D. LuoTianyi and the Function
time limit per test
7 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

LuoTianyi gives you an array $$$a$$$ of $$$n$$$ integers and the index begins from $$$1$$$.

Define $$$g(i,j)$$$ as follows:

  • $$$g(i,j)$$$ is the largest integer $$$x$$$ that satisfies $$$\{a_p:i\le p\le j\}\subseteq\{a_q:x\le q\le j\}$$$ while $$$i \le j$$$;
  • and $$$g(i,j)=0$$$ while $$$i>j$$$.

There are $$$q$$$ queries. For each query you are given four integers $$$l,r,x,y$$$, you need to calculate $$$\sum\limits_{i=l}^{r}\sum\limits_{j=x}^{y}g(i,j)$$$.

Input

The first line contains two integers $$$n$$$ and $$$q$$$ ($$$1\le n,q\le 10^6$$$) — the length of the array $$$a$$$ and the number of queries.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1\le a_i\le n$$$) — the elements of the array $$$a$$$.

Next $$$q$$$ lines describe a query. The $$$i$$$-th line contains four integers $$$l,r,x,y$$$ ($$$1\le l\le r\le n, 1\le x\le y\le n$$$) — the integers in the $$$i$$$-th query.

Output

Print $$$q$$$ lines where $$$i$$$-th line contains one integer — the answer for the $$$i$$$-th query.

Examples
Input
6 4
1 2 2 1 3 4
1 1 4 5
2 3 3 3
3 6 1 2
6 6 6 6
Output
6
6
0
6
Input
10 5
10 2 8 10 9 8 2 1 1 8
1 1 10 10
2 2 3 3
6 6 6 6
1 1 4 5
4 8 4 8
Output
4
2
6
4
80
Note

In the first example:

In the first query, the answer is $$$g(1,4)+g(1,5)=3+3=6$$$.

$$$x=1,2,3$$$ can satisfies $$$\{a_p:1\le p\le 4\}\subseteq\{a_q:x\le q\le 4\}$$$, $$$3$$$ is the largest integer so $$$g(1,4)=3$$$.

In the second query, the answer is $$$g(2,3)+g(3,3)=3+3=6$$$.

In the third query, the answer is $$$0$$$, because all $$$i > j$$$ and $$$g(i,j)=0$$$.

In the fourth query, the answer is $$$g(6,6)=6$$$.

In the second example:

In the second query, the answer is $$$g(2,3)=2$$$.

In the fourth query, the answer is $$$g(1,4)+g(1,5)=2+2=4$$$.