Ayoub had an array a of integers of size n and this array had two interesting properties: 

  * All the integers in the array were between l and r (inclusive). 
  * The sum of all the elements was divisible by 3. 



Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array. 

Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.

Input

The first and only line contains three integers n, l and r (1 ≤ n ≤ 2 ⋅ 10^5 , 1 ≤ l ≤ r ≤ 10^9) — the size of the lost array and the range of numbers in the array.

Output

Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.

Examples

Input


2 1 3


Output


3


Input


3 2 2


Output


1


Input


9 9 99


Output


711426616

Note

In the first example, the possible arrays are : [1,2], [2,1], [3, 3].

In the second example, the only possible array is [2, 2, 2].
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.StringTokenizer;


public class C {

    private static StringTokenizer st;
    private static BufferedReader br;
    private static PrintWriter pw;

    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

        int n = nextInt();
        int L = nextInt();
        int R = nextInt();

        int mod = 1_000_000_007;


        int cnt = (R - L + 1);
        long[]s = new long[3];
        s[0] = cnt / 3;
        s[1] = cnt / 3;
        s[2] = cnt / 3;
        if (cnt % 3 > 0) {
            if (L % 3 ==0) {
                s[0] ++;
                if (R % 3 == 1) {
                    s[1]++;
                }
            }
            if (L % 3 == 1) {
                s[1]++;
                if (R % 3 == 2) {
                    s[2]++;
                }
            }
            if (L % 3==2) {
                s[2]++;
                if (R % 3 == 0) {
                    s[0]++;
                }
            }
        }

        long[]dp1 = new long[3];
        long[]dp2 = new long[3];
        dp1[0] = 1;
        for (int i = 1; i <= n; i++) {
            Arrays.fill(dp2, 0);
            for (int j1 = 0; j1 < 3; j1++) {
                for (int j2 = 0; j2 < 3; j2++) {
                    dp2[(j1+j2) % 3] = (dp2[(j1+j2) % 3] + dp1[j1] * s[j2]) % mod;
                }
            }
            dp1 = dp2.clone();
        }

        System.out.println(dp1[0]);

        pw.close();
    }

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

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

    private static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

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

}