A field channel has cultivable commanded are of $2000$ hectares. The intensities of irrigation for gram and wheat are $30 \%$ and $50\%$ respectively. Gram has a kor period of $18$ days, kor depth of $12$ cm, while wheat has a kor period of $18$ days and a kor depth of $15$ cm. The discharge (in $m^3/s$) required in the filed channel to supply water to the commanded area during the kor period is ________.