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: Wrong Answer)

#include<iostream>
#include<math.h>
#include<vector>
#include<string>
#include<stack>
#include<queue>
#include<map>
#include<algorithm>
#include<bitset>
#include <climits>
using namespace std;
#define _GLIBCXX_DEBUG
#define pq priority_queue
#define mp make_pair
#define pb push_back
#define ff first
#define ss second
#define vit vector<lint>::iterator
#define all(x) (x).begin(),(x).end()
#define rep(x) for(int i = 0;i < (x);i++)
#define repj(x) for(int j = 0;j < (x);j++)
#define REP(i,x) for(int (i) = 0;(i) < (x);(i)++)
#define rrep(x) for(int i = (x);i >= 0;i--)
#define mins(x,y) x = min(x,y)
#define maxs(x,y) x = max(x,y)
#define mod 1000000007
#define graph_set(n) struct edge{int to,int cost;} vector<edge> G((n))
#define dump(x)  cerr << #x << " = " << (x) << endl;
#define debug(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#define range(x,y) ((x) >= 0 && (x) < h && (y) >= 0 && (y) < w)
#define pyes cout << "Yes" << endl
#define pno cout << "No" << endl
#define fin return 0
typedef vector<long long> vi;
typedef vector<pair<long long, long long>> vp;
typedef vector<vector<long long>> vvi;
typedef pair<long long, long long> pi;
typedef long long lint;
typedef long long ll;
lint qp(int a, ll b) { int ans = 1; do { if (b & 1)ans = 1ll * ans*a; a = 1ll * a*a; } while (b >>= 1); return ans; }
lint qp(int a, ll b, int mo) { int ans = 1; do { if (b & 1)ans = 1ll * ans*a%mo; a = 1ll * a*a%mo; } while (b >>= 1); return ans; }
lint gcd(int a, int b) { return b ? gcd(b, a%b) : a; }
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
long long INF = 1e19;

//////////////////////////////////////////////////////////////////////
ll pr(ll a, ll b) {
	ll s = min(a, b);ll l = max(a, b);
	return s + (l - s) / 2;
}
ll dp[100010];
int main() {
	ll n; cin >> n;
	vi a(n); rep(n)cin >> a[i];
	dp[0] = a[0] / 2;
	if (n == 1) {
		cout << dp[0] << endl; fin;
	}
	dp[1] = pr(a[1], a[0]);
	if (n == 2) {
		cout << dp[1] << endl; fin;
	}
	for (int i = 2; i < n; i++) {
		dp[i] = max(dp[i - 1] + a[i] / 2, dp[i - 2] + pr(a[i], a[i - 1]));
	}
	cout << dp[n - 1] << endl;
	fin;

}