A12835 | Print a 1337-string...

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 $1337$ :

1. $337\underline{1}3\underline{3}\underline{3}7\underline{7}$ (you can remove the second and fifth characters);
2. $337\underline{1}\underline{3}3\underline{3}7\underline{7}$ (you can remove the third and fifth characters);
3. $337\underline{1}\underline{3}\underline{3}37\underline{7}$ (you can remove the fourth and fifth characters);
4. $337\underline{1}3\underline{3}\underline{3}\underline{7}7$ (you can remove the second and sixth characters);
5. $337\underline{1}\underline{3}3\underline{3}\underline{7}7$ (you can remove the third and sixth characters);
6. $337\underline{1}\underline{3}\underline{3}3\underline{7}7$ (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.

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 $n_i$ ( $1 \le n_i \le 10^9$ ).

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.