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 $N$, $A_0$, $B_0$, $L_0$, $A_1$, $B_1$, $L_1$ $(3\le N\le 1000,1\le A_0\le B_0\le L_0\le N,1\le A_1\le B_1\le L_1\le N)$.

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.