Tacos Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⠤⣄⣤⣀⡤⢤⠀⢀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⣯⡈⠛⣦⣉⣣⠘⣇⣼⢳⠈⠒⣉⡿⠴⢟⣒⣒⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣒⣓⣾⣿⣿⠈⠧⣈⠭⣤⣙⣻⡾⠛⣛⡥⠖⠛⠉⠛⠣⠍⠙⡚⠭⢷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣾⣿⣿⡿⣫⢟⣻⣿⣶⣦⣼⣿⡿⢋⣠⡜⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⢶⠱⡙⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣄⣾⠛⣭⣭⣭⣗⣓⠿⣿⣿⣿⣿⠟⣡⠶⢛⣡⣤⠦⠄⠀⠀⠀⠀⣤⣤⡀⠈⠻⣈⠷⢸⡿⣄
⠀⠀⠀⠀⠀⠀⠀⢧⣀⣰⣟⣻⠿⣭⣿⣿⣷⡌⣿⣿⢏⡜⠁⠄⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⡀⠈⠉⢦⠓⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢧⣤⣚⡡⠖⠉⠉⠉⠉⠛⢿⣿⣫⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⢆⠀⣿
⠀⠀⠀⠀⠀⢀⡴⠻⠋⠈⠳⢄⣤⣤⣴⣶⣤⡿⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡀⢣⣿
⠀⠀⠀⠀⠀⠀⣿⠓⠲⠴⢚⣿⠿⣿⣿⣿⡿⣹⣁⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⡄⠉⢁⣼⡟
⠀⠀⠀⠀⠀⢀⣘⣦⣠⣾⢻⣸⡇⡏⢸⣿⣿⠉⠈⠓⠀⠀⠀⠀⠀⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⠾⠟⠛⠁
⠀⠀⠀⠀⠀⢯⣿⢁⣿⣿⣿⣿⣧⣿⣿⢳⠇⠀⠀⠀⠀⣀⡀⠀⠀⠈⠍⠁⠀⣀⣠⣤⠶⠞⠛⠋⠉
⠀⠀⠀⠀⠀⡼⢿⣿⢿⣿⢿⡟⢿⣿⢿⡿⠖⠢⠄⠈⠉⠉⠁⢀⣀⣤⡴⠾⠛⠋⠁
⠀⠀⠀⠀⠀⣧⠀⣿⡆⢻⡌⣷⣼⣏⣾⣋⣀⡤⣰⣦⣤⡶⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠹⠤⣿⣽⣾⣷⣿⣫⣿⣿⡷⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⣀⢴⡄⠀⢀⣶⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣧⠼⢿⡛⠋⣽⣿⣿⣿⣿⢛⠛⣲⣶⡴⠟⢾⡇⠀⠈⢛⣡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣴⣾⠯⠙⠀⣇⠀⠀⠙⠚⠁⢻⢱⣿⣟⡍⠛⢩⢟⠀⠀⣨⠿⠛⣿⣭⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⣿⣲⣴⡟⠿⠏⠀⣺⢶⡞⠋⣠⠖⢯⡲⣀⣸⣿⣿⡷⠶⠶⠿⠾⠶⠾⠷⣤⣤⣴⣴⣿⣿⡽⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⠻⣷⣽⣶⡞⠋⡹⣷⣣⢙⣷⣿⡿⠛⠋⣍⣙⢲⠂⠀⠄⠘⠃⣤⠀⠙⠛⠒⡾⢭⣛⠿⣿⣦⣬⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⡄⠀⢿⣿⣿⣝⣦⣐⣿⠿⠛⠙⠿⠃⡀⠀⠶⠾⠍⠀⠀⠆⠀⣤⠀⠀⠛⡇⠠⡍⠛⠾⣝⠲⣝⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣁⣀⡿⣀⡎⡼⣻⣿⡿⢋⠁⠀⠀⠀⢰⡀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠤⠈⢁⠈⠓⢮⠻⣆
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⡆⠀⠊⠉⠚⠛⣇⣷⣿⡿⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⢀⠀⠌⠳⡜⣧⡀
⠀⠀⠀⠀⠀⠀⡾⢿⠿⢀⡿⢹⣄⣤⣤⣖⣴⠟⠛⠻⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠐⣾⣼⣤⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠙⠦⣤⡿⠟⣻⣷⣤⣤⣿⡁⠀⠈⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⢠⠀⠀⠀⡀⡌⠀⠀⠀⠘⠉⠉⢁⣠⡴⠞⠛
⠀⠀⠀⠀⠀⠀⠀⣀⡟⠉⠀⠹⢿⣾⣿⠟⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⡀⠀⠀⣤⠀⣀⣬⡶⠞⠋⠁
⠀⠀⠀⠀⠀⢀⣼⡧⣶⣲⣿⣿⣾⣿⣟⡤⠀⠀⠀⠀⠀⠈⠀⠀⠐⠍⠀⠄⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣀⠀⠀⠋⣀⣼⠶⠛⠋⠁
⠀⠀⠀⢀⡴⣫⣷⣿⣿⣿⠿⣿⣿⣿⡞⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠂⢀⣠⣤⠶⠛⠉
⠀⠀⢠⣟⣾⣿⡿⠛⣡⡶⣶⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠐⠾⠀⠀⠠⠀⠀⢠⠀⢀⣠⣴⢾⣯⣡⡴⠞⠛⠉
⠀⠀⠈⠿⣯⠿⢤⣠⣘⠿⣿⢯⡇⠘⠟⠀⡤⠀⠀⠀⠀⣄⣀⠀⠐⠃⢁⣠⠴⠚⣉⣤⡿⠟⠋⠁
⠀⠀⣠⣖⡲⡄⢰⠋⣡⠶⣿⢸⢡⡄⠀⡶⠀⠀⠀⠀⣰⡓⡾⡄⠀⠚⣉⣤⠶⠛⠉⠁
⠀⠀⢧⣙⠛⣁⡼⢏⠁⢀⣿⢸⠺⠀⠀⠀⢀⠀⢀⠀⠌⢙⣩⣴⠶⠛⠉
⠀⠀⠀⠈⠉⠉⠀⡼⢰⢯⣿⣼⣆⢀⡀⠀⢈⣌⣨⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⢰⣳⣎⢿⣿⣷⢿⣼⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠻⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡤⠤⢄⡀⢀⡠⢎⠉⠳⣄⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡴⠁⠈⢳⢤⡤⠃⡠⠴⡌⠭⠀⠈⠂⠀⢈⠭⣓⣂⣚⢳⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠉⠉⢆⠀⠀⢦⠃⠀⠘⡀⣀⣱⠰⡶⠧⠴⢊⡵⠮⢭⢤⣍⣿⢀⠎⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠒⠲⠤⣀⠀⢦⡱⣀⠮⠁⠀⣊⣉⠭⢵⣿⣭⠥⠤⠽⢊⣉⣠⠤⢾⠋⠉⠑⢤⣀⣠⢷⠛⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣇⠀⠀⢲⠤⠞⣓⡩⠭⠭⠝⣒⣦⣀⣹⡀⣁⣠⠤⠔⠚⠛⢛⣛⣛⣛⣛⣒⠲⠦⢄⡀⠀⢃⠄⢀⣇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠤⠤⢩⠖⣡⣶⠋⣠⡂⠤⠔⡺⠉⢉⡥⠖⠉⢁⣠⠴⠒⠚⠉⠉⠁⠀⠀⠀⠉⠉⠙⠒⠮⣕⡺⡀⠁⠈⠉⡧
⠀⠀⠀⠀⢀⡖⠉⢱⠀⠙⠲⢡⢞⣥⣶⠦⢤⣛⡏⢈⡱⠚⠁⣠⠴⣚⠥⠂⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠲⢍⠻⣦⡀⠘⢑
⠀⠀⠀⠀⠀⡇⢀⡴⣒⣤⢣⣣⠟⠋⠘⡄⠀⢜⡵⠋⢀⡴⢋⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⢷⡔⠋
⠀⠀⠀⣠⠚⠉⡰⡪⠃⣟⢿⣧⠀⠀⡠⣇⡴⠋⢀⠔⢩⠞⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢷
⠀⠀⠀⢇⠀⡰⠃⠀⣸⡟⢀⡾⣖⠊⢠⠎⢀⡴⠃⠔⠁⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡆
⠀⠀⠀⣸⠙⠁⢅⠮⠊⡠⢪⡄⠀⡴⠃⣠⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⢰⠃⢠⡌⡆⠠⡪⡾⠛⠃⡜⠁⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⢀⡏⠀⢾⡀⠀⡇⡇⠳⢄⡞⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤
⠀⡼⠀⠖⠀⢨⠂⢄⠀⠀⡜⢀⡞⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠋⠉⠉⠁
⢠⠇⡆⠠⣀⡴⠒⢲⠁⡼⢀⡞⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡠⠤⢒⣊⠭⠐⣂⡥⠴⠒⠉⠁
⣸⢰⠉⡀⢀⠀⠐⠊⡼⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⢒⣊⠥⠖⠊⠉
⡇⠘⢀⠀⠘⢰⠄⡰⠁⣰⠁⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣀
⡇⡇⠈⠓⢚⣜⡼⠁⣰⠃⠀⠀⢀⣠⠤⠖⠋⠉⠀⠀⠀⠀⠀⠉⢻⡏⠉⠀⣸⣧⠀⠀⣴⠟⠋⠙⠁⣴⠟⠉⠛⢷⡄⢼⡏⠉⠋
⢻⡿⣌⣩⠥⠊⢀⣜⣡⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⣯⣼⣇⠀⣿⡀⠀⠀⠐⣿⠀⠀⠀⢸⡇⠈⠙⠻⣦
⠀⠙⠒⠶⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠠⠟⠀⠀⠹⠆⠘⠻⠶⠶⠆⠙⠳⠶⠶⠋⠀⠲⠶⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣀⠀⣐⠀⠀⠀⢀⠀⢠⠂⠀⠀⠀⠀⣠⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣶⣦⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⣋⣩⣵⣶⣦⣤⣾⠏⠁⣉⣭⣭⣵⣶⣿⣿⣿⣿⣭⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⢡⣴⣾⡿⠛⢻⣿⠋⢉⣡⣶⠿⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣀⣴⣿⣧⣌⣡⣤⣾⠟⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢀⣾⡟⠛⠀⠉⣹⡿⠉⢡⣾⠟⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣿⣟⠁⠀⣠⣤⣿⠇⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⢸⡿⠀⣠⣿⠿⠿⢿⣿⠁⠀⣼⡟⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠁⠀⢀⣼⡿⠀⣼⡟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠰⡶⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⢠⣿⠁⣾⡟⠀⠀⣿⡏⢀⣾⡟⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣠⣿⠇⠀⣀⣿⣇⣾⡟⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⣠⡀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⢰⣿⢉⣾⠏⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠹⣿⣄⣀⣼⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣶⠶⠶⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠿⣭⡾⣿⠛⠛⣻⠶⢦⣍⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣭⠿⠶⠒⠶⠶⢬⣟⡛⢿⣤⣄⣭⠿⣤⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠉⠈⠀⣀⣁⣀⣤⣀⣈⡙⠷⣄⡘⢧⣤⡀⠻⣎⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠡⣀⣤⣶⣛⣽⡿⢶⡴⣬⣍⣙⠳⢦⡙⠷⣼⡷⢦⡉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣻⣯⣥⣬⣭⣍⣳⠶⢾⡏⠈⠙⣻⣆⡙⢦⡨⠙⢾⣷⡾⠇
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠋⠁⠀⠀⡀⠀⠈⠉⠓⢦⣝⡋⢿⣉⡈⠹⣦⢻⡞⠋⠁
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠠⡄⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠛⢦⣍⣿⣄⡘⠻⣿⡀
⠀⠀⠀⠀⠀⢀⡿⠀⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⣀⠀⠈⠻⢮⣿⣤⣿⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠐⠀⠀⠃⠀⠐⠂⠀⠠⠀⠀⠀⠀⣀⣤⠴⠟⠋⠁
⠀⠀⠀⠀⠀⢸⡇⠀⠰⠀⠀⠀⠄⠀⠠⠄⠀⠀⢀⣠⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⡄⠀⠀⠀⣀⣤⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⢻⣄⠀⢀⣠⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠁






⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⠲⠤⠤⠤⠴⠖⠒⠒⠚⠛⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢰⠚⠉⠉⢀⡄⠂⠐⠒⠒⢤⡠⠐⠂⠉⠉⠀⡈⠉⠘⠳⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣒⠉⣀⣀⣠⢚⡁⠤⠶⠁⠀⠀⠠⠤⣤⡎⠀⠠⢒⠉⡁⠉⠉⠛⠳⠄⠀⠁⡙⡦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠄⠊⡀⣄⢀⡠⠈⠁⢀⣠⠠⠄⠀⣀⣀⣀⠀⢈⡟⠁⠀⠉⠃⠀⠀⠀⠀⠐⠺⡦⠜⠀⠀⠛⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠁⠀⡴⠱⠋⠀⠠⠉⠀⣠⢚⠷⠒⠆⡂⣹⠃⠀⠀⠉⠉⣀⡠⠴⠒⠂⠀⠀⠈⠉⠁⠀⠒⠂⠄⣀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⢀⠜⢰⠁⠀⠀⠀⡧⠁⢀⠀⠀⣠⡈⠷⠀⠀⠀⠈⠑⠀⣠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠂⢄⠙⡄
⠀⠀⠀⠀⠀⢀⠎⠀⢺⠀⠀⣰⠃⢸⠀⡈⠀⠘⡠⠲⠀⠀⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾
⠀⠀⠀⠀⢀⡌⠀⡖⠉⡖⠈⠁⠀⠀⢂⡇⠀⠇⡇⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⡼⠀⡔⢀⣼⣇⣀⡀⠀⠀⠈⢁⠀⡇⡃⠀⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⢰⠁⠠⠋⠀⠀⠀⠀⠀⠀⣠⠛⠉⠀⠋⢀⠌⠀⠀⠊⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⢀⢠⡀⢀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⢀⡐⠂⠀⠀⠀⢰⠁⠉⠁⠀⣠⠊⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⣈⠀⠀⣠⠞⠁⢀⠜⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠸⡀⠐⢄⡀⢀⡔⣃⡴⠚⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡾
⠀⠀⠀⠀⢳⢄⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣀⠠⠄⠤⠴⠶⠶⠶⠶⠶⠖⠚⠁
⠀⠀⠀⠀⠈⢦⡈⠀⠈⠉⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⠤⠤⠒⠒⠒⠒⠒⠚⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠒⠶⠶⠶⠶⠒⠚⠉⠉⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠻⠿⠛⡿⠿⡿⢛⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⢺⡄⠀⢠⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣰⡖⠀⠀⢀⣄
⠀⠀⠀⠀⢿⡄⠀⠘⢧⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡤⡀⠀⠀⠀⢠⠾⡄⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⣠⠟⠁⠀⣀
⠀⠀⢀⠀⠀⠙⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡖⠠⣀⠀⠀⡰⠁⠈⠢⣀⡰⠃⠀⠹⣄⣀⠔⠋⠁⠸⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⡾⠋
⠀⠀⠻⢷⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠖⠁⠀⠀⠀⠈⠀⠀⠀⣀⣈⣀⢀⠀⠀⠀⣇⡀⠔⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡴
⠀⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⢸⠉⠐⢒⣤⠼⠤⠄⢆⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠀⠀⠀⢸⠀⠀⠀⠈⣀⡀⠤⠤⠷⠤⣄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠈⠉⠀⠀⠀⢀⣀⠤⢦⡀⢸⠀⠊⠁⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⣀⣀⣸⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⣭⠃⠀⠀⠀⡤⠤⢄⡀⠀⠘
⠀⣀⠠⠔⠚⠉⠁⠀⠀⠈⣧⠺⠀⡆⠀⠀⠀⣦⠀⠀⠈⣆⠀⠀⢰⠃⠀⠀⠀⡴⠉⠀⢠⠀⠀⢺⠏⠀⠀⠀⡤⠒⠦⡀⠀⠀⠈⣆⠀⢀⣾⠁⠀⠀⠈⢳⠄
⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⢆⠁⠀⠀⠀⠿⠆⠀⠀⠘⡆⠀⣿⠀⠀⠀⠀⢷⠛⠒⠚⢠⠇⢽⠀⠀⠀⠼⠠⣄⠀⢹⠀⠀⠀⢹⡖⢩⠃⠀⠀⠀⢀⠎
⠘⣆⠀⠀⣀⠀⠀⠀⢻⣁⠀⠈⠾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⡟⣆⠀⠀⠀⠀⠉⠉⠙⡏⠀⢻⠀⠀⠀⠇⠀⠈⣆⠜⠀⠀⠀⡾⢠⠃⠀⠀⠀⢠⠃
⠀⠘⠾⢋⡈⡆⠀⠀⠀⢇⢑⠀⠀⡇⠀⠀⠀⢰⡞⢷⡀⠀⠀⠸⣇⠈⠳⣄⠀⠀⠀⠀⠀⢧⠀⠘⡆⠀⠀⠈⠒⠚⠁⠀⠀⠀⡰⢣⡏⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠉⢘⡄⠀⠀⠸⡆⡆⠀⢠⠀⠀⠀⠀⢮⠈⣷⣀⣠⠤⠼⡄⠀⠈⠙⠒⠶⠖⢒⣏⠀⠀⠙⢦⣀⠀⠀⠀⠀⣀⣤⠾⣳⣉⣑⠒⡤⠊⠙⡲
⠀⢠⡔⠒⠉⠁⢱⠀⠀⠀⢻⡘⠄⢸⣀⡠⠤⠚⡃⡁⠱⣄⣀⣀⣼⣷⡶⢶⣮⣧⢒⣓⣾⣦⡷⣤⣀⡀⠉⠉⠉⠋⡋⠝⠁⠾⡏⠀⠀⠙⣄⡴⠊
⠀⠀⠈⠲⣄⠀⠘⣇⢀⡠⠔⠛⢱⡀⠁⣀⡀⢤⣿⡿⠻⠍⢉⣍⠑⠣⡔⢉⡬⣷⣄⣴⣛⣶⣦⠤⡛⠳⢶⡐⠂⠉⠀⠀⢸⠀⠈⠲⡶⠚⠛⠤⣄
⠀⠀⠀⠀⢀⠵⠀⠈⠁⠐⠀⠐⡠⢤⣖⣩⣵⣾⣶⡿⠶⠶⠶⠶⠶⠦⣷⣎⡐⠁⢤⣮⣙⡯⣶⠶⠻⣶⣤⣌⠽⣦⡀⠀⠀⠁⠒⠊⠀⠀⠀⠀⠀⠙⣲⠆
⠀⢀⣠⠖⠁⠀⠀⠀⠀⠀⢠⣲⣷⠟⠋⠉⠀⠠⠀⠀⠔⠰⠂⠀⠀⢀⠙⠊⠍⢻⢦⣄⠠⠄⠨⣇⢰⡵⢟⠉⡖⢈⢿⡷⣄⠀⠀⠀⠀⠀⠀⣠⠖⠋
⠀⠈⠐⠒⠤⣀⠀⠀⠀⣠⠟⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠈⡁⠉⠳⣦⡒⢉⢠⣸⣏⣀⠙⡇⠘⣿⢬⡳⣄⠀⠀⠀⠘⢄⡀
⠀⠀⠀⠀⠀⡠⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⠁⠪⠻⢦⡈⠛⣤⡙⣛⠟⢮⡉⢑⡙⢮⣧⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⠎⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠜⢪⠻⣮⠁⠙⣆⣠⣴⣹⠉⢱⠊⢯⠳⡄⣀⡤⠖⠊⠁
⠀⠀⠀⠃⠠⠤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⢌⢳⣏⡾⠀⣉⣹⢛⡿⠻⡏⢣⢻⣅
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠢⠹⣦⠘⣭⠐⠊⡃⣠⢦⡾⡆⢻⣑⡄
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠣⠘⣧⠲⢈⠟⢋⠩⠀⠸⢿⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠱⡘⣷⡄⡀⢨⠀⠀⣀⣾⢸⡇
⠀⠛⠀⠀⠈⠛⠶⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⢌⡻⣤⣠⣴⣮⡿⢣⣾⠃
⠀⠴⠂⠀⠀⠀⠀⠀⠘⠛⠉⠉⠛⠛⠛⠓⠒⠲⠶⠶⠶⠶⠦⠤⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠈⣒⣺⣉⣥⡶⠟⠁⠀⠀⠀⠀⠀⠙
⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡠⠔⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⠋⠉⠙⠛⠻⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀
⠀⠘⠁⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠘⠂⠁⠀⠀⠸⡄⠀⠀⣠⠖⠄⠀⠀⠀⣠⠆⡀⠀⠀⠀⡜⠑⢦⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠋
⠀⠀⠠⡾⠋⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡴⠋⠀⠀⠈⢆⢀⠔⠁⠀⠙⢦⡀⢰⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢻⣄
⠀⠀⠀⠀⠀⣰⠟⠁⠀⢠⡾⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠰⡆⠀⢸⡄⠀⠘⣧⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢄⢠⡄⢠⣤⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠁⠀⣶⡾⢠⠀⠀⠀⠶⣆⣱⠿⠈⢛⢱⡄⡠⠀⠾⠋⡋⢁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠠⠄⠀⣠⡙⠋⠀⢀⢉⠑⠋⢁⠬⠂⠂⠄⠀⠀⠉⠙⠲⢨⣿⡁⣾⡘⠛⡀⣾⡥⠀⠀⡐⢠⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣭⡟⢿⠈⣿⣧⠢⣬⡡⠀⠀⠃⠤⠀⠀⠀⠀⠋⠙⣉⠁⣀⡨⡏⢠⣤⡄⢘⠀⠈⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠫⢬⡄⣥⡴⢇⠨⣤⣶⣄⠻⠄⠛⠆⢀⠀⠀⠀⠈⠑⠅⢁⠇⠟⣡⢉⢀⢄⣀⣀⣀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠡⣀⠀⣘⠀⡟⠁⣎⢥⣤⣤⡼⢟⡆⠀⠀⣄⠀⠀⠙⠣⣄⡘⣒⡀⠯⣨⣿⣧⣚⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠘⣍⠏⢻⣅⣇⠻⢁⠋⠉⠓⠈⠡⣀⠀⢹⣇⠀⠀⠀⠉⠻⡏⡿⠋⠁⡉⣌⢃⢭⣧
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡟⣯⠉⣦⣔⢻⣶⡠⡔⢂⡿⡔⠘⣿⣆⠀⠀⠀⠀⠙⣿⣄⠀⢀⡍⢁⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢭⣘⣏⠂⠀⠠⠠⣿⠫⣾⣷⡀⠹⣿⣔⠀⠀⠀⠀⠀⠹⠛⢿⣴⡿⠷⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠠⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠈⢿⠿⢷⣄⣐⡠⠄⣤⠐⠻⣷⠄⣿⣿⣶⡄⠀⠀⠀⠈⠢⣼⣯⠀⢦⣤⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⡞⠉⢿⣷⡶⣷⠾⣿⣿⡀⢸⣿⣿⣿⣁⠀⢀⠀⠀⠙⠙⣾⣷⡶⠆⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢶⣤⣤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣼⣯⡁⢠⣄⣈⠻⣇⠀⠀⠉⠛⠿⢿⣶⣦⣤⣀⣳⡄⣿⣵⣔⣗⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⠛⠻⠿⣶⣤⣄⡀⠀⠀⠀⠈⠨⢽⣧⣶⣯⣅⠀⢻⡄⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠮⣏⠉⠈
⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠀⠀⠀⠉⠙⠛⠷⢶⣦⣤⣽⣄⢹⣿⣻⡀⢸⡛
⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣝⡿⠛⠇⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⣤⠴⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⣶⡶⣶⢎⡠⢌⣳⣍⠛⠻⣭⣉⣿⡶⠂⠀⣠⠴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠦⢤⣬⣭⣿⣶⣬⣭⣍⣙⣻⠧⠤⠶⠶⣮⠿⠟⣛⠩⠉⠈⠛⢷⡇⢸⡷⠳⣄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢠⣤⣀⡀⢀⣀⣾⠵⢚⣩⠵⠚⣹⡶⢞⣛⣭⣤⣤⣤⡴⠚⣩⣴⡞⢉⣉⡛⢿⣍⣁⣨⡇⣾⠞⣩⣟⣷⣶⣶⣾⣿⣃⣀⣀⣠⣤
⠀⠀⠀⠀⠧⢤⣭⣉⣙⣳⣾⠿⠶⠯⠽⠥⠾⢭⣁⣊⡥⠚⢁⣴⠿⠽⢿⡶⠋⢹⡙⢿⣿⠟⢰⢳⣧⣾⣿⣿⡿⠿⠿⣒⣒⡒⢂⡴⠋
⠀⠀⠀⠀⠀⣰⠟⠉⠁⠀⠀⠈⠉⠉⠉⠁⠒⠂⠒⠬⠭⣝⠻⠿⣿⣶⠋⠀⠀⠀⢯⠀⢈⡇⡾⢸⢷⣿⠁⣶⠶⠚⣩⠽⢻⣷⡾⠤⠤⠤⠤⣤⣀
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢍⡛⠦⣄⡀⠈⣧⢸⣧⢇⣼⣞⡁⢸⣧⣖⣋⣤⣤⣾⣷⣿⣞⢶⠲⠦⠴⠋
⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣙⠷⣿⣻⠃⠀⠀⠉⠉⢙⣛⠶⣮⣿⡟⠛⠛⠛⠛⠛⠓⠒⠒⠶⡄
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⠛⢶⡒⠒⠒⠉⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⡶⠶⠇
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡙⢦⣀⢄⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣄
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡄
⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣇
⠀⠘⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿
⠀⠀⠀⠈⠉⠙⠛⠲⠶⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠶⠶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡹⣿⣿⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⠶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠶⢶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠈⢌⠻⣿⣿⣿⣿⢟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⠶⣦⣤⣀⣀⠂⠈⠛⠟⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⣄⠀⢠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄⠀⢀⡀
⠀⠀⠀⠲⡀⠘⠆⠀⠁⠀⠀⠈⠀⠀⠀⠀⢠⢄⠀⠀⡠⢢⠀⠀⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⠊⠀⠠⠞⠀⣠
⠀⠠⣄⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡀⠁⠀⠑⠂⠀⠀⠳⠀⠁⠀⢱⠀⡠⠔⡆⠀⠀⠀⠀⠀⠀⠀⠚⠁⣀
⠀⣀⠈⠁⠀⠀⠀⠀⢰⠒⢠⡤⠤⠤⡀⠀⠀⠀⢀⡠⠒⠀⠀⠀⡆⠀⠈⣁⠠⠤⠧⢄⡀⣀⠀⠀⠀⠀⠀⠈⢁
⠀⠀⠀⡀⠤⠔⠒⣆⡀⠈⠀⠀⠀⠀⠐⡀⠀⢀⠎⠀⠀⣠⠄⢠⠃⣠⠞⠁⠀⣀⠀⠀⠙⢇⠀⠀⡴⠐⠠⢀⢈
⢔⠊⠁⠀⠀⠀⠀⢸⠈⠀⠀⠀⢹⠄⠀⠱⡀⢸⠀⠀⠀⡿⠀⠎⡰⡟⠀⠀⡼⢁⠙⡆⠀⠈⡤⡺⠁⠀⠀⡘
⠈⡄⣀⣄⠀⠀⢫⡀⠘⢷⠀⠀⠀⣀⠀⠀⢣⡜⢆⠀⠀⠈⠀⢹⠁⢣⠀⠀⠀⢈⡦⠁⠀⢰⣳⠃⠀⠀⠜
⠀⠈⠑⠒⠆⠀⠈⡖⡀⢸⠀⠀⠘⡏⢧⠀⢀⣳⠈⠓⠤⣄⣀⣬⠆⠘⢄⠀⠀⠀⠀⢀⣠⡯⠧⢀⡠⠮⡀
⠀⢤⠒⠂⠙⡀⠀⠱⡣⠈⣄⠠⠔⢙⠘⣏⣠⣼⣷⣶⣶⡤⣤⣾⣴⢤⣀⠉⠒⠒⠺⠋⣹⡋⠉⢒⡠⠚
⠀⠀⠀⠢⡀⠣⠔⡚⢉⠆⢀⠤⣰⣻⣟⣃⣵⣉⣱⡉⢺⠷⡶⣽⣿⣲⣝⡛⠬⡁⠀⠘⠅⣈⠛⠉⠑⠢⢄⡀
⠀⢀⡠⠊⠀⠀⠀⢀⣤⡴⠟⠛⠋⠉⠉⠩⠉⠉⠙⠻⠳⢮⣁⠊⠉⣏⣸⡟⢻⠙⣶⣄⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠉⠒⠠⠄⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠳⣖⠩⣤⡧⣌⣃⣸⠷⣷⣄⠀⠀⠣⣄
⠀⠀⠀⡀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠳⣤⠓⢬⠋⡱⡄⢊⢻⣧⠀⢀⡨⠗
⠀⠀⠚⠠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠳⣺⠉⣉⢟⡿⠺⢣⢿⡁
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡹⣎⡓⢬⣥⠖⢺⡏⣯⠂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⣦⠀⠐⠂⢀⡿⣿
⠀⠁⠀⠈⠓⠦⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣳⣤⡶⢟⣱⠇⠀⠀⠀⣀
⠀⠉⡀⠀⠀⠀⠀⠀⠀⢨⠀⠉⡉⠍⠉⠉⠉⠉⠛⠛⠓⠒⠒⠒⠒⠒⠒⢲⠶⠶⠶⣶⠚⠛⠋⠁⠀⠀⠠⣀⠈
⠀⠘⠁⣠⠄⠀⠀⠀⠀⠀⠂⠉⠀⢸⠀⢀⠴⠀⠀⠀⡠⢀⠀⠀⠰⠓⢄⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠈⠃
⠀⠀⠚⠁⣠⠖⠀⢠⠀⠀⠀⠀⠀⠈⠖⠁⠀⠀⠢⠈⠀⠀⠑⢤⠃⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠘⣆⠀⠳⠄
⠀⠀⠀⠀⠉⠀⠐⠋⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠀⢒⠔⢀⡤⠀⣉⠀⢀⠈⢉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⣀⠀⡀⢆⡴⢁⠔⠁⣀⣤⠵⠖⢂⣈⣉⡋⣛⣁⣒⣀⡀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⢁⡠⠐⣘⣃⡔⢡⢎⡴⡡⢊⢐⡩⢴⣺⠿⠟⠻⠽⠉⠉⠉⠉⠩⠽⠗⣒⠯⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢠⣬⡖⠉⠈⡌⡰⠡⢎⣴⢔⣫⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠑⠩⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠋⠤⣶⠞⠲⠂⣌⢢⡜⡐⣽⡶⣫⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠑⢂⠀⣀⣤⣀⠀⠀⡼⢡⡟⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡏⡀⠔⡊⢈⠁⠀⠝⢈⠳⡾⢫⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠡⠀⡕⠚⠁⢆⠀⢚⠶⢁⠞⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠓⡆⢀⠁⣘⢁⡤⠚⡠⢃⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⢰⡀⢨⠔⠿⠉⠀⡰⣡⠏⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳⢈⡔⢋⠠⠚⢃⡜⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⢖⣒⡫⠭⠴⠒⣚⣃⣭⣤⠴⠶⠖⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢠⠛⠂⠀⢚⠔⠁⠔⢣⢎⡼⠁⠀⠀⠀⠀⠀⠀⢀⠠⠤⢒⣋⠥⠔⢒⣉⣩⡤⠶⠒⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⡸⠂⠀⢠⣀⡠⠚⣠⢋⡞⠁⠀⠀⠀⠀⠀⠀⠈⠀⣐⣈⣥⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⢣⠀⠐⠂⢩⠋⡔⣡⠏⠀⠀⡀⠤⢀⣀⣤⠴⠖⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠘⢶⢤⣉⡳⢎⠜⠁⣀⣠⡭⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠶⠤⠶⠷⠚⠋⠉




⣀⣀⣀⢀⣀⣀⣀⣀⢀⣀⢀⢀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⣀⣀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⠖⠒⢈⡠⠂⠠⠤⣀⠤⠐⠐⠀⠀⠚⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⡠⠍⠀⢠⡪⠤⠒⠂⠀⠒⠢⠴⣁⡠⢂⣩⠉⠉⠓⠆⠀⢩⡲⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⠈⠔⠂⠖⠀⣠⣔⡂⠀⣶⠒⠂⠤⠜⠀⣀⡀⠀⠀⠤⠈⠙⠋⡀⠀⠉⢡
⠀⠀⠀⠀⠀⡠⠪⠀⠉⠁⡆⠀⠀⢀⡘⠮⠀⠈⠑⠂⢀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠄⠀⠈⠁⠢⠈⢣⡀
⠀⠀⠀⠀⡐⠁⣀⢀⡠⠃⠣⠀⠀⣀⠘⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢇
⠀⠀⠀⠰⠁⡊⢠⠁⠀⠀⠀⢦⠀⠘⠀⢀⡀⠋⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⢀⠃⠼⠂⠉⠉⠉⠀⡰⠚⠀⠚⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢡
⠀⠀⠘⠀⠀⠀⠀⠀⢀⣠⠀⠀⢠⠞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀
⠀⠀⠀⠰⠉⠀⠀⠀⠇⠀⢀⡔⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢰⠀⢄⠀⢀⠴⣀⠤⠉⡠⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠳⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠤⠤⠴⠶⠶⠦⠶⠚⠁
⠀⠀⠀⠈⠢⣀⣈⡀⠀⢀⣀⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢄⣀⡠⠂⠂⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⡀⠊⠁⠀⣰⣐⡂⣀⠀⠀⠀⡀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢖⢉⢡⡄⠀⠄⣉⠢⣜⠀⠋⠀⢂⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡊⠈⠂⠐⢄⠀⢠⣄⣀⣀⣴⣷⣶⣿⣿⣧⣍⢙⣷⣶⣮⣅⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠈⣢⠊⠤⣾⣶⢦⣯⣭⣻⣿⣿⣿⡿⠿⠛⠉⠉⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢻⡀⠶⠾⠿⢿⣶⣀⣽⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⣀⠀⠀⠀⡐⡩⢀⠉⢯⠀⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢣⢀⣴⢰⡱⠀⠌⢉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢿⢟⣵⡂⠘⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡉⡯⢶⡟⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠂⠀⣴⡟⣏⣹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊
⠀⠀⠀⠀⠀⠀⢘⠉⠐⠀⠀⢻⣷⡈⡘⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠈⠐⠀⠄⠉⠉⣿⣿⠇⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⡝⢻⠀⠁⢀⢀⡰⡢⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⢾⡇⣄⠄⡈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠊



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⣛⣿⣍⣉⣿⠛⢛⣻⣿⣭⣿⣷⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣡⣶⡿⠛⣿⠟⢉⣵⠾⠛⠉⠉⠁⠀⠀⠉⠉⠛⠻⣧⣄
⠀⠀⠀⠀⠀⠀⢠⡾⠋⣤⣾⠿⣶⣴⠶⢟⣴⠟⠁⠀⠀⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢠⡿⢁⣾⠟⠀⢀⣸⡏⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠠⡄⠀⠀⠹⣧
⠀⠀⠀⠀⠀⣾⠃⣰⡿⠶⢾⡟⠉⣰⡟⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⢰⡟⢸⣏⠀⢠⣼⠇⣴⠟⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠰⠂⠀⠀⢹⡇
⠀⠀⠀⠀⢸⡇⣿⡅⠀⢻⡇⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⢸⣿⡏⠁⣴⠟⣽⠏⠀⠀⠘⠃⠀⠀⠐⠇⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢿⣇⣀⣿⣾⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡶⠾⠏
⠀⠀⠀⠀⠀⠈⠛⠻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠒⠒⠚⠉⠉⠉⠉⠓⠢⠤⣄⣀⡀
⠀⠀⠀⠀⠀⣠⠒⠋⠭⠭⠅⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⠈⠁⠂⣀⣀⠀⠉⠙⠒⠢⣤⣀⡀
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡆
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢀⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡑⠀⠀⠀⠀⡐⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠒⠒⠠⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠡⡀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠆⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⡀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚
⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠂⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⠀⣀⠤⠔⠒⠊⢳⣀⡀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠐⠒⠒⢤
⡎⠁⠀⠀⠀⠄⠀⢀⣉⠉⠉⠉⠉⠉⠓⠋⠀⠀⠘⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠀⠀⣤⣤⡤⢄⣀⠗⠂⠀⢀⡠
⠈⠓⠢⠤⢄⣀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠐⠒⠂⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⣀⡤⠖⠊⠉
⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠤⠤⣤⣤⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣄⣀⣀⣒⡤⠦⠤⠭⠖⠒⠚⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⢸⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡧⣿⡟⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠿⢿⣿⣿⣶⣦⣄⣈⡇⣿⢹⣿⠃⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣟⢿⣿⣿⣧⢿⣸⣿⣿⡿⣟⣻⣭⣭⣭⣍⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⠿⢿⣶⣝⡿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣟⣾⣿⣟⣽⣾⣷⢻⣿⣿⣿⣶⣽⡻⣮⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣼⢟⣽⣿⣿⣿⣿⡟⣿⢿⣿⣿⣿⣿⣮⡋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠿⢿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⡇⡿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⢸⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠛⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⢰⠀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡸⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⣀⠔⠈
⠀⠀⠀⠀⠀⠀⠤⢔⡳⠶⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⠀⡤⠚⠁
⠀⠀⠀⢀⢶⠂⠀⠀⠀⠀⠙⠂⡹⠋⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠒⠂⠸⢤⠴⠀⠀⠀⠀⠀⠁⠀⠀⠋⠁⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠈⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠷⠃⢨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⢰⣮⠃⠀⠀⠀⠀⠀⢀⢾⠁⢆⣀⡀⠀⠀⣠⠅⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠒⠦⠠⡔⠀⠀⡰⢀⡈⠆⠃⠀⠀⠀⠀⠀⠀⠐⣦⠎⣑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠓⠀⠀⠀⠈⠀⠔⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠁⠀⢀⠠⠐⠊⡅⠀⠠⡤⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠠⡆⠀⠠⠴⡅⠀⠀⠀⠀⢀⠁⡉⠒⠢⠄⢧⢴⠂⠕⠁⣃⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠁⠀⠀⠀⠀⠠⢶⡀⠀⠙⠄⠁⠂⠀⠶⠊⡙⡆⠀⠀⢀⠄⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⢰⠊⠀⠀⠨⠁⠀⠀⠀⠢⡄⠀⠀⠀⣈⠩⠀⢦⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠐⢀⡟⢀⠄⠀⠊⠢⠄⠀⠰⠄⠘⠀⢒⡎⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⡄⠀⣆⣤⠋⡀⠀⡀⠠⠨⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣭⣤⣍⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⡉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠉⠈⠑⠂⠂⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠖⠢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⣀⣤⣄⢀⣀⡀⠀⠀⠀⢀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠻⠿⠿⣿⠿⠃⠀⠀⠈⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠶⣶⣶⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣄⠀⠀⠉⣩⠟⠛⠻⢅⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⢡⣶⡿⠀⠹⣾⣿⣂⣀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⢀⣀⣄⡀⠀⢸⣿⡿⣶⡄⠙⣿⣿⡋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡄
⠀⠀⠀⠀⠀⠀⣠⡶⠷⠒⠀⠀⠀⠀⢽⣿⣿⣿⣿⡇⠀⠙⠛⠛⠁⠀⠈⠻⠿⠷⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢸⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠻⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⡇⠀⠀⠀⠈⠿⠿⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢴⠂⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣮⠀⠀⠀⣸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠠⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣯⡀⠀⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⢤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣀⠀⠀⠙⢟⠛⢋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⡳⠀⠀⠀⢤⣄⠀⠈⣿⣿⣿⣿⡇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⢀⣀⣿⣿⣧⠀⢿⣿⠏⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡰⠁⢻⣿⣿⣿⠏⠀⠈⠙⠀⠀⠖⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⠤⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⠴⠋⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠶⡤⠀⠀⣀⣠⠤⠄⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⣀⡀⠤⠐⠂⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠁



⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⢤⠄⠀⠀⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣞⠛⣳⠄⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⢁⣠⣎⣉⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠍⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢯⣁⠡⠝⠃⠀⠀⠀⠀⣐⠲⣤⠤⠀⠒⠈⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⣩⣤⡤⣀⡀⠀⠀⣀⣀⡀⠤⠤⠐⠒⠂⠉⠉⠈⢁⣀⣀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣋⣡⡼⣇⠈⢊⡾⠋⠉⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⢠⠞⠻⠮⡺⣝⢷⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⣯⠀⠀⢘⡩⣲⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⣞⣳⠄⠀⡀⠀⠀⠀⠀⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣴⡟⢫⡄⠐⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠉⠁⠀⠀⠀⠀⠀⢀⡞⠛⠥⣀⡝⢵⡄⠀⠀⠘⠀⠀⠀⠈⠈⠑⠈⠁⠀⠀⡠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢆⠦⠀⠘⣧⡀⠀⠀⢊⡼⠁⠀⠀⠀⢰⠒⣦⠀⠀⠀⠀⠀⠀⠀⠓⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠚⠉⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠋⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠴⠒⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠒⠒⠃⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⡤⠶⢤⡀⠉⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠍⠀⠀⠀⠈⠳⠤⠔⠁⠀⠀⠀⠀⢙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠈⢁⡴⠒⢲⣤⠤⠤⠴⠖⠂⠀⠃⠀⠉⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠾⠷⠖⠒⠒⠋⠉⠉⠳⠤⠼⠁⠀⠀⠀⢀⠤⢤⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡼⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⢠⠖⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢤⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡼⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠂⠐⠒⠂⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⡋⠁⠉⢻⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠿⠟⢛⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠿⠿⠿⠟⠁⠀⠀⢩⣭⣭⣴⣶⣶⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⣿⣿⣿⣦⣤⣴⣿⣿⣿⣿⣿⠋⠙⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠤⠤⠤⠀⠀⠀⠠⠤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠔⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠒⠤⣄
⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⡄
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡇
⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠈⢳⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⣠⢴⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠻⣦⣌⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢤⣲⡺⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣶⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠤⣤⣶⣒⡪⠭⠽⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠊⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠓⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⢄⠀⠀⠀⠀⢀⣠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡀
⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡀⠉⠲⢄⠑⠀⠐⠚⠛⠛⠛⡃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣏⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣤⣼⣧⠤⠤
⠀⠀⠀⠀⠁⠒⠢⢤⣀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠔⠒⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⠓⢶⣤⢀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣡⡀⠀⠀⠘⠁⣕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⠄⠀⢻⡌⠦⡰⠀⢼⣟⣀⣀⣀⣀⣀⡀⣀⣀⣠⣤⣤⡤⠶⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠈⠀⠀⠻⣧⣀⠀⢿⣴⡇⢨⣾⣷⣡⡤⠴⠚⢛⣩⣵⣖⣻⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣀⣠⣤⡤⠤⣤⣌⣻⣷⢽⣿⡀⣾⣿⣴⣦⣶⣿⣿⣟⡛⠋⠉⠉⠉⠛⠂⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠋⠉⠉⠉⠉⠙⣻⠷⠶⣾⣯⣿⣯⢽⣿⣿⣿⣾⣷⣿⣿⣷⣾⣿⣷⣶⣶⣷⣴⣠⣌⢠
⠀⠀⠀⠀⠀⠠⠊⠜⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⠛⠉⠁⠀⠀⠀⠙⣿⣷⡄⠀⠉⠙⠈⠀⠈⠉⠉⠙⠛⠻⣿⣿⣿⣷⡶⡤⠄
⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠉⠹⢷⣷⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⢧
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⣷⣃
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡘⣿⠉
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣯⣿⡆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣿⣿⠃
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢠⢀⣷⣿⡄
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣻⣿⢳⠁
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢿⣿⡟⡞
⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣩⡿⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣠⣘⣿⣿⣟⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣾⣽⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊⣠⣔⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢬⣀⡀⠁⠀⠀⠀⡀⠀⡀⠀⠐⠀⡀⠁⣴⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠓⠶⠴⠶⠶⠶⠷⠶⠦⠷⠾⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠠⣤⢤⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⣴⡠⢀⡀
⠀⠀⠀⠀⠀⣠⠶⢛⣽⣳⢄⣾⢿⡛⢶⡀⠀⠀⠀⣴⣾⢿⣟⣣⣀⣿⣿⣿⣦⡀⠀⠀⠀⣴⠶⣶⣶⣿⣯⣭⣽⣶⣦⡄
⠀⠀⠀⠀⢠⡏⣴⠈⠁⠀⠀⠛⠀⠀⢢⣿⠀⠀⣸⡏⠀⠊⠁⠀⠘⣿⣿⣿⣿⢷⠀⠀⢰⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠈⣸⠀⠀⢻⣧⠀⠀⠀⠀⣠⣿⣿⣿⡿⠘⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢻⣜⠆⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠘⢿⣿⣶⣶⣾⣿⣿⣿⠟⢁⠎⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⡤⠶⠛⠁⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⣯⠥⠒⠁⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠲⣤⣜⣂⣿⣚⣠⡴⠁⠀⠀⠀⠀⠀⠀⠠⣤⢤⣶⣤⠄
⠀⠀⠀⠀⠀⢠⡴⠿⢹⡿⣿⣿⣭⠶⣄⠀⠀⠀⠀⣠⡶⠾⠛⠛⠛⠿⢿⣷⣦⡀⠀⠀⠀⢀⠀⢠⣞⠧⢴⡿⠦⠀⢀
⠀⠀⠀⠀⢰⡏⠀⠀⠘⠀⠈⠃⠈⠃⠘⣧⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⢠⡏⠀⠈⠀⠀⠀⠃⠀⠀⠈⣇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⣠⣾⠇
⠀⠀⠀⠀⠀⠀⠙⠳⠦⢤⡤⠴⠞⠋⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣾⣿⡿⠟⠋⠀⠀⠀⠀⠀⠙⠿⢿⣷⣶⣿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⢀⣤⠤⡴⢲⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠰⣄⡇⡄⢀
⠀⠀⠀⠀⢠⣶⢿⡿⠗⣀⠀⣙⢲⣶⣦⡀⠀⠀⠀⠀⡀⠀⢰⠟⢿⠻⣄⠐⣦⣄⠀⠀⠀⠀⣀⡤⠙⠷⣾⣿⠶⠋⢤⣄
⠀⠀⠀⢠⣿⢤⣼⣷⣿⣿⣷⣿⣿⣿⣿⣿⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⣶⡹⡆
⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⡗⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢹⣿⣿⣦⣤⣤⣤⣶⣿⣿⣿⠇⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⡾⣱⠇
⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⣀⣬⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⡴⠒⣒⠒⣆⣀⣴⢲⣟⣿⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣳⡯⣽⢋⣭⠭⣟⣾⡋⣥⣴⣿⣶⣮⣹⢯⢵⡚⠳⣶⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣚⠽⠖⠻⠵⠋⠠⠾⠽⠛⠧⣑⠦⣽⣟⡚⠻⢿⡇⢠⣠⢰⣶⡇⣠⢜⣴⡫⠿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣞⣽⣷⡶⠬⣟⢿⡼⡿⢚⣠⣴⣿⡇⠀⠀⡈⣽⣂⣤
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⣿⢿⣩⢤⡖⢲⡛⠀⠹⡍⠉⢭⣏⣿⢻⡚⠘⢩⢟⡿⡗⡶⠂
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣀⣀⣀⣹⣦⡙⠻⣖⡓⠚⠾⠶⠿⠮⡭⣝⢯⣱⠹⣽⣳⣆⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⠛⠋⠉⢿⡶⣤⣍⡛⢿⣖⣒⡚⣅⣞⢿⡛⠃⣮⠔⢻⡽⠻⣦⡀
⠀⠀⠀⠀⡼⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢧⣷⣏⡛⠛⢷⡦⣏⠘⣎⢦⡑⢄⠪⣵⡌⢩⣭⠴⠃
⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠕⠛⢿⡯⣗⣌⠢⡱⣿⣞⠙⢲⣧⣮⡛⡶⣾⢵⡆
⠀⠀⠀⢰⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠐⠷⢻⠳⣭⣒⣿⣮⡪⣴⣷⡛⣿⡙⣟⡟⣆
⠀⠀⠀⠸⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣝⣒⣶⠀⢩⠍⣤⠣⣬⣟⡻⣷⢿⡀
⠀⠀⠀⢠⠇⡆⡆⡀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⣹⣜⡶⢃⣜⣁⠹⢼⡼⣩⠏⣩⡛
⠀⠀⠀⢸⡄⡇⡇⡇⢸⢸⢸⠰⡄⡆⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⢹⠘⠲⣟⢮⡛⣟⣫⡞⢧⣀⡞⡇
⠀⠀⠀⢸⠛⢇⠇⡇⣸⢸⢸⠀⡗⢇⢸⠘⡆⢰⢰⢠⠀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠙⠚⣧⣳⣬⣿⡠⠄⠊⢹⣸⣍⠦⣹
⠀⠀⠀⠈⢧⡀⠀⠁⠙⠈⠘⠃⢧⢸⣸⠀⡇⢸⠘⣬⡆⡇⢸⠀⡏⠘⡆⡆⢠⠀⡄⡀⢀⠀⠀⠀⠀⠀⢸⡉⠙⢯⡷⢀⣤⣎⠙⢺⢳⢺⠃
⠀⠀⠀⠀⠀⠉⠓⠲⠮⠤⢤⣀⣀⠀⠉⠃⠳⠈⠇⢧⢧⢻⠘⡆⢳⠀⢇⢹⠸⡄⡇⢳⠸⡄⡇⡄⠀⠀⠀⢿⢳⠦⠽⢤⡞⣽⣇⣨⣿⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⢤⣀⡀⠀⠈⠘⠂⠳⠘⡆⢸⡸⡄⣇⢱⢸⡀⡇⢹⢹⠈⡆⢧⠘⡿⣰⣆⠈⢷⣖⠥⣌⠻⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⣤⣀⠀⠀⡀⠁⠓⠸⠜⡆⡇⢹⡈⡇⣇⢻⢸⡀⢳⣈⢻⠀⢳⡙⢄⠨⣝⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⢤⣀⡀⠀⠃⠀⠃⠹⠘⡌⣆⣇⠀⢷⡀⢾⢨⣇⢸⡀⠹⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⣀⠀⠀⠀⢘⠀⠸⣷⡎⡃⢹⣾⣟⡸⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠬⣄⠀⠹⣧⣿⡦⣽⡿⣧⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢬⣉⡭⠥⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⢀⣠⣄⣀⣀⡀⠀⠀⠘⣷⠀⠀⠀⠀⢈⠉⠉⠛⠛⠳⠶⢶⣤⣤⣀⣀
⠀⠀⠀⠀⢸⣏⠉⠉⠉⠛⠛⠛⠻⢿⡆⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠶⣦⣤⡀
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠰⡶⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠒⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠠⡦⠀⠀⠀⠀⠙⠋⠀⠀⣠⡾⣯⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠻⠂⠀⠀⠓⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠈⠉⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠐⠆⠀⠀⢀⣴⠟⠁⠀⠀⠓⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠰⣿⠆⠀⠀⣸⣧⠀⠀⠀⢀⣴⠟⠁⠶⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⢀⣴⠏⢻⡆⢀⣴⠟⠁⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢀⣴⣿⡁⠀⠀⠛⠛⠁⠀⢤⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠟⠁⠸⣧⠀⠀⡀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠛⠁


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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢶⣶⡶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣡⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⢋⢁⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⢾⡀⡏⢸⣉⡉⠛⠛⢳⡶⠖⢛⣛⣿⣿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣯⢭⡤⣄⣸⡇⢡⠞⢑⠏⣠⠶⢃⡤⠚⠉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢉⡥⠤⠤⠴⠶⢍⠲⢍⣠⠃⠀⡾⢞⡅⣠⣏⡀⠀⠀⠀⠀⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⣑⡄⠀⠀⢰⡏⠀⠉⠀⠠⢍⡓⢤⡀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠉⠀⠀⠀⠀⠀⡠⠎⢁⣀⣤⡀⠡⠐⠂⠋⠓⠒⠶⣌⡂⢹⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡞⠄⡼⠉⠀⠸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠱⡜⠀⠀⣀⣤⠶⠛⠛⠛⠛⠛⠛⠲⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣷⡜⠁⠀⠀⠀⢱⣰⠇⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠉⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⣀⢀⠞⠁⠀⡀⠀⠠⠤⢤⡀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⣀⡠⠤⠤⣿⣊⠜⠀⠀⠈⠀⠐⠀⠀⠀⠙⡄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣠⠞⠁⢀⠀⠄⢀⠀⠀⠀⠔⠀⡔⢅⠶⡀⠒⠄⡘⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡜⠁⢠⠖⠁⢀⠐⡂⠑⢄⠀⣄⠀⡄⠀⢙⣃⠔⢊⡀⣀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡼⠀⢠⠗⢉⠁⢠⠜⠉⠱⢬⠇⠈⠈⠀⠀⠈⢄⡔⠉⠁⢤⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⣝⠋⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⡇⠀⢸⠄⣂⠐⠓⢠⡄⠀⠀⡠⢄⠀⡖⠐⠄⢀⣼⠢⠀⢸⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣂⣈⣳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢣⠀⠀⢧⣀⡈⠵⢊⣠⡄⠀⣠⢼⡆⡻⡤⡈⠟⠈⠠⢠⠏⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡉⠩⣤⢭⣓⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣹⡆⠀⠈⣆⠀⠀⠀⡴⠈⠈⠊⠱⠒⠣⠀⡣⠁⠘⠦⠴⠒⠓⣉⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⢶⡌⠉⠛⢛⠃⠈⣙⠛⠃⠈⢉⠩⠝⠛⠉⠉⠉⠀⢹⣆⠀⠘⣆⠀⠀⠳⡜⠠⠠⠀⡅⣠⠖⠁⢀⣠⣤⣴⣶⣟⣉⣙⣛⠛⡷
⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠞⠋⠁⠀⠀⠀⣀⠀⠀⠙⠒⠋⠀⠀⢀⠄⣀⡤⠶⠒⣾⠈⠳⣤⡈⠣⡀⠀⠉⠒⠢⠴⠖⠁⢀⣴⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⣠⠞⢉⡀⠤⠒⠒⠈⠉⠉⠙⠁⠀⠀⠀⠀⠌⣠⠄⡰⣡⠞⠁⠀⠀⣠⠏⡀⠔⢹⠙⢳⡾⣷⣤⣄⣀⣤⡤⠶⠋⠁
⠀⠀⠀⣴⣧⣬⡥⠤⠤⢤⣤⣤⣀⣀⣀⣀⣤⠖⣃⣠⠞⣯⣼⠞⠋⠀⢀⡴⣛⣥⣤⠀⠀⡦⠀⡀⠳⣄
⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢼⠷⠛⠉⠀⠀⠉⠀⠀⠀⠀⠘⢋⡵⡚⣁⠀⠩⠁⡀⣿⠳⢼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣹⠏⣠⢋⣼⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⡷⠛⠁⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠶⠒⠒⠒⠒⠒⠒⠒⢶⣶⣒⣒⡲⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠁⡁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠀⠀⠀⠀⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠁⠂⢤⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡏⠀⠀⠀⠀⠈⠉⠒⡤⣄⡀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠁⠂⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣴⡂⠀⠀⠀⠁⠒⢤⡜⢀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢀⣀⠀⠀⠀⠘⠓⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⡇⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠰⣇⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⡇⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡌⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠁⠀⡇⠀⠸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⣶⣷⠀⠀⠀⠀⡀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡁⠰⠀⠀⠀⡀⠀⠀⠉⠀⡤⠀⠀⠀⠀⠀⠀⢧⣾⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⢈⠂⢄⠀⠀⠾⠃⠀⠀⠀⠀⠐⠀⡄⠀⠠⡿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣌⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠘⠇⡇⠀⠀⢠⠃
⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣤⣤⣀⣀⠀⠈⠙⠓⠤⣐⡠⠐⢶⡄⠀⠀⠀⣣⠀⡠⠃
⠀⠠⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠉⠑⠒⠤⢤⣠⣼⣿⠔⠁
⠀⠀⣿⣿⣿⣏⣿⣣⣃⣕⣩⣼⣿⣿⣿⠇
⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⠒⠀⠃⠀⠠⠘⠃⠒⠶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⢠⡀⠀⠀⠒⢄⡀⠀⠐⢂⡀⢀⣀⠀⠉⠉⠂⠠⣄⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⠀⡀⠀⠀⠀⠂⠀⠀⠉⠀⠀⠀⠈⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠈⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠒⠈⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠂⠀⠀⠈⠁⠀⠀⠀⣠⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐⠄⠀⠀⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠁⠀⠀⠀⠂⠀⢄⣰⣣⢿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠙⢄⠀⠢⣀⠀⠀⠀⠄⠠⠤⠀⠀⠀⠀⠁⠀⢀⡀⠀⣀⣴⡞⠺⣹⢗⣿⣟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡙⠂⢌⣛⣒⠠⠤⠤⠤⢄⣀⣀⣀⡠⠤⣴⢾⣋⣁⣴⡞⣻⣥⡿⠉⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠐⠦⠬⣍⣙⣓⡒⠲⠦⠵⠴⠤⠤⠤⠴⢾⣿⣭⠿⠿⠋⠉⠁⣠⣶⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡱⠖⡀⠤⠀⠀⢀⠉⠉⠉⢉⣀⡀⠈⠛⠋⠉⠁⣀⣀⣠⡤⠶⠋⣩⠟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⢶⡆⢄⣀⣈⣉⣙⡠⠉⢉⠘⠛⠒⠋⠁⠡⠁⠂⣡⠞⢃⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠅⣀⣛⠚⠐⣲⠶⠤⠤⠶⠶⣞⣋⠥⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠⡄⠀⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⢐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠰⠞⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⣻⠃⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠢⡀
⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠈⠁⠐⢄
⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠂⠁⠠⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢦⡀
⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣠⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠑⢦⣄⡂⠤⠀⠀⠠⠄⢀⢀⣀⣀⣠⡤⢤⢖⡶⢌⠆
⠀⠀⠈⢄⠠⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠽⡹⢿⣿⣿⡯⠸⠳⠉⠚⠹⡘⡸
⠀⠀⠀⠀⠀⠨⡀⢒⠢⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠂⠤⢀⠀⠀⠀⠠⠄⣠⣄⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠶⠒⠚⠋⠉⠉⣡⠞⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠴⠶⠶⠶⠒⠚⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢸⡿⠥⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠉⠛⠲⠦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠿⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⢦⣤⣄⣀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡴⠋⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⣾⡷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣞⣱⠆⠀⠀⠀⠀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⣅⣠⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠺⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠲⠶⢤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠦⣤⣤⣀⣀⣀⣿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠃⠀⠀⢀
⡾⠋⠉⠀⠀⠀⣀⣀⣤⠇⠐⢿⠷⠀⣠⡾⠋⠉⠀⠀⠀⣀⣀⣠⡇⠀⢿⡷⠀⣠⡾⠋⠉⠀⠀⠀⣀⣀⣠⡞⠀⢿⡷⠂⢠⡾⠋⠉⠀⠀⠀⣀⣀⣠⡞⠀⢿
⠀⠀⢀⣀⠀⠈⠛⠋⠁⣀⣀⣀⡀⠀⠿⠁⠀⠀⣀⠀⠈⠛⠋⠁⣀⣀⣄⡀⠀⠿⠁⠀⠀⣀⠀⠈⠛⠋⠁⣀⣀⣀⡀⠀⠿⠃⠀⠀⣀⡀⠀⠛⠛⠉⢀⣀⣀
⠀⠀⠺⠿⠃⠀⠀⠀⠊⠉⠉⠙⠛⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠞⠉⠉⠙⠛⠀⠀⠀⠀⠘⠿⠛⠀⠀⠀⠜⠉⠉⠉⠛⠀⠀⠀⠀⠘⠿⠛⠀⠀⠀⠜⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠒⢶⣄⡀⠀⠸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠒⢶⣦⡀⠀⠸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣦⡀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠒⠲⣦⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆
⣠⡤⠄⠀⠈⠁⠀⠀⠀⡄⢀⣤⣄⠀⠀⣠⡤⠤⠀⠈⠁⠀⠀⠀⡄⠀⣤⣄⠀⠀⣠⡤⠤⠀⠈⠁⠀⠀⠀⣠⠀⣤⣄⡀⠀⣀⣤⠤⠀⠈⠉⠀⠀⠀⣠⠀⣤
⠋⠀⠀⠀⠀⠠⣶⡶⠟⠁⠀⠛⠋⠀⣾⠋⠀⠀⠀⠀⠠⣶⣶⠞⠃⠀⠙⠋⠀⣾⠏⠀⠀⠀⠀⠠⣶⡶⠾⠃⠀⠙⠋⠀⣼⡟⠀⠀⠀⠀⠀⣶⣶⠾⠃⠀⠙
⠀⠀⣰⣶⡄⠀⠀⠀⣠⠶⠶⢶⣦⠀⠉⠀⠀⢠⣶⣄⠀⠀⠀⢠⠶⠶⢶⣦⠀⠉⠀⠀⢠⣶⣤⠀⠀⠀⢠⠶⠶⠶⣦⠀⠉⠀⠀⢠⣶⣦⠀⠀⠀⢀⠴⠶⠶
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡄⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠹⡄⢸⡆⠀⠀⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡆⠀⡇⠘⡇⠀⠀⡇⡇⡠⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣏⡛⠒⠲⠶⣻⠄⡟⠉⡇⠹⠛⠓⠶⢁⡏⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠁⠉⠢⣁⢿⡰⡡⢠⠀⡦⠀⠈⣡⠾⡛⠍⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡼⡁⠀⠀⢠⠜⠊⠉⠉⠈⠉⠛⠻⠚⠉⠉⠉⠉⠛⢣⢤⠀⠘⢛⢦
⠀⠀⠀⠀⠀⠀⣼⠓⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠱⡀⠪⣮⣧
⠀⠀⠀⠀⠀⢀⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡂⠀⠀⠀⠀⠂⡀⡔⢔⢅⠀⣹⣿⡇
⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡇⠀⠀⠀⠀⠺⠱⠰⢈⣎⠃⢿⣿⣷⠀⠀⢀⣀⣠⠤⢦
⠀⠀⠀⠀⠀⢸⡏⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣠⣀⡤⠼⠶⠶⠴⠶⠗⠒⠚⠛⠛⠋⠉⠉⠐⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠈⣇⠀⠀⢰⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⠋⠁⠀⠀⠀⠒⠒⠀⠄⠀⠀⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠹⣤⠀⠘⠀⠀⢀⣤⠀⠸⠀⢰⠏⢀⡀⠠⠀⠐⠒⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣶⡷⠄⠀⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠐⢄⠃⡜⣿⡀⡶⠄⣿⠀⠠⠰⡀⠀⢀⡀⣟⢛⡬⠇⣴⢦⡄⣤⢄⠠⡰⣶⣦⠏⢰⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡉⠂⢷⢟⢽⡇⠂⣿⠀⠀⠣⠳⣄⠀⠙⢮⡚⠲⠊⠊⢸⡁⣿⣾⠘⣷⢘⡷⢠⠊⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⣘⠒⠁⢈⡾⣇⠀⢑⠵⡜⢮⡓⢀⠙⠲⢦⣜⣁⠙⣉⣠⣛⣉⠥⠚⠁⠰⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢤⣬⣧⣀⢈⠚⣷⣿⣦⣀⠰⢦⠀⠈⠁⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢭⣛⣿⣿⣿⣽⡶⣤⠶⠀⠴⠦⢀⣠⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠛⠛⠚⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡐⣤⣤⠀⡎⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠈⣹⣷⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⠀⠀⠀⠀⡀⢽⡄⢀⠆⠀⠀⡤⠄⠀⠄⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⢀⣂⣫⡾⣶⡋⠀⠀⠁⢠⠀⠀⡀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠈⢹⡿⠟⠿⣟⠉⠀⠀⣾⣷⣎⠁⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠀⠀⠀⠈⠂⢠⠀⢈⢹⠧⡄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⡾⡀⢸⡇⢀⣽⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⣀⣴⠏⠀⢧⡾⠉⡍⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠋⣉⣰⣼⣾⣡⡦⢈⣄⠀⠠⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠀⣨⠠⠵⢔⣢⡀⠀⠀⠀⠉⠛⠻⢿⣷⡼⠇⠀⠰⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⢂⡠⠠⠔⠀⣿⢿⡃⠀⠀⠀⠀⠀⠀⠀⠉⡷⠹⣶⡀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠈⠙⠛⠓⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⣀⣠⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠚⠛⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣖⣶⣿⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⣿⣿⡌⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣶⡀⢀⣠⣆⠀⠀⠚⠛⠀⠁⣠⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢹⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢦⣘⣷⣼⢿⡇⠰⠓⠀⠀⠀⢀⠇⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠽⠇
⠀⠀⠀⠀⠀⠀⢀⡄⢺⣀⠀⠠⠤⢭⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀
⠀⠀⠀⠀⠀⠀⠈⠻⣎⢹⣦⡤⠄⢀⡀⠈⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⣽⣇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢀⣴⣾⡿⠀⠀⠀⠀⠀⠀⡄⠀⢠⡀⠰⣶⣀⣡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠣⣎⣹⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⣷⡀⠸⡇⠐⠻⣿⣭⠉⠛⢻⠶⠃⠀⠀⠀⠀⠀⠀⢸⣏⣀⡟⣳⡞⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣉⣀⣀⣠⣴⡇⠀⠀⠈⢿⣦⣇⡤⠀⠻⠟⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⠾⢤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠉⠉⠼⢋⠀⠀⠀⠀⠀⠀⠈⠛⠻⢤⣀⣶⣶⣶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢰⡃⠀⣀⡀⡄⠀⠀⠀⣿⣷⡈⠉⠉⠡⠤⣤⠴⣆⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⡀⣈⢁⢩
⠀⠀⠀⠀⠀⠀⠀⠘⢃⠈⢢⠀⢀⠤⠚⣇⠀⠀⠀⠼⣠⠄⢰⣿⣾⣿⣑⠲⢦⠀⠻⡶⢻⡆⠀⠀⠀⠀⠀⠀⡅⢀⣴⠀⠈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠀⠀⠉⠳⠤⠀⠀⠊⢠⣿⣿⠏⣿⠙⣧⡀⠀⠀⠛⠈⠁⣀⡀⠀⠀⠀⠀⢇⠀⠙⣄⣀⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠿⢃⣘⠿⠶⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠑⠯⠇⠭⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⢀⡀⠀⠀⢠⡏⠀⣀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠰⠾⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣾⠀⠠⣄⣻⠄⢸⠏⠀⣺⡆⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⡀⠐⠀⢀⢅⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠘⢆⠀⠁⣿⣷⡟⡀⢀⡿⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡴⠒⠉⠀⠀⠀⠀⠀⢀⠂⡘⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠛⣿⠀⡈⠁⡤⠀⠀⠀⠀⡀⠀⠠⠝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠸⣎⠘⢇⡠⠃⠌⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠌⠀⠀⠀⠀⠀⠠⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠤⣄⣠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠴⠁⡀⡀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠖⠉⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣥⣦⠀⠀⠀⠀⠀⠠⠶⣀⠀⠀⠀⠀⠀⢀⡀⡆⣤⡄⣠⢠⣤⢴⢢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠛⣇⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠈⢯⣿⣿⣧⣿⣿⣽⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⡇⠂⠀⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀⠸⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣴⣿⣿⠟⢻⣦⠀⠀⠀⢠⢿⣿⡀⠀⠀⠀⠁⠀⠀⠀⢀⣶⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠀⢰⢿⣿⠋⠀⠀⢱⠀⠀⠀⢀⢸⣿⠀⠀⠀⠀⡇⠀⠀⢠⣿⣿⠟⠉⢻⠀⠀⠀⠀⡴⣠⠐⠆
⠀⠀⠀⠀⢨⢸⣟⠀⠀⠀⠀⢸⠀⠀⠀⠘⣿⠀⠀⠀⠀⡅⠀⠀⣿⣿⠏⠀⠀⠨⠃⠀⠀⠀⢇⠸⢀⡤⠅
⠀⠀⠀⠀⠈⠐⣿⠀⠀⠀⠀⠀⠂⠀⢸⠘⣿⠀⠀⠀⢀⠀⠀⠀⢩⣿⠀⠀⠀⠰⠀⠀⠀⠀⠈⠑⠲⠒⠀⠀⣠⡴⣀⣄
⠀⠀⠀⠀⠀⠆⣿⡄⠀⠀⠀⠀⠀⠀⢘⢸⣿⠀⠀⠀⢸⠀⠀⢸⢰⡇⠀⠀⠀⠈⠀⠀⢀⡄⠴⠀⣄⠀⠀⢦⡉⢲⡅⠸
⠀⠀⠀⠀⠀⢸⠸⣿⡀⠀⠀⣤⠀⠀⠀⣿⣿⠀⠀⠀⡋⠀⠀⠀⢸⡏⠀⠀⢰⠇⠀⠀⠀⢷⡉⠴⠪⠀⠀⠀⠙⠓⠒⠋
⠀⠀⠀⠀⠀⠀⣇⣿⣇⠀⢀⡝⠀⠀⠀⣿⣿⠀⠀⢰⠃⠀⠀⣤⣿⡇⠀⢀⡟⠀⠀⠀⠀⠀⠉⠒⠒⠁⠀⠀⠠⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠸⣽⣿⣧⣼⠇⠀⠀⠀⣿⣿⠀⣠⡏⠀⠀⢰⣿⣿⣇⣠⠞⠀⠀⠀⠀⠀⢀⣠⠀⠄⣠⡤⡜⢒⠑⠉⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠀⠀⠀⠀⣿⣿⣼⡟⠀⠀⠀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⣰⡏⢑⠙⡼⠎⢀⢤⣄⡧⠄⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⠿⠋⠀⠀⠀⠘⠟⠛⠉⠀⠀⠀⠀⠀⠀⠠⣥⣀⣤⠾⢟⣛⣘⡈⠈⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⣠⡀⠀⠘⣧⠀⠀⠻⠀⠀⠓⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⡾⠃⠀⠀⣰⠗
⠀⠀⠀⠀⠈⢻⡄⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡰⠓⢄⠀⠀⢀⠞⠙⣆⠀⠀⢀⡠⠞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠞⠁⠀⢀⡶⠄
⠀⠀⢠⣄⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠑⠦⣄⢠⠁⠀⠀⠑⠶⠁⠀⠀⠘⠦⠐⠁⠀⠀⠸⡆⠀⢀⣠⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⡀
⠀⠀⠀⠙⠣⠀⠀⠀⠀⠀⠀⠀⡤⣀⣀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡀⠤⠄⠐⠂⢠⠀⠀⠀⠷⠒⠉⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠰⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡠⠽⠓⠋⠉⠉⢆⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠑⠢⣤⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⢀⣠⠤⠖⠒⠙⢦⢀⡇⠏⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⢠⠃⠀⠀⠀⢀⡤⠒⠒⠎⠀⣠⡾⠁⠀⠀⠀⡀⠀⠀⠀⠈⢻⠁⠀⠀⢠⡞⠙⠲⢤⡀⠀⢀
⢀⠠⠐⠈⠁⠀⠀⠀⠀⠀⠘⡌⠃⠀⠀⠀⠀⢸⣇⠀⠀⠘⡆⠀⠀⡎⠀⠀⠀⢠⠇⡀⠀⡸⠀⡌⣽⠁⠀⠀⢠⠞⠉⠑⡆⠀⠀⠀⢧⢀⡴⡟⠀⠀⠀⠀⢨⠃⠉
⠘⡄⠀⠀⠀⠀⠀⠀⢀⡤⠔⠳⣸⢴⠀⠀⠀⠘⠛⠀⠀⠀⠘⡄⢘⣧⠀⠀⠀⠈⠯⣁⣀⣁⡜⠁⡎⠀⠀⠀⡏⠘⢢⠀⣸⠀⠀⠀⣸⠋⡼⠁⠀⠀⠀⡰⠃
⠀⢹⡀⣀⠤⠄⠀⠀⠈⡷⢄⡀⠜⢻⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⣼⠘⢆⠀⠀⠀⠀⠀⠀⠸⡇⠀⣥⠀⠀⠀⢇⠀⣰⡧⠃⠀⠀⢀⡟⡸⠁⠀⠀⠀⡰⠁
⠀⠀⠙⠠⢤⢸⡀⠀⠀⠸⡀⢅⠀⠸⡀⠀⠀⠀⣻⠈⢧⠀⠀⠀⠙⣄⠈⠳⣤⣀⠀⠀⠀⢀⡇⠀⠘⣆⠀⠀⠀⠉⠁⠀⠀⠀⢀⡞⣱⣃⠀⠀⢀⣜⡀
⠀⠀⠀⠀⣀⡠⢵⠀⠀⠀⢳⠘⡀⠀⡂⠀⠀⠀⣙⢣⣸⡧⠐⠂⠚⣻⡀⠀⠀⢉⠙⢙⠉⢩⢣⡀⠀⠈⠳⢄⣀⣀⣀⣀⣤⡶⢻⣽⠤⠬⣉⠗⠁⢈⠝
⠀⠐⢎⡉⠀⠀⠈⡆⠀⠀⠈⢧⢁⠀⠧⠄⠒⠊⢡⣠⣀⣻⣤⢤⣤⢟⠿⢟⣻⣿⡎⢠⢽⣿⠶⠗⠦⣤⠀⠀⠀⠀⣁⠕⠈⢠⠛⢇⠀⠀⢈⣦⠞⠁
⠀⠀⠀⠈⠲⣄⠀⢹⣤⠴⠒⠉⠀⡦⠈⢢⣴⠀⣾⢿⣋⠷⠀⢵⠖⠋⢲⡈⡠⢾⠿⠭⣦⣽⡿⠿⠚⣍⢛⠳⣬⡉⠀⠀⠀⠺⣀⠈⢙⠟⠉⠙⠒⠦⣄
⠀⠀⠀⠀⣀⠜⠁⠀⠀⠉⠐⠀⠡⢒⣲⣥⣶⡿⠿⠿⠛⠛⠛⠛⠻⠛⢺⠿⣤⣉⡀⢾⠧⠉⠾⢟⡛⢙⠷⢶⣤⠛⢶⣄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣈⠽⠃
⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⢀⣦⡿⠟⠉⠈⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠈⠐⠨⠛⠶⣤⠐⠂⠚⣧⠲⠞⡅⢠⡃⡀⢿⡗⢦⡀⠀⠀⠀⠀⢀⡴⠚⠁
⠀⠀⠁⠙⠒⠢⠄⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡔⠈⡻⢦⡃⢤⣦⣤⣧⣄⢹⡄⢘⣿⡲⡙⣆⠀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⡠⠂⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠦⡙⢧⡀⢹⣤⡈⣯⠛⢣⡂⢄⡼⢮⣷⡄⠀⠀⠀⠈⢳⡄
⠀⠀⠀⢠⠞⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⡢⠹⣧⡀⢈⣧⡤⣮⣽⣀⣘⣂⣷⡹⣄⣠⠴⠚⠁
⠀⠀⠀⠉⠐⠒⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠑⢌⢻⣍⠏⢀⣀⠹⣋⡷⠛⡏⢳⢹⣦⡀
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠹⣧⡨⠥⢖⢊⣃⣴⠲⡿⣇⢻⡝⠦
⠀⠀⠀⠀⠀⡟⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⣧⡃⢨⠏⢛⡠⠀⠸⢿⢸⡇
⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠱⡘⣿⣄⡀⢡⡀⠄⣀⣿⢸⡇
⠀⠘⠀⠀⠀⠙⠳⠦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⢌⡻⣤⣤⣰⣼⠿⢣⣾⠁
⠀⠰⠖⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠙⠛⠛⠓⠒⠒⠲⠶⠶⠶⠶⠴⠤⢤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣈⣐⣪⣭⣴⡾⠟⠁⠀⠀⠀⠀⠀⠙⠶
⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠤⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠉⣹⠉⠉⠙⠛⠻⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⣦⡀
⠀⠈⠋⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠓⠈⠀⠀⠀⢧⠀⠀⢀⡴⠂⡀⠀⠀⠀⡴⢄⠀⠀⠀⠀⡌⠑⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠛
⠀⠀⠀⢴⠟⠁⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠔⠉⠀⠀⠑⡄⢀⠞⠀⠀⠑⢄⠀⡸⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⢻⣄
⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⣴⠃⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢰⡄⠀⢱⡄⠀⠸⣧⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣷⣾⣷⣶⣾⣷⢷⣿⣶⣿⣾⣷⣷⣾⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡷⡷⢾⡷⠾⢶⣶⠶⠿⠶⠾⢿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠈⠉⠓⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠚⠃⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠘⠤⠤⠤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠤⠤⠤⠚⡆
⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⣀⣀⣀⠤⠤⠤⠖⠒⠒⠒⠉⠉⡩⠓⠦⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢰⠚⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⡴⠊⠲⡄⠀⠀⠸⡄⠀⢀⡗⠀⠀⠀⠀⢠⠊⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠳⢄⡤⠃⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠈⠉⠢⡀⢰⠁⠀⠀⢳⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡇⠈⠢⠤⠤⠃⠀⠀⡔⠉⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠶⣏⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡹⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡴⠒⠀⠒⢦⡀⠀⣉⣒⣋⣀⠤⠤⠤⠃
⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⢀⣀⣀⣀⠠⠤⠤⠤⠒⠊⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠘⠒⠒⠂⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠛⠳⢤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀
⠀⠀⣠⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣄⣀⠀⠉⠛⠶⢤⣀
⠀⠀⡇⠈⠉⠓⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠙⠲⠦⢤⣽⠗⠀⠀⠀⠀⠉⠛⠶⣤⣀
⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠉⠙⣳⠒⠒⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠛⠶⣄⡀
⠀⠀⡿⢤⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠴⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣄⡀
⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⠖⠒⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣀⣽⠒⠒⠒⠲⠶⠦⠤⠤⢽⡇
⠀⠀⡇⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⠛⠓⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠁
⠀⠀⡇⠀⠀⠀⢀⡴⠛⠉⠳⡄⠀⠀⠀⠀⠸⣄⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡏
⠀⠀⡇⠀⠀⢰⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⣿⠀⠀⠈⠳⢦⣤⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡏
⠀⠀⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠓⠶⠤⣤⣄⣀⡀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠃⠀⠀⠀⠀⣰⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠿⣅⣀⡀⠈⠉⠳⡄⠀⠀⠀⡀⠀⠀⠙⢦⣄⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣿⣀⡀⠈⠛⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⣰⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠉⠙⠛⠲⠦⣤⣄⣀⢸⠀⠀⠀⠯⠭⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠃

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

⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣶⣶⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⠒⢲⢀⡆
⠀⠀⠀⠀⠀⣀⣤⣾⣿⣶⣿⣿⣷⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢯⢳⣺⠀⢸⢊⠧⣀⣀⡀
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⡜⠻⠶⣖⣚⡀⢸⢀⡇⠮⢔⠽⠛⢦⡀
⠀⠀⣰⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⠎⡀⠀⠀⠀⣀⢎⠤⡉⣄⠐⠥⣀⣀⡀⢳⡀
⠀⢀⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡸⢰⠁⠀⠐⠛⠛⠁⠀⣷⠀⠉⠑⠒⠋⠁⠀⣇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢳⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠸⣇⠀⠠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⢠⡶⠀⠀⠀⣠
⠀⠀⠀⠀⢾⣄⠀⠈⢷⡀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣠⢶⡀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠞⠁⠀⢀⡾⠋⠀⢀⡀
⠀⠀⠀⠀⠀⠙⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠂⢄⠀⠀⠀⠎⠀⠑⢄⣀⡔⠁⠀⢳⡀⢀⠴⠊⠁⢰⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣴⠟⠁
⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠉⠢⠜⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣇⢀⡤⠚⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⡤
⠀⢀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢐⡗⠒⠢⢤⣀⡧⡤⢤⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠀⠉⠉⠉⢸⠀⠀⠀⠈⠁⣀⢠⡤⠧⢤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠈⠓⠀⠀⠀⠀⢀⣀⣤⡀⠀⠁⡔⠊⠉⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠈⠳⣏⡇⠀⠀⠀⢀⢀⣀⠀⠀⠀⠚
⠀⠀⢀⡠⠴⠒⠉⠉⠀⠀⢧⢠⡄⡇⠀⠀⠀⢠⡀⠀⠀⢣⠀⠀⠀⣼⠀⠀⠀⠀⡴⠛⡉⢉⠁⢀⢼⡏⠀⠀⠀⣠⠤⢄⡀⠀⠀⠈⢇⠀⠀⣰⠏⠀⠀⠉⠲⣄⠠
⢖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⢅⠁⠀⠀⠀⢸⣧⠀⠀⠀⢧⠀⠀⡇⠀⠀⠀⠀⣇⠧⠤⠞⢀⡎⣾⠀⠀⠀⣰⢃⠀⠀⢱⠀⠀⠀⢸⣤⢞⡟⠀⠀⠀⠀⣠⠃
⠘⡄⠀⠀⠀⠀⠀⠀⢰⡃⠁⠘⢴⣰⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢰⢿⡀⠀⠀⠀⠑⠒⠒⢲⡎⠀⢿⠀⠀⠀⠂⠀⠘⡆⡸⠀⠀⠀⢸⠁⡼⠀⠀⠀⠀⡰⠁
⠀⠻⡤⠖⠚⡀⠀⠀⠈⣯⠢⠄⠊⢸⠀⠀⠀⠀⣤⢶⡄⠀⠀⠈⢾⠀⠳⣄⠀⠀⠀⠀⠀⠈⡇⠀⢹⡀⠀⠀⠰⠄⠴⠟⠁⠀⠀⢀⡏⡼⠁⠀⠀⢀⡜⠁
⠀⠀⠀⠈⠓⠸⡀⠀⠀⠘⡄⢃⠀⢸⠀⠀⠀⠀⢫⠂⢻⡀⠀⠀⣈⣧⠀⠈⠓⠦⢤⣀⣀⣠⡗⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⢀⣠⣟⠔⠣⠤⣀⡠⠾⢤⡀
⠀⢀⣀⡤⠤⠒⢣⠀⠀⠀⢳⠸⡀⠈⡄⠀⣀⣠⡤⠳⠘⣅⠉⠁⠀⣼⣤⣠⣤⡰⠀⡠⢄⣰⡁⣄⠀⠀⠈⠒⠦⠤⠤⠴⣒⠟⢹⡾⠚⠓⠲⡌⢀⣠⠊
⠀⠈⠓⢄⠀⠀⠈⡆⠀⠀⢀⣷⢠⠀⠣⠋⠁⠀⢠⣼⣤⡼⠶⠞⠻⣯⡋⠱⠞⢛⡏⠹⣛⣿⣛⣉⡉⢶⣇⣀⠀⠠⠔⠊⠁⢠⠇⠳⢄⣀⣠⣿⡋
⠀⠀⠀⠀⠑⢦⡀⠸⠖⢊⡁⢀⠌⠃⢀⡵⠺⣬⣟⣻⣬⣩⣥⣹⣃⣀⣸⣄⠔⣹⠛⢛⡿⢶⣞⣻⣭⣦⣄⠈⠒⢦⡀⠀⠀⠘⠢⠠⠤⠊⠀⠀⠈⠙⠲⣤⣀
⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⣀⣼⣭⣷⠞⠟⠛⠋⠛⠉⡉⢉⠉⠉⠉⠹⣟⠳⢦⣌⡙⠛⢒⡋⢻⡌⢈⢟⣿⠿⣍⠹⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠰⢚⣁⠀⠀⠀⠀⠀⠀⣸⡾⠛⠋⠀⠄⠀⠀⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠄⠁⠪⠙⢶⣍⠁⡈⠷⡙⢫⡵⠀⢧⡤⠘⣿⡻⣆⠀⠀⠀⠀⢠⡞⠋
⠀⠀⠀⠀⠉⠒⡂⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠎⢰⢌⠳⣄⡐⠴⣾⠷⢶⣤⣧⡀⠿⢝⢮⡳⣄⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⣠⠎⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠑⢈⠳⣆⡠⠖⢦⡰⠋⠑⣦⠠⢦⡙⣟⣦⠀⠀⠀⠀⣈⠦
⠀⠀⠀⡔⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⢈⢳⣄⣠⣣⠖⠿⢼⣤⣬⢇⣸⣎⢷⡤⠒⠉
⠀⠀⠀⠀⠀⢉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢⡙⣧⡟⢀⡤⠜⢣⡿⠉⠳⢸⡎⣷⣄
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠑⡌⢿⡄⢖⢈⣅⣧⡼⠙⢟⣻⡘⡧⠓
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡌⢿⣝⠀⠊⢩⡄⠀⠀⢻⡇⣿
⠀⣀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘⢄⢻⣇⠄⠐⠄⠀⣤⣿⢃⡟
⠀⠉⠀⠀⠀⠈⠛⠲⢦⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢝⠳⢤⣮⣷⠟⣡⣾⠃⠀⠀⠀⠀⢀
⠀⠚⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⢹⠉⠉⠉⠛⠛⠛⠛⠛⠒⠒⠶⠶⠶⠶⠶⠶⠤⠤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣉⣺⣦⡶⠾⠛⠁⠀⠀⠀⢀⠀⠈⠛
⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡠⠔⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣸⠁⠀⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡀
⠀⠈⠁⠀⣠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢷⠀⠀⣠⠔⠐⡄⠀⠀⢀⡴⠢⡀⠀⠀⠀⡎⠉⠢⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⠁
⠀⠀⠀⠾⠋⠀⢀⡴⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠚⠁⠀⠀⠘⣄⣠⠎⠀⠀⠈⢦⡀⡸⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠘⣧⡀
⠀⠀⠀⠀⠀⢰⡟⠁⠀⢀⣾⠁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⡦⠀⠘⣆⠀⠈⢿⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢠⣤⠀⡈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⣤⡮⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⣠⣾⡫⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠦⠤⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢔⠃⠁⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠁⠼⢀⠈⢀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⢤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠉⢢⡐⠈⠒⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠎⢲⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠆⡏⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⡅⣄⠡⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⣀⠤⢂⢅⠟⠁
⠀⠀⠀⠀⠀⠀⡀⡗⡘⢆⠱⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠚⠅⢚⠔⠏
⠀⠀⠀⢀⠀⡨⠳⣄⣌⠢⠀⠀⢉⠓⠤⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣀⠤⡀⠆⡑⠨⠁⡒⠌⡤⠊
⠀⠀⠸⠷⣤⣤⡄⠀⠽⠛⢦⣈⠑⡠⢅⣂⠈⠐⠦⠦⠤⠤⠤⡤⠠⠀⠀⠀⠐⠬⠭⠉⠙⡫⠉⢁⣀⣢⣤⣴⣶⣶⠖⠒⠁
⠀⠀⠀⠇⡈⠇⠉⠩⠉⠲⡒⠬⡬⡏⣛⠒⠂⠂⢈⠉⠀⠀⠉⠉⠉⠙⢈⣀⣀⣬⣥⠤⠴⠖⠟⢛⡽⢋⣷⢿⠏⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠡⣀⠈⠫⢯⠲⠒⠤⣉⡈⠁⠀⠉⠀⠠⠨⠐⠈⠀⢀⠀⢂⡄⣡⢾⠟⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⢓⡐⠒⠤⠄⣀⣀⣀⣀⣴⣇⣵⡃⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠠⢈⢀⡌⠉⠹⣿⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠠⠀⡀⡀⡀⠀⠀⡀

⠀⠀⠀⠀⠠⠢⠂
⠀⠀⠀⠀⡄⠆⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡱
⠀⠀⠀⠀⢰⠀⠀⢈⡡⠌⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢂⣍⣐⠀⠀⠀⠀⠀⠀⠱⠁
⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠈⢆⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢰⠋⠀⠀⠀⠀⠀⠀⠀⣸⠀⠆
⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⡏⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠘⡀
⠀⠀⡠⠁⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡇⠀⠀⠀⠀⠀⡴⣀⠀⠀⠀⠀⠈⠄
⠀⢘⠀⠀⠀⠀⠈⡂⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⢀⠷⢤⡀⠀⠀⠀⠀⢀⠔⠺⠀⠀⠀⠐⠄⠀⠀⠀⡈⠀⠀⠉⠐⠀⠐⠀⢃
⢀⠊⠁⠐⠒⠀⠀⠀⠀⠀⠀⢸⣀⣀⠀⠀⠄⠊⠀⠀⠀⠱⠀⠀⠀⢠⠊⠠⠀⣀⠀⠀⢀⣸⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠈⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠰
⠀⢃⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠃⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠇
⠀⠀⢸⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀
⠀⠀⠀⡄⠀⠀⠸⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠆
⠀⠀⠀⠐⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠐⠌⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠐⠂⠁⠀⠀⠀⠃⠤⠐⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠷⠤⣄⠀⠀⠀⠀⠈⠉⠉⠓⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⣎⣀⣤⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⣀⣀⣠⠤⠴⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡎⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠚⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠴⠒⠚⠉⠉⠀⠀⠙⢤⣀⡤⠋⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⣀⣀⡤⠤⠶⠒⠊⡟⠉⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡶⠓⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠳⠤⠖⠃⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⡴⠋⠙⢦⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡞⠁⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠹⢤⣠⣞⣠⠇
⠀⠀⠀⠀⠀⠉⢲⡀⠀⠀⠣⣀⣀⡰⠃⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⢀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢹⠀⣀⣀⡤⠤⠒⠚⠉⠉
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠿⠔⠒⠋⠉⠁
⠀⠀⠀⠀⠀⡇⠀⣀⣀⠤⠴⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⢀⣤⣤⡀⠀⠀⠀⠀⢀⣶⠿⢶⣤⡴⠟⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠻⣿⡿⣿⣶⣄⣠⡶⠟⣉⣉⣉⣉⠛⠿⣿⠙⠳⣤⡴⠛⠲⠟⠁⠀⠀⠹⠁⠀⠀⣴⣋
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠐⣿⡟⠛⠛⠋⠀⠀⢹⣿⠏⣰⡾⠛⠉⠉⠉⠳⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣤⣶⣾⣿⣶
⠀⠀⠀⠀⠀⠀⣾⣟⠉⠉⠉⠛⠛⠻⠆⠀⠀⠀⠀⣼⠏⣼⣿⠟⠛⠛⢷⣶⣄⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢠⣿
⠀⠀⠀⢀⣠⣤⣌⣹⡿⠀⠀⠀⣀⣤⣶⣦⣤⡀⢸⣿⣠⣿⣷⣤⣤⠶⠶⠿⣍⡀⠀⠈⢻⣷⠀⠀⠀⢀⡾⠁⠀⠈⢻⣶⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⢰⣿⣏⡀⠈⠀⠀⠀⠀⣾⣏⡀⠀⠀⠈⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡤⠾⠛⠒⠒⠒⠾⠷⣤⡀⢀⣼⡿⠦⡴⢿⣷⠀⢰⣟⠉
⠀⠀⠀⠉⠉⢻⡄⠀⠀⠀⠀⠈⠙⢿⣷⣦⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣉⣤⣴⣶⡾⠿⠛⠛⠳⠖⠀⠙⣿⡿⠃⠀⢀⡼⠃⠀⣀⠿
⠀⢀⣴⣾⠓⠉⠀⠀⠀⠀⢠⣴⣤⣄⣹⠟⢁⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣤⣾⣿⠟⢋⣁⠀⠀⢀⣤⣄⣀⡤⢤⡟⠀⠀⠀⠘⠣⣤⡄⠙⣦
⠀⣠⡬⠛⠁⠀⠀⢠⣴⣤⣀⣿⠁⠙⠿⡴⠻⢷⡼⠿⣧⠀⠀⢠⡞⠁⣾⣿⡟⠁⢰⣿⠛⠛⠢⠾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠻⡅⢰⡇
⠀⠛⠿⣶⠊⢀⣤⣾⣿⣁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢷⣤⣤⣾⣅⣼⣿⣿⠀⠀⠈⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠿⠾⣿⡿⠃
⠀⣤⠞⠁⠀⠈⣉⣿⢷⣦⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⣉⣁⣤⣤⣄⡀⠈⠙⠢⣄⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⣸⡇⣠⣄⣀⣾⠃⠀⣼⣿⣆⠀⠀⠀⠀⢠⡞⢁⣴⠾⠛⠋⢹⣿⠛⣿⣷⣶⣤⣤⡿⠿⠂⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠙⣿
⠿⠟⠛⠻⣿⡿⠀⠀⣿⣿⢿⣷⡀⠀⠀⢿⣴⠟⠁⠀⠀⠀⢸⣿⠀⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣿⠿⠟⠶⠄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠈⢻⣿⣦⣄⠀⠀⠀⠀⢀⣤⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠿⣿⣿⣦⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣶⣤⡀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⣤⣀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡄⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠰⠆⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠘⠃⠀⠀⠀⠀⠀⣰⣿⣧⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⣴⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣶⣶⣿⣿⡿⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢈⡙⣿⣿⣿⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠦⣴⡀⠀⠶⠚⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠉⢉⠀⠏⠛⠉⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣨⣏⠉⢈⠁⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠚⢼⡟⠿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡰⢀⢘⠀⠈⡻⡧⠁⠀⠀⠀⠀⠀⢀⣠⡎⢡⢖⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⣷⣀⣔⡇⡲⠂⠀⠀⠀⣤⢊⣜⣡⠿⢰⡇⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢈⣁⣴⣖⠴⠍⢩⠃⣴⠃⠀⢀⠸⠇⢮⣩⠕⠃⢐⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢘⠉⠀⠀⢊⡙⠃⣴⠃⠀⠘⠄⠑⠂⠈⠱⣿⣔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠐⠁⢤
⠀⠀⠀⠀⠀⠀⡞⠀⠀⡀⠚⢁⣼⡟⠀⣌⣉⣧⡜⢁⣀⣠⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠚⠁⠢⠀⠈⠆
⠀⠀⠀⠀⠀⠂⢛⡻⠀⡀⠀⡾⣿⠃⠤⡛⠉⠉⠙⠛⠛⠣⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣿⣿⣳⣀⠀⠀⠀⣐⡄
⠀⠀⠀⠀⠀⢀⣠⢧⡜⢐⣽⣾⣿⠄⠆⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⢀⣤⠄⠶⢿⣿⠟⠋⠁⠙⢧⣼⣷⣤⣀⣉⣤⠃
⠀⠀⠀⠀⠀⠈⠙⠫⠚⠛⠛⠛⠙⠀⢸⠇⣴⣴⣾⡿⠁⣀⣀⣠⣴⣶⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠤⣄⣀⣀⠀⠀⢀⣀⣩⡟⣋⣤⣾⠿⠟⠋⠁⠈⠀⠘⡄⠁⣁⡀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠊⠀⠀⠀⠀⠀⠚⠉⠉⠁⠀⢠⠆⠀⠠⡖⣤⣜⣦⣈⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣻⡵⢀⠀⠐⠀⠀⡀⣀⠔⣢⣾⡲⢤⡈⠀⠁⠀⡈⠙⠛⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⡄⠀⠀⡐⠂⠤⠷⠛⠉⠉⠉⠛⠻⠦⠀⠀⠀⠘⠀⠀⠃

⣷⣾⠾⢶⠷⠾⢶⠷⣾⣾⢷⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣾⣾⣶⣶⣶⣾

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


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢱⠃⠀⠀⠀⢀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡙⠘⠦⠶⢮⣽⠟⠋⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣄⡀⠀⠀⠀⠀⠀⣀⣀⡀⠈⠙⠳⡦⠤⣴⣾⠉⣠⢰⡦⣼⡧⠤⣀⠀⠈⠳⣄
⠀⠀⠀⠀⠒⣶⣒⣒⡚⠛⠉⠉⠛⠋⠛⢶⣄⡴⣻⡥⠼⠟⡠⠀⠈⠀⠀⠀⣞⢠⢿⠀⡇⠀⠈⠳⢤⣶⠆⠀⠘⣦
⠀⠀⢀⠔⠁⠀⠀⠈⠉⠛⠓⠶⣶⣶⡷⢢⠋⠸⣤⡤⢤⣴⡃⠀⠀⠀⠀⠀⢯⠊⠈⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⢀⡤⠋⢳⠀⠈⠹⠷⣌⡻⡄⠀⠀⠀⠀⢸⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠰⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡤⠚⠉⠀⠀⠘⡆⢰⠀⠀⠘⢧⣻⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⠀⠈⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠘⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠈⠑⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠈⠀⠀⠁
⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⠿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣭⣶⣖⣒⣀⣀⣀⣚⣒⡒⠲⠂⠨⡍⠙⠻⠿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠟⠛⣉⣉⣉⣉⣉⣉⡙⠛⠻⠿⣿⣟⡛⠛⠿⠶⣦⣤⣈⠳⢦⣍⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⢟⣩⣴⡶⠿⠛⠛⠉⠉⠉⠉⠛⠛⠻⠶⣦⣤⣉⠛⠷⣦⣀⠀⢉⡙⠻⢶⣬⡙⠦⣍⠻⣷⣦⡀
⠀⠀⠀⠀⠀⣰⡿⣫⣴⠟⠋⠁⢀⣠⣤⣤⣶⠶⠶⣶⣤⣤⣄⣀⠀⠉⠛⠷⣦⣈⠙⢿⣟⠛⢻⣆⠉⠻⢷⣌⣷⠈⠻⣿⣆
⠀⠀⠀⠀⣼⣿⡿⠋⠀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣄⡀⠈⠙⢷⣄⠙⢷⣬⣿⣀⡀⠀⠙⢿⠳⠦⣌⠻⣷⡄
⠀⠀⠀⣼⣿⠟⠀⣠⡾⠋⠁⠀⠀⠀⠈⠀⠀⠀⠞⠋⠀⠀⠀⠀⢠⡄⠉⠻⣶⣄⠀⠙⢷⣄⠙⣿⡍⠻⣧⠀⢸⡄⣼⣟⡇⠙⣿⣆
⠀⠀⣰⣿⠋⢠⣾⠋⠀⠀⢀⡄⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠈⠙⣷⣄⠀⠹⣷⡈⢻⣆⣿⣦⣤⡙⢦⣽⣇⢠⡈⢿⣧
⠀⢠⣿⠇⢠⡿⠁⠀⠀⠀⠈⠓⠀⠀⠀⠈⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⠻⣦⡀⠘⢿⡄⠹⣯⠁⠈⠻⣦⠈⢻⣆⠻⡌⢿⣧
⠀⣿⡏⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣄⠀⠀⠀⢠⡀⠀⠀⠀⠀⠙⣷⡄⠈⢿⣆⠹⣧⣀⠀⣿⠀⠀⢻⣇⢻⡌⢿⣧
⢸⣿⠁⣾⠃⠐⠖⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠈⠋⠀⠀⠠⠄⠀⠈⢿⡄⠈⢿⡄⢹⣿⢿⣿⡀⠀⠀⢻⣆⠁⠘⣿⡆
⣾⡟⢸⡟⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠈⣿⡄⢻⣆⢹⣿⣆⣀⡀⢿⡄⠇⢸⣿⡀
⣿⡇⢸⡇⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⠳⠀⠘⣷⡀⠘⣷⡈⢿⡾⠿⠛⢻⣧⠸⣷⠀⡄⢿⣇
⣿⡇⢸⡇⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡆⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠹⣧⠘⣷⣖⣛⣩⣿⠆⢻⡇⣷⢸⣿
⣿⣇⢸⡇⠀⠋⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢻⣇⠀⢻⣆⠸⣿⠿⢹⡇⠀⢸⣧⢸⡈⣿
⠘⣿⣾⣿⠀⠤⣤⣄⠀⢀⡀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠀⠀⠀⠀⠄⠀⠛⠋⠀⠀⡄⠀⠀⢿⡆⠀⢿⡄⢻⣿⠽⣷⠀⠈⣿⠈⠁⣿
⠀⠈⠛⠿⣿⣶⣶⣶⣤⣬⣥⣀⣘⣛⡒⠲⠶⠦⠄⠀⠀⣀⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠘⣿⡀⢿⣞⣿⠀⢰⡿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠻⠿⠿⠿⣷⣶⣶⣦⣤⣭⣭⣁⣈⣓⡀⠀⠶⠤⢤⣤⣄⣀⣀⡀⠀⠀⠘⣷⡀⠘⢷⣄⠻⢿⣴⠿⠁⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⣷⣶⣶⣶⣤⣭⣭⣉⣁⣀⡈⢿⣦⡈⠻⢷⣤⣤⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠻⠿⠿⠿⣿⣷⣶⣾⡿⠟⠉⠁

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⢐⠒⠒⠒⠂⠲⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠯⡢⢄⡀⠀⠀⠀⣼⡧⠟⠓⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠌⠀⠒⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠈⠒⢤⣈⣉⣀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠇⠉⠩⣶⢦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⢯⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣶⣶⣖⣐⣀⣄⣀⣀⠀⢀⣠⣤⡤⡠⣲⡤⡤⣤⣴⣝⣷⣼⣾⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢉⣉⠉⠉⠋⠻⠛⠛⠛⠻⠿⠿⠿⠟⠿⠿⢿⠿⠿⠿⢟⣟⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠒⠒⠦⠤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠙⠻⣟⡶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠈⢀⠀⠙⠲⣌⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢵⡄⠀⠈⠙⠶⣤⡙⢷⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠄⠀⠀⠈⠻⣦⣿⣄
⠀⠀⠀⠀⡴⠃⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠙⢿⣷⡄
⠀⠀⠀⡼⠁⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⢷⡙⢦
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⢳⡀
⠀⢰⠃⠀⣾⣿⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢾⣷⡉⣷
⠀⣿⠀⡄⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠉⢿⣼⡇
⢀⡇⢰⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⢹⣷
⢸⡇⡄⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⢘⡄⠃⣿
⢸⡃⢁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⢈⢇⠀⣿
⢸⡇⢰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡿⠀⡟
⠈⣇⢘⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠀⠀⠀⢠⠀⠀⠀⠀⠌⢠⢶⡇⢸⡇
⠀⢹⣎⢷⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡦⡞⠁⣼⠁
⠀⠈⢿⣮⣎⢠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠄⠀⠀⠀⠀⣤⡄⡀⢠⠏
⠀⠀⠈⢿⣆⠺⡯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⣾⠏⠀⢠⠏
⠀⠀⠀⠈⢿⣦⡉⠻⣼⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠱⠀⣰⡏
⠀⠀⠀⠀⠀⠹⣿⢦⡸⣧⣶⠀⣀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠘⠀⣀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⠈⠳⣝⢿⣏⡷⢿⠟⢧⡀⠀⠀⠀⢠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠠⠂⠐⠀⠀⠀⢀⣴⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⡛⠷⢯⣄⣶⣷⣾⣿⢦⡀⣅⠀⠀⢀⠀⠀⠀⠀⠒⠀⠀⠀⢠⠆⠀⣠⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⢬⣍⣛⠻⢭⣂⣓⡬⠅⠁⣠⡀⢠⡒⠁⠊⠀⠉⢁⣠⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠽⠷⣤⣤⣬⠤⠤⠴⠶⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠘⠓⣷⠟⢀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠘⠛⠀⣶⣆⣀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⣀⠀⣾⡁⠀⢸⣿⠀⠀⠀⠀⣠⡴⢾⡇⠀⠀⢠⡾⢛⣿⠀⣷⠀⠈⡏⢹⡟⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠗⣿⡇⡘⣿⠀⢻⣷⡀⢸⣿⠀⠀⠇⠀⣟⢀⣾⡇⠀⠀⠸⣄⠼⣿⠀⣿⢀⠔⠀⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠉⣿⠀⠘⠷⠃⠿⠠⠈⣿⡷⠸⣿⠀⡸⠀⠀⠈⠉⠸⠇⠀⠀⠀⠀⠀⣿⠀⠉⠁⠀⠀⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⠶⠟⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠿⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠿⠇⠚⠿⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣴⡄⣠⣤⡀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⢸⡏⢻⡄⠀⠀⠀⣿⠀⣿⠀⡇⠀⢰⡿⠀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢿⡄⣀⡀⠻⣦⡇⠀⠀⠀⣿⠀⠻⠞⠁⠀⣼⠃⠄⢡⣾⡋⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠳⡀⠈⢷⠉⢿⡀⠀⠀⠀⠀⠐⠿⠒⠒⠀⠀⠀⠙⠀⠀⣿⠃⠀⡀⠄⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⢸⡙⢷⣌⠢⠀⠀⠘⠛⠀⣠⣤⣤⡴⠶⣤⣤⣤⡀⠀⠀⠀⠀⠉⠀⠁⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡷⠀⠙⠛⠃⠀⢠⠞⠚⠁⣤⠶⠒⢲⣶⣖⣮⣛⣷⣦⣀⠀⠀⠀⠀⢶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠋⣴⠶⢾⣥⠶⠛⠋⠉⠉⠉⠙⠳⢦⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠾⢧⡤⢿⣴⠏⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⡈⠻⣏⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⡧⢠⡏⠀⣼⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⢀⠀⠹⡟⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢾⡀⠸⣇⢰⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢻⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢻⡀⠈⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣭⠿⠋⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⣀⣀⣀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⠟⠛⠀⣰⣿⣿⣇⠀⢀⣾⡿⠛⠛⠿⢃⣼⡿⠛⠛⢿⣷⡄⣼⣿⡛⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣇⣸⣿⣆⠸⣿⡇⠀⠀⠀⠸⣿⣇⠀⠀⢠⣿⡇⢈⠛⠿⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⢠⣿⡟⠋⠙⢻⣿⡄⠙⢿⣷⣾⡿⠂⠙⠿⣷⣶⡿⠟⠁⠻⢿⣶⣾⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⡀⢰⢰⡏⠀⠀⠀⡏⠀⣴⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡎⠹⡆⢻⡙⣼⡟⡇⢲⠀⢀⡇⣼⣿⣸⠃⢠⠞⢳⠀⣀
⠀⠀⠀⠀⠀⠀⢰⣆⠘⢦⠈⠹⡄⢹⡤⠃⠈⠃⠉⠉⠀⠈⠉⠁⠃⢧⠀⡏⣠⠏⠈⢡⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠳⠴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⣀⣀⢰⠃⡰⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠔⠉⠉⠉⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠛⠀⡑⡀⠉⣿⡇⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣀⠀⠀⠀⠀⠀⠁⠙⠀⠀⣈⣧⡀⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⢀⠀⠐⢿⡀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⣠⡴⠶⠿⠿⠿⣿⣿⣶⣧⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠐⠂⠀⠀⠀⣠⠙⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠰⠂⠀⠀⠠⡆⠀⠀⢀⠸⡟⠛⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠳⣏⠙⠉⠓⠛⣩⠟⠋⠈⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠈⠀⠀⡠⠚⠳⢤⣄⡰⠆⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠔⠋⠀⠀⠀⠀⠀⠉⠓⠺⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⠉⠉⠉⠉⠁⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠉⡠⠀⠀⠄
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢧⡀⠀⠀⠀⠁⠢⣀
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠓⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠙⠒⠲⠤⠤⣄⣑⡢⢤
⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⣠⠆⠈⠀⠀⢹⡖⢦⣄
⠀⠀⠀⠀⠐⡇⠀⠀⠈⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣰⠋⢄⠠⠂⣱⠂⠀⠀⡧⠹⢦⡀
⠀⠀⠀⠀⠀⣧⠀⠀⢀⡀⡀⠐⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡀⠂⠀⡀⠐⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⢀⡇⡤⠗⠀⢀⠯⡤⠆⠀⢣⠔⢄⡃
⠀⠀⠀⠀⠀⢸⡀⠂⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠸⡇⠀⠄⠈⠀⠃⠀⡆⠲⡁⠀⠀⢇
⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢧⡀⠀⠠⠀⠁⠀⢀⠀⠘⠳⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⡄⣀⠨⡄⠺⠄⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣁⡀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠒⠒⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠻⣄⠘⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⢀⡤⣪⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡈⠒⠶⠤⣤⣤⣀⣀⣀⣀⣠⣤⣤⡤⠤⠴⠚⣡⠖⠉⣚⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣤⣬⣉⠁⠒⠂⠤⠤⢤⣤⣤⣤⡤⠶⢶⣖⣲⡿⠧⠔⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠙⠳⠛⠻⠿⠿⠷⠒⠒⠚⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⡤⠀⠀⣀⢰⣄⠀⠀⣼⡦⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠠⡦⣸⠷⡘⠈⠘⣇⠨⠟⢡⠟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣠⡆⠑⠛⠹⠾⠗⠚⠓⠛⠳⢦⣇⡶⣏⣧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⢉⡏⡈⠟⠻⠶⠶⣚⡍⢙⠷⢌⠘⢆⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⣶⠄⠀⠋⠀⣠⡶⠠⠯⠀⠐⠀⢁⣁⠀⢀⣶⣶⢦⡉⠉⢦
⠀⠀⠀⠀⠀⠠⣶⣤⣴⡟⠀⠀⠀⠠⡀⢠⢤⠚⠀⢄⠀⠀⠀⠨⠶⠫⡀⠅⠈⢧⡀⢸⠃⡄
⠀⠀⠀⡠⠒⠁⠨⣿⣿⠢⡀⠀⢇⠀⠀⠘⣎⠃⠀⠉⠲⠉⠀⠀⡤⠛⣁⡴⠥⢼⣷⡟⠀⠸⢆⠐⠀⡤
⠀⠀⠀⠀⠀⠠⣠⣿⢿⠀⠰⡀⢹⣄⠀⠀⠈⢢⠀⠀⠤⠠⢄⣾⣿⡀⡀⢞⣨⠿⢋⣀⣴⣷⣿⣾⣀⡟⣶
⠀⠀⡄⡄⠀⢀⣽⠃⠈⡆⠀⢱⡄⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠙⡆⠉⢉⣿⣿⣿⣿⣿⣧⢻⡟⠻⣶⡂⡞
⠀⠀⡇⠀⠀⢺⣿⠁⠀⠹⢶⡄⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⡘⣆⣼⢿⣿⣿⣳⡿⠋⠀⣽⣶⣄⠉⠂
⠀⠀⠃⠀⠀⠰⢿⡄⠀⠀⢼⡁⠀⠀⢀⠀⠈⠴⠃⣠⠔⢋⣄⣸⣅⢿⣿⣿⠟⠋⠁⠀⢀⣾⣿⡞⠟⠁⠀⠃
⠀⠀⠀⢆⠀⣠⠎⠉⣶⠀⠲⠷⡶⣤⣌⣅⣘⣗⣸⣟⣱⣯⣿⣷⠶⠛⠋⠙⠲⠾⣿⣶⣿⣏⠏⠀⠈⠀⣈⣼
⠀⠀⠀⠀⠘⠁⠀⠀⠐⢳⣦⣤⣀⣀⡛⠘⢘⡿⣷⠞⠟⠉⠉⢱⣄⠀⠀⠀⠀⠀⢌⣼⣿⡥⠽⠢⠤⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⠛⠛⣿⣿⡖⠾⠛⠋⠀⠀⠀⠃⡀⠙⠒⠌⣁⣤⣶⡿⠋⠁⠀⠀⢠⠤⢂⡤⠂
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠉⢹⢿⣧⣀⣀⣠⢀⣈⣀⣀⣀⡀⢤⣾⠛⠙⠋⠀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣀⡤⠯⠿⠛⠁⠀⠀⠉⠁⠀⠀⠀⠈⠁⠀⠐⠒⠂⠀⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣾⣿⣶⣶⣶⣶⣶⣶⣶⡖⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣿⣿⣿⣿⣿⣿⣾⣽⣿⣽⣿⣿⠿⠟⠛
⠀⠀⠀⠁⠰⠄⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠿⣿⠿⠿⠿⠿⠿⠛⢛⠛⠂
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠠⣀⠀⠠⠀⠀⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡦⠤⠴⠦⠤⠤⠤⣧⣀⡘⣷⠠⠟⠁⠀⠀⠳⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠺⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣄⡐⢂⣇⣒⣹⣴⡎⠑⠀⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠭⣄⠰⣄⣭⡷⢴⡟⠿⡔⣢⢀⠁⠒⣄
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠓⣤⠀⣉⢀⢷⣆⡁⡸⡿⣡⢣⢶⡐⢄
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠌⠳⣌⣾⢃⣾⣷⣧⠴⠃⠎⠀⡧⣘⡆⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠈⠀⠫⣥⣚⡠⢀⡜⣱⢃⡀⠙⠯
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣤⣤⣀⠙⣿⠿⠓⢉⠙⠳⣷⣀
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⢃⠈⣿⠿⣈⠀⣶⣤⡁⠺⠷⢀
⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣶⡦⠀⠉⢳⠀⠨⣃⡘⠓⢀⡀⢀⠂
⠀⠀⠑⠦⢤⣀⣀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣷⣲⣤⠖⣄⣶⠛⢻⡄⠸⢃⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢦⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡍⢻⣏⠙⠛⢳⠾⡟⢿⣻⡟⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⣿⣧⣉⠁⠠⠟⣮⢱⣎⢹⣿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣬⣖⣄⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠀⠈⠀⢿⣮⣉⣷⣡⡼⢧⣜⠳⣞⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠳⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⢦⡙⣿⣟⠡⠆⢼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢤⣀⣀⠀⠀⠠⠙⢧⣌⣿⠻⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠓⠒⠒⠚⠉⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⠚⣋⣙⣒⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣭⠀⠀⠈⠉⠙⠻⢝⡺⢝⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⢻⡇⠀⠀⠀⠀⠀⠀⠀⠙⠦⠵⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠳⢄⣾⡏⡟⠘⠃⣠⠤⠂⠀⣀⣠⠤⠤⠀⡄⣠⠈⠃⢀⡤⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⠏⠙⠆⣿⡇⡇⢠⠞⠁⠠⠖⣋⡵⣀⣠⣴⡿⠛⢸⡄⣸⢡⠔⢲⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⡴⠁⠀⠀⠀⣿⠃⠁⠚⠀⠀⠒⠛⠻⠿⠷⢯⣥⣤⣀⡸⠃⣿⠀⠀⠀⠙⣄⠹⡄
⠀⠀⠀⠀⠀⠀⢀⡞⣡⠏⠀⠀⠀⠀⠀⡏⠀⠛⣿⡟⢂⣶⣦⢀⣴⠶⠦⢀⣤⠦⣤⡀⣿⠀⠀⠀⠀⠈⢣⡙⣆
⠀⠀⠀⠀⠀⢠⣯⠞⠁⣴⠃⡰⢀⣆⠆⣿⠀⠀⠿⠃⠿⠳⠿⡏⢿⣤⣤⠸⣧⣀⣿⠇⣿⠢⣰⡀⣆⠱⣄⠙⢮⣧
⠀⠀⠀⠀⠀⢟⣁⣠⡞⠁⡴⢁⠞⣸⠀⣿⠀⠀⣿⣛⣷⢰⣿⣛⡓⢰⡆⠀⢸⣏⠁⠀⣿⡆⢇⠳⡘⢆⠘⢦⣄⣙⡇
⠀⠀⠀⠀⠀⠀⠁⠐⠷⢊⡴⢫⡰⠃⢰⡇⠀⠀⠿⣥⡿⠿⣿⣭⣥⢸⣧⣤⣼⣧⣠⡀⢹⡇⠘⢆⠽⢌⠓⠞⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠉⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠭⠭⠭⠭⠿⠉⠹⢿⠿⠟⠋⣛⣻⣟⣛⣓⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠸⠇

⠀⠀⠀⠀⣀⣀⠤⠤⠐⠒⠒⠊⠉⠉⠉⡉⣉⢉⠉⡉⠉⢒⠒⠒⠠⠤⢄⣀⡀
⢀⢶⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠕⠘⠚⠻⠲⠀⠀⡹⡆
⢸⠏⠑⠫⢔⡢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡧
⣿⠀⠀⠀⠀⠈⣑⠊⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⢟⡸⣧
⢻⡄⢀⡀⠀⢸⡹⡷⡀⠀⠉⠑⠫⠖⣢⣄⣀⠀⠀⠀⠀⠀⠀⠀⡠⣻⡿⡆⣡⣿
⠀⡇⠘⠗⠀⠈⠧⣀⡅⠀⠀⠀⠀⣠⡀⠉⠑⠛⠵⣖⡤⣀⡀⡰⣵⣝⣷⡛⣿⣿
⢀⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠙⠁⠀⣠⢲⡶⣄⠈⠙⠺⣻⡇⢹⡿⢁⡿⣿
⢸⡆⠀⣠⣤⡀⠀⠀⣾⣹⠼⠟⡆⠀⠀⢸⣷⠅⠀⢈⠀⠀⠀⣿⣼⡎⠟⢛⢳⣿⡶⢶⣖⠒⠂⠠⠤⠤
⢸⡇⢸⣿⡟⠚⡆⠀⠙⢇⣀⠰⠁⠀⠀⠀⠙⠤⠴⠊⠀⣠⠶⡿⠙⡕⡀⣸⠛⣿⡛⢉⣉⠉⣉⣉⣈⡁⠉
⢸⡧⡀⠙⠢⠤⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠠⣷⣵⠂⢸⣷⡟⣏⣿⡿⠔⠀⠤⠦⠤⠔⠂
⠀⠙⠪⣕⡤⣀⠀⠀⠀⣴⢦⠀⠀⠀⣾⣶⡵⠛⠆⠀⠀⠉⠓⣔⣳⣿⣷⣿⣿⣃⣉⣉⣉⣭⡭
⠀⠀⠀⠀⠙⠳⢽⣦⣀⠈⠊⠀⠀⠀⠙⢏⡀⣀⠇⠀⠀⠀⠀⣿⠄⠦⢶⡿⠷⠺⠿⠖⢳⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⣄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⣿⢿⡏⣿⠍⠉⠉⠉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠮⣒⣄⡀⠀⠀⢠⡶⡄⠰⣷⢁⣼⣽⡯⠍⠉⠉⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣗⣤⡀⠉⠀⠀⠈⡿⣿⣟⣓⣒⣐⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⣦⢄⡀⠀⣧⡯⠌⠥⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣶⣿⣿⠛⠛⡏⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⣿⣿⣿⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣄⢸⣿⣿⣧⣴⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⠟⢻⣿⣿⠋⠹⢿⣷⣔⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠏⢀⣈⠉⢁⣀⠀⣤⣽⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢋⣿⡗
⠀⠀⠀⠀⠀⠀⢀⢋⣾⣿⣿⣿⣾⣿⣿⣿⠁⣾⣿⣷⣍⢿⣿⣿⡿⠶⠀⠀⠀⠀⠀⠀⢠⡆⢾⡿⢸⣿⣁
⠀⠀⠀⠀⠀⢠⢣⣿⡿⠻⢛⣭⠍⠁⠀⣿⣿⣿⡑⢝⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣡⣿⣿⡏⢀
⠀⠀⠀⢀⡆⢀⣿⣿⢁⣾⣿⣿⠿⠛⠀⢹⣿⣿⠃⠀⠉⠙⢿⣿⣧⡀⢠⣴⣿⣿⣿⣟⠉⣽⣿⡿⠋⠾⣿⣽⡿⢄
⠀⠀⠀⣾⠁⣼⣿⡇⣼⣿⣿⣶⣦⣤⠀⠸⣿⠉⠀⠀⠀⠀⣸⣿⡟⠁⢠⣼⣿⣿⡿⠋⢀⣉⠉⠀⢴⣶⣿⣿⣷⢦⡀
⠀⠀⢠⡏⠀⣿⣿⢱⣿⣿⣟⣛⣉⣄⠀⠀⠁⠀⠀⠀⠀⣼⣿⣿⣋⣠⣿⡟⣼⣿⣷⣿⠿⠿⣷⣄⢸⣿⢹⡿⢻⣿⠓
⠀⠀⢨⡇⢀⣿⡟⢸⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢰⡿⠛⠉⠀⠀⠘⠋⢿⣾⡏⣿⡇⣼⣯
⠀⠀⠘⡇⢸⣿⡇⢸⣿⣿⣶⣶⣶⡶⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢀⡀⢀⠀⣈⣿⣴⣿⢰⣿⠇
⠀⠀⠘⡇⢸⣿⡇⢸⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⢀⡈⠙⢿⣿⣿⣿⣿⠃⣼⡿
⠀⠀⠀⠹⠘⣿⣧⢸⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⢠⡀⠙⢿⣿⣾⣿⣿⠃⣾⡿⠁
⠀⠀⠀⠀⠀⣿⣿⡀⢿⣿⣿⣵⣶⣦⡤⠄⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠰⣄⠌⠻⣶⣿⣿⣿⡿⢋⣾⡿⠁
⠀⠀⠀⠀⠀⠙⣿⣧⠸⣿⣿⡿⡟⠁⠀⠀⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⢰⡀⠹⣷⣿⣾⣿⣿⠟⣱⣿⠟⢁⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣆⢹⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⢨⣿⣿⠀⢾⣦⡘⢿⣷⣿⣿⣿⠟⢡⣾⡿⢃⣠⠞
⠀⠀⠀⠀⠀⢀⠈⣿⣿⣆⢻⣿⣿⣵⣶⣤⡤⠀⠀⠀⠈⣿⣿⣦⡾⣿⣿⣾⣿⣿⠟⣡⣴⡿⠏⣠⡾⠁
⠀⠀⠀⠀⠀⠠⣤⣈⠿⣿⣧⠹⣿⣿⣿⣋⣀⡀⠀⠀⠀⠸⣿⣿⣿⣾⣿⡿⢟⣻⣿⣿⠟⢃⣴⠏
⠀⠀⠀⣠⣶⣿⢛⣴⣿⣿⣿⣦⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⢿⣿⡿⣋⣥⣴⣿⡿⠋⣀⣴⠟⠁
⠀⢠⡾⢛⣩⣥⣿⣿⡟⠡⡙⢿⣷⡈⠻⣿⣷⣶⠾⠀⠀⠀⢸⣿⣿⣿⣿⡟⢉⣵⠞⠋⠁
⢠⡏⠁⣿⣿⡿⠛⣋⣀⣔⢾⣦⣿⣿⣄⠘⢿⣿⣷⡶⠀⠀⠀⢿⣿⣿⡋
⢼⠀⣾⣿⣯⣤⡶⣿⡿⠿⢿⣿⣿⣿⣿⣷⣦⡙⢿⣶⡶⠂⠀⠈⢿⣿⣷
⠈⠀⠹⢿⣿⣿⣿⣿⣿⠿⠿⡿⠿⠿⠿⠿⢿⣿⣦⡙⠻⣿⣟⠁⠈⢿⣿⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠳⣄⠈⠻⣿⣷⣆⠉⠓⠀⢨⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣌⡛⠛⠿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠷⠦⣤⡬⠤
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⣡⣤⣤⣀⠀⠈⠉⠑⢲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⢸⣵⣿⣿⣿⢇⠀⢰⢰⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⣤⣤⡀⠀⠉⠹⠿⠗⠃⠀⠘⣞⢷⣝⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⢴⣶⣤⡀⠈⠉⠁⢀⣤⠶⠶⠶⢦⣄⠀⠈⠙⠚⠭⠉⠉⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠘⠻⣿⡿⠏⠀⠀⢰⣿⣶⣿⣿⣿⣿⣿⣷⠒⠒⢒⣛⡉⠉⠉⢹
⠀⠀⠀⠀⠀⠀⣠⠔⣋⣀⣀⣀⣤⠤⠤⠴⠖⠒⠒⠋⠉⠉⠻⢿⣿⣿⣿⣿⠿⣫⠂⠀⢿⣿⣷⡄⠀⢸
⠀⠀⠀⠀⠀⣾⠉⠉⣽⣂⡀⠀⠀⣠⢖⣒⣒⡂⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠋⠀⠀⠀⠈⠙⠋⣀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠸⠿⠇⠀⠘⣱⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⢔⣂⡀⠀⠀⢀⡴⣫⢷⣶⣿
⠀⠀⠀⠀⠀⣿⣀⣀⡠⢄⡀⠀⠀⢿⣿⣿⣿⢿⡟⠀⢀⡤⢤⠤⠀⠀⠀⣿⣿⣿⡆⠀⡞⡾⣱⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⢶⣝⢦⠀⠀⠙⠛⠚⠋⠀⠀⠋⣾⣿⣿⣷⡀⠀⠙⠒⠋⠀⠀⡜⣇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⢻⣆⢧⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣛⡿⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⠿⠿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠈⠀⠀⠀⠀⢀⣀⣀⣀⡤⠬⠥⠤⠶⠒⠒⠚⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢿⣿⡿⠿⠿⠿⠓⠒⠒⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠈⠳⡒⢄⠰⡎⣢⠄⡲⠋⠀⠉⠙⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣀⢤⣀⣸⠈⠢⠃⡇⢰⡥⠤⠐⢒⡩⠃⠸⣆
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠰⠯⠀⠠⠤⣀⡀⠠⠤⠔⠀⢠⠔⠊⠁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⡠⠔⠢⠄⣉⡐⢄⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣀⠔⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⡀⠀⠀⣀⣀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠈⠑⠠⡰⠋⢀⠀⠀⢀⠀⡉⠀⠒⠒⠂⠀⠤⠤⠤⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠀⢀⠀⠀⠈⠑⠲⠵⣤⣄⣀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⢪⠟⢦
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠉⠉⠒⡒⠶⣦⡄⠀⣠⣢⠏⠀⣘
⠀⠀⠀⠀⠀⠀⡴⢄⠄⡀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠀⠁⢀⡼⣪⠋⠙⡆⣠⠝⠁⣠⠞⠉⣧
⠀⠀⠀⠀⠀⢰⠖⡌⠟⠚⠧⢄⣀⡠⠤⠤⠴⠦⠤⠶⠒⠚⠋⠋⠁⢀⣴⠩⠴⠖⠊⠁⢀⠀⠏⡇
⠀⠀⠀⠀⠀⠈⢌⢜⠢⣄⣀⣀⣒⠤⠤⠄⠒⠦⠥⢤⣤⠤⠤⠔⠊⠁⠀⠀⠀⣈⡡⠴⡃⢤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣌⠩⠭⢍⡒⠒⠒⠶⠦⠀⠀⠀⠠⠤⠤⠤⠴⢓⣋⢥⣢⠵⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠉⠭⠓⢒⣒⣒⣒⣒⣒⣲⠾⠿⠓




⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⡀⣀⣀⣀⣰⣿⣿⣏⡀⠀⠀⣠⢶⠀⠀⣴⡖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⢺⠆⠙⢯⣠⢻⣾⢿⣿⣬⣩⢿⠟⠉⢹⣀⣤⡬⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⣄⣀⡴⣞⠋⢨⣄⡬⠇⣀⣀⣀⠀⣯⣿⣇⣂⣠⣮⣆⣠⣞⣁⠘⢛⣶⣖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⢿⣯⡢⣤⠖⠺⣾⡔⢸⣵⡾⠶⠚⡛⠩⠍⠁⠀⠦⣀⠀⠺⠿⠽⣟⡿⢿⣧⣄⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣇⠀⢿⢿⣮⣢⣐⡿⠟⠋⠻⠃⡀⠰⠿⠭⠀⠀⠀⢠⠀⠀⠺⠄⠌⠙⠯⣗⢯⡻⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠿⣤⡼⣠⡏⣎⣿⡿⢫⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠢⡹⣆
⠀⠀⠀⠀⠀⣠⣤⡀⢰⢧⠀⠀⢀⠀⣷⣿⣿⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⢀⣀⠀⠘⠚⣧
⠀⠀⠀⠀⠀⢯⣉⣠⡿⠼⣟⠉⣻⠞⠁⠂⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠞⠞⠛⢂⣀⡼⠇
⠀⠀⠀⠀⠀⠀⢸⠟⠀⠸⢯⣿⠿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠾⠄⠀⠀⠀⢠⠀⢀⣢⡴⠞⠋⠁
⠀⠀⠀⠀⢀⣼⣵⣲⣶⣶⣾⣿⡣⠀⠀⠀⠀⠈⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠘⣁⣤⠷⠚⠉
⠀⠀⢀⣴⣿⣾⣿⠿⠛⣻⣿⡿⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣀⡤⠶⠛⠉
⠀⠀⢿⡾⣿⠋⠀⣟⣿⣿⡏⣡⡄⠀⠀⠀⠀⠀⠈⠀⢀⠁⠀⢐⣠⠴⢚⣿⡷⠖⠋⠁
⠀⠀⣠⢽⡉⢹⠗⣈⣽⢹⢁⠀⢀⠉⠀⠀⠀⡼⣰⡀⠠⠴⢚⣩⡴⠞⠋⠁
⠀⠸⣝⠓⢃⡼⡎⠁⣼⢸⢾⠀⠀⠀⠀⠀⠨⠓⣛⣥⠶⠚⠉
⠀⠀⠀⠉⠉⢀⡇⣾⣿⣼⡄⣀⣀⢈⣄⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠸⢽⣽⠿⣿⣳⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠒⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⠔⠋⠀⠀⠐⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢻⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠈⡀⠀⠀⠀⢀⣹⡩⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣿⢿⣧⢻⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠑⠚⠁⠒⠢⠀⠀⠀⡀⠘⣹⡅⣺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⣛⣛⣿⣿⣿⣘⣿⣿⣿⣿⡿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠢⢴⡱⣶⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣿⣿⣿⣼⣿⣯⣟⣿⣿⣜⢿⣿⣷⡀
⠀⠀⠀⠀⠀⡖⠈⠀⢅⠀⠀⠀⢀⠀⠀⠀⠄⡀⠀⠀⠀⠉⢎⢻⡌⢧⡀⠀⠀⠀⠀⠀⣴⣺⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⡻⣿⣷⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠈⡆⠀⠀⠈⠛⢆⡀⠀⠈⢄⠀⠀⠙⠒⠷⡝⢦⢹⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢿⣿⡄
⠀⠀⠀⠀⠀⠣⣄⡤⠴⠶⣄⡀⠀⠓⠀⢭⡢⣄⠀⠈⠙⣏⢳⣄⠛⣎⢻⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⡇
⠀⠀⠀⠀⢀⠊⠁⠀⠀⢤⣀⣯⣍⣳⣦⡀⠈⠻⢷⣲⢄⡈⠲⣌⡙⠻⠌⣧⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣻⢿⣿⣿⣿⣿⣿⡇⢳
⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠐⠋⠙⠿⠟⠷⠿⠶⣮⣵⣦⣬⣉⡛⠒⠀⣹⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣉⡛⠛⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⠤⠒⠒⠢⠔⠒⠉⠓⠒⠶⠴⠴⠶⠛⠋⠑⠲⠚⠁⠀⠀⠀⠀⠉⠉⠙⠿⠿⠟⠛⠻⠷⠛⠋⠙⠛⠻⠿⠿⠿⠛⠋⠙⠒⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠛⠉⠉⠙⠛⠛⠒⠶⠤⢤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠲⢄⡀⠀⠀⠀⠀⠀⣤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣉⠓⠦⢤⣀⣀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠰⡟⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣠⡤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢧⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⠛⠉⠁⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⡴⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⣀⠈⠙⣦⠤⠞⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢀⡔⠛⠉⠓⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠐⠀⡀⠁⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⠶
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣢⠛⢦⡄⠐⠢⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠑⠋⠀⠀⠀⢁⡽⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⢀⣀⣡⠟⠁⠀⠀⠀⠀⣀⡠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⣀⣠⡥⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⢀⡀⠀⠀⠀⣀⡀⠀⢀⣀⡀⠀⣀⣀⣀⠀⡀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡇⠀⢸⡇⠀⠀⠀⣿⡇⠀⢸⡏⣿⠀⣿⠉⠉⢸⣿⠀⣿⠀⣼⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡿⣿⠀⢸⡇⠀⠀⢸⡟⣧⠀⢸⡇⣿⠀⣿⣤⡀⢸⣿⡄⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡄⢸⡇⠀⠀⢸⡇⣿⠀⢸⡟⠁⠀⣿⠉⠀⢸⡏⣇⣿⠀⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟⠛⣇⢸⡇⠀⠀⣿⠦⢾⡆⢸⡇⠀⠀⣿⠀⠀⢸⡇⢻⣿⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣼⠇⢼⠁⠀⠿⠸⣧⣤⠄⠟⠀⠸⡇⢸⡇⠀⠀⠻⣦⠤⠸⠇⠘⠿⠀⠻⣴⠇