Enormous XOR

You are given two integers l and r in binary representation. Let g(x, y) be equal to the bitwise XOR of all integers from x to y inclusive (that is x ⊕ (x+1) ⊕ ... ⊕ (y-1) ⊕ y). Let's define f(l, r) as the maximum of all values of g(x, y) satisfying l ≤ x ≤ y ≤ r.

Output f(l, r).

Input

The first line contains a single integer n (1 ≤ n ≤ 10^6) — the length of the binary representation of r.

The second line contains the binary representation of l — a string of length n consisting of digits 0 and 1 (0 ≤ l < 2^n).

The third line contains the binary representation of r — a string of length n consisting of digits 0 and 1 (0 ≤ r < 2^n).

It is guaranteed that l ≤ r. The binary representation of r does not contain any extra leading zeros (if r=0, the binary representation of it consists of a single zero). The binary representation of l is preceded with leading zeros so that its length is equal to n.

Output

In a single line output the value of f(l, r) for the given pair of l and r in binary representation without extra leading zeros.

Examples

Input

7 0010011 1111010

Output

1111111

Input

4 1010 1101

Output

1101

Note

In sample test case l=19, r=122. f(x,y) is maximal and is equal to 127, with x=27, y=100, for example.

inputFormat

outputFormat

Output f(l, r).

Input

The first line contains a single integer n (1 ≤ n ≤ 10^6) — the length of the binary representation of r.

The second line contains the binary representation of l — a string of length n consisting of digits 0 and 1 (0 ≤ l < 2^n).

The third line contains the binary representation of r — a string of length n consisting of digits 0 and 1 (0 ≤ r < 2^n).

It is guaranteed that l ≤ r. The binary representation of r does not contain any extra leading zeros (if r=0, the binary representation of it consists of a single zero). The binary representation of l is preceded with leading zeros so that its length is equal to n.

Output

In a single line output the value of f(l, r) for the given pair of l and r in binary representation without extra leading zeros.

Examples

Input

7 0010011 1111010

Output

1111111

Input

4 1010 1101

Output

1101

Note

In sample test case l=19, r=122. f(x,y) is maximal and is equal to 127, with x=27, y=100, for example.

样例

7
0010011
1111010

1111111

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