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 <bits/stdc++.h>
#define INF 1000000000
#define LINF 1000000000000000000
#define MOD 1000000007
#define mod 1000007
#define INF63 1061109567
#define INF127 9187201950435737471
#define UINF 18446744073709551615
#define F first
#define S second
#define ll long long
#define N 800010
using namespace std;
ll n,q,bin[N],sum[N],pre[N],val[N],sz;
vector<ll> vt[N];
void update(ll l,ll r,ll v)
{
	ll i;
	l+=sz;
	r+=sz;
	while(l<=r)
	{
		val[l]=min(val[l],v);
		val[r]=min(val[r],v);
		l=(l+1)/2;
		r=(r-1)/2;
	}
	return;
}
ll getans(ll v)
{
	v+=sz;
	ll ret=LINF;
	while(v>0)
	{
		ret=min(ret,val[v]);
		v/=2;
	}
	return ret;
}
int main(){
	ll i,j,x,y;
	cin>>n;
	sum[0]=0;
	memset(val,127,sizeof(val));
	for(i=0;i<n;i++)
	{
		cin>>bin[i];
		sum[i+1]=sum[i]+(1-bin[i]);
	}
	cin>>q;
	for(i=0;i<q;i++)
	{
		cin>>x>>y;
		x--;
		y--;
		vt[y].push_back(x);
	}
	for(sz=1;sz<=n;sz*=2);
	for(i=0;i<n;i++)
	{
		update(i,i,pre[i]-sum[i]);
		for(j=0;j<vt[i].size();j++)
		{
			update(vt[i][j]+1,i+1,getans(vt[i][j]));
		}
		pre[i+1]=min(pre[i]+bin[i],getans(i+1)+sum[i+1]);
	}
	cout<<pre[n]<<endl;
	return 0;
}