Domestic work Emojis & Symbols

⠀⠀⠰⡿⠀⠀⠀⠀⠀⠀⣀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⢀⣾⣿⣆⠀⠀⠀⠀⠸⢿⣄⣴⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣙⣋⡀
⠀⠉⣿⣿⣧⠁⠀⠀⠀⠀⠀⠉⣿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷
⠀⠀⢹⢿⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⠡⣴⣤⠄⠀⠀⢀⣤⣤⢸⣿⡇⠈⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⡆⠈⢣⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿
⠀⠀⠙⠘⠰⣾⠆⠀⠀⠀⠀⠀⠘⠘⠀⠿⠿⠁⠀⠀⠈⣿⡿⠈⠟⠀⠀⠀⣨⣿⠆⠀⠀⢀⣿⣿⡗⠁⢸⣿⠁⠀⠀⢑⣄⣀⠀⠀⠀⠉⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘
⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣿⣭⡀⠀⠀⠀⠀⠀⠀⢘⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠂⠀⠀⠀⠀⠀⠀⣾⠷
⠀⠀⣿⠏⡳⠤⠤⠀⠀⠀⠀⣾⡿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣰⣿⡿⣆⠀⠀⠀⠀⠀⠀⢸⣿⠿⡄
⠤⢼⣿⡟⠀⠀⠀⠀⠀⠀⢀⣿⣷⠀⠈⡆⠀⠄⠀⠀⠀⠀⠀⣼⣿⡀⠈⠁⠀⠈⠙⠋⠀⠀⠀⢠⣿⣧⠀⣸⣧⢀⠀⠀⠀⠀⣸⣿⡀⠙⣄
⠀⠹⣿⠇⠀⠀⠀⠀⠀⠀⠘⣿⡿⠀⠀⣏⡉⣉⠁⠀⠀⠀⠀⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢠⠙⠿⢻⠀⠀⠀⠀⣿⣿⡇⠀⢸⣶⣿⣷⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠋⠀⠀⠃⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠸⠤⠤⠼⠀⠀⠀⠀⠘⠋⠀⠀⠘⠜⠋⠙⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⢸⣿⠟⣛⡀⢀⡀⠀⠀⠀⠀⠀⢠⢾⣷⢦⡀⠀⠀⠀⠀⠀⠀⣼⣀⣭⣥⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⡀⠞⠀⠀⠀⠀⠀⠀⣴⣿⣶⠁⣾⣶
⠀⢀⣿⣏⠘⢻⣷⣾⡟⠀⠀⠀⠀⣀⣉⣸⣿⣰⣷⣦⡀⠀⠀⠀⠀⠙⢩⣿⣿⢳⡀⠀⠀⠀⠀⠰⢻⣿⣿⣿⠈⣿⡄⠀⠀⣀⣀⣀⣉⣉⡛⠚⣿⣿
⠀⢸⣿⣿⣄⠸⠿⠿⠃⠀⠀⠀⠀⠀⠀⠙⢤⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢠⣤⠀⠀⠀⠀⠀⠺⢿⣿⡿⠀⠻⠃⠀⠀⠁⠀⠀⠀⠀⡇⢰⣿⣿
⠀⠈⣿⠉⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢦⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠈⠉⠀⠀⠀⠀⠀⠀⠸⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠏⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣠⡠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⣁⠂⠐⠋⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢂⢔⣿⠄⢀⣈⡐⠀⢩⠗⣆⠀⠀⠀⠀⠀⢐⣂⣥⣖⢻⣯⢶⣄⠀⠀⢦⣀
⠀⠀⠀⠀⠀⠀⠆⠛⢃⠀⣩⠐⠐⠛⠋⣻⣶⣿⣶⣶⣤⣙⣏⣿⡯⠩⠿⡻⢿⡁⣄⠛⣤⠤
⠀⠀⠀⢀⢸⡇⠰⡇⢼⢾⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣷⣯⣞⣿⣟⡀⠀⢛⣿⣷⠄⡆⢀⠀⠀⠈
⠀⠀⠀⠙⠈⠛⠘⠃⠚⠓⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢢⡾⠟⢻⡿⣿⡾⠃⠁⠀⠁
⠀⠀⢰⣶⠶⠶⢶⣶⢶⣶⣶⣿⠿⣿⠟⠉⠻⣿⣿⣿⣿⣋⣿⣿⣿⣇⣸⣿⢁⣿⣿⠻⢿⣤⣤⣤⡤⡄
⠀⠀⠀⣿⠠⡆⠀⣷⢸⣿⣿⡍⣽⠃⡼⠃⢱⡿⠩⣿⣿⣿⣾⣿⣿⡷⠟⠛⠒⣿⣿⣵⣿⡟⠳⠀⡀
⠀⠀⢠⣿⠀⡂⢠⣿⣿⣿⣿⡿⣧⣼⣧⣶⣿⣷⣤⣶⡾⣿⣿⣧⣿⢹⣦⡀⠀⣿⣿⡋⢻⡇⢸⡀⡀
⠀⠀⠀⡿⠀⡏⢸⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣟⣾⣷⠟⢆⣘⢻⠁⣸⣷⣼⠀⠃⠀⢀
⠀⠀⠀⣿⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢹⣿⣿⡟⠀⠀⠀⠁⠀⣠⠿⣿⣿⡂⡴⠀⠰
⠀⠀⠀⡟⡀⢻⣿⣿⣿⠿⠛⠋⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⠋⠀⣿⣿⣷⡜⠀⠀⠀⡀
⠀⠀⠀⠇⢈⠃⡍⣿⣿⣶⣦⣭⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣄⣼⠀⠀⢸⣷⡿⡇⠀⠀⠀⠆
⠀⠀⠀⠀⢀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡏⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⣿⣦⣿
⠀⠀⠀⠁⡤⢠⡄⣿⣿⡿⠷⠿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣬⠇
⠀⠀⠀⠀⠒⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⢿⣿⣿⣿⡿⠛⠛⠋⢹⣿⠀⠀⠐⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⣤⡀⢻⣇⠀⠀⠀⢸⣯⣤⣤⡄⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢀⡒⠀⠖
⠀⠀⠀⠀⠀⠀⠀⣼⠷⠿⠈⠀⠸⣿⢀⣀⣠⣈⣬⣟⠁⣤⣤⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣙⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠟⠋⠀⠀⠈⠉⠀⠀⠘⢧⣄⣀⣀⣀⣀⠀⠀⠀⠀⢀⣴⠿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠁⠉⠉⠰⠖⠂⠙⠉
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡆
⠀⠀⠀⠀⠀⡇⢸⠀⠀⠺⠂⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⠀⠸⠀⠀⣀
⠀⠀⠀⠀⠀⡇⢸⠠⣲⠔⢤⡑⡐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⡄⢸⢀⠀⡆⡸⢏
⠀⠀⠀⠀⠀⡇⢨⠔⠃⠀⠎⠡⠈⢀⡘⠦⠄⢠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠰⡆⠘⣤⠠⠤⢴⠀⠸
⠀⠀⠀⠀⢸⡁⢉⡃⠀⠀⠀⠀⠀⠃⠙⠀⠘⡾⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡔⠒⣒⣒⣒⣢⣱⡀⠀⣧⠘⠁⡔⠒⡇⢤
⠀⠀⢀⠔⠁⠀⠀⠉⠲⡒⠒⠒⠂⠐⠂⠒⡖⡃⢀⣀⣑⡀⠀⠀⠀⠀⠀⠀⢸⢠⠀⠸⠂⠀⠀⠀⠀⠸⡤⠃⠀⣰⠀⢀⠫⣀⠇
⠀⠀⠸⡤⠤⠤⠤⠄⢠⡇⡀⠀⠀⣀⢀⣀⠜⠀⠀⠠⠄⡇⠀⠀⠀⠀⠀⠀⡆⡌⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⢠⣁⣄⣘⣀⡄
⠀⠀⠀⠇⠐⠀⠀⠀⢸⠀⠑⠒⠒⠉⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢇⠣⡀⡇⠀⠀⠀⠀⠀⠀⢀⢀⠎⠀⠀⠀⠀⡄⢣
⢀⡠⠎⢀⠇⢰⠀⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⠱⣸⠀⠀⠀⠀⠀⠀⠀⠈⡎⠀⠀⠀⠀⠀⠈⢀
⠑⢤⡒⢁⡔⢁⠤⠐⡀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⠤⠤⠤⠤⠤⠤⠠⣄⠀⠀⠀⠀⠀⠊⡜
⠀⠀⠈⠀⠈⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠤⠤⠤⠤⠤⠤⠋⠓⠤⠤⠤⠔⠊



⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⡎⠈⠁⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠤⠠⠀⢠⠀⠠⠀⠠⡀⣀⢄⠀⠁
⠀⠀⠀⠀⠀⢠⣠⠐⠒⠁⠶⠀⢡⠀⠀⢀⠞⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠒⠂⠠⠀⠤⠀⠠⠃⠓⠘
⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⢁⣉⡉⠉⠁⠈⠉⠉⣡⡤⢤⣄⡀
⠀⠀⠀⠀⢖⠆⠸⣉⣉⣁⡀⠀⠀⠀⢀⣀⢀⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠔⠉⠀⠤⠀⡈⠲⠄⡰⠉⠀⠑⠊⠀⠈⢆
⠀⠀⠀⢀⡔⠄⠀⠀⣀⡀⡗⠀⠉⠉⠀⣀⡀⠠⠬⡂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠰⠃⠀⠀⠀⠈⢂⠘⠠⠇⠀⠀⠀⠀⢸⠤
⠀⠀⠀⠓⠠⢌⠢⠠⡑⠁⠑⠉⠉⠉⠁⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⢀⠀⠀⠀⠀⠀⠨⡔⠓⠒⠒⠒⠒⢲⠸
⠀⠀⠀⠮⠂⠘⠤⠋⠀⣘⠙⢄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠱⡀⠓⠄⣀⠠⠔⣰⠉⣀⡀⣀⢘⡀⢈⣱
⠀⠀⡼⠬⠤⠅⢡⡦⣮⠁⠥⠭⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠑⠠⠤⠤⠚⣓⣜⠉⠀⢤⠋⠁⣠⣄⠇
⠀⢰⠀⠀⠀⠘⢷⠋⢢⠟⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔⠐⠒⠢⠀⠀⠀⠀⢡⠀⡱⢆⠀⣱⢞⡁⢸
⣤⣧⣤⣤⣤⣤⣬⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣦⣤⣤⣤⣤⣦⣤⣤⣤⣬⣤⣤⣤⣼⣥⣤⣤⣦⣤
⣿⣿⣁⣍⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢸⣽⡂⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣠⠞
⠀⠀⠀⠀⠀⢰⡯⠤⣷⠀⠀⠀⠀⠀⠸⣄⡀⠀⣠⠇⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣠⣈⣍⣀⣄⣄⣀
⠀⠀⠀⠀⠀⢸⡇⠀⢸⡄⠀⠀⢀⣀⣀⣈⣉⣉⣁⣀⡀⠀⢷⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠈⣿⠁⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⢸⡇⠀⢸⠙⣦⠴⠋⠁⠀⠀⠀⠀⠀⠀⠙⢧⢸⡄⠀⠀⠀⠀⣸⠃⠀⣠⠀⠀⢰⠿⡆⠀⠀⣄⠀⠸⡆
⠀⠀⠀⠀⠀⠈⠛⠛⢻⡀⠀⠀⣠⣶⠀⠀⠀⠀⠀⢠⡄⠈⢷⣧⠀⠀⠀⢠⠏⠀⢰⣿⠀⠀⣾⠀⣷⠀⠀⣿⡄⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠁⣯⣀⣀⣀⣀⣀⣀⣿⣆⠀⢻⡀⠀⢀⡞⠀⢠⡏⣾⠀⠀⠈⠛⠁⠀⠀⡇⢳⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠀⠀⠀⠀⡇⢸⡜⢦⠀⢳⠀⠸⣅⣀⡞⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠈⢧⣀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢸⡀⠀⠀⢀⡇⠈⣇⠈⠙⢻⡀⠀⠈⠁⠀⠀⣿⠀⠀⠀⣤⠀⠀⠀⡇⠀⣠⠽⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠈⠉⠉⠉⠉⠁⠀⢹⡀⠀⠈⣇⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⡇⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⡟⠙⢻⡟⠋⢻⠋⠛⠁⠀⠀⢻⡀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⡇⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⢘⣧⣀⣀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⡇⠀⢧⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⢸⠀⠀⠀⠀⣴⣋⣠⣤⠼⢷⡀⣿⠀⠀⠀⠿⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣸⣇⣀⡼⠀⠀⠀⠀⣏⠙⡇⠘⠇⠀⠃⠹⢄⠀⡀⠶⠄⢀⡰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⣂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⢀⢀⠀⣀⠀⡀⠀⠀⠀⠀⠀⡀⠀⡀⡀⡀⡀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠄⠘⠸⠨⠠⠓⠄⠍⠀⠄⠨⠀⠀⠱⠀⠀⠇⠂⠃⠠⠈⠣⠨

⠀⠀⠠⠠⣦⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⡐⠀⡶⠀⡀⠀⠀⣘⡀⢴⢄⣀⡀⠀⠀⠀⠀⣤⢀⠀⠐⣿⣿⣿⣧
⠀⠀⠲⠞⢹⡇⢀⣿⣷⡆⠀⠀⣎⣟⡀⠀⠈⠉⠉⠉⠁⠀⠀⠠⣻⠏⢻⡇⢀⠀⠀⠀⢸⡗⠋⠀⠈⣿⣿⣿⣿
⠀⠀⠀⢠⣤⠀⠸⢿⡏⠀⠀⠀⡾⢷⣿⣿⣿⣿⣴⠀⠀⠀⢠⣌⠃⣤⡌⠀⣼⡅⠀⠀⠈⡇⣸⠇⠐⣿⣿⣿⣿⡇
⠀⠀⠀⠈⠉⠀⠀⠘⠁⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠉⠀⠉⠁⠘⠋⠁⠀⠀⠀⠃⠘⠀⠈⢉⡉⠙⠉⠣
⠀⠀⠀⢀⡶⠀⠀⠀⠀⣀⠐⣦⠀⠀⠀⠀⠀⣐⣷⡄⠀⠀⢰⣆⠀⠀⠀⠀⣤⠀⠀⢀⣄⠀⠀⠀⠀⣼⣉⣦⡀⣀
⠀⠀⠀⢾⡯⠍⠀⠀⠀⢻⠒⣿⠀⠀⠀⢠⣿⡋⠸⣿⣧⠀⣿⣿⠄⠀⢠⣶⣅⡀⠀⣾⢅⡀⠀⠀⢀⣿⡌⢻⣿⣿
⠀⠀⢀⡼⢻⠀⠀⠀⠀⠀⢸⢻⡀⠀⠀⠘⣿⢳⣶⢹⡏⠀⢻⡏⠀⠀⠀⣹⣿⠃⠀⣿⣆⠁⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠘⠀⠘⠁⠙⠀⠀⠀⠀⠐⣷⣿⣿⣿⡇
⠀⠀⢀⣶⣢⡄⠀⠀⠀⠀⠀⢰⡆⠀⠀⣤⣴⠀⠀⠀⠀⠀⢠⣶⡂⠀⠀⠰⣦⠀⠀⠀⠀⠀⣀⡦⠀⠈⣿⣿⣿⣿⡇
⠀⠀⢹⣿⣿⣿⣿⣆⡀⠀⠀⢹⣿⠀⡤⢽⣿⡇⠤⢤⠀⠀⠸⠏⠛⠰⠯⢹⣿⡆⠀⠀⠀⢸⣿⣄⠀⠀⠛⣿⣿⣿⡇
⠀⠀⢸⠿⣿⡿⠿⠿⠇⠀⠀⣼⢹⠀⡿⢿⣿⠿⠿⢿⠀⠀⠀⣶⡆⠀⠀⢸⣿⠃⠀⣸⣿⢂⡟⣇⠀⠀⠀⠈⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⣿⣷⡄
⠀⠀⢀⣤⣴⣾⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⢠⣿⣿⣧⡀
⠀⠀⣿⣿⣿⣿⣿⠁⣟⠉⠁⠀⠀⠀⠀⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣇⣀⠌⢈⣿⣿⣿⡄
⠀⠀⠘⢿⣿⣿⡿⠀⠠⠀⠠⠀⠀⠀⠀⠂⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⢿⠀⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠉⠀⠀⠀⢷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣈⣋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⡄⢠⠀⠀⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣏⠉⣹⣿⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⢛⡏⠀⢹⠷⡄⠀⠀⠀⠀⢠⠟⠁⠀⠈⠻⡄⠀⠀⠀⠀⣿⣿⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠷⠸⠷⠶⢾⠀⠇⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢿⣿⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠶⠋⠀⠀⠀⠀⢠⣿⣿⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣦⡀
⠀⠀⠀⠀⢠⣾⣿⣿⡏⡽⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⣿⢻⣿⣿⣦⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣧⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠡⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠈⠛⠿⠿⠃⠀⣷⣶⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⡆⠀⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠛⣏⣉⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠿⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢙⣛⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⠰⠥⠀⠀⠀⠀⠀⠀⣔⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣮⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢷⡝
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠸⣿⣇⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠸⣿⡆
⠀⠀⠀⢠⣶⡆⠀⠀⣼⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣿⠃⣿⡇⠀⠀⠀⠀⠀⢰⣶⣶⣶⡆⠀⢀⣿⣿⠀⠀⣿⣇⠀⣶⣶⣤⡀
⠀⠀⠀⠀⠈⠛⠃⠀⠈⠉⠀⠀⠉⠉⠀⠀⠚⠛⠁⠈⠉⠀⠉⠁⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠈⠉⠁⠀⠀⠉⠁⠀⠙⠻⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⣶⠿⠛⠛⢦⣀⣀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠁⠀⠙⠁⠀⠀⠀⠀⠈⠉⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡴⠊⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⣠⡤⠀⠈⠉⡼⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣡⣄⠀⠀⢸⣀⣠⡶⠳⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣧⡼⠀⠀⠀⠙⠉⠀⡀⠀⠤⢼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⡄⠀⠀⠀⠀⠀⠀⡻⠿⠟⣋⡀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠁⠀⠀⢀⣀⣄⠀⢱⠂⠉⠉⢹⣆⣠⣀⠀⠀⣀⡰⢫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣫⠅⠻⣦⣨⠆⠀⢸⣿⣿⣿⣿⡷⡞⡌⢷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⢀⣠⣴⡆⠀⣀⣾⣿⣿⣿⣿⡝⠞⢠⡟⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡽⡂⠛⠓⢤⡀⢀⣠⠴⠒⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢫⠞⠁⢹⣆⠀⠀⠉⢯⡁⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢿⣿⣿⣿⣿⣿⣿⠟⡴⣯⡴⠞⠋⠙⠷⣤⣀⣼⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠙⢢⡜⠉⠉⠉⡹⢫⣎⡡⠾⣷⣖⠒⠒⠒⠀⠭⣥⡤⢄⣀⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣴⠋⠀⠀⢀⠞⡵⠁⠘⣇⠀⠈⠙⢿⣦⡀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢿⣀⣠⡴⣫⠞⠀⠀⠀⡿⠀⠀⣠⣴⣿⣿⠆⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⣠⡴⠞⠉⠁⠀⠀⠀⠀⠀⠙⢦⣠⠋⡰⣸⠃⠀⠀⠀⡼⠁⠀⠸⣿⣿⣿⠋⠻⠏
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡰⣱⠟⠁⠀⢀⡞⠁⢀⣴⣶⣿⡿⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣵⠟⠉⠀⠀⣠⠏⠀⠀⠘⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠞⠁⠀⠀⠀⡴⠃⠀⠀⢰⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡱⠋⠀⠀⠀⢀⣾⣿⣶⣶⣦⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣰⢻⠟⠀⠀⠀⠀⢠⣿⣿⣿⡿⠿⠿⣿⡿⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢿⠀⠀⠀⠀⠀⢠⠞⠉⠉⠉⠛⣿⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⢣⠀⠀⢹⢣⡀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂⠀⠀⢀⠔⠁⠢⣀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⢸⠇⢧⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡠⠀⠈⠳⡄⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⠸⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠠⠞⡡⠀⠀⡀⠈⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣿⠀⠀⢻⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠛⢉⣠⠤⢒⣀⠴⠊⠀⡠⠚⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠘⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⢴⡚⠯⢔⡈⠔⣊⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠪⠭⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⢳⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠾⠛⠃⠀⠀⠀⠀⠀⠀⠀⣤⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠆
⠀⠀⠀⠀⠀⠀⣤⣶⣄⠀⠀⠀⠀⠀⠀⠀⠘⣧⣥⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⢀⣀⡀⠀⠀⠀⢹⣿⣿⣧⠀⠀⠀⣿⠗⠀⠀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣤⠀⡈⠀⠀⠀⠀⢸⡿⢿⡯⠀⠀⡀⠀⠀⠀⠀⠀⢺⣿⡍⠀⢀⡰⠳
⠀⠀⠀⠀⠀⠘⣻⣿⢏⣿⠉⠀⠀⠀⠀⠀⠀⠺⣿⠸⣿⠀⠐⠃⠀⠀⠀⠀⠀⠀⠙⠋⠀⠼⠃⢸
⠀⠀⠀⠀⠀⠀⣿⣇⣸⣿⠁⠀⠀⠀⠀⠀⠀⣾⣿⣀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠒⠳⠰⠁⠀⠀⢸
⠀⠀⠀⠀⠀⢰⣟⠛⠛⢹⡇⠀⠀⠀⠀⠀⢰⣿⣿⢽⣾⡧⠀⠀⠀⠀⠀⠀⠀⣀⣻⣾⣿⣿⡀⠸⡀
⠀⠀⠀⠀⠀⢺⣿⢀⡀⢿⣿⠀⠀⠀⠀⠀⢠⣿⠃⠀⢿⡇⠀⠀⠀⠀⠀⢀⣜⣸⣿⠃⠘⣿⣇⢀⣦⠄
⠀⠀⠀⠀⠀⠛⡣⡀⠀⠀⠛⢡⢀⠀⠀⠀⣚⣥⣀⠀⢘⣣⣄⡀⠀⠀⠀⢸⡟⠝⣿⡿⣶⠜⣿⣤⣁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠙⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣦⣤⣤⣦⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠃⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠢⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠠⠀⣀⣠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠀⠀⡠⠒⢄⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⢱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠈⠐⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣇⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠑⢄⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠢⡀⠀⢀⠐⠁⠘⡀⠀⠀⠀⠀⠐⡲⠙⠚⠁⠫⠗⠂⣀⠄⠲⠖⠁⣹⠖⡲⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠓⠒⢂⢾⡁⠉⠶⠀⢦⡈⠀⠀⠀⠀⠀⠾⡲⠴⢻⢖⠧⠆⠁⠂⠀⠀⠀⠁⠎⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠃⢀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠲⡿⠻⠻⠺⠎⠠⠴⠀⠀⠀⠀⣤⡤⠀⠢⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⠂⠀⢸⠈⠉⠀⠈⠁⢨⠈⠄⠀⠀⠀⢰⣿⣿⣽⣿⡂⢀⠀⠀⠠⠤⢄⡉⢰⠀⠀⢸⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⠄⠀⢁⠀⢨⣀⣀⣀⣀⣀⢸⠀⡄⠀⠀⠀⠈⡋⠉⠈⢈⠍⠀⢀⠀⠃⠀⠈⠃⠤⡀⠀⠀⢈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸⠀⠘⠠⠀⠀⠀⡘⢸⠀⠀⠀⠀⠀⠀⠈⣲⠆⣡⠀⣼⠀⠑⡗⠖⠠⡀⣠⠓⠠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠆⠀⠀⠂⠈⠀⢸⠀⠀⠒⠒⠋⠀⠉⠁⠀⠙⠀⡟⠀⡐⠐⠀⠀⠀⠉⠓⠠⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠱⡀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠖⡃⠀⠇⡐⠌⠀⠀⠀⠀⠀⠀⠙⡄⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡨⠓⢄⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠑⠤⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡤⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡐⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢀⡀⣀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡅⠀⢀⣠⣄⠀⣀⣠⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⢸⠁⠉⣛⢿⣿⣿⠠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠸⠀⠈⠉⠛⠤⣈⡇⠉⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠇⠓⠀⠤⠀⠀⠉⠛⠶⡏⠀⠀⠀⠰⠂⠈⠁⠸⠀⠀⠼⠓⠻⠆


⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠐⣶⡖⢒⠒⠒⢒⠒⠂⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣦⣤⡤⣤
⠀⠀⠀⢸⣿⡿⢛⣛⡻⣿⣿⡇⠀⠀⠀⠀⠀⣴⣶⡜⣿⣿⣿⣿⣿⣧⠏⠀⠀⠀⠀⠀⡏⠈
⠀⠀⠀⢸⣿⢰⣿⣷⢹⢜⣿⡇⠀⠀⠀⠀⠀⣿⠿⡏⠈⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣷⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⢸⣿⣮⣙⣓⣫⣾⣿⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⠏⠲⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⢸⡿⠛⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢞⡷⠀⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡤⢤⡀⣿⠀⠀⠀⠀⠀⠀⠀⠟⣸⣿⣿⣿⣿⣿⣷⢠
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣦⣴⠇⣿⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⡿⢸
⠀⠀⠀⠀⠀⠈⣩⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡄⢠⡄⣿⠀⠀⠀⠀⠀⠀⠀⠿⠀⠙⠻⠿⠟⠋⠀⠾
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠛⠉


⠀⠀⠀⠀⠀⣷⣶⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣻⣃⣿⣚⡇
⠀⠀⠀⠀⠀⡏⢉⣍⡉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⠏⣿⠛⠇
⠀⠀⠀⠀⠀⡇⣿⣼⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⢸⣻⡇
⠀⠀⠀⠀⠀⠇⠿⠿⠧⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠤⠼⠶⠆

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠿⠿⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣀⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⢿⡿⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠗⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠺⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠘⢿⣶⣶⣶⣶⣶⣶⣶⣶⣿⠃⠀⠀⠀⠀⠙⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢠⣤⠀⢀⣤⡄⠀⣤⡄⠀⠀⠀⣿⡇⠀⠀⠹⣿⡆⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⢠⣿⠟⠉⠉⠙⢿⣷⠀⠀⠀⢸⣿⠇⠀⠀⠀⠉⠀⠀⠉⠀⠀⠈⠁⠀⠀⠀⣿⡇⠀⠀⢀⣿⡇⠀⠀⠀⣾⡿⠋⠉⠉⠻⣿⡄
⠀⠀⠀⢺⣿⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⣿⡇⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⡗
⠀⠀⠀⢘⣿⣷⣤⣀⣤⣾⣿⠀⠀⠀⢸⣿⡄⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠟⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣷⣤⣀⣤⣾⣿⡃
⠀⠀⣰⣿⠟⠉⠛⠛⠋⠉⢻⣷⡄⠀⢸⣿⣿⡿⠋⠸⣿⣇⡀⢀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢀⣿⡇⠀⢠⣾⡟⠉⠙⠛⠛⠉⠻⣿⣆
⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠘⠿⠋⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣦⣈⣿⡇⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣯⠿⠿⣿⣿⡿⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣴⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣺⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⠀⠀⢀⣴⠟⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠒⠒⢲⡟⢀⡴⢋⣴⠞⣀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡷⢋⡴⠛⣡⠞⢋⡴⠆⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡴⠋⣴⠋⠠⠞⠁⠐⠋⢠⠶⠃⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣌⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠛⠛⡿⠛⠛⣷⠀⠀⠀⣴⠞⠛⣛⠓⢦⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣀⣀⣧⣤⣤⣿⠀⠀⣼⠃⠀⠋⠗⣫⠆⢻⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠉⠈⣯⠀⠀⣿⠀⠀⡟⠀⠀⠀⠀⠐⠋⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⠶⠶⠿⠒⠚⠛⠀⠀⡇⢀⡀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠻⠃⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⢀⣀⣤⣤⡤⠷⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠛⠒⠶⠶⠶⠶⠶⠾⠧⢤⣤⣿⣄⣀⣀
⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⣤

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⢐⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠒⢲
⢰⠀⠀⢀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⡀⠑⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⡞
⠈⢆⠀⠀⠈⢦⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠹⠛⠛⠁
⠀⠀⠑⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠾⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬



⠀⠀⠀⡄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣄⣠⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⡀
⠀⠀⠀⠀⡠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡧⠤⡧⢤⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⠀⠀⠀⢳
⠀⠀⡀⢴⠃⠐⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣡⠤⠧⢤⣁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣌⠒⠚⠦⢊
⠀⠀⠒⠒⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤
⠀⠀⠀⠀⣠⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣾⣄⠀⠀⢀
⠀⠀⠀⠀⠉⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠛⠁
⠀⢀⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡴⠀⠀⠣⣀⠜
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣁⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠙⠄⠀⠖⠉⠱
⠰⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⣰⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢸⣿⣿⠿⠛⠉⠙⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⣼⡇⠀⠀⠀⠀⠀⠸⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡆⠀⠀⠀⠀⠀⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⢶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⡁⠀⠀⣀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣅⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠉⠙⣦⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣦⣀⣿⣿⣦⣿⡷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣯⡙⢿⣿⣿⣿⣿⣿⣿⣿⣧⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡈⠻⣿⣿⣿⣿⣿⣿⣿⡀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⠿⠿⠿⠿⠟⠛⠁⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣶⣶⣬⣿⣿⣿⠏⠀⠘⣿⣿⣿⡆⠀⢀⣀⠠⠶⠚⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢈⠿⠿⢿⣿⠏⠀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⢠⡾⠁⠀⠀⣀
⠀⠀⠀⠀⠀⢠⡞⠀⢀⣴⡏⠀⠀⠀⠀⠀⠀⠻⣿⡆⠀⠀⠀⣼⡇⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⡾⠀⠀⠈⠉⠓⢦⣤⣤⠀⠀⠀⠀⠹⡷⠒⠖⠚⠹⣷⡀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⢻⡶⠀⠀⠀⠀⣾⠿⠁⠈⠉⠑⠶⠶⣶⡶⠖⠀⠀⠈⠻⠶⣄⠀⠸⣇
⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⡦⢹⡟⠓⢶⣶⣶⣦⡀⠀⠻⡄⠀⠀⠀⠀⠀⠙⣷⠀⠻⣄
⠀⠀⠀⢠⡿⠀⠀⠀⠀⣼⠇⢸⡇⠀⣼⣿⣿⣿⡇⠀⣀⣹⣆⠀⠀⠀⠀⠀⢹⣧⠀⢹⡄
⠀⠀⠀⣼⠇⠀⠀⠀⠀⠛⠀⢸⡇⢰⣿⣿⣿⠉⠓⠈⠉⠁⢀⠀⠀⠀⠀⢀⠀⢻⣇⠈⢧⡀
⠀⠀⠀⠁⠀⠀⠀⠀⢰⡆⠀⣾⡇⣸⣿⣿⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠈⣿⡄⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢾⡇⣿⣿⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⠀⢸⡇⠀⠸⣿⠀⢻⣄⡀
⠀⠀⠀⠀⠶⢦⣀⠀⣿⠃⠀⢼⣿⣿⡏⠀⠀⠀⠀⠀⣀⣠⡾⠀⠀⠹⠀⢸⡇⠀⠀⢻⣇⠀⠈⠈⢻⣦⢀⣀⡀
⠀⠀⠀⠀⠀⠠⣬⣉⡁⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡇⢸⡇⠀⠀⠘⣿⡄⠚⠟⠛⠁⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⡇⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⣼⣿⠃⣼⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⣿⡆⠀⠉⠉⠀⠉⠉⠑⣾
⠀⠀⠀⠀⣰⣿⢇⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠹⣿⣤⣀⣤⣤⣤⡶⠾⢋
⠀⠀⠀⢰⣿⠏⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢿⣏⠉⠉⣉⣉⠀⠀⣸
⠀⠀⢠⣿⠏⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠉⠀⢠⡿
⠀⢀⣿⡏⣰⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⣼⠇
⠀⣸⡟⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠄⠀⠀⢠⠟
⠰⡏⢠⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣷⡆⠀⢤⣤⡶⣞
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⡿⠛⠾⠷⠟⠛
⠒⠦⣤⣌⣙⠛⠛⠟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠉⠙⠻⠶⣤⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣟⣛⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⢉⡽⠿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠶⠶⣤⣤⣤⣌⣉⣉⣉⣁⣀⣤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡄⡟⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢣⡇⢸⡁⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠻⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿

⠀⠀⢀⡴⠓⠛⠛⠛⠛⠓⠛⠛⠛⠛⠓⠳⡄⠀⠀⠀⠀⠀⠀⠀⣠⣴⡴⢤⣦⣀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⠋
⠀⢠⡞⠁⠀⠀⠀⠀⣰⠛⢧⡀⠀⠀⠀⠀⠹⣆⠀⠀⢀⠠⣶⢻⡁⣸⡀⢀⡀⢈⣿⣶⢄⡀⠀⠀⣤⣯⢿⡿⣷⣄⠀⠀⠀⡀⡀⣠⢄⢠⡄⣀⢠⠤
⣰⣟⣐⣒⣒⣂⣢⠞⢡⡶⡆⠙⣆⣂⣒⣒⣒⣚⣧⠀⠀⡎⢉⣉⣉⣉⣉⣉⡉⢉⣉⣉⠁⠀⠀⠚⡞⣓⡛⠚⠚⢳⠓⠀⠐⠋⠃⠳⠜⠘⠻⠛⠸⠭
⠀⠀⢽⠀⠀⠃⠛⠀⠈⠋⠋⠀⠘⠀⠃⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠈⢸⠀⡇⠜⠳⢻⠀⠀⠀⠀⡟⠿⠟⡤⢤⢸⠀⢰⠶⠶⢶⢲⡖⠆⠰⠶⡶⢶⢶
⠀⠀⣾⢸⡇⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠇⠇⠐⢸⠀⠀⠀⠀⣧⢀⢠⡇⢸⣼⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣽⠈⠁⡂⠀⠀⣿⣿⣿⡇⢀⠀⡀⠉⢸⠀⠀⠀⠀⠉⠉⠈⠁⠉⠈⠁⠉⠉⠉⠉⠁⠀⡀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠁⠀⠀⠀⣦⡆⠀⠀⠙⠉
⠀⠀⣿⠀⠀⠟⠛⢠⣿⣿⣿⣧⠘⠛⠇⠀⢸⠀⠀⠀⠀⠀⣠⠞⠙⠢⣀⠀⠀⠀⠀⣨⢗⣵⣮⡢⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⣵⢝⡶⣄
⠀⠀⠻⠤⠴⠦⠤⠼⠿⠿⠿⠿⠤⠤⠶⠤⠼⠀⠀⢀⡠⠚⠁⠀⠀⠀⢈⡷⠀⠀⢾⠷⠻⠿⠿⠿⠿⣽⣿⣳⣄⡀⠀⠀⠀⢚⣉⣀⣛⣒⣛⣛⣚⣙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⢉⠢⣄⠀⠀⡠⠊⡇⠀⠀⢸⠀⢰⣻⠛⡇⠀⠛⠚⠛⠚⠛⡆⠀⠀⢸⣯⣩⣿⣿⣿⣯⣩⣿
⠀⠀⣀⣀⡀⢀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠰⠯⠤⠤⠧⠤⠤⢷⠊⡠⢘⡇⠀⠀⢸⠀⢠⠤⡤⡄⠀⠀⠼⠿⠹⠄⡇⠀⠀⢸⣿⣿⡏⠀⠈⣿⣿⣿
⠀⠀⣾⣿⣶⠿⣫⢬⡙⢿⣦⣀⠀⠀⠀⠀⠀⠃⠀⠄⠄⠄⠀⢸⣀⠜⣡⠇⠀⠀⢸⠀⢸⠠⡇⠇⠀⢤⠤⠤⠤⠤⠇⠀⠀⠘⠿⠿⠇⠀⠀⠿⠿⠟
⢀⣴⡿⢟⡥⠚⢁⣠⡈⠳⣍⠻⣷⣄⡀⠀⠀⠇⠀⠀⠀⠀⠀⢸⣡⠞⠁⠀⠀⠀⠈⠂⠘⠘⠃⠓⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠿⣫⠖⠉⠀⠀⠈⠋⠀⠀⠀⠙⢮⡙⠿⠀⠀⠓⠚⠓⠓⠛⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⣺⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⢫⢝⠷⣄
⠀⣼⠀⢀⣀⣀⡀⠀⢀⡀⢀⡀⠀⡇⠀⠀⠀⣠⠖⠒⠒⠒⠒⠒⢒⡶⠢⡀⠀⠀⠠⣶⣿⠛⠛⢻⣿⡇⣍⣲⢤⣀⠀⠀⠀⠠⠞⠩⠾⠯⠿⠷⠌⠳⠄
⠀⢸⠀⢸⣿⣿⣗⠀⠿⠇⠿⠇⠀⡇⠀⠀⢺⠓⠒⠒⠒⠒⠒⠒⠿⠒⠒⠸⠆⠀⠀⣿⣿⡍⡍⣿⣿⡇⣯⡟⠛⣾⣗⠀⠀⠀⣿⣿⣿⢿⡿⠿⠿⣿
⠀⢸⠀⢸⣿⣿⡏⠀⠿⠇⠿⠇⠀⡇⠀⠀⢸⢰⣶⠠⣶⡆⣶⡆⠀⢰⣶⠀⠀⠀⠀⣿⣿⠀⠃⣿⣿⡇⣿⠅⠀⣿⣿⠀⠀⠀⣿⣯⢽⣿⡷⣯⣏⣿
⠀⢸⣀⣼⣿⣿⣯⣀⣀⣀⣀⣀⣠⡇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⠀⠀⠀⠀⠿⠿⠀⠀⠾⢿⠇⠷⠄⠀⠿⠿⠀⠀⠀⣿⣇⣸⣿⣿⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠀⣛⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠇⠀⣆⡀
⠀⠀⠀⠐⡇⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠡⡀⣏⠰⣿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⢸⠀⠀⣿⠧
⠀⠀⠀⠀⡇⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣟⡼⢿⣿⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠯
⠀⠀⠀⢠⡁⠉⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡿⠟⡃⢀⣀⢀⠀⠄⠂⠀⠀⠀⠀⠀⢸⣀⢀⣷⡶
⠀⠀⠀⢺⡁⣷⣶⠐⢸⣧⣄⠀⠀⢀⣀⣀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠐⢒⠸⣷⣶⣾⣿⣦⠀⣀⠀⠀⠈⠀⠀⠉⠉⠉⠁
⠀⠀⠀⢸⠀⣿⣿⣿⢿⡟⠃⠀⠀⠐⢋⣛⠛⠻⠝⠃⠀⠀⠀⠀⠀⠀⡐⢀⣴⣷⡤⠈⠙⠿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠸⠀⣿⣏⠀⢸⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠀⠒⠀⠀⢦⢉⠉⠉⠳⢾⣀⣀⠈⢿⣿⣿⣿⡄⠀⠁⠀⠀⠠⠼⠂⠐
⠀⠀⠀⠀⠀⢹⡿⡾⣿⣽⣱⠆⣞⣻⠋⠀⠉⠀⠘⡎⠀⡌⡇⠈⠀⠀⠀⠀⠣⡘⠛⣛⣻⣿⣴⠄⠙⢿⣿⡇⠀⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢘⢧⡥⠋⠀⠤⠖⠦⠀⢻⠀⠀⠀⠀⠈⠀⠇⠁⡀⠀⠄⠀⠀⡀⢱⡈⠁⠚⠋⠙⣤⣄⠀⠙⣿⠀⠐⠀⢀⠀⡀⠁⢠⠆
⠀⠀⠀⠀⠀⠈⣨⣷⠀⠀⠀⠂⠀⠀⠀⢳⡄⠀⠀⠀⠰⢶⠖⠀⠀⠀⠀⣴⡀⠸⢧⢀⣤⠶⠶⢿⣷⣴⠆⠀⠀⠀⠐⢀⠀⠀⠠⠋⠐⠤⠄
⠀⠀⠀⠀⠀⢁⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⣛⣲⠀⠀⠐⠀⠀⠚⠃⠀⠀⠈⠁⠀⠀⠸⠟⠉⠒⢔⣳⣼⣧⡍⠀⣀⣰⣤⡀
⠀⠀⠐⠿⣿⣿⣯⣿⣿⣆⢀⠄⢈⣉⡿⠷⠗⠒⠉⠉⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠀⡤⠈⣧⣼⢿⣿⠉⠃
⠀⠀⠀⠈⠉⠛⠛⠉⠉⠙⠛⠋⢩⣴⡄⠀⠀⠀⠀⢤⠘⡦⠀⠀⠈⠉⣉⠉⠉⠉⠉⠉⠀⠀⡀⠸⠀⢸⣿⣿⠘⣿⣧⣰⡆⠀⢀⣀⣠⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣰⣶⠀⠉⠂⢸⣶⡆⠀⠀⠀⠈⠉⠉⢛⣛⣛⡟⠀⠀⠀⢸⣿⣿⠀⢻⣿⣿⣿⢹⡿⢟⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠀⠀⢸⣹⣁⡀⠀⠀⠀⠘⠛⠿⠿⣻⠁⠀⠀⠀⢸⣿⣿⠀⣸⣿⣿⣿⠘⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⣠⣤⣴⣶⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠿⠿⢻⢻⣿⠟⠀⠀⠀⠀⠀⣿⡿⠛⠉⠛⠋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡔⠲⡌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡅⢎⡇
⠀⠀⠀⠀⠐⠒⠒⠒⠒⠂⠀⠀⠛⠀⠒⠒⠒⠒⠒⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⢊⠴⠁⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠸⠃⠀⠈⡆⡔
⠀⠠⠀⠀⠀⠀⣰⣁⡍⢀⡴⠀⢿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⠓⠒⠒⠒⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠀⠀⠀⠀⠀⡠⠂⠉⠉⡇⠢⡀⠀⠀⠀⠀⠀⡇⡤
⠀⠀⠀⠙⠔⠉⠉⠉⠉⠁⡜⢣⠈⠉⠉⠉⠉⠑⠦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢘⠀⠀⢀⡴⢆⠀⢸⠀⠀⠀⠀⢀⠈⡀
⠀⠀⢠⠖⠉⠉⢹⠙⠢⡀⠑⠊⠀⢀⠔⠋⠉⠉⠃⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠙⢦⡀⠀⠈⢹⠈⠁⠀⠀⠸⠛⠀⠀⢀⠔⠁⠀⢈
⠀⢀⠁⠀⠀⢀⠾⡀⠀⢡⠀⠀⢀⠃⠀⠀⢀⠼⣀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠙⠦⣠⡈⢆⡀⠀⣀⠞⢸⡤⠔⠁⠀⢀⠴⠁
⠀⠀⠙⠂⠉⠁⠀⠈⢙⠈⠀⠀⠈⠛⡆⠈⠁⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠀⠉⠈⠉⠀⠁⠀⠀⢀⠔⠁
⠀⠀⠀⢆⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⡔⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⡠⠒⠛⠂⠘⠓⠢⡀⠀⠀⠀⡤⠖⠛⠃⠘⠋⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢸⣁⣀⣀⣀⣀⣀⣀⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠁





⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠊⠙⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠈⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢣⠀⡴⣔⢉⢩⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡔⠒⢄⠀⠈⠁⠒⢄
⠀⠀⠰⠢⢄⠀⠀⡰⠛⢤⡣⠄⠃⠈⢣⠀⢀⠀⢀⡆⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⠢⡊⠗⢄⠀⠀⠈
⠀⠀⢐⠀⠠⠃⠀⠑⠀⠲⡀⠁⡛⠀⠘⠀⠀⠀⡜⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠀⠙⠦⠴⠃⡀⠜
⢀⠄⣈⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠀⠑⡲⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⡀⠑⠄⣀⡠⠎⢠⠒⠄
⠣⠠⠆⠀⠀⠀⠀⠀⡠⠊⠉⠉⠓⢦⠀⠀⠐⠒⠉⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⢬⣊⠀⠀⠀⠀⠀⠀⢈⡓⠅⢠⣄⡀
⠀⢠⠄⠤⡀⠀⠀⠠⣁⣀⡠⠚⠤⣀⡇⠀⠀⠀⡠⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⢠⠀⠑⢄⠀⠀⠀⡰⠋⠀⠀⢠⠀⠉⢆
⠀⠸⡀⠀⠉⠢⡀⠀⢘⡀⠀⠀⠀⡇⠀⠀⡠⠊⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣀⣀⠴⠋⠢⣀⣈⠀⠀⠀⣇⣀⣀⠤⠊⠢⢀⣈
⠀⠀⠈⠢⡀⠀⠈⠒⠤⠵⠦⠤⠾⠤⠐⠉⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⡁⠀⠀⠀⠀⢨⠈
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⣀⣀⣠⠃⠀⠀⠀⠀⡇⠑⣄⣀⣀⣠⠊
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠉⢢⠀⠀⠀⠗⠉⠀⠀⠀⠀⠉⠲⡀
⣀⣀⣀⣀⣀⣀⣀⣘⣤⣄⣀⣤⣤⣤⣜⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣤⣤⣤⣤⣤⣤⣤⣤⣃⣀⣈⣀⣀⣀⣠⣄⣤⣤⣤⣃
⣿⣿⡟⠙⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⡄⠀⠀⠀⠀⢠⠀⠀⠀⣠⣄⠀⠀⣠⠀⣄⢀⣀⡄⠀⠠⢀⡀
⣿⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡄⡇⣬⣷⢾⣉⢸⢿⡁⠠⣟⣯⡆⠀⠸⣾⢻⣾⢠⡏⣷⢸⢸⡇⣾⠽
⣿⠀⠀⠀⠀⡖⠁⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠁⠈⠉
⣿⠀⠀⠀⠀⠁⡀⠀⠀⣀⠀⣀⠀⡀⠀⠀⠀⠀⢰⠋⠉⢉⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠠⠀⢀
⣿⠀⠀⠀⠀⠀⠈⠉⠘⠁⠒⠀⠂⠁⠄⠀⠀⠀⠸⡄⢀⢀⠀⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡞⢿⣛⢸⡏⢙⣦⢼⢸⣉⡇⣿⢹⠀⠀⠀⢀⡀
⣿⠀⠀⠀⠀⠀⠸⠀⠀⠛⣶⠛⡆⠈⠀⠀⠀⠀⠀⠀⠈⠿⠄⠀⠀⠀⠀⠀⠀⢀⡀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠁⠀⠷⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠠⠧⠍⠛⠁⠀⠀⠀⠀⠀⠀⠸⢀⡀⢀⠀⠀⠀⠀⠀⢘⣦⠀⠀⠀⠽⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⠀⢠⠀⠇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⢀⠀⣀⠀⠀⠀⠀⠘⡇⠰⠄⠰⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣠⡄
⣿⠀⠀⠀⠀⠀⠐⠀⣴⡆⠺⣇⡀⠀⠀⠀⠐⣛⡛⠂⠉⢻⠁⡀⠂⠀⠀⠀⠀⠀⠲⠂⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢁⠈
⣿⠀⠀⠀⠀⠀⠐⠒⠚⠚⠉⠁⠀⠀⠀⠀⠐⠊⠟⠉⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⣤⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠔⠀⠈
⣿⠀⠀⠀⠀⠀⣠⠤⢤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⢰⣟⣀⢊⣿⡇⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠰⡂⠀⡁
⣿⠀⠀⠀⠀⣼⠅⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢉⣆⡰⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠛⠣⣜⠁⠀⠶⠀⣡⡀⡀
⣿⠀⠀⠀⠀⣯⡀⠀⠀⠂⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠠⠒⢶⠁⠁⠈⠩⠁⢧⣹⢤⠴⣃⣀⣀⣀
⣿⠀⠀⠀⠀⠈⠸⠛⠹⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠁
⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠊⠐
⣿⠀⠀⠀⠀⠘⠠⠀⡀⢉⣙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠆⠁⠲⢀⣼⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠖⠢
⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⡘⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠀⠀⠀⢐⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠁⠀⠀⠀⠀⠺
⣿⠀⠀⠀⠁⠀⠀⠴⣀⠀⠁⠀⡀⠀⢠⣂⣄⣰⣦⠀⠀⠀⠀⢬⣀⠘⠀⠀⠁⠈⠀⠀⠀⢀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⣽⣧⠀⠀⣀⣠⠌
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠈⠀⠈⢠⠑⠀⠘⣦⡄⠂⢠⠃⢄⣀⡀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠨⠉⠀⠀⠁⠠⠜⠁
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠂⠐⠀⠸⠆⠤⠤⠤⠤⠎⠀⠈⠉⠀⠀⠀⠀⠸⠁⠀⢋⣃⠀⠝⠋⠁⠀⠀⠐⠀⣄⡴⠂⢀⣠⠐⠂⠀⠤⠄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠹⢴⡄⠀⠀⠀⠀⠀⠀⡿⡀⠀⠈⡵
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠥⠀⠁⢁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⡀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠐⠂⠀⠀⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠈⣠⡁⢈⡌⠀⢀⡠⠒⠄⠁⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠊⠁
⣿⠀⠀⠀⠀⠀⠀⠀⡀⢘⠆⠀⠀⠀⠶⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⢴⠀⠀⠐⠀⠀⠘
⣿⠀⠀⠀⠀⠀⠀⠸⠁⠈⢨⠀⡅⡀⢀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠉⠀⠀⠀⣄⣀⡀⠀⠀⠀⢀⡄
⣿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠨⠄⠥⠁⠧⠤⠤⠖⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠊⠉⠻⠄⠀⠀⠀⠈⠚⠉⠁
⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⢀⣀
⠀⠀⠀⣸⣯⠀⠀⠀⠀⢠⣤⠀⣻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆
⠀⠀⠔⣿⣿⡳⠀⠀⠀⠈⠙⢺⣿⡿⠆⠀⠀⠀⠀⠀⠀⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣄⠀⠀⠀⠀⠀⠐⣷⣾⣿⡄
⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠈⣿⡏⣤⣤⠀⠀⠀⣀⣀⢼⣿⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠙⢆⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠘⠉⢰⡶⠀⠀⠀⠀⠀⠋⠃⠿⠿⠀⠀⠀⢿⡿⠸⠇⠀⠀⣨⣶⠆⠀⠀⣶⣾⡖⠁⢿⠏⠀⠀⢡⣀⠀⠀⠀⠉⡿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⣴⡦⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⣿⡷⡀⢀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀⣾⣯
⠀⢀⣠⣿⡔⠉⠈⠁⠀⠀⢀⣿⡉⠓⡄⠀⠀⠀⠀⠀⠀⣸⣟⠙⠦⠀⠴⠷⠆⠀⠀⠀⣾⡏⠙⣶⠀⠀⠀⠀⠀⣿⡋⢳
⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠸⣿⠇⠀⡟⠚⠒⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⡘⠿⢿⠀⠀⠀⢸⣿⡇⠀⣵⣤⣶⠄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠋⠉⠙⠂⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠇⠀⠸⠀⠀⠀⠀⠛⠀⠀⠸⠟⠉⠫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⢚⣟⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⣗⠀⠀⠀⠀⠀⠀⠀⡄⠰⡶⠀⠀⠀⠀⠀⠀⠀⣺⣗⠀⢀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣾⠆
⠀⠀⠀⣾⡟⢴⣦⣰⣦⠀⠀⠀⠀⢰⢹⣿⢱⣄⠀⠀⠀⠀⠰⡷⣾⣿⣄⠀⠀⠀⠀⢀⣾⣿⣿⡗⣭⡀⠀⠀⠀⠀⠾⠿⢿⣼⣿⡇
⠀⠀⢠⣿⣷⠀⣿⣿⡇⠀⠀⠀⠘⠙⠻⡉⣹⠛⠋⠀⠀⠀⠀⠀⣿⣿⢈⡀⠀⠀⠀⠀⢼⣿⣿⡇⢻⡇⠀⠀⠋⠉⠉⠙⠀⢸⣿⡇
⠀⠀⠈⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠣⡀⠀⠀⠀⠀⠀⠀⣿⡟⠘⠋⠀⠀⠀⠀⠀⢻⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉




⣿⣿⣿⣻⣛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣿⣛⣛⣿⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⢶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣴⣿⣿⣿⣿⡏⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠿⠿⠋⠐⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠉
⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⢿⣦⡀⣷⣄
⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⣿⣿⣿⡿⣿⢧⡀
⠀⠀⠀⠀⠀⠿⣷⣿⣿⣿⣿⣿⣷⠙⢿⡷⠁⡀
⠀⠀⠀⠀⠀⢻⣿⣾⣯⣽⢿⣯⣿⣦⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣿⣷⣿⡽⣟⢻⣷⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⢹⣿⡷⠊⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠤⣦
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠈⠑⠂⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠛⢓⢂⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⢙⡛⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⡾⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠰⣷⢿⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⣾⢿⣾⡿⠁⠻⡄⠀⠀⠀⠀⠀⠀⠴⠞⠛⠋⠀⡗⠒⠖⠞⠿⠿⠻⠖
⠀⠀⠀⠀⢀⣻⣿⣻⣿⠀⠀⠀⠀⠀⣤⠂
⠀⠀⠀⠀⣼⣯⣿⠿⣷⡄⠀⠘⠀⠤⠚⠃
⠀⠀⠀⠀⢿⣻⡿⣷⣿⢃
⠀⠀⠀⠀⠈⠻⠷⠿⠿⠿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠈⠔⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢳⠤⠤⡼⠁⠀⠀⠀⠀⠐⠒⠁⠀⠢⠠⣀⠑⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⡤⡘⢄⠀⢠⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⡇⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⡤⣴⠖⢀⠴⠋⠀⠙⢆⠑⢬⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠠⠰⠉⣑⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢋⡠⠞⠁⠀⠀⠀⠀⠀⠙⠦⣑⠢⣴⠀⠀⠀⠀⡆⠐⣆⠱⠂⠀⣘⠤⠀⠀⢓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣉⠂⢄⡀⠈⠑⠄⠀⠀⠄⢄⡨⢀⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣊⣥⠴⠋⠁⠀⡀⣀⢀⣀⢀⠀⠀⠀⠀⣀⣀⡀⢀⣀⡀⡉⠒⠮⣅⡒⣬⠑⣴⣀⢈⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⣏⣉⠊⠄⠸⠀⠀⠀⠀⡽⢠⢠⠀⠀⡀⠃⠀⠀⠈⠀⠉⠀⠈⠞⠾⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣤⣸⣤⣆⠄⠀⠀⠀⢰⣥⣸⣠⣄⣶⠀⠀⠀⠠⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⢄⠀⣠⠀⢀⠄⠀⠀⠀⠀⠐⣤⠍⡤⡤⢤⡜⡀⠀⠘⠆⠀⡀⠘⢼⠀⠀⠀⠀⠔⡀⢀⠒⡄⣧⠒⡀⠀⢂
⠀⠀⠀⠀⠀⠈⣀⠀⢁⡀⠈⣄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⢸⠔⢀⡧⠙⣼⠀⠀⠀⣿⠀⠽⢸⠀⣿⡍⠀⡷⠇
⠀⠀⠀⠀⠀⠀⠋⠀⢈⠁⠀⠋⠀⠀⠀⡄⢸⠀⠀⠈⠁⠀⡇⠀⠸⠶⠬⠴⠶⠿⠀⠀⠀⡀⠀⠀⠀⠀⡇⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡿⡄⢸⠇⢀⢻⣠⣀⣀⡇⡗⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠯⠍⠀⣯⡅⠀⡿⡅⢈
⠀⠀⠀⠀⠰⠌⠗⠷⠰⠺⠶⠛⠗⠖⠴⠶⠳⠆⠖⠶⠤⠿⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠝⠦⠬⠦⠶⠦⠧⠶⠤⠖⠶⠶⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠠⠤⠤⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣠⡀⢭⡀⢘⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⠛⠓⠛⠃⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢴⠖⢂⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠲⡒⠁⡠⠉⠑⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶⢴⢤⣴⠀⡘⢸⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⣀⣣⣁⣐⣋⠧⢇⡀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠀⠀⠠⠤⠭⣽⠢⣀⠀⠀⣡⠀⡀⣀⣀⣀⠀⢀⠆⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠠⠀⠀⠀⠀⢰⠙⣇⠀⠁⠂⢹⠛⠓⠐⠛⠙⠂⡾⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢠⠃⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⡜⠀⠀⠀⠀⠀⡠⠓⢤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢠⠂⠀⠀⠀⠀⠀⡆⠀⠈⣧⠀⡰⠁⠀⠀⠀⡀⢸⠄⠀⡸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠎⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢷⡁⠀⠀⠀⣰⣷⡶⠂⠁⠘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠎⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠃⠉⠛⠛⡏⠁⢼⡇⠀⠀⢠⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢺⣇⠀⡠⣮⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣯⡤⠤⠄⡀⠀⠀⢀⡠⠊⠀⠀⠀⠀⢰⠀⠀⠀⡜⠀⠀⠈⢬⡿⣾⠕⣿⡀
⠀⠀⠐⠀⠀⠀⠀⢀⠃⠤⠤⠀⠴⠁⠀⠀⠰⣂⣿⣿⠁⠁⠀⠀⠀⠀⡇⠀⠀⢠⠉⠀⠀⠀⠈⠀⠀⠀⠏⢿⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⡠⠒⠉⠁⠀⠀⠀⠀⠁⠁⠂⠀⠻⢟⠁⠀⠀⠀⠀⠀⢀⠧⠀⠀⡌⠀⠀⠀⠀⢰⠀⠀⢈⠀⠈⢳⡀
⠀⢘⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⢀⣾⠆⠀⠀⠀⢠⠒⠁⠀⢀⣀⠇⠀⠀⠀⢀⠌⠉⠉⢹⠀⠀⠀⠙⠶⣤⣠
⠀⠎⠀⠀⠈⠉⠁⠀⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠈⠂⠀⠐⠊⠀⠀⠀⠀⠀⠀⠉
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠑⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠁⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠎⠛⠛⠉⠁⠀⠀⣿⢵⣿⣿⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠄⠀⢰⣿⠀⢷⣿⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⣿⣷⠞⠗⠀⢸⣿⢟⣾⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣿⡿⠉⠈⠁⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢶⠦⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⠀⡄⠃⢠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠁⠀⠈⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠄⠀⠀⠀⢀⣠⣘⣛⡳⣴⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⣤⣄⠀⠀⠀⠀⣨⣿⠛⣡⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣶⣾⣿⣿⣿⣿⠿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠈⢹⠏⠉⠁⠀⢾⣷⢿⡄⠀⠀⠀⠀⠀⢀⢴⣶⣆⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠤⠄⣀⣿⡧⠀⠛⢹⣿⣿⡮⣿⣷⢶⣿⣿⣿⢻⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣀⠀⠀⠀⠀⠋⡏⠀⣁⠘⠿⢿⣅⣿⣟⣸⣿⣿⣿⣜⡿⠿⠿⠚⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠉⠀⠐⠲⡏⠉⠀⠀⠀⠀⠉⢻⠛⠛⢿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣾⣿⠙⠿⠿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⠛⢿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠿⠿⡿⢿⣿⣿⣧
⠀⠀⠀⠀⢿⣿⠰⠂⠀⠆⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠘⠀⠘⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠰⠀⠘⢨⣿⣿⠏
⠀⠀⠀⠀⢀⠉⠃⡀⢀⡘⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣐⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⢠⡜⣩⣄
⠀⠀⠀⣐⣽⣷⡎⠓⠚⢛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁⢳
⠀⠀⠀⠝⠛⠛⡃⠀⠀⠈⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠀⠀⠈
⠀⠀⣰⠎⠉⠈⠁⠀⠀⠈⠉⠈⠷⡆⠒⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⠀⠀⢻⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠣⠀⠀⠀⠀⡙⠆
⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠋⠀⠀⠀⠀⠀⠸⠦⢶⣄⠤⡄⡇⠀⢰⠀⢼⣿⣿⡆⠀⠀⠀⠀⠀⡀⢀⡀⠰⠶⠒⠤⠀⠀⢀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣓⠖⢀⣟⣛⡷⠃⠀⠈⠀⣠⡉⠁⠀⠀⠀⠀⡰⣟⣿⣍⣛⣟⣶⠠⢤⣀⡀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢋⡿⠭⣅⠀⠐⠂⠀⢠⠇⠀⠀⠀⠀⠀⠘⠢⠼⠶⣇⠘⢼⡷⣆⡽⣿⣟⠟⢷⣤⣅
⠀⠀⣠⣶⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠁⠀⠂⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠉⠒⠙⠺⡍⠓⠚⣞⡳⢼⠁
⠀⢰⣿⣿⣿⠛⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⡀⠀⠀⠈⠉⠒⠓⠊⠁
⠀⢸⣿⣿⣿⠰⠀⢠⢩⣷⠀⠀⠙⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠛⠿⣿⣿⣿⣿⡇
⠀⠀⠙⠿⠿⡃⡀⠀⠘⠃⠀⠔⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠃⠀⠓⣼⣿⣿⠇
⠀⠀⠀⠀⢻⠒⠛⢦⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠊⠀⠀⠀⠀⠀⣤⠘⣟⠛⢉⣀⢤⣤⠤⠤⣤
⠀⠀⠀⠀⡧⡣⣀⠉⠘⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠮⠂⢀⠀⢀⣀⠀⠀⡼⠉⡹⢃⠀⠈⣄⣀⠱⡶⠶⢺⡄
⠀⠀⠀⠸⠀⠈⣠⣄⣖⣲⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡤⠀⠢⠈⢋⢋⡿⣕⠢⠐⣯⢐⠠⠍⠉⠩⠝⡖⢸⡇
⠀⠀⠠⠂⠃⠀⠈⠈⠃⠥⠂⠀⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠁⡈⠈⠋⠀⠀⠟⠨⢼⡒⠂⠂⠥⣇⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠄⠀⠀⠀⠐⠺⠭⡀⠨⠗⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⢹⠀⣿⢰⡇⢠⡇⢰⠏⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠈⠈⠀⠀⠈⠃⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣄⠀⠀⠉⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣘⡀⠀⠀⠀⠠⣶⣶⡆⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⠀⠀⠈⠉⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⣼⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢠⡿
⠀⠀⠀⢀⣴⣿⣟⣿⣿⣦⡀⢀⡇⠀⠀⢻⠀⢀⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⣿⣿⣿⣿⣯⡿⣿⣿⡾⣅⣀⣀⣼⣷⣿⣿⣿⣿⣟⣽⡄⠀⠀⠐⠠⠄⠀⠀⠀⣀⡀⠔⢫⡍⡉⢻⠒⠚⣉⣍⢉⠐⠀⡀⣀
⠀⠀⣿⣾⣿⣿⣿⣷⣿⣿⣻⢿⡀⠀⠁⠀⠈⢿⡿⣟⣿⣾⣿⠃⠀⠀⠀⠀⠀⠠⠀⠈⠉⠐⡶⠤⠄⢁⣉⡭⠿⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣰⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠻⠿⣷⣽⣻⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣦⡀⠀⠀⠀⣀⣤⠐⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡏⠀⢀⠀⠉⠻⣿⣿⣿⣿⣾⣿⠉⠉⠑⣦⣤⠾⠋⡡⠞⠋⠁⢀⣠⠔⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⡏⠀⠀⠀⠀⠉⠛⠛⠛⠳⠶⠖⠛⠉⠁⣠⠾⠦⠶⠶⠚⠋⣡⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣳⣦⣄⣀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡋⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⣿⣿⣻⣿⡛⠛⠛⠛⠉⠁⠀⠉⠙⠛⠓⠚⠋⠁
⠀⠀⠀⠀⠀⠀⢠⣄⣀⡿⠀⠀⠹⣻⣿⣿⢻⣿⡏
⠀⠀⠀⠀⠀⠀⢘⠀⠉⠛⠀⢲⡀⢹⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠳⣷⡾⢿⣿⢸⣿⡆
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠛⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⠛⠓⠶⣤⡀⠀⠀⠀⢀⣀⣠⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣴⣾⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⣀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⣸⢃⣠⠖⠶⠶⠶⠖⠛⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠈⠙⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠈⠙⢻⣿⠉⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⠤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⣴⠚⠛⠛⠛⠛⠛⠚⠛⠛⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠀⠀⠀⠀⠀⢠⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠀⠀⠀⠀⠀⢠⡄⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⡀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⣸⠇⠀⠀⣿⠀⠀⢸⡇⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⠃⠀⠀⣿⠀⠀⢸⣇⣀⡟
⠀⠄⠀⠀⠀⠀⠈⠉⢹⠀⠀⠀⣿⠀⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠀⠀⠀⣿⠀⠀⢸⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣿⣤⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⠿⠤⠴⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡆⠀⢸⣿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⣿⣄⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⣹⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣶⣤⡄⠀⠀⣿⡿⠋
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢥⠀⠍⢻⣧⠀⠀⣤⣄
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠙⠋
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⠂
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣛⣛⣋⣀⡀⠀⠀⠀⠀⢀⣈⣛⣟⣛⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣦⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⢀⣶⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣷⣶⣼⣿⢹⣿⣿⣿⣿⣿⡇⣿⣷⣾⣿⢹⣿⣿⣿⣿⣿⡇⣿⣷⣶⣾⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⢸⣿⣿⣿⣿⣿⡇⠹⠿⠿⠟⢸⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣿⣿⣿⣿⢿⡇⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣾⢻⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠃⣿⣿⣿⣿⠘⠿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠟⢸⣿⣿⣿⡇⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠸⢿⣿⣿⡿⣿⣿⡿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡟⣿⣿⡇⠀⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢸⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⡇⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠹⠿⠀⠀⠘⠿⠿⠁⠿⠿⠃⠀⠀⠀⠀⠘⠿⠿⠁⠿⠿⠃⠀⠸⠿⠛⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⠀⢻⣦⣸⣆⣠⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣀⢘⡿⣿⣿⠟⠛⠻⣦⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⣥⣾⣿⣿⣿⣶⣤⣿⣿⣎⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠋⠻⣿⠏⠉⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⢏⡀⠀⠀⠀⠀⣼⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠐⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢼⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠴⢤⣄⣨⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠁⠀⠀⠀⠀⠉⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠘⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣠⠀⠀⠀⠀⠀⠀⢰⣿⣤⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡶⠂⢀⣤⠤⠀⢾⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠚⠁⠀⠀⣀⢸⣿⣿⣿⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢂⣤⡶⠛⠙⣿⣿⣿⠋⠉⠉⠉⠁⠀⠀⠉⠛⠛⠦⠀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣻⡿⠛⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⣿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⡿⠟⢁⣾⣇⢼⣟⣿⣿⣿⣿⣷⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠟⠁⠂⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⠦⢤⣤⣤⣤⣤⠆⢄⡀⢀⢀⣠⣄⣀⣀⣐⣿⣿⣄⠀⠈⠣⢣⠾⠿⡿⣯⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠘⣿⣿⣿⣿⣿⡅⠀⠲⣶⣶⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⢿⡧⠤⣾⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⠀⢻⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠈⠀⠀⠈⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢂⣴⣦⣶⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠉⠁⠈⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡁⠈⣀⠀⠴⠉⠰⣰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠈⠁⢀⣀⣤⠀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢿⡿⣿⣿⣷⠦⣤⡉⣁⣼⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣿⣿⠶⢿⣿⣄⡀⣨⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠏⠀⣸⣿⣿⡛⢉⣀⣾⣿⣽⠋⠀⠀⠀⠀⢀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣀⠠⣿⣿⣿⣵⣿⣿⣿⣇⡿⠁⠀⠀⠀⠀⡎⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢨⡟⡷⣮⠙⢿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠁⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣸⢇⢿⡀⠈⠛⢁⣿⣿⣿⣿⠿⢦⣤⣀⣀⠀⠀⡸⠀⢻
⠀⠀⠀⠀⠀⠀⡴⡂⢾⠱⣄⣿⢸⡞⣷⡈⠉⢹⣿⣿⣯⣅⣀⣀⣀⣀⣀⣉⣉⣀⢠⠞
⠀⠀⠀⠀⠀⠀⠣⡙⠚⠛⠺⢿⣿⣧⠈⠁⠀⣼⠟⠁⠀⠀⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡔⢨⡇⠺⣌⢻⡿⣦⣤⠿
⠀⠀⢀⣠⠴⢂⡿⠋⣰⣿⢰⡇⠈⠁⢠⠀⠀⠀⡛⣦
⠀⠀⠣⣀⡴⠋⠀⣰⣿⡏⠀⣷⣀⠀⠈⠀⠀⠀⠃⠈⢷⡄
⢤⡄⠀⠉⠀⠀⢠⣿⣿⠃⠀⠘⠏⢷⡄⢇⠀⠀⢸⠀⠈⠻⣄⠐⢤⡀
⠀⠙⢷⣄⢀⡠⣾⣿⣿⠀⠀⠀⠀⠀⠉⠘⡄⠀⠈⡀⠀⠀⠹⣧⡀⠉⠳⣄⡀
⠀⠀⠀⠱⢛⣽⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢁⠀⠀⠀⠘⢷⣄⢀⣼⢻⣦⡄
⠀⠀⠀⣠⣿⣿⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⡀⠀⠀⠀⠈⠻⣿⣵⠟⡀⠛⠆
⠀⠀⣰⡿⣿⢃⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠁⡄⠀⠀⠀⠀⡽⢿⣆
⠀⣰⡿⣱⠏⣼⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠘⢶⣶⣾⣧⡄⠛⡙⠁
⠀⠟⢱⡟⢸⣿⣿⣝⡻⢶⣦⠴⠶⠶⠦⣤⣤⣤⣄⣠⡧⠀⢠⣟⣛⣉⣥⡄⠑⣄
⠀⢠⡿⢀⣿⣿⣥⣉⠛⠻⠶⠒⠒⠲⠶⠶⠶⠦⣭⡤⠶⢑⣬⡛⢿⣿⣿⣷⠀⣸
⠀⠈⠁⠈⠉⣿⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⡟⢦⠻⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⠿⡿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠙⢧⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡃⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢸⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⠋⢴⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡎⠀⠀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠰⠀⠀⠀⠘⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⡆⠀⠀⠀⠀⢡⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔
⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠈⠀⠀⠀⠀⠀⠈⣀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡢⡀
⠀⠀⠀⠀⠀⠀⢰⠲⡄⠀⡆⠀⠀⠀⠀⠀⠀⠈⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⢄
⠀⠀⠀⠀⠀⠀⠈⣷⢾⣦⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡡⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠈⠻⣿⣿⠆⠀⠀⠀⠀⡻⢄⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡜⠀⠀⢀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣷⣄⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⢀⣠⡶⠉⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⢻⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡒⠀⠀⢀⣠⠾⠛⢉⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣈⣉⣙⡛⢋⣡⣤⡾⠛⠁

⠀⠀⠀⠀⠠⠐⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠒⠒⠒⠒⠒⠂⠀⠀⠒⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⢀
⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠑⠂⠰⠀⠐⠒⠉⢀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⣀⣀⣄⣀⣠⣀⠀⠐⠂⠂⠂⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠉⠀⠢⡀⠀⠀⢈⠔⠒⠃⠈
⠀⠀⠀⠀⢀⠁⠀⡰⠀⠀⠀⣠⡆⣀⣒⢀⠄⠠⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢀⠀⠀⠀⡀⠠⡐⠀⠀⠀⠈⠄⠀⠀⠤⠀⠂
⠀⠀⠀⠀⠀⠈⠀⠂⠀⢈⢠⠟⠀⠀⠉⠉⠓⠺⡄⡇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⡀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠔⠅⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⠼⠀⢀⡀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠐⠀⡼⠴⠀⠠⢬⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡑⠀⠉⠀⠀⠈⠉⠁⡤⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠴⠦⠆⠀⠔⠋⠁⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⠠⠄⠀⡆⠠⢸⡀⠀⠄⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠐⢄⡀⠀⠀⡈⠀⡠⠂⢀⡀⠀⠀⠀⠀⠀⠙⢄⡁⠂⠀⣀⡄⢁⠀⡀⠳⣄⠈⠀⠁⡠⡞⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠢⢄⣀⢥⠚⡇⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠀⠀⠀⠆⠙⠒⠊⣩⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣁⠀⠁⠂⣤⠐⠈⢀⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣤⠒⠓⢤⡀⠀⡠⠓⣥⠤⣇⠸
⠀⠀⠀⠀⠀⡄⠒⠉⠀⠀⠀⠙⠒⠚⠑⠙⠒⠉⠀⠀⠀⠉⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠁⠂⠤⠤⠅⠀⠈⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⢸⠀⠀⠀⠀⡇⠀⠒⠀⢰⠀⠀⡖⡆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⠀⡀⡠⠂⠔⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠁⠁⠊⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢶⣤⡶⣴⡦⣖⠀⡔⢢⣠⢰⣄⣶⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠘⠓⠛⠙⠓⠀⠓⠚⠘⠛⠛⠛⠘

⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⢀⡤⣤⣤⣤⠀⠀⠀⠀⠀⢠⢠⠀⠀⠀⣤
⠀⠀⠀⠀⡇⠨⡀⢈⡉⠀⠀⠀⠀⠀⠀⡴⠞⣿⣿⠀⠀⠀⠀⠀⢰⣿⠟⠻⣿⠀⠀⠀⠀⠀⠸⡿⠀⠀⠘⣿
⠀⠀⠀⠀⡏⠀⡇⠀⡇⠀⠀⠀⠀⠀⢦⢠⠆⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠃⠀⠃⠀⠃⠀⠀⠀⠀⠀⠘⠜⠀⠛⠃⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉

⠀⠀⠀⠀⡴⠞⠈⠳⢤⠀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣦⠀⠀⠀⠀⠀⠀⡠⠶⠶⠦⡀
⠀⠀⠀⠀⣯⠁⠉⠁⡁⠀⠀⠀⠀⠀⣧⣿⣿⣿⣼⠇⠀⠀⠀⠀⣰⣿⡆⢙⢋⣄⠀⠀⠀⠀⢰⣻⣶⣶⣾⣳
⠀⠀⠀⠀⢆⣀⣂⣀⡆⠀⠀⠀⠀⠀⠟⠛⠛⠛⠻⠄⠀⠀⠀⠀⠹⠿⠐⢿⠿⠿⠀⠀⠀⠀⠈⠟⠉⠉⠙⠏

⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⢰⡏⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣾⣿⣿⡆
⠀⠀⠀⠸⣆⣀⣠⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠈⢲⣿⣿⣿⣇⠀⠀⠀⠀⠀⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠉⠁⠘⠿⠂⠀⠀⠀⠀⠀⠾⠿⠿⠂⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠈⡊

⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠐⣱
⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⣤⠀⠛⠚⠀⢠
⠀⠀⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⢿⣿⠋
⠀⠀⠀⠀⠀⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠃⠀⠀⠀⠀⠈⢿⣿⣿⣿⡟

⠀⠀⠀⠀⠀⠀⠀⡠⡊⢕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠑⢄⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠔⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠔⠑⢄
⠀⠀⠀⠀⠀⣠⡪⠈⠀⠀⠁⢀⢀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡘⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⡐⠁⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⢠⢠⠀⢸⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠼⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠄⠠



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣽⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣴⣦⠀⠀⠀⠀⠀⠀⠀⠰⣖⣴⣿⣦⡀
⠀⠀⠀⠀⠀⢠⢾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠰⢻⣿⣿⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⡏⢹⡏⠉⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠃⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠿⠿⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠿⠿

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠿⢍⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⣤⡀⡻⢙⣓⢆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠻⣴⠛⡀⢀⢚⡇⠀⠀⠀⠀⢀⣶⣄⠀⠀⠀⠄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠂⠀⢳⠀⠈⣧⠘⠓⡗⢻⠀⠀⠀⢀⣶⢿⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠑⡀⡏⣧⠀⠈⠂⠀⡇⣧⠀⠀⠀⣲⣒⣚⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣤⣤⣦⡀⣤⣄⣐⣠⣤⣤⣧⣠⡤⠀⠐⠀⡐⠀⢰⣖⣿⢿⣿⣆⠀⠀⢠⢷⣿⠀⢀⣸⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⢛⣛⣛⣧⣬⣿⣿⣿⣷⡿⡿⡿⠃⠉⠁⠀⠁⢀⣿⡟⠃⠚⠛⠛⠲⠤⠊⠉⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠿⢋⠉⢫⠟⡯⠞⠼⢸⠚⠃⠃⠀⠀⠀⠀⠰⢧⠛⠻⠓⠀⠀⣴⣤⣦⣴⣶⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠂⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟
⠀⠀⠀⡿⠀⠄⢀⡀⣠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠉⠩⣡⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠝⢻⡇
⠀⠀⠀⡇⠀⠀⠀⢀⠇⠀⠠⢢⠆⠀⢠⠢⣤⠀⣄⠞⠀⠀⠀⠀⠀⣃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⢸⠃
⠀⠀⠀⣿⣤⣤⣄⡞⠀⡠⠁⡼⠀⢠⠃⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡀⠀⠈⠉⠁⠂⢀⡀⠀⠒⠒⠨⠭⢀⣐⣢⡤⠴⣿
⠀⠀⠀⠘⣫⡇⡈⠀⣰⣧⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠀⠀⠀⠀⢒⣒⡠⠀⠀⣀⣀⣠⡤⢴⣶⣿
⠀⠀⠀⠀⢿⡿⠀⠰⠁⠈⠁⠀⡼⠓⠻⢷⠆⢴⣤⣄⡀⢀⣀⣀⣀⣤⣄⣀⣠⣄⠀⢀⣀⣀⣀⡀⣀⣭⣽⡗⠲⠾⠟⠋⠉⠀⠀⢹⣧
⠀⠀⠀⠀⡾⠁⣠⣾⠆⡸⠀⢰⡁⠀⠀⠀⠀⠀⠀⠉⠛⢻⣿⡿⠛⠛⠉⠁⠙⠛⠉⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⢀⣠⣄⣤⠟⠛⣅⠈⢀⡄⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠉⠉⠁⢀⣤⣿⣾⠿⠋⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠙⠓⠶⣄⡀⠀⠀⣀⣠⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⣠⣀⣀⣀⣠⠴⠚⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢀⡤⠖⠛⠛⠲⣼⡵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠟⠛⠻⢿⣷⡖⠋⠉⠙⠳⣄
⠀⠀⣾⠁⠀⠀⠀⠀⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⢸⡆
⠀⠀⢿⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠈⠳⢤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠞⠁
⡴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⡇⠀⢠⠀⠀⠀⠀⠀⠀⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡄⠀⠀⠀⠀⠀⢠⠄
⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸
⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⠀⠀⠀⢸
⡇⠀⢸⠀⠀⢠⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⢠⠀⠀⢸
⠳⣤⣾⠀⠀⢸⠀⠀⠀⣧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⡇⠀⠀⢸⠀⠀⢸⡦⠴
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠹⣄⠀⢸⡀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣼⣀⣀⡼⠁
⣶⣶⠶⠾⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣿⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⢹⠄⠀⠀⠀⠀⢀⠀⠉⠉⠉⢆⠀⠀⣠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⣶⠀⠀⢹⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⠠⠓⠂⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠇⠀⠀⠲⠽⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣠⠤⠆⣰⠆⠨⠀⠀⠀⠀⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠⠂⠾⠀⠀⠙⠄⠄⠀⡀⡤⠄⠐⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢐⠖⠀⣈⠀⠄⡀⢤⠀⠑⠦⡄⠀⢶⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠑⠀⠀⠀⠀⠁⠆⠀⠀⠡⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠃⠀⠀⠀⠉⠀⠀⠀⠀⢀⢀⡆⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠄⠐
⠀⠀⠀⠀⠀⣤⣄⣤⢼
⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠐⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠐⠀⠘⠀⠊

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

⠀⠀⠀⣀⣀⣀⣀
⠀⠀⢸⡟⠛⠛⢻⡇⠀⠀⠀⢸⠟⠛⠛⠛⠛⢻⡇⠀⠀⠀⣠⠴⣖⣷⠦⣀⠀⠀⠀⠀⠀⢤⠀⢀⣀⣀
⠀⠀⠸⡇⠀⠀⢸⡇⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⣯⢻⢫⠝⡟⢹⠀⠀⠀⠀⠀⢿⠀⢀⣿⣽⡗
⠀⠀⠀⣧⣤⣤⣼⡇⠀⠀⠀⠘⠛⢛⣿⣿⡛⠛⠃⠀⠀⠀⠈⠛⢼⡤⠗⠊⠀⠀⠀⠀⠀⠉⠀⠀⠈⠗
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⣠⣾⣫⣟⣷⣄⠀⠀⠀⠀⠤⢒⣉⣉⡒⠤⠀⠀⠀⠀⠀⢘⣧⡴⢒⣆⠀⠀⠀⢰⠒⠒⡒⠒⣶⣶⡆
⠀⠀⡧⡧⠴⡧⢾⢾⠂⠀⠀⠀⠀⠡⢒⣒⠌⠁⠀⠀⠀⠀⢰⣫⣤⣿⣿⠏⠀⠀⠀⢸⠹⡇⡇⢦⣬⠍⡇
⠀⠀⠙⢿⣾⣷⣻⠟⠀⠀⠀⠀⠀⠀⢱⡦⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⣿⡀⠀⠀⠀⠸⠤⠤⠥⠥⠶⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢀⠀⠀⡆⠀⠀⠀⠀⠀⣤⠤⠤⠤⠤⣤⠀⠀⠀⠀⠠⢲⢶⣀⣶⡲⡄⠀⠀⢠⠒⠉⠀⠉⠉⠐⡄
⠀⠀⠀⣾⣿⣿⣷⡄⠀⠀⠀⢠⢀⠵⠤⠤⢎⠙⠀⠀⠀⢰⣟⠋⣾⣿⡦⢏⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡏⣿⣿⡿⠁⠀⠀⠀⠈⠛⠒⠒⠒⠒⠛⠀⠀⠀⠈⠹⡶⠾⠿⠷⡾⠀⠀⠀⠀⠉⠒⢦⠔⠀⠉
⠀⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠠⡀⢀⢄
⠀⡔⠀⣲⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⡇⢸⠄⢠⠀⠀⠀⠀⣦⣼⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠑⠠⠿⢁⠔⡠⠤⣄⠀⠀⠀⡄⠀⠉⠉⠀⢸⠀⠀⠀⠀⢿⣽⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠮⠥
⠀⠀⠀⠀⠃⠚⢇⡀⠿⠀⠀⠀⡇⠀⠀⠀⢠⠞⠀⠀⠀⠀⣼⣛⣿⣟⣟⡿⠀⠀⠀⠀⠀⢰⢲⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠘⠈⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⢀⡀⠀⠙⠻⣿⣿⣿⣿⣿⣿⡤⠤⠤⠤⠤⢤⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⢀⡤⠞⠉⠉⠳⣄⡀⠈⠙⢿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠈⠛⢿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠉⠳⣄⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠙⠢⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⢹⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠉⠲⣄⡀⠈⠙⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠟⠉⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣸⣄⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠈⠻⢿⣿⣿⣿
⣿⣿⠿⠋⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠉⠻⣿
⣿⣅⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠶⠶⠶⠾⠶⠶⠶⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣀⣴
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⡞⠒⠒⠒⡖⠒⠒⠒⡆⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣶⠒⠒⠒⣶⠒⠒⠒⣶⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⡇⠀⠀⢀⣇⠀⠀⠀⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⡏⠉⠉⠉⡏⠉⠉⠉⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠉⠉⠉⣿⠉⠉⠉⣿⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⣧⣀⣀⣠⣧⣠⣀⣤⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⣤⣤⣤⣿⣤⣤⣤⡿⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⢤⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠓⠚⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢈⡁⡐⢄
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠁⠘
⠠⠀⡶⠉⢫⠑⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡚⠛⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⢼⣉⠀⠀⢖
⡄⢻⡤⠔⠚⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⠴⠊
⠘⢦⣈⣓⣂⡤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠤⠤⠤⣜⣂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠠



⠀⠀⢠⠖⢦⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠄
⠀⠀⢸⣄⣬⡀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠒⡂⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⡆
⠀⠀⠸⣿⣇⠇⠀⠀⠀⠀⠀⠀⢧⣀⣈⣉⡁⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀⠳⡅⠀⠜⢀
⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠘⠛⣿⠟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡶⠄



⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠃⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡍⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⡘⢢⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠻⠄⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣠⢔⠂⢹
⠀⠀⠧⠤⠭⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣒⣒⣒⣲⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⣞⠡⠨⠤⢌⣳⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⣄⢀⣀⢀⣠⠤⣄⠀⠀⣠⡀⠀⢀⣄⠀⠀⢀⡤⡄⠀⣀⠀⡞⠉⠑⠲⢄⡀⠀⠀⠤⠠⡖⣂⡉⣤⠅⣀⠀⠀⣀⠀⠀⡠⠒⠒⠒⢄
⠀⠀⠀⣏⠀⠒⠘⠀⠘⡆⠀⠘⠀⢀⠏⡌⠀⢀⠏⠀⡇⠘⠛⠁⠈⣎⠙⢢⡀⠙⡆⠀⠀⠀⠁⡈⠀⠘⢄⠈⠀⠘⠋⡠⠊⡀⠀⠀⠂⢸
⠀⠀⢰⠙⡄⠀⢞⢂⠀⠹⡀⣠⡄⡜⢰⢃⠀⢸⠀⢸⠁⠠⡦⢀⡴⢡⠋⠉⠓⢊⡀⣠⠀⠀⢀⠁⠀⠀⠄⠆⠀⢀⠔⠁⠀⠀⠀⠀⠀⡎
⠀⠀⡎⠀⢱⠀⠈⢂⠀⠀⢣⠀⢠⣇⠇⠼⠀⢸⠀⡾⠀⣤⠀⣜⢠⠇⢰⡶⣤⠏⠉⣉⣀⡀⠘⠀⠢⠤⠄⠀⠀⢰⠁⠁⠀⠀⠀⠀⢰⣡⡆
⠀⠀⠳⠤⠬⣆⡀⣈⣀⡀⠼⠀⢸⡜⠀⡀⠀⠈⡆⣇⣀⣉⠀⠈⠁⢸⢾⠇⢠⠔⢉⡠⠤⡃⠀⠢⠄⠀⠠⠂⠰⠆⠑⣀⠀⡀⢀⡴⠢⢞
⠀⠀⢰⠱⡀⠀⠀⠀⠠⣦⠆⠀⣿⠇⣰⣯⠄⡴⢋⡥⠶⠦⡍⢢⠀⠈⠀⢰⠁⣞⡁⠔⣊⠝⡂⠀⠀⠀⡄⠀⠂⢀⢊⠜⠀⢀⣁⣀⠀⠈⠁
⠀⠀⠀⢖⠳⡀⢠⠀⣀⣈⣀⡴⠛⡄⠣⠉⢸⠁⡏⠀⠀⠀⢘⡦⠃⠀⠀⠸⣑⡒⣉⣉⠤⠚⣅⡠⠂⠺⡝⠀⡰⢡⠊⡴⣉⠀⠀⠀⠈⢲
⠀⠀⠀⠈⢂⠱⡀⠀⡷⢐⡩⢻⢿⡷⣦⢤⠈⠧⣷⠤⠔⠚⠉⡠⠀⠄⠠⠤⠤⠤⡄⣀⣀⠬⠤⠤⠤⢄⠀⠰⠕⢁⠀⠈⠚⠓⠲⠶⠞⠫⠄
⠀⠘⢹⢙⡄⢢⠱⡀⠈⠯⠴⣇⣧⡱⠼⠃⣄⣠⡀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠒⢐⡇⠀⠤⢈⠀⠀⠃⠀⠂⢀⠀⠤
⠀⢰⢸⠀⡇⠀⠣⠑⡀⠀⠀⠲⠤⠆⠀⢰⠇⠁⠑⠂⠀⡎⢀⡠⢄⠤⣀⠤⣄⠤⡠⢹⠒⠒⠓⡋⠉⢉⡀⠀⠀⢊⣉⣉⣉⣉⣉⣉⡅
⠀⠀⡈⠉⠀⠀⠀⣱⡜⢤⠠⠤⢤⡀⠀⠘⠥⣄⡀⣇⢠⠶⠁⠀⠀⠀⠀⠀⠀⡀⠀⡟⡆⢀⡤⢆⠀⠻⠟⠘⠟⠈⠀⠀⠈⢇⠀⠸⢀
⠀⠀⢣⠀⢰⢎⠁⠀⠈⠘⠀⠀⠀⠙⡕⠄⠀⠀⠱⣌⠢⣉⢣⡀⠀⠀⢀⡀⠀⠀⣠⢋⠠⠚⡄⡼⠀⡠⠊⠉⠑⡄⠆⠀⠀⠀⠁⡟⢁⣤⠄
⠀⠀⠈⠀⠀⠠⢔⠀⠠⣀⡀⠤⠖⠉⠊⠀⠀⢦⠀⠈⠳⣼⠁⠉⠒⠲⢦⡤⠖⠊⠙⣇⠤⠊⡇⢀⢸⣀⣀⠔⡊⠃⠈⠐⠒⠒⠚⢀⣉⣀
⠀⠀⣤⡀⠀⣆⠀⠀⡠⠄⠐⢒⣒⣒⢲⡀⠀⠁⠀⡖⠄⠙⢦⠀⠀⠀⠀⠀⠀⠀⣠⠜⣀⡀⠣⠎⠀⠒⠀⠈⢀⡤⠤⠤⠤⢒⡉⠥⠤⠚
⠀⠀⡇⢳⠀⠻⢇⠀⢋⣉⣉⣁⡠⠤⠖⠁⠀⠉⠀⢃⠘⠀⢸⠀⠀⠀⠀⠀⠀⠀⢇⠀⡝⠓⠀⢟⢉⠀⠀⠀⢏⠀⠀⣀⣾⠁⠀⠀⡖⢆
⠀⠀⢹⡊⢧⠀⠀⣤⠀⠀⢀⠀⠀⢀⡀⡲⢒⠀⠀⡈⢆⠃⠰⣄⡀⠀⠀⠀⢀⡠⠜⠀⠁⢀⠤⠂⠀⠁⢴⠗⠈⠙⠛⠃⠁⠀⠰⠆⠉⠁
⠀⠀⡀⢣⠸⡆⠈⠶⠁⠠⠺⡸⢡⡶⠀⠐⢭⠀⠐⠶⡀⢨⣆⠀⠈⠉⢉⣉⣤⡴⡄⠀⠔⠀⠂⠂⢀⠀⢀⣤⣖⣋⣉⣉⠉⠉⠉⠓⠦⡀
⠀⢀⣑⡄⢧⢱⡀⠀⠀⠀⡰⠀⠀⠀⠆⠀⠂⠀⠀⡚⠁⡈⠀⠀⠐⣄⠀⠙⡨⠡⡀⠸⡀⠀⡀⢊⠌⢠⠫⡥⢠⡆⠀⠀⢈⣭⠒⢄⠀⢱
⠀⢠⣭⠶⠈⢃⢧⠀⠀⠀⢈⠒⢀⠀⠈⠂⡀⡰⠁⡘⠀⢳⡀⠀⠀⢘⠄⡘⢐⠚⠎⣂⠈⠐⠐⠁⠀⡟⠀⠀⠀⠀⠐⠒⠒⠒⠒⠚⡆⠈⡆
⠀⠀⠈⠓⢀⠜⠋⠉⠉⢲⡈⠐⠄⠦⡀⠄⢁⠁⡰⠁⠀⠀⠑⠀⢂⡡⠔⢁⠝⡀⢼⠔⠋⠉⢢⠀⢸⠇⠀⠀⢀⡠⠤⢄⣀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⢻⣀⣀⠤⠴⠊⠙⠦⡀⢠⡀⠀⠘⡰⠁⡴⡄⢀⠔⠋⡠⠐⠛⡵⠋⠀⢸⠀⠀⠀⠸⠀⢸⠀⠀⡔⢁⠔⠒⠢⡈⢣⠀⠀⢸⠀⡇
⠀⠀⠸⠀⠸⡄⠀⠀⡀⠀⢠⡴⠃⠀⡠⠒⠓⢃⠀⠘⠁⢨⢠⡏⠀⠀⠀⡇⠀⣠⢎⣀⡀⠀⢠⠀⠸⡄⠸⡇⢸⡀⠀⢉⡇⢈⠂⠀⢸⠀⡇
⠀⠀⡠⠤⠂⡕⠦⠔⠓⡊⢁⠀⠀⡬⣀⠀⠀⢨⠀⠀⢀⣨⡤⠦⣄⡀⠀⡍⠉⡔⠁⣠⡈⢳⢘⠀⠀⢇⠀⠱⣄⡉⠒⢉⡠⠎⠀⠀⡏⢠⠁
⠀⠀⠱⠀⣀⠗⠀⠀⠈⠢⠊⠀⠀⠈⠀⠈⠐⠚⠀⠀⠃⠴⠀⠀⠐⠃⠀⠘⠢⠷⣀⠉⣀⡼⠜⠀⠀⠀⠓⠤⢄⣉⣉⣁⣀⣀⣠⡾⠴⠃

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⠒⠀⠀⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠊⠀⠀⢀⣀⡀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⣀⠔⠊⠀⠀⢀⣤⣶⣿⣿⣿⣶⣄⡀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡔⠈⠀⠀⢀⣤⣾⣿⡿⠿⠿⠿⠿⠿⢿⣿⣶⣄⡀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⣤⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⡀⠀⠀⠑⠢⣀
⠀⠀⠀⠀⠀⢀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠄⣀⡔⠁
⠀⠀⠀⢀⠔⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠁⢲⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⣀⡀⠀⢀⡠⠔⠁⠀⠀⠀⠀⣼⣥⣥⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠁⢲⣶⣿⣿⣿⠉⠀⠀⠀⠀⠀⣀⠠⠚⠻⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⡟⠛⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣀⣀⡀⠠⣼⣿⣿⣿⣿⠀⢀⣤⣤⡞⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠂⢩⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣾⣿⣿⣿⣷⢸⣿⡇⠀⠀⠀⠀⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀⠀⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⣿⣏⣻⢸⣿⡇⠀⠀⠀⠀⡇⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⡇⣿⣿⣿⣿⣿⢸⣿⣷⣶⣶⣶⣶⣷⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢁⡊⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡠⠼⠿⠛⠉⠈⣥⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠁⠀⠀⠀⠀⠀⡀⠙⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⣇⣠⡄⠀⠀⠘⠉⠀⡻⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢽⣄⠁⠀⠀⢀⡀⠀⢻⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢦⠰⢴⣶⠃⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⡠⠊⣸⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⣠⣤⡄⠀⣠⣾⠟⢤⠮⣰⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠃⣠⣿⣏⡴⠞⡁⣸⣶⣻⠿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠻⠿⠏⢔⢲⣷⣿⣿⡿⣿⣿⣿⡓
⠀⠀⠀⠀⠀⠀⣠⣰⣶⣦⡐⢷⡖⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡿⢟⣩⡿⢻⡁⣾⠁
⠀⠀⠀⠀⠀⡸⠊⠥⠄⠭⡜⠿⣽⣶⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢟⠯⣶⣦⣹⣿⠁
⣀⣄⠀⣀⣦⣅⣩⣬⣥⢬⣖⡚⠻⠟⠛⠄⢹⣧⣀⣹⣿⣶⣶⣶⣤⣴⣆⠀⠀⠀⠀⠀⢠⡞⣯⣷⢶⣛⡻⢟⣿⡿
⠈⠙⠛⠿⠷⣿⣷⣾⣿⣶⣿⣴⣀⡚⠋⠊⠛⢟⣫⣼⣿⣿⣿⣿⣿⡿⣿⣷⣤⣤⣴⣿⣿⣿⣿⣵⣴⣯⢛⡿⢥⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠩⠯⠥⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣯⣟⡿⢞⣿⣷⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢳⣾⠟⠁⠐⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣯⣽⣿⣿⠟⠁⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠸⣷⣄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢷⡾⡅

⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠈⠂⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠙⠛⠿⠿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠠⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⢀⣴⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⡛⠁⠀⠀⠀⠀⠀⠛⣿⣟⠋
⠀⠀⠀⠀⠄⠁⠀⠀⠀⠐⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣷⡄⠀⠀⢀⣾⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣿⠆



⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⢤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣦⡀
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢣⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣧
⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣭⣾⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢀⠎⣀⣀⣀⠤⠤⠶⣚⡉⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⠿⠛⠛⠉⠽⣶⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠦⠤⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠆

⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠰⠩⠀⠠⠑⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣾⣷⡆⠀⠀⠀⠀⠀⢠⣤⠶⡶⢶⡶⣦⣄⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠐⠂⡒⠲
⠀⠀⠀⠀⡐⡄⣦⡄⠀⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⡇⠀⠀⠀⠀⠀⠈⢩⣿⠩⡯⣻⣎⠉⢱⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⠀⢸
⠀⠀⠀⠀⠡⠁⠈⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⢀⡇⠀⠀⠀⠀⠀⠀⠿⠿⠷⠾⠿⠿⠖⠃⠀⠀⠀⠀⠀⠀⡸⠅⠤⠤⠼⣀⠌
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⣶⣾⣿⢶⣤⢀⠀⠀⠀⠀⠀⠀⢰⠶⡐⠂⠒⢂⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡍⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆
⠀⠀⠀⢿⣿⣭⣿⣽⣿⠃⢱⠀⠀⠀⠀⠀⢸⠀⠈⠲⠞⠁⣠⣾⣎⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⡇⣀⣭⣯⣄
⠀⠀⠀⠀⠀⠿⠟⠫⣡⠒⠁⠀⠀⠀⠀⠀⠘⠏⠀⠠⢀⡸⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡸⠀⠀⠀⠀⠀⠀⠀⠘⠲⠶⠆⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃



⠀⠀⠀⠀⣿⣿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⡄⣠⣦⡀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠠⠐⠒⣦⡀⠀⠀⠀⠀⠀⠀⡖⠂⠒⣀⠂⠒⢲
⠀⠀⠀⠀⣿⣿⣀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⣘⣟⣁⠀⢃⣙⣟⣁⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⠀⠀⣽⡇⠀⠀⠀⠀⠀⢀⡥⡄⠠⠿⠄⠀⢸
⠀⠀⠀⠀⣍⣉⣉⣉⣉⣉⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠺⠿⠿⠿⠂⠀⠀⠀⠀⠀⠿⠷⠶⢤⡤⠤⢼⠅⠀⠀⠀⠀⠀⠸⣿⠟⡿⢿⠿⠟⠛



⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠰⡶⠀⠼⠧⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⡛⢍⠉⠉⣉⠝⡇
⠀⠀⠀⠈⠉⠀⣈⣀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⢠⣤⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⡘⡐⢛⡘⢰⠀⠀⠀⠀⠀⠀⠀⠃⡀⠑⠚⢡⢖⡲⡄
⠀⠀⠀⠀⠀⠀⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣭⣭⣼⠀⠀⠀⠀⠀⠀⠀⠀⣇⠐⠀⠂⡛⠛⣰⠀⠀⠀⠀⠀⠀⠀⠛⠀⠂⠂⢣⣛⡓⠃
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠙⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣾⡷⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠛⠻⢿⣿⣿
⠀⠀⠀⠀⢠⣤⡸⠟⠁⢰⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣟⠀⣚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⠀⣀⣘⣿⣿
⠀⠀⠀⣰⢋⡿⠃⠀⣰⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠻⠸⠋⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⣫⣥⡤⠀⡿
⠀⠀⣾⠛⢉⡶⠖⠀⠈⠉⠈⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠛⠀⠀⠠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⠀⠀⠉
⠀⠀⠣⠐⠈⣷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⡃⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠤⢀⠄⠀⠄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠧⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⠀⡀⢵⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠹⠶⠋⠀⣀⡗
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣤⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠐⠋⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢈⠁⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠒⠀⣄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢿⡇
⠀⠀⢀⠀⢄⡀⢰⣿⡷⢼⣁⣃⠤⠀⠋⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠄⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀
⠀⠀⠘⠀⠀⠀⠾⠼⠇⠈⠙⠿⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠉⠀⡀⠀⢻⣿⡇
⠀⠀⠈⠉⡙⣤⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠐⠴⣿⣷⠶⠃⠀⠀⢀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⢠⠀⠀⢀⡠⢴⡇
⠀⠀⢠⣟⡏⡉⠂⡄⠀⠀⣿⠀⠀⠀⠀⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠀⠈⠀⣄⡀⠐⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠈⠉⠐⠆⠀⠀⠓⠊⢀⡀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣁⣀
⠀⠀⠀⠀⠀⢀⠀⢤⣰⠋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣻⣿⣷
⠀⠀⠀⠀⠀⣾⠀⣾⠟⠒⠢⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠉⠙⠛⠻⣿⣿⣿
⠀⠀⠀⢀⡶⠿⡶⠁⢀⡀⠀⠀⣾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡎⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⣠⡀⠠⢻⣿⣿
⠀⠀⠀⣾⣿⣆⠸⠇⠠⢠⣴⣠⠿⠟⠛⢫⡉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⠶⠆⢶⠾⣛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠛⠀⠘⣿⠏
⠀⣠⡄⠉⠉⠀⢀⢀⣰⣶⡿⣧⡗⠈⠃⠀⠇⠀⠀⠀⠀⠀⠐⢀⣀⠙⠛⡃⠀⣀⣄⠛⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡧⠀⠁⠀⠠⠋
⠀⢸⣧⠀⡶⠿⠞⠛⣵⣾⠣⣿⣿⠆⠀⠀⣾⠀⠀⠀⠀⠀⠀⠘⠉⠂⠀⠉⢻⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡁⢳⣶⣾⣛⣛⣛⣿⣿⡆⢰⠄
⠀⣸⡿⠀⡀⠀⣀⣾⣿⣇⠛⡫⣿⣖⠂⠀⠀⠀⠀⠀⠀⠀⢰⣦⡄⣨⣀⣠⣴⡇⠐⡠⠀⠀⠀⠀⠀⠀⠀⣐⣹⡾⣿⣿⣿⣿⣿⣯⣻⣷⣷
⠀⢾⠃⠀⣀⣐⣋⣭⣿⣏⣈⠐⢸⣿⣀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠛⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢮⣭⠁⣿⣿⣥⣤⣤⣾⣿⡿⠡⢓⠛⢒
⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠛⠛⠋⠉⠉⠋⠐⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡿⠋⠙⢿⣿⣿⣿⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉⠛⠋⠃⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠵⠂⠀⠀⠀⠰⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⢋⠃⠀⠀⠀⠀⠀⠀⠀⢠⠞⣿⢿⣿⡷⠂⠀⠀⠀⡠⠀⠀⠀⠀⠋⠀⡀⠀⠉⠛⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣼⣿⣿⠏⠀⠀⢰⡞⠉⠀⠀⠀⠀⢀⣴⣾⡏⠀⠀⠀⠀⠀⢹⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡼⢿⣿⣿⠃⢸⣷⣿⣿⣿⡄⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⣴⣾⣿⣿⡧
⠀⠀⠀⠀⠀⣎⠆⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠋⠀⠘⢿⡟⣿⣿⣿⡶⠃⠀⣼⣿⣿⢁⠀⡀⢌⣷⡽⠿⠛⠫⠄⣤
⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠉⠙⠛⠁⠀⠀⣿⣿⣿⣎⣳⣝⣿⡟⠁⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⡿⠑⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡏⠀⠀⣀⠉
⠀⠀⠀⢀⠀⣠⣤⣴⣶⣦⠀⠀⠴⠶⠆⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⣀⣉⣤⡄
⠀⠀⢀⡀⣀⣈⣉⣙⣛⡙⠒⠒⠛⠉⠉⠁⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠈⠤⠴⠾⢯⡭⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢿⡇⣿⣿⡇⠈⠻⣧
⠀⠀⠀⠀⠀⣷⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇⢻⡟⢿⠀⠀⠻
⠀⠀⠀⠀⠀⠹⡌⡫⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠇⠈
⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⣤⡤⠤⠶⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣹⣟⣿⣩⣿⣬⣏⣿⣋⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣭⣯⣭⣭⣿⣯⣭⣭⣭⣭⣿

⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⡇⠀⠀⠀⠀⠀⠀⢰⣶⢴⡆⣤⣠⠄⣦⠄⢰⣶⡀⠀⣆⣦⣰⢶⢄⡀⣤⢠⣄
⡇⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠛⠙⠂⠉⠂⠈⠚⠃⠀⠘⠈⠃⠉⠈⠁⠙⠈⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⡄⣀⡀⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠻⠙⠏⠙⠈⠗⠋⠣⠟⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠤⠂⡄
⡇⠀⠀⠀⠠⢠⡴⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⡇⠀⠀⢀⠀⢐⢀⡁⠨⡉⠀⠀⠀⠀⠀⡤⠰⢚⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⡇⠈⠐⠘⠀⠈⠉⠐⠒⠠⣄⣀⠀⠀⠀⠀⠀⠀⢈⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⢀⡀⢈⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠶⠀⡀⠀⠀⠀⠀⠀⠸⠥⠄⠠⠀⠔⠂
⡇⠀⠀⡂⠐⠒⠒⠢⠒⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠈⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠳⡀⠀⠀⡰⠠⠤⠀⠄⠀⠀⠁⠀⠀⠀⢬⣁⣀⣀⠀⠀⠀⠈⠄⠋⠀⠀⠑⠀⠀⡔⡁⠘⠀⠠⣢
⡇⠀⠀⢠⠧⠃⠹⣇⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀⠀⠯⣄⡁⠈⣀⠼
⡇⠀⠀⠀⠄⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢫⡉⣁
⡇⠀⠀⠀⠀⢀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠼⢅⢀⠄
⡇⠀⠀⠀⠀⠘⠂⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢈⣀
⡇⠀⠀⢠⠔⠒⢀⠒⠂⠁⠈⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢻⣷⣀
⡇⠀⠀⢠⠐⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠚⠂⠟⠁
⡇⠀⠀⢸⠿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀
⡇⠀⠀⠠⠐⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠐⠀⠀⠀⠀⠀⣄⠀⠀⡀
⡇⠀⠀⢠⡒⢚⡃⠀⠀⠣⠎⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠦⠜⠁⠀⠀⠀⠀⠀⠋⠹⠿⠟⠿⠿
⣇⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠠⠤⠀⣀⣀⣀⣩⣭⣥⣤⡤⠤⠤⠴⠶⠶⢤⣤⣤⣄⡉⠙⠲⢤⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡛⠉⣉⣟⣛⣿⣟⣱⠄⣀⣋⣭⡥⠴⠖⠒⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢁⡿⣿⡶⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⠀⠘⣆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠏⣬⡔⠀⠠⠄⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⡄⠠
⠀⠐⠀⠀⠀⠀⢠⡶⢻⣾⠡⣿⣶⠇⠀⠀⠂⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⣰⠏⠀⠘⢆⣹⡿⡿⠀⠀⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠓⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡿
⠀⠀⠀⠀⠀⣿⢀⣀⣤⣤⣦⡐⠀⠀⠈⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢰⡇⠀⢀
⠀⠀⠀⢀⠐⠉⠙⢻⣿⣿⣿⣇⠀⠀⠀⣾⣿⣷⣦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢀⡾
⠀⠀⠀⡄⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⣰⣿⣿⣿⣿⣏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣼⠁
⠀⠀⠀⡇⠀⠀⠀⢀⣾⣿⣿⠃⠀⣰⣿⣿⣿⣿⣿⣿⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣰⠃
⠀⠀⠀⢷⠀⠀⠀⠸⣿⡿⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣰⠏
⠀⠀⠀⠘⡀⠀⠀⠀⠋⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣰⠏⢀
⠀⠀⠀⠀⠅⢀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣰⠃
⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⣰⠃
⠀⠀⠀⠀⠀⣇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠘⠦⢀⣴⠿⠿⠿⠿⠿⠿⠿⠛⠛⢦⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠈⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠄⠠⠒⠒⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⠀⠀⠀⠄⠁⠁
⠀⠐⢀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢿⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣴⠀⠀⣴⠄⠀⣴⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠆⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣼⣿⣧⣼⣿⣧⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡩⠵⣤⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⡴⠭⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣇⡇⠀⠈⢷⡀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⣰⠏⠀⠀⣇⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⢯⡗⠒⠢⡀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡠⠒⠒⣮⠇⠈⠢⣀
⠀⠀⠀⠀⠀⢀⡠⠔⢺⠖⠊⠁⠀⠀⠀⠘⡞⡄⢀⡇⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣇⠀⡼⡜⠀⠀⠀⠀⠉⠒⢾⠒⠤⣀
⠀⠀⠀⢠⢾⠁⠀⠀⠸⣼⡀⠀⠀⠀⠀⠀⠹⡝⡍⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⡝⡽⠁⠀⠀⠀⠀⠀⡸⡜⠀⠀⠀⢹⢦
⠀⠀⠀⠸⡈⡄⠀⠀⠀⠙⣷⣀⠤⠤⠒⠒⠒⠚⠮⣓⢒⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⢒⡪⠞⠒⠒⠒⠢⠤⢄⣰⡗⠁⠀⠀⠀⡞⡸
⠀⠀⠀⠀⠱⣘⣄⣀⡠⢤⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢦⠤⣀⣀⣜⡰⠁
⠀⠀⠀⠀⠀⠀⠈⠈⢆⠈⢣⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠋⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠑⣌⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⡔⠁⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠈⠳⣌⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⡴⠋⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠘⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡜⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⡀⠤⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⢋⣵⣶⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⢰⣿⣿⣷⣿⣷⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠈⠛⠛⠉⠀⠀⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⡿⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣃⣤⡌⣿⡿⠉⠝⠀⢀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣼⡇⠀⠀⠀⠀⡷⠀⢼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⣿⣿⣿⣧⣴⠖⠀⠀⠲⣶⣾⣿⣿⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠒⠦⢦⡈⣿⣿⣧⡀⠀⠀⢠⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⣿⣿⠻⢿⣿⣆⠀⠉⠋⢹⡏⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⣿⣿⣧⣨⣤⣉⣶⣶⣾⡿⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠋⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⢻⣿⣿⣟⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⢹⣿⣿⣿⣿⡆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣧⡀⠀⢿⣿⣿⣿⣿⡄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢹⣿⣿⣿⣷⡄⠈⢻⣿⣿⣿⣷⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡛⣠⣿⠃⣿⣿⣿⣿⠆⠀⣠⠉⠙⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣴⢿⣿⡟⣸⣿⢸⡇⠉⢶⣦⣤⣶⣶⣷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣽⣿⣿⣿⣧⣿⣏⣼⣷⠄⣍⠀⠀⠀⣻⣷⡘⢧⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣚⡛⣓⠀⢀⣿⣿⣃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄


⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⢉⡉⣢
⠀⠠⠀⠀⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⣞⡀⣀⢀⢀⠈⠬⢵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡀⡀
⣶⡶⠶⣶⠶⢶⡶⡶⣶⢶⢶⢶⣶⢶⣶⠶⣦⠀⠀⠀⠀⠁⠀⠀⠀⡀⠈⡛⠛⠀⠁⠀⠀⠀⠀⠀⢀⠄⡠⠊⠁⠙⢦⡠⡀
⣿⡷⢶⣿⣴⣼⡧⢦⡿⠷⣾⣷⣿⠶⣿⠶⣾⠀⠀⠀⠀⠀⠀⠀⠉⠇⠀⠥⠤⠆⠐⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠙⢢
⣿⣇⣘⣿⢈⢸⣃⣸⣇⣀⣿⠀⢸⢀⣿⣉⣿⠀⠀⠀⠀⠀⠀⡀⠀⢈⢤⣶⠛⢲⠤⠀⠀⠀⠀⠀⠀⠈⠉⠀⠠⣐⠀⠁
⠛⠛⠛⠛⠀⠘⠛⠛⠛⠛⠛⠉⠘⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠉⡠⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣰⣀⣊⣐⣿⢀⠀⢀⣐
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃
⠀⠀⢀⢤⡄⠀⢠⡤⡤⢤⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠎⢄⢗⠰⡢⢀⡊⡀⢀⠀⡄⡐⠝⡇⠀⠀⠀⠠⢤⣠⣮⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢰⠁
⡔⢎⣄⣡⡑⠡⡾⠋⠙⢆⠢⣥⣉⣤⣡⣹⣦⠀⠀⠐⠉⢀⠀⠀⠈⢦⣀⣀⣖⣌⣱⣄⠀⠀⠀⠀⠀⠀⠠⠄⠀⢸
⠑⠂⠐⡀⠒⣲⠁⠻⠓⠀⡉⡌⠉⢩⡉⠉⠁⠀⠀⠀⢠⣀⣀⣀⣀⠀⣿⣽⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸
⠀⠀⣸⣗⠀⡷⠀⠀⠀⠀⢠⠧⠀⡧⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠒⠐⠒⠚⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠠⠤⠀⠤⠤⠴⠒⠒⢣⠤⠤⠀⠠⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡑⡓⢖⡶⢶⢞⠠⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠓⡈⠀⣞⣛⣛⣫⢂⢃⣘⣧
⠀⢀⡞⡡⡀⠉⠉⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⢭⣭⣶⣶⣶⣶⣶⣗⣒⠆⠀⠀⠀⠠⠤⠼⠤⠬⠽⠭⠥⠯⠦⠼⠴⠼⠧
⠀⣎⠔⠀⠈⡀⢀⢀⠀⠈⣣⠀⠀⠀⠀⠀⠀⠀⣼⣏⣉⣿⣿⣿⣉⣸⣿⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠂
⠀⡆⠠⠵⠤⠀⠀⢀⡀⠀⢰⣖⣀⣰⠀⠀⠀⠀⣿⡿⠿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡁⠁⠀⠀⠀⠈⠈⠁⠁⠈
⠀⠁⠄⠄⠆⠀⠀⠀⠈⠀⢸⠁⢰⠁⠀⠀⠀⠀⣿⣧⣬⣿⣿⣿⣮⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡀
⠀⡆⡇⠂⠀⠀⣤⣴⡆⠤⢼⢀⠘⠀⠀⠀⠀⠀⣿⣭⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢐⢐⠀⣶⣿⠠⠀⠀⡶⣿⢀⢐
⠀⠇⠃⠒⠂⠀⢹⣷⡇⢀⢸⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠠⠘⠀⠀⣿⣿⡔⠀⢁⣿⣿⠈⠨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⠿⣒⣤⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⢛⣙⢻⣿⠟⣉⡻⣿⡿⣋⡙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣌⣋⣼⣿⣮⣛⣵⣿⣧⣙⣣⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⣿⣿⣿⣿⣿⣶⡍⠛⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿

⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⣀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⣾⣿⣿⣷⣶⣦⣄⡀
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢿⣿⣿⣷
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿
⣿⣿⣿⢋⣥⣦⣬⣭⣭⣭⣭⣭⣭⣭⣥⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢹⣿
⢻⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣮⣭⣍⣛⣛⣛⡛⠿⣿⣿⣿⣿⠈⣿
⠈⢿⣷⣜⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡝⢿⣿⢰⣿
⠀⠀⠹⣿⣇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⡎⠟⣼⣿
⠀⠀⠀⠀⠉⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣾⣿⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢙⠿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⠿⢟⢱⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣾⠿⠸⢿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⣠⣶⣿⣿⣶⣮⣍⣛⠿⠏⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡘⠿⢛⣫⣭⣶⣿⣿⣷⣮⠉⠁
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣷
⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡿
⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⣿⡧
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⡏⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⢸⣿⣿⡁⠀⢈⣿⣿⡇⠀⠀⢀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠀⢸⣿⣿⣿⣶⣿⣿⣿⡇⠠⠶⠿⠿⠿⠷⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⡏
⠀⠀⠀⠀⠀⢠⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠙⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠃
⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢷⣿⣿⣽⣲⣄⡀
⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠠⠚⢹⣾⣿⣿⣿⣿⣿⣷⡏⠓⠆
⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⢿⣿⣿⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⠈⠁
⠀⠀⠀⠸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠠⣶⡆⠀⠀⠀⠀⣤⠀⠀⠀⠘⠛⠒⠚⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦
⠀⠀⠀⠀⢀⣴⣾⣿⣷⣦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡟⡇
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⣾⣿⣷⠇
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⠀⠀⠀⣿⠀⠀⠀⠀⠀⡔⠢⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⢰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣀⠀⠀⠀⠀⡇⠀⢄⣤⣤⣴⠀⠀⢿⣿⣿⡿⣸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣦⡀⠀⠀⡇⠀⢸⣿⣿⣿⠀⠀⠈⠙⠋⠁⠿⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⢀⣤⣧⡄⢸⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⣀⠴⠶⢦⡀⠀⠀⢀⠄⠂⠒⠂⢄⠀⠀⠀⠀⠀⡆⠨⣆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠍⣶⠦⢤
⠰⡏⠀⠀⠀⠀⠈⢺⠀⠐⠐⠀⠀⠀⠄⠇⠀⠀⠀⠳⣄⢀⠋⠁⠀⣀⢈⣡⠠⠀⠉⠀⠩⠀⢀⠀⡇⠀⠀⠀⠀⠀⡆
⠠⣧⡠⠀⠀⠀⠀⡼⠀⠠⡒⣆⢰⡴⢢⠆⠀⠀⠀⠀⢹⠘⠀⠐⠙⠀⠡⠀⠀⢲⡂⠐⠐⠂⠀⢣⠠⡀⠀⠀⠀⡠⠱
⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠈⠈⡧⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡾⣦⠀⠀⠀⠀⠀⠀⠀⡤⡆
⠀⠀⠀⠀⠉⢴⠀⠀⠀⠀⠀⠈⠸⡁⢤⠀⠈⠀⠈⠑⠤⢀⡲⠜⢻⠵⠚⢻⡉⠀⠩⠀⠀⠀⠀⣠⠒⠒⠙
⠀⠀⠀⢸⡁⠩⣄⠀⠀⠀⠀⠀⠀⠓⠀⠢⠤⠶⠤⠤⠀⢨⡟⠀⠀⠀⠃⠛⠀⠀⠀⠈⠀⠀⠀⡅
⠀⠀⠀⡦⠠⠤⣾⠀⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡼⢓⠒⠀⠐⢰⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠀⠀⠀⠂
⠀⣀⠎⠀⠙⠋⠠⠥⠁⠈⠀⠀⠀⠀⢀⠀⠀⢀⡠⠉⠁⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠠⠦⡐⢤⠀⠀⠀⠰⠄
⢜⠁⠐⠒⠒⠒⠒⠄⠠⣮⠶⢤⣀⠀⢀⣀⡴⠋⠀⠀⠀⠀⠤⠰⠆⠾⠠⠄⠀⠀⢀⣰⠤⠼⢥⣘⠁
⠈⠒⢀⠉⠩⢍⠉⠱⠉⢁⡤⠶⢮⣥⡿⠉⢰⣋⣿⣾⣞⣷⣯⣿⣿⣘⣯⠐⠀⠐⡝⠡⠀⠀⠀⠈⢯⠒⡌⠀⠰⡀
⣰⡛⢫⠝⣳⢦⠉⠀⢠⡏⠀⠀⠀⠣⠘⡆⠂⠉⢩⠾⣮⣅⣥⣭⡭⠉⠉⠀⠁⠀⢇⠀⠀⠀⠀⠀⡜⢀⠀⠢⡀⡀⠂
⡓⠊⠀⠀⠀⢞⡅⠀⠘⣄⠀⠀⠀⠀⣱⠇⡄⢪⠬⠛⠹⠯⠟⠥⠧⠤⠤⠭⠤⣤⡈⠑⠦⣤⠀⠊⣐⠀⠀⢀⣒⣀⣀
⠃⠀⠀⠀⠀⡿⠃⠀⠀⠀⠁⢀⣆⠈⠁⠀⠀⠈⠁⢀⣠⣠⣀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠐⡽⡚⢓⣉⠠⠊⠁⠀⠀⠙
⠀⠀⢸⡄⠀⠁⠀⠀⠀⠀⣬⣮⣴⡦⢄⠀⠀⠀⣴⠽⠓⠛⠉⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⣉⠁
⠀⠀⠀⢺⡀⠸⠳⣶⡅⠀⢿⣿⣟⠏⡈⡂⠀⠀⢿⣀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠄
⠀⠀⠀⠀⠛⢢⠀⠀⡀⣀⠀⠀⠀⠠⠄⠀⠀⠀⠈⡗⠀⠠⣐⢪⡻⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠈⡤⠀⣪⠂⢠⣷⣦⣤⡀⡢⢌⣉⢀⠀⣁⡁⠀⡀⠀⠀⡈⢹⠘⣓⠈⠀⠀⠀⡀⠀⠘⣡⠀⠊⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⠁⠑⠀⠂
⠀⠀⢀⡼⠻⡒⠤⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣶⣶⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠃⠀⢀⢤
⠀⢆⡞⠀⢀⣱⡤⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⢆⠀⢀⡱
⢃⠨⠻⣍⡉⠈⠃⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡛⢍⠢⠑
⠀⠓⠤⣌⣉⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠐⣉⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠬⠂



⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢉⣉⣉⡉⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣄
⠀⠀⠀⣷⣶⡗⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⣒⣒⠒⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⠒⠲⢣⠏
⠀⠀⠀⡻⣿⡷⠁⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⣄⠀⢸⣿⣿⣟⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠳⡄⠀⠋⠠
⠀⠀⢀⣠⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠈⠙⣿⠟⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠿




⠀⠀⠀⢠⠀⠀⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⠤⠤⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⢀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤
⠀⠀⠀⠀⢠⣉⡡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠳⠄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠦⣀⡤⢖⡉
⠀⠀⠰⠤⠬⠥⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣛⣛⣛⣉⡦⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡁⡤⠤⠤⣄⣙⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣄⣀⣤⣤⣴⣶⣾⣿⣿⠿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⡛⢛⣉⡉⠉⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣾⣿⣿⣿⣿⣿⡀⠀⠀⠀⣀⣤⣿⣿⣿⣇⡀⠀⢸⣿⣧⠀⢀⣴⠟⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣿⣿⣿⣿⣿⣿⣧⡀⣸⣿⣿⣾⠟⣁⣴⣷⣄⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣷⣄⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⠾⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⢿⡿⢷⣤⡙⢷⣄
⠀⠀⠀⢀⣴⣤⣤⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⣾⣿⠰⠶⠰⠶⢸⣿⣿⣿⣿⠃⢶⠆⢶⠆⣿⣿⡆⠙⠇
⠀⣀⣴⣿⣿⣿⣿⡟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⠰⣶⠰⣶⢸⣿⣿⣿⣿⠀⣶⡆⣶⡆⣿⣿⡇
⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⢛⣛⣛⣛⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠙⣿⣿⢠⣶⢠⣶⢸⣿⣿⣿⣿⠀⣶⡄⣶⡄⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡏⢹⣟⠉⣿⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣤⣤⣤⣼⣿⣿⣿⣿⣦⣤⣤⣤⣤⣿⣿⡇⢠⣄⡀
⠿⠿⠿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡏⢹⣿⠉⣿⠉⢹⡇⠀⠀⣿⣿⣿⣿⡇⠉⠉⢉⣉⣉⣉⠉⠉⠉⠉⠉⠉⣉⡉⡉⠉⠉⢻⣷⣾⣿⠁⣀
⠀⠀⠀⢾⣿⣿⠿⠿⣿⣿⣶⡄⠘⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⣿⣿⣿⣿⡇⠀⠀⣿⣉⣿⣉⡇⠀⠀⠀⠀⢸⣉⣿⣉⣿⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⠟⠛⠀⠐⠿⠿⠛⣿⣾⣷⣶⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⡇⠀⠀⢿⣀⣿⣠⡇⠀⠀⠀⠀⢸⣄⣿⣀⡿⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣠⣤⣤⣿⠟⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡁⠀⠈⢩⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠐⠂⠀⠤⠀⣀⠀⣀⡀⠘⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣌⠅⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⢿⠇⠀⠀⠀⠠⠀⠀⣿⠀⢀⣰⣾⣷⣴
⠀⠀⠀⠂⢠⣶⣦⣼⢿⣿⣿⣿⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣠⠀⠀⢘⣿⣿⡋⠙⠦⠀⠀⣀⠀⠀⠂⠀⣿⠀⠘⠙⢿⠏⠛
⠀⠀⠀⠠⢸⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠃⠀⣸⣿⣿⣇⠀⠀⠀⣰⣿⣿⣷⡆⠀⣿⠀⠀⠀⢸⠀⠠
⠀⠀⢀⠸⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠅⠀⣿⣯⢿⣿⣿⣿⣿⡇⠀⢸⣿⠀⢀⣿⣿⣿⡿⣷⣆⠀⠙⠿⠛⠿⠁⠀⣿⠀⠀⠀⢸⠀⠠
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⢀⡈⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠙⠃⠀⢸⣛⣹⣿⣷⢿⡿⠀⠀⠀⠀⠀⠀⣰⣿⣆⡀⠀⣿
⠀⠀⠀⠀⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀⠐⠀⢸⡇⠀⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⢶⡧⠀⣽⣿⣿⣿⣷⣿⣇⢀⣤⡀⠀⢀⣼⣿⣿⣿⣷⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠐⠐⠀⠻⠿⠿⠟⠛⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢸⣶⡇⠀⠈⠉⠉⠉⠉⠉
⠀⠀⢀⣤⣀⣣⣄⣸⣯⣷⣄⣿⣿⣿⣤⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⡀⠀⣰⣦⣆⠀⠀⠀⠁⠀⠀⢸⣿⡇⠀⠈⣈⣀⣀⣄⣢⣄⣀⣀⡀
⠀⠀⢿⣽⡿⠿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣶⡔⠂⢸⡇⠈⠀⠀⣀⣤⣴⡟⠁⠀⠠⠁⢸⣿⣿⡟⠻⣦⡀⠀⠃⠀⠀⣿⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⣼⠃⢀⣴⣿⣿⣿⣿⣷⡄⠀⣤⡀⢸⣿⣿⣷⣶⣾⡇⢠⣴⣾⠀⣿⠀⡐⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣿⠀⠚⠿⣿⣿⣿⣿⣿⠃⠀⣿⠁⢸⡿⣿⣿⣿⣿⡇⠀⠙⠟⠀⣿⠀⠠⠄⠈⣿⣿⣿⣿⣿⣿⡿
⠀⠈⢛⣿⣻⣻⣿⣿⣿⣽⣯⣿⣿⣿⡟⠋⠄⠀⠀⣿⠀⠀⠠⠀⠉⠛⠿⠃⠀⠀⣿⡆⠘⠿⠿⠿⠿⠿⠇⠀⠀⠀⠰⣿⡇⠈⠀⠀⢻⣿⣿⣿⣿⣿⠇⡀
⠀⠀⠈⠻⠟⠙⡋⢿⣿⣿⣿⠟⠉⠉⠀⠙⠀⠀⠀⣿⠀⠀⠐⠀⠀⠀⡀⠀⣀⣤⣤⣤⣄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠸⣧⣿⣿⣽⡿⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠉⣿⣿⠀⠀⠠⠀⣰⣶⣶⣶⣿⣶⣶⣶⣆⠀⠀⢠⣾⣽⣿⣿⣿⣿⣷⡀⢠⣾⣷⡄⠀⠀⠀⠀⣿⠀⠀⠄⠀⠀⠉⠉⠙⠛⠃
⠀⠀⠖⠐⣶⣶⣤⡀⠀⢸⣿⡇⠀⠀⠀⠟⠟⠟⠟⠟⠿⠟⠟⠟⢠⠂⣿⣿⣷⣿⣿⣿⣿⣿⡇⢠⣿⣿⣦⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠰⡜⣆⣷
⠀⠀⠀⠘⠋⣼⣿⡄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢻⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣾⣿⠃⠐⠂⢠⣿⣇⠀⠄⠒⠈⢷⣹⣾⣾⡆⣷
⠀⠀⠂⠀⢀⣻⣿⡇⢀⠀⠀⠀⠀⣀⣤⣤⣴⣤⣤⣴⠀⠀⠀⢀⢡⠀⠀⠙⠿⠿⠿⠟⠋⡀⣀⣈⠉⠉⢡⣤⣤⣶⣿⣿⣿⣶⣶⣶⡆⠀⠻⣿⣿⣿⣿⣤⣆
⠀⠀⢠⣾⣿⣿⣿⡇⠀⠈⣠⣶⣟⣿⢿⣿⣿⣿⣯⣏⠀⠀⠀⠠⠀⠀⡀⠃⣠⣤⣀⠀⠈⢿⣿⠟⠀⠀⠸⢿⣿⠿⠿⠿⠿⠿⠿⠿⠇⢀⣀⣼⣿⣿⣿⣿⡿
⠀⠀⣾⣿⣿⣿⣿⠀⠀⢾⣿⣿⣯⣿⣿⣿⣿⣿⣻⣿⠷⠶⢶⣤⣤⠀⡁⠸⣿⣿⣿⣷⡀⠀⠀⠀⣀⣠⣤⣄⠀⣴⣶⣴⣶⣶⣶⡄⠀⣨⣽⣿⣿⣿⣿⣿⠗
⠀⠀⠙⠛⠛⠛⠛⢀⡀⠀⠙⢿⣿⣿⣿⣿⣿⠯⣿⠀⠀⠀⠀⠀⠀⢀⣤⣴⡿⣾⣿⣿⠟⠀⢰⣿⣿⣿⠿⠛⠀⣷⢿⣿⣿⣿⣿⡇⠈⡵⣻⢿⠟⠙⠋
⠀⠀⠢⠄⠀⠀⠀⠀⠑⠀⠀⠀⠙⠛⠁⠀⡀⠀⠁⠀⣠⣤⠄⠀⠀⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠛⠉⠀⠐⠀⠀⠀⠘⠛⠛⠉⠉⠁⠀⠀⠁⠈
⠀⠈⢀⣠⣤⣶⣶⣶⣴⣦⣤⣄⡀⠀⠀⠂⠉⢀⣴⣾⣷⠙⠀⠀⠀⠈⠉⠛⠛⠛⠁⠀⣴⣿⠆⠀⠀⣠⣶⣻⡆⠀⡰⠃⠀⠀⠀⠒⠁⠀⠀⠀⢀⣤⣦
⠀⠰⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠈⠻⠿⠋⠀⠀⢀⣰⣒⣬⣤⣤⣤⠄⠀⠛⢁⣴⢞⣻⣿⠛⠉⠀⠀⣀⣀⣠⣤⣤⣤⣀⠀⠀⢰⣿⣿⣏
⠀⠀⣿⣿⣟⣿⣷⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣴⣤⣤⣄⠀⠀⠈⢹⡿⠯⠿⠿⠟⠀⠀⠀⠸⣿⣿⠿⠃⠀⠂⠀⠈⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠹⠟⢿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠁⠀⠀⠀⠀⢈⣿⡇⠀⠀⠠⢀⣀⣀⠀⢰⣯⣭⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⣶⠶⠶⠞⠚⠚⠛⠛⠛⠛⠉⠀⠄⠀⠀⣸⣿⣿⠀⢸⣿⣿⣿⡇⠀⢴⣾⣿⡇⠀⠀⠀⠺⠿⠿⠿⠟⠛⠃⠀⠀⢸⣿⣿⣿⠇
⠀⠀⠀⢀⠉⠀⠀⠀⠘⢿⣤⣤⣤⣤⣤⡶⠶⠶⠶⠶⠚⠛⠛⠛⠛⢻⣿⣿⠀⣼⣟⣿⣯⣿⠀⢸⣿⣿⡷⠀⢀⣀⣀⣀⣀⣀⣠⣴⣶⣶⠄⠈⠻⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠈⠛⠋⠀⠈⠛⠛⠛⠁⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⡠⡶⠻⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠻⠷⢶⣤⡀
⠀⠀⠀⢠⡞⠁⢸⠀⠀⠀⡀⢜⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣞⠉⢉⠉⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠞⡠⠁⠀⠀⠙⣧
⠀⠀⠀⢸⡇⢠⢚⠀⠀⠀⠡⣠⠿⠛⠀⣩⠃⠀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠠⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠛⠃⣄⢀⡀⢈⡇⠀⠐⢁⠏
⠀⠀⠀⠘⠇⣠⡎⣼⠿⠷⠀⣠⣳⢒⠉⢹⠀⠀⠀⠀⡠⢢⠝⠉⢱⢄⡀⠀⣞⣩⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⢀⡞⠂⠤⢿⢢⣤⣤⠔⠈⠄
⠀⠀⠀⢀⠋⠻⢻⣿⣍⡉⡩⣭⢐⠅⢀⠎⠀⠀⠀⠀⠛⠞⢆⠀⠘⡎⠙⠍⣁⡀⠀⠀⣤⡄⠀⠀⢄⡀⠀⠀⠀⠀⠶⠇⠀⠖⢤⠤⡤⠴⠢⠏⠀⠀⠁
⠀⠀⠀⠈⡖⠆⠀⢻⣿⡔⡐⠉⡄⠒⠁⠀⠀⠀⠀⠀⠀⠀⢸⢹⠊⠈⠒⠤⠾⢿⠿⠍⠉⠉⠉⠑⡟⠉⠀⠀⠀⠀⠀⠀⠀⣨⠘⠒⠂⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠇⠀⠀⠈⢠⠦⠇⠐⠓⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠾⠀⠀⠀⠀⠀⠀⠈⠱⡴⠤⠦⢦⡅⠀⠀⠀⠀⠀⠀⠀⠀⢩⠶⣄⠀⠀⠀⠀⠀⣤⠇

⠀⠀⠀⠀⠀⢰⡦⢤⣤⣤⣤⠤⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⣤⡆⠤⠛⠛⢙⡛⠳⣖⠛⡦⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡉⢉⠉⠣⠀⠀⠀⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡙⢀⠈⠉⢳⡄
⠀⠀⠀⠀⢾⡇⡀⠘⢤⢀⠀⠀⡜⠀⡁⠀⠀⠀⠀⠀⠀⠀⠸⠁⢀⠀⡠⠆⢀⠃⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠁⠀⠀⣰⣾⠿⡄
⠀⠀⠀⠀⠸⡿⢵⠤⣌⣀⣠⠜⠥⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠉⢳⡠⠊⠀⠀⣨⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢈⠿⠿⠙⡳⡆⢈
⠀⠀⠀⠀⠀⢸⣿⡖⠁⢹⣿⣿⠋⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠱⠬⠤⠄⠒⣞⠋⠉⠋⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡛⠲⠒⠻⣛⠤⠊
⠀⠀⠀⠀⠀⢸⠛⣷⣶⣾⠛⠛⣶⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡬⠽⠶⠦⣤⣤⡟⠓⠒⢁⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⣀⣀⡇
⠀⠀⠀⠀⠀⢸⣤⡿⠿⢿⣤⣤⡿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢷⢌⣀⣲⡦⠀⠁⢹⡿⢻⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢸⡇⢰
⠀⠀⠀⠀⠀⠈⣿⣧⣤⣼⣿⡿⡆⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⡇⠸⢷⢲⠘⡇⠸⠇⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⣡⣼
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠉⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣉⣴⡶⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢋⠉⠉⠉⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠁⠐⡄⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢐⠂⠐⠈⢻⡆
⠀⠀⠀⠠⣾⣶⣷⣾⡷⠈⠀⠀⡇⠀⠀⢸⡧⣶⣶⣶⢶⠆⠀⠀⠀⠀⠀⢹⠀⠀⢶⠃⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠖⣲⣞⠲⡟⢦⣀⠀⠘⡏
⠀⠀⠀⠀⠀⢸⠈⠇⠀⠰⡀⠀⠑⡆⠀⡰⠁⠀⡏⡷⠀⠀⠀⠀⠀⠀⠀⠀⢑⠂⣶⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡉⠀⡿⣀⣠⡞⣀⠔
⠀⠀⠀⠀⠀⠀⢢⡈⠢⠤⠜⢳⠶⠶⠛⠤⠤⠚⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⣘⣿⣿⣏⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠙⠯⠝⡡⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠚⣧⣤⣤⡗⠒⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠰⠵⠊⠟⢲⡄⠉⠟⠛⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢖⣊⣀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣊⠠⠊⠀⠀⢀⡀⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠐⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠗⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠻⠾⠁
⠀⠀⠐
⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⠀⠀⠀⠂⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠘
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⢨⣆⢳
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠋⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢸⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠮⠤⠐⠈
⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⠀⠀⠉⢖⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⡅⠀⠀⠀⠑⠢⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⣀⡠⢸⠤⡄⠀⠀⠀⡀⠀⠐⠒⢒⠒⠂⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠃
⠀⠀⠀⢁⠀⠀⠀⠀⠀⠑⡀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⢢⠀⠀⢈⡡⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠑⢀⠀⠀⢀⠔⠁⠀⡠⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠈⠁⠀⠀⡐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡔⢄⣀⡠⢊⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠜⢄⠀⠀⠈⠢⠬⠟⢛⣠⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡶⠤⠤⠵⠦⠤⠠⠤⠤⠾⠟⠒⠒⠒⠚⠿⠛⠛⠛⠛⠟⠻⠟⠛⠛⠛⠛⠿⠿⠟⠿⠛⠻⠛⠦⠄⠤⠄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠉⠉⡏⠙⡋⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠃⠉⠊⠛⠉⠛⠉⠉⠉⠉⠉⠉⠈⠉⠉⠀⡏⠉⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠰⠄⠀⠐⠂⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠰⠀⠀⠀⠀⢠⠀⡄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⢀⠁⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣛⣒⣒⣒⣒⣒⣒⣒⣒⣒⠄⠂⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠃⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠍⢸⠀⠀⠅⠉⠀⠀⠀⠁⠉⢠⠏⢨⡏⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⡆⠃⠀⠀⠀⠀⢰⡧⢾⠸⠷⡶⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠐⠃⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢇⡐⠀⡆⣦⠀⠀⠀⠃⠤⣀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⠉⠒⠓⠛⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠛⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⡀⣀⠴⠶⢦⡀⠀⠀⢀⠄⠂⠒⠂⢄⠀⠀⠀⠀⠀⡆⠨⣆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠍⣶⠦⢤
⠐⡏⠀⠀⠀⠀⠈⢺⠀⠐⠐⠀⠀⠀⠄⠇⠀⠀⠀⠳⣄⢀⠋⠓⠀⣀⢈⣡⠠⠀⠉⠀⠉⠀⢀⠀⡇⠀⠀⠀⠀⠀⡆
⠐⣦⡠⠀⠀⠀⠀⡼⠀⠠⡒⣆⢰⡴⢢⠆⠀⠀⠀⠀⢹⠘⠀⠐⠙⠀⠡⠀⠀⢲⡂⠐⠐⠂⠀⢣⠠⡀⠀⠀⠀⡠⠳
⠀⠀⠑⡢⢀⠀⠀⠀⠀⠀⠀⠈⡧⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡾⣦⠀⠀⠀⠀⠀⠀⠀⡤⡆⠀⠀⠐
⠀⠀⠀⠀⠉⢴⠀⠀⠀⠀⠀⠈⠰⠁⢤⠀⠈⠀⠈⠑⠄⢀⡲⠜⢻⠵⠚⢻⡈⠀⠩⠀⠀⠀⠀⣀⠒⠒⠙
⠀⠀⠀⢨⡀⠩⣄⠀⠀⠀⠀⠀⠀⠓⠀⠢⠤⠶⠤⢤⠀⢨⡇⠀⠀⠀⠃⠛⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⡦⠤⠤⣾⠀⡀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢒⠒⠀⠐⢰⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠂
⠀⣀⠌⠀⠑⠋⠠⠥⠁⠈⠀⠀⠀⠀⢀⠀⠀⢀⡠⠈⠁⠀⠀⠀⠁⠍⠈⠀⠀⠀⠀⠀⠀⠀⠠⠦⡐⢤⠀⠀⠀⠰⠄
⢼⠁⠐⠒⠒⠒⠒⠄⠠⣮⠶⢤⣀⠀⢀⣀⡴⠋⠀⠄⠀⠀⠤⠰⠆⠿⠠⠤⠀⠀⢀⣰⠤⠼⢥⣘⠁⠀⠀⠀⠀⠀⠄
⠈⠲⠂⠉⠉⢉⠉⠛⠉⢁⡤⠖⢮⣥⡿⠉⢰⣋⣿⣾⣾⣷⣯⣿⣿⣘⣯⠐⠀⠀⡝⠡⠀⠀⠀⠈⢯⠒⡌⠀⠰⡀
⣰⡛⢯⠙⣳⢦⠋⠀⢠⡏⠀⠀⠀⠣⠘⡆⠂⠉⢩⡾⣮⣅⣥⡭⣭⠉⠍⠀⠁⠀⢇⠀⠀⠀⠀⠀⡜⠀⠄⢠⡀⠀⠊
⡓⠈⠀⠀⠀⢞⡅⠀⠘⣄⠀⠀⠀⠀⣹⠇⡄⢫⠬⠛⠹⠯⠟⠥⠧⠤⠤⠍⠤⣄⡊⠑⠦⣤⠀⠊⣀⠁⠀⢀⣂⣀⣀
⠃⠀⠀⠀⠀⡿⠃⠀⠀⠀⠁⢀⣆⠈⠡⠀⠀⠈⠁⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠠⡽⡚⠓⢉⠠⠊⠁⠀⠀⠙
⠀⠀⢸⡄⠀⠁⠀⠀⠀⠀⣬⣬⣴⡦⢄⠀⠀⠀⣴⠹⠓⠛⠉⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⣉⠁
⠀⠀⠀⢺⡀⠼⠣⣶⡅⠀⢿⣿⡟⠏⡈⡂⠀⠀⢿⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠄
⠀⠀⠀⠀⠛⢢⠀⠀⡀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠈⡗⠀⠠⢐⢎⡻⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠈⡤⠀⣠⠂⢠⣶⣦⣤⡀⡢⢄⠈⢀⠀⣀⡁⠀⡀⠀⠀⡈⢹⠘⣓⠈⠀⠀⠀⡀⠀⠘⣡⡀⠊⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣷
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢰⣿⠆⠀⠻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠃
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⢺⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⣠⣾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⡀
⠀⠀⣀⣀⣀⢸⢻⣿⣿⢻⡆⠀⠀⠀⠀⠀⠺⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠉⠑⢶⡟⢹⣿⣿⢈⡗⠀⠀⠀⠀⠀⠰⡇⣸⣿⣿⠀⡟
⠀⠀⣿⣿⣿⣀⣹⣿⣿⣏⣀⣀⣀⠀⠀⠀⢀⣿⣿⣿⣦⡀⣀⠀⢀⢀⠀⠀⠀⢸⣇⣾⣿⣿⡏⠀⠀⢀⣀⣀⣀⣀⣵⣿⣿⣿⣶⣧⣤⡄
⠀⢸⣿⣿⣿⠛⢿⣿⣿⡿⠛⠛⢿⠀⠀⠀⠘⣿⣿⣿⠉⠰⣿⣷⣾⣿⡤⠀⠀⠈⣹⣿⣿⣿⣷⠀⠀⠈⠉⠙⠉⠉⢹⣿⣿⣿⢿⡏⠉⠋
⠀⢸⣿⣿⣿⠀⢸⣿⣿⠃⠀⠀⢸⠀⠀⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⣿⠈⠃
⠀⢸⣿⣿⣿⠀⠀⣿⣿⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⠏⠀⠀⠹⠿⠿⠿⠀⠀⠀⠀⠙⢻⡟⠛⣿⠀⠀⠀⠀⠀⠀⠀⠈⣷⣹⣏
⠀⠀⣿⣿⣿⠀⠸⡟⣿⠀⠀⠀⣿⠀⠀⠀⢀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠸⡟⡿
⠀⠀⣿⣿⣿⠀⢀⡇⣸⠀⠀⢨⣿⠀⠀⠀⢿⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⠏⣇
⠀⠀⢿⣿⡿⠀⠈⠁⠈⠁⠀⠀⠸⠀⠀⠀⠀⠀⠘⠶⠤⠀⠒⠀⠀⠀⠐⠀⠀⠀⠀⠸⠃⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⢠⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣶⣿⣷⡄⠀⠀⠀⠀⠀⣾⣿⡗⠀⠀⠀⠀⢠⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠀⠘⣿⣿⣿⢿⣿⣿⣿⡇⣾⡿⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠸⣿⡿⠃⠀⠀⠀⠀⠈⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠁
⠀⠀⠀⣿⣿⡇⢈⣽⣿⣿⣶⣿⡇⠀⠀⠀⠀⢀⣴⣿⣯⠀⠀⠀⠀⠀⣠⣾⣷⣄⠀⠀⠐⠀⣰⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣼⣿⣷⡄
⠀⠀⠀⣼⣿⣷⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣻⣿⣿⡄⠀⠀⠀⢰⠛⣿⣿⠙⠦⠖⠉⠰⡇⣿⣿⡇⣳⠀⠀⠀⠀⠀⠀⣿⣿⣏⡇
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢈⣿⣿⣿⠁⠀⠀⠀⠀⢹⣿⣿⡆⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠙⠉⢹⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣴⣾⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠹⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠆⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⡿⠿⣿⣿⣿⠿⡗⠀⠀⠀⠀⠐⢿⣿⡿⠷
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⡏⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⡇⡀⣿⣿⡇⢸⡇⠀⠀⢠⣤⣤⢸⡏⡇
⠀⠀⠀⠀⠀⠀⣸⠃⠀⡿⢠⣶⣶⣦⡄⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠀⠀⡧⡇⢹⢸⠃⠘⡇⠀⠀⠸⣿⡏⢸⠁⡇
⠀⠀⠀⠀⠀⢀⡟⠀⠀⣇⠘⠛⠛⠛⠋⠀⠀⠀⡇⠈⣇⡀⠀⠀⠀⣄⣀⠀⣇⠸⠀⠀⠀⡻⠇⠾⠸⠆⠤⡇⠀⣠⣶⡧⠈⠉⠔⠃
⠀⠀⣀⠀⠀⠈⡁⢀⠀⠉⠀⣀⠀⠀⠀⠀⠀⢈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠈⠈⠁
⣿⣏⢭⣟⡛⣛⣛⡛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠋⠀⠁⢸⡇⠀⠀⠉⠙⠛⠓⠚⠛⠛⠋⣸⠏⠈⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠛⠷⢶⣤⣤⣤⡴⠶⠛⠁⠀⠀⠈⣠⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢋⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⣀⠀⠀⠀⣘⢷⡒⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢹⣧⣤⢀⡈⢉⣙⡛⠀⠐⠀⠀⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠉⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠂⠀⠀⠀⠀⠴⠀⠈⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡂⠀⠀⠀⠀⠀⠀⠀⠄⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⣤⣤⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⡝⠂⠀⠤⠍⠻⠀⢿⠀⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢛⡛⠀⠀⠀⠀⠀⠀⠄⢨⣄⣠⣩⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⡄⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠳⠆⠠⠀⢤⠄⠀⠀⠀⣉⣸⡁⠀⠀⠐⠀⠒⡗⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣿⠁⡆⠀⢸⠆⠦⠀⢠⡌⣿⠀⠀⠀⢐⣟⠀⣿⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⡏⣤⠀⠀⣿⡖⠂⠀⠰⢷⡿⠀⠀⠀⢸⣿⡉⣿⣈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢣⡌⠀⢀⣙⣛⠀⠀⣳⣾⠇⠂⠀⠓⠚⣿⠗⣿⠁⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⡈⠁⠀⢀⣉⣭⡀⢀⢻⡿⠀⠀⠀⠀⠀⣿⣿⢷⠀⠸⣧
⠀⠀⠀⠀⠀⠀⡙⢘⣿⡇⠛⠀⠀⠠⠤⠤⠀⠀⣾⠇⠀⠀⠀⠀⠀⠸⣿⢉⠀⢠⣿⡀
⠀⠀⠀⠀⠀⡀⠁⢼⣽⠀⠀⠀⠀⠀⠀⠀⠀⢴⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠁⠀⠈⡁⠀⢀⣤⡴⠶⣦⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣿
⠀⠀⠀⢀⠀⠀⠀⠀⠁⣀⣼⠋⠠⣴⡿⠛⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡆
⠀⠀⠀⡈⠀⠀⠀⠀⠀⢻⣿⣶⣶⣯⠀⠄⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣧
⠀⠀⢀⡁⠀⠀⠀⠀⡀⡀⠉⠉⠉⠁⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠈⠉⠉⠛⣇⠀⢀⣠⣶⣶⣶⣦⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢁⡀
⠀⠀⠀⠀⠀⠀⠙⢃⠀⠙⠛⠿⠛⠋⠀⢀⣦⣨⣀⣀⣀⡀⠀⠀⠀⣀⣠⠛⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡀⢠⣀⠀⠀⠀⢠⣾⣿⣷⡄⠁⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⠉⠁⠀⢀⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⣾⣿⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣤⡘⠋⣁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠿⠁⠀⠀⠳⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢠⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠈⢸⠇
⠀⠀⠀⠀⠀⠀⠄⠰⡄⠀⣸⣿⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠘⡟⠀⠇⠀⣿⣿⣧⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣅⣀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠂⢻⣿⣿⣿⣤⣤⣶⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⢿⡿
⡀

⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠤⠼⠇⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠀⢐⡿⠀⠀⠀⠀⠐⠕⡀⠀⠂⠀⠚⠀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⡀⠀⠀⠐⢩⠀⠀⠀⠀⠀⠀⢐⣀⡀⢀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠰⢺⡇⠀⠀⠀⠀⠀⠌⠑⢢⠄⠐⢀⠀⠀⠀⠀⠞⠉⠠⠀⢀
⠀⠀⠘⠢⢀⡄⠔⠆⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡧⠘⠠⡇⠼⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠰⠁⠔⠂

⠀⠀⠠⠀⠀⠀⡀⣠⠀⠀⠀⠀⠀⢀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠘⠛⣒⣗⡓⠛⠀⠀⠀⠀⠀⠈⠀⠸⢺⠍⠃⠀⠀⠀⠀⠀⠁⠊⡄⢑⡌⡄⠀⠀⠀⠀⠠⢎⠀⠊⣆⠀⠠⡄⠀⠀⠀⠀⡈⠑⠀⠀⠐
⠀⠀⠀⠐⣇⢠⡕⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡈⠑⠀⠀⠀⠀⠀⣢⡁⠀⢆⠀⢠⠀⠀⠀⠀⠀⠀⠀⡰⡡⠊⣁⠀⠀⠀⠀⠀⠁⢀⠖⠀⠒⠁
⠀⠀⠰⠂⠈⠋⠀⠰⠀⠀⠀⠀⠀⠀⠐⠚⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠀⠸⠀⠀⠀⠀⠁⠤⠊⠛⠀⠀⠈⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡠⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⡀
⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣀⡀⠀⠀⠀⠀⠀⠒⠐⠀⠊⠀⠀⠀⠀⠀⠀⢀⣁⣂⣀⡀⠈⣀⠀⠀⠀⠀⠀⡇⠀⡀⢀⢸
⠀⠀⢈⢀⠈⢈⢀⢈⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⢡⡄⠀⠀⠀⠀⢀⠄⠀⢁⠄⠖⠀⠀⠀⠀⣅⣀⣀⣀⡀⣀⢀⠅⠀⠀⠀⠀⠐⡇⡆⢸
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠇⠇⠇⠇⠏⠇⠄⠀⠀⠀⠀⠐⠇⠃⠸

⠀⠀⠠⠤⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠒⠂⠐⠐⠀⠀⠀⠀⠀⠀⣤⢢⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠀⠀⠀⠀⠀⢠⡄⠠⠤⠀⠀⡀⣠
⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠠⠈⠓⠇⠀⠀⠀⠀⠀⠀⠀⠻⡼⠇⠠⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉⠁⢠⡖⠀⠀⠀⢁⡀⣘⠂⠡⡤⠹
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢄⠀⠀⠀⠀⠀⢠⡰⠀⠐⠀⠀⠉⠀⠀⠀⠠⠴⠂⠬⡄⠃⠰⠀⠓
⠀⠀⠀⠀⠀⠐⠜⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠸⠀⠀⠀⠀⠀⠀⠄⠠⠅⠀⠡⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣐⡶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡟⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡫⣲⡶⠐⠏⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠠⠂⣰⠀⠀⠀⡇
⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⠂⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠠⠥⢂⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⣀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡆⠀⠀⠀⢠⣴
⠀⠀⠀⠀⠒⠩⣿⣷⠀⠀⠀⢀⣀⣰⣟⣀⠀⡉⠀⢉⣀⣀⣸⣿⣇⣀⣀⡀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⣧⢀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠈⠉⠉⠉⠉⠘⠛⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠈⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡗⣺⡿⠿⠿
⣀⠀⠀⠀⠀⠉⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⣿⣧⡤⠤⢀⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄
⣿⣿⣿⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⣿⣿⠿⠿⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣈⣉⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⣴⢦⣄⠀⠀⠀⠀⢰⡟⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠒⠛⠛⠛⠛⢷⡀
⠀⣾⠁⠀⠙⠷⠶⠒⠛⣋⠉⠀⠈⠳⡄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠁⣀⡠⠤⠴⠲⢶⡀⠀⠀⠘⡇
⢸⡇⠀⠀⠀⠀⠐⢾⡋⠉⣻⠀⡿⠚⠁⣌⣼⠀⠀⠀⠀⠀⠀⣠⠤⢾⣁⠀⠀⠀⡞⢁⣤⠀⠀⢀⣤⠙⠛⠋⠉⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠙⢶⡟⢸⡇⢀⣼⣳⡏⠀⠀⠀⠀⠀⣸⢁⠖⠉⠳⢴⡶⠿⠷⠟⠈⠛⠛⠋⠙⠷⠶⠦⣄
⠈⢿⡀⢀⣄⠀⠀⠀⠀⠀⠑⢿⣅⠈⣵⠟⠀⠀⠀⠀⠀⠀⠹⣌⠳⠤⠤⠿⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢷
⠀⠈⣷⠏⡈⢧⡀⠀⠀⠀⠒⣩⠽⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⣾⠛⠀⠀⠀⠙⠦⣄⣀⣤⠴⠃⠀⠀⠀⠘⡆
⠀⣼⠇⠀⠀⠀⠳⣤⣤⣤⣭⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⢠⡷
⠈⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡿⠋⠉⠉⢻⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣸⠁⠀⠀⠀⣠⣇⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣤⣄⠀⠀⢀⣤⣄⣀⡀⣼⡏
⠀⠀⠀⠀⠀⠀⢀⣤⠿⠀⠿⣤⡀⣰⠟⠑⠒⠲⣝⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠟⠛⣋⣉⣤⡀⢻⡄⠀⡿⢀⠤⢭⣉⡛⢳
⠀⠀⠀⠀⠀⢠⡟⠓⠒⠀⠀⠈⠻⡏⠀⠀⠀⠀⠈⡏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢟⠉⠀⠀⠃⠈⣇⢸⢃⣌⡀⠀⠀⠁⣼
⠀⠀⠀⠀⢠⣟⣀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⡇⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢨⣴⠆⠰⠛⠃⢹⡿⠀⢩⣁⠘⠛⢠⡏
⠀⠀⠀⠀⠘⣯⠛⠀⠀⠀⠀⠀⠀⣼⣄⠀⠀⠠⢞⡼⠷⢎⢻⡄⠀⠀⠀⠀⠀⠀⠀⢷⠀⡤⢦⠒⠊⠁⠈⣧⠀⢀⠃⢪⠇⣼⠁
⠀⠀⠀⠀⠀⠘⢦⣤⣤⠄⠀⢀⣴⠃⠈⠙⠒⠛⠉⣴⠖⠋⣼⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⢹⡭⠄⠀⠀⠀⢸⡄⠀⠀⠸⢠⡇
⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠻⣤⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⠂⠀⢀⣀⣠⣬⠟⠛⠲⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠛⠋⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠀⠄⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⢸⣏⣉⣉⣉⣉⣉⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⢀⣤⠞⠳⣄⡀⠀⠈⠛⢦⣀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⢀⣠⠞⠋⠀⠀⠀⠈⠙⠶⣄⠀⠀⠉⠳⣦⡀⠀⣿⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠙⠳⣯⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⣀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠈⠙⠶⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠈⠛⢦⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠙⠳⣤⡀
⠀⠀⠀⣠⡴⠛⠁⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠛⠓⠓⢻⠓⠒⠚⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠈⠙⠶⣄
⢀⣴⠞⠉⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠈⠛⢦
⠙⢧⣀⣠⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⠚⠒⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⣄⣠⠞
⠀⠀⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡤⠤⠤⠤⣤⡤⠤⠤⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⣶⠒⠖⠒⠒⠒⠒⠒⠲⠶⢶⡆⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⠆⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣤⣤⣤⣤⣼⣤⣤⣤⣤⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣧⣤⣤⣤⣼⣧⣤⣤⣤⣼⠂⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⣄⣀⣀⣀⣼⣄⣀⣀⣀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣧⣤⣤⣤⣼⣧⣤⣤⣤⣼⠄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣤⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡭⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠘⠒⡓⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠊⡠⠂
⠀⠀⠀⠀⢀⡠⠤⠺⢥⣀⡀⢀⣀⣀⣈⣁⣊⣑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⡴⢁⡔⠁
⠀⠀⠀⢀⠋⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⡇⠀⠘⠽⠀⡠⢎⣠⠊⢀⡀
⢠⠊⠉⠉⡤⡀⠀⠀⠀⠀⠀⠉⠑⣄⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⢈⠗⠂⠃⠚⠦⣀⠏⠀⣈⡁
⡇⠀⠀⡘⠀⠘⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡡⠔⠒⠒⠒⣲⠎⠒⢄⠀⠀⠀⠘⡄⠊⠀⠈⣆⡀
⠑⢄⠀⠱⣥⡴⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣠⠞⠁⡰⠀⠀⠉⠢⢀⢀⠇⠰⠖⠀⠀⣸
⠀⠀⢹⠁⡏⡆⠉⠉⠁⠈⠉⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⣂⣉⣠⡴⠀⠀⠀⡰⠁⠀⡰⢉⠔⠒⠢⡤⠌⡀
⠀⠀⢸⠀⠃⡇⠀⠀⢖⠒⠒⠓⠒⠒⠒⠒⢲⠒⠓⠒⢢⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⣎⠁⠀⠀⠠⠊⢀⠄⡔⠁⡀⠀⠐⠲⣧⡘⠚
⠀⠀⠘⠤⣄⡄⠀⠁⠀⠀⠢⠤⠄⠀⠀⠀⣼⡹⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⡃⠐⠒⠈⠑⢸⣋⣀⣤⡫⠊⠀⠚⠁⠀⠀⠐⢁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠉⠈⠁⠁⠀⠀⠀⠀⠉



⠀⠀⠀⠀⢀⠤⢄⠐⠁⠅⡠⢤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⢀⢄⣒⣒⣒⣒⣒⣒⣒⣒⠢⡀
⠀⠀⡤⡔⡁⢠⣤⠁⡵⢲⡗⢢⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠉⢰⠁⠀⢀⡸⠘⡀⠁⠄⡣⠠⠤⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡇⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠈⡒⠂⡎⠄⠀⠅⢤⠔⠁⢄⠀⠢⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡗⡄
⠀⠀⠘⠤⠠⢊⢱⠀⠀⣊⠜⠰⡱⠸⡀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢇⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠇
⠀⠀⠀⡠⠇⠀⠈⠐⢀⠃⢄⠤⣄⡠⠃⠀⡄⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⡇⠀⠀⢀⠤⣤⣤⣤⣠⢄⠀⠀⡇⡇
⠀⠀⢸⠠⢀⠵⠒⡖⠙⡄⠶⠆⠀⠀⠀⢠⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡀⠀⢮⡖⠟⠓⠛⠻⣦⠇⠀⡇⡇
⠀⠀⠈⣦⣄⣈⠔⠁⠀⠸⡄⠀⠀⠀⠀⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠧⡄⢠⠔⠓⠎⠉⠉⡖⠒⢤⡀⣧⠧⠤⡀
⠀⢀⢎⠎⠀⢀⠒⠐⠂⠂⠙⠒⠂⠀⠒⠋⠂⠒⠂⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢘⡧⠃⠀⠀⠘⠐⠒⠁⠀⠀⠡⣟⠀⠘⢃
⠠⡦⠃⠀⠀⢸⠒⠒⢒⣒⡒⠒⢲⡖⠒⢒⣒⣂⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠰⡾⣤⡄⢨⡏⢀⣀⠀⣀⣀⣀⣀⣀⣀⣈⣯⠀⣤⠻⣤
⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣐⣇⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣘⣒⣒⣓⣚⣓⣒⣒⣒⣒⣒⣒⣂⣒⣒⣒⣛⣚⣓⣒⣛
⣿⣿⠋⣋⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣴⣶⣦⣴⣾⣧⣄⢰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣾⣿⡿⠙⢻⣿⣿⣿⣿⢻⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡕⠋⠀⠉⠉⠛⠛⠛⠿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⠒⠋⢉⣀⣤⠏⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣭⠄⠀⠀⣀⣀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⣠⣴⣋⣬⠵⠖⠛⠉⠁⢳⠀⢨⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⣉⣀⡙⠳⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢻⠉⠁⣠⣴⣾⠿⠋⢠⣈⣷⠏⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣿⣟⢩⡆⠀⠀⠀⠀⠙⠛⠛⠀⠀⣠⣦⣝⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⢠⣀⡤⣵⣶⣻⠯⣎⡞⣿⡼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⢿⡛⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⡸⣽⢾⡾⣽⣙⣦⡀⣻⡼⣽⣷⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣯⠳⠀⠀⠀⠀⢠⡤⣤⣈⡚⢋⡼⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠃⡰⡻⣽⣮⢍⣛⣿⢿⣷⢳⢿⢧⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⢄⠀⠀⠈⠻⢷⡾⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼⠀⡀⢳⢹⣁⣸⣏⡁⢬⣽⣯⢟⣏⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠇⠀⠀⠀⠙⠦⣄⣀⣀⡰⠃⠰⠔⠊⠉⣆⠀⠀⠀⠀⠀⠸⠇⠀⠡⡀⢇⢿⣿⣿⣟⣿⠿⣿⣾⣾⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠘⢦⣀⠀⠀⠀⠀⢈⡏⡉⢴⠿⣷⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡀⠀⢘⡞⣜⣿⣽⣵⣿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⢀⣠⠤⠤⣄⠀⠀⢀⣠⣤⣾⠀⠀⠀⠈⠳⣄⠀⢠⣨⣧⣜⣄⣁⣈⣳⣀⠀⠙⠒⠒⢠⠀⠀⠀⠀⢹⠀⠘⢀⡜⠛⠉⠁
⠀⠀⠀⠀⠠⠋⠀⠀⠀⣿⣤⣶⡿⣟⢿⣮⣢⡀⠀⠀⠀⢀⠀⡿⠬⠧⠯⠤⠤⠤⠤⡼⡇⠀⠀⡰⠋⠀⠀⠀⢀⡟⠀⠀⡸
⠀⢀⡠⠤⢂⣴⣿⣷⣾⠋⠈⢻⣿⣮⣧⡳⣝⠧⠀⢀⣴⠟⠁⣋⠵⣻⣀⡛⡛⠛⠃⡇⡃⢀⣾⡇⠀⠀⠀⠀⡼⠁⠀⠀⠇
⡔⠉⢰⣾⣿⣿⣿⣿⣿⡀⠀⠀⣈⣙⣣⣽⡟⢆⣴⠿⠃⡠⠊⡡⠊⠙⠿⡿⣿⣿⠀⣿⡇⠀⢺⣷⠀⠀⠀⣸⠃⠀⠀⢸
⢇⡀⢸⢛⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣿⣷⡁⢪⠴⠊⣉⠭⠉⢛⣻⢖⡍⠀⣿⠟⣆⣼⣿⡄⠀⡰⠃⠀⠀⠀⡘
⠀⠑⠘⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣅⣿⣿⣧⠻⠔⠊⡠⠖⣋⡉⢙⡟⠃⢸⡿⠀⠹⣿⡻⢅⡴⠁⠀⠀⠀⠀⠇
⠀⠀⠀⡆⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣎⢿⡳⡀⠀⠒⡩⢤⣤⣀⣙⣛⡨⠟⠀⢠⣿⢀⡞⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠉⠒⢌⣹⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⠱⠗⡹⠃⠀⠀⡽⠀⠀⢀⣤⡆⡠⢀⣴⡿⠋⡞⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠈⣿⣿⡿⠟⢉⣠⠴⠦⣿⣿⣿⣿⡴⠋⠀⠀⢠⠎⠀⢀⡴⣫⡿⢊⣴⠟⠻⡄⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⢠⠜⢋⡤⠚⠉⠀⠀⠀⠸⣿⡿⠋⠀⠀⠀⣰⣷⣤⡴⢋⡼⠋⠀⣾⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠱⢏⣰⡀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⣴⢿⠟⠁⠐⠋⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠲⢤⣀⠜⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣤⣤⣼⣥⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿