Chorus Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠦⣤
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢰⠋⢻⡇⢰⡋⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿
⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⡄⠀⠈⠛⠛⠁⠈⠛⢛⡁⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⡿⠛⣿
⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⠀⣠⡴⠚⠛⠉⠉⠛⠓⢦⣄⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⠋
⠀⠀⠀⢸⡇⣴⠛⠛⠛⠛⠛⠛⠛⠛⢳⣴⡟⠁⠀⣠⡞⠁⠀⠀⠀⢀⡀⠀⠀⠀⠈⢳⣄⠀⠈⢻⣤⡞⠛⠛⠛⠛⠛⠛⠛⠛⣧⢸⡇
⠀⠀⠀⢨⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣇⠀⢠⡏⠀⠀⢀⣀⣤⠞⠳⣤⣀⡀⠀⠀⢹⡄⠀⣸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠘⣧⡀⠐⠟⠓⠀⠀⠐⠛⠆⠀⣠⠟⠀⢸⠁⠀⣰⡏⠁⠀⠀⠀⠀⠈⢹⣆⠀⠈⡇⠀⠻⣄⠀⠲⠛⠂⠀⠀⠚⠛⠂⢀⣼⠃
⠀⠀⠀⠀⠈⣧⠀⢀⡴⠖⠒⢶⡄⠀⢰⡇⠀⠀⢸⡇⠰⣏⠈⠛⠓⣀⣀⠚⠛⠁⣹⠆⢸⡇⠀⠀⢸⡆⠀⢠⡶⠒⠲⢦⡀⠀⣼⠁
⠀⠀⠀⠀⠀⠘⢆⠀⠙⠦⠴⠞⠁⣠⠟⠀⠀⠀⠈⢷⠀⠘⣇⠀⢻⣍⣩⡟⠀⣸⠃⠀⡾⠀⠀⠀⠀⠻⣄⠈⠳⠦⠴⠛⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⢛⡶⠶⠶⠶⣞⠉⠀⠀⠀⠀⠀⠈⢷⣄⠈⢳⣦⣬⣥⣴⡞⠁⣠⡾⠁⠀⠀⠀⠀⠀⠉⣳⠶⠶⠶⢶⡛⠁
⠀⠀⠀⢀⣀⣤⡴⠿⢧⣄⣀⣤⠿⠦⣤⣄⣀⠀⠀⢀⣠⣽⡷⠿⣦⣄⣀⣴⠿⢾⣯⣄⡀⠀⠀⣀⣠⣤⠴⠿⣤⣀⣠⡼⠿⢦⣤⣀⡀
⠀⠀⡴⢫⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣝⢳⡜⢫⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡝⢷⡞⣫⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⡝⢦
⠀⢸⡇⢸⡇⠉⠛⠳⢦⣀⢀⣤⠶⠛⠉⠀⣿⠀⣷⢸⡇⠉⠛⠶⣦⣀⣀⣴⠖⠛⠉⢸⡇⣾⠀⣿⠀⠉⠛⠶⣤⡀⣀⡴⠞⠛⠉⢸⡇⢸⡇
⣴⠾⠶⢾⡇⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⣿⠶⠿⢾⠃⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠸⡷⠿⠶⣿⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⢸⡷⠾⠷
⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠿⠀⠀⢸⡆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣶⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢘⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⣏⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣼⣧⣤⣤⣤⣤⣴⣧⣤⣤⣤⣤⣤⣿⣤⣤⣼⣧⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣼⣧⣤⣤⣿⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣼⣧
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⣤⣤⣤⣤⣤⣤⣤⣤⡄
⣿⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⠄⢤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⣿⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⣿⣤⣤⣬⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣥⣤⣤
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⢀⣷⣾⣠⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢻⣿⣿⡿⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠙⠛⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠤⠠⢚⡁⠀⠀⠀⣓⠠⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠸⣿⣷⣾⣿⠗⠀⠀⠠⣿⣿⣴⣿⠟⠂⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠀⠀⠀⠠⡀⠀⠀⢀⡞⠀⠀⠠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⡍⣡⣴⡆⠀⠀⢰⣧⣝⢈⣤⣷⠀⠀⢠⣬⡐⢘⣡⣴
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢻⣿⣿⣿⠟⠁⠀⠀⠺⣿⣿⣿⣿⠟⠀⠀⠉⠻⣿⣿⣿⠟⠀⠀⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⢨⠛⠿⠇⠀⠀⠀⠀⠀⡟⠿⠿⠟⠀⠀⠀⠀⠀⡿⠿⠏
⠀⠀⠀⠀⠐⠠⢀⣀⠀⡊⠀⠀⠀⠠⢀⣀⡀⠸⠀⠀⠀⠈⠦⡀⠀⣀⠔⠀⠀⠀⠆⡀
⠀⠀⠀⠀⢸⣶⣦⣴⣶⣿⠀⠀⢸⣷⣦⣀⣤⣾⡇⠀⠀⠀⣷⣦⣁⣭⣶⡇⠀⠀⣷⣬⣁⣤⣴⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠋⠉⠋⠁⠀⠁⠀⠀⠘⠙⠛⠛⠀⠀⠀⠀⠀⠨⠙⠛⠋⠃⠀⠀⠀⠈⠙⠛⠛⠁
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠀⠀⠤⠄⠀⠊⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⡀⠀⢀⠠⠃⠀⠣⠀⠀⠀⠀⠠⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣀⠀⠀⠀⠖⠀⢀⠀⣀⠀⠀⠀⠀⢠⠀⡄⠀⠠⡀⡀⠀⠀⢰⠋⡲⠡⠬⠦⣖⣖⠒⣆
⠀⠀⠀⠀⡀⠀⠀⠰⣽⠃⠀⠀⠱⡄⠀⠀⠠⡸⠓⠓⠲⣇⠀⠀⠀⠀⠀⡠⠂⠙⢳⡇⢠⠖⢊⣶⠁⠀⠀⠈⣿⡇⢸⡀
⠀⠘⠁⠀⠀⠈⠀⠀⢻⡀⠀⠀⢠⠇⠀⠀⠰⡇⠀⠀⠀⡿⠀⠐⠀⠀⠀⡇⠀⠀⢀⡇⠘⢲⠀⣸⢄⡀⠀⣠⠋⠈⢯⡀⠀⠀⠁
⠀⠀⢠⠂⣑⣢⣀⣀⡸⠙⢂⣐⡉⢳⡀⠀⠠⠛⠂⠀⠘⣇⢀⣀⣀⣀⣊⡉⠓⠐⠺⡄⣀⡈⡴⠁⠀⠀⠀⠈⠇⡠⠄⠀⣤⡀⠀⠈
⠀⣦⠜⢸⢃⡏⠼⠜⠉⢳⠀⠀⠤⣷⠿⠿⠿⢶⡀⠀⡴⢱⠋⠋⠋⠙⡿⡝⣆⢠⣷⠋⠀⠈⢳⡂⣰⢀⡄⣠⠚⠧⢶⣀⣙⢧⡀
⠀⠈⠒⠊⠘⣇⠠⠄⠀⡸⠀⠂⢸⡿⠀⠀⠀⠀⡇⠀⠃⠹⣄⢀⠄⣠⠇⠇⠈⠀⣇⠀⢀⠀⢸⡇⠈⡍⠁⢣⡀⠀⣀⢀⡇⠀⠙⡆
⠀⠀⠀⠀⠀⢈⣷⠀⢸⠳⡄⠀⠀⠳⣄⣀⣁⣴⡃⠈⠀⠀⣼⠏⠉⢿⣆⠀⢠⢀⣼⠦⠤⠤⢾⢄⠀⣇⢀⣴⠏⠒⢶⣜⠾⠷⠔⠁
⠀⠀⠀⠀⡔⢁⡇⠀⠈⡇⠹⡄⠀⢀⠞⡇⠒⠘⡟⣄⠀⡼⣸⠀⠀⢸⠘⡆⢀⡎⡏⠈⠧⠏⠘⡆⠳⡍⠁⡼⠀⠀⢸⠈⢦
⠀⠀⠀⠘⠧⣘⠉⠑⠡⢝⡀⠃⠀⡎⠀⡇⠀⠀⢷⢸⢠⠇⡇⠀⠀⠘⡇⢹⠈⢳⣁⣠⣄⣀⣄⣹⠞⠁⢰⠃⠀⠀⠘⡖⠦⠷
⣤⣤⣤⣤⣤⣿⣴⣤⣤⣴⣷⣤⣤⣷⣴⣷⣤⣤⣾⣿⣼⣾⣧⣤⣤⣴⣷⣼⣧⣾⣦⣼⣤⣤⣤⣾⣦⣤⣿⣤⣤⣤⣤⣷⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⠀⠀⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣶⣶⡆
⠀⠀⠀⠀⠀⢀⣠⣤⣄⡐⠧⠀⠀⠈⢹⠋⠀⠀⠀⠟⣀⣤⣤⣀⠺⠄⠀⠀⠉⡏⠁⠀⠀⠸⢃⣠⣤⣄⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⢀⣤⣤⡀⢸⠀⣠⣤⣤⢰⣿⣿⣿⣿⡆⣠⣤⣄⠀⡇⢀⣤⣤⡀⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠙⠿⣿⠿⠋⠸⠛⣿⣅⣸⣀⣽⡿⠻⠈⠻⢿⡿⠟⠀⠟⢻⣯⣀⣇⣠⣽⠟⠇⠙⠿⣿⠿⠋
⠀⠀⢠⣤⣤⣶⣶⣶⣶⣶⣤⣠⡄⠀⠉⠁⠀⣤⣤⣴⣶⣶⣶⣶⣦⣄⣤⠀⠈⠉⠀⢠⣤⣤⣶⣶⣶⣶⣶⣤⣤⡄
⠀⠀⣸⡏⠉⠛⠛⢿⠛⠛⠉⠉⣧⠀⠀⠀⢀⣿⠉⠙⠛⠻⡟⠛⠋⠉⢹⡄⠀⠀⠀⣸⡏⠉⠛⠛⢿⠛⠛⠉⠉⣇
⠀⣴⣿⣇⣀⡀⠀⢸⠀⢀⣀⢀⣿⣧⠀⢠⣿⣿⣀⣀⠀⠀⡇⠀⣀⣀⣸⣿⣄⠀⣼⣿⡇⣀⡀⠀⢸⠀⢀⣀⣀⣿⣧
⠸⣿⣿⣿⣿⡿⠀⢸⠀⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠇⠀⡇⠸⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⡿⠀⢸⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⣬⣭⣟⡻⣛⣭⡅⠀⠀⠀⠀⠀⠀⠀⢠⣭⣝⣛⢟⣫⣭⠀⠀⠀⠀⠀⠀⠀⠀⣬⣭⣟⡻⣛⣭⡅
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢸⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⣿⣿⡇
⠀⠀⠀⠀⢻⣿⣿⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡟⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⡇
⠀⠀⠀⠀⠘⠿⠃⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠻⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠉⠀⠀⠀⠀⠠⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⡀⢀⢚⡀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⣰⠤⠤⣀⠀⠀⠃⠀⣤⢠⡄⢀⠀⠀⠀⠂⠂⠀⠐⣄⡄⡀⠀⠏⡨⣃⠒⠛⠮⣯⡉⢷
⠀⢀⠀⠀⠂⡄⠀⢱⠃⠀⠀⠈⡆⠀⠀⢰⠎⠁⠉⢻⡄⠀⡀⠀⠀⡔⠁⠈⠹⡅⢸⢉⠼⡇⠀⠀⠀⣹⠧⡼⠄⠀⢀
⠀⠀⠀⡀⣀⠀⠀⠈⣧⡀⠀⡰⣇⠀⠀⢘⣄⠀⠀⣸⠁⠀⠀⠀⡀⠧⡀⠀⣰⠁⠀⠗⡠⠛⠢⠀⠰⡅⠀⠙⠂⠀⠀⠀⠤
⠀⡀⡼⢰⢲⠗⡖⡾⢄⠀⠒⠂⣜⣦⣤⣬⡀⠀⠀⡸⣠⢲⢲⠲⣶⣢⡀⠀⣈⠄⠒⢴⣁⠀⡀⠀⠀⡡⡎⣁⠐⢷⡄
⠀⠻⡁⠜⢸⠈⠉⡀⠈⡇⠠⢨⣿⠉⠉⠉⢹⡀⢸⠱⡇⠀⠀⠀⡿⣇⠳⠘⡏⠀⠀⠄⢿⠘⠷⠷⢸⠀⠈⠙⠒⡞⠑⢄
⠀⠀⠀⠀⠈⢢⡬⠠⣮⡀⠀⠈⢯⡀⠀⠄⣸⠃⠒⠀⢙⡶⠓⢲⡅⠀⠀⠀⣳⣀⠁⣠⣏⠀⢸⠀⢈⡦⠌⣃⣸⣱⣆⡸
⠀⠀⠀⠀⡔⢹⠃⠀⢧⠹⡄⠀⠀⡽⡗⠮⢻⢦⠀⢀⢎⡇⠀⢸⡹⡄⠈⡜⡏⠰⣠⠂⢯⠳⡜⠒⢹⠃⠀⢸⠱⡄
⠀⠀⠀⠸⣀⡞⠐⠒⠼⡀⠟⠀⡜⠀⡇⠀⠈⡇⡧⣸⢸⠀⠀⠈⡇⢹⠘⢾⠁⣀⠀⣀⢘⡦⠋⠀⡏⠀⠀⠸⡤⠜⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⡀⣸⣿⣿⣿⣿⣷⣾⣧⠀⠀⣹⡀⠃⡀⠀⠐⠚⠀⡔⠢⠤⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠹⣄⠈⡇
⠀⠀⠀⠀⠀⠀⣴⣿⣿⠿⣿⠏⠉⠀⢸⢿⣷⠈⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠬⡬⡗⠀⠔⠈⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡨⠖⠀⠀⠀⠀⠀⡠⡀⠄
⠀⠀⠀⠀⠀⠠⡾⠟⠈⠁⠉⠠⠁⠈⡘⡋⠿⠁⠀⡤⠀⠀⠀⠋⠀⠀⠀⠀⠆⡁⡐⣴⠶⠎⠁⠈⠡⠦⠈⢣⠀⠀⠢⠊⠀⣀⣠⠄⠀⡠⠀⠈⢃⠣
⠀⠀⠀⠀⡀⠀⠃⠄⠀⠀⠀⠂⠀⡠⠀⢀⠖⠀⠀⠀⡀⠀⠀⠀⠁⠀⢀⠆⣠⢼⡏⠁⠉⡀⠐⠀⠈⠉⢠⢌⡄⢀⣡⠊⠟⠛⠋⠉⠠⠄⠀⠆⢈
⠀⠀⠀⠨⡃⠀⠀⠈⢀⡀⠀⠀⢈⡠⠔⠁⢀⠀⠐⠀⠆⡄⠀⠀⠀⡂⠅⠊⠀⠈⡟⡀⠀⠀⠀⢀⠀⠀⢇⡴⡼⠊⢠⠀⠐⠀⠀⠀⡠⠀⠀⢂⡌⠀⡄
⠀⠀⠐⠑⠀⠀⣠⣶⣟⣡⡄⣸⣷⣀⠄⢢⠍⠀⠀⠀⣠⠟⣡⢰⣧⠀⠀⠀⠀⣀⣇⠀⠠⡀⠀⠁⠀⡴⠋⠔⠁⠀⠀⠀⠀⠀⠒⠂⠀⡀⣀⡩⠤⠚⠁
⠀⠀⠀⡀⠦⠈⠉⠉⠁⠠⠹⠁⠘⠁⠀⠈⠀⠀⠐⠀⠛⠀⠹⠉⣩⣾⣿⣿⣿⣿⣿⣶⣶⣄⣴⡆⢈⡠⠔⣂⣀⡤⠀⠀⣀⣴⣄⠄⠊⠉⠉⠁
⠀⢠⡠⠄⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠈⠀⠀⠀⢀⠅⢀⢶⠸⠋⠱⡄⠉⠈⠉⠘⣛⠻⣯⠹⠒⠟⠉⠉⠉⠁⠶⠈⢀⢈⡙⠠⢤⠴⠟⠀⠞⠄
⠀⢨⠀⡀⢂⡀⠂⠴⠌⠀⠀⢨⠿⠠⠀⠀⠀⠂⠐⢉⠴⢁⡃⣤⠀⠀⠀⠁⠀⢐⠀⠉⠀⠉⡿⠀⠀⠐⠒⠀⠀⠀⠀⠈⡀⡶⠁⠚⠁⠀⠀⠀⠺⠂⢀⣠
⠀⠀⠝⠉⠁⠀⠀⠀⡠⠀⢀⠀⣨⠄⠀⠀⣴⣠⡔⢁⠀⠀⠀⠀⠀⠀⠀⠐⠐⠁⠀⠀⡠⠉⣽⡄⠀⠀⠀⠜⠀⠀⢀⡼⣟⢣⠀⠀⠈⠁⠉⡇⠀⠀⠀⠤
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠔⡩⠔⠁⠀⠂⠚⠛⠿⡿⠛⠃⢈⠆⠖⡀⠄⠀⣄⢀⡄⠐⠁⠀⠀⣨⢬⠆⠀⠀⠀⢀⠔⢡⣴⣿⢳⠁⠀⠀⡀⠈⢀⡠⠔⡗
⠀⠠⣁⠂⢀⢠⣴⣆⣠⣺⡤⢤⠀⠀⠃⠀⠀⠀⡇⠀⠀⠊⠀⠀⠀⠰⠿⢶⡷⠼⠗⠀⠀⠀⢀⡌⠀⣴⣏⣖⢳⡄⠠⣿⡎⠂⠀⠀⠾⢭⣶⣹⠦⠀⠁
⠀⠀⠈⠂⠴⠀⠀⠈⠙⠁⠀⡐⠀⠀⠀⠆⠀⠀⡇⢀⠄⠋⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⣸⠂⠸⠿⣿⠿⠿⠿⠀⠀⠀⠐⠂⠀⠀⠀⡀⠀⠀⠠⠖
⠀⠀⠀⠈⠈⢰⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⣐⠠⠃⠈⠛⠂⠀⠀⠀⠀⠀⠀⠠⢑⠀⠀⢖⠀⠀⠀⠇⠀⠀⡠⠔
⠀⠀⠀⠀⠀⠈⠀⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠀⠀⠉⠈⠀⠀⠀⠀⠀⠐⠂⠀⠉

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⠆⠜⠀⣀⣤⣶⣶⣶⣤⣄⠐⠃⠚⠐⢀⣠⣴⣶⣶⣦⣤⡀⠀⠀⠴⠁⣠⣴⣶⣶⣦⣤⡀⠠⠁⠖⠰⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠎
⠀⠀⠀⠀⣼⣿⢿⡿⡿⣿⢿⣿⣇⠀⠀⢀⣿⡟⢋⠙⢋⡙⢻⣿⠄⠀⠀⣾⣿⡏⠛⠿⢿⣿⣿⡆⠀⠀⢰⣿⡿⡿⣿⢿⣿⣿⣧
⠀⠀⠀⠀⣿⠛⠈⠁⠁⠈⠘⣿⡿⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣿⡇⠀⢰⣿⠋⠀⠀⠀⠀⠀⢿⣇⠀⠀⣻⡟⠃⠁⠈⠈⠀⢿⣿⡀
⠀⠀⠀⠀⠉⠀⠀⠁⠀⠉⠀⠨⠁⠀⠀⠈⠁⠀⠈⠀⠈⠁⠀⠌⠁⠀⢸⣧⡀⠈⠁⠀⠉⠀⣠⣿⠀⢸⣿⣄⠀⠉⠀⠈⠁⢀⣼⣷
⠀⠀⠀⠀⠀⠀⢀⡤⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⣠⢤⢤⣀⠀⠀⠀⠀⠀⠉⠙⣀⡤⡤⣄⠘⠉⠀⠀⠈⠋⠁⢀⣠⢄⢤⡀⠀⠉⠋
⠀⠀⠀⠀⠀⠀⢸⠀⠛⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠃⡇⠀⠀⠀⠀⠀⠀⠀⢸⠈⠛⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠛⠁⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢈⣾⣧⣤⣼⣾⠀⠀⠀⠀⠀⠀⣱⣿⣤⣤⣷⡇⠀⠀⠀⠀⠀⢨⣾⣦⣤⣾⣮⠀⠀⠀⠀⠀⠀⣵⣧⣤⣴⣷⡅
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⠈
⠀⠀⠀⠀⠀⢀⣄⡄⠀⢀⣄⡀⠀⠀⠀⠀⠀⣠⣀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⣀⣅⣇⣄⡀⠀⠀⠀⠀⠀⠀⢀⣨⣭⣠⡀
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠛⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠹⣆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣤⣤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠈⠱⡜⠷⢞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠭⠥⣤⡀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠙⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠽⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠈⠳⣄⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⣀⣰⣤⡀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠘⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢻⠀⠉⠙⠒⠒⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⢸⡇⠀⠰⠋⣉⣀⢸⡆⢴⣦⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⡇⠀⠀⣾⠉⠉⠙⢿⡻⠟⢁⣤⠤⣤⠀⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢸⠃⠀⠀⢻⡀⠀⠸⠟⣷⢤⡟⠀⠀⢸⡟⠁⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢀⡟⠀⠀⠀⠀⣳⣤⣤⣴⡃⠸⠃⠀⢀⡼⠡⡄⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡼⠁⠀⠀⠀⠈⠁⣤⢀⣄⠀⠀⠀⠀⠁⠠⠆⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠴⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢴⣒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢦⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⣀⣠⠖⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡔⠀⠀⣀⣠⠶⠋⠁⠀⢺⡖⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠏⠀⠀⡀⠈⠙⠲⠦⣤⣄⣀⣀⣀⣄⠀⣤⠤⠒⠋⠁⠀⣀⡟⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⣠⡖⢋⣀⣠⠴⢺⡃⠀⠀⠀⠀⠀⠀⠀⣀⣀⣻⠀⢸⣤⠤⠖⠚⠉⠁⠀⠀⠀⠀⢀⡴⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⢽⠹⠆⣼⠋⢦⣀⠀⠀⠀⠀⢀⡤⠚⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣞⣒⣤⡃⠉⠉⡈⠳⣄⡤⠚⠉⠀⢀⠔⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣇⠀⠀⠀⠈⠉⠉⠉⠙⡿⠁⠀⠀⠀⢠⡞⠛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠤⢬⡇⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢼⣉⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠶⢾⠁⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠁⠀⠀⠀⠀⠀⠀⢀⡇⢀⣀⡤⠴⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢓⡶⠶⠶⠶⠶⠶⠶⣾⠿⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡳⠶⣶⠾⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⠉⣯⠉⠁⢀⣏⣀⡉⣹⠋⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠬⠭⠿⠿⠛⠶⠤⠤⠤⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠆⠀⠀⠀⠖⠀⠀⠀⠀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠐⠢⠬⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⠒⡆⠀⠀⠀⠀⣀⡇⠃⠀⠀⠀⠀⡀⠀⠀⠀⣤⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢦⡴⠀⠀⠀⠘⠛⠁⠀⠀⠀⢀⡘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⢀⣶⣶⣆⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⢠⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠘⠿⠿⠁⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠘⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠀⢰⣿⣿⣿⣿⣿⣷⠄⢀⣾⣿⣿⣿⣆⠀⣼⣿⣿⣿⣿⣿⡦⢰⣿⣿⣿⣿⡿⣷
⠀⠀⠀⠀⣰⣶⣶⡙⣿⣿⣿⢩⣶⣶⡍⣿⣿⣿⡏⣴⣶⣮⢹⣿⣿⡏⣵⣶⣮⢹⣿⣿⣿⢣⣶⣶⡅⣿⣿⣿⢃⣶⣶⣆
⠀⠀⠀⠀⠙⠿⠟⠱⣿⣿⠿⠘⠿⠿⠃⠿⣿⣿⠇⠻⠿⠋⢾⣿⡿⠇⠻⠿⠟⠸⢿⣿⠿⠘⠿⠿⠃⠿⣿⣿⠆⠻⠿⠋
⠀⠀⠀⣰⣿⣿⣿⣷⡘⢡⣿⣿⣿⣿⣿⣿⡜⢃⣾⣿⣿⣿⣧⠛⣴⡿⣿⣿⣿⣿⣷⢡⣿⣿⣿⣿⣿⣿⡜⢃⣾⣿⣿⣿⣦
⠀⠀⢠⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⡄⣿⡇⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⡄
⠀⠀⠼⢿⣿⣿⣿⣿⠿⠜⠿⣿⣿⣿⣿⠻⠇⠿⣿⣿⣿⣿⡿⠷⠻⠇⣿⣿⣿⡟⠿⠸⠿⣿⣿⣿⣿⠿⠧⠿⣿⣿⣿⣿⡿⠷
⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⠀⠀⢠⣿⣿⣿⣿⠗⣀⣀⠀⣿⡟⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⡏⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⣽⡇⣾⣿⣿⣷⢘⡇⣿⡇⠀⡀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⢹⣿
⠀⠀⠀⠀⣿⡗⣿⡇⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⡿⠇⠙⠿⠿⠋⠸⠇⣿⡇⠀⡇⠀⣿⣿⣿⣿⠀⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⠙⠁⠙⠁⠀⠀⠀⠈⠁⠈⠃⠀⢰⣦⡈⠋⣴⣾⣿⣿⣿⣿⣷⣦⡙⢁⣴⡧⠀⠘⠃⠘⠁⠀⠀⠀⠈⠋⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠉⣿⣿⣿⣿⡍⠻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢸⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠒⠓⠶⣤⣀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠉⢻⡄⠀⢀⣴⠞⠛⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⣏⣤⣄⣀⡀⣀⣀⣤⣸⡇⠀⣾⠁⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⣠⡶⢷⡀⢸⡇⠀⣿⠇⠈⠉⠉⠉⠉⠈⣿⡇⠀⣷⡟⠶⣤⣤⠴⠾⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟⠛⠋⠁⠀⠈⣳⠀⡇⠀⢻⡀⠀⢀⣀⣀⠀⠀⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⢷⡐⣿⣛⡿⢠⡟⢸⡇⠀⠘⣧⡸⣯⣉⣽⠇⣸⠇⠀⠀⠸⣆⢴⣟⣛⣷⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣈⣿⠶⠴⠶⣿⣀⡘⣧⢀⣀⣼⠷⠶⠤⠴⠾⣿⣄⣀⠀⣀⣿⢦⣭⣭⡵⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⢷⣄⣀⣠⣿⣭⣽⣟⣋⡁⠘⠳⠶⠶⠶⠞⠋⢈⣉⣻⣯⣽⣷⠶⠶⠶⠋⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠁⠀⢸⡇⠀⠉⠉⠉⠛⠛⠓⣶⠞⠛⠛⠋⠉⢉⠁⢀⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣧⣀⡀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣤⣶⠿⣿⠀⢸⡇⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⣿⠀⣾⠓⠒⠒⠚⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⢠⡿⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⣿⠀⠺⠛⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠓⠲⠶⠶⠦⣿⠴⠶⠶⠶⠚⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣴⣾⣿⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⢿⡿⠄⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣆⡀⠀⠀⠀⢰⣿⣿⡿⣿⣷⠀⠀⠀⠸⡏⢁⣀⢹⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣀⣸⡇⠀⠀⠀⠀⠀⠀⢸⣿⠉⡟⠉⢻⣷⠀⠀⠀⣸⠿⣯⣴⣟⢻⠀⠀⠀⠀⡇⢉⡇⠉⣽⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣌⡜⣸⠇⠀⠀⠀⠀⠀⠀⢰⡷⢶⠿⡶⠶⡿⠀⠀⠀⠙⣤⣦⡍⢠⡾⠃⠀⠀⠀⢹⣾⡿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⣀⠄⠙⠿⣿⠋⣠⣠⣴⣶⣶⣄⠀⠀⠸⣄⣶⣆⣾⠀⠀⠀⠀⠀⠸⣿⣾⣸⢇⠀⡠⢠⣴⣧⣙⣾⡋⢠⡷⠀⣠⡄⡇
⠀⠀⠀⠀⢀⠀⣹⣤⠀⢱⣼⡿⠔⣿⣿⣿⣿⣿⣿⣁⠠⢄⢙⣿⣿⠁⣦⣄⡀⠀⠀⣆⢹⣟⢁⡤⠓⠦⡄⠀⡀⠉⠉⠉⣿⣶⣿⣿⢁⠀⢤⡀
⠀⢦⣤⣴⣍⡁⡝⡿⠆⠐⢇⣶⢄⣿⢟⣉⡉⢹⡿⠟⢢⣦⠛⢿⣿⡿⢫⠔⠉⠁⠶⠹⣟⠻⡏⡄⠀⠀⡆⠀⠀⠁⠀⠀⣿⣿⣿⠷⣏⠁⣆⣷⡄
⠀⠘⢿⣿⣿⣿⣶⣤⣸⠀⢺⡿⣸⣿⣎⡅⣠⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⡿⣸⡇⠀⢠⡇⠀⠀⡆⠀⠀⣿⣿⡟⢈⢹⣿⡉⠘⢿
⠀⠈⠀⣬⠛⢿⣿⣿⣿⣿⢩⣛⠟⢿⡈⣻⡝⢋⣨⣦⣤⣀⠀⠀⠀⠀⢀⡀⢣⢧⣶⡀⢢⢣⡟⠀⠀⠸⡇⠀⠀⠇⠀⠀⢿⣟⡴⢟⢰⣿⣿⡄⠸
⠀⡄⠀⣸⣧⣸⣿⣿⡿⠋⠈⣿⣿⣶⣿⠛⠉⠉⠉⠀⠀⠀⠑⢤⠀⢀⠠⡧⠞⣼⣿⣷⣌⠻⡇⣠⣾⣿⠃⢀⣠⣦⡆⠀⠸⡟⠀⠸⣾⣿⣿⣿
⠀⡇⣀⣿⣿⣿⣿⣿⣠⠀⣹⠾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠂⠀⢈⡀⢀⣤⣾⣾⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⠁⠁⠀⠁⡄⠀⣿⠙⣿⣿⣦
⠀⠛⡿⠟⠋⡽⡻⠇⢉⣿⣟⠁⢻⣿⣿⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⢿⣿⣿⣿⣿⣿⠿⣿⣿⢰⣿⣿⣿⣿⣿⣿⠭⢻⣷⣶⠞⢸⠀⢹⡄⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠇⢀⣾⣿⡇⠷⣤⣻⣿⠀⠀⠀⠀⣀⠴⢼⠓⠮⠤⠟⢻⣥⣾⠁⠻⠀⡀⠙⠛⠛⠛⠉⠁⣿⣷⣦⡜⠉⠀⠀⢸⡄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⠃⠀⢹⣷⠶⠶⢿⣿⣿⣿⣭⣷⣄⠀⢀⣼⣿⡏⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠘⠇⠀⣷
⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⡟⠀⡾⠀⠀⠀⠀⠘⠁⠹⠏⣿⣿⣿⣷⣾⣿⣿⡇⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⠒⠒⠒⠒⠛⠉
⣀⣀⣀⣀⣀⣀⣛⣉⣀⣀⣧⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣛⣗⣒⣒⣒⣲⣶⣶⣶⣶⣦⣤⣴⣿⣿⣟⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⢀⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠆
⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠸⠦⠟⠘⠧⠼⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⡄⢀⠸
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⠁
⠀⠀⠀⠸⢃⣶⣶⣶⣶⣶⣶⣌⠋⠀⠀⠀⣴⣿⣿⣿⡟⢿⣿⣿⣷⡄⠀⠀⠈⢋⣴⣶⣶⣶⣶⣶⣆⠹
⠀⠀⠀⢠⣾⡿⠿⣿⣿⡿⠿⣿⡦⠀⠀⢸⣿⡿⣛⣩⣴⣬⣙⡻⣿⣿⠀⠀⠠⣾⡿⠿⣿⣿⡿⠿⣿⣦
⠀⠀⠀⠀⢹⣿⡿⠟⠛⠿⣿⡿⠁⠀⠀⢸⡟⣠⣛⣛⣿⣿⣛⣣⡘⣿⠀⠀⠀⠹⣿⡿⠟⠛⠿⣿⣿⠁
⠀⠀⠀⠀⠀⢻⣦⡛⢛⣡⡿⠃⠀⠀⠀⠘⣷⡌⢿⡏⠤⠌⣿⠏⣴⡟⠀⠀⠀⠀⠻⣧⣙⠛⣣⣾⠇
⠀⠀⠀⠀⠀⠀⢈⣉⣋⡉⠀⠀⠀⠀⠀⠀⠘⢿⡌⢙⣓⣛⠩⣼⠟⠀⠀⠀⠀⠀⠀⠈⣉⣋⣉
⠀⠀⠀⣀⣠⣤⣤⣙⣋⣡⣦⣤⣀⠀⠀⠀⣀⣤⣴⣌⣛⣋⣤⣤⣄⣀⠀⠀⢀⣠⣤⣦⣉⣛⣩⣤⣤⣀⡀
⠀⠀⣾⢨⣍⡛⠿⣿⣿⡿⢛⣋⣥⢹⡄⡇⣬⣙⠻⢿⣿⣿⠿⢛⣩⡅⡇⣼⢡⣍⣛⠿⣿⣿⡿⠟⣋⣭⢸⡆
⠀⣐⡛⢸⣿⣿⣷⣦⢡⣾⣿⣿⣿⠘⣃⠁⣿⣿⣿⣶⡌⣴⣾⣿⣿⡇⢁⡛⢸⣿⣿⣿⣦⢡⣶⣿⣿⣿⠘⣃⡀
⢸⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣸⣿⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿
⢸⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⢹⣿⡇⣿⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⢸⣿⣿
⢸⣿⡿⢸⣿⣿⣿⡿⢸⣿⣿⣿⡿⢸⣿⡇⣿⣿⣿⣿⡇⢿⣿⣿⣿⡇⣿⣿⠸⣿⣿⣿⣿⠸⣿⣿⣿⣿⠸⣿⣿
⠸⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿
⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⢋⣥⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣍⢻⣿⣿
⠸⠿⠿⠘⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠸⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢠⡀⣤⢠⠤⣄⢠⢤⡄⡄⢠⢀⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣸⡋⣿⢸⣤⡟⣸⢻⡅⣧⣼⢀⣽⡆
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⡤⠄⠀⠀⠀⠠⠤⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢀⠀⡀⠀⠀⣀⡀⣀⠀⠀⢀⣀⢀⣀⠀⠀⣰⡀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣇⣀⡙⠳⠛⠁⢀⡼⣿⣿⢿⣆⣀⠙⠳⠛⡀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠿⢃⡀⠰⣌⣩⣶⠁⠈⢹⣿⣿⣯⠀⣰⣆⣵⣶⡇⠀⣸⣿⣿⡇⢠⠾⣿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣾⣷⡉⢩⠈⣿⣿⣿⣧⣿⣾⣿⡿⢿⣤⡿⠿⣿⣿⣿⣴⣿⣿⣿⠀⡀⢠⣌⣡⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡿⠿⣇⣼⡶⠿⣿⣉⠛⢋⡉⠉⣷⣤⣤⣤⣆⠉⣫⡉⠛⣡⣿⠛⠚⠻⡼⠛⢻⡟⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣹⣿⣦⣤⣤⡄⢠⣾⣿⣾⠿⣿⣸⣿⠿⣿⠿⣿⣀⣿⡿⣿⣿⣿⡄⣀⣶⣶⣿⣿⡇⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣤⡿⠿⣿⣿⣿⣷⣿⣿⣿⣿⣦⣠⣭⣤⣶⣿⣶⣀⣭⣠⣴⣿⣿⣿⣶⣿⣿⣿⡟⢻⣿⣿⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣦⡴⠞⢿⣿⣦⡉⣉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠉⣡⣾⣿⣿⠘⠃⣈⢉⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⢀⣾⣿⣿⣿⣿⣿⢻⡇⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⢸⠻⣿⣿⣿⣿⣿⣿⣿⣤⢰⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣉⠛⠞⠋⣉⣿⣿⣿⡟⠘⠃⢹⣿⣿⣿⠀⠋⠃⣿⣿⣿⠈⠀⠋⣿⣿⣿⣿⣿⠿⣿⣿⠿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠙⣿⢿⡇⠀⠀⠸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⡿⣿⠀⠈⢷⣄⣠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⣿⠁⠀⣿⢸⡇⠀⠀⠀⠹⠿⠍⠀⠀⠀⠹⠿⠏⠀⠀⠀⢸⡇⣿⠀⠀⢻⣿⣿⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠈⠁⠙⠀⠀⠈⣿⣿⡏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡾⢿⣿⣿⡟⢷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠠⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠐⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠠⠄⠴⠀⠀⢠⡄⠀⠀⠀⠖⠂⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠖⠐⠂⠀⠀⠀⠀⠀⠀⠀⣉⡁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠦⠀⠀⠀⢀⣀⡀⠀⠀⣴⡿⠏⠻⢷⡄⠀⠀⢀⣠⡀⢀⡶⠞⠻⢦⠀⠀⣀⣠⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⠿⢷⠀⠋⢶⠶⠲⠆⠁⢀⣼⣿⢿⣷⠈⠰⠶⠲⠂⢄⣶⠿⠟⠻⠿⡶
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠸⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠏⣥⣤⣀⣠⠀⠄⢠⢀⠈⠀⠃⢰⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⡀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠙⠉⠁⠙⠀⠀⠈⠈⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢡⠀⠀⠉⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡏⡨⠽⠅⠀⠈⠩⠭⢉⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀⠀⠀⠀⡾⣠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣄⢷⠀⠀⠀⣀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣰⡲⢄⠀⠀⡀⠀⡀⠀⠀⠙⢆⠀⢰⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠘⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⡜⠀⢠⠞⠋⠀⠀⠀⠁⠂⠌⠦⠬⠢⢤⡠⠈⢇⠸⡀⠁⠀⠄⡠⠄⠀⠀⠀⠀⠠⢄⠠⠀⠀⢀⠇⠀⠀⠶⠃⠉⠁
⠀⠀⠀⠀⠛⠂⠀⢀⡇⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢸⠀⢿⠀⠐⠃⢠⠀⠀⠀⠀⠀⠀⡄⠙⠃⠀⡿⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠘⠛⠀⠀⠀⠈⡇⡎⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⠖⢙⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠉⠳⡀⠀⢀⣤⠀⠈
⠀⠀⢀⡠⠤⠀⠀⢀⠗⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣄⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⡰⠁
⠀⠀⠀⠀⠀⣀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠘
⠀⠀⠶⠆⠙⠋⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⢈⠀⠀⠠⡀⠀⠀⢀⡯⡘⡄⠀⠳⡀⠀⠀⠁⢠⠀⠀⡀⠈⠀⠀⢀⠞⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⠞⠑⠘⡇⠀⠀⠈⠲⢤⣀⣈⠐⢂⣀⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣢⢤⣠⠈⢀⣠⣤⡶⣄⠀⠀⣀⠞⠁⠀⠀⢀⡖⠉⠁⡁⢡⡄⢈⠈⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠠⡤⣤⣀⣀⣰⠃⠘⢟⡤⣜⡟⠀⢹⣄⣉⣩⡤⣴⣖⠶⠤⢼⣀⡀⠀⠀⢀⡀⠀⠀⠀⣀⡧⠤⠶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⡀⠈⠉⠙⠛⠛⢤⠴⠓⠛⠉⠉⠁⢀⣴⠃⢸⡦⣄⠀⠀⠈⠉⠁⢲⡖⠊⠉⠁⠀⠀⣠⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠱⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⠉⠘⡇⢸⠀⠈⢆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡰⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠙⣄⠀⠀⠀⢸⠀⠀⠀⢀⣰⠁⢀⡜⠀⠀⠣⡀⢈⡦⢄⣀⠀⢸⡇⠀⣀⡀⢼⡁⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠈⡟⠙⠲⠚⠒⡞⠋⣏⠈⠓⠉⠀⠀⠀⠀⠈⢹⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⡅⠀⠀⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣤⣤⣤⡤⢤⣤⣤⣤⣴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠤⣀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡿⠿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⡀⠀⠀⠀⠉⠒⠤⣀⠀⠀⢿⠛⠉⠁⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⠀⠀⠀⠁⠂⠄⣀⠀⠀⠀⠑⠢⢼⡀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠉⠒⠠⣴⣦⡀⠀⠁⠢⢄⡀⠀⠘⡏⠒⢄⡀⠀⣴⣾⣿⣦
⠀⠀⠀⠀⠀⠀⣰⠋⠉⠑⠒⠠⢀⣰⠻⣿⣿⡦⣀⠀⠀⢈⣵⣾⣷⣆⠀⠈⢺⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⣀⣠⡟⠐⠸⣿⡇⠀⠉⠢⣾⣿⣿⣿⠟⠢⣄⡈⠙⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡧⣀⠀⠉⠈⠑⠤⣀⠙⠿⠟⢯⣀⣠⡤⠟⡺⠛⠉⠉⢉⠉⠉⠛⠛⠒⡶⢤⣄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠟⠁⠀⠉⠐⠢⢄⡀⠀⠙⠲⣤⡶⠋⠁⢠⠎⠀⠀⠀⠠⠃⡀⠀⠀⠀⡰⢡⠇⠈⠙⢦⣠⠞⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣤⢞⡿⠁⠀⢠⠃⠀⠀⠀⢠⠃⡜⠁⠀⠀⢀⠃⡼⠀⠀⠀⠀⠙⢦⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣄⣀⣀⣠⣀⣀⣀⡀⠀⠀⡴⢣⢫⠁⠀⢀⠇⠀⠀⠀⠀⡎⢸⠁⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⣧⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠀⢀⠾⠁⠀⢸⠋⠉⠛⢲⢃⡏⢸⠀⠀⢸⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡰⡝⠈⣇⠀⠸⡇
⠀⠀⠀⠀⠀⢀⣴⠋⣠⢾⠂⣼⠸⠀⠀⣼⠀⠀⠀⢸⡞⢧⠘⣄⠀⢸⢣⡀⠀⠀⠀⢃⢹⢆⠀⠀⠀⠸⠀⡇⠀⠀⢀⠜⡐⠁⠀⣿⠀⠀⡇
⠀⠀⠀⠀⢠⢾⢡⠞⠁⠈⢇⢋⠳⣦⡀⠸⣄⠄⠀⢸⠁⠈⠓⠬⠗⠀⠓⠙⠢⠄⠀⠈⠢⢆⠓⢤⡀⠀⠃⢰⡀⠠⢋⠜⠀⠀⡰⣿⠀⠀⣿
⠀⠀⠀⠰⠟⣿⡏⠀⠀⠀⠈⠙⠂⠈⠙⠒⠽⠟⢶⡞⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠓⠄⠁⠀⠀⡰⠁⣿⢣⠀⠘⣧
⠀⠀⠀⠀⠀⣹⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⡀⠚⠛⠛⠁⠀⠀⠒⠂⠀⠀⠀⡶⣶⠶⠆⠀⠀⠀⠀⠀⡀⢀⠜⠀⣰⠟⢦⣑⠦⣈⠳⣄
⠀⠀⠀⠀⠀⣿⢀⢈⠉⣁⡀⣉⣀⣀⡘⠛⠛⡀⠀⢿⠈⠀⠁⠀⢰⣎⣉⣒⠒⠒⠒⠒⢦⣤⠀⠰⢀⠄⠀⠀⠀⠀⠉⠳⣄⡴⠋⠀⠀⠈⠉⠛⠋⠉
⠀⠀⠀⠀⠀⢸⡄⠀⠸⣷⣶⣤⣤⣤⣬⡷⠈⠈⠀⢘⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠻⣄⠀⠙⢿⣿⣿⠿⠟⠁⠀⠀⣠⠞⠉⠷⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣀⡴⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣠⣤⣤⣶⣿⠁⠀⠀⠀⠈⠛⠶⣤⣄⣈⣉⡉⠉⣀⣀⣀⣠⣤⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡶⢤⣀⠀⣸⣿⣿⣵⣿⣿⣿⣇⠀⠀⢀⣤⣀⡀⠀⠀⣼⣿⠉⣿⠋⢩⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣠⠷⣄⠈⢻⠋⠁⠀⠀⢀⣿⣿⣿⠀⠀⠀⣇⠈⠉⠓⠾⣿⡿⠾⠛⠋⠉⠉⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣄⡼⠀⢸⠀⠀⠀⠀⣏⢀⣼⠏⠀⠀⡞⠉⢻⡄⠀⠀⢸⠀⠀⠀⠀⠀⣰⠞⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠧⣄⠈⡀⢀⣀⣤⠼⠋⠀⠀⠀⠀⠳⣤⡼⠃⠀⠀⠘⡀⠀⠀⠀⠀⣧⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄⡀⠀⠀⡇⠀⠀⠀⠀⣈⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣧⠴⠒⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠶⢮⣽⠷⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⢛⡛⠒⠛⠥⠧
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⣟⢟⠻⣦⡄⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢀⣸⠈⣤⢹⢀⡌⠀⣤⡀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⢜⡁⢂⠀⠹⣟⣵⢻⡄⠀⣠⡶⣿⠏⡟⡝⡳⡄⠀⠀⡜⢸⠀⠀⣸⠀⠀⠀⠀⡇⠀⣴⢾⡛⣿⠷⠿⢷⡄
⠀⠀⠀⠀⠀⢀⣎⡠⠞⠑⠄⠀⠉⣹⡜⠀⢰⣿⡤⠾⠛⠉⣉⢳⢻⠀⠀⠘⢾⠀⢠⡜⢧⠀⢰⡷⠃⣼⣿⢸⡗⡇⠀⠤⠀⢣
⠀⠀⠀⠀⢀⡎⡼⣦⠀⠀⠀⢀⠞⣿⠁⠀⣿⡉⠰⠆⣘⠀⠉⠈⢻⡇⠀⠀⠘⡄⠀⢧⠎⠀⡎⠀⠀⣿⢾⣿⣣⡇⠀⠒⠂⠀⣹⠂
⠀⠀⠀⠀⣼⠐⢥⠃⠀⠀⠀⠐⢻⠇⠀⠀⢸⡇⠀⠀⢠⣶⠀⠀⣼⢹⡄⠀⠀⣙⣶⣀⣀⣰⡃⠀⠀⢹⣷⣿⡏⠀⠀⠀⠀⣴⡛⠀⠀⢀⣀⣤⣤⡀
⠀⠀⠀⠀⠈⠙⠲⣤⣀⣀⣀⣤⣾⠀⠀⢸⣏⢻⣄⡀⠀⠁⢀⣼⣳⢹⣧⣠⠞⢹⡍⡽⡏⡽⠛⣄⠀⣾⢹⡿⡄⠀⣠⢤⣀⢀⡟⠀⣶⣿⣿⡉⡤⢙⠛⠛⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡏⢡⣷⠀⢹⡄⠀⣧⢻⡸⣯⠻⡇⠀⠘⣿⢣⡇⢿⡇⠀⠀⠿⠀⠘⠇⢀⣸⡖⣿⣼⠃⣧⡀⣻⣀⠹⣿⡃⢺⣿⡿⣿⣇⠀⠛⠃⠀⣹⠃
⠀⠀⠀⠀⠀⠀⢠⠏⢣⡞⠈⢣⡼⢳⠀⠸⣾⣣⣿⣴⡇⠀⠀⠿⠶⠿⡿⠀⣀⣀⠀⠀⢀⡴⠋⠀⣧⠈⢀⡎⣏⣷⣟⣿⡦⠀⠀⢿⣾⡿⣿⡿⠀⠀⠀⠛⠋⢹
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⣧⠀⠈⠙⠋⢩⡧⣀⡠⢿⠀⢰⠃⢸⡏⠉⠉⠛⡏⠀⠀⠀⢻⡴⠋⢠⠏⡈⢻⠿⣧⠴⡆⠀⠻⣷⣯⣳⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣸⣧⠞⢣⡞⢷⠏⡴⠚⢳⣦⠀⠀⡇⠀⠀⠀⢻⠦⠤⣏⡀⣷⡰⠚⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣠⠋
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⢼⠓⠤⢴⣇⣀⠄⠤⢴⡞⢧⣸⠀⣨⡽⠀⠀⢻⠀⠀⠀⢸⠀⠀⠀⠈⢹⠀⠀⠀⠀⢹⡀⠀⠀⣿⠀⠀⣴⠇
⠀⠀⠀⢰⠃⢰⠒⠒⠲⢤⡤⠒⠉⡋⠀⢸⠀⠀⢰⡇⠀⠀⠀⠀⡇⠈⢻⡀⢹⡁⠀⠀⢸⠀⠀⣠⢾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣇⠀⢰⣏⡱⢎⡸
⠀⠀⢠⣿⠀⣸⠆⠠⡀⢸⢃⣤⡤⢧⡀⢸⠂⠀⠨⡇⠀⠀⣀⣸⡧⠴⠞⠻⣏⠉⠓⠦⣼⡶⠚⠁⢸⡀⠀⠀⠀⠀⣧⠀⠀⢀⡴⢻⠀⡌⢹⠁⠀⣿
⠀⠀⡞⢸⠀⡗⠩⠭⣗⢸⢸⣟⡧⠀⣩⣿⡀⠀⠰⡇⢀⣴⣦⣈⡇⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢸⡗⠦⢤⣄⣀⣿⣀⡴⠋⠀⠈⣿⠁⢻⠀⢠⢻⡀
⠀⢸⠁⢸⡂⡇⡉⠚⠁⢸⡄⠉⢠⣿⡙⠷⠃⠀⠀⣗⡿⠕⠛⢹⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⠃⠀⠈⢿⡿⠿⣯⣀⠀⠀⢠⣿⠀⢸⠀⡼⠈⡇
⠀⡟⠉⠙⡏⠁⣇⠀⠀⢸⡁⣀⡸⣴⠇⣼⠃⢒⡾⢿⠙⠂⢤⡀⠓⢦⣀⡀⠀⠸⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠓⠶⠦⣌⡻⠲⡾⣿⠀⢘⣤⡇⠀⢹⡄⣠⠴
⢸⠃⠀⠀⣷⠞⠉⠉⠉⢸⡏⠀⡴⠋⠰⢃⡼⠋⣠⠿⣆⣀⣀⡬⢷⣤⣬⠽⠶⢤⣷⠤⠶⠶⠶⠶⡾⠶⡶⠒⠒⠒⠊⠉⢻⡷⣬⣧⠧⣶⣼⣏⠈⠉⢹⠋⣁⣞
⡼⠀⣠⠞⣇⠀⠀⠀⠀⣾⡇⢸⡇⢀⡴⠋⠀⡼⠁⠀⣇⠀⠀⠀⠀⠀⠉⠲⣄⠀⠸⡗⠢⣄⡀⠀⡇⢰⡇⠀⠀⠀⠀⠀⠀⣷⠏⠀⣠⣇⣩⡝⠀⠀⡎⠀⣗⡛
⠓⠚⠁⠀⢹⠀⠀⠀⣸⠃⣷⠀⠙⠉⠀⢀⡾⠁⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡇⠀⠀⠉⢳⡃⢸⡇⠀⠀⠀⠀⣀⣀⣾⡖⠊⠁⢸⠋⠁⠀⢸⠀⠀⢻⠗
⠀⠀⠀⠀⢸⠀⠀⡴⠉⠆⢻⡀⠀⠀⠀⡼⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣸⠋⢻⡗⠒⠋⠉⠉⠁⢠⣇⣹⡤⠚⡻⠀⠀⠀⡏⢀⣠⠞
⠀⠀⠀⠀⢸⣤⠞⠁⠀⣧⠈⠳⣄⡀⣼⠁⠀⢀⣠⡴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⡟⠀⢸⠁⠀⠀⠀⠀⠀⢸⠃⠹⡆⠀⢹⡿⠒⢶⡷⠋⠁
⠀⠀⠀⠀⠙⡇⠀⠀⠀⢹⠀⠀⠈⢹⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠅⠀⢸⠁⠀⠀⠀⠀⠀⣼⠀⠀⣻⡞⠁⣧⠀⢸
⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡇⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⠀⣬⠀⠀⠀⠀⠀⠀⣿⡴⠚⠉⣷⠀⠸⡄⢸
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⣧⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡎⠀⠀⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢹⡀⠀⠙⣿
⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢻⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡇⠀⠀⣹
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣸⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢀⣷⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣤⣷⠤⠄⣼⣤⣤⡤⢤⡤⠴⢶⠾⡟⠛⠉⠉⢹⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣸⠹⡇⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⠤⠴⠶⠖⠖⢺⠃⠀⢸⠄⠀⠀⡗⠈⣧⠀⣸⠃⢀⡿⠐⡇⠀⠀⠀⠸⡆⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠛⠚⢿⠒⠚⠉⢹⣍⣩⡇⢸⣤⠤⡟⠀⠀⠀⠀⠀⣼⠀⠀⡾⠀⠀⢸⠃⠀⢹⡋⢹⡃⢹⠇⠀⣇⠀⠀⠀⠐⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢸⡆⠀⠀⢸⡏⢩⡇⠸⡇⠀⡇⠀⠀⠀⠀⠀⡇⠀⢠⠇⠀⠀⣼⠀⠀⠘⡇⢸⠀⡿⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⣷⠀⠀⢀⡇⢸⠁⠀⢻⣀⣧⡀⠀⠀⠀⢰⠃⠀⣸⡦⢴⣶⠃⠀⠀⢀⣇⣾⣸⠇⠀⠀⢿⠀⠀⠀⠀⣏⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⢸⡇⠀⢸⣇⡟⠀⠀⢈⣧⡤⠽⢶⣤⡤⠟⣉⣉⡏⠉⠓⠛⠛⠛⢓⣮⢱⣣⡜⡇⣀⣠⢾⣀⡠⠴⣆⣭⢠⡀⠸⡆
⠀⠀⠀⠀⠲⠶⠶⠿⠥⢶⣶⣶⡺⠯⢴⣶⡯⢾⡇⠀⠀⠀⠉⠠⠶⠿⠓⠚⠋⠁⠛⠃⠀⠀⠀⠀⠀⠛⠁⠈⠉⠙⢯⠉⠉⠉⠀⠀⠀⠀⠹⠼⠉⠓⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠐⠃⠐⠒⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠒⢋⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠋⠀⠀⢤⠀⠤⠼⠇⠂⠄⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠃⠀⢀⡀⣀⠠⠤⠤⣀
⠀⠀⠀⠀⠀⠀⢠⠊⢀⣀⡀⠀⠀⡀⠈⠱⠀⠀⢀⠔⠁⠠⡀⡠⡀⠑⣄⠀⠀⡠⡪⠒⠉⠀⠈⠑⠢⡱⠄
⠀⠀⠀⠀⠀⠀⢈⡠⠊⠀⠀⠉⠁⠈⠢⡀⡆⠀⡾⠉⠑⠁⠈⠀⠀⠚⠹⡄⢐⡜⠀⢀⠀⠀⠀⠀⠀⠈⣼
⠀⠀⠀⠀⠀⠀⠻⡁⠀⠉⠀⠀⠀⠈⠀⠈⡟⠫⡇⠀⠈⠀⠀⠀⠈⠀⠀⡿⠺⡅⠀⠈⠀⠀⠀⠈⠁⠀⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⡀⠔⠀⠀⠑⢄⡀⠀⠀⠀⠀⣀⠔⠁⠀⠈⠢⢀⣀⠀⢀⣀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⣭⣿⢳⣄⠀⠀⠀⠀⢠⣾⢻⣬⣾⢻⣄⠀⠀⠀⠀⢠⠾⠻⣶⣾⢻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠈⢧⠋⠁⠘⡆⠀⠀⠀⡟⠈⠈⢣⠃⠉⠘⡆⠀⠀⠀⡟⠀⠉⠱⠋⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣇⣀⣀⢀⡀⣀⣀⡇⠀⠀⠀⢧⡀⠀⢤⠄⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢇⠉⢹⠈⢉⠋⠀⠀⠀⠀⠀⢃⠀⢸⠀⢀⠃⠀⠀⠀⠀⠀⢡⠀⢸⡀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⠀⡏⠀⠀⠀⠀⠀⠀⠘⡁⢹⠁⡍⠀⠀⠀⠀⠀⠀⠈⡏⢹⡃⡋
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠛⠉⠙⠉⠙⠀⠀⠀⠀⠀⠀⠘⠁⠙⠉⠙⠀⠀⠀⠀⠀⠀⠙⠒⠚⠓⠚⠁⠀⠀⠀⢰
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡇⣠⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠧⠼⠃⠿⠼⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⢀⡘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣶⣶⣶⣶⣶⣶⡌⠁⠀⠀⢠⣾⣿⣿⡟⢻⣿⣿⣷⡄⠀⠀⠈⢡⣶⣶⣶⣶⣶⣶⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡟⡛⣿⣿⣟⣻⣿⠆⠀⠀⣿⡿⢫⣭⣶⣶⣭⡝⢿⣿⠀⠀⠰⣿⡟⣻⣿⣿⢛⢻⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⣋⣉⠻⣿⡇⠀⠀⠀⣿⠡⣯⣭⠿⠿⣭⣽⠌⣿⠀⠀⠀⢹⣿⠛⣉⣙⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣭⣭⡾⠏⠀⠀⠀⠀⠹⣷⡸⣧⣘⣃⡼⢃⣾⠇⠀⠀⠀⠀⠻⢧⣭⣭⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⠆⠀⠀⠀⠀⠀⠀⠘⠛⠠⣬⣥⠄⠛⠁⠀⠀⠀⠀⠀⠀⠰⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⣿⣷⣶⣶⣾⣿⠶⠆⡀⢠⠰⠶⣿⣷⣶⣶⣾⣿⠶⠦⡀⣠⠶⠶⣿⣷⣶⣶⣿⣿⠶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⣦⣭⡛⢟⣩⣴⣾⡇⣿⠈⢸⣷⣦⣍⡛⢛⣩⣴⣾⡇⠃⣿⢸⣷⣦⣍⡻⢛⣭⣶⣾⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣶⣶⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣶⣦⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⡇⢸⣿⣿⣿⡟⣿⣿⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⣿⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣭⣭⣭⣥⣬⣭⣭⣭⣥⣭⣭⣤⣭⣭⣭⣥⣬⣭⣭⣭⣤⣭⣥⣬⣭⣭⣭⣥⣬⣭⣭⣭⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⣭⣭⣭⣭⣽⣿⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣭⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠊⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠑⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠂⣦⣰⣆⡖⢶⣰⣶⡆⡆⢰⢠⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠆⠛⠘⠋⠳⠞⠘⠋⠇⠳⠞⠰⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⠀⠀⣼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⣿⣿⣿⣇⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢼⣿⣿⣿⠟⠉⠛⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣾⠟⠛⢿⠀⠀⠀⣿⠟⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⣴⡀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢘⠀⢰⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⢸⠀⠈⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⡧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⣿⠀⠀⢸⡆⠀⡆⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠻⣤⠤⠴⠷⠤⠷⠶⠀⠠⠼⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⢀⠂⢮⠉⣅⠀⠰⠤⠔⠀⠀⠐⢠⣄⣀⣀⣠⣄⠐⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣬⣶⣦⣴⠈⢑⠀⢀⣀⠉⠓⣾⡿⠿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠛⣿⣥⡍⠐⠻⣿⣿⣿⣿⡇⢀⣿⣿⣿⡏⠉⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⣽⣿⡿⠗⠐⠿⣿⣦⠀⢤⣿⣿⣿⣯⣄⣀⣩⣿⣿⡃⠀⢙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣤⣼⣿⣿⣶⣶⣾⣿⣦⣤⣴⣾⣿⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣿⣿⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠛⣿⣿⣿⡟⠋⢹⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⠟⠀⠺⣿⣿⣿⣿⣯⣤⣤⣭⣿⣿⣿⣿⣿⡿⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⣿⣿⣿⣿⣿⣿⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈
⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⢿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣿⡯⠠⣿⣿⣿⣿⣿⡿⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣇⠀⣼⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⡇
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠇⠀⠻⠿⠿⠿⠇⠀⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢹⡇⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⠻⡆⠀⠀⣴⣿⠿⣿⣧⠀⠰⠀⠀⠀⠀⠘⠈⠁⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⠀⠀⡟⠁⠀⠀⠹⡇⢠⣴⣷⣶⡦⠀⠀⣀⠀⠘⠁⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣦⡀⣸⣇⠘⠃⣠⣿⣤⣤⡀⠀⠲⠀⠀⠀⣸⢛⡋⠙⡛⣇⣤⣤⣴⣦⣴⡿⠿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠋⠀⠀⢙⣧⣽⣿⣤⠼⣿⡿⢿⡿⢿⣆⣴⣶⣿⣦⡁⠀⢀⡄⠀⣼⣿⠿⢿⢿⣿⠀⠀⠀⠘⢁⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⠀⣾⣿⣿⣿⣿⣷⠏⠁⠀⠈⠀⣿⢩⠁⠈⡍⢳⣴⠄⣤⣴⣿⡁⠀⠀⠀⣿⡇⠻⠀⠀⠘⠋⠉⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿⠠⠀⠠⠄⣿⠀⠀⢛⣀⣀⣋⠀⢀⡄⢰⣏⣿⣷⢿⠻⣯⣾⡖⠗⢀⣿⠅⠐⠚⠛⠧⠀⣄⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡾⣧⠄⣸⣿⠀⢠⠄⠀⣿⣇⣾⣾⣿⡾⢿⣿⡌⠋⢸⣿⠁⠀⠀⠢⠙⣷⣗⠘⢿⣿⣶⣿⡿⣿⣦⡀⢁⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣻⣿⣷⠀⠠⣼⣿⡟⡟⠉⠉⠀⠘⢿⣅⠀⣿⣻⡄⠀⣤⠀⢀⣿⡏⠀⠀⢸⠟⠋⠀⠈⢿⣦⣤⣿⠛⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠀⠀⠀⠉⠉⠓⠧⠀⠀⣀⠀⠀⠀⠀⣼⡿⢿⡆⠠⣤⣾⣿⡇⠀⠀⠀⠀⠠⡆⠀⠜⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⣴⠀⠀⢰⣷⣾⡟⠃⠀⠘⠻⢿⣷⠀⠀⠀⠠⠀⠐⢦⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠘⠃⠀⠘⠋⣀⠐⠂⠐⠃⠀⠃⠸⠄⠀⠀⠀⠐⡶
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⠇⢰⠶⠦⣤⣤⣤⣤⣤⠀⠠⠀⠈⠁⠀⠀⠀⠘⠃⠀⠄⠘⠀⠁⠀⡀⠐⠂⠀⠀⠀⠠⣫
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠀⠀⣄⣭⣙⣓⠲⠶⠦⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠂⢀⠁⠠⠄⠀⠀⠀⠔⣡
⠀⠀⠀⠀⠀⠀⠀⠹⢀⡘⠀⢸⣿⠁⠉⠙⠛⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⢁⡐⠀⠈⠀⠦⣀⠀⠀⠀⠞⣡
⠀⠀⠀⠀⢀⡴⠀⠀⠀⡀⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡀⣨⠁⠆⠤⢀⠀⠀⠠⢎⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠐⠂⣠⠈⠀⠀⠀⢋⡴⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂




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

⠀⢠⠤⡀⢠⠈⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⣼⡀⠀⣼⠀⢰⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢹⠀⡠⠚⣆
⡇⠸⠇⠀⢿⡄⠘⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⡘⠆⠁⣠⠋
⠃⠀⠈⠀⢀⣀⣀⣀⠛⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣴⠀⠘⠛⠀⣼⠁⠀⢀
⠀⢃⠀⠀⠀⠀⠀⠈⠛⢀⣤⢠⡇⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠉⠘⠂⠀⠀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠘⠧⣄⠀⠹⠀⠀⠀⠀⠀⠠⠄
⠀⠈⢦⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⠐⠶⠀⠀⠛⠀⠉⢈⡵⠈⠹⡆⠀⠀⠀⠀⠀⠀⠈⡇⠀⠳⣤⡀⠀⢀⡤⣤⠁
⠀⠀⠀⠉⠲⣄⠀⢾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣀⣀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⡼⠃⠀⠈
⠀⠀⠀⠀⠀⠈⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠉⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠛⠀⠀⠀⢀⡛⠀⢠⡤⠚⠁
⠀⠀⠀⠀⠀⠀⣗⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣹⠶⠒⠋⠉⠉⠉⠉⠁⠒⠲⣤⡀⠀⠀⠀⠀⠲⡅⠀⠀⠀⠀⣴⠋⠀⢀⡎
⠀⠀⠀⠀⠀⠀⢹⡄⠀⢻⡀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠹⠆⠀⢀⡴⠁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠈⢃⠀⠘⢣⠀⢠⠞⠁⠀⠀⠀⠛⠃⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠹⡀⠀⠀⡀⠀⢀⡞⠁⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢀⣼⠦⠶⠛⢻⠇⠀⠀⠀⠀⠀⠀⡠⠒⠲⡄⠀⠀⠀⢀⣠⠾⠀⠀⠀⢫⡀⠀⢹⣦⠛⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠋⢁⣼⠀⠀⠀⠘⣇⡀⢸⡟⠀⠀⢀⠾
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢰⠀⠀⠀⠀⢸⣿⡗⠙⠛⠛⠛⠉⠀⢀⣀⣴⣿⡟⠀⠀⠀⠀⠀⠙⡿⢦⣀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠀⠀⠀⠀⠸⣿⣷⣤⣤⣤⣤⡶⠛⠋⠉⢹⡟⠁⠀⠀⠀⢷⡤⠛⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣷⠀⠀⠀⠀⠹⣿⣿⣿⠿⠟⠐⠒⠒⣴⠟⠁⠀⠀⠀⣠⠟⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⣆⠀⠀⠀⠀⠈⠻⠇⣀⣀⡠⠶⠞⠁⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⠁⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠙⠶⢦⣤⣤⣤⣤⣤⣤⡴⠶⠛⠉⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠳⠾⠙⠛⠛⠛⠋⠁⠰⠶⠶⠦⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠁⠈⠙⠛⠛⠛⠲⠦⢤⣤⡤⠤⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠐⠛⠋⣉⣁⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⠳⣤⡤⠔⠛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⡤⠴⠶⢶⣶⠶⠖⠛⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠀⠀⠀⠈⠉⠉⣿⠉⠙⠛⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠧⠤⣼⡁⠀⠀⠀⠀⠀⠀⡰⠓⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢘⡇⠀⠀⠀⢀⡤⠚⠀⠀⠀⢠⡇
⠀⠀⣀⠀⡀⣀⣠⡴⠖⠉⠀⠀⠀⠀⡀⠘⣧⣀⠰⠊⠉⠀⠀⠀⠀⠠⠺⡇
⠀⢘⠋⠤⠀⣀⣈⣡⡀⣀⡀⠀⢀⡠⠚⠛⠁⠉⢠⡀⠀⠀⠀⠀⡜⠁⣀⠃
⠀⠈⠑⠂⢤⣤⣤⣤⣤⣤⠀⠠⣏⠑⠂⠠⠀⠀⠀⣴⠄⢤⣤⠘⠓⢠⠌⠁
⣤⣤⣀⣤⣤⣤⣤⣤⣤⣠⣤⣤⣄⣉⣤⣤⣶⣶⣶⣤⣶⣤⣤⣌⣁⣠⣤⣄⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣠⣤⣤⣤⣄⣠
⣿⣿⣿⣿⠿⠛⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠠⠤⠤⠤⢤⡀
⠀⡇⠠⠒⠒⠒⠐⠒⢂⠴⠤⡀⡰⠲⡐⢄⠀⢒⡖⣐⠒⠒⠒⠒⠒⠒⠒⠒⠶⣦⢖⠒⠶⠆⠒⠀⠀⢠⠦⠄⣀⠀⠀⠀⠀⠒⠂⠀⠂⠀⠂⠀⠐⠒⠦⠀⡇
⠀⡇⢰⠀⠀⡐⠂⡀⢦⡄⢀⣘⠁⠀⢀⡀⣣⠡⢔⣈⣽⠀⠀⠀⠀⠀⡖⡝⠊⢉⣑⣷⠨⡇⠀⠀⡐⠂⠀⠀⠀⠊⢱⠄⠒⠒⠀⠤⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⡇⢸⠀⠺⡁⠈⡄⠐⠇⠤⠸⢢⣾⢠⠄⢾⣧⠀⠐⠘⡠⢤⣄⣀⠀⠉⣣⠉⢯⢀⡏⠀⣇⠀⡐⠀⡄⢀⡀⠀⢠⠃⠀⠀⠀⠀⠀⠸⡥⡄⠀⠀⠀⠠⠀⡇
⠀⡇⢸⠀⡄⠂⡄⠀⠨⡸⠂⢘⢾⢽⠀⢀⣺⡄⢀⠍⢳⠀⡼⡁⢚⣀⠓⠰⢏⠈⢉⢮⠒⣼⡀⢂⡀⠉⢲⠀⢀⠃⠀⠀⠀⠀⠀⣀⠆⠈⠠⠀⠀⠀⢸⠀⡇
⠀⡇⢸⠀⡦⠂⠭⠒⢆⣣⠈⠐⠘⠂⠄⣐⡚⠤⢦⣁⡾⠀⡗⠀⢬⢳⡅⠀⠂⠭⠥⢤⠗⠸⠋⣏⣀⠒⠁⢠⠂⠀⠀⠀⠀⠀⡴⠈⠀⠀⣶⠀⠀⠀⠀⠀⡇
⠀⡇⢸⢠⠃⠀⠀⠀⠉⠇⠆⡘⠀⠀⠀⠀⠙⠟⢄⡬⣹⡚⢤⣀⡨⠾⢄⠀⠀⠐⢬⣧⠈⠈⣀⡿⠣⣈⡒⠦⣀⡀⢀⠀⠀⠈⠀⢀⠂⣐⣿⡀⠀⠀⠀⠀⡇
⠀⡇⢸⠘⠀⠁⠀⠀⠈⡧⢶⠏⠀⠀⠀⠀⠀⠈⠀⢉⡗⠁⢸⠀⠀⠀⠐⠱⢄⡇⢸⠋⢸⠹⡞⠉⣶⠋⠑⣶⠦⣄⡀⠒⢎⡀⠀⠀⣰⣿⠾⣿⣦⡀⡀⠀⡇
⠀⡇⢸⠀⠀⠀⠀⠀⢰⠀⢈⠃⠀⠀⠀⠀⠀⠀⡞⠈⣆⠰⠨⠈⢢⣄⣀⣁⢈⠷⣎⡠⣯⠢⡇⢺⠁⡆⣌⠈⡖⠀⠉⠛⠿⣥⠀⠀⠀⠀⠂⠠⠤⠔⠀⠀⡇
⠀⡇⢸⣆⡀⢀⠀⠀⠈⡇⠙⡀⠀⠀⠀⠀⠀⠀⢃⠠⠄⠄⠀⣄⠀⠀⠀⢹⣡⠤⡞⠃⠈⠁⢞⡠⠛⠁⠄⠫⣅⠀⠀⠀⠀⢸⠀⣲⣆⠀⣚⣟⡀⠀⠀⠀⡇
⠀⡇⢸⢸⠀⠈⠀⠁⠈⢃⠀⠑⡶⠔⠒⠤⢦⠒⠺⡀⠀⠃⠀⣿⡇⠈⠉⠋⠘⠀⠁⠀⠃⠀⡈⡃⠀⠀⢀⠀⠈⢣⡘⠐⠟⢸⠀⣿⣿⠀⣿⢿⡇⡀⠀⠀⡇
⠀⡇⠈⢸⠘⡐⠀⠀⠀⠈⡀⠂⠃⠃⠀⠀⢨⠂⢀⠁⠀⠀⠀⡯⠄⠀⡆⠈⣄⠀⠀⠀⢱⠀⠰⢳⠘⠀⠈⢣⠀⠀⠇⢁⠀⢸⠀⣿⣿⠀⣿⢸⡇⡇⠀⠀⡇
⠀⡇⠘⠘⡄⠇⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⢀⠠⠈⢸⡆⠀⠀⢠⠀⠠⠇⢸⡏⠀⠸⠀⠸⡃⠆⢸⣇⣀⣀⣀⣑⠆⠜⠁⠀⢸⠀⣿⣿⠀⣿⢸⡇⡇⠀⠀⡇
⠀⡇⠀⠀⡇⠀⣠⠃⠀⠀⡇⡇⠀⠀⠀⠀⢸⠀⠀⠀⡇⢸⠀⠸⠀⠀⡇⠸⡇⠀⢸⠀⠀⡆⠀⣸⡇⢈⠉⠉⠉⡇⠀⠀⠀⢸⠀⣿⣿⠀⣿⣿⡇⡇⠀⠀⡇
⠀⡇⠘⠀⠇⠠⠃⠀⠀⠀⡇⢰⠀⠀⠀⠀⢸⠀⠀⠀⣧⠈⠰⠰⠀⠀⢳⠀⡇⠀⠈⠀⡀⠃⢀⠁⣣⢸⠀⠀⠀⣿⠤⠀⠀⢸⠀⣿⣿⡀⢸⣾⡇⠇⠈⠀⡇
⠀⡇⢐⣀⡴⠃⠑⠀⠀⠀⡇⣸⡀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⢠⠠⠘⢻⢸⠀⠀⠀⠸⣆⠐⠅⡺⠀⠀⠀⠀⠈⠉⠤⠜⢤⠀⡇
⠀⡇⠀⢽⣶⣦⣀⠀⠀⠀⡇⠏⠁⠀⠀⠀⢸⠀⠀⠀⠈⡆⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠁⢸⠀⠀⢘⠘⡆⠀⠀⠀⢿⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⡇⠀⠀⠹⣿⡌⠳⢤⣀⡟⢳⣤⠁⠠⠠⠬⠤⠀⠤⠤⣧⣤⣀⣀⣤⣨⠖⡗⠓⠤⡀⢄⣘⡊⡟⢉⠀⡇⠀⠀⠀⠘⣼⠁⠉⠀⠁⠉⠀⠈⠀⠀⠀⠀⠀⡇
⠀⡇⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠈⠓⠀⠀⠺⢶⣇⠀⠀⠀⠘⠿⠀⠈⠁⠂⠆⠀⢤⣤⡇⠙⠊⠓⠒⠒⠲⣶⡎⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⡇
⠀⣇⣀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣁⣉⣉⣉⣉⣉⣉⣀⣉⣉⣉⣉⣉⣉⣈⣉⣉⣉⣉⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣶⣦⣤⣶⣦⣠⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠄⠀⠀⣸⣿⣿⣿⠟⠿⠿⢿⣿⣿⣿⠿⢷⠀⠀⠘⢻⣿⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠈⠙⠛⠋⠈⠛⣿⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⡏⠛⠁⠋⠀⠉⠀⠀⠈⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣿⠃
⠀⠀⠀⠀⠀⢰⠷⡞⠛⠀⠀⠀⡀⠀⠀⠀⢀⡄⠀⠂⠀⠀⠀⢇⡟⠀⠀⠀⠀⠉⠀⢀⠀⡀⠈⠀⠈⡄⠀⠀⠀⠴⠀⠀⠀⠀⠴⠀⠀⠀⠈⠸⠛⠃
⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⢀⡁⡀⠁⠀⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠛⠿⠍⠀⠀⠀⠇⠀⡁⠀⠀⢰⡂⢐⠆⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠂⢉⠅⠛⠅⡘⠦⡤⢀⣀⠀⠀⢀⠀⣀⠤⠺⡐⠤⣁⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢢⠀⠠⠂⠰⠊⠀⢀⠔⠁⠀⠀⠀⠀⠉⠋⠂⠀⠃⠀⢃⠀⠀⠀⠀⠀⠑⠄⡉⡗⠄⡓⡄⢠⡊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢎⠐⠩⣤⠂⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠈⠂⠤⡄⠀⠀⢏⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠑⢄⡔⢄⢻⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢸⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⡷⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠑⢌⡢⢠⡄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡀⠀⠀⠀⠀⢡⢂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡔⢮⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠛⠶⡇⠀⠀⠀⠀⠀⢀⠌⠀⢀⡔⠀⠀⠀⠀⠀⢸⣇⣢⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⡂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠠⠄⢀⠀⢀⠠⡇⠀⠓⠄⣀⣀⡠⠐⠁⡀⠔⠈⠁⠀⠀⣀⠀⠈⡇⠀⠁⠀⠀⠀⠀⠀⠒⠂⠀⠀⠒⠂⠀⠱⠐⠛⣱⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠠⠄⢀⣀⠠⠊⠈⠐⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠔⠁⠀⠀⠢⡀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡆⠀⡄⢀⡃⠀⠀⠀⠀⠀⠀⡆⠀⠔
⠀⠀⠀⠀⠀⠀⠰⡙⢶⡇⠀⠀⠀⠀⠀⠱⣂⣱⣂⠶⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠇⠀⠧⢠⣇⣀⠀⠀⠰⡉⠻⢤⡜
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠛⠀⠂⠁⠀⠀⠀⠀⠀⠀⠐⠍⠐⠋⠀⠀⠓⠒⠒⠀⠃⠀⠀⠀⠁⠂⠁


⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⣤⣌⣀⡀⠀⠐⠒⢭⡓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢛⣫⣭⣭⣭⣭⣇⣀⣀⣀⣐⣿⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡵⡺⠟⠟⠛⠉⠀⠉⠁⠀⠀⠀⠀⠉⠹⣟⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠏⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⢿⡆⢘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⢹⠆⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠀⠀⠀⢸⠱⠀⠈⠔⠀⢀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⠙⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⠃⠀⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⠖⢣⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⢦⢀⣀⢄⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡆⠀⠀⠀⠀⠀⢴⠒⠚⠉⢀⡠⡾⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⢀⠆⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠈⢶⠒⠚⣉⢴⠇⠀⠀⠀⠀⢀⡾⠁⠀⠀⣀⠔⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠙⠲⠒⠁⠀⠀⠀⢀⣴⠏⠀⢀⡤⣄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⣀⣀⠀⠀⢀⣀⣠⠴⡟⠴⠒⠊⣁⡠⠟
⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠈⢉⡩⠝⠋⢅⣀⡠⠃⡖⠂⠉⠁
⠀⠀⠀⠀⠠⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠤⡏⠀⠉⢉⣠⢴⠆⠀⠈⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠞⠁⠒⠒⠒⠒⠉⠑⠒⠉⠉⢀⡞⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠤⠬⣉⠑⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡀⠀⠀⠉⠓⠢⠤⣈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠺⣆⠀⠀⠀⠀⠁⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣯⠙⡖⠒⠒⠃⠤⠤⠔
⠀⠠⢄⠀⠀⠀⠀⠀⢀⡔⢉⡴⠊⠉⠹⠦⠖⠒⠒⠓⠓⠂⢄⡈⠉⠉⠛⠒⠒⠒⣃⣀⠀⠀⠀⢀⠏⣸⠁
⠠⡑⢄⠀⠒⠤⣀⢠⠎⢨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢇⠀⠀⠀⢀⡏⣀⠠⠔⣚⠖⠁
⠀⠘⢄⠳⣀⠀⠀⠉⠲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⡼⠒⠒⠒⠉⠁
⠀⠀⠀⠙⠢⡑⢤⡀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⣤⣤⣀⡀
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣥⣴⣶⣶⣶⣶⣤⣌⡛⢿⣷⡀
⠀⠀⠀⢰⣿⣿⡿⠛⠛⠻⢿⣿⣿⡿⢿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣶⣿⣧
⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⢀⠿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢟⣣
⠀⠀⢘⠋⡎⠉⠀⠀⠀⣦⠀⠀⠀⠀⢰⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠀⠀⠀⠶⠀⠀⠀⠀⠚⡉⠀⠀⡀⡀
⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠆⠀⢀⠀⠀⠀⠘⣲⠺⠂⠀⠀⠀⠀⠀⣸⡇⠘⠂⠻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠈⠡⠀⠋⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠟⢋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠰⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠈⠑⢄⠙⠻⢿⣷⠀⢰⣿⠿⠛⢉⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠒⣠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠒⢄⢀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠸⠿⠗⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠮⣹⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠐⠀⠀⠁⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⣀⠀⠀⠐⠲⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠴⠈⠄
⠀⠀⠀⠀⣠⠀⡠⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⢁⣠⠼⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⢸
⠀⣀⠇⢎⢷⡶⢤⠀⢰⡶⠶⠶⡄⠀⢀⠦⠦⣤⠀⢀⡔⠂⠢⡄⡀⡀⠀⠪⢤⠘⣧⠀⢴⠃⠈⢢⠀⠀⠀⠀⡀⠶⣤⠀⠔⡐⠠⠷⢴⡖⣦⠀⢸
⠀⠑⠈⠸⡀⠀⣠⠃⠸⡃⠀⠀⡍⠀⢸⡀⠀⠸⠀⠘⣅⠀⢀⡇⠨⠉⢣⡀⡀⡸⣀⢱⢸⢄⠀⢸⡀⠀⢠⢸⣀⠀⡸⠰⡠⢻⡀⠀⠀⠗⣜⠀⢸
⠀⠀⠀⠀⢸⠀⢋⢢⠀⡸⡆⠞⣷⡄⣰⡏⠈⣧⡀⣴⠋⢏⠍⣗⢄⠒⡛⠀⢸⢫⡉⢡⡟⠀⠉⠀⢹⣢⠶⡏⠐⠀⢛⢆⢁⡞⠉⣀⠹⣆⠈⠀⢸
⠀⠀⠀⠇⡓⠒⠸⡀⠳⡁⡇⠀⢸⡜⠸⠀⠀⢃⠃⢻⠠⣤⠤⢸⠊⢠⠃⠀⠸⡆⠑⢨⠃⠀⠀⠀⠀⠏⠀⡇⠀⠀⢸⠈⢀⠁⠀⠈⠀⡍⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⣤⣼⣿⣿⣿⣷⣾⣿⣿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠟⣁⠀⠀⠀⠀⠀⠀⣀⠀⠘⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⠁⠚⠉⠀⠀⠀⠀⠀⠀⠉⠃⠀⠸⣿⣿⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⠋⠀⢠⣤⡀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠙⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣸⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⡊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⠀⠀⠀⠐⠀⠀⢀⢆⠠⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠐⡶⠖⠻⠁⢀⡀⠔⠈⠀⠀⡠⠂⠀⠈⢞⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣠⠄⢴⡈⠠⠠⠠⣦⠒⠁⣀⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠁⢿⣧⣾⡇⠀⠀⠀⢹⡖⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡠⠄⠺⣇⠀⠀⠀⠀⠋⠈⠀⠀⠐⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠃⠈⠁⣀⠠⠄⠛⠒⢺⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠢⠐⠉⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣦⣤⣤⣤⣤⣤⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢻⠛⠈⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠈⠀⠀⢰⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⣆⣀⡇⠀⠀⠀⡀⣠⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠶⢯⣷⣿⠟⠀⠀⠀⠀⢿⣿⣴⣛⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⡨⠊⠀⠀⠀⠀⠀⠈⢛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠁
⣿⣿⣻⣻⣛⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣻⣿⣿⣻⣛⣿⣟⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠤⣀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡿⠿⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⡀⠀⠀⠀⠉⠂⠄⣀⠀⠀⢿⠛⠉⠁⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠀⠀⠀⠁⠂⠄⣀⠀⠀⠀⠑⠢⢼⡀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠈⠉⠒⠠⣶⣦⡀⠀⠁⠂⢄⡀⠀⠘⡏⠒⢄⡀⠀⣴⣾⣿⣧
⠀⠀⠀⠀⠀⠀⣴⠋⠉⠑⠒⠤⣀⣸⠻⣿⣿⡤⣀⠀⠀⢈⣵⣾⣷⣆⠀⠈⢹⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⣀⣠⡏⠐⠸⣿⡇⠀⠉⠢⣾⣿⣿⣿⠟⠢⣄⡈⠙⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡧⣀⠀⠉⠈⠑⠦⣀⠙⠿⠟⢯⣀⣠⡤⠟⡻⠛⠉⠉⢉⠉⠙⠛⠛⠒⡶⢤⣄⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠿⠛⠁⠀⠉⠐⠢⢄⡀⠀⠙⠲⣤⡶⠛⠁⢠⠎⠀⠀⠀⠠⠃⡀⠀⠀⠀⠰⢁⠏⠈⠙⢦⣠⠞⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⣤⢾⡿⠁⠀⢠⠃⠀⠀⠀⢠⠃⡜⠁⠀⠀⢀⠇⡼⠀⠀⠀⠀⠙⢦⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣀⣀⣀⣠⣀⣀⣀⡀⠀⠀⡼⢣⢫⠁⠀⢀⠇⠀⠀⠀⠀⡌⢸⠁⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢸⣧⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠛⠀⢀⢾⠁⠀⢸⠋⠉⠛⢲⢃⡏⢸⠀⠀⢸⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⡰⡝⠈⣧⠀⠀⡇
⠀⠀⠀⠀⠀⢀⡴⠋⣤⠾⠀⣤⠸⠀⠀⣼⠀⠀⠀⢸⡞⢧⠘⣄⠀⢸⠣⡀⠀⠀⠀⠃⢹⢆⠀⠀⠀⠸⠀⠇⠀⠀⢀⡔⡱⠁⠀⣿⠀⠀⣧
⠀⠀⠀⠀⣠⢾⢡⠞⠁⠘⣇⢋⠳⣦⡀⠸⣄⠄⠀⢸⠁⠈⠓⠬⠖⠀⠓⠙⠢⠄⠀⠈⠢⢆⠑⢤⡀⠀⠡⠸⡀⠠⢊⠜⠀⠀⠠⢿⠀⠀⢿
⠀⠀⠀⠴⠛⣿⠏⠀⠀⠀⠈⠙⠂⠈⠙⠒⠽⠗⢶⡟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠓⠄⠁⠀⠀⡰⠁⣿⢣⡀⠘⣧
⠀⠀⠀⠀⠀⣿⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠚⠛⠛⠁⠀⠀⠒⠂⠀⠀⠀⡶⣶⠶⠆⠀⠀⠀⠀⠀⣀⣀⠔⠀⢰⠟⢦⣙⠢⣈⡳⣤⡀
⠀⠀⠀⠀⠀⣯⢀⢈⠙⡁⠀⣉⣀⣀⡘⠛⠛⠀⠀⢷⠈⠀⠁⠀⢰⣎⣉⣓⡒⠒⠒⠒⠦⣤⠀⠠⠀⠄⠀⠀⠀⠀⠉⠳⣄⡴⠋⠀⠀⠈⠉⠋⠛⠉
⠀⠀⠀⠀⠀⢸⡀⠀⢸⣷⣶⣤⣤⣤⣭⡷⠈⠈⠀⢘⣧⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠙⢿⣿⣿⠿⠟⠁⠀⠀⣠⠞⠙⠷⣄⠀⠀⠘⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⡴⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣤⣤⣤⣶⣿⠁⠀⠀⠀⠈⠛⠶⣤⣤⣈⣉⣉⠉⣀⣀⣀⣠⣤⣶⠛⠁
⠀⠀⠀⠀⠀⠀⠠⡶⢤⣀⠀⣸⣿⣿⣴⣿⣿⣿⣇⠀⠀⢀⣤⣀⡀⠀⠀⣼⣿⠉⣿⠋⢩⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣠⠷⣄⠈⢻⠋⠁⠀⠀⢀⣿⣿⣿⠀⠀⠈⣇⠈⠉⠓⠾⣿⡿⠾⠛⠛⠉⠉⠉⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠷⣀⡜⠀⢸⠀⠀⠀⠀⣇⢀⣼⠏⠀⠀⡞⠉⢻⡄⠀⠀⢸⠀⠀⠀⠀⠀⣰⠞⠻⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠘⠧⣄⠘⡀⢀⣀⡤⠼⠋⠀⠀⠀⠀⠳⣤⡼⠃⠀⠀⠸⡀⠀⠀⠀⠀⢿⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣀⡀⠀⠀⡇⠀⠀⠀⠀⣈⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣧⠴⠖⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣴⡄⠀⠀⠀⠀⠴⢿⣆⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡿⠤⠠⠀⠄⠀⠀⠈⠉⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢈⢁⡤⢏⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠃⠀⠀⠈⠳⢄⠠⠤⠄⠆⠀⢂⡈⠁⢢⡀⠈⢧⡀⠀⡀⠠⣀⠁⡀⠀⠡⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⡀⠁⢈⠀⠀⠀⣂⢀⠂⠀⠀⠀⠒⠦⡀⠀⠀⠀⠀⠑⡌⢀⠊⠀⠀⠈⠀⣀⣀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠠⢀⠂⠐⡰⠇⠄⠀⠀⠈⠱⡀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⢰⠀⠀⠀⡠⠤⠀⠠⣄⠑⢆⠀⠰
⠰⣄⡆⠀⠀⡅⠀⠀⠀⢀⡤⡄⠀⢤⡄⠀⠀⠀⠀⠀⡆⠀⠀⠚⡅⠀⠀⡄⠀⠀⠀⡄⠀⠀⠰⠘⠲⠠⠄⠉⠀⢸⠀⡘
⠚⠻⣿⠋⠀⠁⠀⠀⠀⠀⣤⡄⠀⣄⡌⠀⠀⠀⠀⠀⠃⠀⠀⡈⠀⠀⠀⢊⡀⠀⢰⢤⡀⠈⢠⣀⠀⠉⡡⠀⠀⠃⡐
⠀⠀⠈⠳⠦⠴⡀⠀⠀⠈⠘⠀⠐⠒⠀⠄⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠿⠀⢰⣦⣤⡼⠁⡀⢡⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠤⢒⣿⠀⠀⠀⠀⢠⢷⠀⠀⠡⢄⠀⡠⠄⢀⣼⣿⣾⢇⠀⠘⠒⠊⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⣴⣵⣤⡄⠀⠈⠋⠑⢀⡤⢄⡠⢴⣋⣿⠀⠀⠀⠀⣀⠀⠀⠀⣠⠋⢀⣨⠦⢀⣀⣀⡠⢒⡏⣀
⠀⠀⠐⢦⣤⣀⣻⠀⠉⠉⠒⠦⢖⠒⠉⡇⠀⠀⠀⠞⠟⠓⠂⠰⡎⡼⠁⠒⠈⠀⠰⠯⠥⠤⣤⡄⠀⢳⠈⠳⠟⠃
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢠⡟⢧⣰⡇⠀⠀⠀⠀⠀⠀⠀⣠⠿⠴⠶⢲⡆⠀⠀⠀⣀⣴⠟⠁⠀⠈⠷⠤⠤⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠁⠀⠀⠀⠀⠀⢠⣾⣥⣤⡀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢂⢀⢤⠊⠀⠩⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⠀⢀⠀⠀⣠⠐⠱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠹⡨⠄⠉⠁⠀⠀⠀⠄⢠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠆⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠨⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⡀
⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⠀⠀⠀⠃⠌⠠⠀⠀⣀⣀⣀⢠⡀⠀⠤⠆⢒⠀⠀⠀⠀⠔⡀⠌⠀⠀⠁⠘
⠀⠀⠀⢀⡌⡄⠀⠀⠀⠀⠂⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀
⠀⠀⡠⠁⠐⠤⠀⠀⠀⠂⠀⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠄⠀⠊⠐⠠⡀
⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠘⠀⠀⢂⣠⡀⢠⣀⠂⠀⢸⠀⡐⠀⠀⠄⠀⠀⢀⠈⢂
⠀⢜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠐⢩⣆⠀⠀⣶⡙⠀⡈⠀⠡⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⢃⠀⠀⡀⠀⠀⠀⠰⡦⠀⠀⠀⠀⢀⠀⠈⠉⠀⠀⠉⠁⢀⡃⠐⢤⠄⣀⣀⣀⣀⣀⣀⡠
⠀⠀⠀⠆⠈⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠑⢤⣀⣀⣀⣀⠴⢋⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠉⠀⠀⠀⠀⠀⠐⠤⠤⠤⠤⠤⠔⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⢀⢄⡸⠀⠐⢅⡤⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠄⠀⠀⠀⠀⠄⡻⠦⠙⠁⡠⠚⠒⡄⠈⠃⢖⢠⡀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠑⠀⠀⣔⠦⠊⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⠪⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡮⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢕⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠉⡄⠀⢀⠀⠀⠂⠀⢢⠀⠀⠀⠐⠀⠀⠒⠀⠀⠀⠀⠆⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡂⢠⡇⠀⠀⠀⠀⠀⠀⡠⠀⠀⠈⠙⠛⠶⣄⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠂⠀⠀⠀⠀⠠⠁⢈⠀⠀⠀⠀⠛⢈⠇⠀⠀⢄⠄⢀⠏⠀⠀⠀⠀⠄⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⡀⡀⠁⠐⠚⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⡰⠂⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡄⢴⠀⠀⠀⠀⠀⠀⡄⠀⠘⠀⠈⠁⠄⠠⠀⠠⠀⠠⠤⠡⠈⢢⠈⠢⠀⠀⠄⠁⠀⠀⠊⠀⠁⠌⠑⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠤⠀⠀⠢⡀⠀⠀⠀⠔⠁⡀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠈⠲⠤⡤⠤⠴⡊⠀⠐⠂⢬⢶⢰⠎⢠⠆
⠀⠀⠀⠀⠀⠀⠀⢠⡠⠁⠀⠀⠀⠀⠙⠒⡒⠂⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠀⠀⠄⠀⠀⠤⠀⠈⠧⠀⠚⠏⢈⣟⠚⠛⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⠀⠀⠀⠸⠁⠀⠁⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠄⣠⠐⠓⡂⠀⠀⢐⠀⢀⠂⠀⠀⢄⠀⠙⠃⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠃⠀⠘⠲⠄⠀⠀⠀⢀⠀⠀⢀⡤⠊⠁⠀⢀⠂⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠨⠀⢀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠐⠐⠀⠃⠀⠀⠀⠀⠀⣆⠀⢀⡆⠀⠀⠀⠀⠀⠄⠀⠈⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠰⣀⠃⠀⠀⠀⠀⠀⡂⠀⠀⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠈⠳⠀⠀⠀⠀⠀⠶⠂⠀⠰⠤⠀⠀⠀⠀⠠⠬⠉⠀⠉⢥⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⡂⢀⡴
⠀⠀⠀⢠⠈⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠉⠉⠃⢈⠐
⠀⠀⠀⠀⠣⠀⢀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠚⠤⠈⠉⠒⠒⠄
⠀⠀⠢⡈⠢⣁⡄⠛⠁⢠⠀⠁⠐⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠇
⠀⠀⡀⠈⠓⠀⠀⠖⠉⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠲⠀⠠
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠡
⠀⠀⠀⠀⠀⠀⠈⠉⠐⢄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠸⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠂⠁⠘⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡀⠀⠀⠀⠀⢀⡔⠉⠲⠂⠉⠉⠙⠛⠶⣷⡀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠠⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠆⡱⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢠⠁⢠⡤⠄⠠⠤⠤⠒⠒⠉⢀⣠⣾⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢸⠀⠀⠰⣤⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠗⠠⠄⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠙⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡌⠁
⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠻⣿⠁⠀⠀⠀⠘⣩⠏⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠈⡓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠉⠁⠒⠒⢊⡁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⢾⣅⣀⡀⢀⣀⡠⠔⠋
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣤⣤⣠⣤⡤⠶⠛⣁⠰⠌⢣⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢹⢄⠀⣤⠀⠈⠐⠃⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠦⠀⣀⣀⠀⠠⠖⠋⠀⠀⠀⠘⣴⠁⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢋⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⢀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠉⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡄⠀⠀⢸⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢋⣤⠞⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣌⠓⠒⢁⡖⠀⢀⠇⠀⠀⠀⠀⠀⠀⣀⠩⠴⠚⠉⠈⠳⡄⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢶⠛⡀⠰⠿⠤⠤⠤⠐⠐⠛⡏⠀⠀⠀⠀⠀⠀⠀⠹⣄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠑⢄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠓⢤⣀⣀⡴⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠴⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣐⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢆⢎⡄⢀⡴⠖⠚⡳⡄⠀⠐⠁⠉⡀⠁⠈⡁⢠⡶⢺⠭⠶⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠀⠀⠀⡸⠁⢸⢂⠉⠁⠄⢎⠀⠀⠃⠐⠒⠀⠛⠁⣇⢯⡸⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁⠀⠀⠰⠃⠀⣣⠀⠀⡤⠀⣸⣄⠀⢈⡆⣀⣰⠀⠀⢧⣵⠃⠀⠀⢰⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠄⡀⠲⠀⢰⢹⡧⣤⠀⠼⢇⡼⡔⠁⣦⠛⡌⠱⡀⣪⢱⡀⠐⠠⣤⢀⣾⣿⡀⢢⠉⠡
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡔⠑⡼⢇⠸⣼⣿⣬⠀⢸⠶⢾⢃⣀⡀⢀⠀⠊⠃⢉⠜⠣⣿⡤⠈⠸⣿⣿⠷⠀⠐⠛⡲
⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠘⠄⠀⠀⣘⢠⢨⣄⠇⡸⣀⠀⢹⠀⠀⢼⣉⠀⢀⣈⠕⠋⠀⠙⡗⠁⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡀⢸⠀⠴⡍⠀⠡⡞⣼⠀⣸⠀⢸⠀⠀⢸⠀⠀⠸⠁⠀⠀⠃⠀⢱⠀⢰⠃
⠀⠀⠀⠀⠀⠀⣰⠀⡉⠉⠐⠂⣀⡀⢰⠀⠀⠀⠀⠀⣇⣈⢦⠷⢄⣀⣄⠔⢫⠀⠀⠀⡇⠀⠀⣱⠀⢳⠘⢶
⠀⠀⠀⠀⠀⢠⠋⢰⢀⣸⠀⢸⡇⢈⣾⠀⠀⢂⣰⣍⡇⠀⠀⢣⠀⠈⠁⠀⢸⠀⢤⣀⣧⠠⠊⠀⡆⢸⠀⠻
⠀⠀⠀⠀⠀⠬⠨⠄⠀⠁⠀⠀⠀⡃⢙⠄⣠⡿⠃⠈⢇⡀⠀⠈⡄⠀⠀⠀⢸⠀⠀⠋⣙⡂⡤⣠⠇⠸⠀⠀⢇⠀⣀
⠀⠀⠀⠀⢀⠃⠀⡤⠊⠀⢰⡇⡠⠁⢈⠖⡡⢧⠠⠬⠦⢬⡳⠦⣷⠤⠴⠶⠾⠶⠆⠀⠀⠘⠧⡤⠣⢤⡏⠀⠚⢉⣖⡀
⠀⠀⠀⠀⠸⠤⠊⡇⠀⠀⡜⠃⠣⠖⠁⡴⠁⠸⠀⠀⠀⠀⠉⠢⢸⠁⠒⠠⡇⠉⠀⠀⠀⠀⣻⡠⠆⠴⠃⠀⠁⢩⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠃⢀⡜⠃⢂⠀⠀⠘⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠄⠀⢠⠓⡗⠀⠐⠂⠉⣋⡄⢐⡂⠀⠈⣀⠌
⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠸⠈⠓⢤⠥⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⡈⠀⡇⠀⠀⠀⢰⠀⢡⡠⢛⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⡀⠀⠀⠀⢸⠔⠊⡇⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⡇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠂⠀⠁⠀⠀⠀⢸⠀⠀⢸⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠸⠀⢨⠀⠀⠀⠀⠀⡀⢀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢤⡗⠒⡗⠒⡚⢒⠂⠖⠀⠏⡅⠀⠀⡅⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠓⢳⠐⠂⢯⢹⠋⡅⢸⠀⠀⠀⢰⠀⢰⠀⢀⠃⠘⡂⠓⠺⠀⡇⠀⠀⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠐⡆⠀⢰⢀⠀⢁⢸⠀⠀⠀⡈⠀⣆⣀⡼⠀⠀⡇⡁⠇⠀⠁⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⡥⠀⡸⠜⠀⠈⡭⠓⣦⢴⡛⣸⠉⠊⠑⠒⣠⢩⣍⢀⣠⡞⠀⠤⠤⢠⡘⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠙⠛⠋⠠⠟⠉⠃⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣤⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣰
⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⡿⣿⣿⣿⡄⠀⢈⠇⠘⡀⠀⠐⠛⠁⢐⠢⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹
⠀⠀⠀⠀⠀⠀⣾⣿⣏⢿⡿⢁⠁⠀⠿⣿⣀⠀⠂⠀⠔⠀⠀⠀⠀⠀⠀⠤⡴⠗⡠⠂⢁⡀⢂⡠⠀⢀⠀⠁⠀⠤⣡⠕⠒⠀⠀⠀⠀⢤⡂⢄
⠀⠀⠀⠀⠀⠰⠿⠋⠈⠬⠡⠊⠀⠁⢉⠝⠃⠀⡰⠂⠀⠀⠉⠀⢀⠂⠀⠂⡄⣈⣾⣛⠃⠀⠀⢐⡂⠘⡆⠀⠀⠞⢁⣀⣤⣆⣀⣤⠀⠀⢙⡹
⠀⠀⠀⢠⠀⠀⠰⠂⠀⠀⠐⠀⢠⠂⠀⠔⠁⠀⠃⠄⠀⠀⢠⠁⠀⡠⠂⡴⢺⡏⠀⠈⡀⠀⠀⠈⢁⡴⢴⡀⡀⡌⠘⠛⠉⠁⠀⠲⠀⠀⢀⠁
⠀⠀⠀⡈⠆⠀⠀⢈⣠⠀⠀⣈⠁⠐⠁⢀⡄⠀⠂⠚⢶⡀⠀⣀⠨⠐⠁⠀⠀⡟⡄⠀⠀⠀⡐⠀⠘⣠⢾⠏⠀⠅⠀⠀⠀⠀⡠⠂⡀⠈⠮⢀⡖
⠀⠀⠘⠈⠀⠀⣴⣿⡇⠴⣈⡿⣧⠀⠀⡖⠀⠀⠀⢠⠟⣵⣨⣿⣄⣀⣀⣀⣠⣧⡀⠂⢄⠁⠀⡠⠎⠐⠃⠀⠄⠀⠀⢄⠀⠈⢀⣈⢠⡤⠄⠛⠁
⠀⠀⡀⠀⠓⠀⠀⠀⠀⠂⠁⣀⠈⠀⠀⡠⠀⠀⠀⣈⠀⠘⢁⣴⡾⠿⣿⢿⣿⢿⣿⣷⣦⣾⢋⣠⣖⣃⣴⠴⠂⡀⢠⣴⡧⠔⠈⢀⡀⢀⡀⠁⠠
⠀⢠⠔⠀⠀⠀⠀⠠⡠⠀⠀⣌⡇⠀⠀⠂⠀⠀⢀⠌⠀⢾⢀⠃⠘⠓⠀⠀⠀⠈⣭⠙⣧⡘⠉⠉⠀⠀⠀⠘⠓⠘⠄⠤⡡⢒⡚⠛⠀⠛⢑⠀⠂
⠀⠀⣀⢄⡤⠀⠀⠛⠂⠀⠀⠚⠗⠂⠀⠀⠀⠉⣡⠐⠁⠄⠺⠀⠀⠀⠀⠀⡨⠀⠀⠀⡠⣇⠀⠐⠁⠀⡆⠀⠀⠀⣠⣾⠃⠈⠁⣀⣀⣀⠈⠁⠀⠴
⠀⠀⠃⡀⠀⠀⠀⠀⠂⢉⠀⠠⠞⠀⢀⣴⣥⣾⣤⣄⡀⡀⢀⡀⠀⠀⠀⠉⠀⢀⡠⠊⠀⠾⣆⠀⠀⠐⠁⠀⢀⠴⢻⣼⢆⠀⠀⠄⣀⠌⠀⠀⡀⠚
⠀⠀⠀⡀⠀⠀⢀⠀⠀⡡⠂⠁⠀⢈⡀⠈⠉⠛⠉⠀⡠⠅⠈⠄⠂⣠⠒⡤⢢⡀⠀⠀⠀⠖⠗⠁⢠⡀⢠⡂⠀⠺⡻⢏⠃⠀⢐⡤⠀⣠⡔⠈⠇
⠀⠈⠤⡁⠐⠒⠻⠵⡮⠟⠂⡃⠀⠈⢀⠀⠀⢸⠀⠀⣁⠀⠀⠁⠈⠙⠛⠛⠉⠉⠁⠅⠀⢸⠂⣰⣿⣾⣧⣿⡄⠚⠗⠀⣈⠀⠈⠓⠻⠚⠛⠀⢐
⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢠⡁⠀⠀⠈⠀⠀⠸⠄⠊⠀⠀⠀⠉⠂⠀⠀⡀⠀⢠⠈⡀⠠⣿⡁⠉⠙⠛⠉⠉⠉⢀⡀⠀⠀⡃⠀⠀⠀⠀⠀⠰⠉
⠀⠀⠀⠀⠀⠰⠀⠀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡇⠄⠒⠈⠀⠀⠙⠈⡄⡀⢀⡀⢀⡀⣇⠄⠀⠈⠀⠀⡀⡀⣀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⡀⢿⣿⡷
⠀⠀⠀⠀⠀⠀⣰⣾⣷⡄⠀⠀⢀⣀⣤⡴⢒⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠛⠉⠉⣽⣿⣿⣦⣉
⠀⠀⠀⠀⠀⠀⠈⠛⢛⣡⣴⣾⡿⠟⠉⢀⣾⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠛⢛⣀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣾⣿⣿⣿⡆⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣄⡹⠿⠇
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⠿⠛⠛⠛⠛⠻⣿⡌⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠶⠂
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣄⣀⣠⡄⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠁⠀⠀⠈⣿⣿⣿⣿⣟⠁
⠀⠀⠀⣰⡿⠋⢉⣿⠿⢿⣿⠛⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⡿⠁⠀⢸⠏⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠛⠛⠋⠉⠻⠏⠉⠉⠉⠉⠙⠛⠒
⠀⠀⠸⠀⠀⠀⠘⠀⠀⠀⠀⠻⡄





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠘⠿⠇⠀⣠⡴⠂
⠀⠀⠀⠸⣿⡿⢃⣀⣀⣀⣠⣴⣾⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣭⣥⣶⣶⣶⣶⠟⠁
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⣠⡾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢿⣿⣿⣿⣿⣿⡇
⠀⠘⠉⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢿⣿⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⢸⣿⢻⡿⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⢸⡇⢸⠇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠈⠀⠘⠀⠀⠀⠈




⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⣶⣦
⠀⠀⠀⠀⠠⡀⠀⠀⢾⣿⡷⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠙⠿⣛⣀
⠀⠀⠀⢰⡇⢹⣄⣀⣠⣥⣤⡀⠀⣠⡇⣼⣷⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⣿⣿⣿⣿⣶⣤⣤⠦
⠀⠀⠀⣾⡷⢿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣌⣥⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠹⣿⣿⣿⣿⠏⠉⠉
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⢰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣰⣿⡿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⠏⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⡏⠹⣿⡇
⠀⠀⠀⠀⠀⣾⠋⠀⠀⢸⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠿⠀⠀⢹⣷⡀
⠀⠀⠀⠀⡸⠁⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠈

⣿⣶⣶⣿⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠀⠈⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⣠⠞⠩⢀⡤⠶⣾⣷⠶⣄⠀⠀⠀⠀⠀⢀⠀⠌⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡾⠁⠀⣰⠋⠀⠀⠈⠻⣷⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠉⣼⠃⠀⠀⠀⠀⠀⠘⣿⡌⢧⠀⠀⠀⠠⠀⢀⠀⠀⢀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⢸⡄⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⢰⣦⡀⠀⠀⣿⢸⡇⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠈⣧⠀⠀⠀⢸⣿⡝⢦⡀⠏⢸⠇⡁⠀⡁⠀⠀⠐⠀⢸⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⣄⠀⠀⣸⠘⣷⡀⢹⡇⢹⠀⠈⡊⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠹⣎⣡⠙⢦⡀⡟⣶⣿⣧⣼⠀⠸⡆⠀⠀⢆⡀⠀⠀⠀⠀⠈⠐⠢⢀
⠀⠀⠀⠐⡆⠀⡀⠀⠀⠀⠀⠀⠈⣻⣷⣤⣉⣓⣟⣉⣵⡇⠀⠀⢧⠀⡓⠒⠒⡄⠀⣀⡀⠀⠀⠀⠀⠙⢀
⠀⠀⣰⣇⠈⡏⠀⠀⠀⡐⠈⠀⣤⣇⠼⣟⣿⣯⣿⡋⡜⠀⠀⠀⠘⣆⠀⠀⠀⡇⠉⣄⠙⠋⠐⠒⠲⠄⠤
⠐⢠⠇⠸⡄⣇⠥⡀⠇⣘⠀⠐⠿⠿⣽⣧⣟⡗⣏⠟⠁⠀⠀⠀⠀⠘⣆⠀⠀⡇⠀⠀⠀⠀⠀⣌⡉
⣠⡏⠀⠀⢹⡇⠃⠐⠀⠄⠾⠂⢼⡆⣼⣙⡮⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡁⠀⠀⠉⠈⠒⠂
⢸⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠃⠈⠋⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⢂⡡
⠈⠓⠤⠔⠊⠀⠀⠀⠀⠀⠐⠆⠠⡶⠖⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⢶⣤⡼⢃⠈
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠁⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣀⣀⣀⣡⣤⣔⣀⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢧⣼⣿⣿⣿⣿⣧⣼⡿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠁⠈⣿⣿⡇⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⢀⣿⣿⠃⠰⣿⣿⣿⠂⠀⠀⠀⣰⡟⣱⣿⣿⠃⠀⣀⣀⣀⠀⠀⢤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⣼⡿⠃⠀⣠⣴⣤⠀⣰⣶⣦⣼⠏⣰⣿⣿⢏⣴⣿⡿⠛⣉⡛⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠈⠀⢀⣸⣿⣿⠃⢀⣿⣿⣿⠏⢠⣿⣿⡟⢼⣿⣿⠁⣴⣿⣿⣀⣾⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⢷⡏⠉⢻⣿⡏⣠⠞⠻⠿⠏⠀⣸⣿⣿⣁⡈⠻⠿⠚⢹⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⡇⠀⠀⠉⠉⢡⣶⡆⠀⠀⣀⣿⣿⡏⠉⠙⣷⠀⣠⢾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠘⠒⠋⣤⢤⡀⠀⠀⠘⠿⠷⠶⠿⠛⠹⣿⣇⠀⣀⡿⣼⡇⣸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⢀⡇⠀⠀⢸⣿⡾⠁⢀⣀⠀⣠⣤⣤⣀⠀⠀⠈⠛⠛⠉⠀⠙⠷⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡯⠴⢋⣴⡿⢷⠚⣩⣿⡷⠀⣿⡇⠈⠉⣿⣿⣇⠀⠀⠀⠀⣀⣀⡀⣀⣠⣶⣶⡄⠀⣠⣶⡄⠀⠶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⣿⡷⡖⠉⠻⠧⠞⠀⣿⣿⠁⣰⠟⠀⠀⠀⣿⣿⡿⠀⠀⣰⣿⣿⠋⣿⠁⣼⣿⣿⠀⢠⣿⣿⣿⠀⠀⣹⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠁⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⢰⣿⣿⡇⢀⣠⣿⣿⣇⣰⡟⠀⠘⢿⣿⡴⠟⣽⣿⣿⠀⣠⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⠤⠤⠤⠤⣼⣿⣿⠛⠋⠁⠈⠙⠛⠉⣀⣠⣤⠤⠤⠤⣤⣿⣿⡿⠾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⣠⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣠⣴⣶⣶⣶⣶⣶⣦⣤⣄⣾⣿⡿⠁⠀⠀⠀⠀⢸⣯⣠⡤⠤⢤⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣾⣿⣿⣛⡉⠉⠉⠉⠉⠉⣿⣿⣿⣷⣤⣀⠀⣠⣴⡿⠛⠛⠶⠾⠟⠛⠉⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⣿⠏⠀⠈⠙⢻⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⡀⠈⠛⠻⠛⠃⣀⣤⣾⡿⠋⠁⠀⠀⠀⢠⣿⣿⠋⠛⠿⣷⣦⣤⣀⡀⠀⠀⠀⢀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⠚⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠈⢳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆⠀⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠩⣿⡿⢿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣁⣸⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣼⢇⢼⣷⣇⢸⣀⣀⡀⢥⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠬⠿⠿⠿⠿⠏⢹⣿⣿⠈⡡⣿⣿⠿⠿⠷⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣄⡀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡋⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣍⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠧⠔⠊⣩⠿⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢖⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠈⠁⣷⡀⠀⢰⡒⠀⠀⡴⠶⠖⡀⠒⠐⠤⠀⠀⠨⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣥⠬⠁⠀⢘⠁⠀⠉⡰⠿⣿⣷⠤⠤⠴⠆⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⣶⣤⡼⠀⠀⠀⠀⠀⣀⡀⠀⢀⠀⠀⠀⠐⠘⡀⠀⠈⣤⠞⠉⠀⢀⡆⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣧⡀⢰⡀⠀⢀⣾⡷⠋⠀⢋⣄⣀⣰⣆⡠⡯⠀⠀⢿⣥⡴⠞⠋⣷⢀⡟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⡛⠳⣀⢹⣉⡝⣉⣤⣨⣿⣞⡏⢀⠜⡡⠂⠈⡿⠉⢖⡘⣿⡃⠀⢻⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡟⠀⠀⠀⠻⠈⢻⣏⣷⢨⣾⣿⣧⡤⠚⠐⠉⡰⠁⠀⠈⠈⣴⠐⣄⠚⠐⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠿⠀⠒⠒⠚⠒⣲⣿⣿⣿⣿⠟⠁⣤⣰⣦⠔⢲⡤⡤⠀⠀⢋⠁⠉⠉⠓⢦⠀⠶⠄
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠂⢀⣠⢀⡔⠁⠴⠶⠖⠲⠦⠤⠇⠀⠀⣥⠂⢀⣞⣟⢓⣺⣏⣾⣷⢤⠆⡀⠀⠐⠠⠄⠸⢑⣤⠆⠦
⠀⠀⠀⠀⠀⠴⠉⠁⠀⠀⠀⠈⠀⠢⠤⠤⠤⠤⠤⠀⠀⠤⠤⠠⠤⠤⠤⠄⠀⠉⠉⠉⠀⠀⠒⠊⠀⠀⠀⠐⠒⠛⠉⠉⠁⠰⠠⠤⠤⠔⠂

⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⣴⠂⢰⣶⡄⠰⡄⠀⠀⠀⠀⣾⣿⠆
⢀⣬⣿⣄⠀⠀⠀⠀⠀⠀⠀⣻⣏⠀⠀⠀⠀⣀⣜⠛⠃⠀⠀⠀⣀⣼⣿⣧⡀⠀⠀⠛⠦⣬⣿⡤⠶⠃⠀⠀⠀⣶⡦⠁
⡾⣿⣿⡟⣇⠀⢀⡀⠀⠀⡞⣿⣿⢳⠀⠐⢿⣿⣿⠀⠀⠀⠀⢰⠇⣿⣿⡇⢹⡄⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠰⣿⡇
⡇⣿⣿⡇⣿⠀⣸⣇⠀⢸⢀⣿⣿⠸⡇⠀⠈⢿⣿⣳⠆⠀⠀⠸⣦⣿⣿⣧⣼⠃⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⠆
⠀⣿⣿⡇⠀⢸⣿⣯⠇⠀⣼⣿⣿⣧⠀⠀⠀⠈⢿⣿⠀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⠀⠀⣿⢸⣷⠀⠀⠀⠀⠀⠀⣿
⠀⣿⣿⡇⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⢸⣿⠈⣿⠀⠀⠀⠀⠀⢀⣿
⠀⠿⠻⠇⠀⠀⠿⠿⠀⠀⠀⠿⠿⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠿⠻⠇⠀⠀⠀⠀⠸⠇⠀⠿⠀⠀⠀⠀⠤⠬⠥⠤⠶⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⡀⢀⣸⠛⠃⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⢸⡿⠿⠿⣶⣶⣴⣿⣿⣿⣤⡀
⠀⠀⣧⢸⣿⠳⠶⢶⣤⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠙⣷⡀⢸⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣦
⠀⠀⣿⢸⣿⣤⣭⣍⠉⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢰⣾⣝⠿⠃⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⠒⠛⡏⣽⡏⠀⡇⠀⠀⠀⠀⠀⠀⣰⡿⣶⣤⣶⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠸⡿
⠀⠀⠋⠉⠉⠓⠛⠀⠀⠃⠀⠀⠀⠐⠿⠿⠿⠿⠿⠟⠛⠿⠶⠟⠀⠀⠀⠀⠀⣠⠖⢚⣻⠻⢦⡀⠀⠀⠀⣾⣿⡟⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠺⡿⠀⠀⡧⠀⠀⢰⣿⣿⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠸⣿⠗
⠀⠀⣴⣶⣤⣠⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄
⠀⣠⣽⣯⡴⣿⣿⣥⠞⠃⠀⠀⠀⠀⠀⠀⣀⣤⡤⢤⣬⣛⠃⠀⠀⠀⠀⠰⣿⣷
⢠⡿⣿⣿⣿⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠛⢦⡀⢠⡴⣶⣿⡀⣀⡄⠀⠀⠀⢠⡄⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⢠⡄
⢸⡇⣿⣿⣿⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠇⠀⠀⠙⠏⢀⣿⡏⠉⠉⠀⠀⠀⠀⢸⠏⠉⠉⢿⣽⣿⣿⣯⡿⠉⠉⢹⡇
⠀⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣼⡏⠀⠀⠀⠀⠀⢾⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣀⣀
⠀⠐⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠾⠋⠀⢰⡟⠀⠀⠀⠀⠀⢀⣼⠟⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠛⠛⢻⡟
⣀⣈⣿⣿⣃⣚⣛⣛⣂⣀⣂⣀⣀⣀⣀⣀⣀⣀⣿⣁⣀⣀⣀⣀⣀⣛⣋⣀⣀⣻⣃⣀⣀⣀⣀⣀⣀⣀⣀⣈⣿⣀⣀⣿⣁⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠬⢥⡀⠀⠀⢀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣆⢤⢤⣀⠀⠀⠀⠚⠀⠀⣤⡀⣤⠀⢀⠀⠀⠀⠠⠆⠰⠂⠀⠐⣦⢠⠀⠀⠀⠸⠇⡠⢒⡐⠶⠷⢮⣽⣍⢘⣷⠀⠀⠁
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠲⡽⠁⠀⠀⠈⢳⠀⠀⠀⠀⢄⡼⠛⠙⠲⢿⡁⠀⠀⠀⠂⠄⠀⡴⠂⠉⠛⣾⠃⢠⠖⠚⣵⡏⠠⠄⠀⠀⢹⣿⡀⢸⡀
⠀⠀⠋⠀⠀⠀⠘⠁⠀⠀⣧⠀⠀⠠⠀⢸⠇⠀⠀⠀⣼⠀⠂⠀⠀⢸⡇⠀⠰⠂⠀⠀⢸⡁⠀⠐⠂⢸⠇⠸⢲⡊⠁⣧⡀⠀⠀⠀⡸⠃⠉⣿⠀⠀⠀⠘⠃
⠀⠀⠀⢠⠤⠤⣄⠀⠀⠀⣸⠧⢄⣀⠤⠻⣄⠀⠀⠀⣸⢦⣀⠀⡀⣾⠀⠀⠀⠀⠀⡠⠘⠳⢄⡈⠠⣎⠀⠀⠘⢃⡜⠁⠉⠐⠂⠈⢷⠀⠀⠈⠁⠀⠀⠀⠀⠐⠂
⠀⠀⠀⡏⢠⠖⣮⢗⡆⣶⠧⣄⠀⠒⠛⢠⣜⣢⣤⣤⣅⡀⠀⠀⠀⣨⢂⠔⡿⣻⠻⣾⣗⢦⡀⠀⢀⣈⠴⠒⠢⣜⢀⠀⢀⡀⠠⠄⢊⣴⠉⣀⠀⢺⣳⡄
⠀⢻⡚⠁⣸⢠⡧⠚⡓⠁⠀⢹⡆⢀⡈⢹⢿⠓⠛⠓⠊⢻⡄⠀⣼⢡⡏⠈⠁⠉⠀⢹⡼⡆⢷⠐⢶⠏⠀⠀⠀⠘⣯⠀⣏⣰⣶⢰⠃⠈⠙⠛⠦⣤⠟⠳⣄
⠀⠀⠉⠈⠁⠈⢧⡀⠤⡂⢀⡼⠁⠈⠀⢺⡟⠀⠀⠀⠉⠀⡇⠀⡉⠀⠳⣄⢠⠄⣀⡜⠀⠃⠀⠀⢹⡀⠀⢠⠈⠀⡿⠀⠠⡄⠉⠸⣆⠀⠤⡬⠀⡼⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢀⣽⡇⠀⢿⠳⡄⠀⠀⠈⠷⣄⡀⠈⣁⣼⠁⠀⠁⠀⢀⣾⠏⠉⢹⣷⡀⠀⣀⠀⣠⡿⠦⢤⠤⢾⣧⡀⠀⡇⠀⣠⣾⠁⠒⢲⣎⢦⡿⠧⠜⠁
⠀⠀⠀⠀⠀⡠⠋⣼⠀⠀⠸⡆⠹⣆⠀⠀⢀⡼⡏⠭⠷⢹⡷⡄⠀⢀⡏⣼⠀⠀⠘⡇⢳⡀⠀⡼⢱⠃⠸⣆⡞⠈⣧⠙⢦⠛⠋⢡⠇⠀⠀⢸⠈⢧⡀
⠀⠀⠀⠀⢰⡃⢠⡏⠶⠤⣀⢳⠀⣹⠀⢀⡞⠀⣿⠀⠀⠈⣇⢹⡄⣸⢀⡇⠀⠀⠀⣷⠈⣧⠀⣇⠿⠀⠀⠈⠀⠀⠸⣆⡸⠃⠀⡾⠀⠀⠀⠸⡇⣄⢳⡄
⠀⠀⠀⠀⠀⠉⣹⠀⠀⠀⠈⠈⡇⠀⠀⠸⡇⠀⣿⠀⠀⠀⣿⣰⠃⡏⢸⠁⠀⠀⠀⢹⠀⢸⡄⠈⡗⠶⠾⠶⠖⠻⠒⡏⠀⠀⣸⠃⠀⠀⠀⠀⢷⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⡆⢠
⠀⠀⠀⠀⢾⣿⣿⠟⡇⠀⠀⠀⠀⠀⠀⠀⢀⠄⣈⠳⠀⠉⠘⢬
⠀⠀⠀⣠⣼⠀⢠⣴⡇⠀⠀⠀⠀⠀⠀⠠⠀⠎⣀⠆⠀⠀⠀⠀⢂
⠀⠀⠀⠙⠛⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⢤⠇⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣿⣏⣠⠔⠉⠑⠠⠠⡤⠖⠒⠓⠒⠤⠤⠤⠤⠋⠀⠈⢉⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⠗⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠗⠴⠒⡿⠀⠀⠀⠀⠀⠀⠉⢹⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⣰⠁⠈⠀⡀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠃⠀⠀⢀⠞⠉⠉⠙⢆⡀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢸⠀⠀⢠⠃⠀⠀⠀⠀⠀⠉⠂⢄⡀⠀⠈⠢⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡶⠚⠀⠀⢸⣀⣀⣀⡠⠤⠤⠒⠒⠒⠛⢣⠀⠀⠹⡀⠀⠀⠈⠉⠉⠒⠒⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠔⠦⠲⡒⡀⢀⠉⠀⢀⡀⣶⡤⠀⢄⣶⠀⠀⠀⠀⢸⠛⠓⠙⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣾⣿⠓⢀⢉⠷⠹⠇⢀⢎⡴⠤⠷⠈⠪⣿⢢⡀⠀⠀⡀⠀⠀⠀⠠⣀⠀⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠑⢀⡘⠛⠀⢀⠠⠹⢏⠀⠀⠀⠀⡀⠀⢈⣮⡥⢀⣤⣼⣦⢹⡬⠀⢰⣌⠀⡀⠀⢈⣸⠀⠀⠲⠆⣀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠷⣠⣾⠀⢭⣴⣿⡅⠀⡰⢶⣖⠸⣿⣿⣿⡆⠅⠀⠀⠈⠀⣿⣴⣿⣿⠀⠀⠄⠄⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣼⠒⠂⠀⠀⠀⠉⠁⠁⠘⢯⣹⡧⡄⠀⢀⠈⢀⠹⣿⣛⣿⠀⢠⠀⠀⡅⣿⡿⣿⡟⠀⠉⠀⠀⠢⠀⢀⡘⠈
⠀⠀⠀⠀⠀⠀⣁⠀⠃⠠⣶⡶⠀⠀⠤⠐⡈⠋⠔⢠⠔⡙⠂⠀⠐⠤⣍⠘⠀⠀⠰⢀⠇⠘⡆⠀⠀⢀⡄⠀⣂⢐⠀⠈⠁⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠘⢻⡄⠀⣴⣿⣧⠀⢀⡀⢀⣶⣿⠿⠃⠀⢅⠐⢈⠀⢀⣴⣿⣿⠛⢿⣾⠈⠀⠂⡐⢇⡿⢒⣤⡍⠉⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢐⠇⠀⢻⡿⢿⣆⠠⠃⠸⣿⡟⢀⢡⣤⡀⠀⠶⢰⣿⣿⠋⠀⠀⠸⣿⣆⠀⢹⣽⡏⠐⠂⢹⣇⠀⠀⠀⠀⠛⠁⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⡙⠛⠁⠀⠀⢀⣿⠁⡀⠀⠐⠀⠀⠀⣿⣿⣿⠀⢀⣀⣠⡄⠯⠀⣸⣿⢠⣐⣸⣧⢿⠁⠀⠀⠀⠀⠘⠋
⠀⠀⠀⠀⠁⣤⠄⠀⠀⠀⢤⠀⠓⣠⡘⡿⣟⢰⣾⡇⠀⠀⠀⠀⠙⠿⢿⡃⢸⣿⣿⡇⠀⠀⠛⢣⡄⣿⣿⣿⡌
⠀⠀⠀⠘⠇⠀⠀⠀⠠⢀⠁⠙⠂⠀⡿⢈⠘⡟⣿⠷⣄⣀⠀⠀⠀⠀⠀⠁⠈⢯⣹⠇⠂⠀⠀⠉⠀⠘⣯⣿⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠂⠀⠐⠀⠀⠈⠀⠓⢹⣦⣒⣁⠀⣠⡜⠀⠀⠀⠀⠨⡦⢤⠀⠀⠀⢀⠊⢛⠦⠌⣅⠿⡀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠘⠃⠂⠀⠀⠀⠀⠀⠭⠂⣰⢮⠝⠿⠟⠀⢽⢻⣧⠀⠈⡅⡛⠂⠾⣶⡀⡀⠈⠔⢡⠰⠀⠀⠈⠑⠞⢠⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠚⣠⡭⠥⠂⠀⠀⢸⠙⠋⠀⡏⡁⡸⠀⠀⠀⠹⢠⠆⡀⢰⠠⠃⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢿⢏⡈⠃⠀⠀⢘⡀⠀⠀⠓⠂⠇⠀⠀⠀⡄⠈⠸⠁⠀⠸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⢀⣠⣤⣤⣤⣤⣶⣶⣶⣦⣄⠀⠀⠀⢀⣤⣴⣶⣦⣤⣤⣤⣴⣤⣄⠀⠀⠀⢀⣤⣶⣶⣶⣶⡤⣤⣤⣤⣀
⢠⣿⠟⠉⠛⢿⣿⣿⡿⣫⢿⣿⣷⠀⢰⣿⣿⣿⣿⡿⢉⣿⣿⣿⣿⣿⣷⠀⢰⣿⣿⣿⣿⣿⣿⡇⢾⣿⣿⣿⣧
⢸⣿⣆⠀⠀⠀⣿⣏⠀⠑⣫⣾⣿⡇⢸⣿⣿⣿⣿⣷⣀⢙⣻⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠁⠸⣿⣿⣿⣿
⢸⣿⣿⣷⣶⡦⠈⠱⣾⣿⣿⣿⣿⡇⢸⣿⠘⠛⠛⠛⠋⠉⠛⠁⠀⢸⣿⠀⣿⣿⣿⣿⣿⣿⡟⣼⡆⢻⣿⣿⣿
⢸⣿⣿⡟⠋⣠⣾⣦⡈⠻⣿⣿⣿⡇⢸⣿⠀⣤⣤⣤⣤⣤⣤⣤⡄⢸⣿⠀⣿⣿⣿⠛⠙⠛⢁⣿⡟⣸⣿⣿⣿
⠘⣿⣇⣠⣾⣿⣿⣿⣿⣆⣈⣿⡿⠀⠘⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣾⡟⠀⠸⣿⣿⣄⡀⢀⣸⣯⣴⣿⣿⣿⡟
⠀⠈⠛⠿⠿⠿⠿⠿⠿⠿⠛⠋⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⢰⡄⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⣆⣤⢀⢤⢠⢄⠀⠀⠀⠀⠀⠀⠰⢖⢀⢠⢤⢠⢤
⠀⠀⠀⠀⠈⠀⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠈⠀⠈⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⠈

⠀⠀⣠⠖⠒⠒⢦⣀⣀⠀⠀⠀⢀⣠⣀
⠀⢰⠁⠀⠀⡞⠁⠀⠈⠱⡄⡴⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⣇⠀⠀⠱⡀⠀⠀⢀⡿⡇⠀⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠉⠲⡄
⠀⠀⠈⠲⣄⣠⠟⠢⣤⠞⢀⣧⣀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠘⡆⢸⡄
⠀⠀⠀⠀⠀⠻⡇⠘⡟⠀⡽⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡴⠉⠀⠀⠀⠀⠀⠉⠲⡄⠀⡇⠀⠀⠀⠀⠀⢠⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣼⣣⠞⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢜⣾⠁⠀⠀⣀⠔⢁⣠⠔⠀⣹⠀⠸⡄⠀⠀⠀⠀⠆⢀⡞
⠀⠀⠀⠀⠀⡔⠲⡿⠋⢠⠔⠋⠉⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⢴⣮⠭⣿⡖⣊⣉⡀⣈⡩⠤⠔⠊⠟⣆⠀⠘⢄⡀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⢇⢀⣽⠀⡏⣠⠴⠖⠒⠒⠒⠒⠦⡀⢷⠀⠀⠀⢀⠀⠀⠀⠀⢯⡇⠠⠔⠲⠄⠀⠘⠉⠉⢸⠃⠀⠀⠀⢹⣻
⠀⠀⠀⣠⠔⣿⣿⠀⠀⣷⣟⠒⠒⠒⠒⠒⠒⠒⣇⣾⠀⠀⠀⠻⣉⡗⠀⠀⠀⠙⢄⠀⠀⠢⠤⠔⠂⣠⠏⠀⠀⠀⠀⢀⠧⣀
⠀⠀⠀⠁⠚⢹⢻⠀⠀⣿⢉⡭⡛⠒⠒⠚⠻⠥⠈⣽⡄⠀⠀⠀⠈⠳⢄⠀⠀⠀⠈⢑⡄⢤⠄⠐⠞⢹⣦⣀⣀⡠⠤⠺⣯⡼⠃
⠀⠀⠀⠀⠀⠛⠈⢧⠠⡻⡄⠀⢀⣀⠁⠀⣠⠀⣰⠃⠙⡄⠀⣠⡤⢤⠀⠙⠲⠤⣤⠚⠙⠪⡖⠐⡖⠁⠀⠙⣄⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣇⠈⠒⣤⣬⣭⠥⣴⣊⣁⣀⣤⡿⠔⠓⠤⠼⠃⠀⢀⠔⢧⠀⢀⠀⡇⠀⠱⣀⡤⠴⠉⣆⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢪⡀⠉⠉⡇⠈⠉⠀⠈⣧⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡉⠉⢹⠧⠤⠔⢻⣀⡴⠚⠁⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢹⠇⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡲⠊⠀⡀⠀⠀⢻⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⣴⠛⣆⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⢧⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⠖⠋⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡦⠇⠘⠦⡤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⢀⣀⣀⣀⣀⣤⣴⠾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣇⠀⠉⠉⠉⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⣵⡇⠀⠀⠀⠾⣩⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀⠀⠀⠀⢀⠀⠀⠀⢠⠀⠀⠢⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⣂⣠⣄⠈⡋⢀⠁⢢⣀⠀⡁⠀⠀⠀⡁⠀⠐⠄⠄⠀⠀⠀⠉⢀⠠⠈
⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⠀⠈⠉⠈⠉⢁⢋⠤⠊⠀⠈⠁⠀⠚⠁⠐⠅⠄⡀⠀⠉⠑⣡⠄
⠀⢀⠀⠄⠐⠂⢀⠄⠐⠠⠀⡀⠀⠀⠀⡀⠰⠏⠁⠀⠁⠀⠀⠀⠀⠐⣀⡀⠀⠀⢀⠀⠀⠀⠬⠀⠀⠀⠄
⠀⠈⠀⢀⡈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠈⠀⠤⢛⠀⠐⠀⠊⢀⠜⠀⠁
⠀⠀⠀⠐⠙⠀⠀⢀⠂⠠⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠠⠀⠁⠀⠁⠀⠀⠐⠁⠠⠇⠀⠀⠀⠀⠁⠀⠠⠤⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⢳⠀⣀⣀⡀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⢀⡴⠖⠋⠀⠙⠚⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡼⠀⠀⠀⠀⢠⠞⠋⠀⠈⠉⠙⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠙⣛⠉⠀⠳⣄⠀⠀⠸⣄⣀⣀⣀⣀⣀⣹⠆⠀⠀⠙⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⠁⠀⠀⠀⠉⠉⠉⠉⢉⡁⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⡤⠤⣄⠀⠀⣀⠀⠀⠀⠀⢿⠉⢦⢰⡏⠀⠈⡇⢠⠎⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡄⢺⠀⠀⢸⢆⡞⢁⡇⠀⠀⠀⠈⢧⡸⣆⠓⠦⠖⢁⠯⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡤⠿⣄⣙⣛⣁⡼⢤⡼⠀⠀⠀⠀⠀⠘⣆⠈⠉⠉⠉⠉⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠉⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣰⠃⠀⢀⡾⡄⠀⠀⠣⠴⠖⠒⡏⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⣦⠀⠀⠘⡆⠀⠀⠀⠀⠀⡇⠀⠀⣞⠀⠹⣄⡀⢀⣀⣠⠤⠿⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣼⠈⢷⡀⠀⠹⡄⠀⠀⠀⠀⠙⣄⠀⠈⠳⡀⠀⠉⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡇⠀⠀⢳⡀⠀⢹⡀⠀⠀⠀⠀⠈⢳⡀⣠⠟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⠀⠀⠀⠀⠳⣀⡤⠷⣄⠀⠀⠀⠀⠀⣟⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣉⣑⡇⠀⠀⠀⠀⠀⢯⡴⠚⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠃⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠀⡄⡀⠠⡄⢀⡄⠀⡄⡄⡀⠀⡤⠀⠀⠠⠀⠠⡄⢠⠀⡄⡄⠠⡀⡄⡄⠠
⠀⠀⠀⠀⠀⠀⠀⣋⡀⣀⣀⠆⡂⢀⡁⡞⠰⢀⣉⡇⣃⡀⣏⣀⠀⣈⡳⠀⡃⢸⠘⡌⢄⣀⠃⡏⢆⣈⣀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣄⡀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⡷⠀⣀⣀⠀⠛⡤⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢉⣩⣿⡤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣒⣊⡡⠞⠋⢩⣰⠞⠁⣠⡅
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⡦⠀⠀⠐⣤⡷⠀⣏⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢧⣀⣀⣀⣀⡀⠀⢠⠀⢸⡕
⠀⠀⠀⠀⠀⠐⠺⢄⡗⠀⠀⠀⠐⢿⣤⣠⢤⡔⠋⢩⣭⡿⣄⡐⡀⠀⠀⠀⠀⠀⠀⠀⡾⢀⣀⡀⠙⣻⠃⠀⡜⡇⠀⢹⡄
⠀⠀⠀⠀⠀⡇⠠⡞⠷⢶⡀⡆⢱⣤⠼⠟⣼⣁⠀⠉⢁⠥⣍⠀⢰⠀⠀⠀⠀⠀⠀⢠⡟⠉⢰⠃⠀⡞⡀⢠⡁⢁⡀⠘⣣
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⣯⡀⠀⠈⠉⠉⣀⣀⣼⠖⠟⠀⠈⡆⠀⠀⠀⠀⢀⡼⠀⢀⣟⠓⢒⣆⡄⠘⢺⠘⢂⣄⣇⠄
⠀⠀⠀⠀⠀⠥⠤⠤⠤⠤⠜⠉⠋⠉⠀⠀⠚⠋⢿⠁⠀⠀⠀⠤⠤⠄⠀⠀⠀⢶⣯⡀⠀⠐⣗⠐⠐⣗⡇⠂⢢⠐⠀⣼⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⢄
⠀⠀⠀⠀⠀⠀⡴⠊⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⢯⡀⠀⣸⠃⣀⣤⠤⠄⠀⠀⠀⠠⠚⠹⡀⠀⠀⢠⠖⠲⣄
⠀⠀⠠⠤⡄⠀⠻⣄⣠⠜⢁⢠⡀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠙⠲⠭⠿⠓⠉⡁⠀⠀⠀⠀⠀⠀⠀⢤⣀⠱⠀⠀⣾⠁⢀⡼
⠀⠀⠀⠀⠿⠳⣄⣼⠷⣴⡅⠀⡙⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠈⠉⠙⠒⢲⠿⡍⠉
⠀⠀⠀⠀⠀⠀⠛⠹⣇⣤⣧⠈⠁⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢡
⠀⠀⠀⠀⠀⠀⢠⡀⢭⣯⡽⣇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⠂⢤⣀⣤⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠺⠃
⠀⠀⠀⠀⠀⠀⠸⡇⠘⢿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⢀⣹⡄
⠀⠀⠀⠀⠀⠀⢀⡖⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢤⠀⠀⠀⠀⠀⠀⠀⣰⠋⠙⣆⠀⠈⠉⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠈⣧⣀⡤⠏⠀⢦⠀⠀⠀⠀⠀⠀⢀⡀⢻⡀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣙⣤⡴⠃⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⣿⠛⢂⣤⢀⣬⠀⠀⠀⠀⠀⢀⡒⠭⣀⡿⠋⠁⠀⠀⠀⠀⣴⣾⣯⣉⡏⠑⢄⣠⣠⡏⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣼⠈⠷⠋⠁⠈⠁⠀⠀⠀⠀⠀⣘⡦⢅⣾⠇⠀⠀⠀⠀⠀⠀⣹⡃⠈⢙⣳⡶⠌⠁⠀⠓⠦⣶⣧⡀
⠀⠀⠀⠀⠀⢀⣿⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⣤⣼⢻⡀⠀⠀⠀⠀⠀⠛⠋⠁⠸⣿⠁⠀⠀⣀⣠⠔⢫⣽⣏⣛⣶⣄
⠀⠀⠀⠀⠀⡼⠁⠉⠓⠦⣤⠟⠀⠀⠀⠀⠀⠀⠀⠉⠁⢹⡇⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠘⠛⠁⠀⢠⡽⠻⣭⣿⣟⣁
⠀⠀⠀⣠⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠐⠠⠐⠛⠟⠚⠛⠉⠩⠿⠃
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠠⠂
⠀⠀⠰⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⠂⠈⠢⡀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⢀⠈⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⡀⠈⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⡖⠀⠀⠀⠇⠀⠀⠑
⠀⠀⠉⠠⢀⢀⠅⠀⠀⠀⠀⠀⠀⡀⠀⡘⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠐⠉⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠉⠀⠁⠄⠀⠂⠀⠀⠀⠁⠘⠄⠒⠀⠚⠠⠡⡀⠀⠀⠀⣠⠀⠈⠀⠚⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠄⠚⠀⢷⠀⠀⡐⢄⠆⠀⠠⠌⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⡀⢀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠊⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡀⢀⡀⠀⠠⠔⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⣾⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⣿⡇⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⣿⣇⣀⣼⡿⠁⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⡟⠋⠀⠀⠿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣠⣴⣶⣿⠂⠀⣰⣿⣦⣶⣿⡆⠀⢀⣴⡿⢷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠟⣻⣿⠉⢀⣿⡟⠀⣠⣿⡟⠁⣼⣿⠁⢠⣿⡟⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣴⡿⠃⠀⢸⣿⣷⡾⢿⣿⠁⠀⣿⣿⡶⠿⣿⣷⡾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⡉⣀⣀⡀⠀⠉⣀⡀⠈⣁⠀⠀⣈⠁⠀⠀⢈⣠⣼⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣟⡛⣿⣟⣿⣷⣿⠛⣿⣾⣿⣧⣾⣿⠀⠀⣴⡿⠛⣿⡏⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠁⢷⡟⢿⡎⠿⣶⠿⠹⡿⠙⢩⡽⠀⣼⡟⠀⢰⡿⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢀⣀⠀⡀⣀⡀⢀⠀⣀⣄⠀⣠⠀⡀⢠⣄⡀⠀⠀⠀⢻⣷⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣠⣏⣴⣓⡼⢻⣇⣴⣁⠎⣞⣀⣀⠤⠤⠤⢌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠃⣀⡉⠀⣀⡁⣀⣁⣀⡀⠀⠀⣀⣀⠀⣀⣀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡟⠀⣿⡇⠀⣿⡇⣿⡏⠉⠁⢀⣾⠟⣿⠀⣿⠛⣷⡌⢹⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡼⠁⠀⣿⡇⠀⣿⡇⣿⡇⠀⠀⣾⡇⠀⣿⠀⣿⠀⣸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⡇⣿⡇⠀⠀⣿⠁⠀⣿⠀⣿⣤⡿⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⣿⡇⣿⡟⠛⠀⣿⠛⠻⣿⠀⣿⢿⣆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠛⠃⠛⠛⠛⠁⠛⠀⠀⠛⠀⠛⠀⠛⠃⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠐⠂⠀⠀⠀⠐⠂⠀⠀⠀⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠀⠀⢠⣴⣰⣤⠀⠠⣦⣰⠆⠀⢰⣶⣴⣦⠀⠴⣇⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣰⡦⠀⢨⡛⢛⡙⠓⠒⣴⣦⣶⠀⢫⡙⣋⣽⠊⢀⣼⣶⡆⠀⣴⣦⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣧⡔⠓⠀⣿⣿⣿⣠⣤⣿⣿⣿⣄⣾⣿⣿⣿⣆⣾⣿⣿⠃⠈⢉⠛⣋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣸⣦⣿⣟⡛⠿⢛⠛⢳⣄⣭⣡⡄⠛⣟⠻⢛⣽⠿⠶⢷⡼⠿⢿⠏⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢉⣿⣶⣬⣥⡄⣠⣿⣷⡾⣿⣆⣿⡿⣿⢿⣿⣸⣿⢷⣿⣿⡄⢐⣶⣶⣾⣿⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣼⠿⢿⣿⣿⣷⣿⣿⣿⣷⣄⣭⣤⣴⣿⣶⣨⣭⣴⣾⣿⣿⣷⣿⣿⣿⡟⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⣶⡞⢻⣿⣷⣌⣡⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⣿⣿⣦⣉⣤⣾⣿⡇⠉⢠⣉⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣾⣿⣿⣿⣿⡿⣿⠸⣿⣿⣿⠺⣿⡿⣿⣿⡇⡏⢿⣿⣿⣿⣿⣿⣷⣆⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣩⣩⣴⢿⣿⣿⡇⠈⠀⣿⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠿⢿⡛⠿⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠈⣿⢿⡇⠀⠀⠸⣿⡿⠀⠀⠀⢿⣿⠇⠀⠀⠸⣿⣿⠀⠈⣿⣶⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⠀⠀⠿⠸⠆⠀⠀⠀⠁⠁⠀⢀⡀⠈⠉⠀⠀⠀⠐⠏⠿⠀⠀⢸⣿⣿⠃⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢴⣴⢾⣿⣿⡷⣦⡦⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣿⣿⡆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠛⠛⠛⠛⠛⠿⣶⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣰⣿⠏⠀⠀⠀⣴⣾⣿⣦⠀⠀⢠⣾⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⣿⡏⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠸⠿⠿⠛⢀⠶⠄⠘⢿⣉⠀⠀⠀⠀⠀⢠⠃⠀⣿⡟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢀⣼⡿⠁⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠈⣿⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠀⠐⡡⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣴⡟⠋⠀⢀⣤⠟⠀⠹⣿⣿⣿⣶⣶⣶⠆⠀⣰⠀⢀⡷⠀⢸⣶⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣶⠿⠋⠉⣿
⠀⠀⠀⠀⢀⣠⣿⡋⠉⠀⢠⣾⣿⣄⣀⣠⣀⡙⠻⠿⠿⣿⣿⣦⣤⣿⣤⣼⣿⣤⣾⣿⡋⠀⢀⣀⣠⡾⠿⣦⡀⠀⠀⠀⠀⠀⣴⡿⣿⠀⠀⠀⠀⠀⣰⡟
⠀⢀⣴⠾⠛⠉⠉⠉⠻⣆⣸⡟⠀⠉⠉⠙⠛⢿⣦⡀⢀⣼⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⡿⠿⠿⣧⠀⠘⢷⣦⣤⣤⣤⣰⣿⠀⠘⠷⠶⣶⡶⠟⠋
⠀⣾⡇⠀⢀⣤⣤⡀⣀⣿⠟⠁⠀⠀⠀⢠⡄⠀⠙⢷⣿⣟⠛⠛⠛⠻⣿⡟⠹⣿⣛⣉⣀⣀⣠⣤⣶⣿⣶⣦⡄⠉⠁⢨⡿⠟⠃⠀⣠⣶⡾⠟⠀⠴⠂⠄
⠀⠈⠛⠛⠋⠉⠈⠙⡛⠁⡀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠿⠿⠿⠷⠶⣾⣿⠃⠀⣿⡛⠉⠉⠉⢉⣉⣉⣿⠇⠹⣿⣀⣴⣿⣦⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠁⠀⠀⠀⢠⠀⠻⢷⣦⣤⣄⣠⣤⣴⣿⠀⢸⣿⣟⡛⠛⠻⠿⣿⣿⡁⢀⠆⠙⠛⠋⠀⠹⣷⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠉⠉⣉⣽⣿⡄⢸⣿⡛⠿⣿⣷⣶⣤⣽⣿⢠⡇⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡿⠟⢋⣩⣿⣷⣿⣿⣿⣦⣄⡙⢿⣯⡉⠀⠈⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣯⣴⡾⠿⣿⣿⣁⣠⣿⣿⡿⠿⢿⣷⣿⡇⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠿⢿⣶⣤⣶⠟⠙⠷⣦⡤⡈⠙⣿⠟⢁⣤⣶⠟⠉⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡷⣦⡀⠀⠀⠈⢀⣀⡀⣠⡿⠀⠀⣠⣿⠀⠈⢻⣇⠀⠀⢼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠁⢸⣿⣤⣤⣾⠿⠛⠛⢿⣤⣴⠾⠋⠙⠷⣦⣤⣿⣦⠀⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠈⠻⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠈⢻⣧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠀⠈⠙⢻⣦⣤⣄⡀⠀⠀⠀⠘⠟⠀⠀⠀⠀⣿⡷⠾⢿⣷⣾⡏⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡾⠛⣿⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⢈⣩⣿⠆⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⠃⢰⣿⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣾⠟⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⢷⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣧⣤⣄⡀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⢳⡄⠈⢹⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣧⣀⠀⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠶⠶⣦⣀⣠⠴⠶⠶⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⡀⢀⡤⠖⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣠⠟⠹⣶⠋⠀⠀⠀⠻⣄⠀⢀⠀⠀⢠⡴⢰⣾⣇⡼⢧
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢰⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡧⢠⣌⠳⠖⠋⠁⠀⠀⣦
⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠟⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠏⢀⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⠟⠀⠀⠀⢹⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣧⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠸⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⠘⠛⡇⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢷⣿⡄⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠙⠿⠁⠀⠀⢀⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⢻⣆⠀⠀⠀⠀⠰⣤⡀⢀⣠⡄⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⢳⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠙⢷⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣀⠀⢠⣀⠀⢉⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣙⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣾⣇⠀⠀⢿⣷⣤⣽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠉⠉⠛⢳⡶⠤⠶⠚⠛⠉⠀⠀⠘⣏⠀⠴⠤⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣤⣀⣀⣼⣧⣀⣀⣀⣀⣀⣀⠤⠚⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⠃⠀⠀⣿⡉⣹⠏⠉⠉⠉⠉⢁⣀⠀⣼⠿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠏⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⢰⡏⢉⣿⣿⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣼⢋⡴⠲⡄⠀⠀⣠⠖⠲⡄⠀⠀⠀⠉⠊⢹⡟⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠃⠈⠳⠞⠃⠀⠀⠛⣤⠾⠁⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠲⣄⠀⠘⢷⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣼⠋⢙⡆⠀⠀⠀⠀⠀⠀⠘⢧⡴⠇⠀⠀⠀⢳⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⡀⠀⠀⠙⠓⠋⠀⠀⠀⢠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡅⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⡸⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢀⡷⠀⠀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠀⠀⠀⠀⣤⠶⣄⠀⠉⠉⠀⠀⠀⠺⣅⣿
⠀⠀⠀⠀⠀⠀⢸⡿⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠿⠀⠀⠀⠀⠀⠀⢀⣀⢼⡇
⠀⠀⠀⠀⠀⢠⡟⠀⠙⣿⡽⣟⠓⣂⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣶⠾⣿⠛⠊⢳
⠀⠀⠀⠀⢠⡎⠀⠀⢰⡟⠀⡏⠀⠀⠀⠀⠈⠘⡿⢻⡄⠈⠉⠉⠉⠛⠛⢻⣿⠹⠉⢻⠀⢹⠀⠀⠘⡆
⠀⠀⠀⠀⠘⢧⣄⡀⠸⡇⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⢃⢸⡇⠈⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠹⠀⠇⠀⠀⠀⠀⠀⠀⠘⠁⠆⠀⠀⠀⣀⣠⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠛⠿⠶⠶⠶⠶⠾⠿⣶⣶⣶⣶⣶⣶⣶⠶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡀⣠⡀⢻⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠙⠁⠀⠈⣻⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣺⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣀⣀⡜⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢀⣨⠟⠛⠷⣤⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣅⣀⣀⢀⣀⣈⣉⣉⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠿⣿⠿⠿⡿⠿⠿⢏⠹⠿⢿⡿⠿⠿⠿⣿⣿⣿⣿⡟⣻⣛⠛⠛⠛⣛⡛⣛⢻⣿⣿⠛⠛⠛⠿⠿⠟⢻⠛⠛⠻⣿
⣿⣷⣿⣶⣶⣷⣾⣶⣾⣶⣾⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣨⡔⠀⡆⠀⢸⠱⠄⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠠⠈⠁⠘⠄⠉⠂⠀⠤⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠠⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⡄⠈⠣⡀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⡸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⣠⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⡇⠀⠐⣤⡾⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⠙⢿⡅⠀⠐⠀⠀⠀⠐⠓⠚⢄⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠀⠂⠈⠀⠀⠀⠀⠁⠀⠐⠏⠀⠀⠀⠀⠀⠀⠀⠩⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠡⠀⠀⠀⠀⠀⠀⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠈⠐⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠤⠊⠀⠠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⣶⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢀⣤⡶⡶⣦⡀⠀⠀⠀⠀⣿⣿⡿⠿⠛⠛⢿⠀⠀⠀⠀⡄⠀⠀⠀⢀⣜⣉⠋⢟⢦⠎⠀⠀⠀⢀⠴⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⠀⢸⣤⡰⣷⡏⣇⠀⠀⠀⠀⠈⠻⠇⣀⣀⡠⠊⠀⠀⠀⠴⠃⠀⠀⢀⡾⢽⣯⢟⡕⣽⠁⠀⠀⠀⣉⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠉⠙⣗⣓⣊⣩⢽⠀⢀⡀⠀⠀⠀⠀⠈⠾⠁⠀⠀⠀⠀⣀⡀⠔⢊⠸⡟⢶⣬⣉⣓⠇⠀⠀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠈⠉⠉⠳⣌⣰⣠⡞⠀⠀⠀⣩⡉⢛⣲⠒⠒⢲⣒⠚⠋⡉⠥⠤⠴⠊⠀⠙⠞⡾⠵⠋⠀⠀⠀⠙⠲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠹⠈⠁⠈⠉⢀⠘⡁⠠⣀⣀⠌⢠⡉⠫⣄⠀⠀⠀⢀⣀⡜⡰
⠀⠀⠀⠀⠀⠀⠐⢄⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⡊⠁⠤⠄⠊⢁⣴⠁⠀⠀⠀⠀⠀⢷⠤⣀⠉⠀⠐⠁⡤⠜⢡⠀⠀⠀⠀⠀⠠⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⣇⠀⠀⠒⣩⠃⠀⠀⠀⠀⠀⠀⠈⡆⠀⠉⠀⠀⡼⣁⣀⠏⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠹⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⢰⢣⠃⠀⠀⠀⠀⠀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠂⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠈⠒⠂⠤⠤⠤⠤⠤⠤⠐⣒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠈⠒⠤⠀⢠⡤⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠆⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇⢸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠒⠚⠂⠀⠃⢸⠀⠀⠂⠀⠀⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠤⠄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⣾⠏⣀⣤⠞⠋⠉⠉⠉⠉⠉⠛⠛⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠞⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⢿⣄⣀⣀⠀⢻⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣿⣀⣿⣤⡟⠿⠁⢼⡟⠛⠛⣧⣀⣿⣆⠀⠀⠀⠀⢵
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣃⣼⠻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠟⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⡂⢠⠟⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⠄⠀⢸⠃
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⡄⢀⡎
⠀⠀⠀⠀⠀⢹⣸⣇⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⣼⠆⣸⠃
⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡴⠋
⠀⠀⠀⠀⠀⠀⢹⣆⠹⣦⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣠⡾⠃⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠼⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣦⣤⣄⣀⡀⠀⠀⢀⣀⣠⣤⠞⠛⣿⡀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠙⢿⣄⠈⠉⠙⠛⠚⠉⠉⠁⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠛⠿⠶⢶⣤⣀⣀⣀⣤⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣠⡛⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣾⣿⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⠶⣄⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠟⠶⣦⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⢾⡷⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣧⣄⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣀⡀⢠⣴⠀⢶⣾⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⣶⣶⣦⣾⡿⠿⠛⠉⠁⣿⣿⣟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⢻⡃⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠄⢦⣤⠤⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣤⠶⠶⠶⢶⣤⡀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣠⣤⠚⠛⠛⠛⠛⢳⣄⣼⠋⠁⠀⠀⠀⠀⠈⠙⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢾⣧⣄⠀⠀⠀⠀⠀⠀⣨⣿⣤⣤⣀⣤⣤⣤⡤⠶⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢿⣿⣶⣶⣾⡛⠾⠉⠈⠙⠛⠋⠶⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣴⠶⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣠⣤⣤⣶⣦⣤⣤⣀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠈⣉⣭⡶⠶⠶⢦⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠙⠋⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣩⣴⠶⠿⠖⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣡⣴⠟⣁⣀⡀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣍⠻⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣾⡟⢡⣾⠏⠐⠛⠛⠛⢿⣷⡄⠀⠀⠀⣾⡏⠀⠻⠏⢛⣠⣤⣄⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣤⣴⡶⠶⢦⣤⡹⣷⡘⣿⣆
⠀⠀⠀⠀⠀⠀⣼⡿⠀⠈⠁⠀⣠⣴⡆⠀⠀⢹⣿⡄⠀⠀⣿⡇⠀⠀⢀⡞⠁⠀⢻⣧⠀⠀⢠⣿⠇⠀⢀⣴⠟⠉⠀⣠⡀⢀⠀⠉⠈⠁⢸⣿⡀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣈⣤⣤⢀⠀⠀⣿⣷⠀⠀⢿⣇⠀⠀⢸⣇⠀⠀⣸⡿⠀⠀⣼⡿⠀⢠⣿⠃⠀⢀⣀⡉⠀⠛⠁⠀⠀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢰⡿⠁⠀⠸⣇⠀⢸⣿⡄⠀⠈⢿⣦⡀⠈⢿⣶⣾⡿⠃⢀⣼⡿⠁⠀⣾⡏⠀⣴⡿⠛⠻⣆⠀⠀⠀⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⢸⣷⡀⠀⣰⡟⠀⣾⣿⠀⠀⠀⠈⠻⢿⣦⣤⣀⣀⣤⣴⡿⠋⠀⠀⠀⢿⣇⠀⢿⣇⠀⢠⣿⠀⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠙⠿⠿⠛⣡⣾⡿⠃⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠘⣿⣄⠈⠻⠿⠟⠁⣀⣤⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣶⣶⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⣾⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⣀⠀⣀⡀⠀⣀⣀⠀⠀⢠⣤⣄⠀⢀⠀⢀⠀⢀⣀⡀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⣉⠁⣿⡶⣿⡇⣾⡏⢉⣶⠀⣿⣷⣿⠀⣿⣄⣿⡇⢸⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⠙⠁⠈⠃⠘⠿⠿⠟⠀⠈⠁⠉⠁⠈⠛⠋⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡀⠀⠀⠀⠀⢄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣀⢀⠀⠠⠤⠤⠀⠀⠀⠀⠀⠔⠆
⢀⡀⠀⠀⢠⠆⠀⠀⠀⢀⠀⠤⠀⠖⠂⠀⠀⠈⠉⠁⠒⠒⠊⠋⠁⠀⠀⠁⢸⠠⠤⠐⠒⠈⠁⠀⠁⠈
⠆⠁⠔⠀⠘⠀⢀⠠⠀⠤⠤⠤⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄⠀⠴
⠀⠐⠈⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⡀⠀⠈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⡀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⡔⡈⠰⠄⠀⠁⠌⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠤⠤⠤⠐⠒⢒⡔⠃⠀⠈⠐⢲⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢈⠀⠸⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢈⡀⠀⡆⠀⢀⣀⣀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡆⠉⡋⠉⠀⠀⠈⠩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⣃⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠹⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⢀⠒⠈⠀⢘⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠠⢊⡆⠀⣤⠀⠤⢤⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡶⠚⠁⠀⣴⠠⠁⢸⠀⠀⣿⠀⠀⣼⠃⣼⡁⢹⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⠴⠂⣷⠂⠀⢸⡄⢀⡿⠀⠈⠃⠀⢋⡤⣾⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠠⢔⠁⠀⠀⠀⠀⠀⠀⡳⢢⠇⠀⠀⠀⡰⠋⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀⡟⠀⠀⠀⠀⠀⠀⡌⠀⡞⠀⠀⠀⢰⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⠐⢰⡧⢻⢠⡟⡐⢀⡸⣀⠞⠁⠀⣀⠀⣨⠋⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣀⣘⠃⠸⠯⠁⠀⣾⠁⠀⠊⠉⢩⡏⠙⡟⠀⡟⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⡿⠿⠿⢿⠆⠀⠀⢰⡇⢀⠔⢸⠂⣼⠀⢰⡇⢸⡇⣼⠏⢠⠁
⠀⠀⠀⠀⠀⠠⣾⣿⠿⠛⠉⢁⣿⠁⠀⢠⡖⠀⠀⠀⠀⢸⡧⠂⠀⠸⠀⠿⠀⢸⡇⠘⠇⠻⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⡏⠀⠀⡿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠸⡇⠀⠀⠀⠀⠀⣀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢸⠇⡠⠀⣷⠀⠀⠔⣽⠂⢠⣇⠎⢠⡟⠀⢀⣠⡾⣷⠄⠈⠯⣀⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠰⠁⠀⣿⢀⠎⠀⣿⠀⢸⠇⠀⣾⢁⡴⠁⢘⢓⡟⠀⢠⠂⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠈⠁⠀⠀⠙⠊⠀⠀⠉⠀⠀⠀⠀⠻⠋⠀⠠⠁⣼⠃⠀⠧⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⠀⠀⠀⠀⣒⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠰⠀⠀⣀⠀⡀⠀⠀⠀⠀⢀⡄⢠⠀⠀⢤⠀⡀⠀⠀⢰⠋⣢⠥⢤⡵⣤⣲⡒⠳⣄
⠀⠀⠀⠀⢀⡀⠀⠀⠤⡷⠉⠀⠈⠱⡄⠀⠀⠀⣄⡹⠚⠣⢴⡃⠀⠀⠀⠀⠀⢀⡤⠚⠓⢧⠇⢀⡤⠜⣵⠊⠀⠀⠀⠙⣿⠀⢽
⠀⠀⠂⠀⠈⠀⠃⠀⠀⣇⠀⠀⠄⠀⡗⠀⠀⠀⣼⠀⠂⠀⠀⡿⠁⠰⠀⠀⠀⣾⠀⠀⠀⢈⡇⠸⢤⠊⠙⣆⠀⠀⠈⣰⠋⠑⣏⠁⠀⠀⠂
⠀⠀⠀⡤⠠⢤⡀⠀⠀⡼⠢⢤⠠⠞⢧⡀⠀⠀⣸⢦⣐⠀⠴⡇⠀⠀⠀⠀⠤⠚⠲⠄⠠⢾⠀⠀⠘⢡⠎⠈⠉⠀⠀⢳⠀⣀⠈⠁⠀⠀⠀⠀⠂
⠀⣀⢸⠃⡞⢱⢟⡟⡿⠳⣄⠐⠛⢁⣦⣥⣶⣶⢥⡀⠀⠀⢠⢗⠔⡿⣹⠻⣿⣕⢦⠀⠠⣬⠗⠚⠒⢎⡠⠀⡠⠀⠐⣈⢼⣁⣤⠀⢯⣧
⠀⠻⣅⡠⠃⣿⠈⠉⠀⠀⢸⠀⡤⢀⣿⡏⠉⠉⡁⢹⡀⠰⡇⣾⠀⠀⠀⠀⢸⢸⠈⠇⢹⡏⠀⠀⠀⠈⡇⠘⠦⠿⢰⡇⠀⠉⠉⠒⡖⠉⠲⡄
⠀⠀⠀⠀⠀⠘⢦⡈⠀⣤⡋⠀⠀⠈⣿⠀⠀⠠⠀⢸⠃⠠⠀⠈⢳⡤⠤⢴⡋⠈⠀⠀⠈⢧⡀⠐⠀⣠⠃⠀⢸⠀⠀⢳⣄⣀⢂⢰⢣⣤⢀⡿
⠀⠀⠀⠀⠀⡠⢺⡇⠀⢹⠙⢦⠀⠀⠈⢳⡦⢤⣖⣷⡄⠀⠀⢠⢻⠇⠀⢸⡿⡄⠀⠂⡴⡟⢩⡙⣭⠹⡝⢆⠸⣤⠖⡿⠀⠀⣿⢯⡙⠉⠉
⠀⠀⠀⠀⡼⠁⣼⢀⣀⡈⣇⠈⣇⠀⢠⠏⢿⠈⠁⢸⡝⣆⠀⡏⣼⠀⠀⠀⡇⢹⡄⢸⢸⠃⠀⠑⠃⠀⢷⠈⡷⠀⢰⠃⠀⠀⢹⠀⠱⡄
⠀⠀⠀⠀⠙⢂⡇⠀⠁⠐⢻⡂⠁⠀⣏⠀⢸⠀⠀⠀⡇⣸⢸⢁⡇⠀⠀⠀⣷⠀⣧⠈⣻⢤⣴⣤⡤⠢⢼⡊⠁⢀⡏⠀⠀⠀⠘⡏⠓⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠁⠁⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠘⣿⡄⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⣴⡟
⠀⠀⠀⠀⠀⠈⢿⣎⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣛⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢃⣼⠟
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣽⡷⠀⠀⢀⣴⡿⢹⣿⣿⣿⣿⠻⣷⡄⠀⠀⠘⣿⣼⣿⣿⣿⣧⣿⠃⠀⠀⢀⣴⠟⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠉⠀⣾⣿⣿⣿⣿⡄⠈⠁⠀⠀⠀⠈⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠋⢀⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠙⣿⡟⢻⡟⠃⠀⠀⠀⠀⠀⠀⠉⣿⠉⣿⡏⠁⠀⠀⠀⠀⠀⠀⠉⣿⠉⣿⠍⠀⠀⠀⠀⠀⠀⠈⢹⣿⠙⣿⠋
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣀⡀⠀⢀⣤
⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣛⣋⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⣀⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⢸⣿⡿⢀⣾⠏
⠀⠀⠀⠀⠘⠛⠛⠛⠛⣿⣿⣿⡟⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠙⣿⡄⢸⣿⡿⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣶⣤⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡏⢻⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠿⠿⠿⠿⠿⠷⠶⠶⠶⠆⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠀⠀⠀⠻⠇




⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣿⡿⣿⣛⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠹⣿⣿⡟⢿⣿⣿⡿⠙⣿⣷⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⣿⡸⣿⣿⠇⣴⡟⠛⢿⣶⣿⣿⣿⣿⠃⠀⣸⣿⣿⠿⠋⣀⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⣿⣿⡟⠃⠘⠏⣰⣿⠀⠀⣼⠟⣱⡿⣿⣿⣄⣰⣿⡟⢃⣤⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣶⡀⠈⣿⣿⣿⡿⢿⣿⣿⠀⡀⠘⣿⠃⢀⡄⠀⣿⣿⣷⣾⠏⣼⣿⣇⠘⣿⣿⡿⡈⢿⣿⣿⣿⣿⣿⡿⠿⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠀⠘⣿⣿⡆⠀⢹⡟⢰⣷⡀⠘⣦⣼⠁⡀⠈⠛⢿⠏⣰⣿⣿⣿⠀⠻⠋⣼⣷⠈⣿⡿⠿⣿⡿⠃⢠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⢿⣷⣤⣼⠁⢸⣿⣷⣄⣹⣇⣼⣿⣆⠀⠀⢀⣿⣿⣿⣿⡀⠀⣼⣿⣿⡆⢹⡇⢀⡟⠁⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠙⠻⠇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⡿⣿⣿⣷⣾⣿⣿⣿⣷⠀⣿⠏⠀⣰⣿⣿⣿⣿⣿
⣿⣿⣿⡟⠻⣿⣿⣿⣿⣿⣷⣦⣀⠀⢠⡏⢀⣼⣿⣷⡄⠈⣿⣿⠟⠟⣿⣿⣷⣄⢸⣿⣿⠻⣿⣿⣿⡄⠈⠀⣸⣿⣿⡟⣿⣿⣿
⣿⣿⣿⣿⣦⣸⣿⣿⣿⣿⣿⣦⡈⢻⠟⢠⡿⠛⢻⣿⣿⡀⠙⠋⣠⣶⣿⡟⠻⣿⡀⠙⠓⣀⣤⣿⣿⣷⣄⣰⣿⣿⠟⢀⣤⣾⣿
⣿⣿⣿⣿⣿⠁⠙⣿⣿⡁⠀⣿⣿⡄⠀⢾⡇⠀⠀⣿⣿⡇⠀⠠⣿⣿⡟⠀⠀⣸⡇⠀⠠⣿⣿⡿⠁⠈⣿⣿⡟⠁⢀⣿⣿⣿⣿
⣿⣿⣿⣿⣇⠀⠀⠈⢿⣧⡀⢸⣿⠀⠀⠈⢿⣦⢠⣿⡟⠀⢀⠀⢻⣿⣷⠀⢰⡟⠀⡀⠀⢻⣿⣇⠀⢀⣿⠋⠀⢀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⡄⠀⠀⠹⣿⣿⠇⠀⣦⠀⠈⢻⣿⡿⠁⢀⣾⡆⠀⢻⣿⣶⡟⠀⣸⣿⡄⠀⢿⣿⣀⡾⠁⠀⣠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠹⡿⠀⠸⣿⠀⠀⠀⠻⠃⠀⣿⣿⣿⠀⠀⢻⡿⠀⢰⣿⣿⣿⠄⠈⢿⠏⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠁⠀⠀⣿⡄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⡄⠀⢸⡇⢰⡄⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣷⠀⠀⣇⢸⡇⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣀⣀⣀⣀⣹⣀⣀⣀⣀⣿⣀⣀⣋⣸⣇⣀⣀⣀⣀⣀⣸⣅⣿⣆⣠⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠀⠒⠒⠊⠁⠀⠀⠀⠀⠉⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⠄⡀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡠⠂⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠖⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠐⠀⠠⠁⠀⠀⠀⢠⠦⡀⠀⠐⠠⠀⡀⠀⠈⠉⠁⠀⠀⡩⠀⠀⠀⠀⠀⠰⠢⠔⠘⠐⢃⡮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠈⠑⠂⢄⣄⣀⣀⢀⣀⣠⡔⢺⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⣠⣶⠤⢤⢀⠀⣀⣠⡛⢡⡌⢊⡷⠊⠀⣋⠏⠀⠀⠀⠀⠀⢀⠎⠀⠈⠁⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢒⢢⠤⡴⣽⠀⠶⠀⡩⠗⢀⠉⠶⡤⠤⣢⠃⠀⠀⡇⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠆⠀⠈⢓⡒⠚⠋⠀⠠⠴⠀⠀⠀⠮⠹⢀⡜⠀⠀⣀⠤⠒⠁⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡀⠧⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠪⠗⠲⡍⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣠⡜⠢⠤⣄⣀⣀⣀⡀⠤⠴⠊⢡⠃⠀⢀⡁⠘⡀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢰⠸⢀⡀⠀⠀⠑⢄⠈⢢⠄⠲⠀⠃⡤⠔⠉⢡⠀⢃⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠆⠀⠈⡗⠂⠐⠁⠁⠺⡀⠀⡏⢠⠂⠀⠀⠀⡀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠸⠀⠀⠀⠀⠀⠀⠙⠢⡝⠞⡐⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠄⠀⡆⠀⠀⠀⠀⠀⠈⠄⡇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡰⡇⠀⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡌⠀⡇⠘⠀⠀⠀⠀⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠰⠇⢀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢠⣮⢀⠀⠠⠤⠤⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠆⠰⡘⠾⠁⠀⠀⠀⠉⠀⣀⣀⡀⠷⠠⠤⠤⠀⠒⠠⠜⠒⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠄⠀⣸⠀⠀⠈⢻⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⢢⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠐⠞⣰⢠⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠢⢄⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢱⡋⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⣠⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⠲⠙⠓⠉⠓⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠉⡻⠛⠲⢤⡀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠑⠀⡎⠀⢀⣀⣀⣀⠤⣤⣤⠤⢂⣁⣀⡀⠀⠹⡄⢠⠦⠀⠀⠠⠀⠈⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⢉⣉⠀⣤⣤⡄⠀⠀⠀⣤⡀⠀⣉⡑⠂⡗⠀⠋⠀⡀⠀⠑⠨⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⡚⢡⣿⣿⣿⣷⣶⣤⡄⢠⣤⣶⣾⣿⣿⣿⡆⠙⡄⠀⠞⣡⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠀⠻⣿⣿⣽⣿⡿⠀⠀⢿⣿⣯⣿⣿⠟⠠⢚⣷⠀⠀⠁⠀⠀⠀⠔
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡐⣚⠁⠈⠛⠛⠛⠑⠛⠚⠊⠛⠛⠋⠁⠀⣐⠃⡼⢂⡠⠀⠀⠀⠀⠀⠮⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢧⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣠⠏⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⣀⠞⢉⠉⠒⠤⡙⢦⣄⣀⣀⠀⠀⠀⣀⣀⣤⠞⠁⠀⠀⠀⠊⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡀⠀⠀⠀⡍⠀⡀⠀⠀⠀⠈⣦⠤⠽⢿⣉⣉⣹⠿⠷⠦⢤⠀⡀⠤⢄⠄⡀⠀⠀⠀⢀⠀⠤⠤⠒⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⠤⠄⠀⠀⠀⠀⠐⠋⢹⠀⠀⠀⠉⠉⠁⠀⠀⠀⡞⠘⠀⠠⠀⢀⠈⠆⠀⠀⠀⠳⣤⡀⠀⠀⠐⠴⠇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠠⠀⠀⠀⠐⠁⠠⠒⢄⠀⠀⣸⡀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠋⠀⠀⠠⢹⣦⣌⠛⠿⠶⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠰⠀⠀⠀⠁⠐⠙⡇⠀⠀⢀⠘⠄⠀⠀⢠⡇⢀⠀⠀⠀⠂⠀⠀⠀⠁⠌⢉⡙⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⣄⠤⢤⣿⣄⣀⡴⠛⣄⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠀⠀⢀⠢⣀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠘⠁⠀⠀⠀⠀⠉⠑⢄⠀⠘⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⡞⣿⠃⠉⠁⠀⢬⠀⠀⠀⠀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠊⣾⠁⠈⠉⠉⠉⠉⠀⠀⠘⣿⣿⣉⠀⠀⠀⢀⡴⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡷⠀⠀⠀⢠⣴⠀⠀⠀⠀⢿⠈⠻⢃⠂⠤⠞⠁⠀⠀⠤⠀⠴
⠀⠀⠀⠀⠀⡴⠊⠉⠉⠙⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⢸⢹⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡂⠀⠀⠄⡀⠀⠈
⠀⠀⠀⠀⢸⠀⢀⠀⠈⠐⠄⣸⡆⠀⠀⠀⠀⠀⢀⣠⠊⣿⠀⠀⠀⠀⣾⠘⡆⠀⠀⠀⠀⢷⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢄⣸⣀⣀⣨⠉⠑⠉⠉⠀⠀⠉⡇⠀⠀⠖⠋⠀⢧⣤⡀⠤⠄⡞⠅⠀⠀⠀⠁⠘⠁⠀⠘⠀⡄
⠀⠀⠀⠀⠀⠈⠻⠤⣄⣠⠶⣹⠋⠉⣹⠉⡁⠀⠰⠀⠀⣠⣖⣠⠀⡄⠀⠀⠀⠀⠀⠀⠄⣴⡒⠀⠀⠀⠀⠀⠀⢀⡠⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⠈⠠⠴⠃⠠⠁⠀⠀⢀⣴⢋⡽⠁⠀⠀⠀⠀⠀⠀⡲⠘⠻⠶⠻⢦⣄⠀⠀⠃⠉⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣷⡏⠀⠀⠀⠀⡀⠀⡜⠉⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠙⡆⠀⠀⠀⠐⠂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠣⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠡⠀⠀⠂⡠⠇

⡅⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠁⠈⠂⠑⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠀⠀⠀⠠⠀⠀⠂⠔⠁⠀⠁⠈
⡇⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⢀⠁⠀⠀⢀⠀⠈⠢⡂⠀⠘⠀⠀⠢⠀⠀⠀⠀⠀⢁⠀⠐⠀⠀⠀⠀⠀⠊⠀⠀⠀⡠⠊⠀⠠⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠄⠀⠑⠤⡀⠀⠂⠀⠀⠈⠢⠀⢁⠀⠀⠐⠤⠃⣀⠀⠼⠘⠂⠀⠠⢄⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡇⠀⠀⡈⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢀⠄⠈⠁⠀⠈⠁⠐⠉⠀⠀⠉⠀⠀⠀⠀⠀⠈⠐⠠⣃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⡇⢀⠁⠀⠀⠀⠀⢀⠅⠀⠀⠈⠢⡀⠀⠀⠀⠀⡨⠂⠀⢀⣤⠤⠤⢤⣄⡀⠀⠀⠀⠀⢀⣤⠖⠛⠛⠛⠲⢄⠀⠀⠀⠀⢀⠂⠀⠀⢀
⡇⠀⠉⠁⠈⠉⠁⠉⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄⠀⠀⠐⠁⠀⠚⢉⣀⠀⠙⠀⠀⠀⢠⠎⠀⣠⣍⡑⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠀⠀⢀⠔⠁⠀⠀⢀⠠
⡇⠀⠀⠀⠘⠢⠀⠀⠂⠀⠤⠀⠀⠀⠀⣑⠂⠠⡠⠀⠀⠀⠀⢰⠋⠉⢷⠀⠀⠄⠀⡜⠀⠸⠁⠈⣷⠀⠀⠀⠀⠀⡴⠄⠐⠀⠀⠀⠀⠐⠀⣀⠠⠒⠈⣀⠠
⡇⠀⠀⠐⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠞⢄⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⡆⠀⠁⠀⠀⠀⢠⡈⠀⠀⠀⠀⠀⢀⠒⠃⠀⡀⠂⠀⠐⠉⠀⠀⠈⠁
⡇⠀⠀⠀⠀⠠⠄⢈⣁⠒⠂⠁⠀⠄⡌⠀⠴⠈⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠙⠁⠀⢀⣠⠔⠋⠈⠀⠀⠀⠀⠀⠀⠁⡖⠀⠑⠀⠀⠒⠥⠁⠀⠀⠀⠀⠴⠂
⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢷⠀⢃⣄⠀⡀⡤⢠⠄⠾⠇⠶⠽⠻⠟⠻⠟⠛⠐⠃⠖⠏⠻⠚⠇⠆⣠⣀⠈⢴⡗⣠⠀⠀⠀⠀⠀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠱⠐⠃⠔⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠉⠸⠓⡷⢠⢄⢴⡰⠀⡀
⡇⠀⠀⠀⢤⠠⠷⠒⠎⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠴⠀⠀⠀⠉⠁⠀⠀⠐⠁⠀⠀⠀⠀⠄⠆⠄⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠈⠑⣰⣦⠰⣄
⣇⡔⣖⠨⠆⠀⠀⠀⠀⠀⠀⠀⢀⡸⠃⠀⠀⢠⠠⠠⠀⠀⢐⣄⢀⣈⠀⠀⠀⠀⠀⠀⠲⢦⠀⢀⠥⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠄⠁⡒⡀⠀⠀⠀⠀⠀⠀⠈⠑
⡧⠉⠀⠀⠀⠠⣂⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠊⠈⠈⠀⠀⠀⠒⠬⢨⠀⠉⢀⠀⢀⣁⠀⣂⠐⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⡇⠂⠸⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠈⠋⣀⡉⠁⠀⠄⠂⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣂⣤⡆⡠
⡞⣣⠄⠈⠡⠀⠀⠀⠀⠈⠄⠁⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠢⠀⠀⠩⢄⣀⣀⠀⢠⣀⣠⢖⢀⡀⠀⠀⠀⠀⢼⡦⢀⣀⡀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⢈⡀⡷⢆
⢇⡀⡬⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢠⢰⠆⠀⠀⠀⠀⠘⠷⠅⡼⣉⠛⠋⠉⣷⠕⠊⠀⠀⠀⠀⠀⠝⠳⢺⠗⠂⠀⠀⠔⠂⠪⠐⠀⠀⠀⠀⠠⠘⠂⢀
⡇⠀⠀⠀⠀⠀⠐⠂⠄⡀⠀⠀⠦⠄⠀⠀⡃⠈⠰⠆⠀⠀⠀⠀⠀⠂⢀⠇⡴⠶⠶⠶⠲⡄⠐⠊⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠰⠄⠀⠀⢄
⡇⠀⠀⠘⠀⠀⠀⠘⠀⠙⠀⠠⣤⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠐⠀⠺⠃⠀⠀⠃⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡈⠦⠂⠀⠀⠀⢄⠀⠉⠀⠈⠒⢄
⡳⣄⠀⠀⠀⠀⠀⢘⠐⢃⠁⢀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢦⡀⠃⠶
⡇⠘⣎⠀⢀⠄⠀⠈⠀⠈⣤⠀⠒⠀⠀⠀⠀⠂⠠⠀⠀⠄⠀⠳⠙⢇⣴⣄⠀⠀⠀⠀⣠⡆⡹⢋⠞⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠨⠀⠀⠠⠀⢛⠳⡈
⠅⠐⠺⣆⠞⠀⣠⠀⣠⠀⠀⠘⠀⠈⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠦⠓⠀⣀⠐⠉⠠⡄⠙

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡞⠛⣿⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⡾⠷⠀⠻⡿⠇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠳⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠿⠦⣶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⣴⣶⠖⢦⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠘⣀⡿⠧⣷⡼⢋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠿⣦⣤⣴⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠄⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⣀⣀⡀⠀⠀⠈⢷⣄⣀⣁⣶⣿⣦⣄⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⣀⣀⠀⠀⠀⣀⡀⠹⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⣸⣿⣿⢻⡻⡛⡛⡟⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⣿⣿⡆⠀⠀⠈⠑⠲⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡤⠤⠀⠶⣖⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣖⣒⣚⣛⡀⢩⡭⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⢩⣭⠭⠵⠄⠐⣚⣻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡆⠒⠛⠋⠁⠀⠉⢴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡌⠁⠀⢀⡀⢠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡟⠀⠀⠘⣷⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⣻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⢀⣼⡟⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⢀⣾⣿⣷⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⣠⣿⣿⣿⣿⣸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣸⡿⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡏⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠈⠉⠉⠉⠀⠈⠴⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠠⠀⣤⣀⠐⠆⢄⠂⠀⠀⠀⢀⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠈⠉⠁⠀⠑⡐⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠊⠀⠀⠀⠀⠀⠀⠂⠀⠈⢦⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢰⣧⠀⠀⠀⢰⣦⡄⠀⠀⠀⠑⡦⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗⠀⠀⠀⡀⠀⠀⢀⠀⢨⠀⠁⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣦⡀⠀⠀⠉⠁⢠⡄⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠙⢥⠀⠺⣶⡶⠟⠁⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⣀⠈⠉⠁⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠘⠡⠀⠤⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⣀⠤⡀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠒⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠐⠄⠀⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠞⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⡀
⠀⠀⠀⢤⡀⠀⢀⠠⠘⠈⠀⠀⠐⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄⠀⠀⠀⠃
⠀⠂⠐⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠂
⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠤⠄⠤⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡁⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠲⡄⠀⠀⢨⠁⠀⡅⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠰⠶⠇⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠇⠀⠀⠀⡇⠘⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⢀⣠⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⠒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⡅⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃⢲⠂⠋⠀⠀⠈⠳⠒⠲⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠘⠈⠁⡇⠀⠀⠀⠀⠉⠉⢋⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠎⠀⠀⢀⠀⠀⠀⣰⠀⠀⠀⡠⠀⠀⠀⠀⠈⢑⡦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣀⣀⣀⡀⢀⡀⣀⣠⠇⠀⢰⡋⠀⠀⠀⠀⠉⠀⣀⡠⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣴⣾⣿⣯⣶⣶⣶⣶⣷⣷⣷⣶⣿⣿⣶⣧⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⠁⠉⢉⡉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣭⠀⠀⠀⠹⣞⠀⠀⠀⠀⠘⣽⣄⡀⠀⠸⣾⡤⠤⠀⠀⠀⠀⣻⠀⠀⠀⢠⣽⣤⠀⠀⠀⣠⣽⣄⠀⠀⠀⣼⡧⡀⠀⠀⠀⣸⣮⠃⠀⠀⢠⣽⣥⡀
⠀⠀⠀⢁⡿⠀⠀⠀⢸⣏⡉⠀⠀⠰⢒⡿⠀⠁⠀⠀⣿⡇⠀⠀⠀⠀⣩⠿⠀⠀⠀⠘⣿⡟⠀⠀⠀⠙⣿⡏⠀⠀⠀⢻⣇⠈⠀⠀⠸⢿⣧⠀⠀⠀⠐⡟⡎
⠀⠀⠀⠈⠂⠀⠀⠀⠸⠋⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠛⠇⠀⠀⠀⠀⠛⠃⠀⠀⠀⠁⠘⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠛⠘
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⣀⠀⠀⣀⠀⣀⠀⡀⠀⠀⣀⠀⡀⠀⠀⢀
⠀⠀⠀⣉⣷⣠⡀⠈⢳⣷⠊⠁⠀⠒⣲⣾⣅⡀⠀⠀⣆⣀⠀⠀⠀⠀⣼⣤⠄⠀⠀⠢⢾⡤⠤⠀⠀⢸⣿⡏⠀⠀⠈⢳⣿⠞⠁⠀⠘⢯⣥⠏⠀⠀⣨⢾⡛⠆
⠀⠰⠚⡿⠉⠳⡀⠀⡸⠛⢆⡀⠀⢀⡟⢳⠀⠀⠀⠀⣿⠖⡄⠀⠀⠘⣷⠄⠀⠀⠀⠀⡟⢧⠀⠀⠀⢸⡿⡇⠀⠀⠀⢸⠻⡆⠀⠀⠀⠸⢻⠀⠀⠀⠈⡿⢻⡄
⠀⠀⠈⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠘⠃⠇⠀⠀⠀⠉⠀⠁⠀⠀⠀⠐⠘⠀⠀⠀⠘⠁⠀⠃
⠀⠀⢠⢀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⣤⠀⡀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⢀⡀
⠀⠀⠈⣶⣶⡄⠀⠀⢫⣿⣷⠀⠀⠑⠒⢾⡟⠢⠀⢠⣾⡷⠆⠀⠀⠘⢶⡷⠆⠀⠀⠰⣶⡞⠁⠀⠀⣴⣾⣶⠀⠀⠖⢻⡿⠒⠃⠀⠀⣶⣶⠀⠀⠀⠈⢻⣧
⠀⠀⠀⣿⡟⠁⠀⠀⣼⠉⣇⠀⠀⠀⠐⣿⡇⠀⠀⠈⢹⢹⠄⠀⠀⠀⢸⢧⠀⠀⠀⠁⣿⡇⠀⠀⠀⢰⡋⡏⠀⠀⠀⢸⣷⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠉⠁⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢴⣀⣠⠀⠀⠀⠀⠤⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⣤⣀⠀⠀⢠⡀⢠⢄⡤⠀⠀⢠⠄⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠠⡄⠀⠀⠀⢀⡀⣠⠄
⠀⠀⠹⣿⢤⡀⠀⠀⠾⣿⡀⠀⠀⠶⣼⣀⠤⠄⠀⠀⣨⡿⢣⠀⠀⠒⣺⣏⠁⠀⠀⠈⢻⡟⠀⠀⠀⣿⡟⠒⠀⠀⠀⠊⣿⣿⠀⠀⠉⢹⣟⠉⠁⠀⢠⣭⣿⠃
⠀⠀⢠⠇⠀⠁⠀⠀⠀⡷⠘⠆⠀⠸⡍⠛⠛⠂⠀⠰⠁⡇⠀⠀⠀⠘⠉⠹⣄⠀⢠⠴⠋⠙⢆⠀⠀⢿⡇⠀⠀⠀⠀⠔⣻⠁⠀⠀⠀⢸⣿⠀⠀⠀⠈⠀⢹⡀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⢰⠂⠀⠀⠰⣤⠦⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡄⠀⠀⠀⣄⠰⠄⠀⠀⠀⢰⣀⡄⠀⠀⠀⠤⢦⡶⠀⠀⠀⣠⣰⠄⠀⠀⢀⣚⣳⠆⠀⠀⣀⣀⣶⡼
⠀⠀⠦⠶⣿⡄⠀⠀⠜⢻⡇⠀⠀⠀⢞⣿⠳⠀⠀⠉⢹⣿⠉⠀⠀⠀⢻⡏⠉⠀⠀⣴⡿⠒⠒⠀⠀⢰⣟⠣⠀⠀⠈⢠⣏⡉⠀⠀⡜⢻⣧⡀⠀⠀⠀⠈⣿⠁
⠀⠀⠀⢸⠉⢇⠀⠀⠀⠛⡇⠀⠀⠀⠞⠉⠇⠀⠀⠀⠏⠉⠇⠀⠀⠰⠋⠙⠆⠀⢀⡏⢹⠀⠀⠀⠀⢸⠋⡆⠀⠀⢠⠞⠀⠃⠀⠀⠀⢸⠀⠹⠄⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠁
⣿⣿⡟⠛⠿⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⡄⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠀⠈⡆⢡⠀⠁⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠜⠀⠚⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠌⠀⠀⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠠⠤⡅⠀⠤⢤⠁⢀⣀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡁⣄⠈⠐⡁⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢠⠔⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠑⡄⢀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⢀⣀⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⣀⣠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⣰⠋⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢡⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠤⠤⢄⣀⠀⢀⠎⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⠀⠠⠀⠀⣀⣀⣀⣀⣀⡀⠀⠈⢆⠀⠀⠈⠙⢮⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢄⡴⠚⠉⠀⠀⡀⠀⠀⠈⠉⠓⠬⡆⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠋⠀⠉⠁⣀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠐⣲⢤⡀⠈⢦⡀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⣾⡏⠀⠁⠀⠀⠙⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡇⠀⠀⠨⣭⣁⣀⣈⣉⣉⣤⣶⣿⣿⠁⠀⠀⠀⢰⢤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠹⣿⣿⡿⠟⠟⠉⢙⡿⠁⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠈⠛⠧⠤⠠⠔⠋⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣄⣀⣀⣁⣀⣀⣀⣠⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠈⠉⠉⡹⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⡠⠤⡀⠶⢀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠘⣄⠀⠀⠌⠢⡀⠀⠀⠘⠀⠀⠈⠃⠀⠑⢄⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠈⢢⡀⢄⠀⠈⠲⢤⣠⢄⠀⠀⢀⠀⠀⠀⠀⠻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠙⢦⡑⠠⣀⡐⠁⠀⡇⠀⠈⠑⠢⢄⡀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠤⢀⡀
⠀⠀⠀⠀⠀⠈⠒⠬⣀⣀⣀⡆⠀⠀⠀⠀⠀⠈⠁⠒⠠⠄⣙⠲⢤⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⠞⠉⠀⠂⠀⢁⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡈⠙⠓⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠦⣄⠀⠀⠀⠈⠢⣐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠂⠀⡀⠀⠀⠀⠀⠀⡀⠀⠇⠈⠳⡀⠀⠀⠀⡙⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⡟⠂⠀⠀⠠⠐⢀⠜⠀⠀⠀⠙⢆⠀⡰⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠌⠀⠈⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢀⠄⢸⡀⡀⢀⢀⠄⡀⠀⢀⡏⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢀⠀⣀⢄⢠⢰⣉⠀⡇⢁⢘⠀⣙⢈⣢⢸⠁⢸⢸⢸⠒⠁⠀⢸⠃⠀⡇⡈⢁⢀⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⢸⠀⠘⠌⠠⠀⠁⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠊⠈⠤⠌⠘⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⡤⠤⡤⠜⠙⠉⠓⢲⣀⠀⠀⠀⠀⠰⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣀⡀⢀⠔⠃⠀⠀⠀⠀⠀⠀⡤⣀⡀⠀⠀⠋⠙⠊⠳⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣃⠔⠋⠁⠀⠀⠀⠀⢨⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠠⡈⢩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠠⢌⣒⡲⠄⢺⠁⠀⠙⠀⠀⠀⣠⣀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣄⣀⠦⠬⠭⠹⣇⠀⠀⠀⢀⡠⠟⠁⠘⠤⡄⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⣸⢸⠀⡝⣿⢿⠀⠀⠀⠸⢤⣀⡶⠞⠀⠀⠀⠀⠀⠈⠉⠓⠋⠒⠩⡃⠀⠀⠀⢦⣀⠀⠀⢀⡹
⠀⠀⠀⠀⠀⠀⠈⡄⠀⢀⡏⡼⢠⠃⠉⠀⠀⠀⠀⠀⢸⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢅⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⢰⠃⡾⠀⠀⠀⠀⠀⠀⠤⡄⡄⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⡆⠀⠀⠀⠀⠀⠀⢤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢀⠜⠀⠀⢴⠆⠀⠀⠀⠀⢁⠡⡀⠀⠀⠀⠠⣞⡀⠀⠀⠀⠀⣤⠀⠀⠈⢆⣀⠀⡀⢀⡖⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣠⢷⢤⡀⠀⠀⠠⣀⠄⠀⠀⠀⠀⠀⠀⢀⠴⠩⢋⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢷⣦⠤⠤⠤⢤⢴⣖⠉⠁⠴⡄⠸⣗⡲⠤⠄⢤⡤⠤⠤⠤⢶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠡⠀⢻⡇⠀⠀⡾⠞⠉⠒⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠧⠴⠟⠁⠀⠀⠟⠃⠰⢷⠄⢀⡀⠀⢤⠄⢢⢄⡘⠚⠷⡀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠦⠀⣀⡀⠈⠙⠀⢸⠀⠀⠉⠉⠂⠼⠟⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠐⣠⠄⠀⠉⠀⡒⠦⢼⣀⢀⠀⡀⢀⠀⡀⠠⣐⠢⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠖⠩⠧⠤⠾⠦⡤⠴⠾⠳⠈⠀⠑⠚⠂⠈⠁⠈⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡀⢠⠀⠀⠀⢨⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⠀⠈⡀⠀⠀⠈⢂⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡄⠌⠸⡄⡤⠂⠀⠀⠐⠤⢠⠃⠈⠢⡄⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⢄⠀⢠⣀⠧⡀⠀⠀⢠⠲⠴⠀⠀⡠⠆⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⣠⣤⣄⠀⢤⣠⡄⠀⣤⣤⣄⠀⣴⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⠆⠀⢝⢛⡝⠒⢢⣶⣶⠐⣍⣋⣽⠊⢰⣷⡆⢀⣶⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣶⡎⣡⢸⣿⣿⣴⣾⣿⠻⡴⠿⢿⣿⣷⣿⣿⣃⡀⣬⣩⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣏⢓⠛⠛⢻⣎⣥⡆⢸⣷⣷⣾⠀⣷⣭⣶⡏⠉⣙⣩⣽⠃⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⣾⢿⣿⣿⣷⣿⣿⣯⣙⣋⣭⣿⣍⣛⣩⣽⣿⣿⣾⣿⣿⢿⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⡖⠚⣿⣦⣩⣴⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣷⣌⣥⣿⣿⠈⢁⣩⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⡼⠿⣿⣿⣿⠿⠸⣿⣿⠛⠿⢻⣿⡇⠇⠿⣿⣿⣿⣿⣷⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⡟⢻⣿⡏⠀⠀⣿⣿⡃⠀⢸⣿⣷⠀⠀⣿⣿⠉⢳⣍⣥⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠁⠸⡟⡇⠀⠀⠙⠛⠀⠀⠈⠛⠃⠀⠀⠿⢻⠀⠈⣿⣿⠏⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠂⠀⠀⠀⠀⠀⠐⡶⠿⣿⡿⢷⡖⠀⠀⠀⠀⠀⠀⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠒⠄⣠⠤⢤⣄⡀⠒⡄⠀⢠⡒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡔⠈⠛⣦⡤⠬⠝⠻⢦⣄⣀⣁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⠄⠈⢿⣦⠀⣾⠀⣾⡆⢹⡇⢠⡞⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣻⡷⣿⠰⣿⠁⢾⡇⢻⣇⢼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡌⠢⠤⠴⢟⣵⠿⡶⣶⣖⣾⡧⢀⠄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠹⣿⣷⡀⠻⣿⣠⡧⠦⠯⠿⣦⡂⢀⡼⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡗⣦⡘⢣⣶⣶⠁⣶⡄⢰⡆⢠⣾⣿⢠⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⣿⡇⣿⠀⣿⣷⣼⡇⣿⡇⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡾⠁⣿⠛⣿⠀⣿⠸⣿⡇⣿⡇⢰⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡋⣀⢀⡿⣠⣟⡤⡛⠠⡽⡅⣬⠿⠋⠨⣛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠸⡇⢧⡿⡿⡅⠀⡇⡟⣿⣃⠻⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⢀⡞⣶⡄⣶⢰⠀⠐⣦⣦⡟⢰⣾⡄⣞⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⢸⡇⢸⣷⣿⣾⠀⠀⣿⢸⡇⣿⢾⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠈⠉⠉⠁⠀⠀⠉⠈⠁⠉⠈⠀⠁⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣩⣭⣩⣬⣩⣯⣽⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣤⣶⠒⠀⠀⠀⠐⢲⣶⡤⠠⠀⢰⡶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⡿⠁⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠁⠁⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⡂⠀⣿⣿⡀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⣭⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠙⠀⢠⣄⠀⠀⠀⠀⢀⢤⣤⡄⠀⣠⡶⠢⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠘⣿⣷⡀⠀⠁⠀⢈⣁⠀⠀⡀⡐⠁⢸⣿⡇⢰⣿⠁⢠⣶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡠⠊⠉⣿⡆⡸⣿⡆⠀⢸⣿⠁⢈⠻⢛⡡⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡐⢻⡇⠀⠀⠈⠉⠀⢈⣤⣄⠘⢿⡠⠂⠔⠁⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠑⠊⠀⠀⣁⠀⠀⢀⣄⣹⣿⣄⡀⠀⠰⠀⠀⢀⡿⠁⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⣿⣧⠀⠂⠀⠁⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄⠀⠀⠄⠀⢀⣤⣀⠠⠀⠈⠉⣀⣀⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠈⠀⠀⠀⣶⣯⠀⢹⡀⣰⣦⠜⠀⣿⣟⠀⢀⣾⡟⠉⣃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠐⠀⠻⣿⣈⠝⠁⠘⣿⡆⢀⣿⡇⠀⢸⣿⠀⠀⠾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠘⣿⠁⠀⡜⠻⠗⠊⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠀⡏⢆⠀⠀⠀⠀⠀⠙⠂⠊⠀⡠⠄⢄⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⡇⠀⠁⠢⠄⡀⠀⠀⠀⠀⢘⠀⠀⡰⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⢀⣴⣿⣿⠇⠀⠀⣠⣤⣦⣤⠀⠀⠀⠀⠈⠁⠒⠒⠚⢎⠁⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣦⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⣿⣿⣿⣿⠂⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾
⣿⣿⣿⣿⣿⣷⣶⣶⣄⠀⢀⣀⡀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣀⡀⣤⣴⣾⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠾⠿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠠⠾⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠉⢠⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢰⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠋⠹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠛⠀⠸⠷⠶⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⢀⣀⣀⠀⠀⡀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⢣⠞⠉⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡋⠉⠉⢹⠀⠀⠀⠀⢸⠉⠉⠙⡆⢀⠖⡄⠀⢸⠉⠉⠉⠉⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⢠⠀⢸⠀⠛⢺⠚⠰⣏⠉⠉⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⠧⠤⠤⠤⢼⡀⠀⢸⠀⠈⢹⡁⢸⠀⠀⠀⢹⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠀⢸⠉⠁⢸⠀⠰⣏⠉⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣧⠤⠤⣼⣀⣸⠀⠀⢸⣀⣀⣀⣉⣉⢳⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀⠀⠀⠀⢠⣶⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣉⠇⠀⠀⠀⢠⣿⣿⣿⣶⣷⡄⢀⣿⣷⡀⡴⠛⢻⣿⣆⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⡀⠀⠀⢸⣿⣿⣿⠇⠉⣿⡻⣿⣿⣿⠁⠀⢸⣿⣿⣸⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⡄⢸⣿⣿⣏⠀⠀⢸⣿⣿⣿⣿⡄⠀⣸⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣷⣿⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠸⣿⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⢿⣿⠂⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⢰⣿⣿⣿⡏⢿⣿⣿⣷⣾⣿⠿⣿⣿⣿⡏⢸⣿⣿⣿⢿⣿⣿⠀⠁⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⣿⣿⣿⠟⠀⠈⠻⢿⣿⡿⠋⠀⢿⣿⣿⠃⠘⣿⣿⠇⠘⢿⣿⣷⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⣶⡄⢲⡆⢰⣶⡀⣴⡆⣠⡶⢷⣦⠀⠀⣶⡶⢶⣶⡶⠆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣤⡀⣾⡇⢸⡿⣧⣹⡇⣿⠃⣀⣉⠀⠀⣿⡇⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡈⣻⡷⢸⡇⢸⡇⢻⣿⡇⣿⣆⢉⣿⠀⠀⣿⡇⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠙⠃⠘⠃⠀⠛⠃⠈⠛⠛⠙⠀⠀⠙⠃⠀⠛⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠲⠂⠈⠉⠉⠉⠉⠉⠉⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⢂
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡁⠀⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠸⠇⢀⠀⢀⡠⠄⢲⡾⠉⠉⠉⠉⠉⠉⠉⠀⠒⠒⠂⠠⠤⢈⣳⠀⠀⠀⠀⢄⠀⠀⠃
⠀⠀⠀⠀⠆⠀⣾⠞⠁⠀⠀⢈⡴⢂⣈⠁⠢⡀⠀⠀⠀⠀⡠⢊⣡⡌⠑⢤⡈⠑⠤⣀⠀⠀⠀⢸
⠀⢀⡤⠞⠂⢴⡇⠀⠀⠀⠰⠋⣰⣿⣯⣴⣦⣸⡆⠀⠀⢠⣧⠼⠿⠷⠷⠤⣵⠀⠀⠘⡷⠀⠀⢸
⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠙⡗⠒⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣀⠸
⠀⠀⠀⢇⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠀⠀⠀⠀⢀⡏⠀⠉⢿
⠀⠀⠀⠘⢧⡀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠘⣏⠃⠠⠴⠦⠖⠘⢋⡼⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠈⠳⢤⣀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣤⣤⠴⠋⠁⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⣐⠂⠲⡄⠀⢀⠔⠁⣠⠞⣠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠳⢦⣀⡀⠀⠀⠀⠀⠀⠴⠄⠀⠀⠀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⢈⣤⡁⠀⠘⠣⠚⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⡶⠶⠶⣶⠶⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠓⠀⠀⠰⣉⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⠇⠀⠀⢷⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠈⠯⣀⠀⠀⠀⢀⣨⠋⠈⠁⠀⠙⠛⠒⢶⡆⠠⠤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢤⣤⡤⣤⠞⠓⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠤⠤⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣸⡧⣤⣤⠤⠤⠴⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⠘⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠘⢄⢸⣧⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⢶⡿
⠀⠀⠀⠀⣌⠁⠀⠀⠀⠀⠈⠻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⢃⠀⠀⠀⠀⠀⢀⡴⣦⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢤⣀⡘⠀⣴⠀⠘⣧⣈⡄⠀⠀⠀⢀⡏⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠉⠛⠦⠻⡤⠚⠀⠈⠀⠀⠀⠀⣘⠁⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠶⠒⠀⠀⠀⡟⠀⠀⠀⢸⡄⠀⠀⠠⠴⠶⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣀⣀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣰⠇⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣇
⠀⢀⠴⠚⠓⠠⣄⠀⠀⠀⠀⠀⠀⠀⡌⠉⢻⡄⠀⠀⠀⠀⠀⢸⠇⠀⣠⣤⠤⠴⠦⠄⢈⣦
⡰⠃⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠙⢒⠦⣷⠀⠀⠀⠀⠀⢸⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⣧⣀⣀⣀⣀⣀⣀⣀⣘⣁⢀⠀⠀⠀⢘⠋⠀⣼⠀⠀⠀⠀⠀⠸⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣽⣿⣷⣶⣶⣶⣶⣶⣾⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠙⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏⠉⠉⠙⠛⠉⠉⠛⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠐⠋⠀⠀⠀⠀⢀⡀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠄⠀⠀⣀⡀⣀⣄⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠈⠻⠄⠀⠀⠀⠀⠻⠿⠃⠻⣿⣻⠭⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⣷⣤⣄⣀⣀⠀⢠⣴⣿⠿⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⠟⠙⣇⡀⠀⣹⣆⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠁⢠⣴⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣏⢘⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢘⣻⠿⡿⣿⢿⡿⣿⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠚⠑⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⠀⢻⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⠿⢛⠿⢿⢿⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿