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⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠃⣿⣿⣿⡇⠀⡜⢢⠓⡜⢢⠓⡜⢢⠓⡜⢢⠓⡜⢢⠓⡜⢢⡹⢨⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⣟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡜⣡⢋⠼⣡⢋⡜⣡⢋⡜⣡⢋⡜⢥⠂⢰⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⡅⣿⣿⣿⡇⠀⡜⢤⠣⡜⢤⢋⠖⣡⠎⣔⠣⢎⡔⢣⠎⡜⢢⠃⢽⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠆⣽⣿⣿⡇⠀⡜⢢⠓⡜⣌⠮⡜⢢⡙⡤⢋⠖⡬⢃⠮⡱⢩⠁⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡴⢊⠖⣩⢒⡱⢜⡩⢚⡔⣋⠖⣡⣧⠀⣿⣿⣿⠀⢸⣦⣅⣀⣀⣉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠀⡁⣿⣿⣿⡇⠀⡒⢥⢊⡴⢋⡜⡡⢎⠲⣡⢎⡱⣘⣤⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⢀⣀⣥⣿⣿⣿⡇⠀⣭⠶⢷⣌⢣⠜⣱⣪⣵⣶⣾⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣹
⠀⠀⢀⠀⢄⣰⣿⣾⣶⣿⣿⣿⣿⠿⡟⠛⡉⢃⡄⠲⣰⠻⡿⣿⣿⣿⣿⣿⢿⣿⡯⠷⣻⣿⣇⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⢼
⣤⣽⣾⣿⣿⣿⣿⣿⠿⠛⠯⠑⢤⠘⡄⡓⢌⡡⢌⡑⢾⠀⣈⡿⠿⠿⠿⣑⡿⢁⠈⡄⠀⠀⠀⠉⠉⠁⠈⠒⠚⠛⢿⣍⠿⣜⢲⡙⡞⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡬⡂⢍⠢⡑⢢⠉⢆⡔⣊⣴⣾⠞⠁⠀⠀⠀⠄⠫⣽⣦⣂⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠈⠒⠈⢁⡑⠬⠐
⣿⣿⣿⣿⣿⡿⢿⡟⠻⡙⠮⡤⣃⣬⣵⣾⣾⣿⣿⣿⢣⣲⡆⠀⠀⡠⣶⡌⣓⣿⡌⢿⣷⣶⣦⣦⣄⣀⣀⣀⣜⡁⡀⠤⠐⠊⠉⠀⠀⠀
⠿⡟⠻⠙⠀⠉⠀⠀⠀⢀⡔⠉⠉⠉⠛⠛⠿⢿⡿⠿⢌⠛⢡⠄⠀⠻⠟⠋⠘⠻⠧⢻⣿⣿⡿⢿⡛⢩⠃⡥⢚⣿⣷⣤⣀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣠⠶⢞⣢⣤⡔⠉⠁⢢⣀⡠⢟⠋⣕⢪⡡⠜⢢⡉⠴⡁⢎⢻⣟⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠓⠰⢼⣿⣷⡰⢈⠖⣈⠧⡳⡌⢥⠘⢆⡉⠖⢢⠹⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠣⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⣿⣿⣿⣌⠦⣁⠎⡹⢜⢦⡉⢆⠩⢜⣢⡵⠚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⡝⠿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⣰⣿⣿⣟⣿⣿⣿⣷⡔⡘⢤⠉⣧⣷⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠘⠥⠟⠽⣻⢿⡿⣿⣿⣿⣷⣶⣾⣿⣿⡿⣧⣿⣿⣿⣿⣿⣮⣶⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠈⠐⢺⢰⣆⣤⣩⡀⠒⠀⠊⠍⣙⢓⡛⠿⠿⣿⣟⣯⣟⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠘⡶⣬⡽⣃⣀⠀⠀⠀⠀⠀⠈⠘⠁⠒⠌⢍⣺⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠯⣶⣛⡭⠼⡏⣽⣶⡶⡤⢤⣀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣔⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⢤⣈⣉⡐⠛⠭⠧⢈⡀⡿⡄⣬⡅⢰⠒⡠⡤⣀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⢦⣄⣉⡑⠒⠣⠸⣰⠇⣯⢸⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⢿⣻⣞⡷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠶⢬⣉⣁⣚⢘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣽⣞⡿⡽⣞⣯⢷⣞⡿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠩⠙⠉⠋⠊⠉⠎⠱⢩⠧⢞⡳⢽⣋⢎⠯⡜⠳⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠠⣟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡜⣡⢋⠼⣡⢋⡜⣡⢋⡜⣡⢋⡜⢥⠂⢰⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⡅⣿⣿⣿⡇⠀⡜⢤⠣⡜⢤⢋⠖⣡⠎⣔⠣⢎⡔⢣⠎⡜⢢⠃⢽⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠆⣽⣿⣿⡇⠀⡜⢢⠓⡜⣌⠮⡜⢢⡙⡤⢋⠖⡬⢃⠮⡱⢩⠁⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡴⢊⠖⣩⢒⡱⢜⡩⢚⡔⣋⠖⣡⣧⠀⣿⣿⣿⠀⢸⣦⣅⣀⣀⣉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠀⡁⣿⣿⣿⡇⠀⡒⢥⢊⡴⢋⡜⡡⢎⠲⣡⢎⡱⣘⣤⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⢀⣀⣥⣿⣿⣿⡇⠀⣭⠶⢷⣌⢣⠜⣱⣪⣵⣶⣾⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣹
⠀⠀⢀⠀⢄⣰⣿⣾⣶⣿⣿⣿⣿⠿⡟⠛⡉⢃⡄⠲⣰⠻⡿⣿⣿⣿⣿⣿⢿⣿⡯⠷⣻⣿⣇⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⢼
⣤⣽⣾⣿⣿⣿⣿⣿⠿⠛⠯⠑⢤⠘⡄⡓⢌⡡⢌⡑⢾⠀⣈⡿⠿⠿⠿⣑⡿⢁⠈⡄⠀⠀⠀⠉⠉⠁⠈⠒⠚⠛⢿⣍⠿⣜⢲⡙⡞⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡬⡂⢍⠢⡑⢢⠉⢆⡔⣊⣴⣾⠞⠁⠀⠀⠀⠄⠫⣽⣦⣂⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠈⠒⠈⢁⡑⠬⠐
⣿⣿⣿⣿⣿⡿⢿⡟⠻⡙⠮⡤⣃⣬⣵⣾⣾⣿⣿⣿⢣⣲⡆⠀⠀⡠⣶⡌⣓⣿⡌⢿⣷⣶⣦⣦⣄⣀⣀⣀⣜⡁⡀⠤⠐⠊⠉⠀⠀⠀
⠿⡟⠻⠙⠀⠉⠀⠀⠀⢀⡔⠉⠉⠉⠛⠛⠿⢿⡿⠿⢌⠛⢡⠄⠀⠻⠟⠋⠘⠻⠧⢻⣿⣿⡿⢿⡛⢩⠃⡥⢚⣿⣷⣤⣀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣠⠶⢞⣢⣤⡔⠉⠁⢢⣀⡠⢟⠋⣕⢪⡡⠜⢢⡉⠴⡁⢎⢻⣟⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠓⠰⢼⣿⣷⡰⢈⠖⣈⠧⡳⡌⢥⠘⢆⡉⠖⢢⠹⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠣⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⣿⣿⣿⣌⠦⣁⠎⡹⢜⢦⡉⢆⠩⢜⣢⡵⠚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⡝⠿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⣰⣿⣿⣟⣿⣿⣿⣷⡔⡘⢤⠉⣧⣷⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠘⠥⠟⠽⣻⢿⡿⣿⣿⣿⣷⣶⣾⣿⣿⡿⣧⣿⣿⣿⣿⣿⣮⣶⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠈⠐⢺⢰⣆⣤⣩⡀⠒⠀⠊⠍⣙⢓⡛⠿⠿⣿⣟⣯⣟⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠘⡶⣬⡽⣃⣀⠀⠀⠀⠀⠀⠈⠘⠁⠒⠌⢍⣺⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠯⣶⣛⡭⠼⡏⣽⣶⡶⡤⢤⣀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣔⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⢤⣈⣉⡐⠛⠭⠧⢈⡀⡿⡄⣬⡅⢰⠒⡠⡤⣀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⢦⣄⣉⡑⠒⠣⠸⣰⠇⣯⢸⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⢿⣻⣞⡷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠶⢬⣉⣁⣚⢘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣽⣞⡿⡽⣞⣯⢷⣞⡿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠩⠙⠉⠋⠊⠉⠎⠱⢩⠧⢞⡳⢽⣋⢎⠯⡜⠳⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠃⣿⣿⣿⡇⠀⡜⢢⠓⡜⢢⠓⡜⢢⠓⡜⢢⠓⡜⢢⠓⡜⢢⡹⢨⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⣟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡜⣡⢋⠼⣡⢋⡜⣡⢋⡜⣡⢋⡜⢥⠂⢰⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⡅⣿⣿⣿⡇⠀⡜⢤⠣⡜⢤⢋⠖⣡⠎⣔⠣⢎⡔⢣⠎⡜⢢⠃⢽⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠆⣽⣿⣿⡇⠀⡜⢢⠓⡜⣌⠮⡜⢢⡙⡤⢋⠖⡬⢃⠮⡱⢩⠁⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡴⢊⠖⣩⢒⡱⢜⡩⢚⡔⣋⠖⣡⣧⠀⣿⣿⣿⠀⢸⣦⣅⣀⣀⣉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠀⡁⣿⣿⣿⡇⠀⡒⢥⢊⡴⢋⡜⡡⢎⠲⣡⢎⡱⣘⣤⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⢀⣀⣥⣿⣿⣿⡇⠀⣭⠶⢷⣌⢣⠜⣱⣪⣵⣶⣾⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣹
⠀⠀⢀⠀⢄⣰⣿⣾⣶⣿⣿⣿⣿⠿⡟⠛⡉⢃⡄⠲⣰⠻⡿⣿⣿⣿⣿⣿⢿⣿⡯⠷⣻⣿⣇⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⢼
⣤⣽⣾⣿⣿⣿⣿⣿⠿⠛⠯⠑⢤⠘⡄⡓⢌⡡⢌⡑⢾⠀⣈⡿⠿⠿⠿⣑⡿⢁⠈⡄⠀⠀⠀⠉⠉⠁⠈⠒⠚⠛⢿⣍⠿⣜⢲⡙⡞⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡬⡂⢍⠢⡑⢢⠉⢆⡔⣊⣴⣾⠞⠁⠀⠀⠀⠄⠫⣽⣦⣂⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠈⠒⠈⢁⡑⠬⠐
⣿⣿⣿⣿⣿⡿⢿⡟⠻⡙⠮⡤⣃⣬⣵⣾⣾⣿⣿⣿⢣⣲⡆⠀⠀⡠⣶⡌⣓⣿⡌⢿⣷⣶⣦⣦⣄⣀⣀⣀⣜⡁⡀⠤⠐⠊⠉⠀⠀⠀
⠿⡟⠻⠙⠀⠉⠀⠀⠀⢀⡔⠉⠉⠉⠛⠛⠿⢿⡿⠿⢌⠛⢡⠄⠀⠻⠟⠋⠘⠻⠧⢻⣿⣿⡿⢿⡛⢩⠃⡥⢚⣿⣷⣤⣀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣠⠶⢞⣢⣤⡔⠉⠁⢢⣀⡠⢟⠋⣕⢪⡡⠜⢢⡉⠴⡁⢎⢻⣟⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠓⠰⢼⣿⣷⡰⢈⠖⣈⠧⡳⡌⢥⠘⢆⡉⠖⢢⠹⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠣⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⣿⣿⣿⣌⠦⣁⠎⡹⢜⢦⡉⢆⠩⢜⣢⡵⠚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⡝⠿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⣰⣿⣿⣟⣿⣿⣿⣷⡔⡘⢤⠉⣧⣷⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠘⠥⠟⠽⣻⢿⡿⣿⣿⣿⣷⣶⣾⣿⣿⡿⣧⣿⣿⣿⣿⣿⣮⣶⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠈⠐⢺⢰⣆⣤⣩⡀⠒⠀⠊⠍⣙⢓⡛⠿⠿⣿⣟⣯⣟⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠘⡶⣬⡽⣃⣀⠀⠀⠀⠀⠀⠈⠘⠁⠒⠌⢍⣺⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠯⣶⣛⡭⠼⡏⣽⣶⡶⡤⢤⣀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣔⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⢤⣈⣉⡐⠛⠭⠧⢈⡀⡿⡄⣬⡅⢰⠒⡠⡤⣀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⢦⣄⣉⡑⠒⠣⠸⣰⠇⣯⢸⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⢿⣻⣞⡷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠶⢬⣉⣁⣚⢘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣽⣞⡿⡽⣞⣯⢷⣞⡿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠩⠙⠉⠋⠊⠉⠎⠱⢩⠧⢞⡳⢽⣋⢎⠯⡜⠳⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠠⣟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡜⣡⢋⠼⣡⢋⡜⣡⢋⡜⣡⢋⡜⢥⠂⢰⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⡅⣿⣿⣿⡇⠀⡜⢤⠣⡜⢤⢋⠖⣡⠎⣔⠣⢎⡔⢣⠎⡜⢢⠃⢽⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠆⣽⣿⣿⡇⠀⡜⢢⠓⡜⣌⠮⡜⢢⡙⡤⢋⠖⡬⢃⠮⡱⢩⠁⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡴⢊⠖⣩⢒⡱⢜⡩⢚⡔⣋⠖⣡⣧⠀⣿⣿⣿⠀⢸⣦⣅⣀⣀⣉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠀⡁⣿⣿⣿⡇⠀⡒⢥⢊⡴⢋⡜⡡⢎⠲⣡⢎⡱⣘⣤⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⢀⣀⣥⣿⣿⣿⡇⠀⣭⠶⢷⣌⢣⠜⣱⣪⣵⣶⣾⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣹
⠀⠀⢀⠀⢄⣰⣿⣾⣶⣿⣿⣿⣿⠿⡟⠛⡉⢃⡄⠲⣰⠻⡿⣿⣿⣿⣿⣿⢿⣿⡯⠷⣻⣿⣇⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⢼
⣤⣽⣾⣿⣿⣿⣿⣿⠿⠛⠯⠑⢤⠘⡄⡓⢌⡡⢌⡑⢾⠀⣈⡿⠿⠿⠿⣑⡿⢁⠈⡄⠀⠀⠀⠉⠉⠁⠈⠒⠚⠛⢿⣍⠿⣜⢲⡙⡞⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡬⡂⢍⠢⡑⢢⠉⢆⡔⣊⣴⣾⠞⠁⠀⠀⠀⠄⠫⣽⣦⣂⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠈⠒⠈⢁⡑⠬⠐
⣿⣿⣿⣿⣿⡿⢿⡟⠻⡙⠮⡤⣃⣬⣵⣾⣾⣿⣿⣿⢣⣲⡆⠀⠀⡠⣶⡌⣓⣿⡌⢿⣷⣶⣦⣦⣄⣀⣀⣀⣜⡁⡀⠤⠐⠊⠉⠀⠀⠀
⠿⡟⠻⠙⠀⠉⠀⠀⠀⢀⡔⠉⠉⠉⠛⠛⠿⢿⡿⠿⢌⠛⢡⠄⠀⠻⠟⠋⠘⠻⠧⢻⣿⣿⡿⢿⡛⢩⠃⡥⢚⣿⣷⣤⣀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣠⠶⢞⣢⣤⡔⠉⠁⢢⣀⡠⢟⠋⣕⢪⡡⠜⢢⡉⠴⡁⢎⢻⣟⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠓⠰⢼⣿⣷⡰⢈⠖⣈⠧⡳⡌⢥⠘⢆⡉⠖⢢⠹⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠣⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⣿⣿⣿⣌⠦⣁⠎⡹⢜⢦⡉⢆⠩⢜⣢⡵⠚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⡝⠿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⣰⣿⣿⣟⣿⣿⣿⣷⡔⡘⢤⠉⣧⣷⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠘⠥⠟⠽⣻⢿⡿⣿⣿⣿⣷⣶⣾⣿⣿⡿⣧⣿⣿⣿⣿⣿⣮⣶⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠈⠐⢺⢰⣆⣤⣩⡀⠒⠀⠊⠍⣙⢓⡛⠿⠿⣿⣟⣯⣟⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠘⡶⣬⡽⣃⣀⠀⠀⠀⠀⠀⠈⠘⠁⠒⠌⢍⣺⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠯⣶⣛⡭⠼⡏⣽⣶⡶⡤⢤⣀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣔⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⢤⣈⣉⡐⠛⠭⠧⢈⡀⡿⡄⣬⡅⢰⠒⡠⡤⣀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⢦⣄⣉⡑⠒⠣⠸⣰⠇⣯⢸⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⢿⣻⣞⡷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠶⢬⣉⣁⣚⢘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣽⣞⡿⡽⣞⣯⢷⣞⡿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠩⠙⠉⠋⠊⠉⠎⠱⢩⠧⢞⡳⢽⣋⢎⠯⡜⠳⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀::::::::----⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀---:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:::::::::::::::::--------⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:------:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:::::::::::::::::::::::-:::-:--------:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-----------⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀------------:-::::-::--::--:---------------⠀⠀⠀⠀⠀⠀⠀---------------⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:----------------:-:-:---------------------:⠀⠀⠀⠀⠀------------------⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-------------------------------------------⠀⠀⠀:---------------------:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀--⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-----------------------------------------=---------------------------:⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=---:⠀⠀⠀⠀⠀⠀------------------------------=--=+++++++****=---------------------=-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀------⠀⠀⠀⠀⠀---------------------==+++++++***************+==-----------------=⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:-------:⠀:-------====++++++++*++******************###**++==-------------=-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀----------++++++++********************************###****+===----------=⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀----------+*********************************########******+===------=-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:---------=************************#############%##********+===---=⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:=--------=*************####################%%%%#%#*********+===-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=--------=**########################%%%%%%%%%%%%##********++=-:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-==-----=################%%%%%%%%%%%%%%%%%%%%%#*+==---------====-::⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-+=---=####%%%%%%%%%%%%%%%%%%%%%%%##*+=---------==+++++=⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀--=+=--*%%%%%%%%%%%%%%%##*++=---------=++++++==========⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-----=+=*%%%%%#**+=----------=++++++=+================-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-------==+==--------=++++++===========================:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-----====++=+++=++=++=================================⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-=========+++++++=====================================⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-=========+++++++=====================================⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-=========+++++++++=+======+=++===+==+================⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-========+++++++=+=++++=+==+++==+==+====+======+==++=⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-=======+++++++++++++++++=+++==++++=======+=====+++-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-======++++++++++++++++++++=++++++++++=+=+==+=+++=-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-=====+++++++++++++++++++++++++++++++++++++++++++-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=====+++++++++++++++++++++++++++++++++++++++++=-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀====++++++++++++++++++++++++++++++++++-:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-==++++++++++++++++++++++++++-::⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀==++++++++++++++++++=-:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=++++++++++=-:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-++=:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀::::::::----⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀---:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:::::::::::::::::--------⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:------:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:::::::::::::::::::::::-:::-:--------:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-----------⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀------------:-::::-::--::--:---------------⠀⠀⠀⠀⠀⠀⠀---------------⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:----------------:-:-:---------------------:⠀⠀⠀⠀⠀------------------⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-------------------------------------------⠀⠀⠀:---------------------:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀--⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-----------------------------------------=---------------------------:⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=---:⠀⠀⠀⠀⠀⠀------------------------------=--=+++++++****=---------------------=-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀------⠀⠀⠀⠀⠀---------------------==+++++++***************+==-----------------=⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:-------:⠀:-------====++++++++*++******************###**++==-------------=-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀----------++++++++********************************###****+===----------=⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀----------+*********************************########******+===------=-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:---------=************************#############%##********+===---=⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀:=--------=*************####################%%%%#%#*********+===-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=--------=**########################%%%%%%%%%%%%##********++=-:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-==-----=################%%%%%%%%%%%%%%%%%%%%%#*+==---------====-::⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-+=---=####%%%%%%%%%%%%%%%%%%%%%%%##*+=---------==+++++=⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀--=+=--*%%%%%%%%%%%%%%%##*++=---------=++++++==========⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-----=+=*%%%%%#**+=----------=++++++=+================-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-------==+==--------=++++++===========================:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-----====++=+++=++=++=================================⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-=========+++++++=====================================⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-=========+++++++=====================================⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-=========+++++++++=+======+=++===+==+================⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-========+++++++=+=++++=+==+++==+==+====+======+==++=⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-=======+++++++++++++++++=+++==++++=======+=====+++-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-======++++++++++++++++++++=++++++++++=+=+==+=+++=-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-=====+++++++++++++++++++++++++++++++++++++++++++-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=====+++++++++++++++++++++++++++++++++++++++++=-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀====++++++++++++++++++++++++++++++++++-:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-==++++++++++++++++++++++++++-::⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀==++++++++++++++++++=-:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀=++++++++++=-:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-++=:⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⣟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡜⣡⢋⠼⣡⢋⡜⣡⢋⡜⣡⢋⡜⢥⠂⢰⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⡅⣿⣿⣿⡇⠀⡜⢤⠣⡜⢤⢋⠖⣡⠎⣔⠣⢎⡔⢣⠎⡜⢢⠃⢽⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠆⣽⣿⣿⡇⠀⡜⢢⠓⡜⣌⠮⡜⢢⡙⡤⢋⠖⡬⢃⠮⡱⢩⠁⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡴⢊⠖⣩⢒⡱⢜⡩⢚⡔⣋⠖⣡⣧⠀⣿⣿⣿⠀⢸⣦⣅⣀⣀⣉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠀⡁⣿⣿⣿⡇⠀⡒⢥⢊⡴⢋⡜⡡⢎⠲⣡⢎⡱⣘⣤⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⢀⣀⣥⣿⣿⣿⡇⠀⣭⠶⢷⣌⢣⠜⣱⣪⣵⣶⣾⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣹
⠀⠀⢀⠀⢄⣰⣿⣾⣶⣿⣿⣿⣿⠿⡟⠛⡉⢃⡄⠲⣰⠻⡿⣿⣿⣿⣿⣿⢿⣿⡯⠷⣻⣿⣇⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⢼
⣤⣽⣾⣿⣿⣿⣿⣿⠿⠛⠯⠑⢤⠘⡄⡓⢌⡡⢌⡑⡑⠀⣈⡿⠿⠿⠿⣑⡿⢁⠈⡄⠀⠀⠀⠉⠉⠁⠈⠒⠚⠛⢿⣍⠿⣜⢲⡙⡞⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡬⡂⢍⠢⡑⢢⠉⢆⡔⣊⣴⣾⣿⣿⣿⣿⣿⣿⠫⣽⣦⣂⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠈⠒⠈⢁⡑⠬⠐
⣿⣿⣿⣿⣿⡿⢿⡟⠻⡙⠮⡤⣃⣬⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣦⣦⣄⣀⣀⣀⣜⡁⡀⠤⠐⠊⠉⠀⠀⠀
⠿⡟⠻⠙⠀⠉⠀⠀⠀⢀⡔⠉⠉⠉⠛⠛⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⢩⠃⡥⢚⣿⣷⣤⣀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿⣢⣿⣿⣿⣿⣿⣿⣿⢟⠋⣕⢪⡡⠜⢢⡉⠴⡁⢎⢻⣟⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠛⠛⣿⣷⡰⢈⠖⣈⠧⡳⡌⢥⠘⢆⡉⠖⢢⠹⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠣⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⣿⣿⣿⣌⠦⣁⠎⡹⢜⢦⡉⢆⠩⢜⣢⡵⠚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⡝⠿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⣰⣿⣿⣟⣿⣿⣿⣷⡔⡘⢤⠉⣧⣷⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠘⠥⠟⠽⣻⢿⡿⣿⣿⣿⣷⣶⣾⣿⣿⡿⣧⣿⣿⣿⣿⣿⣮⣶⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠈⠐⢺⢰⣆⣤⣩⡀⠒⠀⠊⠍⣙⢓⡛⠿⠿⣿⣟⣯⣟⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠘⡶⣬⡽⣃⣀⠀⠀⠀⠀⠀⠈⠘⠁⠒⠌⢍⣺⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠯⣶⣛⡭⠼⡏⣽⣶⡶⡤⢤⣀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣔⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⢤⣈⣉⡐⠛⠭⠧⢈⡀⡿⡄⣬⡅⢰⠒⡠⡤⣀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⢦⣄⣉⡑⠒⠣⠸⣰⠇⣯⢸⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⢿⣻⣞⡷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠶⢬⣉⣁⣚⢘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣽⣞⡿⡽⣞⣯⢷⣞⡿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠩⠙⠉⠋⠊⠉⠎⠱⢩⠧⢞⡳⢽⣋⢎⠯⡜⠳⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠠⣟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡜⣡⢋⠼⣡⢋⡜⣡⢋⡜⣡⢋⡜⢥⠂⢰⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠐⣏⠀⠀⠀⠀⠀⡅⣿⣿⣿⡇⠀⡜⢤⠣⡜⢤⢋⠖⣡⠎⣔⠣⢎⡔⢣⠎⡜⢢⠃⢽⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⠀⠀⠆⣽⣿⣿⡇⠀⡜⢢⠓⡜⣌⠮⡜⢢⡙⡤⢋⠖⡬⢃⠮⡱⢩⠁⣾⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⡃⢿⣿⣿⡇⠀⡜⣡⢋⡴⢊⠖⣩⢒⡱⢜⡩⢚⡔⣋⠖⣡⣧⠀⣿⣿⣿⠀⢸⣦⣅⣀⣀⣉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠐⣯⠀⠀⠀⠀⠀⡁⣿⣿⣿⡇⠀⡒⢥⢊⡴⢋⡜⡡⢎⠲⣡⢎⡱⣘⣤⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢈⡷⠀⠀⠀⢀⣀⣥⣿⣿⣿⡇⠀⣭⠶⢷⣌⢣⠜⣱⣪⣵⣶⣾⣿⣿⣿⣿⣿⡏⢸⣿⣿⣿⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣹
⠀⠀⢀⠀⢄⣰⣿⣾⣶⣿⣿⣿⣿⠿⡟⠛⡉⢃⡄⠲⣰⠻⡿⣿⣿⣿⣿⣿⢿⣿⡯⠷⣻⣿⣇⢸⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⡿⣿⢼
⣤⣽⣾⣿⣿⣿⣿⣿⠿⠛⠯⠑⢤⠘⡄⡓⢌⡡⢌⡑⡑⠀⣈⡿⠿⠿⠿⣑⡿⢁⠈⡄⠀⠀⠀⠉⠉⠁⠈⠒⠚⠛⢿⣍⠿⣜⢲⡙⡞⢯
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡬⡂⢍⠢⡑⢢⠉⢆⡔⣊⣴⣾⣿⣿⣿⣿⣿⣿⠫⣽⣦⣂⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠈⠒⠈⢁⡑⠬⠐
⣿⣿⣿⣿⣿⡿⢿⡟⠻⡙⠮⡤⣃⣬⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣦⣦⣄⣀⣀⣀⣜⡁⡀⠤⠐⠊⠉⠀⠀⠀
⠿⡟⠻⠙⠀⠉⠀⠀⠀⢀⡔⠉⠉⠉⠛⠛⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⢩⠃⡥⢚⣿⣷⣤⣀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿⣢⣿⣿⣿⣿⣿⣿⣿⢟⠋⣕⢪⡡⠜⢢⡉⠴⡁⢎⢻⣟⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠛⠛⣿⣷⡰⢈⠖⣈⠧⡳⡌⢥⠘⢆⡉⠖⢢⠹⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠣⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⣿⣿⣿⣌⠦⣁⠎⡹⢜⢦⡉⢆⠩⢜⣢⡵⠚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⡝⠿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⣰⣿⣿⣟⣿⣿⣿⣷⡔⡘⢤⠉⣧⣷⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠘⠥⠟⠽⣻⢿⡿⣿⣿⣿⣷⣶⣾⣿⣿⡿⣧⣿⣿⣿⣿⣿⣮⣶⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠈⠐⢺⢰⣆⣤⣩⡀⠒⠀⠊⠍⣙⢓⡛⠿⠿⣿⣟⣯⣟⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠘⡶⣬⡽⣃⣀⠀⠀⠀⠀⠀⠈⠘⠁⠒⠌⢍⣺⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠯⣶⣛⡭⠼⡏⣽⣶⡶⡤⢤⣀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣔⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⢤⣈⣉⡐⠛⠭⠧⢈⡀⡿⡄⣬⡅⢰⠒⡠⡤⣀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⢦⣄⣉⡑⠒⠣⠸⣰⠇⣯⢸⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⢿⣻⣞⡷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠶⢬⣉⣁⣚⢘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣽⣞⡿⡽⣞⣯⢷⣞⡿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠩⠙⠉⠋⠊⠉⠎⠱⢩⠧⢞⡳⢽⣋⢎⠯⡜⠳⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⡔⡉⢃⡄⠲⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⠑⡄⡓⢌⡡⢌⡑⡄⠀⠀⠀
⠀⠀⠀⠀ ⡔⡬⡂⢍⠢⡑⢢⠉⢆⡔⣊⣴⣾⣿⣿⣿⣿⣿⣿⠫⣽⣦⣂⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡙⠮⡤⣃⣬⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣦⣦⣄⣀⣀⣀⣜⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⠉⠛⠛⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⢩⠃⡥⢚⣿⣷⣤⣀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿⣢⣿⣿⣿⣿⣿⣿⣿⢟⠋⣕⢪⡡⠜⢢⡉⠴⡁⢎⢻⣟⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠛⠛⣿⣷⡰⢈⠖⣈⠧⡳⡌⢥⠘⢆⡉⠖⢢⠹⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠣⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⣿⣿⣿⣌⠦⣁⠎⡹⢜⢦⡉⢆⠩⢜⣢⡵⠚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⡝⠿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⣰⣿⣿⣟⣿⣿⣿⣷⡔⡘⢤⠉⣧⣷⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠘⠥⠟⠽⣻⢿⡿⣿⣿⣿⣷⣶⣾⣿⣿⡿⣧⣿⣿⣿⣿⣿⣮⣶⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠈⠐⢺⢰⣆⣤⣩⡀⠒⠀⠊⠍⣙⢓⡛⠿⠿⣿⣟⣯⣟⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠘⡶⣬⡽⣃⣀⠀⠀⠀⠀⠀⠈⠘⠁⠒⠌⢍⣺⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠯⣶⣛⡭⠼⡏⣽⣶⡶⡤⢤⣀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣔⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⢤⣈⣉⡐⠛⠭⠧⢈⡀⡿⡄⣬⡅⢰⠒⡠⡤⣀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⢦⣄⣉⡑⠒⠣⠸⣰⠇⣯⢸⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⢿⣻⣞⡷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠶⢬⣉⣁⣚⢘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣽⣞⡿⡽⣞⣯⢷⣞⡿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠩⠙⠉⠋⠊⠉⠎⠱⢩⠧⢞⡳⢽⣋⢎⠯⡜⠳⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⡔⡉⢃⡄⠲⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡔⠑⡄⡓⢌⡡⢌⡑⡄⠀⠀⠀
⠀⠀⠀⠀ ⡔⡬⡂⢍⠢⡑⢢⠉⢆⡔⣊⣴⣾⣿⣿⣿⣿⣿⣿⠫⣽⣦⣂⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡙⠮⡤⣃⣬⣵⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣶⣦⣦⣄⣀⣀⣀⣜⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠉⠉⠛⠛⠿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡛⢩⠃⡥⢚⣿⣷⣤⣀⠀⠀⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿⣢⣿⣿⣿⣿⣿⣿⣿⢟⠋⣕⢪⡡⠜⢢⡉⠴⡁⢎⢻⣟⠛⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠛⠛⠛⣿⣷⡰⢈⠖⣈⠧⡳⡌⢥⠘⢆⡉⠖⢢⠹⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠣⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⣾⣿⣿⣿⣌⠦⣁⠎⡹⢜⢦⡉⢆⠩⢜⣢⡵⠚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠨⡝⠿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⣰⣿⣿⣟⣿⣿⣿⣷⡔⡘⢤⠉⣧⣷⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠘⠥⠟⠽⣻⢿⡿⣿⣿⣿⣷⣶⣾⣿⣿⡿⣧⣿⣿⣿⣿⣿⣮⣶⣿⣿⣿⣿⣿⣿⠀⠀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠈⠐⢺⢰⣆⣤⣩⡀⠒⠀⠊⠍⣙⢓⡛⠿⠿⣿⣟⣯⣟⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⠘⡶⣬⡽⣃⣀⠀⠀⠀⠀⠀⠈⠘⠁⠒⠌⢍⣺⢗⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠯⣶⣛⡭⠼⡏⣽⣶⡶⡤⢤⣀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣔⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠸⢤⣈⣉⡐⠛⠭⠧⢈⡀⡿⡄⣬⡅⢰⠒⡠⡤⣀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⢦⣄⣉⡑⠒⠣⠸⣰⠇⣯⢸⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⣷⢿⣻⣞⡷⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠶⢬⣉⣁⣚⢘⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣽⣞⡿⡽⣞⣯⢷⣞⡿⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠩⠙⠉⠋⠊⠉⠎⠱⢩⠧⢞⡳⢽⣋⢎⠯⡜⠳⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠈⠁⠀
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При оплате рекомендуется отключить VPN-сервис.
Для проведения оплаты используется Robokassa, принимает: банковские карты Visa (включая Electron), MasterCard, МИР, UnionPay; СБП ; сервисы Yandex Pay, MTS Pay, Mir Pay, Sber Pay
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