Thomas, a computer scientist that works with DNA sequences, needs to compute longest common subsequences of given pairs of strings. Consider an alphabet Σ of letters and a word w = a1a2 ...ar, whereai ∈Σ,fori=1,2,...,r. Asubsequenceofwisawordx=ai1ai2 ...ais suchthat1≤i1 <i2 < ... < is ≤ r. Subsequence x is a segment of w if ij+1 = ij +1, for j = 1,2,...s−1. For example the word “ove” is a segment of the word “lovely”, whereas the word “loly” is a subsequence of “lovely”, but not a segment. A word is a common subsequence of two words w1 and w2 if it is a subsequence of each of the two words. A longest common subsequence of w1 and w2 is a common subsequence of w1 and w2 having the largest possible length. For example, consider the words w1=lovxxelyxxxxx and w2=xxxxxxxlovely. The words w3=lovely and w4=xxxxxxx, the latter of length 7, are both common subsequences of w1 and w2. In fact, w4 is their longest common subsequence. Notice that the empty word, of length zero, is always a common subsequence, although not necessarily the longest. In the case of Thomas, there is an extra requirement: the subsequence must be formed from com- mon segments having length K or more. For example, if Thomas decides that K = 3, then he con- siders “lovely” to be an acceptable common subsequence of “lovxxelyxxxxx” and “xxxxxxxlovely”, whereas “xxxxxxx”, which has length 7 and is also a common subsequence, is not acceptable. Can you help Thomas? Input The input contains several test cases. The first line of a test case contains an integer K representing the minimum length of common segments, where 1 ≤ K ≤ 100. The next two lines contain each a string on lowercase letters from the regular alphabet of 26 letters. The length l of each string satisfies the inequality 1 ≤ l ≤ 103. There are no spaces on any line in the input. The end of the input is indicated by a line containing a zero. Output For each test case in the input, your program must print a single line, containing the length of the longest subsequence formed by consecutive segments of length at least K from both strings. If no such common subsequence of length greater than zero exists, then 0 must be printed. Sample Input 3 lovxxelyxxxxx xxxxxxxlovely 1 lovxxelyxxxxx xxxxxxxlovely 3 lovxxxelxyxxxx xxxlovelyxxxxxxx 4 lovxxxelyxxx xxxxxxlovely 0
2/2 Sample Output 6 7 10 0