longd0_function(ps, pss, pff, n, d)
{
#this program compute the probability P(L0>=d)#
#L0 is the perfect matching run within a sequence of length n# 
# ps is the initial prob. for "s", and pss is the transition prob of 1 given 1#
	a <- matrix(1, d, 1)
	b <- diag(a, d)
	c <- matrix(0, 1, d)
	p0 <- cbind(1, c)
	p0 <- cbind(p0, 0)
	U <- rbind(a, 0)
	U <- rbind(1, U)
	c <- cbind(c, 1)
	M <- cbind((1 - pss) * a, pss * b)
	M <- rbind(M, c)
	M <- cbind(0, M)
	M <- rbind(0, M)
	M[1, 2] <- 1 - ps
	M[1, 3] <- ps
	M[2, 2] <- pff
	M[2, 3] <- 1 - pff
	Mn <- M %*% M
	for(i in 3:n) {
		Mn <- Mn %*% M
	}
	1 - p0 %*% Mn %*% U
}