human
PYTHON3 solution for "CQXYM is counting permutations length of 2n.

A permutation is an array consisting of n distinct integers from 1 to n in arbitrary order. For example, [2,3,1,5,4] is a permutation, but [1,2,2] is not a permutation (2 appears twice in the array) and [1,3,4] is also not a permutation (n=3 but there is 4 in the array).

A permutation p(length of 2n) will be counted only if the number of i satisfying p_i<p_{i+1} is no less than n. For example:

  * Permutation [1, 2, 3, 4] will count, because the number of such i that p_i<p_{i+1} equals 3 (i = 1, i = 2, i = 3).
  * Permutation [3, 2, 1, 4] won't count, because the number of such i that p_i<p_{i+1} equals 1 (i = 3). 


CQXYM wants you to help him to count the number of such permutations modulo 1000000007 (10^9+7).

In addition, [modulo operation](https://en.wikipedia.org/wiki/Modulo_operation) is to get the remainder. For example:

  * 7 mod 3=1, because 7 = 3 ⋅ 2 + 1, 
  * 15 mod 4=3, because 15 = 4 ⋅ 3 + 3. 

Input

The input consists of multiple test cases. 

The first line contains an integer t (t ≥ 1) — the number of test cases. The description of the test cases follows.

Only one line of each test case contains an integer n(1 ≤ n ≤ 10^5).

It is guaranteed that the sum of n over all test cases does not exceed 10^5

Output

For each test case, print the answer in a single line.

Example

Input

4
1
2
9
91234

Output

1
12
830455698
890287984

Note

n=1, there is only one permutation that satisfies the condition: [1,2].

In permutation [1,2], p_1<p_2, and there is one i=1 satisfy the condition. Since 1 ≥ n, this permutation should be counted. In permutation [2,1], p_1>p_2. Because 0<n, this permutation should not be counted.

n=2, there are 12 permutations: [1,2,3,4],[1,2,4,3],[1,3,2,4],[1,3,4,2],[1,4,2,3],[2,1,3,4],[2,3,1,4],[2,3,4,1],[2,4,1,3],[3,1,2,4],[3,4,1,2],[4,1,2,3].":



What is a Python code to print the answer in a single line?
assistant
#Here is Python code to print the answer in a single line.
 from collections import Counter, deque
import math
from random import randint
from bisect import bisect
import sys
import re
from time import time

MOD = 1000000007
MAX = sys.maxsize
MIN = -sys.maxsize

t = 0

class get: 
    def int():
        return list(map(int,input().split()))
    def str():
        return input().split()
    def float():
        return list(map(float,input().split()))
    def map():
        return map(int,input().split())

def sqrt(x):
    return int(math.sqrt(x))+1

def gcd(*args):
    result = args[0]
    for item in args:
        result = math.gcd(result,item)
    return result

def LCM(a,b):
    return (a*b)//(math.gcd(a,b))

def solve():
    global t
    t0 = time()
    # Code is below
    
    n = int(input())
    n = 2*n
    if n == 2:
        print(1)
    else:
        res = 1
        for i in range(3,n+1):
            res = res*i
            res = res%MOD
        print(res)
    
    # Code is above
    t1 = time()
    t += t1 - t0

for _ in range(int(input())):
    solve()
    
#print(f"Time taken = {round(t,3)} seconds")