Let p$1$ and p$2$ be the respective proportions of women with nutritional anemia in each of two developing countries. If a random sample of $326$ women from the first country yielded $107$ women with nutritional anemia, and an independently chosen, random sample of $225$ women from the second country yielded $99$ women with nutritional anemia, find a $90\%$ confidence interval for p$1-$p$2.$ Then find the lower limit and upper limit of the $90\%$ confidence interval.