The little girl loves the problems on array queries very much.

One day she came across a rather well-known problem: you’ve got an array of *n* elements (the elements of the array are indexed starting from 1); also, there are *q* queries, each one is defined by a pair of integers *l* *i* , *r* *i* (1 ≤ *l* *i* ≤ *r* *i* ≤ *n* ). You need to find for each query the sum of elements of the array with indexes from *l* *i* to *r* *i* , inclusive.

The little girl found the problem rather boring. She decided to reorder the array elements before replying to the queries in a way that makes the sum of query replies maximum possible. Your task is to find the value of this maximum sum.

Input

The first line contains two space-separated integers *n* (1 ≤ *n* ≤ 2·105) and *q* (1 ≤ *q* ≤ 2·105) — the number of elements in the array and the number of queries, correspondingly.

The next line contains *n* space-separated integers *a* *i* (1 ≤ *a* *i* ≤ 2·105) — the array elements.

Each of the following *q* lines contains two space-separated integers *l* *i* and *r* *i* (1 ≤ *l* *i* ≤ *r* *i* ≤ *n* ) — the *i* -th query.

Output

In a single line print a single integer — the maximum sum of query replies after the array elements are reordered.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

Copy

3 3

5 3 2

1 2

2 3

1 3

Output

Copy

25

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