CF1556C Compressed Bracket Sequence

William has a favorite bracket sequence. Since his favorite sequence is quite big he provided it to you as a sequence of positive integers $ c_1, c_2, \dots, c_n $ where $ c_i $ is the number of consecutive brackets "(" if $ i $ is an odd number or the number of consecutive brackets ")" if $ i $ is an even number. For example for a bracket sequence "((())()))" a corresponding sequence of numbers is $ [3, 2, 1, 3] $ . You need to find the total number of continuous subsequences (subsegments) $ [l, r] $ ( $ l \le r $ ) of the original bracket sequence, which are regular bracket sequences. A bracket sequence is called regular if it is possible to obtain correct arithmetic expression by inserting characters "+" and "1" into this sequence. For example, sequences "(())()", "()" and "(()(()))" are regular, while ")(", "(()" and "(()))(" are not.

N/A

N/A

In the first example a sequence (((()(()))( is described. This bracket sequence contains $ 5 $ subsegments which form regular bracket sequences: 1. Subsequence from the $ 3 $ rd to $ 10 $ th character: (()(())) 2. Subsequence from the $ 4 $ th to $ 5 $ th character: () 3. Subsequence from the $ 4 $ th to $ 9 $ th character: ()(()) 4. Subsequence from the $ 6 $ th to $ 9 $ th character: (()) 5. Subsequence from the $ 7 $ th to $ 8 $ th character: () In the second example a sequence ()))(()(()))) is described. In the third example a sequence ()()(()) is described.