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 javafx.util.Pair;
import sun.net.www.content.text.Generic;

import static java.lang.Double.parseDouble;
import static java.lang.Integer.parseInt;
import static java.lang.Integer.reverse;
import static java.lang.Long.parseLong;
import static java.lang.Math.abs;
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.System.exit;
import static java.util.Comparator.comparingInt;
import static java.util.Map.Entry.comparingByValue;
import static java.util.stream.Collectors.toMap;

import java.io.*;
import java.lang.reflect.Array;
import java.lang.reflect.ParameterizedType;
import java.lang.reflect.Type;
import java.util.*;

public class Solution {

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer tok;

    void solve() throws Exception {
        int n = nextInt();
        long sum = 0;
        int a[] = new int[n], b[] = new int[n];
        for(int i = 0; i < n; i++) {
            double d = nextDouble();
            a[i] = b[i] = (int)Math.floor(d);
            if(d != (int)d) b[i]++;
            sum += a[i];
        }
        for(int i = 0; i < n; i++) {
            if(sum < 0 && a[i] != b[i]) {
                out.println(b[i]);
                sum++;
            } else out.println(a[i]);
        }
    }

    // call it like this: lower_bound(a, x + 1) ( /!\ + 1 )
    public static int lower_bound(int[] a, int v) {
        int low = -1, high = a.length;
        while (high - low > 1) {
            int h = high + low >>> 1;
            if (a[h] >= v) {
                high = h;
            } else {
                low = h;
            }
        }
        return high;
    }

    private String getFraction(int a, int b) {
        assert b != 0;
        String sign = (a > 0 && b > 0) || (a < 0) && (b < 0) ? "+" : "-";
        a = abs(a);
        b = abs(b);
        int gcd = gcd(a, b);
        return sign + (a / gcd) + "/" + (b / gcd);
    }

    private int gcd(int a, int b) {
        while (b > 0) {
            int temp = b;
            b = a % b;
            a = temp;
        }
        return a;
    }

    private int lcm(int a, int b) {
        return a * (b / gcd(a, b));
    }

    public static int[] radixSort(int[] f) {
        if (f.length < 100) {
            Arrays.sort(f);
            return f;
        }
        int[] to = new int[f.length];
        {
            int[] b = new int[65537];
            for (int i = 0; i < f.length; i++) b[1 + (f[i] & 0xffff)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < f.length; i++) to[b[f[i] & 0xffff]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        {
            int[] b = new int[65537];
            for (int i = 0; i < f.length; i++) b[1 + (f[i] >>> 16)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < f.length; i++) to[b[f[i] >>> 16]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        return f;
    }

    public static boolean nextPermutation(int[] a) {
        int n = a.length;
        int i;
        for (i = n - 2; i >= 0 && a[i] >= a[i + 1]; i--) ;
        if (i == -1)
            return false;
        int j;
        for (j = i + 1; j < n && a[i] < a[j]; j++) ;
        int d = a[i];
        a[i] = a[j - 1];
        a[j - 1] = d;
        for (int p = i + 1, q = n - 1; p < q; p++, q--) {
            d = a[p];
            a[p] = a[q];
            a[q] = d;
        }
        return true;
    }

    void print(Object x) {
        out.print(String.valueOf(x));
        out.flush();
    }

    void println(Object x) {
        out.println(String.valueOf(x));
        out.flush();
    }

    // for Map with custom key/value, override toString in your custom class
    void printMap(Map map) {
        if (map.keySet().size() == 0) return;
        Object firstValue = map.keySet().iterator().next();
        if (map.get(firstValue) instanceof Queue || map.get(firstValue) instanceof List) {
            for (Object key : map.keySet()) {
                out.print(String.valueOf(key) + ": ");
                Collection values = (Collection) map.get(key);
                for (Object value : values) out.print(String.valueOf(value) + " ");
                out.println();
            }
        } else if (map.get(firstValue).getClass().isArray()) {
            for (Object key : map.keySet()) {
                out.print(String.valueOf(key) + ": ");
                Object[] values = (Object[]) map.get(key);
                for (Object value : values) out.print(String.valueOf(value) + " ");
                out.println();
            }
        } else {
            for (Object key : map.keySet()) {
                out.println(String.valueOf(key) + ": " + map.get(key));
            }
        }
    }

    private int[] na(int n) throws IOException {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = nextInt();
        return a;
    }

    private long[] nal(int n) throws IOException {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = nextLong();
        return a;
    }

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

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

    double nextDouble() throws IOException {
        return parseDouble(next());
    }

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

    public static void main(String[] args) throws Exception {
        try {
            boolean isLocal = false;
            if (isLocal) {
                in = new BufferedReader(new FileReader("mr_x.txt"));
                out = new PrintWriter(new BufferedWriter(new FileWriter("solution.out")));
            } else {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(new OutputStreamWriter(System.out));
            }

            //long lStartTime = System.currentTimeMillis();
            new Solution().solve();
            //long lEndTime = System.currentTimeMillis();
            //out.println("Elapsed time in seconds: " + (double)(lEndTime - lStartTime) / 1000.0);
            in.close();
            out.close();
        } catch (Throwable e) {
            e.printStackTrace();
            exit(1);
        }
    }
}