The pooled sums and combined sum of squares form a complete sufficient statistic for two normal samples sharing $\sigma^2$

Let $\{X_1,\dots,X_n\}$ be a random sample from $N(\mu_1,\sigma^2)$ and $\{Y_1,\dots,Y_m\}$ be a random sample from $N(\mu_2,\sigma^2)$. Let $T_1=\sum_{i=1}^nX_i^2+\sum_{j=1}^mY_j^2, T_2=\sum_{i=1}^nX_i,\ T_3=\sum_{i=1}^mY_i, T_4=\sum_{i=1}^nX_i^2,\ T_5=\sum_{i=1}^mY_i^2$. Then which of the following is a jointly sufficient complete statistic for $(\mu_1,\mu_2,\sigma^2)$?