Problem:
Score : 400 points

Problem Statement

Snuke has a large collection of cards. Each card has an integer between 1 and N, inclusive, written on it.
He has A_i cards with an integer i.

Two cards can form a pair if the absolute value of the difference of the integers written on them is at most 1.

Snuke wants to create the maximum number of pairs from his cards, on the condition that no card should be used in multiple pairs. Find the maximum number of pairs that he can create.

Constraints

1 ≦ N ≦ 10^5

0 ≦ A_i ≦ 10^9 (1 ≦ i ≦ N)

All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the maximum number of pairs that Snuke can create.

Sample Input 1

4
4
0
3
2

Sample Output 1

4

For example, Snuke can create the following four pairs: (1,1),(1,1),(3,4),(3,4).

Sample Input 2

8
2
0
1
6
0
8
2
1

Sample Output 2

9

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<bits/stdc++.h>
using namespace std;

typedef long long int lli;
typedef unsigned long long int ulli;
typedef pair<int,int> pii;
typedef priority_queue< int, vector< int >, greater< int > >  minHeap;

#define ones(x) __builtin_popcount(x)
#define onesl(x) __builtin_popcountl(x)
#define onesll(x) __builtin_popcountll(x)

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define scn(n) scanf("%d",&n)
#define scnll(n) scanf("%lld",&n)
#define scn2(n,m) scanf("%d%d",&n,&m)
#define scn3(n,m,w) scanf("%d%d%d",&n,&m,&w)
#define scn2ll(n,m) scanf("%lld%lld",&n,&m)
#define atoz(v) v.begin(),v.end()
#define ratoz(v) v.rbegin(),v.rend()
#define Fill(a,v) memset(a,v,sizeof(a))
#define fi first
#define se second
#define inf 1e9
#define pi acos(-1.0)
#define max3(a,b,c) max(a,max(b,c))
#define min3(a,b,c) min(a,min(b,c))
#define mod 1000000007
#define FastIO ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define bug(x) cerr << __LINE__ << " says: " << #x << " = " << (x) << "\n"

int Set(int N,int pos)
{
    return N=N | (1<<pos);
}
int reset(int N,int pos)
{
    return N = N & ~(1<<pos);
}
bool check(int N,int pos)
{
    return (bool)(N & (1<<pos));
}

inline int addmod(lli x,lli y)
{
    return (x%mod + y%mod)%mod;
}
inline int submod(lli x,lli y)
{
    return (x%mod - y%mod + mod)%mod;
}
inline int mulmod(lli x,lli y)
{
    return (x%mod * y%mod)%mod;
}


inline int nextSubMask(int i, int mask)
{
    return (i-1)&mask;   /// returns next  submask
}

template<typename T>
void we_r_done(T mssg)
{
    cout<<mssg;
    exit(0);
}


int main()
{
    ///freopen("output.txt","w",stdout);
  // freopen("input.txt","r",stdin);
    FastIO;

    int n,k;

    while(cin>>n){
        lli a[n+1] , dp[n+1][2];

        for(int i=1; i<=n; i++){
            cin>>a[i];
            dp[i][0] = dp[i][1] = 0;
        }


        dp[1][0] = a[1]/2;

        if(a[1]%2) dp[1][1] = a[1]/2;

        for(int i=2; i<=n; i++){

            dp[i][0] = dp[i-1][0] + a[i]/2;
            if(a[i]%2 && dp[i-1][1]) dp[i][0] = max(dp[i][0], dp[i-1][1] + a[i]/2 + 1);


            if(a[i]==0) continue;

            if(a[i]%2) dp[i][1] = max(dp[i-1][0],dp[i-1][1]) + a[i]/2;
            else{
                if(dp[i-1][1]) dp[i][1] = dp[i-1][1] + (a[i]-1)/2 + 1;
            }


        }

        cout<<max(dp[n][1],dp[n][0])<<endl;
    }

    return 0;
}

///sin and cos expect input in radians not degrees. so use , sin(degrees * pi / 180)
///using bs = bitset<MX>; // how many distinct number can be form?
///sort(atoz(v), [](const data x, const data y){return (x.a==y.a?x.b>y.b : x.a<y.a);});