John Doe has a crooked fence, consisting of n rectangular planks, lined up from the left to the right: the plank that goes i-th (1 ≤ i ≤ n)(from left to right) has width 1 and height hi. We will assume that the plank that goes i-th (1 ≤ i ≤ n) (from left to right) has index i.
A piece of the fence from l to r (1 ≤ l ≤ r ≤ n) is a sequence of planks of wood with indices from l to r inclusive, that is, planks with indicesl, l + 1, ..., r. The width of the piece of the fence from l to r is value r - l + 1.
Two pieces of the fence from l1 to r1 and from l2 to r2 are called matching, if the following conditions hold:
John chose a few pieces of the fence and now wants to know how many distinct matching pieces are for each of them. Two pieces of the fence are distinct if there is a plank, which belongs to one of them and does not belong to the other one.
The first line contains integer n (1 ≤ n ≤ 105) — the number of wood planks in the fence. The second line contains n space-separated integers h1, h2, ..., hn (1 ≤ hi ≤ 109) — the heights of fence planks.
The third line contains integer q (1 ≤ q ≤ 105) — the number of queries. Next q lines contain two space-separated integers li and ri (1 ≤ li ≤ ri ≤ n) — the boundaries of the i-th piece of the fence.
10 1 2 2 1 100 99 99 100 100 100 6 1 4 1 2 3 4 1 5 9 10 10 10
1 2 2 0 2 9
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