Masonry Emojis & Symbols

⠦⢤⡀⠀⠀⠨⠧⠤⢀⡀⠀⠀⠴⠀⢀⠀⢀⠀⠤⠀⠀⢀⠀⠠⡄⣀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠆⡤⠤⠠⠄⠠⠤
⡴⠒⠂⠀⠀⢀⠀⠀⠀⠷⠤⠤⠤⠌⠀⠤⡤⡤⠠⠧⠤⠬⠤⠠⠶⠂⠀⠠⢠⠀⠌⠄⠀⠀⠄⠠⠆⠀⠀⠤⠀⠴⠤⠤⠤
⠛⠒⠒⠲⠖⠚⠀⠀⠒⡒⠒⠚⠒⠂⠠⠤⠂⠀⠀⠐⠶⠄⠐⠒⠒⠒⠂⠒⠂⠒⠂⠴⠂⠀⠂⠂⢀⡂⠔⠚⠑⠀⡖⠒
⢉⠉⡉⠉⠁⢻⡆⠉⡀⠉⡐⣏⣟⡁⢉⡀⢀⣀⡄⠀⠀⠀⠉⣧⡀⢉⡁⠀⠀⡖⠂⠀⠀⠐⢐⠚⠛⠋⠁⠁⣙⡛⠉⠋⠁
⣠⣤⣉⣯⠀⢀⣀⠁⠓⢦⣉⡁⣈⣀⣉⡁⠀⠀⠀⢉⣭⠈⠁⢀⡁⢈⡏⠉⠉⠉⠉⢙⠉⠉⢉⡁⢉⢋⠉⠀⠈⠀⢰⣀⣀
⠧⠤⠤⠀⠀⠀⠤⠤⠀⠠⠤⠼⠤⠀⠠⢤⠀⠆⢠⢤⠤⠤⠈⠀⢀⠠⠄⢠⠀⠀⢠⣤⡤⠀⣡⣤⡤⢠⡄⠀⠠
⠶⠆⠶⠚⠦⠤⠄⠀⠀⠂⠀⠀⣄⡀⠀⠆⠤⠀⠀⠆⠀⠀⠀⠠⠀⠂⠐⠰⠰⡦⠐⠴⠃⠤⠤⠠⠤⠜⠤⠄⠤⠠⠤⠶⠆
⠉⠀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠐⠓⠀⠐⠒⠀⠀⠀⠀⡔⠒⠀⠀⠒⠲⠆⠒⠊⠐⠒⠠⠖⠒⠛⠒⠒⠒⠒⠀⠀⠐⠒⡒⠒
⠁⣀⣉⣉⣉⣈⠏⠉⠈⠁⣉⢙⡉⢉⠁⠀⠁⠓⠀⠀⠉⣉⡁⠉⣉⠉⠁⣀⢉⣈⠑⠀⠀⡙⣆⡁⠀⡀⠈⠰⠒⠈⠈⠁⠁
⠀⠀⠀⠀⠤⣀⣀⣀⠠⠬⠇⢀⢀⠀⠀⣵⣄⣀⣤⡀⠀⠥⢀⡀⠀⠈⠀⠍⠀⠀⠀⠨⢌⠁⣀⣀⣀⣩⡌⣀⣀⡁⠀⡈
⠀⠤⠤⠄⡤⠄⠧⠤⠤⠠⠤⠶⠦⠠⠄⢰⠣⠴⠤⠤⠄⠠⠔⠶⠄⠤⠄⠤⠤⠃⠤⢤⠤⠤⠶⠀⠀⡤⠀⠤⠧⠤⢤⡤⠤
⢶⠒⠒⠐⠃⠐⠤⠒⠐⠒⠐⠒⡶⠖⠒⠒⠒⢲⠂⠀⠂⠀⠑⠒⠐⠒⠃⠀⢤⣤⠔⠀⠒⠒⢶⡶⠒⠓⠐⠂⡴⠀⠘⠂
⠛⠛⠛⣂⠘⠋⠉⠀⠒⡖⠒⠊⠉⠚⢲⠐⠓⠚⠃⠚⣞⠒⠓⠊⠀⠒⠒⠒⠋⠉⠀⢲⠀⠛⠉⠐⠚⡗⠒⠚⠙⠀⢰⡂⠚
⣿⣋⣉⣉⣉⠉⣏⣈⡉⢉⢉⡉⣏⢋⣉⣉⣁⣰⡏⠉⠉⠉⢉⣵⣋⠉⣉⣑⣉⣿⣉⡉⡉⠉⣙⣃⣉⡉⠉⠉⢙⠉⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠈⠈⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⠙⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣝⠙⠢⠤⠅⠴⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⡏⠳⠆⠶⣤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠘⣿⠻⣄⡀⠲⠌⣰⣿⠗⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢐⣿⠀⠈⠙⠟⠺⣿⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢸⣿⡤⣤⣤⣄⣠⣿⣇⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⡀⢸⣿⣿⠯⣭⡍⠿⡏⢹⡟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⡀⢠⡼⣿⣿⣇⣶⣿⣄⣾⣿⡐⣧⣴⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢘⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡿⣿⣿⣽⣥⣿⣿⣿⢀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣶⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡊⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣤⠠⢆⣼⣿⣿⣿⣿⣿⣿⣽⠏⣿⡀⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠉⢴⣿⣿⡟⣿⣷⠈⣾⣿⣟⣿⣿⡗⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠷⠿⣿⠀⠸⠿⣿⣶⣿⣿⣦⣙⣒⣄⣀⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⡄⣠⣤⣼⣦⣤⣤⣤⣤⠤⠠⠀⣴⣶⢦⣤⣴⠶⠾⠿⠶⠶⠶⠶⠶⠶⠶⠶⡶⠾⠿⠶⠶⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡇⠀⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠠⠠⠄⠂⠐⠤⠂⠔⠀⢤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⡉⠉⠉⠉⠉⠁⠈⠁⠈⠉⠉⠛⢸⣯⣭⣭⣥⣀⣀⣤⣤⠾⣿⣿⣿⠸⠉⠉⠉⠉⠉⠉⠁⠀⠀⠨⡅⣿⣿⣋⣁⣉⣀⡀
⠀⠿⠶⠶⠦⠀⠀⢠⡤⠤⠤⠤⠤⠸⣿⣿⣆⣀⢀⣀⡀⠠⠤⠽⢿⠟⠨⠀⠀⠀⠀⠀⠀⠀⠬⠽⠿⠇⠋⠥⠀⠉⠉⠉⠁
⠀⠆⣶⣶⢶⢲⣶⢰⡖⢲⡶⠆⠀⠀⠀⢰⣷⠒⣶⢰⡖⠂⠐⠒⠒⠒⠋⠀⠀⠀⠀⠐⠰⠿⠛⠉⠁⢠⣤⣰⣾⣗⣲⢰
⠀⠀⢻⡟⠑⢸⣿⢸⣷⣿⠀⠀⠀⠀⣶⠈⠋⢠⡿⢸⣀⣀⣀⣀⢀⣀⣀⠀⠀⠀⢀⣸⠨⣭⣭⣤⣤⣄⣀⣀⣭⣿⣿⢸
⠀⢠⠀⠀⠤⠤⠤⠤⠤⠄⢀⣤⣤⣴⣶⡶⠶⠒⠒⠒⠀⠚⠛⠓⠲⠆⣿⡖⡒⠒⠒⠒⠒⠒⠒⠒⠐⡆⠐⠃
⠀⢸⣤⣶⣶⣖⣀⣀⣀⣐⣒⣺⣽⢈⣋⣋⡉⢉⠉⢉⡉⠉⢉⣉⣉⡇⣿⣦⣄⢀⣀⣀⣀⣀⣤⣤⣤⡇⢟⠀⣀⡀⣀⣀
⠀⠈⢩⡭⠭⣭⣭⢰⣶⡶⠶⠶⠶⠶⠖⢒⣶⣶⣶⡆⣶⡶⣶⠶⠶⣶⢶⣖⡶⠶⣶⡆⣶⡦⣶⣦⠀⢲⣶⠂⣶⣶⡆⢰⡆
⠀⠀⢐⣷⠀⣿⣿⢸⠍⠁⠀⠀⠀⠀⢉⡉⢉⠉⣹⡇⣏⣡⣤⡤⠀⠄⠀⠀⢀⣴⣾⡇⣿⠀⠀⣿⠀⠈⣿⣦⣿⣿⡇⣸⡇
⠀⢠⠤⠥⠤⠭⠁⠈⠉⠩⠭⠭⢭⠉⠉⠛⠛⠓⠛⠒⠒⠒⠒⠒⠲⡄⡆⠀⠔⠐⠲⠒⠲⠶⠶⠒⢲⡀⣶⣶⡀⠄
⠀⢸⠳⠛⠛⠛⠛⠛⠋⠉⣉⣛⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⣇⣀⠀⠀⣀⣀⣀⠀⢀⣀⣨⠁⣿⣯⣭⣧⣀⣀⡀
⠀⠌⠭⠭⠭⢭⢭⡍⣭⣭⡭⠉⠡⠌⠭⠭⡭⢭⣥⠀⡄⠀⠤⠠⠮⠀⠯⠭⠭⠭⠭⢩⡭⡭⠩⡭⠭⢤⣭⣭⣤⣤⣭⣥⡄
⠀⠀⠀⠀⠀⣿⣸⡇⣿⢘⣱⠀⠀⠀⠀⠀⠁⢸⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣇⣁⠀⠇⠀⡸⠟⣡⣿⣿⣻⣗⠃
⠀⠀⡤⠤⠤⠤⠤⠤⠭⠭⠭⠤⢭⣉⣥⣬⣤⡤⠀⠀⠀⠀⠀⠀⠲⢀⡄⠀⠀⠀⠀⠀⠉⠉⠈⠉⠘⡆⣤⡤⠈⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣛⠋⠉⠀⣀⣀⣀⣐⣐⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡇
⠀⠀⠀⠈⢉⣉⣩⡀⣤⣠⣤⣤⣬⠤⠭⠭⠭⠭⠭⡍⡭⠭⠭⠍⠉⠀⠁⠀⠀⠤⢄⣠⠀⠀⠨⠭⠭⠥⠭⠭⠌⣠⡄⣤
⠀⠀⠀⠀⢠⣾⣿⡇⣅⣀⠀⢀⢀⣀⣀⣀⣀⣀⣠⡅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣒⣒⣒⣒⣒⡒⠚⠛⠛⠛⡇⣿
⠀⡐⠒⠒⠚⠛⠛⠁⣛⣙⣛⣛⣉⢉⣭⣍⣉⣉⠉⡁⠉⠁⢀⣤⣬⡁⡀⠀⡁⢈⠉⢉⣋⠉⢀⣀⡀⢈⣁⣀⣀⣺⣥⡿⠆
⠀⣷⣶⣶⡐⠂⠂⠀⠈⠘⢁⣿⣿⢹⣿⣼⡄⠀⢰⠂⠀⠀⠀⡟⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢸⣿⣿⠤
⠀⠥⠤⠤⠤⠠⠀⠠⠤⠴⠾⠿⠿⠸⠻⠿⠷⠀⠚⠟⠀⠀⠀⠓⠛⡁⠒⠀⠀⠀⠀⠀⣒⠒⠒⠒⠊⠘⢛⣛⣛⣛⠛⡉⠁
⠀⠈⠉⠉⠐⠿⣿⡶⣿⣿⡿⠛⠛⠛⠛⠛⣛⣟⡗⢸⣭⣭⠭⠍⠉⠉⠉⠛⠛⠿⡇⣿⣭⣽⡯⠟⠛⠉⠉⣉⣉⣹⡆⠁
⠀⢉⣉⣉⣉⣉⣹⠃⣊⣛⣋⣀⣀⣁⣐⣚⣛⣿⡇⢾⣟⣍⣭⣧⣶⣤⣤⡤⢶⣾⡇⢿⠿⠯⠤⠤⠤⠤⠤⠤⠾⠿⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣿⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣃⣀⣀⣀⣀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁
⣀⣀⣀⣀⣀⣀⣸⣁⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠈⠁⠀⠀⠁⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣆⣀⣀⣀⣀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢹⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⠀⡀⣀⣸⣆⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⡀⢀⣰⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠈⠀⠀⠀⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠁
⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⣀⣀⠀⣀⢀⣀⣀⣀⣀⡀⢀⣀⠀⣰⣀⣀⣀⣀⣀⣀⡀⣀⣀⠀⣀⠀⣀⣸⣄⣀⣀⣀⣀⣀⣀⢀⣀⠀⣀⠀⣀⣰⣄⣀⢀⣀⡀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠁
⡀⢀⣀⢀⣀⣀⣸⣀⣀⣀⡀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣸⣀⣀⣀⣀⠀⣀⣀⣀⣀⠀⢀⣀⡀⣰⡀⢀⣀⣀⠀⣀⡀⢀⣀⣀⣀⠀⣀⣰⣂⣀⣀⣀⣀⣀
⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢙⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠉
⣀⣀⣀⠀⣀⣀⠀⡀⣀⠀⠀⡀⣀⣸⡀⠀⣀⠀⣀⢀⣀⣀⠀⣀⣀⠀⠀⣘⣆⣀⣀⠀⢀⣀⣀⠀⣀⣀⣀⣀⣀⣰⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁
⣀⡀⣀⣀⡀⣀⢰⣄⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣸⡀⠀⣀⣀⣀⣀⣀⣀⡀⣀⣀⡀⣀⣠⣀⡀⢀⣀⡀⠀⣀⣀⣀⡀⣀⣀⣀⣸⣀⠀⣀⣀⣀⢀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣀⣀⣀⣀⣀⣀⣀⡀⢀⠀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⡀⠀⢀⣀⠀⢀⣀⣸⣄⣀⡀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⢠⣀⡀⣀⣀⠀⣀⣀⠀⣀⣀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⣀⣀⣀⡀⢀⣀⣰⣃⣀⣀⡀⣀⣀⣀⣀⣀⡀⣀⣀⡀⢨⡀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⢀⣸⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⢀⡀⢀⣸⣁⣀⢀⣀⣀⣀

⠀⠈⠀⡿⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣿⠉⠉
⣀⣀⣠⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣿⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢙⡏⠉⠉⠉⠉⠁⠀⠉⠉⠀⠀⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉
⣤⣤⣤⣤⣤⣤⣀⣀⣠⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣆⣀⣀⣀⣀⣠⣀⠀⢀⣀⣀⣯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡾⣤⣤⣤
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣀⣠⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣨⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣄⣀⣀⣀⡀⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⣀
⠁⢨⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡟⠙⠙⠛⠛⠛⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⠉
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠒⠋⠉⠉⠉⠉⠉⠉⢻⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⡖⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⢶⠶⠶⠖⠒⠚⠒⠒⠒⠒⠒⢶⠖⠒⠒⠖⠶⠞⠓⠒⠒⠒⠒⠒⠒⡖⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠒⠒⡶⠒⠒⠚⠋⠙⠉⠛⠛⠛⠛⠉⠙⡟⠛⠙⠛⠛⠛⠙⠛⠋⠒⠒⢲⠖⠒⠒⠒⠒⠛⠓⠒⠒⠒⣶⠒⠒⠒⠒⠲⠾⠷⠶⠒⠒⠒⢲⡶⠶⠒⠒⠒⠒⠖⠓⠒
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠤⠼⠓⠒⠒⠒⠒⠒⢶⠶⠶⠤⠤⠤⠾⠧⠤⠶⠶⠒⠲⡶⠒⠲⠦⠤⠾⠤⠤⠤⠤⠤⣤⠤⠤⠤⠾⠷⠶⠦⠤⠴⠶⢶⠶⠤⠤⠤⠤⠼⠧⠤⠤⠤⠤⠤⢤⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠤⠤⢤⠤⠴⠲⠶⠶⠚⠶⠶⠶⠒⠒⢦⡤⠤⠤⠤⠤⠤⠧⠤⣤⣤⠤⣤⡤⣤⡤⠀⠤⣿⣤⠤⠤⢤⡴⠶⠶⠶⠶⠶⠚⠒⠒⠒⠒⠒⠲⡖⠒⠒⠒⠒⠚⠛⠓⠶
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠤⠤⠿⠤⠤⠤⠤⠤⢤⡤⠤⠤⠤⠤⠼⣤⣤⣤⠤⢤⣤⣀⣀⣀⣀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠼⠦⠤⠴⠶⠒⠖⠶⡤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣀⣇
⠉⠉⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⠀⠈⡏⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢹⠃⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣀⡀⣀⡀⠀⠀⣸⡀
⠒⠚⠓⠒⠒⠒⠒⠒⢲⠒⠒⠒⠒⠚⠓⠒⠲⠒⠒⠒⠲⡶⠲⠶⠶⠖⠛⠒⠒⠒⠒⠒⡖⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠤⠤⢤⠤⠤⠤⠤⠤⠾⠤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠤⣤⠤⠄⣀⣀⣼⣇⣀⣠⣤⢤⣤⠤⠤⠤⠤⠤⠼⠤⠤⠤⠤⠤⢤⠴⠶⠶⠶⠶⠶⠶⠷⠤
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⣤⡤⠧⣤⡤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣇⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠞⠋⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⣀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⠙⠟⠉⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠈⡲⠄⠈⢠⠉⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠃⠁⠀⠣⡀⠘⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⢖⠢⡤⣀⠀⡀⠀⠀⠐⠀⠀⠔⢄⠀⠀⠈⠀⠀⠀⠀⠀⠀⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠁⢠⡆⢻⠀⠀⠇⠀⠀⠀⠤⠀⠀⠀⢅⠢⡐⠚⠳⡄⠐⠀⠀⠈⠙⢆
⠀⠀⠀⠰⠶⣆⠀⠦⠾⠯⠓⠛⣁⣀⣓⠒⠒⠠⠄⠀⠀⠀⡀⠀⠀⠑⢌⠀⣀⣴⠀⡀⠀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡄⠙⠁⠙⠳⣄⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠚⠋⠑⠂⠀⠐⢒⠒⠒⠛⠁⠂⠀⢂⡀⠀⠀⠒⠛⠀⠀⣄⡽⠀⠀⠀⠀⠈⠥⡄⠀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢘⠀⠀⠀⠀⠀⠀⠘⡃⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠁⠀⠀⠀⠈⠁

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠦⣤⣀⣤⠳⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣘⡫⠿⠿⠷⠶⠦⣬⢉⣻⣶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⢥⣀⡀⠀⠀⠀⠀⠀⠀⣙⡅⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠠⣴⣿⠀⠀⠀⠀⠀⢀⣀⣏⡛⠯⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣂⠀⠻⠍⠙⣛⠷⠖⠛⢉⣿⠀⠈⠁⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠈⣻⣀⡀⠤⠴⠶⢶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡘⠧⢼⣿⡇⢀⣀⠠⢤⣒⡲⠥⠀⠁⠀⠁⠸⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⢿⣤⡀⠀⡀⠠⠿⠛⠂⠉⡃⡏⠀⠀⠀⠀⢀⣠⡤⠰⠶⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠚⢻⡿⠁⠀⠀⠀⠀⠀⢀⠇⠧⠄⠐⣚⡭⠍⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠙⠷⣽⣧⣤⡤⠔⣒⠉⠉⠀⠀⠀⠀⠀⠋⡇⠀⢀⡀⠤⣐⠲⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢮⣄⡀⠁⠀⠀⠐⠉⠀⠀⢈⢹⠀⠀⠀⢀⡀⠤⠔⠂⠉⠁⠐⠃⠸⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⠟⣿⠀⠀⠀⠀⠀⠀⠀⡀⠸⣗⡒⠯⠱⠴⡆⠀⠀⠀⠀⢀⡠⢐⣒⠗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠝⠳⢶⣳⣀⡠⠤⠒⢂⡭⠀⠀⠉⠀⠀⠀⠀⠰⣆⣠⡴⢒⡾⠗⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣀⡀⠀⠤⠌⠑⠂⠉⠈⡏⡇⠀⠀⣀⡀⠀⣐⠎⠐⠚⠉⠀⢹⠀⢀⡠⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣟⣿⡇⠀⠀⠀⠀⠀⢀⡤⠇⠓⠚⠉⢥⡆⠀⠀⠀⠀⣀⡤⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠿⠙⠻⢷⣿⣧⣠⣤⣶⣾⠟⠂⠀⠀⠀⠀⠀⣈⣅⡤⠔⠒⠉⠁
⠀⠀⠀⠀⠀⠀⣿⠷⣦⣀⣀⡀⠲⠖⠛⠋⠉⠁⠸⢩⠀⠀⣀⣠⠤⠖⠂⠁
⠀⠀⠀⠀⢀⣄⣾⢘⣽⣿⡇⠀⠀⠀⠀⣀⣀⣤⠤⠚⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠛⢷⣿⣇⣠⡤⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣺⣥⣭⣭⣬⣵⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢸⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⣀⣀⣠⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠋⠉⠉⠉⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣄⣀⣀⣀⡇
⠀⠀⢸⠉⠉⠙⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⢸⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⡇
⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⢻⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⠋⠉⠉⠉⡇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇
⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⡀⠈⢀⡀⠁⢀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠤⠄⠠⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠤⠀⠤


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⣀⠀⠀⣀⠈⠀⡀⠉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠁⠀⠀⠀⡀⠈⠀⡀⠀⢀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⣀⠀⠀⣀⠀⠀⡀⠈⣀⡀
⠀⠀⠀⠠⠀⠤⠤⠀⠤⠄⠀⠀⠀⠄⠠⠠⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠠⠠⠀⠤⠠⠀⠄⠤⠠⠀⠀⠠⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠂⠈⠀⠂⠀⠐
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⡀⠀⢀⡀⠀⢀⠀⠀⠀⠈⢀⠀⠁⢀⠀⠁⣀⢈⣀⡀⢉⢀⡀⠀⣀⡀⡁⠀⠈⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⡀⠀⢀
⠐⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠀⠐⠒⠀⠐⠂⠀⠲⠀⠐⠖⠒⠒⠒⠀⠐⠒⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠴⠒⠒⠛⠋⠉⠓⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡖⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠔⠚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⠒⠦⣀⣀⣀⣀⠠⠴⠖⠚⠉⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠧⠤⠤⠤⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠋⠙⠦⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣼⣤⡤⠴⠖⠚⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠛⢿⡟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⣀⣄⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣄
⠀⠀⢀⣴⠞⠉⠀⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣄⣼⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣠⣤⣼⠇⠀⠀⠀⠀⠙⢷
⢀⣴⣋⣀⣀⣠⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠶⠶⣾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⣷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⣿⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶
⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣩⡭⠟⠋⠉⠀⠀⠀⠉⠉⠛⠶⠤⣄⣀
⠀⠀⠀⠀⢠⡶⠒⠲⠶⠶⠤⠤⢤⣤⣤⣄⣀⣀⣀⣀⠀⠀⠀⢰⠛⠷⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣄
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⣷⢸⡆⠀⠀⠈⠉⠛⠻⠶⣤⣄⡀⠀⠀⠀⠀⢀⣀⡤⠖⠋⢻
⠀⢠⣞⣁⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢻⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⣶⠞⠋⠁⠀⠀⠀⢸⡆
⠀⢸⡇⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠶⠶⠶⠶⢦⣴⠋⠀⣸⠀⠉⢛⣲⡤⠶⠦⣤⣀⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣰⣯⠶⠚⠋⠁⠀⠀⠀⠀⠈⠉⠛⠲⣦⡄⣿⢀⣀⠴⠚⠁
⠀⠀⠷⠶⠶⠤⢤⣤⣤⣀⣀⣀⣀⠀⠀⢀⣀⣤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠉⢸⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠲⣤⡀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⣀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠳⢦⡶⠊⠁⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⡇⠀⣠⠴⠚⠁

⠀⠀⠐⠂⠀⠠⠄⠀⠘⠀⠀⢠⠀⠀⠃⠀⠀⢤⠀⠀⠃⠀⠀⡄⠀⠘⠀⠀⢠⠄⠀⠘⠀⠀⢠⠀⠀⠃
⠠⠀⢤⠤⠀⠤⠦⠤⢤⠄⠀⠸⠄⠠⡄⠀⠀⠸⠀⠠⡄⠀⠠⠦⠤⢤⠄⠀⠠⠄⠀⢤⠀⠀⠸⠄⠠⡤⠄
⣀⠀⠠⠄⠀⢀⡀⠀⠸⠀⠀⢀⡀⠀⠇⠀⠀⣀⠀⠠⠇⠀⠀⡀⠀⠸⠀⠀⢀⡀⠀⠸⠀⠀⢀⡀⠀⠧
⣇⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣘⣀⣀⣀⡀⠀⣸⣀⣀⣀⣀
⠀⠀⢸⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡇
⡎⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⢹⠀⠀⠈⠀⠀⠍⠀⠀⠈
⠉⠉⢱⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⢡⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⡏⠉
⡔⠒⠊⠒⠒⠲⠂⠐⠉⠒⠒⢒⠒⠒⠑⠒⠒⡖⠒⠚⠒⠒⠒⠒⠒⠚⠒⠒⢲⠒⠂⠓⠒⠒⠖⠒⠒⠓⠒
⠓⠐⢢⠒⠒⠚⠒⠒⡖⠒⠂⠒⠒⠂⠀⠀⠀⠓⠒⢠⠀⠐⠐⠒⠒⠀⠂⠀⠚⠒⠒⡄⠀⠀⠒⠒⠒⡔⠒
⡤⠤⠼⠤⠤⢤⠄⠀⠳⠠⠤⠤⠤⠄⠀⠠⠀⠤⠀⠘⠀⠀⠠⠀⠀⠰⠀⠠⢤⠄⠀⠧⠤⠤⡤⠤⠤⠧⠤
⠧⠀⢄⠤⠤⠴⠤⠤⣤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠄⠀⠀⠀⠀⠼⠤⠤⡀⠀⠀⠧⠤⢤⡤⠤
⢀⠀⠸⠀⠀⢀⠀⠀⠧⠀⠀⣀⠀⠀⡄⠀⢀⣀⠀⢸⠀⠀⢀⡀⠀⢠⠀⠀⣀⠀⠀⡇⠀⠀⣀⠀⠀⣇
⡇⠀⠀⠀⠀⢨⡀⢀⡀⠀⠀⣈⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣇
⠀⠀⣡⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⢸
⠁⠀⠀⠀⠀⢩⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⡇
⠁⠀⢃⠀⠀⠉⠀⠈⡇⠀⠀⠁⠀⢸⠀⠉⠈⠁⠀⢹⠀⠀⠈⠀⠀⡇⠀⠀⠉⠀⠈⡍⠁⠉⠁⠀⢸⠁
⠀⠀⠉⠀⠀⢰⠈⠈⠁⠀⠁⠆⠀⠈⠁⠀⠐⠂⠀⠉⠀⠀⢰⠀⠀⠉⠀⠀⠂⠀⠈⠁⠀⠈⡆⠀⠈⠁
⠁⠀⢂⠀⠀⠈⠀⠀⡆⠀⠀⠁⠀⢰⠀⠀⠈⠁⠀⢲⠀⠀⠈⠀⠀⡆⠀⠀⠉⠀⠐⡂⠀⠀⠁⠀⢰
⠀⠀⠈⠀⠀⢲⠐⠀⠁⠀⠒⡆⠀⠈⠀⠀⠐⠆⠀⠈⠀⠂⢰⠀⠀⠁⠀⠀⠖⠀⠀⠁⠀⠐⡆⠀⠘
⠒⠒⢲⡂⠀⠘⠀⠀⢲⠀⠀⠓⠀⠀⣆⠒⠒⠂⠀⢀⡆⠂⠘⠀⠀⢠⡀⠀⠓⠀⠀⣰⠒⠒⠃⠀⠀⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣽⣿⣦⣀⠠⠤⠖⠒⠉⠁
⠀⠀⠀⢸⠃⠀⠀⠀⠀⣀⠀⢀⣄⣦⠮⠬⠚⠚⣻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⣀⣀⣄⣼⣶⣦⠴⠖⠓⠋⠉⠁⠀⠀⠀⠀⠀⠀⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢹⣏⡀⠀⠀⣀⣀⡠⠬⠴
⠛⠉⠉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⣤⣤⠾⠿⢾⣿⣿⠉⠁
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡄⠀⠀⠀⠀⠀⠈⠿⠉⠉⠀⠀⠀⠀⠀⢸⡿⠟
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⢀⠀⣿⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⣼⡄⣿⡇⢸⡇⢸⣿⣾⠆⠀⠀⠀⠀⣀⠀⠐⣿⣷⡇⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⡆⠀⠀⠀⠀⢻⠀⠠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠹⣧⣠⠀⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⢠⣤⣦⣿⣇⣰⣿⣆⡄⡇⡀⠀⠀⠀⠘⢿⣦⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠷⠂⠀⠀⠀⢸⠉⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣴⠀⠀⠀⠀⣿⡆⠀⠀⠀⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⣀⣴⣾⣿⣿⣿⣶⣤⣾⣿⣤⣤⣤⣤⣀⣀⣠⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠐⠀⠉⠀⠀⠀⣨⡊⠶⢄⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢨⣌⠉⡬⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠹⣋⢢⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⣀⣀⣀⢀⠀⣀⣀⣀⣤⣀⢀⡀⣄⣤⣤⣠⠀⡀⢀⣀⣄⢠⢘⠀⢼⣾⠳⡅⢲⢆⢄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣧⣰⢎⡫⢛⣤⣦⣼⠊⡍⢙⡵⡧⢼⢮⠫⠘⠕⢷⠾⢦⠡⠝⢡⣮⢸⣦⡙⠧⡆⢹⣧⣤⡗⠍⠂⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠞⠊⠀⠁⠀⠀⠀⠀⠐⠶⠟⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠸⢟⠝⠓⡄⠈⠉⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠔⡨⠒⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢒⣁⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠻⣕⡆⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢂⣡⣴⡾⠟⣉⢻⣦⣑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡐⢎⡅⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣈⣤⠶⠟⠈⠀⣀⠀⠀⠀⠀⠉⠳⢦⣍⠢⢄⠀⠀⠀⠀⠀⠀⠀⠰⢲⢟⢆⡁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠞⠋⠁⠀⠤⠀⠀⣄⠀⠀⠒⡀⠀⠀⠀⠈⠛⠶⠃⠀⠀⠀⠀⠀⠀⠠⢜⣠⡀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡠⠦⠀⠶⠄⠄⠽⠦⠤⠼⠧⠤⠧⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠙⠙⡋⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⢀⡳⡜⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢶⠾⠿⠿⠂⢪⠝⠛⠛⠃⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡻⢊⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠠⠄⠤⠄⠘⠃⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠔⠫⡶⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠤⢅⠒⢔⣰⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠉⢠⣤⠀⠀⠀⢠⠯⠒⠛⢳⢸⡗⠛⠛⠛⠀⣿⠃⠀⡿⡁⠀⠀⠀⠀⠀⠀⠀⢰⠰⡝⢉⠄⢘⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠸⠤⠀⠀⠀⠸⠇⠠⠤⠜⠈⠓⠀⠐⠘⠀⠙⠂⠀⣯⡃⠀⠀⠀⠀⠀⠀⠀⢰⢸⠜⣡⣮⡰⣤⠂
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⠀⢀⡀⢯⡇⠀⠀⠀⢀⠘⠉⠑⠚⠐⠈⠉⠓⠒⠙⠁⢐
⠀⠀⠀⠀⠀⢀⡀⣀⡀⣀⢀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠿⣃⢀⠐⣟⣩⡇⢠⠄⠀⠈⠧⠀⠀⠁⠭⠭⠽⠯⠍⠿⠿⠿⠁⠖⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠉⠉⠉⠉⠉⠀⠉⠉⠀⠉⠁⠉⠈⠁⠉⠀⠙⠁⠓⠒⠒⠒⠒⠒⠒⠒⠂⠒⠐⠒⠂⠘⠉⠋⠛⠁⠀⠁⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢺⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢣⣀⣠⣼⠌⠘⠄⢀⠤⠤⢤⠀⠀⣠⠤⢖⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡈⠉⢁⣀⠀⣸⠀⣸⣤⡼⠼⠒⠚⢋⣍⡦⣧⢙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠤⣝⢦⠀⠀⠀⣀⡩⢵⢶⡌⠢⢘⣥⣤⡀⢀⣀⣨⡴⣚⣿⠇⠿⢐⡇
⠀⠀⠀⠀⠀⣞⡉⠲⡀⠀⠀⠀⠀⣎⣠⠖⠻⢿⣒⠺⣩⣠⣠⣠⠸⢸⢮⡇⠉⠭⣼⡟⡉⣠⡏⢸⣿⣇⣸⣐⣷⣤
⠀⠀⠀⠀⠀⠈⢫⠖⢛⠯⡉⢻⡉⠀⡞⠄⠀⠀⠉⠊⠉⠒⢤⡈⠙⠫⡉⡇⠀⣓⣿⣃⢱⡿⣠⣦⣬⡍⣙⡛⢁⣿⠁
⢎⣙⢦⡀⠀⠀⢸⢸⠤⡷⠷⢌⣧⣡⠭⠿⢷⡀⠀⠰⡆⢤⣦⣈⠣⣄⣌⢇⠀⠀⢿⢻⣿⠃⠈⠛⠻⠿⠶⢋⣾⠛⢆
⠈⠣⣶⠙⠢⣄⢸⠀⠑⠁⡆⡑⡇⢸⠀⡭⡟⢧⣄⣈⠪⣶⡿⢉⣷⡘⣞⣷⣆⠥⣿⣅⠘⡄⣭⡵⠞⠛⠛⣿⠟⢆⠈⣆
⠀⠀⠉⠳⣦⣂⡽⠀⠀⠀⡆⡢⣇⠈⢶⣶⢋⡌⠠⢮⡟⣛⠟⢩⣿⣷⢹⡿⠿⣩⣿⡝⣺⣘⡤⠶⠄⠀⣼⣟⣦⠈⡦⣙⡆
⠀⠀⠀⠀⠈⣹⠃⠀⠀⠀⣇⠂⣿⣇⣹⠛⢶⠁⠨⣼⡿⣿⠰⣿⣿⡾⠋⣿⣶⣿⢿⣿⠃⣻⡽⠧⢶⣶⡿⠿⢲⢋⡇⢒⡇
⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠸⡀⠉⢿⠻⢿⡏⢀⡥⣿⣶⣿⢣⢄⣉⣡⣴⣿⡧⠿⣒⣋⢭⠗⡶⢫⢋⠎⡐⡱⡡⢣⡧⢽⠁
⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠻⣼⠀⢐⣸⣾⣿⣷⡤⢾⣛⡿⡿⣳⢋⠝⡡⢣⢊⠞⡰⡡⢃⢞⠜⡔⡡⢡⠏⢽
⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢈⣦⢒⣛⡿⡿⡻⠫⢋⢎⢎⠔⡡⢋⠞⡔⡡⢃⢎⠜⡰⢡⢊⠞⡔⡱⣹⠤⢽⠢⣀⡀⠠⠠⠄⣀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⠀⢽⢉⢔⢎⠔⠔⡱⡱⢡⢊⠜⡰⢁⢊⠜⡰⡣⢊⠎⡰⠡⢂⢎⠜⡔⣼⠭⣿⡑⢐⠀⠂⣙⡂⠈⠣⠥
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢀⠭⡧⢁⢪⢊⢎⠌⡔⡡⢊⠎⡔⡡⢋⢜⡔⡡⢃⠜⡔⡡⢣⢊⢞⣴⡾⢑⣟⡈⠠⢍⣀⡒⠂⣠⠤⠭
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠥⡷⡑⡡⡣⢣⠎⡔⡱⢁⢎⠔⡡⢋⢊⠜⠠⢊⠌⣔⣱⣥⣿⡻⣽⠷⠞⠩⠭⠉⠐⣒⡐⣃⡈⠉⠉
⠀⠀⠃⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠨⢽⠎⢜⠔⡵⢡⢊⠎⡰⡡⢊⡔⡱⢡⢊⣴⢥⣻⡹⠽⠶⠿⠉⢙⢛⣋⣈⣭⣭⣤⠀⠐
⠀⠓⠤⣘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢽⢨⢊⠎⡔⡡⢃⢎⡔⣡⣮⠼⣶⣻⠽⠾⠭⠭⠥⠭⠭⠭⠉⠁⠒⠒⠒⠂
⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⡀⠀⡀⠽⡡⢣⢎⣼⡵⡗⣞⣽⡽⡶⠏⠩⠭⠥⠦⠤⠭⠭⠭⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⡀⠁⠓⡂⣽⣲⣯⣯⣷⣿⣛⣃⣤⣤⠶⢖⣀⣀⣀⠀⠌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠶⠿⠿⠟⢀⣐⣒⣒⣒⣛⠓⠓⠖⠛⠁

⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠟⠩⠽⠷⠶⠶⠲⣶⠻⠾⠶⠶⠿⠶⠶⠶⠶⢶⡶⠳⠖⠒⠛⠓⠒⠛⠛⢷⠶⠶⠶⠾⠿⠶⠶⠶⠶⢶⡶⠛⠒⠒⠛⠒⠚⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⡿⠿
⠀⠀⠀⢀⣀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠄⠀⠀⠀⠀⢀⡀⠀⣸⣀⠀⢀⠀⠀⢀⣀⣀⡀⣸⡷⠀⠀⡀⢀⣀⣀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡀
⠛⠛⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠒⠚⠙⠛⠛⠛⠛⣿⠛⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⢹⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠛⠛⠛
⣄⣠⣿⣠⣀⣀⣀⣀⣠⣤⣤⣄⣠⣿⣠⣤⣤⣤⣤⣤⣤⣤⣤⣿⣀⣀⣄⣀⣀⣀⣀⣀⣿⣀⣀⣤⣤⣀⣀⣀⣀⣸⣧⣄⣀⣀⣀⣀⣤⣤⣤⣠⣿⣤⣀⣄⣤⣀⣤
⠀⠀⠀⠉⠉⠉⠉⢹⠍⠀⠀⠀⠀⠈⠉⠉⠁⢹⣟⠉⠈⠁⠀⠈⠉⠉⠉⣿⠉⠉⠉⠀⠈⠉⠉⠀⠀⣿⡏⠀⠉⠁⠈⠉⠉⠉⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⣀⣀⣀⢀⢀⡀⣀⣸⡆⠀⠀⢀⣀⣀⣀⣀⠀⣸⣗⣀⣀⣀⣀⣀⣀⣀⣀⣿⡀⠀⠀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣠⣤⣤⣀⣀⣠⣀⣀⣽⣇
⠛⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⠉⠹⡟⠉⠉⠉⠁⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠙⠋⠋⣿⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠀⠉
⣤⣤⣼⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣧⣀⣀⣀⣄⣤⣤⣤⣤⣤⣷⣤⣤⣤⣤⣤⡤⣤⡤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣴⣷⣤⣤⣤⣤⣤⣤⣤⣤⣀⣿⣤⣤⣤⣤⣤⣤
⠀⠀⠈⠉⠉⠉⠉⠉⢹⠁⠉⠁⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡇⠀⠀⠀⠀⠀⠉⠉⠉⢹⡇
⠶⠶⣶⠶⠶⠶⠶⠶⠾⡶⡶⡶⣶⠶⠶⠶⠶⠶⠾⠧⠶⠶⣶⣶⣶⡶⠦⠽⠧⠴⠶⢶⡶⠶⠶⠶⠶⠛⠷⠶⠶⢶⣶⠶⠶⠶⠶⠾⠿⠶⠶⢶⡶⠶⠶⠶⠶⠾⠷
⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⣖⣒⣻⣦⣤⣶⣶⣤⠤⢤⣤⣤⢿⣤⣤⣤⡤⣦⡶⠶⢤⠤⠿⠧⠶⠴⠴⣶⣶⣤⣤⣼⣷⣤⣤⣤⣤⣴⡶⠦⠤⠤⠿⠤⠴⠶⢶⠶⠶⠶⠶⠶⠷⠶⠷⠤⢴⣦⣶
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠶⠶⣾⠿⠿⠷⠶⠿⠷⠶⠶⠶⠶⣶⠶⠶⠶⠺⠷⠶⠶⠶⠶⣶⠟⠛⠒⠚⠛⠒⠛⠛⣿⠛⠛⠛⠛⠛⠓⠒⠚⢳⡶⠾⠶⠶⠾⠷⠿⠷⠶⠶⣶⠶⠶⠶⠾⠿⠷
⣀⣀⣿⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡀⠀⢸⣇⣀⢀⣀⣀⣀⣀⣀⣀⣀⣿⡀⠀⣀⣀⣀⣀
⠛⠛⠓⠛⠛⠛⠛⢻⡛⠛⠛⠉⠉⠙⠛⠛⠛⢻⡿⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠋⠘⠛⠛⠋⠋⣿⡟⠉⠉⠋⠘⠛⠛⠛⠛⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⣻⡟
⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡇
⠶⠿⢿⠟⠛⠛⠛⠛⠛⠒⠓⠒⠲⡶⠚⠛⠛⠋⠛⠛⠛⠛⢻⡟⠛⠛⠛⠛⠓⠲⠶⠶⠶⣶⠚⠛⠛⠛⠛⠛⠛⠛⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠛⠛⠛⠙⠁⠟
⣤⣀⣸⡄⠀⠀⠀⠀⠀⣀⣀⠀⠀⣇⠀⣀⡀⠀⠀⣀⣀⣀⣘⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣸⣧⡀⡀⢀⣀⣀⣀⣀⠀⠀⣿⣀⣀⣀⣀⣀⣀
⠉⠉⠙⠛⠛⠛⠛⠛⢻⠋⠛⠙⠉⠉⠉⠉⠉⠛⢻⡏⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠋⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡟
⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣇⣤⣤⣤⣤⣤⣤⣤⣽⣇⣠⣤⣤⣤⣤⣤⣤⣤⢿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⠤⠤⡼⢧
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⢤⡴⢻⣄⣀⣤⣤⣤⣤⣤⣤⣤⣿⣄⣤⣤⣤⣤⣤⣤⣀⣠⢿⣧⣤⣤⣤⣤⣤⣤⣤⣸⣧⣀⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤
⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⠀⠀⠈⠉⠉⠁⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⠀⠀⠈⠉⠉⠉⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠈
⣴⣷⣶⡶⠶⠶⠦⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⠼⠧⠤⢤⣤⣴⣶⠶⠶⠶⠾⠶⠶⠶⠶⣶⠶⠶⠶⠶⠾⠧⠴⠶⢶⡦⠴⠶⠶⠾⣷⣶⣶⣶⣦⣤⣤⣤⣤⢴⣷⣧
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠻⠿⠋⠺⠿⠾⠟⢻⠟⠟⠛⠛⠛⠛⠟⠛⠛⢿⡟⠛⠛⠿⠛⠛⠒⠛⠛⣿⠷⠾⠶⠒⠹⠖⠒⠚⠛⣿⠟⠛⠛⠛⠛⠛⠛⠿⠟⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠶⠻⣶⠟⠛⠒⠲⠞⠷⠶⠶⠶⣶⠶⠶⠶⠒⠚⠷⠶⠛⠛⣷⡾⠶⠶⠶⠿⠶⠷⠶⠶⡶⠶⠶⠶⠒⠛⠷⠶⠛⠻⣿⠓⠛⠓⠛⠛⠒⠖⠒⢺⡿⠛⠛⠛⠚⠛⠷

⠀⠀⠀⠀⠀⣀⠤⠒⠀⠈⠉⠉⠁⠐⢄
⠀⠀⠀⢠⠊⡠⠐⠈⠁⢀⡀⠀⠈⠑⢄⠑⡄
⠀⠀⢀⠁⠎⠀⡀⠈⠠⠀⠀⢄⠐⡀⠀⢀⠘⡀
⠀⠀⠈⠀⠀⢰⠀⠈⠀⠀⠀⠀⠆⢰
⠀⠀⠸⠀⢂⠀⢆⠐⠄⠀⡀⠄⢀⠂
⠀⠀⠀⠑⠀⡀⠀⢢⠈⢃⠠⠒⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠉⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠑⠤⠴⠉⠉⠉⠧⠀⠄⠤⠏⠉⠉⢱⠤⠠⠤⠞⠉⠉⠹⠆
⠀⠀⡀⠀⠀⠀⠀⠀⠇⠤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠢⡤⢤⣀⠦⠀⠀⠠⢴⠤⠄⡼⠄⠀⠀⠴⠤⠄⣰⠄
⠀⠀⠀⡄⠀⠀⢀⠠⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡄
⠀⢀⠀⡀⠀⠀⠈⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁⠀⢱
⠠⠀⠀⢐⠀⢀⢰⠂⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠆⠈⠃⠀⠀⠀⠀⢡
⠈⠁⠐⠜⠃⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⡠⠊⠀⠈⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡘⠀⢀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⣄⠀⠀⠂⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢨⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠁⠂⠒⠒⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠄⠤⠤⠤⡤⠀⠠⠄⠤⢤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡇⠀⢰⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⡄⠀⠀⠀⠀⣆⢀⣰⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⢀⢤⢔⡁⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠀⠀⠀⠀⡃⠀⣼⠀⠀⠀⠀⢸⠀⢠
⠀⠀⠀⠀⡰⣩⠊⠁⢑⠀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉
⡀⠠⠀⠤⠿⠧⠀⡔⠀⠠⠈⢢⠀⠀⠀⠀⠀⠀⢀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢

⠀⠀⠀⠀⢰⣇⣤⠀⠀⠀⠀⠀⠀⣾⣠⡄⠀⠀⠀⠀⠀⠀⣰⠗⠀⠀⠀⠀⠀⣀⣸⣃⡄⠀⠀⠀⠀⠀⢀⣴⡠⠀⠀⠀⠀⠀⠀⣠⣆
⠀⠀⢀⣴⠟⠉⠁⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⢠⣤⠞⠀⠀⠀⠀⢀⡠⠞⠉⣸⠋⠀⠀⢀⡴⠚⠋⢩⡏⠀⠀⠀⢀⣤⠤⢲⠟⠁
⣠⣴⡟⠁⠀⠀⠀⠀⢀⠠⡾⠋⠀⠀⠀⠀⠀⢠⣶⡿⠉⠀⠀⠀⠀⠀⠉⠀⢀⠜⠁⠀⠀⠀⠈⠀⠀⢀⡞⠀⠀⠀⠀⠋⠀⢀⡾
⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⢀⡴⠋⠳⠄⠀⠀⠀⠀⠀⣠⣶⡖⠀⠀⠀⠀⠀⠲⢶⣄⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠐⣅⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀⢀⣴⠏⠙⠗⠀⠀⠀⠀⢀⡼⠻⠿⠂⠀⠀⠀⢀⡾⠛⠿
⠀⢠⣦⠀⠀⢈⡗⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠠⣎⢻⣿⠏⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⡶⠋
⠐⠀⠀⠑⠴⠛⠁⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠹⠞⠁⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠐⠟
⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⣀
⠀⢸⣇⣀⣰⡆⠀⠀⠀⢠⡠⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⢺⡍⠉⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⢀⣴⣾⣿
⠀⢸⡇⠀⢰⡆⠀⠀⢠⣿⠃⣾⣧⣄⣾⠇⠀⢀⡴⠋⣰⠎⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣾⣿⠟⠋
⠀⢸⡇⠀⠘⠃⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠉⢠⠞⠁⠀⠀⠀⠀⠀⣔⡿⠁⠀⠀⠀⠀⠀⢠⣾⠿⠟⠛⠀⠀⠀⠀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠐⠦⣄⡀⢰⡆⠀⠀⢀⣾⣛⣛⣿⣷⠀⠀⠀⣤⣤⣤⣤⣤⡄⠀⠀⣾⣿⣿⣶⠶⠆⠀⠀⠀⠀⠀⢀⣤⣿⡷⠀⠀⠀⠻⠿⠿⠿⢳
⢀⣤⣤⣬⣿⣿⡇⠀⠀⣸⣟⠛⣿⣿⣿⠀⠀⣸⡟⠛⠛⢸⡆⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠋⠀⠀⠀⠀⠀⢀⡄⠈
⢿⣶⣶⣶⣿⣿⡇⠀⠀⠉⠉⠉⠉⠉⡏⠀⠀⠻⠀⠀⠀⠸⠇⠀⠀⠀⠀⣿⣷⠆⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⣀⣀⣀⠀⠀⠀⠀⠖⠖⠒⠒⠒⠒⠀⠀⠀⣀⣀⠀⣰⠶⣦⠀⠀⠀⠀⠀⢀⣶⣶⡀⠀⠀⠀⠀⠀⣠⣶⠃⠀⠀⠀⣶⣶⣶⣶⡦
⠀⣰⣿⠿⣿⡆⠀⠀⠀⡦⠤⠤⠤⠤⠤⠀⠀⢸⣏⣹⡇⠙⠶⠛⠀⠀⣠⣶⣷⣾⡟⠟⠁⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠺⠿⣿⠿⠗
⢠⣼⣿⣿⣿⣧⡄⠀⠀⣤⣤⣠⣄⣤⣤⠀⠀⠀⠉⠉⢠⡟⢻⡄⠀⠀⣻⣿⣼⣿⡇⠀⠀⠀⠀⠸⣿⠥⠄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⢀⡀
⣴⡾⠛⢷⡄⠀⠀⠀⢰⣿⠶⠶⠶⠶⠶⠆⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣤⣤⣯⣭⣧⣤⡄⠀⢀⣀⣤⣶⣾⡷⠁⠀⠀⠀⣴⣿⣾⣿⣷
⣿⣦⣡⣾⡃⣀⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠛⠚⠁⠀⣿⣭⣿⣿⣯⣽⡇⠀⠉⣙⣿⠿⢍⡁⠀⠀⢀⣴⣿⣿⣿⠿⠟

⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⢶⠁⡹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣮⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠐⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⣂⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡛⢳⠂⢢⡀⠀⠀⠀⠀⠀⡎⢀⠐⠈⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⡂⠈⢣
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠁⢸⠁⠀⠀⠀⠀⠀⢱⢄⠀⠀⢀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠠⠠⠴⠃⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠍⡄⠀⢀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⡠⠎
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠃⠀⡠⢂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⡌⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠄⠐⠦⠐
⠀⠀⠐⡂⠀⠠⠀⢀⡠⢠⠀⢎⠀⠁⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠚⠛⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈
⠀⠀⠀⠀⠀⡁⠀⢰⠈⣀⠀⠀⠠⢀⡀⠄⠀⠀⠠⠀⠀⠀⠀⠸⠔⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡐⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠉⠒⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⢆
⠀⠀⠀⠤⣄⡀⣤⠤⣀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⠸⡤⡤⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⡤⠁⠥⠲⡀
⠀⠀⠐⠄⡏⠀⡘⡀⠃⠀⠄⠀⠀⠀⠀⠀⠤⠰⢀⠀⠀⠀⠀⠀⠀⠈⣁⡉⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⣀⠘
⠀⠀⠀⠀⢸⣄⡁⠀⣀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠤⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠠⠎
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢐⠀⠠⢀⠴⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⡀⠀⠂⠀⠀⠉⢂⠀⠠
⠀⠀⠀⢀⣤⠐⠀⠂⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠉⠁⠀⠀⡀⠄⣀⠀⠄⠀⠀⠀⢀⢀⠈⠁⠐⠪⡑
⠀⠀⠀⠂⡀⠁⠀⠐⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⡀⠌⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⢀⠰⠀⠀⡀
⠀⠀⡠⠄⠐⣂⠀⢀⠂⠚⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠁⣐⠎⢐⢐⠂⠑⢀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠜⠰⠠⠠⠁⠀⠂
⠀⠀⠁⠀⠉⠀⠀⠁⠁⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣦⠇⠰⠀⠸⠀⡰⠀⠆⠀⠃⢀⠇⠀⠂⣀⡂⠸⢄⣦⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡿⣧⣴⣷⣾⣶⣾⣶⣿⣴⣿⣿⣿⣴⣿⣿⣿⣾⣧⣼⣿⣧⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣂⡅⡗⠋⠐⢠⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢠⣷⠒⢄⡀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⢀⣠⡄⡂⣱⣟⡿⣿⣆⡇⢀⣰⢸⠋⣷⣶⣾⣽⣿⣧⠠⠰⠪⣄⣈⣿⢶⣆⡀⡹⠂⠀⠀⠀⣻⡤⢐⠛⣶⠦⢀⡀
⠀⢀⡀⢀⣀⣠⣞⣻⣵⣯⣿⣧⡏⣻⣧⣞⣝⣀⣄⣿⣿⣿⣟⣿⣿⣼⡄⠶⠭⠭⠿⠾⠧⠽⠦⣤⣤⡒⣉⣹⣗⣿⣤⣹⣶⣻⣍⣐⢠
⠀⢩⡀⢺⣶⣆⡂⡂⡶⠃⡆⠀⠀⠐⠒⢏⠉⠀⢈⠁⠀⢲⠀⠀⣶⠐⡆⡍⣿⡇⠀⠀⢴⠀⢬⠀⠀⣤⡄⢰⡄⠀⠀⠈⠀⠈⣤⣤⣤
⠀⢸⡇⣸⠋⡇⡧⡟⡇⢄⣄⠀⠀⠠⠀⡄⠑⣄⢸⠀⠀⢴⠀⠀⣿⠀⡇⠀⠙⠃⠂⠀⣬⠀⢸⠀⠀⣿⡟⣾⣧⣄⠀⠀⠀⠀⣿⣁⣿
⠀⢸⠁⢹⠀⠏⠀⡁⣃⣂⣅⣈⣙⣲⣤⣁⣀⣸⠹⠋⠁⠉⠁⠉⣿⠀⣇⠀⠀⠀⠀⠀⠃⠐⠚⠀⠀⠉⠀⠈⠉⠁⠀⠀⠀⠀⣉⠁⠉
⠀⠘⠐⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠀⠐⠓⠀⠐⠋⠒⠀⠃
⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢬⡾⠷⢒⠀⠀⠀⠚⠁⢀⡆⠒⠂⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠐⠧⠀⠀⢸⣤⡿
⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠈⠲⠛⠁⢀⠀⠀⠀⠀⠀⠀⣀⠀⠋⠶⠏⣠⣀⡼⠂⢤⣦⠘⠂
⠀⠀⠀⠀⠀⢀⡅⠀⠛⢂⠀⠀⢠⠊⠉⠋⠴⢄⠀⠀⠀⠀⠀⣡⡖⠁⠀⠑⣄⠀⠀⡐⠁⠀⠙⢦⡷
⠀⠀⠀⠀⠀⠈⡀⠡⡀⠀⠐⠀⠃⢀⠌⠀⠀⠈⡆⠀⠀⠀⠀⠀⠸⣦⠤⡺⠋⠁⠀⠂⣤⠀⢀⡾⡇
⠀⠀⠀⠀⠀⠀⣽⡢⠈⡒⠠⠈⢠⠈⢀⠀⠐⡄⣿⠈⠒⠀⠀⢠⡀⠀⢌⠁⣤⠀⡁⣲⢋⠐⠟⣀⡄
⠀⠀⠀⠀⠀⠀⠿⢤⠔⠤⡀⠀⠀⡄⠀⠒⠀⢸⡁⠀⠀⠀⢀⣸⠃⡚⢐⣓⣚⣀⠁⠁⠀⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢀⣸⡅⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠟⡴⠏⠉⠒⠚⠙
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠓⠈⠉⠀⠀⠃⠀⠀⠀⠀⠸⠂⠀⢀⠂⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠀⢠⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⢿⠘⠀⢰
⠀⠀⠀⠀⠀⠀⠃⢊⠀⠠⠀⠀⡌⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⢀⠀⠏⠀⠈⠀⠀⡇⠀⠃⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢈⣀⣇⡀⠀⠀⠀⡇⣠⡶⠆⢉⡇⠀⠔⠀⠀⠀⢠⣠⡗⠒⠺⡃⠄⠀⣠⡀⢀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠂⠐⠂⠉⠄⠒⠀⠀⠓⠤⣁⡠⠄⠰⠤⢬⠀⠀⠀⠄⠬⠂⠀⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⣀⢀⡀⣀⡀⢀⠀⣀⠀⣀⠀⡀⢀⢨⣏⢀⡀⢀⡀⣀⢀⠄⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠈⠻⠋⠁⠉⠀⠁⠈⠈⠈⠁⢈⣿⠁⠈⠳⠛⠈⢡⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⡍⠀⠀⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠂⠘⠀⡘⠓⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠁⠤⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠀⠀⠀⠀⠀⠀⡀⠠⣤⡄⠀⠀⠀⣿⣿⡄
⠀⠀⠀⢨⢨⠠⠀⠀⠀⠀⢰⣽⢁⣾⣦⠤⡆⠀⠀⠀⠠⠀⠀⠀⠀⠠⣺⠀⠀⠀⠀⢠⠀⠤⠠⠄⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠐⠐⠐⠀⠀⠀⠀⠠⡴⠆⢶⠶⢶⡀⠀⢀⢀⠀⣤⣀⡄⠀⢀⣿⠠⠀⠀⠀⠠⠀⠤⠀⠄⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⢐⡂⠘⢃⣀⡘⣈⠈⣋⠈⣇⠈⡌⠉⠉⠐⠒⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⡀⡈⡉⢉⠂⠀⠇⠀⠀⡇⠀⠰⡶⠂⠀⠀⠤⠀⠧⠀⠁⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠇⠂⠂⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿

⠀⠀⠙⠢⣀⢀⢀⡴⢄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠀⠐⠀⢉⣉⣀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⡀⣤⠄⢠⢈⠉⠀⡠⠀⠵⠀⠄⠀⠀⠀⠀⠰⠄⠀⠃⠀⠀⣆⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠚⣋⠉⠁⠀⠑⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠂
⠀⠀⠠⠐⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⢰⣆⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠁⢀⡞⠁⠀⠈⠁⠀⠀⢀
⠀⠀⠀⠐⠤⠄⠀⠀⠀⠀⠀⠀⠀⠉⣷⠊⠁⠀⠀⠈⠉⠀⠀⠀⠀⠰⡾⠃⠉⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⡇
⠺⠶⠶⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠒⠠⠤⠀⠍⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳
⡉⠁⠀⠀⠓⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣐⠦⠴⣆⣀⡀⡀⠀⠀⠈
⠁⠀⠈⠉⠁⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⣅⣐⣊⠉⠙⠐
⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⠀⠉⠉⠁
⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠑⠄
⠓⢷⣜⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠠⠒⠈⠉⠉
⠀⠀⢛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠐⠂
⠷⠖⠋⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⢀⡄⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢶⡶⠰⠰
⠀⠔⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠀⠠⣪⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⡄⠀⠀⠀⠈⠐⢲⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⠀⠀⠀⣄⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠈⠙⠁⠀⡘⠀⠀⢀⡀⠀⠰⠉⠀⠀⠀⠠⣄⡀⠀⢀⠀⠀⢀⠀⠀⢨⠀⠀⠀⠆⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡠⠧⠤⠀⠈⣧⠐⠖
⠀⠀⠰⢦⣀⢄⠁⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠂⠂⠀⠀⢺⡷⢀⠀⠀⠪⣟⠆⠸⠆⠀⠀⠀⢰⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⣲⠶⢓⣠⡀
⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣸⣃⣴⣃⣀⣹⣾⣑⣀⣆⣀⣀⣀⣈⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣉⣉⣉⣁⣹⣀⣀⣀
⣿⢻⠿⡿⢿⢛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣛⣻⣿⣟⣛⣿⣻⣛⣛⣛⣛⣿

⠀⠀⠀⠀⠀⣿⢼⠀⢠⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠉⠈⠈⢈⠈⡀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢀⡀⠔⠃
⠀⠀⠀⠰⣄⠀⠠⠰⢌⡀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⠈⠈⠂⠀⠘⠁⠈⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⢀⡀⠀⠀⠀⠆⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠁⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣠⠟⠂⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣧
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠗⠠⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡞⠀⢠⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡟
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠠⠃⠀⠀⠀⠠⠆⠀⠀⠀⠀⠈⠀⠀⠈⠧⠀⢠⠇⠀⠀⠀⠀⢀⠀⠀⢔⡫⠞
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠴⡐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡟⠀⠀⢠⡀⠀⢀⠴⠒⠀⠁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢆⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⡜⠁⠀⠘⡆⠀⠸⡆⠀⠀⠀⠀⠉⠈⠂⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⡀⠀⢠⠇⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⡿⠀⠀⠀⠀⢀⠀⢤
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⣠⣴⠾⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣟⠐⠛⠉⠀⠀⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⢀⣠⣤⡀⠠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⡿⠛⠁⠀⠙⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠘⠇⡄⡀⢹⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠉⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠰⠆⡄⠃⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢻⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⡁⠃⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠃⠆⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⢰⣶⢰⣶⡆⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢈⣉⢈⣉⡁⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⠈⠀⠉⠀⠈⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠸⠿⠇⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⣤⣄⡀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⣀⣼⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠋⠙⠛⠛⠛⠻⠿⢿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁




⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠷⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⠀⢠⠾⠛⠀⠀⠀⠀⠀⢠⠂⠓⢳⣝⢄⠀⠀⣀⠀⠀⢀⠔⠁⠁⠠
⠀⠀⠀⠀⠀⠀⠄⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠘⠧⡀⠀⢻⠁⠀⠠⢀⠂⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⠀⠀⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⣀⢀⠀⠀⠀⠀⠀⠾⠓⠀⠘⠀⠃⠀⠀⡄⠀⠀⠈⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠊⠀⢀⡀⠌⠀⠀⠀⠈⠀⠀⠀⡀⠀⢀⠀⠀⠀⠘⢦⠀⢀⣀⡐⠒⠊⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⡨⠎⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠡⡀⠀⣒⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠇⠀⠘⠰⠀⠀⠀⠀⠀⢀⠈⠀⡀⠀⢰⣾⡄⠀⠀⠀⠀⠀⢀⡰⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠠⠀⠀⠡⡀⠁⠀⠀⠻⡇⠀⠀⠀⠀⠐⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣬⠘⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢢⡀⢠⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠘⠁⠀⠠⡄⠈⠀⠀⡀⠁⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠈⠀⢀⡤⠒⠈⠉⠀⠉⠛⠒⠠⢄⠀⠀⠀⠀⠈⠀⠄⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡴⠃⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⣤⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⢠
⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣸⠀⢀⡿⠁⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⡀⠑
⠀⠸⣄⣀⣤⣤⠀⡴⠆⠀⠀⠀⠰⠁⠀⠀⠀⣐⡠⠔⠀⠀⠀⡇⠀⠈⠀⠀⠙⠀⠀⠘⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⢀⡔⠁⠀⠀⡐⠀⠁⠀⠄⠀⠀⢸⠁⠀⠀⠘⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠈⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⡟⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠐
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣴⡦⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⣀
⠀⠀⠁⠀⠀⠀⠉⠓⠿⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⡠⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠈⠙⠁
⠀⠀⠀⠁⠀⠑⠀⠠⠀⠀⠀⠐⠀⣠⡿⠃⠀⢠⡐⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⢀⠈⠓⠪⣍⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠙⠢⢄⣠⠋⠀⠀⠘⠁⠙⢲⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⣾
⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠤⠀⠀⠷⠀⠀⠀⡄⠀⠨⠇⠀⠀⢄⠀⠀⠾⠀⠀⠠⡄⠀⠠⠇⠀⠀⢠⠀⠀⠸⠀⠀⠀⡄⠀⠀⠧⠀⠀⢠⠄⠀⠸⠆
⣆⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣸⣀⣀⣀⡀⣀⡀⣇⣀⣀⣀⢀⣀⣸⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⢀⣸⣀⣀⣀⣀⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸
⠂⠉⠉⠉⠉⠉⠉⡂⠀⠈⠉⠉⠉⢱⠁⠀⠉⠉⠉⠉⡎⠉⠉⠉⠉⠉⢱⠀⠀⠉⠉⠁⠈⡆⠀⠀⠉⠉⠉⢹⠂⠀⠈⠉⠉
⠒⠀⠦⡠⠶⠦⠶⠓⠶⢦⠶⠶⠶⠞⠶⠦⠄⠀⠀⠀⠃⠐⢤⠤⠤⠦⠞⠶⠶⡤⠦⠤⠤⠳⠶⠦⠄⠀⠀⠘⠲⠶⢤⠶⠶
⢀⣀⣀⣇⣀⣀⣀⡀⠀⠸⠀⣀⣀⣀⡀⣀⢇⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⡀⡀⣧⣀⣀⣀⡀⠀⢀⣄⣀⣀⣀⣀⣀⣸⣀⣀
⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸
⠉⠉⠉⡏⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⡍⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⡍⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⢹⠉⠉
⡐⠒⠒⠓⠒⠒⢢⠂⠀⠚⠒⠒⠒⡔⠒⠒⠓⠐⠒⢂⠖⠒⠚⠒⠒⠒⠤⠂⠒⠛⠒⠒⠢⠖⠐⠒⠓⠒⠒⢦⠒⠒⠚⠒⠒
⠇⠀⢀⡀⠀⠀⡸⠀⠀⣀⡀⠀⠀⠇⠀⢀⡀⠀⠀⠨⠀⠀⣀⡀⠀⠀⠤⠀⢀⣀⠀⠀⠠⠇⠀⢀⡀⠀⠀⠸⠀⠀⣀
⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⢸
⡌⠉⠉⠉⠉⠉⢹⠁⠀⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠍⠁⠉⠉⠉⠉⠩⠉⠁⠈⠉⠉⠉⢹⠉⠉⠉⠉⠉
⠓⠒⠒⡐⠒⠒⠚⠒⠒⢲⠒⠒⠒⠓⠒⠒⡒⠐⠂⠘⠒⠒⢢⠒⠒⠒⠓⠒⠒⡔⠒⠒⠒⠓⠒⢲⡆⠀⠀⠚⠒⠒⢲⠒⠒
⠀⠀⠀⠇⠀⠀⢀⠀⠀⠸⠀⠀⠠⡀⠀⠀⠧⠀⠀⢤⡄⠀⠼⠀⠀⠀⣠⠀⠀⠧⠀⠀⢠⠀⠀⠠⠆⠀⠀⢄⠀⠀⠸⠄
⡇⠀⠀⠀⠀⠀⢸⣀⣀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣅⣀⠀⠀⠀⠀⢸⣆⣀⣀⣀⣀⣀⣾⣀⣀⣀⣀⣀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠹⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠉⠁⠀⠀⠒⠀⠀⠉⠀⠀⠉⠀⠀⠈⠉⠉⠉⢹⠀⠈⠉⠀⠀⠀⡆⠉⠉⠉⠉⠉⢻⠉⠉⠉⠉⠉⠉⡟⠉⠉⠉⠉⠉
⠂⠀⢠⠀⠀⠀⠒⠀⠐⡄⠀⠀⠐⠂⠀⢠⠀⠀⠀⠘⠀⠀⣤⠀⠀⠀⠃⠀⠀⡄⠀⠀⠘⠀⠀⢠⠐⠀⠂⠓⠀⠀⡄
⠀⠀⠸⠄⠀⠀⣀⠠⠀⠷⠀⠠⠄⡀⠀⠸⠄⠀⠀⢀⠀⠀⠿⠀⠀⠀⡀⠀⠠⠇⠀⠀⢀⠀⠀⠸⠀⠀⠀⣀⠀⠀⠧
⡀⠀⡀⠀⠀⠀⣀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⢀⣀⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⣀⣇
⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠈⠁⠀⠀⠂⠉⠉⠉⠉⠉⠁⠂⠀⠈⠁⠀⠀⢸⠀⠀⠉⠀⠉⠀⡆⠀⠀⠉⠀⠀⢰⠀⠀⠈⠁⠀⠉⡆⠀⠀⠉
⠂⠀⠀⡄⠀⠀⠒⠀⠀⢰⡆⠀⠐⠃⠀⠀⠆⠐⠒⠚⠀⠀⠀⡆⠀⠀⠃⠀⠀⢐⠀⠀⠘⠀⠀⠀⡖⠒⠒⠓⠀⠀⢰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⢉⣏⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠀⠀⠀⠀⠀⡀⠀⠀⢰⡆⠀⠀⠀⠀⠀⣿⠀⠙⠛⣷⠒⣲⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⡶⡶⡷⢖⢶⣾⡇⠘⠰⠖⠀⠐⣿⠶⣶⣶⡿⡶⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⡷⢾⡷⠶⠶⣿⣟⣻⣛⣟⣛⣛⣿⡒⠚⠚⣧⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⠶⢴⡷⢦⠴⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⡟⣟⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣶⢾⣧⣴⣦⣾⡟⣛⡛⠛⠛⠛⣿⠘⢺⣇⡿⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⣽⣿⣷⣿⣿⣿⣿⡿⠿⠷⠶⠷⠶⣿⠶⡾⠿⡷⢶⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣦⣤⣿⡋⠉⣿⣧⣠⣤⣤⣄⣠⣿⣀⣇⣤⣧⣬⣬⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣾⣀⣈⣿⣿⣓⣿⣷⠶⣶⠶⠶⡶⣿⠶⠶⡶⣷⣾⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢼⣿⠦⠤⣿⣿⣿⣿⣿⡶⠿⠶⢾⢿⣿⣶⠴⠿⡾⠿⠾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣼⣤⣤⣿⣿⣿⣿⣿⣟⣀⡀⣼⣀⣿⣸⣰⣧⣛⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣼⣯⣭⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⢻⠛⠛⡟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢼⣿⢿⣿⣿⠿⠿⢿⣿⠧⢴⣿⣿⣿⣷⠼⠦⠤⣷⡼⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢼⢿⢼⣿⣿⡦⠾⢿⣿⡶⢴⣿⣿⣿⣿⠤⢴⡷⣿⣦⣼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢼⣼⣼⣿⣿⣤⣤⣼⣿⣤⣾⣿⣿⣿⣿⣤⣤⣤⣿⣧⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⣿⣿⣿⣇⣀⣀⣸⣟⣿⣿⣿⣧⣀⣿⣀⣴⣿⣿⣿⣿⡀
⠀⢀⣄⡀⠀⣀⣤⠶⣤⠀⠀⣧⠀⢹⣻⣿⣍⡏⣍⠉⣹⣿⣿⣿⣿⣿⣿⣿⠉⠉⣽⣯⣯⠉⠁
⣠⢀⣿⣶⣾⡟⠁⠀⣸⠇⢀⣷⠀⢻⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⠛⠛⣟⣿⠛⢻⡃⠀⠀⠀⠀⠀⠀⢸⡀⣀⣀
⣻⣾⣿⣿⣿⣦⣛⣵⣟⣐⣸⣿⣀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣇⣶⣶⣦⣾⣷⣻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⠟⠁⣟⡿⢷⣄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⢥⠶⠵⡌⠉⡴⢫⡿⠉⠛⠙⢒⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢤⣞⣰⠅⣾⠂⢠⠀⠀⠈⠘⡌⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⠀⢸⢧⡀⠀⠀⢽⣷⡌⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠉⢻⣧⠿⣆⣸⣿⡁⣾⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣕⣦⢨⠀⣆⣿⢩⣿⣡⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠙⢻⠛⡿⠂⣻⣿⣻⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⢀⡠⠀⢀⠊⢀⠼⣿⡿⢟⡿⠙⠻⠛⢻⣿⣇
⠀⠀⠀⠀⠀⠐⢏⠁⡤⠠⠛⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣗⣴⣄⠉⠀⡠⢁⣔⠁⠀⢻⣳⣿⣠⠂⠀⠐⢛⣿⣦
⡀⠀⠀⣀⡤⠞⣍⣁⣀⣀⣀⣀⣈⣁⣠⣀⡀⠀⠀⠀⠰⣿⣿⣯⣾⡿⠟⠀⣴⣇⡠⠟⠀⠀⢸⣿⣿⣿⢐⢃⡴⣿⣿⡿
⠟⢳⢒⢿⠿⠿⠿⠿⠟⢟⡛⠒⠒⠒⠒⢺⠁⠀⠀⠀⠀⠀⠈⠉⢉⡴⠞⣱⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⢠
⠀⠀⣽⠉⠀⣰⠁⠰⢂⣀⢳⣤⣤⡶⡶⢺⡄⠀⣠⡄⢐⣛⠂⠀⢰⡖⠋⠉⠀⠀⠀⠀⣀⣀⣿⣙⣿⣿⣏⡎⢉⣿⣿⣧⡤⠶⠒
⡀⣠⠽⠟⠛⠿⢿⣿⡿⠟⢹⡏⣘⠄⡻⣿⣿⣿⣿⣻⠿⠛⠙⠛⣻⠟⠒⠒⣶⣦⣤⣾⣿⣷⣩⣽⣋⣿⡿⠛⣩⣷⣉⣵⣾⢞⠔
⠎⠹⢮⡀⠂⠀⣰⣿⢠⢟⣼⣥⠋⣸⡝⠋⣿⣃⣠⣋⠀⢀⠀⠂⣈⣧⣿⣞⠝⣨⠢⣾⣬⡵⣫⠞⣡⣾⡿⣛⣛⣿⣿⣿⡯⣻⠷
⡠⡪⣪⡝⢛⡛⣙⠾⣦⢭⡽⣯⣿⣿⣷⣿⣿⣿⣏⡹⠋⠉⢉⠋⠐⠀⠛⢳⣯⣶⣾⣿⣍⠘⢁⢾⣿⣣⣶⠀⠉⠤⢞⡿⠿⣴⠕
⣀⠚⠁⢗⠀⠔⠁⠄⠈⢼⡏⡿⣾⡛⠟⣻⡿⣻⠏⡇⠀⠶⢓⢄⣴⠆⢲⣿⢋⡞⠽⣲⠋⣦⠶⣻⡿⣫⠎⠀⠀⢺⡾⢖⠁⣉⡻
⠁⣠⣮⠄⢷⣷⣌⣌⣤⣷⣠⣿⠋⠹⠾⣅⣐⠴⢒⡱⠶⠾⣤⣾⣶⣿⣶⣿⢏⣐⣰⣧⣶⣿⣿⣞⡾⡡⢤⣤⡦⠤⣳⣿⡣⢉⣵
⣾⣿⠔⡃⡠⡈⠅⠁⢱⠏⠹⠋⠀⠀⢊⡜⠩⢣⠾⢓⡴⠛⠻⢿⣿⣿⡿⠿⣻⢻⣷⣿⠟⠛⢋⠙⠩⠠⣢⠿⣫⡾⠃⠙⢺⡿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣛⣭⣭⠥⠶⠶⠶⠶⠶⠶⠶⠶⠮⢭⣭⣛⡲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣡⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢮⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡻⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠙⠲⢭⣝⣓⣒⠶⠤⠤⠤⠤⠤⠤⠤⠶⠶⣒⣚⣫⡭⠖⣋⡵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣀⠀⠀⠀⠉⢭⣉⣛⣛⣛⣛⣛⣛⣛⣛⣋⣭⡥⠴⠖⠋⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣸⣷⣌⡙⠓⠲⠦⢤⣤⣀⣈⣉⣉⣉⣉⡉⠀⠀⠀⠀⠀⠀⠀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⣼⠁⣀⣤⡤⢤⣤⣭⣉⣙⡏⠉⣷⠶⠶⢤⣤⣈⣉⣉⣉⣀⣤⣤⡤⠴⠶⣚⣫⡵⠞⢷
⠀⠀⠀⠀⠀⠀⠀⢹⣾⡉⠳⠶⠾⠛⢛⣩⡽⢷⢴⣟⠶⣶⠶⢤⣬⡉⠛⠶⡶⠒⠚⠛⠛⠉⠉⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣤⠶⠚⡿⠋⣠⣿⢰⡏⠳⣌⠛⠶⠤⠿⢷⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣼⠁⣼⠃⣿⠸⡇⠀⠈⠳⣤⣀⣰⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠙⠛⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⢠⡇⠀⣿⠀⣷⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⡇⠀⣿⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⢸⡇⠀⢻⢠⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⢷⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠘⡇⠀⠈⠛⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢼⡇⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⡇⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠿⢷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣷⠀⠀⠀⢸⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡇⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡾⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⠚⠁⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣠⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⠶⠦⢤⣤⣀⠀⠀⠀⠀⣧⣠⣤⠶⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⡘⠳⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⢋⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡛⠲⠦⠤⣬⣭⣉⣉⣉⣙⣛⣛⣛⣉⣉⣉⣩⣭⡤⠶⠖⢛⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⢤⣤⣤⣀⣉⣉⣉⣉⣉⣁⣀⣤⣤⡤⠶⠖⠛⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠶⠖⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⣭⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡗⣛⣋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠥⠶⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣚⠀⠀⠈⣭⠥⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⣿⣿⣿⠒⣛⣿⣿⣿⠀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣒⡂⠀⠀⠶⠒⠀⠀⠀⡿⡯⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠭⣿⣿⣿⣩⣭⣿⣿⣿⢺⣺⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡇⣷⠀⠀⢀⣛⣉⠀⠀⠀⡯⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⣿⣿⣿⠶⢶⣿⣿⣿⣽⢺⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡯⠽⠀⠀⠠⠤⠤⠀⠀⠀⣗⡗⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⣿⣿⣿⣛⣻⣿⣿⣿⣻⢽⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣀⣀⣀⣾⣆⣀⣀⣀⣗⣃⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠿⠿⠿⠏⠻⠿⠿⠿⠸⠾⠿⠇
⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠤⠤⠤⠤⠄⠀⠤⠤⠤⠤⠤⠤⠤⠂⠤⠠⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤⠄⠀⠄⠤⠤⠤⠤⠤⠠⠄⠀⠤⠤⠤⠤⠔⠐⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠤
⠀⠀⠀⠀⠁⢹⢘⠁⠈⠁⠀⠀⠀⠉⠁⠈⠀⠀⠀⠁⠐⡈⠁⠀⠀⠀⠀⠀⠉⠈⠁⠀⠁⠁⠈⡇⡏⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⡇⠁⠀⠉⠁
⣀⣀⣀⣀⣀⡸⢸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡰⢇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⢇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠇⢀⣀⣀⣀
⠒⠀⠐⠀⠂⠒⠒⠐⠒⠒⠀⠀⠐⠀⠂⠂⠒⠒⠒⠂⠒⠂⠒⠒⠒⠂⠐⠒⠀⠂⠂⠐⠐⠂⠐⠐⠒⠒⠒⠒⠒⠂⠒⠐⠒⠒⠒⠒⠒⠒⠒⠂⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠉⠉⠉⠉⠉⢩⢩⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⢍⡩⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⡍⡍⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠩⡍⠍⠉⠉⠉
⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠒⠒⠒⠒⠒⠊⠈⠒⠒⠒⠒⠒⢒⠒⡒⠒⠒⠒⠒⠒⠊⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃⠑⠒⠒⠒⠒⠒⢒⢒⠒⠒⠒⠒⠒⠒⠁⠑⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁
⠀⠀⠀⠀⢀⠸⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠧⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠇⠇⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠇⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠉⠉⠉⠉⠉⢩⠩⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⢍⡩⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⡍⡍⠉⠉⠉⠉⠉⠁⠀⠉⠉⠉⠉⠉⠉⡍⠍⠉⠉⠉
⠀⠀⠀⠀⠀⢸⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠶⠶⠶⠶⠒⠨⠬⠶⠶⠶⠶⠶⠶⠒⡲⠶⠶⠶⠶⠔⠢⠴⠲⠶⠶⠖⠖⠖⠒⠲⠒⠲⠶⠶⠶⠥⠑⠠⠴⠶⠶⠶⢒⢒⠶⠶⠶⠶⠶⠲⠡⠑⠲⠐⠲

⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠰⣀⠂⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⣐⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣐⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⢸⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⢠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄
⠀⠀⠀⠀⠀⢸⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠠⠌⠐⠀⠀⠀⠀⢠⠒⡔⠀⠀⠀⠀⠀⠥⠌⠂⠀⠀⠐⠀⢀⠒⠀⠀⠀⠀⠀⠀⠥⠁⠄⠀⠀⠀⠀⢄⢂⠀⠀⠀⠀⠀⠀⠥⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⢀⣀⣠⡀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠉⠉⠉⢻⠋⠉⠉⠉⠉⠛⠛⠛⢻⠟⠛⠛⠛⠛⠛⠓⠒⢲⡞⠓⠒⠒⠛⠛⠒⠒⠲⠶⣶⠶⠚⠛⠛⠛⠲⠶⠖⠶⠶⣶⠖⠒⠒⠶⠶⠿⠶⠶⠶⢶⠖⠒⠒
⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⣀⣾⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣀⣀
⠉⠉⠀⠀⠀⠀⠈⢻⡟⠉⠉⠉⠉⠉⠉⠉⢻⡟⠉⠉⠉⠉⠉⠉⠉⠉⢻⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⠋⠀⠀⠀⠀⠀⠈⠉⠀⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠤⠤⢴⣶⠤⠶⠶⠾⠷⠦⠤⠤⣤⡤⠤⠴⠾⠷⠶⠶⠶⣶⣶⣶⣶⣶⣾⠧⣤⣤⣤⣤⣤⡤⠤⠤⠶⠿⠷⠶⠶⠶⢶⣦⠶⠶⠶⠶⠶⠿⠶⠶⠶⡶⠶⠶⠤
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠒⠒⠚⠛⠒⠒⠒⢲⡶⠒⠒⠲⠿⠶⠀⠠⠤⣤⠤⠤⠶⠟⠷⠤⠤⠤⢶⡶⠐⠖⠒⠒⠚⠓⠒⠲⠶⡶⠖⠒⠒⠒⠚⠛⠖⠖⠶⠶⣶⡶⠒⠒⠚⠛⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠶⠶⠒⢶⡶⠶⠾⠿⠿⠿⠿⠿⢿⡿⠻⠟⠟⠛⠛⠛⠛⢻⣿⠛⠛⠛⠛⠛⠛⠛⠛⢿⡿⠿⠛⠛⠛⠛⠛⠛⠓⠛⢳⡶⠒⠒⠒⠛⠛⠛⠛⠛⠛⢻⡟⠛⠛
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⢀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣠⣧⣀⣀⡀⠀⠀⢀⣀⣀⣼⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⢀⣀⠀⠀⠀⠀⠀⠀⣸⣇
⠛⠛⠛⠉⠙⠛⠛⠛⣿⠋⠉⠉⠉⠉⠉⠉⠉⢹⠏⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠀⠁⠉⠉⢿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡟⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢀⣀⣀⣀⣀⣀⣼⣄⣀⣀⣀⣀⣀⣀⣠⣼⣄⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣄⣀⣀⡀⣀⡀⣀⠀⣀⢀⣸⣇⡀
⠉⠉⠙⣿⠋⠉⠉⠉⠉⠉⠉⠛⢻⡟⠋⠉⠉⠉⠉⠉⠉⠛⡿⠉⠉⠉⠉⠉⠉⠉⠉⢻⡿⠉⠉⠉⠉⠁⠉⠉⠉⠻⣿⠋⠉⠙⠛⠛⠛⠛⠛⠛⠛⣿⠛⠉⠉
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣿⠃⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠟⢻⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⣿⣻⣶⣶⣾⣿⠂
⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⡟⢂⣿⡏⢸⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣿⣿⠟⠃
⠀⢠⣦⣠⣿⣿⣿⣿⡟⠈⠛⠻⢿⣾⣯⣤⣾⣿⣿⣿⣿⣛⡻⢿⣶⣦⣄⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠛⠉
⠀⠈⢿⣿⡏⠙⠻⣿⣿⡄⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣷⣶⣭⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⡆
⠀⠀⠈⠉⠀⠀⠀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⢉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣈⣽⣿⣷⣿⣿⣏⠀⢀⣀⣤⣤⣴⣶⠾⢿⣿⣿⣿⣏
⠀⠀⠀⠐⠛⠻⠿⠛⠻⢿⣿⣶⣶⣶⡶⢿⣿⣿⡿⠿⠿⠟⠛⠉⠉⠛⠿⣿⣿⣿⡾⠿⠛⠉⣼⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠙⢿⣿⣿⣧⡀
⠀⠀⠀⠐⠲⠶⠶⢦⣴⡿⢿⣿⣿⡷⣦⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣦⠉⠉⠙⠛⠻⠿⢿⣷⣶⣤⣤⣀⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⣸⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡄⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠻⣿⣿⣿⣿⡿⠟⠉
⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠀⠀⠀⢀⣠⠶⠛⠙⠟⠉⠁
⠀⠀⢻⣏⣹⣿⣿⣿⡿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁
⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠁

⣾⣿⣿⣿⣿⠀⢸⠀⢰⠐⠞⠻⠖⠀⣤⠀⣿⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⡾⠀⠘⠛⠛⠛⠛⠃⢠⣆
⣿⠟⠛⠛⠛⠂⢸⠀⢸⠀⠀⠁⠀⠀⡇⠀⣿⡄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⢸⣷
⢯⡀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⡇⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠰⠂⠀⠀⠀⠀⠀⢸⡇
⠀⠙⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸⡇
⠀⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⢸⣿⠀⠀⠀⡟⠀⠀⠀⢻⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠀⠀⠀⠟⠀⠄⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣒⡒⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣸⣿⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⢻⡏⣤⣶⣟⢧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⡇⣸⡧⢿⣿⣿⣴⠇
⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣉⣉⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠂⠄⠀⢸⢹⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆⢰⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⣴
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⠀⠀⠀⡄⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⢢⠀⣜⣇⠄⡇⡄
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠋⠉⠑⠲⠁
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⢰⠋⢙⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢸⠘⢃⠃⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⢠⠞⠀⠀⢠⠄⠀⠀⠀⠀⠘⠒⠋⠀⠀⡠⠋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⡠⠔⠊⠁⠀⠀⠀⠐⠀⠀⠀⡠⠚⢁⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⡀⠀⠀⠀⠀⠓⠋⠁⠀⠀⠀⠀⠀⣠⠔⢁⡐⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢸⣿⣿⠀⠀⠤⠤⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠠⠠⡀⠀⠀⠀⠀⡀⠀⢀⡀⠀⢸⠛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠘⠛⠋⡅⠀⠀⠀⠘⡀⠠⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠰⠷⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⢱⠀⠀⠀⢀⣃⠀⠀⡨⠉⠉⡆⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣁⡀⠤⠊⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠈⠉⢻⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣶⣶⣤⣤⣄⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⠀⠀⠀⠀⠀⢿⣿⠋⣁⣩⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⡿⠛⠋⣹⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣠⣿
⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⠉⢠⡄⠹⣦⠀⠀⠀⣿⣿⣿⣇⢿⣦⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣯⣿⣿⣿⣿⠏⠀⠀⣠⡆
⠀⢠⣶⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣆⠙⢷⡄⠀⠸⣿⣿⣿⡜⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⣼⣿⣿⣿⣿⣿⣷⠀⢠⠞⠉
⠀⠀⠻⣿⡇⠈⢹⣿⣿⣿⣿⣿⠀⠀⠈⢿⣄⡰⣿⡀⠀⢻⣿⣿⣷⣾⣿⣇⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠃⢠⣾⣿⢿⣿⣿⣿⣿⣿⡴⠃
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠈⠻⣷⣿⣧⠀⠈⢿⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿⣿⣿⣿⠃⣤⣿⣿⠋⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠘⣿⠛⣷⣀⠸⣿⣿⡟⠛⠻⣷⣿⣿⣿⣿⣿⣿⣿⢣⣾⣿⡿⠃⠀⢸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⢹⣧⡘⣿⣧⣹⡟⠻⢷⣦⣼⣿⣿⣿⣿⣿⣿⣵⣿⣿⡿⠁⢀⣶⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣧⠀⠀⠈⢿⣧⠈⢻⣿⡿⢦⣤⡤⣿⣿⣿⣿⣿⡿⣿⣿⣿⠟⢠⣶⣿⣿⡟⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠔⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⣀⣀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⢸⣯
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⣀⣀⢀⣿⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡷
⠀⣴⣿⣿⣿⠿⣿⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⠁⢸⡷
⢸⣿⣿⣿⣇⠀⣿⢠⣤⣼⠀⠀⠀⣰⠀⠀⠀⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠠⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠁⢸⣧
⠘⣿⣿⡄⠈⠀⣿⠈⠉⢿⠀⠀⠀⣬⡌⠁⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣮⣧⣼⣧
⠀⢻⣿⡇⠀⠀⣿⠀⠀⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣍⠻⣿⡷
⣀⣸⣿⣧⣀⣀⣿⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣧⣄⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣸⣀⣀⣀⣀⣀⣠⣂⣀⣀⣀⣠⣿⣿⣿⣟⣃⣸⣿
⠁⠀⠀⠈⠁⠀⣿⠁⠈⢿⡜⠙⢄⣩⠀⠉⠉⠀⢠⠎⠹⡄⠀⠀⠀⠈⠉⣡⠏⢻⡇⠀⠀⠀⢸⠉⣡⠋⠳⡀⠀⠀⠀⠀⠀⡡⠋⠳⣼⠀⠀⢸⣯
⠒⠒⠒⠒⠒⠒⣿⠒⡲⢿⠒⠒⠚⢷⡒⠒⠒⡶⠓⠒⠒⠚⢷⠒⠒⢒⡶⠓⠒⠲⡟⢖⠒⠒⢺⡖⠓⠒⠒⠚⢶⠒⠒⢒⠞⠓⠒⠒⢺⢶⠒⢺⣿
⠀⠀⠀⠀⠀⠀⣿⣼⣁⣹⣀⣀⣠⣼⣝⣤⣞⣀⣀⣀⣀⣀⣀⣱⣤⣎⣀⣀⣀⣀⣇⣈⣳⣠⣾⣀⣀⣀⣀⣀⣈⣣⣠⣋⣀⣀⣀⣀⣸⣀⣳⣸⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣾⣿⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠉⠉⠉⠉⠉⢙⣿⡇⠘⡦⣉⠁⠒⠢⡀
⠛⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⡁⠀⢱⠀⠀⠃
⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠙⠛⠛⠛⠋⠀⡰⢄⡑⡀⣘⣤
⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠉⡻⣾⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⡡⢋⠜⢂⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⠃⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠛⡵⠃⢀⠌⠈⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡅⠀⣀⣀⣀⣀⣀⣀⡀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⡰⢁⡀⠀⠔⡡⣅⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⡈⢆⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢠⠊⠠⢊⣼⡣⠗⠁⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠧⠠⣤⡥⠤⠦⠈⣄⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⡐⠁⠀⠙⠊⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⠀⢾⣦⣄⡀⠀⢸⡂⠀⣀⣤⣾⡆⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠀⡝⠿⢿⣧⣸⣥⣾⠿⠟⠉⠈⡄⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⢄⠀⣿⣿⣿⠇⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⢀⠁⠀⠈⠻⣿⡿⠟⠀⠀⠀⠀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣾⣍⠁⠀⠀⠀⢐⠠⠄⠐⠒⠒⠒⠐⠚⠀⠢⢄⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁⠀⢀⠔⠁⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠁⢾⡇⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠏⢠⠀⠀⡌⠀⠀⠠⠊⠁⠀⠀⢀⠇⠀⠈⠲⡀⠀⠈⠃⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠐⠚⠐⠂⠀⡄⡇⠀⠀⡄⠀⠀⠀⠀⡜⠀⠀⠀⠀⠁⠀⠀⠀⠰⠒⠒⠒⠒⠛⠛⠛⠒⠒⠒⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣇⣀⣀⡧⠤⠤⠤⣴⣁⡤⠤⠄⠔⢦⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⡇⠀⠀⠀⠓⠐⠃⠀⠀⠀⢰⠤⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡇⠀⠀⠀⣶⣶⣶⠀⠀⠀⢘⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⠋⣛⠛⢛⠛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠉⠉⠉⠉⠉⠉⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠒⠒⠂⠀⢰⠂⠀⠀⠀⠒⠀⠀⠚⠁⠀⠀⢸⠀⠀⠐⠃⠀⠀⠉⠃⠀⠀⠛⠈⠉⠉⠉⠉⠉⠉⠋⠉⠉⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⠄⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡼⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⠩⠩⠍⢁⠒⠠⢬
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠜⠁⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠖⠀⣁⠤⠐⠀⠀⠀⠀⠀⠬⡀⢅⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⠃⠈⠐⠲⡄⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⢠⠔⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠁⡠⠊⠉⠑⢄⠈⣤⠜⠀⠀⠀⠀⠱⠄⠠⠂⠀⠀⠀⠀⠢⠀⠔⠁⠀⠀⢀⠊⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢃⣶⣶⣶⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠉⠉⠉⠀⠀⡌⡉⡍⡉⡉⢉⡉⣷⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣺⣀⣨⣀⣀⣀⣀⣀⣀⣀⣀⡀⢀⣀⡀⠀⠀⠀⣸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠒⠉⠀⠁⠉⠉⠉⣉⠙⠛⠋⠭⠝⠋⠉⠉⠉⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣥⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣴⣤⣘⡀⠀⠉⠓⠤⣄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠈⠋⠒⡗⠢⠤⢄⠰⠾⣿⡛⠻⠋⣷⣦⣤⡀⠀⢹⡿⢢⣀⠀⠀⠠⠀⠀⡁⢸⡇
⠀⠀⠀⠀⠀⡇⠀⠀⣀⢀⣀⣻⠛⠿⢒⣦⣭⣀⣀⠀⢈⡇⠀⠀⠁⠀⠀⠀⢈⣀⢸⣻
⠀⠀⠀⠀⠀⡇⠀⢠⠼⢼⠈⢻⠛⠛⠳⠶⡿⡯⣿⠀⠘⡇⠀⠀⠀⠀⠀⠀⣉⣀⢸⣿⡃⠀⠀⢠⣤⣤⣤⣾⣿⣿⡿⠿⠷
⣀⣄⣄⣤⠀⡇⠀⢸⠈⢸⠉⣻⠛⡛⠛⠒⠖⠗⣿⠀⢸⡇⠀⠀⠀⠀⠀⢀⣨⠠⢸⣿⡇⡀⠀⢸⣿⢸⡇⢠⣰⡖⠂
⠀⢸⣟⡇⢸⡇⠀⢸⢐⢸⣉⣻⢙⣟⣙⣩⣟⣛⣿⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⢽⡯⢽⣿⡧⠄⠡⠤
⣾⣾⣿⣿⢸⡇⠀⢸⠉⢸⣬⣽⢩⣿⣴⣤⣦⡥⣿⠀⢸⡇⢀⣠⣄⠀⠀⠀⡙⠀⢸⣿⡇⠀⠀⢸⡿⣾⣿⣿⣿⣧⣭⣭⣁
⠉⠁⢀⠀⠸⡇⠀⠸⣻⣿⣀⣹⠉⢙⢨⣶⣶⣥⣿⠀⢸⡇⠀⠀⠀⠀⠈⠉⠙⠙⢸⣿⠏⡄⠀⠸⠾⠿⠟⠿⣿⡿⣿⣿⣿
⠀⠉⠀⢤⣄⠀⠰⡆⠈⠛⣉⣿⣾⣟⣻⣽⡬⠦⠚⠀⢺⡧⠉⣀⠈⡀⠌⠀⠀⠈⠈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣶⣤⣤⣄⡈⠀⠀⠘⠊⠛⠈⢛⣛⣯⣽⣶⣿⣶⣄⡀⠘⠋⠤⠐⠈⠀⠀⢀⣴⣦⣤⣄⣀⠐⠂⠆⢰⡀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⠟⠛⣻⣿⡛⢵⣶⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣷⣮⡐⠢⢍⡁⠈⠛⠿⠻⠿⣿⣿⣿⣷⣶⣦⣤⣀⣀⠀⠀⡀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⠑⡄⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡗⠠⠄⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⠉⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠈⠢⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠄⠀⠐⠁⠀⠀⠀⠀⢹⠉⠉⠉⠉⠉⠉⡇⠀⠀⠀⠀⠑⡀⠀⠘
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠁⠈⠀⠀⠀⠀⠈⠀⠀⢠⠋⠀⢹⣷⣦⣤⣀⡀⡇⠀⠀⠀⠀⠀⢡
⠱⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⡄⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢡⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⡆⠀⠀⡇⠀⠀⣿⣿⡇⠀⡔⢊⠃⠀⠚⠑⠘⢄⣰⠀⠀⠀⠀⢀⢄⣿⠾⠻⢷⣕
⠀⠀⢃⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⡇⠀⠀⡆⠀⠀⣿⣿⣧⢸⠀⢂⡀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⡌⣿⠁⠀⠀⠀⣿
⠀⠀⠀⢂⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠁⠀⠀⣿⣿⣿⢘⡀⠀⠉⠉⠁⠀⡰⠀⠀⠀⠀⠀⠀⡿⡙⢷⣤⣠⣴⢟
⠀⠀⠀⠈⢆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢹⣿⣿⠀⢙⠂⠄⠀⡤⠊⠀⠀⠀⠀⠀⠀⢀⠀⡀⠐⡬⠍⠒⠁
⠀⠀⠀⠀⠈⡄⠀⢰⡉⠑⠤⣀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠁⠀⠀⢸⣿⣿⠀⠈⠀⣤⡀⠆⠀⠀⠀⠀⠀⠀⢀⠎⣼⡟⡰⠁
⠀⠀⠀⠀⠀⠘⣀⠇⠈⠑⠢⠤⢈⡁⠒⠢⢄⡀⠙⡄⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⢰⠀⣿⠀⡄⠀⠀⠀⠀⠀⢀⢂⣾⠟⡐⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⢲⣿⣿⣷⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠘⢸⣿⠀⠀⠀⠀⠀⠀⢠⢃⣾⠏⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⠀⡇⠀⠀⠀⠀⠀⢘⠀⠀⠀⠘⣿⣿⡇⠀⢸⡟⢸⠀⠀⠀⠀⡠⢁⣾⠏⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠧⠧⠀⠀⠀⠀⠀⠼⠀⠀⠀⠠⠿⠿⠧⠤⠾⠧⠴⠀⠀⠀⠴⠥⠾⠏⠬⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣠⣤⣬⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢹⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⡏⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡏
⠒⠛⠓⠒⠒⡖⠒⠓⠛⠛⠛⠛⡟⠛⠒⠛⠓⠒⠒⡖⠒⠒⠛⠒⠒⢲⠒⠚⠒⠛⠒⠓⢳⠚⠒⠒⠛⠒⠚⢲⠒⠚⠒⠛⠚⠛⢲⠒⠒⠚⠛⠒⠒⢲⠚
⠤⢤⠤⠤⠴⠧⠤⠤⢤⠤⠤⠴⠧⠤⠤⢤⠤⠤⠴⠷⠶⠶⣶⠶⠤⠾⠶⠶⠦⡤⠤⠤⠼⠦⠤⠴⡶⠶⠤⠼⠦⠤⠤⡴⠶⠦⠼⠦⠤⠤⡤⠤⠀⠾⠦
⣀⣸⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣠⣄⣀⣼⣠⣄⣠⣤⣀⣀⣧⣀⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀⣧⣤⣤⣤⣀⣀⣀⣧⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀
⠀⠀⠀⠀⢀⡇⠀⣀⠀⠀⠀⢈⡇⠀⢀⡀⠀⠀⢀⡃⠀⠀⠈⠀⠀⢸⡁⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⢸⡀⡠⢄⠀⠀⠀⢸
⠉⢹⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⡟⠉⠉⠉⠉⠉⠉⠟⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉
⠒⠛⠒⠒⠒⡖⠒⠒⠚⠒⠒⠲⡖⠒⠒⠛⠒⠒⠲⡖⠒⠒⠛⠒⠒⢲⠖⠒⠒⠛⠒⠒⢲⠖⠒⠒⠛⠒⠒⢲⠒⠛⠛⠓⠒⠒⢲⠒⠒⠒⠛⠒⠒⢲⠒
⠤⢤⠤⠤⠤⠧⠴⠦⢤⠦⠴⠴⠧⠤⠤⣤⠤⠤⠴⠧⠤⠤⣤⠤⠤⠼⠶⠦⠴⣤⠤⠤⠼⠤⠤⠤⣤⠤⠤⠼⠤⠤⠤⣤⠤⠤⠼⠤⠤⠤⡤⠤⠤⠼⠤
⣀⣸⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣧⣀⣀⣀⣀⣀⣀⣟⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⠁⠀⠉⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁
⠉⢻⠊⠉⠈⠉⠉⠉⢻⠉⠉⠛⠛⠉⠁⢻⠉⠉⠉⠉⠉⠉⡟⠉⠉⠉⠉⠁⠉⡟⠉⠉⠛⠙⠋⠍⡟⠉⠉⠉⠉⠉⠉⡟⠉⠀⠉⠉⠉⠙⡟⠉⠉⠉⠉
⠤⠾⠤⠤⠤⡤⠤⠤⠾⠤⠤⠤⡤⠤⠤⠾⠤⠄⠠⡤⠀⠠⠿⠤⠶⢶⠖⠐⠀⠓⠀⠀⢠⠤⠤⠤⠷⠶⠶⢶⠖⠒⠒⠓⠀⠀⢠⠤⠤⠴⠷⠤⠤⢤⠤
⣀⣀⣀⣀⣠⣧⣤⣤⣤⣤⣤⣠⣇⣀⣤⣄⣀⣀⣠⣥⣤⣤⣤⣤⣤⣼⣄⣀⣀⣀⣀⣀⣸⣤⣤⣤⣤⢤⣤⠼⠄⠀⠀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣸⣄
⠀⢸⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣀⣀⡀⣸⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⣏⢀⣀⣀⣀⠀⠀⣇⠀⠀⠀⠀⠀⠀⣇⣀⣀⡀⠀⢀⠀⡇
⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠙⠏⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠙⠉⠉⢹⠉⠉⠉⠉⠉⠉⢹⠉
⠒⢲⠒⠒⠒⠓⠒⠒⢲⠒⠒⠚⠓⠒⠒⢶⠒⠒⠚⠓⠒⠒⡶⠒⠒⠚⠓⠒⠒⡶⠒⠒⠚⠓⠒⠒⡖⠒⠒⠚⠓⠒⠒⡖⠒⠒⠚⠒⠒⠒⡖⠒⠒⠚⠒
⠤⠼⠤⠤⠤⡤⠤⠤⠼⠤⠤⢤⡤⠤⠤⠼⠤⠤⢤⡤⠤⠤⠷⠤⠤⢤⡤⠤⠤⠶⠶⠶⢶⡦⠶⠦⠧⡤⠤⢤⡤⠤⠤⠧⠤⠤⢤⠤⠤⠤⠧⠤⠤⢤⠤
⣀⣀⣀⣀⣀⣇⢀⣀⣀⣀⡀⢀⣇⣄⣀⣀⣀⣀⣠⣅⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣸⣀⣀⣤⣤⣀⣀⣸⡀⠀⠀⠀⠀⠀⢸⣀
⠀⢹⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠈⠀⠀⢹⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡇
⠉⠉⠉⠉⠙⡏⠉⠉⠉⠉⠉⠙⡏⠉⠉⠉⠉⠉⠙⡏⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⢹⠂⠀⠀⠉⠈⠉⢹⠋⠉⠉⠉⠉⠉⢻⠋

⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⠐⠀⠀⠀⠀⠁⠒⠒⠒⠒⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠀⠀⠀⠊⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠂⠐
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠
⣀⠀⠀⠀⠀⠀⢠⣀⡀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠐⠀⠀⠈⠀⠈⠀⠐⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠈⠉⠉⠉
⠂⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠀⠀⠀⠚⠀⠀⠠⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠁⠀⢈⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠈
⠄⠀⠒⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠄⠀⠐⠀⠀⠀⠠⠀⠀⠒⠀⠀⠀⠠⠤⠤
⠄⠀⢀⠀⠀⠀⢠⠀⢀⣀⠀⢀⠀⠠⠀⠀⣀⠀⠀⠀⠸⠀⠀⣀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠛⠋⠈⠀⠈⠉⢙⠉⠉⠉⠉⠉⠉⢹⠉⠈⠉⠉⠉⠉⢩⠈⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠀⠀⠘⠀⠀⠈⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠠⠀⠒⠒⠚⠒⠒⣶⠒⠐⠒⠀⠐⠀⡄⠀⠀⠀⠚⠒⠂⡄⠀⠀⠀⠒⠒⠀⠄⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠐⠀⠀⢠⠀⢄⣠⣼⣤⣤
⣀⠀⠠⠀⠀⠀⢀⡀⠀⢥⣀⠀⢀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣅⣀⡀⣀⣀⠀⠀⠆⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠆⠀⠀⠀⣀⠀⢀
⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠠
⠁⠀⢨⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠉⠀⠉⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⣾⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣾⣶⣦⣤⣴⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠷⠲⠶⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡈⠁⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠻⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠠⢀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣄⢀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡤⣪⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢦⣁⠉⢩⠄
⠀⠀⡀⠠⠀⠀⠀⠀⡠⠛⠀⠀⢀⠔⣩⠟⠁⠀⠀⠀⠀⠀⠀⠀⡤⠤⠽⠾⠿⠴⠯⠆⠠⣤⢀⣀⣀⣀⠀⢀
⣀⠊⠀⠀⠀⠀⡠⠞⢄⠀⣀⠔⠁⠈⠀⠀⠀⠀⣠⣤⣠⣆⣠⣤⣅⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠁⠀⠀⠀⠀⠊⠀⠀⠀⠻⠄⠀⠀⠀⠀⣀⠀⡔⠀⠀⠀⠀⠀⠈⠀⠀⣀⠀⡘⠁⠒⠒⠒
⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⠾⠿⠿⠿⠦⠶⠶⠶⢤⠀⠤⠤⠤⠤⠉⠀⠀⠤⠤⠤⡤⠤⠤⠤⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣪⡿⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠁⠀⠀⠃
⠀⠀⠀⢀⡀⠊⠉⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠒⠿⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⢤⡦⣀
⠀⠀⠀⠸⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠤⠤⠒⢻
⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⡇⠀⠀⠀⠃⢱⠀⠇⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢄⠀⠀⠀⢀⡜
⠀⠀⠀⠀⢐⢲⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡀⣀⠔⠋⠑⠊⠁⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠁⠀⠚⡀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐⠠⠦⠄⠀⠀⢄⢀⡀
⠀⠀⠀⠓⠀⠀⠠⠐⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⣑⠀⡇⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⠀⠆
⠀⠀⠀⠀⠀⠄⢤⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣄⣄⠀⣀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠒⠉⠀⠀⠀⠀⠀⠈⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠓⠄⠄⠀⠤⠋⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠒⠒⠂⠀⠑⠢⠼
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡁⠀⠈⠉⠁⠀⠀⠀⠈⠁⠀⠀⠁⠉⠉⠉⠉⠁⢹⡏⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠈⠈⠉⠉⠉⠁⠀⠀⠀⠀⠁
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠓⠖⠒⠓⠒⠲⠒⠲⠶⣶⡒⠒⠒⠒⠒⠒⠒⠖⠛⠙⠛⠓⠒⠒⠒⠒⠒⠒⠒⡒⠒⠚⠛⠛⠛⠛⠛⠛⢁⣓⠒⠒⠒⠒⠒⠒⠒⠚⣛⠛⠛⠛⠒⠛⠛⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⢀⡯⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣀⣀⣀
⠉⢩⡝⠋⠉⠉⠉⠉⠉⠁⠀⠉⠀⠉⠓⠀⠉⠉⠉⠉⢹⣭⠛⠛⠛⠋⠉⠉⠙⠓⠈⠉⠉⠉⠉⠉⠉⠉⠁⠉⣤⠉⠉⠉⠀⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⡤⠼⠳⠦⠤⠤⠤⠤⣤⡤⡤⠤⡤⢤⠤⠤⠴⠶⠶⠶⠾⠃⠤⣤⣤⠤⠤⠤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠤⠴⠇⠦⠤⠦⠤⠤⠤⠤⠤⠤⡤⢤⣤⣤⣤⡤⣤
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠛⠛⠛⠛⣟⠛⠛⠛⠛⠛⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⠛⠛⠛⠛⠻⠛⠉⠙⠛⠛⠛⠛⠟⠛⠛⠛⠛⢛⣛⡛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣀⣀⣀⣀⡿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⢇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠁⠀⠈⠁⠀⠐⠀⠀⠀⠀⠈⣦⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣶⠌⠁⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠶⠶⢤⣤⣤⣤⠤⠤⠤⠤⠴⡟⣶⠴⠶⠶⠶⠶⠶⠶⠦⠤⠤⠶⠶⠶⠶⠶⠶⠶⠟⠳⢶⣶⡶⠶⠶⠶⠶⠶⠶⣶⠶⣤⡤⢤⣤⣤⣤⡼⡳⡶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠛⠛⠉⣍⠛⠛⠓⠛⠛⠿⠿⠿⠟⠌⠛⠛⠙⠛⠉⠙⠛⠛⣿⡛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠉⠉⠉⠹⠿⠿⠟⠛⢻⡉⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⣤⣤⣀⣄⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣠⡿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣠⣄⣀⡿⢧⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⠰⣤⣤
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣾⣾⣶⣿⣶⣾⣶⣷⣾⣿⣿⣿⣶⣶⣿⣶⣶⣷⣶⣶⣶⣿⣶⣾⣾⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⢶⣶⢶⢶⡶⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢀⣨⠽⣖⠒⠦⢤⡇
⢠⠋⠐⠀⠐⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡾⠁⣶⡂⠀⣄⠀⠈⠳⣏⣢
⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠉⠀⠁⢀⠈⢁⡔⠁⠁⠀⠀⠘⢧
⠀⣇⠀⠀⠀⡀⠇⠀⢀⠖⠒⢄⡀⠀⠀⠈⠉⠓⠋⠡⠔⢋⠄⠀⠀⠀⠀⠀⠘⡇
⠀⠘⡄⠀⠀⡀⠑⢤⠋⠀⠀⠀⠈⢢⠀⠀⠀⠸⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢹⡀⠀⡇⢀⣈⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡠⠊⠀⠁⠀⡇⠸⡤⢄⢱⣀⣔⡀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⣀⠀⠀⢠⢿⠲⢤⡀
⢇⠀⠀⠀⠀⡇⠀⠀⡸⠬⢄⡤⠌⢃⠀⠀⠀⠀⠀⠀⠙⠢⣀⡀⠘⠀⣀⡴⢻⠘⡆⠀⠈⠳⡄
⠀⢳⠀⠀⠀⠃⠀⢰⡞⠒⠒⣳⠀⢸⠙⠒⠦⠤⠤⠴⠒⠒⢻⠉⡏⠉⠁⠀⢸⠀⢿⠓⢄⠀⠈⢢
⠀⡌⠀⠀⠀⢸⠀⢸⠫⣉⣹⠧⠴⣇⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⡇⠀⠀⠀⠈⡇⢸⡄⠈⢳⡀⠀⢣
⠀⢇⠀⠀⠀⢸⠀⡨⠦⠄⠱⠀⣠⠏⠉⠓⠒⠒⠒⠚⠋⠉⢸⣆⣷⠶⠶⠒⢲⢣⠀⡇⠀⠀⣧⣀⡴⠓⢤⡀
⠀⠀⠑⠀⠠⢸⠀⠑⡖⠒⠃⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠉⠁⠀⠀⠈⠉⠀⢻⠀⠀⠎⡀⠀⠀⠀⠝⠐⢄
⠀⠀⠀⠀⠀⠀⠳⡀⡇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡀⠀⠀⠀⢸⡄⠀⠹⠑⠒⠊⠁⡀⠤⠨⡆
⠀⠀⠀⢀⠀⠀⠀⠈⠃⠀⠀⣰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⡆⠀⠀⠈⡇⠀⢀⠠⢐⠈⠀⢊⡡⠟⢙
⠀⠀⠀⠀⠑⠂⠀⠠⢀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⡇⣇⠀⠀⠀⢻⠀⠘⠖⠓⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⢹⠀⠀⠀⠘⣇⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠹⡄⠀⠀⠢⡀⢀⣀⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠓⠒⠶⠶⡟⠈⣷⠤⠤⠤⠤⣿⠀⠀⠀⠉⠤⠤⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⣀⣀⣤⠤⠔⠚⠒⠚⠁⠀⠘⢦⣀⠀⠀⢸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⣒⣚⡛⠓⠒⠤⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣛⣭⠭⠽⢿⣭⣭⣛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⠴⢪⣥⣤⡀⡘⠿⠿⠋⢀⣠⣄⡈⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣫⡵⠚⠛⣿⣧⣀⣠⣼⡿⠿⠿⣷⢹⣿⣿⣿
⠀⠀⠀⠀⡔⣁⣀⠙⠛⠋⠀⣿⠀⠀⠀⠘⠿⠟⠁⣹⠀⠀⠀⢸⣿⣿⣿⣿⣫⡾⠿⣦⣤⣴⣿⠈⣿⣿⣿⣧⣀⣤⣾⠏⣿⣿⣿
⠀⠀⠀⡞⠸⠿⠿⠃⠸⣷⡀⣿⡀⠀⣠⣤⣄⠀⢠⡟⠀⠀⠀⢸⣿⣿⣿⢳⣇⣀⣀⣼⣇⠉⢿⠀⣿⣿⠿⠛⠻⣿⡿⢸⣿⣿⣿
⠀⠀⠀⢧⣤⣴⡶⠿⣷⠈⠀⢻⣧⡀⠛⠛⢋⣰⡟⠁⠀⠀⠀⢸⣿⣿⣿⡘⠛⠋⢉⣀⡙⣷⣿⡄⠸⢿⣤⣤⣴⠟⣠⣿⣿⣿⣿
⠀⠀⠀⠀⠉⠁⠀⠀⢸⠀⠘⠚⠛⢁⣠⣴⠿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⣿⡇⣿⣧⣥⣤⣿⠟⠋⣠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⠿⢟⣫⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣭⣭⣽⣧⣈⣉⣉⣁⡤⠶⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠻⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢸⣄⠙⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢹⣿⣿
⠀⠀⠀⣴⣷⡄⠀⠀⣠⣤⠀⠀⠀⠀⢠⠀⠀⠸⣿⣿⡇
⠀⠀⣴⣾⣿⣄⠀⠀⢹⣿⣀⡀⠀⠀⠈⠀⠀⠀⢻⣿⣿⡀
⠀⢸⣿⣿⣿⣿⡆⣾⣿⣿⣿⣿⡄⠀⢸⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⢀⣀⣀⣀⣸⠛⠛⠙⠛⠛⠛⠛⠛⡚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⣻⣿⣿⣿⢹⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⣿⣿⣿⣿⣴⣶⣦⣬⣿⣿⣻⣿⣻⣟⢳⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢿⣿⣿⣿⢸⣿⣿⣿⣿⣿⠇⠀⢸⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠛⠻⠿⣿⣿⣿⣿⣿⣷⣼⣤⡀
⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣶⣿⣾⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣶⣶⣶⣮⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡙⠀⠀⠀⢄⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠔⣂⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⡇⠀⢀⣀⡈⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⢠⣁⣨⠟⢙⡇⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠐⠐⠻⢉⣹⢠⣾⣭⣽⠟⠱⣦⡀
⠈⠛⠛⠛⢻⡀⠀⠀⠀⠀⠀⠀⠀⣢⣤⠀⠉⠉⠉⠉⣽⢲⡞⠀⢠⡄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠙⢦⣀⡄⣠⡤⠶⠿⣿⡇⠀⠀⠀⠀⢨⣿⣿⡃⠀⢸⡇⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⢠⠀⠀⣧⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠤⣍
⠀⠀⠀⠀⠀⠀⠈⠛⢆⠀⠀⠀⠀⠩⡅⠀⠠⠤⢤⣬⣙⣛⡂⠀⠨⣃⣀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢸⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠔⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡄⠐⠀⢸⠅⠀⠀⠀⠀⠩⣿⡗⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠸⠄⠀⠻⠀⣠⠇⠀⠀⠀⠄⠀⠠⠀⠀⠀⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠌⡆⠀⠀⠀⠀⠩⡽⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⣿⠂⠀⠀⠀⠀⢈⣯⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣂⣦⣀⢤⣄⡀⣲⣀⣐⣦⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢨⡎⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢁⣀⡙⠋⠁
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠘⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢀⠒⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣇
⠀⠀⠀⠀⡚⠋⠀⠘⠁⠰⡄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢘⠀⠀⠀⠀⠂⠀⢠⠀⠀⡀
⠀⠀⠀⠀⠇⠀⠀⠀⠘⠀⢓⠀⠀⠀⠀⠀⠹⢀⠀⢘⡆⠐⠀⠀⠀⠀⠐⠀⢠⠞⠊
⠀⠠⢡⣿⠁⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠁⠀⡈⠉⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⡀⢰⡏⠀⠀⠀⠀⠀⠘⡰⣯⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠰⢀⣿⠁⠀⠀⠀⠀⠀⠀⠓⢻⡃⠀⠀⠀⠀⠀⡰⠘⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢰
⡆⢨⡅⠀⠀⠀⠀⠀⠀⠀⠸⡌⢻⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠀⠇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠐⢀
⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⠀⠀⠘⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⡤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠁⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⠀⢀⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠗⠲⠶⠛⢉⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⠀⠀⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⡠⠞⡿⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠚⠁⢸⢉⠉⠀⢠⠇⠈⢱⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠰⠊⠙⠄⠀⠐⠓⢆⡀⠘⠀⠀⠀⠀⠉⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⡤⣄⡀⠀⠀⢠⠀⠀⠀⠠⠀⠀⠀⡴⡁⠀⠁⠈⠑⠢⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⢻⡆⠔⠀⢃⡈⣯⠉⠀⢸⠀⠀⠀⠀⢀⡀⠀⠂⢌⠢⣄⠀⣀⡤⣤⠀⠄⣀⠀⠀⠚⠓⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡷⣄⣀⣾⠁⠹⡆⠀⠈⠀⠀⠀⠀⠉⠁⠀⠀⠀⠱⢌⡑⢄⠀⠈⢑⡀⠀⠀⠀⠒⠀⣈⣧
⠀⠀⠀⠀⠛⠛⢧⡌⠙⠛⠛⠓⠈⠁⠠⠤⠤⣭⠍⠉⠉⠙⠂⠀⠀⠀⢠⡄⠀⠀⠀⠙⢦⡀⣤⣾⣧⢠⠆⠀⠀⠀⠈⠻
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡄⠉⠁⠈⠛⠻⣄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠒⠛⠘⠒⣂⡀⠒⠒⡒⠒⠒⠛⠃⠂⠀⠀⠂⣀⠀⠀⠠⠴⠣⠀⠀⢀⣀⣇⡀⢀⠀⢀⢀⣈⣓⡀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠅⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠤⠼⠚⠤⠀⠀⠀⠀⠀⠀⠀⠌⠦⠄⠀⠀⠀⠀⠠⠄⠤⠰⠤⠤⠤⠄⠠⠀⠠⠤⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣠⡀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⣀⠀⣦
⠀⠀⠀⠀⢰⢯⡀⣶⡄⠀⠀⢰⡆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡌⣿⠇⠀⠀⢸⡏⣷⠀⢸⡇⠀⠐⣿⠀⣿
⠀⠀⠠⠤⣼⢼⢿⣿⡇⠀⠀⢸⡇⠀⢹⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⡇⢴⡇⠂⠀⣷⣧⣼⣧⣤⣤⡾⣷⣿⠤⠾⣷⣶⣾⣷⣟⣿
⠀⠀⠐⠒⠒⠲⢲⣿⣇⣠⣄⣸⣧⣀⢺⣄⣠⣀⣿⠀⣆⣀⣀⣀⣸⣷⣗⣷⢲⢰⣿⣿⣶⣾⣷⣾⣶⣿⣿⣉⣉⣏⣉⣹⣉⣉⣿
⠀⠀⢈⣋⣛⣙⣹⣿⣿⣿⡗⣾⣿⣿⣿⣿⣿⣿⣿⢭⣿⣿⠈⠈⢾⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣷⣿⣿⠤⣤⣧⣭⣼⣥⣥⣿
⠀⠀⢨⣭⣭⣭⣼⣿⣿⣿⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣾⣦⣤⣿
⠀⠀⣰⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡠⠤⠤⠤⠤⠤⠠⠤⠤⠄⠢⠀⠀⠀⠀⠀⠠⡆⠂⠀⠒⠒⠒⠀⠀⠄⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⢄⠀⠘⡀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⠦⠔⣦⠀⠀⢰⠔⠒⠾⣄⠀⡊⠀⠀⡽⠐⠢⢀
⠀⠀⢀⠠⠐⠁⠡⠀⠀⠄⠀⠄⠰⢐⢸⠀⠀⠀⠸⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠚⠀⠀⠻⣄⠀⠀⠀⠘⠀⠀⠂⠀⠀⠄⠀⢠⠈⠢⡼⠁⠀⢀⡞⠉⠢⡀
⠀⠀⢣⠀⠀⠀⠀⢃⠀⠀⠀⠈⠡⣘⠾⡁⠋⠀⠡⢉⠀⢡⡤⠤⠤⠤⣤⣤⣶⣖⣾⢣⡈⠉⠋⠁⣸⠁⠀⠀⠉⠀⠀⠉⠀⠀⠃⠀⢸⠀⠠⠉⠐⡤⢞⡀⠀⠠⠁
⠀⠀⠀⠡⠀⠀⠀⠈⢆⠀⠀⠐⢒⠯⢟⡹⢖⠒⠒⡞⠒⢺⠿⠿⠿⣿⣟⡟⢛⣛⣛⠒⠙⢦⠀⠐⡗⠒⠒⠒⠒⠀⠀⠒⠒⠒⠃⠀⠸⠠⠁⠀⡰⠁⠀⠀⠉
⠀⠀⠀⠀⠑⡀⠀⠀⠘⠃⠀⠀⠈⠀⢠⠃⠨⠀⠀⢠⡀⠘⡋⠉⠉⠉⠉⠉⠉⢉⠝⠀⠀⠸⡆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡐
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⡘⠀⡈⢡⠀⢇⠀⢀⣣⡀⠀⠀⠉⠐⠀⠊⠀⠀⠀⠀⠀⠀⢧⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⡐
⠀⠀⠀⠀⠀⠀⠈⢢⣰⡄⠀⢀⠀⢠⠀⠀⠆⠈⠆⢸⡥⣷⠀⠀⠀⠰⠶⢶⠀⠀⠀⠀⠀⠀⠸⡄⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢘⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠈⠢⡄⠀⠀⠈⠄⠠⠀⠁⠘⡄⠀⠀⠰⠒⠚⠀⠀⠀⠀⠀⠀⠀⣧⠀⠸⡆⠀⠀⠀⠀⠀⠀⡔⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠄⠀⡆⡀⠘⠀⠀⠀⢘⠀⠀⠇⠀⠀⠀⠀⠀⠀⠸⡀⠀⢷⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠊⠒⠐⠒⠀⠃⠃⠐⠒⠒⠀⠚⠒⠃⠂⠀⠀⠀⠀⠀⠀⠀⠓⠂⠘⠂⠒⠒⠀⠚⠀⠒⠂⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠊⠋⠀⠀⠀⠈⠋⠂⠌⠅⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠁⠀⠉⠉⠉⠉⠉⠉⠉⡩⠋⠁⠀⠀⠀⠇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠐⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠲⠤⠤⠤⠤⣄⣀⣀⣀⣀⣤⠤⠤⠤⠴⠒⠒⠐⠚⠉⠉

⡀⣀⣀⢀⡀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⢿⢟⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣟⣿⣿⣛⣿⣟⣛⣿

⠀⠀⢤⡀⠀⢀⡀⠀⠀⢠⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤
⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠒⠂⠒⠂⠀⡛⠓⠀⠤⠀⣹⣅⠀⠀⠀⠀⠠⠁⠀⠀⠐⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⢀
⠀⠀⣄⠀⠘⠀⠀⠀⠀⠐⠀⠀⠀⠈⠉⢀⡄⠀⠀⠀⠀⠈⠉⠀⠐⢰⣥⠔⠄⠀⠀⠀⠀⠀⣠⡀⠀⠀⢄
⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠲⠀⠤⡀⠠⢀⣀⠀⠀⠀⠢⡀
⠀⠈⠀⠈⠁⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⢀⠀⠢⠇⠀⠀⠀⠃⠀⠃⢀⠀⠀⠠⢂⢀⠛⠤⠱⠂⠈⠀⠂⠀⠌
⠀⠀⠀⠸⠀⠀⡴⠀⠀⠀⠤⠄⠀⠀⠠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠄⠀⠀⠈⠑⠂⠀⠀⡇⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⡤⢂⠀⠀⠀⠀⠆⠀⡠⢀⠀⠐⠀⠒⠀⠀⠀⠀⣀⣠⣆⠐⠒⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠁⠀⠉⠰⠀⠀⠀⠤⠄⠀⠀⠀⠀⡀⠒⢀⡀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠸
⠀⢀⠀⠀⢀⠀⠀⠀⠻⠀⠀⠸⠂⡐⠀⢠⠀⠆⠐⠤⠄⠐⠒⠀⠀⠰⡖⢀⣃⣀⣀⣀⣀⣀⡴⠁⠀⠀⠀⠀⢠⠄
⠀⠀⢀⠀⠈⠀⢀⠤⠠⠀⠀⠂⠀⠅⠀⠄⠀⠀⠀⠄⠠⠄⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠁⠀⠀⢘
⠀⠐⠀⠈⡉⠀⢄⡀⠀⠀⠀⢤⠀⠀⠀⠀⡀⡀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠃⠀⠀⠀⠀⠀⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⡄⠀⠀⠀⡄⠈⢳⠄⠀⡠⠀⠀⣠⠀⢀⠀⠀⠀⠊⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⣛⠢⠀⠀⠀⡄⠀⠀⠀⡇⠀⠀⡇⠀⠰
⠀⠈⠀⠉⠁⠀⠣⢄⠀⠀⠀⠈⠀⠣⠀⠀⠀⠀⠉⠀⠀⠐⢰⠀⠀⠀⠀⠃⠀⠀⠃⠂⠠⠒⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠸⠷⠰⢦⣬⣿⣯⣦⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡄⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠥⢀⠀⢰⡿⠻⠺⣿⠛⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣶⣶⣿⢡⣤⡄⣬⣟⢧⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⣷⡶⣶⣶⡄⠛⣟⣛⣿⣿⣿⣿⡟⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⣿⣿⣿⢸⣿⡇⣿⡏⠀⠱⣜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⢸⡇⣿⡆⣿⠀⣫⡉⠛⠛⢛⡛⠓⠃⠀⠀⠀⠀⠀⢸⣶⡖⢀⣠⡤⠴⣸⠟⠛⠛⠓⠘⠇⠀⠀⠈⣖⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠚⠐⠹⢿⠇⠈⠛⠁⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠰⠿⣿⣇⠜⠠⣴⡟⢹⣇⡛⣧⠾⠛⠻⡶⢶⣾⡋
⠀⠀⠀⠀⠀⠀⣀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡇⠙⢧⣶⣾⡿⢿⣻⣯⣥⣭⡆⠌⣷⢰⡀⢹⣽⠄
⠀⠀⠀⠀⠀⠀⣿⡄⠉⣉⣒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⠛⠁⠀⠋⠉⢿⣧⣼⠏⠀⠀⠙⠷⠌⠡⠂
⠀⠀⠀⠀⠀⠀⣿⣇⡸⢿⡉⠙⠒⠛⠛⠛⠓⢄
⠀⠀⠀⠀⠀⠀⣿⠇⠀⠘⠋⠛⠓⠲⠦⣤⣸⣇⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣆
⠀⠀⠀⠀⠀⣸⣿⡗⠁⠉⠀⠀⠀⠀⠀⠈⢿⣷⡆⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣽⠛⠛⠛⢧⡀⠀⠒⢄
⠀⠀⠀⠀⠀⣿⢹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠻⣶⣿⣿⣿⣷⣶⣦⡆⠀⠀⠀⠀⣤⣭⡍⣈⣉⣀⣬⣯⡄⠀⢴
⠀⠀⠀⠀⠀⠚⣛⡿⢠⡀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣿⣿⣟⣀⣐⣉⣁⠀⠀⣆⣽⡿⠿⢿⣿⢋⡍⢻⠿⠃
⠀⠀⠀⠀⢀⣿⠉⣰⠏⡀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⢿⡿⡿⢦⠀⠀⠲⠾⠤⣄⣉⣿⣿⣯⡌⢰⣶⣶⣶⣿⣿⣿⣿⡿⠆
⠀⠀⠀⢀⣙⣹⡀⠀⠀⠠⠰⠀⠀⠸⣿⣿⣿⣿⠿⢿⣿⣯⣧⣧⣴⠷⠞⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠘⠛⠛⠉⠉⠁
⠀⠀⠀⠸⢿⣿⣿⡄⡀⠀⣁⡀⠴⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣿⣽⣯⣯⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿

⠤⠀⠀⠼⠀⠀⠀⡀⠠⠀⠿⠀⠀⠄⡀⠀⠀⠧⠀⠀⠤⡄⠀⠠⠧⠀⠀⢀⠀⠀⠠⠆⠀⠀⢀⠀⠀⠸⠄⠀⠀⢤⠀⠀⠸⠤
⣄⠀⠀⠀⡀⠀⠀⣇⣀⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⠒⠒⠒⠚⠒⠒⠒⡖⠀⠀⠛⠒⠒⠒⡖⠒⠒⠓⠒⠒⠒⡖⠒⠒⠓⠒⠒⢲⠒⠒⠒⠓⠒⠒⢲⠂⠂⠘⠓⠒⠒⢲⠒⠒⠚⠒⠒
⠤⠤⠤⡠⠤⠤⠤⠧⠤⢤⡠⠤⠤⠤⠧⠤⢄⠤⠤⠤⠤⠧⠤⢄⠤⠤⠤⠼⠤⠤⠄⠤⠤⠤⠼⠤⠤⣄⠤⠤⠤⠼⠤⠤⣄⠤⠤
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸
⡎⠉⠉⠈⠉⠉⠉⠋⠀⠀⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠙⠁⠉⠉⠉⠉⠉⡏⠁⠀⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉
⠓⠀⠒⡔⠒⠒⠒⠓⠒⠒⡖⠒⠒⠒⠒⠒⢢⠂⠀⠂⠘⠒⠒⢢⠒⠐⠒⠚⠒⠒⢢⠒⠒⠒⠓⠒⠒⢶⠒⠀⠒⠓⠒⠒⢶⠒⠒
⢀⣀⣀⢇⣀⣀⣀⣀⣀⣀⢇⣀⣀⣀⣀⣀⡸⢄⣀⣀⡀⣀⣀⡸⣀⣀⣀⣀⣀⣀⡸⣀⣀⣀⣀⣀⣀⡸⣀⣀⣀⣀⣀⣀⡸⣀⣀
⡇⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠉⠀⠉⡌⠉⠀⠉⠉⠉⠙⡏⠉⠉⠉⠉⠉⢱⠈⠀⠁⠈⠉⠉⢱⠁⠀⠀⠉⠉⠉⢡⠁⠀⠉⠉⠉⠉⢻⠈⠀⠀⠉⠉⠉⡶⠉⠉
⠠⠤⠤⠳⠤⠤⠤⡤⠠⠤⠧⠤⠤⢤⠤⠤⠼⠤⠤⠤⢤⠤⠤⠼⠤⠤⠤⢤⠤⠠⠼⠤⠤⠤⡤⠄⠀⠼⠤⠤⠤⡤⠤⠤⠿⠤⠤
⣇⣀⣀⢀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣸⣀⣀⡀⣀⢀⡀⣸⣀⣀⡀⣀⣀⣀⣸⣀⣀⡀⣀⣀⣀⣇⣀⣀⡀⡀⠀⠀⣇⣀⣀⣀⣀⣀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢟
⡄⠀⠀⠁⠀⠀⠐⡆⠀⠀⠁⠀⠀⢲⠂⠀⠈⠁⠀⠀⢲⠂⠀⠈⠀⠀⠀⢲⠀⠀⠈⠀⠀⠀⡖⠀⠀⠈⠀⠀⠐⡖⠀⠀⠉
⠇⠀⢠⠀⠀⠀⠐⠃⠄⢤⠄⠀⠀⠸⠀⠀⠄⠀⠀⠀⠘⠀⠀⣤⠀⠀⠀⠘⠠⠄⠀⠀⠀⠠⠿⠤⠤⡤⠤⠤⠤⠷⠤⠤⡤⠤⠤
⣀⣀⣸⣄⣀⣀⣀⡀⢀⣸⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⢀⣀⣭⣀⣀⣀⣀⣀⣀⣥⣀⣀⣀⣀⣀⣀⣇⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⡇
⠁⠀⢰⠂⠀⠀⠈⠀⠀⢱⠀⠀⠀⠈⠀⠀⢂⠀⠀⠀⠉⠀⠀⣶⠀⠀⠀⠁⠀⠀⡂⠀⠀⠀⠁⠀⠀⡆⠀⠀⠈⠁⠀⠀⡆
⠄⠀⠘⠂⠀⠀⢠⠀⠀⠘⠂⠀⠀⢤⠀⠀⠚⠀⠀⠀⣤⠀⠀⠛⠀⠀⠀⡄⠀⠀⠓⠀⠀⠠⡄⠀⠀⠓⠀⠀⠠⡄⠀⠀⠃
⠄⡀⢀⡀⠀⠀⠸⠀⠀⣀⡀⠀⠀⠸⠀⠀⣀⢀⣀⣀⠧⠀⠀⣀⠀⠀⠀⠇⠀⢀⣀⠀⠀⡀⠇⠀⢀⣀⣀⣀⣠⠇⠀⢀⡀
⠀⠀⢸⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠁⠀⠀⠀⠀⠈⢹⠉⠉⠁⠈⠉⠉⢹⠀⠈⠀⠀⠀⠀⡟⠀⠀⠀⠀⠉⠀⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠙⡇⠈⠈
⠒⠒⠂⢰⠀⠀⠘⠀⠀⠀⡖⠀⠀⠘⠀⠀⠐⡆⠒⠒⠃⠐⠀⠐⡆⠀⠀⠃⠀⠀⠐⠂⠀⠐⠃⠀⠀⢲⠒⠒⠒⠃⠀⠀⢰⠂

⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⣶⡶⠶⠶⠶⠶⠾⠿⠿⠏⠉⠉⠩⠑⣒⣒⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⡜⠁⣠⣶⣭⡶⠖⠚⠛⠉⠉⠉⠉⠁⠀⠀⠉⠒⠒⠒⣤⣮⣽⠿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⣿⣶⣾⣯⣤⣭⣭⣉⣉⣑⣒⣒⣒⣒⣒⠒⠒⠒⠋⠙⠯⣭⣶⣶⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣷⣍⣙⠛⠻⠿⢷⣧⣤⣤⣤⣄⠀⢹⣿⠀⠤⠤⠄⢴⣶⢾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣧⣙⣿⣷⠀⣶⡶⠶⠶⢶⣶⣶⣶⣾⣤⣤⡶⠆⠀⠀⠀⠐⢊⣭⣤⣼⡇
⠀⠀⠀⠀⠀⠀⢣⣀⠩⠿⣟⣛⣺⡿⠿⠿⠿⠷⠶⠿⠿⠿⠿⠿⠗⠒⣒⣋⣉⠛⣻⣾⠁
⠀⠀⠀⠀⠀⠀⣠⡧⠭⢶⡶⣦⣤⣬⣭⣭⣭⣉⣉⣉⣩⣩⣭⣭⣭⣭⡤⠶⢶⢿⣿⡟⡄
⠀⠀⠀⠀⢀⣞⣵⠛⠓⡬⠋⠘⠛⠭⠭⠽⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢇⠘⡟⡷⡀
⠀⠀⠀⠀⢸⣀⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠁⢣
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣦⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠈⠣⣝⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢭⣛⡓⠶⠶⠦⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⣀⣠⡤⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠲⠖⠒⠒⠒⠚⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠤⠶⠶⡶⠶⢦⣤⣤⢤⢤⣿⡧⠤⢤⣤⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⡇⠀⠀⠘⠋⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠤⡄⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣀⡏⢢⡜⠂⢳⠃⠸⡄⠀⢸⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⠏⣄⠿⣬⡌⢢⣾⡆⢡⡀⡱⣀⠀⡁⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠒⠻⠿⢯⣄⢻⣻⡀⢫⠽⣤⣷⣻⡿⠒⠚⠋⠀⣽⡃
⠀⠀⠀⠀⡀⣀⠀⣶⡄⠀⠈⢲⠗⢺⣛⠛⣹⢷⠲⠀⠀⠀⠀⠀⠺⡗⣒⣒⠀⠀⠀⣠⡄
⠀⣤⣶⠀⢤⠂⠀⠀⠁⢐⠐⠀⠀⡿⠬⠀⠛⠛⠃⣸⡅⣀⣤⠶⡿⠿⣯⣭⣤⣤⣤⣭⣭⠤⠶⠶⠶⠤⠤⠤⠤
⢠⠚⠁⣀⣨⠑⠀⠀⣿⡷⠈⠀⠀⠀⡤⢲⣤⣷⡏⡐⡶⢖⣿⠐⠒⠨⠷⠋⠙⢃⡽⢑⡺⠃
⢘⠛⠓⠺⠊⠀⠀⠀⠉⠃⠀⢀⣠⣤⣧⣈⣧⣴⡿⠶⠿⠛⠋⠀⡀⠀⠀⠀⠀⠸⠗⠈⠉
⠺⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡲⣮⣴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⢸⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣤⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣄⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠁⠹⡉⠉⠉⠉⠛⠛⢳⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢂⠀⠳⠀⠀⠈⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⡄⠃⠀⠀⠀⠀⠤⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⢆⠀⠠⠀⠀⠀⠠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⢸⣿⠀⠀⠁⠠⢥⣀⣤⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠈⠛⠍⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣖⣲⣿⠁⢸⣿⣿⡀⠀⠀⠀⣠⡿⠋⣿⣶⣶⣶⡄⠀⠀⠀⠀⣠⡾⠀⠀⣄⠀⠀⠙⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⣼⣿⣍⠛⠳⠒⣋⡉⡇⠀⣿⣿⣿⣿⣷⠀⠀⢀⣴⣿⠇⠀⠀⢸⣅⠰⠧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠀⣿⣿⠟⠻⠿⠿⠿⢧⡇⠀⣿⣿⣿⣿⣿⣇⣴⡿⠋⠁⠀⠀⢀⣿⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣤⣿⡏⠉⠉⠉⠉⠉⠙⣷⣠⣿⢹⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⣸⡿⡄⣠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠿⠿⠷⠾⠿⠿⠿⠄⡀⠀⠀⠀⠀⠀⠻⠿⠇⢸⣿⣽⣿⠟⠁⠉⠳⢄⡀⢠⡿
⠀⠀⠀⣼⠶⠶⠶⠦⠤⠤⠤⡤⡶⠶⠶⣿⠁⠀⠀⠀⠀⠀⠀⠀⣤⠷⠶⢶⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠀⠀⠀⠀⠛⠛⠁
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⡌⠀⠀⠀⠀⠀⡆⠀⠀⡟⠀⠀⣼⡇⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣿⣄⣀⣀⣀⣀⣀⣰⣇⡇⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⣿⠇⠀⠀⠀⠀⠀⡏⠙⠦⣄⡀⢀⠌
⠀⠀⠀⣿⣿⠯⠭⠿⣿⣭⣭⣤⣥⣤⣭⣍⣉⣉⣉⣩⣭⣭⣿⣿⣿⣿⣿⣿⣀⣀⡀⠀⠀⠀⣷⠀⠀⠈⠉⠁
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢻⡇⠀⢹⡇
⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⢸⠿⠻⠿⠿⠿⠒⢲⣖⣐⡶⠖⠐⠶⠞⠛⠓⠶⠖⠶⠶⠦⠤⢤⣤⠤⣤⣤⣼⣇⠀⣸⣇
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⠀⠈⠈⠀⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⣿⣯⣭⡛⠛⠛⠛⠛⠻⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⠤⠤⠤⠿⢧⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣿
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠁⠀⠉⠉⠉⠉⠉⠉⠒⠒⠒⠒⢲⡶⠖⠲⠶⠾⠿⠿⠶⠶⠶⢶⣶⣤⡄
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⠶⠶⠶⠶⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠠⠠⠐⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠂⠀⠀⠆⠆⠐⠀⠂

⡀⠀⠀⡀⣀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⡀⡀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⢀⢀⠀⠀⢀⡀⠀⠀⢀⣀⠀⠀⢀⢀⠀⡀⠀⢀⣀⠀⢀

⠀⠀⢀⡀⡀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⢀⣀⣀⠀⠀⠀⢀⡀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠄⠤⠀⠀⠀⠠⠄⠀⠀⠀⠄⠠⠀⠀⠠⠀⠀⠀⠀⠤⠀⠀⠀⠠⠄⠀⠀⠀⠤⠀⠀⠀⠀⠄⠀⠀⠀⠤⠀⠀⠀⠠⠀⠀⠀⠀⠤

⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠠⠄⠀⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠲⠀⠀⠀⠐⠂⠀⠀⠀⠆⠀⠀⠀⠐⠂⠀⠀⠀⠶⠀⠀⠀⠐⠂⠀⠀⠀⠶⠀⠀⠀⠐⠂⠀⠀⠀⠲⠀⠀⠀⠐⠂

⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒

⠀⠀⠁⠀⠉⠈⠀⠀⠈⠁⠀⠀⠀⠉⠈⠈⠀⠘⠀⠈⠁⠀⠉⠀⠀⠀⠘⠃⠀⠀⠁⠉⠈⠁⠁⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠈⠀⠁⠉⠀⠉

⠁⠈⠀⠀⠉⠈⠀⠁⠈⠁⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀⠈⠀⠉⠈⠉⠉⠈⠁⠁⠉⠁⠉⠈⠀⠈⠈⠁⠉⠉⠁⠉⠀⠁⠈⠈⠁⠁⠁⠀⠉⠈⠈

⠁⠁⠉⠉⠉⠉⠈⠉⠈⠉⠉⠉⠉⠉⠀⠀⠈⠈⠁⠁⠁⠁⠉⠈⠉⠉⠈⠉⠁⠀⠁⠉⠈⠉⠉⠉⠁⠁⠉⠉⠉⠈⠁⠈⠈⠁⠁⠁⠀⠉⠀⠈⠈
⡀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠿⠿⡿⠻⠿⢿⡟⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷

⠀⢀
⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀
⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠆⠀⠀⢠⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⣀⡀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⣄⠀⠀⢉⣁⡁⠀⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢠⡀
⠀⠀⠀⠀⡤⠤⠤⠭⠭⠤⠤⠤⠀⠀⠀⠀⠰⠤⠄⠤⠄⢙⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠒⠙⠂⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠒⣦⣤⡖⠉⠁⠀⠀⠈⣤⢀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⢿⣇⡿⡇⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⣀⠀⣼⠁⠀⠂⢰⠀⣀
⠀⠀⠀⠀⠀⠠⠤⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⣦⣤⣼⡿⠾⠇⠀⠀⠀⠀⠠⠀⠀⠀⠀⣁⠀⢰⡦⠻⣿⣿⣦⡀⢀⠐⠀⠋
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠒⠀⠀⠂⠐⠀⠀⠀⠒⠒⠂⠀⠉⠉⠙⠃⠀⠒⠛⠒⠒⠒⠒⠀⠀⠀⠀⠈⠉⠉⠀⠀⠉⠉⠛⠁⠂⠘⠓
⠶⠶⠖⠒⠒⠀⠒⠒⠒⠒⠒⠒⠛⠙⠛⠙⠓⠒⠒⠒⠒⠒⠒⠀⡀⠀⠀⠤⠄⠀⠀⠈⠍⠉⠉⠉⠉⠀⠠⠀⠄⠤⠤⠤⠤⠤⠶⠶⠶⠶⠶⠶⣶⠶⠖⠲⠒
⣄⠀⠀⠀⠀⠀⢀⡀⠀⣄⠀⢀⠀⠐⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⡧⠀⠀⠀⣤⣤⣄⣦⣰⣉⣀⣉⣂⣠⣖⣠⣥⣤⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠆⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⡀⠀⢀⣀⣀⣀⡀⠈⠛⠿⠿⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣫⢠⣌⡽⢶⠁⣉⣀⠀⡈⠉⠉⠉⠉⠩⠭⠭⠭⠥⠤⠤⠤⠤⢤⣀
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠃⡘⢀⠁⠀⠀⠀⢠⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠏⠈⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⡆⠀⠀⠀⣤⣸⠀⡇⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⡄⢀⠷⠀⠀⠀⠉⢸⠃⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢄⢡⡸⡆⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⣦⠠⠇⢓⡾⢃⣅⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠠⠀⠀⠸⠃⠴⠉⠦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠐⠂⠉⠀⠀⠀⠀⠖⠀⠛⠙⠂⠐⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣅⠀⠀⠀⢹⠆⣠⠀⢀⡀⢀⠀⠀⠀⣠⡄⠀⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠏
⢰⣤⣤⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠤⠤⠤⢤⠤⣄⠀⠼⠶⠶⠶⠶⠀⠀⠸⠆⣼⠃⠈⠁⠘⠛⠛⠛⠛⠒⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠰⠶⠦⠶⠶⡆⠀⡼⠟⠟⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⠄⢤⠤⣄⣠⡆⢘⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠩⠈⠁⠀⠺

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠴


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⡠
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠶⠀⠖⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠠
⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂
⣀⠈⢠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐
⠀⢄⠁⠀⢸⠇⠀⠀⠀⢠⣀⠤⠄⠀⠓
⠀⠈⠳⣄⡀⠢⣌⡐⠂⣿⡇⠀⣀⣀⢈⠁⠀⠀⠀⠈⢀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠉⠑⠒⠮⠭⠭⠿⣋⣁⡉⠉⠀⠀⠀⠀⠀⢃⣀⠈⣻⣶⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⠉⠁⠉⠓⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠄⠀⠀⠀⠰⠄⠀⠀⠀⡐⡀⣖⡉⡀⠀⠀⠀⠀⢀⠄⠂⡭⠉⠀⡄⠀⠀⢢
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⡀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠥⠀⠉⠙⠂⠀⠀⠃⠀⠀⣅⠀⠀⠛⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠤⠄⠤⠀⠀⠀⠀⠀⠀⡈⠁⠀⢀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡄⠈⠁⠂⠀⠀⡂
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⠤⠤⠠⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣔⠁⠀⡐⠉⠢⠠
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡄⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢙⡀⠀⠅⢀
⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠠⠶⠮⣤⣉⣸⣧⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠸⠥⠙⠻⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⡀⢲⡔⠀⢄⣀⢴⣀⠉⠉⣭⠥⠬⠭⠥⠤⡆⠀⠒⠀⠀⠀⠘⡇
⠀⠀⢘⡁⢀⢀⣀⣀⣄⠼⠆⠀⠐⠀⠀⠒⠆⠀⠀⠂⠐⠒⠂⠀⠒⠀⠀⠷⠖⠀⡀
⠀⠀⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠂⠀⠀⠉⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⣀⡀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡍⠀⠈⠂⡄⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠒⠁⠀⠑⠒⠋
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢢⡤⢲⠀⠀⠀⣠⠀⡴⠐⢤
⠀⠀⢀⠀⠀⣀⡀⡀⢀⢀⣀⡀⢠⡄⠀⠀⠀⠀⠀⢀⠻⡆⠀⠀⠀⣠⠠⢥⡴⠤⡄⠀⠀⠀⠈⡀⠀⠀⠀⢻⠀⠀⠓⠎⣁⣀⣀⠁⠶⠃⠀⢸⠇
⠀⣀⢨⠂⠊⠔⠌⠂⠑⢐⠂⠀⠀⠠⠄⠀⠀⠀⠶⠦⠠⠄⠀⠀⠀⠸⠀⢐⠂⠀⠧⠀⠀⠀⠸⠇⠀⠀⠀⠈⠳⠖⠂⠀⠹⠷⠞⠀⠀⠒⠶⠋
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠔

⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡷⠤⠤⠤⢤⡤⠤⠤⠤⠤⠼⠦⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠾⠦⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤
⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀
⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡷⠒⠒⠒⢲⠖⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⢶⠖⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⢶⠖⠒⠒⠒⠒⠚⠒⠒⠒⠒⠒⢶⠖⠒⠒⠒
⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣧⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡟⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛
⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣧⣤⣤⢤⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡟⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⠉⠉⠉⠉
⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣷⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠐⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⠆⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠘⠀⠀⠐⠖⠀⠀⠘⠀⠀⠀⠴⠀⠀⠂⠀⠀⠰⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⣀⠀⠀⢠⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡄⠀⠀⢀⡀⠀⠀⠇⠀⠀⣀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠋⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠈⠀⠀⠈⠋⠀⠀⠈⠀⠀⠀⡛⠀⠀⠁⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠤⠀⠀⠰⠂⠀⠀⠀⡄⠀⠀⠐⠀⠀⠀⠤⠄⠀⠀⠂⠀⠀⢠⠄⠀⠀⠃⠀⠀⠤⠀⠀⠐
⠀⠀⢀⡀⣀⣀⠀⠀⠀⠀⣀⠀⣀⣀⡀⠀⠀⣀⠀⢀⡀⡀⠀⠀⢀⠀⠀⠀⢠⣀⠀⣀⣀⡀⢀⢸⠀⠀⠀⣀⡀⣀⡀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠒⠀⠀⠀⠁⠀⠀⠀⠒⠀⠀⠈⠁⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠒⠂⠀⠀⠁⠀⠀⢰⠂⠀⠀⠁⠀⠀⠒⠀⠀⠈⠀⠀⠐
⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⡤⠀⠀⠀⠅⠀⠀⢠⠀⠀⠀⠰⠀⠀⠤⡤⠀⠀⠸⠀⠀⠀⡤⠀⠀⠄⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠘⠀⠀⢠⡄⠀⠈⠀⠀⠀⠀⠰⠛⠁⠀⢀⡀⠀⢰⠉⠙⢿⡧⠀⠀⠄⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠃⠀⢸⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠳⣄⠬⠀⠀⠂⠠⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠠⢀⠀⠀⠀⠀⠀⠠⠂⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠠⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡧⠁⠀⠀⠀⠀⢀⠀⠀⠀⠘⠀⠐⠀⠀⠁⠈⠉⢂⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠈⠀⠀⠀⠀⠠⠀⠊⣀⠀⢠⣶⡄⠀⠀⠀⠀⢀⡠⡀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⢄⠀⠀⠀⠻⠆⠀⠀⠀⠐⠉⠀⠁⠀⠀⠀⠂
⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡄⠀⠀⢰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠂⠄⠂⠀⢀⠀⠄⠠⠄⣀⠀⠀⠀⠈⠀⢀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠊
⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠈⠁⢀⡀
⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠠⠟⠀⠀⠀⠀⠐
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⢠⠀⢀⡟⠁⠀⢠⡀⠀⠀⠀⠀⠀⡀⠘
⠀⢻⣀⣠⣄⠀⠤⠆⠀⠀⠀⠎⠀⠀⠀⣐⡤⠌⠀⠀⡇⠀⠈⠀⠀⠂⠀⠐⠄⠀⠀⠐⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⢎⠀⠀⠀⠀⡠⠂⠀⠀⠐⠀⠁⠀⠀⠀⢰⠁⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠴⣄⣄⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⢤⡄
⠀⠀⠠⠀⠠⡀⠀⠉⠀⠀⠀⠀⣰⡟⠁⠀⣠⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣼⠏⠀⠴⢞⣲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠘⠄⣀⡨⠃⠀⠰⠊⠲⢤⠀⠀⠀⠐⠀⢠⡄⠀⢀⠀⠀⠈⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠁⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⣀⣀⡀⣿⣦⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢹⣿⣿⡏⠉⠉⠑⠚⠒⠒⠒⠒⢦⡤⠤⠤⠬⠤⠄⣠⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠂⠀⠈⠀⠀⢻⡃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣶⠀⢀⠀⡔⠀⠀⠀⠐⠀⠀⠰⣴⣶⢶⠀⠈⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢤⣶⡆⠀⠀⠀⠂⠀⠰⠀⠰⣿⠂⣛⡄⡛⠀⠀⠀⠀⠀⠀⢀⣺⣿⣼⠀⠀⠀⠀⠀⢀⣀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅
⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⢨⣽⣉⣭⣉⣍⠀⠀⠀⠀⢠⠀⢸⣌⣷⣸⠀⠀⠀⠀⠠⢸⢿⢴⠟⣺⢀⡀⠀⠀⠀⡀⢀⡀⢸⢇⣶⣂⡀
⠀⣤⡤⠨⡀⠛⣿⡆⠀⠀⠀⠀⠂⠸⠀⢰⣿⣯⡷⢴⣷⢤⣤⣜⠀⣰⢐⠘⠸⣿⣿⠀⠀⠀⠀⠐⢸⣿⣽⡭⣯⢽⡇⣀⣄⠀⣷⡼⠷⣇⢸⣿⠇⠊⠃
⠀⠉⠁⠀⠈⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠈⠉⠈⠉⠉⠀⠀⠈⠈⠀⠉⠉⠀⠀⠀⠀⠀⠈⠉⠈⠁⠉⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠘⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⡠⠔⠊⠀⠂⢁⢀⠀⠠⠀⠀⠀⠀⠄⡕⠀⠀⠀⠀⡐⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⢀⠀⠄⠈⠀⠀⠀⠀⠀⡠⠀⠈⡦⠄⠀⠀⠀⠀⠀⠀⠀⡠⠂⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠐⠊⠀⠁⠀⠂⠁⠀⣀⠄⠁⡀⠀⠀⠐⠈⠀⠀⠀⠠⡆⠠⡆⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠈⠉⠁⢠⡠⠐⠆
⠀⠀⠀⠀⠀⠀⠊⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⠄⢀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⠀⠠⠀⠉
⠀⠀⠀⠀⢀⡄⠂⠀⠀⡄⠀⠂⠁⠀⠀⢠⠆⠀⠐⠖⠈⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠒⢃⠀⠀⠀⠘⠀⠀⠀⠀⠐⠃⠀⠘⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆⠀⠙⡂⠀⠠⠀⠀⠀⠀⠴⡄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠴⠀⠀⠀⡴⠄
⠀⠀⠀⠀⠀⠢⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠠⣀⠀⠤⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠁⡀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢀⠉⠀⠨⠭⠍⠁⠉⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠣⡦⠀⠀⠀⠀⠈⠙⠀⠀⢀⡀⠀⠀⠀⠀⠀⠨⠀⠀⠘⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⢀⡀⡀⠀⠀⡅⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠆⢀⠈⠁⢀⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠒⠀⣀⣐⠀⠸⠄⠀⠂⠁⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠰⠄⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠰⠄⠈⠑⠀⠀⠰⠀⠀⠀⢐⠂⠀⠀⠄⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠱⢄⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠄⠉⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠁⠈⠂⠠⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⠖⠀⠀⢀⡔⠀⠀⠀⠠⠈⠇
⠀⠀⠀⠀⠀⠙⠀⠀⠈⠃⠄⣀⠀⡀⠀⠀⠀⠊⣀⠀⠠⡀⠘⠁⠀⢁⠰⢦⠐⠝⠶⠂⠀⠀⢀⡠⢎⠁⠀⠀⠀⠀⠐⠀⠐⠂⠂⠁⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢄⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠉⠁⠺⣄⠀⠀⠀⠀⠀⠕⠀⠀⢄⠨⠁⠀⠀⠠⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠂⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠔⠈⠅
⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⡀⠀⠀⠀⠐⠃⠀⠀⢀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⠊⢀⠀⠀⠀⠀⠐⠠⠂⠐⠈⠢⠀⠀⠀⠀⡀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⠀⠄⠀⣀⢀⣀⣠⠀⠄⠈⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠄⡀⡀⠀⠀⠙⢀⠇⠁⢀⠀⠂⠁⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠈⠀⠀⠀⠀⣇⡀⠂⢐
⠀⠀⠀⠀⠀⢰⠁⠐⠠⠁⠀⠒⠀⠀⠠⠐⠃⠀⠈⠃⢀⣀⠨⠀⠀⠀⡀⠀⠀⠀⠀⠀⡘⠀⠀⡠⠆⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠙⢠⠒⣆⠉⠄⠀⠀⠀⠀⠀⠈⠁⢀⠐⠒⠂⠀⢀⠄⠀⠁⠀⠀⠉⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠘⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡤⣀⣀⡀⣀⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠉⠀⡈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡟⠦⡀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⡟⠀⠱⡄⠀⠩⢹⡀⠉⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠈⠀⠀⠊⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠞⠀⠀⡀⠀⢀⣀⣀⣀⠀⠀⠔⡠⠅⠀⠀⠀⠀⠀⠀⢰⡆⠒⢲⠞⡙⠃⠄⢠⡤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⣰⣥⠀⠀⠀⠀⠁⢀⠋⠁⢀⠄⣊⠴⠈⠀⠀⠀⠉⠁⠀⠀⠀⠘⠀⢀⠟⠀⠓⣀⣀⣾⣆
⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠱⣀⣿⠧⣄⡠⠊⠁⠀⠀⠀⣶⠀⠀⠀⠀⠊⠀⠈⠁⣭⠀⠀⠀⠈⠉⠛⠛⠛⠋⢩⡝⠙⠋
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡠⠜⠉⠁⠀⠀⠀⡆⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀
⠀⠀⠀⠀⠀⠀⠙⠂⠀⡗⠒⠂⠀⠀⠂⠀⠐⢷⣴⠀⠀⠈⠉⠁⠀⠀⠰⣄⠀⠀⠈⠀⠉⠉⠉⠩⡍⡉⠀⠀⠈⠁⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠀⠀⣀⣈⢋⠀⠀⠀⠀⠀⠀⠀⢀⡟⡀⠀⠀⠀⠀⠀⠀⠀⡇⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄⡤⠤⠄⠈⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⡁⣁⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⣀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠉⡭⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠈⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠈⠀⠀⠉⠁⠀⠉⠁⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣿⣝⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠉⠉⢁⣐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠒⢉⣉⡥⠤⢶⣾⣷⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡻⠉⠉⠉⠅⠀⠀⠃⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣉⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠂⠀⠀⢰
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡠⠋
⠀⠠⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠞⢦⣈⣻⡾⢯⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⡤⠤
⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠨⢂⡀⠀⢀⠀⢠⠉⠉⠑⠢⡀⠀⠀⠉⠉⠙⠉⠉⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠊⠀⠂⠡⠀⠀⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠙⡏⠈⠀⠀⠀⠀⠀⠘⡆⠀⠀⠐⠲⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠑⠄⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠹⢄⠀⠀⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢷⡀⠀⢰⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⡎⠀⠀⠈⣂⡜⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⣷⢠⢿⡍⠓⠀⠀⠀⠀⡇⠀⠀⠀⠉⣿⣇⠴⠚⠙⠏⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡠⠟⠁⠀⢷⠀⠀⠀⠀⢀⡃⠀⠀⠀⢰⠃⠹⡄⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢸⠁⠀⠀⢀⡏⠀⠀⠘⠦⡀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣶⣶⣷⣴⣆⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣽⣿⣿⣯⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⡄⠐⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠒⠉⠉⣿⠀⠀⢀⡀⡄⢰⣀⣀⡐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢆⠿⠞⢛⡃⠪⣽⣿⣍⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠱⡶⠲⠤⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠨⢽⣿⠡⣛⣻⡭⠥⠕⢿⣿⢯⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⠙⠛⠓⠲⠄⠀⠀⠀⣽⣿⡔⠻⠶⢒⠓⢪⣿⣿⣟⣿⣿⡷⣿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⣄⣰⠀⢀⡀⠀⣲⣶⡖⠮⢵⠲⠦⢐⣿⣿⣷⣿⣿⣟⣻⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣦⣽⣿⣿⣇⣿⣺⣧⡀⠾⠌⠄⣛⣷⡂⢘⢨⣿⣿⣭⣿⣿⣾⡿⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⣰⠶⣧⢒⣿⡿⠽⢿⠗⣿⢺⣿⡫⠭⠄⡍⠭⣷⡄⠨⠰⣿⣿⡷⣿⣿⣿⣿⡁⠀⠀⠂⠀⠉⠉⠁⠄⡤⠄
⠀⠀⠀⠀⠀⠠⠄⡟⢻⡿⠐⣿⣿⠩⢿⡃⣿⣽⣿⣿⡇⠂⠂⣙⣟⠂⠐⢨⣿⣽⣯⣿⣿⣿⣿⡤⣀⣴⡄⠀⠀⠤⣤⣭⣇⣀
⠀⠀⠀⠀⠀⠀⢤⣴⣿⣇⣀⣿⣟⠙⣛⣯⣿⣻⣯⡯⣭⣥⣥⣤⡯⣥⣬⣼⢿⡿⣿⡟⢽⣿⣿⠽⠭⠿⢫⡆⠀⣗⣖⣗⣿⣾⣆⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠁⠈⠀⠉⠉⠙⠛⠉⠉⠛⠙⠷⣶⠅⢈⠀⠁⠈⠓⠓⠊⠛⠋⠀⠈⠉⠀⠈⠉⠀⠂⠁⠀⠉⠁⠉⠉⠁
⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠉⠀⠀⠀⠀⠈⠛⠉⠉⠉⢹⠉⠀⠀⠈⠁⠈⠉⠉⠉⠉⠉⠙⡏⠙⠁⠀⠉⠁⠀⠈⠁⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠐⠒⠂⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠤⠤⠄⢶⡶⠶⠶⠒⠴⠲⠶⠶⠶⠖⠒⠲⡶⠲⠲⠶⠄⠀⠀⠲⠶⠶⠶⠶⠶⠆⠀⠤⠄⠠⠤⠶⠄⠠⠀⠠⠠⡤⠤⠄⠤⠤⠄⠠⠄⠤
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⣄⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣧⣀⣀⣀⣀⣤⣠⣀⣠⣀⣀⣀⣼⣤⣤⣀⣀⣤⣀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠉⠉⠉⠉⡏⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⢻⠉⠉⠉⠉⠈⠀⠁⠀⠀⠁⠉⠈⡏⠁⠀⠁⠉⠉⠉⠉⠉⠉⠉⠉⢻⠉⠀⠀⠀⠁
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠐⠓⠀⠀⠀⠀⠀⠄⠐⠐⠂⠀⠒⠈⠀⠒⠒⠖⠲⢠⠄⠀⠀⠀⠀⠀⠀⠀⠔⠒⠒⠒⡶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠤⠄⠠⢤⣤⡤⣤⣤⠤⢀⠤⠀⠤⣤⣤⢀⣀⡤⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⣤⣄⣠⣀⣀⣠⣇⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢙⠀⢀⢀⣀⣀
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⠁⠁⠀⠉⠉⠉⠉⠉⠈⠉⠁⠉⡏⠉⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻
⠀⠀⠀⢲⠖⠒⠒⠒⠒⠒⠓⠒⠂⠐⠒⠒⡖⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⢻⠒⠒⠒⠀⠀⠀⠒⠓⠛⠛⠛⠓⡖⠒⠀⠀⠐⠒⠒⠒⠒⠒⠒⠛
⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠤⠄⠀⠘⠢⠤⠤⠶⠶⢤⡴⠦⠤⠤⠤⠤⠷⠦⠤⠤⠤⠴⣶⠶⠦⠤⠤⠤⠾⠶⠦⠤⠤⠤⢤⡤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠤⠴⣤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢃⣀⣀⣀⣀⣀⡀⣀⠀⣀⣀⣀⣻⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⡀⣀⡀⠀⣀⠀⢐⣀⣀⠀⣀⣀
⠀⠈⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡏⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⣇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉
⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⡟⠙⠛⠋⠛⠋⠛⠙⠙⠋⠛⠙⣿⠛⠋⠉⠉⠉⠛⠛⠛⠉⠉⠋⠛⡟⠛⠛⠒⠛⠒⠛⠛⢛⣛⠻⢻⣿⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠠⠀⠀⡠⠐⠐⠀⠀⠀⠰⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⡄⠀⠀⣾⣾⣠⠀⣰⠠⠞⢻⠀⠠⠀⡀⠄
⠟⠻⠛⢻⡟⠒⠒⠒⠒⠒⠗⠒⠒⠒⠺⠛⣿⠲⠶⠂⠀⠒⠊⠂⠲⠶⠶⠶⠶⡶⠦⠤⠤⠤⢤⡯⠥⡤⢤⡤⣤⡦⠤⠠⠀⠀⠀⢀⣤⡤⠤⣠⠠
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠾⣿⣨⣇⡗⢩⡸⠷⣿⣷⢤⣸⣷⣠⣯⣿⣿⠧⣭⢁⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠀⢀⠀⣀⠀⣀⡀⣀⡀⢀⡀⣀⡀⢀⡀⡀⢸⣏⢀⡀⢀⡀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠉⠛⠋⠁⠉⠁⠉⠁⠁⠁⠉⠀⢩⣿⠁⠀⠳⠚⠃⢉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢺⠄⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡯⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠀⠈⠀⠌⠩⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⢐⢐
⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠸⢠⣀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠄⠀⠀⠐⠚⠒
⠀⠀⠀⠀⠐⠀⠂⠂⠀⠀⠀⠀⠐⠚⠃⠚⠛⠛⠛⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⠐⠂⠘⠀⢉
⠀⠀⠀⠀⢈⠀⠁⠁⠀⠀⠀⠀⠀⡏⠉⠉⣻⡉⣹⠀⠀⢐⠀⡀⣷⠖⣶⡀⣠⢰⣿⣤⣀⣀⠐⠀⠁⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⡴⠀⠐⢶⠀⠀⢐⣒⡂⠲⠀⠐⠀⢰⡂⠰⠀⠀⠀⠀⠀⡶⠀⠁⠈
⠀⠀⠀⠀⠀⠀⢰⠐⠀⠂⠒⢀⡀⠛⠐⠀⠚⠀⠀⠘⠛⠀⠀⠀⠘⠀⠈⠁⠈⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠈⠈⠀⠁⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠂

⠀⠀⠀⠀⢀⠴⠂⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠀⠐⢄
⠀⠀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠒⠒
⠀⠀⠀⠀⠉⣉⣽⣿⠿⡏⠁⠀⢠⠊⠉⢲⣀⡾⠋⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣽⣿⡿⠏⠁
⠀⠀⠀⠀⠀⡿⠋⣁⣤⡇⠀⠀⢸⠀⠀⣰⠋⢧⡀⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⢁⣠⡆
⠀⠀⠀⠀⠀⣶⣾⠿⠛⡇⠀⠀⠀⠠⡀⠂⠀⠀⠁⡐⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠛⠁
⠀⠀⠀⠀⠀⠟⣀⣤⣶⡇⠀⠀⠀⠀⠈⢔⢄⠀⠀⠂⠀⠀⠀⠠⡈⠁⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⠇⠀⠆⠀⠐⠀⢠⡤⠴⡆⠀⠀⠀⡟⢁⣤⣶⡇
⠀⠀⠀⠀⠀⣿⠿⠛⢁⡇⠀⠀⠀⠀⠀⠈⡀⢱⠆⠀⠀⠀⠀⠀⠙⢀⣀⣀⡐⠁⠀⠀⠀⠀⠀⡜⠀⡘⠀⠀⠀⠀⢐⠒⠿⠅⠀⠀⠀⣿⡿⠛⢉⣀
⠀⠀⠀⠀⠀⣃⣴⣾⡿⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠹⠀⠀⠀⠀⠀⢰⠃⢀⠃⠀⠀⠀⠀⢒⣛⣭⡅⠀⠀⠀⣏⣤⣶⡿⠇
⠀⠀⠀⠀⠀⡿⠋⣁⣤⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢇⠀⠄⠀⠀⠀⠀⠀⠠⣬⣬⡇⠀⠀⠀⡿⠛⢉⣠⣦
⠀⠀⠀⠀⠀⣶⣾⠿⠛⡇⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠜⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠩⠥⢖⡂⠀⠀⠀⣷⣾⡿⠟⠁
⠀⠀⠀⠀⡀⠋⣁⣤⣾⢇⡀⠀⠀⠀⠀⠀⠈⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣃⠀⠀⠀⠀⠀⠀⠀⣘⢒⣲⠇⠀⠀⣀⠛⢁⣤⣶⠗⡀
⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠠⠠⢀⣀⣀⣀⣀⠉⠉⣉⣙⣉⣁⣈⠭⠂⠀⠀⠀⠀⠀⠂⠉⠭⠅⠀⠀⠠⠠⠤⠤⠤⠤⠂
⠀⠀⠀⠀⠈⠢⠄⠀⠠⠊⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣀⠀⢠⠀⠀⢠⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣦⡯⠐⠁⠀⠀⠀⠒⢸⣧⡆⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠠⣁⡟⣤⠀⠀⠀⠀⠀⠀⢠⠙⣅⡔⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠓⠷⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⣀⡱⠃⠀⡀⠀⠀⠀⠀⠀⠀⣀⢘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢀⡀⠀⠀⠀⠀⠀⠀⡰⠁⢠⣥⣤⡦⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠨⠗⠂⠀⠀⠀⠘⠬⣿⡟⠦⡀⠀⠀⠀⠴⢪⣿⡧⠊⠀⠀⠀⠀⠀⠀⢀⡧⠄⢺⡇⠀⣹⠢⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⣦⢀⠀⠀⣌⣠⡚⣉⠀⠀⠀⠀⠀⢀⣤⠊⠍⢹⣆⡌⠛⠛⠁⠀⣶⠋⠁⢦⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⠀⡿⠏⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠈⠓⠒⠒⠒⠉⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠘⠀⠃⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣛⡃
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣭⡅
⠀⠀⠀⠠⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣤⣤⣠⣀⣀⣇⣀⣄⣄⣠⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡬⡄
⠀⠀⠀⠀⠀⠀⠀⣽⠀⡆⠀⣧⣄⣤⣼⣩⣭⣩⣏⣙⣿⣿⣿⣛⣛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠂
⠀⠀⠀⠀⠀⠀⢀⣚⣀⣥⣤⣧⣤⣬⣼⣭⣭⣽⣟⣛⣿⣿⣿⣛⣛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡃
⠀⠀⠀⠘⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣛⣿⣿⣿⣟⡛⠛⠟⠓⠒⠒⠀⠀⠀⠀⠀⠀⠀⡆⠄⠀⢠⡶⡷⠐⠒⣶⣶⣶⣶⣶⣶
⠀⠀⠀⢘⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣟⣛⣿⣿⣿⣛⠛⠛⠻⠻⠒⠲⠀⠀⠀⡄⣤⣴⣴⣷⣷⡶⣶⣿⣿⣯⢭⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣬⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣛⣿⣿⣿⣟⠻⠻⠿⢿⣿⣿⣿⣿⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣲⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣿⣿⣿⣟⣻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠓⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠀⠀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣉⠙⣉⣛⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⠀⠙⠛⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠓⠀⠐⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠁⠀⠀⠀⠀⠀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡉⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠁⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠃⠀⠤⠤⠤⠄⠸⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣄⡀⠀⠀⠀⠀⡤⠄⠀⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢤⠀⠀⠐⡇⠠⣄⡀⣀⣀⠀⠀⣤⠤⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠠⣇⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⣦⣀⢨⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⡏⠀⡀⠀⠀⠀⠀⠀⡅⠀⠀⢻⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠣⠀⠀⡀⠀⠀⠀⠀⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠲⠄⠀⠀⢀⡀⠀⢀⡀⠀⠠⠤⠦⠄⠠⠤⢀⡀⠤⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠄⠤⣈⠤⠤⠤⠤⠤⠤⠴⠎⣡⠦⠤⠤⠤⠤⠶⠶⠎⡱⠶⠦⠶⠶⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠤⠤⠤⠶⠶⠶⣈⠶⠦⠠⠤⠤⠴⠶⠖⣀⠶⠖⠀⠠⠶⠶⠖⠶⢩⠖⠒⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠂


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣶⠒⠲⠖⠚⠒⠒⠲⠲⡶⠲⠒⠲⠚⠲⠒⠒⠲⡶⠲⠒⠒⠞⠒⠒⠒⠲⡶⠒⠖⠲⠞⠒⠒⠒⠲⡶⠒⠲⠲⠚⠲⠖⠲⠲⡶⠲⠒⠒⠚⠒⠒⠖
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀
⠈⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣴⠶⠶⠶⠾⠶⠶⠶⠶⡶⠶⠶⠶⠾⠶⠶⠶⠶⡶⠶⠶⠶⠾⠶⠶⠶⠶⡶⠶⠶⠶⠾⠶⠶⠶⠶⡶⠶⠶⠶⠾⠶⠶⠶⠶⡶⠶⠶⠶⠾⠶⠶⠶
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⣇
⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⠤⠤⠤⠼⠦⠤⠤⠤⣤⠤⠤⠤⠼⠦⠤⠤⠤⣤⠤⠤⠤⠼⠦⠤⠤⠤⡤⠤⠤⠤⠼⠦⠤⠤⠤⡤⠤⠤⠤⠼⠦⠤⠤⠤⡤⠤⠤⠤⠼⠤⠤⠤
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⢹⠋⠉⠉⠉⠉⠉⠉⠉⢹⠋⠉⠉
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⠤⠤⠤⠼⠦⠤⠤⠤⣤⠤⠤⠤⠼⠤⠤⠤⠤⣤⠤⠤⠤⠼⠤⠤⠤⠤⣤⠤⠤⠤⠼⠤⠤⠤⢤⣤⠤⠤⠤⠼⠤⠤⠤⢤⣤⠤⠤⠤⠼⠤⠤⠤
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠙⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛⠛⠛⠛⠛⠛⢻⠛⠛⠛
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉
⡀⠀⠀⠀⠠⠇⠀⠀⠀⢠⣀⣀⣀⣀⣼⣀⣀⣀⣀⣀⠀⠀⠀⠀⠥⠀⠀⠀⢀⡀⠀⠀⠀⠠⠇⠀⠀⠀⢠⡀⠀⠀⠀⠼⠀⠀⠀⠀⣀⣀⣀⣀⣀⣧⣀⣀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠃⠀⠀⠀⠠⡄⠀⠀⠀⠚⠒⠒⠒⠒⢲⠒⠒⠒⠒⠒⠀⠀⠀⠀⡤⠀⠀⠀⠐⠃⠀⠀⠀⠠⡄⠀⠀⠀⠺⠂⠀⠀⠄⢶⠀⠀⠀⠀⠒⠀⠀⠀⠀⡤
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠉⠉⠉
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣸⣆⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⡤⠤⠤⠤⠼⠧⠤⠄⠄⢤⠤⠤⠤⠤⠼⠤⠤⠤⠤⡤⠄⠤⠀⠴⠷⠤⠤⠤⠤⡤⠠⠄⠤⠰⠧⠤⠤⠠⢤⠤⠤⠤⠤⠼⠤⠤⠤⠤⡤⠤⠤⠤⠄⠿⠤⠤⠤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠓⠒⠒⠒⠒⡖⠀⠂⠀⠘⠃⠀⠀⠀⢲⠂⠀⠀⠀⠛⠀⠀⠀⠀⠖⠂⠐⠂⠐⠓⠐⠀⠀⠐⡆⠀⠀⠀⠘⠁⠉⠉⠉⢳⠚⠁⠛⠘⠛⠀⠀⠀⠀⣶⠐⠀⠒
⣀⣀⣀⣀⣐⡇⠀⠀⢀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⢀⡀⣀⢀⣀⣀⣀⣇⣀⣀⣀
⡏⠈⠉⠉⠉⠉⠉⠉⠉⢹⠁⠀⠀⠀⠈⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠀⠀⠀⠈⡇⠀⠀⠀⠈⠁⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠁
⠧⠤⠤⠤⢤⡤⠤⠤⠤⢼⠄⠀⠀⠀⣠⣀⣀⡀⣀⣤⣀⢠⢠⡄⣤⠀⠀⠀⠠⠧⠤⠄⠠⢤⡤⠤⠄⠤⢼⠄⠠⠀⠀⣤⣀⢄⢠⠠⣤⢠⣤⣤⡄⣤⠠⠠⠤
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡆⠀⠒⠒⠐⠓⠒⠂⠒⢲⠆⠒⠒⠂⠚⠒⠒⠒⠒⠶⠒⠒⠖⠒⠳⠦⠤⠶⠰⡆⠀⠀⠒⠐⠃⠒⠒⠂⢲⠶⠶⠶⠶⠞⠓⠶⠶⠶⡶⠒⠒⠒⠒⠓⠐⠒⠒
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠁⠈⠀⠀⠘⡏⠁⠀⠀⠈⠉⠁⠀⠀⣹⠋⠉⠀⠀⠉⠀⠀⠈⠉⡛⠁⠉⠉⠉⠁⠀⠀⠀⠘⡟⠛⠛⠛⠛⠛⠛⠛⠛⢻⡉⠉⠉⠉⠉⠈⠉⠉⠁⡟⠈⠀⠉
⣀⣀⣀⣀⢠⡅⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⢀⣀⣀⠀⣤⢀⡀⣀⢀⣀⠀⠀⡀⢠⣇⣀⣀⣀⣀⣀⣀⣀⣀⣼⣃⡀⣀⣀⣀⣀⣀⣀⡀⣧⠀⡀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠧⠤⠤⠤⢤⡤⠤⠤⠤⠼⠦⠤⠤⠤⢴⠤⠶⠶⠴⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠧⠤⠤⠤⠤⡤⠤⠤⠤⠼⠤⠤⠤⠤⢤⠤⠤⠤⠤⠶⠤⠤⠤⠤⡤⠤⠤⠤
⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡖⠒⠒⠒⠚⠓⠒⠒⠒⢲⠖⠒⠒⠒⠚⠒⠒⠒⠒⡒⠒⠐⠒⠂⠛⠐⠂⠒⠒⡗⠂⠒⠒⠘⠃⠒⠒⠒⢲⠂⠐⠒⠂⠚⠛⠛⠛⠛⠛⠙⠛⠛⠋⠛⠐⠂⠒
⣇⣀⠀⣀⢀⡀⡀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⡀⠀⠀⠀⢸⡀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⡍⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠁⠀⠀⠉⠀⠀⠁⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠈⠁⠁⠉⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⡤⣦⠤⠤⠼⠧⠤⠄⠠⢤⠤⠤⠤⠤⠼⠤⠤⠤⠤⣤⠤⠤⠤⠤⠧⠀⠀⠄⠠⡤⠀⠠⠄⠤⠧⠤⠤⠤⢤⡤⠤⠤⠤⢼⠄⠀⠠⠤⣤⣤⣤⣤⣤⣦⢤⣤⡤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠓⣶⠒⠒⠲⡖⠒⠒⠒⠚⠒⠒⠒⠒⢲⠒⠒⠒⠒⠓⠒⠒⠒⠒⡖⠒⠒⠒⠒⠓⠒⠒⠒⠲⡖⠒⠒⠒⠚⠓⠒⠒⠒⢲⠒⠒⠒⠒⠛⠒⠒⠒⠒⡖⠒⠒⠒
⠀⣁⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⡏⡍⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣰⠛⠙⠳⡄⠀⠀⣀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢠⠉⡄
⠀⠀⠀⢻⣀⠀⣠⠇⠀⠀⢿⣄⣀⣀⣼⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠸⣀⠇
⠀⠀⠀⠐⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⠏⠀⠀⢰⣄⣀⡀⡀⠉⠙⠃⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠈⣿⠙⣿⠀⠀⠀⠀⠹⣿⣿⡋⠙⢳⣦⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠹⣿⠙⠛⣻⡇⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⢀⣼⣼⡄⠀⠀⠀⢀⣿⡀
⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⠀⠀⢸⡇⢈⣿⠀⠀⠀⣿⠛⣿
⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⣧⣼⡇⠀⠀⠀⣿⣀⣿
⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⣏⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣸⡟⠻⣧⠀⠀⠀⣿⠿⣿
⠀⠀⠀⢀⣿⣤⣿⠀⠀⠀⠀⣰⣿⣶⣿⡀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣿⠁⠀⢿⡆⠀⢰⡏⠀⢹⡆
⠀⠀⢀⣼⣿⣿⣿⣧⠀⠀⣰⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⢸⣿⠀⠀⣸⡇⠀⣸⡇⠀⢸⣇
⠀⠀⢸⣿⠛⠉⠙⣿⡄⠀⢿⣿⠋⠀⠀⠙⣿⠀⠀⠀⠀⣿⠾⠳⣾⡇⠀⠀⠸⣿⡷⠾⣿⡇⠀⢹⣷⠶⣾⡏
⠀⠀⠈⢿⠀⠀⠀⠸⠁⠀⠈⢿⡄⠀⠀⠀⠉⠀⠀⠀⠀⢿⣀⢀⣼⠇⠀⠀⠀⢿⣦⣠⣿⠃⠀⠸⣧⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠉⠁
⣶⢖⣶⠶⠶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶