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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;

class Program
{
    const int M = 1000000007;
    const double eps = 1e-9;
    static int[] dd = { 0, 1, 0, -1, 0 };
    static void Main()
    {
        var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
        var sc = new Scan();
        int n = sc.Int;
        long ans = 0;
        int pre = 0;
        for (int i = 0; i < n; i++)
        {
            int a = sc.Int;
            ans += (a + pre) / 2;
            pre = a == 0 ? 0 : (a + pre) % 2;
        }
        sw.WriteLine(ans);
        sw.Flush();
    }

    static void swap<T>(ref T a, ref T b) { var t = a; a = b; b = t; }
    static void swap<T>(IList<T> a, int i, int j) { var t = a[i]; a[i] = a[j]; a[j] = a[i]; }
    static T Max<T>(params T[] a) { return a.Max(); }
    static T Min<T>(params T[] a) { return a.Min(); }

    static T[] copy<T>(IList<T> a)
    {
        var ret = new T[a.Count];
        for (int i = 0; i < a.Count; i++) ret[i] = a[i];
        return ret;
    }
}
class Scan
{
    public int Int { get { return int.Parse(Str); } }
    public long Long { get { return long.Parse(Str); } }
    public double Double { get { return double.Parse(Str); } }
    public string Str { get { return Console.ReadLine().Trim(); } }
    public int[] IntArr { get { return StrArr.Select(int.Parse).ToArray(); } }
    public int[] IntArrWithSep(char sep) { return Str.Split(sep).Select(int.Parse).ToArray(); }
    public long[] LongArr { get { return StrArr.Select(long.Parse).ToArray(); } }
    public double[] DoubleArr { get { return StrArr.Select(double.Parse).ToArray(); } }
    public string[] StrArr { get { return Str.Split(); } }
    public void Multi(out int a, out int b) { var arr = IntArr; a = arr[0]; b = arr[1]; }
    public void Multi(out int a, out int b, out int c) { var arr = IntArr; a = arr[0]; b = arr[1]; c = arr[2]; }
    public void Multi(out int a, out string b) { var arr = StrArr; a = int.Parse(arr[0]); b = arr[1]; }
    public void Multi(out string a, out int b) { var arr = StrArr; a = arr[0]; b = int.Parse(arr[1]); }
    public void Multi(out int a, out char b) { var arr = StrArr; a = int.Parse(arr[0]); b = arr[1][0]; }
    public void Multi(out char a, out int b) { var arr = StrArr; a = arr[0][0]; b = int.Parse(arr[1]); }
    public void Multi(out long a, out long b) { var arr = LongArr; a = arr[0]; b = arr[1]; }
    public void Multi(out long a, out int b) { var arr = LongArr; a = arr[0]; b = (int)arr[1]; }
    public void Multi(out int a, out long b) { var arr = LongArr; a = (int)arr[0]; b = arr[1]; }
    public void Multi(out string a, out string b) { var arr = StrArr; a = arr[0]; b = arr[1]; }
}
class mymath
{
    static int Mod = 1000000007;
    public void setMod(int m) { Mod = m; }
    public bool isprime(long a)
    {
        if (a < 2) return false;
        for (long i = 2; i * i <= a; i++) if (a % i == 0) return false;
        return true;
    }
    public long[][] powmat(long[][] A, long n)
    {
        var E = new long[A.Length][];
        for (int i = 0; i < A.Length; i++)
        {
            E[i] = new long[A.Length];
            E[i][i] = 1;
        }
        if (n == 0) return E;
        var t = powmat(A, n / 2);
        if ((n & 1) == 0) return mulmat(t, t);
        return mulmat(mulmat(t, t), A);
    }
    public long[] mulmat(long[][] A, long[] x)
    {
        var ans = new long[A.Length];
        for (int i = 0; i < A.Length; i++) for (int j = 0; j < x.Length; j++) ans[i] = (ans[i] + x[j] * A[i][j]) % Mod;
        return ans;
    }
    public long[][] mulmat(long[][] A, long[][] B)
    {
        var ans = new long[A.Length][];
        for (int i = 0; i < A.Length; i++)
        {
            ans[i] = new long[B[0].Length];
            for (int j = 0; j < B[0].Length; j++) for (int k = 0; k < B.Length; k++) ans[i][j] = (ans[i][j] + A[i][k] * B[k][j]) % Mod;
        }
        return ans;
    }
    public long powmod(long a, long b)
    {
        if (a >= Mod) return powmod(a % Mod, b);
        if (a == 0) return 0;
        if (b == 0) return 1;
        var t = powmod(a, b / 2);
        if ((b & 1) == 0) return t * t % Mod;
        return t * t % Mod * a % Mod;
    }
    public long gcd(long a, long b)
    {
        while (b > 0) { var t = a % b; a = b; b = t; }
        return a;
    }
    public long lcm(long a, long b) { return a * (b / gcd(a, b)); }
    public long Comb(int n, int r)
    {
        if (n < 0 || r < 0 || r > n) return 0;
        if (n - r < r) r = n - r;
        if (r == 0) return 1;
        if (r == 1) return n;
        var numerator = new int[r];
        var denominator = new int[r];
        for (int k = 0; k < r; k++)
        {
            numerator[k] = n - r + k + 1;
            denominator[k] = k + 1;
        }
        for (int p = 2; p <= r; p++)
        {
            int pivot = denominator[p - 1];
            if (pivot > 1)
            {
                int offset = (n - r) % p;
                for (int k = p - 1; k < r; k += p)
                {
                    numerator[k - offset] /= pivot;
                    denominator[k] /= pivot;
                }
            }
        }
        long result = 1;
        for (int k = 0; k < r; k++) if (numerator[k] > 1) result = result * numerator[k] % Mod;
        return result;
    }
}