  Suppose $u\in \dot{H}^1(\mathbb{R}^n)$. In a seminal work, Struwe proved that
if $u\geq 0$ and $\|\Delta u+u^{\frac{n+2}{n-2}}\|_{H^{-1}}:=\Gamma(u)\to 0$
then $dist(u,\mathcal{T})\to 0$, where $dist(u,\mathcal{T})$ denotes the
$\dot{H}^1(\mathbb{R}^n)$-distance of $u$ from the manifold of sums of Talenti
bubbles. Ciraolo, Figalli and Maggi obtained the first quantitative version of
Struwe's decomposition with one bubble in all dimensions, namely $\delta (u)
\leq C \Gamma (u)$. For Struwe's decomposition with two or more bubbles,
Figalli and Glaudo showed a striking dimensional dependent quantitative
estimate, namely $\delta(u)\leq C \Gamma(u)$ when $3\leq n\leq 5$ while this is
false for $ n\geq 6$. In this paper, we show that
  \[dist (u,\mathcal{T})\leq C\begin{cases} \Gamma(u)\left|\log
\Gamma(u)\right|^{\frac{1}{2}}\quad&\text{if }n=6,
  |\Gamma(u)|^{\frac{n+2}{2(n-2)}}\quad&\text{if }n\geq 7.\end{cases}\]
  Furthermore, we show that this inequality is sharp.
