#include<bits/stdc++.h>
using namespace std;
const int maxn=200005;
int mn[maxn<<2];
void Push_up(int id)
{
    mn[id]=min(mn[id<<1],mn[id<<1|1]);
}
void build(int id,int l,int r)
{
    mn[id]=100000000;
    if(l==r) {
        if(l==0) mn[id]=0;
        return;
    }
    int mid=(l+r)>>1;
    build(id<<1,l,mid);
    build(id<<1|1,mid+1,r);
    Push_up(id);
}
void up(int id,int l,int r,int v,int w)
{
    if(l==r){
        mn[id]=min(mn[id],w);
        return;
    }
    int mid=(l+r)>>1;
    if(v<=mid) up(id<<1,l,mid,v,w);
    else up(id<<1|1,mid+1,r,v,w);
    Push_up(id);
}
int q(int id,int l,int r,int tl,int tr)
{
    if(l==tl&&r==tr)
    {
        return mn[id];
    }
    int mid=(l+r)>>1;
    if(tr<=mid) return q(id<<1,l,mid,tl,tr);
    else if(tl>mid) return q(id<<1|1,mid+1,r,tl,tr);
    else return min(q(id<<1,l,mid,tl,mid),q(id<<1|1,mid+1,r,mid+1,tr));
}
int b[maxn];
struct SHIT
{
    int l,r;
}shit[maxn];
bool cmp(SHIT a,SHIT b)
{
    if(a.l!=b.l) return a.l<b.l;
    return a.r>b.r;
}
void Debug(int id,int l,int r)
{
    if(l==r){
        printf("%d ",mn[id]);
        return;
    }
    int mid=(l+r)>>1;
    Debug(id<<1,l,mid);
    Debug(id<<1|1,mid+1,r);
}
int main()
{
    int n;
    scanf("%d",&n);
    int ans=0;
    for(int i=1;i<=n;i++)
    {
        scanf("%d",&b[i]);
        ans+=(1-b[i]);
    }
    int Q;
    scanf("%d",&Q);
    build(1,0,n);
    for(int i=1;i<=Q;i++)
    {
        scanf("%d%d",&shit[i].l,&shit[i].r);
    }
    sort(shit+1,shit+1+Q,cmp);
    for(int i=1,j=1;i<=n;i++)
    {
        int tmp=q(1,0,n,i-1,i-1);
        while(j<=Q&&shit[j].l==i){
           //printf("%d %d\n",shit[j].l,shit[j].r);
            up(1,0,n,shit[j].r,q(1,0,n,i-1,shit[j].r));
            j++;
        }
        up(1,0,n,i,tmp+(b[i]==1?1:-1));
        //Debug(1,0,n);
        //printf("\n");

    }
    ans+=q(1,0,n,n,n);
    printf("%d\n",ans);
    return 0;
}

### Prompt

In cpp, your task is to solve 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<bits/stdc++.h>
using namespace std;
const int maxn=200005;
int mn[maxn<<2];
void Push_up(int id)
{
    mn[id]=min(mn[id<<1],mn[id<<1|1]);
}
void build(int id,int l,int r)
{
    mn[id]=100000000;
    if(l==r) {
        if(l==0) mn[id]=0;
        return;
    }
    int mid=(l+r)>>1;
    build(id<<1,l,mid);
    build(id<<1|1,mid+1,r);
    Push_up(id);
}
void up(int id,int l,int r,int v,int w)
{
    if(l==r){
        mn[id]=min(mn[id],w);
        return;
    }
    int mid=(l+r)>>1;
    if(v<=mid) up(id<<1,l,mid,v,w);
    else up(id<<1|1,mid+1,r,v,w);
    Push_up(id);
}
int q(int id,int l,int r,int tl,int tr)
{
    if(l==tl&&r==tr)
    {
        return mn[id];
    }
    int mid=(l+r)>>1;
    if(tr<=mid) return q(id<<1,l,mid,tl,tr);
    else if(tl>mid) return q(id<<1|1,mid+1,r,tl,tr);
    else return min(q(id<<1,l,mid,tl,mid),q(id<<1|1,mid+1,r,mid+1,tr));
}
int b[maxn];
struct SHIT
{
    int l,r;
}shit[maxn];
bool cmp(SHIT a,SHIT b)
{
    if(a.l!=b.l) return a.l<b.l;
    return a.r>b.r;
}
void Debug(int id,int l,int r)
{
    if(l==r){
        printf("%d ",mn[id]);
        return;
    }
    int mid=(l+r)>>1;
    Debug(id<<1,l,mid);
    Debug(id<<1|1,mid+1,r);
}
int main()
{
    int n;
    scanf("%d",&n);
    int ans=0;
    for(int i=1;i<=n;i++)
    {
        scanf("%d",&b[i]);
        ans+=(1-b[i]);
    }
    int Q;
    scanf("%d",&Q);
    build(1,0,n);
    for(int i=1;i<=Q;i++)
    {
        scanf("%d%d",&shit[i].l,&shit[i].r);
    }
    sort(shit+1,shit+1+Q,cmp);
    for(int i=1,j=1;i<=n;i++)
    {
        int tmp=q(1,0,n,i-1,i-1);
        while(j<=Q&&shit[j].l==i){
           //printf("%d %d\n",shit[j].l,shit[j].r);
            up(1,0,n,shit[j].r,q(1,0,n,i-1,shit[j].r));
            j++;
        }
        up(1,0,n,i,tmp+(b[i]==1?1:-1));
        //Debug(1,0,n);
        //printf("\n");

    }
    ans+=q(1,0,n,n,n);
    printf("%d\n",ans);
    return 0;
}

```