Pantai Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣭⣭⣭⣥⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣄⢸⣿⣿⣿⣿⣷⣿⣟⣿⠿⠿⢷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠈⠻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡛⠿⠿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⢩⣿⡿⠹⣆⠉⠉⠙⢿⣷⣄⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣸⣿⣧⡀⢹⣆⠀⠀⠀⠹⣿⣦⣬⣍⣿⡆⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣧⣄⣿⣿⣷⣶⣦⣽⣧⠀⠀⡴⠿⠛⠛⣿⣿⣿⣿⣿⡛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢫⣾⣿⣿⣿⣿⣿⣿⣇⡈⠙⢿⣆⠀⠀⣠⣶⠟⢻⣿⣿⣿⣷⣿⡄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣼⣿⣿⣿⣿⣿⠿⣍⠙⢿⣄⠀⠻⣆⠰⠏⠀⡴⠁⢻⡏⣿⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⣿⣿⢹⣿⠀⠘⢦⠀⠙⠀⠀⢹⡆⠀⣼⠁⠀⣿⠀⣼⠇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠈⢹⡇⠀⢿⡆⠀⠈⢧⠀⠀⠀⠀⣿⠀⡇⠀⠘⠁⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠙⠀⠀⠘⣇⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠙⠶⣶⣦⣄⠀⢀⣤⢀⠀⠀⠀⣀⣨⣥⠴⢖⣄⣀⣀⣻⡄⠀⠀⣿⠀⣧⣠⣀⣀⣀⡀
⠀⠀⠀⠀⠒⠻⠿⠿⠿⠟⠛⠛⠋⠀⠐⠋⠉⠉⠛⠉⠉⠀⠀⠈⠉⠁⠀⠀⠈⠀⠉⠉⠹⡇⠀⠀⣽⠉⡿⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢾⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣠⣄⠀⣠⣤⣠⡄⢀⣤⣿⣀⣠⣾⣿⣦⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⣿⡿⠍⠉⢉⣉⣛⣛⣻⠿⠿⠟⠙⠙⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⢀⡀⠀⢀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⠀⠀⣠
⠀⡾⡄⠀⣼⣧⣤⡄⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⡀⠀⠉⣓⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠉⢿⠇⠀⠀⢀⡄⠀⠈⠙⣀⠀⠀⠀⣰⢾⣤⡀⠀⠘⠿⠂⠀⠱⢤⡀⠈⠉⣵⣾⡧⠀⠁⡄⠘⠋⠦
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠰⢿⡁⠀⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢀⠝⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⣄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠞⢋⡀⠀⠘⠉⠉
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠶⠿⠛⠒⠺⠿⢶⣷⣴⣷⣶⣦⡄⠀⢀⢀⢀⠀⠀⠀⠀⠐⠶⣤⣤⣀⣀
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠾⠿⣿⠗⢀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠶⠶⢦⣤⣄⣀⣀⡀⢀⣀
⠀⠀⠀⠦⠀⠤⠀⠈⠂⠐⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠁⠁⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⡠⠂⠀⠀⠀⡀⠀⠂⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⠀⠀⢠
⠀⠀⠀⠀⠀⢀⠄⠄⠀⠀⠒⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⢀⣵⠀⠀⠰⡄⠃⠀⠀⠘⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⠀⠠⣀
⣠⣄⣀⢀⡔⢡⠌⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⡧⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⣴⠐⠀⠉⠀⣼⣷⡀⠀⠈
⠀⠰⢦⣺⡔⠷⣶⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⢀⣰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡿⢻⣤⡀
⠰⡞⠁⠚⢟⠐⢮⡃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠑⣄⠴⠁⡜⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⡜⡀⠸⠍⡤
⠀⡧⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠤⠤⢀⢁⣸⢀⢊⡀⡨⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢰⠀⠣⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠁⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⡶⠉⣰⣷⠈⣦⠁⠛⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡐⠠⠆⠏⠸⠆⢸⣦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⣶⣶⣶⣶⡶⠁⠂⣐⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠂⡁⣶⣠⣖⣀⢰⠄⠂⠀⠀⠀⢀⠀⣶⣶⣶⣶⣶⣶⣶⣦⣤⣴⣶⡇⠐⣖⣶⡶⠶⠶⢤
⠿⢿⡟⠋⠀⣐⠀⡍⠹⣷⣈⡀⠛⠉⠽⠭⠉⠿⣿⣿⡀⠉⡉⢠⢤⣴⣼⣀⡃⡈⠐⢂⣸⠘⣿⣿⣿⣭⣿⣿⣿⣷⣾⣉⡡⢈⡀⠲⣻⠿⢾⣿⠏
⠀⠀⠀⠀⠀⢀⠀⡇⠀⠈⠁⠀⠀⠀⠠⠴⠒⠀⠀⠰⠀⠙⠏⠉⠉⠽⠞⠋⣭⡤⠐⠳⠖⠚⠛⠉⠙⠛⠛⠀⠉⠉⠐⠀⠸⠀⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠂⠀⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠾⠑⡂⠈⠉⠀⠤⠴⠿⠀⠀⡀⠀⠀⠀⠀⡶⠀⠀⠨⠉⠁⠀⠐⠂
⠰⠂⢀⠐⠂⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠂
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠷⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠈⠀⠀⠀⠀⣀⡀⠀⠀⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠓⠂⠂⠀⠀⠀⠉⠑
⣤⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠲⡤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⢎⠳⡄⠀⢀⣤⠒⠉⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡈⢆⢸⢔⠟⠡⢤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣒⠂⠉⠉⡙⠲⢦⣧⡈⢇⠎⢀⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠛⣛⣲⣦⡴⣮⠺⡴⠿⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⢈⡩⠞⠋⠉⢀⣠⡿⠠⡈⢳⡀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡠⠔⠋⣿⢋⢼⡇⡀⠷⠀⣿⠲⢤⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡮⠖⠁⠀⠀⢐⡕⠁⠈⡄⢹⠂⢇⠏⠀⠈⠳⣄⠸⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠘⠁⠀⠀⠱⡸⠀⠸⠁⠀⠀⠀⠈⠢⡟⢼⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣜⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠋⡝⠉⠉⠣⣄⠀⠉⠙⠲⢅⠒⠤⢀⡀⠀⠀⠀⠈⠫⡸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢊⠕⠁⠀⠀⡰⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠙⠢⡀⠈⠑⠢⣀⠀⠀⠑⣜⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⢠⠎⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠑⢦⡀⠈⢶⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⢀⠀⠀⢃⢀⡤⢄⡒⠒⠠⢵⣤⣮⠥⣄⣙⣂⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣀⠀⠀⠀⡎⠀⢀⣀⣀⠀⢰⠀⡠⠒⠙⡝⡍⠉⠑⠼⡫⠶⠅⠘⠓⢢⣴⠭⡍⠀⣩⢁⣼⣷⣗
⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡔⠉⠁⠀⠉⠙⢺⡖⠉⠁⠀⠀⠉⠺⠊⠀⠀⠀⢡⢡⢀⡔⠊⠁⠀⠘⠉⠀⠐⠉⠃⠘⣄⠀⠀⣻⡟⣲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⠇⠈⠉⠀⢈⡴⢠⣤⢬⠭⣭⠭⣥⡍⠉⠉⠩⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⡸⡀⠀⣰⣿⢃⢆⠎⡜⢠⠃⣴⠏⠀⠀⠀⠐⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡄⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⢧⢣⡼⣣⢣⢊⠎⡰⢡⢂⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡳⢖⠕⡡⢋⠜⡰⣣⡞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣲⡒⢒⣊⠥⢊⠥⣊⠔⣡⠞⣴⠋⠀⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠙⠑⢾⢥⡞⢁⣾⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢨⡼⣾⡟⠛⠙⠲⠦⢾⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠳⠲⢤⣤⣀⠀⣴⠏⠀⠀⢀⡤⢦⣤⡀⠉⠁
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠃⠀⠀⢠⣡⢊⠟⢦⠘⡄
⠀⠀⠀⠀⠀⠀⠐⠤⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢧⣸⣀⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠁⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣿⣴⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠐⠛⠛⠳⣾⣿⣿⣥⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢸⡇⣴⠏⠀⣀⡤⠀⠀⢀⣤⢾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣿⣿⡾⠋⠁⠀⠀⠀⠈⢱⢟⣽⣿⠯⡟⣿⣿⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣿⣿⣿⣟⠙⠓⠦⠀⠀⠀⠈⢸⡏⡟⠸⠃⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣼⠃⢩⡟⣿⢰⡀⣿⠀⠀⠀⠀⠈⡌⠀⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠡⠇⣀⣀⣳⣿⣶⣋⣁⠀⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣨⡽⣿⣿⣿⣿⠉⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢁⡴⡻⠁⢹⡉⡇⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⢰⠁⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡤⢤⠧⠠⢤⢤⣾⠄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣷⣶⡾⠶⢶⡶⠾⣏⠀⠀⠀⠈⠉⠉⠉⠭⠭⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠶⠒⠒⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡛⢿⣦⣼⣇⣴⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣽⣿⣿⣿⣿⠶⠛⠛⢻⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡴⣻⡿⣿⢿⠻⡌⣛⣷⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⢸⠌⡇⢿⠁⠟⡙⡏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠶⠶⠶⠶⠴⠶⠤⠄⠀⠀⠀⠀⠀⢀⡖⠙⣷⣬⡀⠠⢾⣧⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⣷⢀⣠⣁⣄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⢀⣤⣬⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠛⠛⠛⠛
⢀⠀⡀⠀⠀⢀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⢀
⣿⣏⢽⣟⡛⣛⣛⡛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠓⠄⢀⠂
⠀⠀⠀⠀⠀⠂⠀⢀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢀⠌⣴⣛⣿⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⡁
⠀⠀⠀⠀⡀⡀⠀⣄⠀⠀⠀⡎⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠦⢱⠂⡘⠀⠀⠁
⠀⠀⠈⡲⠆⣧⢐⠀⠀⠀⢀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦⢩⠼⠖⠒⠂⢰
⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⡼⠀⠀⢀⡀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠀⠙⡇⠠⠀⠀⢸
⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠇⠀⠀⡠⢻⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⡬
⠈⠀⠀⠀⠀⠀⢀⠀⠰⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⣄
⠀⠃⠀⢤⠤⢀⡌⠺⠃⢀⡄⠀⠀⠀⠀⠀⠀⣤⢤⣤⣤⣤⣤⡤⠄⠤⠤⢤⣤⣤⣤⣤⢤⣤⣤⡤⣤⠀⣤⣤⡤⠤⢀⢀⣀⡀⠀⣂⡀⠰⠖⠷⠖
⢀⢠⠀⠀⠀⣤⠟⠃⠀⢉⢀⣀⠀⠠⡄⠀⠀⠀⠀⠀⠉⠉⠁⣬⡉⠀⠀⠀⠺⣿⠛⠓⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢤⠉⠉⠙⠀⠀⠐
⠀⠀⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⢤⣒⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣄⡀⠀⠈⠉⠉
⠀⣀⠸⠿⠷⢦⣴⡆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠁⠀⠀⠀⠁⠐⠀⠀⠈⡀⢀⠀⠉⠀⠠⠄⠀⠀⠒⠚⠋⣉⣁⣀⡀
⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⣄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠉⠩⠍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⢀⡐⠒⠀⠀⠀⠀⠀⠀⣶⣶⠮⠁⠀⠀⠀⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⠦⠦⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠄⠀⠀⠀⠀⠀⠃⢀⣀⠀⠀⠀⠀⠀⠀⠨⠟⡒⠂
⠤⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣭⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣘⣛⣛⣙⣛⠛⠛⠛⠛⠂⡃⠚⠛⠒⢓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣌⣉⣍⣉⣉⡉⠉⢉⠛⠛⠛⠋⠙⠛⠋⠉⠉⠉⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣠⡄⠀⠀⠀⠀⠀⠀⠚⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠛⠛⠓⠛⠟⠛⠲⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢼⡅⠀⠀⢠⣔⣀⠀⣀⣤⣀⢀⢠⠀⡄⢀⠀⠀⠀⣠⡀⣀⢀⢠⣄⣠⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣅⠐⠀⠀⠀⠀⠓⣌⠋⣿⠋⠙⡟⠀⠀⠈⠀⠀⠀⠀⠉⠈⠁⠉⠁⠀⠈⠉⠉⠁⠙⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠈⡃⢈⡀⠀⢀⠀⠀⠜⠀⠈⠀⡿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⡄⢨⠀⠀⠀⠀⠀⠀⡧⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣾⡤⣡⠁⡀⠀⠀⠀⠀⠀⠠⡅⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠠⡤⠀⠀⠀⠀⠠⠀⠀⡀⠀⣘⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠽⠦⠄⠈⠤⠀⠟
⠀⠀⠀⣀⡤⠆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠤⡇⠈⠐⠓⠶⠚⠃⠀⠀⠀⠠⠟⠛⠚⠓⠒⠒⠒⠒⠒⠒⠚⠓⠓
⢀⣀⠾⢉⡠⠤⠄⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠐⠀⠇⠀⠀⠀⠀⠠⢘⡀
⠀⠁⠐⠋⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠙⠛⠗
⠀⠀⠀⠀⠀⠀⠀⢻⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣴⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠗⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⣛⠈⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣾⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣤⣤⣾⢋⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠘⠖⠛⠟
⣤⣤⣤⣤⣤⣤⣤⣼⣯⣥⣬⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣾⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⣉⣻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⢀⣀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠙⠿⠿⠛⠉⠉⠙⠻⠷⠟⢋⣉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣻⣟⣤⣠⣤⣤⣤⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠀⠒⠛⢛⡛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠒⠀⠒⣒⠒⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠿⢿⣿⣿⣿⣿⢏⣿⣿⣿
⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣾⣿⣿⣿⣿
⠛⠉⠉⠀⠀⠠⠤⠔⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿
⠀⣴⡖⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿
⣤⣄⣈⣤⣄⣀⣈⣴⣶⡄⠀⠀⠀⢀⣀⣀⠀⠀⠀⢠⣀⣀⣄⠀⣀⣀⣀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣶⣟⣣⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⢛⠿⠛⠛⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⣴⣾⣿⣿⣿⠟⠁⢀⠀⢸⣶⡎⣉⠙⣷⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⢱⠄⠀⠀⣠⠀⣤⣴⣄
⣰⣿⣿⡿⠛⠫⠃⠀⠀⣀⣴⠟⣹⣀⣿⠻⣿⣇⡀⠈⡆⢀⠠⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣰⣟⠺⣣⣷⡄⠸⡂⠀⠀⡉⣻⣿⣿⣿⡦
⣿⡿⠙⠂⠐⡠⣸⢀⣴⠏⠁⡄⢀⣤⣁⠀⠘⠻⠃⠀⠀⠈⠻⣷⡀⠀⠀⠀⢀⠠⠀⢀⣾⣿⠇⠀⠘⢰⣟⠀⠠⡄⠀⢛⡉⢿⣿⣿⣧⡀
⠟⠁⠀⠄⠀⢁⣿⠟⠁⠀⠠⠄⣞⡿⠋⠀⠀⠀⠁⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⣠⣿⠏⠈⠀⠀⢸⡞⠈⠀⠀⠷⠀⠈⠛⢞⣿⣿⣫⣸⡄
⠀⠀⡌⢜⣠⡾⠋⠀⠀⢸⠆⣠⣤⡅⠀⠀⠀⠀⠈⠰⡵⠀⠄⠀⠘⢿⡀⠀⡀⢰⠟⠁⠀⠀⠀⠀⠀⠏⠀⢀⡄⢸⣷⠶⠀⠸⣯⣻⡿⢷⡇
⠀⢰⢠⡞⠁⠀⠀⠀⡀⠄⢠⣿⠎⠀⠀⠀⠀⠀⠀⠀⣧⣔⠀⠀⠀⠘⡇⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⢣⣀⠀⠀⠸⣿⣷⣯⣷
⠀⢰⠋⠀⠀⠀⠀⠀⠉⢠⣄⣉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠁⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢾⣏⠀⠀⠀⠙⣿⣯⣿
⠀⠈⠀⠀⠀⠀⠀⠸⠶⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠻⣿⣿
⠀⠀⠀⠀⠀⠀⡰⠀⢀⣠⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⡀⠀⠀⢀⣠⣬⡇⠀⠀⠀⠀⠘⣿
⠀⠀⠀⢀⣀⣀⠦⠠⢰⣿⣥⣤⣤⣀⣀⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⣴⢟⠁⠀⠠⡄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢸⠀⠀⢀⠄⢈⡀⠛⣤⣤⠤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠈⠆⠀⣴⡇
⠀⠀⠀⠀⢸⠀⢀⣮⣾⢯⡀⠀⠈⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⢀⠀⠀⣀⡀⡉⠣⣻⣄⠀⠀⠣⡀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⣶⣽⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢋⡀
⠀⠀⠀⢰⠀⢠⣿⣾⠁⠀⠈⠛⢷⣦⣀⠙⠦⣀⠀⠉⠲⠤⣀⣀⠀⢀⡤⠤⠖⣚⣭⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠇
⠀⠀⢀⠈⢀⡈⠙⠋⠀⠀⠀⠀⠀⠈⠙⠻⢦⣬⣝⣶⣤⢤⣤⣤⣤⢶⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢦⡆
⠀⡀⢸⠀⠘⣿⣶⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⡇
⠀⢣⣏⣤⠀⣸⣿⣶⡾⠕⠊⠁⠀⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢄⠀⠠⠼⠁⣀⣤⡶
⢆⢸⡚⠰⠁⠛⡿⡣⠂⢤⡔⢦⠐⢶⡧⠀⢀⠆⢀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⣀⠠⠓⢈⣀⠀⠴⣊⠙⢷⠽
⢺⣷⡼⢂⢓⡗⣪⠴⠒⣠⣿⣤⠞⠛⠁⠙⠃⠐⠐⠴⠂⠀⠀⠀⠐⠂⠀⠉⠁⠀⠒⠀⠀⠀⠀⠐⠀⠒⠒⠀⠁⠀⢀⣈⠅⠐⠶⠈⢠⣤⠼
⠿⠿⠥⠞⠋⠉⠟⠃⠛⠶⠀⠒⠤⠇⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠉⠁⣿⣿⣿⣶⠉⠉⠙⠃⠀⠀⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⢿⠿⠿
⠀⠠⠄⠤⣤⡤⣤⠤⠤⠤⠤⠤⠄⠀⠀⠿⠷⠶⠶⠶⠾⠶⠖⠒⠒⠒⠂
⠀⠀⠀⠟⠹⢁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣾⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄
⠀⠀⠀⠀⠄⢺⣾⣿⣟⡷⢶⠀⠀⠀⠀⣀⡀⠀⠀⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠈⠷⠎⡏⠑⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣯⣽⣶⣶⣾⣿⡇⠀⠀⣿⣷⣶⣤⣤⣥⣥⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣴⡆
⠀⣠⣤⣶⣶⣶⣾⣷⣶⣤⣤⣀⠀⠀⠀⠀⡀⢀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣀⠀⣠⣤⣤⣤⡶⠿⣿⠿⣿⡇
⠀⣻⣿⣿⣿⣿⣿⣿⣛⣛⠛⠉⠃⠀⠀⠿⡿⠿⠿⢿⣿⣛⣛⣛⣛⣛⠃⠀⠀⠍⢉⢤⣥⣤⣤⣄⣁⣤⣍⣭⡄
⠀⠙⠛⢿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠶⢶⣶⣶⣤⣀⣀⣠⣴⡄⠀⠀⠀⠀⠀⠈⠻⠽⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣌⡉⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠠⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠞
⠀⠀⠀⠠⣄⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⣀⠈⠳⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆
⠀⠀⠀⠉⠓⠄⠘⠂⢀⢠⣗⠀⠀⠀⢠⠇⠀⠀⢐⣁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⠇⠀⠀⠀⠎⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣒⣞⡋⠉⠉⠉⠉⠉⠐⠒⠈⠛⠒
⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣶⣄
⠀⠀⠀⠀⠀⣰⣏⠴⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⠤⢶⣦⣶⣦⡼⠦⠶⢶⡖⠒⠒⠶⣶⣞⣻⠛⠛⠁
⠀⠀⠀⠀⠺⠿⠷⠖⠀⠀⠀⠀⠀⠀⠉⠛⣿⣉⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣍
⠀⠀⠁⠂⠀⠀⠀⠀⠀⠐⢀⣀⡶⠛⠉⠑⠢⠤⣀⣀⡀⠈⠙⠒⠀⠀⠀⣀⣄
⠀⠀⠀⠀⢀⣠⣴⣶⣤⡴⠏⠁⠾⠥⠤⠖⠀⠀⠀⠉⠙⠛⠲⠶⠶⠤⠾⠟⠉⠁
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠠⠰⠂⠀⠀⠀⢸⠁
⠀⠀⠀⠸⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠈⠈⠒⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠐⠀⠀⢸⡟⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⢀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠐⡆⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⢀⣀⣀⡔⣂
⠀⠀⠀⠀⠀⠄⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⡄⣤⠃⠤⠤⠤⠤⠶⠤⠤⠤⠤⠤⠤⡤⠤⠤⠤⠴⠶⠒⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠒⠒⠒⠒
⠀⠸⢿⡄⠉⡄⣾⠀⠀⠀⢠⣀
⠀⠀⠀⠀⢡⣿⠃⠀⠀⠀⡀⠈⠙⠂⠀⠀⠀⠀⠀⢀⡤⠒⠛⠉⠀⠉
⠀⠀⠀⠀⠾⣿⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⣐⠾⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⣶⡶⣦⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⢀⠀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠤⠤⠀⠄⠀⠀⠀⠀⠈⠙⠛⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣉⡁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣿⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠘⣸⠁⠀⢸⠧⡄⠀⠀⠀⢀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠄⠀⠈⠀⢶⣇⡀⠀⠀⠀⠀⠀⠀⠀⠋⢻⡷⠆⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠠⢿⡵⠀⠀⠀⠀⠀⢋⣠⣄⣴⣤⣤⣤⣦⣴⡀⠀⢡⡄⠈⢉⠋⠀⠀⢠
⠀⠀⠀⠚⠿⣤⣤⡀⠀⠰⣾⣰⠼⠄⠘⠛⠃⠀⢈⣁⠀⠁⠉⠛⠀⠼⠅⠀⠸⢶⣰⠄⠘⠀⣸⠖
⠀⠀⠀⠀⠀⠘⠿⢷⣶⣄⠀⠉⠁⠀⣀⣀⣴⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣤⣤⡤⠶⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⡿⠿⠟⠁⡀⢿⣧⡀⠚⠛⢿⣛⡛⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠐⠚⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⡁⣸⠀⠀⣿
⡀⠀⣀⣀⣀⣸⣿⣷⣄⠀⡀⣰⣿⣿⣄⡀⣿⡇⠀⠀⠀⣀⣤⣴⣿⣷⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⠀⢀⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⢿⣿⢿⣿⣷⣿⣇⠀⡀⠀⣻⠉⣿⣿⣿⣿⣶⣦⣦⣾⣿⣿⣿⣿⣤⣷⣿⣿⣿⣿⣿⣿
⣿⠟⠟⠉⠁⠘⠁⠙⠀⠀⠀⠤⠇⢨⣯⣥⣿⣿⣤⣅⣀⣈⣀⣀⣁⣋⢉⣉⠉⠋⠛⠉⠛⠋⠙⠉⠋⠙⠋⠙⠻⠇⠂
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢿⣿⣿⣿⣿⣿⡿⠿⢿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡟⠛⠛⠋⡇⣿⣶⣾⣷⣶⣶⣦⣤⣄⣴⣶⣶⠆
⠇⠐⠻⠷⠶⢾⣶⣶⡤⠀⠂⢰⣤⣴⠄⠀⣴⡆⠀⠀⠀⠀⠀⣀⡀⡄⠀⠀⠀⠀⠈⠉⠙⠋⠛⠁⠏⠛⠛⠛⠛⠟⠈
⠀⠀⠀⠀⠀⠸⠛⠏⠀⠀⠀⠘⠟⢿⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠻


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣽⣭⣮⣭⣯⣾⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⡀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⣻⣿⣿⣿⡿⣷⣿⣿⣿⣧⠀⣠⡀⢀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣨⣿
⠀⠀⠀⠀⠀⠀⠀⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾
⠀⠀⠘⠀⠀⠋⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣩⣭⣭⢩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠛⠋⠘⡏⠹⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠟⡿⠋⠁⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠙⠋⠋⠉

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⢀⠤⠀⠠
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⠀⠀⠀⠀⠴⠀⠀⢠⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡄
⠀⠀⠀⠰⠁⠀⠀⠛⠟⢫⠁⠀⠀⠀⠀⠀⠀⠀⣤⣿⠂⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠃⠠⣆⠉⠋⢩⡀⣀⠈⢂
⠀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡧⠂⠀⢫⠁⠬⢴⣏⡠⢰⠤
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠈⢥⠀⠀⠁⠉⠀⠾⢤⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠉⢩⠁⠴⢻⠓⡀⠀⠀⠀⠀⠀⠀⠘⠀⠉
⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⠗⠷⢽⣿⠤⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⡄⠀⠀⠉
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣧⡰⠈⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢐
⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡉⠉⠀⠀⠒⠒⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠒
⠀⢀⠉⠀⠀⠀⠀⠀⠀⢀⠰⠀⡀⠈⠁⠀⠤⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠴⠓⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⡀
⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠢⠤⣤⡀
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠒⠀⠀⠀⠀⠀⠀⠁
⢤⢶⣆⠀⠀⠀⠀⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠘⠒⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠠⠄⠠
⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠀⠀⠀⠠⠿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣦⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣯⣤⣶⣶⣶⣦⣤⣤⣤⣤⣀⡀⠀⣀⠀⣀⣀⣀⢀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠬⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠛⠙⠃⠀⠈⠉⠛⠁⠉⠉⠉⠉⣛⡀⠙⠁⠈⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⢶⡶⠶⠶⡶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⠻⠿⠿⠟⠛⠟⠛⠛⠛⠃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣶⣶⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣶⣷⣶⣾⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠽⢤⣄⠀⠀⠀⠀⢰⠟⠒
⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⢀⡠⣾⡽⢻⠖⡳⠾⢿⣿⣇⠀⠀⠉⡟⠉
⠀⠀⠶⣴⣻⣖⡎⣳⢀⡴⠋⠀⢹⡷⢁⠞⠁⡴⢃⠞⠉⠟⠑⠒⠣⠤⣄⣀
⠀⠀⠀⡇⠉⠉⣠⡷⠋⠀⠀⠀⠸⣷⠎⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣀⡀
⠀⠀⠀⠘⢀⡾⠋⠀⠀⠀⠀⠀⠀⢿⡤⠃⠀⢤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄⡀
⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡰⠃⠘⣆⣀⡈⣏⠙⠒⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡄
⠀⠀⡘⠀⠀⠀⠀⣀⠔⠛⡀⠀⠀⠀⣿⠀⠀⠀⢣⠀⠀⢹⠉⠙⣦⠀⠀⢇⣏⣟⠒⡆⠀⣀⡀⠀⠀⠀⠀⡇
⠀⠀⢹⠀⠀⡤⠊⢱⠀⣀⣷⠀⠀⠀⢹⡌⡱⠀⠸⡀⠀⠈⡄⠀⢸⠀⠀⢸⡁⢸⠉⢳⡄⢡⣉⣓⠢⣤⡀⢶
⠀⠀⠸⡀⠀⢧⠤⠚⢫⠁⢸⡄⠀⠀⠸⡟⠁⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠐⠛⠚⠦⠯⠇⢠⣀⣹⡉⢧⠀⠸⡀
⠀⠀⠀⡇⠀⠘⣆⣀⠼⠖⠊⠁⠀⠀⠀⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇
⠀⠀⠀⢸⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢰⡋⠉⠹⡉⠉⢹⠀⠀⠐⠒⠲⡖⠶⠀⢠⣄⣀⣀⠀⠀⢸
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⢸⡀⠀⠀⠀⠷⠒⠒⢻⠛⠙⡇⠀⠀⠀⠉⢳⠒⢇⠘⠐⠢⣯⣙⡇⠀⡆
⠀⠀⠀⠀⢱⠀⠀⠀⠔⡏⠀⢱⠀⠀⠀⠸⡇⠀⠀⠀⢸⢀⣀⣨⣆⣀⣉⠀⠀⢀⣀⣸⣄⣼⠀⢀⣀⣸⣀⣱⠀⢳
⠀⠀⠀⠀⠈⡄⠀⢶⠀⢇⠀⠈⡆⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⡄
⠀⠀⠀⠀⠀⢧⠀⠸⠀⣸⣤⠤⠗⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⢸⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡀⠤⠤⡤⠤⢤⠀⠀⢠⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⣀⠤⣦⠀⠀⠀⡇⠀⠀⠀⢃⣀⣀⣷⡠⢼⠀⠀⠶⠢⠬⡧⠬⠭⠀⠶⠒⢦⠤⡄⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⣀⢹⠀⠀⣸⣿⢠⡸⣷⡆⠀⠀⢿⠀⠀⠀⢸⠀⣀⣘⣀⣸⡄⠀⢠⡤⡤⣧⣀⣀⡄⢀⣀⣸⡀⣇⠀⠀⠸⣿⣷⡀
⠀⠀⠀⢰⠉⠉⠙⡆⠀⠘⣿⡄⡇⢸⣿⠀⠀⢸⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡇⢀⡷⡄
⠀⠀⠀⡸⠟⠀⠀⢹⠀⠀⠙⠛⠛⠚⠋⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣉⠀⣸⢆
⠀⠀⠀⢷⣆⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡴⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠘⠀⣶⠃
⠀⠀⢰⣎⡋⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠊⢠⢂⡆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠸⣟⣤⣮⠟
⠀⠀⠀⠙⠉⠓⠬⢧⣤⣇⠀⠀⠀⣀⣀⡠⠤⠔⠒⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠛⠗⠲⠤⠤⣀⣀
⠀⠀⣀⣀⣀⡀⠀⣘⣏⠿⠖⠚⠉⠉
⢠⣿⣿⣿⠿⠓⠉⠁
⠈⠛⠉

⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⢒⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢐⠁⡀
⠀⠀⠀⢀⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⢀⡤⠔⢊⡵⠊⣅
⠀⠀⠀⣀⢿⣧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠃⠀⠀⠀⠈⠦⠬⠤⠄⠀⠹⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠈⠁⣤⠏⣽⢀⡀⠀⠀⠀⠀⢤⠖⠀⠋⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠠⣤⠖⣠⠒⣠⠄⠀⠀⠀⢀⣠⠄⠀⢠⠄⡀⣄⡄⣠⢀⢠⠀⠀⣶⠀⡄⢸⣳⣧
⠀⠠⠞⣥⣼⣷⡄⠀⡀⠰⠛⠀⠀⠂⣀⣤⠚⣴⣠⡄⢀⡀⠔⠀⠀⢀⣠⠔⠀⠀⠁⠀⠀⣀⠀⠀⠘⠋⠀⢰⣦⣾⣾⣿⣿⣿⣟⣾⣿⣾⣷⡏⣼⣯⣿⣿⣧
⠀⠉⠿⠾⣿⣇⡁⢀⠀⠀⠀⠀⠀⠉⠀⠀⠰⣿⣽⠿⠿⠧⠠⠶⠾⠾⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠿⠿⠿⠷⠿⠿⠿⠇⠧
⠀⢀⣸⢾⣿⣿⠳⡦⠑⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣀⣀⣼⣿⠿⣷⣠⡀⢁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠤
⣬⣿⣿⣃⣾⣿⢿⣇⡠⠤⠁⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡖⠂⡀
⠂⣸⣿⣿⡿⣿⣦⣹⠷⠖⠀⠀⠀⠀⠸⠿⠧⣴⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢾⠏⣁⡰⠋⣠⣴⣶
⠄⢰⣿⡏⢦⣼⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣾⣦⠀⣀⣀⠷⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣶⠂⠀⢘⠉⠀⣼⣫⣽⣿
⠀⠘⡃⣡⣿⠟⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣋⣀⣀⡬⠋⠀⢀⣈⠿⠿⠿
⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠛⠒⠛⠋⠁⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⡤⠔⠒⠒⠒⠒⠦⢤⣀⠻⣉⣛⡻⠖⡢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢒⠩⠉⠉⠉⠉⣙⡒⠞⠡⡔⠂⠻⢍⠠⣬⣉⠴⢋⣀⠬⠽⠷⠶⠮⣕⡝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠔⠈⣠⠔⠚⠉⠩⠥⠀⠈⡤⢲⠤⠤⠿⠒⠳⢯⣀⠘⠛⠢⠴⢾⣀⢀⣡⠐⠩⡒⠉⣒⠒⡢⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣩⠟⡡⣒⠁⣴⠀⣀⠴⠋⠀⡞⠢⢤⣧⠀⣄⠀⠈⠑⢤⡀⠀⠀⡏⠁⠙⣻⠛⢻⠀⠪⡙⢦⡁⠂⢝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠊⣰⣏⡼⠙⡟⠁⢰⣄⣜⠁⠀⣸⣁⠉⣹⠓⠒⠒⠉⠁⠀⠀⡨⢷⠟⢳⡀⠀⣧⠀⠋⠢⡙⣤⡷⣄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⠁⠀⠀⢰⠃⣠⠞⠀⠈⠉⠉⠹⡟⠛⣩⣆⠀⠀⠀⠀⡠⠞⠙⢦⣀⠏⠈⠉⠉⢣⡀⣦⠰⡜⣆⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠛⣎⠁⠄⢳⡀⢀⠞⠣⣁⢈⡞⠁⠀⠀⠀⠀⠀⠈⠙⢦⣘⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠤⠚⢦⡟⢌⡐⢨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠈⢀⡇⠀⢩⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠚⠡⢘⡍⣿⠀⠻⡅⠉⠀⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⠔⠒⠋⣻⣨⠵⠚⡏⣟⠢⠀⢱⡀⠀⠀⠀⢱⠈⣑⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⢊⠁⠀⠀⠉⠈⠙⠲⠒⠓⠼⠒⠚⠈⠃⠠⢀⣀⡀⠠⠈⠠⠒
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⡀⠐⣀⡤⠤⠬⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⡴⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠢⠀⠈⠳⢤⣀⣠⡤⠔⠒⠒⠦⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⣉⣈⣵⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢩⠥⢤⠀⠀⡤⠤⢤⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠤⠜⠀⠀⠷⠶⠾⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠒⢢⠀⠀⡴⠒⢢⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣄⣠⣈⣀⡀⠀⡇⠈⠃⠀⠀⠀⠙⠒⠚⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡖⡆⠀⢴⢢⠁⠀⡇⢸⠁⡇⠀⠀⢸⠉⡃⠀⢸⡆⠀⠀⠀⠀⡴⠒⠢⠴⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡩⡅⠀⡨⡅⠀⠀⡇⠈⠁⠀⠀⠀⠈⠉⡁⠀⢸⡇⠀⠀⠀⠀⡏⠳⠂⠪⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡓⡀⠀⣑⡀⡼⡞⡇⢸⠉⢱⠀⠀⢨⠀⢹⠀⢸⡧⠤⠦⠤⠀⡇⠃⠇⠮⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠇⠁⠀⠧⠀⡤⠆⡇⠈⣉⣀⠀⠀⠀⠀⠉⠀⢸⡗⠆⠖⠶⣆⡇⠃⠃⠮⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠒⠂⠀⠆⠂⣟⡃⡇⠸⣄⣠⠀⠀⠸⣇⣸⠃⠈⡏⠆⠪⠶⣏⠁⠯⠃⠮⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⢺⠀⣤⡄⠀⡬⠄⢯⠀⡇⠀⡀⢀⡀⠀⠀⠈⠈⠀⠀⣏⡙⠻⠅⡗⠀⠇⠆⣎⡇⠸⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⣓⠁⠀⣃⡀⠗⠀⡇⠀⣇⡰⠇⠀⠠⡏⢩⡇⠀⣯⠙⢺⡀⡯⢰⣂⠆⣆⡄⠀⠆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠰⠼⢀⡀⠧⠅⣾⠀⡇⠀⠀⠀⠀⡤⢤⠈⠀⠀⠀⢿⠚⠘⠉⡏⡀⣀⡄⢐⡂⣇⡂⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢸⠀⠀⠏⢸⠀⣀⡏⢐⣇⣀⣀⣀⣀⣃⣸⣀⣀⣀⣀⣸⡐⠆⠀⡇⢰⠀⡖⡄⠀⡧⣍⣿
⠀⠀⠀⠀⠀⠀⠤⠖⠒⠒⠛⠓⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠓⠲⠷⠶⠯⢥⠿⣤⣀

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠢⠀⢨⡦⠀⢀⠄⠢⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠢⠀⠀⣠⡶⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣢⡄⢲⣄⣦⠀⣤⠎⢀⡲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡘⣢⡔⠵⡄⢁⡔⢨⡡⠂⢑⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠍⠶⠬⠑⠄⣀⡡⢊⠴⢂⡉⠉⡥⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⢀⡉⠲⡐⢈⢁⠋⢠⠶⠅⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠂⠐⠶⢂⠈⢣⡿⡿⣭⢀⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣆⢀⣩⠀⣙⢾⣿⠥⢄⠛⠛⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢷⠖⢉⣠⢺⡇⡛⣄⢢⡉⠣⡁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⡤⢊⡰⠋⣽⡅⠠⣌⠫⡀⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡠⠪⠉⠍⢁⡆⢸⣄⡓⠠⢔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠂⠘⡤⡏⢠⡑⢻⠸⢶⠈⠛⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢠⠃⢿⡼⢿⣄⢸⢹⡷⢂⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⡘⠱⡎⠄⠇⠱⢖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢨⡁⣙⠲⣹⣯⣍⠰⡍⠶⢖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠃⡇⢘⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⡺⢾⠝⢓⣽⢿⠿⣥⡞⢇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠧⡸⢻⠟⡎⣷⢳⠙⡙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⡔⡡⠾⠛⣤⠎⠏⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠎⢰⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡉⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠇⠀⡗⠚⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠓⠂⠠⢄⣀
⠀⠀⠀⠀⢀⠀⡠⠋⠉⠀⠀⠀⠓⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⡸⠀⠀⠀⣀⡨⠉⢰
⠀⠀⠀⠐⠁⠀⠁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠅⠐⢀⠩⠄⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢔⡀⠉⠒⠠⢀⡀
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡻⠀⠀⠀⠈⠁⠂⢄
⠀⠀⠀⠀⠈⠒⠤⠀⣀⣀⠀⠈⠂⠀⠀⠉⠀⠈⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠰⠶⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠹⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠰⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡎⠀⠀⠀⠀⠀⢀⡴⠂⠉⠀⠀⠈⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⢢⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠧⡀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠒⠈⠉⠁⠀⠀⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠈⠉⠉


⣶⣶⣶⣶⣶⡷⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣿⣶⣿⢷⡶⢶⠿⠿⣶⣾⡿⠿⠿⠶⢿

⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⢠
⠀⠀⣼⣗⠀⠀⠀⠀⠀⢀⣾⡄
⣠⣀⣿⣷⣦⠀⡀⠀⣸⣿⣿⡥⠀⠀⡄⠀⣴⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣾⣿⣿⣾⣿⣿⣿⡦⣶⣶⣷⣶⣟⢠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣾⣧⣄⣶⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⣦⣼⠀⠀⠀⠀⢀⢀⣄⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠷⠿⣿⣷⣌⣿⡿⢿⣿⣿⣿⣶⡐⠛⠛⠛⠛⠛⠿⠛⠛⠛⠒⠒⠚⠛⠛⢛⣳⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣭⣭⣭⣿⣷⣶⣶⡾⠟⠋⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠉⠂⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿
⢿⡿⢿⣿⠋⠙⠿⠻⢻⣿⣿⡿⠛⠛⡿⠿⣿⡏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠘⠋⠉
⠀⠀⠘⠃⠀⠀⠀⠀⠈⠉⣿⠃⠀⠀⠀⠀⠹⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣞⣿⣏⣰⢤⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤
⠀⡀⠀⠀⠀⠀⠀⣀⢠⠤⢌⠧⢻⣿⣶⣾⣿⠿⢼⠛⢪⠈⣿⠙⠠⢷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠁⠀⠚⠂⠈⠉⠉⠉⠉⠉⠉⠃⠛⠛⠛⠓⠲⠶⠦⠛⠞⠒⠴⠿⠻⠯⠌⠶⠆⠰⠀⠀⠀⠀⠐⠓⠲⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠂⠀⠀⠠⠠⠀⠀⠴⣦⡤⣶⣄⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠐⠶⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⡈⠉⠁⢀⣀⡀⠀⣀⣀⢀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠉⠁⠁⠀⠀⠀⠀⠈⠀⣀⣀⣀⣉⣀⣭⠤⣤⣤⡄⠤⠥⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠶⠐⠒⠤⠤⠤⠶⠮⠍⠛⠛⠛⠛⠋⢉⣉⣠⣤⣤⣴⣶⡶⠖⠒⠀⠒
⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠠⣤⣤⠤⠄⠀⠐⠺⠓⠂⠶⠂⠀⠀⠀⠀⠉⠁⠉⠉⠉⠉⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠋⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠄⣀
⠀⠀⠀⠀⠀⠠⠠⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⣄⠑⢧⡄⠀⠀⠀⠀⢀⢉⣀⡢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠈⠃⢆⢳⡄⡠⢨⣀⡬⡉⠉⠀⠁
⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⡄⠀⡄⠍⣑⢪⣾⡸⠾⠛⠑⠒⠛⠂
⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠴⡀⠀⠀⠀⠀⠀⠀⠁⡠⣴⡾⢿⣯⣿⣿⡧⡴⠖⠒⢏⢲⡢⡲⡠⡄⡀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡘⠻⠛⠟⣻⡏⣽⢁⣧⢀⠀⠀⠁⠀⠀⠈⠈⠃⠠⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠰⠋⠠⡢⠊⠨⠇⡏⢸⠁⢋⠀⠘⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡱⠁⠀⠀⢶⣇⠏⠀⠀⠘⠆⢠⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠄⠀⠀⠀⠀⠀⡤⠤⠠⠤⠤⢤⣄⣤⣤⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠒⠀⢰⡆⣸⡤⠄⠀⣀⡀⠀⠂⠋⠉⢉⣛⣉⣉⣉⣉⡩⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠁⠁⠉⠁⠈⠀⠀⠀⠁⠒⠢⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠰⠶⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⢹⠗
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠒⠀⠀⠂⠀⠤⠤⠤⠄⠶⠒⠚⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣦⣄⡀
⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠻⠿⠟⠛⠛⠛⠓⠒⠒⠒⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣾⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⣤⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⡆⣶⠀⢠⣰⣆⠀⠀⢀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣢⣤⣦⣴⣾⣷⣶⣿⣿⣦⣾⣿⣿⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⣭⣭⠧⠤⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢠⠒⠢⠀⢀⠄⠀⡤⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠒⠂⠀⠘⠓⠒⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡇⢰⡉⡶⠀⠀⡖⠋⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠦⠶⠶⠦⠤⣄⠀⡇⢈⡀⡁⠀⠀⢉⣉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢾⡹⠀⠸⠽⠈⠀⡇⢸⠄⠇⠀⠀⢢⣠⠇⠀⡇⠀⠀⠀⠀⢸⡍⡉⢚⣖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠲⠀⠐⠂⢀⣀⡇⢀⠀⡀⠀⠀⠠⠤⠀⠀⡇⠀⠀⠀⠀⢘⡩⢅⢘⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠨⢡⠀⠄⠀⠘⠂⡇⠸⠄⠇⠀⠀⠠⠄⠄⠀⣿⣒⢛⡒⠀⢀⡨⡁⣑⡉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⢐⡂⠀⢈⡀⢘⡅⡇⢠⠄⢠⠀⠀⢠⠀⢠⠀⢿⣈⢘⢊⣷⠾⡤⡅⡩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⣘⣀⡇⠠⠀⠀⠠⠌⣰⠆⡇⠈⠒⠚⠀⠀⠘⠶⠾⠀⢸⠨⣨⠎⣿⠂⡩⡁⡩⣅⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡃⡇⢞⡇⠀⢈⠑⢉⠀⡇⢠⡆⢰⠆⠀⢠⠄⢤⠀⢸⠶⣤⠁⣿⠀⡙⡁⡑⠃⠀⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡧⡐⡆⠀⠐⠲⣨⠄⡇⠀⠛⠈⠀⠀⠘⠂⠚⠀⢸⣇⠰⡷⢿⠐⣓⣁⢓⠃⡀⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠉⢰⢲⠈⠁⡿⠂⡇⠀⠀⠀⠸⡏⡏⠀⠀⠀⠀⣇⢤⠀⢸⢸⠙⣩⡈⠁⡗⠆⡇
⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣧⡤⠼⠾⠶⠶⠳⠶⠿⠒⠒⠒⠒⠓⠓⠒⠒⠒⠲⠗⠶⠶⠾⠼⢤⣥⣇⣀⣇⣃⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣐⣈⡂⣺
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢼⠄⠶⠠⢼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢸⠀⡨⠍⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠘⠒⠓⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠈⠉⠉⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⣒⣒⣒⣒⣒⡒⢆⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠠⠀⠀⠀⠤⠄⠀⠀⠄⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡄⠀⢿
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⢸⠰⠭⠂⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⣀⠤⠀⠐⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠼⠼⠤⠤⠤⠤⠤⠦⠼⢄⣀⣀⣀⣀⡼⠀⠀⠀⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠭⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡆⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠙⡿⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⣀⠀⡄⢀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⠠⢀
⠀⠀⠘⠁⡗⠐⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠰⠓⢿⠉⠀⠀⢰
⠀⠀⠀⠀⠃⠀⠀⠀⡎⠀⠀⡲⣶⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡄
⢀⡀⠀⠀⠀⠀⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⢄
⠀⠀⠀⠒⠐⣤⠉⠠⠂⠀⠀⠀⠀⠐⠒⠲⠶⠶⠖⠢⠀⠐⠒⣶⣶⣻⡶⠶⠒⠒⠀⠖⠒⠒⠀⠴⠦⠄⠐⠂⠉⠉⠉
⠈⠁⠀⠀⠱⠀⠀⠀⠀⠀⣀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⢀⠈⠁⠐⠒⠀⠀⠀⠀⠀⠀⠀⠉
⢀⡀⠲⠷⣤⣤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠉⠀⠀⠀⠐⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠖⠒⣀⣀⡀
⠀⠀⠀⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠉⠁⠂⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠊⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⢸⠛⠒⠀⠀⠀⠀⠀⢠⣄⣀
⢠⡄⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⡤⠾⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⢲⠃⠀⠀⠀⠀⠈⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠒⠂⠄⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣀⠀⠁⠢⣀⠌⠀⠀⠈
⠀⠀⠀⢀⠊⠁⠀⠀⠈⠐⠀⠀⠠⠀⠀⠀⠐⠀⠂⠈⠸⠀⠀⠀⠀⠤⢀⣀⠀⠈⢢⡖⡀⠀⠀⠠⠤⠆⠠⠄⢀⣀
⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢈⠩⣦⣴⠼⢤⡶⠖⡀⠀⠀⠀⠀⠀⠀⠈⠂⠄
⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠄⠁⠠⠐⠀⠀⠄⠀⡘⠁⠀⠀⠁⠀⠀⠁⠀⠸⠀⠀⠠⡀⡀⠀⠀⠀⠐⠥⡀
⠀⠀⡀⠀⠓⠤⢀⡀⠠⠔⠁⠀⠀⠀⢀⠄⠀⠀⠀⠀⢀⡄⠐⠀⠄⠀⢣⡀⠀⡠⣇⠀⣠⣇⣀⠜⠀⠀⠀⠀⠀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢁⠀⠀⡠⠠⣀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠘⠒⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⡌⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠋⠉⠉⠙⢛⠻⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢬⡣⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠑⡌⣆⢳
⠀⠀⠀⠀⠀⠀⢀⣠⢖⡫⠟⠋⠁⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⠞⣹⣄⠀⠀⠀⠀⠀⢸⢸⠘⡆
⠀⠀⠀⠀⢀⡴⢋⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣡⠆⠙⢮⡑⢦⡀⠀⠀⠈⠈⢀⡇
⠀⠀⠀⢠⠏⡰⠋⠀⠀⠀⠠⡖⣦⣀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⠞⠁⠀⠀⠀⠳⣄⠙⠳⣄⣠⢰⢸
⠀⠀⢀⡏⢰⠁⠀⠀⠀⢀⡴⡿⠦⣍⠓⢦⣀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣠⠊⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⣆⠈⠻⣮⡞
⠀⠀⠸⠀⡎⠀⠀⠀⠀⣼⢀⡇⠀⠈⠳⣦⡈⠳⣤⡀⠀⡇⠀⠀⠀⠀⢰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠘⣇
⠀⠀⠀⠇⢣⠀⠀⠀⠀⡇⢸⠁⠀⠀⠀⠀⠙⢦⡈⠛⢦⣷⠀⠀⠀⠀⠇⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸
⠀⠀⠀⠸⡘⠀⠀⠀⢸⠁⡼⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠹⡆⠀⠀⢸⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸
⠀⠀⠀⠀⢣⠁⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⢹⡄⠀⠀⣧⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⡇⡸
⠀⠀⠀⠀⠀⢧⢆⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡇⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⡴⠁
⠀⠀⠀⠀⠀⠀⠻⣷⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣷⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡴⢊⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣷⡀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠚⣸
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠹⣜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⢧⠀⠀⢸⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡠⢚⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣘⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣸⡆⠀⠀⡇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣇⠀⠀⢱⢹⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠈⣾⣧⡀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠈⠛⠿⠿⠷⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⢠⡀⣠⣶⠶⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢐⡖⢾⣿⣿⣫⣤⣤⣤⣀⡈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⠿⣿⣟⠶⠲⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠐⣡⣾⠼⡈⢳⣄⠈⠙⠆⠳⡅⠀⠀⠀⣠⣼⣶⠒⠲⠦⠀⠀⣦⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣡⣠⢹⣿⡀⠛⢾⡿⢦⠀⠀⠀⠰⠀⠀⣩⢖⢻⣷⣄⠙⠦⣴⢞⣻⢿⠛⡛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡟⠈⢿⠃⠀⠀⢿⡊⠀⠂⠀⠀⠀⢰⠛⠀⠀⡿⣽⣧⠀⠏⠸⠏⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⢦⡄⠑⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⡀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠒⢒⠂⢒⣒⣀⡀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⡀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⠷⠶⢷⠷⠶⠾⠷⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠉⠲⣄⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣔⠀⠀⠈⠙⢦⣄⠀⢈⡷⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⢄⠉⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠳⣷⡀⠀⠀⠻⡡⣌⡁⠻⣆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠤⢴⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠦⢤⡵⠦⡙⣿⣤⢴⣎⣀⠚⠓⡦⣭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣠⠴⠾⠛⠉⢀⠄⠠⠞⠓⠲⢵⣬⣣⣿⠚⠻⢴⣿⣇⠨⠟⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣛⠂⠀⡰⠀⢠⡿⠋⡄⡆⣠⣿⣄⣻⣿⣮⣷⣄⣠⠀⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⣉⣴⢏⣴⣿⠅⣘⡁⡥⣸⣷⡿⣿⠿⠻⠿⠿⠿⠿⠟⢿⣶⡈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠟⠛⠿⠿⡷⠾⠿⠷⠿⠋⠋⠀⠀⠀⠀⠀⠀⠑⠀⠐⠁⠀⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⠀⠀⠀⣀⣀⠀⠀⠀⣀⣀⢀⠀⠀⠀⢀⣦⣀⣶⣼⣦⣤⣤⣤⣀⣀⣀⣀
⠀⠉⠉⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠉⠉⠉⠉⠙⠛⠿⢛⠛⡟⠛⠋⢻⠉⠋⠛⠋⠉⠉⠉⠉⠉⠩⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠶⢶⣾⣶⣿⣿⣿⣶⣶⣾⣶⣾⣶⣶⠶⠒⠓⠒⠂⣾⣾⣶⣿⣶⣶⣦⣦⣤⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣬⣭⡍⢹⣿⡿⡟⠛⠋⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⣿⣿⣾⣿⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠟⠗⠊⠉⠉⠀⠀⠀⠀⠀⠀⢀⡾⣰⣿⣿⣿⣿⣟⡿⠷⠶⠈⣉⠉⠀⢀
⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡀⠀⣀⠀⢀⡀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⣰⣿⣿⣿⣿⣉⠑⢶⠖⣶⣶⣿⣷⣾⣿
⣿⣿⠿⠿⠿⣿⣿⣿⡿⠿⢛⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠌⢠⣿⣿⣿⣿⣿⡿⢟⣛⢿⡿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠈⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⢀⣠⣀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠰⣿⣿⡆⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠛⢿⡟⠁⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⣀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢡⣤⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⢿⣆
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠛⠙⠗⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠀⣠⡀⢻⡆
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⡀⠀⠀⢰⡦⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⣠⣄⠀⠛⢻⣏⠀⠀⠀⠂⡄⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠒⠀⠀⠀⠰⣿⡷⠿⠀⠘⠛⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⣄⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡗⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡁⠀⠀⠀⠀⣼⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠉⠀⣀⣿⣀⠀⠸⠝⠀⠀⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣤⣤⡀⠀⣀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠙⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⢀⣀⠀⠀⠀⢠⣄⠀⠀⠘⠻⣯⠀⠀⠛⢁⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠊⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠾⠛⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠻⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠇⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⠤⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⢰⠀⠆⠠⢎⠀⡀⢇⠈⡀⣄⠒⠢⣌⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠈
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⡄⠐⠀⡈⠒⠒⠈⠀⣀⢀⠀⠀⠀⠀⠀⠈⠒⠀⣘
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠘⠒⠁⠀⢀⠠⡀⠒⢹⠀⠁⢠⠀⢂⢀⡇⠐⢸⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣘⠉⠀⢃⠀⠈⠤⠓⠘⠂⠈⠉⠁⠀⢇⣘⢠⠀⠁⠀⠘⡆⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠄⢠⡃⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠰⣦⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢾⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⢀⣀⠀⣰⢀⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣄⣀⠀⠀⠀⣠⠀⠀⣦⢠⡀⠀⢈⣿⣯
⣿⣿⣿⣿⣿⣧⣽⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⢿⣿⣿⣿⣿⣿⣿⣷⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣀⠀⠀⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢒⠓⣲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣶⣤⣦⣤⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠻⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⣟⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠳⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣠⣦⣾⣦⣴⣦⣽⣶⣷⣶⣶⣾⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢿⣃⣀⣀⣀⣀⡴⣄⣀⣀⣀⣀⣻⠿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⠀⠀⠀⠀⣷⣾⣯⣿⣿⣿⣿⣷⣿⣽⣿⣿⣯⣿⣶⡇⠀⠀⠀⢀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣻⣤⣤⣤⣾⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣦⣤⣤⣼⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣾⣿⠿⣿⣿⣿⢠⡄⣿⣿⣿⠿⢋⣭⣍⠻⢿⣿⣿⡇⣴⢸⣿⣿⡿⢿⣿⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠈⠉⣿⣿⢸⡇⣿⡿⢇⠞⠋⠀⠈⠛⢆⠿⣿⡇⣿⢸⣿⡟⠉⠘⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣹⣿⢸⡇⣿⣇⣏⠀⠀⠀⠀⠀⢈⣇⣿⡇⣿⢸⣿⡃⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢸⡇⣿⢱⡇⠀⠀⠀⠀⠀⠀⣷⢹⡇⣿⢸⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣿⣿⠻⠙⠿⣿⣿⢸⡇⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿⢸⡇⣿⢸⣿⡿⠟⠻⢻⣿⣷⣶⣶⣶⣶⣶⢶⣶⣶⡶⣶⣶
⠀⢸⡇⠀⠘⣿⠇⠀⠸⣿⠁⠀⠹⣿⣿⠀⠀⠀⣿⣿⢸⡇⣿⢸⡇⠀⠀⠀⠀⠀⠀⣿⢸⡇⣿⢸⣿⡇⠀⠀⢸⣿⡿⠁⠀⢹⡿⠀⠀⢿⡟⠀⠀⣿
⠀⢸⠇⠀⠀⣿⠀⠀⠀⣿⠀⠀⠠⣿⡿⠀⠀⠀⢿⣿⠸⠇⣿⠈⠁⠀⠀⠀⠀⠀⠀⠉⢸⡇⠿⢸⣿⠇⠀⠀⠸⣿⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢼
⠀⠈⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⢀⣄⠀⢠⣠⣤⣀⣀⣀⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣖⠊⠛⠂⠩⠞⢢⣄⠅⢀⡴⠒⠉⠁⠀⠀⠈⠉⠉⣉⣈⡳⠀⠓⢶⠦⡢⢄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠛⠖⠂⠀⠐⠦⣄⢠⣶⣁⠀⠀⡜⠉⠉⠁⢄⣲⠤⣤⣀⡔⠃⠀⠀⠀⠀⠀⠀⠘⠛⠵⣬⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠄⠀⠀⠀⠀⠀⠧⡀⢈⡇⠀⠈⠓⣇⠀⢰⠁⠀⠈⠉⠈⢢⠂⡂⠂⢀⡀⠀⠀⠀⢀⣰⡄⠈⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠑⢤⣀⠐⠀⠀⣀⠀⠀⠀⠀⠘⠜⠀⠀⠀⠀⠉⠂⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣀⣤⡴⠎
⠀⠀⠀⠀⠈⢡⠀⠀⠀⠀⠉⠛⢿⣻⣶⣶⣶⣤⡤⣭⣤⡬⣥⣤⣤⣤⣤⣤⣤⡤⣤⢤⣤⣤⣴⠶⠶⠚⡛⡻⠟⠉⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠉⠻⢮⣁⣩⡳⣮⠋⡇⠀⠘⢸⠁⠂⠞⠁⠀⠈⢀⡺⢣⣦⣤⠴⠊⠁
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⢰⡥⣤⣤⠈⣠⣦⣴⣴⣶⣾⡼⠗⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠘⠉⠀⠀⠀⠀⠉⠀⠒⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣰⠃⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢀⣴⠖⢣⣼⢋⣠⠟⣰⡇⣠⣄⠀⠠⣄⡀⣶⣤⡀⠀⠀⠀⠀⠀⠀⢸
⣀⣤⠀⣤⣤⣤⣤⣤⣶⣿⣿⣿⣾⣿⣧⣾⣿⣵⠟⢃⣶⡿⣹⣏⣉⡠⡴⣠⢥⣭⣿⣿⣷⠶⣶⣶⠶⣦⢸
⠘⠛⠛⠒⠒⠲⠚⠇⠬⠭⠭⠯⠍⠿⢉⣙⣓⣛⢒⣛⣿⣅⡠⠤⠽⠿⠿⠿⠛⠛⠻⠛⠛⠛⠛⠉⠉⠉⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈⠆
⠀⠀⠀⠀⡔⠊⠈⠉⠀⠁⠒⠤⡀⠀⠀⠸⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⢀⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⡇⠀⠀⠀⠀⣌⡠⠤⠄⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⢣⠀⢀⠔⠉⠀⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠁⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢆⠎⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠈⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠒⠂⠤⢢⡀⠀⠀⠀⠈⠀⠀⠀⢀⡔⠁
⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠒⢄⡀
⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⣀⢴⠃⠀⠀⠀⢰⠜⠒⢄⡀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⢠⠀⠀⠀⠀⠀⢀⠠⠊⠁⡆⠀⠀⠀⠀⠸⣄⠠⠐⠉⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢉⠔⡝⠁⠀⠀⡀⠀⠀⠀⠻⠢⢄⣀⠀⠀⢀⠔
⠀⠀⠀⠑⠤⠤⠐⠂⠁⠀⠀⠀⡃⠀⠀⠀⠀⠸⠘⡀⠀⢀⡀⠴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠓⠎⠀⠀⠀⠀⣧⠀⠀⠀⠀⢁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⣠⠃⠀⢰⠈⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠼⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⡦⠤⠐⠂⠉⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠤⣀⠘⢄⠀⠀⢀⠌⠀⠘⢄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⣀⠠⠵⠀⠀⠀⠀⠀⠀⠀⢠⣃⠀⠀⠀⠈⡛⠉⠀⠁⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⠃⠀⠀⠉⠐⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⡠⠄⠒⠀⠉⠙⡀⠀⠀⠀⠀⡘⠉⠀⠒⠂⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠠⠤⠒⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠠⠀⣀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠠⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⡀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠁⠤⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠃⠀⣈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⠀⠒⠒⠠⠤⢀⣀⣀⣀⣁⣀⡀⠀⣀⠤⠒⠐⠀⠀⠒⠠⠄⠀⠤⠐⠂⠉⠀⠀⠀⠉⠐⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⣾⣇⣾⣿⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⣀⣴⣦⡤⠀⠰⠶⠾⠿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣤⣾⣧⣰⣦⣼⣿⣿⣿⣿⣿⣾⣿⣿
⣻⣿⣶⣶⣶⣶⢿⣯⣭⣿⣿⣿⣭⣬⣽⣤⣤⣤⣤⣲⣶⣴⣴⣤⣄⣠⣬⣭⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿
⣛⣛⣛⡛⢛⡛⣛⣛⣛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⣛⣛⣛⡻⠿⠿⠿⠛⠿⠻⠿⢿⣿⣿⣿⣿⣭⣉⣛⣿⣛⣛⣻
⡿⢿⠟⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣟⠉⠍⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠱⠋⠀⠀⠀⠈⠈⠢⠀⠀⠀⠀⠀⠹⠿⠻⣿⡿⠻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿
⡟⠒⠒⠒⣶⣶⠶⣶⣶⣦⣶⠟⢛⣲⣶⣶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⡿⢿⣿⠷⠻⣿
⣉⡉⠻⣿⣿⣤⣀⣈⣻⣿⣿⠿⠿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⣴⡤⣨⣅⠀⠀⠀⠀⠙⠃⠈⠉⠀⠀⠙
⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⡀⣀⣀⠀⡀⢠⣤⣤⡄⣠⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣺⣯⡩⡄
⠀⠀⠀⠀⠀⣠⠀⠀⠀⣭⠷⢿⡿⠯⠥
⠀⠀⠀⠀⡐⣿⡃⠀⠈⢙⣯⣿⣯⢭⢷⡒⠀⠀⣀⠠⠄⣀⡀
⠀⠀⠀⣸⠽⣿⠯⢧⠬⠵⣿⣿⣯⡛⠛⠓⡱⠋⠀⠀⠀⠀⠈⢢
⠀⠀⠀⢙⣭⣿⡿⠕⢚⣛⣿⣿⣟⣛⠛⢹⠃⠀⠀⠀⠀⠀⠀⠀⣃
⠀⠐⣒⣺⣿⣿⣟⡚⣧⣖⣻⣿⣟⣛⣿⢻⡅⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⢒⣪⣽⣿⡖⣭⡭⠭⣭⣿⣟⡛⣛⠛⠛⠋⠑⢦⠀⣀⡤⠊
⠀⣀⣖⣶⢿⣿⢿⡟⣳⣶⣿⣿⣿⡛⠛⠛⠋⠉⠁⠈⢣⡀⢀⠔⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⠑⠤⣄
⠀⣠⣶⣿⣿⣿⡶⠿⡵⠾⣿⣿⣿⣋⣛⠓⠳⠖⠒⠃⠀⠉⠁⠀⢀⠈⠁⠁⠈⠁⠀⠉⡐⠠⠤⠔⠈⠀⠀⠀⠀⠀⣠⠀⠀⠑
⠀⣀⣶⣿⡿⣿⣿⣓⣚⣻⣯⣽⣿⣟⣛⣛⣗⣶⣒⣶⣦⣤⣦⣦⣿⣤⣤⣶⣶⣦⣤⣼⣷⣶⣶⣶⣶⣾⣿⣷⣴⣦⣿⣧⣦⣦⣤
⠩⠿⠿⠿⠿⠿⢿⣛⣿⣯⣭⣬⡷⠛⠻⠿⣿⣋⣚⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠃⠀⠀⠀⠀⢀⣈⣉⣉⡛⠯⠍⠉⠈⠉⠉
⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠄
⠀⠀⠀⠘⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⣴⣶⠀⣀⡀
⠀⠀⠀⠀⠀⠙⠓⠀⠀⣠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣀⣀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣐⣶⣤⣄⣤⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣴⠖⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠉⠛⢶⣷⣾⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣰⠟⢻⣿⣿⡿⠦⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⣀⣠⡶⠺⣿⣿⣤⡘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠁⢠⣟⠺⣿⢧⡀⠈⢿⣆⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡾⠋⢀⣠⠀⣿⡷⠻⣯⠀⠀⠀⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠞⠀⠈⡄⣿⡀⢳⣿⠶⠻⢄⠀⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠋⠀⣀⣾⡏⠀⣾⡇⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢚⣿⡆⢃⠺⢿⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⡌⣿⠀⠀⠈⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠈⠀⠀⠻⠀⠈⡄⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢨⠎⠀⠀⠀⠙⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠀⠠⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⣠⡀⢀⠀⠚⠉⠁⠉⢀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⠦⠀⠰⣀⠀⡀⠙⠻⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣶⡆⠀⢀⠀⠀⣈⠀⠀⠀⣤⠄⠀⠑⠄⠀⠀⡆⡈⠻⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠀⠛⢸⡿⠄⢀⣿⣶⣿⠟⠃⠀⠀⠉⣲⡄⠀⢐⡇⣠⣿⣗⠀⠁⠺⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⢸⣾⣿⠁⠀⠤⠄⠻⠉⣠⠀⠀⠀⠀⠈⣼⣇⣀⡾⠛⠋⡟⠉⠀⢹⠶⠀⠠⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⣠⣀⡀⠀⠀⠀⠉⠈⠛⠶⠔⠿⠶⠶⠿⣶⡶⠦⠾⠾⠿⠿⣿⣧⣴⠶⠷⠆⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢒⠲⣖⣲⣒⡒⠂⠁⣤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠉⢙⡛⠛⠤⠀⣀⡀⠀⠀⢀⣀⣀⠠⠤⠴⠶⢦⣤⣤⣄⣠⣤⡤⠴⢚⣡⣤⣍⠤⠤⠍⠉⠈⣉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⠉⠉⠁⢀⣀⣤⣤⣀⠐⠒⠚⠛⠓⠶⢆⣄⡀⠀⠀⠀⣉⠥⠤⠤⠄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠤⠤⠤⠶⠒⠲⠦⠤⠄⠀⠉⠉⠀⠛⠓⠂



⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣠⠔⣊⡭⣤⠙⠦⢀⡀⢤⠔⠊⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠂⠀⠀⠀⢺⠁⠊⠁⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀⠀⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⣡⠈⡅⠀⠀⠀⠀⠀⠘⢹⠁⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠖⢻⠀⡼⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠁⡅⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⢀⡃⡆⠀⠀⠐⠁⠀⠀⡇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⣖⠀⣀⣀⠀⠀⠠⡄⠃⠀⠈⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠆⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⠃⠀⠀⠀⠀⠀⣠⠀⣄⠀⢀⠀⢀⡄⢀⠛⠋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠘⠀⠀⠀⠀⠀⠐⠀⡄⠀⠀⠄⠈⢁⠸⠶⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠴⠶⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⠠⣤⡆⠀⠀⠀⠀⢤⠙⠣⠀⠐⡃⠀⠀⢲⢀⣀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠠⠀⠀⠀⠀⠀⠘⠲⠐⠒⢇⣩⠀⠀⠀⠀⠀⢸⣳⠀⠀⡇⠀⠀⠘⡅⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⡆⠀⠀⠀⠀⠈⢸⠀⠀⠇⠀⠀⠀⢳⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⢦⣰⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣆⠀⠁⠀⠀⠀⠘⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡜⢧⠀⠀⠀⠀⡀⠀⠀⡆⠀⠸⡇⠈⡆⠀⠀⠀⠀⠧⣼⠘⠀⠀⠀⠀⢠⠀⢰⢧⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⢀⠓⣴⠃⠀⠀⠀⠀⠂⠈⢀⠃⠀⠀⠀⡘⢠⠎⠈⡇⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⠀⠘⠆⡀⠈⠉⠁⠢⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠅⠀⠀⠀⠁⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⠃⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⣬⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡸⢴⢔⡁⠃
⠀⠂⣄⠀⣧⡐⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣦⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⡀⡀⠀⡀⠀⠍⢰⢟⠈⠉⠂
⠀⠐⠡⠈⡿⠙⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠻⠛⠀⠀⠤⠠⠀⢿⠴⡄⠀⠀⠂
⠀⠈⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⣾⣯⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠁⢰⠀⣠⡄⠌
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⢾⣯⠀⠀⠀⠀⠈⠊⠙⠟⠿⠟⠛⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠨⠀⠟⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⢠⠄
⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⡀⠀⠀⠀⠀⠐⠒⠀⠀⠉
⠀⠀⠄⠈⠁⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠄⠀⠀⠀⠒⠂⠀⠠⠄⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠉⣄⠀⠀⠀⠀⢠⣤⠀⠤⠤⠄⠀⠀⡀⠄⠠⠄⠤⠤⣤⣀⡤⠤⠀⣤⠀⣀⣠⣒⠀⠀⠀⠀⢀⣂⠀⠀⠀⠀⠉⠁
⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠁⠈⠀⠀⠈⠙⠛⠦⠀⠀⠀⠀⠀⢀⣉⣀⠀⠀⠃⠀⠀⠉⠉⠀⠀⠀⠘⠋⠛⠉⠀⠀⠀⠀⠠⠤
⣤⠒⠀⠈⠉⠑⠂⠀⣀⠀⠀⠈⠉⠉⢀⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⢀⡀⠤⠤
⣀⣀⣉⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣐⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣃⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀
⣿⣿⢛⡻⢛⡛⢻⡻⣻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⢀⣀⣄⡀⡶⢠⣴⣾⡆
⠀⠀⠀⠀⠀⠠⣾⣯⠀⣀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣦⣶⣶⣤⣄⣀⣀⡘⠀⠀⠀⡀⣄⣤⣼⣼⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢀⢸⣶⣿⣿⣆⣿⣠⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠉⠉⠙⠉⠉⠉⣷⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇
⠀⠀⢠⣾⣸⣿⣿⣿⣿⠿⠿⠞⠀⣤⣤⠀⠠⠦⠀⠀⠈⠀⠀⠘⠃⠀⠀⡤⠈⠛⠻⢿⡿⠒⠒⠲⡶⢛⠛⠛⠗⠂
⠀⠀⡼⠿⢿⣿⣿⠿⢇⣄⡀⠀⠀⠆⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠈
⠀⠀⣤⠄⢀⡟⠁⠀⠎⠩⠌⠀⠀⠈⠀⠀⠀⠀⠈⠀⢄⡀⠀⠀⡴⠂⠀⠀⡀
⠀⠘⡇⠖⠀⣭⠺⠂⠰⠒⣰⣄⡤⣤⡄⠶⠀⠀⠀⠀⠀⠙⡀⠚⠡⣀⠀⡠⠈⢿⠷⠦
⠀⠀⣷⣤⡔⠻⣶⢀⡴⠙⢉⣉⠀⠘⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣪⡥⠤⣄⣙⢶
⠀⠀⢿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣶⣴⣾⣿⣶⣶⣦⣶⣶⣷⣤⣴⣿⣶⣏⣠⣴⣾⣿⣁⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠕⢛⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡄⣰⠀⠀⢀⣼⡋⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⢿⠂⠈⣡⡟⠀⠀⠈⠏⢹⢃⠀⠀⠀⠀⣠⣖⣟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠗⠀⠀⠀⢀⠜⣿⢀⡀⠀⠀⠀⠈⠈⠃⠀⠀⠈⠁⠉⢿⠟⠂⠀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣤⠀⠀⠀⠀⠀⡀⠘⢁⢀⣀⣀⣦⢠⣠⣤⣴⣤⡇⡀⠀⠋⣼⠀⠈⠋⡙⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠴⣶⣆⣀⡀⢀⠁⢀⣆⡇⢠⣀⡇⠀⠸⠿⠏⠉⠉⠛⠉⠈⠉⠙⠻⣷⠀⠰⢿⡄⠀⢠⣧⣾⣴⡄⠰⡷⠀⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆⣀⠀⠉⠛⢿⠍⠁⠀⠀⠀⠀⣴⣶⣶⣷⣶⣤⣄⣀⣠⣀⣀⠀⠀⠀⠈⠙⢛⡛⠁⣂⣤⣾⣿⣿⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣷⣤⣄⣀⣀⣀⣤⣴⣶⡾⠿⠻⣿⡿⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠿⠿⠉⠠⢄⣂⣓⣮⡄⠈⣉⠑⢛⣉⠭⠉⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠃⠂

⢀⣄⠀⢀⣄⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠶⠶⢧⠀⢾⠶⢶⣦⡅⠶⠶⠿⡿⡿
⢼⣿⣽⣾⣿⣦⣨⣷⣤⠀⢸⣇⣰⣿⣇⠀⢀⣼⡁⠀⠀⠀⠘⠰⢤⠉⣻⣿⠀⠘⠷⣞⠻⢟⣛⣏⢲⣿⠗
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣾⣿⣿⡆⣀⠀⢀⠀⠀⠀⠉⠙⣦⣼⣷⢿⣄⣉⣅⢽⣿⢿
⢸⣿⣹⣿⢻⣿⡟⢿⣿⣿⣿⢿⢟⢸⣿⡟⠙⡇⠟⠓⠙⠃⠈⠀⠀⠀⠀⢖⣎⠁⠩⣤⣾⣿⡿⢿⣿⣿⣤
⢸⣿⣶⣿⣿⣶⣶⣾⣿⢿⠿⣿⣷⣮⣽⣻⣶⣭⣿⣽⣏⡀⠈⠀⠀⠈⢫⣌⠩⡅⠐⠈⠿⠷⣿⣾⣇⠙⣾
⢸⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣯⡀⠓⠊⠀⠀⡲⠄⠂⢀⠈⠧⢤⣈⣻⣿⣷⣾⣇⣻⡄⢿
⠈⠻⠗⠺⢟⠁⠙⠉⠿⠇⠈⠉⣿⡿⠛⠁⣶⠌⠉⠀⠀⣀⠦⠁⠀⠀⠀⠀⠈⠙⠤⣉⣻⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡍⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠐⣀⡩⡧⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣇⡀⠀⠀⠀⠰⠗⠉⣤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠈⢿⣿⣿
⠀⠰⠂⠀⢦⡖⣀⣤⣤⣄⠀⠀⠀⢸⣟⣀⠀⠀⠀⠀⣤⡔⠲⠚⣄⠀⠀⠠⠀⠀⡀⠀⠀⠄⢀⠀⠈⢻⣾
⠘⡱⠄⠘⠰⣿⠿⡇⠙⢿⢷⣄⢰⣦⣉⠀⠀⠀⠀⠀⣼⠧⠤⠆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⢸⣿
⡔⢁⡄⣿⢆⣿⣷⡘⢦⡈⢳⡙⢷⠏⠀⠀⠀⠀⠀⠀⠚⡀⠀⠁⡈⣧⠠⠀⡀⠀⠀⠀⠀⣀⠀⠂⠀⣸⣿
⡿⢩⡗⣽⢦⣿⡿⡿⣶⣽⣠⣉⡜⠛⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠈⣣⠀⠇⠀⠀⠂⠀⠀⢀⣠⣻⣿⣿
⣁⢯⠿⢹⣷⣨⡝⠻⣿⣿⣿⣿⡷⠒⠒⠒⠀⠀⠀⠀⠈⠀⠘⣁⠰⠇⣨⠀⠀⠀⠀⣠⣤⠴⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠢⢄⢸⠦⠀⢀⠔⢪⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠎⠢⠀⠀⣠⡖⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⢢⡄⠳⡄⢥⠁⣤⠆⢤⡴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡘⢶⡂⠲⡄⢡⡐⣈⡡⠂⠉⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠌⠶⠤⡑⠠⣇⡦⢊⠴⢊⡉⣀⠧⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡌⠲⡈⢄⡁⠋⡠⠟⠐⣂⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠒⠐⠶⣐⢚⢱⣿⡿⣍⢨⣍⠃⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣦⣈⣭⢁⣙⢾⣿⠥⣔⠋⡉⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠳⠞⢉⣴⣢⡇⠟⣬⢢⡌⠣⡁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⡤⢊⠴⠏⣻⢇⠰⢍⠛⡀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡀⠚⢁⢻⢁⡇⢸⣦⡟⠠⢞⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠃⢹⠴⠏⢠⡈⠿⠚⣖⠈⢏⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁⣷⣮⢿⣧⣌⣙⠷⢂⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢀⡜⢳⡃⠆⠆⠰⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢸⠍⣙⡓⣙⣯⣍⠸⠍⠾⢟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠉⠠⢠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡷⢾⠔⣃⣼⢿⠿⠥⣞⢅⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢈⡷⠦⡺⣹⣛⡎⢿⣱⡉⡍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠌⡴⠟⠉⣥⠈⠇⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣡⠊⡐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡉⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠰⠃⠀⡑⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⢨⠃⠀⠒⠠⣄⡀
⠀⠀⠀⠀⣀⠀⡰⠉⠀⠀⠀⠀⠙⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣀⡀⠀⠀⣀⣀⠬⠉⢱
⠀⠀⠀⠌⠀⠀⠙⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⣁⠀⠤⠐⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⣆⠀⠀⠒⠠⢀
⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡝⠀⠀⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠈⠐⠠⠄⠀⠀⠀⠈⠁⠀⡀⠉⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠠⣤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⡈⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠈⠉⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠳⣀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⠀⠀⢀⣀⣀⡤⠊⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠋⠉⠀⠀⠀⠀⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⣀⣀⣀⠀⣀⣀⣀⣀⡀⣀⣀⢀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣤⣤⣤⠠⢤⣤⠤⠤⠒⢲⣶⣶⠶⠦⠤⣄⣀⣄⣤⣤⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠘⣯⡉⠈⠉⠀⠲⠋⡱⣦⠎⠀⣴⣛⣉⡀⠀⠀⠀⠀⠀⠀⢀⣨⣬⠽⠀⠋⠻⠿⠪⡶⣤⠄⣀
⠀⠀⠀⠀⠀⠀⣠⠖⠈⡗⠒⠃⠀⠈⠳⢶⣄⢰⣿⣀⠀⠀⣰⠋⠉⠉⠑⢄⣶⠦⣴⣄⣴⡚⠀⠀⠀⠀⠀⠀⠈⠂⠛⢫⢷⣬⠑⢄
⠀⠀⠀⠀⠀⡀⢳⡀⠀⠀⠀⡀⠀⠀⠀⠀⠸⣧⡀⢈⡗⠀⠈⠛⢻⡂⠀⣰⡃⠀⠈⠋⠉⠻⣴⠒⠒⠢⢀⣀⠀⠀⠀⠀⢉⣸⡄⠨
⠀⠀⠀⠀⠀⠙⣦⣀⠐⠠⠀⠀⡀⠀⠀⠀⠀⠀⠳⡼⠃⠀⠀⠀⠈⠓⠒⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⡉⠀⠀⢀⠀⣀⣩⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⣶⢦⣬⣥⣬⣄⣀⣀⣒⣀⣒⣢⣀⣀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⠖⠶⣿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⢿⣟⠿⠚⠳⣎⡻⢿⡇⠙⠛⡟⣿⠛⠋⣿⠟⠉⢹⠃⢻⣷⢯⡝⠈⣀⡩⠗⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⠿⢩⣿⡀⠇⢀⢀⠁⠿⠀⠀⣁⢀⣠⣠⡀⣻⣥⠟⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠿⢆⣰⠿⠳⠻⠛⠟⢿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⡀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡤
⠀⠀⠀⠀⠁⠑⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⢤⣬⠁
⠀⠀⠀⠀⠀⠀⡉⠁⠈⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠛⠉⠀⢂⠠⠀⡀⢀⢐⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠆⠐⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠔⠈⡀⣉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢣⠀⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠚⠁⠀⠀⠤


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿