#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;
const int maxn=200010;
struct point
{
	int l,r;
}q[maxn];
int b[maxn];
int s0[maxn],s1[maxn],mn[maxn*4],tag[maxn*4];
int n,Q;
vector<int> a[maxn];

inline bool cmp(const point &x,const point &y)
{
	return x.l<y.l;
}

inline void push_up(int p)
{
	mn[p]=min(mn[p<<1],mn[p<<1|1]);
}

inline void push_down(int p)
{
	if(tag[p])
	{
		tag[p<<1]+=tag[p];
		tag[p<<1|1]+=tag[p];
		mn[p<<1]+=tag[p];
		mn[p<<1|1]+=tag[p];
		tag[p]=0;
	}
}

inline void ins(int p,int l,int r,int x,int der)
{
	push_down(p);
	if(l==r)
	{
		mn[p]=min(mn[p],der);
		return;
	}
	push_down(p);
	int mid=(l+r)>>1;
	if(x<=mid) ins(p<<1,l,mid,x,der);
	else ins(p<<1|1,mid+1,r,x,der);
	push_up(p);
}

inline void add(int p,int l,int r,int L,int R,int der)
{
	if(L>R) return;
	push_down(p);
	if(l>=L && r<=R)
	{
		tag[p]+=der;
		mn[p]+=der;
		return;
	}
	push_down(p);
	int mid=(l+r)>>1;
	if(L<=mid) add(p<<1,l,mid,L,R,der);
	if(R>mid) add(p<<1|1,mid+1,r,L,R,der);
	push_up(p);
}

inline int query(int p,int l,int r,int L,int R)
{
	if(L>R) return 1e9;
	if(l>=L && r<=R)
		return mn[p];
	push_down(p);
	int mid=(l+r)>>1;
	int res=1e9;
	if(L<=mid) res=query(p<<1,l,mid,L,R);
	if(R>mid) res=min(res,query(p<<1|1,mid+1,r,L,R));
	return res;
}

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) 
	{
		scanf("%d",&b[i]);
		if(b[i]==0) s0[i]=1;
		else s1[i]=1;
		s0[i]+=s0[i-1],s1[i]+=s1[i-1];		
	}
	scanf("%d",&Q);
	for(int i=1;i<=Q;i++)
		scanf("%d%d",&q[i].l,&q[i].r);
	sort(q+1,q+Q+1,cmp);
	for(int i=1;i<=Q;i++)
		a[q[i].l].push_back(q[i].r);
	for(int i=1;i<=n*4+4;i++) mn[i]=1e9;
	ins(1,0,n,0,0);
	for(int i=1;i<=n;i++)
	{
		int si=a[i].size();
		for(int nn=0;nn<si;nn++)
		{
			int dd=query(1,0,n,0,a[i][nn]);
			ins(1,0,n,a[i][nn],dd);
		}
		if(s1[i]-s1[i-1]) add(1,0,n,0,i-1,1);
		else add(1,0,n,0,i-1,-1);
	}
	printf("%d",s0[n]+query(1,0,n,0,n));
	return 0;
}

### Prompt

Please create a solution in CPP to the following 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

### Response

```cpp
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
using namespace std;
const int maxn=200010;
struct point
{
	int l,r;
}q[maxn];
int b[maxn];
int s0[maxn],s1[maxn],mn[maxn*4],tag[maxn*4];
int n,Q;
vector<int> a[maxn];

inline bool cmp(const point &x,const point &y)
{
	return x.l<y.l;
}

inline void push_up(int p)
{
	mn[p]=min(mn[p<<1],mn[p<<1|1]);
}

inline void push_down(int p)
{
	if(tag[p])
	{
		tag[p<<1]+=tag[p];
		tag[p<<1|1]+=tag[p];
		mn[p<<1]+=tag[p];
		mn[p<<1|1]+=tag[p];
		tag[p]=0;
	}
}

inline void ins(int p,int l,int r,int x,int der)
{
	push_down(p);
	if(l==r)
	{
		mn[p]=min(mn[p],der);
		return;
	}
	push_down(p);
	int mid=(l+r)>>1;
	if(x<=mid) ins(p<<1,l,mid,x,der);
	else ins(p<<1|1,mid+1,r,x,der);
	push_up(p);
}

inline void add(int p,int l,int r,int L,int R,int der)
{
	if(L>R) return;
	push_down(p);
	if(l>=L && r<=R)
	{
		tag[p]+=der;
		mn[p]+=der;
		return;
	}
	push_down(p);
	int mid=(l+r)>>1;
	if(L<=mid) add(p<<1,l,mid,L,R,der);
	if(R>mid) add(p<<1|1,mid+1,r,L,R,der);
	push_up(p);
}

inline int query(int p,int l,int r,int L,int R)
{
	if(L>R) return 1e9;
	if(l>=L && r<=R)
		return mn[p];
	push_down(p);
	int mid=(l+r)>>1;
	int res=1e9;
	if(L<=mid) res=query(p<<1,l,mid,L,R);
	if(R>mid) res=min(res,query(p<<1|1,mid+1,r,L,R));
	return res;
}

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) 
	{
		scanf("%d",&b[i]);
		if(b[i]==0) s0[i]=1;
		else s1[i]=1;
		s0[i]+=s0[i-1],s1[i]+=s1[i-1];		
	}
	scanf("%d",&Q);
	for(int i=1;i<=Q;i++)
		scanf("%d%d",&q[i].l,&q[i].r);
	sort(q+1,q+Q+1,cmp);
	for(int i=1;i<=Q;i++)
		a[q[i].l].push_back(q[i].r);
	for(int i=1;i<=n*4+4;i++) mn[i]=1e9;
	ins(1,0,n,0,0);
	for(int i=1;i<=n;i++)
	{
		int si=a[i].size();
		for(int nn=0;nn<si;nn++)
		{
			int dd=query(1,0,n,0,a[i][nn]);
			ins(1,0,n,a[i][nn],dd);
		}
		if(s1[i]-s1[i-1]) add(1,0,n,0,i-1,1);
		else add(1,0,n,0,i-1,-1);
	}
	printf("%d",s0[n]+query(1,0,n,0,n));
	return 0;
}

```