Problem: Vus the Cossack has n real numbers a_i. It is known that the sum of all numbers is equal to 0. He wants to choose a sequence b the size of which is n such that the sum of all numbers is 0 and each b_i is either ⌊ a_i ⌋ or ⌈ a_i ⌉. In other words, b_i equals a_i rounded up or down. It is not necessary to round to the nearest integer.

For example, if a = [4.58413, 1.22491, -2.10517, -3.70387], then b can be equal, for example, to [4, 2, -2, -4]. 

Note that if a_i is an integer, then there is no difference between ⌊ a_i ⌋ and ⌈ a_i ⌉, b_i will always be equal to a_i.

Help Vus the Cossack find such sequence!

Input

The first line contains one integer n (1 ≤ n ≤ 10^5) — the number of numbers.

Each of the next n lines contains one real number a_i (|a_i| < 10^5). It is guaranteed that each a_i has exactly 5 digits after the decimal point. It is guaranteed that the sum of all the numbers is equal to 0.

Output

In each of the next n lines, print one integer b_i. For each i, |a_i-b_i|<1 must be met.

If there are multiple answers, print any.

Examples

Input


4
4.58413
1.22491
-2.10517
-3.70387


Output


4
2
-2
-4


Input


5
-6.32509
3.30066
-0.93878
2.00000
1.96321


Output


-6
3
-1
2
2

Note

The first example is explained in the legend.

In the second example, we can round the first and fifth numbers up, and the second and third numbers down. We can round the fourth number neither up, nor down.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;

import java.lang.management.MemoryType;
import java.math.BigInteger;
import java.util.*;


public class Main {
    static final int INF = Integer.MAX_VALUE;

    static int mergeSort(int[] a,int [] c, int begin, int end)
    {
        int inversion=0;
        if(begin < end)
        {
            inversion=0;
            int mid = (begin + end) >>1;
            inversion+= mergeSort(a,c, begin, mid);
            inversion+=mergeSort(a, c,mid + 1, end);
            inversion+=merge(a,c, begin, mid, end);
        }
        return inversion;
    }


    static int  merge(int[] a,int[]c, int b, int mid, int e)
    {
        int n1 = mid - b + 1;
        int n2 = e - mid;
        int[] L = new int[n1+1], R = new int[n2+1];
        int[] L1 = new int[n1+1], R1 = new int[n2+1];


        //inversion
        int inversion=0;

        for(int i = 0; i < n1; i++) {
            L[i] = a[b + i];
            L1[i] = c[b + i];
          //  L2[i] = w[b + i];
        }
        for(int i = 0; i < n2; i++)  {
            R[i] = a[mid + 1 + i];
            R1[i] = c[mid + 1 + i];
            //R2[i] = w[mid + 1 + i];
        }
        L[n1] = R[n2] = INF;

        for(int k = b, i = 0, j = 0; k <= e; k++)
            if(L[i] <= R[j]){
                a[k] = L[i];
                c[k] = L1[i];
                ++i;
              //  w[k]=L2[i++];
            }

            else
            {
                a[k] = R[j];
                c[k] = R1[j];
               //w[k] = R2[j++];
                ++j;

                inversion=inversion+(n1-i);

            }
        return inversion;

    }

    static int []c;
    static int[] v;
    static long gcd(long a, long b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    public static void main (String[]args) throws IOException {
        Scanner in = new Scanner(System.in);
        try(PrintWriter or = new PrintWriter(System.out)){
            int n = in.nextInt();
            double[] a = new double[n];
            int[] b = new int[n];
            //System.out.println(n + " " + in.next());
            int sum = 0;
            for(int i = 0;i<n;++i){
                a[i] = in.nextDouble();
                b[i] = (int)a[i];
                sum += b[i];
            }
            //System.out.println(sum);
            StringBuilder res = new StringBuilder();
            for(int i = 0;i<n && sum != 0;++i){
                if(sum > 0 && a[i]<0 && Math.abs(a[i]-b[i])>=1e-5) {
                    b[i]--;
                    sum--;
                } else if(sum < 0 && a[i]>0 && Math.abs(a[i]-b[i])>=1e-5){
                    b[i]++;
                    sum++;
                }
            }
            for(int i = 0;i<n;++i){
                res.append(b[i] + "\n");
            }
            System.out.println(res);

















        }



    }
    static int getlen(int r,int l,int a){
        return (r-l+1+1)/(a+1);
    }
    static int check(Pair[] a, int c) {
        ArrayList<Integer> trouble = new ArrayList<>();
        int n = a.length;
        for (int i = 0; i < n - 1; i++)
            if (a[i + 1].val - a[i].val != c) trouble.add(i);
        if (trouble.size() == 0) return a[0].idx + 1;
        if (trouble.size() == 1) {
            int idx = trouble.get(0);
            if (idx == 0) return a[idx].idx + 1;
            if (idx == n - 2) return a[idx + 1].idx + 1;
            if (a[idx].val == a[idx + 1].val) return a[idx].idx + 1;
        }
        if (trouble.size() == 2) {
            int one = trouble.get(0);
            int two = trouble.get(1);
            if (one + 1 == two && a[two + 1].val - a[one].val == c) return a[two].idx + 1;
        }
        return -1;
    }

    static class Scanner {

        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(br.readLine());
            }
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++) {
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec) {
                        f *= 10;
                    }
                }
            }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

    }
}

 class Pair implements Comparable<Pair> {
    int idx, val;

    public Pair(int idx, int val) {
        this.idx = idx;
        this.val = val;
    }

    @Override
    public int compareTo(Pair o) {
        return val - o.val;
    }


}

class Tempo {

    int num;
   int index;

    public Tempo(int num, int index) {
        this.num = num;
        this.index = index;
    }
}