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You are given *n* integers *a*1,<=*a*2,<=...,<=*a**n*. Denote this list of integers as *T*.

Let *f*(*L*) be a function that takes in a non-empty list of integers *L*.

The function will output another integer as follows: 
 -  First, all integers in *L* are padded with leading zeros so they are all the same length as the maximum length number in *L*. -  We will construct a string where the *i*-th character is the minimum of the *i*-th character in padded input numbers. -  The output is the number representing the string interpreted in base 10. 
For example *f*(10,<=9)<==<=0, *f*(123,<=321)<==<=121, *f*(530,<=932,<=81)<==<=30.

Define the function 

In other words, *G*(*x*) is the sum of squares of sum of elements of nonempty subsequences of *T* that evaluate to *x* when plugged into *f* modulo 1<=000<=000<=007, then multiplied by *x*. The last multiplication is not modded. 

You would like to compute *G*(0),<=*G*(1),<=...,<=*G*(999<=999). To reduce the output size, print the value , where  denotes the bitwise XOR operator.
The first line contains the integer *n* (1<=≤<=*n*<=≤<=1<=000<=000) — the size of list *T*.

The next line contains *n* space-separated integers, *a*1,<=*a*2,<=...,<=*a**n* (0<=≤<=*a**i*<=≤<=999<=999) — the elements of the list.
Output a single integer, the answer to the problem.
For the first sample, the nonzero values of *G* are *G*(121) = 144 611 577, *G*(123) = 58 401 999, *G*(321) = 279 403 857, *G*(555) = 170 953 875. The bitwise XOR of these numbers is equal to 292 711 924.

For example, <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/53a1c46c7cd2d3d56e89fe99af6328601758b327.png" style="max-width: 100.0%;max-height: 100.0%;"/>, since the subsequences [123] and [123, 555] evaluate to 123 when plugged into *f*.

For the second sample, we have <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/330ab8a9387bb33a82877190f4439f4e9ccd8e92.png" style="max-width: 100.0%;max-height: 100.0%;"/>

For the last sample, we have <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/0e0eeb7662af22bf04ea1a2ea669b162d53ad7ba.png" style="max-width: 100.0%;max-height: 100.0%;"/>, where <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/4f42013cbab8c31325f2cf28b60aa2ccc1cf89d3.png" style="max-width: 100.0%;max-height: 100.0%;"/> is the binomial coefficient.