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].
#    ____                       _   _                _     _ _   
#   / ___| __ _ _ __ __ _      | | | | __ _ _ __ ___| |__ (_) |_ 
#  | |  _ / _` | '__/ _` |_____| |_| |/ _` | '__/ __| '_ \| | __|
#  | |_| | (_| | | | (_| |_____|  _  | (_| | |  \__ \ | | | | |_ 
#   \____|\__,_|_|  \__, |     |_| |_|\__,_|_|  |___/_| |_|_|\__|
#                   |___/                                        

from typing import Counter
import sys
from collections import defaultdict as dd
from math import *

def vinp():
    return map(int,input().split())
def linp():
    return list(map(int,input().split()))
def sinp():
    return input()
def inp():
    return int(input())
def mod(f):
    return f % 1000000007
def pr(*x):
    print(*x)
def finp():
    f=open("input.txt","r")
    f=f.read().split("\n")
    return f
def finp():
    f=open("input.txt","r")
    f=f.read().split("\n")
    return f
def fout():
    return open("output.txt","w")
def fpr(f,x):
    f.write(x+"\n")
def csort(c):
    sorted(c.items(), key=lambda pair: pair[1], reverse=True)
def indc(l,n):
    c={}
    for i in range(n):
        c[l[i]]=c.get(l[i],[])+[i+1]
    return c

if __name__ =="__main__":
    cou=inp()
    for _ in range(cou):
        n = inp()
        f = 1
        for i in range(3,2*n +1):
            f = mod(f * i)
        pr(f)