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Are you lost again ?

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Little soul

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⣠⣤⣤⣤⢶⡶⣞⣷⣻⣞⡷⠆⢀⠀⠀⠀⠀⠀⠈⠑⠊⠳⠾⣱⠾⣵⠾⣵⣖⡦⣤⣳⢦⡤⣤⢦⠳⠶⠌⠺⢵⡒⠶⣽⢲⡓⠚⠲⢳⡬⣄⣁⠈⠀⡀⢀⣀⣽⢲⠀⢀⣠⠴⡞⠀⠀⣀⢈⣀⣄⡤⣤⠤⡤⠤⠴⠦⠖⠶⠒⠖⠶⠲⠖⠞⡦⠀⠀⡀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⣁⣈⣤⣤⡴⣶⢶⣶⣻⣞⣷⣻⣞⡷⣤⡀⠹⣞⡷⣦⠀⢀⣾⣳⣟⡆⠀⠈⠑⠛⠾⢳⣟⣾⣳⣟⣾⣳⢧⣄⣀⠀⡀⣾⣳⣟⡆⠀⢀⣤⣤⢶⡶⣶⢶⡐⢆⠖⣢
⣷⣻⢾⡽⠯⠿⠙⠚⠁⠉⢀⠐⠀⢂⠀⢀⡤⣤⠴⣤⠦⡴⢤⠤⣭⢬⣝⡳⢮⡝⣧⢻⣌⣙⣓⣋⠷⣲⣖⡶⢦⣻⢦⡤⣬⡝⣯⢗⡦⣬⡝⡾⣽⢻⣝⢯⡞⣬⡳⣞⡽⠎⣿⢾⠙⠋⠉⠉⠈⠀⠀⠀⠀⠀⠀⢀⣤⢶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠂⠈⡀⠄⢃⡔⣤⢶⣞⣾⣻⣽⣻⣞⣷⣻⠽⠻⢞⣷⣻⣞⠳⣯⣟⣧⠙⠳⣽⣻⡽⣇⢸⣷⣻⢾⣤⡀⠁⠂⠄⡀⠄⠀⠈⠁⣿⢾⣽⣻⢾⣽⣻⢷⣯⢷⣯⣇⣐⠠⠘⢯⠿⠽⢋⠛⠓⢨⠹⡔
⠁⠀⠀⠀⠀⢀⠠⢀⠂⠈⠀⠀⠀⠠⠀⠀⠙⠲⠤⣄⣀⢀⣀⡤⢤⡒⠦⠝⠎⠙⠊⠁⠉⠈⠁⠉⠛⠑⠊⠙⠫⠳⢯⡥⣄⣀⠀⣀⣀⣠⢤⡴⣴⠲⠝⠎⠛⠑⠋⣁⣽⣻⣽⠛⠆⠀⠀⠀⠀⠀⠀⠀⣀⡴⣞⡿⡞⠛⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠐⡀⠁⠀⠀⢡⠘⡜⣿⣞⡷⠻⢞⣷⣻⣆⠀⠀⠄⣼⣳⣟⣾⡁⠹⣾⡽⣧⠀⠀⢿⣽⣻⣞⡷⣯⣟⡾⣽⢶⣌⠀⠠⠐⠈⡀⠁⣿⣻⣞⡇⠀⠈⠉⠙⣾⣻⢾⡽⣯⣟⡷⣶⣤⣂⡄⠂⠌⡀⢃⠞
⠀⡀⠄⠂⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⢤⠶⡭⠛⠘⠓⠦⠴⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⢤⡤⣖⡯⢖⡾⣹⢏⠷⠝⠊⠃⠁⠀⠀⠀⠀⣀⡴⣾⡽⣞⠓⠀⠀⠀⠀⠀⠀⣀⣤⢶⣻⣽⡻⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡐⣀⠀⠐⡀⠀⠂⠀⡱⠘⡀⠀⠀⡀⠘⣷⣻⢾⡄⠀⠀⢻⣷⣻⢾⡅⠀⠹⣿⣽⣳⡀⠈⣷⣻⢾⣽⣳⢿⠀⠙⠻⣞⡿⣶⣄⡁⠠⠀⢿⣳⢯⣧⣀⣡⠈⡀⢺⡽⣯⣗⠀⠉⡙⠳⠯⣿⣽⣻⢦⣔⡀⢊
⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠁⠀⠀⠶⠄⢀⡀⠀⠀⠀⠀⠀⠁⠈⠀⠉⣈⣡⠼⠭⠓⠉⠀⠀⢲⣌⠁⠀⠀⠀⠀⠀⢀⣠⡄⢰⡿⣽⠻⢳⣟⠃⠀⠀⣀⣤⡴⣞⡿⣽⡞⠯⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣱⣄⡀⠐⡀⠀⠀⠐⡡⢀⠡⠀⢀⠀⢹⣯⣟⣷⠀⠁⠈⣷⢯⣟⣷⠀⢀⡹⣞⣷⣳⡴⣾⣽⣻⢾⣽⣻⠀⠄⢀⠀⠙⠳⢯⣟⡷⣤⣹⢯⣟⡾⣽⢯⡿⣽⢯⣟⣷⣻⣤⢦⣤⣄⣠⣀⣉⣛⡿⣾⡽⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠐⠶⠉⠉⠀⠀⠀⠀⠀⢀⡤⣖⠏⠃⠉⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⢀⡴⣯⢷⠃⠈⠋⠁⠀⣸⢿⡴⣞⡿⣽⢾⡽⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣷⡀⠠⠀⠀⠀⡑⢂⡐⢢⡴⣶⢶⣻⢾⡽⣧⠀⢁⣹⣟⡾⣽⣞⣯⢿⡽⣞⣷⣻⢷⢯⣟⡿⣾⡽⡆⠀⢀⠂⠠⢀⠀⠈⠛⠷⣯⣟⡾⡽⠈⠉⠉⠙⠛⢾⣳⣟⡾⢻⢾⣽⣳⢯⡿⣽⣻⠷⠃⢈
⣀⣀⣠⣄⣀⣄⣠⣀⣄⣘⡷⣤⣤⣤⣤⣤⣤⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠝⠉⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣞⠵⣻⣄⠀⣰⢯⡿⠙⠁⣀⣠⡴⣶⣻⡽⣯⢿⣽⣻⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣻⡀⠐⠀⠀⠠⢃⡄⠣⢻⡽⠯⠟⢯⡿⣽⣆⠉⢷⣯⣟⣷⡻⠞⠋⠉⠙⢾⣽⣻⣆⢿⣽⣳⣟⣧⢀⣄⣤⢦⣤⢾⡴⣶⢶⡼⢯⡿⣽⣻⢶⣞⡶⣶⣬⢧⣯⢧⣤⣤⣀⣄⣈⡀⠁⡀⠄⠈⠄
⠟⠙⣷⡋⠛⠚⠓⠛⠚⠙⠛⠓⠛⠚⠑⠋⣈⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣞⡿⣽⡞⠟⠈⠀⢿⣞⡶⣯⣟⣷⣻⢿⣽⣳⠟⣷⢯⠿⣽⡌⠓⠿⣾⣽⣳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢧⠀⠁⡀⠀⠂⡔⠡⡌⠀⡀⠀⠘⣿⣳⢿⡄⠀⢹⣞⣷⣻⡄⠀⠀⠂⠈⢳⣟⣾⣳⢯⣷⣻⣞⡿⣾⣽⡛⢊⠛⡽⠯⠿⠽⠆⠻⠷⠯⠟⠾⠹⠷⠉⠻⠞⠻⠜⠡⠛⠜⠩⠉⡁⠠⠀⠡⠀
⡀⠐⣯⣟⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⡛⠂⠡⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣤⡴⣞⡿⣽⢾⡽⠏⢻⣇⠀⠀⠀⠀⣻⡎⠻⣷⣻⠾⠙⠋⠀⠁⢰⣯⠏⠀⢿⣇⠀⠀⠀⠉⠛⠻⢾⣽⣻⣟⡶⣶⣤⣤⣄⣀⡀⢀⠀⠀⠀⡀⣀⣀⣀⠄⠠⠀⠀⣀⡼⡏⠀⠀⢀⠀⠐⢨⠡⢌⠡⠀⠀⠂⠘⣯⢿⡽⡆⠀⠻⠞⠷⠇⣀⣤⡵⣞⣷⣻⠾⣙⠻⡞⠷⠯⠟⠁⠉⠀⠈⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠌⠀⠐⠀⠄⠁⠠⠀
⣷⣄⡿⣞⡷⢯⣟⣦⣄⡀⠀⠀⠀⠀⠀⠘⢳⣟⡷⣆⠠⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢿⡽⣯⡛⠉⢁⣠⣄⠀⢿⣄⠀⠀⠀⣿⡇⠀⠈⠻⣷⢦⡀⠀⠀⣿⡞⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠳⢟⡾⣽⢯⣟⣯⣟⣿⣻⡽⣶⢶⡶⣶⢶⣶⣻⣽⠛⠀⠀⠀⠀⢈⠀⢂⠣⢎⠒⡡⠀⠐⠀⠙⠯⠟⠙⠀⣀⣤⠒⠀⠉⠾⣽⡻⠾⠙⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠂⠀⠀⠂⠀⠀⠄⠂⠀⠀⠁⡀⠀⠁⠀⠀⠀⠄⠀⠀⠂⠈⠀⢈⠀⠀
⠻⢾⡽⣯⣟⣦⣌⠁⠛⠽⢻⡷⣶⣤⣄⣀⠀⠈⠘⠹⠀⢂⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⣀⣼⣳⣞⣯⢷⡏⠀⠘⣿⣆⠀⢰⣯⡇⠀⠀⠀⠈⠻⣽⣳⣤⢿⡁⠀⠀⠀⠈⠻⣷⣄⣀⣀⣤⡤⠖⠒⠒⠉⠁⠈⠀⠀⣀⠈⠡⠉⠘⠑⠛⠙⠋⠛⢜⡣⢏⠁⠀⠀⠀⠀⠀⠀⠀⠐⠠⢉⠆⡓⠤⡁⠀⠀⡀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢀⠠⠀
⣤⣤⣭⢷⣻⢾⡽⣞⡷⣞⡷⣞⡷⣽⡎⠛⠿⢳⡶⣤⠀⠂⠄⠀⠀⠀⠀⢨⣷⡃⠀⠈⢿⣞⣷⡻⠞⠉⠀⣀⣴⣻⣞⣧⣼⣳⠇⠀⠀⠀⠀⠀⠀⠛⢾⣯⢷⣤⣀⣠⣤⠶⠞⠙⠫⠟⠦⢀⣀⡰⣒⢆⠐⠊⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣩⠆⠀⠀⠀⠀⠀⠀⢀⡰⡉⠆⠎⠴⡁⢆⠁⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠐⠀⡀⠀⠀⠀⠀⠂⠁⢀⠀⠀⠀⠀⠂⠀⡀⠄
⣟⡚⣽⢯⣭⣁⣈⠀⠀⠀⠀⠀⠉⣱⣟⣤⢶⡾⣽⢧⡶⣶⡈⠄⠀⠀⠀⠰⣯⡇⠀⢠⣼⣻⣞⣇⠀⣠⢶⣻⣞⡷⠋⢾⣳⢿⠀⠀⠀⠀⠀⠀⣀⣠⡼⣯⠟⠺⠽⣳⢦⣆⣤⡤⠶⠒⢮⡙⠀⠀⠩⠞⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢥⣃⠀⠀⠀⣀⡠⢖⣣⠓⠉⠠⢙⠢⡑⢌⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠂⢀⠀⠀⠀⠀⠀
⡿⢽⣯⣟⡾⣽⢯⣟⣿⣳⣞⣿⣻⠷⠛⠞⠋⣙⣩⣭⣟⢷⠳⠀⠄⠀⠀⢘⡷⣧⣞⡿⣞⡷⢻⣞⡾⣽⢯⡗⠋⠀⠀⠈⠻⡏⢀⣀⣤⡴⠶⠛⠉⠁⠀⢀⣠⣤⠶⠞⠋⠈⠁⠀⠀⢘⠦⡙⠀⠀⠀⠙⡼⣡⠀⠀⠀⠘⣙⠦⡀⠀⠠⡴⢤⠤⣄⢌⠶⣡⢒⠶⡙⠦⠙⣊⡀⠀⠀⠀⢀⠣⡘⢄⠊⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠈⠀⠄⠀
⠃⠀⠈⠉⣻⣽⣳⠞⠳⠋⠈⠀⠀⠀⠀⣴⡻⠝⠃⠉⠀⠀⠀⠀⠂⠀⠀⠈⣿⣳⢯⡿⠉⠀⠸⣯⢿⡽⠋⠀⠀⢀⣀⣤⢶⠻⠏⠉⠀⠀⢠⢖⡲⢶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⣎⠁⠀⠀⠀⠀⢰⢃⠧⡀⠀⠀⢨⠳⣱⢀⠀⠀⠉⠈⠈⢨⠳⣥⢋⡀⠀⠀⠀⠒⠹⠀⠀⠀⠀⠐⣡⠊⡔⡈⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣷⢶⣻⡟⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⣀⣀⣤⣤⢶⡶⣶⢦⠁⠀⠀⠘⠯⠋⠀⠀⠀⠀⠈⠋⠀⠀⣤⡞⠯⠛⠈⠀⠀⠀⣠⡴⡞⠯⢎⡵⢣⠄⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡜⡬⠀⠀⠀⠀⠀⢈⢮⡱⢱⡀⠀⠀⣇⠧⣋⡄⠀⠀⠀⠀⢏⠓⠀⢏⠲⣄⠘⠱⠂⠀⠀⠀⠀⠀⠀⠀⢇⠰⠡⡘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠂⠁⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠳⢟⡶⣄⠀⠀⠀⠀⠀⣀⣠⣤⢶⡞⠿⠙⠛⠊⣩⡥⠁⠈⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⡟⠓⠉⣀⠸⡸⠌⢧⣋⠄⠘⡼⣡⠀⠀⠀⠀⠀⢰⢩⠖⠀⠀⠀⠀⠀⡘⢦⡙⢦⠱⡀⡜⡜⠒⠁⡎⢥⠀⠀⠀⢀⠀⡀⠈⠱⣊⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠱⢠⠑⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡂⠀⠄⠀⠀⠂⠀⡀⠀⠀⠀⠀
⣶⣤⣄⣀⠹⣟⡆⣠⡴⣶⡻⠝⠓⠉⠁⠀⠀⠀⢠⣼⣳⠧⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡤⣰⠰⡍⠞⠰⢩⣓⡃⠐⡎⡞⡀⠰⡱⢆⠀⠀⠀⠀⡌⢧⠂⠀⠀⠀⣀⠶⡙⠆⠁⠀⢫⡕⡹⠌⠀⣀⠜⣬⢣⠏⣝⢊⠷⠉⠯⠱⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠒⠠⡑⠄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠂⢁⣤⣞⣯⠟⠀⠀⠀⠂⠀⠄⠀⠀⠁⠀⠂
⠈⠁⢛⣽⣻⣽⣻⣗⣉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣻⢾⡝⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⣀⡀⣤⠰⢦⣍⠳⣌⢳⡁⠁⠁⢰⡒⡄⢣⠞⡀⠀⠘⡥⢣⠀⠱⡩⢆⠀⠀⠠⣙⠦⠀⠐⠎⠳⠉⠖⠉⠚⠩⠙⠦⠙⠔⢦⠛⡬⠙⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠐⡨⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣌⣤⣤⣤⢷⣶⣻⣟⠾⠉⠀⠀⠀⠀⠀⠄⠀⠀⢀⠈⠀⠀⠄
⣶⣻⠟⠚⠁⠀⠉⠘⠫⢟⡷⣾⣤⣄⠀⠺⣟⡾⠝⣯⡇⠀⠀⢀⣤⢾⣝⡾⠆⠀⠀⠀⠀⠘⠵⠊⠕⠈⠉⠀⠀⠀⠈⢖⡱⡀⠀⠠⣋⠖⣭⢚⠀⠀⠀⠘⡥⢣⠀⠱⣉⠦⠀⢰⢣⠞⣔⠢⣄⡀⠀⠰⣙⠖⡤⣄⣀⡀⣀⢠⢫⡔⠀⠀⠚⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠱⣀⠂⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣞⣷⣻⠞⠟⠊⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⢰⡄⣀
⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣻⣞⠃⠀⠛⠁⠀⢺⣷⣠⣞⡿⣞⡿⠊⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⣣⠄⠀⢧⡙⢦⠃⠀⠀⠀⠀⠱⣃⠧⣀⠞⡜⣂⠧⣋⠀⠀⠉⠐⠩⡓⢦⡱⢫⠴⡘⢆⠳⣉⢎⡱⠌⠭⢉⠳⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠢⡐⠨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡷⣤⡀⠀⢸⣟⣿⣻⣟⡿⣞⡶⣾⡽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢯⡗⠂⠀⠀⢀⣤⣞⡿⣞⡷⣯⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡤⠤⣄⢠⡀⣄⠸⡔⢣⡀⢢⡙⣎⣁⡀⢤⡒⡬⢓⠬⡓⣅⠊⢜⣡⢛⡄⡠⢔⠢⢎⡱⠍⢂⡓⢣⠞⡡⢎⡱⢄⢆⡒⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⡷⣦⡴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠣⠑⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄⠀⠀⠀⠉⠳⣟⣶⣘⢿⣞⣦⠀⠉⠉⠙⠓⠻⣽
⣿⣤⠀⠀⠀⠀⠀⠀⣠⢾⣽⠋⠀⠀⣠⢶⣻⢾⣽⣻⢽⣻⢷⣯⣟⣿⣻⢷⡶⣶⢶⡌⠀⠀⠀⣀⠠⢤⡜⡱⢌⡣⠞⡌⠇⠹⣡⢒⡤⣙⠲⢦⠙⠂⠁⠀⠀⠀⡱⣌⢆⠲⣌⠣⠜⣑⠨⣅⠲⡰⡙⠎⠜⠁⠊⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⢀⣰⣤⡀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠷⢯⣟⣿⣻⡟⢶⠳⢶⠦⠀⠈⢂⠅⣂⠠⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣀⠀⠀⠀⢀⡀⢠⣤⢦⡴⣶⢶⣻⣟⣿⣳⣟⣦⠀⠀⠀⠀⠈⠱⢯⣟⡾⣽⣻⢶⡶⣤⣤⣀⣌
⠼⠫⣷⣄⡀⠀⢀⡴⣯⡟⠀⢀⣤⢾⡽⢯⠛⣟⣾⠃⠀⢿⣧⠈⠉⠘⠉⠛⠙⠯⠟⠷⠀⠈⠳⠌⠙⠀⠈⡔⢣⡱⠋⠀⠀⠀⠐⡣⢜⠁⠁⠀⠀⠀⣀⠤⡒⣍⠲⠌⣎⠥⡒⣌⠳⠌⠓⠈⠁⠁⠀⠀⠀⠀⠀⣶⢦⣤⣄⣀⡀⠀⠀⠀⠀⠘⣷⢯⣟⡿⣶⢶⡶⣤⢦⣤⣤⣤⡄⠀⠙⠾⣵⣄⠀⠀⠀⠀⠀⠀⠌⢒⠠⢂⠀⠀⠀⠀⠀⠀⠀⣿⢾⡽⣯⣟⣿⣻⣟⡶⠌⢻⣞⡯⠿⠽⠏⠓⠛⠚⢁⡿⣞⣧⣄⡀⠀⠀⠀⠀⠻⣽⣳⠯⠿⠙⠷⢯⣟⣾
⡄⠀⠀⢻⡽⣳⢾⣽⣳⣥⢶⣻⣞⠏⠉⠀⢰⣻⠎⠀⠀⠈⢞⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠁⠀⠀⠀⠀⠀⠀⠁⠋⠀⢀⡠⢆⡝⢢⠓⣉⢔⡪⢕⠪⠘⠁⠀⠀⠀⠀⠀⠀⠀⣴⢦⡀⠀⠀⠸⢟⡾⣽⢯⣟⣿⣳⢶⣦⣤⣈⠉⠺⣽⢯⡛⠙⠋⠋⠈⠡⢬⣄⡀⠀⠀⠈⠛⣷⡄⠀⠀⠀⠀⠀⠂⡅⢊⠄⠀⠀⠀⠀⠀⠀⠙⣯⡏⠁⠉⠈⠁⠉⠉⠀⠀⠻⣷⣄⣀⣤⣤⣤⢶⣬⢿⡽⣾⣽⣻⢷⣦⣄⡀⠀⢾⣽⣻⡄⠀⠀⠀⠈⠙
⠀⠀⠀⠀⣷⡀⠉⠺⣷⢯⣟⣷⣳⢶⣤⣤⣸⢯⠁⠀⠀⠀⠈⢳⢷⡄⠀⠀⠀⠀⢀⣀⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠓⠊⠈⠀⠀⠙⠂⠁⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠸⢯⣟⡶⣄⠀⠈⢿⣳⣄⣤⣈⣉⣉⠘⠓⠋⠛⠧⣼⢯⣟⣦⡤⠀⠀⠀⠀⠻⣽⣳⣤⣄⡀⠈⠻⣧⡀⠀⠀⠀⠀⠘⡄⢊⠄⠀⠀⠀⢰⠶⡶⡞⠷⠶⠶⠶⠤⠤⠀⠀⠀⠀⠹⠚⠝⠚⠓⠋⠛⠈⠋⠉⠁⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⡶⣆⠀⠀
⣷⣄⠀⠀⢹⣷⠀⠀⠈⠁⠀⠁⠉⠛⠺⠷⢯⣟⣿⣳⣞⡶⣤⢦⣽⣻⢦⣤⡖⠞⠉⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠉⠻⣽⣳⣄⠈⠓⣿⢾⠽⠯⣟⣿⣻⢶⣦⣤⣙⠛⠚⠁⠀⠀⠀⠀⠀⠀⠘⠁⠉⠚⠹⢟⡶⣼⣳⣄⡀⠀⠀⠀⠸⣀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠠⢠⢟⡿⠀⠐⠀⠂⢹⣎⡇⠀
⢻⣞⡷⣄⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣝⠀⠈⠉⣙⣩⢟⠾⠙⠻⢾⡽⣞⠶⠛⢾⣳⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣟⣿⣻⢶⡶⣦⣤⣤⣤⣤⣄⠻⣽⢦⣄⠀⠀⠀⠀⠀⠙⢾⣳⣞⡶⣤⣀⡀⠀⠀⠀⠈⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢯⣟⡿⣞⡿⣔⢢⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣯⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣯⠆⠀⠀⠀⠀⠘⣮⢽⡀
⣾⣽⡻⢽⣳⢾⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣞⣠⡖⠾⠁⠉⠀⣀⡤⢶⣯⢿⡭⠂⠀⠀⢯⣟⣷⡀⠀⠀⠀⠀⠀⢀⣾⣻⣟⣷⣳⢶⡶⣶⣤⣤⣈⠳⣟⡾⣝⠋⠛⠓⠛⠚⠓⠉⠀⠀⠘⢿⣞⡿⣶⢦⣄⡀⠀⠀⠙⠾⣽⣳⢯⣟⡿⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡴⣶⣞⠿⠊⠙⠉⠉⠉⠀⠘⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠐⠈⢠⢳⢧⣛⡀⠀⠀⣤⢄⠀⠀⠀⠀⢰⡹⡞⠀⠀⠀⠀⡀⢸⡵⣫⢖
⣳⠏⠁⠀⠙⢯⣟⣧⠀⠀⠀⠀⠀⣀⣤⠶⢻⡞⠁⠀⣀⡤⣖⠛⠉⠀⢸⣯⢿⡀⠀⠀⠀⠘⣿⣞⣧⠀⠀⠀⠀⠀⢸⣷⣛⣚⠓⠋⠛⠙⠓⠛⠺⠽⠀⠈⢻⣽⣳⣤⣤⣄⣀⣀⣀⣀⣀⣀⠀⠹⣿⣍⠛⠺⢽⣳⢦⣄⣀⠹⠯⠂⠀⠀⠀⠀⢰⢫⡖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡤⣤⢤⡤⢦⡴⢢⣶⣫⠞⣵⢣⡀⠀⢳⣏⡆⠀⠀⢀⢯⣳⠉⠀⠁⠀⠀⢀⡾⣱⠏⡾
⠏⠀⠀⠀⠀⠀⠙⢾⡀⣀⣤⢶⠛⠉⠀⠀⢈⣦⣴⠻⠍⠁⠀⠀⠀⠀⢸⣯⢿⠀⠀⠀⠀⢀⡿⣾⢽⣧⠀⠀⠀⠀⠘⣷⢯⣟⣿⣻⢷⡶⣤⣄⣀⠀⠀⠀⠀⠘⢷⣻⢾⡽⢯⠿⠽⠯⠗⠋⠛⠁⠈⠻⣷⡀⠀⠀⠉⠘⠉⠁⠀⠀⠀⠀⠀⠀⢈⠷⣍⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⠝⠊⠓⢽⡳⡉⠃⢘⡧⣛⠈⣧⢣⠀⠀⣞⡽⠀⠀⢸⢧⡏⠀⠀⢀⣀⡴⣫⢞⠅⠀⠹
⠀⠀⠀⠀⠀⣀⣤⠶⠻⠉⠀⠀⣴⢶⡴⡞⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣟⠀⠀⠀⠀⣼⣻⠇⠈⠺⣆⠀⠀⠀⠀⠉⠉⠈⠁⠋⠋⠙⠳⠯⢟⡿⣶⣤⣀⠀⠀⠈⠿⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣟⢦⡹⠠⠐⠀⠀⠀⢀⣠⢒⡗⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣳⢱⠀⠀⡿⣱⠀⠸⣣⢇⠀⢸⡝⣇⠀⣎⢷⠳⣯⠿⡽⣎⠷⣭⣄⣀⠀⠀
⠀⢀⣤⢶⠻⠙⠈⠀⠀⢀⣠⢶⣯⢿⣽⣳⡀⠀⠀⣶⣳⣆⠀⠀⠀⠀⣺⢷⣏⠀⠀⣠⣼⣳⠏⢀⣀⣠⣌⡄⠀⠀⢰⡶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠫⢟⣦⣄⣶⣻⣞⡷⣦⣤⣤⣤⢤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⢎⣧⣛⠄⠀⣀⢤⡲⣝⠦⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣚⡖⣲⡄⠀⢳⢫⡄⠈⣷⢱⠀⠀⠙⣮⢣⠀⢻⡼⣰⢏⡾⣣⣄⠉⠀⣉⣉⠒⠘⠪⢏⡳
⣾⠛⠈⠀⠀⠀⠀⣠⢶⡯⠟⠉⢸⣻⣞⣷⣻⡄⠀⠘⢷⣻⣆⠀⠀⠀⣽⣻⡎⠠⣞⡷⢯⠟⠟⠛⠚⠃⠉⠁⠀⠀⠸⣟⡷⣯⣟⡿⣶⢦⣄⣀⡀⠀⠀⠀⠀⠀⠈⠳⢯⣗⠉⢛⠓⠿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠡⢀⡤⢤⠴⣤⡜⣦⣛⢮⡻⡜⠧⠙⢈⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠀⠁⠀⠈⡷⣲⣖⣯⣟⢶⣫⢟⡼⣫⢟⡱⣟⢧⣛⠆⠑⠪⢟⣦⡹⣎⡟⡶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣀⣤⢶⣻⢾⡱⢯⣟⣦⠀⠈⢳⣯⢧⡀⠀⣿⣳⡇⡀⠀⠀⠀⠀⢴⣞⡶⣞⡶⣯⢷⠀⠀⠉⠙⠓⠋⠿⠽⢻⠾⣽⣻⣟⡶⣶⣤⣤⡤⣤⢬⣞⠷⠋⠀⠀⠀⠀⠀⠀⢰⢲⡄⠀⠀⠀⠈⢳⡝⣆⠀⠀⠈⠚⠭⠛⠶⢹⢶⡹⣎⡁⠀⢀⣀⡘⠦⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢳⡱⠎⠑⠋⠀⠁⣀⣀⡱⢾⡤⢯⡷⣏⢶⡲⣖⡞⣶⣛⢾⡝⣾⡱⢯⡽
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣻⡽⠞⢋⡿⣯⠇⠘⣟⡾⣧⠀⠀⢻⣯⢷⡀⣿⣳⠿⠽⢻⢿⡽⣞⡾⣽⣻⡽⣤⣴⣲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⠈⠉⠙⠉⠀⠀⠀⠀⠀⣖⠤⠀⠀⠈⠣⣝⢧⡀⠀⠀⠀⡻⣜⢧⡄⠀⠀⠀⠀⠀⣞⢧⠻⣜⡳⢆⠘⠲⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠈⢛⡥⣴⢲⣏⢿⡱⠎⠙⠃⠋⠓⠈⠉⠂⠑⠈⠈⠀⠉⠀⠉⠀⠉⠁⠙
⠀⠀⢀⣤⢶⣻⡽⣞⠓⠉⠀⢰⡾⣽⢯⡇⠀⠈⢿⣽⣳⡀⠀⣿⢯⣟⣷⣻⠀⠀⠀⠀⣀⣤⣽⣳⢯⡟⠗⣋⣡⢬⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢳⠀⠀⠀⠀⠘⣧⠳⡄⠀⠀⠱⣫⢞⡼⣢⠀⠀⠀⠘⠼⠙⠀⠫⣝⢯⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⢆⠀⠀⠈⠓⣉⢃⣈⣀⣀⡠⣄⢤⡠⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡶⣞⡿⡞⠋⠑⢿⡽⣦⠀⠀⠠⣿⣽⣻⠆⠀⠀⠀⢻⣷⣻⢾⣽⢻⣞⣷⣻⢀⣠⡴⣾⡽⡞⢓⣩⣥⢶⣻⡽⠯⠛⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡳⡄⠀⠀⠀⠀⠸⡽⣹⢆⡀⠀⢧⡛⠔⢭⡛⣤⠀⣀⡠⢤⠦⣴⣘⢎⡟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⡄⠀⠸⡹⣌⠳⡜⢦⣣⠳⡜⢦⢳⡹⢆⠘⣦⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠰
⠛⠉⠀⠀⠀⠀⠈⢿⣽⣳⡀⠀⣿⢾⣽⡃⢀⣠⣴⣻⢾⣽⣛⣆⢈⣻⢾⡽⣯⠷⢛⣡⡵⣞⣯⠷⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡱⡃⠀⠀⠀⠀⠀⡟⡥⢏⠶⣰⢫⡝⠀⢀⡹⢦⠻⡼⡙⠎⠓⠈⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢆⠀⠀⠳⣌⡳⡙⠦⠃⠛⠘⠃⠃⠙⠊⠀⢪⢇⠀⠀⠀⣠⢖⡹⢆⡷⢬⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣳⣄⢸⣟⣾⣳⢯⡷⠯⠉⠀⢱⣻⢾⡽⣯⠟⣉⡴⣞⣯⠷⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡱⡃⠀⠀⠀⠀⣰⠹⡜⠈⠙⠁⠋⢀⡴⣫⣝⠋⢃⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠄⠀⠀⢨⠳⡵⢤⢤⡀⠀⢷⡀⠀⠀⠀⢸⡝⢶⡰⢎⡵⢪⡕⣫⠜⢃⠃
⠀⢀⡤⣴⢦⡀⠀⠀⠀⠱⣻⣞⡾⣽⠾⠝⠋⠀⠀⣠⢶⣯⡟⠏⣩⣴⣻⡽⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⢏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣣⠇⠀⢀⡤⣚⢥⡛⡴⣒⠖⡶⢲⡹⡞⡵⡀⠀⠘⠞⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣽⡳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢆⠀⠀⠈⡷⣙⢎⠶⡹⣄⢣⣛⡄⠀⠀⢼⣸⢣⡝⢮⡜⣣⠞⣥⢛⡬⣛
⡾⣯⠿⠙⠉⠀⠀⠀⠀⠀⠘⢽⣻⢦⠀⠀⣀⣴⣻⣽⠛⠊⣴⣞⡷⠏⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣎⠾⣱⢀⠀⠀⠀⢯⡹⢆⠀⠀⠀⠘⣥⢫⡝⣣⠞⠑⠊⠁⠁⠈⠈⠀⠁⠀⢉⠶⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣛⣾⠓⠁⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡐⢮⢥⠀⠈⡞⡄⠀⠀⡱⣍⢎⡳⠑⠊⢰⡹⡞⣥⠀⢺⡔⡳⣎⠳⡜⣥⢛⡴⣋⠶⡩
⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⡾⣽⠞⠃⠁⠀⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⢳⢣⢏⢦⡀⠀⠀⠙⣎⢧⡀⠀⢘⢦⡃⠀⠀⠀⠀⠸⣭⠻⣜⢣⡛⡼⣩⢏⡞⠁⠀⣀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣀⡶⣻⡼⡏⠊⠀⠀⠀⠀⣠⠀⠀⠀⠁⠌⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣙⢎⠎⠀⠀⢙⡖⠀⢰⠳⡜⢮⡄⣀⡠⢎⡵⣛⢖⡣⢞⡼⡱⣏⡟⣜⢲⡉⠀⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡐⢮⡜⣣⢇⠘⢦⡓⣆⠀⠀⠘⢦⠳⣄⠸⣆⠷⣲⢤⢤⡠⠤⣌⠳⡜⡄⠉⠀⣁⡠⢤⣒⢾⡽⣧⡝⠬⠛⠀⠀⠀⢠⡸⣯⡽⠧⠋⠀⠀⠀⣠⢴⣯⢷⡃⠀⠀⠀⠀⠀⠋⡲⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢞⡱⣋⠷⣙⢦⡙⢦⡙⣎⠶⣩⢎⡵⣋⠶⣱⢫⠚⠬⢳⡜⣤⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡌⣎⠧⠙⠂⠘⡱⢎⠆⠀⠙⢬⠳⣄⠀⠀⠻⣌⠳⣬⢋⠑⠊⠃⠙⠓⠬⢳⡹⣜⢧⡛⣶⡙⠇⢋⡿⣽⣳⠇⠀⠀⠀⡠⣚⣮⣟⡳⠉⠀⠀⠀⠀⠸⣽⣻⡞⠷⠁⠀⠀⠀⠀⠀⠀⠀⠨⢝⣳⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠵⣩⢞⡱⢎⡝⢦⡹⣌⢳⡵⣚⡴⣩⠞⡥⡏⠀⠀⠀⠙⢦⡛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡳⣌⠳⠙⣬⢓⡀⠀⠀⠘⣭⢚⠀⠀⠈⠳⡌⢧⣀⢘⢦⡛⡴⣃⠀⠀⢀⡠⣖⢭⢳⡹⠜⠂⠉⠀⠀⢠⢯⣟⡷⣯⣇⠀⣠⠾⣼⢯⡶⠋⠀⠀⠀⠀⠀⠀⠀⠳⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣔⢫⡜⣣⠞⣥⠳⣌⠓⠈⠁⠓⢥⡛⡼⠁⠀⠀⠀⠀⠀⠙⠲⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣽⣻⣟⣿⣻⡽⣯⣟⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠒⠁⠀⠀⠈⣧⠹⡄⠀⠀⠲⣍⡃⠀⠀⢀⡘⢦⡙⣎⠖⢹⠲⣥⢤⢺⡵⢣⠝⠊⠁⠀⠀⠀⠀⠀⠀⣿⣻⢾⡹⢳⣯⣟⣷⣻⣳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⣜⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣀⣀⣀⣻⢷⣻⣞⡷⣯⠟⠕⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡜⣄⠀⠀⢧⡙⡴⣊⢧⡙⠂⠙⡌⡖⣬⢛⢦⡋⠗⠈⠁⠀⠀⠀⠀⠀⠀⢀⣤⠀⠘⡽⠏⠸⣹⢾⡽⣞⡷⣏⣷⣻⣖⡞⣶⢳⡖⣶⢲⡖⣶⣲⢖⡻⣞⡳⣏⢿⡹⣏⢿⡹⣎⢷⡹⣎⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠐⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣾⣽⣻⣞⡷⣯⢷⣯⡟⣾⠽⣯⠷⣯⢿⣽⣛⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢤⡀⠀⢙⡖⣆⢞⡱⣌⠳⠑⠀⠀⠀⣠⢜⡱⠎⠝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡾⣧⠀⠀⠀⣸⡽⣯⢿⣽⢻⠽⣺⢧⡟⡽⠭⡳⠝⣞⠳⡛⠧⠻⠎⠷⠭⠳⠝⢎⠳⡙⢎⠳⠝⠎⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢿⣽⣻⣟⣿⣳⢷⣤⣀⠀⣴⢶⣤⣤⣀⡀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣻⢷⣯⠷⠯⠟⠽⠋⠖⠛⠘⠛⠘⠛⠜⠫⠀⠙⡽⣾⡽⣯⢿⣽⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢧⡜⢢⠃⠀⠀⠸⡸⣌⡀⠀⠀⠀⢀⣤⢛⡴⠋⠈⠀⠀⠀⣀⡶⡆⢦⡀⠀⠀⠀⠀⣸⡽⣻⠁⠀⢀⡴⣳⢿⣽⣻⠞⣧⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠀⣀⡤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣟⡚⠓⠛⠚⠙⠛⠾⠽⠇⠻⣟⣾⣳⢯⣟⣿⣻⢶⡶⢸⣯⣇⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⢘⡷⣯⣟⡶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡳⠟⢽⣻⣞⣷⣻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠑⢼⡰⠀⡠⡜⣎⠶⠉⠀⠀⠀⠀⣠⢞⡽⣞⣽⡈⠿⣤⠀⠀⠀⣷⢻⡅⠀⣠⣞⡽⣏⡿⣞⡷⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣺⡵⣯⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢤⣤⣖⠖⠀⠀⠀⠀⠀⠀⠹⣞⡷⣤⣤⣀⣀⡀⠀⠀⠀⠀⠹⣾⣭⣉⣈⠑⠋⠉⠁⠈⣷⣻⢶⣄⡀
⠝⠂⠀⠀⠀⠀⠀⠀⠈⢟⡷⣯⣟⡿⣮⣟⢷⡞⣤⢄⣤⣀⣀⣀⣀⡀⡀⣀⣿⣳⣟⣾⣳⣟⡾⣽⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣱⠹⠈⠀⠀⠀⠀⣤⢞⡵⣫⡞⡽⠂⠁⠀⠙⡿⣖⡾⣽⢯⡤⣶⣛⣾⢳⠟⠀⡿⣽⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⢀⡤⣖⢯⣞⣳⢳⡻⠝⠊⠁⠀⠀⠀⠀⣀⣠⣤⡴⣶⣞⣯⡟⠿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣳⢯⡿⣽⣻⣟⡷⣶⣤⣀⢹⡾⣽⢯⣟⡷⣶⢶⣤⢿⣽⣻⢾⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣳⢻⣜⡳⣎⢷⣛⡷⣯⢶⡹⣞⡷⣯⢿⣽⣻⣞⣷⣻⣞⡷⣯⣟⠷⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣵⢫⣷⠳⠩⡄⠀⠀⠀⠀⠘⣽⣻⡽⣯⣟⡷⣯⢞⠋⠀⠀⢹⣳⠀⠀⠀⠀⠀⠀⠉⠛⡽⣖⡾⢯⡞⡽⣎⠷⠉⠁⠀⠀⠀⠀⠸⣯⣟⣿⣳⣟⡾⣽⣳⣟⡾⣴⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠁⠉⠁⠉⠚⠙⠓⠫⢟⣯⢿⣽⣻⡞⠙⠋⠛⠚⠃⠈⢻⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡳⡞⠳⠛⠎⠓⠙⠈⠁⠙⠽⠻⠽⠻⠎⠓⠛⠚⣱⢯⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢠⣞⢷⣻⣝⠯⠊⠀⠀⠹⣶⡀⠀⠀⠀⢺⢧⠛⡷⣯⢿⣽⣁⠀⠀⠀⠀⣯⡅⠀⠀⠀⠀⣀⡴⣺⢵⣫⢞⡽⠞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠓⠋⠈⠀⠁⠁⠉⠉⠁⠛⠚⠙⠿⢶⣤⠀⠀⠀⠀⠘⣿⢦⡀⠀⠄⠀⠀⠀⠀⠀⠀⢺⣽⣻⣞⣷⣻⢦⣀⠀⠀⠀⠀⠀⢫⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠖⠛⠁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⢫⡟⡾⣽⢆⠀⣠⣞⡄⢫⢿⣄⠀⠀⠘⣟⡆⠀⠉⠛⠾⣝⡯⣗⡦⣤⣸⢧⡀⢀⡴⣺⢵⣫⢗⡯⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⢶⡶⣾⡽⡏⠀⠀⠀⠀⠀⣀⣀⣀⣈⡄⠀⠀⠀⠀⠛⣯⢿⣤⣀⣀⠂⡄⠀⠀⡀⢸⣷⣻⣞⡷⣯⢿⣽⣻⣟⡷⣶⢶⣦⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⡴⣾⣽⠻⠊⠁⠀⠀⠀⠀⣠⢯⣟⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠉⠁⠸⣯⢿⡵⡾⣽⠆⠈⢟⣧⡀⠈⣿⣹⠀⠀⠀⠀⠀⠀⠉⠙⠺⢽⢯⣟⣽⢺⡝⣮⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣶⣻⣽⣳⢯⡷⣯⢿⣝⣳⢿⣽⣻⣽⣻⣟⣿⠳⠟⠞⠙⠚⠀⠀⠀⠀⠀⠈⠻⣾⡽⣯⢿⣽⣻⢿⣽⣻⣞⡷⣯⢿⣽⣻⣞⣷⡻⠌⠁⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡶⣞⡿⣾⡽⠯⠛⠁⠀⠀⠀⠀⠀⠀⣠⢞⡽⣾⡽⠀⠀⠀⠀⠀⣠⢶⣯⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠐⣯⢿⣽⣳⠏⠀⠀⣟⡾⣽⣆⡷⢯⡇⠀⠀⠀⠀⠀⠀⣠⢴⣫⢞⡽⣎⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡸⣟⣾⣳⢯⣟⣯⢿⣽⣻⢾⣽⠻⠞⠓⠉⠁⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠈⠿⠽⠛⠞⠙⠛⠚⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⢟⡯⢿⡽⠻⠑⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⢣⡟⣽⢳⡇⠀⠀⢀⡴⣾⣽⣻⡞⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣥⠀⠀⠀⠀⠈⢟⡾⣧⠀⠀⢸⡽⣻⡕⠛⣞⡿⢶⠀⠀⠀⢀⡤⣞⡵⣫⠝⡮⠒⠁⠀⠀⢀⣀⣠⢴⣲⢶⣯⣟⣯⢿⡽⣯⠿⡽⠞⠹⣟⡾⣽⣻⢾⣝⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⢞⣧⠻⣭⢟⡎⣤⢖⣻⢞⡷⡯⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⣸⢽⣳⣇⠀⣾⣹⢷⠀⠀⠈⠻⣯⠀⣀⡴⣫⢞⡵⣋⠶⠉⠀⠀⠀⠀⠀⠸⣽⢯⡿⣽⠻⠞⠽⠚⠃⠉⠁⠀⠀⠀⠀⠀⠉⣓⢯⣻⢾⣽⣻⢯⣟⡾⣽⢧⡴⣶⢯⠗⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⢟⣼⢣⡟⠨⣑⠿⣎⡿⣼⣫⡽⡏⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣞⣥⠀⠸⣧⠀⠀⠀⣟⡾⣳⠯⣟⣞⣷⡋⠀⠀⠀⠀⣨⢷⣹⢾⡱⣏⠞⠁⠀⠀⠀⢻⣖⣦⢤⣤⣙⣯⢿⣽⣻⣖⡦⣴⣲⢶⣶⣻⡽⣯⣟⣿⣻⡽⣯⣟⡿⣾⣽⣻⢾⡽⠯⠟⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡰⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⡷⣹⢇⠻⡜⠃⠀⢡⡞⣽⣞⣷⡹⣷⡽⢶⡳⣶⣖⡦⣤⢤⡤⣤⣠⣄⡀⠀⠀⠀⠀⠀⠀⢠⣞⡳⣏⡞⠇⠀⠘⣷⡀⠸⣽⢻⡇⠀⠙⢾⡵⠃⠀⠀⣠⢾⡵⣯⣛⠮⠓⠀⠀⠀⠀⠀⠀⠘⠽⣞⡿⣾⡽⣞⡿⣞⡷⣯⣽⢳⣯⣟⣾⠳⠟⠓⠋⠊⠁⠻⡳⠯⠟⠓⢉⡽⣯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢦⡱⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⣵⢫⡞⠵⠃⠀⠀⠀⠀⢒⡽⣾⡽⣶⣽⢺⡝⣯⣳⣝⣮⣟⣭⢻⡾⣵⢳⡭⢷⡄⠀⠀⠀⠀⠀⠘⣞⣳⡭⠋⠀⠀⠀⠐⢳⡼⡽⣯⠆⠀⠀⠀⠙⣠⣴⣻⢷⣏⢷⠧⠋⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠚⠙⠯⢟⡳⣯⢷⣦⢤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⣞⡯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⢠⡙⢦⢩⠁⢀⡜
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠞⣵⠋⠀⠀⠀⠀⠀⣠⠖⣯⢞⣳⣟⠷⣭⠳⡙⠒⠳⠺⠜⠳⠎⠷⠹⠮⠳⡝⢧⠻⣄⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠈⢳⣻⣞⠁⠀⠀⠀⠀⢳⣯⡟⣯⡞⠋⠀⠀⠀⠀⠀⢸⣻⢶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢰⣖⣶⣻⣞⡿⣞⡿⣞⣿⣻⣟⣿⣳⡟⠾⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣌⠳⡌⢧⠀⢩⠆⠀⠀⢠⡙⢆⡣⡐⢎⡜
⠀⠀⠀⠀⠀⠘⢪⠱⣏⢶⣠⢀⠀⠀⠀⠀⠀⡰⢣⢎⡽⠀⡀⢀⡀⣤⠲⣝⢧⡻⣜⢯⡳⣎⠿⣜⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠯⠀⠀⠀⠀⠀⠈⢷⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⣉⣻⢾⡽⣾⣽⣻⢯⣟⣷⣻⣞⣷⣻⣞⣷⣻⢾⡽⣯⠿⠹⠞⠷⣻⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⡱⢌⠳⣌⠣⠃⠀⢛⡴⣠⠆⡽⣸⠰⡍⣎⠜
⠀⠀⠀⠀⠀⠀⠀⠁⠘⢢⡙⢯⢲⢦⣀⡀⢠⠕⡃⣞⣤⡱⣒⢏⡞⡴⢻⣌⢧⡳⣝⢮⡳⠁⠛⣼⢣⡗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡦⣤⣖⡶⣯⢿⣽⣻⠷⣯⠻⠝⣷⢯⣟⡿⣞⡷⣏⡚⠃⠉⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⢦⠱⡑⣎⠱⣌⠁⠀⠀⠀⢞⣡⢛⡴⣡⢛⡜⢬⢚
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠓⠪⡵⣛⠮⣜⡷⣊⠶⣱⢋⠮⣽⡸⠧⠚⠁⣷⡙⡮⠁⠀⠀⠘⢧⣛⠴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣺⢵⡻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⢷⣯⢿⣽⣻⣞⣷⣻⣽⣻⢿⡽⢯⠎⠉⠙⠹⢯⡟⣷⢶⣲⡴⣦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢣⠜⣢⢣⡙⠤⠃⣜⢲⡀⠀⠀⠸⢤⢋⠶⣡⢏⡜⣪⢅
⠀⠀⠀⢀⠤⢎⠳⣍⠏⠀⠀⠀⠀⠀⠁⠡⡛⡼⢯⣝⢳⣍⡞⠓⠃⠁⠀⠀⡘⢦⡹⠁⠀⠀⠀⠀⠈⢽⣫⠖⡄⠀⠀⠀⠀⠀⢀⡠⣴⢫⢷⡹⢧⠏⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⡶⣶⢾⡽⣯⢿⡽⣯⣟⡿⣞⡿⣞⣷⣻⣞⡷⡯⠛⠋⠈⠀⠀⠀⠀⠀⠀⠈⣁⣿⡳⠛⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠙⡎⡵⢃⠶⡩⡔⠳⣌⠱⣙⠦⡀⣈⠞⣌⢳⡰⢍⡺⢅⡎
⢀⡠⣎⢧⠹⣌⠳⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢣⢊⠧⡼⣹⠧⣄⡀⠀⠀⡝⢦⡋⠀⠀⠀⠀⠀⠀⠀⠹⣻⡜⣦⠀⣠⢤⡖⣯⢳⣭⡛⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣳⢯⡿⣽⢯⡿⠽⠏⠛⠑⠈⠙⠀⠉⠻⣞⡷⣯⢧⡀⠀⠀⠀⠀⣀⣀⣠⢤⡶⣯⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢆⠀⠀⠑⠬⢫⡜⡱⢎⠳⣌⠳⡌⣚⠵⣪⠜⡸⢆⡁⠀⠀⠉⠘
⢯⡱⢎⠶⡹⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢥⢃⠏⢶⡙⢶⣸⡙⢦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡿⣜⢯⡳⣏⢾⡱⠏⠂⠁⣠⢖⡷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢯⣏⡉⠁⠀⢀⡀⣀⣀⣀⡤⣤⢤⣤⣤⣤⢿⡽⣯⣟⡷⣾⣽⣻⢷⣯⡟⠏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣞⡿⣞⡿⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢜⢢⠀⠀⠀⠀⢹⡱⢊⡵⣈⠳⠤⣩⠞⣡⠞⡱⢎⡄⠀⠀⠀⠀
⢧⣙⠎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⢞⣦⣙⢦⣲⡝⡮⡅⢄⠀⠀⠀⠀⠀⠀⣠⢞⡵⣫⢏⡷⣹⠞⡥⣢⢖⣯⢳⣏⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢾⣽⣻⣟⣯⣟⡷⣯⢿⡽⠯⠟⠜⢳⢯⡿⣽⣳⢯⠟⠳⣯⣟⡿⣞⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣞⣯⢷⣻⣽⣻⣽⣻⡽⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢣⠀⠀⠀⠠⣙⠇⡶⡉⠀⢲⡑⣎⠱⣎⡕⠮⡔⠀⠀⢀⢤
⠇⠁⠀⠀⣀⣀⡤⢠⠤⡠⠤⡰⢤⡠⣔⢢⡒⣖⢢⠓⣍⢎⡘⡬⡰⢌⡵⢫⡽⣳⡙⠮⠀⠀⠀⣠⢰⡙⢦⢫⠖⠃⣉⠲⣩⢞⡵⣫⢞⡼⠓⠊⠀⠀⢠⡄⠀⠀⠀⣀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠉⠚⠷⠛⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠫⠟⣁⣡⡤⣖⡾⠳⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⣻⣽⣻⡽⣞⣯⢷⣯⢷⣯⢷⣻⡽⣞⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⡒⢆⠀⠀⢠⢃⡟⡰⢣⠎⡵⡘⣌⠃⠀⠈⠓⡜⢥⠚⣌⠦
⢀⢠⡔⣾⣵⢫⡜⣱⣚⢴⢣⡱⢣⠳⣬⠣⡝⡎⢧⠛⡜⢪⡑⣁⠓⡬⢤⡹⢶⣱⠩⢇⡠⢔⡹⢆⠧⠙⠊⠁⢀⡰⢦⡻⣵⢫⡞⠕⠉⠀⠀⠀⠀⠀⢸⡝⣷⣺⡽⣳⢻⡼⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣤⣤⣤⢶⡾⣽⡳⡯⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣻⡽⣞⣯⢷⣯⢷⣻⡽⣞⡿⣞⡿⣞⣯⠷⢻⡽⣞⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⡌⢆⠀⡜⢪⠴⡙⡬⣓⢥⡹⠄⠀⠀⠀⠀⡜⡬⢓⡌⢞
⣮⣳⡝⣮⠳⣏⡘⢳⢻⠎⢷⡙⠧⠳⠴⠳⠌⠚⠁⠛⠘⠁⠉⠀⠉⠀⠀⠀⢛⠦⠛⣌⠲⣉⠆⠋⠀⠀⢀⡴⢮⡝⣧⠻⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣵⣳⣻⡽⣯⢷⣻⠾⣄⠀⠀⠀⠀⠀⢲⢾⣽⣻⢯⣟⡷⣯⣟⣾⣳⠯⠟⠙⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣞⣯⣟⣯⢷⣻⡽⣞⡿⣞⣯⢷⣻⣽⣻⠽⢛⣩⣴⡂⢹⡿⣽⣞⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣌⢳⠸⣥⠚⡥⠓⡜⢦⢣⠃⠀⠀⡤⢋⢖⡩⢞⡸⠌
⣯⢷⡹⣎⠗⠂⠀⣠⢜⡹⢆⡹⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢃⠌⡓⠤⠃⠀⠀⠀⣠⠲⣭⢞⡣⠟⠈⠀⠀⠀⣀⣠⣄⡤⣤⢖⡶⣲⢯⡗⣯⢳⠷⣽⣫⢟⣷⣻⡼⠆⠀⠀⠀⠀⠈⠟⡾⣽⡻⠾⠝⠓⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢶⣻⣽⣻⣞⣷⣻⣞⣯⢷⣻⣽⣻⡽⣞⡯⢓⣫⡴⣞⣯⢷⣯⡇⢸⣟⣷⣻⢾⡽⡄⠀⠀⠀⠀⠀⠀⠀⠈⡎⡵⢢⡝⠄⠀⠉⠂⠇⠀⣀⠧⣙⠣⢎⠲⡑⠊⠁
⣟⢮⠓⠁⠀⠀⣰⢻⡞⣜⠣⡶⣉⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢆⠡⢎⡰⠈⠁⠀⠀⣀⠴⣙⢦⣛⠴⠋⠀⠀⢠⡖⣯⢻⡵⣳⢎⡷⣹⢎⡷⠹⠎⠙⠈⠁⠀⠈⠛⠯⢶⡹⢶⣄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⣞⣯⣄⠀⠙⣾⣳⣟⣾⣳⣟⡾⣯⢷⣯⠗⣋⣥⣞⣯⢷⣻⡽⣞⡿⣞⣷⢘⡿⣾⡽⣯⢿⡽⡄⠀⠀⠀⠀⠀⠀⠀⠘⢥⠓⡼⠀⠀⠀⠀⢀⠶⣑⡚⡴⡙⢎⠅⠀⠀⠀
⣟⢮⡅⠀⢀⡴⣫⠷⡹⡜⠀⠙⣳⢎⢧⠀⠀⠀⠀⠀⠀⣠⠰⣣⠲⢡⠞⠀⠀⠀⠀⣤⢚⡬⢳⠭⠒⠁⠀⠀⠀⠀⠸⣝⢾⣫⠷⡝⢊⣓⣩⢤⡤⣤⡴⢦⡖⣶⢲⢶⡳⣞⢷⡻⣯⣞⡽⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣻⢾⣽⣻⢾⣽⣳⡄⠀⠙⠾⣳⣟⡾⣽⢯⣟⡶⣾⡽⣾⡽⣞⣯⢷⣻⣽⣻⡽⣾⣸⣟⣷⣻⡽⣯⢿⡽⣄⠀⠀⠀⠀⠀⠀⠀⢈⡹⣜⠀⠀⠀⡰⢍⠶⡑⣞⠰⠩⠀⠀⠀⠀⠀
⣟⣎⢦⡰⣮⡟⣵⢣⠓⠀⠀⠀⠈⠿⡌⠀⠀⠀⢀⡰⢜⡥⣓⠥⠋⠀⠀⠀⢀⡴⢫⠔⣫⠜⠃⠀⢀⣀⡀⠀⠀⠀⠀⠘⠧⣏⢿⡹⣷⡽⣞⢯⡽⢧⣛⣧⠻⠞⠟⢾⡳⠟⠾⠽⠳⣏⡿⡑⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣞⡿⣞⣯⣟⡿⣾⣽⣻⣞⣷⣻⢷⣤⣀⠀⠉⠛⠙⠿⠾⢽⢳⡟⣷⣻⡽⣞⣯⢷⣯⢷⣻⢷⣻⣞⡷⣯⢿⡽⣯⢿⡽⣆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢑⡫⡜⡱⢬⠁⠀⠀⠀⠀⠀⠀
⣯⢞⣮⣟⣧⣛⡼⠃⠀⠀⠀⠀⠀⠀⠁⠀⣠⠴⣣⡝⣎⠖⠉⠀⠀⠀⢠⡜⣣⢚⡥⠋⠁⠀⠀⠀⢸⢣⡟⣽⢲⢦⣄⡀⠀⠈⠑⠻⢜⡿⣽⡛⠚⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⣵⠫⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣻⣽⣻⣽⣻⡽⣾⣽⣻⢷⣯⢷⣻⢾⣽⣻⢾⣽⣻⢶⣲⣤⣤⣠⣀⣀⠀⠀⣰⣻⡽⣞⡿⣞⣯⣟⣯⢷⣯⢿⡽⣯⢿⡽⣯⢿⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠣⠙⠀⠀⠀⠀⠀⠀⠀⠀
⢸⣻⢾⡽⢶⡹⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡱⢯⡵⠋⠀⠀⠀⠀⢀⡼⣓⢮⡵⠋⠀⢀⠀⠀⠀⠀⠀⠋⠾⠱⣏⠾⣼⣹⣛⠶⣤⢤⡤⣤⣤⢤⡤⣤⢤⡤⣤⢤⡴⣤⢖⡶⣺⣝⡯⠳⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣯⢷⣯⢷⣯⢷⣯⢷⣻⢷⣯⣟⡿⣞⣯⣟⡿⣾⣽⣻⢾⡽⠯⠳⣟⣾⠳⠋⣀⣴⣻⢷⣯⢿⣽⡻⢽⡾⣽⣞⡿⣞⣯⢿⡽⣯⢿⡽⣯⢿⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠹⢯⣛⡗⠀⠀⠀⠀⠀⠀⠀⣠⢞⡵⣫⡝⠃⠀⠀⠀⠀⠀⠀⠘⡾⡹⠊⠀⠀⠀⢎⡷⣢⠀⠀⠀⠀⠀⠀⠀⠉⠒⠃⠯⠻⣜⢧⡻⡵⢮⡷⣻⣜⡳⣟⡼⠣⠟⠜⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣞⡿⣞⡿⣞⡿⠞⢻⣞⡿⣞⣯⣟⡿⣾⣽⣻⡽⣾⣽⣻⢷⡯⠏⠁⣠⡆⠐⠋⠀⠐⠚⠙⠚⠉⢋⣈⣡⢶⡼⣯⣟⡷⣯⢿⡽⣞⣯⢿⡽⣯⢿⡽⣯⢿⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣞⡿⣽



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