Problem: You are given a sequence a = \\{a_1, ..., a_N\\} with all zeros, and a sequence b = \\{b_1, ..., b_N\\} consisting of 0 and 1. The length of both is N.

You can perform Q kinds of operations. The i-th operation is as follows:

* Replace each of a_{l_i}, a_{l_i + 1}, ..., a_{r_i} with 1.



Minimize the hamming distance between a and b, that is, the number of i such that a_i \neq b_i, by performing some of the Q operations.

Constraints

* 1 \leq N \leq 200,000
* b consists of 0 and 1.
* 1 \leq Q \leq 200,000
* 1 \leq l_i \leq r_i \leq N
* If i \neq j, either l_i \neq l_j or r_i \neq r_j.

Input

Input is given from Standard Input in the following format:


N
b_1 b_2 ... b_N
Q
l_1 r_1
l_2 r_2
:
l_Q r_Q


Output

Print the minimum possible hamming distance.

Examples

Input

3
1 0 1
1
1 3


Output

1


Input

3
1 0 1
2
1 1
3 3


Output

0


Input

3
1 0 1
2
1 1
2 3


Output

1


Input

5
0 1 0 1 0
1
1 5


Output

2


Input

9
0 1 0 1 1 1 0 1 0
3
1 4
5 8
6 7


Output

3


Input

15
1 1 0 0 0 0 0 0 1 0 1 1 1 0 0
9
4 10
13 14
1 7
4 14
9 11
2 6
7 8
3 12
7 13


Output

5


Input

10
0 0 0 1 0 0 1 1 1 0
7
1 4
2 5
1 3
6 7
9 9
1 5
7 9


Output

1

Solution (in CPP):

Solution:
#include<cstdio>
#include<algorithm>
#include<vector>
#define N_ 201000
#define SZ 262144
using namespace std;
vector<int>G[N_];
int n, Q, w[N_], S[N_], D[N_];
int IT[SZ+SZ];
void Ins(int b, int e, int x) {
	b += SZ, e += SZ;
	while (b <= e) {
		IT[b] = min(IT[b], x);
		IT[e] = min(IT[e], x);
		b = (b + 1) >> 1, e = (e - 1) >> 1;
	}
}
int Get(int x) {
	int r = 1e9;
	x += SZ;
	while (x) {
		r = min(r, IT[x]);
		x >>= 1;
	}
	return r;
}
int main() {
	int i, b, e, j;
	for (i = 1; i < SZ + SZ; i++)IT[i] = 1e9;
	scanf("%d", &n);
	for (i = 1; i <= n; i++) {
		scanf("%d", &w[i]);
		S[i] = S[i - 1] + (1 - w[i]);
	}
	scanf("%d", &Q);
	while (Q--) {
		scanf("%d%d", &b, &e);
		G[e].push_back(b);
	}
	for (i = 1; i <= n; i++) {
		Ins(i - 1, i - 1, D[i - 1] - S[i - 1]);
		D[i] = D[i - 1] + w[i];
		for (j = 0; j < G[i].size(); j++) {
			b = G[i][j], e = i;
			Ins(b, e, Get(b - 1));
		}
		D[i] = min(D[i], Get(i) + S[i]);
	}
	printf("%d\n", D[n]);
}