Teepee Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⡇⢰⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣇⠇⣾⣣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢻⢟⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⠀⠸⡜⡆⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⢡⠁⠀⣧⠹⡀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⠇⡏⠀⡇⢸⡀⢣⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⠎⢸⠀⢠⠁⠈⡇⠀⢧⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⠞⣧⠇⠀⢸⠀⠀⢻⠀⠈⣆⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⠎⠀⣸⡀⠀⢸⠀⠀⠸⡄⠀⠘⡄⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢠⠇⢣⠀⢸⠀⠀⠀⣧⠀⠀⠸⡄⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⡜⠀⠀⡼⠀⠈⢧⢸⠀⠀⠀⢸⡀⠀⠀⢳⡀⠀⢀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡜⠀⠀⢠⠃⠀⠀⠈⢧⠀⠀⠀⠘⡇⠀⠀⠀⢳⠐⢢⡵⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣰⡷⣄⠀⠎⠀⠀⠀⠀⠈⢷⡀⠀⠀⢻⠀⠀⠀⠀⢧⠹⡝⠋⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⡰⠁⡇⠈⠓⢤⣀⡀⠀⠀⠀⠀⠱⡄⠀⢸⡄⠀⠀⠀⠈⠆⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣰⡃⡴⣷⠀⠀⠀⠀⠉⠓⠒⠦⠴⠶⠿⡆⠀⣧⠀⠀⡀⣀⢈⡀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠀⠀⢠⡟⢰⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢹⢀⠚⡬⠒⠠⡐⣆⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢛⡟⢣⠋⡄⣟⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠘⣧⢸⠀⠶⠀⢰⢸⠁⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⢕⣄⠀⢀⠇⠀⢣⣹⠀⠀⡇⠀⠀⡆⡄⠀⠀⠀⢀⣿⣿⣆⠀⠀⢻⣆⠓⠤⠔⡁⠈⢣⠀⢤⣤⢲⡌⢣
⢠⣤⣤⣠⣀⣀⣤⣤⣠⢿⡲⢀⠑⢡⡎⣤⣀⠀⠙⢳⠀⢷⠀⠀⠇⢣⠀⠀⢠⣾⣿⣿⣿⡆⠀⠸⡄⠈⠀⠉⠀⠀⠀⢇⠈⠉⠁⠀⠀⣷⣀⣄⣠⣄⣀⣤⣤
⠀⠘⠺⠻⢟⡋⣿⡿⣇⣀⠸⠯⣐⡖⢀⠀⠀⠊⠁⠒⠠⢼⠀⠀⠸⠘⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⢇⠀⠀⠀⠄⠀⡀⢀⠆⠀⠀⢈⣀⠄⢻⣟⣹⣻⠿⣛⠛
⠀⠀⠂⠀⠀⠄⢸⡁⠈⠪⠱⢄⠈⠻⠞⠜⣃⢠⣰⣄⡀⣸⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠹⠂⠀⡀⢀⡀⣤⠄⢤⡶⠰⡍⠃⢂⠡⢼⡄⠆⣤⠉⡶
⠀⠀⠀⠠⠀⠐⢀⠈⠢⡀⠀⡾⠯⠖⣢⠄⣉⠁⠟⠰⠘⠜⡇⡇⠀⡰⣿⣿⢿⣿⣿⢿⣿⣿⣿⣿⡀⣷⠈⠡⠀⠎⠐⠂⠉⢘⡠⢔⠮⠒⠉⠀⣘⡆⠀⠀⠁
⠀⠀⠀⠀⠀⠈⡀⡰⢀⡈⠸⠤⣄⡀⠀⠉⠓⢿⠗⠒⢒⣒⣧⢁⠞⣈⡽⢻⣿⣿⣿⠋⠹⡻⠿⣿⠣⢹⡄⠤⠖⠒⠉⠁⠀⠀⠻⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠂⠀⠁⠁⠀⠀⠐⠀⠀⠦⠉⠑⠢⣇⣠⣤⣤⣤⡽⠋⠀⠀⠁⠚⠉⠉⠉⠂⠀⠀⠀⡄⠀⠸⣄⣀⡤⠤⠤⠒⠒⠒⠒⠓⠁⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⣬⣄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⡄⠀⠀⠀⠀⠌⠉⠉⠄⠀⠀⠀⠀⠰⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠤⣤⡀⠀⠀⡘⠛⠛⠛⠛⠀⠀⠀⠰⡤⠤⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⣿⠁⠁⠀⣀⠀⠀⣴⣄⠀⡀⡀⠀⠉⢀⣯⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠒⣸⣿⣔⠂⢳⣠⣠⣰⣿⣿⣠⣠⣰⡃⠒⣼⣿⣔⠂⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⡇⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠘⠉⠚⠙⠀⠀⠘⡗⠙⠀⠋⠁⠉⠀⠀⠐⠘⠀⠂⠡⠋⠁
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⢀⡀⢀⡀⢀⡀⢀⠁⢀⠀⢀⠀⢀⠀⢀⠀⢀⠀⢀⠀⢀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠛⠉⠉⠉⢹⠁⠉⠉⠉⠹⠋⠉⠉⠁⣛⠉⠉⠉⠙⡋⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⢀⣶⡄⠀⠀⠀⠌⢄⠀⠀⠀⢻⡀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⣿⣇⠀⠀⣘⠀⠘⡀⠀⢠⠍⠘⡄⠀⡐⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⣧⠀⠀⡌⠀⠀⡅⠀⢰⠆⡔⡇⠀⢁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣹⣿⡟⠀⠀⡏⠀⢀⡃⠀⢨⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠷⢀⠀⠇⠀⡇⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠏⠀⠀⠸⣿⡾⠀⠀⠛⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠐⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⢾⡆⠄⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡞⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢀⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧⣾⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⠋⠈⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠋⠀⠀⠈⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠠⠀⠀⠀⠀⢸⡿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢠⠃⠀⠀⠀⠀⠈⣷⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠌⠀⠀⠀⠐⠄⠀⢸⣏⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡈⢦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⠐⢢⣤⠀⣠⡟⠀⠀⠀⠀⣀⣼⣧⢄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣻⣿⣿⡌⢻⣷⣄⡀
⠀⠀⠀⣀⣄⠀⠀⠀⠀⠰⣾⡟⠀⠀⠀⣠⣞⣷⣿⣿⡞⣦⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣧⣿⣿⣿⣦⠻⣿⣱⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠞⠀⠀⣠⢞⡟⣼⣿⣿⣿⢿⠘⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⢹⣿⣿⣿⣿⣷⡌⠀⠉⠉⠉⠉⠁
⠀⠰⠶⠤⠄⠶⠀⠀⢰⢃⡀⠀⣺⣥⡞⣸⣿⣿⣿⣿⢸⣠⣾⠄⠀⡀⠀⠀⣀⣻⣿⣿⣼⣿⣿⣻⣻⣿⣿⣄⠠⠶⠤⠐⠒
⠀⠀⠘⠁⢀⠀⠤⣴⣷⣭⣿⣿⡿⠏⣱⣿⣿⣿⣿⣿⣸⡿⣿⣾⢖⣩⣶⣧⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⡀⢁
⠀⠀⠀⢰⣥⣣⣿⣀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠟⠛⠿⠿⠿⠿⠿⣿⣿⠿⠁⡎⡿⡿⠿⣿⠿⠿⠿⠿⠿⠟⠋⠉⠙⠿⠿⠶
⠀⠀⠀⠨⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣷⡦⠀⠁⠒⠛⠛⠀⠀⣒⣺⣿⣿⣷
⠀⠀⠀⠒⠛⠛⠛⠛⠒⠚⠛⡿⠟⣁⣼⣿⡆⠀⠀⠀⠀⠀⠀⠠⠀⠀⣤⣿⣿⣿⡿⠀⠀⠠⠿⠆⠀⠈⠉⠙⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁
⣿⣿⢛⢿⠛⠟⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣀⢠⡄⠆⠆⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣷⡈⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⡿⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢸⣧⡖⠀⠀⠀⣆⠉⢰⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢲⣄⣸⣿⣿⣀⠀⠘⠁⠀⣾⠻⣿⣷⡀⠀⢸⣷⠇⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⣤⣈⣉⣙⣿⣿⣧⠀⠀⠀⠚⠁⠀⢿⣿⣷⣶⣜⣧⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠲⣤⣴⣿⣬⢿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣷⠄⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣷⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣧⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢀⣩⣿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⡄⢹⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⣐⡠⠀⠀⠀⠀⠀⠀⠒⣾⣿⣿⣿⣿⣿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢦⣽⣿⣻⠃⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠁⠀⠹⡟⢿⣿⣏⢻⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡁⠀⠀⢀⠔⠀⣼⣿⣿⠏⠦⣀⢰⡄⠸⡄⠠⢿⣜⣿⣿⣷⣿⣿⠧
⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⡆⠀⣷⢇⠀⢰⣿⣿⣿⡈⠢⡈⢻⢷⣄⣽⣀⣸⣿⣾⣿⣿⣿⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠿⠟⠃⠈⢉⡝⠛⢻⣿⣶⠿⠿⠻⢿⣿⠶⠿⣿⣿⡿⠿⠿⠿⠟⣿⡛⠛⠛⠟⠉⠰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣁⠛⠁⠀⠠⠀⠀⠀⠑⠶⠾⠯⠄⠹⠷⠒⠒⠚⠛⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⣿⠛⢛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣴⣶⣿⣿⣿⠿⠾⣯⣠⣄⣀⣸⡏⠰⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠛⠉⠉⠀⠀⣰⣿⠿⠛⠁⠉⢹⣿⣷⣦⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⣿⡃⢈⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⣦⣤⣴⣄⣤⣀⣀⠀⠀⠀⣿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠻⠟⠓⠦⢀⣿⡄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠀⣿⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣳⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢿⠀⢰⡇⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣜⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⡇⣼⠀⣰⠟⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣿⡤⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⣷⣏⣼⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣹⣶⡶⠤⣤⣿⣖⣨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⣿⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣠⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢰⡿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢄⠀⠀⢸⡇⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⣿⣇⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⡄⠀⠀⠀⠀⠀⠀⢠⠄⠀⢠⣿⠏⠸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠶⠖⠒⠒⠐⠒⠒⠂⠐⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠙⠓⠲⢶⡄⠀⠀⠒⢾⡟⠂⣰⡿⠿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⡀⣸⠛⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡍⠀⠰
⣤⣤⣄⣀⣀⣀⣀⣀⣀⣿⣀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠘
⣿⣿⠉⣿⣿⣿⣿⣿⡟⢹⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⣿⡿⠀⣿⣿⣿⣿⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⣠⣴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣼
⣿⡇⠀⠿⣿⣿⣿⡏⠁⢰⣿⠀⠀⠀⠀⢠⣾⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⣠⣿⡄
⡟⠁⠀⠀⢾⣿⠁⠀⠀⡇⢸⡆⠀⠀⢠⣿⣿⡿⢣⣿⣿
⠃⠀⠀⠀⠀⠁⠀⠀⢠⠁⠈⠃⠀⢠⣿⣿⣿⡏⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⣼⣿⣿⣿⢱⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⣿⣿⡏⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣀⠀⠀⠻⣿⣿⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄⠉⠛⠦⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠚⣉⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣄⡉⠛⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⢋⣡⣤⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⣀⠉⠋⠙⠂⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢉⣠⠤⠚⠋⠁
⠀⣀⠀⠀⢛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠒⠒⠒⠒⠒⠒⠒⠚⠛⠋⠉⠁
⠤⢿⠷⠾⠁⣴⠇
⣀⣸⣤⡾⠛⠁
⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⢀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⣿⣿⣞⡄⠀⢠⠀⢀⡏⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⡇⠀⢸⠀⡞⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣷⠀⢸⡼⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⣿⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣦⠀⠀⠈⠉⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣿⠁⢽⣏⠙⠄⠀⠀⠀⠀⠀⠀⠀⠸⡗⠀⢠⠄
⠀⠀⠀⠰⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⣯⢁⠀⠈⡅⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠘⢠
⠀⠀⠀⠀⠈⣉⠀⠃⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠋⠗⠉⠀⠀⢠⠀⠙⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⣈⠐⣵⠀⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠠⡿⣿⣿⠋⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢻⡏⠀⠸⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⢸⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠰⣷⣏⠀⠀⠀⠀⠀⠀⢠⣾⣶⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠃⠀⠀⠀⢀⣿⣿⣿⠿⠏⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⢀⣀⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⣿⣿⡿⡀⠀⠀⠀⠀⠐⠄⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣿⠟⠁⠀⠀⠀⢀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣆⠀⠰⢄⣩⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣿⣿⣿⣿⡀⠆⠀⠀⠀⠀⠻⠇⠀⠀⢸⣿⣦⣿⣿⣿⣿⣿⡖⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡽⣿⣿⣿⡇⠄⠀⠀⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⠠⡄⠈⢿⡞⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⣿⠟⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⡄⠈⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡋⢰⣿⣤⣶⡆⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡑⠪⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⢸⣿⣿⢀⡞⠂⣶⠂⠀⢀⡄⠳⠆⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢙⣤⣧⣸⣿⣿⣷⡂
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇⣸⣷⡾⠃⠀⠀⢸⣿⡀⠄⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⠃⠀⠀⢀⣼⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣧⣴⠂
⠀⠀⠀⠀⠺⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⢤⣄⣈⣽⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣭⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡿⣿⡇
⠀⠀⠀⠰⠃⠀⠀⠈⠿⣿⠏⠈⠀⠛⠉⢻⡿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⡿⠙⠏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢸⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠃⠀⠀⠙⣿⣿⣿⠛⠛⠀⠀⠀⠀⣻⠋⠙⢿⣿⣿⣿⣿⣿⣿⠿⠀⠈⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠿⠃⠈⠛⠋⠉⢹⠋⠉⠉⠀⠀⠀⠀⢿⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣘⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⣤⢜⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣹⡏⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⢦⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⢰⣶⣮⣿⣟⡀⠀⠀⠀⠀⡀⠈⠻⣿⣿⣷⣶⣞⡗⣂
⠀⠀⠀⠀⠀⣀⣠⣄⣤⡄⠀⠀⠀⢹⣿⣿⣿⣿⡿⠟⢯⠽⡩⢫⠭⠋⠀⠀⠙⢿⣿⠛⣿⣯⣈⣆
⠀⠀⠀⠠⣿⣿⣿⣿⣿⠃⠐⠀⠂⠀⢿⣿⣿⣿⣁⠀⠀⠀⠈⠀⠀⢠⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⢀⣾⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⠂⢺⣿⣿⣿⡿⣿⣿⣿⣿⡀
⠀⠀⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢿⠏⠛⠛⠉⠡⠄⣉⡁
⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢶⣶⠦⡒⠰⠦⣤⣌
⠀⢀⣾⣯⣯⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠉⠀⠒⠒⠂⠀⠘⠂
⠀⠀⢀⣈⠁⠀⠀⠀⠀⠀⠀⢺⡶⠖⢠⣶⡀⠤⠄⡤⢾⠓
⠀⠀⠀⠈⠃⠀⠐⠀⠀⠀⠀⠀⡇⠀⠉⣿⠁⠀⠀⡇⢰⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡇⠀⠘⢻⠂⠀⢠⡇⠸⠀⠀⠀⢸⡇⡄⠀⠀⠀⢀⠀⠀⠎⠃⠀⠈
⠀⠀⠀⠀⠀⢀⠀⣀⠀⠈⠀⠀⢳⠀⠐⠿⠃⠐⢸⡇⢸⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⠄⡿⠠⢄⢀⣁⣉⣈⣡⣸⣤⣤⣠⡿⠆⢠⡤⣤⠴⠶⠖⠮⠉⠙⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠛⠛⠬⣋⠈⢠⠍⠈⣶⡒⠋⠀⠀⣌⣃⣀⣈⣉⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠗⠒⠠⢄⣀⠀⠀⠀⠀⠁⠉⠃

⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⢀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢻⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⣖⠒⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠷⠀⠤⠆
⠀⠀⠀⠀⡀⠂⠀⠀⠐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠇⢠⠀⢶⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣀⠳⠈⢰⢃⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠼⠶⠀⠀⠀⠀⠀⠶⠦
⠀⠀⠀⠀⠀⢠⠏⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠉⠐⠈⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠷⠳⠇⠀⠀⠀⠀⠀⠸⠗⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⢀⣀⠴⢊⠁⢸⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⡀⢀⠀⠀⠀⠀⠀⡀⠐⠄⠊⠀⠀⠀⠀⠀⠀⢸⠀⢉⠲⢤⣀
⠀⠀⠀⠈⣉⠤⠚⠁⡆⢸⠀⠀⠀⠀⡁⠰⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⡀⠰⠀⣡⠀⠀⠀⢸⠀⡆⠙⠢⢌⡉
⠀⠀⢘⣉⡤⠖⢡⠂⡇⢸⠀⠀⡀⠀⠈⠀⠠⠀⣈⠐⠃⠀⠀⠀⠀⠀⠀⠓⢈⡀⠠⠀⠀⠀⠀⠀⠀⢸⠀⡇⢢⠑⠦⣌⣉
⠀⠀⠀⠤⠖⢠⢸⡆⣧⠈⠀⠀⠀⠐⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠰⠀⠀⠀⠈⢠⡇⡼⢠⠐⠦⠄
⠀⠀⠀⠀⠀⠘⠀⠁⠀⠀⠀⠀⠁⠤⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠠⠄⠁⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠰⠀⠁


⠀⠀⠀⠀⠀⠒⠒⠲⠂⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠛⢿⠛⡟⣿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⡆⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠉⠀⢡⡀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⢫⠁⠀⣘⠶⣷⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠏⢀⡾⠾⠁⣠⣿⠿⣮⡓⣄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⣴⠻⢀⣠⠞⡽⠋⠀⡾⣿⢸⠟⣧⢻⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⢉⠻⠁⣼⡇⢸⠁⠀⠀⢹⡏⣠⡆⢸⣃⡁⣠⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢠⣌⠈⢳⡶⢼⣧⠀⠀⢰⡀⠘⠟⠉⢿⣏⠉⣧⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢠⠚⢠⢏⠄⢻⣇⠄⠹⠄⢀⣾⠛⣶⡄⠀⢀⡟⠼⢻⡇⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⣴⣧⡟⢷⣼⣮⠙⡆⣠⡟⠁⠀⣿⠇⠀⣿⢵⡆⢸⡇⣿⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⢸⡏⣼⣷⡀⠈⠻⠀⣤⣿⡄⠀⢨⣿⠻⣤⡀⠈⣿⣾⣥⠈⢹⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢲⠧⣿⡈⠁⢰⡀⢸⠁⢈⠿⠀⠀⠹⡄⠙⡗⠠⠋⢰⡏⣼⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡈⢳⣌⠻⣄⢶⡇⡿⠆⠸⡄⠀⠀⠀⢁⡼⣇⠀⠀⡾⣿⠟⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢮⡻⣄⠈⠛⢦⡙⠄⠰⡛⠀⠀⠀⠈⠀⠁⠠⠞⢛⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⢻⣶⣥⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡻⠟⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⢢⡤⠔⠋⠈⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣤⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣊⣥⣤⡦⠞⠑⠂⠀⠀⠀⠰⠿⣶⣿⢷⠿⠿⣿⠋⠛⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⢀⡤⠒⠚⠉⠁⠀⢠⣤⣶⣿⠷⢶⣿⣶⣶⡴⠶⠚⠋⠛⠒⠶⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣦⣶⣿⣟⡋⢙⣻⡁⣾⢛⣿⣿⢻⣿⣿⣴⣶⣦⣶⡷⡯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠙⠛⠻⠟⠛⠉⠳⠷⠞⠛⠈⠛⠃⠀⠀⠈⠉⠙⠛⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡿⢿⡿⠿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣧⠀⢀⠔⠁⠀⠁⠀⠓⢄⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠘⣿⡿⣫⣾⣿⣾⣿⣬⣻⣿⣿⣿
⠀⠀⠀⠀⠀⣿⡿⠿⣿⡇⠹⣴⠀⣶⣄⣠⣦⠊⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⣀⣀⡀⢹⣟⠛⣿⠛⠻⠟⠛⣽⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⣾⣀⣿⣿⣿⣿⠻⡆⠀⠀⠀⣿⣿⣿⣿⣿⠐⣿⣿⣷⢸⣿⡇⠿⠀⠀⠀⠀⣤⢹⣿⣿
⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣠⡟⠀⠀⠀⣿⣿⣿⣿⣿⠠⣿⣿⡿⢸⣿⡇⠀⠀⠀⠀⠀⠟⢸⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠈⠉⠀⢸⣿⡇⠀⠀⠀⠀⢀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿



⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢀
⠀⠀⠀⢠⣾
⠀⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠊⠚⠒⠀⠀⠀⠀⠊⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡴⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠚⡦⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⣄⡀⠷⠀⠀⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠉⠀⢺⡆⣴⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⡄⢂⢠⣦⡀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠠⠂⢀⡿⠀⠀⠀⡘⠃⠈⠀⢻⡆⢀⡡⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠁⣇⢺⡀⠀⠀⠀⠀⠀⠀⠀⠿⠃⠈⠁⣀⠈⠀⠴⠁⠀⠀⠠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠄⠀⠠⠻⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠁⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠈⠀⢠⡟⠀⠀⠀⠀⠀⠀⣤⡴⣣⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠓⠄⠀⠀⢂⡴⠉⣴⠁⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡷⠇⢀⣠⠏⢡⡎⢶⣄⠀⠀⢙⢦⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣴⣿⣿⣣⣷⣿⠕⣠⣻⣿⣄⢹⣄⠀⡼⢤⣙⠶⣤⣰⡟⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣤⣿⠉⣿⣿⣿⣯⣾⣻⠥⣎⠉⠹⠥⢈⡽⠿⣦⡀⣀⣽⡷⠶⢄⣨⣯⣡⡀⠑
⠀⠀⠀⠀⠀⠀⠘⠛⢻⣋⣡⣌⣉⣙⠛⠿⠤⠿⠿⣠⠤⠾⠷⠦⠼⠿⠻⣉⡐⣢⡏⠥⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠉⠉⠓⠒⠀⠶⠶⠶⠖⠒⠒⠌⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡆⠀⠀⠀⠶⡄⠄⠈⠉⠙⠗⢲
⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⣿⣿⡷⠀⠀⣾⣿⣿⠀⠀⠨⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢤⣴⠀⠀⢀⣿⣷⣗⠀⠀⣹⣿⣿⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⡻⠀⣄⣽⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⠼⣿⣿⣟⠀⠈⣿⣿⣿⡂⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⠀⠀⢰⣿⣿⣯⠀⠀⣹⣿⣿⡅⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⣿⠏⠀⠀⢾⣿⣯⠁⠀⠀⡇
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠆⠀⢸⣿⣿⡏⠀⣀⣺⣿⣿⡂⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⢸⣿⡿⡇⠀⠀⢸⣿⣿⠀⠀⠀⢿⡄⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠠⠺⣷⠶⠺⠛⢹⡟⡿⠚⠋⠛⣿⣿⡃⠀⠀⢸⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣺⠚⠈⡷⠶⡶⡶⡯⡉⣵⠀⠀⠈⠁⠀⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠶⢭⣀⣀⣀⣀⠀⡀⠀⡀⠀⡀⢀⣀⣀⣀⢤⠵⠂⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠔⠀⢀⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠂⣸⠱⡄⠈⠈⢳⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⢦⢄⡀⠂⠄⠀⣤⣀⠀⣠⠗⠊⢺⠀⠀⠌⡢⡈⠀⠀⡰⡅⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢟⠀⠀⠀⣇⠉⢦⠀⠀⢸⠈⣶⠇⠐⠃⢸⠀⠊⣠⠥⢹⠀⠀⠁⢃⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡧⣒⠀⠀⣼⠀⠈⢇⠀⢸⠁⠆⠌⠀⠆⢸⠀⡰⠁⠀⢀⠁⣰⢀⠌⠀⢱
⠀⠀⠀⠀⠀⠀⠈⠀⠱⣌⢉⣳⣿⠂⢀⡈⠢⣜⠘⢄⠀⠀⠠⠈⢶⢃⠀⠀⣜⡴⡽⠀⢀⢦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠙⢧⡀⠤⢀⡈⠂⢈⠀⠀⠀⠀⠀⠡⠀⠀⠀⠐⠟⡞⢁⠔⠉⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⢱⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⡀⠀⠈⡤⢰⡔⠁⠔⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢵⣸⠄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠰⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣍⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢠⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠁
⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⢀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢉⣝⠁⠀⢀⡤⡤⢄
⠀⠀⠀⠀⠀⢻⣡⣀⣠⣠⡤⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠤⠶⠲⠶⠶⣿⣿
⠀⠀⠀⠀⢀⡏⠉⠉⠀⢀⠀⢀⠖⡎⠙⢦⡀⠠⣴⠅⠂⠺⡦⣷⡄⠀⠈⠉⠩⠉⠒⢦⡄⠀⠀⣸⢉⣸⡆⠀⠀⠀⡀
⠀⠀⠐⠒⠤⠆⢾⡆⠀⣉⣨⣿⡀⠁⠀⡂⡅⢀⡷⠀⠀⢵⠚⠉⢷⡐⠷⣤⣀⡂⠀⣾⡷⠛⠛⡿⢎⡼⠁⠁⠀⠁⠈
⠀⠀⠀⠀⢀⡘⠶⠓⠛⠉⠉⠉⢻⣀⣢⣴⡧⠛⢛⣉⠠⠛⣢⡒⠛⢦⣰⠀⠹⡁⠿⡿⠷⠤⣤⣶⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠹⠷⠶⠿⠁⠀⠀⠈⠙⠲⠆⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢁⠟⣦
⠀⠀⠀⠀⠀⡠⠤⠤⠤⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣠⣀⡄⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡀⠘⠀⢰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⡆⢨⣿⣶⣷⢊⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⣀⠟⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢃⣿⣿⠝⠹⡍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⠀⣸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⢰⣿⣿⣑⣀⣈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢴⡇⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⢠⠏
⠀⠀⠀⠀⠀⣤⠉⠛⠛⠛⠛⡋⣵⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣏⠀⠀⠀⢸⣄⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠒⡏
⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣀⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡛⠉⠑⠚⠋⠉⠩⢽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢐⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠈⠙⢂⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⢸⠁⠈⢿⣿⡿⠏⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⠋⢦⣤⡉⠓⠁⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠸⠀⠀⠈⠉⠁⠈⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⣬⠀⠀⠀⠀⠀⠀⣼⡀⠀⠀⠰⠶⠶⠤⠤⠤⢤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢠⣴⣶⠀⠀⠀⠀⠀⢠⣿⣶⣦⣶⣶⣶⣴⣶⣶⣶⣶⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣭⣿⠎⠉⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠐⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢠⡀⡀⢠⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡷⠠⠀⡠⠀⠀⠀⠀⠀⠉⠛⠛⠛⣛⡛⠋⠉
⠀⠀⠀⠀⠀⠀⢸⣧⡶⠂⢁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢨⣿⣿⣷⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡴⠆⡀
⠀⠀⠀⠀⠀⠀⢼⣏⣯⣭⢍⡉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠶⠀⠉⠀⠰⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀
⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠉⠓⠒⠒⠛⠛⠲⢦⡀
⠀⠀⠀⠀⢿⡂⠀⠀⠀⢠⣾⣷⣦⣤⣄⣀⣀⣀⡇⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⡟⢹⣶⡀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠹⡇⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⢰⡇⣀⣛⠚⡋⣀⣀⣀⣀⣀⣀⡀⣀⡀⡇⠀⠀⠀⠀⡇⣀⣀⠀⡀⢀⣀⣀⣀⣀⣀⡀⣀⡀⣷
⠀⠀⠀⢸⡇⣿⣿⢰⡇⣿⣿⣿⣿⣿⣿⡇⣿⡇⡇⠀⠀⠀⠀⡇⣿⣿⢠⡇⣾⣿⣿⣿⣿⣿⡇⣿⡇⣿
⠀⠀⠀⠀⡇⣿⣿⢸⣷⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⣇⢿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣷⣿⡇⡏
⠀⠀⠀⠀⢻⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠃⠀⠀⠀⠀⢻⢸⣿⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠇
⠀⠀⠀⠀⠸⡎⣿⡆⣿⣿⣿⣿⣿⣿⣿⣿⡇⡾⠀⠀⠀⠀⠀⠘⡆⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⡏⣾
⠀⠀⠀⠀⠀⢷⢸⣷⢹⣿⣿⣿⣿⣿⣿⣿⢰⠇⠀⠀⠀⠀⠀⠀⢳⢸⣿⢸⣿⣿⣿⣿⣿⣿⣿⢡⡇
⠀⠀⠀⠀⠀⢸⡌⣿⣿⣿⣿⣻⣿⣿⣿⡏⣾⠀⠀⠀⠀⠀⠀⠀⠸⡆⣿⣿⣿⣿⣻⣿⣿⣿⡟⣸
⠀⠀⠀⠀⠀⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡟
⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⢸⠇⠻⠿⣿⣿⣿⣿⡿⠿⠁⢷⠀⠀⠀⠀⠀⠀⠀⢰⠇⠙⠿⣿⣿⣿⣿⡿⠿⠃⢻
⠀⠀⠀⠀⠀⢿⣀⣀⡐⠒⠒⠒⠒⠒⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⢺⣄⣀⡐⠒⠒⠒⠒⠒⣀⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠁⠈⢻⠀⠀⠀⣤⡀⠀⠀⢸⠋⠀⠑⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢎⣦⡴⠋⠀⠀⣰⣿⣷⡄⠀⠈⠳⣤⣎⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠁⠀⠀⢀⣼⣿⣿⣿⣿⡄⠀⠀⠀⠁⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠁⢻⣿⣷⣿⡄⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠀⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠈⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠍⠙⠚⠻⢦⣄⠀⢀⣠⠾⠟⢊⠭⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣬⣅⡀⠀⠄⠐⠩⢝⠲⠥⣀⣤⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠉⡙⠓⣶⣤⣄⡀⠀⢀⠀⠈⣙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣷⣾⡿⠟⠛⠉⠙⠻⠶⣭⣵⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⢾⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⢀⠇⠀⠀⠀⠐⠶⡒⢯⡞⠁⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⡀⠀⠀⠀⠈⠢⠀⠐⡄⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡆⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⢀⠀⠀⠳⣄⡀⠀⠘⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡐⠀⠀⠀⠀⠀⡄⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠈⢲⡀⠈⠀⠀⠀⠀⠠⢌⠹⠃⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢌⠄⠀⢻⣄⠜⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢗⡀⠀⠀⠀⠀⠢⡕⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠳⡀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠤⠨⠥⠌⠘



⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣶⣵⣶⣤⣿⣵⣿⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠔⠁⠀⠀⠀⠘⡄⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠣⡀⠀⠀⠀⠀⠀⠘⢆⠀⠣⡀⠀⠰⠀⠇⠀⠂⠀⡁⢜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢀⠜⢠⡀⠠⠀⠘⠀⠈⢣⠀⠈⠢⣄⠀⠀⠀⠀⠀⠣⡈⠢⡀⠀⠃⢠⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⣆⠈⠢⠀⠀⠀⠀⠀⢹⠀⢡⠀⠀⠀⠈⠁⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣸⠻⣆⠀⠀⠀⠀⠀⢀⠎⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠑⠄⠀⠀⠠⣤⣀⠀⠀⠀⢀⣴⠏⡪⢚⣇⠀⠀⠀⠀⢈⠀⠃⠀⠀⠀⠀⠀⢸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠳⡄⢠⢛⠅⠋⠈⠡⢺⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⡰⢀⠎⠀⠊⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⢠⠀⠀⠀⠻⡳⣄⠀⠀⢸⡗⠹⣗⠅⡠⣾⠀⡪⠼⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢸⠀⡇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢇⠘⣄⠀⠀⠀⢻⠝⠆⠀⢰⡫⠂⠁⡜⠁⠺⠈⠕⡃⠀⠀⣸⡄⠀⠀⢀⣾⡇⠀⢠⠀⠳⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢎⢢⠀⠀⡖⠐⣺⡄⢸⢗⠁⡼⠀⠀⠸⡀⠪⠅⠀⢠⠖⡹⡄⠀⣸⣻⠁⢀⢎⡇⠀⠃
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈⡰⠁⢰⡫⢊⡀⢷⣼⡻⢀⠃⠀⡀⠀⢣⠘⣧⠀⡾⡊⣣⢾⠀⡿⣺⣴⢟⠅⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡛⠔⡬⠱⡄⢙⡞⢸⠀⠀⢀⠀⠀⢣⠘⣶⡋⢰⡀⠹⢠⡋⠞⢑⡡⢊⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢗⠁⡆⠀⠈⠳⣌⢸⠀⠀⠀⡠⠀⠈⣇⠹⠃⣼⡀⣽⡿⢋⡄⡩⣪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡵⠀⡃⠀⠀⠀⠈⢾⡄⠀⢀⠔⠁⠀⢩⢈⠞⡸⢸⡿⣠⢺⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢸⡵⣿⡄⣇⠀⠀⠂⠀⠈⠃⠀⠀⡫⠂⠀⢸⡏⠀⣆⢀⡔⠁⢸⠨⣧⢔⡽⠛⠀⠀⠀⠀⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢦⡼⠆⠀⠐⡡⠀⠀⠀⠠⢖⠄⠀⠈⠁⡆⠈⠁⠠⠂⢸⠐⢱⠎⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⢀⣀⣀⣀⣉⣲⣌⠦⠀⠈⠔⡡⠀⠀⠀⠁⡁⠀⠀⡬⠂⠀⠀⠚⠀⡼⢸⡇⣀⣀⡀⠀⠀⢀⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣔⣍⢈⡶⢳⡲⡶⠈⢣⠀⢀⢀⡠⢄⣶⠤⡀⠀⢀⢀⠈⠀⠐⣲⢖⡺⣅⣞⣙⠀⠀⢳⠀⠠⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠘⠒⣀⢹⢟⠕⠜⡰⣁⠄⡏⡐⠕⠇⣉⣘⣆⡤⠣⢪⢀⢀⡧⡜⣈⣸⡣⠡⠣⢢⢸⡤⠀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⢋⡹⠷⣤⡷⢾⡿⠾⢛⠋⠝⢛⠳⢤⣲⠈⠡⢂⡿⠐⡛⠿⣚⠾⣕⣒⣹⡟⠿⠻⠟⠛⠿⠊⠕⠂⠝⠂⠭⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠉⠀⠒⠁⠠⠛⠉⠵⠊⠁⠀⠉⠔⠊⠽⠋⠡⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠳⠎⠁⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣵⣶⣶⣭⣵⣿⣷⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣫⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⡻⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⢤⡏⡇⠀⡟⠉⠙⢦⣄⡤⠋⢹⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣮⡛⢰⢸⣿⢰⣶⣦⣙⠿⢟⣵⡆⣡⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⡇⢠⠀⡄⠀⠀⢠⠘⠒⠲⢦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⢸⣿⢸⣿⣿⣿⣿⣿⣿⣧⣭⣭⣛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⣀⡇⠐⠀⡇⠀⠀⠐⢸⠋⠙⡆⢹⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⡸⡿⢸⣿⣿⣿⣿⣿⣿⡏⣶⣶⢹⡎⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠉⠀⠀⠀⡇⠀⠀⠐⢸⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⢸⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠠⠀⡇⠀⠀⢘⢸⣄⡤⠇⣸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠻⢟⣸⢇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⡂⠀⠀⠰⠀⡇⠀⠀⢘⢰⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣩⣭⣵⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠈⠀⠈⠀⠁⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠤⠤⠤⠤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣬⣛⣛⣛⣛⣛⣛⣛⣛⣛⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛








⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠃⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⣿⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⠸⡇⠀⠀⠹⣧⠀⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡿⠀⣿⠀⠀⠀⢹⣇⠀⣾⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⡇⠀⢹⡇⠀⠀⠀⢻⡄⢻⡀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⡀⠀⠀⠀⠀⣿⠀⠘⣷⠀⢸⡇⠀⠀⠀⠘⣧⠘⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⢻⣆⠀⠀⠀⢹⡀⠀⠙⠷⠾⠃⠀⠀⠀⠀⣿⠀⢸⡇⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⡇⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡿⠁⠀⢸⡇⠀⣠⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣿⠀⢸⣷⣄⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣼⠋⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⠀⠈⣿⠙⣷⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣿⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⡏⠀⢠⣿⠀⢸⡇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣸⡇⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀⠀⠀⢸⡇⠀⠀⠈⣷⣤⣾⠃⠀⠸⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠟⠁⠀⠀⣿⠀⠀⢀⣀⣤
⠀⠀⠀⠀⠀⠀⠿⣯⣅⡀⠈⠻⣦⠀⢸⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⢻⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢀⣴⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⢹⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣾⠋⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢸⡟⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⢸⡇⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⡀⠀⠀⠀⠀⠀⢺⣿⡇⠀⣸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣿⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢷⡀⢀⣷⡄⠀⢸⡇⠿⠾⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⣧⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠈⠻⠾⠋⣿⠀⣼⠃⠀⠀⠀⣿⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⡌⣿⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⣧⣼⠏⠀⠀⠀⠘⣷⣼⢸⡇⠀⠀⠀⠀⡀⠀⠀⢻⣿⡟⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⢸⣷⣦⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣸⡇⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣿⠹⣧⡀⠀⣀⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣀⣤⡾⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢻⡇⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃
⠀⣤⣤⣤⣤⣤⣀⣀⣘⣿⣄⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣣⣴⠂⠀⠀⠀⠀⠀⣠⣿⣃⣤⣤⣤⣤⣤⣤⣤
⣼⡯⠒⢿⣆⣀⣈⣉⠉⠉⠻⣷⣄⠀⠀⠀⠈⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢋⣽⠏⠀⠀⠀⢀⣤⡾⠛⠉⠉⠉⠀⠀⠀⣿⠀⠘
⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠙⠻⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠟⠁⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠰⡇
⢻⣆⠀⣾⠁⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣷⣦⣤⣽⣿⣷⣦⣤⣤⣀⣠⣠⣤⣤⣶⣾⣿⣿⣥⡶⣾⡿⠿⠿⠶⢦⣤⣤⣤⣀⣀⣀⣀⣀⣀⠐⣷⠢⣺
⠀⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁⠀⣀⣤⡶⠟⠋⠀⠀⠀⠈⢉⡽⢿⡿⠛⠉⠛⠙⣿⠉⠙⢧⡈⠀⡀⠀⠈⠛⠷⣤⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⣠⠔⠀⣠⡾⠋⠁⣼⡇⠀⠀⠀⠀⣿⠀⠀⠈⠻⣦⡈⠀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣾⣟⣁⠄⠀⠀⠀⠔⠉⠀⣠⡾⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⡀⠈⠙⢷⣤⡀
⠀⠀⠀⠀⠀⣾⢏⡥⠖⠠⠈⣦⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢸⡏⠀⠀⣠⠀⠀⢸⡇⠀⠀⠀⠀⠀⠘⢷⣄⢀⠀⠀⠈⢳⠞⣉⣉⡻⢷⣄
⠀⠀⠀⠀⢸⣿⠸⠀⠀⠀⠈⢘⡇⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⣿⠃⡀⡀⠃⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣰⡏⠓⠀⠀⠙⣎⣿⡄
⠀⠀⠀⠀⠈⢿⣄⠁⢰⠀⠀⣸⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⣟⣠⣧⣥⣤⣄⣀⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⡀⠀⠀⠀⠀⢉⣿⠃
⠀⠀⠀⠀⠀⠈⠛⠷⢾⡷⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣉⠢⠀⠚⠀⠙⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣾⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣬⣓⠀⠀⢈⣩⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿
⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣾⣿⣿⣿⣷⡀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠟⠻⠛⠛⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠈⠛⠿⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⢀⣤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠂
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⡿⠿⡿⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄⣀⣠⣾⣿⡄⠀⠀⣠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⣠⠀⠀⢀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣄⣀⣀⣀⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⠉⠀⠀⠘⡀
⠀⠀⠀⠀⣿⠟⠛⠛⠛⠛⠛⣿⡇⠀⢀⣾⣿⣿⣿⣿⣿⣧⠀⠀⢸⡟⠉⠉⠉⠉⠉⢻⡗⠀⢸⣿⠟⠛⠛⠛⠛⢿⣿⠀⠀⣸⣦⣤⣤⣴⣧
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⣯⠀⢸⡏⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠟⠉⠉⠉⠉⠙⢻⡇⠀⢸⠀⠀⠀⠀⠀⠀⢠⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢰⣿⡿⠿⠿⠿⣿⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠂⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⠀⠀⠀⠀⠀⠐⣿⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⣶⣤⣤⣤⣤⣴⣿⡇⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣆⠀⠀⠀⠀⠀⣸⡏⠀⢸⣿⣤⣀⣀⣀⣠⣼⣿⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣶⣤⣤⣤⣤⣴⣾⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣦⣤⣤⣠⣤⣴⡇
⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠹⢿⣿⣿⣿⣿⣿⡿⠃⠀⠸⢿⣿⣿⣿⣿⣿⣿⠏⠀⠘⢿⣿⣿⣿⣿⣿⣿⠏⠀⠘⢿⣿⣿⣿⣿⣿⠇

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣭⣭⣭⣭⣭⣭⣬⣍⣿⣩⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣶⣿⣿⣿⣧⣤⣬⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⣿⡇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⠘⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⢿⣇⠀⠀⢻⣿⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠘⢿⣷⣴⣿⡟⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢿⣧⠀⠀⠈⠉⠉⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⢀⣶⠀⢸⣿⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⣿⡇⢸⣧⣄⣠⡾⣻⠀⢸⣿⣿⡿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢸⣿⠀⠀⠀⢀⣿⠇⢸⡇⠈⠀⢠⡏⢠⣿⢿⣿⠃⡀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⢻⣧⣀⣠⣾⡟⢀⡾⠀⠀⢠⡟⢠⣿⡏⣼⡟⢸⣿⡄⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣀⠙⠛⠛⠉⣠⡾⠁⠀⠀⢸⡅⠈⠻⠿⠟⢀⡾⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⣟⠳⠶⠶⠞⠉⠀⠀⠀⠀⠘⣧⡀⠀⠀⣠⡾⠁⠀⣽⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠹⣆⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠉⠛⠋⠉⠀⠀⢀⡿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠉⢀⣠⣤⠶⠲⣾⠋⠉⣿⣆⠀⠀⠀⠀⠀⢀⣼⠃⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⢛⣉⣁⣤⡶⢻⢿⡀⢀⠇⣿⠻⡓⡶⢦⣤⣈⡁⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣟⣛⣉⣉⠉⠑⠄⣰⢟⡱⢣⢾⣇⣎⠎⢹⡷⣷⣮⣲⣤⣈⣉⠛⠲⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡿⢿⣏⡉⠉⠉⢱⢨⢂⣼⣾⣭⣕⡊⠁⣰⣿⡟⡠⠚⣇⠈⢙⣦⣍⣉⣛⣛⣛⠛⣿⠟⠛⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠻⡆⢀⣾⣷⣾⡿⠒⠉⠀⢹⣼⠃⢻⣷⠁⠀⢻⡀⡏⢀⡽⠿⣶⣤⣄⣸⡇⠀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠓⠲⠟⠛⢡⡾⠗⠂⠉⠉⢢⡾⠁⠀⢸⣿⣤⠤⣼⡿⣧⢸⠀⣀⣬⣷⣄⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠓⢦⣤⡞⠁⠀⠀⠘⣿⠁⠀⠈⣷⠈⢿⣤⡏⣀⡼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⠴⠞⠛⠀⠀⠀⠀⠀⠛⠛⠛⠋⠉⠀⠀⠙⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡇⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⠀⢸⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⠘⢼⠄⡸⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠁⠋⢸⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⢠⡼⠀⠀⠀⠀⢀⠀⡄⠂⠀⠀⠈⠀⠀⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠁⠀⠀⠀⢰⡋⠁⠀⢀⡦⠀⢸⣿⡟⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⠀⠀⣴⣒⡶⣛⣷⡀⣰⣟⠷⣄⢈⠽⣯⣑⡦⣀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠀⠀⣀⣀⡥⢛⡡⣠⠖⢛⣻⣿⣿⡀⠈⠻⡾⠉⠉⠙⣦⣙⠢⣄⡀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⢿⣧⣶⣿⣿⠃⠀⠸⠇⢠⣼⣷⣀⠀⣌⠻⣿⣿⣿⣿⣦⣶⣟⠓⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠠⠦⠀⠀⠀⠉⠹⠿⠿⠷⢤⡴⣿⣾⣿⣿⣿⣧⣹⣴⣿⡏⠉⠁⠀⠀⢁⡀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⢁⡤⠤⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠢⠀⠀⠀⠀⠄⡀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠊⠉⣀⠘⣢⠲⣐⠀⠀⠈⠀⠀⢀⡇⠈⠀⠉⡇⠳⠤⣀⠔⢺⠉⠡⠀⣀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠗⠒⠒⠲⡟⠀⠀⠀⠀⠀⢸⡇⢠⠀⠀⠇⠀⠀⠀⠀⢸⡄⡄⡞⠉⠉⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠯⣝⢉⣁⣹⠀⠠⠀⠠⠄⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⡇
⠀⠀⠀⠀⠀⣀⠀⠀⠙⡂⠀⠇⡄⣀⠀⠀⠀⠀⢠⠇⡇⠀⢀⣤⡀⠆⠙⠀⠀⠁⠀⢱⠤
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠰⡓⢬⣀⡀⠀⠰⣊⣰⠁⠀⠈⡈⢳⡄⠀⠀⠠⠄⣱⠈⡱⠢⠤⠤⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠌⠭⢭⣭⠏⠜⠀⠀⠀⡏⢶⢶⠶⠶⢚⡋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⣴⠆⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⠀⠀⢰⣿⣿⠀⣿⣿⣿⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣇⠀⠀⠀⢾⣿⣿⠀⣿⣿⣿⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡃⣿⠀⢸⣦⢸⣿⣿⡇⢻⣿⣿⠿⣿⡟⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡟⢀⣿⣿⠀⣿⢸⠃⢸⣿⡏⢠⡟⣴⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣠⣾⣿⠃⣸⢣⡏⠀⢸⣿⢠⠏⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣇⣰⠏⣼⠀⠀⣼⠏⣾⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⡿⠋⠉⠛⠄⠀⣿⣀⡼⠋⠀⠙⠦⠞⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⢸⣿⠃⠀⠀⠀⠀⢠⠟⠋⠀⠀⢳⡀⠀⠀⢀⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⣶⡶⠶⢾⠌⠳⠼⣇⠀⠀⣴⡀⠀⠋⠀⠀⠀⣸⡎⡇⠀⢀⡾⠋⠉⠁⣀⣀⣀⡀⠀⠀⠹⡆
⠀⠀⠀⢀⡟⠀⣿⠀⠀⠀⠀⠀⠙⢦⡀⢻⡙⣦⡀⠀⠀⢠⣿⠇⣠⣴⡟⠓⠒⠂⣠⡤⠤⠤⠄⠀⠈⠙⡇
⠀⠀⠀⢸⡇⡀⣿⠀⠁⢙⣶⣶⣶⣶⣿⣶⠿⠿⣧⠀⡴⠛⡿⠻⠉⠙⠻⠟⠻⠿⣿⣿⣿⣿⣶⣦⣤⡼⠁
⠀⠀⠀⠀⣷⣴⣿⠶⠚⠉⠁⠐⠲⠿⠛⠋⠀⠀⠈⣿⡿⣦⣀⣔⡢⢄⡀⠀⠀⠀⠀⢉⣻⠶⢤⡀
⠀⠀⠀⣼⠁⠀⢈⢳⡀⠠⠤⠖⠐⠀⠀⢤⣖⣂⡤⣿⣿⡂⡙⠻⢿⡳⢤⡀⠈⢱⣶⠏⠁⡀⢲⣽⡄
⠀⠀⠀⡇⣆⠄⠇⡇⣧⠀⠀⠀⣀⡶⢿⣿⡿⠿⠚⠁⠀⠉⢻⠰⣶⣌⡑⣀⠀⢸⣧⠃⢘⡇⠀⣼
⠀⠀⠀⢻⣳⡑⠀⠃⡟⠀⣒⣫⠵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠙⠳⢤⣼⡻⡶⠖⢄⡼⠃
⠀⠀⠀⠀⠻⢯⣤⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠚⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉
⠀⠀⠀⡇⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠐⣿⣛⣛⠛⠛⠛⠛⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⣿⡉⠁⠀⠀⠀⠀⠀⠀⠀⠉⢶⣄
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄
⠀⠀⠀⢸⡷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⡿⠖⠒⠀⠀⠀⠀⢶⣤⡀⠀⠀⠸⢻⡄
⠀⠀⠀⢸⠀⠈⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠁⠀⣿⣿⠀⠈⢹⠿⠷⢶⣴⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⢹⡀
⠀⠀⠀⠀⡀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⡄⠀⠀⢸⡇
⠀⠀⠀⠀⣷⠀⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠈⠛⠿⠁⠙⠟⠙⠥⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⡇⠀⠀⠘⡇
⠀⠀⠀⠀⣿⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠃⠀⠀⠀⡇
⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣧⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣭⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣄⣀⣄⣀⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡎⠀⠀⠀⠀⢸
⠀⠀⠀⠀⡛⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⣟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⠀⠀⠀⢸
⠀⠀⠀⠀⠁⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⣸
⠀⠀⠀⠀⣶⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠘⣫⠙⠻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⣈
⠀⠀⠀⠀⣿⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢢⠟⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠀⠀⢀⡏
⠀⠀⠀⠀⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣆⢐⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠇⡀⠀⠘⡇
⠀⠀⠀⠀⣿⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠁⡀⣾⠃
⠀⠀⠀⠀⠛⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⢻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣇⣸⣿⠰⣶⣶⣶⣏⣁⣠⠖⠀⠀⠀⠀⣀⡜⠋
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣿⣿⡀⣿⡿⠟⠋⠁⠀⠀⠀⢀⣤⠞⠉
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣾⣏⣿⡇⣿⠃⠀⠀⠀⢀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠰⡿⣿⣻⣇⣿⣤⣠⣤⠞⠋
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⢼⣦⣿⣿⣿⢀⠟⠁
⠀⠀⠀⠀⢸⣾⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢄⣀⣠⣿⣿⣿⣿⠈
⠀⠀⠀⢀⣌⠿⣿⣿⣧⣔⣀⣀⠠⣄⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⣤⣄⣱⣿⣿⣿⣿⢿⣿⣿
⠀⠀⠀⠀⠙⠻⠶⣭⣝⠛⠿⢿⣿⣿⣶⣾⣿⣿⣷⣦⢠⣦⣤⣴⣦⣤⣴⣿⣤⣦⣼⣿⠿⠟⢛⣩⣶⣿⣿⠁
⠀⠀⠀⠀⢶⣤⠀⠀⠈⠉⠛⣶⣦⣤⣭⣍⣉⣉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠉⣿⡧
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡾⠏⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠀⠀⠀⠀⠀⠉⢁⣀⣀⠠⠐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢸⡆⢰⡇⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣇⣸⢁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣀⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠳⠟⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⣀⡀⠀⠀⢀⣀⡀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠓⠚⠋⠉⠙⠓⠚⠋⠉⠙⠓⠚⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠴⠚⠓⠦⣤⠴⠚⠓⠦⣤⠴⠚⠓⠦⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡴⠲⣄⠀⠀⠀⣠⠖⠛⠛⠛⠓⠲⣄⠀⠀⠀⣠⠖⢦⡀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠻⣄⣠⠞⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠳⣄⣠⠏⠀⠘⣦
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠁⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠈⠁⠀⠀⠀⠈⢧
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⢠⡾⠤⡤⠤⠤⠤⠤⣤⠤⠤⠤⢴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠤⠤⠤⠤⣤⠤⠤⠤⠤⢤⠤⢷⡄
⠀⢠⠏⠀⣀⣇⣀⠀⠀⣄⣿⣠⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⣄⣿⣠⠀⠀⣀⣸⣀⡀⠹⡄
⣰⠏⠀⠀⣉⣟⣁⠀⠀⣌⣿⣡⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣌⣿⣡⠀⠀⣈⣻⣉⡀⠀⠹
⢯⡀⠀⠀⢉⣟⠁⠀⠀⠈⣿⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⣿⠁⠀⠀⠈⣻⡁⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⣀⠀⢀⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⠀⣷⠀⡇⠀⣾⡕⡕⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠋⠉⠉⠁⠀⠀⠀⠀⠉⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⣼⣶⡇⢘⣾⡾⠁⠀⠀⠀⠀⠀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⡸⣿⣇⣾⡿⠁⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⡄⢀⣆⣈⡉⡹⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡇⠀⠀⠀⠱⣿⣿⡟⠀⠀⠀⣐⡆⠠⠁⠀⠀⠀⠀⠀⠀⡠⠤⠒⠲⠂⠸⠐⠰⢆⠜⠀⠀⡠⢂⠌⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⠓⠶⢶⣶⣿⣿⣤⣤⠶⠞⢻⠀⠀⠀⠀⠠⠐⠂⡟⠀⠓⡸⢃⣂⡀⢀⠔⠡⠮⣲⡆⣐⣁⣿⣶⡆⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡦⠀⠉⣿⣿⣯⡁⡀⢀⡄⠀⠀⠀⠀⠉⠉⣬⢠⡄⢰⣁⡼⠽⠇⠸⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⠛⣿⣴⠐⣡⠀⠀⢃⠀⠀⣘⠠⠔⠛⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠆⠀⢨⡹⣿⡆⠇⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠰⠀⡇⠸⠁⢯⣿⠀⠀⠀⠀⠀⠈⠑⠂⠤⠤⠤⡤⠀⠀⠀⢠⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠃⠀⠂⢸⡏⡆⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢰⠀⢨⠐⠀⢿⢚⡀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠈⠓⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⠃⠀⠘⠀⢀⡀⠆⢀⣷⣳⠀⠀⠀⠀⠀⠀⠀⠀⠉⡓⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡌⠀⠀⡇⠀⠀⠀⠠⠨⠘⡎⢇⠀⠀⠀⠀⠀⣀⠔⠊⢀⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⠈⢄⢷⡈⣆⠀⠀⢠⠊⠁⠀⠀⠧⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠀⠀⠀⠨⠀⠀⠈⡀⢇⠜⣆⠀⠀⠁⠒⡂⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡀⠀⠰⠀⠀⠀⠀⠀⠀⢀⡀⡁⠘⠀⠢⢠⣊⠜⡆⠀⠀⡔⠁⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⣸⡇⠀⠀⠃⠈⡆⠵⢊⠸⡤⠊⢀⢐⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡸⠀⠀⠀⢀⠀⠀⠀⣟⢵⠀⠀⠘⠀⢢⠘⡷⠚⠡⣀⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠘⠀⠀⠀⡿⠘⡇⠁⠀⢁⡠⠋⣀⣠⢖⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡘⠀⠀⠀⠀⡄⠀⠀⢠⡇⡭⢷⡠⠔⣉⡤⠒⠙⡥⠀⢊⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠠⢁⠴⠉⠀⢠⠁⠀⣠⠀⠀⡇⠀⠀⣸⢝⣶⢾⠒⢋⠀⠀⠀⣅⢘⡕⣽⢳⣧
⠀⠀⠀⠀⠀⠀⣴⣿⣕⠀⠐⠀⠆⡠⠊⠀⢃⠀⠁⢀⠜⣿⠕⡚⢩⡗⢌⠂⠀⠀⡎⢻⡧⡺⢀⣹⣧⡀
⠀⠀⠀⣔⣆⠀⠜⣉⠿⢷⡤⣾⡞⠡⠕⠀⠘⣰⠠⠊⠀⠯⡁⠨⠁⡇⢨⢳⡄⢀⠃⠥⢻⣭⣽⣿⠛⣿⠆⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠻⢿⣿⣅⢢⢀⣨⠿⠛⠿⠷⣒⠢⣿⢥⠦⢸⡇⠢⠅⡀⢥⣈⣳⣼⣿⣶⣾⠿⢿⣧⣙⣸⣿⣧⣹⡿⠅⡈⢀⠠⠂⢄⠡⡂⢀⠕⡂⢔⠠⡂⢄⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣞⡂⣇⣠⠄⠙⡀⠫⢉⠟⢿⡁⠠⢐⠚⠽⡓⢩⢉⡛⣦⣌⠃⣾⣿⣨⣽⡃⠁⠈⠀⠄⡀⠀⠈⢂⠅⡨⣂⢔⡬⠒⠕⠊⠐⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠷⢤⣷⣖⣣⣂⣾⠶⠬⠐⠶⠩⢿⣦⣜⢥⣽⣾⣿⢋⡿⣿⣵⡟⠄⡢⢐⠠⠂⠄⠊⠔⠉⠊⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠿⠟⠁⠁⠀⠀⠀⠀⠀⠈⠛⠉⠀⠻⠾⠗⠀⠂⠁⠈⠀⠉

⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⣜⣇⣄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠿⠟⢻⣻⠿⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣻⣍⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠠⠀⢼⡧⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⡀⠀⣺⣋⡀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⢀⣽⡭⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠐⢺⠶⠄⠀⠄⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠐⢾⠖⠂⠀⢀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⡛⠁⠀⢠⡄⠀⠀⠀⠰⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⢀⡃⠀⠀⠀⣀⠀⢀⣾⣿⣿⣦⠀⠀⣀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣦⣬⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⣿⣿⡟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢿⣿⣿⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣾⣿⣿⣧⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⣼⣿⣿⣷⣼⣷⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⡀⠀⠐⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠎


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡶⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣦⣄⣄⣀⣀⣀⣀⣀⣉⣻⣦⣄⣠⣴⣟⣋⣀⣀⣀⣀⣀⡀⢀⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠟⠋⠉⠉⠉⠉⠉⠉⠉⢉⣭⡿⠛⠛⠿⣯⡉⠙⠋⠛⠛⠛⠛⠛⣿⠷⠞⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⠀⠀⠀⠀⠈⠙⠳⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠠⢠⠥⢠⡀⠀⠀⠀⢀⡀⢐⠀⠀⠀⠀⠀⢇⣠⠆⠀⠀⠀⠠⣀⣸⣇⠀⠀⠂⡀⠀⢂⠎⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⡼⠻⠹⠀⠄⠀⠀⠐⠚⠛⠃⠀⠀⠀⠈⠉⠉⠐⠀⠀⠀⠀⠀⠀⠌⠒
⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⢤⣄
⠀⠀⠀⢠⢲⡀⠠⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢉⡟⢂⣮⠖⣶⡖
⠀⠈⠸⠛⢲⠚⠑⠈⠄⠰⠀⠐⠁⠐⢄⠂⠀⠀⠐⣂⠁⠓⠥⠔⠀⣾⢉⠺⠁⠀⠀⢠⣴⣀⣀⣀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢄⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡈⠀⠀⠀⢠⠇⠀⡠⣠⠀⡠⢖⡨⢒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢰⢰⢠⣾⠀⢸⣄⠀⠀⠁⣎⣶⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⢢⠸⡜⡜⣿⡄⢆⠉⠳⣄⢂⠘⠯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⢀⠠⠌⡢⣧⡱⣼⡘⣿⣎⣇⡀⢹⡎⣇⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠀⠀⠀⢎⡦⢾⣜⢿⣿⣷⣘⣿⢸⣿⣿⢃⡟⠔⠀⣸⠀⠰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠙⡎⢻⣿⣿⣿⡇⣾⣟⡵⢋⣤⣢⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠇⠀⠀⠀⡀⢠⡇⢀⠻⣿⣿⣿⣿⣿⣴⣯⣍⠉⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡛⢳⠶⡗⡤⢿⣦⣷⣿⣿⠿⠛⠛⠛⠉⠩⠑⠂⠫⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠺⠇⣸⠀⠈⠁⢂⡼⠛⠁⠁⠀⠄⠀⠀⠠⠆⠀⡀⢀⡞⡐⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⠿⠧⠀⣶⠯⣥⣄⠀⠀⠀⢠⣞⣅⢠⠖⠶⠖⣾⣮⣧⣑⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⡖⠄⠀⣷⠀⠘⣮⡇⣀⠼⠛⠙⣯⣼⠀⠂⢠⡿⣿⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⣈⣃⣠⣴⣿⠶⢦⣾⣟⣿⣆⠘⣀⣼⠟⠙⠏⠉⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⠚⠉⠶⠀⠀⠘⠋⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣶⡒⡶⣲
⠀⠀⠀⠀⠀⠀⠀⠀⣷⢻⡶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡆⢸⡇⣼⣇
⠀⠀⠀⠀⠀⠀⣠⢟⠁⣿⣷⡙⢿⣄
⠀⠀⠀⠀⠀⡼⢡⠁⠈⣿⣟⢱⠈⢻⣦
⠀⠀⠀⠀⠀⡇⢸⠀⣷⣿⣿⣿⡇⢸⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠉⠉⠉⠙⠧⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠂⠀⠀⠈⣀
⠀⠀⠀⠀⢸⡧⠀⠀⠀⠠⠀⠀⠀⠖⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠰⣿⣄⣀⡀
⠀⠀⠀⠀⢸⠁⠀⠈⠁⠀⠀⠈⠀⣤⢹⡇⠀⠀⠀⠀⠀⣿⠀⣶⡖⣲⣶⠀⣶⣶⣿⠿⠛⠙⢹⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠒⠀⠀⠀⠉⢾⡇⠀⠀⠀⠀⠀⣿⠀⣿⠁⠸⣿⢠⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢀⠀⠀⠀⠁⠔⠂⠀⠀⠠⢸⡇⠀⠀⠀⠀⠀⣿⠀⠃⠀⠀⠀⠸⣿⣯⣿⣀⣀⣀⣼⠇
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢅⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣉⣽⠇⠀⠀⠀⠀⠀⣷⠀⠀⠆⠀⣁⢰⣤⢿⣿⠿⠇
⠀⠀⠀⠀⠀⡏⠀⠀⣶⣤⣤⣴⡆⣸⣿⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠺⢺⣽⣿⣿
⠀⠀⠀⠀⠀⣧⣤⢀⢿⣿⣿⣾⣧⣿⡿⠀⠀⠀⠀⠀⣰⡿⠛⠓⠒⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠛⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢺⠛⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡅⣦⣖⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⠀⠀⠀⢀⡴⠚⠓⠶⠋⢳⣄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⡸⣿⣿⣿⣿⢫⣵⣬⣭⣶⣎⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠘⣆⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣧⠹⣿⢋⣶⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⠀⠳⣴⣦⢰⠒⠶⣄⠴⢲⠞⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⡇⣿⣜⠋⢹⡏⣭⣝⠻⣫⡍⣱⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠰⢸⠀⠀⢸⣿⢸⠰⠀⠠⠀⢨⣿⡳⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⢸⡇⣿⣿⣿⣿⡷⢚⢭⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⢸⠀⠀⣾⠙⠋⠸⠀⠐⠀⢸⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⣧⣵⣿⣿⣿⣿⡇⣿⢸⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⢸⠀⠀⢿⠀⠀⢀⠀⠀⠀⠘⣶⣫⠇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⣧⢉⠜⣸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⠀⠀⢿⠠⠄⠸⠄⠐⠄⢸⠉⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣿⣿⡇⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠚⠀⠀⠘⠒⠒⠒⠒⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣭⣭⣭⣭⣭⣥⣿⣿⣧⣭⣭⣭⣭⣭⣭⣵⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿








⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢆⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡀⡏⠀⠀⠀⠀⠀⠓⢻⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀⠀⡜⠀⠙⠇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡔⢹⡀⡇⠀⠀⠀⠀⡜⡇⠀⠀⠀⠀⠀⢇⣠⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠁⠀⠀⠀⢸⠁⢱⠀⡀⠀⠀⠀⠘⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠢⣀⣊⠀⠀⠀⠀⠀⡜⠑⠃⠀⠈⠚⠹⡀⠀⠀⠀⠀⢱⢀⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠈⠁⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠖⠇⠀⠀⠀⠀⠀⠀⠀⠸⠊⡆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠈⠒⠤⣀⣀⡠⠴⠊⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⣟⠒⠤⢄⣀⣀⠤⠤⢄⣀⣀⡠⠤⠒⣾⡵⢮⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡏⠏⡿⡀⠀⠀⣰⠁⡆⡞⢝⡟⣄⣀⡀⠀⡿⣝⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠯⠼⠒⠊⠉⠘⢄⠣⣉⡭⢃⠇⠀⠈⠉⠉⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⣀⡀⠀⠀⠠⠂⠈⠀⠀⡄⣤⣥⡀⠀⣀⢀⣀⡁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⣼⣿⣿⡇⠀⣾⣾⣿⣿⡆⠀⢷⣿⣿⡇⠀⣿⣿⣿⡇⠀⣀⠆⠈⠀⢸⡠⡀
⠀⠀⠀⣼⣷⣿⣿⡇⠀⢿⣿⣿⠃⠀⢻⣿⣿⣿⠇⠀⢸⣿⣿⠁⠀⢹⣿⣿⠃⠀⣰⢸⣶⣿⣾
⠀⠀⠀⠻⣿⣿⣿⠇⠀⠸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⠹⡏⠀⠀⣿⣼⣿⣿⣿⡄⢀⠆
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠿⠿⠀⠀⠀⢿⣿⡇⠀⠀⠀⠉⢋⠀⠀⠀⠘⡀⠀⠀⠉⠛⠛⠛⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⠀⠀⠋⠑⣴⣶⣗⣕⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣿⡇⠀⣠⠀⠀⠘⢻⣿⣯⣿⣽⣧⣄⠈⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⣶⣿⡇⠀⠀⢶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣔⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣇⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠁⢀⣠⣀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢀⣄⡀⢠⣶⣿⣾⣿⣿⣾⣿⠛⠀⠀⠀⢰⠄⠀⢀⡀⠀⠀⠀⠀⠈⢻⣿⣿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⢀⡀⠈⢉⠛⠻⠞⠎⢻⣿⠏⠘⢋⣿⢇⣄⣦⡄⠜⢀⠀⣾⡏⣄⠀⠀⠀⠀⠀⢹⠏⠂⢻⡙⣿⣿⣿⣿⠟⠛⠿⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⣦⣴⣾⣿⣦⣠⣀⠀⠀⠉⠀⢶⣿⣿⡟⠛⢿⠧⠀⠈⣭⣿⣿⠏⠀⠀⠀⠀⠀⢠⡆⠀⠀⢃⡈⢿⡿⠁⠸⣦⣶⣬⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣿⡿⠋⣻⣽⣍⠁⠀⠀⠀⠀⠰⣿⠟⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⢀⠀⠀⠀⢠⡀⠀⠀⠀⠘⣄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣾⣻⠁⣘⡛⠋⠁⠀⠀⠀⠀⡀⠀⠈⣦⣶⡆⢀⣶⣞⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⡄⠀⠀⡴⠺⣃⣤⡿⢣⠔⠻⠏⠷⠺⣿⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣷⣶⠀⠊⠙⠙⡁⠉⢡⠢⠀⠀⠆⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⢻⣿⣿
⠀⣿⣿⣿⣇⣉⣠⣤⣤⣤⣤⣶⣾⣿⣷⣾⠖⠀⠀⠀⠀⠒⢤⠂⠀⢀⡀⠀⡄⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠂⠰⠉⢿⣿⡿⣤⣾⣧⣸⣿⣿
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⠟⠿⠋⠁⠠⣤⡀⢰⣶⣆⠀⠀⠀⠛⠉⠛⠀⢀⣼⡇⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⢈⣻⣦⡾⠻⣿⣿⣿⣿
⠀⠘⢻⣿⣿⣿⣿⣿⣿⢏⣿⣿⣇⠀⠀⠀⠂⠀⠹⣦⣿⣿⣦⣠⣾⡀⠀⠀⠀⣿⣿⣿⠀⠀⠀⡀⠀⠀⢀⠀⠤⢶⡟⠛⡁⠈⠳⣌⠻⢿⣿
⠀⣴⣾⣿⣿⣟⡛⠂⠀⣸⣿⣿⣿⣧⣴⣅⣀⡀⢠⣿⢿⣿⣿⣿⣿⡇⠀⢀⣾⣿⣿⣿⠉⠉⠉⠹⡀⠀⠀⠀⠀⠀⠱⡀⠐⢄⢀⣬⣿⣿⣿
⠀⢻⣿⣿⣿⣿⣿⣷⣠⣿⣨⣽⣿⣿⣿⣿⣿⣿⣿⣯⣈⠿⢻⣿⣿⣿⣄⣾⣿⣿⣿⡿⠆⠀⠀⠀⣣⣀⣀⣀⣀⣤⣴⣿⡿⢿⣿⡿⠿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣛⣉⣉⣨⣤⡀⠀⠀⠀⠀⠀⠀⢀⣭⣿⣷⣿⣿⣿⣿⣿⣶⣿⣿⣯⣭⣥⣶⣿⡷
⠀⠈⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣶⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⣿⠿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤⣤⣤⣤⣭⣬⣬⣬⣭⣤⣭⣭⣭⣭⣭⣤⣭⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠂⠉⠰⠖⠚⠉⠑⠲⠒⠒⢤⢄⡀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠾⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠓⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⣀⢀⡤⣄⠀⠀⠀⠀⠀⢠⠤⠖⠀⠒⠒⠓⠒⠊⢳⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡼⢥⠈⢁⠴⢾⡃⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀⠀⡄⠀⡀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⠁⠀⠀⠘⠀⠘⣆⠀⠀⠌⠁⡀⡇⢠⠀⠀⠸⠀⠀⠀⢀⢡⣼⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡏⠀⠀⠀⠀⠀⠀⣼⠀⢀⠀⠀⠀⠃⢸⠀⠀⠐⠀⡀⠀⠈⢸⠐⠀⠒⠒⠀⠈⠉⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣱⣯⠀⢤⡀⢀⡀⢀⣿⠀⡎⠀⠀⠀⣀⢸⠀⠀⠀⡀⣇⠀⠠⢼⣀⡤⠞⠛⠛⠒⢄⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠁⡇⠀⠀⢸⠋⠀⠀⠀⠀⠀⠈⠇⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡇⠀⢀⠀⠀⠀⠀⢻⡴⠀⠀⠀⢰⠀⢠⠀⠀⠀⡆⠀⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⡇⠀⠈⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⡇⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⠀⢸⠀⠀⠀⠃⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇⠀⢰⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠘⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⡇⠀⢸⠀⡄⠀⢸⡃⠀⠀⠀⠀⠀⢠⠘⠀⠀⠀⢸⠀⠀⠀⡄⡇⠀⠀⠀⠀⠀⢀⡅⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⡼⠀⣜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡇⠀⢸⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡁⡏⠓⠲⠤⠀⠊⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢨⡇⠀⢸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⠀⠀⠀⣿⣀⠤⠤⣄⣢⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇⠀⡘⠀⡅⠀⠀⡇⢰⠀⠀⠀⠀⢀⠀⠇⠀⠀⢸⠀⢇⠀⠀⢻⡴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡈⡀⠁⠀⠈⠂⠚⠁⠈⢦⣀⠀⠀⠰⠀⠈⠂⠀⠈⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠶⢭⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠉⠉⠓⠒⡂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠉⠁⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⠤⠤⣤⣥⣄⣤⣤⣤⡤⠤⠶⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⢷⡒⠂⠀⠀⠀⠀⠀⠒⢚⡃⣀⡀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠀⠀⠉⠙⢻⠇
⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠈⢉⢙⣿⣿⡗⠋⠹⡷⡀⠀⠀⢸⣷⣶⠀⠀⠀⢐⠀⡒⠖⣾⣷⣶⣄
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⣷⡇⠀⠀⢸⣿⣿⠛⠞⠉⠞⢳⡿⢻⣿⡇⠀⠹⠆
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⠁⠀⠀⢸⣿⡟⠀⠀⠀⠀⠈⡃⢸⣿⡇⠀⢸
⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⢀⣾⠃⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡃⢰⣿⡇⠀⣼
⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡾⠃⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢰⡇⢰⣿⣧⢴⡏
⠀⠀⠀⠀⠀⢻⣧⣧⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠘⣿⣷⡆⠀⡄⢰⡿⢧⣸⣿⠟⠁
⠀⠀⠀⠀⠀⠈⢿⣿⠂⠀⠀⢐⣚⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣂⠐⠒⠖⣶⣾⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢂⠂⡇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣑⢹⣷⠇⠀⠀⠀⠀⠀⠀⠀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⢰⡜⠀⠀⠀⢠⢠⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢠⡇⢰
⠀⠀⠀⢀⣼⣿⣆⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣼⣷⣇⡀⢀⡀⠀⠀⠰⠆⠂⠈⠁⠀⠀⠀⠀⡀⢠⣄⠀⠀⠀⠀⣴⢸⡗⢨⡀
⠀⠀⠀⣼⣿⣿⣾⣦⢤⣶⣿⡟⠀⠀⠀⠀⠀⣽⡿⣿⠛⠿⠷⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡇⠀⡂⠀⡄⣺⣸⣿⣸⡀
⠀⠀⣼⣿⣿⠏⠈⠛⠀⢻⣿⡇⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⣧⣶⣧⣼⣿⢀⣯⠰⠋⢿⢻⣿⣿⡇⡀⡆
⠀⣰⣿⣿⣿⠇⠀⠀⢲⣿⠟⠀⣼⣿⣦⣀⣼⣿⣿⡛⡿⣀⣠⣴⣇⣤⣿⣀⡀⢤⠰⢰⣿⣿⣿⣿⠟⣾⣿⣼⠖⢺⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⡿⣶⡀⡰⡾⠋⠄⠀⣿⣿⣿⣿⣿⣿⣿⠟⢻⠛⢿⣿⣿⣿⣿⣿⣻⣿⣷⣾⣿⣿⣿⣣⣶⣿⣿⣿⣶⡈⢿⣿⣿⣿⡟⠇
⠀⣿⣿⣿⣿⢻⣿⠣⣷⡤⠀⣤⣯⠙⢻⣿⣿⣿⣿⠁⠈⢧⠀⠉⠉⠽⠉⠿⠛⠛⠁⢀⣿⣿⠋⢻⡹⣽⣿⣿⣯⠁⠙⢿⣿⣿⣧
⠀⣿⣿⢉⣯⣠⣏⠀⢸⣷⣿⡛⠛⠀⡙⣿⣿⣿⣿⡶⠦⠼⣶⠒⡀⠀⠀⣀⣠⣤⣯⣭⡫⢹⡇⣰⣼⣿⣿⣿⣿⣷⣴⣬⣿⣿⣿⣆
⠀⣿⢇⣾⣿⣿⣯⠀⠸⣿⣮⡻⢀⠋⠉⠌⠻⣿⣿⣧⠐⠀⠘⣷⣷⣆⡀⢨⣍⣏⣉⣭⠽⠿⢷⣿⣿⣿⣿⡏⣿⣿⣿⣾⣿⣿⡟⢻
⠀⣷⣼⣿⣿⣿⣿⡂⠀⣿⣿⣿⣮⣩⠀⡐⠂⠙⢿⣿⣦⣤⣤⣿⣿⣿⣿⣦⣤⣾⢶⢿⣿⣿⣷⣭⣿⣻⣿⣶⣿⣿⡟⢿⣿⣻⡿⠒
⠀⣿⣿⣿⣻⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⣿⣶⣤⡀⢝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣷⣶⡦
⠀⣤⣿⣿⣿⣹⣿⣿⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠹⣿⣿⣿⣿⣿⣿⣷⣤⣼⣛⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣊⣿⣿⣿⣿⣿⣿⠻⢿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠋⠃
⠀⠀⠈⠉⠉⠻⠿⠿⡿⣟⣿⣽⣿⣿⠿⠿⠟⠛⠋⠃⠿⠛⠰⠟⠃⠿⠻⠷⠾⠋⠋⢸⣿⢛⠛⠟⠿⡿⣿⡿⠻⠟⠩⠍⠀⠈
⣀⣀⣀⣀⣀⣐⣚⣛⣋⣉⣉⣁⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣈⣀⣈⣁⣀⣀⣀⣀⣁⣁⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣋⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠀⢠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣀⡀⠈⢯⡝⣳⡀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣛⣳⣦⣌⠳⠃⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠹⣟⡯⢷⣚⣷⡀⠀⠀⠀⣰⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⡀⠀⣰⢿⣇⠀⠀⣿⠀⣮⡐⢊⣷⡀⠀⠰⡏⢞⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⠇⣰⡯⠥⢜⣦⢀⣿⠁⡇⢳⠐⣚⡇⠐⡶⣝⢦⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⣟⣠⡈⢗⣻⠾⠒⣸⠁⢸⡇⣲⡇⠀⣿⠽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠧⠹⡾⣟⠦⣘⠽⣰⢏⡯⢸⢠⣿⢁⡼⠗⢀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠰⣦⣄⡀⠀⢻⡍⢆⠈⢳⡇⢰⡃⡟⠬⣧⣞⡫⠁⠰⣲⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣳⠙⣞⣹⡄⢸⠿⢸⠰⡀⠁⡼⠂⡇⢨⠿⠵⠂⣐⡽⠃⣼⡽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⣿⣢⠷⣛⡉⡾⢘⠅⠀⠊⠀⢳⠈⢡⣶⣨⡟⢠⡀⠳⡚⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢋⣦⢻⣓⡜⢁⣵⠂⠀⠀⣰⡀⠳⡏⢻⢰⡇⢸⡽⣦⠹⠃⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢠⠾⠍⡜⠘⣇⠞⠀⣸⠅⠀⠀⠀⠀⢻⣀⠀⠸⡍⣻⣞⡫⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢉⡞⠀⠸⡏⠀⠀⣺⠀⠀⠀⣀⠀⠀⠡⡷⠀⢻⠉⠭⣲⠟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡒⡾⢀⡧⠀⠀⠀⠀⢀⠀⠀⠀⠐⡀⠀⠀⠀⠅⣸⣸⡟⠁⠘⠋
⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⡀⣯⡀⢷⠨⠯⠄⠀⠀⢀⡽⠀⠀⠀⠪⢆⠀⠀⠀⢠⣏⣾
⠀⠀⠀⠀⠀⡞⡅⡀⡀⠈⠉⠙⢷⠘⡆⠀⠁⠀⠀⣲⠍⠀⢀⡀⠘⡵⡃⠀⢀⣘⣧⢿⠑⠒⠒⠋⠉⠛⠒⡆
⠀⣀⣀⣀⡠⣗⡁⣇⣧⣷⣒⡒⠛⠉⠉⢱⣀⡀⢈⣴⣖⣋⡉⠙⠲⡌⠕⡾⠁⠈⠉⠉⠓⣶⢦⡆⣦⡆⣄⣿
⠉⠛⢛⡿⠿⣿⣻⣿⢯⠧⣖⢝⣆⢠⣄⣄⠀⡽⢁⣖⣒⡀⢍⢻⣧⣽⣎⣴⣰⡖⣤⡄⣾⣯⣧⣿⣿⣇⣏⡿⠮⠤⠤⠄
⠀⠀⠀⠀⠉⠁⢺⣏⣇⢧⣏⡼⣿⡾⣿⣿⣇⣇⢯⠯⣿⣳⢮⠇⣿⡿⠯⠽⢿⣇⣿⢸⣿⣧⣼⣿⡛⢻⠩⠭⠭⠭⠭⠭⠭
⠀⠀⠀⠀⠀⠭⢿⣛⣯⡿⠥⢾⠟⠻⣿⠟⢙⣟⠦⢍⣓⣒⣫⡾⠯⠍⠀⠀⠉⠭⢛⣾⣯⣭⣿⣷⣾⣦⣤⣀
⠀⠀⠀⠀⠀⠉⠩⠒⠲⠾⠟⠋⠉⠀⠀⠀⠀⠀⠬⠭⠭⠿⠭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠙⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠲⠀⠀⠀⠘⢀⠀⠀⠀⠆⠠
⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠐⠀⢉⠀⠈⡀⠀⠀⠀⠁⠀⠀⠀⠢⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡰⢄⠀⠌⠀⠀⡇⢀⠀⢰⡄⠀⠀⢀⡂⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂⠐⡀⠅⠈⢳⡀⠀⠀⡇⠈⢠⠇⢸⠀⢂⡜⠁⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣰⠦⣀⡅⠀⠀⠁⠀⠀⢰⠀⡌⠀⢸⡀⠀⠀⢀⠃⠀⠀⢈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠣⠀⠀⠀⠀⠀⠀⠑⡄⠀⠘⡄⠀⢀⠎⣄⣀⣬⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠠⠖⢀⠞⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠐⠀⡐⠀⢀⡀⠀⠀⠃⠂⢀⠈⠁⠀⢈⠸⠃⠔
⠀⠀⠀⠀⠀⢀⣰⡤⠤⠶⠲⢶⣀⠀⠀⠀⠀⡀⠀⠈⢁⠀⠀⡀⠈⠀⠀⠀⢀⣭⣤⣠⡀
⠀⠀⠀⠀⠀⢸⣇⣻⣿⡤⢎⡏⣁⣦⡴⢶⡊⣯⢉⡿⠻⢤⠉⢱⡄⠨⠅⡆⠀⢀⣬⢯⣳⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠛⠳⠚⠁⠘⠦⠴⠞⠙⠲⠼⠏⠉⠛⠚⠚⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⣔⡾⣟⠛⣛⢛⣛⠛⡿⢷⢢⠀⠀⠀⠀⠀⠀⢀⣴⣿⢅⠉⠙⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⣠⠔⠔⠚⠛⠯⠉⠓⠦⣄⡀
⠀⢀⣾⣿⣿⣿⣾⡗⡖⠀⣆⠀⠀⢀⣣⠀⠀⠀⠀⠀⢸⢿⣏⡧⠀⠀⠀⠀⣀⡠⠷⠀⠀⣠⠴⠊⠁⠀⠀⠀⠀⢀⣀⠤⢤⡀⠙⢢⡀
⠀⢠⣿⣿⣋⣿⡟⠃⡃⠀⠁⠀⣀⡿⠿⠀⠀⢠⣾⣿⣿⢻⣿⣷⣼⣶⣿⡍⣀⠲⣼⠀⢠⡇⠀⠀⠀⠀⠀⠀⢡⠴⠃⠀⠀⠉⠑⣄⡇
⠀⣸⣿⣿⣿⣿⢿⢷⡖⠚⠛⠉⠁⠀⠀⡇⠀⣿⣿⠀⠈⠨⣿⢻⣿⢸⣿⡅⢹⠀⣿⠀⢘⠀⠀⠀⠀⢡⠄⢠⡎⠀⠀⠀⠀⠀⠀⠈⡇
⠀⢿⣿⣿⣿⣿⢸⢸⡇⠀⠀⠀⠠⢠⣴⡇⠀⣿⣿⠀⠀⠀⣿⢸⣿⢸⣿⡇⢸⠀⣿⠀⠹⡄⠀⠀⠀⠀⣴⢚⣤⣤⣤⣤⣄⣀⠀⠀⡇
⠀⠸⣿⣿⣾⣿⣿⣍⣄⣀⣀⡤⠴⠚⢋⠁⠀⢹⣿⡀⠀⢠⣿⢸⣿⢸⣿⡇⢸⠀⢿⠀⠀⢰⡀⠀⢀⠟⣿⢸⣿⣿⣿⣿⣿⣿⣿⣆⡇
⠀⠀⣿⣿⣿⣿⣿⡿⡇⢀⢀⠀⠀⣀⡾⠀⠀⠈⠻⣿⣶⢬⣛⣻⡿⠌⠿⠇⣋⢠⢰⠀⠀⠀⢹⠀⢸⠀⢹⣼⣿⣿⣿⣿⣿⣿⣿⣻
⠀⠀⠈⢿⣯⣿⣟⠉⠁⠈⠉⣀⣽⠟⠁⠀⠀⠀⠀⠈⠻⢨⣿⢹⣿⢹⣿⡇⢻⠀⢿⠀⠀⠀⠈⡦⣨⠂⢸⣯⣿⣿⣿⣿⣿⣿⡟⡏
⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣚⣻⣃⣫⣴⠾⠀⠀⠀⠀⢱⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⢻
⠀⠀⠀⠀⢀⣀⡤⠴⠲⢶⡒⠚⠳⣶⡦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠈⠁⠀⣀⣀⢀⡤⣀⠘⡄⠀⠀⢻⣿⣿⣿⣿⣿⡟⡎
⠀⠀⡀⣐⣭⣩⡑⢢⣅⠠⠈⠳⡀⠀⠈⢮⢻⣦⠀⢀⠄⢒⣀⡐⠒⠠⢄⣠⢖⣭⣶⣾⡛⠃⡆⠀⡇⠀⠀⢸⣿⣿⣿⣿⣿⣷⠇
⠀⣴⣽⠋⠀⠀⠙⢣⡸⢣⠀⠀⢘⡄⣶⣾⣧⣿⡇⠀⠱⡝⠿⣿⣿⣶⣤⣿⣾⣿⣟⠋⠁⡰⠁⠀⣿⠀⠀⠸⣿⣿⣿⣿⣿⣿
⠀⣾⡇⠀⠀⠀⠀⠀⢳⠼⣧⣻⣿⣿⢹⣿⣿⣿⡇⠀⣤⢘⢶⣟⣿⣿⣿⣿⣿⣿⣶⣤⠞⢁⠀⠀⣿⡆⠀⠀⣿⣿⣿⣿⣿⣿
⠀⡿⣇⢀⡀⣠⣀⠀⠘⠖⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢰⣏⣻⣹⣿⣿⣹⣿⣾⣯⣻⣿⣧⠈⠀⠀⡏⡇⠀⢰⣿⣿⣿⣿⣿⡿⡄
⠀⠸⡽⣄⠃⣛⡃⠀⣰⣳⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣾⡾⣽⣯⣹⣧⡿⠶⣽⣋⣻⣟⣿⡆⠀⢠⢷⣇⠀⠙⣿⣿⣿⣿⣇⣧⡇
⠀⠀⢈⣮⣜⢿⣥⣶⣵⣿⣿⣿⢱⣟⣉⣭⢽⣮⡄⠀⠙⠷⣿⠾⠟⠻⣷⡾⣭⣿⣏⣻⣿⠃⠀⢸⣼⣿⣷⣾⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠈⠙⠛⠋⠉⠉⠉⠛⢿⣿⣦⢻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢟⣶⣻⡾⠋⠀⠀⠈⠪⣟⡋⠉⠉⡉⠉⠉⣋⡭⠊
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠓⠲⠶⡟⠓⢦⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⢠⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠙⡆⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣀⠈⠳⣴⣿⣦⡀⠀⠀⠀⠀⠀⠀⠲⣤⣀⣰⡟⠛⠒⠒⠋⠁⡼⠛⠛⠛⠉⠛⣆
⠀⠀⢠⣾⣿⣿⣿⣿⢇⣿⣿⢿⣷⣶⣦⠀⠀⠀⠀⠀⠀⠈⢹⣤⣀⠀⠀⠀⠁⠀⠀⢠⠀⠀⢸
⠀⢰⣿⣿⡟⠉⠙⡟⣸⣿⡟⣸⣿⣿⣿⣤⣤⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⠀⣀⣴⣾⣷⡴⠋
⢀⣿⣿⡟⠀⠀⣸⢃⣿⣿⢣⣿⣿⣿⠇⣼⠟⢠⣶⣆⠀⣰⠃⠀⠀⠀⣾⣿⣿⡟⣿⣿⠸⣟⣛⣛⣓⣦
⣸⢻⣿⠁⠀⢀⡟⣼⣿⡏⣼⣿⣿⡿⢸⣿⣀⣼⣿⡿⢰⣯⣄⠰⣿⡟⣿⣿⣿⡇⣿⣿⡇⣿⠛⠛⣿⣿⣧
⣿⢸⣿⡀⠀⣸⢡⣿⣿⢡⣿⣿⣿⠇⣾⣿⠟⣿⣿⡇⢸⣿⣿⠀⢹⣇⢹⣿⣿⣷⢸⣿⣇⢻⠀⠀⠸⣿⣿
⠘⢷⣍⠻⣶⡏⣼⣿⡏⣾⣿⣿⡟⢰⣿⡿⢸⢿⣿⣀⣼⣿⣿⢷⣾⣿⢸⣿⣿⣿⠸⣿⣿⢸⡆⠀⠀⣿⣿
⠀⠀⠈⠻⣿⢱⣿⣿⢰⣿⣿⣿⠃⣿⣿⠇⡿⡿⠈⠉⠁⢹⣿⡈⣿⣿⠈⣿⣿⣿⡇⣿⣿⡌⣇⠀⠀⣻⢿
⠀⠀⠀⣼⣧⣾⣿⡇⣾⣿⣿⡏⣸⣿⡟⣸⣿⠇⠀⠀⠀⢸⣿⡇⣿⣿⡇⣿⣿⣿⣇⢻⣿⡇⣿⣴⠞⣋⣾
⠀⠀⠀⣿⣟⢿⣿⣸⣿⣿⣿⢁⣿⣿⢃⣿⣿⠀⠀⠀⠀⠀⣯⣷⢸⣿⣇⢸⣿⣿⣿⢸⣿⣷⢸⣴⠾⠋⠁
⠀⠀⠀⠹⣷⣄⠈⠛⠻⠷⢶⣾⣿⣯⠾⣻⡟⠀⠀⠀⠀⠀⢿⣿⠸⣿⣿⠸⣿⣿⣿⡌⣿⣿⣸⣧
⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣄⣀⣒⣾⣿⠟⠁⠀⠀⠀⠀⠀⣾⣿⡇⣿⣿⡄⢿⣿⣿⣇⣻⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣝⣛⠿⠿⠿⠟⠛⠋⠉⣀⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣦⣤⣤⣴⣶⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡀⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⢸⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⡀⠀⠑⠀⠀⠀⢸⠃⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠐⠀⠀⠀⠀⢀⣴⢋⠀⡠⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠃⠀⠀⠀⢣⠸⠃⢂⠞⠐⠃⡸⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠜⢆⠀⠘⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⢀⠤⠖⠒⠒⠒⢯⠀⠀⣠⣴⣕⣦⡀⠀⢠⢀⢳⠀⠀⠀⡇⡴⠋⣰⠋⠉⠑⣄⠤⣄⣀
⠀⠀⠀⢀⠤⠾⢄⠀⣠⣤⣤⣜⣁⣀⣿⣶⣶⣧⠝⠊⡀⠠⡂⠀⢀⣀⠸⠃⣤⣬⣷⡀⡀⠀⠀⢀⣌⣧⡀
⠀⠀⡴⠁⠀⠀⠸⣿⣷⣷⣿⣿⣿⡟⣫⡿⠋⣁⠀⠈⣁⡶⢀⠀⠠⡱⡅⢿⣿⣿⣶⣠⣼⣖⢤⠞⠉⠁⠉⠑⢆
⠀⠀⠹⣤⣀⣀⣠⣟⠈⠉⠙⢛⡿⢟⣧⡶⠾⢥⣾⡿⣸⣇⣾⣷⣶⣿⣝⢶⣿⣿⣿⣿⣿⣇⡰⣀⡀⣠⣂⣠⡼
⠀⠀⠀⢠⡏⠁⠀⠀⠉⢢⣶⣯⣶⠟⡥⠶⣿⣿⣿⣿⣿⡟⠉⢙⡿⠙⣿⣿⣷⣦⡿⣿⣿⡉⠣⠖⠉⠀⠈⢻⡄
⠀⡀⣤⢿⣷⡀⠀⢀⡠⠜⠛⠯⣥⢸⣿⡂⢙⣿⣿⣯⡿⠻⠉⠉⠁⠀⠙⣿⣎⡽⡠⠚⠛⠒⠒⢤⠀⠀⠀⣸⣇⡀
⠀⠀⠀⠀⠀⠉⢩⡏⠀⠀⠀⠀⠈⡷⢈⣛⡫⣜⣷⣼⣇⠀⠀⠀⢀⠤⠶⠾⠯⠮⡀⠀⠀⠀⠀⠘⣿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠷⠧⣤⣶⣤⡖⢉⠁⠀⠀⠀⠉⢏⡉⠡⠀⠐⠁⠀⠀⠀⠀⠀⠸⣤⣔⣤⣾⡷⠿⠗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡰⣼⣾⣄⠀⠀⢠⢏⢀⠀⠀⢠⡀⠀⠀⡀⣀⣠⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⠒⠙⠲⢶⠿⠖⠛⠛⠓⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⣶⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠈⢻⣆⠀⠀⠸⡇⠀⠀⢻⡇⠀⠀⣾⠀⠀⢀⡾⠃⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⡀⠀⠀⠙⠆⠀⠀⢻⠀⠀⢸⡇⠀⢸⠇⠀⢀⡞⠁⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⠿⡐⠚⠁⠑⠉⠲⠈⢄⠀⢸⠁⠀⠟⢀⣀⡨⢄⡀⢠⡿⠋⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⡄⡠⠊⠉⣀⠀⣀⡄⠠⠔⠒⡇⠈⠀⣐⡀⠉⠀⠁⠀⠠⠂⡀⢀⣠⡾⠟⠋⠁
⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⡏⠉⠊⠁⠉⠀⠀⠁⡀⡀⣷⠀⠀⠃⠀⠁⠊⠁⠐⠂⠤⠸⡌⠁
⠀⠀⠀⠀⠈⠉⠉⠛⠛⡂⠤⠤⠚⡀⣴⣦⣴⣶⣿⢛⣿⣿⢸⠀⢠⢰⣶⡶⢦⣤⣄⣤⡄⡰⠄⢀⣒⢾⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡏⠉⠉⡇⢿⣿⣷⣿⣿⣿⣿⢹⠸⡀⢸⢸⢻⣿⣿⣿⣽⣿⡇⡏⠉⠐⡎⡆
⠀⠀⠀⠀⠀⠠⠴⠾⢸⢸⡗⠟⠒⢸⢸⣷⣿⣿⣿⣿⣿⠸⡇⡇⠀⣼⢸⣿⣿⣿⣿⣿⢡⠐⠒⠂⡇⡇⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇⣀⣀⡈⡄⣿⣿⣿⣿⣿⣿⡄⢷⢸⢃⡇⣸⣿⣿⣿⣿⣿⠘⢠⣤⠐⢇⠇
⠀⠀⠀⠀⠐⢶⣶⡿⠇⡧⣷⡈⠀⠀⡇⣿⢻⣿⣿⣿⡏⣇⠸⡇⢿⠁⡏⣿⣿⣿⡏⡏⣀⢀⣀⡼⡯⠘⠿⢿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⣛⠷⠶⢷⢸⡸⣿⣿⣿⣷⢹⡀⠻⠘⡼⢱⣿⣿⣏⡇⡇⣋⠩⠝⣪⣥⣀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠀⠉⠑⠾⢘⡃⠃⠛⠛⠛⠨⠥⣶⠧⣸⠤⢤⣩⠤⣴⡆⡁⠀⠀⠈⠙⠻⣷
⠀⠀⠀⠀⠀⠀⠻⠋⠁⠀⠀⣠⣶⠟⢰⣐⡛⢛⣙⣒⣛⠩⠤⢒⠊⠉⢩⡐⠒⢒⡒⠂⠁⢻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠋⠀⠀⢠⣴⠀⠀⣰⣶⠀⠀⣸⠀⠀⢸⣷⡀⠈⢿⣆⠀⠀⠙⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠋⠁⠀⠀⣿⡀⠀⠀⣿⡷⠀⠈⢿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣿⡄⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡇⢸⠟⢱⠜⣇⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠛⠁⡠⠁⠀⠈⠀⢹⡀⠏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠁⠀⠀⠁⠀⠀⠀⠀⢠⠀⠀⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣿⡷⢧⢀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣴⢪⠣⣿⡜⣿⠀⠀⠀⠀⠀⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⡲⠟⠁⠀⠁⡘⢧⢿⡀⢸⠀⠀⠀⡟⢟⢧⣼⡗⠀⡖⣢⡀
⠀⠀⠀⠀⠀⠀⠀⡔⣊⡀⠀⠀⢹⣷⠞⣱⣾⡷⠁⣰⡇⢸⠀⢻⣾⣄⠀⣴⡿⡀⠀⢙⢻⣼⠏⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣸⠟⠻⢮⣦⣤⡾⣣⡾⡿⣹⠁⢠⣿⠀⡇⠀⢿⣦⡌⡟⢻⣷⠸⣦⡀⣱⣭⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠸⣻⡿⠾⠷⢧⠤⠿⠾⢴⣧⠀⣸⣿⣷⣳⠀⠼⣷⠟⠋⠁⢉⠑⣤⠀⠀⠂
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⢐⣿⠀⠈⠀⠀⠀⠀⠀⢺⢻⡏⢀⣀⠀⠀⠀⠀⠘⡇⠐⠋⠁⠀⢸⣷⠊
⠀⠀⠀⠀⠀⠀⠑⢄⡀⢀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⡴⢸⡇⠋⠀⠀⠀⠀⠀⡠⠓⠠⡤⣀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠛⠉⠂⠦⠄⠠⠄⠀⠀⢰⡧⠹⢅⣀⣀⣀⣀⣀⡔⠀⠀⡜⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⣦⠐⠚⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⢠⣦⠀⡟⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⣿⢰⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢶⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⣆⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣷⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⣪⣵⣻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡿⢯⡿⢟⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣋⣵⣶⣭⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠛⣿⠛⠛⣟⠉⢹⣿⠛⠛⣟⠋⠻⡉⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⢡⡰⠁⢄⠈⠘⣦⠋⡇⢣⡌⠘⣤⠃⠡⡔⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣳⣿⣶⣶⣷⣶⣾⣶⣶⣿⣶⣧⠠⣶⣶⣿⣶⣶⣷⣶⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣿⣿⣿⣿⣿⡿⠿⣿⠿⠿⣿⣿⠀⠙⢿⡿⣿⣿⣿⡿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⢳⠀⠌⢣⢀⠘⣆⢠⠛⡀⡐⣿⣿⠹⡀⡸⢳⢀⠏⢦⢠⠛⡄⡼⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣤⣤⣿⣤⣤⣯⣤⡼⠃⠀⠘⢠⣿⣿⡀⠹⠃⠀⠟⠀⠀⢧⣀⣸⣧⣼⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⢸⣿⣿⡇⠀⣤⣤⣤⣤⣀⣠⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣸⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣿⣿⣿⣿⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⢸⢻⢰⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣼⠀⠀⠀⠀⠀⠀⠀⡾⢸⠀⢇⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⢻⠀⠀⠀⠀⠀⠀⣼⠃⣾⠀⠸⠄⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠁⢸⡆⠀⠀⠀⠀⣰⠋⢠⠉⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⠀⠈⢷⣄⣀⣠⡾⠃⣠⠏⢸⠀⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⡆⠀⢨⠉⠁⢀⡜⠁⢠⠃⠀⢀⠃⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢤⣀⠀⠀⠀⠀⢹⣿⡀⡇⠀⠘⡆⠀⡜⠀⣰⠃⠀⠀⢸⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠳⣄⠀⠀⢸⡇⣇⠰⡄⠀⡇⠀⠃⣰⢃⣴⣿⠁⢸⠀⣼⠃⠀⠀⢰⡶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠆⢠⡀⢹⡆⠀⢸⡇⣿⠀⠸⠀⠃⣀⢠⣇⡞⢹⡇⠀⢸⠀⣿⠀⠀⠀⢸⡇⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢸⠆⠸⡃⠀⢿⣤⡾⠁⡿⠀⣠⠞⣻⠟⢸⣾⠁⠈⣧⠀⢸⠀⢿⡀⠀⢀⡾⢡⠃⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣼⠀⠀⢇⠀⠀⠀⠀⢠⢃⡾⠁⣼⠋⠀⠈⢿⠀⠀⠹⣆⠀⢃⠈⠛⠞⠛⠁⠀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⡇⢠⠀⠘⢆⡀⠀⠀⠸⢸⡇⢰⡏⠀⠀⠀⣼⠀⠀⠀⠹⣇⠘⡄⢀⡄⣰⡆⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠁⢸⠀⠀⠀⠙⢄⠀⠀⠈⣧⠈⢷⣄⠀⣠⡟⠀⠀⠀⠀⣿⠠⢃⡜⣰⢿⡇⠀⣿⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠈⡆⠀⣠⡄⠈⢣⠀⠀⠹⡆⠀⠉⠛⠉⠀⠀⠀⠀⣰⠇⡠⢊⡴⠋⢸⡇⢀⡏⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⣇⠀⢳⡀⣿⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠰⣯⣤⡶⠋⠀⠀⣿⠀⡸⠁⢿⡀⠀⣀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠹⡄⠈⣧⣻⠘⢧⣀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣰⠃⠀⠈⠙⡛⢉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠙⣄⠀⢿⣇⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠋⣀⣠⡀⠀⣠⠞⣱⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣌⠳⣄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⣛⣽⢟⡡⢚⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣌⡁⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⢁⣠⡴⠛⠁⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⣴⠞⠛⠲⠶⣤⣀⡀⠀⠀⠙⠓⠦⣭⣛⠷⠶⠶⠶⠶⠶⠶⠶⠚⠛⣉⣁⣠⡤⠶⠛⣋⣁⣤⡤⠶⠚⠛⠉⠉⠹⣆
⠀⠀⠀⠀⢰⡏⠀⠒⠤⢀⡀⠈⠙⠻⠶⣤⣄⡀⠀⠉⠉⠛⠛⠛⠚⠚⠛⠛⠛⢋⣉⣥⡤⠶⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⢸⡇⠀⢀⡀⠀⠈⠙⠀⠀⠰⠤⣈⠉⠛⠶⢤⣤⣀⡀⣀⣠⡴⠞⠛⠉⠉⠀⢀⡀⠀⠀⠀⠉⣀⠠⠔⠚⠉⠀⢀⣠⡾⠁
⠀⠀⠀⠀⠀⠷⣤⣀⠀⠈⠁⠲⠦⢤⡀⠀⠀⠈⢃⣀⣤⠴⠟⠋⣉⠠⠤⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣄⣀⣀⣀⣤⠶⠞⠋⠉⠀⠐⠚⠁⠀⠀⠀⢀⣀⣤⠄⠀⠀⠀⣀⣀⣤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⠛⠉⡀⠠⠄⠀⠀⣀⠀⠀⣀⠤⠐⠊⠉⢁⣀⣤⠴⠶⠛⠉⠉⠛⠛⠶⢦⣤⣀⡀
⠀⠀⠀⢀⣠⣤⣴⠶⠛⠋⠁⠀⠠⠒⠋⣁⡤⠖⠊⠀⠀⠀⠈⣀⣠⡤⠶⠚⠋⠉⠀⢀⡀⠀⠈⠉⠓⠲⢄⡀⡀⠉⠙⠳⠶⢦⣄⣀⡀
⠀⠀⢠⡟⡁⢤⣉⠳⣤⠀⠀⠠⠐⠊⠉⣀⣀⣤⣀⣠⡴⠖⠛⠉⠙⠓⠶⢦⣤⣄⣀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠁⠀⠀⠀⣠⠞⣉⣉⠙⠳⣦
⠀⠀⣿⢡⠛⣲⠈⡇⣽⠀⠀⡤⠔⢒⣩⡽⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⢤⣄⣀⠀⠀⠤⢀⡀⠀⢰⡏⡘⣡⣬⣄⠀⢸⡇
⠀⢀⠿⣌⣳⡤⢚⣰⣯⡤⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⣄⡁⣿⡀⢣⣙⢂⣨⣃⡼⠃
⠀⠠⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⠦⠤⠴⠞⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠰⣬⡖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠸⣧
⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⣷⣾⣭⡟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠠⠌⡿⠓⢶⡉⡏⢹⡟⣀⣶⠠⠀⠀⠀⠀⠀⠀⣠⣤⣤⠄⢸⣇⣀⣀⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠘⢃⡌⠐
⠀⠀⠠⠤⠄⠀⠤⣠⡜⣋⣷⣗⡫⠙⠋⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⢸⣟⠙⠛⠛⡻⣆⠀⠀⠃⠐⠲⢂⣰⡴⠆⢁⡠⠄⠀⠀⣄
⠀⠀⠀⠀⡠⣀⠔⠊⢁⣛⢿⣇⣤⣀⢒⣄⡀⠀⠀⠀⠀⠀⡠⠦⠀⠀⠀⢸⣿⠀⠀⠀⠀⣩⣧⡀⠐⠀⢐⢠⠨⡀⣈⣮⣁⡼⠆⠐⠊
⠘⠈⢺⣶⣪⠘⠦⠀⠀⡍⢾⣿⣿⢻⣏⣷⣶⡆⠀⠀⠀⠀⠣⠀⠀⠀⠀⣸⣿⡆⠀⠂⠣⣽⣷⣳⡄⠀⠀⢃⡡⣟⢿⣟⣟⠱⠔⠛⠶⠂
⢈⡐⢫⡟⡇⠴⡖⡢⠃⠄⢺⡋⢯⣿⣿⣭⣿⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠀⠀⠠⡙⢹⣿⣿⣆⠉⣨⣷⣯⣿⣿⣿⣁⣠
⠀⣤⣤⠀⣿⠤⠆⠆⢠⣔⣿⣥⠙⢺⣯⡾⠀⠀⢀⣿⡶⠃⠀⠀⠀⠀⠀⣿⣿⣿⢀⠠⡀⠋⠿⣿⣿⣿⣦⡈⡿⣿⣿⣿⣝⡀⣀⢠
⠰⠓⡲⠯⣽⣁⣄⠀⠀⣠⣿⢹⣜⣿⡟⠁⠀⠠⣿⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠀⠈⠃⡀⠙⣿⣿⣿⣿⢿⣿⣿⣿⣯⣯⠃⢩⠁
⠀⠀⠀⠀⢸⠀⠠⠀⠀⣹⣿⣿⣿⠏⠀⠀⠀⢠⣾⣿⡷⣄⠀⣼⡆⠀⢠⣿⣿⣿⣷⠁⠀⠁⠊⢹⣿⣿⣿⣿⣿⣿⣿⣿⢩⡄⢸⢀⣀
⠀⠀⠀⠀⠘⠀⠀⢈⠔⣿⣿⠟⠁⠀⠀⠀⢀⣿⣷⣿⢧⣿⣶⣿⡇⠀⣸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠉
⠀⠀⠀⣉⣿⣀⢋⠳⡁⡌⠁⢀⣀⡴⠿⠿⣻⣿⢭⣉⣼⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠂⢹⣿⣿⣿⣿⣿⣻⣿⣿⣿⣗⣠⣏⠁
⠀⠉⠙⣛⡿⣿⣿⡿⢋⡀⣠⠈⠹⠑⠈⠈⡿⢡⣶⣶⣿⣿⣿⣿⣿⢼⣿⣿⣿⣿⣿⣿⡄⢀⣤⣶⣶⣾⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⠧
⠀⠀⠀⠜⠉⠁⠀⠙⠉⢉⢔⠀⡋⠉⠹⢏⣴⣿⣿⣿⣿⡟⠻⠿⢏⡿⢿⣿⡿⠿⣿⣿⣷⠾⣟⣿⣿⣯⣿⣏⣭⣽⣿⡎⠛⠹⠭⠭⠅⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠈⠁⠠⠗⠿⠛⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⢂⠙⠉⢉⠉⡀⠀⡜⠉⠭⣝⠠⠆
⠀⠀⠀⠂⠀⠀⠀⠤⠀⠉⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠁⠈⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠄⠈⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂