Patients Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢁⡈⢹⡄⣀⡴⠊⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠁⣰⠛⢻⡛⠛⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠋⢁⣀⡀⠈⢳⠐⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⠈⠋⠁⠀⠈⢙⣶⡇
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣀⡑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⡠⠀⠀⠀⣌⡿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⡉⠉⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡘⠂⠀⡠⣼⣿⠕⠉⠧⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⢊⡟⠁⠀⢠⡜⠀⠀⠀⠀⠀⠀⠀⠀⡠⢴⠒⠻⡏⠉⢛⣻⡿⠋⢁⡠⠊⠀⠀⠉⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠓⠀⠀⢀⡝⠀⠀⠀⠀⠀⢀⡴⢹⢀⡟⠀⠀⢻⡀⣼⠏⠉⠉⠁⢀⠖⢀⡠⠖⠁⠀⢹⣆
⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⣀⡠⢤⣀⡝⢤⣠⣤⠞⠑⠚⠁⠘⣜⣰⠇⠀⠀⢸⣷⡏⠀⠀⠀⢀⠎⠐⣯⡴⠶⠻⠻⠻⣿⡄
⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠡⠄⡠⢤⣄⣀⣀⣨⡏⠀⠀⢠⡟⣿⠏⠀⠀⢀⢎⡞⣸⠃⢀⠀⠀⢀⡄⣸⠇
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⢸⠉⠓⠦⣄⣀⣤⠶⠖⠶⢦⣭⣩⣺⡇⢀⣠⢟⣼⠏⠀⠀⠠⢂⠎⢠⡇⠐⢁⡠⠔⠋⣰⣿
⠀⠀⠀⡾⠀⠀⠀⠈⡇⠀⠀⢸⣦⣤⣞⡯⢁⣈⠉⢲⡛⠛⠉⠉⢻⠻⠿⠿⢛⠏⠀⠀⠀⣠⢋⡔⠉⠁⠉⠁⠀⠀⣰⡟⣾
⠀⠀⢸⠃⠀⠀⠀⠀⡇⠀⠀⢸⡋⠁⠈⠳⣵⣤⡀⠀⠑⠶⢤⣤⣟⣀⣀⣠⣏⣀⣀⣀⣴⣥⣾⣀⠀⠀⠀⠀⣠⣾⣟⢴⣏⡀
⠀⠀⡟⠀⠀⠀⠀⠀⢿⠀⠀⠸⡇⠀⠀⠀⠀⠀⠙⠦⢤⣤⣸⢰⠇⠈⠉⠁⠀⠀⠀⠉⠁⠀⠙⢮⡛⠀⠠⠚⣱⡟⠁⣼⠀⠉⠛⠲⣄
⠀⠘⣧⣀⠀⠐⣒⡀⢸⡀⠠⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣏⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⣼⠏⢠⠞⠁⠀⠀⠀⢰⡏
⠀⢰⠿⠀⠤⠤⠬⢷⠤⠑⣄⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⣀⡼⠋⠉⠀⠈⠉⠉⠉⠛⠒⠲⠶⠶⠶⠶⠶⠾⠃⡀⣸⡀⠀⠀⠀⢀⡿
⠀⢸⡆⠴⠒⠂⠀⠈⢣⡀⠈⠑⣦⡀⠈⢳⣀⡠⠖⠶⠋⠁⠉⠓⢤⣐⠦⢤⡤⢤⣤⣤⠄⢀⣀⠤⠐⠈⠀⣰⠓⣿⠉⠳⡶⢤⡾⠁
⠀⠘⠃⠀⠀⠠⠴⠆⠰⠷⣒⠞⠁⠉⠳⢤⣈⠁⠒⣦⣀⠀⠈⠑⠒⠀⠛⠉⠐⠒⠒⠀⠉⠀⠀⠀⠀⢠⠜⠁⠀⢸⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠀⠀⠀⠀⠈⠉⠓⠛⠉⢷⡀⠀⠀⠀⠒⠒⠒⠂⠀⠀⠉⠉⠀⠐⠂⠤⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠶⣖⠒⠂⠤⠄⢀⣠⠄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⢀⡾⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢲⣤⠝⠋⠁⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⢀⣾⣇⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠚⠀⠀⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠐⠉⠂
⡄⢰⠖⠀⠀⠀⠨⠀⠁⠀⠀⠙⠂⡶⠂
⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠤⠖⠒⠆⠆⠤⣀⠁⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⠒⠀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⢢⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⠎⠐⠘⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠃⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠷⣼⠿⣕⠻⡦⡀⠀⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⣤⠖⠉⠀⠀⠀⠀⠀⠀⠔⢲⢸⠐⠀⡄⠀⠈⠙⠂⣤⢀⠈⢤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⡑⡈⠼⢘⠒⢢⠆⠓⢂⣠⢃⡎⢠⢬⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡜⠸⣒⠒⠒⡻⠑⠠⣤⠋⣡⠟⠑⠢⢤⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⠀⠀⠀⠀⣈⡩⠛⠀⠓⠐⠊⠁⠘⠝⠶⢈⠃⠀⠈⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙⠉⡙⠁⠀⠀⠀⠀⠀⠀⡜⠀⠐⠈⠀⠀⡐⢩⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡐⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⠎⡀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠒⠳⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⢀⠦⡀⢸⠏
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⣀⣤⠦⣴⣃⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⠀⠂⠀⣠⠏
⡇⢰⢢⠀⣯⣁⠖⠤⣀⡀⣠⡤⠴⠖⠘⣻⡛⠲⡰⢂⠀⠉⠀⠀⠀⠀⠈⠁⡑⠀⢀⠊⠢⢄⢽
⡇⢸⠘⠀⠀⠀⠀⡆⠤⡀⠻⡄⠀⠀⠄⠘⠍⡠⠏⠀⠌⡂⢄⠀⡉⠀⠀⠠⠀⠀⡈⠁⢠⠄⠸
⡇⢸⠀⠀⠀⡀⠁⠀⠀⠀⠀⠃⠀⠀⠀⠈⠐⠀⠀⠀⠀⠈⠑⠪⢛⡙⠻⠃⠀⢰⠀⣐⠟
⠇⢸⢰⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⢇⡀⠀⢦⠔⠵⠄⡀⡂
⠁⢸⣬⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⢸⠉⠉⠠⠬⠄⠀⠃⠀⡇
⠀⠘⠀⠅⠷⡆⠄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠀⠀⠒⠂⠀⡄⠀⠀⠈⡀⠀⠀⠀⠀⠀⡁⠀⠇
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠇⠀⠀⠒⠂⠉⠁
⠐⠂⠀⠀⠀⠀⠀⠀⠐⠀⠠⠤⠄⠀⠒⠒⠒⠒⠀⠈⠈⠉⠀⠒⠂⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣀⣀⡀⢀⡄⠀⣤⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠁⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⠀⠀⠈⢃⡴⢛⡛⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⢸⡇⠺⡟⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢁⣼⠖⠒⠛⠛⠛⠓⠒⠾⣄⠹⡆⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠁⠀⠀⢠⡄⢀⣠⠟⢦⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⡆⢀⣴⡏⠛⢋⣁⡀⠈⢿⠂⡟⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⣟⠉⠀⠀⠀⠀⠀⠀⠀⣿⣼⠃⡴⠋⠀⠀⠀⠀⠉⠻⣆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⣤⣀⣠⡄⠀⣼⠟⠁⢸⡃⠀⠀⢀⣠⡴⠶⢤⣹⡄⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠙⠷⣤⣉⣁⡤⠞⣡⣄⡀⠸⣏⠘⣛⡉⠁⣀⡀⠀⣹⠇⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠰⡟⠳⣄⠀⠀⠉⠀⠀⢀⡴⠛⡇⠀⢹⡄⠉⠁⠀⠉⠁⢰⠇⠀⠖
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢷⠀⠈⠳⣤⡀⢀⡴⠋⠀⢸⡇⠀⠀⠻⣄⡛⠒⢃⣴⠏
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀⡴⠚⠳⣄⠀⠀⠙⠋⠀⢀⣀⣾⠀⣠⡴⠶⣌⡉⠉⢉⣠⡶⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢸⣥⠀⢠⣼⠆⠀⠀⠀⠀⣿⠁⠀⣼⠃⠀⠀⠈⠉⠉⠉⠁⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠘⠛⠀⠘⠛⠀⠀⠀⠀⠀⠙⠓⢸⠏⠛⢳⠀⠀⠀⠀⠀⠀⠀⣶⠛⠋⣷
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⢋⣉⡙⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢠⡞⠉⠉⣙⢳⡀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⡶⠶⠚⠙⢻⡇⠀⠀⠸⡆
⠀⠀⣠⣤⡀⠀⠀⢀⡴⠶⣿⠳⠶⠞⣻⠶⢦⡄⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣈⣷⣀⠀⣠⣾⡁⠀⠀⠀⣿
⠀⠀⢻⠀⢻⡀⠀⣿⠀⠀⠈⠳⣤⡼⠋⠀⠀⣿⠀⠀⡿⠀⡿⠀⠀⠀⠀⠀⠀⠀⢿⠀⣰⠋⠉⠁⠉⠉⠉⠈⠉⠻⡆⢠⡏
⠀⠀⠸⡇⢸⡷⠶⣝⠲⠤⣤⣤⣤⣤⣤⡤⠶⣫⠶⢾⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⢧⡻⠶⠶⠶⠶⠶⠶⠶⠶⠶⢧⡾⠁
⠀⠀⠀⢿⡈⠻⣄⠈⠳⣤⡀⠀⠀⠀⠀⣠⠞⠁⣠⠞⠁⡾⠀⠀⠀⠀⠀⠀⣀⣀⡀⠈⢩⡴⠚⠛⠲⠶⠶⠶⣄⠰⣋⣤⠤⢤⡀
⠀⠀⠀⠈⠳⣄⠈⠁⠀⠈⣷⠀⠀⠀⣾⠁⠀⠈⠁⣠⡞⠁⠀⠀⠀⠀⠀⢿⠉⠉⣿⠒⠛⠀⠀⣤⠤⠴⠶⠶⠾⠋⢉⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠘⣦⣀⣀⣤⣿⣤⠀⣤⣿⣤⣀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡆⠀⣀⣀⣀⣀⣀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⢿⣭⣤⣤⣤⣿⠀⣿⣤⣤⣤⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣈⡟⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣤⣤⣤⣄⠙⠳⢦⣀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⣉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⠳⢦⡄⠉⠛⢺⡍⣿⠀⠀⠀⠀⢀⣰⢶⡄⠀⠀⢸⡷⠶⠞⠋⠓⢾⡇⠀⠀⣠⢶⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⢤⣙⢦⣀⠀⢀⣀⣸⡆⣿⠀⠀⠀⠀⣿⢹⡆⡟⣷⠀⠘⣧⠀⠀⠀⢀⡾⠁⢀⡞⣿⢸⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠙⡆⠉⠉⠉⠉⠹⠶⠿⠀⠀⠀⠀⡏⢸⡇⡇⣿⣀⣠⡼⠷⠶⠶⠿⣥⣄⣸⡇⣿⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣾⠛⢧⣼⠋⠈⠳⢤⣄⣤⡴⠟⠈⢹⣧⡟⢻⡆⢹
⠀⠀⢀⣀⣀⠀⠀⠀⣠⠴⠿⠦⣤⡴⠿⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⢷⡀⠻⢤⣄⠀⠀⠀⠀⠀⢀⣠⡴⠏⢠⡞⢁⡾
⠀⠀⢸⡇⢹⠛⠛⠛⠛⠲⣄⣀⣀⣀⣀⣀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠁⠀⠀⠈⢷⡤⣤⡤⢤⡟⠁⠀⠀⠈⢀⡾⠁
⠀⠀⢸⡇⢸⣀⠀⠀⢤⣄⡉⠻⣍⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣄⠀⠀⢸⡀⠀⠀⢸⡇⠀⠀⣤⠶⠛⠁
⠀⠀⠘⠷⠚⠉⠛⠦⣄⡈⠙⢦⠿⠶⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠶⠶⠾⠷⡆⣴⠾⠷⠶⠾⠷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠶⠶⠶⠶⢾⡷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣤⣀⠀⠀⣤⣼⣧⣤⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⢀⣤⡶⠾⠷⢶⣄⡀⠀⠀⠀⠀⠀⠹⣆⠀⣿⠀⠀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⣠⣾⠁⠀⠀⠀⠀⠘⣷⣀⡀⠀⠀⠀⠀⣿⠀⣿⣀⣀⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡟⠉⠹⣇⠀⠀⠀⠀⠀⠀⣿⠋⠛⣷⠀⠀⠀⣿⠀⠉⢹⡏⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠻⣦⣀⠀⢀⣀⣼⠏⠀⠀⣿⠀⠀⠀⣿⠀⢠⡿⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠶⠶⠿⢷⣤⣤⡴⠾⠛⠛⠛⠛⠷⣦⣤⣴⠿⠷⠶⠾⣿⣴⠟⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣴⠶⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⣤⣤⣤⣴⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣤⣤⣤⣤⣼⣷⡀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣷⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠨⣿⣤⣤⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣿⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⣿⣿⡟⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠖⠒⢄⡀⠀⠀⠀⠀⠀⠳⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢹⡇⣿⣿⣿⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⣄⢀⣀⠀⠀⠉⠉⡆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡴⢻⡇⣿⣿⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠹⢿⠟⢻⣿⣆⢸⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡰⢻⡇⣿⣿⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⠀⠚⠿⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⣿
⣦⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⢸⡇⣿⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣀⡤⣦⢀⡼⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿
⣿⣧⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣶⣰⣿⣿⣧⣼⡇⣿⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢋⣀⣀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠈⣻
⣿⣿⣿⣿⣇⠀⠀⢠⣄⠀⡀⣾⣿⣿⣿⣿⣿⣿⡇⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠋⠀⠈⠙⣄⠐⣿⡄⠀⠀⠀⠀⠀⠀⠀⢨
⣿⣿⣿⣿⣿⣷⡀⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⢸⡄⠈⣷⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡤⣖⢻⣿⣿⣷⠀⠀⠀⠀⠈⡇⠀⢻⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡟⠀⠀⠀⢸⡇⠀⠀⠀⢴⣒⣒⣺⠱⠾⠿⣿⣶⠿⣿⡄⢀⣀⣀⡀⢧⠀⠘⣿
⣿⣿⡿⣫⡟⣽⢟⡿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⢸⡧⠀⣠⠔⢺⡀⣀⡸⢀⣴⡶⣩⠕⠋⠙⣷⡏⠁⠈⠙⣟⠀⠀⠻⡄
⡿⢋⡼⢫⠞⣱⠏⡴⣻⣯⡽⠓⠫⣝⢿⣿⣿⣿⡇⡇⠀⠀⠀⢸⣇⠥⠙⠛⠓⢶⣶⣦⣤⣵⣾⣛⣛⡋⠉⠉⠁⠀⠀⢀⡏⠀⠀⠀⢻⡀
⣠⠎⣰⡯⠶⠓⠛⣿⣿⣿⣿⠂⠀⠾⠯⣿⣿⣿⡇⡇⠀⠀⠀⢸⡗⣊⠥⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⢿⣿⡟⠁⠀⠀⠀⠀⢧
⠖⠋⠀⠀⠀⠀⠀⠻⣿⣇⡈⠀⠀⠀⠠⢯⣻⣿⡇⠀⠀⠀⠀⢸⣯⠔⣊⠥⢂⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⣾⣿⣄⠀⠀⠀⠀⠀⠘⡆
⠀⠀⣀⠔⠀⠀⠀⠀⠹⡿⠁⠀⠒⢤⣤⢼⣿⣿⡇⠀⠀⠀⠀⢸⣗⣫⠔⣊⠥⢂⠀⢀⣀⡴⠒⠚⠩⣻⠟⠁⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⢹⡀
⢖⡫⠖⠉⠀⠀⠀⢀⠀⣿⡴⢒⣊⢭⣍⣙⠛⠿⣇⡀⠀⠀⠀⢸⣯⠔⣫⣔⣪⠴⠚⠉⠉⠳⣤⠖⠚⠁⠀⠀⠘⣿⣿⣿⣿⣧⡀⠀⠀⠀⠈⣧
⡽⣒⠅⠂⠀⠀⠀⠈⠙⠳⡞⠁⠀⠀⠀⠈⠛⠦⣄⠙⠉⠛⠒⢾⣷⠿⠛⠁⣀⠄⠀⠀⠀⠀⢹⠶⠒⠒⠒⠒⠚⠛⠙⠛⠿⢿⣷⣲⣶⣦⣤⣼⣄⣀
⡫⢗⠩⠀⠀⠀⠀⠀⠀⠀⠙⣎⢶⣤⡀⠀⠀⠀⠈⠙⠉⠋⠙⠉⠀⢀⡴⣪⢕⡡⣀⣀⡤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣚⠥⡂⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⣿⣼⣼⣴⣴⣴⣴⣴⣰⣰⣠⣾⣿⣿⣷⣿⣚⡉⠁⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠠⠔⢚⣻⣿⣿⣿⣿⣿⣿
⠕⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⠿⠛⠛⠋⠉⠉⠉⠉⠀⠀⠈⠉⠉⠟⠟⠿⠿⠻⠿⠟⠿⢿⠿⡶⣤⣶⢾⢿⠿⠿⢿⠿⠿⠻⡿⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠲⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠈⢹⠉⠉⣻⠛⠛⠛⡟⠛⠛⢿⠛⠛⢻⠛⠛⢻⠛⠛⢹⡏⠉⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢾⣦⣼⣄⣀⣽⣀⣀⣠⣇⣀⣀⣼⣀⣀⣸⣀⣀⣸⣄⣀⣼⣄⣤⣧⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⢤⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣁⡠⠿⣆
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣼⠷⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⣶⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⠀⠀⠀⠀⣴⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏⠀⣼⠋⠉⠉⠉⡏⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠀⠀⢿⣤⣤⣤⣤⣿⣤⣤⣤⠾⠁
⠀⠀⠀⠀⢀⣤⠶⠶⢶⣤⣤⣭⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡴⠶⢶⣤⡀
⠀⠀⠀⠀⣟⠀⠀⠀⡼⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠁⠈⢹⣧⠀⢀⡼⠛⢶⣄
⠀⠀⠀⠀⠙⢦⣄⣀⣳⡀⠀⠀⢀⣰⠟⢀⣀⠀⠀⣿⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢦⣠⡾⠋⠳⣮⡀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢛⣻⣷⠞⠋⠉⢻⡄⠹⣦⡀⢠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢿⡀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠻⢦⣄⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠈⢧⠀⠀⣠⠟⠀⠈⠻⣧⡀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⣼⠷⠛⠁⠀⠀⠀⠀⠈⠻⢦⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⠿⢰⣇⠸⠿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣇⣛⢻⡿⢛⣃⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣘⣃⣸⣿⣿⣿⡇⠀⠀⣿⡴⠖⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣡⣴⣾⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⡴⠶⠶⠶⠶⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⠳⠶⠶⠦⠴⢿⣿⣿⣿⡿⠟



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠪⢒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠐⠒⠶⣶⣄⡀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠉⠻⢷⡂⠤⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢼⡇
⢀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⣦⡀⠀⠀⠀⠀⢀⡠⠛⠲⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡈
⡟⠁⠀⠀⠘⡄⠀⠠⠄⠀⠀⠀⠀⣻⠀⠈⠳⡀⠀⢠⠔⠁⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠁
⢹⡄⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢳⣤⣶⣷⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⢹⡄⢰⣄⢤⣼⡄⠀⠀⠀⠀⠀⣸⣽⡄⠀⣀⢀⠆⡶⣄⡀⢐⡤⠀⣀⣀⣨⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠃⠀⠀⠀⠀⠀⣰⠄
⠀⠀⢻⣿⣷⡈⢿⣿⡆⠀⠀⠀⣠⡿⠻⠃⠚⠉⠉⠈⠐⠋⠻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⢋⣡⣤⣶⠄⠀⢀⣠⡴⠞⠋
⠀⠀⠀⢿⣿⣷⡈⢻⣿⡄⠈⠈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠣⠛⡄⠀⠀⠀⠀⠀⠘⣧⣴⣾⣿⣿⣿⡿⠷⠛⠉
⠀⠀⠀⠈⢿⣿⣷⣼⠛⡇⢀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⢸⡉⠀⠀⠀⠠⡙⣶⣤⡀⠀⠀⠀⣀⣀⡀⣠⡴⠔⠋⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⢢⣼⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣠⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡱⠂⠈⠛⢿⣿⣤⣌⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢆⠀⠙⠻⣿⣧⣄⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⢀⢂⢀
⠀⠀⠀⠀⢺⢆⡀⠀⠀⠀⠀⣀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠢⣍⣿⣷⣏⣍⣇⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⣀⡤⠖⢒⣶⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠘⠁⢀⠤⠚⣛⡛⢟⣟⣻⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⡄⠀⠀⠀⠁⡰⠟⢛⣿⣮⣭⣧⣤⣤⣝⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢰⢱⣤⣆⡴⢊⠔⢺⣿⣏⡙⣿⣿⣿⣿⣿⣿⢦⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠛⢿⡴⠁⠀⠀⢻⠀⠀⢹⣿⣿⣿⣿⣿⡇⡟⢶
⠀⠀⠀⠀⢀⣠⡤⠶⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠺⠤⠈⠷⡦⠾⠆⠀⣠⣿⣿⣿⣿⣟⡏⢱⣾
⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣤⠄⠀⠄⠀⠘⠻⣿⣿⣿⣿⡟⠀⣾⡟
⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣉⢿⣿⣀⠀⢀⠀⠀⡀⠀⠈⠙⣿⣿⣷⡦⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠆⠀⠀⠀⠀⠀⠀⠻⢆⣿⡿⠋⠉⠁⠉⠁⢀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢈⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠈⠳⣦⣌⡉⠙⠛⠛⠛⠛⠛⢉⡉⠤⠀⡾⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⡀⠀⠀⠀⠐⡆⠀⠀⠀⢹⡤⡤⠐⠁⠀⠀⠀⣆⡀⠀⠀⠀⢸⠤
⠀⠀⠈⠙⠒⠷⠠⠀⠠⠈⠄⠄⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⢀⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣦⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠐⢶⠶⠆⠀⠠⠀⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠁⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠃⠘⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠸⢛⣩⣴⣶⣿⣿⡿⠿⠿⢿⣿⣷⣶⣦⣍⡛⠿⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠻⣏⠀⠀⠠⡾⣿⡿⡦⠀⠀⢴⢿⣿⢷⠄⠀⠀⣹⠟⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢹⡄⢹⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⡟⢠⡟⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢿⡀⠀⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⠄⢀⡿⠁⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠈⣷⠀⠙⠛⠿⠿⠿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠀⣾⠁⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠘⠇⠹⢿⣷⣶⣶⣦⣤⣤⣴⣶⣶⣾⡿⠏⠸⠃⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠠⣌⡙⠻⠿⠿⠿⠿⠟⢋⣡⠄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣶⣶⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⣛⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠻⢦⣤⣀⣉⣉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣁⣬⠟⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⠶⣶⣤⣬⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣩⣥⣤⣶⡾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⢸⡇⢸⡏⢹⡏⢹⡏⢹⡏⢹⡏⠉⡏⠉⡇⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣄⣸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⠀⡇⢀⣇⣠⣧⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠙⠛⠛⠻⠿⠷⠾⠷⠾⠷⠾⠿⠿⠛⠛⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣴⣦⣤⣤⣀⣀⣀⣀⣤⣤⣤⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣤⣤⣤⣀⣀⣤⣤⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣉⣉⣉⣛⣛⡋⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠛⠿⢿⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⠿⠟⠛⢻⡇⠀⠀⠀⠀⢀⣴⣟⡱⠋⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠛⠻⡿⠷⠶⣦⡀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⢰⡿⠃⠈⠹⣦⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⣠⡇⠉⠛⢸⡇⠀⠀⢻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡇⠀⠸⣧⣀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣷⣾⠟⠁⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢟⣛⡛⣟⠛⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠉⣀⣿⣀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠞⠋⣉⡍⠙⠶⠀⠀⠀⡀⣀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⠆⠉⠀⢦⡀⠀⠀⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⡰⢄⠀⠀⠈⠁⠀⠁⠀⠀⠁⠄⣨⡴⢘⡇⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠦⢄⠀⠀⠀⢀⢔⡀⠊⣁⠔⠁⢱⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⢼⡥⠋⠠⠊⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⣀⠠⠄⡀⠀⠀⣯⠐⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⠤⡄⢀⠨⠗⠀⠁⠀⢀⣤⠬⣥⣌⠑⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠃⠀⠉⠀⣴⠀⠀⠀⢠⣄⠁⠰⠶⣆⠀⠐⠉⠀⠀⢐⡻
⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠁⠈⠀⢀⡑⠀⠀⠀⢘⣄⡀⠀⠀⠀⠳⠤⠆⠈⠁⠀⢀⠔⡣⠋⣁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠀⠀⡀⠉⠲⢄⣀⡏⠄⡙⠢⢀⡀⠀⠀⠀⠀⢀⠔⡡⠚⠀⡀⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠙⠦⡀⠙⠣⡀⠀⠁⠠⢍⠂⠀⠀⢐⡭⠊⡁⠄⠁⠀⢀
⠀⠀⠀⠀⠀⠠⡀⠀⠀⣴⠚⠛⡓⠦⠤⠇⠀⠀⠀⠀⠉⣢⡀⠀⠀⠁⠀⣙⠋⢀⠒⠁⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢄⠙⢦⠀⠀⠀⠀⠠⢔⡼⢿⠔⠒⢀⡀⠀⠈⠱⠈⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠈⠢⠈⠂⢄⠀⠀⠀⠀⠀⡠⢄⡹⠖⠋⣀⠞⣱⣄⢤⡈⠀⢄⢐⠈⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠁⢤⣠⠔⣫⠚⠁⡀⠔⠙⠀⠀⡶⠀⠀⠘⣦⠇⠉⠒⢄⠀⡀⢀⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠛⢁⡤⠊⣁⣀⣀⢀⣀⣾⣀⡄⠊⠀⠀⡀⠀⠀⠙⢲⣊⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠉⠀⠀⢸⡃⠉⣀⠈⠉⠉⠀⠀⠠⢿⠛⠿⠟⠷⣤⠉⠿⣭⠍
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠑⠀⡀⠈⢺⡃⣈⡙⠁⠀⠀⠀⠀⣀⡙⠃⠀⡀⠀⠉⠀⠀⢸⣷⡄
⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂⠀⡉⢙⣌⠁⠀⠀⠀⠟⠋⠁⠀⠉⠀⠀⠀⠀⣀⠘⣩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠀⠈⠀⠀⢀⡤⠁⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣩⡤⠊⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⣀⠀⡙⠀⣀⠦⠒⠁⠂⠀⠁⠀⠈⠢⡀⠢⠀⢀⡔⠋⡤⠖⠁⡠⠄⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠚⠡⠄⢀⠀⠀⠀⠀⠀⠀⠢⠀⠀⣬⣤⠞⠁⢠⠤⠂⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠑⢤⠀⢠⠶⠁⠀⠀⠀⠀⢀⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄⠀⠀⠀⠀⠀⢑⠈⠀⠀⠀⠀⣀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⢀⡰⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢸⢀⡰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⡟⣞⢧⡻⡝⠀⠀⠀⠀⠁⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠋⠀⠉⠉⠉⠉⠁⠀⠀⠀⠈⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣲⠀⠀⠀⠀⠀⠀⠀⡀⣦⣶⡶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠢⡀⠀⠈⠀⠀⣀
⠀⠀⠁⠀⠀⠀⣀⣀⠀⠀⠀⢸⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⢮⠀⠈⡇⠀⠀⢸⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡁⣱⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠈⠙⠙⠁⠀⠀⢸⠀⢀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⣀
⠀⠀⡀⠀⠚⠛⠛⠛⠛⠀⠀⢸⠀⠈⠉⠉⠉⠉⢉⢉⣉⣉⣉⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠓⠐⠀⢠⠢⠀⠀⠓⠁
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠙⠉⠙⠉⠉⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⣤⡀⢰⣿⠆⣀⢄⠀⠀⠀⠀⣠⡴⠾⠺⠷⢦⣄⠀⠀⠀⠀⡀⠰⣿⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠗⢠⡄
⠀⠀⠀⠙⠛⠀⠀⠀⠓⠊⠀⠀⠀⣼⠏⠀⠀⠀⠀⠈⢻⣆⠀⠀⠸⠿⠂⠀⠀⠀⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶
⠀⠀⠿⠿⠀⠀⠀⠀⠀⠯⠽⠀⠀⣿⠀⠀⠐⠒⠒⠂⢨⣯⠀⠀⣾⠆⠀⠀⠀⠂⠀⢐⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⣶⡷⢀⣤⠀⢎⣢⠀⠀⠀⠹⣷⡄⠀⠀⠀⣠⡾⠁⠀⠀⠀⣶⠄⣀⠀⢀⢠⡌⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠘⠶⠁⠀⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠛⠁⠛⠁⠀⠀⠀⠀⠀⠈⠁⠐⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠞⣧⠀⠀⢀⣀⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⣠⠋⠀⠘⠚⠉⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠙⠲⢤⠞⠉⠉⠙⠣⡀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⣧⠀⠀⠀⠀⡰⣋⣞⠉⣱⣄⡀⢸⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠙⣄⠀⠈⠉⠉⠉⠀⠈⠉⠉⠀⠀⢠⡾⣽⠣⣼⠃⢌⣇⡜⡸⠀⢀⡤⠲⡈⠳⣄⠀⠀⠀⠀⠘⠧⠤⠤⢤⣤⣀⣀⣀
⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠒⠲⢧⡦⢴⠛⣬⣶⠁⡰⠛⢢⠰⢇⣠⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⢾⣠⣿⠏⠻⣅⣀⠼⣀⡠⠃⢱⠛⡆⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⣨⠆⠀⠀⢠⡇⠀⠀⠀⠀⠠⠁⠀⣼⠟⠁⠀⠀⠘⠷⣤⢼⠒⠒⡇⢀⠇⠀⠀⠀⠀⠀⠐⠛⠲⠤⣄⣀
⠀⢀⡠⠖⠋⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠽⠗
⠶⣉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉
⠀⠀⠉⠙⠒⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡛⢏⣙⡦⢵⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠉⢫⠈⣇⣸⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⣧⣞⡁⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⣀⣀⣈⣶⡄
⠀⠀⠀⣴⣁⣤⠤⠤⠶⠒⣶⠂⠀⠀⠀⡠⢿⡀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠉⠙⠲⢤⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠔⠋⠀⠀⠙⠓⠒⠚⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠑⠢⢌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡠⠞⠁⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡽⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⢀⡴⠋⠸⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠀⠉⠛⠛⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠉⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⠀⠀⠀⠀⠀⠀⣌⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠃⠀⠀⠉⠛⠙⠿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣄⣀⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣄⠀⢀⣠⠾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢾⠁⢶⣶⠂⣳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣞⠉⠉⠉⠉⡷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡖⣻⡉⢷⠞⢇⢸⣧⣰⠳⡾⠋⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣿⠙⢷⠞⡖⣶⡾⣰⠳⡾⢹⡟⢶⡀
⠀⠀⠀⠀⠀⠀⠀⣾⢰⠁⠙⡌⠲⣜⣿⣿⣃⠔⠁⢠⠇⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⡞⢸⠁⠹⡌⠢⣘⡌⢱⣣⠞⠁⣸⠁⠀⣷
⠀⠀⠀⠀⠀⠀⢀⡇⠘⣆⠀⠼⠀⠈⠻⡟⠁⠀⢾⣉⠇⠀⢸⡆⠀⠀⠀⠀⠀⠀⢰⡇⠸⣀⠀⡽⠀⠈⢻⠟⠁⠀⢮⣻⠆⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣸⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢰⡏⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⠉⣷⠀⢘⡇⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⣤⣤⣤⣤⣤⣤⣤⣤⠟⠀⠈⢷⣄⣀⣀⣈⣻⣦⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢹⠀⣾⠋⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⢸⡿⢷⣤⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣾⠃⣼⠋⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢁⡾⠁⣼⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢀⡾⠁⣼⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⣼⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆⠀⣾⣥⣼⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣸⡿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠘⠋⠁⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠏


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠟⡰⢱⠂⡄⡗⡆⡔⢲⢰⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠁⠀⠀⠈⠊⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠉⠉⠉⠉⠓⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠟⠲⢤⡀⠐⠂⡢⢀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡀⠀⠤⣝⠲⢤⣤⡾⠿⠛⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢫⣅⠀⣀⣘⠇⢰⣤⠖⠲⡞⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠀⠁⠈⠁⠀⣻⠏⠀⠈⠁⡠⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⢀⡿⠀⢀⠀⠈⠒⠘⡏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠛⠓⡛⠉⠀⠀⢠⣷⡀⠀⠀⣇⠑⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠈⠒⠀⠡⠀⠛⠀⠀⢹⡛⠁
⠀⠀⠰⡐⠦⣀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠉⠂⢈⣙⠢⢤⣀⣠⡞⠁⣀⠈⣧⠀⠀⠀⠀⠀⠀⢀⡷⣄⣀⠀⠀⠀⠀⠀⣀⣠⣴⠿⣀
⠠⡞⠉⣉⡩⣭⠏⡤⠒⠉⠁⡜⠀⠀⠀⠉⠀⠀⠀⣠⠴⠊⠁⠀⢸⠉⣻⠟⢛⡿⣹⠋⢁⠃⠀⠈⠓⢦⡀
⡠⠀⢹⣀⣼⠃⠈⠷⠀⢀⣠⠇⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠠⠒⠊⠀⢰⡐⢯⢠⠇⠀⣬⡀⠀⠐⢁⠢⠝⠦⡀
⠁⡁⠀⡀⠀⠂⠀⠀⣾⠋⠉⡄⠀⠀⠀⠀⡠⠋⣴⠀⠀⠀⠀⠱⡀⠀⠘⡇⢠⡟⠀⠀⣀⡤⠛⢠
⠀⠉⠀⠀⠀⠀⠀⠀⠹⡄⠀⡇⠀⠀⠀⡐⠁⡼⠁⠀⠀⠀⠀⠀⠙⣄⠀⡇⢨⢁⡴⠚⠁⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢣⠀⣠⠎⢀⠎⠁⠀⠒⠂⠤⠄⢀⠀⠈⢢⣥⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠸⡞⠁⡰⠋⠠⠀⠀⣀⡀⠀⠀⠀⠘⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡠⠚⠁⠀⠆⠀⠀⠀⠀⠉⠑⠒⠃⠀⠀⠘⠀⠀⠀⠀⠈⢦⡀⠀⢀⡠⠃⠀⠠⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣠⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠦⢤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⡴⠶⢶⠖⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠤⠾⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⣀⣀⣀⠀⠄⠂⠀⢀⡄⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⣰⢄⡉⠙⠲⠦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⢀⣠⠴⠚⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠙⠲⠤⣄⣀⣀⣉⣩⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⢲⠋⢀⣈⣹⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢠⠈⠉⠉⠉⠀⣠⠞⠀⠀⢀⡤⠤⣄⠀⠀⢀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠈⡗⠒⠒⠛⣹⡇⠀⠀⠀⡏⢀⡔⠋⠉⢉⡉⠳⣄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣴⡃⠀⣀⠀⠈⣇⠀⠀⠀⢷⢸⣤⣀⣠⡴⢧⡀⢸⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⠦⣤⢤⠞⢻⠀⠀⠀⠈⢹⡆⣷⡀⠀⣸⠃⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣟⠙⣇⢨⡟⣿⣦⣀⠀⠀⢀⣽⣻⡿⣍⠻⠿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⣳⠾⣾⠋⡿⢧⣈⣙⣲⠾⣏⣥⣿⡼⠒⣦⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢳⣀⡧⠀⡷⢤⣈⣁⣤⢶⣿⠓⠒⠒⠒⢻⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⡀⠉⠙⠛⠛⣟⢉⣹⢀⣼⠉⣷⡎⢹⣄⣸⣷⣈⣧⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠙⣟⠛⢿⠉⠉⠀⢾⣽⠤⣿⡧⢼⡏⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣀⡀⣿⠀⢸⠀⠀⠀⠘⢷⣶⣿⣶⣞⣛⣛⣛⣛⣛⣛⣻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠘⠃⣷⠀⢸⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡏⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣧⠀⠸⡇⠀⠀⠀⢸⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢲⡖⠒⢲⠛⢲⠚⠃⠀⠀⠀⢸⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣾⠀⣼⠀⠀⠀⠀⠀⢸⡦⠤⠤⠤⠤⠤⠤⠤⠤⠤⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡇⠀⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠙⢿⡙⢲⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⢀⣿⡿⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⣠⣾⣿⣿⣿⣷⣤⣶⣿⣿⠄⣀⢀⣠⣿⣯⠀⠀⠐⠀⣴⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⢥⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠿⢋⣴⣾⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡿⢿⣿⡏⣰⣤⡄⣾⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⣰⣎⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢿⣿⠉⢻⠏⢠⣿⣿⣷⣿⡟⠑⠋⣄⣠⣿⣀
⠀⠀⠀⠀⠀⠀⢈⣛⣧⣽⣿⣿⠿⢻⡿⠋⣉⣉⠙⢿⡄⢰⡶⠀⣿⡆⠈⠀⠻⣿⣿⣿⣿⣧⣿⣶⣿⣿⣿⣿⣇
⠀⠀⠄⠀⠀⢿⡉⠹⣿⠁⠘⣿⠁⢸⠇⢸⣿⣿⡆⠈⡇⠀⣄⠘⠻⣧⠀⣿⣦⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⢠⣼⣷⡀⠻⠀⣤⠘⠀⢸⣧⡈⠛⠛⢁⣴⣿⣤⣿⣷⣶⣾⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⢃⡀⠁⠀⠀⣤
⠀⠀⠀⠀⠈⠙⣻⣷⡄⠀⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⡏⠙⣧⠀⠙⢿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣉⣃⣄⣤⣴⣿⣤⣤⠖⠛⠛⡦
⠀⠀⠀⠀⢢⢭⣷⣿⣿⣿⣿⣽⣰⣾⣿⣿⣿⣿⣿⣿⣿⠀⢻⡄⢸⣄⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⣿⠏⢠⣤⣼⣇⠀⠻⠿⣧⡀
⠀⠀⠀⠀⠀⠯⢿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣿⡆⢸⣇⣈⣿⣷⣶⠾⠛⠛⢿⣯⠉⣤⡄⠙⣷⠀⠻⠛⢿⣦⣄⣉⠙⢿⡿⣶⠆⠈⡧
⠀⠀⠀⠀⠀⠈⠘⡚⠏⠟⠾⠿⢿⣿⣿⣿⣿⣿⠿⣿⣿⡿⠛⣉⣉⠙⢿⡇⢠⣾⠷⠿⢿⡄⠈⠁⢸⣿⡆⠰⠾⠿⣟⠙⠋⣀⣼⢦⣤⠴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⢲⡟⠛⣋⠙⢻⡀⢠⣦⠈⣿⠁⢸⣿⣿⡗⠈⣇⠘⢿⡶⠆⢠⣇⠈⣷⣄⣉⣷⡤⣶⣶⡿⡿⢿⢉⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠿⠃⣸⣇⠀⡁⠰⢿⣧⡈⠛⠛⠁⣰⣿⠷⢤⣤⣶⣿⡙⣛⠉⠼⣷⣬⣐⠃⠮⢹⢃⠒⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠷⢻⡄⢰⣿⣿⣿⣀⣻⣦⣤⣽⣿⣷⣾⣿⣿⠋⢤⡀⢉⣿⣿⣟⠛⠷⣶⡄⠩⣿⠋⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⡛⡿⣿⣿⣿⣿⠀⣿⣿⣦⣌⠉⢻⣿⢀⣿⠃⠸⠏⠀⠀⠀⠀⠀⠺⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠡⠟⢃⠯⢿⣿⠫⠀⠀⢥⣶⣭⣉⠛⠿⣿⡇⢨⡿⢀⣿⠋⠛⢿⣷⡄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡐⠆⠀⢠⠄⠀⠉⣿⡇⢰⡿⠀⠟⠃⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⡀⡚⠀⠀⢰⠟⠀⠉⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⠿⠿⠋⡰⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠉⠉⠙⠛⠛⠻⠿⢿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠉⠻⣿⣦⣄⣠⣤⣤⣴⣶⣶⣶⣾⡿⠿⠿⠿⠟⠛⠻⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⠻⣿⣯⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣽⣿⣷⣄⡀⠀⠀⠀⠙⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣟⡛⠛⠋⠉⠉⠉⠙⠻⣿⣶⣤⣀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣻⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠈⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⣀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣷⣶⣶⣶⣶⣿⣿⠁
⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣿⠃
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤⡾⠋
⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣿⣿⡿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⣄⣀⣠⣾⠟⣿⣿
⠀⠀⠀⠀⠘⣿⣧⡈⠙⠻⣿⣿⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⠟⠋⢠⣿⣿
⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠈⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣤⣶⠀⠀⠿⠂⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣛⢉⣿⣿⣀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣫⣿⣟⡽⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣨⣮⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡔⣯⣾⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠻⣯⡺⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⡙⢅⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢦⡴⠋⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡛⢋⣴⣦⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⡴⢋⣉⣉⣉⣉⣉⠉⣉⣉⣉⣉⣉⣉⢉⣉⣉⣉⣉⣉⣉⢉⣉⣉⣉⣉⣉⡉⢉⣉⣉⣉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⢦
⡇⢸⠀⠀⠀⢠⢎⡜⠀⠀⠀⠀⣠⢫⠞⠀⠀⠀⠀⣰⢣⠏⠀⠀⠀⠀⡼⣱⠋⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⢸⠀⠀⣠⢋⠞⠀⠀⠀⠀⣰⢣⠏⠀⠀⠀⠀⡼⣱⠋⠀⠀⠀⢀⡜⡱⠃⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢧⠘⠦⠴⠃⠿⠤⠤⠤⠤⠾⠱⠷⠤⠤⠤⠤⠞⠱⠧⠤⠤⠤⠤⠞⠸⠧⠤⠤⠤⠴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣦⡴⢢⣦⣰⣰⢰⣄⡆⡆⠀⡴⢲⢀⣦⢰⡖⣆⡆⣦⣰⢠⠖⡆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣏⣳⣾⣸⣇⣿⣸⣈⣧⣷⣤⣳⣾⣾⣛⣾⣧⣏⣧⣧⣹⣜⣶⣧⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠙⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠥⠤⠤⣀⡀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠏⠀⠀⠀⠀⠀⠉⠓⣄⠀⢀⡼⠁
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡞
⢀⡴⢏⠉⠋⠉⠙⠓⠦⣄⠀⣷⣀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠒⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⣾⡇⠀⠑⢦⡀⠢⡀⠀⠈⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣯⠱⡀⠀⠀⠙⢦⡈⠢⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠹⡄⠱⣄⠀⠄⣀⠙⠢⡘⢦⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠐⠀⢀⡾⠁
⠀⠙⣆⠈⠣⣄⠀⠀⠀⠈⠢⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠈⠛⢦⣀⠉⠒⠦⠤⠤⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⠴⠶⠚⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⠴⠚⠋⠉⠁⢀⡠⠞⠋⣻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⢀⣴⠋⠁⠀⠈⠁⡠⠖⠉⣠⠔⠋⠁⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠈⠛⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⣼⠃⠀⠀⣠⠔⠁⢀⡴⠊⠡⠀⠀⢀⢼
⠀⠀⠀⠀⣠⡞⠻⢭⣀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⣴⠋⠀⣀⠔⠁⠀⢀⣀⠤⠞⢁⡾
⠀⠀⢀⡾⠉⠙⠲⢤⣈⠉⠒⠤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡉⠉⠉⠋⠉⣉⣉⣀⡤⠶⠋
⠀⠀⢸⣧⣀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠒⠤⣄⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢿⡈⠓⠦⢄⡀⠀⠀⠀⠈⠙⠲⢤⣀⣉⣳⠖⢻⡆
⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⠑⠒⠒⠒⠒⠚⠋⠉⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣶⣶⣶⣶⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⠋⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠘⣤⡄⠀⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠲⠁⠘⠊⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠸⠁⠀⢠⣀⠀⠀⠀⠀⠀⠀⠠⡃⠀⠀⠀⠀⠀⢁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⢰⠗⢐⠀⡴⢋⣻⣆⠀⠀⠀⠐⠓⠤⣀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⡜⠰⣾⣚⠀⢿⣿⣋⢀⣠⠴⠖⠛⠙⠛⣉⠙⣷⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣂⣺⠏⠿⠸⠁⠓⠒⠁⣘⣉⡀⠀⠀⠀⠀⠀⠸⣣⡟⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠈⠁⠈⠀⠙⢉⡏⠉⠂⠀⠀⠙⢻⠛⡏⠀⡀⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⡿⢀⠖⣄⠡⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣤⡶⠟⢻⣆⣠⡴⠋⢀⡀⠀⠀⠀⢀⣾⣀⣁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢬⣷⠀⠈⠉⠈⠓⠚⠉⠀⠀⠀⣠⠟⠁⠈⡏⠙⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠀⡟⢧⡀⠀⡴⠂⠀⠀⠀⣠⣾⠃⠀⢀⣸⣀⣀⣀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⢻⠀⠙⠓⠷⠤⣶⡶⠛⢡⡏⠀⠀⠀⢀⡤⠟⠁⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⢀⠜⠁⡏⢣⡾⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⡀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡀⠀⢀⡤⡄⠀⠀⢈⠝⠁⠀⠘⡀⠀⡇⢰⠇⠀⢠⠞⠁⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⡇⠀⠂⡅⠀⠀⠀⠛⠦⣄⠀⠀⠰⠀⢡⡜⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠸⡇⠐⠃⠧⠦⠤⠤⠤⡄⠈⠙⢦⡀⢣⢸⠁⡼⠃⠀⠀⠀⠀⠀⣀⣤⣄⢸⡇⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⣧⠀⠀⠤⠤⠤⠄⠀⣸⠀⠀⠀⠹⡄⢾⡼⠁⠀⠀⠀⣀⡤⠞⠉⠀⠀⠚⢆⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢙⣀⣀⡀⠀⠀⠀⢀⣟⣀⣤⣤⠴⡾⠛⠋⡿⠴⠖⠚⠉⠀⠀⠀⠀⠐⠢⣄⠁⢀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠩⠛⠉⠝⠓⠚⠋⠉⠉⠀⠀⠀⢰⠃⠀⢰⡇⠀⠀⠀⠀⠀⢀⡤⠶⠳⢤⡈⠙⠦⣵⣽
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⢸⡇⣀⣀⣠⣤⡞⠉⡀⠀⠀⠀⠉⢲⡶⠚⡟
⠀⠀⠀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠶⠚⠛⣉⣉⣛⣛⣃⣀⠠⠐⢹⡄⠀⡇⠀⡇⠀⡇⢈⣇⣠⣁⣀⣀⣀⣀⣀
⠀⠉⠈⠉⠉⠉⠉⠳⠶⠶⠶⠖⠒⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠶⠋⢦⡴⠧⡴⢇⡠⢧⡼⠁⠀⠀⠀⢀⣀⡠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠙⡆⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣉⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢠⡄⡎⠉⠀⠹⣏⠙⠛⠲⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡌⢀⠀⣀⠀⠀⠀⠀⠀⠀⢆⢣⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠙⣦⠀⠀⠀⠀⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠤⢘⠀⠀⠑⣦⠀⠀⠀⠀⠈⢄⢳⡀⠀⠀⠀⠀⠀⢀⡀⠙⢦⡀⠀⠀⠀⢀⡔⠒⠒⠀⢄⠀⠈⠳⣄⡀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⣀⠁⠄⠀⠈⠅⠚⠀⠀⠀⠀⠀⠈⢆⢳⡀⠀⠀⠐⣊⡥⠶⠂⠈⠳⣄⠀⠀⢸⡁⠀⠀⢀⠀⠈⠳⣤⡈⠛⠶⠶⠚⠙⠛⠲⢦
⠀⠀⠀⠀⠀⠀⠀⠈⠠⡏⠥⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢳⡀⠐⠉⠁⠀⣀⣠⡤⠶⡞⠃⠀⠈⠳⣄⣘⡤⣈⢢⠀⠈⠙⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠱⠤⠒⣚⠉⠅⠐⠀⠁⠀⠀⠀⠀⠀⢏⠈⢄⠉⣛⢤⠀⠀⠀⠀⠉⠛⠓⠶⠶⠞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣃⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣆⣤⣤⣜⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠂⡆⢰⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣘⣀⣁⣃⣘⣘⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠉⢉⣉⣉⣉⣈⡀⠀⠀⠀⡴⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢨⡇⠀⢀⠎⠈⠢⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠘⣀⠤⡄⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠤⠤⠤⠤⠤⠤⡇⢠⠊⠀⠀⢱⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠣⢀⣀⣀⣀⠠⠔⠊





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠊⠉⠉⠉⠑⠲⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠦⣀⠀⠒⢄⠀⡔⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⣈⡳⢦⣄⣉⣰⣷⣶⠶⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠞⠃⠀⠈⠙⡆⠈⠉⣉⣁⣠⠴⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠠⠄⠸⠃⠀⢶⡷⠀⠁⠻⠁⣠⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⣤⠀⠐⠅⠀⣄⣰⢰⠷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣀⣠⠴⠋⠀⠑⣄⠀⠀⠀⢸⠰⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⢀⡴⠛⣦⠀⠀⠸⣄⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠉⠀⠐⠃⠈⠀⠀⠀⢯⠁
⠀⠀⠀⢏⠑⢤⣀⠀⠀⠀⠀⠀⢀⡤⠴⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣈⡙⠲⢤⣀⣴⠏⠀⣀⠀⢳⠀⠀⠀⠀⠀⠀⠀⡈⠷⣤⣀⣀⣀⠀⠀⣀⣀⣠⣴⠞⢧⣄
⠠⣞⠉⣉⡡⢭⡞⣡⠔⠂⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠈⡽⠟⠛⡿⢩⡏⠁⡘⠀⠀⠈⠳⢦⡀
⠠⠀⠐⡄⢠⡏⠀⠹⠆⠀⢀⣰⠇⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢰⠒⠉⠀⢀⡠⢿⠀⡟⠀⠤⢃⡀⠀⠘⢡⠂⠙⢦
⠁⠀⠀⠀⡀⠤⠀⠀⢀⡶⠋⢹⠀⠀⠀⠀⠀⢀⡞⢠⠆⠀⠀⠀⠈⢆⠀⠀⢸⡇⠈⣾⠀⠀⠀⣠⠴⠛
⠀⠛⠂⠀⠀⠀⠀⠀⠘⢧⠀⠸⡆⠀⠀⠀⣠⠋⢠⡟⠀⠀⠀⠀⠀⠀⠣⡀⠀⡇⢠⠃⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⣧⠀⢀⡴⠁⡴⢣⠁⡠⢠⣀⢀⡀⠀⠀⠱⣄⢁⡬⠖⠁⠀⠀⠄⠀⠀⠉⢉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢻⡤⠎⢀⡜⠡⠄⠀⡃⠀⠀⠈⠉⠀⠂⠀⠈⢿⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠘⠃⡴⠋⠀⡤⠀⠀⠁⠀⠂⠠⠤⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⢀⠃⠀⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠁⠀⠀⢤⡀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠲⢶⠤⣤⣤⣤⣀⣀⣀⣭⣀⣀⣀⣠⣤⣤⣤⣤⣤⠴⣶⠶⠞⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⡟⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⣄⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠐⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠋⠉⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠉⠉⣙⠒⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⢀⡤⣶⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⣤⡟⠳⣄⡀⠈⠉⠛⠶⠶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣀⡀⠀⣀⣠⠴⠚⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⠤⠤⠴⠚
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⣀⣀⣀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡞⠁⠁⠀⠀⠀⠀⠀⠀⠈⣟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢐⣀⣀⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡀⠀⠄⢈⡄⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠈⠑⠢⡈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠥⠀⠐⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣿⢧⠻⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠠⡀⠀⡀⡀⠀⠀⣈⠁⡲⠠⠈⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⣤⠍⠁⣨⠖⡱⠇⡈⠚⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠉⠀⠐⠂⠒⡲⠒⠂⠠⠔⠁⠚⢧⠒⠀⠁⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⠀⠘⠁⠀⠀⠀⠀⠀⠂⠀⠂⠁⢀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠉⡉⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⢀⡞
⠀⠀⠀⠀⠀⢀⠀⢠⠀⣀⡀⠀⠀⠀⢀⡀⠠⣶⠖⠋⡚⠂⠠⠄⠀⠀⠄⠐⡇⠀⠠⠁⠀⡞
⠀⠀⠀⠀⠀⠘⠂⠈⠉⠁⠍⡁⠰⡗⠁⠀⠀⠓⠂⡐⠈⠂⠀⠀⠰⠀⠀⠀⠀⠀⠂⢀⡍⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⠂⠀⡈⠀⠖
⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡄⠘⠀⢀⡄
⠀⠀⠀⠀⠀⢸⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠃⠀⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠠
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠤⠄⠀⠀⠀⠒⠠⠅⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣤⠶⠛⠀⠀⠙⠳⢦⡴⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⣀⣤⠶⠶⣤⣄⠀⠀⠀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡾⢫⡄⠘⠓⠀⣬⢻⣄⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠁⠀⣸⢣⡄⠀⠐⣇⠀⢀⣤⣿⠀⠀⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣄⠀⢸⣆⢡⡀⠀⠙⠓⣄⢁⡿⠀⢀⡴⠟⠀⠀⠀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠙⢮⣅⣐⣗⣀⣽⠟⠁⠀⣾⠁⠀⠀⠀⠀⢉⡽⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡀⠈⠉⠉⠉⠀⣀⣀⣀⡿⠃⠀⠀⣠⡶⠋⢀⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠙⢷⣀⣀⣼⠛⠉⠉⠋⢀⣠⡴⠟⠁⠀⠀⡟⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣁⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⣼⠛⠛⢻⡆⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⣦⠀⠀⣿⠀⠀⢸⡇⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⣿⠀⠀⢸⡇⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣧⣤⣤⣿⣤⣤⣿⣤⣤⣼⣧⣤⣤⣧⣤⣤⣿⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⢸⠛⠓⡆⡖⢠⢠⠲⢰⠒⡄⠒⠰⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠉⠀⠀⠉⠈⠀⠁⠉⠀⠃

⠀⣴⣧⠄⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⡐⢾⠖⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠈⠁⣴⣶⡀⠀⢸⢿⣿⢿⠀⠀⠀⠀⣻⣿⡃⠈⠀⠀⠀⠁⠀⠛⠢⡀⠀⢸⠀⠉⠉⠀⠃⠀⠀⠀⡶⡿⢿⢷
⠀⠀⣸⣇⢨⡗⠀⢸⢽⣿⢽⠀⠀⠀⠘⠿⡿⠯⠀⠀⠀⠀⢀⢀⢀⠀⡇⠀⢸⠀⠀⠀⠀⡅⠀⠀⠀⠉⠉⠀⠉
⠀⠀⠉⠈⢁⡙⠀⢸⢽⣿⢽⠀⠀⠀⢀⣤⣯⣄⠀⠀⠈⢢⠊⠘⢲⠋⢀⠀⢸⣀⣀⣀⣀⡃⠀⠀⠀⠀⢱⠆
⠀⠀⠀⢠⡄⠀⠀⠈⠛⠋⠉⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠁⠀⠁⠐⢾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀
⠀⠀⠀⠻⡇⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡈
⠀⠀⠀⣾⣷⠆⠀⣿⡇⡆⡛⣈⠻⢡⣽⡄⡼⢡⠹⠡⢹⣿⠃⣦⠃⣿⢸⠠⢹⠃⢻⠁⢨⣧⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⣡⣇⠛⣤⠘⣻⡇⣷⡘⣸⢠⡘⣿⡄⢛⡄⠟⢸⢰⣏⣠⢸⡀⡌⣿⢸⣿⡇⢸⡏⣿⠁
⠀⣄⠀⢀⣀⠀⠀⠘⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠀⠀⡇⣿
⠉⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⠴⠆⠆⠀⠂⠂⠸⠀⠲⠐⠀⠂⠂⠀⠐⠐⠐⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⣀⣦
⠀⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠃
⠀⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠛⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠉⠀⢠⣾⣾⣶⣶⣾⣾⡆
⠀⠙⣿⣿⣿⣿⠟⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣤⢀⣠⢤⣤⣤⣤⣦⣤⠀⠀⢸⣿⣿⡑⠗⣽⣿⣷
⠀⠀⠈⠙⠛⠁⠀⠐⢻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠐⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⡆
⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⡿⠿⢿⠿⠿⣿⠟⠻⡿⠛⢻⠛⠛⣿⠛⢻⠛⡙⣿⢉⠙⣇
⠀⣿⢹⡏⣿⢹⢡⡌⡇⣤⢹⠀⣇⣾⣿⡇⡇⢹⡀⣿⣧⢰⠈⠀⡦⢸⢸⡇⡇⢸⣼⡆⡇⢸⠸⢿⡌⢷⣿⡘⢷⣿
⠀⣿⡌⢁⠁⣾⢸⡇⡇⠙⢸⡇⠘⣿⣿⡇⡇⣈⠃⣿⣿⢨⣴⡇⣄⢺⢸⡇⠇⢸⡀⡇⣦⢹⢰⣾⠿⣆⢻⢷⡄⣿
⠀⣿⡇⢸⡀⣿⠸⡇⣇⢸⠀⡇⣧⢹⣿⡇⣇⢹⡀⣿⣿⢸⣿⡇⣿⢸⡌⠃⣾⡘⣁⣇⣿⣸⣀⣉⣆⣁⣼⣄⣡⣿
⠀⢻⣿⣼⣧⣿⣧⣴⣿⣾⣷⣷⣿⣾⣿⣷⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛
⠀⠈⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣶⣾⡛⢶⡀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⡴⠀⣼⡇⠀⠀⠀⢠⠀⠀⡀⢺⡀⠿⣿⣏⠳⣝⠉⠄⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠆⠀⢿⡇⠀⠀⠀⠀⢃⠀⠀⠀⠻⣮⣿⣯⣵⢏⠄⠀⠀⠀⠀⣿⡇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⣸⣟⣀⠆⠀⠀⠈⣆⠀⠀⢠⣿⣿⣏⣷⠀⠀⠀⠀⠀⠸⣿⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⢀⣴⡿⠿⠿⢿⣷⡄⠀⠀⠈⢆⠀⣾⣿⣟⣼⠃⠀⠀⠀⠀⠀⢀⣿⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⣼⣿⠀⠀⠀⠀⢹⣿⠀⠀⠀⠈⢢⡯⡿⣼⠃⠀⠀⠀⠀⡀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠃⠀⠀⠀⠡⡀
⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠘⢾⠇⠀⠀⠀⡠⠊⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡜⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠎⠀⢀⠴⠋⠀⠀⢀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⠁⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡈⠀⡴⠋⠀⠀⠀⠀⡀⠸⣷⣬⡿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⢣⣼⣿⠄⢀⡜⠀⢀⣀⡀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢸⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠸⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠸⠏⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⡆⡄⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂⠀⠀⢤⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠰⠁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⣠⠀⠀⠙⣦⡄⠀⣠⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠁⠘⢛⣄⣋⣁
⠀⠀⠀⠀⠿⠗⠸⠋⠀⠀⠁⠉⠉⠀⠀⠃⠀⢰⣷⠀⠀⠀⠀⠐⢅⠌⠀⠀⢠⠋⠀⠀⠀⡄⠀⢀⡆⠀⠀⠁⠀⠀⠀⠀⠈⠉⠑⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣤⣤⣤⣤⣤⣀⣀⣁⣀⣀⣀⣀⢀⣠⣀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠞⠀⠀⡠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠚⠛⠒⠒⠒⠒⠒⠒⠲⠶⠖⠶⢶⡶⠶⠶⠒⠶⠒⠒⠒⠂⠀⠀⢠⠸⣆⠠⠀⣀⠀⣀⢠⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣦⣿⣿⣧⢶⣋⡥⠒⠠⠀⠀⠀⠀⡸⡀⠈⡁⠈⢉⣹⣿⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠠⠆⠐⠲⠄⣀⣀⠀⠀⢠⣲⣾⣿⣾⠿⣿⡟⠍⢳⡋⠁⠀⠀⠀⠀⠀⠀⠀⠃⠐⡄⠈⠦⠙⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠶⠀⢀⣀⠈⠳⠀⠈⠁⠀⠂⠴⠶⠷⠶⠶⠶⠶⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠈⠂⢀⠊⢀⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠐⠀⡉⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⠤⠂⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣷⣦⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠈⠻⣿⣦⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀⠀⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠻⣿⣦⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠈⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⠙⢿⣿⡋⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠘⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠻⣿⣦⡀⠀⠀⠀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣦⡀⠀⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠁⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠙⢿⣦⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢿⣦⡀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠃⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣠⣾⡟⠋⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⢠⣾⠿⠁⠀⠀⠀⠀⠀⠀⣹⣿⣷⣄⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⣠⣾⠟⠁⠙⢿⣷⣤⣾⠟⠁
⠀⠀⠀⠀⠀⣠⣿⣿⣦⡀⣠⣾⠟⠁⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⣠⣾⠟⠁⠀⠙⠿⠟⠁
⠀⣠⣾⠟⠁
⣾⡟⠁
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣤⣴⣤⣄⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣦⣾⡿⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠞⠿⠿⠟⢿⡿⣦⣠⣶⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⡄
⠀⠀⠸⣋⠈⢉⠀⣿⣿⡏⢀⠀⠀⣻⢿⣿⣿⠀⠀⠀⠀⠀⠀⢖⠂⠐⠦⢸⣿⣿⣿⢿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣠⣴⣶⣶⣬⡋⠁⠘⣿⢿⣿⡧
⠀⠀⠀⠎⠂⠘⠄⣠⠜⠁⠸⠃⠐⡁⢼⡿⠃⠀⠀⠀⠀⠀⠀⡏⠓⠈⠃⠘⣩⠏⠀⠠⡀⠙⣹⣿⣿⡇⠀⠀⠀⢰⡿⣿⢿⣿⣿⣿⡶⠠⠉⠸⡿⠃
⠀⠀⠀⠐⠀⡴⠛⢅⠀⠀⣀⣠⡰⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠎⠁⠀⢈⡀⢀⣂⣽⠛⠋⠀⠀⠀⠀⠈⢃⡉⢀⡁⢻⢿⡄⢀⢬⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠈⣑⠂⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢱⠒⠉⠋⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠈⣱⠐⠈⢀⣀⠀⠀⠀⠀⠁
⠀⠀⠀⢈⠃⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠻⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣳⣧⡚⠁⠀⠁
⠀⠀⢀⡤⠆⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡎⠀⠈⠀⡀
⠀⠀⠀⠜⠁⡴⡈⠧⠀⠀⠀⠀⢠⠢⡀⢀⡀⠁⠄⠀⠀⠀⢸⣿⣿⣿⡋⠣⠀⠀⠐⠈⡤⢤⠤⣀⠈⠠⠀⠀⠀⠀⠋⠇⣴⠚⠏⠀⠀⠀⢠⠢⡄⢀⡀⠁
⠀⣀⣔⣦⢠⠤⠄⠀⠀⠀⠀⣀⣸⠶⣆⣠⣀⠀⠀⠀⠀⣀⣼⣿⣿⠧⠤⠀⠀⠀⠀⢀⣌⠔⣄⣀⡀⠀⠀⠀⠀⠀⣼⡷⢧⠄⡀⠀⠀⢀⣈⠶⢆⣸⣀
⠀⠉⠙⠂⠉⠀⠀⠁⠀⠀⠂⠀⠉⠘⠃⠙⠋⠛⠀⠀⠀⠉⠙⠋⠉⠁⠀⠈⠀⠀⠀⠀⠉⠙⠉⠛⠁⠃⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠉⠈⠛⠘⠋⠙⠃
⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣶⣦⣄⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⢠⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣻⣝⠛⠋⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣆
⠀⠀⣿⢠⠈⢹⡛⣿⣿⣿⠙⠋⠻⡿⣿⣿⣿⠀⠀⠀⠀⠘⠇⡀⠀⣉⢈⣿⣿⡿⣦⠄⡸⠋⣿⣿⠃⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣿⠻⠟⢿⡿⣿⣿⣿
⠀⠀⠙⡈⠁⠈⣴⣿⣿⠟⠅⠲⢀⢰⣿⣿⠟⠀⠀⠀⠀⠀⠐⠓⠀⠩⠈⠛⠋⠀⠉⠀⡰⠈⢟⠁⠀⠀⠀⠀⠀⢸⡏⠸⡏⠈⢻⣿⣆⠀⠄⠠⣾⠿⠟
⠀⠀⠀⠀⡰⠎⠙⣢⣀⢀⣶⣤⡖⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣵⣤⣀⣠⣶⡤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠰⢆⠈⡹⠃⠀⠸⠄⠛⢀
⠀⠀⠀⠀⡇⠀⠀⣤⣭⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣯⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣄⡄⠺⠿⠃⡀
⠀⠀⠀⢀⡁⠀⠀⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡛⠛⠂
⠀⠀⠀⠁⠀⠀⠠⡁⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠩⠋⡉⢹⡃⠀⠀⠀⠂⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠴⣿⣿⣿⣧⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⢤⡠⢳⠀⠁⠀⠀⠀⠘⠉⡋⢹⠂⠀⠀⠀⠀⠀⠀⠀⣸⢸⢒⠀⠁⠀⠀⠀⠀⡍⢀⢰⠀⠀⠀⠀⠀⠀⠀⣰⡦⢹⠀⠁⠀⠀⠀⠘⠉⡋⢱⠂
⠀⠀⠰⡜⠾⠛⠀⠄⠀⠀⠀⠲⢌⡽⢶⡶⢤⠀⠀⠀⠀⠀⠾⡿⠽⠚⠀⠄⠀⢀⠐⠶⢯⡭⢾⡦⣤⠀⠀⠀⠀⠘⠻⠟⠙⠀⠄⠀⠀⠀⠲⣮⣽⢾⡶⢤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣟⣻⡿⣿⠿⠿⠿⣿⡿⢿⣟⣻⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠶⢮⣭⣭⣭⣭⣭⣭⣭⣭⡵⠶⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡶⠛⠛⢶⡞⠉⠀⠈⠉⢉⣭⣭⣿⣿⡛⠉⠉⠉⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣼⣷⡀⠀⠀⠹⢦⣤⣤⣤⣴⣿⣿⣿⣿⣇⣀⣀⣤⣿⡿⣿⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠻⢶⣄⣠⣶⣽⣶⡉⠁⢻⣿⣿⣿⡟⠉⠉⠀⣨⣽⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣀⠀⠀⠀⠀⣩⣛⣿⣿⣇⣠⣴⠿⠿⢿⣻⣿⣶⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣙⠻⠶⣦⣤⣿⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣿⠇⠀⠉⣉⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣌⣉⡙⠛⠋⣄⣀⣠⣤⠶⠟⢛⣉⣀⣤⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⠁⠀⠀⠉⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⣴⡟⢷⣆⠀⠀⠀⠈⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠻⣦⡾⠏⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣀⣠⣤⣤⣤⣤⣤⣤⣀⣸⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⢸⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⡀⢠⣾⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢠⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⢁⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢸⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣀⣙⣛⣛⣛⣁⣾⣿⣿⣇⢹⡟⢛⣛⣛⣛⣛⣛⣋⡀⠀⠀⠀⢸⣿⣿⣿⣿⣷⢄⣀⡀⢀⣀⢴⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⡆⠁⣿⣿⣿⡿⠋⠉⠉⠁⠀⠀⠀⠉⢉⠉⣉⣩⠝⠀⠀⠀⠀⠀⠈⠯⣉⢉⣉⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⢸⣿⣿⣦⣄⡀⠀⠀⢀⣤⣾⣿⡇⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⢇⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⢉⣤⣉⠻⣿⣿⣿⣿⣿⣿⣿⡿⢫⣾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢰⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⡿⢡⣿⠛⠛⠛⠛⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣌⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⡀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⢠⢦⣰⡄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡽⠺⡼⠈⠙⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⠀⢀⣴⠞⢛⣛⡛⣛⡛⢛⣛⠛⣛⡛⢛⣛⠛⣛⡛⢛⣛⢛⣛⡛⣛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢶⣄
⠀⠀⠀⣿⢱⣿⢸⣿⡇⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⢨⣿⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⢻⣜⠿⢸⣿⡇⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠸⣿⡇⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠉⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣤⢄⢠⣄⢠⣤⡄⡄⣤⣠⢠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣇⣸⣸⢾⣸⣀⡇⡇⡟⣿⢸⣰⡆⠀⡀⢀⡀⢀





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣻⣛⣿⣻⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣭⣭⣭⣿⣿⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠤⠤⠤⢤⢤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⣀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠉⠉⠉⠈⠹⢿⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠤⠤⠤⠤⠶⠾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠏⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⡌⠐⢲⡶⠲⠂⠒⠒⢒⣾⢻⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⡔⠺⣾⡟⢀⣦⣀⡸⠟⡀⣸⠀⠀⠀⠀⠀⠀⠀⣥⣿⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⢈⣿⡋⢁⣼⡁⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠓⠲⣶⠶⣾⠟⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠃⠀⠀⢤⣧⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢙⡆⠀⠀⣞⠉⣷⠀⠀⣚⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⠋⠁⣀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢸⡇⣼⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⢀⠀⡤⠠⡄⠀⠀⣠⠒⢠⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⠉⠉⠉⠉⠉⠉⢸⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠼⠃⠀⠀⠢⠴⠃⠀⠀⠙⠶⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣋⣸⡇⠀⠀⢨⣀⣵⠀⠀⠺⣤⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠐⠀⠀⢠⣤⣤⣤⣤⣤⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡄⠀⠀⣔⠀⣆⠀⠂⢠⡁⣰⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢹⠙⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠙⠛⠃⠀⠀⠈⠛⠋⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣈⣀⣀⣼⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⣷⠛⠛⣶⢶⡶⣶⠶⠶⣾⠶⢶⠶⠶⣾⠷⠶⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢶⡶⡶⣾⢿⣿⣿⠾⠿⠷⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⠟⠛⠛⠻⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠠⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠐⠒⠚⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⠀⠀⠀⠀⠀⢸⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣦⣰⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣾⣿⣿⣿⡟⠛⢛⣻⣿⣿⣿⣿⣿⣿⡛⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢉⣉⣉⠉⠉⠉⠉⠉⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⠁⠀⠈⣿⣿⠀⠀⠿⡿⠿⠇⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣹⡄⣿⣿⣿⣿⠋⠀⠿⠿⠿⣿⣿⠀⢰⣿⣿⣿⣷⠀⣿⣿⣿⡃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡏⠀⠀⠀⠀⠀⢹⣿⠀⡦⠶⠶⠶⠶⠶⠶⠶⠶⢶⡶⠈⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢀⣺⣿⠀⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣯⣿⣿⣿⣿⣿⣿⡀⣠⣶⣶⣶⣶⣿⣿⣿⠀⣿⠽⠿⠿⠿⠿⠿⠿⠿⠷⠧⠁⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⠀⣟⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡶⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣁⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠛⠃

⠻⣦⡀
⠀⠈⠻⣦⡀
⠀⠀⠀⠈⠻⣦⣤⡀
⠀⠀⠀⠀⠀⠻⣄⠙⠷⣄⡀⣠⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠘⢧⡀⣨⠟⢁⣽⠟⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣨⠟⠁⣴⠟⠁⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣷⠟⠁⠀⠀⢀⡀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⢁⡴⠀⢀⡴⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡴⠋⣀⠀⠀⣀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⣠⠖⢀⣴⠗⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⠟⢁⡄⠀⢀⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣏⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⡴⠋⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡾⠃⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡴⠋⣠⠞⠁⠀⠀⠈⠻⣦⢀⣤⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠞⠻⣦⡀⠀⠀⠀⢀⣼⠟⣡⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁⠀⠀⠈⠻⣦⡀⣴⠟⣡⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⣡⡾⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣞⣋⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠉⠙⠒⠦⣄⠀⢀⡤⠖⠚⠉⠉⠉⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢶⠖⠉⠛⠁⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢠⠏⠓⠃⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⣤⠄⠀⡞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠛⠀⠂⣠⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠈⠢⣀⣈⣀⠤⠞⢄⣀⣤⠖⠉⠀⠙⢖⢲⠊⢁⣈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠢⠀⣀⠤⢄⣤⣴⠕⠁⠀⠀⠀⠀⠈⡆⢀⡴⠒⠺⠇⠀⡟⠚⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢱⡀⠀⠀⠘⣿⣤⡤⣄⣀⣀⡠⠤⣄⣀⠀⢀⣧⣸⣄⡀⠀⠀⣠⠃⠀⢀⡞⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢳⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠉⠀⠀⣀⠴⠈⠉⠉⠁⠀⠀⡼⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢞⠓⠦⣄⡀⠀⠀⠉⠢⣄⡀⠀⠀⣀⠴⠚⠁⠀⠀⠀⣠⠴⠚⣳⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠈⠳⣄⠀⠉⠓⠒⢤⡀⠀⠉⠒⠋⠁⠀⢀⡤⠖⠚⠉⠀⣠⠞⠁⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠙⠦⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠴⠋⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⠀⠀⠙⠀⠀⠀⠀⠋⠀⠀⠀⡴⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⠇⡠⣀⡠⢤⠀⢀⠤⡄⡆⡤⠀⠠⠄⠀⢰⠉⠈⠀⠂⢀⠤⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⠂⠑⠚⠈⠈⠒⠃⠁⠁⠀⠐⠒⠀⠈⠑⠒⠀⠀⠀⠀⠀⠈⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣿⣷⣄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣴⢋⡴⣫⡼⠛⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠙⢿⣯⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⡿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⡥⠤⣤⠄⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⢰⡏⣠⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣭⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣟⣷⣝⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠶⠶⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠞⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣭⡅⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⢸⡇⣒⡂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⣦⠀⠀⠀⠀⣸⠀⣧⠀⠀⠀⠀⢸⡇⠭⠥⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣼⠀⠀⠀⠀⡟⠀⢹⡀⠀⠀⠀⢸⡇⣛⡃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠉⠳⡄⠀⠀⠐⣇⠀⢸⠇⠀⠀⠀⢸⡇⠶⠆⠀⢸⡇
⠀⠀⠀⠀⠀⢠⡏⠈⣧⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⣤⣤⣤⡄⣿⠀⠀⣴⠋⠀⠈⢷⠀⠀⠀⢸⡇⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠳⠴⠃⡞⢹⠄⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣾⠛⢻⠀⠀⣠⡼⣧⣤⣤⣤⣼⣧⣤
⠀⠀⠀⠀⣰⠻⡄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⣿⠀⢸⠀⠀⠙⠛⠻⡟⣿⢻⡟⠛⠋
⠀⠀⠀⠀⠳⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⡇⣿⠀⠀⣿⠀⢿⠀⢸⠀⠀⠀⠀⢰⡇⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣤⣤⣤⣤⠇⣿⠀⠀⣿⠀⠘⠒⢾⠀⠀⠀⠀⣸⣇⣿⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠶⠶⠞⠃⠀⠀⠙⠶⠶⠶⠋⠀⠀⠀⠘⠷⠿⠿⠿⠾⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠙⠒⠋⢗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⣐⠠⠋⢄⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⡠⠔⠊⠁⠀⢀⡀⠱⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢠⠊⠔⠂⠀⠀⠀⣀⠤⠤⣥⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢡⣸⠴⡞⢩⡉⢹⠉⣇⡛⠀⢛⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣈⡀⠑⠒⠒⠉⠀⣡⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢠⡤⠄⢰⠆⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠬⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣄⠀⠀⠉⠁⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠐⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⠑⠦⢀⠠⠔⢉⢣⡠⢄⡀⠀⠀⠀⠀⠀⣏⡀⠈⣀⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⡇⠘⡀⠀⠀⠀⡠⠋⠈⠉⠅⠌⠉⠁⠈⠳⡄⢹⡆⢀⡀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠂⠀⢁⠀⢈⠦⠴⡉⠀⠀⣼⠀⠘⡀⠀⠀⠀⠀⠈⡃⠓⠄⠠⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠆⠀⠀⠀⡑⠂⡀⡷⢇⠀⠀⡱⢄⠜⡉⠀⡠⠃⢠⠀⠀⠀⠀⠇⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⠀⠀⠀⢇⠆⡇⠃⠈⠃⠘⠀⠀⠀⠆⢐⠁⢀⣼⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢨⡌⣦⠀⠀⠀⠠⠀⠀⠀⠀⠀⡃⢝⠄⢂⠆⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠱⡬⠀⠀⠀⠀⡄⠀⢠⠀⡐⠡⠤⠭⠥⠄⠀⡀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡄⠸⠀⠁⡀⠀⠀⠀⠃⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠠⠀⠀⡇⠀⠀⠀⠃⣶⠀⠀⢰⠀⢰⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇⢀⣌⣲⣅⣹⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠈⠁⠈⠉⢹⠀⠀⠀⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠄⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⡁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠊⠀⢸⡀⠀⠀⠀⠘⡀⠀⠀⢁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡜⡇⠀⠀⠀⠀⡇⠀⠀⠈⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡇⡇⠠⢄⡀⠀⡇⠀⡠⠞⠀⠀⢰⠀⠀⠀⠀⣀⠄⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢠⠃⣧⠀⠀⠀⠀⡆⠉⡅⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢰⡇⠀⠀⠀⠀⠉⢳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⡐⡇⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠻⣤⡀⠈⠳⣶⣤⣈⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡥⠀⠀⢀
⠀⠀⠀⠈⠙⠷⣾⣿⣿⣿⣷⣦⣉⣻⣟⠂⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣼⣷⣔⡁⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⣿⠡⣓⣤⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢜⠁⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠉⠁⢀⣤⠏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢷⠀⢀⠀⠀⢀⠀⣀⣴⣿
⣿⣶⠦⠄⠀⠂⠀⠈⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⠀⢠⣄⣀⣀⣀⣤⣆⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢉⣻⣿⣿⡿⠃
⠙⠻⠶⣤⣤⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠄
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠒⠐⠚⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠞⠓⠂⠐
⠀⠀⠀⠉⢁⢤⠁⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣟⡽⠁
⠀⠀⣾⡤⠴⠐⢦⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⡀⢸⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⢳⡴⠀⠚⠇⠰⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠸⡇⢹⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⢹⣿⢀⣄⣄⣰⡶⠀⠀⠀⠀⠀⠀⢹⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠻⣏⡭⠵⢿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⣭⣿⡇⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡠⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠞⠁

⠀⠀⠀⠀⠀⣾⡟⢻⣦⢸⣟⣛⠃⣿⠟⠻⣦⠰⣿⠀⣸⣿⣆⠘⢻⣿⠛⢸⡟⠛⣷⠀⣿⢠⡾⠛⠻⠆⣿⡆⢠⡿⣷⠀⢸⣷⣄⢸⡇
⠀⠀⠀⠀⠀⣿⡟⠛⠁⢼⣏⣉⡁⣿⣄⣠⡿⢈⣿⢰⣿⣶⣿⡄⢸⣿⠀⢸⡟⢻⣏⠀⣿⠸⣧⣀⣠⡄⣿⣃⣾⣧⣿⣇⢸⡏⠻⣿⡇
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠀⠀⠁⠈⠁⠀⠈⠁⠀⠉⠀⠈⠁⠀⠉⠀⠉⠀⠈⠉⠉⠀⠉⠀⠉⠀⠀⠉⠈⠁⠀⠈⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⢸⣿⠀⠀⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⡾⠛⢷⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠁⠀⠀⠀⠈⠉⢉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠛⠛⠛⠛⠛⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡶⠗⠸⣿⡟⠀⠀⠀⠘⢿⡿⠀⠿⣿⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣠⣷⠾⠋⠀⠀⠀⠉⣿⡿⠿⠿⢿⡟⠁⠀⠀⠈⠻⢿⣥⣀⣤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣤⣿⠶⠟⠛⠋⠉⠁⢀⣠⣤⣴⢶⣿⠛⠿⣶⣾⠟⠻⣷⠶⣦⣤⣀⠀⠈⠉⠛⠛⠿⠿⣦⣴⣆
⠀⠀⠀⠀⠀⢠⣶⡾⠛⠉⠁⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠈⠛⢷⣾⡟⢿⣶⠟⠋⠀⠀⠈⠙⢿⣆⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣄
⠀⠀⠀⠀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠻⣦⣾⠃⢀⡀⢀⢀⡀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡂
⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⣸⡇⠀⣿⠛⠛⠛⣿⡇⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠄
⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠿⠶⠶⠶⠿⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣴⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠃
⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣉⣀⠀⠀⠀⢀⣀⣀⠀⠀⣠⡿⡇
⠀⠀⠀⠀⠀⠋⢛⣠⣴⠶⠾⠟⢿⣿⠻⠷⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠛⢷⣦⡾⠛⠉⠙⠻⣦⡉
⠀⠀⠀⠀⢠⣶⠟⠉⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠰⠾⠃⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⢀⣤⣤
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠘⣿⠈⢿⣄⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⢠⡿⠁⣽
⠀⢀⣾⠇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⢸⣇⡀⠀⠀⠀⢹⣇⠀⢻⣦⣤⡀⠀⠙⣷⣄⠀⠀⠀⢀⣴⠟⠁⢀⣤⣤⡿⠁⣸⡟
⣼⠟⠻⠃⠀⠀⠀⣿⣍⣿⠂⠀⠀⠀⠀⠸⣯⣹⡷⠀⠀⠀⠸⠟⢻⣆⠀⠀⠀⢻⡆⠘⣿⡈⠻⣦⡀⠈⠻⣦⣀⣴⠟⠁⠀⣴⠟⠁⣽⠇⢠⡿
⢿⡆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠈⣿⡀⠸⣷⡀⠘⢷⣤⡀⠈⠛⠁⢀⣤⡾⠋⠀⣼⠏⠀⣾⠃
⠈⠻⣶⡄⠀⠀⠀⠀⢀⣴⠾⠿⠶⠾⠿⠷⣦⡀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠘⣷⡀⠈⠁⠀⠀⠈⢿⣆⠀⢠⡾⠋⠀⠀⠀⠉⢀⣼⠏
⠀⠀⠸⣷⡀⠀⠀⠀⣿⠃⠀⣴⠶⢶⣄⠀⢸⡇⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⣿⠀⣿⠃⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠘⢷⣄⠀⠀⠙⢷⣼⣿⣀⣠⣿⣴⠿⠁⠀⢀⣤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⠀⠀⠀⢀⣿⠀⢿⡇⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠙⠷⣦⣀⣸⣿⡉⠉⠉⢉⣿⣀⣠⣴⠟⠋⠘⢷⣤⣀⠀⠀⠀⢀⣠⣴⡟⠁⣸⡇⠀⠀⠀⢸⡏⠀⢸⣧⠀⠀⠀⠸⣧
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣛⣻⣿⣿⣛⣛⣛⣉⣀⣀⣀⣀⣘⣋⣙⣿⣛⣛⣿⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⢀⠀⠠⠀⠀⠄⠀⠀⠈⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠠⢆⠀⠂⠀⠀⠀⠀⠀⠀⠈⠐⢇⠀⠐⠀⠒⠀⣈⡁⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠙⠋⠀⠈⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⣮⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠃⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠳⠂⢀⠀⠀⠀⠀⠐⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠴⠋⠀⠀⠀⠠
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠃⠀⠀⠀⠀⢠⡂⠀⠀⠁⠀⠀⠀⣀⢀⣀⡀⡀⠀⠀⠀⠁
⠀⠀⠀⢐⠀⠔⢄⢠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠕⢀⠔⠀⢀⠄⠀⢨⠈⠉⠀⠀⠐⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠉⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠠⠀⠀⢀⠂⠰⡂⠀⠀⠀⠠⢢⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⡴⠈⠓⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠃
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣍⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠐⡄⢀⠊⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠠⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠰⠛⠀⠀⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣴⠏⠉⠉⡀⢄⠻⡅⠀⠉⠉⠐⢲⣄⡛
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢦⣴⠷⣤⡼⠆⠀⠀⠀⠀⠀⠛⠙⣷
⠀⠀⠀⠀⠀⠀⠐⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠗⠀⢀⡐⠾⠓⠀⠀⠀⢀⡀⠀⣶⡼⠏
⠀⠀⠀⠀⠀⣿⠛⠛⢻⡆⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⢀⣨⠟⠀⠀⠀⠀⠀⣨⠇⠀⡟
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢧⣤⣤⣴⣾⠛⠉⠀⠀⠀⣠⠴⠊⠁⠀⢠⡇
⠀⠀⠀⠀⠀⢻⡅⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠐⠂⠁⠤⠤⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠈⡇⠒⠈⣧⡀⠂⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢀⠐⠈⣛⠀⣠⣇⣀⣰⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣤⣀⡄⠀⠀⠀⣀⣼⡀
⠀⠀⢚⠙⢷⣚⣉⣁⣠⣤⠜⠏⠀⠀⠀⠀⠀⠀⠀⣸⣃⣀⣀⣀⣀⣀⣤⣴⠖⠋⢉⡇⠉⠳⢦⣄⡀
⠀⣀⣈⢦⡄⠉⢯⡉⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠈⠩⡉⠛⠋⠉⠉⠁⠀⢀⡰⠋⠀⠀⣀⠀⠉⠙⠳⢦⣄⣀
⢿⣅⣀⣉⠙⠷⠌⡇⡆⢰⠀⠃⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⠁⠐⠲⠒⠒⠈⠁⠀⠀⠀⠀⠙⢿⠶⢦⣤⣀⡀⠉⠙⠛⠒⠶
⠀⠀⠉⠉⠙⢳⡀⡇⠋⢸⠀⠸⣆⡀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠉⠉⠓⠚⣳⠋⣰
⠀⠀⠀⠀⠀⠀⢳⡁⠄⢸⠀⢀⡟⢳⡀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢀⡾⠁⣰⠏
⠀⠀⠀⠀⠀⠀⢠⡛⠒⢛⡃⣾⡁⠀⢧⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⣰⠏⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⡋⠀⠉⢻⠈⢷⡀⠈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠁⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠋⠀⠀⠻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⡀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⠇⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⠎⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠟⠙⢛⠟⠻⠛⠶⠶⢶⡶⠶⠶⣶⡶⠶⠶⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣏⠀⠀⠀⠀⠀⣼⠁⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⠳⡄⠀⠀⠀⠘⢦⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢡⡀⠀⠀⠀⠀⢳⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣅⢀⣸⡅⠀⠀⠀⠀⢈⣥⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡉⠉⠙⠟⠒⠚⠊⢉⠩⠆⠀⣌⠁⠹⡄⢀⣠⡴⢋⠀⢀⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠦⠤⣤⣤⣤⣴⣶⣏⡹⠶⠾⡟⠉⠡⠀⢀⣰⠟⣧⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠄⠀⠀⣀⣀⣰⣠⡤⠖⠋⠁
⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠛⠷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⢦⠐⠂⠀⢸⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⠿⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣗⢃⡤⠈⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢹⡆⢀⠔⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⣿⣗⠀⠈⠁⢘⢻⠀⠀⠀⢀⠀⣀⠀⢀⣀⠀⠀⠀⠀⢰⠇⠀⠘⣇⠊⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠠⣾⣭⡿⡆⠀⡒⢋⡜⠀⠀⠀⣌⢣⠿⡿⠒⠢⠘⡆⠀⠀⠎⠠⡆⠀⠀⠈⠛⡆⠀⠀⢀⣿
⡆⢠⠂⠉⢙⣍⠉⢰⠣⡀⠸⠉⡖⠤⣀⠀⠘⡆⢰⡇⠀⠀⢸⠇⠀⠀⠀⠀⣧⡀⠰⣷⣿⠓⠒⠶⣾⡇
⢣⠈⣆⣰⠋⣼⠀⢸⠄⠻⣦⡇⠋⠀⡈⢷⣰⠁⢸⡇⠐⢠⡏⠀⠀⡘⠀⣸⠃⠙⡗⠦⠤⡆⠀⢰⡏⢷
⠈⢧⠘⣇⢀⣿⠀⢸⡇⠀⠈⠀⠀⠱⣧⠔⠉⠀⢸⡇⢠⡟⠀⠀⢰⠁⢠⡏⠀⠀⠳⣀⠜⠁⢀⡞⢀⣼⡇
⠀⠀⢧⡈⢯⣿⠀⠀⡇⠀⠀⠀⠀⠀⣹⡆⠀⠀⢸⣇⡾⠀⠀⠀⠃⠀⡾⠀⣠⠔⠊⠀⢀⣠⠞⠤⠴⠚⣧
⠀⠀⢸⢳⡈⢻⡄⢰⣧⢀⡤⢄⣢⢴⡟⠀⠢⣤⡟⣿⠁⠀⠀⣠⠀⠚⠓⠉⢀⣀⡤⢖⠋⣥⡂⠀⠀⠀⣿
⠀⠀⠸⡆⠹⡄⢻⡞⠁⠀⣈⡥⠤⢼⣇⢀⣀⡀⠀⠿⠒⠒⢶⣥⠀⣢⠴⠚⠉⢁⠔⠁⠀⠀⠀⠀⢀⡾⠉⢞⡒⠒⢲⣄
⠀⠀⠀⣇⢰⡟⢆⣻⡄⢈⡠⠴⠒⠋⠉⠉⠉⠙⣆⠀⠀⠀⠀⡍⠉⣧⠀⠀⡰⠁⠀⠀⠀⠀⢀⡴⠋⠉⠉⢧⠉⠛⠤⢤⣭
⢀⡀⠀⣿⢸⣇⠼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡄⢀⡀⠀⡇⠂⢹⡆⠈⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⣀⡼⠞⠛⠋⠉⠁
⠘⠋⠓⢾⡘⣇⠀⢹⡵⣤⠀⠀⠀⢀⡇⠀⡇⣇⢹⣧⡴⢿⠀⣿⢰⠈⢿⠀⠀⠀⠠⠚⠁⠀⢀⣠⠶⠛⠉
⠀⠀⠀⠀⡙⠿⡇⣸⠂⡈⢳⣄⣠⠾⡇⠀⡇⢹⠈⣿⡀⢸⡆⢹⠘⡀⠈⢧⡤⠀⣄⠀⠀⠚⠉
⠀⠀⠀⠀⠈⠢⣄⠽⣶⡺⢄⠙⣧⠀⡇⠀⡇⠈⠃⢘⢧⡔⠛⣲⠀⣠⢂⢼⡇⠀⡿⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠙⢦⣣⡈⠳⣄⠀⠠⣀⡴⠁⠎⡇⠀⣼⠀⠃⣈⡾⠤⠚⠁⣐⣺⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡉⠻⣄⠙⣧⠐⠑⠁⡌⣼⣃⡴⠇⢚⠩⢀⣠⡵⠖⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢌⠓⣾⡅⠣⠔⠚⠩⢀⣢⡥⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⢀⣶⣦⠶⠚⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⡀⣀⢀⡀⢀⣀⢀⣀⢀⡀⣀⡀⡀⢀⡀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠞⢹⣗⠸⣇⡿⣿⣼⢿⡌⡇⢸⢾⢻⠿⣇⡅⡯⡼⢿⣸⠳⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⡼⣄⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡥⠤⠤⢭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠊⢿⣀⣀⡾⠃⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠛⠉⣡⠤⠶⣞⣳⣞⣻⠶⠤⣌⠉⠛⠚⠦⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⠉⠀⠀⠀⠀⣼⠁⠀⠀⠈⢻⡞⣁⣀⣀⠈⠧⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡿⠀⡆⠀⠀⢸⡇⠿⠤⠼⠀⢐⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠃⠀⠃⠀⠀⠈⠃⠀⠀⠘⢀⣘⡀⠀⣀⣀⠀⣼⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠖⠛⠉⠹⡍⠙⠲⣄⠀⠀⠀⠀⠀⠀⢠⠏⠁⠉⠛⠁⠈⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠘⠁⠀⠀⠈⢳⠀⠀⢰⡶⡄⠘⢦⡀⠀⠀⠀⢀⡼⠁⣠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⢠⣦⠀⠀⠀⣴⣄⠀⠸⣧⡀⠈⢧⢹⡶⣄⠙⢦⢀⡴⠋⣠⢶⠇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠈⢉⣀⣀⣀⡉⠁⠀⠀⣰⠇⠀⠘⣆⠳⠈⠳⣄⠉⣠⠞⠁⠟⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⣏⣠⠖⣆⣹⠀⠀⠠⠁⠀⠀⠀⠈⢢⡀⠀⢸⢰⡇⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣬⣟⣛⣻⣧⠴⠊⢰⣤⣀⣀⣤⡞⠸⠃⠀⠼⠀⠇⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠐⠲⠤⠤⠤⠤⢤⠤⠤⠴⣶⢶⢾⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡽⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣟⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠁⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠛⣛⣿⢿⣿⠑⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣙⡎⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠹⠀⡆⡆⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣱⢳⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠦⠴⠶⠞⠳⠻⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡖⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⢰⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡼⠇⠸⣤⣄⣄⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣮⠉⢧⠀⠀⡎⠘⢿⣿⠉⠉⢏⠉⠉⠉⠉⢩⠉⣴⣦⡶⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣡⡀⣷⠀⣸⣿⡖⠀⢈⢄⠀⠀⠀⣸⢴⡿⠈⢅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⡀⠉⠻⣿⡻⣿⡇⣠⢞⣺⣧⣤⡰⠣⠋⠁⡐⠕⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠈⠻⣾⣿⡿⠋⠁⠀⣨⡧⠁⠀⡰⠋⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣟⣷⠤⣠⣿⣿⣀⡠⣤⣾⢟⣷⣀⣠⣦⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠿⠶⠾⠿⠛⠛⠛⠉


⡿⠿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠶⠶⠿⠟⠛⠛⠛⠛⠻⠿⠶⠶⢦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣅⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⠳⠤⢠⠄⠙⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⣳⠖⣯⠝⢋⣤⡙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⡷⢶⣿⣄⡹⢀⡏⢠⡏⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⡋⠙⢖⣙⣺⡅⠀⠀⠀⠀⠈⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠀⠀⠀⢀⡀⠀⠀⠘⣿⢃⡄⡟⠀⠀⠀⠀⠀⠙⠺⣧⠉⠛⢤⡀⠀⠀⠀⢰⠃⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠘⠿⠍⠀⠀⠀⠀⠘⢃⡇⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠉⠀⠀⠀⠈⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣸⠀⠀⢠⣀⠀⠀⠀⠀⡄⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠠⡀⠀⠦⠔⠀⡾
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠓⣂⡀⠘⠀⠀⠀⡰⠁⢀⣿⢷⣄⣀⠀⠀⠀⠀⠀⠀⠈⢳⣽⡆⠀⠀⠀⢷
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡼⣆⠐⠒⠂⠀⢠⠞⠁⣠⠞⢸⠀⣏⠉⠉⠒⠢⢤⣀⠀⠀⠀⣿⣷⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢸⣇⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠉⠀⡰⠀⣟⢦⣤⣴⠞⠁⡠⠞⠁⠀⡾⠀⢻⠀⠀⠀⠀⠀⠈⠳⣄⠀⣿⣿⡆⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠈⣿⠀⠀⠀⠀⣀⡴⠋⠸⠀⠀⠀⢠⠁⠀⣿⠀⣨⣻⡷⣫⠀⠀⠀⣸⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠸⡆⡟⠈⣷⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⢻⣇⢀⣀⠞⠁⠀⠀⠀⡄⠀⢀⡎⠀⠀⢹⡛⢳⠿⣿⣋⠷⡀⣰⠃⠀⠀⢸⡇⠀⠀⢀⡴⠀⠀⠀⢹⡇⢰⠘⠇⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⢿⡏⠀⠀⢀⡀⠀⢠⠃⢠⠀⠙⢦⠄⠸⡇⣸⠂⣯⠀⠀⡽⠁⠀⣀⣀⢸⡇⠀⠀⣾⠃⠀⠀⠀⡾⣿⢸⡄⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠈⢿⡄⠀⠀⣷⢠⢸⠀⠸⡇⠀⢧⠀⠀⢷⡇⠀⢻⠀⡼⠁⠀⠘⣯⠉⠙⠃⠀⠀⡟⠠⡆⠀⣰⡇⠹⣆⠁⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠈⢿⣄⠀⠈⢸⣿⡀⠀⡇⠀⠈⢧⠀⢸⡆⠀⣸⠞⠀⢀⣤⡶⠿⠂⠀⠀⠀⠀⡿⠀⣇⢠⣿⣧⠀⠙⢦⡀⠀⠀⠀⠀⡴⢻⡇⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠈⢻⣦⣴⡿⣿⡇⠀⠃⠀⠀⠘⣇⠀⣿⣴⠏⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⢡⡷⡜⠋⠉⣏⣄⠀⠀⠙⠳⣤⡴⠚⣡⠟⡇⠀⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣧⢸⡇⢠⠀⠀⠀⠀⢹⠀⢸⡏⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣹⡄⢦⠘⣎⠢⣀⠀⡜⢻⡄⠸⠋⡸⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣇⣿⠀⢿⠀⠀⠀⡀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣾⡁⠘⣧⠀⠙⠿⠟⢡⣠⡞⠁⠀⣠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡘⠀⠀⠀⣇⠈⡟⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢠⠟⢸⠃⠙⢿⣤⡀⠙⢦⣘⠦⣀⣈⡴⢁⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⣀⠈⠣⢻⠀⠀⣠⠞⠁⠀⠀⢀⡴⠃⠀⠋⢠⣟⠀⠀⠀⠈⠙⠛⠶⠾⠷⣾⣿⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣿⣄⣜⠁⠀⣠⣤⣶⠟⠁⠀⠀⡴⠛⣿⠀⠀⠀⠀⣀⣠⣤⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠶⠿⣿⣦⣤⣤⣤⣤⣴⣿⠶⠶⠿⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠻⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⡷⠀⠀⠀⠙⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⣠⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠈⢿⣿⣿⣿⣆
⠀⠀⠀⠀⢸⡿⠿⠿⠿⠿⠿⣿⠀⣿⠿⠿⠿⠿⠿⣿⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣤
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⡅
⠀⠀⠀⠀⢸⣷⣶⣶⣶⣶⣶⣿⠀⣿⣶⣶⣶⣶⣶⣾⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢻⣿⣆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⡿⠟⠀⠻⢿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⢤⢤⣀⣀⣀⣀⣀⣀⣀⣠⡽⡇
⠀⠀⠀⠀⠀⠀⣀⠴⠚⠙⢧⡀⠻⣤⣀⣀⠀⠀⠀⠁⢈⣀⣀⡴⠃
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠙⣆⡧⢀⣈⡉⠉⠉⠉⠉⠁⠀⣶⣛⣉⢉⣙⣦
⠀⠀⠀⢠⣶⠋⠙⢫⡳⡀⠀⠀⠘⡇⠀⠀⢩⢭⠉⢹⠀⠀⢸⡷⠤⠤⠤⠤⢾⣀
⠀⠀⠀⠇⡇⠀⣠⠤⣷⢹⠀⠀⠀⣷⠀⠀⠘⡫⠆⢸⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇⠉⠓⠢⢄⡀
⠀⠀⠀⡇⢧⡠⠗⣶⣹⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⣾⠑⠒⠲⠶⠒⠊⡇⠀⠀⢀⠔⠉⡆
⠀⠀⠀⠘⢾⣤⣞⣡⡧⠏⠀⠀⠀⢸⠉⠒⠦⠤⠴⠚⠀⠀⢻⠀⠀⠀⠀⠀⠀⡇⡌⡀⡜⢰⠁⢩⣦
⠀⠀⠀⠀⠀⠈⢉⣈⣱⡦⠤⠤⠴⠚⠓⠤⣄⣀⣀⣀⡤⠔⢻⡄⣀⣀⢀⣀⣠⠏⠙⠓⠷⠞⠛⠛⠉⠑⠢⢄⡀
⠀⠀⡠⠤⢤⠴⢅⣀⡤⠟⠀⠀⠀⠀⠀⡴⠶⠶⣆⠀⠀⠀⠀⠉⠛⠛⠚⠛⠁⠀⢠⠤⠖⠢⠤⢤⡀⠀⠀⠀⠀⠁
⠀⠀⠑⠲⠦⠤⠤⠃⠀⠀⠀⡆⢉⠉⣹⡯⠭⢭⡿⠶⡉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⣤⡤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠭⠭⠟⠁⠀⣎⠀⣀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣬⣭⣬⣭⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⢠⠒⠒⠚⠀⠘⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⡤⢄⡀⠀⠀⠀⠀⠘⠒⠒⢢⠀⢠⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠤⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⢸⣀⣸⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡄⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢸⠉⠐⠠⠄⢀⠃⠀⠀⣀⢀⡀⠀⢀⡀⢄⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠑⣢⡶⠚⠉⠒⠒⡎⠀⢀⣈⣯⠃⣤⡾⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⡰⠁⢰⣏⣉⡉⠉⠀⣀⡀⠀⠀⢸⢰⡁⠀⠁⠀⠇⠀⣀⣀⣀⡀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⡴⠁⠀⠀⠁⠀⠀⠉⢁⣀⠈⠉⠉⠉⠁⠈⢁⣀⠩⠔⠋⠀⠀⠀⠀⠑⠢⢄⡁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠈⠑⠂⠄⢐⠈⠁⠀⢀⣀⣀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢄⣀⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠱⠐⠄⡂⠀⢐⠘⠐⠀⠀⠀⠀⢄⠀⠀⠐⠀⠀⢀

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣺⣍⠉⠉⠉⠓⠀⠉⢑⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⣸⣶⣿⠟⠀⠀⠀⠀⠀⠸⣿⣷⡀⠙⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⡿⠂⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠙⢿⣿⣿⣿⣀⣀⠀⠀⠀⠀⠀⣿⣿⣿⡋⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠀⠀⠘⣿⣿⣿⣿⣿⣷⣤⣦⠀⠀⢿⣿⣿⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢻⣿⣿⠛⣿⣏⣼⣿⠖⠂⢻⣿⡟⠁⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⠀⣸⣿⣿⡆⣿⣿⣿⣇⠀⠀⠈⣿⡁⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠋⠉⠉⠉⢃⣿⣇⣹⣿⣿⡏⠀⠀⠀⠸⠧⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠋⠀⠐⠊⠀⠉⠉⠉⠉⠛⠷⠶⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠀⢠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠸⣿⣿⣿⣿⣿⣿⠻⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢰⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⢿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⢸⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⢸⣿⣿⡏⠸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣏⣛⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⣟⣛⣛⣛⣿⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡿⠟⣫⣿⡿⠙⣿⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⣷⣶⣶⣶⣿⠟⠋⠀⣰⠏⠀⢸⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⣫⡿⢁⣠⣾⣟⠋⠉⠀⠀⢀⡴⣡⡶⠶⣮⣍⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢿⡿⣡⠎⣼⠴⣿⣿⣿⡿⣦⠀⠀⣠⢫⡾⠋⠀⡀⠀⠙⣷⠀⠀⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢡⡟⠁⣹⠄⡟⠀⣿⣿⣯⠀⠈⢳⡞⣡⠆⢀⣀⣠⡇⠀⢠⡿⠀⠀⠀⠀⠀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣀⡛⠁⣴⠋⠀⡇⣼⣿⣿⣿⠀⣰⠏⡴⠃⠀⣸⡏⠁⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⣸⡟⣼⣿⣿⡆⠘⣧⢰⡇⣿⣿⣿⡟⣴⠃⡼⠁⣠⡾⠋⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⣰⡿⠀⠹⠿⠟⠁⠀⢹⣾⢷⣿⣿⡟⣸⠃⡼⢁⡴⠋⠀⢀⠔⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢀⣴⠿⢷⡀⠀⠀⠀⠀⠀⠈⣿⢸⣿⣿⣱⠇⣸⠁⠎⠀⣠⠖⠁⢀⡞⢀⣠⣴⠞⠁⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢠⡿⠃⠀⠀⠁⠀⡆⠀⠀⠀⠀⣿⢸⣿⢧⡟⠣⢿⡠⠔⠋⠁⠀⢠⡿⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣼⡟
⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢹⣿⣿⡿⠀⠀⠀⢉⣛⣴⣶⣿⣯⣭⠀⠀⠀⠀⠀⢀⠴⠚⠛⢩⡿⠁
⠀⣠⣾⠃⠀⠀⠀⠀⠀⣠⣼⣶⣶⣤⣤⣼⣿⣿⣇⣀⣠⣶⣿⣿⣿⣟⠻⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⣰⡟⠁⠀⠀⠈⠙⠶⣾⣿⣿⣿⡿⠋⠀⠤⠤⠴⠾⠿⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⣿⡃⠀⠀⠀⠀⠀⠐⠋⠛⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⢿⡇⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠘⣷⡀⠀⠀⠀⠀⠀⠀⣾⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣿⡇
⠀⠘⢿⣦⣀⠀⠀⠀⠀⠉⠉⠛⠻⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠠⣤⣄⣀⣠⣤⣤⣤⣴⡶⠋⠀⣿⡇
⠀⠀⠀⠉⠛⠿⣶⣤⣄⡀⠀⠀⠀⣼⡿⠿⠿⠛⠛⠶⢶⣤⣤⣤⣤⣤⣤⡴⠖⠋⣴⠟⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣦⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠀⠀⣿⡇

⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣲⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠙⠉⠁⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠰⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣿⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠈⠁⠂⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⣿⣿⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣴⣻⢛⢻⡟⢛⢿⣿⣧⣀⣀⣀⠀⠀⠀⠘⠀⠀⠀⢀⣴⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠈⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⣾⡆⠈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⠇⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠴⠖⠒⠒⠲⠦⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⣀⣤⠤⠀⠀⠀⢀⡄⠀⢀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢠⠖⠃⠀⠀⢸⠀⠀⠀⠀⠀⢳⠴⠃⡔⠉⢢⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠤⣄⠸⡖⠁⡀⠀⠸⠀⠀⠀⠀⠀⠘⠀⠸⣄⣠⢎⡞⠀⢀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢀⡞⠁⢰⠁⢀⡤⡄⠳⠊⠀⣀⡤⠴⠒⠒⠒⠒⠦⢤⣀⠀⠀⠸⣤⠴⢋⡴⢦⠈⢳⡀
⠀⠀⠀⠀⠀⢀⡞⠀⠀⠸⣄⣀⡴⠃⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠰⢛⠗⠉⠀⠀⢳⡀
⠀⠀⠀⠀⠀⣼⠀⠀⢀⠄⠀⠁⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠸⡀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢀⡇⠀⠀⡼⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡶⠋⢶⡄⠀⢱⡀⠀⠀⠘⡆⠀⠀⢸⡀
⠀⠀⠀⠀⢸⠁⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠴⢏⣀⠜⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⠀⠀⠈⡇
⠀⠀⠀⠀⢸⡀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⠀⣴⠚⢁⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⢀⡇
⠀⠀⠀⠀⠈⡇⠀⠀⠘⡆⠀⠀⠈⢇⠀⠐⣶⣾⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⡞⠀⠀⢸⠁
⠀⠀⠀⠀⠀⢳⠀⠀⠀⠘⠆⠀⠀⠘⢦⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⡄⠐⠁⠀⠀⡞
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⡀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⢀⡐⠛⢦⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⢨⠷⠄⠀⠉⠑⠲⠤⠤⠤⠤⠖⠊⠉⠀⢀⢰⡃⠙⡆⠈⠃⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⡰⠓⠂⣠⠏⠀⢠⠀⠀⡀⠀⢀⡤⠆⠀⣆⡸⣆⠳⠤⠃⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠰⣅⡄⠀⡇⠀⡸⠁⠀⠘⠒⠒⣦⠘⠄⠈⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠓⠚⠁⠀⠀⠐⠒⠋⠁⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠦⠤⠤⠴⠖⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠉⠀⠢⣀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠄⠐⠂⠈⣱⠏⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⠛⠻⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⣂⠀⠀⠂⠂⠀⡁⠆⠀⠀⠀⠀⠀⡀⠀⠰⠚⠛⠀⣤⣀⢠⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣥⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠘⡖⠀⠐⠁⠀⠆⠉⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⢆⠐⠀⠀⠀⠀⠐⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⠏⠢⡀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠈⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⡀⢀⠀⠀⢼⡃⠄⡀⠈⠢⡀⠀⠀⠀⠀⠑⢄⡁⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣤⠀⣀⣀⠛⣷⠀⠈⠑⠓⠒⢤⡀⡀⠄⠂⠉⠀⠀⠀⠉⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⢦⡀⠀⣿⡆⠀⠀⠀⠀⠀⡼⠓⠶⠤⣄⣀⠀⢀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣆⠈⠢⣿⣿⠀⠀⠀⠀⡼⠁⠀⢀⡀⠀⠁⠨⡟⠩⢀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⠈⢻⡆⠀⠀⢰⣧⣴⣾⣿⠟⠀⠈⠁⠁⠀⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣷⣴⣾⣿⣿⢿⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⣿⡿⠿⡏⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡆⠀⠉⢹⡇⠀⠀⠀⡇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠱⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⡁⠀⡇⠀⢣⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡇⠀⠸⡄⠀⢂⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡜⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡇⠀⠀⠈⠳⣄⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⡇⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⣀⠀⠸⣿⣿⡿⣡⣶⣶⣶⣶⣶⣶⣦⡀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣦⠰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣛⣛⣛⣛⣛⣛⣋⣀⣙⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣋⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣭⡍⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣭⣭⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡧⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠦⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣾⠟⣷⡹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢱⡟⢿⡎⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡾⠇⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢰⣿⡿⡆⢸⡇⣠⠀⠀⣂⠇⠂⠀⠀⠀⠀⠀⠸⣦⣀⣰⡆⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⣿⣇⢹⣿⡅⣤⠘⣇⠧⢀⠆⠀⣁⠀⠀⠀⠀⠀⠀⠀⠙⡙⡟⠷⢶⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠈⠀⣠⡙⣾⣿⠧⠟⠀⣿⢇⠾⣐⣤⠭⣄⠄⡢⠀⠀⠀⠀⠀⢈⡾⣸⣷⡻⢿⣿⡆⡀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡗⣼⠏⣾⣿⣶⣶⠶⠾⣃⣀⣆⣀⣠⠀⡙⠢⢀⡀⣀⣰⣿⣛⣛⣛⠿⣿⣷⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠛⣷⢹⢸⣿⠋⠛⠿⢴⣳⣿⣿⣭⣁⣀⡈⢲⠀⠀⠉⢩⠟⠋⢿⠭⢉⣷⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠀⡆⠴⣿⢟⠸⢠⢸⡆⣀⣴⠟⠉⠉⠀⠹⡄⠈⠈⠉⢉⠳⠒⠃⢰⡚⠁⢀⠞⢻⠺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣴⠾⠳⣬⣩⠥⠔⠉⣣⣾⡟⠇⠀⠀⢀⣴⣴⣷⣴⣤⣀⣀⢀⣉⣀⣠⡡⢾⣏⠀⠙⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣿⠁⠔⠄⠄⠔⣡⣶⠾⠛⢹⢞⣂⠤⠒⠉⠙⠻⣿⠛⣿⡿⡿⠉⠀⠀⠀⠀⠀⣻⣖⣿⣼⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠨⣷⠶⠴⡖⠖⠛⣿⣀⠀⠀⣾⠏⠉⠀⣠⠀⠀⠀⠘⣧⠈⣱⠋⠀⠀⠀⢀⡠⠞⠉⠟⣛⡉⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣋⡄⢹⣦⣿⠶⠾⠞⠋⠐⠀⣼⣿⡆⢀⣀⢸⡄⠀⠀⠀⢻⣆⣩⡶⠶⠟⠛⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⢿⡄⢈⣯⣗⠠⢤⠀⢀⣀⡴⠛⢿⣷⠘⢿⣿⡇⠀⠀⠀⢸⠋⠁⠀⠀⠀⠀⠀⠀⠛⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠈⠂⠀⠀⠀⠀⠀⠀⣾⡏⠀⢿⢻⡇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⣿⢠⡇⠘⠼⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠿⣋⠼⢃⠀⠰⠿⠟⢢⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣼⠟⠀⢺⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠂⠁

⠀⠀⠀⠀⠀⢀⡴⣤⠀⠀⣠⠆⠀⠀⠀⠀⠀⣴⠟⢶⠄⢀⣴⡶⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠘⠷⠋⠀⡴⠃⠀⠀⠀⠀⠀⠀⠈⠛⠋⢠⣾⠏⠀⠀⠀⠀⠀⠀⢰⣇⡼⠁⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢡⡶⠿⣦⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⢿⡷⠀⠀⠀⠀⠀⠀⢼⠟⠀⠈⠳⠞⠋⠀⠀⠀⠀⠀⠀⣴⠃⠀⣠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠻⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢠⣶⣶⢀⡔⡶⠀⠀⠀⠀⠀⣴⡿⣷⠀⢠⣶⠀⠀⠀⠀⠀⠀⢰⢵⣻⢝⡆⣠⢹⡟
⠀⠀⠀⠀⠀⠉⢁⣞⠞⠀⠀⠀⠀⠀⠀⠉⠋⠁⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠓⠓⠋⡰⣣⠟
⠀⠀⠀⠀⠀⢠⣯⠏⣀⡠⡀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣳⠏⠀⣀⣤⣀
⠀⠀⠀⠀⠰⡯⠃⠀⠻⠷⠂⠀⠀⠀⠀⠀⢰⡿⠁⠀⣾⣻⡇⠀⠀⠀⠀⠀⠀⡼⣵⠃⠀⠸⡇⢿⣫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢸⠻⢗⡇⢀⢎⡝⠀⠀⠀⠀⠀⣾⣻⣷⠀⢠⡿⠀⠀⠀⠀⠀⠀⢠⣪⢿⣦⠀⠀⡰⡹⠃
⠀⠀⠀⠀⠀⠀⠉⠉⢠⢯⠎⠀⠀⠀⠀⠀⠀⠉⠉⠁⢠⡿⠁⠀⠀⠀⠀⠀⠀⠘⠾⠿⠋⠀⡜⡼⠵
⠀⠀⠀⠀⠀⠀⠀⢠⣯⠋⢀⡠⣄⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡞⠁
⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⡏⠮⢎⡇⠀⠀⠀⠀⢠⣿⠃⠀⣿⣫⣿⠀⠀⠀⠀⠀⢠⢂⢎⡞⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠚⠋⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⢠⣯⠞⠀⠀⢿⣿⣧⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⣶⣶⣶⣮⣿⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠻⢿⠟⢿⣟⠛⠽⣋⣹⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⣾⠃⠀⠉⠛⠉⠀⠀⠉⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣀⣼⣄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣼⣿⣿⠀⠀⠀⠀⠀⠀⠠⣶⠋⣀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⡞⣿⣿⠀⢀⡙⣉⡁⠀⠀⠁⠊⠁⠀⠠⣿⢿⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⡛⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣀⡠⠀⠀⣰⣃⣰⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⢉⡃⣄⡀⠀⠀⠈⠀⠀⠀⠀⢉⠈⡇⠐⠂⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣼⠁⠘⣏⠓⠆⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠲⠀⠤⠖⠀⠀⠀⠀⠀⠓⠀⢀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠑⠠⡈⠆⠀⠀⠀⠀⠀⠀⡀⣘⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠸⠂⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⡀⠀⠀⠀⠀⠇⣿⠀⠀⠀⠀⠱⡂⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⡀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢸⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⢸⡇⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠻⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⡇⠀⠠⠊⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠄⠀⠀⠀⠀⠐⠶⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠄⠀⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⠄⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠀⠀⠀⠈⠀⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠂



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⢀⠀⠍⠒⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠠⠁⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡄⠆⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠈⠀⠂⠠⡄⠀⣀⠄⠬⠀⠈⠈⠃⠀⢀
⠀⠀⠀⠀⠑⢄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠁⠀⠀⢀⠀⠎⠀⣘⠒⡈⠜⠁⠀⠈⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⢑⠂⠠⠤⠀⠀⠀⠄⠀⠐⡊⡬⠤⠀⠀⠀⠀⠀⣀⠠⠐⢘⠆⠀⠀⠈⠀⠌⠀⠒⠀⠀⢰⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠄⠒⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠛⠧⠀⠀⠒⠀⠒⡺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢂⠀⠁⠀⠀⠠⠀⠒⠁⠀⢀⠄⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⣀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⢋⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠡⠊⠠⣖⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⠄⠂⠈⠁⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠐⠃⠂⠈⠉⠑⠒⠢⢄⠀⠀⠀⠀⠘⠁⠀⠰⠀⠀⠀⠀⠰⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠫⡀⠀⠀⠀⠞⠠⣐⡄⠀⡠⠀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⢂⠀⠀⠀⠀⢸⡇⠈⠀⠀⡤⠂⠄⠊⠀⠀⠀⠀⠂⠄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⠘⠃⠐⠀⠀⡄⠡⣦⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠁⠀⠀⠀⠀⠀⠀⠐⠗⠂⠀⢡⠀⠑⠀⠀⠀⠀⡀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠂⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠐⡀⠈⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠱⠐⢄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠌⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠣⠀⢱⣄⡀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠌⠁⡀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⡟⢻⢷⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣄⣳⣼⡌⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠨⢀⡤⠕⠂⠠⠀⠀⠀⠀⠀⡈⠘⠤⠁⡖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠚⢨⠥⢐⠀⠀⠀⠀⠀⠀⠘⠗⢰⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠃⠀⠸⠭⡉⠪⠙⢦⣠⠀⠀⠀⠀⢀⠿⡎⢠⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⡀⢀⠀⢆⣀⡤⠀⠴⠳⠤⡤⠊⣴⠏⠈⠅⣎⠈⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢴⠁⠀⠀⢐⠈⠀⡀⢀⠀⠀⠀⢐⠀⠈⠉⡇⠀⠀⡺⠀⠈⠉⢀⠼
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠊⠀⠀⢁⠤⠒⠁⡠⠀⠔⠈⠀⠀⡄⢨⠀⠄⡜⠁⠀⠀⡄⠀⠀⠐⠁⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠠⠊⠀⠀⠀⠀⢀⠴⠀⠰⣀⡰⠀⠀⢠⡀⠀⠀⠐⠣⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠘⠀⠀⢀⡔⢫⠜⢀⡴⠼⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠙⠄⠃⠀⠲⠝⠁⠼⠀⠁⠒⠀⠒⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠈⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⠦⠄⡴⢦⢠⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠹⠤⠆⠧⠼⠹⠏⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣶⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠗⠀⠙⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠀⢀⣀⣿⣤⣿⣇⣀⠀⢘⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣉⣿⡿⠛⢉⣉⣀⠈⠉⠙⠿⣿⣉⣽⣷⡄⠀⠀⠀⢀⣴⠟⠁⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⡿⠋⣠⡾⠛⠉⣿⠀⠀⠀⠀⠈⢻⣏⠀⠁⠀⠀⠰⠿⠿⣶⡆⠀⢠⣶⠾⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣸⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠿⠷⠶⠶⠶⣶⠆⢸⡇⠀⠀⠀⠀⠀⠀⣿⠇⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢹⣧⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⣾⠃⠀⠀⠀⠀⠀⣰⡟⠀⣀⣼⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠙⢷⣤⣄⣀⣀⣤⡶⠟⢁⣼⠏⠀⠀⠀⠀⠀⣰⡿⠁⢸⡏⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣈⣉⣉⣉⣁⣤⣶⠟⠁⠀⢀⣴⣶⣶⣾⣯⠀⢀⣼⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣴⡿⢻⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⠛⠛⣷⣤⡶⢿⡇⠀⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢸⣿⠀⠀⠀⣿⣷⠶⢿⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠉⠉⣿⡆⠀⢸⣿⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⣸⡇⠀⢸⣿⠀⠀⠀⣿⡇⠀⢸⣇⠀⠀⠀⣿⡀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⡇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣸⣿⣀⣀⣸⣇⣀⣀⣿⣇⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣴⠟⠋⠉⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⠀⣿⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠉⠉⠉⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⠶⠶⣶⠀⠀⣶⠶⠶⠿⠀⠀⠀⠀⠀⣿⣷⠀⠀⢀⣀⣀⣤⣤⣴⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠛⠛⠋⠉⠉⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⣿⡀⢶⡄⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⣧⠈⠻⣦⣤⣤⡀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠁⠀⠀⠙⢷⣤⣀⣀⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⡀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢧⢰⢻⡇⣾⣩⠆⣶⠙⡇⢰⢠⡎⠁⢐⣩⡆⢹⠋⢷⢠⠎⢱⡄⡖⠙⡆⢾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠘⠃⠙⠒⠂⠙⠒⠃⠘⠀⠓⠒⠙⠒⠃⠘⠂⠙⠈⠓⠚⠁⠃⠀⠃⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣪⠭⠭⠭⢑⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡸⢇⠸⢄⣀⣀⡠⠜⡠⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠀⠒⠒⠈⠉⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠒⠒⠒⠒⠊⠉⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠉⠒⢬⡑⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⠴⢒⢤⠀⠱⡘
⠀⠀⠀⠀⠀⠀⡗⢦⡀⠀⠀⠀⠀⠀⢀⣀⠤⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢊⣠⣾⡵⢻⠇⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠂⢬⡉⠉⠉⠉⠉⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⣀⠀⡠⠚⣡⣴⡿⠟⣋⠴⣁⣀⣠⠗
⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⢉⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⠞⠉⠉⠉⠉⠲⡝⢦⣾⠟⢋⡤⠊⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣗⠠⣀⠇⠀⠀⠀⠀⠠⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠧⠚⠉⠉⠉⠑⢄⠘⡞⣧⠔⠁
⠀⠀⠀⠀⠀⠀⠙⠢⣀⡀⠀⠀⠀⠀⢀⣀⠴⣪⠃⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠈⡆⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠢⢍⣉⣉⣉⣉⡡⠤⠊⠁⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠀⠈⠉⠢⡀⠀⠀⢀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡠⠐⠒⢄⠀⠀⢱⠀⠀⣨⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡍⠢⣀⠜⠀⠀⣸⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣫⠖⠛⠊⠁⠀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⢀⡠⣞⠵⠊
⠀⠀⠀⠀⡠⢖⡽⠊
⠀⣀⢔⡫⠖⠁
⣾⠕⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠠⣄⣀⡀⠀⢀⠀⢀⣴⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢱⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠱⠀⠀⣸⢳⡖⠀⠀⠈⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢀⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡤⢺⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⢉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⠀⠛⠛⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠐⣾⠶⠴⠛⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⡿⠇⠀⠀⢱⣌⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⢀⣠⣴⢧⠀⠀⠈⠁
⠀⠀⠀⠠⢄⠀⠀⠀⠀⢀⠀⠀⠐⠤⡄⢶⠾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢽⣛⣛⣯⡅⠀⢣⠁⣠
⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻⣋⠙⠻⠿⢿⡄⠀⠈⠒⠁⠀⠀⡀
⠀⠀⠀⠤⠴⠂⠀⠀⠀⡠⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠾⣿⢽⣯⡷⠄⠀⠀⠉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⡁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⡗⠀⠀⢁⡀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⠀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠈⠉⠙⠲⢤⣀⣠⠴⠚⠉⠉⠀⠈⠉⠑⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸⡋⢁⠉⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⢇⣠⠀⠀⠞⠂⠀⡯⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠡⠔⠀⣠⠃⠀⠀⣀⠤⠤⣀⣀⣀⡠⠤⢄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠈⢒⣶⡶⠋⠉⠓⠒⢺⠁⠀⢀⣈⣧⠏⢠⣔⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⠈⠃⣴⡋⠑⠚⠛⠋⠀⠀⠀⠀⠀⠈⡆⢴⠁⠀⠉⠀⢸⠀⠀⢀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢱⡀⠀⠀⠘⠋⢉⡉⠒⠒⠊⠉⠑⠒⠀⠒⠓⠈⣓⠠⠤⠔⠃⠀⢀⡎⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢃⠤⣀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⣀⠤⡜⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠣⡀⠉⠒⠤⢤⣀⠀⠙⠢⢤⠴⠊⠁⠀⣀⡤⠤⠒⠉⢀⠔⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠓⢄⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⡠⠚⠁⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠹⠀⠀⠀⠀⠏⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡱⢀⢄⠀⠤⡆⢀⠤⡀⡄⡠⠀⠀⠄⠀⠐⠉⠁⠀⠀⠠⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠈⠐⠒⠁⠈⠒⠃⠁⠀⠀⠐⠂⠀⠈⠒⠂⠀⠀⠀⠀⠀⠑⠂

⠀⢀⡀⠀⡀⡀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠂⠛⢛⣤⢄⠀⠀⠀⢠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠔⠃⠀⢀⣀⠤⠇⡾⠷⢭⣀⠀⣈⠥⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⢞⠁⠀⢀⡎⠀⠀⠀⠹⡟⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⠀⠀⢸⠀⢀⣄⠀⠀⡇⣤⠀⠀⣸⠉⠑⠢⣄⡀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⢲⡷⠴⠧⣤⣄⣀⣧⣀⣉⢀⡴⠣⣤⣤⠴⠃⠀⢀⣰⠁⠈⠙⢥⣀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠴⡆⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⢺⠉⠉⠉⣻⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠉⠁⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠐⡉⢱⣀⠇⣸⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⣦⣄⣀⠀⠀⠀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠀⠙⠸⣅⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠸⣿⣿⠏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡱⢀⣀⡠⠦⠩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠹⠬⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠔⠉⡷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⠔⢊⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⣀⠀⠀⣧⣤⣤⣤⣤⣄⡀⠤⠀⠒⠒⠒⣲⠒⠒⢲⡒⢒⡶⣷⡪⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⠛⠢⠬⣑⡣⠌⠒⠬⣁⠒⠢⠬⢉⡑⠒⠂⠉⢦⠴⢦⡈⡁⢀⠏
⠀⠀⠀⠀⠀⠀⠀⡠⠒⠓⠒⠾⣀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠋⠺⠤⠈⣉⣀⠒⠧⣄⣀⡽⢜⣋
⠀⠀⠀⠀⠀⢀⠼⡀⠀⠀⠀⢠⠴⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠀⠋⠋⠁⠇
⠀⢠⠊⠉⠉⠉⠉⠛⠓⠒⠒⠚⠃⠛⠒⠒⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡁⢸⠀⠀⠀⠀⢐
⠀⢸⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁⢸⠀⠀⠀⠀⠈
⠀⢸⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠆
⠀⢸⠀⠀⠀⠀⢰⠿⠉⠻⣧⠀⠀⠀⠀⠀⢸⠤⠤⠤⠤⠤⠤⠤⣤⢤⡤⣤⡤⠤⠤⠤⠴⠳⠤⠤⠤⠤⠧
⠀⡇⠀⠀⠀⠀⠘⢷⣄⣶⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⣦⡐⠲
⠀⠈⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠐⠒⠃⠀⠀⠀⠀⠀⠀⢠⣁⣀⣀⣷⣶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠿⠶⠶⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠈⠛⠛⠛⠛⠛⠛⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠑⢦⡀⠀⠀⠀⣠⠤⣤⣀⣀⣀⣀⣀⣠⠤⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢄⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠀⠀⢀⣠⠖⠀⠀⠀⠹⣀⣀⣰⠃⠀⠀⠈⠉⠉⠉⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢠⠃⠀⠀⠸⢤⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⡰⠉⠀⢙⠦⠤⠤⢄⣀⡀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠙⢦⣀⠠⣌⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⣇⡀⠀⠎⠀⠀⠀⠀⢀⡨⠃⠉⠄⠀⠰⢄
⠀⢠⡖⠛⠛⠛⠋⠉⠁⠀⠀⠀⣀⢠⡏⠀⠀⠱⡀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠻⡀⠀⠀⠀⢰⠋⠈⠢⡀⠀⠀⠀⠀⠁⠙⠐⢦
⠀⠀⠙⣆⠀⠀⠀⠀⣀⡤⠐⠉⠀⠀⠈⢢⣀⡠⠧⠐⠊⠁⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⡠⣴⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠘⡇⠀⠀⠐⠙⠢⣀⡀⠀⠀⠀⠀⡝⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠉⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⣧⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⣠⠏⠀⠀⠀⠀⢸⠁⠰⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⡟⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⣦
⢠⠴⠛⠁⠀⠀⠀⠀⠀⠀⢣⠀⣸⠉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⢀⣾⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢿⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡼⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠈⠢⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⢷⡘⡀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢀⣴⣆⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⡜⢸⠃⠀⠀⣀⣠⠴⠞⠓⠶⠚⠁
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⣤⡔⠉⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠀⠈⠛⠛⠋⠉
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡟⡁⠀⢧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠆⠀⠀⠀⠀⢠⠋⠐⠀⠄
⠀⠀⠣⣄⠀⠀⢀⣄⣀⣀⣀⣀⣀⣀⡿⠈⠑⠚⢧⡀⠀⠀⠀⠀⠀⠁⠀⠤⠄⠀⠠⠤⠄⠒⠊⠁⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠈⠙⠒⠋⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢀⠔⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣄⢘⡀⡁⢘⡁⠓⠊⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠒⠂⢤⡤⠀⣀⡐⡖⠈⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣩⠶⠂⢹⠖⣧⠀⢠⣠⣤⣤⣀⢠⣤⡄⠐⣶⡀⡇⠈⠳⠉⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⠋⠀⠀⡇⢸⠀⠘⡄⠸⠀⠺⠛⠘⠈⠉⠁⠁⠁⠉⠀⡀⠀⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣠⠃⢸⠀⠀⡇⠀⢠⡄⡄⣤⠀⢶⡰⢴⡀⣶⢿⢿⡀⢹⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠢⢤⣀⠼⠋⢀⠆⠀⠀⢰⠀⠘⠏⠧⠻⠀⠘⠂⠈⠁⠉⠈⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⠗⢉⣀⠤⠊⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠐⠒⢤⠂⠉⢂⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡴⠁⡆⢸⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠌⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡜⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡠⠊⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢟⣁⣼⠀⠀⠀⡁⠸⢄⡀⢀⣀⡀⢀⣀⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠶⠖⠒⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣘⣡⡬⠼⡜⡃⠀⠀⡀⠀⢘⠀⠀⠉⠁⠀⠈⣧⠤⠖⠒⠛⠋⢋⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠙⠒⠶⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠸⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠉⠐⠂⢖⠂⡄⠀⢀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠉⢹⠉⠁⢲⠐⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠆⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⡅⢹⡀⠀⣸⣀⣦⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⣠⠀⠃⠀⠀⠁⠀⠀⠀⢰