National Olympiad in Informatics, China, 1999

Given 7 positive integers ~N~, ~A_0~, ~B_0~, ~L_0~, ~A_1~, ~B_1~, ~L_1~, determine a 01 sequence ~S = s_1 s_2 \dots s_i \dots s_N~, such that:

1. ~s_i = 0~ or ~s_i = 1~ for ~1 \le i \le N~.
2. For any of ~S~'s length ~L_0~ consecutive subsequence ~s_j s_{j+1} \dots s_{j+L_0-1}~, the number of 0's must be between ~A_0~ and ~B_0~, inclusive.
3. For any of ~S~'s length ~L_1~ consecutive subsequence ~s_j s_{j+1} \dots s_{j+L_1-1}~, the number of 1's must be between ~A_1~ and ~B_1~, inclusive.

For example, if ~N = 6~, ~A_0 = 1~, ~B_0 = 2~, ~L_0 = 3~, ~A_1 = 1~, ~B_1 = 1~, ~L_1 = 2~, then a sequence that satisfies the above conditions is ~S = 010101~.

Input Specification

The input will consist of one line with 7 space-separated positive integers, the values ~N~, ~A_0~, ~B_0~, ~L_0~, ~A_1~, ~B_1~, ~L_1~ ~(3 \le N \le 1\,000, 1 \le A_0 \le B_0 \le L_0 \le N, 1 \le A_1 \le B_1 \le L_1 \le N)~.

Output Specification

The output should consist of one line. If there does not exist a 01 sequence satisfying the above conditions, then output -1. Otherwise, output any 01 sequence that satisfies the conditions.

Sample Input

6 1 2 3 1 1 2

Sample Output

010101

Problem translated to English by Alex.