Mex

Time Limit : 15000/5000ms (Java/Other)   Memory Limit : 65535/65535K (Java/Other)

Total Submission(s) : 18   Accepted Submission(s) : 3

Problem Description Mex is a function on a set of integers, which is universally used for impartial game theorem. For a non-negative integer set S, mex(S) is defined as the least non-negative integer which is not appeared in S. Now our problem is about mex function on a sequence.

Consider a sequence of non-negative integers {ai}, we define mex(L,R) as the least non-negative integer which is not appeared in the continuous subsequence from aL to aR, inclusive. Now we want to calculate the sum of mex(L,R) for all 1 <= L <= R <= n.
Input The input contains at most 20 test cases. For each test case, the first line contains one integer n, denoting the length of sequence. The next line contains n non-integers separated by space, denoting the sequence. (1 <= n <= 200000, 0 <= ai <= 10^9) The input ends with n = 0.
Output For each test case, output one line containing a integer denoting the answer.
Sample Input 3 0 1 3 5 1 0 2 0 1 0
Sample Output 5 24 [hint] For the first test case: mex(1,1)=1, mex(1,2)=2, mex(1,3)=2, mex(2,2)=0, mex(2,3)=0,mex(3,3)=0. 1 + 2 + 2 + 0 +0 +0 = 5. [/hint]
Source 2013 ACM/ICPC Asia Regional Hangzhou Online