀⠀⢀⣞⢑⡀⠀⠀⣈⣱⠀⠀⠀⠀⠀⠐⠧⠀⠀⠀⢻⠃⠀⠀⠈⠀⠄⢀⢠⠀⢸⠀⠀⠀⠀⠁⠲⡄⠊⠁
⠀⠀⠀⠀⠀⣨⡉⠲⠅⠠⠀⢨⣟⠀⠀⠆⠀⠀⠀⠐⣴⠀⡜⠀⠀⠀⠀⠈⠁⢰⡀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢹⣇⣀⣀⡀⠀⢸⣿⠀⠄⠘⠀⠀⠀⠀⠛⠀⠃⠀⠀⠀⠀⠀⠰⠐⠤⠚⠀⠊
⠀⠀⠀⠀⠀⠀⠙⠦⠧⠤⠤⠼⠋⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠚⠀⠀⠀⠀⠀⠲⠤⠴

⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠉⡋
⠀⠀⠀⠄⠰⠄⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣊⣶⣀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠸⣿⠀⠀⠀⠀⠈⣽⣿⡇⠀⠀⠀⠋⢟⣻⠋⠀⠀⠀⠀⠀⠠⠰⠇
⠀⠀⡤⣤⣶⣶⡇⠀⠀⢨⣌⣉⣀⢄⠀⠀⠑⠈⣿⣧⡄⠀⠠⠀⠀⠈⠀⢤⠀⠀⠀⠰⠀⠀⠼⠦
⠀⠀⡇⣬⣭⣽⡇⢰⣤⣾⣿⡷⣦⣾⠀⠁⠶⠶⠾⢿⡇⠀⠀⠈⠁⠀⠀⠈⠀⢀⢶⣾⣾⡶⠀⠚⣷⡀
⠀⠀⡇⣛⣿⣿⡇⢸⣿⢸⣏⣤⣭⣩⠀⠀⢀⣀⣀⣸⡇⠀⠀⠀⠀⢠⣧⠀⠀⢸⢸⣿⠏⠀⠀⠀⢸⡇
⠀⠀⠅⠩⠭⠿⡇⢸⣿⣼⣼⣤⣮⣷⠀⠀⢸⣿⣿⣿⠁⠀⠀⠐⠤⠴⠿⠀⠀⠸⡿⣿⡶⠀⠀⢠⣿⡇
⠀⠀⢀⠆⠐⣄⠀⠘⠛⢻⣿⣟⠛⢻⠀⠀⣰⣠⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠹⣮⣑⢶⣿⣿⠟
⠀⠀⠁⠀⠀⠈⠁⠀⠉⠙⠋⠉⠉⠉⠀⠈⠉⠉⠉⠙⠁⠈⠀⠉⠉⠉⠁⠀⠉⠀⠀⠉⠉⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⡶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠿⠿⠿⠿⠿⠶⢾⣿⠿⠿⢷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡿⠃⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡟
⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠛⠉⠻⣿⠀⠀⠀⢀⣀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⠿⣿⠿⠿⠿⣿⡇
⠙⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⡿⠀⠀⠀⢠⣿⣀⣀⣴⡿⠋⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠃
⠀⠀⠙⢿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣤⣤⣴⠟⢉⣽⡿⠋⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣿
⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⢠⣾⠋⠉⠉⢁⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⢀⣴⠟⠁⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣿⠇⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠉⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠿⠿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡁⠀⠀⠀⠀⣽⡁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠄⠀⠀⠀⢠⣿⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⠿⢸⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢠⣴⣾⣿⣿⣯⣥⣤⣤⣤⣤⣬⣽⣿⣿⣿⣶⣶⡄⠀⠀⠀⠀⠀⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣂⠤⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣀⣀⣀⢀⡞⠕⠁⠀⠀⠀⠈⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⣾⣉⢥⠦⢤⣄⡀⣾⠁⠀⠀⠀⢂⡴⠇⠂⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⡸⣿⠃⣸⣶⣀⠈⣷⢸⡄⠀⠀⢀⢐⣄⡄⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣵⡾⠀⠁⠈⠉⠿⣧⡄⠑⠀⠀⢠⣤⠾⣧⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠸⠉⠊⠓⠒⠒⠀⢈⠑⠒⣻⣿⠶⠀⠀⡇⠐⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡷⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡝⡂⠠⢄⠀⠀⠀⢠⣾⣿⣿⢗⡜⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠁⢇⣀⡃⣤⣴⡟⣿⣿⣏⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢄⣿⠃⣿⢟⡇⣯⣴⡆⠘⠓⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡆⢸⣟⡃⣶⣟⡃⢏⣉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣦⣷⣦⡸⣿⡇⣴⣿⡅⣸⣿⡅⣀⣼⢽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⣿⡷⢾⢜⡻⠶⣬⣭⣥⣬⣥⣈⢻⡷⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣶⣯⣽⣿⣛⣛⣿⣿⣥⣾⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠿⢦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡛⠀⢠⠞⠀⠀⠀⠀⣾⢉⢍⣸⠇⠀⠀⠀⢰⣿⣿⠟⡄⠀⣤⣶⣄⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⢿
⠀⠀⠀⠀⠀⠀⣀⣠⠇⠀⢃⠆⠀⠀⠀⣶⠋⣠⡟⢹⠀⠀⠀⠀⠈⡟⠀⢰⠃⢰⡇⠀⢻⡄⠀⠀⠀⠀⣇⣙⣿⠃⠀⠀⠀⠀⢀⣤⣢⠧⡉⣀⡇
⠀⠀⠀⣾⣿⣿⣿⣿⡾⠷⢿⣦⣀⠀⠀⢼⡳⢁⡤⠃⠀⠀⠀⢀⠎⠈⠚⣇⠀⠸⣷⠁⡿⠀⡴⣶⣤⣄⠘⠋⠀⠉⠒⠦⡀⠀⢸⢀⣷⠶⠿⣦⣾⣶⣶⣦
⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⣼⠿⣿⠀⢠⡋⠉⠛⠒⡄⠀⠀⠀⡜⢀⡇⠀⢻⣎⠉⢁⠀⢱⠞⠤⠛⠞⠿⠀⠀⠀⠀⠀⢸⠇⣰⣮⣿⡟⠀⠀⣾⣿⣻⣿⣿⡂
⠀⢠⣿⣿⣿⣿⣿⣿⡇⢠⣿⣿⣧⠀⢾⣁⣰⡿⠾⢳⡄⠀⠀⣘⡘⡇⠀⡼⢩⢞⡉⢁⣉⠘⡆⢁⣶⣶⡄⠀⠀⠀⢀⡟⢸⣿⣿⢿⣷⠀⣼⣿⣿⣿⣿⣿⡇
⢀⣾⣿⣿⣿⣿⣿⡿⠧⣿⢿⣿⣇⣀⣀⡹⡁⡀⢣⡾⢁⢼⠷⣀⣲⠞⡃⠘⢸⣶⡇⢸⡟⢦⣨⣿⣿⣿⡏⠀⠀⠀⣼⠁⠈⠛⠋⠀⣿⣶⣿⣿⣿⡿⢻⣿⣧
⠈⠻⠿⢿⣿⣿⣶⣶⣶⣶⣿⣿⣿⡱⠊⠙⡱⠐⡈⠓⣁⠔⠃⢀⡇⠀⢙⣠⡆⣽⠀⣏⣵⠿⠟⡏⠹⠸⠀⠀⠀⠀⠸⠀⠀⠀⠛⢺⣿⣟⡋⢉⣿⣿⣿⣿⡿
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠈⠋⠀⠀⡰⠁⡀⠐⠚⡄⠀⠀⢸⡇⡰⣩⢏⢾⡿⢠⣿⣿⣧⠀⢇⢈⣛⡰⠾⣑⣦⣐⣂⡦⠀⠀⣾⣿⣿⣿⣿⣿⣿⡁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠰⢁⢠⠃⠀⢀⢱⠀⠀⢀⡟⢰⠏⡞⢸⣧⠀⢿⣿⣿⡆⠀⢰⠡⠤⠤⣤⠤⠄⡆⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⢃⡇⢸⢰⡆⢸⠀⡇⠀⡜⢀⡟⣸⠃⢸⣿⣧⠸⣿⣿⣷⠀⡇⠀⠀⣴⡟⠀⢰⠇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡎⣸⠀⣿⢸⡇⢸⡄⢻⡜⠀⣼⠁⣿⠀⠈⣿⣿⣧⢹⣿⣿⡷⠁⢠⢞⠟⠀⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⣿⣿⣿⣿⢻⣿⣿⣿⠀⢸⠀⡇⠀⡏⢸⡇⢸⡇⠸⡆⢰⠇⢸⡇⠀⠀⢸⣿⣿⣸⣿⣿⣿⠀⢃⠎⢸⠂⠀⡾⠀⠀⠀⢸⣿⣿⣿⠘⣿⣿⣿⡄
⠀⠀⢸⣿⣿⣿⡏⢸⣿⣿⣿⢀⠃⢸⠇⢸⡇⠘⡇⢸⡇⠀⣧⠾⠀⣿⡇⢀⣀⣀⣿⣿⣿⠿⠿⠿⠓⠚⠒⠋⠓⡒⢳⡶⢲⡤⠸⣿⣿⡟⠀⢿⣿⣿⡇
⠀⠀⣼⣿⣿⣿⠁⠘⣿⣿⣿⡸⠀⣸⠀⢸⡇⠀⡇⢸⣇⠀⣿⡓⠚⠋⡟⠻⠍⣱⢂⡀⠴⣤⣈⣒⣒⣒⣈⣙⠟⠶⢶⣶⣿⡾⢷⣁⣠⣭⣶⢸⣿⣿⣧
⠀⢠⣿⣿⣿⡏⠀⢠⣿⣿⣿⠇⠀⡿⠀⣸⡇⠀⡇⢸⣿⠀⢿⣷⣶⣦⣿⣷⣶⠶⠶⣷⠶⣎⣭⣭⣭⣿⣿⠿⠿⣟⣛⣺⠿⠯⣭⣿⣷⣾⣿⢸⣿⣿⣿
⠀⣸⣿⣿⡿⠁⠀⠘⣿⣿⡟⠀⢸⡇⠀⣿⠁⠀⡇⠈⣿⠀⢸⣷⢸⣿⠙⢻⣿⠿⣛⠛⣿⣯⣽⣿⣷⡞⢻⣿⠉⢹⠀⠀⠀⠀⣿⣿⣿⢰⣿⠀⣿⣿⣿
⠀⣿⣿⣿⠇⠀⠀⠀⣿⣿⠃⠀⢸⠇⠀⣿⠀⠀⡇⠀⣿⡀⢸⣿⣸⣿⠀⣾⠈⢱⡀⡎⣿⣿⣿⣿⣿⣷⢸⣿⣀⡎⠀⠀⠀⠀⣿⣿⡟⢸⣿⠀⣿⣿⡿
⢰⣿⣿⡏⠀⠀⠀⠀⣿⡏⠀⠀⣿⠀⠀⣿⠀⠀⡇⠀⣿⡇⠀⣿⡇⠗⠀⣿⠀⢸⡇⡇⢹⣿⣿⣿⢿⡿⠸⠝⠉⠀⠀⠀⠀⢰⣿⣿⡇⢸⣿⠀⢸⣿⡇
⢸⣿⡿⠀⠀⠀⠀⠀⡿⠀⠀⠀⡟⠀⢠⡿⠀⢸⠃⠀⣿⡇⠀⢿⣿⡒⠊⠙⠦⢼⢇⡖⠋⠛⠻⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠀⢸⣻⠀⢸⣿⡇
⢸⣿⠃⠀⠀⠀⠀⢠⠃⠀⠀⢸⠇⠀⢸⡇⠀⠈⠀⠀⢻⠀⠀⢸⣿⡇⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠁⠀⠀⢿⣿⠄
⠀⠁⠀⠀⠀⠀⠀⠘⠲⠚⠉⠟⣀⣀⡼⠒⠛⠲⢤⣄⣠⠛⠒⠤⠿⠟⠀⠀⠀⢸⢀⡇

⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣾⢿⣶⣶⠀⠈⠁⠀⠀⠀⠀⣿⣿⣿⣇
⢶⣶⣶⣶⣶⣾⣵⣶⠆⠀⠀⠀⠀⠀⢀⣿⣽⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢧⣿⣿⡟
⠀⠙⢮⡻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢻⡟⠀⢀⣤
⠀⠀⠈⠻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠃
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⡀⣴⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣀⣀⣀
⠀⠀⠠⠶⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠖⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠠⠾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠀⠘⠿⠛⠿


⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⣭⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⣴⣿⣧⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣷⡄
⠀⢰⣿⣿⣿⡇⡸⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣧⠀⣻⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⡇⠹⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢿⡿⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⣠⣤
⠀⢸⣿⣿⣿⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠈⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⡇⣿⣿
⠀⠸⠿⠿⠿⠇⠀⠼⠄⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠀⠠⡇⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠸⠿⠿⠏⠀⠀⠀⠿⠿⠿⠿⠇⠿⠿


⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀
⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⢀⡀⣶⢀⡀⣶⢀⡀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⣾⡇⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣶⠄
⠀⢀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣫⣶⣾⣷⠟⢶
⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⢟⣻⣟⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⣯⣀⣀⣀⣀⠀⠀⠀⠀⠀⣾⣶⣿⣿⣿⣿⠀⢸
⠀⢸⣿⣿⣿⠀⠀⢀⣤⡄⠀⠀⠀⣷⣄⣀⣀⢸⣿⣿⣿⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠉⢹⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡗⠋
⠀⠘⠿⠿⠿⠈⠻⠿⠛⠀⠀⠀⠀⠈⠻⠿⠿⠷⠾⠷⠿⠿⠿⠇⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⢠⡆⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢫⣭⣙⣩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣀⢁⣂⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠶⠶⣴⡏⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡶⠛⠿⠻⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠟⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠀⢣⡃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠆⡆⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⡌⡈⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠊⠘⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠰⢠⠅⠀⠀⠀⠐⣷⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢠⢢⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⡄⡘⠀⠀⠀⠀⠀⠫⠆⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠁⠀⠀⠀⠀⠀⠸⢁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠀⠘
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡆⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢰⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⢦⠦⠤⠐⠒⠀⠐⠂⠤⠤⠒⢒⡠⠃⠀⠀⡇⠈⠢⠤⠤⠤⠤⠔⠂⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠚⠚⠀⠀⠁⠉⠀⠀⠀⠈⠀⠀⠋⠀⠈⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⠊⠑⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⠣⠄⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⣠⠤⡖⠒⠂⠒⠒⠂⠀⡀⠀⡼⠁⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⢰⠀⠀⠀⡠⠂⠀⠈⠉⠀⠀⠀⡧⠖⠂⠀⠀⠀⠐⠲⢁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡋⠀⠌⠀⠀⡀⠀⠀⠀⣞⢈⣉⡂⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⢀⡄⠀⢴⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⢀⡤⠃⠀⠢⠈⠠⡈⠀⠁⣤⠐⠚⠒⠀⠀⠲⠀⠀⠂⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠐⠒⠀⠀⠀⠐⠒⠂⠉⢳⠀⠇⠀⡇⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠅⠀⢉⠉⠉⠉⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⣷⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠁⠈⠀⠀⠁⠀⠀⠁⠀⡟
⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⠀⠀⠀⠀⠂⠀⣯
⠀⠀⠀⠀⠀⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⢸⠀⠀⠀⠠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⡇⠀⠸⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⠀⠂⣿⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⡇⠀⠀⠑⠲⠤⠤⠤⢼⡇⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⠀⠀⠀⠀⠀⠘⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⠤⠂⠐⠂⣀⢴⠛⠀⣄⠠⠄⠉⠀⠀⠀⠀⣿⡄⠀⠀⡐⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣀⣀⣀⡠⠤⠒⠊⠀⠀⡰⠃⠀⠀⠡⠀⠀⠄⢸⠀⢰⣀⣀⠠⠤⠒⠀⠀⡟⠃⠀⠀⠂⠀⠀⠀⢠⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡰⠃⠀⠀⡄⠘⠃⢰⠀⠀⠀⠀⠀⠀⠀⢁⠨⠒⠤⠄⡀⠤⠔⠂⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⣂⣁⣀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⢤⡤⠤⠤⠚⠁

⠀⠐⠀⠀⢤
⠀⠀⠀⠀⠸⡆⠀⠀⠀⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⣤⡀
⠀⠀⠀⠀⣠⣷⡿⠂⡖⠻⢿⣿⣟⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣶⡦⡄⠀⣼⣿⣷⣿⣾⡆
⠀⠀⠀⠀⠀⢿⡇⠀⠃⠀⢸⣿⠁⡼⠀⠀⠪⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⣴⣿⡟⣿⠟⠀⠘⣾⣿⣿⣟⠁⠀⠀⠀⠀⠉⠛⠉⠁
⠀⠀⠀⠀⢀⣻⡇⠀⣾⣷⣾⡟⠀⠀⠀⠀⠀⠐⢶⡀⠀⠀⠀⠀⣿⠗⠁⠀⠀⠀⠈⠻⣯⠁⠀⠀⢀⡿⢋⠔⠋⠀⠀⠀⠀⠒⠒⠚⠓⢦⣴⡆
⠀⠀⠀⠀⣿⠙⠀⠀⣿⣾⠙⠇⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⢹⡇⢧⡀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠘⣿⣷
⠀⠀⠀⠀⡏⠀⠀⠀⡁⠉⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣼⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⡏⠀⠀⠐⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⡞⠀⠀⠈⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠆
⠀⠀⠀⠀⣿⠀⠀⠀⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠶⡆⠉
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⣀⡀⠀⣀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣧⡀
⠀⠀⠀⠀⠻⠤⠤⠤⠤⠄⠴⠇⠀⠀⠀⠀⠀⠀⠀⠴⠆⠚⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⠶⠀⠭⠁⠠⠦⠀⠀⠀⠀⠀⠀⠶⠿⠿⠿⠿⠿⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡏⠙⡆⣀⡀⡲⢀⣀⢰⣿⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠓⠁⠐⠲⠖⠂⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡼⠣⠟⠳⣇⡿⢿⣼⢿⣧⣻⡤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠐⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠲⠀⠒⢻⡓⠂⣿⣶⠒
⠀⠀⠀⠠⡤⠀⠠⣤⣤⠀⢴⡄⠀⢠⡀⣀⡀⠀⢀⣀⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⡀⣠⣤⡄⢰⣿⠏
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡀⠀⠸⣇⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⢠⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠙⠾⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣸⣿⣇⣸
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⡿⠟⠉⠹⣷⠀⠀⠀⠈⢻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⠀⢀⢀⠀⠀⠸⠗⠒⠀⠘⠇⠀⠀⠀⠀⠀⠻⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢸⣟⠐⢺⡿⠛⢛⡟⢻⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⢿⡤
⠀⠀⠀⠀⠀⢠⣤⣤⣤⢀⡄⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢸⠻⣄⣀⣳⣶⢛⣁⡼⣿⠀⠀⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠀⡿⢿⠇
⠀⠀⠀⠀⢘⡟⢩⣭⡇⣭⠁⠀⠀⠀⢀⣀⣬⣛⣓⣠⣤⠆⠀⠀⢼⠠⠀⠁⠀⠀⠀⠀⣀⡿⠀⠀⠀⠀⣀⣀⡀⠇⠀⠀⠀⣤⣾⣿⣿⣫⣤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⣿⡿⠻⡿⠛⠿⢿⡿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡇⠀⢠⣤⡆⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠘⣿⢱⠀⢸⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⢸⣷⣿⠀⠀⠀⠀⠀⡠⠀⠀⠀⣀⣀⠠⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⡄⠀⡀⢸⣿⣇⢸⣿⣿⠀⠀⠀⠐⠂⠀⠀⠀⠘⠉⠀⠀⠀⠰⠂⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⣿⣿⠸⣿⣿⡀⠀⠀⠀⠀⢀⠀⠠⠀⠀⢀⠀⢀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⠀⢸⣿⣇⣿⣿⡁⠀⠀⠀⡰⠁⠀⠀⠀⣐⡁⠀⠘⠒⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣶⢾⣿⣿⣿⣿⣧⣤⣴⣤⣤⣶⣶⢶⠾⠛⠁⠀⠀⠀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⡛⠿⣿⣿⣧⠔⠈⠀⠀⢄⠔⠀⠘⠀⠀⠀⡄⢰⣇⣼⡇⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⢴⣶⢀⠀⢠⣧⣼⣿⣿⣴⣿⠟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⠀⠂⣴⣤⠀⢀⠐⠀⠻⣆⠁⢸⣤⢸⣿⣿⣿⣿⣿⣷⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⣀⠀⣾⠰⢃⠀⠆⠀⠉⡀⠀⢀⡸⠂⠊⢸⡇⣸⣿⢸⣿⣿⣿⠟⣫⣥⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡙⣿⣿⣿⡈⢻⣿⣿⣧⡄⠀⠀⠀⠐⣤⠂⠀⠀⠀⠀⠀⠀⠀⡟⢨⢻⡘⣇⢋⠴⣿⣿⡿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⣈⣿⣿⣧⡀⣿⣿⡿⠑⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠀⣼⠇⢨⠈⢇⣡⣴⣾⣿⡿⢛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡐⠀⠀⢠⡀⠈⠀⠀⠀⠀⣀⡾⠃⠘⢰⡀⢂⣴⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠈⡇⠁⠀⠰⠘⣻⣧⣶⣶⣶⣛⠉⠀⢰⠀⠈⠔⣻⣿⠿⣛⣥⣶⣶⣶⣶⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⡿⢿⣿⣶⣾⣷⣾⣟⣿⠄⠀⣴⠟⠉⢉⠉⠙⠿⣿⣿⣆⠀⠀⢀⣾⢿⣷⣿⣿⣿⡿⠿⠿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠋⢀⣾⣿⣿⠉⣿⣿⣿⣿⢈⣆⠀⠀⠆⠈⠀⠀⠀⠈⢿⣿⡄⠀⠈⠛⢻⣦⣽⠟⢿⣷⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣿⣿⣿⣿⠏⣠⣿⣿⠈⣿⡈⠉⢲⡔⠂⠈⣛⠆⠐⠂⠈⣿⡇⠀⣸⣿⢿⣿⣿⠳⣶⣮⣝⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⣵⣿⣿⣿⣿⣾⣿⣷⣄⣀⠈⠒⠂⠁⠸⠷⠀⢀⣁⡤⢶⣏⣿⣄⣿⣿⣷⣿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⢹⡀⠉⠙⡛⢻⠛⠛⠛⠋⠉⢹⢀⣸⠇⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠓⠚⠓⠒⠚⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠉⠳⡆⠀⠀⠀⠀⠐⠲⢤⡐⡆
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⡎⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⢲⣷⣶⣶⠂⠀⠀⠀⠀⢣⢻
⠀⠠⣤⣤⣤⣤⣤⠜⠒⠒⠀⠀⠀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠘⣾⡆
⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⢾⣿⡟⠁⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⢠⠞⠗⠀⣶
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⠀⠀⣼⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣦⠄⣿⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡆⢘⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⡿⠁⠀⠀⠀⠀⢸⡏⠀⠈⠃
⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⢙⠁⢈⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⡄
⠀⠀⠒⠛⠻⠟⠒⠀⠀⠀⠀⠀⠀⠒⠻⠿⠗⠒⠀⠀⠀⠘⠛⠿⠛⠁⠀⠀⠀⠀⠀⠐⠚⠿⠒
⠀⠀⢀⣀⣀⡀
⠀⠀⢸⣿⣿⡇⠀⠀⠀⣶⣶⣶⣶⣶⣶
⠀⠀⢸⣿⣿⠇⠀⠀⠀⠹⣿⣿⣿⣿⠏
⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠈⢹⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠁⠠
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⣶⣾⣿⣶⡶⠀⠀⢰⣿⠟⠻⠛⠻⡇⠀⠀⢰⣶⣶⡏
⠀⠀⢀⣸⣇⠀⠀⠀⠀⠀⢀⣸⣄⡀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⢈⣹⣿⣋⠀⠀⠀⠸⣷⣤⣴⣦⣤⡇⠀⠀⠸⠿⠿⠇
⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⡆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠛⢿⣦⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣴⣦⣤⡀⠀⠀⠀⠀⠐⠖⠒⠂
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠈⣿⡀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠀⠈⡇⠀⣶⣶⣶⣷⣶⣶⣶⣾⣿⣿⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠶⠴⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣀⣤⣿⠁⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡏⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠉⠁⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠃⠀⠀⣴⣖⡷⠀⠀⢠⣶⡶⡀⣠⣤⡀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⣮⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣄⣍⠀⠀⢺⡥⢊⡅⠀⠀⢠⠯⣴⠁⣷⢬⡇⢀⡀⠘⡬⠿⢀⡀⠀⢠⢶⣊⣄⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠈⣿⣿⠀⡜⠓⠫⡀⠀⠀⢃⡄⢹⡆⢉⠘⡥⠭⠿⡷⠀⠀⠀⢸⢀⣶⣿⠉⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣰⣿⣷⠘⢧⡞⢛⡵⢀⣄⣌⣧⠸⣽⣥⢽⡍⢢⣽⣷⠀⠀⢠⡏⢿⡿⢿⣤⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣥⣭⣿⣿⠟⠛⡃⠈⢓⡩⠋⡙⠙⣠⣼⡏⣿⡽⠿⠛⠛⠀⠀⠘⠀⠀⠒⣾⣟⢛⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇⠁⠀⡜⢠⠈⠉⠀⠀⢧⢪⢿⢿⠁⣿⣷⡀⠠⡝⠛⠻⠖⡗⠂⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠐⡁⡄⡁⠇⢃⢠⢃⡏⡎⢸⣧⢹⣿⣇⠸⠀⢩⡏⠉⡇⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢠⢣⠁⡇⡇⢰⢸⠂⡼⢸⠃⠘⣿⣧⣿⣿⡇⢴⠟⠅⢸⠀⠀⢸⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢻⣿⡇⠀⣸⢰⡇⡇⢸⠀⣧⠇⣿⣀⣀⣿⣿⠿⡿⠧⠾⢖⠦⢼⡤⣤⠼⣿⡏⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⢸⣿⣿⠀⡏⢸⠃⡇⢸⡄⣿⣉⣹⣍⣻⣛⣄⣲⠾⣽⣥⣭⣟⣿⣿⣿⣿⣶⣾⡾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⢸⣿⡏⢠⡇⢸⠀⡇⢸⡇⢿⣿⡿⢻⣿⠿⢿⣿⣿⣿⡿⣿⠛⡏⠉⠀⣿⣿⢿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⢸⡿⠀⢸⠁⣸⠀⡇⢸⡇⢸⣿⡇⢸⠀⣇⠉⣿⣿⣿⣇⣿⠴⠁⠀⠀⣿⣿⢸⡇⢿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⢸⠇⠀⣾⠀⣿⠀⡇⢸⡇⠸⣿⠔⠚⢤⣯⡖⠛⠿⠋⠁⠀⠀⠀⢀⣴⣿⠇⢸⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⢈⣀⢤⠇⠀⣏⣄⡀⠈⠧⣀⣿⡇⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠈⠉⠁⠀⠉⠀⠀⠀⠉⠁


⣿⡿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠆
⠀⠀⠀⠀⢢⢀⠐⠀⢉⡡⣐⠤⠐⠀⠀⠠⠀⠨⠉⠉⠉⠉⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡠⣄⣀⣔⣓⢀⠦⡀⠀⠠⠂⠉⠑⢄⠀⠈
⠀⠀⠀⢈⠀⠀⠀⢀⡎⠀⡀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣧⡆⠀⠀⣿⣶⠀⠀⠃⢀⠀⠀⠁⠀⠀⠂⠀⡀⠐⢷⢦⡤⠉⠉⠠⠤⠅⠂
⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠈⠉⢄⠀⡠⠈⠁⠀⠰⠁⠈⠁⠀⠈⠈⠁⢁⠀⠀⠀⠀⡆
⠀⠀⠀⠠⠈⠀⠀⠀⠸⢐⡊⡃⠀⠀⠀⠀⢠⣴⡆⠀⠀⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⢨⣖⡀⠀⢀⣴⣀⠁⠀⠀⠀⠀⠈⠉⠁⠉⠁⠉⠉⠀⠀⠀⡈⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⣐⣦⠀⠀⣠⣲⣤⢀⠀⠀⠀⠀⠨⠟⠀⠀⠀⠚⠅
⠀⠀⠀⠀⠘⠿⠃⠁⠼⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠨⠛⠛⠀⠁⠘⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣂⠀⠀⠧⠀⠀⡀⠈⠁⠰⠆⠠⠂⠀⠀⠀⠀⠁⢉⡉⠁
⠀⠀⠀⠠⡄⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⢀⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⡀⢇⠠⠰⠦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⠀⢼⣷⠇⠀⠚⣷⣿⠈⢀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠙⡎⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠂⠤⠀⠀⢤⡀⠀⠀⠀⢤⡀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⠀⢉⠋⠁⠀⠀⠉⠁⠀⢠⣼⡆⠀⠀⣬⣷⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠻⣿⠇⠐⠀⡆⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡴⠀⠀⠀⢀⡀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣤⣀⠀⠀⢀⣴⣀⡈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣤⡀⣦⠀⡉⣥⣄⣤⠀⠀⠈⠉⢀⡀⠀⢀⠄⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠈⠻⠟
⠀⠀⠀⠠⠥⠀⠀⢀⠄⠀⠀⠀⠀⠈⠙⠍⡣⠈⠈⠉⠁⠀⠐⠒⠨⡍⢀⠀⢭⠰⠶⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⢠⣀⠀⡆⠂⠀⠊⢤⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⢠⠄⠀⠀⠀⡀⠉⠁⢠
⠀⠀⢠⠀⢉⡁⠀⡀⠀⠀⠀⠚⠁⠀⠠⠤⡌⠁⠀⠙⠂⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠉⠀⠐⠄
⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠐⠀⠐⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⠉⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠰⣿⡶⠀⠀⠰⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣮⡄⠄⠀⣾⣤⡀
⠀⠀⣴⣲⡀⠀⢠⣆⡀⠀⠀⠀⣠⣰⡄⠀⢀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣭⣷⠀⠀⠀⣤⣽⡆⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠂⠙⠛⠁
⠀⠀⠙⠋⠀⠀⠈⠛⠃⠀⠀⠀⠙⠛⠉⠒⠀⠛⠋⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠋⠑⣤⠂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠀⠀⠉⠖⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠊⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠧⠤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠚⠋⠉⠀⢰⢯⡼⠛⠀⢀⣿⣧
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢰⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⢀⣠⣶⣟⢾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠔⠋⠀⠀⣀⠀⠤⣄⠀⠀⣀⠠⠄⣾⢇⠉⢿⡿⣾⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠙⠂⠺⠁⠀⡏⠀⠀⢸⠒⡉⠜⢆⣄⠙⠞⡾⡌⣵⢸⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡷⠶⣶⣿⠛⣇⠀⢁⠀⠀⣭⢁⠁⡸⣤⠯⡙⢶⠘⠀⣹⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣟⢳⡐⡿⡷⣄⡀⢰⠂⠃⠀⠱⠘⢆⡙⢦⢡⠇⢸⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢽⡢⠙⢦⠈⠈⠅⢫⠀⠠⠀⡧⣲⡌⢃⠀⠈⡞⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢔⠿⣿⠀⣧⠀⢲⡀⠣⠀⡀⠀⢌⢷⠈⢰⡇⣣⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⣷⣝⠃⢤⡀⠲⣄⣈⢦⠺⠦⠁⡆⣯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣷⣶⣭⣄⣴⣦⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⡿⠀⠈⠳⣄⣠⣤⣤⠤⠶⠶⠶⠦⢤⣤⣴⣋⠀⠀⢹⣼⡆
⠀⠀⠀⠀⣠⠶⠚⣛⣿⡟⣁⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢤⣹⠿⢿⠓⠦⣄
⠀⠀⣠⣞⣡⠤⣶⣿⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡟⢿⣒⠺⢷⡄
⠀⢠⡟⣿⠒⠛⠁⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⢉⡿⢻⡀
⠀⢸⡇⠘⢷⣄⢀⡏⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠟⠁⢸⡇
⠀⠘⣇⠀⠀⢉⡿⠀⠀⠀⠀⠀⢀⡏⠙⠦⣄⣀⣙⣷⣤⣀⡀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠈⢷⣄⡀⣼⠁
⠀⠀⢿⡀⣴⠞⠁⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⣠⡬⠁⠀⠠⣭⡉⠉⠉⠁⠉⠳⢦⣀⣀⠀⢀⣠⡼⢁⡟
⠀⠀⠘⣇⢹⣷⠶⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⠁⣴⠀⠀⢠⣦⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⡍⢧⣼⠃
⠀⠀⠀⢻⣯⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⡏
⠀⠀⠀⢸⡏⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⣤⣀⣤⠟⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣤⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠳⣤⣀
⠘⢯⣄⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⣠⡿
⠀⠀⠉⠳⢤⣀⣀⣈⣳⣄⡀⠀⠀⠀⠀⢀⡴⠲⠤⢿⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣃⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⢠⡞⠃⠀⠀⠀⠀⠀⠛⣦⠀⠀⣀⣠⡴⠚⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣿⢿⣿⣶⣶⣶⣶⣶⣿⢻⣟⣻⣯⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡞⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⢹⡆⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢸⠃⢸⠀⢀⣀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣿⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠿⣤⠾⠛⠋⠹⣆⣀⣀⣀⣼⠋⠓⠶⣤⣽⠇⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠈⣩⣭⣿⡁⠀⠀⠀⠈⢷⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⢸⡀⠀⠀⠀⠀⠀⢠⣤⣤⠏⠀⠀⠀⠀⢸⠀⠀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⠾⠷⣤⣄⡀⠀⠀⢤⣤⡽⠂⠀⢀⣀⣤⡿⠶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⠙⠛⣶⣴⣯⣤⠶⠛⠋⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠴⠿⠭⠤⠭⠶⠆⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠶⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠶⠞⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⢹⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣀⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣴⣶⣤⣤⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡋⣿⣿⣿⣿⣿⣿⣿⠇⣿⡁⣿⣿⣿⣿⣿⣿⣿⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢦⣤⣀⣀⣀⣠⣤⢞⣿⣟⢦⣄⣀⣀⣀⣀⣤⢴⣿⠁

⠀⠀⠀⠀⠀⢀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⣶
⠀⠀⠀⢠⣴⣿⣿⠋⣀⣀⣾⠛⣷⠂⠀⠀⠀⠀⢰⣶⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⡼⢼⣿⣤
⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣤⠘⠏⠀⠀⠀⠀⠀⠘⡇⠉⢉⡇⠀⠀⠀⠀⠀⠀⠀⣿⠶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣿⡆⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⡳⡄⠀⡜⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢽⠟⠀⠀⠀⠀⢠⠀⠀⢀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡶⣶⣶⣶⠛⠁⠀⠀⠀⠀⢰⣶⣲⣶⣾⣿⣆
⠀⠀⠀⠀⠀⡠⠤⠤⠄⠴⠠⠄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠉⠀⠀⠀⠀⠀⠀⢿⣍⠁⠉⠉⠉⡹
⠀⠀⠀⠀⠀⢸⣧⠴⢿⣦⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⠒⠉
⠀⠀⠀⠀⠀⢈⣧⣤⣼⣄⣨⣏⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠠⠶⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣄⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠈⠟⠿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠿⠟⠛⠋⠁


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

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⣴⣿⣿⣿⣿⣿⣿⠟⠀⠉⠈⠛⠿⠋⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣼⣿⣿⠏⠉⠀⢉⣉⢀⣀⣶⣶⣦⣄⠀⢠⣿⣿⡟⠉⠉⠉⠙⠛⠛⣿
⢠⡿⠏⠋⠀⠀⠀⠈⢙⠋⢋⣀⣡⣬⣿⣷⣾⣿⠿⠁⠀⠀⠀⠀⠀⠀⡇
⣸⠃⠀⣀⣤⣤⣿⣦⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣿⣤⡄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠋⣧⠀⠀⡀
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⣴⣿⠞⠋⠉⠳⣄
⠀⢻⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠚⠉⠛⠁⠀⠀⢠⠞⠁⠀⡠⠊⣹⠈⠓⢄
⠀⠀⠹⣿⣿⡏⢠⠖⠶⣦⠙⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠎⠀⣘⡡⠄⠐⠢⣝⢦⣤⣄⣀
⠀⠀⠀⠹⣿⣇⠈⠀⠠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢠⠁⢠⠞⠁⢀⡤⠒⠊⢁⣴⠈⠳⣄⠉⠲⢄
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠸⠀⠉⠀⠰⠋⠀⡠⠖⠋⣠⠃⠀⠈⠓⢄⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢆⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⢶⡄
⠀⠀⠀⠀⠀⠀⢀⣠⠾⣥⣄⡀⠀⠈⠉⠛⠷⢦⣤⣄⣀⡀⠀⢀⣠⠎⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⡉⢢⡀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠉⠛⢶⣄⡀⠀⠀⢀⣼⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣤⡀⠀⠀⣸⠋⠀⠀⠀⠀⡰⠁⠀⢳⡀
⠀⠀⠀⢀⣾⡷⠞⠋⠉⠓⠂⠀⠀⠀⠈⢙⣶⣤⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠙⣿⣿⣿⣶⣄⠉⠀⠀⠀⣠⠞⠁⠀⠀⠀⢳⡀
⠀⠀⠀⣾⠋⢀⡠⠀⠀⠀⠀⢀⡠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠉⠈⠿⠃⠀⢹⣿⣿⣿⣿⣿⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⢷
⠀⠀⢰⣷⠞⠋⠀⣠⡴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢻⣟⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⣄⠀⠀⠀⠀⠀⢸
⠀⢀⡾⠋⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣿⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠘⢿⣦⠀⠀⠀⠀⢸
⢀⡾⠁⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣷⣤⣤⣽⣿⣶⣤⣶⠟
⣾⡇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠷⠶⠶⠿⠟⠛⠋⠉⠉⠉⠉
⢹⣧⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠙⣧⣿⣿⣿⣷⣤⣀⣀⠀⣠⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⣿⠿⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⡿⠀⠀⠀⠙⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢢⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣬⠠⠀⠤⣷⢦⠌⢀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣀⡦⢽⢞⣬⡤⢚⡽⠁⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠹⣽⣿⣿⣇⣿⣽⣷⠾⠁⠀⠀⠀⠀⠀⠤⠤⢠⣿⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡼⠟⠉⠁⠀⡀⠀⠲⢄⡀⠀⢀⣴⢾⣿⠀⢀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢻⠳⠖⢶⠾⠶⢦⣤⡤⠿⠶⡶⠾⣿⣿⡟⢻⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣌⡇⠀⠀⠀⠀⠘⣯⠂⣤⠤⠀⠼⠿⣉⠀⣼⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠓⠲⠖⠒⠒⢶⣶⠶⠶⠾⣛⠛⠉⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠂⠀⠀⠘⢿⡟⠀⠀⢿⣧⡀⢠⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⣤⣤⡟⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢀⣔⡾⠋⢠⣿⡀⠂⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠀⠀⠀⣬⠋⠀⢠⡾⣿⣷⡃⢼⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⢸⡇⣀⡴⠋⣱⡏⢽⡁⣾⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠑⢄⡀⠀⠋⠁⢠⢾⠟⣽⣿⡁⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣯⣶⣶⣾⠁⢀⣴⣿⡿⠟⣣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠈⠉⠉⠉⠉⠉⠉⠉⠁⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⠒⠒⠒⠛⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢽⣋⣛⣟⣙⣋⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠉⠛⢻⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣄⡈⠀⠘⣛⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⠶⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠶⡄⠠⠉⠃⠌⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⢁⠀⠁⠀⠀⠀⠀⠘⠋⢩⠙⡿⣧⡀⣧⠛⢷⣌⣡⣿⡇⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢧⡀⠀⠄⣤⣤⣄⡀⠀⠡⣤⠀⠐⣿⠁⢋⠆⠀⠈⠉⣻⠤⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡄⠀⠀⢀⣴⣿⡏⢠⡀⣿⠋⢙⣿⣧⡰⡡⡀⠀⠈⡄⠀⠀⠈⣤⠈⠀⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠇⠀⢀⣼⣿⣿⣿⣼⣴⣿⣇⣸⣿⣿⠃⠀⠁⠂⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣄⣾⣿⣿⣿⣿⣿⣿⣿⡇⠸⡿⠃⡑⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠃⠸⣿⣿⣿⣿⡇⠀⠀⣠⣿⣄⣀⣀⡀⢸⠁⢰⡋⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠛⠋⠁⠀⠀⢘⣿⣿⣿⣿⣤⣾⣿⣿⢛⡱⣀⠉⡛⠀⣈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠛⠉⣭⣿⣿⣟⣉⡉⠉⣛⡃⣉⣽⣷⣍⣿⠀⠀⠈
⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠤⠘⠛⠛⠉⠉⡍⠀⠀⠈⠁⠈⠩⣕⡿⠟⠔⠀⠄⠄
⠀⠀⠀⢀⡇⠇⠀⢀⠀⠀⢺⠪⡉⠀⠀⠀⡴⠄⡀
⠀⠀⠀⠀⠁⠀⠶⠤⠠⡤⠈⠀⠈⠁⣀⡀⢨⡶⠐⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⢄⡀
⠀⠶⠿⠿⢿⣿⣿⣿⣿⡿⠿⣿⣿⠿⢻⡄⠚⠁⠀⡀⠁⣄⡈⠣⠘⢶⠬⢽⣟⡉⠉⠛⠛⠒⠚⠂
⢠⣤⣤⣤⣼⣧⣀⣀⣀⣀⣀⣀⣤⣤⠾⠇⠀⢀⠀⣠⡾⠋⠉⠓⢲⣤⣵⣦⡀⠀⠈⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⣒⣯⣽⣵⣒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⣷⣾⣿⣿⣿⣿⣿⣿⠿⠗⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠀⠈⠉⠉⠻⡶⣶⣦⣤⣤⣤⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠑⡎⠩⣿⣿⣿⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠆⠀⠰⠖⠂⠀⠀⠀⢞⣁⣘⣿⣿⣿⣷⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠃⠀⠀⠈⠋⠀⠀⠀⢸⣽⡿⣛⢻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠁⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠈⣠⣶⣅⠀⠀⠀⠀⣠⠏⠀⠠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠀⠀⠂⠐⠂⡆⠀⠀⠀⠀⠀⡴⠚⠀⠐⠊⠁⠣⡰⠙⠃⡸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⣬⠃⠀⣀⠀⠀⠃⠀⠀⣀⠴⠞⠁⠀⢀⠐⠢⠀⢠⠇⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⢀⣹⣄⣈⣀⣵⠒⠔⠉⠀⠀⠀⠀⠀⠎⠀⢠⣣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠄⠀⠀⠀⠀⢙⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡉⢻⡏⣾⣿⡇⠊⠀⢠⠎⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢠⠊⠀⣀⣤⠴⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠉⣻⣿⣼⣿⣿⠁⠀⠀⢸⡄⠀⠀⠀⣠⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠁⢠⠎⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠈⠀⠉⠉⠁⠀⠀⠀⠀⢧⠀⠀⢸⠁⠙⠀⠀⠀⠀⠠⢄⡀⠀⠀⠈⢢⠀⠈⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⠀⠀⡴⠁⠀⠀⠀⠀⣰⠏⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠁⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠈⢣⡀⠀⠀⢀⠀⢧⠀⠀⢺⡁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣇⣠⣖⣁⣤⡜⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⢀⣧⡴⠖⠒⠒⠒⠢⠤⢀⡀⠀⢸
⠠⣄⣀⡀⠀⠀⠀⢀⣸⣦⣤⣤⡔⠒⠙⠛⠉⠉⠁⢸⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸
⠀⠀⠀⠉⠙⣢⠞⠁⠀⠀⠀⠀⠉⠙⠓⠦⡀⢀⣀⣋⣀⣀⣘⠀⠀⠀⣀⡤⠤⠂⠀⠀⠑⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠉⠉⠀⠀⠀⠳⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⣀⠞
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠳⢦⣤⣀⠀⡠⠤⠀⢸⣅⡧⠠⣤⣾⢿⣛⠛⠋⢉⡉⣉⢉⡟⠛⠛⠋⠉⠁
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠉⠛⠦⡀⣀⣠⠼⠒⠋⠁⠀⢀⣿⢠⣆⣼⣷⠿⣾⠃⢀⠂
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⡠⠖⠋⠉⠀⢀⣀⠤⠶⡞⣹⠏⣾⣿⠻⠏⠀⠁⠀⢸
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣠⠋⠀⢀⡤⠖⠋⠉⠀⢲⡄⣷⠏⠀⠀⠁⠀⠀⠀⠀⠀⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡶⠶⣴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣗⣣⣜⣃⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⣿⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠃⣿⡆⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⢀⣿⡇⢘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢰⣿⡧⢼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⡫⠁⣼⣿⣿⣄⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣼⠋⡴⠁⠀⢻⣿⡟⠋⣆⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⡏⢀⡇⠀⣷⣸⣿⣿⣾⣼⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⢰⣇⣰⡄⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠈⠙⢤⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠔⠃⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠠⠀⣀⠀⠀⠀⢀⣴⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠨⣽⣟
⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⢠⡄⠀⠁⠀⠠⠄⠀⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣄⣀⣀⣀⣀⡀⣀⣀⣀⣿⣿⣿⣶⡶⣦⣦
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⡭⢾⣿⣿⡇⣿⣿⣿⣿⡟⠃⠀⠀⠰⣾⡇
⠀⠀⠀⠀⠀⠀⢨⡁⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⡅⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡏⠀⢺⣿⡟⡃⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠆⣀⡤⠄⠀⠀⠀⢀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⡇⠀⠈⠈⠁⢡⣿⣿⣛⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣿⣿⣷⣶⣶⠿⠿⠛
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠓⣸⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢙⣻⣿⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠈⢇⠈⣩⣭⣿⣿⡇⣿⠇
⠀⠀⠀⠀⠀⠀⠐⡿⠀⠀⠀⣀⣀⡀⠀⢀⣠⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⣠⣿⡆⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⣿⣿⣿⣿⡟⣿⡀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣀⣀⠀⢠⣼⢘⣡⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣧⣴⣄⣠⠿⡿⣿⣿⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⣗⡎⠉⢉⠉⠿⢿⣿⣯⣿⣿⣻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠸⢿⢿⣿⣾⣶⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠀⠀⠈⡟⠿⠿⠿⠟⠿⠿⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈

⠰⢆⠀⠐⣄⠀⢠⠊⠀⢠⠀⠀⠆⠀⠐⠁⠙⠀⠀⠸⠀⠠⠀⠀⠀⠸⠀⠀⢆⠀⠁⣅⠀⣠⠊⠁⢠⠀⠀⡄⠀⠘⠃⠙⠀⠀⠸⠉⠠⠃⠀⠀⢠
⠀⠠⠀⠀⠈⠉⠉⠀⠀⠀⠘⡄⠀⢀⣢⣬⠃⣀⠂⠀⠀⣀⣴⣇⠀⠢⠀⠀⠠⠂⠀⠈⠉⠁⠀⠀⠀⠘⡅⠰⢀⢁⣬⠃⣠⠂⠀⠀⣀⣰⣇⠀⠠
⠀⠀⠀⠀⠀⣰⠦⢶⡄⠈⢌⣁⠄⠀⠀⠜⠀⠃⠀⠀⠘⠉⢉⠽⡄⠀⢐⠐⡲⣒⡂⠀⣴⠶⢶⡄⠐⠈⠀⠀⠀⠰⠌⠄⠃⠶⠀⠸⠉⢉⠸
⣊⣷⣘⡄⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠀⠢⣀⡠⠂⠀⢠⡀⠈⢐⡇⠀⢠⣈⣳⣘⣤⠀⠰⡀⠰⠀⠀⠀⡇⠀⠀⠀⠡⣀⡀⠀⠀⢘⡀⢈⢐
⠁⠀⠑⠃⠀⡄⡀⠀⠀⠀⠒⠑⠂⠀⠀⠀⠸⠅⠀⠀⠀⠉⠀⠈⠀⢀⠘⠀⠁⠋⠊⠀⠄⡀⠀⠀⠀⠒⠐⠂⠀⠀⠀⡸⠀⠀⠀⠀⠁⠀⠉⠀⡄
⣄⡄⠀⠠⠤⠬⠤⢄⣀⠠⡏⠉⠉⡵⠀⠈⠁⠉⠀⡒⠒⠐⠀⠀⠂⡞⠐⣄⡄⠀⠠⠤⠥⠤⢄⣀⠠⠏⠉⠉⠷⠀⠈⠁⠉⠀⠆⢲⢰⠀⠠⠀⠎
⠞⠁⠀⠐⢄⣀⣠⠞⠈⠀⠠⣞⠗⠀⠀⠆⠰⡆⠀⣇⣽⣬⠀⠀⢃⠤⢰⠟⠁⠀⠐⢄⣀⣀⠖⠀⠀⠣⣎⠇⠀⠰⠄⠒⠆⠀⣥⣽⣸⠀⠀⡄⢼
⠀⡀⠀⢀⠈⠉⠁⠀⠀⠀⠐⠀⠐⠀⠀⠦⠴⠃⠀⠠⠿⠝⠀⠀⠘⠈⠈⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠀⠐⠀⠀⠦⠴⠂⠀⠢⠿⠏⠀⠀⠐⠉
⠀⠂⠀⠸⠀⢀⢁⣈⢡⠀⢰⣧⠀⣶⣷⠦⠀⡤⣀⠁⠀⠀⢐⠒⣒⣲⠀⠀⡆⠀⢒⠀⣐⢁⣀⢡⠀⠠⣧⠀⣾⣿⠦⠀⡤⣀⠁⠀⠀⢐⠒⢂⣒
⠀⠐⢶⠀⠀⠈⢠⢤⠊⠀⠀⠸⠀⠉⠋⠛⢏⠝⠁⠀⣀⡀⠨⠒⠤⠀⠀⠀⠀⢶⠂⠀⠐⠠⠤⠈⠀⠀⠀⠀⠉⠛⠙⢯⠝⠁⠀⣀⡀⠈⠒⠤
⠀⠠⠍⠤⠀⠀⠉⠈⠁⠀⠈⠀⠀⠀⠀⠀⡸⡀⠀⠀⡁⡇⠀⠌⠀⡄⠀⠀⠠⠌⠤⠀⠀⠉⠈⠁⠀⡂⠀⢱⠀⠀⠀⡘⠀⠀⠀⠁⡅⠀⠎⠀⡄
⠦⡀⠀⢠⠐⠂⠢⡀⠀⠀⡄⢸⠀⠀⢀⠀⣁⠉⠀⢀⠀⠠⠀⠀⠀⠀⠎⠦⡀⠀⢀⠐⠂⠢⡀⠀⠀⡁⠁⢘⠀⢀⠀⢁⠁⠀⢀⠀⠀⠀⠀⠀⠠
⠀⠁⠀⠄⡄⡤⢂⠾⠄⡀⠡⠤⠤⠀⠸⠀⢨⠀⠀⠐⠂⠄⠀⠀⠀⠏⠀⠀⡁⠈⠄⡄⡠⠂⠾⢢⠀⠯⠤⠼⠀⢈⠀⠘⠀⠀⡒⠂⠄⠆⠀⠀⠈
⢈⡀⠀⢀⠁⠉⠈⡸⠚⠀⠤⠤⡀⠀⠀⠄⢼⠀⠀⢠⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⢂⠃⠉⠀⠰⠚⢀⠤⠤⠀⠀⢸⠄⢤⠀⠀⢠⠄⠂⡇⠀⠀⠈
⠈⠑⠀⠀⠓⠒⠚⠀⠀⠘⢰⠂⠃⠀⠔⢀⡤⠀⠠⠀⠀⠀⢠⡄⠀⡌⠉⠁⠑⡄⠀⠑⠒⠚⠀⠀⠘⢰⠂⢃⠀⠴⠀⡤⠀⠠⠈⠀⠀⢠⡄⠀⠈
⠀⠈⠀⡀⠀⢀⣄⣀⠀⠠⠠⠅⠀⠘⠊⢳⣀⣖⡀⠀⠠⠧⠭⢵⡀⠀⢀⠀⠈⠀⠀⠀⢀⣀⣀⠀⢀⠠⠏⡐⠘⢈⢻⡀⣞⡀⠀⢠⠦⠭⢧⠀⠈
⡐⣮⠳⡂⠀⠘⠀⠐⠂⠀⠑⡖⠁⠀⠀⠅⠀⠀⡀⠀⠀⠀⠐⠈⡇⠀⢐⠐⣎⠷⣂⠀⢛⠀⢐⠃⠀⠑⡒⠁⠀⠈⠄⠀⠀⠀⠀⠸⠀⠐⠈
⠂⠛⠒⡧⠀⠀⠒⠀⠀⠀⣀⢃⡀⠀⠀⠈⢲⠎⠀⠀⠘⠲⠒⠖⠁⠀⢸⠒⠛⠒⠿⠀⠀⠒⠊⠀⠀⣀⢃⡀⠀⠀⠈⢲⠊⠀⠀⠘⠒⠒⠖
⠀⠀⠀⠀⠀⡡⡂⠀⠀⢀⣤⡐⡲⢄⠀⠠⠎⠲⠀⡀⣠⢐⠀⠀⡀⣹⠀⠀⠀⠀⠀⠀⡅⡀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠎⠲⠀⡀⣠⢐⠀⠀⡀⣁
⣿⠆⠀⢀⠀⠀⠀⣸⡰⠈⠃⡠⣄⠋⢀⣀⣀⡀⠀⡆⣖⢐⠀⠀⡄⢁⢀⣯⠗⠀⢀⠀⠀⠀⣱⡀⠈⡀⡠⡄⡀⢀⣀⣀⡀⠀⠂⣺⢰⠀⠈⠀⣀
⠁⠀⠀⠀⠱⠶⠞⠁⠀⠀⢈⣉⣠⠀⠀⣅⣈⡇⠀⠛⣿⢿⠀⠀⢰⢭⡼⠁⠀⠀⠀⠱⠶⠚⠁⠀⠀⢉⢉⣁⠁⠀⣅⣀⡀⠀⡟⣿⣾⠀⠀⢃⣭
⠀⣂⣀⢰⠀⠀⠐⠂⠀⠀⢀⡄⠀⣠⣤⡀⠀⢀⠠⠈⠉⠁⢀⠀⠀⢀⠀⠀⣀⣀⣐⠀⢀⠀⠒⠄⠀⠀⡄⠀⣠⣤⡁⠀⢀⠀⠈⠉⠁⢀⠀⠀⢀
⠀⠠⣀⠈⠀⠸⡀⢀⡸⠀⠘⢻⠀⠻⠿⢭⡰⢫⠂⠀⠀⠀⠰⣤⠀⠘⠀⠀⠣⣀⠔⠀⠲⡀⠀⡸⠀⠈⠛⠀⠻⠿⢍⡰⠫⠃⠀⠀⠀⠰⢤⠀⠒
⠀⠀⠽⡀⠀⠀⠼⠹⠄⠀⡐⠈⠄⠀⠀⠀⢱⠁⠀⠀⠎⡆⠈⠠⠉⠀⠀⠀⠀⠸⡀⠀⠀⠴⠱⠄⠀⡄⠀⢂⠀⠀⠀⢹⠀⠀⠀⡎⠆⠀⡠⠉⠈
⡀⠈⠀⠉⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠠⠎⠶⠀⠀⠂⠃⠀⠁⠀⠁⡀⡀⠈⠀⠈⡀⠀⡀⠀⠀⠀⠂⠀⠸⠀⠀⠀⠎⠶⠀⠀⠇⠃⠀⠁
⠠⠆⠀⡚⡀⠀⡈⣢⠀⠀⡇⠘⢀⠀⢸⠉⢹⠀⠀⢰⠀⠈⠀⠀⠀⡮⠠⠬⠆⠠⡒⠀⠀⡈⣢⠀⠀⡆⠀⢰⠀⠸⠉⠹⠀⠀⣈⠀⠈⡄⠀⠀⠴
⢠⣀⣀⣁⣇⣗⣀⣉⣈⣂⣀⣀⣀⣀⣈⣀⣘⣀⣀⣀⣀⣁⣀⣀⣀⣡⡀⣠⣂⣀⣁⣇⣳⣀⣉⣘⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣁⣀⣀⣃⣀⣀⣰
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠤⠒⠂⠉⠉⠉⠉⠉⠁⠒⠢⢄⡀
⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄
⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠄⠀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⢼⡇⠙⠋⣿⢂⡥⡐⡄
⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⠖⣫⣽⠶⠖⠒⠈⣑⣳⣤⡇
⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⢀⣼⠋⣡⣴⣿⢧⠀⠀⠐⢮⣽⣿⣿⣿⡀
⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠛⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠐⡄⢰⠒⠒⠂⢙⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⠋⠀⠀⢙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⣄⠀⠀⢈⣙⠀⠀⠀⠊⠁⢀⠀⠀⠀⢶⣖⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠃⠙⠀⠀⠀⠈⠙⠃⠀⠀⠈⠛⠉⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢨⠤⠤⠤⣀⠀⠀⠀⠀⠀⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠷⠶⠞⠁⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆⠀⠀⠈⠀⠀⣴⣄⣠⣶⠟⠁⠀⠘⠆
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠦⣥⠀⠀⠀⠀⢀⡿⠉⠉⠀⠀⠀⠀⢀⠀⠁⡀
⠀⠀⠀⠀⠀⠆⠂⠀⢀⣤⠀⠀⠀⠈⠁⣆⣀⡐⢏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣄⣀
⠀⠀⠀⠀⢠⠀⠀⠀⢸⡇⠀⠀⣠⣶⣿⣿⣿⢡⣿⣧⠁⠀⢀⣠⣴⣶⣦⠀⠀⢸⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣧⡀⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠊⠗⠀⡀⠀⣴⣰⠛⠇⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⢠⠂⠻⠀⡀⠀⢰⣤
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠁⠀⠀⠀⠀⠣⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣥⠏⠀⠀⡀⠀⠀⠀⠀⠀⠆⠀⠀⠈
⠀⠰⠇⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣤⣤⠶⢄⠀⠀⠀⠱⠀⠀⠀⠀⠖⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⣄⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠁⠂
⢿⠀⠀⠀⠀⠃⠀⠀⠃⢀⠀⠀⡀⠀⠂⠀⠈⠑⠠⠰⠀⠐⠈⠀⠀⠀⠀⡀⠀⢸⠆⠀⠀⠀⠁⠀⠁⠀⠀⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀
⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⣏⡤⠜⠃⠀⠀⠀⠀⢄⠀⠀⢸⡀⠀⠀⠀⠀⠀⢤⠄
⠈⠳⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⡼⠀⠰⠿⠀⠀⠳⣶⡾⠇
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀
⠀⠈⢀⡀⡀⡀⠀⠀⠐⠷⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠾
⠐⠀⠀⠀⠓⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠐⢒⠀⠀⠀⠀⠀⠀⢸⠁⡶⠲⠀⠀⠀⠛⠐⠓
⢀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⠤⠒⠩⠀⠀⠀⠀⠀⣴⡚⠿⠉⣀⡀
⠖⠠⠀⠀⠀⠀⠘⠆⠀⠴⠂⠀⠀⠀⠀⠙⠳⢤⡴⠇⠀⢀⣀⠀⠀⠀⠀⠀⢰⡷⠀⠆⠀⠀⠀⠀⠲⠀⡤⠞
⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠋⠀⠀⠀⠀⢮⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠴⠉⠀⠀⠀⢸⡀⠀⠀⠀⠀⠉⣄⣀⠃⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠏⠁⠀⠀⠘⣡⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠄⠁⠋⠀⠄⠀⠾⡼⠉⠃⠄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠠⠁⠙⠀⠄⠀⠸⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠉⠒⡄⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣬⣅
⠀⠀⠀⣴⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣠⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢻⠿⠿⠿⠇
⠀⠀⠀⢿⣿⣿⣿⣥⣤⣤⣤⣤⣠⣄⣄⠀⠀⠀⠀⠀⣿⣾⣷⣿⣿⣿⡏⠛⠷⠀⠀⠀⠀⠀⢩⢿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠉⠉⠻⢿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣍⣉⣭⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣿⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠤
⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⠤⠤⠤⠤⢤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠉⠟⠁⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣛⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠿⠷⠦
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿