Wings Emojis & Symbols

⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⢻⣧⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣿⠃
⠀⠀⠈⢿⣷⡀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣠⣿⡟
⠀⠀⣄⠈⢿⣷⣄⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⣴⣿⠟⢀⡄
⠀⠀⠘⢷⣌⠻⣿⣮⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢋⣾⣿⢋⣴⡟
⠀⠘⢷⣮⣿⣷⣮⡻⣷⣝⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢟⣵⣿⣿⣿⢿⣫⣴⠖
⠀⠀⠠⣽⣿⣿⣿⣿⣷⣝⡷⣝⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣵⣿⣿⣿⣻⣷⣿⣿⡥
⠀⠀⣤⣌⣻⣿⣿⣿⣿⣿⣿⣮⣝⣟⣻⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣋⡷⣿⢿⣫⣷⣿⣽⣿⣟⣋⣠⡄
⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣷⠭⣿⣿⣷⣦⡀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢰⣿⣿⣿⣿⠽⠾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⢺⣿⣿⣿⣤⣄⢠⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣯⣀⣤⣽⣿⣿⣿⢒⣿⣿⣿⡿⣿⣿⣿⣿⣶⡶⠖
⠀⠀⠠⢤⣴⡿⠟⢛⣩⣭⣤⣴⣶⡶⠾⢟⣽⡶⢷⡚⢛⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣟⣳⣢⣴⣯⣟⠿⣶⣶⣶⣿⣭⣽⣟⣷⣿⣥⣤⣤
⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⢟⣭⣖⣫⣤⡏⠴⣿⣶⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⡹⣛⢿⣿⡟⢯⣜⣲⣯⣟⢿⣿⣿⢿⣿⣭
⠀⠀⠀⠀⠀⠀⣴⡿⠿⣫⡴⢟⣿⣿⡿⠋⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣞⣿⡯⣍⢿⣳⣾⣿⡿⣖⠻⣿⣿⣿⣝⣷⣮⡻⠿⣮⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣩⣶⠿⣛⣭⣴⣾⣽⣾⡴⡿⣻⢿⡿⣿⢽⣿⣷⠀⠀⠀⠀⠀⠠⣿⠿⢵⡪⣗⢿⡻⣷⣾⣿⣽⣿⡮⣟⡿⣿⣯⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⠟⣡⣾⣿⣿⡿⣱⢞⡴⠿⢫⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⣴⣿⣥⣽⣿⣎⠳⢷⣽⣿⡿⣿⣮⣻⣮⡻⢷⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠛⠉⠟⣼⢣⢏⢆⡔⡝⣻⣿⣿⣿⣞⡙⡦⠀⠀⡜⣻⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⡞⡯⠛⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠏⠋⠞⡾⣱⣿⣿⡽⢿⣷⣧⠀⢀⣷⣿⣿⣷⣾⣿⡿⣿⢿⠿⠏⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠻⠿⢿⢾⣆⢿⠀⢸⣿⣽⣾⡿⠿⠛⠻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣁⠀⠀⣠⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣡⠔⠋⠁⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡺⣟⣵⠿⠋⠀⠀⠀⠀⣠⠋⠀⠀⣀⣠⣤⣤⢤⣶⡤⢤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⣹⣿⣾⣿⣇⣵⠊⠀⢀⡴⠚⣁⠴⠚⠋⠉⠀⣀⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠞⠁⠀⠀⢉⣿⣿⣿⡿⠋⠄⢺⣧⠔⠋⠀⠀⠀⠀⠀⠀⢫⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣰⢋⠀⠀⠀⡠⢋⣿⡿⢋⠄⣀⡴⠋⢀⡠⠂⠁⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣸⣷⣯⠂⠀⠊⠀⠋⣯⣾⣯⢞⣵⣢⣶⡿⠁⠀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⣿⡿⠁⠀⠀⠀⠀⢠⣿⣟⣵⣿⣿⠿⠋⠀⠀⣰⡖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣿⠃⠀⣻⠆⡀⠀⠀⠀⠀⢸⢷⣿⣿⣿⠏⠀⠀⢠⣞⠃⠀⠀⣀⣀⣤⣤⣤⠤⢶⣦⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⣿⣤⣡⡾⠁⠀⠀⠀⠀⣱⣿⣿⡿⠋⠀⠀⠈⠠⠞⠛⠋⣉⠉⠁⠀⠀⣠⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣾⢼⣿⣿⠏⣴⣣⠄⠀⠠⠚⠉⣩⣿⡾⢃⣠⣤⣦⠶⠒⠋⠁⠀⠀⠀⠀⠀⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣁⠘⠿⣡⣾⠟⢉⢀⡀⠀⠀⣴⣫⣵⣾⣿⠿⠛⠋⠀⠀⢀⣀⣠⠷⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠈⠝⢡⣾⣿⡏⠀⠀⠀⢠⠾⠛⠉⣀⡀⠠⠶⠤⣴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⣫⡀⠀⢉⣟⣩⣶⡆⠀⢀⣷⡶⠖⠒⠀⠀⠀⠠⠴⠯⠤⠤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⢿⣟⡃⢈⠸⢛⣉⠀⠀⢉⣼⣦⣤⣦⣤⠤⠤⠂⠀⠀⢠⣤⣬⠿⠷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢚⣯⡆⠀⣼⠟⢋⠠⠾⠟⠛⡛⠉⠁⠀⠀⠀⣀⣀⠤⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠰⠿⠧⠤⢶⣾⡶⠆⢀⣠⣖⠀⠀⠀⠀⠴⢟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣚⣉⠀⠀⣠⣅⠀⠐⠚⠿⠿⠛⠁⣀⡀⠤⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠿⠅⠒⢛⣉⠠⢤⣬⣄⣀⣀⠀⠀⠾⢧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⢤⡀⣀⣀⣀⡠⡤⠲⠗⠀⣾⢓⣈⣉⡍⢥⣤⣄⣚⡛⠛⢉⣁⣀⣠⠤⠄⠚⠋
⠀⠀⠀⠀⠀⣠⠚⠁⠼⠿⣤⠶⠇⠐⠶⠀⣀⣾⢟⣀⣬⡛⢉⣀⣬⣭⡉⠉⢀⡀⠝
⠀⠀⠀⠀⠰⠁⠀⠀⠐⠒⠰⣇⡀⠀⢤⠋⢃⠐⣤⣌⠉⣛⡀⠐⡍⣉⡙⠓⠀⠙⠦⡀
⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⢉⢠⣤⣰⡄⣤⣧⡉⠉⣀⡈⢛⠛⠛⠦⠙⢟⠉⠛⠓⠚⠳
⠀⠀⠀⠀⠀⠙⢦⡀⢀⣲⠺⠁⠤⠴⠌⠁⠀⠑⢄⣤⣬⡛⠻⢯⡲⢦⠤⢄⡳
⠀⠀⠀⠀⠀⠀⠀⠙⠶⢮⡳⠦⠺⠦⢀⣠⣽⢛⡛⠋⠉⡉⠱⡦⢄⡈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠼⠃⠚⠉⠒⠤⠽⠏⠉⠉⠁⠛⠀⠈⠒⠧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢠⠖⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡤⠀⠂⠀⠹⠀⠀⠀⢸⠀⠈⠀⠰⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠱⢛⡀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠂⣈⠳
⠀⠀⠀⠀⠀⠀⠀⡠⣿⣷⢀⠀⠀⠀⠈⠀⠀⠀⠘⠀⠀⠀⢀⣰⣿⡷⠀⠀⠀⠀⠀⠀⣤⣶⡿⠃⣤⣶⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣦⣤⠛⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⡟⠻⡄⠀⠀⠀⠀⠀⡿⠿⢷⣾⡟⢻⡿⠳⣄⣠⡀⠀⠀⠀⣀⣄⡴⠺⣿⠟⣿⣶⠿⠿⡇
⠀⠀⠀⠀⠀⣀⠜⠁⡀⠙⣿⠀⠀⢠⠀⠀⠀⠀⠀⠰⠀⠀⣻⠟⠀⣄⣈⢦⣀⡀⠀⠀⢸⣶⣦⣡⡁⢸⡛⠶⠸⠷⢉⠆⠀⢈⠱⠿⠀⠞⣻⡁⢩⣍⣶⣾⠃
⠀⠀⠀⠈⣽⣿⣾⣿⣧⣤⢻⣄⠀⢨⠶⠛⠀⠊⠙⠖⠀⢰⡿⣱⣶⡿⡿⣿⣿⡄⠀⠀⠈⠹⣿⣿⣷⣾⠿⣦⢒⣤⡌⠀⠀⠈⣤⣴⣢⣶⢿⣷⣿⣿⡿⠁
⠀⠀⠀⠰⢻⣿⠈⡅⣉⣽⣿⡵⠦⠀⢀⠰⠀⠙⠀⠀⠸⢻⣷⣯⣦⣄⣇⠻⣿⠹⠀⠀⠀⠀⠉⠿⡈⠉⣧⡀⣿⠋⠉⠀⠀⠈⠉⢻⡇⣠⡎⠉⣹⠏⠀⡀
⠀⠀⠀⠀⣼⢁⣿⣿⢿⣻⡾⢛⣀⠤⠒⠀⠀⠀⠈⠐⠠⣌⠛⢿⣏⡟⣿⣆⢹⡀⠀⠀⠀⠰⣄⡀⠙⢄⣿⡟⣿⢢⡜⠀⠀⠘⣤⢚⡟⣿⣧⠐⠉⣀⡰
⠀⠀⠀⢀⣿⣾⡏⢸⣿⠇⡕⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⣷⡀⢿⣿⣇⠀⠀⠀⠀⠻⢿⣦⣼⣿⣷⡀⣰⠀⠀⠀⠀⢰⡌⣰⣿⡿⣧⣼⠿⠃
⠀⠀⠀⡼⠻⡏⢸⣿⠛⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡹⣷⣀⡟⠻⠆⠀⠀⠀⠀⠈⠹⣿⣏⠃⠹⡟⠀⠀⠀⠀⠘⡛⠁⢋⣷⡟⠉
⠀⠀⠀⠀⠀⣿⣿⡏⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠈⢿⡶⣀⣠⠀⠀⠀⠀⢠⣀⡠⣾⠏⠁
⠀⠀⠀⠀⠀⠛⡏⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠙⡈⠿⠀⠀⠀⠀⠸⠏⡠⠁⠿
⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢱⢸⠀⠀⠀⠀⢠⢠⠁⠆
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⠀⠀⠀⠀⢸⣸⡎
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡆⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⠀⠀⠀⠀⠘⣯⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⣠⠤⠀⠠⣠⣤⣬⣧⣐⣀⡀⠀⠀⣠⣐⣠⣮⣤⣬⡠⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠃⠰⠋⣾⢿⣿⠿⣏⣿⡻⠃⠀⠀⠛⢿⣝⣿⢿⣻⢿⡎⠳⡌⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣠⠘⠀⣰⣿⣿⢿⡼⣯⠃⠀⠀⠀⠀⠀⠀⢫⡿⣯⢿⣿⣷⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⠀⠠⠂⠀⠐⠁
⠀⠀⠀⠀⠘⢠⡃⠿⠻⣸⣾⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⣶⢿⣼⡸⢿⢧⢢⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠖⠶⠶⣶⣶⣶⣳⣾⠯
⠀⠀⠀⠀⠀⠈⠃⢠⡤⣿⡿⢦⡛⠀⠀⠀⠀⠀⠀⠀⠀⢣⠼⣿⡷⣠⠀⠟⠁⠀⠀⠀⠀⠀⠀⣿⡏⢻⣓⢲⣶⣯⣈⠿⢿⣿⣻⣵⣶⠄⠊⠁⣠⣂
⠀⠀⠀⠀⠀⠀⠀⢸⣷⡸⡄⢈⣧⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⡘⣱⣿⡂⠀⠀⠀⠀⠀⠀⠀⢠⣿⢩⣾⣟⠏⠉⢉⣱⣾⣿⣿⣿⡿⠟⠂⠀⠐⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢿⠀⣎⠹⣿⣟⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢁⡅⢸⠗⠀⠀⠀⠀⠀⠀⢀⣾⣳⣿⠿⣱⣶⣶⣿⣿⣭⣭⣿⡿⠗⠢⡤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⡿⠦⠀⠀⠀⠀⠀⠀⠞⢿⣷⣿⣿⠃⠀⠀⠀⢀⠀⢀⣴⣟⣿⣿⠯⣤⡾⠿⠿⢿⣿⣛⣛⣛⣛⣉⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠃⠀⠀⠀⠠⣴⡾⣽⣿⠛⣫⣽⣶⣿⣿⣿⣿⣿⡟⠁⠠⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠈⠱⣦⣿⣿⣿⣶⣾⣿⣛⠻⠟⠁⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⡿⠟⢿⠦⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣄
⠀⠀⠀⣰⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⣆
⠀⠀⡴⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣸⢦
⠀⢸⠀⢹⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡏⠀⡇
⠀⡸⡇⠸⣇⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⣸⠇⢸⢇
⢸⡁⢳⠀⠹⣆⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⣰⠏⠀⡞⢈
⡼⡇⠀⢳⡀⢹⣿⣄⣠⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⣤⣠⡿⡏⢀⡞⠀⢸
⢇⠘⣆⠈⢻⣆⢹⣅⠉⠣⣀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⣀⠜⢁⣬⡏⣰⡟⠁⣰⠃
⠈⣇⠘⢷⣄⠹⡋⠛⢄⡀⠸⣷⣦⢤⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⡤⣴⣾⠇⢀⡨⠛⢛⠟⣠⡾⠃⣸
⠀⠸⠳⣀⠙⢷⣿⣆⡀⠈⣲⣼⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⣧⣶⠉⢀⣠⣾⡾⠋⣀⠞⡃
⠀⠀⢢⠈⠳⣦⣿⣁⡉⠑⠲⢿⣆⡀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⢀⣠⡿⠖⠊⢉⣩⣿⣴⠞⠁⡜
⠀⠀⠀⠑⠶⢈⡙⢿⡷⠖⠒⠻⣿⣀⡀⠈⠑⢦⠀⠀⠀⠀⠀⠀⡴⠊⠁⢀⣀⣿⠟⠒⠲⢾⡿⠋⣡⠶⠊
⠀⠀⠀⠀⠀⠀⠀⢿⣀⡠⠖⠊⢛⣿⣤⡆⠀⠘⢆⠀⠀⠀⠀⡰⠁⠀⢠⣤⣿⡛⠓⠲⢄⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠔⠁⡼⢻⡷⢦⠄⠈⠲⠀⠀⠞⠁⠠⡴⢾⡛⢧⠈⠢⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠴⢥⣼⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣧⡬⠦⠶⠁

⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⠀⠀⡎⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢳
⠀⡦⣀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣀⢶
⠀⢷⠈⢇⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡸⠁⡞
⢠⣜⡆⢌⢆⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⡰⡁⣰⣣
⠀⢣⠙⢆⠪⡳⣄⠀⠈⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠉⠁⠀⣠⢞⠄⡴⢋⡜
⢠⣀⠳⡄⠑⢌⡠⡽⠦⣄⡀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢀⣠⠴⢯⢄⡡⠊⢠⠞⣀
⠀⠳⡉⠛⠦⡐⠍⠙⠪⣒⠭⢓⣦⣄⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣠⣴⡚⠭⣒⠕⢋⠩⢂⠴⠛⢉⠞
⠀⠀⠈⠢⣄⠈⠓⠿⣭⣉⡉⠛⡷⠊⠳⡀⠀⢹⠀⠀⠀⠀⠀⠀⡏⠀⢠⠞⠑⣾⠛⢍⣉⣭⠿⠚⠁⣠⠔⠁
⠀⠀⠀⠳⣞⠛⠒⠿⠯⢍⣈⣋⡺⣗⡂⠹⡄⠸⡆⠀⠀⠀⠀⢰⠃⢠⠏⢐⣺⢟⣙⣁⡭⠽⠷⠒⠛⣳⠞
⠀⠀⠀⠀⠀⠙⠒⠤⠤⠤⡴⢋⡦⢂⡿⣥⡜⢆⢱⡀⠀⠀⢀⠏⡴⢣⣬⢿⠐⢀⠙⢦⠤⠤⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠕⢹⢡⠾⢠⡎⡟⡹⠛⠳⠀⠠⠟⠛⡏⢻⢱⡌⠷⡌⡏⠪⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢧⠊⢧⢳⠃⠀⠀⠀⠀⠀⠀⠘⡞⡼⠑⡼⠈⠃




⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠓⠖⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠖
⠀⠒⠉⠀⠀⠀⡀⠀⠀⠄⠈⠂⠀⠦⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⠆⠀⠊⠀⠄⠀⠀⡀⠀⠀⠈⠓⠂
⠀⠈⢋⡥⢒⠁⢀⠀⠀⠀⠁⡀⠀⠐⠀⠄⠀⠀⠉⠃⠀⠀⠋⠁⠀⠀⠄⠐⠀⠀⡀⠁⠀⠀⢀⠀⢑⠢⣍⠃
⠀⠀⠀⠈⠉⠒⠓⣂⡀⠀⠀⠀⠐⠂⠀⠄⠠⠀⠀⠂⠀⠀⠂⠀⠠⠀⠄⠀⠒⠀⠀⠀⠀⣀⡒⠓⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠘⠉

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢙⠲⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⠶⢚⠁
⠀⠀⠀⠈⣒⠛⢛⣿⣿⣿⣿⣿⡲⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡶⣺⣿⣿⣿⣿⣟⠛⠓⡊
⠀⠀⠀⠀⠀⢉⠉⠉⢝⣛⣿⣿⡙⢿⣟⠿⢯⣟⣻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣛⣯⠿⢟⣯⠟⣳⣿⣟⣛⠍⠉⢉⠉
⠀⠀⠀⠀⠀⠀⠁⢀⠀⣀⣀⣵⣿⣞⡩⢳⢎⡽⢿⣿⣻⣦⣀⠀⠀⠀⡀⡀⠀⠀⢀⣠⣾⣋⣿⠻⣉⢶⠫⣙⣾⣷⣭⣀⡀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣍⡢⠔⠾⣿⣮⠔⡻⢛⣿⣿⣿⣿⣿⣿⣿⡟⠃⠛⣿⣿⣿⣿⣿⣿⣿⣿⠻⠓⢬⣾⣿⠷⠤⣂⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⡹⣿⢿⣿⣮⣎⣝⣻⣿⣿⣿⡿⠛⠁⠀⠀⠙⠻⣿⣿⣿⣿⢙⣍⣮⣾⣿⢿⡯⡓⠖
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠨⢻⣿⣿⣿⣶⣶⣶⢶⣶⣶⣶⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣤⣤⣴⣶⣶⣶⢶⣶⣶⣾⣿⣿⣿⡭
⠀⠀⠀⠀⠒⠒⠿⣛⢻⣿⣯⠻⣿⣝⠛⣶⣾⣿⢿⣦⣀⠀⠀⠀⢠⣄⠀⢀⣤⠀⠀⠀⢀⣠⣾⢿⣿⣶⡞⢛⣽⡿⢫⣿⣿⢛⡻⠗⠒⠂
⠀⠀⠀⠀⠈⢐⡚⣉⣉⡩⢿⣷⡩⡉⢛⣶⣭⣟⣿⣿⣿⣿⣿⣿⣿⠿⠃⠻⢿⣿⣿⣿⣿⣿⡿⣟⣯⣵⣼⠛⡩⣳⣿⠯⣍⣉⡛⣛⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠂⢒⣻⣿⣿⣎⢕⡉⡺⣻⢿⢟⣿⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⡟⣿⢿⠿⡊⣑⢍⣾⣿⣿⣓⠒⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠈⠟⠿⠿⠽⠾⠾⠵⠱⠷⠿⣿⣿⠿⠁⠀⠀⠀⠀⠹⢿⣿⣿⠷⠷⠱⠕⠌⠎⠨⠀⠛⠋⠐

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

⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⡷⡀
⠀⠀⠀⠀⠀⣇⠙⣄
⠀⠀⠀⠀⡀⠸⡄⠈⢧⡀
⠀⠀⠀⠀⣷⡄⠹⡄⠀⠱⣄
⠀⠀⠀⠀⢱⡘⢦⡙⣆⠀⢌⠳⣄
⠀⠀⠀⠀⠀⢧⠀⠙⢮⣳⡀⠱⣮⡳⢄⡀
⠀⠀⠀⠀⠀⠈⢧⠀⢀⠙⢿⣦⡙⢿⣷⣽⡢⣄⢲⡦⣤⡀
⠀⠀⠀⠀⢹⣦⡈⢣⡈⠳⣦⣌⡻⣦⡻⣧⡉⢈⠻⣧⢀⣝⣦
⠀⠀⠀⠀⠀⢳⡙⢦⡱⣄⠈⢻⣿⣶⣽⣾⣿⣬⡿⡷⠿⠿⠿⢷⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢳⡄⠙⠻⣷⣌⠙⢿⣿⣦⡀⣶⡟⢻⣄⢙⣷⣄⢑⣿⣯⣙⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⣌⡙⠿⣦⣙⠿⡿⠾⣿⠷⠿⠾⣏⠛⢿⣟⣻⡿⢿⣶⡍⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡈⢳⣌⠛⣿⣿⣿⠷⠾⠷⡿⠷⣄⠐⣾⡿⠾⢻⣟⢻⣦⣤⣀⠀⠀⠉⣳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡓⠿⣷⣌⠻⢿⣷⣄⡐⠿⣷⣬⠿⢿⣦⣄⣈⣻⣿⣛⣷⡶⠖⠂⠀⠈⠻⣮⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠉⠙⠢⣬⣙⡛⠷⢾⡷⠤⣌⣛⣯⣉⣀⣻⡿⣯⣿⣿⣟⣁⣀⠀⠈⣧⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣉⠻⣿⣿⠛⠋⠩⣵⣶⠞⠉⣾⣿⣟⣉⣀⣬⢿⣾⣏⡿⣷⡦⠀⢻⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠮⣝⡻⢶⣬⣍⣛⠟⠛⢻⡿⠃⠾⠿⠏⣠⣴⣏⣴⣫⢦⠀⣳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡒⠒⠚⢛⣓⣶⣦⣤⡤⣾⣿⣤⡤⠲⣶⠋⠸⠿⠳⡿⠿⢺⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⣉⣙⣿⣉⣤⣽⣿⣿⢳⣾⣯⣤⡴⠚⡇⢁⣠⠊⣀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠹⣿⢁⣠⣽⡏⠿⣃⡌⠿⣻⣿⣶⢿⣄⠉⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠒⠚⢋⡟⠙⣻⡴⠚⣻⡷⣾⢃⣴⠇⢼⡟⢇⢀⣳⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⢸⠧⠚⠁⣿⣰⢻⣤⠞⢦⡟⠼⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⠀⠀⠀⠀⠀⠤⠲⣆⠀⠀⠀⠀⠀⠀⣴⠒⡔⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢘⢺⠀⠞⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠶⡤⠦⠤⠀⠐⠤⣠⠒⠄⠒⡇⢂⠌⠀⠀⠑⠝⢒⠠⠲⡄⠤⠂⠀⠤⠴⢤⠖⠂
⠀⠀⠀⠀⠁⠀⠠⠀⣀⡀⠈⠀⠀⠀⠉⠀⢀⣀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠶⠤⣁⠀⠀⢠⢀⣀⡤⠤⠈⠀⠀⠀⠁⠤⢤⣀⡀⡄⠀⠀⡈⠦⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⠉⠉⠉⠀⠀⠤⠤⣄⢀⡤⠤⠄⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢰⠖⠀⠤⠀⠤⠄⠢⠀⠤⠐⠀⢢⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠁⢀⡀⠀⠀⠀⠠⠠⠒⠂⠀⠀⠀⠒⠂⠠
⠀⠀⠀⠀⠀⠀⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡗⠀⠀⠰⡘⠐⠀⠀⠐⠐⠰⠀⠀⠉⠀⠐⠐⠚⠉⢉⠀⠀⠀⠀⢈⠁⠙⠒⠐⠈⠈⠁
⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡆⠀⠀⢀⣦⠠⠐⢀⣣⢀⠀⠀⢀⠤⠤⠤⠤⠴⠃⣸⡀⢠⣸⠈⠢⠤⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⢁⠀⠀⠀⠈⠁⠀⠀⠀⠈⠁⠀⠉⠁⠀⠠⢄⠁⠂⢶⡄⣀⡔⣰⢇⡟⢘⡆⢷⡁⣄⡀⣴⠔⠂⣁⠤
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠐⡀⠆⠄⢀⠀⡀⠈⠉⣄⡈⠉⢁⠠⠀⠉⠛⠢⠆⢎⢼⠛⣉⠖⠁⠀⠓⣊⠙⢿⣘⠆⠄⠚⠋⠑⠤⢈⠉⠉⣠⠌⠁
⠀⠀⠂⡱⠊⠐⠁⠀⠀⠀⠐⠢⡄⠀⠆⠂⠀⠀⠀⠘⠆⠑⢌⠂⠀⠀⠉⠁⠢⣴⣂⣤⢠⠀⠤⠰⠲⠚⠃⠀⠀⠀⠀⠀⠛⠲⠒⠠⠄⢄⣤⣅⣲⡴⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⢡⡈
⠀⠀⠀⠀⠀⠄⠀⠃⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡴⡄⢤⡀⠀⣀⡄⢠⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠷⢎⣽⢹⣏⡣⠚⡁⠀⠀⢸⡉⢧⡀⠀⠀⢸⡟⣷⠀⠀⠀⠰⡟⢾⠀⠀⠀⢀⠞⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡮⣸⠨⡎⣇⡴⠁⠀⢸⠉⢧⠀⠱⡄⠀⠈⣷⣿⡖⠀⡀⣾⣧⡏⠀⠀⣰⠋⢀⡞⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠏⠀⡟⡜⠀⠀⠀⡼⢦⠈⠣⡀⠘⠄⠀⢻⣿⣶⡗⢧⣾⢿⡇⠀⡐⠁⢠⠎⢀⡜⣆
⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠀⠀⠀⠀⣠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⠰⡿⠀⠀⠀⠀⢳⡀⠑⢄⢈⡺⣌⠰⢬⡀⠉⠀⠈⠉⣈⢴⠖⣠⢇⢁⠠⠋⣠⠏
⠀⠀⠀⠀⠀⠴⣿⣄⡀⠈⢄⠀⠀⡔⠁⢀⣴⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠕⣚⠦⠴⣏⠉⠂⠄⣟⠲⠤⢤⣵⣊⠙⢃⠙⢦⡀⢠⡞⢁⡜⢋⣑⣥⠤⠤⢚⡿
⠀⠀⠀⠀⠼⢶⡀⠙⢽⣦⡦⠂⠪⣦⣶⠟⡉⣰⠶⠆⠀⠀⠀⠀⠀⠀⣈⣀⡞⣹⡇⠀⡿⡝⠤⡦⠌⢛⠒⠒⢚⣩⣄⡘⠅⢀⡇⢿⠀⡸⣐⣠⣝⠒⠒⢒⡏
⠀⠀⠀⢀⠀⠂⢹⠶⣧⡜⠁⠀⠀⠘⢤⣿⠞⠉⠄⠄⡀⠀⠀⠀⠀⠀⣁⣩⣴⢳⠄⠀⢰⡙⠶⣤⡤⠈⠙⠻⣉⡤⠋⢒⠩⡜⠀⠸⢧⢙⠆⠁⢄⣉⠟⠋
⠀⠀⠀⡞⠙⠒⢦⣤⣰⡆⠀⠀⠀⠀⢰⣀⣤⠖⠒⠙⡇⠀⠀⠀⠀⡀⠉⠉⢐⡼⠀⠀⠈⢣⣄⠀⠀⠠⡤⠀⠀⠙⠚⠓⠶⠛⠀⠐⠳⠶⠛⠛⠋
⠀⠀⢠⡇⠇⠀⡄⠂⢸⡆⠀⠀⠀⠀⢠⣆⠀⡂⠀⠆⢳⠀⠀⠀⣸⣥⠤⠶⠋⠀⠀⠀⠀⣠⠬⢼⡃⠓⠛⠂⠀⠀⠀⠀⣀⠤⢤⡀
⠀⠀⢈⠋⠤⠳⢣⠬⡼⠀⠀⠀⠀⠀⠸⡍⢤⠳⠖⠌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡠⠆⠌⠁⡜⡏⠀⡏⡇⠈⠤⠲⣀⠙⠦⡀
⠀⠀⠀⢆⠀⢨⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⡁⠀⠣⣤⠒⠄⠏⡈⡅⠀⡍⢈⠅⠔⠂⡤⠓⠀⠌⢢
⠀⠀⠀⠈⣰⠚⣝⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢓⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⠜⠈⢇⡼⠠⠢⡀⠉⠁⠀⠉⡇⣠⠣⠘⣄⡽⠀⣇⣈⡄
⠀⠀⠀⠰⣿⣶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣾⡼⠀⠀⠀⠀⠀⢀⡠⠔⢀⡠⠁⠈⠀⡈⠀⡘⢀⡉⠁⠀⠀⠀⠉⢡⠀⡄⠈⠄⠈⠀⠱⣄⠑⠤⣀
⠀⠀⠀⠀⠾⣆⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⣾⠇⠀⠀⡤⠖⠊⣁⣠⡶⠋⣠⠎⢀⡼⠀⡴⢧⡼⠀⠀⠀⠀⠀⠀⠘⢤⠼⣄⠘⣦⠀⢣⣌⠳⢦⣄⡉⠒⠦⣄
⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠙⠒⠉⢏⡥⠔⢿⡡⠔⠉⠣⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠊⠙⠦⣉⡗⠦⢍⡿⠉⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⣠⣤⠴⠶⠒⠄⠀⠀⠀⠀⠀⠓⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡴⢌⣇⠀⠀⠈⠃⠀⠀⠀⠀⠀⣤⠀⣰⡶⠋⠀⠀⡬⠙⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⢐⣿⣀⣤⠛⠢⡭⡳⢀⡀⠠⠀⠀⡀⠀⠀⡁⣰⣛⠁⠀⢀⠒⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⡟⠂⠁
⠀⠀⠈⠁⠀⠀⠀⠹⡭⢏⣀⠈⠒⠟⠛⠁⠀⠀⠀⢨⠃⢰⠠⣆⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⣤⣯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠂⣀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁⣞⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⡠⡤⠖⢙⠒⠂⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⢆⠀⢀
⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠐⠀⠀⠀⢀⣀⠄⠀⢀⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠛⠄⡀
⠀⠀⢀⡈⠄⠁⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡈⠑⠀⠀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢿⡿⣠⣄⠙⠆⠀⠀⠀⠀⠀⠀⠠⠀⣸⡛⠇
⠀⠀⠀⠀⡈⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠪⠂⠈⠞⢱⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⣼⡁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⡀⠀⠀⠀⠀⠀⢠⣿⢁⠀⠠⠆⠁⢫⣄⠀⠐⣀⡀⠀⠀⠀⠀⠀⠹⣇⠀⠀⣀⡈⢂
⠀⠀⠀⠀⢄⠀⠀⠹⢿⣄⠐⠀⠀⢀⠀⠀⡞⠹⠈⠀⠀⠀⠀⠞⡽⣿⠺⠜⠃⠀⠀⠀⠀⠀⠀⠛⣧⡄⠙⠿⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠉⠻⢷⣀⠀⠘⠁⠀⠃⠀⠀⠀⠀⡁⠂⠘⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠐⠈⢻⣧⣤⣄⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⢄⠀⠀⠀⠀⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⣙⣕⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣮⡑⣄
⠀⠀⠠⠤⠔⠺⠀⠀⠉⢧⡄⠘⣆⠀⠐⢄⠀⠀⠀⠀⠐⠀⢰⣿⢂⡇⠄⠀⠀⠀⠀⠀⠐⠠⠽⠅⠀⠘⡆
⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠁⠮⢑⠀⠀⠁⠒⠀⠀⠀⠀⠉⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶
⠀⠀⠀⠉⠂⠞⠐⠁⠀⠂⠀⠀⡀⠀⠀⠳⠤⠀⠀⠀⠀⠀⠈⠉⢿⣇⡑⡀⠀⠀⠀⠀⠀⠠⠀⠰⣆⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠻⠶⠶⠃⠀⠀⠀⠈⠀⠀⠾⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠰⣄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢀⡤
⠀⠀⠀⠀⠀⠹⢦⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣰⠇
⠀⠀⠀⢠⠀⠀⢡⡳⣄⠘⣝⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣾⠇⢠⣴⡏⠀⣴
⠀⠀⠀⠈⢳⣄⠀⠹⡈⠣⡘⢎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣴⣿⠏⠀⢸⡏
⠀⠀⠀⠀⠀⠫⡳⣄⠈⠢⡈⠢⣧⠈⢷⡀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡀⣻⣿⣿⣿⣿⣷⢋⣴⣡⠟
⠀⠀⠀⠀⠀⠀⠙⢌⠳⢄⠘⡄⠀⠀⣤⢫⠂⣽⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣶⣼⣿⣽⣿⣻⡿⢵⡿⣻⠏
⠀⠀⠀⠀⢠⣄⠀⠈⠳⢄⠑⠻⣄⠠⣌⠃⠱⡄⠑⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣽⣿⣿⣷⣿⣿⣻⣻⣷⣿⡿⠁⢀⣤
⠀⠀⠀⠀⠀⠙⢅⠢⢄⡀⠱⡀⠈⠣⡹⣗⠀⣀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣩⣿⣵⣿⣻⠿⢋⣠⣶⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠑⠄⣈⠁⠚⢦⠀⠘⣬⡀⢀⠁⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣻⣯⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠉⠢⡀⠑⢦⡈⠢⣀⠀⠀⠀⠀⡀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠟⠋⢡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠫⡁⠒⠬⠶⣄⠈⠻⢞⡓⠢⠀⠀⠄⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣋⣿⡿⢿⣿⣯⣶⣿⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠂⠤⢄⠀⠠⣤⡍⠐⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⡿⠟⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⡐⠒⠶⠷⠦⢀⣉⠓⠦⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⣷⣾⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⡲⠤⠠⢄⠙⠳⠖⠖⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣵⣿⣿⣛⣿⠿⢿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⣤⠄⠊⣹⠋⠀⡄⠀⠀⠂⠈⢁⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⣾⣟⣛⣿⡭⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⠠⢤⡶⠋⠋⣙⣀⡴⠃⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣶⣝⣿⣿⣯⣥⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠐⣲⠋⣉⠁⠶⠴⣾⣿⣿⣿⡿⣿⣿⣿⡿⣿⣿⣹⡿⣿⡟⢿⡧⠼⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠠⠾⠄⣰⢀⡜⢿⣞⡟⠋⠓⢿⠞⣷⢻⡟⢿⠯⣽⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠘⠉⠀⠀⠀⠀⠙⠛⠒⠿⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣴⠀⢀⡄⠀⠀⢀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⢄⡤⠠⣞⣻⠷⠟⣓⣭⠾⢃⠞⠀⠀⠀⠀⡀⠄⢂⡱⢁⠴⠃⣠⠼⠒⠀⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⢒⡟⢓⠃⡼⠯⠭⠗⣒⣚⣩⣥⠴⠊⣥⠆⠀⠀⠐⢪⣷⣾⢟⣫⠵⠒⣉⣀⡬⠶⣺⠍
⠀⠀⠀⠀⠀⣤⡾⠿⡿⢁⢈⣀⣶⣭⣭⡭⠭⠭⠭⠤⠶⠶⢖⣫⠅⠀⠀⢹⢦⡋⣼⡧⠝⠉⠁⣀⡀⢀⡀⠈⠁
⠀⠀⠰⢁⣾⡿⣡⢋⣴⡺⢟⡫⢴⣊⠭⢉⣙⠛⠛⠒⠚⣛⡍⠁⠀⠀⠀⠁⠚⣿⢰⡟⠙⣭⣤⡤⠐⠋⠁
⠀⠀⠀⢸⢿⡼⢁⣼⣿⣯⣷⣌⡓⢮⣝⣓⠶⠯⠭⠿⠟⠀⠀⠀⠀⠀⢠⠂⡄⠹⡾⣃⣒⣚⠟
⠀⠀⣰⠟⡤⠚⠈⠉⠉⠉⠉⠙⠛⠙⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣹⣟⡩⢭⠏
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢹⡏⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠟⠿⢛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⡀⠀⡀
⠀⠀⠀⠀⠀⠘⡝⢦⠹⡀
⠀⣤⣀⠀⠀⠀⠙⣄⢙⢿⣄
⠀⠈⠪⣙⠒⠦⢄⡈⠢⡑⠈⠛⠦⣤⣀⡀
⠀⠀⠲⣚⠳⠦⣔⡀⠍⡉⠓⠤⢀⡀⠉⠉⠉⠉⢝⠉⠉⣉⠟⠛⠒⠦⣤⣤
⠀⠀⠀⣬⣕⣤⣀⡈⠙⠒⠢⠤⠀⣀⡁⣖⠁⠀⠈⣗⠒⠈⠂⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠈⠑⠦⢌⣉⠙⠒⠒⠤⠤⠤⠤⠀⠹⣁⠀⠈⠋⡉⠁⠀⠀⠀⡴⠂⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠐⠮⣉⡙⠛⠓⠒⠒⠒⠒⠒⠒⠊⠉⢹⡭⠀⠀⠀⢀⣰⣉⠓⠀⠀⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠲⣛⡛⠛⠒⠒⠒⠒⠒⠈⠉⣀⠧⠀⣤⢀⡀⢣⠤⠌⠁⠀⠀⢱⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⡶⠶⠚⠒⠒⠈⠉⠀⣀⠄⠊⢉⡠⠌⡖⠂⠀⢄⡀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠿⠭⠝⣟⣁⣠⠖⠁⡠⠔⢚⡥⠀⠀⢤⠀⠀⠘⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⣤⠊⢀⡔⠉⡲⢴⠂⠀⢚⡠⠀⡀⠈⠙⠲⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣃⢴⠋⣀⡔⡑⡨⠂⡦⠈⠡⠔⡣⣠⡀⣀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠒⠹⠬⠚⣧⢾⢀⡆⢰⣀⡇⢰⢸⡅⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠑⠋⠛⠑⠃⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣽
⠀⠀⠀⠀⠀⠀⣆⠀⢳⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣰⠃⢀⡆
⠀⠀⠀⠀⠀⠀⢻⡳⣄⣧⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⣇⡴⣻⠃
⠀⠀⠀⠀⠀⠀⢀⠙⣌⠻⢧⡀⢈⢦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⢎⠀⣠⠿⢋⡼⢁
⠀⠀⠀⠀⠀⠀⠸⣷⢼⣆⠀⠙⠦⣕⢭⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⣿⢕⡥⠞⠁⢀⣾⢴⡿
⠀⠀⠀⠀⠀⠀⠀⡈⠢⣍⠳⢦⣕⠮⣙⢿⣧⡙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⣡⣿⢟⡩⢖⣥⠶⢋⡥⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣗⠮⣧⣀⠨⣙⠺⢿⣧⡙⠳⣮⣝⢦⡀⠀⠀⠀⠀⠀⠀⣠⢞⣭⡶⠛⣡⣿⠿⢚⡩⢀⣤⡯⢖⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢢⡉⠙⠒⠯⢷⣿⣙⠺⣿⣿⡄⢳⠀⠀⠀⠀⠀⢰⠃⣼⣷⡿⠚⣹⣷⠯⠗⠚⠉⣡⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣗⠶⠬⠵⣾⣯⣑⠻⣿⣇⣿⠀⠀⠀⠀⠀⢸⣇⣿⡿⢓⣩⣿⡶⠯⠴⢖⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢿⡒⠲⠶⠿⢦⡬⠿⣿⣜⣆⠀⠀⠀⢀⣞⣼⡿⠯⣤⠾⠷⠖⠒⣺⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⣓⣒⣛⣛⣿⣋⡽⢿⣷⡄⣴⣿⠿⣭⣻⣟⣛⣓⣒⣛⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠭⢥⠤⠚⣫⠾⣵⠝⠀⠘⢵⡽⢮⡓⠢⢤⠭⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠚⠐⠈⠀⠀⠀⠀⠀⠈⠐⠙⠂⠈⠁

⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠃
⠀⠠⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠱
⠈⠀⣄⠀⠠⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢀⡔⠈
⠴⡀⠀⠀⠀⢀⠀⠀⡀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠁⠀⡀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⢑⠀⠑⢄⢈⢦⡐⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠑⣠⢎⢀⠔⠁⢀
⠉⠢⠀⠀⠀⠑⢄⠌⢿⡄⠙⣆⠈⠳⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢀⡞⠁⣼⠏⢄⠔⠁⠀⠀⠠⠊
⠠⢄⠀⢀⠘⢄⠀⠳⡄⠙⠄⠈⡁⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⡉⠀⠜⠁⡴⠃⢀⠜⢀⠀⢀⠤
⠀⠀⠑⢄⠙⠦⣝⣦⠙⢂⡀⣥⠛⢀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⢀⠘⢣⡅⣀⠚⢡⣞⡥⠞⢁⠐⢁
⠀⠰⠲⠄⠙⠲⠬⢭⠛⠂⢁⡌⠑⠼⣜⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣼⠔⠉⣠⠁⠚⢫⠭⠴⠚⠁⠴⠢
⠀⠀⠀⠀⣈⠐⠲⠤⠤⠲⠀⠯⠉⠙⣳⡈⠙⡳⢄⠀⠀⠀⠀⠀⢀⠴⡛⠉⣰⡛⠉⠩⠇⠰⠢⠤⠤⠒⢊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢲⣂⣒⡣⠤⢀⡏⣐⠟⢢⣄⠀⢀⣤⠚⠖⡈⣇⠠⠤⣓⣂⣲⠚⠒⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡩⠥⠚⣠⠞⣡⢔⣊⠈⠋⠤⠀⠠⠜⠏⢈⣒⢤⡙⢦⠘⠢⠬⡉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠡⠠⡄⠁⠘⠀⠘⠀⠀⠀⠀⠀⠘⠀⢘⠀⢁⡤⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣚⣩⣭⣭⣭⣀⣲⣴⣿⣷⣤⣤⡄⣙⣷⣶⣀⡀⠀⣠⣤⣿⠥⠠⠤⠄⠀⠀⠠⠐⢶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⣿⣭⠿⣋⣹⣿⣎⡛⣿⣯⣅⣢⣽⣽⡿⠿⠿⣿⣿⡿⠛⠍⠀⠀⡀⠀⠀⣀⣀⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⡠⣫⣾⣿⣿⣉⠻⣷⡦⡙⢿⠿⣦⣾⣿⣿⢏⡛⢿⣯⡒⠦⠄⠙⠻⣿⣶⣾⣿⣿⠿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⣴⣵⣿⣿⣿⡿⣭⡳⢼⣿⢶⣭⣶⠻⣿⣿⡻⣤⣽⣀⣉⣻⣿⡿⣿⣿⠿⠿⠙⠃⠐⠒⠒⠖⠂⣠⣤
⠀⠀⠀⠀⠀⣐⣾⣿⣿⣿⣿⣟⣮⠙⣦⣽⣷⣦⣿⣀⠘⣿⡕⢌⡻⣟⢟⡻⢿⣿⣶⣤⣉⣂⠀⠀⢀⣀⣀⣤⣴⠟⠁
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣏⢹⡿⢷⣦⣾⣿⡟⠛⢻⣿⣿⣿⣦⣁⠈⣳⣝⠢⣍⠫⢝⠛⠻⠿⠿⠿⠿⠛⠉
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠶⣿⣬⣿⣿⣯⠻⣦⣤⣹⡿⣿⣿⣿⣿⣿⣯⡓⠦⣀⠀⠙⠢⢄
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣯⣷⡿⢺⣿⣿⣿⣦⢹⣿⡛⠳⣌⠻⣿⣿⠿⣿⢿⣶⣦⣉⣓⠒⠀⣙⣶⡄
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡿⣿⡿⡟⠋⢿⣶⣮⡑⠮⠻⣷⣤⣉⣹⣯⡙⠛⠛⠛⠛⠉⠀⠀⠀⠀⣶⡀
⠀⠀⠸⣿⣿⣿⣿⣿⣿⡯⠽⣿⢿⣿⣷⡹⡽⣷⡘⢆⠈⢻⣟⣟⠳⡀⠸⣯⡛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣷
⠀⠀⠀⣿⣿⣿⣿⣧⣙⢻⡶⠾⠀⠉⠘⢷⣾⠿⢿⣾⣀⣸⡟⠻⠷⣼⣦⡿⠟⠀⠀⠀⠀⠠⢶⠀⠀⠀⠀⠀⡞⠠⡟
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡎⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣡⡎⠀⠀⠀⠀⡜⠀⣸⢣⡆
⠀⠀⠀⢹⣿⣿⣿⢿⣿⠿⣶⣾⠆⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣠⢞⣿⣿⠅⠀⠀⠀⣼⣇⣴⡯⠃⡟
⠀⠀⠀⠈⣿⣿⣿⣮⣙⣷⠀⠀⠀⠀⠀⢀⣢⣭⣯⡔⠁⣀⣔⣦⡶⣾⡍⠀⢀⣼⡕⣻⣷⡿⠀⠀⢀⣾⣿⣿⡟⠁⣾⣃
⠀⠀⠀⠀⠘⣿⣿⢿⡛⠋⠀⠀⢀⣶⣿⣿⡷⣟⡟⢀⣾⣿⣿⣿⣿⣿⠃⢰⣯⡿⡿⣶⣯⠏⠀⢠⣾⣾⢟⡿⣠⣾⠗⡿
⠀⠀⠀⠀⠀⠛⠹⣏⢻⡄⠀⢠⣿⢽⣿⣿⣯⣽⠁⣾⣾⣿⣿⣿⣾⠏⠀⣿⣿⣿⣿⣿⣏⡄⢠⣿⣿⡥⢚⣿⡟⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇⠀⠘⣿⢏⣿⠿⣾⠟⠀⠹⣟⣿⣿⣿⣥⠀⠀⢿⣿⣿⣿⣟⣻⠂⢸⣿⣿⣶⠴⢻⡿⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣸⣿⣧⣈⠁⠀⠀⡿⣿⣿⡢⠍⠀⠀⢈⣿⣿⣿⢟⣫⠀⠘⣿⣿⣷⠀⣽⠿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣷⣿⣿⣛⠂⠀⠀⢺⣿⣿⡻⠍⠀⠀⢤⣾⣿⣿⣿⢿⡅⠀⣠⣻⣿⣯⣭⢿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡷⡍⠀⠀⠀⠈⠛⠻⠍⠀⠀⠀⠈⢿⡠⠣⠋⠊⠀⠀⠀⢻⣿⣭⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⣻⢛⡟⣻⠟⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡴⠾⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣉⠉⢉⡉⠀⠄⡀⠀⠈⠁⠀⠐⠢⠤⣄⣤⠄⠀⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢆⠀⠀⠀⠁⠀⠃⠀⠂⠈⠻⣀⠀⠒⠒⠢⢤⡀⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⡆⠀⠀⠀⠂⠀⠀⠠⡀⠀⠈⠣⡁⠀⠀⠀⠈⠑⢄⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠈⠢⠀⠐⡄⠀⠀⠈⢄⠀⠀⠀⠀⠀⠑⠖⠀⠀⠁⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁⡀⠠⠀⢀⠈⠢⡀⠀⠀⠀⢁⠀⢹⢦⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣀⡀⠀⠀⠑⠄⠀⠀⠀⠁⢎⠀⠀⠁⠢⣄⠀⠨⡒⠂⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠑⢀⠀⠀⠈⠄⠀⠀⠀⠀⠳⣤⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠱⡀⠀⠐⣄⠀⠠⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠿⠀⢰⠀⠀⠀⠱⡀⠀⠁⠀⠐⠞⠒⠠⠄
⠀⠄⠀⠀⠃⠀⠀⠢⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠳⠄⡀⠀⠀⠀⠄
⠐⠦⣀⠔⠀⠀⡆⠀⠇⠀⠀⠀⠀⠀⠈⡧⡀⠀⢸⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⢄⠀⠀⠧⡀⠀⠀⠈⠢⠸⠂
⠀⠀⠀⠀⠆⠀⠀⠄⠀⠀⠂⠀⠀⠑⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠁⠀⠀⠀⠀⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠐⢄⠑⠀⠈⢁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠐⢂⠁⠀⠐⣁⠔
⠀⠐⢉⡀⠀⠀⠄⠉⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠡⠄⠀⠀⣈⠑
⠀⠀⠑⢄⡀⠀⠐⠒⠚⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡝⠒⠂⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⢀⡀⠈⠉⢔⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⣐⠌⠉⠀⣀
⠀⠀⠀⠀⠐⠀⠀⠀⠔⠈⠐⢠⢀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢠⠈⠈⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠐⠘⠁⠄⠈⠀⠃⠂⠈⡀⠒⠂⠒⠂⡈⠈⠃⠓⠈⠀⠄⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⡀⠢⡀⠢⠁⠁⠀⠀⠁⠡⠂⡠⠂⡘⠀⠄

⠀⠀⠐⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂
⠀⠀⠀⠘⠮⠙⠛⠛⠛⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠂⠉⠀⠀⢉⠵⠂
⠀⠀⠀⢁⣀⠀⠀⠀⠀⠠⣄⣙⡟⢦⣀⡤⠤⠤⠴⠶⠶⠶⢦⣄⢀⣴⠒⠒⠒⠢⠤⠤⢤⣀⡄⣡⣎⣠⠄⠀⠀⠈⠉⣀⡀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⣀⠀⠀⠀⠀⠀⠈⠁⢿⠉⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⢶⠿⠿⠀⠀⠀⠐⠲⠇⠘⢶⡄⠀⢀⡀⠀⢀⡵⠂⠠⠖⠛⠂⠀⠘⢿⠿⡶⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠉⢿⠀⠀⠀⠋⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠙⣄⠀⢀⡿⠉
⠀⠀⠀⠀⠀⠀⠈⠁⠀⢤⠂⢱⣼⣦⣤⣤⣴⣦⣄⣰⡀⠀⠀⢺⡿⠀⠀⢀⣆⣠⣴⣦⣤⣤⣴⣥⣮⣤⣿⢢⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⠾⣷⣠⠿⠟⣿⣷⣤⣀⣼⣇⣴⣤⣾⣿⠉⢻⡇⠾⠷⣖⠂⠀⠀⢹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠉⠋⢩⡿⠿⠿⢿⡟⠻⠉⠹⣿⠟⠛⢻⡿⠿⠛⠻⢯⡙⠉⠁⠀⠀⢀⡈
⠀⠀⠀⠀⠀⠖⡋⠀⠈⡏⠀⠀⠀⢀⣰⣉⣀⠀⠒⠶⢦⡀⠀⠀⠁⠀⠀⣠⡤⠤⠄⠀⣀⣀⡀⠀⠀⠂⢹⠀⠀⠙⠒
⠀⠀⠀⠀⠀⢰⢁⠀⠀⠇⠀⠀⠀⠋⣤⠞⠛⢛⠋⠈⢻⣷⣄⣀⢀⣐⣊⣁⣶⡶⠒⡛⠛⠳⢬⢻⠀⠀⠸⠀⠀⡈⡆
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢸⠁⡀⢠⣼⠇⠀⠘⣿⠿⣿⣿⣿⠿⣿⡿⠀⠰⢧⡄⢀⠀⣧⠀⡗⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡸⡖⠁⢸⣧⡁⠂⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣼⡇⠈⣆⡿⢸
⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠛⠀⢻⠀⢉⡿⣹⠟⠒⠶⠶⣿⣿⣿⣶⣶⡖⣾⡟⣿⡟⠀⣿⠃⠀⠑⡜⣦⣳⢀
⠀⠀⠀⠀⠀⠀⠙⠱⡀⠀⠀⠀⠀⠀⠀⠣⠘⣧⣾⠀⣿⡗⢱⠃⠿⠻⣎⢹⡅⠸⣷⣿⢃⡜⡿⠀⠀⠁⠛⢠⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⣀⠀⠀⠀⠳⣄⠹⣿⡀⣿⣷⡿⠷⣿⠶⢿⣾⣿⢀⣿⢿⣿⠄⠀⠀⣶⡀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡄⠀⠄⢀⠘⠳⡜⡓⢿⣏⠀⢀⠀⠀⠀⣹⡿⣾⢃⠞⡃⢠⠀⢠⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠀⠐⠀⠀⢹⡄⢃⣰⠀⢛⣠⢆⡌⢠⡏⢠⠀⠀⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠦⠍⢁⠀⠒⠉⣚⠻⢾⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠈⢹⠇⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⢀⣤⠀⠋

⠀⠀⡄
⠀⠀⠀⠀⠂⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠔⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡀⠒⠠⢔⡀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⣇⡄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⢁⠠⠀⠤⠤⠤⠤⡀⠀⠄⠀⠤⢈⠀⡄⠀⢀
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⣾⣧⠃⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢸⡥⠂
⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⠼⣛⡽⠆⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀⠀⢤⠀⠀⣱
⠀⠀⠀⠀⠀⠀⠀⣀⡿⠛⠀⠈⠁⠀⠀⠀⣼⠶⠿⠿⣾⣧⡀⠀⢸⣦⠀⠷⠿⣏
⠀⠀⠀⠀⠀⠨⠉⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡀⠀⠙⢇⠼⣿⣿⡏⠁⠀⠀⠀⠉⠙⠂⠄⡀
⠀⠀⠀⠀⠀⠘⡁⠀⠀⡰⡏⠀⠀⠀⢀⣾⣋⠄⠀⠀⠀⢻⡉⠻⠙⠦⠀⠀⠀⠀⠀⠀⣀⠀⠑⢤⣀
⠀⠀⠀⠀⠀⣸⢀⠀⠀⠀⡷⠀⢸⠀⢸⢋⠴⢶⣦⣸⡄⠁⠀⢀⠀⠀⠉⠉⠢⣄⣠⣸⣯⣤⡈⣱⠋⡆
⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⡈⡄⣿⡇⢳⣄⣾⠉⢻⡀⠰⡀⠑⡇⠀⠀⠀⠀⠀⠈⠉⠉⢹⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢳⠘⢾⣿⠊⡦⠩⢅⣒⣟⠷⣶⣤⣹⡄⠀⠀⠀⠀⠀⠀⣠⣼⠁⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠆⢀⡀⠀⠈⠈⠙⢻⠶⠛⠁⠙⣆⢰⠓⠂⠉⡛⠷⠤⠤⠔⠚⠉⣙⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⣀⣠⣄⣀⣈⣡⣠⣀⣀⢹⡀⠠⠖⠂⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠣⣀⡴⠶⠤⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣶⣶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡘⢦⡀⢄⣠⡶⠒⠛⠙⢷⣚⠛⠛⠒⣋⡿⠗⠒⡲⢤⣆⢠⠇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢷⣄⠉⠲⢿⡦⠀⠀⠉⠛⠶⠂⠀⠀⠶⠚⠉⠀⠀⠐⣿⠁⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⡌⣻⣷⣄⠔⠀⠀⠀⠐⢦⡍⠀⠀⠀⠉⠀⢀⡀⠀⠀⠲⢄⠀⣿⣧⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⣲⣿⣧⣤⣿⠁⢲⣦⠴⣿⢶⣄⠁⠀⠀⢰⠀⢸⢋⣴⡶⢦⡴⠀⣦⣙⣿⡯
⠀⠀⠀⠀⠀⠀⠀⢤⣬⢿⣿⠀⠋⢹⠀⡈⠃⠓⢿⠾⢻⡆⠀⠁⠀⠈⠱⠻⢬⠷⡺⠁⠀⠈⣤⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡿⠶⢦⡞⣰⡷⠈⣲⠟⢤⡀⢠⠤⣄⣀⣠⣄⠠⠀⠙⢄⠰⣧⢫⡁⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢠⣿⠀⢹⢛⣿⢻⣶⣢⠈⠚⠲⡆⢠⢰⠄⠀⢴⣾⣿⠯⢻⡉⣿⡀⢸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⢛⡿⠀⢘⡇⠘⢸⣿⣅⣁⡀⠀⠙⣻⠃⢀⣀⣠⣝⠛⠋⠯⢴⣿⠏⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠂⠹⣦⣾⣁⣀⣼⡿⣿⠉⣙⣛⡛⢛⣛⣋⠙⣿⡏⠙⢻⣶⣶⠏⢩⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠲⢾⠉⣹⠏⡀⣻⡝⡆⡿⠿⢿⡿⠟⣿⠸⣿⣀⢴⣉⢉⡤⠒⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣠⡙⠉⣷⢻⡷⣄⣀⣁⣴⣿⢰⡇⢁⣀⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣴⡟⣾⡇⣛⣛⣛⣃⣿⢷⠷⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⢘⠬⣛⠭⠀⠭⢝⣫⡎⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⢀⡤⠆⠀⠀⠲⠤⠹⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣁⡀⣀⣄⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠛⠹⢧⡿⠅
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣭⣴⣭⣿⣼⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡏⠀⠀⠀⠀⠀⢹⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠏⠋⠀⠀⠀⠀⠀⠀⠀⠙⠹⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⣠⣾⣿⣿⣿⣿⣿⢿⣿⠏⠿⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠿⠹⣿⡿⣿⣿⣿⣿⣿⣷⣄

⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿
⠛⠛⠻⢂⣤⣤⡞⠻⠛⢧⣤⣤⣜⠻⠛⠛⣠⣤⣤⡿⠿⠿⢧⣤⣤⡼⠿⠻⢿⣤⣤⣴⠟⠛⠻⣤⣤⣤⡸⠛⠛⢓⣤⣤⣤⠿⠛
⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣯⠀⠀⠀⣿⣿⣿⡁⠀⠀⢺⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣷
⣶⣶⣾⠏⠉⠉⣹⣶⣶⡎⠉⠉⠁⣶⣶⣶⠈⠉⠉⣷⣾⣶⡏⠉⠉⢹⣾⣶⣾⠉⠉⠉⣾⣾⣶⠏⠉⠉⢹⣶⣶⡏⠛⠉⠙⣶⣶
⠿⠿⠿⣆⣀⣀⡼⠿⠿⢇⣀⣀⣸⠿⠿⠿⣄⣀⣀⡿⠿⠿⣇⣀⣀⣸⠿⠿⢿⣀⣀⣰⠿⠿⠿⣃⣀⣀⡸⠿⠿⢧⣀⣀⣐⡿⠿
⠀⠀⠀⣾⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠁⠀⠀⢸⣿⣿⡇⠀⠀⢨⣿⣿⣿⠀⠀⠀⣽⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣶⣶⣶⡙⠋⠛⢳⣤⣶⡜⠋⠛⢻⣶⣶⡶⠟⠛⠛⠦⣤⠤⣜⠛⠛⢡⣦⣶⣼⢛⠙⠛⣶⣶⣶⠟⠛⠛⢳⣦⣴⡎⠛⠛⢻⣶⣶
⣿⣿⣿⠄⠀⣀⢸⣿⣿⡇⠀⠀⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⢸⡏⠉⠀⠈⠈⠁⠉⠉⠻⠥⠄⡀⢸⣿⣿⡇⠀⠀⠘⣿⣿
⠀⠀⠀⣾⣿⣿⡇⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠄⠀⢰⣿⣿⣯⠁
⣤⣤⣤⠿⠟⠟⢧⣤⢄⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢃⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣠⣤⣼⠛⠛⠷⣤⣤
⣿⣿⣿⠆⠀⠀⠨⣫⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡇⠀⠀⢀⣿⣿
⠉⠉⠉⣿⣶⣾⡉⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⢵⣲⣾⡯⢀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⣶⣷⣾⠈⠉
⣀⣀⣀⡿⠿⠿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣀⣈⣁⣼⠿⡿⢧⣀⣀⣘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣄⣀
⣿⣿⣿⡂⠀⠀⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⣿⣿⣿⡗⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢘⣿⣿
⠛⠛⠛⣷⣤⣦⡾⣻⠟⣽⣯⣿⣿⠁⡛⠓⣴⣤⣤⡟⠛⠛⢷⣦⣤⡞⠛⠛⢻⣦⣦⣦⠐⠐⠀⣀⠀⡀⠀⠀⠈⠢⣵⣤⣴⠛⠛
⠀⠀⠀⢿⣿⣿⡚⠫⠀⣹⣿⣿⣧⠀⠀⢀⣿⣿⣿⠃⠀⠀⣸⣿⣿⣿⠀⠀⢸⣿⣿⣿⠀⡀⢀⣿⣷⣷⡄⠠⠀⢄⣹⢿⣿⠂
⣿⣿⣿⡆⠁⠀⣼⣿⣿⡇⠀⠀⢸⣿⣿⣿⠁⠀⠀⣿⣿⣿⡆⠀⠀⢸⣿⣿⣿⠀⠀⠨⣿⣿⣿⡅⠀⠈⢸⣷⣷⡇⠀⠀⢘⣿⣿
⠿⠿⠟⣣⣄⣠⡞⠻⠿⢣⣄⣤⣸⠿⠿⠿⣆⣀⣠⠻⠟⠻⢃⣄⣀⡼⠿⠻⠿⣤⣠⣴⠿⠟⠻⣤⣤⣤⡼⠿⠿⢳⣀⣄⣌⠻⠿
⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣿⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿
⣶⣶⣶⡍⠉⠉⢱⣶⣶⡎⠉⠉⠙⣶⣶⣶⠉⠉⠉⣷⣶⣶⡏⠉⠉⢱⣶⣶⣾⠉⠉⠉⣶⣶⣶⡉⠉⠉⢱⣶⣶⡎⠉⠉⠩⣶⣶
⠿⠿⠿⢅⣀⡀⠼⠿⠿⣇⣀⣀⡰⠿⠿⠿⢀⣀⣀⡿⠿⠿⣇⣀⣀⣸⠿⠿⢿⣀⣀⡀⠿⠿⢿⣀⣀⣀⡸⠿⠿⢧⣀⣀⣈⡿⠿
⠀⠀⠀⣿⣿⣿⡏⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⠁⠀⠀⢸⡿⣿⡏⠀⠀⢸⣿⣿⣿⠂⠀⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⣯
⣶⣶⣦⠟⠙⠛⢳⣤⣴⡾⠛⠛⢫⣤⣴⣤⠟⠛⠛⣷⣤⣴⣫⣛⣛⣱⣦⣶⣤⠛⠛⠛⣶⣴⣦⡙⠛⠛⢣⣴⣦⡾⠋⠛⢱⣦⣤
⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿⣿⠀⠀⠀⣿⣿⣿⡟⠉⠉⢹⣿⣿⣿⠀⠈⠀⣿⣿⣿⡇⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡤⢀⣀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⡄⠀⠀⠈⠉⠉⠓⠒⠂⠀⠉⠉⣁⣀⡄⣴⠋
⠀⠀⠀⠀⠀⢀⠀⠀⠐⠢⠴⠤⣠⣃⡼⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⢧⣙⣄⡤⠦⠔⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠠⢄⠀⠙⡙⠀⠀⠈⠢⠈⢄⠠⠄⡠⠀⠖⠁⠀⠠⠋⠋⠀⣠⣴⠖⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠈⠦⣀⠀⢀⣣⣴⣠⣄⣠⠀⠀⠀⠈⠀⠀⠁⠀⠀⢀⣄⠀⢠⡀⠘⠛⠁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⡀⠛⢛⣦⠀⠀⠹⡏⠀⠀⣴⡛⠛⠀⠀⢿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠍⠁⢺⣿⠓⠦⠴⠳⡖⠙⣿⡷⠈⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⠀⠀⠀⠙⢧⠈⠀⠀⠀⣽⠋⠷⠤⡴⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⡷⢶⣴⡐⠈⠀⠀⠀⢸⠀⠃⠀⠀⠠⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠋⡟⢁⢈⡀⠀⠀⢘⡄⠩⣄⡐⣌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡶⡻⠁⡬⠥⢤⣀⣘⡡⠀⡾⢵⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣱⢄⡀⠀⠀⠒⣉⢵⡱⠷⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠉⢑⠚⡛⡋⠁⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠤⠴⠛⠁

⡀
⠀⠀⠨⣄⠂⠀⠀⠀⠀⠠⠤⠤⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠶⠖⠒⠒⠂⠀⠀⢀⣈⡭
⠀⠀⠻⣠⠉⢉⣓⠀⠲⠤⢦⣤⣀⣤⣀⣀⠀⠁⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⢀⣀⢤⢤⣤⡶⠶⠶⠒⠂⣉⠩⠄⡠⠋
⠀⠀⠀⠈⠑⢲⠌⢉⣛⣒⠶⢦⣼⣿⡁⠚⣩⠁⣦⣀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣥⣴⡈⠭⡛⢀⢿⣷⡶⢛⣛⣋⠡⣔⡚⠋
⠀⠀⠀⠀⠀⠀⠉⠂⠌⠉⢙⣻⡿⢃⡁⠎⣀⠊⡀⢋⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡅⠠⡙⣀⡸⠠⡘⢻⡫⠍⠉⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠕⠁⠀⢊⡍⠳⣤⠱⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠂⡵⠞⢡⣘⠂⠈⢰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡄⠀⠉⠉⠀⢀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠭⡀⡄⢀⠀⠈⠀⢠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠄⣈⣡⠘⠎⡀⠝⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠡⡠⠐⢃⠦⠠⠤⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠃⢀⠤⢦⢶⠀⠀⠀⠀⠀⠀⠶⠦⠖⡀⠈⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢤⠢⠄⠃⠀⠀⠀⠀⠘⠂⠠⠤⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⢣⡀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠝⢦⡘⣷
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠢⡙⢾⣷⣄
⠀⠘⢿⡓⠦⣄⡀⠀⠀⠀⠈⢧⡈⢢⡙⢿⣷⣄
⠀⠀⠀⠙⢦⡐⠭⣙⠲⠤⣄⣀⠙⢦⡈⠢⢌⠻⢟⡶⣤⣄⣀⡀
⠀⠀⠀⢰⡦⢬⣳⣦⣉⠒⠤⣉⠉⠒⠻⠶⢤⣉⠒⠬⢁⡚⠉⠍⠛⠛⠛⣻⠛⠛⢛⡛⠛⠛⠶⠶⢦⣤⣄⣀⠀⡀
⠀⠀⠀⠀⠙⠦⣄⠨⢉⠛⠲⠦⣍⣐⠒⠤⠄⣈⠙⠒⠦⠤⢉⣀⡀⠠⠤⠽⢦⣀⠀⠐⢯⡉⠉⠐⠒⠀⠉⠙⠻⠛⢤⡀
⠀⠀⠀⠀⠠⣤⠬⣽⣦⣬⣁⠒⠤⢈⣉⡓⠲⠦⠤⣍⣬⣀⡐⣇⠐⠀⠤⠄⠸⣉⠙⠓⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤
⠀⠀⠀⠀⠀⠈⠳⢦⣐⠈⠍⣙⠓⠶⠦⢬⣍⣀⣒⣂⣀⠀⡀⠈⢙⡗⠂⣀⠀⣈⣱⠒⠛⠓⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠈⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣓⣶⣬⣍⣀⣐⡒⠂⠠⠭⠭⠭⠭⠉⠀⣉⣒⣤⢤⣤⡠⠽⠋⠁⠀⠀⠀⠀⢀⣧⣀⣀⠀⠈⠲⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⣄⣀⠀⠤⠉⢉⣉⣉⣙⣋⣉⣉⠉⠩⠅⠀⢀⣀⣳⠶⠀⠀⣀⠀⠀⠀⣀⣫⣀⡀⠉⠀⠀⠀⢣⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⢚⠋⠍⢰⣁⠂⠉⣁⠀⠀⠀⢎⡀⣀⣈⠉⠁⠀⠀⠀⢸⡘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢥⣄⣒⣒⣒⡒⣒⣒⣂⣉⣉⣤⠤⠖⠊⢉⡉⠈⣣⠴⠖⠁⠀⣏⢉⣉⠀⠀⢀⠄⠀⠈⠃⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡛⠛⠛⠉⠉⠉⠤⠄⠀⠒⠐⣈⣠⠔⣋⠅⢒⣈⠤⠖⠺⡉⢁⡀⠀⢸⣀⡄⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⢒⡖⣛⣛⡩⢽⠟⠑⠈⣠⠖⢋⡠⢐⣠⠤⢺⢋⣥⠀⠀⣌⠀⡀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠘⠶⢚⡟⡡⠊⣡⡔⢋⠔⢂⣼⠃⢀⠀⡀⠈⢻⢁⡄⠀⠀⠀⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣤⡴⢃⠔⢁⡴⢃⠌⣩⠓⢾⠁⠀⠈⢹⣀⡞⠀⢠⠄⠀⠀⠈⠙⠓⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡼⠑⣡⣴⢋⡴⢃⡴⢁⡜⣹⠆⢰⡀⠀⠉⢇⣠⠞⢆⠀⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠚⣱⠣⣊⡴⣻⡡⢋⣴⢃⢊⡼⡉⣹⠀⢨⢱⢸⠈⢻⠓⢤⡜⠢⣴⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠁⠀⠷⠶⠋⢸⡤⠞⡇⢠⡇⠀⣿⡘⣸⢱⢸⣇⣸⡇⢰⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠋⠻⡼⠁⠳⠛⠧⠞⠀⠁⠑⠉⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⡠⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡤⡀⠀⠀⠀⠀⠀⢀⣴⡿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠳⣜⢿⣷⡄⡀⠀⠀⠀⠀⠀⠘⣿⣷⣄⡠⠆⠀⠀⠀⠀⠐⢦⣀⣴⣿⠏⠀⠀⠀⠀⠀⣀⣴⣿⢟⡴⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣷⣮⣿⢿⣷⣤⣰⣄⠀⢀⣨⡿⢿⣧⡀⠀⠀⠀⠀⠀⣴⣿⢻⣯⡀⢀⣴⣠⣴⣿⢿⣯⣶⣫⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣽⣻⣿⣖⠦⣬⣿⣉⣷⣭⣄⡘⢆⠻⣿⣆⠀⠀⢠⣾⡿⢡⣊⣤⣼⣏⣹⣭⡤⢖⣾⣿⣻⡵⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⡻⢿⡮⡛⢿⣿⣌⣽⣿⣿⠈⢣⡘⢿⣧⣴⣿⠏⡰⢹⣿⣿⣭⣼⣿⠟⡫⣾⢿⣛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⢿⣿⣿⡍⠍⣻⣖⢻⣿⡄⠀⠱⣨⣿⡿⠃⡜⠁⣼⣿⢓⣾⡋⠩⣿⣿⣿⠿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⣷⣎⡡⢚⣿⣽⠿⣦⣴⣿⠟⢁⣾⣷⡾⢿⣼⣟⠢⣉⣶⣟⡛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢛⣻⠶⣠⣐⣷⣾⣿⠋⣠⢧⠈⢿⣿⣇⢠⣲⠮⣛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡿⠁⡴⠁⠀⠳⡀⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⢀⠞⠀⠀⠀⠀⠙⡄⠙⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠤⠋⠀⠀⠀⠀⠀⠀⠈⠢⢌⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣴⠺⠿⣌⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣡⠿⠗⣤⡀
⠀⠀⠀⠀⠀⠀⡔⠑⢁⣴⣤⠘⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢃⣤⣤⡉⠙⢦
⠀⠀⠀⠀⠀⣮⣤⣿⣸⣿⢿⣆⢌⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⡥⣼⡿⣿⣇⣷⣤⣧
⠀⠀⠀⠀⠀⢠⡁⣸⣧⣠⣶⣟⢱⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⣻⣶⣅⣼⣅⢸
⠀⠀⠀⠀⠀⠸⣿⣿⠛⢸⡿⢉⣌⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡟⠛⣥⡙⢿⡇⠟⣿⣿
⠀⠀⠀⠀⠀⠀⡟⠛⢳⣾⣄⢨⣵⣷⡌⣿⣿⣷⡦⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⣾⣿⣿⣡⣾⣮⣀⣸⣷⡟⠛⣿
⠀⠀⠀⠀⠀⠀⢻⣴⠟⣿⢿⡿⡟⠛⢉⣋⡻⣿⣃⠈⢣⠀⠀⠀⠀⠀⢀⠜⠀⣚⣿⢛⣙⡋⡛⡻⣿⡿⡿⠿⣤⡏
⠀⠀⠀⠀⠀⠀⠈⡿⣦⣿⣀⢀⣝⣷⣿⡟⢣⣿⣿⡄⡀⢣⠀⠀⠀⠀⡎⢀⢸⣿⣿⡘⢻⣿⣾⣯⠀⣀⣷⣴⠿
⠀⠀⠀⠀⠀⠀⠀⠸⡈⢿⣿⣿⣿⡿⣿⣯⡙⠿⠷⠟⢻⣿⡇⠀⠀⢸⣿⠏⠻⠾⠿⢍⣽⣿⢿⣿⣿⣿⡿⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣸⣿⣿⣿⡿⡍⠉⠀⢲⣤⣀⠀⢿⠃⠀⠀⠸⡟⠀⣀⣤⡖⠀⠙⡁⢿⣿⣿⣿⣧⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⡟⠈⢈⠁⠙⣦⣠⡴⣿⣿⣆⣚⡄⠀⠀⢰⣓⣸⣿⡿⣦⣄⡴⠋⠈⠑⠉⣫⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢟⣆⠀⠰⢠⣼⣷⣿⣯⠻⠉⡏⠁⠀⠀⠈⢹⠈⢟⣿⣿⣾⣡⡤⠎⠀⡰⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣦⢿⣶⣍⣿⢿⡟⢻⢶⠇⠀⠀⠀⠀⠸⡴⡟⢻⡿⣷⣩⣶⣷⣾⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢿⡻⣿⣿⣧⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣼⣿⣿⢟⠿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⣷⣟⠻⠯⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠿⠛⣻⡞⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⡿⣷⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⣾⢿⣃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢻⣠⢹⣮⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣵⡇⣄⠟⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡌⠛⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⡘⠙⠻⠰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢵⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄

⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⣷⣾⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⡶⢶⣶⣦⣀⣀
⠀⠀⠀⠀⢀⣶⣽⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣿⣿⣮⣻⢿⢿⣯⣦⡀
⠀⠀⠀⢀⢾⣿⣴⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣟⣿⣿⣿⣿⣿⣻⣿⣟⣷
⠀⠀⠀⣿⣧⣿⣯⢿⣿⢿⣯⣾⢿⣯⣻⣿⣿⣿⢧⣿⡷⠀⢾⣿⣼⣿⣿⣿⣟⣽⣿⣿⣿⣟⢭⣯⣙⣿⣽⣗
⠀⠠⢖⣽⣟⣿⣿⠞⣡⣿⣿⡿⣿⣿⣿⣿⣽⣿⣿⣿⡇⠀⢸⣿⣿⣿⣯⣿⣿⣿⣿⢿⣿⣿⣎⠳⣿⣿⡿⣏⣲⠄
⠀⠀⣿⣿⣿⣿⣯⣾⣿⣿⣿⣯⣼⣟⣏⣿⠿⠛⠋⠋⠀⠀⠀⠛⠙⠻⠿⢿⣻⢉⣄⣽⣿⣿⣿⣷⣿⣿⣿⣾⣿⠆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⢋⣿⣿⣿⣿⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣧⣾⣽⣿⣿⣙⣿⣿⣿⣿⣿⣿⣿
⠀⠈⣹⣿⣿⣿⣿⣿⣧⣟⣿⣯⠛⠏⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠹⠛⣧⣿⣻⣾⣿⣿⣿⣿⣿⣏⠁
⠀⠀⢹⣿⣟⣿⣿⣿⢹⣿⣿⢿⣿⡖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢒⣿⡿⢻⣿⡟⣿⣿⣿⣻⣿⣿
⠀⠀⣼⢯⣿⣿⣿⣿⣿⣏⣿⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣇⣿⢹⣿⣿⣿⣿⣿⡽⣧
⠀⠀⠏⣾⣿⣿⣿⣿⣿⢻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⡟⣿⣿⣿⣿⣿⣷⠹
⠀⠀⠀⣿⣷⣿⣿⣿⣿⣾⣏⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣡⣦⣽⣿⣿⣿⣾⣿
⠀⠀⠀⢸⢿⣿⣿⣿⣿⣿⣿⢟⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠻⣿⣿⣿⣿⣿⣿⡿⡇
⠀⠀⠀⠈⠘⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠇⠁
⠀⠀⠀⠀⠀⠘⣿⡏⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢳⢹⣿⣿⣿⣟⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣫⡿⣿⣿⡇⠞⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣽⢟⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠿⣦⡙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣵⠟⠹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣶⣦⣴⣲⠄⠀⠀⠀⠀⠀⠀⠀⡀⠃
⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠂⠀⠀⠲⣄⠀⠀⠀⠀⠀⠐⡟⣕⢿⢻⣿⠇⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠐⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠠⠊⠀⢀⣤⣶⠛⣻⣿⠶⣦⣄⡀⠑⠄⠀⠀⠀⠀⢹⢣⢷⡼⣿⣷⠀⠀⠀⠀⡠⠊⢀⣠⣴⠶⡿⣿⠓⣶⣤⡀⠀⠑⠄
⠀⠀⠔⠁⢀⠶⢿⠁⣿⡰⢿⣌⣼⡏⢃⣟⣦⡀⠁⡀⠀⣴⣮⣯⣿⣍⡹⣷⡵⠀⢀⠌⢀⣴⣿⡉⢹⣧⣀⡿⢆⣿⠈⣿⠶⡀⠈⠢⡀
⠀⠀⠔⢠⣿⣧⣼⠶⢫⠃⡺⠉⣼⢳⠏⣇⣰⠻⣆⠐⡀⠧⡊⠐⠙⢁⠘⠟⠁⢀⠂⣰⠟⣆⣸⠹⡎⣧⠉⢷⠈⡜⡶⣧⣼⣿⡄⠢⠈
⠀⠀⠂⡸⣿⣯⠋⣆⡾⢷⢡⡿⢉⡦⢪⠙⢠⣆⣩⠀⠁⢰⣯⡢⡴⡿⣿⣽⣏⠏⠀⣏⢰⡀⠋⡕⢤⡉⢿⡊⡾⢷⣰⠉⣽⣟⠇⠐
⠀⠀⠀⠣⢻⡙⢶⡌⠱⡌⣸⡀⣬⠁⡜⣤⢃⠙⣹⠠⠂⢸⡝⢿⣦⡫⣵⢸⠀⠐⠄⣏⠋⡘⣠⢣⠈⣥⢀⣇⣡⠎⢡⡶⢋⡟⡜
⠀⠀⠀⠀⠈⣷⢑⢝⠶⣈⠋⠳⠛⣦⠁⣀⡿⣴⠏⠀⠀⢸⡨⡗⢿⢿⣮⡸⡀⠀⠀⠹⣦⠿⣀⠈⣴⠛⠞⠙⣁⠶⡫⡊⡾⠁⠠
⠀⠀⠀⠃⠀⠈⠈⣷⣅⠈⠻⣄⣸⠀⣰⠉⢀⠁⢠⠀⢠⢾⠷⢾⣿⡴⢝⠿⡀⠀⠀⡆⠈⡀⠉⣆⢀⣇⣠⠟⠁⣨⣾⠁⠁⠀⠘
⠀⠀⠀⠀⠀⠘⡄⠈⠉⡙⠦⣌⢳⡄⠁⣷⣾⠀⠀⠀⠈⠉⠉⣩⡯⠤⢄⠉⠀⠀⠀⠀⠀⣷⣾⠈⢠⡞⣁⠴⢋⠉⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠘⣦⣄⠈⢷⣄⡈⠻⣦⡿⡈⠀⠀⠀⠀⢠⣾⣞⣥⢾⠷⣏⠶⠀⠀⠀⠀⢁⢿⣤⠟⢁⣠⡾⠁⣠⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢜⠟⢦⠈⠎⢙⢗⠾⣧⡀⠘⣦⣀⠀⣮⣿⠐⣿⡙⣮⣭⠆⠀⢀⣴⠃⢀⣼⠷⡲⡛⡱⠁⡴⠻⠣
⠀⠀⠀⠀⠀⠀⠀⢸⣄⠈⠃⢷⡀⢣⡁⠘⣷⣄⢁⠀⠀⢰⣿⣏⢟⢁⠀⣿⡆⠀⠀⡘⣠⣾⠋⢈⡜⢀⡾⠘⠁⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢈⢣⢠⡀⢹⢦⣿⡦⡘⡆⠙⠆⠀⠀⠑⠽⠷⡬⠽⠟⠀⠀⠰⠋⢰⢃⢴⣿⡴⡏⢀⡄⡜⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢣⡉⠙⠈⠣⠀⠀⠀⠀⡠⣲⠎⣑⣢⣀⡀⠀⠀⠀⠌⠁⠋⢉⡜⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠟⢆⠈⢦⡁⠀⠀⣸⣿⠗⣾⠩⡿⣇⠊⠀⠀⢌⡴⠁⡠⠻⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠳⡄⠓⠆⠀⢛⣿⡨⣿⡫⢟⢟⠁⠀⠐⠎⢠⠞⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣆⠀⠀⠘⣿⢧⣹⣉⡴⣣⠇⠀⠀⣰⠏⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢡⠘⠶⠀⢀⠈⢙⣋⢷⡚⠁⠀⠀⠾⠃⡄⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠃⢀⠀⠯⢟⢻⢷⣶⠁⠀⠀⠀⠀⠘⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠠⡞⣿⢸⣿⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢯⣿⣸⢿⡀⢀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣃⡿⠛⣿⠶⣾⠞

⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⡝⢦⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠹⡔⠑⢼⣧⡀
⠀⠹⣖⠦⣄⡀⠀⠀⠙⢌⠢⡙⢿⣦⡀
⠀⠀⠈⠳⣔⡩⢙⠲⠤⣈⡓⣌⡐⠌⡛⠷⢦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠘⢿⡓⠻⠶⢬⣐⡢⠌⣉⠙⠲⠬⣁⡂⠀⠀⠈⠀⠰⣏⠉⠋⢩⠭⠭⠙⡛⠲⠦⣤⣄
⠀⠀⠀⢀⣉⣳⣤⣒⠨⠉⡓⠲⠬⢥⣐⡂⣈⠉⣖⠉⠉⢀⠩⡗⠦⠌⠓⠀⠀⠀⠀⠀⠈⠈⠳⢤⣀
⠀⠀⠀⠀⠙⠦⣍⡉⠙⡓⠶⠤⢭⣒⣀⣀⣉⠉⠉⢓⡖⢀⠀⠉⣶⠒⠒⠀⠀⠀⠀⢀⣠⡀⠀⠈⢹⡀
⠀⠀⠀⠀⠀⠀⢀⡭⠽⠶⠮⢭⣤⣐⣒⣀⣀⣀⣀⣀⡈⠲⠶⣤⠔⠛⠁⠀⠀⠀⢀⠷⢤⡄⠀⠑⡌⣧
⠀⠀⠀⠀⠀⠀⠀⠉⠓⣲⣤⣤⣒⣀⣀⣀⣀⣀⣀⣒⣀⠤⠄⡼⠋⠤⠀⠀⠀⡤⠾⠶⠤⠀⠀⠀⢇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢭⣍⡩⠍⠉⠉⠭⠍⠀⠐⣂⣨⠤⠓⠒⠲⣃⡤⠀⢱⠖⠒⠀⠀⠀⠀⠸⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣽⠛⠛⠛⠋⠉⠉⠅⠀⢂⣈⠔⡪⠄⣀⠤⠄⢟⢉⠀⠀⣅⡄⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣟⣫⠭⠝⡟⢑⣁⠴⡋⠅⣠⠴⠒⣫⠄⠀⠸⣀⡀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠋⠊⡠⢊⠔⣡⠚⠥⣄⣠⠀⠸⠴⢀⡀⠀⠈⠙⠲⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⡽⠑⣡⠞⡡⢊⠎⡠⢣⢀⡀⠐⠾⠀⡸⡅⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢊⡏⣊⢶⣏⢞⣼⠡⣠⠛⡡⠀⡉⢱⡙⠞⢢⡴⢤⡆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠘⠗⠋⠿⠖⣧⣠⡇⢸⣧⣸⡃⡼⣠⣇⣰⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠋⠈⠉⠛⠁⠀⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠛⠉⢳⣄
⢶⣶⣶⣶⡒⠒⠒⠂⠤⠤⢄⣀⡀⠀⠀⠀⠀⠋⡸⠃⠒⠬⣯⡭⢤⡀⠀⠀⠀⢀⠀⠄⠐⠒⠂⠀⠀⠀⠙⣀⣠
⠀⣨⣙⠓⠒⠒⠂⠐⡤⠀⢖⡠⡌⠳⡄⠀⠘⣸⣁⡄⠐⠂⠘⣦⡲⡁⠀⠀⡞⠁⢾⣭⠋⠀⣾⠁⠈⠉⣩⢅⡤
⠀⣈⡙⠒⠀⠄⠀⠘⡀⢀⣬⠉⢀⡶⠁⠀⢼⣸⣷⡀⠀⢀⠘⡿⢓⣻⡆⠀⠙⢦⠀⠫⣤⠠⠄⠂⠀⢀⣈⣁⣀
⠀⠑⠂⠁⠀⠀⢠⠒⠩⠄⣱⠂⠈⢄⠀⠀⠘⢏⡻⣿⡏⠁⠀⢻⣶⣽⣟⠀⢀⠄⢀⣫⡄⠒⡉⠤⠤⠈⠁⠒⠉
⠀⠀⠴⣒⠓⢒⣀⠴⠤⠀⢁⠺⠤⠈⠢⣄⡔⢻⠿⡉⠁⠀⠀⣀⡜⠉⠻⡴⠋⣀⡜⠰⠊⠠⡔⢁⣀⡀⠭⠷⠂
⠀⠀⠀⠰⠞⠍⠁⠀⠸⣏⠀⣄⡀⠹⣆⡜⢀⡏⠁⠈⠙⠿⠉⠈⠀⠀⠀⢳⡞⠋⠀⠰⠤⠄⠒⠀⠈⠭⠿⠂
⠀⠀⠀⠀⣠⠮⢀⠀⠀⢢⡄⢀⡖⢠⣼⠃⣼⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⢷⣿⡛⣅⢢⣑⠦⣔⡪⣶⣄
⠀⠀⠀⠀⠑⠛⢁⣴⠤⢀⡠⢾⣿⣷⡇⠧⣿⡸⠰⣄⠰⢀⠀⠀⡄⣶⡇⠘⠈⢳⣿⡟⢄⡈⢑⣀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠙⠇⢚⣵⠀⢈⣿⡄⠀⣩⣾⡿⠟⠻⢿⠭⡿⠶⠻⣿⣄⡔⠉⠉⣻⣜⡆⣉⡙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⡴⢏⡟⠀⢄⣼⣿⡅⠀⠀⠀⠀⢇⠄⠀⣿⣿⡇⢠⠎⠉⢿⣿⡌⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠁⢀⣼⣿⢸⡇⡆⠀⠀⠀⠈⡠⠀⢹⣿⣷⣤⣦⡀⠘⢯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠏⣠⣾⣿⡇⢸⠁⢷⡀⠀⠂⠬⠂⠀⠈⣿⣿⣿⣿⣷⣄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡏⠹⣿⡇⢸⡄⠸⡷⣄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣻⣿⣇⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣿⠿⢁⣧⢹⡇⢸⣇⢀⢿⣮⡰⠁⠀⠀⠀⣸⣿⣿⠇⣽⣯⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⡆⢻⣯⠘⡇⢸⡟⡌⡎⢿⡇⠀⠀⠀⠀⣿⣿⡿⣆⠈⢹⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⣿⡆⢡⣾⣿⠈⣷⢱⣸⡌⠁⠀⠀⠀⢀⣿⣿⠃⣿⡆⠸⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠇⢸⣿⣿⡄⢿⡆⢻⣇⠚⠀⠀⠀⢸⣿⣇⠸⣿⢁⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣙⢿⣷⠸⣿⡌⢿⣧⠀⠀⠀⠈⣿⣿⠟⡁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠿⢸⣿⡁⢻⡵⠈⢯⢀⠀⠄⣸⣿⣅⠘⢣⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⢀⣿⡿⣧⠈⢷⡁⠈⢧⡃⠐⠋⣹⣿⣷⠀⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠨⢒⣬⠂⣌⢙⣄⢿⡆⠘⢷⡀⠀⠙⠶⠶⠟⣽⣿⡰⢇⣈⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⢇⢐⣘⣇⣻⢿⣿⣿⡄⠈⢷⡀⠀⠀⠀⠛⠽⢾⣷⢠⠆⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⡾⠋⡼⣿⣿⣷⡀⡀⠓⠸⣞⡷⠊⡉⠦⠱⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠲⢜⣇⣿⠋⢋⠻⢝⡀⠀⣉⣐⠋⠨⠱⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠐⠉⠋⣣⡭⠰⠶⠔⠈⠤⠌⣙⡲⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣾⠕⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣴⡋⢉⢿⣿⣦⢠⠀⢀⡀⣰⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣎⣽⣿⣷⣶⣦⠿⣿⡀⠻⠟⠋⠙⣿⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⣿⣿⣫⣾⣿⡍⣝⡷⡄⠀⠀⠀⣜⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣸⣯⣼⣿⣿⠟⠍⢿⣯⣷⣷⠢⣄⣤⣧⣄⣤⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⡿⢿⣿⣿⡓⣤⣼⣟⣿⣅⣤⣿⣩⣽⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠳⣄⠲⣿⢿⣿⣦⢬⣿⣍⡻⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠠⢞⣿⡿⠀⠀⠀⠉⣍⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡊⠽⣷⣦⣤⣾⣿⣿⣷⣬⣶⣆⣺⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢉⡟⠛⢹⡿⣏⠀⠈⠙⣿⣿⣿⣿⣿⣯⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣤⣾⣤⠶⠛⠁⠨⡟⢦⣄⣈⣻⣿⣿⣿⡇⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡴⠦⣄⠱⣌⣠⣿⠿⢿⡟⢿⣿⡙⢿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⠒⠰⠿⠷⠿⠟⢤⣤⣶⣼⣿⣿⣾⣿⣿⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢶⡻⠮⣅⣈⣀⣠⣤⣴⣶⡾⠛⠿⠅⠉⣛⣿⣿⡟⠀⠀⠀⠀⠸⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠈⠉⠁⠀⠀⠀⠀⠉⠙⢻⣷⣦⣌⣿⣿⣿⡇⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣬⣽⣶⣶⣀⣐⣨⣤⣶⣿⣿⡿⠋⣿⣿⡟⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢹⣿⣿⣿⠟⠀⢰⣿⡿⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣀⣀⣿⡿⠁⠀⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠋⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠃

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁
⠀⠀⠺⣝⠿⣶⣶⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣴⣶⡿⣟⡽⠂
⠀⠀⠀⠨⣛⠿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⡻⠿⡿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⡿⠿⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⡷⢟⡯
⠀⠀⠀⠀⠨⣟⡷⢶⣿⣿⣿⣿⣿⣿⣭⣭⣭⣽⣷⠤⠤⢌⢽⣦⠀⠀⠀⢠⣾⢍⠤⠤⢶⣿⣭⣭⣭⣭⣿⣿⣿⣿⣿⣷⠶⣟⡭
⠀⠀⠀⠀⠀⠈⢙⡓⠶⠾⣿⣿⣿⣿⣷⣶⣶⣾⣟⠓⢀⡜⠇⡛⡄⠀⠀⡾⡢⠛⡀⠐⢻⣿⣶⣶⣾⣿⣿⣿⣿⡿⠶⠞⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢓⠶⠾⢿⣿⣿⣿⢿⣦⠄⠰⢈⣱⢟⡝⠀⠀⠀⠱⣝⢷⣁⠴⠀⢤⡾⢿⣿⣿⣿⠿⠶⢖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣛⣿⣿⠗⢂⡒⣴⢟⡵⠋⠀⠀⠀⠀⠀⠈⠳⣝⢷⡔⡂⠲⢿⣿⣟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⣫⣷⠟⢋⠉⣽⣿⠸⣧⣀⠀⠀⠀⠀⠀⢀⣠⡿⣸⣯⠉⠙⠛⢷⣿⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣹⣷⣿⣏⣠⢨⢾⢙⡒⡆⡈⠑⡄⡔⠉⡀⡖⡞⢿⢯⢤⣈⣿⣷⣯⡙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⣽⣿⣷⣖⣠⠁⡛⠃⡷⠶⠃⠳⠾⡇⠛⡃⢠⣐⣮⣿⣿⡍⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠟⢹⣿⣿⢧⣾⣧⣾⡅⠀⠀⠀⠈⣿⣦⣷⣆⣿⣿⣿⠙⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠟⣿⢻⣿⠟⠀⠀⠀⠀⠀⠘⣿⣿⢻⡟⠇⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⢀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠆⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠊⠡⠖⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠩⣁⡈⣘⠽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢏⢈⣀⡭⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠀⡔⠂⠬⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠥⠔⠂⡀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢦⡀⠉⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠉⢀⡠⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠁⠐⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠐⠈⠁⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢀⡊⢁⣁⡉⢿⡶⠶⠀⠀⠀⠀⢠⣶⠶⡾⠉⣀⡅⠉⡀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⢀⣈⣵⣀⣶⣷⡄⠀⠀⠀⢸⣿⣶⣅⣾⣍⣀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣹⣭⣽⡛⠻⢏⣡⠀⠀⠀⢤⡙⠯⠛⣯⣹⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⡵⣿⠀⠘⠁⠀⠀⠀⠈⢹⣤⣿⢧⣅⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠮⠙⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⢧⡀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣀⣀⠀⠀⢀⡼⠁⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⢈⣿⠞⠋⢉⠀⠀⢀⣠⣤⣨⣅⣤⣄⡀⠀⠀⡉⠙⠳⣿⡁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⣀⣴⠟⢁⣴⢿⣷⠖⠛⠉⢞⣡⢭⡭⣌⡳⠉⠛⠲⣾⡿⣦⡈⠻⣦⡀⠀⣠⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⢋⡴⢻⡇⠀⠀⢀⣘⠛⠛⣩⠤⠤⢍⠛⠛⣃⡀⠀⠀⢸⡟⢦⡙⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠞⠉⣰⣿⣇⡀⠀⠊⢁⡠⠖⠒⠒⠒⠒⠲⢄⡈⠓⠀⢀⣸⣿⣆⠉⠳⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢀⡄⠉⣽⡏⠻⡄⠀⠺⠀⠀⣠⠔⠢⣄⠀⠀⠗⠀⢠⠟⢹⣯⠉⢠⡀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⣾⢇⣾⠁⠀⠗⢢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠲⠀⠈⣷⡼⣷⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢸⡏⠈⠙⠲⠄⠀⠙⢺⣿⣏⣀⠀⠀⠀⠀⣀⣹⣿⡗⠋⠀⠠⠖⠋⠁⢹⡇⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⢸⣇⣠⡤⡠⢞⣣⣤⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠤⢤⣜⡳⢄⢤⣄⣸⡇⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣠⣴⡟⣇⠀⢰⣿⣦⡻⢄⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⡠⢟⣴⣿⡆⠀⣘⢻⣦⣄⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣬⣧⠻⠆⢸⣿⣏⠻⢦⡀⠀⢠⡄⠀⠀⢠⡄⠀⢀⡴⠟⣹⣿⡗⠰⢟⣼⣥⣿⣷⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣯⣍⡛⠛⣻⣿⣓⠦⠀⠀⠈⠻⣤⣤⠟⠁⠀⠀⠴⣚⣿⣟⠛⢛⣩⣽⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠹⣿⣿⠿⠳⠶⡶⢤⣴⣦⡴⢶⠶⠞⠻⣿⣿⠏⣴⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣀⣿⣿⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⣿⣿⣀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣆⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⣰⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡏⠖⡀⠀⠀⠀⠀⢀⠲⢹⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣟⣉⣉⣉⣙⣩⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢠⡤⠠⣤⠠⣤⠀⠀⣠⠔⠐⢤⠀⠀⣤⠀⠠⡄⠠⣤⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⣼⠃⠀⠀⠀⠀⠀⣿⠀⢠⠀⠀⣿⠀⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⢻⡄⠀⠀⢻⠃⠀⣿⠀⠈⠀⠀⣿⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠐⠛⠀⠀⠙⠒⠄⠚⠀⠀⠛⠒⠒⠃⠐⠛⠀⠀⠛

⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⢐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡄
⠀⢸⣾⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣾⠀⠀⠀⠸⣌⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣱⠃
⠀⢹⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠁⠀⠀⠈⢿⡣⠙⣧⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣾⠋⢞⡟
⠀⠘⣿⣿⣿⣿⣷⡄⠀⠀⠶⡆⠀⠀⣴⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⢿⡒⠈⢿⣄⠀⠀⠈⠛⠁⠀⠀⣰⡿⠁⣚⡽⠃
⠀⠀⠘⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⠯⣥⡌⢻⣄⠀⠀⠀⠀⠀⣰⡟⢡⣭⠷⠃
⠀⠀⠀⠀⠙⠻⠿⠟⠃⠀⠀⠀⠀⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠛⠃⠀⠀⠀⠘⠛⠘⠒⠃

⠀⠀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⢀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆
⠀⣼⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡄⠀⢘⣿⣿⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣿⣿⠁
⠀⢸⣿⣿⣿⣿⣿⣦⠀⠀⠾⠆⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⠀⢓⣿⣿⣿⣿⣶⣄⠀⠀⢀⣀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡋
⠀⠀⢻⣿⣿⣿⣿⡿⣇⠀⠀⠀⢀⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⢿⣟⣗⠀⠈⢷⡀⠈⠉⠁⢠⡞⠁⠀⣺⣿⡿⠉
⠀⠀⠀⠙⠿⣿⡿⠉⠁⠀⠀⠀⠀⠁⠹⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠫⠥⣤⡈⡇⠀⠀⠀⢸⢀⣤⠬⠝⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠁⠀⢌⠳⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⡡⠀⠈
⠀⠀⠀⠈⢦⡑⠈⠛⠔⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠢⠛⠁⢊⡴⠁
⠀⠀⢀⠀⠀⠙⠦⣼⣜⡮⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⢵⣣⣧⠴⠋⠀⠀⡀
⠀⠀⠀⠢⡠⢄⠢⠈⢙⢻⣮⣮⠙⠦⡠⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⢄⠴⠋⣰⢵⡛⡋⠁⠔⡠⢄⠜
⠀⠀⠀⢀⠈⠀⢝⠦⣤⡠⣍⠊⠑⠦⣄⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣤⠴⠊⠑⣩⢄⣤⠴⡫⠀⠁⡀
⠀⠀⠀⠀⠁⠠⡢⢄⣀⠉⠀⢝⠲⢤⣀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⣀⡤⠖⡫⡀⠉⣀⡠⢔⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠨⣝⡛⠛⠲⠤⣄⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⣠⠤⠖⠛⢛⣫⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠦⢤⣤⡨⢤⡤⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢦⡤⢅⣤⡤⠴⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠤⠑⡲⠶⠆⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠰⠶⠖⠊⠤⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⢶⣖⣒⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣒⣶⡶⠶⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠛⣛⣓⡖⣭⣤⠀⠈⠢⡅⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⣤⡭⢲⣚⣛⠛⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠩⣉⣖⡤⠤⠀⠀⠀⠴⠃⠀⠀⠐⠦⠀⠀⠀⠤⢤⣺⣉⠉⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢭⣭⣗⣓⡀⠀⠒⡲⠀⠀⢖⠒⠀⢀⣚⣾⣭⡭⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠫⠥⠒⠈⠀⠀⠀⠀⠁⠒⠬⠻⠖⠈

⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠠⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁
⠀⠈⠃⠀⠀⠀⢀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠀⠀⠀⠀⠊
⠙⠄⠀⠀⠀⢀⠀⠡⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⡠⠃⢄
⣀⠀⠀⠀⢀⠀⠱⡠⠻⣌⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⢈⡼⠣⡠⠁
⠀⠃⠀⢀⡀⠢⡐⠹⣆⠘⢇⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠟⢀⡾⠓⡢⠂
⠠⢄⠀⢀⠱⡀⠜⣆⠘⠂⠀⡉⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⣁⠀⠚⢀⡞⠀⡀⢀
⠀⠀⠀⠈⠳⣌⡣⡈⢂⡀⣅⠳⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡰⢃⡅⣀⠊⣠⣋⡴⠋
⠀⠠⠤⠘⠲⢤⣍⠛⠦⢁⡈⠣⣢⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣫⡧⠋⠀⠡⠞⢋⣥⠴⠚⠠⠤
⠀⠀⠠⠈⠢⢤⣀⣁⣤⡈⣓⠒⠶⡍⢛⠦⡄⠀⠀⠀⠀⠀⠀⡤⢞⠋⡵⠒⢐⡋⣠⣄⣁⣠⠤⠈⠀⠂
⠀⠀⠀⠊⠓⠀⠀⠤⣰⣤⡍⠵⢂⡛⢰⠎⣔⣄⠀⠀⠀⢀⣔⡌⢶⠈⣁⠲⠍⣥⣴⣢⠄⠀⠐⠋⠂
⠀⠀⠀⠀⠁⠀⠠⠄⠤⠴⠒⡾⠉⡥⠚⡸⠅⢴⠛⠀⠘⢳⠄⠴⡘⠣⣍⠱⣖⠲⠤⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠒⠂⢜⣉⠀⠊⠡⠋⡖⢂⡀⠈⠀⠈⠂⣄⠒⡎⠣⠙⠂⢈⣙⠆⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣥⣠⣤⣀⣀⣀⣀⣀⣀⣀⣠⣬⣠⣼⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣭⣭⣭⣽⣽⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠀⠀⠀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠄⠀⠈⠁⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⣠⠔⠚⠹⣃⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⣹⠉⠑⠢⣀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⠞⢁⡠⠊⠐⢇⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⢤⡝⠈⠓⢄⠈⢳⡀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⡴⡏⢠⠎⢠⠊⢔⠼⠦⡄⠀⠀⠈⠓⠒⠢⣄⠀⢀⡤⠒⠉⠉⠀⠀⡀⢠⠞⠮⡢⠱⡀⢱⡀⢻⢆⡀⠀⠣⡀
⠀⠀⠀⠀⠀⢠⠃⠀⣴⠋⣨⡗⣏⣰⠇⢠⠃⠪⢢⡛⡳⠴⢆⡤⠖⠒⠈⠁⠈⠉⠑⠲⢤⡴⠶⠏⢳⡀⡁⢱⡀⢹⣀⡗⢫⡀⠹⡆⠀⠱
⠀⠀⠀⠀⢠⠃⢠⠔⠋⣴⠇⣠⠏⡹⢒⡿⣤⣇⢠⠁⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡆⢰⡀⡷⡼⢿⠛⡌⠳⡄⠹⣄⠙⢦⡀⠱⡀
⠀⠀⠀⢀⠃⢠⠞⢀⡼⠃⡰⠃⡴⢃⡾⠤⡏⢸⠋⣿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡏⠹⡀⡓⠬⢧⡘⣆⠙⣄⠙⣦⠀⠣⡀⠡
⠀⠀⠀⠂⣠⠋⢠⠞⢀⡜⣁⠜⠓⠉⠀⠀⠙⠻⢤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠴⠋⠁⠀⠀⠉⠚⠦⣈⣦⡈⢧⡀⠹⡀⠠
⠀⢀⣢⠜⠳⠖⠛⠚⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠛⠒⠛⠦⣑⠄

⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠸⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠻⡌⠳⣄⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⠞⢡⠟
⠀⠀⠀⠀⠀⠀⠀⢲⣿⣦⡀⢝⡲⢿⡳⢤⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡤⢞⡿⢖⡫⢀⣴⢷⡖
⠀⠀⠀⠀⠀⠀⠀⠠⣝⣦⡉⠳⢭⣿⣷⣤⡉⢷⣾⡷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢾⣷⠺⢁⣠⣾⣾⡯⠞⢉⣴⣫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡛⠦⣔⡪⣽⣮⣙⠳⢮⣽⣆⠈⠉⠛⠓⠶⢤⣀⠀⠀⠀⠀⣠⡤⠶⠚⠛⠉⠁⣴⣯⡵⠞⣋⣵⣯⢕⣪⠴⢛⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣳⣤⣉⠛⣿⣯⣛⠲⢬⣭⣻⣦⡀⠀⠀⢠⠾⠷⡀⢠⠾⠷⡄⠀⠀⢀⣴⣟⣭⡥⠖⣛⣽⣿⠙⣉⣤⣞⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣍⡉⠛⠻⣿⡓⠦⢤⣀⣒⡛⣦⡀⢸⡀⠀⠀⠀⠀⢀⡇⢀⣴⢛⣓⣀⣤⠴⢚⣿⠟⠛⢉⣩⠽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⡷⠦⣬⣍⣓⣶⣬⣭⣿⣿⣿⣦⣳⡀⠀⠀⢀⣞⣴⣿⣿⣯⣭⣥⣶⣞⣩⣥⠴⢾⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⣦⣤⣜⣹⣷⣶⡶⢶⣶⣾⣿⣷⠀⠀⣾⣿⣷⣶⡶⢶⣶⣾⣏⣓⣤⣴⣶⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⣤⣭⣭⣿⣿⣯⣭⢽⣿⠏⠀⠀⠹⣿⡭⣭⣽⣿⣿⣭⣭⣤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⠶⠶⠾⠷⠛⠁⠀⠀⠀⠀⠈⠛⠾⠷⠶⠶⠖⠚⠛⠉


⠀⠀⠀⠀⠀⠀⠳⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢴⠞
⠀⠀⠀⠀⠀⠀⢤⣈⣢⣌⠑⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠊⣡⣔⣁⡤
⠀⠀⠀⠀⠀⠀⠀⣙⣦⣉⠓⠢⢠⣝⣮⡙⢷⡢⠤⣀⣶⣄⣀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⣠⣶⣀⠤⢔⡾⢋⣵⣯⡤⠔⠚⢉⣴⣋
⠀⠀⠀⠀⠀⠀⠀⠈⠹⢍⠓⠦⢄⣈⣳⣍⠳⣟⠦⢄⣉⠹⢮⠙⢾⢱⡀⠀⠀⠀⠀⠀⠀⢀⡎⠷⠋⡵⠏⣉⡠⠴⣻⠞⣩⣞⣁⡠⠴⠚⡩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣒⠻⠦⣄⡈⠹⠯⣑⢮⡷⠦⢤⡍⢸⡆⠀⢸⠇⠀⠀⠀⠀⠀⠀⠸⡇⠀⢰⡇⢩⡥⠴⢾⡵⣊⠽⠏⢁⣠⠴⠟⣒⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣑⢦⣀⠈⠙⢶⡘⠓⢾⡶⠦⠬⠥⣻⡄⣾⠀⠀⠀⠀⠀⠀⠀⠀⣷⢠⡿⠬⠥⠴⢶⡷⠚⢃⡶⠋⠁⣀⡴⣊⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⣍⠉⠒⠂⠾⣷⡲⠊⢿⣓⣒⣨⣿⣌⢧⡀⠀⠀⠀⠀⢀⡼⣡⣿⣄⣀⣚⡿⠑⢖⣾⠷⠐⠒⠉⣩⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣬⠛⠒⠒⠒⠛⣛⢶⡾⢿⣥⣤⠼⣷⡌⢧⠀⠀⡼⢡⣾⠧⣤⣬⡿⢷⡖⣛⠛⠒⠒⠒⢛⣥⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⣝⠋⠥⠄⣲⣟⣥⣞⣵⣏⢼⡟⢶⠃⠸⡴⢻⡦⣹⣮⣳⣬⣳⣖⠠⠬⠙⣯⣭⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠋⠑⠋⠛⠉⠷⠋⠀⠀⠙⠾⠉⠛⠙⠊⠙⠢⠈

⠀⠀⠀⠀⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⠀⠀⠀⠀⠙⣿⣦⣄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣀⣴⣾⡟
⠀⠀⠀⠐⣦⣽⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣤⠖
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣰⣿⣷⣄⠀⢠⣶⣿⣷⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠟⠉⠀⠉⠙⠿⠿⠋⠀⠘⠻⠿⠟⠉⠀⠈⠛⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⡇⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⡿⠇⠀⠀⠀⠀⠀⠀⠿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⡀
⠀⠀⠀⣠⣴⣿⡿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡿⣿⣷⣤⡀
⣀⣐⣛⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣛⣓⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠃⠀⠀⣿⠁⠘⢠⠄⣴⡢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⣤⣴⣄⣺⣣⣖⣷⡀⠈⠀⢴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠀⠄⠀⠈⠉⠑⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢰⣆⣠⣤⢦⡤⠀⠀⠀⢷⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢂⡀⠚⠳⢾⠋⠀⠀⠀⠀⢸⣿⠎⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⠛⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⢺⡘⠇⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣀⣀⣀⣠⠐⠉⠙⣿⣷⡄⠀⠀⡞⠧⣀⠘⢦⠀⠀⠬⠚⠛⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠁⡹⠀⠀⠈⠀⢻⣷⠀⢀⠀⠀⠈⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠁⠳⠢⠆⢁⠀⢺⡟⢠⡏⠀⠀⠀⠀⣡⠋⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⢠⠆⡂⠀⠐⠲⠶⣫⢠⠏⠀⣠⡴⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠁⠀⢀⠀⠀⠀⠠⠄⠀⠀⡰⠋⠀⠀⠀⡠⠂⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⡔⢀⢇⠀⠀⠀⠘⢀⠎⠀⠀⠀⠀⠀⠀⠀⢈⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠝⠒⠀⠈⠁⠸⠃⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠂⠁⠀⠠⢤⣾⣞⡁⠀⢀⣀⡤⠔⠀⢀⡴⠋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠛⠛⠛⢅⠀⠀⠀⠀⠀⠒⠋⠉⠙⠛⠛⠯⠥⠤⣶⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⡀⠀⠀⠀⠀⠁⢠⠟⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠄⠀⠀⠀⠀⠀⢀⠘⠋⣉⡝⠁⠤⣤⡤⡄⢤⠖⠃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⠂⠈⠙⠐⠊⠁⠀⠀⠀⠀⣀⠴⠀⣤⠖⠃⢰⣴⣶⣤⠴⡾⣷⠒⠈⣭⣤⠂⠀⠀⢀⠤⠊
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠉⣀⡠⠶⣿⠉⠉⣹⠛⠙⣿⠦⣀⣉⣳⠀⠀⠉⠁⠀⠀⠈
⠀⠀⠀⠈⡀⠀⠀⠀⠀⢀⡤⠤⠚⠉⠉⠉⠉⠀⢀⠈⠁⠀⠀⢸⠳⠀⣻⠦⣼⣇⠀⠈⢉⡟⠛⠀⠀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⢨⣿⣧⠀⣿⣤⣈⡏⠁⠀⣼⠀⠀⠀⣀⡤⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠀⠀⠀⠀⠾⠿⠿⠀⠈⠛⠻⠿⠶⠚⠙⠓⠀⠈⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠐⠂⠂

⡀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⢻⠢⡀⢀⡀⠀⠀⠀⠀⢫⢢⡀
⠀⠣⡈⠛⢯⣑⠤⣀⠀⠈⢆⠙⠢⣀⡀
⠀⠀⠙⢄⠀⠈⠓⢦⣙⠲⢬⣢⡀⠠⣉⠙⠒⠤⣄
⠀⠀⣗⠢⢕⣤⡀⠠⣈⠙⠦⣌⠙⠒⠤⣑⠢⣀⠀⠉⠲⢄⡀
⢀⠀⠈⠢⡀⠈⠙⠲⢌⡑⠢⣀⠀⠀⠀⠀⠉⠙⠻⠶⣤⣀⠙⢦⣄
⠈⠇⢄⠀⠈⠐⠤⣀⠀⠈⠓⠤⣉⠒⠤⠀⠀⠀⠀⣠⡤⣉⣙⣒⣯⡁⠒⠒⠢⣄
⠀⠈⢀⠉⠢⢤⣀⠀⠙⠒⠤⠀⠀⢉⠒⠦⢄⣀⠀⠀⠙⠢⣄⡀⠀⠉⠒⠲⠬⢯⠉⠒⣄
⠀⠀⠀⠁⠈⠒⠤⣉⡓⠢⠤⠀⠀⠀⠀⠀⠈⠙⠫⢄⡀⠀⠈⠉⠑⠒⠦⠤⣤⡼⣦⠀⣈⡆
⠀⠀⠀⠘⢏⠒⠢⠤⣍⣑⠒⠤⠄⣀⠀⠀⠠⣤⡒⠒⠚⠛⠚⠉⠉⠉⠉⠉⠣⣉⡁⠘⢄
⠀⠀⠀⠀⠀⠙⠢⠤⣀⡈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⢒⣤⣤⠤⠤⠤⠒⠒⢲⠊⣠⡀⠀⠉⠒⠠⠤⠤⠔⠒⣆
⠀⠀⠀⠀⠀⠀⢤⣀⣀⣬⣭⡽⠶⠶⠶⠦⠤⠴⠾⢍⣉⣀⠀⠀⠀⢀⡠⠔⢺⠖⠁⣩⠶⣄⢦⡀⠀⡄⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠩⠭⠉⠀⠠⠤⠤⠄⠀⠀⠀⣉⠽⠋⠁⠀⠀⣠⠔⠈⠀⠀⡿⠊⣧⢼⠋⢹⠃⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠭⠵⠶⠶⠶⠶⠶⠒⠒⠒⢚⣓⣲⠶⢖⡿⠋⢀⣀⡠⡴⠋⠀⢀⣴⣃⡠⡎⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⢒⣒⣒⣲⣶⠾⠽⠷⠒⠛⠉⠉⢉⣝⣉⣠⠴⠓⣲⠊⢁⣊⣽⢁⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠤⢤⣤⣴⠶⠖⠒⢉⣁⡴⠥⠴⠾⠕⠒⠉⠁⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣶⣶⣶⣦⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠁⠀⠀⠐⢲⡶⣿⣛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠐⠒⢲⠶⣉⠀⠀⠉⠛⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢀⡐⠢⣄⡀⡈⢙⣧⣄⠀⠙⠲⢄⡀⠀⠀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠠⠃⠀⡆⠀⣆⠹⠦⣌⠙⢯⢍⡀⠈⠙⢶⣤⣄⣉⣳⡦⠄⣀⣐⠨⢙⣲⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠆⠀⢠⠣⣀⡏⠲⠃⠈⠛⢾⡁⠉⠓⢦⣤⡇⠑⢤⡀⠉⠲⢤⡀⠉⠉⠫⢍⠁
⠀⠀⠀⠀⠀⠠⣸⡠⠃⢠⠀⢰⡀⠹⡦⣀⠀⠹⣦⡀⠀⠱⡕⢤⡀⠙⢦⣄⠀⢝⣳⡦⢄⣀⡙⠲⣦⠆
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⡄⠈⢳⡀⢱⠘⣷⢞⠃⠈⠒⠦⢿⣀⣹⡶⢤⣘⠻⡷⢿⠷⠄⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡀⢠⠇⠘⡁⠀⠙⡋⠀⠘⣦⠁⠂⠄⣀⡸⠀⠀⠈⠢⣍⠙⠉⠀⠑⢦⡀⠢⢀⠀⠐⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠓⠋⡆⠀⢣⠀⠀⢱⡀⠀⠈⠷⣄⠀⠀⠀⠢⡀⠀⠀⠈⠳⢄⠀⠀⠀⠙⢦⡀⠈⠑⠢⢄⣉⠒⠤⣄⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⣧⡀⠈⣷⡀⠀⠘⡌⠢⡀⠑⠤⡈⠲⣄⠀⠀⠀⠑⢦⡀⠀⠀⠙⢶⣤⢀⠀⠀⠈⠉⠒⢚⣻⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠧⠱⣄⠹⠙⢦⣀⢹⡢⢌⡢⡀⠈⠑⠬⣙⠦⣄⠀⠀⠈⠳⢤⡀⠀⢉⠲⣌⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠈⠛⠷⡀⠉⠙⠓⠢⢄⣀⠉⠚⠻⠶⣤⣀⣀⠈⠓⠦⣌⡚⠽⠶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠙⠦⢤⣀⠈⠻⣍⡙⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠛⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢣⣿⣿⣿⣿⣷⡀⠀⠀⡄⣤⠀⠀⣠⢠⠀⠀⠀⣼⣿⣿⣿⣿⣏⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⣿⢿⡿⣽⢿⣷⣄⣸⣿⡿⠀⠀⢿⣿⣇⣠⣾⡿⣯⣿⡿⣿⣿⣆⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣾⣿⣻⣿⣿⣟⣻⣿⡿⠃⠘⡿⣿⣻⣛⣿⣿⣟⣿⣣⣿⣿⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣻⠃⠀⠀⠘⣛⣿⡻⣝⣧⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣿⣿⣿⣿⣥⡿⣿⣽⣿⡟⠛⠀⠀⠀⠀⠛⢻⣻⣏⡟⢿⣉⣿⣿⣿⣿⢹⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⢹⢻⡇⠙⠁⠁⠀⠀⠀⠀⠀⠀⠈⠀⠋⢹⢿⡏⣿⡿⢸⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⡇⡘⡏⠸⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢸⠁⣹⠃⢸⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣶⠀⣷⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡴⢁⣾⠈⣦⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢱⠹⣎⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⡜⢠⠏⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢃⢙⢆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⡜⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠚⠦⣯⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⡀⠜⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢰⣤⠸⣅⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡰⠀⣠⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⢳⡀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⡤⢷⡀⢀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣿⣿⡻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢳⡀⠙⣄⠙⢦⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣮⡻⣿⣦⣀
⠀⠀⠀⠀⠀⠠⡦⠝⣦⡈⡓⢄⠙⢄⡀⠡⣄⠀⠀⠀⠀⠀⠀⠀⢰⣤⣹⣿⣿⣿⣿⣎⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠑⢌⠢⡄⠀⣌⠀⠑⢕⢄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣝⢿⣿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢈⢢⡈⠲⢵⣄⣄⠈⠢⡐⢤⡑⢵⣦⡀⠀⠀⠀⠀⣙⣿⣿⣝⡿⣿⢿⣷⣿⣯⡻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠙⠢⡀⠌⠛⠳⣕⠪⣦⣵⡂⠻⢿⢆⠀⠀⠀⠹⣿⣿⣿⣟⣧⣤⣝⢮⣛⡟⠈⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⠙⠺⡦⣌⠒⠭⣀⠂⠉⠒⢽⣿⠀⠀⠀⠀⠙⢿⣷⣯⣟⣛⢿⣽⣺⢿⣿⣮⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢌⠒⠲⠤⣈⡛⠛⠛⠏⢀⢀⡾⠃⠀⠀⠀⠀⠘⠿⣯⣭⣝⣻⠷⣬⣭⣤⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⡂⡁⣄⡼⡇⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣶⣿⣽⣿⢿⣻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠔⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢸⣷⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠰⡆⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⢰⠆
⠀⠀⠀⠀⠀⠀⣿⡄⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⢠⣿
⠀⠀⠀⠀⠀⢀⠘⣿⣌⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣠⣿⠃⡀
⠀⠀⠀⠀⠀⠸⣦⡘⣿⣦⣻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⣴⣿⢃⣴⠃
⠀⠀⠀⠀⠀⠀⠹⣷⣌⢻⣷⡽⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢯⣾⡟⣡⣾⠏
⠀⠀⠀⠀⠀⢦⡀⠘⢿⣷⣿⣿⣮⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣵⣿⣿⣾⡿⠃⢀⡴
⠀⠀⠀⠀⠀⠈⢿⣷⣄⡹⣿⣿⣿⣷⣝⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣫⣾⣿⣿⣿⢏⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣾⣿⣿⣿⣿⣷⣝⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣫⣾⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢤⣄⣈⣙⣛⣿⣿⣿⣿⣿⣿⣮⣿⢿⣷⡄⠀⠀⢠⣾⡿⣿⣵⣿⣿⣿⣿⣿⣿⢛⣋⣁⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⡄⢠⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣯⡇⢸⣽⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣭⣴⣿⣿⠿⢻⣿⣿⠁⠈⣿⣿⡟⠿⣿⣿⣦⣭⣉⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⣠⣿⠟⠁⠀⠀⠈⠻⣿⣄⠀⠉⠉⠉⠁

⠀⠀⠀⣀⣀
⠀⠀⢠⣿⣿⣷⢦⣄⡀
⠀⠀⠀⣿⡟⠻⢷⣬⡙⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡀
⠀⠀⠀⣿⡇⠀⠀⠈⠙⠷⣯⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠈⠻⣿⣷⣄⡀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠈⠹⣿⡙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⡄⠈⠻⣿⣿⡆
⠀⠀⠀⢹⡇⠀⠀⠀⠀⢰⣄⠀⢸⣷⡀⢘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⣸⡇⠀⠀⠈⠻⣿⡆
⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⣿⣆⠈⢿⣧⠀⠻⣿⣿⣷⣤⣀⣀⣀⣀⣤⣸⣿⣠⡟⠁⠀⢳⡀⠀⢹⣿
⠀⠀⠀⠀⠀⢻⣦⣄⢠⣼⣿⣿⡄⢈⣿⣆⠀⢹⣿⣿⣏⠻⣿⣿⠿⢿⣿⣿⣿⠿⠿⠷⣾⣷⣤⣀⣿⡀
⠀⠀⠀⠀⠀⠀⢯⡻⢿⣿⣿⣿⣿⣿⣿⢏⠀⠈⠀⠙⠿⢷⡈⢻⣶⡿⠶⡷⠶⢦⣴⣶⣤⣄⣀⢉⡉⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠹⢤⡈⠙⠛⠿⢿⣿⣄⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠈⠉⠛⠛⢦⣠⡄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣓⣶⠶⠿⠿⠿⢛⣷⣶⠖⠀⠀⠀⠀⠀⣸⡟⠋⠙⠋⠉⠂⠈⠲⣤⣄⣀⠀⠉⠛⢦⣀⠙⠿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠴⢾⣿⣥⡄⠀⠒⢛⣿⣿⡏⠀⠀⠀⠀⠀⠀⢤⣽⣿⢠⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⠀⢻⣧⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⣠⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⣀⣀⠈⢉⡀⢿⣶⣄⡀⢠⡀⠀⠀⠀⠈⢻⣿⣆⠀⠛⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡧⠀⠾⢻⡟⠁⠀⠀⠀⢀⣴⣿⠃⠒⠺⢿⣿⣿⡿⣶⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⠀⠐⣿⡟⡄
⠀⠀⠀⠀⠀⠀⠋⣿⠟⠁⣠⣾⣿⠋⠀⣠⠄⠀⣼⣿⡋⠀⠀⠀⢀⡈⠀⠀⠀⢻⣿⣿⠉⠛⢿⣷⣄⠀⠀⠈⢹⣧⠀⠀⠀⠀⠀⢻⠀⢰
⠀⠀⠀⠀⠀⢀⣼⠏⠀⡰⢫⡿⠁⣠⣾⡏⠀⢸⣿⣿⡇⠀⠀⠀⠘⣿⡆⠀⠀⠘⣿⣿⡄⢀⣈⣿⣿⣷⣦⣀⣼⣧⣤⣄⣀⣠⡆⢰⠀⣾
⠀⠀⠀⠀⠀⢸⣿⠇⠀⢠⡿⠀⠘⣫⣿⡇⠀⢸⡛⣿⣧⠀⠀⠀⠀⠙⠃⠀⠀⠀⠘⢿⣿⣾⣿⣿⣿⣿⠋⠙⠻⣿⠄⠀⠉⠉⢳⣿⣤⡆
⠀⠀⠀⠀⠀⣿⡟⠀⢀⣿⠁⠀⠐⣿⣿⡀⠀⠘⠃⠙⠻⣿⣦⣤⣤⣀⣀⠉⠙⠓⠶⠾⠿⠿⠿⠿⠿⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠻⣃⡇
⠀⠀⠀⠀⠀⠋⠁⠀⢸⣿⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠠⠄⠚⠛⠛⣛⠒⠒⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⡀⠠⣄⡀⠠⣀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⣠⡄⢸⣿⠀⠀⠛⣿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣦⣤⡀⠀⢠⠈⠹⠟⠳⠄⠀⠉⠳⣤⣈⠙⠦⠈⠳⠆⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠘⢻⣇⢸⣿⡆⠀⢀⣿⣧⡖⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⡿⣿⣷⡀⢧⠀⠀⡀⠀⠀⠀⡀⠈⠻⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢸⣿⡎⣿⣷⠀⠸⣿⡟⠀⣰⢃⣾⣿⣿⣿⣿⣿⣿⣏⠙⢿⡎⠙⣿⣿⡇⢸⠁⠀⣀⠀⠻⣆⠀⠟⠀⢰⣶⣦⣄⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠈⠙⣇⢹⣿⡀⠀⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠈⣿⠀⠈⠙⣿⡐⣦⠀⠙⢦⠀⠙⠀⠀⠀⠘⠛⠻⣿⣿⣷⣶⡶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣿⡇⠀⠋⠀⣿⣿⣿⣿⣿⠿⠋⠙⣿⠁⣿⠇⠀⠈⠳⡀⠀⠛⣷⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠃⠀⠈⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⠃⠀⠀⠰⠃⢀⠟⠀⠀⠀⠀⠣⢄⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⢸⣿⣿⣿⡧⠖⢨⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠛⠛⠻⣦⣄⡀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢪⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠘⣿⡟⠁⠀⠀⣼⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⡀⠐⠋⠉⠛⠿⣷⣶⣶⣾⣿⣧⣄⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢰⡄⠀⢿⣦⠀⠀⢰⣿⣆⢈⡄⠀⢰⡄⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢉⠏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢿⡀⠘⣿⣧⣤⡟⠀⠉⠉⡹⢁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠘⢷⡀⠈⠻⠿⣿⣷⣶⣾⡤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⡀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠋⠁

⣿⣿⣿⠿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣄⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁
⠀⠈⠳⣝⡻⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⡿⣛⡵⠋
⠀⠀⠀⢨⣛⠷⣾⣿⣭⣿⣿⣟⣛⣛⣛⣛⣛⠻⠿⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠿⢛⣛⣛⣛⣛⣛⣿⣿⣯⣽⣿⡶⢟⣫
⠀⠀⠀⠀⠨⡛⠶⣮⣭⣭⣽⣿⣿⣿⣿⣿⣟⣛⣛⣓⣦⠄⢌⣉⠩⣲⡀⠀⠀⠀⠀⡤⡪⢉⣉⠄⢤⣖⣛⣛⣛⣿⣿⣿⣿⣿⣿⣭⣭⣭⡶⠞⡫
⠀⠀⠀⠀⠀⠈⠓⠶⣭⣭⣛⣛⣻⣿⣿⣿⣭⣭⣭⣛⡿⠦⠀⠀⢷⡁⡟⠀⠀⠀⠘⡏⣱⠆⠀⠠⠾⣟⣫⣭⣭⣽⣿⣿⣿⣛⣛⣫⣭⡵⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠓⠶⣬⣭⣭⣭⣽⣭⣭⣭⣭⣿⡉⠉⢀⠠⠲⣵⡴⣳⠀⠀⠀⢰⡳⣴⡵⠢⢀⠈⠉⣩⣯⣭⣭⣭⣽⣭⣭⣭⣥⡴⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢬⣭⣭⣿⣿⣿⣯⣙⣋⣁⢀⣡⠶⣫⠞⠁⠀⠀⠀⠀⠙⢮⡳⢦⣁⢀⣉⣛⣩⣿⣿⣿⣯⣭⣭⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡾⣟⣟⣉⣤⡤⣾⢣⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⢻⣦⣤⣌⣙⣟⣿⣦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣩⣾⢟⣉⣡⠀⢤⡿⣌⠻⠦⢄⣀⠀⠀⠀⢀⣀⠤⠾⢋⡸⣁⣉⢁⣉⣻⣿⣯⣍⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⣾⣿⡿⣡⣴⠳⠹⡏⣛⣰⢐⡀⠑⡄⡔⠁⣐⢰⣘⣯⣯⢥⢥⣤⣭⣽⣭⣮⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠉⢩⣿⡟⣷⡞⣠⡄⢘⠛⢈⡷⠶⠃⠓⠶⣏⠘⠛⠀⣦⡐⣶⡟⣿⣮⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⢸⣿⣽⡇⣶⣷⣰⣾⠁⠀⠀⠀⠀⢹⣶⣰⣷⡆⣿⣽⣿⠘⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠃⡿⣿⡟⣿⣿⠟⠀⠀⠀⠀⠀⠘⣿⣿⡟⣿⡿⡇⠻⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣟⠷⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠟⣯⣿⣿⣿⣿⣿⣶⣶⡦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣶⣶⣿⣿⣿⣿⣿⣿⣝⢷⣦
⠀⠀⠀⠀⢀⣴⢟⣿⣿⣿⣿⣿⢼⢿⣼⣽⣿⣿⡛⣿⣷⣤⡀⠀⠀⠀⢀⣴⣿⢿⢟⣯⡿⣿⣿⣼⢹⣼⣿⣿⣿⣿⣿⣻⣦⡀
⠀⠀⠀⠀⢨⢟⣿⣿⣿⣿⣿⠛⠟⣼⣏⢻⢱⣿⣷⡇⣏⢻⡇⠀⠀⠀⣼⡏⣽⢸⡾⣿⡟⣿⣹⣿⡞⡟⠹⣿⣿⣿⣿⣿⡛⡄
⠀⠀⠀⠀⣾⣾⣿⣿⡿⢿⢹⣰⣇⣟⢿⣿⣾⣿⣦⣽⣿⣾⡿⠀⠀⠀⢿⣷⣷⣿⣴⣽⣷⣿⡿⢻⣄⡷⣸⢙⠟⣿⣿⣿⣿⣗
⠀⠀⠀⣼⣿⣿⢿⣿⢳⣹⡜⣿⡿⣿⣼⣄⡏⣏⢹⣽⣟⠳⣆⠀⠀⠀⣔⠋⣿⣏⡇⣹⢹⣆⣟⣾⡿⣷⡯⣼⣰⢻⣿⡏⣿⣿⠷
⠀⠀⠀⢸⡿⣿⣿⢹⡈⠻⡟⡟⠷⢸⠙⢳⡟⣿⣬⢿⡀⠡⠈⠀⠀⠀⢠⠌⢀⡿⣧⣿⠟⣿⠉⣹⢰⠟⡟⣿⢻⢰⡏⣷⣟⣿⣇
⠀⠀⠀⣻⣿⣻⢹⡟⢷⠂⡇⣧⢹⠈⡇⠈⣇⣿⠙⡸⡇⠀⠃⠀⠀⠀⠘⠀⢼⢣⠋⣿⢰⠇⢠⠇⢸⢨⡇⠇⢸⡟⣿⢹⡏⣿⣞
⠀⠀⠀⢉⡿⣿⡿⣷⣸⡀⡆⢽⠘⣆⠘⡄⡏⠃⣦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡴⠈⢩⠇⡏⣠⠏⣸⡃⣇⢸⣠⡿⣾⣿⢿⡉
⠀⠀⠀⠈⠀⣟⢻⣿⣿⣧⡇⣿⡘⠃⣿⣇⢻⡄⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡏⢠⢿⠃⢙⣸⡇⣷⡼⣿⢷⣇⣇⢀⠁
⠀⠀⠀⠀⢠⠩⡋⢹⡇⡇⢱⢣⣿⠀⣻⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⣸⠀⢸⡇⠻⠃⠀⣾⡇⢹⠉⡄
⠀⠀⠀⠀⠈⠀⠃⢸⣷⡇⠰⣶⠿⢧⡽⠁⠠⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢻⣴⠿⣧⣷⠀⢸⢹⠃⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢘⠁⠸⠈⠸⡀⠡⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⡈⠈⠸⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡆⠀⡇⠀⠄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢰⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣰⠃⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣧⡈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⠇⢠⣇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⣵⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⢺⡚⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠉⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⡞⠀⠀⡄⠀⠀⠀⠀⠀⡜⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⢣⠀⠀⠀⠀⠀⢡⠀⠀⢳
⢠⠇⠀⢰⠀⡀⠀⡀⠀⡼⠀⡰⠃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢢⠈⢆⠀⢧⠀⢀⠀⢂⠀⡆⠀⠸
⢸⠀⠀⡆⢠⠇⢠⠁⡜⠳⢺⢁⡜⢀⠆⡀⠀⠀⢀⠀⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⡀⠀⠀⢀⠰⡀⢣⡈⡗⠞⢣⠈⡄⠨⡄⢰
⣾⠀⢰⠃⢸⠀⡦⠜⠁⠀⠈⠹⢧⣎⡼⢠⢀⡇⣨⠀⣇⢸⢧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⡼⡇⣸⠀⣅⢸⡈⡄⢧⣱⡼⠏⠁⠀⠀⠣⢴⠀⡇⠸⡆
⡇⠀⢸⠀⣆⡰⠃⠀⠀⠀⠀⠀⠀⠉⠓⠻⠞⠧⠛⠜⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠣⠛⠼⠳⠟⠚⠉⠀⠀⠀⠀⠀⠀⠘⢆⣸⠀⡇
⡇⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣧
⡇⠀⣿⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣿
⣇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻
⢻⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⠺⠸⠉⢶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠙⠇⠓⣍⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢠⠧⠄⠀⠠⣶⡋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣶⠄⠀⠠⠼⡄⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡠⢾⠶⠄⠀⠀⠒⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠒⠀⠀⠠⠶⣯⢄⡀
⠀⠀⠀⠀⢀⠀⠁⠞⠦⠄⠀⠀⠐⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠂⠀⠀⠠⠔⠳⠈⠀⡀
⠀⠀⠀⢠⡖⠁⢀⣤⣤⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⣤⣤⣀⠈⢰⡄
⠀⠀⠀⡈⠀⠘⠁⣀⣀⠀⠀⠐⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠂⠀⠀⣀⣄⠈⠃⡀⢁
⠀⠀⠀⠀⠀⡀⠚⢙⠉⠀⠀⠀⠰⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠖⠀⠀⠀⠉⡛⠐⠀⠀⡀
⠀⠀⠈⠉⡀⠀⠤⠚⣱⡶⠂⠀⠠⠾⢷⣄⣀⠀⠀⠀⣀⣠⣴⡆⠀⠀⢸⣦⣄⣀⠀⠀⠀⢀⣠⡾⠧⠄⠀⠐⢶⣎⠛⢤⠀⢀⠉⠁
⠀⠀⣤⡤⠀⠀⢀⠜⢁⣶⡶⠆⠀⠀⣈⠉⠉⠟⠛⠛⠉⠃⣉⠁⠀⠀⠈⣉⠈⠉⠛⠛⠻⠉⠉⣁⠀⠀⠰⢶⣶⡈⠣⡀⠀⠀⢤⣄
⠀⢠⣿⢀⡤⠀⠀⠀⠀⠀⣠⠞⠉⡩⠿⢦⣶⢷⣠⡾⠷⠛⠏⠁⠀⠀⠘⠙⠟⠾⢧⣄⡺⣦⡴⠿⢍⠉⠳⣄⠀⠀⠀⠀⠀⢤⡀⣿⡀
⠀⢸⡋⣾⢁⡄⢀⣤⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠁⠀⠀⠐⠈⠀⠀⠀⠀⠁⠂⠀⠀⠈⠃⠀⠁⠀⠈⠀⠀⠐⠀⠀⣤⡀⢠⡈⣷⠙⡇
⠀⡏⠀⣿⠋⣱⡿⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⢠⡆⡘⠀⠀⠀⠀⢃⢰⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢿⣞⠙⣿⠀⣹
⠀⢸⠈⡇⠀⣿⠀⢠⡴⢃⠀⣠⡆⠀⣼⡇⢠⣆⠀⢠⡍⣰⡅⠀⠀⠀⠀⢨⣆⢡⡀⠀⣠⡄⢰⣧⠀⢲⣄⠀⡘⢶⡄⠰⣿⠀⢸⠁⡍
⠂⠀⠀⡆⠀⡿⠀⢸⡇⠈⢺⡟⠀⠺⣿⠱⢿⣟⢾⣿⠙⢻⡏⠁⠀⠀⠀⢻⠟⠋⣿⡷⣿⡿⠊⣿⠟⠀⢻⡗⠁⢸⡇⠀⢿⠀⣰
⠀⠀⠀⣿⠀⡇⠀⠘⡇⠀⠸⣷⠀⠀⣿⡇⠀⢿⠁⠈⢇⠀⠇⠀⠀⠀⠀⠸⠀⡴⠉⠉⡟⠀⢸⣿⠀⠀⣾⠇⠀⢸⠁⠀⢸⠀⣿
⠀⠀⠀⢸⡀⠇⠀⠀⣿⠀⠀⣿⠀⠀⢻⣻⠀⠈⠆⠀⠈⠀⢠⠀⠀⠀⠀⡆⠀⠁⠀⠰⠁⢀⣟⡟⠀⠠⣿⠀⠀⣿⠀⡀⠰⢀⡇
⠀⠀⠀⠀⢧⠀⢰⡀⠘⣦⠀⢹⣇⠀⠘⠉⠳⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠞⠉⠃⠀⣸⡏⠀⣴⠋⢀⡂⠀⡜⠁
⠀⠀⠀⠀⠘⡆⠈⣧⠀⢽⡄⠀⢿⠀⠀⠁⠀⡆⠀⠀⠀⠀⠳⠀⠀⠀⠀⢚⠀⠀⠀⠀⢰⠀⠘⠀⠀⡿⠀⢠⡧⠀⣾⠀⢰⠃
⠀⠀⠀⠀⠂⠈⡃⢩⡄⡆⢱⡄⠸⡇⠀⢀⠀⠇⠀⢠⠀⠰⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠘⠀⡀⠀⢸⠇⢠⡎⢰⢠⡍⢘⠁⠐
⠀⠀⠀⠀⠀⠀⢁⠈⠇⠀⠀⡇⠀⢿⠀⠀⡀⢸⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⢠⠁⠀⡟⠀⢸⠀⠀⠸⠁⡈
⠀⠀⠀⠀⠀⢠⠆⠀⠆⠘⠀⡆⠀⡈⡧⠀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠀⢼⠁⠀⣸⠀⠃⡰⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢺⠀⠈⠣⠀⠁⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠇⢨⠀⡘⠁⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⢸⡀⣠⠀⠀⠇⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠸⠀⠁⣄⢀⡇⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠸⠇⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠉⠸⠇⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠆⢠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡄⠨⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢙⢄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⡐⠂⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⢂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣿⠈⠙⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⢿⠀⢀⠀⠀⠀⠀⢀⡠⠀⠒⢒⡨⠭⠭⠭⠭⠭⢅⣐⠒⠠⢀⠀⠀⠀⠀⡀⠀⡟⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡠⠁⣠⠆⠀⠀⠀⠀⢠⠀⢸⠀⠀⠀⠀⢦⡐⠆⢸⠀⠀⠀⠀⠀⠀⠀⠀⢈⠇⠰⠀⡇⠀⠀⠀⡃⠀⡇⠀⠀⠀⠀⠰⡄⠈⣄
⠀⠀⠀⠀⠀⠘⣡⣴⡏⠀⢠⠀⢠⠀⢸⠀⠘⠀⠀⠀⠀⠈⠙⠳⠦⠬⣐⣒⣒⣒⣒⣒⡨⠥⠶⠖⠋⠀⠀⠀⠀⠃⠀⡇⠀⡀⠀⡄⠀⢻⣦⣌⠂
⠀⠀⠀⣠⢠⣶⣿⣿⠀⢠⣏⠀⡜⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢃⠀⣻⡄⠀⢿⣿⣶⡄⣀
⠀⠀⠈⠁⡜⠉⣿⠃⠰⣿⡇⢀⠃⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡀⢸⣿⠆⠘⣿⠈⢧⠈⠁
⠀⠀⠀⢰⠄⠀⣧⠀⠀⢿⠇⣼⠀⢸⠁⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⡐⠉⠃⠀⠀⠈⠁⢆⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠈⡆⠀⣧⢸⡟⠀⠀⣿⠀⠠⡆
⠀⠀⠀⠟⠀⢠⡏⠀⠀⣸⣸⡿⠀⡆⠀⢰⠇⢀⠀⠈⠒⠶⠆⠒⠁⠀⠀⣶⠀⠀⣷⠀⠀⠉⠒⠤⠖⠒⠁⠀⡀⠸⡆⠀⢱⠀⣿⣆⣇⠀⠀⢹⡄⠀⢻
⠀⠀⠰⠀⢀⣾⠃⠀⢠⡿⠃⢻⣰⠆⢠⡏⠀⡞⠀⣠⠀⠀⡀⠀⠀⡀⠀⡟⠀⠀⢻⠀⠀⠀⠀⢀⠀⠀⡄⠀⢳⠀⢻⡀⠸⣆⡟⠘⢿⡄⠀⠸⣷⡀⠀⡄
⠀⠀⣴⠀⣿⣿⠀⠀⣾⡇⠀⣼⠟⢀⣿⢀⡜⠀⢰⡏⠀⣾⠀⣴⢀⣧⣿⠁⠀⠀⠈⣿⣼⡀⣦⠈⣶⠀⢻⡄⠀⢧⠀⣷⡀⢻⣇⠀⢸⣷⠀⠀⣿⣿⠀⣦
⠀⢀⠇⠜⢸⡟⠀⣼⣿⠀⢰⣿⠰⠹⣇⣾⠁⠐⣿⡇⢰⣏⣸⣧⣾⣿⠏⠀⠀⠀⠀⠹⣿⣷⣽⣆⣿⡆⢸⣿⠄⠘⣧⣸⠇⢂⣿⡇⠀⣿⣧⠀⢻⡇⢣⠹
⠀⢨⠞⠀⢘⡇⠀⠘⢻⢀⣿⣿⠀⢰⡟⣧⣾⠀⣹⣤⠻⡏⣹⢉⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⡉⡏⢻⠏⣰⣏⠀⣷⣼⢻⡄⠈⣿⣷⠀⡟⠁⠀⢸⡃⠀⠳⡄
⠀⠈⢰⠀⢸⣿⠀⢀⣸⡌⠈⣿⠀⣸⡇⢰⢿⢠⣿⡇⢰⡣⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠼⡆⢹⡿⡀⡿⡄⢸⡇⠸⡿⠁⢻⣇⠀⠀⣾⡇⠀⡆⠁
⠀⠀⠀⢀⣿⡿⠀⢠⣿⡇⠀⢸⠀⢿⡇⡈⢸⡇⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢼⡇⠁⢸⡟⢠⡇⠀⢸⣿⡆⠀⢿⣷⡄
⠀⠀⠀⢸⠟⠇⠀⢨⢿⡇⠀⢻⣿⠈⣷⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⣷⠨⣾⠁⣿⡇⠀⣸⣿⡀⠀⢸⠻⠇
⠀⠀⠀⢸⠀⡆⠀⠸⠈⢷⠀⢸⣿⠀⣿⡞⡃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⢻⣯⠀⣿⠇⠀⡟⠁⡇⠀⢰⠀⡀
⠀⠀⠀⣸⠀⡇⢀⡇⢀⣿⡀⢸⠘⡄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣷⢸⠃⡇⢀⣷⠀⢸⠀⢸⠀⣇
⠀⠀⠘⠘⠀⠃⣼⠀⢀⣿⡇⢸⠸⡇⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢸⠃⡇⢸⣿⠀⢸⣇⠸⠀⠃⠇
⠀⠀⠀⠀⡆⡠⣿⡄⢨⡁⠁⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠉⢸⡀⢸⡿⢤⢰
⠀⠀⠀⠀⠃⠁⢻⡇⢸⣷⡀⢻⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡟⢀⣾⡇⢸⠟⠈
⠀⠀⠀⠀⠸⢠⡀⡃⡟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢳⢸⢀⡀⠃
⠀⠀⠀⠀⠀⡆⢃⢳⣇⠈⢏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡙⠁⡸⡆⡜⢡
⠀⠀⠀⠀⠀⠀⠘⡄⢸⡆⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢸⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⢹⠀⡿⡄⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢠⣿⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⢀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠣⡀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠱⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⣤⣤⠄⣀⣠⣤⠴⣶⣶⠶⡒⠒⠒⠶⠆⠀⣀⣤⣴⣶⣿⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡷⢖⠛⡩⢶⠃⠿⢟⣫⣽⣶⣶⡜⢟⡴⣛⠽⠻⣟⣭⢾⣵⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⢏⣴⠇⣠⡴⢖⣒⣛⠉⢷⡁⠀⣹⠗⡞⠀⠁⠠⣾⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢻⣿⡾⢸⢏⡶⢋⣽⣧⠶⠿⢃⡤⢂⣤⣦⣄⠀⢀⣶⣿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠈⡏⡼⠋⠘⣠⣴⣯⣵⣦⣤⣬⡽⠞⠫⠵⢦⣌⣧⠸⣿⢡⣟⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡷⣰⠃⠀⣸⣿⢻⣤⡥⣋⠕⡊⡲⣶⣦⡴⢣⡿⠀⠀⠃⣸⣿⣆⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⠄⠁⠀⢰⠋⠀⢀⣤⣬⣤⠄⣽⣇⡴⢂⠀⣯⣜⠏⡀⠀⣿⣿⣹⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⡇⠀⠀⠀⠸⢦⣤⠄⠀⠀⢒⣭⢿⣯⡶⣻⠏⠋⣙⣴⠃⠠⢿⣿⠉⡟⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⣻⡿⠃⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣶⠿⠟⢁⠄⠀⠸⣿⣾⠃⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠙⢿⡁⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣲⣶⠶⠞⢉⡀⠂⠆⢻⡏⡇⣿⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⠳⣤⣀⣙⣿⣿⡿⣿⣿⣿⣿⡿⢿⣿⡿⣾⢁⡀⣴⣃⣾⠀⣾⣿⢸⡿⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣤⣼⣷⢾⠋⠀⠈⣇⣿⡆⢻⡇⣿⢋⡼⣻⣫⡏⠀⣿⡟⣾⠃⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢏⠁⠙⠅⠈⠀⠀⢀⣸⢇⡏⣸⣿⣷⠏⣸⣩⠟⢀⣾⣟⣽⣫⣦⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⣼⢡⣟⡾⠁⢠⡟⣡⣼⠿⣫⣾⢁⣥⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢋⡼⣡⠟⣋⣤⣴⠿⣛⣩⣴⠟⠫⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⣠⠟⣛⡵⣟⣯⣷⠾⠟⢛⣉⣀⣀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⡡⠂⣴⢃⡾⣫⠾⠛⡉⠀⢀⣶⢛⡍⠉⠉⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢠⢺⢇⡞⡽⢁⡞⠋⠀⢸⠟⣙⠋⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡌⢸⢸⠣⠇⠈⢧⣀⣀⣾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠁⢸⢸⡄⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠘⣆⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠈⠆

⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠠⣒⣺⣷⣶⡖⢂⠀⢀⠒⣶⣶⣯⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢐⣶⡿⠛⠢⡀⠀⡰⠚⢿⣿⡂⠀⠄
⠀⠀⠀⠀⠀⠚⢻⣷⡖⢸⡄⡼⠰⣶⣿⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠀⠀⠀⠀⠉⠒⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠊⠀⠉⠊⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⣠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠳⡄⠀⠀⠀⠀⢀⡞⣳⡄
⠀⠀⠀⠀⠀⢀⣾⣿⣟⣸⠃⠀⢧⢺⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣻⣿⣷⣻⣄⡀⢀⣠⣞⣾⣿⣿⠂
⠀⠀⠀⠀⠀⣾⣿⡟⠛⠃⠀⠀⠸⠛⠻⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⢔⡿⣿⣿⡟⠁⠀⠀⠈⠹⣿⣿⣿⡷⡀
⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠠⢺⣾⡿⡹⠀⠀⠀⠀⠀⠀⢻⢻⣿⣟⠆
⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠃⠀⠀⠀⠀⠀⠀⠀⠡⠛⡰⠁⠀⠀⠀⠀⠀⠀⠀⢣⠙⢏
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠠⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢀⠄⠀⠀⠀⠀⢠⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡀⡄
⠀⠀⠀⠠⡱⣴⣽⣳⠶⢶⠀⠀⠐⡖⠶⣚⡯⣢⢎⠀⠀⠀⠀⠀⢺⣿⢾⡷⣤⡤⠆⠀⠀⠐⡤⣤⠾⣫⣷⣿
⠀⠀⠀⠀⠈⠻⣿⣒⠄⢸⠀⠀⠀⡇⢠⣒⣿⠗⠁⠀⠀⠀⠀⠀⠸⣿⣗⣛⠀⢸⠀⠀⠀⠀⣧⠀⢘⣺⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠓⠋⠁⠀⠀⠀⠈⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠁⠀⠀⠀⠀⠈⠀⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⡀⠀⣀⣀⣤⣄⣄⣀⣀⣀
⠀⠀⠀⢀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠋⢉⣉⡀⢀⣈⣉⣉⠛⠛⣉⣤⣤⠀⢩⣍⣙⠛⠶⣦⣄
⠀⠀⠀⣾⠃⢀⣀⡈⠉⠛⠛⠶⢶⣦⡴⠞⠋⠁⠀⢀⡖⠋⠉⠀⣴⠏⣉⠉⠉⣽⣛⣋⣴⠖⡲⠀⠀⢹⡇⠀⠀⠙⢿⣦⣀⣤⣴⠶⠶⠟⠛⣷⡄
⠀⠀⠀⢿⠀⠈⠉⠻⢿⣶⣤⣀⡀⠀⢠⣀⠀⠀⠀⠊⢀⣠⣶⠟⠀⣿⡁⠀⠀⣼⠀⠘⠃⠞⠇⠀⢀⡌⠳⢦⣴⣇⣀⠙⠏⣀⣤⣶⣿⡷⠂⣿⠁
⠀⠀⠀⠸⡇⠀⠀⢰⣿⣿⣿⣿⡏⠀⠠⣬⠳⣄⠀⠙⠛⣩⡿⠷⢿⡟⠃⠀⣈⣵⣀⣀⢀⣐⣶⣾⣋⣭⡙⣾⡷⣄⠸⡆⢀⡉⡻⠟⠉⠀⣸⡏
⠀⠀⠀⠀⢻⡀⠀⠀⣙⣿⡿⠁⠀⠀⣀⠩⣤⣌⠳⡝⣿⣏⣼⣿⣶⣿⡟⠛⣫⡽⠿⠭⠿⠶⠶⢿⡟⠻⠟⢛⣿⢈⡣⠶⣏⠤⠈⠃⠀⣴⡟
⠀⠀⠀⠀⠀⠙⣦⡀⢉⣿⠍⠉⢛⣒⡭⢤⣀⠙⢷⣝⣮⠻⠿⢿⣶⣤⠁⠘⢁⣠⣤⣤⣤⣤⣤⣤⣉⠃⠐⠫⢖⣩⣴⢺⡅⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⣸⠷⣾⣯⠥⢤⣘⣛⠃⠐⠾⣿⠶⢭⣝⡓⠀⠴⢤⡀⠀⠀⢻⣿⣭⣤⣤⣤⣤⣼⡟⠀⠀⠪⢭⣤⣖⣲⣶⢒⡂⢺⣷⡀
⠀⠀⠀⠀⠀⢠⠏⣞⠟⢻⡧⣤⣙⣛⣉⣻⠷⠒⠒⠦⢬⣽⣓⠂⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⠟⠉⠀⠀⠀⠀⢁⣉⣀⠡⢽⡭⠁⢺⣿⠃
⠀⠀⠀⠀⠀⣿⡈⠐⠀⣸⡧⢬⣭⣥⠤⢽⣯⠭⠭⢍⣛⣒⡦⠀⠀⠀⠀⠀⣀⣀⣠⣤⣼⠿⢶⣦⣤⣤⡀⠀⣐⠭⣈⠉⢹⣇⠀⠺⣿⡆
⠀⠀⠀⠀⢠⣯⠔⡢⡀⣸⣿⡀⢻⣿⡀⠘⣿⠀⠀⠄⠶⣖⣻⡅⢀⣤⣶⣋⣉⣁⣠⣤⣤⣤⣤⣀⡤⢍⣻⡾⠋⣑⣈⠁⢸⣇⠀⠙⣮⣷
⠀⠀⠀⠀⣼⠡⡪⢞⠁⣼⣿⡆⠸⣿⡇⠀⠻⣦⣄⠀⠉⢻⣿⣿⣿⣿⠀⠀⣿⣄⣧⣦⣦⣤⣤⣼⠀⠀⣿⠇⠀⣹⠃⠀⣿⡗⠀⠀⠩⣻⣧
⠀⠀⠀⠀⣿⢠⢖⡡⠀⣾⣿⠃⢐⣿⣿⣦⡀⠘⢧⠀⠀⠈⢿⣿⠯⣿⡄⠀⡟⡿⡟⡟⣿⢻⣿⢿⡀⢸⣧⣤⠾⠃⠀⢀⣿⡇⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⢿⡶⣫⠖⢀⣿⡇⠀⠈⠸⣿⣿⣷⡀⠈⡇⠀⠀⠼⣿⣢⠙⣿⣄⣿⠉⠧⡇⠟⠈⠸⣸⣷⡏⣼⠁⠀⢀⣦⣿⠿⠃⠀⡀⠀⣜⣿⡇
⠀⠀⠀⠀⢸⡆⠁⠀⢠⣿⡆⣸⡟⡀⠉⢻⣿⡇⠀⢻⡆⠀⢸⣿⣿⣁⢻⣿⣿⠀⠀⠀⠀⠀⢠⢿⡏⣷⠿⢿⣿⣿⡏⠈⠀⠀⢱⣱⣦⣼⣿⠃
⠀⠀⠀⠀⠈⣿⣴⡄⡄⠻⡿⣿⣿⡅⠀⠘⠛⣗⠀⠈⢳⣄⠸⣿⣿⣯⣾⡇⠸⣦⣤⣤⣤⣴⠏⢸⣇⣿⠟⠀⠀⠈⠀⠀⠀⣠⣣⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠹⣿⣧⣷⢠⢠⠡⢻⣦⠀⠀⠀⠀⠀⠀⣈⠛⣶⣾⣿⣿⠏⢧⣀⣉⣥⣤⣭⣏⣀⣸⢻⣿⡆⠀⠀⠀⢠⣀⣰⡟⢳⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢾⣷⣤⣿⣬⢠⢰⠀⢠⢃⢅⣧⣉⢹⡵⠛⣯⣷⣶⠶⠶⣦⣤⣤⡤⣬⣠⢟⡀⢦⢦⢰⣸⢻⣿⣷⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣷⣧⣦⣧⣮⡿⠿⠿⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣼⢸⡞⡄⢾⣸⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⠋⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡟⠻⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣶⢠⡀⣄⠀⠀⠀⠀⢀⣠⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣦⣼⣶⣴⣾⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠛⠉

⠀⠀⠀⠀⠀⢀⠠⠂⠉⠉⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠉⠐⢄⡀
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠈⢆
⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⡌⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⡸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢇
⢀⠇⠀⠀⠀⠀⠀⢠⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡄⠀⠀⠀⠀⠀⠸
⢸⠀⠰⠀⠀⡀⢠⢇⡐⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⠸⡄⢀⠀⠀⠄
⡆⠀⡇⠘⢀⡡⠃⠉⠴⣃⢆⠂⠀⠀⠀⡄⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⢸⠀⠀⠀⠀⡰⣘⠦⠉⠘⢌⡀⠃⢸
⡇⠀⠃⣅⠌⠀⠀⠀⠀⠈⠛⠺⠾⠜⠶⠑⠁⠁⠀⠀⠀⠀⠀⠀⠈⠈⠊⠶⠣⠷⠗⠛⠁⠀⠀⠀⠀⠡⣠⠘
⡇⢸⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇
⡇⢸⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡇
⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⢠⡀⠀⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠀⢀⡀
⠀⠙⠳⣦⣬⣙⡛⠷⣶⣤⣤⣄⣒⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠶⣒⣠⣤⣤⣶⠾⢛⣋⣥⣴⠞⠋
⠀⠒⠶⠤⣭⣭⣙⣛⣷⣾⣿⣓⣿⣿⣿⣟⢒⡤⡬⣈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣁⢤⢤⣂⣻⣿⣿⣿⣚⣿⣷⣾⣛⣋⣩⣭⠤⠶⠒
⠀⠈⠓⠲⠶⠶⠶⠿⢿⣛⣿⣿⣞⣛⣿⣶⣟⡽⣳⣧⣗⣺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣗⣺⣼⣞⢯⣻⣶⣿⣛⣳⣿⣿⣛⡻⠿⠶⠶⠶⠖⠚⠁
⠀⠀⠀⠀⠉⠛⢛⣛⣯⣽⣿⣿⣿⣷⣿⣿⣿⣷⣥⣾⢿⣷⣤⢁⠀⠀⠀⠀⠀⠀⠀⡈⣤⣾⡿⣷⣬⣿⣿⣿⣿⣾⣿⣿⣿⣯⣽⣛⡛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠠⠖⠛⣩⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠡⠄⠀⠀⠀⠠⠌⣹⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⢧⣍⠛⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⢀⠀⠀⠀⡀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣿⣿⣿⣿⣿⣷⣿⣷⠚⠀⠒⣾⣿⣾⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⢿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣿⣿⣿⡿⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠐⠀⠀⠀⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠐
⠀⠀⠄⠀⠀⠀⠂⠀⡄⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⠂⠀⠀⠀⡄
⠀⠀⠁⠀⡄⢔⠐⡇⢰⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢲⠀⡕⢀⠆⡄
⠀⠀⠀⣀⢀⠨⢧⡸⣎⣧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣏⡾⣠⠯⢀⢀⡄
⠀⠀⠀⢈⠒⢢⣌⢳⣽⡙⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣹⣵⢃⣤⠗⢊
⠀⠀⠀⠢⠳⢠⠙⢷⣽⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⣵⠞⢡⠴⠣⠒
⠀⠀⠀⠁⢀⡎⠐⢤⣇⠱⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣷⠔⠈⣆⠀⠁
⠀⠠⠀⠧⡀⣤⠓⢶⡿⣆⢏⠀⠀⡘⢦⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⠞⠀⠐⢉⢇⡾⣷⠖⢣⡄⡠⠇⠠
⠀⠀⠀⠠⠬⣌⣙⠲⣿⡌⢃⠁⠆⡘⠢⣛⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡫⠚⡀⠖⢁⠋⣼⡷⢚⣉⣬⠤
⠀⠀⠀⠀⠀⡌⢉⣽⣟⣿⠦⠑⠀⣍⡓⢾⣿⡄⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠀⣸⣿⠖⣋⡅⠐⠡⢾⣟⣿⣍⢁
⠀⠀⠀⠀⠁⡠⠤⠤⠼⠿⣷⣌⠀⠄⢭⣻⣿⡦⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠠⣾⣿⣫⡅⠀⢪⣴⡿⠷⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢒⡛⢛⣛⣷⣦⡀⠡⠯⠽⢿⡦⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠠⣾⠿⠭⠯⠁⣠⣶⣟⣛⠛⣓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠙⠛⣻⣦⡄⠐⢛⢿⣦⡝⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⣥⣾⠟⠓⠂⣤⣾⡛⠛⠁⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠴⠿⡿⢧⣤⡜⠻⠦⣭⠢⢄⣀⠀⠀⠀⠀⠀⢀⣀⠤⢪⡵⠞⠛⣤⣤⠿⡿⠷⠭⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠙⠛⠛⠛⠿⠓⠛⠶⠒⠀⠐⠲⠖⠓⠻⠟⠛⠛⠛⠉⠁⠐

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⣿⣿⣋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⢰⣽⣿⣿⣿⡎⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠹⣆⢻⣿⣿⡿⣰⠏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⡳⣿⣯⣿⣿⣿⣿⢞⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⡀⠙⠿⣿⣿⣿⣿⠿⠋⢀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡈⣻⣿⣷⣾⣿⣿⣿⣶⣿⡿⢁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡘⢦⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡴⢃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣴⣟⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⣪⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡕⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢢⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡔⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣠⠀⠀⠀⢷⣄⢻⣶⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⡟⣠⡾⠀⡀⠀⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⡀⠘⣧⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⠁⣼⠃⢀⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⢸⣇⠀⢻⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⡟⠀⣸⡇⠀⡆⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⠀⢸⣿⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⡇⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⡇⠈⣿⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣼⣿⠃⢸⡇⢠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣧⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⠀⣼⠀⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠂⠤⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠄⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠉⠉⠁⠀⠀⠈⠑⢤⡠⡆⢤⠀⠀⠀⠀⠀⠀⡄⡶⢀⠔⠋⠀⠀⠀⠈⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠩⠁⠩⠀⢀⣀⠩⠓⠢⠀⠄⢤⠀⠀⠀⠀⠀⢀⡤⠠⠠⠒⠻⢁⣀⠀⠨⠍⠈⠁
⠀⠀⠀⠀⣠⢀⠀⠠⠀⠀⣈⠀⠉⠀⡀⠐⡂⣤⣲⡀⠀⠀⢀⣎⡄⣐⠂⠀⣀⠉⠀⣁⠀⠀⠀⠀⡀⡄
⠀⠀⠀⠔⠉⠣⠞⡀⠀⠈⠀⠀⢈⠅⢘⣁⢟⠛⠀⠀⠀⠀⠀⠈⢛⣗⢈⡀⠨⡀⠀⠈⠀⠀⡈⠦⠙⠉⠂
⠀⠀⠀⠀⠀⠀⢈⠗⠀⠐⠁⠀⢰⠒⡆⢀⡻⡀⠁⠀⠀⠀⠀⠀⢨⢃⠀⠕⠲⡄⠀⠙⠂⠀⢪
⠀⠀⠀⡀⢠⠄⠈⠋⠀⠀⠠⠃⠀⠆⡰⣃⠂⠗⡄⠀⠀⠀⡀⣠⢪⠂⡙⢀⢢⠀⠹⠀⠀⠀⠙⠀⢢⡐⡄
⠀⠀⠀⠀⠀⡄⢀⠀⣠⠀⠀⠀⡆⠘⢡⠇⠆⡌⠈⠉⠀⠀⠉⠉⢁⠱⢱⠘⠀⠐⠀⠀⠰⡄⠀⡀⠦⠁
⠀⠀⠀⠀⠀⠀⠩⠀⠈⢀⢀⠀⡇⢰⠈⠁⡍⠙⢦⠄⠀⠀⠠⠜⠈⡁⠈⠈⠀⡀⢠⢠⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠆⠸⠸⠀⠱⡈⡄⠡⡘⠞⠀⠀⠀⠀⠀⠀⠳⢡⠃⡸⢠⠃⢸⠸⠇⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢻⠈⠃⠀⠀⠀⠁⠈⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠚⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡌⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⡀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⡠⠊⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠚⠉⢀⣀⣠⣤⣤⣤⣀⡀⠀⠈⠢⡀
⠀⠀⢀⠞⠁⢀⣤⡾⢻⡇⢡⡟⠽⢉⡿⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣤⡶⡿⣿⠛⠙⣧⠉⣾⠻⣶⣄⠀⠈⠂
⠀⠀⡁⠀⣰⡏⢹⡄⣼⢷⠋⡿⣤⢿⡇⢠⣿⠺⢷⡄⠐⡄⠀⠀⠀⠀⡐⠁⣰⠿⢿⣧⡀⣿⠷⡼⡏⢳⢿⡆⣹⠋⣳⡄⠀⠑⢄
⠀⢀⠆⢰⣿⣷⣼⠹⠇⣆⢠⢷⣀⢾⠸⢋⢾⡰⠏⢻⡄⠰⡀⠀⠀⠸⠁⣼⠋⢳⣸⣆⠻⢸⢧⣠⢣⢈⡾⠻⢻⣶⣿⣿⠀⢣
⠀⠈⠀⡜⣿⣧⠁⢳⣼⠻⡏⣘⡿⠀⡶⢸⠘⠁⢶⣀⡆⠀⡇⠀⠀⡇⠀⣦⣰⠆⠙⠸⠰⣮⠘⢟⡘⡿⢿⣠⠇⢡⣿⡟⡆
⠀⠀⠀⡇⢻⡨⡳⣇⠙⢦⡀⣿⠀⣦⠀⡸⢡⠘⡈⠋⡿⠀⠁⠀⠀⠱⠔⡏⠛⠘⢠⠼⡄⢀⡆⢸⡇⢡⡆⢁⣶⠯⣸⠇⡇
⠀⠀⠀⠃⠈⢿⠐⢌⠳⣎⠙⠛⢷⠻⣦⠃⡀⣸⢇⡼⠃⠀⠀⠀⠀⠀⠀⠹⣆⡿⡀⡀⢡⣾⢻⡞⠙⢋⡶⢞⠕⢱⠏⠀⡇
⠀⠀⠀⡇⡄⠈⠌⣦⣑⠈⠳⣦⡀⣰⠉⢀⡝⠃⠘⠁⡄⠀⠀⠀⠀⠀⠀⡄⠙⡃⠛⣡⠈⢱⡄⢠⡶⠋⢐⣡⡞⠘⠀⠀⠇
⠀⠀⠀⠀⠐⠰⡀⠘⠙⠳⢤⣈⠻⣯⠣⠞⢱⣠⡇⠀⠙⠀⠀⠀⠀⠀⠀⠁⠀⢰⣠⠛⠆⢺⡿⠋⣠⡴⠛⡛⠀⡰⠠
⠀⠀⠀⠀⠀⠀⠻⣄⠀⠘⢦⡙⠑⠸⣷⡀⣸⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣹⡄⣠⡿⠐⠉⣩⠞⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣶⣆⠀⢻⠳⣤⣈⢻⣇⠣⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠃⣿⣋⣠⣴⢿⠏⢀⣼⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠰⡕⠙⢧⢀⠃⠨⡳⡝⢿⣦⠀⠸⠢⠄⠀⠀⠀⠠⠀⠺⠁⢀⣾⠟⡱⠫⠀⢊⢠⠞⠱⣱
⠀⠀⠀⠀⠀⠀⠀⠀⡷⡄⠈⠊⠳⡄⠱⣌⠀⢻⡷⣄⠀⠀⠀⠀⠀⠀⠀⡄⡴⣿⠃⢀⡴⠃⣴⠏⠊⠀⡴⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠐⡝⠄⢠⡀⢪⡳⣿⣗⢄⣻⡈⠙⠀⠀⠀⠀⠀⠘⠉⢸⣃⢔⣿⣷⢿⠂⣠⠂⠞⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠑⣄⢳⡑⡑⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⣡⢇⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢟⢦⠀⠲⡀⢄⠀⠀⠀⠀⠀⠀⠎⡠⠂⢀⠔⠟⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠳⡄⠙⢮⠀⠀⠀⠀⠀⢠⠚⠁⡰⠃⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⢀⡠⠡⠀⠠⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⡘⣷⡁⠀⠀⠀⠀⣠⡏⠡⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠈⠉⠀⠀⠀⠀⡑⠀⠃⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠁⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠

⠀⠀⠀⠀⠰⣤⣤⣄⡀⠀⢀⣠⣤⣤⠆⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠠⢤⣤⣤⡄⠀⠀⣤⣤⣤⠤
⠀⠀⠀⠀⠀⠉⠿⠿⠿⠀⠿⠿⠿⠉⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⠀⣀⣴⣾⡿⠀⠀⠀⠀⠀⠉⠹⠿⠗⠀⠐⠿⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠋⠉⠉
⠀⠀⠀⠀⠲⢦⣄⣀⠀⠀⠀⣀⣠⡴⠖⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⢶⣶⣤⡄⠀⠀⣤⣴⣶⠆
⠀⠀⠀⠀⠈⠹⢿⣿⡄⠀⢠⣿⡿⠏⠁⠀⠀⠀⠀⠈⠻⢿⣿⣷⡀⣴⣿⣿⠿⠁⠀⠀⠀⠀⠀⠙⢿⣧⡀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠠⣤⣤⣄⣀⠀⢀⣀⣤⣤⡤
⠀⠀⠀⠀⠈⠻⢿⣿⣧⠀⣼⣿⡿⠟⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⡆⣾⣿⣿⡿⠏⠀⠀⠀⠀⠈⠙⢿⣿⡄⣼⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁
⠀⠀⠀⠀⢤⣤⣤⣄⠀⠀⠀⣠⣤⣤⡤⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢠⣀⣀⣀⡀⠀⠀⣀⣀⣀⣠
⠀⠀⠀⠀⠈⠻⡿⣿⣧⠀⣾⣿⢿⠟⠁⠀⠀⠀⠀⠀⠙⠭⣿⣧⠀⢸⣿⡭⠍⠀⠀⠀⠀⠀⠙⢿⣿⣿⡀⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠸⣦⣄⡀⠀⠀⠀⢀⣠⣴⠇⠀⠀⠀⠀⠀⣦⣄⡀⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⠀⢿⣶⣤⣤⠀⢠⣤⣴⣾⠇
⠀⠀⠀⠀⠀⠻⣿⣿⡧⠀⢾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠸⢿⣿⡆⠀⢰⣿⡿⠟⠀⠀⠀⠀⠀⠈⠻⢿⡇⠀⠀⣿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠐⠂⠤⢤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀⠀⠀⠈⠳⠙⠲⡔⠒⠛⠛⠛⠓⠲⠶⠒⠂⠈⠉⠉⠁⠀⠀⠀⠠⣤⣀⡀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⡀⠀⠀⡷
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢒⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢰⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⢰⠀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠐⠮⣄⣀⣀⣀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠙⢾⣧⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣾⠀⣉⠀⠀⣀⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢸⡏⠛⣿⣧⡀⠈⠂⠶⠶⣦⣌⡉⠉⠉⠘⠛⠉⢻⠀⣼⣟⠷⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠣⣼⣿⣿⣿⣶⣤⠶⡚⠅⠀⠉⠓⠀⠀⠀⠀⣻⡿⠿⢿⡤⢰⡀⠉⠁
⠀⠀⠀⠀⠀⠀⣰⣣⡴⠀⠀⠀⠀⠀⡰⠁⠀⠠⠖⠛⠛⠓⢦⣄⡛⢶⣤⠄⣉⣀⡀⠉⠀⠀⣠⠖⠓⠢⢄⢀⠀⠠⠣⣄⢠⠚⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⢁⡞⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠁⠐⠋⠐⠒⠀⠼⡆⠴⠤⡀⠀⠀⠀⢀⡜⠁⠀⠈⠑⠀⣁
⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢢⡀⠀⣠⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⢠⡤⠀⠀⠀⠀⠀⠀⢀⠀⠉⣤⡄
⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⡉⠂⢿⡀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⠂⢸
⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠿⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣄⡀⠀⠀⠀⠀⣀⣠⠜⠀⢸
⠀⠀⠀⠀⠀⢸⢘⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⣰⠃⢰⣿⣿⣿⣿⣷⣦⣀⣭⠙⣿⠻⠋⠙⠿⠛⠯⠉⢯⠭⠭⠓⢿⡟⠙⠋⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⢿⠀⢸⣿⡟⠋⠛⢿⣿⣿⣿⣿⣿⠂⠀⣰⠷⣄⠤⠤⠤⠤⣆⠴⡟⠁⠀⠀⢀⡾⢦
⠀⠀⠀⠀⠀⠀⠀⢧⢠⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢸⣿⢧⡀⠀⠀⠉⠙⢿⣿⣯⣴⣿⠁⠀⠀⡤⠀⠀⠀⠀⣠⠃⢀⣄⡠⠋⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠈⠳⣄⠀⠀⠀⠀⠀⠀⠙⡆⠘⢻⡄⠱⠾⡤⠲⢀⠀⣿⣿⣿⣿⣀⣀⠢⠀⠀⠀⡠⠀⠄⠐⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠠⢄⠀⢹⡄⠈⢷⣤⣄⣀⣰⣯⠤⠄⠴⠤⠦⣤⡏⣠⠀⢠⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠺⣅⠀⠀⠉⠉⠉⠀⠤⠄⠀⠀⠀⠀⠀⠈⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠞⣧⠚⡧⠊⠑⠸⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠙⢛⣿⣿⣿⣿⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠟⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠾⠟⣿⣿⣿⣷⠀⠀⢰⣿⡿⣿⣿⠿⢷⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⢾⣾⣿⣿⣿⡁⠀⠀⠀⢹⣿⣿⣾⣷⠦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡏⠁⢠⠂⠀⢢⠀⠙⢿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠈⠀⠀⠀⠀⠀⠆⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣶⣴⠶⠤⠤⣤⣄⡀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋⢀⡀⣹⣆⠰⡶⠶⢶⡿⢿⣿⣿⠋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣿⣿⡧⠸⣿⣿⡿⢃⣠⠾⠿⠛⣷⣶⣍⠸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⠋⢰⣟⠁⢠⡞⠋⣡⡾⣶⣵⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⣿⣿⡿⠙⣿⡿⠛⢉⣤⡿⢿⣟⠿⠷⡦⠙⢰⣿⣿⡏⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⣁⠀⠹⣏⠀⣾⠋⣠⣿⡛⣿⣍⡽⣦⣀⣿⣿⣯⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢟⣿⣿⠟⠀⣴⡟⠁⢸⠇⣰⠿⡟⢧⣙⣻⣷⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⣿⡏⠀⣼⣿⡿⠁⠈⢠⣟⠀⠹⣆⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⠁⢹⣿⣷⡏⠀⠘⠛⠛⠛⣿⣶⠋⠩⠭⣉⠛⠻⣯⣝⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⡀⡈⠟⣿⣇⣶⢀⣠⠄⠀⠹⣿⣦⡀⠵⠒⡨⠀⢈⡿⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠘⣿⣷⣷⡀⠙⣿⣿⣿⣿⣴⣦⣤⠌⠻⣿⣿⣾⠿⠿⠿⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣏⠛⢦⣌⠛⢿⣿⣿⡟⠁⠀⠀⢠⣀⣀⣀⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠓⢄⠙⢿⡇⠀⠀⠀⠀⠙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⡠⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢦⡀
⠀⠀⠀⡼⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠹⡄
⠀⢠⠊⣧⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢠⡏⢦
⠀⢸⠄⢸⡄⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣼⠀⢼
⢠⠋⢧⠀⢷⡄⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣴⠇⢠⠏⢣
⡸⡇⠈⣦⠀⠻⣦⣀⣌⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⡄⣠⣾⠃⢠⠎⠀⡿
⢇⠙⣆⠈⢻⣆⢻⣉⠉⠢⣀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⢀⡠⠊⢩⣽⣃⣾⠋⢀⡞⢁
⠈⢇⡘⠿⣤⠹⣍⠙⠦⣀⠘⢿⡶⠤⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠠⠴⣾⠟⢀⡠⠞⠉⡽⢡⣼⠟⢀⠏
⠀⠨⡙⢦⡈⠻⣿⠦⢄⣈⡻⣾⠗⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠐⢿⣾⣃⣀⠤⢾⡿⠋⣤⠞⡩
⠀⠀⠹⢄⣙⠳⢿⣶⣄⣀⣉⣻⡶⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠃⠀⠰⣾⣋⣁⣀⣴⣾⠷⢛⣁⠼⠁
⠀⠀⠀⠀⠈⠀⠂⣿⠉⢀⡠⠼⣿⣶⣀⡀⠀⠱⡀⠀⠀⠀⠀⡰⠁⠀⣀⣰⣾⡿⠤⣀⠈⢹⡇⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠈⣇⢀⡴⠊⡹⢿⣦⣄⠀⠑⢄⠀⢀⠔⢁⢀⣤⣾⠿⡋⠲⣄⢀⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠴⠼⣅⣼⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⣸⣄⡽⠴⠜⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣷⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢰⡿⣸⣿⣿⣷⣿⣿⡄⠀⠀⠀⢀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣿⣿⣼⣿⡟⣧⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠏⣼⣿⡿⣿⣿⡼⣿⣿⣄⠀⢀⣿⣼⣧⠀⠀⣼⣧⣿⡀⠀⣠⣿⣿⢯⣿⣿⣿⣿⣧⠙⠄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣇⢻⣟⣿⣯⡿⣿⣷⣾⣟⣿⣇⡀⢀⣸⣿⣿⣧⣾⣿⢿⣽⣿⣻⡼⣸⣿⣿⣶⣶⡄
⠀⠀⠀⠀⠀⢈⣼⣿⣿⣿⣿⣿⣿⣭⡿⣿⣿⣯⣿⣿⡻⠟⠀⠈⢿⣿⣻⣿⣭⣿⣿⢿⣻⣿⣷⣿⣿⣿⣿⣇⠁
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣟⣿⣿⣷⣯⣿⣿⣿⣏⡟⠀⠀⠀⠀⢿⣹⣿⡻⣯⣷⣾⣿⣿⣹⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢏⡟⣿⣿⣿⣿⣿⣻⣽⣽⣇⣿⣿⣟⠿⠇⠀⠀⠀⠀⠞⡿⣿⢿⡿⣹⢿⣏⢿⣿⣿⣿⣿⣿⢻⡼
⠀⠀⠀⠀⠀⢸⣿⣿⣿⢹⣿⣿⢹⣿⣶⠛⣏⠋⠏⠀⠀⠀⠀⠀⠀⠀⠀⠝⠛⡿⢿⣾⢾⡏⣿⣿⡟⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠈⣿⡿⣿⠈⣿⣿⢸⡇⢿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡟⣾⢧⣿⣿⠁⣿⢻⣿⠁
⠀⠀⠀⠀⠀⠀⣿⢁⢿⢰⡸⣇⡈⣿⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡿⡀⣼⢃⡜⡟⡸⣿
⠀⠀⠀⠀⠀⠀⡇⣿⣎⢸⣷⣁⣧⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⡇⢃⣾⡏⢱⣧⢿
⠀⠀⠀⠀⠀⠀⠁⣿⢻⣟⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣽⢿⣿⠈
⠀⠀⠀⠀⠀⠀⠀⣿⠈⣿⡽⣿⡝⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣳⣿⣳⡿⢸⡏
⠀⠀⠀⠀⠀⠀⠀⣌⡟⣾⢷⡙⣿⡌⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⣴⡿⢡⣟⡵⡞⡃
⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⢉⣮⡻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣖⢫⣾⡇⣿⡇
⠀⠀⠀⠀⠀⠀⣸⠟⠀⣿⣿⠸⣿⡇⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣿⡟⢸⣿⡇⠹⣷
⠀⠀⠀⠀⠀⠀⠁⠀⢀⣿⡏⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⣿⡇⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⠆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣴⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠦⢄⠀⢼⠃⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠘⡥⠀⡠⠴⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣓⠶⠚⣂⠀⠾⠁⡿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠈⠷⠀⣐⠓⠶⣚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠽⣋⠠⣈⡇⢾⢽⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡷⢸⣇⠀⣜⠯⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢞⡿⠾⣿⣷⣯⣾⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣜⣾⣿⠠⢿⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠽⠯⠝⢯⣳⢟⣆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡻⣞⡽⠫⠭⠯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠏⠔⢠⠥⣚⢨⠺⠴⡀⣀⠀⠀⣀⢀⠦⠗⡅⣓⠭⡔⠢⠹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠤⢈⠱⣊⢉⠰⠤⢀⠀⠀⡀⠤⡆⣉⣑⠎⡁⠄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⡠⠉⠛⠺⠈⠀⠀⠁⠓⠋⠉⢄⠂⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠄⠤⠄⠀⠀⠀⠀⢠⠄⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠗⢀⣶⣾⣿⣿⣿⡁⠘⠀⠀⠀⠀⠀⠀⠃⢘⣿⣿⣿⣶⣶⡀⠺⠷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⡶⢀⣤⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣿⣿⣿⡟⣤⡀⠠⣄
⠀⠀⠀⠀⠀⠀⣸⡇⠙⠉⢠⣿⣿⣿⣿⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢿⣽⣿⣿⣷⡄⠉⠛⢸⣇
⠀⠀⠀⠀⠀⣴⠟⣴⣰⣶⣿⣿⡿⣿⢻⣆⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣰⣟⢻⣿⣿⣿⡶⣦⣦⠻⣦
⠀⠀⠀⠀⣸⠿⢾⣿⠛⢾⣿⢉⡇⡇⠠⠙⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠁⠀⢸⠸⠘⣿⠿⢿⣿⡷⡿⣧
⠀⠀⠀⢠⢃⠆⢠⠁⠀⠀⠛⠀⣇⠸⡆⠀⠱⠄⠀⠀⢀⡀⢀⠀⠀⠀⡰⠊⠀⠰⠋⣰⠀⠿⠀⠀⠙⡆⠘⡜⡇
⠀⠀⠀⡜⡎⠀⠃⠀⠀⠃⡀⠆⠁⠀⠁⠀⡌⡀⠀⠀⡨⠅⠨⢁⠀⠀⠀⢰⠀⠀⠀⠈⠰⢀⠐⠀⠀⠘⠀⠸⢹
⠀⠀⢀⣻⠀⠘⠀⠀⣾⠀⡇⢀⡀⡀⢡⣀⠧⠈⠒⠁⠁⠀⠀⠈⠀⠐⠡⠞⣀⠎⢠⢀⡄⢸⠀⣧⠄⠀⠃⡀⣇⡇
⠀⠀⣼⣟⢸⠀⠀⣾⣿⡆⣇⢸⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣾⡇⣸⢸⣿⣷⠀⠀⣇⣿⣷
⠀⠰⠏⣿⡇⡀⣶⣿⣿⣿⣿⣾⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣷⣿⣿⣿⣿⣾⠀⢸⣿⡝⢇
⠀⠀⢠⣿⣧⡇⢻⡙⣿⣿⣿⣿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⡿⠿⡟⢸⣾⡿⡇
⠀⠀⠀⠁⢿⡇⠈⠁⢸⠹⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⣿⣿⣿⠿⠇⠀⠁⢸⣿⠀⡇
⠀⠀⠀⠀⠉⢃⠀⠀⡇⠀⠀⠘⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⠃⠁⠀⣸⠀⠀⡞⠀⠀⠁
⠀⠀⠀⠀⠀⠈⢂⠀⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⣿⠀⡀⠀⠀⢸
⠀⠀⠀⢰⡀⠀⠀⣿⢸⡄⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⢠⠋⣿⠀⠀⢀⡎
⠀⠀⠀⠀⢳⠀⠀⢹⡆⢣⠰⣄⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠃⠀⣠⠆⡎⢸⠇⠀⠀⡞
⠀⠀⠀⠀⠀⠁⠀⠀⢻⡈⠣⠉⠑⠲⠜⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢡⡧⠞⠋⢉⠜⢀⡟⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⡠
⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⢀⠂⢀
⠀⠀⢸⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠒⣐⡴⠖⠒⠛⠉⠉⠉⠉⠉⠙⠒⠃⠉⠛⠀⢈⣉⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠈⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡎⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⠈⠉⠒⠦⣤⣤⣀⣀⡇⠀⠀⠀⠀⠘⡆⠀⢀⡠⠐⠀⣀⡀⠀⠀⣵⡀⢸⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡠⠄⠊
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠢⠤⣀⠀⠀⠉⢻⠀⠀⠀⠀⠀⢁⡴⠋⠠⠒⠉⠁⠀⠀⠀⠀⡷⠾⡷⠾⠛⠛⠶⠖⠒⠂⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠙⠢⣼⠂⠀⠀⢰⣄⣀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠋⠀⠘⠀⠀⠀⢀⣀⣀⣀⡄⠤⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀⠀⠀⠠⢘⡻⣆⠀⠀⢀⡟⠁⠀⠀⠀⢀⣂⣠⣾⡇⠀⠀⠤⢤⣀⠠⣾⠉⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠒⢩⢴⣿⣦⣴⣾⣇⠀⠀⡀⢀⣾⡏⠉⠹⠋⠀⠀⠀⢠⣨⠛⠦⡉⠀⠀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠛⠀⠀⠠⡙⢯⠩⠁⢿⣿⣿⡇⡡⠖⠀⠀⠀⢨⣿⡀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣅⠀⠀⠀⠀⠀⣀⣀⠒⣾⠟⠧⠤⠤⠴⠒⠒⠢⠸⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⣤⠀⡆⠀⠀⠀⠀⡀⠀⢧⠈⠰⠂⢀⡼⠻⠷⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠟⠑⠁⠀⠀⠀⢾⠉⠻⡧⢀⡀⠴⣯⠔⠀⠛⡿⡖⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠏⠀⠀⠀⠀⠸⡃⠐⢹⣉⠷⠐⠛⠒⠒⠟⠁⠁⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡉⣆⠑⠢⠤⠴⠞⠉⠙⠁⠀⡸⠁⠀⢀⣠⠤⠤⠄⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣝⣒⡶⠖⣂⣀⣤⠶⠚⡅⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢏⠉⠁⠀⠙⢦⠁⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠤⣤⣤⡤⠶⠃

⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼
⠀⠀⢿⣆⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣼⡏
⠀⠠⣌⢿⣧⡹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢣⣾⠏⣠
⠀⢤⣝⣷⣝⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⣿⣣⠄
⠀⠀⢽⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡥
⠀⠐⢶⣿⣿⣿⣿⣿⣿⡿⣭⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣽⣿⣿⣿⣿⣿⣿⣥⠶
⠀⠠⣤⣿⣿⣿⣿⣿⣿⡯⣿⣿⣏⣀⣹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡋⣘⣿⣿⡯⢽⣿⣿⣿⣿⣿⣯⣤⠄
⠀⠀⠴⠾⠛⣋⣭⣵⣶⡶⡾⢻⡿⣳⢚⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣰⣿⡿⣏⣶⣾⣿⠻⡶⣶⣿⣿⣿⣿⠿⠦⠤
⠀⠀⠀⠀⢚⣿⡿⢟⣵⣾⣷⡾⣸⣿⣿⣿⣿⣻⣿⡀⠀⠀⠀⠀⢸⣿⡿⣷⣾⣿⣿⣻⣶⣿⡿⣽⡿⣿⣟⠃
⠀⠀⠀⠀⠈⠉⢚⣫⠾⣛⣡⣾⣿⣽⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⣾⠿⣼⣾⣿⢿⣵⣿⣿⣿⣿⣿⣟⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠐⢋⢿⡿⡿⣻⣯⠞⢫⣿⣿⣿⣷⡄⠀⠀⣰⣿⣤⣿⣮⣛⣾⣿⣿⣿⣿⢯⠻⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠧⠵⢜⢮⢞⣿⣿⣷⣼⠀⢘⣵⣿⣏⣿⣿⣿⣿⡿⠿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⢾⠹⠄⢸⣿⣿⠿⠟⠻⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣿⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣖⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⠛⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⢿⠻⠙⠇⠙

⠀⠀⠀⠀⣀⣀⣀⠀⢀⡀⢠⡆⠀⠀⠀⠀⠀⠀⠀⢀⣰⠂⠀⠀⠀⠀⢀⡀⠄⠀⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⢰⡇⠀⠀⠀⠠⢴⡎⠀⠀⠀⡠⠤⠀⠀⣠⣾⠏⠀⠀⠀⡠⠚⠁⠀⡄⢴⠃⠀⠀⠀⢀⡀⢄⠐⢠⡴⣻
⠀⠀⠀⢸⠁⠀⠀⣀⣠⠟⠀⠀⣠⠋⠀⠲⣟⣻⠿⠋⠀⠀⣠⠊⠀⢀⠠⣤⣀⡜⠀⠀⢠⠞⠁⡤⣪⢘⣩⣴⠃
⠀⠀⢠⡯⠤⠶⠚⠉⠀⠀⠀⣼⠃⠠⠶⠟⠋⠁⠀⠀⠀⠰⠋⠶⠧⠜⠦⠞⠁⠀⠀⠀⢸⡴⣀⠛⢤⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⢤⣤⣄⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠒⠒⠒⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⢀⠀⠀⠀⢻⡧⠀⢠⠖⠊⠉⠁⠀⠀⠐⢲⡎⠁
⠀⠀⡀⠀⠈⢀⠔⡠⣐⣮⠛⠀⣧⠀⠀⠀⠀⠀⢠⣯⠖⠀⠀⣏⠁⠀⠀⠀⣐⢷⡄⠀⠱⠀⠀⠀⠤⣬⠽⠁
⠀⠀⠈⠢⣀⡈⡼⡼⠞⠁⠀⠀⠘⢷⣆⣄⠤⣕⣶⠚⠁⠀⠀⠈⠛⠲⠾⢮⣯⣻⠂⠀⠀⠱⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠠⠢⢄
⠀⠀⠀⡔⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠀⠀⢐⡯⠀⢠⠆⠀⠀⠈⠀⣀⣀⣺⠆⢀⡠⠤⠤⠤⠄⠒⣀⣨⠆
⠀⠀⢰⠇⠀⡀⠀⣉⠢⠀⠀⠀⠀⠀⡼⠀⠀⠀⠤⣽⠃⠀⣼⠀⠀⠀⠀⣐⣭⠿⠁⠀⢈⠀⠀⠀⠀⣀⢐⡶⠋
⠀⠀⠺⠴⠓⠉⠛⠺⠓⠼⠓⠂⢀⣾⢧⣤⣶⡎⠏⠀⠀⢀⣿⠴⠷⠒⠚⠋⠁⠀⠀⠀⠘⠦⣄⣀⣰⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⣀
⠀⠀⠀⢀⣀⡤⠤⠤⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⢸⡀⠀⠀⠀⣉⠱⢶⣂⠀⠀⠀⠀⠀⡠⠀⠒⣒⡄
⠀⠀⢰⠋⠀⠀⠀⠀⠐⣪⠟⠀⢀⡖⠋⠁⠒⠀⢀⡠⢾⠀⠀⠘⡇⠀⡐⣓⢬⡽⢟⣥⠤⠀⠀⡠⠊⠀⠀⣩⡏
⠀⠀⢹⣀⣤⣴⡷⠆⠙⠋⠀⠀⢸⡄⡀⠀⠀⠠⠿⣺⠇⠀⠀⠀⢻⣘⣵⣿⡷⠿⠻⠁⠀⠀⠊⠀⠀⠀⣍⣩⠆
⠀⠀⠘⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠚⠛⠋⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠐⠋⠉⠙⠲⠿⠋⠁