Print a 1337-string...

1000ms

262144K

Description:

The subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.

You are given an integer $$$n$$$.

You have to find a sequence $$$s$$$ consisting of digits $$$\{1, 3, 7\}$$$ such that it has exactly $$$n$$$ subsequences equal to $$$1337$$$.

For example, sequence $$$337133377$$$ has $$$6$$$ subsequences equal to $$$1337$$$:

$$$337\underline{1}3\underline{3}\underline{3}7\underline{7}$$$ (you can remove the second and fifth characters);
$$$337\underline{1}\underline{3}3\underline{3}7\underline{7}$$$ (you can remove the third and fifth characters);
$$$337\underline{1}\underline{3}\underline{3}37\underline{7}$$$ (you can remove the fourth and fifth characters);
$$$337\underline{1}3\underline{3}\underline{3}\underline{7}7$$$ (you can remove the second and sixth characters);
$$$337\underline{1}\underline{3}3\underline{3}\underline{7}7$$$ (you can remove the third and sixth characters);
$$$337\underline{1}\underline{3}\underline{3}3\underline{7}7$$$ (you can remove the fourth and sixth characters).

Note that the length of the sequence $$$s$$$ must not exceed $$$10^5$$$.

You have to answer $$$t$$$ independent queries.

Input:

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10$$$) — the number of queries.

Next $$$t$$$ lines contains a description of queries: the $$$i$$$-th line contains one integer $$$n_i$$$ ($$$1 \le n_i \le 10^9$$$).

Output:

For the $$$i$$$-th query print one string $$$s_i$$$ ($$$1 \le |s_i| \le 10^5$$$) consisting of digits $$$\{1, 3, 7\}$$$. String $$$s_i$$$ must have exactly $$$n_i$$$ subsequences $$$1337$$$. If there are multiple such strings, print any of them.

Sample Input:

2
6
1

Sample Output:

113337
1337

Informação

Provedor Codeforces

Código CF1202D