Melon Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⡊⠉⣍⠉⠑⠢⣄⡀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠀⠉⠀⠀⠀⠀⠙⡳⢄
⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⣄
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡠⢀⠐
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢀⡠⠦⠁⢀⠄⠀⠀⠀⠀⠀⢰
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠈⠀⠀⠔⠊⠀⠀⠀⠀⠀⠀⠀⡜
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠄⠤⠐⠀⠈⡈⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠐⡂⢀⠀⠀⠀⠀⠄⠄⣊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠘⣆⠀⠘⡀⠀⢔⠈⠀⠀⠀⠀⠀⠈⠉⠑⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠈⢦⡀⢷⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠙⢾⣧⠀⠀⠀⠉⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠊⠁
⣀⣀⣀⣀⣀⣀⣈⣙⣲⣦⣤⣤⣤⣴⣿⣿⣛⣋⣛⣛⣛⣛⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠾⠿⠿⠛⠛⠛⠛⠿⠿⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠋⠁⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⣰⣷⣤⣬⡿⠷⠜⠳⡶⠛⠛⢷⣿⢦⢀⡈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⣼⣷⣶⠿⡟⠋⠉⠁⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠈⠳⣦⣽⣿⠧⣀⡦⠝⠃
⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⣼⣿⠋⠁⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⠷⣿⠇⠤⠒⠛⣶⣿⣶⣴⣾⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠁⠀⠀⠀⢠⣾⣶⣼⣿⡿⣿⠉⠉⠃⠀⠀⠀⠀⠀⢠⣴⠏⣹⠿⡟⢿⡇
⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⢠⣤⣤⣿⠿⠛⢿⠀⠀⠀⠀⠀⠀⢤⡀⠀⣰⣶⠊⠀⠐⣿⠀⡟⢸⣷
⠀⠀⠀⠀⠀⠀⢸⡇⡀⢰⣶⡮⠍⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠉⠀⠑⣿⡿⢤⣿⠞⣿
⠀⠀⠀⠀⠀⠀⠘⣷⣽⡿⠙⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣤⣾⣿⣿⣿⠋⠀⢠⣀⣿⣿⡁⣲⣿⣥⡟
⠀⠀⠀⠀⠀⠀⠀⢻⣯⠀⠀⠀⠀⠀⠀⠀⢠⣄⣰⣿⣿⡿⠟⠛⠀⠀⠀⠀⣼⣿⣿⢿⢱⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⣳⣤⣠⣿⣿⡿⠛⠛⠿⠀⠀⢀⠀⣠⣽⣿⡿⣿⣃⢻⣿⣿⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣶⡿⢿⡿⠃⠉⠀⠀⠀⠀⠐⣌⣼⣿⣿⣿⠋⠣⣔⣪⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⢀⠀⣀⣠⣿⣶⣾⣿⠿⢟⠉⠀⠒⠀⠛⠛⠛⠻⠁⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣷⣶⣿⣿⣿⣿⠿⠟⠛⣯⡆⢸⡥⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠤⣧⣤⣤⣴⣿⢰⠈⣧⠀⠀⣴⠆⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢀⡄⠠⠀⣄⠐⠀⣸⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⣇⠸⠄⠀⠀⢠⡶⠀⡤⠀⡒⠀⠰⠀⠐⠀⣌⠁⢢⡀⠈⠻⢀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣹⡄⠲⣤⠀⡈⠁⠾⠃⣼⠃⢠⣆⠀⣴⡀⢻⡇⠘⠟⠀⠀⡜⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣹⣆⠘⢷⡀⡀⠀⠀⠋⠀⠘⠟⠀⠻⠃⠀⠁⠀⠀⠀⠜⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠙⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠋⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣈⠙⠓⠢⠄⣤⣤⡤⠀⠄⠀⢁⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠦⠤⠤⠤⠤⠒⠊⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣠⠀⠀⠀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠘⠟⠻⠿⠛⠿⠶⠚⣶⡿⢶⣄⡀⢉⡀⠢⣄⡀
⠀⠀⠀⠀⠀⢀⠠⠚⠀⢀⡄⠀⠀⠀⣠⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⣤⡀⢈⠙⢱⣦⡀
⠀⠀⠀⠀⣐⣥⡶⠖⠳⠿⠷⠾⠿⠿⠿⠿⠿⣷⣿⣤⣦⣀⠀⢀⠀⠀⠈⠙⢻⡄⠀⠙⢏⠂
⠀⠀⠀⡰⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠐⠛⠶⢖⣤⣄⡀⠉⢲⣆⠈⣡⠣
⠀⠀⢀⡏⢠⣤⣴⣶⡾⣤⢦⡠⡄⢀⣀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠈⠙⠳⣤⡌⢆⢨⡇
⠀⠀⢘⠷⠟⠁⠀⠀⠉⠉⠉⢶⠈⠁⠊⠛⠋⠉⠉⠀⠚⠋⠑⠒⠚⠛⠛⠂⠤⣀⠀⠙⢆⠆⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣌⣷⢉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠂
⠀⠀⠀⢿⣄⣀⠀⠀⣴⡀⠀⠀⠀⠀⠀⢀⣀⡠⠶⠒⠋⠾⡥⠉⠐⠒⠂⠀⠀⠀⠀⢀⡨⠟⣁⠸⠀⠀⠀⠀⠀⠰⢀⠈⠀⠘⠂
⠀⠀⠀⠀⢎⠙⠿⠛⠿⣷⣾⣳⣶⢾⣶⣋⣡⣀⣀⣀⣀⣀⣀⣀⢤⣤⣤⣤⣤⡤⠞⢋⠴⠑⢸⠇⠀⠀⠀⠀⠀⠀⠁⢠⡆⠀⠀⡀
⠀⠀⠀⠀⠀⠳⣄⠀⢀⠈⠈⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠀⠋⠁⠁⣠⠴⠞⢁⠐⢠⠂⠀⠀⢀⡐⠀⢠⠀⡤⠨⠁⠀⠈⠿⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠙⠿⡻⠶⣤⡄⣀⣀⣀⣀⣦⣀⣀⣀⣀⣀⣀⣤⣤⠴⠞⠋⠁⠀⠜⢃⡔⠀⠀⠀⢀⡀⠀⠐⠧⣀⠃⠀⠁⠀⠀⠀⣀⡤⠚⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡈⠀⠀⠈⠈⠛⠋⠙⠃⠉⠁⠀⠀⠀⣀⡤⠆⠋⡠⠔⠁⠀⠀⠀⠀⠀⠈⠓⠢⠤⢀⣈⣁⢀⣉⣉⡉⠠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠦⠤⢄⣠⣤⣀⣤⣀⣂⡉⠥⠤⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⢠⠊⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⠀⠸⠊⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢤⠤⠤⠤⠤⠤⣤⣤⣤⢄⣀⠀⠀⠀⠀⢹⡉⠉⠙⠳⢮⢍⠒⠦⡀
⠀⠀⠀⠀⡠⠔⠊⠉⠩⠀⠁⢈⠀⢂⠀⠠⠀⠀⠈⡏⠉⠓⢦⡉⢢⡀⠀⠀⢣⠀⠀⣠⠀⠑⠌⠢⡈⠢⡀
⠀⠀⡠⠋⡀⠃⢀⠔⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⡤⠆⠈⢎⢢⠩⢦⠀⠘⡄⠀⠀⠠⠆⠀⠂⠑⡀⠱
⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠱⠀⠀⠀⠀⠀⠸⡠⠤⠈⡄⢇⢀⢣⠀⢃⠀⣠⠀⢀⣀⠀⢀⢱
⡘⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⢣⠀⠀⠠⠀⠀⢣⢀⡄⠁⠘⡄⠈⡆⢸⠀⠐⠂⠀⢀⠀⠀⠀⡄
⡇⠀⠠⠀⠰⠀⠀⠀⠠⠀⠀⢈⠀⠀⠀⠈⠄⠀⠀⠄⠀⠘⡀⠀⠈⠀⡇⢠⡇⠈⡆⠠⠤⠈⠁⠀⠀⢀⠁
⡇⠀⠠⠀⠐⠀⠀⠀⢠⠀⠀⠈⠄⠀⠀⠀⠃⠀⠀⠰⠀⠀⡇⠠⠄⠀⡇⠀⠇⠀⡇⠀⠀⠀⠉⠀⠐⢈⡴
⢃⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠠⠀⠀⢻⠀⠀⠀⠇⡸⠀⠀⢠⠀⠀⠢⠄⣠⡿⠋
⠘⡄⠀⠀⠀⠘⠀⠀⠀⠄⠀⠀⠡⠀⠀⠀⠰⠀⠀⢠⠀⠀⢸⠈⠁⡘⡰⠃⠀⠀⢸⠀⠀⣠⠴⠋
⠀⠐⡄⠀⠁⠀⢡⠀⠀⠐⠀⠀⠈⡀⠀⠀⠰⠀⠀⠀⠀⠀⢸⢀⣴⠔⠁⠀⣠⡀⠐⠚⠋⠁
⠀⠀⠈⠢⡀⠡⡀⠡⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⣸⠟⠁⠀⡲⡄⢸⣈⠆
⠀⠀⠀⠀⠈⠲⢌⣂⣡⠀⠀⠡⡀⠘⠀⠀⠃⡀⠁⣀⠤⠚⠁⠀⠀⠀⠓⠁
⣤⣤⣤⣤⣤⣤⣤⣬⣭⣷⣶⣶⣶⣶⣶⣾⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠄⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⠀⠀⠀⠀⠠⠀⢀⡄⠀⠀⣠⠀⢀⠀⠑⣦⡀⠀⠀⠈⠁⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠒⢀⡀⢁⣌⠃⠜⠢⠀⡠⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠨⣧⡅⠠⡄⠀⠀⣀⠀⡈⠃⡄⠀⡩⢎⠰⠵⣢⢈⡾⢃⢈⣄⢓⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⢉⡅⡁⠤⠀⠂⠀⠉⣆⢲⣬⣥⡼⢸⢗⢍⣾⡵⠐⢤⢬⡬⡄⠀⡀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠹⣦⣛⡠⠶⡆⠚⠘⠉⢵⢆⢩⡵⣾⡎⠾⢮⣎⣵⣬⣻⠰⣘⠠⠋⠑⣦⢁⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⢿⡴⣷⡜⢇⣲⣜⣧⣅⡳⢳⣞⣷⣷⣿⣰⣽⣯⣧⣭⢧⠂⡤⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣳⣿⣎⣥⠎⡎⢳⣦⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⢺⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢾⣷⣯⣿⣷⣿⣷⣿⣧⢹⣩⣿⣿⣿⣻⣿⣿⣿⣿⡿⠋⠀⠀⣀⠠⣄⣤⣲⣮⠱⢀⠜⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠻⡫⢿⡻⣻⠙⣝⣵⣰⣿⣸⠿⠟⢋⡁⠔⠁⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢷⠨⠹⡆⠀⠉⠑⠣⠽⠟⣹⣭⠏⠽⠥⠀⠂⠉⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢆⣸⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣤⣀⡀⠀⠀⠀⠀⠀⣀⡤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢴⣶⣾⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠀⠀⣴⡀⠀⢰⣦⣄⣰⣔⣀⣤⣤⣄⣠⣄⠀⠀⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⢀⡄⢀⣠⣾⣿⠿⠿⠛⠉⠉⠀⠉⠃⠀⠀⠘⠛⠛⠃⢦⡀⠈⣿⣧⡀⠀⡀⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢰⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⣀⣦⣀⣠⡴⠦⠀⣠⣄⣹⣷⠻⠛⣣⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣠⣴⠿⠿⠁⠀⠀⠀⡀⠀⣰⣤⣶⣾⣿⣿⡟⠛⠿⠉⠙⠉⠉⠹⢻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⣠⣾⣿⣾⡿⠿⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢁⡿⢹⣏⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡋⠀⠀⠀⢰⣶⣶⣽⠿⠉⠻⠁⠀⠀⠀⠀⠀⠀⣢⣄⣀⣰⣾⡇⠀⠀⣸⡧⢐⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⢀⡀⣸⣾⠶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡿⠇⠀⠈⢻⣿⠃⢼⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣦⣿⠟⠙⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣠⣴⣿⣿⣿⣿⠋⠀⠠⣤⣼⣿⣟⢈⣼⣿⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣾⣿⣿⡿⠟⠛⠀⠀⠀⠀⣠⣿⣿⡿⠏⢾⣿⣏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⢷⣄⣀⣾⣶⣿⡟⠛⠿⡇⠀⠀⠀⠀⢀⣹⣿⣿⣿⣟⠲⣿⣿⡟⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣴⣿⣿⣿⠏⠙⠁⠀⠀⠀⠀⢂⡁⣸⣿⣿⣿⠟⠛⣠⠜⣳⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣏⠁⠀⡁⠀⠀⠀⠀⣸⣦⣤⣼⣿⣿⣿⠛⠉⠠⡀⠹⠿⠿⠿⡾⠃⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣴⣦⣤⣶⣶⣾⣿⣿⣿⣿⣿⣇⡁⠰⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣛⣻⠋⢍⣀⣠⣿⢁⠘⣏⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⣇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⢣⢸⡄⢻⡀⠀⠘⠁⢀⡀⠀⠀⠂⡀⠀⢀⠀⢀⠀⠀⠯⢀⠀⠈⢷⡄⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡉⢷⠀⣉⡀⠀⠀⠿⠁⣴⠇⣠⠁⢀⡈⠀⢀⠀⢸⣆⠘⣷⡄⠀⠁⣴⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣧⡈⢳⣄⠠⠀⠘⠃⢰⡟⠀⢸⣷⠀⣾⡇⠘⠿⠀⠈⠀⠀⣠⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣷⣄⠛⢇⡀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠁⠀⠀⠀⠀⢀⠔⠁⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠙⠠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠋⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀⡉⠛⠒⠢⠴⠦⠦⠠⠐⠀⣀⡤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠶⠶⠒⠚⠉⠁



⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⢿⠿⠿⢿⡿⠿⠿⢿⠿⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠙⡄⠀⡰⠋⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⠀⠀⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠶⠶⠶⣶⣒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⢴⠶⠛⠙⢯⠉⠉⠉⠉⠉⠙⢿⠿⢯⣗⡒⠤⣄⠀⠀⠀⠀⢳⠀⠀⠀⠀⠉⠫⡒⢄⠉⠲⣄
⠀⠀⠀⠀⣠⠔⢊⠅⠂⢁⠔⠁⠆⠀⡄⠈⢇⠀⠐⢂⠀⠀⠈⢆⠀⠈⠻⡶⣄⢳⣦⠀⠀⠀⣧⠀⠀⠴⠆⠀⠈⢂⠑⣄⠈⢣⡀
⠀⠀⢠⠞⠁⠀⠁⢀⠤⠂⠀⡄⠀⠀⡀⠀⠰⠀⠀⠀⢡⠀⠀⠘⡆⠶⠀⠘⡌⢦⠢⠱⡄⠀⠸⡀⠀⠀⠠⠦⠆⠀⠡⡈⢆⠀⢳
⠀⣰⠋⠀⠊⠀⡠⠀⠀⠀⢐⠀⠀⠐⡀⠀⠀⢢⠀⠀⠀⢠⠀⠀⠸⡄⣤⠄⢰⠈⢇⢑⠹⡄⠀⡇⠀⢀⡄⠀⣀⢀⠀⠱⠈⡆
⢠⠃⠀⡐⠀⢀⠆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢇⠀⠀⠀⡀⠀⠀⢳⠀⠀⠀⠇⠸⡄⠇⢱⠀⢹⠀⢨⣤⠀⠉⠁⠀⠀⠆⢰
⡎⠀⠀⡀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠠⡁⠀⠀⠀⠐⡀⠀⠀⠈⠀⠀⠈⡆⠛⠃⠰⠀⣧⠨⢸⠀⠸⡄⠀⠀⠀⠰⠜⠂⠀⡀⢸
⡇⠀⢀⠁⠀⢘⠀⠀⠀⠀⠄⠀⠀⠀⡆⠀⠀⠀⠀⡅⠀⠀⠀⢁⠀⠀⢱⠀⠀⠀⡀⢸⠀⢻⠀⠀⡇⠀⠉⠁⢀⣠⠀⠀⠇⡆⢠
⡇⠀⠈⠆⠀⠘⡀⠀⠀⠀⠣⠀⠀⠀⠘⠀⠀⠀⠀⠸⠀⠀⠀⠱⠀⠀⢸⡀⠲⠂⠀⢸⠀⣸⠀⠀⢳⠀⠀⠀⠀⠀⠀⠸⡰⣠⠏
⢳⠀⠀⠠⡀⠀⠇⠀⠀⠀⠠⠀⠀⠀⢨⠀⠀⠀⠀⢈⠆⠀⠀⠰⠀⠀⠘⡇⠀⠀⠀⡏⢀⠇⠀⠀⢸⠀⠀⠀⠢⠆⢠⣿⠟⠁
⠘⡆⠀⠀⠀⠀⠀⠄⠀⠀⠘⡀⠀⠀⠈⡄⠀⠀⠀⠘⡄⠀⠀⢠⠀⠀⠀⡇⠘⠐⢰⢁⡞⠀⠀⠀⢸⠀⠀⠀⣀⡴⠟⠁
⠀⠘⡀⠀⠀⠆⠀⠰⠀⠀⠀⠡⠀⠀⠀⠂⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⡇⢀⢢⣣⠎⠀⠀⠀⠀⠸⣤⠶⠛⠉
⠀⠀⠘⢆⠀⠀⢄⠀⠣⠀⠀⠀⢂⠀⠀⠘⠀⠀⠀⢠⠀⠀⢀⠁⠀⠀⠀⣧⣾⠟⠁⢀⡀⠈⡏⠲⡀
⠀⠀⠀⠀⠑⢄⡈⠢⡀⢣⠀⠀⠀⠄⠀⠀⡇⠀⠀⢈⠀⢀⠂⠀⠀⠀⣰⠟⠁⠀⠀⣸⢹⠀⠳⠴⠃
⠀⠀⠀⠀⠀⠀⠉⠲⢬⣢⣡⡀⠀⠈⠢⡀⠸⠀⠀⡄⡠⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣽⣶⣶⣶⣾⣾⣶⣶⣿⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣭⣬⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠀⠀⠀⣀⣀⠀⣀⡀⠈⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠬⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⡠⠒⠈⠀⠀⣀⠤⠀⠀⠤⠤⠒⠒⠒⠀⠀⠒⠢⠄⣀⣀⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⣠⠞⠀⢀⡠⠠⠊⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠤⠄⢀⡀⣀⠈⠓⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⠀⠘⠀⠀⡠⠃⠀⠀⠀⠤⠊⠁⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣂⣌⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠘⠀⢂⠂⢉⠀⠔⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠤⢀⡀⣀⠤⠒⠒⠀⠐⠉⠀⠀⢹⠒⣌⡇⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢂⢒⠠⠔⠁⡀⢀⠤⠒⠒⠐⠊⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡠⠂⢸⡆⣟⢧⣈⠗⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸⡇⢘⣋⠀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⠤⠐⠀⠒⠁⠀⠀⠀⠀⢀⢾⠁⠘⠲⠶⠚⠁⠀⣠⠶⠚⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠓⠶⠾⡇⠀⣿⠢⢄⡀⠁⠁⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⣾⢀⣠⠖⠚⢛⠉⠉⠁⢀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⢲⠞⠁⠀⠰⡀⠀⢿⡀⠀⠑⠀⠀⠑⠤⠤⢄⡀⠀⠀⠀⢀⡞⠙⠓⠒⠒⠒⠲⠖⠛⠛⢛⠛⠶⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⠛⠒⠢⡄⠳⣆⠈⢧⠀⠀⠁⠐⢄⠀⠀⠀⠈⠉⠉⠀⣿⠁⡇⢸⠀⠀⠀⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇
⠀⠀⠀⠀⣀⣀⣀⣀⣤⡴⠃⠀⠌⡑⠨⢧⡀⠀⠀⠀⠈⠈⠈⠒⢄⣀⣸⠟⠀⢳⠸⠀⠀⠃⠀⠀⠀⠆⠀⠀⠀⠀⣁⠀⠀⢀⠀⠀⠀⡁⠀⠀⠠⠀⢈⢰⠇
⠀⠀⠀⠀⡧⠀⠐⠠⠄⣠⠄⢒⠂⠉⠉⢉⠿⢦⡀⠀⠑⠒⠤⡀⠀⢀⡏⠀⠀⠸⡀⠇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⡌⣸
⠀⠀⠀⠺⣄⠀⠀⢀⠊⠀⡠⢁⡤⠶⢴⡁⠀⠀⠉⠳⠦⣤⣀⣈⠐⢺⠃⠀⡀⠀⢣⠐⡀⠀⠃⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡰⢠⡏
⠀⠀⠀⠀⣸⠀⡠⠀⠀⠐⢰⠋⠀⠀⠀⣷⠀⠀⣇⠀⠀⠢⡀⠉⠛⠻⡆⠀⠀⠀⡀⢣⠐⠄⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡴⢡⠎
⠀⠀⠀⣴⣯⣀⣀⡤⠤⣤⡟⠀⠀⠀⢠⡏⠀⠊⠸⣄⡀⢰⠏⠉⠙⣆⠹⣆⠈⠄⠐⠄⠑⢌⠢⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⢀⡠⠔⣩⡴⠋
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠈⣺⣧⠀⠀⠈⠛⠛⠳⢦⣀⠈⠂⠈⠳⢄⠁⠂⠠⠤⠀⣀⣀⣀⠠⠤⢔⣊⣥⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠶⠦⣭⣶⣶⣤⣤⡤⠶⠶⠖⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⣰⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀
⠀⠀⢠⡾⢿⣄⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⣿⣄
⢀⣴⠏⠀⠀⠙⢦⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⡾⠃⠙⣧⡀
⢾⡁⠀⠀⠀⠀⠀⠙⢶⣄⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⢀⡴⠋⠀⠀⠀⠈⢻
⠀⠻⣦⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⢁⣠⡾⠋⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡈⠉⠛⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠾⠛⠉⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣤⣀⣈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⣁⣀⣤⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠒⠒⠚⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠋⠉⢄
⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠺⣦⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣴⠋⠀⠀⠀⠀⡀⠀⠀⠀⠈⢆⠐⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠸⡄⢀⠀⣀⡰⠞⠁⠀⣤⠀⠀⡇
⠀⢀⡾⠁⠀⠠⣤⡀⠀⠙⠂⠀⠀⠀⠈⢆⢷⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⢰⡇
⠀⣼⠁⢀⡀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠈⢎⣧⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠐⣦⠀⠀⠀⣼
⠀⡏⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠀⠈⢟⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠧⠤⣀⣀⡘⠓⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠈⢎⢳⡄⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠈⠉⠉⠋⠒⠒⠢⠤⠄⣀⣀⠀⠀⠈⢆⠙⢦⡀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⢸⡆⠀⠀⠀⠀⠳⠄⠀⠈⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠉⠈⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠚⠁⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠄⣠⢶⣾⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠉⠉⠁⠀⢀⠔⠊⠁⠈⠠⡀
⠀⠀⠀⠀⠀⠀⢀⢴⡾⠟⢉⣴⠊⢀⡞⠀⢷⡝⣬⡛⢿⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⡀⠀⠀⢀⢔⡥⡄
⠀⠀⠀⠀⢠⠞⣱⡟⠁⣶⡿⠁⠐⣿⣇⠀⣸⡇⢸⡇⠈⣷⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢣⢰⠀⠀⠚⠁⠀⢰
⠀⠀⠀⡰⣡⣾⠏⠀⣾⡟⠁⠀⣾⡿⠋⠀⣿⡇⣸⡷⠀⢻⡇⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⢀⢄⡀⠀⠈⢄⠀⠁⠀⠀⠀⢀⡤⠂
⠀⠀⡰⣽⡿⠋⠀⣾⡟⠁⠀⣠⣿⠇⠀⣼⣿⠘⣿⡇⠀⠻⣿⡆⢸⣿⣧⠀⠀⠀⠀⠀⠀⢅⠀⠉⠙⣄⠈⠆⠀⠀⢀⠔⡡⠐⠢⡀
⠀⠀⡇⣽⠇⠀⢠⣾⡟⠀⢀⣿⣧⠀⢸⣿⣏⠐⣿⣧⠀⠀⣿⣿⠈⣿⣿⡄⠀⠀⢀⠔⠒⡄⣇⠀⠀⠈⠓⠃⠀⠀⠦⠔⠁⠀⠀⢸
⠀⠀⢀⣿⠀⢀⣼⣿⠇⠀⣿⣿⠟⠀⢸⣿⡟⠀⣾⣿⡀⠀⣸⣿⠀⢸⡇⡇⠀⠀⢌⠀⠀⢂⢀⡕⣄⠀⠀⠀⡄⠀⠀⠀⠰⠖⠒⢡
⠀⠀⡞⣿⡀⢿⣿⡏⠀⣠⣿⡿⠀⠀⣿⣿⡁⠀⢹⣿⡇⠠⣿⣿⠀⢸⣿⡇⠀⠀⢔⠛⠂⠀⠁⠰⡌⢱⡀⢰⠀⡔⢒⢶⡢⠶⠴⡁
⠀⠀⢧⣿⣇⠘⣿⣷⠀⢻⣿⡆⠀⢀⣿⣿⣿⠀⢸⣿⡇⠀⢹⣿⠇⣼⣿⠀⠀⠀⠈⠉⠐⠢⣄⠀⠙⣼⠀⢏⢊⠔⠁⠀⠀⠀⡠⠆
⠀⠀⠘⣎⣿⠀⣿⣟⠀⢸⣿⡁⠀⠀⣻⣿⠇⠀⢸⣿⠇⠀⢸⣿⠀⣿⠃⠀⠀⠀⠀⡤⠂⠉⠈⠁⠀⠀⡜⠈⠁⠀⣀⠤⢄⣀⡑
⠀⠀⠀⠈⢿⣆⠈⢻⡇⠀⢿⡅⠀⠀⢹⣿⠂⠀⢸⣿⡷⢀⣼⠏⡠⠃⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢺⠓⢄⠀⠀⠉⠒⠲⡄
⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠈⢷⣄⠀⣼⡿⠀⣀⣿⠋⢀⣿⡣⠞⠁⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⡏⠀⠀⠙⠦⣀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣷⣄⠘⣷⣿⣧⣾⣟⣋⡤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⢝⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡫⠀⠈⠣⠤⠘⢅⠀⠀⠀⠈⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢢⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠙⣦
⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠈⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⠖⠁⠒
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡀⢤⡒⠑⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⢀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠍⠠⠀⠂⡀⠜⠊⢁⠀⠀⠀⠀⠀⠀⠀⠀⣸
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀⠴⠐⠉⠀⠃⢀⠄⠒⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⣧⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡐⠈⠫⠁⠀⠄⢀⠁⠀⣀⡠⠄⠒⢁⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠸⡆⠀⠀⠀⡀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠘⢦⣠⣄⠤⠐⣘⣊⣈⡭⠥⠔⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠹⣄⠀⠀⡇⠀⠀⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠞⠁
⠀⠀⠀⠙⢦⡀⠸⡄⠀⠀⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⠵⠊⠁
⠀⠀⠀⠀⠈⠳⣤⣻⡄⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣀⡀⠀⠀⠀⠈⠉⢳⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠖⠒⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣿⣾⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡃⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠄⣤⢸⣭⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠄⠀⠲⣣⣏⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠐⢻⣷⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⡈⠟⡃⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢰⣄⠀⣀⣀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠐⠸⠀⢸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⡠⠈⠁⠋⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⢠⢴⠀⠠⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠼⣀⢸⠘⠀⠠⠧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠢⢀⡏⠈⠁⠀⠈⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⢆⡀⠀⠁⠰⠊⠀⠀⠀⠀⠀⠘⡐⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠹⠈⣀⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠛⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢀⣶⡽⣟⣷⡂⡤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠄⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⣶⣿⣽⣷⣿⣿⣷⣶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⣀⠴⠚⣫⠵⢊⡷⢣⡏⢹⡙⠫⣉⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⣤⠾⠋⢠⡾⠃⠀⣿⠁⠘⡗⠀⢱⡆⠉⢧⡈⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⣄⡾⠁⠀⣰⡿⠀⠀⣼⠋⠀⢰⡇⠀⠐⣇⠀⠈⢳⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠀⢰⠏⠁⠀⣾⠏⠀⠀⢠⡏⠀⠀⢨⣟⠀⠀⣿⡆⠀⠀⣷⡄⠸⣇
⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢠⣿⠀⠀⢰⡿⠂⠀⠀⢸⡿⠀⠀⢀⣿⠀⠀⢻⡇⠀⠀⢹⡇⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢸⡟⠀⢀⣾⠁⠀⢠⣾⡇⠀⠀⢀⣾⠇⠀⠀⢸⣿⠀⠀⠠⣧⡄⠀⢸⣇⠀⠰⣿⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡷⠀⢀⣾⣿⠀⠀⠀⢺⣿⠀⠀⠀⢀⣿⠀⠀⠀⣿⡄⠀⠘⠛
⠀⠀⠀⠀⠀⠀⢻⠇⠀⢻⡇⠀⠀⢿⡟⠀⠀⠀⢸⣧⠀⠀⠀⢸⣏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⣿⡗⠀⠀⠀⣸⣿⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠸⣿⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠿⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠀⠀⠀⡆⠀⢠⡀⠀⢀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠛⠉⠉⡉⠉⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣖⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡿⣘⢿
⠀⠀⠀⠀⠀⢠⣄⣀⣸⠈⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⢉⣒⡡⠤⠖⠉⠹⡄
⠀⠀⠀⠀⢤⠞⠀⠀⠹⡄⠁⠈⠐⠄⠀⠀⠀⠀⢠⠖⠦⠤⠤⠤⠖⢒⠦⠖⠚⠒⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠉⠉⢳⠉⠂⢱⡀⠀⠀⠠⠤⢀⠀⢠⡇⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢰⠉⠉⠉⡁⠠⠐⠂⠹⢄⡀⠀⠠⠀⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠃
⠀⠀⠙⡄⠀⠀⠀⡠⠒⠲⡄⠀⠉⠓⠲⠤⣤⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⣴⣁⣀⠤⣴⠃⠀⢀⡇⠀⢡⠀⢰⠒⢢⡱⣄⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⢄⡪⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⣄⡠⠽⠀⠀⠉⠉⠓⠤⣄⣈⡂⣄⣀⡂⢀⣀⣐⡦⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⢠⣾⡆⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⣰⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀
⠀⠀⢠⡾⢿⣄⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⣿⣄
⢀⣴⠏⠀⠀⠙⢦⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢠⡾⠃⠙⣧⡀
⢾⡁⠀⠀⠀⠀⠀⠙⢶⣄⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⢀⡴⠋⠀⠀⠀⠈⢻
⠀⠻⣦⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⢁⣠⡾⠋⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡈⠉⠛⠶⢦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡴⠾⠛⠉⣀⣤⠶⠛⠁⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣤⣀⣈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⣁⣀⣤⡴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠒⠒⠚⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠂⠁
⠀⠀⠀⠀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⢈⡭⠍⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣭⡄⠠⠐⠀⠠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠤⢠⡔⢸⢤⠭⢠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⡥⠬⠰⡶⣇⣟⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⢀⡸⢭⢿⣖⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡉⢘⠸⢟⣆⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠛⠠⠀⣧⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⢸⡤⣄⣤⣤⣤
⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣗⠀⠀⢁⢹⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⡰⠈⠃⠀⠀⠀⢀⠔⠉⠀⠋⠀⠀⢸
⠂⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣥⠀⠂⠀⡤⢼⠀⠀⣾⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣿
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⣰⠀⠘⣃⡾⠀⠀⣹⠙⠀⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠐⣿
⠀⠀⠀⠀⢀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⣰⠀⠁⣼⠴⠧⠃⠀⠀⡀⠡⠂⠀⠀⠀⠈⠐⠒⠄⠀⠀⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡀⡴⡀⠛⢠⡥⡠⠀⠀⠀⠀⢢⣠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⠠⠀⠆⠐⢥⠠⢁⠄⠀⠾⠂⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠍⠇⠉⡀⠚⡃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠉⠮⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠐⠠⠤⠄⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⣠⡝⣷⢶⣦⡤⢀⢠⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠳⠽⠦⠦⠋⠓⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠂⠄⠨⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢠⡒⠢⣤⣀⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣾⠁⢿⡀⠹⣧⠀⠛⠷⣄⠈⠳⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⣿⠀⠈⣿⠄⠘⢳⡀⠀⠙⣧⠐⠙⢦
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢬⣿⡄⠀⠞⣶⠀⠘⣷⡀⠀⠹⢧⠀⠀⢧⠠
⠀⠀⠀⠀⠀⠀⡆⢾⠁⠈⢸⣿⡀⠐⠙⣷⠄⠀⢣⡀⠀⠈⢧⡀⢸⡆⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡇⠾⣷⣀⢠⢿⣷⠀⠀⣽⣷⠀⠛⢷⡄⠀⢺⠁⢀⠃⠃⠀⠀⠀⠀⣀⠀⠃
⠀⠀⠀⠀⠀⠀⢣⠀⢿⣧⠀⠀⣹⢷⠀⠈⠸⣇⡀⠹⡟⠀⠘⠀⠀⠀⠀⠀⠀⠐⠆⠤
⠀⠀⠀⠀⠀⠀⠀⢣⠈⢻⡄⠈⠁⢙⣿⣀⠂⠙⢀⠤⠁⠀⠀⠀⠀⠀⠀⡄⠀⠰⠄⠦⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡙⢦⣄⡘⠉⠿⣄⣀⠹⡄⠀⠀⠆⠀⡀⠀⡀⣁⠀⣀⠙⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠬⣙⡓⠶⠬⠽⠆⠈⠢⡀⠀⠀⠉⠀⠁⠈⠀⠈⣠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⠀⠤⠀⠔⠋⠋


⠀⠀⠀⠀⠀⠀⠀⠰⠍⣧⢰⡆⠸⡀⣄⢠⡦⢀⢤⢠⡤⢤⡄⣄⣤⢀⡠⡄⣿⢠⢤⡀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠎⠻⠂⠾⠿⠸⠇⠻⠄⠸⠇⠸⠇⠿⠸⠘⢧⠀⠿⠻⠼⠇⠿⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠠⢄⣀⡠⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⢷⡌⠻⣤⠈⠛⣶⣆⠉⠓⢤⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣿⠃⠘⢷⡀⠙⣧⡀⠀⠉⢿⣄⠀⡳⡄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢠⣿⠀⠀⣸⣏⡀⠀⣳⡆⠀⠀⢿⣄⠀⠘⢦⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣻⠂⠲⢿⣆⡀⠘⢸⣇⠀⠀⢷⡆⠀⠈⠻⣄⠀⠘⡆⢃
⠀⠀⠀⠀⠀⠀⢸⠀⣿⡀⠀⠈⣿⡅⠀⠁⢸⣗⠀⠀⣳⡄⠀⠀⢹⡦⠀⢿⢸⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢸⠀⢿⣷⡄⢠⠾⣿⡀⠀⠲⡿⣇⠀⠙⣷⣄⡀⢸⡇⠀⠬⠘⠀⠀⠀⠀⠀⣤⠀⡉⡀
⠀⠀⠀⠀⠀⠀⠈⣇⠘⢿⣧⠀⠀⣨⡿⡆⠀⠁⢹⣆⠀⠹⡿⠁⠘⠃⠀⠀⠀⠀⠀⠀⠐⠂⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⢿⡀⠀⠉⠘⣻⣇⡀⠄⠹⢀⠤⠑⠀⠀⠀⠀⠀⠀⢀⡀⠀⢦⠄⠶⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠛⢦⣀⠀⠛⢹⣧⡀⠀⢳⡀⠀⠀⠴⠀⠀⠀⠀⠈⡁⠀⡀⠲⠄⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣍⡙⠶⢦⣌⣙⣷⡄⠑⢄⠀⠀⠀⠘⠂⠘⠂⠛⠀⠙⢀⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⣀⠀⠀⠀⢀⡠⢔⠯⠊


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⣿⣸⣷⡰⢰⣰⡆⣺⠃⣴⠲⢰⡖⠒⡶⢶⢲⡆⣴⠲⠀⡇⣴⠲⡆⣶⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠹⠃⠸⠞⠇⠹⠂⠛⠆⠘⠇⠀⠇⠸⠘⠇⠙⠦⠈⠇⠙⠼⠃⠻⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠄⡀⡀⢀⠀⠀⠀⠀⠀⠐⠁⢦⠄⠀⠀⠀⠁⠇⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⡚⡀⠀⠀⢉⡄⠀⠀⠆⠛⡆⠠⠄⠀⠂⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣇⢒⠀⠂⠀⠀⠀⠀⠊⢤⠀⠀⡀⢆⡖⢠⢉⠄⠘⣽⡆⠃⠈⣦⠍⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣿⡽⠆⠱⠀⠀⣀⠃⠰⢆⠈⣁⠐⠈⣴⣬⢍⠞⢴⢋⢘⠐⢳⠐⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⢸⣇⢿⠄⣈⣁⢀⡄⡤⠸⣂⠹⠿⢛⣧⢸⣰⣸⡻⢏⠰⢽⢉⢫⡓⣤⢆⣀⠐⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣶⡍⣹⡀⣤⢀⡂⢩⠰⠸⣩⣞⣩⣭⣜⡗⢋⢿⡾⣦⠶⣌⣁⠀⢼⣴⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣝⣻⣨⣆⠿⢎⠟⢣⣅⣹⡴⣾⣿⣿⣾⣿⣿⣿⣿⡟⢀⣫⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣟⣧⣻⣿⣶⣛⣼⣣⣽⡗⣿⢿⣿⣿⢿⣿⣿⣿⣷⣿⣮⣿⠟⠀⠀⠀⠀⠀⢀⣀⠤⠐⠂⡤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣾⣯⣿⣿⣿⣷⣧⣭⣾⣿⣿⣿⣿⡿⣿⣿⢿⢿⢥⠤⡄⡲⣆⣳⣼⣿⡿⠦⣡⠞⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡏⢭⣄⠀⠉⢼⣛⡼⢾⣇⣷⠼⣽⢿⡷⠋⠉⢠⠄⠊⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡀⢘⣧⠀⠀⠈⠉⠚⠃⠐⠳⠓⠚⠛⠀⠉⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣴⣻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣤⣀⣀⣀⣀⣀⣀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢢⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⢣⣸⠀⣰⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢼⡄⠉⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠔⠒⠉⠉⠀⠦⠀⠀⠈⢸
⠀⠀⡤⠤⠄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠒⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠸⣁⣠⢶⣀⡼⠦⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠑⠂⠀⢃⡢⠀⠀⠀⠀⠀⠀⡆
⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠄⠀⠀⠒⠀⠀⠘⣁⠀⠀⠐⠚⠀⠠⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢰⠃
⠀⠀⠀⢧⢂⠀⠀⠀⠄⠀⠀⢀⢴⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠦⠃⠀⠀⢀⠂⠀⠀⠀⢀⠇
⠀⠀⠀⠈⢎⢆⠀⠀⠀⠢⡀⠈⠁⠀⠀⠀⢆⠅⠀⠀⠠⠢⠀⠀⠀⠰⠜⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠈⢦⡣⡀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠀⠀⠀⡀⢠⠎
⠀⠀⠀⠀⠀⠀⠑⣌⠀⠀⠀⠀⠀⠀⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠁⠀⠀⠀⡠⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣅⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⣪⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢥⣂⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠒⣈⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠤⠤⠤⠬⠭⠥⠤⠖⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀
⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⢤⢦⡀⢀⠀⠀⣇
⠀⠀⠀⢀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡠⠛⠁⠘⠃⠀⢱⠀⠀⠀⠀⠠⡀
⠀⠀⠙⠊⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⢀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⣄⠀⠁⠙⠄⢀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠈⠐⢄⠀⠀⠀⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠳⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⠶⢤⣀⣀⣀⣄⡀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠲⣄⡈⠂⠠⣄⣀⣀⠀⠀⠠⣀⠀⠀⠈⠲⢠⣀⠀⠀⠀⠀⠀⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠐⠤⠼⠮⠑⠛⠛⠋⠙⠲⠤⣤⣦⣈⣁⡉⠀⠀⠙⠋⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⡀
⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⢤⢦⡀⢀⠀⠀⣇
⠀⠀⠀⢀⠀⠀⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡠⠛⠁⠘⠃⠀⢱⠀⠀⠀⠀⠠⡀
⠀⠀⠙⠊⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠊⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⢀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠀⣄⠀⠁⠙⠄⢀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠈⠐⢄⠀⠀⠀⠤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠳⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠘⠶⢤⣀⣀⣀⣄⡀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠲⣄⡈⠂⠠⣄⣀⣀⠀⠀⠠⣀⠀⠀⠈⠲⢠⣀⠀⠀⠀⠀⠀⢀⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠐⠤⠼⠮⠑⠛⠛⠋⠙⠲⠤⣤⣦⣈⣁⡉⠀⠀⠙⠋⠁
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢡⠀⡠⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢪⣉⣢⠑⠎⠰⠧⠦⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⠚⠉⠀⠀⢸
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠤⠔⠒⠒⠉⠉⠉⠀⠀⠀⠀⠀⠁⠀⠀⢸
⠀⠀⠇⠀⠉⠙⠉⠉⠙⢲⡀⢠⡄⢀⡦⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠓⠀⠀⠀⡀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠐⠀⠀⠂⠄⠀⠀⠀⠀⠀⢸
⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢠⠢⠀⠀⠔⠀⠀⠈⣑⠀⠀⠂⠃⠀⢄⠀⠀⠀⠁⠀⠀⠀⠀⢀⠇
⠀⠀⠈⣖⡀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⡜
⠀⠀⠀⠘⡔⠄⠀⠀⠑⢀⠀⠁⠀⠀⠰⠔⠀⠀⠀⣑⠀⠀⠀⠂⠁⠀⠀⠀⠀⢀⠔⠀⠀⠀⡀⡜
⠀⠀⠀⠀⠘⢎⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠱⣕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⡠⢐⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⡨⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠭⢔⣂⡀⠀⠀⠀⠀⠀⠀⣒⣀⠠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣤⣤⣶⣖⣀⣄⣶⣂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠤⠚⢁⠀⠀⠀⡈⠀⠈⠁⠈⠳⠿⠳⣶⣀⠈⠓⢦⡀
⠀⠀⠀⣰⠴⠖⠲⠟⠖⠻⠛⠛⠻⠶⠷⣴⣀⢀⡀⠀⠉⠙⣆⠀⠹⡀⡀
⠀⠀⣸⠀⠀⣀⣠⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠙⠶⠦⣄⠙⢆⠰⡇
⠀⠀⣧⠾⠛⠛⠛⠛⢫⡝⠐⠢⠖⠒⠀⠠⠜⠠⠤⠶⠦⠀⡈⠙⠮⠂⡇⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠑⠢⣳⣉⡅
⠀⠀⠘⣦⣤⣀⣴⣄⣀⢀⣀⣀⠤⠔⠋⠉⠛⠆⠈⠉⠀⠀⠀⣀⡤⢚⢡⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠑⣌⠁⠉⠛⠛⠛⠙⠓⠚⠒⠲⠶⠶⠶⠊⠻⠛⠛⣋⡥⠊⠀⡘⠀⠀⠀⠀⠀⢀⠸⠂⠀⣦⠀⡀
⠀⠀⠀⠀⠈⠳⡶⢦⣄⣀⣀⣀⣠⣀⣀⣀⣀⣀⣤⡤⠖⠊⠀⠔⡣⠀⠀⠀⢀⠁⠰⢇⡋⠀⠀⠀⢀⣠⠜⢂
⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠉⠉⠉⠀⠁⢀⡀⠤⠖⡊⠄⠂⠀⠀⠀⠀⠀⠉⠒⠀⠤⠤⠠⠡⠄⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠒⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⣶⣿⣽⣷⣿⣿⣷⣶⡤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⣀⠴⠚⣫⠵⢊⡷⢣⡏⢹⡙⠫⣉⠻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⣤⠾⠋⢠⡾⠃⠀⣿⠁⠘⡗⠀⢱⡆⠉⢧⡈⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⣄⡾⠁⠀⣰⡿⠀⠀⣼⠋⠀⢰⡇⠀⠐⣇⠀⠈⢳⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣰⣿⡁⠀⢰⠏⠁⠀⣾⠏⠀⠀⢠⡏⠀⠀⢨⣟⠀⠀⣿⡆⠀⠀⣷⡄⠸⣇
⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢠⣿⠀⠀⢰⡿⠂⠀⠀⢸⡿⠀⠀⢀⣿⠀⠀⢻⡇⠀⠀⢹⡇⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢸⡟⠀⢀⣾⠁⠀⢠⣾⡇⠀⠀⢀⣾⠇⠀⠀⢸⣿⠀⠀⠠⣧⡄⠀⢸⣇⠀⠰⣿⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡷⠀⢀⣾⣿⠀⠀⠀⢺⣿⠀⠀⠀⢀⣿⠀⠀⠀⣿⡄⠀⠘⠛
⠀⠀⠀⠀⠀⠀⢻⠇⠀⢻⡇⠀⠀⢿⡟⠀⠀⠀⢸⣧⠀⠀⠀⢸⣏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⣿⡗⠀⠀⠀⣸⣿⠀⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠸⣿⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠿⠆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⣄⠀⠁⠀⠀⠀⠀⠀⡆⠀⢠⡀⠀⢀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣀⣀⣀⣀⣀⣀⣠⣤⣴⣶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠡⡀
⠀⠀⠀⠀⠀⣤⠞⠋⠀⠀⠀⢶⡄⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠁⠀⠱⡀⢰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⢰⡀⠀⠀⠀⢠⠴⠋⠉⣉⡉⠉⢹
⠀⠀⣰⠏⠀⠀⣤⡀⠀⠘⠧⠀⠀⠀⠀⠱⡈⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠲⠋⠁⠀⠀⠀⠈⠁⠀⣾
⠀⣰⠇⠀⠀⠀⠈⠉⠀⠀⣀⠀⠀⠀⠀⠀⠱⡸⡆⠀⠀⠉⠀⠀⠀⢠⡴⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢠⡏
⠀⣿⠀⠈⠳⠄⠀⠀⠀⠀⠈⠃⠀⠀⢶⡄⠀⠱⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠉⠀⠀⠀⡼⠁
⠀⣿⡀⠀⠀⠠⠤⠀⠀⠀⠀⠰⢦⠀⠀⠀⠀⠀⠹⡙⣦⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠈⠉⠉⠙⠓⠒⠂⠤⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠹⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⣴⠀⠀⠀⠀⠀⣤⡀⠀⠘⠆⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠐⠒⡆⠤⠽⠀⠉⠳⣄⡀⠀⠀⠀⠀⠘⠁⢠⡀⠀⠙⠀⠀⠀⠀⠀⠈⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣤⣤⣤⡤⠶⠖⠚⠉⠀⡠⠤⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠞⢋⡴⠛⣻⢻⡟⣟⠳⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⢀⡤⣪⡿⠉⣠⣶⠋⢠⣾⠁⠀⢹⡎⢳⡌⠻⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡄⢆⠀⠀⢠⡮⠚⠱
⠀⠀⠀⠀⡠⢋⣼⡟⢀⣼⣿⠃⠀⣸⣿⡆⠀⣾⡇⢸⡇⠀⣿⡄⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠹⠬⠀⠀⠈⠀⠀⢀
⠀⠀⠀⡜⣱⣿⠏⢀⣼⡿⠁⠀⠸⣿⡏⠀⢠⣿⢇⣾⡏⠀⣸⣷⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠔⠢⡠⣄⠈⢢⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⢸⢸⣿⠁⠀⢸⣿⡀⠀⢠⣾⡿⠁⢠⣿⡿⠈⣿⡇⠀⠙⣿⣧⠸⣿⣿⡆⠀⠀⠀⠀⠀⠀⢢⠀⠀⠘⢆⡀⡃⠀⠀⢀⠔⡰⠊⠉⠢⡀
⠀⠀⡇⢼⡏⠀⢠⣾⣿⠀⢀⣼⣿⡆⠀⢹⣿⡇⠈⢿⣷⠀⠀⢿⣿⡄⢻⣿⢧⠀⠀⠀⡔⠉⠉⡞⢄⡀⠀⠀⠉⠁⠀⠀⠗⠒⠁⠀⠀⢀⠇
⠀⠀⣀⣾⠁⢀⣴⣿⡟⠀⢸⣿⣿⠃⠀⣼⣿⡇⠠⣿⣿⡄⠀⢸⣿⠁⠀⣿⢸⠀⠀⠀⢅⠀⠀⢇⡠⡴⢄⠀⠀⠀⡆⠀⠀⠀⠐⠚⠛⢁⠆
⠀⠀⡏⣿⡇⠸⣿⣯⠀⢠⣾⣿⠟⠀⢸⣿⣿⡀⠀⢹⣿⡇⠀⣿⣿⡀⠀⣿⡟⠀⠀⠠⡚⠋⠀⠀⠀⠱⡄⢱⠀⢸⢀⠔⢒⠶⠖⠒⠒⢥
⠀⠀⢱⢿⣧⠀⣿⣿⠀⠘⣿⣿⠀⠀⢸⣿⣿⡿⠀⢸⣿⡇⠀⢸⣿⡇⢰⣿⠇⠀⠀⠀⠈⠉⠒⠦⣄⠀⠙⡼⢀⢇⣊⠔⠁⠀⠀⠀⢠⠜
⠀⠀⠈⢆⣿⠀⢿⣿⡁⠐⣿⣯⠀⠀⠈⣿⣿⠃⠀⣸⣿⠇⠀⢸⣿⠀⢸⡟⠀⠀⠀⠀⢠⠔⠊⠉⠈⠀⠀⠀⡜⠈⠁⠀⣀⠤⠤⣀⣈⠆
⠀⠀⠀⠈⠻⣇⠈⠹⣿⠀⠸⣯⠀⠀⠀⣿⣿⠀⠀⢹⣿⡷⢀⣼⡟⢠⠏⠀⠀⠀⠀⠀⢇⠀⠀⠀⠠⠀⠐⢺⠓⢄⠀⠀⠉⠐⠒⢦
⠀⠀⠀⠀⠀⠙⢧⡀⠙⢦⡀⠹⣦⡀⢀⣿⡟⠀⢀⣿⠋⢀⣾⣫⠔⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢀⠇⠀⠀⠑⠦⣀⠀⠀⢫
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣑⣦⡈⢻⣼⣿⣤⣾⠿⢋⡠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢆⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⢣⡀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠠⡶⠀⠀⠱⡄⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⡄⠀⠀⠀⠀⠀⠀⠘⢎⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠉⠀⠀⠀⡀⠀⠀⠀⠀⠣⡈⠊⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢰⠇⠀⠀⢀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠙⣄⢀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠈⢦⠃⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠳⡀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢶⠒⠒⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⢀⡼⠓⠒⢒⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁⣠⠴⠋⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠉⠓⠲⠤⢄⣀⣀⣀⣀⣀⣀⣀⣠⠤⠔⠒⠉⣀⣤⠶⠋⠁⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠖⠚⠉⣁⣀⡤⠖⠛⠉

⠀⡀⠀⠀⠀⠀⠀⠀⠈⠢⢝⡂⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⢣⣙⠂⢀⠀⠀⠉⠳⣌⡒⠦⠤⣄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡳⠄⠀⠈⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⡀⢐⠈⡉⠀⠀⠀⠢⣕⢦⠀⠀⠀⢤⡀⠠⠆⠦⠳⠳⠈⠁⢀⡔⠀⠀⠀⠀⠀⢀⣴⢋⠴
⠀⠀⠀⠈⠀⠘⠀⡁⠏⠼⣠⠀⠈⢦⢱⡀⠈⠳⣬⣑⡰⠤⠤⠤⠔⣚⠡⠊⠀⠀⠀⠀⢠⡷⣁⠋⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢴⡀⠠⡆⣧⠀⠀⠀⠘⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣸⢣⠇⢐⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠆⢈⡇⣿⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⢄⣀⠀⠀⠀⠀⢻⢸⠀⠠⠖⡀
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⣸⡝⠀⠀⠀⡀⡀⠀⠈⠉⠉⠙⠒⢨⣙⢶⣄⠀⠘⡌⢇⠀⠚⣡⢀
⠂⠰⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠡⠋⠀⠀⠀⠀⡄⠀⢠⡰⡆⢶⢰⢢⢄⡉⠢⠻⣃⠀⠐⠌⠀⠀⠀⠉
⠒⠈⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡘⠢⠃⠀⠀⠀⠈⠈⠠⠀⢣⢹⡄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣼⢰⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⢰⣿⢨⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰
⢀⡐⠆⡀⠀⠀⢿⡘⡀⠈⠵⢂⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⡆⠇⠘⣠⢀
⠃⠁⠰⠁⠀⠀⠈⢣⡱⣄⠀⠉⠰⠃⠇⠶⠘⡂⠊⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⢾⣌⢦⠀⠋⠞⠰⠆⡇
⣿⡿⠷⠷⠶⠶⢶⣶⢿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣶⣾⣿⣷⣷⣶⣶⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⣿

⠀⠀⠀⢸⣿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⢿⣿
⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿
⠀⠀⠀⠘⣿⡄⠀⢹⣧⠀⠀⢺⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠂⠀⢠⣿⠁⠀⣼⡟
⠀⠀⠀⠀⢹⣧⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⢠⣿⠁
⠀⠀⠀⠀⠀⢿⣇⠀⠈⢿⣦⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⢠⣾⠏⠀⢀⣿⠇
⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⢀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⢀⣴⡿⠃⠀⢠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠈⠻⣷⣄⡀⠀⠀⠙⠃⠀⠀⠀⣿⡇⠀⠀⠀⠛⠁⠀⠀⣀⣴⡿⠋⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠈⠙⠿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠉⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⠀⠀⠉⠙⠛⠿⠿⠿⠶⠾⠿⠿⠟⠛⠉⠁⠀⢀⣤⣶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣦⣤⣄⣀⣀⣀⡀⣀⣀⣀⣀⣤⣤⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⡤⡂⠄⠰⠛⠚⠒⠶⠶⣤⡑⢦⡀
⠀⠀⠀⠀⠀⢦⠀⠀⠈⠑⠀⠁⠀⢁⣴⣾⠇⠀⠀⠀⢀⣎⠠⠤⠤⠶⠶⠶⠶⠶⢦⣤⡙⣜⡟⡆
⠀⠀⠀⠀⠀⠈⠓⠦⣀⣀⣀⣒⣾⠿⠗⠁⠀⠀⠀⠀⢸⠁⠀⠤⣴⠦⣴⠶⠶⠶⠦⠴⠒⠄⣾⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⠉⠉⢀⣀⣀⣠⣤⡴⣾⣵⣧⡟
⠀⠀⠀⠀⠀⣀⣤⣖⣾⣿⡶⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣯⣭⣍⣩⣽⣭⣶⣾⣿⡿⠋
⠀⠀⠀⠀⣼⣿⣿⣿⣯⣤⣤⣤⣄⣀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠋⠁
⠀⠀⠀⢰⣿⣿⣿⡟⠿⢿⣇⣄⣡⣤⣤⢥⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠒
⠀⠀⠀⠈⣿⣿⣿⠁⡀⠸⣭⣴⡶⢟⣿⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠘⢿⣿⣷⣶⣴⣿⣿⢿⡿⠋⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣀⣀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⢹⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣞⢀⣷⡦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⣿⡷⢿⣿⣿⣿⡿⢹⡛⠛⠲⢦⣌⣙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⡟⠉⣰⣿⠋⢸⣿⡇⢸⣧⠀⠀⠀⢈⠻⣷⣮⡳⣄
⠀⠀⠀⠀⠀⠀⣰⢋⣴⣿⠋⠀⣾⣿⠃⠀⣸⡿⠁⢻⣿⡄⠀⠀⠀⠀⠈⠻⣧⡈⢳⡀
⠀⠀⠀⠀⠀⣰⠃⣾⣿⠃⢠⣴⡿⠋⣀⣴⣿⡇⠀⠸⣿⣧⠀⠀⠀⠀⠀⠁⠹⣿⡀⠹⡄
⠀⠀⠀⠀⢠⠇⣴⣿⠇⢰⣿⣿⡇⠀⢹⣿⣿⠀⠀⠀⣿⣿⠈⠁⠀⠀⠀⠀⠀⢹⣷⣀⠹⡀
⠀⠀⠀⠀⣼⠀⣿⡟⠀⢸⣿⣿⠆⠀⢸⣿⣿⡀⠀⠀⣿⣿⡆⣀⠀⠀⠀⠀⠀⠀⢿⣿⡀⢧
⠀⠀⠀⠀⡇⣰⣿⡇⠀⢸⣿⡿⠀⠀⢘⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢸⡄
⠀⠀⠀⠀⡇⢹⣿⡇⠀⢸⣿⣇⠀⠀⣸⣿⡿⠀⠀⠀⣿⣿⡇⠀⠀⠒⠀⠀⠀⠀⠀⣿⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⣄
⠀⠀⠀⠀⡇⢸⣿⡇⠀⣻⣿⡏⠀⠀⢿⣿⡟⠀⠀⠀⢻⣿⡇⠉⠀⠀⠀⠀⠀⠀⡀⢿⣿⡀⡇⠀⠀⢀⣀⡠⠤⠔⠒⠋⠉⠁⠀⠀⢸⡄
⠀⠀⠀⠀⢷⠈⣿⡇⠀⣿⣿⡇⠀⠲⢾⣿⣇⠀⠀⠀⣸⣿⡇⡀⠀⠙⠀⠀⠀⠀⡃⣸⠿⠶⠗⠒⠉⠉⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠘⡆⢺⣿⠃⠈⣿⣿⠀⠀⢹⣿⣿⠀⠀⠴⢿⣿⡁⣁⠀⠤⠀⠐⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⢠⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠹⡜⣿⡀⢀⣿⣿⡁⠀⢼⣿⣿⠀⠀⠀⡎⠉⠁⠀⠀⠀⠀⠀⡀⠈⠀⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⢁⡇
⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⣿⣿⡇⠀⢺⣿⣿⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⡀⠀⠀⢠⡀⠀⠀⠇⠀⠀⠘⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⣿⡇⠀⠀⣿⡇⠀⠀⢾⣿⣷⡈⠂⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣷⣄⠀⣿⡇⠀⢠⣿⡿⠙⢿⣦⣀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠷⠤⠴⠿⠧⠶⠒⠛⠻⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠁⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢷⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠘⣧⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠸⣇⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠹⡆⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠸⣇⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⢹⡆⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⣿⣷⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠈⢷⡀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢀⣶⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⣧⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣧⠀⠀⢀⢞⣷
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⢫⡞⢹⡆
⠀⠀⠀⠀⠀⣼⡧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣷⠏⣰⠏
⠀⠁⠀⠀⢰⡏⠳⣮⡑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣥⠞⠹⣶⠋
⠀⠀⠀⠀⠀⠙⢦⣄⠙⠳⢮⣝⡒⠢⠤⢄⣀⣀⢀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠖⣚⣩⡴⠞⠋⣀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣤⣈⡉⠛⠲⠶⠶⠶⠭⠭⠭⣭⣭⣭⡥⠴⠶⠖⠛⠋⣉⣠⡴⠖⠛⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠶⠦⠤⠤⠤⠤⠤⠤⠶⠶⠶⠚⠛⠋⠉
⠀⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠖⠂⠈⠉⠉⠉⠉⠙⠶⢶⣲⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⢿⠛⠛⡟⠟⢱⢢⣦⣀⠀⠀⢀⠀⠈⠛⣷⣄⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠚⠷⢧⣲⣀⠄⠘⢻⣦⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⢀⣠⡤⢊⠀⠢⠀⣡⣢⠠⡀⠤⡀⢀⠄⠀⠀⠀⠉⠙⠀⣄⠈⠻⡄⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⠛⠉⠀⠀⠁⠁⠀⠀⠀⠀⠃⡦⠺⠿⢾⢶⣵⣄⣠⡀⠀⠀⠑⠂⠡⠀⠈⣷
⢀⡟⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⣀⠠⠀⣠⣀⢀⡀⢠⡀⣀⠀⡀⠀⠀⠀⠀⠈⠁⠙⠶⢶⣤⣄⡑⢿⡼⢈
⢸⠃⠀⠀⠀⠈⠉⠉⠑⠢⠤⢄⣸⠉⠁⠈⠉⠀⠙⠉⠉⠉⠁⠋⠃⠋⠋⠉⠁⠢⠀⠲⠀⠠⠀⠀⠀⠀⠤⠈⣻⣷⢿
⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠉⠑⠂⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣠⡤⡐⠴⠤⢒⠘⢹⣽⣿
⣿⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢷⠠⠠⢔⡤⣶⣲⠿⠎⠝⠊⠙⠀⠀⢀⠄⠃⢀⡿⣼⣷
⢻⡀⠀⠀⠀⠐⠀⠀⠈⢀⠀⢀⠀⢀⠀⠂⠀⡄⠀⠀⢠⠟⢾⠆⠓⠀⠐⠀⠀⠀⠀⠀⣀⣠⡤⠾⠋⠀⣤⣾⢇⡇⠏
⠈⢧⡀⢀⠀⠀⠀⢠⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⢀⢀⡏⣰⢸⠀⠀⢀⣀⣠⣠⣶⢶⠞⠋⠁⠀⠀⠀⣼⠟⠠⢸⠋
⠀⠈⠣⡈⠢⡀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⡠⢡⠞⡴⣿⣸⣶⣰⠶⠞⠚⠛⠀⠀⠀⠀⠀⣠⣴⡿⣛⡰⠙⠁
⠀⠀⠀⠙⢦⣈⠂⠀⡀⠀⠀⠀⠀⠀⢀⠄⢀⣴⣾⣾⣷⣟⢁⠀⠀⡠⡀⠀⢀⢀⠀⢀⣰⣿⣟⠿⠓⠉
⠀⠀⠀⠀⠀⠙⠻⢶⣤⣬⣁⣈⣈⣥⣤⡾⠿⠛⠋⠁⠀⠈⠉⠛⠚⠚⠒⠺⠒⠓⠛⠋⠉⠁
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡸⡿⢸⣞⢇⠟⡦

⠀⠀⠀⠀⠀⠉⣀⠀⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣤⣴⣤⡀⠀⠀⠀⣠⣦⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢿⣤⣄⠀⠀⠀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣿⣿⣿⣿⣗⠀⢀⣼⣿⡿⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⣸⠀⠀⢀⢶⠿⠈⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠠⢤⡴⠟⠁⠀⠀⠙⠿⡿⠿⠃⠀⠺⢿⡿⠖⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⢠⠤⠞⠃⠀⠀⠨⢄⣀⠤⠂⠀⠈⠹⢿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠐⠁⠈⢩⣄⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠤⡀
⠀⠀⠘⠢⠀⠀⠀⠀⢆⠀⠀⠀⢀⢴⠞⠁⠀⠀⠀⠀⠀⠀⠉⢻⡆⠉⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠄⣈⣲⣤⣴⢊⠇⠀⠐⠏⠀⠀⠀⠀⠀⠐⢤⣀⣀⡤⠜⠀⠀⠀⢄⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⢀⢾⡇⠀⠀⠀⢀⠴⠖⠀⠀⠀⠀⠚⢶⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⢈⡿⠀⠀⠀⠀⠤⠀⠀⠀⠀⠂⠀⠀⣳⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠰
⠀⠀⠀⠠⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠖⠀⠀⠀⠀⠀⠀⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⣠⣰⡈⣩⡿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠩⠳⠎⠛⠿⢻⡾⠙⣿⣿⣿⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣄⣀⣀⠀⠀⠈⡑⠰⢤⣀⣀⣠⣤⣴⣾⠟⠋⠛⠛⠤⠉⠉⠁⠀⠠⠤⡤⠄⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡐⠋⠉⠓⣲⣤⣦⣶⠿⠛⠋⠉⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⢈⡩⠝⠚⢋⣧⣶⡿⡿⠋⠩⠇⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠜⠉⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⡀⢀⠚⣶⠒⢛⠓⣶⣲⡾⡟⠉⢀⠀⠀⡀⠀⢰⡁⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠀⢦⣄⣀⣈⣠⣾⡟⠉⠠⠀⠀⡼⠀⢀⠃⠀⠋⠀⠀⢀⣀⣀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧
⠀⠀⠀⠀⠀⠉⢉⡉⢡⣾⠟⠉⠀⠀⡜⠀⢠⣃⢀⠎⠁⠀⠀⠀⢈⠐⠀⡽⠛⢴⠛⢦⣼⣦⠀⠀⠀⠀⠀⣤⣿⣿⡃
⠀⠀⠀⣴⣴⣿⣿⣿⠟⠃⠀⠀⠀⢰⠀⠀⢼⠊⠁⠀⠀⠀⠀⢸⠁⠀⡼⠁⠀⣞⠢⣼⣿⣟⢳⣄⠀⠀⡾⠛⣿⡷⠈
⠀⠀⢰⣁⡽⢯⡿⠁⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠠⠤⣤⣞⠀⢰⡇⢀⣢⣿⣈⣿⣿⣿⣿⣿⣷⠀⠀⢠⣿⡟⠢
⠀⠀⠸⢀⣀⡜⢀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠀⠈⡿⠟⢻⠏⠉⡇⢽⣿⣿⣿⣿⣿⣿⣆⠀⢀⣿⡀
⠀⠀⠐⡋⣽⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣠⣾⠀⡄⠀⡇⢸⡄⢘⣿⠨⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⠛⠢⢄
⠀⠀⠀⢩⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠃⠘⠛⠃⢰⠀⣾⣷⡞⢻⣷⣾⣿⣿⣿⣿⣿⣿⣇⢼⣿⢄⠀⠀⠁
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⣆⣶⡄⢲⡎⢘⡟⢹⠃⢨⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡾⠋⢳⡟⠀⣸⡇⢸⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢷⣿⣷⠀⣠⣷⣤⣿⣇⣼⣿⡟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⡔⠋⣁⣠⡀⠀⠀⠀⢸⠋⠙⠿⣿⠉⣿⠛⡟⠛⣿⣷⣄⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿
⠀⠀⠀⠀⠀⠀⢸⣎⣿⠿⠂⠀⠈⠉⠻⠀⠀⢢⠘⣤⣦⢀⡇⢀⣿⠀⡆⢠⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣷⠀⠀⣴⠃
⠀⢀⣾⡟⠀⠀⠈⠉⣧⣤⣄⡀⠱⢄⠀⢀⠀⠈⠂⢹⣷⣾⢻⣶⣿⣤⣿⣾⣿⣼⣿⣿⣿⣿⣼⣧⣼⣿⡏⣾⣿⠀⢸⡇
⠀⠈⠹⣷⡀⠀⠀⠙⠿⣿⣟⠀⠀⠈⢳⣴⡅⠀⠀⠸⣿⣿⣧⣿⡟⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⣿⣿⡆⢻
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠈⢿⠁⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿⣿⣎⢆
⠀⠀⠀⠀⠀⠀⠚⢆⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉⠓⠻⠿⠗
⠀⠀⠀⠀⠀⠀⠀⢀⣁⡀⢀⣀⣈⣙⣷⣦⡀⠀⡆⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠙⣻⠋⠉⠉⠉⠉⠉⠿⠯⠸⣧⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⠃
⡀⠀⠀⠀⢠⣶⡆⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠟⠋⠁
⠀⢀⢄⠰⠾⠁
⣶⣿⠿⠷⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠠⡀⠰⠀⠋⢠⠆⠔
⠀⠀⠀⠀⠲⠀⢶⡐⢘⠀⡿⣠⡞⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀
⠀⠀⠀⠀⠠⠀⡀⠁⠈⠁⠁⢋⠴⡀⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠿⣓⣳⣖⡈⣿⠫⣭⣛⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠄⠃⠘⠀⠈⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⣰⡿⠛⢡⡾⠁⢸⣷⡄⠻⣷⣄⠙⢦
⠀⠀⠀⠀⠈⠁⠀⠂⣀⠀⠀⠁⣭⣍⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣴⣿⠇⠀⣿⡟⠀⢸⣿⡷⠀⢸⣿⣄⠈⢧
⠀⠀⠀⠀⠀⠐⠂⠠⠀⠀⠀⢄⢐⣀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⣿⡇⠀⣼⣿⠀⠀⢨⣿⣿⡄⠀⢸⣿⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠈⠃⠤⠂⡜⢀⡆⠈⠳⡀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⡀⠀⢻⣿⠁⠀⢹⣾⣿⡟⠀⢠⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⡇⠀⠸⢸⣿⡷⠀⠘⣿⡇⢰
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠐⡀⠸⣿⣿⡆⠀⣿⡇⠀⠀⢻⣿⡿⠀⢐⣿⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⢄⠹⣿⣷⡀⢹⣿⡀⠀⢠⣿⡟⠀⡼⣣⠊
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠿⣷⣄⢻⣧⡀⣸⣟⣠⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠐⠈⠁⠀⠀⠀⠀⠀⠰⣄⠖⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠀⠉⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠏⠉⠀⢁⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⡠⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⣈⠀⠀⢀⣀⠴⠊
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠉⠉⠁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸⠀⠀⡀⠀⢀⠖⢅⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠈⠀⠘⠁⠰⠀⠀⠀⠀⠀⠀⠀⠋⠉⠏⠁⢀⠆
⠀⠀⠀⠀⠀⠑⠢⠤⣀⣀⠀⠀⢀⣀⣀⣀⣠⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡔⣶⡿⣷⡶⢿⣷⣤⡶⣦⣾⣯⣭⠉⠑⠒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠴⠛⠁⠀⠀⠀⠉⠀⠀⠀⠀⠈⠈⠀⠙⠻⡷⣿⢷⣶⣞⡁⠀⠘⠻⢆⣄
⠀⠀⠀⠀⠀⡠⢚⣩⣠⣤⣴⣭⣤⣴⣤⣴⣧⣤⣤⣄⣴⡀⢀⠀⠈⠂⠀⠈⠉⠻⢶⣶⡀⠀⠻⣷⢄
⠀⠀⠀⠀⡰⡖⠛⠋⠁⠈⠉⠉⠉⠙⠋⠉⠈⠉⠙⠟⠛⠻⣿⣶⡆⣤⣆⣀⣀⠀⠀⠈⠿⣄⠀⠈⢦⠱⡀
⠀⠀⠀⢸⠅⠀⠀⠀⢀⣠⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠫⣿⠶⣦⣀⠈⠻⠄⠀⢿⡑⡀
⠀⠀⠀⡿⢀⣾⣶⠿⣿⣟⣶⣳⡴⠶⣦⢤⣄⢠⣄⣀⣀⡀⢀⣀⣴⠀⠀⣀⣠⣀⠀⠀⠙⠳⢶⡘⢆⢸⡁⠂
⠀⠀⠀⡟⡟⠉⠠⠀⠀⠀⠈⠉⠹⡇⠉⠈⠈⠉⠁⠀⠁⠈⠈⠙⠉⠙⠛⠉⠙⠙⠓⠒⠤⣀⠀⠙⣜⢌⣇⣾⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⢆
⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣘⣞⢊⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠌⠁
⠀⠀⠀⢸⣧⣀⡀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⢀⢀⣠⡶⠒⠿⠽⣯⡞⠉⠶⠖⠂⠀⠀⠀⠀⠀⣀⡽⠿⣁⡸⠀⠀⠀⠀⠀⠀⠴⢀⠉⠀⠘⠃
⠀⠀⠀⠀⢱⡛⠻⡶⠿⢿⣷⣶⣶⣴⣶⣷⡶⠛⣉⡀⠀⡀⠀⡀⢈⠀⢀⣤⣀⣀⣀⣠⣄⡴⠖⢫⡜⡃⢹⠇⠀⠀⠀⠠⠈⠀⠐⠃⢠⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠱⣔⠐⠀⠀⠘⠋⠉⠉⠁⠉⠉⠉⠘⠙⠛⠻⠿⡿⠿⠿⠓⠉⠟⠉⠋⠉⣡⣴⠚⠁⠜⢀⠌⠀⠀⠀⠠⠂⠄⡐⠀⡀⢘⠃⠀⠀⣿⡆⠀⣆
⠀⠀⠀⠀⠀⠀⠘⢳⣦⣬⣤⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠛⠁⢀⡶⠃⡤⠊⠀⠀⠀⠀⠃⠂⣴⡇⢼⠃⢠⠂⠀⠀⠀⠀⢀⣨⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣉⡛⠣⠖⠚⠛⠟⠿⣿⠾⠶⡏⠶⠶⠚⠛⠛⠙⠁⢀⡀⡴⠂⢀⡰⠋⠀⠀⠀⠀⠀⠳⢤⣄⠈⠙⠒⠠⠄⠤⠤⠴⠶⠞⠋⣁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⣀⡀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⡤⠰⠚⢋⣁⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠐⠒⠒⠂⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠚⠖⠲⠶⠷⠘⠒⠒⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠀⠀⢀⡄⠀⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⣠⡴⢊⣤⠠⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠵⣦⣤⠠⢀⣀⠀⠀⠄⢶⣀⠹⡍⢻⠆⡀⠠⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠌⣀⡠⠄⠀⠉⠉⡁⢃⠘⠹⡟⠈⠙⡄⢐⡔⢢⡤⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠟⠉⠀⠀⢀⣠⡶⠛⠁⠀⠰⣇⡀⠀⠀⠀⠑⠈⠻⣄⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠐⡠⠋⠁⠀⠀⠀⡤⠞⣿⣿⣶⠀⠀⠀⠀⠘⠛⢷⣌⠸
⠀⠀⠀⠀⠀⠀⠀⢀⠄⣰⠏⠀⠀⠀⠀⠁⠀⠀⠀⢀⡜⠁⠀⠀⠀⣭⣿⣿⡄⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⡀⢠⠏⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⢦⡄
⠀⠀⠀⠀⠸⣾⡇⡠⠁⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⣿⣼⣿⣄
⠀⠀⠀⠀⠀⠻⠈⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠁⠜⡙⣿⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⢐⠘⣋⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⣬⠀⣼⢁⣿⠟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⣸⣿⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠐⢲⣿⢿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠄⡀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠐⠟⣐⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠘⠀⠀⠆⠀⠀⠀⠀⠈⠀⠙⠻⣿⣿⡿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠀⠀⠀⠀⢀⡀⠀⠂⡰⣶⠟⢿⣵⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠈⠁⠀⠀⠀⠀⠀⢀⡄⣿⣷⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠶⣶⣿⠰⢶⣿⣿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⡀⣀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣒⠉⢍⠉⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠙⠒⠘⠃⠀⠀⠀⠈⢿⠦⣀
⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡈⠳⡄
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⠄⡀⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⡠⠴⠉⠀⡠⠀⠀⠀⠀⠀⠀⢸
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⡈⠁⠁⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⡼
⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠠⠄⠒⠈⠃⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠀⠙⠅⠀⠀⢀⠀⢀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠹⡄⠀⠀⡆⠀⠀⢀⠠⠒⠉⠀⠀⠀⠐⠤⠦⣐⣐⠨⠤⠥⠄⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠹⣄⠀⢰⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡤⠚⠁
⠀⠀⠀⠘⢦⡈⣇⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠉
⠀⠀⠀⠀⠀⠙⠿⣧⡀⠀⠀⠀⠉⠓⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⠴⠒⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣉⣛⣲⣶⣦⣤⣴⣾⣛⣛⣉⣉⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠻⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠁⠀⣴⣠⢆⣶⣦⣴⣶⣤⠤⣤⣤⣤⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⠞⢁⣴⣤⣤⣾⠟⠛⠋⠉⠀⠀⠀⠁⠀⠀⠉⠉⠘⢧⣄⣿⣷⡄⣀⡠⠆
⠀⠀⠀⠀⠀⠀⢀⡏⢀⣼⡿⠛⠁⠈⠀⠀⣀⣀⣠⣤⣾⣷⣶⡿⢭⠴⠾⣶⣿⣭⣵⣾⡁
⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⣰⣷⣤⣿⡿⣿⠋⠙⠀⠀⠀⠀⠀⢠⣴⠏⣿⢿⡻⣷
⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⢠⣴⣼⡿⠛⠻⠁⠀⠀⠀⠀⠀⣄⣀⣠⣶⠇⠁⢰⡧⢸⡃⣿⡀
⠀⠀⠀⠀⠀⠀⣯⣀⣸⣿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⡿⠇⠀⣙⣿⡗⢾⣿⢹⠇
⠀⠀⠀⠀⠀⠀⢻⣾⠏⠈⠀⠀⠀⠀⠀⠀⠀⣶⣴⣾⣿⡿⠟⠏⠀⠰⣶⣿⣿⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⡀⠀⢠⣤⣷⣾⣿⣿⠋⠁⠀⠀⢠⣤⣾⣿⡿⣽⣽⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢹⣶⣄⣠⣿⣷⣿⠻⠋⠀⠀⠁⢀⠂⣶⣴⣿⡿⠟⣙⠳⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣏⠉⢉⠀⠀⠀⠀⣶⣤⣼⣿⣿⣟⡋⠡⠌⠿⠿⠿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣼⣶⣾⣿⣿⡿⠿⣧⡀⣒⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠭⣿⣴⣤⣴⡏⡆⢹⡄⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣀⠂⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢼⡀⠧⠀⠀⢠⡾⢀⡄⢀⠂⠀⠃⠐⠀⣌⠁⣤⡀⠙⠃⡈⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣷⡐⢦⡀⠀⠀⠟⢡⡿⠀⣾⡄⢸⡆⢹⡇⠙⠃⠀⣰⠁⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣌⠻⣆⢀⠀⠈⠁⠀⠙⠁⠘⠃⠀⠀⠀⢀⠔⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣌⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠄⠉⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣈⣉⡘⠛⠙⢀⣁⠤⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠐⠀⠀⠀⠀⠀⠀⠉⠁⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢁⡀⠠⠀⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⠀⠀⠀⠀⠂⠀⠀⢀⠄⠀⠀⢀⣐⠀⡀⠀⠣⣦⡀⠀⠀⠀⠛⠀⠄⠂⠀⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠈⠀⢁⣈⠀⠁⠀⠄⠠⠇⣁⠘⢃⣝⠯⢘⠆⡀⠀⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡃⡃⠀⡀⠀⠀⠀⠠⠈⠰⡀⣄⢈⠘⣸⡋⣴⣩⢏⠘⣽⡇⡀⡂⠜⠴⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⢸⣷⠣⠂⠳⢀⡀⢈⠑⠀⠗⡀⢉⡒⡒⡀⡇⣷⢅⠻⠼⢏⢨⡁⡛⡀⣂⢁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⢯⠂⣀⣁⠀⡄⢰⠸⢗⡈⠟⠟⣟⣄⣏⢸⢘⡻⢟⠠⠴⢉⡙⣌⢢⡐⢆⣀⠄⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣦⡝⣛⡂⣡⠀⡖⠹⡅⠆⣷⣡⢛⣈⣉⣻⣷⢟⢻⡶⣦⠵⣦⢈⣒⢢⣽⣴⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣶⡙⢿⢈⣧⢿⡷⠳⠘⣼⡉⢫⠹⣾⣻⣿⣾⣿⣿⣿⣾⣾⡻⣐⣧⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⡿⣯⢹⣿⣧⣶⣃⡳⢉⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣖⣻⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⣠⡤⠂⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣿⣿⣿⢺⣿⡇⣿⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⡟⢋⡀⠀⢠⣄⣖⣤⣾⣿⣯⡙⢀⠜⠁⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⢿⣾⣿⡟⡛⠙⠋⠛⣛⡧⣯⢻⣽⣙⣍⣴⣳⣿⣆⠳⠿⠋⢉⡡⠖⠁⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⡇⠉⠹⣆⠀⠈⠙⠻⠯⣿⣛⣉⣉⣋⣽⡧⠥⠴⠂⠉⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢤⡄⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⣵⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⠶⠤⣤⡤⠤⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣠⣰⣶⣾⣷⣤⣤⣠⣤⠶⢦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡼⣿⣿⣷⣿⠿⣿⣿⣿⣟⣿⣟⡿⢿⠿⣿⣀⡛⣀⣤⡀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⣛⣶⣯⣝⣉⠉⣥⠙⢿⡭⠬⡍⠉⣿⡿⠟⢻⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⡿⣿⣿⣏⣿⡟⢿⡟⠻⠀⠟⠁⡐⠀⠘⢁⡌⠐⡴⠃⢠⠌⣿⣣⠊⢿⡿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣾⣿⢿⣏⣯⣽⣥⢍⣀⣠⡤⠶⢈⣾⠇⢲⢀⣁⠀⠐⠒⢞⠂⠹⣿⣬⣿⠉⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡞⢻⠿⡯⠀⣴⡖⢈⠴⠤⠰⠐⠀⠈⠁⠀⠘⠫⢶⣏⣹⢶⣻⡇⣿⣻⢱⡟⣻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣶⠄⣾⡉⠿⠉⠐⠃⠴⠶⠀⢉⠶⠀⠀⠀⠀⠉⣛⡳⣿⡿⠿⢷⣾⢢⡈⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⡖⠯⢠⣾⠇⠴⠋⠘⢀⡄⠰⢄⠀⠙⠂⠀⠀⠀⢌⣈⣿⣷⣄⠹⣅⢽⠶⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡙⠷⠀⣦⣶⠆⠀⠀⣼⠁⢙⣢⣌⡿⣷⣄⠺⣭⡍⠻⣽⡝⢻⣿⣧⠙⣶⠀⠉⢽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⡁⢼⣿⡴⠶⠂⣀⣠⣼⡿⠯⢃⠺⠐⠇⠉⡠⠠⢀⡹⠌⢿⠷⣿⡻⠧⠹⡧⣀⣄⣈⡄
⠀⠀⠀⠀⠀⠀⠀⣀⢈⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣷⣟⣿⣿⣥⣌⣵⠂⣴⠄⢷⡉⠒⠁⠘⠁⠘⠃⢰⣄⡎⢀⣦⡞⣷⠺⣯⢻⣇
⠀⣤⣠⣤⣶⢤⠼⣇⡈⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⡼⢀⡓⠈⢥⣀⠀⠉⠁⠀⠦⠔⡀⠀⡌⢙⡿⣥⣦⣭⣽⡝⣟⣿⡻⣏⠧
⠀⠘⠋⠉⠻⣷⡄⠀⠉⠳⣄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠿⡿⢀⣛⣬⡥⠒⠃⠤⢦⠠⠺⢦⠀⢘⡷⣀⣿⠿⣅⠜⠣⣼⡿⢿⡞⣿⣷⣿⣏
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠘⣦⣀⠀⠀⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣶⣄⡀⢻⣿⡆⠈⡛⢰⡦⣶⠦⣾⠆⠀⣼⣻⡿⠦⢈⣃⢸⡋⣿⢿⣽⣿⣧⢱⣾
⠀⠀⠀⠀⠀⠑⣦⣠⣦⣤⡼⠉⣿⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣛⠈⠶⠋⠁⢀⡉⢶⠀⢃⣾⣿⡏⢹⡤⠶⠨⠁⢈⣁⠝⢟⣿⠻⣟⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡻⣧⡀⠘⣆⠀⠀⠘⢻⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣿⣧⣴⣶⡷⠤⣨⣷⣎⣴⣿⣅⢸⡏⡀⠛⢶⢦⡉⠛⠹⣾⣿⣧⡾⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣽⣿⡿⠷⠈⢢⡄⠀⠀⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⠛⣤⣞⣿⣿⢿⣷⠙⠏⣰⡶⣯⣤⣠⡈⠋⡤⣼⣟⣯⡉⠳⢜⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢛⣩⣿⠳⣦⡀⠀⠹⣆⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣾⣿⣿⣿⣾⠊⣭⠀⣿⣯⣥⣾⣯⠙⣧⣴⣶⣾⣽⣿⠋⠠⡾⣻⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⢶⣄⠘⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡙⣿⡇⠘⣿⠀⠘⢻⠶⣬⣏⡜⣽⣇⠈⠘⡾⣵⠿⡾
⠀⢄⣀⣴⣴⣷⣶⣶⣶⡄⢤⠤⡀⠀⠀⠉⢻⣿⣿⣇⠈⠷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣿⣄⣥⣤⣰⣅⡛⢛⣿⣭⠾⡯⠸⣿⣶⣿⣆⣦⠁
⢼⣿⣿⣿⣿⣿⣿⣷⠛⣙⣿⣷⣿⣷⣦⠶⠞⠋⢿⣿⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣻⣿⣿⣿⣾⣿⣿⣾⣻⡗⣠⣾⣿⣶⣏⣥⣞⣿⣿⠇⠹
⠀⢸⡿⣿⡿⠿⠟⠹⢿⣿⣿⡻⠉⠉⠉⠀⠀⠀⢸⣿⡇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡿⢿⣿⣿⣿⣿⠿⢿⣿⢟⣝⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠠⠀⠀⠈⠻⢾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡾⣿⣿⣾⡷⣿⡿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⡟⠀⠀⠀⠀⠀⠀⠀⠑⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣠⣤⣤⣼⣿⣎⣀⣤⣤⣤⣤⣤⣴⣶⣦⣶⣾⣽⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣿⡛⢻⠛⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠨⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠧⠼⠾⠃⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠙⡍⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣾⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡎⠳⣤⠃⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⡁⢦⢸⣅⣿⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⣀⡄⠸⠏⠁⡀⣿⠟⠁⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠐⢲⠈⠁⣠⠉⠏⠲⣀⣤⠟⠋⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⡴⠶⠈⠀⠀⠀⠀⠀⠀⠀⣷⣼⡶⠟⠁⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⢠⠀⣶⣷⡶⠛⠉⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠰⢦⣶⣁⡿⣀⡔⡠⠀⠀⢀⠀⠀⠀⡀⣀⣠⡼⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠰⣄⠀⠀⠀⠉⠙⠛⠛⠓⠶⠖⠛⠒⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠀⠤⠤⠤⠤⠴⠖⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠑⠢⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠤⠤⠤⠀⠀⠤⠤⠄
⣶⣶⣶⢶⠶⢶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⢶⣶

⠀⠀⠀⢰⠀⠐⠀⠠⠄⢀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠗⠀⠀⢀⣴⡆⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠛⠁⣀⡀⠀⠻⠃⠀⠀⠀⢀⣶⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠆⠀⡄
⠀⠀⠀⢸⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⠀⠀⠰⣿⠃⠀⠀⠀⣀⠀⠀⠈⠿⠁⠀⠘⢿⠇⢠⣦⡀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠈⣿⣆⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢀⣴⠀⠀⢀⡀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣶⡄⠀⡀⠈⠻⠃⠀⠀⠀⠠⠁⢠⠇
⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠺⠛⠀⠻⠋⠀⠀⣿⠇⠀⠀⠀⠉⠀⣴⡄⠀⠀⠛⠁⢸⣿⠀⠀⠀⠀⠀⡠⠀⢠⠏
⠀⠀⠀⠀⠀⢻⣿⣧⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠻⠇⢠⣶⡀⠀⠀⠉⠀⠀⠀⠀⠈⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣤⣀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⣀⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣶⣦⣤⣄⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠛⠛⠛⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣠⣤⢤⣤⣤⣾⣥⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⢛⣯⣭⢟⡻⢟⣿⢿⢿⡿⣟⠿⢝⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠉⢀⣴⠞⠉⣠⡖⢋⣴⡟⠡⣟⠀⢷⠀⡙⣦⡈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⢠⣶⠟⠉⢀⣼⠟⠀⢸⣿⠀⠀⣿⠁⠀⢷⡀⠈⢻⡄⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⠁⢠⣠⡟⠁⠀⣰⡿⠇⠀⢀⣿⠃⠀⢠⣏⠀⠀⢸⡇⠀⠀⠹⡄⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⣾⠋⠀⠀⣾⡿⠀⠀⠀⣸⠇⠀⠀⠀⣿⠀⠀⢠⣿⡄⠀⠀⣷⣄⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⣼⡏⠀⠀⢰⣿⠇⠀⠀⠀⣿⡗⠀⠀⠀⣹⡇⠀⠰⢿⡃⠀⠀⢘⣿⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢰⡟⠁⠀⢀⣸⡇⠀⠀⠀⢀⣿⠀⠀⠀⠰⣿⡇⠀⠀⢸⡇⠀⠀⢨⣿⠀⠀⣸⣇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⣿⡁⠀⠀⣿⣿⠁⠀⠀⢀⣾⡟⠀⠀⠀⠀⣿⡅⠀⠀⠸⣿⠃⠀⠀⣿⡇⠤⠘⠛⠃⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢠⣿⠁⠀⢸⣿⣿⠀⠀⠀⠀⣿⡇⠀⠀⠀⢰⣿⠃⠀⠀⢀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢻⠃⠀⢘⡟⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⣠⠿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠈⣿⡀⠀⠈⣿⡇⠀⠀⠀⠀⡿⠗⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢿⡇⠀⢠⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⢸⠷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⣀⠀⠀⡆⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣶⣦⣤⣤⣠⣤⣤⣤⣤⣶⣾⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⡶⠶⢶⢶⡶⠶⢶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⣶⣶⣶⢶⠶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣊⣉⣉⡉⡉⠉⠛⠛⢿⣿⡿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣟⣛⡛⠻⠿⣷⣾⣷⣦⣤⣄⡀⠀⠉⠛⠿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⢿⣿⣿⣷⣶⣄⠈⠛⠛⠿⣿⣿⣧⡀⠀⠀⠀⠙⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣦⡜⠻⢿⣿⣿⣿⣷⣆⡀⠈⠉⠻⢿⣿⣶⣄⠀⠀⠈⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡈⣿⣿⣿⣿⣿⣦⠈⠙⢿⣿⣿⣿⣿⣿⣦⣄⡀⠙⠻⣿⣿⣦⣀⡀⠈⢹⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠙⢿⣿⣿⣿⣿⣿⣦⡀⠀⠙⢿⣿⣿⣿⣿⣿⣦⣀⠈⠛⣿⣿⣷⡄⠀⠛⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠸⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⠛⢿⣿⣿⣿⣿⣷⣦⣤⣿⣿⣿⡇⠀⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⠋⢿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣇⡀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡰⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣧⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣿⣷⡀⠀⠋⠉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠉⠹⢿⣿⣿⣿⣿⡇⢨⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣤⡀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠙⢿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣾⣦⣀⡀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣦⣤⣄⣀⠻⠛⠟⠻⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣈⠉⣩⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠙⠛⠛⠛⠛⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡆⠀⠀⠀⠀⠄⠠⠀⠀⠀⠰⠀⠆⠀⠀⠀⠀⠠⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⡤⠔⠀⠛⠲⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠁⢀⠔⠀⠀⠈⠀⢁⠐⠚⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⠈⠀⠐⠁⣠⠄⠀⣠⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠙⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄⢀⠀⠀⡀⠄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡔⢠⣿⠟⠻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣄⡐⢁⠄⠀⡐⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣤⢥⢴⣦⣼⣦⠿⠋⠀⠦⠀⡎⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣐⣯⡿⡥⠏⡔⠀⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⡋⡁⢙⣼⣾⣽⣾⡟⠀⠀⠀⠀⠌⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⣯⡙⠟⣁⠶⠃⡀⠀⠪⠃⠀⠀⠀⠄⠀⠀⢀⠀⣔⣾⡉⢻⣾⣽⠟⠛⡛⠁⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠢⡄⢋⡲⣿⢅⡠⣐⢠⡏⠀⠀⠈⠀⠀⠀⠀⢀⡼⢯⣄⣷⣾⣟⣿⡾⡉⠁⢀⠀⡠⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡼⢁⣾⢧⡙⠀⣄⡋⡄⠀⠀⠀⠀⠀⠀⠀⢐⣉⠦⣼⠿⣯⣉⡹⠫⠋⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⢲⡃⣼⣿⣼⡇⢰⣿⢰⡇⠀⠄⠀⠀⠀⣼⡖⠻⣏⣶⣵⣶⠎⡩⠈⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢁⣷⣟⣿⠇⣸⡏⣸⠀⠐⠀⠀⠀⠆⢩⠷⣷⣿⣍⡥⠗⣉⠀⠈⡁⡴⠁⠀⡀⠀⠀⡠⠀⠀⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣸⣿⠆⢋⡖⣹⣧⡟⠀⠀⢀⡄⠸⣧⡿⠗⠛⠛⠃⠀⠀⠀⡰⢊⠕⠀⠄⠀⡀⡀⠀⠠⠂⠠⠂⠀⠆⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣩⣶⣟⣿⣝⣿⡇⠐⢀⢂⢰⠢⠏⠠⠀⢀⡀⢀⡤⠖⢈⠄⠠⠂⠀⠀⠀⠀⠠⢃⠀⠀⠀⢀⠚⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⢷⣞⣻⠾⣷⡴⠀⣠⡜⠉⠠⠀⢀⡤⠄⠉⠀⡀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠈⢠⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⢿⢁⡾⣆⣦⡖⢖⣀⣀⢖⠈⠷⠀⠀⠀⠁⠄⠈⠀⠀⠠⠂⠀⠄⠀⠀⠀⠀⠄⡠⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⡿⠋⣼⣿⡹⢿⡯⣝⡻⠡⠜⣠⡈⠓⠂⠀⠁⠀⠐⠀⠀⠐⠀⡀⠀⠀⠀⠀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⠞⣻⣿⣿⠛⢡⣶⣌⣾⣳⠁⣠⡄⠀⠐⢀⠄⠀⣀⡀⡴⣠⠂⡜⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⠉⣘⡿⢃⣎⠭⠓⠠⢄⠀⡀⠂⠀⠄⠠⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠯⠼⣟⣱⣾⣙⣶⣺⣿⣄⣴⣷⠼⠷⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⣀⡀⠤⠒⠂⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⠛⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡒⠁⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠠⣢⣨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠖⠀⠁⠀⠟⠙⠀⠀⠀⡙⢿⡂⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠔
⠀⠀⠔⠀⠀⠉⡇⠀⠀⠀⠘⡄⠀⠀⠉⠙⢢⢷⡤⠀⠀⢀⣁⠀⠤⠀⠀⠘⠀⠀⡀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠁⡀
⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠈⠙⠦⣄⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠋⠀⠀⠈⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢰⠊
⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠒⠓⠃⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠏⠀⠁⠀⠀⠀⣀⣰⣿⠃⠀⠀⠀⠉⠉⠒⠖⠂
⠀⠀⠀⠀⠀⠘⠁⠉⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⣠⣿⣤⣶⣶⣶⡿⠿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠐⠞⠃⢀⡼⠻⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⣉⠤⠊⠉⠉⠉⠉⠁⠀⠀⠀⠻⡀
⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢙⠛⢳⣶⣶⣦⣴⣶⣶⣶⡾⠛⠛⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠿⠿⠟⠛⠛⠛⠿⠿⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠾⠛⠉⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⣰⣿⣴⣥⣿⠿⠾⠿⢷⠛⠛⠳⣾⡶⢄⡀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⣴⣷⣶⡾⡟⠋⠉⠁⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⢀⠛⣦⣼⣿⡷⢀⣠⠵⠛
⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⣼⣿⠛⠁⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⡿⣾⠟⠩⠖⠾⢷⣾⣷⣤⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣾⡟⠁⠀⠀⠀⢀⣼⣶⣴⣿⡿⢿⠋⠉⠃⠀⠀⠀⠀⠀⠀⣴⡾⢹⡿⣿⢻⣷
⠀⠀⠀⠀⠀⠀⢰⡿⠋⠁⠀⢠⣤⣴⣿⡿⠛⢿⠁⠀⠀⠀⠀⠀⢠⡀⠀⢠⣶⡖⠉⠀⣾⡃⣽⠈⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢰⣶⣾⠿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⡏⠁⠐⣾⣿⢦⣿⡷⣻⡇
⠀⠀⠀⠀⠀⠀⠈⣷⣹⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⣠⣀⣤⣾⣿⣿⣿⠟⠁⢠⣀⣸⣿⡏⣰⣿⣧⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣿⣿⡿⠿⠛⠃⠀⠁⠀⣠⣿⣿⡿⠵⣿⣿⣹⡏
⠀⠀⠀⠀⠀⠀⠀⠈⣏⡀⠀⠀⢳⣤⣀⣿⣾⣿⠟⠛⠿⠁⢀⠀⠀⢀⣼⣿⣿⢿⣏⠺⣿⣿⣯⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣿⢿⡿⠏⠉⠀⠀⡀⠀⠀⣌⣸⣿⣿⣿⡟⠫⣴⣘⣽⣿⢿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⠀⠀⠄⠀⠀⣀⣀⣿⣶⣶⣿⠿⠿⠭⠥⠐⠂⠚⠛⠛⠻⠏⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣷⣶⣿⣿⣿⣿⣿⠿⠻⣿⣦⠈⣇⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢥⣿⣴⣦⣤⣿⢸⡀⢿⠀⠀⣠⠖⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠄⢠⡀⠂⢨⡇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡮⣧⠸⣆⠀⠀⠀⣴⠆⣠⠀⠰⠀⠀⠇⠀⠂⢠⡙⢰⣀⠈⠛⢂⠐⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⣆⠰⣆⡀⠈⠁⢰⠏⣰⡇⠀⣶⡀⢠⡆⠸⣷⠈⠿⠃⠀⢰⠇⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣝⣦⡘⢷⡄⠀⠀⠀⠛⠁⠀⠿⠃⠸⠗⠀⠉⠀⠀⠀⡰⠋⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠙⠦⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣈⠙⠓⠶⠄⣤⣤⣤⣀⡠⠀⠊⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⠤⠤⠤⠤⠔⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⡋⠉⠉⠉⠉⠙⠒⠲⢤⡀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡡⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡴⢋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠔⠀⠔⠈⠀⠀⢀⠀⠀⠀⢀⠀⠈⠁⠀⠀⢺⢷⣾⡀
⢀⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡐⢁⠀⠀⠀⡀⠐⠀⡀⠀⠂⠀⡀⠀⠂⡠⠀⡁⠠⠀⠙⣿
⡼⢰⠃⠀⠀⠈⠉⠉⠓⠒⠲⠤⢤⣀⡀⠀⠀⡞⠀⠠⠀⠀⡀⠊⠀⠀⠁⠀⠠⠐⠀⡀⠐⠀⠠⠊⠠⠁⠀⠄⡇
⡇⣦⠀⠀⠷⠂⠀⠰⠟⠀⠀⠀⠀⠀⠉⠉⠚⠳⠤⣅⣀⠐⠀⠈⠀⡀⠀⠁⠀⠄⠈⠀⠀⠀⠀⠀⠀⠐⢀⠀⠇
⡇⢋⠀⠀⢀⣠⠀⠀⣀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠉⣝⡳⢤⣈⠀⠀⠊⠀⠀⡠⠀⠀⡀⠀⠀⡐⠀⠀⠀⡄
⢱⠘⠄⠀⠈⠉⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢰⡄⠈⠁⠀⠈⡷⡄⠀⠄⠀⢀⠄⠈⠀⠀⠄⢀⠀⠀⡜⡸
⠈⢧⠩⣄⠀⠀⠾⠇⠀⢠⡆⠀⠀⠀⠻⠂⠀⠀⢠⣄⠀⠀⠀⠀⡸⣸⠁⡀⠄⠀⠀⠀⠀⠐⢁⠐⠁⢠⠞⡴⠁
⠀⠈⠳⡑⢦⡀⠀⠀⠀⠈⠀⠀⣦⠀⠀⠀⣦⠀⠀⠉⠀⠀⢀⡴⣱⠋⠀⠀⠀⠀⠄⠊⠀⠂⠀⠀⠒⣠⠞
⠀⠀⠀⠙⠦⡙⠴⣄⡀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⣀⡴⢋⡔⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⣀⠥⠊⠁
⠀⠀⠀⠀⠀⠈⠓⠬⣁⡁⠤⠤⣠⠤⠀⢤⡀⠤⠖⣋⡥⠖⠉⠛⠺⠦⠤⠤⠤⠤⠴⠶⠛⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣽⣶⣶⣶⣶⣶⣶⣾⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣽⣭⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠤⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠦⠠⠤⠖⣀⡀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⢈⡠⣼⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣀⡠⠖⢋⣠⣌⣀⣤⣬⡐⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⠶⠞⠉⠉⠉⠋⠉⠉⢻⣼⠤⣽⣿⣇⣒⡒⠂⠠⣤⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠉⠉⠉⠛⠛⠳⠶⠶⢾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⣿⠀⢢⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⢾⣿⣿⣿⣃⣾⣿⣟⠿⣿⣿⣿⡷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⣿⣿⡿⠿⠛⣱⡿⢣⣬⣽⣬⣿⡇⠹⣿⣟⣿⡛⣾⠻⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣭⣻⣿⡆⢳⣿⡿⢁⣾⣿⣴⣍⣯⢹⣇⢻⣿⣟⣀⠛⠻⢆⠳⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣣⣾⣿⣼⣯⠓⣿⣿⠓⠿⢙⣯⣼⣛⠟⣴⣿⠀⢹⡯⣿⢣⣾⡘⢧⡈⢿⡽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣿⣿⣿⣿⣿⣴⣿⣾⣿⢅⡸⣿⡯⣿⡹⠿⣿⣾⢛⡇⠈⣿⡌⣧⣾⣿⡮⢷⠈⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣟⡟⣿⣿⢿⣯⢾⣶⣧⢴⣮⣷⡷⣾⢯⣇⣶⠾⠿⡛⢿⠀⢹⣿⡏⠹⢿⣷⡞⡃⠸⠷⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⣿⣿⠟⢹⡾⣵⢷⣾⢟⣼⣧⣿⣾⡻⣿⠇⣤⡉⢿⠆⠘⣿⡽⣯⠲⠀⢺⣷⠐⡷⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢠⣿⣿⢛⣿⡿⣶⡭⣿⣼⢉⣸⡏⠛⡷⢿⢞⣥⠛⣨⠄⠀⣿⣿⣏⣷⡤⣶⢻⡈⢫⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡿⣷⣾⣿⣟⣾⠋⡷⣿⠀⣯⣿⣟⣟⣶⣎⣡⣿⣾⢻⣿⣿⣀⢁⣿⣽⣿⡋⢘⠁⣿⢁⣿⣭⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⢿⣿⣿⣯⢿⣏⣹⡆⣿⡿⠉⠉⠛⠻⠿⡟⠻⣿⣿⣿⢿⣿⣿⣿⣟⡛⣿⢿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣭⣿⣾⣿⣿⣿⣧⣇⣽⣴⣿⡷⣶⠶⡴⠶⢶⣷⠶⠿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣾⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣴⣶⢿⣴⣤⢤⣦⣶⣴⡿⣿⠿⢿⢿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣎⣿⣿⣿⣿⣼⡷⣿⣿⣼⣋⣾⣿⣿⣙⣻⢿⣿⣼⣿⣿⣯⡿⠷⢿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣤⣿⣿⣿⣿⣆⣿⣿⣿⢿⣿⣿⠿⣹⣯⣾⣿⣿⣿⣿⣷⠻⣶⣷⣾⣿⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣯⡿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣯⣿⣿⣻⣟⢻⠿⣿⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠛⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡷⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠉⡈⠀⠀⠀⠄⠀⠀⠀⠃⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⢠⡄⢁⢀⣒⣨⢡⠀⡃⠰⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠌⣬⡰⢴⣞⣯⣾⠾⡖⣓⣲⣩⣀⡄⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⢃⠒⢷⠲⡾⣷⠿⠟⣃⡻⢟⣛⣆⣧⠏⡄⠀⠄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢁⠢⠘⣛⣯⢿⣛⣟⣻⡭⣗⣹⣷⡽⡞⣇⡂⠃⡀
⠀⠀⠀⠚⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢈⠱⠂⣷⢻⡍⣋⣯⡽⣷⣸⡯⢿⢮⡥⢡⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠊⠀⠁⠀⠈⠁⠀⠈⠁⢸⣷⡷⢻⢬⡕⣋⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠈⠀⠀⠀⠀⠀⢀⡘⣧⠩⠰⠆⠶⠫⢁
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠐⠂⠸⠈⠥⠀⠠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡉⠀⠂⠂⠈⠀⠀⢀⡀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⠀⠄⠒⠈⠉⠀⠀⠀⠁⠀⠁⠀⠀⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⡟⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣀⣀⣀⢹⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣭⣭⣴⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣏⡿⠛⠉⠁⢑⣽⢟⣿⡿⠟⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠋⠀⠀⠀⠈⡴⠋⡠⢻⡟⠀⠀⠀⢼⡟⢸⣿⡆⠅⠀⠉⠻⣿⣿⢿⣿⣶⣵⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠐⢀⠞⠀⠈⡴⣿⠀⠀⠀⠀⣿⠱⠈⢻⡇⠀⠀⠀⠀⠘⢿⡣⣉⠙⠛⠻⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣠⠞⠋⠀⠀⠀⠀⢀⠴⠁⠀⢀⡼⢡⡏⠀⠀⠀⠀⡿⣇⢀⢣⠵⡀⠀⠀⠀⠀⠩⢧⠈⢣⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⠁⠀⠀⠀⠀⣠⠎⠁⠀⠀⣰⢟⣴⠟⠀⠀⠀⠀⠀⢹⣿⡈⣾⡆⠳⠀⠀⠀⠀⠀⠻⣄⠀⢣⠀⠀⠀⢸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠇⠀⠀⠀⠀⢀⡾⢣⠖⠈⢹⡞⢡⠞⠁⠀⠀⠀⠀⠀⠀⠈⣿⡇⢹⡇⠀⣇⠀⠀⠀⠀⠀⠙⣷⣄⢷⡀⣀⣼⣯⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⢀⡞⡱⠁⠀⠀⡈⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⡇⠀⠸⠂⠀⠀⠀⠀⠀⠘⢿⣗⡍⠙⠉⠋⢻⣅
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⢀⣾⣾⠃⠀⢀⠃⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣸⣥⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠻⣾⡂⢄⠀⠀⢿⡄
⠀⠀⠀⠀⠀⢠⣿⡁⠀⠀⠀⠀⠀⣸⣿⡏⣆⣠⠊⣰⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⣿⣿⠋⣠⣃⣰⡄⠀⠀⠀⠀⣀⣵⡌⢷⡀⡇⢀⢸⣇
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⣠⢯⣿⢏⠈⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⢹⠏⠉⠉⣉⣿⣦⣶⠂⠀⠁⠀⢿⠈⣷⣿⢘⣾⣿
⠀⠀⠀⠀⢠⡿⠏⠀⠀⠀⠀⢠⣯⣞⠵⢠⡄⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠷⠞⠂⣚⣙⠀⠀⠉⢹⡇⠀⠀⠀⢸⣶⣿⠏⡟⠙⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⠿⠁⠀⠀⠛⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠉⠀⠀⠀⠠⠾⠿⠛⠂⠀⠀⣁⡁⠀⠀⠀⠸⣿⡏⣷⠃⠀⣿
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠐⠀⣿⡆⠀⠀⠀⠀⠈⢁⣿⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⢀⠀⠘⠃⠭⠿⠀⠀⠀⠀⣿⢑⡟⠀⠀⡟
⠀⠀⠀⠀⠈⣿⡄⠀⠀⠈⠀⣿⠃⠀⠀⠀⠀⠀⠛⠋⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠸⢍⠉⠁⠈⢀⡄⠀⢉⡉⠀⠀⠀⢰⡟⣸⠇⠀⢰⡇
⠀⠀⠀⠀⠀⢻⡇⡀⢀⢠⣀⣿⠶⠒⠂⠀⠐⠙⠀⢀⠜⢁⠀⠀⠀⠀⣴⡆⠸⠀⠀⡀⣿⣿⡄⡄⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⣸⣧⡟⠀⣠⡿
⠀⠀⠀⠀⠀⣨⠿⠛⢿⣯⠵⠚⢀⠁⢀⡀⠀⠀⠐⠛⣠⣿⡇⢀⡖⢼⣿⣿⢰⠀⠉⠐⠈⠉⠀⠃⠀⠀⠊⠀⠀⢀⡏⠀⠀⠀⠀⣿⡟⢇⣴⣿⠇
⠀⠀⠀⠀⠀⣿⠀⠀⠈⠶⠛⠀⠀⠀⠛⠡⡂⠀⠀⠀⠈⠛⠁⠛⠀⠈⠉⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠂⠀⠀⠀⢸⣿⢻⣴⣯⡟
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣏⣸⣿⡟
⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠏⡷⣸⣾⡟
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⢏⡾⣹⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣫⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠶⠤⣄⠂⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡵⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠖⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠶⠤⠤⠄⠐⠒⠒⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡠⡖⠂⠒⠒⠐⠐⠂⠒⠆⡤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⠉⠁⢀⣀⡤⣤⡀⢀⡤⠤⢤⣀⣀⠀⠉⠓⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⠀⠀⠠⡜⠉⠉⠀⠧⠻⢰⠂⠀⠀⠡⢋⠇⢠⠤⣤⡀⠡⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠲⠈⢀⡖⡚⠲⣘⣆⠀⢎⡱⢷⣯⠇⠀⠂⡨⡺⡦⡀⠉⠈⠻⢦⡀⠘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡞⠃⠀⠑⠈⢳⣽⢺⠀⠀⢣⡞⠉⢻⡾⣱⢠⠀⠄⣊⡌⠼⢷⡄⠉⠀⡄
⠀⠀⠀⠀⠀⠀⢰⡃⠀⠐⠛⢀⠀⠁⢀⣧⣀⡻⣝⡄⢀⠘⡇⢀⡟⣰⢑⡀⠐⠩⠨⠡⢁⡩⠇⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⣸⠂⠀⠈⣁⣴⢤⣦⣺⡀⠈⠙⢯⠈⣁⠠⠈⢩⡀⢷⣳⠵⠧⣵⡾⣛⠛⡒⠚⠹⣆⠈⣭⡀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡂⠄⠁⠑⣑⡮⢽⣷⡄⢈⠁⠀⠀⠀⠁⠂⢠⠞⠛⠐⠢⣔⣀⠐⠀⠂⣿⡀⠐⠂
⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡄⠀⣀⣄⣧⣠⣤⣀⣁⠀⢀⣀⡀⠀⠘⠉⣈⢰⣶⡤⣖⣻⣀⠈⢀⡊⣼⠃⠘⠙
⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⣠⠞⠉⠉⠁⠠⠀⣡⣩⡴⢦⠑⣀⠈⢀⣌⣟⠓⠾⣛⡩⠉⡢⢙⠳⡈⡁⠀⢤⡄
⠀⠀⠀⠀⠀⠀⠸⣯⠀⠀⠹⡇⠄⠁⠡⣵⠾⢿⠃⣀⣯⣾⠋⠐⡼⢜⠊⢳⣦⣟⢂⠕⠂⡀⠉⢸⠃⠠⣔
⠀⠀⠀⠀⠀⠀⠀⢻⢆⡁⠀⠙⠐⢪⠾⠩⠀⡂⠛⣹⡿⣟⠀⢀⣷⡸⠤⢀⠠⠹⣧⣂⡰⠈⣢⠞⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢮⢳⣆⠄⠀⠷⣌⠀⠀⠀⢠⢏⡄⡝⢗⠋⠏⡇⠀⢆⠠⠁⡸⠉⠘⠛⠁⠀⢬⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⣮⣂⠠⠈⠳⠬⠐⢨⠄⠜⠐⡘⡐⠠⠿⠀⠠⠂⣠⡴⠞⠀⠀⠐⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣶⣦⣠⠀⠀⠈⠲⠶⠶⢥⡤⠤⠁⠙⠛⠛⠁⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠣⠩⣛⡷⣤⣀⣀⣀⣂⢀⣆⣷⣠⣦⣤⣧⠶⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠯⠉⠉⠭⠙⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣶⣶⣦⣄⣤⣴⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣻⠿⠿⢟⢿⣟⠻⠿⣭⣾⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣹⡿⠾⠟⠹⠁⠊⠐⡉⠠⠔⠩⢳⣾⡻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡟⢒⡶⢖⠃⡛⠋⠆⠂⣬⣉⢧⣜⣷⢿⣮⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣧⡿⢡⡞⠷⠀⠂⠴⠐⠢⠀⠀⠉⢛⢿⣿⠾⣷⣏⡙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢾⡎⢐⣟⠐⠁⡁⢆⠓⣤⣉⣀⡀⣬⣽⣿⣎⢣⡟⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⣵⣿⠭⣀⣈⣷⠞⠻⠭⡙⡨⡅⢸⢽⣾⣿⠇⢳⣀⣈⡆
⠀⠀⠀⠀⢀⢀⡴⠻⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⢶⠽⡆⠆⢡⠁⡀⠉⠘⠡⣿⢏⡷⣿⣿⣯⣧⡀
⠀⠀⠐⠟⠛⣮⠉⠒⢄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣲⠤⠍⢤⠀⢦⠈⢶⢀⣷⣏⠻⣽⣿⣾⣿⣿⡇
⠀⠀⠀⠀⠀⡀⠀⠀⢈⣧⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⢿⣀⠇⠶⠶⠺⢂⣼⣿⢛⠨⠤⠏⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢘⣿⣿⣯⠀⢇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣺⣷⣬⣥⡀⣦⣽⣴⡟⣿⠈⢯⣅⠰⠶⣼⣿⡽⣿⣿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⡟⠊⠰⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣳⣾⣿⣿⡟⣃⡶⢧⣤⡌⠣⢸⣿⣭⠓⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠈⠳⣄⠙⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⢹⡗⠻⣧⣽⣟⣿⡟⠳⣼⣿⡟
⠀⠀⣠⣴⣶⣶⣶⣶⣤⡠⣀⠈⢻⣿⣿⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢿⣿⣿⢻⣶⣷⣾⠁
⠀⠀⢻⣿⣿⣿⢿⣷⣿⡿⠟⠛⠉⠀⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠉⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⡟⢀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠋⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠯⠿⠻⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠫⢟⠏⠉⠐⠒⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡏⠱⠏⠙⠀⠐⠁⢀⣤⣤⣤⡄⠀⠈⠑⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣠⠎⡼⠛⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠃⠀⠀⠀⠐⠛⣄
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⡴⠮⠤⠐⠒⠒⠤⠬⢉⡒⠤⣼⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠈⣦
⠀⠀⠀⠀⡠⢒⡩⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⡇
⠀⠀⣰⢋⠔⠁⠀⠀⠀⠀⠀⡀⠲⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡌⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣱
⠀⣰⢃⠎⠀⠀⠀⠀⠀⠀⠀⣿⡄⢹⡿⣷⡶⢀⡀⠀⠀⠀⠀⠀⠘⢆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡏⠸⠀⠀⠀⠀⠀⠀⠀⡚⠩⡙⠱⣰⣶⡿⡆⣱⡦⠀⠀⠀⠀⠀⠀⠳⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢀⣀⠠⡤⡄
⠀⡇⠃⠀⠀⠀⠀⠀⠀⠀⣿⠓⢌⣦⡘⣄⢑⡈⢇⠒⠀⠀⠀⠀⠀⠀⠀⢱⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⣴⣿⠇⠀⠀⠈⠎⢦
⠀⡧⢸⠀⠀⠀⠀⠀⠀⠀⢻⣭⢶⣋⢡⡈⢆⠁⣼⠛⣫⠀⠀⠀⠀⠀⠀⠀⡇⠇⢀⣀⡀⠀⠀⠀⢀⣀⣠⣤⣴⢶⣿⣿⣿⢿⣿⠋⠀⠀⠀⠀⠘⡈⣇
⠀⣷⡀⢇⠀⠀⠀⠀⠀⠀⠀⢶⣃⣙⣟⢷⣌⣆⣀⣠⡄⣤⡀⠀⠀⠀⠀⠀⡇⢸⣿⠿⠛⠉⢻⣾⣿⣿⣿⣿⣿⣧⣿⢿⣏⡾⠃⠀⠀⠀⠀⠀⢠⠁⠸
⠀⠸⣷⡌⢆⠀⠀⠀⠀⠀⠀⠀⠙⣇⣾⠃⠒⠠⢤⡠⢌⡍⢉⣉⡉⠓⠒⠒⠳⠾⢭⣄⣀⡀⠀⠈⠙⠛⠚⠛⠺⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⢀⠎⠀⡏
⠀⠀⠱⡝⣮⠳⡀⠀⠀⠀⠀⠀⠀⢘⣿⠀⠀⠀⠀⠱⣡⡗⠮⠣⠐⠉⡙⠿⣶⣶⠦⣄⣤⣈⣉⠑⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⡸⠁
⠀⠀⠀⠙⢆⡑⢬⡲⢄⠀⠀⠀⠀⠸⠘⠀⠀⠀⠀⠀⠙⢇⠊⢻⡠⠹⠍⠄⠒⠩⢧⠴⣾⠬⠭⣩⣩⠒⢄⠀⠉⠒⠤⣀⠀⠀⣀⠤⠔⠊⠀⡠⠊
⠀⠀⠀⠀⠈⠳⣄⠌⠢⢝⡢⢄⡀⠀⡆⠇⠀⠀⠀⠀⠀⠀⠑⠫⢽⡟⠷⠰⡚⠃⡨⠔⡞⡀⡿⣩⣿⠾⠊⠑⠒⠢⢤⣠⣟⣩⣤⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠑⠧⣔⡈⠁⠛⠷⢿⡘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⢦⡀⠦⠠⠤⠒⠉⠀⠀⠀⠀⠀⠀⡆⣸⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠣⠦⠦⠴⡜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢬⣑⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣁⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠬⠍⣐⣲⣔⣒⣒⣂⣉⠡⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣤⣀⣀⡀⢰⣤⣄⡀⡇⣴⢤⡠⣴⠄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠓



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⣀⡀⠈⠀⠀⠀⠀⠘⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠶⠀⠀⠀⠀⠸⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠀⢸⣏⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢠⡀⠘⠃⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⣿⣿⣿⣿⠁⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⣿⠇⠀⠀⠀⠀⠙⠻⠿⠿⠿⢿⡿⠿⠿⠿⠛⠁
⣿⣿⡟

⣿⡿⠿⡿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⡿⠿⣿
⣿⡇⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⣿
⢻⣇⠀⢿⢹⠀⠀⠀⠀⠀⠀⢠⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⡄⠀⠀⠀⠀⠀⠀⢸⢹⠇⢀⣿
⠸⣿⡀⢸⡾⡇⠀⠀⠀⠀⠀⠈⠋⣠⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠈⠛⠁⠀⠀⠀⠀⠀⢀⡟⡾⠀⣸⡿
⠀⢿⣇⠀⢷⢻⡀⠀⠀⠀⠀⠀⠀⠛⠛⢀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⠃⢠⣿⠇
⠀⠘⣿⡄⠘⣧⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⢀⣾⣧⠀⠀⠀⣿⣧⠀⠀⠈⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠏⢀⣾⡏
⠀⠀⠸⣿⡄⠘⢧⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣱⠋⢀⣾⠟
⠀⠀⠀⠘⣿⣄⠈⢳⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫⡞⠁⣠⣿⠏
⠀⠀⠀⠀⠈⢿⣦⡀⠙⢮⡳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣫⡴⠋⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⠳⣝⡲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣚⡽⠞⠁⣠⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣄⡀⠙⠳⢯⣝⣲⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⢶⣚⡭⠷⠛⠉⣀⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣦⣄⣀⠉⠙⠓⠲⠾⠯⠭⠭⠭⠭⠽⠷⠖⠚⠛⠉⢁⣀⣤⣶⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⢀⠤⠀⠂⠠⢄⠀⠀⠀⠀⠀⢰⠀⢨⠅⠀⢇⢃⢰⠙⡀⢇⡄⠀⠀⠀⠀⠀⠀⢀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠘⠐⠐⠀⠘⠘⠈⠈⠒⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠙⠀⠱⡐⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⠛⠉⠙⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠘⡀⢹⠀⠀⠀⠀⠀⡠⠤⢄
⠀⠀⠀⠈⣀⡀⠀⢀⠀⠀⡜⠄⣱⣖⣆⢸⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢺⢄⠀⠀⠐⠄⡅⠀⠀⠀⢸⣺⡷⡾⠁
⠀⢀⠐⢤⣁⣥⡆⠸⠄⠘⣏⠐⢫⢩⠁⡾⢸⠁⠀⠀⠚⠀⠀⣀⡀⠀⠀⣀⠀⠀⠀⣀⠪⡒⢨⣾⡄⢳⠀⠀⠀⠒⠀⠀⠀⠈⠰⠵⠃
⠀⠀⠡⠛⠉⠉⡛⠛⠀⠀⠘⠤⣶⣤⡿⠔⠁⠀⠀⠘⠄⠄⠀⠉⠀⢠⡄⠀⠀⠀⠀⠈⡀⠑⣄⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⠀⢀⢀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⢈⡀⠀⠀⠉⠒⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠐⢀⠀⡀
⠀⠀⠀⠀⣄⠀⠀⠀⠆⢠⡄⠀⢠⠖⢉⠉⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⡀⢀⠀⠀⡤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢠⣮⢣
⠀⠀⠀⠀⠈⠑⡦⢄⡔⠀⠀⢀⣧⡞⡉⠁⠈⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⠊⠀⣀⡇⠀⠈⠀⠮⠀⢜⠁⣆⠀⠀⠀⠀⢠⠈⢤⣁⡸
⠀⠀⠀⠀⠀⠀⣗⠠⡈⠙⢍⠉⠙⠒⢄⠀⣹⠓⠢⢄⠉⠳⣄⡀⠀⠀⠀⠘⣯⣖⣀⣃⣀⣍⣐⣐⣂⣰⣽⠃⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠉⢦⠡⡴⠚⠖⠤⡀⠚⠋⠀⠉⠒⢄⣈⠐⠂⠘⠃⠀⠀⠀⢿⣿⣹⣿⡏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢐⣤⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠃⢡⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⢸⣿⣹⣿⣯⣿⢻⣿⣯⣿⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠠⡜⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⢻⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠉⠳⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢘⣧⢀⡤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⠟⠋⠉⠉⠉⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠧⠀⢸⣷⣋⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣶⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡋⠀⠀⣠⠞⠫⠧⠵⢭⠶⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣠⣾⠋⠀⠀⠀⠀⣀⣤⡶⠶⠶⣤⣀⠀⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠔⣁⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢒⣚⣻⡿⠁⠀⠀⢀⡴⢾⢣⡶⠔⠛⠈⠁⠀⠀⠀⠀⢠⣥⠀⠀⠀⠀⠀⠀⠀⣠⣾⠯⠚⠉⠀⠀⠈⠳
⠀⠀⠀⠀⠀⠀⡋⠁⢤⡿⠁⠀⠀⡀⠼⠟⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⢠⡟⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠘⠀⣊⣿⠃⣀⡔⠚⠃⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⡏⠈⢢
⠀⠀⠀⠀⠀⠰⠆⣿⡿⠚⢦⠛⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠘⢃⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢉⣿⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠰⣞⣁⠀⠶⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡀⠀⠰⠈⢳⢤⣀⠀⢀⠀⢠⣴⣬⣹⣞⡻⣿⠿⠃⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠙⢭⣳⣴⣄⣠⣄⡄⠀⠀⢠⡄⣦⠘⠴⡈⠁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠻⣯⡀⠀⠀⠀⠈⠉⠘⠛⢿⣾⡴⠒⠘⠚⠂⠛⠉⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⣂⣀⣉⣓⡛⡌⠉⠤⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠢⠀⠉⠿⢷⣶⣤⣤⣤⣤⣴⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⠀⣤⢀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣰⠏⡼⢰⠇⣼⠃⡴⢣⠶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠒⢄⠀⠀⠘⠀⠈⠸⡅⠘⠀⠣⠀⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⢀⣀⣤⣄⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⢀⡠⠚⠙⠤⡴⣟⣦⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢠⠔⡿⣼⣾⣷⣶⣰⡿⢿⡇⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⠴⠀⠃⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⡛⢤⣠⣇⣿⢇⣼⡽⢳⣾⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⣤⠀⢀⠉⠀⠰⡦⠂⠀⠄⢉⡙⠙⠚
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠇⣻⣿⡽⠇⢩⡿⣷⣿⡟⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠢⡀⠀⠈⠀⠇⠎⡀⡀⠔⠊⠨⠤⢼⠁
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠉⠛⠻⣿⡿⠇⠞⠋⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠒⠲⡂⢰⢌⠃⢘⠀⠠⢀⡤⠐⠋⠠⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠹⣿⣦⣄⡀⢀⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠈⠃⣈⠙⠢⣇⠈⣦⠴⠋⢠⣤⠤⠶⠂⡀⠐
⠀⠀⠀⠀⠀⠀⠙⠛⠩⡋⠉⢹⠙⣦⣀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣶⡏⢩⡐⠠⣀⣀⡀⠠⠜⠓⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⣄⢛⣳⣶⡦⣤⡴⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠈⣧⣄⣤⡙⡉⠒⠶⠈⣀⢠⣀⢂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠛⠛⠒⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠘⠆⠁⢤⡁⠉⠚⠦⠤⠦⠀⠀⢤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠚⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⣀⢀⣀⣠⠤⣄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠞⡫⠭⠭⠍⣛⣿⣿⡥⣚⣽⠶⠿⣉⠛⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣒⣶⣤⠲⠾⠛⠽⠿⠿⣛⠛⣻⡿⣷⣾⣏⡁⠀⠀⢀⠀⠐⠒⠤⠐⢄⣢⣀
⠀⠀⠀⠀⠀⠀⢀⣐⣵⣿⠕⣿⢡⠀⡀⠀⠀⢁⢤⣌⣭⣿⣿⣯⢿⡩⡿⣷⣤⡀⡀⠀⢀⠠⢘⡂⡙⣤⢖⡄
⠀⠀⠀⠀⠀⢰⣿⣿⣫⢛⡾⣽⢣⣾⣇⣠⣎⣵⣸⣿⡟⠈⠃⢙⡄⢋⢿⣿⣿⣷⡌⠀⠈⠙⣮⡽⣷⣿⣿⣽⣦
⠀⠀⠀⠀⢠⣿⣿⣿⣷⣷⣿⣿⣿⠁⠋⢁⠁⣿⣿⡟⠀⠀⠀⣜⣵⠝⣿⣾⣿⣿⣷⠘⢰⣄⢽⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣧⣿⣾⣿⡧⣶⡂⢚⢾⠷⣿⠁⠀⠈⠀⡘⢳⢺⢿⣿⣿⣿⣿⡆⠈⡁⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣾⡟⣿⣴⣧⠙⠼⠏⢹⡇⠀⠀⠠⡞⣀⠀⠙⣋⡿⢽⣿⣿⣷⣜⢿⡿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⢹⣿⣷⣲⡸⣿⡇⡀⠀⡰⡀⠈⢤⢀⣸⢻⣼⣿⣿⣿⣿⡾⣷⣿⣿⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⡟⣼⣿⡏⠃⡠⣡⣍⠀⠄⠰⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣇⡸⠁⣀⣠⣼⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣺⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁
⠀⠀⠀⠀⠀⠀⠘⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⠽⠃⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⣈⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣥⣬⣽⣤⣶⢦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⢿⣯⠻⡏⢣⠘⡰⣦⠿⣿⡲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢿⣷⣿⣏⠞⠠⠵⣿⠀⢻⠂⠘⣇⠈⠳⣌⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣯⣿⡟⠥⠂⢰⠂⢻⡄⠈⣷⡄⠠⠛⡷⠸⠈⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣾⣿⣷⢤⢿⡿⠒⢺⣿⢶⣿⠁⠀⠡⣧⡀⢦⣽⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⡅⣘⢸⡧⠀⢌⣿⠃⢠⣿⣦⠔⣿⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡣⣾⣷⠀⣹⣯⠀⠀⠹⣿⠀⢹⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡗⣿⣯⡙⢿⡧⡄⢰⣾⣧⠄⣾⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣷⣊⣿⣃⠴⣸⣿⢳⣼⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣿⣿⣿⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⠞⢛⣿⠟⢿⡟⠓⢠⠀⠀⠈⠙⠻⢦⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡸⠋⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠂⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡔⢒⡀
⠀⠀⠀⠀⠀⠀⠐⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢷⠀⠁
⠀⠀⠀⠀⠀⠀⠤⣜⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⡈⣷⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢸⠆⠰
⠀⠀⠀⠀⠀⠸⢹⣟⠀⠀⠀⡠⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⠀⡙
⠀⠀⠀⠀⠀⠘⣋⣿⡀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⠸⠃
⠀⠀⠀⠀⠀⠀⠨⣿⣷⠆⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠂⢸⣧⠞
⠀⠀⠀⠀⠀⠀⠀⡿⣿⡆⠀⠀⢸⣿⡆⠀⠀⠐⠀⠀⠀⢢⠀⠀⠀⠀⣸⣿⠀⠐⣀⢢⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⣼⣠⡣⢻⣿⣧⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⣾⡟⠡⣖⡈⢸⡟⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣀⠘⢿⣿⣇⣀⠀⠀⢀⢸⡆⠀⠀⢰⣿⣃⣰⠟⣼⠟⠀⠀⣀⡤⠔⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣼⣿⣿⣿⣿⡂⢠⣿⣸⣏⢐⢳⣾⣟⣿⣯⠟⢁⡤⠒⠉⠀⠀⠀⠀⠀⣀⠤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠿⠛⢁⠔⠃⠀⠀⠀⠀⠀⣤⡖⢳⣦⣄⣘⣀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⣤⣠⣿⣏⣱⠼⣿⡅⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠠⠏⠼⠦⠧⠶⠞⠃⠀⠀⠀⠀⠀⠀⣠⢾⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣞⣱⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇⡔⠂⠐⠒⠂⠐⠀⠀⠀⡀⠀⠂⠛⠀⠀⢠⣵⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣷⣀⡀⠀⠀⢀⠀⡀⠀⢀⢀⣤⣞⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠦⠮⠶⠿⠿⠖⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠠⠄⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠔⠛⠒⠙⢉⠉⠙⠉⠙⠋⠹⠗⠤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢃⢀⣤⢦⠶⠶⠷⠞⠾⠲⠾⠲⢶⢦⣤⣤⡉⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠞⢋⡉⠃⢀⠀⠀⠀⠀⢀⠀⢀⠀⢄⠀⢀⡉⠉⠳⣮⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣤⠰⠟⠻⠛⠻⠚⠿⠛⠻⠋⠹⠟⠛⠙⡿⠛⠛⢶⢧⣦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⣤⢀⣀⠀⡄⠀⢀⠀⠀⠀⠀⣄⠀⠀⠉⠀⠠⣄⣨⣶⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢹⣷⣀⢀⠉⠙⡿⠶⠛⢿⡶⢶⣶⢾⠟⢻⡷⡿⢻⣻⡟⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢳⣽⠻⢾⣄⣠⡀⡀⢤⡀⠀⢀⠀⠀⠈⢀⣠⣴⣷⣾⣿⠏
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠙⢷⣶⣄⣜⡉⢟⠛⠓⠞⡶⠛⠞⠋⡻⢻⣿⣿⠿⠋
⠀⠀⠀⠀⠑⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠁⠛⠿⠷⣿⡷⢾⡶⢶⡿⣶⣻⠟⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠀⡼
⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣖⠒⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠉⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣦⣤⣀⡀⠀⠀⣀⣀⣀⠀⣠⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠷⠾⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⡐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣄⣤⠀⠀⠀⠀⢣
⠀⠀⠀⢄⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⢝⠈⡾⠃⠸⠆⠀⠸⠀⠀⠀⠀⠀⡀
⠂⠀⠲⡠⠀⠀⠀⠐⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢨⡇⠀⠠⠂⠁⠸
⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠢
⠘⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠁⠐⠄⠀⠀⠀⠀⠀⣀⠈⠀⠀⡠⠀⠀⠀⠀⡀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⢆⠀⠀⠈⠢⠀⠀⠈⠁⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠤⠾⠦⢄⡀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣄⡀⠐⠶⢤⠤⡤⢄⣈⣦⣤⡀⠀⠈⠛⠴⠤⠀⠀⠀⢀⣤⣤⠖⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣉⣉⣈⣉⣁⣀⣀⣉⣑⣛⣾⣶⣶⣬⣤⣀⣀⣉⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣂
⠀⠀⠀⠁⠐⠒⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠰⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⢀⡾⠏⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⢀⠀⠀⢀⠾⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢄
⠀⠀⠀⠀⠀⠀⣠⡐⠋⣀⡼⠁⠀⠀⣸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠈⠙⢿⢤⣄⡀
⠀⠀⠀⠀⢠⡥⠋⢠⡿⠋⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠈⠉⠉⠋
⠀⠀⠀⠀⠛⠓⠋⠁⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠈⠀⠂
⠀⠀⠈⠐⠂⠠⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠘⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠭⣂⠀⡤⠤⣀⣒⠴⠋
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣚⣉⣉⣭⣭⣤⣤⣬⡙⢦⣝⠷⣲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣴⠾⠿⠛⠋⣉⣭⣭⣭⣿⣿⣷⣽⣦⡟⣸⣛⣲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⣹⣿⣷⠾⠟⣻⣯⠁⠀⠐⢲⡞⠋⢟⢳⠼⠩⣝⣻⠆
⠀⠀⠀⠀⠀⠀⠀⢀⡾⣁⣴⡾⠋⢁⣠⣤⣾⡟⠉⣠⣾⣿⣿⠃⣠⠟⢸⣇⢢⡸⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣡⡶⠶⠿⠋⠀⣸⣵⣿⡿⠛⢁⣿⣾⣏⣀⣾⢻⡟⣷⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡟⣡⣿⡿⠀⠀⣠⣴⣾⡿⠋⠁⠀⢀⣿⣿⠏⢹⣿⠋⢘⡇⢸⡇⠻⣏⣷
⠀⠀⠀⠀⠀⠀⠀⣶⡿⠋⠀⢀⣴⣿⡿⠋⠀⠀⣀⣴⣿⡟⠁⠀⣾⡟⠀⣼⡇⣸⣇⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣤⣿⡿⠉⠀⠀⢀⣼⣿⡏⠁⠀⠀⣴⣿⠀⠈⣿⠀⣹⡟⢠⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣐⡿⠿⠿⢿⣄⡀⣐⣿⡿⠋⠁⠀⢰⣿⣿⠁⠀⢰⣿⡄⣿⢀⣟⣟⣠⠤⠤⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⠙⣿⣿⡿⠇⠀⠀⣰⣿⣿⣃⠒⠒⠛⠛⠉⠉⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⣼⣿⡿⠀⠀⠰⠿⣿⢣⡎⣿⠇⠀⠀⠀⠀⠘⠋⢴⠾⢦⣴⡄⢶⠴⠎⠛⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⢿⣟⠃⠀⢀⣴⡾⠋⢸⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠒⠂⠻⣿⡿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣜⣿⡦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣥⣒⠤⠤⣄⣀⣀⠠⠀⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡀
⠀⠀⠀⣠⣾⣿⡟⡼⢿⠟⡿⢿⣿⣆
⠀⠀⠀⣿⣿⣿⡇⢲⣶⣶⣿⢾⣿⡟⠄
⠀⠀⠀⠘⣿⣿⣶⣈⠏⣏⠁⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠀⠀⠄
⠀⠀⠀⠀⠻⣿⣵⣿⣿⣟⣼⡿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠳⠾⠛⠀⠂⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠠⠚⣡⠞⠁⠀⣠⠀⠀⡆⠀⠙⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠃⠄⢀⡾⠁⠀⣠⢻⢄⠀⠹⡀⠀⠰⣄⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣧⣮⢲⣿⡃⠀⠀⣿⢰⡇⠀⠀⢳⠀⠀⠘⡄⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⡁⠀⠀⣻⡞⠃⠀⠀⢸⡄⠀⠀⣫⠀⢰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣾⡀⢸⣿⠀⣆⠀⠀⢼⡷⠀⠀⣾⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡿⡿⠄⢠⡼⣷⠀⢰⣭⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣿⣧⣏⣷⣘⣿⣍⣲⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⢠⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⢠⠃⣼⣿⠿⢻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠁⠀⠀⠈⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠄⠀⠀⣀⡀⠀⠤⠶⠚⠋⠁⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⢠⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⡴⠃⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⢀⢿⡇⠀⣇⣤⣀⠀⣿⡗⠀⣀⠀⣄⠀⢀⡀⠀⠀⠀⠀⢀⣀⢰⣯⠏⠀⢀⡀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡞⠘⣇⠀⡿⣿⣸⣇⣿⠀⣼⡽⠇⢺⡇⣾⡿⢹⡞⣷⢀⣿⠽⢻⣯⠀⣰⣿⢿⣾⡷⢹⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠙⠚⠁⠉⠁⠉⠹⠄⠉⠛⠁⠈⠁⠈⠁⠈⠁⠈⠉⠉⠋⠀⠻⠟⠁⠉⠉⠈⠁⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠶⠖⠶⣦⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣒⣥⣶⠶⠾⢷⣛⣿⣮⣝⣎⡼⢱⠦⡀
⠀⠀⠀⠀⠀⠀⢀⣼⠟⢩⣶⣶⠶⢻⡟⠉⠉⢭⡟⠻⠧⠝⢋⣻⠆
⠀⠀⠀⠀⠀⠀⠞⣡⠾⠋⣠⡤⠶⡟⣁⣴⡿⠟⢁⡜⢹⣇⣆⢻⣿⣧
⠀⠀⠀⠀⠀⢸⠟⣷⡞⠉⠋⣀⣴⡾⠟⠋⢠⣾⡿⣤⡾⢸⠙⡏⢿⣻⡀
⠀⠀⠀⠀⠀⢨⣾⠛⠁⣀⣼⡿⠋⠀⢀⣴⣿⠋⢀⣿⠃⣸⡀⣿⠈⣯⠁
⠀⠀⠀⠀⠀⢸⠃⢠⣼⣿⠋⠀⢀⣴⣿⠋⠀⢀⣼⠇⠀⡏⢈⡟⢠⣿⠀⠀⠀⠀⢀⣀⡠⠤⠤⠲
⠀⠀⠀⠀⠀⠀⢦⡟⠛⠛⢦⣤⣾⡟⠁⠀⣰⣿⠏⣀⣰⣿⣸⡧⠯⠇⠂⠒⠈⠉⠁⢀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢨⣿⡟⠁⢠⣴⡿⡹⣦⠀⠀⠀⠀⠴⣠⣤⣀⡀⣀⣄⢤⠈⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢿⡟⠀⢀⣴⠞⠻⣧⣿⡀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠂⠙⣿⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡪⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠐⠩⠭⠭⠥⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⣠⠴⠚⠉⠀⢀⠀⢀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⢠⠖⢶⡄⠙⡄⢰⣏⠁⠀⢰⣿⡄⠀⠀⠀⠀⠀⠑⠒⢆⠀⢀⡬⠖⡻⠂
⠀⠀⢀⠞⣁⣀⣠⠿⠶⠛⠋⠙⠋⠉⠛⠓⢤⣈⣷⡄⢀⣀⠀⠀⠀⠸⠦⠾⢃⣼⡇⢸⣿⣦⡀⢘⣿⠃⠀⠀⠀⣰⣆⣦⣀⣀⠘⠯⣁
⠀⢠⣇⣴⠿⠋⠉⠀⢀⣀⣤⣴⡶⡶⠣⠖⠶⣿⣭⣿⡏⠀⠀⠀⠀⠈⠒⠒⠛⠋⠀⠀⠈⠙⠛⠉⠁⠀⠀⠀⠘⡿⢁⢤⡀⠙⢎⠳⣮⠑
⠀⣼⠟⠁⢀⣀⣴⣿⡾⠛⠋⠈⠀⠀⠀⣀⠖⢋⡟⡯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢨⣿⡀⡘⢀⣿⠂⠤
⠀⣿⣀⣶⠾⠏⠁⠀⠀⠀⠀⢀⣼⣿⡿⠏⠀⣾⡧⣷⢻⠴⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⡆⢸⣏
⠀⢹⡟⠁⠀⠀⠀⠀⡀⣶⣶⣿⠟⠛⠀⢰⣾⣿⣴⣿⣿⠀⠚⢰⢃⡆⢠⠀⡄⢲⡘⠆⠀⡰⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⣈⡿⠁⢠⣿⡄
⠀⠈⣧⡀⢀⣦⣴⣾⠟⠛⠃⠀⣀⣠⣷⡿⢟⣻⣿⣿⣏⠳⣄⠀⠈⠁⠙⠀⠛⠈⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⡇⠀⢸⣿⠇
⠀⠀⠘⢿⡟⠛⠋⠀⠀⣤⣤⣶⣿⠿⢋⣘⣷⣿⡿⠁⠙⠳⣬⡐⠲⠤⢄⣄⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠛⠁
⠀⠀⠀⠀⠙⠶⣾⣿⢿⠿⠛⣋⢃⣤⣾⡿⠟⠉⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⢀⣷⡤⠀⣇⠀⠀⠀⠀⢄⠀⠤⢡⣆⡾⠈⡀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡶⠄⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⠀⠀⢠⣿⠿⡇⠀⢯⡤⣀⡀⠌⢆⢾⣾⣻⣿⣇⣆⠢⢂⢄⠀⡆
⠀⠀⠀⣠⣆⢀⡀⣵⡘⠳⠀⠘⠦⣄⣀⠀⣀⠀⠀⠈⠁⠀⠠⠀⡰⠋⠀⠀⠄⠀⠈⢿⣷⣶⣷⣾⢾⣻⣷⣿⣽⣿⣿⣗⣾⡟⠁
⠀⠀⠀⠉⠀⢰⣇⠀⠙⠢⢦⠀⠀⠈⠿⣇⠀⠀⠀⠀⣀⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣿⣿⣿⠿⢿⣿⣿⣯⣤⣤⣴⠾⠿⠈
⠀⠀⠀⠀⠀⠀⠙⠱⢄⠀⠀⠑⡄⠀⠀⠀⣿⣟⠛⠉⠁⠀⠀⠀⢀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⢯⠰⡀⠙⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠐⠻⠇⠀⠈⠛⠦⣤⣀⡠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒
⣿⢿⠿⠿⡿⡿⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠒⠀⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠂⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀⠀⠀⢀⠀⠀⢆⠀⠀⠀⠑⡀
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣀⡀⠀⠈⠀⠀⣄⠀⠐
⠀⠀⠀⢀⠁⢠⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠃⠀⠁⠀⠀⠐⠀⠀⠂⠀⠐
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠑⡈⢡⡈⢹⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢰⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠁⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢳⡐⠇⠈⢦⠀⠀⠀⠈⡆⠀⠀⠀⠰⠐⠂⠀⠀⠀⡁⢀⠀⠀⠀⢀⠀⠆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠅⠉⠀⢸⠀⠀⠀⠀⢄⠀⠀⠀⠸⠀⢠⠀⠀⠀⠀⡀⠀⠁⢠⡈⡤⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠙⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠐⡂⠄⠀⡀⠀⠀⠊⠁⠈⠀⠄⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠂⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠃⠈⠀⠇⠁⠁⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⠀⠤⢀⡀⠀⠀⠀⠀⠀⣠⠴⠁⠀⠀⠀⠀⠀⠀⠁⡠⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⢀⣀⡀⠀⡁⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠄⢀⡀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡤⢤⠤⣄⣀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠄⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠉⠂⠈⠈⠈⠉⠀⠈⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⢀⠞⡠⠃⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠝⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⡔⠣⠁⠀⠀⠀⠀⠀⠔⣠⠀⠀⠀⠠⡀⠀⠀⠀⢉⣆⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⢰⢁⠀⠰⠑⢀⠀⠀⠀⠀⠀⠀⡿⡄
⠀⠀⠀⣰⠁⠃⠀⠀⠀⠀⠐⡀⠒⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠱⠀⠀⠐⠀⠀⠀⠀⣐⠛⠲⠀⢀⡀⠲⠀⢀⠁⠀⠀⠀⠀⠀⣷⣱
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡐⠀⠠⠈⠀⠀⠀⣝⠀⠀⠀⠀⢈⣁⠀⠀⠁⠀⠀⠀⠀⡏⠀⠐⠀⠀⣤⠈⢀⠍⠀⠀⠀⠀⠀⢠⠏⠛⡀
⠀⠀⠸⠃⠀⠀⠀⠀⠘⠦⠀⠀⠀⢀⠀⠀⡈⠃⠀⠀⠀⠀⠜⢨⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⢨⡤⠀⠀⠀⠀⠀⠀⡌⠀⢈⡄
⠀⠀⠀⡀⠀⠀⠀⠀⣮⠁⠀⠀⢀⠀⠀⣨⠏⠀⠀⠀⠀⠜⢀⠇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠂⠀⠉⠀⠀⠀⠀⠀⣠⠊⠀⠁⣸⠁
⠀⠀⠀⢱⠀⠀⠀⠀⠩⠄⠀⠀⢀⡄⡟⠉⠀⠀⠀⠀⠞⢀⠎⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠃
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⡁⣠⠊⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠊⠀⠁⠀⢀⡴⠃
⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠲⣀⠦⠀⡤⠐⢖⠘⠡⠀⡁⠠⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⠈⠁⠤⠤⠤⢤⣤⣤⠥⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣥⣤⣀⡤⠤⠌⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⣛⣷⡶⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢀⣤⣶⡾⠋⢀⣠⣤⣤⣀⠀⠙⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢠⡟⢱⡏⠀⣰⠟⢻⡆⠀⢿⠛⠶⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠛⢿⡇⠀⣿⠛⢻⣇⠀⠻⣤⡼⠇⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠿⠦⣄⣀⣤⢼⣇⠀⢻⡄⣿⡽⢦⣄⣀⣀⣠⣾⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⣠⡴⢿⡄⠈⢷⡄⠀⢴⣾⣿⣛⠛⠲⣽⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⣠⠴⠛⢁⣤⠞⠛⠶⢛⡴⠶⣄⠀⠀⠉⠳⣄⠀⠙⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⢀⡞⠁⠀⠀⠀⢸⡇⠀⠈⢳⡀⠀⠀⠙⣦⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⣧⠀⠀⠀⢹⡄⠀⠀⠈⢳⡄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢻⡀⠀⠀⠀⢿⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢘⡇⠀⠀⠀⢸⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠸⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣿⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢠⣿⡇⠈⣿⠀⠀⢠⢤⡀⠀⠀⠀⡤⢄⠀⠀⠀⢀⠤⡄⠀⠀⠀⣠⢤⡀⠀⠀⠀⡤⣄⠀⠀⣽⠁⢸⡇
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣷⠀⠀⠀⢠⡟⢸⡇⠀⢹⡆⠀⣇⣀⡇⠀⠀⠸⣀⣨⠇⠀⠀⢮⣀⡸⠀⠀⠐⣇⣀⡇⠀⠀⢸⣀⣨⠂⢰⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡿⠀⠀⠀⠘⣇⠈⣷⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡟⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢰⡇⠀⠀⠀⠀⠘⡇⠸⣇⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⣇⠀⠀⠀⠀⠀⡇⠀⠹⣆⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣹⡄⠀⠀⠀⠀⣷⠀⠀⠙⢧⡀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⢸⡄⠀⠀⠈⠻⣦⡀⠀⠀⠈⠛⠶⢦⣤⣀⣀⣀⣀⣀⣀⣀⣤⡴⠶⠛⠁⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣷⣤⣄⣀⣀⣨⣿⣶⣄⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣠⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠙⠳⠶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁