Junk Emojis & Symbols

⠀⢀⡔⠋⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣉⣙⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠒⠒⠦⡄
⠀⢸⠀⠀⠐⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢿⣈⣉⣿⢀⡇⠀⠀⠀⠀⠀⠀⢀⠎⢠⡤⠀⠛⠁⠀⠸
⠀⠈⢧⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠿⠛⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⣯⡔⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠰⠶⠀⠛⠃
⠀⠀⠀⠹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠹⠋⠉⣈⣁⡤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡉⠁⠀⠰⡦⢀⡰
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠒⠒⠋


⠀⣀⣠⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠙⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠊⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣀⠀⢶⢲
⣰⠛⠃⠰⠶⠀⠛⢣⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡅⡽⠀⠀⠀⠀⠀⠀⠀⢰⠉⠈⠀⠈⡈⢱⠀⠀⠀⠀⠀⠀⢀⡞⡡⠒⠒⠚⠀⡸⢸
⢇⠰⠗⠀⠀⠰⠗⢀⠇⠀⠀⠀⠀⠀⠀⢮⠀⠀⠀⠌⡼⠁⠀⠀⠀⠀⠀⠀⠀⢨⡶⡶⠶⠶⣶⢢⠁⠀⠀⠀⠀⠀⠀⠉⠁⢯⡓⣄⢾⡥⠋
⠈⢹⢒⠒⡒⢒⢺⠁⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⣌⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢱⠿⠷⡁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡆
⠀⠸⠼⠦⠧⠾⠼⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠼⠾⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢀⣤⣤⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣎⣁⡉⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀
⣿⠁⠀⣭⢻⡅⠀⢹⡇⠀⠀⠀⠀⠀⠀⡠⠛⠉⠣⠔⢍⢳⠞⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣋⣛⣿⣿⣷
⠹⡆⣀⡜⢧⡀⢠⡾⠁⠀⠀⠀⠀⠀⡎⠒⠀⠄⠁⣠⠞⠊⠀⠀⠀⠀⠀⠀⠀⡞⠹⡇⠀⠀⠸⠈⣇⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⡿⢻
⠀⠚⠋⠶⠦⠙⠮⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠪⡭⠖⠓⠦⠴⠓⠮⢭⠇⠀⠀⠀⠀⠀⠙⠲⠤⢤⡤⠤⠞⠉


⠀⡤⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⡀
⠀⢳⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡋⠉⠉⢑⡄
⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠴⢖⣋⣉⣀⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡤⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⢈⡱⣾⡛⠓⠒⠻⡄
⠀⢸⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠺⠷⣶⣶⣦⣤⣭⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣗⡯⣒⣒⣺⡇
⠀⢧⣠⣴⣖⣒⣈⠆⠀⠀⠀⠀⠀⠀⠐⠒⠒⠦⠤⠭⢭⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡱⠿⣗⣓⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣤⡀
⠀⠀⠀⠀⠀⣀⠤⠶⠖⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠩⠀⡀⠈⣈⢳⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠹⡄
⠀⠀⠀⢀⡞⡁⠒⣀⢁⡀⠆⠙⣆⠀⠀⠀⠀⠀⠀⣤⡤⣤⠴⣷⢴⡤⣤⠀⠀⠀⠀⠀⠀⠀⢀⠧⢀⠀⠀⠀⣀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⡇⠑⢰⠁⠀⢸⠐⠀⣿⠀⠀⠀⠀⠀⠀⢹⡉⠉⠉⠉⢉⠉⡟⠀⠀⠀⠀⠀⠀⠀⠈⢷⠚⡳⠛⡦⣾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⡼⠁
⠀⠀⠀⠘⢧⠈⡀⢙⠛⢣⠀⣠⠇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠙⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡀⢂⢐⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⠃
⠀⠀⠀⠀⠈⠛⠶⠬⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠾⠇

⠀⠀⠀⢀⣠⡤⠶⠶⠶⠒⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡦⣤⢤⣄⡀
⠀⠀⠀⣟⡠⠐⢒⢄⠀⣴⠒⠤⣹⠆⠀⠀⠀⠀⠀⠀⣠⠼⠧⠤⠿⣤⡀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠀⠀⠂⠠⠙⢳⡄⠀⠀⠀⠀⠀⠀⣾⣿⣼⣷⣿⣼⠾⣽
⠀⠀⠀⠸⡴⡩⢊⡉⡜⡇⠛⣠⠋⠀⠀⠀⠀⠀⠀⢘⡧⠒⠒⠖⠒⠺⡅⠀⠀⠀⠀⠀⠀⠸⡧⠤⣤⣤⣤⣤⣤⣤⡇⠀⠀⠀⠀⠀⠀⢹⣿⡇⣿⢸⢹⣾⠏
⠀⠀⠀⠀⠹⣄⣈⣆⢨⣮⣼⠃⠀⠀⠀⠀⠀⠀⠀⠸⡧⢄⢀⠼⡀⣠⠇⠀⠀⠀⠀⠀⠀⢸⣶⣶⣤⣴⣶⣦⣤⣶⣇⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠛⠙⣻
⠀⠀⠀⠀⠀⠹⣏⢡⢦⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣥⣤⡼⠋⠀⠀⠀⠀⠀⠀⠀⠓⣖⡒⠣⠚⠑⠒⠓⣸⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⠿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⠶⠶⠶⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣆⠀⠀⠀⠀⠀⠀⢀⡤⣤⡴⣲⣤⠦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⣼⠀⣗⣇⡽⢿⡄⢹⡀⠀⠀⠀⠀⠰⣯⡻⣿⣿⡟⣆
⠀⠀⠀⡤⢶⠟⠛⠁⠉⠙⠛⢷⣄⠀⠀⠀⠀⠀⠀⢠⠈⢻⣯⣿⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡏⠃⣧⣾⡀⠘⡇⠀⠀⠀⠀⠀⡇⠱⡘⣿⣿⣾⢦
⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠀⢴⡶⣶⣚⣛⣛⣒⡒⣶⠀⠀⠀⠀⠀⠀⢘⡇⠀⢿⣥⡷⠗⡆⢀⡇⠀⠀⠀⠀⠀⡇⠀⠘⢞⢷⣿⣿⣆
⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠈⡇⠀⣿⠿⡤⣿⡇⢨⡇⠀⠀⠀⠀⠀⡇⠀⠀⠈⢣⠻⣿⣿⢦
⠀⠀⠙⠛⠛⠛⠓⠛⠓⠒⠒⠒⠛⠋⠀⠀⠀⠀⠀⣿⢿⣾⣿⣶⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⣦⡦⢿⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠱⡙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⣀⣉⣁⣨⠇⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⢿⣤⠾⠓⠋⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠚⠚⠛⠉
⠀⠀⠀⠀⠀⣀⣀⡀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⢰⠃⠀⠹⡞⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⣀⣀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢹⡄
⠀⠀⠀⠀⣠⣄⣀⣀⣰⣀⣀⣏⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠩⠍⠉⠙⠢⣄⠀⠀⠀⠀⠀⠀⣀⡴⡚⢻⠿⠻⡶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢠⡾⡷⠋⠀⠀⠀⠀⠈⠺⣿⡀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⢸⡇
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⣴⢗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⠀⠀⣿⡔⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢺⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠻⣦⣄⣀⣀⠀⠀⣀⣀⣤⣾⠵⠋⠀⠀⢻⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠹⢤⡤⠞
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠢⢭⣉⣉⠽⠛⠉⠁⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⡀⠀⢀⠀⡀⠀⡠⡀⠠⠀⠀⠀⠀⠀⡀⠀⡠⠀⢀⠐⠀⣀⠁⣀⠄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⡀⢀
⠀⠀⠀⡄⠀⠀⠀⠰⠈⠋⠃⢡⠀⠘⠂⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⣅⡄⣇⡷⠠⡀⢣⡜⠇⡘⠀⣴⡠⡀⠀⠀⠀⠀⠀⠀⠆⣤⠀⠀⠛⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⡆⢏⡃⠸⣱⢇⠙⠄⠑⠐⡆⠆⣸⠃⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠄⠀⠀⠀⠀⠀⠘⠣⣴⡀⡇⢮⠘⣂⡔⢸⣬⢶⣁⢀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠓⠙⠁⠈⠀⠈⠉⣸⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⣭⣁⠒⠠⡀
⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡇⠀⠀⠀⠀⢠⠀⠠⢀⡀⠀⡠⢀⠀⠂⣠⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠂⠀⠦⢤⢤⣤⢶⣠⡾
⠀⠀⠀⠘⠢⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠆⠊⣧⠀⠀⠀⠀⠘⡄⠀⠂⠀⠂⠐⠚⠒⠊⠬⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡈
⠀⠀⠀⡡⠤⣀⠀⠈⠁⠉⠉⠉⠁⠀⠀⠀⠀⢚⡋⣽⠀⠀⠀⠀⠀⠸⠐⠂⠀⠀⠀⠀⠀⠀⠐⠂⠸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠐⠢⠄⢰
⠀⠀⠀⣧⢤⠀⠗⠁⠀⠉⠀⠀⠶⠤⠶⠋⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠉⠈⠱⣦⣁⠀⠀⠀⠀⢀⣀⣠⡀⠀⢀⡴⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⡀⠀⠀⡔⢀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⡉⠁⠉⠀⠀⠈⢁⣠⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠠⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⡆⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⢀⠈⡐⠛⢢⠠⣤⡉⠡⢈⣀⣂⡂⠀⢀⡀⢠⡒⠲⠦⢤⠄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠢⣤⣠⠔⠁
⠀⠀⠀⠀⠀⠀⣆⠘⠉⠀⠀⠉⠁⠀⠀⠓⠦⠖⢠⠄⢀⡙⡤⠀⢀⠈⠀⠻⡄⠀⢁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠀⠘⠁⠈⠁⠈⠁⠈⢣⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠳⢇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⡀⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠃⠄⠒⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠠⠀⢀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌

⠀⠀⢀⠔⠒⠈⠉⠁⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠋⣛⣶⡄
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⡒⣻⠧⠜⣡⠖⠉⣨⠵⣿
⠀⠰⠤⠀⠀⠤⠄⠀⠀⠀⠀⠠⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣞⠹⠉⠀⠥⠬⠴⠖⢋⣡⠔⠋⠀⠀⠀⡇
⢈⡄⠀⠠⠄⠀⠀⠀⠀⠀⠠⠤⠶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠄⠀⠔⡇⠀⠀⠀⠀⠀⠀⠀⠀⡌⣰⠖⠀⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⡴⠁
⠀⠟⠉⠒⠂⠒⠐⠃⠛⠖⠰⠚⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠚
⠀⢞⠉⠉⠀⠒⠒⠒⠒⠒⠒⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠒⠒⠒⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠐⠒⠒⠉⠁
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠤⠀⠠⠄⠤⠄⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠓⠤⠀⠀⠀⠀⠀⠀⠤⠄⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠀⠀⠀⠀⠀⠀⠀⠀⠬⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠒⣍⣱⡞⢉⢹⡉⣧⡀
⠀⠀⠀⠀⠀⡔⠓⠚⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⡉⠘⣀⡀⠀⠁⠀⢙⣉⡗
⠀⠀⠀⠀⢀⡗⠒⠦⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠏⠈⠀⠁⣉⣠⠋⢃⣬⡀⠷⡀
⠀⠀⠀⠀⡼⠂⡊⢳⠄⠱⡄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠶⠒⠒⠳⠲⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠢⡤⠤⡥⠤⢤⡤⣤⢤⠖⠁
⠀⠀⠀⣾⠀⠀⠉⠈⠀⢀⠡⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠞⢈
⠀⢀⣞⠉⣀⣀⠀⠀⣄⠀⣹⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠸⠀⠀⠀⢂⠋⠀⠉⠁
⠀⡜⠁⠀⢣⣬⡥⠶⠞⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠆⠈⠀⠀⠀⣼
⠀⠓⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠩⠭⠥⠬⠭⠭⠋

⠀⠀⠀⠀⠀⠀⣀⡤⢶⡛⠓⠦⣀
⠀⠀⠀⣠⠴⠋⠁⠐⢏⡽⠂⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢚⡉⣉⡁⠒⠢⣄
⠀⣴⣏⣥⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣉⠤⠤⠤⠤⠬⣑⠚⢷⡄
⠀⣧⣀⣀⠤⢄⡀⢀⣠⠤⠤⣀⣠⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠕⠀⠄⠐⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠔⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿
⠀⢏⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠠⠤⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡏
⠀⠈⠉⠈⠑⠒⠒⠒⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠲⠐⠒⠒⠀⠈⠅⠐⠀⠀⠀⠉⠈⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠉⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⡴⢀⡖⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣏⡁
⠀⠀⢀⣀⣀⣀⠀⠄⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢩⠈⡋⠉⠀⠑
⠀⠘⡥⣤⡒⠒⠒⠀⠀⠐⠒⢤⣷⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠉⠉⠉⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡎⠀⡇⠀⠃⠀⡀⡀
⠀⠀⢱⡀⠀⠈⠉⠉⠉⠉⠉⢸⡟⠹⡼⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠤⠀⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⡀⠀⠀⡀
⠀⣠⠀⠱⣦⢀⣀⣀⣀⡀⢶⡇⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠋⠋⠀⠀⢀⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠀⠈⠁⠈⠁⠀⢁⡖⠀⢁
⠘⠦⣤⣤⣈⣁⣀⣀⣉⣉⣁⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠐⠂⢀⠀⣉⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⢠⠘⠀⠖⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣥⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣤⣤⣴⣶⣤⡴⠂⠀⠀⠀⡀⠀⣀⣀⣀⡀⢠⣄⠀⠀⠀⠀⡀⠠⠀⢐⡒⢦⠀⠀⠀⠘⢶⣶⣶⡦
⠀⢺⣿⣿⣿⡿⠁⠀⢀⢔⢔⡝⠂⢉⣁⡤⠞⢉⡻⠸⢤⣤⣄⡀⡏⠉⠀⠀⡄⠚⠂⠠⡄⡄⠈⠹⣿⣇
⠀⣿⣿⡟⠁⠀⠀⠀⠀⢀⣈⣙⡍⠁⠀⠀⠀⢸⠀⠀⣠⣤⡄⠀⠠⢀⣄⡀⠇⠀⠀⢀⠇⠀⠀⠀⠈⠃
⠀⢹⣿⠀⡀⡐⣠⢞⣫⡍⠙⠁⠶⣾⠆⠠⠄⡈⡀⠀⣿⢿⠁⣀⠠⠻⣻⠏⠒⠤⠤⠼
⠀⢸⡇⠀⠸⣇⠘⣧⣁⡁⠀⣀⣤⣔⡂⡐⠉⠁⠙⢈⡧⠀⣹⢃⣤⠀⡇
⠀⠈⠇⠀⠀⠋⢀⡿⠮⠤⢄⡰⢤⣄⠉⠁⣠⣔⡪⡥⠖⠛⣏⠧⠀⠊
⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⣰⠬⠖⡶⣻⠉⠉⢁⣠⠶⢖⡫⡵⠾
⠀⠀⠶⠋⠀⠀⠀⣀⣀⣁⣤⣤⡬⠾⠴⠖⠚⠭⠒⠊⠁⠁
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⢀⣀⡀⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⠀⠀⠀⠀⠀⡴⠒⢦⠀⠀⠀⠀⠀⢀⡤⡤⠒⡶⣀⠤⣤
⠀⠀⠀⠀⢠⠞⠁⠀⠄⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⣠⣖⣚⣓⢳⣄⡀⠀⠀⠀⣞⡉⣙⣏⣱⡀⠀⠀⠀⢠⡓⠁⣼⠑⣏⣜⢛⣭⡗
⠀⠀⠀⠀⢸⠔⢒⡒⢒⣒⠒⣲⠂⢼⡀⠀⠀⠀⠀⢧⠤⠤⠤⠤⣤⠇⠀⠀⠈⢳⢮⣉⠖⢺⠁⠀⠀⠀⠀⢯⠒⠃⠧⠘⠚⠉⢠⠃
⠀⠀⠀⠀⠘⡯⠥⠬⢕⣖⢛⣤⣭⡞⠀⠀⠀⠀⠀⠸⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⣏⡬⠛⡏⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠘⠦⠤⠤⠽⣌⡽⠞⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡭⡞⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠔⠒⠚⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠉⠉
⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠤⣀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⢀⡠⠄⠠⡤⢄⡀
⠀⠀⠀⠀⢠⢊⣡⢚⡖⠒⢒⣤⣷⢮⠙⡄⠀⠀⠀⢰⠋⠀⡀⠀⠱⠀⠀⠀⡎⠘⢃⠰⠂⢚⢙⡄⠀⠀⣀⣠⣖⣒⠤⣀⡀⠤⢠⣄⡀
⠀⠀⠀⠀⡇⢇⢨⢳⠆⣔⣙⣯⣥⡀⣇⡇⠀⠀⠀⢸⠀⠤⠀⠂⢠⠃⠀⠀⠹⠙⡍⢻⠙⢫⠻⠀⠀⠀⢧⡜⠛⠻⢟⡛⣛⠿⡛⢧⡕
⠀⠀⠀⠀⢣⢮⣈⠁⠠⡀⠜⢡⠏⡕⠀⠀⠀⠀⠀⠈⢄⠀⣀⢁⡎⠀⠀⠀⠀⡇⠁⠨⢀⢃⠇⠀⠀⠀⠀⣇⠀⠄⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠈⠢⣘⠒⠳⠷⠒⣃⠴⠁⠀⠀⠀⠀⠀⠀⠀⢹⡉⠏⠀⠀⠀⠀⠀⠈⠉⠒⠉⠉⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡯⠽⠂⠀⠀⠀⠀⠀⡤⠤⢤⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠙⡏⢏⣸⠵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡤⡒⠒⣒⠢⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣧⣘⣆⣀⡀⠀⠀⠀⠀⠀⡇⠘⡷⠒⢻⡀⠀⠀⠀⢠⠒⢤⣴⠊⣙⠢⡀
⠀⠀⠀⠀⢀⡜⢊⠝⠛⠥⠑⢍⣳⣄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⣿⣛⠄⠀⠀⡔⠁⢸⠀⠀⠀⠈⡇⠀⢠⠃⢹⠀⠈⢣⢣⠀⠘⠆
⠀⠀⠀⠀⢼⣡⠃⠀⠀⠀⠀⠀⠙⣾⡀⠀⠀⠀⡤⠧⠠⠤⠤⠴⠾⠯⡤⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢰⠀⠸⣄⡸⡄⠀⣸⠸⢀⡤⠃
⠀⠀⠀⠀⢸⠡⢀⣀⣀⣀⠈⠤⠄⡸⠀⠀⠀⠀⠑⠒⠐⠒⠒⠒⠒⠈⠁⠀⠀⠀⠧⡀⣠⡆⢀⣀⠀⢸⠀⠀⠀⠈⠳⠞⠉⠑⠋
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡦⠀⠀⠀⠀⠀⠀⢠⠤⡶⢶⢤
⠀⠀⠀⠀⠀⡠⠊⠁⠈⢢⠀⢏⠉⢢⡀⠀⠀⠀⠀⠸⡇⢣⠀⠀⠀⠀⠀⠀⡼⢢⣷⡯⠛⢢⠀⠀⠀⢀⡤⢄⣀⠤⢤⡀⠤⣄⡠⣄
⠀⠀⠀⠀⣸⢧⠀⠀⠀⠀⢳⠚⠒⠶⠃⠀⠀⠀⢰⠓⠛⠊⠳⡄⠀⠀⠀⠀⢡⢈⡜⠁⠀⢺⠀⠀⠀⢸⠀⠘⢁⣀⡘⢀⣀⣋⣀⢉⡄
⠀⠀⠀⠀⡧⣄⠑⡦⣄⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⢫⠉⡆⡰⠁⠀⠀⠀⠀⢸⡜⢀⠀⠁⢸⠀⠀⠀⣟⡭⢟⡓⢒⣚⠓⣒⢏⣒⢮⡹
⠀⠀⠀⠀⢱⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠚⠁⢇⠀⠀⠀⠀⠀⢠⠁⠀⠠⠀⠌⡆⠀⠀⠘⠭⠥⠌⠉⠤⠍⠒⠒⠓⠊
⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⣀⣀⣈⠇⠀⠀⠀⠀⠀⢆⠤⠖⠒⠶⠃

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡴⠖⠀⠐⠒⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠧⢐⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⢀⡞⠓⠂
⠀⠀⣰⠊⠀⠀⠀⠀⠀⠠⠀⠀⢳⠆⠀⠀⠀⡠⠚⠁⠐⠁⠀⠄⠉⠂⢄⠀⠀⠀⠀⢸⢡⣤⣤⣤⣤⣤⣼⣵
⠀⢠⢉⠀⠀⠠⠀⠀⠀⠀⠀⠀⢨⡇⠀⢀⠊⢄⢀⠍⣀⠀⠐⠴⠀⠀⠀⠉⠢⢀⠀⠸⢄⠈⠉⣍⣉⣉⠁⠈
⠀⠸⢸⣄⠀⠀⢀⣀⡀⠠⢄⣤⣾⠟⠐⠀⠢⠀⠈⠦⣍⠠⢄⣈⠁⢀⠀⠒⢂⠀⡁⠀⠀⢈⠂⠘⠋⠠⡤⠆
⠀⠀⠀⠻⠘⠓⢒⣲⠒⣊⠩⠟⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠐⠚⣈⣀⠚⠁⠀⣆⠻⢴⣄⣤⣴⡇⡂
⠀⠀⠀⠀⠈⠒⠒⠰⠐⠒⠚⠉⠀⠀⠀⠀⠀⠀⢀⠀⠜⢧⠢⢤⢀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠒⠈⠀⠬⠤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠘⠀⠀⢣⠻⡔⠷⣤⡀⠀⠀⠀⠀⠐⠄⡀⠀⠀⢀⠸
⠀⠀⠀⠀⢀⡀⣠⣶⣾⣿⣶⣤⠄⠀⠀⠀⠀⠀⠠⠃⢀⡀⢀⠑⠂⢄⡤⠐⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀
⠀⠀⠰⢶⡍⣷⣾⣿⣿⣿⡟⣹⣿⠀⠀⠀⠀⢠⢁⠔⣁⢀⠀⡑⢎⠉⠈⢲⠀⠀⠀⠀⣀⣄⣲⢭⣻⠮⠽⠓⠖⢄⡄
⠀⠀⠠⠶⢿⣿⣿⣿⣿⣿⣯⡝⢱⠀⠀⠀⠀⠁⠘⣈⣾⡾⣿⢸⢹⠆⡰⠃⠀⣠⠦⠳⢮⠿⠛⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠐⣇⠀⢩⠙⠒⠘⠚⠉⡀⠘⠀⠀⠀⢎⢦⡐⠓⠄⡐⢀⡠⠂⠠⠁⠀⢰⡇⠀⠀⡌⠀⠀⠀⠀⣀⢤⡴⠄⠈
⠀⠀⠀⠀⢂⠀⢣⠀⡀⢰⡀⡀⠠⠀⠀⠀⠀⠑⢌⠲⠤⣀⠀⠂⡡⠁⠀⠀⠀⠳⢀⠊⢀⠁⠄⠐⠂⠉
⠀⠀⠀⠀⠀⢳⠀⢂⠈⠁⡀⡀⡀⡀⠀⠀⠀⠀⠀⠈⢐⠂⠍⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⢆
⠀⠀⠀⠀⠀⠈⠣⠤⠦⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠊⠉⣁⠵⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢚⣑⡶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣎⠂⠀⠠⠁⢂⣸⡀
⠀⠀⠀⠀⠀⢀⠠⠤⠶⢶⡲⢤⣀⠀⠀⠀⢰⣇⡼⣿⡿⠡⠄⠑⠦⡀⠀⠀⠀⠀⠀⠀⢠⠒⢀⣀⠀⠬⡔⠬⢇
⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠈⢀⠙⢧⡣⠀⠀⢕⢄⠀⠀⢀⠀⠀⠀⠈⠂⣑⠄⠀⠀⠀⠘⠖⠐⡀⠀⠐⠂⡉⠜⡀
⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⡇⡈⢻⡄⠀⠀⠀⠁⠠⡀⠀⠀⠀⢠⡎⡤⠗⣦⠀⠀⠀⠢⡁⣀⡀⡐⣀⠈⠄
⠀⠀⠀⠀⠑⠂⣤⣀⠀⠀⠀⡀⢁⠀⣸⠇⠀⠀⠀⠀⠀⠈⠒⢄⠀⡾⠋⠁⣠⢯⠀⠀⠀⠀⠃⢶⡰⢆⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠜⠛⠁⠁⠀⠀⠀⠀⠠⣊⣱⣊⡒⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣧⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢌⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⢰⠀⠀⠀⠀⣀⣑⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⠄⠸⡄
⠀⠀⠀⠀⢀⠀⠀⠀⠙⢤⠌⠀⠀⠀⠀⢹⠀⢐⡤⠐⠒⠠⠤⣄⣰⣦⣄⡀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠈⡆⠀⠀⠀⢄⣀⠀⠀⠀⠀⣧⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠷⡄⢸⠁⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠀⠀⠀⢰⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠀⣀⠧⠐⣛⢠⣄⠒⠦⣀⣀⠀⠀⠀⣀⣤⣤⡤⠤⠤⠝⣄⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢋⣁⡤⠋⠠⠀⢻⠀⠀⠈⢷⠈⠑⢦⠀⠀⠀⠀⠀⠀⠁⢸⡆⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢀⠞⣴⠉⠀⠐⣀⣤⣔⠈⡛⠲⡄⠘⡦⠀⢀⡱⡤⢴⣖⠒⠲⡀⡀⠠⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⡞⠀⣸⠀⠀⣾⠋⠀⢈⡇⣉⢀⡟⢰⣧⣞⣱⣾⣷⣟⣿⣄⠴⢣⡞⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⡇⢀⡟⠁⠀⠻⢦⣤⣾⣿⡏⣿⠀⣼⢁⠉⠀⠁⠀⠀⠀⢀⣀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⠀⠀⢷⠸⣇⢜⣈⣁⠒⠛⣭⠖⠋⢁⣼⠿⠷⢤⣠⡤⠂⠁⠀⠀⠈⠉⠙⢦⡀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⡉⠁⠈⠛⠓⠋⢀⡴⢿⡙⢿⠅⠀⠹⡁⠀⠀⠀⠀⠀⠀⠀⢠⢹⡍⣉⡉⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠚⠋⠉⠰⠶⠒⣦⠀⠀⢀⡗⠀⠀⠀⠀⠀⠀⠀⠐⢠⠇⠓⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠥⠴⠞⠙⠢⢄⣀⠑⠀⠀⢂⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠃⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠌⠓⣦⣌⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣍⣳⢴⡶⣿⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣯⣹⣶⣆⣻⣔⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠤⣄⠀⡀⣀⠀⠀⠰⠀⠀⠀⢄⠀⣸⡠⠤⠔⠒⠒⠒⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡔⠐⢮⠯⡄⢨⡇⠀⠀⡆⠈⠂⠈⢳⡇⢀⠀⠀⠀⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⡠⠚⣈⠷⠀⠀⠐⠧⣜⣦⣄⣀⣧⠈⡀⣸⢫⠣
⠀⠀⠀⠀⠀⠀⢰⡃⠸⣁⣀⡀⢀⠀⠀⡏⣦⣩⡉⠂⢀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣠⠙⠒⢢⡀⠃⠃⢀⡠⠟⠋⡉⠉⡁⠙⠚⠿⡀⠠⠂⠀⣆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠁⢠⠀⠈⣇⠀⣠⠏⢀⠀⠈⠁⠀⠀⠀⢀⠀⠈⠳⡄⢠⣧⡃⡄⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⡀⠀⠛⠶⠷⠞⠓⢒⡎⠀⠄⠈⡀⢀⡀⠀⢠⠀⡀⠈⠻⠟⠁⢹⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠸⣿⡶⠟⠋⢀⣤⠠⣼⡧⣀⣠⠀⠴⣿⣿⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠉⠭⣅⣀⣤⡀⡀⣰⠗⠒⠒⣿⠁⠀⠀⠀⢈⡿⣿⣿⣿⣿⣟⣀⠠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠈⠳⠤⢤⠴⠟⠁⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⢀⠀⠀⠀⢀⡀⠀⠠⡀⢀⢄⠐⡀⡀
⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡄⠁⠰⠘⡄⠸⡀⠀⡁⡄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⣀⠀⠀⠐⠈⠒⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠉⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢡⠀⠀⠀⠁⢀⠀⠀⠀⠇⠀⠣⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠀⡀⠀⠄⠠⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⡜⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠁⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⡅⠀⢀⠀⠆⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⢠⠁⢰⠀⡌⠀⡆⠀⡇⢠⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡀⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⠀⠁⠀⠃⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠀⣁⠄⠀⠀⠄⠈
⠀⠀⠀⠠⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠀⠈⠀⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠹⠀⠈⢀⠤⠊⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⣈⠠⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠄⠀⠀⠀⠘⢀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣠⡀
⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⠈⠁⠢⡀⠀⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⠀⠠⠊⠀⠈⠀⠂
⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢆⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠀⠀⠀⠀⡀
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠁⢄⠀⠀⠃⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⢀⠀⠈⠐⢀⠀⠀⠈⠀⠀⠠⠇⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠄⠂⠀⠈⠌⠐⠀⠢⠀⠀⡘
⠀⠀⠀⠆⠀⠀⠀⢀⣀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠐
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠈⠃⠀⢀⣀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠀⣤⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢈⠀⠈⠁⣴⡟⠺⡝⡌⡇⣏⢢⠆⠐⠀⣊⠀⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠇⠀⠀⠀⠀⠠⠄⠀⠈⠊⠀⠀⠀⡀⡙⠀⢵⡘⡇⠙⠆⠀⠀⠁⣉⠀⠆⠳⠔⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⣠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠘⡄⠀⠀⠀⡑⠠⡀⠰⠞⢁⣳⡸⠂⢁⡀⢅⠉⢀⢤⢒⠬⢙⣀⣀
⠀⠀⠀⠀⠀⠀⡔⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣐⡀⠜⠋⠛⡉⠂⣎⢲⣿⠋⢳⣶⠟⠁⠃⢧⣍⢽⣃⠐⡩⠛⠁
⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠘⡂⣄⠀⠸⠀⠘⡜⠃⡀⠀⢙⡁⠀⢘⡍⢀⡤⠒⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⠉⠉⠘⠲⣄⠀⠀⠘⣤⣇⠋⢿⡄⠀⠀⡷⠋⠀⠠
⠀⠀⠀⠀⠐⢦⣓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡄⠀⠀⠀⠙⠦⢀⣻⣦⢐⣀⡽⠘⠊
⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢱⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠳⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣤⠀⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢈⠠⠀⠀⠀⠀⠀⠀⠀⢇⢹⠀⠀⠀⣀⢀⡀⠀⠀⠐⠒⠒⠂⠂⠀⠀⠀⠀⣀⠔⢂⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⣄⠀⠀⠀⠀⠀⠈⠙⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⡡⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣁⣠⠦⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠠⠛⠋

⣿⣟⢻⡿⢿⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢶⠂⠈⠁⠛⠓⠀⢰⣤⣴⣚⠀⠙⢛⣩⡤⠒⢪⣿⠋⠐⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣦⡀⠀⠛⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⣴⣇⡀⢀⡀⣄
⠀⠸⠀⠠⠂⠐⠄⠀⠈⠁⣠⡤⠀⠀⠘⣿⣿⡛⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠳⠧⠈⣛⣿⣀⠀⠠⢤⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢿⠿⣟⣀⣀⣿
⠀⠀⠀⠀⠀⠀⢈⢷⠀⠂⠸⠿⠀⠀⠈⠉⢻⠉⠀⠀⢠⣸⣇⣤⠀⠀⠀⠀⠘⠏⠛⢑⠦⠈⠉⢙⠛⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠸⢌⣉⡉⠉⠈
⠀⠀⢻⡁⠆⠀⠀⠈⡇⠀⠛⠛⠋⠀⠀⠀⠉⡇⠀⠠⠘⠏⠀⢙⠀⠀⠀⢡⣤⣄⠀⠘⢀⠉⣠⣭⡨⣇⢉⣆⠀⠀⣾⣳⡄⠀⣸⣷⡄⠀⢀⠡⣿⢿⠂⣤
⠀⠀⠘⡅⠀⢀⢀⠐⠁⠀⠀⡀⠀⠀⠀⠀⣤⠃⢠⠄⠀⡀⠀⠈⢲⣿⣾⢺⢻⡗⠀⠀⢀⡀⠉⠛⠁⢿⠘⠯⠃⠀⢩⣦⣄⢟⡈⠿⠤⠶⢾⣴⣿⣏⣴⠏⡆
⠀⢸⣤⣤⣀⡐⣆⠘⠂⠀⠀⣤⣤⡀⠀⢀⣹⣡⣴⣦⣸⣧⠀⠀⢸⣷⠀⠼⣿⠇⠀⠀⠈⠃⠀⠀⠀⣾⣧⠘⢀⠀⠏⠻⠿⢻⠒⢐⣆⡀⠉⣽⣿⣿⠃⠀⠈
⠀⢰⡗⠃⠸⠁⣶⡄⠐⠀⢠⣿⣿⡇⠀⠀⠀⠀⠈⠁⢉⣹⣧⡀⣼⡿⠀⠐⠃⠀⢙⣦⣤⣠⠰⣶⢾⠃⠀⠀⠀⠀⡐⠓⠻⢈⠀⢈⡁⡃⠀⢹⣿⡟⢶⡀
⠀⠞⠹⣹⠀⠀⠈⠒⠂⠀⢸⣿⣿⠁⠀⡄⠀⠀⠀⠀⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠈⣯⡇⠩⡄⠠⣭⣀⣠⣤⣤⡀⠀⠳⡀⠐⡾⠟⠐⠄⠀⠈⠉⠉⠀⠨⣄
⢠⡏⡗⠈⠀⠉⠉⠍⠀⠀⣸⣿⣿⠀⠠⠀⠀⠀⠀⡀⠠⠀⠀⠀⠂⢀⣁⣺⡇⠀⠀⠨⠤⠀⡠⠀⡀⣠⣵⣿⣧⡀⠀⠀⣈⣉⡄⡎⠀⠀⠀⠀⠀⠀⠀⡚⡛
⢸⠆⣀⣶⣶⡄⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡭⠞⠹⠁⠀⠀⠘⡇⠀⠉⠙⠓⠏⢷⣿⣿⣿⡀⠀⡠⣄⢁⠀⠖⠀⠀⠀⠀⢰⡀⠽⠇
⠈⣼⣿⢿⠛⣻⠀⠀⠀⠀⣿⣿⡇⠀⠀⣄⢀⠀⠀⠂⠠⠀⠀⠈⢁⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠘⠋⠃⣀⣽⠙⠻⠁⠀⠁⠁⠘⠀⠀⠶⠀⠀⠶⠌
⣧⠘⠇⠈⢨⠏⠀⠀⢠⡜⣉⡁⠤⠢⠀⠼⠻⣄⣠⡎⠠⡄⠐⠛⠄⠀⠀⢀⣿⣧⢀⣠⠀⠀⠠⠆⢀⡀⠻⠟⠀⠀⠀⠒⠀⣀⡀⠀⠀⠀⠀⠀⠀⠆
⣿⡃⢠⣀⢀⡄⠀⠀⠀⠀⠘⠆⠀⢠⠀⠀⠄⢉⡋⠀⠈⢄⠄⠘⠁⠀⢀⡀⠙⠃⡟⣇⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠄⡄⡀⠀⠘⠓
⠀⠁⠀⠙⠋⠁⠀⠀⠀⠈⠀⠀⢶⠄⠀⠀⠠⠀⠄⠀⠀⠉⠀⠀⠀⣤⠟⡲⣤⠀⢻⣿⡇⠋⠄⣀⠐⡀⠰⣇⠀⠀⠀⠀⠀⡻⠟⠛⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠀⣠⠀⠠⠄⠟⠗⢰⢀⣠⣼⣶⣶⠔⣿⡿⡉⠂⣿⡿⠛⢏⠂⠛⠃⠻⢷⠆⡀⠀⠀⠃⠀⠁⠀⠈⠀⠈⠂⠐⠤⢀⣰
⠀⠀⠀⠀⠀⠠⣤⠀⠀⠒⠀⡀⠈⡿⠀⠀⠐⠿⠇⢈⡶⠿⠿⠿⠿⠦⠿⠶⠷⠶⠾⠷⠶⠴⠶⠶⠶⣮⡉⠀⠀⠀⠀⣴⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣾⡇⠀⠀⣿⢶⣶⣖⠶⠀⡶⠿⠦⢾⣲⡆⠀⠀⣿⣿⣾⣷⣿⣶⣾⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶
⠉⠉⠉⣍⣉⣍⣉⣉⠉⣍⣉⣉⣉⣉⣉⣉⡍⠉⠉⠉⠀⢠⠦⣤⣦⣤⣤⣤⡤⠰⣶⣄⣤⣤⡴⣄⠀⠉⠉⠉⢉⣉⣉⠉⣉⣉⣉⣉⡉⣍⣉⣉⣉⣉⣉⡉⠉
⣤⣤⣤⣭⣭⣬⣭⣬⣤⣥⣭⣭⣤⣭⣭⣭⣥⣤⣤⣤⡀⠈⠉⠉⠁⠉⠉⠋⠉⠈⠉⠀⠁⠉⠈⠁⠀⣠⣤⣤⣭⣭⣥⣬⣭⣭⣬⣭⣤⣭⣥⣭⣭⣭⣬⣥⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⣦⡀⣇⠀⣿⠀⢠⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠈⢹⡿⣿⣆⣿⣴⣿⣿⣏⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⠀⠠⢀⣿⣿⣿⣿⣿⣿⣿⢿⣿⣦⢙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣺⣿⣿⣿⣾⣧⣶⣮⡄⠹⣿⣿⣿⣦⡀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⡐⠀⠀⠀⠀⠀⠀⠀⠐⡀⢹⣜⣿⣿⣿⡏⠛⢟⣙⣿⣯⣦⡀⠀⠹⣿⣿⣿⡷⣀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⣿⣿⣿⣿⡇⣶⣿⣿⣿⣿⣎⢰⢹⣦⡌⢛⣭⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢉⣟⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣦⣝⣿⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣗⠧⣦⣄⠀⠀⢀⠐⠀⠀⠀⠀⢰⣧⣺⣏⠻⣿⣿⣿⣿⣿⣿⣧⡘⢿⣾⡛⣿⠝⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠫⢇⡀⠘⠿⣆⠠⠀⡄⠆⠀⠀⠀⠰⢺⣿⣿⠄⠀⠙⣿⣿⣿⣿⣿⣷⡸⣿⣿⡙⢀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣷⡡⠀⠀⠀⠉⢳⣤⣭⣁⢀⠀⠠⣹⣞⣾⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⢿⣿⡏⣼⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢿⡇⠠⠀⠀⠀⠀⠈⠙⠟⣿⣿⣾⣤⣿⣿⠀⠀⠀⠀⠀⠰⠀⠈⠉⠉⢁⣾⣿⣷⢹⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣟⠋⠳⣆⡦⠠⠀⠂⠀⠦⠴⡩⢉⣙⣿⣿⠃⠀⠀⠀⠀⠀⠀⠑⢠⡀⣰⣿⠛⣿⢫⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣿⡠⠤⡛⢓⢄⠀⠀⠐⠨⣤⣽⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣱⣾⢔⢡⠂⠢⡥⣿⣧⣤⢒⣾⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣴⡈⠄⡭⣀⢝⣽⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣽⣵⣳⣧⡼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣾⣽⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢄⡀⠠⠀⢀⠐⠦⣀⠀⢀⣅⡄⠀⠀⡤⠒⠀⠀⠤⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠓⠀⢍⠒⠉⠁⠀⠉⠀⠀⣬⣆⠀⠉⠀⠀⠁⠐⢢⠄⠘⠁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢔⡲⠏⢐⡛⠆⠀⠐⠀⠀⠀⢰⡏⠛⡟⡄⠀⠈⠀⠐⠀⠠⠟⣒⡈⠖⣲⠥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠣⣤⡂⠝⠪⠁⠁⠀⠀⠀⠀⠀⠸⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢉⠛⠄⣠⣴⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢙⢘⡯⠶⠚⠛⠻⠿⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀⠛⠁⡛⣘
⠀⠀⠀⠀⠀⠀⠀⠌⠕⠉⠀⠀⠀⠀⣀⠠⠀⠈⠙⣷⢆⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⣤⣖⠲⠓⠨⠟⠈⢠⣤⣑⢍⡄
⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠀⠀⠂⣀⠈⠀⠀⠀⠀⠈⣿⣷⠂⠀⠀⠀⢀⠰⣷⣼⣆⢬⣸⣿⠦⣕⠶⡶⢶⣵⣷⡁⢊
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⠀⠀⠈⢩⡞⠀⠀⠀⠀⡶⣿⡍⣽⢸⣣⠷⠰⣿⣷⣶⣼⣷⣬⠀⡭
⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⠀⠀⠰⠉⢀⠐⠀⠀⠀⠀⢀⡫⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⣠⣼⣿⣿⠿⡿⠟⢈⡁
⠀⠀⠀⠀⠀⠀⠀⢹⣇⣀⡠⠒⠙⠈⠀⠀⠀⠀⠀⡐⣼⠃⠀⠀⠀⠀⠀⠘⢻⣿⣿⠨⡮⠏⢉⠙⠇⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⡻⠁⣹⣦⣄⣀⡜⠀⠀⠀⣀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⡫⣴⣄⣀⠀⠀⠀⡀⠀⠐⠀⠨⠁
⠀⠀⠀⠀⠀⣠⣎⢠⠈⠀⠀⠉⠙⠛⠛⠛⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠐⠂
⠀⠀⠀⣠⣾⣿⡿⠃
⠀⣠⣞⣱⣿⠏
⠾⣥⣾⠟⠁
⣶⡿⠋
⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢰⣿⣿⡆⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⠀⠀⠀⣠⣶⣦⢰⡇⢰⣶⣦⡀
⠀⠀⢀⣤⣭⣭⣤⡀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⢻⣿⣁⠀⠀⠀⠀⣼⣿⣿⡿⣼⢧⡼⣿⣿⣷⡄
⠀⠀⣾⠟⢉⡍⠿⣷⠀⠀⠀⠀⠀⢿⡟⣷⣤⣴⠇⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠈⠈⠉⠁⠀⠙⠛⣿⣿⠀⠀⠀⣸⣿⣟⣄⣾⠀⠀⣶⢦⣜⣿⣿
⠀⠀⣿⣾⣿⣿⡇⣿⠀⠀⠀⢀⣴⣿⣿⣿⣿⡛⣠⣾⣶⣄⠀⢈⠉⣿⣿⣿⠀⠀⠀⣀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⣿⣿⣯⣿⣿⡇⠀⣿⣿⣧⣿⣿⡇
⠀⠀⠛⣽⣿⣿⡇⠛⠀⠀⣴⣿⣿⡏⣻⣿⣿⣿⣿⣉⣙⣿⣷⣘⣈⣇⣸⣿⣃⣀⣾⣿⣿⠀⠀⣤⣾⣿⡟⠃⠀⠀⢸⣿⣿⣿⠿⠟⠁⠀⠙⠿⢿⣿⣿⣧
⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⠉⣿⣿⣟⢿⣿⡿⣿⣿⡿⣿⣿⡿⣿⢿⣿⣿⣿⣿⡿⣻⣿⣿⠀⠀⢻⣿⡟⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛
⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠿⠿⠟⠛⠛⠛⠛⢻⣿⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⡄⣤⣰⡂⠐⢠⡄⣦⠐⠐⢰⡄
⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠐⠒⠒⠓⠂⠃⠒⠐⠓⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠁⠈⠀⠁⠈⠀⠁⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣤⣄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠔⠊⢀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⣾⡿⠷⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣤
⠀⠀⠀⢀⣠⣸⣿⢿⠆⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⠂⠀⠀⠀⠀⣠⣬⣶⣧⣄⠀⠀⠀⠀⣴⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄
⠀⠀⠺⢿⣿⣿⣿⣦⣾⠂⠀⠀⠀⠀⣀⣤⣤⣿⣿⡆⢀⠀⠉⠁⠀⠀⠀⣿⣿⣿⣿⠛⠃⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠰⠶⠟⠛⣿⣿⣿⡟⠛⠷⠆
⠀⠀⠀⣾⣿⣿⡏⠹⠋⠀⠀⠀⣠⣾⣿⡿⢻⣏⣯⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⡇
⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠻⣿⣿⣧⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⣀⣠⣤⣤⠀⣿⣿⣿⡇
⠀⠀⠀⠀⣸⣿⢿⣿⡇⠀⠀⠀⠀⠈⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢻⡿⢿⠟⠀⣿⣿⣿⡇
⠀⠀⢰⣾⠟⠁⢸⣿⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠁⢀⣛⣉⣛⣁⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠙⠈⠙⠀⠁⠈⠉⠁⠀⠀⠀⠀⠈⠁⠁⠉⠉⠉⠀⠀⠀⠀⠉⠁⠉⠈⠁⠀⠀⠀⠀⠉⠙⠁⠈⠁⠀⠈⠀⠉⠁⠉
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⣤⡀
⠀⠀⠀⠀⠸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣏⣤⣤⣄⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⡇⢴⢙⡶⢀⠀⡇
⠀⢐⣆⠀⣾⣿⣿⣷⣶⡀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⢠⣶⣷⣭⣿⠟⢽⠉⣿⠀⠀⠀⢻⡿⣿⠀⠀⠀⠀⠀⠀⠃⠀⢠⣤⠄⠀⠃
⠀⠸⠟⠻⢿⣿⣿⣿⠉⠁⠀⢀⣴⣮⠋⢉⣷⠄⠀⠠⠠⠀⠀⠈⣹⣿⣿⣿⣶⣾⣦⣧⠀⠀⣴⣶⣄⣀⣤⣶⠀⠀⠀⠀⢠⡤⠤⢧⣤⣤
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⢠⣿⣿⠟⣻⣋⣹⣏⣀⣀⣀⣂⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⠉⠉⠉⣀⣀⠀⠀⢀⡘⠛⠻⠿⠿⠿⠂⠒
⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡷⠀⠀⠀⠀⠘⣿⣿⠀⢰⠀⣿⣿⠇⣾⣿⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐
⠀⠀⠀⠀⢸⣿⣿⣿⠀⢰⣶⣶⣦⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⠁⣿⣧⠀⠀⠀⠀⠀⠈⣿⡇⢸⣶⣾⣿⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇
⠀⠀⠀⠀⠸⣿⠻⡿⠀⠼⠿⣿⠿⠀⠿⡿⡿⠿⠿⠿⣿⠿⠇⠀⠸⡿⠀⠸⡿⠀⠀⠀⠀⠀⠀⣿⡇⢸⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⢹⡇
⠀⠀⠀⠀⠖⠠⠀⠂⠄⠀⠀⠀⣀⣀⣀⡀⢀⣀⣀⡀⠀⠀⠀⠀⡀⣀⡀⢀⢀⣀⣀⣀⠀⠀⢸⣿⠃⢸⣳⠄⠀⠀⠀⠀⠆⠤⠤⠤⠤⠠⠄⠀⠀⠀⠀⢸⣳
⠀⠀⠀⠀⠐⠒⠃⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⢶⣶⣶⠶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⠀⠀⣿⡏⢹⣿⠀⠀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⢻⣇⢀⣿⡟⢻⣿⡀⣼⡟⠉⠉⠛⠻⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣠⣶⠿⠀⠀⢸⣿⣾⣯⣀⣀⣽⣷⣿⡇⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⣠⡾⠋⠀⠀⠀⠀⢼⡏⣠⣿⠟⠻⣿⣄⢹⡧⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣼⠟⠀⠀⠀⠀⠀⠀⠸⣿⡟⠁⠀⠀⠈⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢀⣀⣀⡀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠈⠉⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣶⡟⠛⠛⢻⣷⡄⠀⢠⣾⠿⣦⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⢀⣴⣶⣄⠀⣸⡟⠉⣿⡆⣰⡿⠻⣿⡟⢻⣿⠟⢿⣆⠘⠿⣶⠟⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⠀⠸⣷⣴⡿⠀⠘⠿⠶⠟⠁⢻⣧⠀⠙⣷⣾⠋⠀⣼⡟⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠙⠿⣶⣤⣀⢁⣤⣤⣄⡀⠀⠀⠀⠀⠹⣷⣴⡟⠁⢠⣾⠏⠀⠀⣴⡟⠋⠉⠻⠷⣦⣀⣤⣶⠿⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠉⠛⢿⣏⠈⠙⢻⣦⣀⡀⠀⢀⣾⠟⠀⣴⡿⣷⡀⠀⢀⣿⣇⠀⠀⣠⣤⡿⠛⠉⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⢿⣦⣤⣾⠏⠉⠁⢠⣿⠋⢠⣾⣿⡄⠙⣿⣄⠈⠙⣿⣀⣀⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠿⣶⡟⠁⠈⢿⣶⠿⠋⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡃⠀⠀⢘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⢹⣧⠀⠀⣼⡏⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠙⢿⣦⣤⣀⣀⣀⣠⣴⣾⠟⣁⣠⣾⠏⠀⠀⠹⣧⣄⣈⠻⣷⣦⣄⣀⣀⣀⣤⣴⡾⠋⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣤⣶⠿⠛⠋⠙⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠿⣶⣤⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠈⠐⢄⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⢀⠔⠈⠀⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⡇⠀⠀⠀⠀⡇⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡰⠀⠀⠀⠀⠀⠰⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢠⠂⠀⠀⠀⣀⡀⠀⠀⠀⢢⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⡴⠁⠀⠀⢀⠔⠁⠐⢄⠀⠀⠀⠑⡄⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠊⠀⠀⢀⡔⠁⠀⠀⠀⠀⠑⣄⠀⠀⠈⢂⣀⠀⢠⡀⠀⠀⠀⣆⣰⠃⠀⠀⠃
⠀⠀⠀⡘⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⢀⠔⠁⠀⡠⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⡑⣄⠰⣿⠇⢀⣰⣟⠛⠋⡀⠀⠘⡀
⠀⠀⢀⠁⠀⠀⠀⠀⠐⠀⠀⠀⢀⠔⠁⣀⠔⢛⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⢄⣸⣗⠾⣿⡷⠜⣩⣝⡁⠀⠙⡾⠛⢀⡄⠁
⠀⠀⡘⠀⠀⠀⠀⠀⢀⡀⢀⠔⡁⠔⠈⠀⠀⢈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠴⢋⠉⠓⣎⠀⢀⣘⠿⢇⣘⡏⠱⡞⠿⡖⠚⡀
⠀⢀⠁⠀⠀⠀⠀⠀⣀⡴⠑⠈⠀⢀⠘⠀⠐⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠇⠀⠰⣄⣥⡜⠙⠃⢿⡿⠃⠸⠿⢇⠸⣿⡦⠀⠀⢁
⠀⠠⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠉⠉⠽⠃⢿⡀⠠⡄⢾⣷⠺⠂⣟⡿⠍⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⠞⠦⣠⣤⢀⠁⣤⣶⡏⠙⢶⡻⠇⠀⠀⠇
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠙⣻⠞⠖⠻⣄⣀⠀⠀⠁⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⡟⠻⡄⠀⠀⠏⠟⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄
⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀
⣐⣠⣤⣤⣤⣀⣐⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣂⣀⣤⣄⣤⣐
⣿⣿⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⢶⣦⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣴⡶⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⣿⣤⣤⣤⣤⣿⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⣿⠉⠉⠉⠉⣿⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀⣿⠀⠀⠀⠀⣿⡀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡞⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡾⠟⠋⠀⠀⠀⠀⠙⠻⢶⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⢻⣦
⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣀⣀⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⣀⣀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⢠⣾⠃⠀⠀⠈⠋⠙⠛⠻⢷⣦⣄⡀⠀⠀⠀⠀⣠⣴⢿⣇⢀⣀⠴⠞⠳⢦⣀⡀⣸⡿⣦⣄⠀⠀⠀⠀⢀⣀⣴⡾⠟⠛⠋⠙⠁⠀⠀⠘⣷⡄
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⢠⡶⠟⠛⠉⠻⢷⣤⣴⡾⠋⠁⠈⣿⡟⠁⠀⠀⠀⠀⠈⢹⣿⠁⠈⠙⢷⣦⣠⡾⠟⠉⠛⠻⢶⡄⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠁⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⢀⣾⠃⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣠⣾⠟⢹⡟⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⢹⡏⠻⣦⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⠀⠀⠘⣷
⠀⣼⡏⠀⠀⠚⠛⢉⣿⠏⠁⠀⠀⠀⣸⡟⠁⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣸⡇⠀⠈⢿⣏⠀⠀⠀⠈⠙⣿⡉⠛⠛⠀⠀⢹⣇
⢠⣿⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⣸⣿⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣿⣧⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⠀⣿
⢸⠃⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⢠⡿⣿⡄⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⡟⠹⣷⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢸
⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇⠸⠇⠀⠀⠀⢸⣿⢷⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⣾⢿⡇⠀⠀⠀⠸⠇⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⣠⣶⠟⢹⡿⠀⠀⠀⠀⠀⠀⠈⣿⠀⠹⣧⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⢼⠏⠀⣿⠃⠀⠀⠀⠀⠀⠀⣠⣶⠶⣦⣄⣤⣤⣄⡀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠘⠋⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠈⠛⠁⠀⠙⣿⡄⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⢠⡾⠛⠻⠃⠀⣀⣴⠶⣦⡀⢿⣇⠀⢸
⠸⣷⠀⠀⣠⣶⢶⣶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢀⣴⣶⣤⠀⢸⣷⠄⠀⣠⡿⠛⠃⢠⣿⠃⠀⢻⡆⣾
⠀⢿⠀⠀⣿⠁⠀⠀⢠⣿⠀⢀⣤⣴⠶⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⢿⣇⢀⣿⠇⣿⠃⠀⠀⢻⣇⠀⠀⣸⡟⠀⢀⣾⠟⡿
⠀⠘⣷⡀⠹⣷⠀⠀⠀⣿⠂⣿⣅⣀⣀⣼⠇⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⡈⠛⠛⠋⠀⠻⣧⣄⣀⣄⠙⠻⠟⠋⣰⡾⠟⢁⣾⠃
⠀⠀⠘⢷⣄⠙⠿⠶⠿⠋⠀⠈⠉⠉⠉⣉⣀⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⣀⠈⠉⠉⠙⠷⣶⣶⠾⠛⠀⣠⡾⠃
⠀⠀⠀⠈⠙⢷⣶⣖⣶⣖⣒⠒⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠖⣒⣒⣶⣒⣶⡾⠋⠁
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠤⢴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠚⠲⣦⠀⠀⢸⡇⠀⠀⣟⠀⠀⢠⡶⠚⠒⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠸⡇⠀⢸⡟⠛⠛⡧⠀⠀⡟⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣀⠀⠀⠀⠀⠀⠀⣿⣀⣼⠇⠀⠀⢷⣄⣸⡇⠀⠀⠀⠀⠀⢀⡀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣀⣻⣄⠀⠀⠀⠀⠀⠸⡏⠀⠀⢀⠀⠀⢈⡿⠀⠀⠀⠀⠀⢀⣼⣁⡀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢈⣩⠷⢶⣄⣀⣴⠞⢻⡴⠞⠉⠙⠶⣾⠛⢶⣄⣀⡤⠾⢯⣉⠁⠁⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⠀⠀⣠⣾⡏⠀⠀⠘⣇⠀⠀⠀⢀⡟⠀⠀⠈⣿⣦⡀⠀⠈⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠶⢶⡾⠛⠛⢻⡾⠋⢸⡅⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣽⠈⢳⣞⠛⠛⠻⣶⠶⠆⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢠⡟⠀⠀⠀⣾⡇⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⢸⠁⠀⠀⠀⣿⠀⠀⣿⣦⠀⠀⠘⣧⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣼⠻⡇⠀⠀⣿⣤⡀⠀⢸⡆⠀⠀⣾⠀⠀⣠⣴⡇⠀⠀⡿⠘⠃⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣠⠾⢋⡟⠀⠀⠀⠀⢻⠈⠓⠀⢸⡇⠀⠀⣿⠀⠐⠋⢸⠃⠀⠀⠀⢠⠞⠳⡶⠶⢦⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠸⠃⠀⠀⣼⠁⠀⠀⢹⡄⠀⠀⠻⠀⠀⠀⣴⠻⠆⢀⣤⢤⡸⣇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠛⠛⣳⠀⢀⣀⣀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢷⡀⠀⢠⡞⢳⣄⡿⠀⢸⠋⠁⣾⠁⢹⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢹⣆⠀⣹⠲⣏⣍⣽⠂⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⣌⡛⠛⠘⢧⣄⣌⡳⠞⣫⡶⢋⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣭⣛⣡⣤⣤⣤⠴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢦⣤⣬⣿⣟⣩⣴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⠀⢈⢸⢰⠇⠹⠀⠁⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢱⣇⡽⣻⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣝⣙⣢⣓⣘⣋⣫⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠷⣄⠀⣸⠇⠀⢹⡄⢀⣴⠞⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢉⣴⠟⠀⠀⠈⢷⣌⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠶⠞⠛⠁⢀⣴⢷⣄⠀⠉⠛⠲⠆⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢀⡴⠋⠀⠀⣤⡴⠶⠋⠁⠀⠈⠛⠶⣤⡄⠀⠀⠓⣄⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠦⠤⡞⠱⡀⠀⠀⠀⠀⠰⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣰⠋⡦⠤⠖⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢠⡇⠀⠈⢲⠶⠖⠀⠀⣿⠀⠀⠀⣿⠀⠐⠲⢶⠞⠁⠀⣷⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⣠⠏⢹⡀⠀⠈⠇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠚⠀⠀⢠⠃⠳⡀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠉⢹⠁⠀⠀⢳⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⡗⠀⠀⠀⠀⢀⣰⡇⠀⠀⢹⠉⠁⠘⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠂⠀⠀⡞⠈⠳⡦⠤⠤⢀⡿⠀⠀⠀⣿⠀⠤⠤⣶⠋⠀⡇⠀⠀⠘⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣰⠁⠀⠀⢣⠀⠀⣸⠇⠀⠀⠀⢻⡄⠀⠀⡇⠀⠀⠹⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡠⠞⢱⡀⠀⠀⠈⠀⣰⠟⠀⠀⠀⠀⠈⢷⡄⠀⠁⠀⠀⢠⠋⠢⣄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠑⢀⣀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠃⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠤⠤⠶⠶⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠶⠤⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠈⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠡⠀⢀⢑⠆⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠓⠀⠀⠸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠌⠀⠀⠀⠁⠤⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀