Dish Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣴⠶⠷⠶⠷⠶⠶⠶⠾⢻⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡴⢟⡋⣠⣐⣒⣤⣄⠐⣃⡀⣈⡁⠰⢶⣄⣉⡁⠙⠛⠻⢷⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠟⢀⡄⠈⣴⠏⢉⣉⠀⠴⠀⠉⠁⠋⠉⠰⢶⠀⠀⠁⠖⠸⠳⢦⣀⠬⡉⢿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⡟⢋⡉⡡⢖⡚⠁⣥⡾⢳⡄⢀⠀⠀⣛⡛⠀⠙⢁⡀⢀⡤⠶⠖⢲⡀⠲⠆⣈⠐⠀⣤⠀⡍⢿⣤⡀
⠀⠀⠀⣴⡶⠶⠶⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠶⣶⡄
⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠁⣿⣎⠇⠀⠐⠫⠐⠛⠀⠀⢀⠺⠹⠀⠀⠀⠰⠥⠀⠄⠀⠀⣄⣔⠒⠀⠀⠠⠤⠭⠤⠀⠀⠠⠌⡫⠄⠀⠀⠈⠁
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠠⠀⠀⠀⠀⠀⠀⡔⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⣀⡀
⠀⠒⠒⠂⠂⠀⠀⠸⠿⠃⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠈⠒⠁⠀⠀⠘⠯⠽⠃⠀⠀⠀⠾⠥

⠀⠠⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡒⢄⠀⠀⣀⡀⢄⡀⠀⠀⢀⣀⣀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⢀⠘⠀⠀⠈⠉⠉⠁⠀⠀⠛⠛⠛⠁⠀⠀⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠄
⠀⠒⠒⠒⠂⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠐⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠁⠀⠀⠁⠈⠁⠁

⠀⠠⠠⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⣀⣈⡁⠀⠀⢀⠰⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠐⠐⠂⠀⠀⣀⣀⣢⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⢀⡤⠤⢴⡶⠶⠒⠒⠛⠓⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⢤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠉⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡌⠙⠲⠦⣤⣉⣉⠛⠒⠶⠦⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣼⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶⡆⠀⠀⠈⠉⠉⠛⠓⠒⠒⠒⠒⠒⠒⠛⠛⠛⣛⣻⣿⠿⠟⠛⢛⣿⠿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣙⣲⣦⣄⣀⣀⣀⣠⣤⡤⠤⠶⠶⠒⠒⢛⣉⣉⣤⡤⠶⠖⠛⣹⣇⣤⣷⡄
⠀⠀⠀⠀⠀⠀⣀⣠⡄⠙⢯⡉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⣉⣉⣁⣠⣤⠴⣒⣋⣽⣟⣩⠿⡟⠁
⠀⠀⠀⠀⠀⣾⣋⠀⠀⠀⠀⠈⠳⠦⠤⠤⠤⠤⢴⣶⣒⣚⣿⣭⣭⣿⣶⣚⣻⠯⠿⠟⠛⠉⠁⠀⣼⠃
⠀⠀⠀⠀⠀⢸⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠛⠻⡶⢦⡀
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣠⢃⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣴⡶⠶⠛⠋⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢶⣬⣿⠿⠿⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣶⡶⠶⣚⣛⣻⡏⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡞⠉⠒⠾⣄⠀⠉⠱⣄⣀⣀⡤⠤⠶⠒⠒⠚⢋⣭⣭⡉⠉⠉⠉⠛⠒⠒⡶⣦⠤⢤⣀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣹⣦⡀⠀⠈⠛⠙⣄⣇⠈⢧⣀⠀⠀⠀⠀⣠⡿⣽⢿⡟⢿⣿⠶⣤⠀⢰⢃⡷⣴⢳⢠⠏⣼⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠸⣀⠀⠈⣇⠀⠀⢀⠘⢾⠂⠈⠈⢧⠀⠀⢰⡟⢸⣇⣾⣳⣤⣿⠶⣾⡇⡜⣸⢠⢃⣾⢋⡼⢉⠗⡹⠊⠑⠦⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⣹⡆⠀⠉⠓⠪⣕⢦⡳⢄⣦⡘⢦⡀⢿⣁⡞⢹⣿⡋⠁⢻⣄⣼⣧⣇⢇⡎⣸⢣⢞⡴⡡⢊⣤⣖⣽⠧⢚⣹⡿⠂
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠉⣒⠶⣭⡳⣌⠳⡵⡄⠉⢙⠲⣍⢿⣿⡀⡸⢘⡏⠲⣤⠏⢠⣿⡸⣸⢱⣣⢫⢎⣾⣿⣿⢟⡫⠗⠋⢁⡀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⢡⣖⡺⠟⢮⣧⠹⡿⣄⠀⠙⢮⣇⣟⠻⣤⣾⣟⣦⣾⣖⣻⣿⣷⣷⡿⡱⣳⢟⢽⣫⡗⢉⡴⢤⢴⠋⠉⢳⡇
⠀⠀⠀⠀⠀⠀⠀⣷⣰⢫⢮⣻⡻⣦⣀⣳⡳⣝⠮⣗⣶⣪⠽⡷⢚⠽⠀⠀⠀⠀⠀⠉⠛⢿⠿⢵⣵⣟⠵⢫⡏⠈⡹⠧⡤⢦⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⢨⣧⣗⣿⡛⠻⣍⠛⡻⠛⠉⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠇⠀⠀⠉⠲⣍⢠⠚⢁⡴⢦⡞⠀⢸⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⠺⣿⡏⠳⡉⢳⠈⣿⡁⠀⠀⠀⠀⠈⠙⠒⠲⠶⠶⠖⠒⠒⠋⠁⠀⠀⠀⠀⠀⢈⡏⠐⡅⢀⡞⢑⡶⠋⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠈⠙⠢⣌⣹⢀⡟⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠗⢲⣋⠭⠛⠉⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠦⣀⠀⠀⠀⠈⠙⠓⠾⠦⣝⣛⣷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣒⣺⣽⡿⠭⠖⠚⠉⠀⠀⠀⢀⡠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠈⠙⠒⠶⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠶⠒⠉⠁⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⠤⠖⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠉⠓⠒⠶⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠴⠖⠒⠋⠉⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠴⣒⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣉⠉⠙⠛⠒⠒⠚⠛⠋⠉⢉⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣶⣂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠁⠀⣰⠋⠈⠙⢳⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠸⣄⠀⠀⠀⠀⠀⡴⠛⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠙⣇⣠⣤⠞⠛⠆⢶⡰⠛⣧⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣇
⠀⠀⠀⠀⠀⢸⡧⠤⠤⠰⢤⡤⠟⣤⠼⣏⡉⠒⠋⠁⠀⠹⣇⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠰⢟⣠⠤⢼⢀⡞⠉⠳⣄⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠷⣤⣴⡋⠀⠀⠀⢰⡶⠀⠀⠀⠀⣶⢀⣠⡾⠀⠀⠀⠀⡀
⠀⠀⣶⣤⣄⣀⣀⣘⠉⠛⠛⠛⠾⠿⠿⠿⠿⣿⣻⡛⠋⠉⠀⠀⠤⠶⢚⣋⣀⣀⣤⣤⡶
⠀⠀⠈⠙⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠋⠁






⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠚⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⣋⣉⣤⡤⠶⠶⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⢛⣋⣛⡫⠿⣧⣀⣤⠶⣛⣥⠶⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⢃⣎⣋⠒⠄⠴⣈⡼⠁⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣇⣂⣵⠤⠬⠒⢊⣡⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠖⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⢶⠖⠚⢛⠛⠓⠒⢚⠙⠶⠶⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢛⠉⣂⡖⠶⠚⣃⠐⠂⠴⠦⣩⡓⠒⢄⡀⣭⡉⢙⠶⣶⡀
⠀⠀⠀⠀⠀⢀⣀⡶⣛⠛⠵⡞⢁⡼⢦⡈⡁⠀⣖⠂⠐⢂⠀⡠⠤⠴⡄⠠⢍⡃⠍⣌⢹⢻⣄
⠀⠀⠰⡶⠶⠾⠿⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⠒⠒⠓⠒⠒⠲⠲⠶⠶⠶⠾⠷⢶⡆
⠀⠀⠀⠹⣦⡒⠐⠒⠐⠒⠀⠂⠐⠂⠒⠂⠐⠂⠐⠂⠐⠒⠐⠒⠂⠒⠀⠐⠂⠐⠂⠐⠂⠒⠀⢲⡞
⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⣄⣠⣀⣄⣀⣀⣀⠀⣠⣤⡦⠒⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣴⡾⢷⣤⣾⣶⣿⣸⠭⢹⠛⣻⣿⣛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⠭⢵⣜⣯⡷⠿⣏⢵⣿⡿⣋⡙⡀⣁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡰⢶⡦⠨⠗⠂⠀⠩⣍⣉⣉⣈⣉⠉⠀⠀⠈⠀⢈⣷⡑⠀⠀⠠⠤⠴⠦⠒⠲⠆
⠀⠀⠀⠀⠀⠀⢲⣤⠖⠀⣿⣖⠚⠑⠶⡄⠁⠀⠀⠈⠛⠝⠢⣀⣀⠀⠠⡀⣶⣥⣹⣿⣤⣀⣀⣀⠀⢀⣼⠀⠀⠀⡀⠀⠻⠦⣄
⠀⠀⠀⠀⠀⠀⠛⢻⣵⡿⣄⠀⠱⠆⢄⡀⠈⠳⡤⢀⠀⠈⡓⢹⣶⡟⠞⠀⡎⠁⠁⠹⣿⣿⡟⠋⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢠⣤⣕⠤⣈⡻⢿⣞⣿⠆⡬⢉⣠⣶⢤⠈⣥⡜⢿⣼⣿⣇⢄⠘⢀⠀⣂⠀⣿⡏⠙⠄⠀⠀⠀⠀⠰⠤⠄⠀⠀⠀⠀⡼⡐
⠀⠀⠀⠀⠉⠋⠻⢿⣶⣭⣍⣛⡛⠿⠷⠚⠻⣯⣉⡃⠿⠛⠂⠈⠻⢿⣯⣑⠢⢤⣈⣠⣼⣧⣴⣦⣄⠀⠀⠀⠀⣤⣀⠀⠁⢐⣯⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣯⣤⠀⠤⠄⢒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠢⠬⠉⢛⠛⠛⠛⠛⠛⠒⠛⠛⠒⠒⠊⠉⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡽⠾⠯


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⢠⡶⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠾⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠖⠛⠛⠛⠉⠉⢉⣉⣉⣀⣀⣀⣀⣀⣉⣉⠉⠉⠉⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠛⠋⢉⣀⣠⣤⠴⠶⠶⠚⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠳⠶⢦⣄⡀⠈⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣀⣠⡴⠶⠛⠋⠉⠀⢀⣀⣠⣤⣤⠤⠶⠶⠶⠶⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠾⢿⣷⣄⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢀⣠⡶⠛⠉⠀⠀⣀⣤⡴⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠛⠁⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⣼⠃
⠀⠀⠀⢀⡾⠁⠀⢠⡟⠁⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⢀⡼⠃
⠀⠀⠀⢸⡇⠀⠀⠘⣧⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠁⠀⠀⣠⡶⠋
⠀⠀⠀⠈⢷⡀⠀⠀⠈⠻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠛⠋⠉⠀⠀⢀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠛⢦⣄⠀⠀⠀⠉⠙⠛⠶⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠚⠛⠛⠉⠁⠀⠀⠀⣀⣠⣤⠶⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠴⠶⠚⠛⠉⠁⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡛⠛⠒⠲⠶⠶⠶⠶⠶⠒⠒⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⢀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⢀⠀⠀⠠⡦⠥⡠⢄⣠⢤⡄
⡠⠶⠿⠇⢼⠺⢬⠤⢶⠬⠂⠁⠱⠹⠕⠤⡤⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣠⣤⣤⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢠⠀⢸⡏⡄⡄⢹⡇⡄⡆⣿⡇⠀⠀⣀⣤⠤⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠒⠒⠚⠓⠒⠒⠛⠓⠒⠒⠋⠁⠐⠓⠂⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡴⠦⠴⠖⠒⠒⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠈⠉⠀⢀⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢀⣀⡠⠠⠀⣚⣉⡥⠤⠤⠒⠒⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠘⠛⠋⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣺⣯⣽⣯⣿⣽⣽⣭⠿⣷⣦⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣝⡸⢿⡟⣽⣷⡯⣧⣫⡻⢿⠯⣿⣾⢽⣟⣕⡆
⠀⠀⠀⢀⣴⣶⡶⠀⣠⣤⣤⣤⣤⡀⠰⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣿⣾⣿⣾⣿⣿⣿⣿⣷⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠁⢀⣿⣿⣿⣿⣿⣧⠀⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠈⠀⠼⢿⣿⣄⢸⣿⣿⣿⣿⣿⣿⠠⠾⠿⠟⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⣀⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⣉⣠⠤⠐⠂⠉⠁⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢶⢒⣋⡩⠤⠤⠄⠒⠒⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣠⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠠⡍⠀⠀⠀⠀⠈⠉⠑⢄⠀⠋⢐⠃⡠⠀⠈⠳⡀⠀⠀⠀⡎⢁⣀⠆⡀⢀⡻⠌⠒⠀⠀⠀⠀⠀⠃⢔⠀⠀⠀⠈⠁⠈⡆⠘⡃⡑⠀⠀⣀⠤⠤⡄⣄
⠀⠀⠀⠀⠀⠀⡀⣀⠠⢔⣉⠃⠀⠸⡄⠀⠂⡄⡀⠉⡄⠀⢘⠀⠈⡂⠀⡀⠀⠀⠀⠐⡀⠀⠀⠀⠄⠀⠀⡠⠁⡀⠀⠂⡰⠀⢀⡈⠚⠀⢾⠥⠤⣈⠓⡎
⠀⠀⠀⢈⠄⠄⠀⠂⠀⡠⠌⡃⠀⠀⠙⢄⡀⠡⡈⠢⣸⠀⠀⢱⣝⡥⣩⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⡔⡀⠀⠀⢂⡔⠁⠀⠈⠉⠣⡀⢠⠀⠀⠀⠀⡇
⠀⢀⡀⠐⣉⣁⠀⠄⠂⠂⠈⣀⡀⣀⣀⡀⠈⠒⠨⠆⠀⣠⠶⠀⣏⢝⡁⠀⠀⡀⢄⡧⠋⠒⡀⢄⠆⡐⣀⠀⠐⡠⠊⠀⠱⡴⣄⣀⣀⠁⠘⠀⠤⠤
⠀⠘⠇⠀⠀⣤⠀⠀⡠⠔⠋⠃⢠⢃⠂⡀⠉⢢⡀⠀⠀⡿⠛⠀⠸⣎⡆⠀⠠⠬⡞⠀⠀⠀⣍⠀⡀⠣⣀⠥⠊⠠⢀⠀⢀⡀⠀⡠⠁⠀⠀⣀⠀⠀⠐⠢
⠀⠀⢀⣄⡀⠁⢀⡊⢐⣁⣊⠠⠦⠌⢰⡖⡫⠵⠂⢀⣀⣤⣀⠄⠀⢳⠀⠀⠀⠈⢑⠂⠲⠔⠫⠕⠂⠀⠀⠀⢀⢁⠊⣀⡀⠈⠉⠁⠀⠒⠈⠀⠰
⠀⠀⢏⠀⢹⡄⠐⢴⠒⠠⠒⠚⠒⠊⣉⣀⡤⠜⠀⢸⠀⠀⠀⢉⠆⠀⡠⠂⠄⠀⢐⠀⠍⠀⠀⠀⠀⢠⣤⣠⣤⠁⠀⠑⠁⠀⠉⠂⠀⠀⠀⠀⣁⢀⡐
⠀⠀⣸⢀⠤⠱⡀⠀⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⡎⠀⠀⠀⣸⠇⠀⢇⠴⠀⠠⢈⠈⢃⠀⠀⢴⣿⣯⣹⣿⣔⣿⣆⠀⠤⠀⠀⢠⡀⠀⢤⣋⠀⡬⠁
⠀⠀⢱⠈⠒⢀⡇⠀⠀⠀⢶⠙⠒⠀⠤⠄⠒⡶⠀⠙⠃⠒⠖⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⢀⠿⠀⠀⠀⠀⠘⡄⠰⣀⣀⠔⠀⠀⠈⠉⠉
⠀⠀⠀⠙⠘⠉⢠⢴⡀⠀⢄⠁⠀⠐⠒⠂⠈⠁⠀⡀⢄⡢⣠⡀⠀⠀⣎⠀⠀⠀⠒⢲⠶⡄⠀⡉⠁⠀⠁⡛⠫⠈⠉⠀⠀⡸⠄⠀⠀⢀⠄⠐⡄⠐⠐⡄
⠀⣰⠀⣐⠀⢠⠁⠀⠉⠀⠉⠀⠀⠀⠠⠠⠤⠄⡖⣆⡿⠟⢁⠇⣀⠌⣰⠈⠉⠈⡉⠉⠂⠁⠀⠐⠀⠀⠄⠀⠀⠒⠀⡤⠉⠀⠊⠀⠀⠋⠀⠀⡸⠒⢴⡡
⠀⠈⠉⠀⢀⠂⠀⠀⠀⢀⠀⢠⢤⠈⠲⠂⠀⠋⠁⣀⠤⠖⢁⡊⠙⠀⢉⡐⣽⠟⠁⠀⠀⠀⢢⠀⠠⠖⠀⠀⣄⣀⠀⣠⠀⢀⡀⠀⡎⠐⢀⡎
⠀⠀⠀⠀⠂⠀⠀⠐⠀⠂⠀⠈⠁⠀⠈⠁⠀⠉⢁⠀⢀⣔⣡⠥⠴⠖⠚⢉⡠⡄⠈⠀⠀⠀⢸⠀⠀⠀⣄⢒⠄⠥⠠⠄⠨⠄⠋⢄⠈⠉⡠⠗⠀⢀⡀
⠀⢀⢀⠰⢈⠉⠣⣀⠀⠀⠀⢀⠢⠀⠤⠄⠀⠀⠓⠁⠀⠁⢀⣄⠀⠀⠀⡫⠭⠃⣀⠀⡀⠔⢁⡀⠀⢀⡀⠀⠄⠉⠉⠉⠈⠉⡁⢈⠀⠀⠀⢀⠋⠀⠈⡀
⠀⠘⢤⡀⠀⠀⠁⣁⠀⠀⠀⠐⠺⡞⠠⠀⠁⢠⣶⠶⠒⠃⠼⢻⠤⣄⠀⠉⠀⡐⠈⠁⠀⠀⠑⠁⠀⢰⡈⠀⠄⠀⠈⠁⠈⠀⠈⡋⠀⠀⠀⠸⢀⠄⣀⠃
⠀⠀⡀⠀⠶⢈⠜⠁⢀⠀⠂⠀⠀⠁⠄⠁⡠⠋⠀⠁⠀⠈⠂⠉⠉⠁⠀⠐⠡⡀⡄⢀⠀⠠⠂⣑⡄⠈⠒⠀⠤⠤⠤⠤⠤⠤⠒⣛⠆⠀⠀⠆⠁⠈⢨
⠀⢨⠁⠘⠀⠁⠆⠀⡨⢀⡠⠀⠤⢄⠀⠀⠀⠂⠸⠀⠀⣀⠂⢀⠔⠈⠙⠀⠀⠈⠀⠘⢠⠐⠒⠁⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠁⠀⢰⣡⠀⠂⠤⡄⠆
⠀⠀⢇⢐⡀⡠⠐⠀⢠⡃⡴⠉⠠⠀⢄⠀⠓⠀⠀⠐⠚⠋⢁⠂⠀⠀⠀⢰⠀⠰⠀⠠⠊⠠⠊⠑⠀⠸⠃⢀⠠⠀⠀⢀⡠⠂⠄⠀⠈⠺⠀⢸⣀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢱⠈⠈⢀⠀⡠⠁⣎⠑⠒⠒⠀⡀⠀⠂⠀⠠⠀⣾⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠈⠐⠒⢧⠀⡀⢀⡱⠄⠀⠀⠀⢀
⠀⠀⡁⢨⢹⢸⡀⢲⡀⠘⠢⠚⠁⠀⠀⣐⠁⣀⡄⠀⠀⠀⠀⠈⠃⠀⠀⢣⠀⠨⠀⢉⠀⠀⠀⡠⠔⠋⠀⠀⠀⡠⠒⠀⠈⢉⡗⠁⠀⠀⠐⣧⣃⡠⠐
⠀⠈⠁⠀⠠⠀⠀⢈⡀⠀⠘⢁⣈⡢⠀⠈⠁⠘⠘⡀⠀⠢⡐⠀⠀⢀⣠⠃⠀⠀⠀⠘⠁⡠⡐⡁⠀⠀⠠⠤⡀⠁⠀⠀⣠⠎⢴⠇⠀⠐⠆⠉⠁
⠀⠀⠀⠃⠀⠃⢉⠉⠀⠀⠀⠁⠀⢀⠀⠀⡄⠀⠤⠃⠀⠀⠈⠁⠉⠁⠀⠀⠀⠀⠭⠦⠄⡓⠬⠌⣁⣒⣒⠛⡄⢉⠚⠩⠄⠒⠉⢠⠢⠀⠢⠀⠀⠀⣀⢀
⠀⠀⠀⢀⠀⠀⢈⠀⠀⠀⠉⡄⠀⠀⠒⠌⠀⣀⡤⡀⢰⠋⠉⠙⣇⠀⠉⡰⠀⠠⠀⠀⠀⠈⠄⠀⠀⢀⠤⡄⢀⠤⢆⢀⡠⢄⠀⠀⠁⠀⠀⠀⠀⠀⠁
⠀⢠⠀⡄⠢⠄⠤⠀⠀⠀⠲⢱⠊⠀⠀⠀⠀⠣⡤⠜⠰⠁⠀⢸⠀⠀⠀⠁⠀⠘⠄⠀⣤⠎⠀⠀⠀⠘⠜⠁⠨⠰⠉⠈⠀⠌⠀⢠⣤⠄⢈⠛⠑⠔⣀⣀
⠀⠀⠉⣀⢤⠐⢠⡀⠀⠀⢀⠰⠀⠀⠄⠒⠲⡄⠀⠀⠈⠉⠉⠉⠉⠁⠉⠀⠶⠂⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠠⠀⠀⠀⠀⢀⡜
⠀⠀⣜⠳⢉⡰⠟⠈⠀⠜⠄⢠⠔⠁⠀⠀⠂⡇⠀⢠⠊⢁⡠⠤⠴⡂⠀⠄⠠⠐⠂⡏⠀⠀⠀⠠⠂⠁⠀⠑⠞⠿⠯⠅⠀⠀⠀⠀⠑⡆⠠⠤⠤⠤⠊
⠀⠀⢻⡵⠒⠁⠀⠀⡀⠀⠀⠠⡀⠀⣀⠤⢊⣤⠀⡇⡴⠁⠀⠠⠄⠈⠐⠒⠒⠒⠉⢀⠀⠂⢁⣀⣀⠤⠤⠚⠀⠀⠑⠄⡀⠀⠀⠀⠤⠈⠀⠀⢀⣀⡐⡿
⠀⠀⠀⠈⠐⠀⠀⠊⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠀⠀⠀⠀⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠤⣒⣒⣒⣒⣒⡒⠒⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⣠⠴⠚⠉⠁⠀⠀⠉⢉⡿⣷⣦⠀⠀⠀⠀⠉⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠀⠀⢀⠀⢠⠊⠀⢀⡕⠀⠈⠐⢈⣵⡿⠁⢹⠟⠠⡐⠲⣦⣄⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡔⠋⠁⢉⢧⡀⠀⣋⡀⢤⡴⠚⢭⢋⣷⣠⠊⠀⠀⠀⢀⢼⠟⣿⡆⡀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⡴⠋⢣⡀⣀⡬⠞⠿⣿⣋⢐⡾⢻⣢⠶⠴⠋⠐⠓⢀⣤⣴⠕⢳⣏⣟⣼⢃⡆⠀⠀⠀⢳
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣿⡀⠀⠈⡃⠀⠀⣀⠘⡜⠋⠁⠈⠙⢶⡶⠒⠲⠿⣿⣋⣻⣧⡖⣩⡍⠵⣹⠇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠈⠻⣄⡀⠣⣄⣮⣹⢿⠀⠀⠀⢀⡀⣼⣽⠗⠶⠶⠶⠻⠷⠚⣧⣈⣵⠞⠋⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⠛⠶⣶⣤⣤⣷⣷⣾⣶⣾⣋⣛⣒⣢⣭⣿⡿⠷⠞⠛⠉⠀⠀⠀⠀⢀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠔⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠐⢧⣄⡀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣶⣶⠆⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⢈⡗⠀⠀⠀⠹⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢠⣿⠏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢦⠀⠀⠀⠀⣾⡉⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠸⠃⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠸⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠴⠶⠃⠀⠀⠀⠀⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣁⡴⠖⠚⠓⠶⣄⣀⣀⣀⣀⣀⣀⣠⠞⠛⠙⠓⢦⣀⣀⣀⡿⠀⠀⢠⣏⣀
⠀⠀⠀⠀⠀⣶⣿⣿⣋⣉⣉⣉⣉⣟⣀⣀⡀⢀⣀⣹⣇⣀⣀⣀⣀⣸⣃⣀⣀⣀⣀⣀⣻⣉⣹⣇⣀⣀⣟⣉⣉⣉⣉⣽⣿⡿⣶
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⣠⠴⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢤⡀⠀⣿
⠀⠀⠀⠀⠀⢿⠀⢸⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠀⣷⢀⡇
⠀⠀⠀⠀⠀⢸⡄⠈⠳⢤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠓⢦⣰⠞⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠞⠃⣸⠁
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢀⡴⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⣤⡀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢸⣀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣸⠇⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠉⠉⠁⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠉⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⣿⣉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⣹⠆⠀⠀⠀⢀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣀⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡀⠒⠂⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⢁⣐⠀⡈⡂⠀⠀⠈⠒⠤⠴⠶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠀⠁⠉⠉⠛⠾⡋⠛⠐⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣒⠒⠤⠤⠤⡴⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠈⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠈⠲⣄⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢌⣳⡾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠒⠒⠒⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠂⠒⠒⠒⡒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⣶⡤⣀⣀⡀⣀⢀⣄⣀⣀⣤⣠⠤⠴⠖⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⠈⠓⡘⢭⢩⢀⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠈⠒⠚⠃⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠹⠖⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⢀⠈⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣾⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⠶⠖⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⠏⠉⠙⡥⠀⠀⠀⣛⠛⠛⠛⠷⢤⠦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠁⠃⡀⠰⠀⠀⠀⠈⠉⠀⠀⠀⢀⡈⠀⠂⠈⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⠛⠉⠀⠠⠀⠈⠀⠀⠀⢀⡄⠀⠀⠒⠀⠀⠘⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠱⠂⠀⢰⠂⠀⠀⠰⠂⠈⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠰⡦⠀⠀⡔⠂⠀⠀⠀⠀⠀⠀⠈⠀⠍⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⠚⠀⠀⠞⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠂⠀⠀⠀⠀⡀⠀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⢀⣤⢿⠄⣴⠀⠀⠀⣠⠀⠀⠀⠀⢀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⠷⣄
⠀⠀⠀⠀⠀⣴⠋⢠⡟⠀⠰⡂⠀⠀⡉⠁⠀⠀⣀⡀⠀⠀⠀⠈⠃⠀⠀⢠⠀⠀⠀⠋⠀⠀⠀⠀⠀⠰⠄⣿⠀⢸⣧
⠀⠀⠀⠀⠀⣿⡄⠘⢧⣉⠀⠀⠀⠘⠒⠀⡀⠀⠣⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⡼⢻
⠀⠀⠀⠀⠀⣇⠙⠶⣄⡉⠳⢦⣀⡁⠀⠘⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⠂⠀⠀⠔⡆⠀⠀⣀⣠⡾⠋⣠⠞⠁⣼
⠀⠀⠀⠀⠀⢻⡀⠀⠈⠙⠲⢤⣈⡙⢦⡴⢶⣦⣤⣀⣀⣙⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠾⢉⣠⡴⠚⠁⠀⢠⡏
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠈⠉⠓⠲⠶⠤⣤⣉⣉⣉⡉⠙⠛⠛⠛⠛⢋⣉⣉⣠⠤⠶⠚⠋⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠲⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣀⡈⠉⠙⠛⠓⠒⠒⠶⠶⠶⠶⠶⠶⠒⠒⠛⣉⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠦⠤⠤⠤⠤⠤⠴⠶⠖⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠾⠛⢛⣋⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⢟⡛⢛⡯⡽⣧⣄⣀⣤⣴⠶⢟⣛⣋⣭⣥⡷⠾⠟⠛⢛⣉⣉⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠿⠋⣧⠅⠺⣥⢙⡈⢿⣿⠷⠾⣛⣛⣩⣭⣤⡶⠶⣾⣿⣛⣫⣭⣭⡽⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠊⣥⠤⠅⣲⣀⣩⡥⠾⢿⣛⣛⣯⣭⣽⠶⠶⠟⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣴⣯⣭⡿⠷⠞⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⣼⡟⠛⠿⠛⠉⢁⠙⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠾⠛⣋⡭⢀⠈⠋⣤⡤⠘⠃⠉⣠⡙⠷⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⡶⠿⢋⣀⡴⠎⡉⢀⡘⠁⠐⠒⠢⣈⣋⡀⠐⠷⣤⡜⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣿⠆⢉⡤⠿⢉⠀⠛⣀⣥⠀⠻⠿⠋⢙⣉⠉⠷⢤⡃⠈⢛⣀⠈⠻⠶⣦⡀
⠀⠀⠀⠀⣀⣀⣾⣏⣁⣊⣁⣀⣈⣉⣥⣤⣬⣥⣤⣈⣳⣦⣬⣥⣤⣤⣤⣤⣄⣀⣀⣀⣈⣃⣹⣷⣀⣀
⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⣿⣀⣤⠀⢀⣀⠀⣀⡀⢀⣀⠀⣀⡀⢀⣀⡀⢀⣀⠀⢀⠀⠀⢀⡀⠀⢀⣀⠀⢀⣀⢀⣀⣿
⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠉⠁⠈⠉⠁⠈⠉⠁⠈⠉⠀⠈⠉⠀⠈⠉⠀⠈⠁⠀⠀⣿
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠛⠻⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿
⠀⠁
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⠶⠾⠛⠓⢶⣤⠴⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⣤⠾⠁⠈⠑⠚⠉⠁⠀⠀⠀⠀⠈⠉⠳⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣋⡤⠀⣀⡀⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⠟⠈⠁⠊⠙⠁⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠈⠻⠖⠲⣦
⠀⠀⠀⠀⠀⠀⠀⣠⡤⢾⣃⡴⠊⠁⠀⠀⠀⡀⠀⠀⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠉⠀⠀⠿⣄
⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⢀⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠤⠴⠛⠋⠙⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⢀⣠⣼⠇⠀⠀⠤⠏⠀⠀⠀⠀⠠⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⣇
⠀⣠⠞⠉⡤⠛⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣄⣀⠀⠀⠈⡷⢦⡀
⣼⠃⠀⣴⠃⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡇⠀⢹
⡟⠣⡀⠘⢦⡐⠘⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⠖⠂⠀⣀⣀⡖⠋⠀⠀⣠⠴⠋⢀⣠⠟
⡗⠀⠉⠳⣤⣈⠛⠲⠦⣤⣀⡂⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢊⣉⣠⣤⠴⠞⠋⣁⣤⠖⠋⠁⢸
⣿⢤⡀⠀⠀⠉⠙⠳⠦⣤⣉⡉⠛⠛⠒⠲⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠴⠶⠶⠚⠛⠉⢉⣀⣤⡴⠞⠋⠁⠀⠀⠀⢀⣼
⢸⡄⠉⠳⢤⣀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠶⠶⠖⠚⠛⠋⠉⠉⠀⠀⠀⠀⣀⣠⠴⠚⢉⡏
⠀⣷⢀⡭⠳⡌⢙⣲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣶⣯⣉⢘⡍⣷⣼⠁
⠀⠸⣦⡓⠚⠁⣨⠍⣷⠠⠬⣍⠙⢓⣒⠲⠦⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠴⠶⣒⡚⠋⡭⠗⢦⠀⢡⣖⡼⢈⣻⣿⠃
⠀⠀⢻⡉⠓⠦⣍⣉⠁⢰⣯⠾⠀⣭⠍⣧⠀⢚⡋⢳⡄⠰⠖⠓⣦⠀⠰⢛⡛⣦⠀⣫⡍⢹⠀⠰⣯⠼⣁⣠⠽⠚⠉⢠⠏
⠀⠀⠀⢻⡄⠀⠀⠈⠙⠓⠲⠤⣤⣙⣛⠁⠀⠿⡭⠾⠁⠐⣯⣥⠾⠀⠀⢯⣥⠞⠀⣙⣒⣫⠤⠖⠚⠉⠉⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠛⠷⠶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡴⠶⠚⠋⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢀⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠲⣼⣆⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠨⠁⠰⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⠀⠀⠠⢀⡠⢤⣀⠀⠀⠘⢆⢑⠍⠅⠑⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠁⠀⠀⡠⠐⠉⢀⣠⠤⠤⠶⡶⠲⢤⡤⢮⣝⡒⢮⡑⠄⠀⠈⠣⡡⡂⠚⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⢀⠀⠀⠂⢀⠔⠋⠀⠁⠚⠁⡀⠀⡠⢎⡀⠱⢢⢌⠑⠮⡙⢦⡙⣄⢦⡀⠈⠄⢔⠐⣌⠳⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢀⠂⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡄⢌⠑⢤⠀⠰⡀⠄⠌⢧⡘⢦⡙⠦⢀⠂⠓⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠤⢀⠀⠀⠈⢆⠐⢄⠡⡀⠱⡀⠢⡠⠙⠲⢬⡙⢦⡀⢄⠠⢀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠁⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠑⡀⠀⠈⡄⠀⢆⠱⣄⠙⠠⢄⡀⠁⢦⡉⢦⠹⡄⢀⠀⠑⡀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠂⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⡁⠀⠀⠀⠌⡑⠢⢄⡈⠓⣄⠹⡌⢧⡙⢦⡑⠢⣔⡄⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠔⠀⠀⢀⠃⠀⠀⠀⠀⠀⠑⠄⠙⢄⠈⢢⠙⡂⣙⠲⣬⠟⠁⠘⡆⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠊⠑⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢣⡀⢅⡈⠣⣌⡁⠀⠀⠀⠀⠂⠀⢂
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⠃⠠⣀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠣⡆⠀⠃⢄⡭⠃⠀⠸⠀⠀⠠⠀⠡⡀
⠀⠀⠀⠀⠀⢀⠂⠀⠞⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣀⣉⣉⡡⠄⠀⢤⠤⢠⠄⠠⠤⣀⡀⠀⠀⠀⠀⠀⢀⡖⠀⣁⡲⠊⠀⠀⠀⠆⠀⠀⠀⠑⡀⠐⠄
⠀⠀⠀⠀⢀⠂⠀⠌⠀⠀⠀⠀⠀⠀⠀⢀⣀⠛⠆⠁⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠉⠉⠐⡦⢠⡞⠀⠔⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠐⠄⠈⠂
⠀⠀⠀⢀⠂⠀⠌⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠆⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠔
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠔⠁⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⣀⣀⣀⢀⡀⣀⣀⣀⣀⣀⣀⢀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠻⣛⡋⠉⠉⣈⡅⠈⠉⠍⠍⣉⠀⠻⠿⠛⢿⣦⣤⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⠋⢥⠄⣶⢦⣥⠴⠛⠂⠠⠶⠄⣴⢦⡈⢉⠓⠶⢶⡄⢀⢀⣉⠙⠛⠻⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠟⠁⢰⠆⡄⠿⣋⠀⢴⠄⠘⢋⣀⣀⠀⢉⡀⠘⠛⠃⠀⠀⠀⠋⠘⠉⠻⢦⡌⠣⠄⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⢩⡄⢡⠚⢫⠍⠠⠤⠿⢹⡦⠠⡤⠀⠨⢭⡉⠀⠈⢡⠄⠀⠴⠒⠛⠋⢳⠄⠘⠓⢤⠄⠓⠰⠦⠰⠆⠿⣦⣄
⠀⠀⠀⢰⣶⠶⠶⠾⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⢶⣶
⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣞⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⣒⠋⠭⠒⢂⣈⡠⢤⠄⣀⣀⣀⡤⣤⢤⠄⣀⡀⠉⠉⠛⠲⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣠⢞⣫⡴⠞⠋⠁⣀⠔⣩⣤⠆⣹⢭⣋⡿⢶⣻⣷⣶⣧⣏⠉⠛⠏⡏⠛⡿⡖⣶⣄⠉⢷⣦⣀
⠀⠀⠀⠀⠀⣠⣟⠵⠛⢛⣇⣤⡦⣚⣕⣺⢏⣖⡺⠗⠻⣞⣫⠯⣗⣻⡖⢮⡿⣦⣤⣀⣄⣀⣠⣆⣋⠟⢻⡗⣜⢿⡷⡄
⠀⠀⠀⠀⢠⣿⡏⢀⡰⢯⣿⣤⢙⣖⣩⣿⠿⣿⡾⠿⣷⣿⣻⠿⣟⡼⠿⢏⣸⠯⠘⣿⣿⣿⣶⣒⣻⣍⡽⢫⢸⠘⢉⣧
⠀⠀⠀⠀⢸⡿⣷⢬⡳⣯⣽⡯⣟⠛⢷⡾⣷⠿⣶⡏⡼⢿⣭⡿⢭⣿⣳⣿⣤⠞⠋⠒⣿⡔⣫⠿⠭⣯⣵⣾⣗⡷⣺⣿
⠀⠀⠀⠀⠀⣿⠘⠳⢿⣗⡺⠭⠟⡕⣲⣶⠒⣫⣝⣺⣳⣿⣿⣿⣷⣿⣽⣿⣯⣀⠶⣎⡹⣟⣓⣶⢿⣿⣯⣽⣿⡟⢱⡇
⠀⠀⠀⠀⠀⢸⡆⠀⡈⠀⡏⢛⡲⠤⣝⣚⣣⣏⣸⣟⣿⣙⣍⡁⠻⡩⢟⣿⣞⣯⣶⣾⣼⣷⣾⣿⡿⠿⡟⠋⣧⠇⣾⠃
⠀⠀⠀⠀⠀⠀⢿⠀⢇⠀⠀⠈⠭⣓⣒⠢⠭⠉⠉⠉⠛⠛⠛⠛⠒⠒⠒⠛⠛⠛⠛⢋⠩⠭⠁⠀⠀⠈⠁⢸⠋⣸⠏
⠀⠀⠀⠀⠀⠀⠘⣧⠘⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠃⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣦⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⢚⣩⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⢤⣤⣤⣤⣤⡤⠤⠴⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠀⠒⠒⠂⠀⠐⠒⠒⠂⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠁⢀⣀⡠⠤⠄⠒⠒⡒⠒⠒⠒⠢⠤⢤⣀⣀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⢀⡠⠔⠊⠁⠀⠀⢀⣀⣀⠀⠀⠄⡀⠠⡆⠀⡲⠀⣠⠍⠒⠠⣀⠈⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⣠⠖⠁⠀⠀⠀⠀⠉⠒⠤⣀⢩⢉⡗⠢⢬⣵⡧⢠⡦⠈⠥⠀⠀⠀⠀⠙⠢⡀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⡴⠊⠀⠠⠤⠤⠤⢄⣳⣄⣐⣦⠈⡀⡘⢇⠑⠖⣼⢐⡹⣧⣀⠄⠶⠋⠀⠑⢠⢄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⡠⠋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠇⢸⠠⡌⡀⡀⢆⠙⠃⡧⣐⣀⡀⠀⠀⠀⡀⠀⠀⠀⡈⠣⡀
⠀⠀⠀⠀⠀⡰⠁⢀⡔⠀⠐⠹⡋⠁⠴⠄⠀⠀⠂⠂⠀⠬⢥⠤⠶⠒⠒⠆⣠⢄⡠⠀⠇⠀⠈⠁⠀⠓⡔⠀⠀⢀⠜⡀⠀⠐⠄
⠀⠀⠀⠀⡰⠁⠀⠌⠀⡠⡄⢀⡈⠒⠤⢈⣁⡀⡀⢀⠈⠀⠀⠦⠀⣁⣀⠐⠜⠀⠀⠀⠀⠀⠐⢈⠀⡀⠒⡆⠐⠿⠀⠠⠀⠀⠈⠄⠀⠄
⠀⠀⠀⢰⠃⠀⡌⡀⠄⠀⠀⠀⠀⠐⢀⠀⠀⠀⠘⣀⠤⠖⠈⠓⠉⠁⠁⠀⠀⠀⠀⠀⠀⠘⠦⠙⠯⡛⠤⣅⠀⠙⠠⣤⠮⠆⠀⠈⠀⠈
⠀⠀⠀⡟⠀⢰⠀⠀⠀⠈⠁⠔⠒⢄⡀⠀⠁⠀⠂⠈⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⣣⣀⠈⠻⢞⣤⠀⠀⠀⠀⠀⢠
⠀⠀⢠⠇⠀⡆⠀⠀⠑⠁⠀⠀⠀⠀⠱⣄⠢⠄⠀⠢⠀⠀⠀⠀⠀⠀⠐⠀⠒⠢⢄⠀⠀⠀⠀⠀⠀⢿⡮⢈⢳⠲⣞⣀⣳⢀⣀⠀⠀⡄⠐
⠀⠀⢸⠀⢀⡇⡄⠒⠀⠀⠀⠀⠀⡀⠄⠈⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠳⠾⡉⠒⠘⠈⡿⠲⣮⡁⠀⠇⠀⡇
⠀⠀⢸⠀⢸⠃⠰⠀⠀⠀⠀⢀⣀⡰⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠐⠃⣁⣳⢸⣁⣀⣀⠁⠀⠀⠀⡇
⠀⠀⢸⠀⠀⡇⠀⠃⢠⠔⠐⠁⢀⣠⡲⠃⠶⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠚⠛⠚⠋⠉⠁⠁⠈⠉⠃⠀⡆⠀⡇
⠀⠀⠈⡇⠀⡇⠀⠁⠠⡀⠉⠐⠈⠀⡀⠀⠀⡐⠘⣆⠀⠀⠀⠀⠀⠐⠤⢀⣀⡀⠴⠋⠀⠀⠀⠀⠀⠀⢤⣉⣀⠀⠈⠁⠀⠉⠛⠺⠀⠀⢠⠁
⠀⠀⠀⢳⠀⢸⠀⢄⠀⠈⡃⢂⠴⠊⠁⠐⡎⠈⠁⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢉⠉⠁⠲⠦⠤⠴⠃⠀⠀⡜
⠀⠀⠀⠈⡆⠀⢇⠈⠇⡀⠑⡌⠢⡤⠐⢒⢑⡀⠄⠚⣱⠈⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⠒⠉⠒⠒⢎⡠⡅⠐⠂⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠘⡄⠈⢆⠢⡀⠀⠎⡆⠀⠘⠁⠀⣩⠉⢁⠈⠐⠺⠀⢄⠁⠀⠀⢀⡠⠠⠄⣠⡤⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠀⡁⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠘⡄⠀⢣⡀⠅⢘⠤⠠⢆⠀⢀⡇⢈⢶⣀⣀⠤⠐⠊⠀⢹⠀⠄⡠⠀⠈⠀⠀⡀⠀⠀⠀⢆⠀⢃⠐⠊⠤⠉⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠑⢄⢨⠀⠀⢸⠓⠙⡆⠀⠀⠀⠠⡀⠀⠀⣠⠞⠐⠂⠇⠀⠀⠀⠀⠅⠀⠀⢋⠁⠀⢀⣹⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠐⣀⠀⠉⠀⢨⡇⠀⠀⣁⠀⠙⢪⠉⡉⠀⠀⡀⡘⠆⠀⠀⠀⢃⠀⠂⠊⢠⠢⠊⡠⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠐⠀⡀⠀⠈⠂⠖⠉⡆⠀⣠⠁⠐⠀⠚⠠⠁⢠⠀⠀⠀⠈⡄⠠⠄⣚⠔⠊⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠉⠺⠄⠄⠀⠀⠀⠆⠠⠀⠑⠂⢀⣀⠠⠔⠋⠀⠀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⡀⠈⠁⠐⠂⠀⠄⠤⠄⠄⠀⠐⠒⠈⠁⠀⣀⠠⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠢⠤⠤⠤⠤⠤⠤⠄⠒⠒⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⣴⣶⡾⠟⣿⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⣀⣀⣴⣾⡟⠉⣉⣛⠁⠀⢠⢤⢉⣉⠻⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠛⢛⣁⡴⢂⡄⠙⠩⢴⡶⠀⠋⡀⠈⣥⣌⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⠶⠿⠋⠁⣠⡴⠈⠉⠀⠘⠟⠀⠔⠦⠤⠔⠙⠁⠀⠀⠿⣤⣤⠛⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⠈⠛⣀⣾⡏⠉⠐⠟⠁⣘⡉⠱⣾⣶⠞⠂⠞⠛⠻⣇⣀⠟⠀⠙⠦⠀⠘⢿⣦⣶⡄
⠀⠀⠀⠀⠀⠀⣴⡶⠿⢩⠶⠚⠉⠠⠶⠖⠀⠀⠛⠛⠉⠠⠦⣍⡀⠰⠶⠃⠀⠈⠙⠃⠀⠀⠊⠛⠀⠰⡦⠹⣿⡆
⠀⠀⠀⢠⣶⣶⠿⠷⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⢿⣿⣶⣶⡄
⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠿⢶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠾⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣈⣉⣉⣙⣛⣛⣛⣛⣛⣛⣛⣛⣉⣩⣤⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⢚⡔⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠖⢤⠏⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠾⣤⠎⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠄⠀⠀⠀⠐⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢀⢄⡔⢲⠁⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⢃⠾⣡⠎⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿
⠀⠀⠀⠀⠀⣠⢐⡖⠁⡀⢡⠴⠾⡧⠖⠓⠀⠀⠘⠉⠉⠀⠀⠀⠀⢀⡀⠀⠀⠈⠉⠈⢁⣨⠤⠁⢢
⠀⠀⠀⠀⡸⡱⠊⡀⠊⠀⠈⠂⠀⠠⠤⠠⠒⢶⠲⠚⠙⣻⣻⡯⠉⠫⣭⠫⠼⢏⠙⠿⣯⠜⢛⡷⠮
⠀⠀⠀⠐⢻⢠⠊⠀⠀⠀⠐⠀⠁⠊⡁⠀⠀⠀⢳⣤⡴⠏⠁⠛⠻⡹⠊⠁⠠⠼⠷⠈⠤⢿⣛⣽⠤
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠋⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠳⢦⡀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⢀⡴⠛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢰⡏⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⣿⠁⠀⠀⠀⠀⠙⢷⣄⠀⠀⢀⣀⣀⡀⠀⢀⣿⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠷⠟⠀⠀⠀⠀⢰⡆⠀⠀⠀⠹⣦⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠉⠉⠻⣶⠋⠁⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠙⠷⣤
⠀⠀⠈⣧⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢠⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣄⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢀⡿⠀⠀⠀⠀⢻⡄⠀⠐⣦⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠈⠻⣦⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠
⢠⡶⠛⠁⠀⠀⠀⠀⠀⢻⣄⠀⢹⡄⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠉⠉⢿⡀⠀⠀⣰⠇⠀⠀⠀⠀⣿⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢀⡾⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⣼⠃⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⠞⠁⠀⠀⠀⠀⣸⠇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠸⣧
⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⡏⠀⠀⠀⣀⠀⠀⠀⠀⠘⣷
⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⣀⢻⣄⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⢿⡀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡿⠶⠶⠶⠛⠉⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠸⣇⠀⠀⠰⠶⣤⣤⣤⣤⠶⠿⣦⡀⢹⡆⠙⠳⣦⣄⡀⠀⠀⠀⠈⠙⠛⢻⡇⠀⠀⠀⠀⡀⠀⣷⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣷⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⢸⡇⠀⠀⢀⣼⠃⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠘⢷⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⣇⣤⡶⠟⠁⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⣦⡀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢸⡇⠀⠀⠀⢸⡏⠀⠀⠀⠀⣰⡟⠀⠀⢀⣀⣴⠄⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⢠⣤⣤⡴⠶⠛⠛⢷⣄⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣼⠋⠛⠛⠛⠋⠉⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⡀⠀⠀⢸⡇⠀⠀⣸⠇⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠦⣤⠴⠶⠶⠶⣤⡀⠀⠀⢹⡇⠀⠀⢸⠇⠀⢰⡟⠀⠀⠀⢀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⡀⢿⡀⠀⣿⠀⢠⡟⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣄⣿⣰⠟⣀⣤⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⣠⡶⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣠⡴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠞⠛⠛⠋⠉⠉⣉⣉⣁⣀⣀⣀⣀⣀⣈⣉⡉⠉⠉⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠋⢉⣀⣤⣤⠶⠶⠖⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠓⠶⢦⣄⡀⠈⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⣀⣤⡴⠶⠛⠋⠉⠀⣀⣀⣠⣤⣤⠴⠶⠶⠶⠶⠶⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠿⢿⣷⣄⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⢀⣠⡶⠛⠉⠀⠀⣀⣤⠴⠞⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⢸⡇
⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠛⠁⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⣼⠃
⠀⠀⠀⢀⡾⠁⠀⢠⡟⠁⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⣠⡾⠃
⠀⠀⠀⢸⡇⠀⠀⠘⣧⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁⠀⢀⣠⡾⠋
⠀⠀⠀⠈⢷⡀⠀⠀⠈⠻⢧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⠛⠋⠁⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠈⠙⠛⠳⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠶⠖⠛⠛⠋⠉⠁⠀⠀⠀⣀⣠⡴⠶⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⠶⠶⠛⠋⠉⠁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣛⠛⠛⠓⠒⠲⠶⠖⠒⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢛⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣼⠁⠀⠀⢠⠟⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣰⠃⠀⠀⣰⠏⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢰⠏⠀⠀⣰⠋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢠⡏⠀⠀⣼⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⢤⡴⠒⠒⠶⣄⢀⣠⡼⢁⡟⠀⠀⡼⢁⡞
⠀⠀⠀⣀⣤⠤⠤⠤⣤⣄⣀⠀⠀⠀⣀⣀⣠⡏⠀⠀⠀⣠⡄⠀⠀⠀⠈⠉⣼⢃⡾⠙⣦⡾⢡⠟
⠀⢠⡞⣿⠀⠀⢀⡔⠉⠁⠉⠳⣄⡼⠉⠀⠀⠀⢠⡀⠈⠁⠀⠀⠈⠓⠀⣰⠃⡼⠁⢀⡞⣠⠏⠒⣄
⠀⡟⠀⣸⣤⠤⣿⣄⠀⣀⣤⣤⣼⡇⠘⠛⠃⠀⠀⠁⠀⠀⠘⣆⠀⠀⠀⠉⠛⠃⠠⣟⣰⠏⢀⠀⢸
⢸⡷⠶⣏⠀⠀⠀⠈⢿⠁⠀⠀⠀⡇⠀⠐⠶⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠈⠁⠀⠘⠆⠈⠳⣄
⣸⠀⡀⢻⠀⠐⡶⠒⠚⠒⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⣶
⠻⠶⠷⠾⠃⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡾
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣋⣀⣀⣀⣀⣀⣀⣀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⢀⡤⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢼⡁⢡⠂
⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡤⢀⠀⠀⠀⠐⠉⠁⠁⠏
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠁⠀⠀⡈⡂⠢⢀⠀⠀⢆⠀⡀
⠀⠀⠀⢢⠑⢄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠐⠀⠂⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀
⠀⠀⠀⠀⠐⠀⠈⠢⡈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠠⡀
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠑⠄⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠅⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⡀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠁⠂⠄⡁⠂⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠦⢀⠀⠀⠀⠀⠁⠂⠠⠈⠐⠋⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⠐⠠⠀⡀⠀⠀⠀⠀⠀⠐⠠⠤⢁⣀⣐⡀⠤⠤⠤⣄⣀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠜⠀⠠⠤⣄⡀⠀⠀⠂⠄⠄⠀⠀⠄⠀⠀⠀⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠅⡀⠀⡠⡈⡦⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⡈⠄⢲⠁⠀⠁⡘⢍⠐⠄
⠀⠀⠀⠄⠀⠄⠀⠤⣖⠠⠔⠖⠁⠀⢤⠂⠶⣤⠰⠑⢶⢪⠒⢬⠒⠄⠠⠀⠠
⠀⠀⠀⡁⣏⡭⠐⠉⣍⠀⠀⣉⠀⢠⣯⠋⠀⣩⠁⠀⣉⢫⣡⢩⠉⠃⣽⣃⢈
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣄⠀⢤⡒⠔⣒⣀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⢠⠉⣗⢖⡀⠀⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⣭⠠⣨⣧⡰⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣤⠘⢺⡶⠩⣁⠟⠂⠀⢨⣀⠀⠀⠀⠘⠧⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡤⣿⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⢷⣽⠇⣈⣁⢮⠁⠽⡆⠒⢇⢌⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⣌⡲⣭⡟⢛⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠸⠟⠹⠷⠰⣗⠀⠳⠀⣤⣜⣉⣾⡛⡷⣦⣶⣾⡋⣰⡻⢋⣿⣿⣓⣊⣛⣿⡛⡚⣣⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⢀⠀⠒⠏⣤⡀⠑⣷⣤⣼⣿⣿⣷⢾⣯⣿⣿⢿⠟⠞⣻⢋⣂⣴⢟⣾⡷⠽⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢿⣮⣵⠂⢀⢮⣽⠟⠻⣽⣾⣿⣿⣿⣷⡳⢿⣇⣆⢹⡿⢛⣡⡶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠠⠦⠤⢀⣀⣉⣉⣉⢉⣱⣶⣾⠿⠿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁




⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣽⣷⣦⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀
⠀⠈⠐⢀⣄⠀⣀⣭⣥⣦⣤⡄⢄⠀⠂⠀⠀⠂⠀⠀⠰⢋⠩⠦⠀⣠⣔⣮⣿⣓⠀⠀⣠⠴⠠⠀⢀⠋⢠⠢⡀⠀⠰⠅⠀⠀⢉⡄⣶⣦⢤⣍⡐⢄⠈⢀⠀⠂
⠀⠀⠀⢿⢿⡿⣏⠀⠐⣈⣉⡷⣦⡇⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠚⠻⠟⠛⠁⠀⠇⠂⠐⠀⠈⠈⠒⠰⠗⠀⠁⢠⠠⢷⡱⠚⠉⠁⠺⢿⣷⣤⡄⠀⠀⢠
⠀⠀⠀⡛⢉⠝⣶⣽⣟⢹⣿⡥⠊⠛⠂⠐⠀⠀⣨⠭⡩⠒⠀⠀⡤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠔⠀⠘⢶⣾⣧⠀⠀⠀⢀⣺⣽⠿⡇
⠀⠀⢰⡄⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⢄⠉⠂⠋⠈⠘⠀⠁⡇⠈⠉⣈⡨⠁⠀⠐⠀⠈⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠉⠛⠛⠲⠖⠚⠙⢁⡴⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠑⠂⠀⠀⠀⠀⠀⠀⠠⠀⠒⢉⡀⠀⠐⢸
⠀⠀⠀⠀⢀⣴⣆⡄⠀⠀⠀⠂⠀⢦⠀⠘⠀⠠⠀⠀⢠⠂⠀⢀⠀⠀⠀⡆⠠⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠆⠀⠴⠰⠀⠆⠠⠄
⠀⢀⠄⠀⠉⡿⠋⠀⢀⠠⣆⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡀⠀⠉⠀⠀⠔⠀⢀⠀⢐⠠⠤⣀
⠀⠈⠁⠒⠊⠀⠀⠰⠨⠿⡝⠍⠠⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⡀⠀⠀⠠⡄⠁⠀⠀⠀⠀⢠⢁⠀⠠
⠀⢀⠲⢴⠀⠐⠂⠀⠀⠀⠈⠁⠀⠀⢶⠀⠸⣄⠀⠀⠀⠁⡇⠀⢁⣀⣀⣀⣀⣡⠀⠀⢀⡀⢀⡶⠀⠀⢀⣄⣒⣒⣤⡀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠀⠀⢀⠄
⠀⠈⠉⢁⠀⠒⣈⠄⠀⣰⣻⡑⠢⣀⠋⠀⠀⠁⠄⠁⣀⠀⠁⠔⣩⣶⣷⡿⢻⣵⣖⠀⠀⡄⠀⠀⠀⡆⢝⣓⡍⢁⠺⢢⠑⠀⠀⠀⢁⠐⠈⠐⠒⠒⠊⠀⠀⠐⠂
⠀⠀⠀⠁⠀⠾⡃⠀⠀⠀⢛⡈⣠⠄⠄⠀⠀⠀⠀⠀⠀⡀⢐⣪⣿⢯⠙⢿⢿⢿⣏⠄⠀⠀⠀⠄⣾⣿⣿⣯⣁⣸⡮⠯⡕⡀⠀⠀⣀⠀⢀⠀⠁⢀⣀⣠⣄⡀
⠀⠀⠀⠰⡗⠾⠔⠀⣤⠴⢏⡞⡏⠀⠀⠀⠀⠐⠀⢉⡠⠐⠋⣽⣟⠀⠀⠠⣿⣿⣃⠃⠀⠀⠀⠀⢿⣟⣿⣾⣿⣷⡠⣿⠁⠀⠀⡜⠀⢀⡅⢱⠀⠺⣿⢧⣿⣾⠿
⠀⠂⢀⠐⠾⢄⠢⢶⡠⠤⠞⠠⠕⠀⠀⠁⡀⠀⠂⠉⠀⠀⠀⠁⠟⣶⡤⠺⣯⠭⠁⠀⠀⠀⠀⠀⠉⠙⠻⢿⠿⠿⠛⠂⠀⠠⠄⠱⢄⠀⡀⠈⠀⠀⠀⠉⠉⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣠⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠮⢤⡀⢈⠖⠉⠁⠈⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠁⠀⢠⡇⠸⣇⠀⠀⠀⠀⠀⠣⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠞⠋⠀⠀⠀⠀⠀⢇⠀⠙⢧⢰⣠⠞⠉⠉⢻⠉⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠰⠀⠀⠈⠣⣴⠛⠋⠓⠀⠀⠀⠘⢗⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢽⡄⠀⠀⠀⠀⠀⠈⠘⠓⢄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⡀⣡⠊⠀⠀⠀⠀⠀⢷⠀⠀⠀⢠⠀⠀⠀⠀⢸⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⢇⠃⠀⠀⡀⠀⠀⢀⡞⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⣾⠘⢀⡴⠋⠀⠀⠀⣸⠀⠀⠀⠀⠀⣧⢠⠄⠐⣿⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠳⡀⡇⣴⠊⠀⢀⠀⠀⠀⢱⡇⠀⠀⡄⠀⢳⠇⠀⠀⠘⡆⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠱⡇⠃⢀⡔⠕⠈⠀⠀⢾⡀⠀⠀⠃⠠⠘⢀⠆⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠐⡄⡇⣇⠎⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⠆⠖⠉⠀⢀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠘⡇⡿⢀⠔⠋⠀⠀⠀⢯⡀⢰⣄⠎⠌⠀⡀⠸⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⡄⣧⢱⠎⠀⡀⠀⠀⡤⠚⠃⢠⢏⠌⡠⠎⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢸⠀⡰⠁⠀⠀⢳⠀⡠⢃⠞⢉⡶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠸⢸⡜⠁⠀⢠⣢⢞⠟⢡⠋⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⣴⠘⡇⠀⠰⡿⣠⠊⡰⠛⣀⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠀⡇⢶⢺⠟⠁⣼⠕⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡏⠀⢇⣸⠏⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⣇⣠⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣀⣸⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⣰⠖⣿⠛⣿⢽⣷⢠⡉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠿⣋⣿⣴⣿⣾⠟⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠊⠔⠀⠀⠀⠖⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠒⡠⠀⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠟⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈⠉⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⡀⣀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠴⠉⠀⠀⢁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⡁⣁⡂⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⢰⣟⣭⣿⣶⠢⠰⡄⢠⢠⠀⠀⠀⠀⠀⠀⢀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢐⢃⣲⠈⠻⠿⡟⠙⠀⠀⠠⠂⠘⠀⠴⠾⠤⠼⠀⢼⡃⠛⠟⣹⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠀⣢⠄⠅⠙⠱⠇⠀⠀⠀⠀⠀⠀⠒⠐⠃⠀⠉⠁⠀⠉⠁⠀⠀⠐⠀⠐⠀⠂⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠂⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠂⠀⢄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠴⢖⠀⠀⣠⡙⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⠤⢤⡶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⢹⡽⠛⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠖⠀⣸⣯⣽⢧⠀⢸⣭⣳⣿⡆⠻⠿⠛⠟⠃⢀⡀⠀⠠⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡀


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠉⠉⠉⠑⠲⢤⣀⣀⣀⣀⠀⠀⢀⡴⠒⠒⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡖⠉⠀⠀⠀⠀⠀⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⢄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠐⠈⠀⣀⡀⣈⡦⣄⣀⣠⣄⡀⠀⠀⠐⡀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠓⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⢀⠴⠒⠒⠚⠋⣁⡤⠤⣥⣀⣀⣉⠛⠋⠉⠙⠳⣄⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠢⢈⡼⠋⠀⠀⣠⠖⠋⠀⠀⠀⢰⠊⠉⠙⠦⣄⣀⠀⠀⠈⢧⠀⠀⠀⠀⢹⠙⢦⡀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⢧⠀⠀⠀⠀⢀⡠⠖⠉⠀⢀⡴⠋⠁⠀⠀⠀⣠⠤⠊⠀⠀⠀⠀⠐⠉⢳⡄⠀⠸⡆⠀⠀⠀⠘⡄⠀⠻⡄⠀⠀⠸⣥⣀
⠀⠀⠀⣠⠞⠀⠀⠀⢠⠏⠀⠀⠒⣲⠋⠀⠀⠀⠀⠀⢰⠃⠀⠀⠑⠀⠀⠀⠀⠀⠀⢳⡀⠀⢳⡀⠀⠀⠀⠙⠢⢤⡘⣆⠀⠀⠀⠈⠳⡄
⠀⣠⠞⢁⡴⠤⣄⠀⡏⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠘⠤⡀⠀⠀⠀⡀⠳⡄⠀⠙⠲⣄⡀⠀⠀⠀⡇⢹⠀⠀⠀⠀⢠⠇
⠀⡇⠀⢸⠀⠀⠈⠳⣷⣠⠤⣴⡃⠀⠀⠀⠀⡤⠒⠉⠀⠄⠀⡀⠀⠀⠀⠈⠂⠀⠀⠰⠀⠙⣆⠀⠀⠀⠉⠳⣄⠀⠱⣸⠀⠀⠀⠀⣾
⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⡖⠀⠀⠀⠀⠘⡆⠀⢸⠀⠀⠀⠀⢻
⠀⠈⣆⡼⠀⠀⠀⠀⡀⠔⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠘⡀⠀⠀⠀⠀⣷⠀⠀⠀⢀⡴⠃⠀⢸⠀⠀⠀⠀⠈⢣⡀
⢠⡞⠉⠀⠀⢀⠂⢁⠀⠀⠀⢀⡟⠀⠀⢀⠴⠁⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠡⡐⠀⠀⠀⠀⡏⠀⠀⣴⠋⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠹
⣸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⡟⠀⠀⢰⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢠⡐⠀⢰⠧⡀⠀⢧⠀⠀⠀⠀⠀⡇
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠠⠍⢢⡟⠀⠈⠢⢘⡆⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣠
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⠀⠈⢣⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠓⢀⡴⠚⠀⠀⠀⠀⡞⠔⡁⠊⠀⢠⠏
⢹⠀⠀⡇⠀⠀⠀⠠⡀⠀⠀⠀⠂⠈⠛⠲⢤⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠞⠀⠀⠀⠀⢀⣾⠁⠈⠀⠀⠀⢸
⠘⡇⠀⢠⠀⠄⠀⠀⠀⠀⠂⠠⠄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠒⠒⠒⠒⠲⠦⠤⣄⣀⣇⣰⠃⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⣸
⠀⢱⡀⠀⢂⠈⡀⠀⠀⡀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠤⠄⠀⡀⠀⠀⠀⠀⢀⠠⠂⠉⠙⣇⠀⠀⠀⠀⣠⠟⠂⠈⠀⠀⠀⠀⢀⡇
⠀⠀⠳⡄⠀⠡⡈⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠀⠁⠒⠀⠐⠁⠀⠀⠀⠀⡟⠀⠀⢀⠴⡉⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠙⢦⡀⠈⠀⠀⠀⠀⡇⢀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⠀⢀⡤⠞⠛⠛⠉⠁⠀⠁⠀⠀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠇⠀⠠⢀⡀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⠀⡰⠋⠀⣀⣀⠀⠀⣀⣠⠤⣶⠶⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⠘⠀⠀⠀⠀⠁⠒⠒⢂⡴⠒⠲⢤⡀⠀⠀⠀⣠⢞⡴⠚⠉⠉⠉⠉⠉⢉⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣤⣤⣤⡤⠤⠖⠋⢠⠏⠉⠲⣝⠲⠴⠚⡵⠋⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⣏⠀⠀⠀⠈⠓⠶⠚⠁⠀⢀⣀⡤⠖⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣲⣦⣤⣤⣴⣶⣒⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⢀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⢋⡄⣼⢊⡃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⢀⣠⡴⠀⠄⠀⠚⠈⡉⢉⣉⣥⣜⢛⡍⠁⠀⠀⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠒⢉⣁⡤⢤⣶⣶⢿⠟⠛⠏⠃⠖⢦⣉⣉⣁⡐⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠐⢁⡤⠔⠊⠉⠀⠉⠁⠀⠀⠘⡓⣲⣀⠈⠐⠀⠓⢠⣸⠂⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠠⢚⡡⡤⡤⠦⡄⡀⠶⠠⠄⠀⠀⠀⠈⠨⠡⠀⠀⠀⠄⠙⠓⠗⠃⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠕⠀⠠⠚⠋⠀⠉⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠋⠐⠅⠄⠌⢁⢛⣽⣦
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠑⠁⠠⠊⠀⠀⢂⠡⣿⡆
⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠈⠀⠌⠍⠁⢁⠀⣦⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⡀⠀⠁⡂⠘⠁⢠⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣧⣤⣶⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⢸⢿⢠⢰⡂⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠚⠛⠛⠛⠛⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⢋⠥⠊⠀⢀⠠⠀⠀⢀⠔⠁⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⡀⠄⠊⠁⡀⠔⠈⠀⢀⠤⠒⠁⠀⣀⠔⠁⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⢀⡠⠒⠉⠀⡀⠔⠈⠀⢀⠠⠊⠁⠀⢀⠄⠊⠀⢀⠠⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠀⠀⡠⠔⠁⢀⠀⠐⠁⠀⢀⠤⠊⠁⠀⠀⡠⠊⠁⠀⠀⠔⠁⢀⠔⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⣫⠟⠀⠀⡠⠔⠈⢀⠠⠂⠁⠀⢀⠔⠊⠀⠀⠀⠀⡠⠊⠀⠀⢀⡔⠈⢀⠠⠁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⡡⠊⠀⡠⠔⠉⠀⡠⠒⠁⠀⠀⡠⠚⠁⠀⠀⠀⣀⠔⠁⠀⠀⢀⠔⠈⢀⠔⠁⢀⠔⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢋⠔⠉⢀⠔⠉⠀⡠⠔⠉⠀⠀⣀⠔⠉⠀⠀⠀⢀⠄⠊⠀⠀⠀⡠⠂⠁⡀⠐⠁⢀⠔⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢞⣛⠛⠛⠋⣛⠳⢦⣄⠀⢀⠔⠉⠀⠀⠀⢀⠠⠊⠁⠀⠀⢀⠔⠊⠀⡠⠊⠀⡠⠄⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⡡⠂⠁⠀⠀⠀⠀⠀⠈⠐⢌⠻⣦⠀⠀⢀⠠⠒⠁⠀⠀⢀⡠⠊⠁⢀⠄⠈⢀⠄⠊⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠊⠀⠀⠀⠀⠀⠈⠉⢢⠀⠀⠀⠑⢌⢷⡄⠀⠀⠀⠀⢀⠔⠁⠀⣀⠔⠁⢀⠔⢁⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠂⠀⠠⠠⡀⠀⠀⠐⠄⠎⠀⠀⠀⠀⠈⢂⢻⡄⢀⠠⠊⠀⢀⠄⠊⠀⡠⠊⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠠⠀⢘⠀⠀⠀⠀⠀⠀⠔⠀⠂⠀⠀⢃⢿⡀⠀⢀⠔⠁⢀⠤⠊⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠤⠐⠂⠀⠀⠀⠸⣧⠀⠁⡠⠒⢁⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡴⡀⠀⠔⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠊⢀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠳⣔⢄⠀⠀⠀⠀⠀⠠⠀⠑⡀⠀⠀⠀⠀⠀⠀⡿⢀⡴⠋
⠀⠀⠀⠀⢠⡶⡫⠋⠉⠁⠀⠉⠙⠛⣳⣤⠶⠾⣿⣷⣶⣶⡶⣦⣄⡁⠈⠀⠀⠀⠀⢀⠔⣼⠷⠋
⠀⠀⠀⢰⡏⠌⠀⠀⠉⠄⠀⣀⣷⢟⠟⠈⠁⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣄⣀⣒⣀⡵⠚⠁
⠀⠀⢀⣿⡇⠀⠀⠀⠀⠁⢀⣾⣧⠁⠀⠀⠀⡀⠐⡀⠀⠁⠈⡆⠀⠀⠐⠝⢯⡉⠁
⠀⠀⢸⡇⢷⣃⠀⡐⠀⡂⣾⠁⣿⡄⠀⠀⠀⣈⡀⠀⠀⠐⠴⠁⢀⠄⠂⡀⢢⢻⡄
⠀⠀⠘⣧⠈⢻⡢⡀⠒⠀⢿⡀⠙⣧⢀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠃⠀⠴⠁⠀⠇⢿⡀
⠀⠀⢀⣸⣧⡀⠛⢮⣐⠄⠘⣧⠀⠈⠳⣕⢄⠀⠀⠀⠀⡂⠀⡀⠂⢄⠀⠀⠀⢰⢸⡇
⢀⡴⡫⠋⠈⠻⣤⡁⠉⠙⠳⠾⢧⡀⠀⠉⠳⣕⢄⠐⠂⠀⠀⠐⠤⠔⠁⠀⢀⢈⣼⠇
⣾⣱⠀⠐⠒⠊⠈⠙⠛⠺⠶⠶⠶⠻⣦⡀⠂⠈⠳⢮⣔⡠⠤⠄⠤⠄⣐⣨⡵⢻⠏
⡏⠿⣶⡄⠀⠈⠂⠂⠀⠀⠀⠀⠀⣀⣼⠿⢶⣄⣀⠀⠉⠙⠛⠛⠛⠋⠉⣡⡶⠋
⠹⣆⡈⠙⠛⠶⠶⠶⠶⠶⠶⠶⠚⠛⢡⡴⠃⠀⠉⠓⠶⠶⠤⠤⠴⠶⠞⠉
⠀⠈⠙⠲⠶⣦⣤⣤⣤⣤⣤⡤⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⡠⠂⠔⠲⢺⠳⠆⠀⢲⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠌⠀⠀⠐
⠀⠀⠀⢉⠉⠛⠓⠊⠒⠀⠀⠀⠐⠓⢉⡅⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⢰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⢄⠈⠁⠀⢀⠀⠀⠀⠈⠁⡤⠀⠀⠀⠀⠐⢀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠜⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⢺⠛⢣⣑⠙⡏⣓⣦
⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣬⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⢰⠛⢃⡠⠫⡼⢄⢾⡧
⠀⠀⠀⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠠⠀⠄⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠈⠀⠙⠛⠯⡵⣶⠖⠒⠉⠐
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡰⣤⣤⡔⢢⢄⠀⠀⠀⠘⠋⠀⠀⠀⣀⠔⢠⠒⡆⠀⠐⡄⡆⠀⠀⠰⠀⠰⡄⠀⠀⠀⠀⠀⠒⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⢀⠞⠉⠀⡀⡛⢄⡛⠀⢧⠀⠀⠀⠀⠀⠀⠀⠛⢄⠸⣀⠇⡰⢆⠁⡇⠁⢠⠉⠃⠀⠈⣤⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠈⣂⣈⣻⣶⡟⠉⢿⡧⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠔⠳⠛⠃⢱⣤⡞⣩⠩⠋⢅⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⢀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠁⠀⠀⠀⡎⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢦⡀⠀⠘⠉⠛⠀⠀⠀⠀⠀⠀⡠⠤⠀⡃⠀⠀⠀⣅⡀⢰⠁⠃⡌⠈⢸⠈⠣⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⡢⡁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠙⠁⠒⠐⠂⠉⠁⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠇⠀⠘⠤⠂⠡⠰⠸⠤⠊⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠱⠀⠀⠰⡀⠨⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⠶⠆⠀⠀⠀⠀⠀⠀⠐⠒⠒⠶⠤⠤⠤⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⢀⢀⠀⠀⣄⢰⠂⠀⠤⠀⢀⢀⠀⠀⢀⢀⡀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⢠⡄⠀⡄⠀⠀⡀⢀⡀⠀⠑⠀⠀⠀⠀⢜
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠁⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠈⠐⠆⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⢤⠀⠄
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠐⠖⠀⠢⢀⠀⠀⢈⠉⠠⡁
⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⠲⠀⠀⢠⣶⣦⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⠀⠘⣶⣦⠀⣼⢹⠁⠠⡆⠀⡰⠷⠰⢀⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⢻⠀⠀⠀⠘⠁⠀⡿⠞⠀⠀⠹⠞⠃⠀⢀⠄⣀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⡦⠀⠀⢹⡆⠀⠀⣶⠄⠀⠀⠀⠕⠀⠀⢰⢀⡋⠀⠻⣷⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠄⠁⠂⠀⠀⣿⠀⠠⢿⣦⠀⠀⠠⠀⣆⢰⡼⠊⣀⠔⠘⢧⠞⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠸⠀⢀⠘⠒⠀⠀⠈⠀⠘⠃⠀⠀⠂⡄⠙⡌⠀⠊⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡴⠂⠀⠀⡇⡼⠁⠀⢀⢴⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠉⠀⢤⠀⠀⠸⠃⢀⡤⠟⠋
⠀⠀⠀⠀⠀⠤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠏⠀⠀⠀⡀⠀⢀⠄⢀⣬⡆
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠠⠀⠠⠒⠀⡀⠀⠀⠀⠀⠀⠀⠁⢸⠀⠄⠀⠀⡄⣠⠂⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⡧⠀⠀⠈⠀⣀⢤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡅⠄⠘⠀⠌⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠐⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠠⡄⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢻⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⣇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⠈⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠠⠄⠀⠀⠂⠀⠀⠂⠀⠀⠀⠉⠈⠙⠉⠉⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠰⠄⠨⠀⠀⠀⠀⠤
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠃⠀⠀⢀⣀⠠⠘⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣠⣄⡠⡀⠙⢿⣦⣴⡦⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⢔⡼⠞⠋⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⣠⣿⣿⣿⠁⠠⠀⠀⠀⠦⡕⢾⣄⠀⠀⠀⠀⢀⣠⣖⣡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⡀
⠀⠀⠀⠀⡹⠋⠽⠏⡉⣠⣤⣤⣾⣧⣭⡥⣬⡉⠲⠦⠀⠈⠱⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⠁
⠀⠀⠀⠀⠈⠢⡀⠂⠰⠿⠿⠿⠟⠛⡩⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠆⢐⠰⢰⠀⠄⠘⠀⠇⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠂⠁⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠀⠀⠁⠀⠁⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠀⠀⠀⠀⠀⠅⡇⡆⠁⠄⠁⠀⠀⢠⣤⠰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⢄⣀⣀
⠀⠀⠀⠀⠀⢀⠊⠀⣠⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⢿⠭⢿⡇
⠀⠀⠀⠀⠀⢸⢶⡤⠿⠣⢤⠀⠶⠖⠛⠀⠀⠀⠀⠀⠀⠀⢀⡤⡰⠆⠰⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⠸⢿⠿⠇
⠀⠀⠀⠀⠀⠀⡂⠽⠓⠒⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢰⡋⣈⡕⣾⠿⠳⢒⠒⢣⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣖⡢⠼⠦⣦⠤⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⡾⠿⠟⠛⢋⣉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠿⠿⠿⠟⣙⣿⣀⠀⠀⠀⣀⣠⣤⣶⡶⠿⠟⠛⣋⣩⣧⣴⣶⣶⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡡⡆⠿⢂⡸⠏⢽⡜⢻⣷⡾⢿⣛⣩⣭⣶⣶⠾⠿⠟⠛⢋⣉⣁⣤⣤⣴⣶⡶⠿⠿⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⣋⡄⠷⣟⠁⠙⠿⢂⣤⠀⢿⣿⢛⣛⣩⣭⣤⣶⣶⠾⠿⠟⣛⣛⣿⣽⣧⣶⣶⠶⠿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡏⢩⡶⠶⠦⠘⣛⣀⣈⣥⠶⠿⢿⣛⣛⣩⣭⣵⣶⡶⠿⠿⠟⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣌⢣⣾⣛⣭⣭⣿⣶⠾⠿⠟⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠿⠿⠟⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⣤⣴⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣰⣿⠛⠛⠿⠟⠋⠉⠁⠘⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣴⡶⡾⠟⢛⣁⠀⢐⠶⠂⢀⡀⢫⠧⠘⠲⠈⠻⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⣠⣾⠿⠉⠁⠀⠰⠖⠋⠀⣷⠀⠀⠙⠛⠁⡠⣤⠀⠀⢛⡇⠈⠙⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⣛⡛⢁⣠⣤⡾⢋⣠⠄⣠⢤⠁⣀⣉⣉⣉⢓⣤⣠⣤⠀⠈⣛⠻⣷⡈⠉⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⢉⣤⠾⠟⠀⠀⠉⠉⣠⠤⢄⠘⠻⠿⠋⠁⢈⣁⡁⠸⠧⣤⡉⠀⠈⢛⣠⡀⠙⠿⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠡⠟⠉⠁⠀⠘⠛⣁⣀⣀⣉⣉⣀⡐⢚⢲⣤⢀⡛⣃⣀⣀⣀⣈⣀⡀⠀⠀⠉⠀⠀⠻⠂⠙⣿⡆
⠀⠀⠀⠀⠀⣾⡿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⡆
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣇⢠⣤⠄⢀⣤⣤⠀⣀⣀⠀⣀⣀⡀⢀⣀⣀⠀⣀⣀⡀⠀⣀⣀⠀⢀⣀⣀⠀⢀⣀⡀⠀⢀⣀⣀⠀⣠⣤⡀⣤⣤⣿⠇
⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠉⠉⠁⠀⠉⠉⠀⠈⠉⠉⠀⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠛⠻⠿⠿⢶⣶⣶⣶⣶⣤⣤⣶⣶⣶⣶⡾⠿⠟⠛⠋⠩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢐⡀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡆⠀⠉⠀⢀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⣆⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠸⠦⠞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠈
⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⣀⣀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣐⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠦⠶⠆
⠀⠀⠀⠀⠂⠠⠀⣠⠈⡇⠀⠀⠉⠁⠀⠀⠰⣄⡠⠤⠆⠃⠀⠒⠴⠃⠂⡀⠀⠀⠀⠀⠀⠀⠠⠃⠀⢀⡀
⠀⠀⠀⠀⠀⠄⠀⢁⡼⠁⠀⡀⠀⠀⠈⡀⢀⡦⠀⠀⠈⡅⠠⠛⣦⣇⡔⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢛⡥⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠒⠈⠉⠀⠀⠀⢀⡄⠀⠈⠁⡀⠀⠀⠀⠤⠉⠡⡅⠠⠗⠡⠠⡄⡀⠀⠀⠀⠤⠐⢈⠀⠔⠋⠀⠀⠀⠤⠞
⠀⠀⠀⢠⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⢀⣀⠄⠀⠀⠀⢢⠀⠐⠣⠇⠀⠀⠀⠒⠒⠀⠀⠨⡠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⡡⠀⠃⠀⡠⠈⠇⢀⠆⠀⠀⠀⠀⠀⠀⠦⠂⠁⠁⢠⡴⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⠅⠐⠠⠌⡁⣀⠴⠋⠀⠀⣘⡴⠖⠘⣠⠀⠳⠄⠊⠁⣠⢔⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⣤⣄⠁⠀⣀⡐⠀⠉⠉⠁⠀⠠⢂⠆⠌⠇⠀⢀⣼⠀⠀⠐⡶⠚⠁
⠀⠀⠀⠀⠐⢀⠄⠀⠀⠀⠀⢡⠀⢤⡼⠈⠛⠛⠂⠸⣿⣿⠈⠀⠀⠇⠀⠀⠉⠀⠀⠙⠚⠋⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠄⣀⠊⠀⣂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⡀⢤⣾⣿⡆
⠀⠀⠀⠆⡈⠇⠐⠧⠀⢠⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢠⣿⠆⠉⠉
⠀⠀⠀⠀⠀⠁⠈⠁⠀⡞⠀⠀⢬⣾⡄⠀⠀⠀⠐⠓⠁⠹⠰⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⢰⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡀⠨⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠈⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠲⠊⢄⠀⠀⠀⠀⠀⠸⣉⡀⠠⠔⠀⠷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠶⢦⡀⢠⠀⠀⠀⢨⣇⠀⠀⠀⠀⠀⠑⠦⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠱⡄⠀⠠⠙⠂⠀⠀⠀⠀⠀⠀⠌⢧
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⢆⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠓⢄⣀⣜⠁⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢤⣤⣤⣤⣤⠀⡤⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣰⢻⠃
⠀⠀⠀⠀⣶⣿⣿⣀⣿⣏⠷⠀⠘⣛⣩⡅⠰⣖⣤⠆⠀⢀⡏⣷⣄⠀⠀⠐⠀⠀⠀⠀⣠⡾⢃⡏
⠀⠀⠀⠀⠠⡹⣿⣿⣿⣿⣅⠐⠂⣾⡇⠁⠀⠈⢳⣿⠃⢰⠃⠘⣿⣦⡀⠀⠀⣀⣴⣿⠏⠀⢸
⠀⠀⠀⠀⠀⠉⠺⠿⠛⠟⠃⠞⠀⠁⠀⠀⠀⠀⢸⣏⣼⣿⠀⠀⠈⠻⣿⣶⣿⡿⠋⠁⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⡻⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⢀⣀⡀
⠀⠀⠀⠀⢠⣴⣾⣍⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠆⠤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣿⣿⣦⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⠙⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠉⠀⢀
⠀⠀⠀⠀⣿⣿⣧⠈⠐⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠠⠄⠂⠢⠤⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠘⢿⣿⣶⡁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠄⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠠⢁⡉⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣥⣇⡘⠀⠀⠀⠀⠀⠀⠀⠒⠓⡄⠀⠀⠨⠒⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠂⠡⠀⠠⡈⠁⠀⠘⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣶⣄⣆⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢤⡀⠘⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠠⠔⠀⠁⠐⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣿⣧⣤⣴⡆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠻⢦⣀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⠀⠀⠀⠀⣀⣠⠔⠈
⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⡠⠤⠠⣄⡀⠀⠀⠀⠉⠙⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠄⠀⠀⠠⠀⠀⠢⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠘⡿⣆
⠀⠀⠀⠀⠀⠁⠀⢀⠤⡰⠀⠀⡀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠔⠠⡀⠀⢀⡷⣿⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠒⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠁⠀⡼⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠄⠁⠀⠁⠀⠀⠀⠀⠀⣂⠁⡀⠀⠀⡰⠋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡤⠼⡿⠗⠀⠀⡀⠀⠀⠀⠀⠀⠐⠖⠈⠁⢀⣔⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠮⢈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠑⠶⣶⡭⠴⠚⠁⠀⠀⠀⠀⠄⠀⠀⠄⠀⠄⠐⡦⠀⠀⠀⠀⢸⣆
⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠐⠀⠀⠠⠠⠀⠀⠀⠀⢀⡣
⠀⠀⠀⢸⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠃⠹⠃⠀⠀⠀⠀⢀⢊⡇
⠀⠀⠀⠀⠳⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠟
⠀⠀⠀⠀⠀⠈⠻⣶⣤⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠠⠀⠀⠀⢀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄⢀⣥⡽⣆⠀⠀⠀⠀⠀⠱⠀⠀⡑⠈⠉⠘⠛⡻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣦⣤⣀⠀⢄⠐⡄⡠⠀⠠⠀⠀⠀⣈⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⢶⣶⣷⣄⣠⣤⣈⡁⢠⣶⣾⣿⣿⠃⠀⠀⠈⠒⢤⣀⣄⡠⣶⠥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠾⠿⠷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⠙⠓⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⡇⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠀⠀⠈⠙⡳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠀⠀⠀⠀⣸⠀⠀⠀⠀⠟⠀⠀⠳⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⠖⢻⡟
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠶⠒⠛⠉⠉⠁⠀⠀⢀⡎⣠⠏
⠀⠀⠀⠀⠀⣠⠞⠁⠠⠂⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠶⠚⠛⠉⠉⠀⠀⠀⠀⢀⡄⠀⠀⢰⠂⣀⣺⡴⠃
⠀⠀⠀⢀⡾⠃⠀⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠖⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⣁⣠⡤⠶⠚⠋⠉⠉⠓⣦⣄
⠀⠀⢠⣏⠰⠂⠀⢀⡤⠀⠀⠈⠁⠀⢀⣀⣀⣤⡤⠶⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠾⢏⡉⠀⠀⢀⡴⠖⢺⡏⠉⠉⠁
⠀⠀⢸⡏⠓⠲⠶⠶⠶⠶⠖⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⢴⡶⣿⣭⣭⣤⡤⠤⠤⠴⠶⠖⠚⠋⠑⠀⣠⠷⣤
⠀⠀⠈⡇⣇⠀⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠒⠛⢛⡟⠛⠿⠶⠴⠶⠋⠀⠈⡆⠀⠀⠀⠀⠀⠀⠄⢀⣀⡤⠶⠛⣡⣾⠁
⠀⠀⠀⠳⢦⣤⣬⣁⣀⣀⠀⠀⠀⠀⣀⣀⣀⣤⠤⠖⠛⠉⠉⣇⠀⠈⠆⠀⢀⡼⠁⠀⠀⡆⠀⠰⠀⠀⠀⠁⠀⠂⣀⣤⡤⠶⠚⠉⣁⣠⠴⠚⠁⠘⣇
⠀⠀⠀⠀⠸⣇⠰⠁⠉⠉⡍⠉⠉⠉⠉⠉⠉⠉⠛⠓⠒⠶⠶⠾⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⠛⣉⣁⣤⡤⠶⠚⠋⠉⠀⠀⢰⠀⠀⣿
⠀⠀⠀⠀⣰⠟⠳⢤⣥⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠴⠶⠶⠒⣒⣚⣛⣋⣭⣭⠥⠴⠖⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⢀⠄⠀⠈⣠⡼⠃
⠀⠀⠀⠀⠷⣤⣤⠤⠶⠶⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣤⠶⠛⠁
⠀⠀⠀⠀⠀⡟⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠛⠉
⠀⠀⠀⠀⠘⣇⠸⠀⢰⡀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠤⠶⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠈⠛⠒⠶⠷⠶⠶⠶⠶⠖⠒⠒⠒⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⠀⠘⡦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⢤⣀⠜⠀⢰⠂⠁⢸⣆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄⠀⡏⠉⠁⠀⠀⠉⠈⠉⠀⢠⠒⠉⠋⠀⢠⡃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⡟⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠄⠀⢀⠃⠀⠀⠀⡉⠉⠓⠋⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢼⠀⠀⠒⠇⠀⠀⠀⠀⠀⠈⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠁⠀⡁⠉⠀⠀⠀⠂⠀⠀⠀⠀⠸⠀⠀⠎⠘⡀⠀⠀⠠⠀⠀⠀⡀⠂⠀⢀⠀⣹⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠲⠇⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠄⡀⠀⠠⣇⡀⠀⠀⠀⣠⠀⡄⠀⠀⢠⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠸⠀⠠⠀⠀⠒⢤⠠⡀⢈⠀⡄⠐⠂⠘⢂⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠆⠘⠀⡀⠀⡀⢀⢀⠈⢀⠂⢀⠒⠀⠀⠀⠠⠀⠀⠀⠈⠊⡠⠀⢠⠀⠀⠀⢀⣈⣙⠆
⠀⠀⠀⠀⠀⠀⠈⢧⢀⡀⠀⠀⠀⠀⠀⢙⡋⠒⠁⠈⠁⡆⠀⠊⠀⠀⠹⡀⠀⡐⠀⠀⠀⠀⠀⠀⠁⡀⢸⣯⠵⠚⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠧⡄⠀⠀⠀⠀⣯⣄⠀⠀⠀⡠⠔⠀⠀⠀⠀⠴⡁⠰⠃⠀⠀⠐⠀⠀⠃⠁⠀⢨⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⠀⢰⠶⠞⢺⡉⠀⠀⢱⠄⢀⠄⠀⠀⡠⢠⡀⠀⠀⠀⢄⠀⠀⢀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣧⠀⠀⠘⡂⠠⡂⡤⢈⢀⠀⠣⡀⢀⡤⠊⠐⠀⠀⠐⣏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣤⡀⠉⠂⢘⠀⠀⠀⣀⡴⠁⠀⢀⠐⠀⠀⣀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢀⣄⠀⠀⠉⠞⢀⠁⠑⡀⠀⠒⠀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠻⣄⢀⣠⡀⣑⠀⠁⣠⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠉⡇⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠄⢸⡛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠙⢀⡵⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⣴⣀⣴⢂⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣴⠎⢹⢧⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠶⠴⠾⠏⢈⡍⠁⠈⣭⢁⣗⠺⠦⢆⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⠮⠟⠀⢀⠀⢴⠀⣘⣋⡾⠐⠀⠀⠉⣀⣀⢀⣌⠓⠲⠦⢤⡀
⠀⠀⠀⠀⡤⢚⣡⡟⠋⠛⢠⠀⠀⠑⠛⠀⡠⠁⠀⢠⢤⡠⠞⠃⢀⣌⠈⠋⠈⢆⣀⡀⠙⢷⡢⡀
⠀⠀⢀⡎⣰⠟⠋⠁⠀⢈⡼⠃⡀⠘⠂⢂⣺⢆⢤⠦⠀⠀⢀⣤⠀⠉⠀⢠⣄⠀⣈⠂⠘⠈⢻⣎⣦
⠀⠀⠸⡇⣿⣄⠺⠤⣀⠬⠀⢈⣉⣀⡥⠈⠉⠛⠀⢆⣴⣀⠨⠈⠀⠀⠒⠋⠀⠀⠀⣬⠀⠀⢰⡟⢸
⠀⠀⠀⣇⠬⡻⢦⣤⠸⠍⠀⠈⣀⠐⠆⠀⠀⠁⢒⠙⣦⡴⠐⢒⠀⡤⠀⠀⠀⢰⠤⢤⣤⡴⢋⡠⣿
⠀⠀⠀⢹⡀⠈⠲⢌⡛⠶⣦⣬⣑⣀⡂⠐⠶⠟⢆⠟⠏⡛⠮⠙⢃⣄⣚⣹⡦⢶⣚⣯⠵⠚⠁⢠⡟
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⠀⠒⠺⠿⠭⠽⠽⣿⣿⣿⣿⣿⣿⠭⠭⠿⠿⠒⠛⠉⠁⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣤⣄⣀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣠⠤⣶⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠉⠉⠉⠉⠉⠉⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠚⠋⠉


⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⠀⠀⠀⢦⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⡀⠠⢀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡦⠀⠀⢄⡤⠀⣈⡂⠀⠀⣀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠛⠀⣀⠗⢊⡤⠀⢀⢌⡆⠈⢹⣦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⠤⠚⠃⠀⣠⠞⢁⡴⠟⠀⢠⣷⠂⣧⡀⠀⠈⠙⢦⠈⢧⡀
⠀⠀⠀⠀⠀⣠⠶⠡⠘⢁⣠⡶⠿⡿⠋⣠⡏⠀⠀⣠⣿⠟⠀⠈⠛⠷⣤⣀⡈⠑⠢⡙⢆
⠀⠀⠀⠀⠞⠑⣁⡰⠾⠋⠀⣠⠊⡱⠋⢀⣤⣶⠾⠋⠁⠀⠀⠀⠀⠀⠉⠛⠻⣦⣄⠘⠠⠽⢦⡀
⠀⠀⠀⠀⠉⠉⠀⠀⠀⢠⠞⠑⠂⣠⣶⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠷⣦⡀⠂⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⢊⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⠻⢿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣀⣤⣤⣤⣄⣠⣤⣤⣤⣀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡈⠉⠋⠉⠉⠉⠉⠋⠉⢁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⢀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⠒⠀⣬⣍⡛⢛⣩⣥⠀⠚⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⣀⠀⠀⠀⠀⣿⡿⠟⠻⢿⣿⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⣤⣤⣭⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⣛⣛⠛⠛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣛⡛⢉⣉⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⡀⠀⠠⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠈⡆
⠀⠀⢀⠀⠀⠓⠒⠢⡀⢑⣀⣇⠀⠀⠀⠀⠀⠀⠀⢠⢃⡿⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠈⣅⠀⠑⡄⠆
⠀⠀⢀⠵⣴⠦⣀⡂⠘⠮⠿⣈⡿⣄⠀⡄⠀⠀⠀⠈⢸⣇⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢽⠢⢀⡿⡆
⠀⠀⠁⢄⠀⠂⠙⢛⣾⡀⡀⠈⠻⢉⢄⡈⠀⠀⠀⣧⢈⣿⠟⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡄⠸⠛⠸⠑
⠀⠀⠀⠀⠻⢦⣀⠀⠠⡟⠛⠀⡾⢉⠀⢈⠠⡀⠀⡿⣅⢃⣼⡿⠀⠀⠀⠰⣆⠈⠀⠀⠀⠀⠀⠉⠀⠁
⠀⠀⠀⠈⠑⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⣀⠈⠈⠉⠋⠀⠀⠀⠈⠀⡙⣦⡀⠂⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠘⠷⠁⠀⠀⢀
⠀⠀⠀⠀⢀⠀⢀⢀⠀⣠⠀⣴⠀⠀⠀⠀⠀⠀⠀⠠⠤⠷⠀⠤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠒⠒⠁
⠀⢀⠀⡀⠹⣄⡻⠰⡔⠃⠀⠞⡇⠀⠀⠀⠀⢀⡀⢀⡔⠀⠤⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠈⠠⡇⠰⠈⢇⢸⡃⠀⡀⢪⡅⠀⠀⠀⠘⠀⠀⠐⡇⢀⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⣠⠟⢀⠄
⠀⠀⢀⣇⠀⢠⠈⡯⠱⠞⢁⡯⠁⠀⠀⠀⡀⢥⠀⠀⡙⠀⠤⢤⣤⣴⡴⠏⡜⠀⠀⠀⠀⠄⣷⠞⢉⠧
⠀⠀⠈⢻⢀⠘⡙⠓⠀⣼⣿⠃⠀⠀⠀⠀⠳⡨⢠⠞⠁⢠⠖⠋⠁⠀⠀⢰⡀⠀⠀⢀⣴⠞⠯⠀⣄⡀
⠀⠀⠀⠸⡏⣼⡡⠌⢀⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣉⣤⣾⣀⣆⡀⠐⣴⠟⠀⠀⢠⠊⠁⠀⠀⠀⠈⠈⣿
⠀⠀⠀⠀⡏⡬⠩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠉⠛⠛⠚⠋⠁⠀⠀⠀⠂⠀⠀⠀⢠⠁⠹⣶⡃⡀
⠀⠀⠀⠀⠳⢣⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠂⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⡋⡁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡐⠀⣌⠏⢰⠿⣭⡠⠆⠀⠀⠀⠈⢡⣀⣄⡐⠀⠤⡀⠀⠀⠀⠀⠀⡀⠰⢁⡆⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡻⣆⠠⣔⠰⢖⡼⢐⢒⡀⠀⠀⠀⢀⡈⠙⢻⢢⣤⡠⠀⠀⠀⠀⠨⠆⠀⢸⡦
⠀⠀⠀⢀⡃⠀⢤⣞⡈⣩⡏⣁⣖⠒⠒⠊⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⣿⠛⠤⡀⠀⠀⠀⣷⢀⡔⢀⡇
⠀⠀⠀⠀⠂⠀⠀⠃⠀⠀⢂⣀⠀⠐⠒⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠀⠀⠀⠀⠀⠀⠀⠛⢊⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣧⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⣄⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⠉⠙⠓⠒⠒⠒⡶⢯⣤⣔⣙⣉⠑⣂⠀⠀⠀⠠⢀⡠⣤⣾⣿⠟⠉⢃⣸⣶⡤⣄⣀
⠀⠀⠀⠀⠀⠀⣠⠊⣷⣕⡒⠋⠀⢠⡶⠒⠋⡡⠞⠉⠀⢀⣀⠽⠟⠛⠛⣶⡶⠶⠗⠓⣿⡹⠄⠊⢀⣾⠏⣿⣧⠁⠘⢿⣒
⠀⠀⠀⠀⢀⣴⣿⣶⣿⣟⣿⣷⠀⢸⣷⣚⣛⣀⠀⠤⠒⠅⡉⢓⢒⡟⢋⣙⠉⢙⣙⣋⣡⣤⣴⣶⣿⣯⣴⣿⣿⡄⠀⠼⠁⣰⣄⢒⡛⠂⣤⢄⡀
⠀⠀⠀⠀⡽⣿⣿⣿⡉⠛⠷⣀⠀⠈⠉⠛⠚⠿⢷⣦⣤⣤⣌⣭⣵⣾⣿⡟⠃⠸⣿⡿⣭⣽⣿⡟⠓⠞⢩⣠⠄⠁⠀⠀⡌⠋⢸⠆⢀⠀⠀⠀⠀⢢⡄
⠀⠠⣄⣀⠀⣬⣿⡇⠙⠓⠲⡦⠀⠐⢀⡀⠀⠀⠀⠈⠉⠛⠛⠋⢉⣠⠟⠀⠀⠀⠀⡠⠋⣤⠈⠹⠃⠀⠈⠀⠀⢀⣴⠋⠀⢠⠓⠠⠞⠉⡀⢀⣴⡿
⠀⠀⠀⠈⠉⠙⣿⣿⠀⠀⠀⠀⠈⠙⣉⠛⠢⠄⠀⣀⠀⠀⠈⠉⠀⣀⣀⠀⢒⣐⣿⡺⣿⣿⣃⡀⠈⠀⢀⣠⠚⠁⡇⠀⠐⠇⣄⢀⠀⡼⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠑⠒⢛⣋⣉⣥⣽⣿⣷⢶⣿⣿⡏⠉⠀⣠⣴⠎⠋⠀⣰⠷⠃⠀⣷⢐⡴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣶⡿⠿⣿⣿⠿⡿⠟⠛⠂⢰⡃⠛⣿⡀⠉⠱⠍⣀⣀⣴⠋⠀⠐⠄⠈⢃⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠛⠲⢬⡝⠛⠤⠀⠀⠿⠅⠀⠈⢷⡀⠐⠈⡋⠙⢿⣾⣿⠷⢆⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣛⠓⠂⢤⣄⡀⠀⠀⠙⢦⡀⣼⣶⣴⡿⠓⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠐⠢⠄⠙⠉⠉⠁⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢁⣀⠹⢿⣒⠖⣒⢦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡖⠒⢿⣿⠾⠋⠉⢳⣤⣿⣏⢁⣉⠋⠉⣉⣉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⠉⣹⡇⠀⠀⠀⠀⠀⠐⡏⠁⠀⠈⠙⠉⠙⠛⠛⠉⠻⡛⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠽⠾⠁⠀⠀⡠⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡁⣳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡇⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡁⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⣶⠫⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢡⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⢀⣴⢋⠄⠀⢰⠒⠋⠁⠀⡽⠀⢠⠁⠀⠀⠀⠀⠀⣀⣴⡆⢸⡁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⡼⢁⡎⠀⠀⢸⡇⠀⠀⠀⠁⡠⠃⠀⠀⠀⣰⡾⠛⠉⠁⠀⠈⡛⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣄⡇⣼⠀⠀⠀⣸⡇⠀⠀⢀⡜⠁⢀⣀⣀⣠⡏⠀⠀⠀⠀⠀⢠⣿⠂⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣟⡇⡏⠀⢯⠈⠉⠀⠀⣠⠎⠀⠀⠁⠀⠀⢈⣀⡀⠀⠀⢀⣠⣿⠟⠋⣹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠇⠷⣠⠎⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⢠⠽⠛⠶⠟⠋⠀⠀⠀⣏⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⣸⠀⢀⣴⠟⠀⢀⣤⠴⢶⣤⣄⡀⠀⣸⠆⠀⠀⠀⠀⠀⡖⠛⣉⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠠⠟⠀⠞⠏⠀⠀⠀⠀⢀⡾⠀⠀⠉⠛⠁⠀⡀⠀⠀⠀⠳⣽⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣤⣀⠀⠀⣀⡀⣠⣤⠖⠚⣛⣀⣀⣀⣠⣴⠞⠋⠀⠀⠀⢀⣸⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⣷⣈⣩⡽⠿⠛⠛⠓⠛⠿⠿⠿⠿⠻⠟⠛⠲⢦⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠚⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣤⣤⡶⠶⠶⠶⣤⣴⣦⡾⢿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⠞⠋⣠⡙⠒⣠⣄⠐⣃⠀⢀⠀⠰⢦⣀⣉⡁⠙⠛⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡿⢈⡄⠉⣥⠏⠉⣉⠁⠤⠀⠉⠁⠛⠙⠠⢶⠀⠈⠃⠴⠰⠶⣤⣀⢭⡛⢿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⢛⡙⡫⠶⡞⢃⣁⣴⢲⡀⢉⡀⠀⣛⡛⠂⠘⢂⡀⢀⡤⠤⠴⢦⡀⠤⠌⣉⠠⠅⣤⠨⡝⣿⣄
⠀⠀⠀⣤⣤⣤⣤⣿⣯⣥⣭⣤⣥⣬⣥⣤⣤⣤⣬⣦⣾⡦⠶⠾⠷⣶⣴⣾⠶⢶⠶⠶⠶⣾⣶⣶⣦⣥⣤⣤⣤⣤⣤⣤⣽⣷⣤⣤⡄
⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁
⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣀⣀⣼⡆⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠓⢄⡀⠀⢙⣣⠄⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⡄⠠⣚⡉⠀⢀⡴⠂⠀⠀⠀⠀⠀⢸
⠀⠀⢀⣀⣀⡀⢤⣤⢄⣥⣔⣻⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣛⣧⣶⣠⣤⠄⣀⣀⠀⠀⢸
⡶⢿⣿⣿⣿⣿⣿⣶⣨⣭⣟⣻⣯⣥⣭⣛⣛⡿⢿⣿⣿⣿⣿⡿⢿⣛⣻⣥⡭⣿⣛⣿⣭⣆⣶⣿⣿⣿⣿⠷⣾
⠉⠛⠒⠿⠯⠭⣽⣯⣙⣛⣙⣻⣷⣶⣍⠛⠛⠫⠭⠤⠘⠓⠖⠛⠻⠿⣛⣋⣞⣒⣒⣒⣹⣥⣭⠭⠽⠷⠚⠋⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢠⠤⢢⠤⢀⣄⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣢
⠀⠀⠀⠀⠃⠀⠰⠏⣠⣀⣸⣷⣎⣉⣀⡿⣷⣼⣟⠋⣼⣿⡿⣿⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠉⠉⠉⢉⣉⡁⣤⡤⢾⣛⣿⡟⠀⡹⠃⢀⣤⣞⣯⣴⢅⣠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠿⣧⠀⣠⣴⣾⣿⣿⣿⣷⣿⣿⣽⣿⡿⢿⣶⢁⣾⣿⣿⣏⣿⣁⡀⠘
⠀⠀⠀⠀⠶⣤⣤⣤⣿⡛⠋⠉⣉⣽⣛⣛⣺⡿⠋⢡⣶⣾⣿⣾⣿⣿⢧⣿⣏⣹⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⢛⣩⠙⢿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣭⣿⣟⣿⣿⡏⣾⡏⢙⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡿⡿⣹⣿⣿⣿⣷⣿⣿⣿⠃⠀⠀⠘⠃⠐⠠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡷⣿⣿⣿⣿⣿⣷⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣙⣏⣿⣿⣾⡿⣻⣿⣯⣽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠯⡝⠠⣿⢻⣿⣿⡏⠁⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠋⠀⠘⠚⠯⡼⢻⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠥⠤⠤⠤⠬⠭⢉⣀⣒⡒⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠋⠂⢿⣍⡓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡀⠐⠀⠀⠀⠀⠀⡴⠀⠀⢸⠧⡀⠀⠀⠀⠀⡠⢆⠠⠈⠁⠀⡀⢸⠹⡉⠳⢦⡉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠔⡹⠆⠀⠀⠀⠐⠈⡆⢿⠋⠉⡹⠋⠔⠈⣀⠄⠀⠀⠀⢸⠀⡇⠀⠀⠙⠳⣄⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡴⠁⠀⠀⠐⠂⠀⠀⠀⠀⡇⢸⢀⠼⠁⠀⠀⠀⠀⠀⠤⠀⠀⠘⣀⠇⠀⠀⠀⠀⠘⢧⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠚⠁⢤⠀⠀⠀⠀⠈⠀⣀⠀⢃⢿⠣⣀⠀⠋⠀⠀⠀⠀⠀⠐⠂⠀⡏⡷⡀⠀⠀⠀⠀⠀⢳⡄⠘⣦
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡏⠑⢤⡀⠀⠀⠀⣀⠀⠀⠀⠀⢸⢸⣦⣨⠑⢤⡀⠀⠀⠆⠀⠀⠀⠀⣇⢸⠘⡄⠀⠀⠀⠀⠀⢷⠀⠸⡆
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢣⡈⠲⣗⠈⠢⣄⠀⠉⠀⠀⠀⠀⠘⡄⡧⣼⠢⣄⠉⡢⣄⠀⠀⢠⠀⠀⢹⠈⡆⠘⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣿⡙⢦⡑⢄⡘⠑⢤⡀⠐⠃⠀⠀⡇⢳⡈⠑⢌⡑⢄⡀⠑⢤⡀⠀⠀⠸⡀⡇⠀⡄⠀⠀⠀⠀⢈⡇⠀⢸
⠀⠀⠀⠀⠈⡀⠁⠀⠀⠀⠀⠈⠣⣄⠉⠢⣌⠦⣄⠈⠢⣄⠀⡄⢷⢸⠙⠦⡀⠝⠣⣹⡢⢄⠉⠢⣌⠀⣇⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠹⡗⢏⠈⠑⢷⣝⠢⣀⠑⢦⣸⡇⠀⠀⠈⠲⣄⠈⠙⢦⡉⠢⣌⠑⢾⣇⠀⠀⠀⠀⠀⢀⡾⠀⢠⡟
⠀⠀⠀⠀⠀⠘⣄⠠⡀⠀⠀⠀⠀⠀⠙⢦⡑⠦⡠⠌⠓⢌⠱⡦⣈⡿⡄⠀⠀⠀⠀⠑⢬⡁⠈⠲⢜⣍⠺⢛⡆⠀⠀⠀⢀⡼⠁⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠘⢦⠀⢄⠀⠀⠀⠀⠀⠀⠙⠢⣌⡒⢄⡈⠑⠻⣆⢥⡽⠀⠀⠀⠀⠀⠀⠈⠓⣄⡒⠩⠦⣽⠁⠀⠀⣠⡞⠁⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠦⢄⡉⠙⣿⣀⣀⡀⠠⠄⠐⠀⠀⠀⠈⠒⠄⣻⠆⣠⠾⠋⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠛⢁⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣉⡓⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠞⠋⣁⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣬⣉⣉⣛⡒⠒⠒⠒⠚⢛⣋⣉⣉⣤⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⡿⠿⠿⠿⡿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠤⣁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣈⡉⠑⠒⠶⠤⠤⣠⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠂⠀⠰⠟⡉
⠀⠀⠀⠀⠀⠀⠀⡂⠀⠉⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡜⠋⠁⠀⠀⢀⣠⠴⢎⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠈⢄⠀⠀⠉⣿⡩⢙⠶⠦⣤⣀⡀⠀⠀⠀⠀⠉⠐⠂⠠⠄⠀⠀⠀⠀⠐⠂⠁⠈⠿⠀⠀⠴⣶⡉⣀⣀⣀⣡⠀⠠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠒⣲⣾⣷⣌⣀⠀⠀⠎⠉⠛⠶⢤⣄⣀⠀⠀⡀⠀⠀⠀⣶⠀⠀⠀⣀⣤⣶⠁⠀⣀⣀⢙⠉⢉⣽⡃⠀⡀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⢀⡈⠙⠻⢯⣶⣖⣶⣶⣾⠿⣿⣿⡟⠶⠦⣤⣀⣀⣈⡤⠶⠻⠁⢠⡷⠺⠫⢉⡍⣾⡾⠟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠉⠲⣄⠀⠀⢀⣀⠀⠀⠀⢉⣉⣻⣶⡀⠺⠀⠉⠡⢀⡀⠄⣠⣏⡠⠤⠚⠋⠰⠁⠀⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢄⡀⠀⠈⠑⠢⠤⠀⡀⠉⠁⠀⠚⠂⠙⠻⣷⣤⣤⣤⡤⢶⡮⠭⠤⢤⣤⣤⠄⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣁⡀⠈⠐⠠⢄⡀⠀⠀⠀⠙⠢⣄⠀⠀⢀⡀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣯⣿⣿⢷⣜⣿⠞⠛⠳⣤⣀⠀⠀⠈⠷⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡍⠛⠿⣏⣿⣴⠶⠤⣄⣀⠉⠲⢦⣄⡀⠀⠀⠀⣀⠀⠀⣀⣤⡀⠀⠀⠈⠀⢀⡰⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠀⠀⠀⠀⠉⠻⠦⢀⣄⠉⠓⢦⣄⠈⠛⠓⠒⠶⠾⣶⠿⠮⣙⣿⠷⠶⠶⠚⢋⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠓⠄⠄⣈⠳⣤⡀⠀⠀⠀⠀⢀⠠⠀⠛⠛⠃⠒⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠀⠀⠀⠀⠀⠉⠘⠛⠂⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠒⠦⢤⣀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣀⠀⡤⠤⢶⣄⡄⠠⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⢀⡤⣢⣵⢅⠀⠀⠠⠒⠀⠀⡀⠀⠀⢄⠀⠀⠄⠀⠀⡠⠄⣶⡆⣤⣄⠂
⠀⠀⠀⡓⢹⠛⠀⠀⢀⢀⠑⢶⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠋⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠀⢠⠀⢛⡔⠁⠁⠀⠛⣿⣶⣤
⠀⠀⠀⠁⠀⠫⠧⠭⠄⠆⠀⠀⠈⠀⠀⠀⠠⡔⠂⡀⠀⠀⠰⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠛⢿⣇⡀⠀⠀⢠⣳⠞⡫
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢀⠔⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠴⣿⠔⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠈⠌⠁⠈
⠀⠀⠀⠀⠐⠁⠀⠀⠢⢔⠄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢄⣀⠀⠀⠀⠀⠁⠐⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁
⠀⠐⠀⠈⠀⠀⠀⠀⠀⡠⠀⠄⠀⠔⠀⠈⠃⠀⠀⠀⠈⠀⠀⡂⣞⣾⠷⣪⡤⠀⠈⠀⠈⠀⠀⠀⠽⣜⠒⠉⠇⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠖⠁⠀⠀⠙⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣷⠛⢷⡚⣇⡗⠀⠀⠀⠀⢀⣾⣦⣷⠚⠈⣅⢞⡢⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀
⠀⠀⠀⢰⠄⠦⠀⢀⡀⠄⣡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⣻⠂⠀⠈⣺⣞⠃⠀⠀⠀⠀⠀⣿⢿⣽⣿⣧⠁⣰⠀⠀⠀⡐⠁⢀⠀⠀⠀⣿⣯⣹⢱⠶
⠀⠀⠀⠀⠅⠀⠠⣈⡄⠬⠃⠠⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠢⡤⠔⠟⠁⠁⠀⠀⠀⠀⠀⠊⠻⢿⡿⡿⠟⠂⠀⠀⠀⠡⠀⠁⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣷⣤⣤⡀⠀⠀⠀⠀⠀⠀⣤⣶⣏⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⣿⣿⣿⢿⣄⠀⠀⠀⣠⡿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣿⣿⡟⣧⡆⣴⡏⡷⣿⡿⣿⡏⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⡽⢿⣿⣿⡟⣷⢿⣸⣿⣿⣿⢟⡴⣿⠁⠀⠀⠀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⣙⡾⠿⠿⡇⢹⣷⣿⣿⡭⣿⡟⢰⣟⣠⡴⠞⠋⠉⠀⠀⠉⠛⠛⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣉⣛⣷⣦⣙⡌⢿⡇⠀⣸⣿⠶⠛⠉⠀⠀⠀⠀⠀⠐⠀⠀⠠⠄⠀⠀⠉⠳⢦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣙⣻⣿⣿⣿⠛⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⣀⣌⣩⠿⠛⠁⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⠀⠋⠀⠀⠀⠀⠀⠀⠐⠂⣉⡿⠿⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠩⡴⠞⠁⠀⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢀⡀⠀⠠⠀⠀⣀⡴⠖⠛⠁⠀⠀⠀⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠘⢳⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⢀⠐⠂⠀⠀⠐⠂⠀⠁⠀⠀⣠⣴⣛⠁⠀⠀⠀⠀⣀⡴⢾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠈⠙⠓⠶⠤⢤⣤⣤⣄⣀⣀⣀⠀⢀⣀⣠⡤⠴⠶⠶⠶⠖⠒⠛⠋⠉⠉⠀⠀⢀⣠⠶⢋⡉⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠛⠋⠐⠚⠉⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠙⠛⠶⠦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠶⠶⠦⠤⠤⡤⣄⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠾⠿⠴⠶⠒⠒⠒⠶⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠶⠶⠶⢤⣤⣤⡤⠴⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠉⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢿⣦⣀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⢈⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢙⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢛⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣿⣿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠟⠛⠉⠉⠀⢀⣾⣿⡿⠃⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣀⣤⣤⣶⢶⣿⣿⠟⠛⠛⠛⢛⣛⡛⠛⠛⠛⠛⣛⣻⣿⠿⠶⢶⣦⣤⣄⣀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⣿⣭⣄⣀⣀⠉⠁⠀⠿⢶⠆⠈⢩⡄⠀⠿⠃⠀⠉⠉⠻⠇⢀⣀⣀⣬⣽⡿⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⠀⠈⠉⠙⠛⠛⢛⡻⠿⢶⡶⠶⣿⣷⠶⠶⠶⠶⠾⠿⠟⠛⠛⠛⠉⠉⠀⢀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⣦⣤⣤⣄⣘⣋⣀⡘⠛⠷⠈⠋⠀⠀⠸⠇⣀⣀⣀⣀⣤⣤⣤⡶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠻⣇⡤⠞⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠁⠀⠀⣿⠁⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⢠⡏⠀⡀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⣠⡾⠛⠋⠀⠀⠀⢸⡀⠀⠀⠀⢀⣤⠶⠛⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⣠⣾⠁⠀⢀⡶⠛⠁⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⠀⢹⣶⠶⠚⠃⠀⢠⡾⠋⠻⢷⣶⠋⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣰⠋⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣾⡄⠀⠀⠀⢸⡇⠀⠀⢀⣮⡤⠴⠄⠀⢰⠟⠀⣠⠀⣼⠃⠀⠀⠀⠀⠀⣾⣿⣦⡀⠀⣠⡶⠛⠁⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⡏⢳⣀⣤⡀⠈⣧⠀⢀⣞⣁⣀⡀⠀⢠⡟⢰⢋⣿⢾⠃⠀⠀⠀⠀⠀⣤⣿⠿⠿⠟⠉⠁⠀⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⠃⢰⠀⠉⠈⠀⠀⠿⣦⣻⠀⢸⠋⠉⠁⠀⢀⣼⠁⣾⠟⠁⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠘⠷⠶⢶⡄⠀⠀⠀⠹⣦⢸⣷⠞⠁⣠⣾⣿⢠⡟⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢸⠇⣿
⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠙⣦⡀⣶⡄⠿⠸⠃⠀⣰⣿⣿⣿⣼⡇⠀⠀⠀⠀⢀⡶⠛⠇⠀⠀⠀⠀⠀⢰⡾⠔⠀⠀⠈⣴⣿⣤⣄
⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⢀⣠⡶⠟⢉⡴⠋⢉⡇⠙⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡿⠉⢹⡇
⠀⠀⠀⠀⠀⠈⣿⡁⠀⠀⠀⠀⢦⣄⡄⠸⣿⣶⠟⢁⣠⣾⣿⠃⣾⠋⠁⠀⠀⠀⢠⡟⠀⠀⠀⢀⠀⢀⣀⣿⣯⣤⠀⠄⠀⠀⣸⣡⣴⠿⣧⡴⠶⠶⠶⣦⣤
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡀⠹⣷⠀⢻⣷⣴⡿⢿⣿⣿⣠⠿⠀⠀⣤⣤⣤⣾⠃⠀⠀⠀⢸⠀⣼⠟⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⡟
⠀⠀⠀⠀⠀⠀⣾⡿⡄⠀⠀⠀⠈⢳⣜⡇⢸⣿⠋⠀⣼⢻⣉⡿⠂⠀⡼⠁⢠⠀⠈⠀⠀⢀⠀⣸⡿⠥⠤⠄⠀⠀⠀⠀⣰⠃⠀⢀⠀⠀⡐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠱⣦⣝⣿⠸⣿⠀⢰⢏⣿⣇⠀⢀⣰⡇⢀⣸⡇⠀⢀⠀⢸⡾⠇⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠂⢀⡴⠛⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠈⢦⡘⢿⣿⠀⣿⣠⡏⡜⢸⡟⠀⣾⠛⠃⣼⠏⠁⠀⢸⣦⠎⠀⠀⠀⠀⢀⣴⠿⢶⠟⠁⠀⠀⣸⡴⠋⠀⠀⠀⠀⣀⠀⢀⣿
⠀⠀⠀⢠⡾⠋⣿⡀⠀⠀⠲⣄⠈⢿⣌⣿⢰⣿⠋⡐⠀⡘⠁⢀⣿⠀⠀⡇⠀⠀⣶⣞⣉⠀⠐⠀⠀⢀⡾⠁⠀⠀⠀⢠⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⢻⣾⠋
⠀⠀⣰⠏⠀⡜⣿⠗⠀⠀⠀⠹⣧⠘⣿⡟⢸⡟⠀⠀⠠⠁⢀⣿⠁⠀⣤⡇⠀⠀⠈⠉⠉⠉⢀⣠⣴⠟⠀⢰⣀⣤⠶⠛⠳⠄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⢀⡟⠀⢸⠇⠹⣆⠀⠀⠀⢰⡹⣷⣽⠃⣼⠇⠀⠀⠀⠀⣸⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠋⣹⣡⡴⠖⠻⠯⠄⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣰⡎
⠀⢸⠁⢀⠏⠀⠀⠙⣧⡀⠀⠀⢿⣿⠏⢠⡿⠀⠀⠀⠀⢀⡏⠀⣲⠶⠀⠀⠀⠀⢰⣶⣫⠵⠚⠻⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⢳⡆
⢀⡇⢀⡏⢀⡀⠀⣼⠋⢻⠀⠀⢸⠟⠀⣼⠇⣠⠂⠀⣠⠟⢁⠞⠁⠀⠀⣠⣶⣄⣸⡟⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣠⡴⠟⠁
⣼⠀⢸⠁⢸⣅⢠⡏⠀⢸⡇⠀⠈⠀⢠⣿⡴⠃⢀⣾⠋⠀⠀⠀⠀⢀⡾⠋⠀⠉⠉⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠛⠛⠉⠉⠁
⣿⠀⠸⠀⠀⠙⣿⠁⠀⣼⠂⡠⠀⢀⣾⣉⣠⡶⠟⠁⠀⠀⠀⠀⢠⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣤⣤⣤⣴⡾⠟⠋
⣿⡄⠀⠀⢀⡼⠟⠀⠀⣿⡾⠁⢀⣼⣿⠟⠋⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⡿⠿⠶⣶⣦⣤⣤⣤⣤⣤⣤⣶⣿⠟
⢸⣧⠀⠀⠸⣧⡄⠀⢸⣿⡷⠾⠛⠉⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⢉⣴⣿⣀⣶⡶⠿⠃⠀⠉⠉⠉⠉⠁
⠀⢿⣆⠀⢰⡟⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣦⣼⣇⣠⣴⠿⠋⠉⠉⠙⠁
⠀⠈⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣠⡴⠒⠒⠚⠋⠀⢀⣽⣿⠟⠁
⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠟⠋
⠀⠀⠙⠿⣷⣤⣤⣤⣴⣾⡷⣶⡶⠿⠿⠟⠛⠉
⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⢰⣿⣷⣶⣦⣄⠀⠀⠀⠀⣠⣶⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣀⢀⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣿⣿⣻⡾⣹⣿⣿⣫⣾⠁⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⣟⡛⡅⣿⡟⠓⣿⣡⠿⠖⠋⠁⠀⠀⠈⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠈⣙⣛⣛⣺⣿⣿⠞⠓⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠁⣠⢤⣬⠟⢉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠽⠛⠈⣧
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠻⣄⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠂⠀⢀⡤⠚⠉⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⠙⠒⠦⠤⠤⠤⣤⣀⣀⣠⠤⠴⠒⠒⠒⠒⠋⠉⠁⣀⡠⢖⡋⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠦⣤⣀⡀⢀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣤⠤⠴⠒⠒⠋⠉⠀⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠉⠛⠛⠒⠒⠒⠒⠒⠒⠒⠚⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⣸⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⣁⠀⠁⠀⠀⠀⠀⠀⠀⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠦⠶⠒⠶⠶⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠒⠚⠉⠁

⠀⢀⠔⠚⠉⠉⠉⠙⠓⠲⠤⣀
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀
⡏⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⠳⢤⡀
⡇⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠙⠲⣄
⢹⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀
⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠲⢤⣄
⠀⠀⠀⠈⢢⡀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡨⠝⠲⢄⡀
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⢠⠃⠀⠀⠀⠀⣀⠀⠀⢳⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇⠀⠀⠠⡁⠘⠋⢀⠤⠊⠉⠀⣀⣈⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⢲⡖⠁⢀⡠⠖⠉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⡀⠀⠀⠀⠘⡄⠀⠀⠧⢃⠊⢀⠔⠩⡄⠀⠟⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣤⣴⣀⣀⣠⠂⡠⠁⠀⠈⣃⠀⢶⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢽⡰⠁⠀⠀⠘⠊⠀⣠⠔⣉⣛⠶⡶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢲⠦⡖⠒⠚⠉⢀⠀⠈⣁⠀⠘⡄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣌⡓⠤⣀⡘⠃⠀⠉⢀⡴⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢬⣭⣉⣉⣥⡤⠖⠋
⣿⣿⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠚⠗⠦⠂⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄
⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢿⣋⠀⣿⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⡀⠀⠀⢀⠀⢠
⠀⠀⠈⠀⠀⠀⠀⠀⠲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⢄⠀⠀⠀⠀⠀⣾⣴⣦⢡⣤⣤⣶⣦⣤⢠⣵⡶⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣯⣾⡿⠂⠀⠀⠀⡀⠉⠀⢋⣾⣄⣠⣥⣄⣠⡅⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡰⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠐⣚⢁⢛⣛⢹⢛⡛⣃
⠀⠀⠀⠀⠒⠧⢴⣁⠔⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠜⠯⠿⠿⣿⠿⡿⠿⠿⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣼⣁⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⢍⠈⣒⣶⣤⡁⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡜⣡⠖⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣤⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠗⢪⠹⣝⢺⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠻⠇⣽⣠⣷⡖⣦⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢉⠠⠀⠀⠀⠀⣴⣾⢭⣿⣿⣴⣆
⠀⠀⠀⢤⣂⡐⢀⡀⠶⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⠛⠛⠋⠉⠀⠀⠀⠀⠀⣤⣶⣾⣴⣶⡄⣤⡀
⠀⠀⠀⠀⠉⠙⠐⠂⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠛⠛⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠂⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⣿⡿⣿⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠤⢲⣶⣿⣇⣀⣠⡦⠐⠀⠤⢤⠀⠀⠀⠀⠀⠀⠛⠋⠻⠋⠻⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⣀⣀
⠀⠀⠀⠀⡀⢰⠞⢋⢳⠀⢀⠀⠀⠳⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤
⠀⠀⠂⠀⠈⠙⠰⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⡘⠖⠂⣀⡴⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢲⡏⠠⢇⠉⠀⠀⠀⠀⠀⠀⠀⠒⢿⡖⣺⠁⡴⢿⡛⠤⠘⠁
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢡⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀⣤⣤⣤⣄⡀⠀⠀⠀⢀⣾⠋⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⡿⠵⠄⠀⠉⠉⠀⠀⠀⠈⢻⣄⡀⣠⡟⢁⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⢉⣤⡶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⠙⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠏⣰⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⢋⣡⣴⠞⠋⠁
⠀⠀⠀⠀⣀⣤⡶⢾⡿⣭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠦⠀⠀⢠⡾⢃⣼⠏⠈⠉⠛⠳⣄⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⣉⣤⠶⠛⠉
⠀⢀⣴⠟⠋⣠⣤⢾⣱⠶⠀⠀⣠⡴⠦⠀⠀⠀⠀⠀⠯⠀⠀⠀⣴⠟⣠⡿⠃⠀⠀⠀⠀⠀⣻⠛⢶⣄⣠⣴⠞⢋⣡⡴⠞⠋⠁
⢠⡿⢁⣴⢿⣍⠒⠊⠉⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢋⣴⠟⠀⠀⠀⠀⣀⠀⠐⢿⣶⡶⠟⣉⣤⠾⠛⠉
⣿⠁⢾⣗⡶⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⣡⡾⠋⠀⠀⠀⠀⠀⣹⣷⠾⢛⣡⡴⣿⠋⢻⡄
⢿⡄⣼⢿⡁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⠟⠁⠀⠀⢀⣠⡴⠟⣋⣴⠾⠛⠉⠀⣿⠀⢸⡇
⠸⣿⣿⢦⠁⠀⠀⠀⠛⠉⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢛⣡⡶⠟⠋⠀⠀⠀⠀⠀⠻⣦⣿⠁
⠀⠹⣿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠏
⠀⠀⠹⣧⢨⣝⡻⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠟⠋⣱⡟
⠀⠀⠀⠹⣷⡉⣛⣂⠈⠙⠛⠻⠷⢶⣶⣤⣤⣤⣤⣄⣀⣀⣀⣤⣤⣤⣤⣶⠶⠾⠟⠛⠋⠁⠀⠀⣼⠟
⠀⠀⠀⠀⠈⢻⣎⠙⣃⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠙⢷⣭⡛⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣭⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⢶⣤⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⣶⢾⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⣦⣤⣬⣉⣉⣉⣉⣉⣩⣥⣤⡶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠛⠉⠉⠉⠉⢉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⢤⡴⠶⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⣀⣤⢶⣫⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠏⠀⠁⠀⠈⠀⡀⠈⠈⠷⠶⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⠀⢀⣀⡤⠶⣒⣫⠽⠚⠋⠁
⠀⠀⠀⠀⠀⠀⢠⡞⡛⠠⠂⠠⠆⠐⠀⠈⠀⠀⠀⠈⠃⠈⠉⠳⢦⣀⣤⠶⠚⠉⠀⠀⠀⢀⣠⠴⠖⣋⣭⠴⠒⠋⠁
⠀⠀⠀⠀⠀⢀⡼⠁⠀⡤⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠉⠀⢈⢷⠀⠀⠀⠀⣀⡴⢚⣩⠴⠚⠋⠁
⠀⠀⠀⠀⡶⠋⠀⠀⠀⠈⠀⡀⢀⡀⠲⠀⣀⠀⠀⠀⠀⣀⠀⠀⠘⣿⠀⢀⡤⠞⣡⠖⠋
⠀⠀⠀⠀⣷⠰⠀⠲⠂⠀⠀⠀⠉⠋⠀⠀⠁⠀⠀⠀⠘⠁⣀⢀⡼⢃⡴⠋⣠⠞⠁
⠀⠀⢀⣴⣿⠂⢤⠀⠀⢠⠄⠀⠀⠀⠀⠠⡖⠀⠘⠁⢀⡤⠞⣩⠞⠋⢀⡾⠁
⠀⠀⢸⣿⣇⠡⡀⠀⠠⣄⢀⣀⡘⠂⠴⠂⢀⣠⠴⢚⣩⠴⠋⠁⠀⣰⠋
⠀⠀⢸⠙⣮⡛⠶⣤⣄⣀⣤⣬⡤⠴⠒⢋⣩⡤⠖⠋⠁⠀⠀⣠⠞⠁
⠀⠀⠘⢧⡀⠙⠓⠶⠬⠭⠤⠤⠴⠖⠛⠉⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⠶⠒⠚⠋⠉⠁

⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠛⣷⡀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⢀⣴⠟⠋⣉⡉⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣻⣧⣀⣠⡾⠋⠀⠈⢻⡄⠀⠀⢸⡇⠠⡏⠉⡟⠀⠀⠘⠛⠶⠶⠞⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠧⠀⠊⠀⠈⠉⠉⠃⠀⠀⠀⢸⡿⣦⣤⠾⢃⣀⡿⠸⣄⠀⢀⣀⡀⠀⣀⣄⡀⠀⠸⣇⣠⣀⣀⣠⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢸⡅⣰⠋⠉⠀⢠⡇⠀⢸⠏⣇⣠⡏⢠⡷⢁⡞⠋⠀⠉⠉⠁⠀⢹⡇⠀⢀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣦⠀⠀⠀⠀⠀⠤⢦⠀⣰⠃⠀⠀⢸⣀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠈⠁⠀⠸⢦⡿⢀⠀⢰⠚⢶⠂⠀⡈⠷⠶⠛⠁⠀⠈⠛⣦
⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⡾⠁⠀⠘⠢⣝⡄⠁⠀⠘⠶⢤⡄⠀⠉⠙⢦⠀⠐⢄⡀⢀⢀⡄⢀⡴⠶⠶⠶⢃⡞⠛⠋⠀⠙⠲⡾⠃⢠⣀⠀⢰⡟⠛⢲⣏
⠀⠀⠀⠀⣀⣤⠾⠃⠀⠘⢦⡀⠀⠀⠀⠈⢻⡀⠀⠠⠀⣠⠏⠀⠀⠀⠈⠛⠲⢶⣍⠲⣮⠀⡞⠀⣠⠶⠶⠛⠀⠀⠀⠀⢠⠎⠀⣰⠋⠹⠤⠼⠃⠀⠀⠙⣷
⠀⠀⠀⣼⠋⠀⠀⠀⣤⣦⣴⠃⠀⠀⠀⠀⠸⡇⣠⢃⠀⠙⠶⣎⠀⣀⣤⣄⠀⠀⠙⡇⢁⣠⠇⠀⣏⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠋⠀⠀⠀⢀⣠⠾⠶⠶⠋
⠀⠀⠀⠻⣦⠀⠀⠀⠈⢧⢨⠀⠀⠀⢢⡳⣄⣧⢡⡎⠀⠀⢰⠇⠀⣿⠀⠈⣷⠀⢸⠁⡿⢁⠀⢀⣽⠀⠀⡀⠀⠀⢠⠀⠀⢀⠄⠀⠀⠀⠀⠈⣿⣀⣀⡀
⠀⠀⠀⢀⡼⠇⠀⠠⠴⡞⠈⣏⠀⠀⠀⠑⢌⠻⡆⢃⠀⠀⠘⠧⠴⠋⠀⠘⣧⠀⠈⠛⠧⡜⠉⠉⠁⠀⠀⢣⠀⠀⣸⠃⡴⠃⠀⠀⠀⠀⠀⠀⠈⢉⣩⡗
⠀⠀⠀⣿⠁⠀⣰⣄⠀⡟⠀⠙⢦⣤⡀⠀⠀⠑⢿⡌⠄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣀⡟⠀⠀⠀⠀⠀⢸⡇⡼⢃⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⡍
⠀⠀⠀⠻⣄⣰⡟⠉⠻⣇⣀⠀⠀⢀⡧⠀⠀⠀⠀⢳⡈⠀⠀⠀⠀⢀⠃⠀⠀⠀⡴⠋⡭⠀⠀⠀⠀⠀⠀⢸⡿⠁⡾⠀⠀⠀⠀⡀⠀⠀⠠⣀⡀⠀⣿
⠀⠀⠀⠀⠈⠉⠀⠀⠀⢩⡟⠀⠀⣿⡀⠀⠠⡀⠀⠀⢧⠀⠀⠀⣠⢎⠀⠀⠀⠠⡇⠀⠳⡄⠀⠠⠀⠀⠀⢘⠇⣸⠃⠀⢀⣴⠋⠀⠀⠀⢸⡟⠳⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡄⠀⠘⠦⢦⡄⠈⢓⠦⣌⡄⢢⡜⣡⠃⠀⠀⠀⢠⡟⠀⣤⠃⠀⠀⡇⠀⠀⢸⠀⡏⠀⢠⡿⢹⣆⣀⣸⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⡷⠀⠀⠑⢌⡃⠈⠰⠁⠀⠀⠀⠀⣿⠀⡞⠀⠀⠀⢰⡃⠀⠀⡌⢀⠇⠀⢸⣿⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠸⡇⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠘⢆⠀⠀⠀⢿⡀⢠⠁⣸⡀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⢻⠀⠀⠀⠀⢠⠀⠀⠀⠀⣠⢀⡞⠁⠀⢀⡎⠀⠀⠀⠘⢰⡆⢠⡯⠂⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠀⠈⢦⣄⡀⠠⣌⠀⠀⢀⣰⠃⠘⣧⠀⢸⡁⠀⠀⠀⠀⢠⡎⢠⠏⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠈⢳⠀⠈⡃⠀⠈⣇⠀⠀⢘⡇⢀⡷⠀⢰⠀⢀⠎⡰⠃⠀⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣄⠀⢧⡀⠘⢆⠀⢻⠀⠀⠈⢧⡞⠁⠀⢸⡴⠃⡰⠁⣴⠷⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⣄⠙⢦⠈⢂⠈⡆⠀⠀⣠⠃⢀⡼⠋⣠⠞⠁⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡘⣇⠀⠣⠀⠀⠸⡇⠀⠞⠀⣸⣥⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠖⠛⠓⠀⠀⠓⠶⢤⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣶⣶⠶⠶⣤⣤⣀⣀⣨⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⣶⣶⣶⣶⣶⡾⢷⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣾⢷⣶⡿⠿⠿⠶⣶⠶⠾⠷⡶⢿⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠
⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀
⠀⠀⠀⢀⡴⠻⢛⡳⢤⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣟⠃⠐
⠀⠀⠜⢡⣤⠶⠦⠁⠨⣿⡇⠀⠹⡆⠀⠀⣀⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⡙⡄⢀
⠀⠀⠀⠀⠀⢠⣤⣠⣄⣀⠉⠉⠙⢿⡟⠛⠛⠦⣍⠙⠓⠒⠀⠀⠀⢐⣶⠂⠀⠉⠉⠉⢛⣓⠺⠛⠉⠝⠓⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣰⡀⠰⠻⡍⠻⣍⠑⠦⠷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⣀⣀⣐⣚⡋⠂⠀⠀⠀⠀⠠⠄⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠻⣷⡶⠂⠈⠲⣤⣌⣑⡖⣶⣄⠀⠀⠀⠀⠀⠀⢀⠴⠺⠿⢿⣯⣭⠬⣬⣟⠛⣛⡶
⠀⠀⠀⠀⠀⠀⠙⢅⡾⣷⠆⠠⠞⠋⠭⠉⠛⠳⣄⠀⠀⢀⣴⠧⠀⠀⢴⡀⠀⢀⡀⠀⡀⠀⠀⣀⠿⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠁⠀⠈⠁⠀⠈⠂⠰⠧⠀⠀⠀⠀⠀⠈⠧⠀⠀⠠⠷⠗⠂⠋



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

⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⡄⠀⠀⢀⣰⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⣦⡀⣾⢱⣿⡿⣿⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⡛⣿⣿⡟⣿⢣⣿⣿⣿⣳⢺⠇⠀⢀⣠⡤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢾⣟⡛⢇⢻⣿⠛⢚⣿⣡⡿⠶⠚⠉⠀⠀⡀⠀⠉⠉⠓⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠓⠲⠾⣿⣾⣦⠿⠦⠾⠋⠁⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠈⠙⠓⠲⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⢉⣉⣙⡿⠟⠁⠀⠀⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠠⠉⣛⡿⠍⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠩⡖⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⣀⡤⠒⠋⠁⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠙⠶⣄⣀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠄⠀⠀⠀⠀⠁⣀⣀⣀⣴⠾⠁⠀⠀⢀⣠⠴⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠉⠛⠓⠒⠒⠲⠶⠤⣤⡖⠚⠉⠉⠉⠉⠉⠁⠀⠀⣀⣠⡴⢒⡩⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠶⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⠴⠖⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⠙⠙⠛⠛⠛⠒⠚⠒⠚⠒⠓⠻⠿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⣠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⢾⡁⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⢤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣬⣔⣠⡤⠤⣤⣤⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠴⠦⣤⣤⣤⡤⠴⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣀⣀⣀⣀⠤⠤⠤⠤⠴⠒⠒⠒⠒⠚⠉⠉⠉⠉⠁⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠩⠤⠤⠤⠤⠤⠤⠲⠶⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⡀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⡄⢾⣀⠀⠠⣄⠀⣣⡀⣂⣸⢋⡔⢲⠄⡘⠉⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢫⣻⡁⢈⢁⠰⡀⡸⢀⠀⡑⠈⣻⣮⣵⢃⠀⠲⠚⣀⣼⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢯⠉⠉⠛⠛⠛⠲⠿⠾⠷⠶⠷⢿⣿⣿⣿⣿⣿⣿⡿⡗
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣟⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠬⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⢀
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⡁⠀⢀⠒⠲⠴⣐⣠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣼⢴⠾⠉⠀⢃⣀⡤⠀⠁⠁⢠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣠⠲⢓⠀⢈⠴⢚⠍⠁⠀⠀⢀⡄⡀⠀⣡⡈⠁⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢀⡃⠀⡼⢫⠡⠆⠴⠤⠤⢥⡅⠉⠵⠚⢂⡨⠄⠀⠉⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠤⡈⠢⠮⠀⠐⠣⣉⠀⠀⠒⠁⠈⠉⣀⠔⠁⠀⠀⠀⢀⡼⠆⠀⠄
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢴⡂⠐⡎⠀⠀⢀⣀⠨⠱⠆⠀⠀⠀⠂⠁⠀⠀⠀⢀⡐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠐⠁⣠⠤⠒⠾⠯⣉⠀⠀⠀⠀⠈⠳⣀⠙⠢⡀⠀⠀⠐⠨⠣⠄⠀⠒⠀⡀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠈⠢⣀⠐⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠈⠀⡠⠁⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠈⠉⢖⠦⡤⠀⠀⢲⠀⠀⠠⣄⠀⠀⠀⠄⢀⣄⡠⠔⠒⠊⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠁⠘⠉⠈⠃⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣂⡀⠤⠌⠙⠒⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⡈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠈⠀⠀⠀⢠⣄⣄⢒⡧⢀⡺⡶⢄⢀⡀
⠀⠀⠀⠀⢈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠀⠀⠀⠀⠀⠘⠳⠻⠶⠬⠛⠋⢃⡁⠤
⠀⠀⠀⠀⠀⢢⠀⢀⠄⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⡇⠠⠆⠀⠀⠀⠀⠀⠲⣴⠄⠄
⠀⠀⠀⠀⠀⠏⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠁⠁
⠀⠀⢠⠀⠀⣴⠘
⠀⠀⠀⠄⠀⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠰⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣠⢀
⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢰⡲⡞⣮⠗⠶⢜⡛⣳⢲⡢⣤⡄
⠀⠀⠀⠀⠀⠄⢣⡀⠀⠀⠀⠀⠀⠀⠢⡐⠀⠀⡀⠀⠀⠀⠀⠀⢿⣷⡒⠀⠁⠉⠉⠉⠉⠁⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠘⡘⡅⠀⠀⠀⠀⠀⠀⠀⠈⢄⢠⡇⠀⠀⠀⠀⠀⠀⠻⣧⣄⣀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⡄⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⢢⢦⣤⠠⡖⠶⣤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡼⢏⠤⣀⣵⠀⠈⠓⢃⠄⢤⠄⠛⢚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠀⢚⠄⠀⠀⠁⠐⠀⠀⠀⠀⢀⠀⠀⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣇⣌⡒⡆⣀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠉⡩⠟⠻⢾⠽⣥⡢⠖⣀⡀⠀⠒⠆⠀⠀⣷⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠋⠁⠀⢀⠤⠊⠁⠀⠀⠀⠑⣽⠊⠉⠙⢯⣄⠰⡶⣤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉
⠀⠀⣰⣋⣠⣤⠤⠒⠒⣩⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞
⠀⠀⠉⠁⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⣀⡴⠚⠉
⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢀⣠⠶⠊⠁
⠀⠀⠀⠀⢀⡞⣀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠉⠉⠉⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣫⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠁⣠⡾⠷⠰⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⢂⡴⠋
⠀⠀⠀⠀⠈⢧⡡⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣞⡋⠁⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⣠⠶⠛⠉⠁⠀⠀⠉⠙⠳⣦⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣇⣰⣚⣥⡤⠤⠤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡷⠿⠶⠶⣤⣤⡤⠤⠖⣊⡵⠷⠖⠒⠲⠿⢦⣄⡀⠀⠀⢀⣠⣿⠟⠉⠀⠀⠀⠀⠀⠈⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠈⠙⣶⡟⠁⠀⢀⠀⠀⠀⠀⠀⠈⢻⡛⠛⠉⠁⡿⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠀⠀⠀⠀⠀⠀⢀⡠⢻⡓⢤⣀⠀⠀⠀⠀⠀⣀⡤⢚⠇⠀⠀⠀⠙⢦⣉⡑⠒⠒⠒⠒⢋⣩⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⣉⡒⠒⠒⢒⣉⣩⠴⠋⠙⠦⣬⣉⣉⣉⣉⣉⡥⠶⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀⢀⠀⠀⣀⠀⠐⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡢⠀⠘⠗⠀⠠⠑⢦⠄⣄⡀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⡰⢠⠀⢈⠀⠀⠀⠆⡻⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠉⠐⢦⡠⠀⠀⠀⣰⢺⡄⢀⡁⠂⠾⢶⣡⢤⣠⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠻⠹⣦⣀⠁⠀⠀⠀⠀⣈⠂⣆⣙⣄
⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠀⠈⢢⣅⠀⠀⠠⠀⠄⠁⠀⠀⠀⣀⠈⠐⣖⣀⣼⣗⣩⣒⣼⠿⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡂⠀⡏⠳⢤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠪⣽⣓⣤⡟⣁⣠⠿⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⠰⠶⣘⡢⡶⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡶⠿⠛⢻⡞⢫⣵⠂⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢈⡈⠳⣯⡿⠇⣘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠍⣳⡤⢽⡏⠉⠛⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⣻⣆⣧⠑⢆⡟⠀⡀⠈⢄⡀⠄⠤⠀⠁⠀⠀⢐⣎⠓⣬⣧⡴⢄⢂⣴⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡘⣿⠈⢳⠛⣇⠀⠸⡆⠀⠈⠁⠀⠀⠀⠀⠀⣼⢸⡇⠃⡟⠛⢶⠌⠙⠀⣘⡠⢔⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠛⠻⣁⣼⠙⠙⢧⡀⠈⠑⢀⢀⡤⣠⣀⡤⣤⡏⢹⣷⣀⠎⢀⡦⡐⠁⣰⢁⠘⠂⠁⡀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠦⠀⠙⡛⣶⡈⢻⡗⠞⢋⠁⠂⠸⠀⠠⠀⠳⠰⠮⡟⢲⢠⠆⢀⠜⠃⠀⠀⠈⣃⠽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠯⣿⡖⠠⡟⠟⠀⠀⢁⠒⠄⡄⠠⠱⡞⢮⠗⢀⣴⠁⠐⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⡄⠀⠃⢀⡀⡀⠠⠀⢀⡄⠜⠋⣠⢴⡋⠥⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣴⣤⣀⣀⠀⠉⠈⠀⠑⢒⣈⡩⣤⣶⣽⣋⣁⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⢿⣿⣿⣿⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡾⣹⢿⠂⣿⢿⣿⣿⠛⣿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⠏⠉
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣷⠏⣼⣼⣤⣦⣿⣶⣸⣍⣼⡝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠭⠉⠀⠈⠐⠃⠉⠉⠙⠛⠿⣿⣿⣿⣿⣷⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⣉⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢾⡉⠛⠚⠋⠉⠙⢦⡀⢠⡾⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢋⣡⠴⠋⠁
⠀⠀⠀⠀⠀⠀⣼⣋⠉⠉⠉⠋⠲⠀⠀⠀⠀⠀⠀⠀⣹⠏⣴⣯⣀⡀⠀⠀⠀⠀⣀⡴⠚⣉⡴⠞⠉
⠀⠀⣀⣴⣶⣿⣟⡎⠀⠀⠀⠀⠀⠀⠀⣴⠚⠂⢀⡼⢣⡾⠁⠀⠉⠙⣦⣠⠶⢋⣡⠖⠋⠁
⢠⣾⣿⣿⠻⡍⠚⠁⠀⢾⠉⠁⠀⠀⠀⠉⠀⣠⠟⣴⠏⠀⠀⣀⡤⠞⣩⣴⣾⣏
⣿⣿⣟⡮⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡾⢃⣠⠴⣋⡥⢶⠋⠁⠀⢿⣿⣧
⢿⣿⠿⠅⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠈⠑⠟⠀⠈⠴⠚⠉⠀⠀⠀⠀⠀⢸⣿⣿
⠘⣿⣿⡀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⠇
⠀⠘⣯⣻⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠇⠀⠀⠀⠀⠀⣀⣠⣴⠞⢫⡟
⠀⠀⠈⢷⡩⣥⡈⠙⠛⠳⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠞⠛⠉⠁⠀⣠⠟
⠀⠀⠀⠀⠻⣦⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠈⠙⢾⣟⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠶⠤⣤⣤⣤⣤⣤⣤⠴⠶⣿⠋⠁