Problem: Fibonacci numbers have the following form:

F1 = 1,  F2 = 2,  Fi = Fi - 1 + Fi - 2, i > 2.

Let's consider some non-empty set S = {s1, s2, ..., sk}, consisting of different Fibonacci numbers. Let's find the sum of values of this set's elements:

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Let's call the set S a number n's decomposition into Fibonacci sum. 

It's easy to see that several numbers have several decompositions into Fibonacci sum. For example, for 13 we have 13, 5 + 8, 2 + 3 + 8 — three decompositions, and for 16: 3 + 13, 1 + 2 + 13, 3 + 5 + 8, 1 + 2 + 5 + 8 — four decompositions.

By the given number n determine the number of its possible different decompositions into Fibonacci sum.

Input

The first line contains an integer t — the number of tests (1 ≤ t ≤ 105). Each of the following t lines contains one test.

Each test is an integer n (1 ≤ n ≤ 1018).

Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specificator.

Output

For each input data test print a single number on a single line — the answer to the problem.

Examples

Input

2
13
16


Output

3
4

Note

Two decompositions are different if there exists a number that is contained in the first decomposition, but is not contained in the second one. Decompositions that differ only in the order of summands are considered equal.

Solution (in JAVA):

Solution:
/**
 * DA-IICT
 * Author : Savaliya Sagar
 */
import java.io.*;
import java.math.*;
import java.util.*;

public class Fibonacci_Decomposition {

	public static int mod = 1000000007;
	public static FasterScanner in = new FasterScanner();
	public static PrintWriter o = new PrintWriter(System.out);
	static long fib[] = new long[90];
	public static void main(String[] args) {
		new Thread(null, new Runnable() {
			public void run() {
				try {
					Solve();
					o.close();
				} catch (Exception e) {
					e.printStackTrace();
				}
			}
		}, "1", 1 << 26).start();
	}

	public static void Solve() {
		fib[0] = 1;
		fib[1] = 1;
		for(int i=2;i<90;i++){
			fib[i] = fib[i-1]+fib[i-2];
		}
		int t = in.nextInt();
		while(t-->0){
			long n = in.nextLong();
			ArrayList<Integer> s = new ArrayList<Integer>();
			for(int i=89;i>=1;i--){
				if(n-fib[i]>=0){
					s.add(i);
					n = n - fib[i];
				}
			}
			ArrayList<Integer> rs = new ArrayList<>();
			rs.add(0);
			while(!s.isEmpty()){
				rs.add(s.remove(s.size()-1));
			}
			int dp[][] = new int[rs.size()][2];
			dp[0][0] = 1;
			dp[0][1] = 0;
			for(int i=1;i<rs.size();i++){
				dp[i][0] = dp[i-1][0] + dp[i-1][1];
				dp[i][1] = dp[i-1][0]*((rs.get(i)-rs.get(i-1)-1)/2) + dp[i-1][1]*((rs.get(i)-rs.get(i-1))/2);
			}
//			debug(rs);
//			debug(dp);
			o.println(dp[rs.size()-1][0]+dp[rs.size()-1][1]);
		}
	}

	public static long gcd(long n1, long n2) {
		long r;
		while (n2 != 0) {
			r = n1 % n2;
			n1 = n2;
			n2 = r;
		}
		return n1;
	}

	public static long pow(long x, long n, long mod) {
		long res = 1;
		x %= mod;
		while (n > 0) {
			if (n % 2 == 1) {
				res = (res * x) % mod;
			}
			x = (x * x) % mod;
			n /= 2;
		}
		return res;
	}

	public static void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}

	static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

		public long[] nextLongArray(int n) {
			long a[] = new long[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextLong();
			}
			return a;
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

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