The solutions to $x^2+4x+1=0$ are $r$ and $s$, where $r<s$. The solutions to $x^2+10x+13=0$ are $t$ and $u$, where $t<u$. The solutions to $x^2+14x+c=0$, where $c$ is a constant, are $r+t$ and $s+u$. What is the value of $c$?