Vietnam is beautiful

By applying AM-GM inequality we have

${ \left( \frac { V+I }{ 2 } \right) }^{ 2 }\le \frac { { V }^{ 2 }+{ I }^{ 2 } }{ 2 } ,\\ { \left( \frac { I+E }{ 2 } \right) }^{ 2 }\le \frac { { I }^{ 2 }+{ E }^{ 2 } }{ 2 } ,\\ { \left( \frac { E+T }{ 2 } \right) }^{ 2 }\le \frac { { E }^{ 2 }+{ T }^{ 2 } }{ 2 } ,\\ ...\\ { \left( \frac { M+V }{ 2 } \right) }^{ 2 }\le \frac { { M }^{ 2 }+{ V }^{ 2 } }{ 2 } .\\ \Longrightarrow { \left( \frac { V+I }{ 2 } \right) }^{ 2 }+{ \left( \frac { I+E }{ 2 } \right) }^{ 2 }+...+{ \left( \frac { M+V }{ 2 } \right) }^{ 2 }\le { V }^{ 2 }+{ I }^{ 2 }+{ E }^{ 2 }+...+{ M }^{ 2 } \quad \left( 1 \right)$

Furthermore, $R$ is a permutation of $B$ $\Longrightarrow \left\{ { \left( \frac { V+I }{ 2 } \right) }^{ 2 },{ \left( \frac { I+E }{ 2 } \right) }^{ 2 },{ \left( \frac { E+T }{ 2 } \right) }^{ 2 }...,{ \left( \frac { M+V }{ 2 } \right) }^{ 2 } \right\}$ is a permutation of $\left\{ { V }^{ 2 },{ I }^{ 2 },{ E }^{ 2 },...,{ M }^{ 2 } \right\}$

which leads to ${ \left( \frac { V+I }{ 2 } \right) }^{ 2 }+{ \left( \frac { I+E }{ 2 } \right) }^{ 2 }+{ \left( \frac { E+T }{ 2 } \right) }^{ 2 }+...+{ \left( \frac { M+V }{ 2 } \right) }^{ 2 }={ { V }^{ 2 }+{ I }^{ 2 }+{ E }^{ 2 }+...+{ M }^{ 2 } }\quad \left( 2 \right)$

From $\left( 1 \right) ,\left( 2 \right)$ $\Longrightarrow V=I=E=T=N=A=M=\frac { 2016 }{ 7 } =\boxed { 288 } .$