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 $l_i$, $r_i$ $(1 \le l_i \le r_i \le n)$. 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.
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.
def max_sum(arr,queries):
    pre=[0 for i in range(len(arr)+1)]
    arr.sort()
    for i in range(len(queries)):
        pre[queries[i][0]-1]+=1
        pre[queries[i][1]]-=1
        #print(pre)
    for i in range(1,len(pre)):
        pre[i]+=pre[i-1]
    pre.pop()
    pre.sort()
    
   # print(pre,arr)
    sum=0
    for i in range(len(arr)):
        sum+=(pre[i]*arr[i])
    return sum
arr=[5,2,4,1,3]
queries=[[1,5],[2,3],[2,3]]
print(max_sum(arr,queries))
