Round #446(Div 2)

Hands that shed innocent blood!

There are n guilty people in a line, the i-th of them holds a claw with length Li. The bell rings and every person kills some of people in front of him. All people kill others at the same time. Namely, the i-th person kills the j-th person if and only if j < i and j ≥ i - Li.

You are given lengths of the claws. You need to find the total number of alive people after the bell rings.

Input

The first line contains one integer n (1 ≤ n ≤ 106) — the number of guilty people.

Second line contains n space-separated integers L1, L2, ..., Ln (0 ≤ Li ≤ 109), where Li is the length of the i-th person's claw.

Output

Print one integer — the total number of alive people after the bell rings.

Examples

input

4
0 1 0 10

output

input

2
0 0

output

input

10
1 1 3 0 0 0 2 1 0 3

output

Note

In first sample the last person kills everyone in front of him.

题意：前面一个人如果站在了后面一个人的武器长度范围内，就会被杀死

也可以理解为，每个人站在对应下标位置，每个人因为得到自己数组下标及对应值的差，可以往前跑差值距离，前面的人也可以杀死更前面的人，更新可向前的人头数

#include <bits/stdc++.h>
#include <stdio.h>
#include <cstdlib>
#include <algorithm>
using namespace std;
#define lowbit(x) (x&(-x))
#define max(x,y) (x>=y?x:y)
#define min(x,y) (x<=y?x:y)
#define MAX 100000000000000000
#define MOD 1000000007
#define pi acos(-1.0)
#define ei exp(1)
#define PI 3.1415926535897932384626433832
typedef long long ll;
#define INF 0x3f3f3f3f
#define mem(a) memset(a,0,sizeof(a))
const int maxn=1e6+10;
const long long  mod=9932107;
int a[maxn];
int maxx=INF;
int solve(int n){
    int ans=0;
    for(int i=n-1;i>=0;i--){
        if(i>=maxx) ans++;
        maxx=min(maxx,i-a[i]);
    }
    return ans;
}
int main(){
    int n;
    mem(a);
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        ll x;
        scanf("%d",&x);
        a[i]=x;
    }
    int a=solve(n);
    printf("%d
",n-a);
    return 0;
}

You have an array a with length n, you can perform operations. Each operation is like this: choose two adjacent elements from a, say xand y, and replace one of them with gcd(x, y), where gcd denotes the greatest common divisor.

What is the minimum number of operations you need to make all of the elements equal to 1?

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2000) — the number of elements in the array.

The second line contains n space separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the elements of the array.

Output

Print -1, if it is impossible to turn all numbers to 1. Otherwise, print the minimum number of operations needed to make all numbers equal to 1.

Examples

input

5
2 2 3 4 6

output

input

4
2 4 6 8

output

-1

input

3
2 6 9

output

Note

In the first sample you can turn all numbers to 1 using the following 5 moves:

[2, 2, 3, 4, 6].
[2, 1, 3, 4, 6]
[2, 1, 3, 1, 6]
[2, 1, 1, 1, 6]
[1, 1, 1, 1, 6]
[1, 1, 1, 1, 1]

We can prove that in this case it is not possible to make all numbers one using less than 5 moves.

首先可以先判断，如果数组中本来就有1的话，那么只要操作n-1次就可以满足题意

然后判断连续gcd都没有得到1那就没有希望了，就是-1；

最后就是隔了一段距离的情况，那就不断去寻找满足1最小子区间

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 const int maxn=2000;
 4 int a[maxn+5];
 5 int n;
 6 int ans=0;
 7 int gcd(int a,int b){
 8     return b==0?a:gcd(b,a%b);
 9 }
10 int main(){
11     scanf("%d",&n);
12     memset(a,0,sizeof(a));
13     for(int i=1;i<=n;i++){
14         scanf("%d",&a[i]);
15         if(a[i]==1) ++ans;
16     }
17     if(ans!=0) {
18         printf("%d
",n-ans);
19         return 0;
20     }
21     ans=n+1;
22     for(int i=1;i<=n;i++){
23         int sum=a[i];
24         for(int j=i-1;j>=1;j--){
25             sum=gcd(sum,a[j]);
26             if(sum==1){
27                 ans=min(ans,i-j);
28             }
29         }
30     }
31     if(ans==n+1){
32         printf("-1
");
33         return 0;
34     }
35     else printf("%d
",ans+n-1);
36     return 0;
37 }