Hair dryer Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⣴⣶⣬⠐⠄⠀⠀⠀⠀⣴⠟⠛⠻⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⣿⣿⣿⣿⡇⠈⠀⠀⠀⣼⡏⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⡠⠊⠈⠢⡀⠀⠈⠛⠟⠋⠀⢀⠣⡀⠀⠘⢷⣄⣀⣀⠴⡝⢹⠀⠀⢠⠂⠉⢲⡀
⠀⠀⠀⠀⡠⠊⠀⠀⠀⡠⠋⠑⠤⢀⢀⠠⣀⠙⠖⠈⠢⡀⠀⠙⠛⠶⠭⢀⣸⠤⠤⢍⠆⣀⠠
⠀⠀⠀⣔⡁⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠈⡆⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠙⠿⠦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⢎⢢⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠀⠀⡁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠊⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⡆⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⢀⠤⠐⠒⠒⠒⠀⠠⢄⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠑⠤⣠⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⡜⡄⠀⠀⠀⠀⠀⠀⢠⢫⠊⠉⠒⠌⠁⠀⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠤⠴⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⠁⢀⡠⠤⠤⣀⠀⠀⠘⢜⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠁⢀⠔⡡⠊⠉⠒⠌⢃⠀⠀⠀⠢⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠴⠁⡐⠁⠀⠀⠀⢸⠈⠀⠀⠀⠀⢣⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠊⠀⠀⠀⠀⠀⡆⢃⠀⠀⠀⠀⡜⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⠢⢀⠤⢊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣟⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⠿⠟⠋⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡟⠛
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋
⠀⠀⠀⠀⢸⣿⣿⠟⠁
⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠚⠉⠉⠉⠉⠉⠓⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠖⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⣀
⠀⢀⣀⡀⠀⠀⣀⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡀⢸⣿
⣉⣉⣤⣉⣉⣉⣡⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠀⢸⣷
⣤⠤⠤⠤⣤⠤⠤⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠀⠀⣸⡩
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠤⠤⠤⠤⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⢠⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠲⠦⠤⠤⠤⠤⠤⠤⣄⠀⠀⠀⠀⠀⢀⡤⠤⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠹⡄⠀⠀⠳⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⢧⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠿⣿⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠷⣄⠀⠈⢦⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠑⠤⢤⠤⣚⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⣼⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣾⣯⣥⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣀⠔⠶⢍⡉⠛⢍⠉⠁⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⢆
⠀⠀⢀⠜⠓⠐⠒⣆⠉⢦⠀⠳⡀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠢⠤⠤⠄⠠⢤⣤⡀⠀⣠⠤⠔⠁⠸⢉⡙⠷⠆
⠀⠀⣜⢀⡐⣂⡒⣁⢀⠀⢣⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢰⠁⠀⠀⠀⡆⢈⣁⡀⠲
⠀⠀⣇⣀⣀⣀⣀⣀⣀⠇⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢘⠀⠀⠀⠀⢿⣚⣓⡲
⠀⠀⢡⠤⠤⠤⠤⡄⠀⢀⡎⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⡇⢸⢸⠀⠀⠀⠀⠇⢈⣓⣂⡲
⠀⠀⠀⠳⡤⠤⠤⢋⡠⠊⢀⡜⠀⠀⠀⠀⠀⠀⠐⣉⡀⠤⠤⠤⠐⠒⠒⠒⠚⠁⠀⠓⠢⣄⠀⢰⣘⣒⣒⠆
⠀⠀⠀⠀⠈⠑⠚⡭⠤⠴⠉⠠⠤⡄⠐⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢼⠌
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⠄⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⠒⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⠉⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠉⣹⠁⠀⠀⠀⠀⢰⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⣀⣀⠇⠀⠀⠀⠀⠈⠀⠀⠈⠷⠤⠤⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢠⠀⠀⣀⠟⠃⠉⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠘⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⣀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀⠜


⣿⡯⣟⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠤⣤⢤⡤⠤⠤⠶⠖⠒⠒⠚⠛⠉⠉⠉⠙⣟⢦⡀⠈⠉⠛⢶⣄
⠀⢀⣾⣿⣿⡍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠳⣄⣀⣀⣤⣤⠤⠤⠶⠶⠒⠒⠛⠋⠈⣧⠀⠀⠀⠀⠙⣷⡀
⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠸⣧
⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢀⡿
⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠙⠻⠿⠷⠶⠶⠖⠒⠲⠶⠶⠶⠶⠾⠿⠿⢶⣶⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⢀⣴⣿⠇⠀⠀⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣈⡟⠙⠛⠛⣿⣿⣿⣿⣿⣿⣶⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⣾⢹⠛⣆⠀⠀⡿⠁⣸⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠯⡏⡟⠀⣿⠀⣸⠃⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣸⣹⠁⠀⣿⠀⡟⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠹⠤⠏⡇⠀⢀⡏⢸⠃⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢸⠁⠀⣸⠃⣼⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢸⠀⢠⡏⢀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⢤⣼⣠⡞⠀⣸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⢀⠏⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⢸⡇⢀⠞⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠓⢾⡗⠋⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣷⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠙⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⡰⠟⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⠞⠁⠀⢀⡜⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠁⢀⣠⠴⠋⢀⡐⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠰⠋⡻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠂⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⠀⠀⢀⣾⡋⡈⢷
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠖⠂⠀⠀⠀⠀⠀⢠⡏⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢀⣶⠟⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⠀⢩⡠⢝⠀⡀⠀⠀⠀⠀⡀⠈⠊⢀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⡴⠛⠁⣀⡀⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⣁⡀⠀⠀⠀⠠⠜⠉⠀⠀⠨⠀⠀⠀⠀⠀⠀⠘⠧⣄⡛⢀⡴⣾⠟⠙⠿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣬⠡⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⣾⠏⠀⠀⠀⠈⢹⣏⠛⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⣶⣾⡿⠏⣤⣶⠀⢶⣤⣤⣿⣷⣴⡁⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠺⡅⠲⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⡝⠀⠙⣷⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⠀⢀⢰⣿⡄⢀⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠀⠀⡇⠀⠀⠹⢿⡀
⠀⠀⠀⠀⠀⠐⠁⠀⠠⠤⠖⠘⠃⠂⠒⠁⢠⡆⣽⠲⠽⠋⠉⠙⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⡀⠀⢾⡇⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⡔⡉⠀⠀⠀⠀⠙⢫⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠿⡝⠁⣙⢻⠀⠀⠀⠀⢻⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣬⡾⠟⠸⢾⣿⠥⣶⣞⢆⡿⠀⡀⠀⢿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠷⠋⣀⠀⠤⠔⣛⢚⣿⡿⢮⣷⡄⠁⠀⠈⡇⢀⣀⡄⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠈⠀⠈⠀⠠⠨⠞⠉⠀⠻⠿⡿⠦⠀⠠⠙⠋⠙⠶⠊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⢐⠀⠰⢢⡐⠐⢰⠂⡄⡀⡴⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠁⠒⠦⡀⠐⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⢄⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⣄⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⡀⠀⠀⠀⠈⠢⡀⠀⠈⠆⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠷⣄⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠖⠋⡀⠈⢳⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⠶⠶⠾⠟⠛⠋⢉⣠⠴⣊⠀⠈⢧⡱⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠘
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣬⣭⣄⡀⠀⢀⡴⠒⠚⠛⠛⣋⡭⠒⣉⣠⠄⢀⣀⠉⠀⠑⠃⠀⠀⠉⠁
⠀⠀⠀⠀⣠⣶⠟⠋⣉⣏⠉⠉⣛⢿⣶⡄⢉⡄⢀⡤⠞⢁⡴⢚⣡⡴⠚⠉
⠀⠀⠀⣼⠏⣼⣿⠿⡛⠻⠿⣷⣦⡀⡙⢿⣆⠉⣉⣀⠴⣫⡶⠟⠁
⠀⠀⢸⡟⣾⡟⠡⠀⠀⠀⠁⢈⢻⣷⡀⠈⣿⠀⠀⣠⠞⠋
⠀⠀⢸⣇⠽⣷⣔⠀⠠⠀⡂⠀⢈⣿⡇⠁⣼⠀⠜⠁
⠀⠀⠈⢻⣦⡨⠛⠛⠛⠉⠀⢈⣽⡿⠐⠀⠃
⠀⠀⠀⠀⠉⠻⢶⣤⣥⣤⣶⠿⠋⠀⠀⠄⢰
⠀⠀⠀⠀⠀⠀⠐⠦⣤⣄⡆⠀⠄⠘⠐⠀⢾⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣝⢿⣷⣤⠀⠀⠒⠀⢨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡙⣿⣷⣄⠀⠐⠈⠉⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠌⠉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣀⣀⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀
⠀⢠⡾⠛⢦⡀⠀⠀⡾⠋⠉⠉⠉⣿⡆
⠀⠈⢷⣀⠈⠁⠀⠀⠱⣄⡀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⣠⣶⡖⠒⠶⣶⠦⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠉⠳⠦⢤⣤⠤⠄⠉⠙⠛⠓⠒⠒⠒⠲⠄⠀⠰⡏⢿⣿⡆⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⣴⠖⠓⠶⣤⡄⢀⡤⠶⠒⠛⠛⠳⠶⣦⣤⣀⣀⣤⠀⢻⡘⣿⡟⠀⠀⠹⡇⠀⠀⠀⠤⠤⢤⣤⠤⠶⠶⠶⠶⠀⠀⠐⠶⢤⣄⡈⢳⡄
⠀⣧⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢷⣟⡀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠶⣤⡀⠈⠙⢷⣿⡀
⠀⠈⠳⣄⣀⣀⠀⠀⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠙⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⢀⣈⣻⣆⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠀⠀⡄⠀⠀⣄⣀⠲⠦⢬⣿⡄⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠱⡄⠀⠠⣍⡙⠛⢲⡿⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠀⠀⠙⢶⣤⣤⣭⡿⠟⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠓⠀⠀⣤⣀⣀⣠⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⡿⢰⠀⠀⠀⠈⠉⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠙⢡⡏⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡏⠀⢠⡿⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢫⣿⣶⣿⣁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣟⣿⣿⡟⡷⢶⡶⣶⢶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⣱⢿⢡⡇⢹⠁⡻⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣷⣧⣯⣤⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⡀⠀⠁⠀⠀⠀⡀⠐⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢚⠀⣴⠟⢫⣹⡦⠤⡔⠀⠑⢬⣦⣄⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠄⢾⠁⣠⡞⠀⢹⠁⡀⠀⠀⠀⠀⠀⠀⠚⡀⠀⠙⣣⠀⢠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠃⠀⡞⠀⡟⠸⠁⡔⠀⠀⠳⢤⡴⠀⠁⡀⠀⠀⡠⠣⠀⠾⢿⡄⠀⡀⠀⠀⢄
⠀⠀⠀⠀⠀⡠⠊⠀⡂⢀⣤⡃⠈⣇⠀⠁⢢⠀⠣⡀⠀⠁⠀⠀⠀⠀⠑⠀⠀⠀⣶⡋⠁⣀⠇⢸⡅⠒⠀⠘⠖⠐
⠀⠀⠀⠀⠈⠀⠀⠀⢣⣝⠚⢟⡆⠙⠣⠤⠾⡳⢄⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⡹⠁⠀⠈⠄⡀⠐⣄⡀
⠀⠀⠈⠀⠀⠀⢰⠋⠀⠀⢡⠄⠁⠀⠀⠀⠀⠈⣀⡵⠞⠀⠠⣄⠂⠀⠀⠀⠀⢀⣠⡞⠁⢀⣀⣀⠀⡀⠀⠀⠙⠀⠐⠆⢤⣄
⠀⠀⡀⢀⣀⡴⠋⠈⢢⢠⠞⠀⠠⣦⠀⠀⣀⡜⠁⠀⠀⠘⠀⠀⠀⠀⠀⠘⠋⠉⠚⠲⠖⠀⠀⠉⠂⠄⠀⠀⠀⠀⣆⠀⠀⢹⡝⠄
⠀⠀⠚⠛⠉⠀⠀⠀⠈⠀⠀⠀⠀⠫⣤⣴⠟⠁⡄⠰⣤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⡀⠀⢀⠀⡴⠋⠀⢀⠀⠃⢸
⠀⠀⠀⣀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠄⠜⢇⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠹⡄⠀⠀⢢⠀⠁⠀⠀⠀⢀⡀⠎⢀⠀⠂
⠀⠀⠉⠠⠀⢡⠤⠤⠀⡀⢆⠀⣀⠄⠀⠀⡀⣀⠀⠀⠀⢸⣶⡀⠀⢠⡻⣂⡜⠀⠀⠀⠀⠘⠦⠤⡴⠂⠀⢀⠀⠂⠀⠨⠔⠋⠀⣀⡄
⠀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠋⢁⣀⡀⠀⣼⠃⠀⠀⠘⣾⠯⠀⠈⠀⠀⠀⡈⠀⠀⣃⠀⠀⠀⠀⠠⠀⠀⣴⡤⠊⠁
⠀⡻⡀⢻⡀⠀⠸⡀⠀⠀⣵⠀⠀⠀⠁⠀⢤⠸⣄⣣⠜⠃⠀⠀⠀⢰⠃⠀⠀⠀⠀⠐⠀⠑⠀⢸⣿⠀⠀⠀⠀⢠⡆⠘⠋⠄⠄
⠀⣠⠂⠀⠐⠀⠀⣽⠲⢤⣘⡿⠛⡃⠊⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠐⡆⠀⠀⠀⠀⠀⠻⣦⣀⣠⣴⡏⢠
⠀⢸⠀⠀⠀⣤⠀⣿⠑⠖⠠⢒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠁⠀⡈
⠀⠀⠐⠀⠀⠻⡄⢸⣆⡀⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠸⠀⢤
⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡠⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⣸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃
⠀⠄



⠀⡀

⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢒⣈⣻⣦⣾⣿⣿⠷⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢋⠉⣡⣥⣿⣿⣿⣿⡳⠆⠠⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣴⣆⡄⣠⡿⠿⠋⠀⠀⠉⠳⣦⡄⠐⢜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣯⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢯⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠛⡇⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⣤⣧⡇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣿⡟⣁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢰⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠰⡟⠏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢾⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡻⣿⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣟⠛⢌⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⢷⣌⢿⣷⣾⣷⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣿⣿⣿⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡛⣿⣿⣹⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣷⣦⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣛⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠲⠶⠶⠶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣷⣤⡀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠟⠋⣉⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠉⠙⠻⢦⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣯⣴⠶⠛⠋⠉⠴⠶⠶⠟⠛⠛⠛⣛⡻⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠁⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠿⠷⠦⠀⠀⠀⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀⢀⣤⣴⣾⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⠤⠄⠀⠀⢢⡈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠋⠉⠀⠀⢀⣀⡤⠂⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠹⣆⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠋⠀⠀⠀⣠⣴⣾⡿⠋⣀⣤⣾⡿⠿⣛⣯⣿⡿⠛⠉⠀⠀⠀⣀⣀⠀⠀⠀⠘⣷⣄⠀⢻⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣁⠄⠀⢀⣴⣿⣿⡿⢋⣴⣾⡿⠛⣩⣴⣿⠿⠋⢁⣠⣤⣴⡶⠿⠛⠉⠀⠀⢀⠀⠀⠘⣿⣷⣄⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃⢀⣴⣿⢟⣿⢏⣴⣿⠟⣡⣴⣿⡿⣋⣥⣶⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⣾⣿⢋⣾⢃⣾⠟⣡⣾⣿⣿⣿⣿⠟⣻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠈⢷⡀⣿⡼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⣾⣿⠃⣾⠇⣾⢋⣼⣿⣿⣿⡿⠋⠡⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⢣⢻⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸⡿⢸⢣⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⢹⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⣾⡇⢠⣿⣿⣿⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠸⣷⣸⠃⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢿⡇⣾⣿⣿⠋⠉⠉⠙⠛⠿⣶⣶⣤⡄⠀⠀⠀⠀⣤⣤⣶⡾⠟⠛⠉⠉⠉⠂⠀⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⣧⣿⣿⡏⠀⡀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣿⣿⣿⠀⠀⢙⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣖⠁⠀⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠶⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡷⠖⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣉⣯⣹⣩⣯⣱⣍⣍⣏⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣭⣭⣽⣿⣿⣿⣭⣭⣭⣿⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⢈⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠙⠉⣩⣿⣟⠁⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡿⠋⠟⠁⠀⠀⠀⠀⠈⠳⣤⣄⠀⡀⠀⠀⠀⠘⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⡴⠞⡿⠿⣿⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢾⣦⣢⡀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⢀⣴⠞⠋⣠⠟⠀⠁⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣄⡀⠀⠱⡀
⠀⠀⠄⠀⠀⠀⠀⠀⣀⣀⡀⢀⠀⠀⢀⣾⣶⣶⡟⠁⠀⣼⡏⠀⠀⠀⠀⠁⠈⠛⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢃
⠀⠀⢀⣠⠴⠚⠉⠉⠉⠉⠉⠀⢠⣚⣻⣽⡿⠻⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠐
⠀⠈⣸⡇⠀⠀⠀⠀⢴⣾⣿⠟⠋⠟⠉⠁⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌
⠀⠀⠹⣧⠀⠀⠀⠀⠀⠉⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⢹⣆⣄⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⢆⡀⠀⠀⠀⠀⠀⢀⢸⣷⠀⠀⠀⡀⢀⠀⠀⠀⣀⣤⡤⠖⠁
⠀⠀⠀⡸⠛⠋⠉⠁⠀⠀⠈⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠹⡄⠀⠀⠀⠀⢸⣿⢃⣴⣴⣿⡷⠷⠶⠚⠛⠉⠁
⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣍⢷⣄⠀⠀⠂⠰⠚⠁⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸⡷⠋⠁
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣬⣳⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡸⠁
⠀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠴⠛⠋⠉⠉⠉⠉⠙⠛⠛⢿⣦⣤⣤⣤⡤⠆⠊⠀⠀⠀⠀⡠⠃
⠀⠸⡆⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠷⢶⣦⣴⣦⣤⣦⣾⡇
⠀⠀⢹⣠⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⣿⡟⢹
⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⢸
⠀⢠⠇⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⣹⣷⣿⣷⣶⣶⣶⣾⣿⠃⠀⠀⣾
⠀⣼⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⢤⣤⡤⠶⠾⣿⡿⠏⠀⠘⠀⠀⡿⠃
⠀⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠋⠁⠈⠀⠈⠀⢀⣴⠟⠏⠀⠀⠀⣀⠔⠋
⠀⣧⡸⠀⠀⠀⠀⠀⠀⠀⠒⠫⠉⠁⠀⠀⠀⠀⠀⢀⠴⠋⠏⠀⠀⠀⠀⣴⠃
⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠐⠁
⠀⠘⣄⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⣀⡤⡴⠶⠒⠋⠉
⠀⠀⠘⡄⠀⢀⠀⠀⠀⠀⠀⢀⣾⡾⢿⡟⠉⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠈⡆⣾⠀⠀⠀⠀⢀⠞⠁⠀⠘⣿⠔⡠⢀
⠀⠀⠀⢀⢾⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⣿⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⠀⠀⡟
⠀⠀⡈⠀⠀⠀⠀⠀⢀⠾⠁⠀⠀⠀⢸
⠀⢀⡇⡀⠀⣀⣤⠶⠊⢀⡔⠀⠀⠀⡎

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠹⣵⠋⠳⢴⣖⢦⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠬⠦⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠁⣟⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⣠⢤⠀⡹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠉⢆⣀⣀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠳⡄⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠹⠤⡄⠀⠀⠀⠝⠃
⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⡀⢀⡠⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠧⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠣⡄⠀⠀⠀⠀⠀⠀⡇⠉⡵⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡠⠼⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢰⡋⠁⣀⢀⢀⠀⠀⢠⠇⠀⡇⠀⢀⣀⡠⠔⠐⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⢧⡀⠀⠠
⠀⠐⠀⠀⠀⠀⠉⠛⢹⣸⣠⠃⢀⠞⠀⠀⠉⠉⣉⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⡞⡳⠋⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠀⢠⠒⢢⣀⡄⢠⠤⠼⠂
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢹⡙⠁⠀⠀⢰⢇⡠⣢⠖⢠⠤⠤⣄⠀⠀⣇⠀⠀⠈⠁⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣣⠞⣵⡵⢦⡀⣳⠀⠈⠓⠂⠀⠀⠤⠦⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⡡⠚⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣁⣀⣀⣀⣀⣱⣄⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠋⠉⠉⠉⠉⠳⠑⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⣠⠴⠒⠛⠉⠀⠀⠀⢸⡆⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⡔⣠⡶⢋⡵⢊⣤⠖⠀⠀⠀⠀⢸⠇⠀⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⣴⠟⣰⣿⢡⣿⠕⡠⠄⠀⠀⠀⠈⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠸⣿⡏⢰⣿⠃⣾⡏⡜⠁⠀⠀⠀⠀⠀⠀⠀⡰⠻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⣷⠀⢻⠀⣿⣿⢰⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡦⢀⢀⣿⠃⠀⢸⣿⡇⢸⣿⣿⡇⠀⠀⢀⣠⡴⠞⠋⠁⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣛⣻⠵⠂⡀⡼⢻⡇⢸⡿⣿⣿⡄⠀⠙⠁⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡯⠤⠶⠚⠛⠁⠸⣷⣿⠇⢻⣿⣿⣄⠀⠐⠺⢿⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡀⠀⠀⠀⠀⣀⡼⠀⣿⡏⠀⠈⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡞⢁⣠⣤⣶⣶⠿⠋⠁⢘⢹⡇⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢰⣿⣿⣿⠋⣀⣀⣠⣴⡟⢸⠇⠀⡀⠀⣿⡟⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣿⣿⡿⠿⠿⠿⠟⠛⠉⠠⠋⠀⠴⠀⢠⣿⠇⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⢀⣤⣴⣶⠶⠦⠤⠤⠔⣊⣴⣿⠃⠀⢀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡎⠀⣴⣿⠛⠁⠀⠀⠀⠀⠉⠉⣩⣴⡟⠀⢶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⣿⡗⠀⠀⠀⢀⣤⣴⣶⡿⠟⠋⡀⠀⠘⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣠⣮⣾⣿⠟⠋⠁⢀⣴⢆⣷⡀⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠻⣿⣿⠏⠀⣀⣤⣶⣿⢟⣼⣿⡇⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣴⣾⠿⠛⠋⣡⣾⣿⡿⣱⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠀⢠⠎⣼⣿⣿⣟⣿⡿⠋⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⢀⡿⣸⣿⣿⣿⡿⠋⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⣧⢻⣿⣿⢋⡄⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⢿⡏⣾⣧⡪⣀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠸⣿⣝⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⢛⣻⢿⣮⣍⣙⠓⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡫⢔⣤⣶⡟⣽⡲⢕⣨⣍⣛⠳⢮⣝⢮⣙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡾⢋⣴⠏⠀⣿⡙⢦⣉⡙⠛⠻⠶⣮⣷⣿⣷⡝⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⡾⠋⢠⣿⠏⠀⠀⢳⣝⠦⣬⣙⡓⠶⢤⣄⠉⠛⢿⣿⣎⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢰⣿⠁⠀⣿⣿⠀⠀⠀⠀⠙⠻⢶⣮⣽⣛⠲⢮⣝⣦⡀⠙⣿⡎⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣿⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⡉⠻⣿⡄⠘⣿⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠷⣄⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠘⣷⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⢀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⣸⡏⡼⣿⣿⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⣰⠟⡰⢱⣿⣿⣧⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣴⠏⡴⢡⣿⣿⡝⢿⣧⡘⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣼⠏⡰⢁⣿⣿⢡⡙⢦⣙⠻⠦⣍⡓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⡏⡄⠁⢸⡿⣟⢸⡉⠓⠻⠿⠷⣶⣬⣭⣛⡻⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⡇⢸⡄⢸⡇⢿⠸⣯⣑⣒⣒⣂⣒⣀⣀⣈⣉⡁⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠳⡌⣷⠘⣇⢧⣙⠫⠭⣭⣤⣤⣤⣤⣌⣉⣙⠲⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠙⢿⡆⠘⣎⢧⠙⣿⣿⣭⢹⣿⣷⣜⣿⣧⢹⡒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⣿⠘⣌⠪⡳⢌⣛⣋⣼⡯⢻⣿⣾⡏⡎⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⠀⡿⣷⡚⠶⠖⣚⡵⢁⡟⣿⣿⢳⣿⣯⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⠄⠀⠀⠀⢸⡇⣸⣰⣝⠦⣍⣛⣉⣡⠴⢋⣼⣿⠏⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⡀⠀⠀⣠⠞⣰⣿⣅⠪⢷⣦⣤⣤⣤⣶⢿⣯⡅⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⣭⣟⣫⣥⡾⢟⡻⢛⡷⡶⣤⡍⠉⠈⠁⢜⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠭⣙⣛⣉⡭⠔⢻⠀⣧⣿⢠⡋⠙⢿⣬⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠘⣆⣿⣌⠓⠛⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣙⡛⢛⣛⡯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣴⣾⣿⣿⣯⠀⠀⠀⠀⣀⣀⡉⣉⣛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣺⣵⠞⠁⢩⡁⢿⠋⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣶⣝⡿⣦⣄
⠀⠀⠀⢀⣤⣶⣿⢿⣿⣿⣿⣿⠃⢠⡅⡄⠳⣌⠐⡀⠀⠀⠀⠀⠈⠻⣿⣍⠻⣧⠙⢿⣿⣿⣧⡀
⠀⠀⠠⠟⡽⢋⣴⠿⡿⠿⣻⣿⡀⠀⠑⣷⡀⡈⠑⠺⢦⣄⠀⠀⠀⠀⠙⣿⣆⠙⣧⠀⠙⢿⣿⣿⣄
⠀⠀⠀⠘⠁⣾⠃⢀⣠⠞⢻⣿⣧⡰⡀⠈⠻⣿⣾⣄⢠⣍⠻⢮⣦⢳⡄⠘⣿⡆⠈⠂⠀⠈⢿⣿⣿⣆
⠀⠀⠀⠀⠁⣿⣷⠟⠁⠀⠀⠻⣿⡻⣿⣦⣀⠀⠙⠻⢦⣝⣷⣄⢻⣧⢻⡄⠸⣿⠀⣄⠀⢲⡘⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠈⠁⠈⠙⠻⢷⣶⣤⣄⡈⠙⠻⣷⣿⣾⣷⠀⢿⡇⢸⣆⠘⣧⢹⣿⣿⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠤⢤⡀⠀⠀⠀⢠⡴⠖⣛⡉⠉⠉⠙⠻⢷⣄⠈⢿⣿⣿⡆⢸⣷⢸⣿⡀⣿⣾⡟⣿⣷⡁
⠀⠀⠀⠀⠀⠀⠀⠶⢶⣦⡀⠀⠀⠀⠰⠟⢿⡿⢻⠿⠋⠀⠀⠹⣧⠈⣿⣿⡇⢸⣿⣼⣿⡇⣿⣿⡇⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡆⣻⣿⡇⢸⡟⣿⢻⣷⡇⢹⣇⣿⣿⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢻⡇⣿⣿⠀⣼⠇⠟⠀⣿⢀⠈⣸⣿⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡀⣾⣿⣿⡏⢠⡿⠀⠀⠀⠃⣾⢠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⡏⢰⢻⡟⣿⡿⢀⣾⠃⡄⢀⡆⢰⣧⡞⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣷⣤⣤⠀⠀⠀⡾⠀⡿⠈⣽⣿⠇⣼⡏⣰⠃⣼⣧⣿⢏⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⢰⡇⠀⡷⢠⣿⡟⣼⡿⣰⣏⣼⣿⠟⣡⡾⢃⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⣧⢸⣿⣱⡿⣱⣿⣾⠟⢁⡴⠏⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠⢻⣾⣿⣿⣿⡿⠟⠁⠐⠋⠀⣠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣞⣿⣿⠟⠋⠀⠀⠀⢀⠄⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⡼⣿⡿⢀⡤⠀⢀⡴⢃⡾⣳⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠊⠁⠀⠀⠀⠀⡼⣷⡹⣿⣷⣿⣴⡵⢋⣴⠟⣴⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⡇⠘⢷⣿⣿⣿⠟⣠⠞⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⠎⠻⣿⣿⡞⠁⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣸⣶⡼⢻⣿⡾⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⢸⣿⣿⡇⣾⣿⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣿⣿⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃

⠀⠀⠀⠀⠀⠀⠄⠤⠠⠀⠀⠀⠀⠀⠀⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡠⠴⣶⣶⡶⠶⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣾⠟⠛⠛⠿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣴⣾⣯⡩⣿⣿⣟⠷⢶⣿⣿⣳⣮⣻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⣾⣿⣿⡯⠐⢚⣛⣿⠟⠀⠀⠀⠀⠈⠻⢿⣿⣿⣟⢿⡙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⣾⡿⣛⣥⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡍⢻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣾⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⢻⡿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢸⣧⠹⡟⣆
⠀⠀⠀⠀⠀⠀⠀⡼⣿⣿⢳⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⣿⡆⢷⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠁⡟⡯⣿⣿⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⢻⠇⠘⡇⣮⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⠀⠀⢹⣽⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⡸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢿⣿⣼⡇
⠀⠀⠀⠀⠀⢸⣇⣤⣿⣏⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠰⡀⢸⣿⡿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⡀⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⣴⣳⣼⣿⣷⡟
⠀⠀⠀⠀⠀⠀⣼⠈⠛⣷⣌⣢⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢹⠀⡀⢈⣿⣿⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⡇⠙⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠸⣦⣱⣿⣿⣿⣧⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⣿⣿⣤⣿⣿⣿⡙⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠋⣴⣿⡿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⣼⣿⣦⡹⣿⣿⣿⣷⡷
⠀⠀⠀⠀⠀⠀⠰⠚⢸⣿⣫⣾⣿⣿⢿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣇⣿⣿⣧⠹⣿⣿⣿⣟⠁
⠀⠀⠀⠀⣀⢤⣀⣤⣟⣽⣿⣿⢃⢟⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡸⣿⣿⣟⠄⢹⢛⣿⣮⠢
⠀⠀⠀⠌⣥⢚⢟⣿⣿⣟⡟⠃⢀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣅⠙⠿⣿⣦⣸⡟⡀⠈⢳⡀
⠀⠀⠜⣿⡟⠃⡸⣿⠟⠌⠀⢰⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⢏⣻⣿⣿⣷⠶⢶⣿⣟⣷⣿⣤⠊⠁
⠀⠀⠈⡟⣠⠎⣠⢋⠀⠀⣠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡼⣫⣾⣷⣝⢿⣿⠻⠶⣶⣿⣿⠉⠈⢢
⠀⠀⢀⡿⣁⠜⣡⠎⣴⣿⡿⣍⢺⣿⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣵⣿⣿⣿⡟⣷⣽⣀⣧⡈⢿⡃⠀⠀⠸
⠀⠀⢸⣷⢏⣾⢃⣾⣿⣿⣶⣌⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⣽⣿⣿⡿⡼⠡⣸⣿⢿⣿⣿⣦⣿⡄
⠀⠀⠘⣯⠈⣿⢿⣿⠿⢿⡿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢸⢸⣿⣿⣷⡀⠀⠘⠏⢪⢿⡌⠻⡙⢷⡄
⠀⠀⠀⠈⠀⢸⣿⣿⣷⡼⠃⣰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠸⡏⠛⣟⠂⠀⠀⠀⠹⣿⣦⣘⣦⣽⣄
⠀⠀⠀⠀⠀⠀⠻⣯⣅⡀⣀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠽⢝⠦⡨⡛⠂⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠐⠡⠞⣽⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁

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


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠒⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⣴⠾⢿⣿⡿⣦⣄⠀⠀⠀⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⡠⠋⠀⣠⣿⠉⣷⡌⣌⢳⣄⠈⠢⣀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⣠⠞⢁⣿⡄⢿⣷⠘⡆⠹⣆⢣⡈⢷⣄⠈⠻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣀⣤⣴⡶⠞⢋⣡⣴⠟⠹⣧⠈⠁⠑⢿⡄⠹⣧⡣⠀⠈⠛⠶⠤⣍⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣾⠿⠋⣁⣴⣾⠟⠋⠀⠀⠀⠹⣆⠀⠀⠈⢿⡂⠙⣷⣄⠀⠀⠀⢀⣠⠔⠂⢙⠷⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠁⢠⣾⣿⡏⠁⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠈⢷⣄⠠⣙⠓⠒⢚⡉⠄⠀⢀⢀⣴⠿⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠀⣰⣿⣿⣿⣏⡉⠳⠄⠀⠀⠰⠞⢋⣹⣧⣠⣀⠀⠉⠓⠿⠿⣛⣥⠒⢀⣘⡵⣾⣿⣗⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢠⣿⣿⣿⣿⠿⠿⠷⠀⠀⠀⠀⠞⢉⣿⡿⢷⣝⢿⣷⣶⣿⣿⣿⡛⣟⠻⣿⡿⣎⣿⣮⡁⠚⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⣿⣿⡿⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢿⣿⣿⣷⣌⣧⠙⣷⡹⣎⠻⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣜⣿⡿⢡⣿⡀⠀⠀⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢻⣎⣿⠇⣿⡟⢳⡆⢿⣧⢻⡟⢻⡟⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⢀⣾⣿⣷⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢘⡼⠋⢠⡟⠘⢸⡇⣾⣿⡜⣿⡌⣿⣦⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⢟⣻⣿⣿⣧⡘⢿⣟⣉⡻⠓⠀⠀⠀⠀⡠⢊⡴⠋⠁⣠⠞⢠⡄⢺⡇⣿⣿⡇⢸⡇⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⡼⠃⢹⡿⢿⣿⣿⣷⡀⠈⠁⠀⠀⠀⢀⣴⣾⡷⠋⠁⣠⠞⢁⡰⠏⢠⣿⠀⣿⣿⣇⡼⢁⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡃⠀⣿⠇⣜⢿⣿⣿⣷⣤⣀⣤⣴⣾⣿⡿⠋⣀⣴⠟⣡⠴⢋⣀⣠⡿⢻⠀⣿⣿⡿⣡⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡄⠹⣦⣹⣿⣿⣿⣿⡿⢹⣿⠋⣠⡾⢋⡴⠛⠁⠴⣋⣥⠔⣠⡷⣾⡸⣿⣷⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡿⡄⠘⣧⠐⠘⡿⢾⣿⣿⡿⢃⡾⢁⣼⠟⡵⠋⢀⡴⠛⢉⡴⣻⡟⠁⠀⠈⣷⡹⣿⣿⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣱⠁⢹⡄⠈⢧⠀⠈⣀⣿⠟⢁⣾⡇⣾⢟⣼⠁⣴⠏⠀⣠⡟⠼⣿⠀⠀⢠⠞⠉⢹⣯⢹⡻⣎⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⠇⢠⣿⣿⡄⠈⣧⠀⠟⠁⣰⡿⣿⣧⣿⠘⡇⣸⡏⠀⢰⡿⠀⢰⡇⠀⠀⣍⠀⠀⠀⢻⡀⢳⡈⠳⣤⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣯⠛⠀⣿⠛⣿⡇⠀⢸⡆⣠⣾⣿⠃⣿⣿⣿⣇⢱⣿⡇⠀⣾⡇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠻⣦⡈⠻⣦⡉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⠀⢹⡇⣸⣴⠿⠋⡌⡟⢸⣿⣿⣿⣿⡌⣿⠀⠀⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠙⣿⢦⡈⠻⣦⡈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⣤⡼⠟⠋⠁⢠⠞⡼⢁⣿⣿⣿⠸⣿⣧⣿⠀⠀⣿⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⠳⡙⠳⣌⡳⣄⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⣴⠟⠉⢀⣀⡤⠖⢁⡞⢡⣾⣿⣿⡟⣠⣿⣿⣿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⣦⡀⠙⢦⣄⠙⠻⡄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠷⠛⢛⣉⣩⣤⡾⣫⣴⣿⡿⣱⣿⢇⡇⣿⣿⣿⠀⠀⣿⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣮⡻⣦⣀⠙⠻⢶⣤⣼⠁
⠀⠀⠀⠀⠀⠀⣠⠞⢉⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⢠⣿⡟⢸⠇⣿⡏⣿⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢹⣿⣿⣮⡙⠿⣿⠞⠻⡇
⠀⠀⠀⠀⠀⢠⣿⣾⠿⣛⣭⣥⡴⢾⠶⣶⣶⣛⣉⣴⣿⡿⠁⢏⣼⡿⢠⣿⠀⠀⡇⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⣿⢻⡌⢳⣄⡾⢃⡔
⠀⠀⠀⠀⣠⡞⢹⠏⣸⣿⣿⠏⡔⣵⠰⣿⡏⢻⣿⡿⠛⣀⣤⡿⣿⠃⣾⡏⠀⢀⡇⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣠⣶⡿⠁⠸⢣⡾⢏⡵⠋
⠀⠀⠀⠀⢿⡄⠸⣆⠸⣿⣿⡀⡇⣿⣄⠉⠱⣾⣟⣛⣛⣛⣭⡾⠁⡼⣿⠃⠀⣼⡷⠛⢧⣀⣀⣀⣀⡤⠴⠚⠉⠉⡱⠟⠉⠀⣠⢧⣿⠵⠋
⠀⠀⠀⠀⠀⠙⠳⣬⣑⠿⣿⣷⣵⡈⠳⠮⣥⡛⠛⣛⣻⡿⠋⢀⡞⣵⠃⠀⣰⣿⡇⠘⣷⣤⣈⣁⣤⣤⣤⣤⣤⣤⣤⠖⠒⣉⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣍⣛⠛⠷⠶⠾⠿⠶⠛⠉⣀⠴⣋⡾⠁⢀⣴⡟⣱⣧⠟⠋⠉⠉⠉⠁⠀⢠⣿⣿⠏⢹⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠳⣬⣙⡲⢤⣄⣀⣀⣀⣠⡤⠞⣋⣤⡶⠻⣿⠀⣿⡀⠀⠠⠒⠋⣉⣉⣩⡉⠽⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣯⣉⠋⢙⣿⣿⡶⠟⠋⠘⢧⡸⠘⠳⠆⣉⣭⠖⠛⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁

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


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⡀⠀⠀⡀⠀⠀⠀⣀⡀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢂⠐⠂⢄⠀⠀⠀⠀⠀⠀⠀⠞⢁⠤⡈⡆
⠀⠀⠀⠀⠀⠈⠀⠀⢈⢀⠎⠀⢸⠀⡀⠂⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠅⢸⠀⠈⡄⠀⠀⠀⠀⠀⠀⢆⡸⠔⡁⠀⢀⠥⠄⢠
⠀⠀⠂⠐⠀⠀⠀⠀⢀⠠⠊⠀⠂⠀⠀⡀⠁⡆⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠰⠈⠀⠀⠈⠑⠒⠁⠀⢠⠁⠀⠀⠀⠀⠀⠀⡀⠤⠊⠀⠀⠀⡩⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⢂⠐⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠊⠀⠀⠀⠀⣀⠠⠔⠁⠀⠀⠀⠀⠒⠒⠠⣄⠀⠀⠤⠯⠑⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⣀⠈⠠⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢨⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠁⠁⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⠀⠁⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠬⠄⡂⠨⠄⠀⢅⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠂⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢎⢁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⢀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡡⠝⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁⠉⠉⠉⠀⠀⠀⠈⠁⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣶⣴⣶⣶⣷⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣸⣿⡿⣿⡿⢿⣿⣿⣿⣏⣉⡿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢋⡴⣽⡿⠃⠹⠁⠀⠉⠙⠋⠈⠉⠋⠀⠈⠓⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢃⠎⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡎⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⢸⡇⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣸⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⡏⢸⣿⡁⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠱⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢈⣿⡿⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⠁⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⡆⠀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣷⣄⡀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⣧⣿⠁⣦⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⣿⠙⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠞⠉⠀⠀⢿⣿⠀⣿⣷⡄⠀⠉⠻⣷⣦⣀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠃⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣤⡀⠀⠀⠈⠇⠀⠰⢿⣿⣶⡄⠀⠀⠙⡿⢿⣷⣾⣿⣿⣿⣿⠟⠀⠌⠀⠹⣿⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⢰⡟⢿⣷⢎⠋⠠⠀⠠⠛⢿⣿⣿⣿⠃⢀⠀⢀⡄⢠⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⢠⣾⣿⣿⣻⣏⢷⡄⠀⠀⣾⠀⠈⠉⣹⠆⡏⠀⣼⠃⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠙⢮⣧⠀⠀⠹⠀⠀⠀⢿⡀⣷⠒⣿⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⢠⡄⢻⣿⣿⡨⢣⡌⢻⡄⠀⢶⡄⠀⠀⢸⣇⠇⠀⣷⢰⣿⡟⢿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢀⠿⣟⠂⠙⢿⣇⠘⡇⠀⣿⠀⢸⢧⠀⢀⣿⣿⣄⣾⣸⠘⣿⠁⠋⣾⡇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣼⢶⡈⠃⠀⠀⠉⠀⠋⠀⢸⠀⣾⠀⠀⣼⣿⣿⣿⣿⡉⠀⠉⣈⣰⠈⣧⠀⠀⣜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⢀⣀⠀⢠⡾⢀⡏⠘⣧⣿⣿⣿⣿⣿⡁⠀⠀⢻⣷⡇⠁⠾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⡇⠘⠃⣼⡇⣾⣿⢿⣿⡟⣿⣟⠁⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠘⠁⠀⠐⣿⣿⣿⡎⢸⣿⣿⣿⡿⠃⠀⢀⠀⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠸⣿⣿⡿⠃⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠄⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄

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

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣯⣭⣟⠲⢤⣤⣶⡿⠿⡇⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣭⣽⡓⠦⣤⣴⣾⠿⠷⠀⣤⣀
⠀⠀⠀⠀⠀⠀⢸⢹⠸⠋⠛⢿⣷⡄⠀⠀⠀⠉⠙⢿⡌⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇⠟⠙⠻⣿⣦⠀⠀⠀⠈⠉⠻⣦⠻⠁
⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⢻⣿⣄⡀⢀⣀⣠⣤⣭⣖⠒⠶⣦⡄⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠙⣿⣧⣀⠀⣀⣀⣤⣬⣷⡒⠲⢶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣓⠢⠀⢉⣟⠛⠉⡁⠀⠈⢻⣿⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠄⠈⣹⡛⠋⢉⠀⠀⠙⣿⡇⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⢸⡟⣧⡀⢸⣦⡀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠀⠀⣿⢳⣄⠈⣷⣄⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠈⢻⣷⣿⡿⣶⣤⣦⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠹⣷⣾⣿⢷⣦⣶⡴⠞
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢴⣿⡷⠈⣦⡀⣿⡏⡗⠀⢙⠎⣷⠀⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⣾⣿⠆⢱⣄⢸⣿⢹⠀⠈⡓⢹⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⢸⣷⠏⢀⣤⣶⠟⣰⠏⣰⡟⠀⠀⠀⠀⠀⠀⠳⠄⠀⠀⠀⠀⠀⠀⣿⡾⠁⣠⣴⡿⢃⡟⢡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣔⣿⣿⡏⠸⢡⡾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣾⣿⣿⠁⠏⣴⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡏⠙⢿⣮⡻⣄⢻⡅⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⠙⢻⣷⣝⢦⡘⣯⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⣿⡇⠀⠈⣿⠋⣿⡆⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⢸⣯⠀⠀⢹⡏⢹⣷⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠉⠛⢦⣔⠁⣠⣾⣿⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡈⠙⠳⣤⡋⢀⣼⣿⡂⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⢠⡞⣫⠊⠁⢺⣿⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⡴⢛⡖⠉⠐⣿⣿⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠉⠳⡇⠀⠀⡀⠉⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡏⠛⢾⡀⠀⢀⠈⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢧⠀⢻⣆⠀⠓⢄⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⢻⡀⠘⣷⡀⠘⠢⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠈⣠⠞⠃⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢡⠴⠛⠀⠀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⡴⠚⠛⠛⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⢀⠀⠀⠈⠉⠙⢧⠀⣀⡀⣠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠙⠁⠀⠈⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠸⠅⠘⠀⠀⠁⠀⢀⠀⠀⠉⠆⠀⠀⠀⢤⠀⠀⠘⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⣤⣃⡀⠀⠤⠊⠀⠀⠀⢠
⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠉⠉⠙⠛⠿⠿⢯⣭⣍⣉⡉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠲⠶⠶⠦⠤⣤⣥⣤⣦⣤⣀⣀⣀⣀⠀⣀⠀⠀⠀⠐⢶⢺⡇⠀⠀⠐⠠⣄⠀⠀⠀⠁⠈⣂⢀⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠹⣏⡙⠂⠂⠀⣸⠘⣧⡄⢀⠀⠀⠀⡄⠀⠀⠀⠀⢻⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⣤⠶⠃⠀⢸⡀⠈⠀⠉⠈⠀⠀⠁⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠷⣤⣄⣤⡼⠋⠁

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

⠀⠀⠀⠀⠀⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀
⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣄
⠀⠀⣼⣿⣿⠁⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣟⢿⣿⣧⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⠉⠉⠉⢻⣿⡆
⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⢻⠏⠘⣿⣿⡆⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⣿⣿
⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⢠⣿⣿⡇⠻⠟⠁⠏⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠠⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠻⣇⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠘⠉⠷⠀⠀⠀⠀⠀⠀⣼⠷⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠈⠆⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠀⠀⠀⠀⢨⡏
⠀⠀⠀⠀⠀⣠⣴⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠞⢳⣦
⠀⠀⠀⣠⣾⡿⠟⠛⠛⠻⠿⣷⡀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡆
⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣦⣄⡀⠀⠀⢀⡾⠟⠃
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣴⣿⣿⣿⡏⠘⢿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⢠⣿⠿⠿⠿⠿⠿⠿⢿⡄
⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⣸⣿⣿⡛⠇⠀⠈⠻⢿⣿⣿⣿⣿⣏⠉⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠟⣿⣿⣇⠀⠀⠀⠀⠀⠉⢻⣿⣿⡿⠃⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠘⢣⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⡿⣿⡉⠀⠀⠀⠀⠀⠀⣾⠿⠃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⡀
⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣆
⠀⠀⣠⣾⣿⣿⠹⣿⣿⣿⣿⡟⣿⣿⣇⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟⠉⠉⣿⣿⡄⠀⠀⢀⣾⣿⣿⣿⠀⢹⣿⡟⣿⣿⣿⣿⡆
⠀⠀⢸⣿⣿⡏⠀⠻⣿⡇⠸⠁⢹⣿⡟⠀⠀⠀⣿⣿⡿⡏⢻⣿⠁⠀⠀⢸⣿⣇⠀⠀⠊⣿⣿⣿⠙⠀⠀⡟⠀⠘⣿⣿⣿⠁
⠀⠀⠀⢿⣿⡇⠀⠀⠘⠀⠀⢀⣿⡏⠃⠀⠀⠀⢹⣿⡇⠉⠀⠛⠀⠀⠀⢸⣿⠏⠀⠀⠀⠟⣿⣯⠀⠀⠀⠀⠀⠀⢹⣿⡿
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⣞

⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⣤⣀⡀⠀⢀⣠⠴⠶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠙⣿⣷⠋⠀⠀⠀⠀⠀⠀⠉⣧⣀⣤⠤⣤⣀
⠀⠀⠀⢀⣤⣶⣿⠀⠀⠀⠀⠀⠀⣀⣿⠁⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⢙⣦⡤⠖⠒⠲⢤⣀
⠀⠀⡴⠁⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠈⢧
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡴⠟⠋⠉⠉⠙⠲⢤⡀
⠀⠸⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠁⠀⠙⠂⠀⢠⠴⡄⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀
⢀⣴⠿⠦⠀⠀⠀⠀⠈⠛⠶⠶⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠰⠟⠀⢠⣤⠀⠁⠀⠈⠙⠲⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠉⠳⣄
⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠬⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⣧⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠈⢳⠀⣰⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠹⣄⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⢀⠀⠀⠀⠀⠈⡇⠙⠶⢶⣄⣀⣀⣀⡠⠇⠀⠀⠀⡞⠀⠀⠀⠀⠀⠙⠷⠆⠀⠀⠀⠀⠀⠀⠀⡤⠖⠲⢾⡁
⠀⠈⣳⡶⠶⠆⠀⠀⠀⠀⠀⠀⠀⠘⣷⣤⣀⣠⣼⠃⠀⠀⠀⠘⣯⠉⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠘⠧⠀⠀⠀⠙⡆
⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⢸⡽⠀⢀⣀⣀⡀⠀⠀⠉⠳⠶⠤⠶⠀⢀⣀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠠⣄
⠀⢻⡀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠁⠀⠀⠀⠀⠙⣆⠀⠀⠀⠸⠋⠀⠀⠀⠈⠙⠻⣟⡛⢶⣶⣤⣤⣤⣄⣀⣉⣛⠛⠛⠁⠀⠀⠀⠀⢀⣀⣤⠖⠋⠀⠀⠀⣸
⠀⠀⠓⢄⣀⣀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⢀⡖⠀⠀⠀⠀⠀⠉⠲⣍⡛⠿⣿⣿⣿⣾⣭⣭⣭⣉⣛⠛⠛⠛⠿⢿⠧⠤⣤⣄⠤⠴⠋
⠀⠀⠀⠀⡾⠛⠉⠙⢿⡀⠀⠀⠀⠰⣄⣀⣀⣠⠋⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠙⡄⠀⠀⠙⢦⡈⠙⠲⣍⡻⢿⣶⣤⣍⣙⣿⡶⠶⠯⠄⣀⣀
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠙⢦⡀⢠⡝⠳⢮⣙⠳⢯⣿⠲⠤⣄⡀⠀⠉⠉
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢀⣀⣀⣠⠏⠀⠀⠀⠀⠀⠀⠙⣾⠷⠤⠤⠽⠻⢯⡀⠉⠒⠦⣍⡃
⠀⠀⠀⠀⠀⢹⣦⣄⣀⡀⠀⠀⠀⠘⢶⣤⣤⣀⣠⣤⠶⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠙⢶⣦⠤⠤⠖⠋⠉⠳⡄⠀⠀⠀⠀⠉⠲⣄⠀⠀⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠻⣇⠈⠁⠀⠀⠀⠀⣠⠟⠉⠉⠁⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠚⠙⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⣸⣿⠦⢄⣀⣀⣀⣠⡤⠞⠁⡞⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠶⠾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠐⠖⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠁⢀⡸⠀⠀⠀⠀⣠⠚⠉⠉⠈⠲⡀⠀⠀⣀⡀⣀
⠀⠀⢀⡀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠠⠄⠐⠉⠀⠀⢀⡸⠀⢠⠊⠉⣁⠠⢤⡀⠀⠈⠁⠉⣷⠀⠀⠀⠗⠠⡀
⠀⠈⠉⠀⠀⠀⠒⠠⠍⡑⠂⠄⣀⠀⠀⠀⠀⠀⠁⠐⠒⠒⠒⠂⢮⣀⣀⠜⠁⠀⢸⠀⠀⠓⠀⠀⡱⠀⠀⠀⠴⠋⢀⣀⠀⠀⠤⠘⠢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⢀⠉⠒⠤⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⢀⠀⢀⡀⠀⢣⡀⡀⠠⠐⠁⠀⠤⠄⠀⠀⠉⡸⠀⠀⠐⠁⢢⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠬⡐⠀⠀⢀⢀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⣀⠀⠀⠈⠉⠁⠠⢀⣤⡤⠴⢧⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠒⠢⠤⢠⣀⣁⡀⠒⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣒⡒⠢⠭⡂⢄⡀⠀⠀⢠⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠢⡀⠀⠀⠀⠀⠉⠉⠉⠑⠒⠒⠂⠤⠤⠤⠤⣀⠀⢁⣹⡀⡀⠈⡆⠈⠉⠉⠁⠀⠀⠀⠀⠀⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣌⠲⢄⡀⢀⠤⠤⠤⣀⡀⠀⠀⢠⡄⠀⠀⠀⡹⠉⠈⠦⠤⠔⠁⢠⣀⠀⠀⠈⡧⠤⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⢬⠉⠒⠀⠀⠠⢿⠀⠀⠈⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⡦⠄⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⣆⠀⢀⡤⠤⠚⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠲⠄⠠⠴⠆⢀⠠⠔⠁⠈⠁







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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣾⣿⣿⣿⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⢿⣟⣛⣛⣛⣛⠾⠿⣽⣂⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣾⣯⣭⣭⣭⣭⣿⣛⡷⣶⣍⡛⢦⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⣭⣍⣙⡻⠿⣿⣶⣍⠻⢦⡙⢦⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠦⠄⠀⠉⠛⠿⣿⣷⣬⢻⣿⣆⢦⠙⠂⠳⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⣦⡙⢿⣿⣿⣿⡞⣷⡱⡄⡉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⠹⣿⣿⡇⢹⣧⢹⡼⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣻⡄⣿⣿⡇⣾⣿⡄⣿⣿⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢸⡿⢡⣿⣿⢡⣿⡿⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣡⣿⣿⢏⣾⡿⢡⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⣳⣿⠋⣠⠟⣡⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢏⣼⢟⡅⢈⡵⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⣾⣏⣾⠁⣾⢣⠇⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⡘⣿⣾⣿⡈⠀⢈⢅⡶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⢷⣅⠙⣿⣿⣧⡈⢂⣾⣞⣣⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠳⣜⢿⡌⠻⣷⣦⡙⢿⣿⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠲⠀⣹⣷⣌⡀⠢⢝⡻⣦⠹⣆⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢩⣨⡾⢟⣿⣷⡜⠿⣻⢨⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣶⠿⠿⠛⠀⠈⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠀⠀⠀⠀⠀⠈⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣻⡍⢛⣀⢀⣀⠀⡀⡀⣠⢄⡀⡀⠀⢀⣀⠀⣀⡀⣀⡰⠂⠀⢠⠆⣀⡀⢀⢀⣴⡃⡠⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠚⠹⠗⠋⠻⠚⠛⠓⠇⢛⡿⠀⠀⠋⠻⠚⠻⠛⠛⠇⠀⢰⡷⠛⠻⠒⠞⠚⠻⠙⠗⠻⠛⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠚⠛⠓⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠏⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣀⣀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠈
⠀⢀⡟⠁⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣊⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠒⠈⠉⠉⠉⠙⠒⠢⣄
⢠⠟⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠄⠈⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠈⢳⡆⠀⠀⠐⠒⠉⠉⠉⠀⠀⠀⠀⠐⠒⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠸⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠄⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠏
⠀⠀⠉⠒⢲⡶⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⡀⠀⠀⠉⠉⠒⠒⠦⢤⣀⣀⠀⠀⠀⠀⠀⠐⠻⣍⠉
⠀⠀⠀⠀⠈⠓⠤⣀⣀⠀⠄⠀⠀⢀⡴⠒⠲⣌⠢⠀⠀⠑⠲⢄⡀⠀⠀⠀⠉⠁⠀⠀⠀⣀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢄⣀⡼⠀⠀⠀⠀⠀⢀⣈⠑⠄⠀⠀⠐⠒⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢯⠈⣹⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠡⣉⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⡶⣚⠋⠁⢀⣀⠀⠀⠀⡀⠈⠓⠈⢻⡄⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣨⠞⢉⠔⡹⡡⠋⠀⠀⠀⢲⡅⠀⠁⠀⠀⢇⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡁⠀⠀⡘⠰⡇⣴⠀⠀⠀⠊⡇⢠⠀⠀⠀⠈⠀⣰⡔⠛⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⢉⢸⠁⠀⠀⡃⠀⢻⡈⠀⢀⡀⣄⠱⡘⣆⠀⠀⠐⠊⢁⣀⡀⠁⣽⠀⠀⠈⢠
⠀⠀⠀⠀⠀⠀⡤⠂⡟⠀⠀⠀⠈⡌⠀⠳⡄⠉⠓⢤⣽⣦⠈⣍⢸⠂⢀⠨⣓⠦⠔⠚⣉⡤⠶⢦⣿⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⡎⠀⠈⡀⠀⣠⠤⠚⠁⠀⡀⠸⠢⠈⢢⠀⠈⢢⣸⠏⡀⠀⠐⠢⢀⣉⠉⠁⠄⠀⢸⢿⠠⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⣸⠞⠁⢀⣀⡤⠞⠁⠀⠀⠇⠠⠀⠀⠘⢞⠄⠀⠀⠁⠀⠀⠈⠁⠁⠀⢀⢾⠀⠀⠀⠑⡇⣷⠁
⠀⠀⠀⠀⢀⠼⡖⢻⣿⡤⠤⠴⠂⠀⠀⠀⠀⢀⢇⠆⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢤⣹⡧⠐⠀⠘⡇⠹⣄
⠀⠀⠀⠀⢆⠀⡹⢸⡗⠋⠉⠉⠉⠉⢁⣀⡤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠀⣳⠀⠀⠣⣀⠀⠉⠑⠒⢄
⠀⠀⠀⢀⡠⡿⢱⣏⠄⢀⡴⠟⢓⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠃⠀⠈⠀⠐⠢⣌⠋⠁⠁
⠀⠀⡴⠁⠀⠀⠨⣾⡀⡊⠀⡠⠋⠁⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠱⠀⢦⣀⠀⠱⡌⠀⣦⠀⣀
⠀⠈⠁⠀⠀⠀⠌⠈⡛⢇⢠⠁⠀⡞⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⣦⠙⢶⣠⣀⠀⣾⠀⠘⡀
⠀⠀⠇⡀⠀⠀⠀⣀⡀⠀⠎⢀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡄⠀⠻⣹⠀⡇⠀⡀
⠀⠀⡠⠶⠖⠛⣹⠃⠀⠀⠠⣈⠳⢤⡘⢦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡏⠀⠀⠀⠀⡟⠓⢌⠀⠐⠄
⠀⠠⠀⠀⠀⠀⢇⡀⠀⠒⢤⠀⠀⠀⢹⢨⡏⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠘⡅⠂⠀⠀⠀⠹⣦⠀⢳⡴
⠀⠀⠑⠈⡆⠀⠀⠉⢳⠀⠀⡃⠀⠄⡵⡿⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⠛⠂⠂⠀⢠⡴⣹⡗⡿
⠀⣀⣀⡴⡟⠐⠀⠃⣸⢃⠴⠁⠠⠀⠼⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢴⣯⠞⠁⠀⢀⢠⠗⠉⣴⠃⠀⠁
⠀⠀⠈⡂⢰⠋⠀⠀⢰⡃⠀⠀⠀⡀⠣⣀⣈⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⠏⠁⢁⠀⠀⠜⠀⢀⡀⠣⡀⠤
⠀⠀⠀⠐⠨⠀⢀⡀⠈⠓⠀⡀⠘⡧⢀⠀⠈⠙⠄⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠸⠀⡐⠋⠁⢀⡴⠗⠛⠁⣄
⠀⠀⠀⠀⠀⡈⠘⠣⡴⢂⡴⠡⠊⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⢄⢰⡘⠄⠀⠀⠙⠢⠁⠠⡈
⠀⠀⠀⠀⠀⠦⣄⠀⠀⢯⠀⠀⠀⣄⠀⡊⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢌⡼⠁⠢⡘⡄⠀⠀⢘⡼⠁
⠀⠀⠀⠀⠀⠀⠸⠀⠠⠈⠛⠲⣄⢳⠂⢣⣀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠖⠉⠀⣀⣤⣾⠃⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢀⡾⠁⠀⠀⠈⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢇⠀⠀⢎⡴⠛⠁⢀⠴⠋⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠠⠀⡏⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⠀⢿⠀⠀⠘⠁⠀⠀⠈
⠀⠄⠀⠀⠀⠀⠀⠀⡡⠄⠈⠣⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠘⡆
⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠆⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠒⠛⠋⠉⠉⠙⠛⠓⠲⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠴⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣴⣤
⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠀⠈⣿⣇
⠒⠛⠉⠉⠙⠓⠒⠚⠉⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠟⠛⠛⠉⠀⠀⣧⣭
⠒⠚⠋⠉⠛⠒⠒⠚⠋⠁⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧
⠶⠖⠛⠛⠓⠲⠶⠖⠛⠃⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⡷⠀⠀⠀⣼⣵⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣤⠤⠤⠤⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉⠁⠀⠀⠀⠀⣰⣿⡷⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⢤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠳⡄⠀⠀⠀⠀⠀⠀⢰⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⣄⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠈⣧⠀⠀⠀⠘⢷⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣾⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳⣦⡀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠉⣽⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠈⠳⣄⠀⠀⠀⠀⢀⡞⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠉⠳⠦⠴⠖⣫⣼⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠘⠉⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣠⡾
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣻⣶⣶⣾⣋⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠛⠛⠛⠛⠛⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⠋⡎⠀⠀⠉⠁⠀⠹⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠜⠁⠀⠀⠀⠀⠀⠁⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⣩⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢰⣿⣿⣿⡿⢡⠇
⠀⠀⠀⠀⠀⠀⢀⣼⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠸⠿⣿⣿⠇⠈⠣
⠀⠀⠀⠀⠐⠒⠋⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢹⡿⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⠇
⠈⠲⠶⣶⣾⣿⣿⣿⣿⣿⠿⠿⢛⣿⠟⠃⠸⣿⣇⠈⢟⢿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⠏⣿⣿⠀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⠀⠀⠀⠙⢿⣆⠀⠀⠉⠻⠿⣿⣿⠿⠋⠀⣿⣿⣿⠀⠘⢿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠘







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⢀⠀⠀⠀⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢠⣦⣄⣀⣀⣀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣦⡄⠀⠀⠀⢸⣿⣿⡟⠛⠻⣿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠈⠙⢿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡺⣿⣿⣿⠀⠀⠀⢸⣿⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢐⣕⢵⡦⠀⣿⣿⣿
⠀⠀⠸⠿⠟⠋⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣾⣿⡟⠀⠀⠀⢸⣿⣿⣇⣀⣤⣷⣤⣤⣤⣤⣀⡀⠀⠀⠀⠁⠁⠁⣠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣻⣿⣿⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠄⠀⢀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⣴⣿⣿⣶⢿⣿⣦⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢁⣰⣟⢩⣭⢿⣷⠋⣶⣾⣶⣶⣶⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠞⣁⣴⣿⡿⠛⡯⢚⣿⣿⣿⣟⣻⣻⠋⠁
⠀⠀⠀⠀⠀⠀⣠⣿⣰⣿⣿⣿⣿⣿⣶⣿⡿⣬⡟⠛⠛⠟⠛⠦⠐
⠀⠀⠀⡀⠀⠻⢱⠜⣿⣿⣿⣿⣿⡿⢿⠋⣽⠛⠓⠃
⠀⠀⠀⠸⠷⢸⣿⣼⣿⣿⣿⣿⡿⢶⠖⢛⡇
⠀⠀⠀⠀⠀⠹⠿⣿⡿⢿⡛⢿⡷⣬⣀⣿⡀
⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠈⠁⠀⠀⠈⢻⣷⡠⢀⣀⡀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠤⠄⠀⠀⠚⠛⠚⠻⠿⠶⠿⠿⠿⠷⠒⠂

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠒⠂⠈⠈⠉⠉⠉⠉⠁
⣥⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⡇⣿⣶⣶⣶⣤⣀⠀⢠⣾⣿⡇
⣿⣇⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⣤⣤⠀⠀⠀⠀⠀⠀⣌
⣿⣿⣿⣿⣿⣿⣿⣟⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣶⣤⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣹
⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⠿⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⢿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣷⣦⣤⣤⣤⣤⣤
⣿⣿⣁⣉⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠛⠙⠛⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⠖⠛⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⣝⣴⠶⠀⠐⠻⢷⡄⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠺⠀⠀⠀⢈⡔⢢⠀⡴⠋⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡤⠤⠼⣦⢸⠀⣧⡀⣨⠷⠒⠒⠀⠐⠂⠄⠀⠀⠠⠒⠋⠉⠉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠉⢹⠀⠀⠀⠈⠧⠤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠈⡳⢤⣀⡐⢄⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠁⠐⠒⠀⠐⠀⠀⠸⠤⠄⠀⠠⢏⠉⠉⠉⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠐⢶⣚⣠⣄⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅
⠀⠀⠀⠉⠀⠀⠀⠂⠈⠁⢈⢧⡀⠀⠀⠉⠀⠈⠙⠒⠦⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡶⠃⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠓⡤⣤⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⣠⠞⠳⢄⣀⠀⣀⣠⠴⠋⠳⣄⠀⠀⠀⣀⡴⠋

⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣀⣶⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⠟⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠻⣟⠁⠈⠙⠁⠀⠸⠟⠁⠀⠀⠀⠀⢻⣿⡏⠻⠿⣿⠙⣿⣿⡟⠀⠀⠀⠀⢸⣿⠋⠀⠀⠉⠉⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠀⠀⠙⠀⣿⡿⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⢠⣿⣿⣇
⠀⠀⠀⠀⠀⣤⣤⣶⣾⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢙⡗⠀⠀⠀⠀⠟⠃⠀⠀⠀⠀⠀⣾⣿⣿⣦⠀⠀⢰⣿⣿⣿⡿
⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠘⢿⣿⣿⡇
⠀⠀⠀⠀⣿⡿⢿⠟⢿⣿⡿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠹⣿⣿⡀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⢀⣴⣶⣾⣿⣷⣄⡀⠀⠀⠀⠀⠀⢸⣿⠻⠃⠀⠀⠀⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣯⠀⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠘⡿⣿⣿⠀⠀⠀⠘⣿⣿⡟
⠀⠀⠀⢠⣿⣿⠟⠉⠛⠛⠛⢿⣿⣇⠀⠀⠀⠀⠙⢿⣷⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠓⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠿⠿⠿⣿⣿⡅⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣾⣿⣷⣄⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠈⢿⣿⣿⡿⠁⠀⠈⠻⣿⣿⣿⠄⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⢠⣿⣿⡿⠿⠟⠙⢿⡇
⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠹⣿⠉⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⢻⠃⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠰⠛⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠛⠓⢤⣀⠀⠀⠀⠀⠀⠈⡦⠤⠤⠴⠶⠤⠴⠶⠶⠶⠶⠆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡞⠋⢿⣷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠻⠶⠞⣹⣄⠠⠠⠤⠴⣯⣭⣭⣭⣤⣤⣤⣤⣬⣥⣼⣇⣀⣀⣲⠶⣿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⢤⣀⣀⣈⣉⡑⠒⠚⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡷⢶⣶⣷⠏
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⡆⢘⢸⣿⠄
⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢠⠀⣧⣿⡄
⠀⠀⠀⠀⠀⠀⢸⠀⢀⠤⠖⢺⣷⡀⠲⣄⠀⠀⠀⢄⠘⢌⣇
⠀⠀⠀⠀⠀⠀⡞⠀⠌⠀⠀⠏⢁⡼⠉⠉⠻⢦⡀⠀⢹⢿⡇
⠀⠀⠀⠀⠀⣴⡆⢠⠀⠀⠈⠀⠈⡇⠀⠀⢠⠃⠑⡀⠘⡆⣿
⠀⠀⠀⢠⡾⡉⡆⠀⢧⠀⠰⣄⠀⣶⣤⡶⠋⠀⠀⠱⡄⠙⠛⣧
⠀⠀⠀⢸⠃⡷⠋⠀⠀⠳⢄⣈⣹⠛⠉⠀⠀⠀⠀⠀⠙⡄⠀⡏
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁

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

⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⣿⠀⠀⠀⠀⠀⠀⠘⢞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢧
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣇⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡇
⠠⠴⠐⠐⠚⠁⠉⠉⠉⠁⠉⠉⠁⠀⠐⠒⠀⠀⠤⠤⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠠⠠
⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠄⠀⠀⠀⠁⠈⠐⠀⠒⠒⠐⠂⠒⠒⠋⠉⢉⠅⠤
⠀⠀⠀⠀⠀⠀⢀⣀⠐⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠚⠚⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⣾⣷⣿⣟⣷⣾⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⢀⣀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠙⠿⠿⠿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠘⠋⠉⠉⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠀⠐⠷⠶⠓⠀⠀⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠎⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣯⠁⠀⠀⠀⠀⠀⠈⠀⢠⡏⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⢣⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣰⣿⣿⣿⣿⣷⣶⣶⣶⡞⠋⠉⢸⢸⠁⢸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣾⠀⢸⣿⡟⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠸⣿⠀⠈⣿⣿⡈⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢿⡆⠀⠸⣿⣧⠀⠙⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⡿⡀⠀⠘⣿⣧⡀⠀⠈⠛⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣇⢳⠀⠀⠈⢿⣷⡀⠀⠀⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⢸⠀⢃⠀⠀⠀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠈⡆⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠉⠉⠉⠑⠒⢄
⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠐⠒⠠⢄⠀⠀⠀⣀⠀⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠐⠀⠒⠒⢤⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⡀⠀⠄⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠂⠀⠀⢀⠀⠀⠀⠀⠀⣤⠎⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠁⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⣠⡼⠁
⡞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠁
⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⢧⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣾⡿⠉⠓⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡀
⠘⣆⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠈⢿⣅⡀⠀⠠⠀⠀⠅⠀⠒⠠⠄⠀⠀⠀⢀⡀⠀⡐⠁⠀⠀⠈⠑⠀⠀⠀⠐⠢⣀
⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⢄⠀⢌⠐⠀⢈⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠢⡈⠂⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠑⢄⡀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠁⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠄⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠤⠤⠐⠊

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠉⠑⣄⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⣀⡀⠠⠤⠐⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⣀⠤⠲⡄⠀⣀⡤⠴⠒⠋⠁
⠀⠀⡤⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠋⠉⠀⠀⠀⠸⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⡠⠚⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢳
⡇⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠔⠒⠒⠀⠉⠉⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⡀⠀⠀⢀⡼
⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠉⠒⠒⠉
⠈⠢⣀⢀⠀⠀⠀⠀⠀⡠⠤⠀⠐⠈⠁
⠀⠀⠀⠈⠑⢄⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⡠⡲⠯⢔⡒⠉⠉⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⣀⢆⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠱⢄⠼⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠄⠀⠀⠀⠀⠀⠀⢎⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠌⠀⣀⠤⠤⠤⡀⠀⠈⠑⢕⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠡⠁⢠⠎⠔⠉⠉⠲⡘⡀⠀⠀⠀⢣⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⣠⠃⡘⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⡆⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⡠⠔⠁⠀⠀⠀⠀⢁⠱⣄⠀⢀⠜⡠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⢀⣤⣶⣿⡭⠭⣭⣉⠙⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠈⠁⠀⢀⠄⣴⣿⠟⠋⠀⠀⠀⠀⠉⡳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⡾⣻⢋⡴⣊⡭⠽⠿⣶⣄⠙⣦⣙⠲⠤⡀⡀⢀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⢣⡞⢰⣧⢋⢞⣡⠴⠚⠛⠓⠾⣧⢞⣟⠻⣖⡒⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠀⢀⡔⠀⢠⢣⡏⠀⣿⣧⠾⣻⠕⠁⠀⠀⠀⠀⠘⢿⣎⢧⣈⠙⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⡁⠳⠦⠖⢋⠀⡠⢣⡟⢠⡞⣫⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠳⣝⢦⡀⠉⠻⢝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠀⠀⠀⠀⢀⠙⠦⠄⠚⣁⠔⢡⣿⢡⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⢧⡙⢦⣄⠀⠑⡝⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠐⠤⠀⠀⠁⠒⠂⠈⡠⢀⣾⢇⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠈⠳⣝⢦⡙⢷⡀⠈⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⣠⣾⡟⣼⣿⠛⠛⢷⣦⠀⠀⠀⠀⠠⡾⠟⠋⠉⠉⠉⠒⠤⠀⠀⠹⣎⠻⣦⡙⣆⢸⠁
⠀⠀⠀⠀⢠⠖⠲⣄⠀⠀⢠⠀⠀⠀⢀⡀⢀⣠⠾⢋⡿⣼⡏⢸⣤⣤⣤⣤⡀⠀⠀⠀⠀⢀⢥⣶⠾⢷⣶⡶⠂⠀⠀⠀⢹⣷⡈⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠈⢧⣀⠀⠀⠀⠀⠀⣠⣾⣿⠧⢬⣿⡟⠳⠟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣆⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣈⣙⣛⣿⣿⣿⡿⢱⠏⢠⠞⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡀⢸⡿⡇⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⡽⢟⣫⡾⠋⣰⢏⡴⢋⡴⢻⡇⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠋⠐⠁⣸⠁⡟⢸⡿
⠀⠀⠀⠈⠉⠉⠉⠀⣠⡴⠞⢋⡡⢖⡿⠋⢀⣼⣷⣫⠴⠋⠀⡠⣿⡀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢳⠞⢹⣴⡇⣸⠃
⠀⠀⠀⠀⠀⠲⠒⠋⠁⢠⠔⣩⠞⠉⣀⣴⠿⢟⡋⠕⣊⣴⠾⢋⠽⣷⠀⢀⣤⠬⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡇⢸⡟⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡴⣡⠞⣁⣴⣾⣭⠖⢉⣡⠴⠚⠉⢀⣠⡤⠚⡹⣧⠀⠠⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⢠⢠⣟⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡜⢰⡷⠋⣹⠏⢡⢋⡶⠛⠛⠿⠿⠿⣛⣩⡴⠛⠁⠘⣧⠀⠙⠓⠀⠀⠀⠀⠀⠀⢀⠤⣶⠟⠁⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⢰⠁⣿⠀⠀⣿⠀⡏⡾⠁⣠⣴⣶⠿⠟⠛⠉⠀⣠⣤⣶⠟⣧⡀⠀⠀⣀⣀⠤⠂⠀⠀⣼⠋⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⢸⠀⠹⣄⠈⣿⠀⣿⢇⣾⡿⠋⡠⠀⠀⣠⣴⣫⠵⠋⢁⡴⢈⡝⣩⢹⡇⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠈⣆⢀⠙⠳⣜⣧⣿⣸⡿⠁⡜⠁⢀⣼⠟⠋⣀⣤⠶⠋⣠⣾⢞⣿⢸⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣕⣀⠀⠈⠙⣿⡇⢠⡃⢀⡞⠁⣠⡾⠋⠁⡰⣼⡿⢡⠎⣾⢸⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⢿⡌⢧⢸⠀⢰⡟⠀⠀⣼⢡⣿⠁⡎⣼⣿⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⣿⡀⢸⡇⠀⠀⡇⡼⣿⣸⠀⡇⢿⣇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣿⣦⡀⢳⣧⠹⣿⣆⢻⡘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⣍⡓⠽⢿⣦⣕⣄⡉⠛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠉⠙⠛⠓⠂⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡿⣿⠿⡿⡿⢿⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣧⢠⠣⣧⣥⣤⣥⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣺⣏⣾⣻⣛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⢛⢛⠛⠛⠛⠛⢛⡛⡛⠛⠛⠛⠛⠛⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠤⠀⠀⠀⠀⠸⠤⠜⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡴⢚⠭⠕⠒⠂⠭⣙⢦⡄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⡞⡔⠁⡔⠒⡄⠀⢀⣀⠱⡙⣆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣼⢰⢀⣀⣀⣒⣁⣀⣋⣀⠇⢱⢹⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⡸⡔⠒⠂⠀⠒⠠⡀⠀⠀⡘⣸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⢧⡑⢄⠀⠀⠓⠔⠁⢀⠔⣱⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⠦⣭⣒⣒⣒⣪⡵⠚⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣀⣀⣀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠈⠁⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣲⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣼⣿⣷⡼⣿⣿⣿⣿⡿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠰⣿⣿⣿⣿⠷⠛⣉⢉⣝⠻⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠿⠻⣭⣤⣶⣾⣿⣿⣿⣿⣶⣭⣗⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣤⣀⠻⣿⣿⡟⠁⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣷⣙⢿⣿⣄⠀⠴⠾⠿⠿⢿⡿⠟⣽⡿⣿⣿⣿⣿⣿⣿⣇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣷⣍⠿⡿⠟⠀⠀⠀⣠⠖⠛⠷⡶⠤⠾⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢛⣿⣿⣿⣿⣿⣅⣀⡄⣤⣾⣼⡇⢾⣧⠐⣷⣦⣐⣿⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢿⣿⣿⡿⢿⣿⣿⣿⣧⣿⣿⣷⡻⣮⢻⣷⣬⡻⢿⣿⣿⡿⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠽⢿⣿⣿⣝⣿⣿⣿⣿⣧⠻⣷⣝⢿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⣈⣿⣿⣬⣿⣿⢿⣷⣌⡻⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠿⣿⣿⣿⣿⣿⣷⣭⣛⠿⠷⢿⣿⣿⣿⣿⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⢛⣿⣿⣿⡿⠿⣛⣻⣿⣿⣿⣭⣥⣴⣶⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣾⣿⣿⣇⣿⠸⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢿⡟⠟⠻⣿⣿⣿⣧⣻⣿⣿⣿⣬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣬⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠿⣷⣾⣿⣥⣼⣿⣿⡟⠉⣃⡀⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⢟⣧⣾⣿⣿⣿⣿⣿⣿⠟⣡⣾⣿⣷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⣆⠘⢿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⢠⣿⣿⡟⢻⢸⣿⡆⠹⣿⡿⣿⢻⣿⠿⣿⡇⢹⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢼⣿⣿⣇⢸⡄⡿⠃⢸⣿⠓⣿⠸⣿⠇⣿⣇⢸⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆⢸⡇⠁⢸⡇⠀⠀⠸⣿⠀⣿⡇⠉⠀⠉⠁⢸⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⣇⠀⠀⠀⠸⠀⣿⣷⠀⠀⠀⠀⢸⣿⠀⣿⣿⡄⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⢸⣿⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⢸⣿⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣛⣛⣛⣛⣉⣛⣻⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣹⣯⣭⣽⣿⣿⣿⣍⣩⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠰⡄⠀⠀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠠⠦⠠⠀⠈⠚⠀⠮⢗⠀⠀⠀⠀⠀⠐⢋⠄⠪⡇⠀⡀
⠀⠀⠀⠀⠀⠀⡀⢀⡈⢠⠀⠀⠀⠀⠀⠀⠀⡠⡈⠈⠀⣠⡀⠀⠀⠀⢔⡖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡪⠇
⠀⠀⠀⠀⠀⠈⠁⠙⠑⠊⠀⠀⠀⠀⡀⡀⠀⠙⠓⠁⠀⠩⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠇⠰⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠨⠆⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠗⠰⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠧⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⣀⡀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠁⠶⠄⠀⠆⠀⠀⠀⠐⣅⠹⠍⡆
⠀⠀⠐⣃⡀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡇⠐⠓⠔⡄
⠀⠈⢂⠘⢁⡂⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢀⠉⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠪⠂⠟⠆⠉
⠀⠐⠑⠃⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠀⠔⠁