Coffee bean Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠂⠴⣰⣤⠀⠀⠀⠀⠀⠀⠀⢀⣾⣤⣄⡀⠀⠀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⢀⣤⣶⣿⡿⠋⠱⠞⣧⠀⠀⠀⢰⢋⡉⠙⠛⠿⣶⣶⣤⣤⣄⣀⡀⠘⢳⣆
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⢂⣤⣼⣿⡿⠋⡀⠐⠢⣰⣿⠀⠀⠀⢸⣦⡁⠀⣀⠀⠀⠈⠉⠉⠉⠻⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⣴⠅⠀⠐⣫⣴⢿⣧⠿⠋⣠⠆⠁⠀⣴⣿⣿⠀⠀⠀⠈⢿⡻⢦⣤⣬⣠⣀⣀⠀⠀⠐⠴⠶⣰⡟
⠀⠀⠀⠀⠀⠈⣿⠀⣰⡾⣻⡿⠋⠀⠀⠀⠁⣀⡴⣾⣿⣿⣏⡗⣁⣤⡄⠀⠉⠀⠀⡁⠌⣽⡟⠻⢿⢿⣿⣿⡟⠀⣠⣄⠄
⠀⠀⠀⠀⠀⠀⢻⡚⣿⠞⠙⠀⢂⡠⠀⢒⣯⣿⠴⠛⠋⠉⠉⠁⠀⠀⠀⠈⠉⠉⠙⠛⢮⡙⠛⠻⠿⠻⠛⠛⠿⠿⠿⠟⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⣒⡛⢿⣶⠿⠛⠩⠀⠀⠀⠀⠀⠀⢠⣂⣀⣀⣤⣄⣶⠶⠶⠾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⠟⠁⠐⠃⠀⠀⠀⢀⣠⣤⣶⠟⢛⠉⣉⣁⣠⣤⡶⠶⠟⠛⢳⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣴⣶⡴⠶⢛⣛⣉⣭⡤⠴⡶⠿⠿⠟⠋⠁⠀⠀⠀⠊⠐⣺⠇⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠥⠒⠛⠉⠉⠁⠀⠏⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠔⣠⣾⡿⠀⢀⢀⠔⡐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡂⠄⣀⠀⢠⠀⠈⠀⠀⠀⠀⠀⢀⣀⡤⢴⣺⣵⣾⣿⣿⠃⡔⢡⢊⠌⡔⡐⡥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⢳⠲⢤⣤⣭⣀⣀⣀⣤⣤⣭⣭⣶⣾⣿⣟⣿⣿⡿⢁⠈⡐⡡⢃⠌⡼⣱⢫⡯⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⢄⣀⠒⠛⠛⠿⢿⣿⣿⢿⣿⣻⣿⢿⡺⠕⠊⠁⠎⠔⠡⠂⠊⠘⠁⠉⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠂⠤⠴⠒⠒⠋⠉⠉⠈⠁⠀⠐⠶⠤⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣶⠶⢦⡤⢤⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠞⠑⠈⠀⢊⡡⢊⠴⠛⢁⡤⠞⣋⠉⠑⢢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⣟⡶⢶⣎⣀⣠⢔⡋⠀⠀⢀⡰⠟⠊⠡⠄⠒⠒⠚⠓⠛⢢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⢹⡉⠓⠶⣭⠭⣛⡙⠒⠶⢍⣠⠔⠂⡒⠂⠀⠀⠈⠀⠀⠉⠁⠘⡳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣇⢰⡀⢣⠂⠀⠙⡝⠒⠦⣌⡑⠢⣤⡀⢤⣄⣀⡀⠀⣀⣩⡍⠙⠛⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠸⡄⢳⢸⠄⠄⠀⠘⡴⡎⢶⠙⣑⢄⡉⠫⡉⠁⠀⠀⠀⠀⢉⠐⠒⠳⠬⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣌⣧⠄⠸⡀⠀⡆⠃⠀⢀⠈⢿⡜⠢⣈⠳⣆⠀⠀⢀⣀⡉⠒⠒⠲⠾⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⢀⢣⠀⡇⠀⠀⠀⠀⠈⡟⠀⠈⠱⣌⠳⣌⠛⠗⠊⠉⠒⠤⠀⢀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⠸⡆⢁⠀⠀⠃⠀⠀⠘⡀⠀⠀⠘⡢⣈⠣⣄⠀⠀⠀⠀⠀⠄⣌⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣌⠓⠿⡜⡀⡆⢰⠀⠀⡠⠡⠀⢂⠀⢱⡦⠕⠨⢛⠿⣷⡒⠀⠤⠤⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣤⣤⠴⠤⠤⣄⣀⣀⠀⠀⠀⠀⣀⡤⠚⠉⠱⣻⣿⣿⠋⢳⡙⢧⣹⡀⢆⠀⠄⠁⢣⠀⢧⠀⠹⡂⠀⠀⠈⠑⠛⠛⠳⣤⣀⣻
⠀⠀⠀⠀⠀⣴⠺⣿⣿⣆⣤⣀⣀⣀⠉⠛⢶⣤⡾⠋⢀⣀⣠⣶⣿⡿⠁⠀⢸⣧⠀⠉⢳⡈⢢⡘⣆⠈⢢⠈⢳⡀⠘⢄⠀⠢⣀⠀⣤⠀⣈⡥⠛⠳⠤
⠀⠀⠀⠀⠀⣿⣀⠈⠙⠻⠿⢿⣿⣿⣷⣤⣾⠋⠁⣰⣿⣿⣿⠞⠋⠀⠀⢀⣿⣿⠀⠀⠀⠙⠚⠓⠚⠳⣄⣑⣶⡹⢦⣈⣛⡶⠋⠙⠛⠛⠁
⠀⠀⠀⠀⠀⢿⣷⣄⣄⠀⠀⠀⠈⠙⢻⠋⢀⣀⣼⣿⣿⡿⠁⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣾⣤⣤⣤⣿⣾⣿⣿⡿⠟⠉⠀⠀⠀⣼⣶⣿⣿⡟⠁⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⢿⣏⣀⣀⣀⣀⣰⣧⣶⣿⣿⣿⠿⠋⠀⠀⠀⠖⠛⠋⠀⠀⠐⠛⢻⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⡀⢀⡀⢠⠄⠀⠀⠀⠀⠀⠀⣽⣿⣾⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢋⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣿⣤⣆⣠⣤⣤⣤⣼⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⢋⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⣡⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⢇⣾⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⢢⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡏⣼⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠸⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⢸⣿⣿⡿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠛⣉⣤⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠘⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⣛⣋⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⠶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⣋⣴⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⣰⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡸⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣡⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠃⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⢰⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢛⣋⣉⣉⣉⣉⠛⠻⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣭⣉⣭⣉⣙⣛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⣌⡙⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣆⠹⣿⣿⣿⣿⣿⣄
⠀⣠⣾⣿⣿⣿⣿⣿⡿⠟⠛⣋⣉⣙⣛⣧⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣷⠆⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣆⠻⣿⣿⣿⣿⣿
⣰⣿⣿⣿⣿⣿⡿⢋⣤⣾⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⢋⣵⣾⣿⡄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⣌⠻⣿⣿⣿
⣿⡿⢟⣋⣉⣥⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⡿⠟⣡⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⡘⢿⡟
⠩⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⢀⣾⣿⣿⣿⡿⠛⢉⣩⣴⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⡿⠟⠂
⠀⠈⠻⢿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⣼⣿⣿⡿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⡿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⡌⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠐⠘⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⡸⠀⠀⠀⠆⠃⠀⠀⢸⡄⠀⠀⠀⢰⠀⠀⢀⣠⡴⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⢰⢀⠀⣸⡅⠀⠀⠀⠀⠠⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠠⢀⢀⠐⠀⠀⠀⠀⠑⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠘⠿⢶⣯⠶⠀⠀⠀⠀⠙⠂⠀⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠀⠀⠄⠀⠀⣠⣀⣤⣴⣶⡶⠶⠲⠦⠄⠀⠀⠀⠀⣀⣴⡺⠋⠀⠀⠀⠀⠀⠀⠀⢈⣇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⢀⡄⠘⠉⠁⠀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠿⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠖⠈⠁⠀⠈⠓⠀⠠⠔⠚⠉⠀⠀⠀⠀⠀⠀⢄⠀⠰⠓⣤⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⢶⠶⠔⠲⠶⠒⠂⠛⠂⠀⠀⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠉⠋⠓⠲⢦⣄⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⡾⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠛⠁

⠀⠀⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⣼⡥⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣿⡁⠸⢷⡤⡀⠀⠀⠢⠀⠀⢀⠃⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⣤⡴⠶⠶⠗⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠈⠋⠛⣧⣴⠀⠀⠘⠀⣠⡾⠛⠁⠀⢀⡌⠀⢸⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⢡⣦⣄⡀⠀⠀⠈⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣤⣀⡈⠁⠀⠀⠰⣚⠉⠀⡀⢠⠤⠊⠀⠀⠈⠛⠒⠒⠐⠒⠋⠁⠀⠀⠀⠀⠙⠻⠿⠷⠷⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⠒⣛⣳⣶⣶⣤⡀
⠀⠀⠀⠀⢀⣼⣿⢽⣾⣿⣿⠿⠿⠿⠿⠟⡧
⠀⠀⠀⠀⣼⣿⣿⣿⢿⣫⣵⣾⣿⣿⣯⣶⡇
⠀⠀⠀⠀⢻⣛⠛⠛⢛⣉⣥⣶⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣶⣶⣶⣶⣿⣦
⠀⠀⠀⠀⣴⣿⣿⣷⣿⣿⡿⠿⠟⢛⣫⣵⣿⡇
⠀⠀⠀⢸⣿⣿⠿⣋⡥⠴⣶⣞⣿⣿⣿⣾⣿⠁
⠀⠀⠀⢸⣿⣷⣮⣵⣶⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠛⢿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣩⣥⣶⣿⣿⢿⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣱⣿⣿⣽⣿⢟⣵⠏⣰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣿⠟⣵⡿⢋⣼⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣿⣿⣿⣿⠿⣋⣴⣿⣿⣿⡟⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⢿⣷⣾⣿⣿⣿⣿⠏⠀⠀⠀⣠⠞⣩⣸⡟⣽⣿⣦⠀⠀⠀⠀⠀⠀⣠⣶⣾⡿⡿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢡⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⢰⣧⣾⣿⣿⢸⡇⣿⣿⡇⠀⠀⠀⠀⡼⣱⣿⣿⡇⡇⣽⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢎⣎⣿⣿⡏⣼⣿⣿⣿⡇⠀⠀⠀⠀⡇⣿⣿⣿⠃⣧⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⡟⣼⣿⣿⣿⣿⠃⠀⠀⠀⠀⣷⣿⣿⣿⠀⣿⣷⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠏⡼⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠹⣿⣿⣿⡀⢿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣼⣿⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣜⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠉⣀⡠⢤⡐⠟⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⡠⢊⠵⠚⠉⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⢀⢞⡜⠁⠀⠀⠀⠀⠀⠀⠀⡼⢧⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⣠⢫⠞⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣸⠴⠚⠉⠁⡠⠈⠙⠢⡀
⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⣠⢞⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠊⠀⠀⠀⢠⢮⠎⠀⠀⠀⠹⡄
⠀⠀⠀⡞⠀⠀⠀⠀⠀⣠⣾⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⢠⢯⠏⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⣇⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⡏⡎⠀⠀⠀⠀⠀⠀⢸⢹⡀
⠀⠀⠀⣏⠳⢾⣉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⡱⠃⠀⠀⠀⠀⠀⠀⣸⢸⠁⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠘⢦⡀⠀⠉⠙⠓⠒⠒⠒⠚⠋⠉⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣠⢃⡏⠀⠀⠀⠀⠀⠀⠀⡸⠀⣇
⠀⠀⠀⠀⠀⠙⠲⢤⣀⣀⣀⣀⣀⣀⣀⡤⠤⢾⠁⠀⠀⠀⠀⠀⠀⡔⣡⠎⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡴⢋⠔⠁⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡴⣫⠖⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⣐⡡⠊⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢥⣀⣀⣀⣀⣀⣀⣠⠤⠒⠋⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣏⠀⠃⠋⠀⢶⢌⡛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢸⡓⡙⣦⠀⠀⠀⠁⠐⡑⣠⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠠⠀⠀⠳⢦⣬⣳⠦⣄⠀⠈⠀⠡⠪⠣⡠⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠈⠳⣌⢧⡀⠀⠀⠁⠀⠘⠳⡢⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠠⠀⠀⠙⢷⠛⣆⡀⠀⠀⠀⠀⠑⠜⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠿⠿⠶⠶⢶⣤⣤⣀⣀⣀⡀⠀⠀⠙⢷⣅⢄⡀⢀⠀⠀⠈⢳⡄⢝⠲⢦⡀⢁⠀⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⡉⡄⡘⢇⠁⠀⠂⠀⠀⠄⠍⠉⡉⠉⡙⢷⡄⠀⠈⠻⢷⣮⣄⠀⣀⠀⠀⠙⢷⡭⣆⣷⠀⠀⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⡁⢆⠈⠈⠐⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠙⢷⡄⠀⠀⠉⠻⢿⣶⣕⣤⡀⠀⠻⣌⣹⣧⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡀⠐⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣿⢸⡿⠀⠀⠀⠀⢀⣨⡽⠿⠛⠛⠓⠛⠛⢛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠈⠀⠀⣀⣤⡴⠶⠶⠶⠶⢦⣤⣴⣶⣿⢟⣹⠞⠅⣸⠇⠀⢀⣠⠖⠋⠁⠀⠐⠌⠀⠀⠁⠀⣩⡾⢻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⢀⣠⡶⢛⢡⣠⣢⣤⣶⣾⣿⠿⠿⠛⠋⠉⢉⠁⠎⢠⡟⣠⡴⠋⠡⠐⠄⠀⠀⠀⠀⠀⠀⣴⠟⣡⡞⠋⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠛⢋⣡⠴⠖⠛⠛⠛⢛⠉⠅⠄⠄⠀⠀⠀⠀⠀⠀⣠⡟⣴⠏⣐⠄⠀⠈⠀⠀⠀⠀⠀⢠⡾⠡⢰⠏⠀⠀⠰⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡅⢦⠢⠃⠃⠀⠐⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣾⡯⡠⠀⠀⠀⠄⠀⠁⠀⢀⣴⠿⣈⣴⠟⠀⠀⡀⡘⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⣸⡿⠮⡢⠀⠀⠀⢀⣤⠶⠟⢋⢁⡴⠋⠁⠀⠀⠂⡙⣜⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣤⣄⣀⣤⣤⣤⠶⠟⠋⠁⠀⠀⣿⡇⠄⠀⡀⠀⢰⠏⡡⠒⣉⡴⠜⠃⠀⠀⠂⠀⡠⡑⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⣀⣴⠞⢋⠐⣡⠞⠁⠀⠀⢀⠀⢠⢠⡱⢹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣏⠥⢒⣡⠞⠁⠀⠀⠀⠠⡠⡳⠑⣡⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣁⢆⢢⠠⡡⠐⣀⣼⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣀⣀⣀⣤⣄⣀⡤⠤⢶⠒⠒⠋⠉⠱⡄
⠀⠀⠀⠀⠀⠀⢀⣾⣄⣀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⣀⠀⠀⠸⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⣴⠇
⠀⠀⠀⠀⠀⡐⠉⠀⠈⠉⠓⠒⠠⠤⣤⣤⣀⣀⠀⠀⠀⠈⠑⡄⠘⡘⢷⣦⣤⣤⣤⣤⣤⣀⣀⣤⣶⣿⡟⡝
⠀⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠙⠛⠛⠛⢶⣿⠀⠘⣦⠉⠙⠋⠉⠉⠉⠉⠉⣻⣐⣭⣾
⠀⠀⠀⠀⠀⠈⢄⠛⠷⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡯⠔⠈⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠉⠁⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠛⠳⡶⣦⣤⣤⣴⣶⣶⣿⡿⠋⠀⠀⠀⠀⢀⣤⣤⠖⠛⠋⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡂⠑⠀⠌⠉⠻⢟⣻⣿⡇⠀⠀⣠⡴⠾⠛⠭⠁⠀⠀⠀⠀⠀⠀⢀⣼⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠛⠛⠋⠉⠀⢿⣾⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⣣⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠻⣟⢶⣦⣤⡄⠀⢠⣴⣾⣿⣿⠿⣯⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣌⡉⠈⠁⠀⠀⢈⣙⣭⣷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠙⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢶⠛⠛⠒⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣖⡾⠍⠉⠀⠉⢳⣦⠀⠀⠀⠀⠀⠀⠀⣼⢫⠋⠀⠀⢸⡇⠀⠀⠙⣦
⠀⠀⠀⠀⢀⡠⣾⠋⠀⠀⢌⠻⣦⣀⠴⢒⣯⠿⠷⠖⠛⠁⣀⣠⠖⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⣿⡘⠄⠀⣠⣼⠟⠀⣰⠆⣼⠆
⠀⠀⠀⢀⢎⠀⢸⡆⠀⠀⠀⠃⠹⣿⡔⠋⠀⠐⠛⠛⢋⣩⣥⣴⠶⠾⢿⣿⣥⡀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣀⠿⡅⢀⣀⣤⣾⡿
⠀⠀⠀⣼⡜⠀⠈⢿⣄⠀⠀⠀⠀⢻⣷⠈⠉⣠⣶⢟⡫⠭⠀⠀⠀⠀⠀⠀⠉⢻⣷⡀⠀⠀⠀⠀⠈⢿⣿⣦⣤⣤⣤⣾⣿⠟
⠀⠀⠀⢻⢱⠀⠀⠀⢻⣆⠀⠀⠀⢸⡟⣧⣾⠟⠑⠉⠀⠀⠀⠀⢀⣀⣀⣠⣴⣾⠟⢻⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠁
⠀⠀⠀⠘⡆⠀⠀⠀⠀⣿⠀⠀⠀⢸⠇⣿⡏⠀⠀⠀⠀⣠⣴⢿⡿⠿⠛⠛⠉⠁⡀⡾⠀⠀⢀⡤⠴⣒⣒⣒⣒⣒⣒⣒⣶⣢⠤⢄⡀
⠀⠀⠀⠀⠹⡄⠀⠀⠈⢹⣦⠀⢀⡞⣸⣿⣧⡀⢀⣤⣾⠟⠀⠀⠀⠀⠀⠀⢀⡼⡽⠁⠀⢠⡰⠚⠋⢉⠉⣉⣩⣭⣭⣭⣍⡙⠻⠶⡌⣆
⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣉⣓⣬⡾⠋⢻⣿⡛⠛⠙⠁⠀⠀⠀⠀⠀⠀⢐⡯⠞⠀⠀⠀⠘⣯⣓⠲⠤⠤⢴⣶⣶⡶⠶⠶⢶⣶⣶⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠁⠀⠀⠀⠙⠿⣦⣤⣤⣀⣀⣀⣤⠤⠞⠉⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠙⠒⢄⣠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠲⢌⢦⠤⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣸⠋⠀⠀⢀⡀⣀⣟⣴⣢⣦⣴⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠛⢦⣴⡛⣻⡟⣯⠟⣰⢻⣿⠗⠠⠿⣤⣰⠶⢞⣒⣁⣾⣻⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠉⠉⠉⠈⠑⠊⠁⢴⡞⠙⢡⣸⣬⡾⠷⢶⡿⢧⡞⣿⡭⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢦⣀⠀⠀⠀⠀⠀⠀⠀⠐⣵⠏⠙⢿⣀⠌⢔⢙⣫⢑⢋⡼⠙⠐⣌⠯⠱⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣄⠀⠀⢀⣀⣿⠀⠀⠀⠉⠛⠤⠬⠌⣦⡳⠄⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠉⠐⠠⠄⠀⣀⠀⠀⠄⠄⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡼⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆
⠀⠀⠀⠀⠀⠀⠀⠅⠣⠀⠀⠀⠀⠀⠀⣠⢦⣩⢾⣟⡻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡰⡿⢻⣿⡳⠟⣎⣞⣯⣹⢿⡯⣦⣄⡻⠂⣞⣴⢠⣦⡲⢶⣠⡆⣤⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⡾⠕⡛⢸⡿⣿⠏⠒⣾⠛⠋⣣⢏⣙⢫⣷⣓⡽⠻⠏⠁⣩⡿⡚⢿⠇⣀⠟⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠋⠆⠐⠛⠃⣿⠻⠿⣛⣾⡛⣯⢁⠸⠴⣛⡻⢻⢿⠲⠽⠎⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠃⠀⠈⠁⢉⡀⠈⣥⠉⠹⠝⠁⠀⠘⠃⠌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠲⡄⠀⠓⢁⠀⠈⣉⠧⡴⠀⠀⠀⠀⠀⠀⡄⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⠰⡀
⠀⠀⠀⠀⠀⠀⢹⣆⣀⠋⣠⠟⣡⠞⢱⡄⠀⠀⠀⠀⠀⢭⡀⠀⠘⡇⠀⣶⠄⠀⠀⠀⠀⠀⠳⠄⣠⠤⠴⣦⣋⡺⠄⣓⣼⢏⡁
⠀⠀⠀⠛⠃⠀⡼⢿⡵⢋⣴⠞⠁⢀⣬⠀⣤⠀⠀⠀⢀⡀⠱⣤⡀⢗⠀⢨⡄⣠⢄⠐⠀⠀⠀⠀⠐⠦⣦⣤⣼⣶⠧⠜⠉⠾⠆
⠀⠀⠀⠒⠂⢰⠛⣾⣷⣏⠀⢀⡴⠛⠃⠂⠀⠀⠀⠈⠀⠔⠂⠒⠀⠠⣄⠉⠁⠻⠖⠀⠀⠀⢀⣀⣴⣠⡄⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⣰⠀⣀⣙⣉⣙⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠛⢀⡄⠀⢤⣠⣄⠀⠀⠉⠀⠀⠀⠀⠀⠐⠷⠂⠀⠈⠉
⠀⠀⠀⠈⠁⢀⠈⠁⠈⠀⠀⡤⠀⠀⣴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⠐⠚⠋⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠄⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣴⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢘⠀⣠⢛⡀
⠀⠀⠀⠀⠀⠐⠀⠀⠲⠿⣦⠀⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⠀⡀⠀⣀⠞⠀⡄⠾⠞⠉⠡⠀⠂
⠀⠀⠀⢶⡀⠀⠑⢄⠀⠀⢚⡛⠛⠳⠤⣤⣴⣃⠤⠤⠖⢊⠀⠀⠀⠀⠢⠌⢁⣠⠞⢀⡈⠙⠀⠀⡿⠆⠒⠫⠀⠐⠁⢀⡀
⠀⠀⠀⠀⠙⠂⠤⠊⠀⠰⣄⠈⠙⠢⠤⣄⡙⣧⣤⡠⠶⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠢⠭⠁⠀⢒⡥⠠⠄⠄⠂⠀⠀⠀⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠄⠀⠠⠜⠓⠀⠈⠛⠲⠤⣀⡀⠀⠀⠉⠒⠊⠀⠀⠀⠀⠀⠈⠉⠀⠀⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⡱⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⢠⣀⡀⠖⠀⠀⠀⠁⠀⠠⠀⠀⡷⢀⡀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠄⡀⠀⠀⠀⠤⠉
⠀⠀⠀⢈⠒⠀⢀⣀⠐⠆⠀⢀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣠⠤⣤⡄⠺⣁⠀⠀⠀⠀⠠⠀⠀⠀⠑⠠⢤⠤⠄⠤⠄
⠀⠀⠀⠀⠑⠲⠄⠀⠠⠴⠒⣨⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⢀⡼⠀⠙⢦⡈⢣⠀⠀⠀⠀⠀⠁⣀⡤⢄⠈⠑⠒
⠀⠀⠀⠀⠀⠀⠈⠳⠦⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠉⠀⠀⠀⠀⠉⠊⠀⠀⠀⠀⠀⠪⠥⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⡿⠛⣿⣻⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢠⡉⠙⠢⠂⠀⠀⠀⠀⠈⢿⣿⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣄⠀⠻⠈⣀⣤⠔
⠀⠀⠀⠀⠀⠙⠓⠂⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠙⠛⠛⠁⠀⠀⠴⠦⣄⣬⠁⠀⡁⢉⣉⠃⠀⠀⢠⣶⢖⡀
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡖⠻⡛⠻⠟⣷⣶⣆⣄⠀⠀⠀⠈⠛⠋⢛⡆⠈⠁⠀⠀⠀⠈⠷⠟⠁
⠀⠀⠀⣤⡉⣡⠔⢚⣅⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠁⠈⠀⠻⢀⣠⠖⠛⠛⠆⠙⠁⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣀⣀⠀⣠⠞⣧⠀⢶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠨⠷⠞⠃⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⠀⠀⠀⠀⠒⠲⣆⡀⠈⠇⠀⠀⣹⠀⠀⠀⠀⠀⢠⡄⣤⡀⠀⠀⠓⠶⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠚⠉⠩⠉⠍⠭⠒⠰⢶⠄⠀⠁⠉⢢⠀⣰⠃⢠⠀⠠⠀⠀⠀⢺⡇⣿⠇⠀⠀⠀⠀⠀⠤⢶⣦⡀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡔⠁⠠⠶⠀⢰⡟⠀⠠⠀⠘⠀⠀⠀⠀⠀⠁⠀⢀⡔⠉⠛⠿⡆⠀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣶⠋⠋⢉⣼⠀⠀⠀⠀⠀⣾⠃⠀⠄⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣰⠿⠔⠁⠀⣠⠋⠈⠀⠀⠀⠀⠀⢿⡇⢀⠀⠀⡊⠀⠀⣀⠀⠀⠀⠠⠤⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡾⢧⠀⠀⠀⢼⠃⠈⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠌⠀⠀⠈⢥⡁⠠⠔⢒⡞⠁⢠⣟⠋⠉⠛⠆
⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⢻⠉⢀⠌⠀⠀⠀⠀⠀⠀⠙⠕⠈⠀⠀⠀⠀⠀⠀⠐⠟⠛⠁⠀⠈⠡⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⠀⠀⠀⠉⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠉⠡⡀⠀⠀⡀⠀⠑⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠈⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠲⠒⠦⢤⣀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⡄⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⢄⠀⠀⠄⠀⠀⠀⠀⠀⣰⣿⣧⠶⠖⠒⠓⠒⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠐⠀⠀⠀⣰⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣄⣀⠀⠀⣰⣤⡾⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠁⠀⠀⢀⠀⠀⢠⣿⠀⠉⠛⠻⠿⠿⢿⡟⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠐⣴⣿⠃⠀⠀⠀⠀⠀⠀⢿⡇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⣏⡀⠀⠀⠀⠀⠀⠀⠀⣂⣥⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣶⣤⣴⠶⠶⠛⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⡀⠀⠀⠀⠀⢀⣠⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡈⠀⢘⡆⠀⢀⡴⢿⡷⠛⠁⠀⣀⣀⣀⣀⣀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢲⣤⣞⡉⠙⣷⠻⠷⡖⣋⡴⣯⠒⢒⡾⠽⢫⣧⣯⣴⣷⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠻⢶⣼⠁⠀⣳⡶⢿⣄⣀⣿⠿⣾⣷⣾⠷⣶⣿⠻⠟⠃⠈⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣄⣀⣀⣿⡶⠖⢿⣿⠟⠉⠉⣷⣀⣀⣸⣿⡷⣄⣙⣅⣠⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣩⢟⣿⢿⡠⠤⣠⣿⣶⣶⣾⠃⠉⠉⠁⠈⠉⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢿⣤⣀⣴⣿⣿⣿⠳⢦⣀⣉⠙⠲⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣲⣼⡿⣫⢿⡏⠀⢹⠂⠀⠙⢶⣄⡀⢠⡄⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⡖⣫⠕⣿⢏⣴⡇⣻⣥⣰⣾⣆⠀⡄⠘⡏⠙⢦⡤⠤⠀⠀⠈⠳⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⢟⠁⢰⣧⣾⠗⢻⠟⣧⡀⠀⠞⡍⢿⣶⡇⠀⠀⠀⣎⠙⢶⡒⠢⠄⠀⠀⠲⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⡵⢂⣼⣿⠁⠀⢸⡀⢀⡇⠀⠀⠠⡜⡮⣿⡀⠀⠀⠙⠀⠈⣿⢦⣤⣤⣀⠀⠀⠘⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣾⣴⣿⠋⣿⠀⠀⠘⣇⠘⠳⣆⠀⢊⡁⢱⣸⡟⢦⡀⠀⠀⠀⢹⠈⠙⢦⣀⣀⡀⠀⠈⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣟⠁⠀⢳⠀⠘⢡⣿⡄⢰⡟⣠⠎⠀⢀⠻⢧⡀⠉⣧⠀⠐⠀⠀⠇⠈⠳⣦⡀⠀⢀⡀⠙⣧
⠀⠀⠀⠀⠀⠀⣠⢞⠋⢹⠁⠸⡆⠀⠘⢦⡀⠈⠞⣦⡀⠙⣇⠀⢀⣄⠀⢳⣷⠀⠘⠳⠶⠾⠦⣤⡀⠀⠁⠙⠷⣍⠀⠰⢾⣇
⠀⠀⠀⠀⠀⢰⡇⡆⠀⣺⠀⠀⠙⣆⠀⠘⢧⡀⠀⢸⣿⡀⢿⡒⢮⡛⠀⡤⡘⢦⡀⠀⠀⠀⠀⠀⠳⣄⣠⣀⣀⣈⣓⣦⣀⠻⡆
⠀⠀⠀⠀⠀⢸⡗⠇⠀⡿⡇⠀⠀⠹⣄⠀⠀⠙⢧⡜⠉⣿⣦⢻⡌⠓⠶⠧⢷⣌⣇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠛⠻⢿⣆
⠀⠀⠀⠀⠀⠈⢳⠀⠀⠁⢹⣆⠀⠄⡈⠳⡀⠀⠀⠉⠛⠛⠾⢦⡷⠀⠀⠀⠀⠻⢾⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣸⡿⣦⠀⠈⠀⢱⡀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡃⠁⠁⠈⢷⡀⠰⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣆⠸⣷⠈⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡹⣧⣹⡀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⠄⠀⠀⠀⣾⠛⠛⣻⣶⣄⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢒⣿⠿⣴⠤⠤⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣶⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠐⡀⢀⡘⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢘⠀⠀⠀⠀⣹⣚⠀⠀⡁⢈
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣦⣼⣿⣿⡿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⡤⣀⣀⡄⠀⠀⡐⠂⠉⠑⠁⡠⠆⡞⢅⠁⠀⣠⠀⢂⠂⢐⢠
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡄⣾⠿⠿⠽⢧⠀⡄⠀⠀⠀⠀⠀⢙⠀⣬⣋⠻⣼⣟⠂⠐⢎⠁⢦⠀⠼⢄⢊⠑⢬⠞⡈⠛⢡⢀⡤⠀⢀⠀⠀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢛⣡⠱⠶⠀⠀⠘⣽⣷⣄⠀⡀⢀⠀⠌⠄⢸⠶⠀⠅⠙⣥⣧⡽⠓⠊⠂⠘⠚⢻⠈⠐⡯⢀⠀⣸⢾⠒⠚⠣⢅⢘⡅
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⠀⠈⠀⠀⡀⠀⠀⠀⣿⣭⣿⡿⡁⣈⠵⣄⠀⣀⢤⣠⠘⠀⠈⠑⠀⠀⠦⢧⣘⣂⢢⢀⣈⣻⣆⡿⢡⣔⠦⠀⢀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣿⠦⣤⣀⣀⠀⢀⣀⡂⠀⠠⠉⢁⣛⣌⣄⠹⣮⡹⣶⠫⣏⠀⡄⠀⠀⠀⠀⠀⠈⢻⣝⡿⢿⣿⣿⣇⠀⠉⣳⣄⡠⠄⠀⠀⢀⠄
⠀⠀⠀⠆⠀⣀⣴⢚⢓⠊⡱⠀⡌⣂⣤⠍⠉⠛⢷⣤⡀⢠⡄⠀⣀⠍⠝⣵⣿⣿⣿⠶⣭⢋⣓⡄⠀⠀⠀⠀⠀⠀⠘⣿⠀⢹⡉⠁⢱⣄⡨⠙⠻⢆⡀⠠⠊
⠀⠀⢐⣦⠪⠀⣀⠤⠀⠐⣃⡭⣴⠛⠋⠅⣡⠒⠋⠀⠹⠟⡤⠞⠉⣀⠔⠊⠛⠛⣇⣀⠀⠙⢿⣿⣦⣀⡀⠀⢀⣠⣠⣿⣞⣿⣿⡆⠘⣉⠁⠘⠳⣛⣾⡛
⠀⠀⠘⠛⣧⣀⣤⠞⠈⢨⠿⢓⠄⡂⠔⠚⠁⠀⢀⡀⢊⣀⠤⠖⠟⠁⠀⢤⣻⣦⠿⠻⠲⣀⠀⠙⢟⢻⣿⣿⠋⠉⡉⠉⠩⣿⠉⡆⢴⣇⠀⠀⡀⠉⡷⠄
⠀⠀⠀⠀⠀⠈⠁⢀⡔⠁⣂⠕⡉⡰⡡⠶⠒⠚⠉⠀⠀⠀⠔⢁⡀⣠⡔⠻⣭⣍⠁⠀⠀⠀⠑⠠⠀⠁⠀⢹⡀⠀⠀⠄⠀⠗⠈⠈⠹⠛⣶⣏⡱⠒⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣶⢠⣀⣥⡼⠓⠀⠀⠀⠀⠀⠀⠀⠄⠐⠉⠈⠛⠓⠀⠿⠃⣙⣦⣰⠀⠀⠀⠀⠀⠁⠀⠑⠀⠠⠄⠐⠁⠀⠀⠈⠻⠅⠸⢝⣶⣥⣼⡓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠘⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⣈⡁⠀⠐⠝⠻
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠠⣀⠀⢀⡄⢠⡀⢠⣤⡀⠀⢠⡄⡤⣠⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⣿⡇⠀⣿⠀⠹⣷⡀⠀⠀⠁⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠟⠁⠻⠇⠰⠟⠠⠀⠹⠿⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡄⢀⡄⠠⣄⢠⣤⠀⠀⠀⣤⣄⠀⢠⡄⣤⡄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⠀⣿⠸⣿⠀⠀⠀⠈⢿⣆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠆⠙⠇⠰⠛⠈⠻⠄⠀⠀⠀⠈⠻⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠴⢰⣦⢰⢠⣶⠀⣴⡆⢴⡆⠰⠄⠀⣶⡆⢠⣄⠀⣰⡄⠰⣶⡀⠀⣤⠀⠦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠂⣿⡇⢸⡇⠆⠀⠀⣿⡇⢸⣿⠀⠸⣿⡀⢹⣷⠀⠻⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠘⠛⠀⠛⠃⠚⠃⠐⠃⠀⠛⠃⠘⠁⠀⠀⠛⠃⠘⠛⠀⠓⠀⠘⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⠀⣶⡆⠀⣴⡄⠀⣶⡆⡀⠀⢰⣶⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣿⡇⠀⠸⣿⡀⣿⡿⣷⡀⢸⣿⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠛⠃⠀⠀⠛⠃⠛⠃⠙⠓⠘⠛⠐⠃
⠀⠀⠀⠀⠀⠀⠚⢸⣷⠘⢰⣿⠀⣾⡇⢸⡇⠘⠂⠀⣿⡇⠸⣦⠀⢼⣆⠘⣿⡄⠀⣶⣀⠛
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⣿⡇⢸⡇⠃⡀⠀⣿⡇⢰⡿⠀⠘⣿⡄⢸⣿⠀⡈⠛⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠉⠁⠈⠁⠈⠁⠀⠉⠁⠈⠀⠀⠀⠈⠁⠈⠉⠀⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠈⢃⣾⠀⢸⣦⢸⡇⠀⠀⠈⢿⣆⠀⠘⢸⣿⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⢀⡜⣿⠀⢸⡟⢸⣇⠀⠀⠀⠀⢻⣦⠀⢸⣿⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠈⠁⠁⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢟⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢒⣲⡾⠿⣭⡵⠋⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠟⠋⠀⢰⠋⢉⡴⠞⠁⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣠⡤⢤⣘⡴⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⣠⡾⠋⠀⠀⣠⡿⠂⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠋⠀⢠⠃⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠾⠋⣁⡤⠤⢤⣀⠀⠈⢇⢀⣤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⢠⠊⠁⠀⠀⠀⠈⢳⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⢀⡼⢋⠔⠊⠉⠉⠓⢄⠀⡇⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⢀⡴⠋⣰⠃⠀⠀⠀⠀⠀⠸⡀⢇⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⢸⡀⠀⡇⠀⠀⠀⢀⣠⠤⠞⠛⠋⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠹⣄⢧⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠀⢀⣠⠴⠒⠚⡓⠲⣄
⠀⠀⠀⠀⠀⠈⠲⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⣠⠞⠉⠀⣤⠶⠛⠋⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠶⠶⠚⠋⠉⠁⠀⣀⡤⠶⠶⠶⠶⠤⠤⠤⣤⡀⠈⠓⠶⠴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠋⠙⠛⠟⠃⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⣀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⣀⡀⢀⠀⠀⠀⠀⢀⠀⠀⢀⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⣸⣿⡏⠀⣿⣿⣿⣿⣿⣇⠘⣿⣷⠀⠀⣸⣿⡏⠀⣻⣿⣿⣿⣿⣷⠀⢸⣿⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⣿⣿⠃⠀⣿⣧⣤⣠⠆⠀⠀⢹⣿⡇⢰⣿⡿⠀⠀⣿⣿⣬⣤⠤⠀⠀⢸⣿⣤⣾⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⡿⠀⠀⣿⡿⠿⠿⠀⢀⠀⠀⢿⣷⣾⣿⠃⠁⠀⢹⣿⠿⠿⠂⠀⡀⢸⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⡇⠀⠀⣿⣿⣶⣶⣶⣆⠁⠀⠸⣿⣿⡇⠀⠀⠀⢸⣿⣷⣶⣶⣶⠁⢸⣿⡟⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠈⠉⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡆⠀⠀⠀⢀⠀⠰⡄⠀⠀⠀⣶⠀⠀⠀⠀⣠⡦⠀⣠⠒⠉⡂⠀⠀⠀⣶⢴⢠⣄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢠⠁⠀⠀⢠⠃⢀⠜⠀⠀⠀⡴⠇⠀⠀⠀⣰⠃⠀⡴⠁⠄⠊⠀⠀⢀⡜⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡎⠀⠀⠀⣏⠔⠁⠀⠀⢠⠎⠸⠀⠀⠀⡠⠇⠀⢸⠁⠀⠀⠀⠀⡠⠊⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠇⠀⣀⠔⠇⠀⠀⠀⠀⠁⠀⢀⠀⢀⠄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠶⠀⠀⠲⠀⠀⠂⠀⠀⠀⠒⡒⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⢀⠀⠀⠉⠀⠀⠡⠀⠀⠀⠤⠀⠁⠐⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠰⠆⠀⠀⢠⡄⠀⠀⠀⠀⣄⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⠀⠀⠙⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⢀⣀⣀⣀⠀⢀⣀⠀⠀⣀⣀⢀⣀⣀⣀⣀⡀⠀⠀⢀⣀⡀⠀⢀⣀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠛⠁⠀⠸⢿⣿⠿⠀⢹⣿⡀⢠⣿⠇⠀⣿⠿⠿⠿⠂⠀⠀⢸⣿⠀⠀⢸⣿⠀⣿⡟⠛⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⣀⣀⣀⣄⠀⢸⣿⠀⠀⠀⣿⣇⣿⡟⠀⠀⣿⣷⣾⠁⠀⠀⠀⢸⣿⡄⠀⣼⣿⠀⣸⣷⣶⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣿⣿⣿⠀⣤⣾⣿⣶⡖⠀⠸⣿⣿⠁⠀⠀⣿⣦⣤⣴⡀⠀⠀⠈⢿⣷⣴⣿⠇⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠉⠉⠉⠉⠁⠀⠀⠉⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡖⠒⣾⠉⠙⢀⣰⡿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠉⠁⠀⣁⡤⢖⣫⠞⠁⣀⡽⠀⠀⠀⠀⠀⢀⡤⠖⣫⣍⣀⣀⣀⣀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠔⣊⡩⠭⣭⡭⠭⠭⠖⢚⣉⣀⣨⣏⣉⣀⠀⠀⠀⠀⡴⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠇⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠶⡶⡏⠉⢫⡉⠙⢾⡁⠀⠀⢠⠗⢚⣙⡿⠷⣞⣛⣚⣻⣤⡘⠷⡄⠀⠀⠳⣴⠀⠦⠐⠄⠰⠄⠐⠀⠆⠀⠁⠈⣀⠤⠚
⠀⠀⠀⣠⠴⠒⠋⠉⠀⠀⠀⠀⠁⠀⠀⠀⠃⠂⠀⣿⣉⣒⣚⣩⠭⢖⠚⢉⣅⣀⣤⣄⠈⠙⢦⡇⠀⠀⠀⠀⠙⠒⠒⠶⠶⠲⡖⠒⢲⠀⠉⠉
⠀⢶⣙⣶⣖⣹⣞⣳⣒⣒⣒⣒⣒⣒⣚⣋⣀⡤⠞⠁⠀⠀⠀⠈⠋⠉⠛⠉⠈⠉⠀⠙⠶⢶⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢸⡇
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢷⡊⢣
⠀⠀⠀⠀⠀⠀⠀⠰⣝⣳⣌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢧
⠀⠀⠀⠀⠀⢀⣠⠤⣤⣾⣯⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀
⠀⠀⠀⡠⢲⠋⠀⢀⡞⠀⣱⠀⠈⢫⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⢘⣿⡁⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⢿⠉⠢⠊⢱⡖⠒⠒⠦⢤⡀
⠀⢠⠺⡁⢢⡀⠀⢸⡀⢼⠁⠀⠀⢀⠇⡍⢳⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠉⠀⠀⠈⡇⠀⠀⠀⠀⠀⢀⡔⠉⢀⣔⡉⣀⠀⠰⠭⠗⠀⡭⠭⠶⠀⠀⠙⢦
⢰⠃⠀⢸⠆⢹⠄⠀⠙⢮⠳⣄⠀⠘⣄⢣⡀⢳⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⡜⢠⠀⠀⠀⢠⣃⠔⠊⣆⠖⠐⠸⠄⠀⠀⠀⠀⠘
⡆⢠⡖⢡⠖⠉⠀⢀⡠⠎⠀⣸⠆⠀⠀⢳⠱⣼⠀⠀⠀⠀⣠⠇⠄⡀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⣇⢀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠
⢧⠈⠣⣵⣀⠀⠀⡏⠀⢰⠋⠁⠀⠀⡴⠋⡞⡝⠀⠀⠀⡰⠃⠘⠊⠓⠄⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠘⣎⢦⣀⣠⠲⣄⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠘⢆⢰⠋⢨⠇⠀⠙⢲⡄⠙⡆⠀⠀⠙⡆⡻⠁⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠑⠺⠥⠤⠤⠤⠤⠤⠤⠤⠤⠴⠖⠒⠋⠁
⠀⠈⠙⢧⣿⡀⠀⣠⠞⢁⡴⠁⠀⣠⣾⠟⠁⠀⠀⠀⠘⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠛⠢⠷⢤⣼⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⢿
⠀⠀⠀⡴⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣄⣁⣀⣀⣤⡥⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡿⣸⠆
⠀⠀⠀⣇⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠻⠋⢿⡵⢿⣴⡆
⠀⠀⠀⠘⣆⠐⡀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡚⠋⣤⡁⢀⡀⠀⠀⠀⠚⢧
⠀⠀⠀⠀⠘⣆⠘⢆⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠖⠂⠰⡄⠖⠦⢭⡳⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠉⠁⠀⠒⠷⠀⠈⣿
⠀⠀⠀⠀⠀⠘⡄⠘⡆⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡸⣄⠀⠀⢰⢁⠀⠀⠀⣙⠞⢯⠢⡀⠀⠀⠀⠠⣔⠛⠀⠛⠁⠰⠒⠀⠀⠤⠀⠀⣄⠀⠼
⠀⠀⠀⣠⣤⣤⣡⠀⢹⡀⠸⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⠊⠙⠦⡙⢦⣼⠸⢀⡴⢊⡠⢤⠘⡇⠘⡄⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠀⠐
⠀⣰⠟⠁⢀⣀⣈⣳⡄⠀⣠⣷⣟⣉⠉⠛⠦⡀⠀⠀⠀⣼⣘⠀⠀⠀⠈⣣⠁⢚⡥⠊⠁⠀⠐⡆⡇⠀⣿⠀⠀⠴⣉⠀⠰⠇⠀⣄⠀⠉⠀⠐⠃⠀⣄⠀⣰
⢰⠇⠀⢀⢋⣴⡛⡍⢹⡾⢋⣴⣯⡞⢳⡂⠀⠙⣆⠀⠀⢹⡿⢒⣛⠭⠟⢛⢐⢦⡑⣄⠀⠀⣸⢰⠇⠀⡟⠀⠀⠀⣆⠀⢀⠀⠀⠉⠀⠠⠆⠀⠀⠈⠁⢀⡞
⣾⠀⠀⢨⡾⠀⠙⣾⢸⡇⢨⡏⠀⡇⠈⣿⡄⠀⢹⠀⠀⠘⣇⢫⡀⠀⠀⡄⡈⠀⠑⢌⡳⠴⢡⠏⢀⡜⠀⠀⠀⠀⣱⠀⠙⠂⠀⠀⠀⠀⢀⠀⠚⠃⢀⡬⠇
⢹⠀⠀⢸⣇⠀⠀⠘⢾⡷⡏⢷⣀⡇⠀⢹⡇⠀⢸⠀⠀⠀⠈⠣⣙⠢⢤⢁⡃⠀⣀⡴⣋⠴⢃⡴⠋⠀⠀⠀⠀⠰⠗⢆⡀⠀⠘⠃⠀⠈⠋⢀⠀⢠⠞
⠈⢧⡀⠀⣿⠀⠀⠀⢸⢀⡇⠀⠉⠀⠀⠘⣏⣠⡟⠀⠀⠀⠀⠀⠈⠑⠲⠦⠭⠽⠶⠾⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡧⠶⠴⠦⡶⠠⠈⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠄⠐⠀⡄⢉⠀⠂⠄⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠀⠤⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣈⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣀⣀⣅⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠐⢄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⡈⠀⠀⠂⠈⠉⢑⠂⢄⠀⠀⠀⠈⡶⡞⠁⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠠⠁
⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⢀⠀⠀⠀⠀⡄⠀⠈⠆⠀⠃⠀⠀⠀⠁⠁⠀⠀⢀⠎⠀⠀⠀⢀⠀⠒⠠⡀⠀⠀⠀⠀⢁⡄
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢧⡘⠀⠀⠀⢀⠂⠀⠀⠴⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠢⠄⠠⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠐⠀⠐⠊⢀⠄⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⠁⠀⠀⠀⠈⠢⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠤⠀⠤⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠠⠈⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠐⠠⠘⠀⠀⠀⠀⠀⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠋⠀⠀⠀⠀⠨⠅⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡤⠁⠀⠐⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠐⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠀⠈
⠀⠀⠱⡀⠁⠒⠀⠀⠀⣀⣴⣅⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⢒⠂⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠉⢂⠀⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠩⢭⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⠀⠀⢸⡀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⢂⠀⠸⢼⢈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠁⠀⢲⣼⣁⠀⠀⠀⠀⠀⢧⠇⡸⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠙⠟⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⡀⠠⠀⠀⡇⠀⠀⠤⠔⠊⠀⠀⢈⠁⠀⠀⠀⠀⠃⠈⠠⠁⠀⠀⠔⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠈⢄⠀⡰⠀⠀⠀⠤⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⣀⡀⠄⠊
⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡒⡚⢒⠚⣋⢁⣈⡑⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢊⣅⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⢛⣟⣽⡆
⠀⠀⠀⠀⠀⠀⢀⠔⣨⣵⣿⣿⣿⣿⣿⣿⣿⣿⡏⣤⣰⣷⡿⣿⠿⠛⣛⣦
⠀⠀⠀⠀⢀⠔⣡⣾⣿⠏⣹⣿⣿⣿⠿⠋⠕⣠⣶⢿⡿⠞⠋⠁⣠⣾⡿⣿
⠀⠀⠀⢠⠃⣼⣿⣿⣿⣿⡿⠏⣡⣴⣶⠶⣛⣻⡷⠋⢀⣠⣤⣿⡿⠟⢱⡿
⠀⠀⠀⡇⣴⣿⣿⠿⠛⣉⣴⣿⣯⣶⡶⣿⣿⢋⣠⣾⣿⣿⡿⠋⣀⣴⡿⠁
⠀⠀⠀⢳⠿⠿⣏⣴⣾⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠛⢉⣤⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⣠⡶⢶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠘⣷⣶⣿⠷⢻⡿⡿⠛⠙⢿⣿⣿⠿⠟⣁⣤⣶⣿⣿⣿⣟⠓⠀⠀⠀⠀⠀⢠⣾⣯⣻⣷⣤⣈⠙⠛⠛⠛⠿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠽⢧⣤⣴⣟⣷⢶⢶⣾⣿⣯⣷⣶⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⢻⢀⠈⠛⢿⣿⣶⣤⣤⣀⠀⠘⠻⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠻⢾⣶⣷⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⢉⣀⡀⠀⠀⠉⠻⢿⣿⢿⣦⣀⠀⠉⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠙⠿⣶⣶⣄⡀⠀⠈⠛⢿⣿⣿⣶⣆⠀⠨⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⣆⡈⠙⠿⣿⣶⣦⣄⠀⠙⢷⣾⣿⣿⣄⡙⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣻⣿⣿⣿⣦⣀⡀⠈⠛⠿⠷⣤⣀⠀⠉⠛⢿⣿⣻⣍⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡻⣿⣿⣿⣿⣿⣷⣴⣆⣄⣡⣈⡀⢉⣀⣈⣧⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢾⣿⣿⣉⡛⣻⡷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡟⠻⠛⣁⣼⠿⠟⠛⠋⢸⣗⣿⣄⡠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣠⣽⣾⡟⠛⠁⠀⣀⣀⣴⣿⣿⡿⠛⣿⣿⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢠⢪⣿⣿⠏⠀⠀⠀⣸⣿⣿⡿⠛⠁⠀⢸⣿⣿⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⣼⣿⣿⠃⠀⠀⣠⣼⣿⣿⣿⠃⠀⠀⢀⣼⣿⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⢀⣾⣿⣿⠏⠀⠀⣼⣿⢿⣿⠟⠁⠀⠀⢠⣾⣿⡿⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⣿⣿⠋⠀⣠⣶⣷⣿⣿⣟⠋⠀⠀⠀⣼⣿⣿⡟⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠋⢠⣾⣿⣿⡟⠛⠉⠀⠀⢀⣀⣿⣿⠏⣽⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⢰⣿⣿⣿⠏⠁⣀⡤⠴⠿⠟⠋⠉⣀⣾⣿⣿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡾⣿⣟⡁⣀⢈⣉⣠⣤⣤⣤⣶⣿⣿⣿⣿⣛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠁⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣷⣶⣄⠀⠀⢠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⣿⣿⠀⠀⢸⡇⠉⠉⠀⠀⠀⠀⣠⣤⠀⠀⠠⡡⠚⠳⠀⠀⠀⣓⠀⠐⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠟⠋⠀⠀⠸⡿⠿⠛⠀⠀⠀⢸⡏⢹⡄⠀⣦⠀⠀⠀⠀⠀⢠⣿⡄⣸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⢸⣧⣤⣤⡀⠀⠀⣿⣧⣼⡇⠀⢡⠐⡀⠀⠤⠀⢸⣿⠁⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡃⠹⣿⣷⡆⠀⠈⠉⠉⠉⠁⠀⢸⣿⠁⠈⣿⠀⠀⠁⠈⠁⠀⠀⠸⠿⠀⠠⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣷⣾⣥⡤⠄⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⡿⠧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⠈⢇⠀⠀⠀⠀⠀⠀⢰⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⢸⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⣸⣿⣽⣆⠀⠰⣆⠀⠀⠀⠀⣿⣶⣿⣿⣿⠏⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣄⢻⡆⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠀⠀⠀⢰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠟⠃
⠀⠀⠀⠀⠀⢀⡿⢲⢦⡀
⠀⠀⠀⠀⠀⢸⡏⠳⣞⣻⡆⠀⢀⣀⡀⠀⠀⢰⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⠀⢰⣷⠀⠀⠀⣠⣶⣶⣧
⠀⠀⠀⠀⠀⢸⡿⠀⡿⣭⣿⠀⢸⡏⣻⡆⠀⢸⣦⣤⠄⠀⠀⢠⡿⢿⠀⠀⠀⣸⡿⢿⣤⣿⢿⣇⠀⠀⢿⣅⡀
⠀⠀⠀⠀⠀⢸⡗⢾⣱⣾⠏⠀⣿⣿⡛⠁⠀⢸⣁⡀⠀⠀⠀⣼⣧⣼⡄⠀⠀⣿⡇⠈⠿⠃⠸⣿⡄⠀⠀⠉⠻⣷⡄
⠀⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⣿⡟⢿⣆⠀⠘⠻⠛⠛⠀⢀⣿⠋⠹⣇⠀⠘⠛⠀⠀⠀⠀⠀⠛⠃⠀⣤⣤⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉


⣶⣶⣶⠶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡟⠀⢸⣿⢦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⢋⣽⡟⣿⠁⠀⠸⣿⠀⠹⣟⢙⡿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣠⣾⠛⢰⡟⠀⠀⠀⣿⣦⡀⠈⢿⣅⣶⡛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⢀⡟⠟⣠⠟⠀⠀⠀⠀⣻⣏⡻⣷⣾⣿⣿⣾⣶⡚⢻⣧⡀
⠀⠀⠀⠀⠀⠀⢰⣿⡏⠘⢀⡼⠋⠀⣀⡠⠖⢋⣽⣷⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠘⡟⠀⣴⠋⠀⣠⡞⠉⠀⠀⠀⠉⣩⣶⡶⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⡇⣼⠃⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠿⣿⣍
⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣬⣥⣦⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣾⣿⣦⣤⣬⣥⣤⣶⣾⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠽⠈⠳⡀⠀⠀⠀⣴⣾⣽⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡤⠿⢦⣤⣴⣇⣀⣴⠟⣩⢞⣁⣀⣤⢴⣶⣶⢲⠒⣲⣚⣮⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣁⢈⡿⠛⢧⣄⣀⣯⠈⠉⢧⣴⣞⣵⣏⣠⣔⣉⣩⣽⣿⣟⠻⠿⢿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⠟⣿⡇⣀⢠⣿⣛⣿⣷⢶⣾⠛⠻⡿⣿⣿⡙⢿⣿⡍⠓⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⣦⣴⣤⣿⡿⠙⠙⢿⡿⠋⠀⠀⣽⣦⣤⣤⡿⣿⣕⣦⠽⣧⡥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣴⢻⢿⠿⣅⠤⢆⣼⣷⣾⣿⣿⣁⠀⠉⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⢿⣴⣀⣠⣿⣿⣿⡟⠲⣦⣀⣀⡉⠳⢦⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢦⣽⣿⢛⣿⣟⠁⠈⣿⠀⠈⠙⢦⣄⣀⣀⣀⡀⠈⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣖⣫⠭⣿⠟⣱⡏⢸⣏⣀⣶⣿⡀⠀⡀⠘⡿⠙⢦⣀⣄⣀⠀⠀⠙⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡵⢟⡉⣰⣣⢾⡵⢾⡿⣇⠉⠈⣩⢟⠹⣷⣄⡇⠀⠃⠀⣷⠿⢦⡤⠤⣄⡀⠀⠀⠬⣹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢗⡧⢀⣿⣿⠋⠀⢸⡇⠙⣷⠀⠀⠈⢀⢹⡻⣷⠀⠀⠀⠻⡄⠀⢻⣦⣀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢁⢎⣴⣿⢿⡇⠀⠀⢸⡇⢀⣿⣀⠀⢀⡾⠖⠏⢻⣧⣀⡆⠆⠀⠀⠈⣏⢹⢿⡛⠓⠂⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣾⡿⠃⢸⡇⠀⢰⠅⣿⠀⠀⣹⡦⢈⡴⠃⠸⣼⡇⠙⠷⣄⠀⠀⡀⠛⠘⡄⠹⣶⡒⠒⠀⠀⠘⠺⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡏⢻⡀⠀⠀⣿⠀⠈⡼⢻⡗⠐⢿⣰⠟⠀⠀⠰⠘⡟⣦⠀⠸⣆⡀⠁⣀⠀⠃⠀⠘⡛⢦⣤⣠⡴⠂⠈⢷⡄
⠀⠀⠀⠀⠀⠀⢀⡾⡉⠀⢸⡃⠀⢷⡀⠀⠙⢶⡀⠠⠋⢿⣤⡀⢹⡆⠀⣰⣶⠀⠙⢿⡀⠀⠉⠛⠛⠛⠓⢶⡄⠀⠀⡀⠙⠳⣄⡀⠺⠿⣷⡀
⠀⠀⠀⠀⠀⠀⣸⢰⡇⠀⣻⡇⠀⡀⢹⡄⠀⠘⠳⡄⡀⢘⣿⣇⠸⣟⠛⢦⠃⠀⡗⣌⠳⡄⠀⠀⠀⠀⠀⠀⠙⢦⣴⣤⣤⣤⣈⣙⣢⣌⣙⣧
⠀⠀⠀⠀⠀⠀⢿⠘⠅⠀⡿⢇⠀⠀⣈⢷⡀⠀⠀⠙⠳⣜⠉⢹⣿⡎⢷⠈⠓⠿⠷⢿⣄⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠁⢸⣦⠀⠬⣂⠙⢦⠀⠀⠀⠉⠛⠛⠲⢿⣼⡇⠀⠀⠀⠀⠙⢿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢸⣿⣧⡀⠀⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣮⠆⠈⠟⡘⢳⡄⠀⢵⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠦⣤⣆⠈⣿⡄⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠙⣿⡌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣼⣷⣼⣆⠀⠀⠀⠀⠀⣠⣤⣶⣿⡀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠸⣇⣀⣨⣿⣿⣦⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢘⣘⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⣠⣾⣿⣷⠠⡿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠟⢳⣿⠗⠶⣾⠟⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣼⡇⠐⢛⡟⠀⢀⠀⠀⢸⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣼⣿⢫⡘⣿⡇⠀⠈⠇⠀⠸⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⣱⡆⢟⡇⢀⣤⠶⡿⠟⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢀⠙⢀⣾⣷⣿⣿⣶⠆⣿⣧⣿⣟⣧⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⣧⣾⢲⣾⣷⣀⣹⣿⣏⣀⣉⣽⣿⣿⣿⣿⣯⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣿⡍⣽⣿⢿⣿⠟⣿⢋⣽⡏⣽⣟⢩⣗⣿⡋⣽⡇⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡜⣿⠟⠻⣷⢋⢾⣿⡇⣸⣿⠘⣿⣿⡇⣿⣷⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⣤⣾⣧⣤⣾⣿⣿⣃⣘⣿⣄⣉⣥⣧⣉⣩⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠷⠴⠶⠶⠿⠿⠿⠛⠻⠿⠴⠷⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡿⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⢷⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠈⠛⠲⠦⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠴⠖⠛⠁⠀⠀⢸⠆
⠀⠀⠀⠀⡀⠀⠀⠷⠶⠦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⡀⢀⣠⡀⢠⣤⡄⠀⣠⣤⢠⣤⣤⣤⡄⠀⠀⠀⠀⠀⠴⠶⠾⠀⠀⢀
⠀⠀⠀⠀⢿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⣿⣿⣿⡇⠘⣯⣧⢀⣷⡇⢸⢿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡿
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡇⠀⠀⣟⣿⢻⣿⠇⠀⢻⣾⣾⣾⠁⢸⢿⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠠⣄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⣿⣿⡟⠀⠀⠘⣷⣷⠇⠀⣸⢿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣠⠄
⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣷⡶⡆⠀⢻⣿⠁⠀⠀⠀⢻⡾⠀⠀⣼⣻⣲⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠃⠀⠀⠃⠀⠀⠀⠀⠈⠃⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠲⣦⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⣴⠖
⠀⠀⠀⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢼⠀⡛⡄⣄⢠⡀⣠⡀⠀⢀⠀⠀⠀⠀⣤⠀⠸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠉
⠀⠀⢠⣤⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠁⠘⠾⠃⢻⢇⡀⢻⡅⢰⡷⠀⢿⣀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣤⡄
⠀⠀⠀⠀⠀⠁⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠙⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⣠⠎⠉
⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⡀
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠄⣿⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣿⠠⠚⠁⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠁⠠⢈⣇⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡗⠀⠀⣸⡁⠀⠀⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠁⠀⢁⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡈⠀⠈⠻⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠰⣊⠉⠉⡇⢸⠀⠐⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⡀⢴⡅⢸⣀⠀⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠐⠁⠀⠀⠀⠀⠀⠬⣏⡁⢣⡗⠀⠀⠀⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠐⠀⠀⢠⠜⠀⠀⠀⠉⠁⠀⠀⠀⠄⠀⠀⠑⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠁⠈⠠
⠀⠀⠀⠀⠂⠀⢖⠘⠂⠀⡀⠤⠤⢄⡥⣂⡾⠠⢀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠆⠀⠀⠀⠀⠀⠁⠀⠨⠐⡟⠋⠉⠉⠁⠀⢄⠂⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡄⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠂⢤⡀⠀⠀⠁⡄⠉⠀⠰⣌⠋⠄⠀⢀⠀⡀⠀⢤⠁
⠀⠀⠀⠀⢀⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⢀⠀⢿⡆⠐⠁⠀⣀⢀⠀⠁⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⣄⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠠⡧⠄⠀⠈⠃⠀⡠⡐⠉⠈⠙⠐⠀⡀⠀⠤
⠀⠀⠀⠀⠀⠁⡁⠂⠆⡰⢂⠆⠹⠲⠂⠟⣆⠀⠂⠠⠀⠁⠀⣠⠊⠁⠰⠄⢀⡄⠀⠀⠀⠀⡀⠔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢉⠊⢚⠓⣙⣤⠡⠗⠦⠤⢴⠆⡈⠩⠂⠀⠀⠂⠈⠑⠀⠀⠀⠀⠁⠄⠅⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠍⠈⠰⠡⢆⢂⡚⠔⠇⠃⠁⢀⡀⠢⡤⠔⢆⣀⣠⠣⠀⠀⢀⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠦⠄⠄⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠐



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠐⠀⢀⡀⠴⡦⠂⠁⠀⠀⠀⠀⠀⠀⠴⡅⠀⠀⠀⠀⠐⠒⠻⡃⠀⠀⠈⠙⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠁⢀⢶⣟⣦⠰⠃⠀⠀⠀⠀⠀⢀⣤⠀⡄⠱⣄⠀⠀⠀⠀⠀⠀⠘⢃⢶⣤⡄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢠⣩⣄⢉⡝⠁⠀⠀⠀⠀⠀⢠⣎⣉⢦⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⣿⡦⣄⡀⠈⠁⠠
⠀⠀⠀⠀⠀⣤⠀⠀⢀⠆⢠⢿⣧⣿⡟⠀⠀⠀⠀⠀⠀⠀⢷⣿⠿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣟⡛⢣⡀⠀⠀⠱⡄
⠀⠀⠀⠀⠘⠃⠀⠐⠇⠀⠚⢀⠉⡞⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣿⠃⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣵⡟⠓⣄⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⣬⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢋⣰⡖⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⡟⠿⠻⡀⠀⠀⢡
⠀⠀⠀⠀⡄⠀⠀⢠⠇⡇⠙⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⡆⠀⠀⠀⢰⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣏⣴⠶⣇⠀⠀⢸
⠀⠀⠀⠀⡏⠀⠀⠈⠀⢉⡴⠶⣾⡇⠀⠀⠀⠀⠀⠀⠀⡼⠹⠿⠟⡰⠁⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣤⣟⣦⡴⠃
⠀⠀⠀⠀⡇⠀⠀⠀⡀⠸⣷⣴⡟⢧⠀⠀⠀⠀⠀⠀⡔⣡⣦⡂⡌⠁⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⣀⠞⠊
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠳⢄⣀⣸⠀⠀⠀⠀⢀⣐⣿⢟⣹⠿⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠛⠁
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⡰⠋⡉⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠑⢆
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⢰⣤⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢆
⠀⠀⠀⠀⠀⠈⡄⠀⡄⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡞⠋⠉⠻⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣄⠀⢀⣀⠀⠰⠀⠀⠁⠤⠀⠀⠘⠂
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠦⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⢀⠰⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡁⠀⠉⠀⠀⠀⠊⠈⠉⠁⠐
⠀⠀⠀⢀⠾⢌⠀⠀⠀⠀⢫⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠑⠀⠀⠤⠃⠀⠨⡁⠀⠀⠁
⠀⠀⠀⣘⠀⠈⢆⠀⠀⠀⠀⠀⠠⢸⠇⠀⠀⠀⠀⠀⡘⠓⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⠎
⠀⠀⠀⡟⠁⠒⡈⢻⣉⡙⣻⣄⠠⣈⡀⠀⠀⠀⠀⢀⣄⠀⠘⣆⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠐⠒⢄⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢁⠀⢀⠈⢺⠑⠣⡀⠉⠻⣄⡐⠠⡀⠀⠀⢸⠀⠀⠁⡈⡧⣠⠹⢷⣤⡒⠲⠄⠀⠀⠀⠀⠁⠘⠲⠤⣄
⠀⠀⠀⠀⣅⠂⠆⠈⠀⠀⢰⡖⢠⡙⠎⠀⢬⡀⠀⠀⢂⠀⠀⠈⠇⠈⠲⡈⠈⢻⡤⠍⠢⡁⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⠊⠇⠀⠀⠀⠀⠀⠀⠰⡌⠘⠁⠀⠀⠀⢛⡁⣦⠘⠀⠐⠲⠀⠀⠀⠈⠀⠀⠀⠊⠐⠂
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⣀⣤⡥⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠤⠖⠂⠀⠀⢀⠀⠀⠀⠀⠀⢀⣞⣡⠄⢻⣿⡣⡁⠀⠘⣿⣂⠀⠀⠀⠐⠂⠘
⠀⠀⠀⠀⠀⠀⠐⠒⠀⠒⠀⠀⠰⢆⡀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠰⠔⡅⠞⠀⠀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⢠⠀⠡⠀⠀⠀⠊⠀⠀⢳⡄⠀⠀⠀⠀⠀⢩⢠⠈⠤⠓⠀⠀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠠⠄⠐⠁⠂⠄⠁⠀⡞⡶⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⣄⣀⣆⣀⠔⠀⠀⠀⡀
⠀⠀⠀⠀⠈⡀⠀⠐⡀⠀⠂⠀⡀⠠⠁⠖⠂⠀⠀⠰⢤⣄⡬⢐⠴⠚⠘⠀⠄⠀⠁⠹⠁⣄
⠀⠀⠀⠀⡀⠁⢀⠀⠁⠐⠀⡀⠀⠀⠁⠀⠀⠀⢛⠄⡐⢨⢉⠁⠀⠂⠀⠃⠀⡀⠁⠀⠁⢀
⠀⠀⠀⠀⠠⠂⢀⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠁⠀⢛⠈⠀⠂⠨⠀⠀⠁⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠂⡉⠉⠀⠠⠀⠠⠀⠈⠀⠃⠠⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠃⠘⠀⡄⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠐⠊⡚⠂⠠⠔⡄⠀⠀⠀⣀
⠀⠀⠀⠁⠀⠐⠒⠀⠛⠋⠋⠙⠀⠁⠀⠀⠀⠀⠀⢀⠰⣶⡆⢀⠀⠀⠉⠉⠲⢶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣴⠀⠀⠀⠗⠀⠰⠊⠆⠀⠠⠁⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠛⡿⡄⠶⣀⣟⠦⠒⠄⣀⠃⡁⠆⠀⠀⢀⠀⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢀⡀⢾⠀⠘⠢⡡⢙⠘⠈⢀⠠⠠⠘⠁⢶⠘⠛⢿⡗⡄⢠⢾⣶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡁⠀⠐⡀⠀⠑⡈⠀⠀⠀⠠⠆⠀⠐⢀⢐⣀⢐⢇⡷⠀⣌⠘⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢘⠀⡀⡀⢠⠁⠀⠀⠀⠀⠀⠀⢋⠀⠔⡀⠂⠚⠆⠃⠄⣅⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠉⠀⠀⠘⠈⣀⠔⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡿⣿⣿⣿⡿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣟⢱⣿⣿⣿⣧⡀⠉⠉⠀⠀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⣿⡿⠀⠈⣿⡿⢀⣀⣀⡀⣿⣿⣿⣰⣶⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠰⣿⠇⢸⣿⣿⣇⠛⠋⠁⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⠀⠀⣾⣿⣷⡸⠛⠉⢸⠁⢀⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠿⠋⢹⡇⠀⣀⡘⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠸⠟⠉⣿⠀⢀⣘⢳⣾⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⢹⡇⠀⢀⠛⣶⣿⣧⢸⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢳⣾⣿⠀⣿⣿⣿⢸⣿⣿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠃⠘⠟⠿⠀⠻⠿⠗⠘⠿⠛⠃⠻⠿⠟





⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠛⠁⠀⠀⣀⡀⣠⣤⢠⣤⠤⠤⠤⣤⢤⣤⣤⣌⣀⠀⠀⠀⠀⢰⡦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠂⠉⠀⠄⠁⢠⡤⠀⠀⠀⠀⠀⡶⠿⠿⠟⠿⣿⣿⣿⣶⣧⣄⡈⠁⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠦⠀⠀⠀⠀⢠⠀⠰⣖⣀⣠⣤⣤⡶⠂⠀⢀⠀⠉⠉⠙⠃⣭⠉⠻⣿⣿⡇⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢦⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢁⠀⠁⢙⠂⠔⠚⢛⣻⣦⣀⠀⠙⢀⣀⣿⣿⠇⠀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡙⠒⠤⣀⣀⠀⠀⠀⠛⠁⠈⣉⠑⢀⡀⠀⠀⠶⠿⠿⡶⢶⡯⠟⣁⡴⢳⣾⠃⢀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⢶⣦⣮⣍⠁⠀⠀⠀⠀⠠⠶⠿⠷⠤⠰⠿⠒⢛⣍⣡⠀⠀⣿⣿⣰⣿⡟⠉⠉⠻⣖⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠃⠀⠀⠀⢀⣰⢶⠗⠀⠈⠉⠛⡀⠘⠃⣿⢿⣿⠁⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣼⣏⣀⣠⣴⠿⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣰⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣿⣅⣉⣉⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠷⠊⠙⠉⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣻⣿⣟⠿⠿⢷⣶⣤⣄
⠀⠀⠀⠀⠀⠀⢠⠠⠃⠀⠀⠀⠀⠀⠴⣻⣷⣵⣆⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠀⣰⠽⣿⡿⣋⡬⣿⠀⠈⠀⡈⢹⣷⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢴⡁⢹⣧⣠⣹⣿⣆⢀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠁⠀⢀⣩⠾⣿⡾⣥⣾⣷⠤⡀⠀⠐⠀⠘⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠉⣹⣭⣿⡋⠥⣺⠏⣻⣷⣷⣦⣄⣀⡀⠀⣀⠀⡂⢀⣉⣀⣴⣾⣿⣱⢊⣽⣓⣺⣿⣾⡷⠏⠀⠁⠀⢀⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢛⣡⠀⢀⠉⠉⠛⠻⠿⠿⢿⣿⣿⠿⣿⡿⠿⠿⣿⣻⢍⣫⡙⣌⠛⠉⠀⠀⠀⠀⢀⠠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⣥⠬⠋⠀⣴⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠋⠛⠉⠀⠀⢀⣥⢴⢊⡿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣄⣀⣀⣀⣀⠠⣄⣀⠀⡀⠤⣶⢎⢃⠈⠿⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠂⠀⠂⠁⠁⠀⠀⠀⠘⠓⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⡇⣸⣀⡀⠀⢀⠀⡄⢀⣀⡀⢀⠀⡄⠀⠀⣀⢀⡀⣀⠀⣠⠄⣀⣠⡔⣿⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⢸⣆⠀⠀⣾⢀⡇⣾⢸⣿⣼⢀⡇⣠⠀⣿⢸⡇⡿⣾⢰⡇⣿⠀⡇⣿⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⢸⡄⠀⠈⢩⡟⠉⠉⠁⠈⠉⠉⠁⠀⠈⠉⠉⠁⠈⠉⠉⠉⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⠀⠀⠀⢯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡆⢀⡤⣄⠀⠐⣶⠀⠀⣶⠀⣠⣤⣤⢠⡤⣤⢤⡄⢶⠂⠠⣤⠀⣤⠀⢴⡆⠀⢴⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⣇⠘⡆⠀⣿⡄⢰⣿⠀⣿⠀⠈⠀⠀⣿⠀⠀⢸⠀⠀⡇⠀⣿⠀⢸⢧⠀⣼⠀⡞⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣿⠈⠛⡷⠚⡇⢧⡾⢸⡀⣿⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⡇⠀⣿⠀⢸⠘⡆⡿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠦⠀⣧⢸⡀⢠⠇⠀⡇⠘⠃⢸⡇⣿⠉⣀⠀⠀⣿⠀⠀⢸⠋⠉⣇⠀⢹⠀⢸⠀⢹⡇⠈⢧⠘⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⠁⠀⠉⠉⠀⠈⠋⠀⠀⠀⠀⠘⠛⠉⠀⠀⠛⠀⠀⠘⠃⠀⠉⠀⠛⠂⠛⠀⠀⠁⠀⠈⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⢹⡏⣿⢺⡄⡔⡧⣰⠞⡆⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠟⠸⠷⠿⠥⠿⠀⠧⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⣀⣀⠀⠀⣀⣀⠀⠀⢠⣤⣴⠦⣤⣀⠀⠠⢤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⢸⣿⠀⢹⡏⠀⣼⠋⠙⢷⠀⠀⢸⡇⠀⠀⠙⡇⠀⢸⡇⠀⣸⡷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣿⢹⡇⣼⠀⠀⣿⣆⠀⢸⡇⠀⢸⡇⠀⢀⣼⠇⠀⢸⣇⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⡟⠸⣇⣿⠀⢰⡇⠈⠛⠶⣷⠶⠾⣧⡴⣟⠁⠀⠀⢸⡟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⣿⣿⠀⠘⣇⠀⠀⢠⡇⠀⠘⡇⠀⢻⡄⠀⠀⢸⡇⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢿⡇⠀⠀⢿⡀⠀⣼⠃⠀⠀⡇⠀⠀⠻⣄⣀⢸⡇⠀⠀⠻⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠘⠃⠀⠀⠈⠙⠛⠁⠀⠀⢴⣷⠄⠀⠀⠈⠁⠾⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢆⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⢸⡗⢢⡶⣶⢸⢗⡆⠀⢰⡆⣿⠀⢠⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡞⠧⠟⠚⠸⠷⠃⠘⠧⠿⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⢿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠋⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⡀⠀⢀⣀⡈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠛⡇⠙⠛⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣷⣶⣧⣴⣤⣼⣟⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡏⢸⣿⣷⣦⣄⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡴⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⠁⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠶⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠿⠿⠿⠿⠛⢛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣿⣿⣿⣶⡆⠒⠒⠒⠒⠚⠁⣿⣿⣿⢿⣿⣿⣿⣿⣿⣧⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠁⣿⣿⡟⠉⠙⠻⡃⠀⢠⣿⣿⣿⣿⡟⠉⢷⡄⠀⠀⠀⣀⠀⢻⣿⡇⠀⣿⠿⠛⠛⢿⣿⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠙⢿⣷⣄⡀⠀⠙⢦⡈⢿⣿⣯⡹⣿⣆⣀⠁⣠⣶⣯⡝⢿⡬⠿⠗⠋⠁⠀⠄⣀⣠⡿⠀⢀⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⣠⣭⠟⠛⠒⠦⣤⡉⢿⠛⢿⣿⠿⢿⡟⢛⡿⣛⡡⢐⡪⢠⣇⣠⣴⣶⣶⠿⠟⠛⠁⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣦⡀⣹⡇⠈⠉⢹⠹⢿⣿⡯⣘⠶⢭⣿⣿⣷⣿⣿⣿⣧⣵⣴⣿⣿⣏⠁⠀⠀⣶⠳⣾⢀⣰⣟⡁
⠀⠀⠀⠀⠀⠀⠀⣼⣻⣾⣷⣿⣿⡇⠀⠀⠈⣦⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣷⣦⣉⣽⣿⣻⣿⠟⠻⣿⣏⠀⠟⣿⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣧⣿⣯⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢩⣿⣿⡇⣸⣿⣟⣿⣿⠀⠀⠋⣿⣿⢂⣿⣋⣀⣹⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⠉⠻⠿⣿⣿⣿⣿⣿⣿⡿⠿⡋⠁⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣏⣉⣻⣿⣿⣷⣤⣃⠀⢴⢀⡄⢠⠉⢩⡁⠀⡆⠀⠹⢀⣠⣶⣿⣿⣿⣋⣹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠻⢯⣻⢿⣿⣿⣶⣤⣤⣉⣀⣈⣁⣠⣥⣴⣾⣿⡿⢟⣯⠿⠻⠟⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣽⣛⡻⠿⠿⢿⡿⠿⠿⢿⣛⣫⡽⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⣾⣀⣤⣴⣶⣾⣿⣿⡛⢿⣿⣿⣿⣿⣯⣙⣻⣛⣛⣿⣿⠿⣷⣶⣤⣀⠀⢠⡁⠀⠀⠀⢀
⠀⠀⠀⢰⡝⢿⣟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣽⣿⡷⢞⣴⣧⡶⡋⠀⠀⢍⣆
⠀⠀⠀⠘⠃⠀⠊⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⣛⣭⣴⣻⣿⣿⡿⠁⠀⠀⠀⣿
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⢸⣿⣿⢸⡿⠟⠁⠀⠀⠀⠀⡏
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⠁⠀⠀⠀⡠⠈
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣃⣀⡤⠖⣉⠔⠁
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⣿⢟⣋⡡⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠖⠶⠾⠿⠛⠁

⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣒⣛⣓⣶⣶⣤⡀
⠀⠀⠀⠀⢀⣾⣿⣫⣾⣿⣿⠿⠿⠿⠿⠟⡇
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣫⣷⣿⣿⣿⣧⣾⠇
⠀⠀⠀⠀⢻⣛⡛⠛⣛⣩⣵⣾⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⢀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣷⣶⣶⣶⣶⣿⣆
⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠿⠟⢛⣫⢾⣿⠄
⠀⠀⠀⣸⣿⣿⠟⣋⡥⠶⣶⣟⣿⣿⣿⣿⡿
⠀⠀⠀⢹⣿⣷⣯⣴⣾⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠛⢿⣿⣿⣿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⢀⣀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⣭⣴⣶⣿⡿⣿⢿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⣴⣿⣿⣿⡿⢫⣾⢋⣾⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⢟⣵⡟⣡⣾⢿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠟⣩⣾⣿⣿⣿⠏⠀⠀⠀⠀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⣵⣿⣿⣿⣿⡿⠋⠀⠀⠀⡴⢋⣥⣾⢃⡟⣿⣆⠀⠀⠀⠀⠀⢀⣴⣾⣿⢿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣱⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⣸⢷⣿⣿⡏⣼⣹⣿⣿⡆⠀⠀⠀⢠⢏⣾⣿⣿⢸⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠟⠋⠁⠀⠀⠀⠀⠀⢠⣛⣞⣿⣿⢃⣿⣿⣿⣿⠃⠀⠀⠀⢸⢼⣿⣿⡟⢸⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢣⣾⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⡇⢸⣾⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢣⡿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢿⣿⣿⣧⠘⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣼⣷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⣻⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠤⠤⠤⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠈⠁⠀⠀⣀⠀⠀⠀⠀⢀⣀⠀⠀⠉⠙⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢊⠄⢀⠀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠐⠂⠤⡀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣯⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡰⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢼⠁⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠡⢐⠤⣤⣀⡄⠀⠀⠑⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠈⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠇⢇⢀⡤⠛⢇⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡸⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣔⢌⠓⠤⣀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡤⠜⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⠙⠿⣶⣠⣍⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢀⡞⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⠀⠀⠀⠉⠙⠚⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣰⠞⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⣥⣤⠖⠋⠀⠀⠀⡠⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠐⡀⠀⠀⠀⠀⠀⠀⢀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⣾⣿⠟⠋⠉⠀⠀⠀⠀⠀⡰⢡⠇
⠀⠀⠀⠀⠀⠹⡆⠌⡉⠉⠉⠓⠒⢤⡀⢀⢤⠳⣌⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢶⡤⠤⣤⡴⠊⣰⡿⠋⠁⠀⠀⠀⠀⠀⠀⡠⢊⡴⠃
⠀⠀⠀⠀⠀⠀⠈⠢⡀⠉⠓⠓⢤⣀⠈⢳⡄⠃⠈⠑⠦⣉⣲⠤⣤⢤⡀⠀⠀⠀⠄⢀⡤⠴⠛⠁⣴⠞⠋⠁⠀⠀⠀⠀⣀⠤⢖⡩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⣀⡒⠈⠳⣤⣿⡍⠕⢻⠂⣙⡾⠺⠶⣞⠷⠶⡢⠴⠶⠾⠷⠶⠶⠮⠤⠤⠤⠤⠔⣒⣈⠥⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠉⡟⣳⢾⣿⢿⣏⣬⢽⣭⠟⡒⢞⠉⠠⠴⠛⣛⣵⢦⡶⢶⠒⠒⠒⠂⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡟⣇⣹⢶⣾⢽⠦⣼⠴⠚⣴⡟⢲⣟⢳⣤⡽⢛⠓⣭⢪⣆
⠀⠀⠀⠀⠀⠀⠀⠛⠁⡈⢻⣉⣇⠃⢹⣍⣴⢌⣸⣄⢹⡶⠾⠷⢫⣴⣨⠃⢹⣿⣿⣼⣟⣋⣿⠳⢂⠦⣍⡆
⠀⠀⠀⠀⠀⠀⠀⠰⠉⠽⠃⠀⡜⠂⢫⣑⣨⡖⠬⣽⠊⡳⠖⢻⣛⣮⣉⣻⣻⡟⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠩⠝⡩⠉⠚⠳⠭⠶⠙⠦⠤⠖⠀⢼⡫⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠉⠉⠉⠉⠉⠉⠁⠛⠁⠀⠘⠛⠛⠛⠛⠛⠓⠒⠒⠒⠂⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢠⣤⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠻⣧⠀⢸⡿⠀⠀⣠⣤⣀⠀⣿⡿⠀⠀⢸⣿⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠹⣷⣿⠃⢀⣾⠟⠙⣿⡆⣿⣿⠀⠀⢸⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡏⠀⢸⡏⠀⠀⣿⡇⣿⣿⠀⠀⢸⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣼⣇⠀⢸⡇⠀⠀⣿⠁⣿⡟⠀⠀⢸⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠙⠛⠀⠀⠻⠶⠾⠋⠀⠻⣿⣦⡴⠟⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣦⠀⠀⢠⣴⣦⠀⠀⣠⣄⠀⢠⣶⡀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣾⠁⠀⠀⠉⠀⠀⣿⠃⠸⡇⠀⣿⡟⣆⢸⣿⡇⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⣿⡀⠀⠀⢀⡀⢠⣿⣤⣤⡇⠀⣿⡇⠹⣎⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣧⡀⢀⣿⡇⣼⡿⠀⠨⣿⠀⣿⡇⠀⢻⣿⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠙⠛⠛⠋⠀⠿⠃⠀⠀⠿⠀⠿⠇⠀⠈⠿⠃⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⡶⢦⣄⠀⠀⠀⣀⡀⠀⢠⣤⣤⡄⢠⣤⣤⣤⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠹⣆⢠⣾⠛⢻⡆⠀⢸⣧⠀⠀⠀⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⡇⠀⠀⣿⣾⠃⠀⢸⡇⠀⠐⡿⠀⠀⠀⣿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⣠⠏⢻⡄⠀⣸⠃⠀⠈⣷⠀⠀⠀⢻⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠘⠛⠛⠁⠀⠈⠛⠚⠋⠀⠘⠛⠛⠟⠀⠀⠸⠇⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠉






⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣀⣀⣀⣀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⣀⡤⠞⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⢡⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢾⡁⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⠈⢻⡆⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⣠⠞⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡚⠉⠉⠀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⡀⠀⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠱⣏⣤⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣭⣭⣿⣲⣦⣍⣦⢸⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⢸⠦⢤⡀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⡟⠀⠀⡷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⣿⠃⢀⡼⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⣰⡧⠖⠋⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⢧⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣀⣤⠴⠋⠁
⠀⠀⠀⠀⠀⢠⠞⠁⠀⢠⠞⢡⡞⣽⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⢠⣿⣾⡭⠴⠖⣚⣿⣧⣤⡤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠙⠲⣤⣙⠿⣴⠿⣍⣉⣉⣡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠲⠾⠭⠭⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢰⠇⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⢠⡏⠀⢠⡟⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡾⠀⢀⡾⠀⠀⣰⠏⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡿⠀⣸⠇⠀⣼⠃⠀⣰⠏⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠛⠛⢹⡇⠀⣿⠀⢠⡏⠀⢠⡏⠀⢀⡞⠘⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢟⣩⡴⠞⣋⣁⠀⢸⡇⠀⣿⠀⢸⡇⠀⢸⡃⠀⢸⠇⠀⠀⠒⠤⣌⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢺⣿⣾⣟⣭⣤⣴⣾⣇⣶⣿⣰⣾⡇⣶⣾⣧⣦⣾⣠⣄⣈⠙⠲⣦⣝⠂⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠖⠀⣀⣴⠟⢸⣛⡷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣌⠙⠂⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⣁⣀⣠⣤⠶⠟⣫⣴⡇⣚⣛⠲⢤⡈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⠓⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⢋⣉⣩⣥⣴⡾⠿⣛⣥⠀⠉⠉⠙⢷⣷⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠞⠃⢹⣟⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⣉⣉⣭⣴⣶⠿⢛⡅⠀⠒⢂⣠⢿⢏⠄⣾⠁
⠀⠀⠀⠀⠀⠀⢀⣴⠾⣛⡭⠔⣀⠀⠀⠀⢿⡛⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠛⠛⠛⣛⣋⣩⣥⣶⠾⡛⢡⡶⢞⣫⣵⡿⢋⡾⢣⣄
⠀⠀⠀⠀⢀⣴⠏⣡⠞⢫⡴⢋⣡⠔⠀⠀⠈⢿⡷⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠛⣛⣋⣭⣵⣶⠿⢡⣾⣿⠿⣛⣭⠾⠋⠀⠠⡉⢳⣄
⠀⠀⠀⠀⣼⠃⣸⡏⢰⡏⠠⡟⠁⣴⠉⠀⠀⠈⢻⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⣛⣋⣩⣭⣶⠞⣡⣿⣷⣶⣿⣿⣷⡄⢦⡘⢦⢹⡄⢻⡆
⠀⠀⠀⠀⢹⣆⠸⣧⡈⠷⣄⡻⢦⣌⠳⠤⠀⠀⠀⠙⢿⣖⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣉⣩⣭⣭⣶⣾⣴⣿⣯⢿⣿⠹⣿⡌⣿⠈⡧⢸⠀⢁⣼⠃
⠀⠀⠀⠀⠀⠙⢦⣝⠻⣶⣌⡛⠶⢬⣝⡓⠀⠀⠀⠀⠀⠙⠿⣷⣶⠦⢤⣤⣤⣤⣬⣭⡭⢷⣿⣿⣿⣿⠿⣣⣿⡟⣸⣿⢀⣿⢣⠏⣰⠃⢈⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠰⠿⠷⢦⣍⣛⠷⠶⣤⣉⡉⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⠶⠶⢖⣛⣛⣛⣭⣥⡶⠿⢛⣩⣾⠟⠡⠞⠁⢀⣠⣤⣾⣿⡿⠯⠍
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣩⣿⣷⣶⣦⣬⣅⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣉⣭⣭⣭⣭⠵⠶⠶⣛⣛⣉⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣯⣉⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠶⠿⠿⠿⠿⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠶⠶⠶⠶⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣉⣉⣉⣉⣉⣩⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣛⣛⣋⣉⣉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡍⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⢒⣈⣉⣉⣉⣉⣉⣉⣁⡒⠢⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢊⣡⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣟⣿⣶⣦⣌⡉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢋⣠⡾⣿⣿⣿⣿⣿⣿⣿⣿⡿⢉⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣴⣿⣿⣾⣿⣿⣿⣿⡿⣿⠿⢻⣶⣤⡈⣦⣤⡝⣿⣿⣿⣿⣿⣿⣿⣿⡿⣦⡈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣶⡯⠿⠿⠿⠛⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣦⡘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠏⠀⠀⠀⠀⠀⢸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⡄⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣠⣿⣿⣿⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⠀⠹⠶⠀⠾⡏⢰⣾⣿⣿⣿⣿⣿⣿⣯⢻⣿⣿⣿⣿⣿⣿⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⣿⣽⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣠⣀⣄⣀⣼⣿⣿⣿⣿⣯⣽⣿⣿⣷⡹⣿⢿⣿⣿⣟⣿⡄⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣏⢿⣿⣻⣭⣙⣿⡏⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣯⢿⣿⣿⣿⣧⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡎⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⢻⡇⠀⢻⣿⣿⣿⠋⠀⣿⡟⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⡄⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⣿⠗⢀⣾⣿⣿⣿⣷⡀⢹⣿⠀⠀⠀⡐⠁⠙⣿⣿⣿⣞⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢀⠀⢠⣿⠀⠈⠀⠉⠋⠀⠈⠁⠀⣿⡄⠀⢠⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢸⡀⣿⣻⣶⣤⣤⣀⡰⣄⣠⣤⣶⣿⣷⠀⡎⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⣿⣿⣿⡿⠦⡀⠀⠈⢧⣾⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⣠⠀⠀⡠⠘⢻⣿⣿⣿⣿⣿⣿⠇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⣿⣿⣿⣿⣷⠖⠶⠀⠀⠱⣼⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣇⣠⡬⠂⢠⢿⣿⣿⣿⣿⣿⣿⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣉⣭⡑⣿⣦⣻⣿⣿⡟⠀⠤⠬⣽⠉⠉⢉⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⢀⠁⠛⢿⣿⣿⣿⣿⠇⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⣿⣿⡿⠟⠁⠉⠉⠛⠛⠛⠿⠆⠀⠉⢠⣿⣷⣶⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠲⢦⣾⣿⣿⣿⡟⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢻⣿⣧⡀⠀⠀⠀⣀⣠⣴⣿⣷⣶⣶⣿⣿⣿⣿⣿⢀⣼⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⣿⣿⣿⠟⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠹⣿⣿⣿⣾⣿⣿⣕⢿⣿⣿⣿⣿⣽⣿⣭⣏⣁⣸⣿⡿⠻⣿⠿⠋⢠⠀⠀⣀⣤⣾⣿⣿⠋⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣈⡿⠿⡿⢿⣿⣿⣷⣿⢿⣿⣾⣿⣷⡀⢲⣿⣿⣿⠷⡀⠀⣤⣼⠛⠛⢻⣽⣿⣿⠟⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⡏⢀⣿⣿⡁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣈⣤⣼⣿⣿⠀⢀⣼⣽⣟⣡⣔⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣒⢻⢿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣟⢉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠠⠠⡄⢀⠀⠀⢒⠒⠒⠯⣷⣢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣦⣬⣜⠋⠀⣤⣉⡻⣿⢦⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡙⠋⢘⣿⣿⠄⡀
⠀⠀⠀⠀⢸⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣭⣿⡿⢠⣇⡴⠞⠉⠙⣦
⠀⠀⠀⠀⠘⣿⣮⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⣼⡟⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣶⣭⣟⣛⠻⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣻⡍⡋⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣏⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⢡⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣦⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣽⣇⠁⢤⣀⢀⠀⠀⠀⠀⠀⢀⣀⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠿⠿⠦⠧⠤⠶⠛⠋⠁

⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢮⣈⠂⡀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⣬⠅⠈⠉⠉⠉⠚⢶⢄⡀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣿⡀⢀⣤⣴⣦⡶⣽⠛⣿⣽⣿⠁⢹⡆⠀⡀⣀⣄⡠⡄⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢽⡄⡲⣧⣯⢙⢼⣃⢯⠯⣐⡭⡵⠳⡎⢭⢱⡔⣒⣿⡟⡺⣱⠄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣠⣼⡯⡄⠄⡼⢛⢿⢯⢅⢽⠷⢻⠣⠛⣷⢽⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⢼⡋⠀⠙⠯⣤⡐⡈⡍⢎⢌⣰⢎⢡⡐⠿⠙⠚⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠒⠤⠄⠀⠤⢾⣄⠀⠀⠀⠀⠉⠒⠒⠖⠳⠕⠊⠈⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡌⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠑⠂⠠⠀⠀⠤⠀⠒⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡜⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠊⠘⠆⠀⠀⠀⠁⠀⣀⣠⢾⣬⢗⣾⡻⣆⡀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⡝⣹⣿⡿⡿⣮⣞⣯⡝⢟⣿⣤⢭⣖⡷⢸⡃⡆⢒⣶⠲⢲⣀⡖⢤⣒⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⡯⠕⠣⢼⡿⣿⠕⠐⣿⠏⡏⣝⡼⢉⡋⣷⡜⣂⠟⠿⠋⡬⣉⡇⡛⢿⠇⢁⣟⠛⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠣⠄⠊⠻⠗⣻⡻⡿⡟⣾⠾⢳⡝⡠⠥⣾⢓⠟⡻⡼⢼⣿⠝⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⠀⠘⠋⢓⡀⠀⣩⠙⠰⠿⠏⠈⠀⠻⠢⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢹⣆⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡾⠀⠀⠀⠛⠛⠛⠋⠉⣩⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣴⠟⢷⡀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⡞⠁⠀⠀⠙⢦⣌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠋⠀⠀⠀⠀⠀⠀⠙⠋⡀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢿⡻⣆⢻⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⢷⣌⣷⡘⢿⣷⠘⣧⡾⢻
⠀⠀⠀⠀⠀⢰⣦⡀⣿⣇⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣽⣦⠉⠛⠁⠈⠉⠀⠛⢃⡟
⠀⠀⠀⢠⣦⣌⣿⡻⣿⢿⡿⣿⣴⢻⡆⠀⠀⠀⠀⠀⠈⠻⢦⣤⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠹⢮⡛⠃⠀⠀⠀⠙⢣⡞⠀⢀⣀⠀⣤⡀⢠⣄⠀⠈⢿⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢠⡏⠀⠀⢸⡝⣿⡇⣿⣿⢹⠀⠀⠀⣿⠀⠀⠀⠀⠸⣧
⠀⠀⠀⢀⣤⡀⣼⢧⢀⡶⣦⢸⡇⠀⣶⠾⣷⠈⠃⠘⠋⢾⡾⢻⠆⣿⠀⠀⢠⣦⡀⣿⡆⢀⣤⡄
⠀⠀⡶⣼⡏⣷⣿⢸⣿⠃⡿⢸⠁⠀⠈⠳⣄⠀⠀⠀⠀⠀⣰⠏⠀⣿⢀⠀⢸⡌⣷⡟⣿⣸⢃⣇⣴⡦
⠀⠀⢷⡘⣿⠘⠟⠈⠛⢸⣧⡿⣦⠀⠀⠀⠹⡆⠀⠀⠀⣴⠃⠀⠀⣿⣏⠻⣾⡇⠻⠃⣿⡟⢸⡟⣹⠇
⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢁⣴⡃⠀⠀⠀⢠⡇⠀⠀⠀⣿⠀⠀⠀⣿⠙⢷⡀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⢀⡇⠀⠀⠀⢠⡴⠋⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢿⡀⠈⠷⣄⣀⠀⠀⠀⢰⡏
⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⢸⠃⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⠈⣷
⠀⠀⢀⣿⠀⠀⠀⠀⢸⡇⠀⣼⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠸⣇⠀⠀⠀⠘⣧⠀⠀⠀⢸⣇
⠀⠀⣸⠃⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢻⡆⠀⠀⠀⢻
⣿⣿⠟⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢚⣀⣓⡛⣀⠀⠀⠀⠀⠀⠂⠈⠅⠛⠁⠀⠀⠀⠀⠀⡠⡀⢲⢣⠆⠀⠀⠀⠀⣖⡄⠂⣆⣓
⠀⠀⠀⠀⠀⣿⣿⡿⠿⠾⠿⠄⠀⠀⠀⣻⣽⣟⢴⣿⣽⣿⡁⠀⠀⢲⢆⣶⢲⢶⣾⠟⠀⠀⡀⠉⢉⠉⡉⠁⡀
⠀⠀⠀⠀⢴⡶⢂⢰⠏⣦⣄⠀⠀⠀⠘⠉⠉⠉⠉⢉⠉⠉⠁⠀⠀⣼⣫⣽⣬⣼⡽⠷⠀⠀⠳⢩⠊⠈⠘⠚⠥⠂
⠀⠀⠀⠀⠈⠀⠀⠋⠒⠉⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠂⢉⣰⢀⢐
⠀⠀⠀⠀⢀⡤⣌⣤⣴⣶⣶⡆⠀⠀⠀⡄⠀⣀⢀⣀⠀⣠⠀⠀⠀⠘⠷⢶⡄⢳⢷⡇⠀⠀⠀⠆⠂⠐⠈⡂⡄
⠀⠀⠀⠀⡸⠠⡯⠭⠁⢀⣒⡂⠀⠀⠀⠳⢂⣿⣾⡟⢺⠏⠀⠀⠀⠀⢨⡭⡄⠂⣄⡄⠀⠀⠀⢻⡿⣿⣛⢿⡟
⠀⠀⠀⠀⠀⠀⣇⡀⠃⠀⠈⠁⠀⠀⠀⠰⠟⠉⠀⠃⠉⠀⠀⠀⠀⠀⠸⠷⠃⠀⠛⠀⠀⠀⠀⠛⠿⠟⠛⠊⠛⠂
⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⡄⠀⠀⠀⢠⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀
⠀⠀⠀⠀⡀⡀⣀⣐⣐⣒⣀⣀⣀⠀⠀⣸⣿⣿⣛⣿⣞⣵⣇⠀⠀⣠⢏⣚⠘⠆⡿⣩⠅⠀⠀⠀⠀⠚⠃⠛⠃
⠀⠀⠀⠀⢻⢽⠿⠙⢯⢽⣋⣏⡏⠀⠀⠉⠉⠩⠉⠉⠉⠉⠉⠀⠈⢁⣐⣀⣉⣼⣿⣷⡟⠀⠀⢰⢶⢶⣶⣶⢲⣶
⠀⠀⠀⠀⠿⠾⠿⠷⠿⠾⠿⠾⠷⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⢠⣧⣇⣿⣽⣿⣷⠄⠀⠀⠸⠿⠿⠷⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢺⡐⠭⣧⠇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⣸⣥⣤⠖⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⣀⡀⠀⠀⠀⠒⡂
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣷⢶⣄⠀⠀⡀⠀⢖⡲⠀⡊⠁⡆⠈⠉⠁⠀⣼⣤⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⡝⠛⣏⣹⠄⠀⣠⡄⠉⠈⠁⠀⠀⠀⠀⠀⡟⠻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠈⢡⡀⠀⢽⠆⠀⢀⢠⠀⠀⠀⡀⡔⠃⠀⠁
⠀⠀⠀⠀⠀⡀⠖⣀⣀⠀⢠⠖⠒⢄⠀⢿⡀⠀⠀⠀⠀⠄⠂⠀⠠⢇⣹⠃⠀⠄⠒⢌⠂⠀⢀⣼⠃
⠀⠀⠀⠀⣼⣿⠉⠉⠁⠀⠹⣀⣀⠜⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠸⡀⠀⡠⢀⢠⣾⡿
⠀⠀⢀⣴⠟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠉⠀⠀⢨⡿⣿⡀
⠀⠰⠟⠁⠠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠒⠀⠐⢄⣀⠐⢦⣄⠀⠀⠀⣀⠀⠀⠠⠀⢠⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠔⠉⠀⠀⠀⠘⢳⣆⡁⠳⡽⠀⠀⠀⠆⠰⢇⠉⠠⠒⠣⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠢⠁⠐⠛⠉⠀⠰⠖⡄⠀⠰⡄⠀⠉⣳⠄⠉⢀⠘⣡⠶⢀⡖⢠⡀
⠀⠀⠀⠀⠀⢀⠌⠀⢀⡤⠒⠦⠚⠻⠦⣬⡿⣛⠂⠬⣄⡀⢠⡄⠋⠂⣦⢈⡼⠃⠀⣛⠁⢨⣁⣨⣥⠐⠲⠄
⠀⠀⠀⠀⠀⠀⠀⣡⠄⠈⠨⠁⠚⠃⠰⠆⠉⠙⠳⢦⣦⠛⠤⠳⡀⠱⢀⡞⠉⠀⢛⡏⠀⠈⠉⢁⣠⡤⠄⠒⠒⣺⠆⠀⣠⣄⡀
⠀⠀⠀⠀⠀⢴⠒⢈⠀⠀⠀⠀⠀⠀⠀⠠⠙⣤⡀⠈⠉⠏⢲⡀⠈⣣⡸⠅⠀⠈⠸⠎⢡⡴⠾⠋⠀⡀⠀⠐⠛⠀⠀⠙⠆⠉⠅
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠂⠀⣸⢧⡩⣶⣯⣓⣆⣠⣠⣤⣶⡋⢁⠀⠐⠊⢹⠔⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣸⡇⠋⣙⠭⡼⢁⣞⡐⠋⠄⠊⠀⠀⠀⠈⢄⡱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⡴⠟⠀⢁⡤⠎⢻⡅⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡼⠏⠁⣤⠖⠛⡁⠀⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢈⣷⢤⢻⠄⢰⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⡄⢿⡀⠢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⡤⠾⠇⠛⢛⣵⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠠⠀⠐⠻⠏⠙⠋⢹⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡑⢉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠤⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⠍⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡄⢙⠋⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠇⣼⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣼⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⣿⣿⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣽⣿⠅⡀⣀⠀⢀⠀⠀⣰⣾⠿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣴⣾⣿⣤⣿⢿⡯⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢻⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢹⡀⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢜⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⡏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠊⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢉⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠔⠊⠁⠂⣀⢀⣀⠔⡰⠁⠀⢀⠔⠀⡈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⢰⠁⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡿⠯⣁⡈⠀⠀⠀⠀⠈⠁⠠⠤⠀⠀⠀⠸⣀⡂⠔⠩⠄⢐⡂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⣤⣤⣉⣉⣀⣂⡀⠄⠀⠂⠼⠿⠿⠟⠓⠠⠖⢀⣀⣀⣀⣀⡺⠾⣃⠿⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢽⠙⠛⠻⠏⠿⠛⠛⠛⠒⠶⠒⠲⣶⣶⣶⣶⣾⡿⣿⣿⣿⣿⠛⣿⠃⢠⠔⠊⠁⠀⣀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣒⢀⣩⣭⠿⠿⣟⣛⠀⢑⡁⢸⠃⣠⠞⠉⠉⠉⢳⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠂⢀⡲⢒⣚⣿⡿⠽⢖⣀⠡⡂⢻⠞⠀⠀⠀⠀⠀⠀⣧⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣤⠀⠠⠴⠶⣒⣻⡭⠄⣈⠁⣿⠀⠀⠀⠀⠀⠀⢀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠀⠒⣂⣀⣉⣭⡭⠤⠖⢀⠥⠀⡇⠀⠀⠀⠀⠀⣠⠎⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠁⠬⠍⠭⠴⠶⣒⣛⡁⠐⠂⠀⣇⢀⡀⠤⠒⠋⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⢀⣚⣛⣭⡭⠵⠀⢋⠄⢠⡷⠂⢀⣀⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠠⠴⠶⣒⣚⣫⡅⢐⠀⣼⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠈⣉⣭⣭⣵⠖⠤⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⣷⣍⠠⠀⠀⠀⠀⠀⣀⢀⣀⠐⣀⣐⣚⣿⣿⡿⠯⢈⣥⣏⣀⣀⣀⣀⣀
⠀⠀⠀⣀⣤⠴⠖⠒⠚⠹⠏⠉⠀⠀⠠⠤⠤⠿⣗⣦⣔⠀⠀⠀⠐⠀⢛⡀⣺⣿⣿⣿⣯⣧⣴⣿⠿⠿⠿⢿⣯⣍⣍⣉⠛⠛⠲⠶⣦⣤⣀
⠀⠀⢸⡁⣄⢠⡀⠀⠀⢎⠀⠀⠀⠀⠀⠰⠀⠀⠈⠣⠄⣀⣀⣀⣀⣀⣉⣍⣩⣶⣶⣶⣤⡦⠞⠁⣀⡠⠀⠀⡀⠀⠈⠉⣙⠆⠀⣠⢈⣹⣹⡇
⠀⠀⠀⠙⠳⢭⣛⡒⠶⠦⠤⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢉⠉⠉⠉⣉⣉⣡⣄⣀⣀⣀⣰⣶⣶⣶⣦⣤⣤⠤⠤⠶⠖⢛⣫⡽⠞⠋
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠦⣤⣤⣤⣀⣈⣉⣉⣉⡉⠉⠉⠉⠩⠉⠉⠩⠭⠉⠉⠩⠉⠉⣉⣉⣉⣉⣀⣤⣤⣤⠴⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⢿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢿⣫⣼⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⢻⣿⣿⡃⣿⣻⣞⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⠿⠋⠁⠀⠀⠀⢻⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⢛⠉⠂⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠉⠀⠀⠀⠀⠈⠉⠒⠀⠘⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠠⠆⠀⠀⠀⠈⠉⠀⠀⠀⣟⣧⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⢡⠀⢤⠂⠀⠆⠀⠀⠀⠀⠀⣼⣟⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⠉⠁⠀⠀⠀⠀⢨⣼⡿⠋⠀⢆⠀⠀⠒⠋⠀⠀⢀⠠⢾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠈⠣⠀⣀⠠⠔⠈⠀⠀⠀⠑⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⢀⡀⠀⠀⠀⠀⢀⣴⣿⠋⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠤⣁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⠾⠽⠃⠒⠤⢤⡑⢄⡀⠀⠀⠀⠀⣀⠠⠔⢋⣿⣿⠃⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠐⠤⣈⠙⢷⡄⠀⡈⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠁⠂⠭⠭⠍⢥⢄⡀⢠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡃⠀⢀⠑⠂⢬⡳⢂⣽⢶⣦⣄⠀⡰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⢀⠤⢐⠞⠉⠣⣀⣀⣉⣱⣼⣾⣿⣿⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠜⠁⢀⠏⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣧⡀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠠⠖⠁⠀⠀⠀⢱
⡘⢠⠀⡜⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢰⡇⠀⠀⢀⢄⠔⠁⠀⠀⠀⠀⠀⠘
⡇⡘⢄⠓⠠⠴⠚⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⡰⠳⠁
⠡⢈⣀⡀⠀⠉⢙⡩⠻⣿⣿⣿⣿⣿⣿⡿⠟⣋⢀⠀⢐⡀⠀⡀⠀⠀⠀⢀⠀⠀⡐⠀⠀⠀⠀⠀⠀⢸⠀⢠⢁⠃
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠛⠿⠛⠉⠀⣸⣧⣶⣐⣚⣲⣆⣤⣬⣥⣄⡀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢸⠀⠈⡎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢠⠁⠀⠀⠀⠀⠀⠀⢠⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡀⠻⣿⣏⡉⠉⠛⠛⠉⠀⠁⠠⣀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠈⠀⠀⠀⠀⠀⠀⠀⠀⢆⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣀⠈⠛⠛⠻⠗⠆⠀⠀⠀⠀⠀⠀⠐⠤⢀⣄⡀⠀⠀⠈⡻⠒⠒⠠⢄⡀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⣒⠚⡶⢄⣠⣤⡄⠒⠂⠐⠐⠤⡀⠀⠀⠀⠀⠀⡄⠀⠀⠈⢱⠀⠒⢤⣀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⢈⠍⠉⠑⠚⡤⡐⢤⡄⣀⡈⠉⠁⠈⠑⣠⠀⠀⢀⠃⠀⠀⠀⢸⠀⠀⠀⠙⡷⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠂⠀⠀⠀⠀⡆⢘⢦⡑⠮⡁⡀⠀⠀⠀⠙⡀⠒⠎⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠘⠀⡜
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡷⣃⠀⠀⠀⠀⢠⠁⡍⠀⠙⠢⠤⠃⠀⠀⠀⠀⠈⠉⠒⠂⠄⣠⠜⠁⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠛⠀⠀⠀⠀⠈⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠢⠤⠐⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞

⠀⠀⠀⠀⠀⠄⠀⠀⡠⠀⠠⡔⠀⠀⣾⠃⠁⡀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⢐⣷⣦⠀⠏⠀⠀⡧⠃⠀⠃
⠀⠀⠀⠀⠀⠞⠁⠀⠀⠒⣺⣿⡿⠀⠀⠀⠸⠁⠞⢀⡅
⠀⠀⠀⠀⡔⠀⠀⠀⣤⣾⠋⣡⣦⣤⡶⠴⠛⠀⣐⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄
⠀⠀⠀⡀⠀⠀⠀⠼⠛⠻⣿⣿⣷⠶⠤⡤⡦⠀⡤⣀⠈⠂⢠⣤⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠇⠘⡠⠶
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠰⢡⣿⠻⠓⠀⠀⠀⠀⠀⣚⠗⣼⠆⠈⣠⣴⡶⠶⠶⠛⠛⢩⣍⣤⣴⡶⢸⡟⢻⡇
⠀⠀⠀⠀⠉⠲⡖⠚⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡉⠈⣁⡄⢨⡆⢰⡶⠟⠛⣿⠀⣿⡇⣿⣄⡄⢸⣇⣼⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸⢿⣋⣀⣀⣀⣀⡠⠔⠚⠃⠀⣿⣷⣸⡇⢸⣧⣤⠀⢿⣧⣿⠀⣿⣋⣁⢸⡏⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠟⠋⠉⠉⠉⠀⠀⠀⢀⡄⠀⣿⠸⣿⡇⢸⣧⣤⡄⠸⣿⣇⠀⢻⡟⢩⣌⣷⡟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠤⠤⠀⠐⠒⠂⠉⢽⡇⠀⢿⣀⡙⣣⣼⣏⢁⣶⢺⡟⠋⠀⢸⡇⢸⣿⣿⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡟⢉⣋⣿⠙⣿⣸⡇⢸⡿⠇⠀⢸⣇⣸⡟⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⣀⣀⣀⣀⣀⣴⠶⣟⢸⣧⢈⣿⣿⡆⢻⣿⠁⠸⠟⠛⠀⣀⠩⠭⠔⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠛⢛⣋⣉⣥⠤⠶⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⠒⠒⠒⠒⠒⠋⠉⠘⡟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡗⣭⢛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣰⡏⣼⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⣿⢰⣟⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣷⣾⣷⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠛⠀⠀⠀⢀⣀⡿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣶⣶⠞⠀⠀⠀⢤⣤⡴⠀⠀⣤⡄⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠹⣆⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡟⠀⢀⣤⡀⠘⣿⠁⢠⡄⢸⡇⣠⣼⠇⣄⡏⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⢸⣿⣷⣾⣿⠀⣿⣿⣿⡇⠙⢻⡇⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⢸⣿⣿⣿⣿⠀⣿⡿⢿⡇⣶⣾⠻⡆⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⡇⠀⠸⣿⡏⠈⣿⠀⠙⠃⣸⡇⠉⠸⠆⠐⠃
⠀⠀⣠⣴⣶⣶⣿⡇⠀⠀⠀⣤⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠸⣿⡿⠃⠀⠠⣿⣿⡀⠀⠀⠀⠈⠛⠃⠀⠀⠉⠁
⠀⠾⠿⠛⠛⠉⠉⣿⣷⣶⣾⣿⡇⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠛



⠀⡁⣉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡶⠾⠛⠛⠛⢛⡛⠻⠯⣶⣢⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢖⣻⢟⡭⠚⢁⠠⠤⠀⠠⣄⠈⣉⠉⠑⠲⠬⣙⠪⣝⢶⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣩⢞⣟⡵⢋⠔⡨⠔⠊⠀⠀⢈⡫⡠⠀⠀⠀⠀⠐⠪⡙⠦⡙⢿⣮⣙⡦⠄⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡴⠋⢠⢯⠞⡀⣠⠊⠀⣠⠄⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠈⢢⠘⢎⢫⣧⠀⣀⣄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⠋⠀⢀⡏⡏⡜⠰⠃⠀⠀⠴⠄⠠⠀⠐⠀⠀⠀⠠⠆⠀⠁⠄⠀⠀⠀⠈⠈⡏⣿⠋⠀⢠⢧
⠀⠀⠀⠀⠀⠀⢠⡟⡰⠁⠀⠀⢸⢸⠁⠃⠃⠀⠀⠀⠀⠈⣄⠀⡀⠘⠇⢀⠆⠰⠀⠇⠀⢸⠀⠀⠀⠀⢸⢸⣂⡴⠛⠒⠧⠤⠀⣀
⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⣾⠸⡆⡆⢀⠀⡄⢂⠀⠁⠈⠓⠠⠦⣴⡅⠊⢀⠘⢀⠁⡎⠀⠀⠀⠀⢸⢸⣿⣶⣤⣄⡀⠀⠀⠀⠈⠑⠄
⠀⠀⠀⠀⠀⢸⠇⠄⠀⠀⠀⠀⢻⡆⢧⠰⡈⢆⢘⣄⡢⣀⠀⠀⠀⠀⡈⢀⡼⢋⠔⡡⢊⠀⠀⠀⢰⢃⡟⣼⣿⡋⠋⠧⠙⢿⡖⠦⠤⠜
⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣷⡘⣆⠀⠀⠀⠙⠻⣶⡛⠷⢶⣤⡙⠈⣴⣵⠟⠊⠀⠀⠀⡰⢃⡞⣰⣿⠙⢃⠀⠀⠀⠠⣇
⠀⠀⠀⠀⠀⣿⠰⠀⠀⠀⠀⠀⠀⡟⣷⣌⢧⡀⠐⢤⡀⠀⠈⠙⠲⢌⠻⢸⠟⠁⠀⠀⠀⡠⠞⣡⢏⣴⡿⠁⠀⢸⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣝⠲⣄⡈⠑⠢⠤⣄⠀⠐⠘⠀⠀⠀⢀⣠⡴⢋⣵⣾⡿⠃⠀⠀⠈⠘⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣯⡳⠮⣍⣓⠲⠦⠤⠤⠤⠤⠴⠒⣚⣩⡤⠞⣋⡴⠏⢀⢀⠂⠀⢀⠆⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⠙⠟⢷⣤⣈⡍⠛⠛⠛⠛⠛⠛⠋⢉⣠⡴⠞⠋⠀⠀⠡⢂⠄⢀⠌⡀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢢⠣⡈⠲⣍⠛⠻⠿⢷⠶⠶⠷⠛⠛⠋⠉⠀⠀⠀⡀⠜⠁⡁⢠⠊⡔⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⠢⡀⢑⠢⢀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢐⡨⢐⡡⢊⠔⣡⠎⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠨⡐⠀⣀⠈⠁⠐⠂⠒⠂⠐⠀⡀⠤⠒⡡⠒⡡⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠨⢐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⢀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣕⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡠⢖⣡⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢽⣳⡶⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢖⣊⡥⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠾⢭⣭⣭⣽⣭⣭⣭⠭⠶⠖⠛⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡠⠔⠒⠒⠒⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠒⠒⠲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡉⠑⠒⣤⡀
⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡰⣠⠄⠳⡀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣹⡿⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢀⡠⣀⠀⢨⡿⠒⠛⠁
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⠙⠗⠃⠀⢱⠀⠀⠀⠀⠸⣅⠠⣙⠢⠄⠀⠠⠤⣒⠾⢁⡜⢉⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⡩⠷⠤⡜⠓⢦⡗⠻⡅
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢈⠄⠀⠀⠀⠀⢜⠷⢄⣉⡐⠒⢈⣉⡤⢖⠩⣢⢞⠏⢸⠀⠀⠀⠀⠀⠀⢀⢠⠎⢉⠖⠀⠲⣏⠟⠉⠉⡖⢧
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠫⣀⣒⡤⣭⣭⡥⢄⣒⠥⠚⡡⠋⢀⠆⠀⠀⠀⠀⡔⢊⣇⢈⠖⠳⣀⣀⣠⣏⣐⠤⠚⣷⠼⡀
⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⢿⠀⠭⠍⣉⣉⠡⠤⠖⠋⠀⢀⠎⠀⠀⠀⠀⠀⠓⠾⡀⢩⠣⢤⠼⠤⡆⠀⠈⡷⠚⣷⡴⠃
⠀⠀⠈⠲⢄⡀⠀⠀⠀⢂⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠚⠓⠒⠋⠒⠊⠉⠋
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠆⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠘⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⡲⠖⢶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⢀⡈⣇⠙⠈⡞⡿⡆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠘⢦⡈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⡠⠊⢠⠌⢙⠳⣄⠋⠀⡗⢀⡢⠄⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⣠⢟⣀⡀⡀⠀⠀⠀⠀⠀⢠⠏⡄⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠸⡄
⠀⢀⠜⠃⠠⠄⠀⢉⡁⠘⠳⡄⠉⣙⣆⠀⠀⠐⠥⡀⠀⠀⠀⠀⠀⠀⠀⠚⢡⣾⡷⡅⠀⠙⡮⠙⣦⡀⠀⠀⢸⡀⢇⣀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⡇
⢀⡾⠈⠃⢀⢄⠀⠑⠁⠦⠆⠹⡑⢿⡌⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⣀⡴⢻⠥⢷⡦⢵⡪⠔⢒⢼⠹⡄⠀⠀⠳⣄⠘⠦⠤⠀⠀⠀⣠⠏⠀⣀⡴⠃
⡸⠤⠰⠆⠀⠈⠀⠘⠀⠠⣢⢀⡇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⢹⡤⣚⢧⡦⣝⠲⠞⡼⠀⠙⡄⠀⠀⠀⠉⠓⠒⠒⠒⠉⠉⠉⠉⠁
⡷⠂⠰⠀⠀⠃⠀⠐⠓⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣥⣸⢀⣀⢗⡔⢁⡴⠚⠁
⠙⢤⣷⣀⣛⣠⠴⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣄⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⡆⣿⣶⣿⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢲⡄⠀⣠⠖⠒⣓⡲⢶⡶⠀⠀⠀⠀⠀⠀⠀⠛⠻⡗⠦⣿⢹⡟⡷⠟⢫⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⡘⣾⠔⠂⠁⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⠳⡈⡧⠛⢈⣩⠽⠟⠒
⠀⠀⠀⠀⠀⢀⣤⢄⣀⢀⡦⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠉⠉⢷⡹⠲⠤⠤⠤⠾⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣯⠿⣰⣶⠗⠺⣿⢦⡌⠶⡄
⠀⠀⢀⡤⢚⡩⠝⠦⢠⣙⡦⠘⠖⠲⣌⠙⠢⡀⠀⠀⠀⠀⢰⢡⢊⠀⠀⠒⠾⠗⠂⠀⠀⠀⢀⢹⠀⠀⠀⠀⠀⢀⡤⢚⣩⣉⠉⣄⣚⡞⢿⠢⢸⠚⠇
⠀⢠⠏⠰⠟⠒⢸⡣⢶⢰⠦⢬⣯⠉⠉⠀⠀⢹⠀⠀⠀⠀⠘⣆⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⣰⠋⢉⠀⠀⢃⠀⢰⠀⠘⠉⡇⠸⠂
⠀⢼⢀⠀⠀⠀⠈⠀⠘⠇⠀⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡟⠀⠀⠀⢰⢧⠀⠸⠒⠒⢺⠀⠘⠓⠒⣷⠇
⠀⠸⣜⢄⡠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠁⠀⠀⠀⣇⢠⣀⣀⣇⣀⣸⠀⢤⠆⢰⠏
⠀⠀⠈⠳⠤⣤⣅⣈⣉⣡⣠⣤⣤⡤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣠⠤⢄⣀⠀⢀⡴⠃⠀⠀⠀⠀⠸⡼⡄⣀⣇⠀⣘⣀⣸⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣇⣸⠥⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠠⢄⠴⠂⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⣸⠀⠀⠀⠀⠀⠆⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠘⠂⠀⠀⢄⠑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠘⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠐⠒⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⣆⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐⠶⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⢀⠀⠀⡀⠻⡀⠀⠰⠀⠀⠀⠀⠈⠁⢀⡄⠀⡀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠘⠁⠀⠀⠈⠀⠀⠀⠉⠒⠀⠐⠋⠀⠀⠐⠦⣀⣀⡤⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣿⣿⣿⣿⣶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠁⠈⠙⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠿⠋⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⢻⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣤⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣄⣀⣀⣀⣁⣄⣀⣠⣀⣤⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠸⠿⠿⠿⠿⠿⠿⠿⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⣀⡤⠚⣀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡴⠋⢡⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⢾⡁⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇⠈⢻⡆⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⣠⠞⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡚⠉⠉⠀⣀⣀⣀⣀⣠⣤⣤⣀⣀⣀⣀⠀⠀⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠱⣏⣤⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣭⣭⣿⣲⣦⣍⣦⢸⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢿⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⢸⠦⢤⡀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⡟⠀⠀⡷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠻⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⣿⠃⢀⡼⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⣰⡧⠖⠋⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠾⢧⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣁⣀⣤⠴⠋⠁
⠀⠀⠀⠀⠀⢠⠞⠁⠀⢠⠞⢡⡞⣽⣧⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⢸⡄⠀⠀⣿⢠⣿⣾⡭⠴⠖⣒⣿⣧⣤⡤⠴⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠙⠲⣤⣙⠿⡴⠿⣍⣉⣉⣡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠾⠭⠭⣤⣤⣤⣤⣤⣤⣤⠤⠤⠶⠖⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣙⡻⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⡟⠟⠛⠛⠋⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⢠⣽⣦⣄⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⣇⣈⡿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣿⣿⣟⣻⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡛⡶⠦⠄⠀⠀⠀⣠⡶⣖⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠏⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠐⠄⠀⠀⠀⢀⣾⠟⠛⢸⡄⠈⠻⢿⣿⢿⣿⣦⡴⠟⢿⣷⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢀⡿⢄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣠⣻⡿⠂⠀⣸⣷⠀⡇⢈⠻⡐⣿⡇⠀⠀⢰⣿⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⡀⠈⠒⡄⢰⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⣴⡿⣿⣇⠀⢠⣿⣿⣾⡷⢿⡃⠀⠘⣇⡄⠀⠀⣿⣀⡆⠀⣠⡏⠀⣠⠗⡀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⣴⣾⣿⣷⡌⢿⣤⡾⣿⢻⣿⣷⣾⣿⣽⣿⣟⠛⠒⠒⠋⢩⡇⢠⣿⣷⡻⠛⠀⢁⠀⠀⢠⠈⢻⣄⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣽⣿⣿⣿⣿⡿⢷⣼⡿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠖⠉⠀⠐⠈⣇⣸⣿⣿⡶⠀⠠⠌⠀⠀⠀⢦⣬⣴⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣄⡀⠈⠁⠀⠸⠿⢿⣿⣿⣿⣿⣿⡛⠷⠄⠀⠀⠀⢸⡟⢿⣿⣿⣷⣤⣤⣜⡄⠠⣨⣽⣌⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣀⡀⢀⡀⢌⡻⣿⣿⣟⣷⣀⢲⠀⣀⣇⠈⢹⡿⠋⠁⠢⡈⠇⢰⣧⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠙⠛⣋⣉⠉⢉⠉⠉⠉⣿⣿⣷⣝⣦⡹⣮⣟⠉⠉⠉⡝⢿⣛⠓⠒⢉⠀⠀⠀⠀⣸⡇⢸⢿⠏⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⣸⣿⣿⠀⣼⡖⠀⣼⣿⣿⣿⣿⣿⣿⡼⡇⢠⡖⠀⣹⣘⣉⠔⢰⣯⣤⣤⢶⣾⠿⠁⢹⡽⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣨⣻⣽⣿⣦⣿⣷⣞⣼⣿⣯⣽⣿⣿⣿⡇⣇⣼⣷⣿⣿⣏⣶⣾⣿⠅⠀⢢⣰⠃⢀⣀⡸⡷⢁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣽⣿⣿⣿⣿⣿⣯⣾⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣦⣶⣶⣙⣓⣻⣿⣯⣟⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢝⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢉⣋⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣇⢾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠈⠻⠿⠿⠽⠿⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⠃⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡇⢀⡛⣶⠀⢀⣤⡄⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠁⠀⠀⠦⠖⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢠⣄⣳⡠⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡜⣿⡄⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠂⠲⠟⠛⠛⠛⠛⢛⡃⠙⣿⢦⣤⡤⠎⡹⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢠⣤⣶⣦⣶⣾⣿⣇⣀⠀⠒⠄⠀⡀⢀⣾⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠿⠿⣿⣤⡀⠈⠙⢿⣿⣿⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠂⢀⡀⢠⠀⣼⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣴⣿⣿⣿⣿⣿⣾⡿⠁⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠌⠀⠀⣘⣇⡚⢤⡿⡟⢻⢿⠻⣿⣿⣿⣷⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣤⣞⡥⠒⠹⣤⣴⣿⣿⢿⣿⣞⡀⠈⠙⣏⣀⡈⠙⢿⣿⣠⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢠⣿⠟⠉⠀⠀⣠⣿⣿⣥⠀⠀⠉⠉⠀⢀⣼⣿⣿⢿⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠖⠂⠀⠀⢸⡇
⠀⠀⠀⣾⠁⠀⠀⠀⢆⣿⣿⣿⡷⠀⠀⠀⠀⡀⢻⣿⣿⣿⣮⣿⡦⠈⠻⣿⣿⣿⣿⣿⣿⣿⣂⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠸⣇⠰⠄⠀⣨⣶⣿⣿⣧⣀⢀⡀⠀⠉⢸⣿⣿⣿⡿⣿⣷⡀⠀⠀⠙⠻⢿⣿⣿⠿⠧⠀⣀⠀⢰⡏
⠀⠀⠀⠀⠈⠘⠚⠛⠉⠉⠻⣿⣿⣿⣷⣿⣿⣧⣈⣛⣋⣵⣿⣿⣿⣿⣄⠀⡀⠀⠀⠉⠙⠛⠻⢷⣶⣕⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⣿⣧⡀⠀⢀⡀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⣿⣿⣿⣿⡏⣁⢹⣿⣷⣄⡉⠉⠀⢀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠉⠛⢿⣿⣷⣴⣿⣿⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣮⡿⣿⣿⠰⠶⠒⠂⠀⠀⠀⢀⠈⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⢸⣿⣦⣀⠀⠤⠀⠀⠀⢊⣴⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠈⣿⣿⣿⣦⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣽⡞⣿⣻⣛⣿⣯⡿⠿⢿⣿⢿⣛⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠾⠿⠿⠿⡟⠉⠉⠉⠉⠉⠉⠉⠉⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠒

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠘⣄⡰⠙⣄⣤⢀⡿⠀⣠⠴⡇
⠀⠀⠀⡀⠀⠀⢠⡄⣽⠑⠾⠀⠈⠃⠀⠙⠈⠃⠰⠞⠁⠐⠇⢀⣠
⠀⠀⠀⠙⢟⠃⠶⠆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠚⢩⠃
⠀⠀⠠⣤⠦⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⣠⠶
⠀⣀⣀⠨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠏⣀⣀
⠈⠙⠒⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠔⠒⠊⠉
⠀⣠⣔⣋⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠦⠄
⠀⠀⠀⠀⣼⣁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣘⣆
⠀⠀⠀⠈⠁⠀⣯⠴⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠹⡄⠁⠀⠀⠀⠀⠀⡴⠈⠀⣠⠛⢩⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣇⠞⠻⢀⡜⢧⡞⣆⡞⠳⣄⣯⠙⠶⣄⡘⢆⠀⠀⠀⢀⣼⡗⠀⠀⢿⠀⠛⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠟⠀⠀⠀⠈⠀⠀⠀⠙⠀⠀⠀⠙⠺⣦⠀⠀⣼⠏⠀⠈⠁⠀⠀⠠⡀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⢠⡿⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⢸⡇⢀⡖⠂⠀⠀⠐⣒⣚⡇⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠚⠁⠀⠀⠀⣾⢡⡀⠀⠀⠀⠀⠀⠀⠈⣡⠀⢡⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣾⣇⠀⣠⠀⠀⣀⠀⠀⣿⡀⠈⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠹⣤⣤⠋⠀⣴⢟⣧⠀⠈⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣠⠖⠟⠛⠛⣡⣠⠆⣀⣀⣴⡿⠋⠘⣿⣷⣄⠀⠙⣿⡳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠌⣾⠛⠄⠀⠀⠈⠃⠉⠀⠉⠛⣯⠠⠶⣄⠈⠉⠻⠷⣦⡈⠹⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣽⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠱⢦⡀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⣤⣹⡌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡶⡄⢀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠃⠀⡈⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⣀⡀⠀⠀⣦⣀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣠⡤⠀⢀⣴⣿⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠀⠀⢿⠇⠀⠀⠀⠉⣿⠨⠲⠕⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠓⠀⠘⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡗⠀⠀⠀⢧⠀⠀⠀⠀⣿⡄⠀⡢⠀⡀⢅⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠈⢣⠀⠀⠀⠸⡇⠂⠁⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⡏⠀⢦⡄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠫⠄⠀⠀⠀⠇⢠⠈⠃⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⠆⡀⢀⠀⠀⠀⢠⡄⣰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠣⣈⣀⣴⠆⠀⣼⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠉⠑⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⢀⣿⣿⡄⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⠀⠠⠂⠀⠀⠄⠈⠁⠐⠂⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⢠⠀⡀⠀⠀⠀⠀⠤⢀⣀⣀⣀⠠⠖⠀⠀⠀⠀⠆⠈⠑⣷⠀⠃⠠⠓⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⡀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠣⢬⡄⠁⢠⡟⣷
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣀⠈⡷⠀⡀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⢤⠐⠛⢲⡎⢱⣿⡧⠀⣄⠀⡀
⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠁⠘⢄⠀⠠⠀⠴⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠉⠗⠊⢽⣥⠏⢩⡅⣹⡀⢹⣀⣠⡄
⡄⠀⢠⡴⠋⠁⠀⠀⠀⠀⠀⢗⠐⠸⣀⡀⣤⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠡⠆⠰⠆⠠⠄⢀⡤⣀⡤
⡼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠤⢟⣁⣷⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠂⢠⠀⢠⠄⠀⡄⢀⡷
⣼⠇⠀⠐⠲⠦⣀⠀⠀⠀⠀⠀⠀⢸⣾⣵⡛⠻⠅⣠⠄⡀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠂⠆⢠⡄⢨⡄⢀⡆⢀⡆
⠋⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⠀⠰⠄⣀⠛⢠⣏⡐⠶⠀⠀⠀⠀⠉⠁⠀⣀⠄⠒⠐⠒⠐⠂⠀⠀⠣⠀⠄⢈⡄⢈⣅⢈⣧
⠀⠀⠀⠀⠀⠀⠀⡈⢿⣆⠀⠀⡀⠸⠂⡠⠉⠀⡴⠀⢘⠃⢤⡄⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢵⣠⡥⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠁⠂⣀⠁⢠⡴⠀⢀⠛⢤⡴⣠⠀⠀⠰⠇
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠟⢀⠉⠠⡌⠀⢀⠛⠀⡴⠆⣹⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢬⠀⣤⠀⢘⠛⢠⡴⢀⣸⡽⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡄⠀⠀⢀⡀
⠀⠀⣠⡎⢽⠄⢡⠀⢠⠀⢀⠀⠀⠀⠰⢦⣐⡟⣠⣴⡤⠜⠋⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠀⡘⡁⠴⠤⠄⡀
⢀⡞⢉⡄⢠⡄⠀⡦⠠⡤⠈⠀⠀⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠲⠤⠀⠀⠀⠀⡎⢀⡗⠉⠠⠀⠐⡀
⠸⡇⠈⡀⠀⡄⠀⡴⠀⢠⠀⡀⢁⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⣴⠬⣉⢹⠤⢤⡐⣲⠒
⠐⢏⡘⣃⢀⣅⠀⣠⠀⣨⠀⣅⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠬⠀⠰⠀⠂⠈⠃⢾⣿⠖⠻⠁⠀⣀⣀
⠀⠈⠋⣡⡄⢡⡄⢠⠄⠴⠄⢠⢾⠦⢀⡄⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⠀⠀⣀⠀⠆⠐⠂⠀⠓⠈⡃⢉⡀⠀⠀⠀⠀⠀⠈⠑⠢
⢦⡀⠀⠀⠁⠐⠶⣀⣗⠰⣶⣷⡎⢹⣇⣀⠩⠇⠀⠀⠀⠀⠈⠉⠒⠀⢀⠁⣀⠠⠦⠐⠶⠀⠒⠀⡋⢩⡐
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣹⠃⠀⠸⡂⢤⠐⠀⠀⠀⠀⠀⠀⠀⢺⠁⣄⠀⣤⠠⠤⠄⢲⠒⢋⠈
⠀⠀⠤⢤⠀⠀⣀⠀⠀⠀⠀⠘⣋⡄⠈⠀⢰⣄⣁⠰⠂⠀⠀⠀⠠⣀⠈⠣⣥⣀⠤⡄⠰⣤⠘⡆⠛⠁
⠂⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⠀⠀⡅⠀⠀⠘⠀⣥⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠓⢤⣦⣔⡶⠞⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢀⣀⣁⡀⣀⠀⠀⠳⣄⢀⡀⠀⠀⠀⡀
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠓⠶⣄⡀⠀⠀⠀⣠⠴⠒⠋⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⡰⠁⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⢰⡇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠃⠀⢸⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠐⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⢀⣠⠤⠴⠖⠒⠛⠛⠋⠉⢉⣉⣉⣉⣉⣩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣍⣛⣛⣓⣒⣲⠦⠤⢄⣀
⣿⢶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡇
⣿⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠉⠁⢸⡇
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡤⠤⠤⠤⠤⣄⡀
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣀⡀⠀⠀⠙⢦⡀
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠔⠋⠉⠀⠉⠳⣄⠀⠀⢳
⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈
⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⢀
⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⢀⣤⣤⡀⢰⡷⢰⣿⢠⣿⣴⢏⡼⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⢀⡜
⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⣾⢷⣼⣧⣾⢃⣾⠛⠛⢧⡴⠟⠁⠀⠀⠀⠀⠀⢀⡾⠁⢀⣀⣀⡤⠴⠒⠋⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣀⣿⣠⠟⠁⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠉⠁⠀⢀⣀⡠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠠⣿⣷⡿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠯⠤⠴⠖⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠁⠀⢀⣠⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠶⠶⣖⡒⠒⠓⣟⣛⣷⣶⢦⣶⣦⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⠟⠋⠉⠴⠞⠁⣾⡶⠊⠉⠻⠋⠁⠹⣮⣿⣿⣿⠿⣙⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠁⠀⡜⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⣠⣿⡿⠛⠁⠀⢸⣯⡝⠻⢿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠈⢣⠀⠀⠀⠀⠈⠛⠻⢦⠀⣴⠿⠋⠁⠀⠀⢀⣠⣾⠏⠀⠀⢸⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⢻⣿⣿⢿⣿⡟⠀⠀⠈⠢⠐⠠⠔⠒⣒⠠⡀⠀⠋⢀⣤⣤⠶⠶⠛⠉⠀⠀⠀⣠⣿⣿⣿⣿⣿⠏⣄
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣄⡀⠠⣀⣠⣤⣤⣠⣠⣭⡻⣤⣶⠟⢉⣀⣤⣤⣤⣴⣾⣷⣿⣿⣿⣿⣿⠿⡫⣾⣿⠟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣴⣭⣭⣯⣉⣉⠉⠛⣿⣾⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠈⠛⢻⣿⠁⡀⠴⠷⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠄⠠⠀⠀⠀⠀⠀⠐⣾⠆⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⡏⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⡟⠀⠀⠀⠀⣠⠔⢋⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⡏⠀⠢⠐⠚⠉⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠎⠀⠀⣀⣀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⠦⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣠⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠩⠿⡖⣶⣶⣶⣶⣶⣿⣿⡿⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠔⠐⠄⡠⠤⠤⣠⠈⠀⠀⣾⠇⠈⢀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⣼⣆⠀⠀⡿⠀⠀⢰⡰⠁⢰
⠀⠀⠀⠀⠀⠀⢀⣤⠴⠛⠁⢀⣾⣿⣧⠀⠀⠀⠀⡿⠁⡀⠈⡀
⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠚⢋⣿⣿⡟⠀⣀⠀⠐⠁⡜⠃⣠
⠀⠀⠀⠀⠀⡈⠀⠀⠀⢀⣴⡿⠋⣁⡀⢀⣇⣠⡾⠃⠠⠜⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⢠⣟⣿⣦⣶⣿⠛⠻⠭⠭⠀⣀⠒⠛⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⢀⡟⢀
⠀⠀⠀⢠⡁⠀⠀⢰⠟⠉⠉⣿⣿⣿⣿⠿⢷⢶⡶⠒⣢⢤⣄⠈⢀⠰⣦⣤⣤⣤⣤⣤⣤⡤⠤⠄⣀⣀⡀⠀⠀⠀⠘⠃⠈⡴⠟⠃
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠏⣸⡟⣿⠆⠐⠀⠀⠊⠀⠠⠟⢷⢸⠄⠈⠀⣠⣤⣶⣶⡶⠾⠟⢛⣉⣁⣤⣤⡦⣾⡿⢿⣷
⠀⠀⠀⠀⠱⢤⣀⣀⣠⣄⠤⠖⠛⠉⠀⠤⠐⠀⠀⠀⠠⠐⡇⠴⠟⠀⠀⠚⠋⣉⣥⣤⢴⣶⠀⣼⡿⣿⡟⠉⠁⣿⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠻⣋⣉⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣶⡆⢸⣿⢸⣿⠋⠉⠸⣿⠀⣿⡇⣿⣷⣶⡆⣿⣷⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣾⣿⠄⠀⠀⠀⢀⣀⡤⠖⠟⠀⢸⣿⣷⢸⣿⢸⣿⣤⣄⠀⣿⣧⣿⠃⣿⡏⢉⡁⣿⡏⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣴⣿⠛⠛⠛⠛⠉⠁⠀⠀⠤⠀⢸⣿⢻⣿⣿⢸⣿⠉⠁⠀⢹⣿⡿⠀⣿⣿⠿⢏⡛⣣⣼⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠀⢸⣿⠈⣿⣿⢰⣿⣿⠿⡀⣘⣯⣥⡄⢰⣿⠀⢸⣇⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠲⠶⠖⠒⠒⠉⠉⠉⠱⣿⠀⠸⢿⣀⡈⢻⣤⣶⡀⢸⡿⢿⡏⠉⠀⢸⣿⠀⢸⣿⣿⣇⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠀⢰⡿⠛⠿⢻⡇⣿⡇⣼⡇⣿⣷⣷⠀⢸⣿⠀⣸⡟⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡄⢸⡇⢴⣶⣾⡇⢸⣿⣿⠀⣿⣇⣤⡄⠀⠿⣷⠟⠁⣛⣃⣤⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⣤⣄⣀⣀⣈⣤⣾⠟⢿⡇⢸⣇⢀⣿⢻⡇⠘⣿⡿⠀⠛⠛⠋⠁⣀⠤⠶⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⡇⠘⠿⠿⠋⠈⣁⣠⣤⡴⠖⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣄⣀⣀⣀⣠⣤⠴⠞⢧⣴⣶⠶⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⠠⠉⠉⠉⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡆⠾⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣶⣚⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡟⠙⢿⣿⣿⡿⠟⠋⠉⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡟⠀⠶⢦⣤⠀⠀⣠⡴⠖⠈⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠐⠦⡠⠶⠀⠠⠥⣴⠶⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⣠⠀⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠈⠒⠂⢀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⣄⠀⠀⠈⠀⠀⣠⡾⠿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣄⠹⣿⣧⣄⣀⣀⣴⡿⠁⢠⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣗⠈⠙⠿⣿⣿⠞⠀⢠⡿⠛⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⣿⣿⣿⣿⣿⠿⠿⠏⠋⢻⣆⠀⠰⣿⡿⠀⢠⣿⣿⣆⡄⠈⡻⢿⣿⣿⣿⡿⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠘⣿⣿⠿⠟⠉⠀⠀⠀⣀⣿⣿⣧⢀⣿⣿⣀⣿⣿⣿⣿⣿⣾⣶⣦⣝⣿⡿⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠘⡃⠀⠀⠀⢸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠀⠀⠀⢷⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢱⣄⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⢿⣿⣿⣿⣷⡟⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣿⠀⠀⠀⠈⢻⣿⣿⣿⠇⢀⠀⠀⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⣰⣿⡅⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⣫⣽⣿⣤⠀⠀⠈⣿⢿⣿⣤⣾⠄⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⢠⣿⢉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠠⣉⠻⢿⣿⣷⣤⣶⡛⣀⠈⠙⢿⣾⣅⠀⠀⣀⣀⣀⡀⢷⡀
⠀⠀⠀⢀⣿⣁⣈⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⢻⣿⢿⣿⣿⣿⣡⣤⡄⠀⠈⠓⠌⡙⠻⣿⣏⠁⠂⠀⠀⠈⠉⠉⠉⠁⠈⠉⠳⢞⣷
⠀⠀⠀⣸⣫⡵⠆⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⢫⡔⠀⠉⠃⣭⢟⣿⣿⣿⣷⣤⡀⠀⠀⠀⠒⢤⣹⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⢻⣿⣴⡶⠀⣀⣀⠐⠂⣷⠘⠟⢉⣩⠀⠀⠀⢀⡾⠎⢠⣽⣿⣻⣿⣿⣿⣦⣤⡀⠀⢠⣿⣿⠛⢷⣶⡀⠀⠀⡀⠀⠀⠀⢀⡞
⠀⠀⠀⣿⣿⣯⡴⠛⠉⠉⠁⠸⠉⢠⠶⠝⠁⠀⠀⡰⠛⢁⣴⣾⣿⣿⣿⣾⡿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠈⢻⣿⣿⣷⣒⢋⣴⡿⠋
⠀⠀⢸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢈⣀⣀⡤⠒⡩⢏⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠹⢿⣿⣿⠟⠋
⠀⠀⠈⢻⣿⡀⠀⣠⢶⣿⣇⠀⢀⡈⠉⣡⡴⡿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠻⢧⣄⣙⣻⡿⠟⠋⠐⠳⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣙⢹⣏⢻⣏⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠨⠾⢿⣿⣿⣿⠿⠏⠉⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠂⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠈⠉⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡀⢠⣀⠐⠒⠢⡀⠀⢀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⡄⠀⠀⠐⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡈⠀⠀⢻⡒⡶⠶⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⢀⠐⠀⠀⠀⠒⠀⠀⠀⠀⠀⢘⣳⡤⠀⣒⠒⠦⣍⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠈⠑⢤⠀⠙⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠱⡀⠀⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠖⠀⠀⠀⠀⠀⠀⢶⠘⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢧⠀⠰⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠀⢀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸⠀⠠⠿⢀⡀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠄⡀⢠⠈⠁⠀⠀⠀⠀⠀⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⣿⠂⢳⣄⣈⣁⣀⠁⢠⣌⣀⣰⡀⣢⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢤⣞⣁⠁⠀⠀⠀⠀⠀⠀⠀⠸⡄⠸⡄⠀⠀⠀⠀⠀⢀⣾⠀⠀⠆⢀⡉⠉⣉⡀⣼⣥⣌⡽⠦⣴⢛⣿⣿⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣆⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢳⣄⠀⠀⠀⣦⠀⡉⠀⠱⡦⠈⠠⠄⢐⠤⢌⣥⣤⠤⡤⠈⡌⣩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡿⠄⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠙⠓⢶⡾⠓⠀⣓⡴⢤⡴⣂⢁⣒⡊⣐⡧⠴⢶⠶⢳⡞⢋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⣤⣤⣤⣏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⣴⡿⠤⢤⡏⠁⠀⣷⣾⣤⣼⣭⣥⣟⣛⣻⣟⣻⣽⠿⡥⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠷⠿⠿⠶⠤⠤⠤⠥⠥⠤⠶⠶⠿⣿⣄⣀⣀⣿⣿⡛⠋⠀⠀⠀⠈⠁⠈⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢀⠀⠀⠀⠀⠀⠀⣠⠎⢰⡇⢸⡶⠢⢶⢦⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣼⣀⣀⣀⡀⠤⠘⠁⢠⠟⠀⡆⣿⠀⢀⠀⠁⠐⠞⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣤⣤⠤⣤⡤⠀⠰⠄⢄⠈⠀⠀⡇⢸⠃⣆⢀⡐⠀⠀⠐⠦⠀⠱⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠟⠋⠁⠀⠐⠀⠀⡸⣤⠀⠀⡇⢸⠀⢸⡏⠉⠂⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⣴⡿⠛⠁⠀⣀⠞⠁⠀⣴⣶⣧⣾⠄⣰⢀⣿⠀⠘⠀⢦⡀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢠⠀⣼⡴⠋⠀⠀⢀⡴⠉⠀⠀⢀⣿⣿⠏⠀⠀⠀⠸⣿⡄⠀⠀⠀⠳⡄⠀⠘⣄
⠀⠀⠀⠀⠀⡀⠀⠀⣀⣶⡋⢀⡞⠁⠀⠀⣠⠋⠀⠀⠀⢀⣿⠟⠁⠀⠀⢀⡀⠀⢻⣷⠀⠀⠠⢀⠡⣄⠀⠰
⠀⠀⠀⠀⠙⠳⠶⢿⡷⠿⢷⡞⠀⠀⠀⡀⠁⠀⠀⠀⢠⡾⠁⡈⣀⠁⠀⢐⣋⡅⠸⣿⣧⡀⠀⢸⢸⢟⠢⢬⡆
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⡾⠃⠀⠀⠀⣤⡟⠀⠄⢠⠧⠀⡀⣹⠤⠶⠈⣿⣿⣿⣾⣤⣦⣸⣿⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⢲⡟⠀⠐⠀⠜⠂⠰⢶⣟⠒⠂⠀⡏⣿⡟⢿⡿⢯⣍⡛⠛⠛⠋⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢤⠁⠀⠂⠐⣠⣿⠁⠀⠐⠰⡋⠀⠀⢺⣉⣉⡇⠀⢣⣿⣄⠜⢣⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⡄⠈⠒⣀⣶⣿⡿⠀⡈⠀⢪⡀⠈⢐⠦⢠⡼⠀⠀⠈⡟⢿⣆⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣡⣾⣿⣿⣿⡇⠀⡀⣈⠅⠀⣀⡹⠂⢠⠄⠀⠀⢸⠁⠀⠙⠻⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠿⠛⠃⠀⠆⠘⠂⠀⢠⡃⠐⡎⠀⢠⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠘⠀⡉⣋⡀⠀⠏⢌⠉⠀⢀⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠗⢀⣽⠷⠂⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢒⡀⡠⠄⠨⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠀⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⣥⣶⣿⡻⢕⣃⠰⠄⠙⠂⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢍⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⣿⣿⣿⣷⣾⣷⣾⣙⣄⢀⣐⢂⡤⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⢼⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠷⣌⡻⢿⣿⣿⣭⣭⣭⣿⣧⣴⣶⣍⡉⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⠜⣣⣞⣿⢀⣍⣡⣍⣀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠉⠓⠪⢝⡛⠿⠿⠿⣯⣿⣽⣿⣿⣿⣷⣦⣵⠶⠤⠶⢚⣛⣋⣭⠶⠛⡫⣰⣿⡿⠋⠈⠉⠙⢲⣟⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⠀⠐⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢉⡋⢩⣭⡵⢶⣻⣽⠾⣻⣿⡇⠀⠀⠀⠀⣸⢿⡇
⠀⠀⠀⠀⠀⠀⠀⡠⣤⣒⢚⣿⡀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠒⠦⣍⣒⣭⣲⣽⣿⣻⣿⣿⢛⣲⠖⢁⡞
⠀⠀⠀⠀⡠⠂⢴⣪⢏⣩⣿⣼⣧⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠼⠿⣛⣻⣿⣿⣿⣿⣿⡿⠟⢋⣥⣾⣿⣯⡔⠄
⠀⠀⠀⠈⢔⠖⢚⢱⡟⢀⢿⠻⣿⣧⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢁⣚⠿⣿⣳⣿⣿⣿⣛⣩⣴⣾⣿⣥⠪⠁⠣⢸⡄
⠀⠀⠀⡀⡘⠸⢣⠓⠁⠁⠁⠉⠀⠛⢷⡈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣾⣿⣿⣿⣿⣳⠟⠋⢝⠷⠛⠛⠏⡡⠁⠀⡐⠰
⠀⠀⠀⠠⡘⠂⠀⢰⡄⠀⠀⠀⠀⠀⠀⠉⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢉⡙⢯⣜⢺⣹⣿⡻⠃⠔⠀⠀⠀⠀⠀⠀⠀⠀⠊⡠⠃
⠀⠀⠀⠀⠈⠢⢑⠰⢭⡢⡀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⢀⡀⢂⣀⣂⣠⣥⡶⠴⣾⡿⠊⠐⠀⠄⠂⠀⠀⢀⡠⠐⣉⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠁⠢⢌⡀⠠⠀⠀⠀⠀⠀⠀⠑⠄⣀⡈⠉⠁⠀⠉⠁⠉⠈⠉⢁⣀⡤⠖⠋⠈⠀⠀⠀⠀⠀⠀⢂⣡⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢦⠤⢀⡀⠒⠀⠀⠄⠉⠉⠉⢉⣉⡀⠉⠉⠉⠉⡁⠀⠠⠄⠐⢂⡈⠤⡐⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠄⠀⢀⣀⡀⢒⠒⠒⠀⢀⣀⣀⠀⠠⠄⠐





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠂⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠄⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⢄⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠦⣍⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⣸⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⠔⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⢀⢤⣶⠿⠛⠉⠀⠀⢀⢠⠃
⠀⠀⠀⠈⢇⠀⣈⣉⠐⠠⣀⢮⠢⡐⠄⠀⠀⠀⠀⠀⠙⠓⠲⢦⡴⢒⡵⠟⠁⠀⠀⠀⠀⢄⡴⠃
⠀⠀⠀⠀⠀⠑⠄⡀⠁⠲⣈⣧⠦⠬⠱⡾⣽⡴⡦⡄⣀⣰⣯⣥⣔⣉⡀⡀⠠⢀⡂⠬⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣉⣗⣾⡿⣿⠬⡯⢑⢔⡉⣀⠛⣧⣶⡖⡖⠒⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠤⠠⡿⠿⠹⣞⣛⢯⡉⣯⣽⣿⣘⢣⢻⣯⢏⣿⣾⣤⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠜⠀⢘⢐⣝⡭⠨⣽⢛⠖⢚⣿⣓⠾⠏⠉⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠤⠂⠈⠑⠋⠉⠒⠃⠘⠯⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⣩⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⢉⣥⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢇⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀⠟⠤⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠉⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢟⡛⠯⠁⠀⣀⠤⠤⢤⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⡆⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢀⣴⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⣴⠾⠛⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠼⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣁⣀⠤⠒⠉
⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠘⢮⡚⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠩⢄⡈⠑⠢⣄
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡤⠤⣀⣀⣀⣀⣀⣀⣀⣀⡤⡔⠊⠀⠀⠀⠀⠀⠈⠀⠀⠈⢣
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠠⠤⠤⠤⠤⠐⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠙⠢⢄⣀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠁⣀⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠦⠤⠤⢅⣈⣀⣀⣀⣀⣀⣀⣀⣁⣀⠠⠤⠤⠔⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠲⡤⠒⠊⠉⠉⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⠒⠀⠰⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⡼⠀⠀⠀⣀⠤⠄⠐⠓⠒⠤⣀
⠀⠀⠀⠀⠈⠄⠀⠀⠷⠆⠀⠀⠁⠀⠁⠐⡀⡠⠀⠀⠀⠀⠀⠀⠀⠀⡏⣷⠀⠀⠀⠀⠀⠀⢀⠄⠊⠉⠁⠀⠀⠀⣠⢤⢠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠈⠣
⠀⠀⠀⠀⠀⠀⣶⠀⠐⠄⠀⠖⠀⣶⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢠⡞⠡⡞⠤⠀⠀⠐⠒⠂⠒⠤⣀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠁⣰⠎⠀⠐⠀⠀⠁⣤⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⣸⡇⠀⠀⠀⠘⠁⠀⡠⠔⠂⠉⢁⠽⢀⡀⠷⠶⢄⡀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⢰⣶⠄⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⢹⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡆⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡞⠋⠒⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⡎⢰⣾⡇⠀⠀⠀⠏⠀⠀⠀⠀⡜⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡾⠀⢸⡿⠀⠀⠀⠈⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠸⡲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠎⣀⠜⣁⢘⡼⠁⠀⠀⠀⠰⡀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠘⢦⡉⠒⠦⢄⡀⠀⠀⠀⠀⢀⡀⠤⠴⠊⠉⣀⠐⠁⢀⡠⠈⠀⠀⠀⠀⠀⠀⠙⠤⣤⣏⠀⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠈⠙⢶⠤⢤⠈⣉⣁⣀⣀⡄⠤⠄⠐⣈⡠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⡇⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠢⠠⠄⠤⠤⠄⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⢀⣀⣀⣀⠼⠦⣤⣤⠤⠞⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣿⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣶⣾⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣟⠀⠃⠋⠈⠶⢌⡛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠸⡓⡛⣦⠀⠀⠀⠀⠐⡑⣠⠙⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠀⠈⠳⢥⣬⣳⠦⣄⠀⠈⠀⠁⠪⠢⣠⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡔⠀⠀⠀⠀⠀⠈⠳⣌⣧⡀⠀⠀⠁⠀⠐⠻⡂⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠠⠀⠀⠙⣿⠻⣦⠀⠀⠀⠀⠀⢔⠜⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠿⠿⠶⠶⢶⣤⣤⣀⣀⣀⡀⠀⠀⠙⢷⣌⢄⡀⢀⠀⠀⠈⢻⡄⢝⠲⢦⡀⢁⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⡉⡴⡀⢇⠁⠀⠃⠀⠀⠄⠍⠉⡉⠉⡙⢳⡄⠀⠈⠻⢷⣮⡅⠀⠀⠀⠀⠙⢷⡭⣇⣷⠀⠀⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⡉⠆⠈⠈⠐⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠃⠀⠁⢀⠙⢷⡄⠀⠀⠉⠻⢿⣶⣴⣤⡀⠀⠻⣌⣹⣧⣴⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠐⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢸⡿⠀⠀⠀⠀⢀⣨⡽⠿⠛⠛⠓⠛⠛⢛⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠀⠀⠈⠀⠀⣀⣤⡴⠶⠶⠶⠶⢦⣤⣴⣶⣿⢟⣹⢞⡅⣸⠇⠀⢀⣠⠖⠋⠁⠀⠐⠌⠄⠀⠈⠀⣩⡾⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢀⣠⡶⠛⠡⣠⣢⣠⣾⣾⣿⡿⠿⠛⠋⠉⢉⠁⠎⢠⡟⣠⡴⠋⠡⡐⠄⠀⠀⠈⠀⠀⠀⣴⠟⣥⡾⠋⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠛⢋⣡⠴⠞⠛⠛⠛⢛⡉⠅⠀⠀⠀⠈⠀⠀⠀⠀⣠⡟⣴⠏⢀⠅⠀⠀⠀⠀⠀⠀⠀⣠⡾⠡⢰⠏⠀⠀⠠⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡥⢦⢂⠂⠂⠀⠐⡀⠀⠀⡈⠀⠀⠀⠀⠀⠀⣰⠟⣾⡯⡢⠀⠀⠀⠄⠀⠁⠈⢀⣴⠿⣉⡴⠟⠀⠀⡠⡘⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣤⠾⠋⢸⡿⢮⡢⠀⠀⠀⢀⣤⡶⠟⢛⢉⡴⠋⠁⠀⠀⠂⡑⣜⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣦⣤⣄⣀⣤⣤⣤⠶⠟⠋⠁⠀⠀⣾⡇⠄⠀⡀⠀⢰⠏⡡⠒⣡⡴⠜⠃⠀⢀⠂⠀⡠⡑⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⣀⣴⠞⢋⠀⣡⠞⠁⠀⠀⢀⠀⢠⢢⡱⢹⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣏⠥⢞⣡⠞⠁⠀⠀⠀⠢⡠⡳⢑⣡⡶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣁⢆⢢⡢⡠⠑⣀⣼⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⠿⠿⠛⠋⠁

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




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⣀⢀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀⡀⠀⡀⠈⠀⠀⠀⠀⠀⠀⡠⠐⠈⠁⠠⡀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠐⡁⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠀⠀⠀⠀⠐⠈⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠈⠀⠀⠈⠀⢀⡂⣐⣀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢠⠀⠀⡀
⠀⠀⠀⠀⠐⠀⠀⠑⠂⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⢢⠊⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠈⠀⠤⠀⠀⠀⠀⠀⠀⢀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠄⢆⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢂⠒⠈⠉⠢⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⣀⠀⠀⠀⠈⠄⠀⠠
⠀⠀⠀⠀⠂⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⢀⠐⠉⠢⢄⣀⣀⠠⠄⢀⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠒⠀⠀⠀⠁⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿