Ehab and the Expected GCD Problem

Let's define a function f(p) on a permutation p as follows. Let g_i be the greatest common divisor (GCD) of elements p_1, p_2, ..., p_i (in other words, it is the GCD of the prefix of length i). Then f(p) is the number of distinct elements among g_1, g_2, ..., g_n.

Let f_{max}(n) be the maximum value of f(p) among all permutations p of integers 1, 2, ..., n.

Given an integers n, count the number of permutations p of integers 1, 2, ..., n, such that f(p) is equal to f_{max}(n). Since the answer may be large, print the remainder of its division by 1000 000 007 = 10^9 + 7.

Input

The only line contains the integer n (2 ≤ n ≤ 10^6) — the length of the permutations.

Output

The only line should contain your answer modulo 10^9+7.

Examples

Input

2

Output

1

Input

3

Output

4

Input

6

Output

120

Note

Consider the second example: these are the permutations of length 3:

• [1,2,3], f(p)=1.
• [1,3,2], f(p)=1.
• [2,1,3], f(p)=2.
• [2,3,1], f(p)=2.
• [3,1,2], f(p)=2.
• [3,2,1], f(p)=2.

The maximum value f_{max}(3) = 2, and there are 4 permutations p such that f(p)=2.

inputFormat

Input

The only line contains the integer n (2 ≤ n ≤ 10^6) — the length of the permutations.

outputFormat

Output

The only line should contain your answer modulo 10^9+7.

Examples

Input

2

Output

1

Input

3

Output

4

Input

6

Output

120

Note

Consider the second example: these are the permutations of length 3:

• [1,2,3], f(p)=1.
• [1,3,2], f(p)=1.
• [2,1,3], f(p)=2.
• [2,3,1], f(p)=2.
• [3,1,2], f(p)=2.
• [3,2,1], f(p)=2.

The maximum value f_{max}(3) = 2, and there are 4 permutations p such that f(p)=2.

样例

2

1

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