You have a Hexagon, named EUNHAS . Also, you are given that:

- \( m\left(\overline{EU}\right) = m\left(\overline{ES}\right) = 19\)
- \( m\left(\overline{UN}\right) = m\left(\overline{NH}\right) = 180\)
- \( m\left(\overline{HA}\right) = m\left(\overline{AS}\right) = 181\)
- \( m \left(\angle UES\right) = m\left(\angle UNH\right) = m\left(\angle HAS\right) = 120^{\circ} \cdot\)

If the value of \( \left( m \left(\overline{EA}\right) \right)^2 \) can be express as \(a + b\sqrt{c} \) where \(c \) is a prime, what is the value of \( \left\lfloor \sqrt{a + b + c} \right \rfloor \ ? \)

**Clarification:**

\( m \left(\overline{AX}\right) \) means the length or measurement of line segment \( AX \) for example, while \( m \left(\angle RES\right) \) means the measurement of angle \( RES \cdot \)

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