#include <stdio.h>
#include <array>
#include <algorithm>
 
#define FOR(i, a, b) for(int (i) = (a); (i) < (b); ++(i))
#define REP(i, n) FOR(i, 0, n)

using lli = long long int;
constexpr lli inf = 2e18;
constexpr int L = 2e5;
std::array<std::array<lli, 5>, L+1> DP;

int diff(int a, int phase){
    if(phase == 0 or phase == 4) return a;
    if(phase == 2) return (a & 1) ^ 1;
    if(a == 0) return 2;
    return a & 1;
}

int main(void){
    int n; scanf("%d", &n);
    // 0 ... 0 | 偶 ... 偶 ≥ 2 | 奇 ... 奇 | 偶 ... 偶 ≥ 2| 0 ... 0
    DP[0] = {0, 0, 0, 0, 0};
    lli V;
    REP(i, n){
        int a; scanf("%d", &a);
        V = inf;
        for(int j = 0; j < 5; ++j){
            if(V > DP[i][j]) V = DP[i][j];
            DP[i+1][j] = V + diff(a, j);
        }
    }
    lli res = inf; for(int j = 0; j < 5; ++j) if(res > DP[n][j]) res = DP[n][j];
    printf("%lld\n", res);
    return 0;
}
### Prompt

Create a solution in Cpp for the following problem:

Snuke stands on a number line. He has L ears, and he will walk along the line continuously under the following conditions:

* He never visits a point with coordinate less than 0, or a point with coordinate greater than L.
* He starts walking at a point with integer coordinate, and also finishes walking at a point with integer coordinate.
* He only changes direction at a point with integer coordinate.



Each time when Snuke passes a point with coordinate i-0.5, where i is an integer, he put a stone in his i-th ear.

After Snuke finishes walking, Ringo will repeat the following operations in some order so that, for each i, Snuke's i-th ear contains A_i stones:

* Put a stone in one of Snuke's ears.
* Remove a stone from one of Snuke's ears.



Find the minimum number of operations required when Ringo can freely decide how Snuke walks.

Constraints

* 1 \leq L \leq 2\times 10^5
* 0 \leq A_i \leq 10^9(1\leq i\leq L)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


L
A_1
:
A_L


Output

Print the minimum number of operations required when Ringo can freely decide how Snuke walks.

Examples

Input

4
1
0
2
3


Output

1


Input

8
2
0
0
2
1
3
4
1


Output

3


Input

7
314159265
358979323
846264338
327950288
419716939
937510582
0


Output

1

### Response

```cpp
#include <stdio.h>
#include <array>
#include <algorithm>
 
#define FOR(i, a, b) for(int (i) = (a); (i) < (b); ++(i))
#define REP(i, n) FOR(i, 0, n)

using lli = long long int;
constexpr lli inf = 2e18;
constexpr int L = 2e5;
std::array<std::array<lli, 5>, L+1> DP;

int diff(int a, int phase){
    if(phase == 0 or phase == 4) return a;
    if(phase == 2) return (a & 1) ^ 1;
    if(a == 0) return 2;
    return a & 1;
}

int main(void){
    int n; scanf("%d", &n);
    // 0 ... 0 | 偶 ... 偶 ≥ 2 | 奇 ... 奇 | 偶 ... 偶 ≥ 2| 0 ... 0
    DP[0] = {0, 0, 0, 0, 0};
    lli V;
    REP(i, n){
        int a; scanf("%d", &a);
        V = inf;
        for(int j = 0; j < 5; ++j){
            if(V > DP[i][j]) V = DP[i][j];
            DP[i+1][j] = V + diff(a, j);
        }
    }
    lli res = inf; for(int j = 0; j < 5; ++j) if(res > DP[n][j]) res = DP[n][j];
    printf("%lld\n", res);
    return 0;
}
```