Little Girl and Maximum Sum

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⋅10^5) and q (1 ≤ q ≤ 2⋅10^5) — 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⋅10^5) — 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 C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

3 3 5 3 2 1 2 2 3 1 3

Output

25

Input

5 3 5 2 4 1 3 1 5 2 3 2 3

Output

33

inputFormat

Input

The first line contains two space-separated integers n (1 ≤ n ≤ 2⋅10^5) and q (1 ≤ q ≤ 2⋅10^5) — 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⋅10^5) — 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.

outputFormat

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 C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

3 3 5 3 2 1 2 2 3 1 3

Output

25

Input

5 3 5 2 4 1 3 1 5 2 3 2 3

Output

33

样例

5 3
5 2 4 1 3
1 5
2 3
2 3

33

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