Swayamvara Emojis & Symbols

⣿⣿⣿⣷⣴⣿⣿⣷⣶⠀⢠⣤⣴⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⣀⡀⢀⣤⣭⣭⣍⠉⠉⠉⠉⣿
⣿⣿⣿⣿⢻⡿⣛⣛⠁⠀⣾⡟⣿⠿⠿⠏⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶⣬⡛⣿⠛⠁⢻⣿⣿⣿⣿⣷⡄⠀⠀⣿
⣿⣿⣿⢿⣿⣿⡟⢡⠀⠀⢸⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⢹⠟⣋⢻⣿⣿⣿⡅⣀⣽⡿⣛⠻⣿⣿⡇⠀⠀⣿
⣿⣿⣿⠀⣿⣿⣥⣤⡀⠀⠀⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⢿⣿⡿⢻⣿⣽⡋⢫⣫⣼⣿⣿⡧⠀⠀⣟
⣿⣿⣿⣾⣽⣿⣿⣿⣿⠀⣶⣟⣿⠛⣯⡄⠀⠀⠀⣴⣶⣆⢀⣴⣿⠻⣿⣿⡄⢿⣿⣷⡾⣦⣿⣿⣿⣟⠀⠀⣿
⣿⣿⡗⣹⣟⣿⣿⣿⡿⣄⣿⠿⢿⣿⣗⣦⠀⠀⢸⡿⠉⣿⣿⠿⣯⠀⠺⣿⡃⣸⣿⡿⠩⣾⣿⣿⣿⡿⠀⠀⡿
⣿⣿⣧⣿⠿⣿⣿⣛⣿⣿⣿⣿⣿⣿⠿⣿⡄⠀⣿⡇⠀⢸⣭⠛⢹⣶⣿⣿⣿⠉⣿⣶⣤⠾⠿⣿⣿⡇⠀⠀⣿
⣿⣿⣿⢿⣿⣿⣿⣻⣿⡟⣿⣴⣿⣿⣿⣿⢯⡄⢹⣿⠀⣼⣿⠀⢿⣿⣿⣿⣿⡇⣿⣷⣦⣤⣤⣿⣿⣇⠀⠀⣿
⣿⣿⣿⣿⣿⣯⣿⣿⣿⣽⣿⣿⣿⣿⣿⣽⣾⣿⣼⣿⣼⣿⣿⣤⣼⣿⣿⣿⣿⡷⢿⡟⢻⡏⡏⣿⢿⣷⠀⠀⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⡿⣿⢙⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣧⣿⣼⣻⣿⡄⠀⣿
⣿⣿⢸⣿⣿⡋⢻⣿⣽⠋⣿⣿⣋⠻⢯⣿⡛⠋⠁⠙⠓⢃⣾⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣠⣤⣀⡀⠀⢠⣿⣿⣿⣿⣶⣦⣶⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⢈⣩⣭⠅⠀⣸⣟⣛⣛⠛⢿⣿⣿⣷⣜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⣤⣴⣶⣶⣾⠿⠿⣄⠐⠛⠿⣿⣿⣿⣶⣈⠻⣿⣿⣮⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢟⣾⣿⣿⠿⠋⡁⠐⠉⠀⠀⠀⠀⣈⠙⢿⣿⣿⣧⣈⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣼⠋⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡻⣿⣿⣿⡾⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⠀⠀⠁⣸⣿⡿⠁⠀⠀⠀⠀⠀⠀⠤⣤⠦⠂⠀⠀⠀⢳⣾⣿⣿⣿⣮⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢻⠿⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡀⠀⠀⠀⠈⠉⠀⡀⠀⠉⠙⠛⡛⠆⠀⠁⢀⣾⣿⢿⣟⣛⣲⣌⢿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⡓⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠸⣷⡄⠀⠀⠀⢰⡀⠃⠘⠻⣻⣿⣿⠆⠀⠀⠻⠿⣟⣿⣿⣿⠿⠋⢹⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡿⠁⣼⡄⠀⢸⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⢸⣿⣿⡗⠄⠀⠀⠀⠀⠀⠠⣤⡆⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⡷⠀⢹⠃⠀⠘⣿⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣴⡶⢿⡾⠛⠀⢠⠀⠀⠀⠀⠀⢸⣿⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⡆⢀⠁⠀⢻⠀⠄⠀⠫⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠈⠉⠀⡿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠘⠻⠇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠒⠀⢸⠁⢸⡇⢾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⢶⣶⣿⡶⡦⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢰⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡉⠂⠈⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠛⠛⠛⠛⠋⠁⠀⢀⣴⢿⣻⣿⣶⣦⡀⠈⠋⠀⠀⢀⣿⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠃⠱⠀⠀⣴⣶⣿⠃⠀⠀⣽⣿⡦⠀⠀⠀⢀⣀⣠⣤⣤⣶⣿⣿⡸⣿⣿⣿⣿⡳⣦⣀⣀⡔⠀⠉⠱⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⣿⣿⡿⠗⠐⢾⣿⣿⡇⠀⠀⠈⠙⠻⢿⣿⣿⣿⡿⠟⢻⡯⠁⠀⠘⡏⠸⢉⠙⢤⣤⣤⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠓⠀⠨⢀⣈⣀⢾⣿⣼⣿⣿⣷⠀⠀⠀⠀⠀⠀⠙⠻⢟⠻⠿⠦⡐⢄⠀⠂⢑⡀⠈⠁⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⠀⣼⠉⠉⠈⠘⢿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⡴⢼⠶⠂⢀⡀⣀⡁⠀⢠⣿⣦⣄⠀⠀⠀⠀⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⠀⣤⡀⠀⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⠀⣀⣤⠶⢋⠉⠙⣷⣿⠈⣿⣿⣿⢳⡿⠀⢀⡀⣼⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠉⠉⣀⣀⣨⣻⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣼⠋⠀⢸⠇⠀⣄⡿⣿⣶⣿⡿⡿⠀⠁⣤⠤⣙⠃⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠛⣿⣶⣶⣿⣿⣍⣉⣽⣿⣿⣿⡀⠀⠀⢀⣠⣴⡼⠿⣄⡀⢁⡠⢾⣽⣷⠟⣡⡛⢁⣰⢀⠄⠀⠴⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠐⠀⠀⠁⢄⡠⠀⠉⠉⠉⢃⣀⣹⠟⠛⠉⠉⠃⢰⣿⣷⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠐⠈⠀⣰⠇⠀⠀⡁⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠻⠀⠀⠀⠽⠿⠑

⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⢻⡿⠛⠃
⠀⠀⠀⠀⠀⠀⣿⣦⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⢤⡤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠉⣀⠐⣶⣤⣼⣿⣀⠉⣱⠶⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣻⣷⣤⣿⣶⣿⡿⣿⣿⣿⣿⡏⠁⠀⠈⠁⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣕⣿⣿⣿⣿⣿⣿⣿⣿⣥⡿⣻⣿⡿⠲⠂⠘⠃⠀⠙⠶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠟⢛⠿⠿⣿⣿⡟⢋⡀⢀⡀⠠⡆⠀⠀⣴⠌⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡇⠀⠄⠹⠷⢾⣿⣿⣷⣬⣁⠈⠁⠀⠀⠶⠄⠀⠀⠀⠘⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠘⡠⣦⢄⠂⠀⢸⣿⡿⠋⢰⣶⣶⡖⠒⠀⠀⠈⠑⠀⠀⠈⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠤⢮⠀⠀⠈⢉⣀⣴⣿⡟⣧⠀⠀⣰⠶⠂⠀⣠⡄⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠁⢠⣿⣿⣿⣧⣿⣆⣼⣦⣸⡄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⠖⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣥⡟⣤⣹⣿⣟⢳⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⠀⠁⠀⢻⡿⠿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡟⢻⠟⢿⣿⣿⣌⣻⣶⣧⣾⣿⣦⣀⣀⠀⠀⠀⠀⠀⠘⣿⣽⣿⣤⣀⡍⠉⠉⣿⣿⣿⣿⡳⣄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣬⣿⣿⡿⠃⠉⠈⠙⢿⣯⣈⣧⣹⢿⣿⡗⠀⠀⠀⠀⠀⣏⣹⠿⠛⠉⠀⣀⡼⣏⣻⣭⣿⡟⢢⠙
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⢿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠻⣿⢛⣼⣿⣷⠦⢀⣤⡾⣿⣍⢀⠠⠴⢶⣿⣿⣄⣿⢾⡗⢿⡟⠀⠙⠀⢀
⣟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⠁⠜⠛⠀⣹⡿⠛⠉⠀⠰⠀⠈⠻⣻⢶⣿⣹⡟⣿⡿⠂⠠⡄⠘
⡿⠃⠚⠷⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣴⡟⠙⡆⠀⠀⠒⠃⠀⠀⠀⠹⣿⡿⣽⠽⣿⡆⠀⠀⣀⠠
⠀⠠⠄⡀⣤⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣡⠌⣿⣷⣷⡀⠀⠀⠀⠀⠀⠀⠹⣷⣿⡛⣿⠓⠦⠀⠙
⡀⠀⠞⢳⠏⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⣾⣿⡶⢟⣦⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠀⠀⢶⠀⠐
⠇⢠⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠇⣹⢿⡿⢶⡀⠀⠀⠀⠀⠀⠀⠈⣁⢀⡀⠀⠈⣷
⣷⡄⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣦⠀⣀⣎⡿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣼⣇⠈⠟⢀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠐⠇⢸
⣿⣿⣷⣦⣼⣻⣿⡄⠠⣤⡒⠛⢃⠈⠻⣃⠀⠀⣠⠈⠉⡿⢻⣟⣦⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢁⣾⣿⣧⠀⠀⠀⠀⠀⠈⠃⠋⠉⠐⠒
⣿⣿⣿⣿⣿⣿⡏⣀⢴⣿⣿⡀⠈⠀⡠⢌⢥⡀⠁⠀⠀⠀⠀⢻⡝⢫⣙⣳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⢈⣛⣉⣽⡄⠀⠀⠀⠀⠐⠂⣀
⢿⣿⣿⣿⣿⣿⠟⠙⠓⠿⢮⣁⠀⡀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠘⣿⠿⠏⣸⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣿⠟⣉⣿⡀⠀⠀⠀⠀⢤⡌⢴⣆
⠈⠻⠿⠿⠟⠋⠀⠀⠀⣠⣤⣼⡟⠑⠂⠠⠀⠀⢀⡶⡀⠐⠀⠀⠀⠈⠻⡎⢻⣿⣻⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⡿⢷⡄⠀⠀⠀⠁⠈⢆⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠀⠀⣀⣠⣄⣤⠎⠻⣇⠀⡀⠀⠀⠀⠀⠘⢿⣿⠻⣌⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣷⠟⣷⠀⠀⠀⠀⢵⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢀⠀⠿⠶⠿⡟⡿⠻⠏⠀⠀⠈⢿⣦⣀⠀⠀⠀⠀⠀⠛⢠⣿⠻⣾⣷⣠⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⠀⠀⠀⠸⣧⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠐⠃⠀⠀⠀⠀⣠⣿⡽⠟⠁⢄⠀⠀⠀⠀⠀⠙⠿⣿⠙⣼⣷⡶⣦⣀⡀⠀⠀⢀⣿⣿⣍⣼⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠂⡀⢀⣦⣳⣬⡹⡁⠀⠀⠀⠑⢀⡀⠀⠀⠀⠀⠉⠙⢿⣿⣾⣿⣿⣍⣳⣶⣿⣿⣿⣿⣤⣤⡄⠀⠀⠀⠘⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⡿⠇⢈⣧⠙⢘⣦⢄⣀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠿⣿⣻⣿⣿⣿⣉⠈⠛⠛⠂⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠸⠈⠀⠀⠀⢉⠶⠀⠀⠾⠻⡟⠀⠀⠀⠄⠀⠀⢠⡄⠀⠀⠀⠀⠈⢁⣿⠃⠹⣧⠛⣤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠁⠀⠀⠀⠀⢩⣶⠀⠀⠀⠰⢋⣤⠀⠀⠀⠑⢈⠳⣟⢦⡀⠀⠀⠀⠘⣿⣄⠀⠙⠹⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⡄⠀⣀⠀⣠⠀⠀⢀⢀⢸⣿⡗⣀⣶⡀⣨⣿⢇⠀⠀⢀⡈⠳⣯⠾⣇⠀⠀⡀⠀⠉⣄⠀⠀⣀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⠃⡸⠁⢸⡇⠀⣿⠀⣴⠃⢸⠀⣾⠁⢈⣿⠟⣶⣿⣟⠁⠠⣿⠂⢴⠻⣶⡟⠀⣼⠃⢠⠏⢠⠀⠈⡍⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⡇⠀⣼⠄⢨⣇⣸⣧⣠⣦⠰⣍⢀⡼⢃⣰⡍⣿⣿⣿⣾⣼⣔⠃⡇⢸⡟⣠⠋⣀⡦⢀⣼⠀⣴⣧⡴⠋
⠀⠀⠀⠀⠀⠀⢰⡄⢀⠇⠈⡇⡐⠏⢀⡾⢠⣿⠈⢱⡏⢀⡈⢀⠇⢸⡏⠀⢸⣿⣿⡟⠻⢿⣿⡷⣸⣧⡼⢦⣽⠁⢠⡏⠀⣿⠀⣇
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠀⠀⠉⠰⣾⢇⠀⠈⠃⠈⠉⠁⠀⠈⠀⠀⠘⠉⢟⣷⠀⠀⠉⠙⠈⠛⢄⠙⠃⣠⣴⠛⢿⡇⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⣳⣟⣤⣼⣤⣶⣤⠀⠀⠀⠀⠀⢸⠓⣧⠀⠀⠀⠀⠀⠈⢲⣤⡾⠃⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⣤⣽⣎⣿⢾⡷⠄⠀⠀⠀⠀⠛⣼⠀⠀⠀⠀⠀⠀⠹⣏

⣿⣿⣿⣿⠟⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠛⠿⠺⢿⣿⣿⣿⣿⣿⣹⣷⣄⡟⣻⣧⣸⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇⠘⣃⣾⣿⣿⣿⣯⡉⠿⣧⡙⠻⢶⣿
⣿⣿⣿⣃⣠⡄⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣶⣉⠻⣿⣿⣿⡋⠹⣿⠃⣿⣿⡇⣽⣿⣿⣷⢹⣿⣿⣿⡟⢁⣿⡿⣿⡿⠋⠛⣿⣿⣦⠹⢿⣇⡀⠉
⣿⣿⣿⣿⣥⠷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣬⡙⢿⣿⣦⡝⠈⣿⣿⣇⠹⣏⢿⣿⠸⣿⣿⡏⢠⣾⣿⣿⣿⣿⣷⣄⡈⢷⡜⢿⣎⢿⣷⣀
⣿⣿⣿⡿⣿⡿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠛⣿⣿⣧⠘⠿⢿⡿⠃⣸⣿⣿⣦⠹⢸⣿⣷⡝⠟⢁⣼⣿⡟⢿⣯⡉⠳⣮⡙⢿⣿⠄⠻⣷⡝⢿
⡟⣁⡌⠀⠈⠁⠀⠀⢤⠀⣹⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣿⣿⣆⠸⢿⣿⣿⣿⣧⠀⣼⣿⣿⣿⠁⢃⣿⣿⡿⢡⣾⣿⣿⠟⣷⡄⠉⠻⣦⡉⢳⣦⡀⠀⠀⠈⣿⣦
⠟⠛⠇⠤⠀⠀⠀⠀⣬⠁⠙⠛⠉⠉⠉⠛⠛⠛⣿⣿⣿⣿⣿⣿⣷⠘⢿⣿⡿⢃⣼⡿⢿⡟⣿⣧⢸⣿⠟⣵⣿⣿⣿⢿⣦⡈⠻⣄⡀⠈⠻⣷⣿⠻⣦⡀⣾⡇⠉
⠃⠸⡇⠀⠀⡀⠀⢰⠋⠀⡄⣶⠦⠆⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣿⣶⣶⡀⣸⣿⣿⣇⣰⣿⣿⢸⣿⡾⣿⣿⣿⠻⣧⡈⠙⣷⣜⠿⣦⡀⠈⠙⢷⣝⡻⣧⡀
⠄⠀⠀⠀⢰⡇⠤⠌⠀⠀⣿⡇⠀⠳⠄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣧⣤⡌⢻⣿⣇⢿⡿⠿⣆⠀⢻⣦⠀⠙⠿⣮⡻⢶⣄⠀⠙⢿⣟⢻⣤
⡄⠀⠀⢸⣿⣿⡇⠀⠀⠀⠉⠁⢀⠀⠀⠀⡀⠀⠀⣠⣹⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⠿⠟⢷⣿⣤⣿⣿⣿⣷⣄⠹⣶⠀⠙⢿⣄⡀⠈⠹⢶⣍⠻⣦⣄⣽⣿⣿
⡇⠀⠀⠀⢿⣿⠇⠀⠀⠀⢠⡀⠀⠀⠀⠈⣱⠆⠠⡄⠺⣿⣿⣿⣿⣿⣿⣿⣷⣬⣍⢻⣿⣷⣜⣿⣿⣝⣿⣿⢷⣬⡳⣿⣦⣤⢤⣭⣛⣷⣦⣴⣿⣷⣼⢽⣏⣥⣬
⣇⢀⣀⡀⠸⡏⣴⣦⣠⡄⠈⢠⡆⠀⠀⠀⠛⠂⠶⣶⠺⠹⣿⡿⢿⣿⣿⣿⢿⣿⣿⣎⣹⠿⣿⣿⣦⡝⢿⣿⣄⠈⢻⣾⣝⣷⣤⣈⠉⠻⢿⣿⡿⣿⣷⣾⣿⠟⣿
⣿⡋⠍⠁⠐⠇⠉⢉⡏⠑⠀⠀⠀⢀⣀⡀⠀⠀⠀⠹⣄⣀⣽⣴⣼⣿⣟⣻⡇⢿⣿⣟⣻⡇⣿⣿⣿⣿⣎⣷⡈⠻⢷⣏⠉⠻⣾⣟⡷⣦⣤⣿⣿⣿⣿⣿⣷⣼⡟
⠙⠻⠆⠂⢾⣶⡴⠋⠱⠆⠀⠀⠷⡾⣧⣷⣴⡆⠀⠄⠹⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⠿⣿⣿⣿⣿⣿⠻⣆⠀⠙⠷⣦⡀⣉⣻⣽⣿⣿⣿⣿⣿⡟⣶⣴⣾
⢀⣤⡀⠠⣾⡿⠁⠀⠀⠀⢁⡠⠿⣿⣿⡿⢿⣠⣤⠔⢡⠀⣼⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣷⣿⣶⠿⠷⣿⣿⣿⣿⣿⣿⣿⢟⣭⣴⡿⠛⣻⣿
⠘⣿⣷⠀⠈⠀⢀⠀⠀⠹⣿⣦⣀⣯⣻⣿⣿⣿⣿⡆⣠⡾⢻⣿⣆⣉⢵⣿⡟⢉⠟⢛⡿⠻⣿⣿⣿⣟⣈⣻⣷⣬⣙⣿⣶⣾⣿⣿⣿⣟⣉⣥⣾⣿⣿⠒⣿⡿⢏
⣾⣿⡁⣠⡔⢃⣬⣃⣃⣰⣿⣹⣿⣟⣿⣿⣿⢿⣿⣿⣿⠷⠛⠛⠟⢉⣀⠛⢡⣟⣠⡾⢃⡤⠀⣼⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣽⣷⣿⣿⣯⣴⠟⢣⣾⡿⢰⣿
⠻⠃⠙⠉⠛⠋⠉⠉⠉⠿⠟⠟⢻⣻⣯⡞⠁⠀⡴⣄⠀⠀⠰⠁⢷⡜⣡⡿⢋⡿⠿⣷⣏⣤⡾⢁⣴⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⠐⢛⣉⣴⣮⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⡈⠉⢁⠀⠈⠀⠀⣄⢰⢉⡾⠋⠀⠚⠁⠰⠆⠻⣿⣶⣛⣧⠀⠘⢟⡹⠎⣹⣿⣿⣿⣟⣋⣭⣽⣛⢋⣵⣿⣿⣿⡿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⢽⣯⣀⣈⡀⢀⣀⣦⠘⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⣭⣥⣴⣶⣿⣷⠂⣿⡿⣷⣬⡿⢿⣿⣿⣿⣿⠿⢿⣿⡏⣠⣼⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣀⡈⠋⠉⠟⢉⡨⠯⣴⡀⠏⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⡿⢟⣋⡀⣿⣾⣿⣿⣷⣮⣻⣆⢠⣀⣶⣾⠃⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠀⠀⢠⣬⡥⠾⠋⠀⠀⠀⣿⠷⠞⠓⠀⢀⣠⣤⠴⠿⠟⠛⠃⢀⡈⠋⣁⣿⣽⣿⣿⣿⣿⣿⣤⣶⣟⣛⣥⣬⣝⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠟⢻⡷⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠐⣅⠀⡀⣰⡤⠀⠀⠀⠀⠀⠆⠀⠀⠠⠆⠀⠀⠀⢠⠄⢸⣿⣿⣿⣷⡆⢸⣟⣫⡝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠀⠀⢰⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⠐⠃⡇⠀⠈⠉⢙⣻⣿⣿⣿⣿⣥⡾⠛⣉⣩⣿⣿⠛⢿⣿⣿⠻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠰⣶⠇⠈⠲⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⢻⣧⡼⠋⠻⢶⣿⠟⣋⣥⣽⣷⠋⠟⠙⢶⣿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⢰⠟⠀⠀⠀⠚⠀⠀⠈⠀⢀⣄⠘⠎⠀⡄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⡀⠈⠻⢾⣟⣉⣄⣙⡄⠘⠓⢼⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⣾⢶⣶⠆⣸⠟⢀⠒⠀⠀⠀⠠⣄⡦⠀⠀⡄⠀⠈⠀⠀⢃⠀⠀⣹⣿⣍⣉⣻⣦⠀⠀⠀⠙⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⡦⣹⡶⠁⠀⢀⣀⣀⠤⠔⠒⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⣠⣿⣯⣉⣽⠟⠀⠢⡀⠀⠀⠀⠙
⠀⠀⠀⠀⣠⠶⠶⠒⠒⠤⠀⠀⠀⠀⣀⣀⣀⢀⣀⣀⢀⡀⢠⣿⣶⠟⠓⠂⡐⠚⠥⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣶⣾⡟⢻⣬⡽⠋⠀⠀⠀⠰⡆
⠀⠀⠈⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠁⠀⡖⣁⣀⡀⠀⣀⣠⠖⡴⠿⠀⠀⢀⠀⢀⣴⣎⢡⣤⣭⡿⠟⠁⠀⠀⠀⠀⠀⠀⢿⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠶⠿⠟⢀⡿⠋⠀⠀⠚⡇⠀⠀⠀⠈⣴⣮⣤⣿⠟⠋⢀⠙⣄⠀⠀⠀⠀⠀⡀⠀⢸⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⡠⠂⠀⠀⠁⠀⠀⠀⠀⢧⣾⡛⠁⡤⡀⠀⠀⠀⠻⣤⠀⢠⡀⠹⡄⠈⢻⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠘⠃⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠨⣼⠿⠟⣠⡇⠀⠀⠀⠀⣿⡇⠀⣃⠀⢹⡄⠀⠻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡠⢰⣶⣦⣶⣦⣄⡈⠛⠛⠋⠁⠀⠀⠀⠀⠋⠃⠀⣿⠀⠀⢹⡄⠀⠈
⠃⠀⠀⠀⠀⠑⠂⠀⠖⠀⠀⣦⠶⢸⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠀⢤⠇⠀⠀⠂⠼⠿⠟⠙⠛⠲⣤⣄⣠⣤⣤⣬⣿⣿⣷⣶⢋⣀⣤⣤⡔⠀⢀
⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⠷⠶⢿⣿⣿⡿⢿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠿⠋⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠛⠷⢾⣍⣻⠿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣀⣀⣀⡀
⠄⠐⠀⠀⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠉⠋⢹⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⡀
⠓⠾⠿⣤⠄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂⠈⢁⣤⣤⣌⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠉⠉⠉⠉⠉⠙⠛⠛⠛
⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⡶
⣿⣿⣿⣛⣻⣛⣻⣿⣿⣷⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠿⠦⣤⣀⣀⡀⣀⣀⣤⡶⠊⠙⠉⠋⠉⠉⠉⢉⠉⠁⠉⠉⠉⠙⠳⡤⣤⣀⣀⣀⣀⣀⣠⠶⣇⣤⣀
⠀⠙⠶⣤⣀⡀⠀⠀⣀⣤⡶⠻⠃⠀⠀⠀⠀⠈⠙⠋⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠁⠁⠉⠋⠛⠙⠈⠈⠀⠈⠈⠙⠻⢲⠆⠐⠆⠻
⠀⠀⠀⠈⠉⠙⠛⠟⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⢀⣴⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⢠⣔⡄⠂
⠀⠀⠸⣬⣀⢀⢀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢀⣴⣿⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡅⠀⠸⡭⠉⣿⣆⠀⠀⠀⠐⠘⠝⡷⠖⠋
⠀⠀⠀⠸⡧⠰⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠛⢆⠀⢀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⠀⠘⡉⣶⣅⢹⢧⠀⢀
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡃⠚⢁⠃⠀⠈⠀⡀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⢰⢱⠀⠀⠀⠀⣀⣀⠀⠀⢀⡈⠀⠤⠁⠀⠀⠀⠀⠀⠀⠱⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠁⢿⡀⠀⠘⠶⠰⣷⠀⡀⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⣯⣾⠇⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠄⠀⠀⠀⠀⠀⠀⡤⠀⠀⢸⢽⠀⣽⡀⣤⠀⠀⠀⢿⠐⠇⠀⠀⠀⠉
⠀⠀⠠⠤⡄⠀⠀⠀⠈⠁⠀⠀⠀⣿⡇⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⣿⠀⠡
⠀⠀⠀⠀⠹⠀⠀⠀⠀⠰⠃⠀⠀⢹⣿⣶⣶⠀⠀⠀⢠⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣿⣿⠟⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠳⣤⡀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣙⣳⣶⠶⣟⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⣸⠟⠛⠛⠛⠛⠃⠚⠛⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠐⠠⠤

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣠⠟⠡⡄⢤⢠⡕⢠⠴⡉⢄⡀⠠⠘⡮⠁⠀⣀⠠⡄⢠⠀⡄⠠⠄⢠⠄⣀⠀⢠⠄⡀⠀⣄⢀⡀⣀⠀⡀⢀⠀⡀⠀⡀⡙⢤⡂⣀⡀⢀⡀⣀⠀⣢⣀⢀⡁⢀⡠
⠀⠐⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠙⠀⠁⠈⠁
⡀⠀⡀⢀⠀⠀⠀⣀⠐⡠⣄⠠⢄⡀⡐⢀⡀⠒⢀⠠⡢⠄⢐⡂⢀⢘⢢⡀⢘⠢⡀⢐⠰⣤⢂⢄⡀⢐⢢⡤⢈⠠⡄⢘⠀⡀⢚⠠⡀⠐⡃⡄⠀⠀⢄⠀⠀⣄
⣞⢶⣏⠀⠁⣉⣷⢋⣬⠋⢸⡛⢛⠇⠛⢺⡏⠉⠙⠋⠋⢻⠉⠉⣻⠙⣻⣿⣿⣟⡿⣿⣿⠿⣹⡿⢻⡟⠉⡟⠛⠙⡟⠛⠑⡟⠚⠛⡗⠘⠃⡞⠛⠻⠞⢷⣿⡑⢚
⣏⢿⡏⠛⢋⠁⡶⠄⢁⡠⢙⡓⢸⡗⡀⠈⡅⠒⠊⡴⠀⢨⠀⠀⣩⠀⠻⢿⣿⣿⣟⠶⣾⣿⣿⡏⣻⡇⠀⡅⠐⠒⢣⠐⠐⢃⠀⠐⢀⠀⠀⡓⢰⠀⠛⣡⡜⣉⢛
⠢⢤⡢⣾⢡⡞⠄⠀⠂⠀⠔⠛⠶⠊⠃⠐⠂⠁⠰⠅⠃⢢⡈⠀⠀⠈⢀⡉⢿⣾⢹⡿⡷⡛⢫⠟⡏⠀⠀⠔⣠⡀⠈⠀⢀⠀⢁⠀⢀⠀⠀⡀⠈⢠⡿⠤⢁⠉⣃
⣄⢾⣿⣽⠷⣤⡄⢘⠂⠄⠈⠀⠆⠀⠐⠀⠀⠊⣙⣍⣣⠀⡅⠀⠦⠀⣰⡀⠠⡏⠉⠷⠐⠳⠀⠀⠠⠀⣈⣾⣿⡷⠴⠀⠬⡀⠸⠀⠐⠂⠠⠄⠂⠄⢠⠀⠠⣩⠉
⢿⡇⣽⠛⡋⠁⠁⠀⠀⠀⠀⠀⠂⠀⡂⠀⣤⣿⣾⣿⣿⠀⡀⠀⣇⠀⢴⠀⠠⡇⠀⣟⠀⢸⡀⠀⠇⠀⠻⣿⣿⣷⣦⠀⠀⠈⢀⠀⢸⠁⢸⠀⠀⠀⠀⠈⠀⠃⠲
⡆⣸⡿⠟⠃⠀⠀⠀⠀⠀⠀⢀⡁⠀⠇⠀⠘⣿⣿⠡⠤⢅⡃⠀⠒⠀⣸⠀⢘⠃⠀⠶⠀⢸⠀⠀⠆⠀⠙⠉⠿⢿⣿⡇⠀⠀⠀⠂⢰⠄⠐⠀⠀⠀⠀⠀⠀⠀⢠
⣵⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡃⠀⣀⣿⣿⠀⠀⠈⠇⠀⡋⠀⢬⠄⠀⠀⠀⣋⠀⢸⠀⠀⠄⠀⠀⠀⠠⣼⡟⢊⡿⠀⠀⠘⠀⢀⣉⠀⠀⠀⠀⠀⠀⠀⢀
⡟⣧⣤⣠⠶⢂⠀⠀⠀⠀⠀⠠⠄⠀⠆⠀⣿⣿⣏⣀⣄⣀⠃⠀⡆⠀⠂⠀⢲⠂⠀⠧⠀⣨⠀⠠⠇⣀⠤⠀⠸⣍⡛⠛⠉⠀⠀⠀⢑⠀⡸⠀⠀⢀⣀⡀⢀⠀⠈
⢱⡏⠹⡳⡶⢨⡆⠀⠀⠀⠀⠀⠀⠀⡃⠀⠃⠈⠻⢿⣏⢱⢣⡔⠁⠀⣀⠀⢸⠀⢈⡋⠀⠠⠀⠈⡋⠙⣶⣴⠦⠟⠋⠀⠀⠀⠀⠀⠈⡀⡒⠀⠀⣮⡾⣽⣮⠀⠘
⣾⠻⣧⣿⣻⡍⠀⣀⠀⢀⠀⠐⠂⠀⡄⠰⠦⣤⢲⣼⡟⢸⢸⡁⠠⠈⢈⠀⢸⠀⠀⡇⠀⠚⠀⠘⢷⠂⡅⠃⠰⢤⡤⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⢈⣙⣉⣛⢶⡄
⢹⡀⠟⡟⡉⣴⠗⠟⣿⣿⡆⠐⠀⠀⠂⢸⠏⠀⠈⠙⠐⢣⡌⠠⠄⠀⡰⠀⢸⠀⠀⣏⠚⡙⣹⠀⠈⡡⠀⢀⣀⣀⠃⠀⠀⠀⠀⠀⠀⢨⠘⠁⠀⠭⣶⣯⣉⠣⠻
⠈⡿⢠⠿⣇⣴⣾⡛⠿⠌⠁⠀⠁⠀⡇⢸⠀⣄⠈⣿⡆⢒⠀⠰⠁⠀⠛⠀⣸⠀⠀⢹⠈⣓⠉⠈⠃⣺⣈⣉⣉⣉⡄⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠑⠈⠙⣿⡆
⠀⠁⢸⡜⣹⠋⢉⠅⠠⡀⠀⠀⠀⠈⠅⣸⢈⣉⣼⢿⠛⠙⡀⢨⠀⠀⡅⠀⢸⠀⠀⠀⡂⢽⣼⠀⠀⠗⠱⠃⠳⠐⢲⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠋⠉⠳
⠀⠀⠈⣰⢿⣆⣩⣼⡣⠁⠀⣀⠀⠀⠆⣿⣉⠫⢿⣸⢦⡀⡄⢐⠀⠀⠇⠀⠿⠀⠀⠀⠀⡹⡾⠀⡏⠈⢁⢁⡁⡩⠁⡆⠀⠀⠀⠀⠀⠀⡅⠠⠀⠀⠀⠀⠀⠙⠓
⣄⢀⣰⠇⣸⣿⣧⣤⠀⠀⠀⠨⠀⠐⡀⠈⠀⢀⡜⠉⡀⠀⠀⢈⠀⠀⡃⠀⣿⠀⠀⠑⣂⢇⡄⠠⠀⠀⢸⡠⠉⠀⢠⠘⡀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠹
⠘⠀⣿⣼⣏⣠⡀⠀⠀⠀⠀⢐⠀⠠⠀⠘⠒⢉⠇⡀⠗⠴⡆⠠⠀⢀⡅⠀⣿⠀⢨⣿⢀⡿⠀⠄⠠⠀⠀⠁⠀⠀⠼⠀⠃⠀⠀⠀⠀⢨
⠀⠀⢿⠇⣈⠉⠁⠀⠀⠀⠀⣨⠀⠐⣀⢠⠤⠞⠰⡧⠀⢀⣁⡞⠀⠰⠆⠀⣩⠀⠰⠉⠙⠂⠀⣀⠀⠀⠀⡀⠠⠂⠀⠀⢈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⡆⢘
⠀⢀⡞⠙⠁⠀⠀⠀⠀⠀⠀⣬⢠⠼⠓⠛⠀⠀⠠⠈⠁⠿⠿⠯⣆⣀⡁⠀⡶⠀⢸⡁⢸⣥⠿⡛⠃⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠀⣠⠃⠐⠀⠀⠀⠀⠀⢠⡶⠈
⠖⣻⠐⠟⠁⠀⠀⠀⠀⠀⠀⡹⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⣟⠃⠀⣩⠀⠐⠂⣸⡁⠀⠽⣎⣩⡄⠈⠠⣂⣠⡄⠉⠧⡔⢂⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁
⠛⣿⠾⠏⠀⠀⠀⠀⠀⠀⠀⠂⠾⣦⢤⣄⣀⣀⣀⣀⣀⣀⣀⣤⣞⣯⠀⠀⠛⠀⠈⠁⠉⠙⣗⣦⢤⣤⣄⣀⣤⢤⠤⣤⠄⠞⠋⠉
⠀⣇⣰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠙⠿⠉⠙⠽⠛⠷⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠂⠉⠺⠊
⠀⠿
⡠⠆⠆⠠⡰⢆⠲⡠⠆⠀⠀⠤⠰⠆⠠⠆⠠⠀⠦⠠⠄⡰⠆⠴⠀⠄⠰⠆⠠⠄⠴⠀⠲⠐⠓⠐⠂⣐⢃⡘⠲⠂⠀⠂⠘⠀⢘⠢⢒⠐⢃⣜⢢⣈⠛⠛⣘⠀⣳
⠉⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⠀⠈⠈⠉⠈⠉⠈⠉⠁⠉⠉⠉⠉⠈⠀⠀⠈⠁⠀⠁

⠰⠒⣄⠲⢀⡀⠶⣄⠰⠄⡄⠠⠀⠀⠰⠀⠀⠠⠀⠀⠠⠀⡀⠦⠀⡠⡄⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⢄⠀⠆⠠⠐⠶⠀⣰
⢠⡀⠁⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠉⠀⠀⢉⠀⠀⠉⠁⠀⠁⠀⠈⠁⠀⠉⠀⠀⠈⠁⠀⠀⠉⠀⠀⠁⠀⠀⠉⡀⠀⠈⠀⠀⠉⠁⡀⠈⢋
⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠋⠀⠆
⠘⠀⠀⠀⠀⠐⢀⠀⢄⠀⠀⠈⠀⠤⡀⠒⣄⠀⠄⢀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⢀⠈⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠁⠠⠀⠓⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⢠⠂⢀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠒⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠠⠀⠀⠀⠀⠈⠁⠀⡀⠀⢀⣄⠀⣤⠀⠀⠴⠃⠀⠲⠀⠈⠀⠀⠀⠄⠀⠂⠀⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⢗
⠀⠰⠀⠀⠀⠂⠠⠀⠀⢸⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠘⢀⠀⠀⢀⠀⠀⠀⠀⢸⣿⡟⠋⢠⡌⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⣄⠹⢿⣿⡷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠠⠈⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⡿⠷⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠸⠀⡀⠀⠁⠀⣌⢱⣾⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠌⠓⢓⠛⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬
⠈⢀⡄⠋⠁⠀⠀⠘⠻⣿⣿⣃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⢀⠐⠀⠀⠀⠀⠀⠀⠈⠐⡆⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠐⠁⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠈⢠⠀⠘⠀⠀⠈⢴⠀⠀⢼⠆⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⢠⢠⠄⠉⠁⠀⠘⠿⢾⣶⣼⣷⠷⠤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠠⠀⠀⠀⣦⣤⣴⠶⠚⠛⠉⠀⡀⠀⢰⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠐⠈⠀⠹⡅⠄⣄⠀⠠⢀⠀⠃⠀⠠⠙⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠀⠃⠈⠁⠁⠉⠉⠈⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠘⠁⠰⠀⣸⠆⠀⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⠀⡌
⠀⠘⠠⠙⣤⡤⠀⠀⠀⠀⠀⠀⡁⠀⠀⢹⡀⡀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢐⠀⠀⠀⠰
⠈⢀⠐⡂⠁⠄⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠈⠃⠀⠄⠀⠀⠀⠀⠁⣼⠀⡆⢰⠀⠄⡦⠠⠄⣶⠀⠀⠸⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃
⢀⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠈⢁⠘⡃⢀⠀⠀⠀⠀⠀⠀⢠⡀⢀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠁⠈⢁⡀⢀⡄⢀⢠⠄⠆⡴⢢⠲⡄⢀⠀⠀⠀⠂⠀⠀⠀⠀⠘⠀⠤⠀⢩
⢀⠈⠀⡵⠿⢠⡔⠉⠀⠀⡀⠀⠙⠛⠶⠏⠀⠀⠀⠄⠈⠀⠁⠀⢁⠀⡄⠈⠡⢸⠈⢀⣀⠳⣦⠞⡡⢋⠤⡄⠈⡆⠀⠀⠀⠀⠔⠀⠀⠀⡖
⠀⢀⠀⠀⠀⠸⠢⠀⢸⡗⠊⠀⠀⠐⠸⠀⠈⠀⢐⠀⡀⠀⠠⠠⡄⠸⠀⠠⡔⠂⣭⠊⠀⠀⠀⠈⠕⠡⠐⠁⠄⠃⠀⠀⠀⠀⠂⠀⠀⠀⠘
⢠⡈⠀⡁⠀⠀⠀⠄⣴⡧⠀⠀⠴⠛⠚⢣⠀⠠⠏⠙⠺⣤⠀⠀⠀⠦⢂⡰⠆⠒⡆⠓⡖⠒⠒⠐⢚⠓⢓⡦⡜⠣⡤⠈⠄⠀⠐⠀⠀⠀⢋
⠀⣰⠀⠅⠀⠀⢻⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡆⠀⠀⣶⠊⠐⠀⠈⠉⠉⢡⠀⡀⠀⠀⠀⠀⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⢰⡮
⣠⡙⠀⣤⠀⠁⠺⣄⣀⠐⠀⠀⠀⠀⠀⢀⡀⠀⢀⣠⣴⠉⡇⠀⠄⡉⢀⡀⠀⠀⠐⠀⠂⠀⠀⠐⠀⠀⠀⠀⠘⠙⠂⠀⠀⢀⠀⠰⠄⠚⠱
⠡⣰⡠⠴⠒⣤⢆⣹⠉⠙⠛⡛⠛⠺⢀⡈⠍⠐⢉⡀⠈⠀⠀⢀⢀⠀⣉⠀⠲⠂⢀⠠⠠⠄⠀⠒⠶⠀⠂⠲⠂⠀⠀⠀⠀⠀⠘⠀⢀⠰⠖
⡮⠬⡃⠀⡄⠠⠦⠁⢤⠄⠀⠉⠀⠤⠄⠀⠠⠀⠈⠀⡄⠀⠁⠤⠀⠀⠡⠀⠀⠄⠀⠀⠠⠀⠀⠀⠆⠀⠀⠰⠆⠀⠀⠀⠀⠉⠀⠀⡀⢀⡜
⠁⠘⠛⢛⡒⠶⣀⣄⡺⢂⢢⡒⠃⣠⡐⠃⣄⢘⠃⢠⠉⠋⣦⡼⠛⣤⠘⠃⢠⡌⠛⠀⣤⠜⢣⢠⡔⠛⢡⡶⡟⠛⣔⣻⢋⣗⠛⠛⠚⠛⢣
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠁⠉⣉⣉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣿⣿⡍⣉⣹⣿⣟⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⠿⠟⠃⢰⡏⠀⣿⠀⠝⢉⠙⣿⣿⡿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⠚⠉⠀⢸⣷⣀⣽⠀⠀⠈⢡⣿⣿⣳⡃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⠿⣵⣦⣴⣾⣿⣿⣿⣶⣾⣏⣚⣿⣿⣿⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⡟⣈⣿⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⡿⣻⣟⣟⣻⣿⣿⣿⣎⣙⣻⣿⣿⣿⣿⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⡤⢤⠄⠠⢠⢤⡤⡄⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠤⠄⣀⡀⠠⡀⣀⠀⡀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⡀⢀⠀⠀⠀⣀⢀⡀⣀⡀⣀⣀⢀⣀⣀⢀⡀⠀⣀⣀⣀⣀⢀⢀⣀⡀⡀⡀⠀⠀⠀⠀⠀⠀⡀⢨⣵
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠙⠻⣿⠤⠼⡟⠋⠿⠋⠉⡉⠙⠉⠍⠉⠹⣿⣿⣿⣿⣿⡇⠘⠉⠉⠙⠉⠋⠹⠉⢿⡿⣬⡿⡿⣻⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣍⣲⣾⣖⠀⠀⠉⠂⠀⠁⡶⠀⠂⠈⠀⠙⡿⡿⠟⠋⠁⣠⣄⠀⡄⠄⠀⠀⠀⠒⠉⡭⢦⣴⣈⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣰⣆⣈⢫⣏⠉⠀⠀⠀⠀⡀⢴⣿⠗⠀⠀⠠⠀⠄⡃⠀⠀⠀⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠓⢉⠁⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠰⡇⠲⢽⣿⡿⠂⡀⠀⠀⠀⠀⠀⣸⡗⠀⠀⠀⠠⢀⠀⡇⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⣻⣼⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠂⡏⣟⣷⡬⠀⠀⠀⠀⠀⠉⠻⣟⡦⠀⠠⠨⠀⡇⠀⢈⠐⢤⠚⠂⠀⠀⠀⠄⠀⢶⣶⠐⢿⡇⠂⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⣙⠚⡏⣟⡣⢶⣴⠄⠀⠀⠋⠙⠃⡉⠀⠀⢰⠀⢇⠲⠀⡀⢀⣉⠁⠀⠀⠀⠂⠀⢴⣞⡳⢦⠀⠊⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢤⡅⠃⡽⠚⢋⡁⠀⠀⢀⣐⣾⠗⠀⠀⠀⢸⠀⠀⢰⠀⠘⠒⢒⡀⠀⠀⠀⠀⠀⠀⠘⠳⡸⢀⡁⠀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠦⡁⢀⠞⣷⡋⠁⠀⠀⠘⠋⡑⠃⠂⠀⠀⢸⠀⠀⡘⠀⠃⣜⠆⠓⠀⠀⠀⠀⠀⠀⠀⠡⠵⠠⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⡙⠋⠸⡟⠒⠀⠀⠀⠀⠀⠁⢠⠈⠀⠀⠀⠘⠀⠏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡐⢣⠔⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣥⢀⣤⠍⠀⠀⠀⢰⡞⠉⠀⠀⠀⠉⠳⡆⢸⠀⢀⡏⢣⢀⠀⡀⡀⢇⠀⠀⠀⠀⠀⠀⠂⣑⣶⠂⠐⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡂⢤⡾⠛⠑⡂⠀⠀⠀⠈⠓⠦⢤⠤⣤⢤⠖⠃⠈⠀⠀⠑⠶⠦⠤⠤⠐⠐⠁⠀⠀⠀⠀⠀⠀⡠⡼⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⡀⣀⡀⢀⣈⣁⣀⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠁⠈⠉⠀⠀⠈⠁⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠶⠀⠆
⠀⠀⠀⠀⠀⠶⠎⠷⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠄⠀⠀⠰⠀⠄⠠
⠀⠀⠀⠀⠀⢛⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣉⢛⣻⠓⠗⠓⡖⠒⠺⠒⢲⠚⢲⠒⣾⣶⣷⣷⣷⢶⣿⢺⡞⢘⠚⠒⠖⠓⡗⠒⡖⠒
⠀⠀⠀⠀⠀⣀⠠⣭⡀⠂⠀⠰⠀⠨⠆⠈⠀⠠⠀⠙⣿⢯⣟⣻⣿⣽⣹⠇⠈⠀⠈⠁⠀⠡⠀⠡
⠀⠀⠀⠀⠀⣀⣀⡄⢀⠀⠀⠀⠀⠅⠀⠀⠀⢀⠀⠀⠈⡛⠠⡙⠥⠈⠀⠀⢀⣴⣆⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⣴⣶⡷⠀⠀⠀⠀⠀⠀⡄⠀⠂⢀⠀⠀⠀⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠲⠀⠆⠀⠀⠀⠀⣿⡏⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠙⢻⡿⣤
⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠟
⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠀⠈⠉⠻⣿⢩⠄⠀⠀⡀⠀⠀⢐⠀⠀⠀⠀⠐⢤⡤⠚⠁
⠀⠀⠀⠀⠀⠈⣀⡃⠀⠀⠀⡐⠒⠱⢟⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⣉⣉⡁⠀⠀⠀⠁⠀⠠⣤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⢒
⠀⠀⠀⠀⠀⢀⠀⡅⠀⠀⠀⣆⣉⣽⠟⠉⠀⠄⠀⠁⢀⠀⠀⠀⠀⠂⠀⠈⠉⠁⠈
⠀⠀⠀⠀⠀⣤⠀⡄⠀⠀⠀⠏⠉⠁⠖⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⠠⠐⠃⠀⢀⠀⠀⠀⠀⢸⠀⢠⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠲⠐⠆⠀⢀⠀⡀⠀⠰⠄⠀⡀⠀⠀⠀⠈⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠚⠀⠒⣤⠈⠉⠁⠀⠀⠀⠈⠁⠒⣄⠀⠐⠀⠀⠀⠆⠸⡀⠄⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠙⠀⠃⠀⡄⢀⡀⠀⠀⠀⠀⢀⣠⠌⠀⠸⠀⠐⠘⠣⣄⣀⡈⣁⣀⠀⢀⡀⠠
⠀⠀⠀⠀⠀⣉⠈⡁⠀⠀⠁⠈⠙⠉⠙⠙⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠐
⠀⠀⠀⠀⠀⣩⢀⣁⡀⡀⢀⠀⠀⠀⠀⢀⠀⡀⠀⢀⠀⠀⢀⢀⠀⠀⠀⠠⠀⠄⠀⠀⢀⠀⢠⠀⠀⠄
⠀⠀⠀⠀⠀⣤⠠⡍

⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠂⠀⠀⠀⠀⠀⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠃⡸
⠐⠀⠀⠀⠃⢐⡃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠅⠀⠸⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠⣤⡤⣤⣄⡠⣄⢀⡆⠘⢙⡟⠁
⠰⣖⠄⢀⣤⠟⢻⢞⡻⠳⡱⡬⣲⡦⢠⠄⠀⢀⣀⢠⠻⠟⢳⣦⠶⢶⣦⡐⣧⣭⣍⠀⡈⢙⣗⣟⣟⡇⠀⠀⠒⢂⠜
⠀⣲⣄⠰⢛⡎⠙⢤⣴⣀⣶⠀⢇⠐⢸⠦⢰⡋⢛⢛⣃⡈⢸⣥⠀⣌⠚⣼⠋⠙⡅⠤⠄⢸⣷⠏⠉⠁⠀⠀⠀⢘⣆
⢈⣭⣴⡆⢰⠇⠈⣿⠄⠒⣶⠻⢿⢳⣶⣶⣾⢿⢆⣸⣷⣿⣶⡰⠦⠀⣰⣧⡶⣰⣟⠀⢀⣹⣿⡄⠀⠀⠀⠀⠀⢸⠏
⢸⣯⡏⠁⢠⠐⢋⠁⠀⢀⠏⣸⡔⢞⢺⣿⡶⢠⢿⠏⣿⢿⣿⣇⢀⡀⡿⠿⣔⠺⣟⠻⣿⢯⡞⡁⠀⠀⠀⠀⠀⠘⠄
⢸⣿⡍⢀⠈⠄⠀⠀⠀⢀⡞⠹⢧⠘⣾⢿⡅⠀⡞⡦⠇⠀⢿⣛⣿⠇⣿⠋⠀⢰⠄⡜⠊⠸⠖⣤⠤⠶⠀⢸⣗⣈⢠
⠘⠋⣙⠈⠢⠐⡠⣅⠠⠪⣥⡜⠁⣷⡈⢊⡃⠄⠂⢐⣟⣦⣬⣿⡆⣄⠃⢠⣤⠼⢦⠍⢈⠆⠀⠈⠀⠀⠀⠈⠉⡱⣯
⠀⠀⠀⠈⠇⠀⡄⠛⠞⢢⠿⠃⠀⣈⣉⠘⠋⢈⣿⡛⢁⡰⣤⡄⣓⣮⡖⢮⡀⠀⢁⠀⡾⠀⠐⠀⠀⢀⠀⠀⣶⠁
⠀⠀⠀⣀⡘⠀⡇⠀⢰⢨⠀⡿⠂⢙⡻⠄⠙⡜⠛⠡⡄⣼⠁⢀⣷⣱⣧⠄⠿⠒⠁⣤⣯⡢⠄⢁⣄⡙⠀⢰⡏⢂⣍
⢰⣠⡎⠴⢏⠀⠒⠀⢸⣾⣷⣆⣀⠻⡟⠀⠰⠀⠐⡞⣿⢯⣽⡋⡿⢸⠨⠹⠋⠍⠰⠋⠏⠡⢄⠄⠀⡄⠶⣖⠝⣿⠚
⢨⠃⠀⠀⠸⣦⣤⠀⢸⠉⡉⡏⡈⢦⡘⠒⠀⡿⡄⠰⡟⠉⠮⠾⢦⡄⠄⠨⠓⠀⠠⠀⠀⠀⠀⠙⠊⠗⠘⡯⠛⡟⣖
⢸⠀⢄⠀⠀⠻⢏⢀⣜⢈⠛⠳⣷⠘⠿⠆⣤⢀⠇⢸⡇⠀⠀⠀⠂⠀⠈⢩⠀⠀⠀⠀⠀⠀⠀⡀⡘⠴⡧⠅⠚⠫⠁
⢸⠀⠈⢳⠼⠀⠀⢠⠄⢩⣿⠀⠉⠖⢀⠀⠠⣦⡄⣿⣶⡍⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠸⠭⣝⡥⠶⠟⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⣙⠻⣷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣼⡇⠀⣿⣷⠂⢹⡷⠦⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠋⢀⣠⣾⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⢜⣉⣉⣙⣩⣿⠔⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡋⠉⢸⣫⣟⣿⡈⡉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠽⠮⡽⠯⠷⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠅⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⣴⣶⣶⣷⠴⢶⣟⠳⣾⣦⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣟⣿⠿⢋⠃⢐⠛⠚⠁⢿⢿⣿⡻⣿⣿⣿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢞⣹⠁⣠⣯⡀⠀⢨⣇⠚⠁⢀⣬⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣟⡹⢀⠻⠿⢿⣿⡿⠗⢦⡾⠿⠇⠀⠈⠉⣉⣻⣿⣯⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃⠀⠈⢙⡛⣸⣿⣿⡉⢠⣇⣛⡠⡄⠀⣄⣽⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⣀⣰⣾⣿⣿⣿⣿⡄⠻⢿⣾⣷⠄⠀⠡⣤⣼⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣿⣿⣿⣻⣧⣤⣿⣿⣿⣍⠋⠉⠀⠀⠀⠈⠉⠁⠀⠀⢀⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣽⡏⣸⣿⣽⣿⣛⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⠋⠰⣴⣿⣿⣿⣿⣿⣷⣾⣿⣿⡷⢰⣿⣷⡀⠃⡴⣿⣿⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣼⣿⣿⡟⠋⣿⣿⣿⣿⣿⠿⠃⢸⣿⣿⣅⠐⣖⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣹⣁⠀⠘⠧⠹⣧⠀⣿⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠟⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣄⡀⠠⠈⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣄⡀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣟⣻⣿⣿⣅⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣯⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠻⠿⠻⠿⡿⢿⠿⠿⠿⠿⠿⠿⠿⠟⣋⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⡷⠆⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⣀⠀⡀⠠⢾⣿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⡤⢄⠈⣠⠟⠀⣠⠞⠛⠛⢲⣄⠀⠙⣾⡁⡄⠠⠭⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣽⣤⣾⣾⠏⡀⣸⡇⣸⣷⣾⣧⢘⣇⣠⡘⣷⣷⣺⣠⠂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣻⠟⠁⢀⣡⡨⣧⣿⣿⣿⣿⣴⡇⣬⣉⠀⠻⢿⣻⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠋⠀⠘⢉⣡⣥⣬⣵⡶⣾⣿⣥⣄⣤⣋⣿⠐⠘⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠁⠀⠀⠀⢸⣿⠓⢺⣿⣿⣿⣿⡟⢛⣿⡟⢋⠣⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣙⣿⣾⣷⣿⣾⣿⣿⣿⣏⣀⠀⡠⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡿⠛⠉⠉⠉⠙⠻⣿⣿⣿⣯⡦⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠏⡀⣓⣒⣒⣲⣒⣚⠈⢿⣿⣿⡛⠃⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠄⠀⢠⠄⠀⠠⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠄⠄
⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⠈⠀⠀⠀⠀⠁⠉⠉⠀⠈⠉⠁⠈⠈⠉⠉⠀⠠
⠀⠀⠘⠇⠰⠶⣶⡤⣴⠒⠐⡴⢆⠖⡲⠶⠶⢤⠀⠴⠐⠖⠲⡾⣴⣶⣴⣴⣴⣴⣴⡞⢰⠆⠤⠾⠦⠤⠦⠴⠦⠦⠴⣤⠂⢀⣦⣴⡄⠈⢿⡀
⠀⠀⠀⠇⠀⠀⠀⠉⠻⣛⢉⠖⠀⠀⣉⠉⠀⠨⠀⠠⠀⠁⢀⡅⠙⢿⣿⣗⣾⣿⣿⠅⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠛⠾⢩⠿⠁⠋⢄⠀⡯
⠀⠀⠀⠅⠀⠀⠀⠀⣷⣣⣟⡀⠀⠀⠀⠀⠀⠀⠤⡓⡀⠀⠀⠄⠀⠈⡗⠊⠑⠈⠀⠀⣠⣾⠀⠤⠀⠂⠀⠀⠀⠀⢁⠀⡐⢒⠢⣇⣄⠀⢀⡀
⠀⠀⠰⡆⢀⣴⣀⡘⢠⣏⠉⠀⠀⠀⠀⠀⢀⠀⣾⡿⠗⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠢⠘
⠀⠀⢰⡆⢠⡝⢯⣱⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢨⣿⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⣎⣇⠠
⠀⠀⢠⡅⠀⣄⡞⢿⠷⢆⡑⠀⠀⠀⠀⠀⠀⠘⠻⣧⡤⣄⠀⠀⠀⠐⠀⠁⠀⠀⠠⠄⣀⣐⠭⠉⠀⠀⠀⠀⠀⠀⣀⣀⠀⣉⣿⠃⡀⠀⠂
⠀⠀⢠⡁⠀⠠⣤⣨⠶⣾⡅⠀⡀⠀⠀⠀⠀⠠⡤⢠⡗⠹⠀⠀⠁⠀⠀⠂⠀⡀⠲⠀⠉⠤⡤⠀⠀⠀⠀⢀⠀⠀⠉⢛⣴⠀⠏⠀⡠⠀⡞
⠀⠀⠈⠃⠀⠰⢬⠉⡄⢧⠔⣋⢿⠛⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⢘⠀⠱⠀⠁⠀⠄⠀⠔⠆⠀⠀⠀⠀⠀⠀⠀⠛⠷⣬⠙⠃⢀⡀⠀⠐
⠀⠀⠀⡅⠀⠰⢤⠀⢡⡜⡋⠙⣄⠀⠀⠀⠀⣀⣩⣾⠋⠂⠀⠀⠂⢸⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣂⠻⢈⠀⠀⠠
⠀⠀⢀⡂⠀⠰⢈⠀⢀⡎⣷⣞⠉⠀⠀⠀⠀⠛⠈⡰⠃⠂⠀⠀⠀⢸⠀⠀⠀⡁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡇⢨⠀⠠⠈
⠀⠀⠀⠀⠐⠒⠆⠋⢸⡴⢥⠈⠀⠀⠀⠀⠀⠐⠈⠀⠐⠂⠀⠀⠀⠈⠀⠆⡸⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄⣤⠀⢸
⠀⠀⠀⡂⠈⠃⠃⠀⠀⠑⠂⠀⠀⠀⢀⣠⠦⠆⠀⠙⠀⠶⢤⡀⠀⠀⠀⠁⢀⠶⠄⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠲⠄⣏⠀⢘
⠀⠀⠀⠀⠈⢻⡤⣄⡗⡊⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⣹⠀⢤⠀⠃⠦⡀⠂⠠⠀⠐⠀⠀⢂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠶⡣⠄⠠⠠
⠀⠀⠠⠀⠰⡾⠋⠀⢈⡅⠀⠀⠀⠀⠀⠈⠛⠑⠦⠒⠖⠶⠛⠁⠀⠀⠀⠀⠀⠙⠋⠓⠊⠂⠏⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢨⣒⠇⠀⠀⢀
⠀⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⡀⠌⣀⡀⠄⡌
⠀⠀⠐⠂⠛⠋⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠀⠈⠀⠉⠀⠁⠈⠀⠘








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠽⢄⡀
⠀⠀⠀⠀⠀⠻⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢃⣀⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣶⣰⣷
⠀⠀⠀⠀⠀⠀⠈⠢⠹⢦⡀⠀⠀⠀⠀⠀⠀⠰⣿⠋⠛⠉⢻⠆⠀⠀⢀⡀⠀⠀⠰⣟⠉⡉⢉⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⡀⣀⣀⣀⣤⣠⣀
⠀⠀⠀⠀⠀⠀⣤⠀⣨⡾⠟⢦⡀⠀⠀⠀⠀⠀⢰⣼⡇⣶⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⡟⣿⣿⠁⠀⠀⠀⠀⠀⠀⢀⡿⠻⠿⣿⣿⣿⣿⣿⢿⣿⡻⣽⣿⣳
⠀⠀⠀⠀⠀⠰⣿⣿⣷⣅⣀⠈⠙⢦⡀⠀⠀⠀⠸⠋⠃⠛⠀⠀⠀⣠⠟⠛⢦⡄⠀⣀⣁⣥⣤⣦⠀⠀⠀⠀⠀⠀⣾⡁⢰⡆⠀⠈⠙⠙⢻⡟⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢈⡙⠿⢸⡿⠀⠀⢈⣿⣦⡀⠐⠟⠾⠛⠛⠻⡧⠚⠁⢠⣆⠀⠈⠓⢿⠀⠀⠀⢰⠀⠀⠀⠀⠀⣻⢹⡇⠘⠃⠐⢛⡀⠀⢸⡃⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢹⣃⠀⠀⠀⠀⢰⣿⠙⡏⢀⣀⣀⣀⣀⣀⣀⣶⣆⣸⣧⣠⣶⣦⣼⣶⠶⠶⠶⠆⠀⠀⠀⣰⠃⠈⢠⠀⣤⢸⣿⠀⠀⢸⡇⢺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣷⣮⠁⠀⠀⠀⠸⠏⠀⠀⠈⠉⠉⠉⠀⠈⡿⠉⠉⠁⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⢰⡏⣄⣠⢸⡇⣿⢸⣿⠀⠀⢸⡇⠜⠉⠥
⠀⠀⠀⠀⠀⢀⡀⣿⣿⢀⠀⠀⠀⢲⠦⠀⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡶⡆⠀⠋⠁⣿⣿⢸⡇⠟⠈⠁⠀⠀⢸⡇⢠⣀
⠀⠀⠀⠀⠀⢸⠶⠿⡿⢾⡏⠀⠀⣸⢹⡇⡀⠀⠀⠀⣠⠀⠀⠂⠀⢰⣿⢿⣷⡄⠀⣀⠀⣰⡆⠀⡟⠉⠁⢲⠆⡿⠋⠈⠄⠀⢺⡇⠀⠀⢸⡇⢘⣿
⠀⠀⠀⠀⠀⠈⠒⠌⡳⠦⠀⠀⠀⣾⣸⠃⠇⠀⠀⠀⣿⠇⠀⠀⠀⠸⣿⣼⣟⠁⠀⡏⠀⢿⡇⠀⣷⣶⢻⣿⠀⢀⠀⡶⡇⠀⢸⠟⠀⠀⢸⡇⠰⠿
⠀⠀⠀⠀⠀⠀⠈⠛⠤⠀⠀⠀⠀⡀⢁⠀⠃⠀⠀⠀⠿⠆⢀⡀⣠⡖⠉⣍⠈⠓⡤⣡⡀⠈⠁⠀⠼⢿⣦⢻⡌⣿⠀⡯⠟⠀⠻⣏⠁⠀⠈⣇⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡂⠀⠀⠀⢹⡯⠀⢀⣴⠒⠚⠛⠛⣻⡿⠷⠶⠐⠛⠒⠒⠓⣘⡿⠁⠀⠀⠀⢸⡏⢻⡄⢋⠀⠀⠀⠀⠀⢻⡀⠀⠀⣿⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⢸⡟⠀⢸⣿⡆⠀⣀⡀⠀⠏⠀⢉⣽⠷⠷⣦⡀⠀⣇⠸⠥⠃⠀⢰⣧⣾⣇⣤⣿⠀⣄⠀⠐⠜⠿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠠⠚⠛⠓⠲⠂⠀⠘⠉⠀⢾⣿⡇⠀⠀⠀⠀⠃⠀⣭⢳⣿⣿⡌⣷⠀⣇⠀⠀⠀⠀⠸⣿⣿⡇⣿⣿⠀⠀⢠⣤⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠀⠀⣴⣿⣶⡷⠸⠿⠃⠀⠀⠀⠀⠱⣤⣿⡆⣭⣭⢸⡿⢶⣇⠀⡇⠀⠀⠀⠉⠙⠃⣿⣿⠀⠀⢸⣿⠄⠀⠀⠈⣯
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⣿⣟⣸⠇⠀⢀⡾⠀⠀⢰⠆⠀⣿⣶⡇⣿⣿⠠⣷⡾⢿⠚⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠛⢤⡠⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣫⡇⠀⠀⠙⠉⠀⠀⠀⡈⠀⡇⠀⢸⣶⠀⣯⡻⠇⠉⠉⠁⢻⡕⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠐⠿⠀⠰⠄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠟⠋⠁⠀⠀⠀⠀⠀⢀⢼⠟⢻⡇⠀⠘⠟⠀⢿⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡽⠧⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣿⣿⡿⠿⣿⡿⢿⢿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣶⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣦⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⢿⢦⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⣸⠳⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣆⠀⠀⠀⠀⣀⣴⣄⣾⣶⡴⣿⣿⠷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⡀⢀⣸⣿⢹⣿⣿⣿⣾⡅⣿⣷⠿⢿⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠓⠖⠒⠒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⡟⣿⣿⣯⣿⠻⣿⣿⣷⣶⠛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣛⣛⣷⣿⣿⣯⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⢳⣿⣿⣿⡿⢷⣹⣿⣿⡙⢿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠥⠤⠾⣿⣿⣿⣟⣚⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣼⣟⣿⣿⣿⣿⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⣃⣀⣉⣉⣉⣤⣤⣭⣭⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣏⣩⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠷⠶⠶⠶⠖⠒⠒⠒⢒⡒⣒⣒⠒⠒⢻⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⡿⢷⣄⣿⠛⢻⣿⣷⡿⡿⠿
⠀⠀⠀⠀⠀⠀⣠⣿⣿⡏⢉⣩⣯⣽⢿⠻⣿⣭⣭⣭⣭⣭⣥⣤⣬⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠘⣿⣄⡿⠐⠋⠞
⠀⠀⠀⠀⠀⠀⠉⠉⣿⡶⠲⢶⡾⣡⣿⣦⠘⢿⣿⣶⠶⠶⠶⠦⠀⣾⡇⠀⢰⣿⡆⠀⣸⣿⡀⠀⣼⡇⠀⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣩⣿⡽⣣⣿⣿⣷⡈⢿⣯⣭⣍⣉⣉⣛⣿⡇⠀⢸⣿⣯⠀⣿⣿⡇⢸⣿⡗⠀⠀⢸⡇⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⢿⡟⣰⣿⡟⣉⠉⣷⡈⣿⣛⣲⣶⣒⣒⣿⡇⠀⢸⣿⣿⠀⣿⣿⡇⠘⣿⡇⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⣀⣴⣆⣰⣄⣿⣿⣾⣧⣿⡟⣿⣽⣷⣿⡇⣿⠤⠤⠤⠤⢤⣿⠇⠀⢸⣿⣿⠀⣿⣿⡇⠀⣿⣧⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⣸⣿⣿⣿⣯⠿⣿⣿⣿⣿⢹⣿⡇⣿⣿⡏⣿⠄⣿⢭⣭⠛⠋⢙⣿⠀⠀⢸⣿⣿⠀⣿⣿⡇⠀⣿⣿⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⣯⣿⣿⣶⣾⣷⣿⣿⠧⣿⣾⣿⣇⣿⣿⢧⣿⠂⣿⣿⣿⣛⠛⢻⣿⠀⠀⠸⠿⠿⠀⠿⠿⠇⠀⠿⠟⠀⠀⢸⣇⠀⠀⠀⢸⡇
⠀⣉⣿⡿⠿⣬⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣷⣿⣒⡒⠶⠖⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣀⢀⣾⡟
⠐⠛⠻⠿⠿⠿⠿⣿⣿⣟⣛⡒⢒⡀⢠⣤⣴⣿⣿⣿⣶⣿⣿⣿⣿⣿⣾⣿⣿⣶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣾⣶⡶⠿⠶⠾
⣀⣀⣢⣤⡄⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠿⠛⠛⠃⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⡀⠐⠒⠂⠒⠈⠉⠉⠉⠁
⠀⠀⠑⢀⠶⠊⠀⠀⠀⠀⠀⣤⣀⡁⡀⢀⠀⢤⣍⣀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣀⣨⠽⠵⠀⠀⠀⠀⠀⠲⠂⠠⠄⠤⠄⠀⠄⣀⡀⠀⠤⠰⠂⠉⠉⠉⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢀⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠤⠤⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠒⠒⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⣀⣀⣀⣀⣤⣄⣠⣤⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣠⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠿⠻⣿⠟⢻⠿⢿⠿⢻⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣾⣶⣿⣶⣿⣷⣾⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡄⢀⣀⣴⠟⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠻⠟⠙⠁⠀⠀⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⢘⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣋⣤⣷⣄⣈⣉⣃⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠻⠿⠿⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠙⣤⣠⠌⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠁⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⠀⠔⠀⠐⠧
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠈⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣾⡿⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⡀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠿⠛⠛⠛⠛⠛⡛⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠴⢆⣾⡿⣫⡌⢻⣦⡀⠀⠀⠀⠀⣸⣶⡙⠻⡇⠀⠀⢀⣴⣦⠀⢀⠀⠀⢰⣿⡀⢀⡀⢀⣴⣿⠀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣴⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠍⠀⣮⡀⣥⠙⢿⣶⡆⠀⠀⢸⣿⡇⠀⠅⢨⠀⢸⣿⣿⠀⠘⠓⠀⣿⣿⡇⠈⠉⠈⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⡿⢿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠙⠃⠻⠁⠨⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠈⢩⡅⠀⠀⢀⣶⠀⡀⢠⣿⢺⣇
⠀⠀⠀⠀⢀⡄⠀⠀⠀⢸⡜⣿⣿⡇⢸⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣿⣿⡃⠀⠀⠀⣿⣿⠀⠀⠀⢀⣾⡟⠀⠒⢸⣿⠀⠉⢸⣷⢸
⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢱⣿⣿⡇⢸⠀⠀⠀⠀⢸⣿⡇⢸⠀⠀⠀⢸⣿⣿⠀⠀⢠⠀⢿⣿⡇⠀⠰⣆⢹⣿⠀⠀⠀⠈⢻⣏⠀⠀⢸⣿⠀⠀⢸⣿⢸
⠀⠀⠀⠀⠁⠀⠀⠀⡆⠀⠸⣿⣿⡇⢸⠀⠀⠀⠀⢸⣿⡇⢘⠁⠈⠀⢸⣿⣿⠀⠀⠘⠓⢸⣿⡆⠀⠀⠀⠀⣿⠄⠀⠀⠀⢸⡏⠀⠀⢈⣿⠀⠀⡠⣿⢸⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⡿⢿⡇⣸⠀⠀⠀⢀⣼⣿⡇⠈⠀⢘⠀⢸⣿⣿⡄⠀⠀⠀⠈⠏⠛⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢠⡰⠆⣻⠀⡆⠁⢂⣸
⠀⠀⠀⠀⣄⠀⠀⠀⢀⡀⠐⠇⠀⠀⢹⠀⠀⠀⠀⠀⠉⠉⢰⠀⢠⠀⠉⠉⠁⠀⢀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⠆⠂⢸⣿⢸⡇⠀⠹⠂⣿⡄⢈⠱⠂
⠀⢰⡆⡆⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⢈⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⢸⠀⠀⢘⢁⠰⠿⣦⡄⠀⠉⠙⠃
⠀⠀⠁⠀⣠⠞⣻⣄⠅⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠀⠀⠀⣿⠀⢘⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⣿⣿⠀⠀⠐⠚⠀⠐⠂
⠀⠀⢤⣴⠗⣫⠭⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣄⠀⠀⠀⠀⣿⠀⠠⠀⠀⠀⠀⠀⣸⣿⣷⠀⠂⠀⠀⠉⠛⠊
⠀⠀⠀⠀⠉⠓⠯⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠒⠿⠀⢠⡄⠀⠐⠀⠉⠁⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡅⠀⠀⠀⠐⠀⠐⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠠⡀⠀⠀⠀⠀⠛⠒⡀⠂⠆⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⢀
⠲⣶⠶⠀⡀⠄⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⢈⠀⠀⠀⠀⠄⠀⡁⢀⠾⢿⡆⠀⢀⠄⠘⠓⠀⠀⠐⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠔⠀⡀⠠⠄
⠀⠈⡀⠘⢄⠀⡀⢱⣀⡀⠀⢀⠀⠀⠀⡀⢸⣼⠆⠀⠐⠁⠀⠀⡅⠀⠀⠸⣧⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠠⢀⡆⠀⠀⡠⠂⠂⠀⣸⠇⡐⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⠀⠀⠣⢴⣤⣶⡿⠿⢀⡀⠀⡀⠀⠀⠂⠰⣤⣼⠇⠀⠀⠀⠀⣀⠔⠀⠈⠳⢔⡪⢌⡲⠊⠀⡀⠀⠃⠈⠓⠊⠁⣠⣅
⠀⠀⠀⠀⠀⣦⠀⠀⠀⠪⡀⠀⠀⠀⠈⠹⠀⠰⣏⠀⠀⠅⢀⠀⠀⡀⠀⠀⠀⠀⠒⠒⣀⠇⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⡠⠂⠀⢀⣿⠋
⠀⠀⠄⠀⠠⣿⠆⠀⠠⠀⠮⠀⠀⠀⠀⠀⣶⡀⠙⠦⡀⠀⡀⣁⣴⠃⠰⠃⠀⠀⠄⠀⠀⠀⠀⡠⠞⠀⡄⠀⢰⠁⠀⠐⠁⠀⠠⢠⣴⡖⣸⣿⠃
⠀⠀⠀⠀⠉⡠⠄⠁⠐⢤⣀⣀⡠⠔⠀⣠⠇⠀⢀⣠⣈⡉⣁⠡⢤⠎⢠⠓⢀⠤⢤⡀⢈⠺⠥⣐⡨⢘⣧⢸⡀⠀⠀⠀⠀⠐⡰⣿⣿⡞⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠐⣚⣻⣬⣧⠬⠷⠾⠷⠖⠶⠛⠓⠚⠓⢒⡒⢒⠶⠾⠦⢿⣭⣿⣙⣟⣷⠍⣀⣤⢄⣴⣾⡿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⠴⠷⠚⠋⠉⠃⠀⢀⡀⠄⠀⠀⢲⡄⠀⠀⠀⣰⡌⠹⡿⠉⢛⣿⡷⠒⠒⠛⠫⢽⣛⣻⠦⣿⣝⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠁⠀⣠⠀⠸⠀⣠⠼⣏⠀⠀⠘⠛⠁⠀⠈⠓⠛⢡⣦⣿⣦⣬⣿⣇⠣⢤⣤⣸⡆⣿⡿⡛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣄⠀⠊⠀⠀⢀⣀⣉⣀⠠⢤⣴⣴⣶⣶⣦⣶⣴⣴⣦⣦⡤⣭⣭⣍⣙⣳⠶⣶⣶⣿⣎⣱⡏⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣥⢴⣶⣲⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣍⣻⢷⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠒⠃⠀⠓⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⡇⠀⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⠼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣀⠤⢤⡈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢁⡤⠚⠁⠀⠀⠘⠢⣄⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢉⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⣠⡔⠋⠀⠀⢀⡴⣺⠿⢭⠿⢿⣦⡀⠀⠀⠙⣦⡈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢾⢹⡆⠀⠀⢠⣯⡟⠁⠀⢐⠀⠀⢹⣿⡀⠀⠠⡇⡿⠦⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⡇⠀⠀⠸⡿⡇⠉⠉⠙⠀⠉⣨⣿⠃⠀⢸⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⣩⢼⠀⡇⠀⠀⠀⠙⠮⣒⡶⠶⠶⣚⡿⠋⠀⠀⢸⢸⣯⡓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢚⣉⠤⠒⠉⠁⢸⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⢸⢸⠀⠈⠓⠦⣍⡳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣋⡥⠖⠋⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⠀⠀⠀⣀⡀⠙⠳⢬⣙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⢺⣥⢴⡛⡇⠀⠀⣠⡶⠿⢷⣦⡀⢸⡄⣇⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⡿⣿⠀⣰⡿⠻⠛⢷⡄⠀⠈⢳⢦⣉⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣧⠀⠐⣿⠀⠲⠆⣿⡇⢸⡇⣿⠀⠀⢠⢞⡿⠋⢹⠉⠻⣿⣦⠀⠀⠀⡇⣿⠀⢿⡇⢙⠃⣻⡗⠀⢀⡏⡟⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡀⠀⠙⠧⣴⣶⠿⠁⠸⡇⢸⠀⠀⡟⣸⠁⠀⢸⠀⠀⠘⣿⣧⠀⢠⡇⡏⠀⠈⠛⠾⠟⠋⠀⠀⣸⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢠⡇⣿⠤⠤⢼⠤⠤⠄⢿⣿⠀⢸⠃⡇⠀⠀⠀⠀⠀⠀⠀⢠⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢷⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⡇⡗⠀⠀⢸⠀⠀⠀⢸⣿⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡸⡄⠀⠀⠀⠀⠀⠀⠀⣧⢸⡄⢸⡇⡧⠤⠤⢼⠤⠤⠤⢼⣿⠀⡿⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⣴⠒⠒⡖⠛⠛⡆⣿⢸⡇⢸⡇⡇⠀⠀⠸⠀⠀⠀⢸⣿⠀⡇⢸⢰⠖⠒⠶⠒⠲⡆⣼⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⣹⡀⠀⠁⠀⠀⡇⢿⢸⡇⢸⡇⡇⠀⠀⢀⡀⠀⠀⢸⣿⢰⡇⢸⢸⠀⠀⠸⠀⢰⣷⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⣏⠛⠛⠛⠛⠛⠁⢸⢸⡇⢸⡇⡏⠉⠉⠉⠉⠉⠉⢹⣿⢸⠃⢸⠈⠙⠛⠛⠛⠋⡟⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣸⡀⠀⠀⠀⠀⠀⢸⠀⡇⢸⡇⡇⠀⠀⠀⡀⠀⠀⢸⡏⢸⠀⢺⠀⠀⠀⠀⠀⢰⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠻⢿⠛⡿⢿⣿⠿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣻⣯⣋⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣶⠞⠝⢶⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠅⠄⠀⠤⡙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠠⣏⢘⠃⢱⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠉⡈⠔⠃⠀⠀⠀⠙⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⠀⢀⣿⣆⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢀⣾⣏⣿⡀⠀⠉⢱⠀⣠⣤⣤⠠⣾⠿⢽⠿⣿⢿⣿⣷⠄⢠⣄⣀⠀⢰⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⢠⣿⣏⣿⣷⡀⠀⢸⠀⣿⣿⠉⠀⠀⢀⡔⢂⢐⡒⣄⠀⡇⢸⣿⡿⡄⢸⠀⣤⣤⠄⢠⣤⣤⠄⢸
⠀⠀⢰⡿⣟⣯⣿⣯⡁⠀⢸⠀⣿⠋⠰⠀⠀⣮⠛⠛⠛⠛⠋⠀⣧⢸⠟⠀⠇⢸⠀⣿⣃⠀⠘⣇⣋⡆⢸⠀⠀⢀⡆
⠀⠀⠀⣴⣿⣷⣿⢿⣷⡄⣸⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠂⢸⠀⡿⠀⠀⠠⡇⠀⠇⢸⠀⠀⣼⣿
⠀⢀⣾⣿⣿⣏⣿⣿⣿⡄⢿⠀⠋⣶⠐⣠⠖⣯⠀⠀⠀⠀⠀⢠⣿⡎⢠⠆⠀⢘⡀⠃⠀⠀⠀⠃⠀⠠⢼⠀⣸⣿⣿⣧
⣠⣿⣿⣿⣿⣧⣷⣿⣿⣿⣿⠀⠀⢼⠋⢠⠤⠯⠤⠤⠤⠤⠤⠴⣿⡿⠦⣄⣀⣸⣁⣉⣉⣙⣉⣿⣿⣿⣏⣰⣿⣿⣿⣿⣆
⠉⠉⠉⠉⠉⠱⢿⣿⣿⣿⣿⣶⣶⣸⣦⣭⣭⣭⣭⣭⣭⣭⣭⣭⡘⣧⣀⣻⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠹⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡿⠿⠛⠉⠉⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠵⣜⢦⡀
⠀⠀⠀⠀⠀⠘⡗⠢⢄⣀⠀⢀⣴⣦⡀⠀⠈⢧⠘⣰⠟⢠⠏⠀⠀⣠⣶⡄⠀⠀⣀⣠⠴⡶
⠀⠀⠀⠀⠀⠀⢱⡾⠀⢸⠀⢻⣿⣿⣿⠁⠀⢸⠆⠀⠀⢾⠀⠀⢻⣿⣿⣿⠆⢸⠁⢢⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠓⠤⢿⣿⣿⠤⠖⠁⠀⠀⠀⠈⠓⠦⣼⣿⣿⣇⠤⠊⢀⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⣀⣤⢀⡀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡗⣀⠀⠠⠀⠀⠀⠒⠒⡀⠀⠂⣶⠒⠖⠀⠢⠀⠤⠍⢛⠛⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠠⠀⠂⢒⣀⣀⣈⣀⣀⡀⣒⣃⣠⣀⠀⠀⠀⠀⠈⢻⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠗⢶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⡄⢸⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⡀⠀⣠⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣶⡿⠶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠋⠉⢷⣄⠀⠀⠉⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⡟⠁⠀⠀⠀⠙⢧⡀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡇⠀⠀⠀⠀⠀⠈⠗⠲⠶⠶⠦⢽⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣤⣄⠀⢰⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠔⡩⢾⣿⣦⣸⠀⠀⠀⠀⢸⣯⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⠊⠀⠀⠈⠻⣯⡉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠷⠶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⢣⠞⠁⠀⣀⣄⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢁⡴⠃⠀⠀⢸⡅⠀⢱⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⢀⣴⣟⣋⣠⡏⠀⠀⠀⠀⠘⢧⣀⠞⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠊⠉⠉⢦⠀⠀⠀⠀⢸⠀⠀⢀⠤⣄⠀⠈⠉⠉⢉⡙⠛⠒⠒⠶⠤⢤⣤⣙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⡟⠛⢻⠛⠻⡀⠀⠀⠀⡜⠀⢠⠃⠀⢸⠄⠀⠀⡰⠉⢹⡆⠀⠀⠀⢀⡾⠋⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠁⠀⢸⠀⠀⡇⠀⠀⠀⡇⠠⠞⠒⠄⠾⡄⠀⡤⢇⣀⣼⡇⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡀⠀⠘⡇⠀⢸⠀⠀⡇⠀⠀⢸⠁⠈⠛⠓⠒⠒⠁⠀⠓⠂⠤⠤⠜⠀⣰⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠋⠀⠘⠷⠶⢦⡷⠤⠾⠤⣤⣇⣀⣀⣼⣀⣠⣤⣤⣤⣤⡤⠤⠤⠤⠤⣤⣤⣤⠋⠉⠉⠛⠻⢷⣄
⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⣏⡀⠀⠀⠀⠫⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⢺⣯⣀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⣶⣦⣾⣋⠁⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣠⣴⡾⠿⠟⠛⠛⠛⠛⠻⠿⠿⠷⠶⠶⠶⠶⠾⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⠶⠶⠿⠿⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠤⠤⡀⠀⠀⢀⡀⠀⠀⠀⠀⡰⠁⢷⡀⠌⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⢀⣠⣦⠵⠒⠀⢢⡀⢠⣄⣩⡽⠁⢳⡿⢿⣿⣾⠇⡄⣁
⠀⠀⠀⠀⢀⠠⠀⠨⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⢣⢬⣬⣽⠃⣾⡟⠀⠀⣼⣿⣾⣴⣈⣩⣶⣤⣀⠀⡀
⠀⠀⡤⣊⠐⣖⡂⠙⠂⠀⠀⡖⠨⠆⠀⠀⠀⠀⠀⠈⢯⣽⢇⣶⢻⣿⠶⠙⠫⠟⢿⡟⠙⠻⣿⠟⠻⠇
⠀⠀⢧⠉⡘⡎⢉⠀⠀⠀⠀⡀⠀⠂⠔⠈⠀⠐⠀⠀⠘⡧⠿⢿⡞⠁⣀⠀⠀⠀⠀⢀⡀⠀⠁⠀⠀⡶
⠀⠀⠈⢆⠁⣽⡌⠀⠀⢀⠠⡀⠀⠄⠓⠐⠂⠔⠁⠈⠀⠹⠀⢰⡆⠀⠀⠁⠀⢤⢄⠀⣿⣶⣄⡀⡼⢁⡀
⠀⠀⠀⠈⠆⢟⣷⠠⠀⠀⠀⣈⠁⠀⠀⠀⠀⠄⢉⡀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⡀⠺⣿⣿⣿⣿⠿⣿⣆⡀
⠀⠀⠀⠀⠘⣤⢿⣧⠀⠢⠄⠤⠀⠀⠀⢀⠀⠀⠠⠄⠁⠂⠈⢦⣀⠀⠂⠄⢠⣤⣾⡅⣀⡞⣽⠿⢿⣷⣿⣿⠷
⠀⠀⠀⠀⠀⠘⡜⣿⣆⠀⠀⢐⢃⡀⠀⠀⠀⡀⠓⢄⠠⠀⠀⠘⣟⡳⣦⣤⣸⣟⣹⣿⠏⣼⠳⣶⣾⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠘⡌⣿⡄⠀⠀⠂⠀⠉⠈⡁⠀⠀⠄⠀⠀⠀⢀⡹⣠⠏⠛⠻⠻⢻⡿⣼⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡘⣷⡀⠀⠀⠀⠀⠈⠀⠁⠀⠀⣠⠀⠀⢈⣀⠡⠈⠉⠉⢈⡁⣹⣏⡍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣧⠀⠀⠀⠀⠤⠰⠀⠀⠈⠀⠀⠰⢀⣩⣄⣠⠄⣤⡈⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⢧⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠛⡯⠙⡛⠹⢗⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠞⠢⠀⠤⠒⠂⠀⠀⠀⠀⠀⠀⠈⠨⠋⠔⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢒⠏⡒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⣎⡹⣀⡇⠀⡁⡳⢸⣤⣇⣰⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⣤⢠⢴⠾⣤⢿⡟⢻⡴⡶⠐⡅⡕⣰⣯⣽⣻⡞⢤⠷⣦⡄⢠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣘⢞⡍⢩⡍⣾⠒⣮⡸⡋⢑⡄⢀⡬⠂⢦⠀⢹⡶⢩⠁⠘⠗⠻⢸⠌⠊⡁⡚⡀
⠀⠀⠀⠀⠀⠀⠐⠼⡌⠧⠸⡇⢹⠏⠙⠷⣧⠀⣷⠏⠁⡀⡈⠵⣼⠃⣠⠴⠛⠹⡦⢸⡗⢶⠇⡧⡅
⠀⠀⠀⠀⠀⠀⠀⢟⣥⠦⣄⠻⡟⣀⠦⠀⣥⡴⠐⣴⠆⠃⠰⣶⠖⠦⣤⠀⢀⣀⠗⡞⣀⣦⠴⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣢⠰⣾⠉⣻⡥⠀⢺⠷⠀⠿⠃⠀⠈⠿⠀⠾⠵⠀⢨⣽⠋⣳⡆⢁⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣛⠡⢈⡀⠀⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⠀⣄⣀⣉⠈⠛⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠛⢋⡉⢰⡤⠀⠐⠂⠀⠴⠃⠐⠂⠀⢤⡆⢉⡍⠛⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣴⠶⣟⣻⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣛⣶⢦⣬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⠀⠁







⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣛⣛⣻⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠥⠤⠠⠤⠴⡆
⠀⠀⠀⠀⠀⠀⣠⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⡏
⠀⠀⠀⢶⣒⠊⠀⢀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠤⠤⠤⢶⠗
⠀⠀⠀⠀⠈⠉⠉⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠎⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢳⡀
⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢳⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢠⣎⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣷⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡇⠘⠳⠞⠀⠻⠶⠃⠀⠳⠞⠀⡇⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢠⣏⣀⣀⣀⣀⣀⣀⣀⣀⣷⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⣏⣀⣀⣀⣀⣀⣀⣀⣀⣷
⠀⠀⠀⠀⢸⡇⠙⠒⠃⠘⠒⠃⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠁⠛⠚⠃⠙⠒⠃⢸
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠠⠀⠀⢸⣤⣤⡀⠀⣠⣤⡀⡇⣠⣄⡀⠀⣠⣤⡄⠀⣠⣠⣄⡇⢠⣤⣄⠀⢠⣠⣼⠀⠀⢀⠀⠠⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠒⠒⠀⠀⢸⠀⠀⢧⣤⡇⠀⣧⣧⡇⠀⢧⣤⡇⠀⢧⣤⡗⠀⢯⣧⡼⠀⢿⣤⡼⠀⢸⠀⠀⠈⠒⠚⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠈⢢⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠔⠢⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠐⠊⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢻⠉⠀⠀⠀⠉⡟⠦⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠂⠐⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⢠⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⡴⠃⠀⢸⠀⠀⠀⠀⠀⡇⠀⢹⣆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⡄⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣸⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⠸⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠃⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣇⣀⣀⣀⣸⣀⣀⣀⣀⣀⣇⣀⣸⣀⣷⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠉⠀⠈⠈⠁⠈⠀⠁⠈⠁⠀⠁⠈⠀⠀⠀⠀⠀⠁⠈

⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣾⣿⣽⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣧⠐⢠⠀⠀⠀⠊⠉⠉⠀⡀
⠀⠀⠹⣿⣿⣿⡷⠀⠀⠄⠀⠀⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⢶⡾⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⣿⣿⠂⠀⢀⡔⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠙⠦⠀⠀⠀⠼⣿⡆⣠⣿⢉⢓⣀⠀⠀⠀⠀⠀⢠⣴⡦⠀⠀⠀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠒⠋⠀⠀⠀⠀⣸⣧⢋⢇⣼⣿⠇⠀⡀⠠⠤⠶⠛⠉⠀⠀⠀⠀⠁⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⡿⣿⣿⣿⣾⡏⠁⠀⣾⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡈⢻⡿⣿⣿⠃⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣿⣇⣹⣾⣿⣿⡀⠀⠀⠉⣀⠀⠀⠀⡀⠀⠀⠀⢀⡴⢒⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠰⠀⢘⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣶⣄⣀⣠⣀⡀⠀⠀⠀⠑⠾⠋
⠀⠀⠀⡇⠂⡒⢤⣄⣀⣠⡀⠀⠀⠈⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁
⠀⠀⠀⢿⣤⣮⣿⣿⣿⣿⡷⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣠⠂
⠀⠀⠀⢸⡉⠉⢉⠻⠋⠁⠀⢀⣤⢤⣖⣋⠉⠀⠀⠀⠀⣀⢐⠀⢠⣾⡿⠄⢠⣾⣏⣀⣀⢀⢲⢩⣵⡗
⠀⠀⠘⢾⣷⣄⠘⢿⣷⣤⣾⣿⠿⠿⣿⠋⠀⠀⠀⣀⡐⠉⠸⢀⣄⣿⣿⣗⡟⠘⣿⠁⣹⡿⠛⢷⣆
⠀⠀⠀⣺⣷⣿⣿⡺⢿⣿⣿⠋⢾⣿⣿⣦⣴⡂⠀⣿⣛⠛⠂⠀⣿⣟⣏⡙⣿⣽⣿⣿⣴⣧⣤⢶⡌
⠀⠀⢀⣡⡼⣿⣿⣿⣾⣿⡿⢿⣾⣿⣟⣿⠋⠀⠀⠻⢿⣷⣌⣾⣿⣿⣿⣿⣋⣙⣿⡮⣤⣯⡶⠻⠁
⠀⠀⠀⠀⠀⠀⠈⠛⣿⠷⠟⠛⠓⠛⠛⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠐⠒⠂⠀⠰⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠦⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢸⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠇⠠⢸⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⡗⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢸⠀⠠⠦⠴⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡇⡀⠠⠞⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡄⠀⠀⠀⣀⠀⠀⠀⢸⡇⠀⠀⣿⠡⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡇⠀⠀⠀⢿⠀⠀⠀⢸⡇⠀⠀⣿⢏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⢀⣀⣸⣇⠀⠀⠹⠴

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⢷⣦⡀⠀⠀⠀⠀⠘⣿⣆⢿⣿⣿⢆⣾⡏⠀⠀⠀⠀⠀⣠⣾⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣤⣤⣻⡇⠀⠀⠀⠀⠀⠘⠿⣷⣶⣶⡿⠟⠀⠀⠀⠀⠀⠀⣿⢡⣤⣤⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⣵⡿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣭⣽⡿⠏
⢀⣴⡾⠿⢷⣦⡀⠀⠀⠀⠀⠈⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⣠⣶⠿⠿⣶⣄
⣿⡏⠀⣀⣴⢹⣿⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⡿⠀⠸⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⢱⣄⡀⠈⣿
⢻⣷⣜⣛⣫⣾⡟⠀⠀⠀⠀⠀⠀⣿⡿⢿⣷⡀⠀⠀⠀⢰⣿⠃⣴⡄⢻⣷⠀⠀⠀⠀⣰⣿⠿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣮⣻⣛⣴⣿
⠀⠉⠛⠛⠛⣿⣿⣦⡀⠀⠀⠀⠀⣿⡇⠀⠻⣿⣆⠀⢠⣿⠇⣸⣿⣿⡈⢿⣇⠀⢀⣾⡿⠃⠀⣿⡇⠀⠀⠀⠀⣠⣾⣿⡟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠹⣿⡿⣿⣦⡀⠀⠀⣿⡇⠻⣦⠈⢿⣷⣾⡟⢠⣿⠁⢹⣧⠘⣿⣶⣿⠏⢠⡿⠃⣿⡇⠀⠀⣠⣾⡿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢻⣷⠈⠻⣿⣦⣀⣿⡇⠀⠹⣷⡀⠙⠟⠀⣾⡏⠀⠈⣿⡄⠙⠟⠁⣰⡿⠁⠀⣿⣇⣠⣾⡿⠋⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⣇⢿⣎⠻⣿⣿⣿⠀⠀⠘⣷⣄⣀⣼⡿⠀⠀⠀⠸⣷⣄⣀⣼⡟⠀⠀⢰⣿⣿⡿⢋⣾⢇⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠹⠷⠈⠙⠋⢀⣴⣦⡈⠙⠛⠉⠀⢰⣶⣦⠀⠈⠛⠛⠉⣠⣶⣄⠈⠛⠉⠰⠿⠁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢀⣤⣤⠀⠀⠈⠿⠟⠁⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⢠⣤⣄⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣈⣤⣤⣤⣶⣶⣶⣶⣶⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣌⣠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠛⠋⠉⠉⠉⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠛⠛⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣶⣶⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣶⣶⣾⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠘⣿⣿⣿⣿⣿⡿⠁⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠙⣿⣴⣿⡆⠀⠀⠹⢿⡇⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⢹⡿⠃⠀⠀⣸⣿⣴⡿⠋
⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⢸⣷⣤⣀⣀⣠⣿⣿⣿⣷⣄⣀⣀⣴⣿⡇⠀⠀⠀⠘⣿⡿⠁
⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠰⡆⢁⡒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠜⠋⠁⣠⣄⣧⠤⠀⢄⠁⠈⣉⢐⣂⡞⠰⣴⣾⣷⣶⣶⡀⡉⠂
⠀⠀⠀⠀⠀⠀⡀⠀⡂⠁⣀⡴⠶⠛⠉⠁⠀⠀⠀⠀⢇⢘⣉⣻⡟⢠⣶⠏⠀⠉⣷⣧⣞⣨⢛⢂⣤⣀⡀
⠀⠀⢀⠤⠂⣥⠤⠐⡎⠉⠀⢀⠤⢰⡀⠀⠀⠀⠀⠀⠈⣞⢻⡟⢀⡼⣿⣦⡄⠾⢿⡿⣽⡿⠻⣿⣿⣿⣿⡦
⠀⠀⢇⠛⠂⣇⠺⠂⠀⠀⠀⠈⠁⠀⠀⡠⠐⠀⢀⠀⠀⠘⡟⣥⣿⣥⠟⠁⠀⠀⠁⠀⠑⠁⠀⠈⠛⠀⠀⢡
⠀⠀⠘⡆⠳⢸⡄⠆⠀⠀⠀⠐⠀⢀⠀⣅⢀⡀⣁⠆⠠⠄⢻⡀⠈⡍⠀⠙⠳⠀⠀⠀⠀⠐⣤⣀⠀⠀⢠⠯⠀⢀
⠀⠀⠀⠘⡄⣻⣷⡀⠀⠀⠂⠉⢠⠊⠁⠀⠀⠀⠑⠤⠀⠀⠄⢆⠀⠱⠀⢀⠀⠀⠀⠙⠂⠀⣿⣿⣷⣦⣯⣴⣷⣄
⠀⠀⠀⠀⠸⡜⢺⣧⠁⢀⠀⠀⡂⢀⠀⠀⠀⠀⠁⠐⠂⠈⠀⠈⣄⠀⠀⢈⠀⠀⠀⠀⣠⠂⠈⣻⢿⣿⣿⣏⣻⣿⣶⡠
⠀⠀⠀⠀⠀⠹⡝⣿⣗⢀⠉⠈⢣⠀⠀⠀⠠⠀⠀⣈⠁⠀⠀⠀⡘⣷⣄⡀⠈⠀⢶⣿⣿⣴⡴⢣⣟⣉⣹⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠱⡘⣿⡄⠀⡀⢂⡰⠂⡄⢤⠄⠂⠀⠱⠈⠀⠀⠀⢹⡦⠹⣿⣶⣿⣦⣾⡿⢡⣿⣨⣹⣿⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠱⡸⣷⡀⠀⠁⠄⠀⠀⠀⠆⡀⠀⠀⠀⠀⠀⠀⡆⢣⠘⡄⢄⠉⠩⠿⢧⣿⡻⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⢴⠌⠀⠀⠀⠀⢴⢀⣞⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⣇⠀⠀⠀⠀⠐⠘⠀⠈⠀⠀⠀⢐⣃⣤⣶⣤⡖⠀⣶⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⢝⠀⣩⠁⠛⡻⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠢⠄⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⠍⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⡤⣤⢤⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣥⣴⣯⣤⣧⣤⣽⣦⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡹⣄⠀⡇⠀⡼⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣦⣧⣼⣷⣋⡀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠉⠉⠓⠦⣤⡶⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣠⡴⠖⠚⠛⠛⠛⠓⠶⢤⣀⠀⠈⠛⢦⡤⠶⠚⠛⠛⠛⠓⠲⢤⣄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⠏⠈⢳⣦⡀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⠟⠈⢳⡄⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢠⡏⠀⠀⠀⢻⡀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣼⠀⠀⠀⠀⠈⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢿⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢸⡆⠀⠀⠀⢸⠇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⢳⡄⠀⢠⠏⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠹⣶⡋⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠛⠦⣄⣀⠀⠀⠀⠀⢀⣀⣿⣄⠀⠀⠙⠶⣏⣀⡀⠀⠀⠀⢀⣀⣠⠴⠋⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠉⠉⠙⠛⠉⠉⠁⠀⢈⣻⢦⣄⠀⠀⠉⠉⠉⠛⠉⠉⠉⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠦⠤⣤⠤⠴⠶⠚⠋⠁⠀⠈⠙⠓⠶⠦⠤⠤⠤⠴⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣴⠇⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣻⣏⣾⣧⣀⠉⢳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢆⠛⡟⢯⡛⡛⢏⠂⠀⠀⠀⠀⠀⠀⠀⠘⠙⣾⣷⡋⣿⠀⠀⠁⠀⠠⡰⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⣶⣨⣆⡓⠄⠸⠀⠀⢠⠀⠀⠀⠀⢀⢰⣶⣏⣿⡷⣶⡤⣄⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⡀⠀⣼⣿⣿⡿⢩⡇⠀⠀⠀⠀⠘⠆⠀⠀⠀⢸⣆⢻⣿⡿⠁⣾⣧⡹⢧⡀⠀⠠⠀⠠⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⡇⢙⡿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⢿⣿⣿⣶⣿⠙⣿⣿⡷⠀⠀⠀⠀⠈⢹⢷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢨⣿⣿⣿⣷⣤⣴⡼⠉⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢲⣶⣤⣿⣿⣏⠀⠈⢻⣷⡀⠀⠀⠀⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⡀⠈⠀⣿⣿⣿⣿⡟⣅⣾⣿⡇⠀⠀⢀⣀⣄⠀⠈⡘⡆⠀⡸⠞⢿⣿⣽⣿⣿⡇⠀⠀⠈⠁⠀⠀⠀⠚⠻⣷
⠀⠀⠀⠀⢠⣀⡄⠀⠠⠀⠀⠉⠀⠀⠠⠟⠉⠀⠡⢂⣽⣿⣿⡇⠀⠀⢸⣉⠉⠄⠀⠸⡀⢀⠃⡘⠚⠉⢩⢿⡟⣷⠀⠀⠘⢿⠄⠀⠀⠀⣠⡍
⠀⠀⠀⠀⠈⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤⣿⣿⠉⣿⣷⠀⠀⠀⠇⠀⣶⡆⠀⣅⢨⠀⣵⠈⢰⢘⡭⡇⡟⠀⠀⡉⠈⢻⠂⠀⠀⠁⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠞⢩⡿⠿⡿⡟⠀⠹⣷⣄⠀⠀⡀⠀⠀⢠⡀⠹⡇⠀⠹⠼⣒⡉⣈⠇⡇⠀⠀⣉⣹⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣴⡀⠱⣄⠱⣾⣦⠀⠘⠻⣴⣄⣁⠈⠀⣾⠳⠀⣿⡄⡀⢸⠖⢹⠉⢸⠁⠀⠀⢹⣿⢿⠒⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣦⠈⠳⠿⣿⡇⠐⠂⠘⢿⣿⣿⠒⠻⡿⣶⢿⣿⣴⣾⠀⠘⠴⠇⠀⢸⡀⠉⠇⢈⠀⠉⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢻⣷⣿⣿⠷⣄⡀⠈⣿⡀⠀⠀⠀⣷⡄⡀⠀⢱⡜⣾⠛⠛⠃⠀⠀⠀⢸⣦⡼⠏⢠⠀⢈⡀⢠⣷⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢘⠁⢹⡟⠀⠈⠙⣦⢨⣷⠀⠀⠀⢹⡻⣷⡄⠘⣿⣏⢰⡀⠀⠀⠀⠀⠈⢿⣿⣦⣶⡤⠾⠀⠈⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠊⠀⡞⠀⠀⠀⠀⣘⡃⠏⠀⠀⠀⠀⣿⣻⣷⠀⠉⢉⡜⣿⡌⠁⠀⠈⠀⠈⣿⣿⠁⡀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣡⡤⠖⠚⠉⠀⠀⠀⠀⠀⢸⠃⣷⠈⠐⠛⠚⠋⠻⢁⣀⡴⢿⡿⠃⣯⣦⣬⠉⣷⣄⠸⣽⣿⣇⣀⡀⣿⣧⣶⣷⡆
⠀⠀⠀⠀⠀⠀⠀⢈⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠶⠿⠿⠛⠻⠿⠏⠀⣿⣿⣿⣷⣧⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀

⣠⣤⣤⣤⣤⣀⣀⣄⣠⣤⣤⣤⣤⣤⣤⣄⣀⣀⣄⣠⣤⣤⣀⣀⣄⣀⣀⣀⣀⣤⣤⣤⣀⣠⣤⣤⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣄⣠⣀⣀⣀
⣿⣿⣏⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡛⢝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⠊⣏⣸⢀⣝⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⠉⣹⡍⢹⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⠭⠤⠼⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢺⡐⢀⡠⠾⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣴⣿⣷⣦⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢫⠟⠱⢽⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⠔⠀⠀⠀⠄⠂⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢟⠅⠉⠁⠀⠀⠀⠀⠀⠊⠁⡝⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⢟⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢽⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢋⠅⠁⣂⣀⠀⠀⢀⢀⣠⣄⡀⠐⠀⠈⠀⠀⣨⣙⢝⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⠕⠑⠂⠀⠀⠀⠀⠀⣠⣶⡫⠟⢧⣄⠀⠀⠀⠀⠀⠀⠀⠐⢙⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠕⠋⠀⠀⠀⠀⠀⠰⣤⡾⠫⠊⠀⠀⠑⢝⢷⣄⠀⠀⠀⠒⠀⠀⠀⠙⢿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣷⠁⠀⠀⠈⡀⠀⠉⣩⡾⡡⠊⠀⠀⠀⠀⠀⠂⠑⢝⢷⣅⠀⠀⠀⠀⠀⠀⠀⠗⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠄⠀⠀⣴⣶⡤⠘⠛⢺⡧⠭⠥⠍⠁⠀⠀⠀⠀⢽⡿⠛⠁⠀⣢⣖⠀⠐⠂⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⢹⣽⣟⠀⠀⢸⣟⠀⢠⡤⠤⠬⠥⣄⠀⣿⡇⠀⠀⢘⣿⣿⣃⠀⠁⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠆⠠⠴⢺⣿⡷⠀⠀⢹⡷⠀⢸⡅⢠⡄⡂⡇⠀⣾⡇⠀⠀⠰⣿⣿⠂⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣒⠂⣀⣸⣿⣟⠀⠀⢸⣗⠀⠘⡄⢸⡇⡇⡇⢀⣻⡇⠀⠀⢺⣿⣿⡂⠐⠆⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠄⠀⠠⣾⣿⣯⠀⢀⢸⡯⠀⠠⠀⠸⠇⡈⡧⠄⣽⡇⠀⠠⢴⣿⣿⡇⠀⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡂⠀⠀⠛⠛⠛⠂⠀⢸⡷⠀⢰⡇⠐⠐⠆⡇⠀⣿⡇⠀⠀⠘⠉⠛⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣉⣁⡀⠈⡉⠉⣉⣁⣹⣹⡶⠈⠉⢉⠩⠿⢽⣿⣏⣏⣀⣁⣉⣀⣉⣉⣀⣁⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⠛⠛⣋⣉⣡⣦⣴⠍⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⡇⠈⠣⡈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡇⠸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣯⣯⣽⣿⣿⣾⣷⠄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣷⣌⠳⣄
⠀⠀⠀⠀⠀⠀⣰⡿⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣷⡌⠳⣄
⠀⠀⠀⠀⢀⣼⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣦⡙⠦⡀
⠀⠀⠀⣠⡟⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⢦⡀
⠀⠀⣼⡯⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠻⣆⠀⠀⣀⣀⠄
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⠛⠋⠉⠉⠀⠀⠀⡆
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠠⡄⣻⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠃⣿⠂⠀⣀⣠⣾⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣿⣶⣿⣿⣿⣿⡿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢹⣿⣿⣿⣿⣿⣧⠀⣀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⡿⠿⠿⠿⠿⠷⠤⠤
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡇⣾⠁
⠀⠀⠀⠈⠉⠛⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⠃
⠀⠀⠀⠀⣀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠆⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠙⠛⠛⠶⠶⢶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠿⠷⠦

⠀⠀⠀⠀⠀⠦⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⢤⡀
⠀⠀⠀⠠⢠⡆⢠⡆⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠈⠀⠀⢠⣄⠁
⠀⠀⠀⡄⢸⡇⢸⡇⢠⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⡿⣷⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣀⠀⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣶⣄⢹⣯
⠀⠀⠀⣷⣸⣟⣸⣗⣼⡄⠀⠀⠀⠀⠀⣸⣿⠀⣶⣿⣿⣦⢠⣿⡇⠀⠀⠀⢀⣀⠀⣿⠀⣿⣿⠀⣿⠀⣀⡀⠀⠀⣰⣆⢸⣷⢿⡿⡿⡮⡿⢠⣦
⠀⠀⠀⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣠⣿⣿⢴⣶⣿⣷⣶⣾⣿⣷⡀⠀⠀⢹⣯⣼⣿⣿⣿⣿⣿⣿⣧⣿⡇⠀⠀⢻⣿⣶⣾⣾⣷⣷⡗⣶⣿⣿
⠀⠀⠀⢸⣿⡏⢹⣿⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⠟⣿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢦⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠇⢀⡀
⠀⠀⢰⣶⣶⡆⠰⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⢀⡈⣾⣦⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣾⡆⠀⠓
⠀⠀⠠⣯⣼⣤⣤⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⣇⣏⣧⣼⠁⠀⠀⠀⠀⠀⠀⢻⣟⣀⠀⣿⣿⢀⣀⣻⡗⠀⠀⠀⠀⠀⠀⣦⡼⡿⢿⣴⠀⡀
⠀⣠⣠⣿⣿⠛⡟⣿⣿⣅⣄⠀⠀⠀⠀⣀⣺⣀⡟⠛⠛⠿⣰⣇⡀⠀⠀⠀⢀⣾⣿⣉⣉⣿⣿⢉⣉⡿⣇⡀⠀⠀⠀⢸⣧⣬⣻⣿⣟⣡⣤⣷
⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⠀⠀⠹⣿⣿⣷⡶⣷⣾⣿⣿⠃⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠸⠿⠿⠿⠇⠈⠿⠿⠿⠿⠀⠀⠀⠀⠐⠿⠿⠿⠃⠸⠿⠿⠿⠀⠀⠀⠀⠾⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠷⠀⠀⠀⠀⠿⠿⠿⠁⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠃⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⢴⠄⠀⠐⠆⠀⣶
⠀⠀⠀⠀⢰⡇⢹⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢰⢀⠠⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⢶⣶⠀⣿⡇⠀⠀⠀⠀⠀⠠⠾⢧⠀⣼⠄⠰⠿⠆
⠀⠀⠀⣶⢸⣷⣾⣇⢰⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡿⣿⢧⡇⠀⠀⠀⠀⠀⠀⠀⣠⣤⠁⣾⣟⢠⣿⡇⠀⠀⠀⠀⠀⠘⣟⡟⣤⣿⣥⢹⣻⡇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣀⣸⣿⣾⣷⣿⣞⣿⣀⣀⡀⠀⠀⢠⡄⢸⣿⣶⣿⣿⣼⣿⡇⢠⠄⠀⠀⠀⣘⣛⣟⣛⣟⣛⣻⣟⣓⡀
⠀⠠⣤⣿⣿⣿⣿⣿⣿⣤⡄⠀⠀⠀⢘⣟⣿⣛⣟⣛⣛⣟⣻⣛⣻⡁⠀⠀⢰⣷⣾⣿⣿⣿⣿⣿⣿⣷⣾⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⢀⣿⡟⣿⡿⢻⣿⢻⣿⡇⠀⠀⠀⣸⣿⣿⣿⣿⣟⡿⠛⠟⠛⢙⠁⠀⠀⠈⣿⡟⠻⣟⠿⢿⢿⡟⢿⣿⠀⠀⠀⠀⢰⣿⣿⣿⡏⣿⣿⣿⣇
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠉⠉⠀⠈⠉⠉⠁
⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠄
⣤⣤⠀⠀⠈⣿⣿⡇⠀⠀⣠⣤⠀⠀⠀⢴⣶⡦⢀⣿⣿⠀⣴⣶⡆⠀⠀⠀⠀⣤⠄⣈⣿⣿⣿⣿⡀⠠⣤⠀⠀⠀⠀⠀⠀⢰⣦⢀⣿⡦⢼⣿⠁
⢸⣿⣀⣀⣀⣿⣿⣇⣀⣀⣸⣿⠀⠀⠀⢸⣿⠷⠶⠿⠿⠶⣿⡾⡇⠀⠀⠀⠀⣿⡀⣟⣛⣛⣛⣛⣛⢀⣿⠀⠀⠀⠀⣿⡇⢸⣯⢸⣿⡇⢸⣿⠂
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠠⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣯⣤⠀⠀⠀⣿⣷⣶⣷⣶⣷⣶⣾⣿⠇
⣿⣿⣿⣿⣿⡏⢹⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⡟⣻⣿⣿⣿⡇⠀⠀⠀⣸⣿⣿⢻⣿⣿⣿⣿⠟⣿⣿⣇⠀⠀⠀⣾⣿⣿⣿⣿⣿⡏⢹⣿
⠉⠉⠀⠀⠈⠁⠀⠁⠀⠀⠈⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠁⠀⠉⠉⠉⠉⠀⠈⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⣦⠗⠀⠂⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡆⠨⠁⡥⠤⢆⡴⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠗⠀⠔⠈⠀⠀⢹⡅⣬⠠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣙⠀⣴⠀⠀⠄⣴⠘⠃⡈⣢⣄⠡⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠯⠀⠶⠀⢞⡉⢁⣤⠟⠓⠻⠟⢃⠀⠀⠀⠀⠀⠀⠀⠊⠻⠫⠁⠸⠛⠛⠲⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣶⣶⡶⣴⣾⡿⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦⡄⠀⠐⠘⣗
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⢸⣿⠀⠀⠶⠙⠀⣩⡅⠀⠀⠀⠀⢀⣾⠉⠟⠈⢿⣿⣿⣿⣧⡀⠀⣿
⠀⠀⠀⡀⠀⠀⠀⠀⣿⣿⣿⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢤⠀⣀⠤⠈⢿⣿⣽⠃⠀⡉
⠀⠠⡀⠀⠀⠐⡀⠀⣿⣿⣏⡀⠷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⠀⠀⠒⠀⢀⣿⠏⡀⢠⠁
⠀⠢⡀⢠⠀⠁⠀⢨⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⣹⣧⡌
⠀⠀⠈⠀⠀⠀⠀⠊⠉⠀⠀⠀⠦⣀⣀⢀⣀⡻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠗⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣴⣿⣟⠋⠉⠁⡈⡁⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠇⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠟⠁⠀⠀⠠⠀⣴⣦⠀⠀⠀⠀⠀⠋⠀⠀⡗⠄⠐⢈⠡⠂⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⣿⣿⡀⠀⠀⠀⠀⠀⠁⠄⠄⠤⠖⠁
⠀⠀⠀⢀⠷⣧⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠛⣋⡥⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠐⠢⡁⠀⠀⠀⢠⡀⠀⠀⠀⠀⢀⡠⠊⡱⢁⠀⠀⠀⠾⠀⠠⠀⠀⢶⠺⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⡋⠑⠊⠁⢰⣤⣵⠈⡠⠂⠁⠠⠀⠁⠀⠀⠀⠉⠃⢤⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠰⡄⠀⠸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣶⠛⠛⠛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⢅⣀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢺⣿⡇⠀⢀⣦⣄⠀⠀⠀⢀⠀⣤⣾⣗⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠷⣦⣤⣀⣄⣠⣄⣼⣿⣿⠙⠛⠃⠀⠘⠩⠻⡛⡷⠿⣛⠫⠏⡐⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠂⢨⠵⡉⠷⣸⠿⠟⣤⣤⠀⠀⠀⠐⠌⠱⠖⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠰⢉⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣍⣭⣯⣭⣩⣯⣽⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⣥⣀⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣀⣘⣿⣁⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣾⡟⠉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⡛⣷⠶⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠹⣇⠿⢤⣸⠓⠒⠶⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⢀⣤⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⣿⣿⡧⠀⠀⠈⢳⣴⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢹⠲⠷⠶⢤⣤⡔⣂⣀⣀⡐⠲⣶⣾⣦⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⢸⠀⠀⢰⣿⠀⠯⢭⣭⡭⠭⢽⡿⠿⠿⣷
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⠿⢿⠀⠀⠀⠀⢸⠀⠀⢸⣿⡇⠀⢸⡟⡇⠀⢸⣿⠀⠘⡈⠳⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢸⠀⠀⢸⣿⡇⠀⢸⡯⡇⠀⢸⣿⠀⠀⣏⡙⠛
⠀⠀⠀⠀⠀⠀⢸⠀⢀⡤⢤⣇⣶⣾⠀⠀⠀⠀⢸⠀⠀⠘⠓⠀⠀⢸⣿⠇⠀⢸⣻⠂⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣴⡏⣇⣾⢻⣿⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠸⣼⣟⡁⣿⡞⠁⢰⠀⠀⠀⠀⠘⠒⠒⠂⠠⠤⠤⠤⠤⠤⠀⣀⡀⠀⠀⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣸⡆
⠀⠀⢠⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⡄
⠀⠀⠈⠒⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣷⠛⠁
⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢛⡴⣼⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠘⣿⡏⠻⣦⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⣼⣿⣾⠃
⠀⠀⠀⠀⠀⠀⢿⣿⠄⠘⢷⣄⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⠀⠄⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⡀⣠⣾⡉⣿⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠉⠉⠁⠀⣰⣶⣦⣶⣷⣶⣦⣀⣀⣀⣀⣀⣀⣠⣵⣶⣶⣶⣶⣶⣀⠀⠀⠀⠀⠈⠙⠉⢉⣬⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡾⠾⠾⠿⠟⠛⠛⠛⠛⢛⣛⣛⣛⣛⡛⢛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠿⠿⠾⠷⢶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣉⣥⠴⠒⠒⡒⣛⣍⠉⠉⠉⠽⠡⣄⠀⠀⠀⠀⠀⠀⠁⢲⡄⠀⠀⠀⡠⠐⢿⡍⠉⠉⠉⣡⡒⠂⠀⣦⣬⡙
⠀⠀⠀⠀⠀⠀⠈⡟⢹⣇⠀⠠⠀⢸⡿⠀⠀⠀⣄⣤⡾⠂⠀⠀⠀⠠⠤⣶⡿⡗⠀⠀⠀⢁⣠⣼⡧⠀⠀⣁⣰⣿⡀⠨⡟⢹⣿
⠀⠀⠀⠀⠀⠀⠀⣷⣼⣇⣀⠤⠽⠯⠁⠐⠒⠒⠊⠙⠂⠈⠁⠀⠀⠀⠀⠐⠘⣋⣾⣶⠶⠒⠎⠓⠒⠒⠀⠒⠿⠥⠤⢄⣷⣿⣿
⠀⠀⠀⠀⠀⠀⣴⣋⣽⣤⣴⣤⣤⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣤⣤⣤⣠⣬⣭⣿⣦
⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣿⣿⣿⣭⣩⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣀⣀⣀⣠⠤⠤⠤⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢸⣿⡿⣣⡄⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣽⣛⡃⠫⢾⣿⣧⢻⠟⣡⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢸⣷⣶⡾⣠⣜⣛⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢸⣿⠟⣰⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⣤⣴⣶⣿⣿⣧⠈⢿⠘⠋⣼⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠿⠛⠛⠋⠉⠙⠛⠛⠿⢿⣿⣿⣿⣷⣌⡻⠟⠛⠉⠉⠁⠈⠀⠈⢁⣴⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣙⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠙⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄
⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟
⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃
⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣄⡀⢰⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣮⣭⣥⣀⣀⣤⣤⣶⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣬⣙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣦⣤⣄⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⣿⡀⠀⠀⠰⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢶⠀⠀⠖⢒⣻⣷⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠄⠀⠀⢀⣸⡆⡀⠋⠉⢻⡏⢀⣀⣸⡆⠀⠀⠀⠀⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠘⢻⡇⣧⠀⠀⣸⣷⢸⠘⢻⡇⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⢠⣼⣧⢰⡄⣸⢿⣿⣼⣄⣼⣧⠀⠀⠀⠋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣤⣿⣷⡄⠀⢲⣿⣿⡾⣰⡟⣏⣿⣿⣿⢿⣿⠀⢠⣮⣤⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⢠⡀⠃⣹⣿⢉⢹⣿⣿⣿⣿⡏⢸⣿⢀⡄⣤⣤⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢀⣿⡏⣹⣿⠠⣞⡟⠾⠿⡟⡿⢙⣿⢃⣿⣆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠙⡇⣻⡿⠀⣀⣤⣤⣀⠀⠀⢻⣿⡟⣹⣿⣧⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢹⡃⠀⢘⡇⢸⡇⢸⣿⣿⣿⣿⠂⠘⠀⣿⡧⣻⣿⡏⣽⣇⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⡇⣶⣿⣿⣄⣼⡇⣹⡇⠠⣿⣿⢻⣿⠀⠒⢈⣿⣧⣾⣿⣿⣿⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠶⢶⣶⣿⣧⣶⣻⣿⣛⣻⡷⠞⠋⠉⠉⠉⠳⢾⣛⣛⣿⣓⣦⣼⣿⣶⡶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢯⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⣿⡛⢿⣿⣿⢟⣋⣙⣇⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢽⣛⡿⢿⣵⣿⣖⣛⣫⡭⣽⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢿⡏⢻⣿⣿⠋⣽⡟⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣜⣿⣿⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠛⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠻⣿⣿⣷⡄⠘⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣷⠄⠘⢿⣿⣿⡄⠘⠿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠈⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠈⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⢀⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣶⣤⡀⠘⣿⣿⣷⡀⠀⣾⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⡀⠘⢿⣿⣿⣦⡈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠻⣿⣿⣿⣶⣤⣀⣀⠀⠀⢀⣀⣠⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠜⠤⢔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠋⠁⠒⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠄⣀⢉⠙⠷⢦⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠋⠀⠀⠐⠋⠀⠝⢱⠦⣄⠁⡀⣀⠶⢴⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠘⣻⠇⠀⠀⢉⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⢙⡇⢀⡎⠀⣄⠀⠀⠀⠀⠠⠀⠀⠈⣧⠀⠀⠈⡦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⠀⠛⠛⠛⢶⣾⣧⣠⠃⢛⠻⡇⠀⣄⠀⠼⠃⠀⠈⣷⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⡀⠀⠈⠿⣿⣷⣾⡶⣧⣔⡃⢠⣆⠀⠀⠀⣟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠶⠛⠉⠉⠀⠀⠀⠈⠛⠋⠁⠀⢻⣿⣿⡟⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢉⣴⣿⣷⣦⣄⠀⢾⠇⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣿⣿⣿⣷⢀⡾⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣿⣿⣿⣿⣿⣿⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⠏⣰⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⣿⣿⣿⣿⣿⣿⣿⣷⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠁⣰⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣼⠿⠋⠀⠉⠁⠀⠀⠉⢿⣧⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⠐⣄⠀⠐⡫⠟⠙⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠘⠻⠿⣿⡿⡁⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠙⠂⠀⢠⡾⠁⠀⢀⣼⠏⠁⠀⠀⠀⠖⠀⣰⣷⣤⣀⡀⠀⠀⠀⠀⠀⠐⠁⠈⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠠⣶⣿⣶⣤⠟⠁⠀⠀⠁⡀⠃⠀⢀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⣰⠿⠿⣿⡟⠀⣳⣤⠤⡶⠀⠀⠊⠈⠉⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣻⠃⠀⠀⠆⠈⠙⠋⡘⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠰⢿⣦⣤⣆⠀⠀⠀⠈⠁⠠⠀⣰⣿⣷⣦⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢠⠁⠸⠿⠿⡇⠀⢀⡤⠄⢠⡆⠀⡾⢿⣿⣿⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣀⠆⠀⠀⠀⠀⠀⠀⠈⢠⠄⠀⠀⠀⠀⣦⣄⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⣿⣿⣿⡗⠀⠎⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡯⠀⣀⡀⢻⣿⣿⡇⠄⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⡙⠀⢀⠀⢀⠀⠀⠀⠀⠀⠈⠦⠄⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠀⠀⠀⠀⡿⠀⠀⠂⠀⠀⠤⡀⠀⠠⠜⣿⡶⠈⠁⠀⢠⡅⠀⠀⢀⡀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⢀⢰⡖⠀⣶⣤⣤⡗⠀⠀⡀⠠⠀⠀⠉⠐⠁⠈⠋⡁⠤⠀⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠘⠀⢱⢀⣿⣿⣿⠳⡆⠈⠁⡄⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡄⢀⡀⠀⠀⠀⡸⠉⠛⠻⠀⠷⠤⠴⣦⠀⠀⢠⣤⣄⣀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠾⠋⠉⠀⠀⠀⠀⠀⢃⠀⠀⠈⠃⢠⠄⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠖⠀⠳⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣿⡀⠀⡀⣀⠀⠸⠿⢿⡿⠀⠀⢀⠀⠀⡄⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣤⣤⡎⠀⠀⠀⠸⣏⠀⡆⠀⠀⠠⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠳
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠰⠀⠀⠀⠀⣸⡁⠀⠀⣦⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⣴
⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠿⠋⠁⠀⠀⠀⠰⣾⣿⣿⣶⠀⢾⡀⠃⠀⠀⠀⠇⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢤⠚⠀⠐⠀⠻⣿⠟⠁⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡀⢀⢀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⠿⣿⣿⠿⢿⣿⣿⣿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣌⣤⣤⣧⣤⣮⣤⣼⣧⣥⣿⣏⣼⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣀⣠⣤⣴⣶⠶⠶⠿⠛⠛⣿⣿⣍⠉⠉⠁⢹⣿⢷⣄⠀⠀⠀⠀⣠⣶⠟⠁
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠋⢩⣿⣿⣿⡀⠀⠀⠀⣼⡟⣿⡟⢷⣄⠀⠘⣿⠀⠙⢷⣄⠰⠿⠋
⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⢀⣴⡟⢡⣿⠀⣰⡟⣿⡿⢹⣧⠀⠀⣰⡟⠀⢸⣷⠀⠙⢿⣦⣿⡇⠀⣀⣹⣷⡄
⠀⠀⠀⠈⠛⠷⠀⠀⠀⣠⡾⠋⠀⢸⣯⣾⠋⢠⣿⠃⠀⢻⡆⣰⡟⠀⠀⠀⣿⣆⣤⣤⣾⣿⡿⠿⠛⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣏⣀⣀⣠⣿⣿⣥⣤⣾⣿⣤⣤⣼⣿⣿⠶⠶⠾⠿⣿⡟⠛⠉⢩⡿⠁⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣍⠉⠉⢿⣏⡉⠉⠉⢻⣧⠀⠀⠸⣧⠀⠀⠀⠀⣿⠀⠀⢠⡿⠁⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠙⢷⣄⠀⠀⢻⣧⠀⠀⣿⡀⠀⠀⢸⡏⠀⢠⣿⠃⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⠙⣷⣄⠀⢻⣧⠀⢸⡇⠀⠀⣾⠇⢀⣿⢃⣾⠋⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠀⠀⠈⠛⢷⣌⠻⣦⡀⢻⣇⠘⣿⠀⢠⣿⢀⣾⣳⡿⠁⠀⠀⠉⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠙⠿⣮⣿⣦⣻⣆⢿⡆⣸⣇⣾⣿⠟⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣧⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣩⣿⣯⣤⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠟⠛⢋⣉⣉⣥⣤⣤⣤⣤⣄⣉⡉⠉⠛⠛⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⢉⣠⣴⠶⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠷⣦⣤⡀⠈⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⢁⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡈⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁⠀⣠⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⡉⠙⠻⠷⢶⣶⣤⣤⣤⣤⣤⣴⣶⠾⠿⠛⠉⠀⣀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⣦⣤⣤⣤⣀⣀⣀⣀⣠⣤⣤⣴⡶⠾⠛⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⣁⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇
⠀⠀⢀⣶⡄⠀⠀⠀⠀⣧⢠⣉⣓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⣿⣿⣦⡄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠄⣸⠀⠀⠀⠀⢠⡄
⠀⠀⠸⡦⣝⣆⠀⠀⢀⣙⣧⡻⣿⢏⠤⢤⣄⠀⠀⠀⠀⡰⢒⣲⣖⠿⣾⣿⢩⣊⠴⣒⣲⠦⡀⠀⠀⠀⢀⡤⠶⢤⣻⣿⢏⠴⣃⠀⠀⠀⣠⣧⡼
⠀⠀⠀⠙⣿⣿⢦⡀⣿⡭⣙⢷⣸⡿⡿⣷⢀⡇⢀⣠⡀⠻⢇⢸⡛⢳⣝⣿⡜⢡⠊⢹⢆⠕⠁⣀⣀⠀⢿⣦⠾⡑⣿⡋⠾⡛⣽⡇⢀⠴⣿⡟⠁
⠀⠀⠀⠀⠈⢻⣶⣷⢬⡶⣷⣿⡘⣉⡧⢣⠏⠀⣸⠆⢇⡀⠀⠹⠃⢸⠇⠆⠖⢾⡀⠓⠁⠀⢀⠷⢸⡀⠀⣿⠇⣟⣙⣳⣿⣯⣾⠤⣧⣾⠋
⠀⠀⠀⠀⠀⠀⢹⡛⣆⢧⣈⣼⢧⣀⠙⡦⠤⠾⠅⠁⠀⠉⠗⠒⠾⠃⠀⠆⠀⠀⠊⠑⠖⠊⠁⠀⠉⠙⠢⠤⠖⢋⣀⡟⢮⣁⠿⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢷⠧⠒⢉⣁⣤⣤⣴⣴⡶⠶⡶⠚⠛⠿⠿⠟⠛⠿⢛⣥⣔⠲⠒⠒⠂⠀⢉⡀⠀⠀⣶⣶⣦⣴⣦⣤⣬⣷⣤⣭⡏
⠀⠀⠀⠀⠀⠀⠀⠙⣶⠟⣿⠟⣯⡀⠒⢃⣀⣀⡀⠀⠀⣀⣒⡒⠒⠂⢻⣷⠿⣵⣶⣶⣶⣄⢀⣠⣶⣢⣤⣤⠛⢿⣷⡝⢻⣯⣿⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣯⠘⠏⠀⠀⠹⠿⠛⠗⣚⣛⣒⡛⠛⣛⣛⣛⣁⣀⣒⣈⣀⣒⡒⠒⡲⠷⠚⠛⠛⠛⠛⠚⠻⠇⠀⠘⣿⢫⡿
⠀⠀⠀⠀⠀⠀⠀⢰⠻⢿⣿⣿⣿⣶⣾⣥⣭⣭⣭⠍⠛⠋⠉⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣬⣥⣶⣶⣶⣦⣾⣿⠻⢟⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠠⠭⠬⠥⠾⣭⣭⣤⣤⣠⣤⣠⣶⣶⣶⣾⣛⣛⣛⠛⣛⣛⣛⣛⣛⣉⣉⣉⣉⠩⠤⠤⠤⠒⠒⠊⠉










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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⡬⢛⡛⢥⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠶⢷⣶⣻⣟⣩⣍⡙⢶⣧⣘⣃⣼⡶⢋⣩⣍⣻⣟⣶⡾⠶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⡾⠶⣼⠈⠁⠀⠀⢸⡇⣛⣛⢸⡇⠀⠀⠈⠁⣷⠶⢷⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⡿⠿⡇⠀⠀⠀⠀⢸⠈⠿⠿⠇⡇⠀⠀⠀⠀⢸⠿⢿⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠛⠟⢻⠀⢠⣄⠀⠀⢁⣾⣷⡈⠀⠀⣠⡄⠀⡏⠻⠛⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣴⣿⣦⣴⣯⡯⣷⢴⣿⢾⡷⣿⡦⣾⢽⣵⣦⣴⣿⣦⣠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣋⣉⣝⣬⣤⣧⣷⠵⣤⡽⣭⣭⢭⣤⠤⣾⣬⣦⣥⣏⣍⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠹⣙⢇⣽⣐⣦⣷⣸⣄⣫⣝⣠⣇⣸⣴⣂⣯⡸⣛⠏⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠛⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠀⠉⠉⠉⠉⠋⠉⠉⠛⠛⠃





⣿⣿⠻⠿⢻⠿⣿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣤⣤⡎⠀⠀⢀⡀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢠⢂⢱⡜⠉⣡⠀⠂⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⣺⣷⠂⠀⠀⠀⠀⠀⢈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⢻⣀⣀⣀⡀⠄⠞⠁⢰⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⣤⡴⣦⡉⠀⠀⠀⢀⠀⡜⢄⣀⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⡰⠂⠀⠀⠀⠀⠀⠀⢳⣀⣿⡟⠲⠤⠁⠠⠈⠁⠀⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠈⠀⠀⠀⠀⠠⠚⢋⣈⣠⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⢀⠓⠒⡂⠩⠭⢩⠀⠁⠙⢦⠀⠀⠀⠀⡠⠀⠀⢠⠇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠢⣀⡨⠃⠀⠀⠀⠀⠀⢆⠐⢿⠱⢀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠁⡇⠀⠳⠤⣤⡀⠀⠈⡆⠀⠐⣞⣏⠒⠒⢡⡎⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠘⣄⠀⠀⠀⠙⠀⠀⠈⠶⢶⠉⢫⣳⢦⡾⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣠⡟⠉⠒⣄⣄⠀⠀⠀⡸⠘⡆⠀⠈⠓⠚⠙⡇⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠚⠋⠻⣦⣠⡇⢸⡏⠒⣞⢣⠀⠘⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⢸⡇⠀⢸⡈⡄⠀⠘⢦⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⢲⣇⠀⠀⢃⠘⢄⠀⠀⠑⠤⣼⡵⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⢸⠘⣄⠀⠀⢢⡈⠳⢄⠀⠀⡀⠃⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⠓⡦⢇⠙⠢⣤⡭⠋⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⡀⠈⠀⡀⠑⠒⠉⠀⠀⣈⡨⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠇⢀⣦⠤⠄

⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠟⣃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣅⣿⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠟⠷⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣾⣿⣿⣿⣿⣷⣾⣷⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣿⣿⣿⣿⣀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⣤⠌⣋⣉⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⡿⣿⣿⣿⣟⣿⣿⣯⡇⣼⠀⠀⠀⠀⠀⠀⠘⠋⡖⠀⠀⠉⠈⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡽⡇⣿⢹⣿⣟⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣽⣿⡇⣿⣿⢿⣿⣇⣿⠆⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡤⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣸⣿⣿⣿⣿⣿⣿⣿⠯⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠈⠉⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣯⡤⠤⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢠⠀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠏⠀⠀⠀⡀⡄⣴⣦⣹⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⡈⠐⠚⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢠⠀⠉⠻⢿⣿⣿
⣿⣿⣿⣿⣿⠂⢀⢠⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠿⠂⠀⠀⢈⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣧⣠⣿⣾⣧⣰⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⣠⣤⣿⣸⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠖⠂⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣠⢄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣟⣻⡻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡵⠋⠧⠽⠈⢪⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢵⣿⠀⠀⣿⠀⢿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣌⣛⣀⣀⣛⣃⣽⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⡏⠉⠉⠉⠉⠙⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⠇⢰⣯⣿⣦⠀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢒⡭⠚⣿⡀⠘⠾⠽⠋⠀⣿⡓⢯⣒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡮⠕⠊⠁⠀⠀⣹⣧⣦⡀⢀⣴⣄⢿⡇⠀⠈⠑⠺⢵⡢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣪⡵⠚⠁⠀⢀⡀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣸⡇⠀⠀⢀⡀⠀⠈⠓⠮⣕⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢹⡅⠀⡴⢻⣿⣯⠳⡄⠀⡏⣿⣿⡇⢸⣿⣿⢹⡇⢠⠞⣹⣾⡝⢦⡀⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⡇⢸⢁⣀⠉⢁⡀⢸⠀⢧⡟⠉⢃⡘⠉⠛⣿⡇⡇⢀⡈⠉⣀⡀⡇⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⡇⢸⣾⣿⣧⣿⣽⢸⠀⣼⠇⣴⠋⡏⢦⠀⣿⡇⡇⣿⣿⣴⣯⣷⡇⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢸⣷⣿⣦⣾⣿⣼⠀⢿⠠⡇⢰⡇⢸⡆⣾⡇⡇⣷⣗⣽⣻⣆⡇⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣺⡇⢸⣿⣿⡟⣿⣽⢻⢰⣿⡶⡇⢸⡇⢸⢷⣿⡧⡇⣯⣯⣿⢽⡏⡇⢰⣷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⡇⠸⠽⠿⠥⠿⠯⠼⠀⡛⣶⡇⢸⡇⢸⡆⣻⡇⠧⠿⠿⠭⠿⠯⠇⠀⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⣤⣧⣤⡤⣤⣤⣤⣤⣤⣴⣷⣿⣿⣿⣿⣿⣷⣾⣧⣤⣤⣤⣤⣤⢤⣤⣴⡧⢧⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⢒⡖⠲⠢⢄⣀
⠀⠀⠀⠀⠀⠀⢀⣠⡯⣡⠴⢻⣦⡖⠲⣄⠈⣳⡀
⠀⠀⠀⠀⠀⠀⢰⡍⡜⠁⠀⣼⡉⣳⡄⠈⢆⢈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣆⡀
⠀⠀⠀⠀⠀⠀⢺⡶⣀⢤⣾⠩⣶⠈⠉⠲⣼⣈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢟⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠈⣧⠻⣗⣿⠂⠛⠀⢿⣼⣏⣾⠃⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⡟⡘⠎⠲⢐⠒⢣
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠿⠀⠿⠆⡟⡿⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣄⡀⣠⣄⢀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣦⣼⡦⠄⢠⣿⣷⣤⣴⣿⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⡃⡉⠉⠘⣽⡇
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠗⢻⡿⠥⠀⢙⡿⢿⣧⢸⣤⡄⠈⢢⠀⠀⠀⠀⠀⢀⣼⣿⣇⠛⠋⡀⢸⣿⣿⣆
⠀⠀⠀⠀⢀⡔⠉⠉⡏⠀⣿⣔⣂⢒⣿⡇⢸⠈⡿⢻⡷⣦⠄⠃⠀⠀⠀⢰⣿⣿⣿⣿⣟⣉⣀⢠⡿⢿⣿⣄
⠀⠀⠀⢠⣟⢬⣄⠀⣇⠀⡏⠙⠛⢿⣿⠃⠸⠀⣿⠈⣿⣿⡀⣾⠀⠀⢀⡾⠉⠉⠈⣿⣿⣄⣴⣿⠃⠀⢀⠚⣽
⠀⠀⠀⢸⠁⠘⠃⡂⣏⠀⣧⠀⢀⡿⣿⠀⡔⢠⣏⠀⢱⣿⡄⢺⠀⢠⣿⣿⣤⣷⠪⣿⠍⠉⠸⡛⠀⠀⡄⠸⢻
⠀⠀⢀⣸⠀⠀⢠⢤⣯⠀⣿⠷⣼⢃⣿⠀⣧⢼⣿⠀⢸⡏⡄⢸⠀⢸⠻⡼⠋⡏⠀⣎⡀⢀⡇⠀⠀⡀⡀⡆⠈
⠀⡰⢻⣿⡵⢦⡿⢰⡟⠀⣿⣿⣇⢸⡟⠀⣗⠎⣿⠀⢸⣿⠀⡘⠀⡘⣇⠀⢀⣿⠀⣸⡟⢼⠃⢀⠠⢱⡾⠁⢀
⠀⡇⢸⠋⠀⣰⠁⢹⡇⠀⡇⢹⡛⢸⣧⠀⣾⠀⣿⠀⢸⠨⡆⠇⡞⠛⣿⡿⣿⡹⠋⠁⢾⣠⣤⠏⠀⣾⠓⠀⢙
⠀⡇⢸⢲⡞⡹⡆⢸⣇⠀⡇⠈⠃⢸⡇⠠⣧⡀⡇⠀⠸⠀⠇⡇⢇⣀⣈⣼⣿⣧⣤⠔⠒⠉⢋⡀⢸⣿⡇⡀⢠
⠀⡇⠘⠸⢫⣧⣸⢿⣿⠀⣧⣈⣤⣼⡇⢸⠃⢦⡇⠀⠀⡐⢀⠃⠀⢀⣿⣟⣿⡿⠥⣬⡄⢰⠶⠊⣽⣿⡇⠀⠀⡀
⠀⠃⠀⡄⡏⢻⡟⠘⢿⡃⢹⣍⣉⣿⡅⢸⠆⠘⣧⢀⡜⢁⠎⠀⠀⢸⣿⣿⠟⠁⢰⠧⢡⣤⠌⠀⡏⠹⣧⠀⠀⢡
⠀⠀⠀⠃⠘⢶⠀⣈⣺⡇⠘⣁⣠⣿⠇⢈⡀⠘⣷⠏⠀⡎⠀⠀⠀⢸⣿⡏⢀⠶⠀⠀⠀⠀⢀⢁⡏⠀⣽⡄⠀⠀⠆
⠀⢰⠀⢠⠀⢸⠀⠙⣿⣿⣄⠙⠓⠉⣠⣧⡀⠀⡿⠀⡇⠃⠀⠀⠀⠺⣿⡧⠖⠀⠀⠀⠀⠀⢠⣞⣃⣁⢸⡿⢢⡀⢸
⠀⠈⠀⢸⡀⢰⡴⢚⣿⣿⣿⡶⢶⣾⡿⠧⣍⣰⡇⠀⡇⠀⠀⠀⠀⠀⠹⠄⠠⠀⠀⡀⠀⣠⠟⠉⠀⠀⢹⡇⢸⠟⢻
⠐⠚⡉⢁⡄⢸⡶⠛⠉⠟⣿⠀⢸⡟⠀⠀⠈⢹⡇⠂⢷⠀⠀⠀⠀⠀⠀⡶⠃⣰⣾⣰⣶⣿⡁⠀⠀⠀⣼⡇⡰⠋⠉
⠀⠀⣯⣻⠀⠀⡀⠀⠀⠀⣽⠀⠈⣷⠀⠀⠀⢸⡇⢷⠈⢆⠀⠀⠀⠀⠀⣷⣾⢿⢾⣿⣿⡌⢇⠀⠀⢀⡿⣇⢡⡄
⠀⠀⠀⠙⠀⠀⠇⠀⠀⢸⣿⠀⠀⢷⠀⠀⠀⢹⣷⠈⢣⠈⠄⠀⠀⠀⠀⢻⠟⢣⣾⡏⡿⢇⠈⠳⢀⣿⡇⢁⠚⡇⡴
⠀⠀⠀⠀⠀⢸⠄⠀⠀⣿⢨⠀⣁⣼⠀⠀⠀⢸⠉⢁⡼⢧⠘⠀⠀⠀⠀⢣⣤⣿⣿⠄⣧⠈⠠⠐⣾⠁⡇⢸⣴⡔⠁
⠀⠀⠀⠀⠀⢸⠀⠀⢘⣧⣼⣩⣿⠁⠀⠀⠀⢸⠀⠀⠀⠀⠆⠃⠀⠀⠀⠀⢹⡟⣿⠀⡏⠀⠀⢸⡿⠀⡿⠂⡇
⠀⠀⠀⠀⠀⢸⣀⡐⠋⢙⣿⠁⡇⠀⠀⠀⠀⢠⠂⠀⠀⠀⡃⠀⠀⠀⠀⠀⠘⣾⣿⡀⣿⡀⠀⣼⡇⣠⣧⡔
⠀⠀⠀⠀⠀⠘⡭⠀⠀⠀⣿⠀⣿⡀⠀⠀⢠⡎⠀⠀⠀⠀⠃⠆⠀⠀⠀⠀⠀⣿⣿⠁⡿⠶⠾⣿⡟⠁⠸⠁
⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⢹⠐⣏⠁⠀⠀⢰⡇⠀⠀⠀⡘⠐⠀⠀⠀⠀⠀⠀⢻⡯⠀⣿⠀⠀⡟⣿⢀⣠⠃
⠀⠀⠀⠀⠀⢀⣿⣦⢶⠀⢸⢈⡍⠀⠀⠀⢿⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡏⠀⢀⡇⣄⠞⠁
⠀⠀⠀⠀⠀⠘⣤⣥⠞⠀⡌⢰⣷⠀⠀⠀⢸⠀⠀⢀⢣⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣦⡸⡇⠁
⠀⠀⠀⠀⠀⢰⣏⣡⣤⠴⠀⣼⠉⠓⠂⣀⠞⠀⠀⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠀⣿⡁⠀⡇
⠀⠀⠀⠀⠀⣧⠼⠛⢁⣀⠈⠀⢱⠒⠉⠙⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠀⢸⣛⠀⡇
⠀⠀⠀⢀⡠⠗⠚⠉⠉⢹⠀⠀⢸⠄⠀⢁⠀⠀⠀⢞⡀⠀⠀⠀⠀⠀⠀⢠⠏⢠⣿⠀⣾⠟⠒⢧
⠀⠀⢸⣷⠆⣀⣠⣶⠿⠟⠁⠀⠸⣿⣷⣤⡆⠀⠀⠈⠳⠄⠀⠀⠀⠀⣰⡏⢀⡏⣼⠀⣿⠧⡀⠀⢑⣄
⠀⠀⠙⠿⠟⠋⠁⠀⠀⠀⠀⠀⠻⢶⢿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠛⠋⠁⠀⠘⠦⠜⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡳⠀⠀⠇⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠂⠀⠀⠁⠐⢀⠉⠃⠀⠉⣉⡀⠀⠀⠀⠐⠈⠠⢶⡷⠆⠀⠀⠉⠁⠉⠉⠏⠉⠛⠳⣶⣄⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠦⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡎⡀
⠀⠀⠀⠁⠀⢀⡤⠒⠩⠀⠀⠀⠒⠀⠀⡀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⡅
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⡄⠀⠀⠀⠈⢮⣐⢄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠘⠁⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡆⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢠⡤⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠖⢻⠇⠀⠀⠀⠐⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠐⠋⡁
⠀⠀⠀⠀⠤⣾⠁⠀⠀⠀⢀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇⠀⠀⢠⠀⠀⠈⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠘⣓
⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⣘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠠⠋⠀⠀⠁⠀⠀⠀⠈⢹⡄⠀⠀⠀⠀⣉
⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⢸⣹⡄⠀⠀⠀⠀⠀⠀⠀⢐⠀⠈⠀⠀⠀⠀⠠⡀⠠⠀⠀⠀⠂⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⢉⠁
⠀⠀⠀⢠⠼⠀⠀⠀⠀⢀⣸⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠆⠀⠀⠀⠐⣀⣀⡀⠀⠀⢀⡞⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠛⠂
⠀⠀⠀⠄⠰⡇⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠆⣤⣶⠟⠋⠉⠉⡙⠛⣦⡞⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⢈⣭⣶⣶⣦⣤⣄⠁⠀⠀⠀⠀⢀⡇⠀⠀⣀⢀⣰⠏⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⢨⣄⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⢧⠀⠠⠴⠀⠐⠏⠋⣈⡠⠟⠋⠀⠀⠀⠀⣼⠀⠀⢐⣭⠞⠁⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠈⠷⣼⣶⡄⠀⣀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡇⣠⣶⠎⠁⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣾⡇⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢻⡿⣽⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⡟⢇⢏⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣅⣅⠙⢃⠰⡄⡄⠀⠀⡀⢠⣾⡏⠀⣁⣼⠿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠀⣒⣀⠡⢘⣄⣠⠁⢃⣙⡀⠠⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚⠋⠁⠈⠛⠲⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟
⠀⢰⣶⡄⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣛⡀⢀⣛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢠⣶⡆
⠀⠀⠉⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣼⡸⣿⣿⣿⣿⢇⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠺⠟⠛⠈⠻⠟⠁⠛⠻⠗⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠚⠹⠛⢛⠛⢓⠀⣀⠀⣀⠒⡒⢒⡖⢒⡒⢒⡒⢲⠒⣀⠀⣀⠀⡚⠛⡛⠛⠏⠓
⠀⠀⠀⡁⠆⠀⠃⣘⣃⡈⠁⠈⠀⠉⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠉⠀⠁⠈⢁⣈⣁⠘⠀⠲⢈
⠀⠀⠀⢠⣾⣿⣿⣷⡶⣿⠖⠀⠀⠻⠿⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠿⠟⠀⠀⠲⣿⣶⣾⣿⣿⣷⡄
⠀⠀⠀⡈⠿⠿⡛⢛⡚⢡⡀⢠⠀⣤⠀⡤⠀⡄⠠⠆⠰⠆⠰⠄⢠⠀⢤⠀⡤⠀⡄⢀⡌⢓⡛⢛⠿⠿⢁
⠀⠀⠀⢀⣭⣤⡵⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⢮⣤⣭⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⢊⣴⠀⠀⠀⠀⠀⠀⠀⠐⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⢰⡅⠂
⠀⠀⠀⢈⣵⡈⢉⠢⠀⢀⡀⠀⠀⠀⢀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⣀⠀⢀⣾⠋⢴⣅
⠀⠀⠀⠀⠙⡤⡀⣷⠑⡄⢴⡇⠀⠀⣸⣿⣿⣷⣄⠀⠀⣌⡁⠀⠀⢾⣿⣿⣷⡀⠀⠀⣶⢄⠄⢻⡏⠀⠈
⠀⠀⠀⠀⠀⠘⣶⣾⠀⣿⣾⣿⣄⡴⣻⣿⣿⣿⣿⣷⣤⠛⠃⠀⠀⠀⠀⣿⣿⢷⣀⠼⣛⠁⢠⠾⣷⠇
⠀⠀⠀⠀⠀⠀⠈⡁⠀⢹⣿⣿⠿⢾⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣠⣿⣿⣷⣭⣽⠏⠀⣿⠄⠋
⠀⠀⠀⠀⠀⠀⠀⢹⠀⣸⣿⣯⣤⣀⣭⣿⣿⣭⣭⣭⣭⠤⠄⠀⠀⠈⠉⡉⣙⢛⣟⣟⡀⠴⣟⡠
⠀⠀⠀⠀⠀⠀⠀⠈⣨⢱⣾⡇⠀⠀⢸⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⠉⣹⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣦⣴⣿⣿⣭⡭⠤⠤⠄⠀⠀⢀⣀⠀⠈⢉⣉⡭⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢾⣿⠿⠿⢿⣿⡟⠓⠲⠖⠒⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠓⠒⠒⠒⠶⠶⠶⠒⠒⠒⠒⠒⠚⠛⠛⠛⠋⠉⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠔⢋⠉⣈⠀⠀⠀⠀⠐
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠚⠋⠁⠀⠀⠀⠀⠀⢀⠠⣄⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢀⣤⣺⡘⢋⠀⠀⠾⢹⣆
⠀⠀⣠⣇⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣀⢸⡷⣶⠂⠈⢓⣁⣉⡙⠀⠠⣢⢦⣳
⠀⠈⠁⠠⠁⠀⠀⠀⠀⠀⠂⠀⠀⢘⠇⣼⣇⣀⣴⣾⡟⠁⠀⠈⣁⢻⣿⣷⣿⠿⣤
⠀⠀⠘⢷⡄⠀⠀⠀⠠⠀⠰⠤⠄⡺⢀⡟⣻⣿⠟⠋⠀⠐⠠⣄⢹⣿⣿⡿⠃⠀⠙
⠀⠀⠀⠀⠃⡈⡄⠀⠀⠂⡠⠤⠔⣡⡾⠿⣿⡏⠀⠀⡀⠀⢀⡀⠀⠋⠁⠀⠀⠒⢜⠂
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠌⣠⣴⣿⠁⠀⠘⣿⠀⠀⠈⠁⠈⠁⠀⠀⠐⠂⠐⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣆⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⡜⠦⣱⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣼⣿⣿⣿⣿⣷⠄⠚⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠃⠀⠠⣤⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠒⢠
⠀⠀⠀⠀⠀⢸⣴⣿⣿⣿⣿⣿⣿⡿⠿⣄⣀⠀⠀⣠⣿⣆⠀⠤⣡⡀⣴⣦⡀⠂
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢿⡿⠱⣤⠛⢄⠉⠛⢛⠼⣿⡿⣄⠱⣿⣟⡹⢿⡤⡄⡀⠀⠀⠀⠀⠰⠦⣄
⠀⠀⣠⣾⣿⣿⣿⡿⣿⣿⡯⣸⡇⠀⠸⣇⠀⠩⠈⠁⠀⡜⠘⣩⠄⠘⠤⠑⠚⠤⠌⣉⠐⠖⠲⠊⠀⢶⠈
⠀⢀⣿⣿⣿⡯⡴⠄⠋⠀⠰⠋⠀⠀⡀⠙⣧⡄⢿⠀⢣⡀⠀⣝⠖⠂⠁⠠⠄⠠⠄⠠⠉⠀⠀⠀⠀⣨⠀⠻
⠀⢸⡇⠙⡗⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣗⡀⠀⠢⡽⠀⢾⠆⠀⠠⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⢘⠦⢀⣀
⠀⢿⠀⠀⠀⠀⢢⢠⠐⠃⠀⠈⠁⢀⡀⠀⠀⢹⠆⠐⠀⠀⠀⣊⠀⠀⠀⡄⠀⠀⠄⠀⠀⠀⠁⠀⠀⣾⣏⡁
⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⣀⣸⠇⠀⠒⠀⠀⠀⠐⠀⠀⠄⠀⢀⠀⠰⢧⡉⢈⡙
⢠⣤⣀⣄⣄⣄⡤⣃⢂⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⢈⣸⣆⠀⠀⠉⠛⠋
⠈⠀⠀⠀⠀⠈⠸⣳⣟⠆⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠂⢀⣷⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠄⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠂⠶⡄⠀⠀⠀⣀⡄⠀⢘⡈⠀⠀⠀⠀⡀⠀⡰⢤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⣶⡄⠀⠈⠀⠁⠀⣸⠀⠄⠀⠀⠀⠌⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢕⠂⠐⠂⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣍⣬⣹⣤⣏⣽⣭⣽⣟⣵⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣿⣟⠀⠀⢳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠰⡀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠡⠃⡂⠀⢀⣼⢻⠟⣀⣀⠀⠀⣼⣿⣿⣿⠿⠛⠻⠿⣷⣄⡀⠻⠀⠀⠀⠀⠀⠄⠀⠀⠀⣴⠀⠀⣼⠏⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⡆⣴⠀⢀⣾⠃⢸⠇⠘⠇⠀⢺⣿⣿⣿⣯⣤⣤⣄⣄⡀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⣸⡿⠀⢹⣷⡀
⠀⠀⠀⠀⠀⡀⢀⡟⣀⠀⠸⣵⡏⠀⠀⠩⡀⠚⠀⠈⡷⠰⣾⣿⠿⠟⠛⠉⠉⠉⠙⠙⠟⠀⣠⣦⡀⠀⠀⣤⠀⠀⠻⡆⠉⣶⣿⡇⠀⠀⠙⣧
⠀⠀⠀⠀⣼⠁⣾⠡⠁⠀⢸⣿⠀⠀⠀⠀⠙⣿⣿⡿⠉⠭⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠇⠀⠀⠀⢹⣷⣿⡇⠃⠀⠀⠀⠈⢀
⠀⠀⠀⠀⢻⣻⣿⣿⣿⣿⣿⡿⡟⢓⠒⠖⠶⢿⡿⠁⠀⢀⣹⣿⠀⠀⠓⠀⠀⠀⢰⠀⣷⣶⣦⣀⡀⣀⣀⣀⣀⣀⠈⢀⢙⣿⠀⢀⣀⣀⣀⣀⣀⣆
⠀⠀⠀⠀⢸⣿⣧⠬⢴⣯⣾⣿⠀⠀⣠⡄⠀⠚⠀⠀⠀⠀⢉⣷⠀⠀⠀⠀⠀⠀⠀⠀⣫⠏⠛⢻⣟⠛⠛⠛⣟⠉⠉⢹⡋⠉⠂⠸⣿⡍⠉⠉⠉⠛
⠀⠀⠀⠀⠈⣛⣽⣆⠈⠛⣿⣿⠀⠀⠹⠃⣴⡶⠖⢿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠀⣄⠀⡟⠀⠀⢘⠛⢀⣀⣈⣛⣀⣀⣈⡉⢀⡆⢸⡿⠷⠆⠙⠛⠁
⠀⠀⠀⠀⠀⣬⣿⡟⢸⣿⢽⣷⠀⠀⠀⢀⡙⠆⠐⠖⠂⠙⢛⣿⡀⠙⠀⠀⠀⠀⠉⢀⠁⠀⠈⠻⠿⠿⠃⠙⠈⠉⠉⠙⠙⡻⠇⢸⡿
⠀⠀⠀⠀⠀⡹⢿⣿⠸⠿⣿⣿⠀⣿⠀⠸⣄⣀⣀⣠⣤⣤⣬⣿⡇⠀⠀⠀⠀⠀⠀⠹⠿⠁⢰⠬⠃⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣈⢟
⠀⠀⠀⠀⠀⠿⣽⣿⢐⡻⢯⣿⠀⠀⠀⠀⢽⡟⠉⠉⣿⣿⣿⣽⡇⢸⡆⠀⠀⠀⡗⠈⠀⠀⢸⠶⣬⣤⠀⠀⠀⣤⣤⠀⠀⠯⣻⣛⠿⢀
⠀⠀⠀⠀⠀⣰⣾⣿⠀⣋⣹⣿⠀⠀⠀⠀⢘⡇⢠⠀⢸⣿⣿⣞⣇⠸⡇⠀⠀⠀⠉⠀⠀⠀⠀⠀⣥⣭⠀⠀⠀⣷⣽⠀⠀⣶⡿⣿⠅
⠀⠀⠀⠀⠀⣈⣚⣿⠀⣿⣿⣿⠀⣿⠀⠀⢨⡇⠀⠀⠀⠀⠫⣼⣿⠀⡀⠀⠀⠀⠀⠀⠹⣋⢟⡭⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣳⣖⣂
⠀⠀⠀⠀⠀⠈⠛⣿⡏⠼⣿⣿⡄⠀⠀⣿⣿⣛⠀⠀⠐⡿⢿⣷⣿⢠⡄⠀⠀⠀⣶⠀⠀⡟⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠈⢠⡿⡿⣿⡃⠀⠀⠈⠉⣿⠀⠀⠰⣿⣾⣟⣿⠐⡇⠀⢀⠀⠛⠀⠀⣷⠀⠀⢰⡄⠀⠀⠀⢴⡆⠀⠀⠸⢿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠾⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠒⠘⠃⠀⠀⠀⠘⠁⠀⠀⢸⣇⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣥⣈⡅⠀⠀⠀⢀⣿⠀⠀⠀⢐⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣝⣧⢄⣀⣤⣤⣼⣤⣤⣡⣬⡷⡿⠿⠧⡤⢤⠤⠀⠀⡀⠾⠛⠛⠿⠿⠿⠷⠶⠶⠶⠶⠦⠴⠾⠛⠛⠛⠂
⠀⠀⠀⠀⣤⡶⠶⠻⠟⠛⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⢤⣀⡤⠴⢶⡶⣶⡶⠤⣤⠒⢤⡔⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⡛⡞⢩⡦⢀⣀⣤⣄⣬⣤⢀⠐⠏⡋⢹⠾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡘⠓⠛⢂⣤⡝⠏⢮⠃⢋⠏⠙⣷⣦⡟⠀⢣⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢠⡴⠂⠈⠛⠂⠀⠁⠈⠠⠒⠉⠁⠻⢦⡀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⣶⠤⡇⠀⠠⠴⢶⠀⠀⣶⠦⠄⠀⠰⠐⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⠀⠂⢸⣦⡀⠀⠈⠀⠀⠈⠀⣠⠞⢀⠁⢀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢑⣔⢤⢿⡤⠝⠒⢶⡄⠖⠲⢈⠛⠓⣞⡡⣮⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢒⡯⠽⡟⠻⡼⢄⡃⠈⠁⢀⣭⠰⠧⠀⣀⡤⠞⢾⣡⡽⠭⣝⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⣼⣿⣄⣀⣷⠁⠾⠓⣾⣏⡛⠓⢒⣖⣺⣿⢿⠉⠈⢋⣿⣄⣠⣿⠙⣆⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⢀⣴⣾⣿⣿⡯⠭⠍⢣⠀⠀⣿⢛⠉⠙⡈⠉⠝⢃⠇⢀⡴⠛⠒⠛⠹⢿⡶⣟⡀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⣠⡴⠟⠉⠉⠁⠀⠀⠀⠀⢜⣷⡀⠹⡆⣰⣿⢿⡆⡴⠋⣠⣞⣦⣄⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠈⢦
⠀⠀⠀⠀⠀⣰⠫⣞⣠⠞⠁⠀⠀⠀⠀⣀⣤⣴⣾⣾⣿⣿⣿⣤⠤⠬⠭⠭⠶⠶⠾⠶⠦⢬⣭⣍⣁⡀⠀⠀⠀⠀⠀⠀⠑⣄⢧⢣
⠀⠀⠀⠀⡰⣿⡁⠋⠀⠀⠀⢀⣠⡤⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⠦⣄⡀⠀⠀⠈⢻⡎⡆
⠀⠀⠀⡰⢸⠟⠁⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠈⠁⡇
⠀⠀⠀⡇⠛⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢠⡗
⠀⠀⠸⡇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠁⢀⡾⠁
⠀⠀⠀⢧⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⣿⣿⡿⠋⢠⠞⠁
⠀⠀⠀⠈⠳⡀⠈⢿⣿⣿⣶⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠖⡏⢩⢸⢿⢸⡿⢋⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡙⠻⣿⣸⢸⠈⢹⢙⠒⢶⠶⠶⠶⠤⠤⠤⠶⠶⠶⠒⠚⠋⠉⠉⢸⠀⠀⡀⣇⠼⢔⣫⠥⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⣍⣛⠲⠼⢸⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣼⣒⠻⠽⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠚⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣉⣿⣟⣡⣤⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⡼⠋⠁⠀⢈⣿⣟⠉⠁⠀⠸⡆⠀⠀⠀⠀⠀⠀⡆
⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣠⣿⡀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⢀⠐⡴⠒⢀⡀⠀⠀⠀⢀⣹⣼⣷⡶⣴⡄⠀⠀⠀⠀⣌⠛⢛⣄⣀⠄⠀⠀⣴⡴⣶⣾⣼⣃⠀⠀⠀⠀⢀⠀⠒⡄⢀
⠀⠀⢈⢿⣿⡆⠀⠀⠀⠀⢠⠾⠿⢿⣏⠀⠈⠇⠀⠀⡠⢚⡟⣼⡟⢛⠢⡀⠀⠀⠟⠀⢈⣿⠿⠿⢦⡀⠀⠀⠀⠀⣾⣿⢏
⠀⠀⠘⠋⠉⢻⣆⠀⢀⠀⠻⠄⠀⠈⣍⣲⣤⠤⠤⠾⠖⠚⠛⠛⠛⠻⠶⢾⣦⣤⣤⣤⣊⡍⢀⠀⠼⠃⠀⠀⢀⣾⡋⠉⠛
⠀⠀⠀⠀⠀⠙⠷⢴⣧⣀⣀⠤⠚⠋⢙⣲⣤⣤⠤⠶⠒⢒⡶⠒⠲⣖⠒⠺⠿⠭⣭⣀⣈⠉⠙⠢⢄⣀⣠⣷⠴⡟⠁
⠀⠀⠀⠀⠀⠀⠉⠠⣿⣏⣀⡴⠖⠛⠟⠁⠀⣠⡴⠀⠀⢽⣷⠤⢴⣿⠇⠀⠠⣤⡀⠀⠙⠟⠓⠶⣤⣾⣿⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠋⣥⠀⠀⣶⢦⣿⣿⣿⠷⠿⠴⠶⠾⠿⠶⠿⢷⣿⣿⣿⣧⣶⣆⠀⢠⡌⠹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⣹⠼⡟⠉⠉⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣬⣯⣄⣀⣀⠈⠉⠙⠻⢼⣉⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣠⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠛⡉⠉⠉⠛⠻⣍⡉⠉⠉⠉⠉⠉⠉⠙⠻⠟⠛⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣿⣧⣀⣠⣼⣇⣀⣴⣄⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⡀⠀⣿⣷⣶⣿⣿⣿⣿⣿⣯⡿⡿⠼⢿⠿⣿⣿⣿⣿⣇⠀⢰⣶⣶⡄
⠀⠀⣀⣠⣤⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣷⠿⠿⠿⠿⠿⣿⡟⢻⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠶⢖⢲⣶⣞⣾⣶⣲⣾⣿⣿⣷⣿⣿⣲⢒⣶⣶⣶⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠿⢿⣬⢭⣭⣍⣭⣽⣿⣛⣿⣿⣿⣿⣾⣿⣭⣿⣿⣿⣿⡿⡝⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠙⣿⡟⠛⠻⣿⢿⣿⡿⢟⣿⣻⣿⣿⣿⣷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢴⣾⣆⣩⣴⡺⣿⣾⡶⠶⠟⠋⠉⠉⠅⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠋⠉⠈⠉⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢒⡈⠶⠶⠶⠶⠛⠤⢌⡑⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⡔⠁⠀⠀⢀⡠⢄⣀⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠀⣶⠀⢖⡉⠀⠘⣷⡟⠀⠀⣈⠢⠀⡆⢄⠈⠄⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠐⠹⠞⠈⠛⠳⠄⠳⠋⠴⠞⠋⠁⠶⠁⡂⡇⢸⠓⢶⠌⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢤⡋⠀⠀⠸⠇⢀⠙⠆⠰⡇⠀⠀⠀⢗⡡⠁⢸⣶⣿⡗⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⠀⠀⠀⠠⣁⠀⠄⠀⠀⠀⠀⠀⠸⠀⠀⣤⡾⣿⣄⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡜⠀⢰⣿⡁⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠑⠤⢀⣀⡀⠀⣀⣀⣀⠠⠔⠃⠀⠀⠀⢏⠛⣩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⠀⠀⠀⠀⣅⣀⠠⠤⠼⠤⠤⠄⣀⠀⠀⠀⠀⠙⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⠀⠠⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠸⢀⡜
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢥⣤⠶⠓⠦⣤⣤⣴⠟⠁⠀⠀⠀⠀⢋
⡔⢡⣤⣀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠓⢄⠀⠀⠈⡄
⠣⣙⡠⠀⠑⢄⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠸⡄⠀⠀⠒⠛⠂⠀⠀⠀⠀⠉⠀⢸⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠈⠄⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤⠦⠄⠀⠀⠀⢸⠀⠀⠀⢆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠘⡀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡠⠂⢰⠀⠀⠀⢀⣀⠀⣀⡤⠂⠙⣄⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠱⡄⠀⠀⠀⠀⠀⠀⣠⠁⠀⢀⠔⠁⠰⠯⡘⠂⠛⠛⠙⠉⠁⠀⢀⡠⠛⡀⠀⢰⡁⣀⢚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠢⢄⡀⠀⠀⣠⠇⠀⢽⠃⠀⠀⠀⠀⠀⠉⠁⠐⠒⠒⠂⠉⠁⠀⠀⠈⡄⡇⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠀⢯⣀⣸⡻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠙⠤⠤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⡙⢄⡁⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠀⠀⠀⠰⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣍⠒⠒⠒⠒⠀⢉⣀⠤⠐⠒⠈⠉⠩⢶⣦⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠉⡉⠁⠀⠀⠀⠀⠀⠀⠌⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠲⢢⡴⠎⠁⠀⠀⠀⠀⠢⢄⡀⠀⠤⠄⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠖⠀⠙⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠈⠀⠀⢀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢀⡸
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶
⣿⣿⣿⢁⠈⣉⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⡜⠁⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠂⠀⠀⠴⠀⠀⠀⠘⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠁⠀⢀⡸⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⡘⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⠈⠀⠀⡜⠁⠀⠀⠀⠀⡄⠀⠀⠀⠇⠀⠀⠀⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⢰⠇⠀⠀⠠⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣧⠀⠀⠈⠀⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡟⠀⢸⡄⠀⠀⠇⠀⠸⠀⠀⠀⠀⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⠀⢸⡃⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠀⠀⢠⠀⠁⡀⠘⠁⠀⠀⢸⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⢇⠀⢺⠀⠀⠸⠇⢰⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠆⠈⢣⠀⠷⡀⠀⢀⡈⠀⠀⣠⠇⠀⠀⠋⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⠢⣀⠐⠀⠉⠠⠞⠁⢀⡴⠃⠀⣤⠦⣀⠀⠀⠈⠉⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⢶⠀⠀⠒⠉⠀⠀⠀⠀⠰⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⣀⡀⠀⠁⠀⢰⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⡀⠖⠀⢀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠉⠁⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠛⠓⢠⡀⠶⠀⠀⠰⢀⡆⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠶⠁⠀⠀⠀⠀⠁⢀⡇⠸⠀⠘⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⣾⠂⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠀⠰⡀⠰⠄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠖⣀⣶⡤⠞⠁⠀⠀⠀⠀⠤⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡈⠲⠻⢶⣤⣭⣉⣁⠀⠈⠉⠉⠉⠉⠉⠀⠈⢉⠙⣆⡰⠃⣠⠶⠛⠓⠐⠒⠈⣉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠂⠀⠱⠖⠲⠾⠋⢉⣍⣀⣤⣤⣄⣀⣤⣤⡤⣤⡄⠈⣤⢈⣷⠌⢡⣤⠄⠚⠛⠓⢠⡀⠃⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠉⠁⣀⣀⣠⡤⠀⠀⠀⠀⠰⠶⡄⠐⠂⠈⢉⠤⠟⠛⠛⠛⠁⠀⠀⠁⠀⠸⣞⠡⠞⠃⠄⡀⠀⠀⠀⠀⠈⠶⠀⢰⡄
⠀⠀⠀⠀⠀⠀⡰⠊⠀⣠⠖⠊⣉⠛⠉⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠲⠀⠴⣆⠀⠀⢀⣄⡀⠁⠀⠀⣀⠀⠀⠀⣇⣸⠁
⠀⠀⠀⠀⢀⠞⠀⣠⠞⠁⣠⠛⠀⠀⠀⠀⠀⠀⢀⠈⢠⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⢀⡿⣦⡀⠘⠏⠰⠾⢦⣄⠈⠀⠀⣶⠉⣿
⠀⠀⠀⢀⠉⠀⣘⠃⠀⢰⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣹⡇⠀⠀⠀⠀⠈⠙⠃⣠⡞⣀⠇⡸⠃
⠀⠀⠀⠘⠀⠀⠃⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢴⠀⠈⠓⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⢀⣤⠾⢯⠚⠁⡸⠃
⠀⠀⠀⠀⠀⠀⢀⣀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣤⣄⣀⡀⠛⢣⣶⣶⣶⡄⠀⣶⣴⠾⠟⠁⠀⠘⠋⡰⠛⠂⠀⠀⠀⠠⠾⠁
⠀⠀⠀⢀⠀⠀⠈⠉⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⠛⠳⠶⠶⠀⠀⠉⠁⠀⠀⠀⠀⠰⠎⠀⠀⠰⠶⠖⠈⠀⠀⡀
⠀⠀⡄⠈⢀⠀⠀⡆⠀⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠒⠀⣀⠃
⠀⠀⠁⠀⠀⠀⠀⠙⠦⣀⣀⡤⠃⢀⡠⠦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢤⣤⠿⠏⠁⠀⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣴⠎⠀⠀⠈⠉⠉⠁⠀⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠀⢀⣉⣉⠲⠂⠉⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠓⣤⠀⠀⠀⠀⠀⠀⠛⠛⠓⠀⠀⠤⣤⣤⣤⣤⣤⣤⣤⠤⣤⣤⣤⣤⣤⠤⠒⠒⠛⠋⠀⠀⢀⣀⣠⣤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠶⠆⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠤⠶⠶⠆⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⠀⣤⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⣽⠀⢿⡤⠠⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢁⣄⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠁⡼⠹⡆⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⢰⠁⠀⢰⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡰⠃⠀⠀⠀⣦⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⣀⠃⣀⣀⡀⠀⠀⡆⠈⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠁⠀⠈⠉⠀⠀⠀⠀⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡀⠁⠀⠒⠂⠀⠀⠋⠀⠀⢳⠀⢡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⣠⠁⢀⣀⣀⣀⡀⢀⣀⡀⠀⠀⣦⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⣰⠁⠀⠈⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⡄⠀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠁⠸⠇⠀⠲⠖⠒⠐⠒⠒⠒⠲⠶⠶⠃⠀⠰⠆⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⣠⡷⠀⠤⠤⠴⠦⠤⠤⠦⠤⠤⠴⠆⠠⠶⠶⠾⣀⣸⠧⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣀⣀⠠⢠⡄⢀⣀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⡀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⡋⠉⠉⠉⠀⠀⠀⠈⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠉⠑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢉⣉⣉⣉⣉⣀⣁⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⠀⠀⣾⠁⠀⠀⠀⣨⠃⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⡀⠀⡀⠀⢀⡀⢁⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠤⠐⠉⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⢀⣠⠶⠋⠉⡄⠑⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⣠⡴⠋⠀⠀⠀⢀⡇⠀⠈⠛⢤⡀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠊⠉⠀⠀⠀⢀⡴⠞⠻⡄⠀⠀⠀⠙⢦⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⡠⠔⠋⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢀⡰⣿⠛⠋⠉⠉⢻⠶⢆⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠠⠔⠉⠀⠀⠀⠀⠀⢀⠏⠀⠉⠀⠀⠀⢰⡆⠀⠀⢳⠀⠀⠀⠈⠣⡄⠀⠀⠀⠀⠈⢡⡀
⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⢠⠀⠀⠀⠟⠀⠀⠀⡇⠀⠀⡌⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⢠⡀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠸⡇⠀⠀⠀⢀⡠⠀⠀⠀⣴⠚⠻⢆⡰⠏⠀⠀⢸⠶⡀⠀⠀⠃⠀⠀⠇⠀⠀⢀⣴⣿⠀⡆⠀⠀⣀⡀⠙⢆⡀⠀⠀⠀⠀⠙⣤
⠀⠀⠀⠀⠀⠘⣦⣠⠴⡟⠀⠀⠀⠀⠛⠠⠖⠋⠁⠀⠀⠀⠈⠀⠹⣄⠀⢸⡆⣨⠀⢀⡴⠋⠀⠀⠀⠹⢀⠘⠋⣁⠀⠀⠙⢤⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠳⣤⣧⣇⡴⠋⠀⠀⠀⢀⡄⠀⠈⠁⠀⠉⠀⠀⠀⠀⠙⣤⡀⠀⠀⡰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⡆⠙⠋⠙⠑⡆⠀⠀⠈⠛⠀⠀⠀⠀⠙⠛⠛⠤⠦⠄⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣿⠙⠷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⢀⣀⡀⢀⣀⣀⣀⠀⠀⢸⡏⠀⠀⠈⠉⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⠀⡆⠀⠀⡾⠉⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⠉⢹⡇⠀⢸⠃⠀⠀⠀⠀⡇⠀⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡇⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢨⡇⠀⢸⡀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡄⠀⠀⠀⠀⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⠇⠀⠀⠀⣠⡄⣤⠀⣿⠀⢀⠀⡀⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⠈⠷⠃⠀⣯⠐⢯⣤⠃⠀⠀⢠⠀⠀⠀⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠳⠆⠀⠀⠘⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣀⣀⣀⣀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈
⠀⠀⠀⠐⣷⣄⣸⡇⠀⢠⣦⣀⡀⠀⠒⠒⠒⠒⠒⠂⠘⣿⠀⠐⠒⠒⠒⠒⠒⠛⠶⠖⠀⠀⣠⣄⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣀⠀⠤⠀⠉⠁⠉⠉⠋⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠉⠉⠛⠋⠀⠀⠠⠶⠦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠒⠛⠉⢹⡆⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢀⣤⣤⣤⡤⠀⣤⠉⠑⠒⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣤⡀⣴⠊⢳⠀⠀⠉⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⢻⣤⢀⣈⣄⠀⣼⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠛⠋⢀⡴⠞⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢰⡏⠀⢀⡀⠴⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠓⠄⠺⢆⡀⡨⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠘⠛⡆⠀⠀⡶⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠘⠲⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢄⣀

⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣀⣠⣶⠋⠁⣠⠄
⠀⠀⠈⠐⠁⠀⣼⠏⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡘⡌⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠤⠶⠥⣄
⠀⠀⠀⠐⠤⠃⠀⠀⢸⡇⠀⢸⡇⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠰⠤⣤⣤⣤⣤⣤⣔⠊⠁
⠀⠀⠀⢄⡀⠀⠀⠀⢸⡇⠀⠈⢿⡀⠀⠀⠃⠀⠀⠈⠳⣄⠀⠀⠀⠙⠲⠦⢤⣤⣀⣀⡀⡠⠔⠋
⠀⠀⠀⠐⠖⠀⠀⠳⠤⠋⠀⠀⠈⢷⡀⠀⠀⠀⢤⡀⠀⠀⠙⢶⣤⣀⣀⡀⢀⣀⣤⠞⠃
⠀⠀⢠⡠⠀⠀⡀⢀⠀⠀⡸⢦⡀⠘⡟⠦⡀⠀⠀⢹⡦⣄⠀⠀⠉⠓⢦⠤⠤⠄⠀⠂⠤⣀⠀⣸
⠀⠀⡸⣀⠀⢰⠉⣵⠂⡂⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠉⠷⠲⠚⠁⠀⠀⢀⢀⡀⠀⠀⠉⢴⠄
⠀⠀⢣⠀⣴⢘⡄⠈⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢀⠀⢰⡆
⠀⠀⠀⠀⠈⠉⠃⠀⠀⢂⠣⠂⠀⢠⠀⡶⠐⠚⠀⠠⠀⠀⠀⠀⣠⣤⣄⡆⠀⠀⠀⠀⢀⠀⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠸⡄⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⢀⣤⠶⢶⣄⡀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢣⠀⠀⠘
⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⣸⠋⠀⢸⣏⢷⡀⠀⠀⠀⢳⠀⠀⠀⠀⡨⠀⢰⡤⣶⡀
⠀⠀⠀⠀⠀⠀⠉⠀⣀⠤⠤⠤⡐⠁⠀⠀⠀⣿⣾⠃⠀⠀⠀⠀⠀⠀⡥⠚⢤⢤⡄⠿⠛
⠀⠀⠀⠀⠀⠀⢻⠁⠀⣀⠀⠀⢹⠈⢰⡶⣻⡽⠋⠀⠀⠀⠀⢀⡠⣾⠧⠀⠊⠀⡇⢰
⠀⠀⠀⠀⠀⠰⢞⠃⣀⡨⢠⢀⠏⠀⠘⢷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡟⠉⢡
⠀⠀⠀⠀⠀⠀⢸⠃⠘⡇⠀⣜⠀⣼⠤⢾⡟⠀⠀⠀⠀⠀⠀⠸⠀⢄⠀⠀⠀⣰⠇⠀⢸⠀⡶⢠
⠀⠀⠀⠀⠀⠠⠈⠂⠀⠠⠞⠙⠋⠀⠀⣌⡷⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⣀⠔⡇⠀⠀⠀⠀⣬⠃
⠀⠀⠀⠀⠉⠒⠁⠀⠀⢠⡈⠃⠀⠀⢀⡼⣦⠀⠀⠀⡠⠰⠀⠀⢷⠤⠴⠇⣸⠠⣖⢂⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡂⠄⠀⢸⣶⠏⠀⠠⢠⠀⡤⠂⠄⣊⢀⢸⠀⠏⡠⠏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠤⡀⠀⠉⠀⢀⢀⡘⠐⡵⠋⢊⣤⠤⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠓⠓⣤⠾⠄⠀⢐⠶⠛⣈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢣⡀⠀⠠⣦⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣺⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⢠⡼⢇⠤⠒⣷⣖⠂⢄⡀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣾⠠⠁⠀⢰⡅⠈⣆⠀⢱⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣀
⠀⠀⠀⠀⠀⠀⣿⠀⣠⢴⡇⢴⠂⢀⠰⣲⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡁⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠘⣮⢻⣌⢟⠈⢁⡸⣧⣟⡴⠏⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠘⡁⠐⠁⠁⠐⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠛⡇⠘⠓⢘⣹⠁⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⢠⣦⠈⣤⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣼⢷⣔⡟⠒⢀⣿⣿⡶⢼⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠈⢀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢀⣰⢿⡟⢉⡟⠓⠂⢀⡝⠛⡿⣌⣷⣆⠀⢁⡀⠀⠀⠀⢀⣴⣿⣿⣎⣉⠀⠈⢿⣿⣷
⠀⠀⠀⠀⡰⠃⠀⢘⠃⠘⢷⣵⣤⡼⡇⠀⡃⠮⠘⣿⢻⠂⡁⠀⠀⠀⣸⡿⠿⢿⣻⠤⠤⢀⡾⠛⠻⢦⣀
⠀⠀⠀⢸⠑⢲⠆⢸⡇⢰⠁⠈⢨⢹⡇⢰⠀⡒⠀⢹⣿⠀⡗⠀⠀⡴⠇⢀⢀⢸⡟⢳⠖⣯⠁⠀⠀⠀⣼
⠀⠀⠀⠈⠀⠀⠀⢸⡇⢸⣇⡀⡸⢸⠇⢸⢀⡇⠀⢰⡟⠀⠁⠀⢸⡃⢰⢺⡏⠘⠇⠀⢀⠀⠀⠀⠀⠀⠘
⠀⢀⢄⣶⠀⢠⡜⢸⡇⢸⣟⣡⠃⣿⠀⠸⢫⡟⠀⢸⡇⠀⠀⠀⢡⠐⠆⢸⡀⠀⣇⠄⢺⠀⠀⠀⢀⡄
⠀⡆⢸⠛⠁⢉⠁⢸⡇⠀⠹⣿⠄⣿⠀⡞⠆⡇⠀⠘⠳⠀⠇⣠⣬⣦⣤⣼⢧⠄⠊⡜⠂⢠⠀⢀⣟⠀⠠
⠀⡇⢘⣀⡀⢿⠀⢼⠁⢠⠀⠿⠀⣿⠀⣿⠀⡇⠀⠐⠋⠁⢀⠁⠀⠙⢹⣿⠁⠀⣈⠻⠾⠋⠀⣼⡇⠀⠠
⠀⡇⠀⢸⢧⠘⢦⣸⡇⢸⠀⠄⢀⡇⠀⡿⢃⡟⠀⠀⠀⠀⠀⠀⠒⣾⣿⣹⡗⠂⠀⠀⣀⡀⢤⣿⡇
⠀⠁⠀⠐⠈⣾⡇⢼⣧⠸⣷⠟⢻⡗⠀⣇⠈⣇⠀⠠⠆⠀⠀⠀⣾⣿⣰⡿⠉⢉⡋⠀⠉⠀⠸⠿⣷
⠀⠀⠀⠆⠣⡘⠀⠠⣍⠀⡿⠓⣙⣇⠀⠁⠀⣿⡴⠃⡀⠀⠀⠀⢼⣿⠏⠀⡀⠈⠁⠋⠉⠀⢰⠀⢸⡀⠀⠀⡀
⠀⠀⠀⠀⠀⢙⠀⢺⣻⡄⠘⠿⡝⠂⣰⠀⠀⢻⠄⢀⠁⠀⠀⠀⣼⣿⠁⡀⠀⠀⠀⠀⠀⣠⠟⠀⠈⣷⡄⠀⢠
⠀⠀⠀⢰⠀⢀⣠⠴⣿⣿⣦⣤⣤⣼⣏⡑⠀⡘⠀⢸⠀⠀⠀⠀⠈⠻⠁⠀⠀⠀⠀⠀⣰⠟⠋⠉⢰⡿⢸⡵⢼
⠠⠴⠒⠊⡀⢰⣴⠞⠛⠿⡇⠀⣿⠃⠀⠉⠱⡇⠀⢸⠀⠀⠀⠀⠀⢸⡀⠀⢠⡜⣠⣼⡇⠀⠀⠀⢸⡇⢨⡤⠘
⠀⠈⡖⠞⠁⠘⠀⠀⠀⢀⡃⠀⠿⠀⠀⠀⢠⡟⢠⠘⠂⠀⠀⠀⠀⢸⣄⣴⢋⢾⣿⡇⢱⠀⠀⠀⣼⠇⠀⡀
⠀⠀⠉⠻⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⠑⢡⣿⠙⢷⠀⠡⠀⢰⡇⠀⠼⡇⢠
⠀⠀⠀⠀⠀⢨⠀⠀⢠⡏⡁⠐⣀⠁⠀⠀⠀⡟⠂⡸⣧⠀⠀⠀⠀⠀⣁⣠⣿⡏⢀⠀⠀⠀⢴⡏⠁⠀⣠⡁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⣇⣸⠅⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢙⡇⢘⠀⠀⠀⣿⠀⢰⠀⠃
⠀⠀⠀⠀⠀⢰⣀⠐⠀⢸⡏⢸⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⢸⡆⠀⢰⣿⢀⣾⡀
⠀⠀⠀⠀⠀⢨⠅⠀⠀⠸⡇⢸⡄⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇⢸⠁⠤⢿⣿⠋⠘⡇
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡇⢸⠈⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⠀⠀⠘⢿⠀⣠⠅
⠀⠀⠀⠀⠀⢰⣷⡀⠂⠀⠇⢀⠀⠀⠀⠸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⠀⣤⢀⠜⠁
⠀⠀⠀⠀⠀⢨⣤⡤⠂⠠⠀⣿⡀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢸⣆⠀⠏⠈
⠀⠀⠀⠀⠀⡼⢀⣤⠠⠀⢰⠇⠈⠀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡀⠈⡇⠀⢀
⠀⠀⠀⠀⠀⠶⢂⣉⣠⡔⠀⠈⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠁⠀⣏⠀⣹
⠀⠀⠀⠀⠐⠛⠉⠀⡀⣅⠀⠀⡆⠀⠈⡀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⡴⠁⡼⡆⠀⡏⠉⠻⡄
⠀⠀⣸⣷⣂⣤⠴⠇⠓⠁⠀⢀⠹⢟⣶⣶⠀⠀⠀⠑⠂⠀⠀⠀⠀⠾⢁⣰⢁⣇⢘⠏⠢⠀⢈⣶⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⢠⣜⢿⣿⣇⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⠻⡟⣾⣿⡷⠝⢘⣛⣯⡭
⠀⠀⠀⠀⠀⠀⠀⠸⢟⣛⣣⣄⢷⣶⣿⡇⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣦⠻⣿⡇⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣧⠙⠃⡿⠁⣼⣿⣿⣶⣦⣤⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣦⡈⠁⠀⠁⠈⠉⠙⠛⠻⢟⣡⣾⣿⣿⣿⡿⠿⠛⠛⠋⠉⠛⠛⠛⠿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣋⣵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠃⠀⠹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦
⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠀⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧
⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧
⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⠀⠀⠀⣰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆⢀⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⣤⣤⣀⣀⣬⣭⣵⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⣋⣥⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⣠⣤⣴⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⢄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠃⠀⢣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⡰⠳⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡇⠀⠧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⢴⡆⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡒⢲⣞⣛⣿⠟⠿⠿⣿⠿⠿⠿⣿⣛⣳⡖⢒⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢸⡇⣠⠖⠉⠀⠀⠀⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣄⢈⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠈⠙⢿⡄⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢿⡄⣠⠀⣠⠾⠛⢩⠭⣉⠉⣱⢲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⣙⣿⡞⣿⡞⠁⢀⡤⣀⢳⡈⠑⢎⠀⠙⢄⠀⠀⢀⣤⠖⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⣠⠞⠋⠙⠉⢻⣷⣿⣿⡿⣶⣽⡄⠙⣇⠀⠈⢆⠀⢸⡠⠖⠉⠀⢠⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⢼⡇⠁⠀⠀⠀⠈⢳⠀⠹⡀⠀⠸⡀⢸⠀⠀⠀⠀⢸⠤⠒⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢷⣄⠙⢦⡀⠙⣾⠀⣀⡠⠖⠁⢀⣼⠖⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⠤⠜⠙⡄⠀⠀⠀⠀⠀⠀⡸⠀⠉⠓⢚⣿⣽⠉⠉⠉⠑⠒⠊⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠦⣤⠤⠴⠁⠀⣤⠶⠋⠁⠘⢟⠢⣄⣀⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠀⣼⣻⠀⠀⠀⣸⣿⡄⠀⠀⢲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠉⠀⠀⠀⠀⢺⣿⣇⣤⣤⡿⡟⠀⠀⠀⡈⠀⠊⣐⣡⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣝⣍⣿⣦⡀⠀⠀⠀⠀⠀⠩⢟⠛⢛⡿⠄⠀⠀⠀⠀⢀⣸⣿⣯⣩⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣙⣹⣾⠃⠀⠀⠠⠀⠀⠀⣾⣦⣾⡍⠀⠀⠠⠀⠁⠀⡿⣷⣭⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠘⡊⠀⠈⠻⡙⢩⣦⡀⠀⠀⣂⣼⣾⣏⢡⣄⢩⣿⣷⣧⡠⢀⢰⣦⠸⠋⢉⠀⠀⠜⠉⢶⡂⢀
⠀⠀⠀⠀⠀⠀⢠⣌⣀⣄⠀⠀⠀⠂⠠⠀⠈⢫⠈⡤⣺⣿⣿⣥⣬⣤⣧⣤⣤⣬⣿⣿⣎⠰⡁⠀⠀⢀⡐⠊⡀⣶⡞⢿⡟⠡
⠀⠀⠀⠀⠀⠀⢧⣿⣻⣿⣧⠀⠀⠁⡄⠀⠠⠀⣞⣶⢟⣩⡵⠶⠶⠷⠶⠶⡶⣤⣌⠉⣿⣧⠉⣀⡐⠂⠀⠀⣰⠟⣿⣾⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠿⣿⣹⣿⡀⠈⠀⠀⠀⠠⢸⣻⡟⠛⢀⣤⡶⣲⡛⣚⡶⣶⣌⡉⠛⢻⣿⡈⠁⠀⡀⠠⠄⠿⣶⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠻⠍⣶⡄⡀⠉⠤⢸⣿⢧⣿⡛⣹⣟⠮⠤⠿⠦⣉⢬⣿⡳⣽⣿⠀⢂⣄⡸⠿⡷⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠛⠢⠻⢧⠰⣶⣥⠜⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠰⣻⠻⣐⠿⠋⠀⠀⠀⢂⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠈⢠⡞⠁⠋⢡⠖⢛⣦⠀⢀⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡐⣀⠀⠠⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠽⠃⠀⢠⣿⠀⠉⠁⠀⢼⣿⣻⡧⣤⣄⣴⡄⠀⠀⠀⠀⠀⠙⢇⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠏⠀⠀⠀⠹⣿⠀⠀⠀⢠⣾⣿⣿⣋⡾⠟⢹⣿⠀⠀⠀⠀⠀⠀⠀⢿⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⡟⠀⠀⠀⠀⣼⣿⡀⠀⠀⣯⣾⡼⠟⣉⣦⣷⣾⠟⢦⠀⠀⠀⠀⠀⠀⠀⢷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⠀⠀⠀⠀⠀⣸⣿⣇⠀⠈⡟⠩⢔⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣼⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣷⣶⣿⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣿⣿⣿⣄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣲⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢇⡀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣿⣿⣟⠀⠀⢀⣤⢀⡀⠀⠀⠀⠀⠀⠀⢠⣞⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⢳⡄⠀⠀⠀⣀⣤⠾⢽⢿⡟⠛⢿⢿⣶⣿⣿⣿⣿⡄⠀⠀⠀⠀⢀⡯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠸⣤⠀⢰⠿⣧⡀⠀⠀⠀⠀⠈⢧⣿⣿⡟⠋⣿⡿⡄⠀⠀⣠⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⢧⡘⣼⡀⠈⢷⡀⠁⠀⠀⠀⠀⢻⣿⡷⡇⢸⣷⢘⣤⣽⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠚⠬⢓⢾⣷⠂⠀⠀⢠⠀⣸⠿⢆⣗⡸⣚⠿⠐⠃⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⡀⠀⠉⠐⠊⠵⠹⠷⢪⠷⡽⠩⠟⠛⠈⠁⠀⢠⠀⠀⢀⠠⠀⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠰⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⢻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⠈⠉⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢤⠄⢠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⣦⣶⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣏⠉⠹⠉⠀⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⠄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠘⠂⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⣴⣷⣶⣦⢰⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡏⣝⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠙⢻⣿⣶⣶⣿⠏⠋⠉⠀⣹⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆⠒⠒⠀⠈⠉⠉⠀⠀⠀⠴⠦⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠛⠋⠉⠀⠄⠀⡄⠀⠀⠀⠈⡀⠉⡀⠀⠈⠙⠻⠿⣿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⣠⣿⣿⣿⣦⡀
⠀⣴⡿⠋⠉⠙⢿⣧⠀⢀⣿⣿⣿⣿⣾⠇
⢰⣿⠀⠀⠀⠀⣼⣿⠀⠀⠛⠿⢿⣛⣭⣴⣾⡆
⢸⡇⠀⠀⠀⠻⠛⠁⠀⠠⣷⣾⣿⡿⠿⢛⣉⡁⠀⠀⠀⠀⢀
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⣡⣴⡶⣿⠿⠛⠛⠛⠒⠠⣀⣼⡆
⠻⣿⡆⠀⠀⠀⠀⠀⠀⣤⠞⠛⠻⣇⢁⠠⠀⠂⠀⠀⢉⣽⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠹⣿⡄⠀⠀⠀⠀⠞⠁⠀⠀⢈⠿⠀⠀⠀⢀⣌⣍⣽⢇⣿⣷⢱⣀⣀⣀⣀⡀⠀⠀⢉⣿⣷
⠀⠰⠈⣿⡄⠀⠀⢠⠀⠀⠀⠀⠩⠰⣶⣆⣰⣿⣿⣿⣿⡘⠿⠏⣿⣿⣿⣿⣽⣿⣷⣤⡾⣿⣿⡇
⠀⠀⡆⠈⢾⣄⠀⠀⣾⣶⣒⣸⡿⠀⠈⣙⣥⣼⣿⣿⣶⣿⣶⣾⣿⣻⣟⣿⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠁⠀⠈⢻⣦⣤⡟⢀⠙⢋⡀⠀⢸⣿⠭⣿⠶⠟⠞⠋⠙⢻⣧⣿⡿⣿⣿⣿⣿⣾⣿⣿⣿⡇
⠀⠀⢸⠀⠀⠀⠻⣿⡁⠀⣴⣿⣇⣤⣬⢡⣴⠃⠀⠀⠀⠀⠀⢠⣿⣿⣿⢋⣻⣿⣿⠟⠉⠙⣿⣷
⠀⠀⠀⡆⠀⠀⠀⣹⣷⣾⣿⢟⣴⣿⣶⠚⠁⠈⠉⠉⠙⠳⠦⠈⣿⣿⣿⠿⣟⠥⠤⠤⣄⡀⢸⣿⠆
⠀⠀⠀⠃⠀⠀⢸⣿⡿⢌⣯⠚⠹⡟⠀⠀⠀⠂⠀⠘⢿⠟⠀⠀⣿⡿⠃⠀⠠⠐⠲⣶⡶⠅⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣶⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠉⠀⠀⠸⣿⡇
⠀⠀⠀⠸⠀⢀⠁⠀⠀⠠⠘⢳⣆⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠆⠀⠀⠀⠀⠀⠀⠀⢆⡀⣻⣧
⠀⠀⠀⠀⡇⠀⢀⢃⠀⡂⢀⡿⣻⣧⠈⢆⠀⠀⠀⠀⠰⠖⢠⣾⣿⡇⠀⠀⠀⠀⠠⣤⠀⣾⣿⣿⣿⡀
⠀⠀⠀⠀⣧⢠⡇⣼⠀⢹⢸⣇⠘⣿⣆⠞⠀⠀⠀⠀⠀⠠⣾⣿⠛⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣿⡇
⠀⠀⠀⢀⣎⡞⢠⢣⡇⢸⠀⣿⣿⠛⣿⡀⠀⠀⡀⠀⠀⢀⣿⣿⠇⠀⢐⣦⣄⣀⣠⣼⣷⣿⣿⣯⣹⢙
⠀⠀⡠⢊⡾⢡⠏⣸⡇⣼⣾⢡⣿⠀⢸⡇⠀⠀⣸⣯⣿⣿⣿⠛⠀⠀⠸⣗⡽⣿⢭⣿⣟⣼⣻⣿⡿⣧⢃
⢠⠈⠀⣾⠁⠊⣌⣿⣳⣿⡏⣾⡅⠀⠸⣿⠀⠀⢸⣿⣿⣿⣿⣶⣤⣀⣠⣯⣿⣝⡛⣧⢿⣫⣝⣿⣷⣿⣎⢧
⢸⠀⠂⢁⠦⠘⣸⣿⡟⡟⣼⢻⢻⣶⣴⡏⣦⣶⣿⣷⡘⣿⣯⡿⣟⡻⢿⣿⠙⣿⣟⣿⣯⡷⣿⢟⣿⣯⡙⣧⢧⡀
⢸⡀⠀⡬⠰⠈⣽⣿⡷⢃⡁⠈⢀⣿⡟⣷⡟⠋⠁⣾⣿⣌⢫⣼⡿⢿⣮⣍⡛⠿⣏⠹⣿⣻⣽⡿⢿⣿⣿⣏⢷⣹⣦⡀
⢠⢅⠀⠀⢰⢸⠸⣿⡇⠘⠛⠈⡼⢻⣿⣿⣧⣤⣾⡿⢿⣿⣆⢳⡷⢾⠿⡻⣿⣷⣷⣵⡻⣿⣯⢿⣭⢾⣻⢿⣿⣿⢶⣟⢳
⠀⠀⠀⢀⡷⣾⣤⣧⠀⠸⣿⠇⠃⠘⣿⣿⣿⣿⣿⣷⡸⣿⡌⢆⢡⣴⣶⣽⡝⣿⣝⡿⣿⣦⣿⣿⡽⣗⣯⣽⡿⣿⣷⣽⡿
⠀⠀⠀⢨⡀⣌⡛⠋⣿⡷⢰⣿⡇⠀⣿⣯⠛⢿⣿⡿⠁⣿⣧⠈⡆⢯⣥⡘⢻⡼⣿⡿⣮⣿⣿⣿⣟⣯⢾⣫⡼⣫⣿⣿⣷
⠀⠀⠀⢸⢧⣿⠿⢀⣤⡄⢈⣭⡅⠀⣽⣿⡇⠀⠛⠁⠀⢹⣿⠀⢹⠘⣟⢹⣿⢷⢻⣾⣿⣿⣻⣿⣯⣻⣞⣧⢿⡻⢞⣷⣿
⠀⠀⠀⡜⢀⣧⣤⡈⠛⢃⠘⠛⠧⣼⣿⢻⣿⡀⠀⠀⠀⣼⣟⠀⠈⣷⢹⢧⣶⡾⣏⣿⡿⣽⡿⣿⣯⢮⣷⣹⣜⣻⣟⣿⣷
⠀⠀⢀⡧⢸⠛⢛⡀⠸⣿⠃⣾⣿⣿⡿⠈⢿⣷⡀⠀⣠⣿⠇⠀⠀⢹⠈⣷⠉⣵⣷⣽⣿⣿⣶⡿⣞⢻⣺⣯⣿⣩⣏⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣒⣐⣂⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠿⠿⠿⠿⠿⠿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣲⠀⠒⠒⠒⠒⠒⢲⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣤⡶⠶⣦⣤⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠉⠀⠀⠄⡀⠈⠉⠛⠳⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠰⢞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣠⡴⠶⣤⣀⡀⠀⠀⠀⢀⠤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠈⠀⠀⠀⣠⠶⠛⠋⠁⠀⣀⠀⠉⠛⠳⡦⠀⡀⠀⢠⠀⠀⢠⣦⣀⡀
⠀⠀⠀⠀⢴⠖⠛⠉⢁⠀⠀⠉⠀⠈⡇⠀⠀⠀⢠⠊⠀⠁⠀⠀⡀⠀⡄⠀⠁⠀⠈⠀⠀⠘⠀⠈⠉⡟
⠀⠀⠀⠀⠸⡀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⢰⠀⠀⡆⠀⠀⠀⡄⠀⠐⠀⠂⠀⢰⠀⡇⠀⠇⠀⠰⠂⢠⠁⠀⠀⠀⡇
⠀⠀⠂⠀⠀⢇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠄⠀⠇⠀⠀⠀⠀⠀⠘⠀⠇⠀⠀⠀⠀⠀⢸⣀⣀⣀⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠒⠒⠒⠲⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣲⠶⠖⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⣨⡋⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⣛⢱⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⠿⢰⡄⠀⠀⠀⠀⠀⠀⠀⠘⢧⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢸⠂
⠀⣤⣤⠰⣄⠀⠀⠀⠀⠀⠀⠉⡽⣤⣾⠃⠀⠀⣀⠀⢀⡂⠀⠀⡸⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣰⡦⠾⠂⠀⠀⠀⠀⠀⣠⢠⡀⣤
⠀⠙⠦⡰⣿⡀⠀⠀⠀⠀⠀⠀⠀⡏⢿⣆⠀⣶⣾⣷⣾⣷⣾⡿⣡⠏⠈⢷⣤⣀⢸⣤⣤⣴⣄⡠⠁⢿⠀⠀⠀⡀⠀⠀⠀⠀⠙⢀⡴⠏
⠀⠀⠀⠈⢈⡻⣦⣀⢠⣶⣶⣶⡄⣱⠃⠙⠛⠿⢿⣿⡿⠿⢋⡴⢃⣴⡀⠀⠙⠻⠶⠿⠿⠛⣁⡴⠻⡘⢧⣘⣶⣶⣶⡀⠀⣠⡶⠋
⠀⠀⠀⠀⠠⣿⣦⣍⡙⠛⠋⡡⠔⠡⠾⠶⠀⠀⠀⠀⠀⠈⠁⠈⡉⣉⠉⣀⠀⠀⢐⡒⠒⣻⣭⡶⣿⣬⠂⢤⣬⣭⣤⣶⣿⠏
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⠀⠀⠀⢤⡀⠬⠍⡇⠀⠺⠷⠂⠀⢓⢲⣂⣀⡩⠆⠈⠹⠝⠠⣬⠂⠭⡈⢳⠀⢡⣿⠿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣷⣧⠀⠀⠈⠂⠉⠉⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣂⣀⣀⠒⠚⠥⠚⠿⠥⣄⣼⣽⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣯⡽⠶⡒⠒⠛⡉⠉⠉⠭⠉⠩⠅⠀⠀⠆⠀⠁⠏⠉⠩⠍⠉⠩⡍⠛⠛⣲⠲⢶⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠛⣯⣿⣷⣂⣀⣁⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣈⣘⣓⣻⣿⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⡿⣿⣿⡿⢿⠿⠏⠟⠟⠟⠿⡿⠟⡿⣿⡿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠒⠒⠂⠀⠂⠘⠂⠒⠘⠓⠒⠒⠂⠒⠒⠀⠘⠁⠁⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⢠⣝⣛⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠓⠀⠀⠀⠀⠧⢠⡌⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣿⡅⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠻⣿⠀⠀⢀⣀⠢⣤⣤⡌⠀⠀⠘⡟⠫⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆⣴⣦⡏⠀⠶⠈⣿⣷⡿⠓⠀⠀⠀⠀⢣⡆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣶⣧⢸⣿⡀⣰⣿⠉⣩⢷⠀⢶⠶⢆⡴⠀⠁⠄⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⢿⣤⢿⣿⠃⠀⠣⡷⢸⠀⢰⣠⠞⠙⠁⠀⠀⠠⠀⠀⡈⠍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⣀⣀⣠⣤⣴⠀⣀⠀⠚⠸⢜⣃⣠⡁⣀⣀⡤⠔⠚⠉⠀⠠⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡟⢷⣿⣿⣿⣻⡾⠿⠿⢶⣶⣾⡙⠿⡟⠇⠀⡄⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⢣⣻⠑⢀⠿⣿⣯⣤⣴⢄⡀⠀⡤⣄⠨⣙⣛⠀⣠⣚⠴⠃⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢈⡿⢠⣤⡄⠀⠹⠉⠀⣈⠙⠻⢿⣣⣴⡟⠀⠈⠣⣴⠈⡉⠉⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠚⠋⠛⠿⡶⠶⠦⡧⣆⡤⣾⡿⣿⣣⡀⣀⡀⠘⣷⣭⠛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⣿⣿⣿⠻⡝⠜⢿⣭⣄⠀⢹⣯⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡜⢻⣿⣤⣽⣰⣼⣿⡤⠄⠈⢻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠞⠿⣶⣯⣽⡟⠛⠛⠳⠾⢤⡿⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠁⠙⠀⠀⠀⠀⠀⠠⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇
⠀⠀⠀⠀⢠⣄⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣭⠁
⠀⠀⠀⠀⠈⢁⡙⠛⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡛
⠀⠀⣤⠐⠻⠿⣿⣷⡦⢤⣤⠀⠀⠀⠀⠀⠀⣀⠠⢤⣴⣶⣿⣿⣿⡇⠀⠉⠀⠀⠀⠀⢀⣁⣤⠄
⠀⢀⣼⣴⣶⡄⣀⠈⠻⣏⡀⠀⢀⡀⠂⠉⢁⣤⣖⣋⣩⠄⠀⣿⣿⡇⠸⠀⠀⠐⢤⣾⣟⠋⣽⠷⠉
⠀⠈⠉⣹⣵⣄⠄⣭⢀⡈⢉⣰⣾⣶⣶⣿⣿⣿⣿⣿⡟⠀⠀⣼⣯⡄⢰⡄⠓⠒⠛⣋⡉⣿⠨⠟⢲⣮⣿
⠀⠀⡽⢿⣿⣿⣿⣿⠁⢠⣆⣿⣿⣿⢸⣿⣿⡇⢶⣿⡇⠀⣤⢸⡿⠇⢸⠀⢸⠀⣾⣇⣸⣧⣤⣌⣺⣿⣿⣀
⠀⢶⣷⣾⣿⣿⣿⢋⣰⣿⣿⡿⠟⣻⣿⡿⣿⣿⣿⣿⣧⠀⣉⣼⣿⣷⡘⠶⠌⣴⣝⢿⣿⣟⣟⣿⣿⣿⣿⣿⡇
⠀⣭⣭⣭⣥⣿⣿⡿⠏⠉⠉⠈⠛⠛⠂⠒⠛⠛⠛⠛⠛⠚⠛⠛⠛⠛⠛⠃⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣾⣿⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡉⠉⠉⠋⡁⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⣿⣿⢹⡏⣿⢻⢓⣶⣤⣐⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠈⣧⠟⠉⢠⣿⠸⢿⡅⠋⠉⠹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⣶⣶⠂⠠⠀⠀⠀⠐⠋⠀⢀⣿⣿⠀⠋⠀⠀⠀⠀⢻⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡿⢻⠻⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⢠⡄⢀⣀⣠⣤⣿⣏⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡴⡿⠈⢧⣨⣃⢶⣿⣿⣷⣸⠀⠀⠀⠀⣼⠀⠐⡀⣿⣿⠗⣫⡆⠙⠻⡀⢹⣜⣿⣻⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠈⣼⣡⡄⢠⣽⣯⣈⠿⡟⣿⡟⡀⢀⠄⢀⣴⠞⠁⢡⠸⡇⣼⠛⠻⠦⣀⠉⢦⣼⣄⢷⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⡟⣿⣿⣿⡁⠰⡇⢸⣿⡿⢀⠴⣿⡇⠀⠀⠀⠱⣄⣿⠦⠤⠤⢄⠁⣿⣿⣿⣻⣧⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⡽⣿⣿⣯⣍⣻⠃⣼⣿⢁⡏⠀⠘⠿⢦⡀⠐⢄⠘⣷⣦⡠⠤⠀⡆⢿⣿⣿⡧⣽⠸⣼⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢆⣶⣿⡟⠁⣼⠣⠾⢿⣿⢸⡧⢀⠀⠠⣤⣤⣄⣨⣷⡿⠃⢀⣀⠤⡟⣿⣿⡟⢣⣶⠞⢸⣇
⠀⠀⠀⠀⠀⠀⠀⢡⣭⣿⣿⣏⣜⠉⠻⣧⣌⠂⣵⡿⠿⣢⣽⠞⠋⠉⠉⠉⠉⠉⠉⠛⠳⣶⣧⣼⣿⣷⣼⣫⠘⣱⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⣴⣷⣤⠀⠀⢉⠳⢦⡖⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠛⠻⢿⠙⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡄⠀⢹⠏⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢿⣿⣿⣦⡌⣼⣿⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠛⣦⣿⣿⣗⣱⡿⠁⠀⠀⠈⠉⠉⠉⠉⠛⠷⣦⡀⠀⠀⠠⣰⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡁⠀⠙⣿⣿⡟⣿⠁⠀⠀⠀⠀⣀⣀⣀⣀⣠⡀⠈⠹⢦⠀⠈⠄⢀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⣾⠇⣿⣿⣿⠀⠀⠀⠀⠈⠉⠘⢿⣿⠋⠙⣷⡀⠀⠀⠀⣰⢯⣥⢀⠀⢈⠃
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⢿⣷⣾⢹⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢰⣿⣿⡿⢛⡶⣾⡇
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣷⣣⣈⣈⣙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⠉⠁⢰⣿⡇
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣧⠀⠉⠻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣼⣿⣿⣆⡀
⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⣰⡀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣄
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⠿⠿⠷⣄⠀⠀⠀⢀⠀⡀⠀⢀⡌⡲⠤⠋⠀⠀⠀⣸⣿⣻⣿⣿⣿⣿⡿⣷⡀
⠀⠀⠸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣉⠀⠀⠹⢯⣄⡀⠀⠀⣰⣿⣷⣿⣿⣿⣿⣿⡀⠀⠁
⠀⠀⠀⠀⠘⣿⣿⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠘⠻⠷⡚⠉⠁⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡒
⠀⠀⠀⠀⠀⠘⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣅⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠈⠛⠛⠿⢿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠛⠉⠉⣉⣽⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠉⠈⠙⠻⢿⡿⠿⠄⠀⠀⠈⠁⠉⠉⠙⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡯⣷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡿⠋⢏⠏⠻⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⡇⣿⠀⢸⡇⠙⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣧⣿⣤⣬⣇⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣤⣄⠀⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣲⣯⡇⠸⣿⣿⠇⢨⣷⣢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣐⠮⠒⠉⠀⡈⣇⣄⠀⢀⣄⠈⡇⠈⠑⠪⢗⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣨⠗⠊⠀⣀⡀⠀⠀⡇⣿⣿⠀⢸⣿⠇⡇⠀⠀⢀⡀⠈⠓⢯⣐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣥⠀⡴⠻⣿⡏⠢⡀⡇⣿⣿⡀⣸⣿⡇⡇⣠⠊⣷⣯⠓⡄⠀⡏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠀⣇⣤⠀⣤⡀⡇⡇⡏⢉⣥⣍⠉⠁⡇⡇⣠⣄⢠⣄⠀⠀⡃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⠀⣿⣿⣿⣻⡇⡇⣇⡇⡞⢸⠈⡆⢠⡇⡇⣿⣿⣟⣟⠇⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⠀⣿⣿⣿⣿⡟⣇⣽⣇⡇⢸⠀⣇⣼⣇⡅⣿⣿⣿⣿⢲⢀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢻⠀⣿⡿⠛⣿⣇⠇⡏⡏⡇⢸⠀⡇⠉⡏⣇⣿⣟⠻⣿⡰⠈⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡧⣼⣤⣤⣤⣤⣤⣤⣤⣧⣷⣷⣾⣶⣷⣦⣧⣤⣤⣤⣤⣤⣤⣤⡤⢧⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠬⣁⠀⠈⠁⠀⣧⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⡀⣆
⠀⢠⣤⠀⠀⠀⡀⠀⣾⡆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠮⢿⣿⣿⡛⠛⡄⣼⡇⠜⢳⣾⣯⣿⡁⠤⠀⠑⠆⠀⢀⠄
⠀⠀⠈⠀⠀⠈⢁⠀⠛⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣟⡿⢿⣿⡇⠆⣿⣿⣸⢈⣿⠫⢿⣏⠉⠀⠲⠀⠀⡀⢰⡀
⠀⠀⠀⠀⠀⠀⡀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣇⣹⣿⡿⠅⣿⡇⠍⢹⣿⣧⢸⡿⣶⠀⡴⠄⠀⠀⠀⠁
⠀⢠⣤⣴⡤⠰⢵⡄⠀⠀⠀⠀⢰⠀⠰⠀⠀⠀⠀⣤⣿⡇⣿⣿⢟⣻⣿⡿⣿⣦⣘⡿⣿⣾⡇⣿⠀⢱⣿
⠀⡌⠛⢋⣶⡀⠘⠛⠀⠀⠂⠄⠌⠀⠀⠀⠀⠀⠀⢹⣿⠟⢿⣿⣸⣼⡿⠢⠿⣿⣣⣤⠹⡿⡁⣿⣤⡬⣷⡆
⢠⣾⣿⣿⣿⣿⣾⠋⡅⠀⠀⢠⡀⠀⠀⠀⠀⠂⠀⢸⣿⠃⣿⣯⣻⣤⣦⣭⣤⣉⣿⣿⣦⣼⣟⣿⠥⡭⡤⠤⠄⠀⠉⠁
⠀⠉⢻⣿⣿⣿⡏⠀⡇⠄⠀⠸⡇⠚⠛⠃⠀⠀⠙⣶⣟⣀⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢟⡿⡿⣿
⠀⠀⠈⠉⠙⠻⠂⠀⠇⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢹
⠀⠀⠀⠀⠀⢀⣶⠞⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⣦⡀
⠀⠀⠀⠀⠀⠘⣷⣦⣊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣴⣢⠃
⠀⠀⠀⠀⠀⠀⠈⢿⡹⣷⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣞⢯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡗⠈⣕⢄⠀⠀⠀⠀⠉⢍⠀⠀⣀⠜⠁⠀⢀⠄⠠⡀⠀⠈⠣⣄⠀⠀⡩⠉⡆⠀⠀⠀⣠⡪⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣝⣄⠈⠙⠳⠦⠐⢡⣤⣄⠈⠈⠁⠀⠀⠐⡑⠋⠑⢊⠆⠀⠀⠈⠉⠁⣠⣤⡌⠢⠴⠞⠛⠁⣠⣫⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⠀⠀⠀⠀⠀⠸⠀⣟⠀⠀⠀⠀⠀⢰⡱⠤⡤⢎⠄⠀⠀⠀⠀⠀⣹⠀⠇⠀⠀⠀⠀⠀⣿⠇⢈
⠀⠀⠀⠀⠀⠀⠀⠸⣮⡟⠀⠀⠀⠀⠀⠀⠙⢉⣀⣀⣀⣀⣀⣀⣈⣐⡀⢉⣀⣀⣀⣀⣀⣀⣉⠋⠀⠀⠀⠀⠀⠀⢻⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣞⣛⣈⣈⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠭⠭⠭⢭⣉⣉⣚⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡒⠂⠀⠐⠆⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠺⠖⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠰⠂⠀⠐⢒⣽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠷⠀⢀⣀⣀⣀⣒⣂⣀⣒⣦⣄⣀⣈⣭⣭⣭⣭⣍⣀⣷⣖⣒⣂⣐⣒⣒⣀⢀⣀⠀⠾⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠙⢻⣛⠛⠛⠿⠶⠞⠛⠛⠛⢉⣉⠉⠉⠉⠉⠉⠉⢉⣙⣛⠛⠛⠳⠾⠟⠛⣛⣛⡛⠉⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣟⣿⣿⣯⣿⣽⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠧⠘⠿⣫⡿⢛⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢓⣀⣾⣋⣅⣠⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢋⣴⣾⣯⣿⣟⠹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠯⠓⠋⡎⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣭⢀⡀⠀⢰⣿⣾⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⣀⣁⡀⠉⠀⠀⠀⣼⡿⡎⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁⠀⠀⣿⣿⣿⡿⠀⠀⠰⢿⢳⡜⠁
⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⠀⢀⣽⣿⡟⢀⣴⣕⠀⠰⠋
⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠸⢿⣿⣧⣿⣿⣿⣧⣤⣄⣀
⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠛⢉⣲⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⣿⣿⣿⡉⢻⣿⠙⠦⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣋⠁⠀⠘⣿⡿⣿⣿⢿⡟⠀⠀⠴⠓⠽⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡁⠂⠠⡄⠀⠀⠀⠋⠤⠖⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠡⡑⠀⢸⡀⠐⡄⢀⠀⠄⡆⠰⡰⢀⠁⡠⠁⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡈⠀⢈⠂⡐⢌⢜⢄⢳⣀⣿⣼⣴⣥⣇⣅⣁⠆⡔⢡⠂⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡑⢜⢄⣩⡾⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣅⣞⢔⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡈⢱⡟⠁⢀⣖⡽⠿⣿⣿⣿⣿⡿⣿⣿⡉⠙⢻⣅⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠨⠐⣰⠏⢀⣞⣿⣷⣷⢞⣙⣭⣭⣟⠻⣿⣿⣿⣦⠀⠹⣆⠡⠤⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠬⠄⠀⠀⢠⡟⢀⣿⣿⣯⡋⢽⣧⣿⣿⣿⣿⣿⡎⣿⣾⣿⣧⠀⣿⣆⠉⠡⠄
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠤⢼⣧⣼⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡆⣿⣿⠤⠄⠀⠉⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢼⣿⣿⣿⣿⣿⣯⠻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣷⣿⡿⠀⠀⠠⠄
⠀⠀⠀⢀⠀⠄⠒⠊⠉⡀⠀⡺⣿⣿⣿⣿⣿⣿⣿⣬⣻⣛⣛⣿⣿⣿⣿⠿⠛⢿⣿⣿⠇⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠀⠐⠙⣿⣿⣿⣿⣿⣋⡛⠻⠟⠿⠟⠛⠋⠀⢀⣠⣾⣿⠯⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⣽⡟⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⠿⠋⢡
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣒⠠⠭⢒⣀⠀⣀⣀⣀⣐⡀⠠⠄⠒⡺⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠐⠒⠒⠒⠂⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉