Rye bread Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠉⠉⠩⠗⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣊⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠬⢵⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠁⠀⠀⠀⣈⣉⠵⠦⠤⠶⣉⣁⠄⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠈⡳⣄
⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⡠⢊⡴⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⡴⠁⠂⠀⠀⠀⠀⢈⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⡀⠘⣆
⠀⡼⠁⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠘⡆
⢰⠁⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⢹
⡎⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⡇⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢣⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⡸
⠈⠣⡀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠈⠲⠤⣀⡀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣠⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣓⣒⣒⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣖⣚⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣖⣚⠛⠛⠛⠛⠛⣛⣒⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠉⠉⠉⣉⣭⠽⠿⠛⠛⠛⠛⠿⢭⣄⣀⠀⠀⠉⠛⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠛⠛⢓⣶⠶⠿⣭⣀⡀⠀⠀⠀⠀⠀⣀⣠⡤⠿⠛⠿⣯⡉⠉⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠈⠉⠛⢶⣤⣶⠛⠉⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠉⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡤⠴⠶⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠐⠐⠒⡂⠐⠒⠧⠤⣫⣉⠉⠩⠉⠙⠒⠂⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣚⣋⡀⠀⠀⠀⠀⠒⠀⠄⠀⢁⠀⠀⠀⠀⠉⠓⢦⣀⣀⠐⢄⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠌⠠⠒⠔⠲⠈⠭⠩⠉⠙⠛⠛⠛⠛⠒⠒⠤⣌⡐⠠⡀⠉⠁⠀⠈⠙⠲⣄⢀⠀⡰⠐⠈⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠈⣀⢈⣥⣤⣀⣀⣄⣀⣀⢀⣀⡀⠀⠀⡀⠀⢀⣄⠀⠀⠀⠈⠓⠼⠄⢀⠀⠀⡀⢠⡈⠛⢀⡠⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣞⠝⢚⠁⠉⠀⠀⠐⠈⠍⠉⠉⠉⣛⠓⠚⠫⠶⣄⣀⠄⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠨⣆
⠀⠀⠀⠀⠀⠀⡰⡷⠁⠀⠀⠂⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⠀⠂⠀⠠⠈⠈⠑⠯⣂⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠀⡀⠀⠅⢫⡀
⠀⠀⠀⠀⠀⠀⠸⣧⡈⠀⠠⠀⠀⠉⠀⠀⠀⠀⠀⠤⠀⠈⠀⠀⠀⠅⠀⠀⣀⠊⠀⠈⡹⣷⢌⠂⠄⠀⢁⠀⠀⠆⠀⠂⠀⢁⡨⠀⠀⠀⠀⣿⣓⣒⠄⡀
⠀⠀⠀⠀⢀⣀⣴⠿⠿⣦⣄⣈⡀⣀⠀⠠⠄⠠⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠎⠫⣦⠀⡀⢂⡴⠀⠀⠐⠠⠂⠀⠀⠀⠀⠀⣴⡓⠒⠀⠈⠥⠄⡀
⠀⢀⣴⡾⠋⠉⠉⠉⠩⠉⢉⠉⠈⠛⠀⠛⠷⢶⢤⢆⣀⡀⠁⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠂⡀⢳⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡨⠞⢁⡀⠀⠀⠈⠀⠉
⢠⣫⠁⢀⣀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠅⢀⠀⠀⠨⠉⠐⠛⠿⢶⣤⡀⠀⠀⢀⠄⠀⠌⡩⠂⣘⡇⢄⠄⠐⠁⢀⠈⠀⣀⣤⠴⠊⢁⡀⠀⠀⠀⠀⠐⠂
⢺⠉⠛⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠡⠁⢙⢶⡄⠈⠁⠀⠀⢀⡴⡽⠑⡀⠀⡀⣠⠴⠟⠋⠉⠀⠀⠁⠀⠀⠈⠁⡁
⠈⠉⠱⠶⢄⣀⠉⠛⠶⢤⣀⡀⠀⠀⠐⡀⠀⠀⠀⠠⠤⠁⠀⠀⠀⡀⠄⢳⣿⡻⣷⡖⣞⣿⣫⠦⠾⠒⢻⠭⠥⣀⣒⠂⠂⠀⡤⠤⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠈⠉⠓⢶⣄⡈⠉⠓⠶⠠⣀⠀⠀⠀⠀⠀⠀⠆⠈⠄⠀⣠⣞⣼⠦⠩⠀⠀⠉⠑⠒⠒⠬⠥⠒⠒⠠⠤⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⢤⣠⣀⣙⠫⠖⢶⠒⠒⣲⣖⣴⡿⡟⣡⡮⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠤⢴⣂⣲⣧⣴⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠛⠋⠉⠉⠙⠓⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⣀
⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⢀⡴⠋⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠌⢳
⠀⣰⢋⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠱⠑⠤⣀⡀⠀⠀⠁⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⡇
⢰⠃⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢿⠛⠓⠒⠒⠒⠒⠒⠒⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡠⠂⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠠⠀⠀⠀⠀⠀⠀⠀⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢿
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⣃⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸
⠸⡄⠀⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⡀⢀⡞
⠀⠑⣄⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣠⠞⠀⢀⢈⡞
⠀⠀⠈⠓⢄⡀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠕⣠⠞⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠉⠓⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠀⠀⠠⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⠀⠀⠀⠀⠀⠉⠙⠒⠒⠦⠤⠤⣤⣤⣤⣤⣤⣤⠤⠤⠖⠒⠋⠁⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣒⣒⣶⣤⣤⣴⣶⣤⣤⣤⣤⣤⣶⣒⣚⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⢛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⠐⠒⠊⠉⠉⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠦⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⢛⣉⡁⠠⣀⣀⣒⣒⣀⣀⣀⡀⠐⠒⠒⠂⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣶⣿⣿⣿⠿⠿⠿⠟⠛⠛⠛⠛⠿⠿⠿⠿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⣀⣴⣾⡿⠟⠛⠉⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠉⠙⠻⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈
⠀⢀⣾⠟⠋⠁⠀⠛⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⣿⠟⠉
⠀⣾⠏⠀⢀⡤⠀⠀⠐⢈⠀⠀⠀⠀⠀⠘⠀⠀⠡⠌⠀⠀⠀⠀⢠⠀⠀⠀⠸⠀⢰⠀⠀⠀⢀⠀⠉⢿⡆⠀⠀⠀⠀⣀⡤⠖⠊⠁⠀⠀⠀⠀⡼⠁
⠀⢿⣄⠀⠐⠠⠀⠀⠉⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⠀⢀⣼⠇⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠈⠿⣦⡀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠘⠀⠀⠀⠀⠀⠃⠀⠀⠀⠠⠢⠀⠀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⣿⠀⠀⠀⠐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠰⠗⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣿⠀⠀⠘⠀⠸⠀⠀⠀⠀⠀⢀⠄⠂⡀⠀⠐⠁⠄⠀⠀⠀⠀⠀⡰⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣿⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠜⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⢸⡟⠀⠀⠄⠑⠀⠀⠠⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⢸⡇⠀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣎⡠⠀⠀⠀⠀⠀⢠⠢⢄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠖⠋
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠠⢀⠘⠀⠀⠀⣿⠀⢀⠀⠀⠀⠀⠀⢀⡀⠖⠈
⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⡀⠀⠀⠀⠐⠊⠀⠤⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⣿⠀⠸⡀⡀⢠⡤⠖⠈
⠀⠀⠀⠸⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣿⣀⡴⠗⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣄⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢠⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣛⣛⣋⣨⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠅⢀⠔⢀⠔⠉⠤⠤⠄⠀⠳⠯⠟⣠⣤⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠒⢢⠀⠀⠁⠰⠁⠀⡈⠀⡡⠤⠤⠴⠆⠀⠀⠢⣝⠻⠿⣟⣭⠇⡴⣴
⠀⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⢧⠀⠒⠤⡁⠠⡑⠢⢤⡀⠀⢀⢆⡀⠢⣈⢉⣉⠥⠜⠀⠛⠩⡃
⠀⠀⠀⠀⠀⣀⣀⡤⢶⠒⠲⢤⣑⣄⡀⠈⠂⠀⠀⠀⣠⠖⠁⠈⠁⠠⠀⠥⠀⠀⢙⡠⠔⠢⠀⣶⣶⡄
⠀⠀⠀⠀⠘⡉⢿⣽⣾⣟⣾⣿⠽⠀⠙⠓⣒⣚⣉⣉⠁⠉⠈⢉⡒⠠⠀⠐⣀⣥⣶⣦⢤⣤⡀⢀⠽⡇
⠀⠀⠀⠀⠀⠙⢮⣽⣤⡛⠃⢀⠤⠤⠖⠂⣀⣀⠀⠀⠐⠀⠾⣶⠦⠶⠆⣸⡿⣬⡿⠄⢠⠟⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠥⠀⠬⠄⠠⠆⢒⠉⢡⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣛⣚⠿⡧⠶⠟⢁⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠜⠋⡀⠁⡲⢼⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⢻⣍⣙⠷⣛⣾⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠿⣀⡀⠈⣧⣀⣀⣀⣈⡉⢉⣀⣀⣠⠀⠉⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠾⠶⠿⠧⠆

⠀⠀⠀⢀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠘⡴⢄⡴⣰⢄⠚⠆
⠀⠀⠀⠀⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢠⠄⠀⡀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠈⠀⠀⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⡀⢀⣀⠠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡌⠈⠀⠈
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠐⠒⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠐⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⠀⢈⡠⠊⠀⠉⠁⠉
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠠⠄⣀⣀⠀⠀⠀⠀⠀⠀⠠⠴⡋
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠀⠀⠀⠀⠈⠀⠊⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣴⠀⠀⠀⡰⠀⢠⠂⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠺⠏⠮⠧⠍⠿⠅⠸⠚⠳⠞⠰⡓⣖⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡴⣶⣦⡐⢻⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠴⢠⣦⡄⠀⢱⠘⣿⣿⠈⠁⠛⢁⠇
⠀⠀⣠⣶⣦⣄⣀⠙⠶⠦⠈⠁⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠲⠆⡀⠀⠄⢀
⠀⢰⡟⠉⠉⠉⠉⠁⠀⢀⣀⠄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠴⠞⢿⡏⠠⡤⢊⠟⣢⣜⠛⢂⢀⣄
⠀⠈⢿⣷⣶⣤⠤⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⢀⠰⢜⢲⡶⠙⢃⣢⡭⠳⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠀⠴⠟⢷⣤⠚⠛⠃⠀⠀⣀⠖
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠒⠀⠐⠐⠒⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠤⠔⠒⠛⠉⢁⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠒⠒⠈⠉⠁⠠⠄⢀⣀⣤⡤⠄
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠀⠀⢀⣀⠤⠴⠶⠂
⠀⣠⣎⠀⠀⠀⠈⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠈⠳⠤⡀⠀⠀⠀⠈⡳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠉⠓⢤⣠⢤⠠⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠚⣀⣀⠠⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠶⠒⠿⣄⠉⠉⠛⣀⠉⣱
⠀⠀⠀⠀⠀⠀⠀⠀⣧⣿⣿⣟⡄⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠳⠆⠀⠀⠠⠀⠀⠂⢀⣼⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣧⡀⠄⠀⣈⡂⠀⠀⠀⠀⣀⣼⣁⡤⠈⠀⠀⠀⠀⠀⠀⠀⡴⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣗⡆⢠⡁⠇⠀⠀⠀⣰⠵⠈⠁⠀⠀⠀⣀⢀⠀⠴⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠄⠄⠰⠇⠀⠊⠃⠁

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠉⠁⠈
⠀⠀⡀⠀⠂⠉⠉⢁⡠⠊⠀⢠⠁⠀⢀⡑⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢠⠊⠁⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠜⠀⠀⢠⠛⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⡏⠀⠂⠀⠄⠄⠀⠀⠀⠰⠸⡇⠀⢌⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠓⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡄⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡅⠀⠀⠀⠀⠀⠂⠤⠄⢀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠎⠀⠀⠀⡠
⠀⠀⠑⢦⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣢⠤⠊⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠂⠤⡀⠀⣉⠠⠉⠒⠒⠒⠊
⠀⠀⠀⠀⠈⠑⠢⠤⠤⣀⠠⠤⠄⠴⠄⠚⠉⠀⠀⠀⠀⠀⠀⠐⡅⠀⠀⠀⠤⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⢴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢀⣀⠀⠈⠈⠁⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠠⠍⠀⠀⠀⠂⠀⠠⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠤⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠐⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⠂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣄⣀⣀⣀⠀⠀⣀⣀⣀⣀⢀⠀⣨⣄⣀⣠⣀⡀⠠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢠⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⢠⡷⢀⠀⠀⠀⣿⣧⠀⠀⢸⣇⣄⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣽⢾⢸⣣⣟⣷⣼⢧⣷⣩⡞⠀⣬⣹⢫⣄⣶⣢⡖⡀⠄⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡿⠛⠛⠋⠉⠁⠀⠀⠀⠉⠀⠀⠈⠀⠛⠉⠉⠉⠻⠛⢲⣥⠆
⣿⣿⠟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣄
⠀⣿⡑⢌⣠⢡⣝⣓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣚⣫⡌⣄⡡⢊⡿
⠀⠘⣦⢻⡪⢙⣋⣙⡻⢯⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣿⡼⢋⣋⣙⡋⢕⡗⣴⠃
⠀⠀⠘⣎⢧⣏⢲⡆⠀⠭⠟⡿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣿⢿⠫⠩⠀⢰⡔⣹⡼⣱⠃
⠀⠀⠀⠸⡌⣎⠒⠬⢒⠤⡀⡀⠙⠹⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⡿⠏⠊⢀⠀⢤⣒⠥⠒⣱⢡⠇
⠀⠀⠀⠀⣿⢸⡗⠦⠔⢆⡈⠑⡓⠦⣌⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⣿⠞⣡⠴⢚⠈⢅⡐⠢⠴⢺⡇⡿
⠀⠀⠀⠀⢸⠨⡿⣓⣈⣀⢈⡁⠐⠤⠀⠙⠺⣿⡻⣦⠀⢀⡀⠀⣴⢟⣷⠗⠋⠀⠴⠃⢈⡁⣀⢁⡚⢿⠡⡇
⠀⠀⠀⠀⠘⣯⢇⣧⣤⣦⣀⣬⣨⣆⣠⠈⡂⠨⠻⣽⣇⣾⣷⣸⣯⠟⠁⢖⠁⣄⣰⣁⣥⣀⣤⣤⣼⡼⡽⠃
⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⡀⠀⠀⠄⠀⠉⠛⠲⢤⡈⣿⣿⣿⣿⣁⡤⠖⠋⠉⠀⠠⠀⠀⢀⣤⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⡻⢣⠟⡟⣞⠗⠶⣾⣟⣽⣿⣿⣏⣻⣷⠶⠻⣳⢿⠻⡝⠛⠧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠀⢸⠀⡇⣜⠤⠈⠹⢿⡿⢹⡏⣿⡿⠏⠁⠄⣣⢸⠀⡇⠀⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠠⠃⠨⡇⠸⡀⢇⡐⠀⣀⠇⣿⡇⠸⢀⠀⢂⡼⢀⠇⢸⠅⠘⠄⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⠹⣄⠙⢦⣈⢦⡞⠀⢹⡇⠀⢳⡔⣁⠴⠃⡰⠏⠀⡉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⡌⢀⣀⡉⠓⠤⣤⠏⠀⠀⠘⠃⠀⠀⠹⣤⠤⠚⢉⣀⡀⢡⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠒⢦⢊⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⡑⡴⠒⠾

⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⢽⡞⠛⢻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⡟⠛⢑⡮⢭⡿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢻⣷⠏⣻⡍⠿⡽⠓⠞⠛⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠻⠚⢫⡾⢩⣟⠹⢾⣿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢶⠯⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣻⡽⡶⢺⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣞⡷⠊⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠙⠶⣓⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣧⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣴⢷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣬⣗⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⡀⡄⢰⡦⢠⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⡒⣥⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⡷⢤⣀⣠⠤⠤⠄⠀⠀⠀⠀⢿⣼⣷⡿⠂⠀⠀⠀⠠⠤⠤⣄⣀⡤⢾⣥⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡭⠋⣡⠃⠀⢀⠠⠀⠀⠀⢀⡜⣿⣿⠣⡀⠀⠀⠀⠄⡀⠀⠈⢌⠙⢭⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡿⠂⠀⠀⠈⠁⡄⠀⢀⡠⠴⠁⠀⢻⡟⠀⠈⠢⢄⡀⠀⠀⡀⠉⠀⠀⠀⢿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣥⠀⠀⠀⠀⠀⠐⠀⠋⠐⠀⠀⠀⠈⠃⠐⠀⠀⠀⠉⠀⠒⠀⠀⠀⠀⠀⣤⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⣇⣠⠀⠀⡀⠀⠠⠁⠀⠀⠀⠌⠀⢀⡆⠀⠡⠀⠀⠀⠈⢂⠀⠀⠀⠀⢄⣸⢶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣩⣇⣠⠂⢀⡔⠀⣠⣀⣴⡟⠀⠀⠘⠃⠀⠀⠹⣦⣀⣄⠀⠢⡀⠑⣤⣈⣏⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣷⣾⣶⣞⣶⣪⡷⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣕⣶⣟⣶⣿⣾⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠋⣹⠋⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠘⣯⠙⠻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⣦⣤⣤⣤⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⣤⣤⣴
⠀⠀⠸⣿⣶⣩⡟⠋⠻⢾⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢾⠽⠛⠚⣯⣹⣽⡏
⠀⠀⠀⢫⡽⣤⢟⠋⢀⣙⡿⠄⣹⣫⣵⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣭⣿⡁⢾⣏⣉⣉⢻⢧⡼⣿⠃
⠀⠀⠀⠈⢯⣏⣹⣟⠁⠉⡻⢶⣉⣁⣞⣷⣭⣳⣤⡀⠀⠀⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠆⠀⠀⣠⣶⣫⣴⣿⣟⣉⣵⢻⡋⠉⢹⡿⢉⣿⠏
⠀⠀⠀⠀⠈⢻⣿⣽⡟⠻⣽⡏⠁⠈⠑⠀⠀⠈⠉⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠈⠁⠀⢉⡿⡤⠛⣟⣶⣼⠋
⠀⠀⠀⠀⠀⠀⠹⣯⣧⢾⣽⣦⣦⡀⠀⠴⣄⡀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣀⣴⡄⠀⣠⣛⣿⣷⢴⠟⣿⠁
⠀⠀⠀⠀⠀⠀⠈⣟⣽⡏⢿⡏⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠈⣧⠽⣛⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣵⡾⣧⣄⠀⠤⠤⠴⠖⠛⠓⠀⠀⠀⠀⠈⠳⡄⢠⣤⠀⡴⠋⠀⠀⡀⠀⠐⠛⠒⠶⠤⠄⠄⢀⣴⠟⣶⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠘⣾⣿⡞⢀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢯⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⣤⣤⣤⣶⣶⣶⡶⠶⠦⢤⣤⣤⣤⣼⣿⣿⣿⣤⣤⣤⠀⢀⣴⣶⣶⣶⣶⣦⣤⣀⣤⣿⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣩⠅⠀⠉⠉⠉⠉⠓⠈⠀⠀⠂⠀⢀⠿⣿⣿⡿⣇⠁⠀⠀⠈⠉⠛⠉⠉⠉⠁⠀⠈⢭⣉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢻⡤⠄⠀⠀⠀⠆⠀⠀⠀⠀⣠⠔⠉⠀⢹⣿⠑⡈⠓⢤⡀⠀⠀⠀⠀⠆⠀⠀⠠⠤⣼⣙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢳⣾⠁⠀⠀⠀⣠⠄⠀⣀⡤⠖⠋⠀⠀⡔⠀⢿⣿⠀⠐⡀⠀⠈⠳⣦⣄⣀⡀⣄⡀⠀⠀⠈⢻⣾⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢯⠿⣶⠦⠀⠈⣉⠔⠉⠁⠀⠀⠀⠀⠈⢁⡄⢸⣿⠘⣆⠉⠀⠀⠀⢀⡀⠉⠀⢍⡉⠓⠶⣶⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣄⣠⡞⠁⠀⠀⠀⠀⠀⢠⠂⢰⡞⠀⠘⠟⠀⠘⣧⠀⢢⠀⠀⠠⠀⠀⠀⠹⣦⣀⣾⣧⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡿⣛⣿⣦⣀⣀⣴⠃⠀⣰⠃⢀⡞⠀⠀⠀⠀⠀⠀⠹⣆⠀⢳⡀⠀⢳⣄⣀⣠⣿⣋⡻⣽⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣽⣿⣭⣿⣻⣶⢾⣇⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣿⢶⣟⣹⣯⣿⣽⡽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠛⠋⠁

⠀⢠⣤⣤⣤⣀⡀
⠀⣮⣾⣾⣿⣴⣦⡉⠛⢶⡤⠀⡀
⠀⠻⣷⣿⣾⣿⣿⣟⣷⣶⣾⣿⣷⣦⣄⢀
⠀⠀⢸⣯⣇⣻⣿⣟⢛⠛⣯⣽⣿⣿⣿⣿⣧⣆⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢹⣿⡻⡟⢿⣍⣉⣹⡏⠀⠀⣠⣿⣿⣟⣷⡀⢄⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠈⢻⣿⠟⢻⣷⠤⠬⢿⡀⠰⣿⣿⠛⠉⠛⣝⢦⡁
⠀⠀⠀⠀⠘⢿⣿⢿⣿⣦⠴⠐⠚⠳⢬⡁⠀⣤⣿⣿⣷⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠘⡿⠶⠾⢿⡷⠒⠒⠒⠒⢿⣷⣮⣙⠻⡟⠛⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠐⢦⢿⡿⠿⢻⠦⠀⠀⠠⠶⣿⣿⣿⡟⠲⢄⡈⢻⣿⡄⠀⠀⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠈⢙⣿⠻⢻⣴⠂⠀⠒⠒⠚⠻⠿⠷⢤⣀⣹⣿⣿⣷⣤⣞⣻⣿⡿⠃⠀⠀⠀⣀⣀⣤⣴⣦⣦⣤⣆⣴⣶⣒⡲⠶⠤⣤⣤⣀
⠀⠀⠀⠀⠀⣠⣼⠿⣿⠋⣉⣩⡷⠒⠚⠉⠉⠉⠙⠃⠐⠢⢭⣝⣻⣿⣿⣿⣿⣿⣧⡶⠾⠟⠛⠛⠛⠛⢛⣻⣶⡾⠒⢶⣷⣭⡍⣙⡛⠶⢦⣌⣹⣶⣤⣀
⠀⠀⠀⠀⠀⣼⣹⣷⢿⡋⠁⣞⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠋⢙⣿⣿⣛⣿⣟⠿⢿⣿⡟⠿⠻⠶⠀⢤⣰⣿⠿⠃⢀⡽⣷⠇⠀⠈⢿⡗⠲⢶⣿⣿⣞⣛⢷⡆⡀
⠀⠀⠀⠀⢀⣼⣿⣤⣿⡟⢁⡼⠶⣤⣤⣤⣤⣶⠛⠁⠀⢀⡴⢪⣟⠦⣽⣿⡿⠋⠐⠈⡙⠢⣄⣀⣰⣾⣿⣿⣿⣲⢬⣿⣇⣀⣠⡤⡞⠑⢦⣴⣿⣽⣿⡟⣯⣅⣿
⠀⠀⠀⠀⠀⣿⣿⣱⣼⣿⡏⢀⣴⠁⠉⣡⠝⠁⠀⢀⣴⠟⣰⣿⣮⣿⡟⡀⠀⢰⡀⠀⠈⠲⣄⠙⠿⣿⡽⢏⡀⠁⠀⠉⠀⡈⠹⣦⣉⣷⣿⡛⢣⣭⢻⣧⡾⠟⠛
⠀⠀⠀⠀⠰⣿⣛⣫⣼⣿⣿⣿⣿⣤⣤⣧⣄⠀⣠⣾⠋⣰⣿⣿⣿⠏⣰⠇⠀⢰⣧⠀⠀⠀⠘⣿⠢⣬⣿⣶⣽⣆⣀⣶⣴⣼⣿⡟⣻⣞⣽⡷⡮⠟⠉⠉
⠀⠀⠀⠀⠀⣼⣿⡟⢫⣙⣿⡿⣻⣿⣿⣛⣿⡖⣷⠃⢰⣿⣿⠟⢁⡼⠋⠀⠀⢸⠟⣧⡀⠀⢀⡿⣦⣘⣷⣿⡿⣿⣿⣯⣽⣷⣾⣿⠟⠛⠋
⠀⠀⠀⠀⣸⢋⡔⠂⠀⣟⠿⠛⢿⡟⠘⠛⡟⣭⠏⠀⠘⠋⠁⡀⣺⠶⣶⣄⠀⣾⠀⢸⠉⠛⠈⣇⣸⡿⣶⣿⠇⠀⠉⠀⠉⠁⠀⠈
⠀⠀⠀⣴⡷⠋⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠉⠁⠀⠀⠀⠀⣠⠌⢿⡿⣸⣿⣀⡏⠀⣾⡀⣰⣶⡟⠻⣦⣿⣇
⠀⠀⠸⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⣠⣴⣿⣿⣿⣷⣴⣿⣿⣿⡋⢻⣤⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡿⢙⣿⢿⣿⢣⣿⣀⣿⣷⣾⣻⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢻⡿⢷⣤⣿⣿⣿⣿⣿⡿⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠳⣿⣿⡿⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⡟⢡⡀⡍⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⡩⠥⠎⠄⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⣫⠤⣌⠍⠲⣄⠀⠀⠸⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡃⣝⣁⡼⢸⠀⢹⠀⠄⣢⢹⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠛⠷⢄⠀⠐⠁⠀⠀⠆⢉⠁⡘⡇⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣏⣖⡒⢦⠢⠁⠀⠀⠀⠀⠐⡀⠒⠁⡇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣼⠈⠫⠥⠞⡠⠁⠀⠀⠀⢄⠀⠀⠀⢚⠃⠄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⠦⣄⠀⠀⢸⡧⣿⢀⠀⢄⢈⠀⠀⠀⠀⠀⠀⣑⣤⣷⣾⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣛⣤⣼⣧⡀⠈⣷⢻⠘⡡⠜⠘⠀⠀⣀⠬⣴⣿⠟⠛⠛⠁⠀⠀⢀⣴⠾⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⡘⢿⠻⡻⣆⣷⡀⠘⢿⣧⣀⣠⠴⠒⠉⠀⠾⠛⠁⠀⠀⠀⠀⠀⢠⣿⡜⣅⠔⠛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠖⣋⣉⣾⣷⣽⡟⢿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢦⠟⣳⡤⠚⣫⣿⡄
⠀⠀⠀⠀⠀⠀⢀⣿⣻⡄⢿⣟⠿⣧⠈⣇⣘⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡾⡟⣩⢷⡂⢁⠷⣻⡄
⠀⠀⠀⠀⠀⠀⢸⣿⣽⠓⢢⣿⣗⠘⢧⣹⣿⣷⢹⠀⠹⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣓⢿⣿⡡⠞⣯⡠⠞⣹⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠻⣧⣰⣿⡿⠯⠁⠀⠻⣿⠟⣿⡇⠀⠀⠀⠀⠃⠀⠀⠀⢴⠀⠀⠀⠸⠻⠳⠤⣧⣛⡤⠂⢉⣧⠔⠁⠾⡇
⠀⠀⠀⣀⣤⣤⣶⣤⣬⣝⣿⣇⠀⠀⠀⠈⠙⠆⢻⡇⢠⠀⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡷⠋⡷⣳⣯⡴⠚⠉⣹⡖⠁⠘⠓⢲⡀
⠀⢀⣞⣻⡟⢽⣿⡄⢟⣆⣹⣟⣿⢾⣵⢶⡄⢸⣼⡇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⡠⢠⠿⣿⡾⠛⠉⣉⠴⣮⡤⠀⠉⢙⣦
⠀⢸⡭⣝⠰⠶⠦⠼⣏⡁⠐⠬⠝⣺⣿⣓⣽⣶⣿⣷⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⠇⢃⠂⠀⢠⣿⢾⠋⢁⡈⠩⢷⡶⠒⠚⠛⣦
⠀⠘⢗⣻⣇⡚⢃⣬⣉⡝⣻⣿⣯⣽⠿⠿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣦⣄⣠⠀⠀⠹⢾⣝⣇⣀⠀⢘⣷⣂⠀⠈⠙⢂⣤⣄⣀⡀
⠀⠀⠈⠓⠾⠧⠾⠷⠚⠋⠉⠀⠀⠀⠀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣷⠶⠦⠤⣟⣼⣧⡤⠤⣼⣇⡀⢾⣙⣯⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠈⠉⠓⠶⣾⣁⢾⣍⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠃⠀⠈
⠀⠀⠀⠀⠀⠈⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡘⠀⣰⠂⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⡇⡠⠉⣀⠄⠤
⠀⠈⠀⠀⠐⠀⠀⠀⢄⠀⠀⠢⠀⠠⡀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠠⢵⡆⡄⣏⣤⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⠀⠀⠀⢈⡙⠾⣄⠀⠀⠀⠀⠌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠈⠀⠨⠉⠀⠉⠀⢐⣀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⢄⡀⠀⠀⠀⠀⡀⠀⠀⠈⠂⠀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⣀⠀⠀⡀⠂⠀⠀⠆⢠⠀⠩⠑⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡤⠉⠙⠒⠺⢦⣁⣢⡀⢾⠀⢠⠐⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠖⠋⠁⠘⠂⠈⣃⠈⠠⠀⢷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠀⠀⠀⣀⠤⢤⣄⣢⢄⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠉⠀⠒⠠⠀⠐⠂⠀⠀⠙⠒⢛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡀⠙⠋⠉⠑⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣠⢰⢠⠀⣀⠄⡄⢠⠄⡆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊⠉⠘⠘⠐⠙⠐⠁⠘⡘⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡛⠘⢏⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠡⠀⠈⠙⠢⢤⣀⠰⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢱⣄⠀⠀⠀⠙⣷⣾⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠄⠀⣠⡆⢀⠤⠀⣐⣈⡀⠐⢿⡇⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⠰⠖⠉⠒⠓⠳⢰⠋⠉⣩⡶⠛⠁⠙⢦⠀⠀⣹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢸⠃⠀⠀⠀⠀⢨⣷⣾⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠤⠞⠃⠀⣼⠀⠀⠀⠀⠀⡸⠃⢸⡥⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠞⢃⣀⣀⣤⠶⠛⠁⠀⣠⣵⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⣴⠖⠲⠤⠔⠒⠒⠒⠐⠂⣀⡤⠖⠛⠉⠉⠁⠀⢀⣀⣠⣤⣿⣷⣟⡻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠢⣄⡀⠀⠀⠀⣠⣴⠟⠁⠀⠀⢀⣀⣤⣴⣾⡿⢟⡭⠏⠹⡋⣋⢱⣻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠈⠙⠛⠛⠛⠻⠻⠟⠗⠖⠻⠟⠻⠋⠉⠁⢀⠈⢰⣞⣴⣷⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⡦⣤⣄⣠⡄⠀⣀⠀⣀⢀⣀⣀⣁⣘⢠⣂⣠⣤⣼⣾⢿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⢹⡄⢹⡟⠈⢿⠛⣿⠛⢻⡟⢻⠟⢻⡟⢻⡏⢩⣇⣸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⡎⣧⠀⣿⠀⢸⡀⢿⠀⣸⡁⢸⠃⢼⠀⢺⠇⢺⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢠⣸⡆⢿⠂⠸⡇⢸⢢⣼⡇⢸⠂⣿⡀⣿⢓⣿⣿⣿⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠸⣿⣇⢺⣧⠀⣷⢾⡧⣿⣧⣿⢲⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣶⣷⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⣿⡸⣿⣿⡧⣿⡎⣿⣾⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣿⣿⣿⣧⣿⣿⣷⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣶⠧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣿⣾⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢟⡛⠓⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠛⠿⠟⠻⠛⠛⠙⠉⠉⠉⠁



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

⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⣄
⠀⠀⠀⣸⠋⣀⣉⣐⡒⠨⢕⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣚⠭⠒⣂⣈⣀⡈⢳
⠀⠀⠀⢸⡍⡡⠤⠤⠭⣍⣒⡟⠚⠓⢄⠀⠂⠀⠀⠀⠀⠀⠀⠠⠂⣠⠔⠛⠺⣖⣫⡭⠥⠤⢄⡉⣿
⠀⠀⠀⠀⢷⡀⠂⠒⠒⢒⣲⢷⣄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣴⢗⣒⠒⠒⠂⠀⣼⠃
⠀⠀⠀⠀⠈⢷⡈⣉⣉⠀⠈⠩⣍⣳⣦⣀⡀⠑⣄⠀⡀⢀⠞⠁⣀⣤⣖⣉⡭⠉⠀⢈⣉⡁⣰⠃
⠀⠀⠀⠀⠀⠀⠻⢦⣀⣤⠄⠠⠤⠤⠤⠤⣭⠷⢮⡶⢺⣧⠶⢯⡥⠤⠤⠤⠀⠒⢤⣄⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠝⠛⠉⢙⣛⣛⣉⡩⢽⣷⣼⡿⢭⣉⢛⣛⣋⠉⠛⠛⢍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡥⠒⣉⠡⢤⠞⠉⠀⣠⠃⡿⢸⡏⢦⠀⠉⠑⢤⠤⢉⡑⠦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣏⠐⠁⡀⠔⣧⣀⣤⠞⠙⢰⠃⠆⢧⢠⠙⣦⣀⣨⡇⠄⡈⠑⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡠⠋⡠⠊⢀⠃⠘⠀⢠⡞⠐⠆⠸⡜⠀⠸⠀⢇⠈⠢⡈⠂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⠁⢀⠂⠀⠀⠀⣸⠁⠀⠀⠀⢳⡀⢀⠀⠈⢆⠀⢳⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠬⣤⣤⠴⠞⠁⠀⠀⠀⠀⠀⠙⠾⣤⣤⡼⠖⠋

⠀⠀⢀⣾⣟⣿⣿⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣟⣿⣆
⠀⠀⠀⢻⣯⣿⣿⣿⠿⠿⢶⣼⣿⣿⣦⣄⡀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⢀⣠⣶⣿⣿⣿⡶⠾⠯⣿⣿⣯⣿⠋
⠀⠀⠀⠈⣿⣷⣿⣿⣶⠛⣿⣿⡇⠀⢈⣽⣿⣶⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣠⣶⣿⡋⠁⠈⣻⣿⡿⠿⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠙⣿⣼⣿⣿⡟⠋⣙⣻⣦⣿⣿⠏⠁⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⢿⣿⣧⣴⡛⠙⠛⣿⣿⣿⣽⡟
⠀⠀⠀⠀⠀⠹⣷⣽⣿⣿⣿⠉⣉⣡⡽⠿⣆⣀⣠⣾⣿⣿⣦⡐⠀⠀⠀⢀⣴⣿⣿⣄⠀⢀⣼⣿⣉⠉⠙⢛⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠻⣯⣹⣿⣿⣿⡉⣀⡤⠶⠚⠛⢿⣿⣿⣿⣿⣷⣾⣿⣦⣿⣿⣿⣿⣿⠿⠿⠷⣤⣀⠉⣳⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣧⣀⠀⢀⠤⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⢄⠀⠀⣨⣿⣿⣿⣿⣻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣏⣻⣿⣿⣿⢃⠠⠔⠚⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣍⠛⠛⠲⢤⣈⣸⣿⣿⡿⢛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣿⢿⣿⡆⠀⠤⠐⡘⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠙⡌⠒⠠⢀⣼⣿⣿⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣷⡠⠐⢸⡇⢸⣿⣿⡿⣿⣿⢿⣿⣿⡇⠀⣿⠐⢄⢠⣿⣿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣹⣿⣿⣧⣔⠀⠛⢹⡿⣿⡇⣿⣿⡇⣿⣿⡟⢚⠣⠑⢤⣿⣿⣿⢋⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⣟⢻⣿⣿⣿⣷⣦⣼⣧⣼⣇⠸⡿⠁⣿⣧⣇⣤⣴⣿⣿⣿⣿⠿⣿⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣹⣿⣟⣿⣿⣿⣿⣿⡻⣿⡿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡟⣻⣿⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⣽⣿⣯⣽⣿⣽⣷⡴⠁⠀⠀⠀⠑⣴⣿⣽⣿⣛⣻⣿⡉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇

⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⠃
⣿⣿
⡟⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡄
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣑⣦⠀⠀⢀⠀⠀⠀⠰⠀⠈⠄⠉⠁⡦⠀⠀⠀⠀⠰⠧⠤
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣴
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠠⠄⠤⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⣴⡀⠀⠀⠐⠀⣠⡿
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⡀⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠐⠃⠀⠀⠀⠀⠀⠠⠄⠀⠤⠊⠀⠀⠙⠤⠤⠄⠠⢞⠋
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⣦
⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⢠⣤⠏⠀⠀⠀⠀⠄⠀⢰⠇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⣀⣀⡼⠋⠁⠀⠀⠀⠀⠀⢀⠴⠋
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠀⠄⠀⠀⠀⠀⠀⢀⡜⢠⠀⣀⠀⠒⠒⠀⠀⠔⠀⠤⠾
⠀⠀⠀⠀⠀⠀⠀⠀⡤⢒⣠⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠒⠀⠀⠀⠀⠀⠀⢀⢠⡷⣾⣋⠁
⠀⠀⠀⠀⠀⠀⠀⣶⠀⠤⠑⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⣼⣻⣛⣶⣴⠶⡤⠆⠀⠀⠀⠀⠀⠀⠐⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠀⠀⠀⠀⠀⠰⠲⡄⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⣸⠟⠋⠁⡈⠉⠁⠀⠀⠀⠀⠀⠀⢴⠖⠁⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠦⡀⠀⠀⠀⠀⠐⠀⠐
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠁⠀⡹⠂⠀⠀⠀⢠⢸⣆⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠇⠤⠔⠃⠀⠀⠀⠀⠘⠻⠿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠄⠀⡀⢀⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠠⠀⠀⢠⡀⠀⠀⠀⠀⠈⠉⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠉⠋⠀⢀⣀⡔⠀⠀⣠⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠓⠤⠄⠃⠀⢀⣀⣂⣀⣈⣥⣴⠶⠞⣫⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣉⢀⡀⣼⣥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⡀⢀⣀⠄⠈⠉⣉⠉⣁⣤⣤⣄⣾⡃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠛⠟⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⣀⠀⠀⠀⠲⠞⢉⡛⠫⠄⠀⠉⠉⠀⣰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⢺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠇⣀⡀⠀⠀⠀⠀⡀⢠⣔⣤⣿⠿⠋⠀⠀⠀⠀⠀⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠷⠿⠿⡾⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⢠⣾⢻⡏⠙⣿⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣁⣸⣿⠾⣿⡶⠋⠀⠀⠀⠀⣈⠀⢀⣀⣠⣩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡏⢉⣿⡁⠘⣿⡇⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢷⣦⡾⠃⠀⠀⠀⠀⠀⠦⠤⠠⠀⠀⠀⣶⡴⠶⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⣤⡀⢠⣤⣤⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠐⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⡰⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣢⡒⢷⡀⠀⠀⠀⠀⡐⠱⣍⠀⠄⡑⢇⣳⣀⠠⢊⠉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡊⠉⢲⣀⣀⠹⠁⠑⣄⠴⢾⡽⣿⣣⢟⡠⢡⢄⡏⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠱⠘⠃⠀⣤⣋⢌⣛⢻⣷⣟⠋⢠⠁⡼⡀⠘⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⢁⠀⡁⢳⡄⢠⣴⠾⡴⡮⢤⣹⣷⣿⠚⣕⡁⢻⣧⡴⠀⣉⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡄⠁⠀⡡⠉⠠⡜⢁⠰⣦⡀⣋⣿⣼⣄⠑⢾⣟⣾⣫⣭⡽⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠛⡔⠧⠀⠀⡠⠿⣲⣦⣹⣃⣼⠋⣻⣸⣟⢖⠻⣟⢻⣿⣦⡁⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠀⡀⠤⡄⠞⠡⠩⣝⠛⠯⡼⡹⢃⣽⡉⠿⣾⠿⡶⠖⢚⠉⠉⡨⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠒⠶⢄⠧⠰⣴⣤⠐⡟⢗⣼⠏⢷⡀⠛⢻⣒⠶⠲⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠛⣵⡛⡧⡠⢉⡔⠋⢸⠀⣾⠄⢰⡋⠁⠀⠀⠢⣵⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠠⠀⠀⠠⠜⠿⠆⠰⠯⣱⣤⡼⣶⡅⢩⢸⠗⡠⠐⢈⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⢻⣠⠿⣷⣿⠈⣟⡭⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠀⠹⠟⣄⣽⣷⠾⠇⣿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢄⠈⣄⣀⠅⡃⡟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⣤⠾⣧⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠘⠗⢾⣰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡻⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠒⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠘⠃⢀⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠁⠀⢀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠋⠀⠀⡀⠈⠁⠀⠡
⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠘⠂⠀⣤⡀⠈⠁⠀⢀⣀⠀⡗⢄
⠀⠀⠀⠀⠀⢠⠎⠀⠑⠄⣀⣀⣀⣀⡀⠀⠄⣀⡀⣉⠰⣡⢀⠦⡀
⠀⠀⠀⠀⠰⠁⢄⠐⠃⠀⠀⠀⠒⠀⠀⠠⠤⠀⠀⠀⢀⠤⢊⣀⠈⢆
⠀⠀⠀⠀⡆⠀⢀⠉⠒⠀⠤⠀⠀⠀⠀⠤⠄⠀⠒⠈⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠘⣄⠈⠁⠀⠀⠋⠀⠀⠀⠐⠒⠀⠀⠘⠁⠀⠉⢁⡀⡴⠁
⠀⠀⠀⠀⠀⠸⠈⠉⠀⠀⠉⠉⠀⠉⠉⠀⠉⠁⠀⠉⠁⠉⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠩⠶⠦⠀⠀⠀⠀⠤⠶⠭⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠈⠢⠴⠃⠀⠀⣀⢄⢶⠋⢉⠔⠖⢄⣀⡀⠤⠐⠈⠉⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⡤⠠⠤⠄⠀⢀⠔⢠⢂⡆⢀⠊⠘⠀⠱⠱⡤⠄⠒⠁⠀⠉⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⣀⠧⠀⠀⠀⠤⡜⠀⠂⢻⠃⣬⡀⠿⠆⠀⠀⡇⠠⠤⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢄⢰⠀⠸⠈⣻⠏⢀⠀⡜⡰⠁⠒⠠⢄⣀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠀⠈⢀⡠⠘⢢⡀⠀⠄⠰⡀⠈⣎⠔⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠒⠁⠀⠀⠀⠈⠑⠚⠒⠚⠉

⠀⠀⠀⢻⣦⡀⠀⣴⣿⠀⠀⢠⣤⣀⠀⠀⣀⣤⡄⠀⢰⣦⡀⠀⠀⢀⣄⡆⠀⢰⣦⣀⠀⠀⢀⣤⡆
⠀⠀⠀⢈⡏⢻⣿⠉⡇⠀⠀⠀⢃⣤⣵⣾⣥⣜⠃⠀⠈⠻⣾⢶⣶⢷⡞⠃⠀⠈⢿⡿⣦⣴⢿⣿⠃
⠀⠀⠀⢸⣮⠁⠁⢡⣟⠀⠀⠀⠺⠽⠋⠉⠯⠿⠀⠀⠀⠸⣿⠊⠁⢿⠟⠀⠀⠀⠻⣿⠎⠉⢾⡟

⠀⠀⢀⣄⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⢀⢠⡄
⠀⠀⠀⢿⣿⣦⣴⣿⡿⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠘⢇⡀⣠⣦⣀⡸⠇⠀⢠⠀⠒⣢⣆⠒⠀⡀
⠀⠀⠀⢸⣿⠏⠋⣿⡷⠀⠀⠀⠐⠀⠈⠇⠀⠂⠀⠀⠀⢿⣰⡟⠻⣆⣽⠀⠀⠀⠙⢟⠻⢟⡛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁

⠀⠀⠀⣗⠲⣤⣤⠖⢲⠆⠀⠰⡒⠐⢦⡴⠒⢒⠶⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣶⣄⠂
⠀⠀⠀⠸⣲⠚⠛⣖⠏⠀⠀⠀⠀⢳⠞⠳⡾⠁⠀⠀⠀⠀⢠⡄⢡⡄⠀⠀⠀⠀⠸⣯⣻⢟⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠃⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠠⠇⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣀⠉⠈⠦⠄⠃⢥⡤⠀⠄⠐⢀⡜⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣢⠀⡁⠖⣀⠰⢍⡳⠀⠀⣀⣀⡀⠠⠤⠒⠃⠀⠀⢾⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣀⣠⣾⣛⣫⠍⠐⠁⠀⠉⠉⠀⠀⠀⠀⠀⠖⣦⣿⠁⠘⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠞⠛⠋⠉⠉⠉⣀⣦⠴⣶⡾⡋⢻⣤⢤⣤⣿⣟⣿⣽⣦⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠉⠛⡟⠛⡃⢀⡠⣤⣿⣉⠉⢋⠁⣐⠛⠈⢁⠈⢿⣟⣩⡜⣟⣥⣶⡻⣻⣷
⠀⠀⠀⠀⠀⢠⠗⠋⢓⡆⠲⠛⠿⠧⠜⠉⠉⡠⠆⠈⠁⢀⡴⠇⠤⣀⠙⠛⢿⠷⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠙⠓⠛⠳⠄⠁⠀⠂⠒⢂⡽⢣⠴⠀⠀⠈⠑⠠⠄⠻⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⣄⣀⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⢪⡭⠅⡀⠙⢯⡐⢆⠉⢿⣳⢦⠀⠀⠀⠀⠠⣶⠏⢉⠥⠶⠖⢦⣄⡀⠀⠀⠀⣠⠊⠁⠀⠀⢀⠇⠰⡀⠀⠈⠢⡀
⠀⠀⠀⠀⡀⠔⠊⠁⣦⠠⡀⠈⢷⡀⠀⠀⠈⢷⠀⠆⠀⢳⠀⣧⠀⠀⢰⠀⣇⠔⢁⠰⠻⠾⠟⠛⠷⠀⠀⢰⠃⢀⡄⠊⠁⠀⠀⠀⠉⠑⢄⠀⢱⡀
⠀⠀⡠⠊⠀⡿⠙⠄⠹⡄⠘⢆⠈⣷⡀⠀⠀⠸⡇⢸⠀⠈⣶⡏⠀⠀⢷⠀⠀⢠⠂⠀⢀⣀⡠⠤⣤⡆⠀⢸⣆⠀⠀⠀⠀⢹⢀⠇⠀⠀⠈⠃⢸⠇
⠀⢰⠁⠀⠀⢧⡀⠐⡀⠙⣆⠘⡄⠘⢿⡀⠀⠀⢹⣸⣶⡿⠋⠀⠀⠀⠈⢷⣄⠀⠑⠉⠁⠀⠀⠀⣴⠇⠀⢸⣿⣦⡀⠀⠀⠈⠎⠀⠀⢀⣠⣤⡿
⠀⠰⣄⠀⠀⠀⠙⠢⢐⣄⠈⠳⣷⣀⣨⣷⣿⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⢤⣤⣤⠤⠞⠉⠀⠀⠀⠻⣿⣿⡷⣶⣶⣶⣶⣿⣿⣿⠟⠁
⠀⠀⠈⠛⠷⠶⠶⠶⠶⠿⠿⠟⠛⠛⠋⠉⠁⢀⠤⠂⠒⠒⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⠭⠭⢍⣁⡀
⠀⠀⠀⢀⣤⣔⠂⠐⠒⠒⢦⣤⡀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡀⠀⠀⠈⢻⣿⠛⠳⡄⠀⠀⠀⠀⠀⡴⢎⠁⠀⠀⠀⠀⢸⠉⠙⡒⠒⣄
⠀⢀⣴⠋⠀⠠⡙⠄⠀⠀⠈⣿⠉⢣⡀⠀⡇⠴⠀⠀⠀⠀⠀⠀⠀⣀⠀⢰⣁⡀⠀⠀⢀⡟⠀⠀⠸⡀⠀⠀⣤⠚⠙⢦⠠⡀⠀⠀⠀⢸⠀⢠⠷⠊⠁
⠀⡭⠭⠭⣀⡢⢹⣤⡄⢀⣶⠏⢀⡆⢹⠀⣇⠀⠀⠀⠀⠐⠀⠀⢰⠇⢀⡼⠛⠛⠻⢦⡎⠀⠀⠀⣠⣿⠀⡞⠓⣀⠀⠀⠱⡔⡀⢀⣀⠾⠂
⠀⠆⠀⠀⢠⣿⣼⣿⡷⠟⠛⠛⠛⠣⠶⠀⠈⠢⢤⣀⣀⣀⡤⠞⠋⠀⠀⡇⠀⠀⠀⠉⡄⠁⠐⠊⢹⠇⠸⠄⠶⠚⠾⠦⠞⢛⣛⣛⣉⡀
⠀⠦⠴⠚⠋⢉⣁⡀⠠⠀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠰⣄⡇⠀⠀⠱⣄⡀⠐⠃⠀⠀⠀⠀⠠⠴⠶⠿⠥⣄⡀⠀⠈⠉⠓⢤⡀
⠀⠀⢀⠔⡈⠁⠀⠀⠀⠀⠀⠀⠸⣹⡂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣙⡒⠒⠚⠉⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠉⠳⣤⠀⠀⠀⠹⡄
⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠐⠙⠻⣿⡏⠁⠢⣄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡇⠀⠀⣸⠃
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣄⠈⢣⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡟⠋⠉⢿
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⣞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢸⣧⢄⣼⠀⠀⠀⠘⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣾
⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⠀⠀⠉⠓⠦⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡿⠃⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣀⡟
⠀⠀⠀⠀⠓⠤⠤⠤⠤⠤⠤⠖⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠒⠒⠢⠤⠴⠚⠋⠀⠀⠀⠀⠀⠘⠲⠦⠤⣄⣠⣀⣀⡀⡀⠀⣼⠖⠋⠁
⣤⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣬⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣀⣤⣯⣼⣭⣥⣥⣬⣷⣯⣥⣥⣯⣭⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⣿⣿⣿⣿⣭⣭⣽⣽⣿

⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠙⠛⠛⠁⠀⢀⠀⠀⠀⠀⠘⠑⠛⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⠙⠛
⠀⡀⣀⢂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣠⠄⢙⡇⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⢂⠀⠀⠈⠁⠀⠀⠀⠀⢠⣀⠄⢙⡇⠀⠀⠀⠐⣶
⠀⠱⠂⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡄⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢚⠈⢡⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠈⠓⠇⠀⠀⠀⠻⠲⡰⠦⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠓⠇⠀⠀⠀⠻⠲⡰⠶⠀⠀⠀⠀⠀⡀
⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠃⠢⠤⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠙⠶⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠦⠤⠴
⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠂⠈⠁⠀⢀⡀⠠⠀⠀⠀⠉⠀⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠂⠈⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠂⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⢤⠤⠤⣄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⡁⠀⠀⠀⠀⠀⠀⢐⠀⠀⡀⠀⢀⢤⠤⠤⣄
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠂⠋⠁⠀⡋⢠⠂⠂⠀⠆⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠉⠁⠀⡋⢠⠒⠂⠀⠆
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡰⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣀⠀⠀⠀⠀⢣⡀⠀⢁⡠⠃
⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢠⢚⠶⢀⡆⠀⠀⢰⠁⡞⠛⡆⢀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢰⠾⠶
⠀⠀⠀⠸⣦⣀⢀⣡⠟⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠠⠀⠐⠀⠈⠁⠀⢸⠁⠀⠀⠸⣦⣀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠠⠀⠂⠀⠈⠁
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠘⣿⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠰⣶⡆⠀⠀⠀⣿⣧⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣠⡄⠀⠀⠙⠁⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠉⠁⠀⠐⠀⠀⠸⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⢠⠤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠘⢿⣿⡿⠇⠀⠀⠀⠀⠀⠀⣤⢤⣼⠁
⠀⠀⠀⡀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠡⠆⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⢀⣀
⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣡⠰⠇⠀⠀⠀⡀⠟⠀⠀⠀⠀⠀⠀⠀⠀⢂⡒⡐⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣡⡰⠆⠀⠀⠀⠀⠟
⠀⠀⠀⠑⠀⠀⠀⠠⣄⡄⠀⠀⠀⡯⣑⠀⣘⠃⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⢀⣄⡄⠀⠀⠀⣯⣁⠀⣘⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠐⢦⣀⡀⠁⠀⠀⠀⠈⠈⠘⠁⠀⠀⠤⡄⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⡀⠁⠀⠀⠀⠈⠈⠊⠉⠀⠀⠤⡄⠀⠃⢀
⠶⠀⠄⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⢀⠄⠀⠀⠃⡀⠠⠍⠉⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠉⠓⠃⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀⠠⠉⠉⠁
⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈
⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⣀⠤⠆⠀⡴⠉⣉⡉⠃⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣀⠤⠇⠀⡴⠉⢉⡉⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⡅⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠄⠀⡅
⡆⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⢶⡽⠒⠀⠀⠀⠀⠘⠀⠤⠰⠊⠀⣠⣀⠀⠂⠀⠀⢀⠄⣠⣤⡀⠀⠀⠀⠀⠠⠶⠽⠖⠀⠀⠀⠀⠈⠀⠤⠰⠊⠀⣠⣀
⠃⠀⠀⢸⡀⠃⠀⠃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⣀⠀⠸⡄⠉⢰⠇⠀⠀⢸⡀⠃⠀⢃⣴⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⡀⠀⠸⡔⠉
⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⢰⣿⡇⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠻⠶⠴⠞⠁⠀⢀⣀⡀⠀⠀⠀⣿⡇⠀⠀⠀⠨⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⢿⠟
⠀⠀⠀⠤⠄⠀⢀⣀⠀⢸⣶⣶⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⢰⣶⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇

⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⢠⠆⠀⠀⠀⠀⠠⡄⠀⠀⠰⢢⡖⠀⠀⠀⠀⠀⠀⢶⡴⠆⢰⡇⠂⠀⡀⠀⠀⡀⠐⠲⡷
⠀⠀⠀⠈⢦⣀⠀⣰⠀⢀⡠⠏⠀⠀⠀⣿⣰⢩⢄⡰⡍⣆⣻⠀⠀⠀⠈⠇⠀⠀⢠⡄⠀⠀⢾⠀⠀⠀⢳⠀⠀⠨⣶⡌⠀⠀⣺⠁
⠀⠀⠀⠀⣴⠀⠀⢼⠀⠀⢰⠄⠀⠀⠀⢩⣾⠘⣾⣷⠃⣷⣍⠀⠀⠀⠀⣠⡀⠀⠸⠇⠀⢠⡄⠀⠀⠀⠈⣳⢂⣴⢻⢲⣔⢲⠋
⠀⠀⠀⠀⠘⣷⠶⠖⠶⢶⡟⠀⠀⠀⠀⠈⢿⣇⠈⠁⣸⡿⠁⠀⠀⠀⠀⠙⢷⣤⡄⢠⣴⠿⠃⠀⠀⠀⠀⠹⣜⣱⠀⢸⣋⡼
⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⣀⠀⠘⠁⠀⠈⠙⠀⣀
⠀⠀⢶⠆⠀⠀⠀⠀⠀⠀⠀⠐⣶⠀⢰⡂⠖⣤⡀⠀⠀⣠⠰⠂⡆⠀⢰⡂⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠘⣆⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠈⣇⠀⠀⠀⣴⠀⠀⠀⣠⠃⠀⠀⢻⠙⠚⡘⣶⢚⠙⠚⣼⠁⠀⠘⡇⠀⠀⠀⣤⠀⠀⠀⣾⠁⠀⠀⠸⠟⠂⢰⠀⠚⠿
⠀⠀⠀⠈⣷⡀⠀⠹⠀⠀⣸⠏⠀⠀⠀⠨⣗⢆⡙⠻⠊⣠⢆⡏⠀⠀⠀⠻⡄⠀⠀⡟⠀⠀⣰⠋⠀⠀⠀⣆⠀⠀⠘⠀⠀⢀⠆
⠀⠀⠀⠀⠙⠿⠶⠀⠶⠾⠛⠀⠀⠀⠀⠀⠈⠣⠭⠀⠨⠵⠋⠀⠀⠀⠀⠀⠱⠤⠄⠀⠠⠴⠋⠀⠀⠀⠀⠘⢶⡤⠀⠠⣴⠟
⠀⠀⢠⡀⢀⠀⠀⠀⠀⠀⣀⠀⡤
⠀⠀⠈⢷⡈⠊⠀⣀⠀⠙⠈⡼⠃⠀⠀⡀⠀⠀⠰⣿⡆⠀⠀⢀⡀⠀⠀⠐⢰⡆⠂⢀⠀⠂⣶⠐⠀⠀⠀⠀⠀⠠⣿⡆
⠀⠀⠀⠀⣙⠀⠀⢿⠀⠀⢚⠁⠀⠀⠈⠓⠀⠀⠀⢹⠀⠀⠀⠘⠃⠀⠀⠀⢨⠃⠀⢻⠃⠀⢫⠀⠀⠀⠀⢀⣌⡓⣛⠒⣋⡄
⠀⠀⠀⠀⠘⠦⠦⠈⠰⠴⠛⠀⢤⣀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⠀⠀⢳⡀⠀⠀⣰⠃⠀⠀⠀⢠⣶⠯⢍⣩⣏⠭⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉⠉⠈⠁
⠀⠀⣶⠖⣠⡄⠀⠀⠀⢠⣤⠲⣶⠄⠀⣶⣶⣤⡀⠀⠀⢀⣤⢶⣶⠀⠀⣶⣶⢄⠀⠀⠀⢠⣶⣶⠀⠠⣤⣄⠀⠀⠀⠀⠀⢀⣤⡤
⠀⠀⠹⠀⢿⠀⠀⣤⠀⠀⣿⠀⠘⠀⠀⢹⡀⢁⣞⢳⡞⢻⡈⢀⡏⠀⠀⢻⠀⠀⠡⣀⠊⠀⢨⡇⠀⠀⠸⣧⠀⠀⣤⠀⠀⢰⡟
⠀⠀⠀⠀⠘⢧⣀⣿⣀⣴⠋⠀⠀⠀⠀⠈⢓⠘⠏⠈⠁⠹⠃⣚⠁⠀⠀⠘⠦⠀⠀⡿⠀⠠⢴⠁⠀⠀⠀⢙⡗⠀⢹⠀⢰⡏
⠀⠀⠀⠀⢷⣦⣉⠀⢉⣥⡾⠀⠀⠀⠀⠀⠘⣦⡤⠀⠀⢤⣴⠃⠀⠀⠀⠀⢧⣤⠂⠁⠰⣤⡼⠀⠀⠀⠀⠈⢷⣴⠏⣧⡴⠃
⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉

⡾⣿⣿⣓⡲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⢺⣿⣿⡟
⠹⣟⣿⣿⣅⣼⣿⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⠉⣿⣇⣴⣿⣿⣿
⠀⠹⣽⣿⣯⣈⠿⠀⢼⣿⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣿⣧⡠⠙⠓⣿⣿⣽⠃
⠀⠀⠹⡽⣿⣍⣁⠀⠸⣿⠀⣾⣿⣷⣄⠀⠀⠀⡄⠀⠀⠀⠀⢀⡄⠀⠀⣠⠾⣿⡏⠀⣻⠏⠀⠶⣿⣿⢷⡏
⠀⠀⠀⢳⠻⣿⣦⣠⣀⠛⠢⣿⡇⠀⢹⣷⣄⠀⠑⢄⠀⠀⠀⠌⡠⣠⣾⣇⠀⠘⣿⠄⠁⠀⢬⣶⣿⣟⡿
⠀⠀⠀⠈⢷⠻⣿⣧⣤⣠⠀⠾⠃⠀⣿⣿⠙⣷⣌⠄⣿⣿⣄⣪⡾⠛⣿⣿⠀⢀⡛⠀⠀⢠⣴⣿⣿⣿⠃
⠀⠀⠀⠀⠈⢷⣛⣿⣦⣤⡄⠀⠀⢀⣿⠋⠈⢾⣿⣷⣾⣿⣿⣿⠃⣀⣸⣿⣆⠀⠀⠠⢤⣴⣿⣿⡜⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⢦⠄⠙⠁⢰⣆⠀⢹⣿⣿⣿⣿⡇⠈⢿⡇⢈⠩⣯⣜⠒⠛⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠀⠚⠀⢹⡀⠀⠐⣽⣿⢿⠁⠀⢸⠀⠈⡑⢿⣽⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣶⠀⢦⡀⠀⡧⠀⢧⢿⣿⡼⣇⠀⡟⠀⢠⡏⣿⡟⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠙⣿⣷⣤⠀⠅⠀⣷⢠⢸⠘⡟⢰⣄⢠⠃⠰⠋⣤⣼⢷⡟⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠿⣿⣿⣰⡆⠀⢻⠈⣐⠀⠀⣸⠁⣸⠀⠰⣀⣬⡏⡾⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣿⡿⣿⣵⣦⣾⣦⠶⠀⠀⠰⢆⣿⣷⣤⣾⣹⣿⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⣾⣋⣾⣥⣿⠋⠀⠀⠉⣟⣹⣟⣙⣏⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⣹⣯⡞⠀⠀⠀⠀⠻⣽⣏⡙⢿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡄

⢠⠤⠤⠤⢤⠤⠤⠤⠤⠴⠶⠄⠐⠀⠂⠀⠀⠀⠀⠰⠶⠶⠤⠤⢤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢀⠀⡀
⠀⢀⠔⠀⠀⢠⠦⡤⠶⡆⠀⣇⠤⣤⣴⡆⣶⠀⠠⡤⣤⣄⢀⣤⠀⠁⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉⡉⠉⡉⠛⡋⡉⡉⡍⠉⠁⣄⣉⡈⠁
⠀⠀⢀⣤⡄⣈⢀⣀⣀⠀⠠⣧⣤⣄⠀⣀⣀⣰⠆⠀⠀⠁⠀⠀⠀⠂⠀⠀⢸⢸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠃⠈⠀⠉
⠀⠠⡀⠉⠁⠀⠈⠉⠉⠀⠀⠀⠀⣀⣀⠉⠉⡁⠀⠀⡀⠠⠄⠀⠀⠀⠀⠀⢸⢼⠀⠀⢰⡏⠁⠀⠀⠀⠀⠀⢀⣀⠀⠰⠶⠇⠀⠐⠆⠈⠙⠛⠙⠋⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠈⢻⣄⣠⣤⣤⣄⠀⠘⢿⠃⠢⠀⠂⠖⠶⠀⠸⠐⠳⠇⠛⠀⠃⢀
⠀⢀⡤⠠⠀⠀⠒⢤⠠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⣼⣿⣿⢿⣿⣿⣿⣀⣴⠞⠁⣀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠈⠉⣦⠀⡄⢠⣠⣌⣀⠀⣀⡀⢀⡀⣀⠀⣀⣀⣀⣠⠤⠤⠤⠤⠤⠠⠤⢤⡈⠘⠀⢠⡿⣿⣿⣾⣿⣿⣿⠇⠹⣆
⠀⠀⠩⢄⣵⠴⡤⠆⠬⠀⠨⢤⠊⢡⠨⢼⠋⠍⣀⣀⣀⣠⡤⢤⣤⣴⢟⣷⡇⡆⠀⢿⡀⠛⠛⣿⣿⣿⡗⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀
⠀⠀⠀⢀⡄⠀⠁⠀⠈⠀⠈⠙⠀⢸⠈⣹⡆⠀⣬⡡⠀⣤⣶⣿⠟⢋⣨⣽⡇⡆⠀⠈⠛⠶⠟⢹⣿⣿⣷⠤⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⢸⡄⠄
⣉⡂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢹⣳⢅⣿⣴⠚⠛⣫⣵⣾⡿⢿⠽⡇⢃⡀⠀⢚⠀⠀⣺⡟⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄
⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⢟⠀⠈⠈⠉⠉⠉⠉⣀⣀⣠⣤⡇⢸⠄⠀⠑⠀⢠⡿⠀⠀⢸⡇⠀⠀⠀⢰⣀⠀⢀⢠⣍⠀⠀⠀⠀⠁⢐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠑⢓⣶⠀⠉⠉⠁⠀⠀⠹⣈⡇⢸⠁⠀⠀⠀⣾⠁⠀⠀⢸⡇⠀⠀⠀⠸⡃⢥⠑⠈⣉⠤⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⢥⡔⢧⣤⠤⠄⢲⡉⣼⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⠀⠀⠀⠀⢹⡆⠀⠀⠘⣷⠀⠀⠀⠀⠀⠈⠉⣠⢤⡀⠆⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⡴⠋⢸⠀⠀⠀⠀⠀⠀⠀⢸⠆⢸⡀⠀⠀⠀⣼⠇⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠑
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡘⠒⢒⣒⣈⣉⣁⣀⣀⣇⣀⣀⡀⠀⠤⠤⠤⠼⠀⠀⠇⣀⣀⣀⣀
⠤⠤⠤⠤⠀⠀⠤⠤⠤⠤⠭⠭⠥⠄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⡆⠐⠒⠂⠤⠤⠤⠭⠭⠭⠍⠉⠉⣉⠉⡉⣉⡉⣉⢉⣉⣉⣉⣉⣉⣉⡉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⢀⠀⢠⣀⣀⠀⢠⡤⣀⡀⠀⣶⠄⡄⠴⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣄⣄⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⠀⠀⠘⠂⠀⠀⢀⣀⣠⣤⡴⣖⣿⣿⡟⡋⠀⠹⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠐⠒⠒⠉⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⢛⣽⣾⣯⣿⣿⣲⣶⠂⣿⣿⣿⡄
⠀⠀⠀⣀⡠⠤⠒⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠁⠀⢿⣾⣿⣿⣿⣇
⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡏⠉⠀⢀⠀⠀⠀⠀⣒⣤⡲⠶⡀⠈⠁⠀⠀⠀⠘
⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⢶⣶⡄⣇⠀⠀⠀⠀⠀⠀⡄⡇⠀⠀⠀⠀⠀⢱⣠⣶⡓⠠⡀⠀⢰⣭⣿⣿⡆⣘⠀⠀⠀⠀⠀⠀⡇
⠈⢆⠀⠀⠀⠀⠀⣠⣤⡀⠀⠒⢄⠀⠀⣏⠀⠹⣾⣿⠇⢸⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠈⣷⣾⣿⣠⠇⠀⠀⠙⠛⠋⠉⡀⠑⠀⠀⠀⠀⢠⠇
⠀⠘⡄⠀⠀⢠⣾⣈⢿⣷⠀⠀⡸⠀⠀⠀⡉⠉⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⢳⠀⡀⡀⠄⠐⠊⠉⠉⠀⠁⢸⡆⢀⣀⣤⠤⠊
⠀⠀⠹⡀⠀⠈⠻⠿⠿⠿⠔⠊⠁⢀⠠⠀⠸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢿⣭⣄⣴⣶⣶⠶⠤⡴⠚⡻⠉⢧⡀
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠤⠔⠊⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢷⠒⠒⠁⠀⡇⠀⢸⠳⡄
⠐⠈⠁⠀⢣⡀⠀⠀⠀⠀⢀⣀⡀⢤⠔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⡗⠐⢸⠀⢹
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⡇⠀⢸⡀⢸⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣦⡀⠀⠀⠀⠀⠀⠀⢿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⠀⠀⠀⠀⠀⠀⠀⢬⣡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣄⠀⠀⠀⠀⠀⢠⣾⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⣻⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠿⡄⠀⠀⣀⠀⠀⠀⠀⣲⠀⠀⠀⠀⢰⣷⠂⠀⠀⠀⠀⣿⣴⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠘⣷⡆⠀⠀⠙⠀⠀⡀⠀⠛⠁⠀⠀⠀⣺⣟⠄⠀⠀⠀⢠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠂⣙⠂⠀⠀⢼⠁⠀⣤⠀⢺⠃⠀⠀⠀⠿⠁⡀⠀⠀⠀⠘⠿⣁⠄
⠀⠀⠀⠀⠀⠀⠀⢠⣺⣀⠐⠢⠿⠓⠀⠀⢿⠄⠀⢤⠀⣿⠃⠀⠀⠠⣤⣠⡆⠀⠀⠀⢀⣶⡄⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⣤⣤⠄⠔⢠⢼⡄⠘⠇⢉⣠⠄⠀⠀⢻⡿⠇⠀⠀⠐⣿⣇⠀⠀⢿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣤⠀⢩⣇⠀⠙⡿⣩⠆⢱⣿⡴⠀⠀⠱⣤⣿⠀⠀⠀⠀⢻⡞⠀⢠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣛⣤⡞⢯⡆⠀⠀⣽⠂⢪⣽⣧⠈⠀⠢⣬⡉⠂⠀⠀⢀⣀⠸⢟⣄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢷⠀⣾⠃⠀⠀⠫⡜⠻⠛⢷⠀⠀⠀⠹⣿⠀⠀⢀⡀⠟⠀⠀⣿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⣷⠉⣶⠀⢿⠆⠻⠦⢙⡟⠀⠀⢳⣤⣈⠃⠀⠘⣵⣏⠀⢀⣿⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣠⠿⠇⠀⠁⣠⣶⣛⠁⢀⠀⣰⣿⡏⠀⠀⠀⢛⣧⡀⢸⡷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⡾⠁⣿⠆⠸⡇⠘⣧⣾⣿⣇⣻⡇⠀⢿⣄⠴⠀⢼⡋⠐⡏⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡀⢈⠀⠳⡆⢁⡌⢻⣩⣟⢀⣹⡇⠤⣼⠋⣤⣈⢈⡡⠤⣘⢯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⣾⡃⠂⣩⣾⠀⡌⠱⣿⠗⢹⡏⠁⢿⣦⢆⣡⣬⣦⡐⢾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢜⣷⠄⠶⣁⡖⠀⠛⣴⡶⣿⠀⢁⣸⣇⡿⠘⠛⠛⣷⣾⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⡤⢹⡿⠀⠀⢠⡀⢈⠀⠘⡁⠈⣿⣦⠶⠀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡘⣿⢳⣄⠀⢙⠋⠀⢸⣻⡟⢪⣤⠴⢀⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⣯⠀⣾⡿⠄⠘⣿⣃⢹⡅⠲⠿⠗⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⢋⡀⠀⠟⣴⣿⣧⣍⠠⠿⠀⣰⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣷⡀⠛⣽⠋⠈⣤⡀⠆⠈⢿⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡌⢷⠀⣀⣾⡀⠛⣶⠀⠱⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣰⡄⢻⡿⡇⢸⠟⣿⢲⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⢻⡏⢹⣷⣀⠀⢀⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢰⣿⣯⣿⣡⢿⣨⡅⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⢿⣿⠃⣶⣿⡅⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠚⢻⣾⣿⣷⡈⣿⠁⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⣷⣼⣯⣿⣿⣌⠳⣀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣬⣥⣼⣆⣻⡕⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣾⠿⣿⡗⢈⢿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢳⡾⣿⣷⡌⠀⣿⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢣⣏⡟⣡⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠇⣼⠘⠃⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⣟⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣗⢒⣿⢹⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣗⣒⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡧⣤⡼⠿⢟⣬⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣞⠿⠿⢧⣤⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡦⠤⠤⠬⣄⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡴⠤⠤⠤⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣄⡀⠀⠀⠱⢤⡀⠉⢷⡄⠀⣀⠀⣰⠟⠁⣠⠴⠁⠤⠤⠤⢤⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⣀⠀⠀⠀⠀⠀⠈⠑⠠⠙⣾⣿⣞⠡⠐⠉⠀⠀⠀⠀⣀⣀⣀⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣛⣿⣿⣿⠿⠿⠶⠶⢲⣿⢸⣿⠖⠶⠿⠿⢿⠿⢻⣟⣛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠇⠀⠀⢰⠊⠁⢀⠔⠨⢿⣿⠿⠀⠀⠀⠈⠱⠀⠀⠀⢽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣈⣁⠠⠖⠁⡀⠀⢸⣿⡀⠀⠄⠈⠢⠄⣈⣀⠀⠠⢽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⠀⢀⠌⢠⡞⠀⠌⠀⠠⢹⣿⠑⡀⠈⢆⠀⢦⠈⢂⠀⢢⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣎⣀⡌⢀⠌⢀⡔⠀⠀⠛⠀⠀⢆⠀⢂⠀⣅⣀⣷⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣾⣦⠞⠀⠀⠀⠀⠀⠀⠈⠳⣾⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀⠀⠀⡔⠋⠱⠤⢶⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⢠⠒⣄⠀⠀⢀⠚⠠⠂⢀⠤⣄⠓⠛⢢⡑⢄⣆⠀⡀⡱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⣄⠀⡴⢶⠲⡒⠒⡖⡚⢲⠲⣆⣠⠙⠚⡗
⠀⠱⡤⡑⠼⠟⢍⡑⣄⡀⠘⠂⠊⠀⢤⡠⣵⠋⠁⢌⣀⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⢠⣍⣘⢃⠀⢣⢸⠀⢰⢀⠀⡇⣿⣁⠀⠘⢆
⢀⠞⠀⠀⠀⠀⣠⠞⠳⠥⠀⠀⠀⢇⣠⠇⢸⡧⣵⠀⢠⠒⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠀⢀⡀⢹⣤⠂⢸⢀⠀⢸⡄⢠⢇⡿⢹⣱⠒⠋
⢇⠀⢀⡴⢾⡉⠙⠢⣄⣔⡇⠈⡂⢀⠤⣤⠋⠧⣈⣁⡜⠀⠀⠀⠀⢀⡀⠤⡤⠤⠤⢤⣤⣤⣀⡀⠀⠈⠓⢻⠃⣧⠜⠋⠈⠒⠞⠚⠒⠛⠛⠉⠉⠀⠀⠉
⠀⠉⠉⠀⠀⠑⠤⠴⠛⠾⣌⣉⣠⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡎⠑⠠⠀⣌⡶⡷⠷⢶⡀⠤⣍⣣⠀⠀⠘⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⡒⠲⠤⠤⡶⠤⠤⠼⠖⠚⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢁⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⠀⠀⠀⡇⠀⠀⢀⡄⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠒⡩⠤⢕⢤
⠀⠀⠀⠀⠀⡰⠲⡋⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠈⠐⠚⠠⠤⠤⠧⠤⠤⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⢡⠀⡠⢀⠑⠤⠚⠀⣣
⠀⠀⠀⠀⠀⣧⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠒⠁⠀⠢⠴⠃⢀⣀⠸⣄⡆
⠀⠀⠀⠀⠀⢏⠳⣄⠈⠓⠤⣀⡀⠀⠀⢀⣰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⡄⠀⠐⢄⠸⣄⡨⠃⡠⠁
⠀⠀⠀⠀⠀⠘⢦⠀⠑⠢⠤⣀⣉⡉⢉⢉⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⣀⡴⠂⠈⠉⠑⠢⠤⣀⠀⠀⠈⠣⣆⠀⠁⡁⠄⣀⣰⠻⠥⣀
⠀⠀⠀⠀⠀⠀⠀⢹⠦⣀⡀⠀⠈⣉⡡⠟⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠂⠁⠀⠒⠀⠤⣠⠀⠈⠁⠀⠀⠀⠀⣀⠄⠊⠉⡄⠀⠀⠀⠀⠈⠈⡑⢟⡉⢠⠻⡖⠊
⠀⠀⠀⠀⠀⠀⠀⡼⠀⡰⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣎⣁⡘⠊⢇⡀⠀⠀⠀⠂⠀⠀⠀⠉⠓⢂⠔⠊⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠉⠁⠈⠙⡀⠸⡄
⠀⠀⠀⠀⠀⠀⣰⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠊⠁⠀⠀⠈⠉⢀⠿⣓⣦⣀⠀⠀⢀⣤⣀⠂⠀⢸⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠱⡀
⠀⠀⠀⠀⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⣞⡋⠤⡀⠀⠀⠀⠀⠀⠔⠅⠈⠀⠀⠀⢉⡹⠓⡄⠉⡆⠀⣸⠗⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⣄⢑
⠀⠀⠀⠀⢰⠃⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡆⠙⠲⢬⠑⠒⠒⢮⠒⠉⠓⢦⠒⠒⠲⣤⠐⠀⢠⠀⡾⠊⠀⠀⠀⠀⠀⣠⠔⠛⠉⡡⢈⠩⠛⢦⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣆⠠⣀⣔⠠⠤⢄⣍⣀⠀⣀⣸⠀⡠⠞⠉⠁⠀⠀⠀⠀⢠⠞⠁⠀⠀⢀⣀⣀⡀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⢏⠠⡀⢀⡴⢋⢀⢔⢹⡏⠩⢑⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⠚⡟⠀⠰⡉⢁⣼⢅⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠤⣼⠗⠀⠈⠲⡀⠀⠀⠀⠀⠀⠀⠈⢷⡤⢀⣷⣀⠴⡻⠉⠈⠎⣆⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔⠚⠉⠙⠢⡈⢆⠀⠈⣷⡖⠀⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣄⣙⣺⣤⡤⠴⡟⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⠐⠚⠉⠁⢄⠙⢆⠀⠀⠀⢹⠈⣄⡴⠙⠛⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⢆
⠀⠀⠀⠀⡀⠠⣀⡀⠀⠀⠔⠉⢍⡉⠲⣌⠢⠀⠀⠀⠑⠘⣀⣠⠤⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠳⡄
⠀⠀⠀⠐⡀⠀⠸⡈⠑⠚⠒⢀⡀⠱⠀⠈⢆⣷⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠘⢆
⠀⠀⠀⠀⡝⠉⠀⡨⠛⢳⠔⠣⠤⠤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠘
⠀⠀⠀⠀⢇⠀⣸⠽⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣹⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢿⠀⡥⠁⠀⠀⠀⠀⠀⠀⠀⢹⡣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣼⣸⠃⠀⠀⠀⠀⠘⠀⠀⡀⡀⡑⠀⠀⠀⠀⠀⠀⢀⣀⣰⣶⣶⣶⣶⣶⣤⣶⣶⡴⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠈⢿⠁⠀⠊⠀⠀⠀⠀⠀⠀⠉⡷⠁⠈⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⡱⣼⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⠁⠀⠀⠐⠀⠀⡀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡞⠀⠀⠀⠀⠀⠀⠀⠈⢹⣣⠞⠂⠊⠀⠀⠀⠀⠈⠉⠀⠺⠿⠿⠿⠿⠿⠿⠛⢛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⢀⠀⢀⠋⠱⡇⢠⠄⡀⠂⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠳⣘⠶⢴⡷⣶⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠁⠐⡌⢡⠀⢀⣹⡇⠰⠁⡈⠀⢀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⢠⡆⠂
⠀⠀⠀⠀⠀⠀⠑⢈⣀⠇⠀⡀⢀⠀⢰⡇⠀⢀⠀⡀⢠⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡆⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣦⡈⠄⢸⠀⣠⢎⠜⠠⡾⡈⠀⢠⠇⠀⠀⠒⠀⠀⠀⡀⠀⠀⠀⢰⡼⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠈⠀⠐⠄⠘⠀⠀⢫⠏⠒⢼⣠⣴⠋⠀⢸⠃⢀⠄⡱⠂⠀⠀⠐⠀⣤⠀⠸⠀⠀⠀⠀⣟⠉⢀⠀⠀⠄⠀⠰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠑⠷⣄⢄⠀⠄⠀⢸⠕⠁⠀⠀⣼⣴⣠⠜⠁⠀⠀⠀⠀⠈⠘⠧⣼⡀⠀⡀⢤⣼⡰⠊⠋⠀⠀⠀⠀⡟⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠀⠈⠀⡙⠀⠀⠀⠀⠷⠋⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡄⢈⣼⡅⡴⠀⠀⠂⠀⢰⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠠⣯⡠⣄⠀⣠⣐⡠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡀⠙⠏⢹⡜⠀⠀⠀⢠⠀⠀⠠⠇⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠄⠀⢱⡀⡏⠉⢳⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⢸⠀⣄⣠⠂⣰⡧⣀⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡇⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡖⠘⠁⡰⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⡏⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀⢘⡠⠛⠳⢦⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣶⣶⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠈
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠋⠉
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠟⠛⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢻⠾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢟⣴⣤⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠛⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠰⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⣠⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⠀⠀⠴⠞⠁⢀⣤⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡏⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠼⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀⠀⢀⣶⣴⣿⣿⡇⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣿⡇
⠀⠀⠀⠀⢀⣤⡤⠴⢖⣲⠟⠛⠋⠉⠀⠀⠀⠀⠈⠉⠉⠉⡉⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⢠⣾⢟⠅⠂⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⢉⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡇
⠀⠀⠸⣿⣍⣰⠇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣿⣿⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿
⠀⠀⠀⠙⠻⣿⣶⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠰⠋⠀⡿⢿⣿⣿⣏⠛⠦⣄⠀⠀⠀⠀⠀⠀⠠⣄⣨⡟
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣴⣶⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⢿⣦⠀⠀⠁⠀⠀⠀⠤⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⠟⠀⢀⣀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠛⠉⢩⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⡆⠀⣰⠀⠀⢀⠀⠀⠀⠀⡀⢀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢷⣶⣿⣆⣠⣾⡂⢠⣄⣠⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠋


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

⠀⠀⠀⠀⠀⠀⢀⠖⠒⠲⡄⠀⠀⠀⠀⠀⠀⠀⣰⠲⡄⠀⠀⠀⠀⠀⠀⠀⢀⣞⡅⠀⠀⠀⠀⠀⠀⠀⡴⠂⠒⢦
⠀⠀⠀⠀⠀⠀⢮⣀⣄⣄⡼⠀⠀⠀⠀⠀⠀⡰⠣⠭⢽⡀⠀⠀⠀⠀⢀⡴⠋⠉⠉⠦⡀⠀⠀⠀⠀⢀⠷⠔⠒⢺⡄
⠀⠀⠀⠀⠀⠀⠈⢟⠢⡱⠁⠀⠀⠀⠀⠀⠀⣗⢒⠒⢒⡇⠀⠀⠀⠀⠪⣀⢤⣀⡠⣀⡼⠀⠀⠀⠀⠸⡀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢸⠁⠀⠀⠀⠀⠀⠸⣴⣤⣦⠇⠀⠀⠀⠀⠀⠀⠈⢹⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⢠⢾⣱⠦⡀⠀⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⡀⠀⠀⠀⠀⢀⡠⠚⣧⣼⣦⠀⠀⠀⠀⠀⡰⠁⠉⠉⡖⠁⠀⠀⠀⠀⠀⡴⠷⠞⢄
⠀⠀⠀⠀⢰⣫⢤⣀⠤⣄⡠⢌⣲⠀⠀⠀⣏⣩⣭⣤⣤⣤⡇⠀⠀⠀⠀⠳⡒⠒⢲⠞⠀⠀⠀⠀⢀⣠⣏⣙⣉⣹⣄⡀
⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠊⠀⠀⠀⠀⠯⠭⠭⠭⠤⠴⠃⠀⠀⠀⠀⠀⢹⢻⠏⠀⠀⠀⠀⠀⠈⠑⠒⣢⣖⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠽⠦⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⠤⠶⠭⡉⠑⣄⠀⠀⠀⠀⢰⠣⢢⢔⢮⢣⠀⠀⠀⠀⠀⡔⠉⠀⠈⠱⡄⠀⠀⠀⠀⢸⣿⣿⡿⣿⡇
⠀⠀⠀⠀⠀⡏⡞⡉⠳⡈⡆⢸⠀⠀⠀⠀⠸⡰⣐⣾⣮⡾⠀⠀⠀⠀⢰⠳⡖⢶⢲⡖⣷⠀⠀⠀⠀⢸⣿⣿⡛⢻⡇
⠀⠀⠀⠀⠀⠱⣱⢌⣒⣁⠷⠊⠀⠀⠀⠀⠀⠉⢲⣿⠃⠀⠀⠀⠀⠀⠈⣇⣧⢸⢸⢧⡏⠀⠀⠀⠀⢸⠋⠛⠻⠿⣯
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡔⠋⠀⢙⠲⡀⠀⠀⠀⠀⠀⠀⢀⣠⡓⢤⠀⠀⠀⠀⠀⠀⡞⡁⡙⡆⠀⠀⠀⠀⠀⠀⣀⣄⣤⣀
⠀⠀⠀⠀⠀⡜⠡⠆⠀⠈⠀⢳⠀⠀⠀⠀⠀⡴⡏⢣⠈⡞⠁⠀⠀⠀⠀⡖⠚⠈⠘⠒⡆⠀⠀⠀⣰⡎⢱⡀⢀⠎⢑⡆
⠀⠀⠀⠀⠀⢸⣀⠀⠀⠙⢀⠎⠀⠀⠀⠐⣮⠣⣸⡤⠋⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⢏⠀⠀⠀⠀⠙⢌⡏⠙⠋⢹⣡⠃
⠀⠀⠀⠀⠀⠀⠈⠙⣾⠉⠁⠀⠀⠀⠀⠀⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠋⠳⠬⠇

⠀⠀⠀⠀⠀⠀⢀⡠⣖⠾⠍⠋⠯⠽⢶⣲⢤⣀⣠⢤⣖⠾⠭⠟⠹⠿⢷⡢⣄
⠀⠀⠀⠀⠀⣠⣫⠊⠀⠀⠀⠀⠀⠀⠀⢀⣉⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⡳⡀
⠀⠀⠀⠀⢀⣷⠃⠀⠀⠀⠀⠀⠀⠀⢀⠩⢉⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⢹⢷
⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠑⡄⠈⠁⢢⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⢠⠚⠶⠉⢣⠤
⠀⠀⠀⠀⠀⢳⣣⡀⠀⠀⠀⠀⠀⢀⠀⠀⠐⢀⡇⠂⠀⢠⠀⠀⠀⠀⠀⠀⢀⢮⠇⠀⡎⠉⠢⢐⠠⠃⣠
⠀⠀⠀⠀⠀⠀⣧⠇⠀⠀⠀⠠⡀⠈⠲⠤⠴⠊⠐⠤⠤⠊⠀⡠⠀⠀⠀⠀⢸⣧⠀⠀⠈⢣⡀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠀⠀⠘⠢⢀⡀⠀⠀⠀⠀⣀⠠⠚⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⢀⠃⢠⠏
⠀⠀⠀⠀⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⡤⠤⠖⢁⡠⠋
⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡖⠒⠊⠉
⠀⠀⢀⡤⠒⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇
⠀⢠⠋⣠⠊⣟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇
⠀⡎⠀⡇⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡇
⢀⠇⠀⠈⣆⣹⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠃
⡎⢀⣶⠢⠤⠜⠙⠯⣖⣤⣤⣤⣤⣤⣤⣤⢤⢤⢤⡤⣤⣤⣤⣤⣤⣤⣔⡮⠗⠁
⠣⠴⠷⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡏⡏⡏⢹⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣤⣀⣀⡇⡇⡇⢸⣀⣠⡤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣋⣀⣀⣀⣀⣀⣉⣁⡧⣇⣈⣁⣀⣀⣀⣀⣀⣙⡄
⣿⡿⠻⠗⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀
⠀⠀⠀⠐⠦⢳⡋⠀⠀⠀⠂⠀⢠⠁⠀⠀⢆⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠁
⠀⠀⠀⠀⠀⠀⡁⠀⠈⠈⠲⠡⠏⠀⠀⣀⡎⢀⠄⠨⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢉⡁⠀⠀⠀⡘⠀⢐⢤⠁⠋⠘⢨⡅⢱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠰⣤⣘⠅⢰⡞⢃⠃⠉⠰⣿⠊⠳⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇
⠀⠀⠀⠀⠀⠀⠤⠀⠋⢛⣸⠐⠀⡁⣻⢜⠘⡋⣠⢆⠎⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣆⠄⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢧⡏⢩⠄⠈⠁⡯⠈⢸⡏⣭⠜⢱⣫⡴⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠃⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠰⠸⣇⠃⠀⢠⡄⠀⣖⢳⡀⣼⡇⡾⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣧⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠄⠌⢲⢸⡎⢰⡦⠛⠛⠙⠋⣰⠤⠒⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⠀⣠⢼⡖⢋⡔⢙⡐⠁⠀⠀⠀⠀⠀⢀⣤⡶⢀⠀⠀⠀⠀⣆⡃⠀⡀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⣾⣾⡿⢾⣤⣿⡁⠀⠀⠀⠀⠀⢰⠟⠋⠀⠈⠀⠀⠀⠀⣈⣳⠿⠡⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢺⠛⣙⣴⣿⠸⢻⡵⠂⠀⠀⠀⠀⢸⡲⠆⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢠⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣹⣸⣿⡀⠛⠀⠀⡀⠀⠈⡅⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⠃⠀⠀⠀⠀⢀⡴⠗⢺⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁
⠀⠀⠀⠄⠀⡆⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡴⠋⠀⠠⣼⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⣠⡖⠁⢀⣀⡀
⠀⠀⠀⠀⠀⣷⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠋
⠀⠀⠀⠀⠘⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⠀⣠
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁⠀⠔⠂⠀⠀⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢻⣌⣀⠾⠁
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⢳⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡞⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠤⠽⢿⣛⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣛⡿⠯⠤⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡖⠒⠲⢿⡟⠁⢉⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡉⠈⢻⡿⠒⠒⢲⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡾⣷⡒⠒⣚⣧⣰⣿⡿⢉⣿⣄⠀⠰⠀⠀⠆⠀⣠⣾⡉⢿⣿⣆⣼⣛⡚⢒⣾⢷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⢉⣉⣉⢻⣿⡀⢸⣿⡿⣦⠘⡀⣠⠃⣼⢿⣿⡇⢀⣿⡯⣍⣁⡉⣹⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣇⣀⢠⠤⠿⠟⣿⡿⢥⣹⣇⣿⣿⣸⣏⡬⢿⣿⠻⠿⠤⠤⢀⣸⣟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡤⠔⠒⠒⠒⢿⡟⠒⠦⣽⡇⢸⣯⠖⠒⢻⡿⠐⠒⠒⠂⢤⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣿⡟⠛⢋⣉⣉⣽⠿⠛⣿⣇⣸⣿⠛⠿⣯⣍⣉⡉⠛⢻⣿⡛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡿⡟⠋⡹⠋⢠⡿⢀⡼⣹⣿⣿⣏⢧⡀⢿⡄⠘⢏⠉⢻⢿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⡷⠚⡇⠀⢘⣷⡾⢠⡇⢻⡟⠸⡄⢷⣾⡃⠀⢸⠓⢺⣿⣿⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣦⣷⠞⣹⠒⡟⢻⣷⡿⠀⠀⠀⠀⢿⢺⡟⢻⠒⣏⠳⣿⣴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⣿⣍⣧⣧⣰⣧⣼⣽⡇⠀⠀⠀⠀⢸⣯⣧⣼⣦⣼⣼⣭⣿⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡝⣿⣿⣶⣿⣷⣿⣿⠇⠀⠀⠀⠀⠸⣿⣿⣾⣿⣶⣿⣿⢫⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⣿⣽⡿⠾⠟⠁⠀⠀⠀⠀⠀⠀⠈⠛⠶⢿⣯⡾⢿⠿⠁

⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠴⣖⠦⠬⣍⣉⠓⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠌⢉⣉⡰⠖⢦⣤⣀⠁⠒⠨⠍⡒⣄⠈⠛⠄⠀⠀⠀⠀⠀⠰⣿⣿⣿
⡛⠛⣉⣥⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠚⠒⠒⠒⠦⠤⣀⠀⠉⠐⠢⠄⣁⠂⣄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠉⠛
⠁⢣⣿⡏⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠁⠀⠉⠀⠁⠂⠠⠄⣉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢸⢿⡄
⢠⣿⣿⠏⣾⡀⠀⠀⠀⠀⢠⠓⠀⠀⠀⠒⠒⠢⠀⢀⠀⠀⠀⠀⠉⠁⠀⠀⢀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣷
⢸⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⢀⡀⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣻
⠸⣿⡇⠀⣼⡇⠀⠀⠀⠀⠀⠀⠑⠢⠄⠀⠀⠀⠀⠤⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠛⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⢠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢹⡿⣋⡟⢿⣤⢶⣆⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣼⠟⣿⣻⡟
⠀⠀⠀⢻⢻⠗⢿⣤⡀⠨⢿⣿⠛⢷⡦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣶⠟⢻⣿⠯⢤⣤⣼⠛⣿⣿⠃
⠀⠀⠀⠘⣿⣹⢯⣦⣤⠴⠞⣯⣁⡾⡞⢻⡟⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢞⣻⣿⡿⣆⣩⣷⠶⢦⣤⣮⢽⣽⡟
⠀⠀⠀⠀⠙⣷⣴⣿⣦⣀⡠⣏⣹⠶⠶⣏⠛⠳⠾⢿⣦⡀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠀⠀⣠⣾⠷⠶⠿⢿⡷⠶⠾⣭⡧⣀⣠⣟⡃⣼⡟
⠀⠀⠀⠀⠀⠘⢿⣳⣾⠉⢱⣿⠆⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⢠⣞⣷⠈⢹⣾⣷⠏
⠀⠀⠀⠀⠀⠀⠈⣻⣾⡟⣳⣾⢾⡧⠄⠀⠞⠦⢄⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⢀⡤⠿⠆⠀⠴⢭⣿⢿⡳⣟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢹⣵⣿⠝⢿⠁⠀⠀⠀⠀⠀⠀⢁⡄⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⣿⠞⢯⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⣿⣛⣧⣤⠤⠤⠤⠒⠒⠛⠙⠓⠀⠀⠀⠀⠈⠳⡄⢰⣶⠀⡴⠋⠀⠀⢀⠠⠐⠊⠉⠓⠒⠒⠠⠤⢤⣤⡟⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠘⣾⣿⡞⢁⣠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠯⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣦⣤⣤⣤⣶⣶⣶⡶⠶⠦⠤⣤⣤⣤⣤⣽⣿⣿⣿⣤⣤⣤⡀⠀⣤⣶⣶⣶⣶⣶⣤⣤⣀⣠⣾⣿⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣉⠍⠉⠉⠉⠉⠉⠻⠆⠁⠀⠤⠐⠀⢉⡿⣿⣿⣿⣏⠉⠐⠠⠤⠉⠛⠛⠉⠉⠉⠉⠀⠫⣍⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢯⣀⡀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣀⠴⠋⠘⢹⣿⠹⡈⠳⢄⡀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣀⣸⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⣷⠊⠁⠀⠀⠀⡀⠀⠀⢀⣠⡴⠊⠁⠀⡰⠀⣾⣿⠆⠁⡀⠀⠉⠲⣤⣀⠀⠀⠠⡀⠀⠀⠀⠈⢻⣯⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣛⣷⣄⣀⠀⠐⠚⢁⠴⠛⠉⠁⠀⠀⠀⠸⠃⡀⢸⣿⠐⡄⠙⠄⠀⠀⠀⠉⠙⠳⢀⠛⠒⠤⢀⣀⣼⣿⢾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⣬⣿⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⠀⢠⡼⠁⢸⡿⠀⠹⣴⠀⢀⠀⠀⠀⡀⠀⠀⠑⢦⡀⠀⢹⣞⢻⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣛⣿⣷⣾⡇⠀⠀⠀⡔⠀⠀⣠⠃⢀⡿⠁⠀⠀⠁⠀⠀⠹⡆⠀⢣⡀⠀⠐⡀⠀⠀⠀⣿⡶⣿⠿⣻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣭⣶⢿⣿⡶⣶⣾⣇⣀⣴⠃⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢳⣄⣀⣿⣶⡶⣾⢿⢶⣮⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢯⣷⣿⣲⣻⣭⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣾⣯⣿⣷⣺⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣴⣶⡶⠶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣠⣶⠿⠿⠿⠿⠿⠿⠛⢛⠛⠉⠉⠉⠉⠁⠒⠒⠛⠉⠉⢆⢹⣇⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠛⠻⢿⣁⡆⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠠⠀⠀⠀⢈⣼⠟⠉⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠂⠀⡀⠰⣥⣄⠀⣉⣹⠆⠀⠀⠀⠄⠲⢀⣀⡀⠀⠤⠁⠀⠄⠠⠀⢀⠎⢀⡰⡎⢀⠄⠀⠄⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡤⠰⠈⡦⠛⣿⣿⠹⠁⠀⠀⠠⠈⠊⡐⣋⠆⠀⠁⢃⡀⡅⡸⠄⠂⠐⠶⣿⡁⠳⢎⠀⠐⡆⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠑⠦⣌⣵⠞⢿⣿⣧⠁⠀⠀⠘⠊⣝⢌⣁⠈⡄⢀⠀⣄⡲⢠⠈⡄⠀⠀⢸⡟⠻⢦⣀⣈⢀⡀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠚⢇⣰⡾⠛⠁⠀⠘⣿⣿⠀⠀⠀⡀⡐⣦⢟⣙⡃⠴⠠⠀⠠⡍⡾⢛⠠⠀⠀⢸⣇⠀⠀⠉⠙⢷⣎⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⡏⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠠⠌⣉⢳⣩⡗⢂⣄⠂⠄⡳⣇⠈⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢿⡄⡀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⣿⠁⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⡓⠆⢳⠊⠇⡇⡨⣀⠰⠐⡤⠆⠀⠀⠀⠆⢻⡇⠀⠀⠀⠀⢸⣿⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⣿⠀⠀⢀⣤⣶⠿⠛⣿⡇⠃⠀⠁⠀⠄⠂⠐⠀⠑⣆⢁⣉⣈⡁⠀⡀⠀⠀⠸⢸⣷⡀⠀⠀⠀⠀⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⡆⢿⣶⡾⠛⠉⢀⡤⣶⣿⣇⣀⡠⠤⠒⠒⠊⠉⠉⢉⡉⠉⠉⠉⠉⠉⠉⠛⠒⠲⠾⣯⡻⣦⣄⠀⢀⣿⣿⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠸⡇⢄⠀⠀⠻⣾⠿⢛⢩⡀⠠⠀⠀⣀⣀⣠⣤⡤⠤⠤⠤⠶⠶⠤⠤⠤⣤⣄⣘⡀⠆⠈⠻⣷⣼⣿⡏⣸⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢿⣏⢃⠹⡄⠓⢄⠈⠂⠠⠐⣀⡥⠖⠚⠉⠉⠁⠄⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠙⠒⠤⣈⠻⣷⢁⣿⠃
⠀⠀⠀⠀⠀⠀⣰⣟⣿⣭⣍⢿⣎⣿⣅⢷⣝⠦⣄⠱⢈⡴⠋⠁⠀⠠⣞⣛⣛⡂⠀⠀⠈⠀⠀⠀⡄⠀⠀⠐⠀⠀⠀⠐⣛⣛⡒⠀⢀⠑⠼⣿⣏
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢻⣿⠉⠧⣌⢹⢘⡆⣮⠀⠀⠐⢠⡞⠉⠈⣿⣿⣦⠀⠀⢀⣤⠶⠶⠦⢤⡀⠀⠀⡰⠋⠉⣻⣿⣷⡄⠐⢠⠈⣿
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣯⣿⣬⣓⡶⣮⡉⠚⠁⡇⠀⠀⠀⣿⠀⡲⣞⣿⣿⣻⠆⢰⢏⡀⡂⠈⠐⢦⠙⣦⢰⡇⢠⣶⣻⣿⣯⣿⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⣿⠇⠀⠂⡇⠀⠀⠀⠹⣄⠈⠛⠉⢛⡼⠁⣿⢀⣧⡁⡀⡀⠀⡇⢸⠌⢧⡀⠙⠛⠀⣡⠏⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⠈⠛⠶⠖⠋⡀⢀⣹⣄⠱⠕⣺⠣⠔⢁⡟⡀⠈⠙⠒⠒⠚⠁⠀⠀⡘⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⢿⣤⢘⠆⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⣧⣤⣾⣿⡿⠃⠀⠀⠁⠀⠀⠅⠀⢰⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⣦⡘⢠⡦⡇⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠉⠐⢀⡀⠆⠀⠀⠆⠀⢠⢸⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⣿⣶⣍⡇⠀⠧⠀⠟⠀⠀⠒⠀⠀⠂⠃⠂⠀⠀⠀⠐⠀⠀⠀⠐⠘⠃⠀⡀⠀⣀⠂⡘⡘⢐⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣶⡶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠾⠟



⣿⣿⡿⠿⣿⠿⢿⠿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣿⣶⣿⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣈⠣⣰⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⢀⣄⠀⠀⢱⡀⠠⠋⡀⢹⠛⢢
⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⢱⠀⠃⠀⢳⠀⠂⠁⠀⠸⢀⠈⡘⡜⠐⠀⢀⣀⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢠⠿⡇⠀⢠⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⢢⣆⠀⢠⠈⢷⠃⡎⣠⢆⠌⢰⡇⠀⠀⡶⠃⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⡏⢀⠂⢡⣳⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠯⣇⠀⢡⠘⣴⠷⢁⡜⠥⢼⠁⠎⠀⡆⣴⠀⣠⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⡀⠀⠀⠀⢸⠀⠈⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠀⠈⢢⡀⣶⠛⢦⠜⢣⡕⠚⡄⡀⠘⣡⠇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡆⠘⡆⡿⢀⡆⢠⡿⠃⠀⣀⡤⠖⠊⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠶⡛⡇⢐⠈⠒⢸⠀⡀⠜⠁⡄⢀⠀⡀⢺⠁
⠀⠀⣤⠠⠤⠤⠄⣀⣀⠘⣆⣿⣤⠃⣿⣠⡇⢸⠅⢀⠞⠁⠀⠀⠀⠐⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠱⡀⢀⣰⡇⡞⡟⢀⠜⣠⠏⠐⢀⡜
⠀⠀⠈⠓⠦⣤⣀⡀⠀⣉⢪⣉⠣⣀⢺⣿⣥⠂⢠⣏⢀⡀⠔⢃⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠈⣾⢿⡏⠀⣷⣥⣶⠿⠒⠒⠉
⠀⠀⠀⠀⠀⠀⢈⠝⠛⠉⢁⣈⣈⣻⣧⡽⠟⠁⣸⣞⣉⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢍⠹⣿⠁⣰⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢴⣶⠞⢿⡀⡀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢻⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠈⠀⠀⠀⢳⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠟⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⣤⡤⠤⣤⣀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡤⠤⠤⢄
⠀⠀⠀⠀⢀⠠⣔⠊⠉⣷⠒⠂⠙⣆⠡⡈⢻⠳⡄⠀⠀⠐⡟⡡⠒⣉⣭⣷⣆⠀⠀⡰⠁⢀⠠⠔⠁⠰⢄⡀⠑⡄
⠀⠀⡠⢊⡔⢄⠹⡌⢢⠘⣧⠀⠀⠘⡆⠃⠈⣧⡇⠀⢸⠀⠉⠠⠈⠉⢁⣀⣈⡄⠀⣇⠐⠁⠀⢰⢀⠂⠀⠘⠄⣱
⠀⡘⠀⠀⢧⠀⠀⠱⡄⢧⠘⣇⠀⠀⢳⣸⡶⠟⠀⠀⠈⠳⣄⠐⠂⠉⠈⠀⣸⠇⠀⣿⣦⣀⠀⠈⠎⠀⢀⣠⣴⠇
⠀⠳⣄⣀⠀⠑⣠⣦⣘⣾⣦⣬⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⠶⠚⠁⠀⠀⠈⠻⣿⣿⣷⣿⣿⡿⠿⠋
⠀⠀⠈⠉⣉⠉⡉⣉⡉⠉⠉⠀⠀⠔⠊⠁⠀⠀⠑⢄⠀⠀⠀⠀⠠⣤⣤⣤⡀⠀⠀⠀⠀⣀⠤⠒⠘⠙⠲⠤⢤⢄⡀
⠀⢀⡴⠉⢑⢆⠀⠀⢹⡗⢆⠀⢸⠠⠀⠀⠀⠀⠀⢈⠀⢠⡃⠀⠀⢈⡇⠀⠱⠀⠀⢀⡴⠣⡁⡀⠀⠀⠀⠆⢠⠤⠚
⠰⠭⠭⢄⡊⣷⡄⣠⣾⢁⡎⠳⠸⡀⠀⠀⠀⠀⠀⡼⠀⡼⠛⠛⢦⡎⠀⠀⣠⡇⠠⠓⣄⡀⠘⣎⣄⣀⡼⠃
⢰⠀⣀⣰⠿⠟⠛⠋⠉⠉⠙⠃⠀⠙⠲⠤⠤⠖⠋⠀⠀⢃⠀⠀⠀⠆⠀⠉⡹⠃⠐⠐⠙⢛⣚⡭⠍⠭⠤⢄⡀
⠈⠉⢁⠤⠐⠂⠀⠀⠀⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠦⠤⠽⠖⠀⠀⠀⢀⡄⠀⠉⠉⠉⠓⠦⣄⠀⠈⠳⡀
⠀⠀⢧⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠉⠋⠙⠻⠿⣗⠒⠠⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢈⣇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⠈⡄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢺⡟⠋⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢸
⠀⠀⠀⠧⣀⣀⣀⣀⣀⠤⠼⠃⠀⠀⠀⠉⠀⠐⠂⠀⠀⠄⢀⣀⠴⠟⠁⠀⠀⠀⠧⣄⣀⡀⡀⠀⠀⠀⢰⣧⠴⠋
⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣥⣬⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⢖⣛⣛⣛⣛⣛⣛⡲⠶⢤⣄⣀⠀⠀⠀⠀⣀⣠⡤⠶⢖⣛⣛⣛⣟⣛⣛⡲⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⠴⠚⠉⠁⠀⠀⠀⠀⠉⠉⠙⠓⠦⢭⣛⠶⠶⣛⡭⠴⠚⠋⠉⠉⠀⠀⠀⠀⠈⠉⠓⠦⣝⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠈⠳⡜⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠟⠛⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠊⠀⣂⡠⠀⠀⠹⡌⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠲⢄⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠆⠆⠀⠀⠀⠀⠀⣷⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠱⡀⡴⠋⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠤⠀⠒⠐⠛⢉⣿⠈⠛⠐⠒⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⢀⣠⠞⠘⢦⡀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠉⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡋⠈⠉⡝⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢹
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣄⡀
⠀⠀⠀⠀⢀⡤⠞⠋⢹⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢸⡏⠙⠳⢤⡀
⠀⠀⠀⣰⠋⠀⣠⠖⢻⠃⡇⠀⠀⠀⡉⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡟⠲⣄⠀⠙⣆
⠀⠀⣸⠃⠀⣰⠃⠀⢸⢰⡇⠀⠀⢀⠌⡉⠘⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇⠀⠘⣆⠀⠘⣇
⠀⠀⡏⠀⠀⡇⠀⠀⢸⢸⡇⠀⠀⠐⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⢹⠀⠀⢹
⠀⠀⡇⠀⠀⠳⣤⠀⢸⡌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢱⡇⠀⣤⠞⠀⠀⢸
⠀⡴⠃⠀⠀⠀⠸⣇⣀⢷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡾⣀⣸⠇⠀⠀⠀⠘⢦
⣸⠁⠀⣠⡤⣄⠀⠀⢈⡇⠻⣮⡓⠦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠴⢚⣵⠟⢸⡁⠀⠀⣠⢤⣄⠀⠈
⡏⠀⠀⡏⢹⡌⠉⠋⠉⠀⠀⠀⠉⠓⠶⠮⢭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡭⠵⠶⠚⠉⠀⠀⠀⠉⠙⠉⢡⡏⢹
⠳⣄⣠⠧⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠼⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠒⠒⠶⠶⢤⣄⣸⡇⢸⡇⢸⡇⢸⣇⣠⡤⠶⠶⠒⠒⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠸⡇⢸⠇⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣏⣹⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠙⠋⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠤⣀⠀⣀⣤⢠⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣥⣥⣤⣭⢤⣬⣭⣬⢭⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⡀⠀⡀⣟⣛⣛⣛⣸⣛⣛⣛⣸⣛⣛⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡆
⢨⣴⣿⣿⣾⡇⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⠀⠀⠠⠤⠤⢼⣦⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠬⠿⠿⠽⠃⣟⣛⣛⣛⣸⣛⣛⣛⣸⣛⣛⣛⡀⠀⠀⠀⠀⠘⠁⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠸⠿⠿⠿⠸⠿⠿⠿
⠀⢸⠔⠤⡠⢴⠔⠂⠦⡢⠖⢠⡄
⠀⣶⣶⣶⣶⢶⣶⣶⣶⢶⣶⣶⣶⢶⣶⣶⣶⢶⣶⣶⣶⡶⣶⣶⣶⡖⣶⣶⣶⡖⣶⣶⣶⡶⣶⣶⣶⣶
⠀⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿
⠀⣯⣭⣭⣭⢼⣭⣭⣭⢼⣭⣭⣭⢼⣭⣭⣭⢼⣭⣭⣭⡥⣯⣭⣭⡥⣯⣭⣭⡥⣯⣭⣭⡥⣭⣭⣭⣭
⠀⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿
⠀⣯⣭⣭⣭⢼⣭⣭⣭⢼⣭⣭⣭⢼⣭⣭⣭⢬⣭⣭⣭⡥⣯⣭⣭⡥⣯⣭⣭⡅⣯⣭⣭⡭⣽⣭⣭⣭
⠀⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿
⠀⠛⠛⠛⠋⠘⠛⠛⠛⠘⠛⠛⠛⠘⠛⠛⠛⠘⠛⠛⠛⠁⠛⠛⠛⠃⠛⠛⠛⠃⠛⠛⠛⠋⠛⠛⠛⠛
⠀⣿⣿⣿⣿⢻⣿⣿⣿⢹⣿⣿⣿⢹⣿⣿⣿⢻⣿⣿⣿⡏⣿⣿⣿⡏⣿⣿⣿⡏⣿⣿⣿⡟⣿⣿⣿⣿
⠀⣿⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⢸⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⡇⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣰⠂⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢠⡏⠀⠀⠀⠀⠀⠻⣦⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣻⡇⢸⡇⠀⡀⠀⠀⠀⠀⠈⠙⠛⠛⠻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠇⠈⠀⣸⠃⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⠚⠉⢀⣠⠴⠖⠚⢻⡆⠀⢈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠠⠴⠚⠋⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣷⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⢀⠀⠀⠀⠀⠀⠀⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⡾⢷⠄⠀⠀⠀⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⢀⣀⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣀⣀⣀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠠⠞⠋⠁⠀⠀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣻⡿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣦⣤⣤⣤⣤⣤⡶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⣀⣀⡀⠀⠀⠀⠀⠀⡟⠀⡰⠀⠀⢻⡇⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⣦⡀⠀⠀⠁⢠⡇⠀⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠀⢰⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠻⣤⠏⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠃


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

⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠘⣿⣧⡈⠻⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢒⠟⢁⣾⣿⠃
⠀⠀⠈⢻⣿⡤⢿⠀⢀⣑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣊⡀⠀⡾⢤⣿⡟⠁
⠀⠀⠀⠀⣿⡇⢸⣰⣿⣿⣷⢌⡢⡀⠀⠀⡴⠊⡑⠢⡀⠀⠀⠀⠀⢀⠔⢊⠑⢦⠀⠀⢀⢔⡡⣾⣿⣿⣆⡇⣸⣿
⠀⠀⠀⠀⣿⣿⠉⢣⠹⠋⣗⡦⠙⡌⠢⡀⠙⠒⠁⠀⠹⡄⠀⠀⢠⠏⠀⠈⠒⠋⢀⠔⢡⠋⢴⣺⠙⠏⡜⠉⣿⣿
⠀⠀⠀⠀⢸⣿⣀⡸⠘⠤⣈⣀⠜⠦⡀⠙⢆⠀⠀⠀⠀⢹⠀⠀⡏⠀⠀⠀⠀⡰⠋⢀⠴⠣⣀⣁⠴⠃⢇⣀⣿⡇
⠀⠀⠀⠀⣾⡟⠀⢇⠀⠀⢀⣤⣤⣤⣈⠳⣄⠳⡀⠀⠀⠈⡇⢸⠁⠀⠀⢀⠞⣠⠞⣁⣤⣤⣤⡀⠀⠀⡸⠀⢿⣷
⠀⠀⠀⠀⠻⣷⡤⠤⣵⠀⣿⣿⡋⢑⠄⠙⢮⣢⡙⡄⠀⠀⣇⣸⠀⠀⣠⢋⣔⡵⠋⠠⡏⢙⣿⣿⠀⣮⠤⢤⣼⠟
⠀⠀⠀⠀⠀⣿⡇⠀⡇⠀⠙⠿⣉⣉⠀⠀⠀⠑⣕⣜⣆⠀⣿⣿⠀⡰⣣⣫⠊⠀⠀⠀⣈⣉⠿⠋⠀⢸⠀⢸⣿
⠀⠀⠀⠀⠀⣿⣗⠉⠱⢄⡀⠀⠀⣴⣿⣿⣿⣶⣮⣿⣾⣎⣿⣿⣰⣷⣿⣵⣶⣿⣿⣿⣦⠀⠀⢀⡠⠎⠙⣺⣿
⠀⠀⠀⠀⠀⠈⠻⠷⢴⣮⣭⣓⣶⣽⣿⣿⠭⠭⠭⣶⣶⣿⣿⣿⣿⣶⣶⠭⠭⠭⣿⢿⣯⣶⣞⣭⣵⣦⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⢫⠟⠉⣩⢟⡩⠔⠚⣩⣋⡟⠀⣿⣿⠀⢻⣙⣍⠓⠢⢍⡻⣍⠉⠛⡝⠲⣄⡀
⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠘⠢⠚⣵⣿⠀⠀⣰⡷⣿⡄⠀⣿⣿⠀⢠⣿⢾⣆⠀⠀⣿⣮⠓⠔⠃⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡦⠀⠀⠀⢿⣿⣷⡴⢻⠁⠸⣿⠀⢻⡏⠀⣿⠇⠈⡟⢦⣾⣿⣿⣀⠀⠀⢴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⡖⢰⡋⢱⠌⠁⠀⠘⠢⠖⢹⡇⠀⠀⢸⡏⠣⠔⠁⠀⠀⠁⢏⣈⡇⢲⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⠀⠀⠉⠁⠀⠀⠀⢀⣄⠀⣸⡇⠀⠀⢸⣇⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣷⣾⣷⣄⣼⣿⣶⣾⣿⣿⣿⠇⠀⠀⠸⣿⣿⣿⣷⣶⣿⣧⣤⣾⣷⣾⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⠙⢿⡿⠋⠙⠿⠋⠉⠛⠋⠀⠀⠀⠀⠙⠛⠉⠙⠿⠋⠙⢿⡿⠋⠉⢿⣧⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄
⠀⠀⠀⠀⠀⠰⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠒⠉⠉⠄⠉⠑⢄
⠀⠀⠀⠀⢠⠖⠉⠀⣀⠠⠂⠁⠀⠄⠐⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂
⠀⠀⠀⠀⠇⠀⠈⠀⠈⠀⠀⠂⠀⡀⠀⠰⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣬⡀
⠀⠀⠀⠀⢇⠈⢁⠀⠉⠀⠋⡀⠀⠀⠀⠀⠀⡠⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⡎⠐⠾⠓⢹
⠀⠀⠀⠀⠈⡆⠀⠀⠀⣀⠀⠁⢠⠋⠉⢆⠀⠰⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠠⠀⠀⡧⣀⣀⣀⠜⢦⡀
⠀⠀⠀⠀⠀⠸⡌⠀⣾⠉⠙⠒⠋⠀⠀⠈⠂⠐⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠐⠀⡁⠐⠀⠬⠀⠈⠀⠠⠙⡄
⠀⠀⠀⠀⠀⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠈⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢀⡠⡶⡻⠃⣿⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠖⣩⠊⡴⠁⠀⣇⠑⠤⣆⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⡰⠁⢰⠁⠀⠀⠈⢦⡀⠀⠉⠳⣽⢦⡔⢢⢀⣤⡀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣀⣠⡎⠀⠀⠇⠀⢸⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⣦⣹⠃⢸⠤⠻⢖⠚⠉⡦⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠤⠔⠒⡏⠀⢸⣇⠀⠀⡇⠀⠈⢆⠀⠀⠀⠀⠀⡇⠀⠀⣠⠣⣈⠒⢛⣦⣀⠠⢵⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⣱⢄⣾⠀⠑⠒⠚⠢⠄⣈⠷⠤⠠⡤⠚⠉⠉⠉⠀⠏⠉⠣⡀⠀⠑⢦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠓⠂⠉⢸⡁⠒⠪⠕⣤⠊⠉⠢⠔⠉⠑⠤⠊⠉⠲⠊⠙⢦⠖⠻⢶⣀⣉⠯⠽⠥⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠏⠀⡏⠒⢶⠐⠸⡆⠀⠐⡄⠀⠀⡆⠀⠀⡛⠀⠀⣇⡤⠚⡉⠀⠠⠀⠀⠂⠀⠠⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠰⠀⠘⡄⠀⢣⠀⠀⠇⠀⠀⡇⠀⠀⡇⠀⡼⠃⠀⠂⠀⠀⣠⢄⠴⠛⢤⣀⠀⢁⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢣⠀⢱⣀⡈⡆⠀⢸⠀⠀⠁⠀⢰⠁⡜⠀⠈⡁⠉⢔⡲⠗⠂⠉⠉⠐⢦⠇⠄⠐⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⣧⠄⠠⢔⠂⠘⠿⠁⠀⠈⢷⡀⠀⡆⠀⠀⠀⡸⢠⠅⠈⠀⠀⠂⡈⠣⢄⣀⣀⡀⠤⠊⡀⠀⢠⠲⢄⡨
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠘⡂⠀⠀⠀⠀⠀⢸⠥⠄⠁⠀⠀⠤⠅⠤⠵⡞⠦⠚⢢⠀⠀⠀⠁⠄⠐⢀⠁⢀⠤⠃⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⡸⣁⠀⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠓⠒⠉⠑⠤⠔⠉⠁⠉⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠖⠊⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣀⣀⣀⣀⡀⠤⠔⠊⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡷⠀⢀⡿⠹⢷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡶⣿⠷⠒⢀⣀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⠿⠥⠧⠤⣴⠿⣷⣤⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠿⣧⣶⠿⢎⣹⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⢤⠀⠀⠀⠨⢧⡀⠉⠛⣦⡀⠀⠀⠀⠀⠀⢀⡔⠋⠀⣠⡯⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣗⣟⡄⠠⠄⠀⠠⠷⢄⡀⠈⠻⣦⢠⣀⣔⡴⠋⠀⣠⠞⠁⠀⠀⠀⠀⣼⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⣤⣤⣴⣶⣶⣶⣿⣷⢦⣬⣿⣿⡟⣡⣴⡬⠤⢤⣤⣤⣤⣤⣴⣟⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⣉⡅⠞⠛⠃⢠⠄⠉⠲⢺⢿⣿⢏⡷⡯⢤⡄⠂⠉⠛⢿⣿⣍⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣅⡠⠀⢀⡚⠉⡠⠊⢀⠂⢸⣿⠙⡇⡀⢄⠈⠫⠁⠀⠀⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠈⠔⠑⠒⠁⢀⠂⠐⢨⣿⠀⠰⡈⠄⠑⡆⢬⠀⠀⠀⢸⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⡄⠀⠀⠀⠂⢀⠀⢀⠠⢻⣿⠀⠀⢡⠈⣄⠈⠄⠣⡈⣲⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣫⣶⣠⡴⢀⢴⣠⡆⠀⠘⠏⠀⠈⢢⣆⣈⣄⡸⣤⢻⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠓⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡜⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠊⠀⠊⠰⠰⠁⠀⠁⠁⠈⠐⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃




⠀⠀⠀⠀⠀⠠⣄⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠻⣦⢸⡆⠀⠀⠀⠀⠀⠀⠀⢰⠀⡀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢰⣧⣆
⠀⠀⠀⠴⠖⠒⢒⣿⢿⠀⣦⣀⡞⠀⠀⢘⣳⢾⣷⣡⠞⠁⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⡅⠚⠛⠻⢥⡀
⠀⠀⠀⠀⠀⢞⠉⠀⠀⠳⣼⠏⠀⠀⠈⠉⢙⡷⢿⠁⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣤⣀⠞⠉⠙⠓⠲⠤
⠀⠀⠀⠀⠀⠀⠙⠳⠶⠖⠻⠀⠀⡀⠀⠐⠋⠀⠈⢶⣠⡟⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠛⠛⠛⠓⠒⠀⠀⠀⠀⠰⣄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⡼⠀⠀⠤⠤⣤⣄⣸⡟⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⣸⠀⠞⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⠙⡇⠀⠀⠀⠀⠀⠀⠀⠈⣄⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⢥⣤⠀⠀⠀⠀⠀⠀⠀⠙⢲⡿⠥⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠱⠀⢀⠀⠀⠐⠲⠶⠒⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢠⠁⡄⣀⣤⠄⠀⠀⠀⠀⠀⡆⢠⡾⠤⠤⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣈⣶⡆⡸⠀⡄⠀⠀⢰⣠⢧⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠘⠻⣅⠀⠀⠀⠀⠀⢀⠀⢱⣦⡤⠤⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴⠾⠿⠻⣿⠗⠚⠁⠀⠴⡺⢟⡾⠄⣼⣀⠞⠀⠀⠀⠀⡀⠀⢸⣄⢀⠄⢀⠀⠀⠀⠀⠀⠀⠲⣄⡀⠈⣷⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠈⢡⠏⣀⠔⢻⠀⠀⠀⢀⡄⠀⠘⡄⠸⠟⠋⠀⡘⢰⠀⡰⠀⠀⠀⠀⠈⠉⠉⡻⠗⠓⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⣴⣴⣃⡄⠀⠀⡀⠀⠀⢠⡀⣿⣦⡼⠉⠀⠀⠀⠙⢢⡄⠀⢀⠃⣸⡾⠁⠀⠀⠀⢆⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠒⠦⣽⣿⡿⠶⠒⠋⠀⢀⣀⢀⣳⣿⠏⠀⠀⠀⠀⠀⠀⠀⠁⢸⡌⢀⠟⠓⠒⠒⠒⠀⠈⢧⣧⣼⣋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡿⣷⠒⠦⣄⠀⠀⠈⠉⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣇⣬⡴⠚⠁⠀⠀⠀⠀⠈⠻⠿⠷⠶⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠃⠈⠁⠀⠈⠇⠀⠀⠀⢄⢈⣠⠇⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠤⠬⣿⠿⣯⣄⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢄⣠⣬⣿⡯⠤⢤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣸⠀⣀⣀⣀⣀⡤⠀⠀⠀⠀⢩⠀⠀⠉⠙⠂⠀⠈⠓⣤⣼⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠛⠛⠉⠉⠉⠻⡛⠉⠛⠛⠛⠛⠋⠁⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣒⣀⠀⢀⢀⣀⡀⢀⣀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠤⠄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⢀⡀⠠⠤⠉⠡⣀⠈⠉⠁⠀⠀⠀⢠⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⡀⣁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⣀⣀⣀⠀⢶⠄⠉⠀⡈⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣾⣿⣿⣿⡦⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⢬⠁⠀⠀⡀⠀⢠⠒⠁⢀⡀⢀⣠⢷⡞⡇⢸⠙⢿⣿⣿⠥⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢄⡠⠴⣟⣩⡴⡇⡅⠈⠙⠋⣿⢿⡆⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⡈⠙⠚⠉⠉⣤⡄⠣⠀⠀⢸⠇⠀⡇⠀⠀⣀⠀⢠⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⡁⠀⠀⠀⠐⡇⠀⠀⠀⢻⠀⠀⣇⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠉⠂⠀⠀⠀⠀⡁⠀⠀⠀⠸⠀⠀⠸⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠐⠀⠒⠐⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⣶⠾⠏⠙⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⣿⣿⡤⠾⠳⠛⠙⣧⣽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⢴⣖⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠈⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⣿⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣠⣀⡀⡀⢼⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠃⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠈⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⡄⠀⠀⠀⠀⠀⠀⠘⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⡀⠄⠠⠄⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣀⡀⠔⡆⠀⢀⣤⡀⠀⠀⠀⢀⡤⠒⠒⢦⠀⠈⠁⠀⠀⠀⠀⠀⡼⢤
⠀⠀⠀⠀⠶⠀⠀⢀⡠⠔⡶⠔⠉⡆⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣗⢚⣄⣠⡾⠉⠁⠀⠀⠀⠰⢁⡀⢀⠀⠇⠀⠀⠀⠀⠀⢀⠔⠋⠉⠁⠒⡔⠃
⠀⠀⠀⢀⣤⣐⣈⣁⣀⣀⡁⠈⠭⠤⠄⠐⠒⢈⡆⢀⠀⠀⠀⠀⠀⢀⠤⠾⢽⣯⠗⢳⢄⠀⠀⢀⠀⠀⡶⠆⡆⡏⠦⣼⠀⠀⠀⠀⠀⠾⠠⠤⣠⠦⠜⠣
⠀⠀⠀⢸⣄⡂⠄⠀⠒⣒⣒⣖⣒⠂⠤⠘⠛⢀⠀⠀⢱⠀⠀⠀⢀⡟⣶⠚⠓⣿⣙⡏⠭⡄⠀⠈⠁⠀⡇⠀⣇⠃⠀⣿⠀⠀⠀⠃⠀⢂⠱⠀⠇⠀⡇
⠀⠀⡤⠚⠦⠄⣀⣀⡁⠀⠠⠤⠤⠤⠀⠒⠒⠉⢀⡠⠊⠀⠀⠀⠈⡄⡓⠄⢰⠢⠀⠔⢳⠃⠀⠀⠀⠀⢇⠀⠙⠀⠀⣹⠀⠀⠀⠀⢀⠔⢆⠁⠐⠀⢀⠁⢈
⠀⢨⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠒⠉⠀⠀⠀⠛⠀⠀⠘⠪⠬⢈⠀⠈⠔⠋⠀⠀⠀⠀⠀⠈⠈⠩⠈⠃⠀⠀⠀⠀⠀⠘⠤⢀⣁⡐⠠⠥⠒⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠀⠀⢠⡀⠀⡀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⠤⠀⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⢠⣄⠤⠐⠒⠀⣐⠢⡀⠀⠀⠀⠀⢛⡢⠌⢰⡈⠁⠀⠀⠈⠉⠀⠀⢨⠑⠞⠄⢀⠌⠀⠀⠀⠀⠀⠈⠃
⠀⠰⠆⠀⢀⠎⢰⠊⠓⡊⢯⠱⣈⢢⠀⠀⠀⠀⡤⠊⣁⡠⠊⠒⠈⢀⠂⢰⠀⠀⠛⢄⡁⠈⠀⠀⠥⡀⠀⠀⠀⠀⢠⠒⣏⠢⢄⠀⠓⢤⡀⠀⠀⠈⠃
⠀⠀⠀⠀⡆⡾⠅⠠⠋⠉⠘⣷⠌⡙⠇⠀⢠⠊⢀⡌⠀⠀⠀⠀⠀⠸⡀⡞⠀⠀⠀⠀⠈⠁⡏⠀⠀⠈⡆⠀⠀⠀⠈⠢⢌⠙⠲⠏⠉⢈⣀⠀⠀⣀
⠀⠀⠀⠀⡗⠢⡸⠣⡀⠀⣀⠟⣗⡇⡄⠀⡆⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⡐⢄⠀⠀⣀⠀⠀⠱⠄⢠⠖⠀⡉⢑⣲⠄⠀⠀⠉⠊⢠⠆⡵⠲⡤⠒⠒⡍⠢⡀
⠀⠀⠀⠀⠘⢄⠣⠥⢎⡉⡉⡮⢚⠜⠀⠀⠘⣦⣈⠑⢄⠀⠀⠀⠀⠀⠀⠘⡌⠢⡀⠉⠀⠀⠀⠀⠈⢦⢠⠌⣉⣢⠀⠀⠀⠀⢀⢡⠒⠁⡠⠄⠦⣄⠉⠒⣷
⠀⠀⣀⠀⠀⠀⠑⠢⠤⠥⠯⠒⠩⠄⠀⠀⠀⠀⠉⠳⣄⢣⠀⠀⠀⠀⡠⠔⢁⡴⠃⠀⠀⠀⠀⠀⠀⠨⡼⠀⠉⠁⠀⠀⠀⠀⢸⢎⡀⠰⡀⠀⠀⢨⠀⢰⢸
⠀⢀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡉⠐⠒⢉⣠⡾⠋⠀⠀⣀⠤⡐⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢸⠀⠈⠒⠂⠁⣀⢜⠌
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢔⠒⢲⡆⠒⢄⠀⠀⠓⠀⠀⠈⠻⣶⡢⠛⠉⠀⣤⢀⡊⠀⠑⡻⠖⠚⠀⠀⠀⢀⡀⠀⠀⠀⠋⠀⠀⠀⠑⠭⣈⡓⣤⡊⠔⠋
⠀⠀⠀⠀⠀⡠⢖⡛⠄⠈⢲⠀⠀⠃⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣅⠘⠋⠑⣶⠠⣤⠀⢤⣬⠥⠤⣤⡤⣤⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣠⢎⣣⠀⠐⡆⠀⠈⠀⢀⠄⡠⠂⠀⠀⠀⠀⠀⡠⣔⠚⠑⠒⠦⡀⠀⠀⠈⠑⠠⠄⠿⠤⠽⠤⠤⠽⠤⠀⠤⠥⠨⠧⠤⠃⠀⠀⠀⠀⣠⠄⠀⠀⠉
⠀⠀⠐⠀⠀⠘⠇⠀⠀⢀⡠⢔⡡⠚⠁⢀⡀⠀⠀⠀⢌⡴⠋⢠⡇⠘⢷⡌⡆⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄⢀⡀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢀⠻⡀
⠀⠀⠠⣀⠀⠀⢀⢒⡪⠅⠊⠁⠀⠀⠀⠈⠁⠀⡠⢄⠀⠀⠀⠀⠁⠀⠀⠀⡈⢢⠶⠀⠀⠀⢀⠔⠁⢀⣀⡀⣀⡈⠳⡄⠀⠀⠀⠁⠀⠀⡔⠁⠀⠘⡀
⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠑⡆⠉⠓⠒⠊⠒⠒⠉⡹⠁⠀⠀⠀⠀⡎⠀⡔⠁⢀⠤⢄⡀⠀⠘⡄⠰⠆⠀⠀⡰⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⡤⠒⠒⠠⡊⠁⠀⠑⢎⠁⠈⡆⠀⠀⠈⠉⠀⠉⠁⠘⠈⠉⠀⠀⠀⠀⠀⠀⡇⠈⡀⠀⢇⠄⠀⡱⠀⠀⡇⠀⠀⠀⠸⡀⠀⠉⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⡀⠀⠀⠘⡤⠚⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠱⡀⠑⢄⣀⣀⠴⠁⠀⡜⠀⣀⠀⠀⠀⢩⠶⣔⢶⣲⠞⠁
⠀⠶⠀⠀⢈⠦⢀⠀⠀⠀⠀⠰⣀⡠⠞⠀⠀⢀⠔⡩⠰⠒⡐⡶⣕⢆⠀⠀⠀⠀⢀⡀⠀⠀⢠⢞⠦⠤⠀⠀⠤⠔⠊⠀⠀⠉⠀⠀⠀⢸⢲⡋⣹⢥⠆
⠀⠀⠀⠀⡆⠀⠀⠑⠢⢄⣀⠔⠁⠀⠀⠀⡐⡅⢺⠣⡀⢣⠱⡐⡘⡆⠆⠀⡤⠀⠈⠀⢀⠔⡱⠃⠀⢀⡀⠀⠀⢠⠔⣠⡄⠀⠀⠀⠀⠈⠉⣯⡝⢰⠀⢀⡀
⠀⠀⠀⠀⡱⢄⠀⠀⡠⠂⠀⠠⡄⠀⠀⢀⠀⠦⡀⢣⠱⡀⢣⠱⣁⡀⠐⠀⠀⠀⢀⡔⡡⠊⠀⠀⠰⡁⠈⡃⠀⢏⣩⠕⢂⠀⠀⠀⠀⠀⡧⢦⢼⡎⠀⠈⠁
⠀⠀⠀⠀⢇⣀⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⢆⡘⢄⢣⠑⡌⠆⣸⢃⠃⠀⠀⠠⢊⠜⠀⠀⠀⠀⠀⠉⠉⠉⠒⢄⡀⠀⠉⠀⠀⠀⠀⠀⢰⡵⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠈⠢⢌⠒⠷⠧⠜⢋⡥⠋⠀⠀⠀⠓⠁⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠉⠁⠰⠆
⠀⠀⠀⠘⠁⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠃⠀⠀⠀⠈⠁

⠀⠀⠀⣤⣴⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤
⠀⠀⢸⣿⣷⣿⣿⣿⣿⠿⣖⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣲⠿⣿⣿⣿⣿⣾⣿⡇
⠀⠀⠈⢻⣿⣿⣟⢉⣿⣶⡿⢏⣻⣗⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣻⣟⡹⢿⣶⣿⡉⣻⣿⣿⡟⠁
⠀⠀⠀⠀⠙⣿⣿⣿⡉⠉⠙⠻⡋⠉⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡿⠛⠉⢙⠟⠋⠉⢉⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠘⣿⣿⡟⠉⠉⠀⠓⢤⡀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢀⡤⠚⠀⠉⠉⢹⣿⣿⠃
⠀⠀⠀⠀⠀⠀⣿⣿⡷⠒⠒⠒⠒⠒⠚⠓⠢⣄⠈⠻⣄⢰⡆⣠⠟⠁⣠⠔⠚⠓⠒⠒⠒⠒⠒⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠉⠒⢬⣿⣿⡥⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⣿⡿⠿⠿⠿⢿⣛⣻⡿⠿⢿⣿⣿⡿⠿⢿⣟⣛⡿⠿⠿⠿⢿⣿⡋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡯⠤⠒⢒⡲⠋⠀⠀⡠⠖⣡⣿⣿⣎⠲⢄⠀⠀⠙⢖⡒⠒⠤⢽⣿⣄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠤⠒⢉⡝⢀⣀⡤⠊⢀⠜⡱⣿⣿⢏⠣⡀⠑⢤⣀⡀⢻⡉⠒⠤⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣅⡤⠚⢁⠏⠁⡔⠁⢠⠊⡰⠁⣿⡿⠈⢆⠑⡄⠈⢣⠈⠹⡈⠓⢤⣨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣤⠎⠀⡸⠁⡠⠁⢰⠃⠀⢸⡇⠀⠘⡆⠈⢆⠀⢆⠀⠑⣤⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣯⣷⣾⣧⣴⡁⣠⠏⠀⠀⠘⠃⠀⠀⠹⣄⢈⣦⣼⣷⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣸⢸⡄⠀⠀⠀⠀⠠⠄⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠨⠟⠛⠃⣀⡀⣀⠀⠀⠠⠄⠚⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢸⠄⡐⠂⠠⠄⠀⠠⠤⠤⠀⠀⠄⠀⢒⡡⣴
⠀⠀⠀⠀⠀⠀⡠⠐⣂⠡⠄⠒⠐⠒⠒⠀⠌⢁⠒⠄⣸⠈⠐⠀⠐⠊⠉⠉⠉⠉⠉⠑⠒⠀⠂⠉⡅
⠀⠀⠀⠀⠔⢁⠔⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠎⡰⢁⡀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⢰⠀⠁⠿⠇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⢆⠣⠀⠀⠀⠰⠋⠛⠂⠀⠀⠀⠞⠉⠳⠀⠀⠀⢰⠀⠀⠀⣤⡉⠁⠀⠀⠈⣭⡁
⠀⠀⠀⠀⠃⢁⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠠⢩⠀⠀⠼⠉⠳⢀⣀⣀⠼⠉⠳⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣿⡿⢿⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠀⠀⢀⣘⣳⣊⣀⣀⠀⠀⠴
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢨⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠁⠀⠀⠉⠀⠀⠀⠒⠂⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⣀⣤⣀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣾⣿⣿⣿⣿⣿⣿⣿⢷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⣀⣤⠴⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣿⣿⣿⣿⣿⣿⣿⢟⣁⣿⢏⣴⣶⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⠀⣠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣭⣯⡍⠁⠚⣻⣿⣿⣿⣿⣿⣿⢿⣿⣀⠀⠀⠀⠀⠀⢀⣴⠋⣀⢠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠛⠾⡿⢿⣿⣿⣿⣼⣿⣿⡀⠀⠀⠀⣰⡟⠵⠓⡴⠛⢉⣿⠟
⠀⠀⠀⠀⠀⠀⢀⣿⣏⣿⣿⣿⣿⣿⣿⢿⢿⡟⠃⣀⠀⢀⠀⠁⣾⢿⣿⣿⣿⣿⣏⠁⡠⢠⡾⠁⠀⣠⣞⣥⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠿⠖⣛⡁⠀⠙⣼⡟⢻⡿⣿⣿⣆⣰⣿⣶⣶⡾⠿⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⣿⣿⣿⣿⣧⡀⠀⢰⣿⣿⡿⠁⣰⣿⣷⣾⣿⡟⢹⣿⣿⣝⣿⣯⣶⣾⠟⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⣿⡟⠛⠛⣿⠿⠶⣦⣬⣥⣤⣴⠟⣿⣿⠛⢿⣷⣿⣿⣿⣿⣿⣿⠏⠁⢀⠈⠁
⠀⠀⠀⠀⠀⠀⣴⡾⣿⣷⣦⣸⣿⣧⠀⠀⠈⠒⠀⢘⣯⠉⠉⠀⠀⣹⣿⣧⣾⣿⣿⣿⣿⢿⡿⠋⠀⠀⠘⣧
⠀⠀⠀⠀⠠⣾⣭⣿⠿⢟⣿⣿⣿⣿⣦⣀⣀⣤⣴⣾⠻⠀⠀⠀⣀⣿⣏⣿⠟⣻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢸⠿⣫⣾⣞⣩⣶⣿⡯⣿⣿⣿⣿⣿⣷⡟⠀⠀⢰⣿⣿⣿⣿⣷⣶⣷⣿⣿⣏⠙⣧⡀
⠀⠀⠀⠀⠸⣦⠈⠛⠛⣛⣿⣿⡷⣿⣿⣿⣿⣿⣿⠀⠀⠀⢘⣿⣿⣯⣭⣿⣿⣿⡟⣭⠘⢷⡼⣷
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠙⣿⠉⢡⣿⣿⣿⡿⣿⡇⠀⢀⣴⣿⣿⣿⣾⡟⠉⠉⣻⡿⢻⣖⠃⠀⢹⣧
⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣸⡆⣾⡿⣿⣿⡇⣻⡇⠀⣹⣿⣿⣿⣿⣿⡷⠀⢰⣿⣁⡦⠀⢀⠤⣸⣿⣦
⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠿⣦⣿⣷⡝⣿⣿⠿⣷⣾⣿⣿⣿⣿⣾⡏⣱⣬⣿⣿⣿⣆⡀⣀⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠸⣿⣿⣿⣿⣋⠀⢹⢹⣿⣏⣀⣤⣀⣸⣿⣿⣿⣿⣿⣿⣼⣿⣿⠋⠉⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠻⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡏⠁⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⡟⠘⣧⠀⠀⠀⠀⢻⡄
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡏⠁⢹⣿⡟⠀⠀⣿⠀⠀⠀⠀⠈⣷
⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⠈⢿⡄⠀⢸⣿⣿⣿⣿⣿⣿⣻⣿⣧⣴⣿⣷⣮⣾⣿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣆
⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠈⠻⣿⣾⣿⣿⣏⣽⣿⣟⠉⢻⣿⣿⣿⣿⣿⣿⣿⣡⡀⠀⢿⡇⠀⠀⠀⠀⠀⢻⡄
⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠠⠉⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡀⠸⣷⠀⠀⠀⠀⠀⠈⣷
⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣇⠀⠀⠀⠀⠀⢿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠻⣧⠀⠀⠀⠀⢸⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠁⠀⢸⣿⣿⡇⠀⠀⠀⠹⣧⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⢿⣿⣿⡿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠀⠀⠀⠀⠙⣧⣤⡴⠾⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⠒⠀⠈⢿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⡤⠴⠶⠶⠶⠶⠶⠶⠶⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⣀⣀⣤⡤⠤⠶⠶⠒⠒⠒⠒⠒⠶⠶⠤⣤⣈⡉⠙⠲⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢀⣠⡤⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠈⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢸⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⢠⣄⠀⠀⣀⡤⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢸⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠛⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠈⠳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠤⠴⠛⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⢀⣀⣀⣀⣀⣤⡤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⣛⣛⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣼⠀⡆⡤⠀⠀⠀⠀⠀⠀⠀⡰⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⢸⡆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⡀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠳⣾⡽⠁⢠⠀⠀⠀⠀⠀⠀⢠⣠⡲⠀⠆⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁⢀⠹⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⡝⠁⠀⠀⡀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡄⠆⢹⠆⡄⠀⠀⠀⠀⠐⠠⢬⡾⢀⡀⢀⠐⠁⠀⠐⠀⠾⠿⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠁
⠀⠀⠀⠀⢀⠀⠠⠀⠀⠀⡧⢄⣿⢀⠀⠀⢀⠂⠀⠀⠀⢠⡷⠋⠁⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠛⠛⠉⠉⠉⠉⠀⠂
⠀⠀⠀⠀⠀⠁⠀⣰⣄⢰⢁⠈⡏⣸⡋⠔⠁⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠄⢀⡀⢀⠀⠈⢦⡙⠛⡏⠻⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢄⠠⠀⠃⠐⠂⠠⠖⢃⠈⠀⠀⠀⢰⠀⣠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢼⣌⠀⢤
⠀⠀⠈⠐⣤⠀⠀⠆⠠⠀⠘⡇⠀⢠⠀⠎⢀⡇⠆⠁⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠹⠀⡘
⢀⠀⠀⠀⢻⡆⠀⣽⣤⡀⠀⠇⠸⣣⠎⡀⣿⠀⠀⠠⠋⠀⠀⢈⠁⠀⠀⠂⡀⠀⠈⠀⢿⣅⠤⠄
⠀⠀⠈⡀⡈⠁⠠⠁⠃⠈⢳⡶⡿⠁⠀⣠⠇⡀⠊⡰⠁⠀⠀⠀⠀⣰⣆⠀⡇⠀⠀⠠⠸⡄⢀⣤⠄⠐⠀⠀⢁⡰
⠀⠀⠀⠀⠙⢧⣰⠀⢀⠀⢸⠋⠁⠀⠀⢠⣾⡡⠊⢀⠀⠀⠀⠀⠀⠀⠉⠒⣧⠀⠢⠀⠖⣵⠋⠈⠀⢀⠀⠀⣸⣁⠐
⠀⠀⠀⠀⠀⠈⠣⡀⠀⠑⢤⠀⠀⠀⠀⠘⠁⠀⣀⠌⠀⠀⠀⠀⠀⠀⠀⢠⠀⠙⢦⣄⡴⡷⡰⠃⠀⠘⠀⠀⠛⢁
⠀⠀⠀⠀⡀⠀⠀⠱⡄⠐⢶⣄⣦⠀⣰⣤⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⡀⠙⠈⡿⠁⠀⠀⠀⡆⡀⠀⠚⠀⠁
⠀⠀⠀⠀⠀⠉⠒⢀⣸⣄⠃⠀⢘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⡇⠰⣤⠎⢀⣿⣓⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢀⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠁⢃⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠠⠀⡼⢀⣠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡡⠊⠛⠓⠦⠤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠈⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣻⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢸⣧⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠄⢳⣴⣎⠑⢀⠉⢠⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣈⡛⣺⣿⣄⠷⡀⠈⠄⠀⠆⢩⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣉⣽⣿⣿⡥⣶⣷⣦⡴⢾⣿⣥⢍⢼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣹⡇⣊⣶⣦⢿⡿⢻⣟⣉⢁⣄⠀⠛⣿⡎⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⣻⡟⢸⣿⣍⡰⣶⠾⡻⠇⣻⣅⢿⡷⣠⠄⢻⣧⠈⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣾⣿⠻⣽⣇⠈⢯⣿⣿⣶⣾⣿⣋⡈⣧⡼⢾⠃⣀⣻⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢠⠛⡟⣿⣆⠈⠛⠳⠄⣉⠛⣿⡿⢿⠿⠿⣻⣿⣿⠟⠛⠉⣁⡴⠀⠀⠀⠀⢘⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠁⠶⣿⣿⣄⠀⠀⠀⠀⠉⠛⠲⢤⡄⠒⠛⢋⡥⠖⠛⠉⠉⠀⢀⠜⠁⠀⣼⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡄⠀⠈⠻⣿⠳⠦⠤⣤⣀⣀⣀⣽⡷⠒⠉⠀⠀⠀⢀⣤⣎⣠⣤⣤⢾⠁⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠠⣿⣿⣿⠀⡀⢰⣼⣦⣤⣤⣤⡾⠟⢋⡁⣀⣀⣀⣤⣤⠖⣻⠛⠉⡼⠋⠀⠸⠀⠈⣧⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣀⠁⠙⢿⢷⣦⣤⣮⣿⣿⠿⠶⠛⠉⠉⠉⠉⠉⠁⠀⢀⡼⠁⠀⠠⠀⠀⠀⡆⠀⠀⡼⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⠀⠤⣚⣿⣫⣽⡎⠁⠀⠀⠀⠀⠀⢀⣀⡠⠾⠋⠀⢀⡴⠀⠀⠀⠀⠀⢀⣼⠃⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠀⣀⣼⣷⣋⣀⡤⠔⠊⠁⠀⠀⣀⣴⡦⠖⠋⠀⢀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣯⣐⠛⠿⠿⠿⠶⢶⣦⡶⢾⢛⡋⠉⠉⠛⠛⠻⠿⠶⠶⠖⠛⠉⠁⠀⠀⣀⣴⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣶⣤⣀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⢶⠟⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠁⠀⡍⠙⠏⠁⠀⠲⢦⣶⠶⡖⠒⡲⠞⢻⠛⠉⠹⠏⠀⠂⢳⢠⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⢨⡇⠘⡀⢰⠄⢠⠀⢠⠀⠀⠧⠀⠀⠀⠘⠃⢸⠃⠇⢸⠁⡄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣧⣄⣇⢸⡄⠀⠀⠈⡄⠀⢰⠀⠀⠀⢸⠀⢾⠀⠀⡘⢠⡧⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢿⣧⣿⣏⡿⢸⣧⠐⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⡕⠀⠀⣇⣘⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣦⣿⣿⣿⣅⣀⡻⠆⠈⠀⢷⣀⠘⠀⣀⢀⡾⠀⠃⣐⣀⣩⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢿⡿⢽⣿⡿⣿⣿⣶⣶⣶⣷⣶⣶⣶⣿⣶⣶⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡚⢿⣿⢿⣿⣽⣟⣛⣻⣿⡿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠛⠍⠛⠷⠛⠛⠉⠉



⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣡⣟⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⡽⢩⣟⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡟⠻⠛⠉⣿⡿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣠⣴⢁⠔⠋⣀⠽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣿⡏⠀⡟⢁⡠⠚⠁⣀⣼⡿
⠀⠀⠀⣴⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡿⠀⢠⠓⠉⠀⣠⣾⠟⠁⣀⣀
⠀⠀⠀⠻⣿⣟⢲⡟⠫⣿⣷⣶⣤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡎⠀⣠⣾⣿⡿⠛⢉⡻⠿⣿⣷⡀
⠀⠀⠀⠀⠈⠻⣿⣯⣽⠿⠅⣨⡟⠻⢿⣶⣥⣀⠀⠀⠀⠀⠀⢸⠀⣸⣠⣾⢟⣟⡡⠔⢊⠡⠄⠒⠊⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡤⠤⠝⠲⢤⣀⡉⠛⠻⢦⣄⣰⣶⣾⡶⠟⣫⠔⠉⠉⠁⠉⣳⢶⣒⠉⠉⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⡒⠂⠉⠁⠀⠉⢉⣉⣽⣿⢿⣿⣷⣿⣒⠒⠒⠒⠛⠣⠤⣀⠀⠉⡳⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠶⠾⣿⣿⣿⣛⡫⠔⢋⠻⣿⣿⡪⢍⠒⠢⠤⣀⡀⠀⢉⣶⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⣀⠜⢫⠀⢀⠆⠘⡘⡝⣿⡁⠛⠦⣄⡀⢈⣹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⠋⣤⡼⡄⠀⢇⠸⣸⢿⣄⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣥⡑⡘⢄⠘⠀⢹⡄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠷⣷⡾⠁

⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⣶⣶⡶⡶⡶⣶

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣾⣿⣛⣛⣛⣻⣿⣿⠿⠿⠷⠶⢶⣶⣶⣦⣄⣀
⠀⠀⠀⢀⣴⢾⡛⠩⠋⠀⠀⣀⡜⠙⠙⠉⠀⠀⠙⠋⠀⠀⢉⢻⣿⣶⢤⢤⣤⣉⠛⠻⢷⣦⣀
⠀⠀⣴⡿⠑⡴⠀⠀⠀⠀⠀⠈⠀⠀⠀⠔⢣⠗⠃⠀⠀⠔⠁⠙⠊⠀⠀⣀⣁⣭⣥⣤⣶⣬⣿⣿⣶⣤⡀
⠀⢸⠏⡜⠈⠌⡀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠀⢀⣤⠶⠟⠛⠉⠉⠀⠲⠀⠠⠀⡀⠉⠙⠻⣦⡀
⠀⣾⣴⠁⡀⠈⡔⡸⢱⢡⢀⢠⠂⠄⡀⠀⠀⢀⠀⠀⠀⢀⣴⢏⡵⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⣿⡄
⠀⠸⣿⣇⣇⡆⡇⡇⡇⡏⣼⣾⡜⡸⠁⡀⡀⢬⠤⢄⢄⣾⠃⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡇
⠀⠀⠘⣿⠿⣿⣷⣷⣧⣿⣷⣿⣧⣧⣶⡇⣷⢼⠀⠀⣾⣿⠀⠀⠀⠀⠀⠈⡀⠀⠁⠀⠈⠀⠀⠀⠠⠀⠀⠀⣾⡇
⠀⠀⠀⣿⠄⠀⠈⠉⠙⠛⠛⠿⠿⣿⣿⣷⣿⣿⣿⣧⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⡿⠿⠟⠛⠲⠶⣿⡀
⠀⠀⠀⣿⢀⠈⠀⠂⠆⠀⠀⢀⠀⠠⠀⡉⡉⠉⠛⠛⠿⢿⣿⣌⢢⠀⠀⠀⣴⣾⣟⡽⠋⠁⠐⠦⠀⠀⠀⠀⠈⢻⣆⣀⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⢠⣿⠘⠀⠂⠀⢠⠠⠀⠀⠈⠒⠀⠄⠁⠙⠓⠤⠀⠀⠈⢻⣦⠳⠑⣾⣿⣿⠋⠀⠈⠀⠀⠀⢀⡀⢀⣠⡴⣿⠿⠛⠉⠰⠤⡀⠀⠂⠀⠙⢷⡄
⠀⠀⣼⡇⣠⡀⠰⠀⠈⠀⠀⠀⠀⠃⠰⠀⠀⠀⠀⠀⢠⢈⠀⢠⣿⡆⠀⣿⠫⡇⢆⠀⠂⠀⠀⠀⠀⣴⣿⣡⠞⠅⠀⠒⠀⠀⢀⡀⠀⠈⢁⠀⠈⣿
⠀⠤⣿⣇⣿⡗⣶⠀⡀⡀⠀⢡⠀⠀⡀⠀⠀⠃⠀⠀⡆⢠⠗⢾⢈⡇⠀⢿⡀⣰⡘⠆⠀⠀⠀⠀⢰⡟⣿⠁⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠄⠀⠀⣿
⠀⠀⠙⢻⣿⣷⣿⣧⣷⣿⣶⢸⢰⣄⠀⣴⠂⢀⠀⠀⡇⢸⣾⡾⣺⡇⠀⠘⢷⣾⣿⣶⣤⡀⠠⠀⢸⡀⢻⠰⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠠⠀⣏
⠀⠀⠀⠀⠒⠚⢛⣻⣿⣿⣿⣿⣿⣿⢸⢻⡰⣾⣤⣸⠃⣿⣾⣿⣿⠃⠀⠁⠀⠙⢿⣿⠟⢿⣀⠀⠈⢳⣾⣧⡑⠀⠉⠁⠀⠒⠀⠀⠠⢀⣀⣀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣐⣓⣲⣛⣛⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡏⡇⠀⠈⠀⠀⡀⢻⣄⠀⣇⢆⠢⠀⠈⠻⣿⣷⣦⡀⠀⠂⠠⠤⠀⠀⠀⠀⠠⠤⡀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣒⣒⣒⣒⣒⣚⣻⣿⡿⢿⣿⣿⣿⣿⡇⠇⠀⢀⣀⣠⣤⣾⣿⣷⣾⡘⣄⠀⠀⠀⢹⡍⠉⣧⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠒⠚⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⡿⣿⣿⣿⣿⣿⣮⣓⣀⣀⣤⣿⣦⣿⡆⢀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢈⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠩⠭⠭⠿⠭⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣎⡳⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠉⠙⠓⠒⠒⠂⠂⠀⠀⠀⠙⠻⠿⠿⠿⠷⠖⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⢀⡀⢀⢠⠀⣀⠀⡀⢀⠀⢀⠀⡀⠀⡀⢀⢀⠀⠀⢀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠈⠉⠈⠀⠀⠉⠈⠉⠈⠁⠈⠀⠁⠉⠉⠉⠈⠁⠀⠀⠁⠁⠁⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠄⠀⠀⠀⠀⠀⢀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⡀⠀⠀⠀⢀⠎⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢃⠀⠀⠀⣜⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠀⡇⢸⠀⠀⢀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠃⢘⠀⠀⠸⡆⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠰⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠢⣀⠀⠀⠀⠀⠀⢠⠀⠀⡄⠁⠀⢀⠀⠘⡄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⠢⡀⠀⠀⠀⠘⡄⠀⢡⢰⠀⡏⢳⠀⢡⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⡈⢢⡀⠘⡄⠀⠀⠀⠙⣄⠈⠌⣄⡀⠀⢣⠀⡄⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣅⠀⠑⢄⠈⢆⠀⠀⠀⠈⢧⡀⢸⡇⠀⠈⢆⣧⠇⡆⠀⠀⢀⣠⠴⠒⠒⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠣⡈⢢⠀⠀⠀⠀⠱⡈⠙⡄⠀⢸⣇⠀⠀⠀⡰⠋⢀⠠⠔⠒⠒⠒⠤⣉⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢄⠱⡀⠀⠀⠀⢳⡇⠘⠄⢂⠏⠀⠀⣰⠁⣴⠗⠊⠉⠙⠢⡀⠀⠈⠓⢄⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠘⢆⠀⠀⠀⢟⢄⢸⡆⢿⣄⡾⠓⠉⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠁⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠹⢦⣄⡈⣎⢋⢘⡌⡟⢀⣠⣤⡤⠤⠄⣀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⡒⠐⠒⣨⣿⣟⠂⢻⡇⡿⠛⠛⠂⠠⢄⡀⠀⠉⠲⢄⡀⠀⠀⠉⠒⠲⢄⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠔⢀⡤⠒⠉⠉⠉⠉⠑⠄⠣⢳⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡤⠤⠒⠁⠀⢈⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⢢⠈⠣⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⡀⢠⠀⡄⣠⠀⢀⡄⡄⠀⢠⠀⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⠟⡏⢰⡁⡇⢸⢸⠁⡇⠀⢼⢰⠇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⢸⢻⣿⢿⣳⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠛⢵⡞⢣⣾⠸⡏⢷⡏⠳⣌⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡱⢮⢀⢠⡖⠙⠁⢀⡿⢸⣧⠐⣿⠀⣿⡟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠛⠒⣻⣛⣩⡤⠿⠧⠺⠏⢠⣟⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣀⡠⠴⠒⠛⠛⠉⠁⢛⣃⡀⠤⠐⠊⠉⣋⣴⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⢀⣠⣶⣶⣿⠿⠿⠛⠛⣛⣻⡿⢛⣽⠏⣿⣿⡝⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⣀⡴⠟⠋⠉⣉⢹⠭⠤⠒⢊⣉⣻⣅⠴⢛⡯⢃⣿⣿⣿⢸⣇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣠⡞⠋⠀⣠⠖⠋⠁⢀⣤⠖⠂⠉⠁⠀⢀⣀⣨⡤⠞⣹⣿⠏⣸⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⣧⣿⠀⣰⠋⠀⠀⣰⠞⠉⠀⣀⠤⠖⠊⠉⠀⣀⣀⡴⠞⣋⠤⠞⠟⢳⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⠀⠘⢿⡄⣧⠀⠀⣴⠁⠀⣰⠞⠁⢀⣠⡴⠚⠋⠉⣠⡴⠋⠀⠀⣀⣤⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡳⢤⡀⠀⠉⠚⠧⣄⣿⡀⣼⡏⢀⣴⣿⠁⢀⣀⣤⢾⣿⡏⢛⡿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢆⠉⠉⠊⠓⠰⠤⣍⣉⣙⣛⣻⣛⣻⣟⣿⣵⣾⣴⣾⢿⠿⡟⢻⠏⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠈⡍⢩⠉⣏⠉⡯⢹⠇⢹⡇⣾⣼⢸⡇⣿⢸⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡗⢸⠀⣸⢁⡏⡇⣸⢧⡏⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⠀⡄⠀⠀⠀⠄⠀⢸⡆⡿⢘⠀⡾⢸⢃⣉⡏⣿⢸⣿⣿⣿⣆⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠐⡄⢡⠰⢠⠀⡆⢀⠰⠈⡇⡻⣸⢰⡇⣼⣴⢼⢳⣿⣾⣿⣿⣿⣿⣿⣶⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢻⡺⡎⣦⣇⠡⠀⡇⡆⣷⢾⣾⢸⣷⡟⣿⣿⣸⣿⣿⣿⣿⣿⣿⣯⡿⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠷⢿⣿⣄⣧⣓⣱⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡿⣿⡿⡏⠻⢿⠷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠾⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠉

⣲⣿⡟⠉⠉⠉⠙⠒⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠚⠉⠉⠉⠙⣿⣷
⣿⠅⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⢼
⠸⣆⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⢀⠀⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⡾
⠀⠈⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠙⣦⣠⣿⣧⣠⡞⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠟⠉
⠀⠀⠀⠈⢢⡤⠄⠒⠂⠁⠀⠀⠀⢀⣠⠤⠿⠟⠿⢿⣿⣿⠿⠿⠿⠧⢤⣀⠀⠀⠀⠀⠁⠒⠂⠤⣤⠊
⠀⠀⠀⠀⠀⠱⣤⡀⠀⠀⣀⣤⠞⠉⠀⠀⠄⠀⠀⡼⣿⡿⡄⠀⠀⠄⠀⠈⠙⠶⣄⡀⠀⠀⣠⡴⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠛⣿⠋⠀⠀⠀⠀⠀⠀⠀⣸⡇⣿⡇⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠋⠀⠠⠀⠀⠀⠀⠀⣿⡄⢹⠁⣸⡇⠀⠀⠀⠀⠠⠀⠈⢳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⡟⠀⠀⠀⠀⠀⡀⠐⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡔⠀⠠⠀⠀⠀⠀⠀⠀⢡⠀⢠⠃⠀⠀⠀⠀⠀⠰⠀⠐⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠃⢀⠀⢠⠀⠀⠀⣼⠀⢸⡄⡀⠀⢠⠀⢠⠀⢁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⡆⠀⢸⠀⢀⡟⠁⠀⠀⠙⣇⠀⢠⠀⠀⣆⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡶⣾⠶⠿⠃⠀⠀⠀⠀⠻⠷⢾⡶⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⠛⠋⠉⠉⣑⣺⣽⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡃⠀⠀⠤⠖⠒⠀⠉⠿⠟⠛⠉⢇⡀⠀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣉⠀⠀⣠⡄⣀⢀⣠⡄⠰⠞⠛⢿⡆⠜⠉⠉⠀⠀⠀⠈⠉⠂⢄⡈⠉⠒⣅⠐⠢⣤⠤⢄⣀
⠀⠀⠀⠀⠀⢀⣤⡿⣿⣿⣯⣝⣷⣴⡿⠫⡼⠋⠀⢀⢀⣀⣘⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠙⣆⠀⠀⡙⣄⠀⠑⠄⠀⠈⠢⢄
⠀⠀⢀⣴⢾⣟⢿⡟⢧⡀⡝⢿⣿⣿⣄⡴⠆⠒⠒⠋⢉⢉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣿⢄⡀⣱⣿⠀⣀⣾⠀⠀⠀⠀⣧
⠀⢠⣾⢿⣻⣿⢾⡇⣤⣿⣷⡌⠩⠁⠀⠀⠀⠀⠀⠀⢿⢶⠀⢀⣀⣀⠀⠀⠀⠀⠀⢰⣾⣿⠶⣟⣻⣿⣿⣿⣾⣷⣿⣦⣤⣶⢾⡿⡀
⠀⢸⢿⡙⠻⣿⣶⣷⣶⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠆⠛⢿⣿⣿⣿⡶⠲⠒⠚⠠⠴⢦⣭⣥⣞⢿⣿⠤⠄⠒⠊⠉⠉⠀⢠⢇
⠀⠘⣆⠱⣄⠀⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⡸⠯⠞⠛⠻⠴⠾⢲⣦⣤⣤⣀⣀⠀⠀⠈⠉⠀⠐⠒⠦⣤⣀⣀⣴⢋⡜
⠀⠀⠈⠳⢄⡙⢶⣥⣀⠈⠙⠣⠤⠤⠶⠂⠒⠊⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠳⠶⠦⣤⢀⣠⣾⣽⣿⣿⣾⣿⣟⣿⣶⣶⢤⣄
⠀⠀⠀⠀⠀⠉⠛⠷⢬⣙⠓⠲⠦⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠴⠶⠒⠛⠉⣁⠤⠚⠋⠛⠛⠉⠋⠛⠛⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠶⠤⢤⣍⣉⣉⣛⡙⣛⡛⠋⠉⠉⠉⠉⠉⡉⠉⢉⣉⣀⡠⠤⠤⠤⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠒⠒⠒⠲⢟⢿⠛⠛⠓⠒⠦⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣴⡛⣯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠈⢽⡗⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠙⢺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⢀⡜⠉⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⢀⠔⠒⠒⠺⣄⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⣿⡀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠊
⢣⠙⢦⣀⠀⠀⠀⠀⠙⢶⣄⡀⠘⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⠒⠉
⠀⠑⠤⣌⣉⣓⣒⣶⠶⠖⠁⠈⠓⠻⠷⠤⠤⢤⠤⠤⠤⠤⠤⠤⠒⠒⠒⠉⠉⢉⣀⣀⢤⠄⠀⠔⠒⠒⠒⠒⢒⡲⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠄⠀⠀⠒⠒⠒⠒⠀⠉⠉⣉⣹⣹⣏⢡⠀⠄⠀⠀⠀⠀⠀⠀⠀⠉⣈⣼
⠀⠀⠀⠀⢀⣤⢔⣒⣈⡉⢁⡤⠤⠤⠖⠢⠖⠒⠒⠚⠉⠛⠋⠉⠉⠉⠀⠀⠈⠙⠛⠛⠻⠗⠗⠒⠞⠓⠘⠋⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠛⢻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡏⡽⢿⣿⣴⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⠿⣿⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣷⠛⣿⣵⢋⣭⣿⡾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣼⣹⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢾⣿⡶⢻⣿⣯⣀⣿⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⣯⣽⣻⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⢀⣾⣯⡶⠋⠁⠀⠈⣻⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⣷⡇⠀⢹⡟⣷⡄⠀⠀⠀⠀⢰⡿⠛⠋⢻⠏⠀⠀⠀⣠⣶⣿⣿⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠙⢇⠀⢸⠉⢹⣿⡄⠀⠀⢠⣿⠀⠀⠀⣿⠀⢀⡴⠞⠋⠁⠈⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣆⢸⠀⢸⠛⢿⣤⣤⣼⠇⠀⠀⢰⣿⠞⠉⠀⠀⠀⢀⣤⣾⣿⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠲⡜⣆⠀⢸⣿⠀⣸⠀⢸⠇⣸⡟⠀⠀⢀⣿⠁⠀⠀⢀⣤⡾⠋⠁⠀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⡆⠀⣿⠀⡿⠀⡌⢀⣿⠁⠀⢀⣾⣃⣠⣴⠾⠛⠁⠀⠀⠀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠹⡄⢸⣦⡇⢰⡗⣿⠇⠀⢀⣾⠟⠋⠁⠀⠀⠀⠀⣀⣴⣿⣯⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡘⣆⢿⡇⢸⣱⠏⠀⢠⠞⠁⠀⠀⠀⠀⣀⣴⡾⠟⠛⢉⣙⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣬⣧⡑⣸⡟⠀⠔⠁⠀⠀⣀⣤⣶⠿⠿⠭⠴⢖⡉⠉⠁⠀⠀⠙⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣷⣯⣀⣤⣤⡴⠶⠛⠋⢉⣀⣀⡀⠠⢤⣤⣟⡉⠉⠉⠙⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⡿⣿⠭⢍⣉⡀⠉⠙⠓⠶⣤⣀⠀⠀⠉⠉⠲⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣍⣙⠒⠲⠤⣄⣀⣉⣷⣶⡶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠋⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⣒⠺⣄⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣈⣶⣽⣁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡥⡦⡙⡦⡍⢆
⠀⠀⠀⠀⠀⢀⣐⡙⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡈⠈⠀⢇⢣⠀⠀⠀⠀⠀⠀⠀⠈⡄⣦⢧⡑⢧⡆⡌
⠀⠀⠀⠀⠀⠹⣀⣹⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠤⠧⠤⠤⠼⠤⣆⠀⠀⠀⠀⠀⠀⠀⢎⡴⢋⣋⠷⣜⠄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢰⢲⣅⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠠⠄⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⡀⠉⠢⡀
⠀⠀⠀⠀⠀⣼⡓⢓⣲⣒⠛⣲⡄⠀⠀⠀⠀⠀⠀⠀⢏⠉⠀⠀⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⣏⢈⡧⠤⡇
⠀⠀⠀⠀⠀⣿⢿⣻⠇⠿⣻⢿⡇⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⡀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠁⣀⠔⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢠⢖⠫⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣁⣀
⠀⠀⠀⠀⠀⠀⠀⢎⠢⡑⢌⡞⠀⠀⠀⠀⠀⠀⠀⠀⣸⡒⣊⣑⢒⣇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡭⡣
⠀⠀⠀⠀⠀⡠⠚⡵⠑⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠚⠒⠒⠒⠲⡇⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⣨⠟
⠀⠀⠀⠀⠈⠢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠒⠒⠒⠒⠒⠓⠀⠀⠀⠀⠀⠀⠈⠃⠍⠍⠩⠍⠋