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 <cstring>
#include <algorithm>
#define MN 262150
using namespace std;
struct node{int x,y;}b[MN];
int t[MN<<1],a[MN];
int MQ,INF,n,m,ans,f0;

inline int read()
{
	int n=0,f=1; char c=getchar();
	while (c<'0' || c>'9') {if(c=='-')f=-1; c=getchar();}
	while (c>='0' && c<='9') {n=n*10+c-'0'; c=getchar();}
	return n*f;
}

inline void grw(int x,int y) {for (x+=MQ;x;x>>=1) if (t[x]>y) t[x]=y; else return;}
inline int gmn(int x,int y)
{
	int sm=INF;
	for (x+=MQ,y+=MQ;x<=y;x>>=1,y>>=1)
	{
		if ( x&1) sm=min(sm,t[x++]);
		if (~y&1) sm=min(sm,t[y--]);
	}
	return sm;
}
bool cmp(const node& a,const node& b) {return a.x<b.x || a.x==b.x && a.y>b.y;}

int main()
{
	register int i,j;
	n=read(); for (i=1;i<=n;++i) a[i]=read(),ans+=(a[i]==0),a[i]=a[i]?1:-1;
	m=read(); for (i=1;i<=m;++i) b[i].x=read(),b[i].y=read();
	sort(b+1,b+m+1,cmp); memset(t,100,sizeof(t)); INF=t[0]; f0=0;
	for (MQ=1;MQ<n;MQ<<=1); --MQ;
	for (i=j=1;i<=n;f0=min(f0+a[i],t[i+MQ]),++i)
		for (;j<=m&&b[j].x==i;++j)
			grw(b[j].y,min(gmn(i,b[j].y),f0));
	printf("%d",ans+f0);
}