A pilot sterilization was carried out in a vessel containing $1000\; \text{m}^{3}$ medium with an initial spore concentration of $10^{8} \;\text{spores/ml.}$ The accepted level of contamination after sterilization is $1$ spore in the entire vessel. The specific death rate constant for the spore is $2 \; \text{min}^{-1}$ at $121^{\circ}\text{C}.$ Assuming no death takes place during the heating and cooling cycles, the holding time at $121^{\circ}\text{C}.$ (rounded off to nearest integer) is _________ $\text{min}.$