Is the representation $\mathbf{N}\oplus\bar{\mathbf{N}}$ of $SU(N)$ real or pseudo-real?

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Let $N \geq 3$ be an integer. Let us call $\mathbf{N}$ its fundamental representation, and let $\bar{\mathbf{N}}$ be its complex conjugated representation.

Is the direct sum $\mathbf{N}\oplus\bar{\mathbf{N}}$ real or pseudo-real ?