Cute flower fox Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⢠⠞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠱⣤⠃⠀⢸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠖⠓⢦⡹⣀⣀⠟⠉⠉⠓⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⢄⠀⢀⠀⠛⠣⡀⠰⠊⠲⠀⡀⠀⡸⠤⠴⠊⠑⣄
⠀⢠⡤⢄⣀⣀⡀⠀⢠⠇⠀⠐⠄⠖⠂⢹⠄⠀⢹⢦⣀⠐⠴⠃⢰⡁⢠⠔⢄⠀⠉⠉⢳
⠀⠀⠑⣄⠀⠀⠈⠉⠻⡀⠀⠠⣀⠄⠀⠉⠀⣠⠞⠀⠀⠒⠚⠀⣰⣁⠈⡀⠀⠤⠗⠀⣞⡤⠤⠤⠤⠤⢤⠄
⠀⠀⠀⠈⢣⡀⠀⠀⢀⡼⠳⡀⠀⢀⡴⠤⠞⠉⠲⠤⠒⢑⠒⢋⠀⢸⠀⠑⠖⠀⠀⠀⡸⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠙⣄⢠⠎⠀⠀⠈⡉⠉⠀⠇⠘⠀⠀⡄⠀⠚⠀⠃⠴⠂⠓⠦⠤⠚⠙⠉⢧⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⢸⠻⠤⣄⣀⡀⠉⠈⠀⢀⢰⠀⠀⠀⠰⠂⠀⢀⠀⠈⠁⣀⣀⠤⠤⠤⠬⠦⢾⠆
⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠉⠙⢢⡰⠈⠀⡀⠀⡆⢠⠀⠀⠉⣠⠔⠋⠁⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠻⣅⠀⠀⠀⠈⡇⢱⠀⣀⠃⠀⠀⠀⠘⡡⢪⠆⠀⠀⠀⠀⠀⠀⠀⠈⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢼⡃⠙⢦⡴⡟⠀⡇⠈⠀⠃⠘⢀⡜⠡⢿⣀⣀⡤⠀⠀⠀⠀⣤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⢧⡦⠄⠐⢣⠎⠀⠀⠉⠙⠁⠀⠀⠀⠀⣀⠤⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⠉⢙⢾⠀⠠⢦⠏⠀⡠⠤⣄⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠁⠘⡟⢤⠏⠀⠀⠧⠤⠎⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢀⣇⡎⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠈⣳⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠐⢄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡤⠈⡃⠀⠀⢰⣄⠀⠠⠤⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢢⠸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⠄⡄⠈⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⡒⠄⢳⡴⠃⠆⠈⣋⠀⢀⠀⢠⣤⣀⠀⢀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠈⠉⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⢬⠏⠀⠀⠀⠹⠶⣄⠀⠀⠉⠉⠁⠀⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠐⠈⢀⢸⠇⠈⠱⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠠⠀⠈⣀⠑⠂⠀⠀⢀⡀⣀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⢀⣮⡉⡗⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠⠀⢃⠀⠁⠄⡈⠑⠀⠀⠀⣠⠤⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠋⠻⣤⠔⠉⢁⢀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⠃⠀⠀⠀⠀⠁⠐⠁⠀⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⢀⠳⠆⢹⣦⠡⠞⠦⢁⠄⢄⠀⠀⠀⠀⣀⣠⠄⢀⠀⠀⠂⡂⠰⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠂⠐⠑⠈⠈⢼⠓⢲⠴⣇⠀⡈⠄⠁⠀⠜⢅⣀⡔⠁⠁⠶⠋⠀⢁⠤⠐⠢⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠠⠀⠸⡄⠘⡗⠡⡀⢠⡆⣀⣀⡤⢼⣀⣽⠛⠛⢲⠒⠮⢅⡀⡀⠐⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⣊⡀⠓⠀⡗⠖⠊⢯⠉⠁⠸⣀⡸⠁⠈⡆⠀⠏⢉⠈⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠂⡄⠐⠢⠀⠀⠀⠠⠀⡛⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⢀⡀⡀⡀⣀⢀⢀
⠀⠀⠀⢀⢰⡿⣿⢀⠀⠀⠀⠐⠣⣈⡠⠟⠀⠀⠀⠀⣶⡶⠿⠻⢷⣶⡄⠀⠀⢀⣤⣥⣾⣷⣮⣤⡀⠈⣥⣥⣧⣭⣬⡨
⠀⢀⣴⡾⣅⣳⣃⡭⣶⣤⠀⢉⣉⠛⠫⣉⠃⠀⠀⣴⡿⢠⢪⡅⣃⢻⣷⡀⠀⠸⣿⠛⠋⠙⠛⣿⠇⠀⠹⢟⢋⡟⡿⠋
⠀⠈⠛⢛⡏⡽⣍⣝⠛⠋⠀⢀⣁⡘⣂⣉⠀⠀⠀⠙⣿⣄⡃⢖⣃⣿⡏⠀⠀⠀⠈⠀⠻⠟⠂⠁⠀⠀⠠⢖⢸⠔⠴⡄
⠀⠀⠀⠀⠸⣷⡿⠀⠀⠀⠀⢿⢳⠙⠱⣓⠅⠀⣀⣤⣝⠛⢿⡿⠛⣛⣥⣀⠀⠘⠻⢦⡀⢀⣴⠟⠃⠀⢈⠊⣸⡈⢒⡁
⠀⠀⠠⣶⣶⣼⣤⣶⣦⠀⠀⠀⢀⡶⣆⠀⠀⠀⠈⠻⣿⣷⡀⡇⣼⣿⡿⠉⠀⠐⠶⣦⡙⠋⣠⡶⠂⠀⠰⠼⢸⠐⠥⠃
⠀⠀⠀⣙⣛⢹⢙⣛⡁⠀⠀⢠⣿⣟⣿⣷⠀⠀⠀⠀⢙⣛⡛⡟⣛⡋⠀⠀⠀⠀⠀⠈⠑⠞⠁⠀⠀⠀⢘⢠⢹⠫⣊⡆
⠀⠀⠈⠻⠿⢿⠿⠿⠏⠀⠀⠰⣿⡯⢿⡿⠀⠀⡀⠀⢏⢒⠌⡏⣖⢊⠀⠀⠀⠀⢀⣄⣰⣣⣠⡄⠀⠀⢀⣀⣾⣦⣀
⠀⠀⠠⣶⣶⣾⣴⣶⡶⠀⠀⠀⠈⠓⠋⣤⠀⡀⡗⠤⢄⣀⣠⣧⣤⣶⣶⣦⡀⠀⢯⣿⣾⣷⣿⡽⠂⠀⠸⣿⡁⢹⡿⠃
⠀⠀⠀⠈⠉⢹⠈⠉⠀⠀⠀⠀⣀⣠⣾⣿⣾⡇⠳⡀⠀⢘⣿⣿⣿⣿⣿⣿⣿⡄⠀⢉⡤⢤⡉⠀⠀⠀⠀⠻⠟⠻⠟
⠀⠀⢠⣤⣴⣿⣷⣤⣤⠀⠻⢿⣿⣿⣿⣿⣿⣦⣄⠈⠉⠋⠉⠉⠉⠉⠉⠉⠻⡇⠀⠉⠀⠀⠉⠀⠀⠀⢀⣰⣟⣿⣄
⠀⢀⣼⣿⠉⠡⠨⢹⣿⣅⠀⠀⠉⠛⠿⣿⣿⣿⣭⣟⢲⡶⣤⡤⣤⢤⡤⢶⣶⡆⠘⠛⢷⡾⠟⠃⢠⣞⣻⣿⢟⡿⣿⣟⣷
⠀⠘⢿⣧⠀⠘⠡⠠⣾⠟⠀⠀⠀⠀⠀⠀⢻⡿⢿⣹⠿⣿⣿⢲⣿⣶⣿⣿⣿⡇⠐⠿⢶⡶⠿⠃⠀⠹⣻⣿⣝⣣⣿⣿⠋
⠀⠀⠸⠿⢿⣧⣾⠾⡿⠁⠀⠀⢠⣴⣤⠀⠈⣿⣾⠾⠶⠿⠼⠽⠼⠿⠹⣿⡽⠇⠰⡶⣶⣷⣶⡆⠀⠰⣿⣿⣿⣿⣯⡿
⠀⠀⠀⣠⠤⣹⡡⠤⡀⠀⠀⠀⠀⠋⠃⠀⠀⢹⣿⠀⢀⣀⣠⣤⣀⣄⠀⢻⠶⠀⠀⠀⠘⠃⠀⠀⠀⠀⠴⠦⣸⣠⡴⠦
⠀⠀⣀⡣⠝⢸⠘⠥⣃⡀⠀⠀⣿⣿⣿⡷⠀⢸⡇⠀⠘⢿⣿⣿⣿⠏⠀⢸⡏⠀⠀⢿⣿⣿⡿⠀⠀⠒⠳⢶⣝⣡⡶⠟⠒
⠀⠙⢿⣿⣆⢸⢀⣾⣿⠟⠁⣀⣈⠻⠟⣀⣀⠀⠀⠀⣶⡦⣌⣏⡴⣶⠆⠀⠀⠀⣀⣀⠻⠟⣁⣀⠀⢠⢖⣖⢿⡟⣒⡲
⠀⠀⠀⠙⠿⠒⠺⠟⠃⠀⠀⠙⠻⠗⠾⠟⠁⠀⠀⠀⠈⠓⠞⠣⠞⠋⠀⠀⠀⠀⠘⠻⠗⠺⠟⠋⠀⠈⠪⠞⠈⠈⠢⠟
⠀⠀⢀⡀⢠⡀⢀⡀⢠⡀⢀⡀⢠⡄⢀⡀⢠⡄⢀⡀⢠⡄⢀⡀⢠⡄⢀⡀⢠⡄⢀⡀⢠⡄⢀⡀⢀⡄⢀⡀⢀⡄⢀⡀
⠀⢠⣿⣷⡈⢠⣿⣷⡀⢠⣿⣷⡀⢠⣿⣷⡀⢠⣾⣷⡀⢠⣾⣷⡄⢀⣾⣷⡄⢀⣾⣿⡄⢀⣾⣿⡄⢀⣾⣿⡄⢁⣾⣿⡄
⠀⠉⠉⠉⠁⠉⠉⠉⠁⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠈⠉⠉⠉⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠀⡠⢒⠂
⠀⠀⠀⠀⠀⠀⠐⡂⢄⡀⠀⠀⢠⠊⠁⠒⠈⠳⡘⠋⠀⡌
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠈⠒⡔⠁⠀⠁⠁⠠⡀⠻⡁⢊⠀⠈⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢀⠱⡄⠠⠄⠀⠐⠁⢀⢄⠀⠈⢀⠀⢨⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠐⠁⠀⠐⠤⠤⠢⠤⢒⠉⠀⠡⠄⠀⡘⢁⠈⡁⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠢⢄⠈⠰⠀⠁⠂⠀⠈⢈⠑⠒⠚⡇⠠⠀⢁⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⢀⢁⠀⠀⠘⠀⠀⢠⠀⠀⠡⠀⢄⠀⠀⠀⠀⡛⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⡏⠰⣤⡼⢸⠀⡀⠂⠘⠠⠀⠀⠂⠀⠈⡀⠁⠉⠁⡊⠀⠀⣀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠘⠀⠀⠂⠄⢀⠥⣲⠈⠁⠀⠀⠈⠁⠂⠶⢴⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣈⣱⠞⠙⠀⡡⠊⠁⠸⣅⣀⠀⠀⠀⠀⠀⢤⡖⠁⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡘⢂⡼⠋⢀⠤⠀⠀⠀⠀⠀⠀⠀⢤⠒⠊⠀⠀⠀⠀⠀⠀⠀⡰⠆⠲⠀⠀⣀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠧⡊⠀⠀⠘⠒⠂⣀⠠⠤⠐⠒⠐⢊⠁⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⢰⠄⠊⠘⡀⡐⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⠖⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⣄⠀⠀⠀⠀⠠⠃⠤⢠⠀⢀⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢢⠀⠀⢠⢇⢀⠀⠀⠀⠁⠈⠒⠈⠢⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⡆⠀⠁⠀⠑⠄⠂⠑⠤⠄⠤⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⠁⠤⠒⠒⢄⣀⠠⠤⡀⠀⣀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⢀⡀⠀⠀⠀⠀⠈⠉⠀⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠤⠔⠐⠤⠐⠢⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢣⠀⢸⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⢀⠠⠤⢄⣀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⢰⠀⠀⠀⢠⠀⠀⠀⢀⡠⠤⠄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢸⡄⢸⠀⠀⠀⡘⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⢘⠐⠈⠉⠢⠤⠀⠢⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⢸⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢨⣄⡀⠤⢄⠀⢀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡇⣠⠀⠀⢰⠇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⣇⡿⠀⠀⢸⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡌⠈⠉⠀⡨⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠤⠏⣀⠀⣀⣌⢸⢀⣀⣀⣀⣀⣀⠀⠀⠤⠚⠤⠄⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠙⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠢⢄⡀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡛⡍⠢⣠⠚⠉⠙⠛⣉⠛⢣⡴⠶⣏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠐⢻⣆⠀⠀⠀⠹⡳⢦⡀⠀⠀⠀⠀⠀⠀⢴⡖⠢⢧⣹⠶⢳⡶⠒⣲⠯⢭⣙⣦⣧⣀⠈⢦⡀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡄⠀⠀⠘⠿⣦⡀⠀⠀⠀⠀⠙⢦⡤⠤⣤⠤⠴⠾⢮⡓⠤⣿⠀⣸⠀⡎⢉⡷⣤⢧⡈⣷⠈⢳⠀⡏⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⢙⣾⣿⡄⠀⠀⠀⠀⠀⠃⠀⠀⢀⡤⠖⠒⠛⢒⡟⠀⢯⠀⢧⣯⣴⣿⣀⡇⣿⠀⢸⡶⠁⠀⣞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢰⡇⠀⠀⠀⢀⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠰⢿⣒⠒⠒⠒⡇⠙⣄⣸⡗⠦⢷⣀⣠⠿⢾⠁⣠⢾⡀⠀⠀⣏⡉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⠀⠀⣀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢹⡀⣇⠉⠳⠤⣄⣀⣀⡠⠞⠉⠁⠀⡇⠀⣼⣉⣉⣩⠽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢻⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⣆⠀⠀⠻⣍⠁⠀⠀⢀⣠⠼⣗⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⡜⠛⠒⠚⣉⣀⣼⠙⢆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⣀⠀⣀⡙⠒⠖⠋⠁⠀⠈⠳⣬⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⡉⠀⢀⠈⠁⠀⠀⠀⠀⠀⠜⢀⠀⢀⣀⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⣷⣼⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⢿⡿⣿⠿⢻⡂⠀⠀⠀⠀⠀⠀⠀⣿⠻⣿⡿⣿⠟⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢀⣀⣀⣀⣀⣴⡦⣄⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⢰⠇⢀⡴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⡾⠀⠀⠀⡄⠀⠀⠀⠀⢸⡀⣠⠴⠚⠉⠉⠁⠀⠀⠈⠉⠙⠢⢄⡀⢸⡀
⠀⠀⠀⠀⠀⠀⣼⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠃⠀⢀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⡇
⠀⠀⠀⠀⠀⠀⠉⠲⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢿⣄⡀⠀⠀⠀⣀⣀⣀⣸⠀⠀⠀⣠⣶⣶⣶⣦⡄⠀⠀⠀⣿⣀⣀⣀⠀⠀⠀⣀⡤⠛⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡉⠛⠛⠉⠉⠀⠀⠸⣆⠀⠀⠘⢿⣿⣿⡿⠃⠀⠀⢠⠏⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠘⠢⣄⣀⣠⠼⢧⣀⣀⡤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⡆⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠙⠀⢆⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣡⠂⠰⠁⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠙⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠉⠁⠀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⣀⡀⠀⠀⠀⠀⠀⠠⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠲⢤⡀⠀⠀⠀⠖⡄⢀⠀⣀⡀⠀⠀⣸⣀⡤⠔⢒⡆⠀⢀⡠⠄⠒⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢤⡈⠑⠢⣴⣪⣡⡻⠚⠀⢀⢵⣍⠙⠷⣔⡡⢊⡠⠖⢉⠴⠂⠀⢸⣤
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡜⠉⢂⠀⠘⡿⠚⢣⡤⠤⡇⠀⠈⠉⡎⠙⣷⣋⠥⡩⠷⢆⢄⣴⣋⣌⣀⣀
⠀⠀⠀⠀⠘⠀⠁⢺⠋⠐⢣⢀⣘⠀⡠⢧⠀⢸⠀⠀⢸⣶⡴⠊⠉⢺⠙⡇⠞⡱⢮⠑⡗⣹⡡⣀⠔⠁
⠀⠀⠀⠀⣠⠚⠉⢩⠷⠄⢰⣿⣿⣯⠄⣈⣲⠓⠤⡴⠊⠉⢂⣀⣀⠝⠀⡏⡳⣑⣎⠕⠁⡇⣿
⠀⠀⠀⡀⠨⠉⢒⣨⣄⣠⠜⠛⠚⢣⡀⠀⢸⡆⠀⠳⣐⢢⠴⠛⢤⣀⣴⢅⣧⠀⠤⠖⣖⣱⣯⠉⠀⠤
⠀⠀⠀⠀⠒⠂⡺⡛⠱⠦⣀⠜⢄⣀⠏⠁⠁⠈⠐⠂⠑⠄⠤⠒⠃⠀⠈⠒⠞⠲⠴⠒⠻⡏⠈⠱⡤⡀
⠀⠀⠀⠀⡔⢘⠃⢃⠀⠀⠀⠀⠀⠀⠐⢀⡂⠀⠈⠀⠀⠀⠀⠐⠁⠀⣀⠀⠀⠀⠀⠀⠀⠐⢌⠀⠢⣈
⠀⠀⠀⢠⡠⠊⠀⡎⠀⠀⠀⠀⠀⠠⢾⣿⣿⣷⡆⠀⠀⠀⠀⠀⣶⣿⣿⣿⠦⠀⡀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⢀⣀⣀⣄⣀⠉⠋⠁⡇⠀⠀⠀⠀⠀⡇⠉⠋⠁⢀⢀⣀⡀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⣸⣠⠴⠚⠉⠁⠀⠀⠀⠉⠢⢠⠇⠀⠀⠀⠀⠀⢣⡠⠒⠉⠉⠁⠀⠉⠙⠢⢄⣿
⠀⠀⠀⠀⠀⠀⠻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢤⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠙⠲⢤⠤⠴⠒⢺⡀⠀⢸⣿⣿⡶⠀⠀⡸⠶⠦⠤⠤⠴⠋⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠐⡄⠀⠀⠀⠀⠑⠤⣀⠩⠯⣀⡠⠔⠁⠀⠀⠀⠀⠀⡔⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠄⠘⢦⠀⠀⠀⠀⠀⠈⠑⠒⠋⠀⠀⠀⠀⠀⠀⣀⠞⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠆⢀⠠⢰
⠀⠀⠀⠀⠀⠀⠀⡦⢄⡀⠀⠀⠀⡔⠀⠐⠖⠘⢂⠸⠂⢀⡂
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠈⠐⢤⠊⠀⠠⢉⡀⢄⠐⢟⠒⢊⠉⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⣦⠀⠤⠀⠀⠘⠀⢀⡄⠁⠀⢀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⠊⠁⠘⢄⣀⠠⢀⠠⡔⠂⠈⢀⡈⠁⠐⠉⠀⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠑⠠⡀⠀⠂⠀⠐⠀⠀⠈⠒⢐⠢⠤⠐⡅⢀⠀⠁⡀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠐⡞⠀⠀⠈⠱⡀⠀⠀⠆⠀⠂⠀⠈⠐⢃⠐⡁⠑⠀⠀⠁⢴⠅⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠠⡀⢀⡇⠁⠀⠠⠀⠄⡀⠁⢀⠀⠀⠀⠈⠂⠒⠠⡴⠃⠀⠀⢀⡉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠘⠉⠀⠇⠀⠠⢀⡀⠡⣂⣠⠔⠒⠒⠒⠒⠠⠄⣀⣀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠉⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠢⡰⠐⠀⠠⢀⠔⠈⣴⠁⠀⠀⠀⠀⠀⠀⢀⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣡⠀⡢⠒⠁⠀⠀⠙⠓⠂⠀⠀⠀⣀⡀⠍⠃⠀⠀⠀⠀⠀⠀⠀⣴⣋⡀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣀⡠⠋⠀⠀⢏⣈⠂⠀⠀⢀⣀⠀⢠⡽⠆⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠁⡠⠔⡂⠀⣠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢱⣀⠀⠤⠄⠐⠒⠈⠉⠀⠀⠀⠀⠨⣄⠀⠀⠀⠀⠀⠀⣔⠁⠀⠀⠀⠉⠀⠀⢰⡔⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⡘⠀⠀⠈⠢⠔⠒⡄⡀⢄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠘⢄⠀⠰⠑⠄⠒⠢⡀⢀⠀⠀⠀⡀⠉⠩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢧⠀⢀⣀⠀⠀⠀⠀⠑⠁⠈⠂⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠄⠉⠁⠀⠑⠂⠒⠈⠑⠄⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠀⠂⢄⠀⠀⢀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠈⠊⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠑⠄⠂⠐⠄⠐⠢⠀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢃⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠂⠀⠀⠀⢁⠀⠀⣀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⡇⠀⠀⠀⡆⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠈⠒⠊⠈⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠄⠀⠀⠄⠠⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⡇⠀⠀⢸⠀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⢀⣧⠇⠀⠀⡌⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠚⠅⣀⣀⡠⠧⠤⠀⢀⢀⣀⣀⡀⠀⠤⠄⠚⠐⠂⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠸⣄⠀⠀⠀⠠⣌⣄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡥⠘
⠀⠀⢀⡄⠀⠀⠠⠀⠈⠀⢦⠈⠀⠈⠩⠪⠂⠀⣀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠂
⠀⠀⠀⠁⠁⠢⠀⠁⠃⠁⠐⡉⠂⠀⠘⠠⠂⠀⠁⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⡘⠀⠀⠐
⠀⠀⠠⠀⠒⠀⠀⠈⠁⠁⢀⠀⠀⠀⠀⠀⠐⠆⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤
⠀⠀⠐⠂⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠒⠀⠀⠀⠀⠀⠠⠀⢤⠆⠀⠀⠀⢀⡆⠀⠀⠀⠐⠂
⠀⠀⠂⢁⠀⠀⠈⠢⠤⠊⠀⠌⠢⠤⠊⠃⠀⢀⠁⠂⠀⠀⠀⠀⠀⠀⢤⢠⠂⠀⠀⠀⠉⠀⠀⠈⠃
⠀⠀⠀⠈⠐⠶⠀⠀⠀⠀⠁⠁⠀⠀⠀⠠⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠄⠀⡤⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠐⠗⠁⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠀⠀⠀⠀⠀⢂⡂⡀⠈⠤⡀⢀
⠀⠀⠀⠀⠀⢁⠅⠀⠠⠄⢀⠈⠁⠂⡀⠈⠂⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⣀⠠⠄⢄⡂⠠⠀⢂⠰⡆
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡅⠜⠈⠄⠀⠁⠀⠲⠀⠀⠀⠀⠠⠀⠤⣀⣪⠜⢣⡡⠒⣅⠖⠠⣤⠒⢤⣐⣂⡀
⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠈⠡⠀⠈⢁⠃⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢄⣀⠄⠀⡀⡘⠀⢄⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡝⠀⢁⠀⡆⠀⠽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠠⠑⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢈⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠂⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⡠⢲⠂
⠀⠀⠀⠀⠀⠀⠀⡦⢄⡀⠀⠀⠀⡔⠈⠲⠒⠘⢆⢸⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠐⢤⠚⠀⠸⠉⡀⢀⠘⢞⠒⢊⠉⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠈⣦⠀⢄⠀⠠⠜⠀⢀⡄⠁⠘⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡤⠊⠁⠐⢄⣀⠤⢀⠠⡖⠃⠈⢀⡈⠁⡔⠉⣙⠁⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠑⠠⣀⠀⠂⠄⠐⠠⠀⠈⠂⢒⠢⠤⠐⡅⢈⠀⠃⡀⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠐⡞⠀⠀⠀⠱⣀⠀⡀⠂⠀⠃⡀⠈⠐⢃⠐⡀⠐⠄⠉⠁⢴⠁⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⣄⢀⡇⡇⠀⠠⠀⠄⡀⠁⢀⠄⠀⠂⠈⠒⠒⠂⠔⠁⠀⠀⢀⡉⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⠉⠀⠇⠈⠠⢀⠀⠰⣂⣤⠐⠂⠀⠀⠐⠂⠄⣸⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠢⡈⠖⠄⠰⣀⠔⠈⣴⠁⠀⠀⠀⠀⠀⠀⣀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⡥⠀⠦⠊⠀⡀⠀⠙⠓⠉⠀⠀⠀⠀⣀⠌⠃⠀⠀⠀⠀⠀⠀⢀⡠⢋⡀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣰⡠⠋⠀⠀⣏⣈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡇⡠⠔⠆⠀⣠⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⢱⡤⠤⠤⠄⠐⠒⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠉⠀⠀⠸⡔⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⢄⡀⢄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⠑⠄⠂⠂⠀⢀⢀⡀⠀⠀⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢤⠇⠀⢀⣀⠀⠀⠀⠀⠙⠉⠈⠓⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠉⠁⠀⠙⠂⠒⠉⠑⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢡⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⠂⢄⠀⠀⢀⡀⠀⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠁⠀⠀⠈⠉⠀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⡆⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠑⠄⠂⠐⠀⠒⠢⠀⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡇⠀⡇⠀⠀⠀⢸⠀⠀⠀⡠⠔⠒⠂⠀⠀⠀⢡⡀⢀⣀⡀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⡇⠀⠀⠀⡆⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠈⠒⠊⠈⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠀⡇⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠒⠄⠤⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠀⡇⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢈⣤⠇⠀⠀⡎⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠚⠤⢀⣀⠠⠧⠬⠄⠀⠀⠀⠀⠀⠤⠤⠔⠚⠐⠒⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⡀⢀⣀⣀⢀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠉⠙⠶⠀⠀⠀⠀⢀⣀⡀⣀⠀⠀⢀⠨⣿⡀⠀⣰⠈⠁⣠⣁⣴⠂⠀⠀⠀⠀⠐⠎⠀⠀⠙⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠂⠀⠀⠂⢘⣿⣿⣀⣡⣸⣌⣦⡈⠻⣶⣿⣄⠀⢹⣧⣿⡷⠔⢋⡠⠀⣠⡆⣀⣤⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⡀⠁⠀⠀⠀⠀⠠⠛⢀⣩⣥⣾⠙⢿⡇⠀⡟⢹⣿⣷⠈⠓⢈⣲⣶⠋⠀⣸⡿⣿⣿⣿⠟⠒⠛⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⢱⣦⣤⣟⠀⢲⣄⠀⠀⠀⠀⠀⢀⣤⠩⠔⠛⠀⢸⡅⠘⢻⣿⣷⣶⣮⣿⣷⡒⠀⣿⣶⡟⣯⣹⣄⠲⡶⢋⡤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠐⠾⣿⡄⢸⡏⠘⠛⣿⣷⠖⠋⠉⠀⠀⣠⣶⣿⣽⡗⠀⠌⠣⠙⠈⠛⠿⠟⠀⢘⣧⣧⡘⢿⡻⢿⣷⢴⡶⠇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠲⣦⡤⠀⠠⣤⣤⣼⠟⢃⡼⠁⠀⠀⠈⠉⠀⠀⠀⠀⠈⠉⠀⢹⣿⠇⠀⠀⠀⠀⠠⢤⣠⣤⠖⠡⣿⣿⠉⢦⢳⠎⠛⠋⠀⠀⣠⡾⢿
⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⣸⣾⣯⡍⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣤⣼⡿⠖⠒⠀⢩⠟⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣿⠿⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣶⣶⡾⢀⡤⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢦⢎⣿⣴⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⣄⠀⣀⡀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣵⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣷⠀⣠⠀⢸⣿⠀⠀⣿⠺⣿⣿⣿⣿⣿⣿⣧⡤⠀⠀⠀⠈⠇⠈⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣀⣠⣾⣿⣿⣿⣿⣿⣽⣿⣿⣧⡴⠛⠃⣼⣿⡆⠀⠙⣦⣿⣿⣫⣿⢙⣿⣿⣿⣷⣦⣀⠤⠄⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣉⠀⠈⠿⢿⣿⣿⣿⣿⣿⣄⣤⣾⠿⠿⣿⣤⣀⣿⣿⠿⠿⣿⡿⠟⠁⠐⠛⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣷⣶⣦⣀⠀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠙⣿⣿⣿⣤⡀⢀⢀⣰⣶⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤
⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣟⣥⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠴⢤⡀⠛⡁
⠀⠀⠀⠀⠀⢈⡽⠶⠂⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠈⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠏
⠀⠀⠀⠀⢐⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⣀⠀⠀⠀⠿⠀⠀⠀⠀⣠⣤⣴⣦⣤⡀⠀⠀⠀⠸⣏⠀⠀⣀⠴⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⣨⣽⣟⡁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠈⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠛⢿⣿⣿⠟⠁⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣄⣌⠋⢠⣤⣤⣤⣤⣽⣧⣤⣤⣤⣴⢆⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⠂⠈⢹⠟⠦⢤⡤⠶⠛⠋⠡⠨⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠓⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢳⣤⣤⣦⡴⢾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣟⠋⠉⠉⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⢠⣦⢄⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠁⡼⢳⡀⠸⣧⣶⣤⣼⢿⡿⠖⢛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡯⠧⠊⠀⠈⡇⠀⠰⠄⠀⠈⠘⣿⣻⣽⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣻⣇⡀⠀⠀⠀⣐⠂⠀⠀⠀⠘⢢⡀⢸⠟⠉⠉⠋⢤⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣌⠁⠀⣀⠈⢹⡇⠐⠀⠀⠀⢸⣇⢁⠀⠀⠀⠀⢸⡿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣼⣿⣿⣿⣷⣿⡏⠀⢸⣇⣶⠀⠀⣀⠰⣿⣧⣦⡇⠀⠀⢸⠇⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⢹⣿⣿⣿⡇⠀⣾⣿⠛⠈⢢⣿⡟⣹⣿⣿⠀⠀⣰⣿⣦⣤⣾⣤⢀
⠀⠀⠀⠀⠀⠀⠀⢰⢡⠐⣿⣿⣿⡁⢸⣿⣿⣿⡇⢀⣿⣿⠂⢠⡧⠟⢠⣿⣿⡇⠀⣸⣿⣿⣿⠋⠀⠘⣧⠀⣄
⠀⠀⠀⠀⠀⠀⡀⠘⠛⠋⠀⢿⣿⡇⢸⣿⣿⣿⡗⣸⣿⢏⣴⣿⡟⢠⣿⣿⣿⠁⢠⣿⣿⣿⣷⡟⠀⣰⣿⣷⣏⡉
⠀⠀⠀⠀⠐⡚⠁⠘⢻⠀⡀⢸⣿⠇⢸⠿⠿⢿⡇⣿⣿⣿⣷⡿⢠⡿⡹⣿⡏⢀⣿⣿⣿⣿⡿⣡⣾⣿⣷⢖⠢⠹⢉
⠀⠀⠀⠀⠸⠗⡆⢀⠀⠺⠐⠛⢦⠤⠀⠀⠀⢸⣅⡸⠛⣹⣤⠴⠟⠲⠟⠻⠁⡌⠉⠉⣉⠿⣿⠟⠻⣿⢿⣿⣷⡄⢸⡆
⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠳⠴⠃⠀⠀⠘⠒⠀⠀⠀⠀⠀⣠⡽⣁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⠀⢀⡴⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⢸⣦⣏⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣥⣤⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣫⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡿⠋⠉⠀⠀⠉⠙⠻⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠉⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡴⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣼⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⣻⡎⣿⣿⣿⣿⣿⣸⠁⠀⠀⠀⠀⠀⢢⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣽⣿⣿⣌⢿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣆⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣷⣝⢿⣿⣿⣿⣦⡀⡀⣰⣿⡿⢁⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣿⣿⣎⢻⣿⣿⣿⠙⣿⣿⡿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⠿⢿⣿⡿⠿⣟⣈⣯⣿⣿⣾⣿⣿⣿⣷⡝⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢧⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠉⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣄⡀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠛⢿⣦⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⠙⢹⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⢀⣾⣿⣿⡇⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡇⠀⠀⢀⢊⣿⡿⠟⢃⣾⠃⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⣩⣍⠙⠛⠶⠦⢤⡀⠀⠀⣠⠞⠉⠀⢹⡀⠀⣼⣿⠟⠛⢠⣿⣿⣶⡇⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⣷⣄⠘⢷⠶⢬⣷⣄⠋⠀⠀⠀⠀⣧⠀⢟⠀⠀⠀⢸⡿⣿⣿⣷⠀⢹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⢿⣷⣄⣳⣄⠀⢉⡿⡿⠷⣶⣶⣿⠀⢰⣀⣄⣀⣿⡇⠸⠛⢟⢧⣼⡿⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠉⠛⠿⠿⠛⠂⠉⠙⠲⢾⡸⠿⣦⠘⢿⣽⣿⣿⠀⠀⠀⢸⡆⢻⡇⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡆⢀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠈⡇⠀⠈⢻⣿⣆⠀⠀⠀⠈⢸⣿⠂⠛⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⢿⡔⠀⠀⣤⠃⠀⠀⣀⠀⠀⠀⠀⠀⢸⠃⠀⣀⠀⠀⠘⠿⣿⣦⣀⡄⠀⢸⣿⣷⡾⣼⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⣤⣾⢿⣣⡵⢀⣠⣄⣴⣏⠀⣀⡤⠘⠛⠛⠒⠿⣦⠈⠆⠀⠻⠀⠀⠀⠀⠈⣿⠻⣿⣿⣾⠟⠉⢈⣼⣿⠇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⢉⣽⣟⣡⣶⠟⠻⢿⡿⢿⠷⠶⠆⠀⠀⠀⠀⠀⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⣸⣼⣿⣿⣁⣠⣶⡿⢛⡿⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⣽⠁⢠⣶⣽⣾⡏⣀⣤⠄⠐⢦⡀⠀⠀⠀⠀⠀⢸⣦⣤⡄⠀⠀⠀⣼⣿⣿⠟⠁⠀⠋⠀⣼⣷⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠞⡏⣜⠀⣿⣦⠞⣿⣿⠟⢋⣀⠀⠀⢐⠦⣝⣶⣾⣄⠀⠀⢈⣿⣿⠿⠀⠀⠀⡿⠙⠁⠀⢀⣀⣴⣾⡷⢿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢈⣿⣿⡿⢻⣿⣾⣟⣩⣾⣿⣷⣾⣾⡿⠀⠈⣿⣿⡍⢳⣶⠾⠏⠀⠀⠀⠀⣰⣷⣖⣀⣠⣿⠿⠛⠉⠀⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣾⡟⢻⣿⣼⡟⣿⣿⣿⠟⢉⣽⠿⡏⠀⠲⠀⠃⣽⣧⡀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠛⣻⡿⠟⢀⣴⢃⡼⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣧⠉⠀⠙⣧⡀⠸⣟⣡⣠⣼⠏⠀⠹⣦⣀⣤⢀⢻⣤⡀⠀⠀⠀⢀⣾⣿⡟⠀⠀⠘⠁⠀⣰⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣤⣸⡄⠙⣼⣿⣿⠟⣻⠀⠀⠀⣿⢻⣿⣾⣧⣙⡻⣄⣀⡀⠈⣼⣿⣷⠧⠀⠀⠀⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⢦⣹⢿⣿⣶⣿⣆⢸⡆⣷⣆⣿⡏⠙⠻⡶⣾⠿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣷⢹⣿⠿⣇⠹⣷⡟⣿⣷⠀⠀⣾⡄⢘⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢇⠙⠄⢸⠀⢿⣦⣽⣧⠛⣿⣧⠀⠀⠁⢸⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣼⡟⠀⠈⠿⣿⣿⠆⠛⢿⡇⡶⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⣷⢾⠇⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢀⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⣀⡠⠤⠲⢸⣷⡆⠐⠒⠃⣿⣦⢄⣀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⡠⠦⠹⠇⢧⠀⠄⣾⠁⢷⡀⣠⡬⠋⡏⠀⠈⢙⣴⣏⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⣶⣟⣄⠀⠐⣧⡈⢿⠘⠹⡄⢸⠀⢹⡇⢸⠇⡠⡶⠒⣹⠋⠙⢦⡀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⠋⠈⢸⡄⠙⠄⢃⣳⠼⠒⠋⠉⠉⠉⠙⠓⠳⢤⣸⠃⣴⠅⢀⡀⢀⣵⣟
⠀⠀⠀⠀⠀⠀⠀⠘⠶⠶⠶⢶⣷⡦⢤⡌⢏⢲⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣁⢪⡝⠋⣩⠟⠉⢦⡀⢀⡤⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠀⢷⢤⣈⡰⠋⡀⠔⠒⠒⠲⣶⡀⠀⠀⣰⡶⠖⠒⠒⠄⡈⢫⠐⡉⢥⣀⡀⣨⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⣤⣄⣢⣑⣸⠃⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⠚⢉⣠⡽⠟⢻
⠀⠀⠀⠀⠀⠐⠒⠚⠉⢉⠋⢳⣤⣠⣬⡇⠀⢴⣄⡀⠀⣀⣠⠀⠀⠀⠀⠀⢠⣀⡀⠀⣠⣴⠄⠸⡍⢠⣤⣄⠀⠈⠇⢀⡤⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⠉⣀⣈⣧⠀⠈⠜⡝⢟⠿⠋⠁⠀⠀⠀⠀⠉⢏⢿⠟⠟⠂⠀⣰⣟⣭⣁⣉⣵⡿⡟⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣞⡋⢉⣁⣿⠑⠀⠀⠀⠀⠀⠀⠀⠠⠄⠤⠀⠀⠀⠀⠀⠀⠀⠈⢹⣄⣠⢍⠢⡀⢠⠇
⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⢬⠀⠙⠛⠂⣈⣧⠀⡀⠀⠀⠀⠀⡀⣠⣀⣠⡀⡀⠀⠀⠀⢀⠀⢰⠯⢍⣉⠙⢣⣠⣘⣂⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣠⠞⠉⣠⠞⢦⡀⠀⠀⠀⠀⠈⠀⠈⠁⠈⠀⠀⠀⠀⠀⣠⠯⣄⣢⠉⠉⠛⢻⠋⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢛⣓⣡⡴⢙⢦⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⠎⠑⢦⣄⠙⣇⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠈⠣⣀⡴⢋⣠⣋⠄⡘⢹⢺⠓⢦⠤⠴⠞⢓⡚⠡⡈⠳⣔⢠⠈⠑⢟⠷⠦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⡿⢉⠉⠀⡾⢀⣾⠌⡸⠈⣇⡆⣷⠈⢧⡇⠽⣆⣿⠀⣀⠔⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠉⠑⠺⣷⠍⡁⠈⣿⡰⠟⠀⠘⡆⣾⢀⢀⡨⠿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠋⠀⠀⠀⠀⢿⠀⠉⠛⠻⣿⠰⠒⠒⠛⢿⡌⠁⠀⠀⠀⠈⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣍⣍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⠀⣿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢒⣩⣿⣿⠀⠹⢦⡉⠛⠢⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⢤⣳⡿⢟⢿⡃⠀⣓⠀⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢊⣴⠟⠉⠼⠫⢋⠀⠀⡹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣶⠏⠀⠀⣠⢦⣷⣿⡄⢸⡷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠁⠀⠀⢠⣽⣿⣿⢨⡀⠈⡁⢿⣿⣷⣤⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠘⠁⠉⢛⢿⡇⠀⣽⠛⠋⠻⣆⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠠⠞⠊⠳⡄⠁⠿⡀⠨⡤⠀⠘⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠂⠠⠀⡏⠀⡄⠃⠀⢁⣤⡙⢈⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⠶⠞⠀⠀⠁⠀⣄⠀⠐⠋⢩⡔⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠍⠢⠝⠂⣿⠀⢼⡛⣾⡑⣿⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣄⣀⣀⠠⣛⡄⠈⣡⣤⡤⠤⣤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣴⣦⣭⣷⡟⣻⠀⠉⠰⣾⣶⣦⣈⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠙⠀⣸⠟⠀⢺⣦⣭⣙⣋⣈⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣴⣯⣞⠀⠘⢟⡋⠉⠉⠛⢻⣿⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣽⣖⣻⡅⠀⠌⢁⣴⠾⠛⠛⠳⣝⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠛⢉⣿⠃⠘⠂⣾⠁⣴⠳⠒⠀⢸⢻⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣴⣿⠀⠜⣃⠻⡀⢿⣹⠦⣤⢞⣿⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡽⢀⡼⢹⣿⣌⡄⠙⠛⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⢄⡀⠉⠀⢈⣷⣜⠻⢿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣴⣦⠤⠂⠁⠀⠻⣿⣷⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣩⣥⣤⣶⠟⣤⡀⢷⣄⠉⠉⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣩⠟⢂⠉⢻⣾⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢿⠀⣿⡀⢈⡇⢸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠿⣷⠈⣽⣟⣠⢿⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠿⢶⡖⢻⣿⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠦⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂


⣿⣿⣿⡿⠿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⡗⣻⣿⣿⣿⠢⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢶⣾⣾⡿⠞⠛⠿⣿⢿⣿⣿⣨⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⣻⠏⠀⠀⠀⣀⠀⠀⠈⠻⣿⠿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣠⣼⣽⡆⠀⠀⣠⣹⠃⠀⠀⣠⣿⣗⡲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣸⣽⣿⣧⡀⠁⠀⠡⣀⠀⠀⡸⠛⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠏⠷⣿⣿⢷⣶⣾⣤⣿⣯⣴⣾⣟⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠺⠙⢟⠞⢻⠯⣿⡯⠛⠟⡻⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠠⠧⠲⠿⠞⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢤⣀⠀⣼⡷⢀⡄⠀⣦⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⢤⣤⣄⡀⠲⠂⠀⢠⠛⠋⡄⠀⠀⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠘⢿⡆⠛⢳⡿⠃⠀⢻⣿⣦⣤⣤⣶⣿⠃⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⢈⣴⣯⡄⠀⠀⠀⠀⣿⣿⣿⣿⡿
⠀⠀⠀⢠⠞⢉⠓⢦⠀⠀⠀⠙⠻⢿⠿⠟⠁⠀⠀⠀⠘⠁⢠⣿⣿⠇⠀⠀⢐⣿⣻⡂⠀⠠⣤⣤⣾⣿⣿⣿⣷⣦⣤⠄
⠀⠀⠀⢏⠰⢀⠰⢈⠇⠀⠀⠀⠄⠂⠀⠂⠀⠀⠀⠀⠀⠠⠾⡟⢫⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠈⠳⠤⠖⠋⠀⠀⠀⠀⡍⠀⠂⠘⠀⠀⢰⣷⠀⠀⠂⡂⡃⠀⠀⠘⠃⠀⠀⣿⠀⠀⠀⠀⠈⠹⠟⠟⠁
⠀⠀⠀⢴⡄⣀⡀⣤⡄⠀⠀⠀⠀⠀⠀⠨⠀⠀⠘⠋⠀⠀⠀⠃⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⢀⣤⣤⣀⡀⠀⢀⢠⣶⡄
⠀⠀⠀⠈⠀⠙⠃⠈⠀⠀⢤⣤⡄⠀⠀⠀⡀⡄⣄⢠⢄⠀⢠⡤⠀⠀⡄⣠⢤⣀⠀⡀⠀⢴⣿⣿⣿⡟⠃⠀⣸⣇⡉
⠀⠀⠀⠀⢀⣤⣶⣦⣄⠀⠀⠉⠀⠀⢳⣿⡇⢧⢻⢸⡮⠀⢸⣳⡀⢰⡇⡿⡇⡟⢸⠃⠀⠀⠀⠉⠁⠀⠀⠀⠙⠊⠉
⠀⠀⠀⢰⣿⡿⠿⢿⣿⣇⠀⣠⣦⡀⠈⠃⢁⡈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠀⢀⡀⣀⠀⣀⠀⣀⠀⣀⠀⡀
⠀⠀⢀⣼⣿⡇⠀⠈⣿⣿⣀⠈⠛⠁⣠⣶⣿⣿⣿⣷⡄⠀⠀⠁⠀⠛⠀⠐⠇⠀⠼⠆⠀⠈⠀⠈⠀⠈⠀⠀⠀⠁⠀⠁
⠀⠰⢿⣿⣿⣿⠁⣼⣿⣿⣿⠄⠀⠀⠘⡛⠛⡛⢛⢻⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠀⣄⠀⢤⠀⢠⠀⢠⡀
⠀⠀⠠⠍⠠⠅⠀⠈⡅⡉⠄⠀⠀⠀⠀⢁⡅⠆⢀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠇⠀⣨⡄⠀⢄⢁⢄⢁⢄⢉⠤⠈⠤⡈
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠁⠠⠁⠀⠁⠤⠉⠀⠈⠄
⠀⠀⢘⣴⡀⣄⠀⣀⡀⣀⠀⡲⠧⠀⠀⣰⣿⣿⠿⢿⣿⣧⠀⠀⠀⠀⠐⣤⣥⡔⠀⠀⠀⠠⠂⠔⠀⠠⠂⠔⠀⠠⠂⠄
⠀⠀⠀⠻⢿⣈⣿⣿⣿⣏⠺⠿⠀⠀⢠⣿⣿⣧⡀⢀⣿⣿⣄⠀⠀⠀⢁⠻⠿⢃⠁⠀⠀⢠⡄⢠⡄⢠⡄⢠⡄⢤⠄⣤
⠀⠀⠀⠀⠈⠁⠙⠛⠋⠉⠃⠀⠀⠀⠈⠙⠛⠋⠀⠛⠛⠛⠛⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⡲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⡍⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡆⠱⡀⠙⠷⠒⠒⠒⠒⠒⠚⢁⡔⠁⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣀⠀⠀⠀⠀⢹⢇⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠀⠀⠈⠳⣦⡤⠴⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⢸⣆⠀⠀⠘⣖⣄⠀⠀⠀⠀⢠⣾⠞⠀⠀⢸⡃
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠽⣄⠀⠀⠘⠯⡆⠀⠀⠀⡏⠁⠀⢀⣠⣾⠁
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠒⠤⡀⠀⠰⠀⠀⠀⠀⢀⠜⠉⠀⢸⠀⠀⢀⣠⢴⡆
⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡀⢀⣀⡠⠤⠤⠬⠧⡀⢠⠤⣤⠀⡞⠋⠉⠛⢛⡿⠉⠉⠀⡾
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡯⠞⠉⠁⠀⠀⠀⠀⠀⠀⠙⢬⣵⠥⠞⠀⠀⠀⠐⠛⡸⠃⠀⣸⠁
⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠳⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢣⠏⡴⠁
⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠦⠤⢤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠖⠒⠚⠋⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡄⠀⠀⠀⠀⠀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠁⠀⠀⠀⠀⠐⢺⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢶⣴⠀⠀⡀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠘⠀⠈⠙⠛⠁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣄⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⠄⢿⠆⣠⠞⠁⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠆⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡟⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠟⠃⠀⠀⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⡷⡀⣤⠀⠀⠀⢠⣶⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠙⠿⣷⡀⢠⠟⠁⠀⠁⠀⣀⡄⠀⠀⠀⠀⠀⠀⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣦⠀⠘⢳⡏⠀⠀⢠⡄⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠰⣿⣿⣆⠈⠀⠀⢰⣿⣧⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠙⠿⡻⠒⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡎⠀⠀⠀⢿⡦⠀⠀⢶⠾⢶⠀⢸⣿⡿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠺⣧⠀⢰⣶⣾⠀⣴⣶⡆⢠⣦⣤⡀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⣿⠀⣿⣿⠁⠀⠉⠻⠿⣶⠤⠀⢀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣠⣦⡀⢴⣀⡎⠀⢀⣿⣿⣦⣿⣿⣆⠀⣴⣿⣷⣶⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⣦⠛⠈⠛⠀⠙⢇⠀⢺⣿⣿⡿⣿⣿⡿⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢿⠀⠀⠀⠀⠀⠈⠣⡀⠀⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⣀⣀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠦⣤⣄⣠⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻

⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠔⠒⢆
⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⢠⡉⢟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⠎⣡⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⢧⡀⠷⠙⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡟⠱⠆⣪⠏⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠀⡀⢨⡑⠠⡈⢎⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠎⡠⠐⣈⠀⡀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⡤⢨⡄⠀⠀⠹⡂⢯⡔⠚⠆⢂⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢠⠊⠞⠒⣬⠇⡺⠁⠀⠀⣬⢠⡄
⠀⠀⠀⠀⠀⠀⠠⡄⠁⠀⠀⢳⢌⠂⢄⠀⠀⠀⢢⡀⠈⡶⢒⠾⠭⣉⠲⢊⠩⠽⢖⠲⡎⠀⢀⠃⠀⠀⢀⠤⢊⣴⠃⠀⠀⠁⡴
⠀⠀⠀⠀⠀⠀⢠⠽⡄⠀⠀⠀⣑⣌⠁⠚⠓⠂⠀⢢⡘⠑⡌⢦⡀⢸⠀⢸⠀⣠⠎⡴⠑⣀⠂⠀⠒⠛⠋⢉⢔⡁⠀⠀⠀⡼⢥
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⣧⡉⠛⠖⠀⢠⠔⠘⠓⠢⣘⡄⠱⠎⣠⡈⠶⠁⣜⡠⠒⠛⠐⢄⠀⠐⠞⠋⣡⣡⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⡈⢀⠙⣠⡆⢀⣥⢚⠉⠒⢄⠈⠃⢀⠞⢀⠙⢂⠀⠋⢀⠔⠁⢙⢢⣅⠀⣦⡘⢁⠈⡄⠀⠀⣴⠁
⠀⠀⠀⠀⠀⠀⠀⢈⣇⡝⢀⣦⠋⣰⠁⠖⢩⡔⠋⠁⢠⡌⠂⢀⠂⢠⠋⢣⠀⢣⠀⠂⣤⠀⠉⠛⣬⠑⠆⢱⡘⢣⣇⠜⡅⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠊⣿⠀⠁⢀⠤⠤⣈⢱⠄⠀⡈⠁⠈⠀⡇⠀⠀⡇⠈⠀⠉⠀⠀⣴⢉⡠⠤⢄⠀⠁⢸⣏⠒⢠⠁
⠀⠀⠀⠀⣠⡖⠯⠉⠯⠻⡦⣘⣧⠀⢢⡀⠀⠈⠋⠀⢀⣑⡀⢠⠀⢃⠀⢀⠃⢰⠀⣔⣀⠀⠈⠋⠀⠀⣠⠂⢠⣟⣤⡷⠫⠏⠩⠗⣦⡀
⠀⠀⠀⠀⠀⢈⢭⠚⢶⢺⡶⠋⠉⠀⢀⡀⠉⢐⣢⣀⠀⠩⣉⠀⢆⠀⠢⠂⢀⠆⢈⡵⠁⢀⣠⣒⠈⠁⣀⠀⠈⠉⠲⡾⢲⠟⢪⢍
⠀⠀⠀⠀⢰⣃⣄⣘⠖⢛⠓⠋⣠⠄⡈⡙⢦⡤⠠⣌⠛⢦⡈⠳⡄⠣⣀⡠⠃⡴⠋⣠⠞⢫⡤⢠⣤⠞⡉⡠⢤⡈⠛⣛⠃⢞⣀⡄⣲
⠀⠀⠀⠀⠈⠁⢈⡍⠀⠟⡚⢰⡁⠀⠈⠳⡈⠇⢀⠀⢀⡄⢳⡄⠈⡄⠈⠀⡌⠀⢰⠋⣄⠀⢀⠀⠏⣰⠋⠀⠀⣱⠘⡟⠃⠈⣅⠀⠉
⠀⠀⠀⠀⢠⠤⠎⠀⠀⢰⠀⠀⠻⡂⣤⡀⠈⠓⠬⢃⣉⡑⣤⠘⡄⢡⠀⢠⠁⡘⢠⡔⣋⣁⠩⠄⠊⠀⣠⡄⡺⠃⠀⢰⠀⠀⠈⠦⢤
⠀⠀⠀⠀⠀⣱⡄⠀⠀⠸⣠⢦⠀⣘⠇⠴⣋⡰⠂⢤⣀⠀⠈⠀⢡⢸⠀⢸⢀⠀⢈⠀⢀⣠⠄⠲⣈⡱⠄⢟⡁⢀⢦⡸⠀⠀⠀⣴⡁
⠀⠀⠀⠀⠀⢑⣄⡀⠀⠀⠛⡸⠀⠘⡛⢄⠀⠉⠒⢅⣠⠏⠻⠀⠈⢸⠀⢸⠈⠀⠸⠋⢥⣀⠕⠊⠁⢀⡜⡛⠀⠸⡘⠃⠀⠀⣀⣔⠁
⠀⠀⠀⠀⠀⠈⢥⠀⠀⡦⣓⠶⠀⡀⠇⠈⠳⢦⡀⠀⠙⣄⠃⠀⠀⣾⠀⢸⡆⠀⠀⢣⡜⠁⠀⣠⠶⠋⠀⡇⡀⠰⣔⡣⡆⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣴⣤⣄⠊⡙⣀⢀⠀⠀⠙⢦⠀⡍⠀⠀⢀⡇⠀⠀⣇⠀⠀⠈⠅⢠⠞⠁⠀⣀⣀⠘⠙⢂⣤⣤⣥⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢄⡉⠁⠄⣌⠉⠉⠀⠀⡈⠘⢿⠀⠀⠀⠎⠁⠀⠀⠉⠆⠀⠀⢸⠟⠈⡀⣀⠉⠉⣀⡠⠄⠉⡉⠼⡆
⠀⠀⠀⠀⠀⠀⠀⠐⠇⢂⢈⡕⠆⠀⠈⠳⠏⠰⣁⠴⠔⣆⠀⠀⢦⣀⡄⣄⣠⠆⠀⢀⡖⠴⢤⡱⠈⡷⠋⠀⠀⠖⣍⠀⠃⠗
⠀⠀⠀⠀⠀⠀⠀⢐⠳⠈⢄⡯⡱⢶⣶⠀⠀⣀⣉⠀⠀⠈⠳⢤⣀⣉⡴⣈⣁⣠⠴⠋⠀⠀⠈⣁⠀⠀⢰⣶⠶⡩⣇⠌⠰⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣑⣤⣈⠁⠈⠢⢄⢠⣄⠮⠥⠀⣑⠠⠤⠄⢉⠒⠒⠒⣈⡡⠤⠤⢐⡁⠠⠭⢆⣤⣀⠤⠊⠀⠉⣠⣔⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣢⣤⣤⣤⢤⣄⠈⠀⠑⠒⢒⣨⠅⠀⡀⠤⢸⠷⢶⠠⢄⡀⠀⢭⣐⠐⠒⠁⠈⢀⣤⣤⣤⣤⣤⣊
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢠⡷⢾⣹⡏⢠⡄⠔⣱⣋⠁⠀⡞⠀⡔⠁⣠⡀⠑⡄⠘⡆⠀⢉⣳⡑⠀⢤⠈⣿⣿⠶⣦⡘⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣤⢘⡴⢣⣷⡇⠘⠋⡡⢁⠚⢠⣇⠸⠀⡰⠀⠱⡀⠸⢀⣧⠜⢂⠡⡉⠛⠀⣿⣧⠳⣜⢠⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⢹⢓⢢⡇⠀⠲⢈⡀⠈⠀⠀⢈⡇⢀⠁⠀⠀⢃⠀⣇⠀⠀⠀⠀⣈⠴⠂⠠⣧⢒⢻⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⠏⠰⠀⠠⠊⠀⠀⠀⡔⠉⠀⠘⡀⠀⠀⡘⠀⠈⠑⣄⠠⠀⠈⠢⠀⠴⠈⠿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣤⣤⣤⡄⢀⡸⣆⠀⠀⠀⠈⠉⠉⠀⠈⠀⢀⡾⣀⢀⣤⣤⣤⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠝⣫⡽⢿⣿⠈⢇⠉⠉⠉⡇⠀⠀⠀⠀⡏⠉⠉⢁⠏⢸⣿⠻⣭⡛⠱⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⣎⡙⢰⡖⣛⣄⠑⠢⣄⠑⠌⠀⠈⠔⢁⡤⠖⢁⣜⡓⣷⠘⣉⡎⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡴⠋⢲⡉⠽⡗⠀⣈⠑⢤⡀⣠⠖⢁⡠⠀⣿⠍⣱⠊⠳⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣿⠀⠈⠙⠤⣹⡡⠒⠉⠀⢸⠧⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⡆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⠻⣿⣿⣿⡿⠿⣿⡿⣿⣿⠟⠋⣿⠛⠁⠈⠀⠛⣿⣿⣽⣿⣙⣉⣿⣿⣿⣿⣯⢟⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⡇⡇⢹⡫⣾⣷⠴⣾⣧⠈⠙⢀⣴⠃⠀⠀⠀⠀⢀⠘⣿⡏⣸⡟⢻⢩⡤⠹⠿⡏⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⠿⢷⠋⠀⣸⣯⠖⢸⣿⣼⠛⠊⡀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠛⠀⠘⠈⠁⠐⠰⣧⣽⠋⠀⠈⡿⠋⢹⣿⣿⡇
⠀⠀⣿⣿⣿⡿⠀⠀⣿⠉⠀⠒⠇⣻⡆⠐⠛⠀⠀⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⢶⣤⣶⠁⣠⣿⣿⣿⡇
⠀⠀⣿⣿⠿⠃⡀⠀⣠⠀⡶⠀⠆⠀⠀⠉⠀⠀⠀⣿⠄⣷⣄⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⠀⣀⣹⣿⣿⠿⣿⣿⣿⡇
⠀⠀⣿⣿⡁⠀⠀⠀⠀⢠⣍⠀⠀⠐⠆⠀⠀⢀⣴⡿⣾⣏⣿⣆⠀⠀⠀⠀⠀⠀⠘⢧⡀⣼⣓⣿⣿⣏⢉⣦⠘⣿⣿⡇
⠀⠀⣿⣿⡝⠁⠀⣀⣢⣿⠟⠁⠁⠀⠀⠀⢀⣾⣶⣤⣿⣿⣿⣿⣦⠀⠀⠀⢰⠀⡀⠀⣴⡰⣿⣏⡻⢿⣿⣿⣿⣹⣿⡇
⠀⠀⣿⣿⣷⣿⣾⣿⣿⡿⠃⠀⠀⠀⠠⠶⡿⠛⠛⠛⠛⠻⣿⡏⠉⢇⠀⠀⠀⠀⣐⠳⣶⣄⠿⢿⣿⣶⣾⡿⠿⢻⣼⡇
⠀⠀⣿⣿⣿⣿⡿⠫⠑⡀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⣷⠀⠀⡄⣆⠻⣀⡾⠙⠛⢋⡶⣄⣉⡍⠙⢷⣶⣼⣿⡇
⠀⠀⣿⣿⣿⣿⣿⠀⠀⠑⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣧⠈⢰⣿⡗⠀⠀⡼⠋⠁⠈⢡⡀⢠⡉⣧⡜⠇
⠀⠀⣿⣿⣿⣿⡟⠀⠀⠈⠰⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠘⣷⣟⠻⣠⠐⢀⠀⠀⠈⠀⠈⠻⠿⠟⠛⠛⡇
⠀⠀⣿⣿⣿⡷⠀⠀⢢⠀⠀⠀⠀⠀⠀⠠⣷⢀⣠⠀⠀⠀⣇⢀⣀⣰⣿⠟⡽⠟⢻⣬⠀⣠⠄⡀⠀⠠⠄⢀⢠⣴⠆⠉
⠀⠀⣿⣿⣿⣿⣦⣤⣶⡀⠀⠓⢢⡦⣠⠀⢿⣾⠟⠀⠀⠀⢸⣿⣿⣿⣏⠻⢿⣠⣿⣻⣿⠀⠐⢦⠀⠀⢸⠆⢈⣍⣵⡇
⠀⠀⣿⣿⠇⣀⡄⠸⣿⣷⡀⠒⢀⡼⠃⠂⠀⠀⠄⠀⣰⣴⣾⣿⣿⣿⣿⣧⣾⣿⣿⢛⢿⣗⠀⠀⠀⠀⡈⠴⣦⠹⣿⡇
⠀⠀⣿⣿⣤⣌⣤⠀⠉⠉⠻⠀⢺⣇⠀⠀⢰⣦⣤⣰⠋⠁⢸⣿⣿⣿⠋⠂⠀⣿⣿⣵⣿⣿⣧⠀⠀⢰⣷⣤⣶⣾⣿⡇
⠀⠀⣿⣿⣿⣿⡇⠴⠇⠀⠀⠀⠆⠈⢠⣄⣿⣿⣿⡿⣷⠀⠚⣿⣿⠟⢶⣶⣾⣿⡏⣼⣟⣋⠹⡈⢔⣨⡟⢹⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣧⣄⣀⢀⣴⣆⡀⠈⠛⠁⠈⠙⠉⠙⢇⠀⢀⣼⣿⣶⣶⣴⣿⣿⣿⣿⣿⠏⢀⡙⣮⠻⣧⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣅⢉⣀⣶⣾⣶⣄⠀⠄⠀⠀⠀⣹⣿⣟⣻⣿⣿⣿⡿⣌⡍⣡⡀⢀⠂⢈⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠩⠤⠴⢶⣦⠔⢹⡟⠉⠻⣿⣿⣉⣇⣜⠁⢬⣙⣯⣤⣟⣋⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⣠⣴⣿⣠⣿⣇⠀⠀⠘⣿⣿⣿⣧⣷⣮⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣦⣄⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠙⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡟⠁⢸⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡾⠹⠀⠀⢸⠀⠀⠀⠉⠙⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣠⠴⠛⠒⠃⠀⠀⢀⣾⡄⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢏⠉⠛⠩⢙⠲⠞⠁⠀⠀⠀⠀⠀⢠⠊⠀⢓⡆⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡠⠀⢨⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣲⡄⠒⠒⠂⠤⣀⠀⠀⠐⠈⠀⣰⠃⠀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡀⠀⠐⠋⠀⠉⠢⡀⣣⠀⡏⠀⢸⡁⠀⠀⠀⠀⠀⠀⡴⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠛⠛⠛⠲⠦⣤⣘⣛⡿⠁⠀⠀⢧⠀⠀⠀⣀⡤⠞⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢅⡀⠀⠀⠀⠀⠀⠘⣆⠉⠙⠒⠒⠒⠚⠓⠚⠉⠁⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠘⣖⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠦⠤⠤⠶⠒⠚⠉⠁




⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⣦⣄⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⠻⣿⣿⣶⡦⠃⠀⠀⠀⠀⠐⣶⣶⣶⣾⡿⣿⣿⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣯⣿⣿⣷⣋⢿⣿⣧⠀⠀⠀⠀⠀⠀⠨⣻⣿⣿⣴⣿⣿⡇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢿⣿⣿⣿⣿⣇⢉⣿⡏⠀⠀⠀⠀⠀⢠⣴⡟⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣏⣽⣿⣿⠟⠀⠀⣀⡀⠀⠀⢿⣿⣧⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⢿⡁⠀⠀⠘⢿⣿⣇⢀⣿⣿⣯⣭⣻⣿⣿⣇⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡍⣥⣴⣆⣀⡘⡿⢿⠟⢻⡿⢹⠟⢿⣿⣿⣿⠂⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣷⡿⠿⣿⡿⣿⠄⠜⠀⢨⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠞⢁⠀⠀⠀⠀⠀⠹⣟⢛⡁⠿⣿⣿⠏⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢬⣴⣿⣭⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⣘⡟⣡⣶⡏⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⢶⣿⣿⡁⡀⠀⠀⠀⠀⠀⠀⢱⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣶⣾⢿⣿⢿⢿⠿⠃⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣷⣤⣾⢶⣤⡄⢀⣤⣴⣿⣭⣿⠿⣿⣿⣿⠾⠟⠿⣿⣷⡽⠿⠿⣟⢾⡅⠛⡀⣀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⡾⣷⣶⣾⣿⣼⣅⣠⣷⣿⣷⠆
⠀⣀⣴⣀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠻⠿⠿⠿⠿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⢸
⣶⣿⣿⣿⣷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⠤⢤⡀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢠⠇⠀⠀⠈⠣⡀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠋⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡼⠀⠀⠀⠀⠀⠙⣆⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⣀⣠⠤⣄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠘⣆⠀⢳⡀⡀⠀⠀⠀⠀⢀⡤⠚⠁⣠⠖⠋⠁⠀⠀⠈⡇⠀⣸
⠀⠀⠀⠀⠀⠀⣤⣄⡀⡇⠀⡇⠀⠀⠀⠀⠀⠀⣀⣿⣀⣈⣻⡇⠀⠀⢰⠷⠎⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡇⠀⡟
⠀⠀⠀⠀⠀⢀⣙⣎⠙⠛⠀⢹⣄⠤⠖⠒⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠤⣴⡇⠀⠀⠀⠀⠀⠀⠀⣸⠃⢸⠃
⠀⠀⠀⠀⠀⠈⢹⡍⣀⠴⠚⢉⡠⠖⢚⡓⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⣠⠃⢀⠏
⠀⠀⠀⠀⠀⢀⡼⠋⠁⠀⣠⢋⠔⠋⢉⠉⠑⢦⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⠲⢬⡑⢦⡜⠁⢠⣞⣀⣀⡀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⣰⣡⠃⣴⣿⣿⠟⢷⡀⢣⢳⠀⠀⠀⠀⠀⠀⢀⡜⣡⠖⠉⠉⠙⢦⡙⣆⠙⢦⡈⢁⣤⠟⠁
⠀⢀⠞⠁⠀⠀⠀⠀⢠⣧⡇⣼⣿⣿⣧⣤⣄⣧⢸⡞⠀⠀⠀⠀⠀⢀⡎⡜⢁⣶⣿⣿⠷⣄⢹⡸⡄⠀⠙⣤⡜⠛
⣰⢃⣀⠀⠀⠀⠀⠀⢸⣿⣤⣿⠿⠿⠿⠿⣿⣿⢸⢷⠀⠀⠀⠀⠀⡼⡸⢠⣿⣿⣿⣁⣀⣸⡄⡇⣇⠀⠀⠈⢧
⠛⠁⡵⣾⡵⢮⣒⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⢏⠀⠀⠀⠀⠀⢷⣧⡼⠿⠿⠿⢿⣿⣿⠇⡷⣿⠀⠀⠀⠀⢣
⠀⠀⠀⠈⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⣤⣄⡔⠉⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⡇⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠰⡀⠘⢻⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣶⣳⣼⡷⣌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠈⠉⠉⠙⠦⠤⠴⠀⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉⠀⠀⠁⠈⣁⣈⣀⣀⣀⣤⣤⣤⣤⣤⠤⠒⠊⠁⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡳⠒⠠⠤⠤⣤⣤⣤⠤⠤⠤⠔⠒⠲⣍⠁⠀⠀⠀⠀⣠⠴⠚⠉⠉⠀⢀⣀⣠⠤⠔⠒⠉⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⣴⠛⠁⠀⣀⡤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣞⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢸⡄⠀⢠⠟⠀⠀⠀⣀⡤⢤⡀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⢀⣹⣄⡞⠀⠀⠀⣸⠁⢀⡞⠁⠀⠀⠀⠀⠀⠀⡯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⠁⠀⠀⢀⠟⠀⢸⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠉⠑⠒⠒⠒⠒⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣤⠴⠛⠒⠲⠦⣿⠀⠀⠀⢰⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢦⣄⡐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂⣀⡤
⠀⠀⠀⠀⠀⠀⠑⠄⠉⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠈⠀⠐⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⣶⠆
⠀⠀⠀⠀⠀⠀⣠⠼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⠂
⠀⠀⠀⢀⠔⠉⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠
⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠤⢀⡀⢀⠖⠀⠀⠀⠀⠠⠄⠤⠀⠂⠛⠤⠤⠰⠆⠪
⠀⢠⠁⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠠
⠀⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⡁⠀⠀⠀⠀⠀⠀⠀⠸
⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠞⠉⠉⠀⠀⠀⠀⠀⠀⢠
⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠁⠀⠀⠢⠀⠀⠀⠀⠀⠀⠈⠁⠤⡀⠀⠀⠀⠀⠀⠀⠐⠔⠃⠀⠄⠃⠀⠀⠀⠐⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠄⠀⠈⢢⡀⠀⠀⡴⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠘⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣤⣠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⡀⡀⠀⠀⠀⠸⡀⣠⡴⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⠿⠋

⠀⡀
⠀⣁⣈




⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢀⠔⣠⠆⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠢⡙⢦⠀⠀⠀⠀⠀⠀⡴⢋⠔⣡⠞⡡⠂⠀⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⠳⣌⢢⡑⢄⠀⠀⣠⠊⡰⢁⠔⡡⠊⡠⢺⠀⠑⢌⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⠑⣌⢢⡑⢌⠓⠚⡡⢊⡴⢡⠎⣠⢊⠔⢩⢀⡑⢄⠑⢌⠢⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡘⢮⡳⡈⠢⡙⢦⡁⢈⡴⢋⠔⢁⠞⡵⢋⠔⢹⢣⡙⠢⡑⢄⠑⢎⠢⡈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡗⢀⡑⢌⠢⡈⠢⡁⢈⠔⢁⠔⡡⠊⡠⢁⠔⢹⣷⠬⢦⡼⢦⡵⠤⡵⢬⡦⢼⠦⢤⡤⠤⠤⠤⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢢⡑⢄⠑⢌⢢⡀⢀⡴⣡⠊⡠⢊⡴⠃⠀⢸⣯⠖⡩⠔⢁⠔⡩⠔⡁⠔⣡⠖⠁⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠙⢦⡑⠌⠳⡍⢨⠞⠡⠊⡴⠋⠀⠀⠀⢸⣿⠋⡠⢚⡵⠊⡠⢊⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠑⢌⠣⡀⢀⠔⡡⠊⠀⠀⠀⠀⠀⢸⣿⣫⠖⢁⠔⣡⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣀⡀⠀⠀⣀⣀⣼⡇⠀⠀⠀⠀⠈⠳⣄⢠⠞⠁⠀⠀⠀⠀⠀⠀⢸⣿⡠⢊⡡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣀⠀⠀⢀⡀
⠀⠙⠉⠀⠉⠉⠙⠻⢇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣻⣴⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡟⠉⠀⠀⠀⠰⠂
⠀⠖⠂⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣴⣦
⠀⠶⠦⣄⣠⣀⡀⠀⠀⠀⢀⡀⠀⠀⠐⢱⡖⠀⡀⣄⢀⠀⠀⠀⣀⡄⢠⡄⣠⣀⣀⢄⠀⢀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠆⣀⠀⠀⠀⡀⠀⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⡄⠀⠈⠁⠀⢀⠀⠹⠛⠀⠀⠈⣄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠁⠀⢦⠀⠀⠀⠘⠣
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⢠⣾⠀⠀⠀⠈⠁
⠀⠀⠀⣸⣆⠀⠦⠀⠀⠀⠀⠠⠀⠀⠀⠐⣦⠀⠀⢸⡄⠀⢻⣷⢠⡞⠀⢠⣶⠖
⠀⢀⣨⠐⠹⣶⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⢹⣿⡿⡋⣼⣗⣠⣾⡇
⠀⠈⠳⣄⡀⠀⠉⠛⠿⠀⠀⠀⠀⠀⠀⠐⣤⣤⣼⣿⣷⣿⣿⣽⣿⢯⡍⣹⡿⠓⠂
⠀⠀⠀⠀⠉⠓⠒⠶⠃⠀⠀⠀⠀⣄⣀⣠⣶⣯⣠⣿⣿⡏⣴⣾⣿⡿⣿⣿⣥⣤⡾⠶⣄⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⣸⣿⢿⡿⣷⣬⣿⡿⣿⣯⣥⣯⣍⠀⠀⠀⠀⠀⠀⠀⣘⠉⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣴⣾⣿⡿⡷⣿⣟⠓⣿⣏⠀⠈⠃⠀⠀⠀⠀⠀⠀⠏⠛⢷⣤⡀⠀⠽⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡏⠈⢹⡇⣾⡟⠛⢿⡝⠛⠻⣧⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠉⢷⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠋⠀⠙⣷⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⣦⠀⡀⠠⡏⠀⠀⠀⠂⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⡀⠈⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⢏⢩⡔⢠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡄⠀⠂⠀⠀⠛⠿⠄⠀⠀⠐⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⠀⠀⠀⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠒⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣷⠈⠻⣷⣦⣄⣀⠀⠀⢀⣀⣤⣴⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⣿⣿⡇⠀⠈⠿⣿⣯⣙⠻⢿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⣿⣿⣿⠘⢧⠀⠀⢿⡍⠈⠐⠀⠹⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡌⢿⣿⣿⣄⢸⣆⢀⡼⢧⠀⠀⠀⠀⠛⠓⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣿⣷⡄⠹⣷⣬⣙⣿⠘⠁⠈⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣷⣶⣿⡿⠿⠋⠀⠀⠀⣀⣄⣀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣤⣴⣿⣿⣿⣿⣿⣷⡄⢀⣾⠃
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣋⠁⢐⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣯⡄⡿⠟⠛⣿⡿⠛⠉⠋⠙⠿⠿⠿⣿⣿⣿⣧⠀⠘⠂
⠀⠀⠀⠀⠀⣿⣿⣿⣟⣿⣿⣿⣶⠇⢘⠿⠿⣶⣾⣃⣤⣤⣤⣀⣀⣀⣨⣿⣿⡶⠂
⠀⠀⠀⠀⢀⣿⣿⣟⣻⣟⣿⣿⣿⣿⣿⣶⣶⣾⣉⣙⣿⣿⣿⡿⢿⣿⣿⣿⡋⠀⠀⠰⣿⡷
⠀⠀⠀⠀⣾⣿⡿⣿⣿⣿⣷⠟⢻⡿⣟⣿⣿⣿⡿⢿⣿⢿⣿⣿⡿⣿⡿⢿⣿⣿⣾⡿⡟⢦⡀
⠀⠀⠀⢠⡿⣻⣾⣅⢼⢯⣽⠖⢿⠵⣿⠰⢿⣬⡛⠼⢌⠷⠯⠛⠛⠂⣽⣿⣿⣿⣿⣇⠀⠐⢝⣦
⠀⠀⠀⠈⣧⣹⢏⣷⢶⠶⡒⠺⣧⣴⡾⢶⡀⢿⣍⠓⠢⣀⠀⣴⣾⣿⣾⣿⣿⣿⣿⣿⣧⠀⡄⠸⡻⣆
⠀⠀⠀⠚⣿⢿⣾⣿⣿⣿⠷⣶⠶⣦⣙⣮⢣⡼⡏⠁⠠⠀⠁⢻⡟⣿⣿⣿⣿⠿⣿⣿⣿⣤⠲⠄⠈⡛⣧
⠀⠀⠀⠀⣿⣶⠚⣿⣿⣷⣾⣤⣤⠙⣻⣿⡶⠣⢡⠀⠀⠀⠘⣾⣷⢿⣿⡿⠀⠀⣀⠀⠈⠻⣷⣦⢄⣺⣽⣇
⠀⠀⠀⠀⣿⣿⣿⣏⢻⣷⡯⢿⣽⣿⣿⣼⣧⡶⢋⣧⣰⣿⣶⣿⣍⣼⣿⡇⠀⠀⠈⠛⣦⡀⠈⢻⣷⣼⣿⡟
⠀⠀⠀⠀⢼⣿⣿⣿⣴⡸⡷⣼⢷⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣏⣿⣿⠃⠀⠀⠀⠰⣿⣿⣷⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⣬⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⠿⠿⢿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣾⣶⠿⣿⡛⠛⣻⠿⢿⣿⣷⡀
⠀⠀⠀⠹⣿⣿⣿⣿⣿⡿⠟⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣶⣿⣿⣿⣿⣾⣿⣶⣷⣴⣬⠛⢿⣷⡀
⠀⠀⠀⠈⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⠿⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⠀⢙⣿⡇
⠀⠀⠀⡳⣶⠟⢁⠀⠀⠀⠀⣀⣤⣶⣶⣶⣾⡿⠿⡿⠛⠛⠿⠆⠀⠀⡄⠀⠀⠉⠙⠛⠛⠙⠿⠏⠱⠀⣼⣿⣿⠇
⠀⠀⢀⣽⣿⣤⢮⣤⣶⠿⠟⠛⠉⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⡿
⠀⠀⠀⣿⣿⣿⣿⣠⣖⢛⠁⣀⣀⡀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⣟⣠⣴⣶⣂⣤⣤⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠀⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⣀⠀⠉⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⡀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠙⢦⡠⠤⠤⠠⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⢀⡴⠊⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠋⠙⣂⠃⢤⡄⠀⠈⠳⣄⠀⠀⠀⢠⠊⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⣠⠔⠋⠉⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡡⠄⢶⣖⡂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠸⠣⣀⠀⠈⠳⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠉⠐⠀⠋⠀⠀⠀⠀⣠⡴⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠁⢀⡤⠒⠦⣄⡀⠀⠀⠀⠈⠢⡖⢁⣀⢠⠔⢊⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢻⠋⣼⣿⠁⣠⢡⠀⠀⠀⠀⠀⠀⠰⢋⣴⡟⠀⣌⢻⣦⠀⠀⠀⠀⠀⠈⠁⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠀⠈⢀⢿⣿⣿⡟⠀⡀⠀⠀⠀⠀⠀⠇⠸⣿⣿⣾⡟⡰⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠁⠙⠉⠁⠐⢩⣟⣉⣺⡅⠘⠄⠀⠙⠛⠋⠒⠁⠀⠀⠀⠀⢠⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠐⠢⣤⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⢿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣀⠀⠀⠀⠈⠓⠤⠤⠛⠄⣀⠤⠞⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡲⠢⠤⠤⣄⠀⠀⠀⠀⣀⣀⣀⠠⠤⠴⡒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢊⣀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⡎⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠄⠀⣠⠀⠀⠀⠀⠀⠀⠀⢀⠓⣀⡠⠃⠀⠀⠘⠆⠀⠀⠀⠀⣠⡴⠒⠒⠲⠤⡉⢆⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠘⢦⢹⠀⠀⠀⠀⠀⠀⢀⠞⠀⠉⠀⠀⠀⠀⠀⠘⣆⠀⠰⠿⢤⡄⠀⠀⠀⠀⠈⠻⡆⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠳⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢡⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⢢⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢠⠟⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠙⠒⠛⠯⠍⠑⠒⠒⠤⠤⣈⡄⠀⠀⠣⢄⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠀⠈⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠑⣄⣠⠞⢹⠀⠀⠀⠀⠀⠀⠸⠀⠂⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⣶⣄⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡞⠡⢀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⢙⡄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠳⡀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠁⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⢀⠀⢀⠀⠀⡇⠀⠀⠀⠀⡇⢆⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣀⠀⡀⠀⠀⠀⠀⠴⠃⢉⣄⣀⡀⠀⠈⠀⠈⢂⡀⡇⠀⠀⠀⢀⡇⠈⢢⠄⠐⠂⠠⢴⣃⣀⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠚⢂⡏⠀⠀⠀⠀⠀⠠⠆⠒⠉⠉⠃⠀⠀⠀⠈⠉⢢⡇⠀⠀⠀⠀⢠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣘⡀⢰⡀⢀⠄⠀⠀⠀⠘⡀⠠⠀⠀⠀⠀⣧⠓⠲⠤⠼⠤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠃⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠓⠒⠒⠲⡀⠀⠐⠒⠒⠶⠀⠀⠤⠤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠁⠀⠈⠲⠀⢐⠀⠀⠀⢰⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡀⠴⠂⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠈⠃⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⢀⠴⠖⠀⠀⠀⠀⠘⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠄⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠚⠀⠒⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠂⠀⠀⠀⠄⠀⡠⣄⡀⠀⠀⢠⡶⠾⠷⠶⠶⠿⢦⡴⢦⣄⡀⣀⠠⠘⠃⠀⠀⠀⠀⠻⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⡀⠀⠀⠀⠀⠂⠤⠈⠙⢲⣶⣿⠁⣴⠒⢈⣉⣐⠲⢄⠀⠸⣧⠄⠀⠀⠀⠀⠀⣠⡄⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⠶⠐⠀⠀⠉⠉⠉⠉⣳⣀⠉⠶⣤⣭⣭⣥⡼⠃⢰⠯⠈⠁⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣎⠀⠀⠀⠀⠀⠀⣀⠴⠂⠉⠙⣷⠶⢦⣠⣤⣤⣤⡾⠛⠐⢶⡤⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠠⣇⢰⠀⠀⠁⠈⠀⠈⠉⠐⢶⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⠀⠀⠀⡀⡀⠀⠀⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠦⣤⡀⠀⢀⣞⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⣁⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡀⢄⠛⢠⣻⠟⠀⠀⠉⠐⣦⠔⢋⠁⠀⠀⠀⠀⣼⣧⠀⠀⠀⣤⠀⠀⢸⣷⣄⣠⡟⠉⠀⠠⣀⣤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⡁⡌⠃⢸⡏⠠⠀⠀⠀⠀⠀⠀⠘⠶⠠⢠⡄⠈⡇⣏⠧⠤⠄⣹⣦⣶⠾⡙⣿⣿⠉⠀⠠⣤⡼⠛⢦⡀⢰⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⠿⢶⣬⡁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡿⣾⣾⣿⡝⠋⠁⠋⠀⠁⠈⠀⠀⢠⠇⠀⠀⠀⣉⠟⣻⡄⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⡷⠈⠙⠛⠿⠀⠀⠰⢴⡉⡧⣈⠤⠦⠀⠀⠀⠈⠁⠈⠴⠛⠿⣄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⠀⠀⠀⣀⠀⠀⠀⠀⢸⡇⣼⢧⡀⠀⠀⠀⠐⢶⣦⠀⣈⡷⢿⠖⠴⣆⠀⠀⠀⠐⠀⠀⠀⠀⣨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠑⡄⠀⠀⡿⣆⠀⠀⠐⣬⠁⣿⠀⠀⠀⠀⠀⣜⠘⡙⣳⣭⣻⣆⠚⢆⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣀⣀⠀⠈⢲⡄⠐⡇⠀⣠⠆⠀⡏⢠⡟⡀⠀⠀⣀⠀⣸⠧⣜⡙⢩⣦⣎⠛⢿⡉⠛⠦⣀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠈⠀⠀⣁⠀⠀⠃⠀⠘⢷⠀⣿⠀⢀⠀⢸⡇⠀⠀⠀⠀⡴⠃⠀⠀⠄⠸⠉⠳⠀⠀⠙⠀⠀⠀⠀⠈⠁⢛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠆⠀⠀⠉⠀⡈⡀⢆⠸⡛⠁⢿⠀⠸⠀⣟⣧⣤⡀⢀⣼⠁⠀⠀⡘⢰⠀⠀⠈⡀⠀⠀⠀⢀⣀⣀⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠉⠀⠈⡆⠙⣤⣈⡀⠙⢀⡇⢸⡦⠽⠋⠣⣀⣀⣠⢁⡇⢀⡄⡀⣥⠀⣀⣠⠄⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⡤⠂⡹⠉⢹⡃⢈⡛⠘⠠⠀⣠⠞⠁⢉⣧⠞⠋⣈⠁⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⠑⢦⡀⠀⠀⠀⠀⢴⠔⡃⠈⠋⢘⣧⠃⠒⠙⠉⠆⣀⠻⠃⢊⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢳⠀⠀⠐⠒⠚⢿⣄⢀⠀⠀⠀⠾⢤⠆⣠⠼⣿⠀⢰⠇⠀⠀⠉⠀⢤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠑⣤⡝⠶⠚⠛⠒⢧⡄⠀⣀⡾⠊⠁⠀⠘⡀⠀⠁⣀⠶⣅⣀⡀⠉
⠀⠀⠀⠀⠀⠀⡀⠄⢸⡇⠀⢰⣦⣄⠈⠛⠶⣤⣤⣀⣤⠤⠛⠉⠀⠀⠀⠀⠰⠄⠠⠾⠷⠦⠤⠽⢁⣀⡀
⠀⠀⠀⢀⠔⠁⠀⠀⢸⡇⠀⠐⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠸⣇⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠀⡸⢷⠀⠀⠉⠳⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣄⣀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⢀⣦⠄⢸⣁⠀⠀⣠⣤⣄⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⢀⠀⢶⡆⠘⠿⠀⠸⢟⣀⠀⢯⠈⠈⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⢤⣨⢁⡤⠤⠋⠀⠈⠁⠑⠀⠶⠶⣀⡀⠺⣤⣿⣧⣄⡀⠀⠤⠤⠤⠤⠰⣯⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠤⠤⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠐⠀⠀⢠⣄⠀⠀⠀⠠⢶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢦⡀⠀⠀⠀⠀⠈⠒⢤⠀⣀⣐⣀⣠⡄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⢀⡀⠀⢿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⣄⣀⠀⠀⠉⠒⠚⣧⡀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠙⠂⠈⠁⠀⠀⠀⣤⠖⠋⠉⣠⠤⠀⡸⠗⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠒⠠⠄⢀⣀⡀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⣀⣠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⢀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢠⠀⠉⢉⣉⠡⠤⢴⠟⠚⠒⠛⠋⠁⠰⠟⠒⠋⠁⠄⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⣼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣽⣿⣿⣀⠀⠀⠀⠀⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⣰⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⣿⣿⠏⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣄⠀⠸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡅⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡟⣷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣤⢲⡟⣷⡶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣼⣿⡄⠀⠀⠀⠀⠀⠀⣼⣿⣦⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢰⠋
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠶⢄⠉⢑⡆⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠀⣴⣛⣿⣿⣷⡄⠀⠀⠒⢀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠁⡴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠀⣸⠂⢸⣆⣤⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠻⣿⣿⣿⡿⠃⠀⠀⣴⣿⡄⠀⠀⠀⠀⢀⣀⣶⠁⢸⡀⠠⣟⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣄⣻⠀⢸⡿⢿⣿⣷⣄⡄⠀⠈⣿⣿⣷⣦⡀⠈⠽⠍⠀⣠⣴⣾⣿⡯⠀⠀⣀⣠⣿⣿⠟⠿⠀⢈⢣⡄⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⡏⢀⡟⠉⠛⡽⠛⣿⣿⣧⠀⠀⠛⠙⣿⣿⣶⣶⣶⣾⣿⡿⠛⠋⠀⢠⣿⣿⡟⠻⡜⠋⠘⣿⠉⣿⠛⠁
⠀⠀⠀⠀⠀⠙⠂⠈⠹⠷⡴⢯⡼⡿⠛⠳⢦⡾⠉⣩⠟⢀⡀⠀⠀⠈⠛⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⢿⡁⠙⣧⡴⠛⠻⣿⢦⢿⡰⠖⠋⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠿⡖⠻⡆⠀⠀⠀⠀⠀⠀⠀⢹⣦⠘⡿⠆⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠸⡌⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⣾⠓⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀⡿⠂⠀⢤⣄⠀⠀⠀⠈⠛⣶⠃⣰⡀⠀⠀⠀⢹⠀⠈⠀⠀⣀⡀⠑⡞⠋⠀⠀⠀⢀⣤⡄⠀⠰⢇⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠛⠂⣤⣿⡄⠀⠀⠀⠙⠓⢀⠀⠀⢠⣿⠏⠉⢡⣤⠀⠀⠸⠀⠀⠀⣄⠙⠁⠸⣧⠀⠀⢀⡀⠛⠁⠀⠀⠀⣸⣧⣀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢸⡟⣶⡴⢦⣀⡤⠉⠁⠀⠀⣇⠀⠃⠶⣉⡆⠀⠀⠀⠀⡴⢰⡄⠀⠀⡄⠀⠀⠈⠁⣄⣠⠴⢤⡞⣻⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠉⠀⢠⣀⣀⡄⠀⡶⠀⠐⠉⠂⢤⡶⠀⢳⡞⠀⠸⣷⡄⠀⣤⠀⠀⠀⠀⠀⢆⠀⢉⡀⣠⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠈⢳⣾⠀⠀⠀⠀⠀⠀⠰⣴⠛⠁⡼⢇⠘⠹⣧⠀⠀⠀⠀⠀⠀⠠⣶⠎⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠙⠀⠰⢷⠞⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠁⠀⠀⠀⠀⠐⢺⠏⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⠀⢶⢴⠀⠀⡀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠘⠀⠈⠙⠛⠁⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣄⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠹⠄⠿⢆⣠⠞⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠆⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡟⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠟⠃⠀⠀⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠻⡷⡀⣤⠀⠀⠀⢠⣶⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠙⠿⣷⡀⢠⠟⠁⠀⠁⠀⣀⡄⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⣦⠀⠘⢳⡏⠀⠀⢠⡄⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠐⣿⣿⡆⠈⠀⠀⢰⣿⡇⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠸⣿⣷⡄⠀⢸⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡎⠀⠀⠀⠻⣇⠀⠀⢻⣿⡇⠀⢸⣿⡟⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠛⢧⠀⠸⣿⣷⠀⢸⣿⡇⠸⣷⣆⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⠀⣿⣿⠁⠀⠉⠻⠷⣶⠤⠀⢀⣴⠟⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣠⣆⡀⢴⣀⡞⠀⢀⣿⣿⣦⣿⣿⣆⠀⣴⣿⣷⣶⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⣦⠛⠈⠛⠀⠙⣇⠀⠺⣿⣿⡿⣿⣿⡿⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢿⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣧⣀⣄⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠳⠦⣤⣄⣠⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⠦⡔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣤⠈⠑⣯⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆⣧⢼⣓⣀⣤⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢄⣠⣏⠉⡏⢠⠎⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢀⣠⣄⠉⠒⠻⠾⡏⠀⠀⠀⢠⡞⡇⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠄⠀⠀⠀⠐⢊⡁⠁⠀⠀⢆⠀⢸⡀⠀⠀⠈⣿⡄⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠰⠀⠀⠀⡀⠜⣁⢦⠀⠊⠸⠀⡀⣇⠀⢘⡞⠀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⢀⠀⠈⠉⡡⢰⣰⠀⠚⣥⢸⡀⢀⡏⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠄⠀⠀⢷⠉⢀⠤⠈⣱⣤⣴⢃⠺⣡⡞⡴⠂⢀
⠀⠀⠀⠀⠐⠒⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡁⠀⠀⢳⡄⠀⡀⡀⠿⡈⢊⣱⣟⠈⡴⠎⠁
⠀⠀⠀⠀⠈⢢⠀⠠⢄⠂⣈⠁⢲⠠⠶⠂⠓⠐⠋⠀⣨⠟⠁⠀⢈⡿⠗⢋⠀⠳⡀⠀⢊⠙⣈⠝⠒⠠⠂
⠀⠀⠀⠀⠀⡅⠙⣄⠘⣷⠉⠓⡍⠀⠀⠀⠀⠀⢸⠀⠂⡶⠀⠦⣀⡀⠰⠌⠇⡀⢤⢻⣼⡗⠊⡀⠁⠤
⠐⠖⠈⠑⢄⢱⠀⠙⢦⠘⢡⠛⠀⠀⠀⠀⠀⠀⠈⢲⡘⠴⡸⡆⣫⠃⢰⠀⠀⠻⡄⠚⢹⡅⡈⠄⠂⣀
⠀⠀⠢⠤⠄⡉⡄⡤⢈⡅⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣉⠀⠀⠘⢠⡀⠀⠉⣤⠰⢌⠎⢸⡿⠡⠒⡡⠈⡀⠀⢀⠀⡴
⠀⠀⢀⠀⠀⠀⣈⢳⣼⡟⠀⠀⠀⠀⠀⢀⡴⠋⠉⢀⠉⠙⠁⠀⠀⠀⠛⠀⠈⢸⡅⠠⣸⠦⢖⢉⡠⠂⠅⡰⠁⢀⠁⠂⠠
⠀⠘⠀⠀⠔⠋⠀⡦⠳⡏⢉⣗⠀⠀⠀⠟⣵⣿⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠉⢀⡟⢀⡉⠾⠡⠄⣸⡅⢲⠛⠂
⠀⠀⠀⢀⣴⠀⢰⡇⢀⣧⠈⠟⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⢀⡠⠂⠀⠀⢰⡀⢱⠀⣹⠙⠈⢰⠠⠦⠂⠠⠐⠒⠀⠒⠄
⠀⠀⠀⠀⢁⠀⣌⠳⡌⣽⠏⠀⠀⠀⠀⠀⠀⠰⠋⠈⠈⠑⠆⠀⠀⠀⠀⢸⡁⠈⡄⢉⢠⡞⢋⠙⠀⠉⠀⠀⠐⡀⠀⠈⠁
⠀⠀⠀⡠⠈⠁⠰⡴⢺⠧⣤⡤⠀⠒⠲⠶⠚⣀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠆⢆⣼⣁⠐⣀⣠⡴⠂⢉⡷⠆
⠀⠀⠀⠑⢄⠀⠹⠄⢹⣾⣿⣃⡀⠀⢠⠴⠋⡁⢠⣄⠀⠀⠀⠀⠀⠀⠀⠙⢃⣴⣯⡿⠻⢋⡝⠋⢧⡄⠻⣦⣴⡟⠃
⠀⠀⠀⢀⠀⠐⡰⠒⠉⠉⢉⠋⠠⠤⢆⡈⠛⠉⠉⠉⠙⠁⢳⠀⠀⡀⡱⠀⢾⡉⠵⠶⢿⣶⣤⣦⠀⢁⠤⠤⢭⣁⡀
⠀⠀⠀⠈⠠⢄⣱⠀⠂⠒⢄⡀⠀⡸⠆⠛⠁⠀⠈⢷⣄⠀⠀⡶⠖⢻⠁⠀⠈⣗⠈⠑⡦⠡⠜⢏⠒⢾⠒⢀⠤⠄⠈⠓
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⢀⡍⠈⡁⠀⠀⠀⠀⣸⣄⠻⠘⠖⠓⢦⣸⣶⣀⣴⣥⠒⠉⠁⢤⡀⠂⠐⠀⡕⠌⠂⠀⠠⠄
⠀⠀⠀⢀⠐⠀⠀⠲⠀⣀⠈⣷⣤⣷⡀⡀⠀⠠⠀⠈⠐⠅⡀⠀⢀⣹⣿⠿⣿⣇⠀⠀⢀⣸⡅⡀⢁⠞⠠⡄⡇⠁⠂⠀⠑
⠀⠀⠀⠀⠣⢀⡠⠔⣤⣤⣿⡟⢻⣿⣿⠓⠂⠉⠑⢄⡌⢠⠞⠚⢉⡽⠿⣾⣟⠛⢫⣍⠁⡹⢙⡁⡌⣠⠁⡇⠘⡄
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⣹⣿⣿⣿⠳⡄⠀⠀⠀⠀⠓⢀⠦⣴⠋⠀⠀⣃⢺⡀⠀⢘⠁⠀⠈⠀⠓⠁⠀⠆⢠⠁
⠀⠀⠀⠀⠎⣀⠀⠀⠀⢰⠏⡜⠁⠀⠈⠓⠦⠤⢠⣀⡔⠹⡶⠈⠄⣠⠔⡯⢀⡙⠉⠈⢀⣀⠸⠀⠀⠀⠀⠸⠆
⠀⠀⠀⠀⠀⠀⠈⠛⠈⠁⢃⠀⠀⠀⠀⠰⠀⠀⣨⠜⠏⢘⡇⠀⢂⠀⡀⠀⠀⠀⠀⠐⣪⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠐⣀⣠⠔⠃⠀⠀⡠⠛⡈⣰⠟⠂⠀⡈⢏⠳⠰⠀⠁⠀⠀⠀⠀⢾⡍⡸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠐⣈⠂⠀⢠⠠⠀⢄⠙⡖⠁⠢⠀⠀⠀⠀⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢰⠀⠆⢈⡀⠂⢠⣶⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⡀⠀⡆⠀⠀⠁⠀⠈⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠁

⠀⠀⠀⠀⡀⠢⠀⡀⠒⠂⠤⠄⠀⢀⠂⠀⡄⠀⡄⠀⠄⠀⡤⠠⠀⠀⠀⠐⠀⢠⠀⠁⠂⠀⠔⠠⡄⠐⠀⠂⠰⢄⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⣈⡧
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣀⠀⠱⡀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠒⠒⠒⠲⠤⣀⠀⠀⠀⢀⠎⢀⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠃⠀⢀⠴⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠤⠛⢲⣄⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢁⡴⠋⢳⡀⠀⣸⠛⢧⡀⠀⢠⠏⠙⢦⡀⡞⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⣼⣎⣀⣀⣀⣳⣴⠃⠀⢀⣹⣤⣏⣀⡤⠤⠿⠓⠚⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⢠⠤⢤⣀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢤⠀⠀⠀⢀⡇⠀⠀⠀⣧⠀⠀⠀⢀⠄⠀⠀⠀⠀⡇⠀⠀⠀⣀⡠⠤⠖⠒⡆
⠀⠀⠀⢸⠀⠀⠀⠉⠑⠒⢤⠀⢸⠀⠀⠀⠀⠀⠈⢳⡤⣤⠾⠄⠀⠀⠀⠸⠦⡤⢴⠋⠀⠀⠀⠀⠀⡇⠀⢮⣉⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⣀⣀⡤⠤⠒⠊⠉⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⠈⠀⠀⡀⠀⡀⠀⠀⢁⣀⡀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⠑⠲⠤⢤⠇
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢰⠋⠀⠈⡇⠀⠀⠈⠉⠁⠀⢰⠋⠀⠈⢣⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⠢⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠳⠤⠴⠃⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠙⠲⢤⣀⣀⠀⠀⠀⠀⢀⣀⡤⠔⠊⠁⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⢆⠈⠙⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢏⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⣶⣾⣿⣿⣷⣶⣶⣦⣤⣀⠀⠀⠀⠀⣀⠀⠨⡿⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠘⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⣶⣾⣿⡿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣿⠟⠻⠇⠀⢀⣀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠁⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢿⡟⠛⠉⢹⠀⢀⣼⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡇⠀⠀⣴⣷⡄⠀⢸⠀⠸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡏⠀⢀⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⣾⣷⡄⠘⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠨⡏⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠄⢀⣼⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠃

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

⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⣀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠈⠛⠆⣀⡈⠀⣤⣴⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠐⠈⣀⠀⢀⠉⠛⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠻⣏⠻⣿⣄⠀⠀⠀⠀⠀⠀⣰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣓⠺⠟⠉⠁⠀⠀⠀⠉⡤⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠤⠄⠀⠀⣀⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣭⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣀
⠀⠀⠀⠀⢰⣿⣶⣶⣶⣶⡆⢠⣿⣽⣿⢿⣿⣿⣭⣷⡀⠀⠀⢀⠚⡄⠀⠀⠀⣀⠀⠀⠀⠀⣴⣦⣀⡀
⠀⠀⠀⠀⠀⠉⢿⣿⡟⠁⠀⠈⢿⣿⣿⣾⣾⣾⣿⣿⠇⠀⠀⢸⣼⣤⣄⣰⣊⡝⠀⠀⠀⢸⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢠⠦⡭⢴⡄⠀⠀⠀⠙⠛⠻⠿⠿⢟⣁⡀⠀⡠⠾⠿⠿⠿⣿⠋⠀⠀⠀⠀⢸⣿⠟⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣾⡷⣶⣦⣀⠀⠀⠀⠀⠀⠛⠿⠟⣤⠀⠀⠀⠀⢰⣷⣶⣶⣾⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠘⠇⠀⠘⠃⢻⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣹⠛⠛⠛⢏⠱⠄
⠀⠀⠀⠀⠀⢀⣄⣀⣀⣀⣀⠉⠁⠀⠀⡠⡀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⢀
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠀⠀⠀⢰⣿⣿⣶⣶⣶⣾⣷⣷⠀⠀⢠⣄⡀⢀⣀⣀⣀⣞⢹
⠀⠀⠀⠀⠀⠀⠀⡙⠟⡁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠛⠉⠀⠀⠘⣦⡿⢿⣿⣿⠟⠉⢫⣄
⠀⠀⠀⠀⠀⣀⣸⡇⠀⢻⣄⠀⠀⠀⠀⠐⠈⢻⣿⠋⠀⠂⠀⠀⠀⠀⠀⠀⠤⢈⣻⡀⢲⣿⣿⣿⡄
⠀⠀⠀⢶⣿⣿⣿⣷⠶⢛⣿⡆⠀⠀⠀⠀⢀⣶⣷⣶⡄⢀⣾⣷⣦⡄⠀⠀⢀⣿⣿⣿⡌⢿⣿⣿⡇
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣬⣿⣿⡿⠃⠀⠀⢸⢹⡏⡟⣧⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⢿⠟⠛⠛⡟⠛⠛⢻⠿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⡉⢀⣨⣦⣴⣶⠷⢶⣶⣷⣤⣤⡟⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢿⡁⣠⡿⠟⠉⢡⡄⠠⠤⠄⢠⡄⠉⠙⠻⣷⣬⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⢠⡿⠋⠀⠖⠁⢠⠖⣴⣒⣤⢬⠁⡈⠓⢀⣌⠻⣷⡈⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⢲⠟⡠⠛⣃⢼⣡⣿⣿⣿⢿⣿⣿⣷⣬⡤⡄⠁⢄⠹⣿⡈⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣠⣏⣤⠀⣠⣧⣾⣿⠋⡟⢆⡰⢹⠉⠻⣿⣷⣖⢢⠈⣤⢹⣧⠼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣼⢠⠀⠘⣤⣿⡿⢫⢑⣷⡾⠿⢿⣖⡩⠋⢿⣿⡟⢤⠠⡀⣿⡄⢻⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠗⡇⣤⠀⣏⣿⣿⠿⢐⣿⢯⣾⠿⣷⢻⣏⡩⠻⣿⣿⢮⡀⣁⢸⡗⢺⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⡇⠀⢰⢛⣿⣿⢖⣻⡟⣿⢳⣿⢻⡏⣿⣉⡱⣿⣿⣶⡁⢉⢸⣇⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢙⡇⣤⢨⢿⣿⣿⢖⣿⡇⣿⢸⣿⢸⣷⣿⣏⣐⢿⣿⣧⠃⣤⡘⣿⠰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⡇⠤⠘⣾⣿⣿⣖⣿⡇⣿⢸⣿⢸⣿⢸⣟⣒⣼⣿⣇⠕⢠⠀⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⡇⠶⠂⢅⣿⣿⣤⣻⡇⣿⢸⣿⢸⣿⢸⣏⠱⢾⣿⣏⡆⣶⠀⣿⠒⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠃⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠤⠀⣀⣀⡤⢀⠀⠀⠀⠀⡄⢠⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡔⠁⢀⠏⠀⡰⠋⡟⢆⠀⢡⠀⢹⡀⡠⢊⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⡃⠀⣌⠀⢰⠁⠀⠃⢸⠀⠈⣇⠀⠛⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠥⠗⣇⠀⡆⠀⠀⡇⡸⠀⠀⡼⡀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠀⠀⢩⡀⢇⠀⡜⢠⠃⢀⢎⡔⠙⢆⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠚⠀⠀⠀⠉⠚⠋⠐⠁⠀⠘⠋⠀⠀⠈⠓⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠠⠄⡈⠉⠒⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠂⠈⣉⠠⠄⠵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠙⢦⡒⠒⠒⠒⠒⠒⢢⠖⠉⠀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣠⠜⠳⡀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠠⠚⢠⡀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠔⠈⠁⠀⠉⠐⢄⠀⠀⠀⠀⠀⡠⠂⠉⠀⠈⠁⠢⣄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠞⠁⠀⠀⢀⠀⠀⠀⠀⢢⠀⠀⠀⠜⠀⠀⠀⠀⡀⠀⠀⠀⠱⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣃⣀⣐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡀
⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡖⠚⠳⡀⠀⠀⠀⠉⠑⠶⠠⠤⡄⢀⣀⣀⣀⣀⣀⠤⠄⠖⠊⠁
⠀⠀⠀⠀⠀⠀⢰⡖⠁⠉⠁⠀⠀⢱⠀⠀⠀⠀⡜⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⢧⠀⠀⠘⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⢧⠀⡀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠙⠆⢠⡄⠀⠀⠑⠤⠀⡀⠠⠔⠁⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⢴⠉⠙⠢⣸⠃⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡄⠊⠉⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠈⠁⠀⠀⠈⡀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⣀⡀⠀⠀⢀⡃⠀⠀⠀⢸⡀⠀⠀⢨⡄⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠤⠊⠉⠉⠉⠉⠈⠑⠄⠴⠃

⠀⠀⠀⢀⡄⢠⢀⣤⣄⣀⣤⠄⢠⠄⣤⣀⣠⣠⠄⣤⠀⣀⣠⣠⣀⣤⣠⡄⠠⣤⢤⣠⢠⡄⣄⡀⢠⣠⡄⣤⣀⡄⣤⢠⣠⣠
⠀⠀⠀⠘⠃⠚⠚⠚⠘⠃⠛⠀⠘⠁⠛⠑⠓⠛⠂⠟⠀⠛⠛⠓⠛⠛⠛⠃⠀⠃⠚⠛⠛⠛⠛⠃⠘⠛⠳⠛⠛⠛⠛⠛⠛⠸⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢠⠂⠈⠈⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠐⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⢂⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠂⠤⢀⣀⡀⠀⠀⣀⡀⠀⠀⠴⡀
⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠮⡟⢃⠤⠀⠀⠀⢲⡄⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠠⠀⠖⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠃⠀⠀⠀⠀⠀⡠⠂⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⡟⠂⠀⠀⠀⠠⣧⣨⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠘⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⡴⠶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⢦⡿⠁⠀⠻⣽⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣤⠇⣀⣀⠀⣥⠺⠃⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠹⡿⠇⠘⠿⣦⡿⡓⠄⠀⠀⡀⣠⡾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡀⠘⠀⠀⠀⠀⢈⡼⠃⠀⣴⣶⠙⣫⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠿⣿⣾⣦⣀⣀⡀⣊⢋⣙⣁⣾⣿⣷⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⢀⣀⣼⠿⠿⠿⣿⣯⡸⠟⠾⣿⣿⠿⠿⠟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⠀⠀⠀⠀⠈⣻⣧⡤⠸⣧⣤⣤⣤⠶⠦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠉⠀⢀⡾⣢⠀⢿⣿⣿⢿⣶⣏⣭⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡐⠚⠻⣿⣯⣴⣚⡟⠻⡿⢹⣿⡟⡃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋⣿⠟⢻⣷⣼⣛⣿⣿⣤⣤⣼⣉⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠘⠁⠀⠈⣻⣧⣾⣿⣿⣿⣍⣻⡇⠀⠀⢠⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⢻⣿⣾⠐⣯⣽⣿⣿⢿⣿⣿⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⣿⡿⣿⡟⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢷⣶⣶⣿⠋⣿⡀⢻⡇⣿⠀⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠇⠀⣿⡇⢸⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⣇⠁⢸⣿⡿⡃⢸⣿

⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠒⠙⠶⣶⡶⠾⢋⡇
⠀⠀⠀⠀⠀⢰⢃⢀⡈⠁⡀⠁⢹⣦⠴⠶⠒⠒⠦⠀⠤
⠀⠀⠀⠀⠀⠠⠉⣄⣧⠀⠇⣐⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣃⠀⡀
⠀⠀⠀⠀⠀⠀⠑⠌⡁⠛⢠⡛⠂⠡⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⢀⣿⣝⠌⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡙⣆⢀⣄⣀⣄⣤⣴⢶⡟⠀⠀⢀⣴⣿⠙⣿⣦⠂⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠺⣿⣟⠉⠉⠀⠀⢸⣧⣤⠞⠛⠷⣻⣧⡈⢿⣶⣄⡄⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⢹⣿⡀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠈⠉⢻⣶⠻⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣄⣴⣿⠃⠀⠀⣸⣿⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠉⠛⠻⠿⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠀⠉⠁⠄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⠙⠁⠂⠀⠡⢤⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡄⠀⢀⣀⣄⣠⣤⣤⣶⣾⣿⣿⣧⡄⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣻⢿⢋⠁⠂⠄⣉⣹⣼⣧⣎⡠⠈⠇⢽⡏⠁⠈⠙⣷⡶⠖⠆
⠀⠀⠀⠀⠀⠀⣠⡾⢉⣞⠁⠀⠀⠀⠀⠀⢀⡀⠉⠃⠈⠈⠃⠀⢊⠀⡀⠀⠀⠟⠁
⠀⠀⠀⠀⢀⣾⠏⣴⣿⣏⡀⠄⠀⠀⢀⠄⠀⠂⠀⠀⠀⠀⠀⠀⢨⢰⡇
⠀⠀⢀⡴⠋⢈⣸⣼⡟⢻⣧⠀⣤⠀⢨⣴⣤⣴⠀⠀⠀⠀⠀⢠⣬⣹⢁⢷⡠
⠀⠀⠀⢲⣶⣿⠟⠁⠀⣸⣿⠴⠃⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠘⢿⠏⠸⣼⡇
⠀⠀⠀⠠⠋⠁⠀⠀⢨⡿⠃⠀⠀⠠⣻⡇⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢨⡜⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠹⣅⠀⠀⢘⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⣠⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣦⠄⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⢐⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡙⠷⠄⠀⠀⠻⣄⠀⠀⠀⠀⠀⢀⡞⡁⠀⠀⠐⠛⣫⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⣿⢶⠀⠀⠀⡘⢧⡀⠀⠀⠀⠜⢸⣧⡀⠀⣰⡾⣿⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⠈⠄⠀⣀⣀⣨⣯⡛⢶⠾⠿⣷⡄⢻⣇⣤⣤⠀⠹⣇⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣉⣤⣄⢤⡘⠛⠛⢟⡩⠋⠁⣠⡀⢉⣤⣀⡀⠈⠡⣤⣄⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣟⣂⣀⠀⠶⠙⠅⠀⣸⣿⣷⣈⠉⠛⢻⢄⣠⡀⠘⢲⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠞⣁⠄⣉⣽⣾⣷⣾⣿⣿⢿⣿⣿⣷⣤⣴⣿⢆⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⣡⠞⣿⣿⡟⠻⣿⠃⠋⠀⣽⠟⣿⣿⠛⠛⢀⡀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⠶⣤⣤⣈⣉⡥⢀⣸⣗⡀⠀⣼⡀⠈⠉⠀⠀⠀⣈⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡯⠉⠀⠀⠁⠀⠀⠉⠉⠁⠚⢻⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⠉⠁⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣟⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢳⠶⠶⠀⠀⠀⢠⢀⣀⡈⠉⠉⠉⣉⡠⠐⠾⠶⠲⣤⣄⣲⠾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢳⡶⠚⠋⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡀⠀⠀⠀⠰⣯⠀⠀⠀⠠⠋⠙⢾⡤⢤⠀⠀⠀⢸⣿⢿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⢸⡿⠃⠄⡀⠀⡀⠀⠄⠀⠈⠓⠻⣿⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠶⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣴⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠢⡉⢄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⠔⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⠈⡄⠻⠷⠆⠊⠑⠰⠾⠟⢰⠁⠀⠀⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡻⣿⠄⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⣿⢟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠻⣿⣧⠄⠙⠃⠀⠀⠀⠘⠃⠀⠀⠀⠘⠛⠠⣼⣿⠟⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣤⣿⣤⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠇⣤⣿⣤⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⡤⠠⠄⣀⠀⠀⠀⠈⠀⠀⢲⡖⠀⠀⠁⠀⠀⠀⣀⡀⠄⢠⠄⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠐⠂⡀⠈⠀⠀⠀⠉⠈⠫⣛⣢⡀⠀⠀⠀⠀⢀⣔⣛⠝⠁⠉⠀⠀⠀⠁⢀⡀⢊⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⠀⠈⠙⠏⠛⠀⠀⠀⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠛⠻⠋⠁⠀⠶⠄
⠀⠀⠀⠀⠀⠚⠢⠀⡀⠒⠀⡀⠘⣆⡀⠀⠀⠀⠒⠠⡀⠀⠀⠅⠀⠀⠀⠀⠈⠀⠀⢀⠄⠒⠀⠀⠀⠀⣰⠏⢀⠀⠐⠀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠒⡆⠀⢀⡁⠀⠉⢶⡖⠢⠄⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠴⣲⡶⠉⠀⢈⡄⠀⢠⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠉⠝⠃⠀⢀⡞⢉⡽⠚⢲⣦⣯⠀⠢⣶⣦⣴⣶⠜⠀⣸⣴⡖⠒⢯⡉⢳⡀⠀⠘⠛⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠦⠀⠀⡀⠈⠀⠈⢁⠀⠀⢏⠛⢦⣀⣙⣻⣿⣋⣀⡴⠛⣻⠀⠀⡈⠁⠀⠑⢀⠀⠀⠰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡤⠀⠨⠋⠂⡀⢼⣆⠀⡻⠻⣯⣽⠟⢻⠀⣠⡧⢀⠐⠉⠁⠠⢴⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⣀⠀⠀⠠⣠⠄⠠⣿⡧⠸⠀⠈⠀⠀⠇⢸⣿⠄⠀⣄⡄⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡼⢄⡀⠈⠉⠃⠀⠗⢡⡀⠀⠀⢀⠀⢀⡌⠻⠀⠀⠉⠁⢀⡀⢥⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡤⠆⠴⢶⡀⢸⠿⣄⠁⠈⣠⠿⣇⢀⡶⠦⠰⢤⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠎⠀⡀⠀⠀⠀⢱⡆⠘⢷⣾⠃⣰⡏⠀⠀⠀⢀⠀⠱⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠠⠃⠡⠀⠸⠇⠀⠄⠘⠀⠀⠀⢈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠀⠀⠀⠀⠀⠁⠠⠂⠈⠀⠀⠀⠀⠀⠳⠃



⡿⣿⠿⠿⡿⠻⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣖⣴⠒⢀⣒⠈⠉⠁⠉⠉⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡤⠒⠚⢇⠈⠄⣒⠆⠈⢻⢤⡀⠀⠀⠀⠀⡈⠄⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠶⢓⣬⠊⠄⠀⠁⠁⠀⠀⠀⠄⠀⢑⡀⠀⠀⠀⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⠈⠛⣻⡷⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡓⠦⣄⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢀⠀⠀⠀⡠⠀⠀⠀⠿⠁⠠⠁⢄⡂⠀⠀⠐⠀⠀⠹⡟⠀⠀⠀⡙⠲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠔⠁⡠⡂⠀⠀⠀⠀⠀⠀⠀⠐⠑⠂⢀⠀⠀⠀⠀⠀⠄⢣⠀⠀⠀⠀⠀⠨⠒⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠹⢂⡈⠄⡂⠀⠀⣸⠇⠀⠀⣉⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠮⠣⢦⡞⢠⣦⡀⡀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠉⣽⠋⠀⢀⣶⠁⠀⠀⠀⠉⣄⠀⢠⠞⠙⡀
⠀⠀⠀⠀⠀⠀⠀⣼⢀⠀⡈⠀⠀⢀⠈⡜⢀⣴⢄⠀⠀⡀⠈⠀⣀⠄⠀⠴⡆⠠⢻⣤⡾⠃⠀⡀⠀⠀⡀⢀⢅⡦⠀⠀⢸⢆
⠀⠀⠀⠀⠀⠀⠀⣇⠼⠀⠁⠀⡀⠀⡾⠃⠀⠁⠚⠀⣤⡤⠀⢀⠁⣠⢀⣀⡰⠖⠒⢛⠃⠀⠀⠄⡀⠒⠂⠒⠘⠃⠆⢴⠀⣬⢱⣄
⠀⠀⠀⠀⠀⠀⢸⠏⠃⠀⠀⠀⠁⠜⠄⡀⠀⠀⠁⠀⠈⠹⢆⠐⠠⠂⣼⣿⠄⠀⠀⠈⠀⠀⠀⠎⠀⠀⠀⡆⠀⠀⠀⠀⠈⠉⡹⠟⠃
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠇⠄⠀⠀⠠⠀⡄⠀⠀⡀⠈⠤⠒⠁⢂⠢⣦⡈⣟⠳⣤⣀⣀⠁⠀⢉⠀⠀⢀⠼⣐⢀⣀⣤⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠘⡇⠂⠃⢀⠀⠠⠤⠄⠀⠠⣤⣀⠠⡀⠀⠀⠀⠤⠀⠤⣐⣀⠹⢓⣹⠟⠛⠛⠲⠶⢿⡟⢿⣝⡛⡈
⠀⠀⠀⠀⠀⠀⠀⢻⠉⡀⣈⠀⠰⣆⣠⣶⣄⣻⣀⣑⣐⣂⣀⡈⣁⢐⣈⣤⠵⠖⠋⠀⠀⠀⢀⣾⠈⠩⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣃⣠⢡⡞⠉⣁⣤⡤⠤⠤⠿⠿⠿⠿⠿⠿⠭⢭⡤⣤⣤⣤⣠⣤⣤⣴⠛⡄⠀⠀⠘⢣⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⡇⣴⠗⠛⠻⠏⠀⣷⡀⠀⠀⠀⠀⠈⠀⡠⠀⠠⠀⣹⡂⠹⣧⡔⠊⠑⢢⡈⠄⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢇⢏⣴⠉⠀⢀⠀⡛⠠⠄⠀⠢⠠⠤⠀⣒⠤⠉⠀⠈⡁⡃⢻⣷⠎⠂⠸⠒⡀⠐⠀⠀⢐⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⣏⣗⠠⠛⠂⠁⠀⠀⠀⠀⠴⠤⠀⠬⢁⡀⠁⠸⠕⠘⢀⢹⣓⣬⠢⢄⠀⡀⠀⢀⣾⣯⣛⣹⣳⣶⣶⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⣃⢘⡂⠀⢈⠀⠈⠀⠈⠒⠉⠀⠈⠫⣭⡀⠘⣉⢛⠉⡢⠐⢳⣌⣑⠄⠁⠰⡏⠀⠀⠀⠉⠉⠉⠉⠙⠋⠉⠁
⠀⠀⠀⠀⠀⠀⣀⠄⢪⠅⣊⣿⣵⠄⢄⢀⡀⠠⢀⡠⠄⠤⠀⠡⢀⠲⠆⠐⠩⠥⠄⠉⢉⠈⠹⠿⠧⢠⡾⢷⣄⣀
⠀⠀⣀⣤⣄⡈⣄⣨⡴⠚⠉⠀⠙⢦⡀⠉⡧⠈⠄⢐⠁⡈⣀⠀⠀⢻⣬⠆⠀⠷⠆⠀⣊⢅⣀⡾⠷⠿⣤⣿⣠⡍⠹⢳⡶⢶⣦⣤⣤⣄
⠀⠘⠻⠿⠶⠓⠈⠁⠀⠀⠀⠀⣠⠟⠵⣦⡷⢶⣮⣔⣂⣀⣐⣂⠀⠈⣿⣶⣲⣶⡶⠶⠒⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠾⠿⠷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⣧⠔⠂⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣠⣖⣋⡥⠒⠁
⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⢀⣀⡀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⡠⠔⠊⠉⠀⠀⠀⠉⠉⠒⢄⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡜⠀⠀⢀⡠⠔⠂⠉⠉⠉⠒⠢⡀⠀⠀⠈⢆⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡜⠀⠀⡠⠋⠀⠀⣀⠀⢀⣀⠀⠀⠈⢢⠀⠀⠈⡆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢰⠀⠀⡰⠁⠀⡰⠋⠀⠀⠀⠀⠙⢢⡀⠀⢣⠀⠀⠰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⡄⠀⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⢰⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢰⠀⠀⢃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠤⠺⠤⣸⠀⣀⠼⠤⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⡅⠀⣸⡀⠀⡇
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠈⠋⠀⠀⠀⠈⠳⠤⠤⣀⠀⠀⠀⠀⠀⣠⠴⠃⠠⢧⠎⠁⠈⠳⠗⠊⢁⠉⠲⡀
⠀⠀⢀⠔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⡆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠈⢀⡇
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢀⠜⠀⠀⠀⠀⡱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠄
⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠈⠉⠉⠙⡄⠀⠀⠀⠀⣰⢆⡀⠀⠀⢀⠜⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣸⠗⠂⠐⠊
⠀⠀⠀⠀⠀⠀⠀⢸⠒⠤⠤⡞⠁⠀⠉⡏⠉⠁⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠋⠈⠓⢤⠤⠚⠁⡇
⠀⠀⠀⠀⠀⠀⣠⠘⢤⠀⠀⡇⠀⡠⠴⠇⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢢⠀⠀⢸⠀⢀⠔⠲⡄
⠀⠀⠀⠀⠀⠀⠣⣀⠴⠀⠀⡇⠀⠱⡀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢀⠇⠀⢸⠀⠘⠤⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⣄⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⢀⠖⠚⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠘⠄⠂⠀⡀⠈⠀⠈⠠⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠜⠀⠀⠀⠀⡈⠀⠤⠀⠐⠌⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠄⠀⠀⡀⠀⠉⠀⠠⠀⠄⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠐⢠⠀⠀⠀⠀⠀⢀⠴⠈⠀⠁⠀⠁
⠀⠀⠀⠀⠄⠀⠀⢂⠀⠀⠀⠀⠀⠆⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⡑⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡴⠀⠀⠀⠀⢀⠙⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠃⠨⣀⠂⠀⠀⠉⠀⠀⠀⢄⠈⠀⠀⠀⠈⠠⠒⠐⠀⠄⠀⣀⠀⠉⠀⠃⢀
⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠔⠒⣁⠀⠀⠀⠀⠀⠀⠈⠡⡀⠀⠀⠀⠠⠀⠀⠈⠀⠀⠆⠀⠀⠉⠀⠂⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠉⢄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠑⠈⠂⠃⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠄⠈⢀⢀⠀⠀⠃⠀⢀⡀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠀⠀⠈⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠁⣠⠄⠀⣡⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠁⠀⢀⡴⠯⠄⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢁⠀⠀⢀⠀⠀⠂⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡀⢀⠈⠀⠃⠉⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡁⠣⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⣾⣇⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣷⡆⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⣿⠀⡀⠀⠀⠀⠀⣾⠁⠠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠻⠠⣿⣿⢷⠃⣸⣧⣀⣤⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠍⢉⠀⣤⠚⣿⢒⣤⡀⠉⣻⣿⣿⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠩⠐⠃⢈⢿⣼⣄⣜⣿⣩⢭⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣒⣿⣃⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣟⣾⣽⡟⢯⣿⣿⣿⣿⣿⣿⣿⣿⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢏⠃⠀⢸⣿⣿⣿⣿⣿⣿⣯⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣹⣼⣿⠟⢁⡌⢉⣀⣛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣭⠀⠻⢆⣸⣷⣿⡇⠩⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⢹⣿⡛⣀⣴⣿⣿⣿⣿⣆⠠⠛⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠀⠲⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡁⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡷⢠⣆⠉⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢿⣹⣷⡀⠀⠁⠉⢉⣿⣿⣿⣟⢺⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⣼⣿⣿⣶⣶⣄⡀⣾⣿⣿⣿⣿⣇⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠠⣷⠂⠀⣖⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣲⢀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢀⣯⠔⠁⠁⠰⡀⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⡹⠆⠀⠀⠀⠘⡗⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⡇⣹⣿⣿
⠀⠀⠀⠀⡀⢄⡠⠀⢀⣟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿
⠀⠀⠀⠀⢣⣾⣷⠂⠀⢹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿
⠀⠀⠀⠀⠈⣾⣿⣿⣿⣶⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣆⣀⣤⣤⣤⣤⣀⣤⡤⠄⢀⡀
⠀⠀⠀⠀⠺⢻⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⢿⢿⣟⣉⣛⣯⣥⣀⣚⠟⠻⠛⠳⡶⡤⢀⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣾⣤⣭⣯⣰⠖⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠛⢿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣣⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⣿⣿⣏⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢹⣿⣿⣿⣷⣦⡈⠉⠛⠛⠻⠿⠿⢿⣿⣿⣦⣄⡄⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣧⠐⣶⣶⣶⣟⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⣿⣿⣿⣿⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⡿⠿⡿⢙⣿⡙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡅⠀⠀⠀⣤⣬⣙⡿⠦⢴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣧⠀⢰⢷⣶⡬⠻⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢟⠉⠋⣾⣿⣿⣿⣿⣿⣿⣿⢿⡦⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋⠀⡀⠀⣾⣿⣿⣿⣿⣿⢻⣿⡅⠀⢀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣾⠿⠻⢿⣿⣿⣿⣿⣍⣡⣾⣿⣆⡤⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣟⣿⣉⣿⣻⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⠛⠁⠀⣿⡇⠀⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣀⢀⢸⡇⢀⠈⣿⡃
⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⢛⣯⣽⣟⣧⠙⠋⣼⣷⣭⣷⠄
⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠋⢉⢩⣧⡐⣒⣚⠂⠊⠓⡤⣽⣤⣤⣷⣦⣜⠾⠊⠑⠚⠉⠁
⠀⠀⠀⢰⣿⣿⣿⡾⡿⣿⣿⡄⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣶⣤⣤⣀
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠈
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠻⠿⠛⠛⠛⠛⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⢻⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⡄⠙⢿⣷⡶⠲⣶⣾⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣿⣿⡆⢢⠀⠉⣿⡑⠂⠈⢻⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡌⠻⣿⣧⣸⣧⠀⠾⢇⠀⠀⠀⠛⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣀⣹⣷⣬⣿⠋⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡟⠋⠁⢀⣠⣤⣶⣦⣄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠟⠂⠠⣾⣿⣿⣿⣿⣿⣿⡆⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣏⢹⡿⠻⣷⡶⠒⠛⠻⠿⣿⣿⣿⣿⡇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣷⠎⠰⠿⢿⣴⣆⣀⣤⣄⣀⣀⣈⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣯⣭⣽⣿⣿⣿⣿⣿⣿⣉⡀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠿⠿⣿⣟⣩⡿⣿⢟⣿⢿⡛⠿⣻⡿⣿⡻⢯⣿⣿⣿⣿⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢣⡛⣷⣙⡾⣋⣍⠛⣻⣈⠹⣧⠍⡓⠉⠀⣀⣥⣸⣿⣿⣿⣿⡖⠀⠉⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣿⣽⣶⣤⣭⣭⠋⡽⢀⡽⠀⠀⠐⠀⣿⠟⣿⣿⣿⣿⣿⣿⣇⡠⡀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⠛⣿⣿⣿⣧⣉⡙⢿⢷⡌⠁⡀⠀⠀⢰⣾⡷⣿⣿⠉⠁⠉⠉⠻⣼⢃⣤⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠻⣿⣿⣿⣿⣿⣼⣧⠞⣠⣰⣷⣾⣯⣀⣿⡇⠀⠀⠙⢳⡄⠈⢻⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣾⣘⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡇⠀⠀⠀⢻⣷⢿⣷⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⢻⣿⣿⣯⣭⣭⣭⣍⣹⡿⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⠁⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⠋⠀⠀⠀⢀⣠⣤⣴⣴⣾⡿⠿⠿⠿⠯⠉⠀⠀⠀⠉⠙⠓⠛⠻⢿⠛⠀⢈⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣦⣤⣶⣾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⣤⣬⣭⣤⣤⡄⢀⣀⣀⣀⣀⣀⣤⣶⣤⣶⣶⣶⣿⣶⣶⣾⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀
⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣽⢯⣿⣿⢘⣷⣿⠊⠙⠉⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⠀⡠⣣
⣿⣿⣼⣿⣿⣿⣿⣿⣿⠟⢵⠟⢱⣿⣿⣿⣾⣿⣿⠄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⣾⣧⠚⢡⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⢞⠂⠀⣽⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣿⠟⠉⣻⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠈⠀⠘⠋⠃
⣿⣿⣿⣿⣿⣿⣿⡟⠈⢀⠶⣼⣿⣿⣿⣿⠿⠿⢿⡿⠟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠞⠀⢀⡤⠤⠤⢤⠼⠃
⣿⣿⣿⣿⣿⣿⣯⣜⢢⡏⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢸⣿⣆⠀⠸⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇⠘⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⢸⣿⡛⠀⠀⠈⠂⢄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡹⣿⣿⣿⣿⣿⣿⣿⣦⢀⢀⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⣄⡻⣷⡀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠿⣄⠪⠃⠀⠀⠹⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⢻⣆⠀⠀⠀⠀⠃
⣏⣷⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢄⢸⣿⡆⠀⠀⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡠⠀⢠⡇
⣿⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣆⣤⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠤⠊
⣿⣿⣇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠅⠂⠁⠀⠀⠀⠀⠈
⣿⣿⣿⡄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⠏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠻⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄
⣿⣽⣿⣽⣯⣿⣿⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣯⣿⣿⣽⣽⣯⣯⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣍⣈⣀⣤⢤⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⣛⣉⡉⠭⡻⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⡠⠲⠦⠀⠛⠛⠻⠆⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠵⠻⠂⠀⠀⠀⢠⠀⠒⠲⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠂⠈⡀⠀⣰⠄⠰⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡧⢀⠀⡤⠂⡢⢠⡶⢌⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢠⠻⢀⠐⠈⠘⡝⠰⡌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡽⣿⢰⡌⠃⠴⠊⠀⣀⡿⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢻⡄⠇⡓⡤⢀⠇⣸⢸⠀⢈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠷⠄⠯⠙⠛⠒⠶⠶⠤⣤⣀⠀⠀⠘⣇⢸⣷⡆⢀⢤⡇⢸⠘⠀⠀⢝⢦⡀
⠀⠀⠀⠀⠀⠀⣀⠴⠊⢁⡤⠔⠒⠒⠀⠄⠀⠀⠀⠀⢠⡀⠉⡙⠦⣄⣹⡀⠸⣷⠸⣾⡇⢸⠃⠀⠀⠀⡏⡇
⠀⠀⠀⠀⢀⡜⢁⡼⣵⢁⡔⢊⠭⠀⠠⡐⡜⠀⢀⠀⠈⠢⡀⠈⠂⡈⠛⢿⣶⣿⣁⣿⣿⡿⢀⠀⡀⠀⣧⣿
⠀⠀⠀⢀⠏⢀⠞⣇⣇⡏⢀⡏⠀⢀⣀⠠⠃⠠⡘⡆⠀⠀⠈⠒⠀⠙⠫⠶⣬⣻⣯⣼⣿⣇⣤⡾⡿⠟⡉⢿⡀
⠀⠀⠀⣾⠀⡼⡄⠹⢿⡅⢸⡇⠀⢀⠄⠀⠀⣀⣬⡈⢦⣖⢤⣀⡀⠲⢤⣀⡤⢌⠘⢮⠙⢫⠙⠂⢡⡀⢸⡈⢷
⠀⠀⢸⣿⠀⡇⢸⠢⣈⢧⠀⣇⠀⠸⡄⠀⣿⠁⣍⠛⠶⣬⣛⠣⣄⢰⠁⢠⡉⠀⠑⢈⠂⡀⡀⣠⣿⢀⢎⡇⣸⡇
⠀⠀⠈⢿⡄⠹⡄⠣⡈⠙⠳⠌⠳⠤⣈⣓⣌⠧⣘⢕⡢⠤⣍⣙⣶⠿⢷⣶⣬⣉⣉⣁⣋⡡⠞⣡⡷⢋⣾⣞⠟
⠀⠀⠀⠈⠻⣄⠙⢦⣙⠢⠀⠀⢠⣀⠀⠀⠉⠳⡈⢵⡈⠙⠀⢀⡔⠉⠁⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠈⠳⣄⠈⠻⣶⣬⣀⡘⠂⠀⠀⠀⢹⠀⣉⣑⠒⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⣏⠙⠫⠿⠶⠶⠒⠋⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠦⠠⢄⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⠆⠀⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠄⠀⠈⢰⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡾⠊⠁⠀⠘⣧⠀⠰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠁⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡄⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠳⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⢱⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠈⠀⣄⠀⠀⡀⠀⠀⠸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣄⣀⣀⠀⠀⠀⢠⣄⣀⡇⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠉⡟⠀⠀⣠⣿⣿⡏⣿⠀⠀⢸⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢠⠃⢠⠊⠀⢹⡿⠃⢿⣧⠀⠸⡄⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠆⠀⠁⠀⢠⡿⠁⠀⠘⡿⢁⣴⣿⣆⡀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠐⠀⢀⣠⣴⡿⠁⠀⠀⠈⡠⠛⢿⣿⣿⣿⣾⣶⣵⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⠐⠀⠉⠉⠀⠘⠤⠄⠈⠀⠀⠀⠈⠉⠉⠉⠉⠁


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

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢤⠠⡄⠀⠀⠀⠀⡠⠐⢦⣄⠀⠀⠀⠀⢀⣴⠠⠀⠀⠀⠀⠀⣠⣶⣄
⠀⠀⠀⣼⡏⠆⠀⠀⠀⢀⢸⢸⣿⠂⠀⠀⠀⢰⠀⢸⣿⣷⠀⠀⠀⢸⣿⡓⡀⠀⠀⠀⠀⣿⢹⣿⡇
⠀⠀⡸⣿⡇⡄⠀⠀⠀⢸⣿⣸⠃⣾⡀⠀⠀⢸⠀⢸⣿⣿⠇⠀⠀⠁⠹⣧⠗⡂⠀⠀⠀⢿⣼⣿⡇
⠀⢀⣿⣿⠗⠁⠀⠀⠀⢸⣿⣿⣾⣿⠇⠀⠀⢸⣦⣸⣿⠟⡆⠀⠀⣠⠐⡗⡁⡄⠀⠀⡀⠀⢹⣿⡇
⠀⣾⣿⣿⠀⠀⠀⠀⢈⡈⠙⣿⡿⠛⠀⠀⠀⣿⣿⣿⡡⢠⠇⠀⢀⣿⣿⣯⡴⡇⠀⢰⣷⣄⢸⣿⡇
⠀⣹⣿⣿⢀⡤⠄⠀⣮⣳⢴⡋⠀⠀⠀⠀⠀⠙⠻⣯⡴⠋⠀⠀⢸⣿⣿⣿⣻⡇⠀⢸⣻⣿⣿⣿⡇
⠀⠹⣿⡟⠆⠀⠀⠀⠳⣭⡿⠀⠀⠂⠀⠀⢀⣄⠄⡏⠀⣠⠀⠀⢨⠙⢿⡿⠏⠃⠀⠀⠙⣿⣿⣿⡇
⠀⠀⠙⠛⠈⠁⠀⠀⠀⠁⠇⠀⠀⠀⠀⠀⠸⣿⣿⠓⠊⠁⠀⠀⠘⢄⣿⢁⠄⠀⠀⠀⠀⢰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠂⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⢀⡤⢖⣢⣤⣠⡤⢤⣄⡀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠧⠤⣤⣤⣤⣤⣀⡶
⠀⠀⠐⠀⢰⣿⣴⡫⢍⣛⣋⠽⣿⣵⣞⢋⣡⣶⣶⣦⣤⣀⡀⢸⣇⣒⣐⣞⣛⣛⣛⣛⣫⣟⣦⡀
⠀⠀⠀⠀⠀⠙⢿⣿⣤⣂⣀⠐⢄⠑⣄⠙⢿⣿⠿⠿⠛⠋⠁⠀⠙⠋⠉⠓⢬⣻⡿⠿⣿⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠉⠉⠉⠈⠁⢠⣴⣶⣶⣶⣶⡒⠉⠉⠙⠻⣿⣿⣿⣿⣶⣀⣀
⠀⠀⠀⠠⠠⠄⠄⣤⣮⣤⣼⣟⣆⣦⡤⠀⢿⣿⣿⣿⣿⠿⠿⠖⠒⠒⠒⢊⣟⣿⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠛⠉⠉⠉⠀⠀⠀⠉⠙⠛⠃⠀⠀⠄⠀⠀⠤⠡⠏⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠖⢌⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡊⠍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠱⡌⢆⣀⡀⢀⣀⣀⡔⡡⠊⠀⡐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡧⠐⠀⠉⠀⠀⠀⠀⠀⠀⠉⠑⠂⢤⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡥⠒⠉⠑⢢⠀⠀⠀⠀⢠⠖⠉⠉⠒⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⠇⠇⠀⠀⠀⠇⠺⠂⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⢰⠀⠀⠸⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠘⠀⠀⡇⠀⠀⢠⢇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠱⡄⠀⠀⠀⠀⢠⠙⠄⠀⠀⡆⢠⠁⠀⢠⠃⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⢀⡀⠀⢀⠇⠀⢸⠆⢀⣧⣼⡀⣰⠁⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠉⠈⡄⡈⠀⠀⡆⠀⠻⢿⣿⠟⠀⡇⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⠀⠀⠀⠰⡇⠀⠀⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠉⠀⠀⠀⠀⠘⢄⠀⠱⣀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠐⢢⡸⠑⢦⠈⠁⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠤⢄⠘⠀⠀⠀⠀⠁⠢⣀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠉⠀⠒⠓⠒⠂⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠱⠂⠤⠄⢀⣀⣀⣀⣀⣀⣀⠠⠄⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣁⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿