Gardening Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠈⠠⠀⠂⣀⣀⡀⠀⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡼⠁⠀⠀⠀⠀⡀⠀⢴⣤⣠⣴
⠀⠠⠀⠀⠀⠀⡴⣻⣿⣿⣿⣶⣶⣤⡧⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣧⠀⠈⠀⠉⢠
⠀⠀⠆⢸⣄⣼⢷⣿⣾⣿⣿⡿⡿⣿⣿⣿⡀⠀⠐⠀⠀⠀⣠⠀⠀⠀⢸⢸⡇⠀⠀⣰⣤⣾⠿⣧⡄⠈⠐
⠀⠀⠼⣆⣿⣷⣾⣿⣷⣤⣿⠟⠛⣿⣿⣿⣷⠀⠀⠠⠁⢀⣸⠀⣠⠀⣇⣾⠀⠀⣺⣟⡅⢇⣠⢈⢙⠀⠻⢈
⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣂⠠⣴⣿⣿⣷⣦⣤⣀⣸⣮⣡⣸⣼⣷⣿⣛⣻⠋⠙⡿⣿⣾⣿⡆⠂
⠀⠀⠀⣿⣿⡟⢿⣿⡿⣴⣿⡿⣻⣿⣀⣹⣿⣿⡿⣿⣿⢿⣿⢿⣿⠿⣿⣻⣿⡿⣿⣧⣾⣟⡿⢟⣿⣿⣾
⢀⠀⠙⢿⡿⣿⣿⣿⣘⣧⣤⣿⣿⣦⡶⡛⢛⣿⣿⣿⣿⣿⣿⣿⣻⣶⣿⣯⢹⣛⣾⡏⠽⢿⡿⣿⣿⣿⣿⢀⣀
⠙⠀⡀⢀⡿⡿⢂⣿⡻⡿⡛⠋⣩⢎⣙⣛⣇⡻⣿⡇⣘⣿⣿⣿⣿⣿⣿⣿⡳⣿⢻⣇⠀⣸⣿⣟⣻⣯⣿⠀⠁
⠀⠙⡅⠃⢀⣤⣿⡞⢝⣯⣼⠻⣴⣠⠟⡸⣶⢃⣿⣿⣿⣻⣿⣿⡿⡿⣿⣿⣧⣿⡿⡽⣿⣿⡟⣯⣟⡻⢟⡇
⠀⠀⠰⡛⣏⣹⣷⣃⣅⣯⠿⣹⣾⣭⣴⣿⣸⡿⠿⢿⣿⣿⣿⣿⣷⣿⣿⡏⣈⡙⣽⣿⣿⣷⢻⡟⣿⣷⣿⡇⠂
⠀⣀⣀⢰⣿⢿⣯⣭⣙⣿⣿⣿⣿⣿⣿⣿⡏⣠⣷⣗⣿⠿⡇⢉⡉⢘⠛⣓⠾⣷⡏⣿⣿⣟⡟⣋⢿⣾⣉⠁⢁
⠰⠐⠢⢼⡗⢼⣿⣿⣿⣿⣙⣿⣿⣿⣿⣯⣿⣩⣿⣿⣿⣷⣥⣮⣤⠒⣷⣿⣴⣾⣿⣿⡟⠛⠢⡐⠖⣿⣼⡋⠁
⠀⠀⠀⠈⣿⣻⣿⡿⠃⣠⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣽⡟⢿⣧⢴⡿⠟⡛⣿⣃⣸⣇⣴⣾⣷⢴⡏⣹⠋
⠀⠀⠀⠀⢿⡿⣽⡵⣰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣧⣰⣤⣾⣿⣿⣿⣀⣋⣥⣀⣽⣿⠏
⠀⠀⠀⠀⠘⠀⠻⠐⠁⠀⠀⠁⠙⠋⠁⠈⠙⠁⠀⠉⠉⠙⠛⠙⠛⠛⠛⠛⠙⠋⠉⠙⠋⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠗⠀⠀⠀⠀⠀⠡⡐⠆⡄⡰⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣊⣲⣿⡇⠀⣉
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠍⠹⡑⢄⠒
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠄⠀⢸⣑⣿⠄⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠛⠁⢰⣶⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠒⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠰⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⣠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠀⠀⠀⡀⠀⠀⢿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢻⠀⠀⠸⡇
⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠙⠃⠀⢸⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠃⠀⠀⠉⢀⠀⠀⠀⠀⣤⣟⠀⠀⢀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠂⠐⣤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣤⠀⠛⠃⠀⠀⠀⠋⠿⠀⠐⠈⡁⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠱⡆⣾⠀⡠⠀⠺
⠀⠀⠀⠀⠀⠰⠂⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⢱⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⠹⣿⣠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡆⢸⡃⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠐⠦⢉⣡⣰⣆⡔⣄⣆⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣼⣿⣾⠃
⠀⠀⠀⠀⢀⣤⡸⠇⡐⠀⠀⠂⠲⠀⠀⠀⠀⠠⣀⣸⠆⣘⢶⢿⠿⡦⡖⠞⠀⠁⠀⠀⠀⠀⠀⠀⠙⢿⡿⢊⣡⣤
⠀⠀⠀⣰⠞⢉⡔⠊⣩⢀⠀⠠⠈⠀⠀⢀⣻⠧⣄⣸⠇⣼⣷⣿⡟⠁⣉⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⠘⠿⠟⠁
⠀⠀⢰⠏⠀⢼⠀⣼⠦⠦⢤⠀⠀⡆⠀⠀⣿⡖⣳⡀⢐⢛⣻⣿⣿⣿⠛⠿⠘⠄⠀⠀⠀⠀⠀⣰⣾⣅⣦⣶⣤⡀
⠀⢀⡞⢀⡿⢁⣿⢋⣩⠂⠀⠂⠄⠀⠀⠀⠸⠿⣿⣤⣁⣨⢉⣩⠇⡛⠄⠀⠀⠀⠀⡤⠀⠀⣤⣿⣿⣿⣿⣿⣿⡏⡿⢰⡄
⠀⠀⣿⣿⣽⡟⣱⣟⠉⠀⠀⠰⠷⣄⠀⠀⠀⠈⠛⢿⣷⣾⣉⣵⣤⠣⣀⣴⣤⠎⠈⠀⠀⣶⣿⣿⣿⣿⣻⡏⡝⠁⠀⠘⣱⡆
⠀⠈⣿⣯⣾⣿⣻⣄⡄⢡⡄⠁⠀⠀⠑⠀⠀⢀⠤⠀⠁⠛⠩⠿⣧⠀⣧⢉⠂⢀⣦⣼⣿⣿⣿⣿⣿⡿⢿⣿⣀⠀⠀⠈⠉⠰
⠀⠀⠸⣿⣿⣿⠛⠝⠁⠀⠀⠀⠀⠀⠀⢠⣆⣈⡠⢀⣮⠆⠀⣠⠀⠈⣿⠀⢠⠀⢻⣿⣿⣿⣿⣿⣋⣘⠐⣿⡯⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠠⣤⣀⡀⠀⢠⡀⠀⠿⣿⣿⣾⡏⡀⠀⣿⡇⠀⢸⢠⠏⣀⠈⣿⣿⣿⣽⣿⣿⣿⣿⡟⠃⢢⣔⠒⠦⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⣷⣿⣶⠢⠄⠱⡀⢱⢰⣾⣿⣿⣶⢰⡏⠀⠈⣆⠜⢻⢟⣽⡿⠉⢏⡋⡄⠀⠀⢉⣳⣦⠄
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣇⣦⡘⢳⠸⣾⣿⣿⣿⣿⣸⠀⢀⡾⠁⠀⡜⠻⣯⣴⠄⣸⢣⣇⢴⡳⡼⠞⠁
⠀⠀⠀⠘⣿⣇⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⢻⡍⢻⣿⣿⡇⣿⢠⡞⠀⠀⣼⢁⡤⡄⠁⠈⠉⠋⠙
⠀⠀⠀⠀⣉⣉⣳⣞⡠⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠳⣸⣿⣿⣥⣻⠟⠀⡄⠀⠇⢸⠿⠃⠀⣠⠁
⠀⠀⠀⠐⠻⠟⢁⣜⠁⠠⣀⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠞⣿⣀⣃⣿⠀⣶⣾⠗⠁
⠀⠀⠀⠀⠀⠀⠈⠉⢳⣴⡷⠒⠒⠂⣉⣀⡐⢀⣨⣿⣿⣿⣿⣿⣟⠠⠀⣀⣴⣿⢿⣿⣿⣿⣿⣥⣤⠄
⠀⠀⠀⠀⠀⠀⠦⠾⠁⠾⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠿⠏⢰⣿⣿⣿⢿⡜⣸⠟⠛⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢽⣿⣿⣿⣿⣿⡿⠟⣿⣦⡿⠋⢀⣴⣦⣜⠷⣿⡟⣸⣃⣴⣾⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠋⢀⣴⣿⣿⠧⠂⢈⣉⣛⡿⡆⢿⢹⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⠀⠀⠹⢿⣿⣿⢰⣿⣿⣟⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⠿⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠠⡄⠀⠀⢀⡀⠀⠀⠀⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⣬⠉⠉⣷⣦⢶⣄⢊⡀⢳⡀⠀⠘⢿⣷⢀⣴⣿⣿⢠⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀
⠀⠀⠀⣀⣰⣧⠛⠃⠀⠹⠛⠻⠛⢁⡶⠆⠹⡷⡞⠋⢁⠿⢁⣨⡄⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠒⠛⠛⠁⠀⠀⡀⠀⠀⠀⣀⣀⠀⠀⢰⠘⢰⣤⣤⣷⣿⣿⡇⠀⣺⣤⣤⡀⠀⡄⡀⠀⠀⡠⡀
⠀⠀⠀⠀⠄⠀⢀⠢⠷⣦⣀⠀⠉⠙⢶⣤⣿⢃⡁⣩⣏⣿⣿⢿⣿⣅⣈⣿⢉⣐⢾⢟⡄⡀⣀⠁⠠⣄⠀⠈⢀
⠀⠀⠀⢄⠠⠴⠎⠃⠀⣽⣈⣄⣀⠀⠀⢍⡉⣲⣿⣿⡿⣷⣿⣿⣿⣿⣷⣿⠁⢸⡃⣤⣹⣿⣿⡴⣶⢋⢀⣀⡆
⠀⠀⠀⢸⠇⡄⠙⠃⠀⢹⡟⢻⣿⣷⠰⢾⣴⣿⣿⢻⣷⣿⣿⣿⣿⢿⣿⣿⣧⢘⣿⢙⣩⣿⣿⣿⣿⣷⣔⠸⠓
⠀⢰⠀⠰⠀⡇⠀⠀⠀⣾⡆⢸⡟⢙⣀⡀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣍⣸⡿⠀⢀⣿⣿⣇⣼⣶⣛⡑⠓
⠀⢸⠀⣂⢸⣇⣀⣴⣴⣿⡇⢹⣴⣿⣟⣻⣖⣿⣿⣿⣿⢯⣽⣿⣿⣷⣽⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠘
⠀⢸⣁⠈⢘⡏⠛⠡⣭⢹⣏⢹⣯⣿⣿⣍⣫⢿⣿⣿⣿⢿⣿⠏⠉⠹⣿⣿⣿⣿⣿⣇⣿⣿⢋⣏⡴⠠⠆
⠀⠺⣿⢇⡐⡇⠀⠀⠠⣼⣟⣸⡏⣉⣽⠛⠉⠛⣻⣿⣿⣛⣿⣷⠶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠄
⠘⠲⡽⠊⠈⠃⠀⠐⠂⠙⣿⣿⡇⠀⢹⠀⠤⠶⠀⠰⠼⠿⣷⣤⡤⠄⢻⣿⣿⣿⣿⣿⣿⣿⠏
⢀⣠⣽⠏⠀⠀⠀⠀⠤⣿⣟⠋⠀⠀⢹⡀⠀⠀⠀⠀⠀⠠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠠
⢀⠽⡯⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⢀⣈⡄⠀⠀⠀⠶⠿⠉⠉⠛⠛⠛⠟⠛⠻⠿⡋⠙⠻⠿⣧⠠⠀⠀⠀⠒⠲⠶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢱⣿⣿⣿⡏⢘⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡼⢿⣿⣿⡟⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡦⠀⠀⠀⠀⢀⣿⣿⡇⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠹⡟
⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣴⡆⠀⠀⢻⡿⢻⣦⠀⠘⠃⡄⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠛⠛⢠⡀⠀⠀⠀⠀⢨⠢⠀⠀⠀⠀⠀⢄⠑⠶⠀⣰⣦⡀⠀⡇⠀⠀⢰⠇
⠀⠀⠀⠀⢀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣦⠀⢀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣼⣿⣿⣧⠀⡇⠀⠀⠿
⠀⠔⡀⣿⣿⣿⣻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢧⢹⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢻⡖⡋⠿⣿⠏⠀⡇
⠀⠀⠀⢿⣿⡟⠏⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠈⣎⠁⢀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⡆⠁⠀⢸⠀⠀⡇
⠀⠀⠀⢸⠁⠁⠀⠀⠀⢀⡘⠟⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢹⡄⠈⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠀⢸⠀⢀⡇⠀⠀⠀⠀⠀⢀⡄⢰⣿⡄
⠀⢰⠀⢸⡄⢠⣤⠀⠀⠘⠷⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⡇⢠⣤⡌⣧⠀⠀⣮⠛⢀⠀⡀⠀⠀⠉⠀⠀⢹⡌⢆⢠⡄⠈⡗⢤⡀⠀⠀⠀⠈⠀⠾⠛⠏
⠀⢸⡇⢸⣷⣿⣿⠀⠀⠄⠀⣶⠈⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⠿⣄⢹⡄⠔⠉⠀⡏⠀⠛⠀⢀⣀⡤⠀⢸⡇⠘⡎⡇⢈⡇⡀⠳⡄⠀⠀⠀⠀⠂
⠀⠀⢻⣿⠊⢻⣿⣶⣿⢟⣿⠃⠀⠀⢀⠀⠈⠙⢿⡉⠉⠟⣇⠀⢹⡎⣿⡆⠀⣸⡇⠀⠀⠀⠐⠻⠆⠀⠀⣷⠀⢻⣷⢰⡇⢡⠀⢹⡄⠀⠀⠀⠀⠀⢀⡔
⠀⠀⢸⠸⡁⢹⡟⠉⣙⣯⣿⣀⡀⢀⣸⠀⠀⠀⠀⡿⣄⠀⣿⠀⠀⣷⢹⡁⠀⡿⠀⠀⢠⠀⠀⢀⠄⠀⢀⣿⣀⢈⣿⣾⡇⢸⣤⠀⢻⡀⠀⠀⠀⣠⡾
⠀⠀⣼⠀⣇⣹⣿⣿⢿⣿⣿⣯⠛⢉⣿⣶⣾⣷⡄⢹⣿⣷⣼⡆⠀⢸⣾⡇⢰⡇⠀⠀⣴⠀⠀⣼⠀⠀⠈⢻⡙⠛⢿⣿⡇⢸⡿⠀⠈⣧⠀⠀⠾⣿⠃
⠀⠀⣿⡄⠹⡇⢸⢹⡀⢟⠛⢿⣿⠾⣿⣿⣿⣿⣧⠸⣿⣿⣿⡇⠀⠀⣷⣿⢸⡇⠀⣀⠃⢀⣼⣃⣴⠏⠀⣿⡿⡄⣸⣿⡇⢸⡇⢡⠀⢹⡇⠀⢠⡟
⠀⢠⣇⡇⣦⣇⢸⡇⣷⠈⢳⡀⣷⠀⢸⣿⣿⣿⡿⠀⣿⣿⣿⡇⢠⠀⢹⣹⣼⠀⠀⢹⢰⣠⡿⠻⣇⠀⡜⢹⡇⢳⡏⢹⡷⣾⣇⠈⡆⠘⡇⣧⣾⠇⢰
⠀⢸⠉⡟⣿⣿⢻⣷⢸⣵⣾⣷⢸⣆⣼⣷⣽⢻⡇⠀⣟⡏⠈⣇⢸⠀⢸⣿⣿⣶⣿⡿⣿⣿⠿⣷⠿⣸⠁⢸⡇⢸⣇⢸⡇⣿⢹⠓⢷⠀⡇⣿⣹⡀⠀⡇
⠀⣿⠀⣿⡇⢿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⡷⢸⡇⠀⣿⡇⠀⣿⢘⡇⢘⣿⣿⣿⠙⣇⢻⡏⣰⠋⢀⡏⠀⢸⣁⣸⣿⢸⣇⣏⢸⠀⢸⠷⣟⡿⡿⠃⠀⢱
⠀⣿⠀⣽⣧⣼⡿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣷⢸⡇⠀⣿⣧⠀⣿⠸⡇⢸⡿⣿⣯⣠⡏⣼⣡⠏⠀⢸⠃⡤⢾⠏⢸⣿⣿⣿⣿⣸⠀⠈⡇⣿⣇⡿⣼⠀⢸⡀
⠀⣿⢠⣿⣏⢹⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⡇⢠⣿⣿⡀⢿⣐⣇⢸⡇⣿⣿⣿⢻⣿⣾⣦⣦⣿⠟⠀⢸⠇⢸⣿⣿⣿⣿⣿⣢⠖⡏⣿⣿⡇⢹⡀⠀⡇
⠀⣿⣤⣿⣿⢸⡇⣿⡏⣿⣿⣿⠛⣿⣿⣿⣼⣿⣿⣾⣿⣿⣧⣿⣿⣿⢸⡆⣿⢻⣿⢸⣿⣿⣿⣹⣿⣄⠀⡾⠀⠘⢿⣿⣿⣿⣿⡅⠀⡇⣿⣿⣇⠸⡇⠀⡇
⠀⣿⡟⣻⣿⣸⡇⣿⣷⣽⣿⣿⣠⣿⣸⡟⠈⡿⡿⡟⢻⠃⣟⢻⠛⡋⣾⡄⡇⠀⣿⣼⣿⣿⣿⣿⡇⠀⢀⡇⠀⡇⢸⣿⣿⣿⠘⣧⠀⡇⢹⣿⣿⠀⣧⠀⣷
⠀⣿⠁⢹⣿⣿⣷⣿⣿⠿⣿⢻⠿⣿⢹⡇⠀⡇⣿⡇⢸⢰⢸⣸⠀⡃⣿⡇⡇⠀⣿⣿⣿⢏⡟⣼⠁⡀⢸⡇⢠⣧⠿⣿⣿⣿⠀⠀⠀⣧⢸⣿⣿⠀⣿⠀⣿
⠀⣿⠀⢸⣿⡿⡃⢹⡿⣆⣿⢸⠀⢿⢸⡇⠀⡇⣿⠃⢸⠸⢸⣿⠀⠁⢸⡇⡇⠀⢻⠃⡇⣾⣷⣿⣟⡉⢹⡇⢸⣿⠀⣿⣿⠉⠀⠀⠀⣿⡿⣿⢻⠀⣿⠀⣿
⠀⣿⠀⢸⢹⡇⠀⣿⡇⠀⣿⢸⠀⢸⢸⡇⠀⡇⣿⠀⢸⡇⢸⣿⠀⠀⣿⣷⡇⠀⢸⠀⡇⡿⠋⣼⠈⠃⢸⡇⢸⡇⠀⣿⡇⠀⠀⠀⠀⣿⠇⣿⢸⠀⢻⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⣿⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠃⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣙⠖⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠀⠠⠀⠈⢢⠀⣀⠔⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠁⠙⡀⠚⠀⠀⠈⠽⠍⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠇⠀⠀⠀⠀⠀⠀⠛⠄⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠗⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⢤⣤⡀⠀⠀⠀⠀⠀⢀⣤⡶⢈⡦⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠄⠀⠀⢀⠀⠀⠈⠀⠰⢆⢭⣦⢤⣄⣨⣑⣄
⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠘⠻⠷⠚⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠀⢀⡓⠲⡤⠤⠼⢥⣴⣾⣀⣆
⠀⠀⣾⣿⡟⠀⠀⠀⢀⣤⠂⠀⠀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⠠⠄⠀⠀⠄⠀⠀⢀⠀⡉⠹⢯⡽⠒⠒⠏⠀⠀⢁⡠⠷⡀
⠀⠀⢿⣿⡇⠀⢀⣴⣿⡿⠋⠀⠀⠛⠄⠀⠂⡀⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠐⠀⠀⠂⠀⠐⠐⠠⣀⠈⠂⠌⠀⠛⣋⠛⢀⠀⢃⣀⡤⢞
⠀⠀⠈⠿⣿⡄⠉⠛⠻⠷⠀⠒⠋⠑⠊⠂⠀⠲⠆⡤⠀⠀⠀⠀⠀⠁⠀⠔⠄⠀⠀⠘⡇⠀⠆⠀⠹⡔⠀⣀⡀⠂⣠⠖⠀⠀⠰⣯⣭⣭⣴⣾⡿⠀⢀
⠀⠀⠀⠀⠀⢁⠀⠀⠀⡀⠔⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠅⠀⠀⣆⠀⠇⠠⠀⢀⠞⣁⠀⠀⣴⣾⣿⣿⣿⠛⠉⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠒⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠤⠒⠂⠖⠁⠁⢉⣥⠾⢴⣥⣩⠖⠡⢦⣾⣿⣿⣿⣿⣿⠀⡀⣀
⠀⠀⠀⠀⠀⠐⠄⠀⡀⠀⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠿⣯⣖⠤⠋⠀⠉⠂⢄⠉⠉⠉⠉⠉⠀⠀⠐⠅⠠⠔
⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣽⣭⣽⣽⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣷⣿⣷⣶⣿⣷⣶⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀
⠀⠀⠀⠖⠆⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠁⠤⣠⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⠐⠒⠒⠀⠂⠐⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠡⣅⠉⠉⠁⡀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠓⠶⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠁
⠀⠀⠀⠣⣀⠂⣤⠂⢠⠂⡆⠂⡆⢠⠂⣆⠠⢰⠂⡂⡇⡆⠢⠂⡆⢰⠒⡄⠂⡆⢠⠂⡇⠀⡤⠂⣤⠂⡇⢠⠐⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠑⢄⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠴⠤⠖⠒
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠑⡀⠀⠀⡤⠤⠀⠀⠀⠀⢀⠀⠀⠀⢄
⠀⠀⠀⠀⢀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⡥⠠⠀⠀⠀⠒⠒⠒⠞⠂⠠⠐⢃⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠠⠠⠤⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠐⣢⠋
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⢀⠀⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠸⢋⣻⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⢀⡀
⠀⠀⢧⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⣀⠀⠀⠐⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀⠉⠃⣤
⠀⠀⢤⠀⠀⡀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣿⣿⣷⡿⢿⠟⠻⣷⣦⣤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠂⠀⠒⠐
⣆⠀⠴⠀⠀⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡍⠙⠃⢀⣄⣀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠙⠒⣆⢀⠃⠀⢰⠄⠀⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠟⠆⠀⡀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⢀⠆
⠻⣀⠀⠀⣈⠀⠀⢸⡅⢰⠀⠀⠀⠀⠀⠀⠀⢿⣾⣷⠁⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠡⠀⣀⠀⠀⠀⠠⠀⠀⢲⠎⠈⢀⡀
⡀⡷⠶⡄⠀⠀⠀⠸⡇⢀⠰⠄⠀⠀⠀⠀⠀⠀⢹⣗⢁⠔⡟⢀⠈⠐⠁⠀⣀⠰⠀⠰⣤⡿⠄⠀⠀⠀⠒⢄⠚⣠⠴⠈⠁
⠀⢀⣤⡘⠀⠛⠀⢸⣦⣾⡄⠀⠀⠀⠀⠀⠀⠂⡄⢹⠊⢘⡀⢈⡤⠀⠀⣜⢁⡆⠉⠀⢴⡕⠄⠀⠀⠀⠀⠈⠳⢆⡀⢀⠘
⠀⠞⠁⢹⡀⢈⡀⢶⠀⣹⢿⡤⠆⠀⠀⠀⠀⣤⠀⡄⠀⠉⠠⠼⣄⡾⠓⠭⢰⡇⠸⡌⢿⡁⠀⢂⡀⠀⠀⠀⠀⠀⠠⢀⡀
⢀⠀⠠⣌⣣⢾⡃⢻⢆⠋⢼⣷⣄⠀⠀⠘⢸⡏⠘⢥⡀⡀⠑⠰⠀⠀⠉⠓⢀⣝⣧⡈⠁⠀⢀⠀⢘⢐⡂⢰⠂⠐⠄⠀⠁
⠋⣡⢀⠀⠀⣨⣤⣾⣄⠦⢠⢿⠈⣇⠈⣀⣺⣀⠀⢀⡘⢣⡮⢴⠆⠤⠀⠀⠈⣛⣿⠋⢛⠀⠀⠞⠉⣌⡱⠦⠉⠀⠀⢀⡀
⡀⠸⣋⠉⠽⢿⡄⣼⡇⠠⠌⡛⠀⠉⣠⣉⡝⠁⡸⠤⠉⠁⠃⣼⠂⢀⠶⣧⡄⣐⠿⠶⢊⡄⠺⠿⠈⠟⠸⢤⡠⣀⢀⣈⠱
⢶⠜⣿⡗⣠⣛⡛⢿⡷⠂⠀⢱⠈⣦⣤⣿⣷⣴⣥⣄⠀⠀⣠⡾⣫⢿⢰⡶⣏⡰⠀⠗⣺⢁⡃⢀⠀⢀⠀⢈⡛⢐⡍⠯⣴
⡴⢹⣟⡿⠿⢙⢻⡚⠁⠀⣠⡄⢸⣍⣯⡿⠿⣿⡏⠐⠤⠀⠐⣟⡿⠂⠙⡿⠿⡿⠓⢀⠖⠊⢉⠰⢆⣟⡿⣇⣤⣞⡧⣆
⠁⢼⣿⡠⣦⡀⣨⣴⣿⣿⡶⣲⢻⣇⠈⣔⡜⢻⣂⣠⡖⢠⣦⣏⡗⡁⣀⠃⢿⠑⠠⠈⡃⠸⢺⠀⠻⣽⢣⣻⡾⡿⣞⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣀⠀⠀⠀⠀⠀⠀⠀⠸⢃⡀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⣶⣻⣿⠀⠀⠀⣠⣀⡙⣾⡀⠋⠀⠀⠀⠀⠀⠀⠞⠋⣉⣽⣤⣠⣤⡄⠀⢠⣶⣿⠟⠇⣄⣾⣷⣄⣀
⠀⠀⠀⠀⢀⡀⣀⣈⠻⠋⡟⠛⠀⠀⣲⣿⣿⢿⣷⣿⡿⠂⠀⠀⠀⠀⠀⠀⢠⣼⣿⣷⣿⣿⣿⣦⠀⠀⠀⠀⣲⣾⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣀⡿⣭⣷⣿⡗⠀⠁⠀⢀⣤⣿⣿⣿⣿⣿⣧⣿⣿⠂⠀⠀⠀⠀⣴⣷⣿⡟⣿⣿⣿⣿⣿⡟⠀⢀⣩⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⢘⣿⣿⣿⣿⣿⣿⠂⡀⠀⢣⣿⣿⣇⠘⠿⡾⢿⣿⣿⠇⠀⠀⠀⠀⠛⢿⠟⠛⡷⠋⢻⣿⡆⠀⠀⢘⠗⢻⡿⣿⠛⠿⢿⡿⡟
⠀⠀⠸⣽⣿⢺⠚⠛⣫⣤⣦⡀⠀⠀⠿⠂⡆⡾⣿⡟⠉⠁⠀⠀⠀⠀⠀⢰⢶⣶⡄⡇⠀⠈⠛⠁⠀⠀⢀⠀⠀⠀⡏
⠀⠀⠀⠈⠁⢸⠀⠀⠘⢙⢻⡇⠀⠀⠀⠀⡇⠣⠾⠧⢠⣴⣶⣶⣷⣦⡄⠰⠸⢿⠀⣧⣀⠀⠀⠀⠀⡛⣿⣿⠆⠀⡃
⠀⠀⠀⠀⠀⢸⠀⠀⠘⠺⠿⠷⣶⣷⣶⣴⣧⣀⡀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⣤⣷⣶⣶⣶⡄⠀⣦⣿⣿⣀⣀⣇⣀⣀
⠀⠀⠀⢀⣀⣼⣄⣠⣀⣀⣀⣀⡙⠻⢿⣿⣿⣿⣿⡷⠶⢿⣿⣿⣿⡿⢱⣶⣿⣿⣿⣿⣽⡻⠕⠁⠀⠀⠀⠀⢀⠀⡇
⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⢜⡸⢿⡿⡿⠿⠶⢿⢿⣦⣾⣿⣿⣶⣾⣿⣿⣿⣻⣿⣿⣿⣿⣶⡄
⠀⠀⠀⢹⡿⣿⣿⣿⣽⣿⣿⠿⠿⣿⣟⣿⣿⣿⣮⣷⣤⣴⣎⣶⣎⣭⣤⣪⣾⣿⣿⣿⣿⣿⣿⢻⣿⢿⣿⣿⡿⣿⣿⣿⡟
⠀⠀⠀⠸⣿⣿⣿⣇⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣭⣉⠓⠛⢿⡏⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⢺⣿⣿⣿⣿⣾⣽⣿⡿⣿⣿⣿⣿⣿⡏⣹⣿⣿⡗⣿⣿⣿⣇⠀⠈⠃⠛⠛⠛⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡽⣇⣼⣿⣿⡗⠾⠿⠿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠾⠿⠛⠛⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢆⣠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣿⣿⣿⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⣿⠟⠽⠋⠿⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠿⠚⠿⣤⠀⢐⣺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠰⠃⡤⠵⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⢀⣮⡁⢠⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠀⠀⠀⢠⠦⣥⢦⣟⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⣾⣿⣏⠱⣬⡳⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡐⠁⠀⣿⡃⡌⢷⣌⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠎⣀⣠⡞⠁⢀⣼⣿⡿⣮⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠿⠥⠤⣤⣀⣄⣹⣤⣨⣹⣟⣰⣿⣿⡿⣝⡾⠉⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢜⣿⡥⠂⠉⠉⠙⢿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⠻⣷⣾⡿⢾⡦⠆⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠁⠀⠀⠄⠀⠀⣀⣥⣬⣙⠚⠆⠀⠤⠄⠈⠳⡤⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠡⠀⠂⢁⣀⣀⢤⢶⣿⣾⣿⡿⠟⠋⠈⢳⣾⣴⡎⢘⣷⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠰⣿⡀⠀⣀⣄⣤⢾⣿⣿⣦⣬⣿⠿⠋⠀⠀⠀⠀⠀⢻⡝⠻⠿⣥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣺⣿⣧⣂⢰⢿⢉⢻⢿⣿⣾⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⠒⠋⠁
⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣉⣧⣷⣾⣶⡿⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠶⢦⡴⢶⣖⣛⠛⠉⠙⠛⠛⠳⢦⣄⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠹⡆⠀⠀⠀⠀⠀⠉⢷⡀⢠⠾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣩⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠙⢣⠠⢤⣤⣤⣄⡀⢻⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢁⣴⡟⣹⠞⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠸⣄⡀⢿⠀⠀⠙⠾⠁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⣾⣥⠟⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠈⠙⣻⣇⣀⡀⠀⠸⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣼⠏⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⣤⡾⠋⣀⣠⣤⠖⠲⣌⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⠛⠉⠉⠉⠀⠀⠀⠈⠙⢦⡙⢦⡀⠀⣠⠄⠀⠀⠠⡄⢀⡼⣡⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠾⠻⣦⠱⣴⠃⠀⠀⠀⠀⢹⠏⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡄⢴⠤⣤⣤⣀⡀⠀⠀⠀⠀⠈⢳⡉⡄⠀⠀⠀⠀⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣄⣀⠀⠀⢻⡜⡄⠀⠀⠈⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢆⡀⠀⢿⣰⠀⠀⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⡇
⠀⠀⠀⠀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⢀⠀⣤⣄⣀⣀⠀⠀⠈⠀⠀⠀⠀⠈⢣⡀⠀⢇⢇⡀⠻⠒⠂⠀⠀⠀⠀⠀⠀⣠⡶⠊⠉⠀⠀⣿
⠀⠀⠀⠚⢏⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠂⠈⠉⠀⢀⠀⠛⠒⢤⣀⠀⠈⢷⡀⠸⡘⢻⠆⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠉⠓⢿⣍⡉⠙⠳⣤⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠓⢦⠘⣧⠀⠇⢸⡄⠀⠀⠀⢀⣤⠋⠀⠀⠀⠀⣠⡄⠀⠀⢠⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣼⡄⢸⠈⡃⠀⠀⣤⠎⠁⠀⠀⢀⢀⠞⠁⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠯⠐⣦⣀⣀⠀⣤⣀⣰⡶⠛⠛⠉⠀⠙⠷⣄⡀⢳⠀⢰⡇⠀⠀⡀⠀⣸⠋⠀⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⡀⣿⠀⠀⠀⠹⣮⠃⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠉⠉⠙⠿⣄⣀⣀⣠⣉⡀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠙⠳⣄⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠙⠙⢦⣸⢦⣷⣤⠶⠞⠛⠛⠙⠛⠶⣄⠀⢀⣀⣀⣀⣀⠈⢳⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠾⠛⠉⠉⠉⠉⠉⠉⠛⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡴⠞⠁⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠁⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢤⣰⡇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣴⠤⣝⣋⠩⣙⣻⠇⠀⠀⠀⣀⡀⠀⠀⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⡇⠀⠀⠀⣴⠒⢦⣄⠀⠀⣰⣿⠀⣿⡀⠿⠃⢀⣼⢿⣔⢇⡦⠞⠁⠀⠀⠀⠀⠛⠷⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠻⣄⣀⣴⡟⠀⠀⠈⣳⡾⠃⠹⣧⣌⠙⠳⣤⡏⠁⠀⠹⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠀⠀⠀⣼⠋⠀⠀⠀⠀⠙⢷⣄⠟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣀⠠⠤⠤⣀⣾⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢀⡴⠶⠤⠶⢤⡀⠀⠀⢀⣤⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠋⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠘⡇⠀⢀⣴⠏⠀⣠⡴⢶⠉⠉⠀⢀⡿⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⣠⡤⠤⠤⠚⠋⠁⢀⡼⠋⠀⠘⠳⢄⣀⡼⠃⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠙⠷⢦⣄⣀⣀⣴⠞⠉⢩⠟⠁⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠦⣄⣀⠀⠀⠀⠀⠀⠀⢈⣽⠟⠁⠀⠀⣠⡶⣿⠖⠴⠶⠛⠛⡉⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠀⠋⠉⡜⠁⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠷⣤⣀⣀⣀⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⠉⠉⠉⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⣀⣀⣠⡶⠏⠥⠤⠤⢤⣬⡽⢶⣤⣀⣀⣀⣀⣀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⡑⠶⢄⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢂⠀⠂⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣱⠛⡊⠤⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡘⣄⣓⡀⠃⣤⠀⠀⠀⠀⣠⠤⠄⣤⣼⣧⣤⠀⠀⠘⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣯⡮⣝⡶⡅⠢⠀⠀⠀⠈⠳⣦⣤⡀⢛⣿⣿⣿⡃⢀⣤⠄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣟⣫⡓⢨⡚⡷⠀⠀⠀⠀⠈⠉⠁⢀⠃⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣯⣤⣿⢇⠶⢲⠄⠀⠀⠀⢀⠠⡄⣀⠀⣄⢀⠄⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣯⣻⡗⣯⡀⠀⠀⠀⠀⠀⠐⠫⡆⢸⣀⡔⠀⣠⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣾⠿⠟⠁⠀⠀⠀⣶⣆⠀⡀⢠⣾⡟⢀⣘⡟⠀⠀⠠⡒⠄
⠀⠀⠀⢠⣀⡀⠡⠀⣥⡀⣤⠀⠀⠀⠀⠀⠀⢦⠈⠋⠙⣇⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣾⣿⣿⣿⣥⠀⠴⠞⠻⢿⡿⠃
⠀⠀⠀⠈⣿⣿⣦⣒⡈⠼⠤⣱⠀⠀⡄⢀⣘⣷⣀⣤⡀⠛⠀⠀⢀⣤⣤⣤⣀⠜⢹⣿⣿⣿⣿⣿⣦⠀⢲⣄
⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⠿⣄⣾⡷⠛⠚⠻⣿⣿⣿⡗⠂⠀⣿⣿⣿⣾⣧⣴⠋⢀⡼⠛⢿⡿⠿⢧⣄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠰⢶⣶⡄⠈⡏⠙⠳⠀⣠⣿⣿⣿⣿⣿⣿⠰⠋⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠘⠻⢻⡇⠹⡄⠀⠘⠛⠛⢿⣿⣿⣿⣿⣷⣀⡢⢄⠀⠀⠀⠀⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣧⠀⣼⣗⣠⣧⣀⠀⠄⣀⡄⢻⣿⣿⣿⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⣿⣿⣿⣿⡥⠾⠘⠉⠀⢠⣿⣿⣿⣿⣦⣲⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠁⠀⢈⣷⣶⣮⣿⣿⣿⣿⣤⡀⠀⠀⠀⢀⣸⡟⠛⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣾⣿⠛⠁⢳⠀⠉⠛⣿⠥⠤⢴⡾⠋⠀⠀⠀⠈⠉⠉⠀⢀⣀⣠⡤⡴⢼⠓⠣⢿⣐⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡏⣩⠏⠁⠀⠀⠀⢣⠀⠀⢸⠀⠀⣨⡇⠀⠀⠀⠀⠀⠀⢀⠀⡞⠧⣞⢡⣇⣾⣯⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠉⠁⠀⠀⠀⠀⠀⠀⠳⡀⢺⠀⣰⢹⣿⣀⣤⠀⠀⠀⠀⣍⢷⣴⣺⣄⣳⣿⣿⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⢠⣇⡜⢸⣿⣿⠀⣠⡴⠚⠛⠿⠿⠿⠟⠛⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⡏⠀⣉⣉⣀⠀⠈
⠀⠀⠀⠀⠐⣦⣄⣀⣀⠀⠀⠀⠀⠀⢀⠈⣿⣷⣶⣤⣹⣶⣿⣾⣿⠟⠛⠉⢉⣠⣘⡀
⠀⠀⠀⠀⠀⠀⠑⠈⠛⢻⣿⡀⠀⣀⣉⣀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠗⣤⣼⣾⡿⢋⡿
⠀⠀⠠⢤⣠⣀⡔⡤⢠⣿⠟⠁⢾⡿⣻⣿⣿⢿⣿⣿⡿⠛⡿⠏⠀⢹⡉⣿⠑⠒⠉
⠀⠀⠀⠒⠛⠛⠶⠛⠋⠀⠀⠀⠀⠙⠛⠋⠁⣾⣿⣧⡀⠀⠁⠀⠀⢜⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⢀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⢣⡄⠀⠐⠈⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠃⠂⠀⠀⠀⠀⠀⠀⢻⠟⢡⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠏⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡆⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣄⡧⠀⠀⠀⣀⡀⠠⠀⠀⠠⠀⣴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⡀⠀⠀⠀⢀⠀⠙⠁⡀⠠⣶⣄⠟⠡⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⢿⠆⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⢄⠀⠀⢀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⢤⡤⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡇⠸⠉⠀⠀⠀⠀⠀⠾⠁⡤⠀⠀⠀⠀⠀⠀⡀⠀⣄⠀⠐⠀⠀⠀⠴⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠻⠂⠀⠀⠀⠀⠀⠐⠁⠀⣠⣼⣿⣿⣿⣿⣾⡁⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⡇⣤⡀⠀⢀⠀⠀⢰⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⡇⠈⠁⠀⠀⠀⠘⢇⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⢀⣤⣶⠿⠰⢆⣤⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⡀⠀⠀⢀⣀⢸⡀⠀⠈⠙⠙⢻⣿⣿⢻⡇⠰⣿⠋⠀⡀⠛⠻⣏⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣸⡷⠀⠀⠀⣻⡷⣿⠿⠃⠀⠀⠀⠀⠀⠛⢸⡅⠄⠀⠀⠀⣀⡀⢠⠿⢇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣿⡟⠋⠀⣿⠂⠻⠗⠘⢀⣀⢠⠀⠀⠠⣤⣼⣿⡇⠀⠀⢀⠀⠛⣤⠌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⣬⣿⡿⡀⠀⠀⠀⢙⣿⡇⠀⢀⡈⠀⠀⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⡀⠠⡀⠀⠆⠀⠀⠀⠀⠀⠀⡅⠀⠐⢷⣀⠀⢺⣿⣯⡇⠀⣯⣉⣥⣐⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠛⣦⠀⢀⡀⠀⡀⠂⠀⠀⢈⠀⠀⠀⣿⡆⠰⣞⣿⣿⣾⣿⡛⣿⠀⢋⣍⣿⣿⠛⢠⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⠷⡶⠇⠀⠑⣀⣠⡴⡏⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⠉⠀⢻⡆⠉⠛⠋⠁⠀⢀⣥⠀⠂⠀⡖⣠⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡹⠛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣇⠀⣠⣨⡗⠀⣴⣦⣿⠀⠙⣴⠀⣴⣾⣿⣇⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣷⠀⠀⠀⠀⠀⠀⢀⢀⡘⠀⣀⠀⠀⡈⠁⠀⠈⠱⡆⢺⣿⣿⡿⠀⠀⠁⢠⡿⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣋⣼⠂⢀⡄⢠⣤⣾⠉⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣧⣴⠃⠀⠀⠀⠈⠁⠀⠀⠈⠁⠀⠀⠀⢀⡙⣽⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠘⣻⣦⠄⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢠⢤⣤⣄⣄⣿⣿⣶⠟⠁⠘⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠳⠀⠰⣆⡀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠠⠰⠍⠁⠐⢶⣤⢤⣿⣿⠿⢿⣿⡛⠉⠉⠀⠀⣶⠀⢠⣌⣿⣥⣿⡿⠟⠋⠉⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣇⡀⢀⡴⠚⠁⠀⠀⠈⠀⠁⢀⠀⠀⡄⠁⠀⣰⠿⣿⠏⠙⠃⢀⣤⠆⠀⠀⣀⠴⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣽⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢸⠷⠟⠀⢀⡀⠑⢀⠉⠠⠀⠶⠋⣁⡴⠖⠋⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣯⣴⣶⣦⣤⣀⣤⣴⠶⣿⣶⣶⣶⣿⣷⠀⠉⠙⣦⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣉⣿⣿⣿⣿⣿⣤⡿⣿⠿⠏⠈⠁⠹⠿⣦⡞⠛⠁⠀⠀⠀⠀⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣏⣿⡿⡿⢿⣷⠀⠀⠸⠃⡀⠀⣼⣀⡀⠰⠦⠀⢁⠀⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣽⣿⣿⠟⠻⣾⡿⠟⠻⣧⣼⠈⠻⣿⣏⢀⣀⣽⣿⣿⣿⣅⠀⣠⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠋⠀⠀⠠⣈⣁⠀⠀⠹⣿⡇⠀⢹⣿⣿⢹⣿⡿⠛⠛⠉⠀⠁⠀⠈⠈⠉⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣦⣀⠈⢷⣶⠾⢯⡄⢸⣷⡇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠓⢛⣹⣿⣿⣾⣿⠃⢸⡇⠈⣿⠂⢀⣾⣇⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠉⠀⠈⣿⠀⠸⣧⠀⣿⠖⠁⠙⠻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⠄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠁⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣴⡿⠟⠻⣈⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢫⣿⣿⡾⡿⠁⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⠛⠉⢻⡷⢺⣷⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠃⠀⠀⣠⡆⣠⣇⠈⠉⠀⠀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡴⢶⡿⠁⣿⢿⡿⢳⣿⢾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⡁⠘⠁⠘⠁⠀⢸⡇⢠⣿⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣌⠻⣿⠿⠗⠶⠄⢀⣸⡇⠈⣿⣀⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡿⠿⣿⣿⡆⠛⠀⠀⠀⠀⠀⠀⠀⠀⠣⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⢼⠟⣁⢾⣟⣿⣿⠀⢰⣧⠀⠀⠀⣴⠀⠀⠰⠋⠈⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⢻⣄⠀⣶⡄⣿⡿⢻⣾⣿⡇⠈⠁⠀⠀⢸⣿⠆⣴⠇⠀⢿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠆⠉⠀⠛⣤⣬⡆⢾⠿⣉⠀⠀⠀⠀⠀⠸⠋⠠⢀⣶⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⢉⡤⢶⡿⠋⠀⢀⡄⠀⠀⠀⠀⠰⡟⢿⡀⣿⣯⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⣠⡶⠀⣠⣶⢟⣧⣞⠃⢀⣠⣤⠅⠀⠀⠀⠠⡴⢱⡿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣠⡦⠀⠿⠁⢰⠟⣱⡿⣿⣿⠀⢸⠉⡈⠀⢴⠄⠀⠀⢠⣾⠇⣹⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠛⣰⡟⢸⠇⢀⣴⣿⣿⣿⡿⠀⠿⠛⠁⠀⢠⣤⠀⠀⠈⠁⠀⠻⣿⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⡿⢠⣾⣤⣿⣿⣿⣿⣿⠇⢰⡦⠤⠀⠀⠀⠂⠀⢰⡆⣀⠀⠀⣤⡿⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡄⢈⣹⣿⣿⣿⣿⣿⡟⢰⣷⣶⠆⠀⣀⠀⠖⢲⡀⠀⠋⢠⡀⠚⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠐⡇⢸⠃⢸⣿⣟⣼⣿⣿⣿⣡⣿⣿⠷⠀⠚⠇⠀⠀⠘⠃⠈⠀⠈⣽⠇⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢰⠌⣻⣿⣿⣿⣿⣿⣧⣧⡀⠀⠀⠀⠀⠀⢠⠿⠇⠀⣶⠟⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⣼⡇⣀⠀⣸⣟⣹⠟⣿⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⣴⣧⠐⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡀⢻⡇⣿⢰⣿⣿⣧⣾⣿⣿⡿⠋⠀⠙⠀⠀⠀⠀⠀⠀⠀⢰⠏⠁⠀⢠⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣬⣷⠚⠀⠟⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⣾⡟⢋⣭⡀⢀⢈⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠆⠀⢀⠊
⠀⠀⠀⠀⠀⠀⢠⡿⣇⠈⣿⣆⣿⢸⣿⣿⣿⣿⣿⡿⠹⠆⠀⠁⢸⠀⡀⠀⢠⠏⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠸⣿⠉⣡⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⠀⠈⠁⠀⠃⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⢠⣄⠶⠀⢸⣶⠁⣰⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⢠⣾⣿⡶⠀⢸⠟⣰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣽⣿⡅⠀⢀⡀⣠⠈
⠀⠀⠀⠀⣿⣿⡟⠁⠀⢾⣿⣿⣿⣿⣿⣿⣿⣞⢁⣤⣀⣰⣿⣿⣏⠀⣠⣾⡇⠁
⠀⠀⠀⠀⠟⠋⠀⠁⣤⢹⣿⣿⣿⣿⣿⣿⣧⣽⠛⢋⣿⡏⠀⣿⣷⣾⠿⠛⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠰⢉⣾⣿⣿⣿⣿⣿⢳⠟⠀⠀⣼⡿⠇⠀⡀⠛⠛⢲⣾⣷⣄⡀⠀⠁⠐⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠋⡛⢄⡻⠂⣯⣀⣴⡟⠛⠛⠛⠛⠙⢻⠉⠉⣿⠉⠛⢛⡛⢻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠀⡸⠀⠃⠘⠋⣸⣿⡇⠀⠀⡇⠀⣷⢸⠀⠃⠃⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣧⣶⢣⣾⡀⠀⠀⠹⣿⡇⢠⠀⡇⠀⣿⡄⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠡⣿⣿⣿⣿⠁⠀⡀⠀⣿⡇⠸⣦⣧⠀⢿⡇⠀⠀⠀⢸⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⣴⣿⣿⣿⣿⠀⠀⣀⠀⢹⡇⠀⢸⡇⠀⢸⣇⡘⠀⠀⠀⡇⠀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⣸⣿⡟⢿⣿⡇⠀⠀⡀⠀⠘⣧⠀⢸⠃⠀⣼⣿⡇⠀⠀⠀⠃⠀⡏⠈
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⣰⣿⠋⢰⣾⡟⠀⠀⢠⡿⠀⢰⣿⠀⠘⠀⢀⡟⢿⠁⠀⠀⠀⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⢠⣿⠁⢠⣿⡿⠀⣼⠃⠁⠀⢰⣿⠁⢀⡿⣿⠀⠀⠀⠘⠇⠸⠀⠀⠀⠀⠀⠀⠇⢸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⣿⠁⣶⠛⠀⠀⠀⠺⣿⣧⣼⣇⣿⠀⠰⠀⠀⠆⠸⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⣼⠁⢀⣿⠇⠸⠉⠃⠀⠀⠀⠀⢻⡿⢹⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡟⠀⣸⡟⢀⠃⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⢿⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢱⠛⠄⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡻⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣔⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⡵⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⢚⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⣇⢀⠀⢤⣦⡤⠞⠉
⠀⠀⠀⠀⠀⢀⡿⡿⣳⣳⢫⢖⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣞⣽⡿⣣⡆⠚⠁
⠀⠀⠀⠀⠀⢸⢛⣿⣯⣿⣯⣣⠞⢻⢗⡶⣄⢀⣴⣿⡿⠿⠃⠰⣜⣴⠟⢡
⠀⠀⠀⠀⠀⣬⢮⣿⣿⡿⣵⡟⣵⣱⣋⡼⣾⣿⣿⡛⢏⢀⣀⠾⠛⢡⠖⠃
⠀⠀⠀⠀⠀⣯⣷⣽⣷⣿⣟⣿⠿⡿⣭⣽⣭⠋⠉⠁⠑⢸⡮⣡⠾⣇⢄⡀
⠀⠀⠀⠀⠀⠻⢿⠿⣿⡿⣫⡜⠋⠋⠁⠀⠀⠀⠀⢀⣼⣻⣿⣷⣾⣧⣾⣽⠐⠀⣠⠆
⠀⠀⠀⠀⠀⣀⣠⣾⣯⡜⠋⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⡽⣿⣿⢻⣿⣿⣿⣷⠺⠏⠌
⠀⠀⠀⣠⣾⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⣻⣿⣾⣿⡿⢎⠿⣫⠘⠁⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⢠⠿⠿⣴⠄⠒⠂⠀⠀⠀⠀⢠⣴⡿⢿⣿⢯⣿⣿⣴⣯⢾⡯⣷⢄⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⣤⣴⠆
⠀⠴⠿⠷⠂⠀⣄⣤⣤⣶⣶⣤⣴⣾⣟⣷⣾⣟⣿⣿⣿⣿⣿⣿⣏⣵⣯⣪⣽⣫⣟⠼⣋⣤⣟⣭⣟⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣮⣷⣮⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠐⠻⢿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡛⣛⡛⡛⠛⠛⠛⠙⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣻⡻⠼⠴⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠦⠋

⠀⠀⡲⠀⠀⠀⢀⣄⡀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢤⠀⢰⣆⣄⠄⡖⢰⣦⠀⡴⠄⡖⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠘⠁⠀⠀⠀⠸⣿⣷⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠸⡤⠸⠇⠹⠀⠯⠸⠇⠀⢬⠇⢧⠘⠀⠀⠀⠀⠀⠰⠛⣿⣶⣤⡤⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⣶⣦⣌⣻⠈⠠⠂⠛⡇⠀⠀⠀⠀⠀⠧⠷⠷⠇⠸⠿⠸⠾⠾⠇⠆⠅⠇⠟⠇⠿⠉⠇⠀⠀⠀⠴⣶⣿⣿⣿⡷⢦⡴⠂⠀⡇
⠀⠀⠀⠀⠀⠉⠻⢅⡿⠟⢶⡶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⢹⡿⠁⠀⠇⠀⠀⠁
⠀⠀⠀⡄⠀⠀⠀⠄⠀⠀⠼⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⢴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⣄⠋⡀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⣀⡀⠙⣿⡇⣼⠟⠀⠀⠀⠀⣤⠒⠄
⠀⠀⠈⠘⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣹⣿⣦⡬⣿⣷⠚⠒⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠻⣧⣤⣶⣄⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣿⣿⣿⢁⠏⢳⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣷⣄⣾⠟⢻⡇⠀⠉⠋⠁⠀⠁⠊⠁⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠁⠀⣼⣿⡟⠃⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⣿⠣⠖⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠙⠀⠀⠀⠀⠀⠐⠿⠄⠀⠀⠀⠀⠀⢠⡀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠿⠋⠽⣦⡀⠓⣆⠀⠀⠀⠀⠀⠀⠀⣠⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣦⣹⣿⣷⣀
⠀⠀⠀⠀⠀⠄⠀⣦⠀⣄⠀⠀⠀⠀⠀⠀⣸⠷⣾⠏⠀⢰⡾⠷⣄⠀⢰⡿⠿⠻⣶⠀⠀⠀⠀⠀⠀⠀⢀⣶⡏⠀⠀⠀⠀⣸⠉⠉⡿⢋⣿⣷⣄⡀
⠀⠀⢰⣾⣙⣦⣠⡟⣰⠿⣄⣀⣀⠀⠀⠀⠁⠀⠀⠀⠀⢘⣷⣤⣾⣷⣏⡒⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⡿⠉
⠀⠀⠈⠉⠉⠉⣙⣷⣷⣞⠋⠉⠁⠀⠀⠀⣀⠀⠀⠀⠀⠸⢯⠿⠋⢸⣯⠛⠻⡦⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣄⣈⡁
⠀⠀⠀⠀⠀⠘⢿⣿⡁⠀⠠⠀⠀⠀⠀⠈⠙⣷⠊⢿⠀⠀⠀⠀⠀⠀⠹⠆⠀⠁⠀⠀⠀⠘⣿⢀⡄⠀⠀⠀⢀⡁⠃⠀⠀⠀⠀⠀⡏⡷
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠤⢤⡀⣴⣿⣦⣊⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣦⡻⣿⢏⣶⣀⣴⡀⠀⠀⠀⠀⠀⠀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⡅⢿⣿⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠟⠚⣿⢟⣿⣿⢿⣟⡿⠃⠀⠀⠀⠀⠀⠈⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢿⡿⠄⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠷⠛⢿⠋⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠔⠻⢼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠐⠃⠀⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣶⣤⣀⡀
⠀⠀⠀⠘⠿⣿⣿⣿⣿⣷⣦⣄⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣷⣾⣿⣿⣶⣦⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣙⣿⣿⣷⣶⣾⣿⡿⠿⣿⣿⣿⣿⣶⣤⣀⠀⣀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣶⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀
⠀⠀⠀⠀⠠⣄⠀⢀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣌⡋⡻⢿⡿⠋⠁⠀⠘⠻⠿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠘⠿⣦⡀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣴⣾⣷⣶⠿⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⡃⠀⠀⠀⠀⠈⠻⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁⠀⣀⣠⠶⠚⠁
⠀⠀⠀⠀⠈⠳⡦⠀⢀⡎⢻⣶⣦⣄⠀⠀⠀⠈⠳⣄⣠⣽⣿⣿⣿⣿⣯⣉⣤⣴⣶⣦⡀⢻⡁
⠀⠀⠀⠀⠀⠀⠙⣮⠛⠀⠀⠙⠻⣿⣷⣤⣴⡿⣿⣿⣿⣯⣿⣿⣿⣿⡟⠉⠁⠀⠀⠻⠷⢷⣯⣖⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡤⡾⠿⠉⠉⠁⣁⣠⣼⣿⣿⣿⠟⠛⠋⠙⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠆
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⢀⣀⣤⣤⣶⡼⣿⣟⣉⣉⡉⠁⠀⣀⣀⣀⣀⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠙⠋⣽⣿⠟⠉⠁⠀⠀⠀⠉⠉⣩⢟⡿⠙⢧⡉⣦⠀⠙⠍⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠸⣿⡷⢷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⢀⠇⢨⡍⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⢉⡄⠓⢄⠀⠣⠤⢴⠤⠬⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡆⢀⡖⢊⡴⡳⢤⠈⣆⡀⠀⠀⠸⢲⣽⣿⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣤⣤⡀⠈⠁⠘⡧⣦⢱⢁⠴⠃⣼⢉⠆⠀⠳⣿⡯⠊⠀⠀⢀⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢳⢀⠸⣄⢀⡝⠀⢀⠤⣰⡏⠉⠘⠦⢾⠣⣀⠇⠀⠀⠇⠀⠀⠀⠀⢨⣿⣼⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣚⢾⣧⠈⢃⡀⢀⡧⢠⠟⢉⠗⠀⢀⠴⣦⠖⢦⠀⠀⣼⠀⢀⠀⢀⠼⢿⣿⣝⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢷⠿⠋⠲⣼⡇⡋⣠⠼⡁⢸⠀⠀⢈⠆⠾⠄⢏⢠⡀⣧⣴⣿⣔⡅⠀⠀⠈⠊⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢷⠜⠸⣠⣤⢾⡣⡈⢴⡢⢬⡙⡄⠀⢧⡠⢶⠦⠴⠉⢿⣿⣿⣟⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠣⢧⣱⡥⢱⠘⢎⢯⠽⠁⠰⠀⡖⢄⢸⣠⠤⡄⢈⠟⠛⠋⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⡴⠁⠈⡵⠋⠱⣄⣽⣴⣟⡀⡇⠑⢌⣿⠧⠊⢀⠎⣀⣴⣾⣋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⡤⣀⣴⠋⠓⠛⣾⣧⢱⢻⣦⣷⡺⢢⠞⠋⡹⣯⢻⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡴⡖⢢⠛⠿⢯⠘⡄⢹⠁⡴⠁⠀⠀⢧⠋⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠜⠓⠒⠒⢧⡇⣺⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠸⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠻⢿⣯⣟⣽⣿⠛⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⣧⠐⠛⠕⢹⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠐⠂⠀⠠
⠀⠀⠀⠀⠀⠀⢸⠋⡔⠀⢭⡴⠟⢻⣿⣷⣏⠁⠀⠈⢀⡀⠀⠈
⠀⠀⠀⠀⠀⢀⣿⠤⠓⠃⠉⠀⠀⣽⣿⣿⡌⠀⠀⠀⢀⠀⠀⠀⠀⠓⠂
⠀⠀⠀⠀⠀⣸⣿⣷⠃⢀⢠⣶⡻⣿⣿⣿⣿⢶⣵⣾⣧⣤⡀
⠀⠀⠀⠀⠀⠸⣿⣿⡄⣧⡏⣸⣰⣿⣿⣿⣿⡄⠙⢿⣿⣿⢷⡀⡀
⠀⠀⠀⠀⠀⠀⠹⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿⣿⣤⡌⢿⠸⠁⠈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡾⠀⠀⢻⢻⣦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠁⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠗⣠⣾⠉⠁⠹⢿⣿⣿⣿⣿⣿⣧⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡞⣿⠀⣠⠺⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣺⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢾⠋⢣⣿⡟⠻⠿⠃⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡏⢿⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠀⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⢀⣀⠀⠄⡀⠀⠀⠑⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢸⠇⠀⠙⠳⠄⠁⠀⠀⠀⠈⠆⠀⠀⠘⣿⣷⡀⠀⢂⠀⠀⡠⠴⡀⠀⠁
⠀⠀⠀⠀⠀⡀⠑⠄⠑⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⡀⠄⠀⠀⠈⣠⡟⠻⡇⢀⡀⠀⠉⠙⠳⠦⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠲⡀⠠⣄⠀⠀⠈⠳⣄⠀⠀⠀⢀⡠⠂⠊⣀⠤⡀
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠖⠀⢸⡿⡃⣶⠊⠉⣠⠔⠉⠀⠀⢧⣄
⠀⠀⠀⠙⠆⠆⠀⠐⡄⠀⠀⣿⣶⢤⣀⣀⠠⠤⢭⣧⠈⢀⡜⠁⠀⢀⠀⠀⠸⣿⡇⠀⠀⠠⠈
⠀⠀⠀⡀⠀⣀⠔⠀⠈⠀⠀⣙⠻⠀⠀⠁⠀⠀⠀⠈⢢⡎⢸⣿⣦⣤⣬⠴⠂⠙⠳⠄⠀⢠⠁⠂
⠀⠀⢦⡀⡎⠀⠀⠀⠀⢀⠂⠀⠂⡀⠀⠀⠀⠀⠀⠀⢀⣃⡠⠭⢉⡀
⠀⠀⠀⠉⠉⠁⠀⢀⠤⠒⠉⠉⠀⠣⡀⠀⠀⠀⢠⠔⠉⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡀⠆⠀⢀⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⣀⣴⣽⣴⡃⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢠⡴⠃⠤⠿⢿⠿⠀⠀⠀⠤⠤⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠊⡠⠚⠀⠠⢸⠃⠨⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠀⠀⠀⢨⠀⢠⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣬⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣷⣽⣮⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⣠⣤⣶⣹⣿⣽⣿⣿⣿⣿⣽⣏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣛⢿⡙⠢⠙⣆
⠀⠀⠀⢀⣴⣿⣽⣿⣟⡿⣟⣯⣽⣿⣿⣿⣹⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⡲⣝⢧⠑⢈⡀⣟⡄
⠀⠀⠀⠀⠻⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣾⣟⣾⣦⣵⣶⣿⡿⣷
⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣟⣿⣿⣿⣾⠿⣫⣽⢿⣦⣄⣀⡀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣾⠓⠗⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣯⣿⣿⢾⣗⢻⣿⣿⣿⣿⣿⣿⣟⡛⠃⠹⣿⢿⣿⡷⠆⠰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣋⣮⣤⣆⣈⠁
⠀⠀⠀⠀⠀⠒⠲⠶⢶⣤⣤⣄⣀⣤⣄⣄⠟⠿⣿⡿⢟⡉⣙⣛⡛⡻⢿⣿⣿⣿⣟⣿⣿⣿⣿⡏⠁⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⣿⢧⣞⢿⡾⢿⣾⡻⣷⠌⠐⡝⢿⣿⣿⣿⡿⣿⡿⠉⠑⠻⠷⠞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣿⣿⣆⣨⣿⣿⠿⣶⡼⠀⠘⢿⠛⢟⠉⣀⡤⠤⠄⠐⠂⠛⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠨⢟⣊⢯⣰⠄⢀⣼⣄⣄⣹⠟⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠸⠇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢘⠠⠀⠀⠄⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠴⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠓⢀⡀⠀⠥⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢈⢏⣤⠶⡉⠄⡄⢰⡄⠠⠆⠀⣀⣘⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢽⠴⠞⠀⠀⠂⠀⠰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣌⣠⠉⣌⠀⢟⠉⣥⠄⡀⡤⠠⣁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠺⠷⠆⠀⢈⠀⠟⠀⠀⠀⠄⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠸⠟⠐⢟⢒⣮⡛⣤⠴⠅⠈⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠒⠭⠁⣰⣆⠀⡾⠂⠁⢰⠀⣀⢀⣤⢣⣄⡴⠖⠀⠀⠀⠀⠀⠀⠊⠀⢁⠷⡁⠙⠘⠋⠀⠀⠈⠁
⠀⠀⠀⣀⠀⣄⠀⠀⣀⠰⢄⡀⠀⠈⠃⠹⣧⠀⠀⢹⡧⠉⡮⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠉⠔⠃⡈⢣⣤⠁⡀⠀⢀⡀⣿⠂⠁⠸⠏⠈⠑⣾⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠷⠞⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⢙⣿⠀⠀⠈⠱⣿⠀⣄⠀⠂⢹⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣧⡖⠓
⠀⠀⠀⠄⡸⠰⠆⠴⠆⠀⠄⡏⠁⠀⠀⠐⣿⣧⢽⣿⣇⢐⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠊
⠀⠀⠀⠀⠁⠀⠀⠐⠴⢈⣿⣧⣀⣤⠀⠀⣿⠀⠀⠀⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠐⠋⠉⠉⠀⠒⠙⠵⠶⢶⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠈⠀⠀⠨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⢤⠀⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡑⠒⠀⠀⢠⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⡄⠀⠀⢀⣀⠀⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠰⣦⣷⠈⠋⣷⢀⡄⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠁⠀⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠠⢕⣰⡞⠂⠈⣣⣄⡀⢇⡀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⡿⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢠⢀⢪⣍⡼⣦⠟⢙⣻⠗⠈⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⣨⣿⣌⠳⠂⠛⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⡇⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⡀⢀⡀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⡄⠰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠦⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠹
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠃⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠸⠀⢀⡀⠄⠀⠀⡾⡆⣐⡀⠺⠀⢈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⡺⢭⠿⢛⣻⠿⠯⣅⣶⣭⡛⣓⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⣉⣉⣩⠽⠟⠋⠉⠀⠀⠀⠀⠈⠉⠙⠒⠓⢄⢻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠈⠣⣙⣏⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠅⣼⠁⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⡀⠀⣹⠘⢳⡀⠀⠀⠀⠈⢻⡈⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡰⣠⠏⣀⡀⠀⠀⠀⠀⠀⠀⡵⠀⠉⠘⠦⡜⢦⡄⠓⠦⣤⣤⡀⠀⢧⣱⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡖⠁⣠⠇⠙⡹⠒⠢⣄⣠⠤⠭⣒⣦⠋⠐⠳⣼⠀⠀⠀⠀⢀⠇⣀⠈⣏⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡆⡇⠀⠹⢄⡚⠁⠋⡁⡎⠁⣂⢑⠜⠁⣀⠀⠀⣨⣤⣤⣀⡴⠿⢏⣉⠗⣸⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇⡇⡔⠋⠋⡉⠷⣀⠀⡳⡀⡂⠊⢾⣹⣴⡂⠎⢻⣄⢸⡥⠄⠀⠀⣹⢠⢇⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠖⠧⣇⠀⣠⠀⣀⠉⠀⠀⠠⠀⡠⠓⠚⣿⠭⣆⢀⠈⠙⣄⣀⡀⢀⣉⡉⢭⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣀⣠⣷⣿⡰⠃⠀⠀⠀⠀⡖⠀⠀⠀⠀⠙⢻⡯⣈⠎⢀⠔⠚⠛⠁⠄⠫⡞
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠤⣐⠀⠀⢀⡎⠁⠀⠀⠀⣼⠋⠡⡑⡀⠀⠀⢀⡌⠭⢽⠀⡄⠎⠉⠆⢨⢨⡄⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠠⡔⠉⡖⡀⠈⡁⠦⠂⠉⠀⠳⡤⡴⡜⠁⠙⠺⡅⠐⢈⠘⢢⡑⠒⢊⡠⢣⠀⠈⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠧⡄⠀⠀⠀⡄⠣⠄⠰⢡⡀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢈⠄⠀⠠⡤⠊⠉⢣⠀⢙⠈⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣴⡏⠜⠂⠲⠓⢠⣜⣄⠀⡠⢎⢀⠀⠀⣠⠴⣉⢌⠋⢠⠓⢋⢠⠈⠀⠩⠀⡷⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠈⡇⠈⡐⠈⠒⠁⢅⠀⠈⠀⡈⠀⠀⠋⢠⢹⢻⢫⠕⠨⠀⠀⠀⠉⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠐⠀⠀⠀⢁⠨⠄⠀⢀⠀⠀⠀⠈⢙⠈⢡⠤⠐⠁⠀⢐⡈⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⡂⠀⠠⣠⠃⠀⠉⠀⠀⠀⠑⠁⠀⠀⠀⠀⠄⠂⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠢⠁⠀⠀⠀⠀⠀⠀⠀⠀⠬⠍⠀⠀⠀⠀⠁⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣀⠠⠄⠀⠀⠀⠈⠅⠀⣀⡤⠤⠤⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠋⠙⠛⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣸⡗⠀⠀⠀⠀⣨⡀⠙⠴⠦⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⡗⠀⠀⠀⠀⠀⠘⡤⡄⠀⠀⠀⠀⠀⢙⣧
⠀⠀⠀⠀⠀⢓⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⢀⡤⠀⢀⡀⠀⠀⠀⠀⠀⠀⡨⢿⡡
⠀⠀⠀⠀⢀⣀⣰⠍⢁⠶⣤⠖⣰⡾⠄⠁⢰⡯⢟⠀⠀⠀⠀⡞⠀⢰⠀⠀⠀⠀⠴⢷⣃⣤
⠀⠀⠀⠀⠉⢀⣀⡄⣴⠀⠯⢰⡏⠀⠀⠀⠸⡟⠀⡇⠀⠀⢰⠂⠰⢏⠀⠀⠀⣴⠖⡼⠉⣁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⣠⣟⠀⠀⢶⣄⠀⣧⠈⡇⠀⠀⣸⠈⠃⠐⠀⠀⠀⠀⡶⠀⠆⠀⠀⠒⠈⠃
⠀⠀⠀⠀⠀⠀⢀⡤⠄⠄⠀⠀⠀⠀⠾⠈⢁⠹⠀⠀⠀⢺⣏⠛⠙⣁⠀⠀⢀⡼⣤⣾⣦
⠀⠀⠀⠀⠀⠘⠫⣴⣃⣆⡀⣤⠐⣌⢒⠠⠈⠲⠀⠁⠀⠈⠛⠁⠸⠟⠀⣤⡨⣇⠛⡏⠈⠁⣀⣀⣴⡀
⠀⠀⠀⠀⠀⠀⠠⠘⢿⣿⡷⣿⣇⡈⠠⡀⠀⠀⠀⠀⠄⠀⠀⠀⢰⡘⠶⣖⣷⣉⢧⡤⠖⠉⠉⠹⠿⠁
⠀⠀⠀⠀⠀⠀⢦⡀⠈⠱⠳⠋⠛⢤⡀⢹⡄⠐⠀⠀⢰⠄⠀⠀⠈⠛⢑⠻⡾⠛⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⡀⢀⠀⠱⡄⢂⡀⣀⠀⠀⠀⠁⣤⡔⠰⠁⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣾⣇⡓⢰⠂⠃⠉⠗⠀⣀⠀⠉⠀⠀⠀⠀⢀⡆⢀⠀⠀⠀⠀⠴⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣦⣀⡈⠻⣷⡌⠃⡛⠙⡀⠀⠉⢀⣸⠂⡠⠆⠀⠚⢀⡀⠐⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉⠉⠀⠀⣇⠙⢿⣷⣄⡉⠀⠀⠈⠻⠛⠂⠀⣀⡠⠞⠛⠀⠀⠸⠉⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢙⡄⠀⢻⣿⠿⣧⣄⣠⠆⡀⠀⢐⡿⣁⠀⠀⠘⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠓⠀⡀⢃⡈⠉⣿⣯⣾⣷⡞⠁⠀⠻⠀⠿⡧⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂⠾⢿⠛⢻⣿⠛⠒⠤⢀⡠⢯⣶⣏⡴⠶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠹⠄⠀⠘⠃⠈⢠⢥⣠⠄⢀⣀⡴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠀⠀⠀⠀⠌⢠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁




⣶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣷⣋⣻⣥⣬⣭⣭⣤⣬⣤⣥⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣶⣶⠤⢦⣶⢶⣶⣄⠄⣠⣦⠆⣀⣴⣶⡶⠤⡰⠰⢠⢶⣶⠀⠀⠀⠀⠀⠀⢠⣶⡶⣤⣰⣶⣠⣶⣂⣠⣶
⢸⠟⠻⣶⣿⢾⣿⡿⣺⣯⣉⢉⣹⣿⣿⣿⣷⡌⢦⡸⣼⢠⡀⠀⠀⠀⠀⣠⢿⣿⡶⣿⣿⢿⣿⣟⣡⡿⣿
⠀⠀⣠⣿⢻⣿⣿⣙⣫⣿⣿⣿⠋⠉⠙⢻⣿⣟⣦⡃⢿⣿⣧⡀⠀⢀⣠⠖⣻⡥⠶⣻⡵⢾⣯⣬⡿⠇
⡶⣾⡿⣄⠀⣿⣧⣿⣿⠀⠈⠻⠀⠀⠀⠚⠉⠙⣿⣧⢸⣿⢟⣩⠖⠿⣃⡬⢤⣬⣉⡁⢐⣛⠫⣭⣷⢶⣶
⢿⣿⣤⣈⣿⠏⢻⣿⢻⡄⠀⠀⠄⢄⡀⠀⠀⠚⢻⣿⠿⢑⣻⣯⣤⣬⢥⡖⣚⣻⡿⢿⣦⣿⠛⣿⢻⠀⠹
⢰⣿⣾⡻⣿⣷⣾⣯⣋⣽⣦⣌⣀⡀⠠⠀⠀⠀⣼⡏⣴⠟⣻⢛⣿⣿⣿⣿⣿⣿⣿⣿⣏⣣⠀⠀⠘
⣼⣿⣇⣁⣌⡻⣌⢻⠿⣿⡿⣹⣿⣿⣷⣶⣶⣿⢟⣴⣿⠗⠚⢿⠋⠉⠙⠻⣾⠿⣿⣿⣿⣿⣦⣀⠀⠀⢀
⢙⣿⣙⣷⡶⠒⣲⣍⡃⢿⠳⢹⣿⠁⠸⠛⡿⣨⡾⣿⡇⠀⠀⠈⠀⠀⠀⠀⣽⣷⡿⣿⣿⡟⡻⣻⣿⣿⡿
⣛⠽⣿⣿⣋⣽⣧⡴⢛⣮⡻⣿⣧⣷⠶⣿⣿⣿⠺⣽⣧⡀⠀⠀⠀⠀⠀⠞⠛⠛⣿⢰⠿⠋⢺⠋⠟⣿⠷
⡒⠿⣿⣿⡿⣿⠽⣿⣿⣋⣷⡿⣹⠾⣷⣤⣿⢿⡿⠋⢻⣿⣷⡆⡀⠀⠀⠀⢀⣠⡿⢈⠔⢫⣍⣛⣿⢁⠤
⣿⠿⡏⠹⠅⠋⠀⠟⠁⣿⣿⣿⣷⣾⠋⠈⠋⠘⣷⡤⢶⣿⣿⢹⣿⢿⡶⢿⡿⢋⣤⠤⢤⣍⡉⠈⡻⠶⣧
⠬⠓⠧⠀⠀⠀⠀⠀⡰⣿⣿⣿⣻⣧⡀⠀⠀⠀⠋⠀⣸⣿⡟⡾⣿⣶⠱⣋⣤⣿⠶⠿⠋⠛⠛⢿⣾⣿⣿
⠿⣯⡉⢛⣻⣿⣿⣿⣽⣟⣟⣷⣟⣿⣿⢂⣤⣀⣀⣀⣠⠼⠣⠖⠉⣁⣨⣿⣭⢿⡀⠀⠀⠀⠀⣈⣻⣧⣽
⣲⣶⣟⣽⣿⡿⠏⡾⠛⢹⣯⣿⡛⠼⣳⠿⣿⣿⣭⠟⡡⠴⣶⠟⣳⡦⣔⢦⣄⢌⡉⣄⣤⣀⣀⣛⣿⣿⣿
⠿⢿⣯⣿⡏⠀⠀⠀⠀⠀⣿⡻⡿⡶⣣⡾⠴⣛⠵⠶⢦⣭⣛⢿⣯⣿⣬⣷⢿⣷⣽⣮⣁⢾⣿⣯⣿⣷⣾
⠀⢸⠛⠻⡇⠀⠀⠀⠀⢠⣟⠻⡇⣻⣵⣾⣫⣿⣛⣻⣿⣿⣻⡷⣯⣸⣏⡿⢻⡟⣿⡟⠋⠙⡟⠀⠀⠀⠿
⠀⠀⠀⠀⣿⣶⣄⣤⡖⣻⣿⠟⣚⣿⡭⠿⠿⣿⣿⣟⣿⢿⣟⢻⣯⣽⣮⣳⡟⣻⣿⡆
⠀⠄⠀⣰⣿⠁⢻⣿⡿⣫⡴⢿⣿⡅⠀⠀⠀⠀⠙⠿⣿⣿⣏⣿⣲⣿⣭⣬⣶⣿⠁⠀⠀⠀⠐⠂⠀⠀⣀
⣤⣶⣺⣯⣿⣴⡾⣫⣾⣹⣷⣿⣿⣿⢢⡀⠀⠱⣶⣿⣿⣿⠟⠉⠻⠏⠙⢿⣿⡸⣧⣄⣀⠀⢑⣀⣤⣾⣿
⣿⡬⢽⣿⡛⣿⣷⡇⠸⠅⣺⠿⠿⣿⣧⠹⢻⢿⠟⣿⢿⣿⠀⠀⠀⠀⠀⠀⠹⣷⣹⣻⣿⣿⠛⣸⢟⣩⣿
⠉⠁⠀⠀⠉⠈⠈⠁⠀⠀⠁⠀⠀⠉⠉⠁⠈⠈⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠉⠉⠀⠁⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⡟⣿⠳⠈⢻⢿⡆⠀⣠⢚⣿⠟⡷⠆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⡖⣷⠘⡂⠀⠈⣼⢨⣤⢋⡯⠋⡸⢱⣇⢠⡟
⠀⠀⠀⠀⠀⠀⢰⡏⠀⢰⣿⣿⣤⠀⢣⠀⠀⢹⣼⣿⣞⢁⡶⣡⣿⣿⠟⠖⠉⢢⡀
⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⣿⣿⣿⠄⠀⢳⣦⠈⣾⣿⣿⢛⣵⣿⣿⣵⠂⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣦⣽⣿⣿⣿⣾⣷⣿⣿⣿⣿⣯⣾⣿⣿⣝⣦⣤⣾⣿⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⡿⠛⠛⠻⠿⣿⡿⠟⣋⣤⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣶⣦⣀⢀⠀⣰⠆⠈⢿⡟⠀⠀⠀⠀⡀⠀⠀⣶⣿⢻⢻⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⣠⠾⡒⢄⣙⣿⣯⠀⠻⣇⡀⠀⠻⣤⡀⢰⣿⠏⠀⠰⣿⣿⣬⣼⣾⣿⠟⠀⠀⢀⠀⠀⡀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠐⣿⣫⣭⣷⣿⣿⡿⠛⠛⠛⠛⠛⠓⠺⢿⣿⣇⡀⠈⠁⠈⢹⣿⡟⠙⢁⡴⢃⠁⡸⢁⣰⠤⠀⢩⠁
⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⡀⠀⠀⡾⠁⠁⣰⣿⡁⠀⡰⠀⠋⠀⠀⡠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠀⡲⠤⠤⠀⠠⣄⡀⠙⣇⠀⢰⠀⠀⣰⣿⡯⣷⣾⣁⣀⠀⢀⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⢠⣶⣶⣶⣶⣷⣄⠀⠀⢰⣿⠁⠀⢻⣦⣸⡇⠀⢿⠹⣿⣇⣠⢅⣤⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⢠⡞⠛⣸⣿⣻⢻⡿⠄⠀⣼⣿⠀⠀⠈⣯⣿⠇⣴⣣⣿⣶⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠂⣾⡇⢠⠟⣿⣟⣿⢿⣆⣼⣿⠋⠀⠀⠀⣿⠋⣼⠟⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠿⢶⣿⣿⣿⣯⣾⣿⡋⠀⠀⠀⠀⠀⢿⣿⠃⠀⣠⢶⣶⠷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣦⣤⣤⣴⣒⣾⣿⣿⡟⢉⣥⡟⣼⠧⣤⠀⠀⠀⢸⣿⢠⣴⡟⣄⠃⠰⣽⡷
⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠿⠟⠉⠀⠀⠙⣇⢸⣿⣶⣯⣌⣽⠀⠀⠀⢸⡇⠨⣿⣧⣿⣴⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢙⣿⠛⠟⠋⠀⠀⠀⣸⠁⠀⠀⣽⡿⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⡼⣦⠀⠸⣆⢻⡀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠋⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢷⡄⡟⣆⠀⠈⢩⣷⠀⣰⣫⠄⢰⣏⣠⠞⠛⠛⣧⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠶⣻⣇⣻⣷⣤⣄⣹⣧⡟⠁⠀⡞⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣮⣤⣼⣿⣿⡿⠋⠙⠻⣷⣀⣰⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠈⠛⠾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣠⣤⣶⣤⣀⠙⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣦⣤⣀⣼⣿⣿⣿⣿⣿⣦⡘⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⢻⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢸⣋⢻⣿⣧
⠀⠀⠀⠀⠀⢀⡴⣾⡿⠃⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⠀⠀⣼⠟⠁⠟⣿
⠀⠀⠀⠀⣴⣻⡖⡼⢁⣾⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⢠⣿⡇⡛⠀⡿
⠀⠀⢀⡞⢿⡿⣰⠇⠛⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⡀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠋⠉⣽⠁⣸⠃
⠀⠀⣼⡣⣤⣿⣾⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠛⠹⣿⣿⣿⠉⠀⠀⣀⣘⡁⠀⢰⡇⣰⠋
⠀⠀⣏⢷⠈⢻⣿⡀⠀⠀⢽⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⠿⠇⠀⠀⠰⠟⠀⠀⣀⠜⠁
⠀⠀⣟⢂⣿⣾⣿⣧⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠘⢛⡃⠰⢿⣿⠤⠄⣀⣠⠴⠚⠁
⠀⠀⢹⡿⣉⡙⢋⢹⣧⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢳⡳⣆⣱⣿⣟⣿⣤⡀⠀⠉⢹⣿⣿⡟⠛⠋
⠀⠀⠀⠀⠙⣿⠢⠻⠉⠙⣿⣽⡲⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠙⠶⣿⡄⣎⠙⣮⣶⢾⣏⣹⣷⡶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠚⠛⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠉⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢧⠀⡄⠘⠶⠒⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢣⠀⠈⢇⢳⡤⠤⠖⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⣄⡀⠀⠘⡇⢀⠀⢣⡀⢸⠞⠒⠒⠒⠂⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠡⣀⠀⠐⡄⠈⠳⡄⢳⠈⢆⠀⢳⠯⠐⠒⠒⠒⠂⣰⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠀⢤⡈⠳⡄⢹⡀⢀⠘⣎⡆⠈⢣⠯⠴⠒⢂⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⢄⠘⠄⢣⠘⡄⡌⠻⠀⢀⣤⣶⠯⠽⢒⣒⠛⠒⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠀⢈⠖⢫⠋⡩⢋⢟⣠⡀⠈⣀⡠⠔⠊⣉⡤⠤⠖⠂⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣠⠎⢠⠃⡰⠁⢋⢾⢧⡇⠀⢨⠙⡶⣉⣀⡠⠤⠒⠒⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠊⠁⠠⠃⠀⢁⡴⠋⣼⡏⢳⠀⡾⠀⡇⠈⡅⠀⢈⣉⣡⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠤⠴⠚⠉⠀⣸⡟⠀⠘⣆⠃⢀⡇⢠⡇⡄⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠘⢆⠈⡇⠈⠇⠳⡀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⠓⢤⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠘⢧⢄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠁⠀⠄⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠬⣯⠁⠀⠰⠂⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠛⠀⠠⢦⡔⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢀⣀⡀⢨⠍⠙⠔⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣐⣸⠂⡘⢛⣡⡀⠉⠐⠆⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⢀⠾⡒⠙⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠡⠆⣴⠃⠀⠯⢼⠗⠀⠀⢀⡀⠀⠸⢶⣄⡙⢦⣀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣳⣶⠀⠀⠀⠀⠸⣆⣱⡿⣺⣧⡼⢃⡨⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠺⠓⣤⣶⣼⡾⢿⣿⡯⢿⣖⣿⣿⣦⡠⠀⠀⠀⠠⠕⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣰⢀⣐⣭⠈⠑⣿⣼⣿⣗⠀⣹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣽⣗⣠⢫⡟⢡⣀⣀⣿⣿⣿⣿⣟⠀⠤⡀⠀⠀⠢⠔⠐⠀⠀⢀⡠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣶⣧⣀⣿⣿⣿⣿⡿⠿⠉⠀⠀⠈⠢⠒⠄⠀⡀⠠⠐⡑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⠟⠛⠈⣾⢛⡛⠹⢦⠀⠀⠀⠀⠀⠀⠀⠃⠁⢀⠠⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡩⠜⡙⠀⠀⠀⠩⣤⡀⣀⡻⠆⠀⠀⠀⢀⡀⠀⠈⢀⠀⠀⠀⠰⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠟⠁⠀⠀⠀⠀⠈⠀⠉⠁⠀⠀⢀⠀⡤⠣⠆⠀⠜⠀⠀⠀⠀⠁⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠠⠀⡐⠀⠀⠠⠃⠀⠀⠸⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢀⢐⣧⡤⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠡⠟⡡⠀⢀⢀⠤⢀⢦⠄⠀⠆
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠒⡀⠀⢀⡀⣾⡦⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠠⠆⠩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠹⠉⠒⠂
⠀⠀⠀⠀⠀⢠⡄⠐⢤⡷⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠐⠀⢀⢠⣾⡃⠀⠐⣷⣠⠀⣠⡶⠀⢐⣤⠀⠀⠀⠺⠆⠆
⠀⠀⠀⠀⠀⠀⠉⠁⠘⢷⡀⠛⠛⠋⠉⠉⠁⡶⠋⢄⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠑⠖⠊⠁⠰⠀⠋⠈⠁

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⡠⣼⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣿⣿⣿⣿⣿⣿⡃
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⠀⠀⠞⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠦⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⠀⠀⠀⠀⠀⠀⠀⣠⣴⢰⡿⣸⣿⠋⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⡀⠀⠀⠰⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⢀⣼⣿⣿⣿⢸⢧⣿⠏⢰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣧⡀⠀⢀⣽⣿⣿⣶⠀⣦⢠⣦⡤⠀⠀⠆⣠⣶⣾⣵⣾⣿⢀⡇⣿⣿⣿⣿⠘⣼⣿⢀⣼⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⡉⣿⣿⠘⣿⡇⣿⢸⣿⡇⠀⠀⢸⣿⡟⢿⣿⣿⡟⣸⡇⣿⣿⣿⣿⢰⣿⣏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣯⣿⣿⣿⣿⣿⣷⢸⣿⠀⠸⣇⢿⢸⣿⣿⡆⣶⢸⣿⡇⠘⣿⣿⢇⣿⢃⣿⠟⣿⣧⣿⣿⢻⣿⣿⣿⠟⣿⣿⣿⣿⣽⡇
⠀⠀⣿⣿⣿⣿⣿⣿⢽⣽⡎⣿⣧⡤⣿⢸⢸⣿⣿⡇⡟⣼⣿⡇⠀⣿⣿⢸⣿⢸⣟⣯⠟⣼⣿⡟⣾⣿⣿⠏⢠⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⡿⣿⣷⣿⡇⣿⣿⣧⣿⡘⠘⣿⣿⡇⡇⣿⣿⡇⠀⣿⡏⣾⣿⢸⣿⣿⠃⣿⣿⢇⣿⣿⠃⢠⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣷⠙⢿⣿⣿⢺⣿⣿⢸⡇⡆⣿⣿⢹⡇⣿⣿⣿⡍⣿⡇⣿⡇⣾⣿⡟⡄⣿⣿⢸⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⡆⠈⣿⣷⢸⣿⣿⢸⣇⠁⢻⣿⢸⡇⡟⣿⣿⡇⣿⡇⣿⡇⣿⣿⢸⢣⣿⡇⣿⡿⣱⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣷⣔⢻⣿⡎⣿⣿⡸⣿⠀⠸⣿⢸⠇⣝⣽⣫⣷⢹⡇⣿⠇⣿⡇⣿⢸⣿⢱⣿⣳⣿⣝⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠻⠛⠛⠛⠛⠛⠛⠃⠛⠃⠛⠛⠃⠛⠃⠀⠛⠘⠃⠈⠛⠛⠛⠘⠃⠛⠘⠛⠘⠃⠛⠋⠚⠃⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠸⠇⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠸⡁⠀⣁⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠁⢠⣼⡿⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⣿⣤⣛⣴⣿⣿⠁⠀⠀⠀⣿⣿⣷⡀⠀⠀⡀⠐⠂⠈⡐⠀⠀⠀⢀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠈⠉⠙⢦⠀⠠⠀⢰⡟⡛⢻⣧⠀⣠⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⠛⣿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣤⣄⠸⠿⠿⡟⠃⢠⡾⠋⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠾⠃⠀⢠⣶⣦⡠⠀⣀⡀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣾⣷⣦⡄⠀⠀⡾⠛⠉⠀⠀⠀⠰⠠⣾
⢀⣤⣤⣠⠀⢀⡀⠀⠴⡒⢄⠀⡇⢀⡴⣲⡘⠻⢿⣿⡼⠛⠃⠀⠀⠀⠀⣯⠀⠀⠀⠀⢘⡝⡿⠃⠀⠀⠁⠀⠀⢀⣤⣠⠀⠃⠊⠀⠀⢀
⠈⠿⢿⣿⣰⠿⠋⠀⠂⡈⠊⣳⣷⡫⠊⢀⠆⢰⣦⣹⠁⠀⠂⠀⠀⠀⠀⣿⠀⡞⡽⡆⢸⠋⣀⣤⡄⠀⡇⠀⠀⠹⣿⣽⣿⣼⣇
⠀⢠⣤⣹⡇⠀⠀⠀⠀⠈⠑⢺⡗⠐⠊⠀⠀⠀⠉⠻⡆⠀⠀⠀⠀⠀⠀⣿⠀⠙⠚⠻⡾⠶⣏⣪⠏⠀⣇⣶⣶⠀⠈⠀⠙⢺⣿
⠀⠀⠉⠻⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⡇⠀⣀⣠⣤⠀⡟⠁⠀⠀⠀⠀⠀⠀⡿⠀⠀⠰⡶
⠀⠀⠀⢀⡇⠀⠈⠀⠀⠀⠀⢸⡇⠀⠀⠀⠰⣿⣿⣾⢀⣴⣦⠀⠀⠀⠀⡿⠀⠀⡤⢸⠁⣄⠿⠟⡏⠀⡇⢀⢀⣤⡄⠐⡓⠀⢰⠰⡶⠀⠁
⠀⣾⣷⣮⠀⣠⣤⠀⠀⢀⣀⡸⡧⡶⠆⠠⠄⠉⠛⢿⡞⠉⠀⠀⠀⠀⠀⡇⠀⠀⠉⢹⠉⠉⠀⠙⠇⠀⡿⣙⣻⡽⠀⠊⠱⡄⢸⠀⠁⣀⣦
⠀⠉⠛⢿⡼⠋⠁⠀⠂⠈⠯⠁⣷⠘⠀⠂⠀⠸⠿⣾⡇⠀⠀⠈⠀⠀⢀⡇⠀⠀⠀⠸⡆⠀⠂⠀⠀⠀⡇⠀⠀⠉⠦⠈⣉⣠⣼⣶⣿⣿⣿
⠀⠐⢿⣦⡇⠀⠀⠀⠀⠀⢀⠀⢸⣄⣁⣀⣀⣀⣀⣈⣇⣀⣀⣀⡀⠀⢸⠇⠀⠀⠀⠀⢷⠀⠀⠀⡄⣀⣇⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠈⣗⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⢀⡴⠟⠋⠉⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⡚⠻⠏⠀⠢⠁⡇⠄⡄⠀⠀⠈⣿⠀⢰⡏⠀⠀⠀⠀⠀⢀⠘⢠⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣁⡒⡀⠀⠀⠀⠑⢄⠡⠄⡄⡶⠀⡐⢻⡇⣿⠀⠀⠃⠀⠀⢀⠸⢘⡠⠆⠉⠉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠬⠀⠤⠀⠀⠀⠀⠀⠑⢄⠡⠄⡆⡀⢸⣿⣏⠀⠁⡀⠃⠗⣉⡴⠋⠀⠀⠀⠀⠨⠁⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡔⠒⣐⠒⠀⠀⠀⠀⠀⠀⠀⠱⣌⠡⠀⢸⡏⣿⠈⡁⡇⣠⠞⠁⠀⠀⠀⠀⠀⠀⣤⠘⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠩⡄⠤⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⣿⠀⣿⠈⣡⠞⠁⠀⠀⠀⠀⠀⠈⢁⠐⠒⠆⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣳⣤⣃⡤⠅⠀⠀⠐⣀⣀⣀⣁⡀⠻⣶⠯⠞⠁⠲⠄⠀⢡⡀⠈⡤⠘⠒⣂⣥⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠉⠩⠙⠖⢒⣛⠩⠉⢙⡛⠚⣻⢇⣤⠺⠿⣿⣝⣛⣛⣓⣒⠶⠶⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡅⠉⠀⠀⠀⠈⠀⠠⠀⢠⠙⣢⠴⠋⢀⡟⢹⡇⠑⢄⡈⠉⠉⠉⠉⠙⣛⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠦⠀⠀⠀⠀⠀⠀⠤⢈⡤⠊⠁⠀⠀⢸⡇⣸⠗⠆⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⣨⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡌⣃⠀⠄⠀⠠⠌⣡⠞⠉⠀⠀⠀⠀⠀⢸⡇⣿⠠⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢁⡈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣐⠒⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠂⣸⢿⡇⠖⠀⠀⠀⠀⠀⠈⢣⡀⢀⠀⠀⠐⠀⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣷⠀⠄⠆⠀⠈⠀⣀⠐⠂⢆⡿⢸⡧⠆⠀⠀⠀⠀⠀⠀⠀⠹⠌⠤⠈⠤⠭⢁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠆⡄⢙⢸⠀⡛⠰⢇⣾⠃⠘⣷⠚⣰⠂⠆⠠⠀⠀⠀⠄⣠⣤⣤⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣉⠘⠘⠀⣋⣤⢾⡇⠀⠀⠹⣧⡀⠞⡴⢀⠋⡴⠰⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⣿⢸⣇⠀⠀⠀⠈⠻⢦⣥⣉⣀⣥⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⣿⡄⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡌⠠⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣤⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣴⠖⢀⠉⢀⠀⣀⢀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢠⣄⠀⠨⣿⣿⣧⣙⣱⣶⡆⢾⣿⠀⡵⠀⠀⠀⠛⠀⠀⢀⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⢁⡄⠀⠿⠷⠀⠽⣿⠃⢀⣴⣿⠏⢀⠀⠈⠀⢀⣮⡄⢀⣼⠔⠉⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠂⢀⡺⠛⠉⠀⠀⠈⠔⠞⢉⠁⠰⠿⢣⣤⠀⢚⣭⣵⣿⣟⣵⣶⡿⢋⠀⠸⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡘⠟⢟⠻⠿⢻⡾⠆⣠⣿⣿⠿⠀⠀⠏⠰⠾⢿⣿⣯⣿⣿⠟⠀⡼⠀⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⡤⠀⠀⠈⠁⠀⠀⠀⠀⠐⣄⣠⡟⣿⡗⠓⠨⠄⠀⠀⠂⠀⠙⠿⣻⣿⠀⠚⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⣙⠇⠀⠀⠙⢈⢛⣻⡗⠀⣀⣉⣯⣷⣤⢡⡶⢴⡷⠢⠆⠀⠀⠀⠀⢐⡿⠁⣰⣦⢦⣤⢄⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠌⠁⠀⣀⠿⠀⣯⠽⡿⢩⠋⠀⢶⠉⣤⣽⣋⠀⣀⡀⠀⠀⠀⣺⣯⣤⠀⢣⠈⠲⣷⡿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⡀⠢⠣⠰⡜⡫⠉⠦⡴⠁⣰⣧⣿⣿⡦⠸⣷⡄⠀⠀⠙⢿⣿⣆⠼⡆⠰⣿⡘⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⣀⠀⣀⡀⣰⣧⠈⠐⠢⢞⣿⢿⣿⣾⣧⣤⣭⣴⠶⠀⠀⢠⣞⣉⣀⣳⣴⣤⠉⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠻⠀⠂⠀⠁⣈⡠⡄⠀⠀⣙⣴⣿⠿⠷⢿⣷⢛⣉⠶⠊⠈⣿⣿⣿⣿⠷⣿⢄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠈⠂⡘⠃⢈⣱⠎⠐⠂⢁⠈⣠⣴⣴⣷⣡⣿⣿⣟⣣⠀⠀⣤⣤⠀⠀⠀⢰⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠈⠁⡴⠄⠁⢀⣘⠋⢀⠀⢦⡤⣿⠛⠛⠻⠻⠿⢿⣾⡛⠃⠀⢠⣿⣿⡧⠰⠄⠘⠵⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠔⠋⠀⠀⠀⠀⠐⢤⣥⠌⣿⡏⠀⠀⣄⣀⣀⠀⠛⠁⠰⡶⠀⠠⡄⢹⣿⣿⡄⠀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠅⠙⠶⠦⠶⠂⠀⠀⢨⡟⠀⠀⠐⢿⣿⣿⣷⣎⣩⣿⣄⠀⢢⡀⠈⠙⠿⡃⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣧⠀⠀⠀⢁⡀⠘⠢⠀⠉⠻⣿⡿⡟⢤⣾⡷⡘⠀⢀⣱⡄⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠀⠀⠈⠂⠀⣬⠘⠛⣀⡄⠀⡀⠈⡁⠀⠀⠀⣿⠀⠑⠀⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡤⠀⠘⠃⣀⠓⢶⣦⠄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡛⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⠁⢹⣿⣿⣧⠘⢿⣿⠋⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢿⣿⠇⠀⠈⠁⠀⠀⠀⠉⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠙⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣴⣿⣿⡏⠀⠀⠄⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣛⡻⠿⣿⣶⣬⣭⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣦⣄⠀⠀⢠⠀⠀⠈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣶⣶⣿⣶⣿⣿⣿⣿⣿⢿⡿⢿⣿⠟⠀⠀⠋⠀⠨⠿⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢹⡆⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⢰⣮⣝⣻⠿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡜⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡿⢿⣿⣷⣶⣶
⠿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠹⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣿⣬⣭⣽⣯
⡿⣶⢯⣿⣿⣋⣩⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⢿⣜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡆⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣙⠳⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣰⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣟⣛⡿⠋⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣈⣥⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⣃⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠒⠀⠀⠀⠀⠀⠀⠠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠙⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣥⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣽⣯⢿⣿⣿⣿⣿⣿⣿⣟⢷⣶⣌⢿⣿⣿⣿⣭⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣹⡟⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣷⣌⠿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⣧⡙⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣈⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠸⣿⣿⡆⣹⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣷⣏⣙⠛
⣿⣿⣿⣿⣿⡿⢧⣿⣿⢹⣿⣿⣿⣷⣿⣶⣶⣆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣜⢻⣟⣫⡟⣼
⣿⣿⣿⠿⢋⣴⣾⣿⡧⣾⣿⣿⣿⣿⣿⣟⠛⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡽⣿⣿⣿
⢋⣭⣴⣾⣟⢿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⠿
⡜⣿⣿⣿⣿⣶⣽⠋⣾⣿⣿⣿⣿⠉⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣜⢿⣿⣿⣿⣿⢱⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣝⣻⡿⢇⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣴⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢗⣾⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⡿⣣⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠰⡠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⠉⡻⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣤⣴⣾⣿⣿⣿⣛⠁⣠⣿⣷⣦⣝⣛⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣤⣤⣤⣄⣠⣴⣶⣤⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣛⣩⣄⣻⣿⣿⣿⣿⣿⣿⣿⣶⡘⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⢛⣛⣋⣿⣿
⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡳⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹
⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠀⠂⠀⢴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠂⠀⠀⠀⠀⠉⠄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢿⠋⠀⠈⡤⠀⠄⠀⠀⡄
⠀⠀⠀⡀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⢂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠤⠂⠂⠀⠀⠀⠀⠀⢀⣤
⠰⠀⠀⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⢀⠂⠀⠀⠀⠿⣿⣿⢇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢠⡁⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡂⠆⢒⡄⠀⠀⠐⠀⠀⠀⠀⠀⠡⠀⠉
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⠤⡧⢈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠⠎⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⣄
⠀⠀⡀⠋⠀⣤⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠛⠛⠉⠃⠘⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠀⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣆⣦⡿⣦⠇⠘⡽⠻⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢤⠀⠀⠀⡀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠙⠛⢳⣭⡴⣃⡤⢄⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⣿⣿⣿⣧⡁⢤⡘⠓⠀⢀⡁⣿⢦⣴⠀⠀⠀⠀⠘⢦⡄⠀⢀⣿⣿⣟⡉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣼⣿⣿⣿⣿⣿⠹⠃⠀⠰⢸⡿⣏⢙⣎⣻⠃⠀⠀⠀⠙⢛⣫⣿⠟⡘⣟⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⠟⠸⠿⠃⡀⠀⠄⢀⠋⡁⢁⡶⠀⠙⣶⠊⠀⠀⠀⠺⣿⣿⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠀⢰⣤⡤⠀⠂⠶⣶⠆⢠⠀⠉⠄⢠⣴⣻⣠⠄⠀⠀⠀⠀⠉⢩⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣤⣴⣀⣠⣀⣁⡀⢀⣩⣶⡅⠈⠀⠀⠀⠀⠀⠀⢀⡹⠀⠀⢀⢀⡠⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⣿⣽⣿⣿⣗⣿⣿⡿⠛⣹⣿⣿⣿⣿⣿⡏⠉⠀⠀⠀⠀⠀⠀⣤⣁⣤⣾⣾⣿⣵⣿⠀⠀⡘⢎⣥⣶⣷⠤
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⡀⠀⠿⡿⣿⣿⠘⣏⠻⢇⣠⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢿⣿⣿⣿⣿⠀⠀⢰⣸⡿⣻⣷⣶⠃
⠀⠀⠀⠀⠀⠀⣼⣩⣿⣿⣿⣁⠀⠀⠉⠀⠀⠹⣄⠀⠈⠉⠙⠉⡇⠀⣠⣆⣤⣠⣿⣯⠶⠀⡟⠋⢁⣀⠀⠈⢿⣿⡿⠀⠀⣞⠩⢤⡉⠽⣯⣴
⠀⠀⠀⠀⠀⠀⢯⣿⣿⢿⣿⡟⣷⡹⠋⠀⠀⠀⠹⣦⠀⠀⠀⠀⡇⠀⢟⣿⣿⣿⡿⠋⢀⣾⣤⣾⣿⣿⣇⠀⠈⠋⠀⣤⠋⠁⠀⢰⣾⡖⠉⠁
⠀⠀⠀⠀⠀⠀⠘⠻⣽⢸⡽⠟⠋⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⡇⠀⠀⠙⠺⡿⣿⣀⣸⢿⣿⢏⣿⣿⣿⣥⠀⢰⣾⡁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⡇⠀⠀⠀⠀⠀⠙⢋⠗⠊⠀⡼⠻⠛⠋⠉⣰⣿⣛⡛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⢀⡏⠀⠀⣼⠃⠀⠲⢶⣾⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣇⠀⠀⠀⠀⡼⠀⠀⣼⠃⠀⠀⢠⠞⠈⠉⠈⠘⠟⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣧⠀⠀⢠⠇⠀⣰⠃⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⣆⠀⡻⠀⢀⡏⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⣶⡇⠀⡼⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢿⡄⢀⠃⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡸⣷⡜⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⡇⣸⠃⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠃⣽⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢺⣵⡏⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⣧⠀⢻⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣄⠤⢀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⢀⠠⠊⠀⠊⣀⣀⡀
⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠆⠐⠚⠀⠘⠒⠀⠀⢀⣠⡔⠀⠈⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⡀⠀⢣⢀⡄⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⠀⠀⡀⠈⠃⠀⠈⢁⠀⠀⠀⠀⢸⡀⠀⠁⠀⢠⡀⠀⠀⠀⠔⠉⠀⠀⠀⠖
⠀⠠⠀⠀⠁⠀⠀⣀⠀⡀⠤⠏⠠⠄⠉⠀⠑⠀⠀⠀⠈⠁⠂⣀⠈⠀⠀⠀⠀⠈⠀⢀⠊⠀⢠⡮
⢰⡁⠀⠀⠀⠀⠁⠀⠌⠀⢾⡴⠷⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠋
⠀⠒⠤⣄⠀⣡⠀⠀⢆⡀⡀⠀⠀⠀⠀⠈⣃⠀⢀⠀⠀⠤⠂⠀⠓⢃⡐⠂⠒⠀⠀⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠶⠀⠰⠊⡀⠀⢶⠁⠀⠀⠀⠄⡀⠀⠀⠀⠀⠑⣀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⠀⠀⠀⢀⠈⠂⠤⠀⣀⠀⠀⠀⠀⠖⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⢁⠋⠀⠀⠈⠀⠀⠑⠄⢀⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠢⠀⠠⠲⡀⢀⡀⢐⠀⢀⠄⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢀⡴⠐⢀⠁⠈⠖⠓⠂⡉⠠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⢃⡔⡪⢐⠃⢈⢤⠈⠢⡴⠤⠐⣈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠐⣋⡤⠀⠀⡰⠀⠡⠴⠉⠠⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠚⡠⢀⠄⠀⡖⠂⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠠⠀⠀⠀⠈⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠼⠀⣄⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⢀⠤⠂⠉⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠄⠀⠀⠀⠀⠘⡤⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⡄⠈⠀⠀⠀⠀⡀⢡⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠈⢆⢀⣄⣀⡀⠰⡇⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢰⡀⠀⠀⠀⡠⣄⡀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠀⠀⠉⠁
⣿⢿⠿⠿⡿⢟⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣛⣻⣿⣿⣿⣿⣿⣟⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠔
⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠧⠀⠂
⠀⠀⠀⠀⠀⢠⣾⣟⢁⣠⠿⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠻⣿⡛⠛⠿⡗
⠀⠀⠀⠀⠀⠈⢿⡿⢿⠁⡄⠀⠀⠀⠀⠀⠆⠀⠀⠄⠠⠀⠀⠀⠀⠀⣴⣦⠀⣀⠀⠀⠀⠀⠀⠀⣨⣶⣾⢀⠀⡄⣰⣄
⠀⠀⠀⠀⣀⠀⠀⠀⢉⡐⠀⠀⢀⢠⠆⣀⠛⠒⡀⣱⣳⠀⠀⠀⠀⠀⠛⣇⣸⡇⠀⠀⠀⣤⠀⢸⣿⣿⠁⠀⠀⢸⣷⡋⠂
⠀⠀⠀⢸⣿⡆⠀⠀⢿⣶⣾⡇⠀⢠⣿⣴⣠⣿⡇⠁⢐⣶⣶⢦⣶⣄⣤⣭⣽⣷⣦⣤⣤⠶⠶⠀⣿⣿⠀⠀⠀⣀⣃⣀⠀⣀⣤⡄⠀⠀⠄
⠀⠀⠀⢺⣿⣇⠀⠀⢸⠏⢙⠁⣸⣞⣿⡿⠟⢿⣷⠂⠈⠠⣿⣾⠛⠛⠿⣼⣿⣿⣿⣿⣿⣤⠤⡄⣧⡘⢿⡀⠔⠉⠁⠃⠀⣿⠈
⠀⠀⠀⠘⡟⢿⡄⠠⠁⠠⡁⠀⢿⣿⣿⣶⣦⣀⣀⡘⢀⡶⠋⠁⠀⠀⠈⣿⡿⣿⣿⣿⣿⠻⠇⢰⣿⢿⡤⠍⠀⠀⠀⠀⣤⡿⠀⢀
⠀⠀⠀⢾⣿⡶⠀⡀⢦⠀⠀⠀⠘⣿⠟⠋⣿⣿⠁⠀⢸⣷⣶⣄⣤⣦⣤⡿⠟⢹⣟⠛⢷⡴⠆⣾⣿⢻⠀⠀⠀⠀⠀⠀⢻⠁⣠⣿⠂
⠀⠀⢴⡟⠛⠍⣎⠷⠄⢣⠀⠀⠀⠈⣀⡀⢻⡉⠁⠀⠀⣹⠛⣛⣽⡟⣿⣄⢀⣨⣿⣧⡄⠈⠀⣾⡿⠀⠀⠀⡇⠀⠀⠀⢸⣼⣿⡏⢸⣧
⠀⠀⢸⣿⣶⣶⠋⠐⢀⡀⠀⠀⠀⠀⣹⡭⡫⠡⠤⠀⠀⠛⠶⣛⣿⢷⣼⡏⣾⣯⣿⠻⠣⠴⠷⠀⠻⢤⣀⢠⣤⠀⢤⠀⡞⠻⠿⠀⢾⡿⠆
⠀⠀⣿⣿⣿⣿⣀⣀⣼⣧⢈⣠⠶⢸⣿⣶⣶⣶⣾⣆⠳⣄⠀⠘⢦⣐⠋⣁⣌⣛⠉⠚⣷⡾⣿⣿⣷⣾⢿⡅⣠⣹⡇⡀
⠀⢻⣧⣬⣿⠿⣿⣿⡷⣹⡦⠀⣾⣿⣙⠛⠫⠽⢿⣿⣧⡈⠻⣦⣶⣭⡀⢀⣠⠉⠠⠆⢀⠀⠀⠉⠉⠛⠋⠁⠉⠙⠻⡾⠈
⠀⠀⠘⠻⢿⣷⣿⣅⣀⠹⡇⠐⠻⠿⠿⠿⠿⠿⠿⣯⣿⣷⡆⢻⠟⠛⢛⣙⡉⠃⠰⠾⠇⠀⠀⠀⡠⠀⣤⡐⠒⢂⣤⠤⠀⡀
⠀⠀⠀⠀⠀⠉⠛⠿⠿⠷⡿⢄⣤⠀⠀⠀⠀⠀⠁⠉⠉⠛⠃⠈⠁⠀⠈⠁⠀⠀⠀⠀⢀⣀⣴⣿⣿⣷⣻⣷⣾⣿⣇⠀⠟⢻⡒⢶⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠙





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠰⠀⠒⠀⠀⠀⠐⠀⠐⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⣤⣤⣤⣤⡀⣳⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⣠⣿⣷⣸⣿⢹⣿⣽⢿⣏⣉⣀⣤⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣿⣿⣿⣿⣿⣧⠈⠻⣿⣿⣿⡿⠿⢟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⠛⣿⠛⢻⡟⠀⠉⠀⢰⣫⡿⢋⣤⣤⣉⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠋⠁⠀⣧⣄⣀⣸⣿⡛⠓⠙⠛⠻⣿⣿⣮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣴⠛⣿⣧⣴⣿⣿⣿⣿⣿⣿⣦⣤⣄⢀⡀⠉⠙⣿⠀⠀⠀⣀⣿⠆⠐⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠈⣿⣿⣿⣿⡿⢹⢿⡇⢹⠿⣿⠟⡛⣿⠀⣀⠀⢀⣶⠋⠀⠀⠀⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣰⡆⣿⢿⣿⣿⣠⣿⣸⣿⣼⡟⠀⠘⠻⠛⢿⣿⠇⣠⠇⠀⠀⠀⠀⠀⠘⣧⣤⡄
⠀⠀⠀⠀⠀⢠⣤⡀⠙⠿⣦⡀⠀⢀⣿⣿⢹⣧⣾⣿⣿⡿⠛⡛⢩⡀⠈⠣⣀⠀⢸⣿⡄⢻⠀⣇⠀⠀⠀⠀⢸⡏⠜⢋⠤⡀
⠀⠀⠀⠀⣶⣾⡻⣿⣦⣤⢙⣿⣀⡾⠟⠷⣾⣟⠻⣫⣴⠀⠸⠃⠀⠈⠀⠀⠀⠘⣿⡿⣷⠘⠋⠋⠀⠀⡃⢀⠟⠁⠀⠀⠀⠁
⠀⠀⢀⡀⠈⠛⢧⡄⠉⢧⣽⡝⢡⣤⣶⣷⡌⣿⣿⣟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡽⢛⠛⠷⣤⣀⠴⠋
⠀⠀⠋⠙⢿⣦⣀⣈⣉⣢⣌⣻⣶⣿⣿⣿⣿⣿⡿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠈⠁⠙⣿⣴⣿⣻⣷⠌⣥⠀⡃⠀⠀⠀⢀⣀
⠀⠀⠀⠰⠚⣛⣛⣛⣋⣭⢾⣷⣿⣿⣿⣿⢿⡙⠷⣶⣦⡶⠁⠀⠀⠀⠀⠀⠙⠻⡟⢻⣿⣿⣿⣿⡿⢧⣭⡁⠀⠀⠀⠈⠉
⠀⠀⠈⢥⣄⠿⢻⠙⠋⣠⠟⣩⡞⠉⠻⣿⣮⠙⢦⡄⠙⢠⡄⣀⠀⠀⠀⠀⠀⠙⠛⢻⣾⡿⢹⣿⡻⣮⠁
⠀⠀⠀⠀⠿⣿⣷⡶⠀⣴⠾⠋⣀⣾⡆⠻⣿⡦⠀⠀⣀⣤⣤⣹⢧⣠⣄⠀⠀⡀⠀⣸⣿⠁⠀⠈⠁⠈⠁⠀⠀⠀⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡿⠿⣿⣿⢿⣦⣴⡆⠀⣿⠿⠛⣿⠏⢸⣿⣿⣄⣀⡁⠉⠀⠙⠶⠦⠤⠤⣤⡀⠀⣤⡾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠐⠿⣯⠏⠀⢿⣿⡁⠀⠉⠀⢸⣿⠀⠀⠛⢿⣿⣿⣿⠿⣿⣶⣶⣿⣷⣦⣴⣶⣶⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡈⢿⣷⡄⠀⠀⢈⡇⠀⠀⠀⠎⠉⠛⠉⠛⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⣿⣿⢻⣏⣽⢦⣄⡀⠀⠁⠀⣠⣾⣿⣿⣿⣿⣌⠻⣧⡉⠻⣿⣿⠿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠹⢿⣿⡷⣿⣥⣿⣧⣿⠇⠀⠂⠀⠉⢉⣿⣿⣿⣿⣿⣷⣽⣿⣦⡈⣻⡦⠠⣿⣿⣯⣝⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠳⣦⣤⣴⣿⣿⣿⣿⣿⢿⣤⡄⠀⠀⠀⠈⠙⠛⠛⢿⣿⣿⣶⣯⣛⣿⣿⣶⣶⣶⡶⠟⠻⠿⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡻⠟⡹⣿⣿⣿⡏⠛⠻⠆⠀⠀⠀⠀⠀⠈⣀⣸⣿⣿⣿⣯⣤⣹⣯⣿⣿⠆⢰⣶⡶⠶⠞⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠵⣶⠋⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⢸⠟⠻⠿⢿⣿⣟⣻⣿⣿⣿⡿⢛⣛⣁⠴⠖⠋⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠳⠤⣄⣈⣿⣿⡷⠀⠀⠀⠀⠺⠀⠀⠀⡾⠁⣿⣿⣿⣿⡿⠿⠿⡿⠏⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡱⠟⠀⠀⠀⠀⢀⠀⠀⢀⡾⠀⠀⠿⠛⠉⠛⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣣⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠘⡇⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡄⠀⠸⡇⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠀⠈⠀⢀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠄⠘⢀⠎⠀⣴⣤⡄⠈⠡⠀⠀⠀⠀⠀⠀⠈⡀⠂⠀⠀⠀⠀⠀⠀⠀⢆⢀⡠⠀⠀⠀⠀⠤⠂⠐⡆⡀⡄
⠀⢀⠀⠀⠀⠀⠈⡂⠀⠻⠟⠃⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠱⣅⣁⣿⠁
⠀⠀⠀⠄⠀⠀⠀⠈⠧⠤⠂⠀⠁⠀⠀⠀⠀⠀⠠⡀⠀⠀⠁⠀⢀⢀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃
⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠰⠿⡀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠹⡏⠀⠀⠀⠀⠀⠀⢰⡀⠨⠀⠀⠀⡤⠀⠀⠠
⡂⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠻⠄⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⢀⠀⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢁⠀⡀⠙⠠⠂⠀⠀⣈
⠀⠀⠈⠛⠠⠀⠠⠐⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⢀⣴⡄⠀⠀⠀⠆⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢺⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢈⠀⠌⠁⠂⠘⠀⠀⠀⠘⠂
⠠⢜⡣⠀⠀⠀⠀⠀⣤⠀⠙⠉⡄⠀⠠⠀⠀⠂⠈⠂⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠰⠆⠀⠀⠆
⠁⠾⠧⠈⠆⠀⠀⠀⠀⠀⠚⠃⠀⠀⠐⢀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡛⠀⠀⠀⠀⠁⠈⠀⠀⢀
⠀⠘⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠨⠀⢀⠀⢀⣤⡷⠎⠀⠀⠀⠁⠀⠀⠈⠁⠘⠻⠃⠀⠠⠄⠈⢀⠈⠀⠀⠂
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠾⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⡉⠀⠀⠈⠀⠀⠰⠂
⡠⡀⢀⡁⠀⠀⠀⠀⠀⠀⠇⢈⣠⣤⡀⠀⢈⠂⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢄⠓⠀⠀⠀⠀⠀⠀⠂
⠀⠪⠵⢴⠆⠉⠀⠀⠘⠀⠀⢿⡀⢘⣿⠀⠀⠀⠀⠚⠀⠀⠀⠠⢤⣀⢀⣀⣴⠀⠀⠀⠈⠀⠀⠀⠀⣤⡤⠀⠀⠆
⠤⠼⠋⠈⠰⠀⠈⠀⠀⠀⠆⠨⠝⠋⠉⠀⡀⠆⠰⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠐⠁⠀⠀⠀⠂⣟⠀⠀⠀⠀⠀⠀⠂⠠⠀⠘⠑⢀
⠀⠀⠈⠀⠀⠀⠀⢠⡶⢄⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢻⠘⡃⢚⠀⠀⠀⠀⠁⢦⠈⠀⠀⠀⠈⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠠⠚⠡⣭⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣠⠀⠀⡸⠇⡀⢠⠉⠦⠀⠀⠀⠀⠾⡿⠆⠀⣠⡀
⠀⠀⠘⠎⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⡄⠀⠀⠀⢄⡴⠀⠀⠀⠘⠁⠀⢠⠂⠠⠤⠈⠀⠈
⠲⢄⡀⠀⠀⠀⠶⠀⠈⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⡄⠈⠀⠀⠀⠠⠄⠀⠀⠀⠠⠐⠀⠀⠄⠀⠉
⠀⠀⠀⠁⠃⠀⠀⢀⡠⠔⠒⢢⢀⠀⠀⠀⠀⠐⠢⡀⠉⠈⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠠⡙⢦⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠉⠑⢤⡀⠀⢰⠁⠀⠀⠀⠀⠉⠒⠂⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠑⣄⢸⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⣠⠃⠀⠀⠀⠀⠀⠘⣾⠀⠀⣰⠃⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠊⠁⠀⠀⠉⠒⠤⣀⠀⠘⡇⢠⠃⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠴⠚⠛⠓⠒⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⠤⢤⡴⠶⠚⡀⠀⠀⠀⠒⠢⢤⣀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢀⡔⠁⠀⠸⡄⠀⠀⠀⠈⠙⠢⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⢠⠎⠀⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⡌⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⣧⠘⣆⠀⠀⠀⠀⠀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⠠⢄⡀⠀⠀⠀⢠⠟⡆⢹⠑⠦⣄⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣆⠑⠀⠀⢀⠞⠀⢱⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⢰⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠄⠀⡀⠀⠑⠄⢀⡀⠀⠀⠉⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠒⠒⢄⢦⠤⠤⡠⠚⠉⠑⣄⠤⠎⠁⠀⠈⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠈⢣⠀⠀⢁⡀⠀⠀⠴⠒⠢⡂⠀⠑⢀⠀⢅⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠂⠲⡀⠀⠀⠂⠀⢀⠼⢀⠀⠇⠀⠀⠜⠀⠀⠀⡸⠛⠀⠰⠀⢀⠇⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠑⡤⠤⢤⡤⠊⠀⠠⠐⠀⠀⠀⠀⡉⠀⠰⣗⣄⠀⣁⡰⠈⠀⠈⠀⠲
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⡀⠀⠀⢱⣀⣄⡕⠐⡆⠈⠂⡄⢠⠀⠦⠀⢀⠂⠊⠀⠁⠘⠃⠆⡀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣶⠀⠁⡀⠐⠘⢿⡁⠀⢀⣈⠣⡼⣀⡹⠀⠀⠀⠀⠠⠄⡀⠀⢦⡀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⣀⠃⠀⠄⠰⠆⠨⣍⢉⠽⠌⠀⠀⠁⢳⠀⠀⠀⠀⠀⠀⠁⠀⠐⢥⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠐⠀⣠⢻⣃⠀⠈⠈⠀⠼⣇⡀⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⢀⠐⠠⡆⠈⠙⣾⡠⠦⡝⠋⠀⣹⠤⢄⡠⣤⣀⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠲⡀⠀⠀⠀⠱⡆⠇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⢀⠀⠀⠀⠿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣀⢸⡒⠟⢀⠤⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⣰⠻⡙⡐⡌⠙⠒⠒⡏⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡀⡄⢀⠁⢳⢠⠆⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠈⡎⠌⣇⢫⠀⠀⠑⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢠⠻⣹⠐⡜⢎⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⢀⣜⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⠔⣠⣤⠊⣠⠀⠀⣨⡕⢶⣤⠤⣤⠣⠁⢨⣄⡀⢀⣀⣀⣀⣀⡄⢀⣀
⠀⠀⠀⠀⠈⢢⡉⠠⠈⠻⣄⠀⠙⢆⠀⠐⡄⠈⠉⠓⠀⠀⠀⠈⢰⢧⠀⠈⠀⠐⠈⠒⠀⡀⠀⠈⠁⠉⢸
⠀⠀⠀⠀⠀⠂⢀⣀⠈⠉⠀⠀⠁⠈⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⠀⠁
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠸⢶⡦
⠀⠀⠀⠀⠀⠀⢸⠐⠀⢀⡄⢃⠀⢐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠁⠀⢀⡀⠀⠰⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠬⠥⠴⠤⠤⠴⠧⠤⠴⠾⠄⠀⣶⣾⡄⠀⠀⠤⠔⠒⡲⢀⠾⣆⠀⠀⠙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠅⠀⠀⠀⠔⠉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠿⠿⠟⠛⠛⠛⠉⠉⠉⠁⡀⢀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⢀⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣫⠵⠦⠄⠄⡀⠁⠀⠁⠠⣤⣀⣀⣰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢀⠠⠂⢀⡼⠋⡤⠀⠀⠀⠚⠿⠟⠻⠿⠿⠛⠛⠋⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠴⠀⢉⠠⠊⣠⠀⠀⠀⠴⠷⠇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣣⣲⠶⣂⠀⠀⠀⠚⡠⠔⠁⡰⠊⢠⣾⣡⠄⣠⠟⠀⠀⠂⠀⠈⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢊⣥⣦⡤⡖⠊⠛⠙⣠⢖⣀⠴⢚⡡⠈⡽⣷⡟⠁⠀⠀⠀⠐⠀⢠⠀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣞⣛⠭⣖⠯⠀⠀⢀⣠⣼⣏⣑⣚⠽⢚⡭⠖⠋⠀⠀⠄⠀⠀⢀⠀⢀⣇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠯⢍⠀⢈⣠⣤⣴⣾⣛⣻⣿⣿⣿⣖⣪⠟⠁⠀⠀⠀⠀⠀⠀⢀⠀⢳⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣋⠤⠶⠤⠭⣭⣍⣿⣷⣿⣶⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⣪⣭⠟⠁⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣇⣡⣤⣶⣶⣀⣶⣤⣤⢤⠴⠐⠒⠊⠉⠁⠀⠈⠀⠀⠀⠀⠀⢠⣤⡵⠗⠀⠀⠀⡀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠟⠛⠛⣫⠽⠿⡟⢛⣭⢁⡇⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣾⡥⢀⣀⣀⠜⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⢀⡠⠔⠛⠁⠊⠉⠉⠑⠶⠙⠳⢆⡄⠐⠀⠛⠀⠀⠀⡀⠀⠀⠀⠀⠔⠛⠉⠀⠈⠉⣹⣿⡖⣡⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣪⠝⠁⠀⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣶⡈⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣥⡶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣺⠕⠋⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⣠⢖⣭⠿⠋⠛⠛
⠀⠀⠀⠀⠀⠀⣀⠴⣊⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣦⡀⢐⣡⡶⠛⠁
⠀⠀⠀⣀⠴⣊⡵⣚⢅⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣽⣵⣾⣿⡅
⢀⣴⣿⡿⢞⡽⢊⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣲⣿⠿⣧⡭⠿⠛⠉
⠈⠱⣿⣾⣿⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣭⠶⠛⠉
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣄⠀⣠⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠈⠹⣿⠟⠁⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠉⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠛⠿⢷⣦⣄⡈⢻⡄⠀⠀⠀⠀⠀⠀⣴⠏⢀⣤⡶⠿⠟⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠈⠛⠶⣽⣄⠀⠀⠀⢀⣼⡧⠞⠋⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⡠⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠓⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠁⠀⠀⠹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣀⣀⣠⣴⠶⣻⣿⠏⠀⠀⠀⠀⠀⠘⣧⡙⠳⣦⣤⣀⣀⣀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⢁⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⢾⡇⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠘⢿⣦⣤⣴⡾⠋⠻⣷⣤⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠀⠀⠀⠀⠠⠤⠀⣀⠀⠀⠀⠀⠀⡘⠐⠀⠀⠀⡠⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠉⠀⠀⢀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠈⠐⠢⣄⠀⠉⠃⠀⠀⠄⠁⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⡀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⢀⠀⠁⠲⡕⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣐⡀⢀⠀⠀⠀⠀⠀⠀⠈⢆⠈⡄
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠩⡠⠄⠀⠀⠀⠀⠀⡠⢴⠀⠀⠙⢣⠄⠗⠁⠀⠀⠀⠀⠀⠀⠈⠀⢰
⠀⠀⠀⠀⠀⢀⣰⢀⡌⠀⠀⠓⢈⠐⠤⡀⠀⠷⣵⢾⣴⣄⠀⡠⠊⢠⡃⡄⠀⢄⡌⠀⠀⡠⠂⡍⠀⢳⡗⢹⠒⠃⠀⡆
⠀⠀⠀⠀⠀⢘⡉⠉⠈⠂⠀⠀⠀⠳⡄⠈⠢⣘⡢⠯⠆⠁⡜⠁⡠⠏⠀⡂⠀⠀⢃⡠⠊⠀⢀⡠⠊⠀⠯⠏⠁⢸⠀⠃
⠀⠀⠀⠀⠀⠣⣀⠀⢀⡄⢀⠤⠀⠀⠄⢦⡀⠐⡀⠀⠇⡐⠀⡌⠀⠡⠀⠱⠀⠀⠘⠁⠀⡠⠟⠁⠉⠑⢀⠀⠀⡰⢛⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠈⠇⠱⠇⠀⠀⠀⠀⠀⠈⠢⣰⠀⣾⢁⠴⣀⠴⡄⠀⡀⠀⢀⠆⢀⠎⠀⠀⠀⠀⠀⠀⢃⠀⡀⠀⠠⢁
⠀⠀⠀⠀⠀⡖⠺⡀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠈⢂⣉⡤⠊⠁⠀⡇⢰⠉⠲⢎⠀⠎⠀⠀⠀⠀⠀⠀⠀⢸⠊⣝⠰⢶⠉
⠀⠀⠀⠀⠀⠈⢄⣡⠈⡃⢄⢈⡀⠐⠀⠁⠀⠀⠀⡠⠋⠀⠀⠀⠰⠉⠹⠀⠀⠀⠹⠀⠀⠀⠄⠀⠠⢀⡠⠚⠉⠀⣀⠊
⠀⠀⠀⠀⠀⠀⢀⠙⠦⠡⠄⠧⠄⠠⠤⠤⠤⠤⠴⠄⠄⠀⠄⠤⠅⠤⠀⠥⠠⠤⠠⠧⠀⠤⠤⠠⠥⠮⠠⠀⠤⠾⡁
⠀⠀⠀⠀⠀⠀⠣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜
⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠃⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠳⠰⠃⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠑⠆⠚⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠘⠦⠜⠁⠀⠀⠀⠀⠀⠙⠢⠊⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⢰⡆⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠝⠰⣆⠶⠀⠀⣀⠅⢀⡀⠀⠰⠆⠈⠛⣿⠀⠚⣤⠀⠀⣺⡖⠀⠀⠼⢧⠉⠛⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⡛⢶⠆⠉⢀⣻⠃⠉⠀⢀⡁⠀⠰⠂⠀⣠⠄⠀⣼⢃⣀⢀⣀⠄⠀⢾⡀⠀⣄⠀⠈⠷
⠀⠀⠀⠀⠀⠀⡄⠀⠈⣥⢴⡄⠀⠺⠉⠀⠀⠠⠋⣀⡐⡄⡤⢈⡀⠀⠶⠀⠌⠁⠘⠟⠃⠀⢠⠄⠶⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡀⢁⡌⠛⠀⠉⣀⠀⠐⢦⣭⣌⡇⠼⢰⠆⠀⡄⢀⡠⢀⠀⠀⣴⡄⠀⠛⠂⠖⡈⢰⣃⣾⠁
⠀⠀⠀⠀⠀⠀⣰⡶⣆⢤⠀⠈⠁⠀⠓⠀⠉⠀⠀⠉⠻⠯⣭⡁⢊⠇⢾⠆⠿⣏⡁⠀⠀⢀⡄⠀⠀⠈⢀⢻⢀⣀
⠀⠀⠀⠀⠀⠰⠌⠁⠀⣈⢠⡀⠀⠀⡀⠘⠃⡀⣼⣇⣤⠈⠙⣓⠀⠜⠀⠀⠀⠛⢁⠀⠆⡈⠑⠿⠀⠓⠘⠇⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠈⢁⠀⣀⡁⠀⠀⠺⠊⠀⠉⠠⠀⡤⠀⠈⠀⢀⡀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠐⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠛⠁⠎⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠈⠿⠂⠀⠀⠀⠀⠀⠙⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢔⣾⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡰⠊⢐⢀⠀⠂⡭⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠆⠀⠀⢼⠀⠄⠃⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡄⠁⠀⠀⠀⠮⠁⣠⠖
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠁⠀⠠⠀⠘⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢨⠖
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠢⠐⢠⣀⢀⡘⠀⠃⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⠀⠂⠀⠀⠀⠂⠀⠀⢠
⠀⠀⠀⠐⠈⠢⢀⠀⠠⠄⠁⠀⠒⠿⣿⣿⣷⡄⠀⣠⠟⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣷⣴⣀⠉⢩⠀⠀⠀⠆⢀⠀⠈⠁⠀⠂
⠀⠀⠀⠀⠀⠑⠀⠈⠀⠀⠀⡁⠔⢺⠗⠛⠗⠉⠈⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠰⡀⠀⢻⠛⠛⢠⠍⠀⡀⠀⠈⠈⢳⣧⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠈⠀⠁⠀⠀⠀⠀⠂⠀⠘⡏⠙⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⡈⢄⠀⠀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠈⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡠⠀⡄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠈⠁⢀⠀⠉⠂⠤⠘⠰⣦⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢠⡴⠂⠘⠃⣐⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⡄⢀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠄⠀⢼⣿⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠈⠰⣻⠶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠂⡖⠀⠈⠑⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠠⠀⠀⠀⠀⠄⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠡⠐⠡⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢩⡕⠄⠀⠀⠀⠀⠀⠀⠀⠌⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⡆⡌⡰⠀⠆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⣀⠁⢬⣿⣧⣤⠁⠀⠀⠀⠁⠀⢀⣀⠠⠐⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡔⠂⢈⣷⣯⣴⠂⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢨⠏⠉⢉⠉⠀⠀⠐⠀⠀⠀⠋⢠⣦⣴⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⡒⢿⣟⠋⢈⡉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠈⠈⠀⠀⠀⠀⠀⠀⠁⠄⠈⠻⡍⢉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⠔⢫⠄⡀⣸⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠀⢆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡰⠇⠀⢀⣀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠴⠁⠀⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢀⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡸⣧⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠙⣦⣬⡱⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⠒⠀⠀⠀⠤⣀⠀⠀⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⡤⠈⠉⠉⠛⠳⠶⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠞⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢠⠎⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣳⡄
⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠄⠫⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢙⡇⠀⠀⠈⢎⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢛⠀⣠⣐⠝
⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⡜⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢨⡇⠀⠀⠀⠈⢂⡑⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡍⠁
⣄⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⢃⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠈⠑⠢⡈⠁⠢⣄⠀⠀⠀⠀⠀⠀⡠⢚⡴⠛
⢛⣷⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠉⠀⠄⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡑⢄⣀⣀⢠⢟⠐⠋
⠀⠀⠉⠛⢣⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣿⣿⣶⣶⣤⣀⡀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⠿⡈⢛⠃
⠀⠀⠀⠀⠀⠈⠙⠋⢻⠯⣁⣶⠶⠶⠶⠶⠶⠻⠳⢶⠊⠀⢀⣉⢻⣿⣿⡯⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣐⡞
⠀⠀⠀⠀⠀⠀⡠⢾⠟⠃⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠈⠉⠉⣿⣿⠀⠀⠀⠀⠀⠀⠀⠛⣰⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠐⢚⠿⠛⠃⠑⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⡘⢯⠉⠛⠳⠶⠼⠶⣖⢦⡇⢠⡇
⢴⠋⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠂⣠⡀⣤⠄⠄⠀⠀⠉⠀⠈⢳⡀⠀⠀⠀⠀⠈⡁⢀⡟⠁
⠃⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⠃⠀⠀⠀⠀⠠⠀⠐⡀⠀⠈⠀⠋⠀⠀⠀⠀⠰⣡⠞
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣄⠀⠸⠂⠀⠀⢤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠀⢻⣄⢠⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠘⠆⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣄⠠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⢰⡟⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⡀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠠⠈⢃⣻⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢠⣀⠀⠀⠐⠖⠃⢠⣾⡅⠀⢸⠋⠤⠀⠒⠒⢲⢿⢙⠁⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠠⣄⣴⣦⣟⢻⣧⣿⣷⠸⠀⠀⠀⠀⠀⠀⠀⠸⣆⠠⢀⠸⣦⣧⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣿⣿⣿⠻⣄⣘⢿⠠⡟⢹⣽⠉⠀⢀⣰⠂⠀⠀⣘⣃⣠⡿⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡶⢺⠃⠈⠛⣧⠸⡆⠈⠉⣈⡃⣠⣼⣿⡀⠀⢸⣗⣇⣸⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠉⠨⣿⠀⠛⠉⠁⡀⠀⡀⠀⣿⡆⠛⣤⢁⡜⠉⢏⠷⠲⠞⠉⠈⠉
⠀⣀⣀⢄⣀⠀⢀⣀⡠⠔⠒⡀⠒⠒⠂⢈⣍⠀⢰⣦⡶⡀⠀⠈⢀⣰⣷⠓⠲⣟⠶⣉⠃⣨⢋⡿⠁⠀⠈⡄
⠘⠿⠿⠿⠿⠀⣀⣈⣀⡾⠾⠇⠀⠤⠾⠛⠷⣀⡾⠛⠛⠛⠛⢀⠌⠁⠀⠀⠀⠈⠛⠛⣾⣯⠛⣿⡄⠀⠀⢿⣄⣀
⠐⠒⠉⠀⠂⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢧⠀⠀⡘⢀⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⢸⣇⠀⠀⢸⡏⠙⠛⠷⠶⢦⣤⣀⡤⢄⣀⣀⡀⠠⠤⢤⣤
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠸⠦⣀⣣⠈⠀⠀⠀⠀⠀⠀⢀⣴⡏⠁⢇⠀⠘⣿⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠂⢍⡙⢧⡄⠒⠂⠉
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠄⣼⡏⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠘⡆⠀⠙⡇⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣭⣦
⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠀⠀⠀⢶⢹⠀⠀⠀⠀⠀⠀⡔⠿⠁⠀⠀⠀⠀⠘⢆⡀⢹⠇⠀⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡣⡀
⠀⠀⠀⡄⣰⠀⠀⠀⠀⣀⣀⣀⣼⣇⣰⠀⠀⠀⠀⣶⠇⠀⠀⠀⠀⣠⣎⡜⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⣷⠀⠐⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣮
⠀⠀⠀⡿⣿⠀⠈⠉⠉⢀⠠⢊⡙⠀⢠⠀⠀⠀⢠⡟⠀⢀⠠⠔⣩⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⢠⠀⡟⠀⠀⠀⢀⠎⠀⡌⠀⠀⠐⠀⠀⢀⣾⡡⠚⠁⢀⣜⠏⠠⠏⡳⢤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀
⠀⠀⠀⢀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⢃⠀⢳⡄
⠀⠀⠀⣨⠷⢤⣌⣙⠳⠦⣄⣀⠀⠀⠀⠀⠀⠀⣰⠋⠳⣤⠿⠀⠀⠂⠀⠻⣄⣀⣠⣤⠤⠶⠖⠚⠛⠛⠛⠓⠲⢤⡀
⠀⠀⠀⢷⣀⠀⠀⠈⠉⠓⠲⠭⣝⣒⠦⢤⣤⣼⠁⠁⠄⠈⠳⢦⡤⠶⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢻⡄
⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⣀⣀⣀⣈⣉⣿⠀⡜⠀⠀⠀⠐⢄⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠾⠄⠘⣯⡽⠛⠁
⠀⠀⠀⠀⠀⠀⠸⣏⠁⠀⠀⠀⠀⣀⣀⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠉⠹⡇⠀⠈⢣⡀⠀⠈⠀⠀⢠⠁⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠲⢄⣀⠀⠐⠀⠀⠀⠀⣠⠇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠈⠙⠒⠳⠶⠖⠚⠁⠀⠀⢀⠈⠀⢀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣄⡀⠰⡟⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣳⣦⣬⣉⡛⣻⡦⢤⣤⣤⣤⣤⡤⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣿⡿⢿⣴⣿⡆⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠷⢷⣄⡀⠀⣀⡤⠞⠉⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡯⣤⠶⠲⢄⠀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠳⡌⢿⡀⢀⣸⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢳⠖⠛⡏⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠘⣦⡤⢿⡏⠃⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢰⠇⠀⠀⢷⡀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠖⠋⠀⠀⠀⠀⠙⠲⠚⠃

⣀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⢀⣀
⠉⠛⣿⣿⣶⣄⡀⢸⣿⣄⡀⠀⠀⡀⢀⣿⣿⣿⣿⣿⣿⣏⣥⣠⣽⢿⣿⣿⣿⣿⢻⣆⢲⣾⣉⠑⣪⡶⠔⠀⢺⡿⠋
⠀⢀⠈⠙⣿⠟⠉⢹⡇⠀⢹⣄⠀⣀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡟⢿⡀⠻⣿⣿⡿⢛⣿⣿⣿⣿⡏
⠀⣨⡀⢠⡿⢀⣠⡆⠀⣠⣏⠁⠀⢉⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⣿⣶⣾⣿⣿⣿⣿⣿⣿⠃⠀⢀⡀
⣴⠏⠀⠀⡈⠛⣿⣶⣿⣿⣿⣦⣄⣾⣷⣤⣘⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⠃⣾⡀⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠑
⠁⠀⠀⢈⣧⡀⠈⢉⣹⣿⣿⠻⣿⣿⣿⡟⢿⣿⣿⣭⣉⠛⠛⠛⠛⢿⣏⣰⡿⠃⠈⠈⠙⠋⠻⣿⣿⣿⣿⣦⣤⣤⡞
⠀⠀⣠⣾⠏⠹⣿⣿⣿⣿⡇⠀⠘⢿⣿⡇⠀⠈⠙⣿⣿⣿⣦⡀⠀⢶⣿⠋⠀⡄⢀⣿⠶⠄⠀⠛⣿⣿⣿⣿⡿⠉⠠
⠈⠉⠉⠈⠀⠀⢻⣿⣿⡿⠁⠀⠀⠀⠀⢹⣤⣤⡄⠈⠈⢻⣿⣿⣶⣤⣿⣦⣴⣿⣼⣁⠀⠀⠀⣸⣟⣭⣭⣿⣧
⡆⠀⣴⣷⣤⣀⢸⣿⡏⠀⠀⠠⣴⡟⠁⠈⠀⠤⠄⠀⠂⣸⣿⣭⣀⡀⢛⣿⣿⣉⠛⠛⠿⠟⠻⠿⣿⣿⣿⣿⣿⣷⣸
⣿⣼⣿⠋⡙⣿⣿⣿⣷⣄⣰⠀⣽⡄⠀⠀⠀⠁⠀⠈⢬⠉⠹⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣦⣤⣤⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣼⣿⣿⣿⣿⣿⣝⠁⠀⣀⠀⠈⢡⠀⠀⡀⠀⠈⠁⠀⢿⣿⣿⣿⣿⠋⠟⢹⣿⣿⣿⡟⠘⣿⡿⠟⠀⠛⠻⡟
⡙⢿⣿⣿⣿⣿⣿⠉⠀⠈⣷⣦⣙⣷⠄⡀⠀⠀⠁⠐⠒⠂⠀⢸⣿⣿⡿⢁⣠⣴⣿⣿⣿⡿⢷⣸⡏⣀⠀⠀⠀⠀⢹
⣧⠀⠙⣿⣿⣿⠏⠀⠀⠀⠛⣿⣯⡉⠃⣄⡀⣤⠀⠀⠐⠃⠀⢿⣿⣿⣾⣿⣿⣿⣿⡌⠛⠳⢤⣬⣷⣿⣷⠀⠀⠀⠈
⣿⡀⠀⠈⣿⣿⣿⣿⣿⠇⠀⠹⣿⣏⠓⢂⣹⡶⠶⠶⢇⣀⣠⣿⡿⠿⠋⠙⣿⣿⣿⣿⣆⡀⠤⣝⣿⣿⣿⣶⣶⣶⡿
⣾⠿⡄⠀⠘⣿⣿⣿⣿⡀⠀⢀⣼⣿⣮⡉⠉⠙⣶⣄⣀⣿⠟⠷⠶⠶⢾⡀⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⠟⢀
⡏⠀⠈⠙⢶⡈⠻⣿⣿⣧⣾⣿⣿⣿⣿⣿⣷⣾⡟⣸⣿⣧⣶⣀⠀⠐⠀⠹⣟⠛⡉⠁⢀⣴⣿⣿⣿⣿⡟⠿⠏⣰⣿
⡇⠀⠀⠀⠀⢱⣠⢹⣿⣿⣿⠛⢹⣿⣿⣿⣇⢹⣧⣿⠛⠉⠈⢻⣷⣤⠄⠀⢹⣿⣤⣶⣿⣿⣿⣿⣿⣿⣷⡀⢠⣹⣿
⣇⣸⣦⣰⣧⣼⡟⣸⣿⣿⣧⣴⣿⣿⠻⠿⠿⣾⣿⡇⠀⢀⠀⠀⢿⣧⣾⢆⣼⣿⣿⣿⣿⡿⠛⢉⣡⣾⣿⣿⣾⣿⣿
⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣄⡀⠐⢿⣿⣿⣿⣧⣤⣼⣿⣿⣿⠟⠉⠀⠀⣀⠀⡉⠛⠿⣿⣿⡿⠟⠋⠁
⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡖⠸⠏⠀⠀⠀⠀⠈⡙⣠⣤⣀⣼
⠿⢿⣿⣿⣿⣿⣿⣿⠛⠁⣿⠟⠁⣼⣿⣿⣿⣿⣿⣿⣿⣭⣍⣉⣉⣤⣴⠻⠄⢸⠃⠀⠈⠀⠀⠀⠠⠄⠃⠈⠉⠻⣿
⣀⠀⠀⠉⠙⠿⠟⠁⠀⠀⠁⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡌⠂⣀⣤⣄⠀⠀⠀⢀⠀⠇⠀⠀⠈
⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠉⠀⠙⠛⠃⠈⠛⠂⠙⠃⠉⠛⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠀⡀⠄⠀⠤⠀⢀⣠⣶⢀⡈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢁⠈⠰⠁⠉⡰⢰⠂⣠⣤⣷⠀⠨⠁⠁⠶⣤⡇⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠁⣻⠷⠈⡰⠃⠄⢃⣡⣀⠀⣰⣷⢺⣿⣴⣩⣄⠐⡋⢸⡕⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⣠⠄⠑⠦⡹⣶⠀⣂⣀⣐⡆⠀⠉⠟⣘⢻⣿⠚⢿⣏⣿⣼⢷⣉⠃⡥
⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⢀⠀⣶⠛⠂⠁⠛⣧⣹⣯⠙⠙⣧⠔⡆⠀⠱⣿⡸⠄⠋⠻⠂⢾⡿⠛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠡⢊⡁⠀⠀⣸⡲⣿⣿⡯⠁⠀⣅⠀⠰⡀⠀⢸⡗⠐⠦⡄⠀⣀⠂⠘⡁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠀⠠⠋⣹⣿⣧⣄⠺⢁⢅⡆⣀⠁⢢⠸⣧⡔⠂⢸⠆⠁⣀⠂⠄⠹⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠓⡀⠒⠄⠴⠋⣜⣻⣏⠰⠈⢉⠄⡙⣂⠙⠇⠁⠐⠀⣬⠤⠼⣩⡧⡈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⡀⠀⠁⠀⢘⡄⢱⡤⠀⢶⠋⠀⠛⢋⠁⣾⣷⡶⠒⡃⠀⠈⣅⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⢹⡆⠲⠒⣸⣧⠺⠷⡤⣎⠀⢲⡄⢀⠛⠙⣿⢧⣀⡼⠟⠀⠈⠲⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠏⢱⣄⠰⢏⡿⠆⣀⠀⡿⠛⣯⠀⡄⠠⠲⣿⣽⡅⠐⢿⣶⣌⠛⢈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠣⠄⣼⠀⢠⡎⢀⣂⠁⠁⣥⢨⡍⣈⠁⠀⠀⡸⢿⣧⠀⠀⠁⡠⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠐⠞⣷⠛⠋⣱⡶⠇⠈⢸⡇⠐⢈⠈⣴⢞⡁⠀⠚⠀⢀⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⣻⣿⠡⢛⡘⣡⣤⣁⣠⢘⣷⣶⡈⢲⠀⠀⠀⠂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠈⠀⠙⢿⣧⣿⠚⢿⡆⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢻⡎⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠘⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣇⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡟⢃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠅⣿⠇⣿⠸⣆⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡤⠘⠃⠜⠃⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈



⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⢄⠈⠙⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠐⠀⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠁⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠘⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠱⠶⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀⠀⢠⡀⠀⠀⠀⠀⠘⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠂⠠⠄⡀⠀⠂
⠀⠀⠒⠩⠄⠀⠀⠉⠀⠠⣤⠀⠂⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠐⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠋⢈⢂⡚⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⠙⠂⠀⠀⠃⠀⢀⡤⠀⠀⠀⠀⠀⠀⡀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⠃⠊⠀⠀⠀⠉⠁⠀⠂⠁⠀⠐⠀⠀⠶⠄⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠒⠂⠈⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠈⠡⠂⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⠀⠀⣀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠛⠀⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠙⠀⠀⠚⢁⠀⠉⠑⠒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢨⡀⠤⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠈⠁⢠⡤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⣤⠐⣄⣀⠀⢠⡄⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠛⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠀⠀⠁⠄⠈⠉⠀⠈⠁⠰⠆
⠀⠀⢀⡀⠀⠀⠀⣠⠀⢀⡀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⣀⠀⠀⠘⠀⡜⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠘⠃⠀⠄⠀⠀⠀⠀⠁⡄⠐⡀⠀⠀⡇⠀⠀⠀⡈⢉⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈
⠀⠀⠀⠀⠤⠀⠐⡃⠐⠀⠀⠀⠰⠁⢀⡘⠀⠀⠀⠀⡇⠈⢄⠀⠀⠀⠀⣀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡀⠀⠎⠐⠁⠆⠀⠠⠀⠀⢈⡟⠀⢠⠀⠀⡇⠀⠀⠀⢀⠀⠀⠃⠁⠀⡈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠈⠁⠠⡇⠀⠀⢰⣀⠄⠄⠀⠀⡇⠀⠠⠀⠀⡇⠀⠞⠁⠀⠀⠀⠁⠀⠸⠁⠀⢀⡤⠀⢲⡀⡆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠
⠀⠀⠀⡀⠠⣴⡀⠀⠀⠠⠃⠀⠀⠀⠀⠳⠄⡀⢀⡀⡷⠀⠀⠀⠀⠀⠀⡆⢀⡄⠀⠀⠀⠀⠉⠛⠿⣇⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣯⣴⡃
⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⡀⠀⠀⠀⠁⠈⠉⠀⡁⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢛⠉⠉⠉
⠀⠀⠀⡀⠀⢸⠀⠠⠞⠀⠀⠀⠈⠀⠒⠠⠖⠲⠆⠀⠀⠀⠀⡇⠀⠀⠀⠀⠄⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠁⠀⠈⠇⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠈⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⠀⠈⠳⠌⠰⠁⠂⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⢀⠘⡧⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠃⠀⠂⠀⠀⠀⠀⠂⡰⠒⠀⡁⠁⠀⠀⢀⠀⠀⠈⠀⠀⠘⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠆⠀⠄⢈⣰⣋⠁⠀⠁⠀⠀⠀⠀⠠⡀⠐⠀⠠⠈⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢈⠧⠄⠀⠄⠀⢰⠁⠀⠠⠀⢈⢠⡀⠀⠀⠘⢀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠒⠀⢆⠈⢙⠡⢀⣠⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⣀⠤⣿⣇⠀⠀⠀⠀⠁⠉⠀⠀⠘⢀⠤⣀⠀⠀⠀⠂⠀⠀⠀⡀⡾⠁⠈⢀⠀⠠
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠉⠲⡀⠀⠁⠠⠀⠁⠐⠁⠀⠈⢺⡄⢀⣀⠀⠀⠀⡿⠂⠈⣀⠀⠈
⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠖⠒⠲⠾⣿⣿⡅⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠠⠀⢄⡀⠁⠀⠀⠀⠸⠁⠈⠱⣆⠀⠀⠀⠀⠀⠀⠤⠠⠷⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠉⠳⡄⠀⠀⠀⠆⠀⠀⠀⠈⠀⠀⠀⢰⣠⠤⡋⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠁⠀⢄⡀⠀⠀⠈⡀⠀⠀⠀⠰⠂⠠⠄⠀⠀⠒⠉⠙
⠀⠀⠀⠀⠀⠀⠂⠰⠉⠄⠀⠀⠀⠀⠀⠀⢀⠈⠙⢙⣆⢀⠢
⠀⠀⠀⠀⠀⢀⠈⠄⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⣾⡅
⠀⠀⠀⢀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⠀⠁
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠁⠀⠀⠀⠐⠂

⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡤⣤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⢈⡁⠀⠠⡀⡀⠁⠈⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣲⠮⠃⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠉⠁⠱⣄⠀⠀⠐⠀⠀⠔⡤⡀
⠀⠀⣀⠀⢁⡀⢀⠚⠀⢀⡀⠀⠂⠐⠀⠠⠀⠀⠂⢀⠀⠁⠀⠀⠀⠀⠂⠀⡀⠀⠀⠰⠋⡁⠈⠉⠘⠤⠀⠀⠀⠀⠐⠉⠇
⠀⡐⠀⠀⠈⡬⠀⠀⠈⣈⠁⠐⠂⠂⡀⠀⠀⢀⠀⡀⠂⠀⣄⣀⠀⠀⠀⣀⡈⢀⢘⡀⠀⠐⡄⠁⠁⢀⣂⠀⣀⠀⡀⠀⠈⢀⣀
⢸⢡⡀⡼⠀⠀⠀⠀⠈⠀⠉⠚⠇⣀⡀⠈⡀⢀⠁⡀⠠⠈⠉⠛⠓⢀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠂⢀⠀⢀⠀⠀⢀⣀⠐⠋⠉⠁
⡄⠈⠱⠃⠀⡀⠀⠀⠀⢀⠄⠀⢀⠀⠠⣠⠀⢈⠀⠃⡒⠀⠐⠛⠠⠈⠀⠀⢙⠀⠂⠉⣍⠀⠀⠀⠈⠀⠀⡈⠘⠀⠀⠀⠀⠉⢲⢨⠧
⠷⡀⢂⠁⣀⠐⢌⠁⠐⡀⢪⢄⠔⢀⣠⡀⠀⠄⠀⢂⡥⡤⢀⠀⠃⠀⠀⠠⡀⠀⠆⠄⠐⠀⠁⠀⡀⠐⠀⠁⠈⠂⠀⠼⠰⠃⠬⠀⠉
⠀⠀⢸⡀⠈⠀⠈⠀⢀⡐⠈⠀⢀⠙⠟⠓⠀⠀⠀⢵⠣⠀⠀⢀⣀⠂⠀⠀⠈⠀⢀⠚⠀⠀⣅⠀⠈⠃⠀⠀⠁⠀⠀⠀⠠⠀⠂⠁⠸
⡀⠀⢻⠁⠉⢠⣦⡆⠀⠀⠄⡀⢊⣱⠂⠠⠂⠀⢀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⢻⡄⠃⠐⠀⠄⠀⠀⠀⡀⡀⠊⠀⠀⠀⠀⢀
⠀⠀⢀⣠⠄⠈⠉⠀⡂⠀⠀⣀⠀⢻⣤⡠⠄⠀⢄⠀⠀⠐⠀⠀⠀⣠⠶⠞⠀⠠⢀⡅⠀⠁⠀⠆⠁⢀⣁⠄⠈⡙⠛⠄⢀⡉
⠈⠀⠂⢲⣀⠀⠄⠋⣴⡀⠃⠠⢀⠀⢪⢂⠀⠈⣀⠐⠠⠀⠔⠀⡂⠀⠰⠁⠄⠀⡄⠻⢦⣅⢠⠀⢁⡌⢰⠂⠃⣰⡔⠀⠀⠀⠗⣂
⠁⠀⠄⠠⡌⡈⢀⠀⠈⢇⠀⠀⠀⠀⠈⡅⣇⠀⠀⠑⢄⡔⠂⡀⠀⠜⡓⠀⣈⠀⡤⠀⡀⠚⠉⡦⠀⢠⠉⡄⠒⠈⢹⡿⠤⠄⠀⢧⡤
⢕⣦⣠⠰⠂⠐⠏⢱⡀⠾⡀⣅⠘⡍⡄⠰⠵⠿⢠⣄⣲⠵⠧⠤⣦⡀⠋⡀⠈⡾⠻⠧⣤⠺⢄⣁⡄⢈⣄⢠⡀⢅⠽⠈⣔⠴⠤⢾⣶
⠐⠈⠈⠑⣿⢦⣆⠀⠁⠐⠀⠘⢊⡀⡁⠀⠀⢚⣻⡹⠃⠀⠃⠂⠈⠓⠀⠑⠾⠁⠀⠀⠉⡾⢫⠉⢤⠘⠛⣆⠀⠘⠈⠒⠋⢒⢸⠃⠂
⠀⠐⠐⠀⠁⡀⠁⠑⠀⢀⣀⢠⠀⢃⠀⢀⠀⠀⢹⠢⠀⠀⠰⠊⠀⠀⡴⠂⠀⠀⠊⠄⠠⠁⠠⠀⠈⡀⠀⠈⠙⠎⣔⠤⡅⢠⠉

⠀⠀⠀⠀⠀⠀⣤⣄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢻⡈⢳⣼⣧⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢸⡷⢌⣇⠙⢧⡀⠀⠀⣿⣇⣴
⠀⠀⠀⠀⠀⠀⠀⣿⣄⠙⢦⡀⠙⢷⣄⣿⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠻⣌⠓⢤⡉⠢⣄⠈⠻⣦⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠰⣿⡷⢄⣈⠑⢷⠀⠀⠈⠻⣄⢛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣃⡀⠉⠚⢷⠀⠀⠀⢹⣮⡗⠙⢧⡀⠀⠀⠀⠀⣠⠶⠒⠛⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣉⣉⣉⣉⣹⣄⠀⠈⢷⣿⠄⠀⢳⣀⣀⣤⠞⠁⠀⣶⡆⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣤⡤⠤⠤⠚⣆⠀⠀⠙⢦⣀⠀⠙⠀⠀⠀⠀⠀⠉⠁⣀⣾⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡖⠂⣉⠬⠋⣠⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣠⠔⢋⣔⡡⠊⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣠⡼⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣤⣀⢀⡀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢋⡵⠁⣠⣋⣟⣰⣶⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣉⣤⡾⠋⣠⠊⡨⢋⠟⣹⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⢞⡿⠋⢀⠔⠁⡔⢁⠎⣼⠃
⠀⠀⠀⠀⠀⠀⣠⠼⠋⣡⠋⢀⣴⠋⢠⠎⢠⣏⡼⠁
⠀⠀⠀⠀⠀⠀⠛⠒⠛⠙⠛⠉⠈⣻⠃⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡴⠊⠋⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⠑⠉⢉⠳⣾⡅⡀⡀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⢐⠭⣺⢿⣟⠎⢔⠀⡀⢺⠁⣠⣤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡀⠐⡋⠕⠁⠙⡀⠀⠈⡴⣣⠏⠁⠀⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠋⠲⣽⡳⢦⡁⠀⢸⡗⣀⠞⡕⠁⠀⢀⢔⢄⠄⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠠⡀⠄⠀⠈⠲⣌⡳⣝⣯⡯⢾⣠⣢⠤⠤⣯⣿⢿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢐⣬⣂⣅⠀⠨⠷⢽⢾⡿⣿⡿⣝⡉⠀⠀⡢⣟⢝⢕⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⡻⡻⡕⢄⢀⠀⣠⢋⡜⣹⡭⠦⣝⠢⣬⠪⠪⠂⠁⠀⡐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠐⠝⠌⠎⢂⡾⣡⡎⠀⠀⢿⠂⠀⠑⢮⣓⠴⠴⠴⠼⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣂⠀⠀⣀⣠⢞⡟⠩⡪⢂⣄⣸⣀⢄⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡟⠉⠀⢸⠅⠈⢒⢕⢕⢟⣾⢕⠅⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⠸⡅⡀⠀⠁⢡⠟⢯⡀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⡇⠀⠀⠀⠀⠙⠲⠗⠚⠁⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡾

⢠⣿⢿⡍⠀⢹⠆⠀⢰⣯⣿⡄⠀⠀⠀⠰⣶⡄⠀⠀⣤⣤⣹⣿⡿⢀⣴⣦⠀⠀⠀⠀⠀⣠⣦⡲⠆⢹⡀⠈⢉⣿⣅⠀⠀⢿⢆
⢀⣀⠀⠀⠀⠀⠃⠀⠈⠁⣀⠀⠀⠀⠀⠘⣯⡥⠀⠀⢿⣿⣿⣿⣿⣿⠿⠿⠃⢠⡄⣀⠀⠻⡯⠁⠀⠈⣇⠘⠉⠛⠁⠀⠲⡾⠟
⠹⠟⣧⣴⢂⠀⠀⠀⣾⣈⠿⠓⣀⢰⡶⣶⠌⠀⠀⠀⠀⣠⣿⡿⣿⣿⡀⠀⠺⢾⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣷⡗
⣄⣤⣿⣿⣛⠁⠀⠀⠀⠀⠀⢀⣤⣬⣿⣇⠀⠀⠀⣤⣤⠛⠉⠀⠻⡿⣻⡄⠀⠘⠋⠋⠀⢀⡀⠀⠀⠀⠀⣶⢷⡀⠈⠉⠙⠁⠀⠀⢀
⠋⢿⣻⣼⣯⢶⡹⠾⢿⣄⠀⠘⣿⣿⣿⠁⢀⣾⣦⣿⣏⣴⣦⠀⠀⠀⠿⠛⠀⠀⠀⠀⠀⠿⣇⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠈
⣿⣫⣿⢻⣷⠟⣁⣠⡀⠸⠇⠀⠀⠀⠀⠉⠀⣽⣿⢿⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢁⣀⣀⡀⢠⣶⡆⢴⡀⢠⠀⠀⣤⣰⢾
⣿⡶⠷⠟⠁⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠛⠛⠀⠀⠀⠁⠀⠀⠐⢷⣾⣇⠀⠀⠛⣯⡟⠙⠀⠀⠛⠙⠁⠈⠀⠷⣿⣿⣀
⠿⣏⢶⣆⠀⣭⣍⡋⠉⢠⣾⣿⣧⣶⡀⠀⠀⠀⣰⣦⣿⡦⣤⣿⣏⡾⣿⡀⠘⢿⡏⠛⠀⠀⠐⢿⣿⣿⡷⠀⠀⣴⣤⣴⢠⣸⣟⣽⣿
⡆⢹⡆⠿⣿⣿⣿⠁⠀⠘⠟⠋⠻⠿⠁⠀⠀⠘⢿⣿⡟⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠛⠟⠁⠀⣶⠉⡀⠈⣷⣿⡿⣿⣛
⣷⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⢠⣶⣶⡄⠉⠁⣶⣄⠀⠀⠀⠀⠀⠀⣰⢾⣿⣶⡄⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣧⡙⢻⣮⣯
⠁⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⡄⠀⠀⣀⣠⣿⡅⠀⠠⣯⠁⠀⠀⠀⠀⠀⢺⠝⠃⠈⠉⠀⠀⠀⢀⣄⣰⣶⣄⠰⠛⠛⣛⡃⢀⣴⢀
⠀⠠⣿⣿⣿⣿⣿⡆⣠⣼⣶⣰⣧⣄⠀⠈⠈⠉⣀⡐⣶⡾⢃⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠿⠿⣿⠀⠀⢻⣿⣷⣾⠍⠾
⠀⠀⠠⠿⣿⠻⠋⢁⣿⣿⣿⣿⣿⠟⠃⡀⠀⢠⣿⣿⠷⠀⣿⣿⡿⣿⡉⠀⢀⣀⠀⠀⢀⣀⣀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠉⠉⠁⣀⣛
⣠⣤⡀⠀⢻⠀⠀⠈⢻⣿⣿⣿⡯⠀⣿⠏⠀⠀⢀⠉⠀⠀⠀⠘⢙⡇⠀⠀⠛⣿⠀⠀⢺⣿⡉⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⣀⢻⣿
⣿⣿⠃⠀⠘⠀⠀⠀⠀⠙⠋⢛⠁⠠⠈⠁⠀⠀⡌⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⣿⢠⠀⠘⠛⠛⠃⠀⣀⣤⡀⣴⣄⡀⠀⠀⠻⣿⢷⣿
⠻⠿⠀⠀⢀⡀⠀⠀⠀⠀⠀⢻⠿⠀⠇⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠉⣩⣶⣶⠀⠀⠀⠲⣿⣿⣿⣿⣿⣏⠀⠀⠀⢠⣿⡏
⠀⠰⣿⣶⣼⠃⠾⠿⣷⡄⠀⠘⢷⡄⢈⣀⣶⣿⣷⣦⡀⠀⢠⣴⡦⠘⢧⣾⣿⠀⠈⠛⠛⠁⠀⢺⣦⠈⣻⣿⣿⣿⡿⠀⠀⠀⠈⠉⠡
⠀⠀⣿⣿⣿⠀⠀⠀⠀⢀⣠⣻⡛⠁⢿⣿⣿⣿⣿⣿⣇⠀⠉⠁⠀⠀⢸⡿⣿⡀⠀⠀⢂⠀⠀⠐⠁⡄⠘⠛⠛⠟⠀⠀⠀⠀⣀⣀
⡀⠀⠾⠶⣿⠀⠀⠀⠀⠨⣿⣿⠃⠀⠀⡟⠉⠉⠉⣉⡛⠂⠀⠀⠀⠀⠈⡏⠉⠁⠀⠀⠈⡄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠄
⠃⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠚⣿⣷⠶⠀⠀⣀⡀⠀⠇⠀⠀⠀⣀⣴⣷⣦⡀⠂⠀⠀⣀⡀⠀⣴⣶⣶⠘⠛⠁
⠀⠀⠀⠀⠀⣴⢆⣿⣿⣷⠄⠀⠀⠀⣼⢀⣀⡀⠘⠏⠙⠃⠀⢾⣿⡿⠹⠇⠀⠀⢀⣿⣿⣿⣿⣿⣷⠄⠀⠻⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⣽⠁⠈⠛⠛⠀⠀⠀⢠⠇⣿⡟⠃⠀⠀⠀⠀⠀⠈⠋⠁⠀⠹⠀⠀⠾⠟⠛⠛⠛⠻⠁⠀⢀⣶⣿⣿⣿⣿⣷⣿⣿⡆
⠸⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⡜⠀⠸⠿⠛⠃⠚⢿⡆⠀⠀⠀⢀⠀⠀⠁⠀⠀⣀⢰⡄⠀⠀⡇⠀⠸⣿⠿⣻⣿⣷⠉⠛⠛⠁
⠆⠀⠀⠀⠀⡇⢀⣤⣴⣤⡀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡿⣢⢌⠀⠀⢛⣿⣟⠋⠀⢻⠀⠀⠀⠀⠻⠿⣿⠀⣀⡀
⣰⣿⣧⣦⣀⣃⣪⣝⣛⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣾⣷⣀⣀⣁⣛⣀⣀⣈⣉⣉⣀⣀⣈⣇⣀⣰⣶⣶⣄⣀⣀⣿⣿⣀⣀
⣿⣿⡋⡛⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠊⠀⠠⠀⠀⠀⡀
⠀⠌⠀⠀⠠⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⢣⠀⠀⠀⠀⠁⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠛⠀⢀⣀⠀⣁⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⢃⠀⠀⣶⠮⢦⡜⢡⠀⡀⢀⡄⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢀⠴⢈
⠈⡈⠛⠚⠳⣃⠌⢀⢠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠋⠀⠀⠀⠘⡆⡠⠂⢁⠇⠀⠀⠐⠀⠀⣵⡀⠈⠄⠀⠀⠀⢨
⠦⠀⠀⠀⠀⢈⡠⠋⠀⡸⠀⠀⠀⡀⠀⣂⠒⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢠⠌⠀⢠⠒⠔⢀⠀⠀⠀⠁⢌⡀⠀⠀⠨
⠀⠀⠀⠀⡠⠋⠀⢠⠔⠁⠀⢀⠄⠄⠐⠉⠑⠀⣂⠀⠀⠈⠣⡀⠀⠀⢀⠊⡀⠄⠂⠁⠀⠀⠰⠀⠀⠙⠆⠀⠀⠀⠀⢣⠀⠀⠀⠀⢄
⠄⡇⠀⣈⠄⢲⠋⢠⠀⠀⠀⠸⠀⠙⢇⠀⠀⠀⠘⡄⠀⠀⠀⠈⣄⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠢⢀⠀⠀⠀⣆
⠀⠇⠜⠁⠀⠘⠀⠈⠀⠀⠀⠀⠠⣀⠀⠀⠄⠀⠀⢰⠀⠀⠀⠀⡌⠀⠀⠀⠀⢠⠀⡄⢀⠔⠦⣄⠀⠉⠁⠂⠐⠚⠦⢀⣸⡀
⠀⠂⠀⠀⠀⠀⢰⢠⠀⠔⡩⢳⡆⠰⠉⠙⠂⠚⠦⠤⠇⠀⠀⠀⠀⠀⠀⡀⠀⠸⢐⢠⠂⠘⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄
⠀⠀⢀⠀⠀⠀⠇⣼⡶⠈⠀⣸⠁⠁⠀⣠⠦⡌⠀⢠⠀⠑⣠⡱⢴⡘⠓⢤⠀⠀⠀⡾⠁⠀⠈⠀⡤⢠⣰⢂⠀⠘⢄⠂
⢲⠀⠸⠀⠀⠀⠀⠘⠁⠀⣰⢃⡞⠲⡄⠁⠀⠱⢠⡵⡏⣀⢸⡄⠀⠉⠀⢄⡆⠐⠰⠀⠀⠀⠀⠀⠀⠀⠁⠂⡴⠃⠠⠣⡱⡀⠄⠀⢼
⠸⠀⠀⢀⠤⢾⡘⠣⣀⢚⠇⡜⠑⠆⢁⣴⢶⣴⠋⠀⣯⣕⠈⠛⠇⠀⠀⠀⠹⡀⠰⡴⠀⠀⠀⡀⠀⠀⠠⠋⢀⡤⠃⠀⠙⠄⠈⢀⢸
⠀⡄⠰⢼⣠⠊⠉⠀⢽⠀⣀⣇⠀⠐⠎⠀⠀⠈⡃⠞⢁⡎⢦⡀⠈⠢⢀⠀⠀⢱⠁⠰⠀⠀⢄⠀⠀⢀⠀⡄⢏⠀⠲⠀⠘⢂⠀⠨⠘
⠀⡇⠠⠀⠙⢄⠀⠀⠈⣦⠸⠈⢠⡀⢀⠀⢀⠘⢁⡤⠚⢢⡐⠈⡁⠐⠐⠓⠠⡸⢆⠂⠀⡀⠘⠇⢊⢘⠀⠀⡌⠼⠀⣄⡀⡀⡄⠀⡇
⠀⠂⠀⡑⠠⢠⢁⣠⡀⢸⡾⠀⣄⡌⣰⢠⠶⢨⠇⡟⡀⠂⡑⡄⠃⠀⠐⠀⢀⢀⠄⠠⣂⠃⡀⠁⢸⠈⣼⢸⢱⣄⠃⠊⡿⠐⡎⠠⡀
⠀⡅⠀⠀⠀⠀⠘⠀⠀⡯⠁⡴⡘⡅⠹⠀⠈⢸⢰⢠⣧⠒⢳⡌⠀⠀⠂⠀⢂⢢⠀⡀⢁⡄⢻⠀⢸⠸⡃⠀⣸⠏⠀⢠⠃⠆⡇⢠⠙
⠀⠄⠀⠀⠀⠀⠀⠘⠄⢆⠤⠈⢳⠀⡀⢀⣦⡏⠈⢬⠏⠀⡸⠰⡀⠀⠀⠀⠀⠑⡁⠱⠀⣧⠸⠆⠀⠐⠃⠀⣔⢀⡔⠃⠀⡀⠁⡀⠠
⠀⠃⠀⠀⠰⠀⠀⠀⠀⡫⠀⠆⠸⡇⡧⢈⠀⠀⠀⠛⢀⡴⠁⠀⠀⠠⡀⠀⠠⠀⠆⠀⢄⢻⠀⠀⠀⠀⠀⠀⠻⠊⠂⡄⡀⠁⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢒⠻⣩⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣲⠇⣼⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⠀⠀⠀⠀⠂⠳⠞⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠈⠹⣀⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢰⡂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⠠⡀⢻⡄⠀⠀⠰⡄⠃⠀⠀⠀⠀⠀⠀⠈⠹⠷⡄⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠻⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠺⣶⠀⠀⢀⡧⠀⠄⠠⠄⢀⠈⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠒⢂⠀⠛⢊⡄⠟⠉⠀⠠⣆⣟⣡⠞⠀⠴⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠃⠈⠁⠀⠀⠀⡀⠀⠀⣳⣌⡉⠉⠒⣄⢀⣤⡼⢉⣬⣧⣈⣉⠚⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⢲⠞⠛⠀⠈⠀⠀⠈⠉⠉⠀⠤⣈⣍⠹⣦⣄⣦⣌⠁⢰⣦⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣢⡈⠐⢁⠀⠜⢻⠷⡂⢺⡿⠟⠐⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣽⣷⣶⡄⠀⠘⠀⠓⠀⠣⠤⠁⠀⠀⠀⠀⠀⢴⠊⠹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠂⠐⠀⡠⠘⡷⠀⠀⠀⠉⠀⢿⣿⠿⠛⡳⠀⠀⠑⠳⡄⠀⠀⠀⢂⠀⠀⠀⠀⠘⣤⣴⢛⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢡⠎⣠⣄⠃⠀⠀⡀⣠⡆⠀⠀⣄⠀⠿⠀⠀⠀⠠⣫⠤⡀⠀⠀⠀⠀⠀⠀⠁⢿⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠼⣜⠑⠆⠀⢸⡧⢿⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⢁⢦⠙⢄⠀⠀⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣰⠿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢲⡀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠹⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⡚⠀⠀⠄⠀⡀⠈⠌⣽⠁⠀⢀⣈⡻⢀⡀⠀⡍⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠀⠀⢀⣀⡀⠀⠀⠰⠇⢰⣧⢠⣶⡄⠀⢘
⢉⠁⣷⠀⠀⠀⡿⠀⠀⠉⠀⠀⠚⠿⠀⡈⠁⠀⠁⠀⠀⠀⢲⡼⣦⣄⡠⠀⠀⠀⠀⠀⠀⢋⣾⡿⠃⠀⠀⠈⢾⢋⣦⣉⡀⠐⠟
⠀⣾⣙⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⠆⠀⢀⣤⣤⡀⠀⠀⠸⣿⣧⣿⣿⣖⠀⠀⠰⠾⠂⠀⠈⠁⠀⠀⠀⠀⢉⣈⣧⣽⡋
⣎⠢⠔⠀⠀⠠⠀⠀⠀⢰⣥⣟⡧⠀⠀⠘⠙⣿⡃⠀⠀⢀⣹⡉⠙⣯⢷⠀⠀⠠⣄⠊⠀⠀⡀⠀⡀⠀⠀⠘⠟⠓⠀⠀⠀⠀⠸
⠀⣶⠶⠀⠀⢠⡀⠃⠰⠿⡽⢿⡇⠀⠀⢀⣤⣤⠀⠀⠀⠈⠉⠘⡏⠁⠀⠀⠀⣠⠄⠙⠀⢀⢈⣠⠀⠀⠀⢀⠀⠀⠀⣴⣦⣤
⠀⠦⠀⠀⠀⠀⠉⠐⢦⠀⠇⢀⠀⡄⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠥⠤⢙⣇⣤⠔⠁⢀⠀⠘⠛⢻⠟
⠀⠀⠀⠀⠀⠄⠀⠀⠈⢳⡀⠌⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠁⠠⣾⣿⣷⠀⠀⠘⡄
⠀⢀⠀⠀⣤⠀⠈⠛⠀⠀⢷⡘⠀⠀⠀⡀⢀⢀⡀⣀⣀⢀⡀⢀⡀⡀⣀⣀⣀⢀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠀⠀⠀⠈
⠀⢸⠀⠀⠀⠐⠿⠀⠛⠀⠘⡇⠀⠀⠈⠃⠈⠈⠁⠉⠉⠈⠉⠈⠀⠁⠁⠁⠋⠈⠀⠉⠈⠁⠀⠐⠲⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⣬⠀⠸⠿⠀⣠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⠑⣄⡇
⢠⠋⠀⠀⠀⡴⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠀⠆⠀⢠⠀⠘⢿⣼
⡏⠀⠀⠀⠀⢠⡗⠀⠀⠂⠀⠎⠀⠀⠀⣄⠀⣠⡀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠾⢃⡈⠇⠀⠀⠀⠀⠈⠂⠀⠀⠀⢸⠀⠀⠀⣿
⠀⢀⠀⠀⠀⠰⡟⠀⠀⠀⠀⡀⠀⠀⠀⣤⢠⠨⢀⠀⠀⢀⣥⡤⢐⣂⠀⠀⠀⠐⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⢿
⠰⢜⣑⠏⠀⠀⠠⡀⠀⠀⠘⠤⠀⠀⠛⢾⠎⠾⡭⠀⠀⠸⠿⠷⣿⠟⠃⠀⠀⠀⠀⠉⠑⠀⠀⣴⣿⣿⣿⡄⠀⠈⠿⠟⠀⢀⣈
⡇⠈⠈⠀⠀⠀⣀⣀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⡟⣉⠋⠀⢀⣔⡓⠀⢾⣿
⢣⣄⠰⠁⣠⡀⠁⠛⠀⠀⢰⣿⣿⣿⠆⠀⢒⡀⢦⣠⠄⠀⣈⡿⢃⡀⠰⣞⣷⣷⠆⠀⢾⡿⠀⠀⠤⣥⠉⠀⠀⢰⢚⣂⠀⠈⢩

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣚⣚⣫⣶⣿⣿⣿⣷⣮⢳⡄⢀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢟⣫⣶⣶⣮⣝⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⣿⣿⣿⣿⣷⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣇⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣮⡻⣿⣿⣿⣷⢻⣿⣿⢧⣿⣿⠿⣟⣿⣿⣿⣿⣿⣿⣷⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣵⣶⣶⣶⣶⣯⣤⣉⡻⢿⣧⢻⡏⡾⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢷⣮⡁⢐⣛⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡟⣼⡏⣿⣿⣿⣶⣦⣌⡩⣭⣿⣭⡽⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢰⣿⣿⡸⣿⣿⣿⣿⣿⣿⣶⡝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⣿⣿⣿⣿⣿⣿⣿⡟⣼⢸⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⡎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡻⣿⣿⣿⣿⣿⠟⣸⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢮⣽⣛⣭⣴⢧⣿⢡⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⢸⣮⡻⣿⣿⣿⣿⠿⣡⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣿⣿⢸⠈⠙⠲⠶⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣛⣛⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡦⠀⠀⠀⠈⠁⢀⣆⡀⠀⠀⠀⠈⠀⠀⠀⣁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠑
⠀⠀⢀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠐⠿⡗⠀⠀⠀⠀⢀⠐⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢀
⠀⠀⠀⠀⠀⡀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠚⠖⠀⠀⠀⠒
⠀⠀⠀⠑⢆⠘⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⡀⣠⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠈
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠠⠴⢲⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠞⣿⢛⡍⢙⡬
⠀⠀⠀⠀⢀⡠⣾⢘⣳⣬⣎⣨⠉⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡂⠀⠀⠀⠀⠠⠀⢀⡤⢿⣾⣿⣿⣷⣜⠣
⠀⠀⠠⡔⠂⣀⣽⢸⣿⣿⣿⣿⣯⡟⡃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠘⢉⢠⠆⠀⠀⠀⠀⠘⠳⣿⣿⣿⣿⣿⠮⠅
⠀⠀⠀⠀⠀⠜⡻⡺⢿⣿⣟⡟⡢⠔⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠹⠗⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠥⠜⢣⣎⠉⠹⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠳⠄⠜⢃⠏⠁⡗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⣸⣀⣀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡄
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣄⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠠⠐⠶⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠊⡀⠱⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⡉⠋⠀⠀⠀⠀⠐⠀⠀⠀⢀⠁⣠⡭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠆⠹⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠒⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣥⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⣿⣿⣷⣿⣷⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⡀⠀⡄⠀⢀⠀⢀⣀⠀⢀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠑⠃⠀⠃⠀⠋⠂⠘⠙⠀⠈⠀⠑⠂⠐⠙⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⣄⠀⠀⠻⠀⠀⠀⠀⠀⠀⣾⣠⠀⣀⣤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⠀⠉⠀⡀⠀⠀⠀⡉⠁⠀⠀⠀⠀⢀⣿⣦⡿⠟⠰⢛⢡⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠀⠈⢐⡏⠁⠀⠀⠀⡁⢀⣀⠀⠀⢾⢿⣿⡍⠀⣦⣼⠟⠈⢻⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠦⠶⠻⣄⠀⢀⡀⠛⠁⠀⠀⠐⡾⠃⠈⠛⠻⠶⠮⢡⠶⡿⣿⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠢⣀⠀⠀⠂⣠⣤⣄⣣⠠⢔⡒⢳⣆⡠⠆⠈⠽⣿⣿⡻⡥⢘⡿⢚⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰⣠⡙⠁⠀⣴⣿⣿⣿⠏⠐⠀⠘⢀⡎⠀⠲⠖⠀⠀⡈⢀⠀⣾⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢸⣆⣄⡀⠀⠈⠣⡄⠠⠀⢉⠟⠋⣍⠈⢢⢁⠴⠿⠉⠀⣀⡀⣄⠈⠀⠠⠆⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠆⣉⣿⢠⡹⣤⠁⡶⡀⠂⠈⠃⠠⡀⢠⠆⠀⠀⠀⠔⠀⣥⣿⠂⠀⠀⣰⠷⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠗⢠⠞⠙⠡⠤⠙⢤⣴⠑⠙⠲⡁⢤⣀⣅⠀⠁⣸⡏⠀⢈⠼⣿⣿⠺⠀⠀⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠲⠞⠀⣩⡤⠀⠾⠈⠁⠈⠁⠄⠑⢤⣴⣿⣿⣿⣷⡄⠘⣧⠀⣀⢧⠅⠊⡀⠀⠐⠘⠚⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠸⡆⠀⠘⠷⠂⠀⢠⠀⠘⢯⣻⡿⠿⠃⠀⠈⢷⠍⡉⠁⠀⠀⠀⣈⡀⠀⣠⢐⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⢀⡆⢀⠀⠈⠃⠀⠀⠀⠀⠤⡠⠤⠀⠄⠂⠠⠘⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠂⠀⠀⠀⠘⠃⠁⡀⢀⣀⠀⡤⣘⠀⠊⠀⢐⠂⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠠⠀⠈⠉⠉⣄⢀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠎⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⠐⢛⡻⡆⠀⠈⢻⡀⠒⣀⢲⡀⠈⠀⠘⠀⠀⠺⢙⣒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠒⠀⠀⣉⠎⠀⣠⠠⣌⡁⠀⠀⠀⠎⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠰⢫⡀⠈⠻⠄
⠘⠀⠘⠀⠐⠂⠀⠁⠘⠂⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠘⠂⠘⠂⠘⠃⠀⠀⠈⠂⠘⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂