Seperator Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣶⣿⣷⣿⣷⣦⡄⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠐⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣛⣉⣉⠁⠀⠀⠈⣉⣁⣀⡉⢋⣉⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣯⣿⣿⣿⡆⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡿⠛⠛⠛⠛⠋⢩⣄⣠⡌⠙⠛⠛⠛⠿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⡼⠻⣿⣄⠀⠀⠀⠀⠀⠄⣉⣉⠡⠐⠀⠀⠀⠀⢀⣿⣿⡟⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣆⣀⣿⠀⠀⠀⢀⣼⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣯⣀⠙⠀⠀⠀⠀⣴⢇⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠮⠷⠶⠶⢿⣿⣿⣿⠿⠿⠿⠿⣷⣶⣶⣶⡾⠿⠿⠿⣿⣿⣿⡿⠶⠶⠶⠶⠶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⣤⡤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⠉⠹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⠘⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⠀⠀⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⠀⣿⣿⣿⣿⠀⣀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⠂⡞⠁⣰⠋⡁⠉⣧⠙⢿⡿⠋⣼⠉⢈⠙⣆⠈⢳⠐⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠘⠆⢳⡀⢿⡀⠓⠒⠋⢀⡜⢣⡀⠙⠒⠚⢀⡿⢀⡞⠰⠃⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠁⠀⠀⠈⠛⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣺⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⣗⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣈⡭⠤⢤⣉⡢⣠⠖⠲⡄⠀⠀⠀⠀⠀⠀⢠⠖⠲⣄⢔⣉⡤⠤⢭⣅⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠸⣇⠒⡆⠀⠀⠉⠻⣄⣲⣃⣠⠔⠁⠈⠢⣄⣘⣖⣠⠟⠉⠀⠀⢰⠒⣸⠇⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠛⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⡀⠀⠀⢀⣠⠤⠤⠤⣄⠀⠀⣠⠤⠴⠤⣄⡀⠀⠀⢀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⣼⠉⡀⠉⠳⣴⠋⣉⡇⢠⡏⡴⠲⡄⠀⠀⠱⠎⠀⠀⢠⠖⢦⢹⡄⢼⣉⠙⣦⠞⠉⢀⠉⣧
⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠈⠧⠬⠤⠚⢧⡀⢀⡽⠀⠀⠀⠀⠀⠀⢯⡀⣀⡼⠓⠤⠥⠼⠁⠀⠀⠙⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⣫⠵⣏⠭⡝⣾⠩⢤⡉⢢⡴⣋⡉⠙⠲⡄⢠⠖⠋⢉⣙⢦⡔⢉⡤⠍⣷⢩⠭⣹⠮⣽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠘⠲⠴⠃⠘⢦⣁⡼⠀⠀⠘⠃⠀⠀⢧⣈⡴⠃⠘⠦⠶⠃⠈⠙⠉


⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣰⠟⠉⠉⢹⡿⠿⠿⠭⠭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⣬⣭⣭⡭⠭⠽⠿⠿⣿⠉⠉⠙⢷⡀
⠀⠀⠀⠀⢿⠀⠀⠀⠈⡇⠀⠀⣰⢶⡄⠀⣠⣤⠀⠀⣠⣄⠀⠀⢀⣤⣄⠀⠀⣀⣤⡀⠀⢠⣤⡀⠀⣴⢦⡀⠀⠀⡟⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠻⠶⠃⠀⢧⡼⠃⢰⡇⠈⡧⠀⣾⠁⢸⡆⢰⡏⠈⣷⠀⢿⣼⠇⠀⠳⠾⠃⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣴⢶⡄⠀⣴⢦⡀⠀⢙⣛⠁⠀⠙⠳⠛⠁⠀⢙⣛⠁⠀⣠⢶⡄⠀⡴⢶⡀⠠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡛⠶⠃⠀⠷⠾⠃⢰⡏⢹⡆⠀⢰⠏⢳⡄⠀⣞⠉⣧⠀⠻⠴⠇⠀⠳⠾⢡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⡴⢶⡀⠀⢙⡛⠁⠀⠘⠦⠾⠁⠀⠙⣛⠁⠀⣰⢶⡄⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢀⠳⠾⠁⢠⡟⢹⡆⠀⢠⡶⢦⠀⠀⡾⠙⡇⠀⠻⠶⢃⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠛⠚⠁⠀⢺⣄⣸⠇⠀⠙⠞⠃⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠦⠤⣬⡤⠤⠶⠶⠚⠋⠉




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡞⣹⢸⠁⢌⠳⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠓⢺⢁⠇⡇⡞⠠⡀⠕⢄⡇⠉⡆⠀⢼⣻⠄⠀⠀⣀⡤⠴⠖⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡎⡘⢸⢰⠃⢌⠨⡢⣼⠁⢀⡗⢄⡠⠤⠒⠋⠩⠀⠂⠀⣸⢹⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢰⢁⠇⡏⡾⠀⢑⢅⣸⠃⠀⣼⠅⡾⠠⠁⡐⠠⠁⡐⠠⠁⡇⡜⡸⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢠⠃⠀⡞⡸⢰⢡⠇⠪⡢⣑⡟⠀⢰⡇⢠⠃⠤⠐⠀⠤⠐⠀⠤⢸⢠⢃⡇⡟⠒⢲
⠀⠀⠀⠀⠀⠀⠀⠸⠶⠏⠀⡜⠀⢰⢃⠇⡎⡼⢐⢄⠪⣺⠇⠀⣞⠊⡼⠈⢁⡐⠌⢁⠐⠌⠁⡏⡼⢸⢰⠃⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡾⢸⢰⢁⠇⡠⠑⢅⡾⠀⢸⠓⢀⠇⠄⠂⠈⢀⠂⠀⠀⢰⢡⠃⡇⡞⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢠⠇⡇⡎⡸⢀⠨⡢⣰⣇⣄⡯⡂⡸⠈⠀⠀⠈⢀⠂⠌⠀⡎⡼⢸⢰⠇⠀⡞⢀⡖⠲⡆
⠀⠀⠀⠀⠀⢰⠒⢻⡀⢠⠇⠀⡼⢸⢰⢁⡇⡐⢕⢌⠪⡣⡙⢕⢠⡇⢀⠂⠁⢐⠂⠉⡐⢰⢃⡇⡏⡜⠀⢰⠃⠈⠙⠞⠉
⠀⠀⠀⠀⠀⠛⠲⠞⢁⣸⠀⢠⡇⠯⣘⠦⡙⢮⡂⢑⢄⠈⡢⡀⣸⠀⡀⠠⠁⡀⠠⠁⠂⡜⡸⢰⢡⠃⠀⡞
⠀⠀⠀⠀⠀⢀⡤⢚⡭⠓⠚⠙⠛⠳⠮⣝⡺⣷⣝⣦⡑⢕⠌⢀⡇⡐⠀⠁⡐⠀⠁⠐⣠⢃⡇⡏⡼⠀⢠⢧⡀
⠀⠀⠀⠀⡰⠋⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⣻⠽⠿⠿⢿⣦⡁⣸⠐⠀⣈⣡⣤⣒⣚⣭⣤⣼⣰⢃⠇⠀⡼⠀⠙⢆⢀⣖⣆
⠀⠀⠀⣰⢁⡞⠈⠀⠀⢯⡷⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⠼⠛⠉⠉⠉⠉⠛⢿⡋⠁⠀⠀⠀⠀⠉⠢⣠⠇⠀⡄⠈⢇⠈
⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠸⡄⠀⣷⠀⢸
⠀⠀⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⢸
⠀⠀⠀⠹⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠃⢀⡁⢠⠇
⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡠⠋
⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠐⠚⠀⣠⠞⠉⠉⠉⠀⠀⠙⠲⠤⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢹⣏⣛⣛⣛⣫⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣀⣀⣀⣀⡀⠀⢀⣀⡀⠀⢀⣀⣀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⢀⣀⢀⣀⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⢀⢠⡄⡀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠰⠄⠀⠑⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠚⠀⠰⠄⠀⠀⠀⠀⠀⢼⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢀⡀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢀⢀⠀⠀⠀⠀⠀⢀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⡀⣀
⠀⠀⠈⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠈⠉⠁⠀⠀⠀⠀⠈⠀⠉⠂⠀⠀⠀⠈⠉⠀⠀⠉⠉⠉⠉⠉⠻⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠉⠁⠁⠈⠁⠀⠡⠌⠁⠉⠛⠉⠈⠡⠍⠀⠈⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠁⠀⠀⠈⠁⠀⠀⠈⠀⠐⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⡀⠀⠀⣠⠀⠺⣆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⢻⣿⣷⣧⠀⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣼⣿⣿⣿⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⢶⡄
⠀⠀⠀⣀⠀⠀⠀⢀⡀⠰⣎⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⢀⣤⠀⢷⡄⠉⠀⠀⠀⠀⠀⠀⠀⣰⣦⣄⣀⣠⠴⡀⠙⣧
⠀⢀⣼⣾⣿⣶⢶⣯⣧⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⣿⣾⡄⠈⣿⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢫⣽⣿⣿⣷⠀⣼⠃
⠀⢾⣿⣿⣟⣵⣾⣿⣿⣦⡾⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣆⣿⣿⣧⠾⠃⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣾⣶⡿⠿⠿⠛⠁
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢶⡆
⠀⠀⢀⢶⣄⣀⣀⡴⡆⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⣀⣀⣠⢶⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢦⣄⣀⣀⡴⡆⠘⣧⡀
⠀⢠⣿⣿⡏⣿⣿⣿⣿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⢽⣿⣿⣿⡆⢀⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⣹⣿⣷⠀⣸⡇
⠀⠹⠿⣿⣿⣿⣼⡿⠿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⣽⣧⣿⠿⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣼⣿⡿⠿⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⣀⠀⠀⠀⠀⡀⢰⣍⠉⠗⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⣮⠉⠻⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢰⡍⠙⠗
⠀⠀⣰⣽⡷⣶⢶⣮⣇⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣷⢶⡶⣾⣽⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣼⣽⢶⣶⣶⣯⣇⠀⢻⡆
⠀⢼⣿⣿⡇⣭⢸⣿⣿⣆⣼⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣼⡇⣺⣿⣇⣴⠟⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢸⠸⣿⢸⣿⣠⡾⠃
⠀⠈⠙⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠉

⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠀⠀⠀⠀⠀⠀⢤⣤⣤⣠⢤⣤⡶⠿⠿⠷⣄⠀⠀⠀⣀⡾⠿⠿⢷⣤⣤⣄⣠⣤⡤⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠠⠤⠤⠤⠔⠒⠉⠁⠴⠟⠋⠀⠀⠀⠀⠀⠙⠶⠊⠁⠀⠀⠀⠀⠉⠻⠷⠈⠉⠒⠢⠤⠄⠠⠄

⠀⢀⣀⡀⠀⢰⣦⣀⡤⣂⣤⡀⠸⢿⣆⣀⡠⢤⣤⣄⡀⠀⠀⣠⣤⡤⢄⣀⣠⡾⠗⢀⣤⣄⡠⣀⣠⡦⠀⠀⣀⣀
⠀⠈⠋⠙⠒⠤⠐⠋⠘⠟⠁⠈⠑⠒⠊⠁⠀⠛⠋⠀⠈⠒⠋⠀⠈⠛⠃⠈⠁⠒⠒⠁⠀⠛⠗⠈⠂⠤⠐⠋⠙⠉

⠀⠈⠷⡄⠀⠀⠀⠠⣴⣶⣶⠦⢀⡀⠀⢄⣀⡀⠤⠤⠀⠀⠀⠠⠤⠄⣀⣀⠤⠀⣀⠠⢶⣶⣶⡤⠀⠀⠀⠀⡴⠟
⠀⠀⠀⣀⣥⡴⠄⠀⠀⠐⠀⠀⠀⢀⣴⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢷⣄⠀⠀⠀⠐⠂⠀⠠⠤⣤⣅⡀

⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠸⢿⣿⣆⠀⠀⠀⣿⣆⠀⠀⢰⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⢀⣾⡇⠀⠀⢀⣾⣿⠟
⠀⠀⠀⠀⠈⠉⠐⠂⣼⣿⣀⣀⠀⠛⢿⡇⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣿⠟⠁⣀⣀⣸⣯⡔⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢾⡿⠋⠀⠀⠀⣨⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣯⡀⠀⠀⠈⠿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⢤⠀⠀⠀⢠⠄⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢠⣤⠀⡀⠀⠀⠛⠂⢠⡌⠛⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡘⠋⣤⠀⠚⠃⠀⠀⡀⢠⣤
⠧⠀⠀⠐⠃⠀⠀⠀⠀⠈⠀⣠⠈⠉⠀⠰⠋⠈⠓⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⠳⠀⠈⠉⢠⡀⠈⠀⠀⠀⠀⠀⠓⠀⠀⠠
⠀⢀⡀⠀⠀⠀⠀⣤⣀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⢀⣠⡄⠀⠀⠀⠀⣀
⠀⠈⠁⠀⢀⡀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⡴⠖⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠶⡄

⠀⢀⣠⡄⠀⢀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠛⠿⠆⠀⠈⠻⠆⠀⠀⣤⡶⠀⢀⣴⡆⠀⠀⠺⢿⡄⠀⠀⢿⣏⠁⠀⠀⠀⣀⣀⠀⠀⠀⣠⡶⠀⠀⠘⠻⢷⠄⠐⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠛⣿⡍⠀⠀⠀⠛⠿⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠔⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⢴⠶
⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤
⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶
⠀⠀⠰⠖⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠘⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣯⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣬⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡤⢤⡀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⠤⢤⡀
⠀⠀⣈⣪⣭⡿⠋⠁⠀⠀⠉⠉⠒⠢⢤⣀⠀⢠⢖⢦⠘⣦⠋⡴⡲⡄⠀⣀⡤⠔⠒⠉⠉⠀⠀⠈⠙⢿⣭⡕⣁
⠀⠀⠸⢱⢻⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠙⠺⢮⣿⠂⠉⠐⣿⡵⠗⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⡟⡎⠇
⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣠⣤⣤⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡌⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣷⣆⢰⣴⣠⣤⣀⣀⣀⣠⣤⣤⣤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡥⢴⢴⣮⣍⣉⠀⠀⠀⠀⢀⣬⡭⠠⠤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠷⠀⠃⠀⠁⣶⣌⠉⢿⣿⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡷⠇⠀⠀⠀⢠⣽⣿⣷⣼⡿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡯⢄⣀⠀⠀⠀⠀⠀⢀⣀⢄⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⢀⣀⣤⣤⣤⣤⣤⣤⠀⠀⠀⢨⡷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠨⠟⠛⠋⠁⢀⣀⣀⣀⣠⣄⣸⡧⡾⣻⣃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣻⠀⢠⣼⣷⣶⣦⣤⣽⣞⣿⠷⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢹⣿⣿⢿⣿⣿⣯⠃⠀⠈⠛⠀⠻⣱⣿⡛⠙⠻⣿⣶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣛⣂⣀⣚⣚⣿⣿⡿⣽⣇⠀⠀⣿⣩⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠻⣿⣿⡿⠟⢰⣾⣿⠀⠀⢸⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⡏⠀⣿⣿⡇⠀⠁⢙⣯⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⠀⣤⠄⠀⠠⠀⠛⠀⠀⠀⣤⣄⠀⠀⠈⢹⡇⢀⣿⣿⡗⢀⠀⢈⡝⡆⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠈⣀⠀⠇⠀⠀⠀⠅⠀⢀⡀⠀⣿⣿⡇⢜⠀⢸⡇⢸⣿⣿⣧⠘⠳⠾⠙⡇⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⠒⠋⠉⠑⡀⠉⠈⠉⢻⡇⠀⠀⢸⣷⣾⣿⣿⣏⠀⠈⠉⢹⣃⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢠⣼⠇⢀⣀⣽⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⣯⡟
⠀⠀⠀⠀⠀⠀⢸⣿⡿⠅⠀⠀⠀⠀⠀⠀⠀⢈⣽⠀⢸⣿⣿⣿⣿⣿⣿⡇⢀⣀⣤⣄⠦⢷⣦⠀⠀⠀⠀⠈⠀⠀⠠⠄⣀⡀⠀⠤⢀
⠀⠀⠀⠀⢠⣐⣶⣀⣀⣀⣀⣀⣀⠐⢷⡆⠀⠈⣻⠀⢼⣭⣍⣛⡿⣿⣿⠳⠶⣭⣅⠤⠘⡲⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠞
⠀⠀⠀⠀⠀⢹⣿⡿⠹⠿⢿⣿⣯⢾⡿⠁⠀⠄⢿⠀⡆⠈⣻⡿⡿⢯⣤⡴⡟⠿⠿⠶⣿⡇
⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⢰⣿⣇⣼⣷⣤⣀⢀⠸⠀⣧⣤⢩⣿⣻⣿⣿⡇⠅⠰⠀⠀⠂⢂
⠀⠀⣴⡞⢫⡷⠂⠁⠀⠀⠀⠈⠁⠀⠈⠙⣿⣿⣆⢀⣿⣀⢸⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠌
⠀⣸⣿⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠮⢉⣀⡱⠿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠂
⠈⣿⣿⣿⣧⡀⠀⠀⠀⡀⠀⠀⠀⢀⣐⣠⣤⣾⣿⡏⠀⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰
⠀⡿⣿⣿⡟⠙⠻⣗⣛⣛⠛⠛⣻⠟⠛⢻⠁⠙⣿⠀⢠⣿⣿⣿⣿⣿⣿⡇
⠀⡟⣿⣿⠁⠀⠀⢈⠉⠉⠙⠋⠉⠀⠀⢸⠀⢸⣿⠀⣼⣿⣿⢿⣿⣿⣿⡇
⠀⣟⣿⣿⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⣾⣿⣿⣼⡏⢉⣿⠃⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⣿⡏⢿⣿⣿⣿⣿⣿⣿⠃⠀⢀⠀⠈⠉⠙⠛⠻⠻⣶⣄⡛⣦⣤⣀
⠀⡇⣿⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠄⠀⠀⠈⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠛⠛⠁
⠀⡇⣿⣿⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⣿⡆⣇⠒⡄⠀⣀
⠀⣇⣿⣿⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠓⠠⠝⠋⣰⢯⢫⣴
⠀⣿⣿⣿⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠷⣦⣀⠈⠁⠀⣳⣿⡀
⠀⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⠀⠈⠉⠛⠶⣤⡘⠛⠳
⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣿⠀⠀⠀⠀⠀⠀⠉⠋
⠀⠙⠻⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠼⠋
⠀⠀⠀⠀⠉⠂⠠⠴⠀⠀⠀⠀⠤⠄⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠢⠔⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠀⠀⢜⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣀⣀⣀⣀⣂⣁⣑⣂⣀⣀⣀⡀⠐⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡻⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣸⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠔⠊⡐⠈⡳⡋⠐⠉⠒⢄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠛⠛⠒⠒⠒⠚⠛⠒⠚⠛⠒⠒⠒⠚⠛⠓⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠒⠲⠶⠶⠒⠋⠉⠀⠈⠙⠉⠀⠉⠉⠓⠲⠶⠶⠒⠊⠁
⠀⢀⣀⣀⡀⠀⠀⠀⡀⣀⣀⠀⠀⢀⢀⠀⡀⠀⢀⢀⡀⡀⢀⠀⠀⠀⣀⢀⠀⡀⠀⣀⠀⡀⡀⢀⢀⡀⣀⣀
⢐⢐⠒⠒⠒⠐⡐⠂⡒⠒⠒⠂⢂⢒⢐⢒⠂⠐⠒⡒⡒⡒⡐⠐⠀⠒⠒⢒⢂⠂⠒⠒⠒⡒⡒⡐⠐⠒⢒⢒⢒
⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉
⢉⡉⡉⢈⠁⡉⣀⠉⡈⣁⢈⠁⡉⢈⢁⡉⠁⢉⡈⡁⢩⠁⡉⣈⠁⡈⣀⢉⠈⡁⢈⢁⡉⡈⢁⡈⡁⢉⡈⡁⣈
⡠⣀⣄⢄⣠⣀⢀⢄⢄⡀⣀⢀⣀⡀⡀⣀⣄⣀⣀⣀⢈⣀⣠⣀⣀⣀⡀⡀⣀⣀⢀⡀⣀⢀⢄⢀⣠⣈⢄⣄⡠
⠀⣈⢀⡠⢀⢄⠈⠀⠀⡀⢀⡀⡠⢀⠀⡀⢀⡄⠀⢀⠀⣀⠅⠀⡀⠀⡀⠀⢠⡀⠁⠄⡀⢀⠀⣠⢀⠀⡀⡈⡄
⠀⠋⠉⠃⠉⠘⠉⠙⠁⠉⠋⠉⠙⠈⠉⠋⠉⠃⠉⠘⠉⠙⠈⠁⠋⠉⠃⠉⠘⠉⠉⠋⠉⠙⠉⠙⠉⠁⠋⠉⠃
⡽⢯⡽⢯⠿⢯⠿⣭⠿⣭⠿⡽⢿⡽⢯⡽⢯⡽⢯⡿⢯⠿⣭⠿⣭⠿⣭⠿⡽⢿⡽⢯⡽⢯⡽⢯⠿⢯⠿⣭⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠉⢉⠄⠠⡋⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠙⠀⣴⠖⠒⠶⣼⡄⠀⠀⠀⠀⠀⠀⢠⣧⠶⠖⠲⣦⠀⠋⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣱⠀⣛⠚⠀⠀⠈⢿⣆⠀⠀⠀⠀⣰⡿⠁⠀⠀⠓⡛⠀⣎⠟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡚⣿⣯⣁⡀⠀⠀⠈⢿⣧⠀⠀⣼⣿⠃⠀⠀⢀⣈⣽⣿⢓⡋
⠀⠀⠀⠀⠀⠀⢀⠔⠒⢄⠀⠈⠙⢻⡿⠛⠻⠷⢦⣤⡈⠛⢧⡼⠛⢁⣠⡴⠾⠟⠛⠻⡟⠋⠁⠀⡠⠒⠢⡀
⠀⠀⠀⢠⠤⢄⡇⠀⢐⠮⡄⠀⠀⠈⠓⠁⣀⠀⠀⠀⢿⣷⡜⢃⣾⡿⠀⠀⠀⡀⠈⠛⠁⠀⠀⢀⠵⡂⠀⢸⡠⠤⡀
⠀⠀⠀⠈⠁⠀⠙⠢⣧⣐⣠⣤⣴⠶⠿⣛⣛⣛⣛⠦⡀⢹⡇⠸⡏⢀⠴⣛⣛⣛⣛⠿⠶⣦⣤⣌⣂⣼⠴⠋⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠾⠛⠋⠉⠁⠉⠉⢡⣤⣤⣤⣤⡌⠉⠁⠈⠉⠙⠛⠷⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣰⣿⣿⣆⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣤
⠀⠀⣤⣤⣤⣤⣤⠶⢶⣿⡿⠿⠿⠿⠶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⣶⣤⣤⣤⣄
⠀⠀⢸⡇⢀⡀⢀⡰⠋⣡⠄⣰⣷⢀⣴⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⢟⡷⣝⢦⠀⠀⠀⠀⠀⠀⠀⠸⣿⡋⠉⣀⣀⣀⣀⣀⠈⢻⠏
⠀⠀⠸⣷⢸⣧⣾⠁⣼⣿⡾⠟⠁⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⢱⢏⡾⣡⡌⢿⢳⡄⠀⠀⠀⠀⠀⠀⠹⣷⡈⢻⠏⠉⠉⣿⡟
⠀⠀⠀⠹⣷⣿⠟⠀⣠⣶⠾⣿⣿⠛⣿⣯⢨⣿⠀⠀⠀⠀⠀⠀⠀⡇⣿⠘⣧⣿⢃⠈⣇⢷⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⢠⣾⡋
⠀⠀⠀⠀⠈⠛⠀⣴⠟⠋⠀⣿⡿⢀⣿⠏⢸⡏⠀⠀⠀⠀⠀⠀⠀⣧⢹⡀⢋⣿⢻⠀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠉⠻⣷
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠰⠏⠀⡼⠃⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⣧⡻⠞⡼⢣⢇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡳⢾⣡⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠸⠃⡄⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⢀⠀⢸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠛⠛⠿⣾⣷⣤⢠⣤⠄⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠄
⠀⠀⠀⢀⠀⢸⡆⢸⣇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⢤⣤⡀⠀⣙⣿⣟⠁⠀⠀⠀⠀⠀⣸⣿⡟⣠⡄⠀⠀⢰⡄⢻⡿⣯
⠀⠀⠀⠀⢳⡾⠁⣛⣛⠊⢻⡾⠁⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⣾⡿⠟⣋⣵⠞⠋⢸⣿⡇⠀⠀⠀⠀⣰⠏⢸⡀⢿⣷⣦⣴⣿⡇⢸⡇⠸⣷
⠀⠀⠀⠀⠘⢃⣼⣿⣿⣿⣌⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⣀⣬⡶⠟⣩⣴⣾⠀⠈⠉⠁⠀⠀⠀⠀⠻⣷⡜⢷⣄⠙⠛⠛⠋⣠⡾⣡⣼⠟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⡶⠿⣿⣯⡁⠀⠻⠿⠉⣉⣴⣤⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠙⣿⡇⢸⡟⠉⣼⠟⠁
⠀⠀⠀⠀⠀⠛⢿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠷⢶⣶⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠰⠟⠀⠈⠳⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢛⠛⢛⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠙⠁⠋⠀⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢾⣧⣤⣿⡿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠉⠀⠀⠀⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣷⣤⡀
⠀⢠⣴⣾⣿⣦⣶⣾⡿⠋⢿⣿⣿⣿⣷⣤⣴⠖⠀⠀⠀⠀⠈⠃⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢻⣇⠀⠈⠛⠄
⠀⠀⠙⠛⠉⠙⠟⢿⣶⣀⣴⣿⠛⠛⠻⠟⠁⠀⠀⠀⠀⠀⠀⣶⣦⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢸⣿⡄⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣴⣾⣿⣇⣿⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢻⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢾⣿⣿⠙⢿⡟⢹⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢀⠹⣿⣿⣿⣷⣶⡶⠂⠀⠀⠀⠈⠳⣤⡀⠀⢀⣿⢀⡀⣿⡀⠀⢀⣴⠞
⠀⠀⠀⣠⣿⡉⠁⢠⣬⣤⠈⢉⣹⣧⡀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠘⠠⣿⣿⡟⠛⠋⠀⠀⠀⠀⠰⠶⢴⡿⠻⣷⡟⢁⣾⣷⡘⢷⣾⠛⣷⡤⠶
⠀⠀⠘⢿⣿⠟⠃⠸⠿⢿⠀⠛⢿⣿⠟⠀⠀⠀⠀⠸⣿⣦⣄⣠⣤⣤⣽⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⢠⣿⣿⣿⣿⡈⣿⠀⣸⡀
⠀⠀⠀⠀⣻⣷⣶⠀⣴⡄⢰⣶⣿⠃⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠿⠿⢿⣿⠦⠄⠀⠀⠀⠀⠉⠙⣿⡾⠏⢸⣿⣿⣿⣿⠇⠻⣶⣿⠋⠉
⠀⠀⠀⠀⠙⠛⠛⢿⣿⣿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⢻⡆⢰⠏⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠛⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⣾⠁⢀⣠⣤⡀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⣼⠃⣴⠏⠁⠈⠹⣆⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⢿⡀⠀⠀⣠⡿⢠⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⠛⠛⠉⢠⡟⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠳⢶⣏⡀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠈⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠈⠙⠳⢦⣄⠀⠀⢠⡟⠀⠀⠀⠀⣠⡼⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢿⣄⠀⢀⣤⠞⠋⠀⠀⠀⠻⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⠶⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⣀⣤⠶⠖⠒⠶⢦⣄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⢦⣄⠀⠀⠀⠀⠀⠙⢦⡀
⠀⢀⡴⠋⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠈⢻⡄
⢠⡞⠁⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠏⠻⣄⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⢻
⣾⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⡟⠀⠀⠹⣆⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⣼⠃⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢹⡄⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢠⡏⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⢀⣠⡞⠁
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⡤⠾⠋⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⣸
⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⣠⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣄⣀⣀⣀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡶⢶⢞⡻⠛⠛⢟⠳⡶⢶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢹⡏⠀⣡⠋⠀⠀⠀⠀⠙⡌⠀⢹⡏⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⠶⣿⡄⠈⠃⠀⡏⠀⢀⠀⠀⡀⠀⢸⠀⠘⠃⢠⣿⠾⠿⠿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢀⣐⣒⣒⣦⣽⣦⣄⠀⠻⡀⣿⠀⠀⣿⢀⠟⠀⣠⣴⣿⣶⣒⣒⣂⡀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣠⡾⠋⠉⠉⠉⠛⢿⡏⠀⠈⠀⠁⢻⠀⠀⡟⠈⠀⠁⠀⢹⡿⠛⠉⠉⠉⠙⢷⣄⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⡇⠀⠀⠀⠒⣒⣶⡧⢀⣤⣶⣶⣦⡀⢀⣴⣶⣶⣤⡀⢼⣶⣒⠒⠀⠀⠀⢸⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⡄⢀⣴⡿⢟⠉⣴⣿⣿⣿⣿⣿⠁⠈⢿⣿⣿⣿⣿⣦⠉⡻⢿⣦⡀⢠⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣩⣤⣮⣴⡶⠋⣸⣿⡿⣟⢠⣿⣿⣆⣰⣿⣿⣄⣻⣿⣿⣇⠙⢶⣦⣵⣤⣍⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⠿⠗⣫⣿⣿⣿⣯⡄⠀⣿⡍⢽⡭⢻⣡⣾⣿⣿⣷⣌⡟⢥⡫⢩⣿⠀⢠⣽⣿⣿⣿⣝⠺⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣻⣿⠿⠿⣻⣿⣿⡏⠀⢿⣿⣿⣿⣎⡿⣿⣿⣿⣿⠿⣱⣿⣿⣿⡿⠀⢹⣿⣿⣟⠻⠿⣿⣟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⠕⣪⣽⡿⢟⣋⠀⣷⡄⠙⢿⣿⣏⣰⣿⣿⣿⣿⣆⣹⣿⡿⠋⢠⣶⠀⣉⡛⢿⣯⣕⠪⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⢁⣾⣿⣵⣾⣿⡿⠀⠹⣿⣦⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣴⣿⠏⠀⢿⣿⣷⣮⣿⣷⡈⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⡿⢋⣽⣿⣟⣁⣤⣄⡈⢻⣿⣿⣿⣌⣉⠉⠉⣁⣩⣿⣿⣿⡟⢁⣠⣤⣈⣻⣿⣯⡙⢿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⣰⠟⣱⣿⣿⣿⣿⠟⠃⠀⢻⣺⣯⣿⣿⡇⢸⣿⣿⣿⣗⡟⠀⠸⠛⣿⣿⣿⣿⣎⠻⣆⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠃⣰⡿⠛⣩⣿⣯⣤⣾⣿⡌⠻⠿⢿⣟⡁⢈⣻⡿⠿⠟⢡⣿⣷⣦⣽⣿⣍⠛⢿⣆⠸⣘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢀⡟⠀⠀⠉⠉⢰⣿⣿⠟⠀⠰⣶⣿⣿⣦⣴⣿⣿⣶⠆⠀⠻⣿⣿⡆⠉⠉⠀⠀⢻⡀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠇⢠⡄⠀⠀⠀⢿⡏⠀⠀⠀⠹⣿⣿⠛⠛⡿⣿⠏⠀⠀⠀⢸⡿⠀⠀⠀⢠⡄⠘⢇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢾⡇⠀⢀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡀⠀⢸⡷⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣼⣧⠀⢸⡇⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⢸⡧⠀⣼⣧⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡘⣿⡄⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢠⣾⢃⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⠿⣦⣀⠀⠀⠈⠻⣆⠀⠀⣰⠟⠁⠀⠀⣠⣴⠿⡷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣽⣦⣴⣯⣤⣴⠶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣰⡟⢀⣤⠄
⠀⠀⠀⠀⣰⠞⣿⠛⠲⡄⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⢠⣄⣀⣀⣤⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⡟⡁⠞⠥⣐⠺⠛⠛
⠀⠀⠀⢰⡇⣀⣿⣄⡀⢹⠀⠀⠀⠀⠀⠀⢁⠂⠀⠀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡡⢎⡁⠐⢶⣄⣙⠛⠂
⠀⠀⠀⠀⠻⣍⣸⣀⣹⠏⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢀⣀⡆⠀⣀⣸⠀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠻⠷⠴⠄⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠈⠛⠋⠀⠛⠛⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠄⠀⠀⠀⣠⣤⣄⢀⣤⣤⣀
⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⠀⠀⣤⣾⡟⣟⢿⡿⠯⣏⠿⣷⣤⠄
⠀⠀⠀⢠⠮⠅⠡⠄⡉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⣹⠏⡠⠊⣰⣯⣤⠖⠋
⠀⠀⠀⢰⡂⣀⠐⢀⣒⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡔⠁⠐⠁⡀⠜⠉
⠀⠀⠀⠈⠉⢹⣟⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡐
⠀⠀⠀⠀⠀⡿⠛⡟⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠤⠴⠚⠻⢿⠧⠄⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠊
⠀⠀⠀⠀⠀⡇⠀⢱⠀⠀⠀⠀⠀⠀⣈⡉⢐⡀⠀⢀⣐⠠⠤⢔⣂⡀⠂⠀⡐⢒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⣀⣠
⠀⠀⠀⠀⠀⢣⡀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣾⣿⣯⣿⠽⢷⣆
⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠉⡱⠀⠀⠀⠀⠀⣠⠔⠲⠀⠀⠀⠀⠙⢤⣇⣙⣷⣆⡠⠊⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣄⣤⠒⠉⠀⠀⢀⠠⠀⠀⠀⢀⡴⠊⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⠋⢠⢯⠄⢁⡠⠤⣰⠁⢠⣯⠈⡖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠃⡌⢀⠀⠀⠀⠀⠀⠀⠢⡐⠋⣀⠂⠀⠀⠘⢄⡐⠃⠠⠀⠀⠀⠀⠀⠀⡗⠚⠓⠇⠀⠀⠀⠀⠀⠀⢤⠊
⠀⠀⠀⠀⠀⠀⠔⠖⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠃
⠀⠀⠀⠀⠀⡊⠤⠀⠠⣶⣶⠆⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠇⠠⣶⡶⠀⠀⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠐⢤⡀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢢⠀⠞⠁
⠀⠀⠀⠀⠀⢀⣤⣤⣤⠀⣠⣶⡆⢀⣴⢾⡇⢀⣤⠶⢶⡆⠀⠀⠀⢀⠚⠀⠸⠁⠌⢢⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠠⠤⠴⠵⢋⠠⠄
⠀⠀⠀⠀⢰⡟⠉⠀⠹⣶⠟⠹⠷⠟⠁⠘⠿⠋⠁⠀⠀⠀⠀⠀⠀⠈⡈⠃⠚⠐⠂⣺⠀⠀⠀⠀⠀⠀⠀⡧⠤⠤⠤⠄⠤⢴⣅⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠶⠦⠘⠁⠀⠀⠀⠀⠀⠀⠀⠷⠷⠿⠶⠶⠖⠁⠻⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠰⠆⣀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠥⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡁
⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠛
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡏⡞⠀⠀⠀⣠⣿⣆⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⢶⣾⠀⠀⠀⠀⠀⠀⢀⣜⠻⣦⡉
⠀⠀⠀⠀⠀⠀⠀⢇⠇⠀⠀⠀⠛⠚⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠟⠃⠀⠀⠀⠀⠀⠀⠀⠙⠋⠘⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⢠⢻⣄⠀⠀⠀⠀⡹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠤⠜⠀⠀⠀⠀⠀⠀⠀⢠⡜⢦⡰⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠙⠶⠛⠗⠀⠀⠘⢧⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠠⢄⣀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⣧⡃⠄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⢇⡈⡄⠀⠀⠰⡅⠙⢈⠇⠀⠀⡀⠀⠀⠀⠀⣔⢣⣸⠂
⠀⠀⠀⠀⠀⠀⠈⠓⠙⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠓⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣠⢦⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⠄⠀⠀⠀⣠⣄⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⢠⠾⣏⡄⠀⠀⣠⠃⣨⠀⠀⢀⡾⢿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⡰⠀⠀⠀⣞⣳⡖⠂⠀⢀⣷⡡
⠀⠀⠀⠀⠀⠀⠈⠓⠛⠃⠀⠀⠉⠐⠁⠀⠀⠀⠓⠛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠋⠁⠀⠀⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠻⢣⠀⠀⠀⠀⠀⠄⠀⠀⣼⡟⣷⠀⠀⠀⢀⠱⣄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠷⠀⠀⠈⠃⠈⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⡀
⠀⠀⠀⠀⠀⠀⢀⡜⣷⣾⠀⠀⠀⢠⠀⠀⠀⠀⢠⡞⢁⡀⠀⠀⢀⠀⠀⠠⠄⠀⢞⡵⣋⠀⠀⠀⠈⠁⠀⠀⠀⠠⡎⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠙⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⡀⢀⣶⣶⣶⣶⣶⣶⠒⠒⠒⠒⠒⠋⠀⠀⠙⠒⠒⠒⠒⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠁⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⣠⣀⡀⢸⣿⣿⣿⣿⣿⣧⣀⣀⣼⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡇
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣷⡀⠀⠀⢠⡞⠉⠙⠓⠚⠁
⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⡿⠁⠀⠀⠘⢧⣀⣠⠴⢦⡄
⠀⠀⠀⠀⠈⠉⠉⠁⢸⣿⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠃⠀⠀⠘⠛⠛⠛⠛⠛⣤⣤⣤⣤⣤⡄⠀⠀⢠⣤⣤⣤⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⢀⣿⣿⣿⣿⣿⡇⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠖⠋⠉⢳⡄⠀⠀⢀⣾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⣄⣀⡼⠃⠀⠀⠈⢿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⣿⣿⣿⣿⡟⠉⠉⢻⣿⣿⣿⣿⣿⡇⠈⠉⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⢀⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠤⠤⠤⠤⣄⠀⠀⣠⠤⠤⠤⠤⠤⠿⠿⠿⠿⠿⠿⠁⠈⠿⠿⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⠭⣗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡾⠁⠀⠈⣧⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⡾⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡹⣄⣀⡴⠃⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣀⡾⠀⢀⣀⡤⠶⢚⡯⠽⠿⠭⣗⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠧⣞⠉⠁⠀⢰⠋⠀⠀⠀⠀⢸⢺⠆
⠀⠀⠀⠀⠀⠀⣴⠦⠤⣤⣄⣀⣀⠀⣀⣠⡤⠴⠒⣧⣤⣟⣀⣸⣦⡤⠤⣜⠦⣄⣀⣤⠴⣫⠞
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠲⢾⡇⢀⣯⣁⣀⡀⠀⠀⠈⠙⠓⠒⠚⠋⠁
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠃⠀⠉⠉⠉⠛⠓⠒⠶⠤⢤⣤
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠘⠲⠶⠤⢤⣄⣀⣀⣀⠀⠀⠀⠀⣸⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⡏⢠⢯⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠋⠀⠀⠀⠈⠉⠉⠙⠓⠒⠶⠦⠼⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠋⠉⠳⣄⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠈⡇⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡷⢤⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⠀⡠⠚⠛⠛⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠉⠉⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢾⠀⠀⠀⠀⠀⢀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠘⢿⡿⠃⠀⠀⢀⣀⣼⣄⣀⣀⣧⣀⣀⣸⣇⣀⣀⣼⣀⡀⠀⠀⠀⠈⠻⡿⠃⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⢸⣀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⡇⠀⠐⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⡇⠁⠉⠉⠁⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣅⣀⣀⣀⣀⣀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡷⠤⠤⠤⠤⠤⠤⠤⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡧⠤⠤⠤⠤⠤⢴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣦⣉⣉⣉⣉⣉⣉⣡⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠒⠒⠒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠒⠒⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⡀⠀⠀⠀⠀⠙⠿⢿⠿⠿⠿⡿⠿⠿⢿⡿⠿⠿⢿⠿⠟⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⠀⠀⣤⣶⣄⠀⠀⠈⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⣠⠞⠀⠀⣤⣷⣄⠀⢸⡇⠀⠀⠈⠉⠉⠿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⠒⠚⠁⠀⠀⠀⠿⣿⠟⠀⠘⢧⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣧⣤⡀⠀⠘⣷⣦⣀⣾⣧⠀⢀⣿⣆⣠⣶⡞⠀⠀⣀⣤⣿⣇⠁
⠀⠀⠀⠀⠀⠀⢀⠖⠿⠀⠀⢀⣀⠀⣾⠁⢶⣿⠇⠀⠀⠙⣿⣿⣿⣿⡄⣼⣿⣿⣿⡟⠁⠀⠀⢿⣷⠆⢹⡇⢀⣀⠀⠀⠸⠗⢆
⠀⠀⠀⡀⠀⢸⡟⠀⠀⠀⠀⠈⣻⣿⣿⡀⠀⠀⠀⠀⠀⠸⠟⠛⢿⣟⠀⢘⣿⡟⠛⠷⠀⠀⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⠀⠘⣿⠀⠀⡀
⠀⠀⠈⣿⣷⣼⣷⠀⣴⡶⢄⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⢀⠴⣶⡄⢰⣿⣴⣿⡟
⠀⠀⠀⠈⠻⣿⣿⣆⠉⠁⡼⡗⠲⣌⠉⣿⣿⣿⣶⣤⣀⠀⠀⢠⣿⡿⠀⠸⣿⣧⠀⠀⠀⣠⣴⣾⣿⣿⡏⢉⡴⠲⡾⡄⠉⢁⣾⣿⡿⠋
⠀⠀⠀⠀⢀⣴⣿⣿⣷⣼⣅⣿⣈⡛⠀⠛⠉⠉⠉⠉⠛⢷⣶⣿⠿⠁⠀⠀⠹⢿⣷⣶⠟⠋⠉⠉⠉⠙⠃⠘⣋⣸⣇⣿⣴⣿⣿⣿⣄
⠀⠀⠀⠀⠘⣿⡿⠛⠛⡿⢿⣾⣧⣭⣓⣦⣀⣀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⢀⣀⣠⣖⣫⣥⣿⣾⠿⡟⠛⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⡌⠛⠻⠿⠿⠿⠿⠿⠿⢶⣦⣄⠀⢻⡄⠀⠀⣼⠃⢀⣤⣶⠾⠿⠿⠿⠿⠿⠿⠛⠋⣴⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⣴⣶⣶⣶⣶⣶⣶⣤⣄⠙⢷⡄⢣⠀⢠⠇⣴⠟⢁⣠⣴⣶⣶⣶⣶⣶⣶⣤⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣀⣾⣿⡏⠁⠀⠀⣾⡿⠿⠿⠿⣿⣦⣿⣸⡄⡼⣸⣣⣾⡿⠿⠿⠿⣿⡆⠀⠀⠉⣿⣿⣆⣰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠋⠛⠿⠶⠀⠀⠙⠃⠀⠀⠀⠈⢿⣿⣿⠇⣿⣿⡿⠋⠀⠀⠀⠀⠛⠁⠀⠰⠾⠟⠋⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⣭⣭⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣛⣛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⣿⣿⣿⣿⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈




⣿⠿⠿⠿⠿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣻⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢀⣀⣤⣤⣀⡀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠿⠿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣧
⣿⣿⣿⣿⣿⣿⣿⡇⠀⣾⡏⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣼⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⢿⡄⠀⠀⠀⠀⠀⠀⢠⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⢿⣦⣉⠛⠿⣟⣿⡿⠃⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡈⠻⢶⣤⣤⡤⠀⢠⣾⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠉⠛⠛⠛⠛⠉⢀⡀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⣤⣤⣴⣾⡿⣿⣷⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣶⣶⣿⣿⣄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠘⢿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠖⠒⠒⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣶⠀⢀⡄
⠀⠀⠀⠀⠀⣀⠴⠋⠁⠀⢠⡀⣤⠀⡀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣾⣿⣷⣿
⠀⠀⠀⢀⡴⠋⠀⠀⣀⣰⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣄⠀⠁
⠀⠀⠀⡾⠁⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢦⣔⣿⣯⣏⡛⣦⣆
⠀⠀⢸⠃⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣇⠀⠀⠀⠠⣄⣀⡀⠁⠀⠀⢸⣿⡿⢪⡟⠛⠘⢽⡃⠀⠀⠀⢀⣀⣠⠄
⠀⠀⢼⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠂⠀⠀⠀⣻⠀⠀⠀⣀⣨⣿⡏⠀⠀⠠⣾⣿⡏⠘⠋⢦⣁⣾⣷⠀⠀⠀⢹⣿⣅⡀
⠀⠀⢸⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⠀⠀⠀⡛⠀⠀⠀⠉⢙⣿⡇⠀⠀⠀⢿⣿⣿⣧⡈⢁⣈⣻⣿⠀⠀⠀⣸⣿⠋⠉
⠀⠀⠈⣧⠀⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢰⠁⠀⠀⠀⠐⠋⠉⠉⡄⠀⠀⠈⠉⠉⢹⣵⣿⢿⣾⠧⡄⠀⠀⠉⠉⠛⠢
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣟⠷⠃⡀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢀⣼⣿⣿⣿⣿⡀⠀⡠
⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⣴⣿⣿⣿⣷⠏⠘⠂⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢠⣾⣿⣿⣿⣿⡇⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠳⠾⣿⣿⣿⣿⣿⣤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⢠⣰⣆⡤⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢲⣾⡿⠷⠚⠛⢛⠃⠾⢿⣷⠆⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣿⡿⠋⠁⠀⣦⠀⠀⣼⡄⠀⢀⡌⠑⢿⢿⣥
⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⣄⠀⢠⡆⠀⢈⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⣬⠋⠀⠀⠀⠀⢹⣷⣾⣿⣧⣴⡟⠀⠀⠀⠹⣥⣴⣀
⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢸⣷⣿⣷⣾⠇⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⢼⣿⠃⠀⠀⠀⠀⣶⣮⣿⣵⣯⡻⣿⣅⠀⠀⠀⠀⠘⣻⣯
⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸⣿⣟⣿⡾⢿⣆⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠐⣶⡞⠀⠀⠀⠀⠀⣺⣿⡟⣼⡟⢃⡈⢿⡀⠀⠀⠀⠀⣧⣶⠂
⠀⠀⠀⠀⢰⡇⠀⠀⠀⣼⣿⡋⠛⢤⢂⣷⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢉⣿⣇⠀⠀⠀⠀⠰⣿⣿⣇⡊⢁⠢⣀⣾⡗⠀⠀⠀⠀⣿⣿⡉
⠀⠀⠀⠀⠀⣧⠀⠀⠀⢹⣿⣿⣤⣁⣝⣿⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢤⣿⡀⠀⠀⠀⠀⣿⣿⣿⣧⡌⣠⡌⣿⡏⠀⠀⠀⢀⣳⠤
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⢀⣿⣿⣿⡟⠂⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠚⣻⠷⡀⠀⠀⠀⠈⠁⠀⢹⣾⣿⣿⣿⠣⠀⠀⢀⠮⣟⠓
⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⣾⣿⣿⣿⣁⣤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⣿⣦⡀⠀⠀⠀⢠⣿⣿⣿⣿⠧⠀⢀⢴⣽⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠟⣹⣷⣦⣴⣿⣿⣿⣿⣿⣶⣿⣅⠻⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠙⠋⡽⢻⡟⢇⠹⠋⠃⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⡀
⠀⠀⠀⢀⣀⠤⠄⠜⠀⠘⠧⠠⠤⣤⠀⠀⠀⠀⠀⠀⣠⣤⢀⠕⢓⡦⢀⣄⣀⣀⡀⠀⠀⠀⠠⣤⣤⢤⣼⠧⠼⣷⣤⣤⣤
⠀⠀⠀⠈⠙⠢⢀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠉⠠⠠⢔⠭⣠⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠂⣴⡇⠀⠀⣸⣿⠋⠁
⠀⠀⠀⠀⠀⢀⡏⣠⠄⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⡡⠬⣥⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣸⡶⢿⡉⢿⡄
⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠁⠸⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠙⢥⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠉⠀⠀⠉⠻⣧


⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢆
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢢⡀
⠀⠀⠀⠶⠶⠖⠒⣾⠷⠒⢾⡖⠀⠀⠀⠀⠀⠀⠀⢶⣴⣾⣿⣿⣿⣿⣿⣿⣷⡶⠂⠀⠀⠀⠘⢫⡉⠁⠀⠀⠀⠀⠀⠉⡩⠃
⠀⠀⠀⠀⠀⠢⣴⡇⠀⠀⢀⣽⠂⠁⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⢠⠏⠀⡲⢶⣁⠀⣇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠙⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣀⠤⡀⠈
⠀⠀⠀⠀⠀⠭⠀⠀⠀⠀⠈⠓⠼⠄⠀⠀⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠈⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠈⠑⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢧⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣴⣿⣫⣦⣀⣀⣀
⠀⠀⠀⠰⠖⠀⠀⠀⠀⠀⠈⠉⢉⡴⠋⠀⠀⠀⠀⠻⢧⣉⠉⠁⠀⠈⠉⢉⠭⠛⠁⠀⠀⠀⠀⠲⢿⠉⣫⣾⣿⣿⢷⡿⠋⠁
⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣵⣿⣟⣵⣿
⠀⠀⠀⠀⠀⢸⠀⡠⠀⠑⠄⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠠⠐⠲⣄⣳⡀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠙⠁⠉⠻⢟⡀
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢰⡆⠀⠀⢸⣿⢸⣿⠀⠀⠀⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣿⣴⡆⣿⣿⢸⣿⣿⣶⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠷⣄⣴⣿⣿⣸⣿⣿⡷⠶⠾⢸⣿⣿⣿⣿⣿⣿⣿⣶⣤⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢿⣏⣽⣿⣯⠿⠟⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣰⣿⣼⡟⣿⣩⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⣀⣀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠿⠿⠿⣺⣧⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣹⣿⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⣯⣷⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠰⣷⡖⣻⣿⡇⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⡇⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢿⡇⣿⣹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡖⣶⣼⡏⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠹⣿⣶⣯⣿⣙⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⡿⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⣶⢸⣏⣻⣿⣟⣶⣦⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⡶⠛⠸⣿⣿⢹⣿⣿⡷⠶⢶⢸⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠻⠇⣿⣿⢸⣿⣿⡿⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠸⠃⠀⠀⢸⣿⢸⣿⠀⠀⠈⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁

⣟⣿⣍⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⡶⠿⣻⣿
⠛⠉⠻⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⢉⣉⣠⣄⣠⣶⣶⣶⣭⣲⢄⡀⠀⠒⣺⣿⣿⣿⣿⣿⣿⢟⡿⣿
⢀⣤⣀⣸⡆⠀⠀⠀⣀⣴⠾⠋⢁⣴⣿⣿⠿⠿⣿⣿⣿⣿⣻⣟⣻⠟⠃⢿⣿⢿⣼⣿⣿⣿⠿⠷⠛⠁⣿
⣿⣿⣿⠹⡇⣀⣴⡾⠋⢀⣠⣾⣿⡿⠋⠁⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠘⣯⣉⣻⣿⢿⣿⣿⣆⣤⣤⣿
⠀⠉⢉⣀⣹⣿⠋⣠⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⣿⣿⣿⡇⣈⣛⡟⣽⣿⣿⣽
⣆⣴⣈⣽⣿⣷⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠞⢛⣛⡉⠀⢀⣀⣉⣿⣿⣿⣯⣿⣿⡏⣨⣿
⣮⣟⠈⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣶⣤⣿⣿⣧⣶⣿⣿⣿⣿⣿⣨⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠈⠉⠉
⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣄⣽⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣇⣀⣷⣶⣿⣿⠛⠛⣻⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⠷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⣿⣿⣿⣿⣿⡙⠀⠀⠈⠁⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠉⠽⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠅⠸⠿⠿⣿⣇⠀⣤⡄⠀⢠⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣦⣾⣿⡇⠀⠀⠀⠀⠀⢻⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⡟⠃⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣿⣀⣾⣶⣿⣿⠿⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣿⡟⠛⠻⠿⠿⠉⠿⠿⣿⡏⠁⠀⠀⠀⠈⣻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣇⣠⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⠷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⡷⠀⣀⡀⠀⠀⣤⣿⣿⣿⣿⣿⡏⠉⠉⣿⠏⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠇⠈⢱⣶⣿⣷⣶⣶⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠐⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣶⡆⠀⣸⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠⠤⠤⠤⠤⡀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣼⠀⠆⡀⠄⣰⠜⠉⠙⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠠⡆⠂⠀⠑⠀⠁⢀⣼⠁
⠀⠀⠀⠀⠆⠀⠀⠀⢃⠀⠁⠄⠀⠀⠀⠀⠠⠀⣀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⠀⠀⠻⠤⠤⠤⠔⠚⠦⠬⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠀⠒⠒⠻⣤⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠒⣄⠀⠀⠀⠀⢐⠀⡲⠶⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠤
⠀⠀⡎⢁⠀⡀⡀⢀⠀⠀⢣⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢁⣄⣠⡄⡀⠀⠀⢰⠂⠀⠆⠀⠰⣀⣀⣂
⠀⠈⡁⠘⠖⠋⠉⠘⠀⠀⡸⠀⠀⠁⠀⠀⠀⠰⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⢀⠙⠛⠀⢀⠀⠀⠁⣄⠀⠀⢀⠂⣀⠀⢀⡀⠑⡤
⠀⠀⠈⠂⠄⢀⠀⠀⣠⠞⠁⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠃⠈⠀⢀⠀⠁⡀⠀⠀⠀⠅⠒⠺⡀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀
⠀⠀⣀⡇⢠⡘⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠉⠀⠀⡀
⠀⠀⢥⡀⢀⠘⢨⠀⢉⠤⠀⠀⠀⠀⡈⠄⠰⠂⠤⠂⠁⢤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠁
⠀⠀⢸⠃⢸⠀⢘⡀⡇⠀⠀⠀⠀⢀⡅⠀⠠⠀⠒⢁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⢠⠂
⠀⠀⠀⠂⠀⠀⠈⠑⠃⠀⠀⠀⠀⠈⠇⠄⠀⠀⠀⠈⡀⢰⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⡜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⠀⠀⢀⡅⠀⠀⠀⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⡄⠀⡐⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⠀⣄⠁⠀⠈⠃
⠀⠘⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠀⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⠀⠒⠃
⠀⢤⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡇⠀⠄⠀⠀⢀⣀
⠀⠈⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠉⠀⠀⠂⠀⠀⠀⠀⠀⠘⡐⠃⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⢀⠔⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖
⠀⢀⡔⠁⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠤
⠀⠋⠀⠀⠀⠀⠁⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⣘⣠⣈⠀⠀⠀⠀⠀⠀⢁⡀⠠⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈
⠀⠐⢺⠀⡉⠉⠉⠀⢺⠄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠐⢄⠠⠂⠘⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⣦⡤⠖⠚⠛⢳⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⠋⠁⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠏⠀⠀⣀⣀⣤⣤⣀⡀⠀⠀⠀⢀⣈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠁⠀⠀⡴⢾⣿⣿⣭⠀⠀⣠⢞⣿⣷⣤⡀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠟⠉⠀⠀⣴⡷⠁⠈⠛⢻⠇⢀⡇⠀⠉⣸⠙⣇⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣀⠀⠀⠀⡼⠁⣇⠀⢀⡴⠋⠀⠈⠙⠓⢾⡁⠀⢹⡀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠋⠀⠀⣾⠁⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣀⣽⠂⢸⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⠿⠟⣁⠀⢸⣷⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⠀⠘⠛⣦⠀⣏⠀⢠⡴⢯⣀⠀⠀⠀⠀⠀⠀⢠⡟⠙⠘⢋⣄⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢶⢾⡇⠀⢠⡞⠿⡟⠀⠀⠀⠀⠈⠛⠶⢄⠀⠀⡰⠋⠀⠀⠀⢏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢉⣷⠀⠸⡗⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣰⠖⠋⠉⠙⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣩⣭⣿⠀⠀⠻⣄⣙⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⡿⠷⠦⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⣿⢸⠀⢀⣠⣬⠭⠼⠿⠷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣯⡴⠶⠆⢸⡗⠒⠒⠒⠒⠶⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢿⢸⠀⣾⠀⠀⠀⠀⠀⠀⡀⠹⣦⡄⠀⠀⢀⣴⠻⣏⣠⡴⠆⢸⠃⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⢸⢸⠀⡇⠀⠀⠀⠀⡴⠋⠀⠀⣿⡇⠀⠀⢸⣿⠻⡞⠁⣀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣸⠀⣇⣤⠖⠒⠺⠇⠀⠀⠀⠀⠙⠒⠚⠛⠋⠀⠻⡶⠛⢀⣿⣄⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣿⣧⢸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠚⠋⠁⠙⣆⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠹⣿⢸⣿⢦⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠘⣿⡏⠀⣿⠀⡞⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣟⠘⢧⡀⢀⣿⣧⣴⠏⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢸⡇
⢀⣀⣀⣀⣀⣀⣠⡞⣻⠁⢿⠀⠀⢻⣿⣝⣿⣇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⣸⡇⠀⠀⢸⠃
⠀⠀⠀⠀⠉⠹⣿⣀⣽⣄⠘⣧⣀⣼⣿⣭⣽⣏⣉⡙⠛⠒⠒⠶⠶⠶⠶⠶⠤⠤⣤⣄⣀⣀⣀⣀⠀⠉⣹⣿⣿⠛⠛⠁⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⢛⣩⠿⠋⠀⢻⡟⠀⠈⠉⠉⠛⠓⠒⠲⠶⠶⠶⠦⠤⠤⠤⠤⠤⠭⠭⣭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠶⠿⠯⠤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢿⡿⣀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⢻⠳⢤⣖⠉⠀⠠⡇⠀⠉⣲⠤⠚⡟⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⢸⠀⠀⠈⢱⠀⠈⡇⠀⡏⠀⠀⠀⡇⠀⣤⣀⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⡇⠀⣿⣿⣿⣦⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⡇⠀⠀⠀⣇⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠛⠢⣄⡀⢸⠀⢀⡇⠀⡇⠀⣀⠼⠿⠧⡈⠙⠻⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠔⠊⠀⠀⠀⠀⠀⢉⠿⠀⣨⣏⠰⣷⣉⠀⠀⠀⠀⠀⠑⠠⢄⠁⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⢁⠀⠀⠀⠀⢀⡠⠔⠊⠀⣠⠔⠻⠟⠢⣄⠈⠑⠢⣄⡀⠀⠀⠀⠀⡨⠾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠂⠤⠒⠁⢀⡠⠖⠉⠀⣀⢴⣦⣀⠀⠉⠲⢤⣀⠉⠲⠤⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠄⠊⠁⢀⡠⠔⠈⠀⠐⡇⠈⠙⠢⢄⡀⠈⠑⠦⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⡉⠀⠀⢠⠂⠁⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠉⠲⡄⠀⠀⢙⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢼⠀⠀⠀⡠⠔⠊⠉⠉⠙⠢⢄⡀⠀⠀⡧⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⢀⠠⠐⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⢄⠀⠀⠀⠀⠀⠀⡔⠉⢣⠀⢠⠇⠀⡤⠚⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡎⠀⠀⠀⠀⠀⠀⠂⠄⢤⠙⠁⠀⠘⢆⠀⠀⡨⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠂⠒⠋⠀⠀⠑⠒⠒⠊⢳⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠉⠉⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⣀⡀⠀⠀⠀⠀⢀⠤⢄⠈⡆⠀⡠⠊⠀⢀⠤⢤⡀⠀⠀⠀⠀⠘⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⡆⠀⠀⠀⡇⠀⠀⠉⠀⠀⠳⣄⠀⡊⠀⠀⢘⠆⠀⣀⠤⡀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢⣀⡰⠀⠀⠀⠀⠑⠤⠒⠉⡆⠀⠀⢀⣉⡁⢠⡒⠉⠀⡰⠁⠀⠙⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣅⠀⡸⠀⠈⠑⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠉⠉⡇⠀⠀⢏⠉⠉⢉⠧⣀⣀⣀⡸⠐⣅⣀⣀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡀⠀⠀⣀⠇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢀⠖⠢⠤⠞⠀⠀⠈⠉⠉⠀⠀⠀⠸⢄⠠⠲⡄⠀⠀⠀⠰⠁⠉⠒⠎
⠀⠀⠀⠀⠀⠀⠸⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⢀⡇⠀⠀⠀⠰⡀⢀⡤⢄
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢱⠀⠀⡴⠊⠉⠐⠄⠀⢈⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀⠀⢱⠄⠀⢠⠃⠀⢸⡤⠤⠒⠦⠀⠀⡤⠒⠒⠤⠤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⢠⠃⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠔⠁



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⡀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠄⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⠤⣲⡀⢠⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⠛⠻⠿⠃⢾⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⢣⡉⡢⠦⡆⠈⠈⠷⢤⣀⣀⡠⣄⣠⣄⠀⠀⢿⣷⡝⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣶⣭⢃⣀⢀⢀⣀⣀⡤⠤⠭⠶⠈⠉⠀⠀⠀⠘⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⡿⠻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣾⡿⡿⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⠿⣻⢦⡇⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣧⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⢐⡿⣿⣿⣦⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢁⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢰⠋⠀⠘⢿⣿⣧⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⣣⠈⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡏⠀⠀⠀⠈⢻⣿⣯⡆⠀⠀⠀⠀⠀⠀⣸⢿⣿⠋⡙⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⠀⢰⢺⣿⡿⠀⡇⠀⢀⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⢠⡯⠃⢠⡿⠀⠃⠀⠀⠓⠄⠈⠳
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⡠⠶⠁⣀⣠⣴⡓⠀⠀⢣⠀⠠⠤⠕⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢼⣿⡟⠁⠀⠀⠀⠀⠀⢀⣀⣸⣿⣟⢢⣴⠶⠐⠛⠉⠉
⠀⠀⠀⣀⣀⣠⣴⣞⡿⠟⠛⠓⠀⠀⠉⠉⠙⠉⠉⠛⠟⠛⠁
⠀⠀⠉⠉⠉⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⡀⠀⠀⠀⠰⡆⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢏⠀⡗⠀⠀⡇⠀⢸⠂⢸⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠳⡈⢢⠀⡇⡴⠋⡔⠋⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠘⠉⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⡔⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⣀⣀⣀⣀⣀⣿⣿⣟⡍⣭⢹⣭⡍⣭⣩⣩⡝⣿⣿⣀⣀⣀⣀⣀⡤⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⣀⣀⣀⣀⣿⣿⣯⣥⣭⣬⣭⣥⣭⣭⣬⡅⣿⣿⣀⣀⣀⣀⣀⠔⠉⠉
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠉⠉⠉⠉⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠉⠉⠉⠉⠉⣿⣿⣿⣿⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠉⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠢⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡇⢸⠀⡇⡇⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⠔⢁⠜⠀⡇⠳⣄⠣⡀⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣇⠀⡧⠀⠀⡇⠀⢸⠄⢹⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠁⠀⠀⠀⠰⠇⠀⠀⠀⠈⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢻⣇⡀⠀⠠⣤⣀⠀⣴⠀⠀⣤⠀⣀⣤⠄⠀⢀⣸⡟⠇
⠀⠀⠀⠀⠀⢀⠴⠆⠀⢀⡀⢰⡟⢭⣿⠂⠀⠸⣿⣿⣿⡇⢸⣿⣿⣿⠇⠀⠐⣿⡯⢻⡆⢀⡀⠀⠠⠦⡀
⠀⠀⣀⠀⢰⡏⠀⠀⠀⢈⣻⣿⣇⠀⠀⠀⠀⠀⠟⠛⣿⡃⢘⣿⠟⠻⠀⠀⠀⠀⠀⣸⣿⣟⡁⠀⠀⠀⢹⡆⠀⡀
⠀⠀⠹⣿⣾⣧⢰⡿⢲⡈⠻⢿⣿⣷⣄⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⢁⡔⢿⡆⣼⣷⣿⠏
⠀⠀⠀⠈⣻⣿⣧⡀⡞⢏⢹⡆⢾⠿⠿⠿⢶⣄⣀⣼⡿⠁⠈⢿⣧⣀⣠⡶⠿⠿⠿⡷⢰⡏⡹⢳⢀⣼⣿⣟⠁
⠀⠀⠀⠀⣿⡿⠿⢿⣿⣿⣗⣲⣄⠀⠀⠀⠀⠈⠻⣯⠀⠀⠀⠀⣽⠟⠁⠀⠀⠀⠀⣠⣖⣺⣿⣿⡿⠿⢿⣿
⠀⠀⠀⠀⠈⠀⠀⢳⣠⡝⠛⠿⠿⠿⠿⠷⠶⣦⣀⠘⢧⠀⠀⡼⠃⣀⣤⠶⠾⠿⠿⠿⠿⠛⢫⣄⡜⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠾⠿⢿⣶⣶⣤⣙⢳⡘⡄⢠⢃⡾⣋⣤⣶⣶⡾⠿⠷⣶⣤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣴⡿⣿⣀⡀⠀⢿⠛⠉⠛⠻⣷⣷⣧⣼⣾⣾⠟⠛⠉⠛⡿⠀⢀⣀⣿⢿⣦⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⣉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣿⣿⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⢝⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣛⣿⣻⣛⡯⣍⡁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣴⣿⣿⣿⣿⣿⣯⣤⣑⡻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢨⣿⠯⡞⢹⣾⡿⣿⣿⣿⣿⣦⡙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣼⡋⡀⢸⡟⠉⠛⠛⡿⢿⣿⠅⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⡴⣏⡸⢁⠘⠀⠀⠀⣸⡷⣾⡏⡾⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣱⣾⡥⡺⡈⠁⠀⠀⢀⣠⣽⠶⠿⠿⠵⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠛⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⣴⣿⢿⣿⡟⠀⢀⡤⠞⠋⣡⠀⠀⢀⡴⢦⡀⠉⠺⠲⢤⠤⠀⡈⠉⠀⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢛⣴⣿⡿⠟⠛⢋⣠⠞⠉⠀⠀⠀⢀⡄⢫⣀⠁⠀⠹⠀⠀⠀⠈⢀⠛⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⣱⣾⣿⠻⠗⠁⢀⡴⠊⠀⠀⠀⣠⣤⣴⡞⠑⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⡞
⠀⠀⠀⠀⣀⠄⠐⣈⣬⣶⣾⣿⠶⠛⠉⢁⣀⡤⠖⡋⠀⠀⠀⣀⣴⠏⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⡇
⠀⠀⣀⣼⣥⣴⣿⣻⣿⣋⣩⣤⠤⠐⠊⠉⠀⠀⠀⣀⢠⣶⣍⠙⠉⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣻⡄⢸⠁
⠀⠀⠙⣄⠲⣤⡄⣀⡀⢀⡤⠀⣀⠴⠇⢠⠆⠀⠈⠁⠀⠂⠀⢀⠀⢤⠄⠀⠀⢀⠀⡀⢨⠀⡐⣀⡶⠋⣡⠃
⠀⠀⠀⠈⠙⢦⣍⠩⢥⡀⠀⠀⠉⠠⠔⠀⠋⠀⣴⠀⣤⣤⠀⡻⣄⢨⣁⣴⠧⣾⣴⠶⠟⡻⠛⣁⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⠀⠀⠀⠀⠀⠋⠈⠉⠀⠘⠉⠀⠁⠉⠃⠉⠈⠁⠀⠀⣀⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠤⠦⠤⠤⠤⠤⠤⠤⠄⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣤⣀⣀⡀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⣶⡏⣿⣿⣿⣿⠛⠛⣡⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⣤⣤⣝⣾⣧⣈⠀⠿⠾⠀⢠⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣧⠙⢻⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⢧⡀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⡟⠿⣿⣷⣄⠀⠉⠛⠻⠿⠿⣿⢻⣷⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡇⠀⣀⠸⠿⣿⣿⣿⣿⣦⣶⣿⣿⣸⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⣻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠃⢰⣿⠿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⢄⣨⡄⠴⠛⠁⠈⠃⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣻⣿⡖⣶⣿⣶⠠⢄⣀⠀⠀⠀⠈⢹⣿
⠀⠀⠀⠀⠀⠀⠰⠁⠒⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣿⣿⣦⣴⣿⣿⣿⣿⡿⣦⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡆⠀⣿⣿⣿⣿⣿⣿⣿⢿⠿⠿⡿⠃⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⡿⠿⣿⡿⠿⠻⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⣶⣦⠛⠁⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⣙⠃⠀⠰⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣤⡴⠂⣤⣤⠀⡀⠀⠤⣤⣘⣻⣄⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⣾⣿⣿⣦⣤⣀⡀⠀⠸⠏⢤⠀⢰⣯⣿⣿⣿⣄⠃⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⣀⠉⠉⠉⠛⠛⠛⠛⠓⠀⠀⠘⠛⠚⠛⠛⠿⠿⢿⣦⠳⡄⠀⠀⠀⢀⣥⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠦⠄⠠⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⣠⣄
⠀⠀⠀⠀⣀⣠⠤⠤⠴⠶⠶⠶⠶⠶⠤⠤⠤⢤⣤⣤⣀⣀⡀⢧⠀⢱⡾⠋⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒
⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⢧⡀⣠⡾⠋⠒⠒⠶⠶⠶⠦⠤⠤⠤⠴⠶⠒⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣮⣵⣦⣤⣧⣼⣯⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢰⠀⠀⠉⠉⠉⠉⠀⠀⠀⠐⡄⠀⠀⠈⠉⠀⠐⠀⠐⠒⠒⠒⠒⠁⠀⠀⠐⠒⠀⠀⠀⠐⠒⡆
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢲⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠈⠈⠑
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠣⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠸⠀⠐⠒⠒⠒⠒⠄⠀⠀⢀⠤⠤⠤⠤⠄⣀⢐⠀⠀⠠⠤⠤⠤⢄⠀⠀⠀⠠⠄⠄⠤⠤⠄⢘⡀
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠀⠒⠂⢄⠀⠘⣄⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠉⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠉⠒
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠒⠄⠔⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠒⠤⠀⠀⢡
⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠣⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠢⠀⠀⠒⠀⠀⠀⠓⠠⠤⠀⣀⡀⠀⠇⠀⠀⠰⠀⣀⣀⣀⣀⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣤⣤⣄⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠛⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠘⠃⠀⠛⠀⠘⠀⠘⠃⠀⠛⠀⠘⠃⠀⠛⠀⠘⠃⠀⠛⠀⠘⠃⠀⠀⠀⠀⠛⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠛
⠀⢰⠦⠦⠦⠀⠀⠀⠀⠀⠀⠤⠀⠤⠀⠤⠀⠀⠀⠀⠀⠀⠴⠴⠦⡆⠀⠀⠠⣖⣒⣒⣒⣒⣐⣒⡒⡲⣒⡂⠶⠀⣒⣒⢖⣒⣒⣒⣒⣲⣒⣲⠤
⠀⢠⡄⠠⠀⠀⠀⠀⠀⡄⠀⣤⠠⣤⠄⣤⠀⢠⠀⠀⠀⡄⠀⠀⢠⡄⠀⠀⢠⢀⡀⡄⡀⠠⢠⢠⢀⡀⡄⡀⢠⢠⢠⢀⡀⡄⡀⢠⢠⢠⢀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⢀⡀
⠀⠈⠁⠉⠀⠀⠀⠀⠉⠈⠈⠁⠁⠉⠈⠈⠁⠁⠉⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠋⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠤⠀⠀⠠⠀⠀⠀⣶⡦⠄⠤⠠⢴⣖⠀⠀⠀⠄⠀⠀⢤⣶⡄
⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⣤⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⣉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣤⡄⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⢤⠄⠤⡤⠄⢤⠤⠠⡤⠄⡤⠤⢤⠤⠠⡤⠄⣤⠤⢤⠤⠠⡤⠄
⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⢀⢀⢄⢄⢠⢤⣠⣄⣄⡄⣄⠀⣠⢠⣠⣢⡄⡄⡄⡠⡀⡀⡀⣀
⠀⠈⠁⡀⠀⡀⠀⡀⠀⡀⠀⠀⠀⣀⠀⠀⠀⢀⠀⢀⠀⢀⠀⢀⠈⠁⠀⠀⠉⠉⠈⠈⠈⠈⠈⠈⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠁⠉
⠀⠈⠀⠛⠀⠛⠀⠛⠀⠛⠈⠃⠈⠛⠁⠘⠁⠛⠀⠛⠀⠛⠀⠛⠀⠉⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠐⠶⠂⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠅⠀⠸⠯⠂⠀⠀⠷⠲⠿⠗⠾⠀⠀⠀⠭⠇⠐⠨⠭⠐
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⡟⣛⡿⠿⠿⠿⠿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⣶⡾⠿⠛⠛⣿⠛⠛⠿⣶⡶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⢁⡴⠟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠙⠳⣄⠉⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢀⡾⠁⠀⠀⣀⣀⣀⣠⣤⣤⣤⣿⣤⣤⣤⣀⣀⣀⡀⠀⠀⠙⢂⣀⣀⣀⣀⣀⠹⢦
⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣀⣼⠷⠖⠛⠛⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠉⢉⣥⣶⠿⠛⠛⠛⠛⠛⠛⠿⢷⣦⣄
⠀⠀⣼⠃⠀⠀⣠⡴⠞⠋⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⣰⠏⢀⣴⠞⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⢠⡟⣴⠟⠁⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⣸⡿⠁⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⣿⠤⠤⠤⠤⠤⠤⠤⠤⣿⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⢴⣿⠤⡄⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇
⢻⣧⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋
⠸⣟⢷⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡆
⠀⢻⡄⠙⢦⣄⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣶⣶⡾⠿⠟⡛⢿⡿⠟⣡⣶⣷⣄
⠀⠀⢷⡀⠀⠉⠳⢦⣄⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⣀⣤⠶⠋⠁⠀⠰⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⢳⡀⠀⠀⠀⠈⠙⠻⢷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡿⠛⠉⠀⠀⠀⠀⣰⠃⠘⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠘⣧⠀⠉⠙⠛⠛⠓⠶⠶⠶⠶⣿⠶⠶⠶⠖⠚⠛⠛⠉⠉⢠⡟⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠙⢦⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⠞⠁⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣽⣷⣦⣄⣀⣀⣿⣀⣀⣤⣶⣿⡵⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠿
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠐⡖⠊⢤⠄⠀⠠⡀⠁⠊⢄⠀⠀⢀⡀⠀⠀⣼⣗⣧⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣤⣾⣧⣀
⠀⠐⠀⠀⠀⠠⠀⠀⠀⡐⠂⠀⠐⠁⠲⠁⠀⠀⠰⠁⠀⡠⠊⠀⢀⡾⣧⠀⠀⠀⠈⠀⠀⠀⠌⠈⠀⢁⠀⠀⠀⠀⣀⣠⣴⣿⣷⠶⠒⠀⠀⠟⠻⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠈⣆⠠⠀⠀⠠⠀⠀⠀⢠⣤⣤⣠⣾⣁⣽⣄⣀⣀⣀⠀⠀⠈⠀⢁⠐⠀⠆⠀⠀⠀⠀⠀⠈⡿⠻⡇
⠀⠀⠀⠀⠀⠄⠀⠀⠘⠀⣤⠀⠀⠄⢀⡩⠀⠀⠀⠀⠀⠐⢠⡾⠁⠀⠈⣻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⢾⠀⠀⠘⠃⠄⠘⠀⠀⣠⠎⠱⠄⡀
⠀⠀⣷⣿⣀⠈⠂⢄⡒⠀⠀⠀⢀⡐⢍⠀⠀⠀⠀⠀⠀⠀⡜⢉⣶⣶⠞⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡝⣺⡷⠆⠀⠀⠀⠄⠀⠈⢠⠀⡀⠰⠁
⠀⠈⠉⠛⠁⠀⠀⠀⠃⣀⠀⡭⣀⠀⣬⢣⠀⢠⣄⠀⠀⣼⠷⠋⠁⠀⠙⢾⣧⠀⠈⠓⢶⠃⠂⠠⡀⠀⠈⠉⠈⠻⠄⠀⠀⠘⠃⠠⠀⡀⠈⠚⠊⠁
⠀⠀⢀⡤⣀⡀⠀⠀⠠⠔⠈⠀⠀⠈⠀⠂⠀⣸⣿⣦⣤⣤⠆⠀⣀⡀⠀⢀⡈⠀⠀⡀⠔⠃⠌⠀⠀⠀⠘⠃⠲⠆⠀⠀⠀⠀⠀⣠⣴⡇⠀⠀⠀⢠⡄
⠀⢀⢸⠈⣿⣰⢳⢆⡄⢀⠀⠀⠀⠀⠀⠶⢾⣿⣏⣽⣿⣇⠀⢀⣸⣿⣛⣿⣤⡀⠀⠀⠀⠈⠁⠀⠸⣿⠆⠠⣀⢀⣤⣤⠄⣤⣮⣿⠿⠇⠀⠰⠷⠀⠁
⠀⠙⠛⠸⢡⢧⢇⡾⣧⢇⡏⠁⠀⠀⠀⠀⠀⢹⣿⠟⠛⠛⠃⠀⠀⠘⠟⠀⠀⠀⢠⡳⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢂⡻⠟⣩⣶⣺⡽⢦⣄⠀⠘
⠀⠐⣠⢂⠀⠈⠘⠸⠇⣞⠉⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠾⡀⠉⠖⢲⠖⠀⣀⠠⠀⠀⠀⢱⣥⠴⣻⣿⣿⣷⣚⣭⣴⣿⣶⣤
⠀⠀⠀⡁⠀⠂⠠⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡆⢀⡈⠠⣏⠀⠀⠼⠦⡞⠀⢠⣯⣴⣿⣿⣿⠿⣛⣭⡞⠋⠉⠁
⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣄⠀⠀⠀⠀⠀⠀⢰⣤⣶⡀⠀⠀⣧⠞⠉⠳⢿⠀⠀⠀⠀⠀⣠⠟⠛⠩⠟⠛⢶⣾⣿⣿⠀⠀⠴
⠀⠁⠀⠀⠀⡀⠀⠐⣄⠀⣀⡄⠀⠀⠺⡒⠁⠘⠦⣄⠀⠀⠰⠞⠛⢿⣿⠛⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠻⣿⢻⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡅⠀⠀⢰⠣⢤⣠⠎⠁⠀⠀⠀⠀⠀⠈⡏⠀⢀⡀⣤⢺⣢⠀⠀⠐⠂⠂⠀⠀⠀⠀⠳⢀⡀⡤⠀⠀⠘⢿⢀⠀⢠⡰
⠀⠀⠀⠀⠠⠀⠉⠉⢻⣿⠋⠛⠃⠀⠀⠀⠀⠙⠀⠀⠀⣇⠀⠀⠀⠀⠀⣔⠏⢂⠘⡦⠹⠂⠀⠀⠀⠀⠀⠀⠀⡠⠈⡬⣽⠣⡀⠀⠀⢠⣏
⠀⠀⠀⠀⠠⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠱⣡⡟⠉⠀⠀⠈⣷⠄⠃⠁⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⣴⠚⠭⠒⠛⠾⠁
⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡆⠳⠐⠠⠆⠀⠀⠀⠀⣀⣠⣦
⠀⢲⡄⠠⠊⣇⠀⠀⠀⡀⠂⠰⠟⠀⠕⠀⠠⣄⡀⠀⠀⠀⢀⡀⠀⢤⣶⣦⡀⠀⠀⠠⠀⡁⠀⢀⣀⠀⢀⠞⠤⠀⠀⠀⣹⣿⣿⠛
⠀⠀⡹⠀⠀⡀⠉⠓⠀⠀⠐⠆⠀⠈⠀⠀⠀⠆⠙⠲⡄⠐⣸⠃⠀⠀⢽⡛⢷⠀⠀⢐⠋⠜⠀⠘⠉⠁⢀⠈⠂⠠⠀⠀⠁⠀⠙
⠀⠐⠀⠀⠢⣤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡈⠂⠀⠀⠀⠧⣀⠀⠀⠀⠙⣿⠀⠀⠁⢀⡄⢀⡌⠂⠀⠁⠷⠈⠀⠀⠀⠓⣄
⠀⠀⠀⠀⣄⠈⢀⠀⠀⠇⡸⠃⡀⠀⠀⢠⣞⡥⢀⡀⢀⡀⠀⠈⠳⠄⠀⠀⠈⠀⣶⠀⠀⠀⠈⠁⠰⠈⠈⠀⠀⠀⣀⢰⡦⠘⢷⡀⠀⠀⠀⡼⢤⣀
⠀⠀⠛⢦⡹⠆⣸⣧⡀⠀⠱⠚⠋⠀⠀⠀⠀⠀⠀⢇⣼⠀⠀⠀⠀⠀⠀⠙⢻⣿⠟⡓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢼⡄⣀⡐⠃⡀⠀⠛⣵⡷⢿⡀
⠀⠘⠓⠒⠊⣀⣿⣿⣿⣶⣶⡞⠁⢀⡀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠾⠋⠑⠑⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⢸⠀⠈⠉⠁⠘⠀⠀⠉
⠀⠀⠀⠘⠧⢻⣿⣿⣟⣿⡏⠐⠯⣭⣄⠀⠀⠀⣀⠀⠂⠐⠀⡀⠀⠀⠀⠀⡠⠀⡄⠀⠀⠀⠀⠀⣤⡀⠀⠀⢰⠏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡤⠶⣂⠈⣿⡿⠋⠘⠿⠀⠳⠆⠀⠀⠀⠀⠁⠀⠀⠈⠀⠰⠀⠀⠀⠘⣅⢈⠃⣶⣆⢹⡄⠀⠀⢉⡴⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢲⠶⢻⣤⡀
⠀⠀⠀⠾⠃⠀⠋⠀⡆⢳⡄⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢠⣈⠇⠆⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠞⠛⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠇⢣⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠢⢀⡀⠈⢿⣄⠀⡜⠀⡀⠀⣼⠇⠀⠈⠁⡠⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠒⠄⠀⠀⣼⣿⡆⠁⠀⣰⣿⡏⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣈⡄⠀⠙⢿⡿⠆⠒⠛⠿⠇⠀⠀⠀⠀⢁⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣦⡬⠃⠀⠀⠀⠀⠀⠈⠲⣿⣿⠶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠁⠐⠂⠙⢛⡃⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠐⠠⠠⠐⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠑⣢⣤⣴⣇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣯⡉⠙⠒⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⠿⠛⠏⠀⠓⣄⡀⠀⠀⣀⠤⠙⢍⠻⢿⣷⣶⣆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⢿⣿⠇⠈⢸⣿⣦⡤⡀⠀⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⣀⠠⠁⣼⡿⠈⢂⠀⠟⢿⣷⠈⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠸⠊⠀⠀⠀⠀⡿⠁⠀⠸⠀⡀⠘⣿⠀⠈⠢⠧⠄⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠌⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣦⡀⠀⢀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⢋⣡⣶⠿⠟⠛⠋⠉⠉⠉⠛⠻⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣇⠀⠻⠋⢡⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣦⣶⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡉⠻⣿⣿⡿⢉⡀⢤⣥⣤⣤⡄⢀⠈⠋⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⡿⢡⣾⣿⣄⠙⠿⢋⣴⣿⣧⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣆⠀⣤⣤⣤⣤⠀⣤⣤⣤⡤⠀⠀⠘⠛⠛⠛
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣷⡌⠻⣿⣿⠀⣿⣿⠟⠀⠀⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣴⡿⠁⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠉⠀⠀⠀⠀⠀⣠⣾⣿⡷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣩⣭⣭⣭⣭⣭⣤⣤⡀⠀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢁⣾⣿⣿⣿⡛⠛⠛⠛⠛⠛⣃⣼⣿⡿⠋
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠃⠼⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠋

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

⠀⠣⠤⠴⡆⠀⠀⣀⢀⡀⠀⠀⠶⠤⠤⠃⠀⠘⠤⠤⢶⠀⠀⢀⡀⣀⠀⠀⣰⠦⠤⠜⠀⠀⠣⠤⠴⡆⠀⠀⣀⢀⡀⠀⠀⡶⠤⠤⠃
⠀⠀⠀⠀⠇⠀⠘⡇⢀⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡀⣸⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⢀⠇⠀⠀⠇
⢸⡉⠉⢙⠋⠐⠒⠋⠈⠓⠒⠈⢋⠉⠁⡹⠀⢏⠈⠉⠻⠁⠒⠚⠁⠙⠒⠂⠹⠉⠉⢉⠇⠸⡁⠉⢩⠉⠐⠒⠋⠈⠓⠒⠈⢋⠉⠁⡹
⠔⠃⠀⢸⣀⠤⢄⠀⠀⢀⠤⣀⣸⠀⠀⠓⠠⠚⠀⠀⣇⡠⠤⡀⠀⠀⡠⢄⣀⡆⠀⠘⠢⠔⠁⠀⢸⣀⡤⢄⠀⠀⢀⠤⣀⣸⠀⠀⠓
⡀⠀⠀⢠⠤⣄⡰⠀⠀⠸⣀⡤⢤⠀⠀⢀⣀⠀⠀⠀⡤⢤⣀⠅⠀⠀⢄⣠⠤⡀⠀⠀⢀⡀⠀⠀⢠⠤⣄⡸⠀⠀⠠⣀⡤⢤
⢨⠆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢏⠀⡹⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠸⡁⢈⠆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢏
⠘⠂⠒⠒⡓⠈⠉⡗⠰⡋⠉⠐⡗⠒⠀⠚⠀⠓⠐⠒⢺⠀⠉⢹⠆⢾⠉⠁⢺⠒⠒⠐⠃⠘⠂⠒⠒⡗⠈⠉⡷⠰⡏⠉⠐⡗⠒⠀⠚
⠀⢀⣀⡀⡇⠀⠘⠧⠠⠇⠀⠀⣁⣀⣀⠀⠀⠀⣀⣀⢸⠀⠀⠸⠄⠼⠀⠀⢼⢀⣀⡀⠀⠀⢀⣀⣀⡇⠀⠀⠧⠠⠃⠀⠀⡇⣀⣀
⠀⢇⣀⣨⡅⠀⠀⠀⡀⠀⠀⠀⣭⣀⣀⠇⠀⠸⣀⣀⣭⠀⠀⠀⢀⠀⠀⠀⢨⣅⣀⡸⠀⠀⢇⣀⣨⡅⠀⠀⠀⡀⠀⠀⠀⣭⣀⣀⠇
⠀⠀⠁⠀⡇⠀⠠⡏⠉⡆⠀⠀⡄⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⢸⠉⢱⠀⠀⢙⠀⠈⠀⠀⠀⠀⠁⠀⡇⠀⠀⡏⠉⡇⠀⠀⡇⠀⠁
⢰⠒⠒⠲⠆⠦⠤⠟⠘⠦⠤⠆⠗⠒⠒⢲⠀⡖⠒⠒⠾⠰⠠⠼⠃⠻⠤⠴⢸⠒⠒⠒⡆⢰⠒⠒⠒⠧⠦⠤⠟⠘⠧⠤⠖⠗⠒⠒⢲
⡨⠇⠀⢸⠀⣀⡀⠀⠀⠀⣀⠀⢸⠀⠀⢧⣀⠽⠀⠀⡆⢀⣀⠀⠀⠀⢀⡀⠈⡄⠀⠸⣄⡠⠇⠀⢸⠀⣀⡀⠀⠀⠀⣀⠀⢸⠀⠀⢧
⠀⠀⠀⢈⣉⡁⢘⠀⠀⢸⠀⣉⣉⠀⠀⠀⠀⠀⠀⠀⣉⣉⠈⡇⠀⠀⡁⢈⣉⠁⠀⠀⠀⠀⠀⠀⢈⣉⡁⢸⠀⠀⢌⠀⣉⣉
⢑⡆⠀⢸⠀⠉⠁⠀⠀⠀⠉⠁⢸⠀⠀⡖⠉⢲⠀⠀⠇⠈⠉⠀⠀⠀⠈⠉⠀⠃⠀⢰⠊⠑⡆⠀⢸⠀⠉⠁⠀⠀⠀⠉⠁⢹⠀⠀⡖
⠸⠤⠤⠤⠆⠖⠒⡦⢠⠖⠒⠆⡦⠤⠤⠼⠀⠧⠠⠤⢴⠰⠒⢲⡄⣴⠒⠲⢸⠤⠤⠤⠇⠸⠤⠤⠬⡆⠆⠐⣦⢠⠖⠒⠆⡦⠤⠤⠼
⠀⠀⠀⠀⡇⠀⠰⣇⣀⡇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢸⣀⣸⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣇⣀⡇⠀⠀⡇
⠀⡎⠉⢑⠃⠀⠀⠀⠁⠀⠀⠀⣓⠉⠉⡄⠀⢰⠉⠉⣚⠀⠀⠀⠈⠀⠀⠀⢙⡊⠉⢱⠀⠀⡎⠉⢑⡃⠀⠀⠀⠁⠀⠀⠀⣓⠉⠉⡆
⠀⠈⠊⠁⡇⠀⢀⡔⠒⡄⠀⠀⡋⠉⠋⠀⠀⠀⠙⠉⢹⠀⠀⢰⠒⢢⠀⠀⠺⠉⠙⠁⠀⠀⠈⠋⠉⡇⠀⠀⡖⠒⡄⠀⠀⡏⠉⠋
⢠⠤⠤⢤⡅⣀⣀⡧⠰⣅⣀⡀⡧⠤⠤⢤⠀⡤⠤⠤⢬⢀⣀⣸⠆⢾⣀⣀⢸⠤⠤⠤⡄⢠⠤⠤⠤⡇⣀⣀⡷⠰⣇⣀⡀⡧⠤⠤⢤
⢘⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣎⠀⣳⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢰⡁⢘⡆⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣎
⠉⠀⠀⠘⠒⠊⢑⠀⠀⢰⠉⠒⠚⠀⠀⠈⠉⠀⠀⠀⠓⠒⠉⠆⠀⠀⠊⠑⠒⠃⠀⠀⠈⠉⠀⠀⠘⠒⠊⢱⠀⠀⠐⠉⠒⠚⠀⠀⠈
⠢⡀⠀⢸⠉⠒⠊⠀⠀⠈⠒⠋⢹⠀⠀⡤⠒⢤⠀⠀⡏⠑⠒⠁⠀⠀⠑⠚⠉⡆⠀⢠⠔⠢⡀⠀⢸⠉⠒⠊⠀⠀⠈⠒⠊⢻⠀⠀⡠
⢰⣁⣀⣨⣄⡀⠤⣄⢀⡤⠄⣀⣌⣀⣀⣱⠀⣎⣀⣀⣠⡀⠠⢤⡀⣠⠤⢀⣰⣀⣀⣈⡆⢰⣁⣀⣘⣄⡀⠤⣄⢀⡤⠄⣀⣌⣀⣀⣱
⠀⠁⠁⠀⡆⠀⢠⡇⠈⡆⠀⠀⡇⠀⠀⠁⠀⠈⠀⠀⢸⠀⠀⢸⠁⢹⠀⠀⢸⠀⠈⠈⠀⠀⠁⠁⠀⡇⠀⠀⡏⠈⡆⠀⠀⡇⠀⠈⠁
⠀⡔⠒⠶⠇⠀⠀⠉⠊⠁⠀⠀⠶⠒⠒⠄⠀⠠⠒⠒⠾⠀⠀⠈⠑⠉⠀⠀⠹⠔⠒⠢⠀⠀⠔⠒⠶⠇⠀⠀⠉⠊⠁⠀⠀⠷⠒⠒⠄
⠀⡀⣈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⢶⣶⣽⡀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣸⣿⣿⣧⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣜⠛⠷
⠀⠀⣰⣤⣀⣀⣴⡀⢻⡄⠁⠀⠀⠀⠀⠀⠀⢠⣲⣤⣤⣴⣆⠘⢷⠀⠀⠀⠀⠀⠀⢀⣮⣷⠶⣶⣯⡄⠘⡇
⠀⣼⣿⣿⢟⣽⣿⣧⣠⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⣿⣿⣀⡾⠀⠀⠀⠀⠀⠀⢿⣿⣧⣯⣿⣿⣿⡼⠃
⠀⠉⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣦
⠀⠀⣜⣦⣤⣤⣶⡀⠹⡆⠀⠀⠀⠀⠀⠀⠀⢠⣲⣤⣤⣴⣆⠘⢧⠀⠀⠀⠀⠀⠀⠀⣰⣦⣤⣤⣔⡄⠙⣆
⠀⣾⣿⣧⣿⢻⣿⣷⣰⠇⠀⠀⠀⠀⠀⠀⢰⣿⣿⢸⡟⣿⣿⣀⡾⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⣼⣿⣿⣠⠟
⠀⠈⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠉⠉⠁

⠀⠀⢀⠀⠀⠀⢀⠀⣬⠙⠗⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢠⡙⠻⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠀⣼⡉⠳
⠀⢠⣾⡿⣶⢶⣿⡆⠘⡇⠀⠀⠀⠀⠀⠀⠀⣴⣿⣶⣶⣾⣧⠀⣻⠀⠀⠀⠀⠀⠀⢀⣾⣿⡶⣶⢯⣇⠈⣷
⠀⢿⣿⣯⣶⣼⣿⡿⠾⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣷⣿⣿⠶⠟⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⣿⣼⣿⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢻⣏⣀⡀⠀⠀⢶⣦⣄⠀⣴⣶⠀⠀⣶⣆⠀⣀⣤⡶⠀⠀⠀⣀⣹⡟⠛
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠀⠀⠀⠀⣰⠟⢫⣿⣿⠀⠀⠀⢿⣿⣷⣿⣿⡄⢠⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⡝⢻⣆⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⣤⠏⠀⠀⠀⠀⠘⢿⣦⣿⡀⠀⠉⠁⠀⠀⠀⢰⣿⢿⣿⣿⠇⠸⣿⣿⡿⣿⡆⠀⠀⠀⠈⠉⠀⢀⣿⣴⡿⠃⠀⠀⠀⠀⠹⣤
⠀⠀⠀⣶⣤⡀⣿⡀⠀⣀⣀⠀⠰⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⠁⠀⢹⣿⡄⢠⣿⡏⠀⠈⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⠄⠀⣀⣀⠀⢐⣿⢀⣤⣶
⠀⠀⠀⠹⣿⣿⣿⣧⠸⠿⠏⢳⣀⣈⠻⠿⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⣸⣿⡇⢸⣿⣇⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠿⠟⢁⣀⡞⠹⠿⠇⣸⣿⣿⣿⠏
⠀⠀⠀⠀⠈⠛⣿⣿⣧⡀⢠⠞⡏⢩⣷⡄⣾⣿⠿⠿⠿⣷⣤⡀⢀⣴⣿⡿⠀⠀⢿⣿⣦⡀⢀⣤⣾⠿⠿⠿⣿⣷⢠⣾⡍⣹⠳⡄⢀⣼⣿⣿⠛⠁
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣦⢿⡶⢭⣀⠈⠀⠀⠀⠀⠀⠈⠻⣿⣿⠋⠀⠀⠀⠀⠙⣿⣿⠟⠁⠀⠀⠀⠀⠀⠁⣀⡭⢴⡷⣴⣷⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠹⠿⠋⠉⢹⠛⠻⣿⣿⣶⣮⣷⣦⣤⣤⣀⣀⠀⠀⠈⠻⣆⠀⠀⠀⠀⣴⠟⠁⠀⠀⢀⣀⣠⣤⣴⣾⣵⣶⣿⣿⠟⠛⡏⠉⠙⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣾⠆⠉⠙⠛⠛⠿⠛⠛⠛⠻⠿⣶⣤⡀⠹⡇⠀⠀⢰⠏⢀⣤⡶⠿⠟⠛⠛⠛⠿⠛⠛⠋⠉⠰⣷⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡿⠿⠿⣿⣷⣶⣦⣄⡉⠿⣄⢹⠀⠀⡟⣠⡞⢉⣠⣴⣶⣾⣿⠿⠿⢿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣠⣾⣿⡏⠁⠀⠀⢰⣿⠿⠿⠿⠿⣿⣦⣹⡌⡇⢸⢣⣏⣴⣿⠿⠿⠿⠿⣿⡆⠀⠀⠀⢹⣿⣷⣄⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠋⠻⠿⠶⠂⠀⠈⠛⠀⠀⠀⠀⠈⢿⣿⣿⡇⢸⣿⣿⡿⠁⠀⠀⠀⠀⠛⠁⠀⠐⠶⠿⠟⠙⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⣉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⣠⣿⣿⣿⣿⣄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣶⣄⣀⣀⠀⢀⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢈⡿⣯⡶⠿⢾⣝⢿⠠⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀
⠀⠀⠀⠀⠀⠀⢰⣾⣿⡇⠰⣷⠀⣿⢾⣷⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢈⣧⡿⢦⣤⡼⣿⣾⠁⡀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠻⣿⠛⠉⣋⡼⣿⡽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⡃⢶⠄⣄⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⣷⣶⣾⡿⠂⢄⠀⠀⠙⣄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠁⠀⠀⠁⠄⠀⠘⢦⠀⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠘⡇⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠱⠄⠐⢃⣀⠭⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⠔⠚⡈⠁⠀⠐⠢⣶⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣂⠀⠀⠀⠀⠄⠁⠘⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠛⠛⠉⠉⠉⠛⠛⠿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠉⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⣷⣤⣤⣀⡀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣦⣍⡙⠛⠻⠿⠟⠛⣋⣩⣴⣾⣿⠿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠙⠟⣡⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋




⣀⣀⣀⠀⣀⣀⣀⢀⢀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣀⣴⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡬⠥⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣠⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⠐⠂⠒⠐⠀⠈⣉⡁⣀⠀⠀⠤⡢
⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢⡄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢤⠔⠁⠈⠠⢈⡁⠀⠔⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠠⠀⣀⠀⠀⠀⣌⠊⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡨⠩⠉⠣⠀⠀⠀⡀⠀⡈⢀⢀⣀⢀⢀⠄⠸⠁⢀⣀⠀⢐⣤⠗⠋
⠀⠀⢀⠀⠀⠀⠒⠀⠐⠀⢀⠀⠐⠤⣀⣀⣀⣤⠤⢤⠾⠚⢀⠉⠙⠒⠂⠒⢲⠲⠒⠿⠶⠿⠿⢶⣤⣤⣿⣷⣶⣤⡤⠴⠒
⠀⠀⠀⠑⠀⢀⠀⠀⠀⠀⡈⠀⠀⠠⠤⠴⠔⣒⣸⠋⠀⠀⠀⠀⠒⡠⣐⠤⠞⠚⠛⠉⠉⠉⠈⠉⠉⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠒⠈⠉⠉⢤⠄⢀⢠⣐⡬⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠠⢐⡬⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠚⠉

⠀⠀⠀⠀⢀⡴⠞⠛⠛⠛⠻⠶⢶⣤⡀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⣠⣴⠶⠿⠛⠛⠛⠛⠶⣄
⠀⠀⢀⣤⣏⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⡄⣰⠟⠉⠉⠉⠙⢷⡀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣈⣧⣄
⠀⢰⡇⠀⠳⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠃⠀⣷
⢀⡴⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⣄
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁
⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀
⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠘⠢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠚
⠀⠰⡅⠀⡴⢒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠲⡄⠀⡿
⠀⠀⠉⠒⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠹⣦⣀⠀⢀⣠⡼⠃⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡗⠊⠁
⠀⠀⠀⠀⠈⠳⢤⣤⣤⣤⣤⡶⠶⠛⠉⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠈⠙⠳⠶⣦⣤⣤⣤⣤⠴⠋
⣿⣿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⢿⣴⣼⢧⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠦⢤⣄⣀⣀⣀⣀⡾⢻⢿⠟⡷⢋⢉⠉⠳⡛⣻⢿⠻⣆⣀⣀⣀⣀⣤⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢒⣾⠭⠭⠭⡉⢹⢫⠙⢷⠘⠎⠆⢸⠛⢩⢻⠉⡩⠭⠭⢽⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⠟⠋⣨⢏⢙⣾⣷⠲⢺⣿⣞⣩⢯⡈⠛⠿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠈⠈⠋⠘⠈⠋⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠆⠱⢱⠀⠲⢸⠀⠘⠔⠄⠀⠘⠦⠰⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠁⠀⠈⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⡀⢀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣆⣤⡾⠟⠛⠉⠁
⠀⠚⠛⠚⠀⠐⠛⠛⠃⠀⠚⠛⠚⠂⠀⠓⠛⠓⠀⠘⠓⠛⢂⣠⣴⣿⣿⣭⡿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠿⠟⠛⠛⠉⠉⠀⠉⠛⢿⣿⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠛⠛⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⣢⡤⠄⠀⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢌⣻⣉⣠⠎⢹⡯⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣾⣆⠘⣏⣿⡏⠀⣎⠀⠀⣡⠙⠳⣤⡁⠐⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠟⠉⠙⠣⣿⡿⠁⠀⠙⠷⠾⠃⠀⢸⣿⡇⣠⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⢀⣾⡧⠀⠀⠀⠀⢠⣀⡼⢿⢏⣾⠋⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⢀⣿⡏⠉⠁⠀⠀⠀⠀⠀⢀⣯⣿⣇⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠀⠀⠀⠀⠐⣿⣿⣷⡄⠀⠀⠀⠂⢠⢡⣾⠏⣿⣿⡎⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠲⣿⣿⣾⣷⠀⣴⣿⣿⣿⡿⠶⠘⠓⠛⢲⣾⡟⠐⣿⡯⠷⠒⠚⠚⡋⡽
⠀⠀⠀⠀⠀⠈⠀⢀⢀⣊⠉⠛⠛⠛⠛⠿⣿⣿⣿⣶⣶⣖⣰⣶⣿⡷⠞⠋⠀⠀⠠⡀⢕⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⡄⠀⠀⠀⠀⠀⠉⠙⢿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⣠⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠙⣿⣿⣤⣀⣠⡀⣨⢤⣿⣿⠿⠋⠀⣸⣿⣤⣶⣶⣼⣿⣏
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⢧⣙⢿⣿⣿⣿⠃⠀⢹⢃⢀⠀⣰⣿⣿⣿⡿⡛⠉⠉⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⣆⢲⡿⠿⢿⣷⣦⣇⣎⣎⣾⣿⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠈⢡⣽⠶⠦⠔⠚⢿⣏⣛⢳⢽⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡃⢰⡖⠁
⠀⠀⠀⠀⠀⠀⠈⠹⠶⣶⣶⡶⣾⡟⣡⣿⢬⠙⣻⣽⠛⡫⢛⡻⣻⣿⣿⠇⠀⠀⢀⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠹⠻⣷⣾⣿⡿⠓⣿⢛⠎⠻⠟⢓⣟⠳⢛⢻⣿⠀⠀⠀⢸⡿⠊⢓⡒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣓⠀⢉⣉⠄⠟⣳⣿⣿⣼⡦⠿⠿⠿⠤⠦⢾⡇⠀⠀⢀⡿⠽⠳⠊⠑
⠀⠀⠀⠀⠀⢀⠀⠘⠂⠠⠀⣊⣵⠭⠟⠉⠀⠀⠁⠚⠿⣤⣄⡀⠀⣸⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠐⠦⠀⠄⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⢯⡀⢠⣯⠤⠠⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣿⣿⡏⠁⠨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠖⠂⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⢲⠀⠀⡰⢳⡹⣦⡀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢀⡴⠊⠁⠀⠀⠈⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠊⠁⠀⠀⠀⠀⡜⠀⡐⠻⣶⣱⡑⡙⣧⠀⠀⠀⠀⠀⠀⠘⡄⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢀⠞⣆⠀⠀⠀⠀⠀⠀⠀⢇⠈⠩⠭⠭⢻⣷⣠⡟⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣼⢈⠎⢇⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠭⠴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⢀⣀⡼⠁
⠀⠀⠀⠀⠀⢠⡃⠙⣦⡄⣈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡑⡰⠅⠑⠩⢉⢉⡿
⠀⠀⠀⠀⠀⣦⠴⠒⠚⠛⠶⠮⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣞⢓⣧⣷⣷⣾⡇
⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠈⠳⣴⢶⣚⡤⠃
⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠉⠉⠙⢻⣦⠀⠀⠀⠀⠀⠀⠈⠫⡀
⠀⠀⣤⢧⢹⢦⡀⠀⠀⠀⣀⡴⣏⡎⠘⡜⢳⡀⠀⠀⠀⠀⠀⠀⠠⣿⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣀⣼⡠⣄
⠠⠄⢹⣆⢊⢊⠋⠛⠹⢉⠁⢈⡿⠿⡾⡀⢨⢳⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢀⣠⣴⠾⠛⠁⠀⠀⠑⢄
⢹⡃⠀⠛⣮⣇⢊⠁⢡⣛⣱⣟⣛⣓⣿⡰⢃⠚⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀⠀⠘⣿⣤⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠒⠠⠤⠈⠙⠻⠿⠿⠿⠷⠶⡴⠒⢻⡇⠀⠌⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠈⠀⠐⠀⠭⠤⠛⠉⠀⣀⠀⢸⣧⠈⢈⣾⠷⢶⣶⣶⡶⠾⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢋⠙⡷⠶⠤⡴⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣐⣿⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢾⣮⣎⡣⠀⡑⣼⠃⡴⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠐⣻⡿⣹⡇⠀⠀⠀⠀⠀⢀⡤⢴⠶⢦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣯⢭⣔⣟⣻⣿⣾⡯⣼⠃⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢻⣷⠆⣻⡀⠀⠀⠀⢰⠟⡅⢄⠂⠀⠀⠘⢳⡀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⠓⠒⠊⣰⠋⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⢀⠈⣷⡂⢀⠿⣄⠀⠀⣾⠿⠛⣻⣿⣷⣟⢐⢎⡗⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⠤⠤⠞⠁⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢂⣘⣷⢃⢈⠊⢳⡾⠉⠉⠛⠉⠍⠭⢿⣎⢄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠍⠠⠬⠳⣦⠽⠟⠀⡠⠤⠤⠀⣰⣶⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠥⣄⣀⠁⡼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⢒⠚⠛⠙⡉⠈⠌⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣸⠄⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠉⠓⠳⠦⣦⣴⣤⠴⠾⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⢻⡆⡔⠱⠳⡄⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠏⢙⡿⠀⠀⠀⠀⠀⠀⠀⠉⢳⣅⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣁⠀⠹⣾⡕⡐⠙⢦⣄⠀⠀⣠⠶⠛⡀⡀⣤⣾⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠬⢿⣄⠄⢌⢋⠛⠛⠅⢀⣰⣴⠛⣛⣻⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠬⢙⣮⣧⣢⣀⣤⣶⠛⣉⢭⠭⠕⣿⠀⡟⣦⣄⣀⣀⣀⣠⡴⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⡀⢀⠛⠋⠉⠉⠋⠉⠀⠈⠙⢋⡻⣾⣜⣆⢌⡍⡌⢁⣣⡾⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠲⠚⠉⠁⠀⠀⠀⠀⠀⣐⣚⣙⣏⣿⡿⠾⠋⠭⠭⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⢒⣒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠸⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⢠⠀⠘
⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢠⡀⠀⢀⠀⠀⠀⠀⠀⡐⢀⣼⠟⠙⠒⠁
⠀⠀⠀⠀⢀⠀⢰⠀⠈⢃⠀⠀⢌⠐⢄⠆⠀⠀⠀⠀⠙⠁
⠀⠀⠆⠀⠀⠀⠈⣆⠀⢃⠹⡄⠈⠂⠀⠀⠤
⠀⢰⠀⠀⠀⠀⠐⠸⣆⠘⡀⠈⠣⠠⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⡘⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢀
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠐⠒⠠⠤⠤⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠀⠀⠀⢀⣀⡀⠀⠀⠉⠉⠉⠉⠛⠓⠒⠒⠒⠶⠦⠤⠤⠤⠤⠤⣤⠀⠀⣀⣀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠒⠒⠒⠒⠶⠶⠦⠤⠤⠤⣤⣤⡤⣤⣤⣀⣤⣴⠃
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣤⣤⣄⠀⢀⡀⣀⣠⣀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⣿⣟⣿⣷⣿⡇⠘⠓⠛⠛⠚⠐⢠⣺⣷⡄⡀⠀⠀⠀⠰⢆⣂⣂⠈⠀⢀⣀⣠⡶⠋⠀⠀⠠⣀⠀⠀⠀⠀⠳⢎⡸⠀⠀⠀⠀⠄
⠀⠀⠈⠛⠿⠟⢿⠋⠀⠀⠀⣠⠶⢄⠀⠀⠉⠉⠀⠀⠀⠲⢣⣞⠁⠈⢻⣛⣆⠛⠋⠁⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠸⠟⠻⠇⠀⣠⡄
⠀⠀⠀⣠⣴⣤⣌⡀⠀⣀⡤⣷⣤⡾⠃⠀⡀⠀⢠⠀⠀⠀⢾⣿⡄⠀⠈⣿⡏⡇⣰⠆⣠⡦⠀⡴⡄⠀⠀⢠⡶⣦⢠⣶⣦⡸⣧⣸⣿⡀
⠀⠀⢰⠻⣿⣿⡿⠟⠋⠑⠀⡼⠁⡀⠐⡤⡾⣿⡯⠑⢏⠀⠘⢏⡁⣠⣤⣍⡠⠃⠋⠊⠁⠀⠐⣃⡀⢠⣦⠘⢷⡿⢻⣧⣴⣷⠘⠋⠹⣧
⠀⠀⡏⠀⠘⣯⣠⣄⣀⣀⣾⣇⠀⣧⠈⠳⢤⣮⣦⠴⠋⠀⠀⠀⠉⠙⠛⡉⣠⡄⢠⣠⣦⢠⣿⠛⣿⡌⣿⣤⣴⡆⠀⠻⢿⠿⠀⣀⡀⢀⡄
⠀⠀⢿⠀⢤⠁⠉⠻⢮⣿⣿⣿⡇⠈⠷⣶⣆⠀⠀⠀⢤⣰⠚⢣⣤⣄⣺⣧⣸⣷⢻⣿⣿⣎⣿⣦⣿⠇⠻⠿⠛⠋⠀⠀⢰⣾⣿⢿⡇⠈⠇
⠀⠀⠈⢷⣤⡀⠀⠀⠀⣈⡽⠟⠁⠀⠀⠉⠀⣀⣤⣴⡄⠈⣀⣿⡏⠙⠛⣿⡏⢿⡞⡿⠙⠟⠈⡉⠁⠀⠀⠀⣧⠀⠀⠀⣸⣷⣤⣄⣧⣀⡀
⠀⣤⣶⣾⣍⣛⣻⣿⡛⠉⢀⢤⡒⠄⣇⡀⠹⠛⣿⡏⢺⣿⣽⡜⢿⣶⣿⠻⠗⠈⠀⠀⠀⡀⠛⠁⠲⠄⠀⠤⠞⠀⠀⠘⣿⣷⣾⣿⣿⣿⠃
⠀⣿⣟⠛⠛⠛⠛⠛⢻⠃⡜⠀⠀⠀⠀⠂⢀⠀⢹⣿⡘⣿⣷⠶⠀⠉⢁⠀⠀⠀⢹⡀⠀⠸⡄⢠⠤⠒⠀⣀⣠⣤⣤⣀⠀⠙⢿⣿⣿⠃
⠀⣿⠿⡀⠀⠀⠀⢀⡏⠀⢷⠀⠀⠀⠀⢈⡆⠀⠀⠉⠀⣀⡀⠀⠀⢰⣬⣟⣲⠤⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣟⣿⣿⡟⠀⢠⡀⠙⠁
⠀⠻⣧⣇⣀⣀⣀⡼⠁⡀⠀⠑⠂⠔⠐⠀⢀⣠⠤⠒⠉⠙⣁⣀⣤⣼⣿⣿⡿⢿⣿⣶⡆⠀⡁⠀⠀⠈⠙⢿⣿⣿⣿⠀⠰⡏⠘⠳⠆⣀⡀
⠀⠀⠀⠉⠉⠉⠁⠀⢄⠀⠠⣀⡀⠰⠞⠛⢉⣀⣤⣶⣺⣿⣿⣿⣻⣿⣿⣾⣿⣿⡿⠃⠈⡥⠁⠀⠀⠀⢀⡀⠈⣵⡆⠀⣼⣿⣦⣦⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣆⡔⠀⠸⣃⣤⣶⣾⣿⣽⣿⠿⠿⠟⠛⠛⠛⠉⠹⣿⡿⠋⠀⠂⡠⠔⠉⡁⠀⢤⣿⣷⡄⢸⡆⠀⠻⠿⠛⠁⠐⣿⠂
⠀⠀⠀⠃⠁⡔⠀⠀⠉⠉⠀⠈⠛⣛⠋⠉⠉⠀⠀⠀⠀⠀⢈⣶⠃⠀⠀⠉⠈⠆⡆⠀⠀⣀⣀⢿⡿⠄⢉⣩⠥⠔⠧⢄⡀⠀⠀⠀⠬⡁
⠀⠀⠀⠂⠀⠀⠀⠀⠂⣤⡞⢉⣻⣅⣈⠑⣤⠢⠐⠀⠻⢷⣾⠋⠀⠀⠑⠈⠢⣠⠖⣆⠀⡇⠈⡎⠁⣰⠋⣠⣶⣶⣶⣦⣙⡄⠀⠠⣤⣄
⠀⠀⠀⠀⡀⠰⡆⠀⣾⣤⣾⣿⣽⠶⠶⠟⠾⠷⣉⡴⠠⠐⠀⠀⠀⣤⣦⣤⣤⡘⣦⣈⠛⣷⣤⠇⢰⡇⣬⣿⣿⣿⣿⣿⣿⣇⠀⢨⣷⣾
⠀⠀⣠⣾⣷⡀⠉⠘⡿⢋⠉⠀⢻⡀⠀⠀⢤⣤⢸⣷⡀⠐⡅⢰⣟⣛⣿⠻⡟⣿⣎⠙⢻⣿⣿⣆⠈⣧⠸⣿⣿⣿⣿⣿⠏⢹⡀⠘⠿⠟⠂
⠀⠀⠛⣿⡟⠓⠀⢸⣿⡾⠆⢠⣾⣿⣷⣦⣄⣀⠞⠙⣿⡀⢇⢸⣿⣛⣿⣠⣇⣿⣿⠀⠘⣏⡕⡻⣷⣿⡦⠄⣉⣉⣉⡤⠒⠉⢿⡵⣦⡀
⠀⠀⠀⣿⡇⠀⢠⣿⠉⠓⢦⣾⣿⣿⢿⣿⠟⢅⠀⠀⢸⣧⢪⢸⣿⢙⠏⡿⡏⣿⣿⠀⠀⠙⣾⣱⣹⣿⢴⢒⣍⣩⣭⡍⡭⣽⠸⣿⣒⣳
⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠘⢯⣛⣛⠛⣋⡠⠆⠀⠀⣴⣛⢦⡀⣿⡞⡿⣷⣗⢿⣿⡆⢰⠄⠈⠛⠿⣿⡸⣙⠞⠙⢿⠇⢉⡼⠀⣿⣿⣾⡆
⠀⠀⢀⣿⡇⣴⠋⢿⣳⡄⠀⠀⢨⠏⠛⠂⢲⠀⠀⢸⣿⡦⡌⢷⢹⣷⣤⢿⡼⠼⣿⣧⠘⡄⠀⠀⠀⢸⣦⣄⣉⣘⣛⣋⣥⣴⣾⣿⡿⠙
⠀⠀⢸⣿⡇⢹⡀⡏⢿⡷⠀⠀⣸⣀⠀⠀⡇⠀⠀⠈⠛⠓⠘⠉⣿⣿⡆⣾⡿⠾⣿⣿⡙⡄⠀⠀⠀⠈⣿⠿⠿⢿⣿⣿⡿⢟⣹⡞⢷⣰
⠀⠀⣾⣹⣷⠀⠉⢡⣴⣶⠆⠀⠀⢸⠁⠀⢉⠇⢀⣀⣾⣀⡀⠀⣾⡿⣻⢻⡟⢿⢻⣿⡧⡇⠀⠀⠀⢀⣿⣭⣭⣭⣧⢸⣿⣿⣶⡷⣶⣄
⠀⢰⣿⣹⣿⣧⡀⢀⡏⠀⣾⠆⠠⠚⠚⣧⠎⠀⠀⢹⢿⡏⠁⠀⢻⣷⠹⢿⡇⣆⢘⣿⠇⡸⠀⠀⢰⣯⣛⣿⣿⣿⣿⠸⣿⣿⡿⠿⠿⢿⡆
⠀⠈⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⠁⠀⠀⠈⠛⠿⠿⠿⠿⠿⠋⠀⠁⠀⠀⠘⠋⠋⠛⠛⠛⠉⠀⠉⠉⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢿⣿⡿⠛⣿⡟⠛⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⢠⣿⠏⠀⠀⣿⡇⠀⠀⠹⣿⡌⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡁⠀⢠⣿⡏⠀⠀⠀⣿⡇⠀⠀⠀⠹⣿⡄⢀⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠛⠿⣷⣾⣿⣤⣤⣀⣀⣿⣧⣀⣤⣤⣴⣿⣿⠿⠛⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⠀⢀⣿⡏⠉⠛⠛⠛⣿⡟⠛⠛⠉⠉⢹⣿⡀⠀⠀⢹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣤⣤⣤⣼⣿⣥⣤⣤⣤⣤⣿⣧⣤⣤⣤⣤⣼⣿⣧⣤⣤⣬⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠉⠉⢹⣿⠋⠉⠉⠉⠉⣿⡟⠉⠉⠉⠉⠉⠛⠋⠉⠉⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠘⣿⣇⣀⣤⣤⣤⡟⠁⣠⣾⣿⢿⣿⣶⡄⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⣠⣶⣾⣿⣿⠛⠛⠋⠉⠀⢸⣿⠏⠀⠀⠈⢻⣿⡄⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠉⠀⠸⣿⡄⠀⠀⠀⠀⠸⣿⣆⠀⠀⢀⣼⣿⠁⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⠀⢻⣷⡄⠀⠀⣦⡀⠙⠿⣿⣿⣿⣿⣇⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣽⣿⣦⡀⣿⡇⢀⣤⣄⣀⡀⠙⣿⣧⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠀⠀⢼⣽⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣂⣤⡀⣤⣠⢄⡤⢰⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠉⠉⠀⠙⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡀⠀⢀⣴⣿⣿⣿⣦⡀⠀⠀⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⣄⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠳⣄⠀⠀⡘⠁⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⣀⠔⠢⡀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⣎
⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠰⣀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠋⠀⠀⢻⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⣹⣏⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢀⡀⣀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⠀⠀⣠⣾⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠈⢣⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠘⢄⣀⠀⠈⠓⠚⠁
⠀⠀⠀⠀⠀⢰⠋⠀⠀⢀⠔⠢⡀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁⠀⣠⣄⠀⠀⠀⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠹⣄⠀⣀⠆⠀⠀⠈⠢⡀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⣿⣷⣄⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡆⠰⣶⢃⡞⠀⠀⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⣀⠀⡀⠍⠙⠁⠀⠀⠄⠀⠀⠀⠁⣶⣀⠀⠄⠀⠀⠀⢀⡤⡀⠀⠈⣀⣛⠀⠃⡀⠀⠲⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠸⠿⣗⠀⣿⠀⠉⠒⠐⠂⠀⠀⠀⠀⠀⢠⣆⡄⢹⢀⡀⢻⣄⠀⠉⠻⠋⠀⠀⠹⠌⠀⠀⢱⡆⠸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣐⡇⠀⢀⡐⠋⠀⠀⠀⡄⢀⡹⣆⠀⠀⠀⠀⠑⠀⢩⣶⠀⠀⠀⠀⠀⠈⠔⣀⠀⠀⢃⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠊⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⢠⠀⠁⠈⠓⢠⡀⣄⠀⠀⠀⠀⠀⠀⠦⢄⡈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⢠⠀⠉⠀⠓⠀⡀⠃⠀⠀⡇⢀⠁⠈⢳⡏⠀⠀⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⡀⠀⣴⠀⠀⢀⠇⠀⠀⠀⠀⠉⣤⠀⢁⠞⣠⠀⣠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡭⠂⠀⠒⠄⠀⢉⡀⠁⠀⡝⠀⠀⠈⣴⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠐⠀⠾⠡⣀⢀⢠⠐⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡂⠀⠤⠀⠀⠀⠀⠀⠀⠤⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠦⠀⠀⠸⢓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠀⠀⠰⠀⠚⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢛⡅⠀⢠⠀⠀⡀⠀⡔⠀⠀⠀⠇⠀⠈⠀⠀⠀⠀⠀⠀⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠦⠀⠀⢰⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣸⡆⠀⠀⠀⠀⠀⠤⠆⠀⠀⢁⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠀⢤⣀⠀⠀⠀⡤⠿⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⠂⡀⠀⠀⡄⠀⠀⠀⠀⣠⡐⠀⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⠓⠤⣀⠴⠬⠆⣌⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⢈⠀⠀⠀⢠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣀⡀⠀⠀⢰⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⢦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢀⡤⠒⠃⠟⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡜⠃⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠑⠀⠀⠀⠀⠄⠂⠀⠀⠀⣀⠀⣀⠤⠂⠀⠁⠀⠀⠀⠘⣇⣀⠐⠀⠒⡄
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢲⡄⠃⢠⠐⠁⠀⠀⠀⠈⠀⠂⠀⠀⠄⠀⠖⠀⠀⠀⠀⠀⠀⠈⠁⠣
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠠⣄⠀⠀⣀⢀⠀⠢⣀⠴⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠐⠀⠲⠄⠢⠤⡄⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⢀⠂⠀⣠⠉⠘⠷⣆⠀⠈⠇⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠈⠂⣀⠕⣠⠀⠀⠀⠀⢀⡴⠖⢀⡠⠊⠀⠈⣫⡄⣀⡀⠩⠄⠀⠀⢑⢦⣀⠩⣷⠄⠀⠀⠀⣠⠀⢄⣠⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡎⢠⣆⠀⠀⠀⣿⠃⢀⠱⣇⠀⠠⡀⠀⠀⠀⠁⠀⠀⠀⠰⢣⡖⠛⠂⢽⡆⠀⠀⠠⠵⠛⠉⠀⠉⡌
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⠆⠀⠀⢺⡅⠀⠃⢀⣹⡶⠀⠂⠀⠀⠀⠀⠀⠀⡀⠹⣤⠤⠀⣸⠇⢀⣤⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡽⣦⠀⠈⠳⠀⣀⣉⡫⠐⠋⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠔⠀⢁⡴⠛⠉⠰⠄⠀⠀⠀⠈⠁⠐
⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠺⠀⠁⠂⠠⣀⡈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠦⠉⠀⣰⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⡀⠄⠐⠉⠁⠙⡁⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⡠⠃⠀⠃⠀⠀⠀⠈⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⠤⠀⢀⢤⠀⠀⠈⠀⠐⢂⠡⠆⡈⢀⡐⠀⠀⠀⢀⡱⡃⠀⢀⠤⠒⠠⢄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠊⠀⠀⠂⠀⠀⠀⠀⠀⡀⠜⠣⠐⠈⠤⠈⡀⠀⠀⡍⠀⠀⠠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠎⠉⠀⠀⠀⡄⠀⠐⠂⠀⠀⠁

⠀⠀⠀⢀⡄⠀⠀⢀⡄⠀⠀⢠⡀⠀⠀⢠⡀⠀⠀⢠⠀⠀⠀⣠⠀⠀⠀⣠⠀⠀⠀⣤⠀⠀⠀⣤⠀⠀⠀⣄⠀⠀⠀⡄
⠀⠀⢤⡜⠃⣴⣤⡜⢇⣤⣤⡸⢃⣤⣤⡘⢣⣄⣤⡸⣠⣤⣤⠙⣠⣄⣤⠹⣠⣤⣤⠟⣠⣤⣄⠛⣤⣤⣄⠏⣤⣠⣤⠃⣤
⠀⠀⠀⠉⠊⠀⠀⠙⠂⠀⠀⠱⠊⠀⠀⠑⠋⠀⠀⠱⠋⠀⠀⠒⠉⠀⠀⠱⠁⠀⠀⠚⠁⠀⠈⠛⠁⠀⠈⠞⠁⠀⠈⠊⠁
⠀⠀⢀⣶⡀⠀⢀⢲⡀⠀⢀⡶⡀⠀⢀⣴⡀⠀⢀⣰⡀⠀⢀⣰⣀⠀⠀⡰⣀⠀⠀⣰⡄⠀⠀⣰⣆⠀⠀⣰⢀⠀⠀⣰⣆
⠀⠀⠁⣬⠉⠀⠁⣭⠈⠀⠉⣨⠈⠀⠉⢨⠈⠀⠉⢩⠈⠁⠉⢩⠉⠁⠉⢨⠉⠁⠈⢩⠈⠁⠈⢨⡀⠁⠈⢨⡅⠁⠈⢡⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡻⢃⣤⡄
⠀⠀⠀⠀⠀⠀⢀⢂⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⢀⢂⡀
⠀⠀⠀⠀⠀⠀⠉⡎⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠈⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣴⣿⣷⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣙⠛⢦⣿⣯⠞⢛⡁⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢰⠋⣍⠹⣆⢿⢇⡾⢉⡍⢳⠀⠀⠀⠀⢠⣽⡇
⠀⠀⠀⠀⠀⠀⣰⠟⢉⣉⠉⠒⠛⠻⠄⠀⠀⠀⠀⠈⢉⣀⠏⠺⠊⢧⣀⠁⠀⠀⠀⠀⠀⠼⠛⠓⠊⢉⣉⠙⢳⡀
⠀⠀⠀⠀⠀⠀⢻⣀⠻⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⢃⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠸⢁⢤⣀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡄⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠰⢿⢻⢽⡄⣢⢿⢻⢷⠀⠀⠀⠀⠀⠀⠾⠻⠂
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣸⠍⠙⠉⠉⠉⠋⠒⢂⠤⠀⡀⠀⠀⠀⠀⣠⠿⢧⠀⠀⠀⠀⠀⠀⠀⢄⡒⠺⠍⠉⠉⠉⠉⢻⡀
⠀⠀⠀⠀⠀⠀⠃⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⢰⣶⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣄⠀⣰⡀⢀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⡀⠟⠇⡈⠉⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⣀⠐⡀
⠀⠀⠀⠀⠀⠀⠑⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⢠⠀⣶⠆
⠀⠀⠀⠀⠀⠀⡔⣨⡉⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠂⠀⠀⠒⠒⠐⠛⠚⠛⠛⠛⠛⠛⠛⠛⠋⠉⣩⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⣀⣀⣀⣀⡀⣼⣿⣿⣿⣿⡄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⢿⣿⣿⣿⣿⠇⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁
⠀⠀⢀⣂⠀⠀⣠⡀⠀⢠⡀⠀⢀⣄⡀⠀⣠⡀⠀⢀⣄⠀⠀⣰⡀⠀⢀⡇⠀⠀⣰⠀⠀⣀⣀⠀⢀⣀⠀⠀⣠⡀⠀⢀⣂
⣀⣀⣚⣛⣂⣘⣛⣛⣀⣛⣛⣂⣘⣛⣃⣐⣛⣛⣐⣚⣛⣓⣐⣛⣓⣀⣛⠛⢂⡘⢛⢓⣀⠛⢛⢀⣚⠛⡃⡚⡛⠛⢀⡚⠛⠂⣀

⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣒⠒⡖⣢⠨⣡⣶⡔⠦⠃⢀⠀⠂⠀⡤⠀⠒⠒⣂⣀⡐⠒⠒⠂
⠀⠀⠀⠀⣀⠤⣺⠁⢠⣤⣤⣤⣶⣶⣶⣾⠀⠀⣾⣦⣴⣿⣿⡧⠀⠨⢎⠌⠜⡼⠠⣖⡻⠷⣔⠃⡎⠀⠀⡀⢰⣷⠀⠁⢻⣿⡇⠀⠿⠿⠿⠿⠗⠐
⠀⠀⠀⠸⢐⠥⠚⡁⢸⣿⣿⣛⣟⣻⣿⣿⠀⠀⠙⢿⣿⣿⡟⠁⠀⣐⣠⣂⣊⣾⡀⠢⠄⠉⣹⡶⣄⠀⢀⠁⠸⠿⠀⢠⠘⠛⣁⣤⣤⣦⣤⣄⠀⠀⡀
⠀⠀⠀⡋⠤⢂⠥⡇⠈⠛⠛⠛⠛⠛⠛⠻⠀⠀⠀⠄⠙⠉⠀⠀⣸⡿⠿⠿⠿⢿⣧⣀⠀⢀⡟⠃⠙⠆⠘⠀⢠⣶⣦⠸⠀⣼⣿⢟⣩⣍⡝⠻⣿⣄⠁
⠀⠀⠀⡇⠊⡡⠔⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢀⣼⡟⠁⠀⢀⡀⠀⡉⢻⣧⠈⠁⠆⠀⠀⠀⠀⠈⠻⠋⠀⢸⣿⡇⣾⣿⣿⣿⣇⢹⣿
⠀⠀⠀⡇⣈⠔⣊⢸⢰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠹⣿⣇⠀⠀⢘⡁⠉⠁⣸⡟⠀⠀⡃⠀⠀⠀⠀⠀⠀⢠⠀⠘⣿⣧⡹⠿⣿⠿⣣⣿⡟⡀
⠀⠀⠀⣋⡠⢊⠅⠘⠼⡄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣼⠀⠀⠙⢿⣷⣤⣨⣁⣠⣴⠟⠁⠀⠀⠃⠀⠀⢠⠀⠀⠀⠈⠀⠀⠈⠻⢿⣷⣶⣿⠿⠋⠀⠂
⠀⠀⠀⠧⢈⣤⢊⣠⡀⠀⠀⠀⠀⠀⢀⢼⠀⠀⡒⠄⡁⠠⠐⠀⠀⠈⢻⡻⠻⠟⣿⠀⠀⠀⠀⡆⠀⠀⠀⢄⣀⣀⣀⣠⡄⣠⡠⠠⠤⠤⠤⠤⢠⠲
⠀⠀⠀⠀⡀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠐⠊⠀⠀⠈⠢⣿⠤⠚⠀⠀⠀⠘⠒⠀⠒⠞⢀⡴⣤⠀⠘⠀⠠⡶⣦⠈⠓⠓⠚⠓⠒⠒⠂⠋⠂⠈⠈⠁
⠀⠀⠀⠋⠀⠀⠀⣀⠄⣆⣂⣖⡠⡀⠀⠀⠀⡌⠁⡀⡀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠚⠿⠂
⠀⠀⠀⠀⠀⠠⡎⢰⠊⠉⠙⢿⣿⣮⣢⠀⠈⠀⠁⠠⣿⡴⠂⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣥⣥⣤⣤⡀⢱⡀⠀⡊⠁⠰⠈⠀⣧⢀
⠀⠀⠀⠀⣐⢃⡡⠁⠀⠀⠀⠀⠹⣿⣿⣇⠀⠀⣠⣤⣿⢀⡀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠛⠛⠉⠉⣉⣉⡉⠉⠙⠛⢻⣿⡇⢸⡇⠀⠀⡀⠀⠀⣰⠏
⠀⠀⠀⠀⡉⢀⠃⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⠀⢸⣿⣿⣿⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⢷⣆⠀⢸⣿⡇⢸⡇⠀⢀⠀⢠⡴⠃
⠀⠀⠀⢠⡁⣈⠀⠀⠀⠀⠀⠀⠀⡄⣿⣿⣿⠀⠈⠛⠛⠁⠀⠀⢀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⣿⣿⠀⠸⣿⡇⢸⡇⢀⠀⠀⣸⣿⠀⠻⠃
⠀⠀⠀⠀⡁⢌⡀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣆⠀⠀⢠⣄⣰⡆⢀⠀⣿⣿⠀⠀⠀⠀⠐⠘⢿⣷⣿⣽⣿⡛⠋⠀⠀⣿⡇⢨⡇⢸⠀⠀⣿⣿⡆
⠀⠀⠀⠀⢅⠈⣭⣉⠛⢶⣄⠠⠐⠂⢩⣙⢻⣿⡄⠀⠈⢿⡿⠃⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⣿⡇⢠⡇⠸⠂⠀⣿⣼⠇
⠀⠀⠀⠘⠂⠁⠈⢿⣷⣄⠻⣧⠔⢠⣿⣿⡆⣿⣷⠀⠀⠀⠀⠀⠀⢄⠻⠿⠿⠿⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣾⠿⠿⠿⢃⣸⠇⠀⠀⠄⠀⡀
⠀⠀⠀⠀⢰⣾⣿⣆⠻⣿⡄⢻⣇⣿⣿⣿⡇⣿⣿⠀⠁⠀⠀⠀⠄⠂⠀⠀⠈⠉⠁⠁⠈⠻⢿⣿⣿⣷⣾⣟⣃⣉⣀⣀⣉⣑⣒⡄⠀⠀⠸⠀⠰⠁
⠀⠀⠀⠀⣿⣿⣿⣿⡆⢹⣷⢸⣿⣿⡿⠏⣰⣿⡟⠀⠀⠠⠀⠀⢷⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠠⠀⠐⠀⠈
⠀⠀⠀⠀⠻⣿⣿⣿⡏⢨⣟⣿⣧⣤⣴⣾⣿⣿⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣠⣲⠄⣀⡲⠄⢠⠰⠤⠀⣀⣀⡀⠀⠀⠀⢀⠠⠐⣒⣒⣒⡀⠄⠁
⠀⠀⠀⠀⠄⠈⠛⠛⠴⠛⠋⠀⢀⠉⠁⠀⠈⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠁⠀⠘⠛⠀⠀⢹⣿⣷⠀⠁⠀⠓⣿⣿⠿⣿⣿⠿⢷⣾⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⢠⠂⠚⠀⠠⡎⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠸⣿⣿⡆⠀⠀⠀⣿⡇⠀⣿⡏⠀⣾⡿⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠨⠀⠀⠀⠀⠒⠂⢀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠡⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠘⣿⠀⢹⣷⠀⢸⣇⣼⠏
⠀⠀⠀⠀⠀⠀⠒⣴⣶⣶⢽⣿⢿⡍⠃⣉⣶⣶⣿⡙⠻⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⠀⢀⣿⠀⣸⣿⠀⣾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⣿⢾⣿⣼⣿⣽⡧⠧⣿⣿⣿⣿⡷⠀⠀⢐⢂⠀⠀⠀⠀⠀⠉⠉⠈⣈⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢀⣴⣾⣧⣀⣿⣧⣸⣿⣷⣦⡀
⠀⠀⠀⠀⢀⠀⠀⠙⠛⠛⡉⢩⣉⣠⡂⠙⠻⠿⠛⠁⢠⠀⠈⠀⠀⠀⡦⠠⠤⠀⠤⠤⠤⠀⢀⠀⠀⠀⢸⣿⣿⡇⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠓⠒⠐⠂⠂⠒⠒⠒⠓⠚⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢁⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⡯⠈⠀⣾⣧⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⠇⣨⡝⠂⣸⣿⡏⠀⠀⠀⢋⠁⢤⠤⠒⢂⣷
⠀⠀⠀⢀⡀⠀⠀⠐⠀⢠⠥⠄⢹⣿⣿⣿⣿⣿⡿⠀⠀⠒⣞⠀⠈⡀⢠⣿⣿⠁⠤⢤⣄⡐⢠⢯⢐⣦⣍⡿
⠀⠀⠘⡄⠀⠀⠀⢀⣂⣀⣭⣵⣀⣿⡿⠟⠋⠁⣀⣀⣀⣀⠈⠉⠒⠋⠚⠛⠁⠀⠀⠀⠀⠫⠉⠭⠜⠛⠉
⠀⠀⠀⠙⠛⡛⢛⡻⠛⠉⠀⣹⠛⠛⢋⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠀⠀⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⢠⠉⣐⢎⠐⠁⠀⠀⠀⠀⡇⢠⣿⣿⣷⣶⣶⣶⣶⣦⣤⣬⣤⣤⡀⠀⢿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⢸⢰
⠀⡼⠣⢍⡁⢱⠀⠀⠀⠀⢠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡿⠟⠻⣧⣐⣲⣆⡼⣸
⡘⢠⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣨⠛⣙⣤⣶⣿⣿⣿⢟⡠⠋⠔⠁
⠇⢸⡀⠀⠀⠀⠀⢀⣀⡀⣸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⢾⣟⠁⣿⣿⣿⣿⡟⠉
⠈⠀⢱⢤⡒⣈⣭⣤⠄⠀⢀⠗⠘⠛⢛⡿⠿⠿⢿⢿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣶⣿⣿⣿⢤⣤
⠀⡔⠁⠀⠚⠛⠋⣁⡤⠖⠉⠛⢶⣤⣤⣀⣈⣉⠉⠙⢌⠻⣿⣿⣿⣥⠖⣺⣿⣿⣿⢿⣫⣷⣿⣿⠀⣀⡀
⠀⠈⠒⠒⠒⠛⠛⠳⠤⠄⠀⣶⠻⠿⣒⣚⠛⠛⠛⠓⣚⣓⣍⠻⣿⣿⣷⠞⠛⣫⣵⣿⣿⣿⣿⣿⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣐⡒⠫⠉⠩⠉⣙⣓⠒⠓⠾⠛⠿⣶⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠒⠠⠬⠥⢉⣑⣒⠒⠂⠨⠥⠄⠀⣿⣿⣿⣿⣿⣿⠟⠁⠀⡠⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡰⠠⢍⣉⠑⠒⠒⠤⠬⣭⣉⣉⣉⠀⢻⣿⣿⣿⠟⠁⣀⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣈⣉⠛⠓⠶⠤⣤⣄⣀⣀⠀⠀⠉⠁⠀⢸⣿⡿⢃⡴⠊⠑⣢⡾
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣀⡂⠭⢉⡓⠒⠦⠤⢤⣉⣉⡙⠛⠻⠶⠶⠾⠋⠠⡏⠑⢢⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣚⠁⠀⠀⠈⢉⠚⠂⠀⠨⠉⠐⠂⠀⠀⠉⣍⣩⢿⠒⠒⢂⡄⠈⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣤⣤⣀⣀⡉⠒⠒⠀⠀⠀⣠⢮⢟⣰⢃⢞⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣷⣶⣦⣤⣽⣷⣶⡖⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣛⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠟⠻⠿⢶⣦⣀⣴⡶⠿⠟⠻⠷⢦⣄
⠀⠀⢀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⡀⠀⠀⣸⣿⣇⠀⠀⢀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⢠⡾⠋⠉⠀⠈⠉⠛⢶⣄⠀⠀⣠⠖⠢⡄⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⡆⢠⣿⠀⣿⡄⢰⠁⠀⠀⠀⢠⡏⠀⠀⠀⠀⢠⠔⠲⣄⠀⠀⣠⡶⠛⠉⠀⠈⠉⠙⢷⡄
⣿⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⣤⡃⠀⠀⠈⠀⠀⠀⠀⠈⠻⢦⣀⣠⡴⠃⠈⡇⠀⢹⠁⠘⢦⣀⣀⡴⠟⠀⠀⠀⠀⠀⠁⠀⠀⢘⣤⠞⠁⠀⠀⠀⢀⠀⠀⠀⠀⣿
⠘⢦⣀⠀⢀⡔⠀⠀⣠⠔⠒⠊⠷⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠾⠑⠒⠢⣄⠀⠀⢢⡀⠀⣀⡴⠃
⠀⠀⠉⠉⠁⠀⠀⠀⢇⠀⠀⠀⠀⠘⢆⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡰⠃⠀⠀⠀⠀⡸⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣀⣥⣾⠇⣀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠉⠀⠉⠳⢦⣄⡀⠀⠀⠀⠀⠀⣀⠸⣷⣬⣀⠀⠀⠀⠈⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣥⣤⣤⣬⣭⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣤⣤⣬⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠛⠋⠉⠉⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠈⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣿⢿⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⡇⣿⢸⢸⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣦⠀⠀⢸⡇⠁⢹⡆⢸⡇⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⠀⠀⠈⠁⠀⢸⡇⣴⢸⡇⢸⡇⠀⠀⠀⠀⠀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢸⡇⢸⢸⡇⢸⡇⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⢰⣶⣤⣤⣤⣤⣤⡶⠶⢾⠟⣛⣫⣭⣯⣭⣭⣭⣿⣭⣛⣷⠀⢸⡇⢸⠘⡇⢸⡇⢸⣟⣹⣟⣙⣛⣛⣷⠶⢶⣤⣤⣤⣤⣤⣴⢶⡶⠾⢛⣛⣫⣟⠁
⠀⠀⠙⠷⠶⢶⣶⣿⡶⠶⠶⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠘⣿⠀⢇⣷⣾⠃⠈⠉⠉⠉⠉⠉⠙⠛⠻⠷⠶⠶⣷⣶⣶⠶⠾⠿⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠀⠀⠀⠀⠀⠀⢿⡤⣲⠽⣿⠀⠀⡄⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⣼⠿⡄⠀⢻⣆⠀⠹⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⣿⣆⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢁⣾⠁⠹⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣃⣾⠃⠀⠀⢹⣧⡼⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣥⣤⡉⢻⣆⠀⠀⣸⡇⣴⢶⣝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣼⠇⠈⣿⡈⣿⠀⠀⣿⣼⣏⠀⢻⡞⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⣿⠇⣿⠀⠀⠸⣇⢿⣄⢸⡇⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠻⣦⣴⠟⣼⠏⠀⠀⠀⠻⣦⣙⣛⣵⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⢠⡾⠋⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣠⠖⠒⠦⣄
⠀⠀⠀⠀⠀⢸⠁⡎⠉⠙⠢⡙⢦⡀
⠀⠀⠀⠀⠀⠈⢳⡈⠢⡀⠀⠈⠀⢉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠳⢌⡀⠀⠀⠀⠀⠈⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⣀⠈⠑⠦⣄⣀⡀⠀⠀⠀⢀⣠⠴⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢭⣀⣂⠀⠉⠉⠓⢶⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⣿⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⢻⡀⠀⠀⠀⠀⠈⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠉⢉⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠓⠒⠒⠒⠛⠒⠒⠒⠒⠒⠒⠢⠤⣍⡓⠶⣖⠒⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣏⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡈⠙⠲⢄⣸⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⢣⠀⠀⠀⠈⠳⣄⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⣸⠦⣤⣄⣠⣠⢟⡴⠁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⣀⣠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠊⠀⠀⢀⣠⣃⣀⣀⣀⣠⠔⠉⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠉⠛⠒⠒⠶⠶⠶⠤⠤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠖⠋⠁⠉⢉⣩⠥⠤⠤⠤⠤⠶⠶⠶⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⢀⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠒⠒⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠚⠁