Mountains Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣿⡄⠄⠀⠀⠀⠀⠀⢀⡼⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠑⢸⣿⣿⣄⢦⠀⠀⠀⡠⠋⡄⣻⣿⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡶⢭⣸⣿⣦⣄⣀⠀⠀⠀⠀⡴⢫⠖⡂⠸⣿⣿⣿⣿⣷⣮⠭⠀⠊⠐⣱⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠬⠷⠛⢉⣜⣧⡝⡻⢦⣀⢀⡠⠃⠃⠀⠄⠘⢿⣿⣿⣼⣿⠁⠀⠀⠀⣴⡛⠋⢛⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⠞⣉⣩⣍⢻⣦⣿⡟⠀⢠⡄⠀⠀⠀⠀⣿⣿⣿⣿⣧⡞⠋⠛⠁⠁⠘⠉⣿⣿⣿⣿⣵⣳⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠒⢲⡃⠨⢻⣷⠟⣻⠁⠀⠠⠿⣦⣀⠤⢤⣤⣿⣷⣿⣿⣿⣆⣀⠁⠐⠊⠄⡛⢿⣿⣿⣿⣿⣷⣿⣿⡄
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠀⢐⠝⠉⣰⡏⣠⡄⢀⡀⠀⠨⢑⠤⡀⠉⠉⠙⢹⣿⣿⣷⣤⡄⠀⠀⠀⠀⠉⠒⠻⣿⣿⣿⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠐⠁⠀⠀⠁⢀⣿⣷⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⣺⣿⣿⡿⠿⣿⡆⠀⠀⠀⠀⠀⣐⣿⣷⣾⣿⣯⠅
⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⢀⣠⠄⡀⠀⠀⣀⠀⠰⠿⠛⡛⠓⠸⠯⠿⠽⠓⠒⠖⠻⡍⠛⠉⠉⠁⠐⠚⠒⠱⠶⠦⠆⠲⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⢀⡉⢀⢀⡀⠀⠁⠀⠉⠁⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠲⠂


⣿⣾⡾⠿⠾⠾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣾
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⡀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⣿⣧⣾⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡠
⠛⠻⠿⠿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⣹⣧⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠞⠉⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣀
⡄⠀⠠⡤⠀⢉⠁⣀⠀⠙⢧⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢨⡷⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠚⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⢁⡆⠀⠀⠀⠀⠀⠀⢠⣷⢠⣦
⣷⡀⠀⢁⡤⠀⣀⣿⡀⠀⠀⠀⣸⣧⠀⣰⡀⠀⣀⣠⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠾⠱⠦⠀⠀⠀⠁⠀⠀⠀⢠⡜⠃⠀⠀⠁⠘⢦⠀⢀⠀⠀⢸⣿⣿⣿
⣿⣇⠀⠸⠁⣰⣿⣿⣖⠀⠀⠀⠿⠿⢦⣿⡅⠠⣿⡍⠀⣞⠋⠘⠃⠀⢠⡀⠀⠸⠃⠤⠀⠀⠀⠀⢀⠀⢡⣀⠀⡴⠣⢀⡖⠀⠦⠐⠀⣄⢀⠀⠚⠀⠀⠀⠀⠿⠟
⠉⠀⡀⠀⠀⣿⣿⠇⠀⠀⠈⠁⠀⠀⠸⠿⠛⠀⠈⠁⠈⠉⠀⡆⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠒⠛⠠⠆⢨⣤⣵⣄⣠⣄⣆⠰⠇⢱⣿⠈⢠⠂⣴⠀⢀⠀⣤
⢀⡼⠀⡀⢸⣿⣿⡡⠀⠀⠀⠀⠀⠢⣄⢠⣶⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠛⠛⠁⠀⢰⣿⣢⣿⠀⠻⡆
⡜⠁⢠⣿⠀⢀⡀⠀⠀⠛⠷⠖⠆⠤⠀⠈⠛⠓⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠠⠄⠀⠙⠛⣿⣿⡧⠈⠡
⠀⠀⣿⠭⣅⠀⠹⠅⠀⢀⠀⠀⠀⣄⡀⠀⠀⠀⠀⢄⡀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⣤⣀⡁⠲⠤⠀⠀⠀⢤⡄⠀⠀⠀⢒⡀
⠀⢠⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣣⡀⢀⠀⠀⢤⣀⡀⠈⣿⣄⣀⡀⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠋⠀⠉⢭⣦⣀⣁⣴⣶⣶⢾⡇⠀⠀⠤⢀⣄
⠀⠬⠭⠍⠉⠀⠀⠀⣀⣤⣄⣀⣠⣤⣾⣷⠶⠴⠖⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠲⠿⢳⣤⣄⣀⠉⠀⠦
⠀⠀⡀⠀⠀⠀⠁⢀⣀⣤⡾⣟⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠶
⢀⣀⣤⣤⣤⣶⠿⠿⠟⠟⠛
⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⢻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠘⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⣾⣦⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⠁⠀⠹⣿⣿⣶⣄⠀⠀⠀⠀⢿⣿⣿⠟⠁⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⡿⠃⠀⠀⠀⠁⠹⣿⣿⣦⣀⠀⠀⠈⠛⠁⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄⠀⠀⠀⠀⠀⠉⢿⣿⣷⡀⠀⠀⠀⠀⠀⣘⣿⣿⣁⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⠀⠀⠀⠀⠀⠈⠿⢿⣿⣦⣄⠀⠀⢨⣿⣿⣿⣯⣈⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠧⠀⣤⣽⣿⣿⣥⣼⣿⣿
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣤⣆⣿⣷⣾⣾⣶⣿⣿⣷⣷⣷⣦⣶⣶⣾⣷⣶⣦⣤⣤⣶⣤⣤⣦⣤⣤⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⢒⣲⣖⣒⣲⣶⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣼⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⣿⣿⣟⣦⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣆⡀⠀⢰⣷
⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⣾⣿⣿⣟⠉⠻⢿⣗⣦⡀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣧⠀⣤⣾⣿⣿⣿⣿⣿⣿⣦⣾⣿⣼⡇⢀
⠀⠀⠀⠀⣧⣿⣧⣦⣾⣿⣻⣛⣽⡿⢷⣄⣀⣰⣼⣿⣷⣾⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⡿⠾⣿⣭⣉⡙⠛⠿⠟⠙⢺⣿⣿⣷⣿
⠀⠀⠠⣤⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠈⠉⠛⠛⠿⣿⣽⣿⣿⡷⠦⠀⠀⠀⢀⣚⣏⣽⣿⠿⠿⠿⠿⠷⠶⠤⠤⣤⡤⢤⠴⠶⠿⠿⠿⠿⠿⠿⢦



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⢠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣄⣀⣴⣿⣿⣿⣿⣿⣿⣦
⠀⠀⢀⣠⡀⢀⣴⣷⣦⣤⣤⣴⣿⣵⣾⣿⣿⣿⣦⣀⡀⣀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣄
⠀⠐⠛⢿⣿⣿⠉⠙⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠉⠋⣹⣿⣿⣿⣷⠴⠀⠀⠀⢀⣾⣷⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⣷⣄
⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⡠⠔⣁⣻⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣄⣠⠏⠱⣴⢦⡀⠀⠀⠀⠀⠀⠀⣀⡴⠃⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈
⠀⢀⣴⣿⣿⣿⣿⣿⣿⣛⣋⣳⣄⠀⠀⠀⠔⠋⠹⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠹⡶⡀⠀⠀⠀⠀⠀⠘⠁⠀⠂⠀⠀⡠
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄
⠀⠀⠶⠀⠠⠞⠃⠀⠰⠧⠄⠀⠀⠀⠀⠀⢀⠀⢀⣀⣴⣂⢀⣤⣄⣀⣀⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢰⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⢊⣿⣦⣀⠀⣠⣤⣴⠏⠁⠠⣟⣿⣿⠟⣦⠤⢤⣀⡠⠚⠛⢩⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢐⣩⣿⣯⣭⠿⠗⢃⣀⣠⣤⣄⠈⠻⠿⠅⠀⣠⣿⣿⣟⡢⠀⠻⡿⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠉⠛⠋⠉⠀⠀⠐⠋⠉⢠⣾⣿⠧⠀⠀⠀⠘⠻⠿⣏⣻⡯⠀⢀⠀⠀⣾⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⢶⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢷⠜⠂⠁⠀⠘⠿⣿⣿⣟⠛⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣆⣀⣠⣠⣠⣀⣠⣸⠀⠀⢀⣠⣤⣄⣀⣠⣤⣀⣀⣀⣀⣀⢀⣰⣷⣀⠀⠀⡀⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠉⠉⠉⠉⠹⠯⠭⠭⠽⣛⣛⣿⠿⣟⡛⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠯⠭⠭⢝⣓⡚⠻⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣐⣒⠒⠪⠭⠭⣛⡳⠦⢄⡀⠀⠀⢈⣉⡉⠉⢉⣍⣑⣒⡂⠤⠄⣀⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠉⠹⠗⠶⠎⠉⠒⠀⠀⠀⠈⠉⠉⠉⠛⠛⠭⠍⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠄



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⡀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢧⡀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⣴⡿⠖⠃⠀⠀⠀⣤⡄
⠀⣠⣴⡾⠳⢂⡘⢻⡛⠁⣠⣆⣘⡳⣶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⣴⣿⣿⠟⡄⠀⠀⠀⠻⠇⠀⠀⠀⢀⣀
⠀⠀⠀⠶⠛⡻⠛⠛⠛⠀⠀⠀⠈⠃⠊⠁⠀⠀⠀⠀⣠⡄⠰⣏⠼⢛⣱⣿⣿⢿⡟⢀⡖⠀⠀⠀⠀⠀⠀⠠⣶⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⡟⠁⡀⠀⠈⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣞⠀⣸⡿⠞⢀⠀⠀⢠⣤⠂
⠀⠀⠀⠀⠀⠀⣰⡟⠟⣴⣿⡷⠷⡄⠀⠀⠀⠙⢇⠀⠸⠅⠀⣸⣆⣴⣤
⠀⣠⠄⢴⠇⠞⣛⣵⣿⣿⣿⠇⢠⠀⠀⠀⢠⠀⡀⠶⢤⣰⣄⡿⠟⡏⣀⠀⠀⠀⠀⠀⢀⡠⠢
⠀⣀⠀⡆⠀⢠⢿⠋⠀⠐⠁⠀⣼⣇⢰⣦⣿⣦⣿⣿⣤⠿⠿⠷⣾⡿⠋⠀⠀⠀⠀⢠⠃⠀⠀⢁
⢀⣿⣴⣷⡄⢀⣄⣼⣧⣦⣾⣷⣿⡿⠻⠿⠟⠋⠉⠀⠀⠴⠟⠛⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⢆
⠈⠉⠉⠙⠓⠪⢥⣀⡀⡐⢨⡉⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠃⠀⠀⠀⠀⠀⠈⢢⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠺⠷⠤⠿⢷⣆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠁⠀⠀⠀⠀⠀⢂⠤⠊⠀⠀⠀⠀⠀⠀⠈⠑⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣻⣿⣷⣖
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣍⣚⣿⣯⣥⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣚⣿⣿⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⢿⣿⣿⡷⢞⣫
⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⡷⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠠⣄⣛⣿⣿⣿⣿⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠠⣙⣻⣿⣿⣟⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠢⡀⠀⠀⠀⠀⠀⡉⣽⣿⣿⣿⣿⣿⣏⣡⣤⠄
⠀⠀⠀⠀⠀⠀⠠⣭⣿⣿⣿⣿⣯⠔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⣌⠛⢷⣿⣿⣿⣿⣿⣿⠟⢁⣀
⠀⠀⠀⠀⠀⢀⣄⣾⣿⣿⣿⣏⣥⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⣞⡉⠻⣶⣿⣿⣿⣿⣿⣿⡿⠛⣩⡀
⠀⠀⠀⠀⠀⢠⣭⣿⣿⣿⣿⣷⣦⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠬⣿⣿⠾⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣷⠶⠛⠓⠛⠒⠒⠐⠒⠒⠛⠉⠀⢀⣄⣰⣷⣿⣷⣞⣙⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⡥
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣯⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠈⠩⣽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠃
⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣽⣶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠤⠴⢾⢿⣿⣿⣿⣿⣿⣶⣤⡤⠖⠀⠀⣆⠀⡄⠀⠀⠀⡄⢰⣇⣙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⣯⣍⡀⠀⠀⢰⡗⢠⡇⠀⡗⠀⣯⢸⣷⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣶⣤⣿⢀⣟⣾⣿⣭⣷⣿⣿⣤⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣇⣸⣏⣟⣿⣫⣋⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠅⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣼⣿⡿⢠⠀⠿⣿⣿⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠑⢀⣾⣿⡁⣽⣿⡇⠀⠠⠀⠈⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠃⠀⢠⣿⣿⣿⣶⣿⣿⣧⠀⠀⠖⠀⠀⡀⠀⠀⠀⣤⣶⣯⠀⠀⢀⡀⣠⣴⡾⠋⠀⠆
⠀⠀⠀⠀⠀⠀⣀⣴⠀⡀⠀⠀⣠⡞⠀⠰⣦⣾⣿⣿⣿⠃⣴⣿⣿⡿⣿⣿⣽⣿⣿⣦⣀⠀⠀⠀⡀⢀⠀⢀⣼⣯⠏⠀⠀⠋⠈⢹⡾⠃⠀⠐
⠀⠀⠀⠀⢰⢿⣿⣇⠀⢀⣴⣿⣿⡟⠀⠀⠀⠙⣿⢻⣿⡖⠻⣻⡿⡃⠛⠋⡵⢟⠿⢿⣿⣿⣶⡀⠀⠀⣀⡈⠼⠟⢠⢤⡼⠁⢀⠘⠃⠀⣰⡄
⠀⠀⠀⠀⢙⢿⠟⠻⢠⣾⣻⢹⣋⡷⢸⢁⢸⡆⠘⣇⠹⠏⢤⡁⠠⣸⡄⢀⠀⠀⠀⠈⠁⠛⠹⣿⢶⣦⣌⢁⠋⣰⡎⣸⣯⡀⢸⣧⢰⣦⢼⣿⣀
⠀⠀⠀⠀⢀⣆⣶⣶⣿⣿⣶⣾⣷⣷⣿⣾⣼⣷⣶⣿⣧⣿⣿⣧⠀⣽⣿⢠⡆⠀⠀⠀⠀⠀⢀⣀⣴⣹⣇⣨⣤⣿⣇⣸⣿⣧⣶⣿⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣀⣁⡒⠺⠿⠿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡋⡿⣿⣿⣿⢿⣿⣯⣿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠆⠀⠀⠈⠙⢻⣿⣿⣾⣯⢻⢹⢸⣿⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠹⣾⣿⣿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠉⠉⢀⣄⠀⢀⠀⣷⣸⢫⠻⢿⣄⣾⣌⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣿⣡⣿⢿⡿⢻⣟⣿⣿⣿⣿⡿⠿⠛⠋⠉⠁⠀⡄⠀⠀⠀⠀⠀⣰⡀⣸⣿⣦⣴⣇⣿⢾⣷⡦⠊⠉⢡⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣏⢹⢸⣷⠋⣿⣿⣿⣿⣯⡀⠀⣾⣆⠀⠀⢼⣯⠀⠀⠀⣤⣤⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣇⣤⣽⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣸⠉⢾⣬⣿⣿⣿⣭⣠⠌⣿⢗⡀⢈⣾⣿⣞⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣶⣦⣝⣿⣿⣿⣋⡥⢒⣿⡿⠃⡀⣹⣟⣯⡆⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢃⣿⣿⣯⣶⣃⡄⠀⠀⠀⣾⣟⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣦⠀⠰⣶⣿⣿⣵⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠴⠲⣾⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣷⣆⣹⣾⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢣⡀⣙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⣰⡟⠻⡌⢳⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⠞⣫⣝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠁⡰⠋⠀⠀⠈⠀⠙⣿⣿⣿⣿⣦⣄⠀⢀⣤⡾⠛⠕⠊⠁⠈⢀⣙⣷⣦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠹⣯⠻⢿⡿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠙⢦⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠉⠙⠻⢶⣄⡀
⠀⠀⠀⠀⢀⠴⠋⠀⠀⣦⠀⣾⣆⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠓
⠀⠀⠀⠀⠁⠀⣀⣠⡴⠿⠞⢛⣋⣉⣉⣉⣭⣤⣀⣀⣀⣀⣈⠉⠉⠉⠙⠛⠛⠿⠷⢶⣤⣼⣿⣄⣾⡀⠀⠀⣿⡧⢰⡄⠀⠀⠀⣦⠀⣾⡀⠀⠀⠀⢀
⠀⠀⢀⠤⠖⢋⠭⠴⠒⠛⠋⠉⠉⣭⣴⠶⠿⠿⠭⠭⠉⡉⠉⠙⠛⠓⠶⠤⣄⣀⠀⠀⠀⠉⠉⠛⠛⠻⠶⢾⣿⣿⣿⣧⣀⣀⣰⣿⣴⣿⣧⡤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠐⠒⠦⢤⣄⣀⣀⡈⠉⠉⠉⠉⠉⠉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏⠀⢋⣼⡉⠢⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⠇⠀⠀⠀⠀⠀⣩⠿⠋⡀⣠⡿⠟⠁⠀⡀⠀⠀⠀⠹⣇⠀⠀⣀⣀⣠⣴⢾⡁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⡿⠿⠛⡦⠀⠀⢂⣴⣫⣵⣶⣿⠁⠈⠳⢤⠀⠀⠸⣶⠀⠀⠀⠈⠳⣀⠙⠙⢿⠟⠀⠷⣄⡀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠊⠉⠉⠉⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⡿⠿⠋⠻⣦⣄⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠋⠉⠁⠀⠀⠀⠀⠀⠙⠲⢤⡀⠀⠀⠀⣀⣀⣈⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⣰⣿⡿⠁⠀⠀⠀⠀⢀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⢠⣾⣷
⡀⣸⠆⠀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⣠⣞⡿⠃⢰⣿⡇⠀⠀⣦⠀⠀⠀⢀⡁⠀⠀⢸⣿⠀⠀⢀⣠⡀⢀⡉
⣇⣿⠀⣰⠄⢀⢻⣧⠀⠠⠀⠐⠃⠀⣿⡿⣀⣴⣾⣏⠁⠀⠀⠹⠀⠀⠀⠀⢠⣷⠀⠞⠁⣠⠔⠛⠟⠛⠀⠡
⢮⣿⠐⢿⣐⣯⢀⠹⣷⡄⠀⠠⠀⠀⠘⠻⠿⠟⡿⠛⠛⡆⠀⡀⠀⢀⣴⠀⠀⠀⠀⠀⠈⢀⡆⠀⢠⡇⡀⣼⢰
⣿⣿⡀⣸⣷⣇⢺⠀⠈⢀⢰⣄⢄⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⠃⠀⢈⣀⣀⣢⡆⣾⣴⣶⣼⠧⣿⣾⣿⣧⣿⢸
⠉⠉⠉⠙⠻⢿⣾⣶⠿⠺⠲⠟⠛⠀⠘⠃⠀⠘⠙⠛⠛⠛⠿⠂⠀⠛⠿⠿⣿⣿⡿⠿⢿⣿⡄⠿⠿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠉⣀⣲⣶⠂⠀⠀⠀⠀⠀⣀⣀⠀⠂⠤⠀⣀⣀⣤⣤⣄⣀⣀⠀⠀⠀⢉⣁⣀⣴⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⢤⣤⣄⠀⠀⠀⠀⠉⠁⠀⠀⠀⣀⣀⠀⠉⠉⠉⠉⠉⠹⠿⠏⠉⠀⠈⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠔⠒⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⠀⠀⠀⢠⣄⡀⠙⣿⣦⣄⣤⣼⣿⣤⣀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠂
⠀⠀⠀⢀⣼⣶⣤⣽⣿⣿⣿⣿⠟⠛⠻⢿⣿⣿⡛⠉⠁⠀⠀⣤⣦⣤⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒
⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣤⣬⣿⣷⣤⣤⣤⣤⣬⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢶⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣠⣿⠀⢈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡶⠲⠄⣠⠞⢁⡼⠉⢈⡇⠀⠀⠙⢄⠀⠀⠀⠀⣠⡴⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡫⢻⠅⢀⡼⡯⠒⠛⢁⡤⢾⠁⠀⠂⠸⡀⠑⣄⡤⣞⣡⢷⣄⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢰⠒⠉⠊⠰⠃⠐⡩⠊⠀⠀⣀⡟⠀⣸⠃⠀⢐⠀⠁⠄⠈⠻⡑⠁⢠⣿⡀⠃⠉⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⠀⢸⡂⠀⠀⠀⠀⠀⠀⢀⡴⡋⠋⣠⢜⠃⠀⠀⢘⠳⠄⠀⠀⠀⠈⠂⠼⠁⠁⠀⠀⠀⠀⢀⣾⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⢰⣿⡀⣽⡀⣿⡇⢸⡀⠀⠀⠀⠀⠁⠀⢀⠔⠁⢸⠀⠀⠀⠀⠢⠈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢸⡀⢰⣿⡂⣸⣇
⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⣻⣿⣗⣿⢧⣿⣟⣾⡆⠀⠠⡇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⠀⠠⣿⣇⣽⡿⠷⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠚⠛⠚⠿⠿⢿⣿⣿⣿⣿⣿⡇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣸⣿⣇⠀⣸⣿⣅⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢐⡆⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠦⠿⠿⠦⠤⠤⠀⡀⠀⠀⠀⠀⢀⡆⢀⣾⡆⢀⣿⣿⡷⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡝⣲⠂⠒⠚⠛⠊⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣚⠥⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠏⡀⢀⣿⡇⠀⡠⠔⠒⡢⠎⡩⠔⠊⠉⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⢀⣻⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⡑⠢⢬⡦⣘⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠀⢐⣿⡂⠀⠀⡅⠀⠀⠀⢠⣿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠂⠙⢮⡙⠒⢤⡀⠀⠤⢀⣰⣾⣿⡄⠀⠀⢾⣿⡥⠀⢠⣷⠀⠀⢀⣿⣿⣿⠧⠔⠒⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⡽⠀⠀⠙⢆⠀⠀⠀⠈⠉⠉⠒⠞⠿⠿⠿⠆⠾⠿⠗⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠀⠀⠀⢀⠜⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣼⣿⡧⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣰⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠄⠀⠀⠀⣰⣏⠙⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢨⣿⡂⠀⠀⣰⣿⣿⠀⠘⢻⣿⣿⣿⣿⣷⠀⠀⢀⡀⠀⢠⡀⣼⡅
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣼⣿⣿⣿⠆⠀⠀⠳⣝⣯⣻⣿⣷⣶⣴⣿⣾⣾⣿⣿⣇⢀⡀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⣩⣿⣧⣾⣿⣿⣿⣿⠀⠀⠀⠀⠈⡳⢽⣿⣿⣿⣿⣿⣯⠻⢿⣿⣿⣾⡇⢸⣧
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡿⣟⠳⡄⠀⠀⠐⢻⣿⣾⣿⣿⣿⡟⣫⣟⣻⣿⣿⣿⣿⣿⣿⢀
⠀⠀⠀⠀⠀⠀⣄⣸⣿⣿⣿⣿⠟⠦⣬⠿⣶⣵⠛⢛⣿⣿⣿⣿⡿⣿⣿⡿⠟⣿⣿⣿⣿⣿⣿⣿⣼⡇
⠀⠀⠀⠀⣾⢠⣿⣿⣿⣿⣿⣿⣷⣾⣜⣃⠻⣿⣗⡾⣿⣿⡏⣹⣾⣿⣿⣁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡃⣸⣏⣷⡞⢻⣿⣿⡿⠛⠿⣿⣿⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣷⣦⢠⣾⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡖⠛⢿⣿⣿⣛⠻⣿⣿⣿⣿⣯⣶⣾⠟⣟⣙⣿⣿⣿⣿⣿⣇
⠀⣼⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢼⣿⣿⣽⣿⣆⣙⢻⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⣭⣿⡿⠿⣿⢻⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⠿⠛⢉⣤⣶⣿⣯⣍⣩⣤⣤⣤⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠐⣤⣾⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠈⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠄⠃⢸⣿⣿⣯⣤⣤⣌⣉⣛⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣯⣄⠂⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣷⣦⣜⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⣿⡿⠛⠀⠀⠉⠉
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⠈
⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏
⣿⣿⣿⣿⠆
⣿⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠹⠟⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠘⡿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⡞⠀⠀⣀⣿⣚⣳⣄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠰⣗⣒⣒⣒⣛⣦⠀⠀⣀⠀⠀⠀⠀⠀⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣶⡀⣠⠞⠁⠀⠀⠀⠀⠘⠳⣖⠒⠒⠈⢳⡾⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢹⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⡴⠋⠀⠸⣏⡽⣆
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⢠⡞⠀⠀⠀⢸⡯⠷⣄⠀⠀⠀⠀⠀⠀⣠⣶⢶⠟⠀⠀⠀⢠⡄⠻⡙⠛⢷⡀⠀⠀⢀⣦⠀⢠⡄
⠀⠀⠀⠀⠀⠀⢨⣿⣇⠀⣰⠏⠀⢀⣴⡀⠈⠻⢯⣭⡭⠽⢦⣀⢀⡼⠁⠈⠁⠀⣀⠀⠀⣸⣇⠀⠀⣶⠀⠹⣆⠀⢸⣿⠄⢸⣗
⠀⠀⠀⠐⠒⠒⠲⠿⣤⡾⠁⠀⠀⢠⣿⡅⠀⠀⠀⠀⠙⣯⠭⠭⠿⢄⡀⠀⠀⠀⣿⡇⠀⣽⣯⡄⠠⣿⡆⠀⠙⣦⣘⣿⣃⣭⣯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⠀⢾⣿⠆⠀⢠⣄⠀⠀⠘⢷⣒⣒⠀⠁⣤⠀⠠⣿⡗⠀⠾⡟⠂⣈⣿⡥⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡓⠀⢼⡷⠀⠀⠀⠘⠇⠀⠀⢐⣿⠀⠘⢻⣉⡤⠴⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣫⣿⣍⠀⢽⣿⠀⣀⠀⠀⠀⠀⢀⣨⡿⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠈⠀⠀⠁⠀⠈⠙⠓⠶⢿⡿⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠇⢀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠙⠤⠙⠓⠒⠒⠒⠲⠶⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⢠⣤⣀⠎⠀⠀⠀⢨⣿⣿⣷⣄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣸⣿⠋⡨⠟⠁⠀⠀⠀⢀⠞⠉⣿⣿⣿⣷⣦⡀⠘⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠕⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣤⣄⠈⠛⢦⣄⠠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠈⠓⠀⠉⠻⣦⣄
⠀⠀⢀⣀⣀⣀⣄⣀⣴⣤⣀⣤⣀⣤⣤⣀⣀⣤⣀⣠⣀⣠⣠⣀⣀⣀⡀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀
⠀⠀⢈⣭⣉⣏⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠠⢼⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠔⢳⣦⡀⠀⠀⢀⣀⣴⠞⠃⠀⡾⣿⣿⣿⣦⣀⣀⡀⠀⣠⠶⠶⢛⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠉⣡⠴⣻⣿⡛⣳⣖⡭⠋⠉⠀⣀⠀⠙⠿⣿⡇⠘⠉⣩⣿⣾⢧⡄⠀⢾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠺⢽⠿⠛⠉⠀⡠⠶⠖⠋⣽⣷⡦⠀⠉⠁⠠⣾⣿⣿⢿⣷⡦⠀⠈⠋⠀⢹⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠘⠛⠷⠍⠀⠀⠀⠀⠀⠈⠉⠑⣿⣀⢤⡐⠄⠀⢺⣿⣿⣿⣿⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⡄⠀⠀⠉⠛⠻⢿⡪⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣴⣶⡶⠶⠶⠶⠿⣿⣤⣴⣧⣧⣧⣶⣶⣿⣀⣠⣴⣾⠶⠷⠤⣴⣿⣷⣤⣤⠤⠤⠤⠴⣾⣿⣶⣀⣠⣤⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠒⡒⠒⠾⠭⠽⣛⣷⣤⣀⠀⠀⠀⠀⠀⠤⠤⠤⠬⣉⣉⣉⣉⠐⠒⠒⠢⠭⠍⢙⠒⠲⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠭⠍⠉⣙⣒⡲⠭⢍⣓⠂⠤⠀⠀⠠⣤⣤⣄⣀⣶⣦⣬⣭⣭⠓⠒⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠠⠤

⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣼⣿⣧⡀⠀⢀⠀⠀⠀⠀⢀⣼⡏⢻⡗⢄⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢠⣿⣿⣿⣄⢀⣿⣧⠀⠀⣰⠿⠉⢆⠀⢻⡀⠈⠢⢄⣤⣶⣿⡏⢢⡀⠀⠀⢀⣤⣀⣠⡾⠃⠑⣤⣆⢰⣿⡀
⠀⣿⣿⣿⣿⣷⣼⣿⣿⣄⣼⣿⣦⣄⠀⠑⠈⢧⡀⠀⢘⣿⡿⠋⡇⠀⠉⢶⠲⢅⠘⣿⢝⠁⠀⠀⣼⣿⣿⣿⣇
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠉⠓⠀⠀⠀⢁⣴⠿⠋⠀⠀⢻⠀⠀⠀⠑⠀⠑⠘⠀⠀⠀⢀⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠸⠿⣟⣿⣿⣿⣿⢿⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣄⣀⡀⠀⠀⢠⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⢳⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⣡⣿⠈⠢⠀⠀⢱⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⠏⠀⠀⠀⠀⢀⡴⠟⢁⡀⣴⠿⠋⠀⠀⡀⠀⠀⠈⢿⡀⠀⢀⣠⣤⣶⢿⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⢤⣴⣾⣿⠿⠟⠋⡳⠀⠀⣁⣴⣭⣶⣿⣯⡀⠈⠓⠦⠀⠀⠻⣆⠀⠀⠀⠙⠤⠈⠉⠻⠟⠀⠷⢤⣀⠙⠢⢀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣠⠶⠾⢿⣿⣿⡿⠟⠛⠉⠙⢶⡄⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠳⠤⠀⠀⠀⣠⣤⣤⡿⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣦⠀⠀⠀⠀⢀⣴⣿⢦⠀⢀⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⣠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣴⠟⣷⣿⣿⣿⣿⣿⣿⣦⠂⣴⣿⣿⣿⣯⣴⣿⣿⣀⢀⠠⡀
⠀⠀⠀⠀⠀⢀⣶⠿⠮⣿⣿⡘⣿⣿⡄⣌⠀⣠⣦⣦⢀⠸⠃⠀⠀⠁⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⢢⣍⠛⠘⠻⢾⣿⣿⡏⣌⣧⣥⢤⠄
⠀⠀⠀⠀⢀⣾⡜⢂⣀⣽⣿⣿⣽⣿⡑⣿⣿⣆⡻⣿⣥⣤⡚⢿⣎⡀⠐⢳⢯⡿⢿⣋⣙⣛⣬⡉⢿⣿⡏⢰⣷⡞⢴⣾⢏⡙⢿⣿⣿⣿⣌⣃
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣄⡻⣿⣿⣿⣏⣀⠀⣝⠳⡀⣽⡀⢀⣿⠿⢻⣿⡆⢵⣾⣿⣧⠐⢿⠠⣤⡙⠈⠁⣈⠿⣿⠛⣻⣿⣇
⠀⠀⠀⡼⡿⣿⡿⠛⡩⢚⣿⡏⢹⣧⣾⣯⡿⢿⣾⣿⣿⣿⣧⣼⣮⣿⣿⣌⣓⣨⡿⠘⢿⣿⣿⣦⢿⣿⣿⣿⣿⣧⣹⡿⠇⣀⢼⣦⣡⡚⢻⣿⣿⡄
⠀⠀⢠⣇⠀⠃⣀⣸⣿⣿⣿⣶⣿⣿⣿⣷⣦⣦⣼⣿⣿⣿⣿⣿⣿⣿⡿⢛⣽⣿⣿⣶⣦⣬⣟⣻⣷⣿⢿⣿⣿⣿⣿⣷⣄⣼⣎⣿⣿⣿⣼⣷⣆⣄⡀
⠀⠀⠀⠉⠉⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠯⠭⠍⠉⠉⠉⠹⠟⠉⠉⠈⠛⠛⠟⠿⠿⠉⠉⠛⠛⠿⠿⠛⠛⠛⠛⠛⠛⠛⠻⠿⠟⠛⠛⠛⠛⠙⠛⠛





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⣙⡛⣉⣙⣛⡟⣫⣿⣻⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⢀
⠀⠀⠀⠀⠀⢀⡄⢦⣄⠀⠃⠎⠙⠂⠀⢶⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠀⣤⢀⠀⠀⠈⡏⠀⢻⡦⠀⢦⡀
⠀⠀⠀⠀⠀⠀⣁⠀⢉⠰⣄⠀⠀⠀⠐⠦⢙⡀⣜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠸⠃⠀⠁⠈⠃⠀⠀⠁⠀⠈⠀⠀⠈⠃⠀⣀
⠀⠀⣠⠀⠃⠀⠏⠀⠈⠀⠙⢶⡇⠘⠀⠤⣀⠑⠈⡀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⣤⠔⠀⠀⠀⠀⠀⠐⠀⠇⠀⠆⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⢸⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠸⢻⠷⣤⠀⢀⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠸⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠟⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠙⠏⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢢⡀⢠



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠈⠆⠈⢡⡙⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢫⠀⢀⡁⠀⠐⣤⣄
⠀⠀⠀⠀⣠⠂⢠⠀⡜⠑⣀⠀⢀⠀⠀⠀⠙⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⣶⣧⡈⠀⠀⠀⠈⠁⠠⣄⠀⠹⢦⡀
⠀⠀⠀⠀⠁⠂⢘⠀⠀⢀⠉⠀⠜⠀⠀⠀⢼⠁⠘⢿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠛⢿⣿⣦⡀⠐⠁⠀⠀⠀⠑⣄⣀⠉⢲⣤
⠀⠀⡀⠓⢠⠀⠸⣆⠀⠀⡠⠀⠀⠀⠘⢦⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠻⣿⣷⣄⠀⠀⠀⠀⠈⢿⣷⣜⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡦⠤⠤⣄
⠀⠀⠀⠀⠀⢀⡠⠊⠉⠁⠀⠰⣢⣤⡢⣭⣘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠁⡀⠀⣤⠀⠀⠙⢦⡀
⠀⠀⠀⡠⠊⢁⠄⠀⡀⢀⣠⠖⠋⢠⣝⢾⡓⠟⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⡋⠹⢇⠙⢦⠹⡼⠃⣠⠀⣇
⠀⠀⠀⠀⠀⠀⠂⢈⡟⠉⣠⡄⠀⠙⠃⢹⡔⢉⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠈⠷⣄⠻⡄⣷⡡⢋⣁⠀⠈⢳
⠀⠀⠀⠀⠀⡠⠖⠚⢀⡞⡁⢹⣤⡾⠆⣘⠁⡤⠀⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠈⠛⠢⢓⢤⣽⡡⠛⢁⡼⢃⣏
⠀⠀⠀⠀⡼⠁⣀⣀⠞⡼⠉⠲⣄⡬⠷⢽⢁⣤⡳⣲⡖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀⢳⣐⣦⡐⢇⣹⠶⠀⢎⡼⠃⡏
⠀⠀⠀⣸⣁⠴⢁⡤⢊⠴⠲⠄⠒⠀⠀⢸⠋⡠⠤⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢗⣦⢭⣝⠧⣽⡴⢛⡽⣴⠿⠁
⠀⠀⠀⠩⣴⡾⠗⠖⠋⠀⠀⠀⢀⡰⠋⢹⠟⢁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⣿⠔⠉
⠀⠀⠀⠀⠩⣤⣴⣶⣾⣶⣶⡴⠁⠀⢀⣽⢔⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣷⣿⣷⣄⠀⣼
⠀⠀⠀⠀⠀⠈⠻⠿⣿⢟⣩⣢⣴⣾⣿⢇⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣛⠻⠿⢮⣍⡳⠿⣷⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠞⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢼⣁⣙⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣤⢜⠡⠼⠛⠳⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠔⢟⣂⢹⢉⣹⠷⠶⣒⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⣠⡔⣱⠃⢀⣀⢑⡿⠯⣶⣬⣿⣤⣬⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠃⠀⠈
⠀⠀⠀⠀⠀⢠⡟⣰⢃⠎⠸⡏⣾⡃⠤⣤⠦⠭⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠈⠀⢁⠀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⢠⣏⠜⡡⠃⢠⢞⠽⡿⠛⢉⠑⢄⠐⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠢⢬⠀⠀⠈
⠀⠀⠀⡰⡿⠋⠔⢀⡴⠃⢋⡠⣯⡞⠉⢝⠦⣕⣄⡈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⢁⠖⠁⡶⢺⠱⢄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠠⠄⠀⣀⣼⡞⡌⠤⠄⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢔⡷⠂⠉⠀⣸⠀⠀⠉⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠴⠛⠉⠁⠀⠀⠉⠈⠉⠀⠀⠀⠀⢕⢆
⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⣾⡷⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣶⣴⣿⡜⢱⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠛⠿⠂⠀⠀⠂⠀⠷⢀⡀
⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⣿⣿⠋⠀⠀⠀⠝⠡⡄⢄⠀⣲⣿⣿⣼⣷⣶⣎⣦⣀
⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢷⣿⣿⡇⠀⠀⠀⢀⣀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⢐⣿⣧⠀⠀⢠⡀⠀⠀⠀⠀⣰⡈⣤⣂⢀⣤⣁⠀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣺⣿⣯⡀⠀⢾⣧⣤⡜⣁⣾⣿⡇⠨⠃⢈⣵⣟⣨⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡹⣿
⠲⠿⣿⡿⣂⣰⣿⣿⣷⢸⣿⣟⣿⣿⠄⢠⡎⢩⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣾⣻⣿
⣙⣿⣿⣿⣏⡵⣿⣿⣗⣼⣿⣿⣽⣿⣿⣼⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⢿⣿⣿⣿⠿⢿⣿⣿⠿⠿⣿⣿⣿⠻⣿⣿⣿⡻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠹⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠸⠏⠀⠐⢻⣿⠃⠀⠈⢹⡿⠃⠀⠈⠻⠃⠀⠈⠉⠛⠛⠛⠋⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂




⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⡴⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⢠⡾⢿⣿⣿⡿⠛⢸⣿⢁⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⢹⣍⡼⡋⠈⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠿⠿⢻⡇⠀⠁⠀⠻⠂⠛⣏⠛⠷⣿⣿⣿⡇⠸⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⣴⠀⠸⠂⠀⠀⡈⠀⠀⠀⠀⠀⠀⣌⠹⣽⡇⠀⠻⠁⢼⣧⣄⠀⠀⠀⠘⠂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⣄⠀⠀⢰⡷⠀⠀⠀⢀⡀⠀⠈⠀⠋⢋⠀⠀⠀⣿⣿⢿⣿⣿⣆⣦⣤⣦⣷⣇⠄
⠀⠀⠀⠀⠀⠀⠀⢾⣷⠄⠀⢾⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠘⠈⣂⠀⣿⣽⠿⠟⠿⠹⠻⢿⢿⣿⣿⣦⣥
⠀⠀⠀⠀⠀⠀⢠⣽⣿⡷⠀⣼⣿⡗⠂⢀⣿⣧⠀⣦⠀⠀⠀⠀⡟⡀⠁⠘⠀⠇⢠⠀⠀⠀⠘⠙⠛⠛⣿⣿⣷⣆⠀⡄
⠀⠀⠀⠀⠄⠀⢾⣿⣿⣟⣰⣿⣿⣿⠥⢮⣿⣿⡀⣿⠀⠀⢰⣶⠀⣯⠀⠘⠁⠀⣼⠄⠀⣆⠀⠀⠀⠈⠁⠀⣭⣞⡿⣴⣦⣤
⠀⠀⠀⠀⢀⡘⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣮⣿⣆⣠⣿⣿⣼⣿⣶⠀⠀⢠⣿⣿⢰⣿⡀⠀⠀⠀⠀⢀⣧⠈⣰⣌⠹⣿⣿⣦⣄
⠀⠀⠀⠀⣈⢙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠶⢠⣿⣿⣿⣺⣿⣶⡇⠀⠀⠀⣸⣿⢘⣿⣧⠀⠀⠘⢻⡿⠷⣦
⠀⠀⠀⠐⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⡟⢻⣿⣏⡍⣻⣴⡟⠱⡼⣿⣿⣿⣿⣿⡆⠀⠐⣼⣿⣮⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⡉⠀⠀⠀⣈⣿⣿⣿⣾⣿⠟⠀⠀⢳⠹⣿⣿⣿⣿⣷⣀⣙⣿⣿⣿⣿⣿⣦⠆
⠀⠀⠀⠻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⠀⢀⠀⣠⣼⣿⣿⣿⡿⠇⠀⠸⡧⠀⢧⢻⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣟⣁
⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠶⠧⠶⠾⠻⠟⠛⠛⠛⣛⠁⠀⠀⠀⠀⠀⠈⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⡄
⠀⠀⠰⢶⣿⣿⣿⣿⣿⣿⣿⣛⣉⣄⣠⣤⣤⣤⣤⣤⣤⣴⣶⡾⠋⠀⠀⠀⢠⣤⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣤
⠀⡀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⢻⣿⡇⢹⣿⡇⠀⠀⣿⣁⡏⠀⠀⠀⢸⣋⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠂⠀⠀⠀⠀⠀⠉⠉⡭⠉⣿⡧⠀⠼⠿⠇⢸⣿⡏⠀⢀⣃⣹⣧⡀⠀⠀⠘⠃⠀⠀⣽⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢾⣿⣿⣻⣿⣿⣿⠊⣿⣿⣿⣿⣿⡯⣿⣟⡽⣏⡛⣻⡿⣽⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠿⠻⢄⡰⢿⠿⠿⡛⠛⠚⠋⠛⠁⠉⠉⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠹⠟⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠘⣿⣧⡀
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡞⠁⠀⣤⣟⣉⣳⡄⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣠⡀⠀⣠⠋⠀⠀⠀⠳⣖⣒⣒⡛⢦⣠⣦⡀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠘⣷⡞⠁⠀⠀⠀⠀⠀⠈⠳⣖⢀⡔⠁⢿⣛⣆
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡞⠁⠀⠀⡿⠷⣄⠀⠀⠀⠀⠀⣠⡤⡼⠋⠀⠀⢠⠘⣞⠓⢦⡀⠀⠀⣤⡀⢀⡀
⠀⠀⠀⠀⠀⠨⣿⡅⣠⠞⠀⢠⣦⠀⠙⠿⢭⣍⣓⣦⣀⡞⠁⠈⠀⢀⡀⠀⣾⡆⠀⣶⠀⠹⣄⠀⣿⡇⢸⡇
⠀⠀⠀⠈⠉⠙⠛⠾⣇⠀⠀⢺⣿⠀⠀⠀⠀⠘⣖⣒⣛⠢⠄⠀⠀⢸⣇⠀⣾⣷⠀⣿⠇⠀⣹⣦⡽⠥⠾⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⣹⣿⡁⠀⣷⠀⠀⠈⣷⠐⠀⢰⡇⠀⣽⡯⠀⣹⣭⠤⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⠆⢸⣿⠀⠀⠀⠈⠀⠀⢘⣗⡤⠴⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡏⠁⠈⠉⠀⠙⠲⠤⣶⡾⢭⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⢀⢀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠙⠊⠉⠉⠉⠒⠒⠒⠲⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠠⠄⠄⠀⠀⠀⠒⠀⠁⠀⠀⠀⠀⠈⠑⠠⠄⡀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠈⠀⠂
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠠⠀⠀⠀⠀⠀⠀⠁⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠠⠀⡐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⡀⠠⠀⠀⠂⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣎⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⣠⣿⣡⠜⠃⠈
⠀⠀⠀⣠⣤⣀⠀⢰⣤⡠⠆⢈⡐⠠⣤⡀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⣰⣿⣯⣷⠈⠀⠀⠀⢻⡿
⠀⠘⠛⠛⣁⣡⣶⣇⣽⣤⡠⠘⠓⠶⡮⢱⠧⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⣴⡿⣡⣴⣿⣿⣯⠐⢓⠀⠄⠀⠀⠉⠦⠀⠀⢀⣤⠖
⠀⠀⠀⠉⠉⠐⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠙⠳⠛⢩⣴⣿⠟⠟⡻⢃⣴⡏⠀⠀⠀⠀⠀⠀⠈⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⢊⡽⠁⣤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⠟⡁⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⢀⣼⡿⡞⠡⡄⠀⠀⢤⣶⠀⠀⢀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⢀⣾⠛⢏⣾⣿⣿⠿⣤⠀⠀⠀⠈⠻⡀⠀⠻⠄⠀⢸⣧⣸⣦⡄
⠀⣠⡄⢠⣾⡰⠫⢫⣶⣿⣿⣿⠟⢀⡀⠀⡀⠀⡄⢀⠐⠦⣄⣰⣄⣿⠿⢛⢁⠀⠀⠀⠀⠀⠀⠀⡠⠲⡀
⠀⠀⠀⣠⠀⠀⣼⡿⠋⠀⠐⠃⠀⢸⣇⠀⣦⣰⣧⣸⣧⣧⣠⣿⠿⣧⢤⣿⠞⠃⠐⠂⠀⠀⢀⠊⠀⠀⢁
⠀⣸⣆⣿⡄⠀⢀⢁⣼⣤⣀⣴⣦⣿⣿⡿⣿⣿⠿⠛⠛⠁⠉⣴⡶⠶⠛⠁⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠈⢣
⠘⠻⠟⠻⠿⢤⣚⡋⠉⠉⠩⢙⠛⠛⢡⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⠘⠦
⠀⠀⠀⠀⠀⠀⠀⠛⠻⠶⢦⣸⣇⡀⣸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠡⡀⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠛⠃⠒⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠁⠑⡀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠈⠁⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⡀⢰⠡⠀⠀⠀⢀
⢣⡿⠁⢴⠃⠠⡿⠀⢀⡆⠀⠀⡄
⣾⣥⠋⡠⠕⠀⢃⡘⣿⠀⣼⣴⠁⣾⡄⠀⡀
⡛⢷⣄⣐⡂⠀⣴⠀⣲⡆⣿⣏⣉⠸⣷⣴⣧⢄⡄⡠⠀⣶⣠⢀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣄⣠⣄
⠉⠁⠒⠂⠀⠘⠧⣖⠊⢈⢿⠀⣐⠂⢻⣯⡐⢹⣿⠟⣼⠃⢻⣿⡏⣴⣿⣠⣤⠀⠀⠀⣠⣴⣴⣾⣿⣿⣛⣿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⣤⠄⠀⠘⣿⠀⠐⣿⠀⢼⣇⣐⢿⠁⠸⣇⣘⣿⢿⣾⠿⠟⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠚⠒⠛⠧⢬⣹⣆⠈⢿⣒⣸⣆⣄⣻⣆⣽⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡞⠙⡻⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠍⠳⣶⠞⠋⢭⣷⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⣽⠿⢏⣧⣚⣉⣋⠥⠛⠭⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠚⢯⠋⠈⡿⢈⣩⡭⠿⢿⣛⡭⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣋⣀⣠⣀⣈⣻⡁
⠀⠀⠀⠀⠀⠀⠀⣠⣤⢊⡾⠁⡀⠀⠱⢤⣿⣭⣤⣤⣓⣂⣀⣀⣭⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⣋⣁⣹⠀⠉⠹⣿⣦
⠀⠀⠀⠀⠀⠀⣰⡿⢁⡾⢁⠎⢸⡟⢠⣟⠔⠉⠉⢉⠭⠟⠋⢭⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣾⡿⠟⠋⠁⢹⠚⠲⣶⣶⣿⣝⢿⣶⣄
⠀⠀⠀⠀⠀⢠⡟⢡⡞⢡⠋⠀⢘⢆⣸⢏⣊⣩⣟⠫⣉⠙⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣿⣿⠿⠛⠋⠐⢾⡂⣀⣀⣉⣻⡿⣶⣿⣿⣇
⠀⠀⠀⠀⣠⢏⡶⠋⡴⠁⢀⡴⣫⠞⣿⠛⠉⣀⡈⠢⣄⠈⠳⠤⣄⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⢟⣽⣿⣶⠾⠛⠉⣾⡠⡀⠉⠻⢿⣿⠶⣍⡻⢮⣷⡀
⠀⠀⢀⡴⣣⠟⣠⠞⠀⣠⢏⠔⠁⢀⣿⢻⢞⠩⣝⠦⣬⣓⢤⡀⠈⠳⡄⠀⠀⠀⠀⠞⠋⠋⣡⠞⣻⡿⠶⠶⣶⠾⣿⡛⠛⠿⠶⠾⠯⣉⠚⠉⠂⠍⠛⠄
⠀⠀⠈⠘⠁⠈⠀⠀⠚⠁⠀⠀⠀⠁⢸⣧⢧⠑⠀⠁⠀⠉⠙⠛⠲⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⣿⠀⠀⣀⣤⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣩⣵⣶⣾⡿⣾⡆⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡛⣶⣿⣶⣿⣿⣿⣗⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣝⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣮⣽⡿⢛⣥⣾⣿⠿⣻⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠈⢳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡷⠄⡔⢲⠄⠠⠙⠯⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⡺⣟⠿⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⢒⣒⣙⣏⡤⢀⣈⣙⠛⢣⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⣀⠂⠁⣦⣝⠦⣙⡇⠨⣿⡵⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠃⠠⡈⣤⡈⣏⡴⠎⠤⠬⣭⣍⣓⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠁⢀⡀⠑⢄⣻⡮⠶⢬⡇⠤⣌⠶⢋
⠀⠀⠀⠀⠀⠀⢰⣚⣉⣉⣉⢉⣙⣯⡙⡟⢑⣂⣤⠤⠤⠤⠬⣷⣤⡀⠀⠀⠀⠀⠀⠀⢀⠊⠀⡠⠐⡩⠀⠀⠌⠂⠀⣸⠊⢩⡇⠤⣄⣙⣖⣁⠁⠠⡀
⠀⠀⡀⠀⠀⠀⣾⡭⠤⠔⠲⣊⠉⠉⠙⣿⣫⠿⠶⣖⣒⠶⠒⠲⠷⠽⣄⠀⠀⠀⢠⠐⢁⠠⢊⠤⠊⠀⡀⢁⢤⡄⣩⠃⠰⡉⡇⠀⠶⢦⣉⠩⢉⠓⠈⠢⡄
⠀⠀⢡⠀⠀⠀⠀⠀⢀⡴⢺⣍⠳⣄⠀⣿⠁⠀⠀⠀⠉⠙⠣⠞⠛⠛⡟⠂⠀⠀⠘⡁⠀⠀⠁⠄⠔⠋⠀⠠⡚⠛⠋⠉⠐⠠⡏⠁⠑⠢⣌⣳⡤⠀⠁⡲
⠀⠀⠘⣆⠀⠀⣀⠴⠋⡰⠻⢿⢧⡈⠻⣿⣢⠔⣿⡷⣄⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠓⠊⠉⠀⠀⡰⠁
⠀⠀⠀⠘⣦⠞⠁⠀⠈⠔⠁⠀⠑⠈⢰⣿⠁⠐⠋⠉⠊⠳⣄⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣾⣿⣿⣷⣄⣀⣀⡠⠊
⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡤⠖⠲⣬⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⢀⣀⣤⣼⣿⣶⣾⣏⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⢹⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠆⠀⢠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⣿⠏⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠘⣧⢆⡖⡀⠀⢂⣠⡀⠀⠀⠀⠀⠀⠀⣼⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠰⢏⡟⣡⣨⠀⠈⠁⡿⣢⠀⠀⠀⠀⡀⡸⠃⠀⢿⡄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠻⢁⣶⡀⠀⠀⠉⠃⠀⢠⣞⣼⢣⡀⠀⠉⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⢀⡤⠀⠀⠀⢀⡾⢡⣿⣻⣿⣄⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡍⠉⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠸⢡⡮⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯⣿⣿⢣⣿
⠀⠀⠀⠀⢀⡾⠀⠀⠀⠠⠾⢿⣦⡀⠀⠀⠀⠀⠘⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠘⢿⡟⣫⡴⠛
⠀⠀⠀⠀⢸⢁⣶⡶⠀⠀⠀⠀⠚⠷⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⢾⣿⣧⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⣣⠄⣠⣄⠀⠀⠀⠀⠀⢨⣿⣷⣶⡄⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⣠⣾⣷⡦⠀⠀⠀⠀⠀⠀⠉⠀⠙⣁⣾⢿⣏⠀⠀⠀⠀⠀⠀⠈⠛⠱⠷⠀⠠⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡿⠄⠀⠀⠀⠚⠋⠒⠩⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡹⠯⢾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣄
⠀⠀⠀⠀⠀⠀⠀⣠⢲⣻⠁⠀⠀⠀⠄⠀⠀⡾⢶⣿⣆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢢⡀
⠀⠀⠀⠀⠀⠀⡼⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⢠⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠧⠤⠀⠀⠀⠀⣀⠀⠀⠘⣹⠋⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣶⡿⠃⠀⢀⢸⡟⡠⢀⠀⠀⠀⠈⠂⠀⠀⠀⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠂⣄⠀⠀⠀⠀⣠⡾⠛⡀⠀⠀⠀⠁⠚⠁⠀⠀⠀⠀⠉⣠⠊⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠉⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠋⣤⠊⡀⠀⠘⠂⣤⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡁⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⡰⠆⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠉⠠⠀⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⢀⡄⠀⠀⠛⢩⠆⡀⢀⠠⠀⠀⠀⠀⠈⡖⣠⠔⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣷⠄
⠔⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠸⠟⠻
⡠⠂⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⢼⠏⠀⠀⣠⡴⠃⠀⠀⠀⠀⠀⡎⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⡄
⠀⠀⠀⠠⠄⠀⠐⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠹⠋⠂⠀⠀⠟⣰⣷⡏⢀⡀⠀⠀⠁⣠⣾⡶⡀⠀⢀⢀⣾⣀⠀⠀⠀⠀⢸⡿⢸⣧⠀⣰
⠀⠀⢠⡾⣿⡦⠀⡀⠀⠀⠀⠀⠻⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡽⣿⣷⣥⡀⢀⠀⠀⠈⣉⡾⠁⣼⠃⣸⣿⡧⠄⠀⣠⢀⣿⡗⣻⣿⢀⣿
⠀⠀⠀⡀⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⠂⠀⣀⠀⠀⠀⢞⣨⡿⢋⡴⠃⠀⠀⠐⠋⠁⡴⡇⠀⢼⣿⠷⠀⢀⣿⢻⣿⣥⣿⣧⣾⣿
⠀⢀⠀⠘⠀⠀⠀⢀⣀⢰⡀⠠⠤⣄⠀⢚⣆⠀⠀⠀⢄⡀⠀⠀⠀⠐⠋⢁⠴⣿⡿⠀⣤⠀⠀⠀⠀⠁⠀⠐⣾⢻⣿⡆⢸⣿⡀⠿⠛⠛⠉⠉
⢀⠈⠀⢠⡀⠀⠀⠘⠋⠀⠀⠀⠒⠈⠀⠈⠑⠚⠀⢀⡆⠘⠂⠀⠀⠀⠀⠀⠈⠙⠓⢰⡧⣸⡆⠀⠿⠀⠀⠦⣽⣿⣿⣏⠛⠋⠉⠁
⠀⠀⠀⠤⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣰⣼⡇⢀⠀⠀⠀⠀⠀⠀⢀⠖⠀⣾⣟⣻⡇⠀⠀⠀⠒⣶⣿⣥⣿⣯⡄
⠀⠀⠀⠀⠀⠀⢀⣰⡂⠀⠄⠀⠸⣇⠀⠄⠀⠀⠻⠿⣭⣿⠂⠀⠀⠠⣄⠀⠀⠀⠘⠟⠁⠘⠀⠀⠀⠀⢿⣭⣿⣟⣿⣿⠧
⠐⠂⠀⠈⠃⣿⣄⢿⡅⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠐
⠀⠀⠁⠀⠀⢸⢿⡌⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡀⠀⠀⠀⠀⢀⠁⠁⠀⠠⠶⠿⠛⠀⠀⠀⠀⠤⠤⠂⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠐⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠠⠤
⢧⣶⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣐
⠀⠈⢀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠰⠂⠀⠀⠀⢀⡀⠉⠀⠀⠀⠀⠀⠀⣀⠐⠂⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠁⠂⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⠄⣶⡿⠂⠀⠀⠀⠀⢀⢿⣿⣿⣷⣄⠀⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠘⠁⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣷⣄⢻⣷⣄⠀⠀⣀
⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⢰⠇⠀⡆⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⣿⣿⣿⣦⡀⠉⠿⣦⣈⢳⣤⡀
⠀⠀⠀⠀⢸⣗⠀⠀⡄⠀⠁⠀⢸⣿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣾⣿⣿⣿⣿⣿⣿⣿⣶⣤⡄⠻⢧⡙⣿⣶⣄⡀⠀⢀⣀⣤⣤⣄
⠀⠀⡄⠀⣹⣿⡀⢠⣷⠀⠀⠀⢾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⢻⣿⡿⠿⠿⠟⠛⠛⠛⠛⠻⠶⠀⠉⠀⠿⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⣸⣷⠀⣿⣿⠅⢾⣿⡆⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⡖⣿⣿⢖⣿⣿⣗⠀⢠⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣦⣤⡀⠀⢀⣤⣴⡿⠂⠉⢻
⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣤⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠛⣿⣿⡟⢊⠥⠤⠎⢘⣿⣇
⣿⣿⣯⣝⣻⡿⢻⣿⣿⣿⣶⣾⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠁⠀⣀⣤⣤⣿⣿⣶⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡏⢉⢉⣉⡉⣉⢉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉
⡇⠨⡬⢱⣉⡉⣀⠁⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣠⢶⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⢀⣍⡉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡛⠈⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡾⠥⠹⢞⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠒⢺⠒⠖⣖⢲⠖⠒⡆⠀⠀⠀⠀⠀⠀⢀⡀⣑⡋⣁⣀⢀⣀⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠅⠈⠀⠋⠀⡃⠀⠀⠀⠀⠀⠀⢘⠂⠘⠁⠘⠛⠀⢢⠐⢧
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠸⠐⠁⠀⠃⠀⠀⠨⠂⠏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣄⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⡄⠀⠉⠀⢰⠈⡄⠁⢀⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠇⠤⠴⢁⡀⠉⣆⣀⣀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠛⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠆⠀⣈⠉⣻⠀⠂⡀⠀⢁
⡇⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡉⠀⢸⠀⠀⠀⠈⠀⠀⠀⢸⠈⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡍⡄⠉⠈⠛⠸
⡇⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠉⠀⠀⠀⠆⠀⠀⠀⡘⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠰⡏⠀⠐⠀⠀⠁⠸⠀⠒⠄⠀⣆
⡇⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢠⠴⠀⠀⠀⠀⣇⠀⡂⠀⠀⠀⠀⣇⠀⠀⠀⢀⠦⠄⠀⡎⢩⡄⢠⠀⡀⠔⠀⢩⠆
⡇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠸⣀⡈⠉⠀⠈⢡⣿⠁⠒⠀⠐⠒⢉⡆⠀⠀⡎⠀⠠⠀⠁⠘⣣⡼⡈⠀⠀⠄⠸⣢
⡇⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠂⠀⠀⢧⠀⢈⠉⠉⠉⠁⠀⠉⠐⠒⠒⠀⠉⠀⠀⠀⠁⠲⡤⠤⠤⠄⠋⠓⠤⠤⠴⠒⠦⠚
⡧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡏⠢⡄⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡅⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⡇⠀⣆⠀⠀⠉⠑⠂⠠⠤⠤⠄⠠⠤⠤⠄⠒⢺⠀⢸⠀⠀⣌
⡇⠀⠘⢆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠈⠣⣠⠋⠉⠉⠁⠘⠃⠐⠒⠒⠠⠤⠤⠤⠀⣀⣀⡀
⡇⠀⠀⠀⠓⢄⡀⠣⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠒⠒⠒⠲⠠⠤⠄⢠⣄⣀⣀⣀⣀
⡇⠀⠀⠀⠀⠀⠈⢱⠈⠢⣄⣀⡀⠀⠀⡀⣑⡺⠝⠓⠊⠉⠉⠁⠒⠒⠂⠠⠤⠤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠅⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠂⠒⠒⠂⠠⠤⠤⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⣄⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠒⠂⠀⠤⠄
⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⡂⠀⢁⠀⠀⡇⠐⠀⠠
⡇⠀⠀⠀⠀⠀⠃⠈⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡇⠀⠀⠀⠈⠓⠀⠀⠐⠂⠀⠀⠲⠀⠀⠉⠉⠉⠂
⡇⠀⠀⠈⠀⠀⠀⠖⠒⠒⠀⠄⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⣇⣀⣈⣀⣁⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡇⠀⢄⣀⢀⣴⣿⣿⣿⣅⡋⠁⣴⠂⠄⠠⠀⣠⣴⣿⠀⠄⣠⣾⢩⠦
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣚⣽⡿⠀⢀⡀⣠⣾⣿⣿⣷⡌⠙⢷⣾⣿⡧⠀⠰⠦⢌⣩⣽⣶⣚⣿⣏⠤⢢⣴⣄
⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣷⣴⣿⣷⠀⡙⠿⣿⣿⢆⣴⣿⣿⠟⠁⠀⠀⢠⣾⣿⣿⣿⣿⢟⣡⠀⢿⣿⣿⣷⣄
⠀⠀⠀⣠⣴⣾⢿⣿⣿⣽⣿⢿⣿⣿⣿⣷⣄⢻⢷⡬⣙⠾⣿⣿⣿⡈⢤⣠⣴⡿⣿⡿⠟⣫⢷⡽⡏⢴⣿⣿⡿⠿⢷⣦⣄⣄
⠀⠠⠾⠿⠿⠷⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠿⠶⠷⠾⠷⠦⠾⠿⠿⠟⠛⠿⠿⠷⠾⠿⠶⠟⠶⠷⠶⠿⠿⠿⠿⠿⠿⠿⠶⠷




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⢀⣾⣷⣤⡈⣐⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠈⠁⠀⠦⠀⠀⡀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠃⠈⠚⣛⣿⣿⣿⣿⣷⡄⠀⠛⢣⡘⢲⣿⣗⣠⣴⣿⣺⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣯⣿⣿⣯⣠⣶⡌⠻⢿⣿⣿⣿⣯⡁⠀⠀⠂⢈⣴⣾⣿⣿⡿⢋⢱⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⢦⡝⡛⢿⣿⣿⣦⣀⣴⣾⣿⡿⢟⡽⡺⡏⣴⣿⣿⠿⢷⣤⣀
⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠚⠓⠓⠚⠲⠒⠻⠟⠛⠻⠟⠓⠚⠛⠛⠓⠓⠚⠛⠛⠟⠛⠛⠓⠓

⣿⣿⣿⣻⣻⣻⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣻⣿⣿⣻⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢱⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣄⠀⠀⢀⡔⠋⠠⠛⢙⣿⣧⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢁⣼⣿⣷⡄⠋⠀⠀⠀⠀⠸⣿⠙⣿⣷⣀⠀⣠⠾⠻⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢠⠏⣿⣄⡀⠀⠀⠀⠀⠸⣦⠈⠻⢿⣷⣤⣀⠀⠀⠹⣧⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⣴⠏⠀⠘⠟⠛⠷⣄⡀⠀⠠⣿⣦⡀⠀⠈⠻⠿⢶⣤⡀⠈⠋⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠘⠀⠙⢶⡄⠀⠀⠀⠙⠿⠿⠶⠄⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠈⠁⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠉






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⣴⡛⢆⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡖⣦⡀⢤⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⡇⢀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⣰⡋⠔⡉⣸⣧⡚⠃⠀⢿⡦⢀⠀⠀⠀⠀⠀⠀⢚⠀⠣⠙⣇⠈⠉⠷⢯⠀⢿⢀⠀⠀⠀⠀⠀⠀⣠⠎⢈⠷⠄⠈⠀⣰⠏⠇⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⣆⠐⠾⣿⠈⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⣏⣷⣔⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⢶⣿⠀⢶⣿⡁⠢⣠⣶
⠀⠀⠀⠀⠀⠰⠦⡽⠿⠿⠼⠿⠶⠾⠿⠶⠯⠤⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠀⠀⠀⠀⠀⠐⠛⠚⠛⠛⠛⠛⠛⠒⠛⠛⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢠⣖⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡂⡀
⠀⠀⠀⠀⠀⠀⣀⢼⣇⡈⢿⣿⠑⢾⣇⡑⢄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡞⢿⣿⣶⣥⣾⣓⠤⡀⠀⠀⠀⠀⠀⠀⣠⢠⣾⠃⢿⣿⣧⠈⣤⡄
⠀⠀⠀⠀⠀⠘⠓⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠾⠿⠿⠿⠿⠿⠷⠿⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠶⣀⠤⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⡀
⠀⠀⠀⠀⠀⠀⡄⢤⣾⡇⠹⣗⣀⣓⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠏⠛⠃⠐⠻⡦⠌⢀⠿⢤⡀⠀⠀⠀⠀⠀⠀⣀⢤⣴⡇⣻⣿⠀⣼⣻⡄⢀⡀
⠀⠀⠀⠀⠀⠘⠙⠛⠋⠛⠛⠛⠙⠋⠛⠙⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠋⠛⠛⠛⠉⠉⠛⠛⠙⠙⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⢦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⣯⠑⣄⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡎⣅⢤⡤⡀⢀⡀
⠀⠀⠀⠀⠀⠀⢤⡆⠹⠿⢭⠀⠐⢋⣈⠦⢤⡀⠀⠀⠀⠀⠀⢀⣤⣾⣦⠻⢿⣿⣦⠚⢿⠧⡳⠄⠀⠀⠀⠀⠀⠀⢤⠚⠀⠙⠡⠞⠈⠡⠿⠛⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶
⠀⢨⣯⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⢠⣖⣷⠇⠀⣼⣿⡋⠀⠀⢀⡀⠐⠀⠀⢀⠉⠂⠀⠀⠀⣴⣯⠀⠀⠀⠀⣀⠀⠀⠙⠋⠉
⣆⢸⡇⠄⢀⠀⠀⢴⣾⠛⠀⠀⠀⠀⢠⡄⠀⢴⣿⡿⠁⠀⣠⣾⡿⠃⠀⠀⠈⡇⠀⠀⠀⠀⠉⢀⣤⠀⢀⡿⠋⠀⢀⣴⣾⣿⣶⠈⠓
⠷⣾⡧⠀⣾⠃⢠⠄⠿⣿⡀⠈⠁⠀⠈⠀⠀⠘⢻⣣⣴⣿⣿⣿⣦⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠼⠻⠀⠈⠁⣠⠖⠋⠈⠈⠁⡄⠀⠀⡉
⢷⣿⡏⠉⢿⡈⣿⠠⣄⠸⣿⣖⠀⠀⠂⢀⠀⠀⠉⠙⠿⠛⠻⠟⠓⠻⣿⠀⢠⠀⠀⢀⣴⠇⠀⠀⠀⢀⡀⠀⠀⢀⡇⢀⡀⣸⡇⣰⢰⡧⣾
⣿⣿⣧⠀⣸⣿⣿⠘⣿⠀⠀⢀⣜⣧⣀⢆⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⢀⠀⠘⠃⠀⢀⢠⢀⢸⣠⡇⣼⣷⣾⣴⣰⡷⢼⣷⣿⣳⣿⣾⡧⣿
⠙⠛⠛⠛⠻⢿⣿⣦⣿⣴⣾⢾⡷⣮⡷⠾⠀⠀⠿⠇⠀⠘⠟⠿⠿⢶⠾⢾⡶⠀⠀⠺⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⡅⣼⣿⣿⡿⢿⠿⠷⠛
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠉⣀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠂⠀⠀⠀⠀⠉⠉⠛⠉⠁⠀⠘⠛⠟⠉⠀⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠒⠶⠦⠀⠀⠈⠁⠒⠒⠲⠾⠿⠿⡶⠶⢶⣤⣤⣤⣤⣤⠶⠶⠾⠿⣯⣿⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠘⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠼⠛⠂⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢿⣧⣄⣀⣁⣠⣿⣯⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠂
⠀⠀⠀⠁⠀⢠⣦⡀⠙⣿⣷⣴⣾⣿⣿⡿⠿⣿⣿⣿⣿⣿⠿⠦⠚⠓⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣀⣤⣤
⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠉⠛⠿⣿⣗⣂⠉⠁⠀⠈⠙⠿⠿⠿⠷⠚⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⣦⠀⠀⠀⠀⣤⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⠰⠿⣿⣦⠈⡁⠀⣀⣼⠋⠁⠀⠀⠀⡀⠀⠀⢾⡁⠀⠀⠀⢠⡾⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠈⠀⠀⠀⠀⢠⣆⠀⠚⠁⠈⠉⠉⠉⠓⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠏⠁
⠐⡄⠀⠠⠀⠄⠄⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⣠⣀⡀
⡀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣀⡀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⠈⢀⡀⢀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⢀⡤⣇⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠌⠀⢡⠆⠀⠀⠀⢀⠀⠐⠀⡍⠉⠉⠉⠻⠛⢄⠀⠠⠀⠀⢤⡀
⠔⠋⠁⢀⡘⢷⣷⣤⣰⣤⡀⠀⠀⠀⠀⠀⠀⠠⠂⠤⢀⡍⠀⠄⢀⠆⠈⣸⠀⠂⣇⠐⠀⠱⡀⠐⠀⢂⠀⠀⠑⣀⠙
⠀⠀⠀⢀⡤⠛⠁⠀⠘⠉⢉⡿⠛⠠⠀⠀⠰⠊⠀⠁⠖⠀⠀⠀⣸⠀⠀⡿⠀⠀⣯⠀⠀⠀⢇⡀⠀⠂⠱⣀⠐⠈⠣
⠀⢀⢰⠞⠁⠀⠀⣠⠀⣀⡞⠀⠀⠀⢀⡰⠇⠰⠀⢰⠇⠀⠀⢸⡇⠀⢸⠇⠀⠀⣿⠀⠀⠀⠈⣧⠀⠀⠀⢻⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡧⠀⠀⠀⠀⠀⠀⠀⠀⣤⢶⣦⡀⠀⠀⠘⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⠀⢀⡞⠁⠀⣯⣳⡄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⣾⠭⢭⢽⣆⠀⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠴⣦⣀⡴⠁⠀⠀⠀⠈⠳⣞⣛⠈⢳⠾⡷⣄
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⡼⠁⠀⢻⣯⡀⠀⠀⠀⠀⠀⠀⠈⢢⡔⠁⠀⠻⢽⣧⣀
⠀⠀⠀⠀⠀⢸⣿⠀⢀⡞⠁⢀⠀⢸⣭⣷⠤⣤⡀⠀⣠⠞⠿⠋⠀⠀⠀⣿⠈⢂⡌⠳⡄⠀⢸⡇⢀⣇
⠀⠀⠀⠤⠤⢭⣟⣰⠋⠀⢀⣿⡃⠀⠈⠉⠳⣖⣛⣶⣇⠀⠀⠀⣺⡆⢀⣿⡀⢸⣧⠀⠹⣆⠼⣷⣐⣗⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⠐⣿⡇⠀⣤⡀⠀⠹⣖⣒⠈⢡⡄⠀⣾⣇⠨⢿⠃⣘⣯⠴⠖⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣏⠀⣿⡂⠀⠀⠘⠀⠀⢸⡧⢀⣹⠭⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠇⠀⠻⠃⠠⢤⣀⣠⣤⡒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢉⡧⠉⠉⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠳⠜⠓⠒⠒⠦⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠸⣿⠻⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⢸⠇⠈⠋⠛⢿⣿⣦⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⡟⠁⠀⠀⠀⣠⣯⡀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣫⣿⣿⣿⡶⠃⠀⠀⠀⠈⣿⣿⣦⡀⠀⠀⣠⣿⡟⠁⠘⠙⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠾⠛⣿⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣾⠟⢹⣿⣠⣴⠾⠛⠉⢿⣿⣷⣤⡀
⠀⠀⠀⢀⣤⠾⠛⠉⠀⣠⣾⣿⠶⠂⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⠟⠁⠀⣼⣿⡟⠁⠀⠀⠀⠀⠙⠘⣿⢿⣦⡀
⠀⠀⠀⠈⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⣠⣄⣠⣴⣾⣿⣿⠟⠉⠁⠀⠀⢀⣽⡿⠀⠀⠀⢀⣠⣶⣦⣦⣹⣎⢻⣿⣶⣶⣶⣄⡀
⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⣀⣴⣾⡿⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠜⠁⠀⠀⣠⡴⠟⠉⢻⣿⣿⣿⣿⣿⣿⠟⠛⠯⠛⠻⣷⣦⡄
⠀⠀⣠⠖⠋⠀⠀⠀⢀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⣠⣴⠞⠉⠀⠀⠀⠀⠈⠻⡏⠛⢿⣷⣦⡀
⠀⠈⠀⠀⠀⢀⡤⢾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠋⠻⢿⣶⣾⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠂⠉
⠀⠀⠀⠀⢀⣠⣾⠟⠋⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋⠉⠛⠷⠀⠀⠉⠉⠛⠻⢿⣶⣤⣄⡀
⠀⠀⣠⠶⢫⠟⠁⠀⠀⠀⠀⠀⠀⠀⠚⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛
⠀⠈⠀⠀⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⢻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢛⣿⠇⡀
⠀⠀⠀⠀⠀⠀⢠⣇⡀⠀⠀⠀⠲⢩⡿⣿⠖⠁
⠀⠀⠀⠀⠀⢀⢺⡿⠄⠀⠀⠀⠠⣯⣴⡿⣆⠚
⠀⠀⠀⠀⠀⠄⣠⢶⣄⠄⠀⠐⠆⢴⡟⢳⣮⣀⢠⠄
⠀⠀⠀⠀⢠⡀⣻⢾⣅⡄⠀⢄⣠⣾⣠⣿⣮⡧⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢤⣼⠟⣴⢷⠄⠀⢀⢀⡼⠋⢀⠿⣤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣘⢳⣶⣟⣷⣷⠐⣀⢉⡿⠋⣽⣶⣬⠦⡤⠐
⠀⠀⠀⠠⢽⡟⢁⡽⠿⡶⠠⠿⣿⣦⠴⣿⣧⢳⡄⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣲⣤⣿⡿⢳⣤⠷⡄⠾⣿⣁⣀⢾⠛⠙⣄⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠈⠛⠻⢿⠗⠿⢿⡷⠿⢶⣿⡿⣃⣤⣷⢶⡜⠛⠘⠉⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠉⠉⠹⠛⠷⢷⠆⡤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠂
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⢀⡀⠀⠀⠀⠀⠐⡈⢀⠀⠀⣠⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠄⠄⠈⠀⠈⠀⠀⠉⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢰⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡆
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢴⡶⠶⠶⠒⠒⢷⡀⠀⠀⢠⡟⠒⠒⠶⠶⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣄⠀⠈⣧⠀⢀⡟⠀⢀⣄⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠛⢦⣘⣇⣾⣡⠶⠋⠁⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠒⣶⠋⠉⠉⠻⡖⠚⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢠⡞⠛⠛⠛⠛⠛⢛⣻⠿⠛⣻⡿⢿⡛⠛⢿⣟⡛⠛⠛⠀⠘⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⢴⡞⠋⠀⢀⣼⡏⠀⠀⣿⣦⡀⠈⠙⣶⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠙⣦⡴⠋⢸⡇⠀⠀⣿⠈⠻⣦⡾⠋⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠸⠧⠤⠤⠤⠤⠤⠤⠤⠤⢼⡇⠀⠀⣿⠤⠤⠬⠤⠤⠤⠤⢤⣤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⢀⣠⣤⡤⢿⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⣰⠏⠀⠀⠀⣠⠼⠧⣤⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⢀⡏⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠈⣇⠀⠀⠀⠀⠀⠉⠙⢳⡄⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⢻⡄⠀⠀⠀⠳⢦⡴⠞⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⣀⣀⣀⣀⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣦⣀⠀⠀⠈⠁⠀⠀⣀⣴⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠲⠶⠶⠖⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⢀⣀⠤⣤⣀⣀⠠⣤⣄
⣦⣄⣠⣤⣠⢤⡤⠒⠻⢥⣼⣿⣷⣶⡊⢡⠆⠐⣻⣿⣧⠀⠈⣹⣿⣦⣄⣀⣠⣤⣤⡴⢦⣄⣀⠀⠀⠀⠀⣀⣀
⣿⢿⣷⣦⣿⣠⢿⡶⢋⣼⠈⣻⣿⣿⣷⣿⣄⡼⢻⡻⡟⡿⡜⠋⢿⣿⣿⣿⣷⣒⣿⣟⣶⠭⢽⣿⣿⣯⡭⠤⣭⣿⣷
⣾⠟⢛⣿⣿⣷⡸⣄⣾⡈⠘⣹⣿⣿⡻⢿⣿⣿⣿⣧⣑⠿⡈⣸⣆⢹⣿⡉⢻⣿⣿⣧⡞⠆⢲⠹⣿⣄⡞⠀⣨⣿⣿
⢿⣣⣿⢹⣿⣿⣿⣯⡀⠁⠒⠃⠙⣷⡽⡆⢻⣷⡿⣿⣿⣿⣿⡙⣿⣄⡹⠿⣦⡙⠻⡝⢿⣷⣯⣙⣾⡹⣦⡊⡇⠹⣯
⡼⣁⡿⣎⣿⡜⣿⡹⣿⣶⣴⣤⠸⢏⢿⣿⣏⣿⡟⢾⣿⣷⣿⣿⣷⣌⢿⡢⠄⢢⡶⣌⠂⠙⣷⣬⣟⠻⣾⣿⣦⣐⠛
⢘⠽⠉⣿⣿⣀⣼⢿⣔⠛⣿⣿⣶⣄⠨⠿⣿⣤⠒⣶⣟⠻⣮⣏⠻⣿⣷⣧⣐⠛⠁⡿⢷⣤⡁⠙⣷⣤⡨⠛⠓⢮⣟
⠀⠔⠪⠃⡼⠋⣷⠘⣿⢷⣮⡙⡿⢿⣿⡶⣿⡹⣿⣯⡛⢷⣬⣑⠦⡹⣾⣝⢿⣓⠦⣄⡀⠈⠻⣕⡈⠛⢻⢷⣦⠌⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠀⠛⠛⠬⠙⠿⠦⣍⠓⠬⠉⠉⠂⠀⠁⠀⠈⠙⠢⠍⠳⠀⠘⠊⠙⠒⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡶⣲⡷⣹⣷⣾⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣴⡩⠒⠛⠉⢿⣿⡧⡾⠭⠽⠃⣀⣤⣀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⡿⡿⣻⣿⠁⠀⠀⠀⣶⣟⠀⠀⠀⢸⢠⣾⡿⢿⣦⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣨⣏⣰⠿⢾⡀⠀⠀⣸⢳⣿⡀⠀⠀⢸⠘⢻⣶⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠽⠿⠟⠛⠛⠐⠈⠉⠉⠉⠉⠛⠋⠙⠂⠠⢵⣾⣉⡙⠿⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣔⡖⠒⠀⠀⠀⠀⠀⢠⢲⣿⢦⣤⣤⣤⡈⠀⠙⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⡿⢿⣿⣘⡀⣀⣀⢶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠿⠷⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠖⠋⠉⠀⠈⢿⡻⢿⡃⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠒⠲⠒⠓⠒⠖⠲⠛⠉⠉⠉⠀⠐⠤⠀⠀⠀⢘⣿⡆⠈⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢾⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠈⣏⣀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⡦⠙⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠐⠂⠀⠀⠀⠀⢀⠀⠂⠁⠈⠟⢡⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠐⠀⣗⡵⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣼⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣤⣀⡀⠟⢣⡾⢃⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⣴⡟⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠛⣿⣿⢱⣸⠀⡷⠋⠀⣠⣴⠷⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡇⣧⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⡠⠞⠋⢱⠀⡴⡀⠠⠔⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢉⣴⠠⠀⠀⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⠋⠀⠀⣀⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠠⠉⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠃⡀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠈⠁⠊⠀⠀⠀⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⢰⠖⠂⠀⠈⢀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠘⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠄⠀⠀⠀⠈⠃⠈⠙⠄⠀⠀⠀⠘⠀⠀⡢⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⠊⠀⠀⠀⠀⠂⠸⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠂⠀⠈⢃⠌⠀⠀⠀⠁⡀
⠀⠀⠀⢀⡀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠘⠀⠀⠀⣴⠀⠀⠀⠘⠢⠀⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠀⠘⢟⡻⣾⠿⠿⠷⠶⢶⣶⣶⠶⠟⠠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣼⣿⣿⣶⡀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠶⢶⣦⣀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⣶⣟⣭⡟⢀⣿⣯⡽⢇⡀⠈⢹⣿⣏⣹⣿⣿⣿⡟
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⡾⡤⡀⡇⠀⠀⠀⠀⠀⠀⠀⠚⢻⡿⣿⣿⡟⣿⣿⣧⣾⠁⢠⣾⣿⠁⣿⣿⢟⣿⡇
⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⠄⣿⡄⣼⡁⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣞⣴⢟⣻⣙⡻⠛⠃⠀⠛⡿⠟⢰⣿⣿⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⣴⣀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠈⠀⢉⣷⣏⠉⠉⠀⠀⠀⠀⢀⣿⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⠿⠛⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠜⠚⠿⠟⡐⠂⠀⠀⠀⠀⢼⣿⣿⣿⣟⢛⡛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⡄⠀⠀⠀⠀⠀⠉⠉⢻⣧⣾⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣿⣿⣷⣄⠀⠀⠀⣤⡀⠀⠀⠀⠈⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣠⠀⠀⢀⣶⡄⠀⠀⠀⠀⢸⣿⣿⠛⣿⣄⡀⢠⡼⢋⣶⣦⡶⣶⠐⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⢠⣿⡏⠀⠀⣤⢘⣶⣶⣶⠆⢹⣿⡏⢹⣿⣿⣿⣾⣿⣿⡄⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣀⢸⣷⣄⣤⣌⡏⠘⣿⠉⠉⢀⣼⣟⢁⣴⣿⣿⡿⠿⡿⣿⣿⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠸⣿⣿⣇⢹⣿⣿⠇⡹⢛⠀⠀⢀⣷⢀⣸⣿⣿⣿⣿⣿⢿⠇⠰⢀⣀⣤⣄⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⣀⣛⢻⣿⠈⣿⡃⠀⢧⣴⡶⠀⠸⢿⣿⣿⠃⠀⣿⣿⣿⣀⠸⠀⠈⠉⠛⠋⠖
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⣇⣴⣿⣿⣿⣿⣿⡄⠸⣇⠀⠘⣿⢧⣄⣀⣸⣿⣿⣰⣦⣿⣿⣿⣭⣿⣶⡠⠓
⠀⠀⠀⢰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣿⣄⣀⣹⣞⣍⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣻⣶⣤⣴⡄
⠀⠀⠀⠸⠿⣿⡛⠛⠛⠛⠿⠿⠿⠿⠿⠛⠛⠉⠉⢉⣽⠿⡋⠉⠉⠙⣟⠉⠉⠉⠉⠉⠀⠈⠙⢻⣿⣿⣿⣿⣿⡏
⠀⠀⠀⢘⣿⣿⣿⣦⣤⣤⣀⣤⣤⣤⣤⠀⣀⣤⢞⣿⡏⢠⢱⡄⠀⠀⢸⡀⠀⠀⠀⢀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⢀
⠀⠀⠀⢠⣿⣿⣿⣷⡿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣶⣾⣶⣶⣶⣶⣶⣶⣶⣻⣴⣾⣤⣤⣴⣿⢿⣿⣿⢿⣿⣁⡘
⠀⠀⠀⢸⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⣿⢿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣧⠎⣿⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⣴⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣷⣬⣉⣫⢿⡿⣟⣿⣿⣿⣿⣿⢷⣿⡿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣭⣴⡿⣿⣿⠿⠿⠿⢿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⡿⠿⣿⣿⡿⠹⣿⣿⣾⣏⣻⣭⣥⠶⢟⣫⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⣯⣀⣼⣧⡌⠁⣶⣭⠻⠟⣀⣠⣬⣵⣾⣿⣿⣶⣾⣷⣿⣯⣙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣷⠀⣈⣉⠉⠀⠀⠉⠉⠉⠙⠛⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡈⢹⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠘⠿⢿⠷⢸⡿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⢹⣿⣿⣿⠿⢿⣿⣿⠿⠿⠷⠴⠿⠿⠿⠿⠿⠿⠿⠋⠑