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.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;


public class Main {
    private static Scanner sc;
    private static Printer pr;
    static boolean []visited;
    static int []color;
    static int []pow=new int[(int)3e5+1];
    static boolean check=true;
    static ArrayList<Integer>[]list;
    private static long aLong=(long)(Math.pow(10,9)+7);
    static final long div=998244353;
    private static void solve() throws IOException {
        int n=sc.nextInt(),sum=0;
        double []arr=new double[n];
        int  []arrInt=new int[n];
        for (int i=0;i<n;i++)
            arr[i]=sc.nextFloat();
        for (int i=0;i<n;i++)
            arrInt[i]=(int)Math.floor(arr[i]);
        for (int h:arrInt)
            sum+=h;
        //sum = Arrays.stream(arrInt).sum();
        for (int i=0;i<n;i++) {
            //System.out.println("sum:"+sum);
            if (sum == 0) {
                for (int s : arrInt)
                    System.out.println(s);
                System.exit(0);
            } else {
                if (arr[i]-arrInt[i]!=0) {
                    arrInt[i]++;
                    sum++;
                }
            }
        }
        for (int s:arrInt)
            System.out.println(s);
    }
    static int add(int a,int b ){
        if (a+b>=div)
            return (int)(a+b-div);
        return (int)a+b;
    }
    public static int isBipartite(ArrayList<Integer>[]list,int src){
        color[src]=0;
        Queue<Integer>queue=new LinkedList<>();
        int []ans={0,0};
        queue.add(src);
        while (!queue.isEmpty()){
            ans[color[src=queue.poll()]]++;
            for (int v:list[src]){
                if (color[v]==-1){
                    queue.add(v);
                    color[v]=color[src]^1;
                }else if (color[v]==color[src])
                    check=false;
            }
        }
        return add(pow[ans[0]],pow[ans[1]]);
    }
    public static int powerMod(long b, long e){
        long ans=1;
        while (e-->0){
            ans=ans*b%div;
        }
        return (int)ans;
    }
    public static int dfs(int s){
        int ans=1;
        visited[s]=true;
        for (int k:list[s]){
            if (!visited[k]){
                ans+=dfs(k);
            }
        }
        return ans;
    }
    public static int[] radixSort(int[] 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 long []primeFactor(int n){
        long []prime=new long[n+1];
        prime[1]=1;
        for (int i=2;i<=n;i++)
            prime[i]=((i&1)==0)?2:i;
        for (int i=3;i*i<=n;i++){
            if (prime[i]==i){
                for (int j=i*i;j<=n;j+=i){
                    if (prime[j]==j)
                        prime[j]=i;
                }
            }
        }
        return prime;
    }
    public static StringBuilder binaryradix(long number){
        StringBuilder builder=new StringBuilder();
        long remainder;
        while (number!=0) {
            remainder = number % 2;
            number >>= 1;
            builder.append(remainder);
        }
        builder.reverse();
        return builder;
    }
    public static int binarySearch(long[] a, int index,long target) {
            int l = index;
            int h = a.length - 1;
            while (l<=h) {
                int med = l + (h-l)/2;
                if(a[med] - target <= target) {
                    l = med + 1;
                }
                else h = med  - 1;
            }
            return h;
    }
    public static int val(char c){
        return c-'0';
    }
    public static long gcd(long a,long b) {
        if (a == 0) return b;
        return gcd(b % a, a);
    }
        private static class Pair implements Comparable<Pair> {
            long x;
            long y;

            Pair() {
                this.x = 0;
                this.y = 0;
            }

            Pair(long x, long y) {
                this.x = x;
                this.y = y;
            }

            @Override
            public boolean equals(Object obj) {
                if (this == obj) {
                    return true;
                }
                if (obj == null) return false;
                Pair other = (Pair) obj;
                if (this.x == other.x && this.y == other.y) {
                    return true;
                }
                return false;
            }

            @Override
            public int compareTo(Pair other) {
                if (this.x != other.x) return Long.compare(this.x, other.x);
                return Long.compare(this.y*other.x, this.x*other.y);
            }
    }

    public static void main(String[] args) throws IOException {
        sc = new Scanner(System.in);
        pr = new Printer(System.out);
        solve();

        pr.close();
       // sc.close();
    }
    private static class Scanner {
        BufferedReader br;

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

        private boolean isPrintable(int ch) {
            return ch >= '!' && ch <= '~';
        }

        private boolean isCRLF(int ch) {
            return ch == '\n' || ch == '\r' || ch == -1;
        }

        private int nextPrintable() {
            try {
                int ch;
                while (!isPrintable(ch = br.read())) {
                    if (ch == -1) {
                        throw new NoSuchElementException();
                    }
                }

                return ch;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        String next() {
            try {
                int ch = nextPrintable();
                StringBuilder sb = new StringBuilder();
                do {
                    sb.appendCodePoint(ch);
                } while (isPrintable(ch = br.read()));

                return sb.toString();
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        int nextInt() {
            try {
                // parseInt from Integer.parseInt()
                boolean negative = false;
                int res = 0;
                int limit = -Integer.MAX_VALUE;
                int radix = 10;

                int fc = nextPrintable();
                if (fc < '0') {
                    if (fc == '-') {
                        negative = true;
                        limit = Integer.MIN_VALUE;
                    } else if (fc != '+') {
                        throw new NumberFormatException();
                    }
                    fc = br.read();
                }
                int multmin = limit / radix;

                int ch = fc;
                do {
                    int digit = ch - '0';
                    if (digit < 0 || digit >= radix) {
                        throw new NumberFormatException();
                    }
                    if (res < multmin) {
                        throw new NumberFormatException();
                    }
                    res *= radix;
                    if (res < limit + digit) {
                        throw new NumberFormatException();
                    }
                    res -= digit;

                } while (isPrintable(ch = br.read()));

                return negative ? res : -res;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        long nextLong() {
            try {
                // parseLong from Long.parseLong()
                boolean negative = false;
                long res = 0;
                long limit = -Long.MAX_VALUE;
                int radix = 10;

                int fc = nextPrintable();
                if (fc < '0') {
                    if (fc == '-') {
                        negative = true;
                        limit = Long.MIN_VALUE;
                    } else if (fc != '+') {
                        throw new NumberFormatException();
                    }
                    fc = br.read();
                }
                long multmin = limit / radix;

                int ch = fc;
                do {
                    int digit = ch - '0';
                    if (digit < 0 || digit >= radix) {
                        throw new NumberFormatException();
                    }
                    if (res < multmin) {
                        throw new NumberFormatException();
                    }
                    res *= radix;
                    if (res < limit + digit) {
                        throw new NumberFormatException();
                    }
                    res -= digit;

                } while (isPrintable(ch = br.read()));

                return negative ? res : -res;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        float nextFloat() {
            return Float.parseFloat(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            try {
                int ch;
                while (isCRLF(ch = br.read())) {
                    if (ch == -1) {
                        throw new NoSuchElementException();
                    }
                }
                StringBuilder sb = new StringBuilder();
                do {
                    sb.appendCodePoint(ch);
                } while (!isCRLF(ch = br.read()));

                return sb.toString();
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
//				throw new NoSuchElementException();
            }
        }
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

    }

    static class List {
        String Word;
        int length;

        List(String Word, int length) {
            this.Word = Word;
            this.length = length;
        }
    }
    private static class Printer extends PrintWriter {
        Printer(PrintStream out) {
            super(out);
        }
    }
}