A pianist wants to play the piano.

The piano has $10^{100}$ keys, and the keys are labeled $A, B, C, D, E, F, G, A, B, \cdots$ from the left to the right. The pianist wants to satisfy the following constraints:

• He chooses an $A$ key, and starts playing the piano by pressing the chosen key.
• After he presses the $i$-th key, he can press either the $i-1$-th key or the $i+1$-th key in the next step.
• After he presses an $A$ key, he can also stop playing the piano.
• The first $A$ key and the last $A$ key he plays are not necessarily the same.
• He must press $A$ keys (it doesn’t matter which $A$ keys) exactly $C_1$ times.
• Similarly, he must press $B, C, D, E, F, G$ keys exactly $C_2, \ldots, C_7$ times, respectively.

Determine if it is possible to satisfy all the constraints above.

Input

$C_1\ C_2\ C_3\ C_4\ C_5\ C_6\ C_7$

• $0 \leq C_i \leq 10^{10}$
• $\sum C_i > 0$

Output

Print “YES” if it is possible to satisfy all the constraints, and “NO” otherwise.

Examples

Input 1

2 1 1 1 1 1 1

Output 1

YES

Input 2

1 1 1 1 1 1 1

Output 2

NO

Input 3

3 1 0 10000000000 10000000000 0 1

Output 3

NO

Input 4

1 0 0 0 0 0 0

Output 4

YES

Note

In Sample 1, he can play $A, B, C, D, E, F, G, A$.