Maple Syrup Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⡴⠶⠶⠶⠒⠛⠛⠛⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⣇⣀⣀⣠⣄⣠⣥⣤⣿⣟⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠈⠀⢠⣴⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⢠⠖⣦⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⠤⡾⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣄⡀⠀⠀⠀⠀⢀⡴⠶⢦⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠙⣦⠀⠀⠀⣸⠁⠀⠀⠷⡴⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠛⠶⠞⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠲⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⠤⠤⠤⠶⠖⠒⠊⠛⠛⠛⠛⠛⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⢸⡇⠀⠀⠀⠀⠀⣀⣀⣀⠠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣿⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⢸
⢰⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣼⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⡤⠤⣀⣀⡀⠀⠀⠉⠀⠀⠀⠙⣆⢀⣠⣤⢶⠶⢶⣤⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠉⠙⠳⠶⠇⠀⠀⠀⠀⠙⠋⠉⠀⠀⠀⠸⠏⠀⠀⠀⠀⢸⡏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢠⡀⠀⠀⢰⡇⠀⠀⣠⠄⠀⢀⡴⠃⠀⠀⠀⠀⠀⠸⡇
⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⣯⡀⠀⠀⠀⠀⠀⠀⢀⡇
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠞⠁⠀⠀⠀⠳⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢰
⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⣀⣤⣆⠀⢠⣄⣀⣀⣀⣀⣠⣽⠄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠛⠒⠛⠛⠋⠉⠀⣿⠀⢸⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠋⠀⠀⠀⠀⠀⡤⠈⠂⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠋⠁⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢺⣍⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠶⠶⠶⠶⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⡤⠀⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠛⠛⠀⠀⠀⠀⢀⣀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⡄⠀⠀⠈⠙⠋⠈⠁⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣧⡇⡆⠀⠀⠀⠀⠀⡄⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢭⠧⣈⣀⣨⠤⠥⠤⢟⣀⣠⣤⠄⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⠩⠋⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⣀⣤⣄⣀⣤⣤⣄⣠⡀⣳⡶⠞⠛⠲⡄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣉⣏⢀⣀⢀⣉⡈⠭⣿⣿⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⢀⡞⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⠞⠀⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣦⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡠⠂⠁⣀⡤⠔⠲⠖⠶⠢⡤⣄⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠅⠀⠀⠀⠊⠀⡴⢛⣧⡶⠞⢃⠐⠉⠃⠄⡈⠓⣄⠀⠀⠀⠀⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢀⠈⠀⢠⡞⠁⢪⡟⠀⠐⣵⠶⡄⢀⠄⠁⡀⠘⢷⡄⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠁⠀⢠⡟⢀⡴⢃⠀⠀⣰⠃⠀⠉⣠⡄⠀⠀⢂⠈⣶⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⣴⢠⡄⣀⢀⣾⡗⠋⠀⢀⠀⢈⠷⣈⣀⣤⣔⣸⡇⠀⠀⠀⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⣿⣿⡇⠀⠉⠙⠷⠀⠀⠋⠀⠘⠛⠉⠀⣸⡟⣭⢿⠃⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠀⠈⠀⡿⠉⣿⠀⠀⣤⠀⠀⠰⡄⠀⠀⡄⠀⠀⣼⠃⣥⡾⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠠⠀⠀⠀⢿⠠⣾⠃⠀⠀⠀⠀⢀⡄⠀⠈⠁⠀⣺⡿⠊⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠸⣀⠋⠛⢻⠄⠀⠀⣸⡇⠀⠀⠀⠻⣿⠁⢠⣻⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠧⠀⠰⣧⣴⡴⠶⢿⣿⠶⠶⠲⠞⡋⢀⣀⣾⠟⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠸⣄⠐⠈⠠⠀⠤⠘⠿⠀⠀⠂⠀⠀⣿⢡⡟⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⠀⠀⠀⠀⢻⠤⢚⠤⠴⠶⠶⠶⠒⠒⠛⠋⠠⠟⡿⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠰⡀⠈⢧⣤⠐⠶⠢⡄⠀⠐⠄⡠⠘⢡⣼⠃⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣶⠀⠀⠁⢀⠈⠛⠲⠷⠦⢿⣼⠧⠴⠷⠾⠞⠁⠀⠀⢀⣤⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠳⣦⣄⢀⡀⠀⠀⠀⢀⠀⡀⠀⣠⠄⢀⣾⠇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⣀⣀⣤⡤⠀⡤⠄⠀⠀⠤⠀⢠⣤⣤⣀⣉⡛⠛⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢏⣛⠛⠛⠻⠷⢤⣠⣤⣄⣀⣠⣮⣵⡿⠿⠟⣋⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠉



⣿⣿⣿⡿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠒⠒⠚⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⣀⣀⣀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠀⠣⢄⠀⠀⣇⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡜⡠⠎⠁⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⠓⣁⢤⠤⠬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡂⠀⠈⠀⠀⠸⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠀⠀⠀⠀⠂⠠⠄⢀⠀⠉⠑⠢⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠰⡒⠃⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠈⢆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠅⠢⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⢀⠄⠀⡠⠀⠠⢒⠀⡤⠄⠤⢄⠀⠀⠀⠀⠀⠈⡀⠀⢹
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠒⣀⠀⡄⢁⠀⡌⠖⠃⠢⡄⢿⠀⠀⠀⠀⠀⠀⠁⠀⢸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠤⠡⠀⠐⠉⠁⠀⡁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⠐⡔⢆⠊⠑⠁⠄⡱⠀⠖⡖⠡⠀⡀⠀⠀⠀⠀⡀⠀⢸
⠀⠀⠀⠀⠘⡄⠀⠀⠀⡡⠂⡠⡔⡡⠀⡀⡦⡨⠆⠀⠇⠈⠈⠀⠀⠀⠀⢠⠀⠀⡇
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⡰⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠌⣀⠤⠊⠉⠉⠉⠑⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠙⠒⠒⠒⠒⡶⠒⠀⠠⠔⠓⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠠⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠢⢄⣀⡀⠤⠄⠒⠒⠒⠢⠤⠤⠤⠤⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠿⠇⠀⠀⠀⠀⠀⣩⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⢁⠀⠄⠀⠒⠒⠓⠛⢉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡼⢠⢠⠀⠀⠀⠀⠀⢸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣷⣾⣈⠀⠂⣇⣀⣸⣼⡏⠀⣀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠁⠈⠉⠉⠉⠀⠀⢈⡟⡻⠛⠉⠀⠈⠀⠷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢰⣀⡀⠀⠀⠀⠀⠀⢻⣄⣤⠴⠤⣤⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⠻⡿⠉⠉⠙⠿⠛⣿⣿⣶⡟⠁⠀⠀⠈⣇⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠛⠛⠘⠛⠐⠒⠀⠉⢽⣿⡇⠀⠀⠀⠀⡿⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣀⠀⢀⡾⠁⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣯⠁⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠁⠀⠀⠀⡠⠖⠈⠁⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⠳⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠁⠀⠀⡤⠋⢁⣤⣶⣋⣡⡭⢉⣹⣍⡹⠛⢦⡄⠀⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠰⠈⠀⣰⠏⣰⣿⠟⢋⡴⣊⡠⠈⠙⠶⣄⠙⣧⡀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠀⡄⠀⠀⣼⠏⢐⡽⠛⠀⢈⣾⠉⢷⣠⡞⠃⡼⢡⠈⢿⡄⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠈⠁⠀⣸⠃⠰⠏⡔⣀⣄⣿⠋⠀⠀⠶⣿⡀⡠⠊⠦⠘⣿⡀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠀⠀⠀⣿⣴⡗⠦⢤⣽⣿⠁⠐⣤⠀⠀⣿⣵⠶⠾⣿⣿⣿⣧⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡀⠀⠴⢸⣿⣿⣧⠀⠀⠀⠙⠃⡀⠁⠀⠀⠉⠀⠀⠠⣿⣿⠻⡟⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⠉⢿⡄⠀⠻⢄⠀⠈⡷⠁⠀⣴⠆⠀⣰⣿⣾⣼⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠂⠀⠀⠀⢿⣸⣿⣁⣀⠀⠀⠀⢠⣇⠀⠈⠀⢀⣨⣿⠟⢵⣿⠃⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢹⣌⠛⠉⣽⠇⠀⠀⣠⣯⡀⠀⠀⠈⣿⡏⠁⠼⣿⡀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠈⡟⠂⠘⣷⠶⠾⢿⢿⣿⣿⠿⠛⠛⠭⢄⣷⣿⡿⠋⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡤⠀⢀⠀⠀⢹⣦⠘⠁⠘⠀⠛⠀⠛⠃⠂⠃⢀⠀⢸⣿⣿⠁⠀⠀⢠⣜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⢿⡷⢃⠶⠶⠖⠒⠛⠛⠛⠛⠋⠁⠾⢹⡇⠀⠀⠀⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⢢⡀⠘⢷⣤⠶⡶⠒⡴⠂⠐⠲⢠⠟⠉⣶⡟⠀⠀⠀⢠⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢄⡀⠙⠲⠿⠶⠾⣿⠷⠶⠿⠿⠛⠋⠀⠀⠀⢠⡞⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠹⣦⣄⣀⣄⢀⢀⣀⣀⡀⢀⣀⣀⣴⠀⣠⣿⢃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠆⣠⣬⣄⣤⠀⣤⢦⠀⠄⠤⠄⠠⣤⣤⣤⣄⣙⠛⠃⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⡻⠿⠛⠿⠿⢤⣤⣤⣄⣀⣀⣴⣿⣿⡿⠿⢟⣣⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠒⠶⠆⠤⠌⠀⠀⠴⠖⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀⡷⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡦⠈⡟⠒⠒⠒⠛⡆⠰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢃⠀⡀⢠⠞⠁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠇⢸⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢰⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠘⡀⡇⠀⢸⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠃⠀⠀⠀⠲⠃⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠤⠶⠶⠶⢤⡀
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠙⡄⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠤⡀⠀⠘⡆
⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⡤⠤⠤⣴⠃⠀⠀⠀⠳⠖⠉⠁⠀⡜⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠀⠀⢳
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠁⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠇⠀⠀⡾
⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⠀⠀⡀⠀⠀⠈⢓⡄⠀⠀⠀⠀⠀⠈⠢⠤⠤⠒⠁⠀⠀⡼⠁
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠸⠤⠤⠒⠒⠚⢇⣰⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠓⠲⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⡒⢲⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣉⣉⣉⣉⣁⣉⣉⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⠛⠻⠿⠿⠿⠿⠿⠷⠾⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠦⠀⠀⠐⠶⠶⠶⠶⠶⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣧⡀⠀⣀⣤⡄⠀⣤⣼⢀⣴⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⢹⣿⡇⠀⣿⣿⠸⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠇⢰⠀⢸⣿⡇⠀⣿⣿⡄⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⣿⠀⢸⠀⣿⣿⡇⠀⢸⣿⣿⢨⡉⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢛⣾⣿⠀⡄⢀⣿⣿⡇⠀⢸⣿⣿⡼⣇⠀⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣼⣿⣿⠀⠇⢸⣿⣿⡇⠀⢸⣿⣿⡇⢿⡄⠀⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣰⣿⣿⠇⡆⠀⠈⠛⢿⡇⠀⠸⣿⣿⣿⡘⣿⣄⠰⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠃⢀⠃⠀⠀⠀⢸⡇⠀⠀⠙⢿⣿⡇⠻⣿⡷⠆⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣭⣤⣤⣤⣿⣤⣀⣀⣀⣤⣶⣄⣀⣀⣀⣀⣿⣦⣤⠠⡶⠿⠿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣛⣛⣛⣋⣩⣿⣿⣿⡿⠯⣍⣹⡛⠉⠩⣭⣽⠟⢿⣿⣿⣿⡿⠟⠓⠛⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⠟⠋⣉⣿⣿⣋⣴⣤⣴⡶⠊⠀⠙⣿⠗⠈⠳⣦⣬⣿⣿⢿⣿⣿⠿⠛⠺⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠟⠛⣹⡿⢁⣴⡟⢁⣈⠉⠁⢾⣿⣋⣀⡹⠷⠂⠙⣅⡀⢱⣦⣸⣿⣿⣿⠶⠾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⢛⣿⢿⠟⢉⡽⠃⣹⣿⣾⡿⠿⠛⠛⠛⠿⢿⣷⣦⡙⣷⡞⣭⡉⢉⡹⣿⣿⠦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⣩⡟⣥⣿⡷⠻⣷⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⢿⡿⢺⣷⠾⣿⣶⣤⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⢛⡟⠁⢻⣾⣀⣾⡟⠁⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠈⠛⠿⣿⣦⣿⣧⡜⢿⣦⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⣿⣸⣷⠚⠙⢿⠉⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⣴⣿⣿⡷⠀⠀⠀⠀⢽⣿⣿⠿⠟⢿⣿⣧⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⡟⠁⣼⡄⠹⠀⠀⠀⠀⠀⣀⡀⢀⣻⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠻⣿⡔⢷⣼⠙⣿⡉⣣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⡟⣧⡰⠿⠻⡆⠀⠀⠀⠀⣼⣿⡇⠘⢿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠙⣷⢠⡟⢳⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⡇⠙⡇⠸⣇⠀⠀⠀⠐⣶⣿⣿⣿⡖⠈⢻⡿⣿⡿⢿⣿⠟⠋⠁⠀⠀⠀⠀⠸⢻⣿⢧⣦⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡿⢇⠀⣿⡆⠉⠀⠀⠀⠀⠙⣿⣿⡿⠇⠀⡸⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣀⢻⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢾⡇⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⢿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣷⡈⢡⣄⢻⠀⠀⣤⣤⣤⣄⣤⣄⠀⣤⣤⡄⠀⢠⣤⣴⣤⠰⣿⠆⣠⣤⣤⡀⠀⢸⣿⡇⣿⣇⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣿⠃⢼⠋⢸⠀⠀⣿⡏⢸⡿⢸⣿⢠⣶⣿⣷⣤⢸⣯⣸⣿⠀⣿⠆⣿⡷⢻⡇⠀⢸⣿⣿⠏⣿⣿⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣿⣇⣼⠉⠳⠀⠀⠈⠁⠈⠃⠈⠋⠀⠙⠋⠙⠉⠸⠿⠉⠀⠀⠿⠆⠙⠛⠛⠁⠀⣾⣿⠉⣼⣿⣿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⢻⡿⠁⢸⡆⣿⠀⢰⣿⣛⠂⠺⣷⣀⡾⢰⣿⠾⣷⢴⣿⠀⣾⡆⢰⣿⠿⣷⡄⠀⣿⣿⡾⣛⣿⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⠻⣿⣀⡇⠠⠀⡆⢠⣍⣿⡿⠀⢻⣿⠃⢸⣿⡇⠁⠘⣿⣦⣿⡇⢸⣿⣤⣿⠃⣸⣿⣅⣴⢿⣿⠛⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡷⣯⣝⠿⣤⣤⠁⡄⠀⠀⠐⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⢰⣿⣿⢿⡏⣼⡿⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣣⣼⣿⣄⣽⡉⣆⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢿⣿⡁⣼⣷⣿⣤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⢿⣏⢻⡷⢿⣦⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣩⡿⠿⠏⢡⣿⠋⣡⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣝⣛⣿⣿⡿⣶⡤⢶⣌⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⣴⡟⣠⣾⣷⣿⠷⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⣯⡉⠻⣷⣈⣣⣈⣽⠂⣨⡐⠂⣀⠀⠀⠀⠀⠀⢠⡔⢒⣩⡶⠿⣿⠗⣭⣽⡿⣡⣴⠾⣫⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣍⣀⣈⣿⣿⡟⠻⣷⣬⣿⡿⠒⢶⣦⣬⡵⠶⣶⣾⣻⣥⣤⣾⡿⢾⣿⠏⠘⠛⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡛⠻⠍⠉⠛⢿⣄⣹⣏⡈⠻⣷⡦⣉⣭⣿⣿⣿⡿⣫⣽⣷⣿⣶⣟⣥⣤⣶⣿⣿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣶⣶⠀⠀⢈⣿⣿⣿⣷⣉⣲⣿⣿⣷⡛⢛⣾⣿⣿⠟⠋⣀⣩⣽⡿⠿⠛⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡜⠛⢻⣶⣾⣿⣟⣙⣻⣿⣿⣿⣿⣿⣿⠿⣛⣻⣿⣿⣏⣉⣠⣤⣶⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣾⣯⣍⠉⠯⠛⠛⠛⠛⠛⠛⠛⠛⠛⢯⣭⣭⣟⣛⣿⣯⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠒⠶⠲⠶⠖⠲⠶⠖⠲⠒⠚⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠚⠉⠉⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⠤⠤⠤⢼⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠐⡄⢀⡠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⡰⠩⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠐⠈⠋⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⢀⡀⠉⠓⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠈⠑⢄
⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢤⠐⠁⢂⠆⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⢣
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠠⠄⠄⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⡆⠀⠀⠀⢀⠀⠄⠀⠄⠂⠐⡀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⢀⠃⠀⠀⠀⠀⡉⠄⠀⣌⠅⢠⠐⠋⢐⡆⠚⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡄⠀⠀⠀⠒⠁⠀⡉⢀⢀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠈⡀⠊⢠⠁⠁⢐⠠⡃⠉⡩⢐⠠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠸⡀⠀⠀⠠⠅⠒⠢⠀⠐⠈⠐⠉⠀⠁⠂⠀⠀⠀⠀⠀⠂⠀⠎
⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⡐⠀⡜
⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠔⠀⡀⠓⠒⠂⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠀⠤⠤⠤⠤⣤⠤⠀⠀⠰⠖⠂⠁⠀⠀⠀⠀⠀⠑⠠⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠒⠤⣀⣀⣀⠠⠄⠀⠀⠤⢄⣀⣀⠠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠴⠶⠖⠒⠛⠛⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⣈⣠⢤⡤⠤⠤⠤⠤⠴⡧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠀⠀⠀⢀⠣⢤⡀⠀⠀⠜⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠈⠀⠀⠀⢀⠇⣀⡴⠋⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡌⢸⠁⢰⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢄⣀⠤⠦⢄⣈⣁⠤⢼⡖⠶⠒⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠢⠀⠀⠀⡄⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠉⠀⠀⠀⢁⠀⠀⠀⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠤⢀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢀⡤⠤⠇⠐⠤⢠⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠱⡄
⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢣⠀⠀⠀⢹⡀
⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠒⠲⠴⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢷
⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡠⠤⠀⡤⠖⠠⣀⡤⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⢸⡆
⡼⠀⠀⠀⠂⠀⠀⠚⢠⡋⠀⠀⠈⠠⡦⠀⡀⠰⠀⣸⢀⡁⠀⠠⡾⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⣧
⡇⠀⠀⠀⠀⠀⠀⠀⡄⢠⠦⠈⢢⣀⡶⣀⣹⣀⡏⢠⣈⢉⡇⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠠⠤⠋⠼⠀⠑⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⢸⡀⠀⠀⣿
⢷⠀⠀⠀⠀⠀⠀⣠⠤⢄⢠⡴⢤⠔⢦⠒⢉⠉⠂⡤⢀⡤⣤⠴⠒⠦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡿
⢸⡀⠀⠀⠀⠀⠸⣁⠀⠚⢄⠑⣄⢀⠃⠀⠘⠀⢞⡇⠈⠁⢸⠀⣘⣀⡼⠀⠀⠠⠀⠀⠀⡴⠀⠀⢰⠆
⠈⣇⠀⠀⠀⠀⠀⠴⠚⢀⡴⣐⢁⡎⠀⡀⢈⠳⣠⠟⠤⠤⠻⢤⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡾
⠀⠘⣆⠀⠀⠀⠀⠁⠉⠁⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⠃
⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠉⠀⢰⡀⠀⠀⠀⠀⠀⢠⠇⠀⢠⠇
⠀⠀⠀⠈⠳⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣀⠀⠀⢀⠀⠀⠀⠀⢠⠏⠀⠀⢺⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠓⢦⣤⠀⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⠀⠀⠀⠑⠐⠉⠀⠀⢀⡴⠁⢀⡠⠔⠋⠉⠉⠉⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠶⠶⠶⠦⠤⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣰⡯⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⣀⣀⣀⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣠⠤⠶⠒⠚⠋⠉⠉⠓⠒⠶⠦⠤⠴⠶⠖⠚

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠚⠛⠉⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡤⠟⠒⠐⠙⡂⠀⠉⠉⣹⠙⡆
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⢱⠀⣀⠗⠺⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡃⡎⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠈⡇⡀⠄⠂⢄⣉⠤⢸⠖⠒⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠨⠄⠀⠀⡆⠀⠀⢱⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠡⠤⢠⣀⡀⠀⠉⠙⠢⢄
⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠉⠢⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠠⠋⠄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠘⣆
⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠘⡆
⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠓⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢸⡀
⡸⠀⠀⠀⠀⢀⣀⢀⠒⠀⠠⢂⠃⠐⢉⡀⢴⠲⠐⠒⣂⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠋⣠⠀⢀⠈⡅⢰⡄⡖⠋⠐⢰⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⡇⠀⠀⠀⠀⠠⠨⠣⠄⠐⠚⠉⠀⠁⠉⠀⠈⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠇⠀⠀⠀⠀⢀⡠⠤⠀⡔⠠⠒⡴⢊⡉⠂⡔⢀⠤⡔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⢀⠀⠀⠀⠀⠘⠤⡌⠑⠈⡄⠠⠀⠈⡅⠊⡅⠀⢀⡇⡬⠤⠂⠀⠀⠀⠀⠀⠇⠀⢠⠁
⠀⢧⠀⠀⠀⠀⠍⠤⠐⠘⠤⠁⠘⠤⠂⠒⠉⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⡜
⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠀⢀⠀⠀⠀⠀⠀⢀⠄⠀⡸⠁
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⡀⠈⢀⠀⠀⠀⢀⠎⠀⠰⡇
⠀⠀⠀⠀⠈⠑⢦⡄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⡠⠂⣀⠤⠐⠉⠉⠉⠉⠙⢢
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠒⠒⠶⠶⠤⢤⠤⠠⠤⠤⠤⠼⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠦⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠤⢤⣀⠀⠀⠀⢀⣀⣀⡤⠤⢤⣀⣀⡀⠀⢀⣀⣈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣷⣾⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣿⣦⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⢻⣿⣿⡦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣴⣿⣿⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⣟⢾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⡿⢡⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢿⣷⣿⣿⣿⢉⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⣯⣿⣿⣶⣤⣤⣤⣤⣤⣤⣤⡀⣐⣶⡾⠿⠿⠿⠿⠿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⣀⣤⣤⣽⣷⣍⢿⣯⣥⣤⣤⣤⣤⣾⣭⢭⣥⣶⣶⠶⢶⣶⡿⢉⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣈⣤⣞⢿⣿⣟⣙⣿⣿⣆⢻⣿⣿⣯⣯⣽⣫⣵⣯⣥⣾⣧⣴⣾⣿⡟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠶⣿⡿⣿⡟⠛⠛⠛⠛⠛⠛⠻⣦⢹⣟⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⣿⢇⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢠⡿⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣼⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢀⡿⢡⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⡄⠀⠀⠀⠀⠈⣿⣾⣿⣿⣷⠘⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠏⣼⢃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⢷⡀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣧⠹⣞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡘⣧⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢹⡆⠀⠀⠀⣹⣿⣿⣿⡇⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡈⣿⡀⠀⠀⣿⣿⣿⡏⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢹⡇⠀⠰⣿⣿⣿⡃⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣧⠀⠀⢻⣿⣿⣧⢹⣿⣯⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⣿⡄⠀⣼⣿⣿⣿⡜⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢰⣏⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠸⣇⢸⡇⠀⢻⣿⣿⣿⣿⣿⣿⡟⣿
⠀⣀⣀⣤⣴⣶⠶⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠶⠾⣿⡈⣿⣤⣼⣿⣿⣿⣿⣿⣿⣦⣿
⣾⣟⠉⠁⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄⣽⣧⢸⣷⡄⠉⠉⠛⢻⣿⣏⢿⣿
⠉⢻⣿⠿⣷⣶⣶⠶⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⠉⠆⢿⣷⣿⡿⣿⣿⣿⣿⣾⣿
⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣈⣙⢻⣿⣶⣴⣿⣭⠄⣏⣿⣿⣿⣿⡿⣿
⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢬⣭⣽⣻⣿⣿⣿⣿⣥⣴⢄⣻⣿⣿⣿⣿⣗⣿
⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣤⣽⣯⣭⣿⣿⣿⣿⣯⠅⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⢠⣾⣯⣿⣿⣿⡿⠶⠶⠂⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠿⣶⣿⣿⣿⣋⣉⡁⢰⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢉⣿⣿⣿⣿⠿⠏⠉⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣬⣽⣿⣿⢿⡶⠦⠀⣸⣿⣿⢿⣿⣿⣿⣿⠉⣿
⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠶⣶⢾⣿⣿⣿⣿⣶⠶⢀⣿⣿⣿⣾⣿⣿⣿⡏⢸⣿
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣽⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⡿⣿⣿⣷⣏⣿
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣧⣿⡿⢡⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣾
⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠻⣶⣿⣿⣿⣟⣛⡀⣼⡿⠀⣿⣿⣏⠹⣯⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣛⣛⣛⣻⣻⣿⣿⣿⣿⠯⢠⣿⠃⠀⢻⣿⠙⣷⣿⣿⣷⢻⣿
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠤⢴⣶⣿⣿⣿⣾⣛⠁⣾⡏⠀⢀⣼⣿⣷⡘⣿⣿⣿⡞⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⣶⣿⣿⣿⠛⠁⣰⣿⠁⠀⢸⣿⣿⢏⣿⣿⣿⣯⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣻⣿⣿⣶⣶⣟⢀⣿⡏⠀⠀⠀⢻⣿⢾⣿⣿⣿⣻⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢀⣀⣀⣀⣀⣀⣀⣀⣀⣽⣭⣭⣽⣿⣯⣭⣤⣶⣼⣿⠁⠀⠀⠀⣿⣿⣾⣿⣿⣿⣟⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⣛⣉⣉⣉⣉⣉⣭⣭⣭⣭⣍⣉⣩⣭⣭⣭⣥⣥⣼⣿⠇⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⠴⠦⠴⠒⠶⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣌⢀⣄⠀⢀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣮⣥⣤⣤⣤⣤⣷⣽⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢁⣴⣾⣶⣶⣶⣶⣶⣶⣦⡈⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⣿⣿⣿⠉⠉⢹⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣜⡠⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⠀⠀⣿⣿⣿⡟⠻⣿⣿⣶⣦⣞⣳⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡏⠀⢸⣿⣿⣿⣿⡴⠞⠛⠻⢿⡛⠿⣃⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⠀⢸⣿⣿⠋⣿⠁⠀⠀⠀⠀⠹⣄⠸⣧⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣸⣿⣿⣿⠀⢸⣿⣿⢀⣿⠀⠀⠀⠀⠀⠀⢿⠀⢿⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⡆⢸⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⢸⠀⣾⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⣷⢸⣿⣿⡀⣿⠀⠀⠀⠀⠀⠀⣾⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⣿⣿⣿⠘⣿⣿⡇⢿⡀⠀⠀⠀⠀⠀⡟⢰⡟⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣾⣿⣿⣿⣿⣿⡆⣿⣿⣷⢸⡇⠀⠀⠀⠀⣸⠃⡾⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣱⣿⣿⣿⣿⣿⣿⣧⢹⣿⣿⣆⢷⠀⠀⠀⢠⡟⠀⢃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⡜⣧⠀⠀⣼⠁⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣧⣿⣿⣿⣿⣿⣧⣴⣿⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠟⣡⣶⣿⣿⣶⣮⡙⣿⣿⣿⣿⣿⣿⢹⡇⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣌⢻⣿⣿⣿⣿⡄⣿⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⢡⣿⣿⣿⡿⠏⣨⠙⣿⣿⣿⣆⠻⣿⣿⣿⣷⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⢡⣿⡏⢉⡹⠗⠄⡰⠀⡟⣹⢹⣿⣆⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⢡⣿⣿⣿⡀⢧⡘⢢⡄⢀⠰⠋⣙⣿⣿⡄⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⣾⣿⣿⣿⣏⡃⡡⣤⡄⠛⢀⣶⣿⣿⣿⣷⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡏⢰⣿⣿⣿⣷⣭⣭⣵⣷⣶⣶⣾⣿⣿⣿⣿⣿⡆⠸⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠁⣾⣇⡀⠹⣅⠙⢩⡏⢉⣈⡉⢹⠁⣹⠀⣥⠈⣷⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⣿⣯⣤⣄⠻⢀⣾⣧⣼⣿⣧⣤⣤⣾⠀⣤⣴⣿⠀⢸⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢸⣿⣿⡟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠙⠛⠿⠿⠿⠿⣿⣿⣿⣿⠿⠿⠿⠛⠁⠀⠀⢸⣿⡿⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣾⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⣿⣿⣿⠿⢷⣦⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣾⣿⡿⣿⣿⣿⡏⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠙⠿⣿⣿⣶⣦⣬⣍⣉⣙⣛⠛⠛⠛⠛⢛⣛⣉⣉⣭⣭⣴⣶⣿⣿⣿⠟⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⡀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⡿⠟⠁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠛⠛⠛⠛⠒⠒⠚⠛⠓⠲⠚⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠸⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣤⣤⣤⡤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠶⠶⠶⠶⢶⣇⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠘⣧⠤⠶⠦⣄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠤⠤⠤⠤⠤⠤⢷⡀⠀⠀⠈⡆⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠂⠐⠀⠀⠀⠀⣳⠀⠀⣠⠣⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠃⠀⠀⠀⠀⠀⠀⠀⠳⣄⠔⢁⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠲⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⣠⠔⠚⠉⠙⠒⠦⡀⠀⠈⠣⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⢠⠞⢁⠀⢀⠀⠀⠀⢄⠈⢢⡀⠀⠑⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⣰⠃⠀⠣⠤⠀⣁⠉⠥⠔⠀⠀⠱⡄⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣰⠃⠀⠀⠀⠂⠀⠂⠂⠒⠀⠀⠀⠀⠹⡌⢂⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠠⢠⠃⠀⠒⣂⣩⠀⢰⠤⠾⡀⠀⠀⡸⠓⠚⢱⡈⡀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⢀⠃⡞⢀⠀⠉⠁⠀⠀⢈⠄⠀⠙⠤⠔⠁⠀⠀⡀⢧⠁⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡸⠈⢸⠃⢄⠑⠢⢄⡀⠈⢫⠀⠀⡄⠀⡀⠀⠰⣰⠁⠸⡆⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⡜⠀⠀⠑⠂⠠⠌⢉⢉⡇⠀⠘⣤⠃⠀⠀⡏⠀⠀⡇⠀⠃⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡇⠀⡇⠀⠀⠀⠀⠀⢦⠔⠊⠀⠈⠢⣼⠀⠀⣸⠔⠁⠀⣷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⡇⠐⢄⠀⠀⠀⠼⢀⣀⡀⠒⠦⣈⠀⣰⠃⣠⠀⠀⣿⠀⠀⢠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢹⡀⠀⠑⠢⢄⣀⠀⠀⠈⠑⢆⠈⠷⠃⠒⠉⠀⢀⡇⠀⠀⠄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠣⣀⠀⠀⠀⠀⠉⠉⠉⠉⡝⡠⠖⠒⠶⢄⣀⠞⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠦⠤⠴⠼⠴⠶⠖⠒⠚⠁⠀⢀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠉⠓⠒⠒⢒⣂⣀⣀⠀⠀⠀⠀⠀⠤⠤⠤⠴⠒⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢤⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠷⣾⣿⣿⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣯⣿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⣿⠿⠿⠿⣿⣿⠿⣿⠒⠀⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣀⠀⠀⠘⣃⠐⣿⣶⠿⠶⢶⠆⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠘⠿⠿⠿⠿⠟⠽⡦⢻⡇⠀⠀⠀⣾⡧⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣸⣿⣶⠶⠶⠶⠶⣾⣿⡀⢳⣄⣠⢾⣇⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢴⣿⣿⣿⡾⠖⠲⢶⢷⣿⣷⠄⣱⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⣿⣟⣛⣛⣛⣛⣿⣛⣭⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠛⣾⣿⠿⣿⣿⣿⡿⠿⠿⠷⣛⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠁⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣀⡀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⣿⣿⣿⣿⣿⣿⣿⣥⠾⠿⠾⠿⠿⠷⠾⣿⣿⣿⣿⣿⣿⣷⡀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣰⣿⣿⣿⢟⣷⠟⠋⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠉⠛⢿⣿⡮⠹⣿⡄⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⣿⡿⣿⡿⠁⠀⣀⠖⠁⠀⠀⠀⠀⠀⠈⠙⠳⢦⡀⠀⠛⣷⠀⢸⣿⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣸⣿⣿⣳⡟⠀⠀⡔⠀⠀⠀⠀⠀⠸⣧⣀⠀⠀⠀⠀⠙⣦⠀⠘⣇⠀⢿⡇⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣿⠀⠀⠸⠀⠀⢠⠀⣀⣣⠀⢀⣺⣀⡄⢀⡀⠀⢹⡄⠀⢻⡀⢸⣿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⡿⠀⢠⡇⠀⠀⠸⢇⡀⠙⠀⣼⡭⠉⠡⢿⡁⠀⠀⢅⠀⢸⡇⢸⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⣿⣿⣷⠀⢸⡇⠀⠀⠘⢶⣝⣷⣆⣿⣥⡏⣱⠟⠁⠀⠀⡄⠀⢸⡇⢸⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⣿⣿⣿⠀⠀⣧⠀⠀⢠⣤⡉⠒⢿⡿⢿⣃⣹⠶⠄⠀⢠⡇⠀⢸⠇⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣷⣿⡄⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣼⠃⠀⣾⠀⣾⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⡿⣷⠀⠸⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⡿⠀⣼⠏⢠⣿⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⣿⣷⣿⣇⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⣸⡟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣻⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟⠛⠀⣠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡿⣻⣿⡟⠲⠖⠂⠀⠀⠀⠀⠀⠀⡀⠙⠉⠿⠿⢤⣼⣿⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣾⣿⣿⣿⠿⠿⠷⠶⠖⠒⠤⠤⠀⠤⠄⠼⠲⠶⠶⠖⠒⣛⣫⣵⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⢹⣿⣿⣿⢛⣿⣿⣽⣿⠟⢺⣿⣿⣿⣿⠛⢻⡿⢿⡏⣽⢇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⡞⣷⣧⣬⣸⣇⠀⣀⣀⡧⣼⢁⣀⡀⢸⣇⣇⢀⣾⢣⣿⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣧⣹⠿⢿⡟⠿⣷⣦⣼⡇⢸⣦⣤⣴⠞⠻⣷⠿⢋⣸⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠺⠿⠷⠶⠶⠶⠾⠷⠶⠖⠚⠛⠛⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣶⣟⣹⣿⣹⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡤⠴⠖⠒⠒⠛⠉⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡠⠟⠒⠒⠲⡂⠈⠉⠉⣹⠓⡆
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠉⢱⠀⣀⠗⠲⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠁⡎⢡⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠄⠢⠀⣉⠤⠼⠖⠖⠺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠀⠀⠀⡆⠀⠀⢳⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠤⢀⣀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⠙⠢⡀
⠀⠀⠀⡴⠋⠀⠀⠀⠀⢀⣀⣠⠉⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠙⣄
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠢⠀⠀⠘⡆
⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠃⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢹⡀
⡸⠀⠀⠀⠀⢀⣀⢠⠤⠀⠠⠒⠂⠐⢉⠁⢴⠲⠀⠒⢢⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠛⣀⠀⢀⠈⡁⠰⡄⡴⠋⠘⢠⠀⢿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣷
⡇⠀⠀⠀⠀⢠⡨⠣⠅⠢⠘⠊⠈⠉⠉⠁⠈⠀⠙⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⡇⠀⠀⠀⠀⠀⡠⠤⡀⡤⠤⠖⡴⠂⠁⠂⡄⣀⢤⡤⠀⠤⠀⠀⠀⠀⠀⠀⡄⠀⠀⡏
⢸⠀⠀⠀⠀⠘⠄⡀⠃⠈⡦⠀⠀⠈⡁⠪⡇⠀⢠⡇⡬⠠⠇⠀⠀⠀⠀⠀⡇⠀⢠⠇
⠀⣇⠀⠀⠀⠀⡋⠡⠔⠸⠤⠃⠰⠤⠈⠒⠉⠒⠈⠓⠂⠀⠀⠀⠀⠀⠀⢠⠀⠀⡜
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣰⠁
⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⠀⠀⠀⠀⠀⠜⠀⠠⡇
⠀⠀⠀⠀⠈⠲⢤⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠁⠑⠐⠈⠀⠀⡠⠊⢀⡠⠔⠉⠉⠉⠉⠓⣦
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠤⠤⠤⠤⠤⣤⣤⠄⠀⣀⣀⠾⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠈⢉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢹⢛⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡦⠤⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠶⠀⠦⡀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡤⠆⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠶⠀⣷⣀⣀⡴⠂⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠛⣿⡀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠉⠀⠉⢘⣿⠷⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣀⣠⣤⣤⣤⣤⣤⣭⣭⣭⣭⣤⣤⣤⣤⣄⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠛⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠻⡘⣿⠉⠀⠀⠘⠃⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡏⠁⠀⠀⣀⠠⠤⠒⠚⠛⠉⠉⠉⠉⠛⠛⠻⠷⣄⣀⠀⠀⠀⠀⠈⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡶⠖⠃⢀⣀⡤⠴⠖⠛⠛⠛⠛⠛⠛⠒⠤⠤⣀⠉⠐⠠⣄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⠋⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠈⠻⣦⡀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠋⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠻⣆⠀⠈⠃⠈⢦
⠀⠀⠀⢀⣿⣿⠉⣰⡿⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠘⠆⠀⠀⠧⠘⣦
⠀⠀⢀⣾⣿⠁⢠⡿⠁⡜⠁⣀⠀⢀⣤⣄⠀⠀⣴⣶⡄⠀⢰⣿⠟⠷⣶⡀⣶⡆⠀⠀⠀⣠⣄⣀⡀⠘⢀⠈⢦⠀⠘⠣⢹⡄
⠀⠀⣸⣿⠃⠀⣾⠃⢰⠀⣾⣿⣇⣸⣿⣿⠀⣸⣯⣸⣿⡄⢸⣿⠶⠾⠟⠀⣿⡇⠀⠀⠀⣿⣯⣉⣛⠁⠀⠀⠀⣆⠀⠀⠸⡇
⠀⠀⣿⡏⠀⠀⡟⠀⠀⠀⣿⡟⣿⡿⠹⡿⠰⠟⠉⠁⠘⠟⠘⠟⠀⠀⠀⠀⠻⠷⠶⣦⡄⣿⣧⣉⣉⠀⠀⠁⠀⢹⡆⠀⠀⣿
⠀⢰⣿⠁⠀⠀⡇⠀⠀⠀⠙⠁⠈⠁⠀⠀⠀⠀⠀⣀⠀⣀⣀⣄⣀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠉⠉⠛⠁⠀⠀⠀⢸⣿⡃⠀⣿
⠀⢸⣿⠀⠀⠀⡇⠀⠀⠀⢀⣴⠶⢶⡆⠸⣷⣄⣾⠟⢸⣿⣍⣉⣿⠇⢸⣿⠀⠀⣿⡇⢰⣷⠶⢦⣄⠀⠀⠀⠀⢸⣿⣇⠈⣿⡄
⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠙⠿⠶⢶⣦⠀⠈⣿⡇⠀⢸⣿⠉⠹⣿⡄⢸⣿⣀⣀⣿⡇⢸⣿⠶⣾⡿⠀⠀⠀⠀⢸⣿⡏⠀⢹⡇
⠀⠸⡇⠀⠀⠀⠃⠀⠀⠀⠸⢷⡴⠞⠋⠀⠀⠙⠀⠀⠀⠉⠀⠀⠈⠁⠀⠉⠙⠛⠉⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⢸⡇
⠀⠀⣧⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⢸⠇
⠀⠀⢿⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⣿⠃⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣾⣿⠀⠀⠀⣿
⠀⠀⠘⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢰⣿⡏⠀⠀⢀⡿
⠀⠀⠀⢿⡄⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣼⣿⠁⠀⠀⢸⡇
⠀⠀⠀⠘⣧⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⣟⡟⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢻⡆⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⡽⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠘⣷⠀⠀⠀⠈⠇⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡬⠁⡀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠄⠤⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣀⣩⡷⠖⠒⠒⠒⠀⠀⠀⠁⠈⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠛⠛⠛⠷⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⡉⠓⠒⠒⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡤⠤⠴⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⢀⡠⠤⠤⠤⠤⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠣⢤⠀⠀⠠⡇⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⢠⢇⣤⠞⠁⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢇⠸⠀⡇⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠤⠒⠐⠂⠠⠔⠒⢻⠙⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠐⠵⠀⠀⠐⠀⠀⠀⠳⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⣀⡀⠀⠀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⣀⡌⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠐⠢⠴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢧
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡤⠤⠀⡄⠀⠀⡠⢄⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⢸⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠁⡬⠀⠀⠀⠀⠆⠀⡀⢃⣠⠇⣀⡀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⡄⠚⢀⣸⠦⠗⠀⠿⠼⠀⠀⠤⠯⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢀⠀⣀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠂⢉⡆⠪⡑⠁⡙⠁⠄⢀⡰⠁⠖⢰⡋⢠⠉⠂⠀⠀⠀⠀⠀⢠⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢈⡂⠄⢀⣀⠜⡰⠀⠀⢰⡈⢙⡄⠀⣸⠀⠒⠐⠃⠀⠀⠀⠀⠀⠸⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠘⠤⠐⠊⠘⠒⠁⠀⠓⠊⠈⠁⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠖⠀⢠⠀⠀⠀⠀⠀⠀⡰⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠈⠁⠀⠀⠀⠀⡴⠁⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠉⠀⠀⢀⠎⢀⣀⠤⠊⠉⠉⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠶⠶⠤⠤⠤⠤⣤⡤⠄⠀⣀⣀⡸⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⠶⠒⠊⠉⠁⠀⠀⠀⠉⠉⠛⠓⠚⠛⠉⠁

⠀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄
⠀⣿⡑⢌⣠⢡⣝⣓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣚⣫⡌⣄⡡⢊⡿
⠀⠘⣦⢻⡪⢙⣋⣙⡻⢯⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣿⡼⢋⣋⣙⡋⢕⡗⣴⠃
⠀⠀⠘⣎⢧⣏⢲⡆⠀⠭⠟⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⢿⠫⠩⠀⢰⡔⣹⡼⣱⠃
⠀⠀⠀⠸⡌⣎⠒⠬⢒⠤⡀⡀⠙⠹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡿⠏⠊⢀⠀⢤⣒⠥⠒⣱⢡⠇
⠀⠀⠀⠀⣿⢸⡗⠦⠔⢆⡈⠑⡓⠦⣌⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠞⣡⠴⢚⠈⢅⡐⠢⠴⢺⡇⡿
⠀⠀⠀⠀⢸⠨⡿⣓⣈⣀⢈⡁⠐⠤⠀⠙⠺⣿⡻⣦⠀⢀⡀⠀⣴⢟⣷⠗⠋⠀⠴⠃⢈⡁⣀⢁⡚⢿⠡⡇
⠀⠀⠀⠀⠘⣯⢇⣧⣤⣦⣀⣬⣨⣆⣠⠈⡂⠨⠻⣽⣇⣾⣷⣸⣯⠟⠁⢖⠁⣄⣰⣁⣥⣀⣤⣤⣼⡼⡽⠃
⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⡀⠀⠀⠄⠀⠉⠛⠲⢤⡈⣿⣿⣿⣿⣁⡤⠖⠋⠉⠀⠠⠀⠀⢀⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡻⢣⠟⡟⣞⠗⠶⣾⣟⣽⣿⣿⣏⣻⣷⠶⠻⣳⢿⠻⡝⠛⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⢸⠀⡇⣜⠤⠈⠹⢿⡿⢹⡏⣿⡿⠏⠁⠄⣣⢸⠀⡇⠀⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠠⠃⠨⡇⠸⡀⢇⡐⠀⣀⠇⣿⡇⠸⢀⠀⢂⡼⢀⠇⢸⠅⠘⠄⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠹⣄⠙⢦⣈⢦⡞⠀⢹⡇⠀⢳⡔⣁⠴⠃⡰⠏⠀⡉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡌⢀⣀⡉⠓⠤⣤⠏⠀⠀⠘⠃⠀⠀⠹⣤⠤⠚⢉⣀⡀⢡⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠒⢦⢊⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⡑⡴⠒⠾

⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠔⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⡔⠉⠡⠀⠀⠠⣄
⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡜⠁⣠⠀⠀⠀⠆⠀⠑⡄⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠯⠀⢄⣀⠀⠀⠀⠀⠀⠀⢸⠅⠀⡇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢻⠋⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⢀⡴⠋⠠⠄⠀⢄⡀⠱⣆⠀⠀⠀⠀⢸⡆⠀⢇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⣀⣀⣀⡴⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠹⡶⣠⠀⠀⢠⠞⠀⠀⠀⠀⠀⢀⠃⢀⣿⣆⠀⠀⠀⠘⣿⣄⠈⠦⣀⣀⠀⠀⠁⢰⠇⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠌⢀⠞⣿⠟⠀⠀⠀⠀⠈⠻⣦⣄⣀⡀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡅⠰⣠⠤⠤⠊⢁⡤⠊⣸⢦⠃⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣧⣤⣤⡄⠀⠚⢩⣄⣴⠟⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⠦⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠓⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢤⠄⠀⠀⠀⠀⠙⠷⠦⢄⣀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢀⠄⢁⣀⣉⡀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣾⢦⡈⢫⠁⠀⠀⠈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⣿⢹⡇⠀⠧⠄⡀⠀⠀⢀⡆⠀⡆⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣷
⠀⠀⠀⠀⠀⢹⡀⠁⠀⠀⠄⡀⠀⠀⢉⣀⣴⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡏
⠀⠀⠀⠀⠀⠀⠙⢤⣀⡀⠀⢀⢀⣉⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠋⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⡀⠀⠀⢀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⢽⡞⠛⢻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡟⠛⢑⡮⢭⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⠏⣻⡍⠿⡽⠓⠞⠛⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠻⠚⢫⡾⢩⣟⠹⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢶⠯⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⡽⡶⢺⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣞⡷⠊⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠙⠶⣓⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣧⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣬⣗⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⡄⢰⡦⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡒⣥⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⡷⢤⣀⣠⠤⠤⠄⠀⠀⠀⠀⢿⣼⣷⡿⠂⠀⠀⠀⠠⠤⠤⣄⣀⡤⢾⣥⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡭⠋⣡⠃⠀⢀⠠⠀⠀⠀⢀⡜⣿⣿⠣⡀⠀⠀⠀⠄⡀⠀⠈⢌⠙⢭⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠂⠀⠀⠈⠁⡄⠀⢀⡠⠴⠁⠀⢻⡟⠀⠈⠢⢄⡀⠀⠀⡀⠉⠀⠀⠀⢿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣥⠀⠀⠀⠀⠀⠐⠀⠋⠐⠀⠀⠀⠈⠃⠐⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⣤⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⣇⣠⠀⠀⡀⠀⠠⠁⠀⠀⠀⠌⠀⢀⡆⠀⠡⠀⠀⠀⠈⢂⠀⠀⠀⠀⢄⣸⢶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣩⣇⣠⠂⢀⡔⠀⣠⣀⣴⡟⠀⠀⠘⠃⠀⠀⠹⣦⣀⣄⠀⠢⡀⠑⣤⣈⣏⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣷⣾⣶⣞⣶⣪⡷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣕⣶⣟⣶⣿⣾⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⣹⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⣯⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢂⡿⣿⣿⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⠿⢹⡿⢃⠾⣋⣿⠋⠉⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⣯⡿⠁⣿⣵⣫⣒⣁⡠⢤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡠⣄⣿⣿⣋⣿⡅⠊⠀⠘⠛⠉⠉⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠈⢳⣨⢹⣿⢟⡉⠌⠻⣶⡶⡶⠾⠖⢚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⡿⣿⡀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠄⠀⣡⡿⢵⣶⣯⣓⢶⣶⣦⣤⠴⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠈⠿⣄⡘⢮⣀⠀⠀⠀⣂⣤⣦⠴⢏⣆⠀⠀⠀⠈⢉⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠐⠀⠀⠀⠀⣝⣶⣼⣿⣿⠛⠋⠉⠂⢰⣍⣿⠿⠾⠛⣻⣏⣴⣆⣄⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠘⢿⣉⠛⠛⢋⣁⠀⠿⢽⣿⣷⣆⣀
⠀⠀⠀⠀⠀⣀⣤⣴⣄⢙⣓⣧⣿⠶⣬⣁⠀⠀⡀⣀⣜⠁⠦⡔⠁⠀⢀⡄⠙⠁⠀⠀⢃⢝⣬⠂⠈⠙⠛⠁
⠀⠀⠀⢠⠚⣓⣢⠔⣫⠽⢣⣿⠏⢠⣾⣉⣽⠟⠛⠉⢿⠃⠘⠃⠃⠘⠋⠀⠀⠀⣀⢔⡼⠋⠼
⠀⠀⠀⠘⠡⠿⢱⠾⠿⠴⠛⠓⠈⠉⠉⠁⠀⠀⠀⠀⠈⠳⣦⡀⣄⣀⣀⣤⣤⠿⠟⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠂⠒⠒⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⠿⣿⡿⠿⠭⢟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠹⠄⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢷⣦⠄⠀⠀⠀⢰⠆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠼⠃⠨⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣠⣴⡀⠀⠀⠀⠀⢠⣾⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠀⠀⣸⣟⣦⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣟⢠⣸⣿⡇⠀⠀⠀⣀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠀⠀⢠⣷⡿⠉⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠛⢳⣿⢀⣤⣾⣿⣿⣿⣿⣶⡤⠄⠚⠀⠰⠶⣾⣿⣿⣿⣿⣿⣾⡀⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⢠⣾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣷⢣⣾⣿⣖⣾⣿⣿⣿⣿⣿⣿⣿⡆⢸⡆⠀⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡜⠛⠀⢻⣿⣿⣿⣿⠿⠿⠣⢎⣼⣿⣿⣾⡜⢿⣿⣿⣿⣿⣿⡿⠁⠸⣷⣶⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠉⠉⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣉⣄⠀⣀⡀⠉⠀⠄⠀⠀⢸⣍⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣯⠏⠃⠁⠀⠠⠀⠀⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⠀⠉⠺⡿⠁⠁⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢿⣿⣿⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⡌⢿⣿⣷⣄⣀⣀⣀⣀⣀⣀⣠⣤⣠⣤⣽⣿⣿⡏⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣆⠈⠻⣿⡏⣌⠃⡏⢸⡃⡏⣏⣙⣩⣿⣿⠿⠟⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⠀⠀⠈⠑⠓⠦⠶⠸⠿⣹⡤⣭⣴⠿⠃⠁⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠈⠃⠀⠀⠀⠀⠈⠋⠉⠙⠁⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠃⠀⠀⠠⢈⣿⠇⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⣦⣤⣤⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣤⣤⣴
⠀⠀⠸⣿⣶⣩⡟⠋⠻⢾⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢾⠽⠛⠚⣯⣹⣽⡏
⠀⠀⠀⢫⡽⣤⢟⠋⢀⣙⡿⠄⣹⣫⣵⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣭⣿⡁⢾⣏⣉⣉⢻⢧⡼⣿⠃
⠀⠀⠀⠈⢯⣏⣹⣟⠁⠉⡻⢶⣉⣁⣞⣷⣭⣳⣤⡀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⣠⣶⣫⣴⣿⣟⣉⣵⢻⡋⠉⢹⡿⢉⣿⠏
⠀⠀⠀⠀⠈⢻⣿⣽⡟⠻⣽⡏⠁⠈⠑⠀⠀⠈⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠈⠁⠀⢉⡿⡤⠛⣟⣶⣼⠋
⠀⠀⠀⠀⠀⠀⠹⣯⣧⢾⣽⣦⣦⡀⠀⠴⣄⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣴⡄⠀⣠⣛⣿⣷⢴⠟⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣟⣽⡏⢿⡏⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠈⣧⠽⣛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⡾⣧⣄⠀⠤⠤⠴⠖⠛⠓⠀⠀⠀⠀⠈⠳⡄⢠⣤⠀⡴⠋⠀⠀⡀⠀⠐⠛⠒⠶⠤⠄⠄⢀⣴⠟⣶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠘⣾⣿⡞⢀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣤⣤⣤⣶⣶⣶⡶⠶⠦⢤⣤⣤⣤⣼⣿⣿⣿⣤⣤⣤⠀⢀⣴⣶⣶⣶⣶⣦⣤⣀⣤⣿⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⠅⠀⠉⠉⠉⠉⠓⠈⠀⠀⠂⠀⢀⠿⣿⣿⡿⣇⠁⠀⠀⠈⠉⠛⠉⠉⠉⠁⠀⠈⢭⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡤⠄⠀⠀⠀⠆⠀⠀⠀⠀⣠⠔⠉⠀⢹⣿⠑⡈⠓⢤⡀⠀⠀⠀⠀⠆⠀⠀⠠⠤⣼⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢳⣾⠁⠀⠀⠀⣠⠄⠀⣀⡤⠖⠋⠀⠀⡔⠀⢿⣿⠀⠐⡀⠀⠈⠳⣦⣄⣀⡀⣄⡀⠀⠀⠈⢻⣾⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢯⠿⣶⠦⠀⠈⣉⠔⠉⠁⠀⠀⠀⠀⠈⢁⡄⢸⣿⠘⣆⠉⠀⠀⠀⢀⡀⠉⠀⢍⡉⠓⠶⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣄⣠⡞⠁⠀⠀⠀⠀⠀⢠⠂⢰⡞⠀⠘⠟⠀⠘⣧⠀⢢⠀⠀⠠⠀⠀⠀⠹⣦⣀⣾⣧⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡿⣛⣿⣦⣀⣀⣴⠃⠀⣰⠃⢀⡞⠀⠀⠀⠀⠀⠀⠹⣆⠀⢳⡀⠀⢳⣄⣀⣠⣿⣋⡻⣽⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣽⣿⣭⣿⣻⣶⢾⣇⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣿⢶⣟⣹⣯⣿⣽⡽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠛⠋⠁

⠀⢠⣤⣤⣤⣀⡀
⠀⣮⣾⣾⣿⣴⣦⡉⠛⢶⡤⠀⡀
⠀⠻⣷⣿⣾⣿⣿⣟⣷⣶⣾⣿⣷⣦⣄⢀
⠀⠀⢸⣯⣇⣻⣿⣟⢛⠛⣯⣽⣿⣿⣿⣿⣧⣆⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢹⣿⡻⡟⢿⣍⣉⣹⡏⠀⠀⣠⣿⣿⣟⣷⡀⢄⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠈⢻⣿⠟⢻⣷⠤⠬⢿⡀⠰⣿⣿⠛⠉⠛⣝⢦⡁
⠀⠀⠀⠀⠘⢿⣿⢿⣿⣦⠴⠐⠚⠳⢬⡁⠀⣤⣿⣿⣷⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠘⡿⠶⠾⢿⡷⠒⠒⠒⠒⢿⣷⣮⣙⠻⡟⠛⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠐⢦⢿⡿⠿⢻⠦⠀⠀⠠⠶⣿⣿⣿⡟⠲⢄⡈⢻⣿⡄⠀⠀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠈⢙⣿⠻⢻⣴⠂⠀⠒⠒⠚⠻⠿⠷⢤⣀⣹⣿⣿⣷⣤⣞⣻⣿⡿⠃⠀⠀⠀⣀⣀⣤⣴⣦⣦⣤⣆⣴⣶⣒⡲⠶⠤⣤⣤⣀
⠀⠀⠀⠀⠀⣠⣼⠿⣿⠋⣉⣩⡷⠒⠚⠉⠉⠉⠙⠃⠐⠢⢭⣝⣻⣿⣿⣿⣿⣿⣧⡶⠾⠟⠛⠛⠛⠛⢛⣻⣶⡾⠒⢶⣷⣭⡍⣙⡛⠶⢦⣌⣹⣶⣤⣀
⠀⠀⠀⠀⠀⣼⣹⣷⢿⡋⠁⣞⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠋⢙⣿⣿⣛⣿⣟⠿⢿⣿⡟⠿⠻⠶⠀⢤⣰⣿⠿⠃⢀⡽⣷⠇⠀⠈⢿⡗⠲⢶⣿⣿⣞⣛⢷⡆⡀
⠀⠀⠀⠀⢀⣼⣿⣤⣿⡟⢁⡼⠶⣤⣤⣤⣤⣶⠛⠁⠀⢀⡴⢪⣟⠦⣽⣿⡿⠋⠐⠈⡙⠢⣄⣀⣰⣾⣿⣿⣿⣲⢬⣿⣇⣀⣠⡤⡞⠑⢦⣴⣿⣽⣿⡟⣯⣅⣿
⠀⠀⠀⠀⠀⣿⣿⣱⣼⣿⡏⢀⣴⠁⠉⣡⠝⠁⠀⢀⣴⠟⣰⣿⣮⣿⡟⡀⠀⢰⡀⠀⠈⠲⣄⠙⠿⣿⡽⢏⡀⠁⠀⠉⠀⡈⠹⣦⣉⣷⣿⡛⢣⣭⢻⣧⡾⠟⠛
⠀⠀⠀⠀⠰⣿⣛⣫⣼⣿⣿⣿⣿⣤⣤⣧⣄⠀⣠⣾⠋⣰⣿⣿⣿⠏⣰⠇⠀⢰⣧⠀⠀⠀⠘⣿⠢⣬⣿⣶⣽⣆⣀⣶⣴⣼⣿⡟⣻⣞⣽⡷⡮⠟⠉⠉
⠀⠀⠀⠀⠀⣼⣿⡟⢫⣙⣿⡿⣻⣿⣿⣛⣿⡖⣷⠃⢰⣿⣿⠟⢁⡼⠋⠀⠀⢸⠟⣧⡀⠀⢀⡿⣦⣘⣷⣿⡿⣿⣿⣯⣽⣷⣾⣿⠟⠛⠋
⠀⠀⠀⠀⣸⢋⡔⠂⠀⣟⠿⠛⢿⡟⠘⠛⡟⣭⠏⠀⠘⠋⠁⡀⣺⠶⣶⣄⠀⣾⠀⢸⠉⠛⠈⣇⣸⡿⣶⣿⠇⠀⠉⠀⠉⠁⠀⠈
⠀⠀⠀⣴⡷⠋⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠉⠁⠀⠀⠀⠀⣠⠌⢿⡿⣸⣿⣀⡏⠀⣾⡀⣰⣶⡟⠻⣦⣿⣇
⠀⠀⠸⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⣠⣴⣿⣿⣿⣷⣴⣿⣿⣿⡋⢻⣤⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡿⢙⣿⢿⣿⢣⣿⣀⣿⣷⣾⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢻⡿⢷⣤⣿⣿⣿⣿⣿⡿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠳⣿⣿⡿⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣤⡀⡀⠀⠀⠐⢼⡆⠀⡶⡄⠀⢀⡀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠇⠘⠃⢸⣦⣼⠂⠘⢻⣯⡄⠘⠂⣸⡇⣰⣿⣃⣤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠐⠄⠀⠀⠀⠐⠀⡙⣿⣿⣿⡄⠀⣽⣇⠝⠓⣿⣿⣿⣿⣿⣿⣦⠟⠁
⠀⠀⠀⠀⠀⣠⣄⡀⠀⠤⢀⣀⠀⠀⠀⠀⠀⣁⡿⢻⠯⣁⣰⢿⠓⠰⣿⣻⣿⣿⣿⣿⣿⣷⡿⣂⣀⣀⡰
⠀⠀⠀⠀⠐⣿⣿⠟⠶⠜⢿⠃⠀⡀⠀⠀⣀⣶⡊⠀⠀⠤⠘⠋⠀⠩⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣹⣾⣶⣦⡄
⠀⠀⠀⡄⢀⢸⣿⣶⠀⣦⣠⣾⣿⣿⣆⠔⠻⠻⠟⢀⡀⣠⣶⡀⠀⠀⠀⢠⣴⣿⣿⠿⠿⠻⣿⣿⣿⣿⣟⣟⡃
⠀⠀⠈⢗⡊⠛⢻⡏⢙⡓⣿⣿⣿⠻⠓⠀⠀⠒⠀⢀⠘⠁⠀⠁⠠⣠⡀⣠⣼⣟⣙⠶⠛⠓⣏⡰⡾⢷⢿⣿⣦
⠀⠀⠀⢘⣷⣿⣿⣿⠿⠉⠀⠀⠁⠂⢤⠠⣮⣿⣷⣦⡌⠈⣢⠀⠀⣩⣯⣿⣽⣿⣿⣿⣟⣩⡀⣰⣶⣾⣷⣿⡛
⠀⠀⠀⠀⠤⠖⢉⡙⠂⠀⠀⡀⢀⣶⣀⢀⣉⠫⣍⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⠛⣿⣏⡉⣥⣼⣿⣿⣿⣧
⠀⠀⠀⠘⠛⠿⠍⢀⠘⣴⢴⣿⣾⡟⠻⢋⣉⣰⣾⣿⣿⣿⣿⣿⣿⢿⣿⠟⢿⡿⠾⠛⣙⣽⣿⣿⡾⣿⣿⣿⣿⠁
⠀⠀⠘⢛⢻⣿⣇⣰⡤⠖⠛⠋⠀⠠⣠⣿⡿⠟⠛⠻⡿⠿⡿⢋⠘⢦⣭⡾⠶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⣅⢄⢀⡈⢣⠀⠰⣶⡂⠹⠁⠉⠁⠀⢀⣘⣤⣄⣶⡷⣄⡐⡻⣖⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯
⠀⠀⠀⠀⠀⣯⡅⣈⠁⠀⠀⡉⠀⠀⣤⢀⠣⢼⣿⣿⣿⣿⣷⣶⣶⢻⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⣠⢾⣿⠟⠁⠷⠠⣾⣾⣦⣏⣸⣿⣾⡏⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠏
⠀⠀⠀⠀⠁⠘⢁⣴⣆⠙⢻⣿⣿⣿⣿⡿⢿⡟⠹⠇⠈⢿⣿⡏⣼⠛⣿⢿⣿⣿⣿⠿⣿⣿⣿⣿⠻⡃
⠀⠀⠀⠀⠀⢰⣾⢿⠟⠱⣾⣿⣿⠟⠿⠀⠈⠁⣀⡀⠐⢸⣿⡇⠀⠀⠁⠀⠁⠀⠋⠀⠉⢿⡏⠁
⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⠈⢸⠋⠀⠀⠀⠀⠈⠉⠀⠈⢸⣿⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢸⣿⣇⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣀⡶⣦⣽⣆⣳⣤⣿⡞⣸⣿⣯⣥⣗⣶⣶⣘⣮⣷⣦⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣀⣀⣁⣙⣉⣛⣙⣙⣋⣋⢻⣿⣿⣿⣿⣯⣛⣻⡛⣛⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡇⠸⣿⣿⣿⣟⣻⣿⣿⡿⣿⣿⣅⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠉⠉⠉⠉⠁⠙⠉⠩⠿⠋⣢⠙⠿⣿⣭⣧⠭⡭⠭⠭⠀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣀⣐⣀⡀⠀⠀⢂⠀⠁⠐⠚⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠐⠀⠉⠈⠉⠛⠛⠻⠹⠏⠽⠛⠀⠀⠀⣀⠈⣕⡸⠀⢦⣠⣦⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠆⠀⠰⢿⡴⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢠⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⣇⠈⡇⡀⠀⠀⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠲⠚⢻⣿⣿⣿⠿⠶⠶⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡆⢻⡜⡄⠀⢠⠀⠄⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠚⣡⡾⠉⠉⡡⠄⢀⣈⢩⣶⣾⢣⡀⠀⠀⠀⠀⠀⠀⠀⣦⡆⢧⠈⢿⣜⠀⢐⡄⢀⠈⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠘⠹⣦⠟⣿⣿⣷⠀⠀⠀⠀⢠⣶⣼⣿⣧⠈⢇⠈⢿⡂⠀⠀⣀⣠⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠚⣡⣿⣿⣿⣿⠀⠀⡀⠀⠈⠿⢿⣿⣿⣿⣎⠢⣀⠛⠲⣶⣝⣿⣦⣿⠇
⠀⠀⠀⠀⢀⣎⡀⠠⠃⠀⠀⠀⠀⠠⠐⢁⣴⣿⣿⣿⣿⠟⠀⠀⠀⣠⣤⣤⣀⣿⣯⣿⣿⣷⣬⠑⢄⡙⠿⣿⣿⡿
⠀⠀⠀⠀⢠⠟⡄⠁⠀⠀⠀⠐⢀⣴⣀⣨⣿⡿⠛⠃⠀⠀⠀⠾⡿⣿⣟⣻⡿⠛⠙⣿⡿⢹⣿⣿⣦⣬⣑⡢⣝⡗
⠀⠀⠀⠀⠀⣆⠀⢀⣀⢤⣔⠠⢚⣽⣿⡿⠋⠀⣠⠎⠀⠀⠁⣰⠟⠉⠉⠙⢿⣤⣴⡿⢁⣾⡿⠿⠿⠛⠛⠛⠺⠃
⠀⠀⠀⠀⠀⠘⠢⢽⣞⠯⣖⣤⣿⣿⣿⣷⢴⡶⠋⣀⣀⣤⣾⠏⠀⠀⣀⣤⡾⠃⣀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠀⣸⡀⠊⠀⠉⢙⣥⣄⡠⠴⠋⣀⣴⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣍⣙⣒⣒⢒⣁⣀⣠⣤⠖⠋⠁⢓⣿⣯⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⡟⣻⡟⠁⠀⠉⠀⣰⣯⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣽⣷⣍⣀⣠⠀⣀⣭⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠶⠶⠒⠚⠛⠛⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣂⣀⣀⡀⠤⠤⠤⠤⢼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠉⠁⠀⠀⠸⣄⣀⠀⠀⠀⡔⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠂⠀⠁⠀⢸⠆⢀⡠⠛⠉⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡋⠸⠉⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⢀⣠⣀⠀⠓⢁⣀⣡⡤⣤⠤⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠉⠁⠀⠀⠨⠉⠉⠀⠘⡀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠑⠊⠀⠀⠀⡇⠀⠀⠀⠛⠲⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠤⣄⡀⠀⠀⠀⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⢄⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⣀⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠳⡀
⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠪⡉⠉⠀⠀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠹⡄
⠀⢠⠏⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠⣃⣨⡀⡠⠨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢃⠀⠀⠀⢻⡀
⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠈⣧
⢸⠁⠀⠀⡀⠀⠀⣀⡀⢠⠲⠀⠀⠖⠉⠑⠐⠍⣉⠁⣶⠓⠂⠒⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢹
⡟⠀⠀⠀⠁⠀⠀⠇⠀⠆⢀⠀⠄⠀⠘⡃⠀⡀⢩⠤⠟⠸⢄⡄⢨⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠀⠀⢲⡀⡏⢀⣀⡧⠴⠑⠆⠻⠞⠀⠐⠀⠴⠧⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⣇⠀⠀⠂⠀⠀⠀⠓⠃⠉⠁⠀⠀⠀⡀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇
⢻⠀⠀⠀⠀⠀⠀⡤⠒⢒⡆⢮⡁⠚⢉⠎⠁⣄⠀⣡⡎⢦⠖⢲⠋⢉⠑⢂⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠺⠃
⠸⡄⠀⠀⠀⠀⠀⠢⢄⡈⠑⠀⢹⠆⡌⠀⠀⢠⠘⠣⡇⠀⠀⣼⠀⡬⠤⠞⠀⠀⠐⠂⠀⠀⢰⠂⠀⠀⡶
⠀⢷⠀⠀⠀⠀⠀⢘⢉⣀⠴⠣⣅⡼⠁⠸⣀⡄⠑⠖⠉⠒⠒⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠃
⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢠⠏
⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠀⠀⢸⠄⠀⠀⠀⠀⠀⢀⡎⠀⢀⡞
⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⡤⢤⠀⠀⢀⠀⠀⠀⠀⢠⠎⠀⠀⠘⣧⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠉⠳⣦⠄⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⢀⡴⠁⣀⡤⠔⠊⠀⠀⠀⠀⠈⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠶⠤⠤⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣰⡯⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢥⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⣀⣀⠤⠴⠒⠚⠛⠉⠉⠙⠓⠲⠶⠦⠤⠴⠶⠖⠚

⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠠⡇⠑⠦⠀⣀⡀⣠⡀
⠀⠀⠀⠀⠀⠀⣴⡃⠙⢦⡄⠀⠀⠉⠙⠶⠶⠦⣄⣀⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠘⢷⣄⢀⠃⠀⠀⢀⡄⠈⠙⠱⣦⠼⢷⡀
⠀⠀⠀⢠⡾⢟⠁⠀⠄⢠⠤⠽⣦⡀⠀⢀⣈⠤⠄⠀⠀⠀⠀⠈⢷⣦
⠀⠀⢀⡸⠃⠀⠡⢀⠀⠀⠀⠀⠙⢿⣦⡟⠀⠀⠀⠀⠀⡰⠥⠄⠀⠙⢶⡀
⢀⣴⠿⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠂⢿⣷⡀⠀⢀⠄⠁⠀⠀⠀⠀⢀⠈⢷⣄
⠈⣏⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠉⣷⡴⠋⠐⠐⠰⣔⠃⢀⠦⠄⠈⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⢀⣀⠀⠀⢀⡀
⢰⣿⠂⠀⠀⠉⠁⢂⡠⠤⠀⢄⣀⡀⡀⠱⣿⣷⠀⠀⠀⠀⣠⡴⣥⣀⡀⠀⢿⠄⠀⠀⣠⠶⠶⠖⠟⠃⠀⠉⠉⠙⠋⠉⠉⠹⠓⠂⠴⠢⠄⡰⠂
⢸⣇⠀⠀⠀⠂⠞⠀⠀⠀⡠⠄⠉⠉⠉⠻⣿⣿⡀⢀⡴⠋⢀⢴⣿⢏⡁⠖⢸⠆⣤⠞⠉⠀⡁⠀⠀⠀⠀⠀⠐⢤⠀⠀⠀⣀⣀⡤⠖⠁⢠⠃
⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢈⣿⡷⠋⡾⠋⢀⣾⣵⣾⡇⣿⣯⡼⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⣦⣴⠟⠋⠅⠀⠀⠀⡀
⠈⢧⣄⠀⠀⠀⠐⠂⠚⡙⣿⣆⡂⠠⠀⡂⢨⣿⣧⠞⣁⠴⠛⣱⡟⠉⣟⠻⢏⠀⣀⠀⠀⠀⠀⠀⠈⠑⡀⣀⣶⠿⠟⠛⠂⠀⠀⠀⠀⢰⡇
⠀⠈⢧⡀⠀⠀⢸⡶⢾⡿⠻⣌⠛⢓⢦⣼⡟⠉⠀⠈⠀⠀⣴⣿⡄⢠⠌⠀⢰⡆⠀⠀⢀⠀⠀⠀⠀⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃
⠀⠀⠀⠁⠠⠈⠁⠀⠈⠀⠋⡙⣲⣤⣽⣿⣿⠀⠀⠀⠀⠐⠁⠀⣴⡇⣰⣆⣸⣀⠀⠀⠀⢑⠄⣠⣾⠟⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢘⡷
⠀⠀⠀⠀⣤⠀⡄⠀⠀⣀⣠⠿⠗⠀⠀⢻⡟⡀⠀⠀⠀⠀⣠⣾⣿⣶⣿⢿⣿⡿⣀⣴⠾⣛⣿⣿⣿⡦⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⢛⠊⠑⢀⡀⠀⢹⣆⣀⡀⠠⣼⣷⣆⠀⠀⠀⣈⣩⣭⣭⡿⢷⣾⣿⣿⢋⣴⠛⠉⠉⠀⠉⠁⠘⢿⡶⣤⠀⠀⠀⠀⠀⠀⢀⡷
⠠⠄⣀⠐⢼⣄⣷⣿⣟⣛⣛⢛⡛⣻⠿⣿⣟⢛⠛⣿⣿⠋⢀⡾⠋⠈⠀⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⡛⠳⠆⠀⠀⠀⣠⡏
⠀⠀⠀⠋⠀⠹⢿⣿⠻⠿⢿⣿⣿⠁⢀⡟⠋⠙⢻⣿⣯⡖⠁⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⢀⡠⠖⠛
⠀⠀⠀⠠⠚⠀⠜⠋⠁⠲⢿⣿⣷⢀⡾⠓⠀⢀⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣀⣀⣤⣤⣠⣴⣿⣿⣿⣋⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣇⠀⢀⣤⣿⡿⣿⣿⣼⣄⠀⠀⠀⢀⡔⡺⢿⣿⣿⣿⣿⡿⣫⣿⣿⡿⠏⠀⠈⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⢑⣿⠟⠛⠁⠈⠑⠉⢻⣿⣦⣤⠾⠒⣀⣀⡉⠉⠛⠛⣟⢿⣿⡇⠀⠀⠀⠀⠈⢸⡆⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡶⢛⠋⠁⠀⠂⣀⠀⠀⠀⢿⢉⡴⠛⠛⠛⠻⣍⢢⡀⠀⣿⡗⢸⣷⠄⠀⠀⠀⠀⣴⣿⣠⠀⠀⡐⠀⢀⣠⣶⡿⠋⠀⠀⠸
⠀⠀⠀⠀⣀⠄⠒⠂⠀⠈⠉⠒⢝⢻⣿⣧⣀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠆⠀⠀⠀⠀⠈⠇⢹⡀⠸⣧⣾⣿⣶⣦⣤⣤⣼⣿⣾⣧⠅⠀⠁⠀⠈⠉⠀⠀⠀⠀⣰⣿
⠀⠈⡍⠁⢤⣴⣶⣶⣤⠤⠀⣀⣼⣾⣿⣿⣯⡀⠀⠀⢀⣀⣀⣤⣿⣿⣄⠀⠀⠀⠀⢄⠘⣺⡇⠀⠙⠿⣿⣿⣿⣭⣭⣿⠿⠋⠀⠀⠈⠠⡀⠀⠀⢀⣀⠔⣺⣿⠏
⠀⠀⠷⣀⠀⠀⠀⢀⣀⣤⣶⣿⠟⡇⠻⣿⣿⣿⣷⣿⣿⣿⡿⠛⠙⢿⣿⡄⠀⠀⣀⠀⣀⣿⠃⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠐⠲⠶⠞⠚⠉
⠀⠀⠐⡀⠈⠉⠉⠉⠻⠋⣹⣿⡾⠁⠀⠀⠉⠉⠛⠛⠋⠁⠀⠀⠀⠀⠙⠻⠿⠦⠼⠿⠛⠒
⠀⠀⠀⠈⠒⣶⣤⣦⣴⡞⠉⠉
⣿⣿⡟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠿⠓⡢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣦⣴⣇⣀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⡰⠛⡝⠀⠶⠆⠀⠀⠀⢀⠀⠀⢸⡆⠀⠈⡖
⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠟⢨⣿⠀⠁⠀⠀⣢⠀⠀⠀⢢⡠⣼⠇⠀⢀⣿⡀⣷⣆⡄
⠀⠀⠈⠁⠐⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣐⡿⠿⠂⠀⠀⣴⣿⠂⡄⠀⠸⣿⠃⣠⢤⣼⣿⣶⣯⣿
⠀⠀⠀⠀⠀⢀⡟⠛⠻⠷⣶⡶⢤⠄⣠⢤⠘⣆⣤⣴⠰⠟⠿⠉⠁⣐⣾⣿⣿⡯⠀⠀⣶⢲⡆⢠⣌⣵⣾⣿⣷⣿⡿⠇
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠸⢿⣀⣄⠊⠲⣠⡶⠄⣿⣩⣷⣿⡿⠟⠿⠛⠟⠉⠉⢍⣙⠻⠃⠀⢀⠈⠩⣙⣿⡇⢮⠑
⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠲⢿⣿⡇⣰⣿⡀⠀⠀⠀⠉⢻⠀⠠⡠⣦⣵⣤⣶⣾⠁⠀⢨⣁⣈⣠⣴⣿⡿
⠀⠀⠀⠀⠀⠙⠷⠖⠒⠒⠒⠿⢣⠏⣼⣿⣿⣿⣤⣄⠀⠀⢸⣧⣤⣤⣼⣿⣿⣿⣿⣦⠀⠈⢿⣛⣻⣿⣿⣇⡾⣸⡄
⠀⠀⠀⣴⠿⠶⣤⣶⣶⣿⣿⣿⣏⣸⡿⣿⣿⣿⣽⣿⣟⣿⣿⣿⣿⣿⣿⣿⣛⠿⢿⣿⣧⣠⣼⣿⣿⣿⣿⣿⣿⣿⣅⠄⣦
⠀⠀⠀⢋⢾⣽⠟⠉⠡⠀⠉⢋⣾⡟⣷⡘⣿⣿⡍⢹⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠟⢻⣞
⠀⠀⠀⣿⣽⠁⠀⠀⠘⣄⢂⣼⢿⣿⠙⣿⢻⣿⡟⣻⡦⣾⠟⢾⣷⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡿⠟⠁⠐⡛⣿⡀
⠀⠀⣶⣿⡃⠀⢸⡁⢀⣳⡞⡃⠸⠸⠃⣿⢸⣿⡆⣿⣷⡿⢶⢾⣿⣿⣿⣿⠀⣻⣟⣿⣿⣿⣿⣿⣿⣽⡆⢀⠆⠀⡥⠏⠉
⠀⠀⢿⣿⣧⡀⠀⠳⢾⠟⠣⠈⡝⠂⢢⣯⡘⠿⣷⡻⢿⣿⣿⣿⣿⣿⣻⣿⣶⣿⠷⠿⠿⠯⠫⠁⠉⢾⣥⣡⡤⣰⠅
⠀⠀⠈⢻⣷⣍⠀⠀⡀⠀⠀⠊⢀⡴⠋⠉⠉⠀⠀⠉⠻⣟⣾⡿⣿⣿⣿⠿⡿⠋⠉⠉⠻⣿⣿⣻⠿⠯⠟⠛⣿⣏⡀
⠀⠀⠀⠠⣬⣿⣿⣷⣷⣶⣶⣿⣿⣶⣶⣶⣶⡶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟⢡⡀⡍⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡩⠥⠎⠄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣫⠤⣌⠍⠲⣄⠀⠀⠸⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡃⣝⣁⡼⢸⠀⢹⠀⠄⣢⢹⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠛⠷⢄⠀⠐⠁⠀⠀⠆⢉⠁⡘⡇⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣏⣖⡒⢦⠢⠁⠀⠀⠀⠀⠐⡀⠒⠁⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠈⠫⠥⠞⡠⠁⠀⠀⠀⢄⠀⠀⠀⢚⠃⠄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠦⣄⠀⠀⢸⡧⣿⢀⠀⢄⢈⠀⠀⠀⠀⠀⠀⣑⣤⣷⣾⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣛⣤⣼⣧⡀⠈⣷⢻⠘⡡⠜⠘⠀⠀⣀⠬⣴⣿⠟⠛⠛⠁⠀⠀⢀⣴⠾⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⡘⢿⠻⡻⣆⣷⡀⠘⢿⣧⣀⣠⠴⠒⠉⠀⠾⠛⠁⠀⠀⠀⠀⠀⢠⣿⡜⣅⠔⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠖⣋⣉⣾⣷⣽⡟⢿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⠟⣳⡤⠚⣫⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣻⡄⢿⣟⠿⣧⠈⣇⣘⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡾⡟⣩⢷⡂⢁⠷⣻⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣽⠓⢢⣿⣗⠘⢧⣹⣿⣷⢹⠀⠹⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣓⢿⣿⡡⠞⣯⡠⠞⣹⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣧⣰⣿⡿⠯⠁⠀⠻⣿⠟⣿⡇⠀⠀⠀⠀⠃⠀⠀⠀⢴⠀⠀⠀⠸⠻⠳⠤⣧⣛⡤⠂⢉⣧⠔⠁⠾⡇
⠀⠀⠀⣀⣤⣤⣶⣤⣬⣝⣿⣇⠀⠀⠀⠈⠙⠆⢻⡇⢠⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡷⠋⡷⣳⣯⡴⠚⠉⣹⡖⠁⠘⠓⢲⡀
⠀⢀⣞⣻⡟⢽⣿⡄⢟⣆⣹⣟⣿⢾⣵⢶⡄⢸⣼⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⡠⢠⠿⣿⡾⠛⠉⣉⠴⣮⡤⠀⠉⢙⣦
⠀⢸⡭⣝⠰⠶⠦⠼⣏⡁⠐⠬⠝⣺⣿⣓⣽⣶⣿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⠇⢃⠂⠀⢠⣿⢾⠋⢁⡈⠩⢷⡶⠒⠚⠛⣦
⠀⠘⢗⣻⣇⡚⢃⣬⣉⡝⣻⣿⣯⣽⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣄⣠⠀⠀⠹⢾⣝⣇⣀⠀⢘⣷⣂⠀⠈⠙⢂⣤⣄⣀⡀
⠀⠀⠈⠓⠾⠧⠾⠷⠚⠋⠉⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⠶⠦⠤⣟⣼⣧⡤⠤⣼⣇⡀⢾⣙⣯⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠈⠉⠓⠶⣾⣁⢾⣍⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠶⠖⠒⠚⠛⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⠼⠦⠔⠒⣖⠀⠀⠀⠀⡛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠀⠈⠙⡆⠀⢀⠧⢶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢐⢡⠚⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⢀⠤⣀⠘⢊⣀⣣⠤⠤⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠬⠁⠀⠈⡀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠉⠀⠀⠀⣇⡀⠀⠈⠉⠙⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⣠⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⡀⠀⠀⠉⠲⢄
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠱⡄
⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠲⡙⠁⠈⢩⠙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⢄⠀⠀⠘⣆
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢰⡡⢤⣀⠄⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢂⠀⠀⠸⡄
⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠤⢀⢀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢷
⡜⠀⠀⠀⠀⠀⠖⢀⠋⠁⠀⠁⢤⠀⠀⠲⢀⡇⡈⠈⠀⡼⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⡄⠰⢆⠐⣆⡰⢄⠸⣬⠍⢄⢈⣿⣀⣱⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⡇⠀⠀⠀⠀⠀⠖⠁⠚⠀⠉⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⢧⠀⠀⠀⠀⠀⠔⠒⣢⠲⡁⠊⠱⠋⢠⠀⣡⠊⠴⢲⡎⢉⠑⡄⠀⠀⠀⠀⠀⠸⠀⠀⢸⠃
⠸⡀⠀⠀⠀⠀⢓⡤⠈⠂⡸⢂⠀⡀⠠⡌⠑⡆⠀⣸⠃⡖⠐⠃⠀⠀⠁⠀⠀⡏⠀⠀⡏
⠀⢳⠀⠀⠀⠀⠠⠐⠒⠁⠓⠊⠀⠓⠒⠈⠉⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣸⠁
⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⢠⠀⠀⠀⠀⠀⠀⡌⠀⢠⠃
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⣀⡀⠈⢁⠀⠀⠀⠀⠜⠀⠀⢯⣀⣀
⠀⠀⠀⠀⠀⠙⠲⡤⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⡠⠊⣀⡠⠔⠉⠀⠉⠉⠉⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠶⠦⠤⠤⣤⠤⠤⠤⠤⠤⠼⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣉

⠀⠀⠃⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⣘⠃
⠈⠀⠀⠘⠄⠀⠀⠀⠀⣀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠌⠀⠔
⡁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡀⠀⡆⠀⣂⠀⠀⠀⠀⠀⠈⠱⠄⠀⠀⠀⠗⠀⠀⠈⠓
⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡠⢃⠀⠁⠀⠻⣤⠀⠀⠀⠀⠠⠀⠀⠰⠄⠀⠰⣄⠀⠀⠀⠘
⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠺⠉⠁⠀⠀⠀⠀⠉⠳⢄⣀⡀⠀⠀⠀⠒⠂⠀⠀⠈⠽⠠⠄
⢀⡔⠢⠄⢤⣀⠀⠀⠀⠙⠁⣀⡤⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠂
⠋⠀⠀⠀⢀⣿⠆⠀⡴⠚⠉⠀⠀⢠⠏⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠄⠀⠀⠈
⢷⣤⣤⣤⠾⠋⢀⡎⠀⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠂⠀⠀⡐⠀⠄
⠀⠀⠀⢀⣤⠖⠛⠁⠀⠀⠀⢀⡤⠒⠀⠀⠀⠀⠀⢠⠶⠛⠛⠒⠠⠂⠠⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⢰⠋⠁⠀⠀⠀⠀⠐⠀⡸⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠘⠆⠐⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐
⠀⠀⠸⣄⡠⠄⠂⠀⠀⠀⠀⠀⠒⠀⠀⠀⢼⠁⠀⠀⠀⠀⠄⣀⡀⠔⠁⠀⠀⠀⠂⠀⠀⠌⠁⠀⠈⠀⡀⠈⠂
⠤⠄⠀⠀⠀⢈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠐⠀⠀⠀⠀⠀⠁⠀⢂⠄⠀⣢⡷⠀⠐⠏⠀⢀⣠⢄⠔⠀⠀⠀⠀⠀⠠⠔⠂⠀⠈⠀⠀⠀⠠⠄⠀⠀⢰⡇⠈⠙⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠖⠀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⣀⠔⠋⠈⢷⡀
⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠙⢦⡀⢀⠀⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⡁
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠀⠈⠙⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠳⣄
⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤
⢁⡀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠀⠀⠀⠀⠀⠅⠀⠀⠀⠠⠂⠠⠍⠁⠀⠚⠛⠃
⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠈⠂
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠈⠈
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠊
⠀⠈⣆⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠓⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢀⠄⠀⠠⢄⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠛⠃⠀⢰⡁⠀⠀⠀⠀⠱⡄⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⠋⠹⠲⡆⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢉⠏⠱⡀⠑⠒⠦⢄⡀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠴⠃⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣦⣤⡎⠀⠀⡈⡐⠠⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢋⠵⢮⣤⠈⡀⠈⠀⠀⠁⠀⠨⠱⠄⠀⠀⠀⠀⠀⠀⠀⣸⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡴⠃⠀⠀⠀⠉⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣋⠀⠀⠸⠀⠠⠐⡆⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠠⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⢤⡀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⢀⡞
⠀⡠⠖⠉⠉⠙⠲⡀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢰⠒⠊⠀⠀⠀⠀⢠⠎
⡞⠀⠀⠀⠰⠉⢀⣇⣀⣠⠴⠚⢅⡠⣆⠐⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠧⠄⠠⠔⢢⠀⢀⠇⠀⠀⠀⠀⠀⣠⠏
⣇⠀⠀⠀⠀⠀⠀⠁⠀⣀⢴⡴⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⢠⠏
⠈⢦⣀⣀⣀⣀⠤⠔⢊⡵⠋⢠⠞⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠏
⠀⠀⡠⠋⠁⠀⠀⢠⠟⠀⠀⣏⠘⢱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠢⠤⠤⠤⠤⠤⠖⠚⠉⠙⠁
⠀⢰⠇⠀⠀⠐⠀⠙⢆⠀⠀⠈⠉⠉
⠀⠘⡇⠀⠀⠈⠀⢀⡞

⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣄
⠀⠀⠀⣸⠋⣀⣉⣐⡒⠨⢕⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣚⠭⠒⣂⣈⣀⡈⢳
⠀⠀⠀⢸⡍⡡⠤⠤⠭⣍⣒⡟⠚⠓⢄⠀⠂⠀⠀⠀⠀⠀⠀⠠⠂⣠⠔⠛⠺⣖⣫⡭⠥⠤⢄⡉⣿
⠀⠀⠀⠀⢷⡀⠂⠒⠒⢒⣲⢷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⢗⣒⠒⠒⠂⠀⣼⠃
⠀⠀⠀⠀⠈⢷⡈⣉⣉⠀⠈⠩⣍⣳⣦⣀⡀⠑⣄⠀⡀⢀⠞⠁⣀⣤⣖⣉⡭⠉⠀⢈⣉⡁⣰⠃
⠀⠀⠀⠀⠀⠀⠻⢦⣀⣤⠄⠠⠤⠤⠤⠤⣭⠷⢮⡶⢺⣧⠶⢯⡥⠤⠤⠤⠀⠒⢤⣄⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠝⠛⠉⢙⣛⣛⣉⡩⢽⣷⣼⡿⢭⣉⢛⣛⣋⠉⠛⠛⢍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥⠒⣉⠡⢤⠞⠉⠀⣠⠃⡿⢸⡏⢦⠀⠉⠑⢤⠤⢉⡑⠦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠁⡀⠔⣧⣀⣤⠞⠙⢰⠃⠆⢧⢠⠙⣦⣀⣨⡇⠄⡈⠑⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡠⠋⡠⠊⢀⠃⠘⠀⢠⡞⠐⠆⠸⡜⠀⠸⠀⢇⠈⠢⡈⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⠁⢀⠂⠀⠀⠀⣸⠁⠀⠀⠀⢳⡀⢀⠀⠈⢆⠀⢳⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣤⣤⠴⠞⠁⠀⠀⠀⠀⠀⠙⠾⣤⣤⡼⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢪⣵⠖⠒⠛⣩⠭⡄⢐⣒⠒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣪⠋⠁⠀⠀⠀⠀⠐⠻⠈⢠⠚⣡⡾⣯⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠲⠙⠅⠉⠉⠉⠛⠽⢶⣄⠀⠀⢈⣴⣿⢿⣫⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢻⣿⣿⣿⣿⣿⣯⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⡪⠔⠉⠀⢢⠀⠀⠉⠭⡻⢒⠶⣤⣄⡀⠀⠄⡌⣾⣿⣿⣿⡟⢗⢀⣴⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⣫⠕⡾⠅⠀⠀⠀⠀⠀⠙⠢⠤⠤⠴⠔⢊⢟⣥⣿⠈⢞⣼⢿⣿⠿⠗⣠⡾⣿⡿⡿⡧
⠀⠀⠀⠀⠀⠀⣺⣅⠀⠲⠋⢡⠀⠀⠬⠄⠀⠀⠀⠀⠀⠀⠀⢀⠤⣪⣵⣽⣿⣿⠄⣽⣿⡿⠿⠥⠾⣿⢾⣝⣝⡴⠋
⠀⠀⠀⠀⠀⠀⣿⠪⣍⣙⠳⠶⣭⣑⠢⢌⣀⠔⢒⣲⡖⠐⣪⢵⣺⣿⣿⣿⣿⣟⣨⡾⠭⠁⠀⠀⡄⣿⣫⣫⣾⠣⣄⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠩⢝⡳⢶⠬⢿⣶⠤⣒⣫⢴⣾⣽⣾⣿⣿⣿⣿⠿⠿⢎⣁⣀⣀⠀⡄⣶⡃⣾⣿⠿⠧⣭⠁⠘⠿⠓⠢⢤⣀
⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⡒⠬⢅⡋⠃⠊⢹⠒⠾⢵⣟⣻⣿⢻⠿⠻⠉⠉⢁⣀⠤⣞⡽⡷⣽⢧⠻⣟⡿⠶⠒⢙⡧⢠⡁⠞⢚⣠⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣶⠬⣝⡛⠴⡬⠍⣽⣿⣿⠛⠫⠏⠀⠈⠉⠁⡠⢮⣾⣾⡇⡎⢦⣞⠁⠀⠀⡘⠀⠈⠒⠭⢗⣿⣿⣯⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠿⠓⡡⢍⣉⠛⠴⢼⠿⠭⠅⠈⠉⠀⠀⠀⢀⢔⣔⣟⣽⣿⡇⣦⠏⠀⣀⠤⠊⠀⠀⠀⠀⠀⠒⠀⠉⡏⠉⡓⠲⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣶⠥⠤⠪⠁⠀⢃⡀⠤⠬⠷⣒⠂⠀⢀⠤⠄⢲⠖⢒⣵⡷⣳⣫⣿⣿⠛⠍⠁⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⢀⠘⣄⠀⠣⢋⡤⢞⣥
⠀⠀⠀⠀⠀⠀⠀⣯⠍⣉⣀⣒⠒⠂⠠⠬⠍⢉⣙⣒⠊⠥⠤⠬⠥⢒⡽⣫⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣠⠤⡺⠴⣚⡥⢖⣩⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣒⣒⠒⠈⠭⠭⠭⠀⢒⣒⣒⣶⣚⣒⣟⣤⣥⣾⢾⣿⣿⣷⣴⡤⠐⠶⣶⠠⢄⡀⠀⣀⡠⠄⣂⡨⠱⣐⣭⣶⣿⣷⣾⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢱⠶⡰⢬⠭⣭⣩⣀⣐⣒⣒⡒⣲⢒⡒⣒⢒⣚⣺⡿⢕⠅⠀⠉⠺⢗⡦⢭⡙⣂⣨⠭⣔⣲⡯⢷⣿⣿⣿⣟⠿⠒⣉⠤⢖⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢺⡓⠉⠢⠕⠦⣑⠂⠊⠴⠩⢚⡕⣨⠌⡁⢩⢌⠄⡹⣷⣵⠀⠀⠀⠈⠛⡗⠪⣻⣿⣯⣼⣾⣿⠿⠟⣋⠡⢔⣚⣭⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢼⠂⠀⠀⠀⠀⠈⠑⠺⢦⡤⠤⠔⠐⣤⣄⣠⢔⣾⣶⣟⣽⣷⣄⡀⠀⠀⠅⠈⡿⠿⣟⡫⣭⣖⣾⣍⡘⠭⠓⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠒⣽⣦⣜⣛⣩⣤⡾⣻⣿⣿⣟⢿⠭⠊⠉⠒⠤⣀⠀⣿⡽⡼⠾⠛⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠀⠢⡢⠄⠑⣯⣿⢿⣯⡷⠗⠋⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠤⢀⡘⠀⠸⣿⠗⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠠⡠⢔⠀⡀⠐⡨⢀⠁⢊⠔⠁⢔⠀⢂⠔⢁⠄⡀⢂⠔⡀⠀⠠⢀⠔⠠⢂⠄⠀⡠⢒⠔⢀⠄⡠⢂⠔⡠⢈⠔⡡⢂⠔⡀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠐⠡⢊⠤⢂⠤⡢⠐⡡⢊⠥⢊⠔⡈⢐⡥⠊⠔⡠⠀⡡⢂⠔⡠⡪⢊⠔⠁⠐⡡⢊⠔⡡⢊⠔⢡⠎⡔⠡⠊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠐⠁⠐⠁⠊⠀⠉⠐⠡⠂⠠⠊⠄⠁⠊⠎⠀⠀⠘⠀⠊⠀⠁⠈⠀⠈

⠀⠀⢀⣾⣟⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣟⣿⣆
⠀⠀⠀⢻⣯⣿⣿⣿⠿⠿⢶⣼⣿⣿⣦⣄⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⢀⣠⣶⣿⣿⣿⡶⠾⠯⣿⣿⣯⣿⠋
⠀⠀⠀⠈⣿⣷⣿⣿⣶⠛⣿⣿⡇⠀⢈⣽⣿⣶⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣶⣿⡋⠁⠈⣻⣿⡿⠿⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠙⣿⣼⣿⣿⡟⠋⣙⣻⣦⣿⣿⠏⠁⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⢿⣿⣧⣴⡛⠙⠛⣿⣿⣿⣽⡟
⠀⠀⠀⠀⠀⠹⣷⣽⣿⣿⣿⠉⣉⣡⡽⠿⣆⣀⣠⣾⣿⣿⣦⡐⠀⠀⠀⢀⣴⣿⣿⣄⠀⢀⣼⣿⣉⠉⠙⢛⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣯⣹⣿⣿⣿⡉⣀⡤⠶⠚⠛⢿⣿⣿⣿⣿⣷⣾⣿⣦⣿⣿⣿⣿⣿⠿⠿⠷⣤⣀⠉⣳⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⣀⠀⢀⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢄⠀⠀⣨⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⣻⣿⣿⣿⢃⠠⠔⠚⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣍⠛⠛⠲⢤⣈⣸⣿⣿⡿⢛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⢿⣿⡆⠀⠤⠐⡘⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⡌⠒⠠⢀⣼⣿⣿⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣷⡠⠐⢸⡇⢸⣿⣿⡿⣿⣿⢿⣿⣿⡇⠀⣿⠐⢄⢠⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣹⣿⣿⣧⣔⠀⠛⢹⡿⣿⡇⣿⣿⡇⣿⣿⡟⢚⠣⠑⢤⣿⣿⣿⢋⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣟⢻⣿⣿⣿⣷⣦⣼⣧⣼⣇⠸⡿⠁⣿⣧⣇⣤⣴⣿⣿⣿⣿⠿⣿⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣹⣿⣟⣿⣿⣿⣿⣿⡻⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⣻⣿⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣽⣿⣯⣽⣿⣽⣷⡴⠁⠀⠀⠀⠑⣴⣿⣽⣿⣛⣻⣿⡉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢰⡆⣿⣰⡂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣦⢲⣿⣇⣦⡀⠀⠀⠀⠀⠀⠀⡀⠀⣖⣀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣷⠚⣩⣿⢿⣿⣥⡿⠁⡆⡙⠆⠀⠑⠈⢀⡼⠞⠀⠷⣦⠈⣷⣇⠀⢀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠉⡙⠌⣿⣻⣟⣡⡴⢳⣷⠆⢹⣄⣀⣠⠀⠀⠀⠀⠀⠀⠈⣧⢸⠃⢱⡆⠀⠀⢸⢋
⠀⠀⠀⠀⠀⠆⢠⣿⣿⣾⡌⣿⢩⠁⣴⣾⣿⢻⡾⠟⠉⠙⡄⠀⠀⠀⠀⠀⢀⣿⠿⠀⠀⠀⣞⣀⢸⣆⠀⠐⠂
⠀⠀⠀⠀⢀⡴⠀⣀⡠⣤⣭⠻⢦⣄⠀⠀⢢⡽⣀⢀⡀⠀⠘⣦⣀⣠⣶⣴⠏⠀⠀⠀⠀⠀⠉⢁⠿⡉⠿⠷⠶⠁
⠀⠀⠀⠀⢾⠀⠀⠿⠀⠸⣿⡥⢌⣽⣏⣡⡛⣴⡇⠀⠈⢢⣄⣼⡿⣏⠍⢻⣿⣷⡲⢦⡤⢀⠔⠁⠐⠁⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠘⠀⠀⠀⠀⢾⣻⣶⠋⢁⣿⠙⣢⠀⡁⠀⠀⠀⠹⣿⣯⠓⢀⣸⠿⠄⠀⠀⠈⣴⠀⠠⣿⣶⡆⠀⢈⠀⣠
⠀⠀⠀⠀⠉⠙⠇⠦⢤⠈⣿⣿⣤⣾⣿⠀⠉⡤⠀⠀⣤⣀⣀⡼⠙⠛⠏⠀⠀⠀⢐⣶⡏⠁⢲⣀⣈⡍⠳⢆⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡰⡾⠋⠉⠁⠀⠙⠳⠀⠀⠀⠘⠛⠛⠋⠀⢆⣀⠀⠀⠀⠃⣘⠉⠀⣤⡀⣉⡿⡤⣤⠘⢿⠖⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡿⠋⠓⠶⣦⣄⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠙⣿⡄⠀⠁⢉⠀⠂⡜⠀⠈⠉⡀⠀⣀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣤⣤⣿⠀⠀⢀⡈⢉⣭⣤⣄⡀⠀⠁⡟⠁⠤⠐⠾⢦⡀⠘⠁⠀⢡⡼⢦⠉⢰⣅⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠿⠿⠛⢻⠀⠀⠾⢡⡟⢻⣿⣿⣿⡆⠀⣿⣄⠀⠳⢦⡀⠙⣷⣦⣴⡀⠀⠄⠀⠾⠏⠣
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠉⠛⠉⠉⠀⣸⣿⣿⠰⠀⠸⡇⠀⠌⠠⠍⠋⠉⠋⠀⣰⠷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⢧⠀⡀⣖⠀⠀⢦⣤⣤⠶⢤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⡷⠀⠦⢘⡧⠀⠀⠀⠀⠀⣼⡏⢿⡿⠁⠀⣀⢻⣿⡷⠶⣿⢁⢈⣠⣤⣾⣖
⠀⠀⠀⠀⠀⠀⠠⠀⠦⢻⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣧⣿⡃⣤⣾⠇⣾⣻⣧⣐⠁⢿⣯⡄⣠⠻⢸⠇⠁
⠀⠀⠀⠀⠀⠀⠣⠀⠀⠄⣧⠀⣾⣏⣉⡀⣦⣄⠀⠀⠀⠀⠈⢧⠀⢻⣿⣿⢽⡀⠸⠿⣿⠛⠉⢠⠙⢮⣉⣞⣫⣖⡄
⠀⠀⠀⠀⠄⠀⠀⡄⠈⠀⠙⡄⠈⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠿⠋⡬⠁⠂⡀⠧⢐⠈⢀⡀⣄⠈⠛⡁⠨⠄
⠀⠀⠀⠀⣈⠀⠀⡁⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⠳⠖⠀⠀⠁⠀⡁⠈⠀⠱⠚⣅⠀⠉⠁⠀⡠⢀
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⢿⢻⡿⢢⣤⣤⣴⢶⠿⠛⠛⣽⡟⢧⡤⠀⠀⠂⠀⠀⠁⠀⢀⣠⣄⠟⠉⠂⠚⠏
⠀⠀⠀⠀⠀⠖⠂⠀⠘⠆⠀⢈⠦⣷⣿⢿⡇⠀⠀⠀⠀⠀⢸⡖⠹⠁⣿⣄⡠⣔⠔⠀⣴⣷⠿⠻⣿⡀⠀⡴⠂
⠀⠀⠀⠀⠀⠀⠰⠠⠐⡄⠀⠈⣀⠉⢿⣿⡿⢦⠀⠀⠀⢠⣏⣶⢸⣿⣿⠿⢣⣿⠀⠀⠈⠁⠀⠀⣿⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠢⣌⣼⣇⣸⠀⠀⠀⠸⣿⡟⠋⠉⠀⣠⡻⠿⠓⠒⣻⡇⠀⠈⠉⠳⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣠⣤⢶⠞⠃⠙⠟⠀⠀⠀⠀⣿⢷⣄⡀⠀⠀⠀⠀⠀⣠⠀⠀⢠⣤⣴⠖⢀⣤⠀⡆
⠀⠀⠀⢀⣠⣶⡶⠀⠐⣛⣀⣿⡅⢂⠀⠀⣸⡇⠀⠀⠀⠀⠈⢧⠈⠻⠀⠀⠀⢀⠀⢘⣦⣀⣼⣿⡃⣶⠠⡂⠀⣀
⠀⢀⣤⣿⣷⣶⣅⣤⣾⣿⣿⣿⣿⣿⡧⣀⠋⠹⡖⠀⠀⠀⠀⠀⢣⡰⠇⠀⠀⣾⠀⠸⠋⠻⣿⣧⠀⠀⡄⠆⠘⠷⠂
⠀⠙⠉⢿⠠⣿⠻⢟⢿⡄⠀⠈⠙⣿⡷⢍⠀⠀⠀⣀⠀⠂⠀⠀⠋⠀⠀⠀⠀⢀⠴⠀⠀⠠⠿⠈⠉⡲⠀⢡⣄
⠀⠀⠀⠀⠀⢻⡁⢠⠀⢁⡳⣦⣮⣤⡟⠀⠀⠀⠀⠉⠀⠓⢦⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠒⠀⠀⠇⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠁⠂⡀⣤⠙⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠂⠤⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠀⠀⠀⠀⠀⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⡙⢿⣿⣿⣿⣿⣿⠟⣩⣶⡇⠀⠀⠀⠈⡇⠉⠳⣄⡀⠀⠀⠀⠀⢀⡴⠚⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣶⠈⠻⠿⠋⠰⣾⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⢙⣦⣀⣠⣾⡋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⣴⣾⣿⣶⣿⣷⣌⠻⣿⡇⠀⠀⠀⠀⡇⠀⣠⠞⠉⠀⠈⠁⠀⠙⢦⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠴⠿⠿⠿⠿⠿⠿⠿⠿⠷⠎⠁⠀⠀⠀⠀⣷⣞⣁⣀⣀⣀⣀⣀⣀⣀⣀⣉⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⢸⣿⡇⠀⠀⣶⣖⠒⠒⠒⠒⠒⠒⠒⠒⠒⢾⠀⢸⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣙⠿⣿⣿⣿⣿⡿⠟⣹⣿⡿⠟⠁⠀⠀⡇⠈⠳⣤⡀⠀⠀⠀⠀⣀⡴⠛⠳⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⢈⡛⠿⣋⠰⣿⣿⣿⡇⠀⠀⠀⠀⡇⠀⠀⠀⣹⠦⣄⣠⢾⡉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢋⣴⣿⣿⣾⣿⣷⣌⠻⢿⡇⠀⠀⠀⠀⡇⠀⣠⠞⠁⠀⠈⠀⠀⠙⢦⣄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠁⠀⠀⠀⠀⣷⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⡷⡿


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢻⣦⡀⠀⣴⣿⠀⠀⢠⣤⣀⠀⠀⣀⣤⡄⠀⢰⣦⡀⠀⠀⢀⣄⡆⠀⢰⣦⣀⠀⠀⢀⣤⡆
⠀⠀⠀⢈⡏⢻⣿⠉⡇⠀⠀⠀⢃⣤⣵⣾⣥⣜⠃⠀⠈⠻⣾⢶⣶⢷⡞⠃⠀⠈⢿⡿⣦⣴⢿⣿⠃
⠀⠀⠀⢸⣮⠁⠁⢡⣟⠀⠀⠀⠺⠽⠋⠉⠯⠿⠀⠀⠀⠸⣿⠊⠁⢿⠟⠀⠀⠀⠻⣿⠎⠉⢾⡟

⠀⠀⢀⣄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⢠⡄
⠀⠀⠀⢿⣿⣦⣴⣿⡿⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⢇⡀⣠⣦⣀⡸⠇⠀⢠⠀⠒⣢⣆⠒⠀⡀
⠀⠀⠀⢸⣿⠏⠋⣿⡷⠀⠀⠀⠐⠀⠈⠇⠀⠂⠀⠀⠀⢿⣰⡟⠻⣆⣽⠀⠀⠀⠙⢟⠻⢟⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁

⠀⠀⠀⣗⠲⣤⣤⠖⢲⠆⠀⠰⡒⠐⢦⡴⠒⢒⠶⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣶⣄⠂
⠀⠀⠀⠸⣲⠚⠛⣖⠏⠀⠀⠀⠀⢳⠞⠳⡾⠁⠀⠀⠀⠀⢠⡄⢡⡄⠀⠀⠀⠀⠸⣯⣻⢟⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⢀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣿⠻⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣿⣶⠘⢋⣥⡄⠀⠀⠀⠀⠀⠀⠐⣄⢃⠈⠊⠀⡎⡰
⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣮⣶⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣿⠿⠿⠛⠏⠱⡄⠀⠀⠀⠀⠀⠐⠚⠀⠳⣄⢼⡗⡓⠠⠂
⠀⠀⠀⠀⠀⣼⣿⢿⣿⣸⣿⣟⣟⣻⠛⢻⡆⠀⠀⠀⠀⠒⠚⣏⢹⢿⣛⠀⢀⡤⣤⣶⣿⠆⠀⠀⠀⠈⢻⣀⣈⡱⢾⡿⢯⠒
⠀⠀⠀⠀⢀⣿⣾⣿⡻⣿⣿⣿⣿⣵⣷⢄⡀⠀⠀⠀⠀⠀⠞⠓⢁⣰⣷⡶⠉⠀⣈⠋⠻⣦⠀⠀⠀⠀⠀⠀⢸⠶⠠⠂⠀⠁
⠀⠀⠀⠀⢸⣿⣾⡳⣿⡹⣿⣿⣽⠻⣹⢿⢶⡄⠀⠀⠒⢸⡤⡤⣤⠉⣉⣑⣲⠚⠛⡰⣦⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴
⠀⠀⠀⠀⣜⣟⣿⣿⣿⣷⣿⣟⣶⡻⣳⣷⡈⠇⠀⠀⢰⡚⠓⠿⣀⣈⣿⡿⡿⢤⣀⣀⣀⣹⡇⠀⠀⠀⠀⠀⠀⢀⣏⠰⣠⢣⡞⠀⠇
⠀⠀⠀⠀⣱⣿⠿⢿⣟⡘⣿⣼⣫⡾⡿⣿⣿⡄⠀⠀⠀⢰⡶⣶⣛⣿⣿⣉⣁⡀⣰⣿⣻⢿⡁⠀⠀⠀⣀⠀⠀⠀⢯⣤⣠⠇⠐⠀⠀⠄
⠀⠀⠀⠀⢿⡗⠾⢄⣍⡟⣿⣿⢹⡤⠒⠿⣾⠃⠀⠀⠉⣉⣴⣾⣿⣋⣀⣠⣿⡯⠀⢋⣁⣦⡃⠀⢀⣸⡏⠰⠋⠀⠙⢻⠿⡄⢠⡄
⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⢻⣧⠞⠁⠉⠁⠉⠀⠀⠀⠀⠙⠯⠥⠛⠛⢻⢻⡽⠣⣴⠿⠙⠋⠁⠀⠈⢣⣹⣤⡠⠂⢀⠞⣦⢽⡏⠧⠚⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢣⢀⡊⠄⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⣛⢟⣙⠛⣟⢟⣿⢿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢾⡿⣿⣿⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⣦
⠀⠀⠀⣾⣿⣟⢈⠀⠀⠀⠀⠀⢀⡓⠒⠂⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⣿⣿⡇⠈⡇⠀⠀⠀⠀⠀⣷⡥⡁⠀⢪⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⡾⣿⣘⡇⠘⠈⡇⠀⠀⠻⣄⣠⠋
⠀⠀⠀⡿⣿⣧⠞⢁⠀⠀⠀⠀⢀⡆⠤⠤⠀⠒⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⣿⣷⢼⠀⠀⠀⡇⠀⠀⠀⢱⡋
⠀⠀⠀⣷⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠠⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣿⣾⡲⠀⠀⡟⠛⠀⠀⠸⠃
⠀⠀⠀⣿⣿⣿⡆⣠⣤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠁⠇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠱⠷⢱⠸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢳⠛⢆⡀⣀⠀⠀⠓⠂⠰⡇⠀⢈⢇⠀⠂⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠈⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⡀⢦⠀⠀⠀⠀⠀⠀⠘⠁⢢⡌⠀⠘⠀⠋⠀⠀⠀⠀⠀⡄⠀⡰⠀⢴⠄⠀⡃⠀⠀⠀⠀⠀⠀⠀⣷⣿⣷⡶⠇⠠⠇⠀⠀⠀⠐
⠀⠀⠀⠠⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⣑⠈⠱⡀⠀⠀⠠⠀⠀⢀⢀⠊⠀⠀⠣⠀⠀⠀⠄⢀⡤⠀⠀⠀⠀⠀⠘⠿⠩⠥⠀⠀⠀⠓⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣀⠘⠢⡀⠀⠀⠀⠸⠀⠀⢀⠔⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠄⠀⠤⠐⠁⠀⠀⠀⠈⠃⢄⡀⠀⠀⣠⠁⠐⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠉⠀⠉⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⢉⣲⡾⠅⠀⠀⠀⠠⡀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⠀⠀⠀⢤⣴⣹⢿⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⡼⠂⠀⠒⠤⠀⠀⡀⠙⢃⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢻⡇⠀⠀⢠⣙⡿⡄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠠⠖⠀⠀⠰⠃⠀⠀⡇⠀⠀⠁⠀⠀⢀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢛⣦⠀⠈⠉⠛⠋⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠀⡄⠀⠴⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⢰⣿⠀⠀⠀⠀⣿⡈⠀⠀⢈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣧
⠀⠀⠀⢿⡷⠀⠀⠀⢰⡇⠉⠄⠀⠁⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⣠⣤⣶⣶⢶⣦⣤⣷⣶⣷⠟⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢇⠀⠀⠀⢁⠀⡿⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⣿⡇⠀⠀⠉⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠁⠀⠀⠰⠀⠀⠜⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠀⠄⠐⠡⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣄⠀⢀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⢀⠠⠄⠀⠀⠠⠄⠀⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⣾⣓⠲⠶⢤⣌⠁⠀⠀⠀⠀⣀⣠⠤⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠒⠤⠀⢀⠀⠀⠤⠚⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣯⣍⣛⣓⠶⠤⠍⠓⠺⠋⠡⠤⠄⢀⡅
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢆⠀⢹⣶⠭⣭⡙⠒⠤⠤⠤⠄⠒⠒⠋⢙⠀⡃
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢄⡙⠓⠲⠤⠤⢙⣷⡶⠄⠰⠞⠛⣉⠔⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⣀⣀⡀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠠⠤⠀⠀⠤⠀⠀⠐⠉⠁

⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⢠⠆⠀⠀⠀⠀⠠⡄⠀⠀⠰⢢⡖⠀⠀⠀⠀⠀⠀⢶⡴⠆⢰⡇⠂⠀⡀⠀⠀⡀⠐⠲⡷
⠀⠀⠀⠈⢦⣀⠀⣰⠀⢀⡠⠏⠀⠀⠀⣿⣰⢩⢄⡰⡍⣆⣻⠀⠀⠀⠈⠇⠀⠀⢠⡄⠀⠀⢾⠀⠀⠀⢳⠀⠀⠨⣶⡌⠀⠀⣺⠁
⠀⠀⠀⠀⣴⠀⠀⢼⠀⠀⢰⠄⠀⠀⠀⢩⣾⠘⣾⣷⠃⣷⣍⠀⠀⠀⠀⣠⡀⠀⠸⠇⠀⢠⡄⠀⠀⠀⠈⣳⢂⣴⢻⢲⣔⢲⠋
⠀⠀⠀⠀⠘⣷⠶⠖⠶⢶⡟⠀⠀⠀⠀⠈⢿⣇⠈⠁⣸⡿⠁⠀⠀⠀⠀⠙⢷⣤⡄⢠⣴⠿⠃⠀⠀⠀⠀⠹⣜⣱⠀⢸⣋⡼
⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⣀⠀⠘⠁⠀⠈⠙⠀⣀
⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⢰⡂⠖⣤⡀⠀⠀⣠⠰⠂⡆⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠘⣆⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠈⣇⠀⠀⠀⣴⠀⠀⠀⣠⠃⠀⠀⢻⠙⠚⡘⣶⢚⠙⠚⣼⠁⠀⠘⡇⠀⠀⠀⣤⠀⠀⠀⣾⠁⠀⠀⠸⠟⠂⢰⠀⠚⠿
⠀⠀⠀⠈⣷⡀⠀⠹⠀⠀⣸⠏⠀⠀⠀⠨⣗⢆⡙⠻⠊⣠⢆⡏⠀⠀⠀⠻⡄⠀⠀⡟⠀⠀⣰⠋⠀⠀⠀⣆⠀⠀⠘⠀⠀⢀⠆
⠀⠀⠀⠀⠙⠿⠶⠀⠶⠾⠛⠀⠀⠀⠀⠀⠈⠣⠭⠀⠨⠵⠋⠀⠀⠀⠀⠀⠱⠤⠄⠀⠠⠴⠋⠀⠀⠀⠀⠘⢶⡤⠀⠠⣴⠟
⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⣀⠀⡤
⠀⠀⠈⢷⡈⠊⠀⣀⠀⠙⠈⡼⠃⠀⠀⡀⠀⠀⠰⣿⡆⠀⠀⢀⡀⠀⠀⠐⢰⡆⠂⢀⠀⠂⣶⠐⠀⠀⠀⠀⠀⠠⣿⡆
⠀⠀⠀⠀⣙⠀⠀⢿⠀⠀⢚⠁⠀⠀⠈⠓⠀⠀⠀⢹⠀⠀⠀⠘⠃⠀⠀⠀⢨⠃⠀⢻⠃⠀⢫⠀⠀⠀⠀⢀⣌⡓⣛⠒⣋⡄
⠀⠀⠀⠀⠘⠦⠦⠈⠰⠴⠛⠀⢤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⠀⠀⢳⡀⠀⠀⣰⠃⠀⠀⠀⢠⣶⠯⢍⣩⣏⠭⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠈⠁
⠀⠀⣶⠖⣠⡄⠀⠀⠀⢠⣤⠲⣶⠄⠀⣶⣶⣤⡀⠀⠀⢀⣤⢶⣶⠀⠀⣶⣶⢄⠀⠀⠀⢠⣶⣶⠀⠠⣤⣄⠀⠀⠀⠀⠀⢀⣤⡤
⠀⠀⠹⠀⢿⠀⠀⣤⠀⠀⣿⠀⠘⠀⠀⢹⡀⢁⣞⢳⡞⢻⡈⢀⡏⠀⠀⢻⠀⠀⠡⣀⠊⠀⢨⡇⠀⠀⠸⣧⠀⠀⣤⠀⠀⢰⡟
⠀⠀⠀⠀⠘⢧⣀⣿⣀⣴⠋⠀⠀⠀⠀⠈⢓⠘⠏⠈⠁⠹⠃⣚⠁⠀⠀⠘⠦⠀⠀⡿⠀⠠⢴⠁⠀⠀⠀⢙⡗⠀⢹⠀⢰⡏
⠀⠀⠀⠀⢷⣦⣉⠀⢉⣥⡾⠀⠀⠀⠀⠀⠘⣦⡤⠀⠀⢤⣴⠃⠀⠀⠀⠀⢧⣤⠂⠁⠰⣤⡼⠀⠀⠀⠀⠈⢷⣴⠏⣧⡴⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡿⠁
⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⡀
⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠉⠈⠉⠉⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦
⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠋⠙⠛⠓⠦⣄⡀
⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣠⡟⠁⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣰⡏⠀⢀⡎⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⣿⡇⠀⣸⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠀⣰⡟⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢀⣼⠏⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠤⠤⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⡀⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣽⣿⢢⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⠷⠟⣤⠭⣭⠩⡛⡆⠐⢲⡟⠿⠩⠖⢾⣿⠿⢿⣇⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡆⠀⠈⠀⠠⠀⠀⠀⠀⢸⣧⡀⠀⠀⠉⠋⡀⣰⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⣴⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠜⠠⠤⠄⢴⠷⠖⠀⠀⢀⣾⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢰⡀⣠⣴⣿⣷⣶⣾⣿⣷⣶⣆⢸⡇⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣧⣿⠟⠛⠛⠛⠛⠛⠛⠛⢻⣾⡇⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⣿⣀⠀⣾⣿⣿⣷⠀⣀⣮⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣧⣀⣘⣭⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠟⠋⠁

⡾⣿⣿⣓⡲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⢺⣿⣿⡟
⠹⣟⣿⣿⣅⣼⣿⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠉⣿⣇⣴⣿⣿⣿
⠀⠹⣽⣿⣯⣈⠿⠀⢼⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣿⣧⡠⠙⠓⣿⣿⣽⠃
⠀⠀⠹⡽⣿⣍⣁⠀⠸⣿⠀⣾⣿⣷⣄⠀⠀⠀⡄⠀⠀⠀⠀⢀⡄⠀⠀⣠⠾⣿⡏⠀⣻⠏⠀⠶⣿⣿⢷⡏
⠀⠀⠀⢳⠻⣿⣦⣠⣀⠛⠢⣿⡇⠀⢹⣷⣄⠀⠑⢄⠀⠀⠀⠌⡠⣠⣾⣇⠀⠘⣿⠄⠁⠀⢬⣶⣿⣟⡿
⠀⠀⠀⠈⢷⠻⣿⣧⣤⣠⠀⠾⠃⠀⣿⣿⠙⣷⣌⠄⣿⣿⣄⣪⡾⠛⣿⣿⠀⢀⡛⠀⠀⢠⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠈⢷⣛⣿⣦⣤⡄⠀⠀⢀⣿⠋⠈⢾⣿⣷⣾⣿⣿⣿⠃⣀⣸⣿⣆⠀⠀⠠⢤⣴⣿⣿⡜⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⢦⠄⠙⠁⢰⣆⠀⢹⣿⣿⣿⣿⡇⠈⢿⡇⢈⠩⣯⣜⠒⠛⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠚⠀⢹⡀⠀⠐⣽⣿⢿⠁⠀⢸⠀⠈⡑⢿⣽⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣶⠀⢦⡀⠀⡧⠀⢧⢿⣿⡼⣇⠀⡟⠀⢠⡏⣿⡟⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⣿⣷⣤⠀⠅⠀⣷⢠⢸⠘⡟⢰⣄⢠⠃⠰⠋⣤⣼⢷⡟⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠿⣿⣿⣰⡆⠀⢻⠈⣐⠀⠀⣸⠁⣸⠀⠰⣀⣬⡏⡾⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⡿⣿⣵⣦⣾⣦⠶⠀⠀⠰⢆⣿⣷⣤⣾⣹⣿⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⣾⣋⣾⣥⣿⠋⠀⠀⠉⣟⣹⣟⣙⣏⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⣹⣯⡞⠀⠀⠀⠀⠻⣽⣏⡙⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠂⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡀⠀⢀⠀⠀⠁⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢀⠆⢠⠸⡄⠠⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⣿⠀⠀⢸⠀⠀⠀⢱⠀⠀⡀⢸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣀⠙⠉⠁⠞⠓⠲⡶⠧⢤⡾⠗⠋⢈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⣉⣉⣉⠛⠛⠛⠒⠒⠒⠲⠶⠖⠚⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠞⣋⡡⠔⠒⠚⠿⠓⠲⢄⡀⠀⠀⠀⠀⢰⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠰⠚⠉⠁⠔⠂⠀⠀⠀⠀⡄⠈⠻⣄⠀⡆⢀⠏⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠥⠚⠁⠀⠀⠀⠀⠴⠊⠉⠑⠒⠒⠊⠀⢀⡄⢹⡞⣠⠏⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠐⠉⠉⠉⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⢀⣾⠿⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡉⠛⠒⠂⠀⠀⣀⡤⠔⠈⠉⠉⠙⠒⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣦⣤⣤⣤⡴⠶⠛⠛⠛⠛⠛⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⣦⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⢹⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠰⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠶⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⠁⠀⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠻⢄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠁⠀⠀⠀⡀⠳⡀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠘⢃⠠⠚⠁⠀⠀⠀⢉⠗
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠃⠀⠀⠀⡄⠰⠴⠁⠈⠂⡘⠀⠀⠀⡠⠁⠀⢳⠀⠀⠆⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⣀⠄⣠⠎
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠀⠀⠠⠀⠂⠀⠀⠀⠀⡄⠀⠰⠀⠀⠀⠀⠉⠁⡀⠀⠀⠀⠀⣀⠂⠀⠀⢀⡀⠎⠁⡴⠁
⠀⠀⠀⠀⠀⢠⣼⣧⣠⡾⣧⣴⡿⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⡀⠃⠀⠀⠀⠘⠀⠰⠀⠀⠀⠀⡤⠁⠀⠀⠊⠁⠀⢠⡞
⠀⠀⠀⠀⠀⡼⢡⡟⢩⠀⢀⠘⠧⡀⠀⠀⠀⠐⠀⠈⠂⠀⠰⠃⠀⠀⠀⡄⠁⠀⠀⠆⠀⠀⢀⠇⠈⠁⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠠⠀⠀⢀⡀⠦⣾⠆
⠀⠀⠀⢠⣴⣿⢆⡇⠈⡄⣺⠠⣄⣹⠇⠀⠀⠀⣆⠀⠀⠀⠀⡐⠀⠀⠈⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⡠⠐⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⡰⠋
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠛⠉⠀⠈⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠠⡌⠀⠄⠈⠁⠀⠀⠌⠀⠀⠀⡘⠀⡀⠐⠁⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠈⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⡀⡼⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⡠⠖⠊⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢄⡀⠰⠀⠤⣀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⠀⠨⠃⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⣀⠀⡀⠠⠄⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⡠⢀⠉⠋⠦⡀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢀⡇⠀⠈⠀⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⢀⠀⠀⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⣿⣿⣿⠇⠻⡃⠀⢀⣈⢠⣄⠀⠀⠁⠙⡄⠀⣀⣀⡛⠀⢀⠀⠀⣤⣤⣉⣀⠀⠀⠀⠠⠀⠈⢀⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⣠⢟⣴⣿⣿⡏⠀⠃⠴⣿⠌⠠⡀⠀⠈⠳⣆⠀⠈⠃⠀⠀⡌⠁⠄⢀⠄⠘⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉
⠀⠀⠀⠀⠀⠀⢠⣿⠊⡤⣿⣼⡇⠀⠸⠄⢸⡏⣤⠈⠢⡀⠀⠈⠿⡀⢸⠀⠸⠃⡀⠘⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⡀
⠀⠀⠀⠀⠀⢀⣾⠃⢠⡇⣿⢻⡄⠀⠀⠂⠇⠈⠿⢢⡀⠈⠒⠀⠀⠐⢢⣴⣇⠀⣀⠀⠀⠀⠠⣤⣄⠀⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣼⠻⠀⠺⢰⡇⠸⡇⠀⠀⠘⠒⢶⠲⣤⠀⠀⠀⠀⠀⣀⡼⠋⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⠤⡀⢤⠒⠛⠛⠁
⠀⠀⠀⠀⣸⠃⢿⠀⡇⢿⡇⠀⣿⠀⠀⠀⠀⠈⠃⠘⡄⠀⠀⢀⡴⠋⠀⠀⠀⢠⠐⠀⠄⣀⠞⠉⠁⠀⠡⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⡏⠀⢸⠀⡇⣿⣴⠀⢻⡀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⠳⠀⠈⠁⠀⠀⢀⡘⠀⠀⠀⢼⠀⠀⡀⠀⠐⠂⠀⠁⠄⠀⠄⠠⠀⢰⡾⠃
⠀⠀⠀⣸⠁⠀⢸⠸⡇⡇⢻⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣠⠋
⠀⠀⠀⣿⠀⠀⢸⢠⡇⢧⠘⡇⠀⣿⠀⠀⠀⠀⠀⠀⣴⣿⣶⣦⠤⣀⠀⠀⠀⢨⠀⠀⠀⠁⠀⣰⠎⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⠤⠚⠀⠀⢰⠁
⠀⠀⠀⣿⠀⠀⢸⠀⡇⢠⡀⢹⠀⠛⠀⠀⠀⠀⠀⣰⡏⢻⠙⠿⣦⠈⢿⠀⠀⠘⡇⠀⠀⠀⣼⠃⠀⠀⠀⠀⠌⠀⠀⠀⣀⠰⠊⠁⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⣿⠀⠀⢸⡀⢱⠸⡇⠘⣇⠂⠚⠀⠀⠀⣼⢣⡇⠀⠈⠀⠘⣧⠀⠀⠀⠀⠃⠀⠀⣼⠀⠀⠀⠀⠀⠈⣀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠎⠁
⠀⠀⠀⣿⠀⠀⠊⠁⣾⡁⣀⡠⠙⠆⠀⠀⠀⣰⠃⠀⢷⡈⡇⠀⠀⢻⡄⠀⠀⠀⡘⠀⡴⠃⠀⠀⢀⣤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠉
⠀⠀⠀⣿⠀⠀⠻⠟⠛⡋⠉⠀⣶⡖⠀⠀⣰⠇⠀⠀⠈⡄⠃⠀⠀⠀⢷⡀⠀⠀⢁⣘⠁⠄⠒⠋⠁⠀⠈⠉⠀⠀⠀⠀⠀⠂⠀⠀⠘⢀
⠀⠀⡰⠉⠂⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⡀⢾⡄⠀⠀⠀⠈⠓⠤⠿⣿⠉⠤⡀⠀⣀⡀
⠀⠀⢿⣶⠇⠀⠀⠀⠀⠛⢀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⢹⡄⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠈⠉⠉⠙⠛⠁⠀⠀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡀⠀⠀⠀⡤⢤⣄⡀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠌⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⣤⣤⣤⣀⠀⠀⠁⠄⡀⠀⠀⠈⠠⡀⠀⡀⠀⢩⠁⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣼⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢡⣄⠀⠀⠉⠛⠢⣀⠀⠀⠀⠀⠀⠐⣈⠂⠁⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠈⢉⣏⠉⠳⢷⣄⠀⠀⠀⠀⠀⠀⡇⠀⢈⡟⠙⠳⠶⠖⠙⠋⠛⠳⣦⠀⠀⠀⠀⣨⠗⠚⠋⣻⡛⠛⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢠⡟⠉⠦⠀⠀⠙⢆⠀⠀⠀⠀⠀⢇⠀⡼⠃⠀⠀⠀⠑⠀⠀⠀⠀⠀⡼⠀⢀⠞⠁⠀⣀⣴⠎⠱⢦⣀⠀⠘⠓
⠀⠀⠀⠀⠀⢀⡠⡄⠰⠶⠎⠁⠀⠀⠀⠱⠆⢤⣤⢳⣀⠀⠀⠀⠘⢀⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡰⢀⠴⠒⠿⠋⠁⠀⠀⠈⠙⠋⠛⠓⠶⢆
⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣄⠀⡈⠙⢷⡄⠀⠀⢈⡕⠀⠀⠀⢀⠀⠀⠀⠈⢂⣴⠎⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠓⢀
⠀⠀⠀⣴⠁⠀⠀⠀⢀⠁⠀⠀⠀⣸⡄⠀⠀⠨⠀⠀⠀⠀⢹⠀⠀⠀⢡⠀⠀⠀⠈⠀⠀⠀⢀⡜⠁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢦
⠀⠀⡸⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠄⠀⠀⠀⠀⣃⠀⠀⠘⣄⠀⠀⠈⠀⠀⠀⠎⠀⠀⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⡇⠀⠀⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠁⠀⠀⠀⠉⠂⣀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠴⠟
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠤⢶⡶⠿⠿⠿⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠟⠿⠿⢿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠉⠀⠀⠀⠀⠉⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢧⡀
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠛⠛⠛⠛⠓⠶⣤⡀
⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⣰⡟⠁⠀⣠⠒⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⡟⠀⠀⢠⣧⣠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠀⢹⣿⣿⡆⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣿⣿⣿⠇⠀⣼⡟⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠏⠀⣼⡟⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣠⣾⠏⠀⠀⠀⠀⠀⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢶⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣤⣤⣴⣶⠾⠟⠋
⣿⣿⠿⠿⡿⠿⠿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⢒⣿⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣗⣒⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡧⣤⡼⠿⢟⣬⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣞⠿⠿⢧⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡦⠤⠤⠬⣄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠤⠤⠤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⡀⠀⠀⠱⢤⡀⠉⢷⡄⠀⣀⠀⣰⠟⠁⣠⠴⠁⠤⠤⠤⢤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣀⠀⠀⠀⠀⠀⠈⠑⠠⠙⣾⣿⣞⠡⠐⠉⠀⠀⠀⠀⣀⣀⣀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣛⣿⣿⣿⠿⠿⠶⠶⢲⣿⢸⣿⠖⠶⠿⠿⢿⠿⢻⣟⣛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠇⠀⠀⢰⠊⠁⢀⠔⠨⢿⣿⠿⠀⠀⠀⠈⠱⠀⠀⠀⢽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣈⣁⠠⠖⠁⡀⠀⢸⣿⡀⠀⠄⠈⠢⠄⣈⣀⠀⠠⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠀⢀⠌⢠⡞⠀⠌⠀⠠⢹⣿⠑⡀⠈⢆⠀⢦⠈⢂⠀⢢⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣎⣀⡌⢀⠌⢀⡔⠀⠀⠛⠀⠀⢆⠀⢂⠀⣅⣀⣷⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣾⣦⠞⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⡷⠶⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠀⠀⢸⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⣀⠤⠓⠲⠶⠖⠚⠤⣀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢺⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⣧⠀⠀⢰⠃⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠃⠀⠀⣼⠀⠀⠀⠀⢸⡋⠀⢙⠇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣽⣤⣤⡀⠀⠒⠃⠀⠘⠋⠙⢻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠤⣸⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⡬⡇⠀⢤⠀⠀⠀⡤⠖⠚⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⠋⣟⠙⠃⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢾⠀⠀⠰⠶⠶⠶⠶⠶⠶⠶⠶⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣘⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣋⣀⣀⣀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠧⣉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢉⣵⣋⣉⣀⣀⣀⣀⣀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⠾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣴⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠛⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠰⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠴⠞⠁⢀⣤⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠼⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⢀⣶⣴⣿⣿⡇⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⡇
⠀⠀⠀⠀⢀⣤⡤⠴⢖⣲⠟⠛⠋⠉⠀⠀⠀⠀⠈⠉⠉⠉⡉⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⢠⣾⢟⠅⠂⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢉⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡇
⠀⠀⠸⣿⣍⣰⠇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣿⣿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿
⠀⠀⠀⠙⠻⣿⣶⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠰⠋⠀⡿⢿⣿⣿⣏⠛⠦⣄⠀⠀⠀⠀⠀⠀⠠⣄⣨⡟
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣴⣶⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢿⣦⠀⠀⠁⠀⠀⠀⠤⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠟⠀⢀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡆⠀⣰⠀⠀⢀⠀⠀⠀⠀⡀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣶⣿⣆⣠⣾⡂⢠⣄⣠⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣼⢱⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠾⡄⠉⠆⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢳⢧⠄⢰⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡞⡞⡄⢌⣆⠀⠀⠡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⡑⡑⡀⣍⠂⠀⠀⠑⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣹⡱⡔⣌⢦⡀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠋⣀⡠⠀⠠⣄⡀⠀⠀⠸⢧
⠀⣠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⣮⡣⣝⠶⣌⡂⠀⠀⠀⢀⣀⠂⢈⠈⠤⠀⠀⠀⠀⠀⠠⠀⠀⠘
⢀⠁⡠⣐⡪⢥⣐⣒⣒⣒⡆⠤⠄⡀⠀⠀⠀⠀⠀⠀⠐⢌⠳⣮⣕⢮⣍⣛⠒⠤⠤⠤⠤⠤⠄⠐
⠀⠀⠈⠒⠍⢯⠙⠤⠣⠬⠭⣏⡒⠀⠑⠄⠀⠀⠀⠀⠀⠀⠁⠈⢛⣻⢾⣭⣛⡓⠒⠲⠒⠒⠒⠃⡉⡠⠀⠂⡀⠀⠀⠀⢀
⢠⠆⠡⠤⠄⠌⠉⠉⠉⣉⠁⠚⢼⡑⠄⠀⠀⠀⠀⠀⠀⠀⡆⣇⢢⢹⣿⣦⣯⣉⣉⡉⠋⠉⠉⣉⡀⠄⠒⢀⡀⢀⠀⡰⠂
⠀⣦⠀⠀⠀⢀⣒⢒⠤⠤⢈⠑⠤⠉⠀⣠⠖⠂⠀⠀⠀⠀⡇⢸⢸⠀⣏⡓⠺⠭⢭⣉⣉⣉⢉⡁⠤⠄⠒⣀⠔⠁⠊
⠀⠈⠳⠀⠀⠒⠒⠬⠉⠀⠀⠀⠁⠀⡠⠃⠈⠀⠀⡄⡐⢠⠃⠆⠸⢠⡷⠦⠍⣒⠒⠢⠤⠠⠤⠀⠄⢐⣂⡤⠖⠁
⠀⠀⠀⠀⠀⠐⠒⢲⣦⣤⣀⡀⠀⠀⠀⠀⠀⠡⠈⠐⠁⠀⠀⠠⠃⢆⡇⠀⠈⠉⠛⠛⠿⠶⠾⠓⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⢀⠄⣀⠤⣀⡴⣢⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢋⢞⠵⣫⣔⡎⢗⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢯⠞⠓⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠤⠶⠧⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡤⣄⡄⣠⠶⠶⠶⠶⠶⠶⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠛⠛⠛⠉⠉⠁⢠⣬⣥⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⡤⢤⣤⣴⣶⠶⠶⠶⠾⠿⠃⠀⠀⠀⢠⣽⣿⣿⣿⣇
⣤⣴⣶⡶⠶⠿⠛⠛⠋⠉⣈⣧⣬⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣮⡻⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⢍⣡⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣼⣿⣿⣷⡶
⠀⠀⠀⠀⠀⢀⣠⣶⣿⡟⣭⣷⣾⣿⣿⣩⢻⡟⣽⣿⣟⡝⣿⢫⡿⡿⣫⢻⣿⣿⣿⣿⡿⠋
⠀⠀⠀⢀⣴⣾⣿⣏⣷⣿⡸⣿⣿⣿⣿⣶⣿⣷⣶⣿⣷⣶⣿⣷⣾⣿⣶⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠙⠻⠿⣻⣿⣿⣿⣶⣶⢰⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⢰⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠆

⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⢳⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡞⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠤⠽⢿⣛⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣛⡿⠯⠤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡖⠒⠲⢿⡟⠁⢉⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡉⠈⢻⡿⠒⠒⢲⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⣷⡒⠒⣚⣧⣰⣿⡿⢉⣿⣄⠀⠰⠀⠀⠆⠀⣠⣾⡉⢿⣿⣆⣼⣛⡚⢒⣾⢷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⢉⣉⣉⢻⣿⡀⢸⣿⡿⣦⠘⡀⣠⠃⣼⢿⣿⡇⢀⣿⡯⣍⣁⡉⣹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣇⣀⢠⠤⠿⠟⣿⡿⢥⣹⣇⣿⣿⣸⣏⡬⢿⣿⠻⠿⠤⠤⢀⣸⣟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡤⠔⠒⠒⠒⢿⡟⠒⠦⣽⡇⢸⣯⠖⠒⢻⡿⠐⠒⠒⠂⢤⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⡟⠛⢋⣉⣉⣽⠿⠛⣿⣇⣸⣿⠛⠿⣯⣍⣉⡉⠛⢻⣿⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⡟⠋⡹⠋⢠⡿⢀⡼⣹⣿⣿⣏⢧⡀⢿⡄⠘⢏⠉⢻⢿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⡷⠚⡇⠀⢘⣷⡾⢠⡇⢻⡟⠸⡄⢷⣾⡃⠀⢸⠓⢺⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣷⠞⣹⠒⡟⢻⣷⡿⠀⠀⠀⠀⢿⢺⡟⢻⠒⣏⠳⣿⣴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⣍⣧⣧⣰⣧⣼⣽⡇⠀⠀⠀⠀⢸⣯⣧⣼⣦⣼⣼⣭⣿⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⣿⣿⣶⣿⣷⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⣾⣿⣶⣿⣿⢫⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣽⡿⠾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠶⢿⣯⡾⢿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠒⠛⠛⠉⠉⠉⠉⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚⠋⠉⠀⠀⠀⢀⣀⡤⠤⠒⠒⠲⡄⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⢠⠤⠖⠒⠉⠉⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡴⠞⠁⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣳⣹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⣠⡤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠜⢯⣷⣷⣿⣿⡗⠛⠛⠳⢦⣀⠀⠀⠀⡇⢀⣀⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠠⠃⢠⢁⠎⠀⠜⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠚⠛⠉⠁
⠀⠀⠀⠀⢀⣀⣌⣀⣘
⠀⠀⢰⡯⣉⣩⣉⣉⣍⡭⢿⠂⠀⠀⣀⣤⣤⣤⣤⣤⡄
⠀⠀⢸⡗⠲⢚⠲⢼⣄⣀⣾⠀⠀⠀⣿⠉⠛⠛⠉⠉⡿
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢿⣄⣠⣤⣀⣴⠇
⠀⠀⠀⢹⣤⣀⣄⣀⣀⣴⡇⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⣿⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢹⡀⢾⢀⣞⢧⣀⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠤⡤⢾⠀⠁⢸⣾⠊⡾⠋⢁⡾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣝⣄⠀⠀⠑⢄⠀⣏⡉⠀⢘⠠⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢾⣘⠦⣀⠀⠀⠈⣿⣀⡴⠋⠄⣧⢻⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡌⠳⠤⢤⡀⢰⡏⢦⡀⠈⢿⡦⠀⠑⠢⣀⠨⠉⠀⠀⣤⢥⡟⠀⢠⣾⠟⢧⣀⡤⢤⣤⢔⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⣶⠀⢠⠉⠉⠀⠄⠻⣄⣸⠀⠢⠀⠀⠈⠈⢆⣠⡾⠁⢈⢧⡴⠋⡎⠈⠀⠀⠀⠀⣴⠞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢗⡿⣦⣾⠀⠀⠀⠠⠀⠈⠁⠃⠀⠈⠒⢔⡆⣾⡁⠀⡀⠀⠰⠀⢰⠃⠀⠀⢀⣈⠿⣛⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡄⣈⡉⠛⢆⡀⠀⠀⡇⠀⠸⡄⠀⠠⡀⠀⠉⣿⣔⠞⡀⠁⠁⠀⡸⠀⣀⣀⡘⠛⣉⣭⣶⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠈⠉⠛⠋⠙⢶⣄⡇⠀⠀⡇⠀⢀⠈⢢⣐⣿⠗⣦⠁⠀⢀⠀⠰⡄⠉⠈⠉⠀⠀⢨⡽⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⣋⡢⠈⠙⠒⠉⠉⠈⣑⣦⣴⡇⠀⣼⠀⠐⠈⣻⣼⠋⠀⠀⣻⢠⢞⠐⠉⢀⣈⣉⣀⣂⣴⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣝⣓⢘⡒⠒⠒⠛⢉⠁⠙⣷⡄⣺⠄⠀⠀⣿⣧⠊⡄⢀⡿⠃⠀⠀⠀⢉⡉⢩⣭⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣍⢒⢐⠲⡖⠛⢛⣻⣿⠀⠀⢠⣿⣍⠰⣡⣾⣡⡂⣀⢡⣶⣤⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣮⣬⣁⠁⠀⢄⠹⠾⢷⣵⢲⡿⢃⣶⠟⣞⣿⠟⠉⠋⠁⢘⡷⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠙⠥⣀⠀⣀⣨⣵⡦⠴⠦⣴⣦⣿⣿⣿⣿⣥⣿⣏⠀⢀⡤⠂⠀⡠⠾⠻⡿⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣯⣤⣴⡶⠚⠋⠁⠴⠉⠀⢈⠝⠁⣠⢾⣿⣉⡟⠓⢦⣉⡉⠙⠒⠲⣞⠛⠚⠛⣛⣿⠿⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠶⣥⣤⠵⠶⣦⣤⣥⠶⠛⠁⣾⠃⠉⠳⣌⢀⣈⠳⣄⠀⣠⡬⠽⠦⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠉⠈⠙⠺⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢹⡿⣋⡟⢿⣤⢶⣆⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣼⠟⣿⣻⡟
⠀⠀⠀⢻⢻⠗⢿⣤⡀⠨⢿⣿⠛⢷⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠟⢻⣿⠯⢤⣤⣼⠛⣿⣿⠃
⠀⠀⠀⠘⣿⣹⢯⣦⣤⠴⠞⣯⣁⡾⡞⢻⡟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣻⣿⡿⣆⣩⣷⠶⢦⣤⣮⢽⣽⡟
⠀⠀⠀⠀⠙⣷⣴⣿⣦⣀⡠⣏⣹⠶⠶⣏⠛⠳⠾⢿⣦⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⣠⣾⠷⠶⠿⢿⡷⠶⠾⣭⡧⣀⣠⣟⡃⣼⡟
⠀⠀⠀⠀⠀⠘⢿⣳⣾⠉⢱⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⣞⣷⠈⢹⣾⣷⠏
⠀⠀⠀⠀⠀⠀⠈⣻⣾⡟⣳⣾⢾⡧⠄⠀⠞⠦⢄⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢀⡤⠿⠆⠀⠴⢭⣿⢿⡳⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣵⣿⠝⢿⠁⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⣿⠞⢯⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣿⣛⣧⣤⠤⠤⠤⠒⠒⠛⠙⠓⠀⠀⠀⠀⠈⠳⡄⢰⣶⠀⡴⠋⠀⠀⢀⠠⠐⠊⠉⠓⠒⠒⠠⠤⢤⣤⡟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠘⣾⣿⡞⢁⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠯⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣤⣤⣤⣶⣶⣶⡶⠶⠦⠤⣤⣤⣤⣤⣽⣿⣿⣿⣤⣤⣤⡀⠀⣤⣶⣶⣶⣶⣶⣤⣤⣀⣠⣾⣿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⠍⠉⠉⠉⠉⠉⠻⠆⠁⠀⠤⠐⠀⢉⡿⣿⣿⣿⣏⠉⠐⠠⠤⠉⠛⠛⠉⠉⠉⠉⠀⠫⣍⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢯⣀⡀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣀⠴⠋⠘⢹⣿⠹⡈⠳⢄⡀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣀⣸⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣷⠊⠁⠀⠀⠀⡀⠀⠀⢀⣠⡴⠊⠁⠀⡰⠀⣾⣿⠆⠁⡀⠀⠉⠲⣤⣀⠀⠀⠠⡀⠀⠀⠀⠈⢻⣯⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣛⣷⣄⣀⠀⠐⠚⢁⠴⠛⠉⠁⠀⠀⠀⠸⠃⡀⢸⣿⠐⡄⠙⠄⠀⠀⠀⠉⠙⠳⢀⠛⠒⠤⢀⣀⣼⣿⢾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣬⣿⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠀⢠⡼⠁⢸⡿⠀⠹⣴⠀⢀⠀⠀⠀⡀⠀⠀⠑⢦⡀⠀⢹⣞⢻⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⣿⣷⣾⡇⠀⠀⠀⡔⠀⠀⣠⠃⢀⡿⠁⠀⠀⠁⠀⠀⠹⡆⠀⢣⡀⠀⠐⡀⠀⠀⠀⣿⡶⣿⠿⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣭⣶⢿⣿⡶⣶⣾⣇⣀⣴⠃⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢳⣄⣀⣿⣶⡶⣾⢿⢶⣮⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣷⣿⣲⣻⣭⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣾⣯⣿⣷⣺⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠟⠛⠋⠉⠉⠉⠙⠛⠻⢿⣿⡛⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⢀⣀⣀⣀⣿⠷⣄⡀⠀⠈⠙⠳⣦⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⢠⣟⣉⣉⣉⣩⡄⠈⣻⠂⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢻⣴⠏⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⣤⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣄⠀⣷⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⣧⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠉⢿⠀⣿⣀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⢠⡴⠶⠾⠀⠈⠉⣇⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣧⣤⣤⣤⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣠⣤⣴⢶⣄⠀⣾⠋⡇⢠⡶⠛⡆⠀⠀⡾⠫⠦⢹⡇⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⠁⠉⠁⠀⢻⡆⣨⣿⣥⠈⡇⢸⣇⣀⣼⡇⠀⠚⢻⡄⠀⠀⠀⠀⠀⢸⣿⡇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⡇⠀⠀⢸⡄⢰⣦⣶⣌⣇⢿⠀⢸⡄⣧⠈⠉⠀⠈⣿⣦⣄⣸⡇⠀⠀⠀⠀⠀⢸⣿⡿⠛⣷
⠀⠀⠀⠀⠀⠀⢸⡏⠙⢻⣇⠀⠀⠸⠷⠟⠀⠈⠉⠋⠸⠶⠾⠃⠹⣦⣤⡤⠶⠇⠀⠉⠉⠁⠀⠀⠀⠀⠀⢸⠏⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡤⠶⣆⠀⢀⡴⠟⢻⡄⠀⣴⠋⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠘⣧⡀⣰⠏⠉⢷⡀⢀⡼⠋⠀⠀⠸⣦⡏⠀⠀⠀⣧⣼⠃⠀⠀⠀⠀⠀⣼⣃⣤⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠈⢷⠏⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⢀⣿
⠀⠀⠀⠀⠀⣾⡿⣶⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠘⣷⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⣴⣶⣶⡶⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⣿⡏⢭⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⡔⣀
⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠨⣙⡂⠡⡇⢀
⠀⠀⠀⠀⠀⠛⠂⠀⠦⠀⠀⢀⠀⠀⠠⣄⠳⠿⣆⣣⣠⣤⡄⡀⠚⠳⠈⢱⡦⣀
⠀⠀⠀⠀⠀⠀⠋⠀⢀⢐⡟⣨⡀⠖⠲⠆⠖⠲⡄⠠⢭⠈⠄⠶⠊⡠⣥⠚⣽⣆⣳
⠀⠀⠀⠀⠀⠀⠀⠂⠊⡟⡬⡷⢑⣛⡻⠚⠛⢿⣆⡶⠶⢦⡒⢋⣻⣠⣴⢛⣴⢿⣿⣷⡄⠠⠌⠤⡌⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⢿⣟⣓⢀⣹⣠⣷⠉⢐⣀⡉⢥⡟⡻⣿⣿⣼⣿⣳⣾⣿⠧⠖⡶⢒⣦⠶⣶⣦⡄
⠀⠀⠀⠀⠀⣠⣤⠶⠖⠒⠒⠲⢭⣭⣭⣿⣿⢠⣯⣬⣷⣶⣶⣇⢹⣿⣿⣿⣿⣿⣿⣿⣾⣯⣰⣭⣴⡿⠟
⠀⠀⠀⠰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠈⠿⣫⣵⣾⣿⣿⣿⣿⣿⣿⣈⡩⠽⠟⠛⠛⠥⢄
⠀⠀⠀⢱⣬⣲⢤⣤⣀⣀⣤⣴⣤⣴⣾⢟⣿⣿⣿⣿⣾⣿⡿⠿⠿⣦⣄⠀⠀⠀⢀⣠⣷⠆
⠀⠀⠀⠈⢛⣻⣿⣿⣿⣿⣻⠿⢖⡻⠟⠛⠙⠛⢻⠟⠉⠀⠀⠀⠀⠀⠉⠻⣷⣶⣿⣿⡟
⠀⠀⠀⠀⠀⠉⠙⠺⠷⠈⠐⠈⠉⠀⠀⠀⠀⠀⢸⣤⣤⣀⠀⠀⠀⠀⠀⢀⡹⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣧⣠⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠛⢿⣇⠀⠀⠀⢀⣯⡉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠄⠀⡏⠉⠉⠉⠉⠉⡇⠀⠺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡇⠀⠀⠀⢠⠞⠁⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠓⢻⠀⢸⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠘⡄⠸⡀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⢡⠀⡇⠀⠀⢿⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠀⠀⠀⠀⠘⣤⠃⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⢀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣼⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⡷⠖⠛⠋⠛⠛⠶⣄⡀
⠀⣼⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⢰⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⢤⡀⠀⠀⠀⢻
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢳⢀⡠⠶⠒⠒⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢢⠀⠀⠈
⡇⠀⠀⠀⠄⠀⠀⠠⡴⠒⠚⠛⠓⠺⠇⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⡇
⣧⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⣀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢸⠃
⢹⠀⠀⠀⠐⠀⠀⠀⠀⠱⢄⣀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⠏
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣀⣀⣀⣀⠴⠋⠀⠀⠀⣸
⠀⢹⡄⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣠⠄⠀⡤⠤⠤⠤⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢀⡴⠃
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠓⠋⠉⠉⠉⠉⠀⢧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⡟⠀⠉⠛⠲⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠃
⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠘⣿⣧⡈⠻⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⠟⢁⣾⣿⠃
⠀⠀⠈⢻⣿⡤⢿⠀⢀⣑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣊⡀⠀⡾⢤⣿⡟⠁
⠀⠀⠀⠀⣿⡇⢸⣰⣿⣿⣷⢌⡢⡀⠀⠀⡴⠊⡑⠢⡀⠀⠀⠀⠀⢀⠔⢊⠑⢦⠀⠀⢀⢔⡡⣾⣿⣿⣆⡇⣸⣿
⠀⠀⠀⠀⣿⣿⠉⢣⠹⠋⣗⡦⠙⡌⠢⡀⠙⠒⠁⠀⠹⡄⠀⠀⢠⠏⠀⠈⠒⠋⢀⠔⢡⠋⢴⣺⠙⠏⡜⠉⣿⣿
⠀⠀⠀⠀⢸⣿⣀⡸⠘⠤⣈⣀⠜⠦⡀⠙⢆⠀⠀⠀⠀⢹⠀⠀⡏⠀⠀⠀⠀⡰⠋⢀⠴⠣⣀⣁⠴⠃⢇⣀⣿⡇
⠀⠀⠀⠀⣾⡟⠀⢇⠀⠀⢀⣤⣤⣤⣈⠳⣄⠳⡀⠀⠀⠈⡇⢸⠁⠀⠀⢀⠞⣠⠞⣁⣤⣤⣤⡀⠀⠀⡸⠀⢿⣷
⠀⠀⠀⠀⠻⣷⡤⠤⣵⠀⣿⣿⡋⢑⠄⠙⢮⣢⡙⡄⠀⠀⣇⣸⠀⠀⣠⢋⣔⡵⠋⠠⡏⢙⣿⣿⠀⣮⠤⢤⣼⠟
⠀⠀⠀⠀⠀⣿⡇⠀⡇⠀⠙⠿⣉⣉⠀⠀⠀⠑⣕⣜⣆⠀⣿⣿⠀⡰⣣⣫⠊⠀⠀⠀⣈⣉⠿⠋⠀⢸⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣗⠉⠱⢄⡀⠀⠀⣴⣿⣿⣿⣶⣮⣿⣾⣎⣿⣿⣰⣷⣿⣵⣶⣿⣿⣿⣦⠀⠀⢀⡠⠎⠙⣺⣿
⠀⠀⠀⠀⠀⠈⠻⠷⢴⣮⣭⣓⣶⣽⣿⣿⠭⠭⠭⣶⣶⣿⣿⣿⣿⣶⣶⠭⠭⠭⣿⢿⣯⣶⣞⣭⣵⣦⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢫⠟⠉⣩⢟⡩⠔⠚⣩⣋⡟⠀⣿⣿⠀⢻⣙⣍⠓⠢⢍⡻⣍⠉⠛⡝⠲⣄⡀
⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠘⠢⠚⣵⣿⠀⠀⣰⡷⣿⡄⠀⣿⣿⠀⢠⣿⢾⣆⠀⠀⣿⣮⠓⠔⠃⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡦⠀⠀⠀⢿⣿⣷⡴⢻⠁⠸⣿⠀⢻⡏⠀⣿⠇⠈⡟⢦⣾⣿⣿⣀⠀⠀⢴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡖⢰⡋⢱⠌⠁⠀⠘⠢⠖⢹⡇⠀⠀⢸⡏⠣⠔⠁⠀⠀⠁⢏⣈⡇⢲⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠀⠀⠉⠁⠀⠀⠀⢀⣄⠀⣸⡇⠀⠀⢸⣇⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⣾⣷⣄⣼⣿⣶⣾⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣷⣶⣿⣧⣤⣾⣷⣾⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⠙⢿⡿⠋⠙⠿⠋⠉⠛⠋⠀⠀⠀⠀⠙⠛⠉⠙⠿⠋⠙⢿⡿⠋⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄
⠀⠀⠀⠀⠀⠰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠉⠉⠉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⡄⠂⠐⠢⡀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠉⠉⠁⠀⠼⡀⠀⠀⠀⠈⢣⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣁⡘⢹⣆⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⢠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⠃⠘⢆⡈⠉⠓⠢⢤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣛⠗⠣⠀⠠⠂⠀⢁⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣄⠀⠀⠀⠀⠀⠀⠀⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⡠⠊⠉⠚⠦⠦⢄⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⡆⠀⠀⣀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⠈⠑⠲⣤⠀⠀⠀⠀⠀⠰⡆⠈⠐⠓⠀⠀⠉⠉⠁⡜⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠁⠀⠀⡔⠀⠀⠀⠀⠀⠀⣰
⠀⣀⠤⠐⠐⠦⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠠⠬⠃⠀⠀⠀⠀⡴⠁
⡴⠁⠀⠀⢐⠂⢸⠀⢀⣠⠴⣊⣡⡄⠴⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢼⡀⢀⡠⢄⠀⢠⠃⠀⠀⠀⠀⢀⡜⠁
⡇⠀⠀⠀⠀⠀⠉⠉⢁⣠⣤⠞⠁⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⡾
⠘⢦⣀⡀⣀⣀⠤⠖⣩⠟⢁⡔⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡜⠁
⠀⠀⡼⠋⠀⠀⢀⡼⠁⠀⢾⠀⢙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⠤⠤⠤⠒⠋⠉⠋
⠀⢸⠁⠀⠀⡀⠈⢱⡀⠀⠀⠉⠉
⠀⠘⣄⠀⠀⠀⢀⡼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡷⠀⢀⡿⠹⢷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⣿⠷⠒⢀⣀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⠿⠥⠧⠤⣴⠿⣷⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⣧⣶⠿⢎⣹⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⢤⠀⠀⠀⠨⢧⡀⠉⠛⣦⡀⠀⠀⠀⠀⠀⢀⡔⠋⠀⣠⡯⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⣟⡄⠠⠄⠀⠠⠷⢄⡀⠈⠻⣦⢠⣀⣔⡴⠋⠀⣠⠞⠁⠀⠀⠀⠀⣼⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣤⣤⣴⣶⣶⣶⣿⣷⢦⣬⣿⣿⡟⣡⣴⡬⠤⢤⣤⣤⣤⣤⣴⣟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣉⡅⠞⠛⠃⢠⠄⠉⠲⢺⢿⣿⢏⡷⡯⢤⡄⠂⠉⠛⢿⣿⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣅⡠⠀⢀⡚⠉⡠⠊⢀⠂⢸⣿⠙⡇⡀⢄⠈⠫⠁⠀⠀⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠈⠔⠑⠒⠁⢀⠂⠐⢨⣿⠀⠰⡈⠄⠑⡆⢬⠀⠀⠀⢸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⡄⠀⠀⠀⠂⢀⠀⢀⠠⢻⣿⠀⠀⢡⠈⣄⠈⠄⠣⡈⣲⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣫⣶⣠⡴⢀⢴⣠⡆⠀⠘⠏⠀⠈⢢⣆⣈⣄⡸⣤⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣴⠶⠶⢶⠶⠶⡶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⣿⠀⠀⠀⣧⠀⠀⢸⣀⣀⣿⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣤⡤⠾⠶⠶⠶⠛⠛⠛⠛⢋⣩⣭⣉⠉⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣹⣧⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠉⠀⠙⣧⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣋⠴⠋⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢿⣹⣄⣀⣠⡟⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠚⠁⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⣀⣀⣤⣴⠶⠞⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣟⣁⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⢀⣀⣤⡴⠾⠛⠋⠉⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠳⠶⠾⢿⡶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⠞⢹⠇
⠀⠀⠀⠀⠀⣴⠦⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠘⠷⢦⣤⣤⣀⣽⣻⣦⡀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠛⠛⠋⠉⠉⠁⠀⠀⠀⠈⠉⠒⠶⢾⡷⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⡟⣷⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⠹⣿⣻⡿⠿⠿⠿⣟⣛⣛⣛⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣀⡀⣀⡀⠠⡄⢸⡆⢸⣿⡁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⣿⣶⣶⣦⡤⠤⠤⠤⠤⠤⠤⠤⠭⣽⣃⣽⡗⠀⠀⠀⠀⠀⢸⠀⢸⡏⠛⠋⣿⠀⡷⠘⠇⠘⠃⠙⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠈⣿⠸⣯⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⢹⢸⡇⠀⠀⠀⠀⠀⢸⠀⠈⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⢸⡇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣇⣀⣀⣿⣘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⠇⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡏⠀⠀⠀⠀⠉⠉⠙⠒⠒⠒⠒⠋⠉⠉⠉⠉⡇⣼⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⠞⠻⡄⢀⡼⠁⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠛⢢⠀⠀⢀⠴⣿⠒⣄⠀⢀⠇⠀⠀⠉⠉⠀⠀⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡟⠀⠈⠓⠴⠋⠀⣿⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⢓⣠⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⡇⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣸⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⡟⠉⠛⠶⢦⣤⣀⣀⣧⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣍⡓⠦⢤⣤⣀⣀⣀⣀⣀⣠⡤⢞⣡⡟⠀⠀⠀⠀⠀⠈⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠤⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣧⣿⢳⠆⠠⡀⠀⠀⢀⡶⣤⡘⣦⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⣺⣿⡩⢟⣶⡐⣆⣠⠀⠀⠀⠀⢱⡜⠱⠂⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢛⣳⣯⡀⠛⢻⡟⠁⠀⢢⠀⣀⣠⠞⠉⠀⠘⠆⡾⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠘⠀⣿⣄⡿⣧⠎⠞⠀⠠⣤⣿⡏⢻⡶⠶⠦⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠈⢿⣯⣰⡇⠓⡀⢀⡀⣈⠻⠶⠊⠁⢀⡴⠣⣈⡛⠧⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⣈⠁⠙⠀⠀⠈⠉⠁⠢⣄⠀⠀⡌⠁⠦⢈⡷⠄⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣄⣙⡇⠀⠐⢛⣛⣉⠁⢸⠃⡀⠴⡀⠓⠀⢠⢤⠢⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠟⠛⠉⡃⠀⠃⠋⢿⠿⠇⣸⣦⠈⢲⠈⠷⠶⡄⡀⠘⣋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣿⣿⠄⣀⡀⠠⣥⡴⢤⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡄⠀⠓⠐⠘⠁⠀⠀⢰⣏⣿⢁⣴⣽⣿⠛⢥⣰⢒⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢥⠰⣞⠀⢤⡄⠀⠀⠸⡈⣿⣿⠇⠸⢿⠓⣨⠻⢿⣺⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠁⠀⠀⠀⢀⣠⣿⢟⠉⠀⠐⠈⠠⣤⠐⠠⠅⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠿⣷⣤⡤⠶⠞⠛⣿⢫⣄⠀⠀⠀⠀⣀⣤⡓⠂⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢈⠀⠈⠙⣿⣧⡀⠀⠀⣼⣠⣼⣷⣱⠃⠘⠋⠉⣷⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣼⢧⡇⠀⠐⣿⠋⠁⠠⠛⠓⠸⠇⠀⢙⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢸⣂⣾⢉⠀⢨⠀⠀⠀⠻⡙⠆⠀⠀⠀⣇⢀⣿⠯⡔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⡿⣾⣤⣾⠻⢿⣿⡢⠉⠛⠀⠀⠀⠱⠒⠀⠸⠀⠋⢹⡿⠀⠰⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⢠⠈⣰⣤⣩⠇⠀⠀⠀⠠⢄⠀⠀⠀⠐⠣⠀⠈⠁⠰⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡈⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠏⠲⠊⠁⠀⠀⠀⠠⢀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠈⠄⠐⠀⠄⠀⢀⠘⠀⠠⠚⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⡀⠶⣄⣦⠀⠀⠛⠇⠀⣴⠱⠈⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠐⠑⠢⠼⠀⠀⠀⠠⣹⣆⡀⡀⢼⡠⢃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⢀⡀⠰⠀⠀⠀⠀⠈⣿⡁⠀⠸⠏⠀⠀⠀⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠁⢀⣀⠀⣄⠀⠀⠀⠀⢿⡇⠐⠆⠂⠀⢀⠀⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠼⡇⠀⢺⡃⠀⠀⠀⠀⢀⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠰⠋⠁⢻⠣⠆⢉⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠺⠲⡀⠀⠀⠐⠒⠋⢾⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡆⠄⠂⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠇⠉⠀⠀⠈⠀⠈⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣤⣴⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤
⠀⠀⢸⣿⣷⣿⣿⣿⣿⠿⣖⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣲⠿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠈⢻⣿⣿⣟⢉⣿⣶⡿⢏⣻⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣟⡹⢿⣶⣿⡉⣻⣿⣿⡟⠁
⠀⠀⠀⠀⠙⣿⣿⣿⡉⠉⠙⠻⡋⠉⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠛⠉⢙⠟⠋⠉⢉⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠘⣿⣿⡟⠉⠉⠀⠓⢤⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⡤⠚⠀⠉⠉⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⡷⠒⠒⠒⠒⠒⠚⠓⠢⣄⠈⠻⣄⢰⡆⣠⠟⠁⣠⠔⠚⠓⠒⠒⠒⠒⠒⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠒⢬⣿⣿⡥⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⡿⠿⠿⠿⢿⣛⣻⡿⠿⢿⣿⣿⡿⠿⢿⣟⣛⡿⠿⠿⠿⢿⣿⡋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡯⠤⠒⢒⡲⠋⠀⠀⡠⠖⣡⣿⣿⣎⠲⢄⠀⠀⠙⢖⡒⠒⠤⢽⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠤⠒⢉⡝⢀⣀⡤⠊⢀⠜⡱⣿⣿⢏⠣⡀⠑⢤⣀⡀⢻⡉⠒⠤⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⡤⠚⢁⠏⠁⡔⠁⢠⠊⡰⠁⣿⡿⠈⢆⠑⡄⠈⢣⠈⠹⡈⠓⢤⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣤⠎⠀⡸⠁⡠⠁⢰⠃⠀⢸⡇⠀⠘⡆⠈⢆⠀⢆⠀⠑⣤⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣯⣷⣾⣧⣴⡁⣠⠏⠀⠀⠘⠃⠀⠀⠹⣄⢈⣦⣼⣷⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣻⡏⡍⣝⠛⠛⠻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⠙⣿⣿⣿⣿⣿⣿⣏⣿⣇⣿⣧⣿⣹⣹⣼⣵⢹⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣻⣿⣭⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣷⣿⣧⠻⢟⣛⣭⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡟⠋⠁⠀⠀⠀⠙⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⠿⠿⣟⣻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠦⣤⣀
⠀⠀⠀⠀⣀⣤⡶⠶⢶⣶⣿⠁⠀⠀⠀⠀⢈⣿⣶⠶⠶⣶⣶⣶⣤⡀
⠀⠀⢰⡿⣿⣧⠒⡒⠂⠉⠹⠓⠶⢶⣤⠖⠉⠁⠀⠤⣀⣶⣶⣿⣻⣿
⠀⠀⠘⢷⣜⠻⢿⣿⣷⣶⣶⣶⣤⣤⣤⣒⣒⣲⣾⠿⠿⠟⠛⣁⣹⡏
⠀⠀⢠⣾⣟⠻⢷⣴⣦⣦⣶⣤⣍⣥⣀⣀⣠⣤⣴⣶⠶⠾⠟⠛⣻⡟
⢀⣤⣤⣽⡿⠷⣶⣷⣂⣀⣨⣭⣉⣉⣉⣉⣉⣥⣤⣤⣤⡤⠶⠿⠟⣷⣀
⣼⡟⠛⠝⠻⠿⣶⣶⣬⣩⣭⣋⣉⣩⣭⣭⣩⣭⣤⣴⣤⣤⣴⣾⠿⠟⠻⠟⠛⣿⣦
⠙⢷⣦⣄⣀⣀⣀⠀⠀⠉⠉⠉⠉⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿⠟⠃
⠀⠀⠈⠙⠿⠿⠿⠿⣿⣿⣶⣶⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣤⣎⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⡆⠀⠀⢰⡄⣻⣖⢞⡢⡀
⠀⠀⠀⠀⠀⠀⡰⣿⣨⣼⣿⡷⠒⠂⠀⠀⠀⠀⠀⠀⠏⠇⠿⠾⣶⣶⢾⣰⡲⠀⠀⠀⠀⣀⣿⠿⡿⠀⠀⢀⠀⠀⣗⠀⢀⡀⠹⣴⡛⢿⣿⡟⣢⡀
⠀⠀⠀⠀⢀⣼⣁⡁⠈⠋⠹⣿⡶⣦⡄⡀⠀⠀⠀⠀⠰⢯⣀⢀⣘⣁⣀⣀⡀⠀⠀⠀⠸⣤⣿⣿⣷⡀⠀⢸⠛⠛⠟⠿⣿⠇⠀⠘⢷⡟⠋⣽⡿⠇
⠀⠀⠀⠀⢀⡿⢿⠋⠓⢠⣰⡎⠱⠿⣄⠀⠀⠀⠀⠀⠛⠋⢙⣿⠙⠉⢻⡟⠁⠀⠀⠀⠀⣨⣿⣿⣿⣇⠀⠀⠙⠒⠒⠚⠋⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⣿⣥⡜⠿⢤⣤⡛⠛⣅⣠⣠⠢⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣟⠉⠉⠉⠻⣷⡄⠀⠀⢀⣀⢤⣄⣤⣴⣶⣶⣆
⠀⠀⠀⢰⣟⣁⣀⣀⠬⡿⣿⡉⣉⠿⠛⢦⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⣟⡤⢀⢹⡇⠀⠀⢻⣸⠿⡟⢛⣟⠿⢯⣏⣦
⠀⠀⠀⠀⡿⢿⣿⣄⣀⣉⣿⣿⣛⡶⣶⡀⠀⠀⠀⠀⣞⣻⣿⣿⣭⣉⣳⣶⡄⠀⠀⢸⡷⣆⠙⠋⣁⣄⣾⡇⠀⠀⠀⠿⣿⠋⠽⣿⣶⣾⣿⡍⣱⡄
⠀⠀⠀⠈⣷⣤⣄⠀⣿⣧⣠⣬⣿⢿⣦⡌⠁⠀⠀⢀⣿⣿⣿⣿⠭⣽⡾⣊⠅⠀⠀⠨⣿⢿⣖⢒⣲⣿⣿⠅⠀⠀⠀⠀⠈⠛⠻⢤⣀⣿⡛⣫⡟
⠀⠀⠀⠀⠀⠈⠛⠓⠙⢺⠛⠉⠉⠒⠛⠀⠀⠀⠀⠸⣿⣿⣛⣿⣷⣿⣿⢟⡀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣀⣠⣤⣄⡀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠿⣯⣽⡷⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣶⣢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⣺⣿⣿⣶⣤⣬⣼⣟⡿⢷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣋⠙⠫⠻⡯⣿⣿⠟⠡⡄
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣻⣿⣿⣿⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣽⣍⣻⣷⢤⣾⣿⣿⣵⣤⠄
⠀⠀⠀⠀⠀⠀⠙⢏⢦⣠⢒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡉⠙⢛⣛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠽⠟⠋⠁
⠀⠀⠀⠀⢀⠀⠴⡌⢧⣁⣼⠏⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡄⣰⢿⠟⠋⠨⠳⠈⣿⣠⠀⠀⢠⡀⡀⢠⢤⢴⠀⠀⠀⠀⠀⠀⡠⠚⣮⣼⠿⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠤⠲⣼⢹⣿⣤⠢⡀⠒⢤⢾⣴⠃⠀⠀⣞⠁⢑⣫⠀⡤⠂⠀⠀⠀⠀⠠⠛⣻⠄⠀⠰⢤⣿⣿⣿⣙⠀⠀⠀⢀⡀⣄⣢⣼⣏⢡⡗⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠠⢵⣄⠂⠀⠀⠀⠀⢶⡞⣾⣼⣃⣀⣉⣵⠆⠀⠀⠀⠸⣄⠙⠛⠶⠾⢿⣏⣴⣿⡿⠀⠀⠀⣩⣵⣿⣿⣿⣿⠛⣦⡛⣠⡀
⠀⠀⠀⠀⠀⠁⠈⠁⠈⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠒⠙⠟⡉⠓⠒⠂⠀⠀⠀⠑⢀⠈⠻⣷⣶⣶⣾⣿⣿⠏⡀⠀⠀⠀⣰⣿⠻⣿⢛⣿⣶⣾⡱⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠤⠘⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⡀⠀⠀⢀⡤⢀⣤⡅⠀⠈⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠂⠙⡀⠒⠁⠐⠊⠉⠈⠁⢀⣀⣀⠍⠉⠓⠲⠆
⠀⠀⠀⠀⢀⣀⠀⠀⠀⢨⠀⠀⠀⠒⢈⡇⠀⠀⠀⠀⢀⣀⢌⡉⢉⠀⠀⠀⠋⠉⢒⡒⡀⠀⠀⣀⢲
⠀⠀⠀⠨⠁⠀⠀⡅⠅⢀⠀⠀⠀⠉⠉⡔⠲⠄⢙⡦⡗⠒⠳⠬⠙⠛⠗⠡⠒⠤⠀⡤⠶⠖⠁⠀⠀⡀
⠀⠀⠀⠐⠠⢀⡴⠒⠱⠲⠈⠉⠉⠉⠁⡭⡀⠈⡨⡧⢄⠤⣀⣀⣤⣀⣌⣁⠀⠀⡀⠤⠔⣊⡊⠤⠒⠃⠉
⠀⠀⠀⠀⠀⠀⠂⠤⠤⠴⠦⠀⠀⠤⠴⠋⠁⠊⣼⠒⠐⢂⡀⢀⠀⠈⠉⠙⠃⠀⠐⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠿⠿⢿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣦⣤⣀⣀⠀⠀⣀⣀⣤⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠈⣿⣿⣧
⠀⠀⠀⠀⣀⣿⣿⣿⡀⠀⠀⣠⣾⠟⡋⠉⠀⠀⠀⠉⠉⠛⠛⠿⠿⠟⠛⠋⠉⠀⠀⠀⠈⢙⡻⣿⣦⡀⠀⠀⣼⣿⣿⣄⡀
⠀⣴⣿⡿⠿⠿⢿⣿⣇⠀⣼⡿⣡⣾⣿⣷⣦⣄⡀⠀⠘⣧⠀⠀⠀⠀⣰⡇⠀⠀⣀⣴⣶⣿⣿⣎⢻⣷⡀⢰⣿⡿⠿⠿⠿⣿⣶
⢰⣿⡏⠀⠀⠀⠀⣿⣿⢠⣿⡇⠙⢻⣿⡿⢿⣿⣿⣷⣦⣽⣧⠀⠀⣰⣿⣤⣶⣿⣿⣿⠿⣿⡟⠛⠁⣿⡇⢸⣿⡇⠀⠀⠀⢸⣿
⠈⣿⣧⠀⠀⠀⠀⢿⣿⡀⣿⡇⠀⠀⢻⣷⣤⣈⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣟⣋⣁⣠⣼⡿⠃⠀⢀⣿⡇⣿⣿⠁⠀⠀⠀⢸⣿
⠀⣿⣿⠀⠀⠀⠀⣸⣿⡇⢹⣿⡀⠀⠀⠈⠛⠛⣻⣿⡿⢛⣍⠉⠉⢉⡟⠿⣿⣿⠛⠛⠉⠀⠀⠀⣼⡿⢀⣿⣿⠀⠀⠀⠀⢸⣿
⠀⢻⣿⡀⠀⢸⣿⣿⣿⣧⠀⢻⣧⠀⠀⠀⢀⣾⡿⠋⠀⠈⠉⠁⠐⠉⠉⠀⠈⠻⣷⣄⠀⠀⠀⣰⣿⠃⢸⣿⣿⣿⡇⠀⠀⣿⣿
⠀⢸⣿⡇⠀⠈⠿⠿⣿⣿⠀⠈⢻⣷⡀⢠⣿⠏⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠙⣿⣆⠀⣴⡿⠃⠀⣼⣿⠿⠿⠇⠀⢠⣿⡟
⠀⠀⣿⣿⣀⣀⣀⣀⣹⣿⡆⠀⠀⠙⢿⣿⠏⣀⣴⡾⠟⠋⠉⠉⠉⠉⠉⠛⢿⣶⣄⠘⣿⣾⠟⠁⠀⠀⣿⣿⣀⣀⣀⣀⣼⣿⠇
⠀⠀⠈⠻⠿⠿⠿⣿⣿⣿⠇⠀⠀⠀⣸⣿⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⠀⠀⠀⠰⢿⣿⣿⡿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⣄⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣟⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⡽⢩⣟⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡟⠻⠛⠉⣿⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣠⣴⢁⠔⠋⣀⠽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡏⠀⡟⢁⡠⠚⠁⣀⣼⡿
⠀⠀⠀⣴⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡿⠀⢠⠓⠉⠀⣠⣾⠟⠁⣀⣀
⠀⠀⠀⠻⣿⣟⢲⡟⠫⣿⣷⣶⣤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡎⠀⣠⣾⣿⡿⠛⢉⡻⠿⣿⣷⡀
⠀⠀⠀⠀⠈⠻⣿⣯⣽⠿⠅⣨⡟⠻⢿⣶⣥⣀⠀⠀⠀⠀⠀⢸⠀⣸⣠⣾⢟⣟⡡⠔⢊⠡⠄⠒⠊⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡤⠤⠝⠲⢤⣀⡉⠛⠻⢦⣄⣰⣶⣾⡶⠟⣫⠔⠉⠉⠁⠉⣳⢶⣒⠉⠉⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡒⠂⠉⠁⠀⠉⢉⣉⣽⣿⢿⣿⣷⣿⣒⠒⠒⠒⠛⠣⠤⣀⠀⠉⡳⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⠾⣿⣿⣿⣛⡫⠔⢋⠻⣿⣿⡪⢍⠒⠢⠤⣀⡀⠀⢉⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣀⠜⢫⠀⢀⠆⠘⡘⡝⣿⡁⠛⠦⣄⡀⢈⣹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠋⣤⡼⡄⠀⢇⠸⣸⢿⣄⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣥⡑⡘⢄⠘⠀⢹⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠷⣷⡾⠁

⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⣶⣶⡶⡶⡶⣶