Statement

Edoardo is getting interested in making his house smarter. For this reason, he has bought a smart thermostat, which measures the temperature in his room. Edoardo has gathered so far N measures V_i produced by the sensor and would like to calculate some statistics. However, the thermostat is not always able to produce a stable measurement: in the case of an unreliable reading, V_i = -1 is reported as a special value instead of the correct measure of the room's temperature. The N measurements were all obtained at regular intervals in a single morning, starting just after switching on the heating system. For this reason, we are certain that during the whole morning the temperature of the room was non-decreasing. Edoardo wants to fix the errors by changing all the unreliable measurements so that they respect the non-decreasing property (formally, V_i > V_i-1 for each i = 1… N-1). What is the minimum sum of the measurements that he can get?