Two streams of water are fed to a boiler, each with a mass flow rate of $120k\frac{g}{s}$ and $175k\frac{g}{s}$ at $30C$ and $65C,$ respectively. Both streams leave the boiler as water vapour at a velocity of $5\frac{m}{s}$ and a temperature of $200C.$ Calculate the heat input of the boiler.