Site: preserve the search query in the input after a search

RELNOTES: None.
PiperOrigin-RevId: 222248625

site/_includes/header.html

diff --git a/site/_includes/header.html b/site/_includes/header.html
index 8862210..3b30f46 100644
--- a/site/_includes/header.html
+++ b/site/_includes/header.html
@@ -20,10 +20,10 @@
           </ul>
           <form class="navbar-form navbar-right" action="/search.html" id="cse-search-box">
             <div class="form-group">
-              <input type="hidden" name="cx" value="012346921571893344015:xv_nfgpzbu4">
+              <input type="hidden" name="cx" value="009927877080525621790:2pxlpaexqpc">
               <input type="hidden" name="cof" value="FORID:10">
               <input type="hidden" name="ie" value="UTF-8">
-              <input type="search" name="q" class="form-control input-sm" placeholder="Search">
+              <input type="search" name="q" id="q" class="form-control input-sm" placeholder="Search">
             </div>
           </form>
           <ul class="nav navbar-nav navbar-right">