accompanying advances quite a few times: Pick two files I and j (1≤i,j≤n), and an integer x (1≤x≤ai). Leave I alone the source file and j be the sink file. Reduction the I-th component by x, and increment the j-th component by x. The subsequent qualities at I-th and j-th file are ai−x and aj+x separately. The expense of this
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You can change an exhibit utilizing the accompanying advances quite a few times:
Pick two files I and j (1≤i,j≤n), and an integer x (1≤x≤
Reduction the I-th component by x, and increment the j-th component by x. The subsequent qualities at I-th and j-th file are ai−x and aj+x separately.
The expense of this activity is x⋅|j−i|.
Presently the I-th file can at this point don't be the sink and the j-th file can at this point don't be the source.
The all out cost of a change is the amount of the multitude of expenses in sync 3.
For instance, exhibit [0,2,3,3] can be changed into an excellent cluster [2,2,2,2] with absolute expense 1⋅|1−3|+1⋅|1−4|=5.
An exhibit is called adjusted, if it very well may be changed into an excellent cluster, and the expense of such change is particularly characterized. As such, the base expense of change into a delightful exhibit approaches the most extreme expense.
You are given an exhibit a1,a2,… ,an of length n, comprising of non-negative integers. Your errand is to track down the number of adjusted clusters which are stages of the given exhibit. Two exhibits are considered unique, if components at some position vary. Since the appropriate response can be enormous, output it modulo 109+7.
Input
The main line contains a solitary integer n (1≤n≤105) — the size of the cluster.
The subsequent line contains n integers a1,a2,… ,an (0≤ai≤109).
Output
Output a solitary integer — the number of adjusted changes modulo 109+7.
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