Two small particles, each of mass m carrying positive charge q each are attached to the ends of a non-conducting light thread of length 2l. A third particle of mass $2m$ is attached at mid-point of the thread. The whole system is placed on a smooth horizontal floor and the particle of mass $2m$ is given a velocity v as shown in Fig. minimum distance between the two charged particles during the process of motion is expressed as $\left(\frac{a.q^b\mathcal{l}}{cd{\in }_{0}m{V}^2\mathcal{l}+q^e}\right)$ find $a+b+c+d+e$ to nearest integer