Crown prince Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⣿⡇⣠⣴⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠛⣿⣿⣿⡟⢛⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⠀⠁⠀⣸⣿⣿⡆⠀⢀⠤⣒⢦⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⢹⣿⣷⣶⣤⣿⣿⣿⣷⣾⣵⣿⣿⡏⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠹⣶⣄⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⢟⣿⣿⣿⣿⡇⢻⣿⣿⣷⡟⡟⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⢀⣴⣾⠋
⠀⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⢀⣎⢮⣹⣿⣿⡀⣠⣿⡿⣩⡔⣠⣀⣠⣿⣿⡿⠀⣀⡀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⢠⠊⡷⠀⣿⡟⢻⣟⢿⣿⣯⢟⢿⣿⣿⣿⢟⡞⣝⣼⣿⣯⡿⠋⣿⡇⠘⠃⢸⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣀⠓⣤⣔⠻⣧⡀⣿⣼⣿⣿⣷⡣⣯⢿⣏⣎⢮⣾⣿⣿⣿⣀⣼⠏⣽⣶⣮⢁⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⣯⣾⣟⢿⣿⣹⣿⣿⣿⣿⣟⠎⡸⣳⣿⣿⣿⣦⡽⣟⣻⣷⢽⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣭⡽⣿⣞⣻⣿⣿⣭⣭⣭⠎⠰⡹⣿⣿⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⢿⣛⣫⣭⣵⠶⣶⣿⣿⣛⡧⣴⣹⣟⣛⣶⠾⣯⣽⣟⡷⢿⣽⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣟⣿⣽⠿⠞⠛⠛⠉⠉⠉⠉⢞⡟⠉⠉⠉⠉⠛⠛⠶⢿⣽⣻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⣨⡋⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂⣛⢱⠲⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣄⠿⢰⡄⠀⠀⠀⠀⠀⠀⠀⠘⢧⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⢸⠂
⠀⣤⣤⠰⣄⠀⠀⠀⠀⠀⠀⠉⡽⣤⣾⠃⠀⠀⣀⠀⢀⡂⠀⠀⡸⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣰⡦⠾⠂⠀⠀⠀⠀⠀⣠⢠⡀⣤
⠀⠙⠦⡰⣿⡀⠀⠀⠀⠀⠀⠀⠀⡏⢿⣆⠀⣶⣾⣷⣾⣷⣾⡿⣡⠏⠈⢷⣤⣀⢸⣤⣤⣴⣄⡠⠁⢿⠀⠀⠀⡀⠀⠀⠀⠀⠙⢀⡴⠏
⠀⠀⠀⠈⢈⡻⣦⣀⢠⣶⣶⣶⡄⣱⠃⠙⠛⠿⢿⣿⡿⠿⢋⡴⢃⣴⡀⠀⠙⠻⠶⠿⠿⠛⣁⡴⠻⡘⢧⣘⣶⣶⣶⡀⠀⣠⡶⠋
⠀⠀⠀⠀⠠⣿⣦⣍⡙⠛⠋⡡⠔⠡⠾⠶⠀⠀⠀⠀⠀⠈⠁⠈⡉⣉⠉⣀⠀⠀⢐⡒⠒⣻⣭⡶⣿⣬⠂⢤⣬⣭⣤⣶⣿⠏
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⠀⠀⠀⢤⡀⠬⠍⡇⠀⠺⠷⠂⠀⢓⢲⣂⣀⡩⠆⠈⠹⠝⠠⣬⠂⠭⡈⢳⠀⢡⣿⠿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣷⣧⠀⠀⠈⠂⠉⠉⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣂⣀⣀⠒⠚⠥⠚⠿⠥⣄⣼⣽⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣯⡽⠶⡒⠒⠛⡉⠉⠉⠭⠉⠩⠅⠀⠀⠆⠀⠁⠏⠉⠩⠍⠉⠩⡍⠛⠛⣲⠲⢶⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠛⣯⣿⣷⣂⣀⣁⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣈⣘⣓⣻⣿⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⡿⣿⣿⡿⢿⠿⠏⠟⠟⠟⠿⡿⠟⡿⣿⡿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠒⠒⠂⠀⠂⠘⠂⠒⠘⠓⠒⠒⠂⠒⠒⠀⠘⠁⠁⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠉⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣷⣄⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⢀⣴⡿⠛⠁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠙⢿⣷⣄⠀⠀⢰⣿⠇⠀⢀⣤⣤⣄⠀⠀⠀⢻⣧⠀⠀⢀⣴⡿⠋⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⢿⣷⣄⣾⡿⠀⠀⢾⣿⠉⢙⣧⠀⠀⠈⢿⣆⣰⡿⠋⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠙⢿⣿⠇⠀⠀⠈⠻⣷⣾⠟⠀⠀⠀⠘⣿⡟⠁⠀⠀⠀⠀⢰⣿⠀⠀⠀⢀⣠⣤⣤
⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣦⣤⣬⣿⡇⠀⣠⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⢸⣿⣤⣶⠿⠛⢋⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠈⠉⠉⠛⠻⠃⠀⠹⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠸⠟⠋⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣠⣤⣴⣶⠶⠿⠛⠛⠛⠉⠉⠉⠉⣉⣉⣉⣉⡉⠉⠉⠉⠙⠛⠒⠲⠦⠤⣄⣀⠀⠀⢸⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠛⠋⢉⣀⣠⣤⣴⣶⣶⣚⣛⣛⣩⣭⣭⣭⣭⣭⣭⣭⣭⣭⣤⣤⣤⣤⣀⣀⠀⠀⠉⠀⡏⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢙⣛⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢒⠏⡒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⣎⡹⣀⡇⠀⡁⡳⢸⣤⣇⣰⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⣤⢠⢴⠾⣤⢿⡟⢻⡴⡶⠐⡅⡕⣰⣯⣽⣻⡞⢤⠷⣦⡄⢠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⣘⢞⡍⢩⡍⣾⠒⣮⡸⡋⢑⡄⢀⡬⠂⢦⠀⢹⡶⢩⠁⠘⠗⠻⢸⠌⠊⡁⡚⡀
⠀⠀⠀⠀⠀⠀⠐⠼⡌⠧⠸⡇⢹⠏⠙⠷⣧⠀⣷⠏⠁⡀⡈⠵⣼⠃⣠⠴⠛⠹⡦⢸⡗⢶⠇⡧⡅
⠀⠀⠀⠀⠀⠀⠀⢟⣥⠦⣄⠻⡟⣀⠦⠀⣥⡴⠐⣴⠆⠃⠰⣶⠖⠦⣤⠀⢀⣀⠗⡞⣀⣦⠴⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣢⠰⣾⠉⣻⡥⠀⢺⠷⠀⠿⠃⠀⠈⠿⠀⠾⠵⠀⢨⣽⠋⣳⡆⢁⡒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⣛⠡⢈⡀⠀⠀⠀⠀⠀⢶⣦⡀⠀⠀⠀⠀⣄⣀⣉⠈⠛⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠛⢋⡉⢰⡤⠀⠐⠂⠀⠴⠃⠐⠂⠀⢤⡆⢉⡍⠛⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⣴⠶⣟⣻⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣛⣶⢦⣬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠒⠀⠁







⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣛⣛⣻⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢀⠴⠒⠦⡀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⢠⠃⠀⠀⠀⠘⡄⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠉⠢⡉⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢧⡀⠀⢀⡜⠁⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠈⠉⠲⢤⡀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⢀⡞⠁
⠈⠛⢶⡲⠤⣀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⣀⡤⣶⠞⠋
⠀⠀⠀⠈⠢⡈⠑⠦⡀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⡠⠚⢁⠜⠁
⠀⠀⠀⠀⠀⠘⢦⠀⠈⠲⡀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⢙⡦⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣠⠊⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠈⢦⡀⠀⡇⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢸⠁⢀⠞⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠙⣄⢿⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣠⠇⠀⠀⠀⠀⠀⢸⣠⠋⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢠⠊⠉⠉⠳⡄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠸⣀⣨⠂⠀⠀⠀⠀⡏⠀⠈⡇⠀⠀⠀⠀⢻⠀⠀⠀⠀⡅⠀⠀⠀⢰⠁⠀⠘⡆⠀⠀⢎⠀⣱⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠁⠀⠀⠀⠀⠈⠓⠤⠤⠚⠀⠀⠀⠀⠀⠑⠒⠊⠀⠀⠀⠀⠉⠁⢀⣰⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠙⠒⠦⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⠒⠊⠉⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⣀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠔⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⣀⣠⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠦⠤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠴⠖⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⣀⠀⠀⢀⠀⠀⠀⣀⣀⢀⡀⠀⡀⢀⣀⡀⠀⠀⢀⣀⠀⣠⣄⡀⢀⣠⠀⠀⠀⣀⠠⠆⠰⠆⢰⠀⣀⠀⠀⠀⠀⠀⣠⣧⡀
⠀⠀⠀⠹⣶⣬⣿⣥⣶⠏⠀⠀⠀⠀⢀⣀⢀⢀⠀⣀⠀⠀⠀⠀⠀⢯⣶⣵⣯⣵⣼⠃⠀⠀⠀⠈⢄⣶⣼⣧⣮⡤⠁⠀⠀⠀⠹⣷⣿⣿⣷⡟
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠯⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠗⠀⠀⠀⠀⠸⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣀⣄⢸⣇⢠⣀⠀⠀⠀⠀⢀⡀⡀⣰⣦⢀⣀⡀⠀⠀⠀⠀⢀⡀⠿⠇⢀⠀⠀⠀⠀⠀⢀⣀⣄⣹⣁⣤⣀⠀⠀⠀⠀⠀⢀⣸⣃
⠀⠀⢸⣿⣿⣸⡇⣼⣿⣷⠀⠀⠀⠨⣤⣀⣾⣷⣀⣤⠅⠀⠀⠘⢦⣾⣶⣿⣿⣮⣧⡜⠃⠀⠰⡟⣿⠉⢹⠏⢹⡟⣷⠀⠀⠄⣰⣾⢸⡈⣷⡄⡄
⠀⠀⠈⢻⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠙⢜⣇⣸⣀⣞⡜⠁⠀⠀⠘⢿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⡀⠀⢠⡄⠀⢀⡀⠀⠀⢠⣶⣶⣤⣾⣤⣴⣶⣄⠀⠀⠠⣄⠀⣨⠿⡀⢀⣤⠀⠀⠀⠀⣴⣶⣶⣾⣶⣦⠀⠀⠀⢀⡀⠀⢀⣴⡀⠀⠀⡀
⠀⠀⠈⢃⢰⢈⡅⡖⠨⠁⠀⠀⢸⣇⣰⣦⣿⣥⣦⣨⡿⠀⠀⢰⢫⣛⡿⡿⣿⢻⢱⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⠀⠀⠀⠈⢃⣲⣈⣭⣁⣖⡸⠁
⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠿⠿⠯⠿⠿⠉⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠉⠀⠀⠀⠀⠻⠿⠿⠿⠿⠇⠀⠀⠀⠀⠈⠿⠿⠿⠿⠾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠻⣷⣄
⠀⠀⠀⠀⢀⣾⣻⣿⣿⣿⣿⢿⣫⣽⣾⣿⣶⣶⣤⣿⡿⠟⠛⢿⣦⣄
⠀⠀⠀⠀⢸⣿⣝⣿⡽⣫⣴⠟⠋⢉⣴⣿⣷⣿⠛⠛⢷⣦⠀⠀⠹⡟⢷⡄
⠀⠀⠀⠀⣴⣟⣻⣿⣿⠋⠀⠀⢠⣿⣿⣿⣿⡏⠀⠀⠀⠙⢷⣄⠀⢹⡌⢷⡀
⠀⠀⢀⣾⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠙⣧⠀⢳⠨⣇
⠀⠀⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⣿⣼⠟⠉⠀⠀⠀⣠⠖⠀⠀⠀⠘⡆⢹⠀⡇⠀⡀
⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠠⢾⡁⠀⠀⠀⠀⠀⢹⢸⣿⢧⠇⢠
⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢠⢸⣾⡿⢋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠅⠀⢀⡤⢿⣿⠉⣷⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠄⢂⠁⠰⠋⣝⣷⡓⢌⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣩⣾⣻⣿⣿⣦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⠴⣣⣾⣷⣿⡗⣽⣿⣿⡇⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣵⣶⣷⣿⣿⣯⣤⣿⣿⣿⣿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣴⣾⣿⣿⡿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢲⠿⠾⣿⢿⣿⣿⣿⡇⠸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠉⠀⣻⣿⣿⣷⠀⠻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰⠇⠀⠘⢻⣿⢿⣿⡀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣸⠛⢸⣿⡇⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⡇⢸⣿⡇⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠸⣿⠁⠀⠀⠀⠀⡇

⠀⠀⠀⠀⢀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣀
⠀⠀⠀⠀⣈⣽⣇⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠸⡷⢠⣤⣄⠀⠀⠀⢀⡴⠒⢶⣼⣧⣴⠒⢶⡄⠀⠀⠀⠀⣀⣀⣉⣿⣉⣀⣀⡀
⠀⠀⣠⠞⡿⢹⡍⣯⠳⡄⠀⠀⠀⠀⢻⣿⣿⣸⣿⣸⣿⣿⠃⠀⠀⠘⣧⠀⢿⡀⠁⣽⠀⣠⠇⠀⠀⠀⣾⠉⣿⠉⣿⠋⢻⠍⣿
⠀⠀⣯⣼⣷⣾⣷⣾⣦⣿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⠳⣬⣷⣾⣧⡼⠃⠀⠀⠀⠀⠹⣄⠻⡄⣿⠀⡟⢠⠟
⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⢀⠀⠀⠀⠀⢿⡿⠀⠀⠀⢀⡀⠀⠀⡀⢀⣄⣰⣷⣀⣄⠀⡀⠀⢀⡄⠀⢲⠀⢘⡟⠀⠰⠀⢀⡄⠀⠀⢀⣼⡦⠀⣿⠀⢤⣿⡀
⠈⢻⣄⣤⣤⣾⣷⣤⣄⣠⠟⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠐⣦⣼⣧⣾⣷⣴⣿⣤⡎⠀⠀⠈⢧⣴⣿⣾⣿⣷⣿⣧⡴
⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⡄
⠀⠐⣦⢀⣿⣆⣼⣿⢀⣴⠀⠀⠀⠘⣇⠀⢸⣄⢀⣼⠀⢀⠟⠀⠀⠰⣆⠀⢹⡀⠀⡿⠁⢠⠖⠀⠀⠀⢶⡆⢰⣶⠀⣶⡆⢠⣶
⠀⠀⢹⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣦⣼⣷⣶⣷⣴⡏⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠈⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣭⣭⣭⣭⣽⠀⠀⠀⠀⠀⠀⢩⣭⣭⣭⣭⣭⣭


⠀⢠⡀⠀⠀⣼⣦⠀⠀⣠⠄⠀⠀⢀⣄⠀⠀⠸⡿⠀⠀⢠⡀⠀⠀⢀⡀⠀⠀⢰⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣾⣄
⠀⠀⢿⣦⣼⣿⣿⣦⣾⡟⠀⠀⠀⠀⠙⣄⣀⣰⣷⣀⣀⡼⠁⠀⠀⠈⢷⠂⠀⢙⣏⠁⠐⣾⠃⠀⠀⠀⢶⣦⠀⣹⣿⣏⠀⣰⣴
⠀⠀⠈⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⣿⣾⣿⣿⣷⣾⡏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠈⢯⡭⡽⡭⠁⠀⠀⠀⠀⠀⠀⠀⢹⠿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠩⣯⢭⣽⢿⠏⠀⠀⠀⠀⠀⠀⠈⠻⡿⠿⢿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⣴⣄⣠⠟⢧⣀⣼⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⣀⡤⠾⡌⠁⠀⠀⠉⡼⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇⠀⢀⡞⠁⠀⠀⠙⠒⠒⠒⠚⠁⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⣧⠀⠀⢀⣀⣀⠀⠀⠀⢀⣀⣠⣄⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢸⡀⢠⠏⠴⢾⠿⠉⠹⠿⠷⠆⢸⡄⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣀⣇⣀⡈⢧⣸⠀⠀⠿⠇⠀⠀⠻⠇⠀⢀⣇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠤⠤⠤⣤⠜⠀⠈⠳⢤⣀⠀⠀⠁⠀⣀⠴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣾⡀⣠⠾⡟⠛⠛⠛⡻⢟⠛⠛⠛⢻⠖⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡇⠀⠉⠁⠀⢳⠀⠀⠀⢓⡚⠀⠀⠀⡾⣄⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠳⠤⣤⡤⠖⠛⣆⠀⠀⠣⠌⠀⢀⣰⣇⡜⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢹⡉⠉⠉⠉⠉⡏⠀⠀⢳⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⡞⠉⠉⣹⢿⠉⠳⢤⡤⠋⠉⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠘⢳⠤⠴⢋⡘⠦⠤⡶⠃⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡟⠀⠀⡏⢹⡀⠀⢻⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢰⠇⠀⢸⠃⠀⣇⠀⠘⡆⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠚⠙⠲⢤⣼⠀⠀⡾⠤⣄⣹⠀⠀⣷⠲⠤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢰⠇⠀⠀⠘⡇⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣭⣭⣭⡿⠀⠀⠀⠀⢿⣭⣭⣭⣭⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⣼⣿⣯⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⢛⣹⣟⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣿⠛⡛⢽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣐⣆⣶⣰⣐⣄⣄⡀⠀⡟⣿⣿⣀⣳⣻⣟⣇⣀⣀⣄⣴⣐⣂⣶⣶⣐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⣱⡾⠛⡻⣷⢿⣿⣿⠿⣿⣭⣿⣿⣿⣀⣽⣿⣶⣿⣼⡿⠿⣿⣿⡷⣿⣞⠻⣶⣍⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣾⣾⣤⡷⡀⣿⣿⣿⣭⣤⣴⣶⣿⣿⣿⡟⢸⡤⡜⠹⣿⣿⣿⣿⣶⣤⣤⣽⣿⣷⡇⠰⢧⣤⣶⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠸⣦⣿⠟⣽⠶⡗⠆⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠓⠟⢢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠶⡳⢼⣝⢿⣿⡴
⠀⠀⠀⠀⠀⠀⠀⣙⣿⡇⢸⣿⣟⠽⣄⠒⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠊⡰⠟⣿⣿⠀⣿⡟⡃
⠀⠀⠀⠀⠀⠀⠀⠘⢽⣅⠀⢿⣅⡦⡟⠓⡮⣹⣿⣿⣿⣿⣿⡿⣿⣜⡏⢹⡏⣝⣵⡿⢿⣿⣿⣿⣿⣿⡍⣶⠛⢧⣶⣽⡏⠀⣹⡯
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⣶⣾⣿⡿⣨⣄⣨⣻⣶⡌⢿⣿⣿⠣⣽⡄⢲⣏⣱⠂⢰⣧⢼⣿⣿⡿⣰⣾⣋⢄⣬⡰⣿⣿⣶⣾⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠹⣯⢳⡦⡼⡏⢡⣛⣴⣾⠿⢻⣿⣾⣶⡄⢁⡉⢰⣮⣾⣿⠛⠿⣶⣄⣃⡉⢻⠤⢷⠏⣾⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢭⣽⠟⣿⣶⣧⣈⠻⠿⢟⣶⣎⠛⠿⢋⣰⣿⣷⣌⠛⠿⢛⣰⣶⢿⠿⠟⣠⣟⣶⡟⢻⣯⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠋⠃⠸⣿⣶⣟⡛⠙⠋⠁⠉⠉⠉⠉⠉⠉⠉⠛⠛⢛⣷⣶⡿⠁⠙⠛⠻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⡀⠈⢿⢿⣿⣵⣿⣶⠀⠀⠐⠚⡤⠀⠀⠠⣾⣷⣾⣿⠿⡟⠀⢀⣀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡶⢿⣶⣻⣛⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣛⣿⣶⠿⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣡⣶⣾⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣶⣦⣨⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠋⠑⠒⠒⠀⠒⠒⠒⠂⠒⠒⠒⠛⠛⠛⠃⠉⠉⠁







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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠠⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢰⢄⠌⢇⣄⢀⠀⠀⠀⠀⠒⠤⠊⠙⠢⢚⡇⠀⠀⠀⠀⠀⡀⠈⠑⡄⢄
⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠂⠐⢠⠀⠀⠀⠀⠀⠀⢀⠸⢀⠀⡐
⠀⠀⠀⠀⢀⠆⠐⠠⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠁⠀⠀⠀⠀⢀⠀⠀⡀⠉⣀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠐⡄⠈⡎⡐⠀⠀⠀⠀⠰⠟⠞⠳⠙⠚⢴⠀⠀⠀⠀⠈⡑⠶⠙⠚⢁⠇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠤⠄⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈⠑⠤⠋⠔⠙⡀⠀⠀⠀⠰⠀⠁⠀⠀⠁⠀⡁⠀⠀⠀⢀⣀⢄⡆⠱⠶⣤⠀⠀⠀⠀⠀⠄⡀⠀⠣⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠐⠀⠐⠢⡐⠁⠀⠀⠀⠀⠈⠤⠠⠀⠀⠘⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉
⠀⠀⢀⡀⠀⡰⠆⠀⣀⠀⠀⠀⠀⠠⠤⠴⠴⠤⢤⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠈⠲⠃⠘⠒⢹⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⡀⡦⠼⠰⣀⡄⠀⠀⠀⠀⠀⡀⡄⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠈⠀⠀⠉⢈⠇⠀⠀⠀⠠⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣽⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠞⠛⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠓⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢀⠀⣠⣄⢡⣄⡀⢀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠚⢳⠀⠀⠀⢹⣿⢸⡟⠀⠀⠀⢰⠟⠐⠶⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠉⠀⠀⠀⢀⣀⣼⣧⣶⡾⠎⠁⠈⠉⠷⣶⣦⣿⡴⣀⠀⠀⠀⠈⢉⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢰⣿⠛⠉⠉⡀⢀⡀⠃⠈⢃⡀⢀⡉⠉⠘⢻⣧⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢸⣷⠀⠀⠀⠙⠓⠖⠢⡔⠲⠶⠟⠀⠀⠀⢸⣿⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⣿⠀⠀⠴⡄⡀⠀⠸⠇⠀⠀⠀⡄⡀⠀⢸⣿⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⣿⠀⠀⠀⠻⣄⡀⠀⠀⠀⣡⠞⠀⠀⠄⣾⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠑⠀⠄⠀⠈⡈⠳⡁⡱⠞⠉⠢⠀⠀⠀⠙⠇⠀⢸⠁⠀⠀⠀⠀⠀⠀⡠⣴⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡴⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⢀⣀⣠⣄⣤⡄⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠛⠀⠀⢀⡀⠀⠀⣿⡇⠀⠀⠘⠛⠿⣿⣿⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠤⢄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣇⡀⠈⠀⢠⡾⠃⠀⠀⠿⠃⠀⠀⠀⠠⠀⣸⣿⣿⣀⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢩⣿⣶⡶⢉⡤⠦⣄⠀⠀⠀⢠⠔⠒⠀⠸⣿⣿⣏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⣠⣤⣤⣤⣤⣤⣤⡀⣬⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡆⠙⠛⠛⠛⠛⠛⠋⠀⠙⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠁⠀⠀⣠⡆⠀⠀⠰⢦⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠙⠓⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⢀⣼⣿⠟⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠈⢻⣿⣷⡄⢠⣿⣿⠃⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠃⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣄⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⢀⣠⣴⣾⡿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⣿⣏⢻⣿⣷⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⣿⣿⠟⠉⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀⠙⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠃⠸⣿⣄⡀⠀⠀⠀⠀⠀⣸⣿⡿⠋⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣿⣿⢿⣷⣦⣤⡀⠀⠀⠀⠸⣿⣷⣄⣀⣀⣼⣿⠇⠀⠀⠀⣀⣴⣿⣿⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⢀⣿⡟⠀⠉⣿⣿⠁⠀⠀⠀⠀⠘⠻⣿⣿⣿⠿⠋⠀⠀⢠⣿⡟⠋⢻⣿⡀⠀⠀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠺⣿⣷⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣶⣼⣿⣷⡄⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠭⠉⠉⠉⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣦⣤⣬⣭⣽⣿⣿⣿⣶⣾⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣍⠶⢆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⡿⡟⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠠⠀⣼⣿⡇⠠⠤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⢻⠃
⠀⠀⠀⠀⠀⠀⠀⡄⠛⠛⠁⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡣
⠀⠀⠀⠀⠀⠔⡀⠀⠀⠀⠀⠀⡀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠀⣦⣤⡔⢀⢴⠦⢀⡀
⠀⠀⠀⡠⠆⢀⠀⡶⠀⡄⠀⠄⠀⠄⠄⠲⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⡇⠈⠁⢠⣳⣏⠞⠉⠙⠂
⠀⠀⠀⣥⣘⡀⠠⠀⢁⠀⠂⡀⠀⠠⠀⢐⡠⠀⣀⡰⠀⠀⠠⢄⠀⠹⠇⠀⢠⢳⢧⣟⠀⠀⠀⠀⠂
⠀⠀⢰⣿⣿⣿⣿⣿⣶⣶⠖⡂⠀⠁⠹⣿⣿⣤⡤⠫⠁⠰⡦⡀⠑⢌⡄⢀⡏⣿⣼⡫⠄⠀⠀⠀⠰⡀
⠀⠀⣼⣿⣿⣿⣿⣿⡿⣿⠀⠁⠀⠀⢣⠘⣿⣿⣶⠶⠆⠀⠇⠈⠦⣾⣿⣼⣟⣽⣿⣯⠅⠐⠶⣤⣬⡅
⠀⠀⢿⣿⣿⠁⢰⠁⠀⡾⠘⠿⠿⠿⠿⣧⠈⣰⣤⠘⠀⠀⠠⠀⣾⣿⣏⣹⣾⣿⡿⠋⠀⣀⠔⠉⠁
⠀⠀⠘⣿⣇⠀⢾⢈⣿⡇⠀⠀⠀⠀⠀⢻⡇⠹⡇⠂⠀⠀⢠⠀⢻⣿⣿⣿⡿⠟⠁⣠⣾⣿⣆
⠀⠀⢸⣿⣿⣄⣀⣼⡿⠁⠀⠀⠀⠐⠀⠘⣿⠈⠉⠀⠀⢀⣶⡆⢠⣿⣿⡟⠁⢀⣺⣿⣿⣿⣿⡆
⠀⠀⠿⠿⠿⠿⠿⠿⠁⠦⠤⠤⠠⠤⠤⠴⠿⠇⠀⠀⠀⠼⠿⠿⠿⠿⠿⠷⠶⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡅⠀⠀⠀⠐⠀⠐⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠀⠠⡀⠀⠀⠀⠀⠛⠒⡀⠂⠆⠀⠀⠀⠐⠀⠘⠀⠀⠀⠀⢀
⠲⣶⠶⠀⡀⠄⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⢈⠀⠀⠀⠀⠄⠀⡁⢀⠾⢿⡆⠀⢀⠄⠘⠓⠀⠀⠐⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠔⠀⡀⠠⠄
⠀⠈⡀⠘⢄⠀⡀⢱⣀⡀⠀⢀⠀⠀⠀⡀⢸⣼⠆⠀⠐⠁⠀⠀⡅⠀⠀⠸⣧⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠠⢀⡆⠀⠀⡠⠂⠂⠀⣸⠇⡐⠀⠈
⠀⠀⠀⠀⠀⠁⠀⠀⠀⢈⠀⠀⠣⢴⣤⣶⡿⠿⢀⡀⠀⡀⠀⠀⠂⠰⣤⣼⠇⠀⠀⠀⠀⣀⠔⠀⠈⠳⢔⡪⢌⡲⠊⠀⡀⠀⠃⠈⠓⠊⠁⣠⣅
⠀⠀⠀⠀⠀⣦⠀⠀⠀⠪⡀⠀⠀⠀⠈⠹⠀⠰⣏⠀⠀⠅⢀⠀⠀⡀⠀⠀⠀⠀⠒⠒⣀⠇⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⡠⠂⠀⢀⣿⠋
⠀⠀⠄⠀⠠⣿⠆⠀⠠⠀⠮⠀⠀⠀⠀⠀⣶⡀⠙⠦⡀⠀⡀⣁⣴⠃⠰⠃⠀⠀⠄⠀⠀⠀⠀⡠⠞⠀⡄⠀⢰⠁⠀⠐⠁⠀⠠⢠⣴⡖⣸⣿⠃
⠀⠀⠀⠀⠉⡠⠄⠁⠐⢤⣀⣀⡠⠔⠀⣠⠇⠀⢀⣠⣈⡉⣁⠡⢤⠎⢠⠓⢀⠤⢤⡀⢈⠺⠥⣐⡨⢘⣧⢸⡀⠀⠀⠀⠀⠐⡰⣿⣿⡞⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠐⣚⣻⣬⣧⠬⠷⠾⠷⠖⠶⠛⠓⠚⠓⢒⡒⢒⠶⠾⠦⢿⣭⣿⣙⣟⣷⠍⣀⣤⢄⣴⣾⡿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⠴⠷⠚⠋⠉⠃⠀⢀⡀⠄⠀⠀⢲⡄⠀⠀⠀⣰⡌⠹⡿⠉⢛⣿⡷⠒⠒⠛⠫⢽⣛⣻⠦⣿⣝⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠁⠀⣠⠀⠸⠀⣠⠼⣏⠀⠀⠘⠛⠁⠀⠈⠓⠛⢡⣦⣿⣦⣬⣿⣇⠣⢤⣤⣸⡆⣿⡿⡛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣄⠀⠊⠀⠀⢀⣀⣉⣀⠠⢤⣴⣴⣶⣶⣦⣶⣴⣴⣦⣦⡤⣭⣭⣍⣙⣳⠶⣶⣶⣿⣎⣱⡏⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣥⢴⣶⣲⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣍⣻⢷⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⠵⣜⢦⡀
⠀⠀⠀⠀⠀⠘⡗⠢⢄⣀⠀⢀⣴⣦⡀⠀⠈⢧⠘⣰⠟⢠⠏⠀⠀⣠⣶⡄⠀⠀⣀⣠⠴⡶
⠀⠀⠀⠀⠀⠀⢱⡾⠀⢸⠀⢻⣿⣿⣿⠁⠀⢸⠆⠀⠀⢾⠀⠀⢻⣿⣿⣿⠆⢸⠁⢢⣴⠃
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠓⠤⢿⣿⣿⠤⠖⠁⠀⠀⠀⠈⠓⠦⣼⣿⣿⣇⠤⠊⢀⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⣀⣤⢀⡀⠀⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⡗⣀⠀⠠⠀⠀⠀⠒⠒⡀⠀⠂⣶⠒⠖⠀⠢⠀⠤⠍⢛⠛⢻⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣏⡀⠠⠀⠂⢒⣀⣀⣈⣀⣀⡀⣒⣃⣠⣀⠀⠀⠀⠀⠈⢻⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⣇⢠⡿⣦⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⣧⠀⢰⠆
⠀⠀⠀⠀⠀⢸⠚⣿⠉⣛⡏⢻⡟⠞⠀⠀⠀⠀⠀⠀⠀⣆⢸⣇⢰⣇⢰⡇⣰⠀⠀⠀⠀⠀⠀⠘⢧⣼⣷⠟⡙⢷⣾⣤⠟
⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣷⣾⣷⡇⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⡟⢻⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⢸⣶⣿⣶⣷⣶⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠇⠠⠿⠾⠸⠣⠷⠈⠳⠀⠀⠀⠀⠀⢤⣼⣿⣿⣉⣿⣽⣽⣿⣹⣧⡤⠀⠀⠀⠀⠐⠌⠸⠦⠆⠟⠞⠆⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠂⠀⠀⠀⠆⠄⠀⠐⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠸⠀⢀⡀
⠀⠀⠀⠀⠀⢶⡄⢀⣹⢤⢾⡁⠀⣴⠂⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣷⡠⠀⠀⠀⠀⠀⠀⠀⠰⡀⣸⣄⢼⢄⣼⡀⡰
⠀⠀⠀⠀⠀⢘⣾⣁⣹⣿⣿⣁⣹⡟⠀⠀⠀⠀⠀⠀⠀⣴⣩⣍⣯⣼⣭⣭⣥⠀⠀⠀⠀⠀⠀⠀⠀⣿⣭⣤⠶⣢⣬⣽⡇
⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣉⣉⣉⣉⣉⣉⣁
⠀⠀⠀⠀⠠⡆⢸⠿⠾⠸⠩⠿⠈⢳⡄⠀⠀⠀⠀⠀⠐⠏⠹⠷⠆⠞⠾⠌⠳⠄⠀⠀⠀⠀⠀⢶⡿⠽⠯⠽⠿⠯⠽⠯⠿⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠀⠀⠀⠘⠀⠀⠀⠘⠉⠃

⠀⠀⠀⠀⠀⠀⢀⣀⡀⢼⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢠⣿⣿⢿⣿⡿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣠⣿⣧⣼⡄⡀
⠀⠀⠀⠀⠀⠀⢻⣇⣀⣿⣀⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⣿⠀⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣽⣅⣿⣇⣽⣭⠁
⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣾⣯⣷⡿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢛⠛⠛⠛
⠀⠀⠀⠀⢀⡄⢠⣤⣤⢠⢄⣄⠤⣄⠄⠀⠀⠀⠀⢀⣰⣶⣶⣒⣶⣲⣲⣶⢲⣆⣀⠀⠀⠀⠀⠀⡠⢠⣠⣠⢠⣤⣤⠠⣄
⠀⠀⠀⠀⠀⠁⠈⠉⣉⠈⢈⠈⠀⠈⠁⠀⠀⠀⠀⠼⠿⠍⠉⢉⠉⡍⡉⠉⠩⠿⠧⠀⠀⠀⠀⠀⠓⠈⠉⠉⢈⠈⡉⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁

⣿⠿⢿⢷⢿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⡿⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⢴⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⡶⣠⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠬⢇⡠⠁⢦⣀⠘⣦⡀⠀⣰⣧⠀⠀⣠⠖⠀⣀⡌⢠⡸⡯⠘
⠀⠀⠀⠀⠀⠀⠀⢰⡤⠶⣟⢃⡄⠀⠙⣷⣿⣿⣶⣿⣿⣷⣿⣿⣴⠟⠁⢠⡘⣛⠷⠦⣖
⠀⠀⠀⠀⠀⢀⡀⠋⠰⣦⣉⠌⣿⡶⣦⠈⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣶⣿⠃⣌⣱⠆⠸⢀⡀
⠀⠀⠀⢀⡀⠬⣻⠎⠲⠀⣼⣏⡺⣿⣿⣇⠘⠛⠉⠉⠉⠉⠛⠃⢨⣿⣻⡷⣙⣯⡀⠔⠱⢟⠥⠀⡀
⠀⠀⢴⡻⣿⣾⣇⡚⢷⣌⣀⡝⠁⣿⣏⣙⠦⣄⡀⠀⠀⢀⣀⡴⢋⣙⣿⠀⢻⣄⣈⡴⢛⣸⣷⣿⠟⡷
⠀⠀⠀⠈⠋⢿⡨⠅⠈⢿⢌⣁⣽⣠⡽⡉⠿⢁⡉⠀⠀⢈⣁⢿⠉⢹⣥⣻⣈⡡⣾⠃⠀⣍⡾⠏⠃
⠀⠀⠀⠀⠀⠉⠓⠀⠐⠚⠘⠂⢀⢮⡄⢹⡦⣾⣣⡄⢠⣌⣳⢴⡞⠀⣭⠄⠀⠂⠙⠂⠀⠺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠿⠏⠙⠃⠀⠉⠁⠈⠉⠁⠈⠋⠹⠿⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠛⠶⣄⢳⣸⢃⡴⠛⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡏⠀⢀⣠⠼⠎⠧⠯⢤⣀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⣿⡟⠛⣉⣀⠀⠾⠿⠆⢀⣉⠛⠻⣿⠛⠿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⢀⡟⢀⣶⣿⣿⡿⢣⣆⢿⣿⣿⣵⡄⢻⡄⠀⠈⡿
⠀⠀⠀⢀⣠⣶⡾⠶⠶⣤⣈⠳⢄⣾⢀⡀⢻⡿⢀⣀⣿⣿⣆⠀⢿⣿⢁⡀⢻⣠⠞⣁⣤⡶⠶⢶⣶⣤⡀
⠀⠀⠀⢿⣿⣯⡀⠀⠀⣀⣨⠽⢗⣂⢸⡿⢀⡺⢿⣿⣿⣿⣿⣿⠷⣃⢺⡗⢈⡲⠯⣍⣀⠀⠀⢀⣸⣿⡿⠂
⠀⠀⠀⠀⠉⠛⠻⠛⠛⠉⢠⡞⠁⢿⡀⢀⣾⣿⣀⡀⣿⡿⢀⣀⣾⣿⡄⠀⡼⠉⠳⡄⠉⠛⠻⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣄⠀⠈⣷⡀⠛⣿⣿⠿⠞⠳⠿⣿⣿⠛⠃⣼⠃⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣿⡷⠶⣤⡀⠀⠻⠟⠂⣀⣤⠶⢶⣿⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠉⣹⢳⡞⢏⠉⠀⠀⣸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠛⢡⡏⢹⡌⠛⠶⠾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⡆⠀⠀⠘⣿⣿⣿⣿⣿⡿⠁⠀⠀⣼⣿⡆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠙⣿⣴⣿⡆⠀⠀⠹⢿⡇⠀⠀⠀⠀⢠⣿⣿⡀⠀⠀⠀⠀⢹⡿⠃⠀⠀⣸⣿⣴⡿⠋
⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⢸⣷⣤⣀⣀⣠⣿⣿⣿⣷⣄⣀⣀⣴⣿⡇⠀⠀⠀⠘⣿⡿⠁
⠀⠀⠀⠀⠀⠘⣿⣦⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣦⣤⣖⢻⡟⣲⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣀⡀⠀⠀⠀⠀⣷⣿⣿⣯⣻⣿⣿⣿⣟⣟⣼⣿⣗⡿⡀⠀⠀⠀⢀⡀⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣈⠀⢠⡀⠀⢿⣿⣿⣦⣶⣶⣶⣾⣷⣶⣶⣶⣼⣿⣿⡿⠀⢀⡄⠀⣀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⡉⣛⠓⢢⢹⡆⠀⢻⣟⣿⣭⣽⣧⣼⣧⣼⣯⣽⣿⣻⡟⠀⢰⡏⠰⠚⣛⡉⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣟⠁⠠⡿⢿⣃⡼⢁⣤⣻⠿⠿⣿⠋⢻⠙⠁⡋⠙⣿⡿⠿⣟⣤⡘⢇⣛⡿⢿⠄⠈⣛⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡳⣶⣞⣼⣿⣷⣿⣛⠅⣐⣰⣤⣤⣰⣴⣷⣦⣤⣤⣆⣂⠘⡋⣿⣮⣿⣧⣳⣶⢞⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶⢂⣾⣿⡍⡿⣯⣿⣿⣿⣿⣳⣾⣿⣿⠋⠉⠁⣙⣋⠀⠉⠙⢿⣿⣿⣗⣿⣿⣿⣿⣽⢿⠩⣿⣷⡐⡦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣽⣸⡁⠋⡶⢱⣿⣿⣿⠟⠋⣍⣉⣾⣧⣀⣠⣀⠈⠁⢀⣄⣀⣼⣷⣉⣭⠹⠻⣿⣿⣿⠞⢿⠙⢘⣇⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⣯⣷⠀⠀⢸⣿⣿⣟⣰⡿⢉⣿⣷⡄⠘⡛⡇⠀⠀⢸⢛⠋⢠⣾⣿⡙⢿⣦⣻⣿⢻⡇⠀⠀⣾⣽⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣧⣿⡀⣤⣼⣧⣿⣟⣏⣁⣩⣴⣿⣽⣾⠃⣀⠀⢀⣀⠘⣵⣯⣿⣮⣉⣉⣹⣻⣿⣿⣧⣦⢀⣿⣼⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣬⡁⠸⣇⣿⣿⡝⢻⣿⠀⢸⣿⣿⣿⠀⠙⠳⠞⠋⠀⣿⣿⣿⡏⠀⣿⠿⢩⣿⣿⣸⠇⣨⣥⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⢲⣤⣹⠿⡄⠙⣧⣿⣿⡴⢲⣦⡼⡟⢻⣿⣶⠤⢾⣷⠦⣴⣿⡟⠻⠧⣴⡶⢦⣾⣿⣼⠋⢠⠟⣏⣤⡞⠁⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣙⣷⣦⣿⣀⣿⣿⣻⣧⢺⠋⠀⢁⡾⡿⣿⣦⣤⣠⣴⣿⠿⢳⡀⠀⠹⡇⣸⣟⣿⣿⢀⣿⣵⣿⣋⣡⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⡼⠟⢻⣿⣿⣿⣿⣽⡌⣿⣏⠘⣧⡀⢻⡿⢿⡿⢿⡟⢀⣾⠃⣹⣿⢡⣯⣿⣿⣿⣿⠟⠻⢧⣤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠉⠻⠿⡿⣿⣿⣿⣿⣿⣿⣬⣄⣢⡹⠟⢳⣤⣴⠞⠹⢏⡜⣰⣥⣿⣿⣿⣿⣿⣿⢿⠿⠟⠉⠻⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣧⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣾⣅⡈⢁⣨⣷⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣼⣦⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠘⣿⣿⣿⣟⣿⣿⢹⡿⣿⣿⣿⣿⣾⣿⣿⣿⢿⡏⣻⣿⣻⣿⣿⡿⠁⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⢴⣤⣸⣿⣿⣿⣯⣻⣿⣷⣿⣿⣿⡇⢸⣿⣿⣿⣾⣿⣏⣿⣿⣿⣿⣃⣤⡦⠀⣐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣃⣶⢿⣟⣿⣿⣿⣶⣿⣾⣿⣟⠻⠃⡘⠿⣻⣿⣷⣿⣾⣿⣿⣿⣻⠿⣶⣺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣿⣾⣿⣿⣿⣿⣯⡄⢉⡏⢀⣿⣿⣿⣿⣿⡿⣿⣤⣄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠋⠁⠈⠻⢿⣿⣷⣼⣦⣴⣧⣾⣿⡿⠟⠁⠈⠙⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⢷⣦⡀⠀⠀⠀⠀⠘⣿⣆⢿⣿⣿⢆⣾⡏⠀⠀⠀⠀⠀⣠⣾⠿⠿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣤⣤⣻⡇⠀⠀⠀⠀⠀⠘⠿⣷⣶⣶⡿⠟⠀⠀⠀⠀⠀⠀⣿⢡⣤⣤⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣯⣵⡿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣭⣽⡿⠏
⢀⣴⡾⠿⢷⣦⡀⠀⠀⠀⠀⠈⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⣠⣶⠿⠿⣶⣄
⣿⡏⠀⣀⣴⢹⣿⠀⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⡿⠀⠸⣿⡄⠀⠀⠀⠀⠀⣰⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⢱⣄⡀⠈⣿
⢻⣷⣜⣛⣫⣾⡟⠀⠀⠀⠀⠀⠀⣿⡿⢿⣷⡀⠀⠀⠀⢰⣿⠃⣴⡄⢻⣷⠀⠀⠀⠀⣰⣿⠿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣮⣻⣛⣴⣿
⠀⠉⠛⠛⠛⣿⣿⣦⡀⠀⠀⠀⠀⣿⡇⠀⠻⣿⣆⠀⢠⣿⠇⣸⣿⣿⡈⢿⣇⠀⢀⣾⡿⠃⠀⣿⡇⠀⠀⠀⠀⣠⣾⣿⡟⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠹⣿⡿⣿⣦⡀⠀⠀⣿⡇⠻⣦⠈⢿⣷⣾⡟⢠⣿⠁⢹⣧⠘⣿⣶⣿⠏⢠⡿⠃⣿⡇⠀⠀⣠⣾⡿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢻⣷⠈⠻⣿⣦⣀⣿⡇⠀⠹⣷⡀⠙⠟⠀⣾⡏⠀⠈⣿⡄⠙⠟⠁⣰⡿⠁⠀⣿⣇⣠⣾⡿⠋⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⣇⢿⣎⠻⣿⣿⣿⠀⠀⠘⣷⣄⣀⣼⡿⠀⠀⠀⠸⣷⣄⣀⣼⡟⠀⠀⢰⣿⣿⡿⢋⣾⢇⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠹⠷⠈⠙⠋⢀⣴⣦⡈⠙⠛⠉⠀⢰⣶⣦⠀⠈⠛⠛⠉⣠⣶⣄⠈⠛⠉⠰⠿⠁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢀⣤⣤⠀⠀⠈⠿⠟⠁⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⢠⣤⣄⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣈⣤⣤⣤⣶⣶⣶⣶⣶⣿⡿⠿⠿⠿⠿⠿⠿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣌⣠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠛⠛⠋⠉⠉⠉⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⠉⠉⠉⠛⠛⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣶⣶⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣿⣿⣶⣶⣾⣿⠃

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣰⡿⠋⠛⣧⠀⠀⠀⠀⣿⠋⠀⠀⠙⣷⠀⠀⣾⡏⠉⠙⣷⠀⠀⢰⡿⠋⠉⢿⡄⠀⠀⣴⡿⠛⠻⣦⠀⠀⠀⠀⠀⣠⣴⠶⠶⣶⡄
⠀⠀⠀⠀⠀⢿⣇⠀⢀⣿⠀⠀⠀⠀⠻⣧⣤⣤⣼⠟⠀⠀⢿⣧⣠⣴⡿⠀⠀⢸⣧⡀⠀⣸⡇⠀⠀⢿⣄⡀⢀⣿⠀⠀⠀⠀⠀⣿⡁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠈⠻⢿⣿⡁⠀⠀⠀⠀⠀⢸⡿⢿⣄⠀⠀⠀⢠⡿⠛⣿⡀⠀⠀⠀⢹⣿⣿⣏⠀⠀⠀⢈⣿⠿⣿⠁⠀⠀⠀⠀⢀⣽⣿⣶⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡟⢻⣦⡀⠀⠀⢀⣿⠁⠈⢻⣦⠀⢠⡿⠁⠀⠘⣷⡄⠀⣠⡿⠁⠈⠻⣧⠀⢠⡿⠃⠀⠹⣷⡀⠀⠀⣴⡟⠋⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢿⣦⢀⣾⠃⠀⠀⠀⠹⣷⡿⠁⠀⠀⠀⠘⣿⣴⡟⠀⠀⠀⠀⢹⣷⣿⠃⠀⠀⠀⠹⣷⣤⡾⠃⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⢿⠃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠉⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣤⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⣷⠀⠀⠀⠀⠀⠀⣰⠞⢋⡿⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠞⣷⠶⣿⣇
⠀⠀⠀⠀⠀⣸⡏⠀⠰⣄⣿⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠟⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢹⡆⠀⠀⠀⠀⢀⡟⠀⠈⠁⠐⠃⢹⡇
⠀⠀⠀⠀⠀⢻⣧⣀⣳⣼⠏⠀⠀⠀⠀⠀⠘⣷⡀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⣿⡴⢀⡄⠀⣼⠃⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠙⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⠷⠛⠃⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⢿⣇
⠀⠀⠀⠀⠀⢠⣾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣦
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠷⠶⠶⠶⠶⣶⣶⣶⣤⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣴⠶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠉⢀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠂⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠮⢀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢿⣤⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠘⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⢀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠸⠀⢀⣘⡋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡄⢒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠢⡀
⠀⠀⠀⠀⡠⢀⠐⢿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠇⡀⠀⡀
⠀⠀⠀⠀⠲⣿⠆⠀⢦⡱⡀⠀⠔⢀⠀⠀⠀⠀⣾⣿⣿⣄⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⣾⣿⣿⠀⠀⠀⠀⠀⠐⠦⠀⣠⢿⡇⠀⢿⠶⠂
⠀⠀⠀⠀⠀⠈⢆⢆⠸⣇⠈⢆⠲⣿⠀⠀⠀⣰⣿⣿⣿⣿⣦⡀⠀⠸⣦⡀⠀⠀⠰⡿⢿⣿⣿⣧⠀⠀⠀⢸⡿⡢⠊⢘⣿⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⢷⣧⣿⠀⢽⣿⣿⣷⢄⣴⢟⣿⣿⣿⣿⣷⣝⢦⡤⠿⠇⠀⠀⠀⠀⠀⢹⣿⡝⣧⢀⠰⢟⣛⠁⢀⡜⣷⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠟⢸⠀⢸⣿⣯⣟⣛⣵⣿⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣮⣛⣛⣿⠃⢀⣿⡁⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⢀⣿⣿⠏⠀⠈⠿⠿⣿⡿⠿⠿⠛⠛⠓⠀⠀⠀⠀⠀⠴⠾⠿⢿⣿⣿⣿⣿⡇⠀⣸⡿⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠠⠼⠾⣖⠿⠭⠛⢒⣿⣿⣿⣿⣿⣿⡿⠒⠒⠒⠒⠒⠂⠀⠀⠐⣒⣂⣘⣿⠷⣤⣌⣻⣧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡔⠘⣿⣿⠀⠀⠀⢈⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣁⣀⣼⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡴⣟⣛⣿⣦⣴⣿⣿⣯⣭⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠩⣭⠭⠟⠻⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⣭⣭⣽⣿⣿⣿⣿⠷⠶⢤⣤⡴⠤⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⡆⢒⡚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢿⣭⣭⣭⣭⣍⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣽⣿⣿⣿⡿⠿⠿⠟⠫⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠻⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠕⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠰⠆⣤⢠⡄⣠⣶⣯⣤⢀⡄⢠⢠⡄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣐⣒⣲⣇⡀
⠀⠀⣀⠠⠤⠠⡀⣀⡤⣾⠃⡀⠀⠠⣤⠤⣄⠀⠀⠤⠁⠊⠉⣐⣀⣀⡂⡇⣻⣹⠓⣒⣒⣒⠐⠢⢳⡦⠀⠀⠀⣀⣴⠾⠛⠉⡏⣿⡋⠛⠷⣦⡀
⢨⠃⠀⠀⠀⠀⠀⠒⢹⣿⡜⠑⠂⣁⡀⠉⠢⢂⠀⢒⢀⠀⠀⠛⣿⠁⠀⠁⢐⠀⢰⣿⠟⠻⣶⠀⢸⠓⠀⢠⡾⠛⠁⠀⠀⠀⡇⡗⡇⠀⠀⠈⠻⣆⡀
⠺⢠⠚⣏⢹⣤⣻⣿⣟⣫⠾⡅⡜⠿⢻⣦⣔⡼⠂⠘⢈⢇⠀⢸⣟⣦⣂⢧⢨⣶⣴⢠⠈⣿⡿⠇⠚⠁⠀⡼⠡⠀⢰⠄⣄⠀⡀⣰⠋⠄⣀⢰⡀⠝⢿
⠀⢣⣽⣾⢼⣿⣿⣷⣶⣿⣶⣿⣿⣧⣼⣿⣵⠁⠀⠀⢿⣴⣿⣦⣿⣿⣿⣶⣿⣦⣷⣿⣺⣯⣭⣽⡧⠀⠀⢷⡀⠋⣽⡏⠃⠞⣺⣷⠀⠖⢩⡼⠁⠈⡿
⠀⠸⢟⠛⢻⣿⣉⠛⡉⣿⡛⣿⣿⣿⣿⢿⠇⠀⠀⠀⢼⣫⣭⣭⣭⣥⠽⠿⡿⠿⢶⣿⣿⣯⣭⣿⡇⠀⠀⢸⠽⢼⣽⣯⣤⣼⢫⣨⣯⡐⢹⡽⣅⢌⡥
⠀⠨⣿⣭⣭⣽⣬⣦⣾⠿⡷⠿⠿⢿⣿⣿⠁⠀⠀⠀⢤⠶⡥⠤⠶⠸⠄⢤⠴⠶⠸⢿⣤⣿⣿⣿⡇⠀⠀⡼⠁⠉⠛⢈⡀⠃⢘⠋⠘⣃⠹⢿⡿⢿⡧
⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠣⣤⣥⣤⣬⣤⣤⣥⣤⣬⣶⡥⠼⠶⠼⢭⡷⠀⠀⠉⠛⠐⠒⠒⠐⠀⠀⠀⠐⠒⠐⠒⠑⠊
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢠⢒⣯⣄⣈⣡⣼⣶⣲⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⢹⣿⣵⣽⠀⡀⠀⠀⠀⣤⢼⣎⠋⠛⠿⠏⠋⣹⣿⣤⡀⠀⠀⠀⠀⢸⣵⣽⣷⠈⢻⣄
⠀⢀⡤⣶⣶⡄⠀⠀⠀⠈⣿⣧⡛⠉⠁⣿⣻⣿⠀⠀⠀⡏⢿⡟⠳⠄⠀⣀⠴⠛⣽⣿⣅⠀⠀⢸⣿⢿⡇⠉⠙⣧⣿⡏⠀⠀⠀⠀⣴⣶⡦⣄
⠀⠘⠛⠻⡉⣿⣿⣦⣄⠀⢹⡏⠻⣄⠘⡃⢿⠊⣧⠀⠘⣿⣸⡇⠀⠰⣤⣿⠀⢸⣟⢈⣿⠀⢠⡟⢸⠇⠛⢀⡼⠋⣿⠁⢀⣤⣮⣿⡏⡹⠛⠛
⠀⠀⠀⠀⣵⠽⠀⠉⢻⡇⢹⣎⠿⠿⠶⡂⠈⣳⣿⣊⣱⣿⣽⡥⣠⣶⡖⣶⣦⡀⣽⣾⣿⣉⣶⣷⡏⠀⡰⠾⠿⢏⣾⠁⣿⠋⢁⢼⣷⡅
⠀⠀⠀⠰⣁⣽⠇⣤⣴⡗⣊⣿⣷⣿⣿⣛⣹⡿⢟⡿⢉⠿⣬⣞⣡⡇⣸⡛⣿⣙⣻⡽⢏⠹⣟⠿⣿⣙⣻⣿⣷⣿⣏⡚⣿⣤⡄⣿⣅⡵
⠀⠀⠀⠀⠈⠛⢻⢞⣾⣿⠟⣟⣻⣾⣿⠿⠿⠿⠟⠉⠟⠷⠶⢿⣧⣼⣿⡷⠤⠿⠿⠚⠛⠻⠚⠿⠿⠿⢿⣿⣾⣛⣟⢿⣿⣾⢾⠛⠋
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣏⠠⡤⣤⠤⣄⣀⢀⡀⣤⣤⣽⡟⢷⠤⣤⣤⣄⡀⣐⢒⣒⡲⢦⣴⣤⣬⣿⣾⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⢳⣟⣾⣶⣷⢻⢏⠉⠹⣶⣶⡜⣿⡜⠋⢘⡏⠩⣞⣛⣙⣿⠝⣝⡏⡛⣴⣿⢡⣶⣶⠋⢉⢺⣦⣿⣭⢝⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣽⣯⡗⣴⡿⣮⡻⠛⣛⡛⣰⣿⡼⣿⠸⠿⠷⠶⠭⠽⠶⠿⠿⠙⣿⠸⢿⣄⢛⡛⠛⠋⣾⣧⣜⣯⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣷⣏⣩⣭⣍⡉⢉⣉⣩⣥⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣤⣤⣤⣤⣶⣶⣶⣭⣉⡉⠋⠉⣁⣓⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠚⠃








⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⢩⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡃⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣸⡆
⠀⠀⢠⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⡄
⠀⠀⠈⠒⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣷⠛⠁
⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⠟⢛⡴⣼⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠘⣿⡏⠻⣦⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⣼⣿⣾⠃
⠀⠀⠀⠀⠀⠀⢿⣿⠄⠘⢷⣄⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠄⠀⠄⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⡀⣠⣾⡉⣿⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠉⠉⠁⠀⣰⣶⣦⣶⣷⣶⣦⣀⣀⣀⣀⣀⣀⣠⣵⣶⣶⣶⣶⣶⣀⠀⠀⠀⠀⠈⠙⠉⢉⣬⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⡾⠾⠾⠿⠟⠛⠛⠛⠛⢛⣛⣛⣛⣛⡛⢛⣛⣛⣛⣛⣛⣛⡛⠛⠛⠛⠛⠿⠿⠾⠷⢶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣉⣥⠴⠒⠒⡒⣛⣍⠉⠉⠉⠽⠡⣄⠀⠀⠀⠀⠀⠀⠁⢲⡄⠀⠀⠀⡠⠐⢿⡍⠉⠉⠉⣡⡒⠂⠀⣦⣬⡙
⠀⠀⠀⠀⠀⠀⠈⡟⢹⣇⠀⠠⠀⢸⡿⠀⠀⠀⣄⣤⡾⠂⠀⠀⠀⠠⠤⣶⡿⡗⠀⠀⠀⢁⣠⣼⡧⠀⠀⣁⣰⣿⡀⠨⡟⢹⣿
⠀⠀⠀⠀⠀⠀⠀⣷⣼⣇⣀⠤⠽⠯⠁⠐⠒⠒⠊⠙⠂⠈⠁⠀⠀⠀⠀⠐⠘⣋⣾⣶⠶⠒⠎⠓⠒⠒⠀⠒⠿⠥⠤⢄⣷⣿⣿
⠀⠀⠀⠀⠀⠀⣴⣋⣽⣤⣴⣤⣤⣴⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣶⣤⣤⣤⣠⣬⣭⣿⣦
⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⣿⣿⣿⣭⣩⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣀⣀⣀⣠⠤⠤⠤⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢸⠏⠀⣼⡇⠈⢻⠈⢹⡆
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠲⠤⢤⣀⡤⠂⠀⣀⣀⣤⡀⠀⠘⢣⣞⣦⣥⣿⣧⣧⣞⣦⠚⠀⠀⣠⣄⣀⡀⠀⠢⣄⣠⠤⠴⠒⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠒⠲⣄⠀⡎⠉⢳⠮⠤⠠⠏⠉⠛⠋⠉⣿⣿⣻⣻⣛⣻⣛⡏⠉⠛⠋⠉⠧⠤⠬⢶⠊⠉⡇⢀⡴⠒⠒⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢧⠀⠈⢄⠀⠀⣎⡗⠀⠀⣀⣤⡤⠴⠦⠶⠤⣤⣄⣀⠀⠀⢏⡆⠀⢀⠈⠀⢠⠇⢸⡀
⠀⠀⠀⠀⠀⠀⠲⠤⣀⡀⠠⠔⠃⠀⠈⠓⠦⣤⣤⣬⣧⡶⠚⠋⠉⠀⠀⠀⢐⠀⠀⠀⠈⠉⠛⠲⣦⣯⣤⣥⡤⠖⠋⠀⠀⠑⠤⣀⠀⡀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠈⠉⠉⠑⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⣴⡿⣷⡄⢀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣅⣀⣹⣿⣿⣁⣀⣭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠉⠉⠓⠲⠤⣄⠀⠀⠀⠀⠀⢩⢭⣭⣭⣯⣽⣽⣭⢯⠁⠀⠀⠀⠀⢀⡤⠴⠒⠋⠉⠉⠁⠐
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⠂⠂⠀⠐⠲⡄⠀⠀⠈⠳⣤⠖⠋⠉⠒⠒⠒⢒⡖⣖⠓⠒⠒⠊⠉⠓⢦⡴⠋⠀⠀⠀⡴⠒⠀⠀⠂⠒⠲⣄⡀
⠀⠀⠀⠀⠀⢠⠎⠀⠘⢦⣐⢠⡀⢀⡴⠃⠀⠀⠀⣼⠉⠳⣀⠀⠀⠀⠐⠈⠁⠉⠐⠀⠀⠀⢀⡰⠋⢹⡀⠀⠀⠀⠳⣄⡀⣠⢐⣠⠞⠀⠈⢦
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠈⢉⡏⠁⠀⠀⠀⠀⠀⠸⣄⠀⠈⠓⠤⣆⡀⣦⠀⢠⡆⣀⡤⠔⠋⠀⢀⡼⠁⠀⠀⠀⠀⠈⠉⣏⠉⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠉⠒⠦⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠄⣀⠠⠶⠃⠀⠀⠳⠦⢀⡀⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣆⠀⠀⠶⢿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠛⠉⠁⠀⠀⠀⠀⠈⠙⠃⠀⠀⠈⠉⠙⠻⠿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠇
⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⢠⣤⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷
⠀⠀⠀⠹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢛⣿⣿⣿⣿⣶⣶⣶⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⡀
⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃
⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⣀⣰⣦⣄⡀⠀⠀⠀⣠⣴⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢿⣿⣿⠿⠛⠀⠀⠘⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⣄
⠀⠀⠀⠀⢰⣿⠭⠵⠖⠲⣌⡷⣄
⠀⠀⠀⠀⢸⢫⠄⠀⠚⠛⢻⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⣿⠀⠞⠂⣉⣉⠙⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⢁⣀⣀⣀⣠⡴⠊
⠀⠀⠀⠀⡇⠀⠀⠐⠻⣭⡼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⡇⢰⡂⠀⠀⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣀
⠀⠀⠀⠀⢷⡈⠙⢛⣯⡵⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠰⣫⠿⠭⠋⠁
⠀⠀⠀⠀⠈⣇⢀⠀⠈⠘⣆⠻⡄⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠙⠛⠾⣷⡶⣄⠀⢤⡀
⠀⠀⠀⠀⠀⣿⠀⢷⡀⠀⠈⠃⠹⣦⡀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢷⡀⠹⣦⡀
⠀⠀⠀⠀⠀⣿⠀⠈⢧⠀⠀⠀⠀⠈⠻⣦⡿⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠻⣦⣀
⠀⠀⠀⠀⠀⣿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠈⠻⣶⣀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠉⠳⣄⠉⠛⠛⠒⠒⠒
⠀⠀⠀⠀⠀⢻⡰⡀⠘⣽⢦⠀⠀⠀⠀⠀⠀⢹⡍⢷⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⡇⣸⠀⠛
⠀⠀⠀⠀⠀⠘⣧⠫⠀⣿⠙⠿⠟⠂⠀⠀⠀⢨⣷⢾⠠⢤⣤⣤⣤⠞⠋⣠⣴⠄⠀⣧⡏
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠹⣆⡀⠀⠀⠀⠠⠴⠚⠸⡇⠀⠀⠀⠀⣀⢄⡰⡝⠁⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠨⡉⠛⠛⠒⠒⠀⠀⠘⢁⡼⠀⠀⠀⠀⠑⠒⠺⠀⢀⣼⠋⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⢦⣀⣀⣀⠀⠔⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟⠁⠀⠈⠙⠷⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣬⣉⢁⣠⡴⠶⠛⠛⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡽⠿⠿⣅⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡴⣦⣴⢞⡿⢋⡙⠛⢧⣼⡀⠻⠃⣸⣤⠟⠛⣉⠻⣟⢶⣤⡶⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠁⢀⣯⣬⡿⠛⠋⠉⠉⠀⣿⡃⣿⡇⣿⡇⠈⠉⠙⠛⠻⣯⣬⣇⠀⢹⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⢸⣤⣥⡇⠀⠀⠀⠀⠀⡟⢳⣶⣶⠞⡇⠀⠀⠀⠀⠀⣧⣥⣼⠀⢠⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⡀⢸⣬⣅⡇⠀⠀⠀⠀⠀⢧⠈⣩⡉⢰⠃⠀⠀⠀⠀⠀⣇⣭⣼⠀⢸⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠃⠈⢉⣅⠡⠀⣰⣷⣄⠀⣠⡜⢿⠿⣤⡀⢀⣴⡷⡀⠀⢀⣍⠈⠀⢛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⣾⡿⡷⢾⡷⡿⢿⠟⢿⣟⢯⢟⣿⠟⢿⢻⡷⣿⠶⡿⣯⣧⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣬⣤⣵⣯⣤⣤⡷⢿⠶⢶⣾⢿⣾⣶⢿⣶⠶⢾⠷⣽⣦⣬⣧⣧⣬⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠟⡹⢂⣿⣐⣷⣾⣠⣷⣜⣡⣙⣴⣧⣸⣶⣗⣸⣇⠺⡙⠇⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠟⠛⠣





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣀⡀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣽⣿⣿⣿⣦⡀⢀⣾⣿⣿⣿⣿⣾⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⢧⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣻⣿⣯⣵⣶⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣽⣿⣿⣷⣝⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣾⢿⣿⣿⣿⣿⣿⢻⣿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡷⠶⢟⣼⣿⣿⣭⣭⣭⡾⢿⣾⣻⣶⣿⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⢏⣽⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⡇⣿⣿⣿⣯⣿⢧⣿⣿⣻⣿⣿⣿⡿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣻⣵⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⢿⣿⣻⢿⣾⣽⣿⣿⢋⣾⣿⡿⣿⣿⣿⣿⣴⢿⣛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣎⣿⣿⣿⣶⣯⣿⡷⣾⢯⣿⣿⣿⡎⣿⣇⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣯⡻⣿⣷⢿⣧⣟⣻⣿⡿⣯⣾⣷⣽⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣽⣿⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣯⣽⣟⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠙⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢀⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣿⣿⡿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⡂⠁⢉⠉⢙⣥⡤⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⡆⣷⣿⠋⠀⠀⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⣿⡉⡷⣇⣀⠀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⢙⠷⡀⡷⣬⣼⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡶⢚⣾⠃⢳⠶⠾⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣷⡼⡠⣶⣿⣰⡿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣤⣶⡶⢶⣾⠟⣻⠯⠈⢡⠷⣿⡅⠉⠲⠿⠻⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⠛⣋⡵⠤⠒⢞⣻⠶⢚⣩⠐⠊⠀⠀⠀⠃⢀⡏⢻⠀⠀⠀⠀⠈⠙⠻⢭⢻⣯⠻⠹⢿⣿⢿⣿⣰⣤⣀
⠀⠀⠀⠀⠀⠀⠦⠞⠃⠀⠚⠁⠀⠀⠀⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⡀⠀⣊⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⠙⢪⡽⠀⠀⠀⠁⠈⠛⢿⣿⣷⣄⡀
⠀⠀⠀⠀⡶⠎⠁⠐⠀⠀⠀⠀⠀⢀⣰⠏⠰⣰⣶⣶⣶⣿⣿⠟⢁⠃⠀⣀⣽⡆⢻⠽⠻⡟⠓⣶⣶⣄⠀⠀⠛⣉⡇⡀⠀⠀⠀⠀⠙⢿⣿⢧⡄
⠀⠀⠀⠶⠃⠀⠀⠀⠀⠀⢀⣤⠀⢤⡁⢠⢁⣿⣿⣿⠟⠉⠀⠀⠈⠀⠀⡀⣈⡁⠸⡆⢀⣠⣶⣯⣏⣹⡇⢀⠀⡁⢾⡤⣄⠀⠀⠀⠀⠀⢻⣟⣷⡄
⠀⢀⠐⠂⢠⠀⠀⠀⣠⣶⠟⠀⠀⢼⡆⠈⢸⣿⣿⠃⠀⠀⠀⠀⠀⢀⡜⠁⠘⢷⠀⣼⣾⣿⣿⣿⣿⣿⣿⢠⠄⠀⢼⡇⣿⣷⣦⡀⠀⠀⠈⣿⣽⣦
⠀⣘⢺⢀⠈⠀⢀⣜⣿⠂⠀⠐⠢⢶⡇⠀⢸⣿⡧⠀⠆⢀⡀⠀⢨⠃⠀⠀⠀⠀⠰⣿⣿⣿⡿⠏⠉⣄⢭⢸⡃⡠⠶⠗⢻⣿⣿⣷⣄⠀⠠⣽⣿⣷
⠀⢈⡻⢈⠈⠀⣾⣉⠋⠀⠀⠀⠀⠀⠀⢰⠸⣿⣦⣀⠆⠈⢡⠔⠘⠄⣀⠀⠀⢄⡴⠻⢿⣿⣃⢹⣯⡿⡖⣸⠃⠀⠀⢠⡸⣿⣿⣿⣿⡆⠀⣼⣾⣿⠄
⠀⣈⣽⣽⡄⣾⣷⡟⠂⠀⠀⠀⠀⠀⠀⡦⠃⡠⠀⠑⣧⣀⡎⢠⡴⠀⠈⢀⠉⠂⣴⠒⠀⢸⣭⡥⢋⡤⠄⠙⣴⣶⣠⡟⣳⣿⣿⣿⣿⡇⠤⣿⣿⡷
⠀⠉⠉⠛⠻⡹⠷⠿⠦⢤⠀⡤⠀⠠⠘⠃⢸⢘⣦⠀⣾⠗⠁⢻⡀⢻⠀⠠⠀⣸⣯⡷⢀⡬⠻⡇⢺⣶⣦⠀⡿⣳⢏⣵⣦⢸⣿⡿⠿⠫⣼⠟⠛⢃⡼
⠀⠀⠀⢤⡀⡁⣰⢲⠀⡺⢌⠧⣴⡆⡄⠠⠈⠇⢻⣶⡟⠒⠀⣾⣿⣉⣁⢀⣀⣈⢹⣿⣿⠃⠐⢿⣾⠇⢻⣀⠁⢁⣾⡏⣸⣿⡿⢡⣶⣇⣿⣾⡿⠟
⠀⠀⠀⠀⠉⢁⡘⡩⠣⡧⢰⠛⣾⣧⡤⠖⠖⠻⠞⣿⣿⠏⠻⠿⡿⠇⣡⡈⣧⡈⠻⠿⠿⠋⠻⣿⣏⠰⡿⢻⠷⣾⣿⣟⣿⠠⣧⣸⡾⢳⠟⠁
⠀⠀⠀⠀⠀⠀⠩⣘⣤⣵⡾⢉⡛⢙⡁⠖⠒⠋⠒⠠⠰⠊⠙⠲⠆⠈⠐⠸⠇⠈⠄⠐⠆⠿⠶⠤⡄⣨⣷⣼⣷⣿⡟⣛⢹⣿⠯⣤⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡵⠃⣀⢀⠤⠤⠀⠄⠒⠂⠂⠀⠀⠀⠀⠀⠒⠒⠖⢲⡲⢚⢒⣢⣤⣤⣴⢖⠰⣟⣿⣿⣿⣼⣿⣯⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠞⠉⣀⣀⠀⠀⢪⣭⢽⡆⠘⢣⣶⣜⠀⠠⢠⡴⠾⠒⣿⣰⢮⡵⣷⣿⠛⢠⡾⠉⣿⣟⠿⣿⢿⡟⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⠈⢿⡁⡂⠀⠾⠷⠶⠃⠀⠚⠁⠘⠀⠀⢽⢭⠛⠫⠓⠸⠾⠶⣦⢿⣀⣾⣤⣠⣿⣟⣾⡽⣿⠃⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡀⢁⣀⢀⣀⠤⠄⠄⢀⡄⠠⠄⠀⠀⠐⠀⠂⠀⠐⠀⠄⠀⠀⠂⠐⠧⠤⠠⠭⣿⣯⣿⣿⣿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣅⣿⣁⠀⢨⡦⠄⢠⣨⢇⡰⠀⠐⠢⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠉⠊⠛⠛⠛⠛⠛⠙⠂⠐⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠐⠲⣄
⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠙⡆⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠀⠀⠀⣀⡀⠀⠀⣼⡗
⠀⠀⠀⠀⠀⠀⠘⡿⠀⢰⠋⠉⡟⢻⠛⠛⠋⠀⠀⠀⠀⠀⣀⣀⣠⣤⡀⢀⣀⣈⠑⢲⣤⠾⠿⠿⠷⠚⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠊⠁⠈⡇⠀⠀⠀⠀⠀⢠⣶⣿⣿⠙⠉⢿⣿⡿⣿⣷⣅⠀⡇⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⣴⣆⠀⠀⠀⢻⢏⠁⠈⣇⠀⠀⡋⢀⡵⢾⢿⣷⡏⠙⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢾⡿⣿⣿⣯⠀⢠⣶⠙⠃⠀⠀⢸⣀⣀⡼⠋⠀⠐⠋⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣏⠀⠉⠉⠁⠈⠁⣸⣯⣤⣀⠠⠄⢾⣿⡿⠁⣀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣆⠀⠀⠀⠀⠀⢻⣟⠉⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣽⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢹⠶⡄⠀⠀⠀⠘⢿⣷⣄⡀⠎⠀⢀⡇⠀⠘⢶⣼⡿⠋⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⡖⠚⡀⠙⣆⠀⣠⣄⣀⠉⢻⣿⣠⣤⣾⣿⣦⣶⣿⠧⣤⣴⣟⣉⣙⣖⣢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⣈⣶⣿⡿⢿⡟⢻⡀⠈⣹⠛⠛⡿⠟⡟⠛⢋⣴⣾⣿⣿⣿⣋⠻⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠟⠀⢠⣾⡻⣏⠉⠀⠸⠃⢀⡆⢰⠃⠀⠠⣤⠊⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡤⠄⠁⣤⣄⣷⣿⣧⡾⠀⠀⡼⡇⠀⣴⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣬⣭⣤⣀⣸⣿⣿⣿⣿⡇⠀⢸⠁⠸⣀⡿⠃⠀⠀⠉⠛⠛⠻⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣡⣤⠤⡼⠿⠧⠽⣿⣷⣄⠘⣄⠀⣸⠶⣄⠀⠀⢠⣶⣶⡤⠀⠈⠻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⡠⣀⡏⠙⢢⠀⠹⠉⠙⢎⢣⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣷⣀⣀⣸⣇⠤⢎⠀⢣⣠⣄⣸⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⠈⡆⢸⣿⠻⠇⠀⠻⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣧⡀⠛⠡⡀⠙⣶⣄⣙⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢻⠁⢀⠀⢱⣄⣸⣿⣿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠹⡄⠀⠀⠀⢠⢿⣿⣾⣯⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠙⠋⠁⢀⠇⠀⠀⢹⡀⠀⠀⢘⣨⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⡸⠀⢠⡟⠲⣧⠀⡠⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡇⠀⠛⠀⠀⢸⡞⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠰⢻⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⢀⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⡟⣠⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⣼⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⡇⢻⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⢠⣿⡿⠿⠛⠛⠿⢃⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⠈⣿⠿⠟⢋⣉⣤⣤⣶⣾⣿⣷⡀⢺⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⣿⣿⣿⣿⠇⠹⣿⣿⣿⣿⣿⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣈⣉⣙⢋⣠⣄⡙⠛⠻⠿⠟⠀⠹⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣦⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣧⠀⣉⣉⣉⣙⣛⠁⣼⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⠛⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⠿⠿⠿⠻⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡛⣛⣛⡛⢛⣻⣿⣿⠿⠿⢿⡿⠿⣿⣿⢿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⣁⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡇
⠀⠀⢀⣶⡄⠀⠀⠀⠀⣧⢠⣉⣓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⣿⣿⣦⡄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁⠄⣸⠀⠀⠀⠀⢠⡄
⠀⠀⠸⡦⣝⣆⠀⠀⢀⣙⣧⡻⣿⢏⠤⢤⣄⠀⠀⠀⠀⡰⢒⣲⣖⠿⣾⣿⢩⣊⠴⣒⣲⠦⡀⠀⠀⠀⢀⡤⠶⢤⣻⣿⢏⠴⣃⠀⠀⠀⣠⣧⡼
⠀⠀⠀⠙⣿⣿⢦⡀⣿⡭⣙⢷⣸⡿⡿⣷⢀⡇⢀⣠⡀⠻⢇⢸⡛⢳⣝⣿⡜⢡⠊⢹⢆⠕⠁⣀⣀⠀⢿⣦⠾⡑⣿⡋⠾⡛⣽⡇⢀⠴⣿⡟⠁
⠀⠀⠀⠀⠈⢻⣶⣷⢬⡶⣷⣿⡘⣉⡧⢣⠏⠀⣸⠆⢇⡀⠀⠹⠃⢸⠇⠆⠖⢾⡀⠓⠁⠀⢀⠷⢸⡀⠀⣿⠇⣟⣙⣳⣿⣯⣾⠤⣧⣾⠋
⠀⠀⠀⠀⠀⠀⢹⡛⣆⢧⣈⣼⢧⣀⠙⡦⠤⠾⠅⠁⠀⠉⠗⠒⠾⠃⠀⠆⠀⠀⠊⠑⠖⠊⠁⠀⠉⠙⠢⠤⠖⢋⣀⡟⢮⣁⠿⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢷⠧⠒⢉⣁⣤⣤⣴⣴⡶⠶⡶⠚⠛⠿⠿⠟⠛⠿⢛⣥⣔⠲⠒⠒⠂⠀⢉⡀⠀⠀⣶⣶⣦⣴⣦⣤⣬⣷⣤⣭⡏
⠀⠀⠀⠀⠀⠀⠀⠙⣶⠟⣿⠟⣯⡀⠒⢃⣀⣀⡀⠀⠀⣀⣒⡒⠒⠂⢻⣷⠿⣵⣶⣶⣶⣄⢀⣠⣶⣢⣤⣤⠛⢿⣷⡝⢻⣯⣿⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣯⠘⠏⠀⠀⠹⠿⠛⠗⣚⣛⣒⡛⠛⣛⣛⣛⣁⣀⣒⣈⣀⣒⡒⠒⡲⠷⠚⠛⠛⠛⠛⠚⠻⠇⠀⠘⣿⢫⡿
⠀⠀⠀⠀⠀⠀⠀⢰⠻⢿⣿⣿⣿⣶⣾⣥⣭⣭⣭⠍⠛⠋⠉⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣬⣥⣶⣶⣶⣦⣾⣿⠻⢟⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠠⠭⠬⠥⠾⣭⣭⣤⣤⣠⣤⣠⣶⣶⣶⣾⣛⣛⣛⠛⣛⣛⣛⣛⣛⣉⣉⣉⣉⠩⠤⠤⠤⠒⠒⠊⠉










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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣦⣀⠀⢀⣾⠟⠻⣷⡀⠀⣀⣴⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⢿⣿⠋⠀⠀⠙⣿⡿⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄
⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⣼⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣧⠀⠀⢀⣴⡦
⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⢿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡿⠀⠀⠛⠋
⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⣿⡇⠀⠀⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⣤⣤⣤⣤
⠀⠀⠀⠀⠀⣈⡁⠀⢈⣉⠀⠀⣉⡀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⢀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠛⠃⠀⠘⠛⠀⠀⠛⠃⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣿⣿⣶⣤⣤⣶⣾⣿⣁⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⠿⠟⠛⠻⣿⣄⣉⣉⣠⣿⠟⠛⠻⠿⣶⣦⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣷⣄
⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⢰⣿⣅⡀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⠀⠀⠈⣿⡆
⠀⠀⠀⢀⣾⡟⠛⠛⣿⣆⠀⣿⡇⠀⠀⠀⣴⡿⠛⠛⢿⣦⠀⠀⠀⠀⠀⠀⣰⡿⠋⠙⢻⣿⠀⠀⠀⣿⡇
⠀⠀⠀⢸⣿⡀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣿⠇
⠀⠀⣀⣤⣿⣷⣶⣶⣿⣧⣤⣶⠿⠿⣶⣤⣽⣿⣶⣶⣿⣿⣤⣶⠿⠿⣷⣤⣼⣿⣶⣶⣿⣿⣤⣴⡿⠿⣷⣄
⣴⡿⠛⠉⠁⠀⠀⠀⠀⠉⣿⡇⠀⠀⢸⣿⠁⠀⠀⠀⠀⠈⣿⡏⠀⠀⠘⣿⡍⠀⠀⠀⠀⠈⣿⡏⠀⠀⠈⣿⡆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣄⣠⣾⣟⠀⠀⠀⠀⠀⠀⣻⣷⣄⣠⣼⣿⠀⠀⠀⠀⠀⠀⢹⣷⣄⣀⣴⣿⡁
⣿⡇⠀⠀⠀⠀⠀⣠⣶⠿⠛⠋⠙⠋⠙⠛⠿⣶⣤⣠⣶⠿⠟⠋⠙⠋⠉⠛⠿⣷⣤⣠⣶⡿⠟⠋⠙⠛⠉⠛⠿⣷⣦
⠿⠃⠀⠀⠀⠀⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣶⣶⠶⠶⠶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟
⠀⢰⣶⡄⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣛⡀⢀⣛⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢠⣶⡆
⠀⠀⠉⠀⠀⠀⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣼⡸⣿⣿⣿⣿⢇⣧⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠺⠟⠛⠈⠻⠟⠁⠛⠻⠗⠀⠀⠀⠀⠀⢀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠚⠹⠛⢛⠛⢓⠀⣀⠀⣀⠒⡒⢒⡖⢒⡒⢒⡒⢲⠒⣀⠀⣀⠀⡚⠛⡛⠛⠏⠓
⠀⠀⠀⡁⠆⠀⠃⣘⣃⡈⠁⠈⠀⠉⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠉⠀⠁⠈⢁⣈⣁⠘⠀⠲⢈
⠀⠀⠀⢠⣾⣿⣿⣷⡶⣿⠖⠀⠀⠻⠿⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠿⠟⠀⠀⠲⣿⣶⣾⣿⣿⣷⡄
⠀⠀⠀⡈⠿⠿⡛⢛⡚⢡⡀⢠⠀⣤⠀⡤⠀⡄⠠⠆⠰⠆⠰⠄⢠⠀⢤⠀⡤⠀⡄⢀⡌⢓⡛⢛⠿⠿⢁
⠀⠀⠀⢀⣭⣤⡵⠶⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⢮⣤⣭⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⢊⣴⠀⠀⠀⠀⠀⠀⠀⠐⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⢰⡅⠂
⠀⠀⠀⢈⣵⡈⢉⠢⠀⢀⡀⠀⠀⠀⢀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⣀⠀⢀⣾⠋⢴⣅
⠀⠀⠀⠀⠙⡤⡀⣷⠑⡄⢴⡇⠀⠀⣸⣿⣿⣷⣄⠀⠀⣌⡁⠀⠀⢾⣿⣿⣷⡀⠀⠀⣶⢄⠄⢻⡏⠀⠈
⠀⠀⠀⠀⠀⠘⣶⣾⠀⣿⣾⣿⣄⡴⣻⣿⣿⣿⣿⣷⣤⠛⠃⠀⠀⠀⠀⣿⣿⢷⣀⠼⣛⠁⢠⠾⣷⠇
⠀⠀⠀⠀⠀⠀⠈⡁⠀⢹⣿⣿⠿⢾⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⣠⣿⣿⣷⣭⣽⠏⠀⣿⠄⠋
⠀⠀⠀⠀⠀⠀⠀⢹⠀⣸⣿⣯⣤⣀⣭⣿⣿⣭⣭⣭⣭⠤⠄⠀⠀⠈⠉⡉⣙⢛⣟⣟⡀⠴⣟⡠
⠀⠀⠀⠀⠀⠀⠀⠈⣨⢱⣾⡇⠀⠀⢸⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⠉⣹⣭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⣿⣦⣴⣿⣿⣭⡭⠤⠤⠄⠀⠀⢀⣀⠀⠈⢉⣉⡭⠿⠿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢾⣿⠿⠿⢿⣿⡟⠓⠲⠖⠒⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⡤⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠓⠒⠒⠒⠶⠶⠶⠒⠒⠒⠒⠒⠚⠛⠛⠛⠋⠉⠉






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣤⣉⣿⣟⣡⣤⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⡼⠋⠁⠀⢈⣿⣟⠉⠁⠀⠸⡆⠀⠀⠀⠀⠀⠀⡆
⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣠⣿⡀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺
⠀⠀⢀⠐⡴⠒⢀⡀⠀⠀⠀⢀⣹⣼⣷⡶⣴⡄⠀⠀⠀⠀⣌⠛⢛⣄⣀⠄⠀⠀⣴⡴⣶⣾⣼⣃⠀⠀⠀⠀⢀⠀⠒⡄⢀
⠀⠀⢈⢿⣿⡆⠀⠀⠀⠀⢠⠾⠿⢿⣏⠀⠈⠇⠀⠀⡠⢚⡟⣼⡟⢛⠢⡀⠀⠀⠟⠀⢈⣿⠿⠿⢦⡀⠀⠀⠀⠀⣾⣿⢏
⠀⠀⠘⠋⠉⢻⣆⠀⢀⠀⠻⠄⠀⠈⣍⣲⣤⠤⠤⠾⠖⠚⠛⠛⠛⠻⠶⢾⣦⣤⣤⣤⣊⡍⢀⠀⠼⠃⠀⠀⢀⣾⡋⠉⠛
⠀⠀⠀⠀⠀⠙⠷⢴⣧⣀⣀⠤⠚⠋⢙⣲⣤⣤⠤⠶⠒⢒⡶⠒⠲⣖⠒⠺⠿⠭⣭⣀⣈⠉⠙⠢⢄⣀⣠⣷⠴⡟⠁
⠀⠀⠀⠀⠀⠀⠉⠠⣿⣏⣀⡴⠖⠛⠟⠁⠀⣠⡴⠀⠀⢽⣷⠤⢴⣿⠇⠀⠠⣤⡀⠀⠙⠟⠓⠶⣤⣾⣿⣧⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⠋⣥⠀⠀⣶⢦⣿⣿⣿⠷⠿⠴⠶⠾⠿⠶⠿⢷⣿⣿⣿⣧⣶⣆⠀⢠⡌⠹⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⣹⠼⡟⠉⠉⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣬⣯⣄⣀⣀⠈⠉⠙⠻⢼⣉⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣠⣵⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠛⡉⠉⠉⠛⠻⣍⡉⠉⠉⠉⠉⠉⠉⠙⠻⠟⠛⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠌⠀⠀⠀⠀⠄⡌⡸⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⡀⠀⢀⣤⣤⡄⠀⢀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠃⠀⡼⠛⠿⠓⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⡶⢾⡀⠀⢰⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠠⠀⠀⢸⠇⠘⡇⠀⠘⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⢀⠄⠀⠎⠀⠀⠃⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢠⠤⠀⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠸⠇⠀⠀⠀⠀⠀⢀⡀⠤⠀⠐⠒⠊⠉⠁⠀⣠⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢐⡂⠤⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡪⠛⠁⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣋⠔⠀⣠⠔⠊⠁⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣠⣶⠗⠋⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡿⢛⡡⢔⡠⢔⠮⠐⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣟⣉⣔⡩⠦⠥⠬⠤⠤⠥⠤⠤⠤⠤⠤⠤⠀⠀⢡⣀⣀


⣿⣿⡟⠛⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⢀⡠⣿⣏⣹⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⣠⣿⣯⢿⣿⣶⡤⢤⣄⠐⣿⡿⢽⣧⣿⡭⢿⣿⠒⣤⡤⢠⣶⣿⡿⣴⣿⣄⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠙⣷⣶⢤⡄⣤⡎⢿⡏⢹⣿⣏⠙⠿⣾⣿⣶⡝⠆⢨⣿⣿⡁⠸⢯⣶⣿⢧⢿⠋⣽⣿⡟⢹⡿⣰⣆⢤⣤⣶⣿⠏
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣞⣿⣿⣍⣴⣿⣿⣷⣶⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣾⣿⣿⣿⣶⣾⣿⣿⣦⣬⣿⣿⣳⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣟⣳⡿⣟⢻⢹⣟⣛⣻⡽⠯⣿⡿⢭⢩⣿⣛⣻⡟⡝⣻⢿⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣴⣾⠷⠖⠛⠓⠚⣚⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣙⣓⣒⠚⠛⠾⠿⢷⣶⣿⣯⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠟⣋⣭⣥⣶⣶⠟⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠈⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠳⣶⣶⣬⣭⣛⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⠿⣿⣿⣿⣿⠶⠶⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡶⠶⠶⣿⣿⣿⣿⠿⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⡄⠀⠀⠀⣠⣿⣶⣤⣤⣤⣾⣿⢿⣷⣤⣤⣤⣴⣿⣄⠀⠀⠀⢀
⠀⠈⢀⣤⡀⠀⠈⠃⠈⠀⠠⠀⠈⠁⠀⠄⠀⠀⠘⠁⠀⠀⣠⣄⠁⠀⠀⠘⠷⠲⣾⣿⣿⣽⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣯⣿⣿⣷⠖⢾⠃
⠀⠀⢨⡿⢉⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⡉⠻⡇⠀⠀⠀⠀⠘⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣄⠃
⠀⠀⠐⠋⣭⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣭⡝⠃⠀⠀⠀⠀⢠⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠄⠈⠄⠀⠀⠀⠀⠀⠀⠀⡾⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠌⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⣐⠀⠀⠉⠈⠉⠟⠀⠀⠀⠀⠈⠀⡀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠉⠀⠀⠀⠀⠀⠀⣠⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⢀⣤⣤⠀⡆⠀⢀⠔⠀⠀⠀⠀⠔⣠⣤⣄⢠⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⡑⠛⠀⢀⣤⣾⣦⣠⣶⣦⡀⠀⠙⢂⣿⡆⠄⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠙⠻⠶⢿⠟⠋⠉⢈⡁⠉⠙⠻⡿⢶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠂⠄⠜⠣⠀⠄⠊⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣌⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣈⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀⠀⠀⠀⠘⠛⠛⠛⠢⠀⠀⠀⠀⠀⠀⠀⡀⠘⠛⠛⠛⡄⠀⠀⠀⡀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠛⠛⠛⠛⠛⠛⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠸⠉⠉⢹⠀⠯⠉⠉⠽⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⡈⠀⠰⠀⠀⡄⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣷⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣀⣀⣠⣄⣠⣄⣀⣀⣥⣀⣇⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⣿⣿⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠸⠟⠋⠁⠀⠀⠀⠈⠙⠻⠷⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣽⣯⣿⢷⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄⢀⣀⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⣿⣿⡏⢘⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⣿⣿⣧⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣻⣿⣋⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⡿⢿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⣾⣿⣿⣿⡆⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠾⡿⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠙⠿⡿⠟⠁⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⡀⠒⡗⠂⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣦⣼⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣽⣿⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠬⠀⠀⠀⣀⡀
⠀⠀⢠⣄⣾⣦⡀⣠⠤⡹⠻⣆
⠀⢀⣠⣼⣿⢿⠄⠂⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠖⠓⠘⠛⣿⢰⡄⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢈⣧⣿⣞⣋⠉⠈⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡄⠀⠐⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣤⠾⢻⡙⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣽⣿⡃⠉⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠸
⠁⠀⠸⢳⣿⢳⡦⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⢙⢹⣧⡄⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠑⠒⢰⣾⣖
⠀⣀⣴⣶⣿⠻⠇⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢾⠯⠅⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢈⣽⡟⠙⠢
⠛⠁⢘⠹⣿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠰⢸⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠘⠀⠉⠨⣿⣿⣤⡀
⠀⠀⡝⢂⣿⠄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⢴⣾⣟⠇⠀⠙⠆⠀⠀⡠⠖⡀⣠⣤⠀⠀⠀⠀⢀⣤⢤⣾⡶⠀⠈
⠀⠀⡄⠘⣿⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⢹⡏⠃⠀⠀⠀⠀⠀⠀⣀⡀⣹⡿⠲⢄⡀⠀⠁⠀⢘⣽⡿⠖⡤
⠀⠰⠈⢤⣿⠃⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⡇⠃⠀⠀⠀⠀⠀⠘⠉⠉⢿⣿⣤⡀⠀⠀⠀⠀⢀⢸⡇⠂
⠀⠐⠀⢸⣿⡂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣼⡇⠤⠀⠀⠀⠀⠀⠀⡠⠀⢺⡏⠀⠈⠀⠀⠀⠀⡀⢼⡇
⠀⠁⠈⣺⢿⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣸⡇⢈⡀⠀⠀⠀⠀⠀⠀⠀⢾⡟⡉⠂⠀⠀⠀⠀⠁⣸⡇⠰
⢸⣳⣄⢼⣾⡧⣀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⡀⣭⣧⡀⠂⠀⠀⠀⠀⠀⠀⠀⢊⡇⠀⠀⠀⠀⠀⠠⠁⣼⡇⢀⡄
⣻⣀⣈⣻⣻⣃⣉⣹⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣏⣈⣿⣗⣉⣵⣀⣀⣀⣀⣀⣀⣀⣠⣇⣀⣀⣀⣀⣀⣸⣉⣻⣟⣉⣇
⣿⣿⠋⠛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠇⠀⠀⢀⣴⣿⣿⠆⠀⢀⠀⢀⢄⠘⠻⡂⣠⡞⢻⣿⠇⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣩⣾⣿⣆⢸⣿⣾⠿⣄⡀⣘⣄⣨⠝⠳⢄⣹⡝⠛⠛⣧⠸⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢦⣥⣬⡽⠂⣶⡎⣽⢂⣬⡅⢂⣶⣦⡁⠾⡛⠦⣈⠃⢀⢸⡅
⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⢀⠲⢀⡠⠔⠁⢀⡈⠀⢄⠀⠀⢫⠘⣯⠀⣾⣯⣻⣷⣞⣴⣶⡈⠓⢈⢠⡶⠂⣈⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠛⢁⡁⡤⠐⢉⡀⠘⠀⣈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠠⣘⠋⠀⠃⣀⢀⡄⡌⠛⠛⣿⠏⣁
⠀⠀⠀⠀⠀⠀⣀⠴⠃⢪⠀⠀⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡉⠀⠀⠀⠀⠸⢦⡀⢲⣄⡸⠆⣿
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⡔⠀⣩⣴⢄⡀⠑⢀⣈⡁⠀⠹⠇⢄⠠
⠀⠀⠀⠀⢠⠁⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠘⠃⠈⠤⣬⡭⡄⠠⡀⠐⠈⠟
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢰⠂⠀⠺⠗⠂⠀⡀⠀⠇⠈⢹⣶⣿⣿⣧
⠀⠀⠀⠀⢸⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠠⠀⠀⢠⡾⠷⠄⠠⣆⠸⣿⣥⣿⣿⠆⠀⠀⠁
⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠄⠀⢤⡀⢀⡄⠀⡐⠄⠙⠀⢈⡏⠛⠷⢰⡄⢶⡾⢶⣄
⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠾⣀⠀⣀⣀⢻⡿⣷⡘⡀⠲⡄⠁⢀⠇⠰⣽⡇
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⢙⡿⢿⡿⠉⠀⠈⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⡘⡧⠿⣧⣹⡏⢬⣦⠀⢰⡫⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⢿⣧⣝⡫⠸⣷⣼⣇⣀⣴⣾⠯⠠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠠⢴⣶⠌⢀⠄⠠⠙⠁⠌⠉⣠⠈⢹⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣟⠲⢾⣯⡁⠀⣿⣿⣿⣿⣿⣥⣴⡒⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣠⡄⠀⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡷⢀⡼⠷⠒⠘⢻⡩⡛⠛⣯⣉⣃⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢠⣿⠇⠀⠀⠀⡼⠀⠀⠀⠀⠀⠄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⡷⢌⠃⢀⢠⡄⢸⣿⣿⡰⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⣿⡇⢸⣁⣠⣤⣄⡀⣶⣿⣿⣦⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠚⢿⣯⡿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠏⠙⠦⡿⢶⣾⠿⠋⢸⣿⣼⣿⡷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡅⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢠⠀⠰⠦⣀⢳⠈⣤⢟⠁⠈⢄⣰⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣥⣴⡅⠂⠈⢌⠀⠈⠢⠀⠀⢄⢈⣿⣧⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢻⣿⢀⣦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣟⡣⠀⠀⠈⠁⠀⠀⠠⠀⠀⠉⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣟⣸⠃⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠁⢀⠿⡧⣀⠀⠀⠀⠀⠀⠈⠠⠀⠀⡀⠀⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡢⡆⢯⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢋⣿⣷⢢⠀⡌⠑⣀⣀⠀⠘⡑⠁⠲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣡⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢤⠀⠀⠟⠁⣥⣠⣅⣼⣿⡉⢛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠑⣢⣤⠆⠀⣿⠻⣿⣏⣻⣿⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠯⠉⠀⢀⣿⣠⠟⠻⠿⠟⠧⡄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠁⠘⣤⠀⠀⢊⠙⠗⠶⠄⠁⠀⢄⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠐⠀⠢⠀⠠⠀⠀⢰⣦⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠀⠂⠀⠀⠐⠀⠈⠙⠤⣄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠒⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⣀⠰⠆⢠⢀⡀⠀⣀⣤⣧⣤⡀⠀⢄⢀⠐⠀⣄⡀⠀⣀⡤⠤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠠⡄⠆⠈⠃⠴⢠⠄
⠀⠀⠻⣷⣴⣆⣺⡟⠁⠘⢿⣯⣧⣿⠟⠀⠀⠶⣾⠷⠶⠀⠀⠙⣶⣼⣏⣿⠏⠁⠀⣠⠴⠶⠒⠋⡛⣉⠑⢶⡤⣄⠀⠀⢸⣿⠀⢸⣿⠅
⠀⠀⠀⠀⠀⠀⠀⢤⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣇⣒⢼⣮⣡⣿⡌⣭⣼⢗⣺⠇⠀⠈⠉⠛⡉⠉
⠀⠀⠀⠀⠀⢀⡀⣿⣷⣀⠀⠀⠀⠀⠀⠐⠊⣀⣅⣩⣍⠒⠀⢰⣟⣾⢿⣿⣷⠀⠀⠀⠙⡭⠕⢲⢒⡐⠘⣭⠛⠉⠀⠀⣠⣄⣼⢧⣄⣄
⠀⠀⡴⢛⣿⡏⠈⣿⣿⠀⢻⣿⡛⢦⠀⠀⠀⠿⠥⠽⠇⠀⠀⠀⠙⠯⠬⠟⠁⠀⠀⠀⠀⠹⠨⠬⠬⠥⠬⠞⠀⠀⠀⠀⠙⣿⣃⣔⣛⠏
⠀⠀⢷⡈⠻⣧⢀⢩⡇⡀⣝⡟⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠀⠀⢠⠠⠤⠖⠄⠄⡀⠀⡀⡄⠠⢀
⠀⠀⠀⠱⣷⣿⠏⠈⠁⠀⢝⣾⠏⠀⠀⠀⠀⣶⣲⣆⣲⡌⠀⠙⣭⠁⠡⢹⠝⠁⠀⢰⡎⠈⣿⡆⠀⠀⠑⣶⠈⣶⠀⠀⠀⢐⣿⣯⣯⡶
⠀⠀⠀⠀⠛⠛⠛⠓⠛⠛⠛⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⣀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠉⠛⠉⠀⠀⢀⡀⠈⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡐⠳⣆⠀⡄⢉⣷⠀⠀⠘⡆⠀⠀⡤⠀⠀⠀⠀⢀⣀⣄⡀⠀⠀⠀⠀⢀⣼⣄
⠀⠀⠐⢄⣷⣈⣃⣴⣦⠆⠀⠤⣤⡀⣄⣹⡇⠘⢶⡟⠀⠙⣿⠋⠀⢰⡾⠃⢸⣠⡿⠀⠀⣴⠀⠐⠷⠿⠀⠀⢠⡶⠛⠃⣿⡄⠙⠻⣦⡀
⠀⠀⠀⠈⠛⠿⠟⠙⠃⠀⠀⠢⣼⣟⠈⠙⠃⠀⠀⠁⠀⠀⣸⡀⠀⣼⡁⠀⣸⠋⠁⣰⠶⠏⠀⠀⣀⠀⠀⠀⠟⢒⣉⡄⢠⠀⣀⣉⠘⠇
⠀⠀⠀⠀⢀⡀⢀⡄⠀⣀⡀⠀⠀⠈⠷⣤⣤⡐⠖⠂⠸⠶⢿⣿⣿⣿⣿⣿⣿⣤⠔⠁⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠙⠁⠈⠀⠛⠁
⠀⠀⠘⠲⣼⣗⣈⣉⣠⣾⡴⠋⠀⠀⠀⢹⡷⠾⠒⠘⣛⣈⣛⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⡤⠖⠋⢓⠑⠲⢤⡀⠈⠀⠂⠒⠂
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠁⠀⠀⠀⠀⠘⠛⠛⠿⠿⠟⠚⠃⠒⠀⠀⠉⠙⠛⠃⠀⠰⠵⣒⡟⠋⠈⠙⢿⣶⣼⠆⠀⠀⠀⠄⠨⠇
⠀⠀⠀⠀⠀⠀⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⣀⢠⢠⠄⡄⡀⠀⠠⠀⣐⣆⡀⠤⠀⠀⠈⠛⠃⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⢰⡞⢳⡆
⠀⠀⡠⣤⣄⠠⠷⠤⡿⠿⡧⠴⠧⢀⣤⡤⡀⠈⠛⠛⠛⠚⠁⠀⠀⠙⠻⠿⠛⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠉⠁⢀⣀⣼⣆⣀⡀
⠀⠀⠀⠈⢋⡠⡔⠤⠦⢢⠔⡤⡤⣌⠉⠀⠀⣀⡀⡄⠄⡠⣀⡀⠀⠀⠀⡄⠀⠀⠀⠀⣀⣀⣄⣀⡀⠀⠀⢰⣿⣿⢶⣾⣻⣶⣿⣷⡆
⠀⠀⠀⠀⠀⢛⡩⠭⢯⣯⣯⡭⢿⠇⠀⠀⠙⢷⣦⣤⣴⣶⡦⠉⠁⠘⣿⣿⡿⠀⠀⠐⠿⣇⣈⠿⠗⠀⠀⠀⠙⣿⣯⢭⣭⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠈⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠉⠉⠙⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣷⠀⠀⣀⠹⢦⣄⣀⣤⠞⢁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡄⠀⠒⠒⠒⠒⠒⠒⠒⠀⣿⠀⣾⠋⠁⠀⠈⠉⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠐⠷⠟⠁⠀⣛⣛⣛⣛⣛⣛⣛⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⣤⡼⠃⠀⠶⠶⠶⠶⠶⠶⠦⠀⣿⠀⠻⣦⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠁⠀⠀⠶⠶⠶⠶⠶⠶⠖⠀⣿⠀⠀⠻⡶⠶⠶⠶⠶⢶⡞
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡶⢶⡄⠀⣉⣉⣉⣉⣉⡉⠉⠀⣿⠀⠀⠀⡇⠀⢰⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⠾⠃⠀⣭⣭⣭⣭⣍⠁⠀⠀⣿⠀⠀⢰⡇⠀⢸⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠘⣧⣀⣸⣇⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣾⣿⣿⣷⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⣶⠀⢰⣶⠀⠀⢀⣉⣉⣉⣉⣉⣉⣉⣉⡀⠀⠀⢀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⢈⣿⠀⠀⠘⠉⠋⠉⠉⠉⠉⠉⠙⠁⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠿⠀⠘⠿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⢶⠀⠠⡶⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡄⠛⠶⠶⠃⣠⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠹⣿⠀⣿⣿⣿⠏⢡⣤⣄⠹⣿⣿⣿⣿⣿⠏⣠⣤⣄⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⢀⣿⣿⠿⣿⣿⡀⢿⣿⡿⠀⣿⣿⠿⣿⣿⡀⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣤⣈⠉⢠⣴⣄⠉⣁⣤⣀⣤⣄⠉⣠⣴⣄⠉⣁⣤⣀⣤⣀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠻⣿⡿⠀⣿⣿⣿⣿⣿⡀⢻⣿⡿⢀⣿⣿⣿⣿⣿⡀⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⢋⣁⣤⣤⣤⣄⡉⠛⠿⠟⢋⣁⣤⣤⣤⣄⡉⠻⠿⠟⢉⣡⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠃⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧




⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢉⠀⠈⠐⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣈⡑⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣉⣡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⣉⡑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡀⢨⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠨⠀⠨⢀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠑⠢⡔⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠰⠀⠠⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡶⢤⠖⠋⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡜⡁⠌⢦⠀⠀⠀⠀⢣⠘⢆⠀⠀⠀⠃⠀⠀⠀⠀⡰⢡⠂⠀⠀⠀⢣⠀⠀⠀⠀⠀⠁⠀⠀⢀⡜⡀⡇⠀⠀⠀⠀⡔⠁⢌⠳
⠀⠀⠀⠀⠀⠀⠱⢤⣤⡎⠀⠀⠀⠀⢸⠸⣎⢣⡀⠀⠀⠀⠀⠀⡰⢡⠃⠀⠀⠀⠘⠄⢂⠀⠀⠀⠀⠀⠀⢠⠎⠸⢳⠃⠀⠀⠀⠀⢱⣬⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⢆⠀⠀⠀⠈⡇⠈⠢⡙⢦⡀⠀⣀⠞⡰⠁⠀⠀⡀⡀⠀⠈⢄⠢⡀⠀⠀⢀⠔⡡⠊⠀⢸⠀⠀⠀⠀⡰⢃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢂⠳⡀⠀⢀⠇⡆⠀⠈⠢⠄⠀⠤⠊⠀⠀⠀⢸⠀⠈⠂⠀⠀⠑⠬⠁⠈⠅⠈⠀⠀⠀⠸⡀⠀⢀⠞⡵⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⢆⠑⠌⣁⡋⠰⢀⠔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⡀⠢⡉⣉⠡⠊⣰⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡀⠀⠀⠘⣄⢰⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠐⠁⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠑⠁⠀⠀⢀⣁⡀⠤⡤⠤⠠⠤⠀⠐⠒⠒⠂⠒⠒⠀⠀⠀⠤⠤⠠⠄⢀⣀⡀⠀⠈⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠤⠒⣂⢉⠥⠠⠄⠐⠒⠒⠂⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠒⠒⠒⠠⠤⠠⠈⣉⠒⠢⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⠁⡀⡀⠀⠀⠀⠀⡐⠐⠀⠀⠀⠀⠀⠁⠈⠂⠀⠀⠀⠀⠒⢢⠀⠀⠀⠀⢀⡀⠈⠁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠂⠀⠁⠜⠀⠀⠀⠀⠈⠈⠀⠀⠀⢀⣀⣁⣈⣀⡀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠣⠘⠀⢸⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡤⠀⠐⠀⠀⠀⣀⣀⣀⡀⠀⠀⠠⠤⠤⠤⠤⠤⠤⢀⠀⠀⢀⣀⡀⠀⠀⠀⠐⠂⠠⢬⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⣀⣠⣥⠤⠄⠒⠲⠒⠒⠲⠖⠒⠒⠒⠒⠒⠒⡖⠒⠒⠒⠒⠒⠦⠀⠤⢤⣤⣀⣂⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠠⠌⢭⢀⣐⣒⣒⠒⠒⠂⠀⠀⠒⠀⠀⠠⠃⠀⠀⠒⡀⢒⣚⣒⣂⠈⠭⠱⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠠⠀⠀⠀⠀⠀⡀⠐⠶⠀⠀⢘⠃⠀⠀⢄⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣯⠢⡀⠀⠀⠾⠳⡄⠀⠀⠀⢀⠘⠀⠀⠀⠐⠁⠠⡀⠀⠀⠀⠀⠀⣤⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⣽⡆⠈⠲⣏⡀⠀⠘⡂⠄⠀⠀⠀⠀⠀⠀⠀⡠⠴⠳⡖⠂⠙⠆⠠⢼⣟⣋⣉⠐⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠐⠀⠀⠀⢠⡄⢹⡀⠀⣉⣉⠀⠀⣿⡌⠠⣠⠀⡠⢀⠄⠈⠀⠐⠣⡁⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠄⠀⠀⠀⣹⠦⢿⡈⠀⢁⢼⡌⠉⠻⢆⢿⣄⡿⣳⠆⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠈⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⣀⠀⠴⣷⡿⠁⠀⠘⣑⠀⠀⠀⠛⠦⠀⠪⠞⠋⠷⠁⠀⠘⠀⠄⠀⠀⣿⣤⡼⠀⠀⢀⡤⠶⠛⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠦⢿⠓⠖⠉⠀⠀⠀⠀⠘⣶⡴⢦⠐⠀⠀⠀⠀⠀⠀⡁⠐⢃⡀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⣀⠤⠤⠀⠐⠂⠈⠹⠋⠙⠛⠒⠒⠂⠀⢴⠇⠀⠀⠑⠀⠀⢠⠀⠀⠜⠀⠀⠀⠏⠀⠀⠀⠹⡿⢿⣷⡆
⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⣀⠣⠄⢀⠀⠈⠄⢢⢸⡀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⡘⢻⠈⠁⠀⠢⡄⠠
⣠⠞⠁⠀⠀⣦⠄⠀⢀⡐⣈⠅⠀⣀⠀⠀⢴⣽⡶⠂⠀⠀⠀⠀⠠⣼⣌⣿⣷⣾⠦⠀⠀⠈⠀⠀⢁⠀⠀⠜⠀⠈⡀⠀⠀⠀⣼⡃
⠀⠀⠀⠀⠰⣈⣆⣱⡉⠙⠓⠒⢈⠀⠐⠚⠋⠉⠁⠑⠀⠀⠀⠀⠀⠈⢻⠿⣿⢧⠶⠛⠂⠀⠀⠀⠉⠀⠤⠤⠀⠀⠓⠂⠐⠈⠀⠀⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠏⠛⠁⡁⠀⠀⠀⣾⠻⣶⡤⠄⠤⠤⠤⠠⣔⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⢀⡀⠐⠂⠀⠉⠁⠀⠠⣄⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠃⠀⠀⠹⣏⡀⠀⠀⠈⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⢏⠒⠚⠀⠀⣎⣀⢀⡀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⡋⢄⣤⠂⠁⠘⣿⣿⣶⠁⠠⠙⠖⠀⠀⢢⣤⣼⠖⠀⠀⢀⡴⠁⠀⠐⣶⣿⡻⠿⠛⠓⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⣴⠄⠠⢤⠔⠒⠈⠈⣟⠉⠀⠀⠀⠄⠉⠿⡷⠀⡀⠘⠀⠀⠀⡘⠙⠉⠀⠀⠀⡘⠁⢠⣾⣿⣿⡏⠃⠀⠀⠈⠁⠐⢀⠁
⠀⠀⠷⠊⠹⡶⠰⠁⠀⠀⢀⣾⠋⣠⣠⠀⠀⠀⠀⠀⠴⢻⡅⣰⠀⢀⡼⠁⠀⠀⠀⠀⠠⠀⡠⠁⠸⠟⠋⠙⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢃⡾⠁⠣⣀⠀⣠⠎⠀⠀⢸⣷⡏⢀⠚⡅⢢⡐⠀⠀⢀⣀⠜⠁⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣔⡈⠹⠊⠀⠀⠀⡩⢺⡁⠀⠀⠀⠊⠙⣦⠧⠄⠠⠟⢳⣶⡆⡅⢸⡀⢀⡀⠀⠀⠀⠀⠹⡄⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⢰⡶⢚⣿⡤⠔⠉⠀⠀⠀⠀⠀⠉⠘⠓⠠⠛⠁⠀⠇⠁⠀⡰⠉⠀⢁⠀⠀⡉⠀⡶⠂⠒⠦⢍⣁⣀⣀⢈⣼⠋⠀⢠⣀
⠀⠀⠀⠀⠀⢀⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠀⠀⠀⠀⠀⠀⢆⠐⡿⠢⡀⠀⠀⠀⠀⠀⠀⢹⡁⠀⠉⠉
⠀⠀⠀⠠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡔⠀⠀⢀⣄⢀⣯⠑⠀⠤⠒⣵⡀⠱⡄
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⠀⠈⠃⠀⢘⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣨⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣹
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣼⣽⣿⣿⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⣤⣴⣶⡟⠉⠹⣿⠀⢨⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⢊⣉⣩⡍⠙⠛⠻⣆⠸⣿⣧⣼⣿⣗⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢁⡒⠛⠛⠿⢿⣧⢠⣆⣿⡛⣯⡭⠏⠛⠉⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡈⣽⣵⣁⡃⢀⣸⣿⣦⡿⣿⣿⣷⣶⣶⣶⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⣿⣿⣿⣿⢿⢺⡇⣿⣯⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⣸⣘⣿⣿⣿⣿⣿⣿⣿⣿⠻⠀⠉⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⠈⢁⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⡟⡕⡻⢻⣿⣿⣿⣿⠙⢿⣍⠢⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣹⢏⠌⠀⠉⣟⢅⠙⣆⠻⣢⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡎⣀⡀⢀⣬⣺⣶⣌⣷⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣷⣶⣾⣿⣿⣿⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⡿⣿⢸⣿⡟⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣷⣿⣽⡿⣧⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠉⠹⡇⣿⣿⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢿⣿⠀⢘⡇⠻⠋⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣾⡇⠄⢸⠇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢸⠇⠀⢸⡄⡄⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⢸⠀⠀⠈⡇⡇⠀⣿⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣷⡇⠀⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⡇⠀⢸⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡇⠀⠀⠀⠀⠘⣿⠀⠘⣷⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⢹⠀⠀⢸⡼⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣃⣀⣀⣀⣀⣀⣈⣀⣀⣀⣓⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢲⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢁⡀⢀⡀⢀⡀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡲⠆⠰⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠉⠉⠛⠶⣤⣠⣀⢻⡖⠐⠂⢲⣖⣁⣠⣤⠖⠛⠉⠉⠉⠉⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢀⣠⣤⣶⣦⣤⣤⣄⣀⣉⣹⡇⣿⣿⢸⣏⣉⣀⣤⣤⣤⣴⣦⣄⡀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⣿⣿⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣤⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡘⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⢿⢇⠛⠛⠸⠿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢹⣿⡿⢶⣾⣿⣿⣿⡏⢿⣦⡀⠶⠶⢀⣴⠟⢹⣿⣿⣿⢱⣦⣿⣿⡟⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢾⠟⠔⠜⣥⣄⢹⡇⢠⡌⠁⣴⣦⠉⢡⡄⢸⠏⣶⡌⠣⠦⢻⡿⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⡀⢨⡮⢸⡇⢈⣡⡦⠙⠋⣴⣌⠀⢸⡆⣶⡄⣀⣀⡿⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣐⣋⣀⡀⠘⢧⣿⣷⠿⠋⠀⠛⠓⠈⠛⠷⣼⣷⡼⠁⢀⢀⣛⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠩⠿⢟⠛⠲⠶⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠖⠖⠛⠻⠯⠍⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠐⠟⣢⠀⡌⢵⡌⡀⠀⢰⣿⣷⠀⠀⡀⣴⡍⠄⠀⠐⡻⠀⢸
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠓⠚⠿⠤⠤⣤⣜⣈⣀⣀⣘⣻⣛⣀⣀⣈⣐⣣⣤⡤⠴⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⣀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⣀⠀⡄⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠋⠉⠉⠉⠉⠉⠛⠛⠉⠉⠉⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢹
⠀⠀⠀⠀⠀⢀⣶⠞⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠲⣦⡀
⠀⠀⠀⠀⠀⠘⣷⣦⣊⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣴⣢⠃
⠀⠀⠀⠀⠀⠀⠈⢿⡹⣷⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣞⢯⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡗⠈⣕⢄⠀⠀⠀⠀⠉⢍⠀⠀⣀⠜⠁⠀⢀⠄⠠⡀⠀⠈⠣⣄⠀⠀⡩⠉⡆⠀⠀⠀⣠⡪⠈⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣝⣄⠈⠙⠳⠦⠐⢡⣤⣄⠈⠈⠁⠀⠀⠐⡑⠋⠑⢊⠆⠀⠀⠈⠉⠁⣠⣤⡌⠢⠴⠞⠛⠁⣠⣫⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠸⣿⠀⠀⠀⠀⠀⠸⠀⣟⠀⠀⠀⠀⠀⢰⡱⠤⡤⢎⠄⠀⠀⠀⠀⠀⣹⠀⠇⠀⠀⠀⠀⠀⣿⠇⢈
⠀⠀⠀⠀⠀⠀⠀⠸⣮⡟⠀⠀⠀⠀⠀⠀⠙⢉⣀⣀⣀⣀⣀⣀⣈⣐⡀⢉⣀⣀⣀⣀⣀⣀⣉⠋⠀⠀⠀⠀⠀⠀⢻⣵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣞⣛⣈⣈⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠭⠭⠭⢭⣉⣉⣚⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡒⠂⠀⠐⠆⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠺⠖⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠰⠂⠀⠐⢒⣽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠷⠀⢀⣀⣀⣀⣒⣂⣀⣒⣦⣄⣀⣈⣭⣭⣭⣭⣍⣀⣷⣖⣒⣂⣐⣒⣒⣀⢀⣀⠀⠾⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠙⢻⣛⠛⠛⠿⠶⠞⠛⠛⠛⢉⣉⠉⠉⠉⠉⠉⠉⢉⣙⣛⠛⠛⠳⠾⠟⠛⣛⣛⡛⠉⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣼⠥⠀⠀⠀⠈⠑⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣿⠾⠃⠀⠀⠀⠀⠀⢀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣴⣶⣶⡶⠶⢶⢶⡏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠀⠀⣼⢸⡇⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣸⠃⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠺⠛⠛⠛⠻⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⠇⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣠⣴⠶⠿⠛⠷⠶⣦⣀⡏⠈⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀⠀⠀⠀⠀⢰⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠛⢧⣄⣀⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⢀⡴⠞⠛⠒⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠺⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡏⠀⠐⠀⠶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⣌⣡⡿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⣄⠀⠀⠀⠈⡀⣴⣿⣿⠾⣟⣶⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⣀⡈⠁⠀⠘⣦⢃⡀⠸⣿⡿⠛⠁⣼⡟⠛⠙⠋⠈⠳⡄⠀⠀⠀⠀⠀⠀⢀⡖⠁⠀⡠⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣶⣤⣟⣾⣿⣴⣟⣡⡴⠟⠉⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⣠⡎⢀⣤⠞⠁⠘⠉
⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣀⣤⣴⣦⣶⣿⣿⣿⡿⢋⠁⠀⠀⢀⣀⢠⣜⠛⠃⠀⡸⠀⠀⠀⢠⣾⣋⣀⡟⠁⠰⠊
⠀⠀⠀⠀⣠⠊⠀⠀⣴⣾⠿⠛⠉⣉⡤⠀⢠⡞⠁⠰⣎⠲⣄⠀⠀⠉⠀⠀⠀⠀⢀⡏⠀⠀⣠⣿⣿⣿⣿⠿⠗⠒⠉
⠀⠀⢀⢀⡁⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⣰⡿⢁⠀⠀⢻⣦⠈⠛⣄⠀⠀⠀⠀⠀⣸⠃⢠⡜⠛⠉⠉⠁
⠀⣠⢻⣿⡃⠀⠀⠀⠀⢰⣿⣅⠀⠀⢰⣿⠃⢸⠀⠀⠀⠈⠠⣾⣿⡃⠀⠀⠀⢀⠋⣰⠋
⠠⢛⡏⢻⠀⠀⠀⠀⠀⠀⠉⠀⠀⠐⠿⠇⠀⡇⠀⠀⠀⠀⢲⣿⣿⡆⠀⠀⠀⣮⠾⠁
⠀⢻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠹⣿⡃⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣰⠏⠀⠀⠀⠀⠀⠀⠀⢛⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣼⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⢄⡀⠀⠀⠀⡿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣾⡿⡟⠁⠀⠀⠀⠀⠁⢦⠀⢸⡇⢰⠃⠀⡀⠲⢦⡀⠀⠀⠀⢰⣿⣿⣧⠠⡤⠆
⠀⠀⠀⠀⠀⠀⢀⡤⠴⠾⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⢇⢸⢁⣼⠀⠊⠁⠀⠀⠈⠀⢸⣾⣿⣿⣟⠉⠐⠒
⠀⠀⠀⠀⠀⠀⣀⠄⢂⣠⡟⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣾⡟⠁⣃⠀⠀⠀⠀⠈⠁⣿⣿⣿⣿⡏
⠀⠀⠀⢀⣀⠌⣴⣾⡿⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢿⣿⣿⣿⣿⡧⠀⠀⠀⢀⠀⠙⣿⣿⣿⣿⣿⣶⠄
⠀⠀⢠⠠⠋⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⡿⠁⠀⠉⠀⠲⠚⠉⢂⢿⠀⣾⠟⣿⣿⡿⣿⡇
⠀⠀⠀⠃⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣴⡅⠀⠀⠀⠀⠀⠀⠀⠁⠘⠁⣾⠐⢿⣿⣾⡿⠃
⠀⠀⣨⣾⣿⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢹⣿⠁
⠀⠀⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⡄⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⢸⡇⢀⣤⣶⣟⠋⠉⠁⠀⠉⠙⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⣄⢸⣧⣿⣿⣿⣿⣆⡀⢀⣀⣀⡀⠄⠀⢉⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣾⣷⣿⣸⣿⣿⣋⡭⠉⠉⠙⠻⠿⢤⣴⣶⣶⣿⣿⣿⡿⢦⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⠉⠻⣦⠱⢆⠠⠶⠀⠀⠀⢈⣉⣻⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣰⣾⣿⣿⣿⣛⣿⠻⣿⠀⠀⠈⠑⠚⠐⠒⠒⠚⠛⠛⠛⠻⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣟⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⡷⠂⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⣼⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦
⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏
⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⢰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠠⢾⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢋⠙⠷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⠰⣿⣿⠆⠈⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣾⠿⠶⠶⠶⠶⠾⠷⠶⠶⠶⠶⠿⣷⡶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⡇⠀⢿⡶⠶⣶⠶⠶⠶⠶⠶⠶⣶⠶⢶⡿⠀⢸⣇⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⡉⢹⡇⠀⢸⡇⠀⣿⠀⠀⢘⡃⠀⠀⣿⠀⢸⡇⠀⢸⡏⢉⡉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠃⢸⡇⠀⢸⡇⠀⣿⠀⢰⠋⠙⡇⠀⣿⠀⢸⡇⠀⢸⡇⢈⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠃⢸⡇⠀⢸⡇⠀⣿⠀⢸⠀⠀⡇⠀⣿⠀⢸⡇⠀⢸⡇⠘⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣏⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣹⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣄⡈⠛⠛⠁⢿⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⣽⣿⠿⠉⠛⢃⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⣠⣾⣿⣿⣿⡶⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⡆⠀⠻⢿⣿⣿⢻⡟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣧⣴⡿⠛⠁⠀⠀⣼⣿⠁⠀⣼⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣯⣄⠀⠀⠀⠀⠉⠀⢀⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣦⣶⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠈⢛⣿⣿⣿⠩⣿⣿⡟⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠔⡻⢿⡿⢿⣿⣿⣿⣿⣷⠀⣧⠀⢸⣿⣿⣿⡇⣿⣿⡇⠀⢠⡇⢰⣿⣿⣿⣿⣿⠿⣿⠿⡓⠼⠿⠿⠛⠁
⠀⠀⠀⠀⣘⢧⢶⡀⠀⠀⠀⢶⣾⣿⣿⣍⠺⣿⣛⣿⡿⣻⣿⣶⣿⠀⢸⣿⣿⣿⣷⣿⣿⣷⠀⢸⣷⣾⣿⡻⣿⣝⣿⡷⢊⣽⣿⣿⣶⠆⠀⠀⢀⡶⡼⣃
⠀⠀⠀⠀⠹⣗⣪⢷⡄⠀⠀⠀⠈⢉⣥⣶⣿⣷⢌⣽⡒⢻⡼⢫⣟⠀⣸⣿⣿⣿⣿⣿⣿⣿⡄⢘⣯⠻⣽⠓⣺⣍⢼⣿⣷⣦⣍⠉⠀⠀⠀⢠⡾⣑⣲⠏
⠀⠀⠀⠀⠀⠘⢷⣉⠟⣦⡀⠀⠀⠀⠈⠉⠉⣴⣿⡿⢣⣿⡿⢹⣿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⠹⣿⣧⠻⣿⣷⡌⠉⠉⠀⠀⠀⢀⣴⠻⣉⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠛⣯⣜⡹⢷⣤⣀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠿⠋⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠈⠻⠇⠙⠛⠃⠀⠀⠀⠀⠀⣀⣤⡾⢏⣣⣽⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣧⣎⡏⡛⢳⠶⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⠀⣀⡀⢀⡀⣀⣀⣀⡀⣀⣀⣀⡀⠀⠀⡶⡞⢛⢫⣱⣼⠾⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠳⠎⠀⢸⣿⣽⡿⢰⡟⠉⢻⡆⢿⣶⡿⣧⣿⠁⣿⡯⡭⠀⣿⣯⣽⡇⠀⠀⠻⠞⠋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠀⠀⠈⠻⠶⠿⠃⠘⠿⠁⠻⠿⠀⠿⠶⠶⠆⠿⠇⢻⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣤⡶⢿⣭⣿⣽⡿⢶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡓⠀⢼⣿⠿⠿⠿⠟⠛⢶⣿⣻⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠶⢀⠇⠃⠀⠀⠛⠀⠀⠀⣀⣀⠀⠻⣯⣿⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢛⢿⡄⠚⠙⢶⠤⠐⡿⠟⢿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠍⠀⠀⠀⠀⠀⢐⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣘⣃⠀⠀⠀⠀⣻⣦⣿⠁
⠀⠀⠀⠀⡄⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⣀⣤⠞⣿⢇⡽⣿⣦
⠀⠀⠀⡈⠀⠀⠀⢠⡇⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⡀⠀⠙⣾⠿⠋⠀⠀⠸⣼⣛⣯⡟
⠀⠀⠀⡧⠀⠀⠐⠀⠉⠉⠉⠉⠉⠉⠉⠛⠻⣝⣟⠁⠈⢹⣷⣾⣿⣄⠀⠀⠀⠀⠙⣿⢯
⠀⠀⠀⣧⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹⡆⠀⠈⠻⠿⠉⠛⢦⠀⠀⢀⡴⠃⣰⠷⣄
⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⠀⠀⠀⢠⣴⣾⡟⡼⠁⠀⠀⠠⣤⠴⢻⡞⣷⣞⣉⡀⢰⡇⠀⠈⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢻⣷⣶⣿⣿⣦⡆⣸⠇⠀⠀⠀⠀⠘⢻⡿⠁⠀⠳⣸⠁⡠⠂⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠻⠛⠿⢾⠏⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠇⠀⠘⠟⠒⠒⣤⠶⣦⣶⣶⣿⣷⢔⠤⣄⣄⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⡄⠀⢚⠃⠀⠀⠀⠀⠀⠐⠟⣿⢛⣻⣿⣿⣯⣗⡆⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠙⠄⢻⡅⠀⠀⠀⠀⠉⠉⣼⢣⣏⣭⣵⣾⣯⣟⠭⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠠⡄⠸⡘⡇⠀⠀⠀⠀⠀⢸⣧⠜⠋⠁⠀⠀⠀⠙⢷⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢀⡈⠣⠐⢧⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠉⢂⣀⡨⠤⠖⠋⠁⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠁⠀⠀⠀⣀⠀⠤⠤⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠁⠀⠀⠀⣠⠆⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢤⣄⠀⡀⡰⡀⠀⠀⠀⠠⠤⣀⠠⠤⠄⠒⠒⠒⠉⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⢀⡔⢋⡏⠁⠀⠀⠀⠀⠈⠀⢀⢻⡢⣁⠃⢠⠀⡀⠀⡀⠂⠈⠀⠄⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⢀⠂⠁⢠⠖⠒⠉⢯⡀⠀⡄⠀⠀⠀⠀⠀⡠⠈⠉⢁⢑⠿⢜⠛⠀⠀⠀⠀⢈⠀⢸⡤⠶⠚⠊⠁⠀⠀⠀⠀⠀⣀⣀⣠⡴⠮⠋
⠀⠀⠀⠀⠀⠀⠘⣠⠶⡋⠀⠀⠀⠈⠈⠳⠐⣰⠀⣀⠜⠉⡀⠀⠀⠀⠀⠀⠀⠉⠑⡦⡄⠀⠤⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠁
⠀⠀⠀⠀⠀⠨⡞⠁⠉⠉⠀⠁⠒⠩⣈⣃⠀⠃⡎⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣼⠁⠚⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠔⠙⢄⠀⠀⠒⠈⢄⠀⠀⠀⢀⠜⠃⠀⠀⡄⠀⠀⠀⠀⠀⡠⢂⠀⠙⠣⡞
⠀⠀⠀⠨⡀⠁⢀⠲⣄⠀⠀⢀⠈⠀⡄⠀⢀⡀⠀⠀⠕⠤⠀⠡⡀⠈⠂⠀⢸⡒⠀⠀⠀⠁⠀⠀⠀⠀⣠⢠⡏⡔⠀⠀⠘⢄
⠀⠀⠀⠀⠀⢉⣲⡿⠖⢲⠃⠀⠁⠠⢃⠜⡂⢀⡀⠀⠰⡀⡀⠀⠑⢄⢀⣀⠃⡷⠛⠉⠁⡷⢁⡀⢠⠔⠚⢺⡏⠁⠀⠀⠂⠈⡆
⠀⠀⢀⠄⢩⣰⠁⠀⠠⢊⡀⢢⠼⠉⠉⠀⠁⠉⠉⠑⠒⠁⠁⠁⠂⠌⠤⠿⡤⠁⠀⠀⡠⠃⠈⠀⠞⢀⠀⡃⡐⢖⠀⠄⢠⡜⠁
⠀⡴⠉⣀⡾⠁⠀⢀⠁⢀⡔⠃⠘⠆⠀⠀⠐⣀⠀⠠⠀⠀⠀⠀⠀⢰⠖⢻⠀⠀⠀⠰⣃⣹⣧⠁⠀⠀⠆⠑⠡⠈⠲⡀⠸⡁
⠈⠇⠘⠁⠀⠀⠀⠐⡀⠞⢀⡤⠟⠃⠒⠈⠉⠑⡀⠀⡀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠐⠹⠟⠉⠙⠚⢑⠖⠀⠒⠂⢁⡐⠙⠲⢵⣄
⠀⠀⠀⠀⠀⠀⠀⢠⢏⠔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠤⠁⠸⠄⠀⠒⠸⢃⡜⠁⣀⠄⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠄⠊