human
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].
Solve the task in PYTHON3.
assistant
#Here is Python code to print the answer in a single line.

from collections import deque
import heapq
from math import sqrt
import operator
from operator import itemgetter
import sys

import copy

 
inf_var = 0
if inf_var == 1:
    inf = open('input.txt', 'r')
else:
    inf = sys.stdin
 
input = inf.readline
# sys.stdout = open('output.txt', 'w')
 
def read_one_int():
    return int(input().rstrip('\n'))

def read_one_float():
    return float(input().rstrip('\n'))
 
 
def read_list_of_ints():
    res = [int(val) for val in (input().rstrip('\n')).split()]
    return res

def read_list_of_ints_zero():
    return [int(val) - 1 for val in (input().rstrip('\n')).split()]

def read_str():
    return input().rstrip()

def bfs(q, graph, dist):
    while len(q):
        cur_v = q.popleft()

        for to in graph[cur_v]:
            if dist[to] == -1:
                dist[to] = dist[cur_v] + 1
                q.append(to)

def sort_vert(n, graph):
    dist = [-1] * n
    q = deque()
    dist[0] = 0

    q.append(0)
    bfs(q, graph, dist)

    vertices = []
    for vert, dist in enumerste(dist):
        verticies.append((dist, vert))

    verticies.sort()
    res = [vert for (dist, vert) in verticies]

    return res

def main():
    # tests = read_one_int()

    # for _ in range(tests):
    #     vert = read_one_int()
    #     v_w = []
    #     for _ in range(n):
    #         v_w.append(read_list_of_ints())

    #     graph = {}
    #     for _ in range(n - 1):
    #         u, v = read_list_of_ints_zero()
    #         if u not in graph:
    #             graph[u] = [v]
    #         else:
    #             graph[u].append(v)
    #         if v not in graph:
    #             graph[v] = [u]
    #         else:
    #             graph[v].append(u)

    #     vertices = sort_vertices(vert, graph)

    #     cache = [[None, None] for _ in range(n)]

    #     def f(prev_v, op):
    #         pass

    tests = read_one_int()
    mod = 10**9 + 7

    def mult(a, b, mod):
        return ((a % mod) * (b % mod)) % mod

    for _ in range(tests):
        n =...