Найду корень уравнения: y+2=(3-x)^3
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________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________ _________________________________________________________________ \\ ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________ _________________________________________________________________ \\ | / 2 2 | | / 2 / / 2 2 \\ / 2 / / 2 2 \\|| / 2 2 | | / 2 / / 2 2 \\ / 2 / / 2 2 \\||| / 2 2 | | / 2 / / 2 2 \\ / 2 / / 2 2 \\|| / 2 2 | | / 2 / / 2 2 \\ / 2 / / 2 2 \\|| | / / _________________________________________________________________ \ / _________________________________________________________________ \ | | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/| 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/||| / / _________________________________________________________________ \ / _________________________________________________________________ \ | | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/| 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|||| / / _________________________________________________________________ \ / _________________________________________________________________ \ | | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/| 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/||| / / _________________________________________________________________ \ / _________________________________________________________________ \ | | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/| 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/||| | / | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------| \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------||| / | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------| \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|||| / | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------| \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------||| / | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------| \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------||| | / | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| / | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /||| / | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| / | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| | / | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------|| | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|| |atan2|-------- + -----------------------------------------------------------------------------------------------------------------------------------------, 27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------|| | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|| |atan2|-------- + -----------------------------------------------------------------------------------------------------------------------------------------, 27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------||| / | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------|| | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|| |atan2|-------- + -----------------------------------------------------------------------------------------------------------------------------------------, 27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------|| | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|| |atan2|-------- + -----------------------------------------------------------------------------------------------------------------------------------------, 27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------|| | / |27*im(y) \ 2 /| | 27*re(y) \ 2 /| | \ 2 2 2 2 /| ___ / |27*im(y) \ 2 /| | 27*re(y) \ 2 /| | \ 2 2 2 2 /|| / |27*im(y) \ 2 /| | 27*re(y) \ 2 /| | \ 2 2 2 2 /| ___ / |27*im(y) \ 2 /| | 27*re(y) \ 2 /| | \ 2 2 2 2 /| |6 / |-------- + -----------------------------------------------------------------------------------------------------------------------------------------| + |27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + -----------------------------------------------------------------------------------------------------------------------------------------| + |27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 6 / |-------- + -----------------------------------------------------------------------------------------------------------------------------------------| + |27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + -----------------------------------------------------------------------------------------------------------------------------------------| + |27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| |\/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 /| \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 / x1 = 3 + I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- \ 6 6 / 6 6
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729*im (y)/| 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/||| / / _________________________________________________________________ \ / _________________________________________________________________ \ | | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/| 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|||| / / _________________________________________________________________ \ / _________________________________________________________________ \ | | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/| 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/||| / / _________________________________________________________________ \ / _________________________________________________________________ \ | | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/| 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/||| | / | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------| \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------||| / | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------| \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|||| / | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------| \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------||| / | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------| \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------||| | / | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| / | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /||| / | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| / | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| | / | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------|| | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|| |atan2|-------- + -----------------------------------------------------------------------------------------------------------------------------------------, 27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------|| | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|| |atan2|-------- + -----------------------------------------------------------------------------------------------------------------------------------------, 27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------||| / | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------|| | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|| |atan2|-------- + -----------------------------------------------------------------------------------------------------------------------------------------, 27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------|| | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|| |atan2|-------- + -----------------------------------------------------------------------------------------------------------------------------------------, 27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------|| | / |27*im(y) \ 2 /| | 27*re(y) \ 2 /| | \ 2 2 2 2 /| ___ / |27*im(y) \ 2 /| | 27*re(y) \ 2 /| | \ 2 2 2 2 /|| / |27*im(y) \ 2 /| | 27*re(y) \ 2 /| | \ 2 2 2 2 /| ___ / |27*im(y) \ 2 /| | 27*re(y) \ 2 /| | \ 2 2 2 2 /| |6 / |-------- + -----------------------------------------------------------------------------------------------------------------------------------------| + |27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + -----------------------------------------------------------------------------------------------------------------------------------------| + |27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|| 6 / |-------- + -----------------------------------------------------------------------------------------------------------------------------------------| + |27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ 3 *6 / |-------- + -----------------------------------------------------------------------------------------------------------------------------------------| + |27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| |\/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 /| \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 / x2 = 3 + I*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- \ 6 6 / 6 6
________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________ _________________________________________________________________ \\ ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ / / _________________________________________________________________ _________________________________________________________________ \\ / 2 2 | | / 2 / / 2 2 \\ / 2 / / 2 2 \\|| / 2 2 | | / 2 / / 2 2 \\ / 2 / / 2 2 \\|| / / _________________________________________________________________ \ / _________________________________________________________________ \ | | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/| 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/||| / / _________________________________________________________________ \ / _________________________________________________________________ \ | | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/| 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/||| / | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------| \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------||| / | / 2 / / 2 2 \\| | / 2 / / 2 2 \\| | | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------| \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------||| / | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| / | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | 4 / / 2 2 \ 2 2 |atan2\54*(54 + 27*re(y))*im(y), (54 + 27*re(y)) - 729*im (y)/|| | |27*im(y) \ 2 / 27*re(y) \ 2 /|| / | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------|| | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|| |atan2|-------- + -----------------------------------------------------------------------------------------------------------------------------------------, 27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------|| / | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *sin|--------------------------------------------------------------|| | \/ \(54 + 27*re(y)) - 729*im (y)/ + 2916*(54 + 27*re(y)) *im (y) *cos|--------------------------------------------------------------|| |atan2|-------- + -----------------------------------------------------------------------------------------------------------------------------------------, 27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------|| / |27*im(y) \ 2 /| | 27*re(y) \ 2 /| | \ 2 2 2 2 /| / |27*im(y) \ 2 /| | 27*re(y) \ 2 /| | \ 2 2 2 2 /| 6 / |-------- + -----------------------------------------------------------------------------------------------------------------------------------------| + |27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------| *cos|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| I*6 / |-------- + -----------------------------------------------------------------------------------------------------------------------------------------| + |27 + -------- + -----------------------------------------------------------------------------------------------------------------------------------------| *sin|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| \/ \ 2 2 / \ 2 2 / \ 3 / \/ \ 2 2 / \ 2 2 / \ 3 / x3 = 3 - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 3 3