In the Isle of Guernsey there are *n* different types of coins. For each *i* (1 ≤ *i* ≤ *n*), coin of type *i* is worth *a*<sub class="lower-index">*i*</sub> cents. It is possible that *a*<sub class="lower-index">*i*</sub> = *a*<sub class="lower-index">*j*</sub> for some *i* and *j* (*i* ≠ *j*). 

Bessie has some set of these coins totaling *t* cents. She tells Jessie *q* pairs of integers. For each *i* (1 ≤ *i* ≤ *q*), the pair *b*<sub class="lower-index">*i*</sub>, *c*<sub class="lower-index">*i*</sub> tells Jessie that Bessie has a strictly greater number of coins of type *b*<sub class="lower-index">*i*</sub> than coins of type *c*<sub class="lower-index">*i*</sub>. It is known that all *b*<sub class="lower-index">*i*</sub> are distinct and all *c*<sub class="lower-index">*i*</sub> are distinct. 

Help Jessie find the number of possible combinations of coins Bessie could have. Two combinations are considered different if there is some *i* (1 ≤ *i* ≤ *n*), such that the number of coins Bessie has of type *i* is different in the two combinations. Since the answer can be very large, output it modulo 1000000007 (10<sup class="upper-index">9</sup> + 7). 

If there are no possible combinations of coins totaling *t* cents that satisfy Bessie's conditions, output 0.
The first line contains three space-separated integers, *n*, *q* and *t* (1 ≤ *n* ≤ 300; 0 ≤ *q* ≤ *n*; 1 ≤ *t* ≤ 10<sup class="upper-index">5</sup>). The second line contains *n* space separated integers, *a*<sub class="lower-index">1</sub>, *a*<sub class="lower-index">2</sub>, ..., *a*<sub class="lower-index">*n*</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">5</sup>). The next *q* lines each contain two distinct space-separated integers, *b*<sub class="lower-index">*i*</sub> and *c*<sub class="lower-index">*i*</sub> (1 ≤ *b*<sub class="lower-index">*i*</sub>, *c*<sub class="lower-index">*i*</sub> ≤ *n*; *b*<sub class="lower-index">*i*</sub> ≠ *c*<sub class="lower-index">*i*</sub>).

It's guaranteed that all *b*<sub class="lower-index">*i*</sub> are distinct and all *c*<sub class="lower-index">*i*</sub> are distinct.
print("_RANDOM_GUESS_1690488944.6073928")# 1690488944.6074166