Let the position vectors of three vertices of a triangle be \( 4\vec{p} + \vec{q} - 3\vec{r} \), \( -5\vec{p} + \vec{q} + 2\vec{r} \) and \( 2\vec{p} - \vec{q} + 2\vec{r} \). If the position vectors of the orthocenter and the circumcenter of the triangle are \( \frac{\vec{p} + \vec{q} + \vec{r}}{4} \) and \( \alpha \vec{p} + \beta \vec{q} + \gamma \vec{r} \) respectively, then \( \alpha + 2\beta + 5\gamma \) is equal to:
