Seafront Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣆⠀⣰⡿⠉⢀⣙⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡉⣤⣾⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣧⣿⠁⢀⡿⡻⠀⠈⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⢾⡰⠛⢿⣿⣿⡆⣤⣴⡆⢴⣤⡴⠖⠂⠀⠀⠀⠀⢀⣠⢄⣤⡤⠖⠀⠀⠀⣀⣬⣤⡈⠀⠀⣀⠈⡉⠁⡀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢋⣤⠶⠾⢿⣿⣿⣿⣟⣥⣊⠁⠀⠀⠀⠀⠀⢀⠴⠫⠞⠫⠋⡅⠀⠀⠲⠋⡏⠀⠘⣷⠘⠃⠈⠁⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⠰⡿⣷⣿⣿⣿⣿⡿⣷⡄⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⠃⠀⢰⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣟⣴⠟⢹⣿⠛⡟⠙⣻⡄⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⡀⠀⠸⠀⠘⡆⠀⠀⢀⠀⠀⠀⢼⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠟⠁⠀⣸⣯⣸⠃⠀⠘⡡⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠸⡀⠀⠀⠸⠄⠀⠈⠀⠂⠀⡾⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠿⠿⠁⠀⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⢧⠀⠰⠀⠄⢸⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠘⠄⠀⡞⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢀⣺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⢣⢀⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣈⣲⣄⠀⠀⢀⣹⣇⠀⣿
⠀⠀⠀⣀⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⣎⠠⢡⣏⠜⢛⡉⠭⢣⣿⠀⣿
⠀⠠⢽⡿⣿⡟⣻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣬⢆⠤⡄⠤⠉⣤⠔⡉⠐⢖⢾⣿⣣⣿⡦
⠠⠤⢼⡿⣿⣿⣿⣶⣃⠢⣄⣂⣤⣦⣄⡀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠸⡉⣀⡬⠽⠤⠐⣈⣈⠤⣌⣱⣾⣽⣿⣿⣿⣿⣓⣚⡂
⠀⢰⣾⣿⣿⠟⠾⠿⣭⠭⢿⣿⣿⣿⣿⣿⠦⠀⢸⠃⠃⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⢿⣿⣿⠿⣟⠋⠁
⠀⠸⣿⣿⠏⠀⠀⠀⠀⣺⣿⣿⣿⣿⡩⠟⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠩⠽⢭⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⢿⣧⣤⣬⣉⣿⣇⠙⠻
⠀⡤⢟⠋⠐⠎⠻⠿⣿⠿⠛⠆⠐⠒⠏⠀⠀⠀⠘⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠋⢠⣴⣿⠿⣿⠿⠛⠿⣭⣡⢿⠿⠛⠚⠛⠛⠛⠈⢻⣆⠀⠙
⣠⡼⠁⠀⠀⠀⠀⠉⠉⠀⠺⠁⢀⠀⠐⠂⠀⠀⢸⢸⡆⡇⠀⠀⠀⢀⣀⡤⠤⣤⣰⣲⡏⣉⣉⣭⣽⡛⣟⡻⢷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂
⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠂⠉⠒⠛⠒⠒⠀⢺⢻⠃⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠉⠙⠛⠒⠊⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣎⣍⣬⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠤⠈

⠀⠀⠠⠀⢄⠀⠐⠃⠀⠀⠀⣤⣴⡀⠀⡷⠀⡦
⠀⠀⠀⠀⠀⠀⠖⠠⠴⠀⢸⠃⠉⠄⠀⠀⠀⠀⠈⠳⣤
⠆⡀⡀⢠⠘⠁⠀⠀⠀⠀⡈⠀⠀⠈⠠⢀⣀
⠀⠀⢳⠂⠀⠀⠁⠀⢀⢠⠆⠀⣠⠄⢀⣾⣉⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠉⠋⢠⣾⣿⠿⠁⠀⢠⡾⠆
⠂⠃⢀⣀⠀⠀⠀⣁⢀⡆⠀⠀⣠⡞⣁⣰⣦⣖⠀⠚⠖⠀⠀⣀⡀⠀⡛⠀⠀⠀⣤⣿⣦⣄
⠀⠀⢠⠛⡔⢀⠀⠈⣩⠉⠙⠀⠈⠂⠨⠟⢛⠻⣽⣶⣾⡁⠀⣼⠿⣿⠧⠀⠆⠀⠘⠋⡛⠇⣀⣆⡀
⠀⠀⢾⠀⣧⠀⠀⡾⠯⠰⠆⠀⠀⠀⠀⠀⠈⠀⠘⡋⠙⠀⢠⠊⠀⠈⠀⠀⠀⠁⠀⡖⡇⠀⠛⠻⠁
⠀⠙⠀⠦⠈⡀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⡇⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠇
⠃⠀⠀⠀⠀⢡⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢠⡇⣤⠇⠠⠾⠄⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠤⠤⠤
⠀⠀⠀⠀⠀⠰⠀⢈⡇⠀⠀⠀⣀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠞⠉
⡀⠀⠀⠀⠀⠀⡆⢰⠁⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⡿⠟⢿⣿⠷⠛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠠⠂⠀⠀⠶⣠⠥⠈⠄⢀⣤⣶⣿⣿⡿⠿⠿⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠃⠸⠟⠿⢏⣛⣛⠏
⠀⠀⠲⠒⠆⠀⠀⠀⢨⠀⠀⠀⠀⠉⠉⠀⠓⠂⠤⢤
⠂⠀⠀⠀⡀⠀⠠⠄⠀⠀⠀⠘⠒⠧⠔⠠⠀⠀⠀⠀⠈⠙⠷⣦
⠀⠀⠀⠚⠓⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠈⠐⠂
⠀⠀⠀⠀⠴⠦⠀⠀⠀⠀⠀⠀⠛⠓⠚⠃⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢈⣁⠀⠀⠤⠦⠄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠷⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠓⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠐⠂⡀⡀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠉⠙⢳⡀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠀⠀⣀⡼⠋⠉⠁⠀⢦⣄⠀⢸⡆⢀⣠⡴⠆⠀⠀⠀⠈⢷⡀
⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⣀⣠⣀⣀⢻⣶⣿⣧⣿⣋⣄⣀⡀⠀⠀⠀⠈⢷⡀
⠀⢰⡏⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣩⣭⣽⣿⣿⣿⣟⣻⣿⣿⣉⠛⠙⠃⠀⠀⠀⠘⣷
⢀⡿⠀⣀⣀⣀⠀⢻⣆⣾⣡⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣬⣍⣉⡉⠙⠋⠉⣩⣿⣯⣽⢿⣿⣿⡻⣾⡛⢷⠀⠀⠀⠀⠀⠀⢹⡇
⢸⡇⠈⢉⣩⣭⣿⣾⣿⣿⣿⣾⣿⡛⠶⠄⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⣴⡟⢁⣿⣿⣿⣿⣿⡟⠻⣷⡀⠀⠀⣀⠀⠀⠀⠀⣿
⣿⠀⠀⢨⠏⣩⣴⢿⣿⣿⣿⣿⣭⡙⠳⠆⠀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣏⢸⣿⡇⠙⣿⠀⠈⣣⣀⡄⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣮⣿⡍⠻⣆⢀⡴⠞⠉⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⣿⡧⠤⠭⢶⣿⣿⣿⣿⣥⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠸⣁⣾⡿⠉⢻⡇⠈⣷⣤⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⡹⣦⣀⣤⠤⠤⢤⣄⡀⠀⠀⠀⠐⠂⠀⠈⠁⢸⣿⣆⠀⠀⠀⠉⢻⡏⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⣿⣿⡧⠀⠸⢷⡾⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣽⣿⣿⡤⠄⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⢸⣿⠈⠳⡀⠀⠀⠀⣷⠀⠀⢀⣠⣶⣿⣿
⣿⡀⠀⠀⠀⣿⡿⠀⠀⠀⣼⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⣹⢿⣿⣿⡟⠂⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢸⣿⡆⠀⠙⠆⠀⠀⢸⣦⣴⣿⣿⣿⣿⣿
⢸⣷⣶⣶⣤⣿⣇⠀⠀⣀⣼⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠚⢹⡇⠙⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⣠⣴⣾⣿⣿⣿⣿⣶⣤⣀⣤⣾⣿⣿⣿⣿⣧⣿⣿
⠀⣿⣿⣿⣿⣿⣽⣷⣄⣿⣩⢭⡍⠁⣰⡿⠛⠛⢻⣟⠁⠸⣿⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⡏
⠀⠸⣿⣿⣿⣿⡟⣿⣿⣿⡇⠀⣷⣿⣿⣇⢐⣺⢰⣿⣖⡂⢸⣿⣷⣾⣥⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠼⣿⣿⣿⣿⣿⣯⣻⣯⣿⣿⣿⡿
⠀⠀⢻⣿⣛⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢻⣏⠛⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠋⠙⠛⠛⠋⠉⠉⠉⠉⠛⠛⠛⠋⠙⠛⠛⠛⠉⠉⠉⠉⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠙⢿⣿⣿⢿⣿⠿⠿⠛⠛⠋⠉⣉⣉⣭⣛⣲⣄⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢯⡿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠿⠿⢟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣛⣿⣛⣻⣿⣿⣿⣿⣿⢿⣟⣻⣿⣿⣿⣿⣟⢏⣾⣽⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣹⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡽⢛⣿⣟⣶⣷⣿⣿⡿⣿⣿⣛⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣯⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢉⣭⣿⣿⣿⣯⣭⡀⠀⠀⣲⣶⣷⣖⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⣿⠇⠡⣧⠀⠀⠹⡆⠈⣽⠟⠀⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠃⢠⠀⠀⠀⠘⠁⠀⡇⠀⢈⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣢⣄⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⡇⠐⢩⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⢿⠟⢯⠁⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⣸⣧⡤⣧⡤⣀⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⠙⣲⡤⣰⣴⣶⣦⣼⣟⣷⡝⢡⣿⣿⣷⣿⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢶⣾⡾⠾⠷⠾⠾⠿⠿⠿⠿⠿⠷⠿⠿⠿⠿⣿⣾⣿⣿⣿⣿⣿⣿⣽⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠓⠐⠒⠤⠤⠤⡄⠀⢈⡉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠶⠖⠒⠉⠀⠀⢀⣀⡤⠶⠾⠐⠂⠂⢀⣀⣠⠤⠖⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣐⣒⣲⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣐⣶⣶⡶⠼⠟⠛⠉⠀⣤⢀⠀⠀⠀⠘⠄⠢⠤
⠀⢀⡀⠀⢀⢀⣀⣀⣀⣀⡤⠤⠤⠶⠶⠚⠛⠛⠛⠛⠍⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⠖⢶⡀
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣠⡒⢒⠾⠛⠟⠛⠛⠉⠀⠀⡾⠀⠀⠀⠀⠠⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡾⠟⠛⠋⣉⣉⣀⣀⣠⣤⣤⣄⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠖⣋⡅⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠠⠄⠠⠤⠀⠈⠙⠛⠓⠒⣒⣛⣉⣉⣡⡴⡶⠞⠟⠟⠛⠉⠉⠙⠉⠏⠋⠉⠈⠛⣛⣛⠿⠟⠚⠓⠛⠓⣛⡹⠍⠝⠉⠑⠲⠾⢿⠤⠔⠒⠉⠁⠀⠀⠈⢣
⠀⠐⠒⠒⠂⠋⠉⠙⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠒⢊⠉⠥⠜⢛⠁⠄⠐⠀⣀⡤⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡴⣤⡟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⣁⣀⠄⠀⠀⠀⠀⠀⠀⣀⡠⠄⢀⠐⣯⠁⠀⠀⠀⠀⠀⠀⠀⢀⡔⢣⡴⣦⡦⠦⢻⡿⠃⠉⢛⡓⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠂⠠⠤⢤⣠⣤⣤⣤⠴⠖⠛⠉⠀⠀⣀⣤⡴⠚⠛⠉⠀⠠⠂⠁⠀⠀⠄⠀⠀⠀⠄⠀⠠⠖⢁⡽⠛⢛⡯⠉⠹⠛⠇⠀⠭⠿⠣⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠀⠠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠈⢦⠁⢈⣀⠀⠄⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠁⠈⠀⠀⠀⠂⢨⠀⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣬⠐⠀⠐⠀⠠⣢⢠⢁⠀⠀⠢⢠⡾⠀⠉⠠⠿⠇⠄⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠾⢮⡁⠁⠈⠉⠹⣘⠉⣀⡄⠀⠀⠆⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠐⠁⠐⠋⠓⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣠⡇⢀⠶⣾⣤⣤⡿⡦⠀⡀⣾⣷⣴
⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠉⠉⠀⠀⠁⠘⠚⠀⠀⠀⠀⠙⠀⠈⠁⠈⠋
⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠂
⠀⠀⠀⠂
⣀⣀⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣐⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⣤⣦⡶⠟⠓⠲⠦⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠜⠤⠶⠢⠆⠴⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣽⣿⣿⣚⣟⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿⣡⣟⠓⣏⠙⠿⢆⢤⠄⠀⠀⠀⡀⣤⡤⣤⡀⠀⢠⠀⠀⠀⠀⠀⠈⠙⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠘⣀⡜⣿⡇⠷⣼⣷⡀⠈⠀⢀⠀⠀⣪⣿⣿⡄⠲⣄⣤⢾⣿⠷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠃⢻⡇⠀⠨⣗⠁⠂⠀⠀⠀⠸⠃⠀⣽⣽⣆⠸⠏⢿⠈⢓⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢦⡌⠳⢄⡀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠈⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⡀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠈⠑⠦⡀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠀⠈⠳⣄⣀⠘⣆
⠀⠀⠀⠀⠀⠀⠟⠛⠲⠶⠂⠀⠈⠁⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣄⠀⠈⠻⣧⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⠤⡤⠤⠤⠤⠖⠛⠡⢀⡀⠐⠙⠁⠀⠀⠀⠀⠈⠻⣷⣄⠀⠙⣆
⠀⠀⠀⠐⠒⠒⠂⠈⠉⠉⠉⢉⣁⣀⣀⣀⣀⣀⣀⡤⠀⣀⠤⠴⠴⠖⠋⡹⠀⠀⠀⠀⣀⡤⠤⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠤⠀⠠⠴⢖⣫⣭⡥⠶⠶⠶⠶⠶⠶⣤⣤⣤⠤⣤⠤⠖⠊⠁⣀⡠⠀⠊⢁⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠠⠤⠄⠒⠀⠀⠊⠉⢀⡠⠒⠈⠀⠀⠀⡠⡊⣨⢧⠷⢾⣋⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠄⠤⠤⠤⠒⠈⣀⠤⠔⠂⠀⠄⠀⠀⠀⠀⠠⠴⠻⢚⠏⠑⠛⠰⠖⠠⠀⠀⠀⠀⠒⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⢀⡄⣚⠿⣿⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠉
⠀⠀⠀⠀⠚⣙⣿⣿⣯⣾⡟⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⠩⣦⠉⠁⠀⡴⣗⢂⣤⣶⠄
⠀⠀⠀⠀⠀⡿⠁⠋⢡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠝⠀⡀⠈⠀⠙⢇⠉⠘
⠀⠀⠀⠀⡐⠁⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⡀⠑⠠⡀
⠀⠀⣠⠞⠀⣠⠊⠀⠐⠂⠶⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⠁⢄⣀
⠀⠘⠁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠿⠿






⣀⠀⠀⠀⡆⠀⡀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣷⣷⣦⣀⣿⣦⣤⣦⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⡀⣄⣤⣀⡀⣀⣠⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⡉⠀⠐⠒⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠏⠉⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡉⠙⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⠑⠀⢁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠿⡛⠛⠉⠉⠋⠀⠀⠀⠀⠀⠈⠃⢀⠈⠀⠄⡀⠠⠀⡀⠀⠀⠀⠀⠉⠉⠙⠛⢉⣀⣹⣿⣿⣿⣿⣿⣿⣿⡿⣿
⡶⠄⠀⠁⠀⠀⣈⠓⠀⢲⣄⡀⠀⠘⠀⡠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠑⠦⢻⡿⠿⣿⣿⣿⣿⣿⣿⣵⣿
⠠⠤⢀⠀⠀⠜⢀⣠⠍⠈⢁⣔⠒⠀⠀⠀⠨⠀⠐⠂⠀⢘⡂⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣛⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣽⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢯⣿⣿⣭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠭⣿⣿⢚⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡷⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢻⣿⣿⣿⣭⡤⣂
⠀⠀⠀⠀⠀⠀⠀⠀⣓⣾⣿⣿⣋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠄⠀⠀⠀⠀⠀⠀⠀⡈⠻⢶⣿⣿⣿⣷⣾⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠲⢬⣿⣿⣿⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠨⠀⣀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⢀⠓⣶⣿⣿⣷⣶⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⢠⠀⠀⢶⣼⣹⣿⣿⣿⣿⣯⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⡿⠿⠋⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠾⣦⣌⣿⣿⣿⣿⣿⣿⣯⣤⣶⠖
⠀⠀⠀⠀⠀⠀⠺⢾⣿⣿⣿⣿⡚⠋⠁⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣾⣷⣞⣌⣻⣿⣿⣿⣿⣿⣿⣿⣥⣴⣾⠄
⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣛⣡⣤⣠⣄⣀⡀⣀⣀⣀⣠⠰⠂⠀⠀⠀⣉⣻⣿⣋⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠧⠶⢯⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠓
⠀⠀⠀⠀⢠⣄⣘⣿⣿⣿⣿⣿⣿⡷⠛⣉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤
⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢌⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠘⠚⠛⠛⢿⣿⣿⣿⣿⣿⢿⡾⠈⠁⠀⢸⡆⢰⡆⠀⡄⠀⣧⠘⣧⠠⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡛⠶⢢⡂⢀⣀⢸⣇⣼⡇⣀⡏⠀⣷⢸⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣾⣇⣸⣿⣿⣿⣾⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠁

⣠⣄⣤⣀⣠⣀⣄⣀⣠⣀⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣠
⣿⣇⣺⣯⣍⣭⣭⣍⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⣾⣆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⢸⡇⢰⢸⠀⠀⣇⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⡀⡀⢀⢀⣯⣿⣀⠀⠀⠀⠀⢠⡄⣹⠀⡀⠀⠀⣼⣿⣧⣾⣿⣶⡎⣿⣰⣷⣿⡷⢶⣦
⠀⠀⠀⠀⠀⠀⢀⠀⣼⣷⣾⡇⠣⢺⣿⣿⣿⡇⠀⠀⢨⣶⣾⣷⣿⣿⠃⠀⠑⠛⣿⠃⠈⢻⡿⠥⣏⡷⢻⣾⣡⡎⣻⡆
⠀⠀⠀⠀⠀⢀⣶⣶⣿⣿⣿⢷⡞⠐⢿⣿⠏⠃⡀⠀⠈⠋⢻⣿⣿⠛⠂⠤⠦⢴⡇⠀⠀⠀⢿⣩⡿⡗⢺⣋⣾⣷⣨⡇
⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣟⣼⠁⠀⢸⡟⠄⢸⡵⣶⡎⠀⠈⣿⣇⡀⠀⠈⢀⠬⠃⠈⠉⠒⠠⣿⡀⣿⣾⠛⣷⡉⡦⠄
⠀⠀⣼⣿⣿⠿⠿⠛⠛⠉⠉⠃⠀⠀⢸⠃⠤⠈⢷⡿⠁⠤⠐⠙⠛⠛⠛⠿⢾⠀⠀⣤⢴⣤⣤⣏⣿⣷⡟⠀⢿⡙⠫⡀
⠀⠀⠋⠁⠠⡆⠀⠀⠐⢺⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠠⠀⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠒⠀⠩⡥⠚⣽⡦⢘⣲⣄⣀⣐⣢⡄⠀⠀⠀⠀⠠⣤⣀⣄⠐⢢⡄⠁⠲⡆⠈
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠒⠶⠶⠶⠄⠲⠚⠃⠀⠼⠖⠒⠛
⠀⠁⠀⠀⠒⠿⠿⣥⣶⣤⣿⣆⡀⢰⣦⠀⡀⣰⡄⡄⠀⣦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣦⣽⣿⣯⣿⣼⣿⣯⣿⣧⣷⡄⠀⠀⡀⠀⠀⣸⣶⡄⠀⣦⠀⠀⠀⢢⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢹⢿⣶⢶⣿⣿⣻⡃⠀⠆⣿⣷⣶⣿⣿⣇⠘⢻⡇⠀⠐⣘⣧⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠀⢐⡒⠈⠃⠈⠁⣥⠛⢛⡻⣿⣿⣚⣉⣁⠤⠠⣿⣿⠗⠛⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠉⠈⠛⠉⠉⠝⢿⣦⠤⢴⣾⡿⢿⠭⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣲⣱⣦⣄⣀⢀⠀⠀⡀⢀⣀⣴⣦⡀⠀⠀⢠⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⡉⢛⠙⠉⣴⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠌⠛⣿⣛⠟⠛⢭⡈⠟⢆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠍⠉⠓⠦⢥⣅⡔⡚⣷⣶⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠋

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⣤⣴⣬⢛⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⠯⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠁⣾⠻⠟⡻⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠘⠇⠀⠀⠛⢧⠚⠻⠁
⠀⠀⠀⡠⠁⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠄⡀
⠀⣀⠔⢁⡴⠁⠀⠂⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢤
⠀⠉⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣯⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⠀⣤⠀⣤⣴⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢀⣤⢽⣷⣿⡾⢚⣉⣀⣀⠈⠈⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢾⣶⣾⣿⣿⣿⣭⣏⡛⠉⠉⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡴⢛⡟⣡⡞⡟⠲⡅⠈⠻⢷⡆⢤⢤⠀⠀⠀⠀⠀⢠⣄⣀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⣼⣿⡇⢱⣀⢻⣦⠀⠀⠙⠀⠡⠀⠀⢀⣤⢺⣷⣿⠍⠠⣍⠁⢀⣲⣿⣴⣮⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡼⣼⠘⣿⣧⠈⡙⢿⡟⢷⡀⡀⠀⠀⠇⠀⢀⡾⠫⠺⡿⣷⣀⠘⢰⣿⢣⣾⢻⣅⠤⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢹⡇⠀⠀⠐⢿⡁⠀⠁⠀⠀⠀⠀⢸⠉⠁⠀⠿⢷⣽⠄⡘⠃⠘⠃⠰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡄⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣉⢉⣉⣀⢄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣄⡀⠀⠀⠀⠀⠈⠙⠦⣀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣂⣦⠀⣠⠒⣄⢲⠒⢖⣒⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠈⠓⢦⡀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣟⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠀⠀⠈⠲⣄⠈⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⠄⡀⠀⠈⠻⣶⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⡇⠀⢂⠀⠠⠄⢀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢳⣕⡄⠀⠀⠈⣛⡀
⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠤⢼⣆⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡵⡀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂⠶⠚⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠂

⣿⢿⠿⡿⡿⠟⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣿⣛⣻⣿⣿⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣴⣿⢿⡿⠷⢦⣅⠀⣀⣿⡿⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠇⠀⡟⠀⠀⠙⠀⠸⠋⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⡠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣶⣿⡟⠂⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡆⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠞⠀⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⠀⣆⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢦⣄⢠⣠⣤⣄⣷⢶⣴⠛⣽⣿⣯⣿⣻⣶⣿⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣽⠦⠾⠿⠷⠿⡿⣿⠷⣿⣿⠿⣿⣯⣶⣿⣿⣿⣿⣿⣷⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠦⠀⠤⠄⠀⢉⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠒⠊⠁⠀⣀⣄⡤⠒⠚⠐⠂⠀⢀⣤⡤⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣐⣀⣠⣤⣤⣤⣽⣶⣶⡶⠶⠦⠤⠶⠶⡶⠶⠾⠗⠛⠉⠁⠀⠴⢀⣀⡀⠀⠑⠈⠒
⠀⠀⠀⠀⠠⠤⠤⠤⠤⠖⠒⠒⠛⠋⠉⠉⠉⠉⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣤⡽⠟⠋⡧⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⠶⠶⠶⠖⠒⠒⠒⠒⠒⠒⠛⠁⠤⠶⠖⠉⠈⠉⠉⠁⠀⠀⣀⡤⠃⠀⠀⠀⠀⠀⢀⡤⠚
⠀⠀⠀⠀⠀⠀⠠⣤⢄⣀⣀⠤⠶⠶⠛⣛⣩⣤⣤⡶⠶⠶⡶⢶⠿⠶⠖⢾⠶⣦⣤⣤⣤⣠⣤⣠⢤⠤⡶⠾⢟⣁⣲⡄⠀⣀⡀⠄⠂⠁⢠
⠀⠀⠄⡤⠠⠤⠤⠤⠤⠶⠒⠒⠂⠈⠉⠉⠁⠀⠀⠀⠀⣀⣀⡬⠤⠄⣒⡤⠖⠒⠉⠀⠀⣀⠠⠒⠋⠁⠀⠀⠀⠀⠉⠉⠀⣠⡀⢀⠀⣤⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠒⠚⠋⡉⠁⠀⠀⠀⠀⠀⢀⡀⠀⠠⡖⠋⠁⠀⠀⠀⠀⠀⠀⠠⢀⣠⣀⣀⠼⣾⠏⠿⠷⠤⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⣀⣀⣀⣀⣀⣠⡤⠶⠚⠉⠀⢀⣠⡤⠖⠒⠈⠁⠄⠀⠀⠡⠀⠀⠀⢀⠀⠀⡠⢊⡵⠞⢶⡛⠒⠾⠧⠀⣂⡾⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠁⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⣠⣸⠔⠂⠒⠂⠠⠠⢀⠀⠀⠀⠀⠀⠀⠈⠠⠀⢀⠐⢴⡄⠘⣋⡉⠉⠁
⠀⠀⢸⣾⠂⠀⢀⣼⣳⢶⡴⡗⢐⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣠⣆⣿⣦⣾⣿⣈⡉⠙⠃⠋⠀⠄⠁
⠀⠀⡯⠇⠠⣔⠈⠉⢸⡦⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢉⣠⣴⠊⢹⡽⣴⠆⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡄⠀⠀⢾⡧⠤⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠃⠀⢸⡯⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⣤⠄⠀⠐⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⢀⡀⠀⠀⠀⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠐⣆⠀⠀⠀⠐⠐⠀⢒
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠘⠛⠀⠉⠉⠀⠀⠀⠀⠀⠀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠈⠉⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠈⢉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠀⠀⠀⠀⠀⣠⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠰⣻⣿⣃⡀⠀⠀⠀⢀⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠈⠀⠀⡀⢀⠀⠀⠀⠀⠈⠛⠻⠿⠇⠀⠀⣠⣿⣿⡿⠟⠀⠀⠀⡖⠀⠀⢀⠀⠀⠀⠀⠈⡇⡂
⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢠⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠘⠿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠠⠀⠁⢠⡀⠀⠀⠀⠂
⠾⠿⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠙⠙⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⡁⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣤⣄⣀⠀⠀⠀⠀⢠⠆⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣭⣽⣿⣽⣷⣄⠀⣀⣤⣀
⠀⠀⠂⠀⠀⠀⠁⠈⢀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠀⢠⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠘⣻⡻⣿⣿⣿⣿⣿⣿⣿⣿⢶⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠿⠖⠾⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠛⠷⣴⣤⣿⣿⣿⣿⣷⣶⣒⠛⠠⠈⠉⠹⣛⣩⣽⣽⣿⣿⣧⣯⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠠⠀⠙⠚⠀⡠⢸⣿⣿⣿⣟⡶⠾⣿⣟⡁⠈⠰⠀⠀⠈⠁⠈⠛⢷⣿⣿⣕⣄⡀⠀⣀⣿⣿⣷⣤⣶⣦⣴⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡠⠀⠀⡀⠀⠈⠀⠀⠙⠛⣻⣿⣿⣿⣿⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣦
⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠂⠃⠀⠀⠀⠀⠀⠀⣽⣿⣿⣟⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠟⠿⢿⣿⣿⣿⣿
⠀⠀⠰⠀⠒⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⣿⣿⣿⣟⡛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⢀⣱⣴⣴⢛⣋⠐⠒⠢
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠿⣭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⡟⠈⣾⡗⣌⣷⡈⠙⠈⠀⠀⢀⣰⣿⠋⣓⠀⣠⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠶⢻⡇⠈⢻⠙⠠⠀⠀⠀⡾⠁⢻⣷⡌⠸⢳⠏⣦⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠑⢤⡀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠉⠠⢄⠀⠀⠀⠀⠉⠒⠦⢄⡀⠀⠈⠑⠦⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠺⡞⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠈⠓⢄⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢦⣀⠀⠙⢶⠀⠾⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢐⠤⡹⣧⣠⣄⡈⠶⣬⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⡤⠖⠋⠉⣀⠀⠚⢑⠻⣮⡾⠛⠓⠾⣧⡘⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣹⢀⣴⠡⠜⡉⣤⣦⣾⣷⣿⣿⣿⣶⣄⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠟⠳⠿⠿⠾⠷⠷⠛⠁⠁⠀⠀⠐⠀⠐⠈⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠈⠉⠀⠀⠠⠀⣴⣿⡿⠛⠿⠍⠠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⣤⠤⣀⣀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⠿⠿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠰⠀⢀⣀⢿⣿⣟⣉⣉⣈⡉⣉⣉⣩⣽⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠀⠘⠛⠛⠋⠀⠻⠋⠛⠛⠻⠿⣿⠿⡿⠟⢁⣸⡽⢃⣤⡄⠀⣠⣼⣧⣼⣶⣿⣦⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠈⠙⠁⠁⠁⠉⠉⠈⠀⠈⠉⠉⠉
⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠶⠶⠶⠶⠂⠒
⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⣦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠉⠁⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣈⣀⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣧⣤⣤⣀⣀⠀⠐⠿⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⡿⠟⠛⢛⣛⣻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣷⣿⣿⣷⣶⣶⣶⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠶⠶⠶⠶⠖⠲⠲⠶⠶⠶⠶⠶⠤⠶⠆⠀⠀⠀⠤⠦⠼⠽⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣴⣦
⣤⣀⠀⠀⠠⠀⠀⢀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣛⣛⣿
⣿⣿⡿⠿⣋⣬⣿⣿⣧⣬⣿⣿⣦⣤⣶⣦⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⡿⢿⠿⠟⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣾⣿⣿⣿⣿
⣦⣶⣿⣥⠉⠛⠛⠛⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿
⢿⣿⡿⠃⠙⠂⠀⢀⣀⣠⣄⣀⣤⣶⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣲⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣅⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣠⣼⣿⣿⠷⢦⣌⠀⠀⢐⣶⣷⣿⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡿⠀⢸⠆⠀⠈⠷⠀⣼⠟⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠀⠄⠀⠀⠀⠁⠀⠀⠀⢀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣾⣴⣄⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⡇⠀⠁⠏⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡞⡻⠋⠓⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠘⣆⣀⢠⣤⢷⣶⡷⣶⣤⣖⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⣠⣤⣦⣨⣿⣦⣷⣛⣿⣶⣿⣽⣶⣠⣿⣿⣷⣿⣿⣿⡻⣳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠛⠋⠉⠉⠋⠛⠛⣛⣛⣛⣛⣛⡛⢛⠿⠛⠛⠛⠻⠿⠿⡿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠐⠒⠒⢂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠉⣀⡀⣀⣤⣴⠖⠋⠉⠉⠀⠀⠀⠴⢒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣂⣠⣤⣤⣴⡶⡶⠶⢶⠿⠿⠿⠟⠛⠓⠚⠛⠛⠞⠛⠛⠛⠉⠁⠀⠀⠐⠃⠦⣤⣄⣀⠉⠀⠉
⠀⠐⠂⠀⠀⠴⠶⠒⠒⠒⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⣤⣤⣤⡴⠗⠋⢈⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠐⠒⠒⠒⠀⠀⠁⠀⠀⠀⠀⣀⣠⠜⠁⠀⠀⠀⠈⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠠⠤⠤⢤⣀⠤⠴⠶⠟⠛⣋⣥⣤⣴⡶⠶⠖⢿⠟⡿⠿⠛⠛⢿⠿⢦⣤⣤⣤⣤⣤⣤⠤⠴⢶⠚⠿⣉⣀⣷⠄⠀⣀⡤⠄⠊⠁⠀⠄
⠀⠀⡄⣠⠀⠤⠤⠤⠤⠴⠖⠒⠒⠂⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣠⡬⠤⢀⣲⡴⠖⠒⡁⠀⠂⣀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠉⠁⠐⣦⡀⢀⡀⣤⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠶⠒⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⡈⠀⢠⡔⠛⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤⣀⣀⠽⢿⡯⠿⠶⠆⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⣀⣀⠀⠀⢀⡀⣀⣠⡴⠖⠋⠁⠀⢀⣀⣤⠴⠒⠂⢁⠄⠂⠀⢉⡀⢀⠀⠀⡀⠀⢀⠔⢋⡦⠿⣼⠛⠡⡼⣯⠀⢀⣰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠠⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣘⠒⠒⠊⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠘⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠑⠠⡀⠀⠀⣠⠔⢪⠃⠀⠑⠦⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠈⢇⠀⠑⠀⠀⠀⠀⠘⠒⠦⡁⠀⠀⠀⠀⠐⠀⣄⠀⢄⡠⠊⠁⢠⠂⠀⠀⠀⠀⠈⠑⠢⢄⣀⡀
⠀⠀⠀⣀⠄⠊⠀⠀⠀⢨⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⡡⠄⠚⠉⠀⠀⠀⠁⠀⢀⠀⠘⣄⠀⠀⠀⠀⠈⠉⠉
⡠⠴⠊⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠄⠋⠉⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⡀⠀⠈⠦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠉⠂
⠀⠀⠀⠀⠸⡄⢁⠀⢠⢦⠤⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣀⡄⠀⡄⣰⠃⠀⢅⣘⢘⠂⠄⠀⠀⠀⢀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠛⠡⠎⢥⠀⢨⡤⠔⠀⠰⠤⠀⢀⣌⣀⣘⣃⡐⣲⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠁⢁⢀
⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠠⡄⠠⡀⣀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢐⠃⠇⠁⡇⠀⡇⠀⣼⠏⠀⠁⠀⣦⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⡀⢉⣥⡁⠀⠒⠀⢰⠻⠀⠀⠀⡐⡝⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⡟⠉⠙⢡⠣⢀⠁⠀⠐⣸⠁⠀⠀⠀⡌⠀⠀⠀⠀⠠⠀⠀⠀⠰⡀⠀⠀⠆⠀⠀⢀⠄⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠁⠄⠄⣈⢐⠍⠀⠀⠀⢰⠀⠀⠀⠀⠀⠰⢦⠀⠀⠀⠁⠀⠘⠀⠀⠀⣰⢆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⢧⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⠙⠋⠀⠀⢸⠀⠀⠀⠀⠔⠁⣠⠑⠄⠀⢠⠀⡇⠀⢀⠄⣠⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠈⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠓⠚⠆⠀⠀⡀⠀⢀⠌⢀⠜⠀⠑⠌⠢⠈⠀⡇⠠⢂⠔⠀⠑⢄⠈⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣃⣧⡤⢤⣤⣀⠀⠁⠀⠌⡠⠂⠀⠀⠀⠈⠢⡘⡀⡱⠡⠂⠀⠀⠀⠈⠢⡈⠆⢀⠁
⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠨⡀⡜⠐⠁⠀⠀⠀⠀⠀⠀⢱⡜⣰⠁⠀⠀⠀⠀⠀⠀⠐⠌⡌
⠀⠀⠀⠀⠀⠀⢸⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⡆⢿⠃⠀⠀⠀⠀⠀⠀⢀⠏⡸⡉⢇⠀⠀⠀⠀⠀⠀⠀⠺⠇
⠀⠀⠀⠀⠀⠀⢸⡇⢰⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠈⠄⠀⠀⠀⠀⠔⢡⠎⠀⠈⢢⠑⠄⠀⠀⠀⠀⡐⠠
⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⣀⣠⣤⡶⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠠⠓⠐⠒⠒⠀⠤⠀⠀⡇⠀⠀⠀⠘⠊⠀⠀⠀⠀⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⠍⣐⣂⣒⣛⣛⣛⣛⣛⣛⣛⣓⣒⣀⠨⡁⠢⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠣⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡘⣐⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢘⠸⡀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠀⠀⠀⡇⡟⡈⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠑⠀⠠⠤⠤⢌⢧⣀⠀⠀⣀⢎⣔⣀⣢⡡⣀⠀⡀⣀⡼⣰⠇⠧⢀⡀⠀⡀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⠉⠩⠐⠀⠀⠀⠀⠈⠂⠽⡟⢋⡊⡐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡶⠀⠀⠀⢀⡴⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⡇⠀⡼⠁⠀⢀⡴⠋⣀⣘⠛⠃⢀⣠⡤⠖⠃⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠘⢂⣀⣁⡘⠃⢀⡴⠋⠀⠀⣀⡤⠶⠚⠉⠀⠀⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⡄⢠⠞⠉⠀⠀⠉⠳⡄⢠⠴⠚⠋⠁⠀⠀⠀⠲⠶⠃⠀⠀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⠄⡏⠀⠀⠀⠀⠀⠀⢹⠀⣤⣤⣤⢤⣤⣤⣤⣤⣤⠄⠀⣼⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣀⡤⢻⡄⠀⠀⠀⠀⢀⡟⠠⣄⡐⠶⠶⣶⣦⣤⣀⠀⠀⢰⣟⢁⣤⡴⢾⡛⢯⡙⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠚⠉⠁⣠⡄⠉⠓⠶⠶⠞⡋⠰⣄⠀⠀⠀⠐⠦⠈⠉⢹⣛⣶⡾⣶⣛⣩⣭⣤⣬⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⣰⠃⢐⡇⠀⢷⠀⠈⠳⠄⠀⣀⡴⣾⢻⠏⣫⣽⣿⡿⡿⣯⣬⣈⠃⢻⠸⡝⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣠⠞⠁⠀⠀⢠⠏⠀⠀⡇⠀⠈⢧⠀⠀⣠⣾⢹⠃⠇⠈⣴⡻⡜⠃⢳⡿⡄⠁⠏⡷⣦⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣀⠀⠀⢀⡟⠀⠀⠀⠇⠀⢀⡈⠀⣼⡇⡿⠈⠀⠀⣼⣏⠧⠁⠀⠈⣧⢿⡄⠀⠀⠏⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡭⠤⠀⠈⢀⣠⠴⠚⠛⠛⠲⣄⠀⠁⠀⠀⣠⠄⠀⡟⣎⠃⠀⠀⠀⢸⡤⢿⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⣠⡞⣳⢼⡆⣨⣷⠀⠈⠙⠃⠀⠀⠟⠀⠀⠀⠀⠀⠀⣧⠼⡇⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢠⣤⢤⡾⠓⣇⠚⠗⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠐⢦⠴⠀⠀⣿⣤⣿⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣠⠞⡛⢃⡲⠀⠹⠌⠦⣄⣈⣠⠴⣄⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣑⣉⣀⣁⣤⠴⣚⡶⣄⠈⠐⠛⠳⠯⣝⣒⠶⠶⠤⠤⠤⠤⠤⠤⣼⠁⢸⡦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠿⠿⠆⠀⠈⠉⠙⠶⢽⣓⠶⠤⢤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⡿⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⡀⠀⣤⣤⣄⠈⠳⣄⠈⠀⢙⢛⣙⣋⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⢀⣠⠴⠶⠒⠒⠛⠁⠄⠰⠶⠶⠶⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⠀⠛⠛⠛⠛

⠀⠀⠀⣀⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣉⣀⠀⠀⠈⠳⡄⠀⠀⠠⠂⠀⠠⠀⠀⠐⢁⡀⠁⢀⠀⠀⠂
⠀⡐⠀⢀⠀⠀⠰⠀⠡⠀⠀⠀⠀⠋⠀⠀⠀⠑⡆⠀⠀⢹⠀⠀⢀⠀⠀⠀⠀⠁⠄⠈⠀⠀⠀⠀⠀⠀⠘⠀⣶⠾⠛⠛⢛⠒⠦⣄
⠰⠀⠀⠀⠢⡔⠁⠀⠀⡅⠀⠀⠀⡄⠀⠀⠀⠀⣸⠀⠀⢸⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠰⠀⠀⠹⣄⣀⠔⠛⡆⠀⠀⣷
⠀⠑⠒⠒⠉⠈⠑⠒⠚⠀⠀⠀⠀⠐⣄⠀⢀⡴⠃⠀⢀⠜⠀⠀⠀⢰⠄⠀⠰⠀⢠⠀⠀⣠⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠙⠶⠚⠉
⠀⣏⠐⠒⠀⠀⠒⠂⢈⠇⠀⠀⠀⠀⠈⠉⠃⠒⠐⠊⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⢢⠴⠁
⠀⠀⠠⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⡙⠀⠀⠀⠠
⠀⠀⠀⠐⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠈⠑⠢⢀⠀⠀⠀⠀⠀⢀⡠⠖⠛⠓⢦⠀⠀⠀⠀⠀⠈⠒⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠰⠒⠀⠀⠠⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⣄⠐⡦⡌⢀⢴⠀⡀
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠈⠢⡀⠀⠀⠂⠀⠀⠃⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠤⡴⡼⠋⠁⠉⠙⢤⢠⠄
⠀⠙⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⠏⠀⠀⠀⠈⠢⡀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠙⡖⠒⢊⠒⣺⠉⠁⠀⠀⠠⠆⣹⠀⠀⠀⠀⠀⢸⡉⠤
⠀⠀⠙⠿⠿⠟⠁⠀⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠘⢦⣀⠇⠀⠀⠀⠀⠀⠀⠀⢻⢀⠠⢐⡇⠀⠀⠀⠀⠀⠚⠰⠣⣀⠀⢀⣠⠺⠔⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠀⠀⠀⠀⠈⣇⠀⡽⠀⠀⠀⠀⠀⠀⠀⠋⠸⡞⢃⠝⠮⠀⠃
⠀⠀⠀⠈⡄⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠘⠃⢀⡤⠀⠀⠀⠀⠀⠘⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⢶⠿⠀⠁⠰⡀⠅⠀⠀⠀⢴⠿⠿⣿⣿⣿⠿⢗⡆⠀⠈⠀⠀⠏⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠉
⠀⠀⠀⠈⡄⠀⠀⣴⠁⠀⠀⠀⠀⠈⣖⠒⠂⠒⠒⠂⡉⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣄⢸⣷⣄⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠠⠁⠀⠀⢻⠄⠀⠀⠀⠀⠀⡷⢌⢄⠀⠀⠠⠂⠀⠀⠀⠠⢀⠀⢰⣿⠿⠛⠉⠉⠀⣶⠀⠈⠂⠀⠀⠀⠀⢸
⠀⠀⠀⢀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⢸⠀⠁⠐⠒⢰⠀⠀⠰⢐⠪⠜⠀⠘⠁⠀⠀⠀⠀⣼⣿⣧⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⢀
⠀⠀⠀⠈⠂⠩⡭⠐⠁⠀⠀⠀⠀⠀⠈⠂⠤⠠⠄⣊⣀⠀⡐⠁⠀⠀⠀⠀⠂⠀⠀⢀⣼⣿⣿⣿⡔⠀⠀⣀⣂⣴⣿⣀⣀⣀⠴⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠒⠺⠿⠟⠛⠁⠀⠀⠀⠈⢙⡙⠛⢋⡋⠛⠋⣙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣩⣽⣿⣿⣿⣭⣕⠀⠀⢐⣶⣷⣶⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣹⡟⠘⣽⠀⠀⠉⢧⠀⣹⡿⠁⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠉⠐⡀⠀⠀⠀⠃⠀⠰⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣆⣤⡀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⡄⠀⠊⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣩⠿⡿⢻⠍⠉⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⣀⣿⣀⢼⣤⢄⡠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡘⢳⣤⢀⣆⣶⣶⣼⣟⣻⣮⠋⣽⣿⣿⢿⣿⣿⣾⣯⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣤⣶⣶⡶⠷⠾⠿⠿⠿⠿⠿⠿⠿⠾⠿⠿⠿⢿⣷⣿⣿⣿⣿⣿⣿⣯⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠚⠒⠂⠒⠂⠀⠤⣄⠀⠈⣉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠶⠒⠂⠁⠀⠀⣀⣠⠤⠶⠇⠀⠐⠀⢀⣀⣤⠤⠖⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⣒⣲⣦⣤⣤⣤⣤⣤⣀⣤⣤⣀⣴⣶⣶⡴⠟⠛⠋⠁⢠⠄⠀⠀⠀⠀⠥⠐⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣤⠬⠴⠶⠖⠚⠛⠛⠛⠋⠍⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢙⣿⡷⠰⡄⠀⠀⠰
⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⡤⢀⢀⣐⣒⠖⠒⠿⠿⠿⠛⠋⠁⠀⢰⠇⠀⠀⠀⡀⠄⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠿⠛⠛⢉⣉⣉⣁⣀⣠⣄⣀⣀⣠⣀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⣫⠀⠀⠀⠀⠀⢀⡤⠚⠉
⠀⠀⠀⠀⠤⠄⠀⠙⠓⠒⠒⠒⠛⣋⣉⣩⣤⡶⠾⠟⠿⠛⠛⠉⠙⠋⠿⠙⠉⠉⠙⢛⣛⡿⠿⠶⢖⠾⠒⢚⣛⠯⠭⠛⠙⠲⠴⢿⡡⠄⠐⠒⠉⠁⠀⠀⠙⡀
⠀⠐⠂⠐⠂⠒⠚⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠖⢒⠛⠩⠽⠛⠋⠩⠐⠂⢈⣠⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⣄⣤⢦⣼⠲⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠉⠉⠉⣁⡠⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⡐⢾⠉⠀⠀⠀⠀⠀⡀⠀⠀⡠⠚⣄⢶⡤⡤⠘⣻⠗⠚⠛⡛⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠤⠄⣀⣀⣀⣠⣤⣤⠶⠞⠋⠀⠀⢀⣠⣤⠶⠒⠉⠉⠀⠐⠁⠀⠀⠤⠀⠄⠀⠠⠀⠀⠠⠎⣸⠞⠛⣾⠉⠒⠾⠿⠀⢰⡶⠟⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠭⠈⠉⠁⠀⠀⠀⠀⠀⠐⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣻⣻⣛⣻⣻⣛⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣯⣭⣿⣿⣭⣽⣯⣭⣽⣽

⠀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠄⠀⢤⠃⠼⠛⣡⠁
⠀⣤⠀⠀⠠⠀⢨⠴⠀⢀⡠⡔⠂
⠀⠀⠐⠇⠀⠀⣞⠀⠀⣄⣁⠀⢤⡀⠀⠀⢤⠄
⠀⠀⠀⠀⠄⠛⠿⡀⠀⠭⠉⠙⠆⠰⣚⠴⠓⣀⠆
⠈⠉⠀⠀⠀⠀⠅⠈⠀⠠⢦⠴⠂⣰⡇⠰⣆⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠋⠰⠀⠘⠁⠁⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢀⡺⡏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠄⠀⠀⠀⠀⠀⣤⣴⡂
⠀⠘⠧⠀⠀⠀⠅⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡿⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠉⠐⠃⡂⠤⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠖⢂
⠀⠀⠀⡀⠀⠀⡇⠀⠂⠠⢀⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠒⠂⠠⠔⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠚⠃⠂⠀⠀⠬⠤⠀⠀⠀⠐⠠⠀⠀⠂
⠀⠀⠀⠉⣤⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠒⠀⠤⠤⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠀⡉⠀⠁⠀⠀⠀⢠⠀⠁⠀⠠⣾⣀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠉⠁⢀⠀⣄⣄⠀⣀⣈⣧⣀
⠁⠀⠀⡀⠀⢀⣠⣷⣷⣾⠵⠟⠛⠓⠐⠛⠉⠉⠁⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠷⠶⠦⠴⠶⠿⠿⠛⠛⠛⠛⠛
⠛⠻⠻⠿⠋⠉⠉



⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⡁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠐⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⢀⠀⠀⠘⠳⣆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡱⠀⠀⠑⢄⠂⠀⠈⢃⡘⣷⢴⣤⡀⡀⠀⠀⠀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⣞⣂⠱⣾⢶⣄⠀⠀⠃⠀⢐⣄⣶⣿⣴⣟⣦⣿⣿⣶⣿⣦⣼⣼⠦
⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡀⣁⠈⠉⠙⠛⠛⠿⠿⠿⣷⡤⠶⠿⠛⠋⠙⠋⠁⠀⠀⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠘⠻⠷⠾⠻⠿⠗⠀⠀⠀⠀⠀⠀⠀⠙⠱⠶⠿⠖⠀⠀⠀⠀⠲⠖⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢠⠀⢀⢀⠰⢾⡗⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⠶⠀⠠⠤⠼⢧⣿⣿⠿⣶⣷⣶⣿⣿⣴⡶⠶⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀
⠙⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠉⠉⠉⠛⠃⠁⠀⠈⠉⠉⠁⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢼⣿⣷⠄⠐⣀⠀⣠⣄
⠉⠉⠉⠉⠁⠀⠉⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⠇⠀⠀⠀⠀⠀⠀⣀
⠐⠒⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠛
⣿⣿⣿⣿⣿⣿⣦⣤⣴⣦⣶⣶⣦⣤⣤⣴⣶⣦⡄⠀⢀⣤⣶⣶⣶⣶⣴⣶⣶⣴⣶⣶⣿⣿⣦⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠈⣩⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢻⣯⣭⣽⣿⡿⠿⣿⣿⣯⣽⣯⣿⣿⣿⣿⣿⣿⡄⠀⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣂⠀⡒⡺⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠖⡳⠾⠷⠴⣶⣽⣿⣿⣿⣿⣿⣛⣻⣷⣶⣤⣛⣷⠶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠤⢭⣽⣛⣻⣿⣿⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠐⠛⠙⠛⠿⢶⠿⠳⣦⡉⠿⠿⠿⠿⠫⣭⣄⣨⣉⡻⠿⠿⣿⣿⣿⠿⠿⣾⣭⣵⣿⣽⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⠒⠒⠦⠿⠿⠷⠛⠻⠗⢶⣾⣿⣿⣿⣟⠉⠁⢉⡿⣿⣿⣿⣶⣭⣽⣟⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠰⡔⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢈⠇⣠⣀⣀
⠀⠀⠀⠀⠀⠤⠀⡰⠈⠉⡗⠀⠀⢶⡀⠙⠗⠂⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⣸⣿⣆⠀⠘⠙⠀⠈⠀⠀⠀⠀⡤⠀⠴⣟⣦⢩⠃⡀
⠀⠀⠀⠀⠀⠈⠀⠀⢠⠇⢻⠟⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⢐⡎⣳⣭⡹⣭⣁⠀⢶⠀⠀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠒⡏⠐⠀⢳⠙⠼⠬⢷⠾⣿⣝⢶⠦⡄
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠇⠀⢰⡥⢻⠿⠛⠾
⠀⠀⠀⠀⠤⠄⠀⠼⠀⠀⠤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠤⠄⣀⠀⠀⠀⢸⡄⢀⣀⡏⣀⠤⠤⠀⠀⣠
⠀⠀⢀⡀⠒⠶⢤⠀⢨⣤⡄⠀⠀⠀⣤⣤⡀⠀⠄⠐⠂⠀⠀⢀⡀⠀⢤⠀⣇⠈⢸⠃⠦⠀⠀⠈⠷⠂
⠀⠀⠀⣛⠖⠲⠆⡔⠀⠀⣀⣠⢀⡄⣀⠀⠉⠐⠾⡶⠦⠄⠀⢀⣈⣀⠀⠉⠉⠁⠌⠀⠛⠛⠉
⠀⠀⠀⠛⠛⠀⠀⠉⠀⠈⠉⠉⠋⠉⠉⠉⠈⠠⠤⠤⠤⡄⠈⢉⢉⣉⡉⠁⠐⠀⠖⠒⠐⠃⠈
⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⣀⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠻⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠼⠄⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⢀⡤⠂⠊
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⢀⡴⠋⠀⠀⣠⠆
⠀⠀⠻⡀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠚⠉⠀⠀⠀⠈⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⣤⣤⣀⠀⢳⡀⠀⠀⠀⠀⢢⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠗
⠀⠀⠈⠳⣬⠙⠄⠀⠀⢠⣮⡿⠙⠢⡄⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠈⠻⣦⠀⢀⣺⣿⡇⠀⠀⡄⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡀⠀⣸⣿⣄⠀⢀⠀⠀⠀⠘⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⡼⠁⢀⡄⠀⣀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡗⠀⠀⣴⣾⣄⠀⠀⠉⠻⢆⡀⠳⠆⠀⠀⠀⠠⣾⢿⣇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡁⠀⣉⡴⠂⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢰⣿⠋⠁⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠁⣠⠖⠀⠀⠀⠀⠉⠈⠉
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⢰⠞⠁⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠼⠅⠀⠀⠀⠀⠀⠀⠹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣟
⠀⠀⠀⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠀⢀⣾⣿⡏
⠀⠀⠀⠀⣼⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡘⠛⠛⠷⠶⠶⣤⣤⣀⡀
⠀⠀⠀⣼⡿⣉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡀⢉⠉⠛⠻⠶⣦⣦⣤⣦⣤⣠⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⣼⣿⣿⡿⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠒⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢀⣼⣿⣿⣿⡿⠤⠸⠘⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠛⠛⠻⠿⢿⣶⣶⣤⣤⣀⡀
⠛⠛⠛⢿⠿⡁⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣷⣶⣧⣤
⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠻
⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠈⠉⠊⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⣶⡿⢿⡿⠿⢟⣿⣽⣛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢪⣶⣿⡿⠞⠟⠙⣉⡤⢾⣿⢿⣳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣰⣿⡟⣀⢤⣽⣶⣽⣾⠟⠛⠃⠀⠈⠙⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣠⣿⢟⡐⢿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢘⣿⣿⠋⢰⣧⣿⣿⣿⣿⠀⣀⣤⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣞⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⣠⣿⣿⡇⠘⣇⣾⣿⣿⣿⢻⠾⠛⠋⠁⣀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠔⠊⠠⢲⡞⠿⠛⢁⢠⣀⣲⣿⣿⡿⢇⡠⠥⠤⢾⣿⣿⣿⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢠⣴⣦⣠⢀⣶⣼⣾⣿⣿⣿⣏⡑⠀⠀⠀⣀⠠⣶⣽⣿⣿⣷⣶⠾⠛⠿⠟⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⣈⣛⣿⣿⣿⣿⣿⠿⢿⡿⢗⠩⠐⠀⠀⢻⣿⣾⣿⣿⣿⡿⣿⡄⠀⠀⠀⠀⢐⣩⣶
⠀⠀⠀⠀⠀⢴⣿⣿⣿⣷⣶⣾⣿⣿⠿⠧⠄⠂⢀⣴⣶⣞⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠋⠹⠿⠋
⠀⠀⠀⠀⣀⡈⠛⠙⠙⠻⠿⡛⠛⠹⠳⠀⠀⢀⣀⣽⣿⣿⣯⡻⣿⣧⣀⠀⠀⠀⠀⠀⠀⢀⣠⣶
⠀⠀⠀⣸⣿⣿⣷⣴⣀⠈⢠⡄⣤⠀⣶⣷⢐⣮⣿⣿⣿⣿⣏⠁⠀⠉⠙⠀⠀⠀⢀⣠⣾⠿⠛⠁
⠀⠀⠀⠛⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠿⠷⠶⠤⣤⣤⡤⠤⠴⠖⠋
⠀⠀⠀⠀⠀⠙⠿⠿⠿⢿⣿⣿⡿⠿⠿⠛⠛⠛⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⠆⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠘⣦⣿⠁⣴⠎⠙⠟
⠀⠀⠀⠀⠀⠀⠀⣠⣷⠟⠻⣿⣿⣠⣴⣢⡦⠴⠂⠀⠀⠀⣀⣄⣤⠔⠀⢀⣨⠥⡌⢁⢀⡀⠉⣀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠛⣣⠞⣩⣽⣿⣿⣿⣾⡀⢄⡀⠀⠀⠊⠉⠉⢱⠀⠀⠁⡇⠀⠿⡌⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣞⡽⢻⡿⢿⠻⣯⠑⠀⠀⠂⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃⠹⠀⠀⢀⠀⠀⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢰⣧⠋⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⣨⠀⠀⢃⠀⠁⠀⢰⠋⠅
⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠈⠁⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡄⢀⠀⡎⠀⠸
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢰⠃
⠀⠀⠀⡀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢻⠀⢸
⠀⠀⣠⣷⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⣹⡹⣓⠺⢫⡇⣾
⠀⢚⣿⣿⣭⣀⣀⠀⠀⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠶⡶⠒⠰⢎⠥⣙⣿⣿⣿⣦⣀⡀
⠀⣽⣿⡿⣿⣿⣆⣿⣿⣿⣷⣤⠄⡞⠋⠀⠀⠀⠀⠀⢀⣴⣾⣷⣶⣶⣭⣬⣤⣿⣭⣿⣿⡿⣿⣿⢿⡗⠂
⠀⢻⡿⢃⣀⣀⣸⣿⠿⣿⡟⠃⠀⠃⠀⡇⠀⠀⠀⠀⠀⠈⣙⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣿⣆⠙⢀
⢀⡝⠀⠁⠈⠽⠋⣭⠄⠀⠠⠀⠀⠀⡀⠆⠀⠀⠀⣀⣀⣠⣬⠰⢿⣿⣿⣥⣍⠓⠋⠉⠉⠉⠁⠀⠙⠆⠈
⠉⠀⠀⠀⠀⠀⠀⠐⠂⠁⠒⠂⠀⢟⢣⠀⠀⠀⠉⠁⠉⠉⠛⠛⠛⠛⠒⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⢢⣀⡖⠀⠀⢤⢾⣿⠯⠀⢀⣱⣶⡷⠂
⠀⠀⢹⢿⣿⣿⠈⠀⠈⠈⠙⡀⡤⠀⢟⠻⡆⠁⠐⢦⣷⣴⠒
⣀⠀⠀⠀⠀⠠⣴⣤⠀⠀⠰⡟⠿⠆⠆⠀⠀⠀⠐⢾⡟⠻⡉
⡄⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⢀⠌⢺⢿⠃⡠⠀⠈
⣿⡀⠀⠀⠀⠀⠀⢠⠀⠀⡀⢀⠜⠀⠀⢀⠌
⣟⣠⢀⠀⢠⣶⣴⡼⣶⣿⣿⣏⣴⣦⣴⣾⣶⣄⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⣔⠟⢿⡯⠰⠾⣿⣭⣷⣿⣿⣿⣯⠉⠛⣿⡫⠀⠀⠐⢿⣧⡀⠀⠀⢀⣀⡀⢀⡀⣀⣀⣀⣀⠀⢀⡀
⠹⡞⣘⣽⣹⣤⣧⠑⡤⠩⣹⣿⠟⠉⠛⠷⢤⣾⡿⢿⡄⠀⠀⠘⠛⡃⢀⡀⠙⠳⠦⠈⠛⠛⠫⠭⠭⡩⠒⠻⠒
⣶⣽⠿⢻⣤⢽⣿⣿⣿⠀⠈⢁⣴⣶⠀⠀⠀⠹⡧⠀⠙⠀⠀⠀⠈⠰⢿⠇⠀⠀⠀⠲⠀⠈⠉⠘⠛⠲⢦⠈⠁
⠀⠀⠀⠀⠀⢀⠈⠉⠉⠓⠀⠈⠛⠻⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠑
⠀⠀⠀⠈⢠⡌⠀⠒⠀⠀⠀⢀⡀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠺⠃⠀⠀⠀⠒⠂⠀⠒⠤⠤⠈⠀⠀⠀⣀
⣦⠀⠐⠛⠀⠀⠀⠀⠶⠀⠀⣴⡄⠀⠒⢀⣀

⠀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⠀⣀⠀⠀⣀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⡀
⣒⣒⣿⡷⠾⡿⢿⢿⣿⣛⣛⣿⣿⣿⣖⣖⣒⣲⣦⣭⣭⣤⣭⣭⣷⡾⢯⣭⣿⣿⣿⣶⣛⣫⣭⣿⣭⣽⣽⣿⣿⣖⣿⡿⢿⣯⣭
⠐⢶⣶⣾⣿⣟⢻⣻⣿⣿⣿⣿⣿⣿⣫⣽⣭⣿⣯⣽⠶⢿⣻⠿⣟⣻⡿⣿⣿⣿⣿⠿⠟⣿⣟⠛⣉⣭⢿⣟⡻⠙⠋⢉⡉⠩⠶
⠷⠶⠌⠋⠒⠐⢒⣻⣮⣉⠙⠛⠐⣬⣽⣿⠛⠛⠛⠛⠉⣁⠐⠒⠂⣉⡁⠀⠀⠉⠙⠃⡤⠀⠀⠀⠁⠒⠂
⠶⠄⠀⠀⠀⠀⡀⠀⠀⠤⠶⠶⡄⠀⠀⠀⠀⠀⠶⠄⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠀⠀⠀⠀⣀⣀⣀⡔
⣀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠐⠁⠂⠖⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⣧⣀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣷⣶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⣄⣤
⠉⠋⠉⠉⣿⣷⡤⠀⠀⠀⢠⠀⠀⣀⣀⠀⠘⠓⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⡀⢀⡀⠀⠀⠐⠶⠄⢀⣄⣀⠀⠀⢹⡿⠿
⠸⠷⠶⠀⠰⠇⠀⠀⠴⣷⣦⣀⠀⠿⠟⠀⠈⠀⠀⡀⠀⢠⠄⢀⡀⠀⠀⠀⠀⠈⠉⣽⣄⠀⠉⠀⠀⠀⠀⠉⠉⠉⠩⠅⣠⣄

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔
⠀⠀⠀⠠⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠌⠀⠀⠀⠀⡠⠀⣀⠀⢰⡛
⠀⠀⠀⠀⠀⠀⠈⠃⠈⠉⣰⠿⠟⠁⢠⡾⠂⠀⠀⠀⡀⠀⠀⢀
⠀⠀⢤⠀⠀⠠⠤⠀⠀⠸⠁⢼⣷⡥⢈⣉⠀⠐⣤⣤⠁⠀⠀⠺⢷⡆
⠀⢠⠀⡄⠀⣠⡆⢀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠸⠁⠋⠀⠀⠀⢀⠄⠀⠿⠇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⠀⠸⠀⠠
⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠠⠴⠀⠚⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣶⣶⡶⢾⠿⠿⠿⠗⠶⠶⠶⠶⠶⠶⠛⠛⠉
⠀⠀⠀⠀⠈⠀⠀⣠⣴⣾⣿⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠂⠁⠈⠙⠉⠭⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠉⠀⢤⣀
⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠐
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠁⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠒⠀⠀⠀⠀⠠⠀⢀⡀
⣿⡿⠛⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⡐⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⡂⠀⠁⠊⠁⠀⠀⠁⠠⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡿⢊⠀⠅⠃⠀⠁⠀⠈⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⢂⡒⢥⣀⡆⠀⠠⠠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢈⠻⢧⣛⠝⠸⠄⠦⠀⠐⠀⠀⠁⠀⠁⠀⠀⠀⠀⢀⠠⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠐⠆⠀⠀⠀⠂⠀⠀⠠⣰⠪⣼⣏⠆⢢⢄⢿⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⣤⡶⠂⠃⠄⣠⠀⡀
⠀⠀⠀⣀⣂⡠⢠⣰⠶⣼⣶⣶⣤⡠⠔⠁⣠⡀⠀⣰⣿⢥⠼⠍⠑⠺⢦⡙⠷⠆⠤⣤⣐⣡⣅⣂⠤⢀⢲⡲⠞⣧⣁⣀⡮⣴⣦⣄⡠⠬⣄⡀
⠀⠀⠀⣵⠮⠒⣓⣤⠄⢼⣻⡿⡁⠒⠴⡞⠁⠝⡉⣘⠝⠁⣤⣠⣄⡠⠴⢹⢃⠀⣀⡤⢿⣭⣭⣥⣶⣉⣁⣸⣏⣲⠿⠏⡛⣉⡠⣽⣒⣂⣑
⠀⠀⠀⠻⠯⠹⠒⠦⣄⠰⣖⠭⣙⠶⢦⣤⠥⠷⠚⡡⠄⣀⠼⡷⠹⣗⣚⣷⣶⣟⣁⢮⣽⣠⣤⡬⣵⣬⡉⣤⣹⣿⣶⣾⣿⣏⣷⣿⣿⣛⣛⠁
⠀⠀⠀⠄⣀⣠⠼⠲⣤⣙⣦⡽⣎⢛⡦⠄⢶⣚⣉⣠⠤⠚⡑⠶⣤⡼⠞⠛⠷⣄⣀⣑⡾⡷⠿⢷⣶⣷⠿⠬⢽⡿⢟⣿⠿⠿⠿⠿⠻⡿⠛⠁
⠀⠀⠀⠈⠉⢀⠔⢦⡸⢭⡭⠭⡙⠶⣵⣶⣤⡤⠤⠔⠒⠉⠄⠰⢝⣿⡍⠫⠠⣄⣸⣷⣍⢡⢔⣫⠔⢬⡙⠛⠓⣻⠽⠒⢌⡓⠠⢤⠀⢀⡀
⠀⠀⠀⠒⠊⠁⠀⠀⠈⠋⠃⠑⠛⠲⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠍⠓⠑⠑⠀⠀⠀⠉⠒⠒⠉⠀⠀⠀⠉⠛⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡞⠙⡀⢸⡇⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⣴⡇⠀⠀⠀⠜⠀⠀⢿⡀⢀⣠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⡴⠛⠀⣠⠂⠠⠀⠠⡀⠀⠀⡇⠘⠃⠈⢧⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠈⢀⠤⠚⠉⠀⠀⠀⠐⠃⢠⠆⠀⠀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⡸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⣼⠀⠈⠉⠉⠁⠀⠀⠐⠤⠤⠀⠄⠀⠈⠁⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣸⣿⣇⢠⣿⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣷⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⣸⡀⢀⣿⣿⣿⠼⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢼⣿⣿⡀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠿⠷⠖⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡯⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠙⠙

⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⠀⣀⠀⣠⡤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠲⣭⠄


⠀⠀⠠⢄⡄⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⢄⡠⠈
⠀⠀⠀⠈⠁⠀⠀⠀⠘⣦⣼⡄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡻⡇⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠑⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⡟⣄⠀⠀⠀⠀⠀⠀⠈
⣀⠠⣤⣀⣀⣤⡶⢿⡶⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢻⣆
⣻⣿⣿⣭⣯⣿⣿⣧⡤⠤⠶⢿⣛⣛⣰⣻⣶⣤⣶⣄⠤⠀⣛⣻⣧⣈⣛⣆⡀⠀⠰⠾⠷⠶⠄
⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠁⠈⠉⠉⢉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠈⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠒⠒⠀⠂
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠄⠀⠀⠀⠀⠀⡀⠐⠒⠀⠀⠀⠀⡠⠄⠤⠄⠠
⠠⠒⠲⠆⠀⠴⠶⠶⠤⠖⠒⠒⠂⠐⠚⢒⠀⠀⠀⠥⠲⠮⠀⣒⠖⠂⠀⠀⠐⠒⠂⠀⢒⠒⠀⠒⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡻⠗⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠙⢈⣤⣶⣿⣿⣿⣿⣟⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣦⣄⣧⣿⣽⡟⢛⣶⣿⣿⠿⠿⣛⣻⣭⠛⠂⣹⡙⠙⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⡿⢛⣛⣻⣧⡘⣯⣽⣿⣿⣶⣿⢿⣶⣾⣯⠴⣛⡀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⢨⠟⠙⠉⣏⣬⣾⣾⣿⣽⣿⢿⣜⣿⣿⣿⣿⣿⣏⣻⣫⣿⣿⣿⣿⣿⣶⣦⡤
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢏⣿⣿⣿⣿⣼⣿⣞⢿⣽⢿⣿⣿⣿⣯⣽⡏⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡝⣾⣿⣿⣿⡛⣿⣿⣷⣫⣿⣸⢉⢿⢻⣿⣿⡇⠇⠛⠛⣿⠿
⠀⠀⠀⠀⠀⢠⣿⣿⣿⠍⢏⢹⣿⣿⢿⢿⡳⣿⣿⡿⣟⢹⣇⠀⠁⢸⢿⣿⣿⡳⠀⠀⠈
⠀⠀⠀⠀⠀⢸⠃⠁⠈⠀⠀⣿⣿⣿⣆⠙⠁⢻⣿⡓⠦⠀⣿⠀⠀⠀⠈⠋⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⡜⢎⠁⠀⠸⣿⡷⠤⠀⣿⣧⣾⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⣀⣘⣡⢾⣿⢿⡧⠉⠟⢿⡙⢿⣟⠛⠋⠓⠦⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣖⣒⣛⡻⠋⠐⠋⠹⢼⡇⣀⣀⣀⡣⢀⠋⠙⣂⡐⠦⢬⡛⢶⡽⢷⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⣀⣤⣀⡀⠀⠉⢉⣉⠉⠉⠉⠿⠿⠿⠯⡽⠷⡶⣸⡯⣁⡈⣍⠁⠨⠽⢿⢋⣙⣷⣽⡿⠿⠛⠛⠛⠋⠉⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣀⣤⠶⠶⠒⠒⠂⠀⠀⠉⠉⣿⡇⢀⡄⣼⣿⢀⡆⣠⠆⠠⠤⢤⣵⣒⣛⣛⣛⢛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⠁⣼⢡⢇⣇⣼⢞⡕⣆⡀⠒⠒⠒⣶⣿⣿⣷⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣬⠍⢀⡞⣸⡄⡴⢮⡘⢷⣿⣦⣄⣀⣈⣿⣟⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠊⠉⠀⣨⠟⠋⠋⠀⠘⠳⠑⠃⠙⠂⠈⠙⠛⠛⠻⠽⠿⠿⠟⠛⠛⠉⠁

⠀⠀⢀⣀⣀⣀⣀⠀⠀⢠⠀⠀⢄⠀⠀⠐⡄⠀⠀⠀⢀⡠⠤⠄⠠⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣄
⠊⠉⡀⠀⠀⠀⠀⠈⠱⠒⠦⡀⠀⠆⢀⠀⠚⠀⠀⣀⠨⠤⠀⢀⠠⠀⠛⠁⢄⡀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠂⠀⠈⠤⠶⢤⣖⡀⠀⠉⠈⠀⠀⠲⡀⠔⠓⢤⠚⠃
⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⠀⠈⠢⠚⠀⠀⠀⠄⠀⠀⠐⡖⠂⣠⣤⠀⠀⠀⠀⠙⣤⠤⠀⠒⠂⠀⠉⠁⠀⠀⠀⡀⠐⠀⠀⠀⠉⠢⡀⠀⠀⠴⠦⡁⠀⠀⠀⠡⠶
⠀⠀⠀⠀⢌⠀⠀⠀⢁⢀⣀⠀⠀⡡⠀⣛⡀⠀⠀⠐⠃⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⢄⠀⠀⠀⠀⠀⠂⠁⠀⡠⠠⠀⠀⠄⠀⢈⠳⢄⠀⣀⡕⠄⡠⠔⢥⡀
⠀⠐⠒⠂⣀⠔⠂⠉⠈⠀⢉⠈⡙⣤⢤⠇⠙⢤⠠⠄⢀⡀⠋⠀⠐⢄⠒⠒⠀⢀⠠⠼⠀⠀⠧⠄⣀⠀⠀⠀⠀⠀⠠⠁⠀⠀⡀⠀⠀⠡⡀⠑⢌⠀⠐⠗
⠀⠀⡠⠀⠓⠀⠀⡤⠀⠒⠉⠀⢀⡈⣎⠀⡠⠊⠉⠉⠀⡇⠀⠒⢀⠀⠑⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠡⠁⠀⠀⠀⠧⠀⠀⠀⠐⠄⠀⠑⢄⠀⠀⣀⠄
⢀⠎⠀⡰⠉⠈⠣⣀⠀⠀⠀⣩⣄⡄⠈⣱⣷⡄⠀⢴⠏⢀⣄⣀⠀⠈⠀⠈⠆⠈⠂⢀⣤⠀⠀⠀⠀⠀⠀⠀⠝⠳⠄⠀⢤⣀⠀⠈⡀⠀⠀⠀⠄⠀⠠⡑⢎
⢃⠔⢨⠅⠠⠀⠊⠀⢁⡦⠁⡸⠂⠘⡏⠀⠀⢰⠀⣈⣶⠂⠈⡄⠀⠉⠁⠒⠬⡄⠒⠀⠀⠀⠤⠤⠤⠤⢤⠎⠰⠇⠀⠀⠀⠀⠓⠢⣄⠠⠤⠤⢈⣂⠀⠀⠄⠳⡄
⠠⠄⠚⠀⠀⠀⠀⠈⢣⡀⠀⢠⣴⡈⠉⠑⠲⡗⠻⣄⢈⣶⣍⠈⢑⠶⠀⠀⠀⠀⠒⠢⠀⠐⠒⠒⠒⠒⠚⠒⠓⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠠⠀⠈⢩⠉⠉⠁⠚
⠀⠀⡆⠀⠀⠀⠀⠀⠀⢹⠂⠉⠛⠉⢲⠖⠋⠀⠀⠈⠁⣉⡇⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠆
⠀⢠⠄⠀⠀⠐⠠⠄⠀⠨⠤⢤⠚⠤⣈⡆⠀⣴⣦⠉⠉⣶⡎⠉⠁⣰⠲⡀⠀⢰⠋⠉⠉⠙⢲⣼⠋⠉⠉⠑⢦⢰⡖⣄⠀⢠⢤⡄⠀⠀⠀⠀⡁⠪⠥⠤⠤⠤⠄
⠀⢸⡠⠀⠀⠢⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⣏⣿⢀⣠⡏⡇⠀⢠⠏⣀⢳⠀⢸⡇⠀⠛⠀⣸⢻⠀⠈⠛⠀⣸⠃⠹⣼⢶⣫⠎⠀⠀⠀⠀⠀⠁⠀⠀⠀⠖⠆
⠀⢻⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣉⢹⠛⠒⡗⡇⢠⣏⣀⣉⡀⢧⢸⢰⡖⠒⠋⠁⢸⢰⠖⠒⠋⠁⠀⠀⠘⣲⡇⠀⠀⠀⠀⠀⠀⣄
⠀⢸⠀⠀⠃⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⢨⣿⠀⠀⣷⠇⣾⠼⠁⠀⠱⠼⠦⠶⠇⠀⠀⠀⠸⠾⠀⠀⠀⠀⠀⠀⠘⣯⠇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣀⢠⣤⡀⣠⢤⠀⠀⡴⢦⣴⢲⡀⠀⠰⠒⠆⠖⣦⠀⢀⡖⢶⢠⣤⣤⣤⣤⡀⣤⣤⣤⣀⡀⠀⠀⠀⡗
⠀⠀⡆⠀⢀⠠⠀⡀⠀⠀⠾⠀⡇⢠⠏⡴⠒⢦⣿⣜⢺⠀⠀⡏⣿⡿⣀⣇⢠⢷⡀⣆⡆⣸⡄⡸⣧⢸⢾⣰⠒⠚⠚⠃⡆⠀⣤⠀⠙⡆⠀⠀⡇
⠀⠈⣵⠚⠀⠀⠀⠈⠁⠀⢸⠀⡇⠈⠳⢯⣷⠲⣄⢸⣼⠀⠀⡇⣼⣯⣿⣸⡼⣸⠞⢃⣤⣧⣷⡇⣿⢺⢸⢈⣯⣉⣹⠀⡇⡀⢀⣠⠜⠁⠀⠀⡃
⢀⠞⢰⡀⠆⠁⠀⠀⠀⠀⢺⠀⡇⠸⡟⢧⣬⡷⣹⢳⡜⠦⠴⢃⡽⡇⣺⣏⢣⡟⣤⣾⠀⡿⡈⣼⢋⣸⢸⣹⣀⣀⣀⡀⠇⡟⢦⡑⢦⡀⠀⠀⡅⠀⠈
⠊⠀⠀⣇⠰⠀⠀⠄⠀⠀⢸⠀⡇⠀⠉⠓⠒⠛⠁⠀⠙⠓⠒⠚⠁⠻⠏⠙⠚⠀⠛⠛⠿⠇⠓⠋⠘⠛⠸⠾⠶⠚⠺⠋⠛⠃⠀⠉⠉⠁⠀⢠⠄⣀⠤⢄
⠠⡀⠀⢹⠀⢃⠘⠀⠀⠀⠘⠤⠇⡀⣀⠀⢀⢀⡀⠀⠀⡀⡄⠀⠀⣠⢠⡄⠀⠀⠀⠄⠀⠄⠒⠀⠀⠀⠤⠤⠤⠄⠤⠰⠀⠠⠖⠀⠐⠐⠒⠘⠁⠁⠂⠀⠀⠐
⠀⠈⠚⠀⢃⠈⢄⠠⠂⠀⠀⠀⠄⠠⠀⢀⠸⣀⣠⣶⡄⡅⡇⠐⠴⢁⠎⠄⡀⠀⠀⡀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠠
⢀⠖⠀⠀⠘⣄⠚⠄⠀⠀⠀⠀⠤⠠⢰⡁⡀⠈⣧⡉⠀⢱⣇⣠⢁⡆⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⢠⣔⡂⠁⠀⠀⡤⠓⢌⠑⢤⡀⠀⠀⠀⠈
⠁⣀⠀⠀⠀⠸⡀⠚⠀⠀⠀⠀⠀⠠⡉⠀⠀⠠⠿⢶⠀⠉⠐⡄⠉⢢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡗⠉⠀⠀⠀⠀⠀⠦⢤⡼⠁⠐⠙⢆
⠙⠛⠛⠁⠀⠀⢱⠀⠀⠀⠀⣶⡀⠐⠉⢢⣰⠁⠀⠀⣣⣠⡾⢔⡊⣡⣷⡆⠀⠀⠀⠀⠀⢀⡠⠒⠒⠆⠀⠀⠀⡎⠀⠀⠀⢀⠂⡀⠀⠀⠀⠀⠀⠀⠱⡈⠆
⠀⠀⠀⠠⠄⠤⠀⢧⠀⠀⠀⠽⡓⠉⠞⠙⠴⢇⢲⡖⣏⠀⠀⠀⠵⠈⠁⠐⢄⠀⠀⠀⢠⠋⢀⠎⣁⠛⡄⠀⢸⡇⠀⠀⠔⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠈⠐
⠀⠀⠀⠀⢀⠠⠀⠀⢣⡀⠈⠓⠿⣶⣀⠀⠀⠘⠷⠎⠁⠀⠈⢳⣤⡆⠀⠰⠦⡀⠀⠀⠘⢆⠈⠎⠾⣰⠃⠀⠘⡇⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉
⠀⠀⠀⠀⠃⠒⠊⠁⠀⢣⡀⠀⡰⠋⠛⠄⠀⠀⢴⡰⣀⠀⡠⠊⠙⢃⠐⠀⠀⡘⠴⠆⠱⠀⠙⠒⠊⠁⠀⠀⢀⡐⣆⠀⠃⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡰⠁
⠉⠀⠀⠀⠀⠀⠄⠂⠀⡐⠁⢲⡀⡀⠀⠘⠒⠖⡁⢠⡌⠉⢀⡀⠀⠀⣦⠴⠚⠁⠀⠀⠀⠀⠀⠐⠒⠂⠁⠂⠁⠀⠈⠢⣀⠀⠀⠀⠀⢀⠌⠀⠀⡠⠞⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠤⠘⠉⠑⠠⠤⠤⡼⢀⠄⠈⠉⠣⢈⠁⢀⠁⠀⠀⠀⠀⢀⣠⠄⠀⡤⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠤⠾⠐⠒⠉⢀⡀⠤⠂
⠀⠀⠀⠁⠉⠐⠈⠀⠀⠁⠀⠀⠀⠐⠒⠀⠐⠒⠂⠈⠁⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠘⠓⠒⠒⠒⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⣁⠀⠀⡀⣀
⣿⣿⡟⠻⠟⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠊⡀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠠⢀⣀⣀⢠⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠄⠀⠠⠂⠀⠲⣀⣀⡀⠀⠀⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⢀⠀⠀⠀⠠⠀⠑⠄⠀⢈⣉⣉⣯⣉⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⠂⠀⠀⠀⠀⠆⠀⠀⢈⢉⣁⠀⡀⠀⠠⠈⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢈⠠⡈⢠⣠⠂⠙⠒⠒⠓⠒⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠈⠀⠅⠀⠈⢩⠁⠂⠀⢀⣆⢀⣇⣁⡂⠰⠄⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⢀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡩⠉⠉⠉⠈⡹⠆⠂⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀⠠⠝⠄⠐⠈⠉⠁⠂⠤⠅⠀⡇⢀⠡⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⣀⠀⠀⢠⣠⠀⠄⠀⠒⠀⠉⠀⠂⠀⡇⠤⠤⠤⠄⠘
⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⣾⣿⣯⣿⣯⣭⣽⣿⣷⡀
⠀⠀⠙⠿⢶⣶⣿⣷⡶⠿⠋

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠠⠀⠀⠀⠤⠀⠀⠠⠀⠀⠠⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠐⠄⠁⠀⠀⠂⠀⠀⠠⠀⠀⠀⠠⠖⠒⠓⠒⢄
⠀⠀⠀⣀⠀⠀⠂⠀⠀⠈⠂⡀⠂⠀⠀⠐⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢀⡀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣠⡦⠶⣂⡠⣀⣰⠦⢴⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢡⠀⠀⠀⡀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣗⣾⠀⠀⠀⠘⠋⠈⠀⠀⠠⠀⠁⠀⠀⠂⠀⠀⠬⣘⠒⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣀⠑⠂⠴⠊⠁⠈⠱⢦⠀⢄⡤⠀⢆⠁⠀⠀⠀⠀⡌⠈⠀⣀⡠⠋⠁
⠀⠀⠀⠀⠀⠅⡀⠘⠀⡀⠊⠁⢠⠀⠃⣀⣾⣒⣛⣋⠉⠉⠉⣙⢂⣋⣛⣺⢄
⠀⠀⠀⠀⠀⣀⠁⠠⠂⠀⠰⠀⠀⠐⠀⠀⠀⠀⠁⠉⠈⠉⠉⠉⠉⠈⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣈⠂⡀⠈⢠⠀⠁⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂
⠀⠀⠀⠀⢀⣐⣄⠐⠂⠤⠌⠠⠤⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣠⢦⣐⠂
⠀⠀⠀⠈⣞⠐⡼⠆⠐⠆⠀⠀⠠⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⣂⢸⠡
⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠊⠁

⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⡇
⠀⠀⠀⢘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⡋⠀⠀⠀⠀⠀⠀⢠⠆
⣀⠀⠀⢸⣖⠀⠀⠀⠀⣠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⠀⠈⠻⠻⣿⣦⣤⠀⠐⢤⡀⠈⠀⡀⢰⡄
⠿⠆⢨⢊⣵⠄⠀⠁⠐⡫⠀⠀⢐⠀⠀⠀⠀⠀⠤⠄⣈⠉⠉⠀⠐⠠⠀⠈⠋⢻⡆⠀⠀⠉⣶⠀⠋⠿⠃⠀⠈⠁
⠰⠀⠠⠋⣙⠧⣀⢰⠊⢠⡀⢀⡎⠱⠲⠦⢀⡄⠲⢤⠍⠀⡒⠄⠄⠀⡀⠀⠀⢈⠙⠆⢀⠆⠽⠂⣰⠄⠤⠀⡀⠰⠆
⠇⡀⢀⣾⢁⠢⡀⣲⣿⣾⠲⣿⣟⣼⣧⣦⣼⣷⣶⡆⣶⣰⡇⣸⣤⣦⣟⣴⣶⣿⣴⣴⣿⣠⣴⣠⣿⣿⣠⣼⣇⡄⣀
⡟⡟⢁⠜⢁⡤⠸⠿⢿⣿⠊⠿⠟⠛⠻⠿⠿⠷⣿⠿⠗⠿⠤⠟⠟⠻⠿⠿⠿⠿⠿⠻⣿⠿⠿⢿⣿⣿⣿⢿⠿⠾⠿
⠀⣴⣋⡼⠛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠛⠿⠛⠛⠋
⠄⠈⣹⠴⠺⣿⡭⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠋⠉⠉⠁⠀⠀⠀⠉⠉⠉⠙⠋⠙⠛⠛⠿⠿⣷⣶⣦⣄⡀⠀⠀⡄⠒
⠤⠜⠃⣤⢠⣯⣗⢆⠀⠀⠐⠀⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⠟⢀⠀⠐
⠀⠠⠞⠁⣸⣟⢯⠁⠀⠀⠀⠀⠀⠉⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣯⡀⠀⠀⣀
⠁⠀⣼⡟⠹⣿⣧⠧⡄⠀⠀⠀⠀⠀⠀⠘⢠⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣋⠀⠀⠀⠈⠉
⣀⠀⠉⠀⠀⠈⠉⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠒⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠞⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣤⠂⣀⣤⠄⠀⠀⠈⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠤⠖⠀⠀⠀⠀⠀⢀⢰⠃⠈⠁⠀⠀⠘⠓⠠⣤⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠥⠀⠂
⠀⠀⢀⠉⠀⠐⠁⠈⠁⠂⠀⢸⣿⡀⠀⠀⠐⢤⠀⠀⠀⠐⠂⠀⢀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡗⠐⠀⠀⠀⠀⢀
⠀⠀⣁⠀⠀⢀⠒⠀⠀⠀⠀⠈⠁⠀⡄⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠀⠀⠀⠄⠈⠀⠀⠀⠀⡴⠉
⠀⠀⢀⠀⠀⠀⠐⡶⠀⢀⣄⠀⠀⢄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢂⡠⠂⠀⡄⠀⠀⠀⠀⣨⡇⠐⠄⠈
⠀⠀⢸⣎⠀⠘⢶⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢸⠀⠀⠀⠀⡇⠀⠀⠀⣠⠋⢈⠀⠀⠁
⠀⠀⠸⡀⠀⠐⠀⠀⠀⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⡅⠀⠀⢠⠇
⠀⠀⠀⡇⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡇⠀⠀⡎
⠀⠀⠀⢷⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⣧⢠⣼⢳⠶⠶⠿⠿⠷
⠤⠤⡶⢸⣇⡶⣦⣄⣼⣟⠂⢤⠤⠤⠤⠴⠤⣤⣤⣤⡤⠤⠤⠤⣤⡤⠤⠤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣤
⠀⡜⣵⣸⣿⣣⠆⡀⣻⣇⠀⠀⠀⠀⣀⡀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠰⠦⠒⣀⣤⠀⠀⠀⠀⠀⠐⠒⢚⠀⠀⠀⠀⡀
⣿⣸⣿⣿⣿⣿⣾⣿⣿⡇⢰⢶⡄⢀⠀⠀⠀⠆⠠⠰⠲⣦⢶⢤⣀⣀⣠⣿⣿⣿⣶⣦⡀⢤⣿⣦⣾⣟⠷⠉
⡏⠹⠫⡋⣽⣿⣿⣿⣿⡅⣸⣯⣾⣿⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋
⣿⣿⣿⣿⣿⠷⠛⣻⠯⠁⠛⠛⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠉⠀⠀⠉⠁⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠉⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠥⢀
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠤⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠤⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣁⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣄⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⣀⣀⠀⢀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠳⣿⠀⠄⢀⠈⣿⣷⣰⠀⠀⠀⡄⡷⠋⠠⠇⠀⠀⠀⠀⠠⣀⠁⢸⡆⠀⡏⡼⠀⡘⠀⡇⢺⡇⣴
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠰⡀⢠⡸⡇⡘⠁⠀⣿⠊⠁⠀⡴⠒⠃⡧⠀⠀⠀⣠⠆⠀⠀⠀⠸⡄⢸⣧⡮⠁⠖⠀⠘⠀⡇⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠼⠃⣿⠁⠀⠀⣿⣿⠀⠆⠀⠀⢠⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠑⢾⡛⠃⠂⠀⠀⠀⠓⣧⠀⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⡀⠸⡆⠀⠀⣿⣿⠀⢀⡀⠀⠘⠒⠛⠉⢅⡀⠀⠀⠀⠀⠀⠀⢸⣏⡘⠀⠈⠀⠀⠀⣿⡁⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣧⡀⠀⣿⣟⠐⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡏⠓⠀⠀⠀⠀⠁⠸⣅⣤⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣇⢸⠀⡀⠄⠀⠀⠀⢸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣿⣿⡶⣄⡴⠒⠒⠒⠀⠀⠀⠀⠀⠀⣀⣴⣦⣄⠀⡟⢸⣼⣤⣤⡀⠀⢰⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢷⡿⠁⠀⠀⠀⠀⠀⠀⣀⣴⣾⣻⣿⣿⣿⣿⡿⡼⠀⠛⠻⠷⠀⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠃⢀⠀⠀⠀⣠⣴⡾⠋⠉⠛⢿⣿⣿⣿⣿⣷⡅⣷⣤⡀⠀⠀⢾⡄⡤⠞⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⢈⣿⣿⡇⠀⢁⣠⣴⠟⢛⠁⠀⠀⠀⠀⠀⢙⠻⢿⣿⣿⣠⢻⣿⣿⣶⣄⢸⣇⡗⢦⡾⣷⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢹⠀⡙⠛⣿⣿⢣⡶⠛⠉⠰⠊⠐⠀⢀⠄⢀⠀⠠⠜⡆⢄⠙⣿⡉⢸⣿⣿⣿⣿⣿⣷⣇⠈⠿⢿⠯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠌⠀⣀⡴⣿⡿⠓⡇⠀⠀⣸⠞⠛⠚⠛⠒⠋⠀⠀⠁⡟⢸⠶⣿⣧⡼⢿⣿⣿⣿⣿⡿⣿⠷⢀⣡⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⢉⣠⡶⠛⠉⣠⣿⣿⠀⠇⣠⠞⢯⡠⠐⠉⠆⡇⠀⠀⠀⠀⠀⠘⣷⣿⡏⠇⠀⠙⣿⣿⢻⣷⢶⣞⣻⣧⢠⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠾⠋⠁⢀⡀⢠⠀⢹⣶⠦⡾⢻⠀⠀⠉⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⣠⣾⣿⣿⣾⡏⢸⡏⡿⢿⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠡⣾⠀⣀⢀⡷⠾⢄⢸⣿⠀⢉⠘⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⣿⠇⣼⣿⣿⣿⣿⢸⡇⢸⡿⡇⢸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡀⠀⡅⠀⠈⢻⣿⡃⢈⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡄⣿⣿⣿⣿⣿⢸⡏⢨⡇⢇⠀⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡃⠀⠃⠀⠀⢸⣿⠃⠬⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣾⣿⢁⢸⣿⣿⣿⣿⢸⡇⢸⡇⣸⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⠀⠀⠀⡀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠁⠇⠀⣠⣾⣿⣿⢼⡸⢿⣽⣿⣿⢸⡇⠈⡇⣿⡅⣇⡄
⠀⠀⢠⣠⡠⠖⣶⣤⣿⣿⣯⠀⠀⠀⠃⢀⠀⢸⢿⣿⢨⠀⠁⠀⠀⠀⠀⠁⠀⠀⠂⢀⣾⣿⣿⣿⣿⢛⠁⣾⣿⣿⡿⣸⡇⣠⠃⣿⡇⣟⡆
⠀⢰⣿⣿⣿⡷⣿⡟⣻⣿⡧⠀⠀⠀⠀⠈⠀⣸⣿⣿⣚⠀⠀⠀⠀⠀⠀⡄⠀⠀⣴⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⣿⡇⣿⠷⣿⡄⣿⠁⣏⡇
⠀⢸⣿⣿⣿⢣⡟⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣿⣿⡿⢹⠀⠀⠀⠀⠀⠀⠏⠠⣾⣿⣿⣿⣿⣿⣿⣿⣇⡞⣿⣿⣿⡇⢻⡆⣿⣷⣿⣶⣿⠁
⠀⠈⠛⠉⠉⠉⠋⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⢹⡏⢿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣦⠀⠀⡀⣿⣷⠐⠀⠘⠈⠀⣸⡿⠇⠁⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠿⠀⠈⠀⠀⢐⣿
⠀⠠⠀⢠⣄⣤⡤⠄⠀⠤⢤⠤⢤⡤⠶⠴⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠀⠘⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡄⠰⡆⢻⢀⡟⢀⡦⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⡈⠻⠀⠉⣈⣀⠁⠘⠁⢴⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠌⢁⣴⡾⠛⠋⠉⠙⠿⢦⡀⠐⠋⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠆⢠⣿⠏⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⢹⣿⣦⡀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠚⠓⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠾⠃⡈⢻⣿⣯⣤⣌⣰⣀⢠⣿⡿⠃⠀⠳⠦
⠀⠀⠀⠀⢀⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣹⡷⠶⠚⠛⣋⣉⣭⣉⣽⣿⣿⣶⣶⡦⠀⠀⠀⠀⠀⠠⠚⠃⣤⠉⠻⠿⠿⠿⠿⠟⠋⣀⠘⠳⣄
⠀⠤⠤⠒⠚⠢⣀⡀⠀⠀⠉⠀⠀⠀⠀⠀⣠⠞⣁⣤⠶⠟⠛⢛⢛⡿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⣰⠇⢰⡄⢠⡄⠰⣆⠈⢷⠀⠈⠁
⠃⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣠⠞⢡⡾⠋⠁⠀⣠⢶⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⠀⠘⠇⠀⠻⡆
⠀⠘⠢⠔⠒⠒⠁⠀⠀⠀⠀⠀⠀⣰⣟⣼⡟⡁⠔⠈⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣰⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠮⠄⠦⢵⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠡⠀⠀⢠⢠⣤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢞⣿⠈⣆⢱⣤⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⢤⣀⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀⠀⢀⣀⣀⣤⣀⡀
⠀⠀⣴⡂⢀⣁⠀⢈⠁⠀⢄⣀⠑⠼⠿⠶⠧⠀⠀⠀⠀⠀⡠⢪⠺⠛⠛⠛⠛⠛⠓⠂⢒⡂⠁⠀⣴⠀⠀⠀⠀⠀⠀⢀⠖⠐⠻⠋⠀⠀⠖⠛⠃⠀⠧⡄⠤⢠⠠
⠠⠀⢙⢺⡟⠏⢐⠚⠂⡁⠚⠞⠡⣰⣤⢂⠋⠀⠀⠀⡠⢫⣌⡂⠁⡾⢀⠖⡤⠐⡲⠭⣔⠻⠇⣠⡞⡳⣶⣤⣀⡠⣤⡴⣖⣾⣝⣝⠳⠶⡶⢒⡀⡇⠔⠃⡄⠘
⠰⠁⠈⢳⠙⠈⣉⠑⠉⠀⠀⠤⡐⣻⢿⠓⡸⠄⢄⣠⡀⠰⢀⡀⢠⠠⠒⣨⣶⠂⡂⠈⢉⡉⠠⢈⡙⠛⠛⢧⣿⠟⣿⠴⣏⣈⡟⣻⣭⣿⣷⡦⠁⠁⠂⠠⢐⢺
⠸⠀⠀⢸⠀⠠⠀⠀⠀⠀⠀⠈⠞⠼⡀⠖⣠⠄⠾⣿⡗⢂⡤⢦⠌⣭⢰⠬⡍⢐⣹⣒⢹⡄⠀⣤⢀⠀⠀⢰⣿⡿⢧⣴⣏⣉⣿⣿⣟⣩⠏⠀⠀⣂⡄⠀⠀⠘
⠀⠄⠀⠘⡄⠤⡄⠀⠀⣠⡴⠀⢈⣷⣷⣆⢀⠲⠄⣁⠐⠋⠐⠟⢼⠹⠆⡛⠀⠘⠀⠀⠙⠐⠀⣊⠂⢄⠀⠸⣿⣧⢫⣾⠭⠭⠿⣿⣿⣅⠂⠀⠈⠍⠑⠀⠀⠁
⢰⣷⠀⠀⡇⡠⠀⠐⠏⡽⡚⠁⠐⡉⠏⠃⡿⢰⢰⡖⡆⠀⠠⠀⢀⣀⣀⣀⠤⠔⡒⠤⢀⣈⣀⡈⠀⠘⡐⢀⣸⡿⠧⡝⠓⠘⠀⠚⠁⠁
⢸⡟⡀⢀⠅⣂⠀⠉⠐⠀⠀⢠⠈⢡⡼⣷⡇⠀⠰⡃⡇⢠⣭⠭⠉⠙⣛⢛⡀⠈⢋⠄⢘⣻⢛⡛⠋⢭⢡⠸⠘⡖⢫⡇⢴⠭⠶⠥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠀⠀⠀⠐⠒⠒⠒⠂⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠄⠤⠤⠀⠀⠀⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠄⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣈⡉
⠀⠀⣀⠀⢀⡀⢀⠀⡀⠀⠀⠀⠀⣈⢡⢎⣼⣿⣾⣷⣤⡒⢤⡀⠀⠀⠰⠶⠒⠀⢀⣐⠂⣠⡀⠀⣀⠀⠄⢀⡀
⣀⣨⣤⣤⣀⠒⣀⣈⣉⣀⡈⢉⣿⡏⠐⣩⢟⣵⣿⢟⣿⣯⠀⠤⣄⡀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⡷⢶⠛⡿⡲⠮
⠈⠙⠉⢉⣁⣈⡉⠛⠙⠛⠋⢉⡭⢒⡠⣸⡽⣛⣵⣿⣿⣿⣦⠀⠈⢝⣆⢠⣰⣠⣀⣀⣈⠉⠛⠛⠛⠻⠿⠾⠞⠛⠒
⠤⢆⣚⠫⠭⣛⣫⣭⠤⣒⡨⠔⣪⠵⣚⣽⣾⣿⡿⣿⣿⣿⡟⣄⡀⠐⠛⠍⡿⢤⡈⣍⣬⠍⣉⠈⠙⢃⡴⣧⡦⢴⡃
⡉⠄⣐⣚⣭⠵⠶⢚⣩⠵⣒⡭⣒⣯⣟⠽⣛⣥⢞⣿⡿⣿⣿⣯⣋⣐⢀⠀⡉⠐⠉⠁⠉⠩⣘⠉⠈⠉⠀⠀⠩⠟⠉
⣫⣭⣽⡥⢴⣒⣫⢽⣾⡿⣗⡿⢟⣫⠥⣐⢭⡾⢟⣽⡾⢟⣽⢿⣿⣿⣶⣤⣬⣥⣤⣬⣴⣮⣵⣍⣱⣀⣒⣵⡶⣾⢣
⠩⠽⠖⣛⠭⢑⣚⢭⣶⠏⣁⡡⢈⣠⡴⠞⣉⡤⠞⣩⠾⣫⣵⠟⣫⣴⠟⣋⢜⣹⠟⡯⢚⣿⣿⣻⣿⣿⠿⣫⠾⢃⣟
⣶⣶⠶⠶⠿⣷⣶⣿⣶⣿⣷⣿⣿⣷⣶⣿⣷⣶⣾⣶⣾⣿⣶⣾⣿⣷⣾⣷⣿⣶⣿⣶⣿⣿⣿⣿⣿⣷⣶⣷⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢒⣶⣿⣶⡂⠀⠀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠏⢻⠉⠉⠷⠈⡿⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠈⠐⡀⠀⠈⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⢿⠓⠀⠀⠀⠀⢠⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢠⡀⠀⠀⠀⠀⣆⡀⣠⣷⣴⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣽⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠑⠒⠓⠒⠉⠏⠉⠍⠉⢉⡙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠒⠂⠂⣉⣁⣀⣤⡴⠒⠚⠀⠀⢠⢤⠖⠂⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣢⣤⠤⠶⠶⠶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠈⠑⣶⣤⢤⠈⠁
⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠾⠿⠛⠛⠉⢀⡸⠀⠀⠀⠀⠀⣀⠔
⠀⠀⣀⠀⠤⠤⢄⡠⠤⠶⠞⣛⣩⣭⣤⠶⠶⡶⡶⠶⠶⢶⢦⣤⣤⣤⣤⣤⠤⢤⡶⢞⣉⣦⠀⣀⠠⠔⠈⠠
⠠⠠⠀⠒⠒⠒⠒⠚⠛⠉⠉⠉⠀⣀⣀⣀⡤⠤⠒⠒⠴⠒⠉⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠉⠀⣦⣤⣤⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠤⠂⠀⠀⣀⡠⠤⠐⠀⠘⠇⠀⠀⠀⠀⠀⡠⢎⣤⡷⢖⣸⡟⢈⣩⡁
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠚⠛⠉⠉⠀⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⣑⡫⠔⠋⠀⠉⠁⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⢿⣿⣶⣦⡀⠀⠀⠀⡀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣾⢿⣯⡉⠑⠀⠀⢠⣬⣿⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠂⠙⠂⠀⠀⠀⠙⢻⠻⠋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⡀⠠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠃⠀⠀⢀⠀⠀⠀⠀⣄⠐⡔⣼⣷⡤⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⢀⠀⠀⢀⡘⣁⡀⢀⣄⣱⣶⣿⡿⣿⣿⣫⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣶⡞⣿⣻⢟⣽⣿⠟⣿⣛⣿⡿⣟⡿⣾⣿⡷⠾⡛⢽
⠷⠟⠒⠀⠉⠁⠉⠀⠀⠈⠁⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠋⠙⠉⠋⠉⠉⣉⣉⣉⠍⠩⢉⣩⠥⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣀⣀⣠⡤⠶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠐⠂
⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡤⠀⠀⠀⠀⡠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠖⠀⠀⠀⠀⠤⣠⢢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⡒⠀⠀⣀⠠⡺⠉⠀⠀⠀⠀⠀⠀⣸⡌⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠴⠷⠀⠀⠀⠀⡀⠀⠀⠈⢩⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⣰⠁⢀⣀⠀⠀⠀⣀⡀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠤⠐⠂⠀⠀⠀⠀⠀⠀⠉⠒⢺⠁⠀⠀⠀⡀⠀⠀⡀⠉⢨⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⠀⠀⠀⠘⠂⠀⣀⠉⠉⠉⠘⠢⣀⠀⢀⣀⠀⠀⠀⠙⠿⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠘⠀⠀⠀⠀⣲⠖⠀⠀⠀⠉⠱⣶⡏⢀⠀⠀⠀⠀⠘⠲⣄⠉⡁⣤⣤⣶⣏⣉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⣌⣻⠠⣤⣿⣍⠒⠉⠀⠀⠀⠀⡠⠄⠀⣸⠁⠁⠃⠘⠀⠀⠀⢰⢼⡷⣼⡿⢋⡀⠀⠙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⣶⠶⠈⢥⣠⣤⣤⣤⣈⣁⣛⣻⣾⡾⢁⠈⠁⠀⠲⠳⠠⠀⣄⠀⠤⣈⢷⣶⣶⣦⠼⠶⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠁⠀⠶⠟⠛⠁⠠⠄⢹⡿⣷⣶⠶⠤⠶⣶⣶⣤⠶⠿⣿⡿⠉⢩⣭⣅⡀⠀⠁
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⡀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠠⢄⡘⢁⡤⡀⠀⠀⠈⠉⢉⣶⣶⣿⠧⠀⠀⠩⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠚⠁⠐⠀⠤⠄⠀⠉⠠⠶⠿⢿⣛⣯⡭⠭⠞⠵⠚⠀⠔⠀⠀⢀⠙⠍⠁
⠀⠀⠀⠀⠀⠀⠤⠤⢤⣤⣤⣤⡀⠀⠀⠀⢀⣀⣀⣀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠉⠉⠛⠊⠀⠈⠁⠀⠀⠀⠀⠀⢀⣒⡒⠒⠂⢤⣤⣤⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠯⠉⠉⠉⠉⠉⠉⠩⠥⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣔⣒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠃⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⡀⠄⠀⠐⠄⢀⠀⢀⠀⡆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠐⠀⠀⠀⠀⠄⠀⠀⠲⢂⠁⠇⠀⠀⠀⣸⡿⠃⠈⠀⠀⠀⠀⠀⢴⣧⠇⠀⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠀⢠⠀⠙⢂⡀⠀⠰⠋⢁⡔⠡⠀⠈⠀⠀⠀⠈⡞⣀⠀⠀⠀⡄⠀⠛⢡⣀⣀⣠⣤⠶⠶⠦⠤⠤⠤⠞⠉⠈⢀⣶
⠀⠰⠀⠀⣁⡗⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢶⢀⡀⣬⣯⡄⢀⠀⡀⣠⠀⠠⠀⠀⠀⠀⠀⢰⠌⠀⠀⠀⠀⠀⣴⣾⣭⠿⠚⠛⠚⠛⠓⠂⢄⠴⣤⢠⣍⣉⣉
⠀⠀⠀⠀⢈⡃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠙⢿⣿⢶⣤⣴⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡗⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⢺⣇⡀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⢀⠀⠈⠿⣭⣟⣻⡾⣷⣦⠘⠤⠶⢖⢀⠛⠁⠂⠀⠀⠀⠀⣇⢸⠀⠀⡃⠰⠀⣀⡀⠀⠀⡀
⠀⠀⡀⠀⢈⣧⠀⠀⢸⢸⡱⠀⠸⢀⣿⣴⠤⣾⠁⠰⠀⠀⠴⠀⠀⢤⠙⡚⠰⠒⠉⠁⡤⠀⡀⠀⠀⠈⠉⠒⠦⢀⡀⠀⠀⠛⢀⡄⠈⠀⢠⡄⢹⢩⢾⢤
⠀⠐⡏⠀⠛⡷⠄⠀⢻⠆⢿⠶⣼⣬⠿⠛⠀⢨⠄⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⡡⠄⠐⠂⠀⠀⠀⠀⠙⠀⣄⠀⠀⠀⠈⠀⠀⠐⡀⣘⠃⢆⠀⢀
⠀⠀⣧⢀⡰⡧⠄⠀⣽⠁⠀⠀⢾⡀⢀⠀⠀⢸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠄
⠀⠈⠉⠀⠰⠀⠀⠁⠀⠐⠆⠀⡸⡀⠀⠀⠐⠚⠄⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠠⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣏⠔⣟⣋⣛⣛⣛⣛⣛⣛⣙⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠔⠠⠀⢲⡶⢶⣦⣴⡶⢶⠆⠀⠂⠤⢀⡀⣀⣠⠄⢀⣀⠠⠀⠂⠒⠴⠠⣤⢤⣤⣄⣠⣶⣄⣀⣤⢆⣤⠤⣤⣶⠶⣶
⠊⠉⠠⠈⠀⠈⠙⣀⠀⠁⠠⠀⠋⠀⠘⠊⠈⠑⠚⠘⠀⠄⠀⠀⠉⡓⠋⠉⢀⣈⠁⠀⠲⠄⠀⠈⣉⠉⠁⠠⠍⠉⠐
⠁⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⢐⡃⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣀⡀
⠈⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠤⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠁
⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠀⠈⠁⠀⠀⡠⠴⠈
⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣥⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣔⣾⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠣
⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠐⠀⠰
⠀⠀⢢⢸⡆⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡄⡀
⠀⠀⠀⠰⠀⠀⠀⠸⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠙
⠀⠀⠀⠰⠀⠀⠀⠂⠀⠀⠁⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰
⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠠⡀
⠈⠁⠐⠂⢤⡙⠁⠄⠀⠀⠀⠀⠰⠶⠶⠴⠶⢶⡴⠖⠶⣶⣶⣶⣤⠴⠶⠶⠶⠖⠒⠠⠤⢄⠀⠤⠘⠛⠓
⠀⠁⠀⠀⠏⠀⠀⠂⠀⣀⣉⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠙⠀⠠⠤
⠀⡀⠜⠷⣤⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠒⢒⣂⣀⣀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠈⢀⣀⡀⠀⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⢐⡦⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣞⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣁⣀⣀⣀⣀⣈⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⢀⠀⠠⠀⠀⡔⠀⠀⠀⠀⡀⢆⠀⡤⢀⠊⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡌⠐⠀⡁⠀⠀⠀⠀⠀⠊⠀⠐⠁⠀⠌⠀⠀⠀⠀⡀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠰⠄⡀⡄⠀⡀⠀⠀⠀⠀⢀⣈⠀⠤⠠⠠⠀⠦⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⡀⠀⠳⢠⣶⣶⣶⣶⣶⣶⣦⠑⠄⠔⣀⣀⣒⡂⠀⠀⢈⠐⠀⢀⠀⠀⠀⠖⡚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⡠⢌⣿⣿⣿⣿⣿⣿⡿⣀⠀⣾⣿⣿⣿⣿⣿⣶⣦⡈⣱⠦⢈⠢⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠤⠄⠀⠠⠀⠀⡠⠊⠀⠈⢮⣻⣿⣿⡿⠛⠁⠉⠃⢿⣿⣿⣿⣿⣿⣿⡿⣱⠳⠤⣀⠀⠈⠒⠤⢀⠈⠁⠀⠂⡐
⠀⠀⠀⢀⠔⠀⠀⠐⠀⠀⠀⠔⠀⠀⠀⠀⠀⠈⠉⠛⡀⠀⠀⠀⠀⠀⢩⣟⣻⠿⣟⣫⠞⠁⠀⠀⠈⠙⠦⣀⠀⠀⡰
⠀⠀⠀⠈⠐⠠⡀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠤⠤⠐⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠡⠀⠀⠃⠐⠠⠆
⠀⠀⠀⡠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠆
⠀⠀⠈⠁⢀⡀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢀⠂
⡄⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡀
⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣄
⠀⠀⠀⡠⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠐⠂⡀⠦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠀⡀
⠀⠀⠀⡈⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⡠⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠢
⠀⠀⠐⠁⠀⠀⠠⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⡠⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⡠⠀⠄⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡀⠤⠆⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⣀⠀⠇⠀⠀⠐⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡌⠀⠀⠀⠀⠤⠀⠐⠒⠀⠀⠀⠀⠀⠒⠀⠁⠀⢀⠀⠀⠀⠠⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⡐⠁⣀⠰⠃⠀⠀⠙⢀⠀⠀⠀⠡⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠡⠀⠃⠀⠀⡂⠀⠄⠀⠁⠀⠀⠁⠂⠄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⣼⣿⣿⠏⠀⡀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷
⠀⢠⣯⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⠇⠀⣼⣿⡋⠀⠀⢠⡀⠐⠀⠀⢀⠉⠀⠀⠀⠀⣴⣯⠀⠀⠀⠀⣀⠀⠈⠙⠋⠉
⣇⢸⡏⠄⢀⠀⠀⢴⣾⠛⠀⠀⠀⠀⢠⡄⠀⢴⣿⡿⠁⠀⣠⣾⡿⠃⠀⠀⠈⡏⠀⠀⠀⠀⠉⢋⣤⠀⢀⡿⠋⠀⢀⣴⣾⣿⣶⠈⠓
⠷⣿⡧⠀⣾⠃⢠⠆⠿⣷⡀⠈⠁⠀⠈⠀⠀⠺⣿⣣⣴⣿⣿⣿⣦⣄⡀⠀⠀⠛⠀⠀⠀⠀⠀⠼⠿⠀⠈⠁⣠⠖⠋⠈⠈⠁⡄⠀⠀⡉
⢷⣿⡇⠉⣿⡊⣿⠠⣤⠸⣿⣗⠀⠀⠂⢀⠀⠀⠉⠙⠿⠛⠻⠟⠛⠿⣿⠀⢠⠄⠀⢀⣴⡇⠀⠀⠀⢀⡀⠀⠀⢀⡗⢀⡀⣸⡇⣠⢰⡧⣾
⣿⣿⣷⠠⣸⣿⣿⡐⣿⠀⠀⢀⣜⣧⣀⢆⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠀⠘⠃⠀⢀⢠⢀⢸⣠⡇⣼⣷⣾⣴⣸⡷⢼⣷⣿⣷⣿⣾⡧⣿
⠙⠛⠛⠛⠻⢿⣿⣦⣿⣴⣾⢾⡷⣮⡷⠞⠀⠀⠿⠇⠀⠘⠟⠿⠿⢶⠾⢾⡶⠀⠀⠺⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⡍⣼⣿⣿⡿⣿⠿⠷⠛
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠉⣀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠘⠛⠟⠉⠀⣀⣀⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠒⠶⠦⠀⠀⠈⠁⠒⠒⠲⠾⠿⠿⠶⠶⢶⣤⣤⣤⣤⣤⠴⠶⠾⢿⣿⣿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠘⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠛⠂⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠘⢿⣧⣤⣀⣁⣠⣿⣯⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠂
⠀⠀⠀⠁⠀⢠⣦⡌⠙⣿⣷⣴⣾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⡦⠞⠓⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣠⣤⣤
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠉⠛⠿⣿⣗⣂⠉⠉⠀⠈⠙⠿⠿⠿⠷⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠢⣄
⠀⠀⠀⠀⣠⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠴⣿⠖⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠈⠙⡗⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤
⠀⠀⠀⠀⠰⠝⣒⣶⢠⡿⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠐⠄⠀⠀⠈
⠀⠀⠀⠀⠈⢁⢻⠿⣿⣟⣿⣗⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠚⠀⠀⠈⡷⠀⠀⠀⠈⠰⡐⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⢓⡀⠂⠀⠀⠐⠛⠛⠛⠒⢚⠂⠒⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠉⠀⠀⠀⠀⠀⠀⠐⢢⠀⠀⠈⠙⠒⠲⠶⠶⢶⣤⡤⠤⠴⠂⠀⠀⠀⢉⠒⠤⠄
⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣖⣉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣁⡀⠀⠀⠠⠤⢤⣄⣀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠂
⠀⠀⠘⠛⠟⠛⠏⠋⠉⠈⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⣀⡀⠀⠈⠉⠙⠛⠛⠛⠛⠓⠲⠿⠟⠉
⠀⠀⠀⠀⢤⠀⡤⠄⠀⠘⠂⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠙⠟⠃⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁