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C. Little Girl and Maximum Sum

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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 $$$l_i$$$, $$$r_i$$$ $$$(1 \le l_i \le r_i \le n)$$$. 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 $$$n$$$ ($$$1 \le n \le 2\cdot10^5$$$) and $$$q$$$ ($$$1 \le q \le 2\cdot10^5$$$) — the number of elements in the array and the number of queries, correspondingly.

The next line contains $$$n$$$ space-separated integers $$$a_i$$$ ($$$1 \le a_i \le 2\cdot10^5$$$) — the array elements.

Each of the following $$$q$$$ lines contains two space-separated integers $$$l_i$$$ and $$$r_i$$$ ($$$1 \le l_i \le r_i \le n$$$) — 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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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