Park Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀
⠀⡀⠀⠀⠀⠸⠇⠀⠀⣿⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡇⠀⠀⢀⣿⣶⡄
⠘⠳⡄⠀⠀⠀⠐⠀⢸⡇⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣈⡇⠀⠀⢸⠈⠁
⠀⠀⠈⠢⡀⠀⠂⠀⠸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠘⠀⠀⠀⣀
⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⣄⠃⠀⡼⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣴⠏
⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⠀⠘⢆⠀⠁⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢀⡀⠘⠁⢼⠟
⠀⠀⠀⠀⠀⠘⡅⠄⠀⠀⠀⠀⠀⠀⠈⡆⠈⠀⠀⠀⠷⠘⠃⠀⣀⠀⢀⠀⠀⠀⣀⠀⠀⢀⡆⠀⠘⢎⢠⡄⠀⠈⠀⠰⠃⠀⠇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⢸⠀⠀⠀⠉⠀⠈⠀⠀⠀⠁⠀⠀⢨⠉⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢸⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⢀⠀⠀⠀⢸⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠃⠀⠀⢸⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠂
⠀⡀⠠⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠀⢀⡀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠠⠀⠀⢘⠃⠀⠀⠀⠀⠀⠈⠠
⠐⣿⣃⠀⠀⣷⠀⢠⠀⠰⠞⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠄⠀⠆⠀⠀⢼⠀⡄⠀⠀⢀⠀⠀⠐⠀⠀⠀⡀
⠘⠋⠉⠀⢼⣷⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⡀⠀⠀⣴⡦
⠀⠀⠐⠀⠘⠛⠠⠤⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡿⡀⢡⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠆⠀⠈⠃⠑⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠈⠀⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⢀⠤⠒⠉⠙⠂⠄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠂⠀⠀⠐⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⣄⠀⢀⡄⡹⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠁⠉⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⣀⡰⡄⠴⢀⠈⠠⢤⣆⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⠀⠠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⠀⠀⢡⠀⠀⢈⠓⠂⠀⣈⣹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⢣⠔⠠⡔⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠈⡀⠀⠹⠀⠀⠀⠈⢀⠐⠀⠀⠀⠀⣈⡍⠑⠓⢠⣀⠀⠀⠀⠐⠀⢤⣂⠒⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⢀⠤⠉⢃⠀⠀⠰⠀⠢⠀⠀⠀⢰⠂⠀⠀⠀⠠⠥⠈⢢⡀⠀⠀⠙⠒⠷⢤⣀⣀⡉⠀⠀⠀⠀⡀⠉⠌⠑⠦⢠
⠀⠀⠌⠀⠀⠁⠀⡤⠄⠰⠆⣀⠶⠤⣆⡈⠀⠀⡀⠀⠄⠀⠀⠀⢳⡀⠀⠀⠀⣠⡀⠀⠙⠢⠀⠀⠀⣀⣀⠀⠈⠩⠭⠷⠒⠊⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠚⠁⠴⡨⠀⠀⠐⠀⠆⠀⠀⡀⠀⠱⡀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢅⡀⢆⢀⠀⠀⡆⠀⠀⠣⠀⠀⠙⣄⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠰⠒⠎⠴⠀⠀⠀⢀⡆⠀⠀⡆⢡⠀⠀⠈⢆⠀⠀⠀⠀⢐⡆⠀⠀⢀⠔⠤⢤⣄⡄⣀⠀⠀⠓⠲⡂⠠⠈⠁⠀⡠⢦⠧
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠁⢈⠃⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢁⠀⠄⠀⠀⠈⢆⠀⠀⠀⠀⢡⠀⠐⡅⠀⠀⠈⠀⠙⢋⡅⠀⠔⢄⡤⠈⠀⠐⢍⠡⠚⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠚⠀⠀⠀⠀⠀⠀⠈⡀⠀⢀⡠⠀⠀⠤⠄⠠⠬⡀⠀⠀⠁⠁⠀⠀⠀⡄⣀⠠⠺⠉⠁⠆⠀⡲⠙⠀⠈⠀⡀⢈⡤⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠘⠂⠀⠘⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠪⠀⠀⣀⡠⠤⠀⠀⠀⠐⠃⠰⠇⠒⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⡭⠶⠽⠋

⠀⠀⠀⠀⠀⠀⡀⡀⢀⢀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⡄⢠⡀
⠀⠀⠀⢸⢸⡇⡇⣿⢸⢸⢸⡇⠈⡟⢻⠋⠀⠀⠀⠀⠀⠀⢀⢴⣄⠀⠀⠀⠀⠀⠀⠠⢦⠈⢉⢈⠁⡉⢡⠶⢀
⠀⠀⠀⠈⣦⣤⠁⠁⣈⣈⣰⠁⠀⠇⢸⠀⠀⠀⠀⠛⠛⣛⠛⣿⢛⡛⠛⠛⠀⠀⢘⠓⠤⡐⡬⠂⠪⡔⡡⠄⠚⡂
⠀⠀⠤⢤⣿⣿⣼⣿⣿⣿⡷⠀⢸⡇⢸⡇⠀⠀⠀⠠⣄⠈⠁⣿⡀⠉⢠⡀⠀⠀⠛⠓⠐⡂⢅⠿⢷⡸⣐⠀⠚⠃
⠀⠀⠀⣠⢼⣇⣿⣿⣿⣸⡧⣄⠀⡇⢸⠀⠀⠀⠀⣰⣶⣶⣶⣿⣷⣶⣶⣶⠀⠀⠚⢃⡁⠔⢩⢁⠹⡕⠂⢈⠚⠃
⠀⠀⠀⢇⣉⡹⠉⠉⠈⢏⣉⡸⠀⡇⢸⠀⠀⠀⠀⠉⢉⠉⠉⠉⠉⠉⣌⡉⠀⠀⠀⠙⠃⣰⡇⢠⡀⢱⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠷⡾⠆⠀⠀⠀⠀⡏⠐⠀⠀⡄⠄⠈⡅⠀⠀⠀⠀⠀⠴⠤⠭⠥⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⢀⣤⣴⡀⠀⠀⠐⣀⡄⣰⡈⠀⠶⡀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠈⠉⠉⠉⠀⠀⠰⢶⡟⠃⡇⠀⠒⠧⡶⠴⠆⠃⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣟⡋⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠧⠤⠤⠤⠧⠤⠤⠄⠀⠀⢀⡠⢀⡖⡔⡕⠦⣀
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⡿⣿⣿⢿⣿⡿⣿⣿⢿⣿⡇
⠀⠀⠀⠀⠀⣀⣀⣘⠉⠉⠁⠁⢠⣶⠏⠀⠀⠺⢻⣷⣤⣤⡀⠙⣿⣿⣶⡄⠀⠀⠀⡇⡇⢸⢸⠀⡇⡇⢸⢸⢸⡇
⠀⠀⠀⠀⠀⠙⢿⣿⣶⣦⣤⣴⣾⠇⠀⠀⠀⠀⣸⣿⣿⢿⡥⠀⠻⣿⠟⠃⠀⠀⠀⡇⡇⢸⢸⣾⣷⣇⢸⢸⢸⡇
⠀⠀⠀⢀⣄⣤⣤⣉⣉⣭⣤⣤⣄⠀⠀⠀⠀⠀⣉⣿⣿⣋⡀⢀⣠⣿⣄⡀⠀⠀⠀⡇⡇⢸⢸⣿⣿⣿⣿⢸⢸⡇
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁⠀⠀⠀⠁⠁⠉⠈⠉⠉⠉⠉⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠆⠀⠀⣀⣠⠴⢚⡽⣽⢆⠠⣀⡀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢀⣦⣄⣠⠀⠀⠀⣴⣄⠐⠟⠋⠁⢋⣸⣷⣿⣜⡷⡊⢹⠿⡶⢄⣤⡀⢀⡀⣠⣠⣤⡄
⠀⠀⠀⢶⣤⡄⣉⣱⣿⣾⣷⡱⣄⢿⣿⣆⠀⣆⢀⢯⣭⣭⣍⣭⡽⡿⡆⡬⠁⣼⣿⠇⡌⠡⣾⣿⣞⢛⠠⡀⣀⠔
⠀⠀⠶⢾⣷⡘⣮⣙⣟⣋⣵⣿⡿⠎⢿⣿⣽⠯⠠⢷⣏⣻⣿⣏⣷⣾⠽⣛⣴⡿⣿⣼⢇⣻⣿⣴⣿⢉⣤⣾⣿⣿⣦⡀
⠀⠀⣇⣚⣻⣷⡟⣻⣿⣿⣿⢡⣶⣶⠤⢛⣴⣿⣿⣷⣣⣟⠿⣣⣿⣼⣿⡶⣍⢛⡝⠂⢪⡛⣿⡷⣾⠺⢿⣿⣽⣿⣿⠁
⠀⠀⠙⢿⠿⢿⠿⣿⣿⣿⣿⣛⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣚⣮⣿⣷⣞⣯⢿⠿⠉
⠀⠀⠀⠀⠘⠛⠿⣿⣾⣿⣿⣽⣿⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⣿⣿⣿⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠛⠛⢛⠛⠟⡿⠛⣿⣷⣿⣿⣙⣿⣛⣹⣿⣿⣿⣿⣿⠿⠿⠿⠟⠻⠋⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢴⣿⣿⣿⣧⣤⣼⣿⣿⣿⣍⣿⣿⣿⣿⣯⣽⣿⢿⣷⣴⣰⣤⣦⡀⣄⣀⣀
⠀⠀⠀⢠⡄⠀⣿⡿⢿⣿⢼⣿⡿⣿⣿⣿⣿⣿⣏⣿⣿⣻⣿⣿⡟⣿⣿⣿⣌⣿⣿⣿⢿⣿⣿⣿⣿⣟
⠀⠀⣤⣤⣷⣤⡇⣳⣜⡁⢸⢏⣴⣼⣫⣽⡟⠳⠣⡿⠿⣿⡿⠏⣍⣙⣿⣟⠙⠯⠅⠸⠟⣾⠿⣾⣿⣿⣷⡇
⠀⠀⣿⣿⠹⣿⠟⠹⣿⠀⠺⣽⣿⣿⣿⣽⣷⠷⡘⠛⠏⠉⠠⢪⣽⣿⡿⠿⡷⡶⡁⠀⠈⢉⣿⣿⣿⣿⣟⡿
⠀⠀⠃⢸⣿⢻⣿⣀⣁⠀⠀⠸⣶⣿⣿⣿⣟⡢⠀⠀⠀⠀⠀⢸⣶⣾⣿⣄⣻⡙⠄⢄⠤⣾⠿⣿⢟⡏
⠀⠀⠀⡟⠛⠀⠋⠈⠀⠀⠀⠈⠟⡿⠿⠿⠃⠑⠆⠀⠀⠀⠀⠞⠻⠿⡏⠀⠀⠀⠀⠀⢶⠃⠠⠷⠋
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢛⠙⠛⢉⣉⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⢤
⠀⠀⠀⢀⠤⠤⠜⠀⠀⠀⠱⠀⠀⠀⠀⠀⢀⣴⠋⢉⠚⢃⣴⠞⠛⠻⣿⣿⣍⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠛⠀⠀⠀⠦⠄⠠⠤⢀
⠀⠀⣀⠇⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⢠⡟⠁⠀⠀⣠⠟⠁⠀⠀⠀⠈⠹⣿⣷⡄⢻⡄⠀⠀⠀⠀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢠⡟⠁⠲⠄⣼⠏⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⡆⢻⡄⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⢨⠆
⠀⠘⠢⠀⢀⢀⡀⠀⠀⠀⠀⠀⠒⠀⣾⠁⠀⠁⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⢿⠀⠀⠀⠀⠉⠉⠠⠤⢄⠀⠀⣠⠄⠠⠄⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠑⠂⠐⠊⠉⠁⠀⠉⣿⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⣿⡇⢸⡇
⠀⠀⠀⠀⡀⠀⠐⠀⠂⠀⠠⠀⠀⠀⣿⢀⡠⠄⣿⠀⠀⠀⠀⠀⠀⣿⣿⢦⡀⠀⠀⢾⠇⢸⡇⡠⠂⠐⢢⠀⠀⠀⠀⢐⠂⠀⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠐⠀⠁⠀⠀⠀⠀⢿⡀⠐⠀⢸⡇⠀⠀⠀⠀⢀⡟⣿⣇⠙⢦⣄⡛⠀⣼⠃⢻⡀⠀⣸⠁⠀⢀⠀⠈⠂⠦⡇⠀⠀⠂⡁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢻⡄⠀⠀⠀⢸⡇⢹⣿⡄⠀⢹⡗⠀⣿⠀⠀⠙⡋⠁⠀⠀⠨⠱⡀⠀⠀⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡠⠷⠉⠻⣆⠀⠀⢸⠁⣄⢿⣷⡀⢸⠇⠀⢹⡄⠀⠀⠇⡀⠄⣐⠀⠠⠀⠂⠂⠑⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⡠⠤⢄⠀⠐⠀⠀⠀⠀⠀⠘⢷⣴⣷⣄⠙⢶⣄⣾⢸⣿⣯⣿⢷⡿⠀⠀⠈⣇⠀⠀⡆⠩⢲⠠⠤⣀⡀⠀⠀⠀⠀⠀⠁⠋⠲⢄⢄⡀
⠀⠀⠀⠀⠀⠸⡀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣶⣈⣙⣺⣉⣁⣤⣾⠇⠀⠀⠁⢻⡄⠀⡛⠛⠉⠚⣤⠀⠄⣉⣈⠀⠒⠀⠄⠄⣀⠀⠋⠁
⠀⠀⠀⢀⣶⠀⠙⣶⠁⠀⠀⠀⠀⣠⠔⠃⠠⡀⢸⠇⣨⣿⣿⡻⣿⣹⣭⠟⢁⡟⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣿⠈⠋⠈⢉⠿⠉⠒⣶⠠⣤⣄⠁⣙
⢀⠐⠀⡾⠘⣆⠀⣙⠠⡀⠀⢬⠀⣣⠀⠀⠀⣿⣿⣾⣁⣿⠶⣿⣿⢹⣟⣦⡾⠀⠀⠀⠀⠀⠀⠘⣧⠁⠀⠀⠀⣇⠀⠈⠹⠘⠀⠀⠂⠀⠦⠰⠀⠂⠭
⠀⠁⡼⠁⠀⠹⡆⣿⣰⠳⠄⠜⠠⣋⢄⠉⣉⢛⡩⠛⢦⣿⠾⣅⣿⢸⣵⠏⠀⠀⠀⠀⠀⠐⠀⠀⠘⢧⡀⠀⠀⣇⠀⠀⠀⢈⠀⠈⠀⠰⡦⢄⠀⠀⢀
⣀⣼⠃⠀⠀⠀⢻⣯⠘⠚⠢⠤⢀⡆⢸⡳⠤⢰⣷⢂⣸⡏⢳⣜⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⢦⡀⠀⠀⠀⠈⠘⠀⠀⠀⠀⠉⠘⠓⠒⠃
⢳⡏⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⢷⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡀⣙⠷⣤⠤⠔⠚⠀⠀⠀⠀⠠⠀⠀⡀
⠘⣇⠀⠀⠀⠀⢠⠏⠐⠒⠂⠀⠀⠀⠠⡈⠈⠀⠀⠀⠉⠀⠈⠀⠀⠀⠈⠀⠈⠐⠂⠀⠁⠀⠂⠀⠀⠀⢀⠀⠀⢓⠂⢤⡞⠀⠀⠀⠀⠀⠀⡄⠉⠁
⠀⠈⠓⠶⠖⠚⠁⠀⠀⠁⠀⠀⠀⠀⠀⠙⠆⠠⣾⣶⡶⠀⠀⠀⡀⠀⠀⠐⠀⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⣀⣀⠄
⠀⠀⠀⠀⠁⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⢤⡔⠀⢡⣾⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠇⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⣀⠀⠀⠀⢈⠛⠟⠛⡡⠚⣀⡀⡀⠈⠀⠄⠀⠀⠀⠈
⠀⠀⠀⡄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠰⠐⡀⠀⠀⠈⢈⠁⠀⠀⡄⠂⠰⠐⠀⠐⠈⠁
⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⡆⠁⠁⠀⠈⠀⠉⣠⣀⡠⠄⠀⣀⣀⣀⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠺⣿⣿⣿⣿⣿⣿⡿⠛⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠾⠿⠿⠿⠿⠿⠿⠿⠶⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⢰⣿⣿⠀⡀⠀⣾⣿⡆
⠀⠀⠀⠀⠀⣯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢠⡀⣠⠀⣿⡄⠀⠀⣠⣼⣿⣿⣰⣿⡄⣿⣿⡇⠀⠀⠀⠀⢰⡆
⢠⣄⡀⠀⠀⡷⣇⣄⠀⣀⢀⡄⠀⠀⣀⢠⣄⣼⣿⣿⣧⣼⢸⣿⣿⣿⣿⡇⢼⣷⣿⣿⣿⣿⣿⣿⣧⣿⣿⣧⢸⣷⠀⠀⢸⡇⢀⡀
⠈⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣧⣿⣷⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⡷⠗
⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⢃
⠀⠀⠀⠀⠀⠻⠿⠛⠛⠁⠀⢸⣿⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠌⠁⠀⠀⠘⠻⠿⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠈⠀⠁⠀⠀⠀⠈⢹⡿⡟⠻⢿⠿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠃

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣬⢢⡢⣀
⠀⠀⠀⠀⠀⣄⣴⣳⢹⣦⣄⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⢲⣤⣖⣶⣪⣠⣋⣄⣟⣌⣑⣨⣁⣴⣖⣦⣴⠂
⠀⠀⠀⠀⠀⢇⡟⢸⡜⡏⡇⠀⠀⠀⡒⣾⠹⡛⡟⡆⠂⠀⠀⠀⠀⢸⢿⢿⢿⢿⢿⣿⣿⣿⣿⣿⣿⢿⢿⡿⢿⠿
⠀⠀⠀⠀⡘⡼⢁⣾⣿⣄⠹⡄⠀⠠⠱⠏⣴⣿⣌⠙⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣿⣿⠁⣿⣿⣿⡿⠿⣇⣀⢀⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⢀⣀⣯⣄⡀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠘⢱⡏⠉⡟⠁⠛⠿⠋⠀⣴⡟⠏⡿⠛⡿⠆
⠀⠀⠀⠀⠀⠀⠐⣶⠿⣏⠉⠉⣏⠉⠉⢳⠿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⣶⡆⣼⡇⠀⠁
⠀⠀⠀⠐⠒⢤⣞⠁⢀⠜⣏⠉⣯⠉⣱⠯⡀⢈⣧⡴⠒⠀⠀⠀⠀⢰⢶⡶⡶⢶⢶⡿⣿⢿⠿⡿⣷⢶⡶⣶⢶⠶
⠀⠀⠀⠙⠛⡟⠈⢹⠳⢄⡘⢇⣻⡰⣃⡤⠞⣏⠉⣿⠛⠃⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠠⠤⠴⡧⠤⡷⠴⠴⠍⣏⠀⡱⢹⠶⠶⢾⠶⢾⠶⠦
⠀⠀⠶⠶⠂⢧⠀⢸⡤⢶⣭⡎⣍⢰⣟⡳⢤⣇⠀⡞⠰⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⣷
⠀⠀⠀⠀⣀⡼⢿⡉⠘⣖⣏⡀⣇⢀⣳⣱⠃⢈⡟⠣⠤⠀⠀⠀⠀⠀⣀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡙⡇
⠀⠀⠀⢠⣤⡄⠀⠙⢶⣺⣀⠈⣏⠁⣀⡯⡶⠋⠀⢰⣶⠆⠀⠰⠶⠾⡷⣷⠷⡷⠶⠆⠀⠀⠀⣠⠊⠀⠀⠁⢷
⠀⠀⠀⠀⠀⠀⠀⠴⣯⠇⠉⠉⣟⠉⠉⢸⣽⠄⠀⠀⠀⠀⢠⣄⡄⢠⠀⣿⡀⢰⡀⢠⡀⢤⣜⣁⡀⠀⠀⠀⡞⡄
⠀⠀⠀⠀⠀⠀⠐⢾⡽⠀⠀⢈⣉⡀⠀⠀⢗⡷⠀⠀⠀⠀⠈⠩⠧⢹⣲⣿⢻⣀⠻⠌⠉⠀⠙⢿⣶⣭⣼⠀⢦⣧
⠀⠀⠀⠀⠀⠀⢀⣓⠃⠀⠀⠈⠉⠁⠀⠀⠸⣺⠀⠀⠀⠀⠀⢠⣤⣤⣼⣿⣦⣤⣤⡄⠀⠀⠀⠀⠀⠉⢹⠀⢨
⠀⠀⠀⠀⢀⣤⣾⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣾⣶⣦⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣦⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣠⢰⣦⢀⣀⣤⡄⠀⣶⣿⣧⢠⣤⣤⣤⠀⠀⠀⣿⣰⡆⣰⣦⡄⢀⡀⣿⣶⣾⣿⠀⢠⣤⡀⢀⣀⣿⣿⠀⣤⢸⣧⣄⠀⠀⠀⠀⠀⢸
⣿⣼⣿⣿⣿⣿⣇⣤⣿⣿⣿⣸⣿⣿⣿⣷⣶⣤⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⣼⣿⣿⣿⣿⣿⣾⣿⣿⣇⣴⣠⡄⣰⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⡟⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⢿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⡿⣿⣿⣿⣿⡿⢿⠿⠟⢿⣿
⠈⠘⠇⠉⠋⠛⠃⠀⠻⠛⠟⠀⠛⠋⠉⠁⠀⠀⠙⠛⠃⠸⠟⠛⠙⠃⠈⠉⠙⠋⠉⠈⠙⠃⠘⠛⠛⠏⠁⠸⠀⠛⠛⠁⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⣸⣿⣷⡆⣤⡀⠀⢠⡄⢀⠀⣀⡄⣤⣤⣠⠄⡀⢀⣠⢤⡄⣤⢤⡄⠀⢠⢄⢠⡄⣤⣄⣄⡄
⠀⠀⠀⠀⠀⠹⣿⠿⠻⠏⣿⣷⠄⣸⣧⢸⣾⢿⡇⣏⢳⣸⠂⢻⣾⣿⠂⡿⣿⢸⡇⠀⢸⠞⣸⣧⣿⣏⡿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠟⠀⠀⠋⠙⠂⠃⠊⠳⠋⠛⠛⠂⠚⠛⠛⠒⠃⠛⠘⠃⠀⠘⠀⠋⠙⠟⠟⠁⠉


⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸⠁⡇
⠀⠀⠀⠀⠀⠌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡇
⠀⠀⠠⢨⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡜⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⡇
⠀⠀⠀⢠⠁⠀⠠⠖⠀⠀⠀⣠⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⡞⠀⠀⠀⡼⢸⠀⠀⠀⠀⠀⠀⢤⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠠⡚⠀⠁⠂⢂⡀⠀⠀⠀⠀⡰⠁⠀⠀⢠⠎⠀⠀⠀⣰⠁⢰⠀⠀⠀⠀⠀⢠⡍⠵⠀⠀⣇
⠀⢀⠀⠀⠠⠡⠉⠀⠚⠀⠀⠀⠠⢨⠇⠊⠀⠀⠀⠔⡁⠀⠀⠀⢠⠇⠀⡈⠀⠀⠀⠀⠀⢸⣿⠜⡄⠀⡟
⠀⡟⠀⠐⠀⠆⠀⠀⠼⠀⡀⠀⠀⠀⠂⡤⠄⠤⣢⠎⠀⠀⠀⢠⠏⠀⠀⣿⠀⠀⠀⠀⠠⠳⠶⠶⠿⠀⣇
⢠⠃⢀⡑⢒⡚⣇⢂⠐⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⡀⠀⡠⣤⢀⡄⠤⠿⠤⠤⡤⠤⣐⡀⠀⠀⠀⠀⣿⢀⣀
⠈⠀⢸⡏⠈⠑⡀⠀⠀⠠⠄⠀⢀⡀⠠⠄⠔⠠⠂⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠠⣀⡄⠠⠄
⠀⡤⠾⠂⠀⠀⠙⠀⠠⠰⠋⠀⠈⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠒⠺⠦⠺⠶⠮⠲⠴⢶⠓
⠠⠄⠀⠀⡀⠀⢰⠀⠀⢢⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⣀⡖⠀⠀⠈⠃⡁⠀⠐⠂⠈
⢰⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠈⠀⠀⠀⠀⡆⠀⢓⡀
⠀⠀⠀⠀⠐⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁⠚⠀⠀⠀⠠⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠠⠅⠘⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⢈⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣈⠀⢾⠀⠀⠀⡄⠀⠀⠀⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠑⠾⠀⠀⠀⣇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠘⠆⠠⠄⠀⠈⠀⠀⠀⢠
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣬⣽⣥⣮⣩⣯⣥⣿⣹⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢲⣊⣯⠭⠭⠭⠭⣹⣃⡖⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢒⡭⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⢭⡒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢊⡐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢂⡑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢬⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⣤⣤⡀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣿⡉⢉⣿⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢸⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡅⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⣾⡟⠛⠛⢻⣷⡀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢨⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢼⡀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⡁⠀⠀⢈⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⢀⡯⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⢣⠀⠀⠀⠀⠀⠀⣰⣿⣱⠁⠈⠉⠉⠁⠈⣏⢿⣆⠀⠀⠀⠀⠀⠀⡜⡒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⠳⡀⠀⠀⠀⣼⣿⣳⠃⠀⠀⠀⠀⠀⠀⠘⣞⣿⣧⠀⠀⠀⢀⠞⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠽⠦⣀⣾⣿⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⣿⣷⣀⠴⠩⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢫⡟⠊⠭⣑⣒⡲⠲⠖⣖⢒⣊⠏⠑⢻⡝⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⢇⡞⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⢳⡸⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣘⣛⣻⣯⣾⣀⣀⣀⣀⣀⣤⣶⣾⣷⣶⣤⣀⣀⣀⣀⣀⣷⣽⣟⣛⣓⣀⣀
⠀⠀⠀⠀⠀⣀⣤⣀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⣀⣀⣤⣀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠈⠻⠿⠿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠙⠻⠿⠿⠟⠉⠉⠉⠙⠻⢿⣿⣿⡿⠟⠉⠉⠉⠉⠻⠿⠿⠟⠋⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣀⡀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⣯⡇⠀⢸⣿⡇⣽⡇⠀⠀⠀⠀⠀⠀⢀⡀⢾⣿⣦⣤⠀⠀⠀⠀⢀⣀⣀⠀⢸⣿⡇⠀⣿⡇⡟⢻⣠⡄
⠀⠀⠀⢀⣄⣀⣠⣿⡇⢀⣷⣿⡀⢸⣿⡇⣿⡇⠀⢰⣿⣤⣄⢸⣿⡇⣿⣿⣿⣿⠀⠀⣶⡆⣸⣿⣿⣿⣿⣿⣇⢀⣿⡇⡇⣽⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⡥⢼⣟⣿⢇⢸⣿⣇⣿⣇⣀⣿⣿⣿⣿⢸⣿⡇⣻⣿⣿⣿⣟⠂⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⣿⣿⡇
⠀⢠⣶⣾⣿⣿⣟⣿⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⡿⠜⣿⣷⣿⣿⣿⣿⣿⡃⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠀⠀⠈⢻⠤⣅⣀⣀⣐⣒⣖⠒⡶⠄⠀⣋⡂⠈⠉⢉⠁⠉⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠛⠛⠛⢛⠛⠉⠁⠀⠒⠒⠒⠀⣀⠐⡒⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⠠⠄⠠⠴⠶⠶⠦⠤⠀⠀⠀⠐⠒⠒⠒⠂⠀⠉⠉⠁⠀⠈⠉⠁







⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢠⢠⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⢀⣀⠀⠆⠀⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠚⠛⠃⠀⠀⠁⠀⠀⣀⣨⠤⠀⠀⠀⠀⠀⡀⢄⡀⢀⠀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄
⠀⠈⠿⠄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣥⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⠀⢠⠀⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⢨⣵⡆⠀⠀⠀⠀⠀⠀⢠⠠
⠀⠀⠀⠀⣴⡦⠀⠀⢀⠀⢶⠀⠐⠀⠿⠀⠈⠀⣿⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠁⠰⣄⠀⠃⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠧⠀⠀⠀⡀⠀⠔⠀⠤⠢⢀⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠩⡀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠸⢀⣀⠀⠰⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⡀⠀⠀⠔⠈⠁⠂⠀⠀⠀⠈⠁⠀⠀⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠭⠄⡀⠀⠀⠁⠐⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠈⠷⠀⣕⠦⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡌⢢⣴⣌⠀⢁⣡
⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⡞⠳⢄⡀⠰
⠀⠀⠀⠀⣉⠉⡀⣉⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⢀⡆⠀⢂⡆⣄⡒⢆⠀⠀⠈⠠⣭⠓⣒⣃⠔⠂
⠀⠀⣀⡴⠃⣿⠇⢿⣮⠓⢶⠤⠀⠀⠀⠀⠈⠀⠉⠀⠀⡠⢂⣀⣤⣄⣀⠌⠏⠃⠄⠀⠀⠀⣀⣀⡀⣠⡀
⠀⠈⠙⠀⠀⢹⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡆⢀⠊⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤
⠀⠀⢀⠀⡀⢘⡆⠀⢿⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠀⠀⠙⢁⠀⠀⠀⢈⠄⠀⠀⠀⠠⣎⡌⠧
⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡲⡻⡿⢆
⠀⠀⠀⠀⢀⢀⣾⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢊⠔⢁⠁⠇⢡⠡
⠀⠀⠀⣰⠉⠀⠉⠈⠉⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠓⠠⡌⠀⣈⠀⣀⡤⡴
⠀⢀⠜⡦⠀⣀⠀⠀⠀⡀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣸⡀
⠀⠀⠈⠐⠒⠀⠒⠂⠀⠘⠒⠀⠀⠀⠉⠉⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢻⡀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣀⣤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠉⠓⢦⠀⠀⢀⡰⠃⠀⠀⢀⡾⠀⠀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢢⡀⠀⠀⠙⠲⠶⠶⠤⣄⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣤⠴⠶⠶⢦⠀⠀⣀⡤⠴⠖⠚⠛⠛⠳⠶⢦⣄⠀⠀⠰⠚⠁⢀⡖⠋⠓⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠴⠋⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⣠⠞⠁⠀⡜⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⢀⠖⠉⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⠒⠂
⠀⠀⠀⠀⠐⠂⠀⠀⠒⠒⠒⠒⠚⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠒⠒⠒⠒⠶⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⠤⠤⠤⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠛⠉⠉⠉⠁⠀⠀⠀⠀⢀⣀⣠⡤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣍⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⠀⣠⡀
⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣠⣜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣟⡀⠀⠉⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⡀⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⣀⡄
⠀⠀⡼⢫⣿⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠶⠾⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⢽⣿⣻⠛⣄⣀⣸⣇⠀⠀⠀⠀⠀⠀⣠⣤⠀⣾⣿⣤⣼⡶⣖⣦⡦
⠀⠀⠀⣿⣧⠀⠈⠳⢤⣼⡋⠀⠀⠀⠀⠀⠀⠾⢹⣿⡇⠀⠀⠀⣯⣀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠥⢿⡿⣿⣼⣷⣾⠷⠟
⠀⠀⣸⠏⠹⣇⠀⣀⡾⣏⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⣤⣦⣭⣁⡉⠉⠀⠀⠀⠀⠀⠐⠛⠋⢀⣀⣹⣯⣀⣀
⠀⠐⠋⠀⠀⠻⠄⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠇

⠀⠀⢀⡔⠺⠁⢙⢈⠓⢢⡀⠀⠀⠀⠀⠀⠀⣠⠾⠟⠛⠿⠿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⢠⠏⢀⠂⠁⠀⠈⠐⢈⠩⡆⠀⠀⠀⠀⠀⢄⠀⠀⠀⣀⡀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⢀⢀⣴⣿⣿⣿⣦⡀⡀⠀⠀⠀⠀⠟⠉⠉⠹⡄⢀⣀⡀
⠀⣬⠀⠄⠀⢸⣿⡧⠀⠠⠄⣽⠀⠀⠀⠀⣤⠀⠷⠐⢾⣿⣿⣤⣀⡄⠁⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⡿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⢠⠜⠏⠀⠙⣆⣠⠏⠉⢳
⠀⢸⡄⠀⢄⡞⠉⢳⡠⠈⢠⡆⠀⠀⠀⠀⠀⠈⠁⠚⢺⣿⣿⠤⠌⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⣀⠀⠀⠀⠀⠀⠀⠁⠒⠊⠀⠀⠸⢆⠀⠀⠀⠀⢀⡼
⠀⠀⠸⢦⣞⠁⢀⠈⣳⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠃⢻⣿⡇⠙⠶⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⠒⠉
⠀⠀⢠⡎⠉⠈⠛⠁⠉⢹⡄⠀⠀⠀⠀⠀⠰⠿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠀⠀⠀⠀⠰⠾⣿⣿⣿⣿⣿⣿⣿⠷⠆⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⢠⡄⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡒⣤⣶⡞⠁
⠀⠀⢸⣾⣆⣀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⣍⢾⡿⣉⣯⣥⣤⣄
⠀⠀⢸⡟⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠸⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢟⣴⣾⠕⡩⠭⢗⡁
⠀⠀⢸⣀⣀⣘⣀⣀⣀⣀⡁⠀⠀⠀⠀⠀⠀⢀⣾⠷⣤⡀⠀⠀⠀⢸⣺⠀⠀⠀⠀⠀⠀⢸⣇⣿⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⣫⠖⣩⠔⠊⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⡾⢯⡀⠀⠉⠐⠀⣴⢸⢼⠀⠀⠀⠀⠀⠀⠿⡿⣾⠛⠃⠀⠛⡟⠂⠀⠀⠀⠀⠀⠘⡿⢋⡤⠋
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢴⠛⠁⢸⡇⠀⠀⢠⣤⣿⣾⣿⣤⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠈⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠶⡶⠶⠶⢶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢴⡀⢺⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⡻⠗⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢠⣶⣄⣤⣤⢴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠙⣹⣿⣉⣉⣀⣀⣀⣀⣈⣁⠀⠀⠀⠉⢠⣿⢿⡄⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠘⣿⣿⢡⢐⠑⢻⣿⡇⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⣠⣄⣠⣤
⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⡀⠙⠋⠀⣀⣀⣠⣠⣾⣿⣿⡇⠀⠀⠀⠀⠈⠛⠷⢶⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢴⠏⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡠⢄⡠⢼⡧⢄⡠⡄⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣄⠀⣸⣿⡀⢠⣿⣧⢸⣿⡇⢰⣷⠀⠀⣶⣶⠀⣀⣀
⠀⠀⠀⠀⢸⣿⡇⢀⣀⣀⢸⣿⣿⢸⣿⣿⣇⢸⣿⣿⢸⣿⣷⣸⣿⣶⡆⣿⣿⠀⣿⣿⡀
⠀⠀⠀⣾⣿⣿⡇⣾⣿⣿⣼⣿⣿⣸⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⢠⣿⣿⣧⣰⣿⣿
⠀⢐⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠀⣀⡄⠀⠀⣰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⢀⣀⢸⣿⡇⢸⣿⣷⣆⢸⣿⣿⠀⣴⣶⡀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⢰⣿⣆⣾⣿⡇⣿⣿⢾⣿⡧⣼⣿⣿⣿⠈⣿⣿⣶⣿⣿⣧⣴⣦⢸⣿⣿⠀⣀
⠀⢀⣤⣸⣿⣿⣼⣿⣿⣿⣿⣷⣿⣿⣸⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡦⠤⡀
⠀⠀⠀⠀⠀⠀⠀⡤⣄⠀⠀⠀⠨⡼⣌⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠅⡇⠀⠀⠀⡇⠘⡩⡇⠀⠀⠀⢀⠂⠉⠠⠀⠀⠀⠈⠉⠢⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠠⠄⢀⠀⠄⠆⠁⠀⠁⡇⠂⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠠⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠠⢠⠀⠄⠄⠀⠀⡇⠀⡔⠓⠀⠀⠤⠀⠀⠀⠀⢛⠧⡀⠀⡇⠋⠀⠀⠁⡌⠀⠀⠀⢘
⠁⠏⡇⠀⠀⠀⢸⣹⠧⠇⠶⢄⠀⡇⠀⡇⠀⠐⠗⠾⣷⡄⠀⠀⢸⠠⣧⠀⡇⣁⠀⠀⠀⣇⣘⣿⠀⢸
⠀⠚⡗⠤⠀⠀⢸⡇⠀⠀⠀⢸⣀⢧⣬⡇⠀⠀⠀⡃⡸⠧⣄⡀⢸⡴⠓⠒⢻⠷⣀⠀⠀⠁⠸⠙⢳⢸
⠀⠀⠃⠠⡆⠀⠀⡇⠀⠀⠀⢸⡇⢸⠀⡇⠀⠀⠀⠄⠇⠀⡷⡇⠘⠆⠀⠀⢨⠀⣹⣇⣰⣀⣨⠀⣾⣸
⠨⠀⠠⠘⠇⠀⠸⠷⠀⠀⠀⠤⠅⠠⠀⠆⠀⠀⠠⠢⡆⠀⡇⡗⡄⡆⠀⠀⢠⠠⠀⠀⠀⢰⠉⣷⣾⠁⠀⡀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣛⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡂⠚⢾⡃
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡀⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⡦⢤⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢐⡏⠽⢻⡄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠈⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢙⢳⠀⠀⠀⢀⠉⡏⠙⠲⠶⣧⠀⠀⠀⠀⠀⠀⣀⢠⠄⠀⠀⠀⠀⠀⠀⢲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣇⠀⢀⠔⢸⠀⠀⠀⠀⠀⢠⠍⠄⠀⠠⠀⠀⠸⠀⠀⢸⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢐⢸⠀⡇⠀⠈⠀⡇⠐⠀⢀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⡅⠀⠀⠀⡇⠀⠠⢈⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⢸⠀⠰⠀⠠⠄⠒⠀⠠⠄⡀⡃⠀⠀⡇
⡀⠠⢄⡀⠀⠀⠀⠀⠀⣁⣽⢰⢨⠀⡏⠀⠀⠀⡇⠀⢀⡇⠀⠀⢸⠈⡙⣫⠀⠀⠀⠀⠀⠀⠎⠙⡂⠀⢸⠀⠰⠀⠀⠀⠀⠈⠃⠀⡆⡇⠀⠀⡇
⠀⠰⡇⡇⠀⠀⠀⠀⠀⣟⣹⠼⠼⠄⠷⢦⡀⠀⡇⠀⢀⡇⠀⠀⠘⠒⠲⠿⣿⡆⠀⠀⠀⠀⠇⠠⣾⠀⢸⡅⢠⠀⠀⠀⠀⠠⡇⠀⡇⡇⠀⠀⡇
⠀⠠⠧⡧⣀⡀⠀⠀⠀⡻⡇⠀⠀⠀⠀⢀⡇⠀⣇⡀⢸⡇⠀⠀⠀⠀⠖⠀⠀⣇⣀⡀⠀⠀⠃⣀⣿⢠⠸⢥⣮⡀⠀⠀⠠⠈⠉⠉⡝⠳⢦⡄⡇
⠀⠀⠀⡇⠀⠆⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⠐⠙⠏⠹⡇⠀⠀⠀⠀⡂⢰⠋⠉⢹⠓⡆⢰⢟⠃⠀⠀⠁⢠⠆⠙⢿⡆⢀⠀⠀⠀⠅⠀⢸⡇⡇
⠀⠀⠀⠃⠀⢼⠀⠀⠀⢀⡇⠀⠀⠀⠀⠈⢻⠀⠠⠇⢨⡆⠀⠀⠀⠀⠗⢰⠀⠀⢸⠘⣧⠘⠸⠀⠀⠀⠀⢰⠂⢠⣺⡧⡼⠧⢄⣰⡆⠀⢹⣁⡇
⠀⡅⠀⣄⠀⢻⡄⠀⠀⢿⣷⠠⠀⠀⠀⣐⣈⡀⠀⣀⠀⡂⠀⠀⠀⢀⡇⢸⡄⠀⣅⠐⡷⢀⢐⡀⠀⠀⠀⢠⠀⣠⠀⠀⠀⠀⢰⠀⠙⡇⣼⠀⠀⠀⡂⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠈⠉⠈⠈⠀⠀⠀⠐⠉⠀⠘⠀⠀⠀⠀⠸⠀⠜⠇⠿⠠⠀⠠⠇⠠⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠿⠿⠿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡙⣉⣦⣶⣶⣶⣶⣾⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⠋⠄⢹⡖⢈⠙⠻⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⡏⠀⠘⠃⡠⠈⠁⡀⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣽⠀⠲⠄⠀⠀⠀⠐⠁⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡏⡦⣀⠀⠀⠀⠉⢀⡔⠁⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⣀⣴⡢⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡙⢰⣿⣿⣷⣄⣸⣿⣿⡃⠀⠀⠠⣄⣤⢦⣧⡆⣸⣯⣬⣦⠰⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢅⣾⣿⣿⡏⠉⢻⡁⣙⣷⣤⣶⣿⣾⣿⣿⡟⢣⣿⠻⢽⣿⡿⢽⡹⣻⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡇⠖⠃⠕⠦⢫⢻⡗⠦⠄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠷⡎⠙⠛⢹⣿⣿⠿⠛⣿⣿⣿⣿⣿⡟⠁⠀⣸⣧⡄⢰⡖⡰⢻⣶⡌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⠀⠀⢀⣾⡿⠁⢀⣴⣶⣿⣿⣿⡏⠀⠀⠀⡟⢱⡀⠀⣰⠁⠧⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣽⡇⠀⣠⣾⡏⠀⠀⣠⣽⣿⡿⠋⠀⠙⢦⡀⠀⢿⠈⣱⡜⣋⣀⣀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡓⠗⠾⢾⠿⣿⠀⢀⣼⣿⠿⠋⠀⠀⠀⠀⠀⠉⠳⢌⣳⣴⡛⣋⣉⡁⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠎⠀⠀⠰⠁⣼⡏⢀⣾⣿⠋⠀⠀⢄⠀⠀⠀⠀⡰⠁⢀⢛⣻⠟⠸⡿⠀⠠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⡆⠀⠀⢠⠁⢸⣿⣷⣿⣿⢡⠀⠈⠢⠀⠆⠀⠀⠠⠁⠀⡎⠀⠛⢾⠦⠀⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⠀⠀⠀⠘⠀⣾⣿⣿⣷⡇⢀⠀⠀⠀⠁⢸⠀⠀⠀⠀⡌⠈⡄⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⡰⡄⠀⠀⠰⣀⢹⣿⣿⢹⡿⠈⠀⠀⠀⠀⠌⠀⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⢡⢰⡀⠀⠡⡀⠑⣿⡿⣿⣴⠀⠀⢀⣉⠐⠀⣤⣤⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢋⣉⠉⢂⠀⠈⠦⢉⠁⠻⡁⢆⠀⠀⠀⠀⣠⣿⣿⡿⢦⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡎⢨⠀⣤⠛⣄⣴⡎⠈⠁⠉⠉⠑⠐⠛⠀⠠⡄⠉⠢⣀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡱⠋⠱⠈⣿⣆⡹⣿⣉⣉⠉⠑⠄⠀⠀⠀⠀⢰⠀⠀⡐⠉⢢⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢛⠅⢺⠀⠀⢸⠛⡇⠀⠀⠀⠑⠀⠈⣢⠀⠀⠀⣤⣤⡔⠁⠀⠸⠤⠤⠘⡄
⠀⠀⣰⣼⣤⢠⠀⠀⠀⠀⡜⡧⢤⠂⠀⠀⢰⠀⢡⠀⠀⠀⠀⢣⡈⢁⡵⠀⢠⣿⣿⠇⠀⠀⠐⠄⣀⡀⠔
⠀⣻⣿⣿⣿⣿⣄⠀⣀⣴⣿⠔⠂⠀⠀⠀⠈⡀⠨⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡋
⠀⠙⠻⠿⠿⠿⠟⠃⠘⠋⠁⠀⠀⠀⠀⠀⠀⠃⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠑⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⠤⠄⠀⠀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣀⡤⠶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠀⣀⣿⣤⣤⣄⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠄⠀⠈⠷⣤⣄⠀⠈⠉⠁⠀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢓⠐⠒⠘⢖⠀⠀⢙⡟⣠⠶⢲⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠧⠀⠀⠤⠳⣰⠟⣰⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠰⡀⠀⠀⠑⣄⣠⡞⠃⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠀⠐⡄⠀⠀⠀⠙⠶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡈⢃⠀⠙⠂⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢣⡈⠳⠐⠒⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠙⠁⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⡄⠈⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⢦⠈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠋

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣄⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠾⣳⠿⢋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢠⡦⢠⣻⣤⣤⣶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡐⣶⣿⣾⣿⣷⣿⣦⡀⠉⠛⠋⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣦⣄⡠⣀⡀⣈⡼⠛⠛⠛⠛⠉⢸⣿⣿⣷⣆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠈⠛⠿⣿⢌⢽⣿⣧⡤⡄⠀⠀⠀⣸⣽⣿⣿⡿⠀⢀
⠀⠀⠀⠀⠀⢀⠔⣩⠶⣚⣛⡻⠶⣤⣀⢤⢔⣱⢿⣇⣿⡏⠐⠲⡶⠂⠀⠉⠉⠙⠛⠁⢠⠄
⠀⠀⠀⠀⠠⠂⡞⠁⠀⠀⠀⠈⠗⢬⠛⢀⣾⣿⡞⣿⡟⠟⡄⣦⡁⠀⠀⢠⡀⠀⠀⡴
⠀⠀⠀⠀⢨⣸⠃⠀⠀⣰⢋⣬⡕⠀⠰⠙⣿⣿⣿⠟⢿⡸⣽⣿⣏⣷⠀⠀⢡⣄⠈
⠀⠀⠀⠀⢸⣿⡇⠀⠀⣻⡘⠿⠿⠓⠀⠀⢹⡅⣡⣿⡞⣿⢹⣿⣛⣌⠀⠀⠈⠉⠛⠶⣄
⠀⠀⠀⠀⠀⢿⣿⡄⠈⠀⠝⠓⡂⠁⢀⠀⣼⣗⣸⣿⠧⣎⢜⡿⣿⣿⡄⠀⠀⠀⠀⠀⢀⣡⣤⣄
⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⠠⢊⣴⠟⠀⢹⣠⣤⢒⣼⣷⣿⣻⡧⠀⠀⢰⣶⣦⠀⠉⠙⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣶⡿⠿⠋⠀⠀⠀⠠⠀⠀⠙⠿⣾⣷⣿⣦⢿⣿⠿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣷⠅⠈⣀⣀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢹⣷⣤⡉⠀⠁⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⠻⣿⡉⠒⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠘⠳⠄⠐⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣄⡠⢀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠶⣶⣿⣷⡶⠦⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡖⠫⠁⠂⠃⠀⠁⠸⣼⡼⠀⠁⠀⠃⠂⠭⠓⣦⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣋⣙⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠀⠀⠀⢀⣟⣉⣻⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢄⠀⠙⠋⠁⢢⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠊⠈⠛⠁⢀⠜⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠑⠁⠀⠑⢀⠀⠀⠀⢣⠀⠀⠀⡀⠀⢸⠀⡀⡀⠀⠀⢠⠃⠀⠀⢀⠐⠁⠀⠐⠙⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡦⢄⡀⠀⠀⠀⠑⢄⠀⢀⠱⡈⠀⠀⠀⢸⠀⠀⠁⠈⡰⢅⠀⢀⠄⠁⠀⠀⠀⣀⠤⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⠆⠀⠈⠒⠤⡀⠀⢀⠙⢄⠀⠑⡄⠀⠀⢸⠀⠀⠀⡔⠁⢀⠜⢁⠀⠀⡠⠔⠊⠀⠀⢶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠴⠀⠀⠀⠀⠀⠀⠈⡑⠢⢄⠀⠑⠄⠘⡄⠀⢸⠀⠀⡜⠀⠔⠁⢀⠤⠒⡉⠀⠀⠀⠀⠀⠀⠰⠼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠉⠒⢤⡀⠘⣦⣼⣴⡞⠐⣠⠔⠊⠁⠀⠀⠤⠀⠀⠀⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣈⣻⣿⠟⢿⣿⣋⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣿⡀
⠀⠀⠀⠀⠀⠀⡶⠿⢷⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣠⠿⣿⣷⣿⡿⢧⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢰⠿⠷⡆
⠀⠀⠀⠀⠀⠀⠲⠶⡞⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⡠⠔⠉⠀⣼⠛⢹⠙⢻⡄⠈⠑⠠⣀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠘⡶⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠀⣀⠴⢖⠁⠀⠄⢀⡾⠁⠀⢸⠀⠀⠹⣆⠐⠀⠀⢑⠶⢄⡀⠀⠀⠀⠀⠀⠘⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠂⠀⢀⡠⠔⠊⠀⠀⠈⠰⣀⢀⡾⠁⠠⠀⢸⠀⠠⠀⠹⣆⢀⡰⠌⠀⠀⠈⠓⠤⣀⠀⢀⢢⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣧⠒⠉⠀⠀⠀⠀⠀⠀⠀⣠⡟⠠⠀⡀⠀⢸⠀⠀⣀⠠⠘⣧⡀⠀⠀⠀⠀⠀⠀⠈⠑⢢⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⠷⡐⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠐⡰⠿⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠙⢦⡃⢀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⣣⠞⠁⠙⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣅⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡒⠬⣐⣠⠆⠀⠀⢀⣸⣀⠀⠀⠀⢦⣐⡨⠴⣺⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣭⣭⡅⠀⠀⠈⠉⠙⠓⠒⣾⡖⠒⠛⠋⠉⠀⠀⠀⣭⣭⡝⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢘⣛⣛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢳⡄⠀⢠⣲⣲⣲⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣬⣿⣯⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢹⣄⠀⣿⣩⣹⡇
⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠾⠥⠤⠤⠤⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠧⠤⠤⠤⠤⠴⠽⠦⠿⠿⠿⠧⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠡⠁⠀⠀⡀⠀⠀⠁⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠀⡈⠀⠀⠃⠀⠀⠢⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠅⠀⠄⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⣐⠀⢀⡀⠐⠈⠀⢀⡀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⢄⣂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⡤⠜⠻⠦⠄⠩⠤⠀⠁⠙⠦⠤⠄⠨⢥⠤⠀⠔⠉⠷⡄⠀⠦⢈⢤⡤⠤⠴⠒⠖⠀⡈⠽⡻⢟⠛⣷⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢴⢠⠀⠐⠀⠂⠰⠀⡄⠀⠀⠀⢠⠀⠀⡆⠀⠂⠀⠀⠃⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⡄⢰⠀⢀⠀⠀⠀⠁⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠾⠤⠶⠀⠤⠶⠆⠤⣄⣄⠀⠀⠤⠴⣤⡀⢤⡀⢁⣀⣄⠀⠤⣀⠄⠀⢀⠘⣀⡀⣀⣄⣤⣌⣀⢀⣄⣠⣱⣥⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢠⡏⠀⡄⢀⣶⠀⠀⠘⠀⠈⡍⠃⠀⠀⠀⠃⢠⡄⠈⢩⠉⡄⠀⠀⣡⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⡇⠀⡇⢸⡟⠀⢨⠐⠀⢠⡇⠄⠀⠌⢀⠀⢰⡇⠀⢸⠇⡇⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡇⠀⠁⣬⡧⢀⢷⡄⡀⠈⡇⠠⠃⠄⠠⠀⠈⡇⠀⢘⠀⡇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⠘⢺⡇⠳⣀⠘⡟⡀⠄⢸⠁⠀⡇⠀⠀⠀⠃⠀⠠⠇⠀⣌⢸⡇⠀⡀⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⠀⠹⠀⠁⠾⠟⠑⠄⠃⠀⠄⠀⠀⠃⠀⠀⠀⠐⠂⠚⠂⠀⠡⣌⡤⠀⠔⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣀⣀⠄⡀⠐⢦⡚⠀⠀⠀⡇⠀⠀⠑⠀⠀⠀⠀⠀⠴⠂⢰⡄⠀⠀⢀⡀⠘⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡿⠀⠀⡈⣭⣍⠀⣠⠀⠀⠃⢀⠀⡠⠀⡉⠠⡁⡀⠀⠼⡔⢺⠠⡯⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⠀⠛⠟⠀⠈⠀⠀⠁⡇⠀⠈⠀⠀⠀⠈⠋⠁⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⣀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣀⡀⠠⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠫⠀⠀⠀⠘





⣿⣿⡿⠿⣿⠿⢿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⢠⣄
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠹⣿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢠⣤⣶⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣄⠀⡀⠀⠸⡿⠀⠀⠀⠀⠀⠀⣤⣼⣁⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠴⣀⣀
⠀⠀⢋⣾⠏⠹⣆⠀⢀⡄⠀⠀⠀⠀⠀⢸⢿⣿⡏⠋⠁⢠⠄⠀⠀⠀⠀⠀⠀⠀⣿⣷⣆⣧⣤⣼⣧⡀⠀⠀⠀⠀⠴⢶⣦⣿⢿⡞⣿⣻⡞⠟
⠀⠀⢸⠟⣧⠀⠈⢩⡿⠦⠀⠀⠀⠀⠀⠈⢸⣿⡇⠀⠀⢸⠗⠂⠀⠀⠀⠀⠀⠀⠿⠿⠛⣛⠿⠟⠽⠅⠀⠀⠀⠀⠈⣹⡿⠛⠛⢿⡟⠉
⠀⢠⡏⠀⢸⡄⠚⠋⡽⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣿⣿⣿⣆

⠀⠀⢀⠠⠆⠐⠂⠲⢄⡀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⣠⠉⡐⠈⠀⠀⠁⢊⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠙⢷⠀⠀⠀⠀⠀⠀⣀⣠⣼⣿⣿⣤⣀⡀⠀⠀⠀⠸⠋⠉⠹⡄⢀⣀
⠀⡧⠠⠀⠀⣿⡷⠀⠀⠀⡧⠀⠀⠀⢠⠀⡻⠐⢺⣿⣷⠤⣄⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⣿⡿⠿⠿⠗⠀⠀⠀⠃⠀⠀⠠⠘⡅⠀⠱⣄⠞⠉⢱
⠀⠸⡀⠡⣴⠁⠘⡆⠌⠰⠇⠀⠀⠀⠀⠈⠁⠚⢺⣿⣿⠖⠁⠚⠀⠀⠀⠀⠀⠀⠀⣀⢠⣿⣇⣠⠀⡀⠀⠀⠀⠈⠐⠊⠀⠀⠘⢄⠀⠀⠀⢀⠜
⠀⠀⠘⣶⡅⢠⡀⢼⣞⠃⠀⠀⠀⠀⠀⣀⣀⣀⣼⣿⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⣚⣉⣈⣿⣧⣈⣛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠈⠁
⠀⠀⠘⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠚⠚⠓⠒⠒⠒⠒⠒⠒⠒⠚⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⣀⡄
⠀⠀⢻⣽⠀⠀⠀⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣴⣦⠻⣿⣀⡀
⠀⠀⢸⠿⢿⡄⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⡅⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⣨⣷⠯⢻⣻⠟⠃
⠀⠀⣿⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⣄⠀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⣴⣰⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢟⠝⡪⠕⠊⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣸⢿⡀⠈⠁⠀⢠⡄⣿⡅⠀⠀⠀⠀⠠⡿⣿⠟⠛⠀⠛⠓⠀⠀⠀⠀⠀⠀⣻⠟⡵⠊⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠠⠞⠁⠸⡇⠀⠀⢠⣼⣷⣿⣧⠀⠀⠀⠰⢿⣿⣿⡷⣚⣛⣛⣿⣿⡷⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⡟⠛⠛⠟
⠀⠀⣠⡀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⢀⡀⠀⠀⠘⣿⣿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠘⠟
⠹⠦⢿⡶⠶⠖⠀⠀⠀⠠⠀⠀⠀⠰⠞⣶⣮⠁⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⢸⣿⡾⢛⠛⢿⣿⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠛⣿⡘⠚⠛⠛⠛⠓⠃⠀⠀⠀⣰⣿⡉⠳⠤⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠈⠿⣧⣈⣈⣾⠿⠁⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⣷⣿⡇
⠀⠀⣼⠏⢳⡀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢸⡇⢰⣶⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⠀⣉⣏⡀⢀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠈⠀⠁⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣴⠶⠟⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡉⣉⣭⣉⢉⣩⣯⡉⢉⣭⣍⡉⣡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣼⣷⣿⣿⣿⣾⣿⣿⣿⣾⣿⣿⣷⣿⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⢿⣿⣿⡿⠿⠿⣿⣿⣿⠿⠿⠿⣿⣿⣿⠿⠿⢿⣿⣿⡿⠿⠿⢿⣿⣿⡿⠿⠿⣿⣿⣿⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⠈⠿⠁⠀⠀⠀⠈⠟⠁⠀⠀⠀⠙⠏⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⣶⠰⡖⢶⠰⡶⢶⠶⡶⢲⠆⡶⢰⡆⣶⢰⡆⣶⣷⡆⣶⢰⡖⣶⢰⡖⣶⠰⡆⢶⠰⡶⢶⠶⡶⢲⠖⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠈⡇⠀⠀⠀⠁⠀⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢤⡄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⡀⠀⡄
⠀⠀⠀⠀⢴⣷⣦⠀⠀⠀⠀⠀⠀⡰⠋⠀⢈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡆⠀⠀⠀⠀⠀⠀⢠⠋⠁⠈⠧
⠀⠀⠀⠀⠈⠉⠙⡇⠀⣀⣄⢀⣒⡁⣀⡠⠔⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡇⠀⡴⣻⣿⡛⠀⠴⠀⠈⠻⢷⡀⠀⢀⡂⠀⡀⠃⠀⣀⠤
⠀⠀⠀⠀⠠⠤⠄⠈⠉⠙⢿⡿⠟⠁⠀⢾⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⢨⣿⣿⠿⣷⡄⠀⠀⡀⣀⡀⠁⠒⠹⣿⣾⡿⠁⠉⢴
⠀⢐⠒⠀⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⣰⢶⢦⢀⡤⠏⢸⣿⣻⠚⠈⠀⠆⠈⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠁⠈⢀⡰⢦⣤⣿⠿⢿⣦⢀⣴⣿⣿⣧⣀⣠⣌⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠷⠟⠀⠀⠉⠁⠀⠀⠩⠘⡟⠛⠙⠿⠋⣠⡦⠗⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⡖⢲⠒⡖⢲⠒⡖⢲⠒⡶⢲⠒⡶⢲⠖⡶⢳⡖⣖⢲⡖⣖⢲⡖⣶⢲⡖⣶⢲⡖⣶⢲⡞⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⢛⣞⠓⠛⠚⠓⠛⠚⠓⠛⠚⠓⠛⠚⠓⠛⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠟⠛⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠛⠉⠉⠙⠛⠿⠿⠿⠛⢿⣿⣇⠀⢀⡀⠀⠀⠀⠀⠀⠐⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⡈⠂⢤⣤⣶⣾⣿⣷⣦⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡄⠀⢀⠀⠙⠟⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠸⠛⠠⠀⠀⠀⠠⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡓⠃⠀⢒⠂⠃⠀⡀⠀⠀⠀⠉⠀⠀⠀⠘⠃⠀⠰⠃⣴⣷⣄⡀⠀⠐⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠀⠃⡀⠀⠀⠱⡀⠀⠀⢳⣀⡀⣁⠀⠀⢀⠂⠰⣿⣿⣿⣿⣦⠀⠀⠀⠉⠉⠉⠋⠙⠻⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈⠢⢀⠀⠈⠠⡀⠈⠻⠟⠃⡀⠔⠁⠀⢀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣙⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠉⠀⠀⠚⠀⠀⠐⠦⡀⠀⠀⠀⣼⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠂⠘⡄⢠⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠈⣁⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⠿⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⢰⣾⣿⢿⡿⠃⠀⠀⠀⠀⠡⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠒⠚⠀⠀⠀⠀⠀⠀⢀⣈⣄⡽⢿⣿⣦⣀⡀⠀⠀⠀⠀⠐⢀⣼⣿⠏⠀⠀⠀⠀⠂⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠖⠁⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠉⠛⠿⢿⣷⣶⣶⣶⣿⣿⠿⡇⠀⠢⡀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣄⡀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠳⠄⣁⠀⠀⠘⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣶⣾⣿⣿⣧⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠒⠒⠀⠒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠻⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠉⠀⠀⠀⠈⠂⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢀⠀⠈⢿⣿⡄⠀⢀⠤⠘⢄⠀⠀⠀⠀⠀⠸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠀⢀⠊⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡇
⢄⡀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⡐⠀⠀⠀⠀⠠⠈⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧
⠈⢿⣶⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⠋⠀⠀⠀⠀⠐⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿
⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠑⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣠⣬⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣶⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠒⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠁⡀⡀⠐⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠉⠀⠀⠀⠀⡠⠈⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⡠⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠁⠤⠤⠠⠄⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⠀⠀⠀⠀⠀⠈⢀⠀⠀⠆⠀⡰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣈⡂⠤⣀⣈⠀⠀⠀⡀⠈⠀⠀⠀⡊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠓⠀⠀⠄⠄⢀⢀⣱⠀⢠⠴⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠰⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⠀⠈⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠐⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⢸⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠦⣄⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠘⢦⣄⡀⠀⠀⠀⠀⣻⠀⠀⠀⠀⣸⠇⠀⠀⠀⢠⡴⠚⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠠⠔⠃⠀⠀⢀⠴⠋⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡆⠀⠀⠀⠉⠉⠛⠛⠛⠶⠀⠀⠈⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠚⠛⠛⠛⠳⠀⢀⡤⠶⠛⠋⠉⠉⠉⠉⠙⠛⠷⣦⣀⠀⠘⠉⠀⢀⡴⠋⠀⠙⠓⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⠀⠀⢠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠰⠋⢀⣠⠤⣄
⠀⠀⠀⠀⠀⠀⠀⣠⢤⣄⠀⠀⣠⠞⠁⠀⠰⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⡴⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠐⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠓⠒⠛⠒⠒⠒⠲⠶⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⡤⠤⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠚⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⣀⣤⣤⠤⠶⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⢛⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠦⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠶⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣲⡂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡇⠉⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠿⡞⠉⢹⠉⠙⢲⢯⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣬⡄⠀⢀⡇⣀⡤⡟⠙⢯⣉⡉⢑⡶⢴⡖⠒⠀⢰⠒⠢⣄⡀⠀⠀⠀⠀⠀⠀⠐⢦⣴⡁⣠⠿⡌⢹⠉⣱⠧⡀⣙⣤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⡇⠁⠀⡇⠀⠀⠈⡷⢇⡀⠀⠓⠀⠀⢸⠀⠀⠨⠑⡀⠀⠀⠀⠀⠀⠛⢻⠀⢹⠓⢤⣽⣾⣶⣧⠴⠛⡁⠸⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡧⡄⠀⡇⠀⠀⠀⡇⠀⠈⢙⡶⠦⠤⣼⣀⠀⢰⢀⠀⠀⠀⠀⠀⣐⡒⢻⠒⢻⠒⢺⣿⣿⣿⣿⡒⠛⡗⢚⣟⣓⡀
⠀⠀⠀⣀⡠⢤⠄⠒⢺⠓⠒⠘⡇⠙⠣⣏⠉⠉⠉⠛⠛⠛⠉⣃⣁⡲⢾⠀⠀⣹⠏⠘⣯⢹⠒⠒⠛⠛⡞⣦⠼⢮⣿⣟⢹⠉⢿⣏⠟⠦⣼⠈⠉⠁
⠀⠀⠸⣅⣀⣰⠀⣄⣸⡇⣀⣠⣧⠤⠤⡿⠷⠶⢶⡗⠋⠉⠉⠇⠀⠀⢸⣤⠞⢸⠄⠶⡤⢸⠀⠀⠀⣒⡏⠙⠦⣴⡿⠒⢻⡖⠚⣿⡠⠞⢀⣉⡀
⠀⠀⠀⠀⠀⢉⣼⡋⠉⠁⠀⣰⡇⠀⠀⣇⡀⠀⠀⠉⣽⣖⣲⣦⣴⣮⣿⣿⣷⣶⣤⣀⣀⣸⣀⣄⢀⣉⡏⠠⢤⣾⣿⠚⢻⡗⠚⢻⣧⠀⠀⠉⠁
⠀⠀⠀⠀⣠⣾⣿⣿⣶⣧⣾⣿⣿⣦⣴⡿⣷⠒⢚⠟⢹⡏⠀⠋⠛⣛⠛⣿⣿⠛⠛⠛⢉⣽⣿⣿⣧⣄⡇⠰⢾⡿⣿⢿⣿⣧⢠⡼⣿⣆⣴⣶⣀
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⠿⠲⢦⣄⣸⣧⠠⠴⠶⠿⢠⣿⣿⢴⡾⡯⢠⣿⣿⣿⣿⣿⡧⠦⣿⡇⣿⡄⢯⣿⢛⠶⢿⣿⣿⣿⣿⣇
⠀⠤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠶⠶⢶⣿⣿⣷⣶⢷⣶⣶⣾⣿⣿⣾⣶⣶⣾⣿⣿⣿⣿⣿⣷⢾⣿⣿⣿⣿⣿⡷⠾⢿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠈⠉⠙⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⢀⣔⠒⢢⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⠀⠀⣀⠤⣠⣀⢀⠀⠀⠀⠀⣠⣴⠀⢤⣄⣀
⠀⠀⣘⣷⡄⢰⠉⣠⠒⠚⠢⠀⠔⠒⠢⡀⣴⣿⣯⣼⡁⠀⠀⠀⠀⢰⣿⣾⡛⠟⢷⡀⠀⠀⢰⡇⠸⣆⠀⡽⠿⢷
⠀⣾⣛⢧⣿⠜⣲⠧⠀⢀⣐⠆⠆⠀⠤⡇⢿⣯⣿⣿⢁⣤⠀⠀⢰⡸⣿⣽⣇⣉⣬⣷⠀⠀⢺⣿⣦⡈⠉⣳⣾⣿
⠀⢸⣿⡿⡟⠀⠙⣷⣾⣴⠋⠀⢴⣶⡶⠁⠘⣿⣳⡟⢛⣉⣀⣀⣸⠀⠻⣿⣯⣿⣼⠏⠀⠀⢸⣿⣿⣻⣷⣿⣿⡟
⠀⠘⣿⣿⠃⠀⠀⢿⣻⡍⠀⠀⠘⡝⠁⠀⠀⢿⣿⠇⠀⢿⣭⣼⠃⠀⠀⣠⣿⢹⣀⠀⠀⠀⠀⣇⠀⠈⡉⠈⣿
⠀⠀⢹⡇⠀⠀⠀⠈⣭⠃⢀⠀⠀⠑⠀⠀⠀⢸⣻⠀⠀⢸⣗⣿⠀⠀⠀⠉⠁⠈⢉⣴⠖⠂⠀⠻⣄⡀⣀⣠⡿
⠀⠀⢈⠁⠀⠀⣀⣀⡙⠀⣿⢯⣿⠀⡞⢻⡆⢀⣭⣤⣀⠀⠃⠃⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣨⣄⠀⠈⠉
⠀⠀⠈⠀⡄⢠⣿⣿⣽⡄⣿⣾⡟⠀⡃⢸⡇⣾⡏⢹⣿⣇⠀⠀⠀⠀⠀⠀⢀⡀⠸⣷⢦⣤⠿⠿⠿⠿⠿⠿⣶⡄
⠀⠀⠀⠀⢡⢸⣿⣿⡇⡁⣿⣽⣿⠀⡆⢸⡇⣿⡇⢈⣿⣿⠀⠀⠀⠀⠀⠀⢙⣇⣤⣶⣭⣁⡄
⠰⡟⠀⢬⣿⣾⣿⣿⡇⡅⣿⣿⣿⠀⡇⢸⡇⠻⣧⣠⣿⠏⢀⣀⣠⢤⣄⠀⢈⢻⣿⣿⣯⣿⠧⠄⣶⠀⠀⡀⡴⡄
⠀⠉⠉⠋⠉⠘⠻⠿⠓⠀⠙⠛⡏⠀⠳⠾⠃⠀⠀⠈⠀⣼⣿⣥⣿⣿⣿⠢⣀⣼⢀⣀⣘⣿⠀⣦⢸⣦⣶⣶⣶⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠇⠀⠈⣻⠿⠿⣿⠁⠀⢸⣯⣻⣸⣟⢻⡬⡀
⠀⠊⠁⠉⢳⠀⢠⠖⠒⢤⡀⡠⠒⠒⢦⢀⡴⠒⠒⢆⢹⣶⣾⣿⣬⣿⡆⠀⠀⠉⡀⣠⠃⠀⠀⠘⣿⣷⠿⣿⢿⣿⠇
⠀⣷⠀⣀⣼⠆⣗⠀⠀⢰⠇⣷⠀⢀⣸⠘⣆⠀⣠⣾⠰⣟⠀⠀⢹⣯⠁⠀⠀⢞⡓⣻⡄⠀⠀⠀⠈⣿⢿⢻⣿⡇
⠀⠈⠉⠉⠉⠀⠈⠁⠉⠉⠀⠈⠉⠉⠀⠀⠈⠈⠉⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⠂⠘⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠑⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⢂⡕⠉⠉⠑⡤⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠀⢀⠤⠂⠁⠀⠀⠀⡠⠁⠸⠂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡠⠐⠈⠀⠀⢀⡀⠄⠐⠈⠠⠂⢀⠥⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⢁⠀⠠⠶⠠⠬⠄⠒⠀⠈⢉⠰⠂⠁⢀⢆⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⢀⠤⠂⠁⠀⠀⢀⠤⠐⠈⠀⢀⠠⠐⠁⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡠⠊⢁⠀⠠⠐⠈⢁⠀⠠⠐⠂⠁⠀⠀⢀⠴⠄⠒⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠔⠁⡀⠄⠂⠁⠀⠀⠀⣀⡀⠤⠀⠀⠁⠀⠀⡠⠊⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠔⠉⠀⢠⣊⠀⠀⢀⠀⣀⢀⡄⠀⠁⠀⠀⠀⠄⠀⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠄⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠠⡤⠀⢄⣄⠀⣀⡀⠀⠄⣤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⣀⠈⠙⠢⢀⡀⠀⠠⠒⠂⢤⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠓⠲⣀⠉⠉⠑⡠⠤⠊⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠢⢤⠄⠑⠒⠄⢀⣀⠄⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⣈⠰⠤⢄⠈⠈⡡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡁⠈⠑⠠⣀⡀⠠⠈⠉⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠑⠌⡉⠀⠉⡀⠖⠮⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠛⠃⠀⠒⠂⠉
⣿⣿⣻⣻⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣛⣿⣿⣛⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣹⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣀⣀⣀⠀⢀⡀⠀⢸⣷⢸⣟⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⢺⡗⣿⢸⣿⡿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⢿⠿⣏⣿⣹⡿⣿⢹⡆⢸⣷⣺⣗⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠛⣿⣿⡟⢻⣿⣧⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⣿⣿⠿⡏⣿⣽⡿⣿⢿⡇⢸⡯⢼⡧⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⡿⢾⣿⣿⣿⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣀⣐⣯⣽⣭⣿⣿⣿⡟⣯⣽⡇⢸⣯⣹⣯⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠽⣿⣿⡯⢽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣟⣻⣛⣇⣿⣻⣟⣿⣻⡇⣸⣗⣺⣗⣺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣭⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣿⢻⣟⢻⡖⢲⡞⣿⠛⣿⣿⣿⣶⣷⣿⣻⣟⣷⣾⣿⣿⣿⣾⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⣶⣿⣾⣿⣿⠭⣿⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⠭⡯⢽⡯⢽⡯⢽⠭⣿⣯⣽⣬⡷⣿⢸⡷⣿⢿⣿⣿⣿⣽⣿⣿⡇⠀⢴⣶⢶⣶
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠭⣿⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⠭⡯⢽⡯⢽⡭⢽⠭⣿⡯⢽⣭⣿⣿⢿⣯⡿⢿⣿⡟⣿⣾⣿⣿⣧⣤⣾⣽⢿⣿
⠀⠀⢀⣤⣴⣶⣿⣿⣿⣿⣿⣿⠭⢽⣿⡯⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⠭⡯⢽⡯⢽⠭⢽⠭⣿⣟⣻⣽⣯⣿⣻⣏⣿⣿⣿⡗⣿⣿⣿⢿⣿⣿⣿⣽⣿⣽
⠀⠀⢸⣿⣿⣿⡟⣿⣿⢻⣿⣿⠭⢿⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠭⣿⢭⡯⢽⡯⢽⡯⣽⠭⣿⣷⣾⣶⣿⣿⣿⣿⣷⣾⣿⡗⣿⣿⡯⣿⢽⡯⣿⣽⢿⣿
⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⠭⢽⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠩⣿⢹⣿⢹⡏⢹⡇⣿⠁⣿⣟⢻⣶⡇⣿⣻⣟⣷⣾⣿⡧⣿⣿⡇⣿⢸⡇⣿⣿⢿⣿
⣾⣿⣿⣿⣿⣿⣇⣿⣿⣼⣿⣿⠭⣿⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣺⣟⣺⣗⣻⣗⣿⣓⣿⡿⢿⠿⣯⣿⢽⡿⣿⢽⣿⡇⣿⣿⡇⣿⢺⡇⣿⣿⣻⣿
⣟⣿⣿⣟⣿⣿⡷⣿⣿⢸⣿⣿⠭⢽⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣚⣗⣺⣗⣺⣗⣻⣒⣿⣿⣿⠿⣯⣿⢹⡿⣿⢿⣿⣇⣿⣿⡧⣿⢼⡧⣿⢾⣻⣿
⣯⣷⣿⣧⣿⣿⣷⣿⣿⣻⣿⣿⠭⣿⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣒⣗⣺⣗⣺⣓⣺⣒⣿⣿⣾⣾⣿⣿⣿⣟⣿⣾⣿⡇⣿⣿⣇⣿⣸⣇⣿⣾⣻⣿
⣟⣟⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⠭⣽⣿⡯⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣒⣗⣺⣗⣺⣓⣺⣒⣿⣟⣻⣿⣗⣿⣻⣟⣿⣻⣿⡇⣿⣿⡗⣿⢸⡇⣿⣿⣻⣿
⣟⣿⣟⣷⣿⣿⣏⣿⣿⢿⣿⣿⣭⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣶⣷⣾⣷⣾⣷⣾⣶⣿⣿⣿⣶⣧⣿⣹⣏⣿⣾⣿⣏⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠲⠢⡀⣀⠠⡀⢄⠀⠀⢀⠀⠠⠚⠁⠐⠀⡶⢀⣞⡐⡄⣴⢀⡠⠎⠀⠄
⠀⠀⠀⠀⠀⢠⡠⢂⣰⣦⠀⠠⠀⠃⠘⣍⠉⣀⡇⠀⠘⠃⠂⠀⠀⠀⠉⠁⣂⠀⠀⢠⠁⠉⠁⠀⠐⠤⢠⣮⣀⡔
⠀⠀⠀⠀⠀⢨⠟⠉⠉⠀⠀⠀⡀⠀⢀⡇⠈⠁⣯⣀⠀⢠⣤⣤⡤⡀⡀⢀⣄⠀⡀⢨⡄⣀⢀⣠⡀⠀⠐⠃⡟⠳
⠀⠀⠀⠀⠀⠀⢂⣤⡄⠀⠚⠋⠉⢍⣛⡉⠉⠋⠉⠡⠁⠈⠉⠈⠁⡀⡷⠀⠙⠏⠉⠉⠉⠁⠘⠛⠁⠘⠞⢢⣦⣤
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⠷⢧⣶⣦⣤⣤⣽⠀⣀⣥⣠⡶⡤⠤⠄⣧⡧⢠⠀⢇⠠⣤⡀⢒⠢⣿⡷⡶⠗⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠄⢀⢰⠀⢹⠹⠃⡟⡷⠦⣿⠿⣶⠶⡯⢻⡶⡤⢪⠚⠻⢰⡏⠀⢠⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣤⣌⠘⢘⣬⢱⡂⣂⡓⠤⠳⠀⢡⣀⡇⣈⡃⡁⠀⠠⠀⠀⢁⣄⢈⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠛⠛⢯⣼⣿⣇⣧⠏⠀⠀⢠⠶⠟⠹⠃⢄⣀⠀⠤⣧⢠⣤⢦⣿⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠨⠿⣇⡠⡄⠤⢋⣼⠥⠭⢗⠀⢴⡋⠑⠸⣿⣷⡿⠝⠀⠠⢽⣼⣿⡼⣿⠄⠉⡅
⠀⠀⠀⠀⠀⠀⠀⠛⠿⠷⠶⢦⣤⣤⣤⡼⡿⣾⣀⡄⠤⠄⠀⠀⠀⢀⣛⣃⣀⠂⠀⠀⠀⣬⠷⣠⣴⣶⣷⡶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣲⣄⡀⠀⠀⠀⠀⡠⠖⣾⠻⠀⣛⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠈⠁⠠⠀⢀⡾⠀⠀⢣⠊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠙⠉⢧⡀⠄⠀⠀⢰⡿⠀⠀⠀⣿⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠔⣀⡂⣼⠂⠀⠀⠀⢧⢷⣀⡠⠴⠆
⠀⠀⠀⠀⠀⠀⠣⠀⠆⠀⠀⠀⠀⠀⡄⠀⠀⠀⠆⠀⢹⡃⠀⠀⠀⣄⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⡁⢤⠀⠘⣇⠀⠀⠀⠈⠈⠁⠀⠈
⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠃⠈⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⡀⠀⠀⠐⢄⠀⠀⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢰⠘⠀⠀⠁⠀⠀⠲⠐⠉⠀⡇⠀⣈⡀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠐⠀⠀⠀⠁⠀⠈⠛⠛⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣿⣆⠀⠀⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⡀⠀⠐⠁⠀⠀⠴⠈⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠀⠁⠂
⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⠐⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⢁⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⣀⠀⠀⠀⠀⢠⡄⠀⠈⣿⡇⠀⠀⠀⣿⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡦
⡀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⠀⠀⠀⠀⣾⣷⠀⠀⣿⡇⡇⠀⢠⣿⣿⡇⢨⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠄⠀⣷
⣧⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠁⠀⠀⣀⣿⣿⠀⢺⣻⡇⡇⠀⣺⣿⢿⡇⢸⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠠
⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⠀⣧⣿⣿⠀⣼⣿⣷⣿⠀⣯⣿⣰⣿⣼⣿⣤⠾⣧⣾⣿⣆⢀⣄⠀⠀⠀⢀⡄⠀⠀⠀⠀⣿⠀⢸⣿⠂
⣿⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣜⣣⣤⠌⣧⣼⡇⠀⠀⡇⠀⣿⡄⣼⣿⡄
⣿⡇⠀⠀⣿⣿⢚⣿⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⣦⣷⣴⣽⣷⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⡿⠿⠋⢻⡿⣥⣮⣿⣿⣿⣿⣿⡿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⣿⣯⣿⣿⣿⣿⣿⣿⡷⠝⣿⣻⣿⣿⣿⣿⣟⣛⠿⠿⠿⠿⠿⠿⣿⣿⡿
⠀⠀⠀⠈⠀⠀⠛⠇⠿⣿⣿⠋⠁⠀⢹⣿⣿⣿⣿⣿⣿⡏⠉⠉⠛⢉⣟⣻⣏⠉⠉⠻⣷⣿⡧⢤⣾⣿⡿⠛⠻⠿⠛⠻⠿⠿⠲⠷⠾⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠂⠀⠀⠈⠉⠉⠛⠙⠛⠙⠃⠀⠀⠀⠀⠀⠋⠁⠀⠀⠈⠀⠀⠀⠀⠨⢽⠿⠛⠙⠶⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣸⡷
⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠂⠀⠛⢸⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣧⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠧⠾⠿⠀⠹⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡧⠀⠀⠀⢠⣶⣶⣆
⠀⣠⣀⠀⠀⠀⠀⠒⢲⡆⠀⠀⣾⣷⠀⠠⠤⢤⡀⣽⢿⡗⠰⠒⢦⡄⡆⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢸⣿⣿⣧⣄⠀⠀⠀⣸⣇⠀⠀⣿⣿⣷⣶⠀⢸⣷⣿⣿⣟⠀⠀⣺⡇⣧⣴⢻⣾⣦⣀⣛⢳⡆⣀⡀⢸⣿⣷⣤⣼⡆
⡾⣿⣿⣿⣿⣤⠤⣴⣿⣿⣿⣷⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⡇⢻⡇⣿⢬⢸⠂⠀⡀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠧⠾⠿⠿⠿⠿⠠⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦⠼⠿⠿⠿⠿⠿⠷⠿⠷⠿⠾⠾⠶⠶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠷⠶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⠀⠀⠀⢠⣴⣤⣄
⠀⣀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣶⣶⠀⢀⣤⣄⡀⣿⣿⣿⢰⣶⣦⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢸⣿⣿⣧⣄⠀⠀⣿⣿⣇⡀⠀⣿⣿⣷⣾⣿⣿⣷⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣶⣦⣀⣶⣶⣆⣀⡀⢸⣿⣷⣤⣴⡆
⣼⣿⣿⣿⣿⣤⣤⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣿⣿⣿⠀⣀⡀⢰⣿⣿⣿
⢠⣶⣶⡄⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣄⣀⣿⣿⣆⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣀⡀⠀⣠⣄⡀⠀⠀⢠⣶⣦⠀⠀⣀
⢸⣿⣿⣿⣷⡆⠀⣿⣿⣿⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣴⣦⣸⣿⣿⣿⣿⣿
⢾⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⠈⠉⠉⠉⠁⠀⠂⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⣷⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣀⠀⠀⢀⠤⠂⠐⠠⠀⢀⠀⠀⠀⣠⠀⠀⠀⠁⠀⠡⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠁
⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣷⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⢯⣣⠙⠁⢀⡇⠀⠀⣀⠀⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣠⡈⠀⠀⠀⢉⠉⡇⠀⠀⠉⠀⠀⠀⢠⠄⠀⠀⠀⡀⠀⠀⠀⢀⣿⠇⠠⠁
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⠃⠀⠀⢀⣤⣾⣿⣿⡄⢡⠀⠘⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⠏⡠⠁
⠀⠀⠀⠻⢿⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠁⠀⢂⠀⠈⠪⣄⠀⠰⣤⡤⠒⠀⠀⠀⠀⠀⣠⣴⣿⡿⠃⡔⠁
⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⠀⠀⠑⢀⠀⣰⣷⣤⡀⠀⠀⠀⠀⣀⢤⣾⣿⣿⠟⠀⠈
⠀⠀⠀⢀⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠀⠀⠀⠀⠱⣿⣿⣿⣤⣤⣾⣿⣿⣷⠀⢻⣿⡇
⠀⠀⠠⠃⠘⠁⠀⠀⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⡀⠀⠀⠀⠀⢀⣿⣿⣿⠟⢿⣿⣿⠏⠀⠀⠉⠓⠀⠀⠘
⠀⠀⣾⣿⣿⣷⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠸⣿⣿⣿⣷⣀⠀⠀⠄⠼⠟⠋⠁⠀⣠⣿⣯
⠀⢀⡀⠀⠀⠀⠉⠙⠻⢿⣿⣦⠀⠀⠀⠀⠁⠀⠀⠀⠙⢿⣿⣿⡿⠛⠄⢀⣀⣠⣤⣶⣿⣿⣿⣿
⠀⠈⠋⠀⠀⠈⠒⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣅⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠿⠿⢷⣶⣶⣶⡾⠿⠛⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⠲⣶⣿⣶⣶⣄
⠀⠀⠘⠠⡀⠉⠀⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠠⠒⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡏
⠀⠀⠊⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠁
⠀⢀⠀⠀⠎⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇
⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⡐⠉⠂⠄⠀⣴⣿⡟⢀⠠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⢸⣿⣿⣿⣿⣿⣿
⠀⢘⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⢀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄
⢠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⠂⡀⠘⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣴
⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠆⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠃⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣐⠁⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⣀
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⡿⡿⣿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣞⣯⣴⣿⣬⣧⣽⣷⣬⣗⣦⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⡶⣾⡟⠻⠿⠬⠟⠃⢘⣙⣛⡒⢚⣛⣉⡂⡒⠲⠬⠾⠿⠻⣿⠶⣦⣄⡀
⠀⠀⠀⠀⠀⢰⣿⣻⣶⣷⣶⣾⣿⣷⣦⣬⣙⣿⣿⡇⣾⣿⣟⣫⣥⣶⣿⣿⣿⣶⣶⣿⣭⣙⣷
⠀⠀⠀⠀⠀⠀⠉⠠⠭⣭⣽⣽⣿⣿⣿⣿⣿⢿⣷⣾⣶⣿⡿⣿⣿⣿⣿⣭⣿⣭⣭⣭⠤⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠘⠋⠛⢻⡟⠛⠛⠃⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢷⠀⠀⠀⠀⠀⢸⡇⠀⣴⣦⡀⠀⠀⢠⣄⣀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠠⣶⣴⣶⣾⣿⡀⠈⣿⣆⣄⣤⣿⣷⠀⢁⣿⣥⣤⣠⡌⢻⣿⡿⠿⢿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠊⡿⡋⠁⠈⠛⠻⠛⠻⠿⢹⣿⣿⡀⠿⠉⠙⢻⠛⠀⠈⠱⠉
⠀⢀⣀⣀⣀⣀⣠⣶⣶⣿⣿⣶⣶⣶⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣀⣀⣀⣀
⠀⠻⠯⠿⠶⠾⠟⠾⠿⣿⣛⣻⣿⣿⣏⢛⣿⣿⣿⣍⣉⣹⣿⣿⣿⠙⢻⣿⣿⣟⣻⣿⣶⣞⣷⣾⣿⡿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡾⠲⣇⢐⢐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠁⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠁⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⠻⣌⠀⠀⢀⠰⣾⠃⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⣛⣛⣯⣟⣋⣬⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣁⣤⣄⢠⣦⣐⡎⠀⠀⣴⣯⣬⠁⠀⠈⣧⠀⠀⣿⣿⣟⣭⣭⣿⡿⣻⡦
⠀⠀⢀⡴⠖⠛⠲⣤⡀⢛⣿⡏⠙⢉⣹⡿⠁⡴⠏⠁⠀⣀⡵⠶⠴⢿⣀⠀⢾⣿⣶⣤⣿⣶⣾⡉⠁⠀⢀⡿⣦⣀
⠀⢠⡏⠀⠀⠁⠀⢈⣷⠈⡿⣿⡿⣿⣿⠇⢰⡝⠂⠀⣼⠇⠀⠀⠀⠀⢈⡄⠸⣯⣏⣻⡟⢋⣿⡏⠀⠰⣏⣆⢻⣿⢳⡀
⠀⠈⢏⠀⠀⠀⣠⣬⣟⠀⢹⣿⡷⣾⢿⠀⠈⢹⢲⡴⣯⡀⢀⠀⠀⠀⠠⣾⠀⢹⣿⣟⣛⣿⡿⠀⠴⣴⠿⠼⣿⢘⣿⣧⡄
⠀⠀⢋⡀⢀⢠⣀⢢⡼⠀⠸⣿⡷⢮⣿⠀⠀⠺⣼⣗⠀⠣⣠⡀⠤⠤⢶⡋⠀⠀⣿⢹⣿⣿⡇⠀⠼⣯⣾⣱⠚⣜⣿⣹⠃
⠀⠀⢠⡾⣷⡾⡿⡾⠀⠀⠀⠛⠓⠚⠃⠀⠀⠀⠈⢿⣿⣶⣶⣦⣴⡻⠉⠀⠀⠀⢽⢾⣤⣿⠃⠀⠀⢻⣿⣿⣾⣛⣿⡿
⠀⠀⠀⠜⣧⣻⠓⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣧⠃⠀⠀⠀⠀⢸⣿⣩⣿⠀⠀⠀⠘⣟⣿⣹⣯⣽⠇
⠀⠀⠀⢸⣶⢋⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠻⣖⡏⠀⠀⠀⠀⠀⠀⣿⣻⡿⠀⠀⠀⠀⢻⣿⣙⣯⣿
⠀⠀⠀⠈⡟⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣻⣽⣩⠁⠀⠀⠀⠀⠀⠀⠹⢿⠇⠀⠀⠀⠀⠈⣿⡟⣿⠇
⠀⠀⠀⠀⠙⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣧⣿⠀⢸⣤⠀⠀⠀⠴⠊⠀⢀⣤⡄⢰⣷⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⢰⢷⡄⣧⣿⠀⠈⣿⣦⢼⡇⠀⠀⢠⠀⠀⠄⣿⣿⡇⠀⠀⠀⠀⣿⠠⠠
⠀⠀⠀⠀⠀⣿⡿⣿⡟⣿⠒⠂⣿⡇⢸⡇⠀⠀⠀⢠⠀⠄⣿⣿⡇⣶⣶⣶⣄⣿⡈⢈⢩⣯⣽
⠀⠀⣀⣀⣀⡈⢀⡈⣟⣿⠀⣴⣿⣷⠞⢷⡶⠶⣶⡶⠶⣶⣿⣿⣷⣿⣿⣿⣿⣿⣧⠠⢬⡿⣿⢷⣤⣴⢶
⠰⠿⠿⠿⠿⠿⠿⠭⠽⠛⠀⠺⠿⠿⠀⠘⠃⠀⠘⠃⠀⠟⠛⠛⠛⠛⠛⠛⠛⠙⠛⠶⠖⠓⠛⠘⠛⠛⠘
⣿⡿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⠟⡿⠛⠁⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⣠⣤⣴⣶⣍⣹⣶⣶⣄⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢀⣙⣋⣿⣿⡿⠷⠒⠛⣿⣃⢿⣇⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠐⠛⣶⣴⠞⠁⠀⠀⠀⠀⣻⢟⣫⣿⣿⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣷⡖⣾⡟⠁⠀⠀⠀⡄⣠⢞⣵⣫⣄⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⡏⣻⢣⣾⢳⣼⣤⣯⠊⠙⡏⢸⣁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⠏⠙⠚⠛⣿⣜⣾⡏⢳⡴⣻⣽⠟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠒⠁⡠⢀⢀⡞⣩⣿⣿⠏⠀⠀⠀⠀⣿⠀⣿⠀⢸⠻⠅⣇⢰⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡛⣗⢤⣄⣀⣀⣀⣐⠁⢈⡼⡿⣯⣿⣤⣤⣀⣤⣤⠷⠶⠿⡆⠀⠙⠃⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢊⣻⣿⣟⣒⡫⠷⣶⣶⣶⡶⠾⣗⣭⣾⣯⣿⣷⣶⡒⣶⣶⣒⢲⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣒⡤⣉⡿⠿⢶⣶⡞⣱⣿⡜⢜⣿⡿⣿⣟⠿⣿⣿⣿⣻⣿⣿⣿⡿⢡⣿⣾⣿⣧⡏⣻⣿⡹⢳
⠀⠀⠀⠀⠀⠀⠀⢀⡟⡴⣡⣾⣿⣮⠞⣹⢫⣾⡟⠻⣿⣮⣦⡱⣿⠿⠟⠒⠈⠭⠭⠭⠭⠉⢒⢿⣽⢿⠟⢻⣯⣾⣷⣇⢾⣾⠃
⠀⢀⠀⣀⣀⡀⠀⣸⠘⡵⣵⣻⣿⠣⠀⣇⠻⣿⣷⣴⡿⢃⡼⠛⠶⠊⢐⣐⡄⢿⣿⣿⣿⡗⣜⣿⣶⠟⡀⢯⣿⡞⢁⡿⣿⣧
⢠⣿⣹⣿⣍⠁⢠⡡⣾⢞⡵⣹⠃⣰⠆⣿⠃⢝⠻⠟⣰⠋⠀⠀⡄⠀⠀⠉⢹⡌⣿⣷⣿⢃⡿⠫⣮⡄⠀⡀⠈⠁⠈⢻⠿⣿⣶⣶⣲⡆
⢀⠙⣿⣿⣿⣶⠯⣚⣵⢟⡵⢃⡼⣡⣦⠸⡌⠀⠙⠾⠁⠀⠀⣸⣃⠀⠀⠀⢀⣧⣙⣛⣛⣸⣥⣷⣿⠿⢿⡁⠀⠐⠒⠉⠀⠀⠉⠛⠿⣇
⠿⣶⡿⠿⠿⣖⣛⣭⠶⠋⠀⣫⡾⠛⠁⢠⡷⠀⢠⠀⠀⠀⣴⠟⠙⠛⠛⠛⠉⠋⢰⣶⣦⠋⢸⡇⢸⠀⠀⠙⠒⠀⠤⠤⠤⠥⣥⣀⣄⠈⣷
⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠀⢀⡴⢋⣤⢸⠸⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠸⠷⢿⠆⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⣴⣿⢿⣸⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⢛⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣝⡃⠻⣿⣯⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⢨⣬⣈⣀⠀⢸⡇⣾⠀⠀⠀⠀⠀⠀⢀⢴⣯⠻⠏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣝⢍⢻⣿⣿⡄⠰⣴⡄⠀⠀⠀⠀⠛⠛⠛⠀⢸⡇⣿⠀⠀⠀⠀⠀⣠⣿⣿⣿⣆⡠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⢻⢿⣿⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠈⠻⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣇⣀⠾⢃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠠⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣶⣾⣿⣿⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⢛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣶⣾⣿⣿⣿⡗⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⡄⣿⢟⡻⣉⣿⢋⡿⣷⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡰⣻⡟⣿⣿⡟⡏⣷⠙⣧⣶⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⣼⢳⣿⣿⣿⢧⣿⣸⡀⡇⣼⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠀⠀⡆⣿⠇⠈⢷⣿⠏⡜⠙⣿⣿⣿⣿⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⣿⣍⠛⢾⣦⡻⣾⡇⢠⣛⡝⣿⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⣆⢠⣄⣀⣀⣀⣀⣀⣀⣠⣤⣄⢨⣼⢻⡉⣽⣷⣮⣺⣿⣸⠃⠀⠙⠁⠘⠋⠁
⠀⠀⣀⣤⣤⣄⣀⣠⣶⣿⣿⠿⣿⠀⠈⢳⣮⣝⣻⠿⠿⢿⣿⣿⣿⣿⢸⠁⠀⠻⣿⡈⠉⠉⢿⣿⡆
⢠⣾⣟⣯⠿⠛⡟⠛⠛⠉⠀⢸⣏⣠⣴⣾⡧⠀⠉⠉⠙⢦⡻⣿⣿⢏⡞⠁⢀⣠⣴⣤⣀⣀⣀⣙⣷⡀
⣿⠘⡿⣿⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⣯⣼⣿⣀⣀⣀⣀⣀⣙⣺⣖⣋⣀⣰⣾⣿⣿⡟⢉⣽⣿⣿⣿⠁
⢿⡰⣧⠹⣧⡀⣦⣶⣶⣶⣼⣿⣿⣿⣿⠙⠻⣿⣿⣿⣿⡟⣿⡏⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⡀
⠈⢧⡹⣧⠈⠻⣟⢿⣿⣿⣿⣿⣿⡟⠃⠀⢠⡿⠿⣿⣿⣷⢹⣧⢹⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣷⣶⣾⣿⣿⣿⣷
⠀⠈⠳⡌⢳⡤⡙⣦⢻⣿⣿⣿⡿⠃⠀⣠⡿⠁⠀⠀⠀⠉⠀⠛⢲⡟⣶⠚⠋⠉⠀⠛⠿⢿⣿⣿⣿⣿⣿⣏⠿⠁
⠀⠀⠀⠹⡄⢹⣰⣸⣾⣽⣿⣿⣣⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⣹⣿⣿⠆
⠀⠀⠀⠀⠸⣼⣻⣟⣻⣿⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⠀⠀⠀⠀⠀⠀⠀⢰⡞⣴⣿⡿⠁
⠀⠀⠀⠐⢢⠎⠝⠻⣿⣯⣛⢿⣿⣿⣿⣿⣷⣦⣠⠀⠀⠀⠀⠀⠀⡷⡇⠀⠀⠀⠀⠀⢀⠀⢸⣟⣿⠟
⠀⠀⠀⠉⠈⠀⠀⠀⠈⠛⠿⣷⣮⣳⡄⡀⠈⣿⠋⣆⠀⠀⠀⠀⢀⣷⠃⠀⠀⠀⢀⣀⣉⣉⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡷⠇⠀⠻⠆⠘⠀⠀⠀⠰⠿⡏⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠐⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⢀⠀⠀⠀⠀⠀⣮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠆⠁⠀⠉⠁⠀⠘⠀⠀⠁⠒⠀⢈⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡀⠀⠞⠀⠉⠡⠀⠀⠀⠁⠀⢠⡄⠀⠀⠀⠀⠀⠀⢠⠆⠀⠳⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠄⢠⠀⡀
⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠠⠆⢉⠁⠀⠈⠀⠀⠀⡤⢄⠀⠆⠀⢀⠀⠈⠅⠀⠐⠉⡀⠄⠀⣀⡴⠂⠀⠞⠀⠃⡌⠀⢀
⠀⠀⠘⠀⠅⢀⡊⠉⠀⠃⠚⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠀⠚⡦⠅⠈⠉⠀⣠⡀⠠⠄
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠂⠀⠠⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣤⠀⠠⡄⠀⠀⢀⡀⠀⠔⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠇⢰
⠀⠀⠀⠀⠀⠘⠇⠐⠀⠀⠀⠋⠀⠀⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠄⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠁⠀⠀⠤⠠⣆
⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠞⠂⠂⠀⠀⠀⠀⠀⡀⠀⠀⠁⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠸⢶⣤⣀⠘⠄⠀⠀⣀⠀⠀⠙⠀⠀⠆
⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⣰⠀⠀⢄⠀⠀⠀⣌⠉⠉⠉⠁⠈⠀⠀⠀⠀⡀⠠⠀⠀⠀⠈⠉⡤⠉⢹⡀⠁⠰⣞⠁⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠘⠻⠿⠷⠶⣦⣤⣤⣀⣀⣈⣀⣀⠀⠈⠃⠀⠀⠀⠂⠀⠐⠀⠀⠁⠀⠐⠀⠀⠀⠀⠓⠀⠀⢉⣁⣀⣀⣠⣤⣤⣴⣶⣾⡿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠐⠀⠀⠀⢀⠀⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢀⠌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠁⠘⠘⠒⠓⠒⠒⠈⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠾
⠀⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄
⢨⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⡀⠀⠀⠀⠘⢢⣤⣠⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⢄⡀⠀⠀⠠⠐⢦⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠹⠂⠓⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠠⠔⠉⠰⠄⠀⠀⠀⠀⠈⠓⢶⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠘⠁⠀⠀⢀⣰⠂⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢐⠂⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⣿⣿⢟⠿⡟⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣬⡉⠀⠀⠀⠀⠀⠀⠀⠀⣸⡙⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠒⠀⠀⠀⠀⠀⢀⠀⢀⡄⠀⡀
⠀⠀⠺⠛⣿⠻⠓⠀⠀⠀⠀⠀⣴⣿⣿⣿⣶⠄⠀⠀⠀⠀⠘⣀⡾⢧⣈⠃⠀⠀⠀⠀⡼⣧⣼⣷⣤⣿
⠀⠀⣛⣃⣿⣛⣁⠀⠀⠀⠀⠀⣿⡿⠋⢿⣿⡀⠀⠀⠀⠀⠀⣸⣙⣙⣄⠀⠀⠀⠀⠀⢿⡿⠟⠹⠿⣿


⠀⠀⠀⠀⠀⡤⠤⠄⠀⠀⠀⠀⣷⣄⡀⣄⠀⠀⠀⠀⠀⠀⠀⢆⡇⢹⢢⠀⠀⠀⠀⠀⠶⣄
⠀⠀⢶⣛⣓⡶⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢃⡄⠀⠀⠀⠀⠀⠫⣇⣸⠎⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⣀
⠀⠀⠸⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⣴⣯⣶⣿⣧⠀⠀⠀⠀⠀⠀⢙⡁⠀⠀⠀⠀⠀⠀⣤⣤⣭⣶⣮⣥


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀⠀⠀⠀⠀⢠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢠⣧⣸⡄
⠀⠀⡗⡖⡖⡖⡇⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣼⢻⡟⣧
⠀⠀⠃⠃⠃⠃⠃⠀⠀⠀⠀⠈⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⣿⢼⡇⢿


⠀⠀⢠⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣠⣦⠀⣴⣦⡀⠀⠀⠀⠀⣤⡄⣀⡀⢤⣴
⠀⠀⢰⣿⡂⢠⠿⠀⠀⠀⠀⢀⣤⣤⡀⣿⢿⡇⠀⠀⠀⠀⣿⣿⠀⢻⡿⠁⠀⠀⠀⠀⣜⣁⣈⠁⢀⣁
⠀⠀⡈⠋⠂⠉⠀⠀⠀⠀⠀⠸⣿⣿⠇⢶⣶⡆⠀⠀⠀⠀⠈⠇⠀⠈⠃⠀⠀⠀⠀⠀⠘⠁⠘⠏⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠢⠀⠀⢀⢄⣀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠉⢙⣇⣰⠬⣈⡴⣿⣧⢤⠁⣔⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡤⢠⠟⠇⠀⠸⣿⣾⢑⣲⡿⣛⠀⣮⡀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠧⠐⢃⠶⠰⠋⠀⠁⢀⠈⠈⡂⠄⠒⠛⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣈⢭⠇⠙⠢⡀⠐⠇⡤⢋⢠⣎⠀⣳⣆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⡀⢈⢴⣦⠀⠠⠠⡇⠀⠟⡴⣏⠆⢠⠞⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠮⠜⣉⡴⠓⣠⢶⠆⡠⠼⢀⡔⢰⠀⠀⠠⢛⠤⠀⠈⣀⠀⠐⠄
⠀⠀⠀⠀⠀⢀⡴⡁⠀⠀⠀⣠⠈⠉⠁⢆⠘⢄⡠⠃⠑⢁⡔⣈⠒⠁⡠⢒⠝⠁
⠀⠀⠀⠀⠀⣾⠎⠤⠠⢆⡜⠘⠔⣟⣰⠀⠰⡴⡢⠒⠲⣣⠊⢀⠄⠈⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠫⡔⡅⣌⡢⢀⡴⢙⠀⡼⡘⡼⡸⠑⠲⢸⢁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢸⡅⠈⠁⠘⠴⣇⣠⠼⠚⠀⡇⢿⡇⠀⠠⡠⠋⠀⡀⠀⠈
⠀⠀⠀⢀⠜⣧⠁⠀⠂⠀⠈⠀⠀⠀⣠⣷⣪⠋⠠⠊⠀⠀⡄⢀
⠀⢀⠔⡡⠚⠮⠑⢦⣀⣀⣄⣠⠼⠚⢳⠞⢁⠔⠀⠀⠀⠀⠀⡄
⡠⢃⢜⣓⣢⠤⢄⣀⠈⠙⠂⠤⣀⡴⠃⡴⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⣠⠋⠀⠀⠈⠁⠀⠉⠑⠒⣤⠊⣠⠊
⣿⡿⠿⠿⠻⢿⠿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠒⠒⠚⠑⠚⢒⡗⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⣰⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⣿
⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⣼⡟⠛⠛⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⡆
⠀⠀⠀⣾⣿⣹⡀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⣤⡄⣄⢹⣿⣻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⣄⠠⡀⣤⣀⠀⢀⡠⠀⣀⣀⣶⠀⠀⠀⠀⡀⣠⠀⠀⣰⣿⣿⣿⣿⣿⡟⢡⣠⣤⡄⢀⡄⠀⠀⣴⠀⢠⡦
⠁⠅⢻⣸⣿⣉⣿⣿⣿⣿⣿⣿⣿⠀⣲⣦⣀⣤⣿⠾⠧⠀⠂⠰⠆⢷⡄⠙⣽⠙⠲⠶⠤⠰⢷⣿⠁⠀⢸⣿⣿⣿⣿⣿⣷⣿⣿⣿⢻⣾⣶⣾⣿⣿⣤⣼⢇
⣇⣴⣾⣿⣼⣋⣿⣿⣿⣿⣿⣿⣿⣚⣟⡤⠷⠿⡇⠰⠄⡻⣂⣲⠒⡶⡇⣰⣿⠀⣿⣿⣀⠿⠨⣏⣁⢠⣼⣿⢻⢿⡏⠉⢸⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠃⣐⣿⣿⣿⣴⡟⣿⣿⣿⣿⣿⣿⢀⠀⠀⠴⠤⡵⣴⣴⠓⠒⠛⠁⠛⢡⠉⢸⠀⠄⠹⢿⢿⣻⣿⣿⣿⣿⣿⠀⠈⠀⠀⣾⣿⣿⣷⢼⣿⣿⣿⣿⣿⣿⠿⠿
⣭⡼⣿⣽⣿⣿⠓⣛⣛⣻⣿⣭⣭⡼⢅⠀⠈⠹⠇⣸⠀⠉⠲⡆⠒⢲⣼⡃⣿⠁⣟⡇⠀⢠⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⡇⠀⣸
⠶⡃⠘⣿⡿⣷⡙⠉⢩⣽⣿⣷⡶⠀⢻⠀⠰⣦⣠⠚⠫⢤⡤⠶⠂⣾⣿⡆⣿⠃⣿⣇⣀⠸⢿⣿⣿⣿⣿⣿⢀⣴⣤⣶⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⠃⣰⣿
⠶⠡⢁⡘⠛⠻⠄⠀⣿⣿⡿⠿⠛⠀⠀⠀⠀⡆⠀⠀⣸⣷⣤⣤⣧⡏⠹⠇⣾⠀⣿⣿⣻⡇⣒⣖⣷⡦⠉⢙⣟⣿⢿⣿⠿⣣⣼⣶⣃⢈⡿⠿⠿⢹⡞⣿⣿
⠛⡀⠃⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠹⠿⠿⡳⠤⢄⡐⠉⠲⡆⢀⢉⠁⠿⠿⢅⡀⠀⠙⠹⣗⠐⠛⠸⠟⣿⣿⣿⣿⣿⣻⣶⣤⣥⣉⠉
⠆⠰⠔⠰⠀⡄⠀⠍⠊⠀⠲⠄⢀⠀⢠⡄⠶⠰⣆⠀⢀⡤⢿⠀⠙⠶⣾⣿⣷⣦⣀⠙⠃⠘⠛⢯⣀⣈⣁⣢⣀⣈⣉⣡⣿⣾⣿⣿⣭⠉⣹⣿⣿⣿⣷⣞⣷
⣿⣄⠒⠂⢂⡿⠜⢲⡀⡀⠀⠀⠈⠀⠀⠰⣶⠀⠶⣖⠂⠀⠀⠒⠀⠀⠈⠛⣿⣿⣿⣿⣆⢒⡒⣯⠁⠨⣥⡼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢿⣿⣿
⢿⣿⠄⠒⠛⠈⠖⣾⠵⢰⡀⠒⡀⢀⠀⡄⠙⢣⣴⢿⣷⣦⣀⠒⠙⠐⠈⠀⣿⣿⣿⣿⣗⢒⣲⣆⠸⢸⣿⣿⡿⢾⡿⣾⣿⣿⣿⣧⣿⣿⣿⣿⡿⣿⡟⠿⣿
⣿⣿⣶⣤⡤⢤⠤⣥⡥⣔⠄⢀⣵⣾⣯⢻⣿⣿⣿⡿⣿⣿⣁⣬⡀⠀⠀⠀⢿⣿⣿⣿⣟⣴⣿⣿⣿⣉⣙⣳⣿⣶⣙⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⡀⠀⣰⣯⣿⣯⣫⢢⣿⡿⣿⣾⣷⣼⡿⠷⢿⣿⣿⡿⣷⠠⢠⣀⣾⣮⣿⣿⣿⣿⣿⡷⡿⢿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⡤⡶⠒⣛⣹⣋⣛⠓⣤⣄⡀
⠀⠀⠀⠀⠀⣠⣞⣡⠔⠻⡉⠁⢸⠀⠉⣹⠓⠦⣙⣦⡄
⠀⠀⠀⢀⡜⢡⠞⠳⡀⠀⢳⠀⢸⠀⢠⠃⠀⡠⠛⢣⡘⢆
⠀⠀⠀⡾⢲⠧⣄⡀⠈⠢⣀⢣⣸⢠⠏⡠⠊⠀⣀⡠⢷⠚⣇
⠀⠀⢰⡇⡟⠀⠀⠈⠑⠲⣬⣿⠿⢿⣿⡴⠒⠉⠁⠀⠈⡇⣹⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠸⡏⣏⠉⠉⠉⢉⣩⠿⣿⣤⣼⣿⢯⣉⠉⠉⠉⠉⡏⣹⠀⠀⠀⠀⠀⠀⢀⡾⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡀
⠀⠀⠘⣇⣹⡤⠒⠋⠁⡠⠊⡹⣿⡟⣌⣣⡀⠉⠓⠢⢴⣁⡏⠀⢀⣀⣀⣠⠔⠽⠁⠇⠱⠕⠤⢀⠀⢀⣀⣀⣀⡞⡺⠁⠑⠄
⠀⠀⠀⠙⣆⠳⡀⣠⠊⡀⣰⢡⣿⣿⠻⡉⠙⢦⡀⣰⠇⡼⠁⣴⠛⠁⡱⠻⡷⠲⡖⠖⣶⠒⡖⡖⠉⣀⢠⢤⣸⣗⣏⣢⠀⠼⣷⣦⡀
⠀⠘⠛⠽⠛⢦⡟⢻⣍⢹⠃⢸⢹⣿⠖⢷⣶⣾⠟⣣⠞⠀⣀⣧⣴⢾⠻⢻⡷⣶⡇⠀⠼⠀⢰⣿⣭⣁⣰⣴⣂⣉⣭⣾⠀⣰⠃⢳⡀⠀⠀⡀⠁⠈⡀⠐
⠀⠀⠀⠀⠀⠒⠘⠷⢤⣏⣒⡞⣾⠛⣷⣏⣯⣼⣋⣥⣴⠾⠋⠙⣶⣇⣴⣟⣴⣷⠓⡖⢳⡄⠈⣟⠿⣿⣿⣿⣿⡿⠗⠋⡀⠌⠀⠀⠃⡀⣀⠟⢑⡤⠗⡗
⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣭⣽⣭⣬⣿⣬⣯⣼⣭⣤⣭⣤⣬⣥⣤⣤⣤⣤⣴⣶⣦⣶⣶⣶⣶⣮⣤⣭⣿⣤⣥⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣗⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡺⡻⢻⠹⡟⡝⣗⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢒⡡⢊⠔⠱⢱⠘⡐⡘⢌⠲⢕⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠪⡥⠖⠡⡴⠋⢴⠣⡦⠀⠧⠱⡄⠱⠤⠉⠲⠬⠑⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤⡧⠤⠤⠧⠤⢾⠤⠦⣤⠶⢤⠧⠤⠶⠤⠤⣦⠤⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡤⢤⡀⠀⢸⠀⠀⣟⣠⠼⡀⠀⠀⠀⠀⣿⢠⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡟⠉⠛⢡⠊⠀⠀⢸⣽⠉⠙⠋⣾⠁⠀⠀⣽⠋⠉⠋⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⠉⡏⠉⠃⠀⠀⢹⠿⠉⣿⠉⢻⡀⢀⣘⣹⡋⣿⠉⠙⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠚⡏⠉⠉⠁⠒⢺⠀⠀⣟⠀⢸⠀⠀⠀⠀⠈⣿⠂⠐⠒⢒⣤
⠀⠀⠀⠀⠀⡔⠉⠀⡠⠮⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠧⠄⠉⠒⠤⢀⡀
⠀⠀⠀⡔⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⢻⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡠⠀⢻
⠀⠀⠀⠈⢮⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣁⠔⠀⠁
⠀⠀⠀⠀⠀⠑⠢⣀⠉⠐⠂⠤⠄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠤⠄⠒⠊⢁⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠤⣀⣀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢀⣀⡀⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⣼⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡘⡛⡀⣀
⠀⠀⠀⠀⣀⣤⠶⠚⣩⠞⢡⠇⠹⡌⠳⣍⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⣫⣾⣹⣿⣹⣮⡻⣶⣤⣀
⠀⠀⢰⣛⣉⣀⣠⣞⣁⣀⣟⣀⣀⣳⣀⣈⣳⣄⣀⣉⣛⡆⠀⠀⠀⠴⠾⢿⠟⠩⡾⠿⠣⠿⠿⠧⠻⠿⡮⠝⢿⠿⠶⠄
⠀⠀⠀⠉⢠⡏⠈⢹⡏⢹⠉⢹⡏⢩⡏⢹⡍⠀⢹⡀⠉⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⢸⣿⢸⣿⠀⠀⡆⠀⠈⡄
⠀⠀⠀⠀⣼⠀⠀⢸⠃⢸⠀⢸⡇⢸⡇⢸⡇⠀⠈⣇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡇⠀⢸⣿⢸⣿⠀⠀⠇⠀⠀⢰
⠀⠀⢀⣠⣇⠀⢀⣸⡀⢸⠀⣸⣇⢸⡇⢀⣇⡀⠀⣸⣄⡀⠀⠀⠀⢀⡄⠀⠀⢀⠀⠀⢸⣿⢸⣿⠀⠀⢠⠀⠀⠈⣄
⠀⠀⠸⢤⡽⠁⢿⣭⡿⢸⠸⣯⣽⢟⡇⢿⣭⡿⠘⢯⡴⠇⠀⠀⠀⠙⠛⠀⠀⠻⠃⠀⢸⣧⣤⣿⠀⠀⠻⠃⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀
⠀⠀⢀⣤⣴⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣦⣤⡀⠀⠀⠀⠤⠤⠯⠭⠭⠭⠭⠭⠭⠭⠬⠭⠭⠭⠭⠭⠧⠤⣄
⠀⠀⠘⠓⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡀⠀⠀⠀⠀⠀⣀⣿⣾
⠀⠀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣀⣀⡀⠀⠀⢀⣀⣠⣴⣦⣀⣀⣀⣠⡀⣠⡆⠀⠀⠀⠀⠀⠀⠉⢉⣦⣄⡠⢀⣀⠛⢹⣿
⠶⠶⠿⢿⠿⠂⠛⠒⠰⠿⠺⠖⠶⠟⠟⠻⠉⠛⠁⠈⠂⠈⠛⠛⠛⠛⠻⣿⠿⠓⠚⠛⠃⠀⢠⡄⠀⠀⠀⠰⣹⣿⣿⣧⣿⣿⣿⣷⣿
⢀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⡁⠘⠂⠬⣉⠲⢌
⡀⠰⠀⡆⢁⠀⠠⡀⠁⠠⡀⠀⠠⠈⠐⠤⠀⠐⠀⡀⠀⢀⠀⠂⠀⡤⠀⢀⡠⠄⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠂⠄⡉⠒⠤⣀⠉⠢
⠁⡾⠀⡄⠀⠆⠀⠑⡀⠀⠘⠢⡀⠀⠑⠀⠀⠑⢄⠈⠒⢄⡈⠢⣀⠀⠈⠉⠀⠐⠃⠀⠀⠂⠀⠀⠄⠒⠈⡀⠤⠐⠀⠈⠀⢤⡀⠑⢦
⠀⢶⠀⢰⠀⠘⠀⠀⠘⡆⠀⢀⠘⠀⠀⠀⠀⠢⠀⠑⠂⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡤⠘⠛⠂⠀⠀⢐⠂⠉⠠⡀⠉⠢⡄
⠀⠘⠀⠈⠃⠀⠃⠀⠀⠀⠂⠀⠀⠀⠀⡀⠂⠄⠀⠀⢀⠈⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠒⠂⠀⠰⠖⠀⠘⠂⡀⠁
⠐⠀⣉⠀⣈⠀⠠⠆⠀⠂⠀⠑⠀⠉⠀⠀⠀⠠⡀⠀⠀⠠⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠒⠀⠀⠋⡠⠄⠀⠒
⠻⠄⠈⠀⠀⠀⠀⠠⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠓⠂⠀⠀⠰⠒⠀⠀⠀⠠⠖
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⢀⠀⠀⠈⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠶⠖⠂⠀⠀⠤⠒
⠈⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠂⠀⠀⠀⠀⠛⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠠⠖⠒⠂⠀⠀⠀⠲⠋⠁
⠀⠀⠀⠸⠶⢤⣄⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠐⠳⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⠐⠂⠀⠀⠀⠀⠐⠋
⣤⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠦⣀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠒⠂
⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠤⠖⠒⠂
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠶⠂⠀⠀⠀⠀⠀⠴⠀⠠⠰⠀⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠄
⣿⣾⢶⢷⣶⠷⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣷⣶⣷⣷⣶⣶⣶⣶⣶⣶⣶⣷⣷⣶⣶⢶⣶⣶⣶⡶⢿⣷⡶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠘⡆⠀⠀⠀⡇⠀⢠⡏⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠉⠓⢦⣀⠀⠀⠀⠠⡀⠈⢦⠀⠀⠹⡄⢀⠀⡇⡄⡼⢠⠀⡰⠋⠀⢀⡤⠀⠀⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠈⠢⡀⠑⠌⢢⠐⠸⠀⡇⢡⠡⢃⠜⡡⢂⠴⠋⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣐⠈⠀⠈⠂⢀⠀⠰⠇⠀⡡⠊⠈⠔⢁⡤⠚⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠲⠤⣄⡢⠅⠠⡠⠂⠤⠒⠀⠀⠂⢌⠀⠠⠊⠡⠐⡈⠤⠒⠋⠉⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠒⠦⠤⠤⢀⣀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠃⠀⠀⢈⠀⠤⠤⢖⡶⠦⠖⠒⠚⠉⠉⠉⠉⠉⠉⠉⠁
⢀⣤⠤⠤⠤⠴⠚⠋⠉⠙⠒⠢⢄⠀⠐⠀⠀⠈⠀⡄⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⢠⠴⠋
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠙⠦⢤⣄⠤⠘⠒⠒⠒⠒⠚⠉⠀⠀⠀⣀⠴⢃⣠⠒⠁⠀⠈⠉⣀⠤⠤⠀⠐⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠤⠀⣀⠀⠢⠀⠠⠠⠵⢶⣒⠒⠒⠒⠒⠒⡶⠋⠉⠁⠀⠒⠀⠀⠶⠄⣚⠬⣄⡀⡀
⠀⠀⠒⠀⠚⠂⠂⠀⠐⠀⠈⠛⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣰⠚⣡⣄⣄⣰⣂⠆⠀⠀⠊⠁⠊⠀⡀⠲⠶⠂⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⣡⣤⠼⠵⠋⠉⢉⣉⣀⣈⣙⡛⣒⡒⠚⠉⠙⠓⠒⠒⠓⠒⠛⠂
⠀⠀⠀⢀⣠⠤⠶⠒⠒⠒⠒⠲⢴⣊⠉⠉⠉⠁⣀⣠⣜⠄⣀⢘⡁⠉⠁⠀⠀⠀⠤⠤⢄⡀⠤⠤⠀⠠⠤⠤⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⣭⢩⣭⣭⣭⣩⡭⣭⢭⣭⡭⡭⢭⣩⢭⠍⢩⣍⣍⢩⡍⣭⡍⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣈⣀⣉⣈⣉⣉⣉⣉⣁⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣦⠀⠀⠀⠀⠀⠠⣾⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠈⢻⠀⠀⠀⢰⢺⢸⡷⡄
⠀⠀⠀⠀⣤⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠸⣿⡿⠁⠀⠀⠀⠀⢴⡤⠀⠀⠈⢹⢸⠷⠁
⠀⠀⠀⠀⠛⠋⠛⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠆⠀⠀⠀⠀⢀⡆⢦⠀⠀⠀⠀⠀⡞⠁⠀⡀⠀⠰⠿⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⣾⢦⡀⠀⠀⣸⠀⢸⡄⠀⠀⣀⢾⡆⠀⠘⠉⢦
⠀⠀⠀⣀⣄⡀⢀⡠⢺⢻⡢⣄⠀⠀⣠⡀⠀⠀⣀⣤⡉⠐⢤⣧⡀⣀⣧⠴⠈⠁⠀⠀⢠⠁⠀⠀⠑⢄⣠⠄⠒⠂⠠⡄
⠀⠀⠀⡏⠋⡏⢸⡷⣛⣚⡛⣾⣧⠉⢹⠉⢁⣩⠉⣯⠍⡍⠸⠀⠀⠀⠸⡀⠀⠀⠀⢀⠎⠀⡀⠀⠀⠀⠉⠛⢇⣉⣭⠷⠒⠒⢢
⠈⠋⠀⣷⣶⡧⣾⣿⡿⣿⢻⣿⡇⠈⣼⡄⠁⣿⣾⣿⣴⣷⣥⣿⣾⣿⣧⣥⣴⡿⠶⠿⠼⠟⠟⠉⠉⠉⠓⠈⠁⠀⠀⠉⠉⠉⠉⠘⠓
⠀⠀⠀⠀⠀⠀⠘⠐⠂⠀⠒⠙⠀⠀⠀⠀⠀⠈⠀⠂



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⢴⣿⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⠀⢈⠁⠠⣴⠖⠫⠅⡿⣽⠽⣮⡓⢦⣤⣄⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠰⢟⣯⣽⣤⢠⡀⣿⣷⡀⢀⡀⢠⣚⡛⠛⠛⣻⣦⣘⣹⠋⣼⣿⠀⠻⣈⣿⣿⠿⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⣿⡍⢷⣻⡿⠿⣫⣶⣿⣝⣿⣷⣾⡧⣣⣽⢻⣿⡟⢯⣽⣲⡷⣠⣿⣯⣼⠐⣽⣋⣿⡗⢀⣴⣾⣧⣄
⠀⠀⠀⠀⠀⠀⢐⡳⡟⣿⣾⢟⣿⣿⣿⢋⣤⣤⡝⢛⣵⣦⣶⣭⣹⠿⢏⣿⣵⣶⣭⡛⢿⠷⠤⡛⢿⣷⣿⠿⢿⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡿⣿⣿⣿⣿⣛⣿⣿⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣟⣻⣧⣶⣿⡶⣷⣻⣷⣞⣯⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣾⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠉⠋⣛⢛⠛⠟⢻⣿⣿⣿⣏⣻⣟⣽⣿⣿⣿⣿⡿⠟⠿⠻⠛⠋⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⣀⠰⣿⣿⣿⣷⣶⣾⣿⣿⣯⣽⣿⣿⣿⣯⣽⣿⢿⣧⣷⣲⣴⣦⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⢸⢿⠛⡿⢺⣿⡿⢿⣿⣿⣿⢿⣼⣿⣿⣿⣿⣟⣿⣿⣿⣼⣿⠿⣿⡿⣿⡿⣿⣿⡀⡀
⠀⠀⠀⠀⠀⠀⢰⣶⡾⣷⣾⣨⣧⡄⢸⡷⣾⣾⣷⣿⣉⡋⣘⣛⣻⠟⠛⢴⣬⣿⣧⡈⠓⠀⠉⡹⣟⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢠⠟⣧⣻⣏⡀⠿⠃⠘⢺⠿⣿⣿⣾⣏⠱⠈⠁⠀⠀⠰⡚⢿⣟⠩⣿⣣⠀⠀⠁⣼⣿⣿⣷⠷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡍⣿⠷⠶⠀⠀⠈⣿⣿⣿⣿⠴⣃⠀⠀⠀⠀⣈⣿⣿⡿⠓⠲⠀⠈⢒⣻⠋⢿⣩⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠠⠀⠏⠉⠉⢠⠈⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠈⠃⠀⠩⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡆⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠃⠀⠀⠀⠃⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣠⣴⣾⣿⣿⣿⣿⣷⣦⣌⠁⠀⠀⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠤⣀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣀⣖⣶⣄⣼⠿⠿⠿⠿⠿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣧⣠⣖⣂⣉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣫⣛⣩⣛⣿⣻⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠈⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠞⡿⡅⠂⠀⠀⠀⣼⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠰⠿⣷⡿⠟⣙⣭
⠀⠀⠀⠀⠀⠀⠀⠘⢊⣁⢨⣀⢀⣠⡀⡜⠀⠀⣰⣏⡉⠀⠈⠱⡄⠀⢰⣾⣿⣛⣛⣿⣿⢿⡄
⠀⠀⢀⡤⠔⠶⢤⡄⠘⢿⣿⠛⠚⢻⣿⠇⣠⠞⠉⠀⣉⣰⣤⢼⣇⠀⠨⣿⣯⣭⡭⣭⣶⡛⠃⠀⠀⣦⣄⡀
⠀⢠⠏⠀⠀⠀⠀⢹⡆⢹⢿⣷⣿⣿⡇⢠⡓⠂⠀⡼⠅⠀⠀⠀⠈⣣⠀⣿⡽⢻⡿⠛⣿⡟⠀⢠⣌⡞⣻⡟⣆
⠀⠈⣇⠀⠀⠀⡤⣽⡃⠘⣿⣳⢼⣿⠇⠈⢱⢢⡼⣧⡀⠀⠀⠀⠀⢼⡆⠈⣿⣟⣛⣿⡿⠁⢠⣴⠯⢼⡧⢰⣿⣤
⠀⠀⢁⠀⡀⢀⡀⣠⠇⠀⢿⡵⢾⣿⠀⠀⠸⣼⣗⢈⠣⣤⡠⠴⡶⡞⠁⠀⢹⡟⣿⣿⡇⠀⠰⣯⣾⣔⢻⣞⣯⡟
⠀⠀⢰⠟⣶⢻⢷⠇⠀⠀⠈⠓⠚⠋⠀⠀⠀⠈⢿⣿⣾⣶⡦⣾⠏⠁⠀⠀⢸⡟⣷⣿⠇⠀⠀⢻⣿⣿⣾⣹⣿⠇
⠀⠀⠀⣏⢤⣟⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠾⡞⠀⠀⠀⠀⠀⣿⣯⣿⠀⠀⠀⠈⣟⣯⣹⣦⣿
⠀⠀⠀⢹⣞⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣻⣽⠃⠀⠀⠀⠀⠀⢹⣭⣿⠀⠀⠀⠀⢻⣿⣭⣷⡏
⠀⠀⠀⠈⡉⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡙⢻⡎⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠈⣿⣛⡿
⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢡⡀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢃⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠙⣀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠘⠀⠈⡄⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠉⡄⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠄⠀⡀⠂⠁⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⣠⠞⠉⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⢀⠎⠁⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⢀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢀⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⢛⡰⠃⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠹
⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠒⠉⢠⠃⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣠⠎⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⠀⠁⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⢀⡴⢫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢀⠀⠒⠉⠀⠀⠀⣀⠤⠒⠉⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢋⠙⢶⡶⠠⢤⡴⠶⠚⠉⠛⣇⠀⠈⡙⠁⠈⠳⢄⡠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠀⢠⡀⡴⠀⠐⠀⠀⠈⠳⡄⠀⠀⠀⢀⠌⠁⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠠⠀⠘⡀⠳⡀⠀⠀⣠⠂⠈⠂⠀⡀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⢨⡇⠀⠀⠘⢠⠜⠁⠀⠀⢀⡜⠁⢄⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠃⠐⠄⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠞⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠜⠂⠀⠀⠀⠀⠉⠰⣄⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠁⠀⠀⠀⠆⠀⠀⠀⠀⣀⠝⠂⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢀⡰⠊⠀⠀⠀⠀⣀⠞⠁⠀⢠⢊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠑⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠒⢆⠀⠀⢀⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠈⡲⠊⠀⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⠈⠀⠀⠈⠐⠞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠠⢀⢀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⡠⠉⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠶⠈⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠖⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠤⣸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠀⠀⠀⢹⣿⠋⠈⠀⠀⠀⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣿⠀⠀⠀⢀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠋⠁⠐⠀⠈⡹⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⣂⠀⠀⠊⠀⢰⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣂⣴⣶⣷⣷⣶⣄⡀⠀⠀⠀⢠⡾⠀⠀⠀⣼⣷⡂⠀⠀⠀⢸⣮⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁
⠀⠀⠀⠀⠀⠀⣦⣾⣿⣿⣿⡿⠿⡿⠿⡿⣿⣧⣤⣾⣇⡀⠀⠉⢻⣿⠁⠀⠀⢀⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣧⣴⢶⡞⢆⣙⣯⡉⣿⣿⣷⣶⣵⣇⢼⣿⠀⠀⢠⣾⡽⠁⠀⠀⠀⠀⠀⠂⠀⠀⢸⣿⡄⠀⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣼⣻⡿⣻⣤⡿⠶⢟⢷⣿⣻⣏⣭⣧⣷⡾⣿⣿⣿⣿⣿⣿⣦⣶⣿⣷⣤⣤⣴⣷⣴⣶⣾⣷⣶⣶⣾⣿⣷⣶⣶⣶⣶⣦⣾⠁
⠀⠀⠀⣶⣿⣿⡇⢾⣾⠶⣿⣿⣟⣻⣿⣯⣭⣧⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⠋⠛⣟⣟⣿⡿⢻⣿⣟⣿⣿⣿⣿⣿⣿⡄⢀
⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣥⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⡠⠔⣗⠭⢽⠭⠝⣲⠦⣄⠀⠀⠀⠀⠀⠀⠀⡠⠖
⠀⠀⠀⠀⡰⢻⢔⠋⠹⡀⢰⠀⢰⠁⢑⡴⡓⡄⠀⠀⠀⣠⠎⣪⠞⠣⡀
⠀⠀⠀⡼⢥⢁⠀⠑⢄⢣⣈⢠⢃⡴⠋⢀⣱⡼⡆⠀⠀⡗⣭⡕⡂⠠⣑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣀⠴⠦⣀⠀⠀⠀⢀
⠀⠀⠰⣇⣇⣀⣉⣐⣢⣿⠿⢿⣯⢖⣊⣁⡀⣃⣹⠀⠀⡇⢺⣀⣀⠉⠴⠾⣻⢿⣄⡀⠀⠀⠀⠀⠈⡉⠦⠔⠁⠉⠦⠔⠁⠙⠆⠔⢩
⠀⠀⠘⡇⠇⠀⡀⠤⢚⡿⣷⣾⣟⠢⠄⣀⠀⡍⢼⠀⠀⠋⠈⠁⠀⠀⠀⣰⠏⠹⡄⠀⠀⠀⠀⠀⠀⠙⠒⢲⡖⣲⡒⠒⠒⡖⡒⣖⠁
⠀⠀⠀⢳⠚⡁⢀⡴⠋⡌⣿⡏⠄⠑⢄⠀⣹⢳⠃⠀⠀⠀⠀⠀⠀⠀⡰⡏⠀⠀⢻⢄⠀⠀⠀⠀⠀⢀⣀⠼⠿⠋⠾⣤⠤⠿⠏⡶⠃
⠀⠀⠀⠀⠻⣼⠫⡀⡰⠠⡏⢷⠘⡄⣠⢗⡵⠋⠀⠀⠀⠀⠀⠀⠀⡰⢱⠁⠀⠀⠈⡌⢆⠀⠀⠀⠀⠘⣧⠒⠐⢲⡷⢾⡔⠂⠒⣿⠂
⠀⠀⠀⠀⠀⠀⠛⠶⢅⣞⣻⣚⣆⡽⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⣧⣤⣤⣤⣤⣶⣼⣦⠀⠀⠀⢰⡃⠐⠂⠘⠂⠛⠂⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠂⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢧⡀⠀⠀⠀⠀⠀⢀⣀⣤⢤⣤⣀⡀⠀⠀⠀⣀⣠⣄⣀⣤⣄⡀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣊⡏⣸⡘⣕⢢⣀⡀⠀⠐⠣⠿⣼⣇⣷⠼⠤⠃⠀⠘⠶⠷⢾⣶⡧⠾⠞⠁⠀⡰⠋⠀⠀⠀⣤⢤⡀⠀⠀⠉⠳⡀
⠀⠀⠀⠀⠀⢣⠤⣤⠤⣤⣤⢤⡤⢤⡤⢬⠂⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⣷⣔⠚⠫⠅⡁⢸⡡⠝⠓⢲⣼⠇
⠀⠀⠀⠀⢀⠃⢠⠀⠀⢇⢸⢸⠇⠀⠆⠈⠆⠀⠀⠀⠀⠀⠀⠀⡨⠳⢒⢺⠡⡀⠀⠀⠀⠀⠀⠀⠀⢿⡺⡗⡖⣶⢿⢾⢶⡖⡞⡿⣸⠇
⠀⠀⠀⠀⠌⠀⡨⠀⢰⣸⣸⣸⣰⠀⢸⠀⠘⡀⠀⠀⠀⠀⠀⠸⡀⡅⢸⢈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠧⣿⣽⣸⣼⡧⠷⠛⠁
⠀⠀⠠⠾⠀⠴⠇⠠⢾⠄⠿⠄⡿⠄⠠⠷⠀⠱⠆⠀⠀⠀⠀⣤⠘⢚⡖⠺⢚⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⠉⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢀⣀⡀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢸⢀⣀⣤⣤⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡾⠟⢻⠻⠿⠿⢿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⠟⠛⡏⠉⣹⡾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢾⣦⡀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢀⣤⣶⣿⠿⣿⣅⢸⠀⠀⣇⣴⡿⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠙⠿⣿⣤⣄⣀⣸⣀⣴⣶⣾⡿⠟⠋⡇⠀⠙⠻⣿⡦⣴⣿⣯⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⢿⣶⣦⣼⣭⣽⣿⣿⣿⣿⣯⣴⣶⣶⣶⣷⣶⡾⠿⢿⠋⠉⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣠⣤⣄⢠⣿⣿⣤⣤⡄⠀⠀⣻⣿⣿⣿⣿⣿⡯⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⡀⣿⣿⣿⠀⠀⠀⢨⢼⣿⣿⢸⣿⣿⣿⣿⣧⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⣧⣼⣿⣿⣿⣿⢀⣶⣶⣾⢸⣿⣿⣾⣿⣿⣿⣿⣿⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⢙⢙⠉⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⡿⠇⡇⡇⡇⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣒⢰⠂⣿⣿⣿⡦⠀⣠
⠀⢀⣴⣶⢲⡒⡞⢳⠓⡗⢳⠓⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⠛⢛⣛⠛⢻⣿⣿⣿⣟⣻⣿⣿⠅⠬⠸⠄⣿⣿⣿⣷⣄⠘
⠿⢿⣿⣿⢾⡷⣿⢿⠿⡿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⠿⣿⣿⣿⣿⣿⠿⠿⠿
⠀⠀⠛⠛⠘⠃⠳⠜⠄⠧⡞⠄⣿⣿⣿⣿⠿⣿⡏⣿⣿⡿⢸⣿⣿⣿⡿⣿⣿⣿⣿⣦⣶⣷⣶⣾⣿⣿⣿⣟⣿⣿⣿⠂⠒⠘⠂⣿⣿⣿⡟⠃⣰
⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣅⣄⣿⣿⣿⡏⠀⠀⠣⢺⣿⡇⢸⣿⣿⣿⠀⠇⢿⣿⣿⠉⠻⢿⣿⡿⣿⣿⣿⡇⠀⢺⣿⠀⠀⠀⠀⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠈⠋⡇⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⢠⡍⠿⠟⠀⠀⢸⣿⡇⣿⣿⣿⠃⠀⢸⣿⠐⠀⠈⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⠄⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠇⣿⡿⣿⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣥⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣽⣿

⢀⣠⣶⣦⣀⡀⠀⠀⠀⠀⠀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⣺⣺⣿⣿⡇⠀⠀⠀⠀⢲⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣷⣦⡀⠀⠀⣿⡇
⢸⣺⣺⣿⣿⣷⣶⣦⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣰⣆⠀⠀⣠⣶⣦⡀⠀⣿⣿⣿⣿⣿⡇⠀⢰⣿⣷
⢸⢿⢿⣿⣿⣿⣿⣿⡀⠐⣾⣿⣿⣿⣿⡆⠀⠠⢼⡤⡄⢀⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⡇⢠⣽⣿⣿⣧
⢸⢿⢽⣿⣿⣿⣿⣿⣇⣀⣿⣿⣿⣿⣿⡇⡀⢐⣲⣂⡇⢘⣿⣿⣿⣏⠀⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡸⣿⣿⢉⢨⣿⣿⣿⣛⣛⣻⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡀
⢸⣺⣺⣿⣿⣿⣿⣿⣿⣿⣿⢾⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣒⣒⣺⣿⣿⣿⣿⣇⣸⣿⣻⣟⣿⣻
⣸⣿⣾⣿⣿⣿⢽⢿⢿⡿⣿⣽⣿⣿⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⣿⠶⠶⢾⣿⡧⡧⡧⣿⢿⣿⣾⡗⣿⣾
⣿⣼⣼⣾⣷⣿⣽⣿⣽⣯⣿⣾⣿⣷⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣧⣯⣿⣯⣿⣽⣿⣽⣿⣿⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠡
⠀⠀⠀⠀⠀⠀⠀⣾⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢠
⠀⠀⠀⠀⠀⠀⠀⡀⡀⠙⠀⠀⠀⠀⣠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠜⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡚⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡔⡰⠃⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠙⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠟⠀⠯⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠔⢃⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣦⣿⡄⠀⠀⠀⠀⠀⠈⠁⠱⡆⠀⠀⠀⠀⢀⠃⠚⠁⠠⢤⠀⠀⠁⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⣥⠞⡄⠀⠀⠀⠀⠀⣀⠐⡻⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢧⠀⠀⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠝⠋⠀⠀⢐⡒⠀⠀⢒⣆⠁⢰⠃⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⢀⣤⣾⠁⠛⠿⠿⠁⠀⠘⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⣀⡤⢘⡩⠿⣧⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⣩⡤⢒⠋⠛⠀⠚⢆⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠀⠀⠀⠘⡀⠀⠀⠐⠆⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡀⢀⠀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡀⠐⠉⠉⠻⠟⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⢠⠔⠀⠀⠀⠀⠀⠈⠁⠀⢸⠆⣠⠀⢀⡔⣠⠀⡤⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠁⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠉⠀⠈⠀⠉⠈⠁⠀⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣤⣀⢀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⣴⣼⠋⣿⣿⣿⣿⠻⠿⢃⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣩⣉⣙⣲⣾⣇⠙⠉⢭⣼⠃⢀⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⣿⣿⣚⠻⢿⣿⣿⣦⣄⣀⣠⣾⣿⣿⣿⣿⡻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣏⡍⠁⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣿⢿⣿⣿⣇⡀⠈⠛⠿⢿⣿⣿⣿⢻⣧⣹⣾⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠉⠀⠈⣿⣿⣷⣶⣦⣶⡄⣠⣴⣿⢰⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠃⠉⣴⡟⣻⢿⣿⣿⣿⣿⣷⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠏⢹⣿⣿⣾⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠁⠀⠸⠋⢉⣽⠟⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⣿⣧⣀⣑⣾⣃⠉⠀⠀⠀⠀⠀⠐⢷⣤⡆
⠀⠀⠀⠀⠀⠀⢀⡴⢀⡀⠀⠀⠀⠀⠀⠀⠀⡎⢠⣿⣿⣏⡛⢛⣿⣬⣵⣶⣤⡀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠸⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⣆⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡽⠋⠉⡟⡉⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢋⠛⣻⡛⠋⠉⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢰⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣷⡌⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⠤⠶⠞⠑⠶⢶⣀⠄⠀⠒⢶⣔⣫⣷⡀⢀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢀⣣⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣶⣦⣤⡀⠀⠐⠧⢠⡄⢰⣿⣿⣿⣿⣧⡘⢄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣦⡀⠀⠀⢠⣄⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⣷⣜⠧⠀⠀⠀⠀⣠⣶⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠤⠄⠴⠿⠛⠋