Fruit basket Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡂⠄⠄⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠑⠀⠀⠀⠀⠀⠀⠈⠰⣱⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣀⠀⠀⠀⠈⠯⠍⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠐⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⡀⠠⠤⠔⠂⠌⢉⣀⡹⠟⠁⠐⠂⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣟⠃⠈⢈⣀⣠⣤⣤⡴⠖⠊⠉⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠈⡀⢀⡎⠠⠽⠀⠋⠙⡿⠀⠀⠀⠀⠀⠠⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⠀⠀⢀⠀⡇⠀⣼⠀⠡⠀⢾⠀⠀⣷⠒⠂⠚⠛⠺⠋⠀⠀⠀⠀⠀⠀⠀⢀⣆⡠⠀⠀⠀⢀⠀⢑
⠀⠀⠀⠠⡚⡇⢢⠀⠘⠄⠀⠀⠀⠑⠀⠈⢀⡀⠀⠀⠀⠈⠒⠤⠀⠀⠀⠀⠀⢸⡁⠀⡀⡀⠀⡠⢀⡏
⠀⠀⠀⣿⠥⣇⠀⠉⠀⡈⠀⠠⡀⠀⠀⠀⠈⠂⠀⡀⠀⠀⡘⠄⠀⠀⡀⠦⢀⣾⡉⢃⡰⠄⠠⠐⠈⠁
⠀⠀⠀⠈⡀⠈⢑⠤⢀⣈⠠⠀⠈⠐⠄⠀⠀⢀⠀⢀⡠⢤⡄⠀⣀⣴⠖⠙⠓⣼⣁⡌⠁⠨
⠀⠀⠀⠀⠈⢶⡄⢀⡡⠀⠋⠻⢴⠒⠉⠀⠀⠀⣎⠀⢰⡂⠂⠀⡿⠄⠀⣿⠀⠀⠀⠄⠀⠸⠀⠀⠆
⠀⠀⠀⠀⠀⠈⢷⡸⡅⠈⠀⢤⡅⠁⠀⠐⡮⠀⠀⠰⣇⠀⠉⠀⡇⠀⠀⢹⠀⠀⠀⠄⠀⠠⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠣⡹⡀⠀⠈⢷⠀⠀⠀⢰⠀⠀⠀⢻⠀⠀⠀⣳⠀⠀⢸⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠄⠀⠸⡅⠀⠀⠈⡆⠀⠀⠸⡇⠀⠀⠻⠄⠀⢸⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⡄⠠⢽⣤⠀⠀⠳⡀⠀⠀⣷⠀⠀⠘⠄⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠤⢤⠂⠀⠁⠀⠀⠀⠀⠀⣠⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢉⣾⠃⠀⠀⠀⠀⣒⠲⢄⡁⠂⠀⠀⠀⠈⠸⣯⣶⣆⣴⢄⣄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⢠⣀⢀⡇⣿⡟⠀⠀⠀⠀⢈⡇⠀⠀⠙⠁⣤⡤⠀⠀⠀⠈⠻⠿⢿⣿⣿⣶⣰⠄⣀
⠀⠀⢀⡀⣤⡆⢾⣟⣛⣖⡻⣦⡵⣎⢷⣤⣤⣤⣤⠾⠷⣦⣤⣿⠈⠁⠀⠀⢀⣄⣆⣴⣾⣿⡿⣿⣾⣥⡞⣊
⠀⣠⣼⣹⢮⡟⣿⣟⣿⣟⢷⣏⣿⢹⡰⡭⠏⠁⣀⡀⠀⠈⢾⠿⣿⣤⡄⠀⠀⠈⠛⣿⣿⣿⡷⡿⣼⢿⣇⣷⣴⠀⠀⠀⣠
⢰⡟⢇⣿⢹⣧⣿⣦⣿⣿⣷⣯⡛⣾⢥⡅⣰⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣅⠀⣀⣾⣿⣿⣻⠿⠿⠛⠈⠉⣉⠡⠄⠀⢸⡟
⢰⣿⡾⣿⣯⡱⢯⣿⣼⣿⣻⣯⢵⣍⡶⣸⣿⣿⣿⡄⠀⠀⣀⣀⣼⣿⣿⠿⠛⠛⠋⠉⠀⠀⠀⠤⢖⡋⡡⠠⢀⣀⣴⠛
⢻⣾⡟⠷⣟⢿⣼⠹⢿⣿⣿⡿⠞⠉⣷⣿⣿⣿⣿⣶⣿⣷⣿⣯⣍⠁⠀⣀⣀⣠⣦⣄⣒⠲⠒⣒⣥⣴⣶⣾⣿⣿⢿⣷
⠀⣻⣽⣿⠋⠹⣿⣿⣦⣉⠀⢰⣿⣿⣿⣿⣿⣽⣭⣿⣿⣯⣿⣿⣛⣿⣿⣿⣟⣟⣻⣿⣿⡿⢿⣿⣿⣿⣛⣿⣿⣿⡟⠃
⠀⠀⠀⠉⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠿⠿⣿⢿⣦⢥⠲⠞⠯⢉⣿⣿⣿⣿⣯⣭⣽⣍⣟⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣛⣥⣼⣿⣯⣿⣖⣓⣐⣿⣿⣿⣿⣿⢧⣬⣚⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠙⠋⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠻⠔⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡻⠒⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠖⠛⠄⠳⡀⠀⠁⠀⢀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⣀⡤⠖⣃⠨⡍⠑⡺⢀⠣⡀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠛⠒⠃⠉⠐⠤⣀⡀⠁⠀⠀⠸⡄⠀⠀⢀⠦⡀⢀
⠀⠀⡴⠙⡂⠱⣄⠀⠈⠀⣀⣤⢁⠀⠳⡜⢦⡜⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡠⢤⡀⠀⣞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⡶⠒⠒⠃⠀⢠⢼⠀⠈⠩⠶
⠀⢸⠓⠚⡇⠀⠈⠉⠉⠉⠁⢸⢘⠀⠀⢡⢸⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣰⠗⠊⠉⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠒⢚⠂⠀⠀⠀⠰⢦
⠀⡿⠀⠀⠙⣄⠀⠀⠀⣠⠖⠛⠜⠓⢶⠛⠊⠉⠉⢳⡀⠀⣠⡤⠤⠤⠤⣼⠀⣯⣤⡴⠿⢤⣄⠀⠀⠀⠀⠀⠀⡤⠖⠛⠓⠦⣤⠟⠉⠙⠲⡜⢏⡀⠀⠺⠀⢀⠆
⠀⡇⠀⠀⠀⠈⠑⢦⣰⡁⠀⠀⠀⠀⢨⠀⠀⠀⠀⢠⠇⡜⠁⠀⠀⠀⠀⠈⠳⠟⠁⠀⠀⠀⠈⢳⡄⠀⢀⣠⠼⣅⣀⠔⠋⠐⡇⠀⢀⡀⠄⣿⠀⣩⠖⠒⠒⠓⢢
⠀⣧⠀⠀⢀⠀⠀⠀⠈⠙⠲⢤⣄⣀⣞⣤⣀⣀⣤⠾⠾⠀⠴⠖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢠⠋⠀⠀⠀⡇⠀⠀⠀⠑⡖⠁⠀⠀⠀⢻⠖⠂⠈⠉⢙⡁
⠀⠹⣄⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠼⡄⢠⠖⠋⠳⢄⣠⠖⠚⣇⠀⠀⣀⠤⣼⠀⠀⠀⠐⠽⡇
⠀⠀⠹⣆⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢻⠀⠀⠀⠀⡇⠀⠀⠈⠓⠎⠀⠀⠀⢣
⠀⠀⣠⣬⡷⠤⠤⠤⠤⣤⠴⠦⠤⠤⠤⠤⠤⠴⠶⠤⠤⠾⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠷⠴⠤⠶⠾⠶⠶⠶⠶⠷⠶⠦⠤⠴⠧⠤⠤⠤⠾⣄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠙⣟⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡟
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠹⣖⠒⠛⠛⠛⠛⠛⠛⠛⠃⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡿⠁
⠀⠀⠀⠀⠀⠈⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⣀⠚⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠉⠀⢀⡀⠐⠁⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡵⠊⠀⠀⠀⠙⠀⠑⠄
⠀⠀⠀⠀⣀⠔⠊⢉⡉⠁⠲⣄⠀⡌⠀⢀⡎⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂⡏⢀⣀⠀⠄⠠⡀⢀⣀⠈
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢈⠗⠋⠁⠀⢸⠏⠒⠄⡀⠀⠀⠀⠀⠔⠁⠉⠈⠁⠇⠀⢁⣦⠀⠝⠀⢀⢀⡃
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⠉⠀⠀⠀⠘⠄⢀⠠⠂⠀⠀⠀⠀⢃⠜⠙⣇⣀⠨⡧⢔⠉⠀⢀⠅
⠀⢠⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠘⠂⠎⠀⡠⢾⠀⢈⠈⢻⡠
⠀⠐⠤⢅⣀⢐⠒⠂⠀⠲⠤⠦⠀⠀⠀⣀⠀⠀⢀⣀⣼⡀⠀⠀⠀⠀⠀⠀⠀⣤⠒⠉⠋⠀⢠⠃⢫⠐⢷⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃⠀⠒⠂⠀⠤⠤⠀⠀⠀⠤⡤⡤⠄⠀⠀⠀⠤⠄⠐⢇⣠⠞⠂⡶⢇⠀⡠⢄⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⢂⠀⣠⠀⠀⡉⠈⢲
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠊⠀⢹⠢⠔⠑⢤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡔⡇⢀⡆⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⡘⠋⠘⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠺⠿⠶⠶⠶⠷⠶⠶⣶⣾⣿⣶⣶⣶⠾⠿⠶⠶⠶⠿⠷⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠄⠂⠁⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⡀⠀⠀⠐⢠⡀⠈⠑⡤⠀⠂⠀⠀⢀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢢⣲⡀⠀⢳⠀⠰⠁⡈⡀⠀⢾⡨⠄⠀⠂⠔⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣷⣄⠜⠃⠂⠀⠀⠛⠁⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⢀⡝⠯⢀⣀⠃⠘⠃⠀⠀⠉⠀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⢳⡆⠀⠀⠨⠁⠀⡃⠀⠀⠀⠼⠉⢉⠙⣦⠀⠀⠀⠀⡀⠀⠐⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢢⡈⠂⠤⣿⡼⠀⡁⠀⠀⠀⠀⠀⠀⢱⣼⡇⣀⠀⡰⠀⠀⣸⡿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠓⢤⠈⠒⠦⣀⡉⠐⠂⠀⠀⠀⢀⡆⢀⡜⠁⠀⣀⣳⣀⠈⠟⢉⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⢀⠀⠀⠠⢿⠨⡆⠀⠀⠀⠈⠉⠒⠒⠂⠤⠤⢤⢤⡤⠤⢤⡤⠤⣴⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠬⣶⡳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⡛⠿⢟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠌⣽⣟⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠈⢉⣿⣿⡟
⠀⠀⠀⠀⠀⠡⠔⠚⢆⢀⡀⠓⣤⣀⠘⢗⢌⣋⢿⣿⡷⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡞⠁⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢾⣁⠀⠈⠁⠉⠉⠀⠀⠀⠀⠈⣷⣂⠀⠀⢀⠀⣀⣀⣼⣽⣇⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⢀⣀⣼⠿⠛⠋⠉⠉⠁⠉⠁⠀⠀⠀⠙⠒⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⣠⢺⣏⠉⠙⣿⠋⠻⣷⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢫⢻⣶⣄⡀⠀⠀⢠⣿⣼⣿⠿⣾⣿⣷⣷⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣶⣿⢋⣭⠈⠉⢡⡌⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⡟⢀⡢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠈⠉⣻⠾⠛⢻⣿⣧⡆⠀⣠⣄⢤⡑⠲⡄⢻⣿⣿⣿⣿⣿⣿⣤⣼⣷⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⢰⠿⠹⠗⢰⣼⣿⣿⣿⣿⣿⣿⣿⣷⣖⣿⣾⣿⣿⣿⣿⣿⣿⠋⠀⠀⠉⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡆⠀⡄⢠⠠⣯⣿⣿⣿⣿⣿⡟⣿⡿⣿⠟⠿⢻⣿⣿⣿⡿⠋⡳⢦⣤⣤⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣷⣿⣾⣞⣿⣿⣯⣿⣿⣠⣿⣷⣷⢦⣼⣿⣧⢚⣿⣿⣥⣺⡶⣛⠿⣿⠿⡯⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣏⠀⠈⣿⣿⣿⡿⠉⠉⣿⠙⣿⠛⠉⠙⠙⡏⢻⡿⠟⠙⠛⠉⡇⠉⡟⠁⠁⠀⠘⠀⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠳⢹⣮⣿⣷⣦⡶⠿⣼⡿⠤⠀⠀⠸⠇⣸⠿⠄⠀⠀⠀⣃⡀⢃⣄⠀⣠⣴⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣶⠛⠃⢻⣿⣥⡀⣿⠃⠁⣀⡀⡘⡛⠋⠐⢀⡀⢠⣮⠛⠉⠲⡆⣰⠀⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡉⠹⢵⣖⣍⡹⠟⠛⢻⡄⠀⣹⠿⠗⢧⡀⠀⣈⠿⠿⢐⢀⣠⢀⠟⠛⢉⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣦⣽⠿⠻⡀⣀⡀⢈⣿⠶⠛⣀⠀⠺⠿⠦⢧⠀⢀⡐⠾⠿⢻⡆⣀⠘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠟⣿⣶⡀⠽⣿⡿⢏⢀⠀⠘⠿⠿⠼⣄⠀⣠⣿⡾⠧⠄⣀⢸⠿⠏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢿⣿⣿⣿⠿⣄⣬⡿⣷⣿⡻⠀⡐⣿⣴⡸⠁⠀⠰⣶⠟⠻⠀⠚⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⣬⣿⣿⣷⣾⣿⣈⣿⣦⣷⣿⠁⠀⢼⣾⣧⡁⣀⡷⠞⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣿⢿⣭⢤⡭⠆⠤⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠻⡜⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⣀⡠⠞⡽
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⢀⡤⠚⡡⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆
⠀⠀⠀⠀⠀⠀⠠⡟⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⡜⣳⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣠⠎⢀⠞⠁⠀⠀⡇⠀⣠⠄⣀⡔⠊⠑⡄⣰⣟
⠀⠀⠀⠀⠀⠀⠀⣷⣿⣴⡒⠒⠒⠢⢼⡁⠀⡼⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠁⣠⠋⠀⠀⠀⣸⢁⣞⠀⠀⢸⢧⣀⣠⡿⢻⡅⠉⠳⡄
⠀⠀⠀⠀⡠⠞⢉⡝⢻⠋⠉⠳⣄⠀⣀⣹⣦⡇⣏⣠⡤⢀⡀⠀⠀⠀⠀⢀⠞⢀⡜⠁⠀⠀⠀⢠⡟⠁⢉⡶⠒⠳⡏⠀⠀⣷⠀⠓⠤⣀⣹
⠀⠀⢀⡞⠁⠀⡼⠀⠘⡇⠀⠀⡼⠋⠀⠠⠴⣿⡷⠂⠀⠀⠈⢢⡀⠀⣰⠋⢠⠎⠀⠀⠀⠀⢠⠏⢳⠖⠘⢄⠀⢀⣿⠖⠚⢧
⠀⠀⣸⠀⠀⢰⠃⠀⠀⢷⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠞⠁⡰⠃⠀⠀⠀⠀⢠⣿⠴⣿⡀⠀⣼⠛⠛⢿⡀⢀⡼
⠀⠀⡿⠀⠀⢸⠀⠀⠀⠘⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⡜⠁⠀⠀⠀⠀⢠⣿⠁⠀⠈⣿⠁⠹⣀⢀⣾⡉⠁
⠀⡴⠿⣄⣀⣘⡆⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠎⠀⠀⠀⠀⠀⡰⠃⠘⢦⣤⣞⡹⠶⠒⠋⠉⣈⡟
⠀⠙⣤⣀⠀⠉⠉⠉⠛⠓⠒⠓⠒⠒⠒⠒⠒⠒⠀⠠⠤⠤⠴⠾⠷⠶⠖⠒⠒⠒⠚⠉⠉⠉⠉⠀⣀⣀⡤⠴⠒⠋⡏
⠀⠀⠘⡇⠉⠛⠒⠒⠶⠤⠤⠤⠤⠤⢀⣀⣀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠒⠒⠉⠉⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⢻⡀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣴⡀⠀⠀⢀⡔⠀⠀⢀⡟
⠀⠀⠀⠈⢧⠀⠀⠀⢳⡀⠀⢀⣸⣶⠋⠀⠀⠘⡄⢀⠴⠋⠙⣆⢀⡴⠋⠈⢧⡀⣠⠞⠀⠹⣄⣠⠋⠀⠀⠀⡾
⠀⠀⠀⠀⠘⢧⠀⠀⠀⢷⡞⠉⠀⠘⣆⠀⢀⡤⠻⡅⠀⠀⢀⡼⢯⠀⠀⠀⣠⠿⡅⠀⠀⣠⠞⢧⡀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠳⡀⠀⣀⡼⢶⠉⠀⠀⠘⣦⠞⠁⠀⠀⠳⣤⠞⠁⠀⠙⣦⡞⠁⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠿⣏⠁⠀⠈⠳⣀⡴⠊⠉⢣⡀⢀⡠⠞⠙⢦⡀⣠⠞⠉⠳⠄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠈⠀⠀⠀⠈⠙⠦⠀⠀⠀⠽⢯⠀⠀⠀⠀⠛⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣄⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣠⣤⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠠⠀⠀⠀⠀⠠⠄⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⢀⣀⡀⠠⠤⠤⠤⠄⣀⡀⠀⠀⠉⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⣀⠤⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢄⡀⠈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠎⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⡄
⠀⠀⠀⠀⠀⠀⡘⠀⡜⠀⠀⠀⠀⢸⠉⠒⢄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢡
⠀⠀⠀⠀⠀⢠⠃⢰⠁⠀⠀⠀⠀⠈⢆⠀⢄⡇⠀⠀⠀⠀⡆⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠀⠀⠀⠀⢃⠈⡄
⠀⠀⠀⠀⠀⠸⠀⡆⠀⠀⠀⠀⠀⠠⡆⠘⠻⣇⠀⣠⠖⠉⠋⠢⡀⢸⠀⠘⢄⠀⣀⢀⠛⡄⠠⡃⢀⠆⠀⠀⠀⠀⢸⠀⢃
⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠀⠀⢀⡤⡌⠁⠊⠁⢢⠃⠀⠀⡀⠀⢘⡀⠳⣀⢈⡞⡥⠊⠦⣸⣤⠽⠡⢄⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⢀⠀⡇⢀⡄⢤⠀⡎⠀⢸⢀⡠⠔⠊⠀⠀⠀⠀⠀⣨⠆⠒⠒⠻⠞⢤⡀⠀⢀⣈⣐⠒⢉⠜⡝⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠇⠀⠉⠢⣹⡇⢀⣦⠊⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠠⠈⢫⠁⠀⠀⠉⠪⣞⣒⣉⠽⢁⠀⡌
⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⡠⠜⠟⠃⢸⠀⠀⠀⠀⣀⠤⠄⠾⠠⠤⡀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠈⠑⡄⡌⢠⠃
⠀⠀⠀⠀⠀⠀⠘⡀⢣⠊⠀⠀⠀⠀⠈⡄⠀⡴⠋⠀⠀⠀⠀⠄⠀⠈⠳⡀⠀⠀⠀⠀⢠⠆⠀⠐⠀⡀⠂⠀⠀⠘⠁⡎
⠀⠀⠀⠀⠀⢠⠄⠳⠾⡐⠀⠂⠀⠢⢤⠘⠾⠂⠰⢤⠒⠢⠐⠚⠢⣔⠀⠳⠒⠂⠲⢤⠞⠰⠰⠦⣄⠀⠀⠤⡄⠐⠾⢄
⠀⠀⠀⠀⠀⠑⢤⠤⠄⠈⠑⢤⠀⠀⠀⠙⢤⠀⠀⠀⠙⢦⠀⠀⠀⠈⠑⢤⠀⠀⠀⠀⠱⡤⠀⠀⠈⠣⠄⠀⠈⠦⢤⠜
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠒⠚⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠰⢄⡠⠀⠀⠀⠀⠠⡀⢀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⠒⠃⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠠⣀⡠⠀⠀⠀⠀⠀⣄⣀⡄⠀⠀⠀⣄⠀⡀⠀⠀⠀⠀⠀⠑⠤⠖⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠈⠢⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⢀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⢀⣀⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠒⠂⠀⠀⠀⠀⠖⠒⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⣂⣭⣴⡾⠿⠿⠿⠿⠷⢷⣿⢕⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣵⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣩⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣦⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣩⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡬⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢆⡇⠀⠀⠀⠀⢈⡏⣥⣄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣍⣷⠀⠀⢾⡧⠟⠛⠋⢉⡷⠖⠈⢴⠀⠻⣿⣿⠿⣶⣢⡎⠀⠀⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣷⣷⣷⠖⠀⠀⢲⣼⠇⣀⣈⣀⠀⢠⡈⣾⣷⠾⠿⠿⣜⢂⡋⣶⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⣷⣿⠉⠛⡇⠀⠿⠂⢄⣵⠟⠋⠙⢻⣿⠾⠷⠛⠾⠷⢾⡀⠈⠉⠁⠈⣿⡽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣿⣿⠿⢇⣤⣷⣄⢀⡀⣸⣏⡣⣀⣀⣸⣷⣨⣄⣐⠀⢾⣇⣿⡶⢤⣶⠶⢟⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠌⣙⡓⠛⠶⠊⠶⠯⠽⠥⣯⣵⣯⣿⣭⣹⣿⣿⣫⣽⣦⣻⣿⣶⠶⣟⣚⠉⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠁⠐⠒⠀⠀⠀⠒⠂⠐⠀⠤⠬⣭⠛⠻⣽⣿⣻⢇⠈⣹⡧⢄⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠲⠴⣥⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠹⢿⣦⣤⣿⣷⡶⢦⣝⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠆⢶⣂⣀⣬⣭⣁⣀⣀⣀⣀⠒⣀⣘⣃⣀⣀⣀⣨⣤⠒⢛⡍⢾⣻⣿⣏⡥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡿⠮⠿⣏⡃⣛⣻⣦⣤⣭⣼⡿⠯⠽⠿⣭⣍⣩⣥⣟⠛⠙⣻⣿⡘⣿⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⡾⠇⢾⣟⣃⣚⣻⣦⣤⣴⣿⣿⠿⠽⢿⣿⣭⣤⣴⣟⠋⣙⣻⡶⠳⣿⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢿⡿⠽⢿⣉⣈⣩⣷⡤⢤⣾⡟⠿⠛⣻⣧⣤⣤⣾⣛⣃⣋⣿⠏⢾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢯⡍⣭⣷⡶⠲⢾⣿⣛⣛⣻⣶⡤⣴⣾⣽⣩⣽⠿⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠿⠿⠿⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⠦⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⢠⢠⠏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠙⢷⢄⢁⡿⢿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣎⠛⣾⣮⣧⠿⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢤⡂⠘⣿⡵⢋⡖⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⢿⢲⣿⠟⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⠁⠊⡙⣦⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢠⠎⠉⡆⠀⠀⠀⠀⠀⢀⣤⣾⣧⡿⡾⣻⣕⣇⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣀⠔⠁⡠⠃⠀⠀⠓⠀⠀⠐⠀⠀⣰⣄⣷⣦⠿⠿⢭⡵⢾⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠁⠀⠐⠁⠠⡀⠀⢄⡔⠀⠀⠀⣀⢿⡾⠿⠁⠀⠀⠀⣱⣿⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⣀⡀⠀⠀⠈⣆⠀⠀⠀⢐⣤⠁⠀⢀⠤⢄⠀⢠⠊⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⢦⢚⠈⣧⠄⡄⣆⠩⡵⠒⠐⠳⣌⣤⠆⠁⠠⠁⢀⣼⠇⠀⠀⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠹⢊⣸⡆⣏⠡⢸⡇⠀⡖⠀⢹⠃⢀⣠⠇⣰⡿⠁⠀⢀⠄⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⣎⠤⠆⢸⡡⠠⡇⠀⢀⡤⠚⠛⠙⠈⣛⢿⢀⣀⠔⡏⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⣟⠰⠛⣇⠀⠀⡇⠀⠀⡇⠀⠀⠙⠋⠀⢸⠋⠀⢀⠇⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢸⠀⠀⢫⠀⠀⠀⠀⢰⡇⠀⠀⡇⠀⠀⣸⠀⠀⢸⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⣆⡀⢰⠀⠀⡄⠀⢸⡇⠀⠀⡇⠀⠀⡇⣀⣀⠦⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠚⠓⠒⠚⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡝⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣰⣟⣁⣀⡀⠀⠀⠀⠀⢀⠴⢋⠞⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡀⣀⡀⠀⠀⡜⠁⠀⠀⠈⠙⠟⠂⠀⠀⠈⠱⡄⠀⣰⢣⢲⠁⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⣣⠀⠧⡄⠀⢸⠆⢚⣢⡜⠂⢶⣒⠢⣄⣀⠠⠤⠤⣄⡀⠀⡇⡰⢃⢀⠇⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⢰⠊⠉⠚⠉⣣⠔⠂⣈⣈⣈⣱⡞⣝⡡⠤⣽⣠⠋⠀⢀⡀⣴⠂⠀⠉⠙⢿⡡⢃⠎⠀⠀⠀⡀⠀⣸
⠀⠀⠀⢀⠤⡼⠊⠉⢱⠖⠣⢰⠋⠀⠀⠀⠠⠶⠗⠀⠀⠀⠈⢣⠀⠒⠉⠉⠁⠀⠀⠀⢘⡷⠋⠀⠀⠀⡰⠁⠀⡇
⠀⠀⠀⢏⡀⠓⢀⠄⠉⠉⢢⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⣀⠤⣓⠭⠊⠀⠀⠀⡴⠁⠀⣸⣇⣀
⠀⠀⠀⠀⣇⠀⠀⢳⡄⡠⠜⠛⣦⠤⠤⠤⣤⣀⣀⣀⣀⣀⣀⣀⣇⣀⣠⣚⣉⣴⣨⡤⠤⠤⣤⠴⠚⢒⠞⠉⠉⡆⣈⡷
⠀⠀⠀⠀⠈⠑⠒⡟⠒⢶⠴⠮⠤⣤⣤⣴⣊⣀⣀⣀⡴⠋⠁⢀⣀⣴⣉⣠⡤⢮⡤⠤⠤⠼⢤⠶⠒⠚⠒⠲⡋⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠣⣀⠞⠁⢄⡰⠊⢣⡠⠋⠑⢄⣀⠎⠘⠀⠀⠀⠀⠂⠑⢄⠀⡐⠁⠀⢄⠀⡐⠁⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠔⢇⡀⠐⢏⠀⡠⢮⠀⠀⠀⡠⠋⠀⠀⠀⠑⡔⠁⠀⠀⠀⡘⠁⠀⠀⠀⠜⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠜⠁⠀⣠⠟⠀⠀⢐⠴⠊⠙⢄⠀⠀⠀⠚⠠⡀⠀⡀⠈⠀⢀⣀⡠⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⠉⠢⣤⠴⢅⠀⠀⠀⢀⡕⠂⠀⠀⠀⣀⠾⢀⠀⠀⡠⠊⠑⢂⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣴⣈⠣⣀⠀⣁⢶⡂⠀⠈⠢⣤⠤⢎⠀⠀⢀⡽⠫⣀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⡉⠛⠛⠲⠶⠬⠶⠶⠮⠷⠶⠤⠴⠿⠛⠛⢋⡿
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠢⠤⠤⠤⠤⠤⠤⠶⠒⠒⠋⠁
⠐⠲⠫⠖⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢚⣽⡶⠴⠷⠶⠧⠮⠶⢵⣝⣔⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣭⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢵⡙⡢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣱⠝⠉⠀⠀⠀⢠⡾⣷⠒⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣬⠳⡄
⠀⠀⠀⠀⠀⠀⠀⡰⣣⡿⠁⠰⣶⠯⢶⢖⣚⡷⠟⠉⠉⠛⠙⠛⠓⠶⢤⣀⡀⠀⠀⠈⢆⡊⢆
⠀⠀⠀⠀⠀⠀⡼⢙⠝⠀⠀⠀⠹⠻⣦⣨⠏⠀⠀⣠⠄⢄⣀⠀⠀⠈⠐⠐⡝⢢⡀⡀⠀⠣⡆⢧
⠀⠀⠀⠀⠀⣸⣴⡟⠀⠀⢀⠤⠄⠐⠾⢧⡀⠀⠀⣘⣣⠔⠈⠉⢓⢒⠶⡤⢫⠬⣀⣈⠒⡀⢳⡆⢇
⠀⠀⠀⠀⢀⠗⡽⠀⢀⠔⠹⠃⠀⠀⠀⠀⠙⢆⣠⠿⠃⠀⢆⡼⠋⠉⠉⠉⠹⣔⣻⣜⡉⢉⡀⢇⡺⡀
⠀⠀⠀⠀⣈⡼⡇⠀⠘⠀⠀⣀⡠⠤⣤⣠⡶⣿⢿⠿⠛⠢⣾⠀⠀⠀⠀⠠⠚⠛⡧⠛⠿⠿⠢⣸⡇⡇
⠀⠀⠀⠀⣷⣽⠀⣀⢴⠶⠿⠣⡄⣠⢫⡿⠷⡿⠁⠀⣀⡠⡾⠶⡚⠛⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⣷⣼
⠀⠀⢀⠔⠓⠾⠶⠿⢇⡀⢀⣰⣴⣁⣿⣿⣿⠀⢠⣿⣿⡟⠀⠀⣳⠀⠀⣡⣀⣀⣀⣀⢀⡀⠠⠿⠷⠚⠢⡀
⠀⠀⠀⠓⡤⠤⣤⢄⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡠⣤⠤⢤⠚
⠀⠀⠀⠀⣧⣤⣤⢸⣀⣀⡀⠉⠉⡉⢸⠉⠉⠉⠉⠉⡏⠙⠉⠉⠉⠉⠉⡇⢉⠉⢁⣀⣀⣀⡀⣧⣤⢼
⠀⠀⠀⠀⡗⠂⠚⠛⠥⠭⠍⠉⡉⣳⢼⡟⣛⣛⣛⣛⣇⣚⣛⣛⣛⣛⣙⡏⡏⣉⠉⠭⠥⠼⠃⠓⠒⢺
⠀⠀⠀⠀⣻⠰⢶⣢⡤⡀⣄⡠⠤⣤⢀⠀⣀⣀⠀⢀⣀⣀⣀⣀⢀⡀⢀⣠⣤⣄⣠⣤⠤⢤⠶⠖⠒⣛
⠀⠀⠀⠀⢇⠈⢙⠀⠃⠐⠀⠒⠒⢻⢸⠏⠉⠭⠤⠤⡏⠹⠬⠭⠍⠭⠸⡇⡗⠒⠒⠒⠀⢸⠀⡋⣁⡸
⠀⠀⠀⠀⠘⡍⢹⣒⡟⠓⠒⠒⠶⢾⢸⡦⠶⠶⠶⠦⡧⢴⠶⠶⠶⠦⠴⡇⡷⠒⠒⠒⢛⣻⢲⡍⢩⠃
⠀⠀⠀⠀⠀⠱⠄⢀⣀⣀⣉⣉⠁⠉⠈⠁⠀⠀⠒⠀⠃⠘⠒⠂⠀⠀⠈⠁⠉⢉⣉⣀⣀⣀⡀⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠈⠳⡴⠖⠒⠒⠒⠤⣀⠀⠀⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣩⢃⡤⠐⠮⣁⠀⢩⢍⡂⠈⢳⠢⣱⣨⣑⡆⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⢡⠊⠀⢰⠀⡀⣤⢀⡵⠚⠒⠬⣕⠰⣾⢋⡀⠂⡑⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠡⡖⢢⣀⠀⢸⠀⠁⠘⡄⠈⠓⢦⡐⠁⡹⣷⠀⢳⡁⢀⠒⠈⠢⣈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠀⠀⢩⠾⢖⡀⠀⢱⠀⠀⠀⠙⢶⢁⢾⡠⠀⠹⣄⠠⠈⠠⠈⢳⡕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⣸⢵⡪⠦⠀⠈⢑⠒⠧⢤⣀⢀⠈⢫⠴⢣⢀⡐⠈⠑⢎⠀⠀⠂⠹⣎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡃⣨⠗⢢⠛⢐⠤⣄⠀⠀⡎⠖⣣⢼⠉⢙⣳⡛⢿⢱⢺⣢⣀⠐⢤⡄⢠⠈⢎⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣢⡇⢹⠤⡴⠉⡙⡌⠾⡚⠉⠵⢤⣏⣜⣝⢀⣶⣍⠬⠜⢚⠠⠀⠙⡄⠹⣄⠐⡈⢾
⠀⠀⠀⠀⠀⡀⡀⠀⠀⢀⠃⠌⠯⠄⣸⣤⣕⣧⡦⠂⠄⠄⠀⠀⠙⠄⡏⠘⠀⠀⠀⠀⠀⠄⣀⣹⣠⡸⠦⠴⠞
⠀⠀⠀⢠⠊⠉⡝⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣁⠉⠓⠀⠐⠒⠓⠀⠐⠋⠉⠉⠉⠁⠀⠀⡀⠀⠀⠂
⠀⠀⣠⠦⢀⣮⡀⠀⠀⠀⢳⠠⠦⢄⣀⣀⣠⠔⠛⢍⡜⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⣀⣁⣀⣤⠦⢴
⠀⠜⠁⠀⢸⠈⡜⢄⡀⠀⠸⠀⣰⡠⠔⠊⠀⡠⠂⢰⠉⡉⠋⠉⠉⠉⢉⠟⠋⠉⠉⠉⡉⠉⢄⠀⢀⠄⠀⠀⣸
⡄⠀⠀⠀⢸⡀⠈⠢⣈⡉⠉⠉⠁⠀⣀⠄⣊⡠⠔⠓⠺⣩⠃⠑⣀⠔⠁⠀⠀⠀⢀⠀⠀⠀⠀⢱⠆⠀⠀⠠⡇
⡇⠀⡀⠀⠘⣕⠄⡀⠀⠈⠉⠙⠛⠉⠉⠉⠀⣀⠠⠀⢠⠏⠀⡠⠊⢄⠀⠀⠀⡠⠊⠂⠀⠀⡠⠁⠀⠢⡐⢰⠁
⢣⠀⠐⢄⠀⠈⠑⠤⠬⠥⣀⣒⣀⣒⡂⠈⠁⢀⡤⠚⠑⢄⠌⠀⠀⠀⠢⠀⠔⠁⠀⠀⠑⡔⠁⠀⠀⣀⣁⠎
⠀⠳⣄⠀⠑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢩⣛⡳⠤⠤⠤⠌⠤⣀⣀⣀⣠⣿⡄⠠⠤⠤⠴⠴⠒⠒⠊⠉
⠀⠀⠈⠑⠤⣄⣀⠀⠀⠈⠉⠁⠀⢀⣀⠤⠚⠁
⣶⣶⠶⠶⢶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢰⠛⣏⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢈⠄⠘⢦⡓⢤⠀⠀⠀⠀⠀⣀⣀⣉⣷⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⡸⠀⠀⠀⠱⠠⢳⡀⠀⡔⠉⠀⠀⠐⠺⠟⠉⠀⠀⠀⠱⡄⠀⠀⣀⢀⡠⠄⣀⢀⡀
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢇⠀⠳⡀⡇⠀⣀⡤⠤⠄⣀⢀⡔⠒⣲⠔⠓⣤⣃⠠⠏⠀⢀⠼⠀⡜⠓⠢⡀
⠀⠀⠀⠀⠸⡇⠀⡀⠀⠀⠈⢆⠣⣹⠟⠉⠁⠀⢢⣀⣀⠀⠉⢃⣽⣡⣄⣉⢩⣔⣈⣁⣀⠐⠢⣜⠉⠓⠉⠑⡄
⠀⠀⠀⠀⠀⡇⠀⠠⡀⠀⠀⠈⠳⣏⠀⠀⠀⠈⠉⠈⠑⠀⣰⠋⠀⠀⠀⠚⠦⠄⠀⠀⠈⠙⣆⠼⠲⡎⠉⠑⣇⢀⡀
⠀⠀⠀⠀⣀⣸⡀⠀⠱⡀⠀⠀⠁⠨⣓⠧⣀⡀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡔⠊⠉⢠⡀⠞⠀⡱
⠀⠀⠀⣎⠉⡌⠑⠒⠶⠺⠦⢤⡤⣤⣀⣉⣢⣉⣒⣤⡀⢘⡇⠀⠀⠀⢀⣀⣀⣀⣀⣠⢤⡤⠿⠧⣀⣀⡔⠀⠀⣸
⠀⠀⠀⠈⠙⡗⢲⠶⠾⠦⠤⢤⣵⣤⣀⣈⣙⣄⣈⣉⣫⣉⣉⠉⠙⢍⡉⣁⣈⣑⣄⣀⣀⣈⣵⢤⡤⠤⢷⠖⠒⠁
⠀⠀⠀⠀⠀⢹⠀⠡⡀⠀⠀⠀⠡⠀⢀⠔⠉⠀⠀⠀⠀⠈⠉⡄⢀⠔⠙⢌⡨⠙⢄⣀⠈⠢⣀⡔⠁⢤⡟
⠀⠀⠀⠀⠀⠈⣆⠀⠘⠄⠀⠀⠀⠳⠁⠀⠀⠀⠢⡀⠀⠀⠀⠘⢅⠀⠀⠀⠱⢄⠀⢱⠄⠀⢈⢆⢀⡞
⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠔⠄⠀⠀⠀⠜⠑⢄⡄⠀⠈⠶⡁⠀⠘⢇⣀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠄⠛⢄⠀⠀⠀⠰⡈⠁⠀⠀⠀⠴⡈⠀⠀⠀⠙⣦⣀⡠⠚⠂⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⢑⢶⠈⠀⠈⠂⣄⣀⠠⠄⠁⠀⢤⡐⠊⠀⡩⠂⢄⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠶⠿⣶⣦⣈⣠⣭⣒⣤⣤⣔⣥⣬⠶⠾⠖⢊⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠤⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢶⣶⡚⠿⠭⣭⣭⣉⡀⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡫⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠤⠘⠒⣂⣀⠩⠭⠥⠤⠀⠀⠐⠒⠀⠒⠒⠂⠀⠐⠒⠀⠀⠤⠬⠭⢉⣀⣒⠲⡇⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡡⠄⠒⢉⡉⠤⠤⠐⠒⣒⣀⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣐⣒⠒⠀⠤⠄⣹⠀⡞⠠⡉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠣⠴⣊⣁⡤⠒⠂⢉⣁⠤⠤⠤⠀⠐⠒⠒⠒⠒⠒⠒⠒⠀⠤⠤⠤⠄⣈⡉⠒⠲⠇⢠⡓⠤⠜⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⣉⠒⠂⠤⠄⣉⣉⠁⠒⠒⠒⠓⠂⠠⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠒⠒⠒⠈⢉⡋⠀⣈⠖⠒⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠬⣉⡓⠒⠂⠤⠤⢈⣉⣉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⣉⣉⣉⠠⠬⠍⠒⠒⣋⡉⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡒⠦⠤⣉⡑⠒⠲⠦⠤⠤⠈⣉⣉⣉⣉⣉⠉⠉⠉⠉⣉⣉⣉⣉⣁⠠⠤⠤⠴⠒⠒⣊⡉⠤⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡒⠤⢄⣀⡉⠉⠒⠒⠂⠤⠤⠤⠤⠄⢀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠀⠒⠒⠂⠉⣁⣠⠤⠔⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡑⠢⠤⣀⣉⠉⠀⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠐⠒⠒⠂⠉⠉⣁⣀⠤⢒⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢑⠒⠤⠤⢉⣉⣙⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⢈⣉⣉⡉⠥⠤⢒⡪⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠒⠒⠂⠉⠉⠉⠉⠉⠍⠉⠉⠉⠉⠀⠒⠒⠒⠒⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠈⠀⠀⠂⠀⠐⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠙⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠹⠿⠿⡟⠓⠀⠀⠀⠀⠀⠀⠀⠀⣐⠀⢨⣇⠤⡄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⣾⡄⠀⠀⠀⠀⠀⠁⠘⠋⠰⠃⣀
⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⠀⠀⠁⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⣸⣆⣴⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⡿⠀⢲⠈⠹
⠀⠀⠀⠀⠀⠀⠉⠀⢠⡾⣿⡿⢷⠌⢀⣼⠁⠀⠀⠀⢸⢠⣼⣿⣿⡿⠟⠛⢻⠿⡁⠀⠀⠀⠀⠀⠀⠀⣁⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⢧⣾⣶⣬⣿⢦⠀⣀⣤⣿⢸⣿⡿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⡇⠀⢅
⠀⠀⠀⠀⠀⠀⠀⠴⠀⣴⣿⡿⠟⣻⣴⠂⠀⠉⠁⠟⠛⣾⡻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠻⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠉⡀⠠⠿⠶⠛⠿⣿⣿⣳⠆⣾⡆⢠⠀⠈⠁⠀⠀⡄⠀⠀⠀⠀⠀⢰⠀⢂⡀⢾⣧⣤⣤⡟⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠿⠂⠀⠀⣤⣀⡈⡁⠀⢀⣿⡃⡀⢀⡀⠀⠀⢠⢇⣸⣤⣰⣶⣦⡿⠘⠿⢿⡒⠀⠉⠉⠀⢠⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠌⡭⠈⣴⣷⠖⢈⡛⠻⠾⢷⡆⠞⠋⠙⠟⠉⠉⠩⠉⠁⣄⢼⣿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠉⠀⠭⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠁⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠐⠖⠲⢄⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠂⠐⠀⠈⣀⠈⠀⠀⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠘⠒⠂⠉⠀⠀⠀⠀⠉⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠒⡚⠀⠀⡐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠩⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠔⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠄⢠⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⣰⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣇
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠉
⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡄⠠⠀⠠⠤⠤⠀⠄⠐⠂⠀⠂
⠀⠀⠀⠀⠀⢐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⡄⠀⡆⢀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠒⠀⠈⠀⠀⠀⠂⠀⠀⠐⠀⠂⠀⠁⠈
⠀⠀⠀⠀⠀⠨⠁⠀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⢠⢀⠄⠀⠤⠤⠀⢰⢀⡆⠀⠒⢲⠀⠀⠅
⠀⠀⠀⠀⠀⠀⡀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠂⠐⠀⠘⠀⠁⠀⠁⠈⠀⠈⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠠⠀⠄⠨⠀⢱⠄⠀⠀⠀⢀⠈⠐⠀⡂⠐⠂⠐⠀⠐⠐⠂⠀⡆⢘⠀⡹⠀⡄⠠⠆⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣀⣀⡀⠉⠀⢈⠀⠁⠀⠁⠈⠀⢈⠀⡁⠀⠀⣀⣀⣀⠀⣄⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⠈

⣿⣿⣿⣿⣿⣿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡿⠟⢉⣠⣴⣾⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀⠻⠿⠋⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⠂⣠⣤⣤⣀⣀⣀⣀⣁⣉⣉⣉⣉⣉⡉⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡈⠁⠈⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⣼⣿⣿⣶⣤⣌⡉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢉⣠⣤⠀⣀⠙⢿⣿⣿⣿⣿⣿⣷⣤⣈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣰⣿⣿⡏⢠⣿⣷⣄⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⣸⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⠛⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠒⢒⣒⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢉⠠⠔⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢮⡠⠠⢤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠚⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⣀⢱⣄⠀⠈⢧⠀⠈⠱⡍⠁⠐⢴⠒⠒⢤⠖⠛⠢⢞⠉⠁⠑⢏⠀⠉⠙⢄⡀⡀⣡⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠀⡏⠉⠀⠑⠒⠀⠘⠒⠀⠠⠒⠠⠤⡵⠶⠀⠤⠓⠒⠒⠒⠉⠉⠉⠉⠀⡇⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠉⠉⠚⠃⠐⠀⠠⢤⠤⡤⠤⠀⠠⠤⠀⠠⠄⠤⠤⠤⠤⠤⠀⠤⠤⠐⠐⠒⠈⠉⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠑⠲⠶⠤⠤⠤⠄⢠⣀⣆⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡶⠤⠤⠄⠒⢐⠂⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⠴⢠⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⡁⢸⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠘⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⣀⣀⠀⠀⠀⠀⠈⠀⠏⠉⠉⠁⠀⠀⠉⠁⠈⠉⠉⠉⠁⠀⣩⢨⠀⢀⠀⢤⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣈⣹⠉⠉⠀⠐⠒⠒⠃⠐⠒⠒⠒⠒⠲⠖⠶⠂⠀⠀⠂⠀⠉⠉⠁⠀⠀⢸⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃⠐⠒⠒⠠⠤⠤⠤⠤⠤⠠⠰⠄⠥⠤⠤⠤⠄⠀⠀⠐⠒⠋⠉


⡶⠶⠶⠶⠖⠲⠶⠶⠶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣯⣭⣭⣭⣭⣭⣭⣤⣒⣒⣒⣒⣒⣒⡒⠲⠶⠶⠶⠤⠤⠤⠤⠤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⠶⣶⣶⣬⣭⣭⣍⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣇⣤⡶⣿⣿⡟⠂⠒⠂⠙⢻⡖⠚⠒⢛⡇⠠⠼⢧⠄⠀⠰⣶⣖⠒⠒⢶⣤⣤⣀⣤⣤⣀⣀⣀⣀⣀⢀⡀⠀⣀⠀⢸⡇⢸
⠀⠀⣀⣀⣄⡶⢿⣶⡄⡸⠏⠙⣸⣿⣿⣶⣷⣶⢾⠿⡿⠶⠦⣤⣿⣦⣤⣄⣷⣀⣀⠀⣿⡄⠀⠀⢩⡍⠉⠁⠉⣧⠀⠐⠊⠹⡛⠛⠃⠘⣃⢻⡇⣸⠰⣇
⣰⣯⣹⣿⣛⣠⣾⣿⣼⣿⣾⣿⣿⣿⣇⣿⡟⠈⠀⠀⡀⠀⠀⠀⠀⡎⣿⠉⠉⠉⠉⠉⠉⡛⠛⠛⢻⠟⠓⠒⠒⠛⡿⠶⠖⠲⣿⣶⠒⠒⠿⢿⡇⣿⢴⣽
⣿⡅⠀⠀⠘⠟⠄⠀⠀⠙⠿⡇⠉⠉⢻⡿⠛⠛⠛⢿⣧⠄⢀⣀⣠⣄⣉⣀⣾⣀⡀⠀⠀⠃⠀⠄⢸⠄⠀⠀⠀⢰⠇⠀⠀⠰⠸⠃⣀⣠⣴⣏⡛⢳⣼⢿
⠉⡻⠤⢄⠀⢘⣾⣄⡀⠀⠐⣴⡀⠀⠀⢃⣀⠀⠀⠀⠉⣢⠀⠀⠀⠻⣂⠀⠀⠙⠟⠉⠁⠻⡿⠓⠛⠒⢶⣖⠒⠒⠒⢾⢷⣴⣿⣿⣿⣿⣿⣟⣥⡌⣿⣿
⠀⣇⢠⡆⠀⠰⠉⠉⠉⠙⠛⠙⢻⠛⠛⠛⠛⠒⠒⠲⠶⠿⠶⢤⢤⣤⣼⣧⣄⣀⣈⣶⣄⣀⢡⣤⣀⠀⠀⢀⣦⠀⠀⢀⣸⣿⣿⡿⢿⡿⣿⢻⡍⣿⣿⡿
⠀⣜⡀⠃⠀⢐⣄⡀⠀⠀⠀⠀⢸⠀⠀⢀⠀⠥⠀⠀⠀⠀⠀⠠⠀⠀⠠⡁⠀⠀⠈⠉⠙⢙⠙⠩⡭⠍⠉⠋⠛⣉⠛⠹⠋⠀⢾⣿⣿⢳⣿⡐⣢⡿⣏⡗
⠀⣯⠬⠉⠉⠉⢹⡟⠛⠿⠛⠛⠛⠒⠒⠛⠿⣷⣦⣤⣴⠾⠧⠀⢀⣤⣄⡁⢀⣀⣠⡆⢠⠀⢀⠀⠑⠀⠀⠀⠀⠹⠀⠀⢀⣄⢙⣓⣿⠼⠛⣿⡏⠀⡟⠃
⠀⣿⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⡃⡁⠀⢰⠀⠑⠀⠀⠀⠉⠉⠉⠉⠉⡉⠉⠉⠙⠿⠷⡶⡶⠲⢟⡚⠂⠓⠚⠛⡿⣿⡏⠀⢰⣿⣿⢶⣿
⠀⠸⢿⠻⠛⠛⠛⠿⠤⠤⠼⠿⢷⣦⣴⣶⡶⠧⠀⠀⢼⣦⣄⣀⣀⣠⡄⠀⠀⢀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠀⠀⠀⢠⠳⣿⣷⣤⣿⠏⠀⢸⡟
⠀⠀⡏⣀⠀⢁⡁⠈⠀⠀⠀⠀⢸⠨⢹⠹⠀⠒⠀⠀⠀⢘⠿⠛⠛⢹⠇⠌⠁⠚⠛⣿⣷⡶⡾⢷⠧⠤⠤⠷⣤⣴⣤⣤⠶⡿⠃⠉⢹⢸⢿⣤⣤⣬⡇
⠀⠀⡌⠛⠛⠛⢷⣾⣤⣤⣤⡶⠿⠶⠴⠾⣦⣤⣤⣤⣤⣎⣀⣀⡀⢸⣄⣁⡀⠀⣠⠇⠈⠀⠃⣠⠈⠀⠀⠀⠘⠁⡏⠙⠀⣇⠁⢀⡾⠛⠛⣿⠃⣿⠇
⠀⠀⣧⠀⠀⠀⢰⠎⠉⡏⢿⠀⠉⠀⠀⠀⣿⠉⠉⠉⢨⠀⠌⠉⠁⠉⡉⠛⠛⠛⠉⠒⠓⠒⠓⢿⣬⣥⣤⣤⣶⣤⠤⠔⠲⢿⡟⣿⠃⠀⣸⢻⣠⡿
⠀⠀⠹⢶⣶⣤⣼⠦⠀⢤⣼⣄⣀⣀⣀⣠⣿⣀⡀⠀⢸⣄⠀⠀⠀⠀⠁⠀⠀⠀⡀⢘⠛⠂⠀⠀⡏⠉⠉⠁⡅⠀⠀⠀⠀⣿⣗⣿⢶⣾⠏⠉⢩⡞
⠀⠀⠘⣿⠁⠀⢹⠸⠀⠀⠀⠉⡟⠛⠛⠉⡇⠀⠀⠈⠉⠉⠻⡿⠿⠿⠒⠒⠒⠚⠳⣮⣤⣤⣤⣇⣁⡒⠀⢀⣦⣀⣀⣠⣼⠛⠉⠀⢸⣸⡆⢇⣸⡁
⠀⠀⢀⣿⢀⣀⣼⣄⣀⣀⣀⣼⠁⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠈⠨⠙⠀⠀⠄⠉⠉⠉⡛⠉⠙⠁⢸⡇⠁⢀⣼⠟⢻⢿⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠈⠙⢙⠉⠛⠛⠛⠛⠚⠻⠶⣶⡶⢾⠖⠓⠒⠂⢾⣤⣤⣠⣤⣥⠤⢤⡀⣤⡀⠀⠀⠀⠀⠁⠠⠀⠀⣾⣥⣶⢿⡗⠀⢸⠸⣿⠃
⠀⠀⠈⢿⣀⣀⢀⣠⠀⠸⠀⢰⣬⡄⠀⠀⠀⠀⠀⠁⢸⠤⠄⠀⠀⠀⠉⠙⠉⠉⠀⢤⠀⠀⠈⠙⠛⢿⠿⠛⠃⠀⠀⢂⠙⢃⠀⣹⣀⣠⡾⠛⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠷⠖⠛⠒⠲⠶⠶⢾⣥⣄⣀⣴⣦⣀⣀⣀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣼⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠒⠶⠶⠾⢦⣤⣤⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠰⠋⠀⣰⣶⣒⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣶⣾⣧⣂⠄⡀⠀⠁⣀⠀⢾⡆⢸⣿⢷⢽⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⢿⣖⠴⠆⣤⡹⡏⠀⠣⣸⠿⠍⣀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⢊⠱⡟⠠⣤⣵⡇⣼⣠⠜⡓⠚⠁⣂⠡⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠟⠛⣬⢙⢏⠃⡄⣽⣿⢰⡟⡡⢆⣠⣀⠺⠙⠉
⠀⠀⠀⠀⠀⠀⣤⣠⣸⡋⠴⠶⢦⣷⣦⣳⢲⡈⢿⣿⣾⣣⡖⠁⠉⢀⠀⡠⠦⠤⡤
⠀⠀⠀⠀⢤⣷⠀⢿⣧⣠⠂⠬⠭⢟⡋⡙⢿⡇⣴⢮⡱⣏⣠⠞⠡⡽⠋
⠀⠀⢀⣶⣦⣌⣷⣿⡿⡿⡦⠶⠀⢻⡏⠊⠘⢿⣿⣿⡷⠸⢟⣊⠔
⠀⠀⠟⠋⣻⡷⣾⣯⣽⠟⠀⠄⠲⠄⢣⢑⣴⣼⢉⣿⡧⣟⢀⡺⢮⣁⣀⠄
⠀⠀⠀⠀⢶⡿⠿⢿⡿⡴⠒⠀⠀⠀⠀⢹⠟⢿⣸⣦⠙⠚⢋⣠⠆⠘⠁
⠀⠀⠀⠀⢲⠿⣶⢫⣿⣦⠃⠀⠀⠀⢈⢇⣿⣸⣿⢻⣇⣣⡹⣻⡂⣠⣆
⠀⠀⠀⠘⣾⣸⣿⣼⣿⢻⣋⠁⠀⠀⠈⠣⣸⣷⣯⠀⢻⡿⣷⣯⣎⠙⠃
⠀⠀⠀⣴⡿⡿⣷⣽⣿⣿⣯⢀⣀⣠⡞⠩⡷⢿⣿⡕⣾⣿⠟⢏⣽⠇
⠀⢠⡾⠿⣿⣿⣿⣿⣿⣿⠿⠓⠀⠈⠉⢛⣿⣶⣿⣿⢸⣿⠘⠌⣽⣀⣠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢴⣍⡏⣿⣿⡿⣻⡆⠘⣸⠀⢿⡏⠡⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢡⢲⠇⣿⡟⣽⣤⢸⢱⡆⠁⣷⣙⣧⡄⣀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⣿⡾⡖⡿⡃⢹⢿⠄⢾⡇⢜⢹⣿⢿⣷⣿⣼⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠈⣸⡿⣶⣧⡿⣈⢀⣻⣼⡏⡟⡞⣿⣿⢟⡍⢿⢿⡀
⠀⠀⠀⢀⢄⣀⡀⢀⠤⣤⣄⡴⣿⣇⣿⣿⢱⣿⣦⣘⢿⣷⣿⣇⣿⡟⣾⣷⣾⣾⡧
⠀⠀⠀⠀⢾⡎⠄⡴⢂⡘⠳⢿⢟⠻⡳⣷⣿⢸⣿⣿⢨⢟⡿⢿⣿⣿⣿⣿⣿⣿⠷⠓⠒⠶⢶⣶⢷⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄
⠀⠀⠀⠀⠸⣿⡞⢰⠏⠀⠀⣸⢨⡇⣰⢸⣏⠙⢿⣿⣾⡾⣬⡘⣿⢻⠹⣿⣿⠋⢠⠄⢀⠆⠀⠈⡏⢃⠉⠙⡆⠀⠀⠀⠀⠀⡀⠀⡔
⠀⠀⠀⠐⠀⠉⢅⣽⠀⣰⡾⠟⠚⠛⢳⠏⠱⣦⣴⣆⢛⣿⢻⣿⣝⣷⣿⣿⣿⡄⣼⢀⡆⠀⠀⣼⠃⣼⢸⣧⣿⢀⣶⣤⣴⡯⠈⣶⣼
⠀⠀⠀⠀⢀⣴⡶⣿⠗⢯⡶⠛⠃⣄⠁⢆⠠⠿⠛⠽⡟⠟⠢⠹⣿⣻⠹⢏⡭⡝⠛⠁⣥⡾⠿⢉⣾⣿⣿⣿⣋⢙⣓⠑⢤⢻⡇
⠀⠀⠀⠀⠀⠛⠲⠁⡄⢼⠀⡄⠀⠈⣧⣸⣿⡿⠓⠲⠲⠤⡆⢤⣤⣁⢚⡻⠆⠀⠉⠁⠻⡂⣬⠙⣽⣝⣉⣝⠛⠓⠛⠂⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢆⠷⣼⣦⡘⢶⡶⠿⣦⢸⡿⣧⡴⠞⠓⠛⠛⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠛⠙⠀⠘⠛⠞⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠛⠿⢿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣿⣧⡄⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣿⣿⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣟⣿⣿⣿⣿⣦⣿⣦⡇⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢿⣿⣿⣿⣿⣯⡹⢯⣿⡀⢀⡟⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠲⣀
⠀⠀⠀⠀⠀⠤⠤⣤⣾⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⡀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣶⣄⣉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢸⡿⣿⣞⣿⣿⣿⣿⣿⣿⣏⠀⠉⠉⠓⠺⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⢸⡇⣿⣿⠃⠘⢿⣿⣿⣿⣿⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣏⡻⣿⣿⣿⣦⣶⣤⣾⣷⣿⠏⠀⢠⣼⣿⣿⣿⣿⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣤⠞⠋⢩⣿⣿⡟⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣟⠛⣉⣿⣿⣿⣿⣿⣿⣿⠉⠁⢀⣄⣸⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣿⡟⠲⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠁⣴⣿⣿⣿⣿⣿⣦⣀⠉⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⠃⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠐⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⢹⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣦⣀⣙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢸⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⢀⣾⡗⢿⡇⠀⠺⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠐⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⢰⣾⣿⣿⣿⡿⢿⣿⣿⣿⡌⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣿⣿⣿⣿⡛⢿⣿⣿⣿⣿⣥⣶⣄
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⡀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣾⣿⣟⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣾⣿⣿⣶⣶⡟⣉⢁⠸⠂⣴⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⢰⣿⣿⣿⠟⠿⢿⣿⣿⣿⣿⣿⣿⣦⣶⠛⢋⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠆
⠀⠀⠀⠀⢸⣿⡟⠁⠀⢠⣾⣿⣿⠋⠙⠿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣿⢿⣿⡿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠀⣿⡟⣱⡏⠀⠀⢠⡏⠈⠛⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠈⣿⡇⠀⢸⣿⣷⣿⠀⠀⠀⢸⠁⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⢤⣿⡏⠛
⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⢀⣴⣿⣿⡷
⠀⠀⠀⠀⠀⢹⡇⠀⢸⣿⣿⢹⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⣿⣿⣠⣶⠟⠋⣸⠋
⠀⠀⠀⠀⠀⠘⣇⠀⠈⢻⣿⣄⠙⢧⣄⠀⡄⠀⠀⠀⠀⢀⣰⣿⠟⠉⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠙⠻⢿⣿⣿⣿⣷⣶⣶⣶⣿⣿⡿⣏⢀
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠉⠉⠀⠸⡶⠶⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⢀⣄⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣄⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠒⠀⠠
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⢠⣟⠐⢤⣀
⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣁⡀⢀⡀⠀⠉⠒⠬⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣛⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡟⠛⠛⢣⣤⣤⡝⠛⠛⢣⣤⣤⡝⠓⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡟⠛⠛⢥⣤⣤⡝⠛⠛⢡⣤⣤⡝⠛⠛⢦⠀⠀⠀⠀⠚⢣⡄
⠀⠀⠀⠀⠀⠀⠀⠈⣭⣭⡿⠿⠿⢭⣭⣭⡽⠿⠿⢭⣭⣭⡽⠿⠿⢯⣥⣄⠀⠿⠿⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡿⠿⠿⢏⣉⣉⡽⠿⠿⢏⣉⣉⡽⠿⠿⢏⣉⣉⡽⠿⠿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⡷⠶⠶⢏⣉⣉⡷⠶⠶⢏⣉⣉⡷⠶⠶⢏⣉⣉⡵⠶⠶⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡷⠶⠶⣊⣉⣉⡳⠶⠶⣎⣉⣉⡳⠶⠶⢎⣉⣉⡳⠶⠶⠆

⠀⠀⠀⠀⠀⠐⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⣀
⠀⠀⠀⢠⣠⣵⣿⣟⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣟⠿⣿⣿⣶⣄
⢀⢢⣐⣤⣿⡿⣿⣝⣿⣿⣿⣭⣽⠿⠟⠲⣶⣶⣿⡿⣿⣾⣿⣿⣿⣧
⠈⠳⣽⣿⣿⣿⣿⣿⣽⣿⣿⣯⡿⣯⣽⣷⣿⡿⠟⠛⠛⠿⠿⣿⣿⣿⡇
⠀⣜⣮⣻⣿⡿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢤
⢀⠺⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣉⢉⡓⠀⣴⣖⠒⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣾
⠀⠑⠿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣷⣌⠀⠀⠀⠀⠉⠛⠉⠀⣿⡏⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇
⠀⠐⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⣸⣧⡄
⠀⠀⠁⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢦⣈⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣘⠳⠤⠆⡅
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢉⣿⣇⠀⠀⢲⣄⡀⠈⣿⣿⣿⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠌⢉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⡿⣿⣷⣤⡀⠹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣠⠞⣻⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣲⣿⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣴⠟⠁⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣴⣶⣿⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣹⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠿⠟⠛⠉⠉⠉⠀⠀⠈⢉⣽⠟⠉⠘⣿⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⣀⠀⣿⢿⡎⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣿⡿⣋⣀⡤⢀⣠⣤⣴⣶⣶⣤⣤⣤⣤⣴⡾⠷⢄⣘⣿⣾⣣⠞⠁⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⢿⡐⣿⢏⣴⣿⣿⣿⡴⠶⢿⣿⣶⣶⣶⣴⣿⣿⡿⠿⠛⠉⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠋⠀⠀⠙⢮⡙⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠛⢉⡩⠖⣸⡧⠴⢛⡹⢶⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠙⠷⣤⣄⣀⣀⣀⣀⣀⣤⡤⠶⠋⠀⠀⠀⠐⠫⠅⣀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣺⡥⠟⣻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣤⣤⣤⣤⣤⡴⠾⠟⠛⠛⠛⠉⠉⠉⠁⢪⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣦⣶⣦⣤⣴⡶⠾⠟⠛⠉
⣿⣿⠟⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⢀⠀⠀⠀⠀⡠⠐
⠀⠀⠀⡀⠀⢀⣿⣄⣀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣐⠶⠤⠤⡀⠀⠈⠁⠐⠄⠀⡀
⠛⠓⠣⠼⢀⣹⣿⡆⠀⠀⣿⣻⡧⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⠄⠈⣏⠉⠉⠉⠙⠓⠀⠀⣴⠀⠀⡄⠐⠄
⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠉⠀⠉⠙⠓⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⠀⠨⠀⠀⢤⡀⠙⢮⣷⣿⠀⠀⣿⠀⣆
⠀⢀⡀⠠⠄⡄⠀⠀⠀⢄⠀⠀⠄⢐⠠⠀⡀⠀⠀⠉⠉⠋⠿⣷⣶⣤⣄⡀⠀⢀⠀⠀⠀⠀⠄⠀⠀⣷⡀⠀⢻⣦⠈⢿⡇⠀⣸⣿⠀⣿⠐⢒⠒⠚⠓
⢀⠀⡀⠄⠀⠄⠀⠀⠀⢀⡉⠒⢄⡀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⣷⢾⡇⠀⠀⢸⡂⠀⠀⢹⣷⠀⠈⣿⡇⢸⡏⢠⣿⡏⣸⡏⠀⠀⠂⢁
⠡⠐⠂⡂⠂⠅⠏⣠⡒⢆⠀⢀⠄⠉⠢⣄⠀⠈⠀⣀⣠⠤⠶⠒⠛⠉⠉⠀⠀⠀⣇⠀⠀⢸⡇⠀⠀⠘⣿⡇⠀⢹⣿⢸⠟⠋⠙⠲⠟⣀⣠⡀⠀⠈
⠁⠐⠠⢅⠁⢎⠐⠢⠁⠬⠡⠃⢴⣃⣤⠼⠗⠛⠉⠁⠐⠀⡀⠒⠀⡀⠀⠠⣴⣆⠘⡄⠀⠀⢻⠀⠀⠀⢾⣧⠰⠈⠉⢻⡆⠀⠀⠈⠺⠿⠋⠀⠀⠠
⠸⢁⡇⠀⠐⠂⡠⠚⣀⣤⠷⠚⠋⠡⠀⠀⠀⠀⠄⠀⠀⠉⠀⠀⢴⡁⠐⠖⠒⠶⢤⣌⣦⡀⠈⠦⠀⠀⠺⣿⣥⠄⠀⠀⠠⠀⠀⠤⠀⡀⠀⠈⠀⣀⠐
⢤⢉⠹⢐⣪⡴⠞⠋⠁⠠⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠌⠁⠐⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠀⠀⠉⠅⠀⠂⠠⠖⠀⠀⠀⠀⠋⠁⠀⠀⠀⠁
⣠⡵⠞⠋⠁⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⡀⠀⠹⠶⠷⠿⠶⠄⠀⢀⠀⠀⠀⠁⠀⠤⠀⠀⢀⡔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠆⠐⠂⠄⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⢀⡀⠀⠀⠐⠄⣀⣁⡀⠀⠂⠀⠁⠀⠁⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠮⠄⠀⢀⡤⠄⠉⠉⠀⠀⠀⠀⠀⠀⠉⠲⠠⠀⠀⠀⠀⠣⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⢠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⢡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡀⠀⠈⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠘⠢
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠰⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠌⠀⣀
⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠠⢀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠜⠀⡘⠂
⠀⠀⠀⠀⠀⡁⠀⣀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠴⢀⡇
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠤⠀⠄⠀⠐⠈⠁⠀⠀⠄⠀⢁
⠀⠀⠀⠀⠀⠐⠠⠄⣀⠈⡉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⣀⡠⠄⠒⠂⢉
⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠉⠀⠈⠀⠀⠂⠀⠀⠠⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠠⠀⠀⠀⠐⠒⠀⠀⠁⠀⠈⠀⢀⡀⠀⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠲⠒⠀⠀⠄⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠉⠀⠀⣀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠐⠀⠠⠄⠀⠀⠀⠀⣀⠀⠀⣀⠀⢀⣀⠀⣀⣀⣀⡀⣀⠀⠀⠤⠄⠐⠂⠀⠒⠈⠉⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠠⠄⠀⣀⠀⠀⡀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠒⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠄⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⣀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠁⠀⠈⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠉⠉⠀⠂⠒⠂⠀⠐⠀⠠⠀⠀⠄⠀⠀⠀⠐⠒⠂⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡈⠉⠐⠀⠀⠀⠠⠀⠠⠄⠠⠄⠀⠠⠀⠤⠤⠠⠔⠂⠐⠀⠐⠀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠀⠀⠄⠠⠄⠤⠄⠀⠠⠄⠤⠀⠀⠀⠀⠒⠒⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠻⢽⠂⢀⣀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⣶⡀⣐⣰⡷⡦⠦⢵⠾⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢆⡲⠀⠀⠀⠄⠀⠀⠂
⠀⠀⠀⣸⣿⣧⢀⢈⡯⢐⣦⡞⠉⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢬⣭⠄⠀⠀⠀⠀⠀⠈⠶⢦⠐
⠀⠀⠀⣿⣿⢻⣸⣯⣶⠰⣿⣬⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠖⠋⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣏⠸⠿⢿⠟⢧⣬⡷⠌⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡂⠀⠀⠀⠀⢂⠠⣅⠀⠀⣐⠉
⠀⠀⠀⠀⣹⣤⡀⠙⠟⠁⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⡀⠀⠀⠀⢨⣴⠀⣷⠀⡁⣼
⠀⠀⣠⣾⣟⠻⢍⡟⣿⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠠⢴⣿⣿⣏⢉⣼⢗⡡⠄
⠀⠀⣿⣿⣿⣧⡀⣿⣿⢢⣿⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⡤⠶⠂⠀⠈⠉⢁⣘⠄⠀⢀
⠀⠀⣻⣿⣿⣿⣷⣸⣿⣆⣿⣿⣿⣿⣿⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣴⣮⣛⠛⠻⣿⠧⠄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠞⠖⠀⠀⠙⠿⠿⠛⠓⠒⠀⠀⠀⠓
⠀⠀⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣯⣭⣭⣭⣭⣭⣥⣄⣒⣒⣒⣒⣒⣒⡒⠒⠶⠶⠦⠤⠤⠤⠤⠤⢤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⢶⣶⣶⣬⣭⣭⣉⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣇⣤⡶⣿⣿⡟⢂⠒⠀⠙⢫⡖⠚⠒⠛⡇⠀⠼⢦⠄⠀⠐⣶⣖⠒⠒⢶⣤⣀⣀⣤⣤⣀⣀⣀⢀⣀⠀⠀⠀⣀⠀⢸⡇⢸
⠀⠀⣀⣀⣄⡶⢿⣶⡄⡸⠏⠙⣸⣿⣿⣶⣷⣶⣾⠿⡿⠶⠦⣤⣿⣤⣤⣤⣷⣄⣀⠀⣷⡄⠀⠀⢨⡍⠉⠁⠉⣧⠀⠒⠊⠹⡛⠛⠁⠘⣃⢺⡇⣼⠰⣆
⣰⣯⣹⣿⣛⣠⣾⣿⣼⣿⣾⣿⣿⣿⡇⣿⡟⠈⠈⠀⡀⠀⠀⠀⠀⡎⣿⠈⠉⠉⠉⠉⠉⡻⠛⠛⢻⠟⠓⠒⠒⠛⡿⠶⠖⠲⣿⣶⠖⠒⠿⢿⡇⣿⢴⣿
⣿⡇⠀⠀⠈⠟⠄⠀⠀⠙⠿⡇⠉⠉⢻⡿⠛⠛⠛⢿⣧⠄⢀⣀⣠⣄⣉⣁⣾⣀⡀⠀⠀⠃⠀⠄⢸⠄⠀⠀⠀⢰⠃⠀⠀⠰⠼⠃⣀⣤⣴⣏⡛⢣⣼⢿
⠉⡻⠤⢄⠀⢘⣾⣄⡀⠀⠐⣴⡀⠀⠀⢂⣀⠀⠀⠀⠉⣢⠀⠀⠀⠛⣂⠀⠀⠙⠟⠁⠁⠻⡿⠒⠛⠒⢷⣖⠒⠒⠒⢾⢧⣴⣿⣿⣿⣿⣿⣟⣡⡌⣿⣿
⠀⣧⢠⡆⠀⢰⠉⠉⠉⠉⠛⠙⢻⠛⠛⠛⠛⠒⠒⠲⠶⠿⠶⢤⢤⣤⣼⣧⣀⣀⣈⣶⣄⣀⢡⣤⣀⠀⠀⢢⣤⠀⠀⢀⣸⣿⢿⡿⢿⡿⣿⢻⡍⣿⣿⡿
⠀⣜⡀⠃⠀⢘⣄⡀⠀⠀⠀⠀⠸⠀⠀⢀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠉⠙⠙⠙⠩⡭⠉⠉⠛⠛⣋⠛⠹⠋⠀⣾⣿⣿⢳⣿⡐⣢⡿⣏⡗
⠀⣯⠩⠉⠉⠉⢹⡟⠛⠻⠛⠛⠛⠒⠒⠛⠿⣷⣶⣤⣴⠾⠦⠀⢀⣤⣄⡀⢀⣀⣠⡂⢠⠀⢀⠀⠑⠀⠀⠀⠀⠹⠀⠀⢀⣄⢙⣓⣿⠼⠛⣿⡏⠀⡟⠃
⠀⣿⣀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠁⠀⢠⠀⠉⠀⠀⠀⠉⠉⠉⠉⠉⡉⠉⠉⠙⠿⠶⠶⡶⠲⢟⡚⠀⠓⠚⠛⡟⣿⡏⠀⢰⣿⣿⢶⣿
⠀⠘⢿⠻⠛⠛⠛⠿⠤⠤⠼⠿⢷⣦⣶⣴⡶⠧⠁⠀⢼⣤⣄⣀⣀⣀⡄⠀⠀⢀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠀⠀⠀⢀⠣⣿⣷⣤⣿⠏⠀⢸⡟
⠀⠀⡇⣀⠀⢄⡀⠈⠀⠀⠀⠀⢸⠈⣹⠹⠀⠒⠀⠀⠀⢈⠿⠛⠛⢹⠁⠌⠀⠚⠛⣿⣷⡶⡾⣷⠧⠤⠤⠷⣦⣶⣤⣤⠶⡿⠋⠉⢹⢸⢿⣤⣤⣬⡇
⠀⠀⡌⠛⠛⠛⢷⣾⣤⣤⣤⡶⠿⠾⠴⠾⣦⣤⣤⣤⣤⣎⣀⣀⠀⢸⣄⣁⡀⠀⢀⠇⠈⠀⠇⣠⠉⠀⠀⠀⠘⠁⡏⠙⠀⣇⠁⢀⡼⠛⠙⣿⠃⣿⠇
⠀⠀⣧⠀⠀⠀⢰⠌⠉⡏⢿⠀⠋⠀⠀⠀⣿⠉⠉⠉⢈⠀⠌⠉⠀⠉⡍⠛⠛⠛⠉⠒⠓⠒⠓⢿⣬⣥⣤⣤⣶⣤⠤⠔⠲⢻⡟⣿⠇⠀⣸⢻⣠⠿
⠀⠀⠹⢶⣶⣤⣼⠤⠀⠤⣼⣄⣀⣀⣀⣠⣿⣀⡀⠀⢸⣄⠀⠀⠀⠀⠁⠀⠀⠀⡀⢐⠙⠂⠀⠀⠏⠉⠉⠁⡇⠀⠀⠀⠀⣿⣇⣿⢶⣾⠏⠉⢡⡞
⠀⠀⠘⣿⠁⠀⢹⠸⠀⠀⠀⠩⡟⠛⠛⠉⠇⢀⠀⠈⠉⠉⠻⡿⠿⠿⠒⠒⠒⠚⠳⣮⣤⣤⣤⣧⣁⡂⠀⢀⣦⣀⣀⣠⣼⠛⠉⠀⢸⣸⡆⢁⣸⣁
⠀⠀⠀⣿⢀⣀⣼⣄⣀⣀⣀⣴⠁⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠈⠨⠙⠀⠀⠄⠉⠈⠉⡋⠙⠉⠁⢸⡆⠁⢀⣼⠟⢹⢻⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠈⠙⢙⠉⠛⠛⠛⠛⠚⠻⠷⣶⡶⢾⠗⠓⠒⠂⠾⣤⣤⣠⣤⣥⠤⣤⡀⣴⡀⠀⠀⠀⠀⠀⢠⠸⠀⣼⣥⣶⢿⡇⠀⢸⠸⣿⠃
⠀⠀⠈⢷⣀⡀⢀⣀⠀⠸⠀⢰⣬⡄⠀⠀⠀⠀⠀⠁⢸⡤⠄⠀⠀⠀⠁⠙⠉⠉⠀⢄⠀⠀⠈⠙⠛⠿⠿⠛⠃⠀⠐⢒⠙⢡⠀⣸⣀⣠⡾⠛⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠷⠖⠛⠒⠲⠶⠶⢾⣥⣄⣀⣴⣦⣀⣀⣀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣼⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠒⠶⠶⠾⢦⣤⣤⡴⠞⠋⠁

⠀⠀⠀⡠⣞⠛⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⢶⣄
⠀⠀⡜⠀⠈⠦⣄⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠀⣀⡴⠋⠘⡄
⠀⠀⠘⢄⠀⠀⠀⠁⠂⢀⠀⠉⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⢀⣠⡶⠟⠉⠀⠀⡰⠃
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢁⠠⠀⠀⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⡢⠕⠉⠀⠀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠑⠠⡐⠄⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠀⠀⠔⠈⠀⠀⣠⠔⠉
⠀⣀⣤⠤⠤⠤⠀⠐⠚⠓⢄⠀⠀⠈⠲⢔⠂⠒⠀⠈⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠐⠓⠁⠀⠀⢀⠔⠚⠓⠒⠒⠒⠒⠲⠦⣤⣄
⣺⠃⠀⠶⠤⠤⠤⠄⠠⠀⠀⠐⠆⠀⠀⠀⣀⢤⡤⠤⠄⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⢤⡆⠀⠀⠀⠀⠤⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠻
⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠧⡤⠃⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠃⠈⠉⠉⠀⠀⠄⠀⠘⠀⠀⠐⠛⠘⣳⠤⠀⢼⡉⠉⠉⠉⠉⠉⠀⠀⢈⣳⣄⡠⠈⠉⠀⠈⢉⡉⠉⠉⢉⠈⠙⠉⠉⠉⠯⠈⠉⣨⣝
⠀⠹⠼⠍⠀⡀⠀⠀⢁⣀⠈⠀⠀⠀⠤⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⣀⣉⠍
⠀⠀⣂⣒⠀⠃⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⠁⠀⠀⣀⠀⠀⠀⣂⣀⣀⣈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠨⠀⢀⠀⠀⢀⠀⠤⠾⢚⠄
⠀⠀⢣⠄⡀⠩⠀⠀⠈⠅⠀⠁⠀⠀⢀⠀⠈⠇⠀⠀⠧⠀⠀⠀⠀⠀⠀⠄⠠⠄⠸⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠐⠀⠀⠐⠂⢰⣆⡏
⠀⠀⠸⣉⡁⢐⠀⠀⠀⡀⠀⠂⠀⠀⠐⠂⠀⣒⠀⠀⢰⣀⣀⢈⠀⠀⠀⠉⠀⠀⠲⠂⠀⠀⠀⠀⢈⠁⠀⠀⣉⠈⠩⠀⠀⠨⠁⠠⠤⡇
⠀⠀⠀⠓⠐⠀⠄⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠠⠄⠀⠐⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠂⠀⠀⣐⠀⢈⣩⠃
⠀⠀⠀⠘⠦⠀⢁⢀⣀⡀⣀⢐⠀⠀⠀⡀⠀⠈⡁⠀⠈⡁⠀⠀⠀⠀⠀⠨⠀⠀⢀⠀⠀⢀⠀⠀⠸⠀⠀⠀⠌⠀⡁⠀⠀⢤⠀⠚⣻
⠀⠀⠀⠀⣤⠄⠒⠀⠀⠀⠂⠠⠀⠀⠀⡤⠀⠐⠃⠀⠀⢃⠀⠀⠀⠀⠀⠰⠀⠀⣩⠀⠀⠨⡄⠀⠄⠀⠀⠀⠆⣀⡁⠀⠀⣈⠉⢽⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠶⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠠⠄⠀⢀⣀⣲⣿⣦⣀
⠀⠀⠀⠀⠀⣠⠤⠤⢀⣀⡄⡀⣠⡏⠀⠤⠀⠀⡤⠀⠙⣁⠀⢩⠁⠙⣷⣄⣀⣀⣤⠤⠶⠒⡒⠒⠒⠲⣦⣄
⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⣉⣻⣾⣽⣳⣶⣴⡞⠋⠠⢀⡴⠖⠲⢦⣤⡿⠛⢋⣡⡴⠖⣛⣭⠶⠂⣀⣼⣿⣿⡆
⠀⠀⠀⠀⢻⡀⠠⠴⠾⠛⠛⠛⠛⣛⣿⣿⣿⣧⠀⠀⡟⠀⣀⡴⠚⣁⣴⠞⠋⢁⡴⠞⢋⣠⠶⣛⣽⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠠⠭⠟⠒⠒⣻⣿⣧⣄⠀⣿⡿⠋⣠⠾⠋⠁⡠⠞⠉⠀⢐⣩⣴⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢰⣟⠛⡗⠲⠤⣀⣀⣀⡀⠉⠛⢻⣿⡷⠾⠋⠀⠚⠁⠀⠀⠀⠀⠀⠤⠾⣛⣛⣿⣿⡿⠿⣿⢹⠄
⠀⠀⠀⠀⠈⠛⢿⡾⣦⣄⣀⣀⠀⠙⠋⠉⠙⠳⠛⠉⠛⠲⣞⠛⠛⠓⢾⣯⣉⠉⠙⠿⣦⣭⣙⣛⠛⡖⠁
⠀⠀⠀⠀⠀⠀⠘⣷⠋⢉⣉⠙⠿⡛⢛⣿⡶⠶⢿⡷⠶⠶⢾⣿⡶⠶⢶⣾⣿⣛⣻⠿⢿⣿⣟⡟⡼
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠞⠻⣀⠀⠸⡏⠉⢙⣶⠋⠉⢳⣶⣏⣉⣙⣿⣿⣥⣴⣿⠿⣿⣿⣻⡿⣱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠦⠛⢃⡀⢠⢿⣋⠉⣹⣾⣉⣀⣉⣿⣿⣉⣩⣿⣿⣷⣶⡿⢻⣿⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠠⠈⠓⣀⠀⣸⣿⣅⣀⣩⣿⣍⣀⣩⣿⣿⣷⣶⡿⠟⣿⣿⢃⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⢦⡴⢶⣉⣙⣤⣤⡼⠻⣅⣠⣼⡿⠿⣧⣴⣿⣛⣿⣿⣿⠷⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠿⣦⣌⣦⣈⣻⣍⡉⠙⢿⣉⠛⢿⣯⣙⣻⣿⣤⣭⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠉⠉⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢲⠃⣀⠘⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢣⡠⠚⠁⠀⠉⠙⠢⡔⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠲⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠒⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠯⢉⡒⣿⣉⣩⣉⣉⣉⣉⣹⣋⠁⠒⢒⠶⠼⠒⢾
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⣀⠄⠚⠛⠉⣉⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠙⠓⢴⡒⠤⡗⠦⣀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠴⠋⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⣀⠀⠐⠒⠀⠀⠤⠀⠀⡃⠒⢗⠲⢌⡱⢦⡀
⠀⠀⠀⠀⠀⡐⠀⠀⡄⠁⠀⠁⠀⠐⠂⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠈⠐⠀⣏⠑⢾⠀⠀⠑⣄⠁⡀
⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠨⠀⠀⢀⠒⠂⠀⠀⠤⠀⠀⢀⠀⠀⠰⠤⠖⠀⠔⠂⠀⣏⠙⢺⠍⣂⢁⡿⠁⡇
⠀⠀⠀⠀⠀⡟⣄⠀⠙⢄⠀⠀⠀⢐⠒⠂⠀⠀⡈⡀⠀⢍⢁⠀⠈⢡⣤⠄⡢⠉⠀⡏⠑⢾⡒⣬⡵⢁⡰⡇
⠀⠀⠀⠀⠀⣷⡈⠢⢄⠀⠙⠢⠤⣐⡭⠅⠀⠀⣀⡀⠀⢀⣀⠄⠰⠐⢂⣀⠂⢉⡴⠭⠠⢾⣿⣁⠼⢋⡴⡇
⠀⠀⠀⠀⠀⢓⠦⠀⣄⠉⠒⠢⢤⣀⡈⠉⡖⠒⠒⠦⠤⠬⡭⡥⠤⠤⠤⠴⠖⠚⠛⢷⠖⣤⣈⡇⠐⢐⣠⡇
⠀⠀⠀⠀⠀⢹⠀⠠⡌⢑⠀⠀⠠⠠⢉⠉⠛⠓⠲⠤⠤⠤⠧⠤⠤⠤⠄⠐⠘⠀⠘⠛⠚⢁⡠⠀⠀⢰⢺⠇
⠀⠀⠀⠀⠀⢸⠦⠐⣢⡀⠀⠀⠨⢄⠂⠀⠀⠀⠁⠒⠂⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢺⢹
⠀⠀⠀⠀⠀⢸⠭⠀⢁⠊⠄⡀⢈⠠⢌⡁⠀⠀⠡⠒⠆⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢼⣿
⠀⠀⠀⠀⠀⢸⠓⠀⡾⠄⡀⠀⢘⣑⠠⠄⢀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⢺⣿
⠀⠀⠀⠀⠀⢸⡒⠂⡆⠑⠤⠤⠐⠢⠍⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡌⠁⠀⠀⠅⠐⠠⡿⡇
⠀⠀⠀⠀⠀⣨⣯⠤⡂⠑⠄⠀⠠⡝⠤⠀⠀⡐⠠⠄⠀⠐⠒⠈⠉⢀⠀⠀⠀⠐⡂⠀⠀⠨⡇⠀⡀⣿⣧⡀
⠀⠀⠀⠀⠀⠡⡘⣥⡬⢍⠢⠀⠈⠭⢉⡉⠀⠀⠈⠀⠀⢀⢀⣃⣀⡠⠄⠀⠀⢨⡥⠀⠀⠺⢶⡺⠓⣅⠔⠃
⠀⠀⠀⠀⠀⠀⠙⠣⣈⣹⠶⢤⣀⣩⣐⣒⡀⠄⡀⠀⠀⠀⠀⠀⠠⠐⠲⠤⠤⢚⣑⡤⠴⢚⡩⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠮⠬⠉⣙⠒⠓⠒⡖⠒⠑⢺⠏⠓⠒⣒⣊⡉⠽⠆⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠀⢈⣁⣈⠀⡀⢁⡈⠁⠐⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⣠⠤⠒⠈⠉⠁⠀⠀⠀⠀⠀⠈⠁⠒⠄⣀⠀⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠃
⠀⠀⠀⠀⠀⠠⠁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠄
⠀⠀⠀⠀⠀⠂⡐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢰
⠀⠀⠀⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢰⡁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢈⡅
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠘⠓⠒⠲⠀⠤⠤⠤⠤⠤⠤⡀⢀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣀⡀⢠⡤⠤⠤⠤⠤⠴⠀⠖⠒⠚⠃
⠀⠀⠀⠀⠀⠆⠤⢤⠀⣄⣀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⣀⣠⡀⡤⠤⠰
⠀⠀⠀⠀⠀⠃⠀⠘⠙⠂⠀⠤⠈⠁⠀⠡⢰⣃⠈⠉⠉⠉⠉⡃⢘⠉⠉⠉⠁⠀⢈⡁⠉⠈⠉⠠⠀⠀⠐⠀⠂⠀⠈
⠀⠀⠀⠀⠀⠆⠐⢠⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⢤⢀⡔⠂⠲
⠀⠀⠀⠀⠀⠁⠀⠐⠀⠂⠀⠀⠀⠀⠀⠔⠐⠖⠀⠀⠀⠀⢀⡃⢐⠀⠀⠀⠀⠀⠨⠀⡭⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉
⠀⠀⠀⠀⠀⢓⠂⠰⠀⡤⠀⠤⠄⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⣀⣀⠀⣄⠀⠤⠤⠤⠤⢦⢀⠒⠚⡛
⠀⠀⠀⠀⠀⠈⠈⠈⠀⠂⠀⠀⠀⠀⠀⠰⠠⠇⠀⠀⠀⠈⠈⠅⠨⠁⠀⠀⠀⠀⠨⠁⠃⠀⠀⠀⠀⠀⠀⠈⠉⢁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠀⠀⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠄⠐⠒⠒⠒

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

⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⡞⠀⠀⠙⠿⢦⣿⣧⣌⣿⣇⠀⢠⢠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣇⣤⣼⡀⠀⠀⠀⣇⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢷⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦
⠀⢀⣠⣤⣄⠀⢀⢼⠹⡉⠻⣷⣦⣤⢾⣿⡟⢻⣿⠀⠀⢹⣿⣿⣿⣿⡟⡆⠀⠀⢣⠀⠈⠑⠢⣄
⠀⣾⣿⣿⣅⣽⣿⣾⡰⣏⠶⣧⣿⣧⣾⣿⠀⠀⡏⡆⠀⠈⣿⡻⠿⣿⡿⣷⣄⠀⠰⣄⠀⠀⠀⠀⠉⠲⢄
⢰⡏⣿⢡⡟⠙⢿⣿⡏⢃⠀⣿⣿⣿⠟⠸⠀⠀⡇⢣⠀⠀⣹⡇⠀⠙⣧⠈⠟⢷⡄⠘⠃⠀⠢⣄⡀⠀⠀⠉⠢⣄
⢸⣧⡷⠻⣄⣀⣸⣿⣬⣶⠿⣿⣿⡟⠀⠀⡇⠀⢳⠘⡀⢀⣿⡿⠀⠀⠈⠳⡄⠸⡇⠀⠀⠀⠀⠀⠉⠳⢦⣄⠀⠈⠑⢄
⠘⡿⠀⠀⠈⠂⠀⢻⡏⠀⠀⣿⣿⠃⠀⠀⠀⠀⢸⠀⡇⢸⣿⣇⠀⠀⠀⠀⠈⢲⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣤⣀⠳
⣼⠃⠀⠀⠀⠀⠀⢻⡇⠀⠀⡿⠁⠀⠀⠀⡀⠀⢸⠀⢐⣿⣿⣿⡄⠀⠀⠀⠀⣸⠋⠙⠓⠶⠶⠶⠶⠶⠒⠒⠻⣿⡗⠚⠛
⠋⠀⠀⠀⠀⠀⠀⢸⡏⠓⠂⢻⠀⠀⠀⠸⠁⠀⢰⠀⠈⡿⢿⣿⢿⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠘⠣⠤⠶⠃⠀⠀⢸⠀⠀⢃⠸⣿⡇⢿⡄⠀⢠⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⢛⡟
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⠀⣿⣿⡈⢷⡀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⣇⣿⡇⢧⠈⣷⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠘⣿⡇⠈⢷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠐⢀⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠀⠀⠀⠀⠰⣀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠠⠀⠀⠀⠀⠠⣸⣿⣤⣀⢀⠀⢁⠀⢀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡄⠋⠁⠀⡠⠚⣠⡷⠃⠈⠉⠈⠻⣬⠐⠦⠁⠀⠈⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠜⠁⢰⠋⠁⠀⢸⣧⠈⠂⢙⣳⠀⠃⠀⠀⠀⠀⠐⢤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠁⠀⠀⠀⠀⠀⡃⠐⣼⡇⠀⢀⣯⣽⠄⠠⢼⣿⠃⢠⠁⠀⠂⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡀⠀⠀⠀⠀⠀⠂⢡⡀⠿⣿⠞⠊⠉⠁⠀⠻⡾⠟⣀⠄⠀⠀⠀⠀⠀⠀⠠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⡌⠀⣽⣠⣬⠀⠈⣥⣬⡇⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣰⣧⣀⣴⠀⠀⠀⠀⠀⢀⣷⣾⣿⣷⡀⠀⣀⠠⡴⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠉⠈⣽⠀⠒⣾⣟⣿⣿⣿⣷⡄⠀⠀⢠⡿⠿⣿⣿⣟⣷⣀⠀⠀⡷⠀⠀⠀⠀⠀⠁⠀⠀⠰⠄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢓⠀⠀⠀⢀⣰⠏⢠⣿⣻⣿⣿⣿⣇⡾⠃⠀⠀⠈⣿⣭⣿⣿⣿⣿⣿⣦⠀⢤⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂
⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠀⠀⠀⠀⠁⢠⣿⣷⣿⡿⢹⠇⢹⣷⠀⠀⠀⠀⣿⡿⡏⠻⣿⣿⣿⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠐⠓⠀⠀⠀⠀⠀⠀⢰⠦⠾⣿⣿⣿⡇⢨⡄⠀⠿⡷⣿⡟⡼⠟⣆⠁⢀⠿⣿⣿⡾⠃⠸⡄⠀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⡀⠀⠹⣿⢟⣧⣀⠲⣁⢄⡙⠊⠘⢀⣐⠋⠀⢘⠄⢿⣿⡟⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠠⠄⠀⠉⠀⠀⠀⠀⢀⣿⣥⠀⠀⠀⠀⠈⣿⣷⡍⠀⠃⠲⠈⠁⣥⣼⣷⡎⠀⠀⢻⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⡀⠈⠁
⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢀⣾⣷⠟⠃⠀⠀⣀⣼⣿⣿⠁⠁⣤⣤⡄⠀⣿⣿⣿⣷⡄⠀⠀⠀⠀⠈⠉⠛⣧⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⣾⣻⡏⠀⠀⠰⣟⡛⠛⠻⣿⠀⠀⠟⠟⠃⠘⣿⣿⣿⣿⠁⠀⢂⣤⣔⠀⠀⠀⠈⡃⠀⠀⠀⠶⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣼⡿⠏⢱⣤⠀⠰⠟⠁⠀⠀⠘⢷⢄⡀⠀⠀⠀⢈⠿⣿⣿⡄⠀⣨⠀⠉⡐⠀⢀⠆⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠰⠃⠁⢠⣾⡇⠀⠀⠀⠀⡀⠀⠀⠀⠢⡁⠉⠈⠁⠠⣶⣖⠀⠑⢚⡄⠈⠓⠉⣠⣦⡆⠀⢰⣄⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠡⠀⠀⠀⠀⢠⡖⠀⢀⣼⣿⣁⣄⠀⠀⡾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠀⠀⠀⠀⠈⠉⠁⠻⣿⣤⣶⣿⣸⠇⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠄⠀⠀⢀⣿⣀⣀⣙⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠶⡄⠀⠀⠰⣾⠇⠀⠀⠀⠀⠂⠀⠸⠧⠛⣿⣷⠘⢷⡀
⠀⠀⠀⠀⠀⠄⠀⠀⢛⣽⠏⣿⣟⣉⡙⢻⡀⠀⠀⠀⠸⢿⠀⠀⠀⠘⠃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠙⢷⠆⠀⢀⡄⠀⠈⠁⠈
⠀⠀⠀⠀⠀⠀⠈⢳⠜⠃⣾⡿⣣⣉⠗⣾⣷⡀⠀⠀⠁⠈⠀⠀⠀⠀⠐⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡉⢻⣿⡎⠃⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠘⢀⣾⠋⣡⣿⡏⣾⣇⣸⡿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⡴⣶⡻⣿⡆⠻⢷⡄⠈⠛⠂⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⣠⣿⠁⣾⠇⣼⣟⡴⠿⠛⠡⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠰⠿⣧⡍⢿⡆⠈⠳⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠗⠁⠁⠀⠀⠁⠀⠀⠋⠀⠛⠺⡀⠀⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⠈⠷⡀⠀⠀⠀⠄⠀⠀⠤⠠⠄⠀⠀⠀⠐⢒⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠰⠀⠀⠀⠀⠀⠀⠒⠒⠠⠄⠀⠄⠀⠀⠀⠀⠐⠈⠓⠤⢤⣀⣀⠀⠀⠀⢀⣀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠇⡐⠁⢀⣀⠁⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠐
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣏⠠⠉⠥⠂⠀⠀⠀⠀⢀⡜⢉⣃⡔⢓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢘⡞⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠳⢄⣀⠀⠀⠀⠀⠀⠀⢈⡠⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠈⠐⠒⠂⠀⠀⠒⠶⠒⠙⠉⠁
⠀⢀

⠀⠈
⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠹⣿⣿⣷⣼⣾⣼⣾⣇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠖⠀⢀⡀⠱⠜⣾⣿⣿⣿⣿⣿⣿⣿⡟⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡇⢀⠀⠀⠙⠪⢢⣎⣿⣿⣿⣿⣿⣿⣿⣏⠵⠓
⠀⠀⠀⠀⠀⠀⢤⣿⣩⣴⣷⣿⡷⢄⣿⠅⣀⠇⢽⣿⣿⣿⣿⣿⡿⠛⠂⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⢘⠿⣿⣿⣿⣿⣤⣤⡁⢠⣐⢄⣸⣿⣿⣽⣽⣯⡇⠐⣄⠉⠀⣠⡄⢐⡤⠛⠛⠁⡂
⠀⠀⠀⠀⠀⠀⠄⠓⠿⢻⢯⣉⣹⠟⠿⡟⢻⢾⣿⣿⣿⣿⣿⣿⣄⢀⣈⣠⠄⣈⠉⠁⠀⣱⣸⡔⡇
⠀⠀⠀⠀⠀⠰⣤⣤⣀⣀⣾⣿⣿⣿⣄⣉⠘⣽⣿⣿⣿⣾⢻⣿⣿⡉⣍⠉⠉⡉⢩⣾⣺⣴⢿⣻⣶⣷⡀
⠀⠀⠀⠀⠀⢢⣸⣿⣿⡿⣿⣿⣿⡌⣿⣿⣴⣿⣿⣽⣿⣿⣿⣿⣿⣧⢀⣿⣿⣷⣷⣿⢿⣻⣿⣟⣿⢽⣿
⠀⠀⠀⠀⡀⠘⣽⣿⣿⣿⣿⣿⡏⠙⢿⣿⣽⣿⡟⡛⢿⠿⠛⠟⠛⠛⠐⠿⣿⣿⣿⣿⣯⢻⣞⣿⣾⣿⢿⣃⡄
⠀⠀⠀⣌⢱⣼⣾⣿⣿⣿⠿⡿⠛⡠⠿⠿⠿⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⠿⠿⠿⠙⠁
⠀⠀⠀⠉⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠙⠌⢦⡀⠀⠀⠀⠀⠀⠀⣤⠼⣿⣩⣤⠄⠒⣰⣖⡢⠆⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢡⠁⠐⣀⡄⠀⠀⠾⠀⠀⠣⠀⠀⠈⠃⠠⠤⠦⠀⠀⠀⢡⠀⠨⠞⣠⠚⣡⠜⠋⠁⣀⠚⠛⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡀⠀⢘⣻⡆⢢⣦⠀⠀⣀⠀⠀⡇⡵⠐⢈⡙⢁⠀⠀⣠⣦⢀⠤⠇⠚⢵⡾⠋⠀⣧⠀⠀⣠⣿⡀⢠⡅
⠀⠀⠀⠀⠀⢰⣶⠎⠁⡄⠈⠚⠻⣿⡷⠀⠈⢰⡄⠻⠀⢀⡇⠦⡀⠀⠃⡜⠃⠺⠏⠀⠀⠀⠀⠀⠈⠇⠀⣴⣿⣦⣎⣀⠈⣤⠀⠓
⠀⠀⠀⠀⠰⣯⡟⠁⠘⠋⠀⣠⡆⠘⢿⠀⠀⣾⡁⢀⠀⢨⠁⠀⠀⠁⠒⠳⠀⠀⡀⠀⠀⠀⠀⠀⡄⡃⢄⠁⠂⠄⠉⣉⠃⢀⠈⣥⡀⢀⡂
⠀⠀⠀⠸⣿⠉⠶⠶⡤⢀⣻⢨⡛⠄⠈⢨⠀⢸⡀⢸⢠⢼⡒⠀⠤⠀⡄⠰⠀⠠⣛⠀⠤⣶⢲⡼⠀⠡⠄⠂⠠⠈⢀⢀⠈⢀⡆⢿⡅⣜⠃
⠀⠀⡆⠀⠉⠀⢰⡎⠀⢠⠇⣀⡉⠃⠀⠘⠃⠈⡷⠾⠚⠛⠟⡂⣄⠐⢡⠐⠅⠘⠙⠶⠤⠀⠉⣈⣥⠀⠀⠀⠀⠀⠀⠀⠀⣸⣁⡜⠀⠀⠉⠳⠆
⠀⠀⠀⠀⠀⠀⢸⠁⣀⣠⠀⠛⣡⡀⡀⢄⡀⠉⠀⠀⡀⢤⡀⠀⠠⣛⡄⠙⠀⠀⠚⠤⢀⠂⠀⣀⠙⠇⠀⠀⠀⠀⠀⣠⠄⠀⠾⣄⡀⠀⠀⣠
⠀⢠⡿⠂⠀⠀⠀⠀⠈⠹⠀⠰⠿⣀⡷⠈⣁⠃⢀⠙⡟⠠⠅⠀⠀⠈⠀⠀⠀⠘⠃⠀⢠⠅⢈⠋⠀⠀⠈⠳⣶⣿⣛⠃⠀⡀⠀⣄⠀⡀⠠⡿⠄
⠀⠈⠁⠀⠀⢶⠄⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠀⠓⣂⢡⠴⠗⠂⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣾⡄⠀⠀⠀⠀⡩⡄⢹⡄⠈⠀⠀⡅⠀⠁⡰⢂⡀
⠀⣠⠗⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠺⠁⠀⠀⠰⢟⣁⣀⣷⣦⣱⣿⠆⠀⠀⠐⠀⠁⠀⣸⡧⠈
⠀⠸⠀⠸⡇⣀⡞⢀⡟⠀⠀⠀⠀⢀⣰⠷⡄⠀⣰⡂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠃⠀⠋⠸⣷⢞⡉⣥⡩⣹⣶⣦⣤⣀⡀⠀⠀⠈⠅⡀
⠀⢀⣐⣀⣈⣽⣅⣸⠃⠀⠀⠀⠿⠋⠁⢀⡀⠱⣿⡧⠀⠀⠀⠀⡀⠀⠰⢺⣄⠀⠀⠲⠀⠘⠁⢸⡟⠻⠖⠿⠛⠞⠉⠉⠛⠻⠿⣷⣶⠒⢮⣀⡀
⠀⠀⠽⠓⠘⠓⠚⢿⠄⠀⢤⡴⢠⡄⠀⠀⠁⠀⢰⡦⠀⠀⢄⣠⡄⠀⣀⠓⣈⡡⠴⢪⡉⠵⠲⢒⣤⣀⠀⠀⠀⠀⠀⣿⣶⣤⣤⣀⣀⠀⣼⡉
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⡇⠈⠉⣤⠉⠠⡄⠀⠀⠀⠀⠀⢹⣫⢁⣩⠄⠀⠀⠤⢉⠐⠌⢃⠠⠤⠹⠳⡄⠀⠀⢠⣿⣿⣿⣿⡿⣿⡿⢶
⠀⠀⣀⠀⠀⡺⠘⠓⣦⣄⠺⢇⢀⡀⢼⡀⢠⠃⠀⠀⠀⠀⠀⢀⠛⣠⠍⠀⣤⡐⠂⣉⠑⠆⣀⠤⠂⠠⣘⢣⣤⠖⠁⠀⠉⠿⠉⠙⢶⡍⠒⢀⡄
⠀⠀⠓⠁⠀⠀⠀⢀⡁⠈⣾⣻⡈⠅⢀⠁⠀⢠⡀⠀⠀⠙⠶⠾⣦⠉⠐⠒⢠⣄⣂⡈⠌⢠⣭⡀⠾⠛⢡⡀⠙⢦⢄⠀⠀⣰⣦⣌⢂⠱⠞⠁⠁
⠀⠀⢺⣄⢀⡴⡠⠞⠓⠘⠋⢱⡄⠀⣼⠆⠀⠀⡁⠀⠐⣀⣀⠀⡉⢓⠠⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠔⢉⠱⣷⠦⠑⠀⠀⠉⠙⣻⡿⢇
⠀⠀⠘⣿⡟⠆⠀⣶⠂⠀⣤⠋⢀⡄⠀⠀⣰⠀⣠⠟⠀⠍⣩⠔⠟⢸⡄⠹⠗⠀⠀⠀⠀⠤⠂⡀⠀⢶⡟⠋⠀⠀⠀⠀⣀⣀⣠⠟⠀⠀⠀⠓
⠀⠀⠀⡿⠀⠀⠀⠈⠦⠀⠛⣦⣬⣿⡦⠀⠈⠁⠈⠃⠐⠦⠛⠃⠠⠜⠁⣴⡀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠉⠚⠯⣤⣤⠎⠙⢏⠀⠀⡠
⠀⠀⠀⠀⠠⡄⠀⠀⠀⢀⠀⠁⠁⡈⠀⠊⠐⣦⢠⢠⣤⣄⠀⢚⡀⠐⠀⠀⢳⣄⡀⢀⣀⠜⣇⠳⠀⠀⠀⠀⠀⠀⠉⢀⠀⣀⠀⣿⣿
⠀⠀⠀⠀⠀⠘⠒⠋⠀⡏⠀⠀⠀⡌⠀⢀⠀⠈⠡⠋⠁⠀⢨⡀⢀⠐⠁⡆⢀⡹⠿⠛⠇⠀⠸⣬⡀⠀⠀⠀⠀⠀⣰⠞⠋⠀⠀⠉⠀⠀⠀⠐
⠀⠀⠀⠀⠠⣀⣀⠀⢀⠙⠆⠀⠀⠀⢀⡁⠐⠀⠀⠰⠋⠀⢋⡐⠋⠁⠘⠓⢫⢤⡆⠀⢲⠇⠐⠀⠉⢢⣤⣤⡤⠖⠁
⠀⠀⠀⠀⠀⠀⠉⠀⢈⣁⠛⠒⠒⠚⠁⠀⢀⠀⠰⠖⠃⠀⢼⠃⠀⠀⠀⠀⢸⢆⠀⣠⠊⢠⡄⠀⠄⠀⢨⠻⠦⣤⠄⠃⠀⠛⠃⠄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣟⠀⠀⠀⡼⠉⠃⣤⠃⠀⠀⠀⠀⠀⠀⢸⡈⠿⢄⡖⠤⠵⠶⠶⠀⠁⠠⠆⠉⠛⠂⠡⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⠋⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠘⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⣼⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣀⣀⣀⣀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢻⣿⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿⣿⣥⣠⡍⢿⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⣿⣿⣿⣿⡄⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣶⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠉⠙⠻⣿⣿⣿⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣏⠁⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣇⡴⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣤⣛⣷⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⣠⣀⣿⠹⠛⠛⢋⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢀⡀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡁⣤⡤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣠⢰⣿⣿⡿⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣍⡿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢀⣄⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣅⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣼⡻⢿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⡎⢿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⣤⣀⢸⣿⣧⣼⠃⠀⠻⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣷⢀⣏⢸⣿⣿⡏⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣾⡟⢻⣿⣿⠃⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣟⣱⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⢛⣉⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⡥⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠋⢉⡀⠀⠠⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣀⠶⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⣁⠤⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠻⡟⢀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣧⠈⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡟⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣤⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣷⡄⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣹⣶
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣛⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣏⣿⣿⣿⣿⣿⣿⡙⠓
⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣶⣶⡶
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠋⠙⠛⠿⠿⠿⠿⣿⣿⡿⠿⣿⣿⣿⡿⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠛⣿⣿⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠸⡟⣿⠟⠇
⠀⠀⠀⠀⠀⢿⡿⠟⠁⠀⠀⠀⠸⣶⣦⣴⠶⣦⣀⠀⠀⠀⠀⣈⡹⣿⣧⣅⣘⡁⠀⠀⠀⠀⠀⣀⣠⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣾⣿⣿⣟⣻⣿⡷⠺⠿⢲⣦⣤⡿⣿⣶⣿⡿⠛⢿⣷⢾⣯⣼⣶⠁⠈⡿⠀⠘⠋⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁⠉⠉⠉⠉⠀⠀⠁⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠾⠟⠛⠛⠛⠛⠻⠶⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠉⣡⡞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣭⣽⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⣠⡶⠛⠋⠉⠀⠀⠀⠀⠈⠉⠙⢷⣦⡀
⠀⠀⠀⠀⠀⢀⣼⠟⣧⠀⠀⠀⠀⡿⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⢠⡿⠁⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⢰⡿⠁⠀⠀⣾⣤⣤⡴⣾⠷⠶⠒⠒⣿⠓⠒⠶⠶⠶⠶⢤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⢠⣿⢁⣠⡶⠛⣿⠁⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠶⣤⣀⠀⠀⠀⢹⣇
⠀⠀⣸⣷⠟⠁⠀⢀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣄⠀⣿⡀
⠀⠀⣿⠁⠀⠀⠀⣸⠇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣼⡇
⠀⠀⣿⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⣿⡀⠀⠀⣸⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠈⢿⡄⢰⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠘⣷⣸⡇⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀⡀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠷⠶⠾⠿⠶⠶⠶⠟⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠋⠀⡈⢿⣄
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠃⠀⠀⡇⢸⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣶⣤⣀⡠⢤⣀
⠀⠀⠀⠀⣸⣿⣿⣿⣿⡿⠀⣷⠀⠁⠈⣿⡄⠹⡀⠀⠀⠀⠀⠀⢀⣾⡿⣋⠀⠤⠴⣦⡀⠉⠉⠓⢶⣭⣂
⠀⠀⠀⠀⢿⣿⣇⢻⣿⡿⣄⠘⢧⡀⠀⠘⢷⣄⠀⠁⠀⠀⢀⣀⣿⣿⡆⠻⠤⣄⠀⠀⠉⠁⠀⠀⠀⣙⠻⣷⡐⡀
⠀⠀⠀⠀⠸⣿⡿⣆⠻⡷⣝⡲⣄⠁⠀⠀⠀⠉⠓⠶⠾⠯⠽⣿⣿⣿⣝⣶⣶⡤⢅⡀⠀⠀⠀⠀⠀⠈⢳⡈⢻⣜⣆
⠀⠀⠀⠀⠀⠹⣿⣝⢦⡈⠻⣿⣿⣷⣶⣶⡶⣶⣦⣄⠀⠒⠄⠸⣿⣿⣿⣿⣿⣟⡿⢶⣄⠀⠀⠀⠀⠀⠀⠱⡀⠹⣎⢦
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠛⣩⣅⣴⠶⠂⠈⣿⣷⣀⣀⠀⠙⠿⣿⣿⣿⣿⣷⣒⡬⣷⣄⠀⠀⠀⠀⢀⠓⢣⢻⣌
⠀⠀⠀⠀⠀⣠⣴⡿⢟⠋⣁⣴⣻⣵⠏⢀⡄⣰⢠⣿⣿⠙⠛⠿⣷⣦⣾⢿⠏⠉⠉⠉⠛⢿⣿⣧⠀⡀⠀⠀⢧⠸⠈⣿⡄
⠀⠀⠀⣠⣾⠟⣫⠾⣿⣿⣿⣿⠟⢁⠔⠋⠰⢣⣿⣿⡿⠀⠓⠦⣄⠙⢿⣎⠀⠀⠀⠰⣔⠀⠙⣿⣇⢹⠀⠀⠸⠂⠀⢿⡇
⠀⢀⣾⣿⣷⢟⣷⣿⡿⠟⢉⡄⠀⠀⠀⡀⠀⣾⣿⣿⡏⢰⡀⠀⠉⠁⠈⢿⣆⠀⠀⠀⠸⠀⠀⣿⣿⠠⣦⣤⢦⡆⠀⣸⣷
⢀⣾⣿⢿⣷⣿⣿⣁⢄⡼⠋⢀⡄⠀⡴⠁⣼⣿⣿⣿⢿⡄⢳⡄⠀⣆⠹⠌⣿⡆⠀⠀⠀⠀⠀⣿⣿⡳⣌⣛⣋⣠⠞⣿⡟
⢸⣿⣯⣿⣿⢟⡵⡵⠋⠀⣰⠋⢀⡾⠁⣼⣿⣿⣿⣿⣄⠹⣦⠻⣄⠙⣄⠀⢸⣿⡀⠀⠀⠀⠀⠹⣷⣝⣛⣒⣫⣤⣾⡿⠁
⢘⣿⣿⣿⠏⣾⠞⣁⠄⠀⠀⣴⡟⢡⣾⣿⣿⣿⣿⣟⢯⡳⣌⢳⡝⠧⠙⣦⡀⣿⣇⠀⠀⠀⠀⠀⠈⠙⠛⢛⣛⡛⠉
⠘⣯⣿⣿⡈⢁⠞⠁⣠⣴⡾⢋⣴⣿⠃⠈⢿⣿⣟⢮⡳⡙⢿⢦⡹⣦⠀⠘⣷⣿⣿
⠀⠈⠙⠻⢷⣬⣹⣿⣿⣿⠾⠛⠉⠀⠀⠀⠀⠙⠻⣷⣽⣺⣄⠁⠑⠝⢷⣵⣦⣿⣿⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⣖⣛⡿⠛⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣶⣾⣿⣿⣿⠟⠉⠀⠀⠀⣠⣴⣿⣿⢿⡿⠉⠀⣀⣤⣴⣶⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⣿⠿⢷⣄⠀⣀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢀⣼⣿⢕⡫⠊⢁⣠⣶⣟⡿⠿⠟⠒⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⠍⠀⢀⣾⡏⣼⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣾⣿⡷⠋⣠⣴⡟⢹⣿⣁⣠⣴⠾⠛⠉⠉⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣥⣤⣶⠿⠋⠀⣿⣿⣥⢹⣷⠀⠀⠀⠀⠀⠀⣿⣿⣎⣾⣿⢋⣤⣾⠿⡋⢉⡤⠖⠉⠀⣡⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⣀⡀⠀⢻⣟⣟⣆⣿⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⢋⠴⣫⢞⡭⢂⡴⣠⠞⣡⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⣿⣆⠀⠹⢿⡿⠟⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣵⢐⡵⣫⠖⣉⣤⡴⣞⣵⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣻⡘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠷⢯⣿⣥⣤⣽⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣮⣙⠃⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⡟⠈
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠢⡍⠀⢨⢀⡀⣠⠴⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣼⠋⢃⡀⠀⠁⠐⠊⠈⠾⠆⠰⠧⣺⡵⢦⠀⣄⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡽⢤⣙⡛⠶⠦⢴⠤⣄⣤⠀⢀⣺⡽⢃⣼⠀⠈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣾⣇⠀⠈⠁⠉⠐⠚⢀⣱⣖⣤⣉⢥⣼⣧⡁⠡⢀⠏⣰
⠀⠀⠀⠀⠀⠈⠁⢀⠀⢠⠂⠀⠸⠎⠓⠀⢀⠀⠀⠀⠀⡈⠟⠛⠛⠋⠉⠙⠒⣚⣡⣬⣼⡶⠀⠡⠰⠆
⠀⠀⠀⠀⠀⠀⡷⠿⠛⠛⠀⠀⠀⠀⠀⡄⢸⣿⣦⡖⠋⠀⠀⠀⠀⠒⠊⠉⣉⣉⡥⠕⣶⣶⠒⠋⡩⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢎⢻⣦⣤⣤⡿⢿⣭⣁⡀⠀⠐⠶⠿⠾⠏⠩⣬⡅⠀⠀⡹⢿⣫⠑⣿⣾⠿⡽⡀
⠀⠀⠀⠀⠉⢁⠀⠢⠹⣯⣗⣿⣿⣿⣷⡭⣙⠓⢦⣌⡛⣙⡛⠂⠉⠀⠐⠛⢾⡓⠺⢮⠙⣤⠁⠈⠻⠞⠂⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠒⠤⠼⣺⡷⣿⠟⠧⠆⠉⠉⠠⠍⠉⢭⡗⠀⣀⣦⢾⠿⡏⠷⠿⠁⠀⠉⠂⢉⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⣠⣿⣽⠃⠀⢀⣀⣀
⠀⠀⠀⢀⣨⣤⣥⡤⠈⠀⠁⠠⠴⠖⠒⠒⠂⠒⠖⠒⠲⠲⠶⠄
⠀⠀⠐⣆⠀⠀⢤⢀⡀⢠⣧⡄⠄⠀⠀⠀⢀⠀⠀⠰⣛⣳⣢⠐
⠀⠀⠀⢻⡣⠀⠈⠷⠀⠀⠈⠀⠀⠀⡀⠀⠈⠁⠀⠀⠉⠉⠁⠀⢷⠄
⠀⠀⠀⠀⢱⠃⠀⢀⣴⡁⠀⠀⠀⢸⣿⢀⠀⠀⠀⠀⠰⡀⠀⣧⠘⠂
⠀⠀⠀⠀⠈⣶⡆⢰⡏⠑⠲⣤⣄⡀⣿⠀⢂⠀⠀⢧⠘⢷⠀⠉⡀
⠀⠀⠀⠀⠀⠸⣆⠀⣇⠀⠀⠀⠙⢀⣧⡀⠘⠀⠀⠘⣶⠘⡅⠀⡅⠀⢘⡆
⠀⠀⠀⠀⠀⠀⢹⡤⠹⡄⠀⠀⣠⠞⠉⠻⡲⡇⠀⠀⣼⣶⢷⠿⢻⡿⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⢿⣥⡹⣄⣰⡏⠀⠀⠀⠘⠃⠀⠀⠘⠿⠀⠛⠈⠁⠀⣷⠂⠀⠠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣷⣡⡈⠛⢃⣶⡆⠀⠀⠀⠀⠀⡀⠀⠀⣄⠤⣀⣠⣬⡉⢚⢛⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢿⡟⠚⠏⠈⠠⠀⠘⠱⣾⡷⣪⠋⣀⣀⠈⠣⣀⣀⠀⠶⠆⢠⣙⣒⠒⢂⠾⣿⣶⣦⣴⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡂⠙⣆⣄⣁⠲⢶⣶⡁⢰⣴⣿⠟⣽⢞⣧⡄⢢⣤⣬⣗⣰⣶⣀⡴⢿⣭⣟⣤⡄⠈⣿⣿⣿⡟⣤⣴⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠣⣭⡒⠩⣽⠦⡈⠙⠾⠿⣿⣾⡅⠀⠛⢀⠋⣹⠋⢹⣧⣈⣿⡞⣻⡿⣿⣤⣤⡴⠮⢛⡛⠏⢭⠑⢠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠢⢭⠐⢤⣀⠁⢐⡄⢀⠨⠙⡟⠶⣾⠟⣿⠻⠿⠛⣛⣁⠸⠟⠙⠛⠉⠁⠀⠀⠀⠐⢂⠂⣈⣭⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡍⠀⠉⠢⢈⠁⠀⠀⠀⢽⠚⠅⠀⡤⢅⡀⠈⠀⠈⠉⠀⠀⠀⠀⠀⠀⢿⣽⠯⠗⠀⠀⠈⡀⡄⠈⠒⠸⠛
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⢷⣌⣺⠡⠀⠀⠑⠠⣙⠀⠁⡉⠢⠀⠀⡁⡀⠠⡀⠀⠀⠀⠐⠀⠀⣀⣠⣴⣶⣾⣿⡇⠀⠀⠤⢥⣳⣷⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣝⡻⣵⠦⡀⠀⠁⠀⠉⠂⠀⠀⠀⡀⠀⠄⠀⠀⠀⢀⣆⣶⣿⣿⣟⠛⠉⣩⠋⠁⠀⠀⢀⣀⣠⡛⠛⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣽⡈⠓⠤⣄⠀⠑⠄⠀⠀⠆⠀⠀⠀⠀⠸⣾⠿⠛⢉⠙⠛⠀⠈⠀⠁⠀⠀⣀⣤⣾⣷⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡉⠑⠐⠰⠠⠀⡕⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣢⣴⣶⣾⣿⣿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣌⡶⠁⢰⠀⠀⠀⠶⣀⣠⣴⣶⣶⣿⣿⣿⡿⠿⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣀⣥⣤⣥⣶⣿⠿⠿⠟⠛⠛⠛⠁

⠀⢿⣏⣾⣿⣿⣿⣿⣿⡿⣟⣯⣵⣶⣾⠾⠿⠷⠶⠶⠶⠶⠶⣶⣤⣤⣄⣀⡉⠛⠿⣿⣿⣿⣿⣯⣙⠚⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠈⠙⠿⢿⣿⣿⠿⠽⠿⠛⣉⣁⣀⣀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠐⠈⠙⠻⢿⣿⣶⣤⡉⠻⣿⣿⣿⣿⡟⢻⣎⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠛⠷⣿⣿⣿⣿⣿⣤⡤⠄⠈⠀⠉⠉⠙⠛⠓⠶⢦⣤⣀⠀⠈⠛⠿⣿⣿⣷⣼⠿⢿⣿⣿⡀⠹⣯⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣀⣈⣹⣯⣶⣄⠀⠀⠙⠻⣿⣷⣬⣿⣿⣷⣄⠽⣿⣿⣿⣿⣿⣿⣿
⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣟⣛⡻⣿⣿⣿⣿⣛⡛⠀⠀⠀⠀⠀⠙⢿⣿⣿⣻⣿⣦⠹⣿⣿⣿⣿⣿⣿
⣿⡟⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠈⠻⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠙⢿⣿⣿⣿⣧⢿⣿⣿⣿⣿⣿
⣿⡇⠀⠸⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢲⣿⣿⣎⠻⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣶⣄⠀⠀⠙⢿⣿⣿⣾⣿⣿⣿⣿⢏
⣿⠀⠀⠀⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣌⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⢻⣿⣿⣿⣧⣽⣿⡗
⡏⠀⠀⠀⡇⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣆⠀⢂⢻⣿⣿⣿⣹⣾⣷
⠃⡄⠀⠀⡇⣼⣿⣿⣿⣿⣨⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣹⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠹⣆⠈⣾⣿⣿⣿⣿⣿⣿
⠀⡇⠀⠀⠁⣿⣿⣿⣿⣿⣿⣷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣾⣿⣯⠻⢿⣿⣿⣿⣿⣿⣿⡆⠹⣆⣿⣿⣿⣿⣿⣿⣿
⠀⠇⠀⠀⠀⣿⠀⢿⣿⢿⣿⣿⣧⠹⢰⡀⠀⠀⠀⠀⢀⠀⡀⢰⡄⠘⣿⣷⣿⣿⣿⣷⣷⣽⢿⣿⣿⣿⣿⣿⡄⠙⣹⣻⣿⣿⣿⣿⣿
⣧⠀⠀⠀⢠⣿⡀⣼⣿⠸⣴⡉⣿⡀⠀⡇⠀⠀⠀⠀⠉⠀⠀⢸⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿
⠈⢷⡀⠀⠘⣿⣾⢸⡿⠀⢸⣧⣿⣧⣠⡇⠀⢰⣄⠀⠢⠤⠃⢸⣿⡆⢸⣿⠿⣃⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠉⠂⠀⠸⣿⣎⣷⡀⠘⢿⣿⣿⡟⡡⠀⠺⠟⢷⣄⣀⣠⡾⠁⡃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⣄⠀⠀⠀⡀⠈⠻⢷⣽⣶⣤⣭⣥⡾⠁⣀⠄⠀⠀⡉⠉⠉⠀⠀⢀⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟

⠀⠀⠀⢀⡠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⣠⣊⣁⠀⠀⠉⠑⢆⠀⠀⠀⢀⠊⠀⢠⡀⠁⠀⠊⠀⠈⠀⠀⠀⠀⠆
⠀⠠⠁⢠⠀⠀⠀⡄⠈⠄⠀⠀⠀⠀⡞⠁⠀⠈⠙⢦⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠘⢨⠀⠙⠀⠀⠰⠀⠀⠀⠸⠀⣠⣴⠖⠒⠒⠶⠤⣄⡀
⢠⠁⠀⠀⠢⠀⠜⠀⠀⠈⡄⠀⠀⠀⡅⠀⠀⠀⠀⠘⡆⠀⠀⢸⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢠⠀⡄⢻⡇⠀⢀⡴⢷⠀⠀⠙⣦
⠀⢢⣀⡤⠄⠭⠤⢄⣀⠔⠁⠀⠀⠀⢣⠀⠀⠀⠀⡸⠁⠀⠀⡜⠀⠀⠀⢠⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⠉⠀⠘⢦⣠⡴⠛
⠀⡤⠄⠀⠀⠀⢀⠀⠀⠤⡀⠀⠀⠀⠀⠑⠶⢖⣊⣀⡀⠔⠊⠀⠀⠀⠀⠘⠀⠀⠀⠀⠰⠁⠀⠐⡃⠀⠀⠀⠀⠃⢠⠀⠀⠄⠀⡤
⠀⠑⠄⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠠⡀⠀⡠⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠋⠁
⠀⠀⠈⠢⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⡠⠃
⠀⠀⠀⠀⠑⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠐⡀⠀⡀⠁⠢⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠉⢣⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠐⠀⠋⠁⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢲⠄⣝⣲⢈⣔⣣⠠⠆
⠀⣠⣤⣤⣤⣤⣤⣀⣠⣤⣤⣤⣤⣤⡀⠀⠑⢄⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⣀⡗⠀⠀⠀⠰⢖⡶⠉⠀⠀⠀⠑⣖⡰⠂
⠀⠈⣿⣿⣿⣿⣿⠋⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠑⢄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⢟⠩⠛⠉⠛⡟⠁⠀⠀⠀⠐⠂⣨⡇⠀⠀⠀⠀⠀⢨⡁⠒
⠀⠀⠘⠿⠿⠿⠋⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠑⣄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⡀⠄⢸⠁⠀⠀⠀⠀⠀⠘⢑⠗⣄⡀⠀⣀⡔⠳⠑⠂
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢀⡄⠀⠀⠀⠀⠀⠀⠀⢳⡀⢈⡏⠀⠀⠀⠀⠀⠀⠀⠚⠈⣷⠛⣩⠣⡏⠐⠃
⠀⠀⠀⠀⣇⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⠂⣀⠀⠀⠀⠀⠀⠈⢇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢠⢼⡄⠐⠀⣄⠈⠀⠀⠀⠀⣰⣶⣾⣿⣿⣿⣿⣶⢦⠀⠀⠙⠁⠀⡾⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠛⠃
⠀⠀⠀⠈⠆⠀⠀⢀⠐⠀⠀⠀⠀⠀⠘⡄⠤⠭⠭⠭⠥⠔⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⣄⠈⣷⣦⡀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⡀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⢟⠀⠄⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠿⠟⠛⢃⡝⠛⠛⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠐⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⢸⠈⠈⠂⣀⡀⣩⠀⠀⠀⣈⡩⡰⠀⢸⠟⠉⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠘⢄⢀⣤⠾⡣⠃⠀⠀⠀⠀⠀⠸⣀⠀⠀⠀⢀⡅⠀⠀⢈⠔⠊⠁⠀⠀⠄⠀⠀⠀⠀⣰⣿⣿⣧⢀⠂⠀⠀⠀⠀⢰⡇⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠁⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠅⠒⠂⠠⠁⠀⠀⠀⠀⠀⠈⠢⡀⢀⣼⣿⣿⣿⠿⠃⠀⠀⢰⡭⢭⣭⣥⡤⣤⣬⣭⣥
⠀⠄⠀⠀⣄⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⣀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠡⣚⠃⠌⠔⡛⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⡤⠴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠕⠛⠪⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡖⠻⠀⠀⠀⠂⠀⠀⠱⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠣⡄⠀⠋⠀⠀⣤⠞⠋
⠀⠠⠚⠈⠉⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠀⠀⠘⠀⠀⠀⠘⠁⠀⢰⠂⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠⢉⣉⣉⣌⣠⣭⣤⣄⣤⡝⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠉⠀⠈⠀⠈⠉⡾⠸⠏⠻⠉⢻⠋⠁⠀⠁⠈⠀⠀⠀⠀⠀⠤⠖⠁
⠀⠀⠀⠀⠈⠁⣂⠄⠀⠀⠀⠑⠦⢀⠀⠀⠀⢠⣄⠀⡀⠀⠀⢉⡀⢀⡉⠀⠑⠤⢄⣀⣠⣄⣀⠤⠚⠃⠀⠀⠀⠀⢀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠁⠐⠚⠈⠁⠀⢢⠀⠈⠉⠉⠃⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒
⠀⠀⠀⠀⠀⠐⠀⠀⠔⠛⠈⢠⡄⠀⠠⡀⠀⠀⡀⠀⢀⠜⠷⣄⠀⢀⣸⡾⢁⠀⠈⢄⣀⣀⡀⠀⠀⠀⣾⠁⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠠⣴⠀⠒⣋⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠈⡆⠀⠀⠘⠋⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠄⠀⠀⠉⠒⠀⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠂⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠈⠉⠙⠚⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠋⠉⠁⠉⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡔⠚⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⡖⠺⠿⣿⠛⠟⠛⠟⠿⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⣠⣶⠀⠀⠀⡄⠀⢀⡀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠈⡘⢻⡀⠀⠄⠒⠀⠸⠟⣁⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢤⡀⠀⠘⣿⣧⣴⣜⣴⠇⠀⠈⣾⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣀⠃⠀⠀⠀⠀⠀⠉⠋⠹⠏⠀⠀⠀⠉⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠴⡆⣀⣰⣧⡄⠘⠓⠐⡀⠀⣀⡀⠁⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠭⣀⠛⢃⡠⢏⣹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⢁⣰⠚⠃⢾⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠒⠂⠀⠈⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⢶⢶⢷⣶⠾⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⣠⡴⠋⠁⠀⠀⠀⠉⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢾⣄⠀⠀⠀⠀⢠⡾⠁⠀⠀⣀⣀⣀⣤⣤⠤⠤⠦⠤⠠⠄⣀⡈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠉⠛⠷⠶⢶⣿⠗⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢾⣦
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⣾⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⡼⢀⣠⣴⠶⠾⠟⠛⣻⡟⠛⠛⠛⠛⠿⠶⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢀⠟⠋⠁⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣤⣤⣶⣿⣶⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢶⣄⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⣠⠞⠋⠁⠀⠀⣿⠀⠀⠀⠉⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⣄⣾⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⢈⡇
⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⣠⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣀⣀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣴⣶⣤⣾⣷⣿⣶⣿⣿⣿⣿⣿⣥⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠃⠉⠉⠉⠋⠉⠉⠉⠉⠉⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢀⣐⡒⣒⣂⠒⠂⡐⠠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⣂⣀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠃⠂⠄⡐⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢁⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⡙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣨⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⣄⠐⠦⢚⠂⠍⠃⠉⠀⠀⠀⠱⠄⣧⡀⠂⠀⣲⢐⡀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠉⠅⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠸⠈⠒⠘⠯⢃⡠⠰⡄⣀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣰⡔⠋⣄⠓⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⠀⠆⠀⠂⠀⠀⠀⠂⠐⠀⠐⠀⠘⠀⠃⢙⠿⣷⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣆⣫⣶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠂⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠃⠐⠀⠘⠀⠈⠀⢉⠞⡿⢞⣦⠐
⠀⠀⠀⠀⠀⠀⠀⠁⠱⢿⡀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⢙⣿⠷⢥
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠂⠠⣄⠀⠀⠀⠁⠐⠀⠀⠀⠠⠀⠄⢀⠀⢠⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠉⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣠⠄⡈⡅⠃⠠⡆⠀⡄⢀⣀⣀⢠⠀⣠⠀⡀⢀⠀⠄⠀⠄⠀⠄⠀⠠⠀⠔⢀⠆⠀⠒⠀⠉⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠐⠃⠸⠀⡶⠀⡦⢩⠌⣿⡈⢣⣈⡁⣻⣄⠙⢅⣒⡀⢀⡄⠰⣠⣀⠠⠀⡠⠄⢸⠔⡦⠚⡄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠆⢰⠀⡄⠀⡀⠈⠀⠈⠀⠋⠀⠟⠀⠿⠀⡆⠀⠚⠁⠁⡅⠀⠁⠌⠀⠭⠀⠚⢀⡁⣀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠸⠀⠆⠠⡄⢉⡀⢁⠀⠂⠚⠀⠰⠄⠶⠀⠶⠀⠤⠀⢠⠄⠠⠄⠀⠐⠀⠰⠆⠈⠃⠘⢀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⡀⢁⠈⣁⠘⠂⠸⠈⠧⠀⠆⢰⠆⢰⡀⢰⡀⠠⡄⠀⡄⠀⣐⠀⠲⠀⠞⠀⠓⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠆⠘⠇⠐⡀⢤⠠⠀⣄⢀⡄⢠⡄⢀⡀⠀⠀⠀⠄⢠⠄⠰⠄⠸⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠘⠁⠈⠂⠈⠦⠀⡆⠀⡄⢠⠀⣨⠀⣉⠀⡁⢈⡁⢀⠀⢀⠁⡄⠀⡆⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠎⢃⠀⠂⠀⢦⠠⡄⠠⡈⢁⠉⡀⢉⠀⢉⢈⡁⢈⠀⡉⢀⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠂⠐⠂⠰⠆⠠⠄⠄⡇⢈⣃⣉⢈⡁⣉⢀⠁⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢶⡂⠤⣎⡉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡜⠉⠑⡦⡈⠓⢤⡀⠙⠢⣄⠀⠀⢀⣴⢲⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡜⠀⠀⠀⢣⠈⣧⡀⠙⡗⢄⠀⠑⡄⣸⠁⢺⠁⠀⠀⠀⢀⡠⠚⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡸⠁⠀⠀⠀⠈⡇⠘⡇⠀⢸⠀⢣⠀⠸⡇⠀⡞⠀⠀⠀⡴⣋⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢰⠁⠀⠀⠀⠀⠀⠸⡀⡇⠀⡇⢀⡤⢇⠀⢱⡀⣇⠀⣠⠊⠀⠁⠘⣠⣋⠤⠒⠂⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢀⠇⠀⠀⠀⠀⢀⣀⣀⡿⠀⣸⣥⡏⠀⠈⡆⠀⢣⢙⡞⠁⠈⠱⢄⠜⢋⡀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⠃⠤⠞⠻⠚⠛⠉⣋⣩⢩⣹⠃⢠⣯⠄⠀⠐⠀⠸⡄⠈⢇⠀⠓⠆⠠⢀⡀⠀⠑⢀⡴⠋
⠀⠀⠀⢠⣶⣟⢙⡉⣅⣶⡛⢦⠀⡶⠀⡟⠃⠈⡀⣅⣠⣰⠇⠀⡌⡌⠀⣄⣀⠀⠀⢱⡀⠘⡄⠀⢄⣀⠀⠘⢠⣴⠋
⠀⠀⠀⠸⣯⢯⠣⡄⢤⠠⠌⠈⢢⡇⠀⠹⡝⠀⣉⡿⢂⡎⠀⣸⠉⠂⣤⡈⢩⣀⡀⠀⢣⠀⢱⣁⣤⣭⠴⢾⣒⣚⣿⡄
⠀⠀⠀⠀⢹⣿⢸⢸⢦⡠⠶⡀⠀⠙⠢⣄⠳⣐⠄⢋⡽⠀⢸⣃⣥⢯⠴⠿⡖⣞⡓⠯⢽⣦⣤⢻⣶⣚⢈⣈⢠⣤⡾⠁
⠀⠀⠀⠀⠘⡛⣮⡣⣙⢷⡤⠼⠦⠒⠖⢚⢛⣙⣩⡿⡁⢀⠟⢘⢉⢩⢈⠭⠇⡓⡃⡍⣿⡙⠛⢉⢠⡟⠚⡋⠉⣽
⠀⠀⠀⠀⠀⡗⡌⢻⣮⣿⡂⡂⣚⢀⡍⠥⠰⣾⠹⠭⢿⢟⣿⡸⠾⠼⡾⠚⠚⢛⠉⠉⢨⠿⢤⣐⡾⠁⠈⠁⢀⡇
⠀⠀⠀⠀⠀⣷⡀⠳⢈⠳⠤⠧⢴⡤⠶⠶⠼⠻⣆⠐⢀⡼⢁⠀⠀⠀⠖⠀⠀⢈⠀⠀⠰⣠⢾⣿⣿⣆⢈⠀⣸⠃
⠀⠀⠀⠀⠀⣿⡄⠳⢀⠙⡇⠀⠠⠄⠀⠖⠀⢀⣽⣿⣿⣄⢠⠀⠀⠐⡂⠀⡈⣩⠀⠀⠰⠛⠓⣿⠊⠉⠉⠀⡿
⠀⠀⠀⠀⠀⢸⡆⡓⢀⠙⡧⠀⠰⠀⠂⠒⠸⡯⢻⣟⣏⠾⠧⠀⠀⠈⠁⠀⠀⣀⠀⠀⠤⠀⠀⠓⠀⠀⡋⢸⠃
⠀⠀⠀⠀⠀⠈⢷⡅⠠⡁⡧⠀⠰⠂⠀⠒⠀⠀⠸⣇⠃⡀⠤⠀⠀⠐⠁⠀⠀⡀⠀⠀⡤⠀⠀⢒⣀⡩⠥⠞
⠀⠀⠀⠀⠀⠀⠈⠳⡠⡄⢣⠀⠰⠄⠀⠒⠀⠀⠀⣉⠀⠀⣀⠀⠀⠐⠂⠀⢀⣁⣀⡤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⢹⠀⠠⠄⠀⠖⠀⠀⠀⢁⢀⣠⣤⡤⠶⠶⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠤⠴⠖⠒⠛⠛⠉⠛⠉⠉

⠀⢀⢊⠀⣼⠗⡇⢠⠁⣿⡇⠀⠀⠀⢀⠄⣣⣴⣫⠖⠋⢝⣩⠞⣋⠂⡴⠀⢠⡟⣰⠃⠀⡄⠘⠗⢰⠀⢨⡽⢆⠑⡁⣍⠲⣄⣊⡸⢿⡹⣆⠀⠈⢻⣿⣷⡔⡌
⠔⡡⣪⣾⠏⠀⣿⠏⢠⣿⣷⣤⣤⣴⣷⡿⠟⠋⣀⣤⢞⡫⠒⠁⣠⠇⠀⣰⠏⡴⠃⠀⢀⡇⠀⢠⠃⠀⡄⠳⢿⣦⡈⢪⡱⣌⠳⣶⣼⠇⣿⠀⠀⠸⠀⠀⢻⡜⡆
⢊⣴⡿⣃⡀⣠⣴⠁⣼⣿⣿⣿⡿⣽⠟⣀⣴⣾⠿⠋⠁⠀⡠⠖⠁⢀⡴⣣⠞⠁⠀⢀⡾⠀⢀⠎⠀⠀⢃⠀⠈⢻⠕⡀⠱⡝⣦⠘⠶⣾⡿⠀⠀⡇⠀⣧⢸⣷⢱
⣿⣋⣥⣤⣽⠟⠁⣰⡿⢋⠍⣂⣤⣴⠾⠛⠉⠀⠀⠀⡠⠂⠀⢀⣴⣫⠞⠁⠀⠀⠀⣼⠃⢀⠞⠀⠀⡔⣼⠀⡆⠀⠁⠡⡀⢹⡄⠀⢄⠀⠀⠀⠀⣭⠀⠁⠀⢿⡀
⠉⠉⠉⢉⡶⢠⣾⠏⢐⣵⠞⣋⠁⢀⣤⡄⠀⠀⡠⠊⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⣸⠏⣰⠏⠀⠀⡐⣠⠇⠀⣿⢠⣤⢠⠁⢈⡇⠀⠈⠳⠴⠀⢀⡏⢰⠀⣼⣿⡇
⣦⡿⠟⠉⢠⡾⠃⣴⠟⠃⠄⠀⠘⠆⠛⠁⢠⠊⠀⢀⣴⠟⠁⠀⣠⠄⠀⠀⠀⣴⢯⣿⠋⠀⠀⠜⡴⠃⠀⢠⡇⠈⡁⡸⢸⣀⡇⠀⠀⠀⢀⡀⣾⠀⠉⢀⣿⢹⠁
⠟⢀⠔⣡⡿⢡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠔⠁⣠⡴⠛⠁⠀⢀⠔⠁⡀⠂⢀⣼⣧⠞⠁⠀⠀⠀⡼⠁⠀⠀⠸⡿⠟⣱⠃⠹⠟⢡⠁⠀⠀⢉⠌⡜⠀⠀⣼⡏⡞
⡠⠃⣴⡟⣠⡟⠁⠀⠀⢰⠀⠀⠀⠠⠊⣠⡾⠋⠀⢀⡤⠊⠁⠀⠈⠁⣠⡾⠋⠁⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⠀⣴⣧⠆⠀⣠⢃⠀⠀⡀⢈⡼⠀⠀⢰⣿⣾⠁⠰
⠀⣸⡟⣰⠏⠀⠃⠀⠀⠈⠀⠀⠠⢁⣼⠟⠀⢀⣴⡋⠀⠀⠈⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠄⠻⣤⡀⠀⢀⣤⣾⣿⠃⠀⠔⡡⠂⠀⠀⢠⠋⠁⠀⠀⣾⣿⠇⢠⢣
⢰⣿⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠀⠐⠋⢁⣀⠴⠂⢠⣾⠟⣡⠊⠀⡀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣿⣿⣟⣧⠖⣠⣾⣧⠔⢈⡴⡡⠁⠀⠀⢸⣿⡏⢠⠆⡼
⢺⡇⣸⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠖⠋⢁⢴⣫⡾⡣⢺⠃⠀⣄⠙⠆⠤⠀⢀⣠⠚⡩⠖⢹⣿⠾⢋⣡⣾⣿⢫⣀⣴⣋⠖⠀⠀⠀⠀⣿⡟⢠⠃⢰⠇
⢸⣧⢿⢀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢞⣵⡿⢋⡾⠁⠳⠄⠀⣀⣤⣤⡶⠟⠋⣠⠾⠄⠠⢀⢠⣴⠋⠱⣧⠿⡿⠛⡋⠁⠀⣼⣿⡞⢰⣿⢡⠃⢠⡿
⠘⢿⣞⢎⠣⣀⠉⠓⠂⠀⠀⢀⣠⣤⠶⢛⡥⠞⡡⠀⣴⠟⣋⢀⠤⠶⠋⠁⠀⠁⠐⠆⠀⢀⣠⠴⠊⢡⣿⣃⣀⠤⣐⣼⣷⠊⣰⠀⢰⡟⣿⠀⣿⣧⠇⣰⣿⠇
⣦⡈⠻⢷⣿⣶⣦⣤⣤⠤⠖⠚⣉⣤⠞⢋⡴⠋⢠⢸⡇⣾⠋⠀⠀⠀⠈⠀⠀⣀⣠⣴⠞⠋⠀⠃⠀⠀⠀⠀⠀⢀⡽⣻⠃⠀⡇⠀⢸⡇⡇⢠⣿⡟⣰⣿⣿
⠈⠛⠲⠀⠀⠀⠀⠀⣀⡤⢶⠾⠋⠁⣴⠋⠀⠀⠈⠪⠷⠿⠷⠒⢚⣉⡤⢒⣫⡿⠋⣡⡴⠖⠚⠙⠋⠉⢀⣦⠞⡟⢰⠇⢠⣆⢳⠀⠸⣷⡇⠸⢻⣧⣿⣿⡟
⣹⣷⣤⣤⣶⠶⠚⠋⢁⠔⠀⠀⢀⡞⣇⠀⣑⠀⠀⠀⣀⣤⠶⠚⠉⢀⡴⣻⡏⠄⠞⢡⣦⠅⠀⢁⣰⡿⣫⠵⣆⡀⢸⡄⢼⣿⣧⡣⡀⢻⣷⠀⢼⣿⣿⣿⣧⣀⣤
⠟⣿⡡⠉⠀⣀⣴⡾⠁⡄⢴⣿⠌⠓⠚⢿⣞⣿⠿⠟⠋⠀⢀⡔⠀⣾⣇⣛⠿⠖⠋⠉⢀⡠⣺⢿⣿⠋⣁⣑⠊⣦⡈⢧⠸⣿⣿⣷⠄⠄⠻⣆⠀⠹⠿⣿⢿⡿⣣
⠿⢟⣩⣷⣿⠞⠋⠀⠘⠳⠬⠷⠾⠀⢛⣋⡍⠈⠀⠀⠀⠀⠘⠧⠀⠀⠁⠀⢀⡴⢂⣴⡟⣱⢃⣿⠁⠚⣉⣀⡀⠈⠙⣌⠣⡻⣿⠿⣷⣄⡀⠈⠙⠒⠒⣊⣥⣾⡿
⣾⣿⡽⡻⠃⠀⣠⠄⠘⠁⣡⡴⣶⣿⡟⢹⡇⠀⠸⢧⣤⡤⠄⠀⢀⣠⢔⣦⠎⠀⡞⣿⢡⡿⢸⡇⢰⠿⠉⠉⣛⣛⠦⣄⡑⠌⡪⠻⢤⡠⣭⣵⣶⡶⣿⣿⣿⠿⠷
⠑⣻⠞⣠⠄⣶⠇⢠⣾⣿⣿⣾⠉⢿⠠⣥⣽⠒⠀⣀⠀⠀⣠⣴⣿⡠⠋⣿⠀⠀⡇⣿⠘⣧⢸⡇⠎⠴⠿⠶⠭⠽⣿⣿⣿⣷⣦⣄⣀⣨⣥⡤⣴⣾⢟⣿⡃⠚⢋

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠤⠂⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣦⣜⠒⠒⠒⠒⠀⢐⣀⣾⠃⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢿⡞⠋⠁⠀⠀⠀⠀⠈⠈⠁⠉⠙⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣒⡿⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠇⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠨⠰⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡐⠀⠀⠀⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠷⠌⠀⠙⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠂⢛⣩⣴⣶⣥⡀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠠⠸⠄⠴⡀⠠⣬⡤⠀⠠⠀⠀⢤⠄⡠⠄⢒⡠⢴⣞⠩⡛⠿⡭⢪⠭⢯⡛⠶⣆⠶
⠀⠀⠀⠀⠀⠀⠐⠂⡤⠐⠠⣴⡟⢗⡤⣤⣀⠈⠃⣤⡖⢻⣛⣲⣩⠷⢻⣇⣵⠗⢼⡃⣩⠎⢷⣯⡖
⠀⠀⠀⠀⠀⠀⠀⠂⠁⠾⢿⣿⣷⣦⣁⣛⠿⣷⣄⣼⡇⣿⣿⣿⣿⣶⣰⣿⠈⠉⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠈⠉⠉⠀⠁⠉

⡂⠙⠿⠧⠤⠀⠤⢠⣀⢹⠇⢀⠡⠀⡈⠑⠀⠐⠀⢀⠈⠱⣧⠀⠄
⠀⠔⢤⠀⠜⠳⡄⠈⣿⠢⠂⠈⠑⠁⣄⠀⠀⠀⠀⠉⢄⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⢸⣧⣨⢤⠐⠊⠙⣆⢫⡴⢂⡀⠀⡀⠈⢿⡇⠀⠀⠀⠀⠠
⠨⠋⠀⢸⡇⡐⢾⡟⠀⠀⠀⡉⠢⣌⡐⠊⠁
⠀⠀⠀⠘⠃⠘⠀⠈⠀⠀⠀⠀⠀⣿⡇⠂⠀⠀⠀⠌
⠀⠐⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣀⠠⣠⡾⠿⡚⢿⣦⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢷⡄⢴⡆⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⢀⠀⠘⡏⠀⢰⣿⠂⠀⣛⣿⠀⢀⣿
⠀⢸⡇⣤⡄⢽⠀⠀⣾⡿⢿⣇⣬⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⢐⠀⠀⠚⡟⠒⡟⢫⡟⣤⠊⣏⡄⢀⣀⣀
⠀⠀⠀⠘⠃⠀⠀⠀⠉⠁⠈⠁⠀⠉⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠁⠀⠁⢘⣿⣿⣿⣧⠈⠉⠉⠉
⡒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⢄⡢⣀⢄⡠⣀⣁⣰⠦⠴⠒⠛⠋⡸⠀⠀⠀⠀⠁⠀⡇⢸⡇⣿⢸
⠭⣓⡪⢭⣒⠦⢄⡀⠀⠀⠀⠀⠀⠀⢈⣳⡽⠶⠓⠋⠉⠀⠀⠀⠀⠠⠘⠁⢡⡀⠀⠀⠀⠀⠀⡇⢸⢠⡇⣿⠄⡄⡠
⠭⣒⡫⢵⣒⠭⣓⡪⠅⣂⣠⠴⠒⠋⠉⠀⠀⠀⠀⠒⢷⣆⠀⠀⠠⡤⠀⠁⠠⡿⠀⠀⠀⠀⠀⠁⣉⣿⠋⠙⣘⠟⠣⢀
⣯⢕⣚⡭⢖⣫⠵⠒⠋⠅⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠉⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠋⢉⠿⡀⢠⡿⢡⡀
⢞⣫⠵⠚⠉⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠐⠞⠃⠀⠀⠐⠀⠀⠀⠠⠀⠀⠀⠀⠃
⣿⣷⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠒⠒⠒⠒⠒⠛⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⠟⠉⠙⠻⣆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⣀⣀⣀⡀⢸⡇⢮⡀⠀⠀⠀⣴⠀⡇⣤⠤⡤⣤⣤⣤⡤⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⣉⣉⠉⠉⢹⢸⡇⠈⠻⠶⠴⠾⠃⠀⡇⡿⢠⢰⠀⠐⠀⠠⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢊⣼⣵⠇⠀⢸⠘⢓⣒⣒⣒⣒⣒⣒⣚⠃⡏⢸⠈⢰⠀⢸⢸⡆⣿
⠀⠀⡶⠒⠒⠒⠒⠒⠒⠒⣦⢸⠀⠀⣾⣿⠇⠙⠀⢸⢸⡏⣉⡉⢉⣉⠉⠉⠉⡇⡗⢸⣼⢸⢸⢸⣸⡇⣿⢸⠉⠉⠉⠉⠉⣉⠉⢹
⠀⠀⡇⠐⢦⡲⣄⢦⠻⠀⣿⢸⠀⠘⠛⠋⠀⠀⠀⣸⢸⡇⠿⣾⣿⣥⣿⡀⠀⡇⣯⣬⣤⣬⣬⣬⣤⣤⣿⣸⠀⣰⣮⣿⣿⣿⡂⢸⡆
⠀⠀⡇⠘⢦⡑⢬⠡⣔⠀⣿⢨⣭⣭⣭⣭⣭⣭⣭⣭⢸⡇⣾⣿⣋⣟⣿⣷⠀⡇⣶⠒⠒⠒⠒⠒⠒⠒⣦⢸⠀⣿⣿⡽⠾⠿⠇⢸⠃
⠀⠀⡇⠘⢦⠓⢤⠰⠘⠀⣿⢸⠀⠀⢠⣤⣤⣤⡄⢸⢸⡇⠙⠛⠛⠛⠋⠛⢀⡇⣷⠀⠀⠔⠚⣿⣞⠀⣿⢸⠀⠛⠉⠀⠀⠀⠀⢸⠁
⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠟⢸⠀⠀⠀⠠⠶⠶⠆⢸⢀⣭⣭⣭⣭⣭⣭⣭⣭⡅⣿⠀⠀⠀⣠⣿⣿⠀⣿⠈⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣛⣛⣛⣛⣛⡃⢸⣸⡇⢀⣀⣀⣀⣤⣦⠀⡇⣿⠀⢠⣾⣿⠿⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣉⣉⣉⣉⣉⣁⣼⢺⡇⢦⣍⡙⠛⣽⠟⠀⡇⠿⠶⠶⠶⠶⠶⠶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣉⣉⣁⣀⣀⣀⣠⡇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡧⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠤⡼⠀⠀⠀⠀⠠⢄⣀⣤⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣶⡍⠉⠉⠡⠄⣀⠀⠀⠠⣄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠴⣆⣿⠿⠿⠽⠿⠭⠭⢽⣶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣫⠿⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠫⢿⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠪⡑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢪⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡕⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣏⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠜⣋⠃⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡁
⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⢀⣠⣤⣶⣶⢿⣿⠟⢻⠛⢻⠟⢛⡟⢻⠿⣿⠿⣿⣿⣷⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣓⡍
⠀⠀⠀⠀⠀⠀⢀⣇⣥⢶⣿⡷⠛⠁⠃⠀⠦⠀⠠⠀⣀⠀⢈⠁⣈⠀⡉⢀⡉⢈⠁⡍⢩⡟⣿⢿⡿⣶⣤⣀⠀⠀⠁⠃
⠀⠀⠀⠀⠀⠀⣺⣿⣿⠿⡄⢁⠘⡀⠂⠀⠤⠀⠤⠀⣤⠀⣬⠀⡍⢀⠁⡈⢁⡈⢀⠁⡤⢠⠀⣴⠀⠏⠿⣿⣷⣦⡄⣤
⠀⠀⠀⠀⠀⠀⠿⣿⣿⢀⡆⢨⡀⠁⠐⠀⡠⠀⡀⠀⡄⠀⡁⢀⠁⡈⠀⢁⡈⣁⢁⡀⢀⠄⣠⠀⡖⠰⠀⠏⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣽⣷⣤⣈⡁⠈⠀⠧⢰⠀⠠⠀⡄⣠⠀⡈⢀⡁⠀⠈⡄⣁⠈⣀⠉⠠⠀⡠⣠⠃⢜⠸⢱⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠌⠛⠻⣺⢿⣿⣾⣤⣴⣠⣆⣄⣀⣄⡍⢠⠁⣈⣀⢀⡀⢀⠈⣠⠀⣠⠀⡴⣠⣂⣴⣆⣚⣟⣻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡁⠘⠁⠏⣹⠛⡿⢿⠿⣿⢿⣿⣿⣿⣿⣿⣿⣶⣷⣶⣶⣾⣿⢶⣟⣿⡿⡿⣿⢿⡿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠸⠀⠆⢠⠀⣅⢈⠐⡃⠘⠃⠾⠁⠿⠸⠇⠸⠿⠈⠿⠁⠹⠏⠸⠟⣘⠃⣉⢠⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢙⠘⠁⢶⢠⡄⢩⠈⣀⢛⡘⠃⠘⠃⠻⠀⠆⠀⠶⠀⠷⠀⠸⠅⢘⠇⡛⢈⣥⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢷⠐⣆⢠⡈⢡⠉⡘⠃⠙⠈⠇⠸⠇⠿⠀⠿⠀⠿⠀⠾⠀⠛⣀⠁⣌⣥⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠐⣦⠠⡄⢡⡈⢃⡘⠘⠃⠁⠹⠐⠧⠸⠄⠶⠀⠾⠀⠯⠸⢃⡛⣩⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣴⢦⠡⣤⠉⡈⢃⠘⠈⠇⠻⠆⠷⠰⠆⠶⠠⠇⠸⠁⡛⣘⠣⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠰⠆⢵⠌⣥⢙⡘⡋⣇⠸⡆⠗⢾⠰⠃⡟⣘⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⢀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⠀⠀⠀⡔⠄⠀⠀⠀⠀⢀
⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡽⠁⠀⠀⠀⠀⠀⠀⣜⠀⠀⠀⠀⠀⠀⠀⡀⡀
⣠⠄⢼⣿⠄⣄⠀⠀⢀⣤⣾⣶⣄⠀⠀⠀⠠⠘⠀⠀⠀⡀⠀⠀⢎⠀⠁⠜⠓⡄⠀⢠⠐⠉⠿⠀⢀⠀⠀⢠⠓⠈⠃⠀⢣
⢻⣷⣶⣶⣾⢟⠀⠀⣉⣀⣀⣀⢈⡱⠀⠀⣅⣀⣀⣠⣴⡎⠀⠲⣔⣤⣤⡤⡴⡆⠀⠸⣄⣠⣀⣤⣴⡇⠐⢯⡉⠑⢒⣂⣉
⠸⣿⣿⣾⣿⡇⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⢹⣿⣷⣿⣿⡇⠀⠀⢳⣧⣇⣷⣷⠃⠀⠀⣿⣿⣿⣿⣿⠀⠀⠘⣿⣽⣽⣽⡿
⠀⠙⠛⠛⠋⠁⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣤⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⣶⣶⡆⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⢠⣴⣦⣶
⣠⠄⢶⡷⠄⣄⠀⠀⢀⣬⣿⣿⢄⠀⠀⠀⠠⠛⠁⠠⡶⠀⠀⠀⠊⠈⠀⠼⠢⡄⠀⢠⠔⠛⠛⠛⢄⠀⠀⢠⠓⠭⠌⠁⢧
⢿⣷⣶⣶⣾⢿⠀⠠⡉⣁⡀⣀⠈⡱⠀⠀⣁⡀⣀⣠⣤⡆⠀⠲⣐⣄⣀⡤⡤⡆⠀⢸⣀⣠⣀⣠⣤⠇⠐⢯⡉⠐⠒⢚⣉
⢸⣿⣿⣾⣿⡏⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⢹⢿⣷⣿⣿⡇⠀⠀⢷⣇⣧⡷⣿⠃⠀⠀⣿⣿⣿⣿⣿⠀⠀⠘⣿⣹⣽⣽⡿
⠀⠙⠛⠛⠛⠁⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠈⠓⠛⠛⠋⠀⠀⠀⠈⠛⠛⠓⠋⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⢀⠀⣠⣠⡄⡀⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⢀⡀⠀⠀⢤⠀⠀⠀⡔⠛⢛⡫⠢⡀⠀⢀⠀⠀⠀⠀⢄⠀⠀⢀⠾⠥⠄⠭⣦
⠿⢶⣦⣴⣶⠿⠀⠀⡉⢉⠀⡈⠉⣡⠀⠀⡀⠂⡂⣀⣤⡗⠀⢢⣠⣁⣀⣠⡤⡄⠀⢸⡀⢀⣀⣀⣤⡇⠠⣾⡒⠒⠂⠒⢛
⢸⣿⣿⣽⣾⡏⠀⠀⢹⣯⣿⣿⣿⡇⠀⠀⢹⣏⣿⣿⣯⡇⠀⠀⢯⡗⣇⣇⣿⠇⠀⠀⣿⣿⣿⣿⣿⠀⠀⠸⣽⣻⣻⣹⡿
⣀⣻⣿⣿⣟⣁⣀⣀⣈⣻⣿⣿⣟⣁⣀⣀⣈⣻⣿⣿⣟⣁⣀⣀⣈⣿⣿⣿⣏⣀⣀⣀⣙⣿⣿⣿⣋⣀⣀⣀⣹⣿⣿⣿⣁
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠈⢿⠀⠈⣷⠀⠀⢸⡇⠀⠀⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢲⠀⠀⢸⡏⣆⠀⢀⣠⢸⣷⡾⠏⠠⡀⣼⠁⠀⠀⢸⣿⠀⣴⠛⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⣸⠋⠀⢀⣼⣿⠙⣧⠈⡗⣿⡟⣛⣦⡊⢱⣿⣐⡡⢀⣿⠙⣷⡇⠀⠈⢀⣠⣤⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠲⠀⠀⠈⢷⡉⢧⡀⣀⣸⣿⣇⣼⢿⣟⣻⢿⣟⡚⣿⠟⣻⡛⢷⠿⣏⡀⣸⡇⠀⣰⡿⠉⠀⠀⠀⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣴⣶⣄⠈⣷⢨⠛⠛⠛⠼⣌⢳⡼⢏⣼⢢⡏⢰⣿⢇⣽⡾⢶⣉⡎⢤⣿⠳⠀⣿⡁⠀⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣸⣿⠛⠛⡼⢻⢻⣵⡂⢿⣿⣄⣿⣶⢎⣏⣿⣿⣛⢢⣝⣷⣧⣾⣯⣵⣿⡍⠈⠳⠤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⠋⠁⠀⠩⠗⢸⠿⠝⡻⣿⣿⢿⣄⣿⠿⣯⣿⡟⣺⢵⠿⡟⢙⣉⢩⡟⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠉⠰⣺⣇⣿⣯⣽⣟⣩⣿⣧⣽⣿⣿⣻⣶⠲⠋⡉⢙⡗⢻⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠓⠚⠉⡝⠁⠼⠇⠉⠙⢿⣿⣿⣿⡟⠁⠀⠑⠃⠌⠀⠙⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠠⠄⠀⡤⠄⡠⠠⢄⠀⣿⣛⣿⠓⡤⠀⠀⠠⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣠⠀⠀⠐⣀⢀⠀⠀⢿⡟⢻⡀⠀⠐⡁⢑⠂⡈⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⣀⣠⣤⣤⣤⣶⣶⣿⣿⣿⣿⣦⣤⣤⣍⣀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⢀⣠⣴⢶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣤⣀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠳⠶⠶⠚⣧⠖⠉⠀⠈⠉⢻⢿⠿⠋⠉⢇⠘⠃⠛⣽⡿⠟⢹⡟⡿⣜⣿⡛⣿⠙⠛⠏⠀⠀⠉⢉⠽⠉⠈⠡⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢀⡴⠋⢳⡀⠠⠂⠀⠀⠈⠀⠀⠀⠁⡱⢸⠏⡠⠁⣠⡼⠄⠈⠀⠐⠀⠀⠒⠀⠀⠁⢠⠶⡦⠻⣤⡦⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣀⡴⠋⠛⣶⠛⢀⡴⠆⠀⠀⠠⠀⠁⠀⠈⠄⠾⠳⠁⠚⣈⠟⠰⠈⡀⠀⠀⠀⠀⢀⡤⡀⢿⠀⠀⠀⠈⠻⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣴⠟⣠⠟⠁⠀⢠⡷⠀⣤⡀⠀⠀⠀⢀⠃⠀⠠⠌⠠⠀⠀⠀⠀⣀⣀⠀⠸⣄⠀⠘⢧⡀⠀⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠀⢀⣴⠟⠀⠀⡿⣏⢀⡾⠋⠲⣶⠓⠲⡅⠀⢠⡞⡇⠀⠈⢻⣟⠒⠻⣶⣄⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠋⠀⢀⣼⠇⠘⣿⠁⠀⠀⣿⡀⠀⠹⡄⢸⡧⢿⡄⠀⠀⢹⣧⠀⠈⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⢀⣿⠀⠀⢀⣿⠀⢀⣼⠇⣸⡇⠀⠙⣆⣀⡸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠋⠙⠛⠛⠉⠒⠋⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⢣⢳⡀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣅⠀⠀⠀⠀⠀⠀⠀⢀⢠
⠀⠀⠀⠀⠀⠀⠀⢢⠣⣀⠿⡂⠀⠀⠄⡰⠀⠀⡀⠎⠀⠀⠁⠀⠀⠀⠚⡄⢸⢀⠆
⠀⠀⠀⠀⠀⠀⠐⢢⡓⠏⠒⠀⣈⠁⠟⠉⠁⠉⠢⠀⠀⣀⠆⠐⠐⠂⠕⠲⢎⠑⠤
⠀⠀⠀⠀⠀⢐⠤⠒⠒⠒⡲⣤⢂⣿⣀⠀⠀⠀⠀⡁⢀⠁⠀⠀⠀⠀⢸⣀⢢⠄⣠⢣⡄
⠀⠀⠀⠀⡔⠁⠀⠊⠀⢀⠀⠉⠉⠉⠀⢌⢑⡴⠉⠀⡠⠛⠉⠀⠑⣎⠁⠀⠈⠺⢉⡔⠉⠧⢲⢀⠀⠀⠀⠀⠀⠀⡀⡀⠤⢀⠄
⠀⠀⠀⠀⠁⠌⠀⠀⢀⠁⠀⠀⠀⠁⠀⢰⠁⠀⢠⠈⠐⠆⠀⠀⠁⣀⡍⢂⡠⠊⠁⠹⢄⠤⣜⣉⠠⠤⢐⡀⠨⠅⠒⢀⣉⠀⠀⡀
⠀⠀⠀⢀⣦⡀⠀⢀⣨⢀⠀⠀⣀⣠⠀⣀⣦⡀⠀⠀⢠⣴⢀⣩⣬⡴⢃⣨⡅⠀⢠⠇⣊⠥⠴⢖⣚⢊⡀⠨⠭⠀⠁⠐⠒⠀⠉
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠠⠄⠀⠲⡖⠀⠈⠁
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠠⠄⠈⠡⠤⠀⠄⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡰
⠀⠀⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠈⣄⣀⡀⠀⣀⡀⠀⠀⠀⠀⠠⠀⠁⠐⠒⠒⠘⠋⠉⠁⠒⡚
⠀⠀⠀⠀⠀⠀⢀⡾⢻⣍⠹⣇⠀⢀⠀⣀⠀⠠⠤⠠⠀⠀⠒⠂⠀⠀⠀⢩⢸
⠀⠀⠀⠀⠀⠀⠘⣯⡈⡛⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⡔⢋⠉⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⡳⢆
⠀⠀⠀⠘⠄⠀⠙⠂⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠠⠋⠁⢀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢄⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠊⢀⣀⠀⠀⠀⢀⡠⠊⠁
⠀⠀⣴⣖⣋⣉⣉⣈⠈⠉⠂⡀⠀⠉⠁⣀⢀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠁⠀⣀⣀⣁⣀⣀⣀⣈⣉⣙⣳⣆
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠪⡨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠐⡛⡂⠰⠉⠁⠀⠂⠓⠂⠈⠁⠱⠦⠀⠿⠁⠈⠁⠃⠀⠐⠓⠂⠐⠉⠋⠀⠉⠐⠂⠀⠈⠃⠃⠘⠉⢂⣸⠁⠒
⠀⠀⠀⠉⢁⠐⠀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣔⡆
⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠰⠀⠀⠀⠀⠀⠁⠀⠰⠀⠀⠄⠀⠀⠀⠀⠀⠨⠀⠀⠁⢠⢄⠃
⠀⠀⠀⠀⢭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠰⠄⠀⡀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠂⢠⣴⠁
⠀⠀⠀⠀⠨⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⠃⡠⡎
⠀⠀⠀⠀⠀⣉⠠⠄⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢘⠀⠀⡂⠀⠀⠀⢠⠀⠂⠀⠀⠂⣰⠇
⠀⠀⠀⠀⠀⠈⠃⠄⠀⠤⠦⠤⠤⠬⠤⠴⠷⠶⠼⠶⠶⠶⠶⠒⠒⠒⠒⠒⠓⠶⠶⠶⠶⠶⠷⠶⠶⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠛⠛⠉⠉⠉⠉⠐⠠⣀⠈⠉⠉⠙⡙⠛⠛⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⢀⣀⣬⡵⠶⠞⠛⠛⠛⠛⠛⠛⠛⠛⠳⠾⢦⣄⡀⠀⠉⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⢈⣭⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠯⠄⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢨⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡌⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡠⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣼⠇⡠⣿⠀⠀⣀⣀⣤⣤⣤⡤⠶⠶⠶⡶⠖⠒⠛⡻⠟⠛⠛⠛⢛⠿⠛⠲⠶⠶⡶⠶⢦⣤⣤⣤⣄⣀⣀⡀⠀⠀⣿⠁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⡤⠿⢛⠟⠉⠉⣀⣊⣀⣤⣤⣤⣮⣤⣤⣤⣾⣤⣤⣤⡤⠴⣧⣤⣤⣤⣴⣥⣤⣤⣤⣴⣈⣀⣀⢉⡩⠛⠛⠳⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣰⡟⠉⢀⣠⣦⡶⠾⡟⠛⠋⣩⠭⠅⠀⠀⡰⠖⠒⠒⠀⣀⡀⠒⠒⠒⠂⠀⠀⠐⠒⠒⠶⠄⠉⠩⢭⣝⠛⠛⠳⠶⣦⣿⠊⢸⣷⡀
⠀⠀⠀⠀⠀⠀⢿⡉⠁⠻⣭⣁⣐⣉⡁⠠⠶⠂⠀⣀⡋⠉⠁⣠⠤⠤⠉⠉⠁⡤⠤⠀⠉⠉⠉⠠⠤⠄⠀⠚⢛⣂⣐⣲⣦⠬⠭⡷⢺⡿⢀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⣷⢶⣦⣅⣀⣀⣈⠍⠋⠉⠉⠉⡹⠛⠛⠛⠛⡛⠗⠛⠛⠓⢒⠲⠒⠛⠛⠛⡻⠛⠋⠉⠉⡩⠋⠁⠀⣀⣠⣬⣤⣼⣧⡾⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠠⢤⣈⡉⠉⠙⠛⠛⠛⠛⠛⠛⠒⠲⠶⠞⠷⠶⠶⠶⠶⠿⠶⠶⠶⠶⠾⠖⠒⠒⠚⠛⠛⠛⠛⠛⣉⣉⡁⠀⠤⠴⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡔⠒⠀⢠⣀⣀⣈⠉⠉⠁⠀⠀⠀⠒⠒⠒⠂⠀⠀⠒⠒⠒⠀⠀⠀⠒⠒⠒⠂⠀⠒⠚⠛⢃⣀⣈⠉⠀⠤⠴⠂⠀⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⢀⣤⠀⠀⠀⢀⣀⣀⣈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠀⠀⠀⠛⠓⠓⠀⠀⠈⠉⠉⠉⠀⠀⠉⠁⠀⠀⣀⡀⠀⠤⠤⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠠⠤⠤⠤⠀⠀⠀⢤⣄⣀⠉⠉⠉⣀⣀⡀⠉⠉⢉⣀⣀⡀⠙⠛⠉⠤⠤⠌⠛⠉⠁⠤⠤⠉⠁⠲⠶⠂⠠⢶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡠⠤⠤⠄⠀⠤⣤⣤⠀⠀⠀⢠⣀⣀⡈⠉⠁⣠⣤⣤⠀⠀⠀⠤⠤⠤⠄⠀⠤⠤⠤⠄⠀⠀⠤⠤⠄⠐⠒⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠒⠒⠒⣀⣀⣀⠒⠒⠒⠀⠀⠐⠒⠒⠒⠀⠀⠒⠒⠒⠀⠀⠀⠒⠒⠀⠀⠀⠙⠙⠉⠀⠀⠋⢉⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⡠⠤⠀⠀⠤⠤⠄⠉⠉⢡⣤⣤⠍⠉⠉⠠⣤⡤⠍⠉⠉⣤⣤⠛⠛⠡⠤⠄⠉⢉⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⣤⣤⣤⣉⣛⣃⣀⣀⣼⣛⣣⣤⣤⣤⣴⣶⣦⣤⣤⣿⣭⣴⠶⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⢻⢿⢛⠻⠿⡿⠟⣿⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢻⡆⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣸⣧⠾⠋⠉⠀⠀⠀⠀⠀⠀⢰⡟⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣨⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣿⣤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠶⠛⠋⠉⠉⣿⠉⠉⠙⠛⠶⣦⣀⠀⠀⠀⢀⣀⣀⣨⣿⣁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠐⢦⣄⣉⣀⣀⣴⠆⠀⠀⠙⢷⡰⠟⠋⡉⠉⢽⠍⠉⡉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⢿⡀⠀⠙⠛⠓⠛⠛⠁⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠠⣦⣄⣀⡀⠀⠀⢀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⣤⣤⣤⣤⣤⠶⠶⠛⠉⠀⠀⠀⠀⠈⠉⠉⠋⠉⠉⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⢰⣦⣄⠀⣶⣴⣆⣰⣷⠀⣤⣾⡆⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⢿⣷⣼⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣿⠁⠀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠘⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣥⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣿⠿⣿⣿⣿⣿⡿⣿⢿⣻⡟⡯⣿⣿⣛⣿⣿⣻⣿⣿⡷⣻⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣻⣿⠿⡿⣿⡻⢟⡟⣪⣿⣿⣿⣿⣾⣟⣇⣷⣟⣶⣾⢾⣿⡿⢻⣿⣯⠿⣾⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⠿⠿⠛⠋⠋⠙⠳⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣟⣯⠵⠛⠙⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⣽⣶⣔⡦⢴⣶⣦⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣷⣦⠔⠒⢶⠖⣍⠉⠙⢤⠀⢜⣿⣿⣌⠟⠛⠻⣿⣿⣿⣿⣿⡿⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢹⡏⠀⠀⠀⢺⣿⡒⠋⠊⠀⠙⠋⣵⠉⠀⠀⢸⣿⡇⡄⢀⠀⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡦⠄⠀⣈⢣⠀⠀⠀⣿⣿⠃⠀⣀⣤⣿⡇⣿⡇⠀⠀⣸⣿⠇⢻⣿⣿⣿⠿⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣡⡇⠀⠧⠀⠁⠛⠉⠙⡍⠉⠉⢩⠉⠉⣹⡟⠁⣴⡆⠈⡧⢸⣸⣿⣿⠁⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣖⠚⠀⠀⠀⠀⠀⠇⠀⠀⠼⠀⣠⣿⣷⣶⣿⣷⣾⠻⢉⠸⠿⠯⠀⠚⠋⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠷⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣫⣉⠛⢛⡟⠛⠛⠛⠤⠀⣀⠀⠀⠈⣧⠀⠀⠻⣦⠘⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡄⠀⠀⠀⠀⣏⠀⠀⡿⠋⠉⠀⠀⠈⠳⡐⠀⠀⠀⠀⣈⢁⠀⠀⢼⣧⠀⠀⢻⣧⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠙⣦⡀⠈⢷⡗⠀⢸⣿⡆⠀⠘⣿⡇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣂⠀⠀⠀⠀⠀⠀⠃⣰⠀⠀⠀⠀⠄⠀⠀⠀⣿⡄⠀⠘⣿⣆⠈⣿⡄⠸⣿⣷⠀⠀⣿⣿⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠒⠛⠀⠀⠀⠀⠒⢿⠀⠀⠀⢀⡶⠀⠀⠀⢸⣿⡀⠀⢻⣿⡀⢸⡇⠐⣿⣿⠀⠀⣿⣿⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡶⠤⠀⢀⠀⠀⠀⠸⡄⠀⠀⠈⣧⠀⠀⠀⠸⣿⡇⠀⠸⣿⡇⢸⠃⠀⢸⣿⠀⠀⣿⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠳⡀⠀⠀⢻⠀⠀⠀⠀⣽⡇⠀⠀⣿⠇⡜⠀⠀⢸⡟⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⣇⠀⠀⠀⢸⡇⠀⠀⠿⠋⠒⠒⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠘⠓⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠈⠢⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢠⡖⢟⠟⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠠⠨⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠁⠃⠀⠠⡆⢸⠁⠠⠁⠀⠀⢀⡄⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠐⡄⣹⢸⡄⠀⠘⠇⠀⢸⠀⠀⠀⠀⠈⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠘⣆⠀⠀⠰⡏⠈⣧⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣥⣤⣢⠘⣆⠀⠀⠀⡀⡘⣇⠀⠎⣼⢣⡀⠀⠀⠀⠀⠘⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡀⠸⡆⠀⡄⣴⠂⠙⠀⠀⣿⠸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡀⠹⡄⠀⠈⡑⠂⠀⢰⡇⠰⠁⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣿⣾⠛⡓⢦⡁⠀⠾⢠⡇⠀⠀⡔⣤⣾⣶⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡥⢟⣿⣆⠘⢀⠇⢰⡼⠃⠈⠉⡙⠛⢦⡠⠐⠋⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡧⢀⡅⠀⢀⣤⡷⠟⠉⠀⠀⠀⠀⢀⣠⣾⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣟⠻⣿⣿⡷⢻⢋⣀⣿⡍⠀⠀⠀⠀⠀⡠⠔⠋⢉⣿⣿⣿⣿⣶⣿⡦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠾⢿⣿⠟⣵⡿⣣⣶⢟⣿⣷⣾⡏⠛⣿⣧⠀⠀⠀⡄⠊⡀⠀⢀⣾⢿⠿⠿⠛⠛⠛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣪⣿⣿⡿⢻⣿⣥⣨⠿⢳⣦⣤⣍⣈⣡⣈⣠⣤⣤⣠⣤⣴⣦⣶⣟⠶⠾⢿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠿⢿⣿⣍⣽⣶⠟⠀⣟⠯⠉⠉⠉⠩⠭⣍⠉⠉⠉⣄⣶⠀⢐⣝⡛⠀⣹⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⡟⣿⣯⣿⣿⠻⠟⠀⡀⠊⢑⠂⠀⠀⠀⠍⠀⠀⠀⢀⠸⡏⠀⠀⢈⡁⢀⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣾⢧⣿⢿⣯⡿⠟⠀⠠⠁⠏⣒⡀⠀⠀⢍⣑⡂⠀⠀⠨⢭⡁⠀⢀⠿⠁⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡾⢷⣷⣶⠒⠁⠀⠀⡠⠀⠀⠀⠘⣳⠂⠀⠀⠬⣽⠂⠀⣰⡟⢀⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⠴⡶⣾⣿⠻⣿⣿⣻⡿⠟⢿⠀⠀⠀⠀⠨⠅⠀⠀⢝⡒⠀⠀⠐⢷⡏⠀⢸⣿⠥⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠉⠁⠀⠀⠀⠨⣿⡀⢸⣿⡍⠀⠀⢗⡇⠀⠀⠀⢝⡃⠀⠀⣲⠆⠀⠀⠤⡾⠀⠠⣿⠃⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⣃⡀⢿⣧⠀⢀⣶⣦⠀⠀⢀⠽⠂⠀⠀⢽⠁⢀⣤⣽⠃⢀⣺⢋⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠆⢘⣿⡇⠀⢨⣽⡀⠀⢀⣹⠀⠀⢠⡝⠀⠀⣬⠟⣰⠿⠓⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣉⣙⠃⠐⠢⢴⡇⠀⠠⣽⡄⠀⠈⠂⠀⠞⠃⠀⠈⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠯⣽⢟⣿⠿⠿⢷⢶⣶⣾⡶⢶⡶⠆⠰⠖⠘⠀⠛⠙⠒⠋⠁



⣿⡿⡛⣻⡿⣿⣿⣿⢿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣥⣽⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣴⡞⠓⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠲⠶⣦⡀
⠀⠀⢠⠏⠀⠳⣄⡀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⣠⡴⠋⢧
⠀⠀⠘⢆⠀⠀⠈⠙⠖⢄⡀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⢀⣤⡶⠟⠁⠀⠀⣸
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠈⡂⢄⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠁⠀⣀⢔⡪⠟⠉⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣁⠢⡀⠀⠈⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⡠⠔⠉⠀⠀⢀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠈⠑⢄⠑⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢀⠀⡀⠐⠉⠀⠀⢀⡠⠖⠉
⠀⣠⡤⠶⠒⠒⠒⠒⠒⠒⠛⠓⢄⠀⠀⠀⠙⠻⡉⠀⠁⠀⠀⠉⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠀⠀⠀⡠⠔⠉⠉⠉⠉⠉⠉⠙⠛⠓⠶⣦⣄
⣸⠋⠒⠒⠶⠶⠶⠶⠄⠀⠄⠀⠀⠑⠂⠀⠀⠀⢀⡠⣤⠤⠤⠤⠤⠠⠤⠠⠤⠠⠤⠤⠴⠶⠶⠶⢶⡶⠈⠀⠀⠀⠀⠴⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠤⠾⠽
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⣄⡸⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⢹⣀⣀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⢩⠧⠀⠐⡛⠀⠀⠀⡀⠀⠀⠦⠀⠀⠀⠶⠖⠓⣤⡀⠀⣴⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠺⢄⠀⢀⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠒⠒⠒⣒⡒⠒⠂⢚⡿
⠀⢰⡤⡤⠄⠐⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⢐⠀⠒⠓⠈⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⠉⠁⠀⠈⠉⠉⠁⢘⠁⠀⠀⠈⠉⠉⣉⠀⠀⠀⠁⠀⠀⠬⠇⡗
⠀⠀⢉⣉⡉⢉⡂⠀⠀⢐⡒⠀⠀⠀⠀⠀⢈⣉⠀⣭⠀⡁⢈⣏⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⠀⠭⠠⠀⠠⠥⠄⠀⠤⠀⠄⠠⢠⠀⠀⠐⠀⠀⠀⠂⠀⢐⡖⣺
⠀⠀⢰⠴⠦⠀⡀⠀⠀⠀⡀⠀⠨⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠂⠤⠤⠤⢤⠀⠀⠀⠠⠐⠂⠐⠀⠀⠀⠈⠀⠀⠒⠀⠀⠐⡂⠉⠉⢉⡼
⠀⠀⠘⡒⣒⠀⠐⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠛⠀⠀⠀⡀⠀⠀⠀⢐⠐⠒⠂⠛⠀⠀⠀⠈⠀⠀⢐⠀⠀⠀⢐⠀⠀⠁⠀⠉⢉⣁⡀⠯⠴⡇
⠀⠀⠀⢣⣈⡁⠸⠀⠀⠀⢠⠀⢈⠁⠀⠀⠀⡁⠀⠈⡇⠀⠀⠸⠤⠀⠀⣁⠀⠀⠀⢉⠀⠀⠤⠽⠀⠀⠀⠠⠀⠀⡈⠁⠀⠀⢀⠁⠭⠥⠤⠠⠀⠂⠀⣶⣺⠁
⠀⠀⠀⠸⠂⠂⠀⠄⠀⠀⠤⠄⠀⠀⠄⠀⠀⠀⠀⠀⢤⠀⠀⠠⠄⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠠⠀⠀⠠⠤⠀⠀⠒⠀⠀⠀⠐⠀⠒⠂⠀⠐⢲⠂⠈⣉⡜
⠀⠀⠀⠀⢳⣀⡀⠃⠀⠀⠒⠒⠒⠒⠒⠒⠂⢀⠀⠀⠘⠀⠀⠀⠉⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠈⡈⠀⠀⠄⠀⠀⠀⣀⠀⢈⠁⠈⠉⣁⠠⠴⠛⡇
⠀⠀⠀⠀⢀⣀⠀⠭⠀⠀⠀⢨⠁⣀⠀⠀⠀⢀⠀⠀⠬⡅⠀⠀⠽⠀⠀⢠⠀⠀⠀⠀⡄⠀⠀⢹⠀⠀⠀⡓⠀⠀⠀⠀⠀⠀⣤⠀⠘⠀⠀⠀⠘⠒⢒⣾⠁
⠀⠀⠀⠀⠀⢳⡆⠠⠄⠀⠀⠀⡄⠐⠂⠀⠒⠚⠂⠀⢀⣇⠀⠀⠘⣢⣀⣈⣤⣤⣤⣤⣀⣀⣈⣩⣀⣀⣠⣭⣭⣭⣥⣤⡀⠉⠉⢥⣿⣄⣀⣀⣨⣨⡼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢤⡤⢛⣁⡿⠒⣭⡀⠷⢦⡒⢂⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⡶⠚⣶⠊⣦⢼⣁⡹⠖⣭⡰⠷⣜⠛⣮⡉⣬⡉⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣴⠑⡾⠙⡿⠙⡶⢱⡤⣏⡸⠖⣍⡸⠦⡛⣱⡉⣵⡍⣽⣉⣵⠙⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡫⣴⡗⢾⢋⡻⣉⣟⣙⠗⢶⢬⣘⠗⣅⠿⢞⢩⣍⠼⠄⠾⢠⣶⣨⣏⠛⡢⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢙⡧⣼⠘⢟⣙⣇⣽⢠⡟⣘⠓⡾⣅⠗⣅⠷⡉⣧⠸⡆⢻⠸⡇⠾⢆⣽⠙⣣⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡅⢛⡣⣴⠙⡃⣭⠤⡏⢶⠣⡭⣽⣱⢮⡟⡥⢆⡹⠜⡗⣣⣩⡞⣛⠺⡧⣼⠙⡻⣤⡗⠣
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢈⣵⠛⡣⠶⠍⣳⠴⠖⢳⣙⣘⡗⡇⢍⡲⡕⡕⡫⢞⡏⠧⡾⢴⢨⡍⣛⠣⠾⣙⡣⣤⠑⢾
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⣩⡜⢛⡔⢧⡩⡆⢻⡩⢆⢷⡲⡩⠵⣵⡝⡜⠇⡕⡸⡩⢡⣟⡺⢤⣏⣺⢃⡽⢤⡞⠲⡆⠻
⠀⠀⠀⠀⠀⠀⠀⠠⡄⣼⡍⣵⡍⣵⡙⣣⡚⣣⡑⣌⠳⣑⠴⣊⢽⡽⢷⢣⠯⣙⠵⡣⠾⣽⠫⡬⠣⡶⠱⡶⠱⡞⠙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⡼⢆⠾⢆⠾⢢⡚⣢⣟⡶⢫⢖⡍⡶⢯⣳⣾⠯⡽⡷⢍⢢⡩⢜⢫⡬⢫⣈⢏⣘⢟⡘⠟⠙
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠸⠦⡸⠓⣞⢡⡮⣹⠓⡮⣱⣃⣊⡎⢗⢻⡾⡜⢱⢝⣊⠮⢷⠰⣚⣥⠹⣊⢳⠌⣥⡜⣋⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢤⠛⢪⣍⡾⢢⣭⣸⣃⠗⡶⢺⣸⡵⡊⢜⣜⠮⣑⠸⢼⡍⣍⠧⠴⠖⢫⣙⠶⢪⣤⢟⡁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢼⠛⣬⣄⡟⢺⡤⣭⣜⣉⢫⠼⡄⣆⠱⢚⣼⣳⢏⣟⣚⢂⠷⣼⠒⣛⢩⣄⡟⢪⣥⢘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⢫⣄⣟⠑⡶⢸⠄⣧⠸⡖⢛⣨⢶⢙⢴⢙⡾⢤⡍⣽⠓⣟⢹⣍⣵⠄⡟⢺⣅⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⣤⣹⣋⠿⠊⡶⠐⡖⡙⣃⡵⡶⢙⢴⡍⡓⠷⠴⣍⣽⣉⣯⣡⡷⢴⠛⣪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣄⢟⣉⣟⣙⢟⣘⢏⣬⠲⡎⣙⢴⡎⣩⠚⢇⠾⣄⣾⣄⠶⢄⠟⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣈⡛⣈⡻⣤⡍⢶⠎⣛⠴⡆⢉⡗⠛⡠⠿⡤⠾⠆⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠡⠬⠳⢶⠈⣛⠴⣾⢉⣵⠚⠓⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⣴⣿⣿⣷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣐⣾⣷⡆⢀⠀⠀⠀⠖⢙⡀⠀⠈⠃⠁⠀⡴⠶⠀⠀⠀⢰⠶⠶⣤⠀⣀
⠀⠀⠀⠻⠿⠛⠟⠀⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⢀⣬⣿⣿⣷⣢⡔⠂⠀⠀⣿⣾⡞⢧⡄⠀⣄⠙⠆⠀⠀⠀⠈⢁⡄⠉⠈⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⢠⣚⢄⣹⡇⠸⢄⠀⠀⠀⠀⠀⠀⠀⠴⠇⣰⣋⠀⠀⠀⠀⠀⣿⠋⠀⠰⣷⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠀⠀⠀⠀⢺⣹⢺⡛⣇⡐⢘⣤⡄⠀⠀⠀⢰⡕⠐⢲⠀⠹⠇⠀⠀⠀⠀⠀⠀⣰⠂⡌⠛⠁
⠀⠀⠀⠈⣛⡦⣀⣤⣄⠙⢿⠛⠙⠀⠀⠀⠀⠈⢕⢺⢯⡝⢩⣽⣿⡃⠀⠀⠀⠀⠀⠀⢹⣦⠀⠀⠀⠀⢀⠀⠀⠀⣨⣶⠉⠆
⠀⠀⠀⠹⣿⣷⢾⣿⡾⠀⠀⠀⠀⠀⢠⡄⠀⠀⣟⡻⢶⣿⣿⠋⠙⠁⠀⠀⣤⡄⠀⠀⠀⠙⠀⠀⠀⢠⠁
⠀⠀⠀⠀⢸⣿⢾⡋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢫⣼⣿⠉⠛⠀⠀⠀⣠⡶⠿⣷⣶⣄⠀⠀⠀⠀⠤⠀⢰⡄⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠙⠛⠁⠀⢺⣿⢻⠀⠀⠀⠀⠀⠀⠀⠔⢿⠆⠀⠀⠀⠀⣷⣷⠾⣾⣿⣿⠀⠀⠀⠘⠁⣆⣿⠀⠀⠀⠀⠐⠾⢣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠻⣧⣿⣿⡿⠟⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠲⣴⣿⣟⡷
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠈⣩⡟⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠰⠃
⠀⠀⢠⣿⣻⣿⣿⣿⡆⠀⠀⠀⣰⢾⣿⣧⡀⠀⠰⠟⠀⠛⠀⠀⠀⠀⠀⢀⡤⣤⡀⠉⠇⠀⠀⠀⠀⠋⠀⠀⡀
⠀⠀⠘⠿⢟⢿⣿⣿⠇⠀⠀⠀⡉⠀⠈⠙⢻⡆⠀⠀⠀⠀⠠⠀⠀⠀⠀⣬⡾⣿⠀⢠⣄⠀⠀⠀⠘⠻⠿⠐⠁⠀⠀⣠⣴⡆
⠀⠀⠀⠀⠛⠻⠛⠋⠀⠀⠀⠸⡿⣄⣀⣤⣼⠇⠀⠀⢀⣠⠐⣀⠀⠀⠀⠻⠅⣠⢸⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⢛⣩⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠣⠏⠀⠀⠡⠊⠁⠀⠐⠺⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠉⠀⠀⠠⠄⣀⠈⠈⠀⠀⠉⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⡷⢹⣿⣾⣿⣅⠀⡀⠁⠀⠠⠦⢬⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⡄⠀⠀⠀⠈⠻⠛⢯⣠⣠⠀⠴⣶⣿⢧⣹⡇⠰⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣄⠀⢀⠀⠠⡤⣼⡟⠓⠴⣈⡉⢙⠣⡹⣧⡀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⢿⣿⡾⠟⢻⡿⢓⡀⠉⠲⠗⠍⠈⢀⣠⣹⡯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⠚⠂⠀⠈⠉⠁⠸⣶⣊⣀⣉⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣤⣤⣠⣤⠆⠀⢈⠛⠉⠉⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣟⣿⣿⣟⣁⣠⣔⠁⠀⠀⠀⠀⠀⠈⢳⣦⣄⡀
⠀⢀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣽⣿⡿⣿⣦⣄⣀⣀⣀⣄⣤⣶⣾⣿⣿⣿⣤⡀
⠀⢇⡰⠌⠻⢩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣻⣿⣭⣿⣿⣿⡿⣿⣿⣿⠿⣯⣟⣿⣿⣾⣻⣏⡿⣆
⠀⠘⢤⡜⢃⠐⡉⠀⠀⡀⠀⠀⠀⠀⠀⠠⣿⣶⣟⣯⣿⣽⣿⢿⣻⠿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⡄
⠐⠬⠁⠉⠚⠃⠑⠀⠀⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣼⣿⣿⣯⣿⡿⣿⣿⣵⣿⣻⣿⣿⣯⣿⣿⣿⣿⣇
⠀⠀⠀⠑⠢⢄⡀⠀⠁⠐⠀⠀⠀⠀⢰⡿⢷⣽⣿⣯⣟⣿⣗⡿⣿⣿⣽⣿⢿⡿⣿⣿⣿⣞⣻⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠈⠢⡀⢠⣿⣿⣿⣿⣶⣿⣿⡿⣿⣷⣽⣷⣿⢯⣿⣟⣻⣿⡏⣻⣯⣻⣾⣾⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠈⠻⣷⣿⣿⣻⡾⣿⣿⣿⣿⣿⣿⣟⣻⣘⣿⣼⣿⣯⣿⢟⣻⣧⣿⣏⣷⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⢰⣿⣿⣿⣯⣿⣿⣽⣿⢿⣿⣿⣿⣿⣿⡻⣯⣽⣯⣿⣿⣿⣩⣻⣭⣿⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣦⠴⠶⠿⠿⠛⠟⠿⣟⣻⣿⣿⣦⣿⣿⢿⡟⣿⣿⣽⣿⣿⡿⣷⣴⠿⣿⠿⢹⣾⣇
⠀⠀⣀⠠⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠙⠯⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣮⣭⣟⣿⣿⣟⣻⣿
⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡚⠤⢖⠟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠙⣿⣯⣿⣿⠿⠟⠛⠛⠉⠉
⠧⡀⡈⠁⠀⠀⠀⠁⢀⠀⢄⠀⣂⠉⡀⠀⠀⠄⠄⠐⠒⠠⠤⢀⣀⣀⡀⠀⠀⣀⠀⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠠⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⡉⠄⠀⠀⠒⠀⠀⠒⠀⠀⠤⢉⠐⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠄⠀⠐⢂⣈⠉⠩⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡬⠍⢉⣀⡐⠂⠀⠠⢀⠀⠰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡜⢁⠄⢒⠈⢁⣀⠀⠠⡄⢰⠀⠀⠀⠀⠀⠰⠆⠃⠀⠀⠀⠀⠀⢰⠀⡴⠀⠤⠄⣈⡹⠒⠆⡈⢣⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⣗⠈⡭⡅⠀⠀⠀⠀⢣⠘⠒⠀⠀⠀⠉⠉⠉⡏⠉⠉⠀⠀⠀⠙⢠⠉⠀⠒⠀⢠⣈⠛⢄⢈⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠐⠓⠲⠶⠤⠄⣀⣘⣚⡃⠀⠀⠀⠀⢸⡄⡗⠀⠀⠀⠀⢀⡁⣈⣀⣀⡀⠠⠶⠐⠛⠊⣁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣍⡐⠂⠠⡄⡄⠤⠤⠈⠉⠉⣁⣀⡀⣈⣉⣁⣀⣀⣀⣀⡉⠉⠁⠤⠤⠠⠤⡄⢀⣂⠩⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠈⠉⠁⢡⡟⡀⢀⣀⠀⠀⢰⠀⠄⠀⠀⠀⠀⠀⠇⠰⠀⠀⢀⣐⢂⡞⡸⠁⠀⠐⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣐⡀⠀⢆⢱⡄⠀⠀⣀⣉⣀⣏⠉⠀⠀⢀⣈⠋⣏⡁⡀⢀⠀⠴⠴⣀⠠⠄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠉⠆⠗⠐⠂⠀⠀⠄⢤⠄⠀⠀⠀⠸⢠⠃⠐⠂⠀⠉⢉⠃⣀⠀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠩⠁⢙⣚⠂⠀⠀⠀⢄⠘⠄⠀⠀⠀⠲⣘⠀⠤⠀⠢⡏⠼⠀⠐⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⢥⠙⡄⢉⠉⢹⢀⣏⡈⠁⠀⡅⡥⠠⠄⠀⠐⣚⠃⠩⢥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⡈⣆⣋⣉⠀⢐⠂⠒⠒⠒⠒⠃⠋⠉⠉⢀⢁⣃⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⣁⠐⡒⡆⠀⠘⡃⢸⠉⠉⢹⠻⠋⠉⠉⡛⡘⢉⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡈⠉⠁⠀⠐⠛⠚⠒⠒⠚⠛⠒⠀⠀⠉⢁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣻⠀⠠⣄⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⣤⠐⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢸⠀⠀⡀⠀⢠⡇
⠀⠀⠀⠀⢀⣿⡁⠒⢤⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠘⡗⠀⢺⠀⠀⢱⠀⠀⡇
⠀⠀⠀⢀⣾⣿⣇⠀⠈⣿⡀⠀⠀⠀⣠⣿⣿⣇⡀⠀⠀⠀⠀⠀⠀⣽⠀⢸⡄⠀⠰⣿⢀⡇
⠀⠀⠀⠉⢉⣙⣿⣷⣄⡜⠓⠀⠀⠈⣙⣋⢿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡧⠈⢷⡀⠀⠁⠹⣿
⠀⠀⠀⠠⠈⣿⣿⣿⣿⣧⠄⠀⠀⠈⠩⡍⠋⠹⠟⠀⠀⠀⠀⠀⠀⢻⣷⡀⠘⢷⠀⠀⠀⣬
⠀⠀⠀⢴⢦⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⣤⣤⡄⠀⠈⢻⣧⡆⢸⡇⠀⢰⣿
⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣦⠀⠄⠀⠀⠀⣰⣤⣤⣄⠀⣿⣿⣁⣰⣶⠈⢿⡇⠀⢻⠀⠘⢻⣧
⠀⠀⠈⠋⠡⣿⣿⣿⣿⣿⣿⠀⢢⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⠀⢻⣯⡀⠈⣷⡀⢈⣿⣷⡀
⢀⣠⣀⣈⣁⣙⠙⢿⣿⣿⠏⢀⣾⣰⣾⣿⣿⡏⣭⣻⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠀⢻⡇⠈⢿⣿⡇
⠘⣿⠛⢻⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠷⠿⠟⢻⣿⣿⢻⣿⣿⡇⠘⣿⣷⡀⠀⣵⡰⣾⣿⡇⡄
⢰⣿⣿⣿⠿⢻⣟⣿⡯⠽⠗⠈⠉⠁⠀⣀⣀⡀⠤⠤⠠⣿⣿⣦⣿⣿⣧⣄⢻⣿⣟⠀⢹⣷⣿⣿⣧⡁
⠘⣟⣶⠿⠟⠋⠉⠁⠀⠀⠐⠀⠐⠛⠛⠛⠿⠛⠚⢶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠃⠘⣿⣿⡿⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⢻⣿⣿⣿⣿⣿⣟⠳⣶⡀⠛⠛⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠶⣭⣿⣿⣿⣿⣿⣆⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣣⣴⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⣀⣤⣾⡿⠟⠛⣿⣿⣿⣿⣿⢿⣞⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣤⡖⠐⠋⠁⣸⣿⣷⠀⠘⣯⣿⣿⣿⣿⣯⢿⡤⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⢼⡿⣿⠀⠘⢛⣿⣿⣿⣿⣿⡖⢿⡖⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡖⠀⢹⣿⣿⣿⣿⣿⣿⣟⣿⣟⣻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣿⣿⣿⣿⡉⠉⠉⠉

⠀⠙⠿⠀⠀⠰⢠⣄⠹⠀⡀⠀⠈⠁⠀⠀⠀⠀⠁⣷
⢀⡒⠂⠀⠙⣆⠀⡿⠐⠀⠀⠁⠦⣀⡀⠀⠀⠀⠀⠋
⠸⡷⠊⣄⠀⢀⣧⠐⠀⠠⠀⠀⠀⡻⠃
⠈⠀⠀⠯⠀⠈⠁⠀⠀⠀⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⢤⠻⠂⢻⣦⠀⢀
⠀⢀⠀⠀⢀⠀⠀⢰⣟⣷⠐⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣼⡇⢀⣬⣲⠀⢸⡇
⠀⠹⠒⡶⠚⠀⠀⢿⠉⠿⠶⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠸⠀⠨⠱⣏⣴⣰⠄⠤⠤⠶
⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠌⠁⠀⠀⠀⠀⠀⢰⡖⡟⣻
⣞⠴⣑⠠⢀⡀⠀⠀⠀⠀⠀⠀⠑⢮⣪⡵⠵⠚⠚⠉⠉⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢸⠃⡇⡏
⡮⣝⡢⢍⡲⢌⡂⠄⣀⡠⠤⠒⠊⠁⠀⠀⠀⠰⣄⠀⠀⢀⡄⠀⠀⠵⠀⠀⠀⠀⠀⢘⡺⠃⠓⡺⠏
⡭⣗⡯⢕⣪⠵⠒⠩⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⢈⠐⠀⢰⠟⣤
⣫⠵⠚⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠃⠀⠀⠀⠠⢶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⡿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣭⣭⣿⣯⣭⣛⠛⠿⣯⣍⡒⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣿⣥⡶⠶⠞⠛⠉⠉⠉⠉⠙⠛⠛⠒⠛⠻⠷⣬⣮⡙⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢟⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡹⣿⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⣡⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⣿⣌⢧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡿⣣⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⢻⣄
⠀⠀⠀⠀⠀⠀⢠⢫⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣆
⠀⠀⠀⠀⠀⠀⣾⠟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡎⣿⣆
⠀⠀⠀⠀⠀⢸⡏⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⢸⡄
⠀⠀⠀⠀⠀⣿⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇
⠀⠀⠀⠀⢰⣟⠀⣿⣀⣤⣤⣤⡤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⢤⣤⣤⣤⣀⣀⣀⠸⣇⡼⣧
⠀⠀⠀⠀⢸⡏⣽⠋⣉⡤⠴⠖⠒⠒⠒⠒⠒⠂⠀⠒⠒⠒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠶⠦⢤⣉⠙⣧⢤⣿
⠀⠀⠀⠀⠘⡇⣿⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⣿⣿⡏
⠀⠀⠀⠀⠀⠻⣿⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⢹⡿⠁
⠀⠀⠀⠀⠀⠀⢹⣆⠈⠙⠛⠿⢶⣦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⡴⠶⠞⠋⠁⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠻⠿⠿⠷⠶⠶⠿⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣯⡑⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⣻⡟
⠀⠀⠀⠀⠀⠀⠀⢰⣷⠄⣉⣧⡄⢉⢛⣛⠒⠶⠶⡶⠶⠶⠤⠤⠤⣤⠤⠤⠤⠤⣶⡶⠶⠶⠖⡻⠛⢋⣩⠓⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡂⠨⡷⠄⢉⣹⡦⠀⢉⣩⣝⠲⠀⠰⠀⢲⣯⠥⠀⠀⣭⣭⣛⠂⢀⣩⡝⠃⢈⢽⡇⠠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⢺⡃⠀⠤⠗⠀⠠⠤⢾⣛⡀⢘⣉⣩⡗⠲⠆⠀⠶⢢⣭⠀⠠⠴⡍⠀⠴⠾⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢙⣭⡀⠒⢾⣁⠐⠛⣻⠤⠄⠠⠤⢾⣭⣉⡁⢈⣛⡻⠶⠀⠒⣻⠆⠀⣚⠓⢀⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠡⡤⠈⢙⠦⠀⠩⠽⣒⠂⠀⠒⢛⡦⠤⠄⠠⠭⣿⡁⢀⣭⡝⠂⣨⣍⠁⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣀⠛⡀⠀⢟⣂⠐⣚⡯⠭⠀⠩⢬⠗⠒⠀⢐⣚⡗⠂⠀⠲⠍⠀⠶⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⣄⣘⣧⠄⠠⢼⣒⠀⠀⣘⡯⡭⠁⢭⣽⡍⠁⣭⠓⣀⣸⠷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠛⠳⠶⠶⠾⠷⠶⠶⠞⠳⠶⠖⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠿⠆⠀⣠⢶⣾⣅⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠤⢞⠀⡇⠘⣿⡈⣆⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⡀⣇⠀⢻⣧⢸⡀⠸⡄⠀⠀⠀⠀⠀⠀⢠⠊⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⡀⢣⡟⠀⢸⣿⡀⡇⠀⣇⠀⠀⠀⠀⠀⢠⠃⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣿⣿⣧⠀⠈⣿⡇⢳⣯⠍⣉⣩⡿⠀⡰⠁⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⠁⠈⢆⠀⢻⣟⠘⡧⣀⣀⣠⡧⠔⠁⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠠⢼⡖⠒⠢⡀⠘⡆⠸⣻⡾⠀⠀⠂⠈⡆⢀⡶⠶⣗⣠⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣞⣀⠀⠀⠀⢱⡀⠀⠘⡄⢒⠀⣿⠃⠀⠀⠀⠀⡇⢨⣟⣒⠒⠠⠭⠭⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠀⠀⠀⢉⣉⣉⣩⣭⣭⠉⢉⠇⠘⡇⢹⠀⠀⠀⠀⠀⣧⡟⠙⠛⠛⡇⠀⠀⣿⣀⣠⠤⠶⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠷⠼⣇⠀⠀⢻⠿⠟⠛⠛⢻⠀⡼⢀⡴⠟⠛⠒⢤⠀⠀⣠⠿⣁⠀⠀⢠⣧⠚⠉⠀⠀⠉⠲⡀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠑⠦⢠⣆⣀⣀⠀⠀⡿⠁⡏⠀⠀⠀⠀⠀⢳⠊⠀⠀⠀⠈⠉⠙⡇⠀⢀⠀⠀⢀⠀⢱⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠓⠒⠓⠒⠓⠒⠒⠒⠒⠒⣚⣲⡶⠶⠒⠒⠉⣉⢉⣉⣉⣉⣉⠉⡀⣉⣉⣉⣉⡹⢆
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠉⣉⡛⠛⣋⠋⡙⠛⣛⢉⣉⣉⡥⠤⠤⠶⠶⣿⠤⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⢒⣻
⠀⠀⠀⠀⠀⠀⠈⠑⠒⢺⠲⠠⠤⠤⠒⣒⣚⣁⡀⠀⢀⣠⡤⠞⢿⡿⠥⢤⣤⡤⠤⠤⠤⢤⠼⣿⡛⠦⣤⠤⠤⠤⠄⠲⣒⠶⠞⠛⠋⣉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣉⢉⡉⠉⠉⠀⠀⢈⡭⠟⠋⢁⡤⠞⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣈⣓⣦⡈⠓⢶⣚⠟⠛⠒⠛⢉⣉⣁⡄⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⠈⢉⣩⠟⠋⢁⣠⠴⠾⠭⢩⣉⣁⣀⣤⣄⣤⣤⣤⡂⠤⠒⠚⠉⣉⣁⣭⠷⢦⣌⠙⠻⢭⣉⡥⠤⠤⠒⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠯⠜⠋⢁⣠⠤⢾⣋⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣄⣠⠤⢬⣭⣛⣋⣉⣄⣠⠤⣤⣶⣚⣛⡷⣤⣬⡓⠲⠤⠤⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡤⠒⠚⠛⠒⠒⠒⠒⠒⠒⠛⠈⠡⠬⠭⠭⣥⣤⣤⣄⠀⠤⠤⠤⠤⠀⠀⠒⠂⠀⠀⠀⠀⣀⡠⠤⠚⠛⠛⠒⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠄⠀⠀⠠⢠⣤⣤⡔⣒⣒⣚⣛⣉⠩⠭⠭⠓⠚⠒⠛⠛⠛⠛⠛⢒⣒⠲⠶⠶⠛⠋⠉⢁⣀⡠⠴⠒⢚⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠤⠴⠶⠶⠦⠴⠛⣉⣉⣉⡙⠒⠐⠒⠒⠒⠒⠒⠒⢐⣒⡓⠥⠞⠛⠛⠓⠚⠛⠓⢊⣉⣉⡤⠔⠒⠊⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠒⠒⠲⠤⠦⠤⠤⠤⠤⠤⣄⣉⣉⣉⣉⣉⣉⣉⣙⣓⡲⠶⠶⠶⠒⠒⠂⠒⢒⣫⢝⣋⡡⠤⠤⠖⠒⠠⠠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⠒⠒⠒⠒⠲⠴⠶⠶⣤⣤⣤⣤⣀⣉⣉⣉⣉⣁⣒⣒⣒⡒⣲⠶⠶⠚⠛⠉⠉⠀⠀⢀⣀⣀⣤⣤⣤⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⢶⣶⣖⣊⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀⠈⠉⢐⣒⣒⠒⠒⠒⠒⠒⠚⢉⣉⣁⣀⣀⣀⡤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠈⠁⠁⠀⠀⠁⠉⠀⠉⠈⠁⠉⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣄⣀⡀⠀⠑⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠘⠉⠉⡉⡍⡉⡋⢳⢲⢤⣀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⢉⢂⢂⢂⠃⠀⠐⠰⡰⠐⠈⠆⠆⠈⠑⠦⣤⠐⠀⠀⠀⢀⡠⠔⠒⠒⠂
⠀⠀⠀⠀⠀⡠⠊⣁⡀⠀⡆⠄⢎⢆⠇⠆⠂⠡⢡⠡⠁⡌⡈⡀⠀⠠⠠⠉⢂⠒⢠⡴⠔⠀⠀⡀
⠀⠀⠀⢠⠊⠀⠀⠋⠁⠀⡓⠀⠨⠈⠘⡜⠀⢀⢃⢣⢀⢠⠘⡐⡀⡀⠀⠂⠂⠀⠀⣇⠀⠀⡌
⠀⠀⠀⠘⢻⢤⣠⠄⢀⠼⠇⡀⠀⠀⣀⠐⡐⡐⠀⠂⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⣴⡃⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠄⠀⠠⡤⠤⠘⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠙⠥⣄⢀⠀⠀⠈⠐⠠⠀⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠲⢴⣖⠀⠀⠰⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠘

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠠⠁⠀⠀⠀⠀⠀⠀⣠⡀⠀⣤⠀⠀⠀⢀⡼⠀⣀⢰⣿⡟⠋⢂⠀⢢⣄
⢐⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣻⣶⣴⣶⣾⡓⣠⣿⣿⣿⣿⠧⣄⠁⢈⣿⣿⢦⡦⠴⠛
⠀⡀⠀⠀⠠⠛⠻⢿⣿⣿⣿⣿⣿⣿⢿⡿⠛⢼⣿⣿⣤⣤⣈⣭⡤⠈⠻⣯⡀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠿⠷⠂
⠀⡇⠀⠀⠀⠀⠀⠀⢟⣿⣯⣿⣿⣿⡯⡉⢁⣾⣦⡟⠏⠋⡌⢿⣧⣬⣀⣁⠰⢆⠈⠁⠀⠑⠒⣶⣶⢏
⠀⡇⠀⠀⠀⠀⠁⢠⣿⣿⣿⣿⣾⣿⠾⣅⣠⡿⢴⠶⠈⠀⠘⡉⠙⠯⠁⠁⠀⠉⠀⠀⠀⠈⠁⠈⠱⠓
⠀⠃⠀⢀⣴⣦⣤⡸⢿⣾⣿⣿⢛⣿⣿⣭⣷⡷⠖⠀⠤⠀⠉
⠀⠀⠀⢸⣿⡏⠋⠀⠀⠀⠹⡇⠙⠿⡿⠟⠁⠰⡴⠂⠐
⠀⡇⠀⣸⠟⠃⠸⣿⣷⠂⡀⠩⡈⠐⠋⣀⠀⡴⢋⡀⡖
⠀⡇⠀⠉⠓⠀⠀⠙⠁⢠⡇⠀⠛⠓⠀⠁⠀⠙⣿⡄⠀⠀⠺⡿⠂
⠀⡿⠀⠀⡀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣀⢤⣤⠈⠻⠗
⠀⣷⠀⠀⠀⣀⠀⠀⠀⡀⢠⠀⢠⠀⢻⣨⠉⠁⠘⠾
⠀⣿⠀⠀⠀⠘⡷⣶⡾⠿⠀⠀⠈⠇⠈⠷
⠀⣿⠀⠀⠀⠀⠳⣾⣷⠆⠀⡈⠁
⠀⢽⠀⠀⠀⠀⠀⢸⣿⡀
⠀⢸⠀⠀⠀⠀⠀⣿⣿⣷⡦⣴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠐⠂⢀
⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⡄⠰⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣈⣡⡀⣀⠐
⠀⢸⠀⠀⠀⠀⠀⣿⣿⣿⡇⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢷⣻⡝⠓
⠀⢸⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠼⠁⠩⠂
⠀⢨⡁⠀⠀⠀⣀⣿⣿⣿⡇⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠸⠄⠀⠀⠀⢙⣿⣿⣿⣷⠀⡄⠀⠘⣁
⠀⠨⠅⠀⠀⠀⠠⣿⣿⣿⣿⡄⡅⠀⠀⠈⡅
⠀⢈⡁⠀⠀⠀⢐⣽⣿⣿⣿⡁⠁⠀⠀⠀⢤
⠀⢀⡁⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⢐⡀
⠀⠀⠅⠀⠀⠀⠐⠟⣿⣿⡯⠠⠀⠄⠀⠀⠀⠁

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢹⠟⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⡀
⠀⣀⠠⣿⡆⣀⠀⠀⣠⡴⢦⣄⠀⠀⠀⠒⠀⠀⠀⠀⠠⠂⠈⠠⠢⠀⠀⡄⠒⠿⠠⠀⠀⢠⠦⠚⠀⢦
⠀⢻⣷⣶⣾⣟⠀⠨⣁⣄⣄⣀⠆⠀⢀⣀⣤⣴⡾⠀⠢⣤⣤⣤⣶⠆⠀⣦⣠⣤⣴⡆⠀⢯⣉⣀⣀⣩⠆
⠀⠘⣿⣿⣿⠇⠀⠀⢿⣿⣿⡿⠀⠀⠸⣿⣿⣿⠇⠀⠀⢿⣿⣿⡿⠀⠀⠸⣿⣿⣿⠇⠀⠈⣿⣿⣿⠏
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⣠
⠀⢀⠀⣴⡄⠀⠀⠀⣀⣿⣿⡀⠀⠀⠀⠶⠀⢤⡀⠀⢀⠘⠛⡱⠄⠀⠀⡠⠿⠿⠆⠀⠀⢀⠜⠋⠛⢄
⠀⢻⡶⣦⣶⢿⠀⢀⣉⣀⣈⣉⡆⠀⢀⣀⣀⣤⣤⠀⢢⣠⣀⣤⣤⠆⠀⣅⣀⣀⣤⡄⠀⢯⡐⠂⣐⣛⠄
⠀⠸⣿⣿⣿⡏⠀⠀⢿⣿⣿⣿⠀⠀⠸⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⠇⠀⠘⣿⣿⣿⡟
⠀⠀⠈⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⠉⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠉
⠀⠀⠀⣀⡀⠀⠀⠀⢠⣶⣾⠆⠀⠀⠀⠀⠀⢁⠀⠀⢀⠸⠿⢦⡀⠀⠀⢀⡄⠄⢀⠀⠀⢀⡴⣀⠄⡄
⠀⢾⣬⣭⣥⣿⠀⢀⠛⠉⠉⠓⡄⠀⠀⠀⠀⣀⣷⠀⢌⢀⣀⣁⣀⡄⠀⡃⢀⢀⣀⡀⠀⣾⠀⠠⠤⠛⡄
⠀⢸⣷⣿⣾⡎⠀⠈⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⡇⠀⠈⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⡇⠀⠸⣿⣿⣿⡿
⠀⠀⠙⠛⠋⠁⠀⠀⠈⠛⠛⠁⠀⠀⠀⠙⠛⠋⠁⠀⠀⠉⠛⠛⠁⠀⠀⠈⠙⠛⠉⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠦⢦⠀⠈⣓⡉⢀⡔⠖⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠠⠖⣈⠁⠀⣿⠃⠎⢀⡰⣆⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣄⠀⢀⠀⠀⢠⣦⠀⣿⠀⠀⣿⠀⠀⣿⠃⣼⡄⠀⠀⠀⠀⠀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠠⣾⣅⠸⣿⡄⢠⡹⣇⡘⢶⡄⠛⢸⡇⢃⢰⠟⣀⠀⢠⡶⠀⢈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣛⠛⠳⢤⡀⢤⡈⠁⠈⠷⠘⣿⠈⣴⣿⡄⢰⡟⠀⠾⠃⠀⠛⠁⠈⣩⠵⠾⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠈⠀⠀⠠⡈⠻⠀⣿⡆⢰⣄⠀⠉⠈⠀⣰⡦⢀⣴⠇⠴⠟⢀⠌⠀⠀⢀⣅⡐⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠃⣾⣡⡀⠀⠄⠀⠀⠈⣠⣶⣮⠁⠘⠟⠀⣰⣆⠈⠛⠃⠀⣡⡄⠠⠂⡀⠀⠀⠀⠰⠾⢟⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠹⠶⣭⠽⣊⠄⠂⠀⣠⣶⣾⢯⣍⠸⣿⠦⢸⣛⣛⢠⣶⡟⢈⣙⣡⣷⣤⢴⡖⠠⠄⠀⠈⠉⠁⠀⠀⢀
⠀⠀⠀⠀⢢⣄⠀⠀⢒⣄⡼⠁⠀⣦⣤⣀⠸⠿⣿⠉⠙⢷⣶⠿⠛⠿⣷⡾⠟⠉⣿⣠⣿⠈⢁⣈⠀⢄⠐⢄⢀⠀⠀⠰⠏
⠀⠀⠀⠀⠀⠁⠀⠀⢈⣻⠀⡠⠄⠙⠿⣿⣾⣷⣿⡀⢀⡀⠯⣀⣭⣀⣿⢀⡄⠀⣿⣶⣼⡔⠿⠟⠀⠀⢧⠀⣌⡓⠀⠀⠴⠃
⠀⠀⠀⠀⠘⠻⠆⠀⠠⡗⠀⠓⠾⡿⣸⣿⠋⢆⣠⣽⣨⣋⣶⡉⠒⢉⣵⣉⡇⢾⠄⠀⠹⣿⡆⣲⡶⠂⠘⣳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢴⡖⠛⠛⠛⠧⣸⢮⠔⠸⠟⠉⢀⣶⣀⠙⠙⠓⠲⠎⢴⠴⠛⠋⠙⠓⣶⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣰⣶⣿⣦⡀⠐⢶⣺⣾⠂⢻⣶⡗⣘⠿⣏⣹⣾⡟⠀⢷⣇⢀⠖⠂⣠⡾⣡⣤⢼⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣱⡭⣿⡿⠋⢩⣎⡹⠛⢀⣞⣭⣏⣹⢂⠯⣸⣧⣸⣄⠀⢟⣡⣮⠙⢻⣦⠙⣫⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢰⣿⣇⠘⢫⡴⢄⡘⠻⡿⢿⡬⢧⣛⣡⢦⣾⢷⠛⢃⡴⢧⣿⠟⢺⣿⠀⠿⠿⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣴⠿⣼⠿⠋⢊⡴⢻⣷⡀⢑⣶⡷⢾⣭⡿⢾⣷⣎⠀⣀⡟⠣⡔⠒⠻⣿⣿⡦⠀⡀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣴⣏⡀⠀⢉⣩⣽⣙⡁⠛⠋⠙⠞⣿⠓⠋⠈⡛⠀⡏⣩⣀⡉⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣭⡟⢻⣿⠀⡩⢦⣿⢽⠷⣦⠶⡉⡠⣶⡿⠯⢩⡴⢏⡁⣻⡟⣿⣋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡜⢿⣦⣥⣤⠊⢠⠗⣩⠲⣿⡷⢫⠲⡆⠘⣦⣤⣴⡿⢣⡙⠉
⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠿⠟⠫⣿⣽⣿⠀⠀⣀⣿⣄⠘⢀⣼⣄⠀⠀⣻⢯⣬⠜⠛⠷⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡛⠁⣿⣴⢞⣯⣙⠿⠿⠿⢯⣽⠛⣦⡿⠀⢹⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⡻⠀⠀⢸⡟⠋⣥⣾⣿⣿⣄⠙⠻⢳⠀⠀⠸⣀⡀⢚⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣉⡠⠄⠀⠀⠃⢸⢁⣁⢄⣀⢻⡀⠁⠈⡄⠠⠀⠀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⢦⣼⠺⣤⠞⠈⡇⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⢀⠀⠀⠂⠀⢠⢀⣿⠁⠀⠀⢧⠀⠀⠀⡈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡅⣿⣥⡦⢀⠈⠀⠐⠀⠸⣿⠇⠈⠀⠸⡆⢰⣌⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡭⠔⠋⠀⠀⠠⠀⠀⠀⠀⢰⡄⠀⠘⢦⣙⣛⣡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠁⠀⠀⠀⠙⠋⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠄⠤⡄⣀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠁⡠⠄⠢⢄⡈⠉⠢⡄⠀⠀⠀⠀⣻⠇⠀⠀⠀⠀⠀⣷⣮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢀⠊⠀⠀⠀⠀⠈⢢⡀⠈⢦⠀⡠⠴⢿⡀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢀⠇⠀⠀⢀⠄⠀⠀⠀⠰⡄⠀⢫⠀⠀⠀⢑⠀⣀⠤⠴⣿⠃⠀⠀⠀⡠⠂⠀⣠⠔⠀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠀⠙⠛⠋⠐⠂⠄⣀⣹⠘⣧⠀⠀⠀⢡⡀⠘⠆⠀⠀⢈⡾⠁⠀⠀⠀⡇⢀⠔⠁⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣞⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠙⢤⡽⠂⠀⢀⠘⢃⠀⢺⠀⢠⠞⠀⠀⠀⠀⢠⡕⢡⡶⠞⡡⠔⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠙⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢒⣿⡆⢙⠀⠰⡆⠚⠒⣶⡄⠀⡠⢋⢔⢟⠅⠊⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡊⡄⠁⠸⠃⠀⣃⠀⠀⠀⢠⢜⠕⢕⡵⠁⠀⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠀⠁⠀⠀⣀⠄⠂⠀⢀⠀⠀⠀⠀⠰⡆⠀⠉⢀⡄⡀⣸⡣⠚⠉⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⣠⠞⡇⣸⠄⠀⠀⠀⠀⠱⡀⠀⠀⠀⢀⠔⠈⠉⠀⠀⠛⠀⡀⠀⠀⠀⠀⣇⠀⠸⢆⠀⠀⠀⠐⢄⠀⠀⠀⠀⣀⣤⠖⠁
⠀⠀⠀⠀⢠⠇⢀⣷⠃⢀⠄⠀⠀⠀⠀⡇⢠⠀⣰⠃⢀⡠⠖⠀⠀⠀⡄⠄⠑⠀⠀⠀⣇⠀⢸⠀⢣⠀⠀⠀⢈⣦⣠⡴⠋⢁⡜
⠀⠀⠀⠀⢸⡄⠐⢿⢀⠁⠀⠀⠀⠀⣰⣤⢼⡒⠛⠒⠺⡀⠀⠀⢠⠂⠀⠀⠀⠈⠀⠀⣞⡀⢛⡀⢸⠀⠀⢂⣠⠞⡛⢀⣠⠎⡁
⠀⠀⠀⠀⠀⢳⣀⠘⠛⢄⡀⠀⢀⡾⠁⠀⠀⠋⠀⠀⠀⠈⠀⠀⡎⠀⠀⠀⠀⠀⠀⠩⡇⠀⠀⣷⡸⠷⠓⠉⠁⣀⣴⠊⠱⢨
⠀⠀⠀⠀⠀⠘⣏⡷⢤⣀⡉⠁⠺⠧⠄⣀⣀⠀⢀⠀⠀⢀⠀⠀⣇⢀⢀⣀⡀⠤⠤⠔⠓⠐⠘⠁⠀⣀⡤⠔⡊⠁⠄⠀⡈⠸
⠀⠀⠀⠀⠀⠀⣷⢸⡀⢹⠛⠛⠶⠤⢤⣤⣀⣀⣉⠀⣉⠁⠈⡁⠀⣀⠀⣀⣀⣀⣠⣤⣇⠠⠟⠚⠉⠁⠀⠀⠅⠀⡁⠀⢂⡇
⠀⠀⠀⠀⠀⠀⢹⣝⡆⠸⡅⠂⢹⠀⠀⠀⡁⠈⠉⠩⠉⠉⠉⠛⠉⠉⠉⠉⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢈⠱
⠀⠀⠀⠀⠀⠀⠘⣧⢭⠀⡃⠀⠐⠄⠀⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠃
⠀⠀⠀⠀⠀⠀⠀⢹⡜⡄⢸⡀⠀⡁⠀⠀⠁⠀⠀⢀⠀⠀⠀⠂⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⣐⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⡈⡃⠀⠠⠀⠀⢀⠀⠀⠐⠂⠀⠀⡀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢸⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠸⡄⠨⣂⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠂⣔⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣑⡄⢳⡀⠀⢡⠀⠀⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⣠⠾⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠻⠤⣬⣆⣀⣨⠀⠀⠤⠀⠀⠀⠀⣀⣂⣠⡴⠷⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠛⠋⠉⠀⠀⠀⠀⠀⠉⠙⠻⢹⣆⠂⡀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⣔⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣦⣬⡍⠌⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠋⠉⠉⠛⠿⣿⣿⡆⣠⣤⣤⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡾⠇⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠠⠺⠀⣶⣼⣿⡅⠁⠈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠀⠀⢀⣀⡐⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢀⢿⣿⣿⡀⠀⠀⠀⠈⠛⠛⠛⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣀⢠⣿⣿⠏⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣏⡀⠀⠀⠀⠀⢯⠀⠀⠀⠀⡀⢀⣄⣀⠀⠀⣿⣿⡇⠀⢠⣤⡀⣀⣴⡿⠋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠻⠿⢿⣿⣿⣿⣿⣶⡍⠘⠋⠈⠁⠀⠀⠀⢻⣿⣇⢀⣼⣿⡿⠿⣿⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠤⠤⣬⣥⡌⠋⢹⣿⡇⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⢸⣿⡇⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⢸⣿⡇⠀⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡟⠁⠀⠀⠀⢸⣿⡇⠀⣿⡇⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣷⣶⣶⣶⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣉⣙⣛⣛⣛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣿⣿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣧
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⡇⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⡸⠁⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⠿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠢⠔⠚⠂
⠀⠀⠀⠀⠀⢀⣀⣷⠴⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀
⠀⠀⠀⠀⠀⠨⠀⠝⠲⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡶⢃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⡴⢶⠦⠄⣠⣀⡀
⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢁⠀⡀⣀⣀⡀⠀⠲⣼⡿⠟⢁⡍⠲⠀⠀⠀⠀⠅⣀⠀⢀⣀⣾⣿⣦⡟⠃⠸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣾⣿⡇⠓⣿⢏⠹⣝⢣⢤⠀⠐⡾⠇⠀⠀⠀⠀⣸⣆⡟⠀⠀⣤⣷⡬⣭⡄⣾⣾⡇⠁
⠀⠀⠀⠀⢀⠀⠀⠀⠈⣺⢷⡖⠆⠉⡁⠁⢈⠻⡟⣀⡋⠓⣾⠀⢰⠀⠀⠀⠀⠀⠀⠋⠘⠀⠀⠀⠙⠓⢃⡨⢰⣯⣴⣴
⠀⠀⠀⠀⠀⠐⠀⠀⡈⠫⣴⠟⠇⢤⣶⣾⠬⠀⠁⠀⠀⠝⠟⠀⠀⠀⠀⠐⡏⣃⢠⢄⠀⣀⣌⣏⡀⠰⠞⣡⠋⠹⢿⣶⡦
⠀⠀⠀⠘⠶⣾⠆⠞⠁⢐⡿⣤⡄⢸⣿⡟⠳⠀⣶⠓⣆⠀⠀⠀⠀⠀⣘⠀⣰⣿⣻⣿⣿⣿⠉⢹⡷⡦⠠⠋⠘⠟⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠒⠒⠒⠢⠠⣄⠀⠀⠀⠀⠀⢸⢧⠄⠀⠀⠀⠀⡀⠰⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠄⠃⠘⠂⠦⠀⠙⢆⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠆⠀⠀⠀⠀⠀⠘⠄⠀⠳⡴⠂⠉⠣⡀⠀⠀⢀⣴⡏⠀⠀⠀⢀⡀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⣼⠄⢌⠀⠀⢰⠇⣄⠀⠀⠈⠆⠀⢳⠀⠀⠀⢀⡔⠉⠉⠙⡄⠀⠀⠐⠋⣀⠴⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⠺⡄⢹⡄⠀⠀⢸⠀⠀⡄⠀⢀⠏⠀⠀⠀⠀⡁⠔⣠⡴⢊⣁⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡰⠒⠉⠑⠢⡄⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠠⣼⡄⡏⠀⢡⠠⠯⣤⣄⠀⠀⡔⣡⡾⡋⠔⠉
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠞⡉⠃⢰⠀⠘⠀⠀⠈⠀⡠⣫⠚⣩⠊⠀⠚⠀⠈
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠁⠀⢼⡄⠐⠇⢀⠀⢀⣏⠵⠋⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡴⢿⢀⡂⠀⠀⠀⠈⠣⠀⠀⠀⠀⣠⠔⠊⠁⠀⠘⠀⠀⠀⠀⠀⠀⡆⠀⠶⡀⠈⠁⠑⢄⠀⠀⠀⠀⣀⣤⠒⠁
⠀⠀⠀⠀⠸⠁⢻⡞⠀⡤⠀⠀⠀⠀⡇⢀⠀⡜⠁⠀⠄⠀⠀⠀⠄⠀⠁⠀⠀⠐⡇⠀⡀⠘⡄⠀⠀⢘⢷⣀⡴⠋⢁⡎
⠀⠀⠀⠀⢱⡀⠸⣇⠀⠀⠀⠀⠀⡰⠄⢾⡂⠁⠐⠠⠀⠀⢀⠆⠀⠀⠀⠀⠂⠀⠃⠀⢁⠀⡃⠀⢀⣠⠞⠋⢀⡤⢋
⠀⠀⠀⠀⠈⢦⡄⢙⠣⣄⡀⢀⡞⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡂⠀⣸⠤⠷⠊⠉⢀⣠⢴⠋⠐⠔
⠀⠀⠀⠀⠀⢸⢽⡓⢦⣄⣀⠙⠛⠀⠤⠄⠠⡤⠀⡠⠤⡀⠼⠠⠄⠠⠴⠀⠐⠊⡃⠀⡁⣀⣠⠶⠚⡉⠀⠄⠀⠅⡉
⠀⠀⠀⠀⠀⠘⡏⡆⠈⡅⠉⢹⡓⠒⠶⡦⠤⠤⣤⣤⣤⣤⣤⣤⠤⡤⠤⠤⠶⠖⠓⢊⠉⠀⠀⠀⠀⠂⠀⠄⢐⢡⠁
⠀⠀⠀⠀⠀⠀⢷⢫⠀⣓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠸⡟⡆⠸⠀⠀⠅⠀⠀⠅⠀⠀⠠⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⢻⣺⠈⢆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢐⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣧⠸⡄⠸⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡫⡀⢅⠀⠐⡂⠀⠈⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⡠⠀⠈⠀⣠⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠦⣀⣐⡀⠀⣂⠀⠈⠀⠀⢀⠀⠀⠀⢀⣠⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠒⠛⠊⠉⠉


⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣧⣶⣴⣶⣴⣾⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠤⠤⢄⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠙⠀⠀⠃⠀⢠⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡠⢀⠀⣀⢠⢚⣩⢀⠙⣉⠁⠀⠈⣇⡤⠄⠞⠚⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠑⠒⠍⠉⠾⠟⠂⠧⠧⠒⠒⠈⠰⠀⠀⠁⠀⡀⣠⠤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⢀⠀⣀⠀⡠⠄⠀⠁⠀⢈⠹⠄⠐⠚⠁⠀⡀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⡀⡈⠀⢄⠀⠂⠀⠑⠃⠀⠈⠀⠀⠀⠀⠉⡡⠤⡀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡄⠀⢐⠀⠀⠀⡀⠀⠈⠉⠉⠑⠒⠖⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠀⠀⠀⠿⠷⠕⠒⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⣀⣤⣤⣶⣶⣀⡶⠀⠀⠈⠈⠈⠁⠉
⠀⠀⠀⠠⠄⢄⡂⠀⡀⠀⠀⠘⠐⠀⠁⡀⠀⠌⣛⠒⠒⠠⢤⣀⣀⣠⣤⣦⣖⣶⣾⠿⠿⢊⢉⠁⠁⠀⠂⠐⠊⠨⠍⠐⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠈⠐⠠⣀⠂⠀⠄⠈⠀⠀⠀⠤⠔⠒⠉⠀⠉⠉⢉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠈⠑⠒⠤⠄⣀⡀⠀⠠⠀⢀⠁⠐⠂⠀⠀⠀⣀⠀⠠⢄⡀⠀⠁⠁⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠉⠀⠒⠂⠠⠤⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠄⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠆⠀⠀⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠄
⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠰⠆⠀⠀⠈⢹⣟⠠⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠈
⠀⠀⠲⣤⡀⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠚⠀⠐⠐⠢⠈⢧⠀⡀⠀⣀⡠⠔⠂⣸⣾⠀⠱⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠹⠆⠘⠓⠀⢈⡆
⠀⠰⠀⠀⢀⠀⠀⠊⠁⠀⣀⣼⠇⢠⣶⣄⣀⣀⠀⠙⠀⠀⠀⠀⠀⠀⢀⣼⠀⠃⠀⢱⡖⠛⠋⢿⠟⠀⡀⠐⠻⢿⣿⠗⠒⢲⣤⡀⠀⠀⠀⣠⠤⣄⠀⠈⡇
⠀⠀⡀⠘⠩⡁⢢⠀⠀⠀⠛⢿⡆⠸⣿⡟⠛⠉⠁⡀⠘⢿⠟⠀⠀⠀⢈⢿⠀⠀⠀⠀⠇⠀⠀⠘⠠⣾⡏⠀⠀⡀⠈⠘⡃⣸⠟⠁⠄⠀⠈⡁⠀⣷⣂⠰⡇
⠀⠀⠈⠀⠀⣡⠏⠀⠀⠺⢆⠈⣿⡀⠙⠦⣤⣀⣠⣿⠀⠈⡀⠀⠀⢀⣾⡞⠀⠠⡴⠀⢴⣶⡇⠀⠀⠀⠓⠀⠀⠀⢰⡶⢋⠁⠀⠉⠀⠀⢰⡇⠀⠀⣿⡀⣠
⠐⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⢡⣿⣿⡆⠀⠀⠉⠁⢀⣄⠀⢿⡷⠦⡿⠋⢠⢐⠀⠀⠀⢈⣿⡆⠀⢀⠀⠀⢠⠀⢀⡿⠄⠛⠂⠐⠾⠿⣶⣾⠟⠢⠀⠀⠀⠛
⡀⠹⡦⠀⠀⢀⡴⠚⠉⢱⠒⠾⣿⡟⣠⠜⠂⠐⡿⠋⠉⠑⠻⢆⡀⠘⠃⠠⣆⡀⢡⡇⠾⠿⢷⣾⣣⣴⣄⣴⠟⠁⢀⣀⠀⠀⠀⠀⢀⣿⣏
⢱⠀⠁⠀⠀⠺⠈⢀⠀⢾⠇⠀⠀⠉⠛⣀⢠⠄⠀⠀⠀⢀⣤⣤⣿⠷⠦⣄⡈⠁⡿⠀⠀⠀⠀⠈⠁⢻⡿⠁⢀⠀⠀⠻⡀⢀⠴⡞⠃⢹⡛⠉⠲⣤
⠙⠀⢀⣀⣀⠀⠀⠈⢢⣌⡀⠱⣆⠀⠐⢸⡟⠀⠀⠤⠐⠋⠉⠉⠙⠒⠦⣈⣍⣠⠃⢀⣠⣤⠀⣠⣔⠛⠀⠀⣾⣠⠀⠈⠀⠀⢠⡇⠀⢺⢉⡿⣠⡙⣄⠀⡀
⠈⢁⡿⠁⠉⢧⡀⠀⠀⠉⢉⡁⠛⣦⠀⢸⡷⠂⢀⣀⢠⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⢉⠃⠀⢻⣿⣿⠀⠀⢫⡁⠀⠀⢠⢟⠘⠁⠀⡿⣼⢡⠿⣻⡏⡖
⠐⠛⠁⠀⠐⠿⠛⠉⠆⠀⠈⠋⢀⢻⣦⣻⣴⠿⠛⠋⠉⠉⠉⠻⣿⠖⠠⠥⠐⡰⠿⢿⠂⣾⣇⠀⠉⠛⢣⡀⠀⠑⠒⠂⠀⠈⠁⠀⣰⡟⣁⠀⠈⣿⣇⢸⣿
⡀⠀⠀⣤⠀⠀⣴⠶⠂⣄⠰⠚⠉⠉⡉⢙⠃⠀⢀⣠⠄⠒⣶⣰⠿⣄⠀⠀⢠⡇⠰⠁⢈⠀⠈⠱⠖⠲⢀⡿⠦⡀⠀⠈⠀⠀⣀⡾⠋⠙⠻⣷⡶⣼⠟⠉⣀
⣹⣄⠀⠈⢳⠾⢿⠀⠀⠁⠀⡀⣠⣿⠡⣿⣿⣿⡟⠁⠀⠀⢀⠟⠀⡟⠀⣴⣾⠟⢀⡰⠶⠶⣤⡊⠀⠀⢸⠂⣀⠬⢷⡄⠀⠀⠹⡆⠀⠀⠀⠉⣴⣿⢷⠞⣽
⠉⠉⠀⠈⠟⠉⡀⠼⠃⣴⣾⡇⠙⠉⠬⠘⠋⠉⣆⠄⢲⣶⣷⡆⠀⢴⣼⢿⣃⣴⡻⠛⢩⣿⣿⣻⣄⣀⠬⣽⣿⢾⣿⠇⠀⠀⠀⡇⠀⠀⠀⠀⠈⡅⣴⢸⣿
⠀⠀⠀⠀⡠⠊⠉⣛⡶⠁⠀⡇⢘⡚⣁⣤⣴⡞⠕⠀⠈⣭⠵⢶⠞⠋⠀⠀⣿⣯⡴⠙⠻⣍⡽⠛⠉⠀⠀⠘⣿⡔⠻⢶⣶⣶⠶⠑⣼⣶⢦⡀⠀⠸⠃⣼⡏
⠀⢀⣀⢒⡀⠀⣀⣤⣴⣎⢸⣇⠸⢃⡴⣞⢯⣵⡄⠄⠀⠙⢿⣏⠀⣀⣠⣄⣸⣟⢦⣤⠀⠈⡀⠀⠀⠀⢀⣀⣸⡇⠀⠿⣀⡈⢀⢴⣇⡼⢾⣿⠀⠀⣿⠿⠐
⢀⡻⢍⣁⣴⢀⣀⢱⡿⣤⣦⣝⣴⣫⣾⣵⠋⠀⠀⠀⠀⠐⢾⣿⢟⡭⠍⠉⠉⠛⠛⠿⢧⣼⡟⠒⠒⢾⣿⣖⣠⣷⣶⠻⣋⠀⠀⠀⠹⣷⢄⣽
⢠⡿⡿⣿⣧⣿⣥⣦⣀⣼⠟⠛⠁⠀⠀⠙⣧⡠⣔⣼⢾⠟⠓⣤⣀⣀⣄⣀⣀⡀⠀⠀⠀⠙⠇⠀⠀⠀⢻⣯⠟⡹⢻⡇⣀⡀⠀⠈⢺⣿⡿⠋⠀⢀
⠀⣀⣀⣉⠟⠁⣨⢿⣤⠀⠀⠀⠀⠀⠀⠀⢻⣾⢟⠀⠉⠀⣼⡗⠻⠾⣶⣿⣶⣿⣭⡓⡄⢠⢇⣠⡴⢀⡟⠀⠈⠀⣭⠜⢻⠡⣔⠀⠸⣿⡀⠀⠀⡈
⢸⣿⡟⠁⠠⠊⠁⡠⠋⢀⣤⡴⠶⠾⢿⣶⣤⡿⣴⣷⠶⠄⢹⣷⡀⠀⠀⢙⣷⣮⣿⣷⣽⣿⢞⣉⣡⠾⡴⠾⠃⠀⠁⢀⣼⡄⠛⠛⣡⣿⣧⠀⣼⣷⣦⡀⠐
⣼⣿⣿⣦⠤⠠⠤⠷⣾⣟⣥⠶⠛⢿⣿⣿⡿⠻⠞⠛⠛⢷⡆⠸⠇⠀⢐⣿⡿⠏⢰⣿⣷⠁⢼⡿⣧⡖⣿⣶⣤⣤⠀⠀⠈⠉⠉⢾⡛⠀⠿⠛⠙⡀⠉⠻⢾
⠙⠋⠀⡀⠒⣒⡶⢶⠞⠁⠀⢄⣀⣿⡿⣿⡀⠀⠀⠀⠀⠈⢿⡧⡀⢀⡾⢳⣷⡤⠃⠈⡜⠀⠸⣧⣼⢿⡐⣵⡿⠃⠀⠀⠀⠀⠀⠈⢏⠘⠉⠁⠈⣙⣶⡄⠼
⢀⠠⢊⠴⢻⡏⢰⣧⣀⣀⣈⣘⣏⣾⡇⠻⣇⢠⠀⠀⠀⠀⠀⢻⣾⣋⠀⠘⢿⣶⣶⡿⠁⠀⠀⣿⣼⡘⠛⡟⠁⠀⠀⣀⣀⣠⠤⠴⡾⠀⠀⢀⡴⣻⣿⠇
⢀⠀⠁⠀⣠⣀⡘⣛⣻⠿⣿⣿⣿⡯⣄⡀⣼⠘⠀⠀⠀⠀⠀⣀⣶⣿⣿⣶⡶⣿⣟⡁⠀⠀⠀⣽⢿⡟⠙⣷⣶⣿⣿⣿⣯⣤⣴⡄⠐⠀⢠⠞⠉⣽⠋⠀⣀
⢿⣴⢂⣩⣥⣤⣤⣿⣿⣟⣶⣄⡇⠙⢦⣼⡇⠁⠀⠀⠀⠀⠀⠘⠟⠻⣏⡴⣣⠟⠓⢧⣭⣉⣟⠡⠾⠛⠋⠉⠉⠉⠉⠉⠉⠙⢏⠧⠀⢀⡞⠀⡼⠉⢷⣄⡿
⡽⠃⠉⢉⡋⠀⠉⠛⠿⠿⣿⡿⣣⢀⣠⡸⢶⣷⣤⣄⡀⠀⠀⢠⣄⠀⠙⠺⠿⡧⠄⠊⠉⠁⠀⠀⣀⣤⡞⠀⠀⠀⢀⣀⣀⣠⣤⣿⣆⣾⣴⣾⣇⠂⠂⣹⣿
⣀⣀⣀⣼⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠿⠦⡿⠛⣿⣽⣷⣦⣼⣧⣍⡀⢀⡀⠀⠀⣀⣠⡄⠀⠀⠻⣿⣉⣁⣉⣩⣤⣤⣤⡤⠬⠏⣝⣽⣯⡙⢌⢷⣵⡿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣤⡄⠀⢀⡀⡀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠙⠛⠛⠛⠛⠛⠒⠒⠶⠶⠶⠶⠶⠿⠭⢭⣭⣭⣭⣭⣵⣶⣶⣒⣒⣒⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠳⣌⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣇⣤⣶⣿⡳⠔⠚⠛⣦⠶⠔⢶⠀⠶⡄⠀⣴⣤⠀⢤⣤⣀⣀⣤⣀⢀⢀⣀⡀⣀⢀⠀⣸⢸
⠀⠀⠀⠀⠀⣀⣤⣤⡞⣿⡆⣘⣋⣽⣿⣿⣿⢿⣿⠿⠲⠶⠾⠶⣤⢼⣦⣄⣸⣧⣀⣈⣧⣈⡉⣻⣈⣙⢙⣏⠙⠈⣫⣻⢸⢸⣧⣦
⠀⠀⠀⠀⣸⡗⠛⠻⣿⠛⠛⢿⣿⠻⠿⣿⡿⣤⣤⣦⡀⠀⠀⠃⠿⢨⠀⠀⠀⢸⢉⠉⡏⠀⠉⢩⠉⣯⠉⣿⡏⠉⣉⣿⣼⣺⣿⡏
⠀⠀⠀⠀⠙⣧⡀⡀⢠⣤⡀⠀⢨⡄⠀⠙⣀⠀⠀⠙⣁⠈⠉⠛⣍⠉⠙⡶⠒⠲⡦⠐⠃⢦⡄⠼⠤⣷⣤⣾⣶⣿⣿⣟⣬⣿⣿
⠀⠀⠀⠀⠀⣧⢳⠀⢸⠩⠉⠉⠉⢙⠛⠛⠋⠓⠒⠒⠛⠲⠶⠤⠿⠦⠤⣼⣦⣄⣠⣦⣀⣀⣴⡄⣀⣠⡿⣿⣟⣟⣿⢿⢹⣿⡇
⠀⠀⠀⠀⠀⡷⡤⠤⠼⢶⣤⣤⣤⣤⣄⣠⣤⣍⣀⣀⣠⡄⠸⣀⠈⠀⠀⠀⠅⠀⠀⠸⠆⠀⠈⣵⠉⠉⠀⢽⣿⣧⣿⣦⠟⣹⠇
⠀⠀⠀⠀⠀⣿⠁⠀⠀⢸⡂⠀⠀⠐⠀⠀⠀⠙⠋⠉⠉⡍⠀⠉⡛⡖⠚⠻⠂⠓⠻⣶⣤⡤⢴⠼⠤⠖⠿⣶⣿⠋⢰⣿⣦⣷
⠀⠀⠀⠀⠀⢸⠟⠛⡛⠛⠧⠤⠚⢳⣶⣶⡶⠿⠤⠴⢦⣤⣤⣤⡆⣃⢀⣀⣁⠀⢀⡀⠀⠀⠀⠭⠀⠀⢀⣿⣿⣦⣾⠋⠀⣟
⠀⠀⠀⠀⠀⠀⢧⣤⣷⣄⡁⠀⢀⣸⣷⣃⣀⠉⠀⠀⡸⠙⠉⢸⠀⠀⠀⢹⢻⠟⠛⡛⡒⠂⠛⣿⣷⡞⢛⠁⢀⣾⣿⣶⢶⡏
⠀⠀⠀⠀⠀⢸⡆⠀⠀⡝⠛⢻⡏⠠⠀⠈⢹⡟⡟⢛⢛⡒⠒⠚⢳⠶⠶⠚⠴⠤⠤⣧⣂⣀⣠⣌⡁⠤⣼⣶⣾⠁⢸⣏⣸⠇
⠀⠀⠀⠀⠀⠀⢳⣶⣦⡷⠀⠤⣷⣤⣀⣠⣼⣄⠀⣸⣬⣀⣀⣀⠉⠀⠀⡀⡝⠂⠀⣸⢙⠉⠉⠀⠀⠀⣸⣿⠿⣶⡏⠉⡵⠁
⠀⠀⠀⠀⠀⠀⢸⡁⠀⡿⠁⠀⠀⡏⠉⠁⠀⠠⠀⠀⠀⠙⠛⠋⢀⠉⠉⠙⡷⡶⠚⢃⠦⠄⢼⣶⣴⠖⡏⠀⠀⣿⣧⣴⣧
⠀⠀⠀⠀⠀⠀⢾⠁⠈⠙⠻⠿⠻⠗⠦⠤⠶⣤⣤⣤⡤⠄⠀⣤⣈⣀⣀⣀⣁⡀⣀⠈⠀⠀⠀⢀⢸⢠⣇⣤⣾⡇⢸⢼⡟
⠀⠀⠀⠀⠀⠀⠸⣦⣀⣀⣄⣸⣀⣮⣄⠀⢀⠛⠘⠸⣤⠀⠀⠀⠹⠛⠙⠡⠄⠀⠉⠛⢿⠶⠒⠀⠐⡚⢿⣽⣯⣀⡾⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠉⠉⠙⠛⠛⠶⠦⠚⠳⠴⠴⣦⣁⣀⣤⣀⣈⣀⣀⠀⠀⢆⣼⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠉

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇⠀⣿⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⠛⠛
⣿⠀⠀⠀⣡⠷⣶⢦⢲⣂⢦⡆⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠠⠤⣼⡷⡖⠠⠄
⣿⠀⠀⠀⠮⠴⠋⣯⢑⢬⠐⡀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣠⣄⣾⣷⣠⡤⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠈⣆⠺⠁⢺⡷
⣿⠀⠀⠀⡁⠢⠁⢿⢐⠅⢑⠁⠀⠀⣿⠀⢸⡇⠀⠀⠀⣻⣿⣤⣥⣽⣧⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣬⡈⣠⢀⡄⠱⠄
⣿⠀⠀⠀⠬⡥⠧⣿⣆⡁⠵⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢩⣿⠿⠟⣬⡋⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣯⠅⠀⠀⠀⠀⡀
⣿⠀⠀⠀⡇⢭⡨⣿⠬⢀⣀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠚⠛⠙⠃⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠁⠀⠀⠖⠠⠠⠵
⣿⠀⠀⠀⠀⠀⠁⠉⠀⠈⠁⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠀⢰⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡆⠀⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⢀⣀⠀⢀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⢠⣷⣤⣤⡀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⣇⡎⡠⣽⡧⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠘⣿⣿⣿⣿⡆⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠏⢯⣁⡰⠃⠇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⢀⣾⡿⠛⣿⣿⣿⡄⠀⠀⢸⡇⠀⣿⠀⠀⠀⢘⠀⡤⠋⢵⠃⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⣼⢿⣤⣶⣾⣿⣿⣃⠀⠀⢸⡇⠀⣿⠀⠀⠀⠈⢄⠃⡀⠔⠀⡸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠉⠈⠉⠉⠉⠉⠉⠉⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠈⠉⠉
⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠇⠀⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢀⣤⡄
⣿⠀⠀⠉⠛⠛⢛⣛⣿⣿⣷⡄⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⡿⣿⢸⣿⢩⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢤⣽⣥⠄⣤⣶⣄
⣿⠀⠀⢀⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⡇⣿⢸⡇⣾⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠶⣶⡶⠂⠶⠿⠶
⣿⠀⠀⢤⣭⣭⣭⣭⣤⣤⣤⡄⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⡇⣿⢸⡇⣿⡆⠀⠀⢸⡇⠀⣿⠀⠀⠀⠲⠶⠶⠂⣚⣿⣓
⣿⠀⠀⢈⣙⣛⣛⣛⣋⣉⡁⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣿⡇⣿⣿⡇⣿⡇⠀⠀⢸⡇⠀⣿⠀⠀⠀⢘⣻⣛⠈⣩⣭⣍⠁
⣿⠀⠀⠠⠤⠤⠴⠶⠶⠶⠦⠄⠀⠀⣿⠀⢸⡇⠀⠀⠀⠛⠃⠟⠙⠃⠛⠃⠀⠀⢸⡇⠀⣿⠀⠀⠀⠈⠉⠁⠈⢩⣿⠍⠁
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡇⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠩⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡸⠀⠐
⠀⠂⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡐⠁⠀⠀⡤⠄⠐⠂⣀⠉⠉⠉⡉⠉⢉⠐⠒⠀⠤⢀⡀
⢠⠈⠦⡀⠈⠑⠤⡀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⢀⠅⠀⠐⠲⠦⠬⠥⠒⠤⠅⠠⢌⠀⢈⠢⠐⢌⠑⠂⢀⡀
⠈⡄⠀⠀⠁⠂⠀⠈⠢⠀⢀⠀⠤⢄⠀⣠⠄⠀⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⢁⠈⢀⠈⠐⢄
⠀⠈⢄⠀⠀⠀⠀⠀⠤⠄⡇⠀⠀⠀⠥⠄⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢁⠈⢄⠙⠢⡀
⠀⠀⠈⠃⠀⠀⠀⠀⠠⠔⠛⣄⢠⡄⠆⣀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠇⠐⠈⠓⡁⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⠀⢡⠑⡄
⠀⠀⠀⢀⠀⠀⠀⢀⠠⢊⠃⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠄⠈⢀
⠀⠀⠀⠀⠀⢰⢊⠁⢊⡼⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢂
⠀⠀⠀⠀⢠⠇⠁⢀⠆⠂⠀⠀⠀⠀⠀⠈⠄⠀⠀⣀⡀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⢃
⠀⠀⠀⠀⠂⠐⠁⠈⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡀⠆
⠀⠀⠀⡐⠀⢂⠴⠀⠀⠄⠀⠀⢆⠠⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⡇⠈⡀
⠀⠀⠀⡄⢁⠪⠇⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁⠄⣠
⠀⠀⠈⠀⡑⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈
⠀⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⢠⡄
⠀⠀⡖⠒⠓⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠚⠚⡇
⡠⠈⠓⠒⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠤⠗⠒⠒⠛⠠
⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠃⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣀⣀⣀⣀⣀⣠⡄⠠⠄⠐⠒⠐⠒⠂⠋
⠀⠀⠀⢀⡀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⣀⡅
⠀⠀⣀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⢀⡀⠀⡀⠀⠠⣄⠀⡠⠤⠀⢤⣀⣲⠒⠀⠈⡇⠀⡇⠀⠀⢀⡀
⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⢸⠀⠀⢠⠃⠒⣧⠀⠀⠤⠀⠤⠀⠀⠴⠀⢸⠂⠀⠘⠁⠀⠉⠁
⠀⠀⠲⠀⠠⠤⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡀⣀⣀⡀⠀⠤⠄⠀⠰
⠀⠀⠰⠠⠄⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠒⢲⠀⣰⠒⠒⠒⣄⣀⡓⠒⠐⠒⠒⠒⠈⠉⢹⠀⢸⡀⠀⢈⠁⠉⡄⠠⠤⠴
⠀⠀⢀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠓⠀⠀⢾⠀⢸⠆⠀⠐⠂⠀⠃⠀⠐⠇⠀⡚⠀⠀⠈⠀⠈⠁⠀⠈
⠀⠀⠘⠋⠁⠀⢂⣀⣰⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⣸⠀⢸⡀⠀⠀⠀⠀⠀⢀⢀⡆⠀⣇⣀⠀⡠⠤⢤⠄⠀⢶⠀⢠⠃⠈⠉⠛
⠀⠀⠀⢙⠐⠂⠒⠠⠴⠀⠀⣸⠂⠀⠀⠀⠀⠀⠀⡄⠀⠀⣁⠀⡉⠀⠀⢹⠐⢸⠁⠀⠈⠁⠀⡁⠀⢀⡇⠂⣇⠀⢀⡜⠀⢺⠄⠠⠜⠀⠘⠒⠀⠈⠇
⠀⠀⠀⠀⠢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠉⠀⠀⠋⠀⠉⠀⠀⠉⠀⠈⠁⠀⠈⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠚⠂⠐⠛⠒⠂⠀⠀⠠⠤⠤⠦⠀⠤⠤⠤⠤⣤⠤⠤⠤⢤⣀⣀⠦⠤⠤⠄⠀⠒⠒⠒⠒⠄⠘⠋⠉⠉⠁
⣿⣿⡿⠛⠟⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡮⠀⠠⡌⢸⡀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠉⠕⢧⡖⠁⠀⠀⠀⠀⠀⠀⠀⣠⣔⠂⠉⣉⣁⣠⣈⡙⠲⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢸⢠⠊⡀⠀⠀⠀⠛⠀⠒⠒⠒⠒⡰⠋⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⢻⣆⡙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢠⡿⣿⣿⣿⣿⣿⣿⠛⠻⠛⢘⠿⢿⢦⡈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇⠀⠁⠀⠀⠀⠀⠀⠀⡘⠁⢠⣿⣿⠁⠐⠛⠻⢿⡇⠀⠀⠀⠀⠀⣘⡀⠈⠋⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣾⣿⣿⣧⡥⠤⢄⠀⢡⠀⠀⢀⣀⠠⡈⠓⠀⢑⢆⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⠀⠀⠀⠀⠀⠀⢰⡎⣠⠿⠏⠀⢀⠀⡀⢀⣃⣀⠧⣤⡅⡯⡤⢷⡀⠰⣌⢊⢢⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⡇⠀⠀⠀⢸⠎⠀⠀⠀⠈⢀⠀⠀⡆⠹⠐⠳⠄⠀⠰⠎⠛⠈⢹⣯⣭⣿⣿⣦⠴⠖⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⠀⢰⠀⡇⠀⠀⠠⣤⠤⣾⡞⠚⢆⡁⢀⠀⠀⠀⠀⢠⠔⢚⡁⠐⠰⠀⠈⠷⣄⠀⠀⣰⠇⢀⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡇⠇⠈⠑⠀⢸⠷⣨⢇⠀⠄⣱⠊⠳⡀⠀⢠⠃⢰⠏⠀⠀⠀⠀⠀⠀⠈⠑⢣⡀⠋⢃⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠸⡌⠒⢶⠒⢻⣿⣿⡄⡀⠀⡏⠀⣦⣑⠀⢰⡆⠄⠀⠀⠀⠀⠀⠐⡤⠀⢀⡜⠀⠀⠀⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⣄⠈⢆⢰⠘⢿⣧⣇⣀⠙⡀⡽⠛⠛⠻⠗⠒⢦⡀⠈⠢⡀⣰⡃⣀⣽⣠⡦⣀⡰⣄⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡻⠿⠋⠉⢠⡨⢧⣺⠁⠀⠀⠀⢀⡄⠀⡟⠋⠁⠉⠉⠉⠉⠁⠀⡀⣀⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠰⠃⢰⠉⠱⡄⠟⣣⡀⠀⠀⢾⣷⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⡌⠀⢺⠀⠐⡄⢠⠟⢳⠦⠔⠃⠘⠻⠢⣄⣀⣠⣤⣤⣶⢶⣭⣤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢫⠀⡴⠁⢀⠯⣅⠀⠀⠀⠀⠀⠀⢸⡭⣏⠼⡁⢯⣜⣧⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠒⠺⢄⠼⠢⠄⣀⢀⡀⠴⠋⠈⠉⠁⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣉⣈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣤⠤⢄⡀
⠀⠀⠀⠀⢀⣠⠤⠤⠶⠒⠒⠒⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⢒⣲⠶⢊⠽⠋⠯⠭⠷⣀
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠈⢉⡠⠖⠁⠀⢀⣀⠤⢶⢬⡇
⠀⠀⠀⠀⠀⠀⠈⢷⣀⣀⣤⣤⣴⣮⣭⣤⣤⠤⣤⡤⠴⠾⣝⣒⠖⠺⠿⣿⣓⠢⡘⢄⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣇⡔⡩⠊⠁⠀⠀⠀⠘⢾⡃⠐⠶⡾⢃⣏⡤⠤⠤⢤⣤⣄⢼⣜⠛⢁⡇
⠀⠀⠀⠀⠀⢀⡤⢺⡌⠳⢽⡛⣄⣀⣀⣠⣠⣴⡿⢾⠶⠊⠁⠀⠀⠀⡴⠋⢁⣀⣾⣟⠉⠻⢧⣀
⠀⠀⠀⢀⡔⡩⠞⠁⡯⡦⢄⠈⠛⠿⠿⠯⠽⣿⣿⣭⡒⠀⠀⠀⢀⠞⣾⣏⣁⣞⡉⢹⠏⣳⣦⣤⣉⠒⠤⡀
⠀⠀⢠⢪⠊⠀⠀⠀⡷⡟⠉⡏⣒⡤⢤⡤⠊⣠⢟⣗⡳⣄⠀⢀⠾⠴⣇⣀⠈⡟⢩⠟⠤⡷⡮⣍⣉⣙⢢⡏
⠀⠀⠸⡐⢄⠀⠀⠀⢳⠛⡏⢩⣡⠕⢋⣤⠮⣄⡼⠁⡜⠫⠵⡿⠤⣤⠏⢠⡏⠑⢻⠒⣶⣵⠁⠀⠀⠈⠁
⠀⠀⠀⠈⠢⣍⠲⢤⣈⣶⠟⢊⡡⣖⠝⢯⣠⣏⠑⣺⠓⣦⣴⣃⣼⣈⣉⣹⠋⡹⢧⡴⠓⠁
⠀⠀⠀⠀⠀⠀⠉⠒⠢⠔⠚⠣⣽⣞⣑⣶⡊⢀⠟⠧⢴⠧⣤⣤⣏⠤⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠑⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⡀⠤⢦⡤⠶⠖⠢⠀⠲⢺⣶⣖⡲⠿⠗⣒⣶⢺⡦⣴⣤⣶⣶⣶⣤⣠⣠⣤⡀⣨⠄⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⠀⢙⣾⣁⡲⠖⢛⠓⡂⠀⠈⠩⠈⠁⠀⠩⠉⡛⢣⡧⠨⠤⢼⢽⣛⡶⠷⣮⣭⡟⣬⣟⠿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⣮⠞⣦⣴⣝⠋⠩⠭⠤⠤⠿⠯⠤⠭⣥⣀⣀⣬⠍⠚⢽⠒⢀⢠⣬⡈⣽⣻⣿⣿⣽⣿⣶⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠈⠸⣉⣘⠐⠶⠦⢛⠓⠶⠶⣶⢞⣒⢒⠒⠒⠲⠖⣲⢆⡒⠒⠚⠋⠹⠶⠖⣍⣉⠁⣤⡈⠉⣽⣵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢾⣿⣋⠐⠨⠓⢂⡷⠄⣈⠠⣭⠽⠓⢲⠌⠁⠚⠦⠿⢛⡋⠡⠤⠥⠶⣛⣋⠁⠀⡤⡨⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⡿⣭⣃⠽⠀⠈⠙⡒⠒⠂⢈⡍⠒⡒⠒⠒⠒⠋⠨⠉⠉⠉⣉⠂⣀⣀⠐⠆⠢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠬⠥⡀⠁⠡⠂⠐⠂⣒⠒⠀⠐⡂⠒⢀⡬⠁⣀⠀⠉⠀⠠⠀⠠⠰⡞⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠭⠕⠩⠭⠥⢔⣒⣒⡐⠤⠤⣠⣤⠤⠀⠁⠄⠨⠍⢀⡐⠂⢄⣽⡩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠨⠅⠡⠭⠤⢀⡐⣒⡊⠐⠒⣒⠂⠀⠂⠀⠨⠁⡀⡂⣈⣜⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠀⣀⡦⠄⠀⠤⡀⠒⠀⢀⣀⡀⠈⢂⠠⠜⡀⠀⠚⠴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠰⠄⠒⠛⣷⠉⠉⠉⠉⠈⠁


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

⠀⠒⡴⠂⠀⣠⣤⠀⠀⢰⣶⡄⠀⠀⠀⠐⠀⠀⠀⠀⢲⣶⣶⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣶⣶
⠘⠾⡤⠀⠀⠹⠿⠀⠀⠈⠛⠀⢀⣀⡀⠀⠀⠀⠀⠀⠈⠙⠉⠀⣶⡆⠀⠀⣤⣦⡀⠀⠀⠀⠀⠀⢰⠃⢀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡗⢦⠀⠀⠀⠀⠀⠀⠀⠙⠁⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠈⢰⣿⣆
⠀⠀⠀⠀⠀⢠⣤⣤⣤⡄⠀⠀⢿⣿⣿⠧⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠃⣴⣶⣶⣶⣦⠈⠈⠛⠉
⠀⠀⠀⠀⠀⠘⠿⠿⠟⠁⣶⠀⠈⠉⣉⠀⠀⠠⠁⢰⣿⣿⣿⣷⠴⡄⠀⠀⣰⡄⠀⠈⢙⠛⠛⠁⠀⠀⠀⠀⠀⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠀⠀⠀⠛⠀⠀⠀⠐⠾⣿⣿⣿⣿⠾⠀⠀⠀⢹⣽⠀⠰⡾⠀⡀⠂⠀⣀⣠⣀⣀
⢀⠀⠀⠀⢠⣤⣤⣄⣀⠀⠀⣾⠇⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠸⠇⠀⢘⣿⣿⣿⣿⡭⠃
⠻⠃⠀⠀⠸⠿⠿⠗⠋⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣋⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠻⢿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠛⠿⠿⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠠
⠀⢾⣿⣿⠒⡆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⢀⣤⣤⣄⠀⠀⠄
⠀⢸⣿⣿⠒⠁⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠐⣿⣾⣿⣿⣿⣧⠴⢦⡄⠀⠀⢀⠀⠀⠀⣀⣶⠀⢹⠿⣿⡟⠀⠀⠠
⠀⠈⠉⠉⠀⠀⠐⠚⢿⣿⠯⠁⠀⠐⠒⠂⠀⠀⠈⣿⣿⣿⣿⣿⣀⣠⠇⠀⠠⠀⠃⠀⢀⣿⡇⠀⠀⠛⠛⠁⠀⣤
⠀⠀⡉⠀⠀⠀⡀⠀⢘⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⣷⣾⡄⠀⣀⡀
⠀⠀⠁⠀⠀⠀⠀⢰⣏⣹⡇⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠻⠃⢘⣿⣏
⠀⠀⠄⠀⠀⠀⠀⠀⠉⠉⠀⢀⣀⣀⠀⠀⠀⣿⣷⠀⠁⣤⣤⣄⠀⠀⠀⠀⢠⠀⠀⣴⣿⣿⣷⠖⣦⠀⠀⠀⠈⠛⠉
⠀⠀⠅⠀⣼⣿⣶⡆⠀⠀⠀⣸⣾⣿⡏⠂⠀⠹⠟⠀⢸⣿⣿⣿⠀⢠⠀⠀⠐⠀⠀⢿⣿⣿⣿⡠⠋
⠈⠀⠀⠀⣽⣿⣿⡇⠀⠀⠙⠿⠿⠿⠛⠀⠀⡀⠀⠀⠀⠉⠋⠁⠀⠛⢀⣾⡆⠀⠀⠘⠛⠛⠃
⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⡿
⣠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⡇⠀⢁⠁⠀⢰⣶⣶⣾⡇⠀⠉⢀⣤⣴⣶⣶⣶⣤⠀⠀⠀⠀⠀⢀⠀⠀⠈⠋⠀⣰⣶⠀⠀⠀⣠⣤⣤⡀⠀⠠⣿
⢉⠁⠈⢠⡀⠀⠸⢿⣿⡷⠏⠀⠀⠈⠿⠿⠿⠿⠿⠋⠀⠀⠀⠀⠀⠈⠁⠀⡿⠀⠀⢿⣿⠃⠶⠀⠿⠿⠻⠃⠀⠀⠉
⠸⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠐⠀⠐