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In this paper, we prove that N(u) is bounded by a polynomial function of degree 2n-3 with respect to |u| under the hypothesis that if two letters x, y occur in u, then the total number of x and x^{-1} occurring in u is not equal to the total number of y and y^{-1} occurring in u. We also prove that 2n-3 is the sharp bound on the degree of polynomials bounding N(u). 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In this paper, we prove that N(u) is bounded by a polynomial function of degree 2n-3 with respect to |u| under the hypothesis that if two letters x, y occur in u, then the total number of x and x^{-1} occurring in u is not equal to the total number of y and y^{-1} occurring in u. We also prove that 2n-3 is the sharp bound on the degree of polynomials bounding N(u). 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