Puranas Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⣀⣤⣤⣌⣤⣤⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣤⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠈⠀⠈⠄⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⡿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⠿⢀⣉⣉⣩⣙⠉⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠁⣴⠟⠋⠉⣙⣿⣷⣿⣷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⡐⠀⢀⣳⢰⡿⠿⣿⣿⣽⣧⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣿⡄⠙⠋⡀⣹⣄⣿⡟⠻⣄⢹⠷⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡤⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣁⠀⠀⠀⠀⠀⠀⠠⣷⡴⠃⠀⢙⣷⣆⣠⡥⠽⣻⣿⣧⡑⢚⣿⣦⣬⡿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠛⠃⠀⠀⠀⠀⠀⠀⠉⢀⣀⣥⢈⣻⣿⠛⠓⠚⠋⣩⣿⡇⢻⣏⡉⠛⠿⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠺⢷⣄⣀⠀⠀⠀⣀⡴⠟⠉⢠⣿⣿⠄⢻⡷⣾⣿⡿⢋⠆⣸⣿⢿⣀⣰⠎⠡⢃⣀⠃⠀⠀⠀⠀⠀⣾⠃⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠸⣄⣠⡟⠻⣿⣆⠀⠀⠘⢣⢀⣾⣯⣹⣷⠘⣷⣼⢯⣿⡿⢠⣟⣻⣿⣿⣿⣿⠓⠈⠻⣆⡀⠀⠀⠀⢠⡿⠁⢹
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠛⢏⡠⠀⣿⡟⣿⣾⢳⣾⡿⠛⢷⡿⠛⣦⢹⡏⠀⠙⡇⢸⡏⠭⣿⣿⠻⣿⣦⢀⣾⢿⡇⠀⠁⣰⣿⠃⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⢸⣦⣀⣼⡇⣼⣿⣧⡍⠀⠀⠘⣧⠀⠰⠈⢃⠀⢼⠃⣿⣿⣶⣿⠇⠀⠙⢁⠺⠃⣨⡀⢀⣰⠿⠁⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⠇⢿⣿⣿⣿⣆⠀⢸⣟⡀⢀⢀⣌⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⢮⠁⢰⣿⣷⣿⣿⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⢸⣿⣿⣿⣿⢻⣿⣿⣿⣿⢰⣧⣄⣴⡆⣿⣿⠟⠀⣰⣆⠀⠀⠀⠀⠉⣿⣿⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⣿⣿⠟⠀⠀⢈⠿⠛⠁⠀⠀⠿⣿⣿⢄⡘⣿⠉⢙⠇⣿⣿⠀⣴⣿⣿⣆⠘⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠂⠀⠀⠘⣿⣷⠀⡠⠄⣲⡿⠋⠀⠀⠆⠀⠀⢠⡀⠠⠀⠀⠙⠻⣷⣅⣈⣑⣡⣾⣿⣿⣾⣿⣿⣿⣿⡇⡀⠀⠀⠀⢡⡆⠀⢺⣷⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢘⠀⣿⣿⡀⠀⠐⠛⠀⠘⠀⠀⠠⡀⠀⠀⠈⠀⠀⠀⣰⡆⡀⠹⠿⠿⢿⣿⣿⣿⣿⣿⣿⣼⣿⣇⠀⠀⠀⠀⠀⠓⠀⠿⣿⣿⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠈⢠⢸⣿⡇⠀⠀⠀⠁⡀⠀⠀⠄⠀⠀⠀⠀⢀⣠⣴⣿⣷⣇⡀⢠⢜⣿⣯⡉⠉⠉⠁⠙⠻⣿⣍⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⢻⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⡇⠀⠀⣄⠀⠐⠄⠁⠂⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣶⣶⣿⣿⡿⠿⠿⠟⠂⠀⠀⠀⠛⣧⡀⠀⠀⠀⠀⠀⠈⠺⣿⣿⣶⡇
⠀⠀⠀⠀⠀⠆⠀⠀⢸⣿⣧⠀⠀⠙⣦⡀⠀⠁⠒⠒⠒⠦⠀⣿⣿⣿⣿⡏⡏⡌⠉⢻⣏⢿⣦⠀⠀⠀⠀⠐⠀⠀⠀⣱⡄⠀⠀⠀⠀⠀⠀⠈⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⠀⠀⠀⠈⠻⢶⣦⣤⡤⠤⠐⠚⠋⢀⡟⣽⠆⠀⠀⠀⠰⠿⣶⣤⡤⠄⠀⠀⠀⠀⠀⠚⠛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠈⠿⣿⠀⠀⠀⢀⠞⡹⢀⣴⣤⣠⡀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠔⠁⢸⣿⡿⠀⣿⣿⣧⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠲⠄⡀⡠⠀⡼⠟⣷⣼⡿⠻⠿⠟⢛⡿⠟⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠑⠂⠈⠑⠲⣷⢸⣿⡏⠤⠤⠘⠓⢉⡠⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⢻⣬⣿⣇⣠⣤⣤⣍⣁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠀⠀⠀⠘⠛⢿⣟⣛⢉⠉⣉⢛⠿⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠙⢿⣿⣄⢠⡄⢠⣾⠟⠉⠀⠀⠀⠀⠺⣶⣿⠿⠉⢿⠧⢠⡬⠼⠂⠂⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢶⣿⠧⠀⠀⠀⠀⡀⢀⡆⠈⡀⠀⠀⠀⢀⣀⣤⣶⣤⣤⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠀⢳⡀⡘⠀⠁⣀⣠⣤⣶⣿⣿⠿⠛⠋⠁⠈⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⣬⣤⣤⣤⣶⣶⣿⠿⠿⠛⠋⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⠀⠀⢐⠂⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⢷⣀⠶⠻⣦⠐⠚⢷⣀⠚⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣁⣀⣾⣉⣰⣿⣉⣉⣉⣽⣿⣿⣩⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠭⠿⣿⠿⠿⢿⠿⠿⠿⠿⣿⣿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠏⠀⢀⠟⢀⣀⣀⣀⣻⣷⠄⠸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠶⣾⡶⠿⠶⠂⠛⢋⣙⠋⣉⣛⡂⢳⣶⣷⡏
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢯⠆⠙⠿⠝⡦⣴⠀⠾⠟⢼⡿⠿⣷⣿⣿⢻⣿⡀
⠀⠀⠀⡀⠀⠀⣁⠙⡆⠀⠀⠀⠲⣄⣀⣿⣧⣴⠙⢫⠀⢠⣶⣴⣦⣴⠟⠛⢿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄
⠀⠀⠀⡅⢠⣶⣿⣟⠀⠀⠀⠀⠀⠘⠛⣿⣿⣣⣀⠂⣀⡿⠿⠿⠿⣿⡘⠘⣰⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢴⠀⣾⣶⣧
⠀⠀⠀⠀⠙⡻⢏⡍⠀⠀⠀⠀⠀⣠⠄⣿⣿⡘⠯⠏⢹⣷⠦⢴⣿⡿⠉⣿⣿⠙⣧⢹⣿⣄⠀⠀⠀⠀⠀⢻⣟⠛⣛⡿
⠀⠀⠀⠀⠀⠁⠘⢷⠀⠀⠀⠀⣶⣟⢰⣿⣿⡟⡀⢀⣼⢻⣄⠁⣈⡔⢰⣿⣿⣴⣿⢻⣿⣿⣷⠀⠀⠀⠀⢼⣿⣶⠁
⠀⠀⠀⠀⠀⠀⣶⡿⣷⣄⡀⡀⠀⠉⢸⣿⣿⡇⠐⢼⣿⣿⣿⠉⠻⡄⢸⠋⢹⣿⡇⢸⣿⣿⣿⡦⠆⠀⠰⣾⡿⠏
⠀⠀⠀⠀⠀⠀⢸⣷⡌⠛⠁⠀⣀⣤⣤⣿⣿⣷⠘⢺⠍⢉⠟⠀⠀⠃⣼⣿⣾⣿⡇⣹⣿⠿⠿⠿⠀⠀⢱⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⣠⣤⣴⣿⡋⠀⠀⠈⣀⣼⣧⣈⣿⣷⣄⠤⣀⠄⣙⠩⣿⡾⠟⠿⢦⣤⡙⢷⣄⢠⡾⠃⢀⣤⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⡰⡹⣿⡿⢻⣿⢿⣿⣿⣿⣿⣿⡿⣯⢸⣟⠾⣡⡾⣻⣦⣿⣶⣤⣴⣾⣿⣿⣾⣿⣿⣴⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢠⠌⡐⢱⣿⣿⣾⢏⣼⣿⣿⣿⣿⣿⣷⣋⠘⢁⣴⣿⣶⣿⣿⣿⠟⢧⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡀⠖⢁⠞⣰⢏⣿⣿⢃⣾⣿⣿⣿⣿⣿⠘⢟⣛⠴⠛⣛⣩⣿⣿⡿⠋⠀⢳⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢃⠐⠋⣰⢏⠞⠁⢠⣾⣿⣹⣿⣿⣟⣉⠶⠁⠁⠀⠀⠙⠉⠉⠀⠀⠀⠀⠈⠿⣌⢿⣏⣉⠉⢻⣿⣿⣿⣿⣿⢿⣿
⠀⠀⠀⠈⢀⠸⢣⣆⠀⣴⣿⡟⣵⣿⡿⠁⠘⠿⣦⣤⣀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢻⠉⠁⠀⢹⣿⣿⣿⠇⢠⣬
⠀⠀⠀⠀⢌⣰⡿⢋⣴⣿⣟⣴⠿⢻⡀⠀⠀⠀⠛⢿⣭⣿⣿⠀⣴⣣⣴⠀⠀⠀⠀⠀⠈⠷⡐⣷⡄⣠⣼⣿⠋⡜⠁⢠⣸
⣀⣀⣀⣄⣼⡿⢀⣾⣿⣿⠟⠁⠀⠀⠱⣄⠀⠐⠀⢀⣿⣿⣿⣶⠿⠿⠿⢿⡿⢿⣿⣶⣿⣾⣷⡜⣿⣿⣿⣿⡿⠀⢠⢉⣿
⣿⣛⢻⣿⡟⣱⣾⣿⠹⣿⡀⠀⡀⢀⣴⣿⡟⣦⣄⣼⠿⠛⠋⠀⠀⠀⢀⣀⣤⡾⠟⠁⠀⠀⠙⣷⡹⢿⡈⢽⣷⡶⣷⣾⣿
⣿⣷⣾⣉⣼⣿⣿⣇⣀⡘⣧⡀⢠⠞⢹⣿⠇⠃⠁⠀⠈⠙⢑⣚⣫⡽⠛⠉⠉⠀⠀⠀⠀⠀⢹⢿⣷⡘⣿⣿⣿⣿⣿⣾⣿
⡛⠛⠛⣻⣟⠛⡛⣻⠉⡹⠈⠳⠿⡷⠶⠀⣀⠀⠴⠶⠾⠿⠛⠋⠁⠀⠀⠀⠀⠈⣦⠀⠀⠀⢸⡟⣿⣷⣺⣿⣿⣻⠿⣿⣿
⡄⣼⣘⣻⣿⠛⠛⠛⠛⢛⡀⠀⠀⣤⣤⣶⡿⠁⠀⠀⡄⠀⠀⠀⠀⣰⣄⡀⠀⢀⣿⢷⡆⠐⢛⢀⣿⠟⠛⠛⠛⣿⣿⡿⣿
⠁⠹⠉⢿⣿⠀⠀⠀⠀⠈⠙⠻⢛⡉⢾⡟⠦⣀⣤⢾⡟⣄⡀⣀⡴⢋⡿⠛⠶⠿⠋⡼⠁⠀⣿⠿⠇⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠻⢿⡟⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣦⣶⠶⣋⣠⣤⣙⢋⣴⣾⣅⣼⠿⢶⣾⡷⠶⣶⣿⠀⠀⠀⠀⠀⠀⣿⠛⣿⣿
⣀⣈⣀⣈⣃⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣛⣃⣀⣀⣉⣉⣀⣙⣛⣁⣀⣈⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣋⣉⣋⣙
⣿⣿⡟⠻⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣿⣷⣶⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢸⣿⣿⣛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠘⣿⣇⣡⣼⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀⠼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠉⣾⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠸⣷⠒⠲⡟⠒⢶⣿⡇⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣴⣿⡿⠿⠥⠀⠀⢁⣀⡈⣁⢈⣿⣿⡇⠀⠀⠈⣇⠀⠑⣆⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⢿⣛⣁⠀⠴⠁⣽⡄⠒⠒⢿⣿⣇⠀⠀⠐⢘⡇⠀⢱⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣧⣶⣶⣿⣿⣽⡕⠀⠈⠛⠀⠀⠠⠾⠿⠛⣆⢀⣀⡀⣧⢁⣾⣿⣇
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢀⣤⡀⠀⢀⠤⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠁⢀⣴⣿⣿⣷⣴⠿⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠛⠋⠁⠀⢀⣀⣤⣴⠶⣤⡙⢿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣴⣶⣾⣿⣿⣿⣿⣿⣿⣤⣼⣿⣼⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠛⢉⣩⣿⣿⡿⣿⣿⣿⡿⠛⣿⣿⢿⣿⣿⣿⣉⣝⠋⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢰⣿⣿⣁⣹⣶⣿⣿⣿⠏⠀⢀⣼⣿⢧⡄⠈⢙⣛⢿⣿⣤⣤⡀⠉⠀⠈⠿⣿⣷
⠀⠀⠀⠀⠀⢘⣿⣤⣿⣿⢿⠿⠋⢡⣤⣶⣿⣿⣿⢒⡠⣀⣿⣿⣏⣛⠿⣟⣩⣞⣁⡰⠀⠙⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣿⣷⡶⠿⠿⢿⣿⢿⣿⡀⠓⣿⣿⣿⣿⣿⣿⣾⣿⣯⣿⣥⣶⣤⣼⣷
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣷⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢀⣔⣊⣉⣉⢓⣂⣿⣧⢰⠒⠗⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠒⣁⢻⠟⢉⡽⠛⢉⡹⢝⣿⠛⠋⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠂⢚⡁⠈⠊⠄⠐⠂⠶⢄⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣇⣠⣿⢙⠟⠰⣌⢢⠏⠨⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⢉⠤⢃⠬⡈⠐⠀⡀⠈⠐⢈⡀⠡⠌⠄⡀⠐⠀⠐⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⢠⣶⣦⣶⣋⣨⣷⣂⣀⡈⡏⠀⠀⠇⠀⢠⡰⣄⡀⠀⠀⠀⣀⡋⢄⠀⣠⠊⠖⠀⠀⠀⠈⠃⠄⠀⠈⠐⠢⠠⠄⠉⣀⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡜⠀⠀⠈⢧⠈⣾⣧⣴⡏⠁⠀⠀⠀⣲⣿⣇⠉⡀⠁⢀⠀⠤⠀⢠⠈⠀⠀⠀⡰⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⠀⠀⠀⠀⠅
⠀⠀⠇⡠⢄⠀⠸⡸⡌⢸⠹⠁⠀⠠⠠⢞⡱⣀⠸⢀⠀⠀⠀⠀⠈⠑⢈⠀⠀⠠⠒⠀⠀⠀⠀⠐⠲⠐⠂⠂⠀⠴⠀⠠⠤⠤⢀⠠⣠⠐⡀⠀⠐
⠀⠀⠸⠀⢸⠀⠨⡖⣃⠀⠀⠀⣀⡠⠊⢡⣿⠛⣷⠐⠀⠀⠀⠀⠀⠀⠀⢗⢀⠤⡀⢒⡶⡿⠂⠁⡀⠀⠀⠀⡠⠥⠊⠉⠁⠀⠠⢜⠙⠮⠁⠀⠀⠐⠐
⠀⠀⠀⠇⢸⡀⠀⡧⢽⠆⣀⠎⠈⠀⡱⠡⢈⣉⠨⡤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠂⠀⠀⠀⠀⠈⠀⠨⢁⠈⠀⠀⠀⠀⠀⠀⠐⠁⠙⠀⠀⢄⠀⢀⡀
⠀⠀⠀⢰⡀⡇⠀⡇⢘⡠⢿⣁⣤⠊⠀⠀⢏⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⢀⣀⠀⠀⠷⠀⠒⠀⠀⠀⠁⠀⠀⠀⠀⢀⡤⠈⡁⢒⠈⠀⠐
⠀⠀⠀⠀⡇⢻⠀⡴⠊⠀⡰⠉⠁⠤⠀⠈⠏⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠀⠄⠐
⠀⠀⠀⠀⡇⣼⠀⢉⡡⡎⠀⠀⠀⠀⠚⠀⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠎⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡯⢀⠠⠄⠠⠁⠁
⠀⠀⠀⠀⡇⠀⠁⣩⣴⠇⡴⣀⣀⣀⣀⣠⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢨⢃⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⡙⢈⠀⢈⠁⠀⠈
⠀⠀⠀⢸⡶⣖⣪⣿⣿⢟⣷⣿⠈⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡎⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠎⠘⠀⡄⠀⠈
⠀⠀⣠⢰⣛⣫⡽⢾⣻⣿⣿⣥⠀⢀⣀⣀⣠⣜⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠉⠁⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⠈⠘⠈⠀⠁
⢠⣶⣶⡏⣙⣠⠴⣛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⡀⠀⠠⠁⠞⠀⠄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠰⠄⠠⠀⠀⠀⠀⢀⠠⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈
⠀⢻⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀
⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠺⠯⠟⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠂⠀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠂⡤⠈⠀⡤⠐⠀⠀⠀⠀⠐⡀⠀⠐⠍⠑⠂⠘⠈⠙⠀⡤⡌⠀⠀⠀⢠⢸⠀⠁⠀⠈⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠊⢐⠀⠀⠀⢐⣘⣟⠁⠀⢀⠆⠉⢠⠈⡀⠀⡠⠒⠢⠄⠄⠠⠤⠌
⠀⠀⠀⠀⠀⠀⠈⠂⢨⠾⠀⢘⠈⠉⠀⠀⠀⠀⠐⠈⠀⠐⠀⠀⠑⠦⠀⠤⠊⠁⠁⢀⠀⡀⠈⠀⡀⠐⢣⠀⢰⣈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣄⢣⠄⡈⠑⠀⠰⠀⢠⠠⡀⣀⣤⠆⠀⠀⠀⠀⠠⠁⡰⠠⠂⠆⣀⠁⠈⠁⠀⠀⠘⢎⡉⠡⠆
⠀⠀⠀⠀⠀⠀⠀⢈⢤⢥⠊⠀⡀⠀⠀⠀⠐⠁⠀⡀⡍⠢⡀⠀⠀⠀⣀⠄⠁⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠨⠉⢳⣇
⠀⠀⠀⠀⠀⡀⠀⠈⠠⠖⠂⡀⢦⠀⠀⠆⠀⠠⡔⠁⠀⠀⢀⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆⠀⣠⠚⠄⠀⠐⠒⠂⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠐⢪⢉⠀⠔⠈⠊⠁⠀⠀⠰⡁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠐⠊⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⢀⠀⠀⠆⠒⠒⠂⢸⠀⡇⠀⠀⠀⢱⠂⠀⢂⠀⢠⠀⠂⠀⠐⠊⠈⠀⠀⣀⠈⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡔⠀⡁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⠀⠀⢀⠀⣼⠀⠀⠀⠀⠀⡄⠀⠘⠆⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠣⢀⠂⠀⠘⠓⠀⣄⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠂⠂⠀⠑⠂⠠⡖⠄⢖⠦⡄
⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⢀⠸⠃⠀⠃⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡤⠀⠀⠀⠠⢀⠀⠂⠀⠉⠉⠉⠈⠰⠁⠀⠀⠀⠘⡀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⢀⠀⢀⠀⣢⠀⡀⠀⠀⠰⠂⠲⠄⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠐
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠉⠨⠔⠂⠛⠘⡇⠁⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⡀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⡀⠈⡀
⠀⠀⠀⠀⠲⣀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⡀⠀⠀⠁⠋⠁
⠀⠀⠀⠀⠀⠈⠠⠆⠠⠤⡄⠒⠲⠂⠤⠀⠲⠨⠀⠀⠆⠀⡀⠀⠒⠀⠘⠁⡘⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠁⠀⠀⠣⠈⠀⡀⠀⠀⠀⠈⠢⡈⠀⠀⠀⡠⠈⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢄⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⢀⡀⠄⠂⠁⢀⠄⠀⠠⡄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠔⠑⠄⠀⠈⠀⠄⠀⠀⠈⠉⠁⠀⠈⠉⣀⡀⠠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠸⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠄

⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿
⣿⣇⡀⣥⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠉⠀⠀⠀⠀⠀⠀⠀⢴⣿⣟⣿⡇⠀⢀⣔⢀⠀⠁⠀⠒⣊⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⣄⣀⣀⣀⢀⠀⠀⣀⣠⣽⣿⣿⣿⡦⠀⠈⠙⠒⠒⠛⠓⡋⣉⣁⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠛⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠃⠀⢀⣴⣿⣿⣿⣻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢀⠤⠚⠛⠛⠓⢶⣿
⣿⡇⠀⢀⠀⠙⠛⣿⠋⠽⣛⣿⣿⣿⣿⣷⢠⣾⣿⣿⣿⣿⣿⠿⠋⠀⠰⢤⡛⠈⣠⡬⠲⠀⠀⢠⣿⠺⡺⢾⣿
⣿⡇⠈⠁⠐⠒⡄⢸⡿⢶⡟⠛⠟⢿⣿⣿⣿⣿⣿⣿⠟⡩⠄⠀⠀⠀⠀⢀⠈⠀⠀⠀⡇⠀⢹⣯⣬⣯⢥⣬⣿
⣿⣧⠒⠋⠉⠙⠲⣺⡷⠿⠂⣠⣇⣼⣿⠉⢻⣿⠋⢤⣰⣁⡔⣶⠓⢪⣤⣤⣤⣀⡰⠄⠺⣾⠟⢺⠟⠋⠈⡿⣿
⣿⡷⠒⡶⡀⢄⣤⣿⣗⣶⠦⣯⣽⡄⠙⢿⣿⡏⡇⠀⢹⠙⠻⠍⢺⣿⣵⠞⠡⠣⢻⡴⠂⠈⠀⠚⠀⣤⠂⠀⣿
⣿⣯⣴⣭⣝⡯⠿⢤⣀⣨⡟⠛⢻⣿⣄⣀⣿⣽⣧⣤⣿⣷⣶⣴⡾⣿⡇⠀⢀⣀⠞⠁⠘⠂⠠⠂⠀⢠⠀⠀⣿
⣿⡇⡰⠟⠂⢠⣴⠶⣼⣿⣿⣿⢟⡉⠁⠀⡈⠻⡷⣤⣅⣠⣈⣉⡉⠭⣟⡻⠛⠉⠀⠀⠒⠀⠀⠈⡥⠅⠀⠀⣿
⣿⡏⠀⠀⠀⠀⠀⠴⠇⢰⣽⡇⡓⠀⢀⣾⣿⡆⣷⠀⢉⠉⢁⠄⠉⠙⠛⠀⠀⠀⠀⠢⠠⠆⢀⣤⣶⠶⣶⣴⣿
⣿⡇⠀⢠⡰⠗⠒⠒⠶⣿⣿⣧⣯⠀⠘⣿⣿⣧⣿⡀⠀⠈⠙⠄⠀⠀⢉⡀⠀⣄⠀⠀⠀⢠⡿⣯⢽⡿⣺⠏⣿
⣿⡇⡴⠋⠀⠀⠀⢞⣀⡼⠋⡹⠿⣷⣤⣬⡿⠏⠁⠈⠢⡀⠂⠀⠀⡜⠁⠀⢠⠄⢀⢀⠔⠛⢻⠻⠿⠾⣟⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠀⠠⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⣾⣿⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠿⣭⣿⠀⠀⣶⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⢹⡏⢹⠠⠀⠀⠈⠡⠀⠉⠘⠻⡀⠀⡀
⠀⠠⠀⠀⠀⠀⢀⡀⠰⡄⠌⢠⣄⣥⡆⠀⠀⣀⡀⠀⣥⣤⣀⠈⠁⢸⡅
⠀⠀⠀⢢⠴⢦⠈⢿⡇⠳⠠⢼⡿⢽⠇⣀⠒⣿⡇⠘⡿⡇⣿⠀⣶⡟⢧
⠀⠀⠒⠈⠀⠟⠈⠻⠁⠤⢀⠤⣿⣸⠀⠀⢀⠀⠅⠐⠛⡓⠿⣠⠋⠁⢐⠁⠀⠀⠀⠀⢀⡄⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣤⣄⠀⠂⠀⠀⠀⡀⢉⡀⠀⠀⠚⢾⣿⣎⢺⣿⣿⣦⣌⠀⠀⠀⠀⠒⠄⠁⠀⢠⡼⢇⡀
⠀⠀⠀⠀⢲⣯⢭⣿⠀⠐⠀⠀⠀⡥⠸⠃⠀⣀⢀⠸⣿⣿⢸⢻⡟⡇⢸⠆⠈⢀⠐⢀⢠⣤⣆⢤⡐⡇⠁
⠀⠀⠀⠀⣿⠀⠈⠉⢧⠈⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⠉⢘⣘⣁⡇⢸⡇⠆⢀⡆⠈⢸⢀⢹⡆⣯⡀
⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣻⠆⡼⠁⠈⠏⠉⠙⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⠀⠀⠰⠀⠈⢂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠘⠳⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣄⠀⠀⠀⠀⠒⠀⢤⠔⠒⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠋⠀⠀⠒⠀⢠⣤⡏⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⣯⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠿⠿⣿⠻⣿⣷⣿⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢉⡙⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠛⠋⠉⠉⠹⠿⠿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠁⠀⠀⠀⢀⡀⠀⠀⠘⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣤⠖⠀⠉⠁⠀⠀⠀⢸⣇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⣤⠄⡀⢈⡛⠛⡓⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⢆⣀⠀⠀⠀⢀⡻⣿⠀⣾⣏⠀⠀⠀⢾⠀⢀⣤⣾⣷⣾
⠀⠀⠀⠀⠀⠘⠂⠀⠸⠃⠘⠁⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡘⡟⠀⠀⠀⠈⠁⠿⣶⣿⣯⣤⣤⣷⣾⠃⠀⠙⣿⡈⣻⡤⠄
⠀⠀⠀⠀⠀⠀⠾⠶⢧⡌⠙⠁⠀⢠⣶⡟⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠸⡇⠀⠀⠀⠀⣽⣝⢻⣿⠗⠃⠀⠀⠀⡼⠟⠉⠀⠀⢶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⣇⣠⡾⠦⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⣀⢀⣤⣾⣄⣤⣤⣾⣯⣽⢿⣿⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⢿⣍⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠄⠀⠘⠀⠀⠀⠀⠀⣀⣠⠛⠰⠿⣿⠟⢿⣿⣿⣿⣿⣿⡍⢻⣄⠻⣆⠀⠀⠀⠀⠀⠀⢀⢀⣀⡈⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣶⣾⣿⡿⣿⡀⠀⠀⠁⠀⠀⣿⠋⠀⣿⠀⠀⠀⣿⠀⢻⡆⠀⠀⠀⣠⡶⢟⡉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢹⡆⢸⡧⠀⠀⠃⠀⠀⣿⠀⠀⣿⠀⠀⠀⠈⣀⣾⠀⠐⠀⢰⣿⠁⠀⠙⠂⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠐⠈⠉⠀⠀⠀⠀⠀⠀⡄⠸⣧⣤⣿⡀⢀⣠⣼⠏⠁⠀⠀⠀⠈⢻⣷⣤⣤⣤⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣿⣶⣤⡀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⠉⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠄⣹⣿⣿⠿⠯⣼⠛⠛⠿⣿⣏⠰⠆⠀⠦⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⢰⠏⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢚⠺⣧⠬⣍⣐⣻⣧⣴⣶⣴⣿⣿⣟⣶⣿⣞⣷⣤⣤⣤⣶⡿⠛⠀⠀⣤⣿⣦⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣥⡾⣦⠽⣭⢛⠉⠉⠉⠉⠉⠛⠟⢳⣿⣿⣿⣿⣿⣿⣿⠁⠀⣠⠾⠁⠈⣻⡏⠁⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣿⠖⣀⣨⡷⣶⣤⣀⣤⣶⣿⣿⢿⣿⡗⢿⣿⣿⣿⣤⠾⠋⠀⠀⢰⡟⠀⠀⣤⣽⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⢻⡋⣱⠙⣿⣤⣽⡿⣿⣿⣶⣿⣿⣿⡿⢿⣿⣏⣴⡤⣤⣄⣼⣷⢀⡿⠦⣆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠈⠀⢘⠣⣼⡟⣼⠟⠀⠘⢿⡿⣿⣿⣿⣿⣾⢿⣿⣿⣷⣿⡿⣿⣧⡾⢦⣻⡞⠁
⠀⠀⠀⠀⠀⣀⠐⠠⠐⠂⣠⡆⠁⠀⠀⠈⠻⠏⠀⠀⠀⢈⣿⣯⣼⣿⣽⣗⣾⡛⣹⣿⡭⣶⣿⡟⠳⣾⣿⡄⢀
⠀⠀⠀⠀⠀⠉⢀⣠⣴⣶⣿⣶⣤⣆⣀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣿⠿⣷⣾⣿⡿⢿⡿⢏⠀⠈
⢠⡤⠰⠤⣶⡶⢿⣿⣿⡿⢾⡿⣶⣿⠳⣿⣦⡀⠀⠈⠰⠿⠟⠉⠉⠙⢧⣬⣿⣿⢧⣼⣿⡌⢻⡿⢿⣿⣋
⠀⠀⠈⠀⢤⣝⠿⠷⠁⠀⠀⠠⣈⣿⣦⣽⠿⠛⡤⣄⡀⠀⠀⠀⠀⠀⢸⣥⣿⣿⣿⡟⢣⣻⡟⢁⣹⣿⣛
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⢿⡯⠯⣭⣩⡆⢀⣶⡿⠁⠀⠀⠀⣤⠾⣏⣿⡁⢿⣏⣷⣿⣿⠛⢛⣻⣿⢿⡀
⠀⠀⠀⠀⠀⠀⠐⠛⠉⣽⡿⠿⢵⣾⣧⠿⡀⣹⠟⠁⠀⣠⡴⠟⠻⠛⣹⣿⠛⣼⣭⣿⣷⣄⣿⣿⣽⣿⣦⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⣤⠋⣛⡀⠒⣻⣯⣥⡀⣿⠟⠉⠻⣧⣿⣏⡹⠋⢻⣿⣿⣾⣿⣿⣿⠃⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠛⠛⠉⠉⠉⢩⠆⠀⠘⣿⣿⡆⢡⣼⠛⠿⠿⠻⠿⣏⠀⢿⣤⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢳⡄⠛⢩⣿⣎⠠⣿⢗⠐⠟⠐⠿⣀⣹⣯⣿⣿⣿⣿⣿⣶⢾⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡹⢶⣌⣼⣿⠧⣭⠛⣤⠘⡳⠂⣹⣿⡧⠈⠛⠛⠾⠿⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢆⣡⣼⣿⣾⣿⣿⣧⣎⠛⢲⣯⣭⣶⣿⣤⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⣄⣽⣿⣽⣛⣿⣷⣾⠛⠁⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⡟⢿⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡟⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⠿⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⢶⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠌⠑⢦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠻⣅⡽⠟⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡏⣉⣀⣉⢻⣶⠶⠒⣛⡿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣏⣉⡁⠚⣋⣠⣾⣿⣿⢸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣏⠻⠿⣿⡿⠀⣹⡍⠛⠋⢁⣼⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⣿⣉⢻⠇⠀⠈
⠀⠀⣄⣤⠀⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⣖⡞⠣⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣿⢸⣆⣿⡀⠀⠀⠀⠀⡰⣿⣿⢃⡴⣞⠀⠀⡀⣾⠀⠀⠀⠀⠀⢀⣤⣶⠲⣻⠛⠓⢶⣀
⠀⠀⢿⡿⢿⡟⡡⠖⢆⠀⢠⡷⡿⣷⢯⣤⠀⢱⢄⡹⠀⠀⠀⠀⣤⡾⠻⡏⠑⡽⣇⣆⠺⠃⢫⡤
⢀⠆⣄⠒⠺⣿⠀⠀⠈⡄⣼⢱⢸⠁⠀⢹⣧⠃⠀⠀⠀⠀⠀⠀⣼⠄⠀⠉⠑⣿⡫⢽⢷⡄⢸⡗⢢
⢸⣰⡼⡀⠀⣿⡀⠀⢀⣧⣿⢸⣿⢰⠀⠈⣿⣇⡀⠀⠀⠀⠀⠀⠧⠤⡤⠤⠰⢷⣝⣭⡾⣡⡿⠁⢸⣂⣀⡀
⢸⠘⠃⡇⡴⣿⣧⠈⠉⣼⢸⣸⣿⡄⣷⡆⢣⢸⠁⢀⡰⠒⠒⠂⡾⢁⡿⠓⠐⠊⠉⠻⣚⠜⠁⣠⣿⣿⡗⢿⣧
⠀⠃⠘⠋⠀⡏⣿⡀⢀⡇⡞⢻⢸⣇⢸⠁⠘⡄⣆⡼⢳⣾⠏⠉⢀⡎⠀⡀⢀⡀⠀⠀⠈⡍⠹⠆⣿⣉⢁⣼⢻
⠀⠀⠀⠀⢸⢱⣿⣇⢸⡇⠃⢸⡆⣿⠀⡇⠀⢳⠋⢀⠇⠉⠀⠀⢸⢿⠈⠀⠈⣏⡢⢄⠀⠸⠀⠀⠘⠺⠽⠽⠟⠂
⠀⠀⠀⠀⣼⠾⡟⣿⡜⣧⣾⢸⡇⡇⡇⢸⡀⠘⠂⡜⠀⠀⠀⠀⠘⡜⢇⠀⠀⢱⠈⠒⢍⣉⡇
⠀⠀⠀⠀⠀⢰⠇⢻⣏⣿⢹⢸⡇⢁⡇⠘⠒⠒⡎⣰⠋⠈⢆⠀⠀⡇⠘⡄⢀⡠⢷⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣸⡆⠘⣿⣿⢸⢸⡇⠸⢇⠀⠀⠀⡿⠁⢀⠀⣞⡧⡀⠱⢄⣻⡟⣶⠙⣄⠀⠀⢀⡆
⠀⠀⠀⢀⢔⡾⠄⠀⣿⣿⠘⠀⠹⠀⢸⣤⣤⠞⠀⠀⠀⠉⣿⠀⠈⠢⡀⡾⣵⠀⠀⠀⣗⣊⠭⢇
⠀⠀⠀⡎⡉⣸⠀⢠⡿⣿⠀⡇⡀⡄⡏⣠⠋⠀⠀⠀⠀⣼⣸⠤⢀⣀⣹⠉⠙⡄⠀⣠⣾⠀⠀⢸
⠀⠀⠀⢛⢻⣹⠉⠁⢡⣿⡆⠀⠃⠁⡷⠁⠀⠀⢀⡤⠊⠎⠀⠀⠀⠀⠈⡀⡠⠘⢿⣿⣼⣀⣠⠃⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠑⠒⠒⢒⣁⣸⣷⣀⣀⠞⠀⢀⣤⣒⣁⣀⣠⣏⠤⠤⠴⠒⠺⠾⠥⠤⠽⠛⠒⠋⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⡻⠶⠞⠋⢈⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⣠⣤⣄⠈⢻⣶⡶⠾⠿⠿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣾⣿⠿⠟⠀⣸⡟⠀⣰⣿⣷⡌⢿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⣤⡀⠉⣉⣀⣴⣿⣿⣿⠃⢸⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠻⣿⣿⣿⣿⣿⠀⢸⣿⡍⠛⠋⠁⢀⣼⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠈⠛⠛⠛⠁⠀⣸⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⢿⣿⣿⣶⣷⣶⣶⣶⣿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡟⠉⢡⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡁⠀⢸⣿⣿⣿⣋⣉⢩⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⢾⣿⣿⡃⠛⠃⠸⣹⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⣿⣷⣴⣶⣿⣿⣿⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡀⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣩⣍⡉⠛⡿⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣿⠃⠈⠋⠙⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣀⣄⢀⣀⣿⣄⣀⣀⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⣴⢰⣶⣄⠀⠀⠀⢻⣿⡏⠁⠉⢉⡁⢀⠈⠙⣿⣿⣿⡇⠀⠋⠱⠷⣲⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⣇⢠⡞⣿⢸⡿⡿⣋⡀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠃⠀⠀⢲⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⠆⠀⠀⠀⢦⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⡟⢸⠇⡇⣿⢀⣉⣉⠙⠀⠀⠀⢀⡴⠶⣤⡄⠐⠓⠂⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⢀⠈⠿⡄⠁⠀⠸⡀⠞⢹⡇
⠀⠀⠀⠀⠀⠀⣰⡇⢸⢨⠇⡽⣘⣉⣉⠉⠀⠀⡠⣿⠀⢀⣷⡴⠖⠚⠒⠚⠿⣿⣿⣿⡄⠀⠀⠀⠀⠉⠐⣈⡇⢀⠀⠂⠁⠟⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡃⣿⢸⠀⣧⣦⣽⣋⠳⠦⠀⠃⠀⠀⠾⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⣤⠨⣵⠈⠀⣀⠳⣴⣿⡆
⠀⠀⠀⠀⠀⢀⣈⣧⣿⢸⡞⣿⣿⣷⣾⣶⣦⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⣿⣀⠀⠀⢀⣀⡀⢹⡔⠀⡅⣿⣾⣿⣧⡀
⠀⠀⠀⠀⢨⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣷⠿⠃⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⢀⣠⣤⣝⣿⣾⣿⣿⣿⣿⡟⣼⣶⠿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣠⣿⣿⡇⠀⠀⢠⡟⠉⠈⢿⣿⣿⣿⣿⣿⣿⡿⣟⣱⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣬⣿⣿⣿⣿⣷⣧⣰⣿⡇⠀⠀⠈⠋⢉⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⣤⣿⠿⠟⠛⠛⠛⠛⠉⠉⠀⠀⠀⢀⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⣾⣿⣿⣟⣉⣿⡾⣛⣿⣿⠏⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⡿⠿⢿⣦⣄⠙⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣧⣧⣾⣿⣿⣿⣄⣀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣟⣛⣛⣿⣄⠀⢀⣿⣿⣄⢀⣿⣿⣿⣯⣿⡿⠿⠿⣿⣿⣿⣧
⠀⠀⠀⠀⢈⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⣷⣾⡿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣠⣿⣿⣿⣿⠿⠟⠻⠋⠀⠀⣠⣟⣻⣿⣽⣿⣿⣽⣿⣿⣿⣿⠏⠟⢿⣿⣿⠿⣿⣿⣿⡟⢿⣧⡀⢀⣉⠛⠋⠐⢿⣟⣿⣿⣿⣿⣷
⠀⠀⢀⣼⣿⣿⠛⠛⢛⣀⣠⣀⣴⣾⣿⣟⣿⠟⠈⠀⠛⠛⢹⣿⣿⠋⠀⠀⠘⠿⠷⣤⣼⢾⣿⣻⡜⠛⠃⠈⠉⠀⠀⠀⠂⠙⠿⣶⣾⣿⣿⡄
⠀⠀⢸⣽⣾⠿⣦⡀⣸⣛⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢠⣾⡾⠿⢠⡤⠀⠀⠀⠀⠈⡉⠀⡾⣹⣷⣦⡐⠷⣄⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⢳
⠀⠀⢸⣿⡇⠈⡹⣡⣽⣿⣿⣿⣭⡏⠉⠉⠀⠀⣠⣀⠃⣾⠟⣿⣆⡴⠀⢁⠀⠀⣙⠟⡛⠃⠘⢿⠿⣿⣿⣶⠛⠃⢴⡆⠖⢀⣀⠀⠀⠟⠿⣿⡆
⠀⠀⣼⣿⣴⣿⣶⣾⣿⣟⣫⡍⠉⠀⠀⢰⣿⣷⣿⣷⡽⣿⣨⣼⡁⠀⡴⠛⢲⣦⡟⣷⣟⣦⡄⠠⣀⠉⢡⡄⡠⢳⣧⣤⣤⣤⠍⠀⠀⠀⠐⢿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣴⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠜⠿⢁⣿⣿⣿⣿⣧⣷⣽⣷⣷⣨⡤⣤⣏⣠⣴⣄⢀⠴⣄⡀⢀⣽⡛⡄
⠀⢠⣭⣿⣿⣿⣿⣥⣤⣤⣭⣿⣿⣯⣥⣤⣤⣤⣭⣭⣭⣥⣶⣿⡶⠆⠀⣤⢄⢸⣿⣿⣿⣬⣿⣿⣿⣉⣽⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣽
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠀⢨⣶⠓⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠲⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⢾⡆⢛⣿⡿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄
⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠊⠁
⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣯⣽⠄⠖⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣸⡏⢻⠿⢷⣰⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣦⣿⣿⣿⣼⣷⣤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣾⢿⣿⣷⣿⣑⡙⢛⣿⡿⢿⣿⣿⣿⣦⡀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⡠⢶⡄⠠⠀⠀⣻⡛⣿⠛⣿⡧⠿⢿⡿⠿⠦⣸⡿⢿⡟⠻⢿⠀⣀⣾⠱⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡸⠇⠀⠀⣘⠛⢛⠛⠛⣻⣿⣴⡄⣼⣶⢸⣾⡗⠂⠁⡘⠋⣀⠀⠛⣄⠻
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠁⠀⠀⠀⢹⡄⠘⠇⢠⡾⢷⡀⢰⡷⠀⣼⣿⣆⠀⢸⠁⠸⠃⠀⠀⠈⠻⢄⣀⢀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠍⠀⠀⠀⠀⠀⣠⣿⣲⣛⣹⢧⡴⣟⡐⢃⣺⣅⣠⣯⡔⣊⠻⢧⡀⠀⠀⠀⠀⠻⣿⡝⠁
⠀⠀⠀⠀⠄⡒⢀⠀⡇⠀⠀⠀⣠⣾⡕⢩⠃⣿⡟⢀⣶⡌⢉⡉⢩⣿⠇⣴⣿⠘⠁⢂⠹⡄⠀⠀⢀⡀⠉⠷⠤
⠀⠀⠀⠀⠀⡸⢋⠀⣻⠄⠀⠀⢧⡿⢦⣜⣻⣿⢢⣿⣿⡟⠦⠶⢛⡟⠀⣸⣿⠤⡄⠀⣏⠘⡆⠀⠿⠷⠾⠃
⠀⠀⠀⠀⠀⠀⠈⢻⠁⠉⣰⣴⠾⡿⢶⣧⢼⣿⡟⠈⢹⡇⠀⠀⢸⡇⢦⣿⣿⣙⣁⣤⢼⣿⣤⣤⣀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣰⠾⠷⠛⠮⢧⡴⠐⢊⡝⠉⠁⢸⠇⡇⢰⣿⠠⠷⣲⡿⠋⡉⠁⢱⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢏⠀⠀⠀⠀⣀⢸⢽⠆⠹⡗⢐⡔⠉⠙⣿⠛⠉⠉⠁⠉⠀⠉⠁⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⡦⢣⢨⣷⡆⣿⠀⣶⢠⣴⡟⢻⣶⡖⢤⣤⣤⣤⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⡟⣿⢹⣾⣿⠁⣯⠀⣿⣴⡏⠃⣸⣿⡇⢦⣸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢙⡏⣿⠀⡇⣹⣿⣿⠙⢿⣦⡼⠛⢣⡖⠁⣿⣗⢺⠝⣿⣿⡹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢌⠑⡿⢀⠧⣾⣿⡏⠢⡀⢛⢶⣖⠊⠀⢀⣿⣿⡚⠆⠹⣿⣇⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⣀⠄⠉⢀⢀⠀⡱⠆⡘⢲⣿⡏⢳⣅⠀⠀⢀⡈⠿⠿⣴⠛⣿⣏⢙⠀⢻⡜⠆⠀⠈⢿⢦⣄⣀
⠀⠀⠀⠀⡄⢰⡚⡍⠂⠀⠀⠀⡠⠍⠀⠠⣿⣿⠁⢠⠙⠻⢦⡀⠑⠀⠈⠔⠁⣿⣿⣅⠧⠀⠹⣄⠀⠀⣿⣸⡇⢸⠁
⠀⠀⠀⠀⠑⡀⢳⡘⢆⠀⢀⡤⠀⠠⠦⣼⣿⣁⡦⠀⣁⣀⢾⣿⣷⢤⣤⢶⡂⡟⢿⣿⠴⢃⠀⠈⢦⣬⠃⣸⠇⢸
⠀⠀⠀⠀⠀⠐⣄⠙⢦⣱⡞⠀⠀⠣⣼⣿⠉⣯⡶⡿⠏⣼⣿⡿⣿⢂⣫⠿⣴⡇⠘⣿⣷⠊⡄⠀⠀⠙⣔⡟⠀⡞
⠀⠀⠀⠀⠀⠀⠈⠃⢄⡙⠀⡀⠁⣜⣿⠏⠀⡇⠘⠀⢐⡾⢻⡇⠿⣃⠀⠟⢽⠀⠀⢹⣿⣏⢰⡄⠀⠀⢸⡡⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣉⣾⣿⠃⠀⠀⣧⠄⡰⠏⠀⠘⠁⠀⠻⢂⡀⡾⠀⠀⠀⢻⣿⣦⠘⡄⠀⠀⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣴⠯⡽⠁⠀⠀⢀⡷⠮⢁⡐⢦⣤⠶⣶⢾⣯⡧⡗⠀⠀⠀⠀⢻⣿⣆⠰⢄
⠀⠀⠀⠀⠀⠀⠀⠠⣈⣞⣿⠿⢄⠖⣠⠛⠡⡝⠲⢤⣈⣉⣉⣉⣛⣹⡝⠒⠞⢣⡜⣁⠖⠀⢿⣿⣗⡊⣢
⠀⠀⠀⠀⠀⢀⠐⠀⣽⡟⢃⣳⡌⠶⢠⡜⠁⢶⡤⠤⠆⣽⠉⠹⣯⠙⠛⢶⡳⠆⣤⣉⠶⠂⣼⠻⣯⣥⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠻⣾⣀⢉⡇⢸⠃⠎⣁⠶⣀⣀⠤⢿⠀⢰⠏⠑⠢⣼⣱⠛⣤⢉⡴⠐⠇⢀⠈⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠁⢤⠇⡸⣉⠖⢈⡰⡥⠄⠰⠟⡦⠛⠶⠤⠤⡿⢡⡛⠰⢏⣐⠀⡗⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠠⠥⠉⠰⠦⠀⠆⠠⢰⠌⠱⠏⠠⠲⠴⠗⠠⢌⡁⠮⠉⠦⠼⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣶⢦⣤⡠⣤⣤⡤⣤⣤⣴⣦⣀⡤⣦⣤⣤⣤⣤⣤⣽⣦⣤⣤⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠤⣤⣷⣀⣡⣼⣿⣤⣼⣿⣤⣤⣿⣯⣤⣼⣥⣬⣿⣤⣿⣧⣼⣤⣿⣤⣧⣤⣥⣽⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⢿⣿⠟⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⠀⠀⠀⠁⠀⢀⣠⣾⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⢶⣶⣶⣦⣤⣀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠛⠛⠉⠉⠉⠙⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠟⠛⠛⠛⠻⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⣀⣀⣀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠃⠀⣠⣶⣿⣿⣿⣶⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⠋⠙⢿⣿⣿⠿⠛⠉⠀⠈⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠋⠀⠀⠀⠈⢻⣿⣧⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁
⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⢻⣿⣿⣶⣤⣤⣴⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣶⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢄⠀⠰⡄⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣁⠁⠀⠀⠀⠈⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⣓⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢡⠀⠠⢠⣬⣤⡤⢤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠘⠀⠇⠀⠀⠀⢷⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠰⠹⠃⠿⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢠⠀⣬⣷⠀⠀⠀⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡠⠂⠀⠀⠀⢀⣠⣤⡘⠰⠇⠀⠀⠀⠀⠎⡷⣄⡀⠀⠀⡼⠀⢷⡀⢄⣰⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⡀⠦⠀⡈⠉⣷⠀⠀⠈⠀⡇⠀⠂⠤⠜⡀⢮⠓⢨⠁⠐⣆⣸⠃⠀⠉⠗⢠⣎⢀⡠
⠀⠀⠀⠀⠀⠀⠁⢀⣬⠄⡻⠤⠁⢰⢠⠔⠉⢀⣄⠀⠀⢻⠀⠀⠂⠳⣾⠄⠈⠁⠀⠀⣽⣇⣀⢀⡀⠠⢃⠿⣦
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⣴⢀⣠⡴⠆⠢⡘⠛⠡⠀⢸⠏⠀⡐⠉⠀⠀⡄⡠⠀⢨⣩⠃⠻⠆⣹⢦⣍⠀⠈⡃
⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠋⠙⢉⡀⠤⣀⠈⠁⠀⠒⢉⣲⣿⡣⡀⡠⢀⡇⠀⠐⢥⣊⠇⠀⡔⠁⠘⠟⠟⠋⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⢤⡄⣰⡊⠁⠲⠬⠭⠅⠤⡄⠉⢀⠀⠙⠺⣵⡿⠁⠀⢠⠏⠉⠀⠜⠀⠀⡈⠲⣷⡀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⡯⡤⠀⠀⠀⠀⠀⢰⢡⠠⠘⠃⡠⠀⢸⡇⠀⣰⠆⠀⢠⠂⠚⠀⠠⠂⠀⠀⠹⣤⡀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⡜⡶⣡⠃⠀⠀⠀⣠⠚⠈⠀⠻⠃⠀⣀⣾⣪⠷⠯⠄⠀⠻⠀⣿⠃⢤⣧⠀⢀⠀⢈⣹⣿⠧⠂
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠼⣱⡣⠆⠀⡐⢉⡁⠀⠀⠀⠀⣁⠀⡟⡣⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠤⡌⢼⣿⡟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⢀⡾⠻⢼⣢⣋⡁⠀⢀⣞⡢⠏⠁⠀⠀⠀⠀⠀⠀⠑⠒⠶⠢⣴⣶⣷⣦⢻⡀
⠀⠀⠀⠀⠀⠀⠀⡤⡤⡄⢀⠀⠠⢠⣼⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠿⠿⠛⠀⠀⠛⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⣤⠀⠀⣠⣄
⠀⠀⠀⣀⠴⠶⠶⠛⠋⠉⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣿⣿⠃⠈⠀⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠟⠀⠀⠀⠛⠀⠦⡄
⠀⠀⠀⠀⢄⣀⡀⠀⠀⠀⡄⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠠⣄⠀⠀⢀⡆⢀⠀⣀
⠀⠀⠊⠉⠉⠉⠉⠀⢀⡈⠀⠈⠀⠒⣎⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⣿⠀⠀⢸⡇⢸⠈⠀⠂
⠀⠀⠀⠀⠀⢀⡤⣤⠴⠀⢰⠓⠉⠉⠁⠀⢰⡟⠂⠀⠀⠀⠀⠀⠀⠶⠱⠜⠃⢀⠙⠀⠀⠙⣠⣾⣄⠀⢀⢰
⠀⠀⠀⠀⡀⣿⠁⠻⠎⣰⠃⠀⠀⠀⠀⠀⡸⠮⣺⣿⢀⡆⠀⠀⠠⡐⠀⠀⠀⣀⣽⠂⠐⡊⠀⠈⠙⠻⣦⡀⢰⠦
⠀⠀⠠⠿⠰⣧⡛⠀⣽⡇⠀⢲⣤⣤⣤⣤⠁⠀⢸⡟⣧⡀⠀⠀⠉⣀⡀⣀⣀⣤⠤⠴⠤⠄⣠⣀⡀⣀⣹⡏⠉
⠀⠀⠀⠀⠈⢿⠇⢠⣿⣧⠀⣿⣶⣮⠙⣿⣆⠀⠸⣉⣁⡀⠀⠀⡀⠠⡤⠄⠀⠐⠒⠒⠒⠒⠂⠨⢿⣿⣿⡏
⠀⠀⠀⠑⠀⠀⣠⣥⠽⠿⢒⡉⣿⠏⢰⣿⠿⠏⢀⣿⠏⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣿⣿⣛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠸⠿⠿⠿⠿⠧

⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡆⠰⠀⣤⢜⡈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣹⡄⢲⡟⣓⢂⣹⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡮⣉⢈⣣⠽⠅⠤⠀⠹⢦⡒⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠳⠦⠤⢤⣝⣋⣈⣉⣋⣛⣺⡁⣈⣤⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡟⣫⠶⣒⢢⣽⣥⣧⣿⣤⣧⣻⢭⡤⠤⢚⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣶⣿⡿⡛⠯⠉⢉⠩⠝⡻⣿⣟⣻⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠩⠐⠈⢻⣤⠁⣀⡾⠛⢧⡃⢸⣌⣛⠫⡥⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⠀⠿⣿⠆⠀⣾⠝⠗⠛⠃⠀⠚⠛⢺⢟⡧⢀⣥⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⣻⣤⠟⠀⠆⠀⠀⠀⢡⣿⡄⠀⣀⣐⣂⠀⣾⣯⠁⠀⠉⠘⠀⠀⠀⠀⠀⠀⠀⡠⠴⠊⡷
⠀⠀⠀⠀⠀⠀⠀⣠⢀⡠⢋⢀⡴⠛⠉⠀⠀⠀⠈⡶⢀⡠⢠⡧⢫⣀⠜⠙⢁⣠⠋⣍⠣⡀⢶⠎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢶⣦
⠀⠀⠀⠀⠀⠀⠀⡟⢇⣠⣚⠏⠀⠀⠀⠀⠀⠀⠀⣡⢀⠰⠁⣠⡎⠙⠦⣠⠞⠙⢦⡈⢦⣀⣴⠀⠀⠀⠀⠀⠀⠀⡠⢫⠇⠀⢸⡚
⠀⠀⠀⠀⠀⠀⠀⣧⡼⠟⠁⡄⠀⠀⠀⠀⠀⣀⠨⢏⣛⡟⠁⢨⡀⠀⠀⠀⠀⠀⢴⠙⠖⢷⣼⠀⠀⠀⠀⠀⠀⢰⠀⠸⡀⠀⢸⡁
⠀⠀⠀⠀⠀⣠⠞⢻⣦⠤⡎⠀⠀⠀⠀⢠⠎⠁⠀⣈⣾⣏⠀⠈⢣⣀⠀⠀⠀⢀⠎⣠⢈⡿⠄⠉⢦⠀⠀⠀⠐⣍⠁⢀⣇⠠⠴⠃
⠀⠀⢀⣴⠟⠁⠀⠈⠀⠀⢀⠀⠀⠀⢠⠃⠀⠀⠀⡤⢹⣫⠄⠀⠀⠈⠻⡿⠛⠁⢀⡄⢸⠗⠆⠀⠘⡇⠀⠀⡜⠀⠀⢻⠁
⠀⠀⠈⠁⠀⠀⠀⡄⠀⠀⠸⠀⠀⠀⡎⠀⠀⠀⠀⡶⢈⣏⠄⠀⠀⠀⠀⠀⠀⡐⠁⠆⣹⣯⠂⠀⠀⣇⡠⠊⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢃⠀⡞⠀⠀⠀⠀⡰⢛⠠⡧⠕⠒⠒⠒⠊⢀⠼⠄⢴⠠⣼⡏⠀⠀⠀⢹⠁⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢈⡄⠑⠀⠀⠀⢴⠁⢨⡄⢳⡣⠀⠀⠀⡰⠃⠀⠀⠈⣐⣟⢻⠀⠀⠀⣈⡇⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡜⠀⠠⠤⣀⡝⠁⠀⠈⡖⢩⡑⡀⢀⠔⠁⠀⠀⠀⡆⣬⣻⠁⣗⠌⠓⠈⢙⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⣼⠀⠀⠀⠀⠀⢳⡀⠀⢠⠋⢒⣚⣥⠀⠀⠀⠀⠀⠐⠡⡘⣇⠀⢨⡄⠀⠀⠈⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠰⠋⠙⢆⡆⠀⢌⢯⣆⠂⡀⠴⠀⠠⢠⣖⠇⠙⡄⠀⢣⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢥⣦⣀⠈⢏⢵⣄⡤⠘⡃⠞⠰⠧⠿⢊⠋⠀⣠⢇⠀⠈⣧⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠙⣱⢞⣒⡋⠈⠂⠠⢀⠁⠀⢁⠠⡔⠉⠀⠈⢳⡄⠘⢆⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠼⠁⠀⠄⠀⢺⠔⢫⡀⠀⠀⠀⠀⠀⠁⠀⢰⠀⠀⠈⠀⠀⠛⠦⣈⢣⡀⢠⠴⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⢀⣀⣀⣤⣠⣄⣠⢆⣸⡅⣀⣤⠀⠦⠄⠉⠉⠲⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡀⢨⣉⢳⡄
⠀⠀⠀⢀⠔⣊⠔⠋⣀⡠⠖⠋⠉⠀⠀⠀⠀⠀⠀⠈⣥⠀⠀⠀⠂⡆⠀⠀⠀⠀⠈⠙⠢⢄⡀⠀⠀⠀⠀⠀⢀⡝⠢⡽⠋⣅
⠀⢀⡔⠁⡜⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢀⡀⠬⠧⠳⠖⠶⢤⣄⣀⡀⠀⠈⢻⣿⡉⠉⠉⠁⢾⠀⠀⠘⡷⡟⠑⢤⡀
⠀⡞⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠒⢉⡀⢀⡠⠤⠤⠤⢼⣂⠀⠀⠈⠑⠒⠒⠀⠓⠀⠀⠀⠈⠳⠶⠒⠁⠘⡄⠀⠑⡄
⠀⣧⠀⠀⠙⠤⢤⣀⣀⡠⠴⠒⠒⠒⠋⠻⠥⠴⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸⡄
⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠤⣤⣄⣀⡀⠀⠀⣀⠼⠁⠀⠀⢸⠃
⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠠⣪⠎
⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⣀⣀⠂⠀⠠⠤⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣀⣠⣴⣊⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠀⠤⠤⠤⠤⠤⠄⠀⠀⣀⣈⣉⡁⠀⠬⠬⠤⠤⠤⠤⠒⠒⠒⠊⠉⢙⡏⢩⣷⠦⢮⣤⣥

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⣿⣿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⡶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣾⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠖⠒⢻⣦⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⠉⠁⠀⠀⢻⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣩⣤⣤⣿⣷⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠺⢿⣷⡄⠀⢀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠄⠀⠆⢻⡇⢠⠏⢘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠶⣄⠀⠀⠀⠀⢀⡴⡆⠀⠀⣠⡟⢃⠀⠀⢀⡉⣧⣘⡆⡼⠃⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠳⡌⣮⠓⢢⠀⠀⢎⠀⡷⡆⢰⣿⢿⠋⠁⠀⠙⣿⣿⣿⡜⠀⠀⠀⠀⠀⠀⠀⡐⢙⣠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠒⠁⠀⠀⣸⠀⣠⣣⠋⢸⢈⠣⢄⣘⡠⠟⠀⠀⠙⢢⣀⠀⠀⠀⠀⢀⡧⣿⣯⡽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣟⡶⢤⣀⡻⠶⡾⠁⢠⣈⠦⠨⠋⠉⣁⣨⣤⠴⣄⠀⠘⠣⣄⠤⠚⣝⡤⠬⠭⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠈⡅⢀⠧⢾⣿⣄⠀⢤⠐⠀⣹⠃⢸⠀⠈⠒⠦⡀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡈⠀⡸⠋⠙⣄⠈⠢⠔⠀⢀⠸⣄⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⣀⠔⠋⠉⠁⢳⠒⡦⢤⣼⣽⣍⣩⣍⣙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⠀⠀⣠⢄⡀⢸⡆⠑⡌⠏⣿⡇⠀⣿⣋⣯⡤⣖⣲⠶⣶⣶⡖
⠀⠀⠀⠀⠀⠀⠀⢴⠤⠐⠒⠒⠃⢡⣀⡬⠤⠒⠋⠁⣾⠙⣶⣿⢀⠁⠈⣽⠁⠀⢿⣉⣉⣁⡀⠠⠤⣼⣭⡋
⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⠔⠢⠜⠋⠁⠀⠀⠀⠀⢰⡖⡺⠧⢿⢘⣧⣿⠛⢦⣀⡀⠉⠙⠋⠉⠛⠛⠷⣬⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⢹⣴⠋⢸⡄⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠋⠁⠀⢺⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠈⢣⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣬⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠐⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠉⠙⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣹⣏⣛⣛⣙⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⣠⠀⠀⠀⠀⢼⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠁⢀⣴⡿⠃⢀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣤⣘⠿⣁⠀⣿⡿⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠋⠉⠛⠛⢣⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⡿⠀⠀⠡⠄⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⣿⣷⣦⡷⠷⣴⡄
⣀⠘⠃⠀⢀⡀⠀⠀⠀⠀⠀⣠⣴⣾⣷⣼⠃⠀⠘⠋⠀⠰⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣧⡈⢷⣧
⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⠃⠉⠛⣿⣿⣿⣷⣼⡏
⠀⠀⠀⠀⠐⢀⠀⠀⠀⢸⣿⣿⣿⡟⠹⠟⠀⠀⠀⢀⣠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠹⠧⠂⠐⣗⠀⠹⣿⣿⣿⡇⣀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠻⢿⣳⣠⠀⠀⠀⠠⡞⢃⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠾⢀⣤⣠⣴⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣦⠀⣄⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠹⣿⣿⣋⠀⠁⠀⠀⠀⠀⠀⠀⢄⣀⠸⡏⢻⡿⠃⠀⠀⠀⠀⢸⡛⠻⠟⠿⢿⡄
⠀⠀⠀⠘⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⢹⡀⢈⡛⢮⠈⠃⠀⠀⠀⢀⡀⠀⢸⣿⣇⠀⢀⣤⣄⣀⢀⣠⠐⠋⠀⠀⠀⠀⡀⢹
⠀⠀⠀⢠⡞⠀⠹⠗⠄⠀⠀⠀⠀⠀⢸⠂⢃⣼⣷⡈⠙⠂⠀⠀⠀⡈⠁⢀⠘⠛⠃⢴⡟⢿⣿⠃⠈⠁⠀⠀⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⡅⠙⠳⠆⠀⠀⢀⡘⠃⡤⠻⣄⠀⠀⠈⣄⠠⠛⠀⠀⠀⠀⠀⠀⠂⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠛⣳⠄⠀⠀⠀⣈⠣⠀⠙⠦⣿⣿⡇⠀⠹⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠛⣳⠆⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠛⠻⠁⠀⢻⠃⠀⢀⡈⠿⠀⠠⠀⣀⠀⠱⡦⠴⠐⠂
⠀⠀⠀⠀⢀⡜⠁⠉⠀⠀⠀⠀⠖⢠⡿⠃⠀⠀⠀⠀⢀⡀⡟⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⠀⠸⡿⣦⠀⢀⠀⠉
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠘⠃⠀⢠⠀⠀⠘⠒⠀⢀⡸⠋⠁⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠀⠀⠀⠀⠀⢠⣤⣀⣀⠄⣠⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⠢⠷⢷⣾⣷⣼⣿⣿⡍⢣⡵⠦⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣄⠠⢼⡟⢻⡉⠉⠹⡛⠧⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⣰⣾⣿⠿⣿⣿⣿⡉⢆⠀⠀⠀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡀⢀⡀⢠⠄⠔⠀⠀⠀⠸⠿⠿⠋⠅⢸⣆⣼⡿⠿⣿⣧⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠈⠉⠁⠁⣀⠀⠄⠀⠀⠀⠀⠀⠀⢢⡀⠋⢁⠄⠀⠀⠙⡃⠀⠰⠀⡄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⠂⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠛⠀⠀⠀⠀⠀⠀⡄⣠⡁⣴⡚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣴⠎⠙⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢹⣶⡆⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠟⠛⠀⠲⠾⠇⠀⠀⠀⠐⣷
⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣤⠀⠸⠁⠀⠀⠀⠀⠀⠀⢩⠆
⠀⠀⠀⠶⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⠀⠐⠂⠀⣤⡦⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⣠⡀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠈⠋⠑⠂⠀⠒⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢠⣶⠂⠀⠀⠀⣴⠆⢠⣤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠀⠀⠀⠀⠊⠙⡿⢠⠀⠼⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⡀⠁⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠄⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠠⠈⢁⠀⠻⠆⠀⣄⢀⡀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⢉⠠⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠶⠇⠀⠀⡀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢤⠉⠠⣾⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⣀⠀⠀⠀⠀⣡⠏⡈⠠⠜⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡈⠀⠀⠀⣤⡄⠀⠀⠶⠀⠀⠀⠸⠛⠀⢠⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⢀⠂⠉⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⡄⠀⠀⠀⢦⡈⠀⠀⠀⠀⠀⠀⠁⠀⠖⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⢦⠀⠂⠉⡆⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡤⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠃⡈⠙⢋⠀⡸⢉⡉⣯⠹⢈⣿⠟⡻⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢴⠗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡿⡟⢿⡄⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣄⡨⣊⣙⣤⠾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⣾⣯⢶⣿⣿⣿⣷⣿⣿⣦⡀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⣴⣿⣻⣿⣾⡯⣸⣬⣇⣷⡟⢲⢽⣿⣷⣿⣦⡀⠀⠀⣤
⠀⠀⠀⠀⠈⣠⠚⣳⠄⠃⠀⢠⣿⣉⣿⣍⣿⣞⠛⠹⢯⠙⠓⢼⡟⠙⢏⢉⡻⠇⠰⣺⡆⢳⡆
⠀⠀⠀⠀⠀⠟⢠⠏⠁⠀⠠⣥⠈⢄⡈⠉⠿⡷⠾⢂⡶⠶⠠⣿⢃⠉⢀⡦⠁⣸⠄⠈⠲⣈⡃
⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⢹⡀⠘⡀⣰⡞⠻⡄⢸⡗⢀⡾⠿⣾⡀⢘⡁⡈⠃⠀⠀⠀⠘⢡⢤⣄⣠⠄
⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⣀⢖⣻⡴⣡⣝⠣⠜⢯⣈⣀⣽⣧⡤⢷⣜⢡⡈⠱⢄⡀⠀⠀⠀⠘⢺⣿
⠒⠮⣀⡄⢨⡀⠀⠀⠀⢴⣷⠋⡜⢲⣿⠇⣀⣼⡆⠠⠄⣠⣿⢳⢰⣾⢂⡁⠈⢌⣣⡀⠀⢀⣤⠀⣫⠓
⠀⠠⠋⣄⣨⢷⠀⠀⠘⣬⠿⠤⣍⢽⣿⣠⠻⣽⡙⢓⠚⢉⡏⢘⡸⣿⡢⠖⠀⢹⣐⡹⠀⠘⠙⠺⡏
⠀⠀⠀⠙⠄⠀⢈⡶⠾⠛⡛⢿⡧⢺⣿⠈⠀⢺⡄⣤⠈⢸⡇⢠⢿⣿⡍⣥⡤⠴⣿⣧⠶⢤⡀⣰
⠀⠀⠀⠀⠀⠀⣿⠂⢀⠴⠛⠚⠛⠋⣷⡆⠐⢋⡍⠀⠀⢸⢁⡎⢰⡿⠖⠷⢺⣿⠞⠉⠁⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠀⠀⣀⠴⡝⠎⠹⡇⢀⠚⠨⠉⢿⠙⠁⠀⠀⠀⠀⠀⠉⢱⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢹⣿⣿⡴⣠⢤⣶⠂⣇⠀⣦⠀⣴⡟⠛⣷⡆⢰⡤⣤⣤⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⣌⣿⠙⣟⣱⣾⣿⠀⣯⠀⢿⣠⡏⠑⠀⣿⡗⠺⣠⣿⣿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡎⢢⡉⣿⠈⢅⣹⣿⡏⠻⢾⡤⠼⠛⢃⠔⠁⣿⣿⠒⡅⢻⣿⡏⠿⣄
⠀⠀⠀⠀⠀⠀⢠⠞⢀⠂⡘⡇⠰⠤⣾⣿⡧⠀⠀⡙⡶⣄⡀⠀⠀⢹⣿⡒⠃⠘⣿⣧⣀⠈⠢⡀
⠀⠀⠀⢀⣀⠐⠁⡀⠀⠐⡐⢀⠷⣲⣿⡏⢦⡀⠀⢀⢄⠀⠘⠷⣤⠚⣿⣿⠛⠀⠸⡏⠃⠀⠀⠹⡷⣤⣀
⢀⠀⡄⢮⠑⠀⠀⠀⠀⠐⠀⠠⠤⣿⡟⠁⠀⠙⢶⣄⠀⠀⠀⠈⠀⠑⢼⣿⣏⡹⠀⠘⢆⠀⠀⢨⠓⣿
⠘⡀⠘⠀⢣⡀⠀⠀⠀⠀⠠⢀⣾⣿⠑⡀⠀⠀⣀⡼⣿⣷⣀⣌⠀⠀⣹⢿⣿⡄⠷⠀⠀⠳⣀⡎⠐⣿
⠀⠀⢄⠈⢢⡙⢴⠋⠀⠐⢆⣾⣯⠻⢈⡴⠖⠏⡙⣶⣿⣿⠆⢉⢶⣤⡎⠈⢿⣷⡐⢃⠀⠀⠘⢅⢸⡇⢀
⠀⠀⠀⠳⢄⠘⠏⠀⠐⢠⣚⣿⠃⢸⠅⠐⠈⠠⣽⠻⡿⢹⡎⠀⢒⣩⡇⠀⠘⣿⣿⠉⡆⠀⠀⠈⡿⠂⡞
⠀⠀⠀⠀⠀⠘⢀⠈⢳⣟⣾⠃⠀⠘⡥⠂⣠⠎⡈⡀⡇⠠⠹⠄⠀⢸⠁⠀⠀⢸⣽⣯⡨⢀⠀⠀⢘⠜
⠀⠀⠀⠀⠀⠀⢂⣼⡙⠹⠃⠀⠀⠀⣧⡔⠁⠠⣄⣁⣧⣤⣴⡞⣭⡾⠀⠀⠀⠀⠻⣾⣆⠈⣄
⠀⠀⠀⠀⠀⢠⡼⢾⡎⢠⡄⠀⠶⢈⡣⢤⡉⠐⠚⠃⠲⠚⢻⣟⠥⣥⢆⣀⠒⢠⠀⢽⣿⣧⠠⠃⡀
⠀⠀⠠⢀⢰⣿⡟⠡⣄⢣⡤⢉⠲⢈⣀⣀⣈⡍⣺⠚⢻⡟⠛⠷⣄⠦⣄⣉⠒⢢⡄⢠⠿⣟⣓⡂⣡
⠀⠀⠁⠂⢼⣯⣄⠁⣺⠀⡶⢍⡰⠂⣭⠀⠀⢀⣿⢠⢸⡛⠤⣄⣸⠇⡤⢉⡰⢢⡄⡞⢀⡙⢋⡉⠁
⠀⠀⠀⠀⠀⢼⢃⠀⢽⠀⡑⠂⣄⠓⢴⠀⠈⢁⡿⣌⡸⢁⠀⣀⣹⠓⠢⢎⡰⢫⡄⢐⠀⠀⣹⠆
⠀⠀⠀⠀⠀⠈⠁⣀⡇⣈⡁⠂⢤⠛⢀⡉⠀⢨⡠⢉⡶⢈⠀⠀⣏⠘⠑⠎⣀⠛⢆⠈⣤⠀⠋
⠀⠀⠀⠀⠀⠀⢀⣜⡁⠉⠉⠂⠀⢀⢀⠀⢀⢨⡀⠈⢀⣄⢈⣈⣀⣀⣉⣳⣌⠀⣈⡉⣀
⠀⠀⠀⢀⡀⣐⣉⠐⢁⣎⣰⣊⣿⣋⣈⣛⣳⡞⢹⡆⣴⠉⣿⠉⣿⢉⣿⠝⠯⢙⡏⠛⠙⠓⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠈⡀⠈⡂⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠂⠀⠀⠂⠖⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⠄⠛⠈⠐⢂⣀⣼⠯⣼⡀⠀⠌⠁⠀⣸⠆⠐⠴⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢧⠄⣤⠀⠐⠎⠀⠀⠳⠀⠈⡁⠀⢀⡴⠔⠀⠈⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⣍⠀⠀⠛⠀⠀⢰⠂⢂⠩⡀⠀⠠⠀⠀⠰⠉⠂⢀⢓⠀⠀⠀⠀⠀⡁⠀⠀⠐⠘⠳⠦⠄⢀⠔⡀⠀⣠⠀⠀⢀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠰⠄⢊⠀⠂⠀⡇⠂⠁⣶⣀⠀⠠⠀⠀⠀⢠⠀⡀⠀⠐⠒⢦⣀⠀⠀⢀⡀⠀⢀⣀⡀⠼⢇⣀⡀⣈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡏⣠⣄⠈⠀⠀⣰⣾⠉⠀⠐⠠⡄⠦⠀⠀⠀⡠⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢸⡆⠈⡁⠁⠈⡠⠊⠁⠈⠑⠀⠀⢀⢁⡀⠋⠈⠩⠁⠀⠀⠥⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠂⠀⠀⠀⠅⡆⠀⠀⠀⠥⠀⠀⠄⠄⠀⠀⢤⡀⠠⠀⠀⠀⠀⠁⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠐⠒⠶⠦⣠⢀⠀⣡⡈⠀⠀⠀⢀⠀⣀⠀⠃⢀⠀⠀⣰⣀⠀⢀⡀⠙⠆⠀⠀⠀⠀⠧⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠆⠆⠈⠋⣃⠉⠀⡀⢰⡟⠀⠁⠀⢀⠍⡀⠊⠁⠀⠀⠚⠄⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠠⣗⠀⠀⠀⠀⠀⢭⡀⠰⠛⠸⠇⠀⠀⠀⠉⠀⠁⢠
⠀⠀⠀⠀⠀⠀⠀⢠⢠⡖⠡⣄⠠⠀⠙⡠⠀⠀⠈⠪⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⡄⠐⢶⠀⠱⠆⢸⠂⠀⠀⠉⢈⡁⠂⣴⠆⠀⠀⠐⠲⡈⠀⠐⡊⠄⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⠀⠀⠤⣁⣀⣀⣀⠀⠀⠀⠀⢧⡀⠈⠫⠁⠀⠀⠀⠀⠀⠀⠕⠀⠀⠀⠀⠀⠀⠀⢀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠂⠀⠉⠙⠛⡦⠴⠖⠒⠋⠀⠀⠀⢠⠀⠀⠠⠐⠀⠀⠂⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠠⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⡀⢉⠴⠡⠄⠀⡠⠀⠑⠄⠀⡀⠀⠈⠀⠀⠤⠂⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠻⠄⠀⠀⠀⡤⠀⢀⡀⠀⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⠿⠀⠄⠀⡁⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠁⠀⠈⡄⠁⠀⠄⢦⡰⠀⠙⠂⠉⠀⠴⢠⡀⣀⠀⠚⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣈⠀⢢⡀⠀⠀⡀⣘⡄⠀⠀⠀⠀⠀⢆⡇⠀⡀⠀⡀⠸⠋⠶⠆⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠒⡐⠋⡉⠉⠐⠉⠑⢳⣦⣴⣤⣚⡉⠀⠀⢈⡁⢆⠀⠀⠀⡅⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠈⠋⠔⡲⠦⠄⢸⣇⢧⠙⡇⠐⠀⠉⠀⡈⡗⢀⢀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠂⠀⠀⠀⠀⠇⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⣄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⢰⣦⠀⡟⢦⣠⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠑⣤⡭⠧⣧⡚⠁⠀⢹⠁⠹⢄
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⡀⠀⠀⠀⠲⣦⣄⡀⢇⠀⢰⠍⠀⠀⠀⠙⢆⠀⠀⠀⠀⢨⡦⡴⢤⣀⣀⢀⣀⠤⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡍⠓⠦⣀⠀⠈⢇⠈⢻⣄⣸⣆⠀⠀⠀⠀⠈⠀⣄⣆⣠⠋⠀⠀⠀⠋⠘⢿⣇⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⡀⣾⣧⡴⠚⠿⣿⣿⡿⠿⣄⣖⠙⠢⣄⠀⠉⠛⢿⣦⡀⣠⠖⠛⠛⠻⣿⠓⠒⠲⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠁⠀⠀⡿⠁⠀⣠⠿⣯⠄⠀⠘⠫⠿⢶⢤⣿⢿⣇⠀⣠⣄⣠⣾⣥⠴⠚⠋⠉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠛⢷⡀⠀⠀⠇⠀⠞⠁⠀⡼⠷⢖⣰⣋⠙⢻⡀⠁⠀⠈⣾⠃⠀⠈⠛⠖⣤⣴⡊⠉⣻⠟⠉
⠀⠀⠀⠀⠀⢀⣠⣤⠒⣾⠀⠀⠀⠀⠀⠁⠐⢓⡀⠀⣀⡤⠾⢧⠀⣜⠉⠉⠉⢢⠱⣄⠀⢀⡎⠀⠠⠄⠀⠈⠉⠛⣇⠴⠁
⠀⠀⠀⠀⠀⠈⠉⢉⣲⣿⣄⣀⡠⠲⡤⣥⣚⣛⣉⠵⠿⠀⠀⣰⠋⣹⣤⠶⣦⣸⣶⠿⣶⣿⣦⠀⠀⣀⣠⣤⣤⣴⣧⠤⣀⡀
⠀⠀⠀⢀⣤⣴⣞⣁⠬⠿⠛⠛⢣⡄⡠⠋⠁⠀⢀⠀⠀⢀⡾⠁⠀⠙⢦⣴⠄⠌⠃⠲⣶⣾⠻⡏⠉⠁⠀⠀⠹⣿⣏⣀⣀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠚⠦⠔⠋⠉⠓⠋⠀⠀⠀⠀⠀⠙⠶⢦⣖⡆⠄⣅⣸⡧⠀⢀⣀⠀⠀⠀⣽⣿⣿⣋⠉⠉⠉⠷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠾⠿⢤⡀⠀⢘⡇⠀⠀⣿⣿⣯⠛⠻⣕⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠧⠴⣾⣿⣿⣷⡀⠀⠈⢳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠌⢿⡌⠙⠒⠒⠾⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠤⠔⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⣶⡆⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⠀⣠⠖⠀⣀⣈⡉⢤⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⢇⣾⢁⡞⠓⠒⠤⠴⢶⣶⣮⣝⣷⣌⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣴⣿⣼⡇⡞⠀⠀⠀⠀⠀⠀⢀⠍⠻⣝⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⣿⣿⠟⠳⠁⠀⠀⠐⠀⢀⠔⠋⢠⠂⠘⡏⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢝⣿⣷⣉⢅⠈⠒⠢⡄⠈⠀⠴⠃⠀⡆⣱⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠝⠟⣉⠉⠑⠈⡄⠀⠀⠀⠀⠈⣥⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠢⡀⠀⢉⣀⢤⡀⢀⡐⠸⠉⠁⢀⡤⠒⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢀⣇⣠⡬⠶⢞⠚⠋⠉⠙⠀⢆⠠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡤⠬⠶⢖⠊⠉⠉⠏⡡⠤⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⢶⡖⠚⠉⠉⠈⠑⠲⡄⠀⠈⠣⠀⠀⡩⠊⠀⠀⠐⢤⡤⡠⠔⠁⠀⠀⠀⡎⠀⠀⢀⠈
⠀⢀⣾⡤⠤⠒⠚⠉⠻⣄⠀⠀⢠⠀⠑⠄⠀⠀⠀⠀⠀⠱⢄⠀⣠⢵⣤⡌⠉⠀⠀⠈⠒⠒⠂⠀⠀⠀⢀⡾⠶⠶⡶⣄⢣
⠀⢀⢜⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠘⢉⣦⠀⠀⠀⠀⠀⠐⠡⡯⠙⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⣯⠎
⠀⠁⠈⠢⢀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠨⢤⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠄⣀⠀⠀⠔⠁
⣠⠄⢄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠉⠊⠚⠀⢠⣠⠑⡄

⠀⠀⠀⠀⠀⢘⡔⢁⠀⠀⡠⠃⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⣶⣾⣛⠀⠈⠢
⠀⠀⠀⠀⢀⡈⠀⡜⢀⠴⠡⣚⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠒⠂⠄⠐⠖⠋⠀⠘⣿⠋
⠀⠀⠀⢠⣼⣧⡄⠀⠀⠀⠉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠀⠀⠰⠋⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠏⠉⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⡗
⣶⣤⣾⠂⠀⠒⡄
⠉⢻⡿⠃
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠑⠦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠤⣉⠊⡆
⣀⣴⣄⣠⠔⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣁
⠀⣽⣿⡏⠁⠐⠄⠀⠀⡠⠊⠠⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⢀⣷⣶⡾⠆
⠴⠋⠀⠀⠀⢀⡁⢀⣌⠀⢐⠀⠀⠠⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⣿⠟
⠀⠀⠀⠀⡠⠜⢻⣿⡇⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠀⢠⠈⢠⡌⠐⡖⠁⡆⠂⡄⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢤⡀⠀⣇⠈⢂⣐⠂⠴⠃⠀⠀⠾⠅⢘⡏⢀⣧⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠐⢦⠀⣃⣤⣶⡿⠉⠀⠈⠒⠒⠒⠶⠒⢋⡄⠀⠱⣦⣄⡋⢀⡤
⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠈⢂⣴⣾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠿⠿⣿⣦⣅⠴⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠡⣀⢈⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⡗⣻⣶⠂⠀⠁⠁⠀⠀⠀⠈⠙⣿⣧⡰⡏⢁⡇
⠀⠀⠀⠀⠀⠀⠠⣀⢀⣾⣿⡛⠀⠧⣠⠀⠀⠀⠀⠀⠀⣿⠁⠸⡿⠠⡀⠀⠀⠀⢀⡀⠖⠀⢹⣿⣿⣌⠊⢀⡄
⠀⠀⠀⠀⠀⠁⣠⢁⣾⣿⣿⠀⠀⠀⠀⠀⠂⠆⠦⠆⠀⠈⠳⠛⠁⢶⡀⡄⣄⠄⠛⠀⠀⠀⢸⣿⣿⣿⡎⠉⢁⡀
⠀⠀⠀⠀⠡⢄⡎⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⣄⠀⠀⡆⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡈⡈⡁⠄
⠀⠀⢀⠐⢂⣠⡴⠤⡤⢭⡛⢷⣤⡀⠀⠀⠀⠀⠉⠁⠀⠁⠀⡈⠁⠀⠀⠀⠀⠲⢦⣤⡴⠟⣋⣉⣉⣙⠻⣇⠉⠁
⠀⣠⢃⠔⠋⠀⢁⡞⠁⠀⠈⠢⠻⣀⡀⠄⠂⠁⠀⠀⠀⠠⠀⠁⠈⠘⠁⠁⠒⠦⣤⣏⣔⠋⠁⠀⠀⠀⠙⢤⠫⣁⡄
⣴⣽⠉⡄⠀⠀⠈⠚⠠⠀⡀⣀⠑⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢹⣯⠼⠀⠀⠀⠀⠀⠀⠀⠃⠳⡄
⠙⠛⢿⡘⠱⠂⠆⠆⠒⠒⠊⠋⠒⢇⣁⣀⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⣠⢐⣊⣥⡼⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⣄⡹
⠀⠀⠀⠈⠲⣀⠀⠀⠀⠀⠀⠀⠀⠈⡭⡑⠆⠐⠁⠀⠀⠀⠤⠀⠀⡜⠡⠉⠴⠄⢻⢐⡀⠀⠀⠀⠀⠀⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠆⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡇⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⡆⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡜⠁⠀⡔
⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⢠⣿⣷⣀⣠⠎⠀⠀⠀⠀⠀⠀⢀⣆⠹⣦⣴⡎
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠰⠥⣚⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠈⣟⢦⣀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡥⠘⡻⡿⠒⢀⡀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⣭⡓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣭⡄⠀⢠⣾⣇⠀⠀⠀⡆⠀⠀⠀⠀⢠⣾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⢖⡦⣼⢻⠀⠀⠀⠗⠀⠀⠀⠀⠘⠁⣠⡶⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⢧⠀⠀⠘⢄⠀⠀⠀⠈⠒⠓⢲⠶⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡥⢤⡤⣨⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡲⢗⡶⣖⣲⡽⠶⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢰⡔⣷⠄⠐⡁⠐⢶⣿⣿⠃⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠂⠀⢤⠀⠀⠈⣿⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⢀⠈⢄⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡑⠆⢀⡥⠘⠉⠀⡀⠀⢰⡉⠁⠛⠉⣹⠂⠀⠀⠀⠈⠀⠁⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠋⠁⠀⢸⠀⠉⡿⠉⠁⠐⠁⠀⠀⠀⠀⠀⠐⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣤⠴⠆⠀⠘⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠑⠀⠀⡆⢰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠘⠜⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢄⠁⠀⠀⠀⠀⠀⠀⠀⢤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣰⠀⠀⠒⠀⠀⠀⢸⣈⣹⠄⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠰⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣦⣤⠴⠟⣡⡼⢡⡆⠀⠀⠂⠀⠀⢀⠀⠀⠖⠚⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠶⠚⣡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠶⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠈
⠀⠀⠀⠀⠀⡀⠀⠀⠄⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠇⠀⡀
⠀⠀⠀⢀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠛⠛⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀⡠⠂⠀⠠⠼⠇⠀⠠⠯⠀⠀⠀⠈⠀⠈⠙⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠴⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠦⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠼⠟⠀⠀⠀⢀⣀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⣧⡀⢸⣿⡿⢿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣠⠀⢡⢤⣶⣟⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠳⣁⠴⠿⠀⢸⣬⣾⠿⣿⣿⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣺⢿⣦⣠⣤⣾⠿⠃⠐⠿⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⣷⣦⣾⡿⠛⠋⠀⠀⠀⠀⢀⡠⠬⠙⢿⡿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢘⢿⣦⠐⣿⣿⣿⡀⠀⠀⠀⠀⡀⢰⠟⠀⠀⠀⠀⣇⠀⣿⣄⢀⠀⣀⣤⣴⣶⣤⣄⡐⣶⢀⡰⠿⢿⢷⣄⣀
⠀⠀⠀⠀⠀⠀⢼⡆⣿⣿⣾⣿⡿⢃⣠⠴⠶⠈⠀⠀⠀⠀⠾⠃⠀⠉⢠⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣧⡐⠀⢌⠹⠿⣷⡀
⠀⠀⠀⠀⠀⠀⣾⡁⠻⣿⣿⣿⡁⠊⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣿⡿⣋⣷⣿⣿⣿⣿⣷⣶⣜⠛⣿⣿⣷⣦⡘⠻⠻⣿⡆
⠀⠀⠀⠀⠀⠀⣿⠁⠀⣿⣿⣿⣧⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣽⣿⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣷⣤⡓⣽⡏
⠀⠀⠀⠀⠀⠀⡿⠁⠀⠙⣿⣄⡈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠈⠙⠛⠛⠻⣿⡏⠈⣿⠋⠹⠯⠱
⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⢿⣿⣧⣘⣶⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⣿⣿⠏⠀⠛⠀⠀⢀⡴⠚⠉⠉⠀⠀⠈⢷⠀⢻⣾⣷⣾⣦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⣀⣀⡀⠀⠈⠀⣤⣬⠁⠀⠀⠀⠈⠀⣸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣿⣿⣷⣤⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠿⣄⣀⣤⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⣩⣿⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⢻⠯⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠑⣰⠁⣬⡁⠀⠀⠀⠐⠀⠖⠀⠀⠀⠀⠀⠹⠟⢿⣿⣿⣿⡿⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠘⡃⣆⡀⠀⠀⠠⠄⠄⠀⢀⢀⠁⡀⠐⠞⣽⣿⣷⣄⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡄⣈⠁
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠆⠀⢀⠀⡀⠈⢷⠱⡞⠃⠈⠀⠠⠀⠀⠸⣷⡄⠀⠊⢲⠊⣻⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⠃⣽⠳⢿⠇
⠀⠀⣸⠀⠩⠸⡁⠀⠀⠙⠃⠉⠘⠿⠀⠈⠀⠷⠰⠆⠶⠀⠰⣆⠘⠇⠀⠄⠀⢠⣾⠿⠿⢿⣿⡷⠾⢿⣷⡖⠁⠀⠀⠀⠀⡤⠚⠉⠁⣀⠀⠀⠈⠛⣤
⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠉⠃⠀⣀⡀⢠⡤⢤⠄⣦⣤⣭⠤⠄⠀⣉⠁⠀⠀⠿⣇⠘⠃⠘⠀⡽⠁⠀⠀⢀⣤⠺
⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠸⠀⠿⠋⠀⠀⣠⢮⣇⠀⠀⠀⠠⡭⠁⠀⣐⠂⢀⡠⠴⠂⠀⢀⡵
⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⠼⢇⣤⡤⡀⢆⠓⠃⠀⠆⢠⠀⠈⡀⠤⠖⠀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⢰⠦⡀⠀⠀⣀⠀⠀⢨⠁⠐⣦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠴⠟⠘⠁⠀⠹⠿⠀⡁⠰⠀⠀⠀⢰⢁⠆
⠀⠀⠀⠤⠀⠀⠀⢠⡄⠀⣨⡟⠛⠙⠀⠀⠐⣛⠀⠈⠀⠀⠀⠀⠀⠂⣾⣆⠀⠀⠀⠀⣀⠎⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⢀⠉⠚
⠠⠀⠀⠀⢱⠔⠃⠀⠀⠀⠙⠻⠂⠀⠀⠀⠀⠽⡄⠀⠀⠀⠀⠰⠈⢸⣿⡟⠀⠀⠀⠀⡿⢣⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⢸⢋⠟
⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⡐⠀⡈⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⢈⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠
⡃⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⢀⠔⠀⠀⠀⠀⠠⣶⠀⠀⠀⠐⢠⢿⣒⣀⣀⠀⠀⠀⠀⠀⡠⠛
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠉⠛⣶⣀⠀⡀⠀⢰⡠
⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠂⡈⢿⠖⠀⠀⠛⠁
⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⡇⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠀⠀⠀⠀⠀⣀⣀⣀
⣿⣿⣿⡿⢿⣿⠿⢿⣿⣿⣿⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣦⣽⣦⣧⣴⣿⣬⣾⣯⣼⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢠⠀⢸⡄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣾⣿⣥⡿⣦⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⢰⠃⣸⡇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⡴⠖⠊⠿⣛⣛⣻⠗⠛⠲⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⢸⣄⣹⣇⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠞⠉⠀⠀⠘⣿⣩⢨⣹⣟⠀⠀⠀⠙⢷⣌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠙⢹⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡴⠃⠀⠀⠀⠀⠸⣿⣜⠾⣻⠹⡄⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣸⠃⠀⠀⠀⠀⠀⣾⡿⢣⣷⠺⣿⡆⠀⠀⠀⠀⠀⠸⡆⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣤⡟⠀⠀⠀⠀⢰⠶⣩⣾⣇⠇⣸⣿⡡⢶⠀⠀⠀⠀⠀⡷⢀⣜⢫⣄⠀⠀⠀⠀⠀⠈⣿
⠀⢀⣿⣶⣄⠀⠀⠀⠀⠀⠶⣾⣯⣻⣿⣷⠆⠀⠀⠀⠀⢂⣳⣿⣽⣿⣽⣧⣇⢃⠀⠀⠀⠀⠀⠟⠇⣆⠖⡥⡟⠃⠀⠀⠀⠀⠸⣷⡄
⢠⣿⣿⠛⠀⠀⠀⠀⠀⡀⠀⢜⠛⣿⠋⢻⣠⠀⢸⠀⢸⢏⣿⣿⣿⢾⣿⣿⣏⢻⣀⣠⡤⠀⢠⡇⠈⢚⣉⡆⠀⠀⠀⠀⠀⠀⢸⢿⣿
⠙⣿⣿⠀⠀⠀⠀⠠⠤⠼⢿⣿⣤⠤⠤⠬⠽⣿⣿⡦⢾⣦⣶⣿⣿⣽⣿⣯⣢⣿⣿⣏⠁⢀⡟⠠⠁⠀⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣙⣻⡄⠀⠀⠀⠀⠀⢀⣿⣿⠇⠀⠀⢀⠀⣿⣿⢻⣼⣹⣧⠾⣝⠻⣿⢛⣿⣳⣿⢿⣶⣯⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠈⢹⣶⣦⡀⠀⠀⠀⠘⢿⣏⢀⣤⡾⣿⣷⣿⡿⣠⢻⣿⣿⣷⣮⣤⣷⢿⣿⣿⣷⣾⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢶⡟⢿
⠀⠀⢸⢿⣿⣿⣦⡀⠀⢈⣻⣿⣾⢻⣿⣿⣿⣋⣙⣻⣿⣿⣿⣿⣳⠖⢣⣍⡻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⢀⣴⣿⣿⡶⠀⢰
⠀⠀⢸⠀⢻⣿⣿⣷⢸⣮⢻⣿⣿⣿⣭⡻⣿⡿⣿⢻⣿⡻⣿⣿⣿⣷⣿⣿⣿⡌⣿⠿⠛⠿⣿⣿⣿⣿⡟⣰⣦⣰⣿⣿⣿⠟⠀⠀⠘
⠀⠀⢘⠀⠀⠹⣿⣿⣿⣿⠸⢿⣿⣿⣿⣿⠉⠀⣿⡀⠙⢿⣿⡿⣿⣿⣿⡿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠫⣾⣿⣿⣿⣿⣿⠋
⠀⠀⢸⠄⠀⠀⠈⠉⠀⠀⠀⠈⣿⣿⠟⠀⠀⠀⢻⣇⠀⠀⢩⡷⠘⣉⣸⣿⣁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠟⠁
⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡀⠀⠀⢾⠏⣿⣿⣿⠻⢗⡄⢹⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢣⣶⣧⣝⣈⠽⣺⣥⣴⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⣿⣿⣿⣿⡿⢿⣾⣿⣾⣽⣺⣿⣿⣿⣿⣿⣿⡿⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣭⣿⣿⣭⠝⢀⠾⣿⠟⣛⣿⣛⡳⣿⠉⠉⠉⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠋⠀⢀⣴⣿⣿⡾⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⢸⡇⠀⠀⣀⡀⣶⣶⣿⣿⠟⠉⠀⠀⠀⠀⣾⣿⣿⣿⣿⣝⣛⣻⣾⠏⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⢘⣷⣶⣿⣿⣿⠿⠿⠿⣿⠇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⡭⠛⠋⠁⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣟⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣼⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⠿⠿⠿⠟⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠈⠙⢏⠛⠃⢤⠀⠀⠉⠉⠳⣄⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣶⡟
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠳⠀⢄⣠⣄⡈⢦⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣴⢺⠝⣧
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢦⣀⣃⠀⠉⠋⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⣿⠞⠋⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⠀⣨⠟⠒⢀⣀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠘⠁⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠗⠒⠛⠉⠀⠈⠲⢝⢢⡀⠀⡀⠀⠀⣀⠀⡼⣠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠳⡑⡾⠁⠀⠀⠈⢏⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠂⠛⠐⠒⠢⢄⣀⠀⠀⠙⣜⡄⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠘⣞⡄⠐⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡏
⠀⠀⢀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠤⠤⣄⡀⠀⢀⠀⠀⠀⢳⡀⠘⢂⡔⠓⠂⠀⠀⠀⠀⠠⠶⠊⠁⠀⣷
⠀⠀⠈⠑⠤⣄⣤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢤⡀⢳⠀⣄⢹⠀⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡇⢰⠸⠀⠀⣠⠚⠁⠀⡀⡠⠊⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠏⢲⣄⣀⠠⣄⡰⠖⠛⠁⠈⠛⢦⡀⡆⢰⠃⠀⢀⢀⠟⠁⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢀⡤⠧⢤⣿⠀⠀⠈⠿⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠈⠑⠚⠛⠒⠦⣄⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠓⢦⡦⣾⠤⠖⠛⠛⠛⠲⣄⠀⣀⣀⣀⡈⢳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠚⠋⠉⠀⣀⠴⠚⠁⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠃⠀⠀⢀⡀⠀⠀⠀⣼⢰⡖⣪⡅⠪⣽⢃⠀⢀⡤⠀⠀⠀⣤⣟
⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣆⠀⣀⡇⠉⠓⣤⡾⢻⣌⠳⢭⣠⠞⠉⢧⠞⠁⠀⠀⠀⠀⠈⠉⠑⡄
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣨⠟⠋⠀⠀⣼⠋⠀⠀⠉⠳⣄⠟⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠤⠐⠒⠠⡏⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⡏⠀⠀⣠⠞⠒⣒⢦⡄⠀⣠⡶⠶⠋
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠹⣦⡀⠀⠀⣀⣉⠤⠞⠁⣠⠎⠹⣄⠀⢠⠏⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⡠⠞⢋⠟⠉⠀⠀⠀⣀⡾⠁⠀⠀⠀⠉⠉⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⢤⣄⠀⠀⠀⠀⠰⢟⣁⢀⣠⢞⠟⠒⠒⠉⢩⠑⢀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠳⣤⣀⣀⣀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠉⣉⡩⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠶⠚⠉⠂⠈⠙⠓⠛⠛⠲⠶⠴⠖⠚⠁

⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣴⡿⠂⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢀⠈⠛⠡⠞
⠀⠀⠀⠀⠀⠀⠀⢠⣭⠜⢓⣶⡰⣁⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⢠⣶⡾⣧⣼⣿⣿⣿⣿⣿⣿⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⢾⢿⣿⣿⣿⠟
⠀⠀⠠⠴⣀⠈⡙⠀⣸⣽⣧⣿⣿⣿⣿⣿⣿⣍⡳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣶⣮⣉⣁⣌⠜⠁
⠀⠀⠀⢴⠟⢿⡿⠺⢿⠛⠛⠋⣳⣸⣿⣿⣿⡛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣛⣿⣿⣿⣿⠄
⠀⠀⢀⢀⣠⣼⠃⢐⣱⣆⠠⠶⠿⣅⣻⣯⣿⣧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠺⠭⠽⠿⠞⣛⡿
⠀⠀⠀⠉⢛⣷⠿⠿⣿⠛⣦⣄⣐⣿⣇⡙⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠭⠏⣿⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣉⢹⣿⣿⣿⣿⡿⣋⣩⣷⣶⡄⠀⠀⠀⠀⠀⡼⠀⢀⡞⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠈⠈⠙⠃⠀⠀⠘⢿⣿⣷⡟⣿⠀⠀⠀⠀⣼⠁⢠⠏⠀⢠⠊⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠠⠄⡠⠄⠀⢀⡀⠹⣿⣿⣿⣀⡀⠀⠀⡇⢀⠇⠀⢀⠎⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⠞⠻⠶⡆⠀⠰⠞⠋⠉⠀⣿⡿⢫⡊⢹⠀⠀⠃⠈⢀⣀⣌⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡄⢘⡄⠀⠐⣦⠀⠀⠈⠀⠈⢀⡎⠀⠀⢀⡾⣋⠶⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠐⠈⣁⠀⣀⣠⠀⠠⣤⣀⠀⠀⡶⠋⠀⠀⠀⣸⣫⡍⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⡾⠋⠀⠈⢉⡀⠤⠚⠉⠃⣰⠃⠀⠀⠀⠀⠿⣠⢄⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠉⠉⠉⠱⠶⠂⠀⢀⣴⣁⣤⣀⡀⠀⠀⢠⠃⣾⣤⡴⠞⣁⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣦⣤⣀⣀⣀⣤⡴⠊⣿⡄⠀⠈⠙⠳⣤⠃⡼⢁⡞⠀⠉⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠒⢬⣳⡽⣆⠀⣼⡿⢤⣿⢿⠀⡴⠀⢀⠎⣼⠋⠉⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⡀⠙⣿⡿⣷⣠⣿⣼⠏⣺⣗⣁⣀⡎⣰⠃⠀⠀⠀⠀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠙⠂⣿⣿⣹⣿⣿⡇⡡⣿⠉⠉⡟⢠⠿⠶⠶⠶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡀⠀⠀⠀⠀⠀⣾⣟⣿⣿⠏⢎⣿⠏⠀⡸⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡺⣿⣿⣿⣷⠀⠀⠀⠀⠀⠙⣿⡿⣿⣶⠟⠁⠀⢰⢃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣷⣟⢿⣿⣧⡀⠀⠀⠀⠀⠘⢿⡋⠀⢀⠤⢶⠇⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣽⣷⣄⡀⠀⠀⢀⡞⠉⠷⠃⠀⠙⠚⠿⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⠻⣦⣄⣸⣇⡘⠀⠀⠀⠀⠀⢸⡟⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠉⠛⠿⠿⢤⣀⠀⣀⣠⠟⠀⢀⡟⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡰⢩⡟⠉⠁⠀⢀⡞⠁⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣰⣻⡟⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⠆⠈⠉⠀⠉⣷
⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⣄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⠀⠀⠀⣸⡾⣿⢀⠆⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠘⠀⣀⡠⠔⠒⠸⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⡿⠋⠉⠉⠛⠛⠛⠛⠿⢿⡏⣬⠀⠀⠀⠀⠀⠀⠱⠞⠀⠀⠀⣿⣠⡾
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⡇⠀⠀⠀⠀⠀⠀⣀⠱⠦⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠠⡇⠀⣀⠀⠀⠀⢸⣿⣿⡿⣽⣿⣿⣿⠀⠀⣿⠀⡆⠀⠀⠀⠀⠀⢠⠀⣿⠀⠹⠀⠀⢀⠤⠖⠊⠁⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠱⡾⠥⠄⠀⠀⠸⣿⣿⣿⡿⣿⣿⣿⠀⠀⣿⠀⡇⠀⠸⡄⠀⠀⢸⡄⣿⡂⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣿⣿⣿⣾⣯⣿⣿⠀⠀⠹⣆⢳⡀⠀⠱⡀⠀⠀⢧⠹⣿⠦⣤⣠⡄⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣤⣤⣤⣭⣿⠿⣿⣿⠟⠛⠉⠀⠀⠙⢦⡙⢦⡄⢙⣦⡀⠀⣱⣬⠳⠦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣤⣤⣼⣽⠀⠀⠀⠀⠀⠀⠀⢀⡤⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡶⠟⢛⡋⢻⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⣧⣀⡀⠁⢻⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠈⠉⠁⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣄⠀⢀⣀⣶⣤⣶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⣻⠛⠁⣼⡟⠋⢛⣿⠿⢿⡅⠀⠠⠂⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠨⠀⠀⢿⡀⠀⠺⠃⠀⠀⢺⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⣀⠀⠀⠀⠘⠙⠛⡀⠀⠀⠀⢻⡿⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠳⡜⠛⠃⠄⠀⠈⠀⢀⠀⠠⡟⣀⣙⣽⠃⠠⡶
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠞⠀⠀⢀⡄⠀⠀⡀⠀⠀⠀⠀⣿⡉⢳⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠘⡉⣈⠀⠀⠀⣸⣿⣖⣠⡇⠠⠀⠀⠀⢼⡇⠾⣆⠀⠀⠐⠀⠀⠀⢙
⠀⠀⠀⠀⠀⠀⠈⢏⣩⠀⠀⢀⣿⡁⣹⣿⡁⠄⠀⢀⡀⢙⣇⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢈⣤⠀⠀⡸⣽⣿⣿⠋⠀⠀⢠⠊⣀⣼⡟⣼⣿⡁⠠⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⡀⠀⠀⢤⣼⡁⣸⠀⠂⡼⡁⣀⡤⢈⣩⣘⣻⣿⣷⣿⣷⠈⠂⠀⠀⠀⠀⠀⣽⡇
⠀⠀⠰⢋⡤⠒⠁⠀⠀⠀⠁⠀⠀⠐⠋⣻⣧⠀⢿⣭⣭⣉⣿⣿⣇⠹⠟⠰⡷⠀⠿⠇⣉⠁⠀⠀⠀⢠⠄
⠀⠀⢰⡎⡀⢀⣤⠀⠀⠠⠄⡁⠀⠠⠀⠈⠠⠆⠀⠁⠀⢻⡛⣿⡟⢡⠆⠰⡀⠀⢢⠖⠀⠃
⠀⠀⠀⠁⣸⣿⡋⠀⠈⠁⢀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇⢿⣷⠀⠀⠀⠀⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠈⠛⠡⣾⠁⠀⢼⠁⠀⡀⠀⠀⠀⠀⠢⣼⡶⢿⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢻⣄⣼⠇⠀⣧⢀⣤⣴⣿⠷⣾⣷⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠾⣿⣿⠿⠟⠋⣸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠘⠛⢻⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢨⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠘⢿⠈⠙⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⠀⠀⠈⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣤⠀⠀⠀⠘⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡓⢤⣄⢼⣤⣴⣶⡟⣢⣤⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠾⣤⡙⢃⢉⣥⣿⣿⠃⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢻⡛⢷⣾⣿⡉⢀⡤⠀⠠⣤⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣇⣹⣿⠓⢲⡶⢻⡆⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉⠁⠀⠒⠛⠀⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠤⠀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣲⣾⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠛⠛⢿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠉⠁⠀⠘⠛⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣀⡀⠀⠒⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠠⡄⠀⢠⡀⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⣏⠀⢄⡀⠀⠀⡘⢿⢀⣾⠀⠀⢰⡀⢠⣴⢾⡆
⠀⠀⠀⠀⢈⣄⡌⡄⡤⠀⢉⣦⠀⠀⠀⠀⠀⠀⠀⠈⢳⡎⠁⢠⡀⠀⠙⠛⣿⢶⣶⡻⠁⠀⠙⣦⠿⠒⣀
⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⠹⣗⣠⡦⠀⠀⠀⠀⠀⠀⠋⣀⠀⣀⣶⣀⣀⣴⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⢀⣀⣬⠕⠚⢿⠟⠻⣿⢟⣿⠿⠻⡌⢳⡀⠀⠀⠀⢀⣀⣀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⠙⣇⠀⢠⠀⢰⡏⠀⣇⠀⠀⠳⢘⠇⠀⠀⣴⠟⠣⢄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠦⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⢷⣤⣟⠀⣀⣴⠟⠁⠀⠀⢻⣦⣀⣀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣶⡦⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⡽⠃⠀⠀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⢱⢟⣟⠻⣞⣁⣈⣹⣧⡬⣤⡁⣄⣀⣀⣀⣤⠞⠀⣰⡇⢀⡜⠁
⠀⠀⠀⠀⠀⠘⢭⢷⠼⠿⠛⠋⠛⠛⠛⠾⣿⣿⣿⣿⣿⡿⠁⣠⠞⠉⢻⡟⠁⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠸⢷⣤⣾⢷⣦⢰⣶⣿⣟⣿⣯⣿⣿⣷⡞⠁⠀⠀⡟⠀⣄⡾⣹
⠀⠀⠀⠀⠀⠂⠁⠀⠄⠉⠶⣠⣿⣿⠏⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣾⣟⣼⠹⣽⠋
⠀⠀⠀⠀⡀⠀⠀⢀⡄⠂⠀⠉⠿⠁⠀⠀⢹⣟⣿⣿⣿⣿⢋⣿⣯⣿⡿⢳⣿⡇⣀
⠀⠀⠀⠀⣀⣴⣾⣿⣿⣾⣶⣀⠀⠈⠂⢀⣿⣿⠿⣿⢿⣿⣾⢛⣿⣿⣿⣿⣿⠄
⠘⠃⠈⣛⣻⣿⠛⠋⠉⣻⣧⣹⢷⢄⣀⡈⠉⠀⠀⠈⣟⣿⣿⡿⢿⣶⠋⣿⣷
⠀⠀⠀⠀⠀⣀⣀⣤⣶⡯⢽⣭⠀⣰⡾⠁⠀⢀⣤⢾⣽⡉⣿⣵⡿⠟⢛⣿⡿⡆
⠀⠀⠀⠀⠀⠉⠚⠛⠛⠻⢿⠚⡤⡟⢁⣤⡶⠋⣙⣽⢿⣭⣷⢿⣷⣾⣿⣿⣿⣧⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠰⠞⠛⠓⢋⠀⠘⣟⣿⢊⡴⢿⣿⢿⢿⡋⣴⣉⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢞⣡⠟⢿⣯⣱⣾⠖⣃⠺⢡⣽⡿⣿⣿⢿⣶⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⠻⢒⣽⣻⣦⣰⣩⣍⣼⢿⣧⡉⣉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢟⣋⣿⣿⢿⣷⣤⠿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣝⣻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉⠉⠉⠀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⢉⡙⠓⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠉⠉⠉⠐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⠢⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢀⡠⠴⠒⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⠀⢸⠀⡏⠀⠀⡰⣡⠔⠁⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢌⢇⠘⠀⠀⢀⣾⠞⠁⣀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⡈⠓⠄⢀⠼⠚⠓⠒⠲⡟⠁⠠⠊⢀⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡏⠀⢛⢀⠘⠃⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⢒⣒⠭⠛⠧⡀⠘⠚⠀⢀⡼⢍⠑⠒⠤⣄⣀⣀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠁⢀⠤⠀⠀⢨⣷⠒⠒⠁⠀⠀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠴⠁⡰⠁⢀⣿⣿⠀⢰⠀⠳⡀⠀⠀⠀⠈⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⠻⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡿⠟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡸⢰⡇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣀⠤⠒⠉⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⠳⢄⡀⢀⡰⠁⠸⡇⢸⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⡠⠊⢁⡠⠖⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡇⠀⠣⡀⠀⢀⡠⠴⠊⠁⠀⣠⠊⢀⠴⠋⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠑⢄⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠁⠀⠀⠀⢀⠜⢁⡔⠁⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⠣⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡠⠃⠴⠋⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠈⠢⣄⠀⠳⡄⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢀⠜⠁⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡈⠁⠀⠈⠢⡀⠀⠀⠀⠘⡌⡄⠀⠀⠀⢠⠎⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⠀⠈⢦⡀⠀⠀⢃⢱⠀⠀⢠⠃⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⠢⣀⠸⡈⡆⢠⠇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢌⡓⢧⠱⣎⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣵⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⡍⠄⠌⡝⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⠁⠤⡠⠔⠠⡄⠤⣉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠴⠚⠛⡁⠎⠖⠙⠛⠲⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠥⠴⠐⠛⠣⠀⠈⠛⠓⠐⠤⠽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣋⡠⢂⣴⠀⢹⣤⢉⢡⣼⠃⢑⣔⠠⡈⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠻⣼⠛⠊⠉⠉⢹⣿⠀⢸⡿⠉⠉⠉⠚⠻⡼⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣣⣶⠋⢉⠋⠓⠸⠦⠾⠔⠋⢋⠉⢱⣦⣣⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠒⠒⠒⢾⡿⢻⠯⠐⠁⠀⠀⣄⢠⢀⠄⠀⠀⠁⠨⢿⠻⣿⠖⠒⠒⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣥⡳⠟⢻⣿⡞⢳⠏⢠⠤⣤⣀⠀⢷⣼⣵⠇⢀⣠⡤⢤⠈⢷⠛⣾⣿⠛⠶⣣⣍⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠋⠀⠘⢄⢈⣿⡗⠺⡆⢀⣤⣀⠙⠃⠀⠀⠀⠀⠛⢁⣠⣀⠀⡾⠚⣿⣏⢀⠐⠀⠈⠃⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠐⡟⠟⢧⣴⠁⠈⠠⠝⡆⠀⠀⠀⠀⠀⠀⡾⠡⠈⠀⢳⣤⠟⠏⡗⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠈⠀⢀⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢆⠀⠈⠂⠀⠀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠇⠙⣦⣄⡄⣰⠀⠀⠲⠀⠀⠀⣷⣄⣤⡞⠀⠇⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡐⠄⠀⠀⠀⠀⣿⡿⢃⠇⠀⠴⠤⠀⠀⢠⡇⢻⣿⡇⠀⠀⠀⠀⠔⣊⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣀⠔⢁⡴⡻⠃⣽⠀⠀⡤⡄⠀⠀⣾⣾⡁⠻⡳⣄⠑⢄⡰⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⡶⠟⢊⣠⠶⣻⠀⠀⢀⡀⠀⢀⡏⠕⠱⢦⣈⠚⠷⣦⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣽⠛⢯⡢⡀⠘⣇⠀⠉⠁⠀⠸⣇⠂⠀⡡⣪⠟⣻⡅⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢈⡟⠮⣂⠈⣦⡀⠘⠉⢀⠈⠳⣬⠞⣷⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢧⠀⠈⠙⠒⠽⢦⣀⠋⠀⠀⠈⠳⡏⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠈⠳⣄⡀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠘⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⣦⣄⡀⠉⠙⠒⠒⠒⠛⠉⠳⡄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡽⠟⠻⠶⢶⡖⡖⠖⢚⣻⠇⣸⠃⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠐⠁⠀⠀⣠⠈⠙⠛⠛⠶⠚⠁⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣎⡵⠚⠉⠓⠶⠤⠤⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠙⢿⡿⠁⠀⣀⣴⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⡀⠹⣿⣷⣶⣶⣶⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⠛⠿⠿⠿⠿⢛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⠉⠉⠀⠉⠻⣿⣿⠀⠀⠀⢠⣴⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⣰⣿⣿⣿⡿⠋⠉⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⣿⡿⠋⠀⠀⣠⣿⣿⣿⡟⠁⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣿⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢰⣧⡀⠀⠀⠀⣀⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⡿⠀⠀⠘⠿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣏⣀⣽⣭⣭⣭⣭⣯⣯⣭⣽⣍⣩⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣽⣿⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠘⠛⠃⢀⠤⣿⣿⡷⢄⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠰⠿⠷⢿⠇⢀⠀⠀⠀⢀⡀⢀⣿⣿⡀⢀⠀⠀⠀⠀⠛⣸⣿⡇⠀⢦⠀⠀⠀⠿⣄⣤⣴⣮⣿⣵⣤⣠⡾⠃⠀⠀⢸⡀⣸⣿⡀⡼
⠀⠀⠀⠛⠶⣾⣿⣿⣷⠞⠁⠀⠀⠈⢳⡮⠈⠈⢵⡞⠀⠀⠀⢰⣼⣿⣿⣿⡆⠈⠆⠀⠀⣄⣈⣼⣿⣿⣿⣿⣿⣯⣶⡶⠀⠀⠀⣸⠍⢹⣿⡆
⠀⠀⠀⠀⠀⠘⠛⠛⡇⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠀⠀⠈⠉⠀⠻⣿⣿⡿⠇⠀⠁⠀⠀⠀⠘⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠛⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠿⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣥⡀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠏⢠⢀⣰⡀⢀⠁⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⡀⠀⢘⣿⣇⣀⠀⠀⠀⠀⠀⠱⣼⣿⣯⠀⠀⠀⠀⠀⠀⢀⠀⢠⣿⣿⡀⣀⡄⠀⠀⠻⠐⢦⣸⡤⣿⣧⣼⡠⠆⠀⠀⠀⠀⠠⣿⣧
⠀⠀⠀⠃⠙⣿⢿⣿⡇⠀⠀⠀⠀⠠⢠⣿⣿⡿⢧⣀⠂⠀⠀⠀⠈⢓⣷⡠⠖⣿⢃⡀⠀⠀⠀⠘⠓⣫⠇⣀⡸⣏⠓⠋⠀⠀⠀⢀⠇⠀⠰⣆
⠀⠀⠀⠀⡎⠀⠈⠁⠉⠁⠀⠀⠀⠀⠘⠏⠉⠙⠀⠈⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠛⠁⠀⠀⠀⠀⠐⡋⠈⠉⠁⠈⠃⠀⠀⠀⠀⠋⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠟⠀⠐⠉⠀⠿⠀⠀⠀⠀⠈⡛⠃⠘⠂⠙⠟⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠘⡄⠀⣼⣷⠀⢠⡇⠀⠀⠀⢻⡄⢸⣿⣿⡄⣰⠃⠀⠀⠀⢀⣀⣸⣿⡀⠀⠀⠀⠀⠘⡇⣰⣿⣆⠀⣠⡄⠀⠀⠀⠀⠀⢰⠟⡇
⠀⠀⠀⠀⠙⢻⣿⣿⣟⠋⠀⠀⠀⠀⠀⠙⣳⣶⣷⡟⠋⠀⠀⠀⠀⠀⣭⣽⣿⣡⠀⠀⠀⠀⠀⢹⣿⣿⣿⡟⠉⠿⠃⠀⠀⠀⠀⣴⣶⣶⠄
⠀⠀⠀⠀⠀⢈⠿⠿⠙⠲⠤⠀⠀⠀⠀⠀⠙⠿⠿⠙⠲⠄⠀⠀⠀⠘⠋⠹⠿⢸⡇⠀⠀⠀⠶⠚⣙⣛⣏⠙⠲⠖⠂⠀⠀⠀⢸⡿⠿⢿⡇
⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⢿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠌⢁⡠⣌⢁⠠⠄⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⠀⠀⠀⠀⠀⠐⠿⠀⢿⠁⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠼⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠶⣿⢿⡿⢧⣹⣿⣿⢟⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⣿⠿⠾⠿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⢿⣿⣿⡯⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣧⣠⡄⠀⠀⠀⢸⣿⣿⣿⣟⢻⣆⠀⠀⠀⡴⠛⠻⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣿⡿⠃⠀⠀⠀⠀⠙⣿⣿⣿⠿⢿⠀⠀⠀⠿⠋⢠⣿⡇⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠇⠀⠀⠀⠀⠀⢠⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⡔⣶⢻⣿⠟⠀⠀⠀⠀⠀⢠⣾⠀⣿⣿⣿⣧⣄⠀⠀⠀⢀⣿⣿⣿⡆⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣹⣿⠞⢡⠆⠀⠀⠀⠀⣼⣿⢃⣼⣿⣿⣿⣿⣿⠀⠀⠀⣿⡛⣿⡟⣷⡤⠀⢿⡗⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⢀⣤⠟⠛⠿⢿⣄⢹⣿⣿⣿⡀⠀⠀⢿⣿⣧⣾⣯⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣄⠀⠀⠀⠀⣾⡁⠀⠀⠀⠈⣿⡦⢿⠿⣿⣷⡀⠀⠸⠟⣻⣿⠁⠀⠀⠀⠀⢹⡆⠀⠀⠀⠸⠧⠄
⠀⠀⠀⠀⠀⠀⠘⣿⠿⠋⠀⠀⡄⡀⠘⢳⢄⣤⠀⠀⠘⡇⠀⢦⠀⢻⣿⣶⣄⠀⣿⠋⠀⠀⢠⠀⠀⠀⣿⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢀⠰⡇⣤⣰⣿⡄⣿⡄⠀⠀⣹⡀⠀⣱⣿⣿⡷⢻⠀⡸⢀⡀⠀⣾⠀⠀⣰⡏⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⢰⣿⠁⣿⠟⠀⣿⣿⣿⣿⣿⣿⠀⠻⢿⡛⠛⠃⣠⡧⣼⡗⠈⠻⣿⣧⣠⡅⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣾⣿⣦⣿⣥⣰⣿⣿⣿⠛⠙⣿⠂⠀⢤⣿⡆⢀⣿⡇⠀⠀⠀⠀⠈⢳⣾⣿⣶⠋⠲⢰⡦⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠈⠉⠀⠸⠇⠀⠀⠀⠀⠀⠀⠸⣿⡿⠁⠆⠀⢺⣡⠎
⠀⣴⣦⣄⣀⣀⢀⣠⣦⢸⣿⣿⣿⣿⣿⣽⣿⣿⣿⣇⠀⠀⣿⣄⡀⠀⡀⠀⢀⣇⠀⠀⠀⠀⠀⠀⢸⠟⠳⠶⡶⢿⣛⡩⣤⠶
⢠⣿⣿⣿⣿⣿⣿⡞⠉⠘⠋⠉⠿⠛⢁⣹⣿⣟⣿⣿⣷⣄⣿⣿⣵⣿⣤⣤⣸⡇⢀⠀⠀⠀⠀⣠⣼⠄⠀⠢⠀⠀⠉
⣿⣿⡿⠿⠁⠘⠃⠀⠀⠀⠀⠀⢀⣴⡾⠛⠙⣿⣿⣿⣿⣿⣿⣿⣄⢈⡻⢛⡏⢀⣼⣿⣶⠶⠟⠉
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⠁⠀⠀⠙⠛⠿⣿⣿⣿⣿⠿⣿⣿⣿⣟⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣶⣿⡿⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣲⣶⣿⡟⣻⡇
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣷⣶⣿⠿⠋⡩⠟⢀⣿⠃
⣿⣧⠀⠀⠀⠀⠀⠀⣈⠀⣿⣿⣏⢻⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠠⣾⠏⠀⣸⣿
⣿⣿⣧⠀⠘⠀⠀⣰⣿⣿⣿⣿⢹⡄⣿⣷⡀⣦⢀⠀⠀⠀⠀⠠⣉⣛⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⣼⡿⣿⡗
⣿⣿⣷⣄⠀⢡⠀⢻⣿⣿⣿⣿⡟⣿⣼⣿⣿⣿⣼⣶⣠⣀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢀⣼
⣿⣿⣿⣿⣦⣀⠱⣄⠙⢿⣿⣿⣾⡋⠉⣿⣧⣿⣿⣿⣿⣿⠳⣤⡀⠂⢤⣤⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿
⠀⠀⠀⠈⠭⠛⠛⢩⠳⣤⣙⠻⣿⣿⣄⣹⣿⣿⣯⣽⣿⣿⣿⣮⣿⣶⣤⣈⣭⣽⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠈⠉⠋⠉
⢶⣶⣶⣤⣄⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⢀⣠⣔⣤⡤⠚⠛⠛⠓
⠤⢿⣿⣿⣿⣷⣤⣄⣀⣀⣘⣿⡿⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣯⣶⣶⣶⣶⣿⣿⣿⣿⣿⣆⡀⠀⠀⢈⡻⠟⠛⠉⠉
⠀⠀⠈⠉⠙⢿⠻⡿⣿⣿⣿⣿⠃⠸⣿⣿⢿⣿⣷⠾⢻⣿⣟⢛⠛⠛⠛⠛⠻⠿⠿⠿⠏⢠⣿⣾⣭⣭⣥⣤⣤⣶⡾⠟⠉
⠀⠀⠀⠀⣤⠴⠶⢶⡿⠿⣿⣿⣷⣶⣶⣶⣮⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⡿⠿⠛⠋⠉⠁
⣴⣿⣷⡆⠀⠁⡄⠸⡇⢠⡟⠋⢉⣳⣄⣈⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⣼⣿⣿⡷⠶⣶⣾⣾⣿⣿⣿⣿⣿⣿⣏⠙⠛⠦
⣿⣿⣿⣷⠿⠋⢩⣿⣿⣿⣿⣿⣿⣿⠛⠛⠳⠶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⢿⣿⡿⠃⣀⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⣀⣉⣥⣾⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣶⣤⡀⠈⠻⢿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠿⠛⠛⠛⠻⢿⣿⣿⣆⠀⠀⠀⠉⠉⠀⠀⢀⣠⣤⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃⠀⠀⠀⠀⢠⣾⣿⣿⡿⠋⠀⠀⠙⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠁⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣦⣄⠀⣀⣴⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢿⣿⣿⣿⡟⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏
⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣦⣤⣤⣴⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡇⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⣦⣤⣴⣶⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⡀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⠉⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣷⣄⣤⠶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⠳⣦⣄⣀⡀⠀⣀⣠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣤⣄⣀⣀⣀⣀⣠⣤⣴⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⡀⠀⠀⠀⢀⣶⣶⣶⣶⣤⡈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⣤⣴⣶⣶⣶⡄⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⣿⣿⠇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠙⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⠏⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⣿⣿⣧⣀⣀⣠⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣄⣀⣀⣼⣿⣿⣿⣿⣷⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠉⣉⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣉⠉⠛⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠈⣿⣿⣿⣿⡁⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣦⣶⣾⣿⣿⣿⣿⣷⣶⣴⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁





⣿⣿⡿⠿⣿⠿⢿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢺⣩⣏⡹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢉⣿⠛⠋⠝⡷⣄⢠⣠⡤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⢺⣴⠞⠁⠀⠀⠀⠘⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠰⠐⠦⣠⣾⡁⠀⠀⠀⠀⠀⠀⠀⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣙⠻⠂⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠌⣷⣀⡜⠂⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠉⣿⣷⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣀⠐⣸⡿⠟⠀⠀⠀⠂⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠠⠄⢁⡾⠻⠃⠀⠀⠀⠀⠀⠀⢠⣠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⡀⢀⡾⠋⠀⠀⡗⠂⠀⢀⣀⣤⣾⢟⣥⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣄⠈⣻⠋⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠔⠁⠈⠁⠀⠀⠀⠀⠀⡘⣜⡿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣿⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣿⣿⣿⣿⡿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣾⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡹⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠨⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣭⣟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣠⣝⠶⣤⡀⠀⣴⢃⠀⡀⠀⣰⣶⡤⠀⣤⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣏⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠐⠿⣿⣷⣤⣈⠙⠢⣙⡲⢷⣼⡟⣩⣤⣶⣷⡷⢠⣶⣶⣆⡀⠀⠀⠀⠀⠀⠀⠈⢼⣿⣿⣿⠿⢿⠧⡀
⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⠙⠲⣍⣛⣡⠚⠛⣿⠀⣬⠹⣟⠻⠀⠶⠀⠀⠀⠀⠀⠸⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⡟⠉⠁⢠⣴⣿⣿⡇⠀⠁⠀⠀⠀⠀⡀⠀⠠⣿⣷⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣷⣶⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡑⢢⣷⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠀⢠⡏⠒⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢻⡆⠀⠀⠀⠀⠀⣰⡣⢌⣇⠀⠀⠀⠀⠀⣼⠇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡐⠡⢸⡇⠀⠀⠀⠀⠀⣿⠁⠀⢿⡀⠀⠀⠀⠀⣿⢠⠉⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣡⡀⣼⠃⠀⠀⠀⠀⢸⡇⠰⢂⢸⡇⠀⠀⠀⠀⢹⣄⣄⢡⡏
⠀⠀⠀⠀⠀⠀⣀⣀⣈⣙⣟⣁⣀⣀⡀⠀⠀⠈⣇⢁⠀⣸⠃⠀⠀⣀⣀⣀⣙⣿⣋⣀⣀⣀⡀
⠀⠀⠀⠸⠁⠘⠿⠿⠭⠭⠿⠭⠽⠿⠟⠂⠙⠀⠙⠻⡷⠋⠀⠋⠐⠻⠿⠿⠯⠿⠯⠿⠿⠿⠃⠘⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠸⣿⣿⣟⣻⣿⣛⣿⣿⡷⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠰⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⠶⠦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⡀⠉⠁⠀⠀⠈⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⣀⠀⠐⡢⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡤⡄⠀⢧⡴⠓⠀⢀⠇⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠋⠀⠀⠀⠀⣦⠈⢉⡆⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡤⠀⠀⠀⠀⠘⠛⠯⡀⠀⠀⠀⠀⡠⡻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠴⡚⢧⣘⠄⢠⣿⣾⣶⡴⢾⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣠⣴⣆⣠⣾⣿⣿⣯⡋⣼⠀⠀⠀⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⢟⠜⢰⡀⠉⢲⡊⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡻⣿⠿⢿⡿⡣⢧⡖⢋⡙⠦⠴⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡜⠁⢀⣜⠝⢲⠉⠻⢦⣄⠀⣸⠃⠀⠘
⠀⠀⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⣀⡀⠀⠀⠈⢧⠘⣦⠤⡿⠃⠀⣸⠀⣠⣾⣿⣇⡏
⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⢻⡡⣰⠆⠀⡰⠁⣀⣽⡿⠃⠈
⠀⠀⠀⠀⢰⠃⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡠⡪⠛⠁⢀⡜⠁⠀⣻⣿⠃
⠀⠀⠀⠀⣿⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⢀⣔⠕⠁⠀⢠⣾⣤⣄⣿⣿⣿
⠀⠀⠀⠀⢻⠀⢸⡇⠀⠀⠀⢀⡠⠄⣠⡻⠋⠀⠀⠰⠿⠿⡟⠛⣿⠛⠻⡄
⠀⠀⠀⠀⠈⠢⠈⠃⠀⠀⡐⠁⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠁⠀⣟⢆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠸⡀⡇⠘⡄⢸
⠀⠀⠀⠀⠀⠤⢒⡉⠄⡨⠐⢀⠄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⢃⢸
⠀⠀⠀⠀⠀⠈⠒⢖⣃⢠⣢⡵⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡲⣟⣿⠲⠶⡄⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⢲⢞⠠⣮⣯⣵⡏⠻⠏⠳⢙⠳⢸⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣕⠱⣢⢽⣿⠸⣿⣏⡋⠀⣀⣰⣠⣆⣽⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣔⢙⢾⡜⣯⡗⣦⣼⡹⣖⣽⣿⣿⣿⣿⣿⣷⢟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡱⡬⢥⣬⣮⢿⣿⣶⣼⣿⡻⢻⡻⠹⣿⣿⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣬⢶⣿⡿⠿⠿⢶⣿⢋⠖⢿⣠⢾⣽⣿⠟⣡⢶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡿⣷⢚⢊⣾⡿⡹⡟⣿⣙⡿⣿⠁⠀⠻⣛⢰⠝⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣜⣥⠷⣯⡭⢾⢛⣷⡟⠸⣿⣿⣪⣦⢄⡀⠉⠻⣿⢻⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣉⠐⠾⣥⢀⡊⢿⣟⢿⣇⣽⣜⣩⣿⢿⣽⣯⡻⠆⠀⣿⣽⡛⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠯⡽⣸⠶⣿⣏⢉⣀⣿⡍⣚⢿⣴⠽⣛⣇⣭⣻⣿⣿⡾⣧⡷⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠐⢴⠗⣀⣿⣿⣨⣉⣿⡇⠊⢯⠈⢻⣷⣏⣻⠉⢯⠟⣥⡶⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢲⣛⣯⣄⣠⢰⢯⡠⢀⠙⠇⠘⡛⠱⢶⡳⣭⣿⠛⠿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡒⠍⢽⢤⡦⠟⣓⢂⡨⠈⣦⣦⡇⣚⣸⣎⣟⡿⣿⣝⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠷⠟⣇⡅⠜⣷⣄⠼⡣⡐⣹⣥⠟⠳⡟⠐⡷⡫⢻⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢋⣟⡡⣥⡦⣉⣿⢷⣣⢜⠿⢥⠐⠦⣙⡽⠷⡟⠥⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠾⣅⣀⠀⠀⣭⢥⠈⣹⣩⣮⣥⠖⢲⠒⠋⠋⠋⡿⠀⠠⠜⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠢⠀⠈⠓⠲⣯⣀⣂⡿⣽⢃⠀⡅⠄⢃⠄⠀⡼⠉⠁⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⠢⢄⠂⠀⢀⢂⠘⡉⢫⢌⡽⡀⠀⠐⠀⠀⢀⣀⣀⡤⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠑⢄⠀⠀⡱⡘⢨⢯⢯⣿⠄⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⢀⠀⠑⠀⡮⢄⡬⡆⠳⣝⢷⣷⣀⡤⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠠⠀⠈⠀⠚⢈⠙⣮⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣒⣢⣀⠀⠀⠠⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢼⠋⣷⡟⣧⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠶⣮⣁⣀⡰⢚⠵⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠉⢮⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⠤⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣰⠁⠀⠹⡈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠇⠀⠀⠀⠱⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠾⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⡜⠙⡆⠀⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⠀⠀⠸⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣧⢀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣇⢸⡇⠀⣇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣿⣦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⣀⣀⠺⣍⣡⣴⣒⣒⣚⣀⣀⣿⣇⣀⣐⣒⣒⣲⣤⣨⣽⢂⣀⡨⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⠖⠲⣶⣶⣶⣶⣶⣶⣶⡶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣄⣠⣿⣴⣶⣼⣤⣴⣦⣷⣤⣴⣾⣤⣥⣤⣤⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣶⣶⣾⣿⣶⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠠⠤⢶⢄⠤⢤⣀⡀⠀⠀⠀⠀⠀⢀⠤⠐⠀⠉⠉⠉⠁⠂⠰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠚⠈⠁⠀⡤⠀⠀⡀⢀⠈⣌⢨⠉⠓⠤⠀⡠⠎⢅⢠⠂⠈⡄⠈⠀⠐⣀⠁⠀⠀⢉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⡀⢁⡵⠞⠁⠀⠀⠀⠈⠉⠁⠉⠐⠢⡔⣊⡴⠁⡀⠀⢈⣿⠐⢆⠀⠀⠀⠀⠀⠀⠠⡄⠀⠠⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠎⢢⠈⡱⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⠄⣀⠀⠀⠟⠀⠒⣡⠘⡁⠴⠆⢨⣤⡄⢀⠀⠀⠀⠀⠈⠀⠀⠰⠟⢠
⠀⠀⠀⠀⠀⠀⠀⡘⢀⠠⡞⠀⠀⣠⡞⢍⠀⢔⡠⠐⠁⣆⣠⣀⣥⠟⣣⠄⣠⠀⠀⠀⠀⠀⠘⠛⣣⡜⣄⢭⠀⠀⠀⠀⠀⠦⢀⡈⢁
⠀⠀⠀⠀⠀⠀⠀⡇⢀⡈⠁⠀⣸⠇⠠⢛⠈⠁⠀⠀⠀⢈⡩⠀⠸⠏⠉⠀⠴⠤⢀⠠⠀⠀⠄⠘⠧⠘⢏⣿⠁⠀⠀⠀⠀⠀⠀⠀⡨⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠄⣡⡆⠀⣃⠈⠀⡧⠀⠀⠀⠀⠀⠁⠀⢀⣾⡃⠀⠺⠧⢁⠄⢲⡾⡀⠐⢤⡀⢜⣀⠱⣦⡴⠀⠀⠀⠀⢸⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠁⣷⠀⠩⣄⠈⠁⡀⡀⠀⠀⠀⠀⠀⠀⠛⠓⣤⡶⠀⡋⡀⢀⠴⠈⠀⢾⣿⡹⢉⡆⠉⡁⠀⢀⣤⣔⣚⠒⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢁⢇⠀⠈⠻⢾⣇⠳⠄⠀⠀⠀⠀⠉⠀⠄⠀⠓⠈⠀⠀⠀⠀⠘⠓⠂⢈⣧⣸⠷⠄⠀⠀⠜⠑⣿⠟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢀⡷⠊⠐⢷⣙⡣⢦⡆⠛⠟⢹⠥⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣌⣁⠐⠁⠀⠐⡁⠀⠀⠠⣿⠂⣇⠡⣰⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢋⠄⠀⠀⠀⠩⠄⡨⣼⠳⣈⠯⠜⠀⠀⠀⠀⢀⣀⢠⠄⢲⠄⠬⣿⡿⢤⠄⡢⣶⠾⣜⠂⠀⡙⢤⣭⣓⢃⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠆⠀⠀⠀⠀⠰⣶⣳⠀⠄⣠⣤⠀⠂⠲⠄⠁⠀⠀⠀⠰⠂⠀⠉⠳⢛⡌⢻⣴⢀⣷⣾⣦⣈⣾⣙⣞⡌⣧⣾⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⡶⣯⡉⣀⣀⣀⡀⠤⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠹⣯⠀⣿⣿⣿⣿⡟⢉⣭⡼⠟⢧⣄⠘⣿⣯⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠢⢀⠀⠐⠻⣾⣿⡟⠋⠉⠀⠒⠉⠉⠙⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠙⡇⣹⡿⢛⡠⠖⣈⠩⡔⢂⠒⡄⠘⠶⣝⢻⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡅⠹⠀⢸⣿⠀⠀⠐⢲⠄⠀⠀⣤⣤⡀⠹⠇⠀⠂⢠⡴⠖⠓⠠⣴⣫⠔⣋⣴⡾⠋⠀⠈⠐⠡⠀⠀⢀⣈⢻⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⠀⠀⣸⡿⠀⠀⠀⠀⠉⠢⠄⠻⠿⠋⠀⠀⠀⠀⠀⢲⡦⣄⣠⣿⣵⣾⠅⠀⠀⠀⠀⠀⣀⠀⠀⡴⠋⠁⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡄⡠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠛⣟⣻⠟⠉⣀⣤⠴⣦⣤⡀⠉⠀⢈⣵⣦⠈⠂⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣏⣻⣴⠻⠟⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡧⢼⠀⠞⠁⣀⡀⠀⠈⠁⠀⠀⠈⠙⠃⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠁⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⣼⣿⡷⢺⡆⠰⠺⣿⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠏⣄⠠⠀⠣⡀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠄⣀⠀⠀⢀⠸⣿⣿⣿⢘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢧⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⠟⠿⢯⡸⠟⠄⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⣠⣽⣿⣿⠀⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠆⠀⠀⢠⠟
⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⢠⣄⠀⣈⢭⡀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠸⢋⣹⣿⣿⣄⣼⠻⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢶⡉⠀⠙⠻⣧⡄⠀⠀⠀⢀⣀⠀⢀⣀⡀⠤⢀⣤⡀⠆⠄⠠⠀⠾⢻⣿⣿⡯⠹⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⡐
⡄⠠⠄⠰⠶⠋⣛⠀⠶⣖⠀⠀⠀⠀⠀⠈⢤⡘⢋⣤⠌⠉⠠⠦⠉⠁⠐⢂⣤⣰⣧⣶⣤⣶⣶⣾⣿⡏⢾⣷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉
⠁⠈⠀⠀⠀⠀⠉⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠹⣾⣷⣀⠆⣠⣤⠤⣴⣢⣽⠻⢉⣿⣿⣿⣿⣿⠿⠿⣿⣄⣖⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢶⠒⢲⡖⢤⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠂⠈⠌⠛⠙⠟⠛⠉⠀⠒⡠⢾⠁⠈⠉⠉⠉⠀⠀⠀⠈⠻⡧⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠙⢶⠁⠓⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠷⡈⠷⠀⣷⣠⢄⡀⣀⣀⣀⡤⣰⡯⠒⣶⣄⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣝⠓⡦⣀⠀⠀⠀⠀⠀⢢⣍⠀⠀⠀⠞⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⣑⡶⢚⠚⣍⠫⡝⢠⡑⠘⣿⣿⣿⣿⣿⡇⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠋⠐⠓⠲⢿⣋⣬⡦⠀⠀⠰⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣹⠉⣡⠛⢤⠶⠀⢉⠀⡐⠀⠉⠙⠛⠛⠁⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⣯⢷⣼⣇⠀⠀⡃⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣤⡄⠈⠭⢀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⢻⣿⠾⡏⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠥⠀⠀⠀⠀⠀⠀⣾⣷⣶⣤⣤⡿⠛⠁⠀⠀⠀⠀⠀⠙⢇⠡⠀⠀⠀⠀⠀⠀⠀⡄⠀⠘⠙⠃⠀⠸⠂⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠰⠦⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢇⠀⠀⠀⠀⠀⠀⠠⠀⠀⡴⠂⡶⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣷⣶⣤⣤⣤⣤
⣿⣿⣟⠋⡙⢻⡉⣽⠛⣻⡙⢹⡿⢻⡏⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡌⢡⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⠐⠖⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⡥⢼⡿⡆⣹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⣤⣀⡟⣮⣶⣶⢟⡴⢶⣌⡵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⠀⠀⠀⠀⠀⢤⣝⡷⠂⢾⣷⣬⣟⣵⡾⠿⣴⠋⠀⠀⠀⠀⠀⠀⢫⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡏⢳⠾⠐⡄⠂⠀⠀⡸⣦⡌⠛⣦⡟⢹⡯⠦⠈⣴⢟⣧⣍⡦⠀⠀⠠⡀⢨⡈⠥⠸⡄⢍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠦⣀⣝⠀⠸⠇⠀⠀⣸⡉⣯⣴⣤⣿⣄⠀⠾⠟⠃⢿⣶⡜⣯⣠⡅⠀⠀⢠⣌⠋⢠⣇⢸⡦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡿⠀⠀⠀⢀⢶⣾⣭⢨⡷⠉⢼⣭⣿⡠⠚⢳⣦⣤⢈⢡⣄⡴⣿⣄⠀⠈⠀⠙⢥⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣽⢻⡇⠀⠀⢀⢮⠟⢻⠦⠻⢃⣴⣶⣿⠉⢣⡞⠀⢰⡆⠀⢸⠇⡠⡟⢛⡆⠀⠀⠐⡀⠛⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⡏⢋⢀⣄⠀⢞⡻⠀⣙⠻⢃⡜⣿⠟⢿⣶⠦⠽⠀⣻⡇⠀⠛⠣⢰⠁⢨⠜⡀⠀⠀⠀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣸⢛⣧⣀⠉⣩⡷⠒⣶⣙⣹⠂⣧⠀⠻⣧⣤⣆⠀⢰⡆⢰⡙⠲⡆⠀⠐⣏⢡⡀⣤⠓⠶⢩⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢶⡟⣳⣤⣶⢟⣷⣬⡝⢿⡌⢢⣴⠉⠛⠙⠀⣺⠁⣸⣛⣋⡱⠄⠘⠛⠀⠀⠀⠳⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡖⣸⠉⣀⢡⠟⠁⡼⣧⣈⡿⠶⣹⡇⣀⣀⠰⣽⡓⢋⣩⣭⡴⠶⠶⣦⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠛⠘⢵⣧⡀⣤⣶⢿⡟⠐⢦⣼⡇⢹⡏⠿⡶⠟⡛⢭⣿⡴⠲⢦⡷⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣱⣿⡿⣤⣼⡧⠀⢈⡇⣀⣄⠰⡇⠚⠃⣠⣽⡀⠀⠘⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢴⢳⣿⣆⣸⣿⡝⠀⢺⡿⠫⠿⢠⡧⠀⢈⣹⣧⣧⣀⣴⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡼⢁⡿⣯⣈⡿⣿⢤⡀⠀⣿⠀⠀⣨⠀⠀⠂⢍⣣⣉⢥⡆⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⡼⢡⡞⢡⣀⣉⡷⣟⠢⡁⠀⠹⠶⠾⠛⠠⢌⠑⠤⣿⠤⢜⣿⣦⠖⢸⠉⠂⠚⠁⠘⣳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⣁⢦⣴⣏⠘⣌⣩⣼⡁⢈⡳⣍⠢⣄⠀⢀⡀⠲⢤⡙⠲⣿⠦⡌⣧⢀⠳⠀⠀⠀⠀⢴⠾⠯⣽⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⡀⣡⢦⡰⢎⡵⣭⣄⢹⣆⠁⠌⠈⢷⣌⠳⣤⡈⠳⣤⡉⢷⡏⡁⡴⢿⠀⠁⠐⡆⠀⠐⠺
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣠⢞⣷⠦⡢⠉⣴⠳⡄⢿⠀⣿⣠⢢⠕⢊⣉⡴⢦⡙⠢⣌⠻⡾⠃⢑⠴⠎⣄⠴⠋⠘⠲⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣆⠠⢿⣴⠞⣿⣾⣭⠐⠛⠃⠀⠘⢃⣰⠖⣯⡴⠖⣤⠙⠂⣤⡙⠇⠀⠈⠳⠞⡣⠀⠴⡀⠀⠠⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡴⢿⡿⣤⣹⣄⠛⡇⠀⠀⠐⣏⠷⢞⣁⡀⢠⣟⢠⣴⡆⢻⡆⠀⠀⡾⠲⢁⣄⠀⠀⠉⣭⡻⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣆⡈⢿⠇⣘⡩⠀⠀⠀⢺⡅⠸⣏⡽⢃⣀⣿⡘⠻⠃⢈⡇⠀⠀⠈⡶⠎⣰⡄⠐⣀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠞⢀⣩⠇⠀⠀⠀⠈⣷⣀⣤⣄⢻⡿⢿⣛⠦⢀⣾⠇⠀⠀⠀⠀⠛⢈⢆⡁⠙⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣄⣈⠕⠀⠀⠀⠀⠀⣴⣯⡹⠾⠋⣀⣈⠙⠶⢤⣷⡀⠀⠀⠀⢸⡙⠟⣸⠋⣰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⣁⢈⡘⠂⠀⠀⠀⠀⢀⡲⠇⣠⣶⡆⣹⠏⣠⠶⢀⡇⡅⠀⠀⠀⠀⠉⠻⢉⠠⡈⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢌⠉⢠⡇⠀⠀⠀⠀⠀⠈⠉⢃⠹⠟⠋⣡⡄⠛⠺⠋⡏⠀⠀⠀⠀⠀⠈⠁⢉⠶⣿⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠏⠼⠛⠃⠀⠀⠀⠀⠀⠀⠀⢨⢂⣤⠶⣋⡟⠀⠤⣰⠇⠀⠀⠀⠀⠀⠀⠀⢙⣛⡛⠛⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣩⡵⠶⣻⡟⠯⠒⠦⢀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠋⡐⢳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣁⣴⣾⡏⠟⢠⣤⣶⠈⠀⠀⠀⠀⠀⠀⠀⢦⡀⢈⣁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣻⠁⣽⡬⢧⣥⠴⢄⣀⣀⠀⠀⠀⠀⠀⠈⣉⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡿⠋⣻⠁⢀⡀⢛⠀⠀⠀⠀⠀⠉⠛⠿⠦⣄⠀⠀⢴⡄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡲⡞⠛⠛⠛⠛⣋⠋⣹⠛⠹⢉⠓⠈⠋⣙⠛⡘⢃⡟⠐⠏⢚⢇⡀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⣀⣁⣄⣤⣆⣐⣀⣌⣁⣨⣅⣌⣀⣀⣁⣨⣁⣎⣀⣏⣰⣍⣠⣅⢈⣝⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠁⠉⠉⠉⠁⠉⠀⠈⠁

⠀⡀⠀⠀⠀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⢠⣤⠀⠀⠀⠀⣠⣌⢠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀
⢰⣿⣷⣄⡀⣈⠿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡘⣷⣄⢈⡿⠧⠀⢛⡀⠀⠈⠁⣼⣯⠈⣀⣈⡠⠞⠀⠂⠀⠖⠀⠀⠀⠈⠛⠁⠀⠀⣴⣿⣿⣿⡇
⠈⣻⣿⣿⡛⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣭⣝⠻⢮⣿⡾⠿⣤⠆⠈⠉⢻⡿⠂⢁⡌⠀⢹⡏⠁⠀⠈⠓⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡥
⠀⣿⣿⠏⠁⣿⡟⢛⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢿⣯⠉⣹⣿⣶⣜⠛⠀⣤⠤⠈⠀⠊⠁⢰⢈⣅⢆⢉⡄⢀⡀⠘⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⣹⣿⣇⣹⣿⠃⣤⣿⡏⠱⣮⣿⣷⡀⠀⣠⣶⣿⣮⣥⣤⣿⠛⠈⠻⠷⠈⠉⠄⠻⣷⣿⣿⠟⢯⡽⠋⣿⣿⣏⠛⠄⠀⠀⠡⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠸⠿⠿⠟⠻⠿⣿⣿⣿⣇⣠⣿⡿⢉⣿⣿⣿⣿⣿⣿⡿⠋⠀⣀⠄⠀⠀⠀⠐⢦⡀⠠⣿⣧⣦⣼⠷⣴⡎⢻⠋⠀⠐⣀⡀⠀⢀⠘
⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⠂⣸⣿⣿⣿⣿⣿⣿⠃⠀⠀⣴⡆⠓⣀⠹⣿⣦⡹⣦⠀⣿⣿⠀⡀⢈⣿⠆⣰⢆⣴⣿⠃⠀⢁⡀
⠀⣴⠟⢗⡀⣤⡀⠀⠈⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⠀⠺⣷⣾⣷⡦⢀⡄⢻⣿⡗⢠⠆⠈⠻⣾⣷⣿⠁⠀⡏⢸⣿⣯⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒
⠀⢿⣶⢛⣩⡙⠶⢰⡦⠈⣹⡿⠟⢠⣾⣿⣿⣿⣿⣿⣄⢀⣁⡹⣿⣧⠀⠀⢉⠛⢋⡠⠦⣈⠖⠋⠀⠑⠠⢀⡀⢂⡉⠁⠀⠀⣼⣿⣷⣶⡄
⠀⠘⢿⣟⠙⣁⠴⣿⠄⢶⣏⠠⣾⣿⡟⣉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣴⣿⣄⠀⠁⣠⣶⣶⣦⠀⠠⣴⣛⠽⠓⣶⣾⣿⣿⣿⣿⣿
⠀⣠⣿⣯⣵⡏⢠⣶⣤⣶⣭⣴⣿⢀⡿⠛⠿⠿⢿⣿⠿⠿⠟⠻⠟⢛⠛⠋⣠⡴⠟⠃⠸⠀⠹⣿⣿⠟⠀⡀⠈⠉⠚⠷⣭⣡⡙⠛⢿⣿⣿⡆
⠘⣿⣀⣰⣮⣡⣾⣿⠋⠙⢛⣿⣿⣋⡁⣀⢠⣴⣾⠷⠶⠶⠖⠛⠛⠛⠛⠋⣠⣤⣶⣾⣿⣤⣶⢠⣄⣶⠎⣷⣶⣿⣿⣶⡆⢀⠉⠛⢦⣈⠻⡿
⢠⡿⢛⣣⠈⠙⣻⣿⡌⢿⣿⣽⣿⣿⡿⣿⠟⢉⣠⣦⠀⣶⣾⣿⣷⡼⠿⣧⣿⣿⡿⢻⣿⣿⠇⠀⠈⠛⢿⣿⣿⣿⣿⣿⣴⠛⣹⣿⣦⠈
⠀⣧⣽⣿⠋⢻⣿⣿⢿⣶⣿⡿⠟⠿⣿⣿⣾⣿⣯⣤⣤⣿⣿⣿⣿⠿⡶⠋⠀⠀⠀⠈⠱⡆⠀⠀⣀⠀⠀⡼⠃⠙⠿⣿⣿⣿⣯⠻⢿⣧⡀
⠰⡷⠀⣿⣿⣉⠁⢴⣾⡻⢿⣇⠰⢄⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⣿⠄⠘⡇⠀⠀⠀⠈⠙⢿⡁⣶⠘⡿⠁⠀⠀⠀⠀⡀
⢠⣴⢺⣿⡏⠉⢀⣤⣿⣿⣿⣿⣷⣾⣻⡟⠉⠸⢿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⣷⡄⢀⡅⠀⠀⠀⠀⠀⠀⠑⢲⣦⡀⠀⠀⢿⡄
⠀⠀⠚⣻⣿⣦⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠺⠷⣸⣿⡷⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⡀⠀⠀⢿⡀⢻⠃⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠀⠂⠀⢀
⠀⠘⢶⣿⠿⢿⣿⣶⣿⣿⣿⣿⠁⢻⣿⣿⣷⣾⣿⡟⠃⠀⠰⠾⠟⠛⠛⠛⠛⠻⢿⣿⣿⣶⣄⠛⢋⣛⠃⢀⣤⣶⣾⣿⣿⣿⣷⣦⢸⣿⣿⢿⣦
⠀⠀⠀⠹⢷⣾⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣼⣿⣿⣿⠀⠻⠟⢠⣿⣿⣿⣯⣤⣤⣤⣈⠻⣿⣿⣿⣿⡏⠀⠻⠇
⠂⠀⣀⣴⣮⡻⢿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⠷
⡆⠀⢡⣼⣿⣿⣿⣿⣿⣿⠿⡃⠀⠀⣿⣿⣿⣿⠇⠀⠀⠈⠙⠛⢣⣼⣿⣿⣿⠃⢀⡿⠻⠟⠁⠀⠀⠀⢹⣿⢹⣿⣿⣿⠇⣹⣿⣿⣿⣿⣿⣿⡿
⡀⠀⣾⣿⣿⣿⣿⣿⣿⣽⣿⡛⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠻⢿⠿⠾⠿⠿⢻⣿⣿⣿⣋
⠃⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣿⣿⠆
⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶
⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡿⣿⡿⠃⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇
⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠻⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⣀⣀⣤⣤⣤⣄⣤⣶⣾⣶⣆⠀⠀⠀⠀⣾⠻⣿⣿⣿⣿⣿⣆⣀
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣴⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠙⠻⣿⣿⣿⣿⣿⡿⠻⠟⠃⠀⠀⢀⣼⣯⣴⣿⣿⣿⣿⣿⣿⣿⣦
⢰⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⣿⣿⡏⠀⠀⠀⠀⡀⣠⣿⣿⠤⣨⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣁⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣶⠇⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣶
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡟⠉⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣧⣄⣤⣀⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣷⣶⣀⡀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣿⣇⠀⠀⣠⣀⣤⣀⣀⣀⣤⣶⣾⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣄⠉⠻⢿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠙⠛⠿⠟⠛⠻⠿⠷⠄⡀⠀⠀⠻⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢀⠈⣿⣿⣿⣿⣿⣏⠙⠿⠂⢤⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⠁⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢴⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⢹⣿⠁⠉⣿⠟⠙⠃⠀⠀⠀⠈⢻⡟⠛⣻⣿
⠘⢿⣿⣍⠙⢀⣿⣧⡀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠈⢱⣌⢻⡟⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⣾⡿⠀⣹⣟⠀⠀⠀⠀⠀⠀⠀⠀⣱⣄⠙⠛
⠀⠀⢈⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠱⣦⣸⣿⣶⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣽⠿⠇⠀⠹⣿⠀⠐⠷⠾⣿⠿⠂⠀⣹⣻⣿⠚
⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠘⠷⠛⠋⠀⠀⠀⠀⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⢠⡤⡀⠐⠆⠀⠀⢀⠀⢨⡀⠀⠀⢢⣙⠷⠀⣀⣤⣤⣤⡀⠾⣿⡿⠛⢀
⠀⠀⣿⡏⠀⢸⣿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠁⠌⠛⠛⠀⠀⣀⠀⢀⡀⠀⠀⢸⡇⠀⡀⠀⠀⠛⣿⣄⡠⠿⣿⣬⣿⠟⢀⣼⡿⣶⠋
⠀⠀⢿⡇⠀⢸⣿⣮⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣤⠀⢀⣤⡀⠀⣾⣿⣶⠿⠶⣦⡀⠂⠀⠈⠀⢈⠁⠀⢀⡼⠃⢠⣄⠀⠀⣰⣿⣿⣿⢾⡶⠿⣷⣤⣼⣿⣦⣉⡀
⠀⠀⣸⡇⠀⠘⣿⡇⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⢠⣿⣿⠃⢀⡀⠘⣷⠄⡄⠀⢰⣦⡀⠈⠉⠀⠀⠁⠄⠀⠀⣿⡟⠀⠁⠀⠀⣀⣀⡛⢻⣿⠿⠿⠃
⠀⠀⣿⡇⠀⠈⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣿⡟⢷⣤⣥⡼⠃⣠⡧⠀⠛⢌⣁⠀⠀⢀⡐⠋⠀⠀⢰⣏⢱⣦⡀⣀⡈⠻⠿⠧⢺⣿⣀
⠀⣸⡿⠁⠀⠀⣿⠀⠁⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⣿⡕⠒⠠⠆⠀⢢⠈⠀⠈⢀⡀⠻⠏⠉⢸⠋⠁⠀⠀⣸⣿⡾⣿⡿⢿⣿⣶⣤⠀⢸⣿⡿
⢠⣿⡧⠀⠀⠀⣿⣄⠀⠀⣼⣷⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⢠⠀⢀⠀⢀⠀⠀⠼⣳⣦⡤⠀⣿⠇⠆⠀⢰⣿⠋⠀⠈⠀⠀⠸⠿⠿⠿⣿⣿⠇
⠘⣿⣷⠀⠀⠀⣉⠉⠀⠚⢩⣿⣿⣿⠁⠀⠀⠀⠀⠀⣠⠔⠂⠀⠀⠀⠀⠘⡷⢸⡇⣼⠀⠀⠀⣍⠙⠁⢸⣿⡆⠀⣠⣾⡏⠀⠀⢲⣤⡜⠀⠀⢰⣾⡿⠉
⠀⢸⣿⡄⠀⠰⡏⠀⢀⣠⡄⢿⠟⠻⢧⠀⠀⠀⣴⠞⠁⠀⠀⢠⡀⠰⠀⠲⠆⠛⠃⢾⣄⠀⣰⠇⠀⠀⢸⣿⠀⢠⡿⢿⠏⣡⡆⠀⠀⢀⠀⣸⣿⣿⠇
⠀⠙⠛⠁⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠈⠁⢠⠘⠀⠀⠀⠀⠛⠀⠁⠀⠀⠀⢀⡰⠀⠀⢻⣿⣿⣶⣤⠀⣾⣿⠁⣬⣿⣷⣶⣿⣿⣿⠻⣟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢠⣤⣶⡀⠀⠈⠃⠀⢀⠈⠙⠙⠿⠟⢢⣿⡟⢐⣿⣿⣿⣿⣿⣿⣿⣶⡿⣉⣿⡏
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠘⠁⠙⠋⠁⢀⠀⠂⢴⣄⠀⣀⡀⠛⠀⢛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣄⠚⠁⠷⠿⠶⠟⠷⠋⠻⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⢄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣄⣀⠀⢀⠀⠁⢪⣥⡜⢻⡄⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠈⠛⢿⣿⣤⣄⠈⠉⠻⣿⣿⣿⣿⣿⣿⣷⡚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡇⠀⠀⣀⣤⣿⠀⣈⣁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠙⢿⣿⣿⣶⣤⣼⣿⡛⠻⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡂⠀⠈⣉⣿⣆⢻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣤⣀⠉⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠘⠿⠟⠛⠛⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛⠿⠗⠘⠛⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⢉⠉⠁⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⡀⢀⠄⣠⠄⡀⢀⡀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢡⡾⠁⢠⠎⠁⢼⠃⣜⢟⡀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⣥⡤⡀⢂⠴⠋⢬⣾⡌⢱⡀⠆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⡇⢀⠙⠁⠐⠋⠘⠛⠙⠁⠈⢘⣇⢸⡆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠳⡀⠀⠀⠀⠨⠉⠒⣾⠚⠶⠀⡀⠀⠀⠤⠶⠄⠈⠉⠷⢦⣄⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠘⡄⠀⠀⢀⣠⠞⢻⡆⠀⠀⣀⢀⡀⠀⠀⠀⠀⣞⠀⠀⠙⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡈⢂⠀⠈⢣⣀⣈⡷⢄⡀⠣⣀⠎⡠⠔⠊⠁⢻⣤⠰⠎⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠳⣀⣀⡀⠉⢃⡤⢬⠿⣆⠟⢲⠄⠤⣀⠀⠀⠂⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡎⠉⢻⡗⣰⠋⠀⠐⠆⣾⠤⠎⠀⠀⠀⠁⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡜⠳⡁⢸⡇⠀⣜⢙⡇⠀⢠⠄⢤⠆⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡄⠘⢇⠆⠀⠀⠀⠀⠀⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠘⢇⠀⠀⠀⠀⠰⠀⣸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠌⠳⣲⠂⡲⠁⡠⠉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⡜⣤⠟⠉⠁⣴⠁⠀⡄⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⠘⠀⠈⡷⢤⠚⢤⡀⠀⢁⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠀⡄⠀⢀⡷⣀⠑⠔⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠀⠉⠢⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡦⡀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⣉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠈⠢⣀⠑⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢐⢀⣴⣁⡐⠂⠄⡀⠀⠀⠀⠀⠀⢠⣦⣤⢴⠀⡶⠶⠒⡆⠀⠀⠀⢳⣶⣿⣷⣶⣦⣦⣤⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⣶⣀⡀⠿⠀⠀⠁⣁⠉⠀⠨⣦⠀⠀⠀⠀⠀⣃⢀⡀⠀⡡⢔⣦⠁⠀⠀⠀⠈⠉⣿⣾⠛⢿⡎⠁⠩⡐⠬⣑⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣄⣈⣀⣱⡷⠖⡀⠘⢯⡂⠀⠀⠀⠹⠤⡀⢀⠀⢀⠞⢟⡡⠂⠀⠛⠥⠔⢠⠀⠀⠀⠀⠀⢫⣏⢣⡠⡻⡐⢦⣌⠣⣀⠇
⠀⠒⠂⠀⠉⣭⡥⢀⠀⠀⠯⠀⠀⠫⠄⠀⠒⠒⠒⠂⠒⠈⠉⠀⠀⠀⢸⡄⠀⢀⣠⣰⣄⣠⣤⣼⣀⣀⣀⠀⠀⠈⣷⠀⠳⡜⢆⢄⡉⢳⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠰⠈⢙⡻⢿⠿⡿⠿⠻⡿⠿⣿⣏⠛⡓⠀⠀⠀⠀⠘⢇⠑⢌⠢⡑⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠒⠂⢐⡶⠋⠁⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠉⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠖⠚⠿⠯⠽⠟⠛⠛⠒⠒⠲⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⡴⠶⠶⠶⠶⠶⣧⡄⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⡀⠀⣘⢒⠃⠟⢩⣏⠛⠛⠓⣌⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⢏⠉⠁⠀⢸⢿⠀⠀⠈⠹⣄⠀⠀⠀⠁⠀⠐⠀⠁⠀⠀⡀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠶⠄⠀⠀⠀⡸⠻⡀⠀⠀⠀⢸⣷⣤⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠣⡀
⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠁⠀⠀⣀⣤⣾⠇⠠⠀⠀⠀⠀⠀⢸⣶⣇⠀⠀⠀⠀⠘⢿⣿⣿⣶⣄⡀⠀⠀⠈⠀⢀⠀⠀⡀⠙⢦
⠀⠀⠀⢠⠞⠀⠀⠈⠀⠄⠁⠀⠀⣠⣾⣿⣿⡟⠀⠠⠀⠀⠀⢠⣠⠟⠛⢹⣤⡀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣦⡀⠀⠀⠁⠀⡀⠁⠀⠈⢳⡄
⠀⠀⢠⠏⠀⠀⠀⠀⠈⠀⠀⣠⣾⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⣼⡏⠀⢀⠀⠹⣇⡄⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⢀⠀⠀⠀⢻⡄
⠀⣠⡏⠀⠐⠒⠂⠀⠉⠉⡉⠙⠻⢿⣿⣿⠁⠀⠀⣀⣀⣀⣀⣿⡀⢀⣌⡔⠀⣹⡁⢀⠀⠀⠀⠀⣽⣿⠟⠋⠁⠀⠒⠀⠀⠘⠷⢤⣀⠀⠀⢻⡀
⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⡈⠉⣄⣶⣞⡯⠳⠛⠂⠋⠀⠀⢨⠁⠀⠻⢯⡽⣟⣶⢤⡠⠊⢀⠔⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠤⠷
⢸⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣡⠀⢘⠚⠁⠀⠀⠀⠀⠀⠀⣠⣿⣆⠀⠀⠀⠀⠈⠈⠋⣧⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⣾⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⢟⡀⠀⠀⠂⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿
⡇⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⠀⡀⠸⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟
⣧⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⡇⠀⠛⢻⣿⣷⠄⠀⠃⠀⠈⠀⠀⡴⢿⡿⡹⠁⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃
⢻⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠳⠭⠡⠆⠀⠀⠀⠀⠀⠀⠄⠒⠚⠁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⢸⡄⠀⠀⠘⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⢰
⠈⣧⠀⠐⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⡇⢣⡀⣸⡆⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠀⣦⣠⡏⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠙⠂⠀⠀⠀⡾
⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉⣿⠁⢀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⢹⣿⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠹⣆⠀⠁⠀⠀⡐⠀⠀⠀⠀⠀⠀⠐⠁⣀⣼⡟⠀⠘⡀⠀⠀⠰⠆⠀⠀⠀⢠⠇⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠀⠀⠀⣴⠃
⠀⠀⠀⠙⣦⠀⠀⣨⠅⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠁⢀⣼⠃⠀⠀⠒⠀⠀⠀⠀⣾⣧⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠠⠀⠈⠁⠙⠛⣋⣠⣴⣿⠏⠀⠀⠐⠀⠀⠀⢀⣾⣿⣿⣷⣶⣿⣿⡿⠓⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠈⠒⢶⡀⠁⠀⢀⠀⠀⠀⠀⠀⠈⢉⢻⠏⠀⠀⠊⠀⠀⠀⣠⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠰⠀⢀⠀⠀⢡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠠⠀⠀⠀⠀⠀⡉⠀⠐⠃⠈⠀⠐⠚⠋⠙⠢⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⢀⠃⠁⠶⠀⠠⠀⠀⠀⢀⠀⠀⠠⠀⠄⠀⠐⠀⠀⠀⠀⠀⢀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡘⡈⠀⠒⠀⡘⠄⡀⠀⡘⠤⠰⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢄⠈⠁⠤⠀⡄⠰⢘⣶⣀⣤⡤⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢩⡉⢙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠐⢙⡀⠘⠯⠤⠄⢀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠀⠀⠀⢆⠁⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠁⠀⠑⠠⡖⢀⡀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠠⠖⠶⠢⠀⠀⠁⠀⠀⠈⠃⠀⠈⠐⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⡆⡘⠀⠀⠀⠃⠀⠐⠉⠛⠱⠀⡎⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡂⠀⠄⢀⠩⢄⠀⠠⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠒⠀⢀⣐⠦⠀⠀⢀⠠⠔⠁⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⢰⡇⠃⠀⠁⠀⠀⠂⠀⢠⠌⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠄⠐⡄⠀⠠⠀⠘⠒⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⡄⠀⠀⢀⠀⠈⠻⢇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠠⠒⣄⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⠘⠂⠀⠀⠳⣄⡀⠀⠂⠰⠘⢃⡀⠀⠀⠀⣨⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠁⠂⢀⠀⠈⠉⠙⠓⠂⠭⠕⠚⠑⡠⠔⠂⠀⠀⠀⠙⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠚⠂⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠐⠉⠀⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠄⠈⡣⢄⡀⠀⠀⠀⠀⠈⠂⠀⡀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⡖⠁⡠⠀⠈⠑⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠑⠀⢻⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠠⠒⠅⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠔⢠⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠇⢨⠄⣉⣀⡀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠐⠒⢲⠊⠁⠑⣄⡈⠀⠀⠀⠀⠀⠀⠀⠔⠧⣀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠔⠋⠀⠈⠑⠦⡀⢀⠔⠈⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣄⠀⠱⣤⣀⠀⠀⠙⠛⠋⣀⣤⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠻⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣧⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⣤⣀⣀⢀⣀⣠⣴⣾⣿⣿⠟⠋⠉⠉⠙⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠻⢿⣿⣿⠻⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⣰⡿⠿⠿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣄⡀⠀⠀⠀⣀⣴⣿⣿⠇⠀⢹⣿⣿⣶⣤⣤⣤⣴⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠲⠆⠰⠖⠀⠀⠶⠂⠲⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠒⠒⠒⠀⠐⠒⠒⠒⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣳⠓⣿⣿⣿⡟⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡛⣩⠆⣩⡽⣼⡇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⢻⣿⣯⣥⣽⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄⣀⣀⣀⣀⣀⣈⠉⣉⣋⣉⢉⣉⠋⣉⣉⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠈⠃⢀⠈⡈⠁⠀⠉⠀⡁⠈⠉⠀⠁⠉⠀⠈⠀⠉⠈⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠈⠀⠉⠈⠉⠁⠀⠉⠉⠁⠘⠁⠀⠉⠙⠈⠃⠀⠈⠉⠁⠈⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠈⠛⠐⠂⠂⠐⠋⠘⠃⠐⠃⠐⠒⠀⠓⠒⠀⠂⠘⠂⠂⠀⠐⠒⠂⠐⠂⠐⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠒⠐⠒⠐⠒⠂⠐⠀⠀⠰⠖⠲⠆⠆⠀⡆⠦⠰⠖⠦⠖⠶⠀⠶⠆⠦⠀⠆⠀⠶⠂⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠄⠀⠀⠤⠄⠠⠤⠤⠤⠤⠤⠄⠀⠤⢤⠄⣤⡤⠀⡄⠀⠄⠀⣤⠀⢤⠄⠠⣤⠄⠠⠤⡄⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⢤⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⣀⣀⣀⣀⡀⠀⣀⢀⡀⣀⠀⢀⡀⢀⠀⠀⣀⠀⡀⠀⡀⠀⡀⢀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⢀⠈⢀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠈⠀⢉⠁⠈⠀⠈⠉⠀⠉⠉⠁⠀⠁⠈⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠉⠁⠈⠁⠁⠀⠈⠉⠁⠉⠀⠉⠉⠀⠉⠉⠁⠘⠋⠀⠀⠘⠉⠋⠛⠂⠘⠛⠛⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠃⠀⠋⠀⠀⠀⠈⠂⠘⠀⠒⠀⠀⠐⠛⠙⠀⠒⠒⠀⠘⠃⠐⠐⠓⠒⠀⠆⠀⠒⠖⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠃⠐⠒⠒⠀⠐⠒⠂⠀⠒⠲⠲⠀⠶⠀⠴⠰⠆⠀⠲⠀⢰⠤⠄⠀⠀⠶⠠⠆⠀⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠄⠰⠠⠄⠠⠆⠰⠂⠀⠤⠔⠤⠴⠦⠀⠤⠤⠤⠄⠠⠤⠤⠠⠄⣤⠠⠤⣤⣄⣤⠀⡀⠠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠤⢤⡤⡄⢠⢠⢤⠀⢠⠄⣀⠀⣀⣀⠀⡄⡄⠀⣀⡀⢠⠀⢠⣀⡀⠀⢀⡀⢀⡀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⠀⣀⠀⣀⣀⢀⡀⠀⡀⣀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⢁⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⣈⠀⠀⠀⠀⠀⠀⠁⠉⠀⠁⠈⠀⠀⠈⠉⠉⠁⠈⠉⠁⠈⠁⠈⠁⠉⠁⠈⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠉⠀⠉⠈⠉⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠃⠘⠓⠚⠂⠀⠃⠐⠂⠐⠒⠂⠰⠖⠲⠄⠂⠀⠆⠖⠖⠀⠂⠀⠀⠒⠀⠲⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠀⠐⠒⠀⠐⠂⠐⠖⠶⠀⠲⠤⠒⠴⠄⠲⠤⠤⠀⠠⠤⠤⠤⠀⠠⡤⠀⠀⠠⠤⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠰⠀⠰⠆⠀⠤⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢤⢀⣀⣀⣠⠀⣄⢀⠀⣀⡀⣀⡀⣀⡀⢀⣀⣀⡀⠀⠀⡀⢀⣀⡀⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠉⠉⠉⠁⠘⠋⠁⠙⠓⠚⠋⠛⠛⠀⠛⠑⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠛⠓⠂⠛⠀⠛⠀⠒⠺⠒⠂⠂⠔⠒⠂⠐⠒⠒⠆⠐⠦⠒⠒⠲⠀⠒⠰⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠒⠒⠂⠒⠒⠀⠐⠒⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀

⣀⣀⠀⣶⠀⣤⣾⢿⣧⣤⠤
⣽⣿⣟⣿⣽⢻⣽⣿⣛⠉
⣿⣾⣛⣻⡿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣥⣏⣹⡯⢵⠿⢽⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠⣤
⣯⡹⠏⣷⡏⠐⣨⣭⣙⡲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣿⣿⣿⣿
⠼⣧⢀⣰⣾⢍⡶⣮⠹⣠⣬⠈⠉⠛⠦⢀⡀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⡀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣤⣤⣴⣿⣹⣿⣿⣿⣿⣾
⠿⠿⠷⢖⣯⣿⣭⣆⠫⠋⣭⢠⠀⠀⢲⡀⠀⣬⣶⡖⠚⢛⠛⠛⠛⣓⡚⢳⡾⠷⠾⠿⠾⠶⠴⠶⢿⣤⣤⣾⣿⣿⣿⣿⣿⣿⢣⣟⢻⣏⣿⣽⣛
⣿⣿⣟⢿⣶⣶⡶⠿⢿⣿⣿⣿⣶⣶⣆⣬⡼⣷⣿⡷⠀⠴⢀⠒⠂⠐⡀⣄⡀⠂⠀⣀⢀⡱⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣸
⡽⢯⢿⡷⣼⣵⣦⣤⣾⡽⣡⣿⣿⣿⡏⢟⢻⣟⣻⣆⢀⣴⡾⠓⠲⠆⠠⠶⠮⠽⣭⠿⣭⠿⡩⠯⣩⣽⣿⣿⣿⣭⣭⣭⣭⣬⠭⣭⠥⣤⠤⣤⠦
⢁⠻⣹⢟⣯⣫⠩⣹⣏⠈⣿⠀⣶⢰⡆⣶⣶⣿⡇⠦⢸⡟⠀⠀⢐⠂⢀⣠⣴⡆⠀⢀⠀⠀⠄⠀⢬⣿⣿⣿⡿⡻⡿⠿⣶⠖⡿⢵⢣⣬⣦⣬⢭
⡤⣾⢫⣿⣿⣿⢼⠿⣿⠀⣿⡀⣿⢸⣇⣿⣿⣿⡗⠀⢸⡇⠤⠒⢀⣾⣿⣿⣿⣿⣿⣷⣤⣀⠠⠀⢠⣼⣿⣿⣿⣷⣿⣸⣏⣼⣆⣴⣷⣶⣿⣿⣯
⡇⣿⢸⣻⣿⣿⠿⡌⣿⠛⣿⠃⡿⢸⡇⣿⣿⣿⠉⠦⢸⡇⠀⣤⣿⣿⣿⣿⡟⠟⢻⣿⣿⣿⡄⠈⠀⣼⣿⣿⣿⣿⡗⣿⡧⣿⣿⣿⣿⣟⣿⣿⣿
⡇⣿⠸⢻⢹⣿⠼⠀⣿⠀⣿⠀⡇⢸⡆⣿⣿⣿⡄⠀⢸⡅⢸⣿⣿⡿⡉⢀⣿⣦⣍⣼⢎⣿⣿⠀⢃⢹⣿⣿⣿⣿⡇⣿⣧⣿⣷⣿⣿⣻⣿⣿⣿
⡇⣿⠠⠉⢸⣏⠠⠸⣿⠀⣿⠀⣁⢸⣗⠿⢉⣝⣛⡀⢸⡄⢸⣿⣿⣷⡟⠛⣫⡉⠉⠁⠀⣙⣿⢗⡀⢸⣿⣿⣿⣻⠇⣿⠷⣿⡯⣿⣿⣿⣿⣿⣿
⡇⣿⠰⠐⣺⡟⠗⠰⣿⢸⣿⡄⠟⠔⠉⠀⣐⢚⠧⠀⢸⣀⣼⣿⣿⡟⢁⣾⣿⣿⡆⠀⡀⢠⣿⠟⠷⣿⣿⣿⣿⣿⣷⣏⣹⣿⣿⣿⣿⣿⣿⣿⣿
⡇⣿⠀⠐⣿⡇⠂⢴⡿⠈⠙⠂⠀⠀⠀⢈⣰⣾⠦⠀⢸⣟⣼⣿⣿⠞⢸⣿⣿⣿⡇⢹⠋⢨⣿⠰⠀⢺⣿⣿⡿⣿⣿⣿⣿⣦⣜⠿⢿⣿⣿⣿⣿
⡗⠿⠀⢸⠿⠧⠃⡤⢀⠁⠀⠀⠀⠀⣴⢾⣿⣿⠂⠁⢼⠷⠿⠿⠛⠛⠚⠛⠛⠛⠓⠚⠛⠛⠋⠐⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣮⡻⠿⢿⣿
⣇⣿⠁⠀⠠⠀⠁⠀⠃⠀⠈⠁⣶⡋⣿⢸⣿⡟⠂⢀⡔⠂⢲⣶⠶⣶⡶⣿⣿⣿⢿⣿⠿⣿⡷⢰⣆⠀⠹⣿⡿⣿⣿⢯⣯⣿⢻⣯⣿⣿⣷⣬⡻
⠋⠁⢀⣁⡂⠀⠢⠀⠀⢠⡄⢺⣿⡄⣿⡟⠏⠀⢠⣿⡇⠀⣾⣿⣋⣁⣴⣿⣿⣿⣷⡀⣤⣸⡇⠰⣿⣦⠀⠈⢹⣿⣿⣸⣿⢠⣞⣿⣿⣷⡾⡿⢿
⠁⠘⠋⠖⣀⠰⡀⠀⠁⣿⡇⢸⣿⣧⡿⠅⠀⣠⣿⣿⡇⡄⣿⣇⠀⢸⣿⣿⣿⣿⣿⡇⠈⣿⡏⢰⡟⣿⣧⡀⠀⠐⠿⢹⣿⢽⣿⢛⣿⣿⣿⣿⣿
⠰⠆⠶⠀⠈⠲⢰⣿⠀⣿⣏⡸⠿⠏⠀⠀⣴⣿⣿⢿⡇⠀⣿⡷⠞⢸⣿⣿⣿⣿⣿⡇⠤⣿⣧⣰⣿⡌⢿⣭⡄⠀⠀⠹⢿⣾⣿⢸⣿⣿⡿⣿⣿
⠶⠄⠀⣀⡀⠀⢾⣿⠗⣿⣷⡔⠀⠀⠀⣼⣿⣿⢣⣿⡧⢒⣿⣶⣶⣾⣿⣿⡿⣿⠿⠛⢻⡏⣿⠀⠹⣿⣆⠻⣿⣤⠀⠀⠀⠹⢿⣾⣿⣇⣵⣿⣻
⡞⠈⢰⣿⣿⡄⣼⣿⡧⠋⠉⠀⠀⢀⣞⣿⣿⢣⣿⡽⠀⣼⣿⠿⣟⠃⣨⣿⣿⣷⣬⢏⡍⠁⣿⣇⠀⠘⢿⣦⠙⣾⡶⣀⠀⠀⢈⣿⣿⣿⣿⣿⣷
⠙⣁⣿⣿⣿⡇⣿⣿⡇⠁⠀⠀⢠⣾⣿⡿⢣⣿⣯⠀⣰⣿⣿⣿⡿⠐⣿⣿⣿⣿⣿⣘⡶⠂⢿⣿⣆⠀⠸⢿⣧⡉⣿⣿⣆⠀⠀⠀⠀⢿⣿⣿⣿
⠦⢰⣿⣿⣿⣇⣿⠍⠀⠀⠀⣰⣿⣿⣿⢣⣿⡘⠃⢀⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣌⣉⣁⣸⣿⡿⣆⠀⠘⢿⣿⡌⢻⣿⣷⡄⠀⠀⠳⣿⢿⣿
⡑⢸⣿⣿⣿⡿⠁⠀⠀⠀⣰⣿⣿⣿⢡⣿⢣⠀⠀⣾⣿⣿⡿⢿⠿⠞⠛⠛⠛⠁⠈⠉⢩⣭⡹⣿⣿⣿⡄⠀⠈⢿⣿⣎⠻⣿⣿⣦⣄⣀⣨⡤⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠛⠛⠒⠲⠤⡀⠀⠀⣼⠀⠀⢳
⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⢠⠇⠀⠀⡼⠒⡄⠀⠀⠀⠀⠀⢀⡤⠤⡄
⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⣀⣀⣤⠴⠊⢠⠏⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⡴⠋⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡏⠀⠀⠀⠀⠠⠚⡆⢀⡤⠞⠉⠀⠀⣀⡴⡅
⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣳⣀⣠⣤⣤⣤⣞⢠⠏⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⢠⡞⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⡿⣏⢹⣿⣿⣿⠟⠋⣹⠀⠀⠀⠀⠀⠀⡶⠋
⠀⠀⠀⡾⠀⡇⠀⠀⠀⠀⠀⣠⣾⣿⣇⣼⠃⣿⠀⠉⠉⠁⠀⢠⠏⠀⠀⠠⢴⣒⠺⠥⣄⡀
⠀⠦⣔⡇⠀⢻⠀⠀⣀⡤⣾⣿⠿⠛⡿⠁⠀⣿⡴⣷⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⡄⠀⢹⣷⣦⣄
⠀⢆⠈⢳⡀⠈⠑⠋⠁⠀⠀⠀⠀⠈⠀⠀⠐⠋⢀⡇⠀⢠⣤⣤⣴⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⡆
⠀⠈⠓⢦⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣸⣋⠀⠀⠀⠀⠀⠀⡠⠖⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡏⠀⠀⠀⠀⣴⣿⣿⣤⣿⢰
⠀⠀⣌⠉⡏⠀⠀⠀⠀⠀⢸⠁⣀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠻⠿⣿⣿⡟⢸
⠀⠀⠹⡟⡇⠀⠀⠀⠀⠀⠸⡄⠛⠁⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠃⢸
⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡜⠠⠀⢄
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⢠⠃⠀⠣⣀⡇
⠀⠀⠀⠀⠸⡄⠀⠀⠀⢀⡆⠀⠀⡄⠀⠀⠀⠀⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⢸⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⢦⣀⠀⠉⢀⣠⢾⠀⢄⠀⠀⠀⠈⢧⠀⠀⡄⠀⠀⣀⣀⣠⠤⢶⠆⠀⠒⢹⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠘⡇⢸⡏⠉⠉⠉⠹⡆⢰⡏⠉⠉⠉⠀⢸⠀⢸⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠸⠀⡼⠀⠀⠀⢸⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⠀⣧⢸⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠀⠰⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⡎⠀⠀⠀⢀⠀⢨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣠⢌⢳⡕⠂⣉⠀⠤⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠬⠤⢾⣷⠎⠈⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⠀⠀⠀⠀⡀⢠⠂⠁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⣀⣨⣏⠛⠉⠁⠀⠀⠀⢠⢆⠁⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⣤⠀⠀⠀⠀⠀⠀⠈⢯⠁⣿⡷⢄⣀⠐⢈⡡⠋⠀⠁⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠄⠀⠀⠀⠀⣀⡴⠆⠐⠚⠚⠛⠁⠠⠉⠉⠁⠀⠀⠀⠰⡎⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⣆⠠⠤⠤⠔⠖⠒⠫⠦⡀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢣⠀⠑⢤⠀⠀⠉⠁⠙⠀⡀⢀⣽⢄⠀⠀⠀⠊⠀⠀⣴⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠵⢲⠃⠠⣀⠀⠀⠀⠀⢱⠀⠈⢨⡱⡤⣀⣀⠤⣪⠃⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠙⡄⠀⠉⠉⠓⣦⠀⠀⢣⣀⣀⡵⣽⣄⡀⣀⣷⡀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⡦⣄⡀⠀⠀⠀⠀⠀⢫⢹⡀⠈⠺⣝⣛⡼⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣠⢾⣅⠀⢸⠖⢳⣄⣀⣠⡜⠀⢣⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠙⢷⣼⠀⢸⠀⠀⢧⢹⠀⠈⢣⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣀⢸⡄⠀⠸⡄⢧⠀⠀⠱⣄⠀⠀⣾⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡝⣇⠀⠀⠱⡈⠣⡀⠀⠀⠑⠺⢷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠇⠘⢆⡀⠀⡱⣄⠈⠢⣄⣀⡠⠊⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⢙⠗⠢⡈⠑⣦⠴⠋⠀⡀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⢁⡀⠈⠂⡄⠈⠋⠉⠄⠀⠌⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠇⡀⠢⠤⠄

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠉⠉⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⣀⡤⠶⠙⠁⠀⠀⠀⣀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠪⠀⠀⡇⣠⠀⣠⠔⠉⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠂⠀⣨⠰⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣁⣙⡋⡀⠀⠀⠈⠐⠋⠀⠀⠀⠀⠤⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠑⡦⠤⣀⣀⣀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠸⣕⡄⣀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠱⣄⢠⡔
⠀⠀⠀⠀⠀⠀⠀⠠⠸⠀⠿⡣⡀⠃
⠀⠀⠀⠀⢠⡀⠀⠠⠆⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠁⢀⣠⡶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠀⠀⣀⠠⠛⣧⡁⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⢠⠀⠈⠻⣷⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣀⣀⣀⠀⡰⠀⠀⠣⠩⣤⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢫⡁⠀⠀⠀⠀⠀⠀⠈⢷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢀⡄⠀⠠⠔⠂⠀⠈⢐⡄⠀⠀⠰⣦⠤⠠⢤⡀⠈⠻⢾⣧⡀⣀⣀⣀⣀⣤⡄⠀⠀⠊⠀⠃⠈
⠀⠀⠀⠈⢷⣀⣀⡼⠷⠒⠊⠉⠉⠑⠚⠾⢧⣀⣀⡾⠃⠀⠀⠀⠘⣶⣶⣶⣾⣤⣶⡏⠀⠀⣀⠔⠐⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢹⣇⣽⣿⣿⣭⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠾⠿⠏⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⢀⡶⢺⡇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢀⠎⠀⠀⠀⣤⣿⣿⣿⡇⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣴⣿⠀⠀⠀⠀⠥⠹⡟⣻⠆⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⡓⡏⢩⠀⠀⠀⢘⡀⢰⣾⣇⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠈⠜⢀⣠⠄⢸⣏⣼⡯⠆⢱⠀⠰⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠇⠐⠩⢯⡠⢺⠿⢟⠰⣌⣬⢦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠐⢠⡞⢗⣿⢀⡾⠀⠧⢒⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠉⠉⢀⣄⠂⠘⣸⣤⣯⡖⣩⢵⡈⢻⡂⠑⠂⠀⣤⡔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠓⠺⠇⠀⠛⠲⡤⠟⢣⢿⣤⠇⢸⠇⢀⠙⠢⢄⠀⠸⠃⡅
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠂⠀⠀⠀⠀⠐⠀⢰⡇⢠⠋⠠⢀⡸⠋⠀⠀⢸⠊⣔⣦⠙⠢⠁
⠀⠀⠀⠀⠀⡀⠀⠀⣀⠠⠀⠀⠀⣀⠶⣤⡘⣿⠉⠒⡖⠁⠀⠀⠀⠈⢸⠈⣻⢵⢈
⠀⠀⠀⠀⠀⠿⠖⠒⠃⠈⠀⢩⣯⡵⠟⢻⢿⣏⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡍⢸⡾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢀⣼⣿⡛⢻⠿⢥⠬⠥⠤⠄⠀⡞⡈⣿⣷⢀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠱⣖⣫⡿⠟⠠⣿⠿⠿⣭⠼⢿⣿⠤⣾⡿⠿⢇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠉⠈⠁⠈⠋⢛⣒⡒⣒⣲⠀⠀⠐⡂⠀⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⠀⠀⢨⠀⠈⠉⠉⠉⢉⠁⠀⠀⠂⠀⠀⠀⠄⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣄⠐⠀⠐⠣⠀⢠⠆⢁⠀⠀⢸⠀⠀⠀⠀⠀⠀⡐⠀⠀⡘⠀⣄⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⢟⣰⠀⠀⠃⠀⠀⠁⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠊⠐⠒⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⣀⠀⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣩⠶⡀⠰⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⠂⠀⠀⠀⠀⠀⡴⠀⠈⠐⣀⣧⢞⠁⢠⠀⠀⢀⠠⠀⠀⠄⠚⢢⡄⠊⠉⠹⡄
⠀⡲⠐⠄⡀⠀⢀⣼⣗⠇⠈⠀⠀⠈⠀⠀⢧⠀⢀⢸⠏⠜⢈⣶⡋⠈⠓⠀⠀⣠⠞⠀⠀⠀⡁⠀⠀⢠⢃⠄
⠀⠸⡂⠬⣟⣴⡯⠦⠯⠋⠀⠀⠀⠀⠀⠂⠈⠿⣿⣴⣮⠜⠉⠜⢁⠠⠀⠀⠀⠘⢄⡢⣀⠢⠁⣀⣀⡜⠁
⠀⠀⠄⠀⡐⡿⠗⠀⠀⠤⠀⠀⠀⠀⠀⢀⡴⠚⢹⠋⠟⣛⣿⢣⡀⠀⠀⠀⠀⠀⠀⣉⡻⠛⢻⠛⠓⡀
⠀⠀⠀⠈⠁⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠜⠀⠀⠀⠈⡆⠀⠉
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣿⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⢰⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣿⣿⣿⡄
⠀⠀⠀⠀⣼⣿⣿⣿⣧⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⣼⣿⣿⣿⣧⡄
⠀⠀⠀⠀⢹⣹⠿⡏⡏⠀⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⡇⠀⢹⣿⡿⣯⣿
⠀⠀⠀⢀⣿⣿⣤⣿⣷⡀⢸⣿⣿⣷⣼⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣇⢀⣾⣿⣇⣿⣿⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⢿⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠿⡿⠀⣿⣿⣿⣿⣿⡅
⠀⠀⢴⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢾⠁⠀⠀⢈⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢄⡀⠀⠙⢦⠔⠋⠀⠀⣠⠞⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⢄⡀⠙⢄⠉⠓⠒⠤⠴⠒⠒⠉⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠉⢢⠈⠓⢤⣀⠀⠀⠀⠀⠀⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣀⠤⠒⠒⠒⠢⡀⠀⡇⠀⠀⠈⠉⠉⠉⢉⡭⠕⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠋⠀⠀⠀⠀⠀⠀⢹⠀⡞⠀⠀⠀⠀⠀⡰⠋⠀⢀⠴⠒⠒⢤⡈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⠴⠃⣴⠁⠀⠀⠀⢀⡜⠁⠀⡰⠋⠀⠀⠀⠀⠱⡀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠉⠉⠀⢀⡤⠊⢿⢄⡀⠀⣠⠎⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⢣⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠉⠒⢌⡲⢍⣉⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⢦⠀⠱⡄⠀⠁⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⠀⠀⠀⠀⠀⡟⣄⠀⠀⠀⠀⠀⢀⠇⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⢸⠀⠀⠀⠀⠀⢇⠈⠦⣀⠀⢀⡠⠋⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠑⠤⣀⡀⠀⠀⠀⣀⠴⠋⠀⠀⣸⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⣀⠀⠀⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢤⣄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠘⣏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢦⡘⢶⡿⢈⣷⣫⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡒⣾⣆⠃⠋
⠀⠀⠀⢠⣴⣶⣶⣶⣾⣶⣦⣸⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⠀⠙⠶⠚⠀⠀⠀⠀⠀⠀⠀⣀⠛⠶⠟⠀⠀⠀⠀⠀⠀⢲⣤⡀⠀⣥⣭⣿⡆⠺⠟⠁
⠀⠀⠀⢼⣿⡟⣻⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣄⠘⠻⢋⢻⣷⣶⠆
⠀⠀⠀⢾⣿⣸⣿⣿⣿⣿⣃⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣇⢰⣿⣿⣿⠟
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⡿⡾⠿⠛⠁
⠀⠀⢰⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠓⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣿⣆⠀⠘⢀⣐⣒⢢⣄⡀
⠀⠀⠀⠙⠺⣬⣿⣿⣿⠟⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⡟⢿⣿⣠⣴⢿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⣦⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣭⣿⡟⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⣏⡿⣿⣿⣿⣒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⣿⠃⣴⠀⠀⠀⢀⣴⣤⣄⠀⠀⠀⠀⠀⠘⣿⣿⠋⠀⡜⢿⣿⠟
⠀⠀⠀⠀⠠⣤⡀⠀⢀⢀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠓⠀⢸⡿⠀⠀⠀⠹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⢿⣿⣷⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⠁⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠻⠿⢧⠄⠀⠀⠀⣾⣤⠀⠁⠀⠀⠀⠀⢀⣿⣿⠿⠃⢸⣿⣦⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⢤⣤⣶⡚⣠⣶⠀⣠⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠈⠙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣾⣿⣿⣿
⠀⠀⠀⢴⣦⡈⢻⣿⣿⡟⠁⠈⠁⢠⡜⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣼⣿⣿⣿⡿⠀⠀⠀⢠⣼
⠀⠀⠀⠸⣿⣿⡄⠈⠛⢿⠟⠃⢤⣜⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⡟⣿⣿⣿⣿⠇⢠⢀⣴⠿⡟
⠀⠀⠀⠈⢻⣿⣿⡏⢀⣰⣾⣆⡰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠈⣿⣿⣿⣿⠟⢀⣼⣿⡿⠞
⠀⠀⠀⣀⣼⣿⣿⣷⡀⠈⠉⠉⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⢄⠹⣌⠛⢃⣴⣤⣤⣤
⠀⠀⠀⠉⠻⢿⣿⣿⣇⠀⢀⣴⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠂⠉⠁⠈⢉⣥⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠠⠼⠿⠂⢸⣿⣿⣿⣿⡿⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠻⠛⠀⠠⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠿⠿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⠀⠀⣠⡶⠆⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡉⠉⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠈⠀⠘⢿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠈⢣⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠙⣤⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢠⣧⠋⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢣⠀⠁⢀⡸⣧⡄⠀⣸⡀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡘⠀⣴⠋⠀⢹⣿⣦⠙⠁⢸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⣠⣾⣏⣀⣀⣈⣿⣿⣷⡄⢸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢹⣿⡟⠛⠛⠛⣿⣿⣿⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⣾⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣶⡶⠟⠛⠻⠷⣾⡟⠉⠰⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣶⣋⣤⣥⣍⣠⣭⣤⣥⣄⣶⣶⣶⡄⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⣿⣏⣤⣿⣷⣿⣷⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢳⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⣤⠏⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⣤⢿⣹⣿⣿⣿⣿⣿⣿⡿⣿⣿⣣⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⡿⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣼⣿⣿⢿⡿⣿⣿⣿⡟⣤⣿⣿⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠃⢀⣨⣽⣛⠛⠿⢿⣿⣿⣷⣬⣙⣭⣷⣻⣦⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠛⠋⠉⣿⣛⣻⣶⣟⣛⣿⡏⠛⠟⠛⠉⡟⢿⣮⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣂
⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠀⢄⠘⣿⣟⠉⢻⣿⡿⠁⢠⠇⣰⠀⡇⣸⡞⠉⣿⣦⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠾⢿⡿⠟⡆⠀⠀⠀⠠⠶⠦⡀⠘⡀⢠⣸⣷⠀⠀⢀⠈⢠⠈⠻⣶⣿⠟⠁⢠⠋⢰⣿⣿⣇⣿⠏⡁⠬⢻⣿⣶⡄⢀⡀⠀⠀⠀⠀⢠⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡇⠀⠀⠀⠀⡼⠆⠰⡄⠱⣾⣿⣧⠀⠆⠀⠂⠀⣉⣀⣼⣥⣀⣐⠁⢠⣿⣿⣿⣿⣿⣁⠤⢈⡁⠿⣿⣾⡿⠁⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⡀⢠⡤⠾⠆⠀⣤⣿⣾⡿⠋⢹⣦⣴⠶⢈⡁⠀⢈⣧⠾⣯⣌⣻⣿⣿⣿⣿⣿⠏⠁⠆⠀⠀⣀⣽⣧⣴⣄⣀⡀⠀⠀⣷⡶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣏⣠⣤⣤⣼⣿⢿⣿⣄⠀⠈⢿⣿⣿⣿⣿⠀⢸⣿⣷⣿⠻⣿⣿⣿⣿⡿⣿⡄⠀⢸⣿⣿⣿⣿⣿⣿⡏⢩⣽⣶⣤⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠾⣻⣿⣿⣿⣿⣿⣿⣯⣠⠀⣠⣾⣿⣿⣿⡄⢸⣿⣿⣿⠀⢸⣿⣿⣁⣴⣿⣤⣀⣼⣿⣿⣿⣿⣿⣿⣷⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⠀⣼⣿⣿⡟⠀⠉⠛⠻⠿⣿⣿⣿⣿⠿⠟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⡿⣉⣿⣿⣿⣿⣧⡈⠛⠛⠉⣠⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢰⠆⣰⣭⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠻⣿⢟⠻⣟⡿⢿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣦⣴⣶⣶⣶⣶⣤⣀
⠀⠀⣀⠐⣂⣠⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢠⣤⠀⢤⣿⣏⣳⡘⢧⡉⠮⡛⠿⢿⣿⣿⣿⢿⣿⣿⡿⠿⠿⠟⠛⣛⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠧⣀⠀⠀⠁⠠⡉⠻⠿⣿⡤⢽⣦⣬⣶⣤⠙⣛⣛⣓⣭⣭⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠑⠒⢤⣤⣀⣉⠱⢦⣄⡀⠉⢛⣻⣿⠿⣷⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⣛⣛⣻⡌⡤⠊⠉⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣉⣁⣹⣶⣿⡏⠻⡙⠣⡈⠛⡉⠳⣿⣿⣿⡟⠛⢶⣭⣿⣟⣻⣿⣿⣿⣷⣶⣶⣴⣶⣿⠟⠛⠉⡩⠛⣀⡞⢁⡴⠛⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢿⣿⣿⣿⡟⠛⢭⡾⢿⡟⢧⡈⢢⡈⠠⠈⢢⠈⠢⠀⠀⠁⢈⣳⡶⠲⢾⣿⣿⣿⣿⣿⡯⠉⣻⣶⡾⠁⠀⠀⡔⠁⢠⠏⢠⠎⣠⠞⣡⢛⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⠏⠰⣦⠈⢷⡋⠳⣄⠱⡄⠱⡀⠱⡀⣣⣀⣇⣀⡀⠘⣇⣀⣦⠀⣜⠓⢻⣿⣿⣃⣼⣽⣿⠃⠀⠀⣼⠀⢀⠇⢀⡇⣰⢋⡞⣡⣏⣬⣥⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠀⠀⠘⢷⣶⣷⣾⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣧⣿⣶⣤⣿⣿⣿⣿⣿⡋⠀⠁⢠⣧⣴⣾⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⠖⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⠻⢮⣙⠻⢿⣿⣯⣽⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢛⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡟⠋⠉⠙⠻⣛⢶⣍⠓⣾⣿⣿⣿⣿⣭⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠟⢛⣡⡶⢛⡽⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠉⢾⣿⣿⣿⢷⣤⣤⣬⣭⣍⣉⣉⣉⣭⣭⣭⣭⣷⣴⠶⠿⢛⣫⣶⣫⣶⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣶⣤⣀⠀⠁⢄⣰⣿⣿⣿⣟⠲⠶⣶⣤⣬⣍⣉⣉⣉⣉⣩⣤⣤⣤⣶⠾⠿⣛⣫⣥⣿⣟⢀⡠⠖⠉⢈⣹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡐⢠⣼⢿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣷⣭⣭⣭⣭⣭⣭⣤⣶⣶⣾⣿⣿⢿⠿⠋⠙⣏⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠿⣄⣐⠀⠉⠉⠉⠉⠛⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⢈⣠⡴⠞⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡈⠉⠛⠻⠷⠶⠶⠶⣤⣤⣠⣤⣤⢤⣤⡤⠶⠶⠟⠛⠋⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣈⣉⣁⣉⣉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣉⣉⣉
⣿⣿⣿⣿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣇⣀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣤⣤⣤⣤⣴⣤⣶⣤⣤⣄⣤⣤⣴⣦⢠⣶⣴⣦⣤⣶⣤⣶⣤⣴⣴⣤⣦⣦⣤⣤⣤⣤⣦⣤⣴⣦⣴⡆⣴⣦⣤⣦⣤⣤⣤⣤⢠⣤⣴⢲⡶⡦
⠀⠀⠀⣿⣾⣿⡷⣿⠻⣿⢿⣿⡏⣿⣿⢾⣿⢘⣻⣿⣿⣿⣿⡿⣿⡿⣿⣿⣟⣿⣿⠟⢸⣿⢾⣿⣿⢿⣷⣿⡇⣿⣿⡧⡿⣿⣿⣼⣿⢸⡿⣿⢻⣻⡧
⠀⠀⠀⣿⣿⣿⡇⠈⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⣶⣶⣶⣆⣠⣴⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⡿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠰⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⡆
⠀⠀⠀⣽⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢹⣿⢿⣾⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣧⣿⣿⣿⠿⢻⡍⠀⠈⣿⢿⣿⣿⣷⡿⣿⡇
⠀⠀⠀⣿⣿⣿⣽⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠛⢻⡉⢡⡇⠀⡸⠋⢀⣰⠃⢸⣿⣿⣿⣯⣿⡇
⠀⠀⠀⣭⣭⣭⣽⣿⣿⡟⢹⡇⠀⠺⠃⠀⣸⠉⠉⢉⠉⠉⢛⡉⠛⢛⠋⠉⢹⡋⠉⢹⣧⠀⢀⣿⡀⠀⣾⣷⠿⣧⠁⢰⣇⣾⣿⢷⣾⣯⣿⣯⡭⣭⡅
⠀⠀⠀⣾⣿⣿⢾⣿⣿⠁⢸⣶⣤⣇⠀⣴⠉⠲⡴⣿⣄⣠⣿⣇⣴⡟⠀⣀⣾⣇⣀⣈⣿⣤⣼⠿⠿⠛⠉⡄⠀⣻⣠⣼⣿⠃⠘⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣿⣾⣿⡏⠀⢸⣿⣿⣿⣿⣧⣤⣼⢃⣤⠊⢀⣭⠉⠉⣙⠛⣻⠋⠉⡍⠉⢹⣦⠀⢸⣆⢀⣸⣷⣾⣿⣿⡿⣿⢣⣴⣿⠻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣿⣿⣽⣽⠿⠇⠀⠈⡿⠿⣿⠿⠿⢿⣿⣿⠿⢿⡿⢷⣦⣾⢧⣾⡧⠴⠾⢷⠴⣶⠿⠷⣿⣿⠿⠿⠟⢿⣿⡏⣧⣸⡟⠛⢻⠘⡟⠛⢿⣟⣿⡋
⠀⠀⠀⢿⣿⣿⣧⣤⣤⠀⢤⣧⣤⢤⡤⣠⠄⢤⡤⣠⠄⣠⣤⣤⡤⠘⠀⠀⠀⠀⠀⠐⢤⣀⡤⣤⢄⣤⠤⠂⠀⢀⣯⡿⢤⣿⡠⣮⢼⣧⣴⣾⠿⡿⠗
⠀⠀⠀⣹⣿⣿⣯⡟⣵⡤⠒⠉⠙⢻⣿⣿⠻⢏⣳⠿⣿⣯⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠷⠏⠁⠀⠀⢀⣘⣹⣟⣌⣼⡓⢿⣿⣿⡏⣹⣿⣿⡗
⠀⠀⠀⣾⣿⣿⢾⣴⡟⢹⣤⡀⠀⣸⠋⡽⠿⢿⡿⠟⢿⡛⣦⡀⠀⠀⠀⠀⣀⡤⠶⢶⣤⣤⣸⣇⡀⠀⣠⣴⡦⠻⣿⣏⢿⣾⣧⣤⣋⣛⠷⣾⣿⣿⡧
⠀⠀⠀⢿⢻⣿⣟⣏⣿⡸⠿⢽⣷⣿⣞⡀⣂⡾⠁⠄⠀⣇⠸⣧⠀⢀⣴⡿⠛⣃⠤⠤⠀⠉⠙⠛⠻⢿⣯⢻⣥⣿⣼⣯⣿⣷⣿⣾⣟⣿⣵⡿⠲⣿⡇
⠀⠀⠀⣹⣟⣷⡮⠿⣿⣷⣷⡎⠉⣹⣿⣿⣿⡶⣶⣦⣤⣯⣴⣿⠼⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢩⣏⣿⣽⡟⣿⠻⣷⣿⣯⢿⣾⡷⣬⣽⣿⡅
⠀⠀⠀⢿⣼⣿⢟⣻⣯⡉⠉⠟⠆⠻⣿⣏⣹⠻⣿⢿⡿⡟⠋⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⡿⢸⣿⢙⣿⣼⣿⣧⣼⣞⣻⡧
⠀⠀⠀⣾⠟⢿⡇⣽⣮⠀⠀⡀⠠⠊⣸⠀⢻⣿⣿⢻⡿⢿⡏⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣻⠀⣿⠸⣿⣼⢿⡄⣯⣽⣾⣿⣻⡇
⠀⠀⠀⣹⣾⣿⠿⠿⠶⠀⣠⠇⡀⠀⢻⠀⢈⣿⡛⠋⢩⣿⡧⠀⠸⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣍⣽⣿⠀⢿⠓⣿⢏⣿⣇⣿⣷⠶⢿⣿⡇
⠀⠀⠀⣿⢽⣿⢕⣥⣀⣼⠏⠀⢀⠀⣿⠀⠸⡏⢹⠈⡳⠮⠵⠦⢤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣷⣿⠀⢸⡇⣿⡿⣻⣏⢿⣍⣽⣿⣿⡇
⠀⠀⠀⣿⣿⣿⡶⠳⠉⠀⣀⡀⣚⠀⢼⠀⠆⣇⢸⡄⢠⣾⠓⠶⣶⣧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⢞⠽⣿⡄⢘⡇⢹⣍⣿⣿⢸⣟⢿⣿⣿⡷
⠀⠀⠀⣽⣿⣿⡷⡶⣶⢉⣉⠉⣿⠀⣾⡃⠀⡿⠸⡇⠀⡿⢥⣆⣠⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣹⠾⡿⢇⠨⣿⠘⣿⢸⣿⣨⣿⣿⣿⣿⡋
⠀⠀⠀⣿⢶⣾⠷⢚⣓⣶⠻⡽⢧⡘⢹⡏⠰⣧⠀⣿⠀⢺⣝⠚⠏⠹⡇⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⡜⢛⣾⣧⡾⡀⣟⠰⢿⣸⣿⢴⣥⢸⣿⢿⡇
⠀⠀⠀⣿⣿⣿⡇⣛⠋⢉⣡⣜⣻⣀⢸⣇⢀⣷⠀⣿⠀⢸⠿⠗⣠⣴⣷⣀⠀⠀⠠⡀⠀⢹⣿⣄⠀⠀⢻⣜⠫⠍⢠⣷⢹⣰⣏⠻⣿⢋⣤⣿⣿⣿⡇
⠀⠀⠀⢹⣿⣿⠟⠛⠃⢛⠻⣽⣷⣏⠀⣿⡹⢙⡄⠸⡇⣤⣴⣌⣻⣭⣿⣽⣁⡐⢒⣵⡀⢸⡟⣿⢷⣦⣼⣯⣁⣾⣷⣎⣻⣿⡟⠳⣄⡹⢏⢻⣿⣿⡇
⠀⠀⠀⢻⣟⣿⡃⣨⠿⣾⠶⣛⡛⠛⠦⣼⠗⠛⢻⣌⠷⠿⠯⠩⣷⣾⣉⠀⠹⠳⢺⣿⠣⠀⢿⣿⡐⣿⣿⡇⣽⣉⡉⢩⣥⡤⠋⡻⣃⣀⡂⢺⣿⣿⡗
⠀⠀⠀⣩⣽⣯⣵⣷⠄⠀⠠⠀⡀⠀⠀⡨⠀⠠⠤⠿⠿⠅⠀⠀⠀⠈⠉⠒⠴⣤⣶⣿⣦⠄⠈⢀⠁⠈⢽⡇⠸⢿⣿⠏⡡⢐⣀⠴⠋⠳⠿⣛⣉⣛⡃
⠀⠀⠀⠿⢟⢻⣣⣼⡖⠒⠓⠊⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⢄⡀⠀⠀⠉⠀⠘⠂⢂⡀⠁⠰⡎⠀⣘⠏⠈⢑⡤⠈⠁⠀⣠⢼⣷⢛⣟⣻⡗
⠀⠀⠀⢛⣛⣟⣋⣼⡏⠀⠀⢀⣀⠀⠠⣴⠂⠀⠶⠒⠒⠄⠠⠤⡀⠀⠀⠀⠁⠂⠤⠄⣀⡀⢈⣉⡁⢂⣉⠉⠀⠔⠋⠁⠀⢀⣠⣾⡵⣟⠓⣻⣾⣾⡇
⠀⠀⠀⢿⣿⣿⠷⣶⠏⠙⠋⠁⠈⠀⣀⠀⠤⣤⠀⠠⠤⠄⣀⠀⠀⠒⡆⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠘⣣⠟⠃⠘⠿⠿⢻⣿⢿⡗
⠀⠀⠀⢛⣿⡟⠃⢘⡂⠂⠀⢈⣩⡀⠀⠰⠾⠻⠿⠂⣠⣄⣀⠀⠉⠒⠢⠀⡀⠙⠛⠶⠶⠂⠐⠰⠖⠂⢒⠾⠒⢉⢫⣗⠊⣡⡒⢳⣶⡄⠀⠻⠿⠿⠛
⠀⠀⠀⣻⠿⢿⣃⣈⡁⢰⣛⣻⢛⡏⣡⣿⡉⣠⡚⣋⢻⣈⣟⢀⡛⢛⣛⡃⠵⣟⣁⣀⣲⡶⢲⣦⣤⣀⣴⣶⡃⣀⣚⣿⡛⢂⣉⣉⣋⣰⣿⣿⣿⣿⡟
⠀⠀⠀⣿⣾⡿⣿⣿⢳⣿⣿⣿⣿⣿⣽⣿⡇⣯⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣻⣮⣿⣿⣿⣿⢾⣿⣿⣿⣿⣿⡇⣿⣿⣭⣿⣿⣿⣿⣿⢸⣿⣿⣿⡷⡗
⠀⠀⠀⠙⠙⠛⠋⠙⠃⠛⠛⠛⠙⠋⠘⠛⠃⠙⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠛⠛⠛⠛⠛⠛⠛⠛⠘⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠛⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠐⠀⠀⠀⡠⠂⠈⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣴⣶⣶⣶⣄⣴⠎⠀⠀⠀⠀⠀⣸⠇⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠙⠿⠿⠀⢠⠿⠿⠋⠉⠉⢙⣿⠿⠋⠀⢀⠀⠀⠀⠀⠀⢿⣦⡀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⢀⠀⠀⠀⣰⣿⠯⠓⠁⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣧⡀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⢀⣠⣤⣾⡿⠁⠀⠀⠀⠸⣯⠀⡀⠀⠀⡠⠂⠀⠀⠄⢀⣾⣿⣿⣿⠇⠀⣀⣀⡀⠀⠀⢠⡄
⠀⠀⠀⠀⣠⣼⠋⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠶⣶⠊⠀⠀⠀⠀⢀⠞⠈⠛⠛⠳⠾⠿⠿⢿⣿⡄
⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣤⣴⣿⣷⣦⣴⣦⣄⣈⣉⣒⣐⣓⣛⣁⣀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠛⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⢰⣀⣀⣀⣴⣇
⠀⡆⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰
⠀⢦⡄⢠⠀⣍⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃
⠀⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⠄
⠀⠀⠀⠀⠂⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠠⢿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠠⡠⣿⣤
⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢀
⠀⡄⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣥⠀⠀⠟⢷⢲⡄⠀⠀⠀⠀⠀⠰⣀⣨⡟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘
⣬⠹⣿⣓⣒⣒⣾⣯⣧⠀⠀⠀⠀⠀⠃⢼⠀⡧⠄⠧⠃⠀⠀⠀⠀⠀⠀⠸⢻⡄
⠀⠉⠓⠒⢃⡖⠛⠋⠁⠀⠀⠀⠀⠀⠀⠨⠀⣭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⡄⠀⠀⠀⠀⠀⠀⠇⠀⠐⠄
⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⢄
⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⡠⣄⠘⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⡤⢴⣴⠦⠼⣷⣶⣦⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠒⠈⠩⡿⣭⠿⠞⠃⠀⠀⠀⠀⠸⠤⠄⢀⣧⣾⣿⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉⠀⠀⠀⢠⡤⣴⡧⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⢸⡿⠿⠿⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

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





⣿⣿⠿⢿⡿⠿⠿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢐⠶⣄⡄⠀⠀⡴
⠀⠀⠀⡈⣿⢋⣬⠬⢾⡀⢞⣯⡄
⠀⠀⠀⠈⣇⠘⠁⣠⣤⠁⠈⡵
⠀⠀⠀⠀⠙⠿⣄⠛⠟⠀⢔⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢉⡌⢡⡀⠈⠌⠻⠟⠿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⢰⣿⠢⠤⣀⣀⣾⡼⠒⣁⡐⣶⣿⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣧⡸⠟⠶⠚⠁⠀⠈⠑⠺⣿⡿⣦
⠀⠀⠀⠀⠀⢸⣯⡍⡆⠀⠀⠀⠀⠀⠀⡴⠚⢀⡈⢧⣿⣧⣄⠀⣀⣠⣂⣄⣀⣀⡀⠴⢦⡀
⠀⠀⠀⠀⠀⠸⣹⣷⣿⠀⢀⡤⠶⠂⠀⠀⠀⠉⠀⠈⠿⣷⣿⣿⢿⣟⣛⣛⣿⡿⣿⣦⡀⠙⢻⣄
⠀⠀⠀⠀⠀⠀⠉⢻⣿⣤⠈⠀⠒⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⢿⣿⣿⣿⣿⣼⣿⣖⢰⠽⣇
⠀⠀⠀⠀⠀⠐⠂⠘⢿⣿⣧⠀⠀⠀⠀⠀⣀⠔⠀⠀⢼⣿⣿⣿⡉⠀⠀⠈⠛⠿⢿⣿⠈⢻⢣⡺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣿⠑⣦⡀⠀⠀⠀⠁⠀⠀⠸⣿⡃⠈⠂⠀⠴⠋⡀⠀⠀⠈⠣⠉⠀⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⣾⡏⠀⠀⠀⠀⠀⠀⠀⠉⣳⡂⢒⠄⠀⠈⠁⠀⠀⠀⠀⣤⣾⣧⣼⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢠⠾⡋⠉⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⡿⢦
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡨⢿⡽⣿⢣⡄⡀⠀⡴⠁⠦⠚⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠮⡽⠃
⠀⠀⡁⠀⢀⡀⠀⠀⢠⠀⣰⡁⠤⣌⡃⡀⢡⣦⠑⢱⡿⠀⠀⠀⠀⠀⠐⠿⠀⠀⣀⠀⠀⠀⢀⢠⠀⠀⠀⠀⡄
⠀⠀⡟⠀⠀⠁⠉⠉⠉⠉⠈⠉⠉⠉⠁⠙⠁⠃⠈⠁⠀⠀⠠⠀⠄⠀⠀⠀⠀⢁⠄⠀⠀⠀⠀⣉⠀⠀⠀⠀⠈⠒⠄
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⠀⠴⠎⠁
⠀⠀⡷⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠄⠁⠈⢶⢴⠆⠀⠀⠀⠀⢐⠀⠀⠐⡃⣀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠓⠁
⠀⠀⠀⠀⠘⠀⠘⠁⠸⡦⠀⠀⠀⠀⠀⠤⠀⠀⠀⣠⣿⠄⠀⠀⠜⢣⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢒⠀⠀⠜⠀⠀⢸⠇⠀⠀⠀⡀⠀⠅⠀⡀⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⣗⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⡀⠀⠀⠀⠀⠀⠀⣾⣷⣝⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡝⠀⠀⠀⡀⢀⠀⢿⣿⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡤⢚⠥⣾⠿⠆⣰⣿⣿⣿⣧⣶⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣡⢠⢇⣜⣵⣾⣼⣿⣿⣟⢿⠘⣿⡦⡄⠁⠉⠛⢿⣷⡲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠔⠀⢁⡼⣸⠿⠛⠻⠿⠿⢯⣼⣷⣼⣿⣧⠀⠀⠀⠀⠀⠀⠙⢜⡛⠷⣖⢄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⣔⣵⠞⠁⠆⠀⠀⠀⣀⠀⠈⠻⣿⡏⣀⢡⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⠙⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡾⠟⠉⢀⠂⠀⠀⢀⠀⠀⠀⢹⣦⠠⡆⠘⣦⡈⢨⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣎⣀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠄⠈⠁⠀⡇⢠⣿⣿⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠻⣦
⠀⠀⠀⠀⠀⠀⠒⣿⣦⠃⠀⠀⢀⠜⠁⠀⠘⠋⣴⣷⣿⣿⣿⣿⣿⠃⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀⠐⠉⠻⠿⢿⣿⣿⠏⠀⢸⣿⣰
⠀⠀⠀⠀⠀⠀⠈⢹⠇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⣾⣿⠏⠀⠀⠈⣿⠃⠀⠰
⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠈⣼⣿⡏⠀⠀⠀⠀⣿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⣼⣿⠏⠀⠀⠀⠀⢠⣿⡆⠀⠀⠰
⠀⠀⠀⠀⠀⢠⣞⣾⣿⣿⣶⣶⣄⡀⢠⠀⠉⠋⣾⣿⠏⠀⠀⠀⠐⢁⣾⣿⡧⡀
⠀⠀⠀⠀⠀⠻⠁⡞⠀⠐⠉⠻⢿⣿⣷⣄⢀⣾⣿⠏⠀⠀⠀⢀⣰⣾⣿⣿⠃⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣿⣿⢏⣴⣦⡴⠖⠀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠳⣿⣿⣾⣿⠟⠁⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⢲⣄⣤⠄⠀⣀⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⢰⡘⣇⢀⠜⢁⣤⣾⡿⡚⢠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⡷⣿⣎⣇⠸⠉⠉⡴⢡⣿⣿⢿⠛⠁
⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣻⣴⣿⣼⡷⠾
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠵⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⢠⣠⢄⣤⣤⣀⣀⣀⣀⣤⣤⠀⡀⠀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠉⠘⠁⢘⢿⣷⡤⢞⠄⣪⡽⠁⢹⠙⢄⠁⣤⠤⢍⣶⡽⡿⠯⢽⣤⡒⢦⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠻⠠⡄⡔⠉⡹⠓⠻⣿⣷⣏⡀⡁⣀⣼⠓⢄⢲⣼⣤⣻⠿⠾⠃⠀⢦⠳⣍⠟⣷⠘⢒⡂
⠀⠀⠀⠀⠀⢠⡾⢃⡉⠈⠁⠱⣿⡿⠒⠒⣽⡝⢏⠓⢻⡛⠻⣼⣾⣿⣯⠤⠿⠛⠛⡶⣄⠁⠂⠁⠐⠒⠉⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⡾⠁⠀⠠⠀⠰⠆⠚⡄⢾⠉⠀⢡⠞⡏⡨⢡⡏⣹⢲⣇⢦⡰⢦⠘⢆⠙⠬⠟⡎⠃⠶⠀⠀⠀⠲⠀⡐⠉
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠉⠠⠀⢠⠀⣾⠄⢡⠳⠜⠁⠀⠸⠀⠸⠸⡘⡆⠋⠸⡄⠀⠰⠤⠐⠃⠐⠀⠈⠁⠀⡀⠒
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠘⠂⢄⠀⠁⠽⢓⣮⡠⢦⠪⡆⠀⢣⡉⣠⠂⢀⠞⠈⠑⠀⣀⠀⠀⠗⢀⠐⠂
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠀⡈⠋⠀⠠⠀⠠⠈⠀⠈⠀⠀⣀⠀⠁⠀⠀⡀⠤⢠⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⢀
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠐⠄⠆⠠⣆⠴⡠⢄⢹⡀⠒⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡀⠀⡀⠈⠀⠀⠀⠀⠠⠀⠀⠐⠄⠀⠘⠓⢀⠠
⠀⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢃⠀⠀⠀⠀⢰⡀⠈⠀⠄⠀⠀⣉⠔⠂⢳
⠀⠀⠘⠛⠓⠀⠀⠀⠀⠀⠀⠡⠀⠀⠢⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠗⠊⠀⠀⠀⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠐⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡀⠀⠀⢰⣔⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡄⠘⡇⡀⢸⠀⠀⠀⠀⢀⣇⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠃⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⠿⠿⠛⠀⠀⠀⠀⠀⠉⠐⠊⠀⠀⠉

⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠎⠀⠴⣾⣿⣿⡇⠈⠃⠉⠛⠂⠀⠀⠂⠀⠀⠀⠰⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠀⠀⠤⠒⠚⣸⣿⣿⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠈⡇⠀⠀⢀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠞⡿⠋⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼
⠀⣀⠔⠂⠀⠦⢄⠀⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠠⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡄⢀⣾⡟
⠴⠁⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠈⠙⢂⣀⣀⣀⡀⢀⡠⠐⠒⠦⢄⠀⠀⠀⠑⠇⡀⠀⠀⠀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⣾⡿⠋
⠆⠤⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢡⠀⠀⡀⠀⠐⢄⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⢤⣶⣶⣼⣷⣷⣤⣾⣿⣿⣿⠖⠈
⠀⠀⠀⠀⠠⠀⠀⠐⠠⠀⠄⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⢳⡎⠀⠁⠈⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⠛⢛⣟⣿⣿⣿⣷⣶⣖
⣦⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠎⢳⠀⠀⠀⠀⣠⠤⠀⠠⠤⢺⣿⣿⠘⠻⠟⠿
⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠊⠁⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣆⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄⠀⠀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⣀⠐⠀⠀⠀⠀⠹⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣻⣷⡀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣤⡄
⠀⠀⠀⠈⠀⣦⢄⡀⣀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣤⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠐
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠤⠱⠶⣦⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⣿⣿⡇⠀⣾⡇⠀⢀⠔⠀⡠⠊⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠢⣀⣀⣀⠀⠉⠙⢿⣿⣿⣇⢰⣿⣷⣾⣿⡵⠄⠀⠀⠀⠀⠀⠀⠀⡚⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠘⠛⠛⠛⢻⣿⣾⣿⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠂⠸⡄⠀⠀⡼⠀⠀⣠⡄
⠀⣠⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠈⠁
⠀⠠⢀⣸⣆⠀⠀⠀⠀⠀⢉⡂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠶⠒⣈⡽⠟⠉⠉⠻⣧⠀⠉⠀⠀⠀⠶⠤⢄⠀⢀⠌⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣠⠂
⠀⠀⠀⠀⠹⠞⠀⢀⠂⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⢒⢀⠝⠉⠡⠚⠐⠆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢠⠀⠀⠀⠀⠀⠀⣠⣄⡀⢸⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠋⠉⠉⠻⢟⢿⣇⣠⡀⡀⠀⠀⠀⠀⠐
⠊⠁⠀⠀⠀⢀⠀⠀⢀⠈⠈⠲⠤⢶⡀⠀⣀⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡄⠀⠀⢀⠀⢠⠀⠀⢀⣴
⠀⠀⠀⠀⡤⣈⣀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢳⣇⠀⢸⣧⣤⣤⣶⡿⠛
⣀⠀⠀⠀⡎⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠹⣆⣧⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⣿⠿⠿⠛⠂
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⡄⠀⡌⠀⠀⠀⢀⣴⣾⡥⠂⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⢿⣍⠀⠀⠀⠐⠊
⠀⠀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⠀⠀⠀⠤⣄⡀⠀⠀⠀⣹⣿⣿⣄⣄⡆⠀⣴⣾⣿⠯⢀⡄⠀⠂⠐⠀⠀⠲⠀⠠⠁⠈⠀⠈⠳⣍⡀⠒⠒
⠒⠠⢀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠀⠀⠙⢿⣿⡏⠃⢠⣿⣿⣯⠖⠁⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣷⣶⡅⣤⠛⠲⣹⣿⣣⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠆⠀⠀⠀⠐⠚⠋⠉⠁⠘⠞⠛⠙⠋⢻⡿⢿⠅⣀⣶⠋⣵⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠙⢿⡿⠁⣠⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠘⢷⣶⣤⣤⣶⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠙⠿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⠿⠛⠛⠛⠛⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡗⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⡿⠁⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠋⠉⠉⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣶⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣭⣄⣀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⣿⣿⣿⣿⣿⣦⣀⣴⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣏⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⣿⠿⡆⠀⠀⠀⣦⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⡷⠷⣶⠀⠀⠀⣿⣿⢶⣤⣤⡴⣾⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⣶⣶⡿⠀⠀⠀⠰⣿⣶⣶⣿⣿⣶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⣤⣀⣀⣀⣤⣴⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⠛⠿⠿⡿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡀⠀⠀⠀⠀⠀⠀⠠⣟⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡘⠆⠙⠳⠋⠹⠏⣹⣦⣀⣤⣥⣭⡈⣤⣠⢀
⣀⣀⣀⡠⡐⠀⡀⠀⠀⠀⣀⡘⢸⣿⡀⣤⣄⠒⠂⠀⠀⠀⠁⣟⢁⢀⠀⢰⡄⠄⣾⣘⢿⣿⣯⣿⠉⢤⢥⣯⡉⠀⠀⢀⣀⣀⣀⣠⣀⣀⣀
⣏⣉⣏⡁⠁⠀⠘⢤⡀⡠⠜⠇⢸⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⢿⡾⠄⠰⠾⠃⠀⣿⣧⣾⣿⣿⠖⠂⠘⠀⠃⠁⢠⣴⣿⣟⣿⣿⣿⣿⣿⣿
⠀⠇⢰⠹⠉⠰⠄⠶⡇⡀⣎⠠⢼⣿⣇⣼⠃⠁⠀⠀⠐⠀⠀⠂⠀⠒⣀⣤⣄⣀⠀⠉⣿⣿⡷⡆⠀⠀⠀⠀⠄⢸⣿⣿⣿⣶⣿⣯⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⢸⣿⣿⡪⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠙⢋⣻⣿⠀⠀⣿⣿⢛⡀⠄⠀⠀⣀⠀⠈⣶⣤⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⢸⣿⣿⣋⠀⣀⠀⠀⠃⠀⠀⠀⠀⠀⣀⣀⢽⣿⠀⠠⣿⣿⣟⡋⠀⠁⠀⠙⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢿⣿⡉⠐⠒⠂⠀⠀⡁⢸⣿⣿⣾⣿⡀⢠⣯⣿⣟⣁⡀⠀⠰⠤⠀⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⣿⡻⠟⠒⠀⠁⠀⠀⡀⠀⠀⡀⠸⠿⠿⠛⢿⡷⢸⣿⣿⡟⢿⣿⣆⣐⠺⣿⢆⣿⣿⣿⣿⡋⡛⢯⡛⠿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠉⠛⡃⠲⠶⣴⣤⢤⣤⣤⠴⣴⠢⣿⡟⠒⣦⣦⣤⣀⠀⠀⠀⠀⠈⠁⡉⡛⠚⠀⠯⠈⠉⠛⠛⠻⠿⣟⣾⣷
⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⡄⠀⠉⠉⠙⠛⠚⢟⡴⠋⠀⠈⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠉⢲⣶⣤⣤⡀⠀⡀⠀⢀⣀⠠
⠀⡃⠀⠀⠙⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⢉⣙⣽⣿⡿⡿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡙⠿⢻⣿⣾⡗⢦⣅⡑⢠⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠙⠉⠀⠀⠥⠌⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠤⠚⠋⠩⠤⠶⣿⣿⣿⠿⠾⣛⣓⣯⣿⣵
⠀⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡶⠦⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠤⠔⠐⠤⠄⠀⣠⣤⣤⣤⣄⣀⢐⣖⣂⣠⣾⡿⠿⢿⣿⣥
⣶⣷⣦⣴⣶⣶⣴⣿⣥⣤⣤⣤⣤⣴⣤⣤⣥⣤⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣦⣤⣬⡥
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⣘⠧⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢆⠀⠀⠺⣿⠷⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢠⣀⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠛⠀⠇⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠈⠀⠈⢻⠄⣑⠶⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠿⠉⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠃⠘⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠏⠛⠀⠀⣀⠀⠀⢀⠁⢀⡄⠴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡉⠙⡆⠀⠀⠁⢀⣠⣿⣇⠀⠀⠀⠀⠀⠙⠈⢠⠏⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠛⠁⠀⠀⠀⠀⠀⠺⠟⠻⠛⠁⠀⠀⠀⠀⣠⡏⠀⣆⡀⠀⠆⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢁⡴⠂⠈⠛⠀⣯⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠛⣄⡐⢂⣩⠃⠀⠐⠀⠀⢌⠷⣄⠀⠀⠀⠁⢳⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠁⠀⠀⠘⠐⠏⠀⠀⠀⠀⠀⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠖⠀⠀⣴⠀⠀⠀⠀⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⣤⡎⠀⠀⠀⠘⡆⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⠠⡀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⡈⠁⠈⢻⠀⠀⠀⠀⢡⠀⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣤⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠀⠀⠀⢠⠄⠀⠀⠀⠈⠉⠀⠀⠀⡄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠙⠒⠤⠤⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠰⡤⡎⣁⠀⢠⣶⠶⢇⠀⠀⠀⠿⢻⡿⠂⠠⠀⠀⠀⡆⠀⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⡆⠀⠀⠂⡑⠋⠀⠠⣷⠴⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢉⣇⠀⠀⡄⠠⡤⠀⢰⣿⡴⣩⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣼⣷⢾⡿⠀⠀⣞⠂⡜⠀⠘⣿⠛⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠂
⠀⠀⠀⠨⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠛⠉⠐⠂⠀⠀⡐⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠊⠁
⠰⣎⠃⣴⣬⡿⠐⠀⠀⠀⠀⠀⠀⡀⣸⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⢰⣰⡷⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠀⠀⠀⢀⡇
⠀⢧⠾⠿⣿⡇⣙⠶⢀⠀⠀⠀⢸⢯⡿⠀⠘⡛⠀⠀⠀⠀⠀⢹⡆⠋⠁⡀⠶⠁⠀⠀⠀⠀⣸⡅⡀
⠀⠀⠀⠀⢸⣾⡟⣳⣾⣷⡀⠀⣼⣧⣾⠀⠀⠋⠀⠀⠀⠀⠀⢸⣟⣷⠐⣿⢢⠀⠀⠀⠀⢂⣾⡧⢩⣴⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⢻⣿⢟⣹⡿⠇⠀⠀⠉⢿⣷⠿⠀⠀⠀⠀⠀⠀⠸⢁⣹⡆⣿⣠⡆⠀⠀⠠⣟⣿⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠛⣽⡷⣀⠀⠀⢀⣾⣽⢇⣀⠄⠀⠀⠀⠀⠀⠿⠋⠀⠉⢙⠁⠀⠀⠀⠉⠿⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠈⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠾⣧⣹⣄⠀⠀⠁⠘⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠀⠀⠀⢀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠰⣿⣭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣝⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠈⠁⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣽⣿⢤⡀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣝⣠⠂⠀⠀⠀⢰⠃⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢘⡆⠀⠈⠳⡀⠀⣴⠀⠀⠀⢀⡀⠀⠀⢀⠀⣠⠀⠃⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢸⣧⠀⠠⠀⡹⢷⣟⡀⠀⠀⢊⠀⠀⠀⠈⠈⠀⠀⢀⣠⠞⠇⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣼⢁⣴⠀⡤⢀⣈⣷⣠⣴⠟⠁⠀⢹⣧⠐⠀⠘⠀⠀⡀⠀⢀⡄⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⡟⣿⣿⣿⣷⣼⠋⠉⠉⠉⢠⡀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠿⠉⠛⠛⠠⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣦⠤⣄⣀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠀⠀⠀⣀⠊⠀⠠⠀⠙⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢀⡀⠀⡿⠉⠑⣶⠟⠀⠀⠀⠀⠀⣅⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠀⠀⠀⠁⠈⣾⠇⠀⠀⠀⠀⠀⠢⠐⠀⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⡀⢀⠂⠀⠀⢠⡟⣇⡀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠐⠀⠀⠀⠠⣧⡄⠀⣺⣵⣷⠆⠀⠀⢀⢁⠎⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠙⢯⠁⠀⠀⠘⣿⡏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠙⠺⠟⠯⡀⠀⠀⠈⠓⣄⣀⠀⠹⠧⢂⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠓⡄⢸⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠜⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠉⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠤⠄⠀⠤⠀⠀⢀⡀⠀⢀⡀⢠⡔⠋⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⡀⡘⠁⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⢀⠀⠠⠋⠉⠦⠄⠀⠀⠀⠀⠀⢇⠀⠀⣀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⢲⣾⣿⣿⡟⠀⠈⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠉⠀⠀⢀⠀⠀⠀⠀⢀⣰⡿⠁⢻⡏⠈⠉⢄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠚⠁⢁⠀⠀⠀⠐⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣿⣿⣷⣦⣀
⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⢿⡿⠿⠛⠛⠻⢿⣿⣿⣿⣦⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠁⠻⣿⣿⠀⠀⠀⠐⠀⠀⠐⠀⣿⣏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠶⠀⢤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⠴⠄⠀⡶⠈
⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⣀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⢠⡙⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣷⣶⣶⣷⣤⣀⣀⣀⡾⡿⠃
⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠂⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠿⠟⠉⠙⠛⠉⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⣠⣦
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣼⣿⡆⠀⣮⣹⣿⣿⡀⠀⠀⠀⢀⣼⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⣟⣷⣿⣿⣎⣴⣿⣿⣿⣿⠀⠾⠁⣿⣿⣿⣦⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣯⣾⣿⣿⣽⢿⣿⣿⣿⡆⠂⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⡿⣿⣻⣿⡟⢽⣿⣿⣿⣿⣾⣿⣿⣿⣿⣏⡏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⠀⠀⠀⠀⠙⠛⠿⡿⣿⣿⣿⣏⣿⣿⠃⢧
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⡀⠀⠀⡀⠀⢻⣳⣿⣯⣽⣿⣿⣷⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣼⣼⢟⣿⣿⣿⢿⣷⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⡀
⠀⠀⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠒
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠈⠉⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⠀⠐⠶⠀⠉⢿⡏⣿⠹⡙⢯⠻⠟⠋⠁⠀⡀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣄⡀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢿⣿⢫⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣏⢠⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⡟⣡⣎⠹⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣽⡟⢻⣻⡿⠶⣿⣋⠠⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⠋⠀⠀⠀⠀⠀⠈⣿⠃⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡒⢊⣉⣴⡆⠀⠀⠀⠀⠀⠘⠁⣈⣁⡀⠀⢰⣶⠦⠀⠀⠀⡦⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠂⠀⠤⠀⠀⠠⠄⠰⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢠⠄⠠⣀⠄⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢀⠀⢰⡄⠀⠀⠀⢀
⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⣶⣶⣄⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣿⠿⡶⠶⢾⠋
⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⣋⡹⠛⠁⠀⡄⠀⡰⠀⠀⢼⡀⠀⠀⠀⠀⠀⠐⢀⡜⠀⠀⠐⠀⠀⠀⡠⠂⠈⠉⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⢦⡄⠀⣠⠐⢂⣩⡿⠀⠀⠀⠀⡠⠊⠀⠀⢀⡀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆⢠⣴⣶⢦⣴⣶⢾⠉⠁⠀⠀⠀⢀⠌⠀⠀⠀⣠⣎⢳⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣻⣇⡀⠀⠀⠋⠀⠀⠠⠀⠁⠘⠍⠛⠞⠛⣹⣾⠁⠀⠀⠀⠴⠋⠀⠀⠀⣼⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠂⡽⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡸⢦⠋⢱⣆⠀⠀⣠⠀⠀⠀⢀⣠⣦⣤⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠱⢤⡉⠛⠛⠋⠀⠀⢠⣿⠿⠉⢀⣈⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠠⠈⠀⠀⠀⠀⣀⣦⣄⠙⣀⣀⣾⣿⠿⠛⢂⡀⠀⠀⠀⠀⢀⣤⠀⠀⠀⡴⡀⠀⠀⠉⠐⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠉⢨⠟⠀⢈⡿⣿⡁⠀⠀⠀⠀⢂⣀⣠⡶⣻⠇⠲⢀⣼⣟⢄⠀⠠⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⣦⣄⠀⠀⡀⠀⠠⠀⠀⣼⣑⡿⠉⠀⢤⡀⣠⣲⠝⠻⠋⠁⠀⠀⠘⢻⢯⡿⣵⣲⠌⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⢰⡂⠀⠠⠌⠙⠁⠄⠀⠀⠛⠙⠿⢄⠀⠀⠀⠀⠀⠀⠀⠉⠳⠾⠏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠷⠀⠀⠀⠰⠀⡤⠦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠃⠀⠀⠀⠛⠀⠀⢀⡔⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠛⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠂⠀⠐⠀⠀⠀⠘⠂⠈⠁⠀⠀⠀⠀⠀⣴⣦⣤⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⣤⠤⠶⠶⠞⠛⠻⠖⠷⡆⠀⠀⠀⠀⠀⠀⠀⢴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡆⠀⢰⡀⠀⠘⠀⢠⠃⠀⠐⢠⠀⠀⠀⠀⠐⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠛⠀⠀⠉⠀⢀⠰⠂⠀⢁⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠀⠞⠁⠀⠔⠈⠀⢴⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⢬⡀⢠⣾⠈⠀⠀⢣⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⣄⣠⡄⠀⠀⡄
⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⠓⠛⠉
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣀⣤⣰⣾⡿⠝⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠙⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠢⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠲⡄⠀⠀⠊⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠚⠀⠁
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠄⠀⠐
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠉⠁⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠜⠁⠙⢤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⠃⠠⠢⣆⠈⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⣿⡟⢁⠄⠂⣙⡀⠢⡄⠙⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⢹⣿⡇⠊⠀⠠⠛⡥⠠⢐⢠⣿⡟⠋⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣾⣿⠟⠁⠀⠀⢀⡄⠀⠀⠀⠈⢿⣿⣶⣾⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠀⡌⡷⠀⠀⠉⠀⠀⡤⡄⠈⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢿⣿⣿⣦⡀⠁⠀⠀⠃⠀⠄⠀⣠⣾⣿⡿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣾⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣾⣿⣿⣿⣧⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⡄⢈⠿⣿⣿⣿⣿⢛⣿⣿⣿⢿⣿⣿⡟⣿⣿⣿⣿⡟⠁⣏⠟⠖⢤⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡨⠓⠞⢲⠈⠀⠉⢻⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⣿⡿⠿⡋⠀⠀⣇⠀⢢⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠻⢆⣀⡠⠊⠀⠈⠛⢿⣿⣿⣼⣿⣿⠟⠋⠀⠀⠈⠦⣀⡨⠗⠀⢶⡈⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⢀⠔⡆⠀⠏⠻⠿⠋⢰⠀⠀⢰⠲⣄⠀⠀⠀⣀⠔⠐⠂⢓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠵⢶⣊⠁⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⡟⠀⠈⠉⡈⠉⠀⠀⠀⢠⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠈⠙⢖⢦⠀⠀⠄⠀⠀⠂⠀⢀⡷⢊⠉⠛⠉⠛⢦⠀⠀⢇⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠹⡧⣀⡀⠀⠀⠀⡠⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠘⣦⠁⣉⢛⣨⠴⠁⠀⠀⠀⠀⠀⠠⠾⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠢⠀⠀⠀⠀⠀⠘⠓⢶⠒⠎⠀⠀⠀⠀⠀⠠⠚⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⠀⠀⠀⠲⢦⠐⠁⠀⠈⠂⡖⠀⠒⢈⣀⣀⣤⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⠉⠉⠑⠄⠈⠓⠶⡛⠲⠞⠁⢀⡠⠚⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣩⠞⠓⠢⢄⠀⠐⠒⠒⠒⠚⣉⠤⠚⢇⠑⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠵⠋⠀⠀⠀⠀⠀⠀⠉⠀⠁⠉⠀⠀⠀⠀⠑⠒

⠀⠀⠀⢀⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⢸⣿⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⣿⡇
⠀⠀⠀⠘⣿⡄⠀⠻⣷⣄⠀⠀⠀⢠⣾⠟⠋⢿⣏⠁⠀⠀⠀⠀⠀⠀⠈⣽⡟⠙⢿⣷⡀⠀⠀⠀⢠⣾⠟⠀⢠⣿⠃
⠀⠀⠀⠀⢻⣧⠀⠀⠈⢿⣷⣄⢀⣿⠏⠀⠀⠈⠻⣷⣤⣀⣀⣀⣠⣴⣾⠟⠀⠀⠀⢹⣷⠀⣠⣄⠈⠁⠀⠀⣼⡟
⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣴⣿⠁⠀⠀⢀⣴⡿⢿⣦⡀⠀⠀⠀⠀⢠⣶⠿⢿⣦⡀⠀⠀⠘⣿⣄⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣟⠀⠀⠀⠸⣿⣄⣀⣿⠇⠀⠀⠀⠀⢸⣿⣀⣠⣿⠇⠀⠀⠀⣿⡟⠉
⠀⣠⣴⣶⠿⠿⠿⠿⠿⢷⣾⣿⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⣿⣷⡾⠿⠿⠿⠿⠿⣶⣦⣄
⢾⣿⣍⡀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣩⣿
⠀⠈⠙⠿⣷⣦⣤⣀⣀⣤⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣄⣀⣀⣤⣴⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠉⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣶⡾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⢷⣶⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣾⡿⠻⣷⡀⠀⠀⣴⡿⠻⣷⡄⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠉⠁⠀⠉⠁⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣷⣶⣤⣤⣾⠟⠻⣷⣤⣤⣶⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⡉⠉⠀⠀⠀⠈⠉⢉⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠂⢀⣴⣿⣅⠈⡏⠁⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⣦⠶⣻⡉⠠⠸⣟⠁⠀⠀⠀⠀⠀⢡⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⣿⠳⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⣷⣆⡀⠉⠲⣴⡟⠀⠀⠀⠀⠀⠀⣴⠀⢀⠆⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡧⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠉⠁⠁⠈⠙⢿⣷⣄⢈⢷⡄⠀⠀⠀⠠⠴⣟⡁⣇⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⠀⠘⠇⠀⠀⠀⠀⣐⡛⠛⠑⠰⡛⠀⠀⠀⠀⠀⢻⠀⠀⠡⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠀⢀⢀⡀⡀⠀⠀⠀⢀⠿⠯⠑⢆⠀⠀⢡⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡴⠇⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠁⠖⠈⡽⠁⡀⠀⠁⠈⠐⠄⠀⠀⠀⢀⡴⣀⠀⠀⠀⠀⢸⡂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣴⡂⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡄⣀⣩⣵⣏⡀⠀⡀⣀⡹⣄⣠⠐⣋⣴⠏⠀⠀⠀⠀⠁⡎⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡄⢈⣦⠀⠀⠀⠀⠀⢰⡀⠀⠀⠹⣟⠿⣾⢹⣟⠿⢹⡙⣧⢯⠆⠉⠛⢥⡀⠀⠀⠀⣸⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡜⠁⠀⠡⢄⠀⠀⠀⠆⠑⢄⠀⠀⠙⠘⠿⠀⡈⠿⢨⢣⣿⢃⠀⠀⠀⠈⡷⠀⠀⠠⠛⠳⣇
⠀⠀⠀⠀⠀⢠⣦⣦⠄⠀⠀⠀⠙⠀⠈⠄⠀⠀⠑⢄⣠⢁⣼⠀⣳⡀⠀⣆⣰⡟⠁⢠⢆⣟⠃⢸⠀⣤⣤⣀⡅⢀⠔⠁⠀⡈⢸
⠀⠀⠀⠀⠀⠀⣡⢟⠶⠀⠐⢤⣀⠀⠀⠈⢀⠀⠀⠈⠁⠀⡉⢠⢿⡇⠸⣢⡈⠀⢀⠏⣼⠇⠒⢹⡟⠛⠞⠛⢳⠎⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠤⣴⡏⠀⠀⠀⠈⠉⠘⠁⠀⡠⢁⣾⡟⠑⢤⣤⡐⠤⣞⣸⣃⣀⣦⠮⠦⠄⠀⠀⢸⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠠⣀⡀⠀⠀⣰⠁⡾⣹⠃⠀⠨⡍⠁⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⠤⢴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠈⠉⢉⣅⢨⠏⡏⢀⡀⠀⡼⠂⣶⡟⠙⠁⠒⢲⡆⢤⡤⠄⠒⠁⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⢀⠤⠤⠀⠒⠀⠀⠀⠀⠀⣀⠠⠤⠒⠀⢬⡿⠄⣧⣀⣀⡞⢁⣾⢏⣠⠔⠒⠛⠛⠁⠀⠉⠢⡀⠀⠀⠀⠀⠀⠈⠐⠤⣀
⠀⠀⠀⠀⠠⠃⠘⠀⠀⠀⠀⢀⡠⠂⠁⠀⠀⠀⠀⢠⡿⠑⠀⠈⠙⠇⢁⣿⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⡸⢰
⠀⠀⠀⠀⠎⠠⠁⠀⠀⠀⡠⠊⠀⠀⢀⡀⠄⢀⣬⣏⣀⠀⠀⠀⠀⣠⣾⠋⠀⠀⢠⠀⠀⣀⠤⠤⠤⠠⢀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠳⠠⡀
⠀⠀⢀⠈⣀⣉⠠⠀⠀⢘⠁⠀⠐⠈⠀⠀⠀⠐⣿⠀⠉⠉⠉⠉⣿⡿⢷⡎⠉⢲⡛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠡⠁⠠⠀⠀⠀⠀⠀⠱
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⢨⣽⡀⠀⠀⣰⣾⣋⣀⣠⡇⠀⠈⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⠀⠀⢄⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣀⠤⠤⠤⠤⠿⠷⢶⠿⠟⠉⠉⠉⠉⠉⠒⢤⠄⠑⡀⠉⠀⠀⠀⠒⢂⠴⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠀⠀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠒⠀⠀⠀⠒⠒⠂⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⠤⠤⡤⢤⣄⡀⠀⠐⠿⡧⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡖⣾⡂⠀⠀⣀⠀⠀⢀⠼⢿⡆⠁⠁⢉⠀⢉⡬⣿⣶⣷⣿⠷⠸⢶⠦⠂
⡖⠶⡶⠹⠀⠲⡀⠀⢐⣾⠀⣿⡇⢹⣿⠀⠀⠀⠀⠀⢸⣰⡒⢢⣼⠈⢸⣿⣻⣿⣿⡱⠈⠏⢻⠳⠀⢀⣶⣶⣶⣾⣿⣶⣶
⠉⡏⣷⡖⠀⡄⠉⠁⠉⡈⣀⣿⣧⣸⠏⠆⠐⠀⠄⠀⢸⠉⠠⢀⣀⡀⠈⠙⢻⣿⡿⡀⠠⠀⠀⢀⠘⠋⠛⠉⣻⣿⣿⣿⣿
⠀⠀⠁⠀⠀⠀⠀⠉⠁⠉⠀⣿⣿⡯⠂⠀⠀⢀⠀⠀⠀⠀⠐⠻⠟⣿⡇⠀⢸⣿⢟⡁⠀⠐⢀⠀⠀⣯⣥⣯⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠐⠈⠁⠁⠀⠀⠄⣿⣿⣟⡀⣀⠀⠘⠃⠀⠀⠂⠀⢀⡉⣿⡇⠀⣾⣿⣟⡋⠈⠁⠘⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢿⡁⠐⠃⠀⠀⢀⢰⣿⣿⣽⣇⠀⣿⣿⣟⣀⡀⢀⠶⣂⡂⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠿⠛⠉⠐⠐⠀⠠⠈⠀⣄⣙⡛⠛⠘⠿⠂⠿⠿⠏⢿⠿⣯⣝⣻⣳⢿⣿⣿⣿⣩⣽⡏⣙
⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⣥⡈⠙⠻⠶⣷⣶⣖⣻⡝⡿⠋⠭⣿⣷⣶⡄⠀⠀⠀⠀⠀⠠⣍⣁⠙⠀⠠⠈⠉⠙⠛⠛⠿
⠀⠀⠒⠲⡄⠀⠀⠄⠀⠀⠀⠈⠙⠓⠠⠤⠤⠤⠬⣭⣾⣥⡦⠼⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣷⣢⣀⡠⠠⡖⣪⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠒⠛⣛⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠀⠀⣈⣽⣿⣿⣧⣽⠿⣤⣛⣃
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢈⣀⣤⢤⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠄⡀⠀⢀⣀⣀⣁⡀⠩⣭⠉⣩⣴⣿⣿⣿⣛
⣴⣦⣤⣤⣶⣤⣖⣂⣠⣤⣤⣤⣤⣤⣦⣤⣤⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣾⣶⣤⣶⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣤⣭⣯
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣷⣶
⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿