Stupidity Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡴⡀⢀⠀⡔⠆⠈⠁⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢱⠞⣶⡙⠀⠀⠀⣀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⠁⠀⠄⡀⠀⡰⢄⠀⠁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⠀⠀⠀⠰⠇⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣀⣤⣆⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⣇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠾⠛⠁⠀⠈⠉⠉⠐⠊⠉⠉⢀⠖⠊⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣿⡀⠀⠀⣰⣿⣶⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⠿⠿⠇⠀⠀⠈⠙⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠰⠠⡀⢤⠄
⠀⠀⠀⠀⠀⢹⡿⠿⠄⠀⠀⠀⠀⣴⠀⠀⡀⠀⠀⠀⠀⣏⠉⠁⠔⠈⢁⠉⠀⠀⣶⣾⣦⠀⢢
⠀⠀⠀⠀⠀⢘⣅⡈⠀⠀⠀⠀⠀⠈⠀⣀⡥⠀⢀⢂⣠⣯⣀⡀⢣⣄⣀⡂⢀⠀⠈⠁⢉⣄
⠀⠀⠀⠀⠀⣸⣿⣿⣦⡠⣄⠀⠀⢐⣿⡿⠟⢷⠿⣿⣿⡃⠉⠿⣀⠀⣸⠏⠉⠃⠀⢒⣻⣿⣷⡄
⠀⠀⠀⢸⣿⣿⣿⣿⣿⠛⠀⠀⢠⢮⡿⠃⠀⠀⠀⣿⠃⠀⢰⣾⣷⣶⠿⣀⡂⢰⣆⣨⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣻⣿⣿⡇⠆⠀⠘⢷⣆⠤⠀⢀⣰⠟⠡⡖⠙⠟⠋⠀⠈⠋⠷⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡆⢰⠀⣿⣿⠀⠀⠉⢻⣄⠀⢩⠆⠀⠀⠀⠀⠀⢀⣿⣿⣷⣌⡻⣿⠟
⠀⠀⠀⢸⠟⢿⣿⣿⣿⣼⣿⣿⣾⣿⣿⠀⣰⠀⠸⣿⣿⡗⢲⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣍⠙
⠀⠀⠀⠸⣟⣶⣶⣤⣈⡇⢈⣿⣿⣿⡏⠀⣿⠀⠀⣿⠛⠀⢘⣿⣿⢸⡞⣿⣿⣿⡿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⣿⣿⣿⠙⢿⡇⠀⡿⣿⣿⡀⠀⣿⣇⠀⣿⣀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣧⠟⠻⠁⣿⣿⠃
⠀⠀⠀⠀⠛⢻⣿⡶⠘⠀⠀⢰⣾⣿⣾⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⣿⣿⡘⣿⣿⣇⠀⠀⠀⡟⠿
⠀⠀⠀⠀⠀⠀⡿⠿⠀⠀⠀⠀⠘⠛⠛⠋⠻⣿⡟⠻⠿⠿⠿⣿⠛⠟⠙⠃⠈⠿⠟⢻⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢰⡈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⠀⠀⠀⠀⢠⡞⢿⣀⣤⣆⠀⠀⠀⠀⠀⠀⢀⣀⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⠤⠤⠀⠀⠤⢤⡿⠤⢼⠿⠤⣿⠒⠒⢒⠀⡉⠉⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣖⠂⠀⠀⠀⠀⠀⠀⣀⣼⣧⣄⡀⣀⣤⣾⣤⡀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠒⣾⠛⠀⠀⠈⢿⠯⠤⠤⠤⢿⡦⠤⠤⠤⠤⠤⠤⠄⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣠⠾⣇⡠⠐⠒⠢⣼⡤⠒⠒⠢⢀⡿⢦⡀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⢉⡉⠉⠻⣦⡾⠁⣠⠾⡧⠄⠤⠤⢼⠄⠤⠠⠀⡿⢧⡀⠙⣦⡾⠋⠉⣉⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⠊⠀⢀⡁⢠⡟⠀⣼⠃⠀⣹⣦⡤⠴⠿⠷⠦⣤⣶⣁⠀⢹⡆⠘⣧⠀⣁⠀⠈⢠⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣢⣠⣤⣤⣾⣁⠀⢿⡴⠛⠉⠀⠀⢀⠀⢀⠀⠀⠀⠙⠳⣼⠇⢀⣸⣦⣧⣤⣠⡌⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠉⠀⠀⠀⠀⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠁⠀⠀⠀⠈⠙⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⡱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢘⠀⠘⠓⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠢⠤⠒⠁⠉⠓⠦⠄⣀⣀⣀⡀⠀⠀⢀⣀⣀⡀⠤⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣞⠁
⠀⠀⠀⣀⡤⠶⠶⠒⠶⠦⣄⡀⠀⠀⠀⣼⠃⠀⠉⠛⠳⠶⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣤⠴⠶⠛⠋⠁⠀⠘⣆
⠀⣠⠞⠁⣠⠴⠶⠶⠶⢤⣀⠙⢳⣄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠸⣆
⢰⠏⢠⡞⠁⠀⠀⠀⠀⠀⠈⢳⡄⢹⠇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢹⡄
⡿⠀⣾⠀⠀⣴⠶⡆⠀⠀⠀⠀⣷⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢷
⣧⠀⣧⠀⢰⡇⢠⡇⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠘⣇
⢹⡄⠸⣆⠀⢿⡉⠙⠶⠶⠖⢻⡇⠀⠀⠀⠀⢀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⡿⢳⠀⠀⠀⠀⠀⢻⡀
⠀⠻⣄⠘⢧⣀⠙⠳⠦⠤⠶⣾⠁⠀⠀⠀⠀⣼⠁⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠘⣇⠀⠀⠀⠀⠘⣇
⠀⠀⠈⠳⣄⠈⠓⠦⣄⡀⢠⡏⠀⠀⠀⠀⢠⡏⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢻⡀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠈⠙⠶⢤⣀⡉⣿⠁⠀⠀⠀⠀⣸⣥⣤⣤⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠸⡇⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡟⢀⠀⠀⠀⠀⣿⣤⣴⠞⠋⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠉⠙⠳⣄⠀⣧⠀⠀⠀⢀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠛⣇⢀⣾⡄⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⡟⣰⣧⡀⣼⠛⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⠛⠁⠙⢿⡌⣧⠀⠀⠀⠀⠀⠀⢹⡟⠛⠛⠛⠛⢿⡉⠀⠀⠀⠀⠀⠀⣾⣰⠟⠋⠈⠛⠃⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⣀⣀⠀⠀⢹⡘⣧⡀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⢀⡾⢣⡏⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿⢻⣿⠀⠀⣾⠀⣨⠿⠶⣦⣀⣤⣠⣼⣧⠀⠀⣾⣥⣄⣤⣀⡴⠶⢿⡄⠘⣧⠀⠀⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⢀⣿⡼⠛⠓⠚⠁⢰⡏⠀⠀⠈⠉⠀⠉⠀⣹⠆⢸⡇⠀⠉⠀⠉⠀⠀⠀⢹⡄⠘⠳⠚⠙⣧⣷⡀⢀⣼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣀⣀⣀⣀⣀⣈⣻⣶⣶⣞⣛⣛⣛⣛⣋⣀⣀⣙⣛⣛⣛⣛⣲⣶⣶⣛⣀⣀⣀⣀⣀⣈⣉⣉⣉⣁
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡏⠉⠉⠉⢉⣭⣍⢉⡉⠉⠉⣉⣭⣍⠉⢉⡉⠉⢉⣉⠉⢉⣭⣭⡉⠉⠉⠉⢙⠃
⡇⠀⠀⠀⠀⣥⠼⠚⠇⠀⠀⣯⣤⠀⠀⣜⣷⠀⠿⣤⡄⢸⣥⠄
⡇⠀⠀⠀⠘⠃⠀⠘⠷⠶⠂⠿⠶⠖⠾⠉⠙⠇⠶⠶⠋⠺⠷⠶⠆⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⡇⠀⡄⠀⣦⠀⣄⠲⠄⢰⡶⠖⠀⠀⠀⢶⣀⡄⢀⣤⣄⢠⠀⣀⢠⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⢢⡀
⡇⠀⣧⣀⡿⢤⣙⣳⡆⢸⡗⠀⠀⠀⠀⠈⣿⠀⣿⣀⡿⢸⣄⡏⢸⣷⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⢀⠟
⡇⠀⠈⠉⠁⠈⠉⠉⠀⠈⠉⠉⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠉⠀⠈⠀⠙⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⢈
⡇⠀⠀⠀⠀⠀⢸⣟⣷⠀⣟⣻⠆⢀⣾⣆⠀⣶⠀⣿⣆⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠠⠜⠀⠀⠀⠀⠈⠳⡄
⡇⠀⠀⠀⠀⠀⢸⣏⡿⠒⠟⠷⠤⠼⠛⢻⡄⠯⠸⡇⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡘
⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠄⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠀⠘⢷⠖⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠤⠙⠛⠉⠁⠀⠀⣘⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⡠⠆⠀⠀⣀⡈⠃⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣴⡦⢸⣿⡇⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⣙⠃⠀⠅⠖⢠⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⢧⡄⣠⠖⠳⢦⡼⠛⢛⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠉⢉⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠁⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠶⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠄⠒⠒⠀⠉⢩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⠚⠓⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⣸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⠀⠀⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⡆⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡔⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⢀⠀⢠⠀⠀⠀⣤⢠⠀⣀⠀⠀⡀⢠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠄⢀⣄⠀⠀⠀⡤⢀⡄⠠⠄⠀⠀⠀⡤⢀⡀
⠀⠈⠂⠈⠀⠐⠂⠃⠘⠀⠉⠀⠀⠐⠂⠘⠀⠛⠀⠘⠃⠀⠃⠀⠀⠈⠉⠀⠃⠀⠀⠀⠆⠀⠂⠉⠙⠀⠌⠀⠛⠈⠉⠒⠀⠑⠄⠈⠓⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⢉⣉⣩⣭⣉⣉⠙⠛⠁⠀⠀⠀⠀⠀⠈⠛⠛⢉⣉⣉⣭⣉⣉⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⠞⠉⠁⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠈⠙⢦⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⡴⢛⡋⠀⠀⠀⠘⢧⠀⠀⠀⢰⠏⠀⠀⣴⠛⡛⠁⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⡇⠿⡷⠀⡶⠀⠀⢸⡇⠀⠀⡟⠀⠀⠸⣇⠸⣷⠆⣰⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⠶⠶⠂⠀⠀⠀⢸⡇⠀⠀⣧⠀⠀⠀⠙⠳⠶⠆⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠀⠀⠀⠈⠓⠲⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⣤⣤⣶⣶⣶⣤⣤⣤⣴⣾⣿⣷⣶⣤⣶⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⠿⠟⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠖⠛⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠠⠄⠀⣴⣦⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠊⠀⢸⡏⠙⣦⠀⠀⣼⠏⠀⢿⠀⠀⠀⣴⡿⣿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡏⠙⢧⡀⠀⢸⣿⣤⠸⣧⣴⡟⠰⠆⠘⣧⣠⣼⢏⡃⣼⠀⠐⠀⣠⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠘⣧⢰⡎⠛⠖⡺⠉⠀⠀⠀⠙⠀⢠⠀⠀⠟⠋⠀⠘⠃⢸⣦⣤⣾⡻⢹⡇⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡍⠉⠓⢦⣤⠟⡃⠀⠀⠐⡀⠀⠠⠄⠒⠒⢤⠋⠘⡤⠔⢲⠀⢀⣐⠁⠀⢘⡾⠇⣸⡁⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠻⡂⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠘⠷⢶⠤⢤⠦⠴⠃⠀⠀⠈⠀⠀⣸⠁⠀⠈⢳⠶⠾⠻⢛⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣟⠛⠶⢶⣶⠟⠀⠠⡀⠀⠀⠀⠀⠀⢠⣶⠀⠐⣷⠀⢠⠐⠀⠀⠰⢛⠓⢶⣤⡀⠄⠀⠑⢤⠟⠉⠐⠿⢠⡟⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣝⠖⠀⢀⠀⠀⠈⠀⢀⣤⡄⠀⡿⠁⣴⣿⢸⠁⠀⠐⠠⠀⢀⠸⣿⡞⣻⣇⠛⣯⡀⠀⠀⠀⠀⣿⠿⣧⣀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⡠⠟⠋⢠⣾⢿⡉⣿⣁⣾⣡⣴⣦⣀⣄⣌⣦⣿⢧⣿⣿⣯⡛⠿⢄⠀⡀⠰⠃⠀⠈⢻⠟⣩⡾⠃⡀
⠀⠀⠀⠀⢰⣿⠛⠛⣛⡉⠀⠡⠄⡄⠀⠀⣬⡁⠀⣾⣿⡿⠟⣨⣯⡿⡟⠛⠉⠟⠈⠋⠙⡳⢦⣗⣌⠻⣿⣿⣷⢴⣷⡀⡀⢲⡦⠦⠴⣾⠁⠀⠘⠢
⠀⠀⠀⠀⠀⠙⠻⢷⣝⠁⠀⠀⠘⠀⠀⠔⠋⢁⣼⣿⣧⣤⣾⣟⠁⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠙⢿⡒⢼⡿⣿⣷⣙⢓⠈⠀⢀⠀⣀⣹⣿⣿⠿⣿⠄
⠀⠀⠀⠀⠃⠀⠀⠀⣿⠀⠀⠀⠠⣤⡀⠐⠄⠈⠉⡁⠼⣿⠃⠀⢀⠀⠠⢀⠂⢀⡄⢂⢀⣀⡀⠀⠋⣿⡀⠙⣀⠙⢋⢙⠇⢃⣈⡅⠉⠀⣩⡶⠟⠋⣡
⠀⠀⠀⠀⣀⣤⠴⠞⠋⠀⠀⢀⠦⠠⣿⠀⠀⠈⢉⡀⢈⣏⠃⠀⠀⠈⢑⡟⠀⡸⡄⢈⣿⠿⠤⠂⠀⣘⡧⠂⠐⣄⠀⠀⢸⡯⢀⡆⠀⠚⣻⣦⣤⣀⣙
⠀⠀⠀⠘⠿⣤⣤⣚⠃⠀⠘⠣⣄⢐⣯⠈⠆⠈⡉⠀⢣⡗⠀⠀⢠⣄⠃⣀⣚⠀⣿⣀⡜⠐⣄⠀⠀⢀⣿⠀⢀⡇⠱⠤⣼⣆⢀⡘⠃⠀⠸⢟⣛⣿⠿
⠀⠀⠀⠀⠄⠀⠉⠙⣿⠐⠂⠀⡀⣨⡟⠀⢀⠤⠠⢄⠀⢻⡅⠀⠀⠀⠈⠙⠀⠀⢩⠀⢙⠀⠀⠀⠂⣸⣿⣴⢟⣳⣳⣦⡌⢧⣬⡇⠑⣶⣾⠋⠉⢀⡀
⠀⠀⠀⠀⢀⣤⠶⠛⣡⠀⠀⠀⢀⠀⠀⢺⣧⣤⣴⣄⠘⣯⢿⣅⠤⠀⠀⠋⠀⠀⠀⠀⠈⠀⠀⢁⣴⣿⣾⣿⣾⣻⣍⣽⠄⠀⠀⠀⠀⢩⣿⣦⣄⡀⡑
⠀⠀⠀⠀⠸⣷⣦⣾⣿⣶⠤⣀⡀⢀⠀⠌⣶⣮⡙⣿⣿⣟⠲⠛⢶⣦⣠⡄⠀⠀⠀⠀⢀⣀⣵⣿⡟⣽⣾⡿⠟⠚⢛⠟⠐⢠⣥⣤⣤⣼⣯⣉⣛⣿
⠀⠀⠀⠀⠀⠤⠤⠀⢀⣼⠃⠀⠉⠸⠄⠀⠈⠩⠉⠘⢿⣮⣿⣶⠀⠙⡛⣿⡿⡗⢾⡛⢟⡿⢛⣿⣾⣿⠿⠀⣠⣴⠏⠐⢠⣯⣀⠀⢻⡏⠀⠉⠉⠍
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⣾⣄⡖⠃⠀⠀⠀⠀⠘⢷⣦⡘⢻⣿⣷⣾⣝⢿⡀⠣⣬⠏⢸⠀⣿⡟⢛⡏⢀⣼⠟⠡⠀⣀⡀⠈⢿⣰⣾⠿⣶⣄⠙
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠛⢷⡶⡤⠖⠃⢦⡀⠂⢉⠷⣬⣿⣿⣿⣿⣼⠉⣿⡿⠀⠘⣧⢏⣡⣾⡧⠈⠁⢀⣠⠈⠙⢿⣯⣿⠋⠙⠛⠾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠⡟⢀⣤⢀⣠⣿⠀⠀⢀⡀⠈⠉⠙⠛⢿⣯⣴⣯⣷⣤⣀⠜⣚⠩⠁⠀⣠⠀⠀⢹⡦⢀⡰⠿⣿⣦⡀⢲⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣠⣺⣽⡷⢾⡅⢀⣀⡴⠋⠹⠶⠄⠀⠾⠠⢾⠉⣩⣃⣻⢀⠠⠀⣾⠅⠉⢛⠀⢰⣷⠛⠛⠷⣦⣽⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢟⠛⠡⠀⢸⠇⣼⣷⣤⣄⣼⡗⢀⠀⢀⣔⠀⠙⠃⢠⣉⠹⣀⠀⢸⣅⣤⣌⠻⣿⣿⠀⠠⣀⣀⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠀⣿⣀⣿⠟⠁⢹⡇⠾⢿⣶⠾⣿⠀⢠⡤⢼⡿⢶⡝⠷⢾⡏⠀⠙⢷⣜⣿⡇⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢡⣄⣀⢸⣆⣶⡞⠀⠀⠸⣆⢸⣶⡟⠀⠀⢲⡄⣶⡇⢀⣤⣤⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠯⠤⢤⣤⣀⢻⣾⣿⡀⣠⣤⣤⠿⠛⠓⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⡿⠛⣿⠟⣛⠻⣿⣿⠯⠭⣓⠛⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠡⠞⠗⠉⠁⠐⠚⠃⠐⠒⡒⠅⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⢀⠔⣠⣴⡶⣞⠀⠀⡼⣛⣻⣦⣿⡟⣿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⣿⣿⡀⣼⠟⣫⠝⠻⣆⢰⣧⠖⠛⣯⡿⠳⡜
⠀⠀⠀⠀⠀⠀⠀⠛⠸⢻⣿⢿⡟⠏⠀⡼⠁⠀⠀⠘⠞⣧⢀⡀⠈⢿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢚⢿⠀⢰⠁⠀⠀⠰⠀⠸⠈⠳⣄⣀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠠⣮⠇⠘⡷⣄⣀⣠⡴⢷⣄⠀⠀⠉⠛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣀⢙⠀⠀⠀⠺⠛⢋⠔⣯⡙⠆⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢦⣿⣄⠀⣠⡏⠀⠘⣿⣄⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠃⢠⠙⢿⡜⠘⠳⣦⣤⣽⣿⣿⣶⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠸⣇⠈⣟⢧⡲⢤⣤⣤⣄⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢶⠀⠀⠼⡦⠘⢢⣝⣛⣻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠘⠁⢀⠀⣿⠀⠀⣙⢶⣤⠶⠚⢻⣿⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣿⣠⡿⠛⠛⠻⡷⣄⡚⠁⠀⢿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠰⣿⣦⡆⠀⠸⠏⠀⠀⠀⠀⢀⣸⣇⣤⠀⣶⣆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠈⣅⣹⡀⡀⠉⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣆⠀⡀⠀⢷⡀⠀⠀⡀⡄⣀⣀⣉⣸⣧⣤⣤⢼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣧⠤⠶⠉⢿⣉⡍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⡀⠀⢀⡼⠋⠀⢠⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠻⠷⠚⠉⠀⠀⠀⣾⠀⠀⢀⣾⡁⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⣸⡴⠃⠀⠀⣾⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⠟⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢠⢤⡄⠀⠀⣛⣩⣷⡀⢠⣶⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣄⢹⠻⣷⣄⡤⣽⠇⠀⠀⠹⢿⣿⣷⣾⣟⣤⠾⣷⣿⡿⠉⣉⠽⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠷⠄⠭⡓⠿⣿⣿⣿⣿⣶⡶⠒⠚⣷⣾⡛⠉⠻⢀⡘⠛⢋⣠⠞⠁⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⣸⠷⠦⠴⠤⣤⡁⣀⣉⠘⠋⠸⠋⠀⣠⠊⠁⠀⣻⣦⣀⢀⡀⣀⠀⢀⣤⣠⣾⠿⢋⡄
⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣤⠐⣎⠛⠷⠬⣭⣙⣐⣋⣉⣁⣠⣤⠾⠟⡩⠛⠢⢭⣭⣿⠿⣭⡭⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠢⠤⠭⠭⠩⠥⠄⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠋⠉⠉⠁⠐⠛⠻⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠏⠛⠋⠙⢁⣀⠀⢀⢐⠒⠠⠄⠺⢿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠍⠀⠀⣂⡬⠛⢃⣉⡩⣤⣤⣬⣅⡐⢦⠀⢶⡹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠈⠡⠔⢒⡉⠁⠀⠀⠀⢤⣄⡙⢦⡐⠈⠇⢼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠠⠀⣠⣶⡿⠃⠀⠀⠀⢀⣀⣉⠻⢦⡙⢢⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢠⡾⠋⢀⣠⠴⢦⡀⠀⡌⠁⠉⠳⣄⠙⠃⠀⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡷⠋⢀⡴⠋⠀⡀⣀⠃⣀⠀⠘⠃⠀⢹⡆⠀⣰⠋⣉⠍⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢻⣆⡎⠀⣀⡠⠝⠁⠀⠸⣆⠀⠀⠀⣴⡏⠀⠁⣾⢟⠆⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡿⠛⠀⠀⠀⠀⢀⡀⠘⣷⠶⠾⠛⠁⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⣀⠀⠀⣠⡾⠛⣆⠀⠉⠀⠀⢸⡅⠞⠲⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣿⡿⠋⠀⠀⠘⣦⠀⠀⠀⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢠⣤⠤⠀⠀⠟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠆⠀⣧⡛⠷⣶⣤⠞⠀⠀⢻⣿⣿⠙⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣿⣿⣶⣤⣄⣀⣀⣴⣿⣿⣿⠀⠀⠈⠙⠳⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⢴⣤⣄⡀⠙⠻⠿⠋⠠⣿⡿⠛⠁⠀⠀⣀⣀⣤⣶⡾⠆⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠈⢻⣷⣆⠀⠀⠀⢻⡇⠀⠀⠀⢸⣿⣿⡍⠁⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠈⣿⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣶⣤⣤⠀⣼⣿⡟⠀⠀⠀⣿⢀⣿⠀⣆⠀⠀⠈⢿⣿⣷⣤⣶⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⡟⠁⠀⠀⢰⢁⡌⢹⡇⠻⣄⣤⣀⠈⠛⠿⠟⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠁⠀⠀⣀⡴⠟⠉⠀⢸⣏⠀⠈⠉⠉⠁⠀⠀⠀⢀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣄⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠋⠛⠛⠛⠛⠉⣄⠛⣯⠙⠛⠛⠛⠿⢛⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢸⠟⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠘⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⠠⣔⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣽⠀⠀⠀⠀⠀⠀⠸⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡿⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⣎⣡⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⠛⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣶⣿⣿⣿⣿⠿⠿⠳⠶⠶⠞⠛⠛⠀⠀⣀⡠⠶⣴⡿⠟⠛⠉⠉⠉⠉⠙⠛⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣤⣴⣎⡀⣼⠛⠶⣄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⡿⠉⠀⠈⠳⠶⠶⠿⢿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⢀⣀⣀⣤⣤⡿⣿⠳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠻⣿⡷⠶⣶⣶⣶⠶⢾⣿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣬⡿⣷⠿⠟⠛⡛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣉⣙⣛⣙⣉⣿⣉⣄⣹⣏⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣥⣬⣿⣥⣼⣿⣿⣭⣭⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣾⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠭⠋⠻⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⠟⠃⢐⣛⢿⠄⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣻⣸⣇⣀⢀⢉⠀⠩⠀⡿⢻⣟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢡⣿⢛⣿⣿⣌⣉⣍⠐⠒⢷⣈⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⢿⣿⠟⢉⣉⡴⡉⠀⢀⡼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣈⡉⡉⢉⣀⡁⣿⣏⠀⢨⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠻⡟⠀⠘⣧⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣻⣿⣿⠀⡄⡃⠀⠀⠘⢧⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣍⣉⣡⢻⡾⠁⠁⠀⠀⠀⠈⣷⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢷⣶⣾⣻⡇⢰⡀⠀⠀⠀⠀⠹⡇⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣾⠏⢿⡟⢦⣇⠀⠀⠀⠀⠀⢿⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣾⠁⠀⢸⠓⠀⠛⠀⠀⠠⠐⠲⠾⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣾⠉⠀⠀⣯⠀⠀⠀⠀⠀⠀⢀⣠⣤⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣟⠲⠶⠧⠤⠤⠤⠴⠴⡚⡋⣩⢰⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠛⠒⠺⠃⠚⢘⠂⠸⡇⡆⢀⣀⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠀⢸⠓⠶⢸⡀⢘⡃⡅⢸⠄⡏⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢙⠐⢒⠒⢊⢸⣠⢀⡁⡇⠀⣄⡅⠢⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣧⣨⣁⣉⠀⢉⠈⣿⣏⡁⣇⠀⢷⣰⣀⣹⡄
⠀⢠⠴⠖⠛⠛⠉⠉⠉⠉⠙⠛⠛⠒⠻⣏⡈⠙⠯⠭⡭⠽⠷⢾⣧⡖⠮⣧⣏⠀⣿⠉⠓⣄
⠀⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣉⠛⠳⠶⣦⣬⣅⣿⠉⠁⣠⠿⠛⠒⠛⠒⠦⣿⣤⣄⣀
⠀⠓⠮⣽⣛⣒⣒⣒⣚⣋⣉⣉⣉⣭⠤⠬⢭⣛⢒⠒⠒⢛⣁⣯⠛⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠉⠛⠢⣙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠮⣝⡒⠶⠤⣄⣀⣀⣀⣀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠈⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⠿⠿⠿⠷⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠾⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠿⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣦⡀
⠀⢀⣴⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡷⠀⠀⠀⠀⠀⠀⠰⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿
⠀⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⢀⣴⣿⠟⠛⠉⠉⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠛⠉⠙⠻⠿⣿⣦⣄
⠀⠀⠀⠀⣾⣿⠀⣀⣀⣠⣤⣄⣀⣀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⣿⣿⠟⠋⠉⠻⣿⣭⣿⠟⠛⠻⢶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣀⣀⣠⣤⣄⣀⣀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠉⠉⠉⠘⢿⣿⡿⠛⠿⣦⣼⣿⠇
⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⣤⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⠿⣶⣶⣶⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⣀⣀⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠸⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠙⠻⢿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣤⣄⣀⣀⣠⣾⣿⡿⠛⠉⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⢰⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁
⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀
⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠉⠁
⣴⣿⡟⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣻⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣤⡄
⣻⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣴⡿⠉
⠘⣿⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠿⢛⣡⣶⠟⠁
⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠿⠛⠉
⠀⠀⠀⠙⠻⢿⣷⣦⣤⣤⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⠶⠲⠶⠶⠶⢶⣶⠲⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠛⣀⠐⠛⠈⠓⣤⡀⠀⠙⠛⠷⣄⡙⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⠀⠀⠈⠒⠂⠀⠀⠈⠀⠶⠀⠀⠀⠈⢳⡀⠈⢡⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡰⠉⡄⠀⠶⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠻⡀⠀⢷⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠀⠀⠀⢀⠀⠀⠉⠙⠶⠤⣄⠀⣀⠀⠀⠣⣀⠀⢻⡀⠀⠙⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠡⠀⠀⠀⠻⢦⠜⢀⠀⢀⣤⠀⠀⠈⠿⠛⠓⢄⣠⡉⠁⢸⡇⠀⠿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⠑⣀⠀⠀⠀⠀⠳⡌⣀⠸⡆⠀⠀⠀⠀⠀⠀⠈⢦⡘⢃⡴⠃⠀⠀⠀⠀⠀⡇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠄⠫⠀⣆⠀⠀⠀⠀⠀⠇⠀⠛⠛⠧⠤⣤⡀⣰⣟⣁⣴⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⠀⠒⡀⠘⠳⣦⣄⠀⠠⣤⡠⠴⠶⠂⣀⡾⣛⠛⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢀⠁⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⣿⣶⡟⠷⣿⣿⠶⣶⣤⣴⠟⠻⠛⠂⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠐⠀⠱⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠛⡋⣠⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠈⠀⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆
⠀⠀⠀⠀⠠⠄⠈⠉⠙⠋⠁⠦⣀⠀⠀⠀⠀⠀⠘⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠋⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠢⠈⠳⡄
⡀⠁⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠿⠗⠿⠇⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠃⡀⠀⣠⣶⣄⣀⡀⠀⠶⣠⠆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠙⢶⣤⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠉⠒⠀⣤⣤⣤⡀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡗⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⢳⠐⠛
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠐⠒⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠴⠤⢀⣀⡀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢄
⠀⠀⠀⠀⠀⠀⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠘
⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠀⠀⠀⣿
⠀⠀⠀⠀⠸⠇⠀⠀⡇
⠀⠀⠀⠀⠘⢣⠀⠀⡇
⠀⠀⠀⠒⠐⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠃⣀⠀⢀⡀
⣤⣤⣤⣤⣶⣶⣾⣥⣤⣭⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⠿⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⡀⣤⣶⡀⠀⢺⣿⠀⣿⣿⠁⠹⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡀⠐⣶⣆⡀⠈⣿⣇⢸⣿⡇⢸⣿⣿⣆⠸⣿⡇⢻⣿⡄⠶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⣤⡄⢰⣶⣿⣆⠀⠸⣿⡏⠉⢻⣿⠄⣿⣿⣿⣄⢿⣿⠀⣿⣿⠈⣿⣇⠻⣷⣿⣧⠸⣿⣇⠀⣹⣿⡆
⠀⠀⠀⠀⠐⣿⣇⠀⣿⣿⡆⢸⣿⠃⢸⣿⠻⣿⡄⠀⣿⣿⠶⢿⣿⡄⢸⣿⡌⢻⣿⣿⡆⢻⣿⡄⢿⣿⠀⠉⢻⣿⠄⠙⠻⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠸⣿⡆⣿⡟⣿⡼⣿⠀⢸⣿⣠⣿⣿⡄⢹⣿⡄⠀⣿⣿⠘⣿⡇⠀⠙⠿⠇⠘⠛⠃⠈⡉⢀⣀⣠⣤⣤⡄⣶⣦⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣹⠇⠹⣿⡿⠀⣿⣿⠉⠉⢿⠿⠸⠟⠃⠀⠉⠉⠀⠁⣀⣄⢠⣤⡴⣶⣶⡄⢸⣿⡈⠉⢹⣿⡀⠀⠈⢿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⠷⠀⠀⠙⠃⠀⢉⣁⡀⣠⣄⠀⢰⣶⠀⣿⡟⠛⣿⣧⢹⣿⠀⣿⣇⠀⢿⣿⠘⣿⡇⠀⠸⣿⡇⠀⠀⠀⢺⣿
⠀⠀⠀⠀⠀⠀⢀⣤⡄⣶⣦⡐⠿⢿⣿⡛⠁⢹⣿⠀⠸⣿⡇⢻⣿⣴⡿⠟⠘⣿⡇⢻⣿⠀⢸⣿⡆⣿⣷⠀⠀⣿⣧⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠸⣿⣥⣈⠉⠁⠀⠈⣿⡇⠀⠸⣿⡇⠀⣿⣧⢸⣿⡄⠀⠀⠀⣿⣷⠸⡿⠾⠿⠛⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⠀⠀⢿⣿⠀⠀⠻⣷⡴⡿⠏⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡆⠾⠟⠀⠀⠘⠋









⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠢⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣧⠀⠀⣸⠳⢦⣀⣄⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢳⠙⠳⢶⡟⠠⠀⢹⡿⣆⡴⠟⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⣄⣀⡴⠋⠈⠀⠈⣇⢱⢟⠄⢀⠀⠈⠀⠋⠅⣄⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⠉⠀⠈⠶⠡⢀⢹⡈⢾⢷⠐⡆⡀⠀⢸⣰⡟⡜⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⢻⡘⣷⠀⠀⠈⠄⠀⠀⢷⠀⠆⠀⠇⢠⠠⣏⣻⣼⠼⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠷⣿⣤⡙⢧⠀⣀⡴⠛⠉⠉⠉⠉⠀⠀⠚⠉⠉⠀⢀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢿⡌⢓⠨⠒⠁⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⢠⡿⠿⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢦⡹⣆⢻⠀⠀⠀⠀⣴⠿⣛⣛⡁⠀⠀⠀⠀⠀⣴⠞⠋⢹⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⢺⣷⡱⣌⠻⡄⠀⠀⠀⣰⠞⠉⠉⠉⠓⢦⡀⠀⢸⠃⣴⡦⢸⡀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣮⣢⣻⠀⠀⢸⠏⠀⣠⣶⠲⠀⠈⢷⡾⢿⣇⠸⠟⠀⢧⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡤⠬⡍⠀⠀⠸⡆⠀⠉⠟⠃⠀⠀⣸⠀⠀⢙⣦⣄⣀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠦⠒⠄⠀⠀⠀⠹⣆⡀⠀⠀⣀⣴⠏⠀⢀⡼⠃⣈⡽⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣇⠀⠀⠀⠀⢩⣛⣫⣭⡤⠤⠴⠖⠚⠋⢹⡇⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠈⢧⣤⣤⣤⣶⣶⣿⣿⣇⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠈⣿⣿⣿⣯⠿⠟⢛⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣷⡦⠤⢄⣈⠉⠀⢀⣀⢴⡟⠁⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠋⠁⠀⣧⠀⠀⠀⠀⠉⠀⠀⠸⡏⠙⡇⠀⠀⢹⣦⣤⣀⣀⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⡇⠀⠲⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹⡀⡀⠀⠙⠲⣄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠉⠀⢠⡇⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡟⠁⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠙⢟⡒⡲⣾⣿⠹⣚⡞⣾⠏⠀⠀⢀⣠⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣤⠤⠤⢤⣄⡙⣄⢹⣧⠰⡻⣵⠇⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿⡿⠆⠿⠋⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣠⠄⢀⣿⣿⣿⣿⡄⠈⢉⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣯⡙⠿⢿⣿⣿⡿⠿⢋⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⢀⣀⣠⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢷⣤⣾⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠁⠀⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⣿⠀⠈⠿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡧⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣟⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⡿⠿⠃⠀⠀⠘⠿⣿⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠰⠀⢀⡀⠏⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠀⠦⠀⠀⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠠⠔⠀⢆⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠁⠑⠀⠀⠈⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠁⠀⠒⠀⠆⠀⠀⠀⠀⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠀⠛⠉⠀⠀⠀⠠⠀⠙⠃⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠐⠚⠀⠀⢳⠔⠀⠀⠐⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡔⣠⠶⠟⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡋⠙⠈⠉⠁⣀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠈⠈⠁⠛⠉⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠁⠀⠀⠂⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⣅⣀⠀⠀⠀⠀⡦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠸⠤⣄⣀⣀⠁⡀⢶⣎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⡋⠀⠀⠀⠰⣖⡠⢀⠀⠉⠀⠈⢿⣦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠀⡀⠉⠀⠐⠢⠟⠁⡘⠦⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⢄⠀⠀⠀⠀⢀⡀⡀⠄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⡠⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⢤⣐⠆⢀⣠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⠠⠁⠀⠀⠂⠠⠤⠀⡀⠀⠄⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠑⠢⠴⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠖⠂⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⡀⠈⠁⠀⣉⣉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣭⣯⣵⣭⣯⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿⣿⣿⣷⣷⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⠶⣿⡿⠛⣛⠻⠿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠾⠟⣧⢀⣀⠹⠿⣶⣄⠙⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡦⠶⠎⠁⠨⡉⠑⠠⣐⠄⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢯⠭⠐⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠔⠒⣦⠀⠀⠀⢡⢢⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣶⣄⣤⣤⡤⠒⠁⠀⣠⢿⠈⠆⣷⠀⢹⣾⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣌⠙⡿⠬⢤⡤⠴⠶⠋⠁⢸⠀⠀⡟⢠⠌⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⢦⣀⣴⣆⣀⣴⣤⣴⣿⠀⠀⡗⠈⡷⢴⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣀⣀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣀⡇⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡋⠓⠢⣭⣀⣈⣋⣁⣨⠟⠀⢰⣿⡿⢠⠖⠋⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠶⢤⣀⣀⡉⠉⠉⠀⢀⣧⢊⣼⡧⡏⠀⠀⠀⢹⡏⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⠀⠀⠀⠀⢀⡠⠞⣱⣿⠏⢰⡇⠀⠀⠀⢸⣇⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠟⠓⠐⠛⢉⣴⠞⢡⠋⠀⢸⡇⠀⠀⠀⠀⢻⡄⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⢳⡄⠀⣴⠟⠁⠀⡼⠀⠀⢸⡇⠀⠀⠀⠀⠘⣷⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠙⠓⣾⠥⠶⣄⣸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⡏⠀⠀⠘⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢹⡇⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠘⠀⠀⠀⠀⠉⠀⠀⠀⢸⠇⠀⠀⠀⠀⢀⣺⡇⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢠⢠⣻⡇⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣀⣤⣴⣦⣾⣷⡿⣷⡛⠦⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣹⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏⠉⢙⡋⠉⣁⠀⢷⡘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢩⡇⠀⠀⠀⢦⣄⠀⠀⠀⠀⣿⡀⠀⣼⣇⠀⣿⣄⣾⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠀⠀⠀⠉⠛⢿⡄⠀⠈⠻⠞⠁⠙⠋⠀⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠿⠗⠾⠿⠶⣶⡖⢦⣤⣤⣴⣿⣤⣴⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠋⠁⠀⠀⠀⠀⠀⠉⠛⠛⠦⡍⠛⠿⠿⠶⢶⣤⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣦⣄⣀⣀⣀⣀⣀⣠⣿⣅⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠴⠶⢶⣄⣀⣀⣀⣬⣽⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣍⣉⣉⣉⣉⣹⣿⡙⠛⠶⠶⠶⢶⣾⣟⡻⠯⠭⠵⠒⠛⠻⢧⡭⠭⠭⠥⠤⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁



⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⠿⠿⠿⠿⣿⣿⡿⠿⠿⠿⠿⠿⣿
⣿⣶⣶⣶⣶⣾⣶⣷⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡶⠶⠿⠟⠛⠛⠛⠻⠿⠷⠶⢶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⢀⣸⡏⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⢰⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⣿
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⠀⣿
⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡾⣷⠀⠀⢀⣿⡄⠀⠀⠀⠀⣼⣇⠀⠀⠀⣀⡿⣧⡀⠀⢠⡟⢻⣿
⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠙⠓⠊⠁⠀⠈⠳⠤⠞⠀⠙⠓⠦⠴⠚⠁⠈⠛⠒⠚⠉⠀⠀⠉⠉⠉⠀⠈⣿⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠛⠲⡀⠀⠀⠸⣷⡀
⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠞⠀⠀⠀⠀⡴⠚⠉⠉⠉⠓⢤⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⣀⣀⠀⠀⢹⠀⠀⠀⠹⣷
⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡞⠀⠀⢀⣀⡀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠿⠟⠀⠀⢸⠇⠀⠀⠀⢹
⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠰⡞⠋⠀⠀⠀⢸⡇⠀⠀⠘⠿⠃⠀⠀⡶⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠘⢷⣄⣠⠴⠶⠦⣤⡴⠃⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⣠⠇⡀⠀⠀⠀⠀⣀⠈⠛⠲⠦⠴⠶⠛⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢻⡏⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠶⠖⠛⠁⠸⢛⠟⠻⡟⠛⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠘⢷⣄⣈⣁⣀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⠴⠃⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠈⠉⠑⠒⠢⠤⣤⣤⣤⣤⣤⠤⠶⠒⠛⠉⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⣀⣤⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢦⣄⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣏⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠙⣷⠏⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠷⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠞⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠋⠉⠉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⢻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠈⣿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠛⢻⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣐⣿⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⣈⣉⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⠤⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⠤⡀
⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⢽⣿⣿⣿⣿⣽⣿⣿⢿⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻
⠀⠀⠀⠈⠒⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠍⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣿⣿⢟⣫⡔⠓⠆⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣀⣀⣀⠀⠙⣫⣶⣿⣿⣿⡷⣾⣛⡻
⠀⠀⠀⠀⠀⡾⠻⣯⡭⢉⠉⠙⠛⠯⣿⣿⣿⣿⢋⡏⢸⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⣼⣿⠅⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣷⡀⠙⠛⠛⣷⠰
⠀⠀⠀⠀⠀⢠⣿⡿⡔⢂⣀⣀⣀⣘⡿⠛⣿⣿⣿⣻⣷⣄⠀⣴⡿⠭⡅
⠀⠀⠀⠀⠀⢸⣿⣷⠇⠍⠉⢉⠝⠋⠁⣀⠀⠙⣻⣿⡿⠿⠖⢛⠉⠁⠙⠃⠀⢀⠟⠛⠛
⠀⠀⠀⠀⠀⢸⣯⣿⠤⠀⠀⠋⣀⡴⡚⠍⠈⢱⣿⣿⣿⣶⢴⠖⡀⢲⠊⠀⠀⠈⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣗⠦⡤⡾⣭⢮⢤⣀⠀⠀⣿⣿⣙⡿⢿⣤⢣⡎
⠀⠀⠀⠀⠈⠉⠉⠻⠿⣿⠟⡻⠿⢿⣼⢈⢦⡀⣿⣏⣽⣯⣿⢼⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠄⠠⠀⠤⠍⢿⣼⢹⠿⣿⣟⡛⠿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠘⠀⠀⠀⠀⣠⣼⣿⣾⣰⡏⠶⢬⣳⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢸⢁⠇⠀⠀⢀⡾⣫⣯⠟⡟⡟⣿⣭⣓⡟⠁⠀⠀⠀⠰⡔
⠀⠀⠀⠀⠀⠀⠀⢹⢸⠀⠀⠀⣼⢊⠜⠁⣰⣿⣱⣻⣗⣒⡆⠀⠀⠀⠀⠀⢸⢰
⠀⠀⠀⠀⠀⠀⠀⠸⢬⣄⣠⣼⣵⡟⠀⢰⢳⡷⡳⣟⠯⣲⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠹⡉⠉⠁⠀⠀⢈⣿⣑⣷⡼⠋⠁⠀⠀⠀⠀⠀⢀⡟⠰
⠀⠀⠀⠀⠀⠄⠀⠀⠘⣦⠱⣄⠀⠀⡴⠮⢵⣽⠿⠋⢀⠀⠀⠀⠀⠀⢀⡞⠡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠂⠀⣸⣿⣷⣅⠀⠀⠉⠀⣀⣀⣠⡶⢋⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⢿⣿⡻⣿⣿⣿⣶⣶⣶⣶⣾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⠆⠀⠀⠀⠘⣧⡀⠀⠀⢀⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣠⣴⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠈⣷⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢶⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢹⡄⠀⠀⠉⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢺⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠈⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣤⣀⣀⣀⣀⣠⡴⠾⠿⣤⣤⣤⡴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠈⠉⠉⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡟⠳⠶⣤⣀⡀⢀⣤⠞⢻⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣩⣿⣿⣄⠀⢸⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣴⠞⠻⣿⣿⡟⠻⢾⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠸⠿⠿⠿⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠈⠀⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢐⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣘⣫⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⢣⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢆⡀⠀⠀⠀⠀⠀⠻⠀⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⡄⠀⠀⠀⠀⠀⣀⡠⣄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠳⣄⠀⠒⠀⠁⠀⠈⠊⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀⣀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⢀⡀⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠀⠇
⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⢄⣀⠀⠀⠀⠘⠀⢠⠀⠸
⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⡆
⠀⠀⠀⠀⠀⡇⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢀⠁⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⢀⣀⠇⠀⠀⠀⠀⠀⣃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⡀
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣶⣶⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣀⣀⣀⣀⣀⣀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⣾⣿⣿⣿⣿⣿⣿⣷⣌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣽⣿⣽⣿⣯⣻⣿⣽⣿⣍⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢾⡟⣥⣿⣭⣾⣼⢷⣧⣵⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠛⠛⠛⠛⠛⠟⡣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢼⣏⠀⠀⠀⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣤⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠓⣶⣦⣶⡀⠰⣴⣴⣆⠀⠻⣿⣶⣆⠀⢲⣶⣴⣆⠀⢶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠈⢻⣿⣷⡄⠈⢿⣿⣷⡀⠘⢿⣿⣧⡀⠙⣿⣿⣦⡀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠧⠤⠹⠿⠿⠦⠤⠹⠿⣿⣦⠬⠿⠿⠿⠤⠌⠿⠿⠷⢤⠨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠢⣤⣤⣤⠀⠠⣤⣤⣤⠀⢿⣿⣤⣄⠀⢤⣤⣤⡄⠀⢤⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠈⢿⣿⣷⡀⠘⢿⣿⣧⡀⠙⣿⣿⣦⡀⠹⣿⣿⣦⠀⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡿⠦⠀⠹⠿⠿⠆⠈⠻⠿⣿⣄⠈⠿⠿⠷⠄⠈⠿⠿⠷⣄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠆⠀⠄⠀⠀⠀⠀⠀⠄⠀⠿⠿⠀⠠⠀⠀⠀⠀⠀⠠⠀⠐⠀⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⣷⣤⣾⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⣶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣴⣧⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣄⠀⢀⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣷⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣶⣾⣴⣶⣦⣤⣤⣤⣖⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠀⠀⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣤⣴⣾⣿⡿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⣀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠠⠴⠶⠮⢽⣿⣿⣿⣿⣿⣶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣶⣶⣶⣿⣿⡟⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢅⣠⣄⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣿⣿⣿⣿⣿⡟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣽⣦⣧⡤⠤⠼⠿⠿⠟⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠒⠛⠛⠉⠉⠉



⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡄⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠀⠇⠀⢸⣿⣿⣿⣿⣿⢟⡭⢇⡴⠔⣤⠢⡵⠙⢿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣻⠇⣤⠚⣉⠀⠖⠠⡍⢳⣿⣿⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠑⡉⢸⣿⣿⣿⡗⣃⡸⠃⢸⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⣿⣿⣥⢾⣷⠀⣯⣿⣶⣾⢰⣪⣾⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⣿⣿⣿⣙⣷⣻⣠⣈⡹⣿⣷⠿⣿⡿⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣝⠳⣠⣴⣟⣫⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠶⡒⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠉⠂⠄⣀⣀⣀⣤⡀⠀⠀⠤⠤⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠑⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⠤⠄⠀⠐⠒⠂⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠘⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠤⠀⠐⠂⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠤⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣀⠀⠀⠀⣀⣀
⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠈⠣⡀
⡀⠀⠀⠀⠄⠋⠀⠀⠛⠦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠷⢀⠃
⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⣾⠇
⡇⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣻⣿⣛⣿⣟⣿⣿⣄⣀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⣆⣹⠀⠀⠀⠀⠀⠀⠀⡾⠛⠋⠉⠀⠈⠁⠀⠉⠁⠋⠁⠉⠙⠛⠛⢳⣾⠁⠀⠀⠀⠀⠀⢀⡄⠈⠹⡆
⠀⠈⠟⠳⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⣦⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠑⠾
⣄⠰⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠈⡇
⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠀⠀⠀⠀⣀⡀⠠⠴⠤⠤⠀⠀⠀⠀⠀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢲⠚⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⣿⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⣿⣿⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⡇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⣿⣿⠏⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡏⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⢠⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⣿⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠃⠀⠀⠀⢸⠀⠀⡈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⡇⢸⠀⠀⢇⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣟⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠺⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠈⠓⠀⠀⠺⠇⠀⠀⠠⠓⣀⣀⡀⠊⠨⠆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠛⠉⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⠟⠛⠛⣿⣿⡿⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢀⣾⣿⡛⠉⠁⣼⣇⠀⢠⣶⡄⠀⠸⣿⡄⠀⢰⣿⠏⠀⣴⣄⠀⠘⣿⠃⢠⡀⠀⢉⠉⢻⣿⣷⡀
⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⣿⡇⠀⢸⡿⠀⠘⣿⣿⡄⠀⢸⣶⣿⡇⠀⣿⣧⣾⣿⣿⡇
⠀⠀⢸⣿⣿⡿⠀⠘⣿⡿⠀⢸⣿⣿⠀⠀⣿⡇⠀⢸⣷⠀⠀⢿⣿⡇⠀⣸⣿⣿⡇⠀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⢻⣿⣇⣀⣀⣙⣃⣀⡈⠛⠋⣀⣼⣿⠃⠀⠘⣿⣆⠀⠀⠉⢁⣰⣿⣿⣟⣀⣀⣨⣿⣿⣿⡟
⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠿⢻⣽⣽⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣞⣛⠢⠀⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⣿⠋⡹⢟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠠⣤⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣀⡀⠀⠀⠀⢠⣄⡄⢹⣿⠏⠙⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣤⣴⣿⣿⣇⣼⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⡇⠀⠀⠀⠀⠀⣰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡻⠟⢋⣟⣿⣿⣿⣿⣋⣀⠀⠀⢀⣤⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣻⣟⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠐⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⠀⣈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠣⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣧⣻⣿⣿⣿⠇⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣜⡂
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⡙⠧
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠨⠖
⠀⠂⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⣀⠰
⠀⠀⠀⠈⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠑
⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠁
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠦⠘
⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣥⣤⣤⣤⣭⣬⣤⣭⣤⣭⣤⣤⣬⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⢸⠀⠀⠀⡀⢀⠀⡀⠀⣀⡀⠀⣀⡀⢀⣀⡀⠀⣀⡀⠀⣀⣀⠀⢀⡀⠀⣀⣀⠀⠀⠈⡇
⠀⠀⠀⢸⠀⠀⠀⡇⢸⢧⣿⢸⡉⠁⢸⡉⣻⢸⡯⡟⢸⡯⣽⠀⡿⠍⠠⡏⠉⠀⢹⡏⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠀⠁⠈⠀⠉⠈⠉⠁⠈⠉⠁⠈⠀⠉⠈⠁⠈⠀⠉⠉⠀⠉⠉⠀⠈⠁⠀⠀⠀⡇
⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢐⠆⠀⠀⣀⠤⠒⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⠀⠀⠀⣰⣫⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠀⢻⡆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠉⣆⠀⠀⢀⣀⠤⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⠼⣶⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠟⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠉⠻⣿⣿⡇⠀⢠⣤⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠺⠂⠀⣿⣿⣿⣶⣤⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⡟⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠛⠿⠿⠛⠋⠁⣠⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⡀⢀⣶⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⡇
⠀⠀⠀⢰⣿⣿⣿⣿⡿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣧
⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⡇
⠀⠀⠀⠛⠿⠿⠟⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠃⠘⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠛⠁⠀⠀⠈⠛⠻⠿⠛⠁

⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣬⣯⣭⣭⣬⣭⣵⣤⣭⣽⣭⣤⣤⣿⣿⣿⣿⣿⣿⣶⣿⣷⣾⣷⣶⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣾

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⡿⡿⢿⣿⣇⣾⣿⠻⣟⠻⡋⢉⣻⣿⣷⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⣿⣛⣊⣿⡿⡟⣿⣿⣿⣿⣝⣽⣷⣾⠏⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⢿⣿⣿⣿⢸⣇⣿⣿⣟⣾⣟⣽⣿⣯⡴⣾⣿⣿⣿⣯⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⡼⠋⠁⣻⣿⣿⢱⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⣿⣾⡿⣟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡷⠀⠀⢀⡌⢹⣿⣻⣿⣿⣻⣿⣛⣿⣷⠏⢻⣇⠹⢧⢶⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣿⣀⣀⣃⣠⣿⣟⣿⣿⠿⢻⣿⣿⡏⠀⣾⠙⠃⢀⡄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⣯⣷⢿⣿⢿⣶⡿⣿⡏⠀⠀⣿⣶⣈⣈⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⣿⣏⣰⢻⣿⣿⣿⣿⠁⠀⠀⣾⢿⣿⢿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣗⣉⢛⣿⡍⡟⣿⡾⢏⣮⣿⣙⢶⡄⠀⢹⣿⣿⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣛⣵⣷⣿⣽⣾⣿⣿⡉⣾⡷⢀⣨⣿⠛⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⡛⣻⣿⣿⢶⣿⣷⣿⣟⣻⣿⣴⣿⣹⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣷⣿⣿⡶⣿⡟⠀⡬⣿⢤⠍⢿⣿⣿⣯⣿⣿⣷⣽⣿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⢻⣟⣿⣿⡿⢁⣴⣿⣿⣿⣿⡄⠛⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⣿⢿⣿⣥⣾⣿⣿⣿⣷⣶⣿⣬⡿⣿⣿⣿⠿⣇⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⣿⣿⣿⣿⣽⠉⡋⣹⡏⣉⢡⣿⣿⣛⣛⣿⣇⣾⢶⣛⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣜⣛⣿⣿⡌⣿⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣹⣯⠿⢛⣛⣻⣿⣿⡟⣿⣿⣿⣿⣿⣩⣿⣿⣯⡴⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣷⡦⢿⣿⣿⣿⣟⣛⣻⠉⡟⠛⢻⣭⣿⢿⣻⣻⣿⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⠻⣿⡞⢋⣥⣶⠮⢧⠀⢸⢿⠿⣻⢏⣿⢺⣿⡛⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣼⣷⣷⣿⣗⣿⣶⣶⣸⡄⢀⣴⡀⣿⡆⣤⠀⠀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣶⣰⣶⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⡀⣠⣿⣾⣇⣾⣤⠀⣀⠄
⠀⠀⠀⠀⠀⢀⡳⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡞⠁
⠀⠀⠀⠀⢙⣿⣿⣾⣿⣿⠀⠀⣀⣠⡅⠀⣀⠀⢹⠀⢀⡀⠀⣹⠁⢀⡀⠀⣯⠀⢀⠀⠈⣿⣿⣿⣿⣶⠂
⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠀⠀⠉⢹⡇⠀⠛⠀⢸⠀⠀⠃⠀⣹⠀⢸⡅⠀⡏⠀⠘⠀⢀⣿⣿⣿⣍⡁
⠀⠀⠴⠶⠾⢿⣿⣿⣿⣿⠀⠀⠿⠿⡇⠀⡄⠀⢿⠀⠀⡀⠈⣿⠀⠸⠃⠀⡗⠀⢠⠀⠹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣶⣶⣶⣶⣷⣴⣿⣦⣼⣶⣶⣷⣶⣾⣶⣶⣶⣶⣷⣶⣾⣦⣶⣿⣿⠟⠓
⠀⠀⠀⠀⠀⠐⡽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢠⠞⠋⢸⣿⣿⡿⣿⠟⣿⠟⣿⣿⢣⡟⠹⢿⡇⠀⠉⠃⠹⢸⣿⡏⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠺⠉⠀⠻⠀⠹⠀⠘⣿⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠟⠁⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⡄⠀⢀⣤⢠⡄⠀⢠⢀⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⡀⢀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⣠⣤⣄⢠⠏⠉⠙⣆⢸⢻⡀⣼⣿⢸⡇⠀⠈⣿⢳⡟⢹⣤⡄⣿⢳⡟⡆⢰⡏⠀⠉⠁⣿⣿⡗⢸⣿⣇⠺⣭⡃⣿⣼⠀⠇
⠀⠀⣶⢲⢴⡇⠀⢸⣾⡀⠀⠀⡿⢸⠀⢿⠇⣿⢘⡃⠀⠰⠟⠏⠿⠞⠀⠀⠋⠛⠛⠁⠘⣧⣀⣠⠄⡿⣷⡀⠼⠏⠿⠐⠶⠃⠛⠘⠀⠁
⠀⠀⡿⠙⣾⠳⣤⠞⠀⠙⠲⠚⠁⠀⠀⢠⢀⡄⢀⣄⠀⠀⠀⣤⣄⢀⣤⡀⣠⡀⣄⠀⢠⡀⠉⠁⣀⠀⠀⢀⡀⢀⣀⠀⣀⠀⠀⠀⡀⣤⡄
⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⣼⢿⡀⠶⠀⣿⣿⣸⣿⣿⣿⣿⣿⣆⣿⡇⠀⠀⢿⣤⣆⣾⢳⣿⣏⣷⢹⣇⣦⣸⡇⢻⠃
⠀⠀⠀⣶⠒⢰⣶⣶⣴⣶⣶⣶⣶⣦⠀⠘⠈⠃⠃⠈⠃⠀⠀⠛⠋⠈⠛⠁⠙⠁⠋⠙⠘⠁⠀⠀⠸⠟⠹⠟⠈⠻⠟⠃⠈⠿⠙⠿⠀⠰
⠀⠀⠀⣿⣁⢸⣿⡉⢸⢯⡁⣿⢯⠁⡀⣀⡀⠀⠀⠀⠀⣤⣶⣦⣄⠀⣤⣤⠀⢀⣤⣤⢀⣤⣶⣦⣄⠀⢠⡆⠀⠀⡀⣀⠀⣀⢀⢀⢀⣄
⠀⠀⠀⠈⠉⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⢹⣧⣿⣿⣆⣾⣿⣿⢸⣿⣟⠉⣉⣀⢸⡇⠀⠀⡇⣿⣼⣏⢸⢺⣿⢨⠆
⠀⠀⢠⠶⠤⣴⡀⢠⡆⢠⣦⠀⣴⠶⠄⣆⡴⢰⠀⠀⠘⠿⣿⣷⠟⠁⠿⠏⠿⠏⠿⠿⠘⠿⣿⣾⠟⠉⠨⠇⠀⠀⠁⠁⠁⠉⠈⠈⠈⠉
⠀⠀⢈⣛⣶⣿⢷⡟⡇⣾⠻⡆⣧⣀⡀⡿⣄⢸⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⠀⢠⣤⡄⢠⡄⠀⠀⠀⢠⡀⠀⡄⢠⢀⡄⢠⠤⠄⡄
⠀⠀⠀⠉⠁⠀⠈⠀⠁⠁⠀⠁⠀⠉⠀⠁⠈⠈⠀⠀⠀⣶⠛⠆⠉⡏⢱⠋⠀⠈⣧⢸⣿⠏⢸⠃⠀⠀⠀⢸⡇⠀⡧⢸⣎⠀⣽⠖⠀⡇
⠀⠀⠀⣴⠞⠶⢠⣶⣶⡄⣴⣾⣦⢰⡆⠀⠀⣶⠀⠀⠀⠈⠓⣦⠀⡇⠸⡄⠀⢀⡿⢸⠀⠀⠠⠀⠀⠀⠀⠘⠓⠂⠃⠘⠈⠃⠙⠒⠂⠂
⠀⠀⠀⣿⠀⢀⣸⣧⣼⡇⣿⣤⣿⢸⡇⠀⠀⠻⠀⠀⠀⠙⠶⠋⠀⠁⠀⠉⠛⢋⣤⡀⢀⣠⣀⢠⣤⣄⡀⢀⣀⡀⣠⠀⢰⡄⢂⡎⢢⢰
⠀⠀⠀⠙⠓⠛⠀⠛⠛⠀⠈⠛⠋⠘⠛⠛⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⣼⣿⢹⣾⣿⣿⠇⢿⣍⠃⣿⠀⠸⠈⠎⠧⠜⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⢀⣿⢸⡇⣿⣷⢸⡇⢸⡇⠀⠻⣷⡞⠹⣿⡾⢹⡇⠀⠀⣦⣽⠇⣩
⠀⠀⢰⡿⡇⠀⢠⣤⠀⠀⣀⠀⠀⠀⠀⠘⣿⡿⣿⡇⢸⡇⣿⠹⣿⡇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠀⢀⡀⣀⠀⣀⡀⢀
⠀⠀⣾⠗⢿⠀⣾⢼⡆⢸⣿⡄⣆⣰⢰⠀⠙⠀⠙⠁⠈⠃⠙⠀⠙⠁⠈⠁⢀⣿⣷⣿⡞⠀⡇⠀⠀⢸⣿⣏⢰⣿⡆⢼⢷⣿⢸⠁⣁⣸
⠀⠀⠏⠀⠘⠗⠇⠀⠓⠛⠀⠃⠃⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠿⠳⠄⠅⠀⠀⠘⠛⠛⠚⠀⠛⠘⠈⠛⠈⠓⠋⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣬⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠰⠦⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣀⠀⠀⠀⣀⣀
⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄
⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠈⠳⡀
⡄⠀⠀⢀⠄⠋⠀⠀⠛⠦⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠈⠷⢈⡃
⡇⠀⢤⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⣿⠃
⡇⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣻⣿⣛⣿⣟⣿⣿⣄⣀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⣆⣘⠀⠀⠀⠀⠀⠀⠀⡾⠛⠋⠉⠀⠈⠁⠀⠉⠀⠉⠁⠉⠙⠛⠛⢳⣾⠁⠀⠀⠀⠀⠀⢀⡄⠀⠹⡆
⠀⠈⠟⢷⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢠⣦⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠑⠶
⣄⠰⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠈⡇
⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠀⠀⠀⠀⣀⡀⠠⠶⠤⠄⠀⠀⠀⠀⠀⠀⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢲⠒⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠛⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠐⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠰⡇⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⣿⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠃⠀⠀⡀⢸⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⡇⢸⠀⠀⢇⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣟⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠺⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠓⠀⠀⠺⠇⠀⠀⠠⠓⣀⣀⡀⠊⠨⠆
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠛⠉⠛⠛⠛⠛⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⡟⠀⠀⣿⡟⠁⣤⡄⠘⣿⣿⡿⠁⠀⣿⣿⡇
⠀⠀⣿⣿⠏⣠⡇⠀⣿⡇⠀⣿⣿⠀⣿⡟⢁⣾⠀⣿⣿⡇⠀⠀⠀⠀⣴⣶⣦⣀⣀⣤⣄
⠀⠀⣿⣧⣀⣀⡀⠀⣸⣇⠀⢿⠏⢀⣿⣀⣀⣀⠀⣨⣿⡇⠀⠀⠀⠀⠻⡿⠛⢿⣿⣿⣿⠃
⠀⠀⣾⣿⣿⣿⣧⣴⣿⣿⣶⣤⣴⣾⣿⣿⣿⣿⣤⣿⣿⡇⠀⠀⠀⠀⠀⠔⠐⠌⢸⣿⡀
⠀⠀⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷
⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡴⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣤⣾⣿⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡖⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣾⡿⠿⣿⣿⡿⠿⣿⡄⠀⠀⠀⠀⢘⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⣷⣴⣿⣿⣷⣴⣿⣿⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⣿⣿⣿⣋⣙⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠙⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣠⣤⣶⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⣿⣿⣿⣿⠿⣿⣿⡻⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⣿⣿⣿⣋⡛⣻⡸⡿⣸⣑⡋⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⢸⣿⠀⠀⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣽⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡃⠀⠀⣀⡗⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣀⣤⠴⢤⡀⠈⠁⠉⠁⠀⣠⠜⠁⠀⢈⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠼⠃⠀⠀⠀⠀⠀⠳⢤⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠘⠦⠴⢄⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⢀⡤⠋⣀⡤⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠓⠒⠒⠁⠀⢠⠋⠀⠀⠀⠉⠀⠈⠣⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠆⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠈⠇⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⢄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡄⢰⠏⠀⠀⢠⠴⠒⠊⠉⢀⡠⠤⠒⠉
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢡⠄⢡⠀⠈⠒⠛⢦⣤⡤⢾⠀⠈⠀⡀⠀⠀⠑⡄⠀⠙⢡⡀
⠙⠫⡑⠢⢄⡀⠀⠦⢄⠀⠀⠀⠀⡆⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⡜⠀⠒⠈⡇⠀⢀⣜⡡⠔⠚⠉
⠀⠀⠈⠢⣀⠉⠲⠆⠀⢉⠲⣄⡀⠓⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠇⠤⠠⠀⡇⠀⠈⠁
⠀⠀⠀⠀⠈⠑⢤⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠤⠤⣶⠒⠻⢷⠤⠤⢤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢉⣋⣀⡤⠤⠤⢖⠒⠒⠉⠉⠀⠀⠀⠀⣀⠀⢁⣀⡠⠥⠤⠠⠛⢀⡀⠀⠀⠩⠙⠛⣇
⠀⠀⠀⠀⠀⠀⡛⠛⠀⠀⠤⢄⣀⠉⠒⠀⢠⣀⣐⠂⠌⣁⠂⠨⠄⠀⠀⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠁⠐⠂⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡠⠏
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠴⢌⠂⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⠚⠿⠇
⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⢄⣨⢀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣵⠒⠦⢤⣀⠀⠀⠀⠸⠀⠀⣀⣤⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢶⡞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⠿⠿⠿⠿⢿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⣷⡀⠀⠠⠄⠀⠀⠈⠉⠛⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⣀⠶⣄⡀⠀⠀⠀⠀⠀⠈⠀⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢿⣿⠿⠿⠿⠛⠓⠘⡇⠀⠀⣰⡶⠆⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⣷⣶⣶⣤⢴⢦⢿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢠⣿⣿⣿⣿⣿⣷⣯⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢨⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣛⠿⠛⢿⣿⡿⠋⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠿⢀⡀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣀⡀⠀⠀⠃⣻⠿⠟⠻⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣟⣣⣴⣴⣦⣬⣤⣤⣤⣿⣿⣗⣶⣾⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⠿⣽⣿⣞⣯⣘⡁⣇⣛⣙⡭⣯⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⢙⠓⠶⢯⣿⣽⣿⣉⣏⣹⡧⣶⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠘⠪⠯⢽⣿⣦⣽⣯⣽⣿⣏⣿⣿⠿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣷⣾⣿⣿⠿⠶⠐⠉⢙⠩⢉⣩⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠐⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⢋⠉⠛⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠁⠀⠉⠁⣶⢄⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⢀⣼⡾⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠁⠈⣤⣀⣿⡗⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⣤⣄⣉⢀⠀⣀⡼⠿⠻⠖⢺⠟⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠸⠏⠈⠁⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡎⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣶⠀⠾⣷⠀⠀⡟⠀⠀⠀⠳⠄⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⣷⠟⠛⢻⡛⠀⠀⠀⠠⠊⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣇⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⢿⡃⡀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢹⡄⠀⠀⠀⢰⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠐⠿⣧⣸⠀⠀⠀⠀⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⢻⡀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣀⠀⠀⢸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣧⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢛⣷⣄⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⢻⡿⣾⣷⠊⠀⠀⠀⠀⠀⠀⠀⣠⡾⢧⣾⣿⡿⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢨⡇⣿⡏⠀⠀⠀⠀⠐⠤⠖⠛⠁⠀⠘⣿⣿⠁⠀⠈⣿
⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠑⣼⡇⣿⡇⠀⠀⠀⠀⠀⡶⠃⠀⠀⠀⠀⣿⣿⡀⠀⠘⣷⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣹⡇⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⣿⣿⣅⡀⠸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⣿⣿⣿⠟⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢤⡦⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣿⢿⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⢸⣟⠀⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡇⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠠⡟⠈⣿⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠉⣤⠁⠀⠀⠀⠀⣰⣅⠀⠀⠀⠀⢰⣇⣠⠄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠎⠀⣀⣤⣿⣷⣤⡀⠀⣠⡿⠃⠀⠀⠀⣠⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠉⠀⢀⡟⠛⠋⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢸⡇⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠱⡀⠦⣄⡀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⣀⡀⠀⣀⡀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⣸⠀⠀⠀⢰⡀⠀⢀⡄⠈⢄⠀⠈⠑⠦⣄⣀⠀⠀⡁⠀⠀⠀⡀⠀⠈⡏⠀⢀⠀⠀⠀⠀⢸
⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠙⠲⠵⠤⣀⠀⠀⠈⠁⠈⠓⠒⠲⠤⠤⠤⠤⢧⣀⣘⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀
⠐⠶⢶⠶⠾⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣼⣮⣕⡲⠄⢠⣀⡀⠀⠀⢨
⠀⠬⠵⠴⢤⠦⠤⠢⠦⠠⠤⠮⠤⢤⣀⣀⡙⢿⢿⣷⣦⣤⣄⣙⡒⠲⠢⠤⢤⣤⠀⡤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢢⠀⠀⠀⢀⠀⠀⠀⠀⠀⡆⠀⠙⠓⠳⣌⠛⠿⢿⣫⣽⣿⡿⠶⣾⡲⠶⣦⣤⣤⡤⣦⣠⢤⣄⣄⣀⢀⣀
⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⢀⠀⠀⠀⣀⠀⢠⠀⠀⠘⢦⡀⠀⠈⠙⠙⠓⢋⠲⠴⢤⣶⣶⣀⣐⣲⣆⡠⣀⣀⡀
⠀⠈⢛⣛⢛⣛⡋⠙⠫⢭⠽⠛⡛⣛⣋⡝⠛⢶⢶⣤⣆⡹⡢⢄⣅⠀⠀⢸⠀⠀⠀⠀⡇⠁⠀⠀⢹⠉⠉⢩⠉⠁⠀⠁
⠀⠀⠀⢁⣗⣛⣛⣓⣚⣉⡤⠤⢰⣶⣤⠤⢶⣿⢿⣽⣭⡿⡟⣦⡈⠉⠛⠛⠒⠦⠤⢤⣤⣀⡀⠀⢸⠀⠀⠈⠀⠠
⠀⠀⠀⣬⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣫⣛⣻⡿⣷⣦⣄⣀⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠃⠒⠒⠒
⠀⠀⠀⠎⠾⠿⠟⠻⡾⠼⠜⠒⠿⠿⢯⠒⠾⠿⠧⠝⢿⣿⣿⡿⣿⣿⣯⣉⠛⠟⠿⠷⢶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⢀⠉⠉⠛⠋⠉⠉⠋⠉⠉⠉⠉⠉⠛⢛⢉⠛⠻⠺⢟⣲⣒⡼⣭⣹⣫⡙⠓⠰⠤⣄⣀⣂⡀⠉⠉⢉⠍⠉⠉⠉⠁
⠀⠀⡄⠀⣀⠠⠤⠤⠤⢤⡤⠴⠶⡖⠒⠒⢺⠛⡖⠒⢻⠚⠛⠗⠻⢿⡟⣿⣿⣄⠀⠀⠀⠀⠈⠉⠙⠋⠉⠛⡉⠇⢠⠃
⠀⠀⠀⣀⣸⣀⣀⣀⣀⣰⣆⣀⣀⣇⣀⣀⣨⣠⣅⣤⠼⢤⣤⠦⢤⣀⣇⣀⡀⠙⠳⣄⡀⠀⢨⠀⠈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠐⠸⢿⣟⣾⣲⣶⣦⣤⣤⣤⣤⡐⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠙⠻⠭⠍⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠴⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⢳⡠⠃⢿⠈⢆⠀⠀⣿⣿⣿⣿⣯⣿⣟⣿⣀⣷⡻⣿⣿⠀⠀⠀⠀⢰⢳⣠⠃⣿⠘⢆⠀⠀⣿⣿⣿⣿⣯⣿⣟⣿⣀⣷⡻⣿
⠀⢀⠔⠂⠁⠘⢥⠤⣿⠤⠬⠂⠀⣿⣿⣯⣿⣾⣷⣾⣿⢶⣿⣟⣽⣿⠀⢠⠖⠒⡉⠘⣧⡤⣿⠤⠬⠂⠀⣿⣿⣯⣿⣾⣷⣾⣿⢢⣿⣟⣽
⠀⠈⠉⠀⢹⢸⠀⠈⠁⠀⠀⠀⠀⣿⣿⣾⣿⣿⡷⣿⣿⣾⣿⣿⣿⣿⠀⠈⠉⠁⣹⢸⠈⠉⠁⠀⠀⠀⠀⣿⣿⣾⣿⣟⡷⣿⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠓⠒⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣬⣭⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠓⠲⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣬⣭⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠿⢿⣿⣛⣉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⠀⣈⠉⠛⢷⣄⠀⠀⠀⣼⠀⠀⣼⠀⢀⣴⠶⡄⠀⣼⠃⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠻⠋⠛⠀⠀⠀⢹⣇⠀⠀⣿⣀⣤⣿⠀⣾⠁⢰⡷⠀⣿⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⢸⣿⡄⠀⠛⠉⢸⡿⠀⠻⣶⠟⠁⠀⠉⠀⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣤⣼⣿⠀⠀⠀⠀⢀⡾⣹⡇⠀⠀⠀⣼⣿⡁⠀⠀⣀⣈⠁⠀⣀⠀⠀⢀⡀⠀⠀⠉
⠀⠀⠀⠀⠀⣿⠀⠀⣾⢻⣆⠀⠀⠀⠸⠃⡿⠀⠀⣠⣾⡟⠘⣇⠀⠐⣏⣹⡗⣼⢋⣇⢰⠏⣥⡄⣰⣯⠁
⠀⠀⠀⠀⠀⢻⡄⢰⡇⠀⠙⢿⣶⣤⣤⣤⣤⣶⡿⠛⣿⢿⣄⣿⠀⠀⣿⠁⠠⠟⠙⠟⠸⢶⠾⠃⠻⣶⠆
⠀⠀⠀⠀⠀⠀⢿⣼⡇⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢸⡏⠈⠛⠁⠀⠀⠀⠀⠀⣴⣦⣤⣠⡶⣦⡴⣶⠖
⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⠃⢹⡟⠹⣶⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣿⠇⠀⠀⣤⠶⠆⢀⣤⠄⡀⣠⠀⢠⡄⢀⣤⡀⣰⡄⣶⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⣿⠉⠀⣸⠇⠀⠀⠀⠀⠀⠀⣿⠞⠃⢿⣁⣠⡿⣿⣤⣾⡇⣸⠛⢷⣾⡇⣿⣠⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠉⠉⠀⠈⠉⠀⠁⠈⠀⠈⠉⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠲⠶⠶⠶⠿⠃⠀⠸⠿⠿⠿⠿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡛⢿⣿⣿⡿⢛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⠙⠋⣴⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⢋⣴⣦⡙⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⢩⣽⡏⣭⢻⡏⣭⡻⡿⣩⡹⣿⣩⡙⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢨⣽⡇⣋⢸⡇⢙⢱⡇⣿⡇⡇⣙⢱⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣌⣹⣧⣿⣼⣧⣼⣾⣷⣍⣼⣧⣿⣤⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣬⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⠶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡖⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡶⠶⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣾⡛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣍⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣷⣦⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣻⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠋⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⡄⠀⠀⠀⣠⣾⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢛⣙⠻⣿⡀⠀⢰⡿⢛⣙⡻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡅⢷⣿⢇⣿⠁⠀⢸⣇⠷⣿⠇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣶⣶⡿⠋⠀⠀⠀⠻⣷⣶⣾⣿⣿⣿⠇
⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⢀⣀⣀⣀⣀⣀⠈⠉⠛⠛⠉⠁
⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⡿⠟⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⡴⢧⣄⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠈⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡇
⠀⠈⢻⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠹⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠛⡁⠸⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠤⡀⠀⣠⣴⣿⢿⣿⣀⡂⠑⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠘⠡⣗⢈⣵⣾⣾⣻⠟⠷⠿⣿⣿⣷⡷⠂⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⣿⣿⣦⠀⠀⠀⠈⡼⢿⣻⣿⠏⢰⠆⠀⠈⣿⣿⣠⢰⡏⠀⠋⠙⠂⣤⠀⠠⢶⠒⠂⠠⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠏⠋⣻⣿⣿⠀⠀⠈⢀⡤⠖⢙⣿⣧⡄⠀⠀⢰⡷⢻⡇⡈⠁⢠⣇⡖⠀⠈⠀⢸⠈⣷⠐⣷⣴⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⢄⠀⠉⣿⠋⠀⠀⡠⠋⣴⣾⣿⣿⣿⡆⠐⠛⣋⣀⠘⢿⠧⡄⠈⠙⣷⣦⡀⠀⠀⣾⣿⡇⡿⣧⡁⠀⠀⢸
⠀⠀⠀⠀⢸⣿⣿⢟⡿⢿⠄⠀⢠⣤⠀⠀⠊⠡⣴⣿⣿⣿⣿⡿⣷⡄⠀⢿⣿⠆⠈⣧⢸⣄⢺⣿⣿⡇⣞⢵⡀⠀⠠⠃⠛⠀⠀⠀⢸
⠀⠀⠀⠀⣾⣿⣿⣻⣧⣸⣆⣼⣿⣿⠀⠀⠴⡁⢼⣿⣟⣟⣴⡀⢸⡇⠀⢸⣿⣓⠀⣿⡧⢟⡛⠁⠹⠀⣈⡤⣧⣄⣽⡀⠀⠀⠀⠀⢸
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣼⣿⡿⠋⠙⠀⣿⣽⠀⢸⣿⠊⠨⣽⡗⢜⡵⡄⠰⠂⠉⢙⣼⣧⣿⡃⠀⠀⠀⠀⢸
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⣜⠀⠚⠻⡿⠁⣺⣿⡄⡁⠿⡴⠠⣿⠀⣼⣏⠀⠈⢈⣷⡼⠠⢀⣼⢿⣿⠟⠁⠀⠀⠀⠀⢸
⠀⠀⠀⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡛⠁⢰⡿⠁⢌⠁⠀⠀⠀⠋⣠⣿⣯⠀⢸⣿⢿⠇⢀⣿⣿⣿⢏⠄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⣼⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠃⢀⣾⡇⠨⠻⢃⣰⣶⣄⣤⣾⣟⣿⣤⣿⡿⡞⠀⢸⣿⣿⠟⠊⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢸⣿⣯⣿⣿⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢸⡿⠀⠀⠤⢼⣿⣧⣫⣿⠉⢻⣿⣿⠿⡃⠀⣴⠏⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣿⣿⣿⡇⠈⣿⣿⣿⠆⠀⠀⠀⠀⠀⣖⠈⠀⠀⠀⠀⣿⣿⣿⣿⠋⢀⣨⣿⣿⡄⢀⣿⣿⣶⣤⡀⢠⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢿⣿⣿⡁⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠉⠑⡄⠀⠈⢸⣿⠿⣿⠇⠀⣈⣿⣿⣿⣿⣾⣿⣽⣿⣟⡁⢀⡆⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣾⣿⣿⡅⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⣇⠁⠀⣾⣿⣶⡾⢿⣿⣿⣿⡿⠏⠻⣿⣿⣿⣭⣽⡃⠸⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⣿⡇⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠉⠈⡿⡛⠈⢁⣿⣿⡿⣿⡇⢠⠄⣿⣿⣿⣿⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣿⣻⠁⠀⠀⢿⣿⣇⠀⠀⠀⠀⡠⠦⠸⣿⡆⢀⠏⠂⠀⡚⣻⣿⠂⣻⠀⠘⠀⠁⠀⣹⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠈⠙⠿⣧⠀⠀⠀⠰⣢⣤⡟⠃⠈⠀⠀⠨⡄⠈⠛⠀⠉⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠐⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠉⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠢⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⡀⠀⠀⠂⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⢄⠀⠀⠨⠐
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⢁⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⡠⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠄⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠁⠀⡐⠀⠀⠀⠂⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠔⠀⠀⠂⠒⠀⡄⢠⠀⠀⠀⠀⠐⠀⠀⠀⠒⠀⠀⠀⠁⠠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⠀⠈⠀⠂⠀⠖⠂⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⠄⠀⠒⠂⠀⠀⠂⠀⠀⠀⠀⠀⢂⠀⠈⠀⠐⠂⠀⠀⠀⠒⠦
⠀⠀⠀⠀⠀⠀⠐⠂⠄⠠⠀⠀⠀⠀⠘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡊⠀⠀⠉⠐⠂⢰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⡤⠔⠢⢄⠀⠐⠤⠄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀
⡎⠀⠀⠀⠈⣱⠒⠢⠠⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⣀⠠⢀⠜⠀⠀⠀⠱
⢉⠀⠀⠀⠂⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡄⠀⠀⡰⠃⠀⠀⠈⠁⡀⠀⠀⠐
⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠼
⠀⡀⠀⠀⠀⢀⡀⠘⡎⠉⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠣⠤⡴⠀⠀⠀⠀⠀⠀⢠
⠀⠉⠐⠂⠚⠙⠁⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡔⠁⠀⠺⠢⢄⡠⠄⠊
⠀⠀⠀⠀⠀⠈⠒⠛⠒⢄⡉⠢⡀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡠⠊⢀⠴⠦⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢌⡒⢄⣺⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢂⢀⠔⢉⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡽⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⡠⠀⢀⠍⠀⢀⠆⠀⠀⠆⠀⠀⠀⠐⠂⠀⢂⠀⠀⡄⠀⠰⡀⠀⠢⡀⠀⢦⠈⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠁⢀⠒⠀⠀⠂⠀⠀⠒⠀⠀⢐⠀⠀⡂⠀⠀⡂⠀⠀⡀⠀⠘⡀⠀⠘⣂⠀⠙⣄⠈⠱⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠠⠁⠀⠀⠌⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠐⠐⠒⠀⠘⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠂⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⠤⠀⠠⠤⠤⠤⠒⠒⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⢤⡀⢀⡠⠔⠒⠈⠉⠉⠉⠐⠒⠤⣀⠀⡠⠖⠒⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠞⠉⠉⠢⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠰⠊⠉⠑⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠗⠒⠀⠀⠀⠀⠀⢈⠈⠀⠀⠀⠀⠉⡈⠀⠀⠀⠀⠀⠐⠒⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡠⠚⠉⠻⣿⣿⣿⣿⡿⠋⠑⢢⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡜⠀⡠⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠙⡄⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠔⠒⢢⡀⠀⠀⠈⢆⡀⠀⠘⡄⠉⠱⢄⣀⢠⡜⢑⣤⣀⡀⠔⠉⠀⡆⠀⠀⣠⠊⠀⠀⠀⡴⠒⠲⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣠⣤⠴⠓⠒⠒⠈⠈⠙⠢⣀⠘⠢⣄⠀⠀⠀⠈⠉⠀⠀⠀⣀⠤⠊⣀⠴⠊⠁⠁⠒⠒⠐⠷⢤⣤⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠛⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠬⠭⠔⠒⠒⠂⠬⠭⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠋⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⣀⣠⠴⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡷⢄⣀⣀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣀⡠⠞⡇⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡗⠤⣀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢄⣀⣠⣾⣄⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣦⣄⣽⣦⣀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⣀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢉⠖⠂⠤⠤⠤⠤⠤⠤⠄⠲⣎⠁⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⣀⣀⣀⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣄⣀⣀⡠⠔⠋




⣷⣶⣶⣾⣶⡷⢾⣾⣿⡿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣾⣶⣶⢷⡶⠿⠿⠶⢷⣶⠶⠶⠶⠿⠶⢾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣠⠔⡤⣀⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣸⣷⡿⢾⣴⣻⣆⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢼⣻⢟⣯⣿⢿⢿⣿⡏⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣹⠞⣭⣿⡟⢿⣿⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠛⢄⠛⠾⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⣠⡤⣤⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣦⡮⠘⣃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠹⠴⢋⡇⠀⠀⠀⠀⠀⢀⡴⣉⠉⠛⠛⠛⢛⣉⡽⢒⣤⠤⢀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠐⡏⠀⠀⠀⠀⠀⠀⡸⠁⠂⠈⠉⠉⠉⠉⠖⠊⢡⠃⢰⠚⢻⢩⣋⣝⡓⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢼⣋⣟⡆⠀⠀⠀⠀⠀⡇⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠣⢤⠟⣩⠍⠋⡩⠷⢮⣈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣩⢿⡏⡷⣄⠀⠀⠀⣰⡇⠀⡟⠿⢋⢹⣿⣿⡇⠀⠀⢸⠸⡞⠀⣀⠀⠀⣀⠀⢱⡤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠻⣤⠎⢸⠒⢻⣹⠀⠀⣿⡶⣯⢟⠍⠿⡇⠀⠀⢸⢰⡇⠚⠑⠀⠐⣹⠤⡜⠃⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠉⠉⠒⠉⢹⠀⠀⠿⣷⣄⣿⣷⣘⡇⠀⠀⢸⢸⡇⠠⢄⡠⣤⣭⡼⢣⣄⣀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣲⠀⠀⠀⢀⣀⣤⡀⠀⢰⣹⣿⠀⠃⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠈⡇⠀⠀⠀⠀⠓⢻⠟⣧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⢞⡸⠆⣹⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠏⠐⡲⡀⠀⠀⠀⠋⢀⣤⣆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⣁⣞⠛⠙⣳⡀⠈⢁⣒⠒⠒⠒⠒⢒⠒⡚⠉⠀⠀⠘⠣⠋⠀⠀⠀⠀⠸⣀⣅⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢤⠀⠀⠀⣠⠖⠉⠀⠈⠉⠉⢁⡇⠀⠏⠸⠇⠀⢠⡖⠉⢰⠞⠀⠀⠠⢸⡇⣿⣸⢇⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠀⠀⠀⠣⢀⣀⣀⣠⣤⣶⠭⡖⠲⡋⢦⠀⠀⣇⡠⠴⣇⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⡒⠉⠱⡀⠀⣸⣀⠵⠞⠁⠀⠙⠦⣔⠉⡽⢻⠋⡴⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢀⣥⣠⠴⠓⠋⠁⠀⣀⣰⠖⠢⠀⠀⠀⠈⢩⠃⡞⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⠐⠃⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⣤⣤⣤⣾⣉⣉⡉⠁⠀⢤⣀⠀⣠⣴⡶⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠛⣒⢾⣿⠟⠋⠉⠉⣹⣿⣽⣿⡿⣿⣦⣤⡀⠻⣿⣿⠧⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⢸⣿⡇⡀⠀⠠⣾⢿⣿⣯⣟⠻⢿⣽⣿⣿⠆⠹⣯⡄⠀⠈⣦⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⡈⠻⣾⣿⡶⣬⡻⠟⣉⡀⢈⡅⠀⢹⣿⡏⣼⠀⠈⠓⢠⡴⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣈⣿⠿⠿⠟⣷⣦⣤⣤⣤⣴⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣚⣋⣉⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⡏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢉⡉⢉⡉⠉⣉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⡉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣉⣁⢈⣉⣀⣉⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⢷⣄⠀⠀⠀⠀⣠⡾⢷⣄⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⢻⣷
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠙⢷⣄⣠⡾⠋⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⣠⣾⠏⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⣠⣾⠟⠻⣷⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⣷⣾⠟⠁⠀⠀⠈⠻⣷⣾⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠋⠉⠙⠛⠛⠛⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⢀⢠⣤⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣺⣷⡾⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡠⣥⢠⣔⣁⣤⣿⠀⠀⠀⠀⢀⠀⠂⠀⣀⡀⠀⠈⢻⡟
⠀⠲⢶⣶⣿⡿⠁⠁⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠈⢹⣿⢿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⣿⣿⡟⠉⠁⠀⠀⠠⠀⡀⠠⠀⡼⠉⠀⠀⠀⢸⡇
⠀⠀⠛⡟⢹⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⢹⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢈⡁
⠀⠀⠀⠁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠾⠷
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢠⡏⠃⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠾⢣⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⢹⡄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠀⠀⠀⢀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣸⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠐⢢⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠁
⠀⠀⠰⠺⣷⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⡎⠑⢦⡀⠀⠀⠀⢠⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢷⡼⠿⣽⠇⠀⠀⠀⠀⠠⠤⠀⠆⠀⠀⠲⠾⠛⠳⣶⠾⠃⠀⠀⠀⠂⠃⠀⠀⠃⠀⠀⠀⠀⣤⣴⠟⠻⡿⠋⠀⠀⠀⠀⠀⠰⠋⠓⠤⠀⠀⠀⠀⠾⠧
⠀⣠⠤⡄
⠀⣧⣀⡄

⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂
⠄⠀⠀⠀⠀⠀⠀⠀⠉⢉⠀⠈⠉⠉⠁⠁⠁⠚⠋⠅⡀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠘⠃⠀⢒⠒
⡀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⢀⢀⡾⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠁
⡀⠄⠀⠐⠂⠀⠀⠁⠀⠲⠔⠓⠋⠒⠖⠒⠂⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡞
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡅
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃
⡃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⡍
⣧⣤⣴⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣼⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣶⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢄⡀⠒⠂⣀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢐⠦⢥⠈⡀⠂⠐⠀⡀⠀⠈⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠰⠂⠁⡐⢧⡶⢳⣖⢾⣦⣤⣤⡀⠀⠀⢀⠐⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠚⢐⠈⢁⣯⣦⢿⡧⣽⣷⣿⣿⠯⣒⣦⠄⢀⡈⠠⠈⡠⠉⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠐⠤⣈⣿⣷⣿⠏⢉⣁⣉⡐⠲⢶⣤⡀⣅⠢⢤⡀⠤⠀⠠⠀⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠆⢸⡘⣿⣿⠀⣿⣿⣿⣿⣷⣦⣌⡙⠻⢿⣄⣹⣷⣶⣄⡈⠀⠐⢀⠓⣚⢣⡀⠰⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠸⢌⠙⣿⡆⢹⣿⡶⠀⡻⣿⣿⣿⣷⣤⣈⠙⠻⢿⣿⣝⣷⣦⣍⣀⡀⠆⠐⠀⠉⢨⠡⢀⠉⡄⠄⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠓⠎⠀⠚⣿⡄⢹⣿⣧⠤⣿⣿⣿⣽⠻⠷⣿⣦⣤⣀⡙⠛⢿⣿⣿⣿⣷⣾⣌⣁⡀⠒⢈⠀⠄⠐⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠎⡄⠘⢠⣿⣿⠄⢿⣿⡿⠋⠉⠛⠿⢝⡡⣶⡍⡻⣷⠯⣶⣦⣤⣉⡉⠛⠻⢿⣿⣿⣿⡿⣒⣖⣷⢦⣤
⠀⠀⠀⠀⠀⠀⠤⢀⡠⠔⠦⠄⠚⠐⡃⢀⢿⡿⣿⡇⢘⣿⣇⠀⠀⠀⠀⠀⠉⠛⠿⣿⣾⣿⡻⣭⡿⢿⣿⣷⣶⣦⣤⣌⣉⡙⠛⠛⠿⠿⢽
⠀⠀⠀⠀⢀⠀⠖⢨⡤⠘⡁⠤⢀⣨⢴⡃⡾⠛⣹⠃⣼⣿⣿⡐⠄⠰⣷⢦⣀⡀⠀⠈⠉⠻⠿⢿⣿⣿⣟⣯⣿⣿⣿⣦⣬⡽⠻⣶⠶⠤⢤⠄
⠀⠀⠀⣄⣤⣤⠬⣥⣴⣶⣶⢾⢿⢴⣹⣥⠷⠛⣀⡼⣿⣿⣿⣇⠀⠀⣻⡿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠉⠙⠻⠯⢴⣿⣽⣛⣉⣙⣿⣷⣠⣾
⠀⠀⢀⣿⣭⣤⣼⡿⠿⠿⠿⠾⠛⠛⢉⣁⡴⡾⣿⣿⣻⣿⡿⡿⠀⠀⣸⣷⣿⣭⣽⣟⣯⠻⣷⡲⣤⣄⡀⠀⠀⠀⠀⠈⠉⠉⠛⢛⠳⠒⠚⠃
⠀⠀⠠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣿⣟⣣⣋⣍⣾⣿⣿⣟⠝⠁⠀⢠⣿⢩⣿⠏⠀⠉⠉⠛⠺⠽⣿⣿⣿⣟⣓⠒⠦⣤⣀⣀⡀⠐
⠀⠀⢀⣽⣿⣿⣼⣿⣿⣿⣿⣭⣿⣛⣝⣿⣷⣿⡿⠿⠋⠁⠀⢀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠷⠦⠽⣮⣽⣽⣯⠶⢶
⠀⠀⢰⣿⡶⠿⠿⠿⠿⠿⠟⡚⠟⠉⠉⠉⢁⠀⠀⢀⣀⣤⡶⣛⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⡀⠀⠴⠀⡁⣁⣀⣈⣀⢤⣤⣴⣶⣻⣿⣿⣿⠿⠛⠁
⠀⠀⠀⣻⣶⣿⣻⣿⣿⣟⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣲⣯⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⣀⣉⠉⠀⠐⠊⣋⣉⠉⢸⣇⣉⣤⣤⡤⠠⠀⢤⢤⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠈⣹⠉⠉⠉⠩⠉⠇⠀⢸⠙⢿⣿⣯⣽⣿⣤⣿⣯⣤⣭⣠⣿⣥⣁⣤⣴⣶⣴⣦⣿⣿⣿⡍⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣹⣀⣀⠀⣠⣤⡇⢀⡼⡀⠀⠙⣍⠉⠉⢹⠉⠉⠉⠉⠉⢉⠉⠉⠉⡉⠉⠉⡉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⣂⣀⣤⣄⣁⣀⣀⣳⡀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠓⠀⠀⡇
⠀⠀⠀⠀⠍⠉⠉⠉⠉⠉⠙⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠘⣬⣄⣀⣀⡀⠀⠸⠀⣀⢀⣀⣀⣀⣀⣀⡀⢀⣀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣯⣷⣤⣤⣤⣿⣿⣯⣿⣿⣿⣼⣾⢶⣄⣀⠀⠀⠄⠄
⣀⣀⣀⣀⢃⣀⣀⣀⣀⣀⣐⣠⣠⢄⣀⣸⣦⡄⣤⡤⠤⠤⢤⣬⣷⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠂⠀⠀⠐⠂⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠬⠉⠉⠉⠉⠻⠿⠿⡿⠶⠾⠿⢶⠿⢗⠛⠻⡛⠿⠟⠿⣆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠄⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⢀⢀⡀⠑⠀⠁⢈⠄⡄⠈⠁⠈⢠⡉⠀⠀⠅⠀⡨⡀⡹⡖⠒⠒⠒⠚⠒⢲⠐⠂⠓⠀⡄⠐⠓⠒⠂⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⣀⣀⣁⣀⣀⣐⣀⣀⣀⣄⣀⣀⣐⣇⣄⣠⣄⣢⣀⣼⣾⣠⣷⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢉⣟⣙⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣛⣻⣿⣿⣟⣂⣶⣛⣆⣳⠲⠶⡖⡶⠺⠦⠤⡤⠤⠷⢤⠤⠤⠷⠤⡤⠤⠤⠥⠤
⠀⠀⠀⠀⢀⡀⢈⠉⠉⣃⣉⣩⣍⣛⣟⣛⣛⡿⣿⣿⣽⡿⢿⠿⠿⢿⣿⣿⡾⡆⠀⠀⡇⠀⠀⠀⡇⠀⠀⣼⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⠁⠀⠀⠀⠐⡄⢸⠀⠀⠀⠀⠀⣸⠀⠀⠀⡇⢸⠀⢹⠲⠖⠓⠒⠒⠒⠓⠒⢒⣚⡒⠒⣒⡂⡃⠠⢤⣠⠄⠀⡀
⠀⠀⠀⠀⠀⡃⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⢸⠀⠈⣧⠤⠀⠄⢤⠤⠬⠉⣤⠤⠌⠀⠁⣤⠀⠦⠥⠤⠤⠈⠤
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢀⡇⠀⠀⠀⠇⢸⠀⠀⠘⢦⡀⠀⢈⠀⠀⠀⢃⠀⠀⠀⠀⠋⢀⠀⠰
⠀⠀⠀⠀⠤⠽⠤⠤⠤⠧⠤⠠⠤⠤⠤⠧⠼⠤⠤⠴⠶⠘⠓⠒⠒⣒⠒⠾⣶⣒⣒⣂⣻⡄⢠⠀⠀⠀⢀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣭⢭⡥⣭⣭⣤⣩⣭⣭⣭⣭⣤⣠⣤⠤⠤⠤⠤⠤⠤⢼⣿⣷⣾⣿⣯⣶⣷⣶⣶⣶⣒⣲⣶⣶⣶⣓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⣀⣠⣤⢤⡤⢤⣤⣤⣽⣏⠈⢫⠉⡁⠁⠒⡾⠱⠂⠀⢈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠉⠋⠀⠀⠉⠀⠀⠀⠉⠀⠀⠙⠳⣏⠀⡀⠀⠔⡀⢀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣦⣤⣬⣬⣤⣤⣤⠤⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣥⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⢡⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀⢠⣴⠎⠙⣦⢭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⣻⢿⣼⣿⡿⣶⣴⢧⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⣌⣁⣀⠀⠀⢀⡤⢻⣛⣯⣿⢛⢻⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢷⣴⣯⣿⣿⣁⣉⣳⣾⣋⣻⣀⣏⠀⢿⣸⣿⣿⡽⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⢿⣟⠉⠉⠙⢷⣾⣯⣿⣿⡷⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡹⣧⠀⠀⠀⣿⡦⣿⣿⣟⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⣠⣿⣵⢿⠟⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢙⢃⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣝⣿⣷⣄⣀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⣽⣋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣴⢞⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠬⠹⡿⢭⠵⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣿⣿⣿⣿⣿⠟⠛⡿⠛⠛⢿⢿⣿⣿⠟⠛⢿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡀⠀⣇⠀⠀⣸⠀⠹⣧⠀⠀⣸⣿⣿⠟⠀⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⢻⠀⠀⢸⢀⣼⠁⣼⣿⣷⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣾⣦⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⡖⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⣹⡟⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣽⠀⢠⣿⣿⣽⣿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣿⡀⢸⣿⣿⣿⣿⢄⡀⠉⠀⠉⠌⠛⢿⣿⢾⣟⠋⢁⣿⣿⣿⡗⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣾⡇⠀⠻⣿⣿⣿⣿⣶⣭⣤⣤⣤⣶⣟⣵⣟⣿⠷⠋⢀⡉⢩⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢿⣦⡀⠈⠛⠿⠿⠿⡇⠀⠀⢀⣵⡿⣿⡼⠿⣷⡀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣰⣺⡁⣸⢦⣤⣿⡙⠓⢶⣦⣶⠶⢿⣿⡋⠫⡃⢚⡠⣧⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣾⠋⠀⣻⠡⠠⣾⡎⢻⣾⣿⡁⠟⠀⠐⠁⠀⠀⠈⠁⠀⠀⠉⢀⣴⡇⠀⢸⠟⣹⠟⠁⣰⡇⠀⢸⠟⠀⢸⠟⢹⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠋⣸⢿⣿⢛⡿⠿⠄⠈⠀⣜⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢈⡁⠀⠀⠀⠀⠩⠃

⠀⠀⠀⠀⠀⠀⢀⠀⠀⣩⣤⣷⣄⣤⡄
⠀⠀⠀⠀⠀⠀⣿⣀⣼⢻⡏⠈⠋⢸⡟⢢⡀
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⣀⡀⠀⠸⢇⡀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢿⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⠀⣥⠀⣘⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⣶⣄⡀
⠙⠢⣄⢀⠀⠀⠀⢦⠙⢄⡋⣠⣆⢠⠢⠠⠀⠀⠀⠈⠤⠭⠉⠛⠛⠛⠻⠶⠶⠶⠶⢤⣤⣤⣤⣀⣀⣀⢀
⠀⠀⠈⠳⢤⡴⣤⠼⢒⢊⡵⠹⣭⡆⢀⣀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠢⠭⢽⣿⠯⠟⠓⠒⣀
⠀⠀⠀⠀⠀⠚⠦⣄⠀⠁⠉⢂⡴⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⢄⣤⢀⠀⠠⠄⠀⠀⠀⠀⠀⣀⣀⠤⠴⠶⠶⠤⢤⡀⠀⠀⠀⠀⠀⠀⠄⠚⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠺⢆⣀⡰⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠀⠠⢠⠀⠀⠠⣔⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠥⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⠀⠀⠀⢀⡀⢀⣀⡀⠀⣀⡀⠀⠀⠪⣤⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⡖⠒⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣦⣤⠶⠾⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣀⣾⡿⣿⣿⣿⣿⠟
⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡟⠁
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟
⣀⣤⣶⣿⣿⣿⣿⣿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⣿⣿⣿⣿⣿⣿⠿⠛
⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢈⠐⠀⠀⠀⠀⠀⠀⠤⠤⠑⠂⠠⢄⡀
⠀⠀⢰⣄⢠⡄⢠⡤⣠⣀⢀⢄⢸⡂⡀⠀⢰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠈⠙⠘⠂⠈⠁⠉⠉⠘⠊⠙⡇⠛⠀⢸⠀⢠⠰⡧⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⡤⠀⣤⣠⣄⠀⣀⠀⣀⣁⠀⠀⢸⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠧⠀⠛⠈⠫⠸⠤⠃⠻⠝⡄⠀⢸⠀⠀⠀⠀⠀⠀⠢⠑⠄⠀⠀⡠⠁
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⢸⠀⠀⠀⠀⠀⠠⠄⠀⠠⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠚⠀⠉⠉⠉⠀⠀⣤⠀⠠⠉⠉⠉⠉⠁⠱⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠤⠀⠸⠉⠁⠾⠿⠿⠷⠿⠿⠶⠿⠶⠿⠾⠭⠤⠄⠄⠀⠀⠄⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⣀⣀⡀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⠒⠀⠤⠴⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⠀⣀⡉
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠟⠁⠀⠀⠀⠀⣴⠟⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⣦⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡰⠋⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠠⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⠁⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠤⠄⠐⠂⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠠⣤⣤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠖⠀⠀⠀⠀⠀⠻⢷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡀⠀⣠⣶⠛⠀⡀⠀⠀⢳⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣽⡇⠀⠙⠋⠀⣸⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⢠⠄⢹⡆
⠀⠀⠀⠀⢀⡴⢦⣄⠀⠀⣠⠟⠁⣠⡼⢻⡇⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⢠⣴⠶⠟⠁
⠀⠀⠀⠀⠘⢦⡀⠙⣧⡼⠋⢰⣞⠉⠀⠘⣿⠀⠀⠀⣸⠃⠀⢀⡀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠙⢷⡞⠁⠀⠀⠈⣷⠀⠀⣿⠀⠀⠀⠙⠳⢶⠋⠉⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠻⣆⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢀⡼⠀⠸⣧⠀⠀⠀⠀⢀⣠⣾⣿⣿⡆⠀⠘⠇⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣶⠋⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣿⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢛⣀⣤⣤⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠶⠟⠋⠉⠀⠀⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⢋⡿⠁⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡰⣶⠆⠀⠀⠀⢀⡿⠀⢻⡀⠀⠀⣀⣠⡤⠶⠛⠉⠁⠀⣴⠏⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣠⡴⠶⠛⢿⡄⠀⠀⢸⣷⡞⠛⠉⠁⠀⠀⣀⣠⣴⣿⠃⠀⠀⠀⠀⠀⢀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⠈⣷⡀⠀⣾⣿⣿⣆⢀⣤⠶⠛⠋⢩⡿⠁⠀⠀⠀⠀⣠⡶⠛⠁⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠘⣧⠀⢻⣿⡟⠉⠉⠀⠀⠀⣰⠟⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢹⣇⢸⣿⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢻⣾⣿⣇⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣿⣿⣿⠀⢠⡾⠁⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢹⣿⣿⣶⠟⠀⠀⠀⢀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⢸⣿⡿⠋⠀⠀⣠⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠋⠀⠀⡰⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⠿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣫⡖⠠⢚⡄⠂⠑⠀⣘⡻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏⣿⡼⢃⣾⣤⣶⣠⡅⣰⠆⣿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠿⢡⡄⠘⠿⢿⠻⣁⠖⠫⣠⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢾⡝⢿⠈⠻⠿⣿⣃⡬⣾⣏⢹⣿⣿⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⣿⣶⡖⢦⣎⠛⢛⣭⠿⣧⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣴⣾⣿⣷⣾⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡅⠀⠀⠀⠀⠀⠀⡆⠀⠙⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠢⡈⠂⠄⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠐⠂⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠰⠐⠒⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠶⠚⠋⠙⠛⠛⠛⠛⠛⠛⠙⠉⠐⢶⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠳⣤⡀⣿⢦⣴⠋⠙⠳⣤⡀⢰⣦⣴⡈⠙⢦⡄⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠈⠙⠓⠀⠁⠀⠀⠀⠀⠉⠛⠃⠙⠃⠀⠀⠈⠙⠶⠶⣄⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢀⣴⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⡄⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⡁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡁⠀⠀⠀⣿⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠞⠛⠳⣴⡇⠀⠀⠀⣮⢁⣀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦⢀⣀⢹⠀⠀⠀⣏⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠴⠒⠀⠈⠀⠀⠀⠀⠛⣌⢩⡴⠃⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⢣⡌⣩⡝⠀⠀⣼⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣹⣿⠛⠛⠛⠛⢿⡏⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠘⠓⠀⠀⠒⠁⠀⠈⠻⣦⡀
⠀⣀⡀⠀⠀⣀⣀⣴⡉⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⢉⣧⣀⣀⠀⠀⢀⣀
⡞⠋⠀⠀⠠⣤⠁⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⢀⣠⡜⠃⠀⠈⣤⠄⠀⢁⠙
⠙⣆⣀⡀⠀⣀⣀⠠⢤⣞⡈⠉⠛⠶⢄⣀⠀⠀⣼⡋⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢙⣷⠀⠀⣀⡠⠄⠛⠉⢁⣳⡤⠄⣀⣀⠀⣀⣀⣰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠉⠒⠢⠜⠛⠓⢤⣄⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡤⠚⠛⠣⠔⠚⠉⠀⠀⣀⡤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⢀⠟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠛⡄⠀⠀⠀⠀⠀⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⢠⣀⣠⠏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠙⣤⢀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⠶⠶⠶⠶⠶⠶⠶⠦⢤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠂⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢰⣿⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢸⠟⡆⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡿⠀⣷⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⡟⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⣷⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣠⣤⣤⣤⣾⠏⣶⣤⣤⣤⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢉⣟⠁⠀⢀⣉⣹⣿⡉⣠⠀⠀⠈⣿⡉⠳⣦
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣷⣤⣤⣤⣶⣶⣶⣤⣬⣛⣧⣤⣶⣶⣦⣤⣤⣤⣾⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⠿⠻⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⢀⣀⢀⣀⣀⡀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢄⡃⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠛⠀⡀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠑⢉⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⢠⠀⠀⠀⠀⢀⡀⠀⢈⢭⠁⠈⠀⠀⠈⣄⠀⡠⢂⣸⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⢁⢄⢀⠴⠠⡁⣐⣀⠀⢦⠄⠀⠀⢰⠀⠀⠻⠉⠀⡀⠁⠈⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠅⠔⠙⢠⠀⠀⠩⠠⢄⣀⣄⡀⠀⠰⠀⢨⠁⠀⠀⠀⠤⠤⠀⠈⠧⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠚⠉⢀⢀⡀⠠⠆⠀⠀⠀⠀⠀⠀⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠉⠀⠀⠀⠀⣀⠤⠀⠀⠙⠄⠱⠀⠀⠀⠀⣄⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⢐⣋⠂⠠⠃⠐⠠⠀⣤⠀⠲⠂⠀⠴⠒⢒⣒⡉⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠞⢀⡌⢫⠖⠁⠈⠀⡁⡦⢠⢀⢀⠀⠁⠀⠀⠀⠒⠉⠁⠀⠈⠹⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠜⠁⠀⠀⠀⠘⠀⢁⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡃⡒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡉⡄⠀⠀⠀⠀⠠⠴⠦⠤⢀⣀⠒⠀⣼⠒⠦⠴⠒⠁⠀⠀⠳⠇⠶⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠰⠅⠁⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠠⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢻⣷⡀⠀⠀⠀⠀⠀⠀⠠⠀⡠⠒⠉⠐⠠⡄⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⡐⣠⣶⣾⣶⣄⠆⠀⠀⠀⠀⠠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠤⠈⠈⢳⣿⣿⣤⣾⡟⠠⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠠⠔⡆⠰⠔⠦⠙⠛⠟⠋⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠿⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢔⠒⠁⠈⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠈⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠆⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠈⠁⢀
⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡠⠐⠋⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⣀⠀⠀⠀⢀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠒⠀⠐⠂⠐⠒⠒⠒⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣅⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⢶⡄
⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⢸⡇⠀⠀⠀⠀⢀⣠⢤⣄
⠀⠀⠀⠀⠀⠀⠈⢳⣦⣴⠏⠀⠀⠀⠀⠀⣾⠁⠀⢹⡇⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣸⠇⣷⠀⠀⠀⠀⠀⠀⠙⣦⣤⡼⠃⠀⠀⠀⠀⡟⠁⠈⢻⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡿⠀⢸⡆⠀⠀⠀⠀⢀⡾⠃⢻⠀⠀⠀⠀⠀⠀⢧⣀⣠⡞⠀⠀⠀⠀⢠⠟⠉⠙⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⠀⠀⢀⣴⠏⠀⠀⢸⡄⠀⠀⠀⠀⣠⡾⠙⡏⠀⠀⠀⠀⠀⠸⣄⣀⣠⠏⠀⠀⠀⠀⢠⠶⠶
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣷⠀⣠⠞⠁⠀⠀⠀⠸⣇⠀⠀⢀⡴⠋⠀⠀⢱⠀⠀⠀⠀⢀⣴⡟⣿⠁⠀⠀⠀⠀⠠⡏
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣿⠞⠁⠀⠀⠀⠀⠀⠀⣿⠀⣴⠏⠀⠀⠀⠀⢸⠀⠀⢀⣴⡿⠋⠀⢿⠀⠀⠀⠀⠀⠀⢻⣦⡾
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⠀⢸⡇⣠⡾⠋⠀⠀⠀⢸⡀⠀⠀⠀⣠⡾⢫⡏
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⠀⠀⠀⢸⡇⠀⣠⠾⠉⢀⡟
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠾⠋⠀⠀⣾⠁
⠀⠀⣴⠿⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⣹⡇⠀⠧⠨⠀⠀⠀⠐⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⢷⡄⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⢀⣴⠟⠳⠶⢶⣄⢀⣀⡀⠀⠀⠉⠀⠐⠀⠀⠀⠑⠒⠀⠀⠀⠀⢠⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⣼⠇⠀⠀⠀⠀⠉⠉⠉⠙⠲⠴⢶⣄⣀⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⣸⡃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠳⠶⠶⣄⣀⣄⠀⠀⠀⠀⠀⠀⠤⠀⣀⡀⠘⠀⠀⢀⢉⣷
⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠶⠶⢿⣦⣤⣤⣄⠀⠀⠉⠀⠐⠾⣟⠁
⠀⢻⣆⠀⠀⠀⢀⡀⠀⠀⢀⣠⣤⡀⠀⠀⠀⣀⣤⢶⣄⠀⠀⠀⠀⣠⣾⠁⠀⠀⠙⠳⠶⠶⠷⣤⣠⡿
⠀⠀⠙⣷⡶⠶⠋⠙⠛⠚⠛⠋⠉⠉⠛⠛⠛⠉⠀⠀⠉⠛⠛⠛⠋⢹⣇⠀⠀⠀⠀⠀⠀⠀⢠⡿⠉
⠀⠀⠀⣿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣤⣀⠀⠀⠀⠀⠀⠀⣹⡶⠀⠀⠀⠀⠀⠀⢿⡁
⠀⠀⠀⣿⠀⣴⠋⠙⣆⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⢀⣿⠀⠇⠀⠀⢿⠀⠀⠀⠀⠀⡿⠀⢀⡀⠀⠀⣷⠀⠀⠀⠀⠀⠈⢳⣦⠀⠀⠀⠀⠀⢸⡏
⠀⠀⢸⡇⠀⠀⣾⡇⢸⡂⠀⠀⠀⢰⡇⠀⣿⡷⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⢸⡟
⠀⠀⢸⡇⠀⡀⠙⠃⣸⠁⠀⠀⠀⠸⣧⠀⠈⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢳⣤⠀⠂⠀⠂⠺⣧⡀
⠀⠀⢸⡇⠸⡇⢀⣠⡿⡀⠀⠀⠀⠈⡟⠲⢄⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⣷
⠀⠀⣾⠁⠀⠐⣤⠞⢁⠃⠀⠀⠀⠀⢻⣤⢤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⣿⡇
⠀⠀⣿⠀⠀⣀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⢠⡿
⠀⠀⣿⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁
⠀⠀⣿⠀⠀⠀⠀⠈⠑⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠛⠛⠋⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⣴⠉⠉⠉⠉⠉⠉⠁⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⢸⣿⠀⠀⠀⠀⠳⠼⠉⠀⢁⡉⠉⠉⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠣⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠻⣦⣀⣀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠉⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⡀⠀⠀⠀⠀⠀⢀⣴⡟

⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⡟⠛⢻⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣿⠟⠛⣿⣿⡇
⠀⠀⢸⣿⣿⣿⠏⢀⠀⢸⣿⡏⠀⣾⣷⡄⠈⣿⣿⡿⠃⡀⠀⣿⣿⡇
⠀⠀⢸⣿⣿⠃⣠⣿⠀⢸⣿⡇⠀⣿⣿⡇⠀⣿⡟⠁⣼⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⢠⣾⣿⣦⣀⣀⣤⣤⣄
⠀⠀⢸⣿⣇⣀⣀⣀⠀⢀⣸⡇⠀⢿⣿⠇⢀⣿⣀⣀⣀⡀⠀⣀⣿⡇⠀⠀⠀⠀⠀⠘⢿⡿⠿⢿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣀⣸⣿⣿⣦⣀⣀⣤⣾⣿⣿⣿⣿⣇⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢈⠄⢠⡈⠹⣿⡏⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⣻⡄
⠀⠀⢸⣿⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⣿⣷⡀
⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣤⣷⠾⠛⠀⣀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣶⣾⣿⣿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠛⠛⠛⠛⠿⢿⢿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣼⠃⠀⠀⠀⠀⠙⣦⠀⠀⠀⠼⠛⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢠⡶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠛⠻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠐⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⣀⣀⠀⠀⣀⣀⣤⠾⢯⣤⣤⣤⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠛⠛⠉⠉⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠶⣤⣄⡀⠀⠀⠀⣠⡴⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⡄⠀⠉⠙⢛⣶⣟⠉⠀⢸⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣠⡶⣿⣿⣿⡿⣦⣸⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠘⣿⣿⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠙⠛⠛⠛⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⣛⡋⣙⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡴⢫⣀⡨⠓⠒⠆⢳⠹⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣓⣭⡾⢄⣉⣁⡩⡡⢺⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⣀⠀⠤⠀⠀⠀⠈⠓⢤⡀
⡶⣤⣀⠰⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡑⢀⠀⠨⠑⠦⢀
⠧⠀⠈⠁⠐⠤⣭⠖⠒⠓⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠤⠀⠈⠀⠐⠂⠀⠬⠂⢄⡀
⠈⠂⠀⠀⠀⠀⠀⠉⠑⠒⠀⢄⣈⢉⣀⠒⠀⠀⠄⠒⠈⠀⡀⠀⠀⠠⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠦⠤⠤⠔
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⢀⠃⠀⠀⠀⠀⠀⠀⢊⡁⠄⠐⠐⠐⠰⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢸⠓⢵⡤⢄⣀⣀⠀⡄⣀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠃⠂⠀⠀⢍⣁⠒⠂⠠⠀⡉⡙⠉⠙⠉⢉⢉⠀⠒⠦⠤⢤⣀⡀
⢠⡀⠂⠈⠉⠉⠉⠁⠀⠀⠉⠳⢦⣤⣅⣀⠀⠀⠀⠄⠞⠀⢸⢣⣀⣬⣭⠒⠓⢆⣐⡆⠀⠀⠠⠠⢀⠐⣀⠀⠄⠐⠀⠠⠀⠉⠒
⣼⠊⠲⡩⢞⣛⣰⡶⣖⢖⢆⣀⡁⡉⡇⠉⠀⠀⠀⠀⡀⠀⠉⠓⢿⣤⠉⠈⠉⢉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠬⠀⡂
⢻⠀⠀⠀⡀⠁⠀⠘⡷⠞⣁⠐⠠⢅⡉⣉⠉⠁⣁⡀⠀⠀⠀⢀⣀⡩⠱⣬⣄⠖⠈⢐⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠠
⣻⠝⡣⣡⡍⠖⡉⢷⠎⠢⠄⠀⡈⢀⡇⠃⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠐⠛⠲⠧⠟⡂⠀⢀⠀⢀⠄⠄⠀⠡⠐⠀⠀⠂
⠀⠈⠐⠛⠺⠭⠛⣐⡊⠏⠠⢗⠨⢈⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⡀⠀⠀⠙⠀⠀⠉⠙⠃⠸⡥⣁⣀⡀⠀⠀⠀⠐⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠀⢀⣃⣀⡀⡀⢀⣁⡀⣀⣀⠀⣀⠀⡀⠀⣁⣀⣀⣀⣀⢈⣀⡀⡀⠀⠀⣀⡀⠀⠤⢤⡀⢀⠀⠀⠠

⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡟⠀⠀⠀⠀⢸⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢸⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢄⣀⠄⡖⡶⡶⢤⣀⢠⠔⠂⣄⢠⡤⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠤⣀⠀⠀⠀⠀⠀⡔⠁⢀⠤⢠⡌⠈⠘⠜⢠⠋⠀⣼⢲⣶⡆⢸⠲⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⠢⡀⣀⠈⡆⠀⠀⠀⠀⡐⡁⠁⠀⡜⠀⠀⠀⠀⡆⠀⠀⢇⠉⣩⠃⢨⡉⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⡘⢆⡍⠢⣱⠃⠀⠀⠀⠀⠏⠀⠀⡸⠀⠀⠀⠀⡘⠁⠉⢉⠏⠉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠚⣼⠠⠂⠀⢀⣤⣶⣾⣄⠀⡰⠁⠀⠀⠀⢠⠁⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣉⠆
⠀⠀⢀⡀⠤⠄⣀⠀⠀⠀⠀⣔⡆⠀⠀⠁⠁⠀⠀⣰⣿⣿⣿⣿⣿⡶⠁⠀⠀⠀⠀⠇⠀⠀⢠⠃⠀⠀⠀⠀⡀⠤⠂⠉
⠀⠀⡋⠁⠒⠤⣀⠉⠢⣀⠀⠀⠈⠢⡀⠀⢠⠀⣸⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⡜⠀⠀⠀⠆⠀⢀⠠⠒⠉⠀⠀⠀⣀⡀⠠⠤⠤⠤⠄⠀⠀⡤
⠀⠀⠑⢄⠀⠀⠀⠉⠢⣈⠉⠀⠂⢄⠈⢆⢸⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣸⣠⣤⣤⣌⠠⣊⠁⠤⠐⠂⠉⠉⠁⠀⠀⠀⡀⠄⠀⠀⠤⠊
⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠑⠤⡀⠀⠱⣀⠱⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠈⠑⠠⣀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢀⡔⠒⠒⠐⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠠⠤⡀⠀⠀⠈⠐⠻⣿⣿⣿⣿⣿⡿⢛⣁⣀⠠⠄⢀⣀⣀⡀⠤⠒⠁⠀⠀⠉⠐⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⣀⡠⠊⠉⠉⠉⠉⠙⡍⠉⠉⠛⠛⠒⠢⢐⡒⠒⠂⠀⠀⠤⠀⠤⠤⠤⠬⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠤⠤⢄⡀⠀⠈⠁⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⡀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⣼⣿⠿⠿⠿⠃⢸⣿⣿⠿⣿⣷⠀⢸⣿⡿⢿⣿⡆⠀⣾⣿⠿⣿⣿⡀⢸⣿⡿⢿⣿⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣷⡆⢸⣿⣿⣶⣿⡟⠀⢸⣿⣷⣾⣿⠇⠀⣿⣿⠀⣿⣿⡇⢸⣿⣷⣾⣿⠟
⠀⠀⠀⠀⣿⣿⣍⣉⣍⡀⢸⣿⣿⣿⣿⣄⠀⢸⣿⡿⣿⣧⡀⠀⣿⣿⣤⣿⣿⠇⢸⣿⡿⣿⣷⡄
⠀⠀⠀⠀⠈⠛⠿⠿⠟⠃⠈⠻⠋⠈⠻⠟⠀⠘⠟⠁⠙⠻⠃⠀⠘⠻⠿⠟⠋⠀⠘⠿⠃⠈⠻⠋

⠀⠀⠀⠀⠀⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡃⠀⠀⣀⡇⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣀⣤⠶⢦⡀⠈⠁⠋⠁⠀⣠⠜⠁⠀⠈⠉⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠼⠃⠀⠀⠀⠀⠀⠳⢤⡀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠘⠦⠴⢄⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⢀⡠⠋⣀⡤⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠓⠒⠚⠁⠀⢠⠋⠀⠀⠀⠉⠀⠈⠧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢆⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢈⠃⣯⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⢄⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡄⢰⠏⠀⠀⢠⠴⠒⠊⠉⢁⡠⠄⠒⠉
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢡⠌⢡⠀⠈⠒⠚⢦⣤⣤⢾⠀⠈⠀⡀⠀⠀⠑⡄⠀⠙⢡⡀
⠙⠫⡑⠢⢄⠀⠀⠶⢄⠀⠀⠀⠈⡆⠀⣀⠈⡆⠀⠀⠀⠀⠀⠀⡼⠀⠒⠈⡇⠀⢀⣔⡠⠔⠚⠉⠁
⠀⠀⠈⠢⣀⠉⠲⠆⠀⢉⠲⣄⡀⠑⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠇⠄⠠⡀⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠑⢤⡀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠤⠤⢶⠒⠺⢷⠦⠤⢤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢉⣋⣀⣤⠤⠤⢖⠒⠒⠉⠉⠀⠀⠀⠀⣀⠀⢀⣁⠠⠥⠤⠤⠛⢀⡀⠀⠀⠩⠙⠛⣇
⠀⠀⠀⠀⠀⠀⡛⠛⠀⠀⠤⢄⣀⠉⠀⠀⢠⡀⣒⡂⠌⣑⡀⠨⠄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠀⠂⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡠⠏
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠴⢌⠢⡀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠿⠇
⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⢄⣸⢀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⠒⠦⢤⣀⠀⠀⠀⠘⠀⠀⣀⡤⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢶⡞⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⢤⣌⣻⡒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠻⠦⠤⠤⣤⣄⣀⠀⠀⠉⠛⠄⠀⠙⢦⣿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣊⣉⣀⣀⡀⠀⠀⠀⠀⠀⠘⠂⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣯⣀⣀⠀⠀⠀⠀⠀⠞⠂⠉⠉⣉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡜⠁⠩⠿⣥⣀⠀⠀⠀⠀⠀⣈⣉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⢲⡖⣤⡠⠤⠶⠒⠒⠲⢦⣘⣤⠞⠉⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠈⠙⢦⡈⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠸⣅⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⢀⡽⠋⠀⠀⠀⠀⠀⠀⠀⣤⣀⢳⡀
⠀⠀⠀⠀⠀⠐⢧⣀⠀⠀⠉⠲⡖⠛⠉⠻⡴⠆⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⣰⠥⠤⠤⠤⡀⠀⠀⠀⠀⢠⡘⡎⠙⠃
⠀⠀⠀⠀⠀⠀⢠⡞⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠀⠀⣒⡤⡀⠀⠀⠀⠈⠁⠴⠚⠛⠃⡸⠀⠀⣰⡆⢸⠏⠛
⠀⠀⠀⠀⠀⠀⠸⣍⠵⠖⠤⣤⣤⣤⣤⡤⠤⠴⢶⣒⠛⠋⠉⠁⠀⠀⠈⠀⢀⡤⠚⠙⠒⠒⠒⠋⠉⠁⠈⠀⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠁⠳⠴⠋⠀⠀⠀⠀⠈⠉⠲⡄⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡜⠀⢀⣞⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠌⠉⠉⠁⠀⢹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢰⢸⠇
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⡇⠀⠀⠘⢸
⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠸⢷⣶⡶⠋⢸
⠀⠀⠀⠀⠁⣰⠒⠲⡄⠀⠀⠀⠀⠀⢀⡞⠁⣀⣀⣀⣀⡟⣻⠀⠀⢸
⠀⠀⠀⠀⠀⢹⠀⠀⢹⡤⠤⠤⠴⠒⠋⢉⠟⡻⠛⠙⠿⣧⡿⢶⣆⣸
⠀⠀⠀⠀⠀⠀⢳⠖⢻⡀⠀⠀⠠⠤⢤⣏⣼⠁⠀⠀⠀⠀⢠⠀⢸⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠳⡄⢧⠀⠀⠉⣁⡤⠿⡌⠉⠓⠀⠀⠈⠁⢠⠞⢀⣧⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠷⠚⠋⠁⠀⠀⠙⠲⢤⣀⣀⠤⢞⣁⣴⢋⡼⠙⠚⠁⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⣉⣡⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣴⠀⠀⠀⠀⠀⢀⡴⠛⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿⠀⠀⠀⠀⠀⠈⠱⠴⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠒⣻⠆⠀⠀⠀⠀⣿⣷⣄⠀⠀⠀⠀⠀⢸⠃⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠳⡄⣠⠹⠄⠀⠀⠀⠀⣿⡿⣿⣷⣄⡀⠀⠀⢸⠀⢸⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣿⡇⠈⠻⣿⣿⣶⣤⣘⣀⣀⣠⣴⣿⣧⡀⠀⠀⣀⣠⣴⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠉⠙⠿⣿⣿⡿⠿⢻⣿⡿⠁⠀⢀⣀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣀⣀⣀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢿⡉⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⢻⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠶⠚⠛⠛⠛⠳⠦⣤⣼⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠙⣦⡾⡁⠀⢀⣠⣤⣀⠀⢀⣼⠏⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠁⠀⢀⣼⣿⣤⣤⣀⡀⢰⣿⣛⢧⡀⠀⠀⠀⡿⠀⠀⠹⣿⡄⣾⠟⢋⣩⡿⠿⠞⠛⢻⣿⡆⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⣶⣶⣾⡿⠛⠉⠀⠀⠀⠈⠙⠻⣿⣯⠢⠻⣦⠀⢰⡇⠀⠀⠀⢻⣾⣏⠀⢸⡇⠀⠀⠀⠀⢸⣿⣷⣀⣀⣿⠙⠃
⠀⠀⠰⡦⠴⢣⠀⠀⠀⠀⠀⠀⠈⣻⣿⡠⠀⢀⣤⣤⣤⣀⠀⠀⠈⢿⡥⣀⠈⢳⣼⠃⠀⠀⠀⠀⢻⡟⢦⣬⣷⡾⠟⠀⠀⣸⠋⣿⠁⠀⢸⣦⣤⣄⣀⡀
⠀⠀⠠⡾⢄⣠⠆⠀⠀⠀⠀⠀⠀⣿⣿⡗⣼⡟⠉⠉⠉⠻⣧⠀⠀⠘⣿⣥⡀⠀⠉⠀⠀⣼⡄⠀⠈⣿⡀⠀⠀⠀⠀⣀⣼⢏⣤⣿⣶⣶⣾⡏⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⢾⣿⣄⠀⠀⠀⡟⢿⡀⠀⢘⣿⣶⣶⡾⠿⠛⢡⡟⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⢧⣀⠀⠀⣠⠞⠀⠀⢠⣿⡿⣿⠻⣷⣄⣼⡇⠘⠿⠿⠛⠛⠀⠠⡀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠒⠀⢶
⠀⠀⠀⠀⠐⠒⠛⠋⠉⠉⠉⠉⣉⠿⢿⣿⣿⣮⠉⠛⠋⠁⠀⠀⢠⣾⣿⣿⣿⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⢐⣤⠞⢶⡒⠒⠚⠛⠆⠀⠀⠀⠈⠑⣤⠞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⠞⠛⢿⣷⣥⣤⣀⣤⣤⣾⢿⣿⣍⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡎⠈⢳⣄⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⢀⡴⠋⠀⠀⢀⠾⠋⠙⠛⠉⠉⠀⠀⠈⢿⣦⠀⠀⠀⢀⡴⠞⠉⠉⠉⠓⢦⣇⠀⠀⠙⣦⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣰⠟⠁⣀⣤⠶⠶⢄⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠜⡀⡠⠀⠀⠀⠀⠀⠸⡇⣰⠏⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⣨⠗⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠗⠚⢦⡇⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⠤⠤⢤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠁⠀⠀⠀⠀⣀⣀⡀⠀⠈⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣶⣤⣄⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣿⣿⣿⣿⣦⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣦⠀⠘⣆
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠉⠀⠀⠀⠀⠉⢻⣿⣿⣧⠀⠸⡆
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠷⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡆⠀⢹
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠘⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⢿⣷⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣾⣿⣿⣟⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣦⠀⠙⠻⣿⣿⠿⣿⣿⡿⢿⣿⣿⢿⣿⣿⡿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣶⣶⣶⣶⣶⣶⣶⠂⠀⠀⠀⢰⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⡏⢩⠉⠙⠋⢉⠉⠙⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡄⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡇⠀⠀⠀⣴⣿⣿⣿⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⠁⠀⠀⠸⣿⣿⣿⡀⠀⠀⠀⠀⣴⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢀⣾⣿⣿⠋⢸⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣏⣀⣀⣿⣿⣿⣇⣀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀⣰⣿⣿⣿⣁⣀⣸⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⣿⣿⣆⣀⣀⣼⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣿⣿⣿⡏⠉⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠀⡀⢀⣤⢾⣿⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣾⣿⣾⣿⣿⣷⣦⣀⣠⣾⣿⣿⣿⣿⣶⠂⠙⠟⠛⠛⠁
⠀⠀⠀⠀⠀⢀⣀⣀⡶⠿⢛⢻⠁⠉⣿⠿⣿⣿⣿⣿⢿⣷⣭⣽⣼⣿⣿⡇
⠀⠀⠀⠀⠀⣸⣿⣿⣧⣄⣼⢺⡆⣰⣿⠰⠀⠈⠙⣿⣟⢁⣨⡿⠁
⢀⣄⡴⢆⣾⣿⣿⡿⢟⣿⣿⣿⣷⣿⣧⠀⠀⠀⠀⠈⠋⠉⠉⠁
⣾⣏⣻⣿⣿⡿⢿⡁⣌⣽⠟⠛⠃
⠁⠈⠻⠯⠿⠿⠞⠚⠛⠁

⣿⡿⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣠⡀⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣧⡤⠠⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣶⣶⣦⣼⣼⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢲⣤⣤⣤⣿⣿⣿⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣦⣀⣀⣀⣀⣀⣀⣠⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣤⣴⣶⣶⣿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠿⠿⠿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣀⣀⣀⣤⣤⣤⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣼⣿⣿⣿⣿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠾⠿⠒⠒⠚⠛⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠁


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣿⣟⣿⣿

⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⢹⣻⡃⠀⠀⠀⠀⠀⠀⠀⣠⢛⢶⣩⢷⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⢠⠀⡤
⠀⠀⠀⠈⠉⡉⠁⠀⠀⠀⠀⠀⡴⢯⠽⣫⣞⡱⠞⠀⠀⠀⢀⠀⠢⡀⠐⢤⠀⡀⠀⠀⠀⡇⢸⠀⢸⠀⠋
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢷⣫⠟⣵⠋⠀⠀⠀⠀⠀⠈⠀⠀⠘⠂⠈⠁⠁⠀⠀⠀⡇⠘⠀⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠘⠛⠇
⠀⠀⣁⢀⣐⣀⣀⣀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⡜⠀⠀⠀⠀⡾⡭⠭⢭⠍⢷⠀⠀⠀⠀⠀⠐⠁⠀⡈⡀
⠀⠀⠒⠀⠀⠀⠀⠒⠀⠀⠀⠀⡇⠀⠀⢀⡴⠋⠀⠀⠀⠀⠘⠓⠚⠓⠚⠓⠒⠃⠀⠀⠀⠠⣀⠂⢀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⡤⢒⡒⢤⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⢠⠒⠒⠲⠖⠒⢲⡄⠀⠀⠀⡎⠁⢠⠀⠀⠈⢱⠀⠀⠀⠀⢼⢸⢡⡎⡇⢣⠀⠀⠀⠀⣀⡇⠀⠛⠂⠂⣄
⠀⢸⣀⣀⣠⣶⣛⣉⠇⠀⠀⠀⠰⠐⠘⣞⠒⠂⠎⠀⠀⠀⠀⢸⣮⣓⣚⣵⡇⠀⠀⠀⠀⣙⡣⠭⠶⠭⢾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠸⡴⢦⠗⠃⠀⠀⠀⠀⠉⠐⠀⠉⠁⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄
⠀⠀⢰⠿⢶⡿⠆⡿⠆⠀⠀⠀⢠⢤⢀⠴⡄⢤⣄⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⠧⠮⠤⠧
⠀⠀⡞⣢⡞⢣⡞⢳⠀⠀⠀⠀⡤⠃⠈⠈⠁⠑⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣤⠒⢤⡆
⠀⠘⠯⠭⠭⠭⠭⠽⠃⠀⠀⠀⠓⠛⠉⠀⠙⠛⠚⠀⠀⠀⠐⠎⠒⠒⠒⠒⠲⠂⠀⠀⠀⠀⠨⡍⠐⠉⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣴⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⢀⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢸⣿
⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢸⣿⠇
⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⣸⣧⣸⣿⡄
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣴⠟⣿⡀⠀⠀⢀⣿⣧⡀⠀⠀⠀⠀⢀⣼⣿⡀⠀⠀⠀⢀⣴⠿⢷⣄⠀⠀⣠⣿⠋⢿⣿⠁
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡛⠛⠛⠛⠋⠁⠀⠘⢷⣤⣴⡟⠀⠘⠻⠶⣤⣤⡴⠿⠃⠈⠛⠳⠾⠿⠛⠉⠀⠀⠙⠛⠛⠛⠁⠀⠸⣿⡄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⣤⣀⠀⠀⠀⠀⢻⣿⡀
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠈⢿⣷⡀
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⠛⠁⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⣤⣤⠀⠀⠀⢸⣇⠀⠀⠀⠈⢿⣷
⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣀⣀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢿⡿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠈⣿
⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠶⠟⠀⠀⠀⠀⠀⣏⠀⠀⠀⠸⣿⣿⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢹
⠀⠀⠙⣿⣦⠀⠀⠀⢀⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣀⠀⠀⢀⣠⡴⠏⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠻⣷⣤⡾⠛⠉⠉⠛⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠀⠀⠀⠀⢀⣰⠟⢀⣀⠀⠀⠀⢀⣀⣴⣦⠀⠀⠉⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⢹⣿⠃⠀⢴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠳⠶⠶⠚⠛⠁⠀⠾⢛⡿⠛⢻⡟⠛⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣧⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⢿⣦⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠉⠛⠷⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⡶⠾⠛⠛⠛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢛⣛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣾⠛⠛⠛⠛⠻⢷⣶⣤⣤⣀⣀⣀⣀⣀⡀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠶⠶⠿⠛⢻⡟⠋⠉⠉⠙⠛⢿⣆⠀⠀⠀⢸⡏⠀⠉⠉⠉⠉⠉⠉⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣦⣄⣀⣀⣀⣀⣀⣿⣤⣤⣴⡶⠟⠋⠛⠻⠷⢶⣿⣷⣤⣤⣤⣤⣤⣴⣶⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⠉⠉⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠉⠉⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⣼⡿⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⢿⣧⠀⠀⣿⡇⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠸⣿⡀⢸⣿⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡤⠀⢀⣿⡇⣾⣏⠀⢠⣶⣿⣇